diff --git a/-fCLJ1pGht4.txt b/-fCLJ1pGht4.txt new file mode 100644 index 0000000000000000000000000000000000000000..55f714fcd3840c3946530519a66c04e2b5d0c342 --- /dev/null +++ b/-fCLJ1pGht4.txt @@ -0,0 +1,12472 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay welcome + + align:start position:0% +ocw.mit.edu okay welcome + + + align:start position:0% +ocw.mit.edu okay welcome +back um at the end of last time we said + + align:start position:0% +back um at the end of last time we said + + + align:start position:0% +back um at the end of last time we said +we built up a pretty good arsenal of + + align:start position:0% +we built up a pretty good arsenal of + + + align:start position:0% +we built up a pretty good arsenal of +optimal control tools now we're going to + + align:start position:0% +optimal control tools now we're going to + + + align:start position:0% +optimal control tools now we're going to +start pushing them in in exciting + + align:start position:0% +start pushing them in in exciting + + + align:start position:0% +start pushing them in in exciting +directions okay so uh many of you know I + + align:start position:0% +directions okay so uh many of you know I + + + align:start position:0% +directions okay so uh many of you know I +I work on walking robots it's one of my + + align:start position:0% +I work on walking robots it's one of my + + + align:start position:0% +I work on walking robots it's one of my +passions I think it's one of the sort of + + align:start position:0% +passions I think it's one of the sort of + + + align:start position:0% +passions I think it's one of the sort of +clear unsolved problems in robotics + + align:start position:0% +clear unsolved problems in robotics + + + align:start position:0% +clear unsolved problems in robotics +right we we know we have so many things + + align:start position:0% +right we we know we have so many things + + + align:start position:0% +right we we know we have so many things +we can do with robotic arms relatively + + align:start position:0% +we can do with robotic arms relatively + + + align:start position:0% +we can do with robotic arms relatively +we have almost nothing that we can do + + align:start position:0% +we have almost nothing that we can do + + + align:start position:0% +we have almost nothing that we can do +with walking robots walking down the + + align:start position:0% +with walking robots walking down the + + + align:start position:0% +with walking robots walking down the +street is still a challenge okay so in + + align:start position:0% +street is still a challenge okay so in + + + align:start position:0% +street is still a challenge okay so in +my mind one of the essential problems in + + align:start position:0% +my mind one of the essential problems in + + + align:start position:0% +my mind one of the essential problems in +in the robotics it also happens to be + + align:start position:0% +in the robotics it also happens to be + + + align:start position:0% +in the robotics it also happens to be +the thing that animals do just + + align:start position:0% +the thing that animals do just + + + align:start position:0% +the thing that animals do just +incredibly well and they do it you know + + align:start position:0% +incredibly well and they do it you know + + + align:start position:0% +incredibly well and they do it you know +even the really dumb animals you know + + align:start position:0% +even the really dumb animals you know + + + align:start position:0% +even the really dumb animals you know +locomote very very very well so um some + + align:start position:0% +locomote very very very well so um some + + + align:start position:0% +locomote very very very well so um some +people might even argue it's a it's a + + align:start position:0% +people might even argue it's a it's a + + + align:start position:0% +people might even argue it's a it's a +predecessor to higher cognitive function + + align:start position:0% +predecessor to higher cognitive function + + + align:start position:0% +predecessor to higher cognitive function +well we'll see um okay so there's lots + + align:start position:0% +well we'll see um okay so there's lots + + + align:start position:0% +well we'll see um okay so there's lots +of good reasons why walking robots are + + align:start position:0% +of good reasons why walking robots are + + + align:start position:0% +of good reasons why walking robots are +tough um there's mechanical problems uh + + align:start position:0% +tough um there's mechanical problems uh + + + align:start position:0% +tough um there's mechanical problems uh +of course the you know suddenly if + + align:start position:0% +of course the you know suddenly if + + + align:start position:0% +of course the you know suddenly if +you're walking robot you have to start + + align:start position:0% +you're walking robot you have to start + + + align:start position:0% +you're walking robot you have to start +carrying your actuators so you don't + + align:start position:0% +carrying your actuators so you don't + + + align:start position:0% +carrying your actuators so you don't +didn't have to do that as a robotic arm + + align:start position:0% +didn't have to do that as a robotic arm + + + align:start position:0% +didn't have to do that as a robotic arm +and that's created lots of interesting + + align:start position:0% +and that's created lots of interesting + + + align:start position:0% +and that's created lots of interesting +work in actuator Technologies how do you + + align:start position:0% +work in actuator Technologies how do you + + + align:start position:0% +work in actuator Technologies how do you +control how do you carry an actuator + + align:start position:0% +control how do you carry an actuator + + + align:start position:0% +control how do you carry an actuator +that can produce torque accurately let's + + align:start position:0% +that can produce torque accurately let's + + + align:start position:0% +that can produce torque accurately let's +say um if you have to carry its own + + align:start position:0% +say um if you have to carry its own + + + align:start position:0% +say um if you have to carry its own +weight that's a that's been a + + align:start position:0% +weight that's a that's been a + + + align:start position:0% +weight that's a that's been a +challenging problem there's lots of + + align:start position:0% +challenging problem there's lots of + + + align:start position:0% +challenging problem there's lots of +interesting work there but I will stand + + align:start position:0% +interesting work there but I will stand + + + align:start position:0% +interesting work there but I will stand +by I I think that the reason we don't + + align:start position:0% +by I I think that the reason we don't + + + align:start position:0% +by I I think that the reason we don't +have walking robots today is not + + align:start position:0% +have walking robots today is not + + + align:start position:0% +have walking robots today is not +actuators it's not power density these + + align:start position:0% +actuators it's not power density these + + + align:start position:0% +actuators it's not power density these +are problems but I think the fundamental + + align:start position:0% +are problems but I think the fundamental + + + align:start position:0% +are problems but I think the fundamental +challenge is in + + align:start position:0% +challenge is in + + + align:start position:0% +challenge is in +control okay and we are now well suited + + align:start position:0% +control okay and we are now well suited + + + align:start position:0% +control okay and we are now well suited +to to make progress on that control + + align:start position:0% +to to make progress on that control + + + align:start position:0% +to to make progress on that control +problem okay so + + align:start position:0% +problem okay so + + + align:start position:0% +problem okay so +um based on what we've learned so far + + align:start position:0% +um based on what we've learned so far + + + align:start position:0% +um based on what we've learned so far +walking robots aren't that different + + align:start position:0% +walking robots aren't that different + + + align:start position:0% +walking robots aren't that different +than the acrobot and the cart pole + + align:start position:0% +than the acrobot and the cart pole + + + align:start position:0% +than the acrobot and the cart pole +there's two things that that are + + align:start position:0% +there's two things that that are + + + align:start position:0% +there's two things that that are +different dynamically speaking about a + + align:start position:0% +different dynamically speaking about a + + + align:start position:0% +different dynamically speaking about a +walking robot the first is we have to + + align:start position:0% +walking robot the first is we have to + + + align:start position:0% +walking robot the first is we have to +think about limit Cycles instead of just + + align:start position:0% +think about limit Cycles instead of just + + + align:start position:0% +think about limit Cycles instead of just +trajectories and we're going to talk for + + align:start position:0% +trajectories and we're going to talk for + + + align:start position:0% +trajectories and we're going to talk for +some minute for some time about that + + align:start position:0% +some minute for some time about that + + + align:start position:0% +some minute for some time about that +okay the second thing the first thing + + align:start position:0% +okay the second thing the first thing + + + align:start position:0% +okay the second thing the first thing +was limit Cycles yeah the second thing + + align:start position:0% +was limit Cycles yeah the second thing + + + align:start position:0% +was limit Cycles yeah the second thing +is uh impacts okay walking robots every + + align:start position:0% +is uh impacts okay walking robots every + + + align:start position:0% +is uh impacts okay walking robots every +time their feet hit the ground um we + + align:start position:0% +time their feet hit the ground um we + + + align:start position:0% +time their feet hit the ground um we +have to start dealing with impacts okay + + align:start position:0% +have to start dealing with impacts okay + + + align:start position:0% +have to start dealing with impacts okay +so so dealing with periodic motions and + + align:start position:0% +so so dealing with periodic motions and + + + align:start position:0% +so so dealing with periodic motions and +dealing with impacts are the two big + + align:start position:0% +dealing with impacts are the two big + + + align:start position:0% +dealing with impacts are the two big +technical hurdles to taking the um and + + align:start position:0% +technical hurdles to taking the um and + + + align:start position:0% +technical hurdles to taking the um and +they're not even that big necessarily + + align:start position:0% +they're not even that big necessarily + + + align:start position:0% +they're not even that big necessarily +but they're the the technical hurdles of + + align:start position:0% +but they're the the technical hurdles of + + + align:start position:0% +but they're the the technical hurdles of +taking the techniques we've already + + align:start position:0% +taking the techniques we've already + + + align:start position:0% +taking the techniques we've already +developed and applying them to walking + + align:start position:0% +developed and applying them to walking + + + align:start position:0% +developed and applying them to walking +robots Okay + + align:start position:0% + + + + align:start position:0% + +and impacts more generally um might be + + align:start position:0% +and impacts more generally um might be + + + align:start position:0% +and impacts more generally um might be +called uh sort of hybrid + + align:start position:0% + + + + align:start position:0% + +Dynamics where you have a a mixing of + + align:start position:0% +Dynamics where you have a a mixing of + + + align:start position:0% +Dynamics where you have a a mixing of +discrete time and continuous time + + align:start position:0% +discrete time and continuous time + + + align:start position:0% +discrete time and continuous time +Dynamics + + align:start position:0% + + + + align:start position:0% + +okay so before I launch into some of the + + align:start position:0% +okay so before I launch into some of the + + + align:start position:0% +okay so before I launch into some of the +models of walking which we'll get to + + align:start position:0% +models of walking which we'll get to + + + align:start position:0% +models of walking which we'll get to +pretty quick let's do a toy example to + + align:start position:0% +pretty quick let's do a toy example to + + + align:start position:0% +pretty quick let's do a toy example to +start thinking about limit cycles and + + align:start position:0% +start thinking about limit cycles and + + + align:start position:0% +start thinking about limit cycles and +limit cycle stability okay so you can + + align:start position:0% +limit cycle stability okay so you can + + + align:start position:0% +limit cycle stability okay so you can +get your head around limit cycle + + align:start position:0% +get your head around limit cycle + + + align:start position:0% +get your head around limit cycle +stability with some very simple + + align:start position:0% +stability with some very simple + + + align:start position:0% +stability with some very simple +oscillator type + + align:start position:0% + + + + align:start position:0% + +circuits um my my favorite simple + + align:start position:0% +circuits um my my favorite simple + + + align:start position:0% +circuits um my my favorite simple +oscillator is the Vander Poole + + align:start position:0% + + + + align:start position:0% + +oscillator okay so it's a second + + align:start position:0% +oscillator okay so it's a second + + + align:start position:0% +oscillator okay so it's a second +order + + align:start position:0% + + + + align:start position:0% + +system these are + + align:start position:0% +system these are + + + align:start position:0% +system these are +the standard equations for a Vander + + align:start position:0% +the standard equations for a Vander + + + align:start position:0% +the standard equations for a Vander +Poole oscillator where mu is some + + align:start position:0% +Poole oscillator where mu is some + + + align:start position:0% +Poole oscillator where mu is some +parameter you can + + align:start position:0% +parameter you can + + + align:start position:0% +parameter you can +choose um you can look at it pretty + + align:start position:0% +choose um you can look at it pretty + + + align:start position:0% +choose um you can look at it pretty +quickly and start thinking about it like + + align:start position:0% +quickly and start thinking about it like + + + align:start position:0% +quickly and start thinking about it like +almost like a very simple spring Mass + + align:start position:0% +almost like a very simple spring Mass + + + align:start position:0% +almost like a very simple spring Mass +damper + + align:start position:0% +damper + + + align:start position:0% +damper +system the only complicated part is it's + + align:start position:0% +system the only complicated part is it's + + + align:start position:0% +system the only complicated part is it's +got State dependent nonlinear + + align:start position:0% +got State dependent nonlinear + + + align:start position:0% +got State dependent nonlinear +damping okay so think about it almost + + align:start position:0% +damping okay so think about it almost + + + align:start position:0% +damping okay so think about it almost +like a spring Mass system but it's got + + align:start position:0% +like a spring Mass system but it's got + + + align:start position:0% +like a spring Mass system but it's got +nonlinear damping State dependent + + align:start position:0% +nonlinear damping State dependent + + + align:start position:0% +nonlinear damping State dependent +damping and in particular if you look at + + align:start position:0% +damping and in particular if you look at + + + align:start position:0% +damping and in particular if you look at +it um you can think of it as having + + align:start position:0% +it um you can think of it as having + + + align:start position:0% +it um you can think of it as having +um if the magnitude of X is less than + + align:start position:0% +um if the magnitude of X is less than + + + align:start position:0% +um if the magnitude of X is less than +one then does it have positive damping + + align:start position:0% +one then does it have positive damping + + + align:start position:0% +one then does it have positive damping +or negative + + align:start position:0% + + + + align:start position:0% + +damping it's it's it's there's a sign + + align:start position:0% +damping it's it's it's there's a sign + + + align:start position:0% +damping it's it's it's there's a sign +change in the word damping somewhere in + + align:start position:0% +change in the word damping somewhere in + + + align:start position:0% +change in the word damping somewhere in +there too it's going to add energy to + + align:start position:0% +there too it's going to add energy to + + + align:start position:0% +there too it's going to add energy to +the system if x is less than one yeah + + align:start position:0% + + + + align:start position:0% + +which I think is negative damping + + align:start position:0% +which I think is negative damping + + + align:start position:0% +which I think is negative damping +typically + + align:start position:0% +typically + + + align:start position:0% +typically +yeah and if x is greater than + + align:start position:0% +yeah and if x is greater than + + + align:start position:0% +yeah and if x is greater than +one it's going to remove energy right + + align:start position:0% +one it's going to remove energy right + + + align:start position:0% +one it's going to remove energy right +it's going to dissipate + + align:start position:0% + + + + align:start position:0% + +energy + + align:start position:0% +energy + + + align:start position:0% +energy +right so it's not too hard to believe + + align:start position:0% +right so it's not too hard to believe + + + align:start position:0% +right so it's not too hard to believe +that you're you're going to end up with + + align:start position:0% +that you're you're going to end up with + + + align:start position:0% +that you're you're going to end up with +something that + + align:start position:0% +something that + + + align:start position:0% +something that +oscillates right if it's if it's adding + + align:start position:0% +oscillates right if it's if it's adding + + + align:start position:0% +oscillates right if it's if it's adding +energy for small x's and removing + + align:start position:0% +energy for small x's and removing + + + align:start position:0% +energy for small x's and removing +removing energy for large X's it's not + + align:start position:0% +removing energy for large X's it's not + + + align:start position:0% +removing energy for large X's it's not +too surprising maybe that you get this + + align:start position:0% +too surprising maybe that you get this + + + align:start position:0% +too surprising maybe that you get this +thing going and it starts oscillating + + align:start position:0% +thing going and it starts oscillating + + + align:start position:0% +thing going and it starts oscillating +okay + + align:start position:0% + + + + align:start position:0% + +um I might as well show you the the real + + align:start position:0% +um I might as well show you the the real + + + align:start position:0% +um I might as well show you the the real +trajectories instead of drawing them + + align:start position:0% + + + + align:start position:0% + +badly for + + align:start position:0% + + + + align:start position:0% + +so if I do a phase plot of this system + + align:start position:0% +so if I do a phase plot of this system + + + align:start position:0% +so if I do a phase plot of this system +which is two-dimensional + + align:start position:0% +which is two-dimensional + + + align:start position:0% +which is two-dimensional +right it's got a walking robot in the + + align:start position:0% +right it's got a walking robot in the + + + align:start position:0% +right it's got a walking robot in the +middle sorry close + + align:start position:0% + + + + align:start position:0% + +figures there we go okay + + align:start position:0% + + + + align:start position:0% + +uh and just yeah that's good that's ex + + align:start position:0% +uh and just yeah that's good that's ex + + + align:start position:0% +uh and just yeah that's good that's ex +good okay so these are three plots three + + align:start position:0% +good okay so these are three plots three + + + align:start position:0% +good okay so these are three plots three +trajectories from three different + + align:start position:0% +trajectories from three different + + + align:start position:0% +trajectories from three different +initial conditions one that started off + + align:start position:0% +initial conditions one that started off + + + align:start position:0% +initial conditions one that started off +with some large negative initial + + align:start position:0% +with some large negative initial + + + align:start position:0% +with some large negative initial +conditions in both Theta and Theta dot + + align:start position:0% +conditions in both Theta and Theta dot + + + align:start position:0% +conditions in both Theta and Theta dot +or x and x dot sorry okay and damping + + align:start position:0% +or x and x dot sorry okay and damping + + + align:start position:0% +or x and x dot sorry okay and damping +took the energy out and started going to + + align:start position:0% +took the energy out and started going to + + + align:start position:0% +took the energy out and started going to +this stable oscillation yeah from + + align:start position:0% +this stable oscillation yeah from + + + align:start position:0% +this stable oscillation yeah from +another very large trajectory did + + align:start position:0% +another very large trajectory did + + + align:start position:0% +another very large trajectory did +roughly the same thing went to that same + + align:start position:0% +roughly the same thing went to that same + + + align:start position:0% +roughly the same thing went to that same +basic oscillation and then even from + + align:start position:0% +basic oscillation and then even from + + + align:start position:0% +basic oscillation and then even from +very small initial conditions near the + + align:start position:0% +very small initial conditions near the + + + align:start position:0% +very small initial conditions near the +origin it'll swing out and start going + + align:start position:0% +origin it'll swing out and start going + + + align:start position:0% +origin it'll swing out and start going +to these um same characteristic + + align:start position:0% +to these um same characteristic + + + align:start position:0% +to these um same characteristic +oscillation in in phas space + + align:start position:0% +oscillation in in phas space + + + align:start position:0% +oscillation in in phas space +okay so this is exactly the picture you + + align:start position:0% +okay so this is exactly the picture you + + + align:start position:0% +okay so this is exactly the picture you +want to have in your head of a stable + + align:start position:0% +want to have in your head of a stable + + + align:start position:0% +want to have in your head of a stable +limit cycle Behavior okay it's a + + align:start position:0% +limit cycle Behavior okay it's a + + + align:start position:0% +limit cycle Behavior okay it's a +periodic motion when I'm away from that + + align:start position:0% +periodic motion when I'm away from that + + + align:start position:0% +periodic motion when I'm away from that +that uh motion I return to it right this + + align:start position:0% +that uh motion I return to it right this + + + align:start position:0% +that uh motion I return to it right this +is exactly what we want to capture with + + align:start position:0% +is exactly what we want to capture with + + + align:start position:0% +is exactly what we want to capture with +by saying a stable limit cycle turns out + + align:start position:0% +by saying a stable limit cycle turns out + + + align:start position:0% +by saying a stable limit cycle turns out +it's not sort of trivial to identify to + + align:start position:0% +it's not sort of trivial to identify to + + + align:start position:0% +it's not sort of trivial to identify to +write down what what you mean by a stab + + align:start position:0% +write down what what you mean by a stab + + + align:start position:0% +write down what what you mean by a stab +stability in the limit cycle context and + + align:start position:0% +stability in the limit cycle context and + + + align:start position:0% +stability in the limit cycle context and +I'll show you we'll say more about that + + align:start position:0% +I'll show you we'll say more about that + + + align:start position:0% +I'll show you we'll say more about that +in a second but but first if we just + + align:start position:0% +in a second but but first if we just + + + align:start position:0% +in a second but but first if we just +sort of let's just use our imagine and + + align:start position:0% +sort of let's just use our imagine and + + + align:start position:0% +sort of let's just use our imagine and +talk about some ASM totic stability to + + align:start position:0% +talk about some ASM totic stability to + + + align:start position:0% +talk about some ASM totic stability to +this this + + align:start position:0% +this this + + + align:start position:0% +this this +orbit would you does anybody know from + + align:start position:0% +orbit would you does anybody know from + + + align:start position:0% +orbit would you does anybody know from +this system whether this system is uh is + + align:start position:0% +this system whether this system is uh is + + + align:start position:0% +this system whether this system is uh is +globally stable + + align:start position:0% + + + + align:start position:0% + +why is it not globally stable good + + align:start position:0% +why is it not globally stable good + + + align:start position:0% +why is it not globally stable good +there's I think it's true that it's + + align:start position:0% +there's I think it's true that it's + + + align:start position:0% +there's I think it's true that it's +globally stable except for a set of + + align:start position:0% +globally stable except for a set of + + + align:start position:0% +globally stable except for a set of +measure zero is the way you say it right + + align:start position:0% +measure zero is the way you say it right + + + align:start position:0% +measure zero is the way you say it right +because darn it if you start at the + + align:start position:0% +because darn it if you start at the + + + align:start position:0% +because darn it if you start at the +origin it's not going to get there right + + align:start position:0% +origin it's not going to get there right + + + align:start position:0% +origin it's not going to get there right +it'll never start moving from the + + align:start position:0% +it'll never start moving from the + + + align:start position:0% +it'll never start moving from the +origin okay any other initial conditions + + align:start position:0% +origin okay any other initial conditions + + + align:start position:0% +origin okay any other initial conditions +will find their way back to the uh to + + align:start position:0% +will find their way back to the uh to + + + align:start position:0% +will find their way back to the uh to +that stable limit + + align:start position:0% +that stable limit + + + align:start position:0% +that stable limit +cycle okay so why is it not trivial to + + align:start position:0% +cycle okay so why is it not trivial to + + + align:start position:0% +cycle okay so why is it not trivial to +say what I mean by um + + align:start position:0% +say what I mean by um + + + align:start position:0% +say what I mean by um +a stable limit cycle well let's plot + + align:start position:0% +a stable limit cycle well let's plot + + + align:start position:0% +a stable limit cycle well let's plot +that same + + align:start position:0% + + + + align:start position:0% + +system um in the time + + align:start position:0% +system um in the time + + + align:start position:0% +system um in the time +domain same initial + + align:start position:0% +domain same initial + + + align:start position:0% +domain same initial +conditions everything's the same + + align:start position:0% + + + + align:start position:0% + +um here we + + align:start position:0% +um here we + + + align:start position:0% +um here we +go okay same exact trajectories you can + + align:start position:0% +go okay same exact trajectories you can + + + align:start position:0% +go okay same exact trajectories you can +see they all go to their characteristic + + align:start position:0% +see they all go to their characteristic + + + align:start position:0% +see they all go to their characteristic +oscillation pretty quickly in fact + + align:start position:0% +oscillation pretty quickly in fact + + + align:start position:0% +oscillation pretty quickly in fact +right but you can it's Crystal Clear + + align:start position:0% +right but you can it's Crystal Clear + + + align:start position:0% +right but you can it's Crystal Clear +here that they the trajectories never + + align:start position:0% +here that they the trajectories never + + + align:start position:0% +here that they the trajectories never +synchronize themselves in + + align:start position:0% +synchronize themselves in + + + align:start position:0% +synchronize themselves in +time okay and that's not too + + align:start position:0% +time okay and that's not too + + + align:start position:0% +time okay and that's not too +surprising so you're on the limit cycle + + align:start position:0% +surprising so you're on the limit cycle + + + align:start position:0% +surprising so you're on the limit cycle +the these Dynamics never Force if you're + + align:start position:0% +the these Dynamics never Force if you're + + + align:start position:0% +the these Dynamics never Force if you're +if you're if there's two trajectories + + align:start position:0% +if you're if there's two trajectories + + + align:start position:0% +if you're if there's two trajectories +that are a different place in phase on + + align:start position:0% +that are a different place in phase on + + + align:start position:0% +that are a different place in phase on +the limit cycle there's nothing that's + + align:start position:0% +the limit cycle there's nothing that's + + + align:start position:0% +the limit cycle there's nothing that's +forcing them to come together okay so + + align:start position:0% +forcing them to come together okay so + + + align:start position:0% +forcing them to come together okay so +they'll continue to be aart in time such + + align:start position:0% +they'll continue to be aart in time such + + + align:start position:0% +they'll continue to be aart in time such +a simple thing but actually that + + align:start position:0% +a simple thing but actually that + + + align:start position:0% +a simple thing but actually that +complicates our our ability to Define + + align:start position:0% +complicates our our ability to Define + + + align:start position:0% +complicates our our ability to Define +stability we can't talk about + + align:start position:0% +stability we can't talk about + + + align:start position:0% +stability we can't talk about +trajectories ASM totically converging + + align:start position:0% +trajectories ASM totically converging + + + align:start position:0% +trajectories ASM totically converging +anymore because they don't right they + + align:start position:0% +anymore because they don't right they + + + align:start position:0% +anymore because they don't right they +ASM totically converge to some manifold + + align:start position:0% +ASM totically converge to some manifold + + + align:start position:0% +ASM totically converge to some manifold +but that's harder to describe okay as + + align:start position:0% +but that's harder to describe okay as + + + align:start position:0% +but that's harder to describe okay as +such we actually have relatively few + + align:start position:0% +such we actually have relatively few + + + align:start position:0% +such we actually have relatively few +good tools for describing limit cycle + + align:start position:0% +good tools for describing limit cycle + + + align:start position:0% +good tools for describing limit cycle +stability okay + + align:start position:0% + + + + align:start position:0% + +um the standard tool well let's actually + + align:start position:0% +um the standard tool well let's actually + + + align:start position:0% +um the standard tool well let's actually +let me say a few things about + + align:start position:0% +let me say a few things about + + + align:start position:0% +let me say a few things about +um about more about limit cycle before I + + align:start position:0% +um about more about limit cycle before I + + + align:start position:0% +um about more about limit cycle before I +tell you the standard tool but there's + + align:start position:0% +tell you the standard tool but there's + + + align:start position:0% +tell you the standard tool but there's +actually a few things that are + + align:start position:0% +actually a few things that are + + + align:start position:0% +actually a few things that are +interesting just good general knowledge + + align:start position:0% +interesting just good general knowledge + + + align:start position:0% +interesting just good general knowledge +about limit Cycles + + align:start position:0% + + + + align:start position:0% + +um turns out if you have a closed region + + align:start position:0% +um turns out if you have a closed region + + + align:start position:0% +um turns out if you have a closed region +in state + + align:start position:0% +in state + + + align:start position:0% +in state +space meaning trajectories that are + + align:start position:0% +space meaning trajectories that are + + + align:start position:0% +space meaning trajectories that are +inside this region never leave this + + align:start position:0% +inside this region never leave this + + + align:start position:0% +inside this region never leave this +region yeah and if that trajectory if + + align:start position:0% +region yeah and if that trajectory if + + + align:start position:0% +region yeah and if that trajectory if +that St region State space has no fixed + + align:start position:0% +that St region State space has no fixed + + + align:start position:0% +that St region State space has no fixed +points then it's got a closed + + align:start position:0% +points then it's got a closed + + + align:start position:0% +points then it's got a closed +orbit there has to be some there's + + align:start position:0% +orbit there has to be some there's + + + align:start position:0% +orbit there has to be some there's +there's got to be something it doesn't + + align:start position:0% +there's got to be something it doesn't + + + align:start position:0% +there's got to be something it doesn't +have to be a stable limit cycle but it + + align:start position:0% +have to be a stable limit cycle but it + + + align:start position:0% +have to be a stable limit cycle but it +has to repeat itself if you stay inside + + align:start position:0% +has to repeat itself if you stay inside + + + align:start position:0% +has to repeat itself if you stay inside +a region + + align:start position:0% +a region + + + align:start position:0% +a region +forever and you don't go to a fixed + + align:start position:0% +forever and you don't go to a fixed + + + align:start position:0% +forever and you don't go to a fixed +point then you have to have a closed + + align:start position:0% +point then you have to have a closed + + + align:start position:0% +point then you have to have a closed +orbit that's the panre um bendixon + + align:start position:0% +orbit that's the panre um bendixon + + + align:start position:0% +orbit that's the panre um bendixon +theorem + + align:start position:0% +theorem + + + align:start position:0% +theorem +you and it's also interesting to note + + align:start position:0% +you and it's also interesting to note + + + align:start position:0% +you and it's also interesting to note +that if you have a a dynamical system + + align:start position:0% +that if you have a a dynamical system + + + align:start position:0% +that if you have a a dynamical system +described by a potential + + align:start position:0% +described by a potential + + + align:start position:0% +described by a potential +function like any system that's + + align:start position:0% +function like any system that's + + + align:start position:0% +function like any system that's +described by a lopov function that + + align:start position:0% +described by a lopov function that + + + align:start position:0% +described by a lopov function that +cannot have a limit cycle right anything + + align:start position:0% +cannot have a limit cycle right anything + + + align:start position:0% +cannot have a limit cycle right anything +that's uniformally going down a gradient + + align:start position:0% +that's uniformally going down a gradient + + + align:start position:0% +that's uniformally going down a gradient +can't have a a a limit cycle Dynamics + + align:start position:0% +can't have a a a limit cycle Dynamics + + + align:start position:0% +can't have a a a limit cycle Dynamics +okay so a lot of leopo theory doesn't + + align:start position:0% +okay so a lot of leopo theory doesn't + + + align:start position:0% +okay so a lot of leopo theory doesn't +apply directly + + align:start position:0% + + + + align:start position:0% + +right and another thing is that + + align:start position:0% +right and another thing is that + + + align:start position:0% +right and another thing is that +um people are don't always call any + + align:start position:0% +um people are don't always call any + + + align:start position:0% +um people are don't always call any +closed orbits these are just random + + align:start position:0% +closed orbits these are just random + + + align:start position:0% +closed orbits these are just random +factoids about limit Cycles before we go + + align:start position:0% +factoids about limit Cycles before we go + + + align:start position:0% +factoids about limit Cycles before we go +in but they're good good culture here + + align:start position:0% +in but they're good good culture here + + + align:start position:0% +in but they're good good culture here +right but um if you have a closed orbit + + align:start position:0% +right but um if you have a closed orbit + + + align:start position:0% +right but um if you have a closed orbit +in state + + align:start position:0% +in state + + + align:start position:0% +in state +space if it's stable people would call + + align:start position:0% +space if it's stable people would call + + + align:start position:0% +space if it's stable people would call +it a limit cycle if it's unstable people + + align:start position:0% +it a limit cycle if it's unstable people + + + align:start position:0% +it a limit cycle if it's unstable people +call it a limit cycle if it's marginally + + align:start position:0% +call it a limit cycle if it's marginally + + + align:start position:0% +call it a limit cycle if it's marginally +stable people don't really use the word + + align:start position:0% +stable people don't really use the word + + + align:start position:0% +stable people don't really use the word +limit cycle okay so for instance on the + + align:start position:0% +limit cycle okay so for instance on the + + + align:start position:0% +limit cycle okay so for instance on the +undamped + + align:start position:0% +undamped + + + align:start position:0% +undamped +pendulum yeah the marginally stable + + align:start position:0% +pendulum yeah the marginally stable + + + align:start position:0% +pendulum yeah the marginally stable +orbits there's no stability properties + + align:start position:0% +orbits there's no stability properties + + + align:start position:0% +orbits there's no stability properties +on these people would typically not use + + align:start position:0% +on these people would typically not use + + + align:start position:0% +on these people would typically not use +the word limit cycle to describe those + + align:start position:0% +the word limit cycle to describe those + + + align:start position:0% +the word limit cycle to describe those +closed orbits on the phase space okay + + align:start position:0% +closed orbits on the phase space okay + + + align:start position:0% +closed orbits on the phase space okay +but anything that has this sort of + + align:start position:0% +but anything that has this sort of + + + align:start position:0% +but anything that has this sort of +converging or diverging property around + + align:start position:0% +converging or diverging property around + + + align:start position:0% +converging or diverging property around +a single trajectory so another way is so + + align:start position:0% +a single trajectory so another way is so + + + align:start position:0% +a single trajectory so another way is so +what's another good good way to say + + align:start position:0% + + + + align:start position:0% + +it they basically there's there's some + + align:start position:0% +it they basically there's there's some + + + align:start position:0% +it they basically there's there's some +words that I that I I liked about the + + align:start position:0% +words that I that I I liked about the + + + align:start position:0% +words that I that I I liked about the +trajectories have to be isolated in + + align:start position:0% +trajectories have to be isolated in + + + align:start position:0% +trajectories have to be isolated in +space basically if it's if a if these + + align:start position:0% +space basically if it's if a if these + + + align:start position:0% +space basically if it's if a if these +closed orbits are not isolated in space + + align:start position:0% +closed orbits are not isolated in space + + + align:start position:0% +closed orbits are not isolated in space +if there's not something sort of + + align:start position:0% +if there's not something sort of + + + align:start position:0% +if there's not something sort of +separating between them then people + + align:start position:0% +separating between them then people + + + align:start position:0% +separating between them then people +don't use the word limit cycle to to + + align:start position:0% +don't use the word limit cycle to to + + + align:start position:0% +don't use the word limit cycle to to +describe it + + align:start position:0% + + + + align:start position:0% + +okay okay so we can't talk about ASM + + align:start position:0% +okay okay so we can't talk about ASM + + + align:start position:0% +okay okay so we can't talk about ASM +totic convergence of trajectories on + + align:start position:0% +totic convergence of trajectories on + + + align:start position:0% +totic convergence of trajectories on +limit Cycles we can't use vanilla + + align:start position:0% +limit Cycles we can't use vanilla + + + align:start position:0% +limit Cycles we can't use vanilla +liapunov functions to talk about + + align:start position:0% +liapunov functions to talk about + + + align:start position:0% +liapunov functions to talk about +stability on limit Cycles so what do + + align:start position:0% +stability on limit Cycles so what do + + + align:start position:0% +stability on limit Cycles so what do +people do all right there's a standard + + align:start position:0% +people do all right there's a standard + + + align:start position:0% +people do all right there's a standard +trick that that most people play and + + align:start position:0% +trick that that most people play and + + + align:start position:0% +trick that that most people play and +that's the idea of panker sections and + + align:start position:0% +that's the idea of panker sections and + + + align:start position:0% +that's the idea of panker sections and +po maps how many people have seen pank + + align:start position:0% +po maps how many people have seen pank + + + align:start position:0% +po maps how many people have seen pank +Maps + + align:start position:0% +Maps + + + align:start position:0% +Maps +before okay here's the + + align:start position:0% +before okay here's the + + + align:start position:0% +before okay here's the +idea so I've got + + align:start position:0% +idea so I've got + + + align:start position:0% +idea so I've got +a + + align:start position:0% +a + + + align:start position:0% +a +um some orbit in uh in state space this + + align:start position:0% +um some orbit in uh in state space this + + + align:start position:0% +um some orbit in uh in state space this +is XX do of my of my Vander Poole + + align:start position:0% +is XX do of my of my Vander Poole + + + align:start position:0% +is XX do of my of my Vander Poole +oscillator + + align:start position:0% +oscillator + + + align:start position:0% +oscillator +yeah instead of talking about convergent + + align:start position:0% +yeah instead of talking about convergent + + + align:start position:0% +yeah instead of talking about convergent +to some orbit I'm going to define a + + align:start position:0% +to some orbit I'm going to define a + + + align:start position:0% +to some orbit I'm going to define a +particular + + align:start position:0% +particular + + + align:start position:0% +particular +surface in this state space let's say I + + align:start position:0% +surface in this state space let's say I + + + align:start position:0% +surface in this state space let's say I +Define that's a bad + + align:start position:0% +Define that's a bad + + + align:start position:0% +Define that's a bad +choice I've got 40 colors here I had to + + align:start position:0% +choice I've got 40 colors here I had to + + + align:start position:0% +choice I've got 40 colors here I had to +pick the one that's not a very good + + align:start position:0% +pick the one that's not a very good + + + align:start position:0% +pick the one that's not a very good +choice + + align:start position:0% + + + + align:start position:0% + +either Green's got to work for me + + align:start position:0% + + + + align:start position:0% + +yeah they're + + align:start position:0% +yeah they're + + + align:start position:0% +yeah they're +all fairly toned down okay let's pick a + + align:start position:0% +all fairly toned down okay let's pick a + + + align:start position:0% +all fairly toned down okay let's pick a +particular section in state space + + align:start position:0% +particular section in state space + + + align:start position:0% +particular section in state space +and instead of talking about the + + align:start position:0% +and instead of talking about the + + + align:start position:0% +and instead of talking about the +convergence in this continuous Dynamics + + align:start position:0% +convergence in this continuous Dynamics + + + align:start position:0% +convergence in this continuous Dynamics +to this orbit let's just look at the + + align:start position:0% +to this orbit let's just look at the + + + align:start position:0% +to this orbit let's just look at the +Dynamics of that limit cycle every time + + align:start position:0% +Dynamics of that limit cycle every time + + + align:start position:0% +Dynamics of that limit cycle every time +it crosses this section okay this is + + align:start position:0% +it crosses this section okay this is + + + align:start position:0% +it crosses this section okay this is +called a surface of + + align:start position:0% + + + + align:start position:0% + +section often referred to as some big S + + align:start position:0% +section often referred to as some big S + + + align:start position:0% +section often referred to as some big S +and a surface of + + align:start position:0% +and a surface of + + + align:start position:0% +and a surface of +section if it's the the + + align:start position:0% +section if it's the the + + + align:start position:0% +section if it's the the +case that all trajectories that leave + + align:start position:0% +case that all trajectories that leave + + + align:start position:0% +case that all trajectories that leave +the surface of + + align:start position:0% +the surface of + + + align:start position:0% +the surface of +section eventually return to the surface + + align:start position:0% +section eventually return to the surface + + + align:start position:0% +section eventually return to the surface +of + + align:start position:0% + + + + align:start position:0% + +section I'm going to write this down + + align:start position:0% +section I'm going to write this down + + + align:start position:0% +section I'm going to write this down +then a surface defining a surface of + + align:start position:0% +then a surface defining a surface of + + + align:start position:0% +then a surface defining a surface of +section allows you to convert The + + align:start position:0% +section allows you to convert The + + + align:start position:0% +section allows you to convert The +Continuous time stability of a limit + + align:start position:0% +Continuous time stability of a limit + + + align:start position:0% +Continuous time stability of a limit +cycle into the discrete time stability + + align:start position:0% +cycle into the discrete time stability + + + align:start position:0% +cycle into the discrete time stability +of a fixed + + align:start position:0% +of a fixed + + + align:start position:0% +of a fixed +Point okay + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +okay so we know a lot about defining + + align:start position:0% +okay so we know a lot about defining + + + align:start position:0% +okay so we know a lot about defining +stability for fixed points the big idea + + align:start position:0% +stability for fixed points the big idea + + + align:start position:0% +stability for fixed points the big idea +is we're going to turn limit cycle + + align:start position:0% +is we're going to turn limit cycle + + + align:start position:0% +is we're going to turn limit cycle +stability into fix Point + + align:start position:0% +stability into fix Point + + + align:start position:0% +stability into fix Point +stability + + align:start position:0% + + + + align:start position:0% + +okay and the name of the technique is is + + align:start position:0% +okay and the name of the technique is is + + + align:start position:0% +okay and the name of the technique is is +the pank CR map technique let's + + align:start position:0% + + + + align:start position:0% + +say okay so I've got some continuous + + align:start position:0% +say okay so I've got some continuous + + + align:start position:0% +say okay so I've got some continuous +dynamical system + + align:start position:0% +dynamical system + + + align:start position:0% +dynamical system +let's make it simple let's say it's just + + align:start position:0% +let's make it simple let's say it's just + + + align:start position:0% +let's make it simple let's say it's just +let's say there's no control to speak of + + align:start position:0% +let's say there's no control to speak of + + + align:start position:0% +let's say there's no control to speak of +No Time dependence let's just keep the + + align:start position:0% +No Time dependence let's just keep the + + + align:start position:0% +No Time dependence let's just keep the +simpl sort of analysis I've got some + + align:start position:0% +simpl sort of analysis I've got some + + + align:start position:0% +simpl sort of analysis I've got some +continuous time dynamical + + align:start position:0% + + + + align:start position:0% + +system let me call um T + + align:start position:0% +system let me call um T + + + align:start position:0% +system let me call um T +C the time of crossing the surface of + + align:start position:0% +C the time of crossing the surface of + + + align:start position:0% +C the time of crossing the surface of +section okay so I'll say + + align:start position:0% +section okay so I'll say + + + align:start position:0% +section okay so I'll say +TC n is the + + align:start position:0% +TC n is the + + + align:start position:0% +TC n is the +nth Crossing + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% + + + + align:start position:0% + +s + + align:start position:0% + + + + align:start position:0% + +yeah that allows me to define a discrete + + align:start position:0% +yeah that allows me to define a discrete + + + align:start position:0% +yeah that allows me to define a discrete +time + + align:start position:0% +time + + + align:start position:0% +time +system which I'm going to call + + align:start position:0% +system which I'm going to call + + + align:start position:0% +system which I'm going to call +XP of n or XP of + + align:start position:0% +XP of n or XP of + + + align:start position:0% +XP of n or XP of +n is X at + + align:start position:0% +n is X at + + + align:start position:0% +n is X at +TC of n + + align:start position:0% + + + + align:start position:0% + +just trying to be very careful about my + + align:start position:0% +just trying to be very careful about my + + + align:start position:0% +just trying to be very careful about my +notation I'm going to use P for anytime + + align:start position:0% +notation I'm going to use P for anytime + + + align:start position:0% +notation I'm going to use P for anytime +um the vector X I'm talking about lives + + align:start position:0% +um the vector X I'm talking about lives + + + align:start position:0% +um the vector X I'm talking about lives +on the Pointon map this is just a trying + + align:start position:0% +on the Pointon map this is just a trying + + + align:start position:0% +on the Pointon map this is just a trying +to be careful about the transition from + + align:start position:0% +to be careful about the transition from + + + align:start position:0% +to be careful about the transition from +continuous time to discreete + + align:start position:0% +continuous time to discreete + + + align:start position:0% +continuous time to discreete +time + + align:start position:0% +time + + + align:start position:0% +time +okay and I'm the + + align:start position:0% +okay and I'm the + + + align:start position:0% +okay and I'm the +result is a discrete Time + + align:start position:0% + + + + align:start position:0% + +map which I typically call P for a pank + + align:start position:0% +map which I typically call P for a pank + + + align:start position:0% +map which I typically call P for a pank +gray map + + align:start position:0% + + + + align:start position:0% + +that takes me it can be linear or + + align:start position:0% +that takes me it can be linear or + + + align:start position:0% +that takes me it can be linear or +nonlinear right in general it's + + align:start position:0% +nonlinear right in general it's + + + align:start position:0% +nonlinear right in general it's +nonlinear for + + align:start position:0% + + + + align:start position:0% + +us defining that surface of section + + align:start position:0% +us defining that surface of section + + + align:start position:0% +us defining that surface of section +defines for me a map which says if I + + align:start position:0% +defines for me a map which says if I + + + align:start position:0% +defines for me a map which says if I +cross the surface of section at the nth + + align:start position:0% +cross the surface of section at the nth + + + align:start position:0% +cross the surface of section at the nth +time at State XP then the next time I + + align:start position:0% +time at State XP then the next time I + + + align:start position:0% +time at State XP then the next time I +cross is going to be x p n plus1 + + align:start position:0% + + + + align:start position:0% + +right right so if I'm + + align:start position:0% +right right so if I'm + + + align:start position:0% +right right so if I'm +on the the um Vander Poole oscillator + + align:start position:0% +on the the um Vander Poole oscillator + + + align:start position:0% +on the the um Vander Poole oscillator +idea let's say + + align:start position:0% +idea let's say + + + align:start position:0% +idea let's say +xpn is something here I've defined my + + align:start position:0% +xpn is something here I've defined my + + + align:start position:0% +xpn is something here I've defined my +Surface of section in this case to be + + align:start position:0% +Surface of section in this case to be + + + align:start position:0% +Surface of section in this case to be +the place where x equals z x dot is + + align:start position:0% +the place where x equals z x dot is + + + align:start position:0% +the place where x equals z x dot is +greater than zero right just to Define + + align:start position:0% +greater than zero right just to Define + + + align:start position:0% +greater than zero right just to Define +only half of the that line there it's a + + align:start position:0% +only half of the that line there it's a + + + align:start position:0% +only half of the that line there it's a +line + + align:start position:0% +line + + + align:start position:0% +line +segment okay this thing we saw is going + + align:start position:0% +segment okay this thing we saw is going + + + align:start position:0% +segment okay this thing we saw is going +to go around like this it's going to get + + align:start position:0% +to go around like this it's going to get + + + align:start position:0% +to go around like this it's going to get +a little closer to the nominal + + align:start position:0% +a little closer to the nominal + + + align:start position:0% +a little closer to the nominal +trajectory it's going to come back here + + align:start position:0% +trajectory it's going to come back here + + + align:start position:0% +trajectory it's going to come back here +right so this mapping is what I'm + + align:start position:0% +right so this mapping is what I'm + + + align:start position:0% +right so this mapping is what I'm +capturing in P + + align:start position:0% +capturing in P + + + align:start position:0% +capturing in P +right if I go around + + align:start position:0% +right if I go around + + + align:start position:0% +right if I go around +again I'll come here yeah the key idea + + align:start position:0% +again I'll come here yeah the key idea + + + align:start position:0% +again I'll come here yeah the key idea +is that if that map exists for all + + align:start position:0% +is that if that map exists for all + + + align:start position:0% +is that if that map exists for all +states for any time I'm on this map I go + + align:start position:0% +states for any time I'm on this map I go + + + align:start position:0% +states for any time I'm on this map I go +around and I can get back to the + + align:start position:0% +around and I can get back to the + + + align:start position:0% +around and I can get back to the +map then knowing that you have stability + + align:start position:0% +map then knowing that you have stability + + + align:start position:0% +map then knowing that you have stability +on this map that your that that points + + align:start position:0% +on this map that your that that points + + + align:start position:0% +on this map that your that that points +in XP if XP as it evolves in time goes + + align:start position:0% +in XP if XP as it evolves in time goes + + + align:start position:0% +in XP if XP as it evolves in time goes +to a fixed point then that must also + + align:start position:0% +to a fixed point then that must also + + + align:start position:0% +to a fixed point then that must also +imply that you go to a limit cycle fix + + align:start position:0% +imply that you go to a limit cycle fix + + + align:start position:0% +imply that you go to a limit cycle fix +point in continuous domain nothing else + + align:start position:0% +point in continuous domain nothing else + + + align:start position:0% +point in continuous domain nothing else +is allowed to happen if I'm on this + + align:start position:0% +is allowed to happen if I'm on this + + + align:start position:0% +is allowed to happen if I'm on this +state in my continuous time world then + + align:start position:0% +state in my continuous time world then + + + align:start position:0% +state in my continuous time world then +nothing else is there's no time + + align:start position:0% +nothing else is there's no time + + + align:start position:0% +nothing else is there's no time +dependent functions here there's no + + align:start position:0% +dependent functions here there's no + + + align:start position:0% +dependent functions here there's no +other state that I'm not looking at if + + align:start position:0% +other state that I'm not looking at if + + + align:start position:0% +other state that I'm not looking at if +I'm on this trajectory I'm going to stay + + align:start position:0% +I'm on this trajectory I'm going to stay + + + align:start position:0% +I'm on this trajectory I'm going to stay +on that trajectory of course a + + align:start position:0% +on that trajectory of course a + + + align:start position:0% +on that trajectory of course a +disturbance or something could knock me + + align:start position:0% +disturbance or something could knock me + + + align:start position:0% +disturbance or something could knock me +off but that's not we're just looking at + + align:start position:0% +off but that's not we're just looking at + + + align:start position:0% +off but that's not we're just looking at +the nominal system + + align:start position:0% +the nominal system + + + align:start position:0% +the nominal system +right so fixed Point stability on the + + align:start position:0% +right so fixed Point stability on the + + + align:start position:0% +right so fixed Point stability on the +map implies limit cycle stability in + + align:start position:0% +map implies limit cycle stability in + + + align:start position:0% +map implies limit cycle stability in +continuous + + align:start position:0% +continuous + + + align:start position:0% +continuous +time + + align:start position:0% +time + + + align:start position:0% +time +okay awesome so + + align:start position:0% +okay awesome so + + + align:start position:0% +okay awesome so +um if I I don't really need that + + align:start position:0% +um if I I don't really need that + + + align:start position:0% +um if I I don't really need that +yet if I work out the map for the Vander + + align:start position:0% +yet if I work out the map for the Vander + + + align:start position:0% +yet if I work out the map for the Vander +Poole + + align:start position:0% + + + + align:start position:0% + +oscillator let me draw this map + + align:start position:0% +oscillator let me draw this map + + + align:start position:0% +oscillator let me draw this map +now as XP at the nth step going to XP at + + align:start position:0% +now as XP at the nth step going to XP at + + + align:start position:0% +now as XP at the nth step going to XP at +the N plus one + + align:start position:0% +the N plus one + + + align:start position:0% +the N plus one +step + + align:start position:0% +step + + + align:start position:0% +step +yeah okay at zero it's doesn't go + + align:start position:0% +yeah okay at zero it's doesn't go + + + align:start position:0% +yeah okay at zero it's doesn't go +anywhere so that's an easy point to + + align:start position:0% +anywhere so that's an easy point to + + + align:start position:0% +anywhere so that's an easy point to +draw yeah I know a cross is + + align:start position:0% + + + + align:start position:0% + +zero I'm being a little loose here so + + align:start position:0% +zero I'm being a little loose here so + + + align:start position:0% +zero I'm being a little loose here so +what I what I really care about is since + + align:start position:0% +what I what I really care about is since + + + align:start position:0% +what I what I really care about is since +I know the + + align:start position:0% +I know the + + + align:start position:0% +I know the +position is um the position is zero + + align:start position:0% +position is um the position is zero + + + align:start position:0% +position is um the position is zero +really what I'm drawing is sort of the + + align:start position:0% +really what I'm drawing is sort of the + + + align:start position:0% +really what I'm drawing is sort of the +Velocity at that let me call it XP dot + + align:start position:0% +Velocity at that let me call it XP dot + + + align:start position:0% +Velocity at that let me call it XP dot +should I well XP at n has has two + + align:start position:0% +should I well XP at n has has two + + + align:start position:0% +should I well XP at n has has two +elements the way I've defined it here + + align:start position:0% +elements the way I've defined it here + + + align:start position:0% +elements the way I've defined it here +right only one of them has anything + + align:start position:0% +right only one of them has anything + + + align:start position:0% +right only one of them has anything +interesting going on I'm not going to + + align:start position:0% +interesting going on I'm not going to + + + align:start position:0% +interesting going on I'm not going to +write a DOT on top of my discrete time + + align:start position:0% +write a DOT on top of my discrete time + + + align:start position:0% +write a DOT on top of my discrete time +system just because that that I don't + + align:start position:0% +system just because that that I don't + + + align:start position:0% +system just because that that I don't +like that notation but but I'm going to + + align:start position:0% +like that notation but but I'm going to + + + align:start position:0% +like that notation but but I'm going to +draw the only interesting variable of + + align:start position:0% +draw the only interesting variable of + + + align:start position:0% +draw the only interesting variable of +the two-dimensional object + + align:start position:0% +the two-dimensional object + + + align:start position:0% +the two-dimensional object +xn + + align:start position:0% +xn + + + align:start position:0% +xn +yeah if I look at my velocity at the nth + + align:start position:0% +yeah if I look at my velocity at the nth + + + align:start position:0% +yeah if I look at my velocity at the nth +Crossing going to the velocity the N + + align:start position:0% +Crossing going to the velocity the N + + + align:start position:0% +Crossing going to the velocity the N +plus one Crossing turns out if it's in + + align:start position:0% +plus one Crossing turns out if it's in + + + align:start position:0% +plus one Crossing turns out if it's in +here I know from simulation there that + + align:start position:0% +here I know from simulation there that + + + align:start position:0% +here I know from simulation there that +it gets bigger every time okay getting + + align:start position:0% +it gets bigger every time okay getting + + + align:start position:0% +it gets bigger every time okay getting +big bigger on this discret map means + + align:start position:0% +big bigger on this discret map means + + + align:start position:0% +big bigger on this discret map means +that it's it's greater than the line of + + align:start position:0% +that it's it's greater than the line of + + + align:start position:0% +that it's it's greater than the line of +slope + + align:start position:0% + + + + align:start position:0% + +one yeah let me draw the + + align:start position:0% +one yeah let me draw the + + + align:start position:0% +one yeah let me draw the +line of slope one here this is + + align:start position:0% + + + + align:start position:0% + +okay on the Vander Poole oscillator it + + align:start position:0% +okay on the Vander Poole oscillator it + + + align:start position:0% +okay on the Vander Poole oscillator it +starts off getting bigger bigger + + align:start position:0% + + + + align:start position:0% + +bigger and then at some point it crosses + + align:start position:0% +bigger and then at some point it crosses + + + align:start position:0% +bigger and then at some point it crosses +here and goes off like + + align:start position:0% +here and goes off like + + + align:start position:0% +here and goes off like +this I think I can + + align:start position:0% +this I think I can + + + align:start position:0% +this I think I can +even tell it to generate that so you + + align:start position:0% +even tell it to generate that so you + + + align:start position:0% +even tell it to generate that so you +believe + + align:start position:0% + + + + align:start position:0% + +me + + align:start position:0% + + + + align:start position:0% + +p and I did it on top of my other plot + + align:start position:0% + + + + align:start position:0% + +again so that's + + align:start position:0% +again so that's + + + align:start position:0% +again so that's +the panc map now of this + + align:start position:0% +the panc map now of this + + + align:start position:0% +the panc map now of this +system the Blue Line This is xpk versus + + align:start position:0% +system the Blue Line This is xpk versus + + + align:start position:0% +system the Blue Line This is xpk versus +is xpk + 1 and that red line is the line + + align:start position:0% +is xpk + 1 and that red line is the line + + + align:start position:0% +is xpk + 1 and that red line is the line +of slope + + align:start position:0% +of slope + + + align:start position:0% +of slope +one all right this is a luxury of the + + align:start position:0% +one all right this is a luxury of the + + + align:start position:0% +one all right this is a luxury of the +two the the the sort of low dimensional + + align:start position:0% +two the the the sort of low dimensional + + + align:start position:0% +two the the the sort of low dimensional +systems here if I have a map from one + + align:start position:0% +systems here if I have a map from one + + + align:start position:0% +systems here if I have a map from one +variable to another variable then just + + align:start position:0% +variable to another variable then just + + + align:start position:0% +variable to another variable then just +like the the flows on a line This is a + + align:start position:0% +like the the flows on a line This is a + + + align:start position:0% +like the the flows on a line This is a +discreet Time map but I can actually + + align:start position:0% +discreet Time map but I can actually + + + align:start position:0% +discreet Time map but I can actually +analyze everything + + align:start position:0% +analyze everything + + + align:start position:0% +analyze everything +graphically okay so what do I know I + + align:start position:0% +graphically okay so what do I know I + + + align:start position:0% +graphically okay so what do I know I +already I already told you um by writing + + align:start position:0% +already I already told you um by writing + + + align:start position:0% +already I already told you um by writing +that equation that if I look at my + + align:start position:0% +that equation that if I look at my + + + align:start position:0% +that equation that if I look at my +panare map there the place where it + + align:start position:0% +panare map there the place where it + + + align:start position:0% +panare map there the place where it +crosses the line of slope + + align:start position:0% +crosses the line of slope + + + align:start position:0% +crosses the line of slope +one is a special Point what what is + + align:start position:0% +one is a special Point what what is + + + align:start position:0% +one is a special Point what what is +it it's the fix Point + + align:start position:0% +it it's the fix Point + + + align:start position:0% +it it's the fix Point +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +right and just by inspection I've + + align:start position:0% +right and just by inspection I've + + + align:start position:0% +right and just by inspection I've +actually got another fix Point here at + + align:start position:0% +actually got another fix Point here at + + + align:start position:0% +actually got another fix Point here at +this uh the + + align:start position:0% +this uh the + + + align:start position:0% +this uh the +origin okay just by inspection I can + + align:start position:0% +origin okay just by inspection I can + + + align:start position:0% +origin okay just by inspection I can +tell you about the stability of that fix + + align:start position:0% +tell you about the stability of that fix + + + align:start position:0% +tell you about the stability of that fix +Point + + align:start position:0% +Point + + + align:start position:0% +Point +okay so when I'm over here I'm getting + + align:start position:0% +okay so when I'm over here I'm getting + + + align:start position:0% +okay so when I'm over here I'm getting +bigger + + align:start position:0% +bigger + + + align:start position:0% +bigger +when I'm over here I'm getting + + align:start position:0% +when I'm over here I'm getting + + + align:start position:0% +when I'm over here I'm getting +smaller yeah so I can actually just by + + align:start position:0% +smaller yeah so I can actually just by + + + align:start position:0% +smaller yeah so I can actually just by +inspection tell you that that's going to + + align:start position:0% +inspection tell you that that's going to + + + align:start position:0% +inspection tell you that that's going to +be a stable fix point we have to be a + + align:start position:0% +be a stable fix point we have to be a + + + align:start position:0% +be a stable fix point we have to be a +little careful about it I'm going to + + align:start position:0% +little careful about it I'm going to + + + align:start position:0% +little careful about it I'm going to +show you in fact the right way to think + + align:start position:0% +show you in fact the right way to think + + + align:start position:0% +show you in fact the right way to think +about it is this staircase technique + + align:start position:0% +about it is this staircase technique + + + align:start position:0% +about it is this staircase technique +okay so if I want to follow the Dynamics + + align:start position:0% +okay so if I want to follow the Dynamics + + + align:start position:0% +okay so if I want to follow the Dynamics +of this iterated map you how many people + + align:start position:0% +of this iterated map you how many people + + + align:start position:0% +of this iterated map you how many people +seen the staircase + + align:start position:0% +seen the staircase + + + align:start position:0% +seen the staircase +pictures yeah something yeah okay so + + align:start position:0% +pictures yeah something yeah okay so + + + align:start position:0% +pictures yeah something yeah okay so +let's say I start in my system and XP is + + align:start position:0% +let's say I start in my system and XP is + + + align:start position:0% +let's say I start in my system and XP is +some small number here + + align:start position:0% +some small number here + + + align:start position:0% +some small number here +then the right way to think about that + + align:start position:0% +then the right way to think about that + + + align:start position:0% +then the right way to think about that +is the next time I I'm going to go to + + align:start position:0% +is the next time I I'm going to go to + + + align:start position:0% +is the next time I I'm going to go to +this new + + align:start position:0% +this new + + + align:start position:0% +this new +value I can sort of graphically copy + + align:start position:0% +value I can sort of graphically copy + + + align:start position:0% +value I can sort of graphically copy +that down to my next XP by drawing a + + align:start position:0% +that down to my next XP by drawing a + + + align:start position:0% +that down to my next XP by drawing a +line to the line of slope + + align:start position:0% + + + + align:start position:0% + +one and then I can from there evaluate + + align:start position:0% +one and then I can from there evaluate + + + align:start position:0% +one and then I can from there evaluate +what the next XP is going to + + align:start position:0% + + + + align:start position:0% + +be and off it goes right into the fix + + align:start position:0% +be and off it goes right into the fix + + + align:start position:0% +be and off it goes right into the fix +point that should have been a little + + align:start position:0% +point that should have been a little + + + align:start position:0% +point that should have been a little +flatter than I ended up making it but + + align:start position:0% +flatter than I ended up making it but + + + align:start position:0% +flatter than I ended up making it but +and then on this side similarly yeah I + + align:start position:0% +and then on this side similarly yeah I + + + align:start position:0% +and then on this side similarly yeah I +can go to + + align:start position:0% +can go to + + + align:start position:0% +can go to +here right into the fix Point yes did + + align:start position:0% +here right into the fix Point yes did + + + align:start position:0% +here right into the fix Point yes did +you kind of emulate a flow diagram by + + align:start position:0% +you kind of emulate a flow diagram by + + + align:start position:0% +you kind of emulate a flow diagram by +plotting xpn + - + + align:start position:0% + + + + align:start position:0% + +xpn and then instead of you know + + align:start position:0% +xpn and then instead of you know + + + align:start position:0% +xpn and then instead of you know +reaching the line of slope one when it + + align:start position:0% +reaching the line of slope one when it + + + align:start position:0% +reaching the line of slope one when it +crosses the absolutely sure sure you + + align:start position:0% +crosses the absolutely sure sure you + + + align:start position:0% +crosses the absolutely sure sure you +could subtract out xpn from there and + + align:start position:0% +could subtract out xpn from there and + + + align:start position:0% +could subtract out xpn from there and +get it in terms of zeros yeah the thing + + align:start position:0% +get it in terms of zeros yeah the thing + + + align:start position:0% +get it in terms of zeros yeah the thing +that that's might be misleading about + + align:start position:0% +that that's might be misleading about + + + align:start position:0% +that that's might be misleading about +that you have to careful and because + + align:start position:0% +that you have to careful and because + + + align:start position:0% +that you have to careful and because +discret time systems can do something + + align:start position:0% +discret time systems can do something + + + align:start position:0% +discret time systems can do something +that continuous time systems can't do is + + align:start position:0% +that continuous time systems can't do is + + + align:start position:0% +that continuous time systems can't do is +they can jump + + align:start position:0% +they can jump + + + align:start position:0% +they can jump +right so I could actually Define + + align:start position:0% +right so I could actually Define + + + align:start position:0% +right so I could actually Define +something that that looked a little + + align:start position:0% +something that that looked a little + + + align:start position:0% +something that that looked a little +benign but is actually unstable yeah if + + align:start position:0% +benign but is actually unstable yeah if + + + align:start position:0% +benign but is actually unstable yeah if +I had a something that looks like + + align:start position:0% +I had a something that looks like + + + align:start position:0% +I had a something that looks like +this + + align:start position:0% + + + + align:start position:0% + +um what does that do right go + + align:start position:0% +um what does that do right go + + + align:start position:0% +um what does that do right go +here here and you know well I guess it + + align:start position:0% +here here and you know well I guess it + + + align:start position:0% +here here and you know well I guess it +goes down to here that one might + + align:start position:0% +goes down to here that one might + + + align:start position:0% +goes down to here that one might +actually catch shoot I didn't make my + + align:start position:0% +actually catch shoot I didn't make my + + + align:start position:0% +actually catch shoot I didn't make my +point like you could limit cycle here + + align:start position:0% +point like you could limit cycle here + + + align:start position:0% +point like you could limit cycle here +like this or something right I need a + + align:start position:0% +like this or something right I need a + + + align:start position:0% +like this or something right I need a +more dramatic uh uh plot to make my + + align:start position:0% + + + + align:start position:0% + +point it's pretty funny that sort of you + + align:start position:0% +point it's pretty funny that sort of you + + + align:start position:0% +point it's pretty funny that sort of you +know it's all unitless right so it's the + + align:start position:0% +know it's all unitless right so it's the + + + align:start position:0% +know it's all unitless right so it's the +fact that I had gave myself that problem + + align:start position:0% +fact that I had gave myself that problem + + + align:start position:0% +fact that I had gave myself that problem +is ridiculous + + align:start position:0% + + + + align:start position:0% + +but you could imagine starting up here + + align:start position:0% +but you could imagine starting up here + + + align:start position:0% +but you could imagine starting up here +getting + + align:start position:0% +getting + + + align:start position:0% +getting +bigger and bigger and off you go right + + align:start position:0% +bigger and bigger and off you go right + + + align:start position:0% +bigger and bigger and off you go right +okay so what are the conditions for + + align:start position:0% +okay so what are the conditions for + + + align:start position:0% +okay so what are the conditions for +stability local stability on that fix + + align:start position:0% +stability local stability on that fix + + + align:start position:0% +stability local stability on that fix +point you all know what they are but + + align:start position:0% +point you all know what they are but + + + align:start position:0% +point you all know what they are but +just now you can maybe see them + + align:start position:0% +just now you can maybe see them + + + align:start position:0% +just now you can maybe see them +graphically by my exaggerated + + align:start position:0% +graphically by my exaggerated + + + align:start position:0% +graphically by my exaggerated +example what are the conditions on the + + align:start position:0% +example what are the conditions on the + + + align:start position:0% +example what are the conditions on the +local stability what what does the slope + + align:start position:0% +local stability what what does the slope + + + align:start position:0% +local stability what what does the slope +of that line have to + + align:start position:0% + + + + align:start position:0% + +be the magnitude has to be less than + + align:start position:0% + + + + align:start position:0% + +one right + + align:start position:0% +one right + + + align:start position:0% +one right +it could + + align:start position:0% +it could + + + align:start position:0% +it could +be sloped like this sloped like this + + align:start position:0% +be sloped like this sloped like this + + + align:start position:0% +be sloped like this sloped like this +what matters is it's not sloped past the + + align:start position:0% +what matters is it's not sloped past the + + + align:start position:0% +what matters is it's not sloped past the +line yeah the other the simpler thing to + + align:start position:0% +line yeah the other the simpler thing to + + + align:start position:0% +line yeah the other the simpler thing to +draw for instability it would be if my + + align:start position:0% +draw for instability it would be if my + + + align:start position:0% +draw for instability it would be if my +plot had gone like this that it's + + align:start position:0% +plot had gone like this that it's + + + align:start position:0% +plot had gone like this that it's +clearly + + align:start position:0% +clearly + + + align:start position:0% +clearly +unstable + + align:start position:0% + + + + align:start position:0% + +right because then I go like this this + + align:start position:0% +right because then I go like this this + + + align:start position:0% +right because then I go like this this +this this and off off I go to Infinity + + align:start position:0% +this this and off off I go to Infinity + + + align:start position:0% +this this and off off I go to Infinity +but it also + + align:start position:0% +but it also + + + align:start position:0% +but it also +happens if I'm unstable like this + + align:start position:0% +happens if I'm unstable like this + + + align:start position:0% +happens if I'm unstable like this +because I + + align:start position:0% +because I + + + align:start position:0% +because I +I oscillate myself out off to + + align:start position:0% + + + + align:start position:0% + +Infinity + + align:start position:0% + + + + align:start position:0% + +right if I look at the gradient of p + + align:start position:0% +right if I look at the gradient of p + + + align:start position:0% +right if I look at the gradient of p +with respect to to X at some fixed + + align:start position:0% +with respect to to X at some fixed + + + align:start position:0% +with respect to to X at some fixed +point right the igen values of that had + + align:start position:0% +point right the igen values of that had + + + align:start position:0% +point right the igen values of that had +better be less than one for it to be + + align:start position:0% +better be less than one for it to be + + + align:start position:0% +better be less than one for it to be +stable yeah so you're linearizing it + + align:start position:0% +stable yeah so you're linearizing it + + + align:start position:0% +stable yeah so you're linearizing it +basically at that point right so that's + + align:start position:0% +basically at that point right so that's + + + align:start position:0% +basically at that point right so that's +a statement about local + + align:start position:0% +a statement about local + + + align:start position:0% +a statement about local +stability one of the cool things about + + align:start position:0% +stability one of the cool things about + + + align:start position:0% +stability one of the cool things about +these Maps actually is people have + + align:start position:0% +these Maps actually is people have + + + align:start position:0% +these Maps actually is people have +stronger you know certainly graphically + + align:start position:0% +stronger you know certainly graphically + + + align:start position:0% +stronger you know certainly graphically +I did sort of a stronger thing I said I + + align:start position:0% +I did sort of a stronger thing I said I + + + align:start position:0% +I did sort of a stronger thing I said I +could just look at this and know that it + + align:start position:0% +could just look at this and know that it + + + align:start position:0% +could just look at this and know that it +was stable people actually know quite a + + align:start position:0% +was stable people actually know quite a + + + align:start position:0% +was stable people actually know quite a +bit about the prop of these Maps it + + align:start position:0% +bit about the prop of these Maps it + + + align:start position:0% +bit about the prop of these Maps it +turns out this is just again for culture + + align:start position:0% +turns out this is just again for culture + + + align:start position:0% +turns out this is just again for culture +it turns out if you have a unimodal map + + align:start position:0% +it turns out if you have a unimodal map + + + align:start position:0% +it turns out if you have a unimodal map +like + + align:start position:0% +like + + + align:start position:0% +like +this if the gradient doesn't change + + align:start position:0% +this if the gradient doesn't change + + + align:start position:0% +this if the gradient doesn't change +sign okay then and if it's locally + + align:start position:0% +sign okay then and if it's locally + + + align:start position:0% +sign okay then and if it's locally +stable then you can infer global + + align:start position:0% +stable then you can infer global + + + align:start position:0% +stable then you can infer global +stability okay there's a citation in the + + align:start position:0% +stability okay there's a citation in the + + + align:start position:0% +stability okay there's a citation in the +notes where you can see that the careful + + align:start position:0% +notes where you can see that the careful + + + align:start position:0% +notes where you can see that the careful +result of that okay some of the kod + + align:start position:0% +result of that okay some of the kod + + + align:start position:0% +result of that okay some of the kod +hopping work uh exploited that uh that + + align:start position:0% +hopping work uh exploited that uh that + + + align:start position:0% +hopping work uh exploited that uh that +result okay so people do know some some + + align:start position:0% +result okay so people do know some some + + + align:start position:0% +result okay so people do know some some +things more more strong Global + + align:start position:0% +things more more strong Global + + + align:start position:0% +things more more strong Global +properties of these Maps yeah but the + + align:start position:0% +properties of these Maps yeah but the + + + align:start position:0% +properties of these Maps yeah but the +trivial one to think about is this local + + align:start position:0% + + + + align:start position:0% + +stability okay + + align:start position:0% + + + + align:start position:0% + +so we know a bit now about how to talk + + align:start position:0% +so we know a bit now about how to talk + + + align:start position:0% +so we know a bit now about how to talk +about whether a limit Cycle System is + + align:start position:0% +about whether a limit Cycle System is + + + align:start position:0% +about whether a limit Cycle System is +stable right it was it's a little more + + align:start position:0% +stable right it was it's a little more + + + align:start position:0% +stable right it was it's a little more +subtle than fixed Point stability but + + align:start position:0% +subtle than fixed Point stability but + + + align:start position:0% +subtle than fixed Point stability but +not too bad + + align:start position:0% +not too bad + + + align:start position:0% +not too bad +right the hard part is it comes if you + + align:start position:0% +right the hard part is it comes if you + + + align:start position:0% +right the hard part is it comes if you +can't find a mapping that it always + + align:start position:0% +can't find a mapping that it always + + + align:start position:0% +can't find a mapping that it always +where it always returns to itself and + + align:start position:0% +where it always returns to itself and + + + align:start position:0% +where it always returns to itself and +then you have problems right but in this + + align:start position:0% +then you have problems right but in this + + + align:start position:0% +then you have problems right but in this +case you can say strong things about the + + align:start position:0% +case you can say strong things about the + + + align:start position:0% +case you can say strong things about the +stability okay now we're set up to talk + + align:start position:0% +stability okay now we're set up to talk + + + align:start position:0% +stability okay now we're set up to talk +about walking okay so my favorite topic + + align:start position:0% +about walking okay so my favorite topic + + + align:start position:0% +about walking okay so my favorite topic +here let me actually um say historically + + align:start position:0% +here let me actually um say historically + + + align:start position:0% +here let me actually um say historically +I mean people have obviously been + + align:start position:0% +I mean people have obviously been + + + align:start position:0% +I mean people have obviously been +interested in Walking for a long long + + align:start position:0% + + + + align:start position:0% + +time some people say that the first sort + + align:start position:0% +time some people say that the first sort + + + align:start position:0% +time some people say that the first sort +of uh serious study of legged Locomotion + + align:start position:0% +of uh serious study of legged Locomotion + + + align:start position:0% +of uh serious study of legged Locomotion +was by a photographer what's his + + align:start position:0% +was by a photographer what's his + + + align:start position:0% +was by a photographer what's his +name mbridge + + align:start position:0% +name mbridge + + + align:start position:0% +name mbridge +good yeah so a + + align:start position:0% +good yeah so a + + + align:start position:0% +good yeah so a +photographer had a sort of a a fast + + align:start position:0% +photographer had a sort of a a fast + + + align:start position:0% +photographer had a sort of a a fast +shutter speed camera and he had animals + + align:start position:0% +shutter speed camera and he had animals + + + align:start position:0% +shutter speed camera and he had animals +run in front of U graph paper basically + + align:start position:0% +run in front of U graph paper basically + + + align:start position:0% +run in front of U graph paper basically +right and he tried to uh win a bet I + + align:start position:0% +right and he tried to uh win a bet I + + + align:start position:0% +right and he tried to uh win a bet I +think was the story um because people + + align:start position:0% +think was the story um because people + + + align:start position:0% +think was the story um because people +weren't sure when when horses were doing + + align:start position:0% +weren't sure when when horses were doing + + + align:start position:0% +weren't sure when when horses were doing +their sort of certain gate whether they + + align:start position:0% +their sort of certain gate whether they + + + align:start position:0% +their sort of certain gate whether they +I think it was a Gallop they asked if if + + align:start position:0% +I think it was a Gallop they asked if if + + + align:start position:0% +I think it was a Gallop they asked if if +when a horse gallops does he ever + + align:start position:0% +when a horse gallops does he ever + + + align:start position:0% +when a horse gallops does he ever +actually get all four feet off the + + align:start position:0% +actually get all four feet off the + + + align:start position:0% +actually get all four feet off the +ground right and the guy who sort of + + align:start position:0% +ground right and the guy who sort of + + + align:start position:0% +ground right and the guy who sort of +proved that it was a photographer that + + align:start position:0% +proved that it was a photographer that + + + align:start position:0% +proved that it was a photographer that +took a picture of all four feet coming + + align:start position:0% +took a picture of all four feet coming + + + align:start position:0% +took a picture of all four feet coming +off the ground okay and you can get his + + align:start position:0% +off the ground okay and you can get his + + + align:start position:0% +off the ground okay and you can get his +books which are these fantastic books of + + align:start position:0% +books which are these fantastic books of + + + align:start position:0% +books which are these fantastic books of +all sorts of animals just pictures and + + align:start position:0% +all sorts of animals just pictures and + + + align:start position:0% +all sorts of animals just pictures and +pictures and pictures of all sorts of + + align:start position:0% +pictures and pictures of all sorts of + + + align:start position:0% +pictures and pictures of all sorts of +animals you sort of almost strobe + + align:start position:0% +animals you sort of almost strobe + + + align:start position:0% +animals you sort of almost strobe +photography of this in front of these + + align:start position:0% +photography of this in front of these + + + align:start position:0% +photography of this in front of these +animals walking in front of a a graph + + align:start position:0% +animals walking in front of a a graph + + + align:start position:0% +animals walking in front of a a graph +paper you know you get elephants and + + align:start position:0% +paper you know you get elephants and + + + align:start position:0% +paper you know you get elephants and +camels and you know humans and babies + + align:start position:0% +camels and you know humans and babies + + + align:start position:0% +camels and you know humans and babies +and um horses and dogs you name it so if + + align:start position:0% +and um horses and dogs you name it so if + + + align:start position:0% +and um horses and dogs you name it so if +you uh if you ever sort + + align:start position:0% +you uh if you ever sort + + + align:start position:0% +you uh if you ever sort +of are curious what the Gate of a + + align:start position:0% +of are curious what the Gate of a + + + align:start position:0% +of are curious what the Gate of a +certain animal looks like you can go to + + align:start position:0% +certain animal looks like you can go to + + + align:start position:0% +certain animal looks like you can go to +mybridge and he also sort of started + + align:start position:0% +mybridge and he also sort of started + + + align:start position:0% +mybridge and he also sort of started +defining this language for describing + + align:start position:0% +defining this language for describing + + + align:start position:0% +defining this language for describing +the gates of different animals like you + + align:start position:0% +the gates of different animals like you + + + align:start position:0% +the gates of different animals like you +know which feet are on the ground at + + align:start position:0% +know which feet are on the ground at + + + align:start position:0% +know which feet are on the ground at +which time and stuff like that so so + + align:start position:0% +which time and stuff like that so so + + + align:start position:0% +which time and stuff like that so so +this was in the the turn of the century + + align:start position:0% +this was in the the turn of the century + + + align:start position:0% +this was in the the turn of the century +the you know late 1800s early 1900s this + + align:start position:0% +the you know late 1800s early 1900s this + + + align:start position:0% +the you know late 1800s early 1900s this +photographer sort of started our our + + align:start position:0% +photographer sort of started our our + + + align:start position:0% +photographer sort of started our our +field okay um more recently though + + align:start position:0% +field okay um more recently though + + + align:start position:0% +field okay um more recently though +people started the first sort of serious + + align:start position:0% +people started the first sort of serious + + + align:start position:0% +people started the first sort of serious +modeling that's which is with the impact + + align:start position:0% +modeling that's which is with the impact + + + align:start position:0% +modeling that's which is with the impact +that's sort of remain today I think was + + align:start position:0% +that's sort of remain today I think was + + + align:start position:0% +that's sort of remain today I think was +was McMahon at uh at Harvard he was um + + align:start position:0% +was McMahon at uh at Harvard he was um + + + align:start position:0% +was McMahon at uh at Harvard he was um +uh biomechanist yeah and uh uh he + + align:start position:0% +uh biomechanist yeah and uh uh he + + + align:start position:0% +uh biomechanist yeah and uh uh he +observed that EMG in your leg if you + + align:start position:0% +observed that EMG in your leg if you + + + align:start position:0% +observed that EMG in your leg if you +look at the muscle activity electrom + + align:start position:0% +look at the muscle activity electrom + + + align:start position:0% +look at the muscle activity electrom +myographic activity in your legs just + + align:start position:0% +myographic activity in your legs just + + + align:start position:0% +myographic activity in your legs just +the electrical signal sent to your + + align:start position:0% +the electrical signal sent to your + + + align:start position:0% +the electrical signal sent to your +muscle that um uh your stance + + align:start position:0% +muscle that um uh your stance + + + align:start position:0% +muscle that um uh your stance +leg has almost very little EMG sorry + + align:start position:0% +leg has almost very little EMG sorry + + + align:start position:0% +leg has almost very little EMG sorry +very a lot of EMG and your swing hug has + + align:start position:0% +very a lot of EMG and your swing hug has + + + align:start position:0% +very a lot of EMG and your swing hug has +very little EMG with the exception of + + align:start position:0% +very little EMG with the exception of + + + align:start position:0% +very little EMG with the exception of +right when you begin swing there's a + + align:start position:0% +right when you begin swing there's a + + + align:start position:0% +right when you begin swing there's a +there's a lot of EMG and right towards + + align:start position:0% +there's a lot of EMG and right towards + + + align:start position:0% +there's a lot of EMG and right towards +the end of Swing there's a lot of EMG + + align:start position:0% +the end of Swing there's a lot of EMG + + + align:start position:0% +the end of Swing there's a lot of EMG +activity so your muscles are doing + + align:start position:0% +activity so your muscles are doing + + + align:start position:0% +activity so your muscles are doing +seemingly a lot of + + align:start position:0% +seemingly a lot of + + + align:start position:0% +seemingly a lot of +work at the beginning at end but the the + + align:start position:0% +work at the beginning at end but the the + + + align:start position:0% +work at the beginning at end but the the +surprising thing and your stance leg is + + align:start position:0% +surprising thing and your stance leg is + + + align:start position:0% +surprising thing and your stance leg is +doing a lot of work right but the + + align:start position:0% +doing a lot of work right but the + + + align:start position:0% +doing a lot of work right but the +surprising thing was that the inside a + + align:start position:0% +surprising thing was that the inside a + + + align:start position:0% +surprising thing was that the inside a +phase your muscles almost turn off okay + + align:start position:0% +phase your muscles almost turn off okay + + + align:start position:0% +phase your muscles almost turn off okay +and that got people so McMahon um told + + align:start position:0% +and that got people so McMahon um told + + + align:start position:0% +and that got people so McMahon um told +the produced for the world uh uh the + + align:start position:0% +the produced for the world uh uh the + + + align:start position:0% +the produced for the world uh uh the +ballistic Walker model + + align:start position:0% + + + + align:start position:0% + +he was at + + align:start position:0% + + + + align:start position:0% + +Harvard and he + + align:start position:0% +Harvard and he + + + align:start position:0% +Harvard and he +basically did some modeling of a + + align:start position:0% +basically did some modeling of a + + + align:start position:0% +basically did some modeling of a +three-link + + align:start position:0% + + + + align:start position:0% + +pendulum something like that and and + + align:start position:0% +pendulum something like that and and + + + align:start position:0% +pendulum something like that and and +showed that um that even with a straight + + align:start position:0% +showed that um that even with a straight + + + align:start position:0% +showed that um that even with a straight +leg on your stance leg if you let your + + align:start position:0% +leg on your stance leg if you let your + + + align:start position:0% +leg on your stance leg if you let your +swing leg just go then you can get very + + align:start position:0% +swing leg just go then you can get very + + + align:start position:0% +swing leg just go then you can get very +natural Gates coming out very very + + align:start position:0% +natural Gates coming out very very + + + align:start position:0% +natural Gates coming out very very +reasonable kinematic descriptions of + + align:start position:0% +reasonable kinematic descriptions of + + + align:start position:0% +reasonable kinematic descriptions of +what human walking looks + + align:start position:0% +what human walking looks + + + align:start position:0% +what human walking looks +like + + align:start position:0% + + + + align:start position:0% + +okay hence the name ballistic Walker + + align:start position:0% +okay hence the name ballistic Walker + + + align:start position:0% +okay hence the name ballistic Walker +this this is a passive phase so the one + + align:start position:0% +this this is a passive phase so the one + + + align:start position:0% +this this is a passive phase so the one +of the dominant ideas that that came out + + align:start position:0% +of the dominant ideas that that came out + + + align:start position:0% +of the dominant ideas that that came out +of that work was the notion that um + + align:start position:0% +of that work was the notion that um + + + align:start position:0% +of that work was the notion that um +people talk about now is walking by + + align:start position:0% + + + + align:start position:0% + +vaulting if you want a first order + + align:start position:0% +vaulting if you want a first order + + + align:start position:0% +vaulting if you want a first order +approximation of what walking is they + + align:start position:0% +approximation of what walking is they + + + align:start position:0% +approximation of what walking is they +said think about your stance leg as a + + align:start position:0% +said think about your stance leg as a + + + align:start position:0% +said think about your stance leg as a +rod and you just Vault over your stance + + align:start position:0% +rod and you just Vault over your stance + + + align:start position:0% +rod and you just Vault over your stance +leg and in fact people Center of mass do + + align:start position:0% +leg and in fact people Center of mass do + + + align:start position:0% +leg and in fact people Center of mass do +tend to go up over the course of a + + align:start position:0% +tend to go up over the course of a + + + align:start position:0% +tend to go up over the course of a +stance and then back down okay so the + + align:start position:0% +stance and then back down okay so the + + + align:start position:0% +stance and then back down okay so the +dominant Theory really was that you + + align:start position:0% +dominant Theory really was that you + + + align:start position:0% +dominant Theory really was that you +could think about this as a stiff leg + + align:start position:0% +could think about this as a stiff leg + + + align:start position:0% +could think about this as a stiff leg +right and then an almost passive swing + + align:start position:0% +right and then an almost passive swing + + + align:start position:0% +right and then an almost passive swing +phase + + align:start position:0% +phase + + + align:start position:0% +phase +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now I remember last year's uh Dynamic + + align:start position:0% +now I remember last year's uh Dynamic + + + align:start position:0% +now I remember last year's uh Dynamic +walking meeting um basically you know + + align:start position:0% +walking meeting um basically you know + + + align:start position:0% +walking meeting um basically you know +half the talks were saying walking is + + align:start position:0% +half the talks were saying walking is + + + align:start position:0% +half the talks were saying walking is +not vaulting anymore it's like it's like + + align:start position:0% +not vaulting anymore it's like it's like + + + align:start position:0% +not vaulting anymore it's like it's like +just in the last year or so people are + + align:start position:0% +just in the last year or so people are + + + align:start position:0% +just in the last year or so people are +really really changing their mind about + + align:start position:0% +really really changing their mind about + + + align:start position:0% +really really changing their mind about +this including you guys in the media lab + + align:start position:0% +this including you guys in the media lab + + + align:start position:0% +this including you guys in the media lab +are talking a lot about the role of + + align:start position:0% +are talking a lot about the role of + + + align:start position:0% +are talking a lot about the role of +compliance in The Stance leg in energy + + align:start position:0% +compliance in The Stance leg in energy + + + align:start position:0% +compliance in The Stance leg in energy +storage during walking which was left + + align:start position:0% +storage during walking which was left + + + align:start position:0% +storage during walking which was left +out of these initial models but I think + + align:start position:0% +out of these initial models but I think + + + align:start position:0% +out of these initial models but I think +if you want a zero order model of + + align:start position:0% +if you want a zero order model of + + + align:start position:0% +if you want a zero order model of +walking thinking about your Str your + + align:start position:0% +walking thinking about your Str your + + + align:start position:0% +walking thinking about your Str your +stance leg as a as straight is not is + + align:start position:0% +stance leg as a as straight is not is + + + align:start position:0% +stance leg as a as straight is not is +not a bad way to + + align:start position:0% +not a bad way to + + + align:start position:0% +not a bad way to +start + + align:start position:0% +start + + + align:start position:0% +start +okay and the other thing that happened + + align:start position:0% +okay and the other thing that happened + + + align:start position:0% +okay and the other thing that happened +because of this work was this this idea + + align:start position:0% +because of this work was this this idea + + + align:start position:0% +because of this work was this this idea +of passive Dynamic walking yeah + + align:start position:0% + + + + align:start position:0% + +so this guy Tad + + align:start position:0% + + + + align:start position:0% + +mcgear so McMahon's model was just a + + align:start position:0% +mcgear so McMahon's model was just a + + + align:start position:0% +mcgear so McMahon's model was just a +model of the Swing phase it didn't talk + + align:start position:0% +model of the Swing phase it didn't talk + + + align:start position:0% +model of the Swing phase it didn't talk +about stability it didn't even talk + + align:start position:0% +about stability it didn't even talk + + + align:start position:0% +about stability it didn't even talk +about ground ground attct it wasn't a + + align:start position:0% +about ground ground attct it wasn't a + + + align:start position:0% +about ground ground attct it wasn't a +sort of a a periodic motion it was just + + align:start position:0% +sort of a a periodic motion it was just + + + align:start position:0% +sort of a a periodic motion it was just +saying something about the kinematics of + + align:start position:0% +saying something about the kinematics of + + + align:start position:0% +saying something about the kinematics of +Swing phase and this guy Tad mcgear + + align:start position:0% +Swing phase and this guy Tad mcgear + + + align:start position:0% +Swing phase and this guy Tad mcgear +who's actually an arrow engineer he + + align:start position:0% +who's actually an arrow engineer he + + + align:start position:0% +who's actually an arrow engineer he +works on uavs now yeah um came in and + + align:start position:0% +works on uavs now yeah um came in and + + + align:start position:0% +works on uavs now yeah um came in and +turned the robotics World on its head by + + align:start position:0% +turned the robotics World on its head by + + + align:start position:0% +turned the robotics World on its head by +building a bunch of machines that had no + + align:start position:0% +building a bunch of machines that had no + + + align:start position:0% +building a bunch of machines that had no +motor no controller and walk down a + + align:start position:0% +motor no controller and walk down a + + + align:start position:0% +motor no controller and walk down a +small ramp basically using these + + align:start position:0% +small ramp basically using these + + + align:start position:0% +small ramp basically using these +ballistic walking kind of ideas + + align:start position:0% + + + + align:start position:0% + +okay so Tad's a good guy uh + + align:start position:0% +okay so Tad's a good guy uh + + + align:start position:0% +okay so Tad's a good guy uh +um Let me let him + + align:start position:0% +um Let me let him + + + align:start position:0% +um Let me let him +describe I've got a video of him talking + + align:start position:0% +describe I've got a video of him talking + + + align:start position:0% +describe I've got a video of him talking +about passive walking here + + align:start position:0% + + + + align:start position:0% + +this familiar toy is a passive Dynamic + + align:start position:0% +this familiar toy is a passive Dynamic + + + align:start position:0% +this familiar toy is a passive Dynamic +Walker with energy supplied by fall we + + align:start position:0% +Walker with energy supplied by fall we + + + align:start position:0% +Walker with energy supplied by fall we +and right + + align:start position:0% +and right + + + align:start position:0% +and right +start it settles into a steady walking + + align:start position:0% +start it settles into a steady walking + + + align:start position:0% +start it settles into a steady walking +cycle sustained by an entirely passive + + align:start position:0% +cycle sustained by an entirely passive + + + align:start position:0% +cycle sustained by an entirely passive +interaction of gravity and + + align:start position:0% +interaction of gravity and + + + align:start position:0% +interaction of gravity and +inertia this machine is also a passive + + align:start position:0% +inertia this machine is also a passive + + + align:start position:0% +inertia this machine is also a passive +Dynamic Walker for that matter I may be + + align:start position:0% +Dynamic Walker for that matter I may be + + + align:start position:0% +Dynamic Walker for that matter I may be +a passive Dynamic Walker as you'll see + + align:start position:0% +a passive Dynamic Walker as you'll see + + + align:start position:0% +a passive Dynamic Walker as you'll see +our gates are quite similar the camera + + align:start position:0% +our gates are quite similar the camera + + + align:start position:0% +our gates are quite similar the camera +was running the day when the analysis + + align:start position:0% +was running the day when the analysis + + + align:start position:0% +was running the day when the analysis +and my intuition were brought + + align:start position:0% +and my intuition were brought + + + align:start position:0% +and my intuition were brought +inclusively into + + align:start position:0% + + + + align:start position:0% + +lot God those few steps convinc us that + + align:start position:0% +lot God those few steps convinc us that + + + align:start position:0% +lot God those few steps convinc us that +we had the Dynamics right the reason the + + align:start position:0% +we had the Dynamics right the reason the + + + align:start position:0% +we had the Dynamics right the reason the +machine failed was a problem called knee + + align:start position:0% +machine failed was a problem called knee + + + align:start position:0% +machine failed was a problem called knee +bounds so for later experiments we went + + align:start position:0% +bounds so for later experiments we went + + + align:start position:0% +bounds so for later experiments we went +to a set of mechanical catches and the + + align:start position:0% +to a set of mechanical catches and the + + + align:start position:0% +to a set of mechanical catches and the +next sequence shows our Tri with + + align:start position:0% + + + + align:start position:0% + +those I guess they + + align:start position:0% +those I guess they + + + align:start position:0% +those I guess they +work that's a big deal that's when it + + align:start position:0% +work that's a big deal that's when it + + + align:start position:0% +work that's a big deal that's when it +that's that started you know a lot of + + align:start position:0% +that's that started you know a lot of + + + align:start position:0% +that's that started you know a lot of +research right is that 1990 1990 exactly + + align:start position:0% +research right is that 1990 1990 exactly + + + align:start position:0% +research right is that 1990 1990 exactly +so uh + + align:start position:0% + + + + align:start position:0% + +the KNE latch is the last time where the + + align:start position:0% +the KNE latch is the last time where the + + + align:start position:0% +the KNE latch is the last time where the +de bouncers of + + align:start position:0% + + + + align:start position:0% + +today no motor no controller that's just + + align:start position:0% +today no motor no controller that's just + + + align:start position:0% +today no motor no controller that's just +falling down a ramp that's beautiful + + align:start position:0% +falling down a ramp that's beautiful + + + align:start position:0% +falling down a ramp that's beautiful +right I love this video because it shows + + align:start position:0% +right I love this video because it shows + + + align:start position:0% +right I love this video because it shows +you + + align:start position:0% +you + + + align:start position:0% +you +the sort of the honest uh capabilities + + align:start position:0% +the sort of the honest uh capabilities + + + align:start position:0% +the sort of the honest uh capabilities +of this these things there's a few + + align:start position:0% +of this these things there's a few + + + align:start position:0% +of this these things there's a few +outakes + + align:start position:0% + + + + align:start position:0% + +yeah that's what it's like working with + + align:start position:0% + + + + align:start position:0% + +them that was pretty benign + + align:start position:0% + + + + align:start position:0% + +it's a pretty robust phenomenon right so + + align:start position:0% +it's a pretty robust phenomenon right so + + + align:start position:0% +it's a pretty robust phenomenon right so +this is he's + + align:start position:0% +this is he's + + + align:start position:0% +this is he's +changing he's changing the ramp angle + + align:start position:0% +changing he's changing the ramp angle + + + align:start position:0% +changing he's changing the ramp angle +quite a bit right and getting + + align:start position:0% +quite a bit right and getting + + + align:start position:0% +quite a bit right and getting +these really graceful motions + + align:start position:0% + + + + align:start position:0% + +out this guy walks sideways for some + + align:start position:0% +out this guy walks sideways for some + + + align:start position:0% +out this guy walks sideways for some +reason + + align:start position:0% + + + + align:start position:0% + +it's really good + + align:start position:0% + + + + align:start position:0% + +yeah you got to realize this was at a + + align:start position:0% +yeah you got to realize this was at a + + + align:start position:0% +yeah you got to realize this was at a +time when The Walking robots of the + + align:start position:0% +time when The Walking robots of the + + + align:start position:0% +time when The Walking robots of the +world were going like this right + + align:start position:0% +world were going like this right + + + align:start position:0% +world were going like this right +you know moving like like that this guy + + align:start position:0% +you know moving like like that this guy + + + align:start position:0% +you know moving like like that this guy +says I got a robot with no motor no + + align:start position:0% +says I got a robot with no motor no + + + align:start position:0% +says I got a robot with no motor no +controller look what it can do yeah + + align:start position:0% +controller look what it can do yeah + + + align:start position:0% +controller look what it can do yeah +really amazing and he was an aerospace + + align:start position:0% +really amazing and he was an aerospace + + + align:start position:0% +really amazing and he was an aerospace +engineer go figure yeah this is stealing + + align:start position:0% +engineer go figure yeah this is stealing + + + align:start position:0% +engineer go figure yeah this is stealing +the show hold on that's the next + + align:start position:0% + + + + align:start position:0% + +bit okay so uh so these passive walking + + align:start position:0% +bit okay so uh so these passive walking + + + align:start position:0% +bit okay so uh so these passive walking +ideas have really had a big impact on on + + align:start position:0% +ideas have really had a big impact on on + + + align:start position:0% +ideas have really had a big impact on on +the world of walking robots they had it + + align:start position:0% +the world of walking robots they had it + + + align:start position:0% +the world of walking robots they had it +in two waves I guess they had it this + + align:start position:0% +in two waves I guess they had it this + + + align:start position:0% +in two waves I guess they had it this +initial everybody knew that a purely + + align:start position:0% +initial everybody knew that a purely + + + align:start position:0% +initial everybody knew that a purely +passive um Walker could could walk down + + align:start position:0% +passive um Walker could could walk down + + + align:start position:0% +passive um Walker could could walk down +a small slope and then you know people + + align:start position:0% +a small slope and then you know people + + + align:start position:0% +a small slope and then you know people +have been reworking for the for the the + + align:start position:0% +have been reworking for the for the the + + + align:start position:0% +have been reworking for the for the the +second part of that video was a video + + align:start position:0% +second part of that video was a video + + + align:start position:0% +second part of that video was a video +finally someone had put Motors on it and + + align:start position:0% +finally someone had put Motors on it and + + + align:start position:0% +finally someone had put Motors on it and +make it walk on the flat because it took + + align:start position:0% +make it walk on the flat because it took + + + align:start position:0% +make it walk on the flat because it took +it took a surprisingly long time to make + + align:start position:0% +it took a surprisingly long time to make + + + align:start position:0% +it took a surprisingly long time to make +that leap okay um so now people I think + + align:start position:0% +that leap okay um so now people I think + + + align:start position:0% +that leap okay um so now people I think +don't just think they're a nice party + + align:start position:0% +don't just think they're a nice party + + + align:start position:0% +don't just think they're a nice party +trick but they're actually may be useful + + align:start position:0% +trick but they're actually may be useful + + + align:start position:0% +trick but they're actually may be useful +for design of real Walking machines + + align:start position:0% + + + + align:start position:0% + +okay well because they don't know how to + + align:start position:0% +okay well because they don't know how to + + + align:start position:0% +okay well because they don't know how to +do underactuated control + + align:start position:0% +do underactuated control + + + align:start position:0% +do underactuated control +yeah I think that's quite quite honestly + + align:start position:0% +yeah I think that's quite quite honestly + + + align:start position:0% +yeah I think that's quite quite honestly +that's my answer + + align:start position:0% + + + + align:start position:0% + +yeah it's hard to we don't have any good + + align:start position:0% +yeah it's hard to we don't have any good + + + align:start position:0% +yeah it's hard to we don't have any good +control ideas I mean what you want to do + + align:start position:0% +control ideas I mean what you want to do + + + align:start position:0% +control ideas I mean what you want to do +here is just push a little bit of energy + + align:start position:0% +here is just push a little bit of energy + + + align:start position:0% +here is just push a little bit of energy +into the system in the right way we + + align:start position:0% +into the system in the right way we + + + align:start position:0% +into the system in the right way we +don't know how to formulate those + + align:start position:0% +don't know how to formulate those + + + align:start position:0% +don't know how to formulate those +control problems when the systems are so + + align:start position:0% +control problems when the systems are so + + + align:start position:0% +control problems when the systems are so +nonlinear and discontinuous and + + align:start position:0% +nonlinear and discontinuous and + + + align:start position:0% +nonlinear and discontinuous and +everything plus I think the people that + + align:start position:0% +everything plus I think the people that + + + align:start position:0% +everything plus I think the people that +are good at building those things maybe + + align:start position:0% +are good at building those things maybe + + + align:start position:0% +are good at building those things maybe +not the same people that are good at + + align:start position:0% +not the same people that are good at + + + align:start position:0% +not the same people that are good at +control right takes a special uh Talent + + align:start position:0% +control right takes a special uh Talent + + + align:start position:0% +control right takes a special uh Talent +to turn enough screws so you should know + + align:start position:0% +to turn enough screws so you should know + + + align:start position:0% +to turn enough screws so you should know +that right um the way that the knee + + align:start position:0% +that right um the way that the knee + + + align:start position:0% +that right um the way that the knee +stayed attached how do you think the + + align:start position:0% +stayed attached how do you think the + + + align:start position:0% +stayed attached how do you think the +knee stayed attached in that why did the + + align:start position:0% +knee stayed attached in that why did the + + + align:start position:0% +knee stayed attached in that why did the +knee not Bend during The Stance + + align:start position:0% +knee not Bend during The Stance + + + align:start position:0% +knee not Bend during The Stance +phase magnetic or something wasn't + + align:start position:0% +phase magnetic or something wasn't + + + align:start position:0% +phase magnetic or something wasn't +magnetic is that's close you could + + align:start position:0% +magnetic is that's close you could + + + align:start position:0% +magnetic is that's close you could +imagine maybe the curvature of the foot + + align:start position:0% +imagine maybe the curvature of the foot + + + align:start position:0% +imagine maybe the curvature of the foot +doing it but that's not it there's + + align:start position:0% +doing it but that's not it there's + + + align:start position:0% +doing it but that's not it there's +suction cups yeah it goes and the + + align:start position:0% +suction cups yeah it goes and the + + + align:start position:0% +suction cups yeah it goes and the +suction cups don't just stick there's + + align:start position:0% +suction cups don't just stick there's + + + align:start position:0% +suction cups don't just stick there's +you poke a hole in the back of the + + align:start position:0% +you poke a hole in the back of the + + + align:start position:0% +you poke a hole in the back of the +suction cup and you tune the leakage of + + align:start position:0% +suction cup and you tune the leakage of + + + align:start position:0% +suction cup and you tune the leakage of +the suction right + + align:start position:0% +the suction right + + + align:start position:0% +the suction right +so that at the right time it pops off + + align:start position:0% +so that at the right time it pops off + + + align:start position:0% +so that at the right time it pops off +and goes like this this is not you know + + align:start position:0% +and goes like this this is not you know + + + align:start position:0% +and goes like this this is not you know +for the weak of heart there's a lot of + + align:start position:0% +for the weak of heart there's a lot of + + + align:start position:0% +for the weak of heart there's a lot of +tuning that goes in into these things so + + align:start position:0% +tuning that goes in into these things so + + + align:start position:0% +tuning that goes in into these things so +our most dramatic failure I think was um + + align:start position:0% +our most dramatic failure I think was um + + + align:start position:0% +our most dramatic failure I think was um +we had a we were doing a point foot + + align:start position:0% +we had a we were doing a point foot + + + align:start position:0% +we had a we were doing a point foot +version of these of mcgear Walker and + + align:start position:0% +version of these of mcgear Walker and + + + align:start position:0% +version of these of mcgear Walker and +for the point foot to work and get this + + align:start position:0% +for the point foot to work and get this + + + align:start position:0% +for the point foot to work and get this +nice swing without the curved feet we + + align:start position:0% +nice swing without the curved feet we + + + align:start position:0% +nice swing without the curved feet we +had to put a lot of Mass on the upper + + align:start position:0% +had to put a lot of Mass on the upper + + + align:start position:0% +had to put a lot of Mass on the upper +leg not a lot on the lower leg Yeah so + + align:start position:0% +leg not a lot on the lower leg Yeah so + + + align:start position:0% +leg not a lot on the lower leg Yeah so +we had these little fiber glass lower + + align:start position:0% +we had these little fiber glass lower + + + align:start position:0% +we had these little fiber glass lower +legs and big heavy upper legs and our + + align:start position:0% +legs and big heavy upper legs and our + + + align:start position:0% +legs and big heavy upper legs and our +failure was not just sort of falling + + align:start position:0% +failure was not just sort of falling + + + align:start position:0% +failure was not just sort of falling +down it was exploding the lower leg into + + align:start position:0% +down it was exploding the lower leg into + + + align:start position:0% +down it was exploding the lower leg into +pieces right and completely crashing + + align:start position:0% +pieces right and completely crashing + + + align:start position:0% +pieces right and completely crashing +John you remember that yeah Vanessa's + + align:start position:0% +John you remember that yeah Vanessa's + + + align:start position:0% +John you remember that yeah Vanessa's +Walker just kind of I I'm the one that + + align:start position:0% +Walker just kind of I I'm the one that + + + align:start position:0% +Walker just kind of I I'm the one that +pushed it too I had a reputation in lab + + align:start position:0% +pushed it too I had a reputation in lab + + + align:start position:0% +pushed it too I had a reputation in lab +for a little while was I had just broken + + align:start position:0% +for a little while was I had just broken + + + align:start position:0% +for a little while was I had just broken +Rick's airplane and I went around and + + align:start position:0% +Rick's airplane and I went around and + + + align:start position:0% +Rick's airplane and I went around and +turned around and broke Vanessa's Walker + + align:start position:0% +turned around and broke Vanessa's Walker + + + align:start position:0% +turned around and broke Vanessa's Walker +and they're all on tape + + align:start position:0% + + + + align:start position:0% + +um so mcgear apart from building these + + align:start position:0% +um so mcgear apart from building these + + + align:start position:0% +um so mcgear apart from building these +beautiful machines gave us this + + align:start position:0% +beautiful machines gave us this + + + align:start position:0% +beautiful machines gave us this +beautiful model to think about the + + align:start position:0% +beautiful model to think about the + + + align:start position:0% +beautiful model to think about the +essential dynamics of walking okay the + + align:start position:0% +essential dynamics of walking okay the + + + align:start position:0% +essential dynamics of walking okay the +ballistic Walker um told us about the + + align:start position:0% +ballistic Walker um told us about the + + + align:start position:0% +ballistic Walker um told us about the +swing phase but that's actually sort of + + align:start position:0% +swing phase but that's actually sort of + + + align:start position:0% +swing phase but that's actually sort of +secondary what you really matters is + + align:start position:0% +secondary what you really matters is + + + align:start position:0% +secondary what you really matters is +this passive interaction between inera + + align:start position:0% +this passive interaction between inera + + + align:start position:0% +this passive interaction between inera +and gravity as as Tad said + + align:start position:0% +and gravity as as Tad said + + + align:start position:0% +and gravity as as Tad said +okay and it turns out you can you can + + align:start position:0% +okay and it turns out you can you can + + + align:start position:0% +okay and it turns out you can you can +understand that um if you just think + + align:start position:0% +understand that um if you just think + + + align:start position:0% +understand that um if you just think +about this little system called the + + align:start position:0% +about this little system called the + + + align:start position:0% +about this little system called the +rimless wheel okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so I'm going to put it on a slope of + + align:start position:0% +so I'm going to put it on a slope of + + + align:start position:0% +so I'm going to put it on a slope of +height of of angle + + align:start position:0% +height of of angle + + + align:start position:0% +height of of angle +gamma the model is going to + + align:start position:0% +gamma the model is going to + + + align:start position:0% +gamma the model is going to +be a simple pendulum with a mass at the + + align:start position:0% +be a simple pendulum with a mass at the + + + align:start position:0% +be a simple pendulum with a mass at the +end but a massless leg okay we'll Define + + align:start position:0% +end but a massless leg okay we'll Define + + + align:start position:0% +end but a massless leg okay we'll Define +Theta to be this + + align:start position:0% +Theta to be this + + + align:start position:0% +Theta to be this +the angle from from vertical now I I + + align:start position:0% +the angle from from vertical now I I + + + align:start position:0% +the angle from from vertical now I I +sort of despise the fact that my + + align:start position:0% +sort of despise the fact that my + + + align:start position:0% +sort of despise the fact that my +theta's no I'm not using the right- hand + + align:start position:0% +theta's no I'm not using the right- hand + + + align:start position:0% +theta's no I'm not using the right- hand +rule here but otherwise you end up + + align:start position:0% +rule here but otherwise you end up + + + align:start position:0% +rule here but otherwise you end up +walking backwards with negative velocity + + align:start position:0% +walking backwards with negative velocity + + + align:start position:0% +walking backwards with negative velocity +so so this is the way it is yeah so so + + align:start position:0% +so so this is the way it is yeah so so + + + align:start position:0% +so so this is the way it is yeah so so +it's almost like the simple pendulum + + align:start position:0% +it's almost like the simple pendulum + + + align:start position:0% +it's almost like the simple pendulum +except my coordinate systems from the + + align:start position:0% +except my coordinate systems from the + + + align:start position:0% +except my coordinate systems from the +top and Thea is sort of reversed okay + + align:start position:0% +top and Thea is sort of reversed okay + + + align:start position:0% +top and Thea is sort of reversed okay +and in addition to this simple pendulum + + align:start position:0% +and in addition to this simple pendulum + + + align:start position:0% +and in addition to this simple pendulum +I've got a few extra legs yeah + + align:start position:0% + + + + align:start position:0% + +that are all + + align:start position:0% +that are all + + + align:start position:0% +that are all +massless and they're separated + + align:start position:0% +massless and they're separated + + + align:start position:0% +massless and they're separated +by two alpha an angle of two alpha + + align:start position:0% +by two alpha an angle of two alpha + + + align:start position:0% +by two alpha an angle of two alpha +there's actually reasonably good + + align:start position:0% +there's actually reasonably good + + + align:start position:0% +there's actually reasonably good +pictures of this cartoons of this in the + + align:start position:0% +pictures of this cartoons of this in the + + + align:start position:0% +pictures of this cartoons of this in the +notes so you can think about this as a + + align:start position:0% +notes so you can think about this as a + + + align:start position:0% +notes so you can think about this as a +bicycle wheel right where somebody took + + align:start position:0% +bicycle wheel right where somebody took + + + align:start position:0% +bicycle wheel right where somebody took +the rim off and just left the + + align:start position:0% +the rim off and just left the + + + align:start position:0% +the rim off and just left the +spokes so what happens if you take this + + align:start position:0% +spokes so what happens if you take this + + + align:start position:0% +spokes so what happens if you take this +bicycle + + align:start position:0% +bicycle + + + align:start position:0% +bicycle +wheel and you put it at the top of a + + align:start position:0% +wheel and you put it at the top of a + + + align:start position:0% +wheel and you put it at the top of a +small ramp and you give it a push + + align:start position:0% + + + + align:start position:0% + +Falls over okay let's say it's + + align:start position:0% +Falls over okay let's say it's + + + align:start position:0% +Falls over okay let's say it's +constrained to be in the in the plane + + align:start position:0% +constrained to be in the in the plane + + + align:start position:0% +constrained to be in the in the plane +yeah that was a fair answer so we've + + align:start position:0% +yeah that was a fair answer so we've + + + align:start position:0% +yeah that was a fair answer so we've +made an additional assumption that it + + align:start position:0% +made an additional assumption that it + + + align:start position:0% +made an additional assumption that it +stays stays upright then what + + align:start position:0% + + + + align:start position:0% + +happens starts rolling down okay is it + + align:start position:0% +happens starts rolling down okay is it + + + align:start position:0% +happens starts rolling down okay is it +going to roll faster and faster + + align:start position:0% +going to roll faster and faster + + + align:start position:0% +going to roll faster and faster +forever no some point losses are going + + align:start position:0% +forever no some point losses are going + + + align:start position:0% +forever no some point losses are going +to catch up with it you know in the + + align:start position:0% +to catch up with it you know in the + + + align:start position:0% +to catch up with it you know in the +bicycle wheel you might think of it as + + align:start position:0% +bicycle wheel you might think of it as + + + align:start position:0% +bicycle wheel you might think of it as +rolling + + align:start position:0% +rolling + + + align:start position:0% +rolling +friction okay in this model we're gonna + + align:start position:0% +friction okay in this model we're gonna + + + align:start position:0% +friction okay in this model we're gonna +we're going to do it by dissipative + + align:start position:0% +we're going to do it by dissipative + + + align:start position:0% +we're going to do it by dissipative +impacts which are very + + align:start position:0% +impacts which are very + + + align:start position:0% +impacts which are very +real okay but that's actually the only + + align:start position:0% +real okay but that's actually the only + + + align:start position:0% +real okay but that's actually the only +thing we need we're not going to model + + align:start position:0% +thing we need we're not going to model + + + align:start position:0% +thing we need we're not going to model +any damping in the + + align:start position:0% +any damping in the + + + align:start position:0% +any damping in the +system so we can really think about this + + align:start position:0% +system so we can really think about this + + + align:start position:0% +system so we can really think about this +system as um let me list all my + + align:start position:0% +system as um let me list all my + + + align:start position:0% +system as um let me list all my +assumptions carefully + + align:start position:0% +assumptions carefully + + + align:start position:0% +assumptions carefully +here we're going to assume that this pin + + align:start position:0% +here we're going to assume that this pin + + + align:start position:0% +here we're going to assume that this pin +this this um the foot so so so to speak + + align:start position:0% +this this um the foot so so so to speak + + + align:start position:0% +this this um the foot so so so to speak +The Stance foot + + align:start position:0% + + + + align:start position:0% + +is a pin joint so I'm going + + align:start position:0% +is a pin joint so I'm going + + + align:start position:0% +is a pin joint so I'm going +to artificially assume that that foot + + align:start position:0% +to artificially assume that that foot + + + align:start position:0% +to artificially assume that that foot +doesn't come off the ground as soon as + + align:start position:0% +doesn't come off the ground as soon as + + + align:start position:0% +doesn't come off the ground as soon as +it C catches the ground it turns into a + + align:start position:0% +it C catches the ground it turns into a + + + align:start position:0% +it C catches the ground it turns into a +pin joint on the ground + + align:start position:0% + + + + align:start position:0% + +okay instantaneous transer of support + + align:start position:0% + + + + align:start position:0% + +which means as soon as this leg comes + + align:start position:0% +which means as soon as this leg comes + + + align:start position:0% +which means as soon as this leg comes +around hits the ground it becomes the + + align:start position:0% +around hits the ground it becomes the + + + align:start position:0% +around hits the ground it becomes the +pin joint and this guy's free I only + + align:start position:0% +pin joint and this guy's free I only + + + align:start position:0% +pin joint and this guy's free I only +think about one ground contact at a time + + align:start position:0% +think about one ground contact at a time + + + align:start position:0% +think about one ground contact at a time +I assume that is an instantaneous + + align:start position:0% +I assume that is an instantaneous + + + align:start position:0% +I assume that is an instantaneous +transfer of + + align:start position:0% +transfer of + + + align:start position:0% +transfer of +support okay the limit of standing on + + align:start position:0% +support okay the limit of standing on + + + align:start position:0% +support okay the limit of standing on +two legs is just modeled as switching + + align:start position:0% +two legs is just modeled as switching + + + align:start position:0% +two legs is just modeled as switching +back and forth really fast between those + + align:start position:0% +back and forth really fast between those + + + align:start position:0% +back and forth really fast between those +two and it works out + + align:start position:0% +two and it works out + + + align:start position:0% +two and it works out +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yeah and then I'm going to assume that + + align:start position:0% +yeah and then I'm going to assume that + + + align:start position:0% +yeah and then I'm going to assume that +the collisions with the + + align:start position:0% + + + + align:start position:0% + +ground are inelastic + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +impulsive impulsive means it's + + align:start position:0% +impulsive impulsive means it's + + + align:start position:0% +impulsive impulsive means it's +instantaneous yeah in elastic means that + + align:start position:0% +instantaneous yeah in elastic means that + + + align:start position:0% +instantaneous yeah in elastic means that +all energy going into the ground is lost + + align:start position:0% +all energy going into the ground is lost + + + align:start position:0% +all energy going into the ground is lost +to the ground there's no bouncing right + + align:start position:0% +to the ground there's no bouncing right + + + align:start position:0% +to the ground there's no bouncing right +and I need that so to make sure that + + align:start position:0% +and I need that so to make sure that + + + align:start position:0% +and I need that so to make sure that +this that there's always exactly one + + align:start position:0% +this that there's always exactly one + + + align:start position:0% +this that there's always exactly one +foot on the + + align:start position:0% +foot on the + + + align:start position:0% +foot on the +ground in this model yeah as soon as the + + align:start position:0% +ground in this model yeah as soon as the + + + align:start position:0% +ground in this model yeah as soon as the +thing bounces we have we built rimless + + align:start position:0% +thing bounces we have we built rimless + + + align:start position:0% +thing bounces we have we built rimless +Wheels with two wheels that's the way + + align:start position:0% +Wheels with two wheels that's the way + + + align:start position:0% +Wheels with two wheels that's the way +they don't fall down in practice you + + align:start position:0% +they don't fall down in practice you + + + align:start position:0% +they don't fall down in practice you +just like MC's Walker had mcgeer's bipad + + align:start position:0% +just like MC's Walker had mcgeer's bipad + + + align:start position:0% +just like MC's Walker had mcgeer's bipad +had four legs right you they call it a + + align:start position:0% +had four legs right you they call it a + + + align:start position:0% +had four legs right you they call it a +four-legged + + align:start position:0% +four-legged + + + align:start position:0% +four-legged +biped uh right but that way you don't + + align:start position:0% +biped uh right but that way you don't + + + align:start position:0% +biped uh right but that way you don't +have to worry about falling over + + align:start position:0% +have to worry about falling over + + + align:start position:0% +have to worry about falling over +sideways okay and on the real rimless + + align:start position:0% +sideways okay and on the real rimless + + + align:start position:0% +sideways okay and on the real rimless +wheel you put it on a ramp it bounces + + align:start position:0% +wheel you put it on a ramp it bounces + + + align:start position:0% +wheel you put it on a ramp it bounces +like crazy right so this is just a model + + align:start position:0% +like crazy right so this is just a model + + + align:start position:0% +like crazy right so this is just a model +right don't but it's actually captures + + align:start position:0% +right don't but it's actually captures + + + align:start position:0% +right don't but it's actually captures +the essential + + align:start position:0% + + + + align:start position:0% + +Dynamics Okay so + + align:start position:0% +Dynamics Okay so + + + align:start position:0% +Dynamics Okay so +now you see why it was good to know + + align:start position:0% +now you see why it was good to know + + + align:start position:0% +now you see why it was good to know +everything we know about pendula + + align:start position:0% +everything we know about pendula + + + align:start position:0% +everything we know about pendula +yeah how is this thing going to + + align:start position:0% + + + + align:start position:0% + +work show you the answer real quick + + align:start position:0% + + + + align:start position:0% + +okay so here's my rimless wheel that was + + align:start position:0% +okay so here's my rimless wheel that was + + + align:start position:0% +okay so here's my rimless wheel that was +a simulation so I'm going to start it + + align:start position:0% +a simulation so I'm going to start it + + + align:start position:0% +a simulation so I'm going to start it +every time I hit go it's going to start + + align:start position:0% +every time I hit go it's going to start + + + align:start position:0% +every time I hit go it's going to start +it with some random initial velocity + + align:start position:0% +it with some random initial velocity + + + align:start position:0% +it with some random initial velocity +forward uphill or downhill you name + + align:start position:0% +forward uphill or downhill you name + + + align:start position:0% +forward uphill or downhill you name +it that's going + + align:start position:0% +it that's going + + + align:start position:0% +it that's going +uphill oh just enough energy turned + + align:start position:0% +uphill oh just enough energy turned + + + align:start position:0% +uphill oh just enough energy turned +around came back down the hill okay + + align:start position:0% +around came back down the hill okay + + + align:start position:0% +around came back down the hill okay +starts speeding up a little + + align:start position:0% +starts speeding up a little + + + align:start position:0% +starts speeding up a little +bit but actually quickly settles into a + + align:start position:0% +bit but actually quickly settles into a + + + align:start position:0% +bit but actually quickly settles into a +stable forward rolling speed okay where + + align:start position:0% +stable forward rolling speed okay where + + + align:start position:0% +stable forward rolling speed okay where +the losses from Collision exactly + + align:start position:0% +the losses from Collision exactly + + + align:start position:0% +the losses from Collision exactly +balance the energy that's gained from + + align:start position:0% +balance the energy that's gained from + + + align:start position:0% +balance the energy that's gained from +converting potential to kinetic as you + + align:start position:0% +converting potential to kinetic as you + + + align:start position:0% +converting potential to kinetic as you +go down the hill + + align:start position:0% +go down the hill + + + align:start position:0% +go down the hill +okay that is the essential idea in + + align:start position:0% +okay that is the essential idea in + + + align:start position:0% +okay that is the essential idea in +Walking is a the conversion of certainly + + align:start position:0% +Walking is a the conversion of certainly + + + align:start position:0% +Walking is a the conversion of certainly +passive walking the conversion of + + align:start position:0% +passive walking the conversion of + + + align:start position:0% +passive walking the conversion of +potential energy and the balance with um + + align:start position:0% +potential energy and the balance with um + + + align:start position:0% +potential energy and the balance with um +dissipation in the ground okay so this + + align:start position:0% +dissipation in the ground okay so this + + + align:start position:0% +dissipation in the ground okay so this +is started with a slow initial speed and + + align:start position:0% +is started with a slow initial speed and + + + align:start position:0% +is started with a slow initial speed and +it speeds up a little bit goes to that + + align:start position:0% +it speeds up a little bit goes to that + + + align:start position:0% +it speeds up a little bit goes to that +rolling + + align:start position:0% + + + + align:start position:0% + +speed if you start it really fast it + + align:start position:0% +speed if you start it really fast it + + + align:start position:0% +speed if you start it really fast it +actually slows down pretty quick goes to + + align:start position:0% +actually slows down pretty quick goes to + + + align:start position:0% +actually slows down pretty quick goes to +that same rolling + + align:start position:0% +that same rolling + + + align:start position:0% +that same rolling +speed can you see where I'm going with + + align:start position:0% +speed can you see where I'm going with + + + align:start position:0% +speed can you see where I'm going with +this we got a stable limit ccle C right + + align:start position:0% +this we got a stable limit ccle C right + + + align:start position:0% +this we got a stable limit ccle C right +it's + + align:start position:0% +it's + + + align:start position:0% +it's +periodic clearly it's not going to be + + align:start position:0% +periodic clearly it's not going to be + + + align:start position:0% +periodic clearly it's not going to be +stable in the trajectory sense but it's + + align:start position:0% +stable in the trajectory sense but it's + + + align:start position:0% +stable in the trajectory sense but it's +going to be stable in the limit cycle + + align:start position:0% +going to be stable in the limit cycle + + + align:start position:0% +going to be stable in the limit cycle +sense okay just I want to see the one + + align:start position:0% +sense okay just I want to see the one + + + align:start position:0% +sense okay just I want to see the one +other thing that can + + align:start position:0% + + + + align:start position:0% + +happen the cool thing about simulating + + align:start position:0% +happen the cool thing about simulating + + + align:start position:0% +happen the cool thing about simulating +rimel Wheels is you get all these + + align:start position:0% +rimel Wheels is you get all these + + + align:start position:0% +rimel Wheels is you get all these +aliasing effects and stuff right so if + + align:start position:0% +aliasing effects and stuff right so if + + + align:start position:0% +aliasing effects and stuff right so if +the if it's going up uphill too fast it + + align:start position:0% +the if it's going up uphill too fast it + + + align:start position:0% +the if it's going up uphill too fast it +looks like it's going + + align:start position:0% +looks like it's going + + + align:start position:0% +looks like it's going +downhill there you go uphill uphill okay + + align:start position:0% +downhill there you go uphill uphill okay + + + align:start position:0% +downhill there you go uphill uphill okay +let see what happens yeah okay so that + + align:start position:0% +let see what happens yeah okay so that + + + align:start position:0% +let see what happens yeah okay so that +one just ran out of energy and stand + + align:start position:0% +one just ran out of energy and stand + + + align:start position:0% +one just ran out of energy and stand +still that's still my instantaneous + + align:start position:0% +still that's still my instantaneous + + + align:start position:0% +still that's still my instantaneous +transfer support the simulation is + + align:start position:0% +transfer support the simulation is + + + align:start position:0% +transfer support the simulation is +going changing ground contacts + + align:start position:0% +going changing ground contacts + + + align:start position:0% +going changing ground contacts +infinitely fast and that that's a + + align:start position:0% +infinitely fast and that that's a + + + align:start position:0% +infinitely fast and that that's a +perfectly good there are serious + + align:start position:0% +perfectly good there are serious + + + align:start position:0% +perfectly good there are serious +simulation people that say that's a + + align:start position:0% +simulation people that say that's a + + + align:start position:0% +simulation people that say that's a +that's the right way to handle um handle + + align:start position:0% +that's the right way to handle um handle + + + align:start position:0% +that's the right way to handle um handle +even some say that you can you should + + align:start position:0% +even some say that you can you should + + + align:start position:0% +even some say that you can you should +simulate your rigid + + align:start position:0% +simulate your rigid + + + align:start position:0% +simulate your rigid +body you should simulate a pin joint by + + align:start position:0% +body you should simulate a pin joint by + + + align:start position:0% +body you should simulate a pin joint by +constantly modeling impacts at the + + align:start position:0% +constantly modeling impacts at the + + + align:start position:0% +constantly modeling impacts at the +joints right this guy and Brian Merk who + + align:start position:0% +joints right this guy and Brian Merk who + + + align:start position:0% +joints right this guy and Brian Merk who +was at Merl for a while uh I think said + + align:start position:0% +was at Merl for a while uh I think said + + + align:start position:0% +was at Merl for a while uh I think said +did some pretty convincing work in that + + align:start position:0% +did some pretty convincing work in that + + + align:start position:0% +did some pretty convincing work in that +world all right so that's the answer + + align:start position:0% +world all right so that's the answer + + + align:start position:0% +world all right so that's the answer +we're going to get now can we see how + + align:start position:0% +we're going to get now can we see how + + + align:start position:0% +we're going to get now can we see how +that works on the face + + align:start position:0% + + + + align:start position:0% + +portrait + + align:start position:0% + + + + align:start position:0% + +okay if I look at um Theta and Theta dot + + align:start position:0% +okay if I look at um Theta and Theta dot + + + align:start position:0% +okay if I look at um Theta and Theta dot +I Robot + + align:start position:0% + + + + align:start position:0% + +here there's a couple key angles right + + align:start position:0% + + + + align:start position:0% + +Theta is only going to live between so + + align:start position:0% +Theta is only going to live between so + + + align:start position:0% +Theta is only going to live between so +it turns out to be gamma minus Alpha and + + align:start position:0% +it turns out to be gamma minus Alpha and + + + align:start position:0% +it turns out to be gamma minus Alpha and +Gamma plus Alpha see if you can work + + align:start position:0% +Gamma plus Alpha see if you can work + + + align:start position:0% +Gamma plus Alpha see if you can work +that out for yourself so this angle is + + align:start position:0% +that out for yourself so this angle is + + + align:start position:0% +that out for yourself so this angle is +is 2 Alpha right when when this leg hits + + align:start position:0% +is 2 Alpha right when when this leg hits + + + align:start position:0% +is 2 Alpha right when when this leg hits +the + + align:start position:0% +the + + + align:start position:0% +the +ground that angle has to be + + align:start position:0% +ground that angle has to be + + + align:start position:0% +ground that angle has to be +Alpha plus + + align:start position:0% + + + + align:start position:0% + +gamma okay and in the other direction + + align:start position:0% +gamma okay and in the other direction + + + align:start position:0% +gamma okay and in the other direction +it's gamma minus Alpha those are the + + align:start position:0% +it's gamma minus Alpha those are the + + + align:start position:0% +it's gamma minus Alpha those are the +conditions where this leg is about to + + align:start position:0% +conditions where this leg is about to + + + align:start position:0% +conditions where this leg is about to +change into a different coordinate + + align:start position:0% +change into a different coordinate + + + align:start position:0% +change into a different coordinate +system and I forgot to say when this + + align:start position:0% +system and I forgot to say when this + + + align:start position:0% +system and I forgot to say when this +foot changes it hits the ground I + + align:start position:0% +foot changes it hits the ground I + + + align:start position:0% +foot changes it hits the ground I +quickly redefine Theta to be the the + + align:start position:0% +quickly redefine Theta to be the the + + + align:start position:0% +quickly redefine Theta to be the the +Theta around the new PIN joint right I + + align:start position:0% +Theta around the new PIN joint right I + + + align:start position:0% +Theta around the new PIN joint right I +just reset my coordinate + + align:start position:0% +just reset my coordinate + + + align:start position:0% +just reset my coordinate +system okay so there's some there's a + + align:start position:0% +system okay so there's some there's a + + + align:start position:0% +system okay so there's some there's a +couple key um places in this plot + + align:start position:0% +couple key um places in this plot + + + align:start position:0% +couple key um places in this plot +somewhere there's some small gamma and + + align:start position:0% +somewhere there's some small gamma and + + + align:start position:0% +somewhere there's some small gamma and +that bcts two very important lines here + + align:start position:0% +that bcts two very important lines here + + + align:start position:0% +that bcts two very important lines here +which are + + align:start position:0% +which are + + + align:start position:0% +which are +gamma um theta equals + + align:start position:0% + + + + align:start position:0% + +gamma minus + + align:start position:0% +gamma minus + + + align:start position:0% +gamma minus +Alpha and Theta + + align:start position:0% +Alpha and Theta + + + align:start position:0% +Alpha and Theta +equal gamma plus + + align:start position:0% + + + + align:start position:0% + +Alpha okay my coordinate system is zero + + align:start position:0% +Alpha okay my coordinate system is zero + + + align:start position:0% +Alpha okay my coordinate system is zero +around the unstable fix Point that's + + align:start position:0% +around the unstable fix Point that's + + + align:start position:0% +around the unstable fix Point that's +what happened when I flip my coordinate + + align:start position:0% +what happened when I flip my coordinate + + + align:start position:0% +what happened when I flip my coordinate +system to the + + align:start position:0% +system to the + + + align:start position:0% +system to the +top so if I want to superimpose the + + align:start position:0% +top so if I want to superimpose the + + + align:start position:0% +top so if I want to superimpose the +phase portrait of the + + align:start position:0% + + + + align:start position:0% + +pendulum say zero is going to be the uh + + align:start position:0% +pendulum say zero is going to be the uh + + + align:start position:0% +pendulum say zero is going to be the uh +the unstable fix point so I get the eyes + + align:start position:0% +the unstable fix point so I get the eyes + + + align:start position:0% +the unstable fix point so I get the eyes +going out this way + + align:start position:0% +going out this way + + + align:start position:0% +going out this way +right that's the hom Clinic orbits if + + align:start position:0% +right that's the hom Clinic orbits if + + + align:start position:0% +right that's the hom Clinic orbits if +you remember yeah and the smaller orbits + + align:start position:0% +you remember yeah and the smaller orbits + + + align:start position:0% +you remember yeah and the smaller orbits +come in and do + + align:start position:0% + + + + align:start position:0% + +this right and the ones up + + align:start position:0% + + + + align:start position:0% + +here do this + + align:start position:0% + + + + align:start position:0% + +does anybody have + + align:start position:0% +does anybody have + + + align:start position:0% +does anybody have +the the foresight to sort of jump ahead + + align:start position:0% +the the foresight to sort of jump ahead + + + align:start position:0% +the the foresight to sort of jump ahead +and tell me where my limit cycle is + + align:start position:0% +and tell me where my limit cycle is + + + align:start position:0% +and tell me where my limit cycle is +going to live on my picture + + align:start position:0% +going to live on my picture + + + align:start position:0% +going to live on my picture +here above okay what's it going to + + align:start position:0% + + + + align:start position:0% + +do keep the trough in the same place in + + align:start position:0% +do keep the trough in the same place in + + + align:start position:0% +do keep the trough in the same place in +each awesome very very good yeah very + + align:start position:0% +each awesome very very good yeah very + + + align:start position:0% +each awesome very very good yeah very +good okay so here's everything we just + + align:start position:0% +good okay so here's everything we just + + + align:start position:0% +good okay so here's everything we just +saw in the uh in the rimless wheel okay + + align:start position:0% +saw in the uh in the rimless wheel okay + + + align:start position:0% +saw in the uh in the rimless wheel okay +if I'm rolling fast if I start with some + + align:start position:0% +if I'm rolling fast if I start with some + + + align:start position:0% +if I'm rolling fast if I start with some +initial velocity rolling fast say I'm + + align:start position:0% +initial velocity rolling fast say I'm + + + align:start position:0% +initial velocity rolling fast say I'm +high up on this line then what happens + + align:start position:0% +high up on this line then what happens + + + align:start position:0% +high up on this line then what happens +okay I'm going to ride this this guy + + align:start position:0% +okay I'm going to ride this this guy + + + align:start position:0% +okay I'm going to ride this this guy +over + + align:start position:0% + + + + align:start position:0% + +here it turns out the Collision model + + align:start position:0% +here it turns out the Collision model + + + align:start position:0% +here it turns out the Collision model +I'll tell you the Collision model in a + + align:start position:0% +I'll tell you the Collision model in a + + + align:start position:0% +I'll tell you the Collision model in a +second but the the angular + + align:start position:0% +second but the the angular + + + align:start position:0% +second but the the angular +momentum the the inelastic collision at + + align:start position:0% +momentum the the inelastic collision at + + + align:start position:0% +momentum the the inelastic collision at +the at the base essentially takes out a + + align:start position:0% +the at the base essentially takes out a + + + align:start position:0% +the at the base essentially takes out a +fraction of your velocity at every step + + align:start position:0% +fraction of your velocity at every step + + + align:start position:0% +fraction of your velocity at every step +it's a linear fraction of your velocity + + align:start position:0% +it's a linear fraction of your velocity + + + align:start position:0% +it's a linear fraction of your velocity +every + + align:start position:0% +every + + + align:start position:0% +every +step + + align:start position:0% +step + + + align:start position:0% +step +okay so I I move I take my coordinates + + align:start position:0% +okay so I I move I take my coordinates + + + align:start position:0% +okay so I I move I take my coordinates +over to here and then it's going to + + align:start position:0% +over to here and then it's going to + + + align:start position:0% +over to here and then it's going to +reset to a velocity over here but with + + align:start position:0% +reset to a velocity over here but with + + + align:start position:0% +reset to a velocity over here but with +some fraction of the uh of that velocity + + align:start position:0% +some fraction of the uh of that velocity + + + align:start position:0% +some fraction of the uh of that velocity +dissipated and I get a new trajectory + + align:start position:0% +dissipated and I get a new trajectory + + + align:start position:0% +dissipated and I get a new trajectory +like this it comes over to some + + align:start position:0% +like this it comes over to some + + + align:start position:0% +like this it comes over to some +something like this and at some point + + align:start position:0% +something like this and at some point + + + align:start position:0% +something like this and at some point +that fraction exactly + + align:start position:0% +that fraction exactly + + + align:start position:0% +that fraction exactly +balances right so because this thing is + + align:start position:0% +balances right so because this thing is + + + align:start position:0% +balances right so because this thing is +not symmetric right when I start here I + + align:start position:0% +not symmetric right when I start here I + + + align:start position:0% +not symmetric right when I start here I +end up a little bit higher with a little + + align:start position:0% +end up a little bit higher with a little + + + align:start position:0% +end up a little bit higher with a little +bit more + + align:start position:0% +bit more + + + align:start position:0% +bit more +velocity at the end than when I + + align:start position:0% +velocity at the end than when I + + + align:start position:0% +velocity at the end than when I +started and I lose a little bit of + + align:start position:0% +started and I lose a little bit of + + + align:start position:0% +started and I lose a little bit of +velocity in my impact and at some point + + align:start position:0% +velocity in my impact and at some point + + + align:start position:0% +velocity in my impact and at some point +those things exactly balance and end up + + align:start position:0% +those things exactly balance and end up + + + align:start position:0% +those things exactly balance and end up +with a stable limit cycle that looks + + align:start position:0% +with a stable limit cycle that looks + + + align:start position:0% +with a stable limit cycle that looks +like + + align:start position:0% +like + + + align:start position:0% +like +that + + align:start position:0% + + + + align:start position:0% + +right what else can happen + + align:start position:0% + + + + align:start position:0% + +if I start with too little energy the + + align:start position:0% +if I start with too little energy the + + + align:start position:0% +if I start with too little energy the +whole thing runs out of energy and + + align:start position:0% +whole thing runs out of energy and + + + align:start position:0% +whole thing runs out of energy and +stands + + align:start position:0% +stands + + + align:start position:0% +stands +still what's the critical energy + + align:start position:0% +still what's the critical energy + + + align:start position:0% +still what's the critical energy +level homin the homoclinic orbit right + + align:start position:0% +level homin the homoclinic orbit right + + + align:start position:0% +level homin the homoclinic orbit right +if I'm actually if I'm if I'm too if I'm + + align:start position:0% +if I'm actually if I'm if I'm too if I'm + + + align:start position:0% +if I'm actually if I'm if I'm too if I'm +just above the hom Clinic orbit it + + align:start position:0% +just above the hom Clinic orbit it + + + align:start position:0% +just above the hom Clinic orbit it +actually speeds up and goes to that same + + align:start position:0% +actually speeds up and goes to that same + + + align:start position:0% +actually speeds up and goes to that same +nominal limit cycle but if I'm just + + align:start position:0% +nominal limit cycle but if I'm just + + + align:start position:0% +nominal limit cycle but if I'm just +below the homoclinic orbit then I never + + align:start position:0% +below the homoclinic orbit then I never + + + align:start position:0% +below the homoclinic orbit then I never +actually make it across to this thing I + + align:start position:0% +actually make it across to this thing I + + + align:start position:0% +actually make it across to this thing I +just end up going over to here + + align:start position:0% +just end up going over to here + + + align:start position:0% +just end up going over to here +and then it actually comes in if you + + align:start position:0% +and then it actually comes in if you + + + align:start position:0% +and then it actually comes in if you +have to think about it but trust me + + align:start position:0% +have to think about it but trust me + + + align:start position:0% +have to think about it but trust me +comes in like this bnk like this and + + align:start position:0% +comes in like this bnk like this and + + + align:start position:0% +comes in like this bnk like this and +just ends up running out of energy and + + align:start position:0% +just ends up running out of energy and + + + align:start position:0% +just ends up running out of energy and +standing + + align:start position:0% + + + + align:start position:0% + +still + + align:start position:0% +still + + + align:start position:0% +still +right you start just above it but then + + align:start position:0% +right you start just above it but then + + + align:start position:0% +right you start just above it but then +the Collision knocks it down but that + + align:start position:0% +the Collision knocks it down but that + + + align:start position:0% +the Collision knocks it down but that +can happen + + align:start position:0% + + + + align:start position:0% + +too um depends on the parameters y yeah + + align:start position:0% +too um depends on the parameters y yeah + + + align:start position:0% +too um depends on the parameters y yeah +but in the parameter regime um I'm + + align:start position:0% +but in the parameter regime um I'm + + + align:start position:0% +but in the parameter regime um I'm +in uh which I think is the standard one + + align:start position:0% +in uh which I think is the standard one + + + align:start position:0% +in uh which I think is the standard one +you want to think about this has got in + + align:start position:0% +you want to think about this has got in + + + align:start position:0% +you want to think about this has got in +order for it to be have some stable fix + + align:start position:0% +order for it to be have some stable fix + + + align:start position:0% +order for it to be have some stable fix +so basically what you're talking about + + align:start position:0% +so basically what you're talking about + + + align:start position:0% +so basically what you're talking about +is a parameter regime where you have um + + align:start position:0% +is a parameter regime where you have um + + + align:start position:0% +is a parameter regime where you have um +no stable fix + + align:start position:0% +no stable fix + + + align:start position:0% +no stable fix +point no stable rolling uh limit + + align:start position:0% +point no stable rolling uh limit + + + align:start position:0% +point no stable rolling uh limit +cycle assuming your velocity if I'm just + + align:start position:0% +cycle assuming your velocity if I'm just + + + align:start position:0% +cycle assuming your velocity if I'm just +Epsilon above here and I go down then + + align:start position:0% +Epsilon above here and I go down then + + + align:start position:0% +Epsilon above here and I go down then +I'm only going to stand + + align:start position:0% + + + + align:start position:0% + +still if if your Collision model is that + + align:start position:0% +still if if your Collision model is that + + + align:start position:0% +still if if your Collision model is that +you always lose a + + align:start position:0% +you always lose a + + + align:start position:0% +you always lose a +a particular fraction of your velocity + + align:start position:0% +a particular fraction of your velocity + + + align:start position:0% +a particular fraction of your velocity +yes okay + + align:start position:0% +yes okay + + + align:start position:0% +yes okay +MH so in the case where we have a + + align:start position:0% +MH so in the case where we have a + + + align:start position:0% +MH so in the case where we have a +rolling fixed point it has to be that + + align:start position:0% +rolling fixed point it has to be that + + + align:start position:0% +rolling fixed point it has to be that +Epsilon above here actually gets you the + + align:start position:0% +Epsilon above here actually gets you the + + + align:start position:0% +Epsilon above here actually gets you the +other thing the one maybe you're + + align:start position:0% +other thing the one maybe you're + + + align:start position:0% +other thing the one maybe you're +thinking about too is that um there's a + + align:start position:0% +thinking about too is that um there's a + + + align:start position:0% +thinking about too is that um there's a +place over + + align:start position:0% + + + + align:start position:0% + +here where if I start with this energy I + + align:start position:0% +here where if I start with this energy I + + + align:start position:0% +here where if I start with this energy I +actually come out with a little less + + align:start position:0% +actually come out with a little less + + + align:start position:0% +actually come out with a little less +energy and I can actually then go and + + align:start position:0% +energy and I can actually then go and + + + align:start position:0% +energy and I can actually then go and +get caught in either this standing fix + + align:start position:0% +get caught in either this standing fix + + + align:start position:0% +get caught in either this standing fix +point + + align:start position:0% +point + + + align:start position:0% +point +or I can transition over into this fix + + align:start position:0% +or I can transition over into this fix + + + align:start position:0% +or I can transition over into this fix +point and go up and and get + + align:start position:0% +point and go up and and get + + + align:start position:0% +point and go up and and get +caught + + align:start position:0% +caught + + + align:start position:0% +caught +okay there's an easier way to see all + + align:start position:0% +okay there's an easier way to see all + + + align:start position:0% +okay there's an easier way to see all +this I want you to see it in the phase + + align:start position:0% +this I want you to see it in the phase + + + align:start position:0% +this I want you to see it in the phase +portrait because we thought a lot about + + align:start position:0% +portrait because we thought a lot about + + + align:start position:0% +portrait because we thought a lot about +it the easier way to see what all this + + align:start position:0% +it the easier way to see what all this + + + align:start position:0% +it the easier way to see what all this +stuff is is by defining my Surface of + + align:start position:0% +stuff is is by defining my Surface of + + + align:start position:0% +stuff is is by defining my Surface of +section and looking at the pon CR map + + align:start position:0% +section and looking at the pon CR map + + + align:start position:0% +section and looking at the pon CR map +okay so let's do that now in this in the + + align:start position:0% +okay so let's do that now in this in the + + + align:start position:0% +okay so let's do that now in this in the +rimless wheel because it can be going in + + align:start position:0% +rimless wheel because it can be going in + + + align:start position:0% +rimless wheel because it can be going in +either direction I'm going to define a + + align:start position:0% +either direction I'm going to define a + + + align:start position:0% +either direction I'm going to define a +little bit of odd surface of section I'm + + align:start position:0% +little bit of odd surface of section I'm + + + align:start position:0% +little bit of odd surface of section I'm +going to Define + + align:start position:0% + + + + align:start position:0% + +it it sure feels like I've got a lot of + + align:start position:0% +it it sure feels like I've got a lot of + + + align:start position:0% +it it sure feels like I've got a lot of +colors + + align:start position:0% + + + + align:start position:0% + +but I don't know some sort + + align:start position:0% +but I don't know some sort + + + align:start position:0% +but I don't know some sort +of red and purple + + align:start position:0% +of red and purple + + + align:start position:0% +of red and purple +makes let me just make it really thick + + align:start position:0% +makes let me just make it really thick + + + align:start position:0% +makes let me just make it really thick +here good + + align:start position:0% + + + + align:start position:0% + +Lord let me Define this to be my Surface + + align:start position:0% +Lord let me Define this to be my Surface + + + align:start position:0% +Lord let me Define this to be my Surface +of section and this also to be part of + + align:start position:0% +of section and this also to be part of + + + align:start position:0% +of section and this also to be part of +my Surface of section + + align:start position:0% +my Surface of section + + + align:start position:0% +my Surface of section +okay so anytime I have an impact with + + align:start position:0% +okay so anytime I have an impact with + + + align:start position:0% +okay so anytime I have an impact with +the + + align:start position:0% +the + + + align:start position:0% +the +ground I'm going to look at I'm going to + + align:start position:0% +ground I'm going to look at I'm going to + + + align:start position:0% +ground I'm going to look at I'm going to +use that as my my return + + align:start position:0% +use that as my my return + + + align:start position:0% +use that as my my return +map okay + + align:start position:0% + + + + align:start position:0% + +so is it just before or just after I do + + align:start position:0% +so is it just before or just after I do + + + align:start position:0% +so is it just before or just after I do +just after but it doesn't matter as long + + align:start position:0% +just after but it doesn't matter as long + + + align:start position:0% +just after but it doesn't matter as long +as you're consistent it doesn't + + align:start position:0% + + + + align:start position:0% + +matter it's a little bit + + align:start position:0% + + + + align:start position:0% + +better okay here's the analytical return + + align:start position:0% +better okay here's the analytical return + + + align:start position:0% +better okay here's the analytical return +map of the um rimless wheel okay so just + + align:start position:0% +map of the um rimless wheel okay so just + + + align:start position:0% +map of the um rimless wheel okay so just +because um in the I should say the + + align:start position:0% +because um in the I should say the + + + align:start position:0% +because um in the I should say the +rimless wheel is the one walking system + + align:start position:0% +rimless wheel is the one walking system + + + align:start position:0% +rimless wheel is the one walking system +that we actually understand completely + + align:start position:0% +that we actually understand completely + + + align:start position:0% +that we actually understand completely +and I mean uh when I talk about these + + align:start position:0% +and I mean uh when I talk about these + + + align:start position:0% +and I mean uh when I talk about these +quank gray Maps I can write them down + + align:start position:0% +quank gray Maps I can write them down + + + align:start position:0% +quank gray Maps I can write them down +analytically because I can tell you if + + align:start position:0% +analytically because I can tell you if + + + align:start position:0% +analytically because I can tell you if +I'm in this velocity where am I going to + + align:start position:0% +I'm in this velocity where am I going to + + + align:start position:0% +I'm in this velocity where am I going to +end up because I just have to do a first + + align:start position:0% +end up because I just have to do a first + + + align:start position:0% +end up because I just have to do a first +integral on the pendulum Dynamics it's + + align:start position:0% +integral on the pendulum Dynamics it's + + + align:start position:0% +integral on the pendulum Dynamics it's +energy conserving we're all we're all + + align:start position:0% +energy conserving we're all we're all + + + align:start position:0% +energy conserving we're all we're all +happy so I can tell you everything about + + align:start position:0% +happy so I can tell you everything about + + + align:start position:0% +happy so I can tell you everything about +the the rimless wheel I can tell you + + align:start position:0% +the the rimless wheel I can tell you + + + align:start position:0% +the the rimless wheel I can tell you +about where its fix points lie the gray + + align:start position:0% +about where its fix points lie the gray + + + align:start position:0% +about where its fix points lie the gray +is actually the basins of a ction of the + + align:start position:0% +is actually the basins of a ction of the + + + align:start position:0% +is actually the basins of a ction of the +fixed points right I can tell you + + align:start position:0% +fixed points right I can tell you + + + align:start position:0% +fixed points right I can tell you +everything there is no other walking + + align:start position:0% +everything there is no other walking + + + align:start position:0% +everything there is no other walking +model that I know of that I can say that + + align:start position:0% +model that I know of that I can say that + + + align:start position:0% +model that I know of that I can say that +about but this is what you should aspire + + align:start position:0% +about but this is what you should aspire + + + align:start position:0% +about but this is what you should aspire +to get with all of your walking machines + + align:start position:0% +to get with all of your walking machines + + + align:start position:0% +to get with all of your walking machines +okay okay so um so the blue the red line + + align:start position:0% +okay okay so um so the blue the red line + + + align:start position:0% +okay okay so um so the blue the red line +is the line of slope one the blue line + + align:start position:0% +is the line of slope one the blue line + + + align:start position:0% +is the line of slope one the blue line +is the analytical solution to the first + + align:start position:0% +is the analytical solution to the first + + + align:start position:0% +is the analytical solution to the first +return map with the surface of section + + align:start position:0% +return map with the surface of section + + + align:start position:0% +return map with the surface of section +defined the way I did okay this is post + + align:start position:0% +defined the way I did okay this is post + + + align:start position:0% +defined the way I did okay this is post +Collision all right so it turns out um + + align:start position:0% +Collision all right so it turns out um + + + align:start position:0% +Collision all right so it turns out um +my lines just got thick enough that it's + + align:start position:0% +my lines just got thick enough that it's + + + align:start position:0% +my lines just got thick enough that it's +it's a little hard to see but there's a + + align:start position:0% +it's a little hard to see but there's a + + + align:start position:0% +it's a little hard to see but there's a +blue line here that's it says if I'm + + align:start position:0% +blue line here that's it says if I'm + + + align:start position:0% +blue line here that's it says if I'm +going too fast I'm slowing down + + align:start position:0% +going too fast I'm slowing down + + + align:start position:0% +going too fast I'm slowing down +yeah and it'll do its little staircase + + align:start position:0% +yeah and it'll do its little staircase + + + align:start position:0% +yeah and it'll do its little staircase +right down to this black fixed point in + + align:start position:0% +right down to this black fixed point in + + + align:start position:0% +right down to this black fixed point in +just above this green + + align:start position:0% +just above this green + + + align:start position:0% +just above this green +line which is um the rolling fix point + + align:start position:0% +line which is um the rolling fix point + + + align:start position:0% +line which is um the rolling fix point +on the pank CR map this is Theta dot at + + align:start position:0% +on the pank CR map this is Theta dot at + + + align:start position:0% +on the pank CR map this is Theta dot at +the N step versus Theta dot at the N + + align:start position:0% +the N step versus Theta dot at the N + + + align:start position:0% +the N step versus Theta dot at the N +plus one step right so there's a rolling + + align:start position:0% +plus one step right so there's a rolling + + + align:start position:0% +plus one step right so there's a rolling +fix point and it's actually stable + + align:start position:0% +fix point and it's actually stable + + + align:start position:0% +fix point and it's actually stable +there's it goes the blue line goes just + + align:start position:0% +there's it goes the blue line goes just + + + align:start position:0% +there's it goes the blue line goes just +above the red line before it goes + + align:start position:0% +above the red line before it goes + + + align:start position:0% +above the red line before it goes +down okay there's also a a standing fix + + align:start position:0% +down okay there's also a a standing fix + + + align:start position:0% +down okay there's also a a standing fix +point with a velocity at zero which is + + align:start position:0% +point with a velocity at zero which is + + + align:start position:0% +point with a velocity at zero which is +the standing on two legs oscillating + + align:start position:0% +the standing on two legs oscillating + + + align:start position:0% +the standing on two legs oscillating +back and forth okay that one's stable + + align:start position:0% +back and forth okay that one's stable + + + align:start position:0% +back and forth okay that one's stable +too and then when you're rolling + + align:start position:0% +too and then when you're rolling + + + align:start position:0% +too and then when you're rolling +backwards up hill it always says I'm + + align:start position:0% +backwards up hill it always says I'm + + + align:start position:0% +backwards up hill it always says I'm +speeding up every time I'm when I'm + + align:start position:0% +speeding up every time I'm when I'm + + + align:start position:0% +speeding up every time I'm when I'm +rolling up the hill this is negative + + align:start position:0% +rolling up the hill this is negative + + + align:start position:0% +rolling up the hill this is negative +initial + + align:start position:0% +initial + + + align:start position:0% +initial +velocities at every time I'm going to + + align:start position:0% +velocities at every time I'm going to + + + align:start position:0% +velocities at every time I'm going to +have a little bit more forward velocity + + align:start position:0% +have a little bit more forward velocity + + + align:start position:0% +have a little bit more forward velocity +on every step um but because this thing + + align:start position:0% +on every step um but because this thing + + + align:start position:0% +on every step um but because this thing +jumps discontinuously in that staircase + + align:start position:0% +jumps discontinuously in that staircase + + + align:start position:0% +jumps discontinuously in that staircase +fashion it's actually a little + + align:start position:0% +fashion it's actually a little + + + align:start position:0% +fashion it's actually a little +non-trivial about where whether it's + + align:start position:0% +non-trivial about where whether it's + + + align:start position:0% +non-trivial about where whether it's +going to end up in the rolling fix point + + align:start position:0% +going to end up in the rolling fix point + + + align:start position:0% +going to end up in the rolling fix point +or the standing fix Point those gray + + align:start position:0% +or the standing fix Point those gray + + + align:start position:0% +or the standing fix Point those gray +stripes are actually the Basin of + + align:start position:0% +stripes are actually the Basin of + + + align:start position:0% +stripes are actually the Basin of +Attraction of the Rolling fix + + align:start position:0% +Attraction of the Rolling fix + + + align:start position:0% +Attraction of the Rolling fix +Point okay so turns out if you go if you + + align:start position:0% +Point okay so turns out if you go if you + + + align:start position:0% +Point okay so turns out if you go if you +roll uphill and you stop with just + + align:start position:0% +roll uphill and you stop with just + + + align:start position:0% +roll uphill and you stop with just +enough energy you don't quite get to the + + align:start position:0% +enough energy you don't quite get to the + + + align:start position:0% +enough energy you don't quite get to the +top and then you roll back down then you + + align:start position:0% +top and then you roll back down then you + + + align:start position:0% +top and then you roll back down then you +go into the other fix Point yeah but if + + align:start position:0% +go into the other fix Point yeah but if + + + align:start position:0% +go into the other fix Point yeah but if +you end up at the top of the hill pretty + + align:start position:0% +you end up at the top of the hill pretty + + + align:start position:0% +you end up at the top of the hill pretty +much losing your energy like this then + + align:start position:0% +much losing your energy like this then + + + align:start position:0% +much losing your energy like this then +you're going to + + align:start position:0% +you're going to + + + align:start position:0% +you're going to +stop but I can tell you everything about + + align:start position:0% +stop but I can tell you everything about + + + align:start position:0% +stop but I can tell you everything about +this this return ma okay what's the + + align:start position:0% +this this return ma okay what's the + + + align:start position:0% +this this return ma okay what's the +green Dash + + align:start position:0% + + + + align:start position:0% + +lines the green Dash lines are places + + align:start position:0% +lines the green Dash lines are places + + + align:start position:0% +lines the green Dash lines are places +where my return rap are IL defined what + + align:start position:0% +where my return rap are IL defined what + + + align:start position:0% +where my return rap are IL defined what +could what could that possibly + + align:start position:0% + + + + align:start position:0% + +be balance yes very good right there is + + align:start position:0% +be balance yes very good right there is + + + align:start position:0% +be balance yes very good right there is +some initial velocity + + align:start position:0% + + + + align:start position:0% + +for which I never return to my return + + align:start position:0% +for which I never return to my return + + + align:start position:0% +for which I never return to my return +map what's + + align:start position:0% +map what's + + + align:start position:0% +map what's +that so if I'm on the home Clinic orbit + + align:start position:0% +that so if I'm on the home Clinic orbit + + + align:start position:0% +that so if I'm on the home Clinic orbit +right never happens in practice no big + + align:start position:0% +right never happens in practice no big + + + align:start position:0% +right never happens in practice no big +deal but there is a set of measur zero + + align:start position:0% +deal but there is a set of measur zero + + + align:start position:0% +deal but there is a set of measur zero +if you started with just the wrong + + align:start position:0% +if you started with just the wrong + + + align:start position:0% +if you started with just the wrong +velocity it'll go up and sit like this + + align:start position:0% +velocity it'll go up and sit like this + + + align:start position:0% +velocity it'll go up and sit like this +and never come back okay so those are IL + + align:start position:0% +and never come back okay so those are IL + + + align:start position:0% +and never come back okay so those are IL +defined points in the bank gray map okay + + align:start position:0% +defined points in the bank gray map okay + + + align:start position:0% +defined points in the bank gray map okay +but everything else we completely know + + align:start position:0% +but everything else we completely know + + + align:start position:0% +but everything else we completely know +you know + + align:start position:0% + + + + align:start position:0% + +sorry what's that you said like if you + + align:start position:0% +sorry what's that you said like if you + + + align:start position:0% +sorry what's that you said like if you +initialize it with velocity of zero then + + align:start position:0% +initialize it with velocity of zero then + + + align:start position:0% +initialize it with velocity of zero then +it would stand still there yes + + align:start position:0% + + + + align:start position:0% + +why oh um why is there a green line on + + align:start position:0% +why oh um why is there a green line on + + + align:start position:0% +why oh um why is there a green line on +zero on one + + align:start position:0% +zero on one + + + align:start position:0% +zero on one +SC it's like green line at Thea Z + + align:start position:0% +SC it's like green line at Thea Z + + + align:start position:0% +SC it's like green line at Thea Z +Z it's Theta do0 um so why do I have to + + align:start position:0% +Z it's Theta do0 um so why do I have to + + + align:start position:0% +Z it's Theta do0 um so why do I have to +draw a green line there I don't know why + + align:start position:0% +draw a green line there I don't know why + + + align:start position:0% +draw a green line there I don't know why +I have to draw a green line there I + + align:start position:0% +I have to draw a green line there I + + + align:start position:0% +I have to draw a green line there I +don't remember that green line being + + align:start position:0% + + + + align:start position:0% + +there yeah but I don't think I should + + align:start position:0% +there yeah but I don't think I should + + + align:start position:0% +there yeah but I don't think I should +have drawn I think that's actually just + + align:start position:0% +have drawn I think that's actually just + + + align:start position:0% +have drawn I think that's actually just +a mat lab typo there's no there's no + + align:start position:0% +a mat lab typo there's no there's no + + + align:start position:0% +a mat lab typo there's no there's no +reason why that should be there I don't + + align:start position:0% +reason why that should be there I don't + + + align:start position:0% +reason why that should be there I don't +know why that's + + align:start position:0% +know why that's + + + align:start position:0% +know why that's +there yeah it's not in the + + align:start position:0% +there yeah it's not in the + + + align:start position:0% +there yeah it's not in the +notes there's no reason why that should + + align:start position:0% +notes there's no reason why that should + + + align:start position:0% +notes there's no reason why that should +that should be there I don't know why + + align:start position:0% +that should be there I don't know why + + + align:start position:0% +that should be there I don't know why +that's there yeah John + + align:start position:0% +that's there yeah John + + + align:start position:0% +that's there yeah John +orbit doesn't separate the rolling ones + + align:start position:0% +orbit doesn't separate the rolling ones + + + align:start position:0% +orbit doesn't separate the rolling ones +on the right side of the up right the + + align:start position:0% +on the right side of the up right the + + + align:start position:0% +on the right side of the up right the +base + + align:start position:0% +base + + + align:start position:0% +base +PL your homic orbit is the boundary on + + align:start position:0% +PL your homic orbit is the boundary on + + + align:start position:0% +PL your homic orbit is the boundary on +the left side but not on the right side + + align:start position:0% +the left side but not on the right side + + + align:start position:0% +the left side but not on the right side +right because the that's not true the + + align:start position:0% +right because the that's not true the + + + align:start position:0% +right because the that's not true the +ones on the right side that roll and + + align:start position:0% +ones on the right side that roll and + + + align:start position:0% +ones on the right side that roll and +then go back they're inside the Hom OR + + align:start position:0% +then go back they're inside the Hom OR + + + align:start position:0% +then go back they're inside the Hom OR +they're inside right they just they + + align:start position:0% +they're inside right they just they + + + align:start position:0% +they're inside right they just they +bounce across to the left go up it so + + align:start position:0% +bounce across to the left go up it so + + + align:start position:0% +bounce across to the left go up it so +okay good so there's actually green + + align:start position:0% +okay good so there's actually green + + + align:start position:0% +okay good so there's actually green +lines every fraction of the way is that + + align:start position:0% +lines every fraction of the way is that + + + align:start position:0% +lines every fraction of the way is that +what you're asking about I was actually + + align:start position:0% +what you're asking about I was actually + + + align:start position:0% +what you're asking about I was actually +say even even the first one this one the + + align:start position:0% +say even even the first one this one the + + + align:start position:0% +say even even the first one this one the +hom orbit is not the boundary for what + + align:start position:0% +hom orbit is not the boundary for what + + + align:start position:0% +hom orbit is not the boundary for what +marks the stable rolling Gates the face + + align:start position:0% +marks the stable rolling Gates the face + + + align:start position:0% +marks the stable rolling Gates the face +plot right it is on the left side maybe + + align:start position:0% +plot right it is on the left side maybe + + + align:start position:0% +plot right it is on the left side maybe +but on the right side you can be inside + + align:start position:0% +but on the right side you can be inside + + + align:start position:0% +but on the right side you can be inside +oh that's correct that's correct so I + + align:start position:0% +oh that's correct that's correct so I + + + align:start position:0% +oh that's correct that's correct so I +can I can end up here um with enough + + align:start position:0% +can I can end up here um with enough + + + align:start position:0% +can I can end up here um with enough +energy to to transfer over that's right + + align:start position:0% +energy to to transfer over that's right + + + align:start position:0% +energy to to transfer over that's right +down here only here is it the is it the + + align:start position:0% +down here only here is it the is it the + + + align:start position:0% +down here only here is it the is it the +that's good yes that's true this is the + + align:start position:0% +that's good yes that's true this is the + + + align:start position:0% +that's good yes that's true this is the +only place where it's the defining part + + align:start position:0% +only place where it's the defining part + + + align:start position:0% +only place where it's the defining part +the the transition across from over here + + align:start position:0% +the the transition across from over here + + + align:start position:0% +the the transition across from over here +is more complicated which is why we end + + align:start position:0% +is more complicated which is why we end + + + align:start position:0% +is more complicated which is why we end +up with these traj iies which get get up + + align:start position:0% +up with these traj iies which get get up + + + align:start position:0% +up with these traj iies which get get up +started up going the other way yeah and + + align:start position:0% +started up going the other way yeah and + + + align:start position:0% +started up going the other way yeah and +it's also the case that um any for some + + align:start position:0% +it's also the case that um any for some + + + align:start position:0% +it's also the case that um any for some +there's actually Stripes of these green + + align:start position:0% +there's actually Stripes of these green + + + align:start position:0% +there's actually Stripes of these green +lines going up at every boundary between + + align:start position:0% +lines going up at every boundary between + + + align:start position:0% +lines going up at every boundary between +the the gray and the white there's a + + align:start position:0% +the the gray and the white there's a + + + align:start position:0% +the the gray and the white there's a +place where I could have rolled 10 steps + + align:start position:0% +place where I could have rolled 10 steps + + + align:start position:0% +place where I could have rolled 10 steps +and ended up you know balanced perfectly + + align:start position:0% +and ended up you know balanced perfectly + + + align:start position:0% +and ended up you know balanced perfectly +right and then go + + align:start position:0% +right and then go + + + align:start position:0% +right and then go +back so I skipped over the impact + + align:start position:0% +back so I skipped over the impact + + + align:start position:0% +back so I skipped over the impact +Dynamics the impact Dynamics are good to + + align:start position:0% +Dynamics the impact Dynamics are good to + + + align:start position:0% +Dynamics the impact Dynamics are good to +know but we can we can um avoid them but + + align:start position:0% +know but we can we can um avoid them but + + + align:start position:0% +know but we can we can um avoid them but +just to give you the intuition + + align:start position:0% +just to give you the intuition + + + align:start position:0% +just to give you the intuition +um you can decide you can you + + align:start position:0% +um you can decide you can you + + + align:start position:0% +um you can decide you can you +can Define the energy loss at impact by + + align:start position:0% +can Define the energy loss at impact by + + + align:start position:0% +can Define the energy loss at impact by +just looking at this rimless wheel + + align:start position:0% +just looking at this rimless wheel + + + align:start position:0% +just looking at this rimless wheel +immediately before the impact here and + + align:start position:0% +immediately before the impact here and + + + align:start position:0% +immediately before the impact here and +it's got + + align:start position:0% +it's got + + + align:start position:0% +it's got +some momentum that's um got to be it's + + align:start position:0% +some momentum that's um got to be it's + + + align:start position:0% +some momentum that's um got to be it's +moving along this pin joint so it's got + + align:start position:0% +moving along this pin joint so it's got + + + align:start position:0% +moving along this pin joint so it's got +to have um some momentum like that + + align:start position:0% +to have um some momentum like that + + + align:start position:0% +to have um some momentum like that +immediately after the Collision it's + + align:start position:0% +immediately after the Collision it's + + + align:start position:0% +immediately after the Collision it's +going to have a momentum + + align:start position:0% +going to have a momentum + + + align:start position:0% +going to have a momentum +that's orthogonal to this new PIN joint + + align:start position:0% +that's orthogonal to this new PIN joint + + + align:start position:0% +that's orthogonal to this new PIN joint +right so any energy that's lost that's + + align:start position:0% +right so any energy that's lost that's + + + align:start position:0% +right so any energy that's lost that's +that's going into the ground is lost so + + align:start position:0% +that's going into the ground is lost so + + + align:start position:0% +that's going into the ground is lost so +if you model an angular momentum + + align:start position:0% +if you model an angular momentum + + + align:start position:0% +if you model an angular momentum +conservation around this point the + + align:start position:0% +conservation around this point the + + + align:start position:0% +conservation around this point the +angular momentum around this which is + + align:start position:0% +angular momentum around this which is + + + align:start position:0% +angular momentum around this which is +the component of this here is is remains + + align:start position:0% +the component of this here is is remains + + + align:start position:0% +the component of this here is is remains +and the other part is lost okay it turns + + align:start position:0% +and the other part is lost okay it turns + + + align:start position:0% +and the other part is lost okay it turns +out that in um in the rimless wheel you + + align:start position:0% +out that in um in the rimless wheel you + + + align:start position:0% +out that in um in the rimless wheel you +get that as a simple mapping saying + + align:start position:0% +get that as a simple mapping saying + + + align:start position:0% +get that as a simple mapping saying +Theta dot after a collision if I use + + align:start position:0% +Theta dot after a collision if I use + + + align:start position:0% +Theta dot after a collision if I use +that notation turns out to be cosine of + + align:start position:0% +that notation turns out to be cosine of + + + align:start position:0% +that notation turns out to be cosine of + + align:start position:0% + + + align:start position:0% +Alpha time Theta dot just before the + + align:start position:0% +Alpha time Theta dot just before the + + + align:start position:0% +Alpha time Theta dot just before the +Collision turns out to be a trivial + + align:start position:0% +Collision turns out to be a trivial + + + align:start position:0% +Collision turns out to be a trivial +mapping + + align:start position:0% + + + + align:start position:0% + +okay so you now know the essential + + align:start position:0% +okay so you now know the essential + + + align:start position:0% +okay so you now know the essential +dynamics of walking this is actually + + align:start position:0% +dynamics of walking this is actually + + + align:start position:0% +dynamics of walking this is actually +most of what you need to know if you if + + align:start position:0% +most of what you need to know if you if + + + align:start position:0% +most of what you need to know if you if +you think about a walking robot okay the + + align:start position:0% +you think about a walking robot okay the + + + align:start position:0% +you think about a walking robot okay the +dominant source of energy loss is not + + align:start position:0% +dominant source of energy loss is not + + + align:start position:0% +dominant source of energy loss is not +friction in the joint + + align:start position:0% +friction in the joint + + + align:start position:0% +friction in the joint +that's pretty small right unless you I + + align:start position:0% +that's pretty small right unless you I + + + align:start position:0% +that's pretty small right unless you I +mean you could make a robot that + + align:start position:0% +mean you could make a robot that + + + align:start position:0% +mean you could make a robot that +friction in the joints but um the + + align:start position:0% +friction in the joints but um the + + + align:start position:0% +friction in the joints but um the +dominant dynamics of our walking are + + align:start position:0% +dominant dynamics of our walking are + + + align:start position:0% +dominant dynamics of our walking are +dominated by impact at the ground even + + align:start position:0% +dominated by impact at the ground even + + + align:start position:0% +dominated by impact at the ground even +for human walking right so so um most + + align:start position:0% +for human walking right so so um most + + + align:start position:0% +for human walking right so so um most +people think that the um the places you + + align:start position:0% +people think that the um the places you + + + align:start position:0% +people think that the um the places you +spend the most energy to recover from + + align:start position:0% +spend the most energy to recover from + + + align:start position:0% +spend the most energy to recover from +the the ground Collision are push off + + align:start position:0% +the the ground Collision are push off + + + align:start position:0% +the the ground Collision are push off +with the + + align:start position:0% +with the + + + align:start position:0% +with the +toe and then you're mostly passive + + align:start position:0% +toe and then you're mostly passive + + + align:start position:0% +toe and then you're mostly passive +through or Nest correct me if the if the + + align:start position:0% +through or Nest correct me if the if the + + + align:start position:0% +through or Nest correct me if the if the +theories have changed you're mostly + + align:start position:0% +theories have changed you're mostly + + + align:start position:0% +theories have changed you're mostly +passive through and then there's one + + align:start position:0% +passive through and then there's one + + + align:start position:0% +passive through and then there's one +other time where you spend a lot of + + align:start position:0% +other time where you spend a lot of + + + align:start position:0% +other time where you spend a lot of +energy not a lot but some energy you + + align:start position:0% +energy not a lot but some energy you + + + align:start position:0% +energy not a lot but some energy you +actually decelerate your leg before knee + + align:start position:0% +actually decelerate your leg before knee + + + align:start position:0% +actually decelerate your leg before knee +strike maybe just to protect your + + align:start position:0% +strike maybe just to protect your + + + align:start position:0% +strike maybe just to protect your +kneecaps or maybe just to not walk like + + align:start position:0% +kneecaps or maybe just to not walk like + + + align:start position:0% +kneecaps or maybe just to not walk like +like this or something I don't know but + + align:start position:0% +like this or something I don't know but + + + align:start position:0% +like this or something I don't know but +you actually spend a little bit of + + align:start position:0% +you actually spend a little bit of + + + align:start position:0% +you actually spend a little bit of +energy doing negative work to slow down + + align:start position:0% +energy doing negative work to slow down + + + align:start position:0% +energy doing negative work to slow down +that swing leg before it collides with + + align:start position:0% +that swing leg before it collides with + + + align:start position:0% +that swing leg before it collides with +the kneecap okay and that's it right so + + align:start position:0% +the kneecap okay and that's it right so + + + align:start position:0% +the kneecap okay and that's it right so +people um have talked about and the + + align:start position:0% +people um have talked about and the + + + align:start position:0% +people um have talked about and the +Collision dominates so much to the point + + align:start position:0% +Collision dominates so much to the point + + + align:start position:0% +Collision dominates so much to the point +where you um if you want to make an + + align:start position:0% +where you um if you want to make an + + + align:start position:0% +where you um if you want to make an +energy efficient robot and you're ruin + + align:start position:0% +energy efficient robot and you're ruin + + + align:start position:0% +energy efficient robot and you're ruin +says you can make it four times more + + align:start position:0% +says you can make it four times more + + + align:start position:0% +says you can make it four times more +efficient if you put this push off just + + align:start position:0% +efficient if you put this push off just + + + align:start position:0% +efficient if you put this push off just +before the the Collision because if + + align:start position:0% +before the the Collision because if + + + align:start position:0% +before the the Collision because if +you're coming down and you suddenly use + + align:start position:0% +you're coming down and you suddenly use + + + align:start position:0% +you're coming down and you suddenly use +your push off to redirect your energy + + align:start position:0% +your push off to redirect your energy + + + align:start position:0% +your push off to redirect your energy +just before that Collision you can + + align:start position:0% +just before that Collision you can + + + align:start position:0% +just before that Collision you can +reduce the velocity at collision and he + + align:start position:0% +reduce the velocity at collision and he + + + align:start position:0% +reduce the velocity at collision and he +says that makes a four time Improvement + + align:start position:0% +says that makes a four time Improvement + + + align:start position:0% +says that makes a four time Improvement +in the Energy Efficiency of your + + align:start position:0% +in the Energy Efficiency of your + + + align:start position:0% +in the Energy Efficiency of your +robot so they've been trying to build + + align:start position:0% +robot so they've been trying to build + + + align:start position:0% +robot so they've been trying to build +walking robots that sense the ground + + align:start position:0% +walking robots that sense the ground + + + align:start position:0% +walking robots that sense the ground +just before by having a you know a + + align:start position:0% +just before by having a you know a + + + align:start position:0% +just before by having a you know a +little limit switch sticking down in + + align:start position:0% +little limit switch sticking down in + + + align:start position:0% +little limit switch sticking down in +front of the foot right and push off + + align:start position:0% +front of the foot right and push off + + + align:start position:0% +front of the foot right and push off +right before ground contact that + + align:start position:0% +right before ground contact that + + + align:start position:0% +right before ground contact that +Collision Dynamics with the rimos wheel + + align:start position:0% +Collision Dynamics with the rimos wheel + + + align:start position:0% +Collision Dynamics with the rimos wheel +tells us about is the dominant essential + + align:start position:0% +tells us about is the dominant essential + + + align:start position:0% +tells us about is the dominant essential +dynamics of walking it's the only loss + + align:start position:0% +dynamics of walking it's the only loss + + + align:start position:0% +dynamics of walking it's the only loss +in this system but it's enough to get + + align:start position:0% +in this system but it's enough to get + + + align:start position:0% +in this system but it's enough to get +stable limit cycle out right the + + align:start position:0% +stable limit cycle out right the + + + align:start position:0% +stable limit cycle out right the +mathematicians like this Phil Holmes + + align:start position:0% +mathematicians like this Phil Holmes + + + align:start position:0% +mathematicians like this Phil Holmes +likes this because um he was surprised + + align:start position:0% +likes this because um he was surprised + + + align:start position:0% +likes this because um he was surprised +initially that and that that these peie + + align:start position:0% +initially that and that that these peie + + + align:start position:0% +initially that and that that these peie +wise this is this is a um energy + + align:start position:0% +wise this is this is a um energy + + + align:start position:0% +wise this is this is a um energy +conserving + + align:start position:0% +conserving + + + align:start position:0% +conserving +system inside the inside each um cycle + + align:start position:0% +system inside the inside each um cycle + + + align:start position:0% +system inside the inside each um cycle +it's a piecewise homic system they call + + align:start position:0% +it's a piecewise homic system they call + + + align:start position:0% +it's a piecewise homic system they call +it and uh uh it can have stable limit + + align:start position:0% +it and uh uh it can have stable limit + + + align:start position:0% +it and uh uh it can have stable limit +Cycles + + align:start position:0% +Cycles + + + align:start position:0% +Cycles +out so people have gone farther than + + align:start position:0% +out so people have gone farther than + + + align:start position:0% +out so people have gone farther than +this now we can do a little bit better + + align:start position:0% +this now we can do a little bit better + + + align:start position:0% +this now we can do a little bit better +than a rimless wheel if you understand + + align:start position:0% +than a rimless wheel if you understand + + + align:start position:0% +than a rimless wheel if you understand +the rimless wheel and now you want to + + align:start position:0% +the rimless wheel and now you want to + + + align:start position:0% +the rimless wheel and now you want to +make it a walking robot all you have to + + align:start position:0% +make it a walking robot all you have to + + + align:start position:0% +make it a walking robot all you have to +do is um take away the the rigid joint + + align:start position:0% +do is um take away the the rigid joint + + + align:start position:0% +do is um take away the the rigid joint +at the hip make it a pin + + align:start position:0% +at the hip make it a pin + + + align:start position:0% +at the hip make it a pin +joint to model the swing leg Dynamics + + align:start position:0% +joint to model the swing leg Dynamics + + + align:start position:0% +joint to model the swing leg Dynamics +you can add some smaller masses in the + + align:start position:0% +you can add some smaller masses in the + + + align:start position:0% +you can add some smaller masses in the +leg so that the so it's now um exactly + + align:start position:0% +leg so that the so it's now um exactly + + + align:start position:0% +leg so that the so it's now um exactly +the acrobot Dynamics you can imagine + + align:start position:0% +the acrobot Dynamics you can imagine + + + align:start position:0% +the acrobot Dynamics you can imagine +putting a torque at the hip okay and + + align:start position:0% +putting a torque at the hip okay and + + + align:start position:0% +putting a torque at the hip okay and +that's called the compass gate + + align:start position:0% +that's called the compass gate + + + align:start position:0% +that's called the compass gate +model for obvious + + align:start position:0% + + + + align:start position:0% + +reasons and wouldn't you know it if you + + align:start position:0% +reasons and wouldn't you know it if you + + + align:start position:0% +reasons and wouldn't you know it if you +take a compass + + align:start position:0% +take a compass + + + align:start position:0% +take a compass +gate put it on top of a small hill give + + align:start position:0% +gate put it on top of a small hill give + + + align:start position:0% +gate put it on top of a small hill give +it a push right only losses come from um + + align:start position:0% +it a push right only losses come from um + + + align:start position:0% +it a push right only losses come from um +collisions with the ground otherwise + + align:start position:0% +collisions with the ground otherwise + + + align:start position:0% +collisions with the ground otherwise +it's a passive even if I have no torque + + align:start position:0% +it's a passive even if I have no torque + + + align:start position:0% +it's a passive even if I have no torque +at the hip a passive uh stance + + align:start position:0% +at the hip a passive uh stance + + + align:start position:0% +at the hip a passive uh stance +phase this + + align:start position:0% +phase this + + + align:start position:0% +phase this +thing walks stably down a small hill + + align:start position:0% + + + + align:start position:0% + +yeah are you letting the leg free + + align:start position:0% +yeah are you letting the leg free + + + align:start position:0% +yeah are you letting the leg free +between everything is just zero torque + + align:start position:0% +between everything is just zero torque + + + align:start position:0% +between everything is just zero torque +the only trick I'm playing is that I'm + + align:start position:0% +the only trick I'm playing is that I'm + + + align:start position:0% +the only trick I'm playing is that I'm +ignoring the foot scuff + + align:start position:0% +ignoring the foot scuff + + + align:start position:0% +ignoring the foot scuff +here which in if you want to build the + + align:start position:0% +here which in if you want to build the + + + align:start position:0% +here which in if you want to build the +robot you got to build a little + + align:start position:0% +robot you got to build a little + + + align:start position:0% +robot you got to build a little +retracting toe to make your leg a little + + align:start position:0% +retracting toe to make your leg a little + + + align:start position:0% +retracting toe to make your leg a little +bit shorter when it goes through but + + align:start position:0% +bit shorter when it goes through but + + + align:start position:0% +bit shorter when it goes through but +otherwise you can do this and we built + + align:start position:0% +otherwise you can do this and we built + + + align:start position:0% +otherwise you can do this and we built +these + + align:start position:0% +these + + + align:start position:0% +these +okay right now this guy has um the + + align:start position:0% +okay right now this guy has um the + + + align:start position:0% +okay right now this guy has um the +rimless wheel actually I showed you the + + align:start position:0% +rimless wheel actually I showed you the + + + align:start position:0% +rimless wheel actually I showed you the +basins of Attraction the two fix points + + align:start position:0% +basins of Attraction the two fix points + + + align:start position:0% +basins of Attraction the two fix points +the rolling and the standing together + + align:start position:0% +the rolling and the standing together + + + align:start position:0% +the rolling and the standing together +are globally attractive except for those + + align:start position:0% +are globally attractive except for those + + + align:start position:0% +are globally attractive except for those +sets of measure zero where you end up + + align:start position:0% +sets of measure zero where you end up + + + align:start position:0% +sets of measure zero where you end up +standing on your toes yeah that's not at + + align:start position:0% +standing on your toes yeah that's not at + + + align:start position:0% +standing on your toes yeah that's not at +all true of the compass gate the compass + + align:start position:0% +all true of the compass gate the compass + + + align:start position:0% +all true of the compass gate the compass +gate is pretty frail you have to find + + align:start position:0% +gate is pretty frail you have to find + + + align:start position:0% +gate is pretty frail you have to find +Initial conditions that put it into this + + align:start position:0% +Initial conditions that put it into this + + + align:start position:0% +Initial conditions that put it into this +walking gate I can show you many + + align:start position:0% +walking gate I can show you many + + + align:start position:0% +walking gate I can show you many +simulations of it falling down + + align:start position:0% +simulations of it falling down + + + align:start position:0% +simulations of it falling down +catastrophically yeah um but within some + + align:start position:0% +catastrophically yeah um but within some + + + align:start position:0% +catastrophically yeah um but within some +initial conditions you get a nice stable + + align:start position:0% +initial conditions you get a nice stable + + + align:start position:0% +initial conditions you get a nice stable +limit cycle out okay and not + + align:start position:0% +limit cycle out okay and not + + + align:start position:0% +limit cycle out okay and not +surprisingly you can go + + align:start position:0% +surprisingly you can go + + + align:start position:0% +surprisingly you can go +further it's + + align:start position:0% + + + + align:start position:0% + +a and here's the put one more set of + + align:start position:0% +a and here's the put one more set of + + + align:start position:0% +a and here's the put one more set of +links in there + + align:start position:0% +links in there + + + align:start position:0% +links in there +um this is point feet walking um with + + align:start position:0% +um this is point feet walking um with + + + align:start position:0% +um this is point feet walking um with +knees we modeled a collision at the + + align:start position:0% +knees we modeled a collision at the + + + align:start position:0% +knees we modeled a collision at the +kneecap and the ground but the Dynamics + + align:start position:0% +kneecap and the ground but the Dynamics + + + align:start position:0% +kneecap and the ground but the Dynamics +are are the same okay the limit cycles + + align:start position:0% +are are the same okay the limit cycles + + + align:start position:0% +are are the same okay the limit cycles +that you see in these guys look a little + + align:start position:0% +that you see in these guys look a little + + + align:start position:0% +that you see in these guys look a little +bit more appealing + + align:start position:0% + + + + align:start position:0% + +it does not work if the knees have you + + align:start position:0% +it does not work if the knees have you + + + align:start position:0% +it does not work if the knees have you +need something that keeps it a a stance + + align:start position:0% +need something that keeps it a a stance + + + align:start position:0% +need something that keeps it a a stance +like for the I mean you might get a + + align:start position:0% +like for the I mean you might get a + + + align:start position:0% +like for the I mean you might get a +totally different gate out that that + + align:start position:0% +totally different gate out that that + + + align:start position:0% +totally different gate out that that +could be just during the + + align:start position:0% +could be just during the + + + align:start position:0% +could be just during the +swing but I guess you you'd have to sort + + align:start position:0% +swing but I guess you you'd have to sort + + + align:start position:0% +swing but I guess you you'd have to sort +of somehow you have to end up with a + + align:start position:0% +of somehow you have to end up with a + + + align:start position:0% +of somehow you have to end up with a +straight leg so you if it went past and + + align:start position:0% +straight leg so you if it went past and + + + align:start position:0% +straight leg so you if it went past and +came back you're exceptionally Lucky in + + align:start position:0% +came back you're exceptionally Lucky in + + + align:start position:0% +came back you're exceptionally Lucky in +that regard you might you might do it + + align:start position:0% +that regard you might you might do it + + + align:start position:0% +that regard you might you might do it +but kneecaps are a good thing yeah + + align:start position:0% + + + + align:start position:0% + +feel a little silly walking down the + + align:start position:0% +feel a little silly walking down the + + + align:start position:0% +feel a little silly walking down the +street without + + align:start position:0% + + + + align:start position:0% + +kneecaps so the Dynamics of this if you + + align:start position:0% +kneecaps so the Dynamics of this if you + + + align:start position:0% +kneecaps so the Dynamics of this if you +sort of project it onto a + + align:start position:0% +sort of project it onto a + + + align:start position:0% +sort of project it onto a +single um plane you get this nice long + + align:start position:0% +single um plane you get this nice long + + + align:start position:0% +single um plane you get this nice long +limit cycle of the of the stance leg you + + align:start position:0% +limit cycle of the of the stance leg you + + + align:start position:0% +limit cycle of the of the stance leg you +got an impact which instantaneously um + + align:start position:0% +got an impact which instantaneously um + + + align:start position:0% +got an impact which instantaneously um +decreases your velocity then you get + + align:start position:0% +decreases your velocity then you get + + + align:start position:0% +decreases your velocity then you get +your stand leg cycle which is actually + + align:start position:0% +your stand leg cycle which is actually + + + align:start position:0% +your stand leg cycle which is actually +it's basically a snapshot of your + + align:start position:0% +it's basically a snapshot of your + + + align:start position:0% +it's basically a snapshot of your +rimless wheel cycle and then you get + + align:start position:0% +rimless wheel cycle and then you get + + + align:start position:0% +rimless wheel cycle and then you get +another discrete impact which loses + + align:start position:0% +another discrete impact which loses + + + align:start position:0% +another discrete impact which loses +energy on the other side and you get + + align:start position:0% +energy on the other side and you get + + + align:start position:0% +energy on the other side and you get +this nice limit cycle for the compass + + align:start position:0% + + + + align:start position:0% + +gate this is the Theta of the of leg + + align:start position:0% + + + + align:start position:0% + +one and it's the it's the stance leg + + align:start position:0% +one and it's the it's the stance leg + + + align:start position:0% +one and it's the it's the stance leg +here and it's the swing leg here yeah + + align:start position:0% +here and it's the swing leg here yeah + + + align:start position:0% +here and it's the swing leg here yeah +and trajectories that neighbor this + + align:start position:0% +and trajectories that neighbor this + + + align:start position:0% +and trajectories that neighbor this +converge to it just like you'd expect + + align:start position:0% +converge to it just like you'd expect + + + align:start position:0% +converge to it just like you'd expect +the need Walker has another Collision + + align:start position:0% +the need Walker has another Collision + + + align:start position:0% +the need Walker has another Collision +that happens somewhere in the the middle + + align:start position:0% +that happens somewhere in the the middle + + + align:start position:0% +that happens somewhere in the the middle +of your swing but it all works out + + align:start position:0% + + + + align:start position:0% + +right okay so + + align:start position:0% + + + + align:start position:0% + +um I've given you enough sort of to uh I + + align:start position:0% +um I've given you enough sort of to uh I + + + align:start position:0% +um I've given you enough sort of to uh I +think to understand the basic limit cyc + + align:start position:0% +think to understand the basic limit cyc + + + align:start position:0% +think to understand the basic limit cyc +Dynamics and the the basic stability + + align:start position:0% +Dynamics and the the basic stability + + + align:start position:0% +Dynamics and the the basic stability +property of these + + align:start position:0% +property of these + + + align:start position:0% +property of these +things um next time we'll talk a bit + + align:start position:0% +things um next time we'll talk a bit + + + align:start position:0% +things um next time we'll talk a bit +about um how you'd actually apply some + + align:start position:0% +about um how you'd actually apply some + + + align:start position:0% +about um how you'd actually apply some +of our previous methods for instance to + + align:start position:0% +of our previous methods for instance to + + + align:start position:0% +of our previous methods for instance to +this now that we got a limit cycle and + + align:start position:0% +this now that we got a limit cycle and + + + align:start position:0% +this now that we got a limit cycle and +we've got hybrid Dynamics with these + + align:start position:0% +we've got hybrid Dynamics with these + + + align:start position:0% +we've got hybrid Dynamics with these +switching if you want to do things like + + align:start position:0% +switching if you want to do things like + + + align:start position:0% +switching if you want to do things like +compute the gradients to do um + + align:start position:0% +compute the gradients to do um + + + align:start position:0% +compute the gradients to do um +optimization so you have to be a little + + align:start position:0% +optimization so you have to be a little + + + align:start position:0% +optimization so you have to be a little +careful about those impacts and how they + + align:start position:0% +careful about those impacts and how they + + + align:start position:0% +careful about those impacts and how they +affect things but it's not too + + align:start position:0% +affect things but it's not too + + + align:start position:0% +affect things but it's not too +hard and we'll tell you a bit about the + + align:start position:0% +hard and we'll tell you a bit about the + + + align:start position:0% +hard and we'll tell you a bit about the +state-ofthe-art and walking control + + align:start position:0% +state-ofthe-art and walking control + + + align:start position:0% +state-ofthe-art and walking control +right they're all sort of based on this + + align:start position:0% +right they're all sort of based on this + + + align:start position:0% +right they're all sort of based on this +this + + align:start position:0% +this + + + align:start position:0% +this +model and then Thursday's the midterm I + + align:start position:0% +model and then Thursday's the midterm I + + + align:start position:0% +model and then Thursday's the midterm I +promise to have a practice exam for you + + align:start position:0% +promise to have a practice exam for you + + + align:start position:0% +promise to have a practice exam for you +it might not be tonight unfortunately + + align:start position:0% +it might not be tonight unfortunately + + + align:start position:0% +it might not be tonight unfortunately +but it'll be very soon tomorrow or early + + align:start position:0% +but it'll be very soon tomorrow or early + + + align:start position:0% +but it'll be very soon tomorrow or early +Saturday morning I promise yeah okay and + + align:start position:0% +Saturday morning I promise yeah okay and + + + align:start position:0% +Saturday morning I promise yeah okay and +feel free to ask me any questions some + + align:start position:0% +feel free to ask me any questions some + + + align:start position:0% +feel free to ask me any questions some +of you are are finding me to ask to run + + align:start position:0% +of you are are finding me to ask to run + + + align:start position:0% +of you are are finding me to ask to run +project ideas by that's a great idea if + + align:start position:0% +project ideas by that's a great idea if + + + align:start position:0% +project ideas by that's a great idea if +you want to talk about your project let + + align:start position:0% +you want to talk about your project let + + + align:start position:0% +you want to talk about your project let +me know let John know + + align:start position:0% +me know let John know + + + align:start position:0% +me know let John know +um see you next time \ No newline at end of file diff --git a/-yfdG4BRFBY.txt b/-yfdG4BRFBY.txt new file mode 100644 index 0000000000000000000000000000000000000000..f4168b1e1d69fe2b9ba0d6a1154965a32ff31eac --- /dev/null +++ b/-yfdG4BRFBY.txt @@ -0,0 +1,435 @@ +align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +becoming the next bill NY was a monthong + + align:start position:0% +becoming the next bill NY was a monthong + + + align:start position:0% +becoming the next bill NY was a monthong +class that we taught at MIT it was a + + align:start position:0% +class that we taught at MIT it was a + + + align:start position:0% +class that we taught at MIT it was a +class to teach students how to use video + + align:start position:0% +class to teach students how to use video + + + align:start position:0% +class to teach students how to use video +to engage an audience in the things + + align:start position:0% +to engage an audience in the things + + + align:start position:0% +to engage an audience in the things +they're excited about in science + + align:start position:0% +they're excited about in science + + + align:start position:0% +they're excited about in science +technology engineering and math it was + + align:start position:0% +technology engineering and math it was + + + align:start position:0% +technology engineering and math it was +Workshop based very intensive we held it + + align:start position:0% +Workshop based very intensive we held it + + + align:start position:0% +Workshop based very intensive we held it +every day and we had everyone from + + align:start position:0% +every day and we had everyone from + + + align:start position:0% +every day and we had everyone from +undergrads freshmen to grad students + + align:start position:0% +undergrads freshmen to grad students + + + align:start position:0% +undergrads freshmen to grad students +coming in from all sorts of different + + align:start position:0% +coming in from all sorts of different + + + align:start position:0% +coming in from all sorts of different +disciplines um and they basically had a + + align:start position:0% +disciplines um and they basically had a + + + align:start position:0% +disciplines um and they basically had a +chance to learn how to script + + align:start position:0% +chance to learn how to script + + + align:start position:0% +chance to learn how to script +pre-produce and host a 5minute YouTube + + align:start position:0% +pre-produce and host a 5minute YouTube + + + align:start position:0% +pre-produce and host a 5minute YouTube +video we had everything from videos on + + align:start position:0% +video we had everything from videos on + + + align:start position:0% +video we had everything from videos on +how braces work to how time travel Works + + align:start position:0% +how braces work to how time travel Works + + + align:start position:0% +how braces work to how time travel Works +to fractals and then we took some of our + + align:start position:0% +to fractals and then we took some of our + + + align:start position:0% +to fractals and then we took some of our +favorite projects and turned them into + + align:start position:0% +favorite projects and turned them into + + + align:start position:0% +favorite projects and turned them into +the third season of mit's original web + + align:start position:0% +the third season of mit's original web + + + align:start position:0% +the third season of mit's original web +series science at LAD we had a teaching + + align:start position:0% +series science at LAD we had a teaching + + + align:start position:0% +series science at LAD we had a teaching +team that was about as big as our class + + align:start position:0% +team that was about as big as our class + + + align:start position:0% +team that was about as big as our class +itself we had Educators producers hosts + + align:start position:0% +itself we had Educators producers hosts + + + align:start position:0% +itself we had Educators producers hosts +I think the most valuable member members + + align:start position:0% +I think the most valuable member members + + + align:start position:0% +I think the most valuable member members +of our teaching team were a group of + + align:start position:0% +of our teaching team were a group of + + + align:start position:0% +of our teaching team were a group of +middle schoolers that we had come in one + + align:start position:0% +middle schoolers that we had come in one + + + align:start position:0% +middle schoolers that we had come in one +day as our class consultants and our + + align:start position:0% +day as our class consultants and our + + + align:start position:0% +day as our class consultants and our +students actually had to pitch their + + align:start position:0% +students actually had to pitch their + + + align:start position:0% +students actually had to pitch their +video ideas to them because who better + + align:start position:0% +video ideas to them because who better + + + align:start position:0% +video ideas to them because who better +to know the YouTube landscape better + + align:start position:0% +to know the YouTube landscape better + + + align:start position:0% +to know the YouTube landscape better +than a bunch of preen so on the MIT open + + align:start position:0% +than a bunch of preen so on the MIT open + + + align:start position:0% +than a bunch of preen so on the MIT open +course for site you'll pretty much get + + align:start position:0% +course for site you'll pretty much get + + + align:start position:0% +course for site you'll pretty much get +as close of an experience to actually + + align:start position:0% +as close of an experience to actually + + + align:start position:0% +as close of an experience to actually +taking the class as these students did + + align:start position:0% +taking the class as these students did + + + align:start position:0% +taking the class as these students did +cuz you'll find the syllabus and you'll + + align:start position:0% +cuz you'll find the syllabus and you'll + + + align:start position:0% +cuz you'll find the syllabus and you'll +find all the assignments but then on top + + align:start position:0% +find all the assignments but then on top + + + align:start position:0% +find all the assignments but then on top +of that you'll find video lectures where + + align:start position:0% +of that you'll find video lectures where + + + align:start position:0% +of that you'll find video lectures where +we've really um tried to capture every + + align:start position:0% +we've really um tried to capture every + + + align:start position:0% +we've really um tried to capture every +single candid moment that happened in + + align:start position:0% +single candid moment that happened in + + + align:start position:0% +single candid moment that happened in +the class and then in particular if + + align:start position:0% +the class and then in particular if + + + align:start position:0% +the class and then in particular if +you're an educator there is a special + + align:start position:0% +you're an educator there is a special + + + align:start position:0% +you're an educator there is a special +section called this course at MIT where + + align:start position:0% +section called this course at MIT where + + + align:start position:0% +section called this course at MIT where +you'll get uh very specific instructor + + align:start position:0% +you'll get uh very specific instructor + + + align:start position:0% +you'll get uh very specific instructor +insights as to how we approached + + align:start position:0% +insights as to how we approached + + + align:start position:0% +insights as to how we approached +designing this class how we ran it + + align:start position:0% +designing this class how we ran it + + + align:start position:0% +designing this class how we ran it +you'll get our confessionals and sort of + + align:start position:0% +you'll get our confessionals and sort of + + + align:start position:0% +you'll get our confessionals and sort of +insights into our pedagogical approaches + + align:start position:0% +insights into our pedagogical approaches + + + align:start position:0% +insights into our pedagogical approaches +in teaching a class like this the great + + align:start position:0% +in teaching a class like this the great + + + align:start position:0% +in teaching a class like this the great +thing is all these materials all of our + + align:start position:0% +thing is all these materials all of our + + + align:start position:0% +thing is all these materials all of our +experiences and resources they're all up + + align:start position:0% +experiences and resources they're all up + + + align:start position:0% +experiences and resources they're all up +online on open courseware for free + + align:start position:0% +online on open courseware for free + + + align:start position:0% +online on open courseware for free +there's no sign up required you can pick + + align:start position:0% +there's no sign up required you can pick + + + align:start position:0% +there's no sign up required you can pick +and choose what you want to learn and + + align:start position:0% +and choose what you want to learn and + + + align:start position:0% +and choose what you want to learn and +you can do it at your own + + align:start position:0% +you can do it at your own + + + align:start position:0% +you can do it at your own +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +pace \ No newline at end of file diff --git a/00LNy0Q_i6c.txt b/00LNy0Q_i6c.txt new file mode 100644 index 0000000000000000000000000000000000000000..dbca4894a9b5ea77491b88b8cbb3f5ba0875bf36 --- /dev/null +++ b/00LNy0Q_i6c.txt @@ -0,0 +1,1197 @@ +Good morning. Good morning. + +So, what I would like to do today is pick up on our basic theme of + +molecular biology. We've talked about DNA replication. + +The transcription of DNA into RNA, and the translation of RNA + +into protein. We discussed last time some of the variations between + +different types of organisms: viruses, prokaryotes, + +eukaryotes, with respect to the details of how they do that in + +general that bacteria have circular DNA chromosomes typically + +that eukaryotes have linear chromosomes, + +etc. What I'd like to talk about today is variation, + +but variation not between organisms but within an organism from time to + +time and place to place, namely, how it is that some genes or + +gene activities are turned on, on some occasions, and turned off on + +other occasions. This is, obviously, + +a very important problem to an organism, particularly + +to somebody like you who's a multi-cellular organism, + +and has the same DNA instruction set in all of your cells. + +It's obviously quite important to make sure that the same basic code + +is doing different things in different cells. + +It's important, also, to a bacterium to make sure that + +it's doing different things at different times, + +depending on its environment. So, I'm going to talk about a very + +particular system today as an illustration of how genes are + +regulated, but before we do that, let's + +Ask, where are the different places in this picture? + +DNA goes to DNA goes to RNA goes to protein, in which you might, + +in principle, regulate the activity of a gene. Could you regulate the + +activity of a gene by actually changing the DNA encoded in the + +genome? So, why not? Because what? It becomes a + +different gene. Yeah, that's just a definition. + +Why couldn't the cell just decide that I want this gene now to change + +in some way? Oh, I don't know, I'll alter the DNA + +sequence in some way. And, that'll make the gene work. + +Could that happen? Is that allowed? Yeah, it turns out to happen. + +It's not the most common thing, and it's not the thing they'll talk + +about in the textbooks a lot but you can actually do regulation. + +So, the levels of regulation are many, and one is actually at the + +level of DNA rearrangement. As we'll come to later in the + +course, for example, your immune system creates new, + +functional genes by rearranging locally some pieces of DNA, + +some bacteria, particularly infectious organisms control whether + +genes are turned on or off by actually going in there, + +and flipping around a piece of DNA in their chromosome. + +And, that's how they turn the gene on or off is they actually go in and + +change the genome. There's some protein that actually + +flips the orientation of a segment of DNA. Now, these are a little + +funky, and we're not going to talk a lot about them, + +but you should know, almost anything that can happen does + +happen and gets exploited in different ways by organisms. + +So, DNA rearrangement certainly happens. It's rare, + +but it's always cool when it happens. + +So, it's fun to look at. And, something like the immune + +system can't be dismissed as simply an oddity. That's an incredibly + +important thing. The most common form is at the + +level of transcriptional regulation, where whether or not a transcript + +gets made is how it's processed can be different. First off, + +the initiation of transcription that RNA polymerase should happen to + +sit down at this gene on this occasion and start transcribing it + +is a potentially regulatable (sic) step that maybe you're only going to + +turn on the gene for beta-globin and alpha-globin that together make the + +two components of hemoglobin, and you're only going to turn them + +on in red blood cells, or red blood cell precursors, + +and that could be done at the level of whether or not you make the + +message in the first place. That's one place it can be done. + +Another place is the splicing choices that you make. + +With respect to your message, you get this thing with a number of + +different potential exons, and you can regulate how this gene + +is used by deciding to splice it this way, and skip over that exon + +perhaps, or not skip over that exon. That alternative spicing is a + +powerful way to regulate. And then finally, you can also + +regulate at the level of mRNA stability. + +Stability means the persistence of the message, the degradation of the + +message. It could be that in certain cells, + +the message is protected so that it hangs around longer. + +And, in other cells, perhaps, it's unprotected and it's + +degraded very rapidly. If it's degraded very rapidly, + +it doesn't get a chance to make a protein or maybe it doesn't get to + +make too many copies of the protein. If it's persistent for a long time, + +it can make a lot of copies of protein. + +All of those things can and do occur. Then, of course, + +there is the regulation at the level of translation. + +Translation, if I give you an mRNA, is it automatically going to be + +translated? Maybe the cell has a way to sequester the RNA to ramp it + +up in some way so that it doesn't get to the ribosome under + +some conditions, and under other conditions it does + +get to the ribosome, or some ways to block in other + +manners than just sequestering it, but to physically block whether or + +not this message gets translated, what turns out that there's a + +tremendous amount of that. It's, again, not the most common, + +but we're learning, particularly over the last couple of years, + +that regulation of the translation of an mRNA is important. + +There are, although I won't talk about them at length, + +an exciting new set of genes called micro RNA's, + +teeny little RNAs that encode 21-22 base pair segments that are able to + +pair with a messenger RNA and interfere in some ways partially + +with its translatability. And so, by the number and the kinds + +of little micro RNAs that are there, organisms can tweak up or down how + +actively a particular message is being translated. + +So, the ability to regulate translation in a number of different + +ways is important. And then, of course, + +there's post-translational control. Once a protein is made, + +there's post-translational regulation that could happen. + +It could be that the protein is modified in some way. + +The proteins say completely inactive unless you put a phosphate + +group on it, and some enzyme comes along and puts a phosphate group on + +it. Or, it's inactive until you take off the phosphate group. + +All sorts of post-translational modifications can occur to proteins + +after the amino acid chain is made that can affect whether or not the + +protein is active. Every one of these is potentially a + +step by which an organism can regulate whether or not you have a + +certain biochemical activity present in a certain amount at a certain + +time. And, every one of these gets used. This is the thing about + +coming to a system that has been in the process of evolution for three + +and a half billion years is that even little differences can be + +fought over as competitive advantages, and can be fixed + +by an organism. So, if a tiny little thing began to + +help the organism slightly, it could reach fixation. And, + +you're coming along to this system, which has had about three and a half + +billion years of patches to the software code, + +and it's just got all sorts of layers and regulation piled on top + +of it. All of these things happen. But, what we think is the most + +important out of this whole collection is this guy. + +The fundamental place at which you're going to regulate whether or + +not you have the product of a gene is whether you bother to transcribe + +its RNA. But I do want to say because, yes? And, + +which exons you used and which aren't? Yeah, + +well, there are tissue-specific factors that are gene-specific + +that can influence that. And, surprisingly little is known + +about the details. There are a couple of cases where + +people know, but as you'd imagine, you actually need a regulatory + +system in that tissue to be able to decide to skip over that exon. + +And, the mechanics of that surprisingly are understood in very + +few cases. And, you might think that evolution + +wouldn't like to use that as the most common thing because you really + +do have to make a specialized thing to do that. So, that's what + +happens on these. That's one in particular where I + +think a tremendous amount of more work has to happen. + +mRNA stability, we understand some of it but not all the factors in + +this business. I was telling you about translation + +with these little micro-RNAs is stuff that's really only a few years + +old that people have come to understand. So, + +there's a lot to be understood about these things. I'm going to tell you + +about initiation of mRNAs, because it's the area where we know + +the most, and I think it'll give you a good idea of the general paradigm. + +But, any of you who want to go into this will find that there's a + +tremendous amount more to still be discovered about these things. + +So, the amount of protein that a cell might make varies wildly. + +Your red blood cells, 80% of your red blood cells, + +protein, is alpha or beta-globin. It's a huge amount. That's not + +true in any other cell in your body. So, we were talking about pretty + +significant ranges of difference as to how much protein is made. + +How do things like that happen? Well, I'm going to describe the + +simplest and classic case of gene regulation and bacteria, + +and in particular, the famous lack operon of E coli. + +So, this was the first case in which regulation was ever really + +worked out, and it stands today as a very good paradigm of how + +regulation works. E coli, in order to grow, + +needs a carbon source. In particular, E coli is fond of sugar. + +It would like to have a sugar to grow on. Given a choice, + +what's E coli's favorite sugar? It's glucose, right, because we + +have the whole cycle of glucose. The whole pathway of glucose goes + +to pyruvate, which we've talked about, and glucose is the preferred + +sugar to go into that pathway, OK, of glycolysis. + +Glycolysis: the breakdown of glucose. But, suppose there's no glucose + +available. Is E coli willing to have a different sugar? + +Sure, because E coli's not stupid. If it were to refuse another sugar, + +it wouldn't be able to grow. So, it has a variety of pathways that will + +shunt other sugars to glucose, which will then allow you to go + +through glycolysis, etc. Now, given a choice, + +it would prefer to use the glucose. But if not, suppose you gave it + +lactose. Lactose is a disaccharide. It's milk sugar, and I'll just + +briefly sketch, so lactose is a disaccharide where + +you've got a glucose and a galactose. + +Glucose plus galactose equals lactose. So, if E coli is given + +galactose, it is able to break it down into glucose plus galactose. + +And it does that by a particular enzyme called beta galactosidase, + +which breaks down glactosides. And, it'll give you galactose plus + +glucose. How much beta-galactosidase does an E coli + +cell have around? Sorry? None? But how does it do this? + +When it needs it, it'll synthesize it. When it needs it, + +like, there's no glucose and there's a lot of galactose around, + +how much of it will there be? A lot. It turns out that in + +circumstances where E coli is dependent on galactose as its fuel, + +something like 10% of total protein + +can be beta-gal under the circumstances when you have + +galactose but no glucose. Sorry? Sorry, when you have + +lactose but no glucose. Thank you. So, when you have + +lactose but no glucose, E coli has 10% of its protein weight + +as beta-galactosidase. Wow. But when you have glucose + +around or you don't have lactose around, you have very little. + +It could be almost none, trace amounts. So, why do this? + +Why not, for example, just have a far more reasonable some compromise? + +Like, let's always just have 1% of beta-galactosidase. + +Why do we need the 0-10%? 10%'s actually extremely high. + +So what. It's a good insurance policy. So, if I only have + +galactose, I need more. Well, I mean, 1% will still digest + +it. I'll still do it. What's the problem? Sorry? + +So what, I do it at a slower rate. Life's long. Why not? Ah, it has + +to compete. So, if the cell to the left had a + +mutation that got it to produce four times as much, + +then it would soak up the lactose in the environment, + +grow faster, etc. etc., and we could have competed. + +So, these little tuning mutations have a huge effect amongst this + +competing population of bacteria. And so, if E coli currently thinks + +that it's really good to have almost non at sometimes and 10% at other + +times, you can bet that it's worked that out through the product of + +pretty rigorous competition, that it doesn't want to waste the + +energy making this when you don't need it, and that when you do need + +it, you really have to compete hard by growing as fast as you can when + +you have that lactose around. OK. So, how does it actually get + +the lactose, sorry, keep me honest on lactose versus + +galactose, into the cell? It turns out that it also has + +another gene product, another protein, which is a lactose + +permease. And, any guesses as to what a + +lactose permease does? It makes the cell permeable to + +lactose, right, good. So, the lactose can get into + +the cell, and then beta-gal can break it down into galactose plus + +glucose. These two things, in fact, both get regulated, + +beta-gal and this lactose permease. So, how does it work? + +Let's take a look now at the structure of the lack operon. + +So, I mentioned briefly last time, what's an operon? Remember we said + +that in bacteria, you often made a transcript that had + +multiple proteins that were encoded on it. + +A single mRNA could get made, and multiple starts for translation + +could occur, and you could make multiple proteins. + +And, this would be a good thing if you wanted to make a bunch of + +proteins that were a part of the same biochemical pathway. + +Such an object, a regulated piece of DNA that makes a transcript + +encoding multiple polypeptides is called an operon because they're + +operated together. So, let's take a look here at the + +lack operon. I said there was a promoter. + +Here is a promoter for the operon, and we'll call it P lack, promoter + +for the lack operon. Here is the first gene that is + +encoded. So, the message will start here, actually about here, + +and start going off. And, the first gene is given the name lack Z. + +It happens to encode beta-galactosidase enzyme. + +Remember, they did a mutant hunt, and when they did the mutant hunt, + +they didn't know what each gene was as they isolated mutants. + +So, they just gave them names of letters. And so, + +it's called lack Z. And, everybody in molecular biology + +knows this is the lack Z gene, although Z has nothing to do with + +beta-galactosidase. It was just the letter given to it. + +But, it's stuck. Next is lack Y. + +And, that encodes the permease. And, there is also lack A, which + +encodes a transacetylase, and as far as I'm concerned you can + +forget about it. OK, but I just mentioned that it is + +there, and it actually does make three polypeptides. + +We won't worry about it, OK, but it does make a + +transacetylase, OK? But it won't figure in what we're + +going to talk about, and actually remarkably little is + +known about the transacetylase. There's also one other gene I need + +to talk about, and that's over here, + +and that's called lack I. And, it too has a promoter, + +which we can call PI, for the promoter for lack I. + +And, this encodes a very interesting protein. + +So, we get here one message encoding one polypeptide here. + +This mRNA encodes one polypeptide. It is monocystronic. This guy here + +is a polycystronic message. It has multiple cystrons, which is + +the dusty old name for these regions that were translated into distinct + +proteins. And so, that's that mRNA. + +So, lack I, this encodes a very interesting protein, + +which is called the lack repressor. The lack repressor, actually I'll + +bring this down a moment, is not an enzyme. + +It's not a self-surface channel for putting in galactose. + +It is a DNA binding protein. It binds to DNA. But, it's not a + +nonspecific DNA binding protein that binds to any old DNA. + +It has a sequence-specific preference. + +It's a protein that has a particular confirmation, a particular shape, + +a particular set of amino acids sticking out, that it combined into + +the major groove of DNA in a sequence-specific fashion such that + +it particularly likes to recognize a certain sequence of nucleotides and + +binds there. Where is the specific sequence of nucleotides where this + +guy likes to bind? It so happens that it's there. + +And this is called the operator sequence or the operator site. + +So, this protein likes to go and bind there. Now, + +I've drawn this, by the way, so that this operator site is + +actually right overlapping the promoter site. + +Who likes to bind at the promoter site? RNA polymerase. + +What's going to happen if the lack repressor protein is sitting there? + +RNA polymerase can't bind. It's just physically, + +blocked from binding. So, let's examine some cases here. + + Let's suppose that we look at here + +at our gene. We've got our promoter, P lack. We've got the operator site + +here. We've got the lack Z gene here, and we've got the lack + +repressor, lack I, the repressor sitting there. + +Polymerase tries to come along to this, and it's blocked. + +So, what will happen in terms of the transcription of the lack + +operon: no mRNA. So, that's great. + +So, we've solved one problem right off the bat. + +We want to be sure that sometimes there's going to be no mRNA made. + +This way, we're not going to waste any metabolic energy, + +making beta-galactosidase. Are we done? No? Why not. + +We've got to sometimes make beta-galactosidase. + +So, we've got to get that repressor off there. Well, + +how is the repressor going to come off there? When do we want the + +repressor off there: when there's lactose present. + +So, somehow we need to build some kind of an elaborate sensory + +mechanism that is able to tell when lactose is present, + +and send a signal to the repressor protein saying, + +hey, lactose is around. The signal gets transmitted all the + +way to the repressor protein, and the repressor protein comes off. + +What kind of an elaborate sensory mechanism might be built? + +Use lactose as what? So, this is actually pretty simple. + +You're saying just take lactose, and you want lactose to be its own + +signal? So, if lactose were to just bind to the repressor, + +the repressor might then know that there was lactose around. + +Well, what would it do if lactose bound to it? Sorry? Why + +would it fall off? Yep. More interested in the lactose. + +So, if you're suggestion, this is good. I like the design + +work going on here. The suggestion is that if lactose + +binds to this here, binds to our repressor, + +it's going to fall off because it's more interested in lactose + +than in the DNA. Now, how is the interest actually + +conveyed into something material? Because the actual level of + +cognitive like or dislike for DNA on the part of this polypeptide is + +unclear, you may be anthropomorphizing slightly with + +regard to this polypeptide chain. So, mechanistically, what's going + +to happen? Shape. Yes, shape? Change confirmation, + +the binding act, the act of binding lactose creates some energy, + +may change the shape of the protein, + +and that shape of the protein may, in the process of wiggling around to + +bind lactose may de-wiggle some other part of it that now no longer + +binds so well to DNA. That is exactly what happens. + +Good job. So, you guys have designed, in fact, + +what really happens. What happens is what's called an + +allosteric change. It just means other shape. + +So, it just changes its shape, that it changes shape on binding of + +lactose. And it falls off because it's less + +suitable for binding this particular DNA sequence when it's bound to + +lactose there. So, in this case, + +in the presence of lactose, lack I does not bind. + +And, the lack operon is transcribed. Yes? Uh-oh. OK, all right + +designers, here we've got a problem. You have such a cool system, + +right? You were going to sense lactose. + +Lactose was going to bind to the lack repressor, + +change its confirmation falloff: uh-oh. But, as you point out, + +how's it going to get any lactose, because there's not a lactose + +permease because the lactose permease is made by + +the same operon. So, what if, in fact, + +instead of getting one of these DOD mill speck kind of things of some + +repressor that is absolutely so tight that it never falls off under + +any circumstances, what if we build a slightly sloppy + +repressor that occasionally falls off, and occasionally allows + +transcription of the lack operon? Then, we'll have some trace + +quantities of permease around. With a little bit of permease + +around, a little lactose will get in. + +And, as long as even a little lactose gets in, + +it'll now shift the equilibrium so that the repressor is off more, + +and of course that will make more permease, and shift, + +and shift, and shift, and shift. So, as long as it's not + +so perfectly engineered as to have nothing being transcribed, + +so no mRNA is really very little mRNA. See, this is what's so good, + +I think, about having MIT students learn this stuff because there are + +all sorts of wonderful design principles here about how + +you build systems. And, I think this is just a very + +good example of how you build a system like this. + +Now, all right, so we now have the ability to have lack on and lack off, + +and that is lack off, mostly off because of your permease + +problem: very good. Now, let's take a little digression + +about, how do we know this? This kind of reasoning, + +I've now told you the answer. But let's actually take a look at + +understanding the evidence that lets you conclude this. + +So, in order to do this, and this is the famous work in + +molecular biology of Jacobin Manoux in the late '50s for which they won + +a Nobel Prize, they wanted to collect some mutants. + +Remember, this is before the time of DNA sequence or anything like + +that, and wanted to collect mutants that affected this process. + +So, in order to collect mutants that screwed up the regulation, + +they knew that beta-galactosidase was produced in much higher quantity + +if lactose was around. The difficulty with that was that + +wild type E coli, when you had no lactose would + +produce very little beta-gal, one unit of beta-gal, + +and in the presence of lactose, would produce a lot, let's call it 1, + +00 units of beta-gal. But, the problem with playing + +around with this is lactose is serving two different roles. + +Lactose is both the inducer of the expression of the gene by virtue of + +binding to the repressor, etc., etc. + +But, it's also the substrate for the enzyme because as beta-galactosidase + +gets made, it breaks down the lactose. So, there's less lactose + +in binding, and if you wanted to really study the regulatory controls, + +you have the problem that the thing that's inducing the gene by binding + +to the repressor is the thing that's getting destroyed by the product of + +the gene. So, it's going to make the kinetics of + +studying such a process really messy. It would be very nice if you could + +make a form of lactose that could induce beta-galactosidase by binding + +to the repressor, but wasn't itself digested. + +Chemically, in fact, you can do that. Chemically, + +it's possible to make a molecule called IPTG, which is a + +galactoside analog. And, what it does is this molecule + +here which I'll just sketch very quickly here, it's a sulfur there, + +and you can see vaguely similar, this is able to be an inducer. + +It'll induce beta-gal, but not a substrate. It won't get digested. + +So, it'll stick around as long as you want. It's also very convenient + +to use a molecule that was developed called ex-gal. + +Ex-gal again has a sugar moiety, and then it also has this kind of a + +funny double ring here, which is a chlorine, and a bromine, + +and etc. And, this guy here is not an inducer. It's not capable of + +being induced, of inducing beta-galactosidase + +expression. But, it is a substrate. + +It will be broken down by the enzyme, and rather neatly when it's + +broken down it turns blue. These two chemicals turned out to + +be very handy in trying to work out the regulation of the + +lack operon. So, if I, instead of adding lactose, + +if I think about adding IPTG, my inducer, when I add IPTG I'm going + +to get beta-gal produced. When I don't have IPTG, I won't + +produce beta-gal. But then I don't have a problem of + +this getting used up. So now, what kind of a mutant might + +I look for? I might look for a mutant that even + +in the absence of the inducer, IPTG, still produces a lot of + +beta-gal. Now, I can also look for mutants that no + +matter what never produce beta-gal, right? But, what would they likely + +be? They'd likely be structural mutations affecting the coding + +sequence of beta-gal, right? Those will happen. + +I can collect mutations that cause the E coli never to + +produce beta-gal. But that's not as interesting as + +collecting mutations that block the repression that cause beta-gal to be + +produced all of the time. So, how would I find such a mutant? + +I want to find a mutant that's producing a lot of beta-gal even + +when there's no IPTG. So, let's place some E coli on a + +plate. Should we put IPTG on a plate? No, so no IPTG. + +What do I look for? How do I tell whether or not any of + +these guys here is producing a lot of beta-gal? Yep? + +So, no IPTG, but put on ex-gal, and if anybody's producing a lot of + +beta-gal, what happens? They turn blue: very easy to go + +through lots of E coli like that looking for something blue. + +And so, lots of mutants were collected that were blue. + +And, these chemicals are still used today. They're routinely used in + +labs, ex-gal and stuff like that, making bugs turn blue because this + +has turned out to be such a well-studied system that we use it + +for a lot of things. So, mutants were found that were + +constituative. So, mutants were found that were + +constituative mutants. Constituative mutants: meaning + +expressing all the time, no longer regulated, so, + +characterizing these constituative mutants. + +It turns out that they fell into two different classes of constituative + +mutants. If we had enough time, and you could read the papers and + +all, what I would do is give you the descriptions that Jacobin Maneaux + +had of these funny mutants which they'd isolated and were trying to + +characterize, and how to puzzle out what was going on. + +But, it's complicated and hard, and makes your head hurt if you + +don't know what the answer is. So, I'm going to first tell you the + +answer of what's going on, and then sort of see how you would + +know that this was the case. But, imagine that you didn't know + +this answer, and had to puzzle this out from the data. + +So, suppose we had, so if there were going to be two + +kinds of mutants: mutant number one are operator constituents. + +They have a defective operator sequence. Mutations have occurred + +at the operator site. Mutant number two have a defective + +repressor protein, the gene for the repressor protein. + + How can I tell the difference? + +So, I could have a problem in my operator site. + +What would be the problem with the operator site? + +Some mutation to the sequence causes the repressor not to bind + +there anymore, OK? So, a defective operator site + +doesn't bind repressors. Defective repressor, the operator + +site is just fine, but I don't have a repressor to bind + +at it. So how do I tell the difference? One way to tell the + +difference is to begin crossing the mutants together to wild type, + +and asking, are they dominant or recessive, or things like that? + +Now, here's a little problem. E Coli is not a diploid, so you + +can't cross together two E colis and make a diploid E coli, + +right? It's a prokaryote. It only has one genome. But, + +it turns out that you can make temporary diploids, + +partial diploids out of E coli because it turns out you can mate + +bacteria. Bacteria, which have a bacterial chromosome + +here also engage in sex and in the course of bacterial sex, + +plasmids can be transferred called, for example, an F factor, is able to + +be transferred from another bacteria. And, through the wonders of partial + +merodiploid, you can temporarily get E colis, or you can permanently get + +E colis, that are partially diploid. So, you can do what I'm about to + +say. But, in case you were worried about my writing diploid genotypes + +for E coli, you can actually do this. + +You can make partial diploids. So, let's try out a genotype here. + +Suppose the repressor is a wild type, the operator is wild type, + +and the lack Z gene is wild type. And, suppose I have no IPTG, I'm + +un-induced. I have one unit of beta-gal. When I add my inducer, + +what happens? I get 1,000 units of beta-gal. + +Now, suppose I would have an operator constituative mutation. + +Then, the operator site is defective. It doesn't bind the + +repressor. Beta-gal is going to be expressed all the time, + +even in the absence. All right, well that was, of course, what we + +selected for. Now, suppose I made the following diploid. + +I plus, O plus, Z plus, over I plus, + +O constituative, Z plus. So, here's my diploid. What would + +be the phenotype? So, in other words, + +one of the chromosomes has an operator problem. + +Well, that means that this chromosome here is always going to + +be constituatively expressing beta-gal. + +But, what about this chromosome here? It won't. So, + +this would be about 1, 01, give or take, because it's got + +one chromosome doing that and one chromosome doing this, + +and this one would be about 2, 00. Now, that quantitative + +difference doesn't matter a lot. What you really saw when you did + +the molecular biology was that when you had one copy of the operator + +constituative mutation, you still got a lot of beta-gal here + +even in the absence of IPTG. So, that operator constituative site + +looked like it was dominant to this plus site here. + +But now, let's try this one here. I plus, O plus, Z plus, over I plus, + +operator constituative, Z minus. What happens then? + +This operator constituative site allows constant transcription of + +this particular copy. But, can this particular copy make + +a working, functional beta-gal? No. So, this looks, when you do + +your genetic crosses, you find that the operator + +constituative, now, if I reverse these here, + +suppose I reverse these, I plus, O plus, Z minus, I plus, O + +constituative, Z plus, same genotypes, + +right, except that I flipped which chromosome these are on. + +Now, what happens? This chromosome here: always making beta-gal and it + +works. This chromosome here: not making beta-gal. + +Even though it's regulated, it's a mutant. So, in other words, + +from this very experiment, you can tell that the operator site is only + +affecting the chromosome that it's physically on, + +that it doesn't make a protein that floats around. + +What it does is it's said to work in cys. In cys means on the same + +chromosome. It physically works on the same chromosome. + +Now, let's take a look, by contrast, of the properties of + +the lack repressor mutants. If I give you a lack repressor + +mutant, I plus, O plus, Z plus is the wild type. + +I constituative, O plus, Z plus: what happens here? + +This wild type is one in 1, 00. This guy here: 1,000 and 1, + +00, and then here let's look at a diploid: + +I plus, O plus, Z plus, I constituative, + +O plus, Z plus. What's the effect? The I constituative doesn't make a + +functioning repressor. But, I plus makes a functioning + +repressor. So, will this show regulation? + +Yeah, this will be regulated just fine. This works out just fine, + +and in fact it'll make 2,000, and it'll make two copies there. + +But again, the units don't matter too much. And, + +by contrast, if I give you I plus, O plus, Z minus, and I constituative, + +O plus, Z plus, what will happen? + +Here, I have my mutation on this chromosome. But, + +it doesn't matter because I've got my mutation on this chromosome in + +the repressor. I've got a mutation on lack Z here, + +but as long as I have a functional copy, one functional copy of the + +lack repressor, it works on both chromosomes. + +It will work on both chromosomes, and so in other words this lack + +repressor, one copy works on both chromosomes. In other words, + +it makes a product that diffuses around, and can work on either + +chromosome, and it's said to work in trans, that is, across. + +So, the operator is working in cys. It's operating on its own + +chromosome only. A mutation in the operator only + +affects the chromosome it lives on, whereas a functional copy of the + +lack repressor will float around because it's a protein, + +and that's how Jacobin Maneaux knew the difference. + +They proved their model by showing that these two kinds of mutations + +had very different properties. Operator mutations affected only the + +physical chromosome on which they occurred, which of course they had + +to infer from the genetics they did, whereas repressor, a functional copy + +repressor, could act on any chromosome in the cell. + +So, OK, we've got that. Now, last point, what about glucose? + +I haven't said a word about glucose. See, this was a big deal to people. + +This model, the repressor model, we have this repressor. What + +about glucose? What's glucose doing in this picture? + +So, glucose control: so here's my gene. Here's my promoter, + +P lack. Here's my operator, beta-gal. + +It's encoded by lack Z. You've got all that. When this guy + +is present, sorry, when lactose is present, + +the repressor comes off. Polymerase sits down. Wait a second, + +polymerase isn't supposed to sit down unless there's no glucose. + +We need another sensor to tell if there's glucose, + +or if there's low glucose. So, we're going to need us a sensor + +that tells that. Any ideas? Yep? + +Yeah, if you work that one through, I don't think it quite works. But, + +you've got the basic idea. You're going to want another + +something, and it turns out there's another site over here, + +OK? There's a second site on which a completely different + +protein binds. And, this protein is the cyclic AMP + +regulatory protein, and it so happens that in the cell, + +when there's low amounts of glucose, let me make sure I've got this right, + +when there's low amounts of glucose, what we have is high amounts of + +cyclic AMP. Cyclic AMP turns out, + +whereas lactose is used directly as the signal, cyclic AMP is used as + +the signal here. When the cell has low amounts of + +glucose, it has high amounts of cyclic AMP. Now, + +what do you want your cyclic AMP to do? How are we going to design this? + +It's going to bind to a protein, cyclic AMP regulatory protein, it's + +going to sit down, and now what's it going to do? + +Is it going to block RNA polymerase? + +What do we want to do? If there's low glucose, + +high cyclic AMP, we sit down at the site, we want to turn on + +transcription now, right? So, what it's got to do is + +not block RNA polymerase, but help RNA polymerase. So, + +what it actually does is instead of being a repressor, + +it's an activator. And what it does is it makes it more attractive for + +RNA polymerase to bind, and it actually does that by, + +actually it does it slightly by bending the DNA. + +But, what it does is it makes it easier for RNA polymerase to bind. + +It turns out that the promoter is kind of a crummy promoter. + +It's actually just like, remember the repressor wasn't perfect; the + +promoter's not perfect either. The promoter's kind of crummy. + +And, unless RNA polymerase gets a little help from this other + +regulatory protein, it doesn't work. + +We have two controls: a negative regulator responding to an + +environmental cue, a positive activator responding to + +an environmental cue, helping polymerase decide whether to + +transcribe or not, and basically that's how a human egg + +goes to a complete adult and lives its entire life, + +minus a few other details. There are some details left out, + +but that's a sketch of how you turn genes on and off. \ No newline at end of file diff --git a/0M_kIqhwbFo.txt b/0M_kIqhwbFo.txt new file mode 100644 index 0000000000000000000000000000000000000000..19e8054e9567341b34a97211ccc0bee5cd25c920 --- /dev/null +++ b/0M_kIqhwbFo.txt @@ -0,0 +1,2557 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: All right. + +Let's get started. + +Today we start a brand +new section of 006, + +which is hashing. + +Hashing is cool. + +It is probably the most used +and common and important + +data structure and all +of computer science. + +It's in, basically, every system +you've ever used, I think. + +And in particular, +it's in Python + +as part of what makes +Python fun to program in. + +And basically, every modern +programming language has it. + +So today is about how to +make it actually happen. + +So what is it? + +It is usually +called a dictionary. + +So this is an +abstract data if you + +remember that term from +a couple lectures ago. + +It's kind of an old term, +not so common anymore, + +but it's useful to think about. + +So a dictionary is +a data structure, + +or it's a thing, +that can store items, + +and it can insert items, delete +items and search for items. + +So in general, it's going +to be a set of items, + +each item has a key. + +And you can insert an item, +you can delete an item + +from the set, and you can +search for a key, not an item. + +And the interesting +part is the search. + +I think you know what +insert and delete do. + +So there are two outcomes +to this kind of search. + +This is what I call +an exact search. + +Either you find an item with a +given key, or there isn't one, + +and then you just say +key error in Python. + +OK. + +This is a little +different from what + +we could do with +binary search trees. + +Binary search trees, if +we didn't find a key, + +we could find the next +larger and the next smaller + +successor and predecessor. + +With dictionaries you're +not allowed to do that, + +or you're not able to do that. + +And you're just +interested in the question + +does the key exist? + +And if so, give me the +item with that key. + +So we're assuming here that +the items have unique keys, + +no two items have the same key. + +And one way to +enforce that is when + +you insert an item +with an existing key, + +it overwrites whatever +key was there. + +That's the Python behavior. + +So we'll assume that. + +Overwrite any existing key. + +And so, it's well +defined what search does. + +Either there's one +item with that key, + +or there's no item +with that key, + +and it tells you what +the situation is. + +OK. + +So one way to solve +dictionaries is + +to use a balanced binary +search tree like AVL trees. + +And so you can do all of these +operations on log n time. + +I mean, you can ignore the +fact that AVL trees give you + +more information +when you do a search, + +and still does exact search. + +So that's one solution, but it +turns out you can do better. + +And while last class was about, +well, in the comparison model + +the best way to sort is n log +n and the best way to search + +is log n. + +Then we saw in the +RAM model, where + +if you assume your items are +integers we can sort faster, + +sometimes we can +sort in linear time. + +Today's lecture is about how to +search faster than log n time. + +And we're going to get +down to constant time. + +No-- basically, no +assumptions except, maybe, + +that your keys are integers. + +We'll be able to get +down to constant time + +with high probability. + +It's going to be a +randomized data structure. + +It's one of the few instances +of randomization in 006, + +but it'll be pretty simple +to analyze, so don't worry. + +But we're going to use +some probability today. + +Make it a little exciting. + +I think you know how +dictionaries work in Python. + +In Python it's the +dict data type. + +We've used it all +over the place. + +The key things you can +do are lookup a key + +and-- so this is the +analog of search-- + +you can set a key to a value. + +This is the analog of an insert. + +It overwrites +whatever was there. + +And what else? + +Delete. + +So you can delete +a particular key. + +OK. + +We'll usually use this +notation because it's + +more familiar and intuitive. + +But the big topic today +is how do you actually + +implement these operations +for a dictionary, D? + +The one specific thing +about Python dictionaries + +is that an item is +basically a pair + +of two things, a +key and a value. + +And so, in particular, +when you call d.items + +you get a whole bunch of ordered +pairs, a key and a value. + +And so the key is always-- +the key of an item + +is always this first part. + +So it's well defined. + +OK. + +So that's Python dictionaries. + +So one obvious motivation +for building dictionaries + +is you need them in Python. + +And in fact, people +use them all the time. + +We used them in docdist. + +All of the fastest versions of +the document distance problem + +used dictionaries for counting +words, how many times each word + +occurs in a document, and +for computing inner products, + +for finding common words +between two documents. + +And it's just it's the +best way to do things, + +it's the easiest way to do +things , and the fastest. + +As a result, dictionaries are +built into basically every + +modern programming language, +Python, Perl, Ruby, JavaScript, + +Java, C++, C#. + +In modern versions, all have +some version of dictionaries. + +And they all run in, +basically, constant time + +using the stuff that's in +this lecture and the next two + +lectures. + +Let's see. + +It's also, in, basically, +every database. + +There are essentially two kinds +of databases in the world, + +there are those +that use hashing, + +and there are those +that use search trees. + +Sometimes you need one. + +Sometimes you need the other. + +There are a lot of situations +in databases where you just + +need hashing. + +So if you've ever +used Berkeley DB, + +there's a hash +type of a database. + +So if things like, when +you go to Merriam-Webster, + +and you look up a +word, how do you + +find the definition +of that word? + +You use a hash table, you use +a dictionary, I should say. + +How do you-- when you +spell check your document, + +how do you tell whether a +word is correctly spelled? + +You look it up in a dictionary. + +If it's not correctly +spelled, how + +do you find the closest +related, correct spelling? + +You try tweaking +one the letters, + +and look it up in a dictionary +and see if it's there. + +You do that for all possible +letters, or maybe two letters. + +That is a state of the art +way to do spelling correction. + +Just keep looking +up in a dictionary. + +Because dictionaries +are so fast you + +can afford to do things like +trial perturbations of letters. + +What else. + +In the old days, which +means pre-Google, + +every search engine +on the web would + +have a dictionary that +says, for given word, + +give me all of the documents +containing that word. + +Google doesn't do it that +way, but that's another story. + +It's less fancy, actually. + +Or when you log +into a system, you + +type your username and password. + +You look in a dictionary +that stores a username + +and, associated +with that username, + +all the information +of that user. + +Every time you log into a +web system, or whatever, + +it is going through +a dictionary. + +So they're all over the place. + +One of the original +applications is + +in writing +programming languages. + +Some of the first +computer programs + +were programming languages, +so you could actually + +program them in +a reasonable way. + +Whenever you type a variable +name the computer doesn't + +really think about +that variable name, + +it wants to think about +an address in memory. + +And so you've got to +translate that variable name + +into a real, physical address +in the machine, or a position + +on the stack, or whatever +it is in real life. + +In the old days +of Python, I guess + +this is pre-Python +2 or so, 2.1, I + +don't remember the +exact transition it was. + +In the interpreter, +there was the dictionary + +of all your global +variables, there's + +a dictionary of all +your local variables. + +And that was-- it +was right there. + +I mean you could +modify the dictionary, + +you could do crazy things. + +And all the +variables were there. + +And so they'd match the +key to the actual value + +stored in the variable. + +They don't do that anymore +because it's a little slow, + +but-- and you could +do better in practice. + +But at the very least, when +you're compiling the thing, + +you need a dictionary. + +And then, later on, you can +do more efficient lookups. + +Let's see. + +On the internet there +are hash tables all over, + +like in your router. + +Router needs to know +all the machines that + +are connected to it. + +Each machine has an IP address, +so when you get a packet in, + +and it says, deliver to +this IP address, you see, + +oh, is it in my dictionary +of all the machines + +that are directly +connected to me? + +If so, send it there. + +If it's not then it has +to find the right subnet. + +That's not quite a +dictionary problem, + +a little more complicated. + +But for looking up local +machines, it's a dictionary. + +Routers use dictionaries because +they need to go really fast. + +They're getting a billion +packets every second. + +Also, in the network +stack of a machine, + +when you come in you +get it packet delivered + +to a particular port, you need +to say, oh, which application, + +or which socket is +connected to this port? + +All of these things +are dictionaries. + +The point is they're +in, basically, + +everything you've ever +used, virtual memory, + +I mean, they're +all over the place. + +There are also some more +subtle applications, + +where it is not obvious +that's it a dictionary, + +but still, we use +this idea of hashing + +we're going to talk about today. + +Like searching in a string. + +So when you hit-- I don't +know-- in your favorite editor, + +you do Control-F, or +Control-S, or slash, + +or whatever your way of +searching for something + +is, and you type start typing. + +If your editor is +clever, it will + +use hashing in order to +search for that string. + +It's a faster way to do it. + +If you use grep, for example, in +Unix it does it in a fancy way. + +Every time you do +a Google search + +it's essentially using this. + +It's solving this problem. + +I don't know what algorithm, +but we could guess. + +Using the algorithms we'll +cover in next lecture. + +It wouldn't surprise me. + +Also, if you have +a couple strings + +and you want to know what they +have in common, how similar + +they are? + +Example, you have +two DNA strings. + +You want to see how similar +they are, you use hashing. + +And you're going to do that +in the next problem set, PS4, + +which goes out on Thursday. + +Also, for things like file +and directory synchronization. + +So on Unix, if you rsync +or unison, or, I guess, + +modern day-- these +days, Dropbox, MIT + +startup-- Whenever you're +synchronizing files between two + +locations, you use +hashing to tell + +whether a file has changed, +or whether a directory has + +changed. + +That's a big idea. + +Fairly modern idea. + +And also in +cryptography-- this will + +be a topic of next +Tuesday's lecture. + +If you're transferring +a file and you + +want to check that you +actually transferred that file, + +and there wasn't some person in +the middle corrupting your file + +and making it look like it +was what you wanted it to be, + +you use something called +cryptographic hash functions, + +which [INAUDIBLE] will +talk about on Tuesday. + +So tons of motivation +for dictionaries. + +Let's actually do it, +see how they are done. + +We're going to start with sort +of a very simple straw man, + +and then we're going to improve +it until, by the end of today, + +we have a really good way +to solve the dictionary + +problem in constant +time for operation. + +So the really simple approach +is called a direct access table. + +So it's just a big +table, an array. + +You have-- the index into +the array is the key. + +So, store items in an +array, indexed by key. + +And in fact, Python kind +makes you think about this + +because the Python notation +for accessing dictionaries + +is identical to the notation +for accessing arrays. + +But with arrays, the +keys are restricted + +to be non-negative integers, +0 through n minus 1. + +So why not just +implement it that way? + +If your keys happen +to be integers + +I could just store all my +items in a giant array. + +So if I just want to store +an item here with key 2, + +call that, maybe, item +2, I just put that there. + +If I want to store +something with key 4 + +I'll just put it there. + +Everything else is going to +be null, or none, or whatever. + +So lots of blank entries. + +Whatever keys I don't use I'll +just put a null value there. + +Every key that I want to +put into the dictionary + +I'll just store it at the +corresponding position. + +What's bad about this? + +Yeah. + +AUDIENCE: It's hard to associate +something with just an integer. + +PROFESSOR: Hard to associate +something with an integer. + +Good. + +That's one problem. + +There's actually two big +problems with this structure. + +I want both of them. + +So bad-- badness number one +is keys may not be integers. + +Good. + +Another problem. + +Yeah. + +AUDIENCE: Possibility +of collision. + +PROFESSOR: Possibility +of collision. + +So here there's no collisions. + +We'll get to +collisions in a moment, + +but a collision +is when two items + +go to the same +slot in this table. + +And we defined the problem +so there weren't collisions. + +We said whenever we insert +item with the same key you + +overwrite whatever is there. + +So collisions are OK. + +They will be a problem in a +moment, so save your answer. + +Yeah? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Running time? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: For deletion? + +Actually, running time +is going to be great. + +If I want to insert-- I +mean, I do these operations + +but on array instead +of a dictionary. + +So if I want insert I +just put something there. + +If I want to delete I +just set it to null. + +If I want to search I just +go there and see is it null? + +Yeah? + +AUDIENCE: It's a +gigantic memory hog + +PROFESSOR: It's +gigantic memory hog. + +I like that phrasing. + +Not always of course. + +If it happens that your keys +are-- the set of possible keys + +is not too giant +then life is good. + +Let's see If I cannot +kill somebody today. + +Oh yes. + +Very good. + +But if you have a +lot of keys, you + +need one slot in +your array per key. + +That could be a lot. + +Maybe your keys are +64-bit integers. + +Then you need 264 slots just +to store one measly dictionary. + +That's huge. + +I guess there's also the +running time of initialize that. + +But at the very least, +you have huge space hog. + +This is bad. + +So we're going to fix both of +these problems one at a time. + +First problem we're +going to talk about + +is what if your keys +aren't integers? + +Because if your +keys aren't integers + +you can't use this at all. + +So lets at least get +something that works. + +And this is a notion +called prehashing. + +I guess different people +call it different things. + +Unfortunately Python +calls it hash. + +It's not hashing, +it's prehashing. + +Emphasized the "pre" here. + +So prehash function +maps whatever keys + +you have to +non-negative integers. + +At this point we're not +worrying about how big + +those integers are. + +They could be giant. + +We're not going to fix the +second problem til later. + +First problem is if I have +some key, maybe it's a string, + +it's whatever, it's an object, +how do I map it to some integer + +so I could, at least +in principle, put it + +in a direct access table. + +There's a theoretical +answer to how to do this, + +and then there's the practical +answer. how to do this. + +I'll start with +the mathematical. + +In theory, I like this, keys +are finite and discrete. + +OK. + +We know that anything +on the computer + +could, ultimately, be written +down as a string of bits. + +So a string of bits +represents an integer. + +So we're done. + +So in theory, this is easy. + +And we're going to +assume in this class, + +because it's sort +of a theory class, + +that this is what's happening. + +At least for +analysis, we're always + +going to analyze things as +if this is what's happening. + +Now in reality, people +don't always do this. + +In particular-- I'll +go somewhere else. + +In Python it's not +quite so simple, + +but at least you get +to see what's going on. + +There's a function called hash, +which should be called prehash, + +and it, given an +object, it produces + +a non-- I'm not sure, +actually, if it's non-negative. + +It's not a big deal if it has +a minus sign because then you + +could just use this and +get rid of the sign. + +But it maps every +object to an integer, + +or every hashable +object, technically. + +But pretty much +anything can be mapped + +to an integer, one +way or another. + +And so for example, if +you given it an integer + +it just returns the integer. + +So that's pretty easy. + +If you give it a string +it does something. + +I don't know exactly +what it does, + +but there are some issues. + +For example, hash of +this string, backslash 0B + +is equal to the hash of +backslash 0 backslash 0C 64. + +It's a little tricky +to find these examples, + +but they're out there. + +And I guess, this is +probably the lowest one + +in a certain measure. + +So it's a concern. + +In practice you have to be +careful about these things + +because what you'd +like-- in an ideal world, + +and in the theoretical world-- +this prehash function of x, + +if it equals the +prehash function of y, + +this should only +happen when x=y, + +when they're the same thing. + +And equals equal sense, I guess, +would be the technical version. + +Sadly, in Python this +is not quite true. + +But mostly true. + +Let's see. + +If you define a custom +object, you may know this, + +there is an __hash__ +method you can implement, + +which tells Python what +to do when you call hash + +of your object. + +If you don't, it +uses the default + +of id, which is the +physical location + +of your object in memory. + +So as long as your object +isn't moving around in memory + +this is a pretty +good hash function + +because no two items occupy +the same space in memory. + +So that's just implementation +side of things. + +Other implementation side +of things is in Python, + +well, there's this distinction +between objects and keys, + +I guess you would say. + +You really don't want +this prehash function + +to change value. + +In, say, a direct access +table, if you store-- + +you take an item, you +compute the prehash function + +of the key in there, and you +throw it in, and it says, + +oh, prehash value is four. + +Then you put it +in position four. + +If that value change, then when +you go to search for that key, + +and you call prehash of that +thing, and if it give you five, + +you look in position five, and +you say, oh, it's not there. + +So prehash really +should not change. + +If you ever implement this +function don't mess with it. + +I mean, make sure it's +defined in such a way + +that it doesn't +change over time. + +Otherwise, you won't be able to +find your items in the table. + +Python can't protect +you from that. + +This is why, for example, +if you have a list, + +which is a mutable object, you +cannot put it into a hash table + +as a key value because it +would change over time. + +Potentially, you'd append +to the list, or whatever. + +All right. + +So hopefully you're +reasonably happy with this. + +You could also +think of it is we're + +going to assume keys are +non-negative integers. + +But in practice, +anything you have you + +can map to an integer, +one way or another. + +The bigger problem +in a certain sense, + +or the more interesting +problem is reducing space. + +So how do we do that? + +This would be hashing. + +This is sort of the magic +part of today's lecture. + +In case you're +wondering, hashing + +has nothing to do with hashish. + +Hashish is a Arabic root word +unrelated to the Germanic, + +which is hachet, I believe. + +Yeah. + +Or hacheh-- I guess, +something like that. + +I'm not very good at German. + +Which means hatchet. + +OK + +It's like you take your +key, and you cut it up + +into little pieces, and you mix +them around and cut and dice, + +and it's like cooking. + +OK. + +What? + +AUDIENCE: Hash browns. + +PROFESSOR: Hash +browns, for example. + +Yeah, same root. + +OK. + +It's like the only two English +words with that kind of hash. + +OK. + +In our case, it's +a verb, to hash. + +It means to cut into +pieces and mix around. + +OK. + +That won't really be clear +until towards the end of today's + +lecture, but we +will eventually get + +to the etymology of hashing. + +Or, we've got the etymology, +but why it's, actually, + +why we use that term. + +All right. + +So the big idea is we +take all possible keys + +and we want to reduce them +down to some small, small set + +of integers. + +Let me draw a picture of that. + +So we have this giant +space of all possible keys. + +We'll call this key space. + +It's like outer +space, basically. + +It's giant. + +And if we stored a +direct access table, + +this would also be giant. + +And we don't want to do that. + +We'd like to somehow map +using a hash function h down + +to some smaller set. + +How do I want to draw this? + +Like an array. + +So we're going to have possible +values 0 up to m minus 1. + +m is a new thing. + +It's going to be the +size of our hash table. + +Let's call the hash table. + +I think we'll call it t also. + +And we'd somehow like to map-- + +All right. + +So there's a giant space +of all possible keys, + +but then there's a subset +of keys that are actually + +stored in this set, +in this dictionary. + +At any moment in +time there's some set + +of keys that are present. + +That set changes, +but at any moment + +there's some keys that +are actually there. + +k1, k2, k3, k4. + +I'd like to map them to +positions in this table. + +So maybe I store k2-- or +actually, item 2 would go here. + +In particular, this is when +h of k2, if it equals zero, + +then you'd put item 2 there. + +Item 3, let's say, +it's at position-- wow, + +3 would be a bit of a +coincidence, but what the hell. + +Maybe h or k3 equals 3. + +Then you'd put item 3 here. + +OK. + +You get the idea. + +So these four items each +have a special position + +in their table. + +And the idea is we would +like to be, m to be around n. + +n is the number of keys In +the dictionary right now. + +So if we could achieve +that, the size of the table + +was proportional to the +number of keys being stored + +in the dictionary, that would +be good news because then + +the space is not +gigantic and hoggish. + +It would just be linear, +which is optimal. + +So if we want to store +m things, maybe we'll + +use 2m space, a 3m +space, but not much more. + +How the heck are we going +to define such a function h? + +Well, that's the +rest of the lecture. + +But even before we +define a function h, + +do you see any +problems with this? + +Yeah. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yeah. + +This space over here, this +is pigeonhole principle. + +The number of slots for +your pigeons over here + +is way smaller than the +number of possible pigeons. + +So there are going +to be two keys that + +map to the same slot +in the hash table. + +This is what we +call a collision. + +Let's call this, I +don't know, ki, kj. + +h of ki equals h of kj, +but the keys are different. + +So ki does not equal kj, +yet their hash functions + +are the same, hash +values are the same. + +We call that a collision. + +And that's guaranteed to +happen a lot, yet somehow, + +we can still make this work. + +That's the magic. + +And that is going +to be chaining. + +We've done these guys. + +Next up is a technique for +dealing with collisions. + +There are two techniques +for dealing with collisions + +we're going to +talk about in 006. + +One is called chaining, +and next Tuesday, we'll + +see another method +called open addressing. + +But let's start with chaining. + +The idea with chaining a simple. + +If you have multiple items +here all with the same-- that + +hash to the same position, +just store them as a list. + +I'm going to draw +it as a linked list. + +I think I need a +big picture here. + +So we have our nice universe, +various keys that we actually + +have present. + +So these are the keys +in the dictionary, + +and this is all of key space. + +These guys map to +slots in the table. + +Some of them might +map to the same value. + +So let's say k1 and k2, +suppose they collide. + +So they both go this slot. + +What we're going to store +here is a linked list + +that stores item 1, +and stores a pointer + +to the next item, +which is item 2. + +And that's the end of the list. + +Or you could-- however +you want to draw a null. + +So however many items +there are, we're + +going to have a linked list +of that length in that slot. + +So in particular, if there's +just one item, like say, + +this k3 here, maybe it +just maps to this slot. + +And maybe that's all +that maps to that slot. + +In that case, we just +say, follow this item 3, + +and there's no other items. + +Some slots are going +to be completely empty. + +There nothing there so you +just store a null pointer. + +That is hashing with chaining. + +It's pretty simple, +very simple really. + +The only question is why would +you expect it to be any good? + +Because, in the worst case, +if you fix your hash function + +here, h, there's going to +be a whole bunch of keys + +that all map to the same slot. + +And so in the worst case, those +are the keys that you insert, + +and they all go here. + +And then you have this +fancy data structure. + +And in the end, all you have is +a linked list of all n items. + +So the worst case is theta n. + +And this is going to be true for +any hashing scheme, actually. + +In the worst case, +hashing sucks. + +Yet in practice, it works +really, really well. + +And the reason is +randomization, essentially, + +that this hash function, +unless you're really unlucky, + +the hash function will +nicely distribute your items, + +and most of these lists +will have constant length. + +We're going to prove +that under an assumption. + +Well have to warm +up a little bit. + +But I'm also going to cop +out a little m as you'll see. + +So in 006 we're going to make +an assumption called Simple + +Uniform Hashing. + +OK. + +And this is an assumption, +it's an unrealistic assumption. + +I would go so far as to say +it's false, a false assumption. + +But it's really +convenient for analysis, + +and it's going to +make it obvious + +why chaining is a good idea. + +Sadly, the assumption +isn't quite true, + +but it gives you a flavor. + +If you want to see why +hashing is actually good, + +I'm going to hint at it +at the end of lecture + +but really should +take 6.046 Yeah. + +AUDIENCE: [INAUDIBLE] question. + +Is the hashing +function [INAUDIBLE]? + +Like, how do we know the +array is still [INAUDIBLE]? + +PROFESSOR: OK. + +The hashing function-- I guess +I didn't specify up here. + +The hashing function maps +your universe to 0, 1, + +up to m minus 1, +That's the definition. + +So it's guaranteed to reduce the +space of keys to just m slots. + +So your hashing function +needs to know what m is. + +In reality there's not going +to be one hashing function, + +there's going to be 1 for each +m, or at least one for each m. + +And so, depending on +how big your table is, + +you use the corresponding +hash function. + +Yeah, good question. + +So the hash function +is what does + +the work of reducing +your key space down + +to small set of slots. + +So that's what's going +to give us low space. + +OK. + +But now, how do we get low time? + +Let me just state this +assumption and get to business. + +Simply, uniform hashing +is, essentially, + +two probabilistic assumptions. + +The first one is uniformity. + +If you take some +key in your space + +that you want to store +the hash function + +maps it to a uniform +random choice. + +This is, of course, is +what you want to happen. + +Each of these slots here is +equally likely to be hashed to. + +OK. + +That's a good start. + +But to do proper analysis, +not only do we uniformity, + +we also need independence. + +So not only is this true +for each key individually, + +but it's true for all +the keys together. + +So if key one maps to +a uniform random place, + +no matter where it +goes, key two also + +matches to a uniform +random place. + +And no matter +where those two go, + +key three maps to a +uniform random place. + +This really can't be true. + +But if it's true, we can prove +that this takes constant time. + +So let me do that. + +So under this assumption, +we can analyze + +hashing-- hashing with chaining +is what this method is called. + +So let's do it + +I want to know-- I +got to cheat, sorry. + +I got to remember the notation. + +I don't have any +good notation here. + +All right. + +What I'd like to know is the +expected length of a chain. + +OK. + +Now this is if I have n keys +that are stored in the table, + +and m slots in the +table, then what + +is the expected +length of a chain? + +Any suggestions. + +Yeah. + +AUDIENCE: 1 over m to the n. + +PROFESSOR: 1 over m to the n? + +That's going to be a +probability of something. + +Not quite. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: That's +between 0 and 1. + +It's probably at least +one, or something. + +Yeah. + +AUDIENCE: m over n. + +PROFESSOR: n over m, yeah. + +It's really easy. + +The chance of a key going to +a particular slot is 1 over m. + +They're all independent, so +it's 1 over m, plus 1 over m, + +plus 1 over m, n times. + +So it's n over m. + +This is really easy when +you have independence. + +Sadly, in the real world, +you don't have independence. + +We're going to call +this thing alpha, + +and it's also known as the +load factor of the table. + +So if it's one, n equals m. + +And so the length +of a chain is one. + +If it's 10, then you have +10 times as many elements + +as you have slots. + +But still, the expected +length of a chain is 10. + +That's a constant. + +It's OK. + +If it's a 12, that's OK. + +It means that you have a bigger +table than you have items. + +As long as it's a constant, +as long as we have-- I + +erased it by now-- as +long as m is theta n, + +this is going to be constant. + +And so we need to +maintain this property. + +But as long as you set your +table size to the right value, + +to be roughly n, this +will be constant. + +And so the running time of +an operation, insert, delete, + +and search-- Well, +search is really + +the hardest because when you +want to search for a key, + +you map it into your table, +then you walk the linked list + +and look for the key that +you're searching for. + +Now is this the key +you're searching for? + +No, it's not the key +you're searching for. + +Is this the key +you're searching for? + +Those are not the keys +you're searching for. + +You keep going. + +Either you find your +key or you don't. + +But in the worst case, you +have to walk the entire list. + +Sorry for the bad Star +Trek reference-- Star Wars. + +God. + +I'm not awake. + +All right. + +In general, the running +time, in the worst case, + +is 1 plus the length +of your chain. + +OK. + +So it's going to +be 1 plus alpha. + +Why do I write one? + +Well, because alpha can be much +smaller than 1, in general. + +And you always have +to pay the cost + +of computing the hash function. + +We're going to assume +that takes constant time. + +And then you have to +follow the first pointer. + +So you always pay constant time, +but then you also pay alpha. + +That's your expected life. + +OK. + +That's the analysis. + +It's super simple. + +If you assume Simple +Uniform Hashing, + +it's clear, as long as your load +factor is constant, m theta n, + +you get constant running +time for all your operations. + +Life is good. + +This is the intuition +of why hashing works. + +It's not really +why hashing works. + +But it's about as far as +we're going to get in 006. + +I'm going to tell +you a little bit more + +about why hashing is actually +good to practice and in theory. + +What are we up to? + +Last topic is hash functions. + +The one remaining thing +is how do I construct h? + +How do I actually map from +this giant universe of keys + +to this small set of slots in +the table, there's m of them? + +I'm going to give you three hash +functions, two of which are, + +let's say, common practice, and +the third of which is actually + +theoretically good. + +So the first two are +not good theoretically. + +You can prove that they're +bad, but at least they + +give you some +flavor, and they're + +still common in practice because +a lot of the time they're OK, + +but you can't really +prove much about them. + +OK. + +So first method, sort +of the obvious one, + +called the division method. + +And if you have +a key, this could + +be a giant key, huge +universe of keys, + +you just take that +key, modulo m, + +that gives you a number +between zero and m minus 1. + +Done. + +It's so easy. + +I'm not going to +tell you in detail + +why this is a bad method. + +Maybe you can think about it. + +It's especially bad if m has +some common factors with k. + +Like, let's say +k is even always, + +and m is even also +because you say, + +oh, I'd like a table the +size of power of two. + +That seems natural. + +Then that will be really +bad because you'll + +use only half the table. + +There are lots of situations +where this is bad. + +In practice, it's pretty good. + +If m is prime, you always +choose a prime table size, + +so you don't have +those common factors. + +And it's not very close to +a power of 2 or power of 10 + +because real world powers +of 2's and 10's are common. + +But it's very hackish, OK? + +It works a lot of the +time but not always. + +A cooler method-- I think +it's cooler-- still, + +you can't prove much +about it-- Division didn't + +seem to work so great, so +how about multiplication? + +What does that mean? + +Multiply by m, that +wouldn't be very good. + +Now, it's a bit different. + +We're going to take the key, +multiply it by an integer, a, + +and then we're going to do +this crazy, crazy stuff. + +Take it mod 2 to the w and +then shift it right, w minus r. + +OK. + +What is w? + +We're assuming that +we're in a w-bit machine. + +Remember way back in +models of computation? + +Your machine has a +word size, it's w bits. + +So let's suppose it's w bits. + +So we have our key, k. + +Here it is. + +It's w bits long. + +We take some number, +a-- think of a as being + +a random integer among all +possible w bit integers. + +So it's got some zeros, +it's got some ones. + +And I multiply these. + +What does multiplication +mean in binary? + +Well, I take one of these copies +of k for each one that's here. + +So I'm going to +take one copy here + +because there's a one there. + +I'm going to take one copy here +because there's a one there. + +And I'm going to +take one copy here + +because there's a one there. + +And on average, half +of them will be ones. + +So I have various copies of k, +and then I just add them up. + +And you know, stuff happens. + +I get some gobbledygook here. + +OK. + +How big is it? + +In general, it's two words long. + +When I multiply two +words I get two words. + +It could be twice +as long, in general. + +And what this business is doing +is saying take the right word, + +this right half here-- let +the right word in, I guess, + +if you see vampire +movies-- and then shift + +right-- this is a shift right +operation-- by w minus r. + +I didn't even say what r is. + +But basically, what +I want is these bits. + +I want r bits here-- +this is w bits. + +I want the leftmost r bits +of the rightmost w bits + +because I shift right here +and get rid of all these guys. + +r-- I should say, +m, is two to the r. + +So I'm going to +assume here I have + +a table of size a power of +2, and then this number will + +be a number between +0 and m minus 1. + +OK. + +Why does this work? + +It's intuitive. + +In practice it works quite +well because what you're + +doing is taking a whole +bunch of sort of randomly + +shifted copies of k, adding +them up-- you get carries, + +things get mixed +up-- This is hashing. + +This is-- you're taking +k, sort of cutting it up + +while you're shifting it around, +adding things and they collide, + +and weird stuff happens. + +You sort of randomize stuff. + +Out here, you don't +get much randomization + +because most-- like +the last bit could just + +be this one bit of k. + +But in the middle, everybody's +kind of colliding together. + +And so intuitively, +you're mixing + +lots of things in the center. + +You take those r bits, +roughly, in the center. + +That will be nicely mixed up. + +And most of the time +this works well. + +In practice it works well-- I +have some things written here. + +a better be odd, otherwise +you're throwing away stuff. + +And it should not be very +close to a power of 2. + +But it should be in between 2 +to the r minus 1 and 2 to the r. + +Cool. + +One more. + +Again, theoretically, +this can be bad. + +And I leave it as an exercise +to find situations, find + +key values where this +does not do a good job. + +The cool method is +called universal hashing. + +This is something that's a +bit beyond the scope of 006. + +If you want to understand it +better you should take 046. + +But I'll give you the flavor and +the method, one of the methods. + +There's actually +many ways to do this. + +We see a mod m on the outside. + +That's just division method just +to make the number between 0 + +and a minus 1. + +Here's our key. + +And then there's +these numbers a and b. + +These are going to be +random numbers between 0 + +and p minus 1. + +What's p? + +Prime number bigger than +the size of the universe. + +So it's a big prime number. + +I think we know how +to find prime numbers. + +We don't know in this +class, but people + +know how to find +the prime numbers. + +So there's a subroutine +here, find a big prime number + +bigger than your universe. + +It's not too hard to do that. + +We can do it in polynomial time. + +That's just set up. + +You do that once for +a given size table. + +And then you choose two +random numbers, a and b. + +And then this is the +hash function, a times k + +plus b, mod p mod m. + +OK. + +What does this do? + +It turns out-- here's +the interesting part. + +For worst case keys, k1 +and k2, that are distinct, + +the probability of h of k1 +equaling h of k2 is 1 over n. + +So probability of two keys +that are different colliding + +is 1 over m, for +the worst case keys. + +What the heck does that mean? + +What's the probability over? + +Any suggestions? + +What's random here? + +AUDIENCE: a and b. + +PROFESSOR: a and b. + +This is the probability +over a and b. + +This is the probability over the +choice of your hash function. + +So it's the worst case +inputs, worst case insertions, + +but random hash function. + +As long as you choose +your random hash function, + +the probability of +collision is 1 over m. + +This is the ideal situation + +And so you can prove, just +like we analyzed here-- + +It's a little more work. + +It's in the notes. + +You use linearity +of expectation. + +And you can prove, still, +that the expected length + +of a chain-- the expected number +of collisions that a key has + +with another key is the load +factor, in the worst case, + +but in expectation for +a given hash function. + +So still, the expected +length of a chain, + +and therefore, the +expected running time + +of hashing with chaining, +using this hash function, + +or this collection of hash +functions, or a randomly chosen + +one, is constant for +constant load factor. + +And that's why hashing +really works in theory. + +We're not going to go into +details of this again. + +Take 6.046 if you want to know. + +But this should make you +feel more comfortable. + +And we'll see other ways +do hashing next class. \ No newline at end of file diff --git a/0Q5IimX-AAc.txt b/0Q5IimX-AAc.txt new file mode 100644 index 0000000000000000000000000000000000000000..b157a6f650472be0f1255807645b18f224a834b2 --- /dev/null +++ b/0Q5IimX-AAc.txt @@ -0,0 +1,12891 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +today I'm going to talk about signatures + + align:start position:0% +today I'm going to talk about signatures + + + align:start position:0% +today I'm going to talk about signatures +and all sorts of different signature + + align:start position:0% +and all sorts of different signature + + + align:start position:0% +and all sorts of different signature +kind of things in the in the problem set + + align:start position:0% +kind of things in the in the problem set + + + align:start position:0% +kind of things in the in the problem set +you're you're working with signatures + + align:start position:0% +you're you're working with signatures + + + align:start position:0% +you're you're working with signatures +but you're working with hash based + + align:start position:0% +but you're working with hash based + + + align:start position:0% +but you're working with hash based +signatures which are not actually used + + align:start position:0% +signatures which are not actually used + + + align:start position:0% +signatures which are not actually used +in Bitcoin at all but we'll talk about + + align:start position:0% +in Bitcoin at all but we'll talk about + + + align:start position:0% +in Bitcoin at all but we'll talk about +those okay so if you've gotten through + + align:start position:0% +those okay so if you've gotten through + + + align:start position:0% +those okay so if you've gotten through +the homework + + align:start position:0% +the homework + + + align:start position:0% +the homework +there's Lamport signatures right these + + align:start position:0% +there's Lamport signatures right these + + + align:start position:0% +there's Lamport signatures right these +are hash based signatures and they use + + align:start position:0% +are hash based signatures and they use + + + align:start position:0% +are hash based signatures and they use +hash functions so it's fairly + + align:start position:0% +hash functions so it's fairly + + + align:start position:0% +hash functions so it's fairly +straightforward like you know you can + + align:start position:0% +straightforward like you know you can + + + align:start position:0% +straightforward like you know you can +understand them there's nothing super + + align:start position:0% +understand them there's nothing super + + + align:start position:0% +understand them there's nothing super +crazy going on the code is fairly + + align:start position:0% +crazy going on the code is fairly + + + align:start position:0% +crazy going on the code is fairly +compact so that's cool what are some + + align:start position:0% +compact so that's cool what are some + + + align:start position:0% +compact so that's cool what are some +disadvantages of these Lamport + + align:start position:0% +disadvantages of these Lamport + + + align:start position:0% +disadvantages of these Lamport +signatures does anyone like yeah yeah + + align:start position:0% +signatures does anyone like yeah yeah + + + align:start position:0% +signatures does anyone like yeah yeah +okay so okay plus ashes that's cool + + align:start position:0% +okay so okay plus ashes that's cool + + + align:start position:0% +okay so okay plus ashes that's cool +one-time use other possible + + align:start position:0% +one-time use other possible + + + align:start position:0% +one-time use other possible +disadvantages of them relative to other + + align:start position:0% +disadvantages of them relative to other + + + align:start position:0% +disadvantages of them relative to other +systems you're aware another is they're + + align:start position:0% +systems you're aware another is they're + + + align:start position:0% +systems you're aware another is they're +kind of huge kind of big right not you + + align:start position:0% +kind of huge kind of big right not you + + + align:start position:0% +kind of huge kind of big right not you +know you can deal with it + + align:start position:0% +know you can deal with it + + + align:start position:0% +know you can deal with it +but if you are looking in the like Forge + + align:start position:0% +but if you are looking in the like Forge + + + align:start position:0% +but if you are looking in the like Forge +or that that file with the signatures + + align:start position:0% +or that that file with the signatures + + + align:start position:0% +or that that file with the signatures +but it's like what eight eight K first + + align:start position:0% +but it's like what eight eight K first + + + align:start position:0% +but it's like what eight eight K first +signature eight kilobytes kind of big + + align:start position:0% +signature eight kilobytes kind of big + + + align:start position:0% +signature eight kilobytes kind of big +keys are 16 kilobytes kind of annoying + + align:start position:0% +keys are 16 kilobytes kind of annoying + + + align:start position:0% +keys are 16 kilobytes kind of annoying +private keys are also 16 kilobytes so + + align:start position:0% +private keys are also 16 kilobytes so + + + align:start position:0% +private keys are also 16 kilobytes so +yes sig 8k 16 K proved palm key so + + align:start position:0% +yes sig 8k 16 K proved palm key so + + + align:start position:0% +yes sig 8k 16 K proved palm key so +that's some disadvantages so since I + + align:start position:0% +that's some disadvantages so since I + + + align:start position:0% +that's some disadvantages so since I +don't have slides you make this sort of + + align:start position:0% +don't have slides you make this sort of + + + align:start position:0% +don't have slides you make this sort of +more fun and interactive what are some + + align:start position:0% +more fun and interactive what are some + + + align:start position:0% +more fun and interactive what are some +solutions for these problems so we can + + align:start position:0% +solutions for these problems so we can + + + align:start position:0% +solutions for these problems so we can +actually mitigate + + align:start position:0% +actually mitigate + + + align:start position:0% +actually mitigate +solve both of these things to a pretty + + align:start position:0% +solve both of these things to a pretty + + + align:start position:0% +solve both of these things to a pretty +pretty good extent so how about the + + align:start position:0% +pretty good extent so how about the + + + align:start position:0% +pretty good extent so how about the +first one one time use what would be a + + align:start position:0% +first one one time use what would be a + + + align:start position:0% +first one one time use what would be a +fairly obvious way to mitigate the + + align:start position:0% +fairly obvious way to mitigate the + + + align:start position:0% +fairly obvious way to mitigate the +one-time use problem and like don't + + align:start position:0% +one-time use problem and like don't + + + align:start position:0% +one-time use problem and like don't +think the answer is is too stupid like + + align:start position:0% +think the answer is is too stupid like + + + align:start position:0% +think the answer is is too stupid like +it may be a fairly stupid answer into I + + align:start position:0% +it may be a fairly stupid answer into I + + + align:start position:0% +it may be a fairly stupid answer into I +work yeah + + align:start position:0% + + + + align:start position:0% + +there's probably some clever way but + + align:start position:0% +there's probably some clever way but + + + align:start position:0% +there's probably some clever way but +that might be too clever like something + + align:start position:0% +that might be too clever like something + + + align:start position:0% +that might be too clever like something +really simple for okay I can only use a + + align:start position:0% +really simple for okay I can only use a + + + align:start position:0% +really simple for okay I can only use a +key once how can I use a key + + align:start position:0% +key once how can I use a key + + + align:start position:0% +key once how can I use a key +quote-unquote more than once + + align:start position:0% +quote-unquote more than once + + + align:start position:0% +quote-unquote more than once +yeah so you can say well I've got this + + align:start position:0% +yeah so you can say well I've got this + + + align:start position:0% +yeah so you can say well I've got this +16 kilobyte public key well I'm gonna + + align:start position:0% +16 kilobyte public key well I'm gonna + + + align:start position:0% +16 kilobyte public key well I'm gonna +make a 32 kilobyte public key and it's + + align:start position:0% +make a 32 kilobyte public key and it's + + + align:start position:0% +make a 32 kilobyte public key and it's +just two public keys stuck together and + + align:start position:0% +just two public keys stuck together and + + + align:start position:0% +just two public keys stuck together and +now when I mean you know and now when I + + align:start position:0% +now when I mean you know and now when I + + + align:start position:0% +now when I mean you know and now when I +make a signature I just put an extra bit + + align:start position:0% +make a signature I just put an extra bit + + + align:start position:0% +make a signature I just put an extra bit +in the front and I say well this + + align:start position:0% +in the front and I say well this + + + align:start position:0% +in the front and I say well this +signature is using key 0 or this + + align:start position:0% +signature is using key 0 or this + + + align:start position:0% +signature is using key 0 or this +signature is using key 1 and it's got + + align:start position:0% +signature is using key 1 and it's got + + + align:start position:0% +signature is using key 1 and it's got +the whole signature after and then you + + align:start position:0% +the whole signature after and then you + + + align:start position:0% +the whole signature after and then you +look through this 32 kilobyte public + + align:start position:0% +look through this 32 kilobyte public + + + align:start position:0% +look through this 32 kilobyte public +keen you say okay well it starts with a + + align:start position:0% +keen you say okay well it starts with a + + + align:start position:0% +keen you say okay well it starts with a +0 so that means it's using the first key + + align:start position:0% +0 so that means it's using the first key + + + align:start position:0% +0 so that means it's using the first key +you know the first sub key in this 32 + + align:start position:0% +you know the first sub key in this 32 + + + align:start position:0% +you know the first sub key in this 32 +byte public key block and in this case + + align:start position:0% +byte public key block and in this case + + + align:start position:0% +byte public key block and in this case +that's using 1 so that means it's using + + align:start position:0% +that's using 1 so that means it's using + + + align:start position:0% +that's using 1 so that means it's using +the second you know the latter sub key + + align:start position:0% +the second you know the latter sub key + + + align:start position:0% +the second you know the latter sub key +so that would work that would let you + + align:start position:0% +so that would work that would let you + + + align:start position:0% +so that would work that would let you +use the signature the your public key + + align:start position:0% +use the signature the your public key + + + align:start position:0% +use the signature the your public key +twice at the cost of doubling your + + align:start position:0% +twice at the cost of doubling your + + + align:start position:0% +twice at the cost of doubling your +public key size which is not really + + align:start position:0% +public key size which is not really + + + align:start position:0% +public key size which is not really +great right it that's not a great if + + align:start position:0% +great right it that's not a great if + + + align:start position:0% +great right it that's not a great if +it's not very efficient but it does sort + + align:start position:0% +it's not very efficient but it does sort + + + align:start position:0% +it's not very efficient but it does sort +of work okay any any clever ways to do + + align:start position:0% +of work okay any any clever ways to do + + + align:start position:0% +of work okay any any clever ways to do +it more efficiently or wait so okay also + + align:start position:0% +it more efficiently or wait so okay also + + + align:start position:0% +it more efficiently or wait so okay also +so I'll give you sort of a hint in this + + align:start position:0% +so I'll give you sort of a hint in this + + + align:start position:0% +so I'll give you sort of a hint in this +case let's say this is you know pub sub + + align:start position:0% +case let's say this is you know pub sub + + + align:start position:0% +case let's say this is you know pub sub +0 and pub sub 1 right and then like + + align:start position:0% +0 and pub sub 1 right and then like + + + align:start position:0% +0 and pub sub 1 right and then like +you're 32 byte pump key is the stem + + align:start position:0% +you're 32 byte pump key is the stem + + + align:start position:0% +you're 32 byte pump key is the stem +concatenated together right of 0 1 what + + align:start position:0% +concatenated together right of 0 1 what + + + align:start position:0% +concatenated together right of 0 1 what +would happen to the private keys in this + + align:start position:0% +would happen to the private keys in this + + + align:start position:0% +would happen to the private keys in this +case right + + align:start position:0% +case right + + + align:start position:0% +case right +how would private keys work here same + + align:start position:0% +how would private keys work here same + + + align:start position:0% +how would private keys work here same +expansion of size I guess and you can + + align:start position:0% +expansion of size I guess and you can + + + align:start position:0% +expansion of size I guess and you can +anyone think of a way to to mitigate the + + align:start position:0% +anyone think of a way to to mitigate the + + + align:start position:0% +anyone think of a way to to mitigate the +expansion of size of private keys in + + align:start position:0% +expansion of size of private keys in + + + align:start position:0% +expansion of size of private keys in +this case so the private keys are sort + + align:start position:0% +this case so the private keys are sort + + + align:start position:0% +this case so the private keys are sort +of you know the Prima + + align:start position:0% +of you know the Prima + + + align:start position:0% +of you know the Prima +here right they lead into these public + + align:start position:0% +here right they lead into these public + + + align:start position:0% +here right they lead into these public +key blocks so you could just say okay + + align:start position:0% +key blocks so you could just say okay + + + align:start position:0% +key blocks so you could just say okay +well I have twice the size private key + + align:start position:0% +well I have twice the size private key + + + align:start position:0% +well I have twice the size private key +leading into twice the size public key + + align:start position:0% +leading into twice the size public key + + + align:start position:0% +leading into twice the size public key +could you do that more efficiently yeah + + align:start position:0% + + + + align:start position:0% + +yes so how would you tell let's say you + + align:start position:0% +yes so how would you tell let's say you + + + align:start position:0% +yes so how would you tell let's say you +have this 16 K block and you want this + + align:start position:0% +have this 16 K block and you want this + + + align:start position:0% +have this 16 K block and you want this +to turn into two public keys so that's + + align:start position:0% +to turn into two public keys so that's + + + align:start position:0% +to turn into two public keys so that's +that's the that's the basic good way to + + align:start position:0% +that's the that's the basic good way to + + + align:start position:0% +that's the that's the basic good way to +do it and it sort of like turns in like + + align:start position:0% +do it and it sort of like turns in like + + + align:start position:0% +do it and it sort of like turns in like +that + + align:start position:0% +that + + + align:start position:0% +that +how exactly like what's a way you did + + align:start position:0% +how exactly like what's a way you did + + + align:start position:0% +how exactly like what's a way you did +that yeah so so this is a hash function + + align:start position:0% +that yeah so so this is a hash function + + + align:start position:0% +that yeah so so this is a hash function +right and so before we just said okay + + align:start position:0% +right and so before we just said okay + + + align:start position:0% +right and so before we just said okay +hash of you know this is like block 0 + + align:start position:0% +hash of you know this is like block 0 + + + align:start position:0% +hash of you know this is like block 0 +this is block 1 this is block 2 so the + + align:start position:0% +this is block 1 this is block 2 so the + + + align:start position:0% +this is block 1 this is block 2 so the +idea of you know pub let's say this is + + align:start position:0% +idea of you know pub let's say this is + + + align:start position:0% +idea of you know pub let's say this is +invisible this might be kind of too + + align:start position:0% +invisible this might be kind of too + + + align:start position:0% +invisible this might be kind of too +small right yes okay let me let me put + + align:start position:0% +small right yes okay let me let me put + + + align:start position:0% +small right yes okay let me let me put +this bigger okay so in these in these + + align:start position:0% +this bigger okay so in these in these + + + align:start position:0% +this bigger okay so in these in these +diagrams + + align:start position:0% +diagrams + + + align:start position:0% +diagrams +you've got your your private key right + + align:start position:0% +you've got your your private key right + + + align:start position:0% +you've got your your private key right +now and it's in these big blocks and + + align:start position:0% +now and it's in these big blocks and + + + align:start position:0% +now and it's in these big blocks and +there's 256 of them but let's keep it + + align:start position:0% +there's 256 of them but let's keep it + + + align:start position:0% +there's 256 of them but let's keep it +small and the idea is these are 32 byte + + align:start position:0% +small and the idea is these are 32 byte + + + align:start position:0% +small and the idea is these are 32 byte +blocks with random numbers in it and + + align:start position:0% +blocks with random numbers in it and + + + align:start position:0% +blocks with random numbers in it and +then you hash it to get your public key + + align:start position:0% +then you hash it to get your public key + + + align:start position:0% +then you hash it to get your public key +and this is you know so we say okay pub + + align:start position:0% +and this is you know so we say okay pub + + + align:start position:0% +and this is you know so we say okay pub +2 and this is you know public this is + + align:start position:0% +2 and this is you know public this is + + + align:start position:0% +2 and this is you know public this is +private let's say secret pub 2 is just + + align:start position:0% +private let's say secret pub 2 is just + + + align:start position:0% +private let's say secret pub 2 is just +the hash of secret - right well yeah + + align:start position:0% +the hash of secret - right well yeah + + + align:start position:0% +the hash of secret - right well yeah +what we could do is we could put them to + + align:start position:0% +what we could do is we could put them to + + + align:start position:0% +what we could do is we could put them to +have two different hash functions and + + align:start position:0% +have two different hash functions and + + + align:start position:0% +have two different hash functions and +then a a real simple way to make a whole + + align:start position:0% +then a a real simple way to make a whole + + + align:start position:0% +then a a real simple way to make a whole +bunch of different hash functions is we + + align:start position:0% +bunch of different hash functions is we + + + align:start position:0% +bunch of different hash functions is we +sort of define okay well hash 0 is + + align:start position:0% +sort of define okay well hash 0 is + + + align:start position:0% +sort of define okay well hash 0 is +defined as the hash function of you know + + align:start position:0% +defined as the hash function of you know + + + align:start position:0% +defined as the hash function of you know +whatever your input X is concatenated + + align:start position:0% +whatever your input X is concatenated + + + align:start position:0% +whatever your input X is concatenated +with the number 0 and then the hash 1 we + + align:start position:0% +with the number 0 and then the hash 1 we + + + align:start position:0% +with the number 0 and then the hash 1 we +define as just X comma 1 and so on and + + align:start position:0% +define as just X comma 1 and so on and + + + align:start position:0% +define as just X comma 1 and so on and +this is this is actually secure you + + align:start position:0% +this is this is actually secure you + + + align:start position:0% +this is this is actually secure you +could do this + + align:start position:0% +could do this + + + align:start position:0% +could do this +any questions or possible objections yes + + align:start position:0% +any questions or possible objections yes + + + align:start position:0% +any questions or possible objections yes +so so this is like you know there's no + + align:start position:0% +so so this is like you know there's no + + + align:start position:0% +so so this is like you know there's no +real entropy or secrets in this zero and + + align:start position:0% +real entropy or secrets in this zero and + + + align:start position:0% +real entropy or secrets in this zero and +one so but it's it's purely riding on X + + align:start position:0% +one so but it's it's purely riding on X + + + align:start position:0% +one so but it's it's purely riding on X +right so but the idea is well if I do + + align:start position:0% +right so but the idea is well if I do + + + align:start position:0% +right so but the idea is well if I do +this and like you know I say okay well + + align:start position:0% +this and like you know I say okay well + + + align:start position:0% +this and like you know I say okay well +pub to you is secret to concatenated + + align:start position:0% +pub to you is secret to concatenated + + + align:start position:0% +pub to you is secret to concatenated +with zero yeah if you no secret to you + + align:start position:0% +with zero yeah if you no secret to you + + + align:start position:0% +with zero yeah if you no secret to you +can go back because zero is obvious but + + align:start position:0% +can go back because zero is obvious but + + + align:start position:0% +can go back because zero is obvious but +the idea is if you don't know secret to + + align:start position:0% +the idea is if you don't know secret to + + + align:start position:0% +the idea is if you don't know secret to +the fact that you know the last you know + + align:start position:0% +the fact that you know the last you know + + + align:start position:0% +the fact that you know the last you know +bite of this what the hash input doesn't + + align:start position:0% +bite of this what the hash input doesn't + + + align:start position:0% +bite of this what the hash input doesn't +really help you because there's all this + + align:start position:0% +really help you because there's all this + + + align:start position:0% +really help you because there's all this +you know all this data that you don't + + align:start position:0% +you know all this data that you don't + + + align:start position:0% +you know all this data that you don't +know and so you're not going to be able + + align:start position:0% +know and so you're not going to be able + + + align:start position:0% +know and so you're not going to be able +to find a pre-image you're like okay I + + align:start position:0% +to find a pre-image you're like okay I + + + align:start position:0% +to find a pre-image you're like okay I +know the preimage to public to ends with + + align:start position:0% +know the preimage to public to ends with + + + align:start position:0% +know the preimage to public to ends with +a zero byte what are the other 32 bytes + + align:start position:0% +a zero byte what are the other 32 bytes + + + align:start position:0% +a zero byte what are the other 32 bytes +that come before that like you can't you + + align:start position:0% +that come before that like you can't you + + + align:start position:0% +that come before that like you can't you +still can't go back to make a pre-image + + align:start position:0% + + + + align:start position:0% + +the second to last byte is gonna be in + + align:start position:0% +the second to last byte is gonna be in + + + align:start position:0% +the second to last byte is gonna be in +so the attack is I've got pump two which + + align:start position:0% +so the attack is I've got pump two which + + + align:start position:0% +so the attack is I've got pump two which +is a 32 byte hash output I want to find + + align:start position:0% +is a 32 byte hash output I want to find + + + align:start position:0% +is a 32 byte hash output I want to find +what this thing is now I do know what + + align:start position:0% +what this thing is now I do know what + + + align:start position:0% +what this thing is now I do know what +the last byte is right it's gonna be + + align:start position:0% +the last byte is right it's gonna be + + + align:start position:0% +the last byte is right it's gonna be +let's say 33 bytes and the last fight is + + align:start position:0% +let's say 33 bytes and the last fight is + + + align:start position:0% +let's say 33 bytes and the last fight is +a 0 and this is gonna be some you know + + align:start position:0% +a 0 and this is gonna be some you know + + + align:start position:0% +a 0 and this is gonna be some you know +random numbers all the way back so I + + align:start position:0% +random numbers all the way back so I + + + align:start position:0% +random numbers all the way back so I +have sort of you know I have some + + align:start position:0% +have sort of you know I have some + + + align:start position:0% +have sort of you know I have some +insight into what the preimage is I know + + align:start position:0% +insight into what the preimage is I know + + + align:start position:0% +insight into what the preimage is I know +the last byte is a zero but that doesn't + + align:start position:0% +the last byte is a zero but that doesn't + + + align:start position:0% +the last byte is a zero but that doesn't +help because I don't know all the the + + align:start position:0% +help because I don't know all the the + + + align:start position:0% +help because I don't know all the the +bytes before that so I can't really do + + align:start position:0% +bytes before that so I can't really do + + + align:start position:0% +bytes before that so I can't really do +any you know I can't I can't sign + + align:start position:0% +any you know I can't I can't sign + + + align:start position:0% +any you know I can't I can't sign +because I don't I need to be able to + + align:start position:0% +because I don't I need to be able to + + + align:start position:0% +because I don't I need to be able to +reveal all these things and the way the + + align:start position:0% +reveal all these things and the way the + + + align:start position:0% +reveal all these things and the way the +hash function if it's a good hash + + align:start position:0% +hash function if it's a good hash + + + align:start position:0% +hash function if it's a good hash +function the fact that you know some + + align:start position:0% +function the fact that you know some + + + align:start position:0% +function the fact that you know some +part of the preimage shouldn't give you + + align:start position:0% +part of the preimage shouldn't give you + + + align:start position:0% +part of the preimage shouldn't give you +insight into the other parts of the + + align:start position:0% +insight into the other parts of the + + + align:start position:0% +insight into the other parts of the +preimage because it's like looks really + + align:start position:0% +preimage because it's like looks really + + + align:start position:0% +preimage because it's like looks really +random and you know adding adding stuff + + align:start position:0% +random and you know adding adding stuff + + + align:start position:0% +random and you know adding adding stuff +to the end here + + align:start position:0% +to the end here + + + align:start position:0% +to the end here +like reveal and thing there are hash + + align:start position:0% +like reveal and thing there are hash + + + align:start position:0% +like reveal and thing there are hash +functions where this can be dangerous + + align:start position:0% +functions where this can be dangerous + + + align:start position:0% +functions where this can be dangerous +and you can consider those like broken + + align:start position:0% +and you can consider those like broken + + + align:start position:0% +and you can consider those like broken +hash functions where if I if I + + align:start position:0% +hash functions where if I if I + + + align:start position:0% +hash functions where if I if I +concatenate a lot of known data at the + + align:start position:0% +concatenate a lot of known data at the + + + align:start position:0% +concatenate a lot of known data at the +end it might give me you know properties + + align:start position:0% +end it might give me you know properties + + + align:start position:0% +end it might give me you know properties +of the public key that I can find shot + + align:start position:0% +of the public key that I can find shot + + + align:start position:0% +of the public key that I can find shot +to v6 as far as we know doesn't you know + + align:start position:0% +to v6 as far as we know doesn't you know + + + align:start position:0% +to v6 as far as we know doesn't you know +it works fine most of the hash functions + + align:start position:0% +it works fine most of the hash functions + + + align:start position:0% +it works fine most of the hash functions +work fine this way so yeah you can do + + align:start position:0% +work fine this way so yeah you can do + + + align:start position:0% +work fine this way so yeah you can do +this and then you can say okay well I'm + + align:start position:0% +this and then you can say okay well I'm + + + align:start position:0% +this and then you can say okay well I'm +gonna use hash function 1 or hash + + align:start position:0% +gonna use hash function 1 or hash + + + align:start position:0% +gonna use hash function 1 or hash +function 0 to make pub keys 0 right this + + align:start position:0% +function 0 to make pub keys 0 right this + + + align:start position:0% +function 0 to make pub keys 0 right this +is funky 0 and if I use hash function 1 + + align:start position:0% +is funky 0 and if I use hash function 1 + + + align:start position:0% +is funky 0 and if I use hash function 1 +I make punky one now I have a 16 + + align:start position:0% +I make punky one now I have a 16 + + + align:start position:0% +I make punky one now I have a 16 +kilobyte this so now what I can do is I + + align:start position:0% +kilobyte this so now what I can do is I + + + align:start position:0% +kilobyte this so now what I can do is I +can say okay well I have a 16 kilobyte + + align:start position:0% +can say okay well I have a 16 kilobyte + + + align:start position:0% +can say okay well I have a 16 kilobyte +secret key private key but I have a 32 + + align:start position:0% +secret key private key but I have a 32 + + + align:start position:0% +secret key private key but I have a 32 +kilobyte public key that's that I can + + align:start position:0% +kilobyte public key that's that I can + + + align:start position:0% +kilobyte public key that's that I can +use twice that is two sub keys so I + + align:start position:0% +use twice that is two sub keys so I + + + align:start position:0% +use twice that is two sub keys so I +don't have to store as much of my + + align:start position:0% +don't have to store as much of my + + + align:start position:0% +don't have to store as much of my +private key data so that's cool that + + align:start position:0% +private key data so that's cool that + + + align:start position:0% +private key data so that's cool that +makes it quite a bit more efficient does + + align:start position:0% +makes it quite a bit more efficient does + + + align:start position:0% +makes it quite a bit more efficient does +anyone have an idea of how to get it + + align:start position:0% +anyone have an idea of how to get it + + + align:start position:0% +anyone have an idea of how to get it +even more efficient for private key + + align:start position:0% +even more efficient for private key + + + align:start position:0% +even more efficient for private key +storage you can actually get it very + + align:start position:0% +storage you can actually get it very + + + align:start position:0% +storage you can actually get it very +efficient using this kind of idea it is + + align:start position:0% + + + + align:start position:0% + +what would you you so some hints this is + + align:start position:0% +what would you you so some hints this is + + + align:start position:0% +what would you you so some hints this is +pretty useful right the idea is well + + align:start position:0% +pretty useful right the idea is well + + + align:start position:0% +pretty useful right the idea is well +even if you know what the sort of suffix + + align:start position:0% +even if you know what the sort of suffix + + + align:start position:0% +even if you know what the sort of suffix +of all these things are if you don't + + align:start position:0% +of all these things are if you don't + + + align:start position:0% +of all these things are if you don't +know X you're not gonna be able to find + + align:start position:0% +know X you're not gonna be able to find + + + align:start position:0% +know X you're not gonna be able to find +the preimage right so maybe add some + + align:start position:0% +the preimage right so maybe add some + + + align:start position:0% +the preimage right so maybe add some +more stuff here any idea of so another + + align:start position:0% +more stuff here any idea of so another + + + align:start position:0% +more stuff here any idea of so another +big yeah right right so instead of just + + align:start position:0% +big yeah right right so instead of just + + + align:start position:0% +big yeah right right so instead of just +saying 0 & 1 we can say like we can say + + align:start position:0% +saying 0 & 1 we can say like we can say + + + align:start position:0% +saying 0 & 1 we can say like we can say +here well why not just have one chunk + + align:start position:0% +here well why not just have one chunk + + + align:start position:0% +here well why not just have one chunk +and you say hash 0 you know hash hash + + align:start position:0% +and you say hash 0 you know hash hash + + + align:start position:0% +and you say hash 0 you know hash hash +like let's list one chunk and it's got + + align:start position:0% +like let's list one chunk and it's got + + + align:start position:0% +like let's list one chunk and it's got +you know random number X well this is + + align:start position:0% +you know random number X well this is + + + align:start position:0% +you know random number X well this is +hash x comma 0 this is hash x comma 1 + + align:start position:0% +hash x comma 0 this is hash x comma 1 + + + align:start position:0% +hash x comma 0 this is hash x comma 1 +this is ash x comma 2 okay so yeah so + + align:start position:0% +this is ash x comma 2 okay so yeah so + + + align:start position:0% +this is ash x comma 2 okay so yeah so +what you can do is you can this was + + align:start position:0% +what you can do is you can this was + + + align:start position:0% +what you can do is you can this was +before right where I said okay yeah but + + align:start position:0% +before right where I said okay yeah but + + + align:start position:0% +before right where I said okay yeah but +this is basically how to do a 32 byte + + align:start position:0% +this is basically how to do a 32 byte + + + align:start position:0% +this is basically how to do a 32 byte +private key where your private key is + + align:start position:0% +private key where your private key is + + + align:start position:0% +private key where your private key is +actually quite small and you just derive + + align:start position:0% +actually quite small and you just derive + + + align:start position:0% +actually quite small and you just derive +all of the public keys by adding numbers + + align:start position:0% +all of the public keys by adding numbers + + + align:start position:0% +all of the public keys by adding numbers +at the end concatenating them into your + + align:start position:0% +at the end concatenating them into your + + + align:start position:0% +at the end concatenating them into your +hash and now you're like okay cool I + + align:start position:0% +hash and now you're like okay cool I + + + align:start position:0% +hash and now you're like okay cool I +have a 32 byte private key and I can + + align:start position:0% +have a 32 byte private key and I can + + + align:start position:0% +have a 32 byte private key and I can +make enormous public keys from them and + + align:start position:0% +make enormous public keys from them and + + + align:start position:0% +make enormous public keys from them and +it's still secure right because I can + + align:start position:0% +it's still secure right because I can + + + align:start position:0% +it's still secure right because I can +add whatever number I want here and I + + align:start position:0% +add whatever number I want here and I + + + align:start position:0% +add whatever number I want here and I +can do this a million times and no one + + align:start position:0% +can do this a million times and no one + + + align:start position:0% +can do this a million times and no one +will be able to find the preimage even + + align:start position:0% +will be able to find the preimage even + + + align:start position:0% +will be able to find the preimage even +though I'm giving you all these related + + align:start position:0% +though I'm giving you all these related + + + align:start position:0% +though I'm giving you all these related +hashes right it's X comma zero X comma 1 + + align:start position:0% +hashes right it's X comma zero X comma 1 + + + align:start position:0% +hashes right it's X comma zero X comma 1 +X comma a million I can give you + + align:start position:0% +X comma a million I can give you + + + align:start position:0% +X comma a million I can give you +millions of them and it each time I do + + align:start position:0% +millions of them and it each time I do + + + align:start position:0% +millions of them and it each time I do +it it doesn't give you any insight into + + align:start position:0% +it it doesn't give you any insight into + + + align:start position:0% +it it doesn't give you any insight into +how to find what X is if it's a good + + align:start position:0% +how to find what X is if it's a good + + + align:start position:0% +how to find what X is if it's a good +hash function so that's really powerful + + align:start position:0% +hash function so that's really powerful + + + align:start position:0% +hash function so that's really powerful +and now I can say okay the private key + + align:start position:0% +and now I can say okay the private key + + + align:start position:0% +and now I can say okay the private key +problem is solved I have like o of one + + align:start position:0% +problem is solved I have like o of one + + + align:start position:0% +problem is solved I have like o of one +growth in my private key I can make as + + align:start position:0% +growth in my private key I can make as + + + align:start position:0% +growth in my private key I can make as +many public keys as I want never gets + + align:start position:0% +many public keys as I want never gets + + + align:start position:0% +many public keys as I want never gets +any bigger cool still have this problem + + align:start position:0% +any bigger cool still have this problem + + + align:start position:0% +any bigger cool still have this problem +with the public key so let's say I want + + align:start position:0% +with the public key so let's say I want + + + align:start position:0% +with the public key so let's say I want +to sign for x okay while I make a 64 + + align:start position:0% +to sign for x okay while I make a 64 + + + align:start position:0% +to sign for x okay while I make a 64 +64 kilobyte pump key now I can sign four + + align:start position:0% +64 kilobyte pump key now I can sign four + + + align:start position:0% +64 kilobyte pump key now I can sign four +times great but my my public key size + + align:start position:0% +times great but my my public key size + + + align:start position:0% +times great but my my public key size +expands with the number of signatures I + + align:start position:0% +expands with the number of signatures I + + + align:start position:0% +expands with the number of signatures I +ever wanted to any any ideas on how you + + align:start position:0% +ever wanted to any any ideas on how you + + + align:start position:0% +ever wanted to any any ideas on how you +could mitigate that or how you could + + align:start position:0% +could mitigate that or how you could + + + align:start position:0% +could mitigate that or how you could +still make a usable system despite this + + align:start position:0% +still make a usable system despite this + + + align:start position:0% +still make a usable system despite this +fact there's a there's a couple sort of + + align:start position:0% +fact there's a there's a couple sort of + + + align:start position:0% +fact there's a there's a couple sort of +different techniques any ideas + + align:start position:0% +different techniques any ideas + + + align:start position:0% +different techniques any ideas +okay so one would be every time I sign I + + align:start position:0% +okay so one would be every time I sign I + + + align:start position:0% +okay so one would be every time I sign I +also sign my next pub key you can do + + align:start position:0% +also sign my next pub key you can do + + + align:start position:0% +also sign my next pub key you can do +that it's got some some downsides right + + align:start position:0% +that it's got some some downsides right + + + align:start position:0% +that it's got some some downsides right +so the idea is I just commit you know I + + align:start position:0% +so the idea is I just commit you know I + + + align:start position:0% +so the idea is I just commit you know I +first published one 16 kilobyte pub key + + align:start position:0% +first published one 16 kilobyte pub key + + + align:start position:0% +first published one 16 kilobyte pub key +and then I say okay when I sign I'm + + align:start position:0% +and then I say okay when I sign I'm + + + align:start position:0% +and then I say okay when I sign I'm +going to sign my message and + + align:start position:0% +going to sign my message and + + + align:start position:0% +going to sign my message and +concatenated that message will be my + + align:start position:0% +concatenated that message will be my + + + align:start position:0% +concatenated that message will be my +next pub key and so I'm signing + + align:start position:0% +next pub key and so I'm signing + + + align:start position:0% +next pub key and so I'm signing +something and also indicating what my + + align:start position:0% +something and also indicating what my + + + align:start position:0% +something and also indicating what my +next public key will be that I signed + + align:start position:0% +next public key will be that I signed + + + align:start position:0% +next public key will be that I signed +with then I can still maintain a small + + align:start position:0% +with then I can still maintain a small + + + align:start position:0% +with then I can still maintain a small +private key and then keep signing the + + align:start position:0% +private key and then keep signing the + + + align:start position:0% +private key and then keep signing the +problem is in order for someone to + + align:start position:0% +problem is in order for someone to + + + align:start position:0% +problem is in order for someone to +verify they're gonna need to look at all + + align:start position:0% +verify they're gonna need to look at all + + + align:start position:0% +verify they're gonna need to look at all +of my previous signatures right so if I + + align:start position:0% +of my previous signatures right so if I + + + align:start position:0% +of my previous signatures right so if I +if I'm saying hey here's my 500th public + + align:start position:0% +if I'm saying hey here's my 500th public + + + align:start position:0% +if I'm saying hey here's my 500th public +key that I'm signing with here's the + + align:start position:0% +key that I'm signing with here's the + + + align:start position:0% +key that I'm signing with here's the +message you're gonna have to go back and + + align:start position:0% +message you're gonna have to go back and + + + align:start position:0% +message you're gonna have to go back and +look at my entire history of signing + + align:start position:0% +look at my entire history of signing + + + align:start position:0% +look at my entire history of signing +it's not great okay so other ideas of + + align:start position:0% +it's not great okay so other ideas of + + + align:start position:0% +it's not great okay so other ideas of +how to how to deal with large pump keys + + align:start position:0% +how to how to deal with large pump keys + + + align:start position:0% +how to how to deal with large pump keys +what's the way you could do this + + align:start position:0% + + + + align:start position:0% + +so hints is there any kind of data + + align:start position:0% +so hints is there any kind of data + + + align:start position:0% +so hints is there any kind of data +function we've seen here where it takes + + align:start position:0% +function we've seen here where it takes + + + align:start position:0% +function we've seen here where it takes +an arbitrary sized amount of data and + + align:start position:0% +an arbitrary sized amount of data and + + + align:start position:0% +an arbitrary sized amount of data and +outputs a fixed size in fact it's the + + align:start position:0% +outputs a fixed size in fact it's the + + + align:start position:0% +outputs a fixed size in fact it's the +only thing we've been talking about so + + align:start position:0% +only thing we've been talking about so + + + align:start position:0% +only thing we've been talking about so +far so what would you do to make your + + align:start position:0% +far so what would you do to make your + + + align:start position:0% +far so what would you do to make your +public he's smaller - yeah right okay so + + align:start position:0% +public he's smaller - yeah right okay so + + + align:start position:0% +public he's smaller - yeah right okay so +you say well yeah 32 byte pump key well + + align:start position:0% +you say well yeah 32 byte pump key well + + + align:start position:0% +you say well yeah 32 byte pump key well +you just commit to the pump key with the + + align:start position:0% +you just commit to the pump key with the + + + align:start position:0% +you just commit to the pump key with the +hash of the whole thing right and I say + + align:start position:0% +hash of the whole thing right and I say + + + align:start position:0% +hash of the whole thing right and I say +well I've got I've got my I've got my 16 + + align:start position:0% +well I've got I've got my I've got my 16 + + + align:start position:0% +well I've got I've got my I've got my 16 +kilobyte pump key + + align:start position:0% +kilobyte pump key + + + align:start position:0% +kilobyte pump key +I just hash it right and now I have a 32 + + align:start position:0% +I just hash it right and now I have a 32 + + + align:start position:0% +I just hash it right and now I have a 32 +byte public key and I've committed that + + align:start position:0% +byte public key and I've committed that + + + align:start position:0% +byte public key and I've committed that +that works right I've committed to my + + align:start position:0% +that works right I've committed to my + + + align:start position:0% +that works right I've committed to my +public key however when I sign I need to + + align:start position:0% +public key however when I sign I need to + + + align:start position:0% +public key however when I sign I need to +provide the whole public key in order + + align:start position:0% +provide the whole public key in order + + + align:start position:0% +provide the whole public key in order +for you to verify you know I need to + + align:start position:0% +for you to verify you know I need to + + + align:start position:0% +for you to verify you know I need to +provide this whole 16 original pub key + + align:start position:0% +provide this whole 16 original pub key + + + align:start position:0% +provide this whole 16 original pub key +you know original version pub key after + + align:start position:0% +you know original version pub key after + + + align:start position:0% +you know original version pub key after +when I sign so now my signature goes + + align:start position:0% +when I sign so now my signature goes + + + align:start position:0% +when I sign so now my signature goes +from 8k to what 24 K so I haven't really + + align:start position:0% +from 8k to what 24 K so I haven't really + + + align:start position:0% +from 8k to what 24 K so I haven't really +made it more efficient right in that + + align:start position:0% +made it more efficient right in that + + + align:start position:0% +made it more efficient right in that +like the total thing with like public + + align:start position:0% +like the total thing with like public + + + align:start position:0% +like the total thing with like public +keys and signatures stays the same size + + align:start position:0% +keys and signatures stays the same size + + + align:start position:0% +keys and signatures stays the same size +actually slightly larger but this is + + align:start position:0% +actually slightly larger but this is + + + align:start position:0% +actually slightly larger but this is +kind of a gain because the public key I + + align:start position:0% +kind of a gain because the public key I + + + align:start position:0% +kind of a gain because the public key I +mean it might be like I'm showing it to + + align:start position:0% +mean it might be like I'm showing it to + + + align:start position:0% +mean it might be like I'm showing it to +you beforehand and it we're space + + align:start position:0% +you beforehand and it we're space + + + align:start position:0% +you beforehand and it we're space +constrained there and then when I'm + + align:start position:0% +constrained there and then when I'm + + + align:start position:0% +constrained there and then when I'm +doing the signature have more space or + + align:start position:0% +doing the signature have more space or + + + align:start position:0% +doing the signature have more space or +time or something like that so this is + + align:start position:0% +time or something like that so this is + + + align:start position:0% +time or something like that so this is +actually useful and actually this + + align:start position:0% +actually useful and actually this + + + align:start position:0% +actually useful and actually this +technique is used in you know Bitcoin + + align:start position:0% +technique is used in you know Bitcoin + + + align:start position:0% +technique is used in you know Bitcoin +and all different crypto currencies + + align:start position:0% +and all different crypto currencies + + + align:start position:0% +and all different crypto currencies +where you know you can call this a punky + + align:start position:0% + + + + align:start position:0% + +punky hash or they say pkh and the main + + align:start position:0% +punky hash or they say pkh and the main + + + align:start position:0% +punky hash or they say pkh and the main +benefit is size right you could say well + + align:start position:0% +benefit is size right you could say well + + + align:start position:0% +benefit is size right you could say well +if I've got a really big punky I can + + align:start position:0% +if I've got a really big punky I can + + + align:start position:0% +if I've got a really big punky I can +commit to it by sending to the hash of + + align:start position:0% +commit to it by sending to the hash of + + + align:start position:0% +commit to it by sending to the hash of +the pub key and then when I later want + + align:start position:0% +the pub key and then when I later want + + + align:start position:0% +the pub key and then when I later want +to sign I reveal the actual pub key you + + align:start position:0% +to sign I reveal the actual pub key you + + + align:start position:0% +to sign I reveal the actual pub key you +do it that way okay so then this is + + align:start position:0% +do it that way okay so then this is + + + align:start position:0% +do it that way okay so then this is +pretty cool right we've now got we've + + align:start position:0% +pretty cool right we've now got we've + + + align:start position:0% +pretty cool right we've now got we've +taken our system which had fairly large + + align:start position:0% +taken our system which had fairly large + + + align:start position:0% +taken our system which had fairly large +16 kilobyte private keys turn them into + + align:start position:0% +16 kilobyte private keys turn them into + + + align:start position:0% +16 kilobyte private keys turn them into +32 byte private keys great and also this + + align:start position:0% +32 byte private keys great and also this + + + align:start position:0% +32 byte private keys great and also this +is o of 1 never expands awesome we've + + align:start position:0% +is o of 1 never expands awesome we've + + + align:start position:0% +is o of 1 never expands awesome we've +taken a system with large potentially + + align:start position:0% +taken a system with large potentially + + + align:start position:0% +taken a system with large potentially +you know huge 32 kilobyte 64 kilobyte + + align:start position:0% +you know huge 32 kilobyte 64 kilobyte + + + align:start position:0% +you know huge 32 kilobyte 64 kilobyte +public keys we've got it down to 32 + + align:start position:0% +public keys we've got it down to 32 + + + align:start position:0% +public keys we've got it down to 32 +bytes awesome ok + + align:start position:0% +bytes awesome ok + + + align:start position:0% +bytes awesome ok +we've now made this thing much more + + align:start position:0% +we've now made this thing much more + + + align:start position:0% +we've now made this thing much more +efficient much more useful the problem + + align:start position:0% +efficient much more useful the problem + + + align:start position:0% +efficient much more useful the problem +the signatures are still big they + + align:start position:0% +the signatures are still big they + + + align:start position:0% +the signatures are still big they +actually got a little bit bigger because + + align:start position:0% +actually got a little bit bigger because + + + align:start position:0% +actually got a little bit bigger because +they include the full public key + + align:start position:0% +they include the full public key + + + align:start position:0% +they include the full public key +in the signature and let's say we had a + + align:start position:0% +in the signature and let's say we had a + + + align:start position:0% +in the signature and let's say we had a +you know one of the things where we make + + align:start position:0% +you know one of the things where we make + + + align:start position:0% +you know one of the things where we make +a bunch of public keys and commit to + + align:start position:0% +a bunch of public keys and commit to + + + align:start position:0% +a bunch of public keys and commit to +them at the outset so he said okay I've + + align:start position:0% +them at the outset so he said okay I've + + + align:start position:0% +them at the outset so he said okay I've +got a 64 kilobyte pub key I can commit + + align:start position:0% +got a 64 kilobyte pub key I can commit + + + align:start position:0% +got a 64 kilobyte pub key I can commit +to the whole thing by hashing it however + + align:start position:0% +to the whole thing by hashing it however + + + align:start position:0% +to the whole thing by hashing it however +then when I reveal and want to give you + + align:start position:0% +then when I reveal and want to give you + + + align:start position:0% +then when I reveal and want to give you +a signature my signature is now whatever + + align:start position:0% +a signature my signature is now whatever + + + align:start position:0% +a signature my signature is now whatever +it'll be like 72 right signature would + + align:start position:0% +it'll be like 72 right signature would + + + align:start position:0% +it'll be like 72 right signature would +be 72 kilobytes kind of huge so I can + + align:start position:0% +be 72 kilobytes kind of huge so I can + + + align:start position:0% +be 72 kilobytes kind of huge so I can +add a bunch of keys but I'm just sort of + + align:start position:0% +add a bunch of keys but I'm just sort of + + + align:start position:0% +add a bunch of keys but I'm just sort of +like pushing the problem somewhere else + + align:start position:0% +like pushing the problem somewhere else + + + align:start position:0% +like pushing the problem somewhere else +into the signature right there's a + + align:start position:0% +into the signature right there's a + + + align:start position:0% +into the signature right there's a +better way to commit too many public + + align:start position:0% +better way to commit too many public + + + align:start position:0% +better way to commit too many public +keys it's maybe not super obvious unless + + align:start position:0% +keys it's maybe not super obvious unless + + + align:start position:0% +keys it's maybe not super obvious unless +you've seen it before but if you have do + + align:start position:0% +you've seen it before but if you have do + + + align:start position:0% +you've seen it before but if you have do +you know what the better way to commit + + align:start position:0% +you know what the better way to commit + + + align:start position:0% +you know what the better way to commit +to many public keys is or you could come + + align:start position:0% +to many public keys is or you could come + + + align:start position:0% +to many public keys is or you could come +up with a day on the spot and to be like + + align:start position:0% +up with a day on the spot and to be like + + + align:start position:0% +up with a day on the spot and to be like +wow you should have gotten this stuff + + align:start position:0% +wow you should have gotten this stuff + + + align:start position:0% +wow you should have gotten this stuff +named after you any idea okay so what + + align:start position:0% +named after you any idea okay so what + + + align:start position:0% +named after you any idea okay so what +you can do it like it's a little + + align:start position:0% +you can do it like it's a little + + + align:start position:0% +you can do it like it's a little +non-obvious you can make a tree right so + + align:start position:0% +non-obvious you can make a tree right so + + + align:start position:0% +non-obvious you can make a tree right so +the idea is instead of just saying oh + + align:start position:0% +the idea is instead of just saying oh + + + align:start position:0% +the idea is instead of just saying oh +I'm going to take all four of my big pub + + align:start position:0% +I'm going to take all four of my big pub + + + align:start position:0% +I'm going to take all four of my big pub +keys stick them all in a row take the + + align:start position:0% +keys stick them all in a row take the + + + align:start position:0% +keys stick them all in a row take the +hash of that whole thing and publish + + align:start position:0% +hash of that whole thing and publish + + + align:start position:0% +hash of that whole thing and publish +that as my public key hash I'm gonna + + align:start position:0% +that as my public key hash I'm gonna + + + align:start position:0% +that as my public key hash I'm gonna +have a little bit more complex design + + align:start position:0% +have a little bit more complex design + + + align:start position:0% +have a little bit more complex design +and that design is a binary tree okay so + + align:start position:0% +and that design is a binary tree okay so + + + align:start position:0% +and that design is a binary tree okay so +the idea is here are my four public keys + + align:start position:0% +the idea is here are my four public keys + + + align:start position:0% +the idea is here are my four public keys +that take up you know 64 KH I can make + + align:start position:0% +that take up you know 64 KH I can make + + + align:start position:0% +that take up you know 64 KH I can make +these intermediate hashes so I make a + + align:start position:0% +these intermediate hashes so I make a + + + align:start position:0% +these intermediate hashes so I make a +binary tree where I say okay this is the + + align:start position:0% +binary tree where I say okay this is the + + + align:start position:0% +binary tree where I say okay this is the +hash of the first two keys stuck + + align:start position:0% +hash of the first two keys stuck + + + align:start position:0% +hash of the first two keys stuck +together this is the hash of the second + + align:start position:0% +together this is the hash of the second + + + align:start position:0% +together this is the hash of the second +two keys stuck together the top is the + + align:start position:0% +two keys stuck together the top is the + + + align:start position:0% +two keys stuck together the top is the +hash of these two intermediate hashes + + align:start position:0% +hash of these two intermediate hashes + + + align:start position:0% +hash of these two intermediate hashes +stuck together and then this top is sort + + align:start position:0% +stuck together and then this top is sort + + + align:start position:0% +stuck together and then this top is sort +of my root which is equivalent to my pub + + align:start position:0% +of my root which is equivalent to my pub + + + align:start position:0% +of my root which is equivalent to my pub +key hash and so I can publish this and + + align:start position:0% +key hash and so I can publish this and + + + align:start position:0% +key hash and so I can publish this and +it is committed it commits me to all + + align:start position:0% +it is committed it commits me to all + + + align:start position:0% +it is committed it commits me to all +four of my public keys so what it might + + align:start position:0% +four of my public keys so what it might + + + align:start position:0% +four of my public keys so what it might +not be obvious are there do you see any + + align:start position:0% +not be obvious are there do you see any + + + align:start position:0% +not be obvious are there do you see any +advantages that this could have + + align:start position:0% +advantages that this could have + + + align:start position:0% +advantages that this could have +over just concatenating all four of the + + align:start position:0% +over just concatenating all four of the + + + align:start position:0% +over just concatenating all four of the +keys and hashing it the private key is + + align:start position:0% +keys and hashing it the private key is + + + align:start position:0% +keys and hashing it the private key is +down here right the private key is not + + align:start position:0% +down here right the private key is not + + + align:start position:0% +down here right the private key is not +shown but it turn you know I have a + + align:start position:0% +shown but it turn you know I have a + + + align:start position:0% +shown but it turn you know I have a +private key turns into this bump keys + + align:start position:0% +private key turns into this bump keys + + + align:start position:0% +private key turns into this bump keys +and we can use the technique here where + + align:start position:0% +and we can use the technique here where + + + align:start position:0% +and we can use the technique here where +we just have really one 32 byte private + + align:start position:0% +we just have really one 32 byte private + + + align:start position:0% +we just have really one 32 byte private +key and create all the different chunks + + align:start position:0% +key and create all the different chunks + + + align:start position:0% +key and create all the different chunks +of all the public keys right by + + align:start position:0% +of all the public keys right by + + + align:start position:0% +of all the public keys right by +concatenating different indices yeah so + + align:start position:0% +concatenating different indices yeah so + + + align:start position:0% +concatenating different indices yeah so +if I want to exactly I can prove that + + align:start position:0% +if I want to exactly I can prove that + + + align:start position:0% +if I want to exactly I can prove that +hey this is public key zero which is in + + align:start position:0% +hey this is public key zero which is in + + + align:start position:0% +hey this is public key zero which is in +here this root hash and I don't have to + + align:start position:0% +here this root hash and I don't have to + + + align:start position:0% +here this root hash and I don't have to +reveal all four in order to do it so + + align:start position:0% +reveal all four in order to do it so + + + align:start position:0% +reveal all four in order to do it so +yeah then II did someone else have + + align:start position:0% +yeah then II did someone else have + + + align:start position:0% +yeah then II did someone else have +probably the same idea yeah okay okay so + + align:start position:0% +probably the same idea yeah okay okay so + + + align:start position:0% +probably the same idea yeah okay okay so +how are we going to do that maybe I mean + + align:start position:0% +how are we going to do that maybe I mean + + + align:start position:0% +how are we going to do that maybe I mean +you obviously know anyone else have ya + + align:start position:0% + + + + align:start position:0% + +right yeah and then you can prove up to + + align:start position:0% +right yeah and then you can prove up to + + + align:start position:0% +right yeah and then you can prove up to +the top so I have little colors the idea + + align:start position:0% +the top so I have little colors the idea + + + align:start position:0% +the top so I have little colors the idea +is the the receive you know the verifier + + align:start position:0% +is the the receive you know the verifier + + + align:start position:0% +is the the receive you know the verifier +who's verifying a signature and already + + align:start position:0% +who's verifying a signature and already + + + align:start position:0% +who's verifying a signature and already +he already knows the route right because + + align:start position:0% +he already knows the route right because + + + align:start position:0% +he already knows the route right because +you've sort of pre published that as + + align:start position:0% +you've sort of pre published that as + + + align:start position:0% +you've sort of pre published that as +your public key + + align:start position:0% +your public key + + + align:start position:0% +your public key +it's your public key route your public + + align:start position:0% +it's your public key route your public + + + align:start position:0% +it's your public key route your public +key hash and then you're provided that + + align:start position:0% +key hash and then you're provided that + + + align:start position:0% +key hash and then you're provided that +verifier is provided with public key + + align:start position:0% +verifier is provided with public key + + + align:start position:0% +verifier is provided with public key +zero saying hey here's a signature + + align:start position:0% +zero saying hey here's a signature + + + align:start position:0% +zero saying hey here's a signature +here's the message + + align:start position:0% +here's the message + + + align:start position:0% +here's the message +here's public key zero so you've got + + align:start position:0% +here's public key zero so you've got + + + align:start position:0% +here's public key zero so you've got +both of these things now the prover + + align:start position:0% +both of these things now the prover + + + align:start position:0% +both of these things now the prover +needs to prove that public key zero is + + align:start position:0% +needs to prove that public key zero is + + + align:start position:0% +needs to prove that public key zero is +contained within the route and to do + + align:start position:0% +contained within the route and to do + + + align:start position:0% +contained within the route and to do +that the only two things you need to add + + align:start position:0% +that the only two things you need to add + + + align:start position:0% +that the only two things you need to add +the prover needs to add is pub one okay + + align:start position:0% +the prover needs to add is pub one okay + + + align:start position:0% +the prover needs to add is pub one okay +so the prove ourselves once the verifier + + align:start position:0% +so the prove ourselves once the verifier + + + align:start position:0% +so the prove ourselves once the verifier +to compute this and then the prover says + + align:start position:0% +to compute this and then the prover says + + + align:start position:0% +to compute this and then the prover says +hey here's hash two three which allows + + align:start position:0% +hey here's hash two three which allows + + + align:start position:0% +hey here's hash two three which allows +the verifier to compute the route and + + align:start position:0% +the verifier to compute the route and + + + align:start position:0% +the verifier to compute the route and +then check that it's equal so yeah you + + align:start position:0% +then check that it's equal so yeah you + + + align:start position:0% +then check that it's equal so yeah you +only need two extra hashes instead of + + align:start position:0% +only need two extra hashes instead of + + + align:start position:0% +only need two extra hashes instead of +all four so save some space it doesn't + + align:start position:0% +all four so save some space it doesn't + + + align:start position:0% +all four so save some space it doesn't +save that much space when you only have + + align:start position:0% +save that much space when you only have + + + align:start position:0% +save that much space when you only have +four it saves a lot of space when you + + align:start position:0% +four it saves a lot of space when you + + + align:start position:0% +four it saves a lot of space when you +have a thousand right so you can add you + + align:start position:0% +have a thousand right so you can add you + + + align:start position:0% +have a thousand right so you can add you +know event n elements and the route the + + align:start position:0% +know event n elements and the route the + + + align:start position:0% +know event n elements and the route the +route stays the same size the route say + + align:start position:0% +route stays the same size the route say + + + align:start position:0% +route stays the same size the route say +is 32 bytes regardless of how many Leafs + + align:start position:0% +is 32 bytes regardless of how many Leafs + + + align:start position:0% +is 32 bytes regardless of how many Leafs +leaf nodes you have and you can prove an + + align:start position:0% +leaf nodes you have and you can prove an + + + align:start position:0% +leaf nodes you have and you can prove an +element with login no parentheses are + + align:start position:0% +element with login no parentheses are + + + align:start position:0% +element with login no parentheses are +wrong Oh + + align:start position:0% +wrong Oh + + + align:start position:0% +wrong Oh +login intermediate hashes so if you have + + align:start position:0% +login intermediate hashes so if you have + + + align:start position:0% +login intermediate hashes so if you have +a thousand keys your route stays 32 + + align:start position:0% +a thousand keys your route stays 32 + + + align:start position:0% +a thousand keys your route stays 32 +bytes and your proofs are going to be + + align:start position:0% +bytes and your proofs are going to be + + + align:start position:0% +bytes and your proofs are going to be +not too too big right 320 bytes of + + align:start position:0% +not too too big right 320 bytes of + + + align:start position:0% +not too too big right 320 bytes of +overhead which is somewhat like a bunch + + align:start position:0% +overhead which is somewhat like a bunch + + + align:start position:0% +overhead which is somewhat like a bunch +smaller than a signature right so this + + align:start position:0% +smaller than a signature right so this + + + align:start position:0% +smaller than a signature right so this +is really cool and you can use this much + + align:start position:0% +is really cool and you can use this much + + + align:start position:0% +is really cool and you can use this much +more practically than the sort of raw + + align:start position:0% +more practically than the sort of raw + + + align:start position:0% +more practically than the sort of raw +Lamport signatures that were in the + + align:start position:0% +Lamport signatures that were in the + + + align:start position:0% +Lamport signatures that were in the +first problem set because those you know + + align:start position:0% +first problem set because those you know + + + align:start position:0% +first problem set because those you know +if you're just doing one key in one + + align:start position:0% +if you're just doing one key in one + + + align:start position:0% +if you're just doing one key in one +signature it's about the same size but + + align:start position:0% +signature it's about the same size but + + + align:start position:0% +signature it's about the same size but +this actually lets you use it multiple + + align:start position:0% +this actually lets you use it multiple + + + align:start position:0% +this actually lets you use it multiple +times lets you store a much smaller + + align:start position:0% +times lets you store a much smaller + + + align:start position:0% +times lets you store a much smaller +private key commit to much smaller + + align:start position:0% +private key commit to much smaller + + + align:start position:0% +private key commit to much smaller +public keys it's a more usable system + + align:start position:0% +public keys it's a more usable system + + + align:start position:0% +public keys it's a more usable system +the signatures though still are + + align:start position:0% +the signatures though still are + + + align:start position:0% +the signatures though still are +of huge right you'd have your signatures + + align:start position:0% +of huge right you'd have your signatures + + + align:start position:0% +of huge right you'd have your signatures +are gonna be a little over eight + + align:start position:0% +are gonna be a little over eight + + + align:start position:0% +are gonna be a little over eight +kilobytes which is okay right computers + + align:start position:0% +kilobytes which is okay right computers + + + align:start position:0% +kilobytes which is okay right computers +can be able to eight kilobytes + + align:start position:0% +can be able to eight kilobytes + + + align:start position:0% +can be able to eight kilobytes +that's called a Merkel tree and made by + + align:start position:0% +that's called a Merkel tree and made by + + + align:start position:0% +that's called a Merkel tree and made by +Ralph Merkle in like seventy six or + + align:start position:0% +Ralph Merkle in like seventy six or + + + align:start position:0% +Ralph Merkle in like seventy six or +something and it was originally made for + + align:start position:0% +something and it was originally made for + + + align:start position:0% +something and it was originally made for +exactly that purpose anyway so these are + + align:start position:0% +exactly that purpose anyway so these are + + + align:start position:0% +exactly that purpose anyway so these are +called Merkel trees + + align:start position:0% +called Merkel trees + + + align:start position:0% +called Merkel trees +Ralph Merkle he doesn't really work on + + align:start position:0% +Ralph Merkle he doesn't really work on + + + align:start position:0% +Ralph Merkle he doesn't really work on +Krypton I work something like biotech + + align:start position:0% +Krypton I work something like biotech + + + align:start position:0% +Krypton I work something like biotech +stuff and I think cool and he gets like + + align:start position:0% +stuff and I think cool and he gets like + + + align:start position:0% +stuff and I think cool and he gets like +everything named after I'm so you will + + align:start position:0% +everything named after I'm so you will + + + align:start position:0% +everything named after I'm so you will +see the word Merkel like everywhere and + + align:start position:0% +see the word Merkel like everywhere and + + + align:start position:0% +see the word Merkel like everywhere and +it's like you know he invented something + + align:start position:0% +it's like you know he invented something + + + align:start position:0% +it's like you know he invented something +cool awesome this is one of the kind of + + align:start position:0% +cool awesome this is one of the kind of + + + align:start position:0% +cool awesome this is one of the kind of +things though where it seems like yeah I + + align:start position:0% +things though where it seems like yeah I + + + align:start position:0% +things though where it seems like yeah I +might have been able to think of that + + align:start position:0% +might have been able to think of that + + + align:start position:0% +might have been able to think of that +right it's sort of a binary tree and + + align:start position:0% +right it's sort of a binary tree and + + + align:start position:0% +right it's sort of a binary tree and +hash functions like it's nothing that + + align:start position:0% +hash functions like it's nothing that + + + align:start position:0% +hash functions like it's nothing that +crazy but so there's all sorts of you + + align:start position:0% +crazy but so there's all sorts of you + + + align:start position:0% +crazy but so there's all sorts of you +know Merkel trees you can make it + + align:start position:0% +know Merkel trees you can make it + + + align:start position:0% +know Merkel trees you can make it +different you know it's used in Bitcoin + + align:start position:0% +different you know it's used in Bitcoin + + + align:start position:0% +different you know it's used in Bitcoin +it's used in a bunch of different crypto + + align:start position:0% +it's used in a bunch of different crypto + + + align:start position:0% +it's used in a bunch of different crypto +currencies it's a very cool it's a very + + align:start position:0% +currencies it's a very cool it's a very + + + align:start position:0% +currencies it's a very cool it's a very +you know powerful way to take a whole + + align:start position:0% +you know powerful way to take a whole + + + align:start position:0% +you know powerful way to take a whole +bunch of different things and commit to + + align:start position:0% +bunch of different things and commit to + + + align:start position:0% +bunch of different things and commit to +them in one small thing okay so this is + + align:start position:0% +them in one small thing okay so this is + + + align:start position:0% +them in one small thing okay so this is +very cool but we can do better and so + + align:start position:0% +very cool but we can do better and so + + + align:start position:0% +very cool but we can do better and so +the next things are things that I + + align:start position:0% +the next things are things that I + + + align:start position:0% +the next things are things that I +definitely would never have thought of + + align:start position:0% +definitely would never have thought of + + + align:start position:0% +definitely would never have thought of +because it's much more complex than just + + align:start position:0% +because it's much more complex than just + + + align:start position:0% +because it's much more complex than just +like hey let's use a binary tree with + + align:start position:0% +like hey let's use a binary tree with + + + align:start position:0% +like hey let's use a binary tree with +hashes and I will mention RSA and then + + align:start position:0% +hashes and I will mention RSA and then + + + align:start position:0% +hashes and I will mention RSA and then +go into ECDSA and I left a curve blare + + align:start position:0% +go into ECDSA and I left a curve blare + + + align:start position:0% +go into ECDSA and I left a curve blare +in evidence signatures which do + + align:start position:0% +in evidence signatures which do + + + align:start position:0% +in evidence signatures which do +different things and are not based on + + align:start position:0% +different things and are not based on + + + align:start position:0% +different things and are not based on +just ash functions so I'll talk about + + align:start position:0% +just ash functions so I'll talk about + + + align:start position:0% +just ash functions so I'll talk about +RSA for a few minutes and then we'll + + align:start position:0% +RSA for a few minutes and then we'll + + + align:start position:0% +RSA for a few minutes and then we'll +have a look a little break like + + align:start position:0% +have a look a little break like + + + align:start position:0% +have a look a little break like +intermission and then we'll go into the + + align:start position:0% +intermission and then we'll go into the + + + align:start position:0% +intermission and then we'll go into the +elliptic curve stuff + + align:start position:0% +elliptic curve stuff + + + align:start position:0% +elliptic curve stuff +okay so RSA was invented by locals the + + align:start position:0% +okay so RSA was invented by locals the + + + align:start position:0% +okay so RSA was invented by locals the +are is is Ron no I think the R stands + + align:start position:0% +are is is Ron no I think the R stands + + + align:start position:0% +are is is Ron no I think the R stands +for Rivest but Ron Rivest is at csail + + align:start position:0% +for Rivest but Ron Rivest is at csail + + + align:start position:0% +for Rivest but Ron Rivest is at csail +and he's you know working on still + + align:start position:0% +and he's you know working on still + + + align:start position:0% +and he's you know working on still +working on cool crypto stuff it's not + + align:start position:0% +working on cool crypto stuff it's not + + + align:start position:0% +working on cool crypto stuff it's not +used in Bitcoin or any currency actually + + align:start position:0% +used in Bitcoin or any currency actually + + + align:start position:0% +used in Bitcoin or any currency actually +that well any currently operating + + align:start position:0% +that well any currently operating + + + align:start position:0% +that well any currently operating +cryptocurrency + + align:start position:0% +cryptocurrency + + + align:start position:0% +cryptocurrency +because they the signatures and keys are + + align:start position:0% +because they the signatures and keys are + + + align:start position:0% +because they the signatures and keys are +a bit larger than the later systems will + + align:start position:0% +a bit larger than the later systems will + + + align:start position:0% +a bit larger than the later systems will +see smaller than the hash based things + + align:start position:0% +see smaller than the hash based things + + + align:start position:0% +see smaller than the hash based things +but still a bit larger was used in cha + + align:start position:0% +but still a bit larger was used in cha + + + align:start position:0% +but still a bit larger was used in cha +me and blinded cash because you can do + + align:start position:0% +me and blinded cash because you can do + + + align:start position:0% +me and blinded cash because you can do +what blinded signatures where you say + + align:start position:0% +what blinded signatures where you say + + + align:start position:0% +what blinded signatures where you say +okay I'm gonna have you + + align:start position:0% +okay I'm gonna have you + + + align:start position:0% +okay I'm gonna have you +sign something for me and then after you + + align:start position:0% +sign something for me and then after you + + + align:start position:0% +sign something for me and then after you +give me the signature I can sort of pull + + align:start position:0% +give me the signature I can sort of pull + + + align:start position:0% +give me the signature I can sort of pull +apart the signature and you won't + + align:start position:0% +apart the signature and you won't + + + align:start position:0% +apart the signature and you won't +because you I'll have you sign something + + align:start position:0% +because you I'll have you sign something + + + align:start position:0% +because you I'll have you sign something +that you don't know what you're signing + + align:start position:0% +that you don't know what you're signing + + + align:start position:0% +that you don't know what you're signing +right I'm gonna like mask this message + + align:start position:0% +right I'm gonna like mask this message + + + align:start position:0% +right I'm gonna like mask this message +and blind it so that you sign the + + align:start position:0% +and blind it so that you sign the + + + align:start position:0% +and blind it so that you sign the +message and then I can get your + + align:start position:0% +message and then I can get your + + + align:start position:0% +message and then I can get your +signature on the real message without + + align:start position:0% +signature on the real message without + + + align:start position:0% +signature on the real message without +you knowing what you signed so basically + + align:start position:0% +you knowing what you signed so basically + + + align:start position:0% +you knowing what you signed so basically +the idea is well I actually have you + + align:start position:0% +the idea is well I actually have you + + + align:start position:0% +the idea is well I actually have you +know message prime equals message plus + + align:start position:0% +know message prime equals message plus + + + align:start position:0% +know message prime equals message plus +randomness and I say hey can you sign em + + align:start position:0% +randomness and I say hey can you sign em + + + align:start position:0% +randomness and I say hey can you sign em +Prime and you say okay I produce a + + align:start position:0% +Prime and you say okay I produce a + + + align:start position:0% +Prime and you say okay I produce a +signature on M Prime with my you know + + align:start position:0% +signature on M Prime with my you know + + + align:start position:0% +signature on M Prime with my you know +private key and we'll call that s Prime + + align:start position:0% +private key and we'll call that s Prime + + + align:start position:0% +private key and we'll call that s Prime +and then what I can do is I can sort of + + align:start position:0% +and then what I can do is I can sort of + + + align:start position:0% +and then what I can do is I can sort of +s equals s prime minus the randomness or + + align:start position:0% +s equals s prime minus the randomness or + + + align:start position:0% +s equals s prime minus the randomness or +really some function of that randomness + + align:start position:0% +really some function of that randomness + + + align:start position:0% +really some function of that randomness +and now I have a signature and this is a + + align:start position:0% +and now I have a signature and this is a + + + align:start position:0% +and now I have a signature and this is a +valid signature on em so that's kind of + + align:start position:0% +valid signature on em so that's kind of + + + align:start position:0% +valid signature on em so that's kind of +cool it's like hey can you sign this + + align:start position:0% +cool it's like hey can you sign this + + + align:start position:0% +cool it's like hey can you sign this +message for me and I'm not gonna tell + + align:start position:0% +message for me and I'm not gonna tell + + + align:start position:0% +message for me and I'm not gonna tell +you what you're signing and then it + + align:start position:0% +you what you're signing and then it + + + align:start position:0% +you what you're signing and then it +seems sort of useless like why would I + + align:start position:0% +seems sort of useless like why would I + + + align:start position:0% +seems sort of useless like why would I +sign something I have no idea what I'm + + align:start position:0% +sign something I have no idea what I'm + + + align:start position:0% +sign something I have no idea what I'm +saying but it can be used in that that + + align:start position:0% +saying but it can be used in that that + + + align:start position:0% +saying but it can be used in that that +Chou Mian blinded cache because I then + + align:start position:0% +Chou Mian blinded cache because I then + + + align:start position:0% +Chou Mian blinded cache because I then +have a proof that well this bank didn't + + align:start position:0% +have a proof that well this bank didn't + + + align:start position:0% +have a proof that well this bank didn't +know what they were signing but they + + align:start position:0% +know what they were signing but they + + + align:start position:0% +know what they were signing but they +they signed this and this is their + + align:start position:0% +they signed this and this is their + + + align:start position:0% +they signed this and this is their +signature and they gave it to me and I + + align:start position:0% +signature and they gave it to me and I + + + align:start position:0% +signature and they gave it to me and I +can use that as like a thing to + + align:start position:0% +can use that as like a thing to + + + align:start position:0% +can use that as like a thing to +represent money that there's all sorts + + align:start position:0% +represent money that there's all sorts + + + align:start position:0% +represent money that there's all sorts +of cool things you can do with this um + + align:start position:0% +of cool things you can do with this um + + + align:start position:0% +of cool things you can do with this um +the basic setup of RSA is make two prime + + align:start position:0% +the basic setup of RSA is make two prime + + + align:start position:0% +the basic setup of RSA is make two prime +numbers P and Q and then compute n which + + align:start position:0% +numbers P and Q and then compute n which + + + align:start position:0% +numbers P and Q and then compute n which +is the product P times Q so this seems + + align:start position:0% +is the product P times Q so this seems + + + align:start position:0% +is the product P times Q so this seems +fairly straightforward right it's not + + align:start position:0% +fairly straightforward right it's not + + + align:start position:0% +fairly straightforward right it's not +too hard everyone knows the prime + + align:start position:0% +too hard everyone knows the prime + + + align:start position:0% +too hard everyone knows the prime +numbers are now you have this composite + + align:start position:0% +numbers are now you have this composite + + + align:start position:0% +numbers are now you have this composite +number P times Q what how do I like make + + align:start position:0% +number P times Q what how do I like make + + + align:start position:0% +number P times Q what how do I like make +a leading question for the next slide + + align:start position:0% +a leading question for the next slide + + + align:start position:0% +a leading question for the next slide +does this have any relation to things + + align:start position:0% +does this have any relation to things + + + align:start position:0% +does this have any relation to things +we've looked at like does this look this + + align:start position:0% +we've looked at like does this look this + + + align:start position:0% +we've looked at like does this look this +doesn't look at all like a hash function + + align:start position:0% +doesn't look at all like a hash function + + + align:start position:0% +doesn't look at all like a hash function +right but are there any properties + + align:start position:0% +right but are there any properties + + + align:start position:0% +right but are there any properties +similar to a hash function here yeah + + align:start position:0% + + + + align:start position:0% + +yeah it's a one-way function in that if + + align:start position:0% +yeah it's a one-way function in that if + + + align:start position:0% +yeah it's a one-way function in that if +I know if he and Q I can compute n right + + align:start position:0% +I know if he and Q I can compute n right + + + align:start position:0% +I know if he and Q I can compute n right +but given n I can't necessarily find P + + align:start position:0% +but given n I can't necessarily find P + + + align:start position:0% +but given n I can't necessarily find P +and Q right if they're small sure I just + + align:start position:0% +and Q right if they're small sure I just + + + align:start position:0% +and Q right if they're small sure I just +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +check and there's all sorts of + + align:start position:0% +check and there's all sorts of + + + align:start position:0% +check and there's all sorts of +algorithms to find factors but if P and + + align:start position:0% +algorithms to find factors but if P and + + + align:start position:0% +algorithms to find factors but if P and +Q are pretty big like hundreds of bits + + align:start position:0% +Q are pretty big like hundreds of bits + + + align:start position:0% +Q are pretty big like hundreds of bits +long thousands of bits long finding it + + align:start position:0% +long thousands of bits long finding it + + + align:start position:0% +long thousands of bits long finding it +may be impractical + + align:start position:0% +may be impractical + + + align:start position:0% +may be impractical +whereas if P and Q are really long + + align:start position:0% +whereas if P and Q are really long + + + align:start position:0% +whereas if P and Q are really long +finding the product of both of them will + + align:start position:0% +finding the product of both of them will + + + align:start position:0% +finding the product of both of them will +be very practical even if even if huge + + align:start position:0% +be very practical even if even if huge + + + align:start position:0% +be very practical even if even if huge +multiplying two integers is like really + + align:start position:0% +multiplying two integers is like really + + + align:start position:0% +multiplying two integers is like really +easy so this is a one-way function but + + align:start position:0% +easy so this is a one-way function but + + + align:start position:0% +easy so this is a one-way function but +not a hash function and so a lot of + + align:start position:0% +not a hash function and so a lot of + + + align:start position:0% +not a hash function and so a lot of +these signature systems use one-way + + align:start position:0% +these signature systems use one-way + + + align:start position:0% +these signature systems use one-way +functions but trickier one-way functions + + align:start position:0% +functions but trickier one-way functions + + + align:start position:0% +functions but trickier one-way functions +that aren't hash functions and still + + align:start position:0% +that aren't hash functions and still + + + align:start position:0% +that aren't hash functions and still +have things that you like cool things + + align:start position:0% +have things that you like cool things + + + align:start position:0% +have things that you like cool things +that you can do so I'm not gonna go into + + align:start position:0% +that you can do so I'm not gonna go into + + + align:start position:0% +that you can do so I'm not gonna go into +RSA in super detail I'm going to sort of + + align:start position:0% +RSA in super detail I'm going to sort of + + + align:start position:0% +RSA in super detail I'm going to sort of +like run through it really quick and + + align:start position:0% +like run through it really quick and + + + align:start position:0% +like run through it really quick and +you'll be like huh how does that work + + align:start position:0% +you'll be like huh how does that work + + + align:start position:0% +you'll be like huh how does that work +but if you think it's interesting you + + align:start position:0% +but if you think it's interesting you + + + align:start position:0% +but if you think it's interesting you +can look it up and then maybe go to C + + align:start position:0% +can look it up and then maybe go to C + + + align:start position:0% +can look it up and then maybe go to C +cell and ask Ron how it works although + + align:start position:0% +cell and ask Ron how it works although + + + align:start position:0% +cell and ask Ron how it works although +maybe try to look it up first he's + + align:start position:0% +maybe try to look it up first he's + + + align:start position:0% +maybe try to look it up first he's +probably explained it a lot of times and + + align:start position:0% +probably explained it a lot of times and + + + align:start position:0% +probably explained it a lot of times and +but it has different properties so you + + align:start position:0% +but it has different properties so you + + + align:start position:0% +but it has different properties so you +could say I'm gonna use this P times Q + + align:start position:0% +could say I'm gonna use this P times Q + + + align:start position:0% +could say I'm gonna use this P times Q +equals n as like a hash function and + + align:start position:0% +equals n as like a hash function and + + + align:start position:0% +equals n as like a hash function and +make a Lamport signature out of it where + + align:start position:0% +make a Lamport signature out of it where + + + align:start position:0% +make a Lamport signature out of it where +my private key is a whole bunch of P and + + align:start position:0% +my private key is a whole bunch of P and + + + align:start position:0% +my private key is a whole bunch of P and +Q pairs and my public key is a whole + + align:start position:0% +Q pairs and my public key is a whole + + + align:start position:0% +Q pairs and my public key is a whole +bunch of ends and I reveal them and + + align:start position:0% +bunch of ends and I reveal them and + + + align:start position:0% +bunch of ends and I reveal them and +stuff you could do that that would work + + align:start position:0% +stuff you could do that that would work + + + align:start position:0% +stuff you could do that that would work +but you can do much more powerful things + + align:start position:0% +but you can do much more powerful things + + + align:start position:0% +but you can do much more powerful things +because of the mathematical properties + + align:start position:0% +because of the mathematical properties + + + align:start position:0% +because of the mathematical properties +of these things so yeah I'm just gonna + + align:start position:0% +of these things so yeah I'm just gonna + + + align:start position:0% +of these things so yeah I'm just gonna +go through it really fast cos but if you + + align:start position:0% +go through it really fast cos but if you + + + align:start position:0% +go through it really fast cos but if you +think it's you know if you if you know + + align:start position:0% +think it's you know if you if you know + + + align:start position:0% +think it's you know if you if you know +anything that's kind of cool the idea is + + align:start position:0% +anything that's kind of cool the idea is + + + align:start position:0% +anything that's kind of cool the idea is +you can do a bunch of multiplication and + + align:start position:0% +you can do a bunch of multiplication and + + + align:start position:0% +you can do a bunch of multiplication and +exponentiation modulo n and so because n + + align:start position:0% +exponentiation modulo n and so because n + + + align:start position:0% +exponentiation modulo n and so because n +is like almost prime there's some + + align:start position:0% +is like almost prime there's some + + + align:start position:0% +is like almost prime there's some +interesting properties where if you know + + align:start position:0% +interesting properties where if you know + + + align:start position:0% +interesting properties where if you know +the factors of n you have these + + align:start position:0% +the factors of n you have these + + + align:start position:0% +the factors of n you have these +shortcuts you can do and if someone who + + align:start position:0% +shortcuts you can do and if someone who + + + align:start position:0% +shortcuts you can do and if someone who +doesn't know the factors of n can't do + + align:start position:0% +doesn't know the factors of n can't do + + + align:start position:0% +doesn't know the factors of n can't do +these shortcuts so you publish E which + + align:start position:0% +these shortcuts so you publish E which + + + align:start position:0% +these shortcuts so you publish E which +is a constant this is sort of a + + align:start position:0% +is a constant this is sort of a + + + align:start position:0% +is a constant this is sort of a +parameter system usually today so RSA is + + align:start position:0% +parameter system usually today so RSA is + + + align:start position:0% +parameter system usually today so RSA is +used today all over the place if you're + + align:start position:0% +used today all over the place if you're + + + align:start position:0% +used today all over the place if you're +on if your computer is open and you've + + align:start position:0% +on if your computer is open and you've + + + align:start position:0% +on if your computer is open and you've +been using the web in the last five + + align:start position:0% +been using the web in the last five + + + align:start position:0% +been using the web in the last five +seconds your computer has performed RSA + + align:start position:0% +seconds your computer has performed RSA + + + align:start position:0% +seconds your computer has performed RSA +calculations every time you connect to a + + align:start position:0% +calculations every time you connect to a + + + align:start position:0% +calculations every time you connect to a +website you're doing RSA so generally at + + align:start position:0% +website you're doing RSA so generally at + + + align:start position:0% +website you're doing RSA so generally at +six five five three seven they just make + + align:start position:0% +six five five three seven they just make + + + align:start position:0% +six five five three seven they just make +this up you can do also use three + + align:start position:0% +this up you can do also use three + + + align:start position:0% +this up you can do also use three +some small number and then D is a number + + align:start position:0% +some small number and then D is a number + + + align:start position:0% +some small number and then D is a number +that you can compute if you know what P + + align:start position:0% +that you can compute if you know what P + + + align:start position:0% +that you can compute if you know what P +and Q are so this is sort of the private + + align:start position:0% +and Q are so this is sort of the private + + + align:start position:0% +and Q are so this is sort of the private +key right P and Q itself can be seen as + + align:start position:0% +key right P and Q itself can be seen as + + + align:start position:0% +key right P and Q itself can be seen as +the private key but you can actually + + align:start position:0% +the private key but you can actually + + + align:start position:0% +the private key but you can actually +compute this demon number and then + + align:start position:0% +compute this demon number and then + + + align:start position:0% +compute this demon number and then +discard P and Q and then yeah so this is + + align:start position:0% +discard P and Q and then yeah so this is + + + align:start position:0% +discard P and Q and then yeah so this is +how you compute D or whatever but the + + align:start position:0% +how you compute D or whatever but the + + + align:start position:0% +how you compute D or whatever but the +idea is n is their public key and D is + + align:start position:0% +idea is n is their public key and D is + + + align:start position:0% +idea is n is their public key and D is +your private key E is always the same + + align:start position:0% +your private key E is always the same + + + align:start position:0% +your private key E is always the same +and P and Q you can discard afterwards + + align:start position:0% +and P and Q you can discard afterwards + + + align:start position:0% +and P and Q you can discard afterwards +and then what you can do and this is + + align:start position:0% +and then what you can do and this is + + + align:start position:0% +and then what you can do and this is +like not going to get into it but you + + align:start position:0% +like not going to get into it but you + + + align:start position:0% +like not going to get into it but you +can say okay my signature s is message + + align:start position:0% +can say okay my signature s is message + + + align:start position:0% +can say okay my signature s is message +right I can take the hash and make a + + align:start position:0% +right I can take the hash and make a + + + align:start position:0% +right I can take the hash and make a +message message to the D power modulo N + + align:start position:0% +message message to the D power modulo N + + + align:start position:0% +message message to the D power modulo N +and if I verify if I take that signature + + align:start position:0% +and if I verify if I take that signature + + + align:start position:0% +and if I verify if I take that signature +to the e power modulo n it should equal + + align:start position:0% +to the e power modulo n it should equal + + + align:start position:0% +to the e power modulo n it should equal +M again which is like crazy and kind of + + align:start position:0% +M again which is like crazy and kind of + + + align:start position:0% +M again which is like crazy and kind of +awesome because the idea is to sign okay + + align:start position:0% +awesome because the idea is to sign okay + + + align:start position:0% +awesome because the idea is to sign okay +I just raised to the D power mod n it's + + align:start position:0% +I just raised to the D power mod n it's + + + align:start position:0% +I just raised to the D power mod n it's +gonna be some some number on you know + + align:start position:0% +gonna be some some number on you know + + + align:start position:0% +gonna be some some number on you know +the same size as n right and then I give + + align:start position:0% +the same size as n right and then I give + + + align:start position:0% +the same size as n right and then I give +that to someone they take that signature + + align:start position:0% +that to someone they take that signature + + + align:start position:0% +that to someone they take that signature +to the six hundred you know six five + + align:start position:0% +to the six hundred you know six five + + + align:start position:0% +to the six hundred you know six five +five three seven power modulo and again + + align:start position:0% +five three seven power modulo and again + + + align:start position:0% +five three seven power modulo and again +and see if n comes back out em the + + align:start position:0% +and see if n comes back out em the + + + align:start position:0% +and see if n comes back out em the +message comes back out and if it does + + align:start position:0% +message comes back out and if it does + + + align:start position:0% +message comes back out and if it does +they know I signed and I have the + + align:start position:0% +they know I signed and I have the + + + align:start position:0% +they know I signed and I have the +private key the private key that + + align:start position:0% +private key the private key that + + + align:start position:0% +private key the private key that +corresponds to n now this the cool thing + + align:start position:0% +corresponds to n now this the cool thing + + + align:start position:0% +corresponds to n now this the cool thing +is I can use this any number of times I + + align:start position:0% +is I can use this any number of times I + + + align:start position:0% +is I can use this any number of times I +can use it the same thing a bazillion + + align:start position:0% +can use it the same thing a bazillion + + + align:start position:0% +can use it the same thing a bazillion +times with different M's and that + + align:start position:0% +times with different M's and that + + + align:start position:0% +times with different M's and that +doesn't give any help on to how to + + align:start position:0% +doesn't give any help on to how to + + + align:start position:0% +doesn't give any help on to how to +factor n or how to compute D so this was + + align:start position:0% +factor n or how to compute D so this was + + + align:start position:0% +factor n or how to compute D so this was +you know late 70s also RSA and sort of + + align:start position:0% +you know late 70s also RSA and sort of + + + align:start position:0% +you know late 70s also RSA and sort of +one of the first like hey we you know we + + align:start position:0% +one of the first like hey we you know we + + + align:start position:0% +one of the first like hey we you know we +can do better than hash functions it + + align:start position:0% +can do better than hash functions it + + + align:start position:0% +can do better than hash functions it +sort of was developed at around the same + + align:start position:0% +sort of was developed at around the same + + + align:start position:0% +sort of was developed at around the same +time as hash based signatures all of + + align:start position:0% +time as hash based signatures all of + + + align:start position:0% +time as hash based signatures all of +these things were sort of coming out of + + align:start position:0% +these things were sort of coming out of + + + align:start position:0% +these things were sort of coming out of +the same time you can do lots of cool + + align:start position:0% +the same time you can do lots of cool + + + align:start position:0% +the same time you can do lots of cool +stuff because there's like these + + align:start position:0% +stuff because there's like these + + + align:start position:0% +stuff because there's like these +properties where we can you know make em + + align:start position:0% +properties where we can you know make em + + + align:start position:0% +properties where we can you know make em +you know M prime plus m and like take + + align:start position:0% +you know M prime plus m and like take + + + align:start position:0% +you know M prime plus m and like take +the exponentiation of all that and still + + align:start position:0% +the exponentiation of all that and still + + + align:start position:0% +the exponentiation of all that and still +it works ok so that's really cool you + + align:start position:0% +it works ok so that's really cool you + + + align:start position:0% +it works ok so that's really cool you +can do lots of cool stuff but this is + + align:start position:0% +can do lots of cool stuff but this is + + + align:start position:0% +can do lots of cool stuff but this is +also not used in Bitcoin one of the + + align:start position:0% +also not used in Bitcoin one of the + + + align:start position:0% +also not used in Bitcoin one of the +things that + + align:start position:0% +things that + + + align:start position:0% +things that +sighs Sookie sizes are smaller than then + + align:start position:0% +sighs Sookie sizes are smaller than then + + + align:start position:0% +sighs Sookie sizes are smaller than then +with Lamport signatures and they're + + align:start position:0% +with Lamport signatures and they're + + + align:start position:0% +with Lamport signatures and they're +often about two kilobits or 256 bytes + + align:start position:0% +often about two kilobits or 256 bytes + + + align:start position:0% +often about two kilobits or 256 bytes +which is fine and that's about the same + + align:start position:0% +which is fine and that's about the same + + + align:start position:0% +which is fine and that's about the same +size as signatures so if you use your + + align:start position:0% +size as signatures so if you use your + + + align:start position:0% +size as signatures so if you use your +like web browser secure well how secure + + align:start position:0% +like web browser secure well how secure + + + align:start position:0% +like web browser secure well how secure +certificate valid no this browser might + + align:start position:0% +certificate valid no this browser might + + + align:start position:0% +certificate valid no this browser might +not show me okay anyway well in Firefox + + align:start position:0% +not show me okay anyway well in Firefox + + + align:start position:0% +not show me okay anyway well in Firefox +that tells you more okay well anyway + + align:start position:0% +that tells you more okay well anyway + + + align:start position:0% +that tells you more okay well anyway +anyway anyway but yeah you there's RSA + + align:start position:0% +anyway anyway but yeah you there's RSA + + + align:start position:0% +anyway anyway but yeah you there's RSA +keys in basically every certificate for + + align:start position:0% +keys in basically every certificate for + + + align:start position:0% +keys in basically every certificate for +web browsers and websites and they're + + align:start position:0% +web browsers and websites and they're + + + align:start position:0% +web browsers and websites and they're +generally 2048 bits long that scene is + + align:start position:0% +generally 2048 bits long that scene is + + + align:start position:0% +generally 2048 bits long that scene is +like pretty secure that's like you know + + align:start position:0% +like pretty secure that's like you know + + + align:start position:0% +like pretty secure that's like you know +even a thousand four thousand twenty + + align:start position:0% +even a thousand four thousand twenty + + + align:start position:0% +even a thousand four thousand twenty +four bits has not been hacked but people + + align:start position:0% +four bits has not been hacked but people + + + align:start position:0% +four bits has not been hacked but people +think it probably could be by a very + + align:start position:0% +think it probably could be by a very + + + align:start position:0% +think it probably could be by a very +motivated actor so this is decent size + + align:start position:0% +motivated actor so this is decent size + + + align:start position:0% +motivated actor so this is decent size +one thing about RSA is that it's a + + align:start position:0% +one thing about RSA is that it's a + + + align:start position:0% +one thing about RSA is that it's a +little tricky to implement right there's + + align:start position:0% +little tricky to implement right there's + + + align:start position:0% +little tricky to implement right there's +a whole bunch of weird math there it's + + align:start position:0% +a whole bunch of weird math there it's + + + align:start position:0% +a whole bunch of weird math there it's +not like the Lamport signatures where + + align:start position:0% +not like the Lamport signatures where + + + align:start position:0% +not like the Lamport signatures where +it's like okay I have a hash function + + align:start position:0% +it's like okay I have a hash function + + + align:start position:0% +it's like okay I have a hash function +use it right it's it's kind of hard to + + align:start position:0% +use it right it's it's kind of hard to + + + align:start position:0% +use it right it's it's kind of hard to +shoot yourself in the foot with the + + align:start position:0% +shoot yourself in the foot with the + + + align:start position:0% +shoot yourself in the foot with the +Lamport signature scheme you can write + + align:start position:0% +Lamport signature scheme you can write + + + align:start position:0% +Lamport signature scheme you can write +but it's sort of obvious if you do so + + align:start position:0% +but it's sort of obvious if you do so + + + align:start position:0% +but it's sort of obvious if you do so +like if you're doing the homework and it + + align:start position:0% +like if you're doing the homework and it + + + align:start position:0% +like if you're doing the homework and it +just like doesn't work at all and you're + + align:start position:0% +just like doesn't work at all and you're + + + align:start position:0% +just like doesn't work at all and you're +like oh I was hashing twice or oh I was + + align:start position:0% +like oh I was hashing twice or oh I was + + + align:start position:0% +like oh I was hashing twice or oh I was +like reversing the order or you know + + align:start position:0% +like reversing the order or you know + + + align:start position:0% +like reversing the order or you know +things that were like it it it just + + align:start position:0% +things that were like it it it just + + + align:start position:0% +things that were like it it it just +didn't work but there's no like subtle + + align:start position:0% +didn't work but there's no like subtle + + + align:start position:0% +didn't work but there's no like subtle +ways where like oh I was off by one and + + align:start position:0% +ways where like oh I was off by one and + + + align:start position:0% +ways where like oh I was off by one and +now it reveals all my private keys + + align:start position:0% +now it reveals all my private keys + + + align:start position:0% +now it reveals all my private keys +that's hard to do whereas an RSA it's + + align:start position:0% +that's hard to do whereas an RSA it's + + + align:start position:0% +that's hard to do whereas an RSA it's +actually quite easy if if your P and Q + + align:start position:0% +actually quite easy if if your P and Q + + + align:start position:0% +actually quite easy if if your P and Q +values for example what's it what's a + + align:start position:0% +values for example what's it what's a + + + align:start position:0% +values for example what's it what's a +really crazy gotcha if P or Q minus one + + align:start position:0% +really crazy gotcha if P or Q minus one + + + align:start position:0% +really crazy gotcha if P or Q minus one +so if like P minus 1 or Q minus 1 is + + align:start position:0% +so if like P minus 1 or Q minus 1 is + + + align:start position:0% +so if like P minus 1 or Q minus 1 is +smooth essentially a number that's + + align:start position:0% +smooth essentially a number that's + + + align:start position:0% +smooth essentially a number that's +highly composite has many small factors + + align:start position:0% +highly composite has many small factors + + + align:start position:0% +highly composite has many small factors +you can find someone's private key you + + align:start position:0% +you can find someone's private key you + + + align:start position:0% +you can find someone's private key you +can factor it so it's not just that P + + align:start position:0% +can factor it so it's not just that P + + + align:start position:0% +can factor it so it's not just that P +and Q have to be prime P minus 1 and Q + + align:start position:0% +and Q have to be prime P minus 1 and Q + + + align:start position:0% +and Q have to be prime P minus 1 and Q +minus 1 have to be not two unprimed not + + align:start position:0% +minus 1 have to be not two unprimed not + + + align:start position:0% +minus 1 have to be not two unprimed not +like it can't be like a power of two or + + align:start position:0% +like it can't be like a power of two or + + + align:start position:0% +like it can't be like a power of two or +something otherwise you can lose your + + align:start position:0% +something otherwise you can lose your + + + align:start position:0% +something otherwise you can lose your +project so there's all sorts of like you + + align:start position:0% +project so there's all sorts of like you + + + align:start position:0% +project so there's all sorts of like you +know crazy things that happen with RSA + + align:start position:0% +know crazy things that happen with RSA + + + align:start position:0% +know crazy things that happen with RSA +Bitcoin and other coins use elliptic + + align:start position:0% +Bitcoin and other coins use elliptic + + + align:start position:0% +Bitcoin and other coins use elliptic +curve signatures which I'll talk about + + align:start position:0% +curve signatures which I'll talk about + + + align:start position:0% +curve signatures which I'll talk about +next + + align:start position:0% +next + + + align:start position:0% +next +that have our sort of displacing RSA in + + align:start position:0% +that have our sort of displacing RSA in + + + align:start position:0% +that have our sort of displacing RSA in +many cases so it hasn't really taken off + + align:start position:0% +many cases so it hasn't really taken off + + + align:start position:0% +many cases so it hasn't really taken off +for for like web certificates but a lot + + align:start position:0% +for for like web certificates but a lot + + + align:start position:0% +for for like web certificates but a lot +of other types of encryption signing + + align:start position:0% +of other types of encryption signing + + + align:start position:0% +of other types of encryption signing +things like that like crypto currencies + + align:start position:0% +things like that like crypto currencies + + + align:start position:0% +things like that like crypto currencies +are also one of the big uses of elliptic + + align:start position:0% +are also one of the big uses of elliptic + + + align:start position:0% +are also one of the big uses of elliptic +curve signatures because they're + + align:start position:0% +curve signatures because they're + + + align:start position:0% +curve signatures because they're +somewhat more powerful and somewhat + + align:start position:0% +somewhat more powerful and somewhat + + + align:start position:0% +somewhat more powerful and somewhat +smaller and really cool and we will talk + + align:start position:0% +smaller and really cool and we will talk + + + align:start position:0% +smaller and really cool and we will talk +about those in three minutes so + + align:start position:0% +about those in three minutes so + + + align:start position:0% +about those in three minutes so +intermission three minutes stretch ask + + align:start position:0% +intermission three minutes stretch ask + + + align:start position:0% +intermission three minutes stretch ask +random questions talk to the neighbors + + align:start position:0% +random questions talk to the neighbors + + + align:start position:0% +random questions talk to the neighbors +okay so they're using these elliptic + + align:start position:0% +okay so they're using these elliptic + + + align:start position:0% +okay so they're using these elliptic +curves which are curves of the form y + + align:start position:0% +curves which are curves of the form y + + + align:start position:0% +curves which are curves of the form y +squared plus X cubed plus X some + + align:start position:0% +squared plus X cubed plus X some + + + align:start position:0% +squared plus X cubed plus X some +coefficient x squared plus some constant + + align:start position:0% +coefficient x squared plus some constant + + + align:start position:0% +coefficient x squared plus some constant +and in the case of Bitcoin it's very + + align:start position:0% +and in the case of Bitcoin it's very + + + align:start position:0% +and in the case of Bitcoin it's very +simple it's y squared equals x cubed + + align:start position:0% +simple it's y squared equals x cubed + + + align:start position:0% +simple it's y squared equals x cubed +plus seven and that's the curve bitcoin + + align:start position:0% +plus seven and that's the curve bitcoin + + + align:start position:0% +plus seven and that's the curve bitcoin +uses and this is what it looks like if + + align:start position:0% +uses and this is what it looks like if + + + align:start position:0% +uses and this is what it looks like if +you plot it and that seems really simple + + align:start position:0% +you plot it and that seems really simple + + + align:start position:0% +you plot it and that seems really simple +like we can totally understand that but + + align:start position:0% +like we can totally understand that but + + + align:start position:0% +like we can totally understand that but +it gets a little weird with elliptic + + align:start position:0% +it gets a little weird with elliptic + + + align:start position:0% +it gets a little weird with elliptic +curves you have these points on the + + align:start position:0% +curves you have these points on the + + + align:start position:0% +curves you have these points on the +curves right and another property is if + + align:start position:0% +curves right and another property is if + + + align:start position:0% +curves right and another property is if +you draw a straight line that intersects + + align:start position:0% +you draw a straight line that intersects + + + align:start position:0% +you draw a straight line that intersects +this curve you could also draw a line + + align:start position:0% +this curve you could also draw a line + + + align:start position:0% +this curve you could also draw a line +which doesn't intersect at all fine but + + align:start position:0% +which doesn't intersect at all fine but + + + align:start position:0% +which doesn't intersect at all fine but +if you draw a line that intersects the + + align:start position:0% +if you draw a line that intersects the + + + align:start position:0% +if you draw a line that intersects the +curve it will intersect in three places + + align:start position:0% +curve it will intersect in three places + + + align:start position:0% +curve it will intersect in three places +so if I draw a line here it intersects + + align:start position:0% +so if I draw a line here it intersects + + + align:start position:0% +so if I draw a line here it intersects +these three dots if I draw a line here + + align:start position:0% +these three dots if I draw a line here + + + align:start position:0% +these three dots if I draw a line here +and intersects here here and then it'll + + align:start position:0% +and intersects here here and then it'll + + + align:start position:0% +and intersects here here and then it'll +intersect somewhere down here it'll + + align:start position:0% +intersect somewhere down here it'll + + + align:start position:0% +intersect somewhere down here it'll +intersect in three places unless I take + + align:start position:0% +intersect in three places unless I take + + + align:start position:0% +intersect in three places unless I take +a tangent if I draw and I like try to be + + align:start position:0% +a tangent if I draw and I like try to be + + + align:start position:0% +a tangent if I draw and I like try to be +like oh I'm gonna only intersect in two + + align:start position:0% +like oh I'm gonna only intersect in two + + + align:start position:0% +like oh I'm gonna only intersect in two +well I can take a tangent here and it'll + + align:start position:0% +well I can take a tangent here and it'll + + + align:start position:0% +well I can take a tangent here and it'll +intersect in one more place what we can + + align:start position:0% +intersect in one more place what we can + + + align:start position:0% +intersect in one more place what we can +do those we can say well if you + + align:start position:0% +do those we can say well if you + + + align:start position:0% +do those we can say well if you +intersect at a tangent that's kind of + + align:start position:0% +intersect at a tangent that's kind of + + + align:start position:0% +intersect at a tangent that's kind of +like intersecting twice or you know we + + align:start position:0% +like intersecting twice or you know we + + + align:start position:0% +like intersecting twice or you know we +can we can deal with that + + align:start position:0% +can we can deal with that + + + align:start position:0% +can we can deal with that +if you draw a vertical oh yeah vertical + + align:start position:0% +if you draw a vertical oh yeah vertical + + + align:start position:0% +if you draw a vertical oh yeah vertical +line then there's like a point at + + align:start position:0% +line then there's like a point at + + + align:start position:0% +line then there's like a point at +infinity which shouldn't happen + + align:start position:0% + + + + align:start position:0% + +yeah yeah it there's a point up there + + align:start position:0% +yeah yeah it there's a point up there + + + align:start position:0% +yeah yeah it there's a point up there +sort of it in the practice of signing + + align:start position:0% +sort of it in the practice of signing + + + align:start position:0% +sort of it in the practice of signing +and stuff you probably shouldn't hit it + + align:start position:0% +and stuff you probably shouldn't hit it + + + align:start position:0% +and stuff you probably shouldn't hit it +like if you yeah but so what we do is we + + align:start position:0% +like if you yeah but so what we do is we + + + align:start position:0% +like if you yeah but so what we do is we +say okay well three points in a line + + align:start position:0% +say okay well three points in a line + + + align:start position:0% +say okay well three points in a line +equals zero and so if we take this point + + align:start position:0% +equals zero and so if we take this point + + + align:start position:0% +equals zero and so if we take this point +plus this point plus this point that's + + align:start position:0% +plus this point plus this point that's + + + align:start position:0% +plus this point plus this point that's +zero another way to say that is P plus Q + + align:start position:0% +zero another way to say that is P plus Q + + + align:start position:0% +zero another way to say that is P plus Q +minus R equals 0 or P plus Q equals + + align:start position:0% +minus R equals 0 or P plus Q equals + + + align:start position:0% +minus R equals 0 or P plus Q equals +negative R and another property is the + + align:start position:0% +negative R and another property is the + + + align:start position:0% +negative R and another property is the +negation of a point is just that same + + align:start position:0% +negation of a point is just that same + + + align:start position:0% +negation of a point is just that same +point with the you know y-coordinate + + align:start position:0% +point with the you know y-coordinate + + + align:start position:0% +point with the you know y-coordinate +flipped so this is you know if this is + + align:start position:0% +flipped so this is you know if this is + + + align:start position:0% +flipped so this is you know if this is +negative R we just go down to the bottom + + align:start position:0% +negative R we just go down to the bottom + + + align:start position:0% +negative R we just go down to the bottom +side of this and this is positive R + + align:start position:0% +side of this and this is positive R + + + align:start position:0% +side of this and this is positive R +similarly you know minus P would be here + + align:start position:0% +similarly you know minus P would be here + + + align:start position:0% +similarly you know minus P would be here +minus Q would be here and if you had a + + align:start position:0% +minus Q would be here and if you had a + + + align:start position:0% +minus Q would be here and if you had a +point + + align:start position:0% +point + + + align:start position:0% +point +you know Z here negative Z would be up + + align:start position:0% +you know Z here negative Z would be up + + + align:start position:0% +you know Z here negative Z would be up +here this is how it's constructed + + align:start position:0% +here this is how it's constructed + + + align:start position:0% +here this is how it's constructed +however we don't actually use these nice + + align:start position:0% +however we don't actually use these nice + + + align:start position:0% +however we don't actually use these nice +curves we sort of chop them up and + + align:start position:0% +curves we sort of chop them up and + + + align:start position:0% +curves we sort of chop them up and +modulo something yeah + + align:start position:0% + + + + align:start position:0% + +no in this case are as I hit right P in + + align:start position:0% +no in this case are as I hit right P in + + + align:start position:0% +no in this case are as I hit right P in +this case P wait hold on + + align:start position:0% + + + + align:start position:0% + +people speak equals R right sorry okay + + align:start position:0% +people speak equals R right sorry okay + + + align:start position:0% +people speak equals R right sorry okay +normally yeah + + align:start position:0% +normally yeah + + + align:start position:0% +normally yeah +the this picture is correct + + align:start position:0% +the this picture is correct + + + align:start position:0% +the this picture is correct +but so basically P plus Q equals R + + align:start position:0% +but so basically P plus Q equals R + + + align:start position:0% +but so basically P plus Q equals R +because R is down here sorry yeah that's + + align:start position:0% +because R is down here sorry yeah that's + + + align:start position:0% +because R is down here sorry yeah that's +why okay this is our this is negative R + + align:start position:0% +why okay this is our this is negative R + + + align:start position:0% +why okay this is our this is negative R +so so yeah people ask you equals + + align:start position:0% +so so yeah people ask you equals + + + align:start position:0% +so so yeah people ask you equals +negative if equals are not negative R + + align:start position:0% +negative if equals are not negative R + + + align:start position:0% +negative if equals are not negative R +sorry when you want to multiply a point + + align:start position:0% +sorry when you want to multiply a point + + + align:start position:0% +sorry when you want to multiply a point +you can because you can take a tangent + + align:start position:0% +you can because you can take a tangent + + + align:start position:0% +you can because you can take a tangent +right so you can add these points right + + align:start position:0% +right so you can add these points right + + + align:start position:0% +right so you can add these points right +you can say okay I want the sum of P and + + align:start position:0% +you can say okay I want the sum of P and + + + align:start position:0% +you can say okay I want the sum of P and +Q which will be down here are I want to + + align:start position:0% +Q which will be down here are I want to + + + align:start position:0% +Q which will be down here are I want to +pee for example well with two P I can + + align:start position:0% +pee for example well with two P I can + + + align:start position:0% +pee for example well with two P I can +take a tangent and then find where it + + align:start position:0% +take a tangent and then find where it + + + align:start position:0% +take a tangent and then find where it +intersects and then go down below okay + + align:start position:0% +intersects and then go down below okay + + + align:start position:0% +intersects and then go down below okay +so for example if this is you know G I + + align:start position:0% +so for example if this is you know G I + + + align:start position:0% +so for example if this is you know G I +say okay well G starts here take the + + align:start position:0% +say okay well G starts here take the + + + align:start position:0% +say okay well G starts here take the +tangent find where it intersects and + + align:start position:0% +tangent find where it intersects and + + + align:start position:0% +tangent find where it intersects and +then drop down and this is to G so I can + + align:start position:0% +then drop down and this is to G so I can + + + align:start position:0% +then drop down and this is to G so I can +you know it's a simple way to say well + + align:start position:0% +you know it's a simple way to say well + + + align:start position:0% +you know it's a simple way to say well +I'm not I'm not really multiplying I'm + + align:start position:0% +I'm not I'm not really multiplying I'm + + + align:start position:0% +I'm not I'm not really multiplying I'm +just adding it to itself which is sort + + align:start position:0% +just adding it to itself which is sort + + + align:start position:0% +just adding it to itself which is sort +of what multiplication is and I can do + + align:start position:0% +of what multiplication is and I can do + + + align:start position:0% +of what multiplication is and I can do +this again and again so I say oh I want + + align:start position:0% +this again and again so I say oh I want + + + align:start position:0% +this again and again so I say oh I want +for G I take the tangent at to G find + + align:start position:0% +for G I take the tangent at to G find + + + align:start position:0% +for G I take the tangent at to G find +the intersection here drop down okay + + align:start position:0% +the intersection here drop down okay + + + align:start position:0% +the intersection here drop down okay +here's for G take the tangent here it'll + + align:start position:0% +here's for G take the tangent here it'll + + + align:start position:0% +here's for G take the tangent here it'll +go you know I can keep doing that and + + align:start position:0% +go you know I can keep doing that and + + + align:start position:0% +go you know I can keep doing that and +get to g4 g AG and if I want + + align:start position:0% +get to g4 g AG and if I want + + + align:start position:0% +get to g4 g AG and if I want +intermediate things like well I want + + align:start position:0% +intermediate things like well I want + + + align:start position:0% +intermediate things like well I want +three G well I'm draw a line between G + + align:start position:0% +three G well I'm draw a line between G + + + align:start position:0% +three G well I'm draw a line between G +and two G find the intersection and find + + align:start position:0% +and two G find the intersection and find + + + align:start position:0% +and two G find the intersection and find +the sum so what we yeah yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah so so it looks I the pictures + + align:start position:0% +yeah yeah so so it looks I the pictures + + + align:start position:0% +yeah yeah so so it looks I the pictures +look nice in this case right it's like a + + align:start position:0% +look nice in this case right it's like a + + + align:start position:0% +look nice in this case right it's like a +this is this curve and it looks so + + align:start position:0% +this is this curve and it looks so + + + align:start position:0% +this is this curve and it looks so +simple and we can like graphically do it + + align:start position:0% +simple and we can like graphically do it + + + align:start position:0% +simple and we can like graphically do it +on graph paper but when you're actually + + align:start position:0% +on graph paper but when you're actually + + + align:start position:0% +on graph paper but when you're actually +doing it on the computer it looks more + + align:start position:0% +doing it on the computer it looks more + + + align:start position:0% +doing it on the computer it looks more +like this + + align:start position:0% +like this + + + align:start position:0% +like this +everything is modulo some giant prime + + align:start position:0% +everything is modulo some giant prime + + + align:start position:0% +everything is modulo some giant prime +number + + align:start position:0% +number + + + align:start position:0% +number +the you could still draw lines it's just + + align:start position:0% +the you could still draw lines it's just + + + align:start position:0% +the you could still draw lines it's just +that the curve is now all these + + align:start position:0% +that the curve is now all these + + + align:start position:0% +that the curve is now all these +crazy-looking dots and you still have + + align:start position:0% +crazy-looking dots and you still have + + + align:start position:0% +crazy-looking dots and you still have +that symmetry from the y-axis but the + + align:start position:0% +that symmetry from the y-axis but the + + + align:start position:0% +that symmetry from the y-axis but the +way the computer does it is all modulo + + align:start position:0% +way the computer does it is all modulo + + + align:start position:0% +way the computer does it is all modulo +number so you can't it doesn't actually + + align:start position:0% +number so you can't it doesn't actually + + + align:start position:0% +number so you can't it doesn't actually +map to a nice like curve however all the + + align:start position:0% +map to a nice like curve however all the + + + align:start position:0% +map to a nice like curve however all the +properties so the fun thing about when + + align:start position:0% +properties so the fun thing about when + + + align:start position:0% +properties so the fun thing about when +you're doing modulo is all the + + align:start position:0% +you're doing modulo is all the + + + align:start position:0% +you're doing modulo is all the +properties stay the same right like you + + align:start position:0% +properties stay the same right like you + + + align:start position:0% +properties stay the same right like you +can still do with with regular numbers + + align:start position:0% +can still do with with regular numbers + + + align:start position:0% +can still do with with regular numbers +you can still do addition multiplication + + align:start position:0% +you can still do addition multiplication + + + align:start position:0% +you can still do addition multiplication +and division all modulo some number and + + align:start position:0% +and division all modulo some number and + + + align:start position:0% +and division all modulo some number and +it still all works right so same with + + align:start position:0% +it still all works right so same with + + + align:start position:0% +it still all works right so same with +this you still have the same you know + + align:start position:0% +this you still have the same you know + + + align:start position:0% +this you still have the same you know +draw a line between P and Q and you get + + align:start position:0% +draw a line between P and Q and you get + + + align:start position:0% +draw a line between P and Q and you get +to here and then you flip over the + + align:start position:0% +to here and then you flip over the + + + align:start position:0% +to here and then you flip over the +y-axis and now this is R similarly you + + align:start position:0% +y-axis and now this is R similarly you + + + align:start position:0% +y-axis and now this is R similarly you +can like take a tangent + + align:start position:0% +can like take a tangent + + + align:start position:0% +can like take a tangent +although tangent is harder to visually + + align:start position:0% +although tangent is harder to visually + + + align:start position:0% +although tangent is harder to visually +see because there's no like obvious + + align:start position:0% +see because there's no like obvious + + + align:start position:0% +see because there's no like obvious +curve here but the equations work the + + align:start position:0% +curve here but the equations work the + + + align:start position:0% +curve here but the equations work the +same okay so you don't need to like know + + align:start position:0% +same okay so you don't need to like know + + + align:start position:0% +same okay so you don't need to like know +exactly why these things work or curves + + align:start position:0% +exactly why these things work or curves + + + align:start position:0% +exactly why these things work or curves +but we're gonna go through what you can + + align:start position:0% +but we're gonna go through what you can + + + align:start position:0% +but we're gonna go through what you can +do with these and what properties you + + align:start position:0% +do with these and what properties you + + + align:start position:0% +do with these and what properties you +have okay so we've now have we've + + align:start position:0% +have okay so we've now have we've + + + align:start position:0% +have okay so we've now have we've +defined these points on a curve and like + + align:start position:0% +defined these points on a curve and like + + + align:start position:0% +defined these points on a curve and like +how this curve works and then we also + + align:start position:0% +how this curve works and then we also + + + align:start position:0% +how this curve works and then we also +have regular old numbers right so a and + + align:start position:0% +have regular old numbers right so a and + + + align:start position:0% +have regular old numbers right so a and +well what we'll do from now on is say + + align:start position:0% +well what we'll do from now on is say + + + align:start position:0% +well what we'll do from now on is say +like a and B are lowercase numbers these + + align:start position:0% +like a and B are lowercase numbers these + + + align:start position:0% +like a and B are lowercase numbers these +are scalars scalars just means regular + + align:start position:0% +are scalars scalars just means regular + + + align:start position:0% +are scalars scalars just means regular +old numbers the upper case a and B will + + align:start position:0% +old numbers the upper case a and B will + + + align:start position:0% +old numbers the upper case a and B will +refer to points on the curve okay so + + align:start position:0% +refer to points on the curve okay so + + + align:start position:0% +refer to points on the curve okay so +from now on lower case is regular number + + align:start position:0% +from now on lower case is regular number + + + align:start position:0% +from now on lower case is regular number +upper case is point on this curve or + + align:start position:0% +upper case is point on this curve or + + + align:start position:0% +upper case is point on this curve or +point on this mashed-up thing that we + + align:start position:0% +point on this mashed-up thing that we + + + align:start position:0% +point on this mashed-up thing that we +still call a current okay so I'll go + + align:start position:0% +still call a current okay so I'll go + + + align:start position:0% +still call a current okay so I'll go +through what operations we can do and + + align:start position:0% +through what operations we can do and + + + align:start position:0% +through what operations we can do and +then we can see what use those that + + align:start position:0% +then we can see what use those that + + + align:start position:0% +then we can see what use those that +so first scalars you can add subtract + + align:start position:0% +so first scalars you can add subtract + + + align:start position:0% +so first scalars you can add subtract +multiply divide you can do + + align:start position:0% +multiply divide you can do + + + align:start position:0% +multiply divide you can do +ever you want right these are just + + align:start position:0% +ever you want right these are just + + + align:start position:0% +ever you want right these are just +regular numbers like five or 17 or 20 - + + align:start position:0% +regular numbers like five or 17 or 20 - + + + align:start position:0% +regular numbers like five or 17 or 20 - +everything is okay + + align:start position:0% +everything is okay + + + align:start position:0% +everything is okay +right easy everything here is integers + + align:start position:0% +right easy everything here is integers + + + align:start position:0% +right easy everything here is integers +we're doing modulo some big prime number + + align:start position:0% +we're doing modulo some big prime number + + + align:start position:0% +we're doing modulo some big prime number +so there's no decimal points you know + + align:start position:0% +so there's no decimal points you know + + + align:start position:0% +so there's no decimal points you know +you never have to use I think in this + + align:start position:0% +you never have to use I think in this + + + align:start position:0% +you never have to use I think in this +class we'll probably never have to use + + align:start position:0% +class we'll probably never have to use + + + align:start position:0% +class we'll probably never have to use +floating-point which is great because + + align:start position:0% +floating-point which is great because + + + align:start position:0% +floating-point which is great because +floating-point always scares me it's + + align:start position:0% +floating-point always scares me it's + + + align:start position:0% +floating-point always scares me it's +like it's also like you int these are + + align:start position:0% +like it's also like you int these are + + + align:start position:0% +like it's also like you int these are +like unsigned integers you can do it + + align:start position:0% +like unsigned integers you can do it + + + align:start position:0% +like unsigned integers you can do it +with sine but since you're modulo some + + align:start position:0% +with sine but since you're modulo some + + + align:start position:0% +with sine but since you're modulo some +big number it's like unsigned numbers + + align:start position:0% +big number it's like unsigned numbers + + + align:start position:0% +big number it's like unsigned numbers +that loop around so it's really nice for + + align:start position:0% +that loop around so it's really nice for + + + align:start position:0% +that loop around so it's really nice for +computers computers deal very well with + + align:start position:0% +computers computers deal very well with + + + align:start position:0% +computers computers deal very well with +these things computers are good at + + align:start position:0% +these things computers are good at + + + align:start position:0% +these things computers are good at +floating-point as well but the thing is + + align:start position:0% +floating-point as well but the thing is + + + align:start position:0% +floating-point as well but the thing is +in cryptography a lot of times + + align:start position:0% +in cryptography a lot of times + + + align:start position:0% +in cryptography a lot of times +floating-point ends up with error right + + align:start position:0% +floating-point ends up with error right + + + align:start position:0% +floating-point ends up with error right +where you're like pretty close but like + + align:start position:0% +where you're like pretty close but like + + + align:start position:0% +where you're like pretty close but like +you're you've got some you know fixed + + align:start position:0% +you're you've got some you know fixed + + + align:start position:0% +you're you've got some you know fixed +amount of decimal places you can store + + align:start position:0% +amount of decimal places you can store + + + align:start position:0% +amount of decimal places you can store +your floating-point goes out to some + + align:start position:0% +your floating-point goes out to some + + + align:start position:0% +your floating-point goes out to some +precision and then air can sort of + + align:start position:0% +precision and then air can sort of + + + align:start position:0% +precision and then air can sort of +accumulate and in a lot of cryptography + + align:start position:0% +accumulate and in a lot of cryptography + + + align:start position:0% +accumulate and in a lot of cryptography +you want zero error right like in a hash + + align:start position:0% +you want zero error right like in a hash + + + align:start position:0% +you want zero error right like in a hash +function it's pretty exact so in a lot + + align:start position:0% +function it's pretty exact so in a lot + + + align:start position:0% +function it's pretty exact so in a lot +of times the cryptography you you use + + align:start position:0% +of times the cryptography you you use + + + align:start position:0% +of times the cryptography you you use +integers instead of floating-point or + + align:start position:0% +integers instead of floating-point or + + + align:start position:0% +integers instead of floating-point or +rational numbers okay so with scalars + + align:start position:0% +rational numbers okay so with scalars + + + align:start position:0% +rational numbers okay so with scalars +these are just regular integers natural + + align:start position:0% +these are just regular integers natural + + + align:start position:0% +these are just regular integers natural +numbers even you can do these all the + + align:start position:0% +numbers even you can do these all the + + + align:start position:0% +numbers even you can do these all the +operations you're familiar with that's + + align:start position:0% +operations you're familiar with that's + + + align:start position:0% +operations you're familiar with that's +fairly straightforward with points so + + align:start position:0% +fairly straightforward with points so + + + align:start position:0% +fairly straightforward with points so +you can add and subtract the points + + align:start position:0% +you can add and subtract the points + + + align:start position:0% +you can add and subtract the points +right we showed how you sort of do that + + align:start position:0% +right we showed how you sort of do that + + + align:start position:0% +right we showed how you sort of do that +visually and then the equations for it + + align:start position:0% +visually and then the equations for it + + + align:start position:0% +visually and then the equations for it +the computer can do that pretty quick + + align:start position:0% +the computer can do that pretty quick + + + align:start position:0% +the computer can do that pretty quick +however these this is not defined + + align:start position:0% +however these this is not defined + + + align:start position:0% +however these this is not defined +multiplication and division with two + + align:start position:0% +multiplication and division with two + + + align:start position:0% +multiplication and division with two +points is undefined it's just not it's + + align:start position:0% +points is undefined it's just not it's + + + align:start position:0% +points is undefined it's just not it's +not clear how you do it like it's it's + + align:start position:0% +not clear how you do it like it's it's + + + align:start position:0% +not clear how you do it like it's it's +not something in this system right it's + + align:start position:0% +not something in this system right it's + + + align:start position:0% +not something in this system right it's +a group you've got one operation you + + align:start position:0% +a group you've got one operation you + + + align:start position:0% +a group you've got one operation you +don't have this other one so you can add + + align:start position:0% +don't have this other one so you can add + + + align:start position:0% +don't have this other one so you can add +them subtract points if you can't + + align:start position:0% +them subtract points if you can't + + + align:start position:0% +them subtract points if you can't +multiply them + + align:start position:0% +multiply them + + + align:start position:0% +multiply them +any questions about this this is a + + align:start position:0% +any questions about this this is a + + + align:start position:0% +any questions about this this is a +pretty important yeah make sense yes + + align:start position:0% +pretty important yeah make sense yes + + + align:start position:0% +pretty important yeah make sense yes +when you adding points what is defined + + align:start position:0% +when you adding points what is defined + + + align:start position:0% +when you adding points what is defined +as addition are you adding them either + + align:start position:0% +as addition are you adding them either + + + align:start position:0% +as addition are you adding them either +you use both the x and y coordinates to + + align:start position:0% +you use both the x and y coordinates to + + + align:start position:0% +you use both the x and y coordinates to +add right so right so when you're doing + + align:start position:0% +add right so right so when you're doing + + + align:start position:0% +add right so right so when you're doing +it in the computer saying okay + + align:start position:0% +it in the computer saying okay + + + align:start position:0% +it in the computer saying okay +well what are the x and y coordinates of + + align:start position:0% +well what are the x and y coordinates of + + + align:start position:0% +well what are the x and y coordinates of +P what are the x and y coordinates of Q + + align:start position:0% +P what are the x and y coordinates of Q + + + align:start position:0% +P what are the x and y coordinates of Q +draw you know find the slope find the + + align:start position:0% +draw you know find the slope find the + + + align:start position:0% +draw you know find the slope find the +slope here and the like where it + + align:start position:0% +slope here and the like where it + + + align:start position:0% +slope here and the like where it +intersects the axis and then see where + + align:start position:0% +intersects the axis and then see where + + + align:start position:0% +intersects the axis and then see where +it'll intersect the curve at another + + align:start position:0% +it'll intersect the curve at another + + + align:start position:0% +it'll intersect the curve at another +point you know but the equation would be + + align:start position:0% +point you know but the equation would be + + + align:start position:0% +point you know but the equation would be +like you don't the sense the computer + + align:start position:0% +like you don't the sense the computer + + + align:start position:0% +like you don't the sense the computer +doesn't actually look at the curve you + + align:start position:0% +doesn't actually look at the curve you + + + align:start position:0% +doesn't actually look at the curve you +just say okay find the PX and y + + align:start position:0% +just say okay find the PX and y + + + align:start position:0% +just say okay find the PX and y +coordinate find the Q X&Y coordinate + + align:start position:0% +coordinate find the Q X&Y coordinate + + + align:start position:0% +coordinate find the Q X&Y coordinate +like find the slope and then find where + + align:start position:0% +like find the slope and then find where + + + align:start position:0% +like find the slope and then find where +it intersects and then like you know + + align:start position:0% +it intersects and then like you know + + + align:start position:0% +it intersects and then like you know +compute for that Ferrar okay so yeah you + + align:start position:0% +compute for that Ferrar okay so yeah you + + + align:start position:0% +compute for that Ferrar okay so yeah you +can add and subtract + + align:start position:0% +can add and subtract + + + align:start position:0% +can add and subtract +you cannot multiply and divide these + + align:start position:0% +you cannot multiply and divide these + + + align:start position:0% +you cannot multiply and divide these +points sounds good any other questions + + align:start position:0% + + + + align:start position:0% + +you just go down right so if I want P + + align:start position:0% +you just go down right so if I want P + + + align:start position:0% +you just go down right so if I want P +minus Q I just say P plus negative Q and + + align:start position:0% +minus Q I just say P plus negative Q and + + + align:start position:0% +minus Q I just say P plus negative Q and +negative Q is just right here right down + + align:start position:0% +negative Q is just right here right down + + + align:start position:0% +negative Q is just right here right down +on the y axis so I say okay I want + + align:start position:0% +on the y axis so I say okay I want + + + align:start position:0% +on the y axis so I say okay I want +people ask you go here but it's gonna be + + align:start position:0% +people ask you go here but it's gonna be + + + align:start position:0% +people ask you go here but it's gonna be +up there somewhere so yeah you just add + + align:start position:0% +up there somewhere so yeah you just add + + + align:start position:0% +up there somewhere so yeah you just add +the negative of the number I guess + + align:start position:0% +the negative of the number I guess + + + align:start position:0% +the negative of the number I guess +that's another thing I you know B minus + + align:start position:0% +that's another thing I you know B minus + + + align:start position:0% +that's another thing I you know B minus +B like negative B is also an operation I + + align:start position:0% +B like negative B is also an operation I + + + align:start position:0% +B like negative B is also an operation I +can do I can negate something which lets + + align:start position:0% +can do I can negate something which lets + + + align:start position:0% +can do I can negate something which lets +me do subtraction okay + + align:start position:0% + + + + align:start position:0% + +natural numbers modulo and just some + + align:start position:0% +natural numbers modulo and just some + + + align:start position:0% +natural numbers modulo and just some +easy birthday curve so this is a and the + + align:start position:0% +easy birthday curve so this is a and the + + + align:start position:0% +easy birthday curve so this is a and the +only things to find is addition and + + align:start position:0% +only things to find is addition and + + + align:start position:0% +only things to find is addition and +subtraction or not right you can do the + + align:start position:0% +subtraction or not right you can do the + + + align:start position:0% +subtraction or not right you can do the +same group operations without using + + align:start position:0% +same group operations without using + + + align:start position:0% +same group operations without using +elliptic curves and so you can just do + + align:start position:0% +elliptic curves and so you can just do + + + align:start position:0% +elliptic curves and so you can just do +exponentiation modulo a big prime number + + align:start position:0% +exponentiation modulo a big prime number + + + align:start position:0% +exponentiation modulo a big prime number +I'm gonna use curves because it's what + + align:start position:0% +I'm gonna use curves because it's what + + + align:start position:0% +I'm gonna use curves because it's what +is used in all the actual systems and + + align:start position:0% +is used in all the actual systems and + + + align:start position:0% +is used in all the actual systems and +it's but but you you can sort of forget + + align:start position:0% +it's but but you you can sort of forget + + + align:start position:0% +it's but but you you can sort of forget +about the curve after this right if you + + align:start position:0% +about the curve after this right if you + + + align:start position:0% +about the curve after this right if you +say well look we just have these + + align:start position:0% +say well look we just have these + + + align:start position:0% +say well look we just have these +uppercase numbers and these you know + + align:start position:0% +uppercase numbers and these you know + + + align:start position:0% +uppercase numbers and these you know +these uppercase variables and these + + align:start position:0% +these uppercase variables and these + + + align:start position:0% +these uppercase variables and these +lowercase variables and the fact that + + align:start position:0% +lowercase variables and the fact that + + + align:start position:0% +lowercase variables and the fact that +it's on a curve we can sort of abstract + + align:start position:0% +it's on a curve we can sort of abstract + + + align:start position:0% +it's on a curve we can sort of abstract +away and just know that we have these + + align:start position:0% +away and just know that we have these + + + align:start position:0% +away and just know that we have these +different types essentially and when you + + align:start position:0% +different types essentially and when you + + + align:start position:0% +different types essentially and when you +do when you're in the computer you're + + align:start position:0% +do when you're in the computer you're + + + align:start position:0% +do when you're in the computer you're +just like yeah that's the point + + align:start position:0% +just like yeah that's the point + + + align:start position:0% +just like yeah that's the point +that's a scalar here are the operations + + align:start position:0% +that's a scalar here are the operations + + + align:start position:0% +that's a scalar here are the operations +I can do and I just run the functions + + align:start position:0% +I can do and I just run the functions + + + align:start position:0% +I can do and I just run the functions +okay so the next part when you mix + + align:start position:0% +okay so the next part when you mix + + + align:start position:0% +okay so the next part when you mix +scalars and points so mixed operations + + align:start position:0% +scalars and points so mixed operations + + + align:start position:0% +scalars and points so mixed operations +you cannot add a point and an integer or + + align:start position:0% +you cannot add a point and an integer or + + + align:start position:0% +you cannot add a point and an integer or +subtract a point in an integer like + + align:start position:0% +subtract a point in an integer like + + + align:start position:0% +subtract a point in an integer like +that's not defined right you say okay + + align:start position:0% +that's not defined right you say okay + + + align:start position:0% +that's not defined right you say okay +here's this point P minus seven like + + align:start position:0% +here's this point P minus seven like + + + align:start position:0% +here's this point P minus seven like +well does that mean move the x axis does + + align:start position:0% +well does that mean move the x axis does + + + align:start position:0% +well does that mean move the x axis does +that move do y like it's not defined + + align:start position:0% +that move do y like it's not defined + + + align:start position:0% +that move do y like it's not defined +however you can do this right you can + + align:start position:0% +however you can do this right you can + + + align:start position:0% +however you can do this right you can +multiply and divide so you can say well + + align:start position:0% +multiply and divide so you can say well + + + align:start position:0% +multiply and divide so you can say well +a times two what you know you take the + + align:start position:0% +a times two what you know you take the + + + align:start position:0% +a times two what you know you take the +tangent right it's just a plus a or a + + align:start position:0% +tangent right it's just a plus a or a + + + align:start position:0% +tangent right it's just a plus a or a +times seven is we just break it out as a + + align:start position:0% +times seven is we just break it out as a + + + align:start position:0% +times seven is we just break it out as a +plus a plus a plus a 17 times we can + + align:start position:0% +plus a plus a plus a 17 times we can + + + align:start position:0% +plus a plus a plus a 17 times we can +also divide which is a little weird + + align:start position:0% +also divide which is a little weird + + + align:start position:0% +also divide which is a little weird +because we have to find the the sort of + + align:start position:0% +because we have to find the the sort of + + + align:start position:0% +because we have to find the the sort of +like inverse of B and then multiply by + + align:start position:0% +like inverse of B and then multiply by + + + align:start position:0% +like inverse of B and then multiply by +that like the multiplicative inverse of + + align:start position:0% +that like the multiplicative inverse of + + + align:start position:0% +that like the multiplicative inverse of +B modulo the the order but anyway you + + align:start position:0% +B modulo the the order but anyway you + + + align:start position:0% +B modulo the the order but anyway you +can do these this is a little trickier + + align:start position:0% +can do these this is a little trickier + + + align:start position:0% +can do these this is a little trickier +because you have to compute what sort of + + align:start position:0% +because you have to compute what sort of + + + align:start position:0% +because you have to compute what sort of +like B to the negative one is and + + align:start position:0% +like B to the negative one is and + + + align:start position:0% +like B to the negative one is and +multiply by that you can do it so you + + align:start position:0% +multiply by that you can do it so you + + + align:start position:0% +multiply by that you can do it so you +can do these things where you have + + align:start position:0% +can do these things where you have + + + align:start position:0% +can do these things where you have +points times scalars but you cannot have + + align:start position:0% + + + + align:start position:0% + +yep yep to it so that was here you know + + align:start position:0% +yep yep to it so that was here you know + + + align:start position:0% +yep yep to it so that was here you know +if this is G this is to G find the + + align:start position:0% +if this is G this is to G find the + + + align:start position:0% +if this is G this is to G find the +tangent find the intersection and then + + align:start position:0% +tangent find the intersection and then + + + align:start position:0% +tangent find the intersection and then +the gate okay so you can do you can do + + align:start position:0% +the gate okay so you can do you can do + + + align:start position:0% +the gate okay so you can do you can do +that that's cool you cannot do that + + align:start position:0% +that that's cool you cannot do that + + + align:start position:0% +that that's cool you cannot do that +okay so roster of operations we can do + + align:start position:0% +okay so roster of operations we can do + + + align:start position:0% +okay so roster of operations we can do +this is it and this is sort of if you + + align:start position:0% +this is it and this is sort of if you + + + align:start position:0% +this is it and this is sort of if you +think of that you can do all these cool + + align:start position:0% +think of that you can do all these cool + + + align:start position:0% +think of that you can do all these cool +things it's sort of amazing all the + + align:start position:0% +things it's sort of amazing all the + + + align:start position:0% +things it's sort of amazing all the +crazy things you can do with just these + + align:start position:0% +crazy things you can do with just these + + + align:start position:0% +crazy things you can do with just these +operations right with regular numbers + + align:start position:0% +operations right with regular numbers + + + align:start position:0% +operations right with regular numbers +you can do whatever you want that's + + align:start position:0% +you can do whatever you want that's + + + align:start position:0% +you can do whatever you want that's +obvious and with these points you can + + align:start position:0% +obvious and with these points you can + + + align:start position:0% +obvious and with these points you can +add them subtract them and when you mix + + align:start position:0% +add them subtract them and when you mix + + + align:start position:0% +add them subtract them and when you mix +you can multiply and divide and that's + + align:start position:0% +you can multiply and divide and that's + + + align:start position:0% +you can multiply and divide and that's +it okay any questions so far you don't + + align:start position:0% +it okay any questions so far you don't + + + align:start position:0% +it okay any questions so far you don't +you don't have to worry too much about + + align:start position:0% +you don't have to worry too much about + + + align:start position:0% +you don't have to worry too much about +the curves and all the math and stuff + + align:start position:0% +the curves and all the math and stuff + + + align:start position:0% +the curves and all the math and stuff +but you just sort of say okay here's my + + align:start position:0% +but you just sort of say okay here's my + + + align:start position:0% +but you just sort of say okay here's my +sort of toolbox here's what I can do + + align:start position:0% +sort of toolbox here's what I can do + + + align:start position:0% +sort of toolbox here's what I can do +okay any questions good so now what we + + align:start position:0% +okay any questions good so now what we + + + align:start position:0% +okay any questions good so now what we +can do is we can define a one way + + align:start position:0% +can do is we can define a one way + + + align:start position:0% +can do is we can define a one way +function sort of like a hash function + + align:start position:0% +function sort of like a hash function + + + align:start position:0% +function sort of like a hash function +sort of like multiplying P times Q to + + align:start position:0% +sort of like multiplying P times Q to + + + align:start position:0% +sort of like multiplying P times Q to +get n what we will need in addition to + + align:start position:0% +get n what we will need in addition to + + + align:start position:0% +get n what we will need in addition to +this is everyone picks some point on the + + align:start position:0% +this is everyone picks some point on the + + + align:start position:0% +this is everyone picks some point on the +curve and we call it G and it's random + + align:start position:0% +curve and we call it G and it's random + + + align:start position:0% +curve and we call it G and it's random +and we want it to be somewhat verifiably + + align:start position:0% +and we want it to be somewhat verifiably + + + align:start position:0% +and we want it to be somewhat verifiably +random we just all have to agree on a + + align:start position:0% +random we just all have to agree on a + + + align:start position:0% +random we just all have to agree on a +point and we'll call this the generator + + align:start position:0% +point and we'll call this the generator + + + align:start position:0% +point and we'll call this the generator +point another property is that if you + + align:start position:0% +point another property is that if you + + + align:start position:0% +point another property is that if you +keep since it's all modulo this number + + align:start position:0% +keep since it's all modulo this number + + + align:start position:0% +keep since it's all modulo this number +if B is too big you'll sort of wrap + + align:start position:0% +if B is too big you'll sort of wrap + + + align:start position:0% +if B is too big you'll sort of wrap +around right because it's all modulo + + align:start position:0% +around right because it's all modulo + + + align:start position:0% +around right because it's all modulo +let's like n so it's called the + + align:start position:0% +let's like n so it's called the + + + align:start position:0% +let's like n so it's called the +generator point because and every point + + align:start position:0% +generator point because and every point + + + align:start position:0% +generator point because and every point +on the curve can be one if you keep you + + align:start position:0% +on the curve can be one if you keep you + + + align:start position:0% +on the curve can be one if you keep you +know say 2g 3G 4G 5g eventually you'll + + align:start position:0% +know say 2g 3G 4G 5g eventually you'll + + + align:start position:0% +know say 2g 3G 4G 5g eventually you'll +get back to G right it's all finite okay + + align:start position:0% +get back to G right it's all finite okay + + + align:start position:0% +get back to G right it's all finite okay +so does anyone have an idea okay how + + align:start position:0% +so does anyone have an idea okay how + + + align:start position:0% +so does anyone have an idea okay how +would we make some cool one-way function + + align:start position:0% +would we make some cool one-way function + + + align:start position:0% +would we make some cool one-way function +given these operations and the fact that + + align:start position:0% +given these operations and the fact that + + + align:start position:0% +given these operations and the fact that +we have an agreed upon point it's not + + align:start position:0% +we have an agreed upon point it's not + + + align:start position:0% +we have an agreed upon point it's not +super obvious but it's actually fairly + + align:start position:0% +super obvious but it's actually fairly + + + align:start position:0% +super obvious but it's actually fairly +straightforward once you see it + + align:start position:0% + + + + align:start position:0% + +any ideas yeah scaler yep yep okay so + + align:start position:0% +any ideas yeah scaler yep yep okay so + + + align:start position:0% +any ideas yeah scaler yep yep okay so +your private key let's say you private + + align:start position:0% +your private key let's say you private + + + align:start position:0% +your private key let's say you private +private key lowercase a it's just some + + align:start position:0% +private key lowercase a it's just some + + + align:start position:0% +private key lowercase a it's just some +256 bit random number scaler exactly the + + align:start position:0% +256 bit random number scaler exactly the + + + align:start position:0% +256 bit random number scaler exactly the +same as you know it's 32 bytes like in a + + align:start position:0% +same as you know it's 32 bytes like in a + + + align:start position:0% +same as you know it's 32 bytes like in a +LAN port signature and your public key + + align:start position:0% +LAN port signature and your public key + + + align:start position:0% +LAN port signature and your public key +is just eight times G and your public + + align:start position:0% +is just eight times G and your public + + + align:start position:0% +is just eight times G and your public +key is now a point on a curve we're + + align:start position:0% +key is now a point on a curve we're + + + align:start position:0% +key is now a point on a curve we're +gonna call it uppercase a and you have a + + align:start position:0% +gonna call it uppercase a and you have a + + + align:start position:0% +gonna call it uppercase a and you have a +32 by x-coordinate right because the the + + align:start position:0% +32 by x-coordinate right because the the + + + align:start position:0% +32 by x-coordinate right because the the +x dimension is 256 bits 32 byte + + align:start position:0% +x dimension is 256 bits 32 byte + + + align:start position:0% +x dimension is 256 bits 32 byte +y-coordinate so it's 64 bytes pretty + + align:start position:0% +y-coordinate so it's 64 bytes pretty + + + align:start position:0% +y-coordinate so it's 64 bytes pretty +small anyone have a another quick + + align:start position:0% +small anyone have a another quick + + + align:start position:0% +small anyone have a another quick +optimization on how you could reduce + + align:start position:0% +optimization on how you could reduce + + + align:start position:0% +optimization on how you could reduce +this so like there's a lot of + + align:start position:0% +this so like there's a lot of + + + align:start position:0% +this so like there's a lot of +optimization going on in like all these + + align:start position:0% +optimization going on in like all these + + + align:start position:0% +optimization going on in like all these +different cryptocurrency systems because + + align:start position:0% +different cryptocurrency systems because + + + align:start position:0% +different cryptocurrency systems because +they don't scale too well but any idea + + align:start position:0% +they don't scale too well but any idea + + + align:start position:0% +they don't scale too well but any idea +of how to get that down you could so you + + align:start position:0% +of how to get that down you could so you + + + align:start position:0% +of how to get that down you could so you +can hash it keep making them 32 bytes + + align:start position:0% +can hash it keep making them 32 bytes + + + align:start position:0% +can hash it keep making them 32 bytes +there's a cooler there's a more sort of + + align:start position:0% +there's a cooler there's a more sort of + + + align:start position:0% +there's a cooler there's a more sort of +useful way because but if you hash it + + align:start position:0% +useful way because but if you hash it + + + align:start position:0% +useful way because but if you hash it +you still have to reveal it later right + + align:start position:0% +you still have to reveal it later right + + + align:start position:0% +you still have to reveal it later right +so like it helps making a funky hash and + + align:start position:0% +so like it helps making a funky hash and + + + align:start position:0% +so like it helps making a funky hash and +that's that's what Bitcoin did initially + + align:start position:0% +that's that's what Bitcoin did initially + + + align:start position:0% +that's that's what Bitcoin did initially +is you'd have the 64 byte public keys + + align:start position:0% +is you'd have the 64 byte public keys + + + align:start position:0% +is you'd have the 64 byte public keys +and then you'd sent to the hash and then + + align:start position:0% +and then you'd sent to the hash and then + + + align:start position:0% +and then you'd sent to the hash and then +there's a nicer way any ideas okay so + + align:start position:0% +there's a nicer way any ideas okay so + + + align:start position:0% +there's a nicer way any ideas okay so +the thing is its symmetric right so the + + align:start position:0% +the thing is its symmetric right so the + + + align:start position:0% +the thing is its symmetric right so the +curve is symmetric about the y axis + + align:start position:0% +curve is symmetric about the y axis + + + align:start position:0% +curve is symmetric about the y axis +or sorry x axis any ideas and then let + + align:start position:0% +or sorry x axis any ideas and then let + + + align:start position:0% +or sorry x axis any ideas and then let +them figure out exactly where it is + + align:start position:0% +them figure out exactly where it is + + + align:start position:0% +them figure out exactly where it is +right so you can encode the x coordinate + + align:start position:0% +right so you can encode the x coordinate + + + align:start position:0% +right so you can encode the x coordinate +only and one bit for Y and then you're + + align:start position:0% +only and one bit for Y and then you're + + + align:start position:0% +only and one bit for Y and then you're +down to 33 bytes it's a little annoying + + align:start position:0% +down to 33 bytes it's a little annoying + + + align:start position:0% +down to 33 bytes it's a little annoying +because the 33 bytes well one of those + + align:start position:0% +because the 33 bytes well one of those + + + align:start position:0% +because the 33 bytes well one of those +bytes is gonna be like empty they're + + align:start position:0% +bytes is gonna be like empty they're + + + align:start position:0% +bytes is gonna be like empty they're +just gonna have one bit in it for like + + align:start position:0% +just gonna have one bit in it for like + + + align:start position:0% +just gonna have one bit in it for like +up or down but whatever um so you can do + + align:start position:0% +up or down but whatever um so you can do + + + align:start position:0% +up or down but whatever um so you can do +that and that's also really cool + + align:start position:0% +that and that's also really cool + + + align:start position:0% +that and that's also really cool +okay any questions so far probably but I + + align:start position:0% +okay any questions so far probably but I + + + align:start position:0% +okay any questions so far probably but I +don't think would be smaller I think + + align:start position:0% +don't think would be smaller I think + + + align:start position:0% +don't think would be smaller I think +you'd have to probably have the same + + align:start position:0% +you'd have to probably have the same + + + align:start position:0% +you'd have to probably have the same +size if you use some other coordinate + + align:start position:0% +size if you use some other coordinate + + + align:start position:0% +size if you use some other coordinate +system + + align:start position:0% +system + + + align:start position:0% +system +I haven't eivin yeah you could sort of + + align:start position:0% +I haven't eivin yeah you could sort of + + + align:start position:0% +I haven't eivin yeah you could sort of +encode a slope and you say it intersects + + align:start position:0% +encode a slope and you say it intersects + + + align:start position:0% +encode a slope and you say it intersects +and it's at the slope and which side of + + align:start position:0% +and it's at the slope and which side of + + + align:start position:0% +and it's at the slope and which side of +the axis you probably could I think it + + align:start position:0% +the axis you probably could I think it + + + align:start position:0% +the axis you probably could I think it +would end up the same size but yeah then + + align:start position:0% +would end up the same size but yeah then + + + align:start position:0% +would end up the same size but yeah then +but it might be faster for some things + + align:start position:0% +but it might be faster for some things + + + align:start position:0% +but it might be faster for some things +there's all sorts of different encoding + + align:start position:0% + + + + align:start position:0% + +yeah so you might not be on the curve + + align:start position:0% +yeah so you might not be on the curve + + + align:start position:0% +yeah so you might not be on the curve +but there's a similar problem here where + + align:start position:0% +but there's a similar problem here where + + + align:start position:0% +but there's a similar problem here where +it might not be on the curve you can + + align:start position:0% +it might not be on the curve you can + + + align:start position:0% +it might not be on the curve you can +encode a point that's also off the curve + + align:start position:0% +encode a point that's also off the curve + + + align:start position:0% +encode a point that's also off the curve +and so when you actually get a public + + align:start position:0% +and so when you actually get a public + + + align:start position:0% +and so when you actually get a public +key like over the wire in these systems + + align:start position:0% +key like over the wire in these systems + + + align:start position:0% +key like over the wire in these systems +the first thing you usually do is make + + align:start position:0% +the first thing you usually do is make + + + align:start position:0% +the first thing you usually do is make +sure like this is a valid public key and + + align:start position:0% +sure like this is a valid public key and + + + align:start position:0% +sure like this is a valid public key and +it's actually on the curve because + + align:start position:0% +it's actually on the curve because + + + align:start position:0% +it's actually on the curve because +there's a lot of points that aren't and + + align:start position:0% +there's a lot of points that aren't and + + + align:start position:0% +there's a lot of points that aren't and +sometimes you can screw around with the + + align:start position:0% +sometimes you can screw around with the + + + align:start position:0% +sometimes you can screw around with the +code that way yeah okay so scalar + + align:start position:0% +code that way yeah okay so scalar + + + align:start position:0% +code that way yeah okay so scalar +multiplication a times G is basically + + align:start position:0% +multiplication a times G is basically + + + align:start position:0% +multiplication a times G is basically +break it out as G Plus G Plus G Plus G + + align:start position:0% +break it out as G Plus G Plus G Plus G + + + align:start position:0% +break it out as G Plus G Plus G Plus G +Plus G a times and G Plus G is find the + + align:start position:0% +Plus G a times and G Plus G is find the + + + align:start position:0% +Plus G a times and G Plus G is find the +tangent of G and then find the + + align:start position:0% +tangent of G and then find the + + + align:start position:0% +tangent of G and then find the +intersection right so this is G this is + + align:start position:0% +intersection right so this is G this is + + + align:start position:0% +intersection right so this is G this is +to G right tangent intersect and then go + + align:start position:0% +to G right tangent intersect and then go + + + align:start position:0% +to G right tangent intersect and then go +to the negation and so you just do that + + align:start position:0% +to the negation and so you just do that + + + align:start position:0% +to the negation and so you just do that +a bazillion times however since you can + + align:start position:0% +a bazillion times however since you can + + + align:start position:0% +a bazillion times however since you can +find two G and then you can double to G + + align:start position:0% +find two G and then you can double to G + + + align:start position:0% +find two G and then you can double to G +to get for G and double for G to get a + + align:start position:0% +to get for G and double for G to get a + + + align:start position:0% +to get for G and double for G to get a +chi you can come up with like powers of + + align:start position:0% +chi you can come up with like powers of + + + align:start position:0% +chi you can come up with like powers of +two of G and then add those powers of + + align:start position:0% +two of G and then add those powers of + + + align:start position:0% +two of G and then add those powers of +two to do a much more efficient addition + + align:start position:0% +two to do a much more efficient addition + + + align:start position:0% +two to do a much more efficient addition +so that you can practically make you + + align:start position:0% +so that you can practically make you + + + align:start position:0% +so that you can practically make you +know his little a is gonna be some huge + + align:start position:0% +know his little a is gonna be some huge + + + align:start position:0% +know his little a is gonna be some huge +you know 50 digit you know decimal 50 + + align:start position:0% +you know 50 digit you know decimal 50 + + + align:start position:0% +you know 50 digit you know decimal 50 +digit number or whatever so you're gonna + + align:start position:0% +digit number or whatever so you're gonna + + + align:start position:0% +digit number or whatever so you're gonna +have to do this like sort of two four + + align:start position:0% +have to do this like sort of two four + + + align:start position:0% +have to do this like sort of two four +six eight binary expansion and then add + + align:start position:0% +six eight binary expansion and then add + + + align:start position:0% +six eight binary expansion and then add +them all up okay so yeah + + align:start position:0% +them all up okay so yeah + + + align:start position:0% +them all up okay so yeah +if you're chucking everything into into + + align:start position:0% +if you're chucking everything into into + + + align:start position:0% +if you're chucking everything into into +some green says to get to get these your + + align:start position:0% +some green says to get to get these your + + + align:start position:0% +some green says to get to get these your +district I think opinions curve yes it + + align:start position:0% +district I think opinions curve yes it + + + align:start position:0% +district I think opinions curve yes it +feels like you do a 32-bit you use + + align:start position:0% +feels like you do a 32-bit you use + + + align:start position:0% +feels like you do a 32-bit you use +basically originally you should be able + + align:start position:0% +basically originally you should be able + + + align:start position:0% +basically originally you should be able +to get all the way down to 32 bits yeah + + align:start position:0% + + + + align:start position:0% + +or you can do some a little what you can + + align:start position:0% +or you can do some a little what you can + + + align:start position:0% +or you can do some a little what you can +do is you can just say look I'm only + + align:start position:0% +do is you can just say look I'm only + + + align:start position:0% +do is you can just say look I'm only +going to allow public keys that are on + + align:start position:0% +going to allow public keys that are on + + + align:start position:0% +going to allow public keys that are on +the top you know on the positive have + + align:start position:0% +the top you know on the positive have + + + align:start position:0% +the top you know on the positive have +positive Y component and everything else + + align:start position:0% +positive Y component and everything else + + + align:start position:0% +positive Y component and everything else +is disallowed + + align:start position:0% +is disallowed + + + align:start position:0% +is disallowed +you could you could have that as like a + + align:start position:0% +you could you could have that as like a + + + align:start position:0% +you could you could have that as like a +rule of your system and then you can get + + align:start position:0% +rule of your system and then you can get + + + align:start position:0% +rule of your system and then you can get +rid of the Y bit but the thing is some + + align:start position:0% +rid of the Y bit but the thing is some + + + align:start position:0% +rid of the Y bit but the thing is some +of the things do you know the y + + align:start position:0% +of the things do you know the y + + + align:start position:0% +of the things do you know the y +coordinate does affect some of the + + align:start position:0% +coordinate does affect some of the + + + align:start position:0% +coordinate does affect some of the +things like signatures things that + + align:start position:0% +things like signatures things that + + + align:start position:0% +things like signatures things that +you'll later use so you can just say + + align:start position:0% +you'll later use so you can just say + + + align:start position:0% +you'll later use so you can just say +okay look implicitly Y bit is positive + + align:start position:0% +okay look implicitly Y bit is positive + + + align:start position:0% +okay look implicitly Y bit is positive +and you you lose them like one bit of + + align:start position:0% +and you you lose them like one bit of + + + align:start position:0% +and you you lose them like one bit of +security because there is a difference + + align:start position:0% +security because there is a difference + + + align:start position:0% +security because there is a difference +between the positive and negative thing + + align:start position:0% +between the positive and negative thing + + + align:start position:0% +between the positive and negative thing +if you're doing signing oh but yeah it's + + align:start position:0% +if you're doing signing oh but yeah it's + + + align:start position:0% +if you're doing signing oh but yeah it's +it's so some systems do do that and + + align:start position:0% +it's so some systems do do that and + + + align:start position:0% +it's so some systems do do that and +makes things easier there's some signing + + align:start position:0% +makes things easier there's some signing + + + align:start position:0% +makes things easier there's some signing +systems that do that okay I'm gonna go + + align:start position:0% +systems that do that okay I'm gonna go + + + align:start position:0% +systems that do that okay I'm gonna go +to the next part + + align:start position:0% + + + + align:start position:0% + +there's ECDSA is used in Bitcoin I'm + + align:start position:0% +there's ECDSA is used in Bitcoin I'm + + + align:start position:0% +there's ECDSA is used in Bitcoin I'm +actually not going to explain it it's a + + align:start position:0% +actually not going to explain it it's a + + + align:start position:0% +actually not going to explain it it's a +worse signature system so the reason why + + align:start position:0% +worse signature system so the reason why + + + align:start position:0% +worse signature system so the reason why +this was used was the better system was + + align:start position:0% +this was used was the better system was + + + align:start position:0% +this was used was the better system was +patented and so there's a clearer sort + + align:start position:0% +patented and so there's a clearer sort + + + align:start position:0% +patented and so there's a clearer sort +of more like obvious cleaner more + + align:start position:0% +of more like obvious cleaner more + + + align:start position:0% +of more like obvious cleaner more +powerful + + align:start position:0% +powerful + + + align:start position:0% +powerful +signature system that was patented by + + align:start position:0% +signature system that was patented by + + + align:start position:0% +signature system that was patented by +this german guy + + align:start position:0% +this german guy + + + align:start position:0% +this german guy +Klaus noir and so no one used it or + + align:start position:0% +Klaus noir and so no one used it or + + + align:start position:0% +Klaus noir and so no one used it or +maybe a few people used it but in + + align:start position:0% +maybe a few people used it but in + + + align:start position:0% +maybe a few people used it but in +general with like open-source things and + + align:start position:0% +general with like open-source things and + + + align:start position:0% +general with like open-source things and +and like web standards patents are sort + + align:start position:0% +and like web standards patents are sort + + + align:start position:0% +and like web standards patents are sort +of really hard to work with and so all + + align:start position:0% +of really hard to work with and so all + + + align:start position:0% +of really hard to work with and so all +the cryptographers said well we'll make + + align:start position:0% +the cryptographers said well we'll make + + + align:start position:0% +the cryptographers said well we'll make +this other system that's different + + align:start position:0% +this other system that's different + + + align:start position:0% +this other system that's different +enough that it doesn't infringe on the + + align:start position:0% +enough that it doesn't infringe on the + + + align:start position:0% +enough that it doesn't infringe on the +patent and it's kind of ugly it does + + align:start position:0% +patent and it's kind of ugly it does + + + align:start position:0% +patent and it's kind of ugly it does +work as a signature scheme + + align:start position:0% +work as a signature scheme + + + align:start position:0% +work as a signature scheme +but actually I'm going to explain the + + align:start position:0% +but actually I'm going to explain the + + + align:start position:0% +but actually I'm going to explain the +Schnoor signatures which make a lot more + + align:start position:0% +Schnoor signatures which make a lot more + + + align:start position:0% +Schnoor signatures which make a lot more +sense are easier to understand and + + align:start position:0% +sense are easier to understand and + + + align:start position:0% +sense are easier to understand and +manipulate and the patent has expired + + align:start position:0% +manipulate and the patent has expired + + + align:start position:0% +manipulate and the patent has expired +so we can all use it and it will + + align:start position:0% +so we can all use it and it will + + + align:start position:0% +so we can all use it and it will +probably be going into Bitcoin and some + + align:start position:0% +probably be going into Bitcoin and some + + + align:start position:0% +probably be going into Bitcoin and some +some cryptocurrencies use our signatures + + align:start position:0% +some cryptocurrencies use our signatures + + + align:start position:0% +some cryptocurrencies use our signatures +I think Manero uses a snore like + + align:start position:0% +I think Manero uses a snore like + + + align:start position:0% +I think Manero uses a snore like +signature but Bitcoin will probably be + + align:start position:0% +signature but Bitcoin will probably be + + + align:start position:0% +signature but Bitcoin will probably be +it will be they'll be putting it into a + + align:start position:0% +it will be they'll be putting it into a + + + align:start position:0% +it will be they'll be putting it into a +Bitcoin in the next year or so so all + + align:start position:0% +Bitcoin in the next year or so so all + + + align:start position:0% +Bitcoin in the next year or so so all +these things will be much more + + align:start position:0% +these things will be much more + + + align:start position:0% +these things will be much more +applicable and you can use them and you + + align:start position:0% +applicable and you can use them and you + + + align:start position:0% +applicable and you can use them and you +can and there's code out you can use + + align:start position:0% +can and there's code out you can use + + + align:start position:0% +can and there's code out you can use +them now okay yeah sorry patent expired + + align:start position:0% +them now okay yeah sorry patent expired + + + align:start position:0% +them now okay yeah sorry patent expired +free to use the better I'll go that must + + align:start position:0% +free to use the better I'll go that must + + + align:start position:0% +free to use the better I'll go that must +not be named so yeah we're maybe not + + align:start position:0% +not be named so yeah we're maybe not + + + align:start position:0% +not be named so yeah we're maybe not +like people don't call it Schnoor + + align:start position:0% +like people don't call it Schnoor + + + align:start position:0% +like people don't call it Schnoor +signature as much because it's like well + + align:start position:0% +signature as much because it's like well + + + align:start position:0% +signature as much because it's like well +this is the guy who prevented us from + + align:start position:0% +this is the guy who prevented us from + + + align:start position:0% +this is the guy who prevented us from +using this for 20 years and like and and + + align:start position:0% +using this for 20 years and like and and + + + align:start position:0% +using this for 20 years and like and and +there's modifications to it okay so the + + align:start position:0% +there's modifications to it okay so the + + + align:start position:0% +there's modifications to it okay so the +elliptic curve signature for lack of a + + align:start position:0% +elliptic curve signature for lack of a + + + align:start position:0% +elliptic curve signature for lack of a +better name and this is something of a + + align:start position:0% +better name and this is something of a + + + align:start position:0% +better name and this is something of a +simplification and there's like reading + + align:start position:0% +simplification and there's like reading + + + align:start position:0% +simplification and there's like reading +about how you can really do it the right + + align:start position:0% +about how you can really do it the right + + + align:start position:0% +about how you can really do it the right +way but this does give you the right + + align:start position:0% +way but this does give you the right + + + align:start position:0% +way but this does give you the right +idea and for a single signer this is + + align:start position:0% +idea and for a single signer this is + + + align:start position:0% +idea and for a single signer this is +also this is secure and it works but + + align:start position:0% +also this is secure and it works but + + + align:start position:0% +also this is secure and it works but +later things you might want to actually + + align:start position:0% +later things you might want to actually + + + align:start position:0% +later things you might want to actually +adds other stuff so the idea is you've + + align:start position:0% +adds other stuff so the idea is you've + + + align:start position:0% +adds other stuff so the idea is you've +got your message M right same as in + + align:start position:0% +got your message M right same as in + + + align:start position:0% +got your message M right same as in +Lamport same as in RSA you've got a + + align:start position:0% +Lamport same as in RSA you've got a + + + align:start position:0% +Lamport same as in RSA you've got a +message m in a private key lowercase a + + align:start position:0% +message m in a private key lowercase a + + + align:start position:0% +message m in a private key lowercase a +and your public key is a times G like we + + align:start position:0% +and your public key is a times G like we + + + align:start position:0% +and your public key is a times G like we +said and then when you want to sign you + + align:start position:0% +said and then when you want to sign you + + + align:start position:0% +said and then when you want to sign you +actually make a one-time use key pair + + align:start position:0% +actually make a one-time use key pair + + + align:start position:0% +actually make a one-time use key pair +for the signature only and they usually + + align:start position:0% +for the signature only and they usually + + + align:start position:0% +for the signature only and they usually +call that K and K is a new random number + + align:start position:0% +call that K and K is a new random number + + + align:start position:0% +call that K and K is a new random number +it's the private key and you're gonna + + align:start position:0% +it's the private key and you're gonna + + + align:start position:0% +it's the private key and you're gonna +multiply it by G and so R is sort and + + align:start position:0% +multiply it by G and so R is sort and + + + align:start position:0% +multiply it by G and so R is sort and +they call this R I don't know why they + + align:start position:0% +they call this R I don't know why they + + + align:start position:0% +they call this R I don't know why they +use these letters but anyway K times G + + align:start position:0% +use these letters but anyway K times G + + + align:start position:0% +use these letters but anyway K times G +is our R is sort of the other public key + + align:start position:0% +is our R is sort of the other public key + + + align:start position:0% +is our R is sort of the other public key +you're using just for this signature and + + align:start position:0% +you're using just for this signature and + + + align:start position:0% +you're using just for this signature and +then the signature itself is quite + + align:start position:0% +then the signature itself is quite + + + align:start position:0% +then the signature itself is quite +straightforward as the signer you + + align:start position:0% +straightforward as the signer you + + + align:start position:0% +straightforward as the signer you +compute S which is K this new private + + align:start position:0% +compute S which is K this new private + + + align:start position:0% +compute S which is K this new private +key you just made up - the hash of your + + align:start position:0% +key you just made up - the hash of your + + + align:start position:0% +key you just made up - the hash of your +message concatenated with are this + + align:start position:0% +message concatenated with are this + + + align:start position:0% +message concatenated with are this +public key so you encode the public key + + align:start position:0% +public key so you encode the public key + + + align:start position:0% +public key so you encode the public key +and 33 bytes stick it in there + + align:start position:0% +and 33 bytes stick it in there + + + align:start position:0% +and 33 bytes stick it in there +multiplied by a your your you normal + + align:start position:0% +multiplied by a your your you normal + + + align:start position:0% +multiplied by a your your you normal +private key and then your signature is + + align:start position:0% +private key and then your signature is + + + align:start position:0% +private key and then your signature is +the pair the R point and the S scalar + + align:start position:0% +the pair the R point and the S scalar + + + align:start position:0% +the pair the R point and the S scalar +this is you know a little bit of a bunch + + align:start position:0% +this is you know a little bit of a bunch + + + align:start position:0% +this is you know a little bit of a bunch +of the process but it's actually not too + + align:start position:0% +of the process but it's actually not too + + + align:start position:0% +of the process but it's actually not too +bad right this is scalar 32 bytes you + + align:start position:0% +bad right this is scalar 32 bytes you + + + align:start position:0% +bad right this is scalar 32 bytes you +made up the hash when you you know this + + align:start position:0% +made up the hash when you you know this + + + align:start position:0% +made up the hash when you you know this +is a message also gonna be however long + + align:start position:0% +is a message also gonna be however long + + + align:start position:0% +is a message also gonna be however long +this is 33 bytes you concatenate them + + align:start position:0% +this is 33 bytes you concatenate them + + + align:start position:0% +this is 33 bytes you concatenate them +together hash you end up with another 32 + + align:start position:0% +together hash you end up with another 32 + + + align:start position:0% +together hash you end up with another 32 +byte scalar you multiply those two + + align:start position:0% +byte scalar you multiply those two + + + align:start position:0% +byte scalar you multiply those two +scalars so actually there's no the only + + align:start position:0% +scalars so actually there's no the only + + + align:start position:0% +scalars so actually there's no the only +elliptic curve operation here is + + align:start position:0% +elliptic curve operation here is + + + align:start position:0% +elliptic curve operation here is +calculating what are s when you're + + align:start position:0% +calculating what are s when you're + + + align:start position:0% +calculating what are s when you're +actually calculating s this is all just + + align:start position:0% +actually calculating s this is all just + + + align:start position:0% +actually calculating s this is all just +scalar so it's very fast so in terms of + + align:start position:0% +scalar so it's very fast so in terms of + + + align:start position:0% +scalar so it's very fast so in terms of +practical computer stuff doing these + + align:start position:0% +practical computer stuff doing these + + + align:start position:0% +practical computer stuff doing these +operations is a little bit on the slow + + align:start position:0% +operations is a little bit on the slow + + + align:start position:0% +operations is a little bit on the slow +side because you're doing those point + + align:start position:0% +side because you're doing those point + + + align:start position:0% +side because you're doing those point +additions quite a number of times so + + align:start position:0% +additions quite a number of times so + + + align:start position:0% +additions quite a number of times so +come so a decent code can and like a + + align:start position:0% +come so a decent code can and like a + + + align:start position:0% +come so a decent code can and like a +decent CPU can do 10 like foul on the + + align:start position:0% +decent CPU can do 10 like foul on the + + + align:start position:0% +decent CPU can do 10 like foul on the +order of thousands of these types of + + align:start position:0% +order of thousands of these types of + + + align:start position:0% +order of thousands of these types of +operations per second which is decent + + align:start position:0% +operations per second which is decent + + + align:start position:0% +operations per second which is decent +you know like you can do a decent amount + + align:start position:0% +you know like you can do a decent amount + + + align:start position:0% +you know like you can do a decent amount +but it is kind of slow and it's it's + + align:start position:0% +but it is kind of slow and it's it's + + + align:start position:0% +but it is kind of slow and it's it's +considerably slower than hash functions + + align:start position:0% +considerably slower than hash functions + + + align:start position:0% +considerably slower than hash functions +you can do you know a million iterations + + align:start position:0% +you can do you know a million iterations + + + align:start position:0% +you can do you know a million iterations +of hash function for a second on a core + + align:start position:0% +of hash function for a second on a core + + + align:start position:0% +of hash function for a second on a core +or you can do maybe a thousand or two + + align:start position:0% +or you can do maybe a thousand or two + + + align:start position:0% +or you can do maybe a thousand or two +thousand of this kind of thing + + align:start position:0% +thousand of this kind of thing + + + align:start position:0% +thousand of this kind of thing +so still pretty fast but slower and so + + align:start position:0% +so still pretty fast but slower and so + + + align:start position:0% +so still pretty fast but slower and so +this signing procedure this takes a bit + + align:start position:0% +this signing procedure this takes a bit + + + align:start position:0% +this signing procedure this takes a bit +of time this takes actually very little + + align:start position:0% +of time this takes actually very little + + + align:start position:0% +of time this takes actually very little +time because you're just subtracting and + + align:start position:0% +time because you're just subtracting and + + + align:start position:0% +time because you're just subtracting and +multiplying scalar you know 32 bytes + + align:start position:0% +multiplying scalar you know 32 bytes + + + align:start position:0% +multiplying scalar you know 32 bytes +scalar integers which is much faster ok + + align:start position:0% +scalar integers which is much faster ok + + + align:start position:0% +scalar integers which is much faster ok +so does this make sense we'll go a + + align:start position:0% +so does this make sense we'll go a + + + align:start position:0% +so does this make sense we'll go a +little bit about how you can't Forge + + align:start position:0% +little bit about how you can't Forge + + + align:start position:0% +little bit about how you can't Forge +this okay sorry first verification sorry + + align:start position:0% +this okay sorry first verification sorry + + + align:start position:0% +this okay sorry first verification sorry +so how would you if anyone knows how I + + align:start position:0% +so how would you if anyone knows how I + + + align:start position:0% +so how would you if anyone knows how I +can think about how would you verify + + align:start position:0% +can think about how would you verify + + + align:start position:0% +can think about how would you verify +this right I know I know their public + + align:start position:0% +this right I know I know their public + + + align:start position:0% +this right I know I know their public +key capital a which is a you know a + + align:start position:0% +key capital a which is a you know a + + + align:start position:0% +key capital a which is a you know a +little a times G and then they're giving + + align:start position:0% +little a times G and then they're giving + + + align:start position:0% +little a times G and then they're giving +me a message m and they're giving me a + + align:start position:0% +me a message m and they're giving me a + + + align:start position:0% +me a message m and they're giving me a +signature which is R and s and they've + + align:start position:0% +signature which is R and s and they've + + + align:start position:0% +signature which is R and s and they've +computed it this way I can't verify this + + align:start position:0% +computed it this way I can't verify this + + + align:start position:0% +computed it this way I can't verify this +equation myself because I don't know + + align:start position:0% +equation myself because I don't know + + + align:start position:0% +equation myself because I don't know +what K is I don't know what little a is + + align:start position:0% +what K is I don't know what little a is + + + align:start position:0% +what K is I don't know what little a is +right I'm just given R + + align:start position:0% +right I'm just given R + + + align:start position:0% +right I'm just given R +s M + + align:start position:0% +s M + + + align:start position:0% +s M +and so how would I verify this so the + + align:start position:0% +and so how would I verify this so the + + + align:start position:0% +and so how would I verify this so the +basic idea yeah you're right + + align:start position:0% +basic idea yeah you're right + + + align:start position:0% +basic idea yeah you're right +multiply this side by G then you also + + align:start position:0% +multiply this side by G then you also + + + align:start position:0% +multiply this side by G then you also +have to multiply the other side by G + + align:start position:0% +have to multiply the other side by G + + + align:start position:0% +have to multiply the other side by G +right so you say okay well I'm gonna + + align:start position:0% +right so you say okay well I'm gonna + + + align:start position:0% +right so you say okay well I'm gonna +multiply it I I'm as the verifier I've + + align:start position:0% +multiply it I I'm as the verifier I've + + + align:start position:0% +multiply it I I'm as the verifier I've +got our got s I multiply F by G and now + + align:start position:0% +got our got s I multiply F by G and now + + + align:start position:0% +got our got s I multiply F by G and now +I have to multiply this side by G and + + align:start position:0% +I have to multiply this side by G and + + + align:start position:0% +I have to multiply this side by G and +what will that look like + + align:start position:0% +what will that look like + + + align:start position:0% +what will that look like +well what's K times G all right what's + + align:start position:0% +well what's K times G all right what's + + + align:start position:0% +well what's K times G all right what's +little a times G big a so so yeah I want + + align:start position:0% +little a times G big a so so yeah I want + + + align:start position:0% +little a times G big a so so yeah I want +to verify I want to verify this that + + align:start position:0% +to verify I want to verify this that + + + align:start position:0% +to verify I want to verify this that +this equation was used right s equals K + + align:start position:0% +this equation was used right s equals K + + + align:start position:0% +this equation was used right s equals K +minus this hash times little a multiply + + align:start position:0% +minus this hash times little a multiply + + + align:start position:0% +minus this hash times little a multiply +both sides by G I get s times G equals + + align:start position:0% +both sides by G I get s times G equals + + + align:start position:0% +both sides by G I get s times G equals +to K times G minus the hash thing times + + align:start position:0% +to K times G minus the hash thing times + + + align:start position:0% +to K times G minus the hash thing times +little a times G this is big a this is + + align:start position:0% +little a times G this is big a this is + + + align:start position:0% +little a times G this is big a this is +our hey now I know everything here as + + align:start position:0% +our hey now I know everything here as + + + align:start position:0% +our hey now I know everything here as +the verifier right I know what s time + + align:start position:0% +the verifier right I know what s time + + + align:start position:0% +the verifier right I know what s time +she is I know what R is I know what big + + align:start position:0% +she is I know what R is I know what big + + + align:start position:0% +she is I know what R is I know what big +a is I know what's going into this hash + + align:start position:0% +a is I know what's going into this hash + + + align:start position:0% +a is I know what's going into this hash +function and so I just say okay well you + + align:start position:0% +function and so I just say okay well you + + + align:start position:0% +function and so I just say okay well you +know I rearranged it a little and say is + + align:start position:0% +know I rearranged it a little and say is + + + align:start position:0% +know I rearranged it a little and say is +R equal to this and if it is that's a + + align:start position:0% +R equal to this and if it is that's a + + + align:start position:0% +R equal to this and if it is that's a +good signature if it's not it's not a + + align:start position:0% +good signature if it's not it's not a + + + align:start position:0% +good signature if it's not it's not a +good signature any questions about this + + align:start position:0% +good signature any questions about this + + + align:start position:0% +good signature any questions about this +is this + + align:start position:0% + + + + align:start position:0% + +make sense mostly so for the + + align:start position:0% +make sense mostly so for the + + + align:start position:0% +make sense mostly so for the +verification there's a bit it's a bit + + align:start position:0% +verification there's a bit it's a bit + + + align:start position:0% +verification there's a bit it's a bit +more CPU intense right you're you're + + align:start position:0% +more CPU intense right you're you're + + + align:start position:0% +more CPU intense right you're you're +given a scaler you multiply by G you're + + align:start position:0% +given a scaler you multiply by G you're + + + align:start position:0% +given a scaler you multiply by G you're +also you also have to multiply a this is + + align:start position:0% +also you also have to multiply a this is + + + align:start position:0% +also you also have to multiply a this is +actually more costly you have to + + align:start position:0% +actually more costly you have to + + + align:start position:0% +actually more costly you have to +multiply a by this hash the reason + + align:start position:0% +multiply a by this hash the reason + + + align:start position:0% +multiply a by this hash the reason +that's more costly it's still a scalar + + align:start position:0% +that's more costly it's still a scalar + + + align:start position:0% +that's more costly it's still a scalar +times a point + + align:start position:0% +times a point + + + align:start position:0% +times a point +the thing is since G is used for + + align:start position:0% +the thing is since G is used for + + + align:start position:0% +the thing is since G is used for +multiplying a lot you pre compute all + + align:start position:0% +multiplying a lot you pre compute all + + + align:start position:0% +multiplying a lot you pre compute all +sorts of coefficients times G and you + + align:start position:0% +sorts of coefficients times G and you + + + align:start position:0% +sorts of coefficients times G and you +store them like in RAM or in your like + + align:start position:0% +store them like in RAM or in your like + + + align:start position:0% +store them like in RAM or in your like +CPU somewhere so so multiplying by G is + + align:start position:0% +CPU somewhere so so multiplying by G is + + + align:start position:0% +CPU somewhere so so multiplying by G is +a little bit faster because you you do + + align:start position:0% +a little bit faster because you you do + + + align:start position:0% +a little bit faster because you you do +it a lot you can pre-compute a lot + + align:start position:0% +it a lot you can pre-compute a lot + + + align:start position:0% +it a lot you can pre-compute a lot +whereas multiplying by a is different + + align:start position:0% +whereas multiplying by a is different + + + align:start position:0% +whereas multiplying by a is different +each time for all the different + + align:start position:0% +each time for all the different + + + align:start position:0% +each time for all the different +signatures so this is a little bit + + align:start position:0% +signatures so this is a little bit + + + align:start position:0% +signatures so this is a little bit +slower in general so it's a little bit + + align:start position:0% +slower in general so it's a little bit + + + align:start position:0% +slower in general so it's a little bit +it takes a little bit more CPU time to + + align:start position:0% +it takes a little bit more CPU time to + + + align:start position:0% +it takes a little bit more CPU time to +verify a signature than to create one + + align:start position:0% +verify a signature than to create one + + + align:start position:0% +verify a signature than to create one +something like twice as much but still + + align:start position:0% +something like twice as much but still + + + align:start position:0% +something like twice as much but still +you can do this pretty fast on a modern + + align:start position:0% +you can do this pretty fast on a modern + + + align:start position:0% +you can do this pretty fast on a modern +computer you can do thousands of these a + + align:start position:0% +computer you can do thousands of these a + + + align:start position:0% +computer you can do thousands of these a +second okay any questions so far and + + align:start position:0% +second okay any questions so far and + + + align:start position:0% +second okay any questions so far and +I'll go a little bit into why this is + + align:start position:0% +I'll go a little bit into why this is + + + align:start position:0% +I'll go a little bit into why this is +not for Jim all right so I want to forge + + align:start position:0% +not for Jim all right so I want to forge + + + align:start position:0% +not for Jim all right so I want to forge +a signature well why don't I make up a + + align:start position:0% +a signature well why don't I make up a + + + align:start position:0% +a signature well why don't I make up a +kit you know I don't know little a but + + align:start position:0% +kit you know I don't know little a but + + + align:start position:0% +kit you know I don't know little a but +why don't I make up a K and compute SNR + + align:start position:0% +why don't I make up a K and compute SNR + + + align:start position:0% +why don't I make up a K and compute SNR +but I need a right so I'm gonna say okay + + align:start position:0% +but I need a right so I'm gonna say okay + + + align:start position:0% +but I need a right so I'm gonna say okay +I this is the equation I want I'll just + + align:start position:0% +I this is the equation I want I'll just + + + align:start position:0% +I this is the equation I want I'll just +make up my own K and make up my own K s + + align:start position:0% +make up my own K and make up my own K s + + + align:start position:0% +make up my own K and make up my own K s +that solved that you know that's the + + align:start position:0% +that solved that you know that's the + + + align:start position:0% +that solved that you know that's the +satisfy this without a I really can't + + align:start position:0% +satisfy this without a I really can't + + + align:start position:0% +satisfy this without a I really can't +make a valid s right I can make + + align:start position:0% +make a valid s right I can make + + + align:start position:0% +make a valid s right I can make +something up here but I can't compute it + + align:start position:0% +something up here but I can't compute it + + + align:start position:0% +something up here but I can't compute it +cuz I don't know here right I can try + + align:start position:0% +cuz I don't know here right I can try + + + align:start position:0% +cuz I don't know here right I can try +keep I can try to grind through hash + + align:start position:0% +keep I can try to grind through hash + + + align:start position:0% +keep I can try to grind through hash +functions but it won't work the basic + + align:start position:0% +functions but it won't work the basic + + + align:start position:0% +functions but it won't work the basic +problem is if I make up an S and solve + + align:start position:0% +problem is if I make up an S and solve + + + align:start position:0% +problem is if I make up an S and solve +for R right I can say well I know what R + + align:start position:0% +for R right I can say well I know what R + + + align:start position:0% +for R right I can say well I know what R +is but the thing is are is in the hash + + align:start position:0% +is but the thing is are is in the hash + + + align:start position:0% +is but the thing is are is in the hash +function as well it's the it's the + + align:start position:0% +function as well it's the it's the + + + align:start position:0% +function as well it's the it's the +one-wayness of the hash function that + + align:start position:0% +one-wayness of the hash function that + + + align:start position:0% +one-wayness of the hash function that +actually breaks this right so let me + + align:start position:0% +actually breaks this right so let me + + + align:start position:0% +actually breaks this right so let me +solve for R well R is the hash of M + + align:start position:0% +solve for R well R is the hash of M + + + align:start position:0% +solve for R well R is the hash of M +our times a plus s times G if I can come + + align:start position:0% +our times a plus s times G if I can come + + + align:start position:0% +our times a plus s times G if I can come +you know if I can come up with a random + + align:start position:0% +you know if I can come up with a random + + + align:start position:0% +you know if I can come up with a random +with a valid are here I can do this + + align:start position:0% +with a valid are here I can do this + + + align:start position:0% +with a valid are here I can do this +the problem is R is defined by the hash + + align:start position:0% +the problem is R is defined by the hash + + + align:start position:0% +the problem is R is defined by the hash +of R in this case I can't compute this + + align:start position:0% +of R in this case I can't compute this + + + align:start position:0% +of R in this case I can't compute this +and I can't cancel this out right so if + + align:start position:0% +and I can't cancel this out right so if + + + align:start position:0% +and I can't cancel this out right so if +you can see this like okay I need to + + align:start position:0% +you can see this like okay I need to + + + align:start position:0% +you can see this like okay I need to +solve for R well but it's already in + + align:start position:0% +solve for R well but it's already in + + + align:start position:0% +solve for R well but it's already in +here like I'm stuck if I don't know K I + + align:start position:0% +here like I'm stuck if I don't know K I + + + align:start position:0% +here like I'm stuck if I don't know K I +can't come up with a signature either + + align:start position:0% + + + + align:start position:0% + +one okay there is one sort of foot gun + + align:start position:0% +one okay there is one sort of foot gun + + + align:start position:0% +one okay there is one sort of foot gun +with EC signatures if you use the same R + + align:start position:0% +with EC signatures if you use the same R + + + align:start position:0% +with EC signatures if you use the same R +value for different signatures with the + + align:start position:0% +value for different signatures with the + + + align:start position:0% +value for different signatures with the +same pump key you reveal your private + + align:start position:0% +same pump key you reveal your private + + + align:start position:0% +same pump key you reveal your private +key so K has to be random and new every + + align:start position:0% +key so K has to be random and new every + + + align:start position:0% +key so K has to be random and new every +time I you you mean that if you if you + + align:start position:0% +time I you you mean that if you if you + + + align:start position:0% +time I you you mean that if you if you +look through the question you'll see how + + align:start position:0% +look through the question you'll see how + + + align:start position:0% +look through the question you'll see how +you can solve if you know if you have to + + align:start position:0% +you can solve if you know if you have to + + + align:start position:0% +you can solve if you know if you have to +live the same case with differences you + + align:start position:0% +live the same case with differences you + + + align:start position:0% +live the same case with differences you +can solve for K and then once you solve + + align:start position:0% +can solve for K and then once you solve + + + align:start position:0% +can solve for K and then once you solve +for K given given this if you know what + + align:start position:0% +for K given given this if you know what + + + align:start position:0% +for K given given this if you know what +K is you can find what little a is right + + align:start position:0% +K is you can find what little a is right + + + align:start position:0% +K is you can find what little a is right +as a verifier you can say well I know + + align:start position:0% +as a verifier you can say well I know + + + align:start position:0% +as a verifier you can say well I know +you you gave me s that's part of the + + align:start position:0% +you you gave me s that's part of the + + + align:start position:0% +you you gave me s that's part of the +signature I know this whole coefficient + + align:start position:0% +signature I know this whole coefficient + + + align:start position:0% +signature I know this whole coefficient +if I know K I can solve for a little a + + align:start position:0% +if I know K I can solve for a little a + + + align:start position:0% +if I know K I can solve for a little a +by dividing this out so always use a new + + align:start position:0% +by dividing this out so always use a new + + + align:start position:0% +by dividing this out so always use a new +K value there have been many cases where + + align:start position:0% +K value there have been many cases where + + + align:start position:0% +K value there have been many cases where +people don't probably the most famous + + align:start position:0% +people don't probably the most famous + + + align:start position:0% +people don't probably the most famous +one is Playstation 3 used ECDSA and they + + align:start position:0% +one is Playstation 3 used ECDSA and they + + + align:start position:0% +one is Playstation 3 used ECDSA and they +used a fixed K value for signing all + + align:start position:0% +used a fixed K value for signing all + + + align:start position:0% +used a fixed K value for signing all +their code and that allowed people to + + align:start position:0% +their code and that allowed people to + + + align:start position:0% +their code and that allowed people to +calculate their private keys and then + + align:start position:0% +calculate their private keys and then + + + align:start position:0% +calculate their private keys and then +run pirated games that was actually the + + align:start position:0% +run pirated games that was actually the + + + align:start position:0% +run pirated games that was actually the +first time I learned it occurs like 2010 + + align:start position:0% +first time I learned it occurs like 2010 + + + align:start position:0% +first time I learned it occurs like 2010 +or sup so actually there's there's kind + + align:start position:0% +or sup so actually there's there's kind + + + align:start position:0% +or sup so actually there's there's kind +of interesting tutorials written by like + + align:start position:0% +of interesting tutorials written by like + + + align:start position:0% +of interesting tutorials written by like +the hackers who broke a Playstation 3 + + align:start position:0% +the hackers who broke a Playstation 3 + + + align:start position:0% +the hackers who broke a Playstation 3 +about how this works and that's what I + + align:start position:0% +about how this works and that's what I + + + align:start position:0% +about how this works and that's what I +first write about it + + align:start position:0% +first write about it + + + align:start position:0% +first write about it +okay we're almost out of time any + + align:start position:0% +okay we're almost out of time any + + + align:start position:0% +okay we're almost out of time any +questions about this stuff so far okay + + align:start position:0% +questions about this stuff so far okay + + + align:start position:0% +questions about this stuff so far okay +so other so this is + + align:start position:0% +so other so this is + + + align:start position:0% +so other so this is +this is a signature algorithm it's like + + align:start position:0% +this is a signature algorithm it's like + + + align:start position:0% +this is a signature algorithm it's like +okay fine this works I can sign same as + + align:start position:0% +okay fine this works I can sign same as + + + align:start position:0% +okay fine this works I can sign same as +Lamport signatures same as RSA what's + + align:start position:0% +Lamport signatures same as RSA what's + + + align:start position:0% +Lamport signatures same as RSA what's +really nice about the elliptic curve + + align:start position:0% +really nice about the elliptic curve + + + align:start position:0% +really nice about the elliptic curve +stuff is you can do more than just + + align:start position:0% +stuff is you can do more than just + + + align:start position:0% +stuff is you can do more than just +signatures there's all sorts of fun + + align:start position:0% +signatures there's all sorts of fun + + + align:start position:0% +signatures there's all sorts of fun +things you can do and it seems like a + + align:start position:0% +things you can do and it seems like a + + + align:start position:0% +things you can do and it seems like a +fairly unexplored area in that like I've + + align:start position:0% +fairly unexplored area in that like I've + + + align:start position:0% +fairly unexplored area in that like I've +found fun things that you can do that + + align:start position:0% +found fun things that you can do that + + + align:start position:0% +found fun things that you can do that +are you guess our novel and like I don't + + align:start position:0% +are you guess our novel and like I don't + + + align:start position:0% +are you guess our novel and like I don't +I'm not an expert on this at all it's + + align:start position:0% +I'm not an expert on this at all it's + + + align:start position:0% +I'm not an expert on this at all it's +just that it's a fairly new area of + + align:start position:0% +just that it's a fairly new area of + + + align:start position:0% +just that it's a fairly new area of +research and like how to do cool Bitcoin + + align:start position:0% +research and like how to do cool Bitcoin + + + align:start position:0% +research and like how to do cool Bitcoin +e cryptocurrency things with these + + align:start position:0% +e cryptocurrency things with these + + + align:start position:0% +e cryptocurrency things with these +curves and points and stuff so I'll go + + align:start position:0% +curves and points and stuff so I'll go + + + align:start position:0% +curves and points and stuff so I'll go +through a couple fun things you can do + + align:start position:0% +through a couple fun things you can do + + + align:start position:0% +through a couple fun things you can do +fun with points okay so I'm not using an + + align:start position:0% +fun with points okay so I'm not using an + + + align:start position:0% +fun with points okay so I'm not using an +asterisk so I'm just you know B times G + + align:start position:0% +asterisk so I'm just you know B times G + + + align:start position:0% +asterisk so I'm just you know B times G +so let's say Alice has a public key a + + align:start position:0% +so let's say Alice has a public key a + + + align:start position:0% +so let's say Alice has a public key a +Bob has a public key B right which is + + align:start position:0% +Bob has a public key B right which is + + + align:start position:0% +Bob has a public key B right which is +little a times G or little B times G + + align:start position:0% +little a times G or little B times G + + + align:start position:0% +little a times G or little B times G +well this is weird little a times big B + + align:start position:0% +well this is weird little a times big B + + + align:start position:0% +well this is weird little a times big B +Alice's private key multiplied by Bob's + + align:start position:0% +Alice's private key multiplied by Bob's + + + align:start position:0% +Alice's private key multiplied by Bob's +public key you can do that right is + + align:start position:0% +public key you can do that right is + + + align:start position:0% +public key you can do that right is +equal to Bob's private key times Alice's + + align:start position:0% +equal to Bob's private key times Alice's + + + align:start position:0% +equal to Bob's private key times Alice's +public key right it's commutative the + + align:start position:0% +public key right it's commutative the + + + align:start position:0% +public key right it's commutative the +multiplication is commutative that's + + align:start position:0% +multiplication is commutative that's + + + align:start position:0% +multiplication is commutative that's +weird right it's just a times G times B + + align:start position:0% +weird right it's just a times G times B + + + align:start position:0% +weird right it's just a times G times B +which is the same or you know it doesn't + + align:start position:0% +which is the same or you know it doesn't + + + align:start position:0% +which is the same or you know it doesn't +matter the order it's the same as B + + align:start position:0% +matter the order it's the same as B + + + align:start position:0% +matter the order it's the same as B +times G times a which is the same as a + + align:start position:0% +times G times a which is the same as a + + + align:start position:0% +times G times a which is the same as a +times B times G and let's call that C + + align:start position:0% +times B times G and let's call that C + + + align:start position:0% +times B times G and let's call that C +see this is called the diffie-hellman + + align:start position:0% +see this is called the diffie-hellman + + + align:start position:0% +see this is called the diffie-hellman +key exchange point Diffie and Hellman + + align:start position:0% +key exchange point Diffie and Hellman + + + align:start position:0% +key exchange point Diffie and Hellman +are two also like late 70s PhD students + + align:start position:0% +are two also like late 70s PhD students + + + align:start position:0% +are two also like late 70s PhD students +who came up with all this cool stuff no + + align:start position:0% +who came up with all this cool stuff no + + + align:start position:0% +who came up with all this cool stuff no +wait if he was a PhD student Hellman was + + align:start position:0% +wait if he was a PhD student Hellman was + + + align:start position:0% +wait if he was a PhD student Hellman was +his advisor I don't remember + + align:start position:0% +his advisor I don't remember + + + align:start position:0% +his advisor I don't remember +anyway they came up with this idea and + + align:start position:0% +anyway they came up with this idea and + + + align:start position:0% +anyway they came up with this idea and +this is this is like a shared point what + + align:start position:0% +this is this is like a shared point what + + + align:start position:0% +this is this is like a shared point what +would this be useful for it's actually + + align:start position:0% +would this be useful for it's actually + + + align:start position:0% +would this be useful for it's actually +super useful and can you think of like + + align:start position:0% +super useful and can you think of like + + + align:start position:0% +super useful and can you think of like +oh okay we can do this we can compute C + + align:start position:0% +oh okay we can do this we can compute C + + + align:start position:0% +oh okay we can do this we can compute C +why would we want to do that like any + + align:start position:0% +why would we want to do that like any + + + align:start position:0% +why would we want to do that like any +applications you can think of yeah + + align:start position:0% + + + + align:start position:0% + +yeah it's really cool to share keys so + + align:start position:0% +yeah it's really cool to share keys so + + + align:start position:0% +yeah it's really cool to share keys so +this is also done if you have a web + + align:start position:0% +this is also done if you have a web + + + align:start position:0% +this is also done if you have a web +browser I think it's all looked a curve + + align:start position:0% +browser I think it's all looked a curve + + + align:start position:0% +browser I think it's all looked a curve +diffie-hellman now mostly but if you + + align:start position:0% +diffie-hellman now mostly but if you + + + align:start position:0% +diffie-hellman now mostly but if you +have a web browser and you go to a + + align:start position:0% +have a web browser and you go to a + + + align:start position:0% +have a web browser and you go to a +website this is happening basically for + + align:start position:0% +website this is happening basically for + + + align:start position:0% +website this is happening basically for +every HTTP request because you can use + + align:start position:0% +every HTTP request because you can use + + + align:start position:0% +every HTTP request because you can use +see as they sort of shared key and + + align:start position:0% +see as they sort of shared key and + + + align:start position:0% +see as they sort of shared key and +encrypt things with it the idea is a can + + align:start position:0% +encrypt things with it the idea is a can + + + align:start position:0% +encrypt things with it the idea is a can +be public big a can be public big beep + + align:start position:0% +be public big a can be public big beep + + + align:start position:0% +be public big a can be public big beep +can be public point C will not be public + + align:start position:0% +can be public point C will not be public + + + align:start position:0% +can be public point C will not be public +the only way to compute it is to know + + align:start position:0% +the only way to compute it is to know + + + align:start position:0% +the only way to compute it is to know +either a is private you know Alice's + + align:start position:0% +either a is private you know Alice's + + + align:start position:0% +either a is private you know Alice's +private key little a or Bob's private + + align:start position:0% +private key little a or Bob's private + + + align:start position:0% +private key little a or Bob's private +key little B even though you can see you + + align:start position:0% +key little B even though you can see you + + + align:start position:0% +key little B even though you can see you +can see the public keys you can't + + align:start position:0% +can see the public keys you can't + + + align:start position:0% +can see the public keys you can't +compute C by from just the public keys + + align:start position:0% +compute C by from just the public keys + + + align:start position:0% +compute C by from just the public keys +right because big a times big B that's + + align:start position:0% +right because big a times big B that's + + + align:start position:0% +right because big a times big B that's +not defined and that would that wouldn't + + align:start position:0% +not defined and that would that wouldn't + + + align:start position:0% +not defined and that would that wouldn't +even be that like you can't multiply the + + align:start position:0% +even be that like you can't multiply the + + + align:start position:0% +even be that like you can't multiply the +points you have to multiply the point by + + align:start position:0% +points you have to multiply the point by + + + align:start position:0% +points you have to multiply the point by +a scalar and since you don't know the + + align:start position:0% +a scalar and since you don't know the + + + align:start position:0% +a scalar and since you don't know the +scalars from viewing this exchange + + align:start position:0% +scalars from viewing this exchange + + + align:start position:0% +scalars from viewing this exchange +you can't compute C but Alice and Bob + + align:start position:0% +you can't compute C but Alice and Bob + + + align:start position:0% +you can't compute C but Alice and Bob +can both compute C so this is really + + align:start position:0% +can both compute C so this is really + + + align:start position:0% +can both compute C so this is really +useful you can compute C you can use it + + align:start position:0% +useful you can compute C you can use it + + + align:start position:0% +useful you can compute C you can use it +for encryption you can use it to prove + + align:start position:0% +for encryption you can use it to prove + + + align:start position:0% +for encryption you can use it to prove +you are who you say you are you can use + + align:start position:0% +you are who you say you are you can use + + + align:start position:0% +you are who you say you are you can use +it as like an interactive verification + + align:start position:0% +it as like an interactive verification + + + align:start position:0% +it as like an interactive verification +where you say okay I'm gonna I'm Bob I'm + + align:start position:0% +where you say okay I'm gonna I'm Bob I'm + + + align:start position:0% +where you say okay I'm gonna I'm Bob I'm +gonna make a random point I'm gonna give + + align:start position:0% +gonna make a random point I'm gonna give + + + align:start position:0% +gonna make a random point I'm gonna give +that to you prove you know your private + + align:start position:0% +that to you prove you know your private + + + align:start position:0% +that to you prove you know your private +key little a by telling me what C is + + align:start position:0% +key little a by telling me what C is + + + align:start position:0% +key little a by telling me what C is +right so I can I can I can make like a + + align:start position:0% +right so I can I can I can make like a + + + align:start position:0% +right so I can I can I can make like a +random key here give it to you you + + align:start position:0% +random key here give it to you you + + + align:start position:0% +random key here give it to you you +return see I verify that that's the + + align:start position:0% +return see I verify that that's the + + + align:start position:0% +return see I verify that that's the +right C I say okay well you must know + + align:start position:0% +right C I say okay well you must know + + + align:start position:0% +right C I say okay well you must know +little a you haven't shown me little a + + align:start position:0% +little a you haven't shown me little a + + + align:start position:0% +little a you haven't shown me little a +but I even that you know it so proof of + + align:start position:0% +but I even that you know it so proof of + + + align:start position:0% +but I even that you know it so proof of +knowledge of the private key so you can + + align:start position:0% +knowledge of the private key so you can + + + align:start position:0% +knowledge of the private key so you can +use that for like logins instead of + + align:start position:0% +use that for like logins instead of + + + align:start position:0% +use that for like logins instead of +passwords and it's like much simpler + + align:start position:0% +passwords and it's like much simpler + + + align:start position:0% +passwords and it's like much simpler +than a signature so that's really cool + + align:start position:0% +than a signature so that's really cool + + + align:start position:0% +than a signature so that's really cool +all sorts of things you can do with that + + align:start position:0% +all sorts of things you can do with that + + + align:start position:0% +all sorts of things you can do with that +the last part you can have fun with + + align:start position:0% +the last part you can have fun with + + + align:start position:0% +the last part you can have fun with +points and I use this in my software so + + align:start position:0% +points and I use this in my software so + + + align:start position:0% +points and I use this in my software so +you say ok well there's a public key a + + align:start position:0% +you say ok well there's a public key a + + + align:start position:0% +you say ok well there's a public key a +there's a public key B + + align:start position:0% +there's a public key B + + + align:start position:0% +there's a public key B +and well we'll define D as the sum of + + align:start position:0% +and well we'll define D as the sum of + + + align:start position:0% +and well we'll define D as the sum of +these two public keys the thing is if + + align:start position:0% +these two public keys the thing is if + + + align:start position:0% +these two public keys the thing is if +it's if you're selling these two public + + align:start position:0% +it's if you're selling these two public + + + align:start position:0% +it's if you're selling these two public +keys it's community it's the same as + + align:start position:0% +keys it's community it's the same as + + + align:start position:0% +keys it's community it's the same as +saying the sum of the two private keys + + align:start position:0% +saying the sum of the two private keys + + + align:start position:0% +saying the sum of the two private keys +times G right a times G Plus B times G + + align:start position:0% +times G right a times G Plus B times G + + + align:start position:0% +times G right a times G Plus B times G +is the same as a plus B times G which is + + align:start position:0% +is the same as a plus B times G which is + + + align:start position:0% +is the same as a plus B times G which is +another really cool property so what if + + align:start position:0% +another really cool property so what if + + + align:start position:0% +another really cool property so what if +I compute this prior to this public key + + align:start position:0% +I compute this prior to this public key + + + align:start position:0% +I compute this prior to this public key +D and I say I want a signature from + + align:start position:0% +D and I say I want a signature from + + + align:start position:0% +D and I say I want a signature from +public key D you can and you saw the + + align:start position:0% +public key D you can and you saw the + + + align:start position:0% +public key D you can and you saw the +private key little D which can sign for + + align:start position:0% +private key little D which can sign for + + + align:start position:0% +private key little D which can sign for +this is just little a plus a little B so + + align:start position:0% +this is just little a plus a little B so + + + align:start position:0% +this is just little a plus a little B so +you can make a combined key and then + + align:start position:0% +you can make a combined key and then + + + align:start position:0% +you can make a combined key and then +either party you know Alice has a little + + align:start position:0% +either party you know Alice has a little + + + align:start position:0% +either party you know Alice has a little +a Bob has little B and they could reveal + + align:start position:0% +a Bob has little B and they could reveal + + + align:start position:0% +a Bob has little B and they could reveal +it to each other and allow the other + + align:start position:0% +it to each other and allow the other + + + align:start position:0% +it to each other and allow the other +person to make a signature with D later + + align:start position:0% +person to make a signature with D later + + + align:start position:0% +person to make a signature with D later +this is this is yet like I use this in + + align:start position:0% +this is this is yet like I use this in + + + align:start position:0% +this is this is yet like I use this in +the lightening up network software I've + + align:start position:0% +the lightening up network software I've + + + align:start position:0% +the lightening up network software I've +had where basically you say look we'll + + align:start position:0% +had where basically you say look we'll + + + align:start position:0% +had where basically you say look we'll +compute D and like I can give you the + + align:start position:0% +compute D and like I can give you the + + + align:start position:0% +compute D and like I can give you the +private key right I know I'm you know + + align:start position:0% +private key right I know I'm you know + + + align:start position:0% +private key right I know I'm you know +I'm Bob and I say okay here's here's + + align:start position:0% +I'm Bob and I say okay here's here's + + + align:start position:0% +I'm Bob and I say okay here's here's +point be yours point a we add them + + align:start position:0% +point be yours point a we add them + + + align:start position:0% +point be yours point a we add them +together and then Alice I if I give you + + align:start position:0% +together and then Alice I if I give you + + + align:start position:0% +together and then Alice I if I give you +my private key now you can sign but I + + align:start position:0% +my private key now you can sign but I + + + align:start position:0% +my private key now you can sign but I +can't write so I'll like sort of give + + align:start position:0% +can't write so I'll like sort of give + + + align:start position:0% +can't write so I'll like sort of give +you the private key to D from some + + align:start position:0% +you the private key to D from some + + + align:start position:0% +you the private key to D from some +information I have or you could give me + + align:start position:0% +information I have or you could give me + + + align:start position:0% +information I have or you could give me +the private key to D by sharing a little + + align:start position:0% +the private key to D by sharing a little + + + align:start position:0% +the private key to D by sharing a little +a with me so this is another useful + + align:start position:0% +a with me so this is another useful + + + align:start position:0% +a with me so this is another useful +thing where you can have something where + + align:start position:0% +thing where you can have something where + + + align:start position:0% +thing where you can have something where +both parties know that neither party can + + align:start position:0% +both parties know that neither party can + + + align:start position:0% +both parties know that neither party can +sign unless they give them something and + + align:start position:0% +sign unless they give them something and + + + align:start position:0% +sign unless they give them something and +you can use that for like Bitcoin + + align:start position:0% +you can use that for like Bitcoin + + + align:start position:0% +you can use that for like Bitcoin +addresses things like that this is like + + align:start position:0% +addresses things like that this is like + + + align:start position:0% +addresses things like that this is like +sort of before you even get to + + align:start position:0% +sort of before you even get to + + + align:start position:0% +sort of before you even get to +signatures you can share keys and stuff + + align:start position:0% +signatures you can share keys and stuff + + + align:start position:0% +signatures you can share keys and stuff +there's a there's all sorts of super fun + + align:start position:0% +there's a there's all sorts of super fun + + + align:start position:0% +there's a there's all sorts of super fun +things you can do with these points and + + align:start position:0% +things you can do with these points and + + + align:start position:0% +things you can do with these points and +curves and systems multi signatures is + + align:start position:0% +curves and systems multi signatures is + + + align:start position:0% +curves and systems multi signatures is +like the the reading I put a link to a + + align:start position:0% +like the the reading I put a link to a + + + align:start position:0% +like the the reading I put a link to a +PDF file it's like very recent and like + + align:start position:0% +PDF file it's like very recent and like + + + align:start position:0% +PDF file it's like very recent and like +kind of overkill and like over my head + + align:start position:0% +kind of overkill and like over my head + + + align:start position:0% +kind of overkill and like over my head +as well but you can do signatures where + + align:start position:0% +as well but you can do signatures where + + + align:start position:0% +as well but you can do signatures where +you a great the signatures but there's + + align:start position:0% +you a great the signatures but there's + + + align:start position:0% +you a great the signatures but there's +ways to sort of say okay well I'm gonna + + align:start position:0% +ways to sort of say okay well I'm gonna + + + align:start position:0% +ways to sort of say okay well I'm gonna +add all these are points and I'm gonna + + align:start position:0% +add all these are points and I'm gonna + + + align:start position:0% +add all these are points and I'm gonna +add all these s points and I can have + + align:start position:0% +add all these s points and I can have + + + align:start position:0% +add all these s points and I can have +signatures that are + + align:start position:0% +signatures that are + + + align:start position:0% +signatures that are +from a bunch of different people that + + align:start position:0% +from a bunch of different people that + + + align:start position:0% +from a bunch of different people that +collapse into the same size as a single + + align:start position:0% +collapse into the same size as a single + + + align:start position:0% +collapse into the same size as a single +signature and I can verify that they're + + align:start position:0% +signature and I can verify that they're + + + align:start position:0% +signature and I can verify that they're +all signing the same thing or possibly + + align:start position:0% +all signing the same thing or possibly + + + align:start position:0% +all signing the same thing or possibly +that they're all signing different + + align:start position:0% +that they're all signing different + + + align:start position:0% +that they're all signing different +things so I have you know ten different + + align:start position:0% +things so I have you know ten different + + + align:start position:0% +things so I have you know ten different +signatures from different people signing + + align:start position:0% +signatures from different people signing + + + align:start position:0% +signatures from different people signing +different messages but I can add up all + + align:start position:0% +different messages but I can add up all + + + align:start position:0% +different messages but I can add up all +the s values I have to keep the R values + + align:start position:0% +the s values I have to keep the R values + + + align:start position:0% +the s values I have to keep the R values +but now these ten signatures instead of + + align:start position:0% +but now these ten signatures instead of + + + align:start position:0% +but now these ten signatures instead of +being 64 bytes each are more like 32 + + align:start position:0% +being 64 bytes each are more like 32 + + + align:start position:0% +being 64 bytes each are more like 32 +bytes each and there's one extra 32 byte + + align:start position:0% +bytes each and there's one extra 32 byte + + + align:start position:0% +bytes each and there's one extra 32 byte +value for all of them + + align:start position:0% +value for all of them + + + align:start position:0% +value for all of them +so there's a lot of really cool ways you + + align:start position:0% +so there's a lot of really cool ways you + + + align:start position:0% +so there's a lot of really cool ways you +can like combine things make things + + align:start position:0% +can like combine things make things + + + align:start position:0% +can like combine things make things +smaller make things really versatile + + align:start position:0% +smaller make things really versatile + + + align:start position:0% +smaller make things really versatile +where we can share keys things like that + + align:start position:0% +where we can share keys things like that + + + align:start position:0% +where we can share keys things like that +which you can't do with hash based + + align:start position:0% +which you can't do with hash based + + + align:start position:0% +which you can't do with hash based +signatures hash functions and so it's + + align:start position:0% +signatures hash functions and so it's + + + align:start position:0% +signatures hash functions and so it's +really fun one worry is that if quantum + + align:start position:0% +really fun one worry is that if quantum + + + align:start position:0% +really fun one worry is that if quantum +computers ever become really a thing all + + align:start position:0% +computers ever become really a thing all + + + align:start position:0% +computers ever become really a thing all +this stuff stops working all the + + align:start position:0% +this stuff stops working all the + + + align:start position:0% +this stuff stops working all the +elliptic curve stuff doesn't work + + align:start position:0% +elliptic curve stuff doesn't work + + + align:start position:0% +elliptic curve stuff doesn't work +anymore you can you can figure out what + + align:start position:0% +anymore you can you can figure out what + + + align:start position:0% +anymore you can you can figure out what +people's private keys are + + align:start position:0% +people's private keys are + + + align:start position:0% +people's private keys are +whereas hash stuff hash things like limp + + align:start position:0% +whereas hash stuff hash things like limp + + + align:start position:0% +whereas hash stuff hash things like limp +or signatures still work so there's some + + align:start position:0% +or signatures still work so there's some + + + align:start position:0% +or signatures still work so there's some +some talk of like hey we should sort of + + align:start position:0% +some talk of like hey we should sort of + + + align:start position:0% +some talk of like hey we should sort of +prepare for if that ever happens and + + align:start position:0% +prepare for if that ever happens and + + + align:start position:0% +prepare for if that ever happens and +make you know efficient effective hash + + align:start position:0% +make you know efficient effective hash + + + align:start position:0% +make you know efficient effective hash +based signatures and use them in + + align:start position:0% +based signatures and use them in + + + align:start position:0% +based signatures and use them in +something like Bitcoin or aetherium + + align:start position:0% +something like Bitcoin or aetherium + + + align:start position:0% +something like Bitcoin or aetherium +people haven't yet because the overhead + + align:start position:0% +people haven't yet because the overhead + + + align:start position:0% +people haven't yet because the overhead +is really high it's really big but and + + align:start position:0% +is really high it's really big but and + + + align:start position:0% +is really high it's really big but and +it's the the real thing is all these fun + + align:start position:0% +it's the the real thing is all these fun + + + align:start position:0% +it's the the real thing is all these fun +things might disappear in the next 10 20 + + align:start position:0% +things might disappear in the next 10 20 + + + align:start position:0% +things might disappear in the next 10 20 +years who knows but there's lots of cool + + align:start position:0% +years who knows but there's lots of cool + + + align:start position:0% +years who knows but there's lots of cool +stuff what do we do with this + + align:start position:0% +stuff what do we do with this + + + align:start position:0% +stuff what do we do with this +so we we're not gonna do anything yep in + + align:start position:0% +so we we're not gonna do anything yep in + + + align:start position:0% +so we we're not gonna do anything yep in +terms of problem sets it's a little hard + + align:start position:0% +terms of problem sets it's a little hard + + + align:start position:0% +terms of problem sets it's a little hard +to program it directly but there's + + align:start position:0% +to program it directly but there's + + + align:start position:0% +to program it directly but there's +libraries and the libraries have fairly + + align:start position:0% +libraries and the libraries have fairly + + + align:start position:0% +libraries and the libraries have fairly +easy use where it's like you know x G is + + align:start position:0% +easy use where it's like you know x G is + + + align:start position:0% +easy use where it's like you know x G is +a function and like x this point as a + + align:start position:0% +a function and like x this point as a + + + align:start position:0% +a function and like x this point as a +function so this is ground worth for + + align:start position:0% +function so this is ground worth for + + + align:start position:0% +function so this is ground worth for +cool stuff you can do and it's really + + align:start position:0% +cool stuff you can do and it's really + + + align:start position:0% +cool stuff you can do and it's really +nice because it's a new area and like + + align:start position:0% +nice because it's a new area and like + + + align:start position:0% +nice because it's a new area and like +I'm not an expert on this but I've come + + align:start position:0% +I'm not an expert on this but I've come + + + align:start position:0% +I'm not an expert on this but I've come +up with stuff that I don't know people + + align:start position:0% +up with stuff that I don't know people + + + align:start position:0% +up with stuff that I don't know people +have sighted me on and they're like yeah + + align:start position:0% +have sighted me on and they're like yeah + + + align:start position:0% +have sighted me on and they're like yeah +I guess no one thought of that before + + align:start position:0% +I guess no one thought of that before + + + align:start position:0% +I guess no one thought of that before +there's a lot of things there's one very + + align:start position:0% +there's a lot of things there's one very + + + align:start position:0% +there's a lot of things there's one very +recent one called taproot where it's + + align:start position:0% +recent one called taproot where it's + + + align:start position:0% +recent one called taproot where it's +like one line you're like oh yeah that + + align:start position:0% +like one line you're like oh yeah that + + + align:start position:0% +like one line you're like oh yeah that +works and it's just these sort of + + align:start position:0% +works and it's just these sort of + + + align:start position:0% +works and it's just these sort of +elliptic curve operations it's like yeah + + align:start position:0% +elliptic curve operations it's like yeah + + + align:start position:0% +elliptic curve operations it's like yeah +that works that's really useful how did + + align:start position:0% +that works that's really useful how did + + + align:start position:0% +that works that's really useful how did +it know one thing is that like it's one + + align:start position:0% +it know one thing is that like it's one + + + align:start position:0% +it know one thing is that like it's one +line like wow so there's just not a ton + + align:start position:0% +line like wow so there's just not a ton + + + align:start position:0% +line like wow so there's just not a ton +of people working on this kind of stuff + + align:start position:0% +of people working on this kind of stuff + + + align:start position:0% +of people working on this kind of stuff +and so it's kind of fun \ No newline at end of file diff --git a/0ZxeQqtAVl0.txt b/0ZxeQqtAVl0.txt new file mode 100644 index 0000000000000000000000000000000000000000..483abf05629c99940519b8d2dd03c8cc1bd7c971 --- /dev/null +++ b/0ZxeQqtAVl0.txt @@ -0,0 +1,1611 @@ +PROFESSOR: Let's talk about what +was probably the first + +energy producing system +that evolved. + +The thought is when the earth +first formed and the first + +primitive organisms, perhaps +resembling a present-day + +bacterium in some way came +out, there were a lot of + +organic compounds that had +been aided by lightning + +strikes and cosmic radiations +triggering chemical + +reactions and so on. + +So there was food around, but +they depleted those resources + +in the same way we're depleting +the petroleum + +resources right now. + +If life was going to continue, +somehow a way had to be found + +to make energy. + +Glycolysis, it looks kind +of complicated. + +It takes a molecule of sugar and +then there are a series of + +10 chemical reactions, each +catalyzed by a separate enzyme + +that give two molecules of this, +molecules of pyruvate, + +plus two ATPs, plus two NADHs. + +Which tells you there must +have been some kind of + +oxidation step as part of this +sequence of events, because + +electrons got taken off and +got stashed on this NADH. + +There are a couple of things +that are important about this. + +One is its a pathway. + +It evolved probably 3.7 billion +years ago or sometime, + +nobody really knows. + +But a long time ago. + +It's pretty much universal. + +Not perfectly so, but it's +in bacteria, it's in + +yeast, it's in humans. + +And another really important +thing is that it evolved early + +in the evolution of earth, so +it evolved when there was no + +oxygen around. + +So it's a way of making +energy from glucose in + +the absence of oxygen. + +Which is a really important +thing as you'll + +see as we go along. + +You're not going to have to +memorize this pathway. + +We'll give it to you +if you need it. + +But you're going to need to +understand its implications. + +And just let me point out +a couple of things. + +You're going to see a sequence +of 10 chemical transformations + +that in the end are going to +end up with a couple of + +pyruvates being produced. + +And I'll try to explain +to you why you + +should care about this. + +There's a concept that you're +familiar with, that if you + +want to make something and you +get a little start up company, + +what's the very first thing +you have to do? + +You actually have to +make an investment + +before you can get going. + +And you're out looking for +venture capital things. + +Well one of the odd things about +this, here's probably + +the first sequence of reactions +that arose on earth + +within some organism and enabled +that organism to make + +energy out of glucose. + +And look, the first thing +that happens. + +Trying to make ATP, the very +first thing it does is it + +spends an ATP. + +And it takes glucose, and it +makes glucose 6-phosphate. + +Go down a couple of steps. + +There's an enzyme that takes +another molecule of ATP. + +And now you've got this point. + +You're at fructose with +two phosphates on it. + +If this was your venture +capital, we'd say, guys, how + +about some product? + +Stop spending, stop +spending money. + +But at this point then, this +is a 6-carbon sugar. + +And it gets split into two +3-carbon compounds that are + +going back and forth. + +Oh I can see it. + +It's over there, OK. + +In equilibrium over here. + +And this particular 3-carbon +compound then + +goes on to be oxidized. + +You get the production +of NADH. + +And at that point, this molecule +has a lot of energy + +stored in it, and in the next +transformation this cell is + +able to make two ATPs. + +And it gets back the +initial investment. + +It goes all the way through +the rest of the pathway. + +And the very last step, you +get two more ATPs back. + +There's your net yield. + +So what you get out of this +are 4ATP+2NADH, and your + +investment was two ATPs. + +So your net 2ATP+NADH. + +Why is this cell going and +doing these initial + +investments? + +Well if we look at the changes +in free energy associated with + +what's going on, there's glucose +up in the upper left + +starting up there, and there's +pyruvate down there. + +So you're going energetically +downhill in the end. + +So this is a sequence of events +that, in principle, you + +should be able to get some +energy out of it. + +But for reasons that may seem +obscure to you at this point, + +before it gets to the point of +making energy, it undergoes a + +set of transformations that's +pushing the reaction. + +It requires the reactants to go +energetically uphill, i.e. + +in an unfavorable direction. + +So what the cell does is, by +coupling ATP hydrolysis to + +this step, it makes +that reaction go. + +Here's another unfavorable one +that makes that one go by + +coupling ATP hydrolysis to it. + +This is an uphill reaction, +but look over here. + +This is an immensely favorable +reaction that goes essentially + +to completion. + +It goes all the way. + +So that means this product is +just being continually taken + +out of the system, so the +equilibrium is basically being + +pulled over the edge by the +removal of that product. + +This is where the oxidation +takes place. + +You get the NADH made +right there. + +And it's finally down here +where you've got to lose. + +This transformation gives you +two ATPs and later there's + +another one. + +Let me just give you +a sense of why you + +get ATP at that step. + +The compound that you have +at that point is 1, 3 + +diphosphoglycerate. + +Or sometimes this is +called bis, is also + +used to describe this. + +But what is this compound? + +It's a 3-carbon compound. + +So glycerate is basically an +oxidized version of glycerol + +that has been oxidized up +to a carboxyl acid. + +So this is a mixed anhydride +between carboxyl acid and a + +phosphate ion. + +So that's a very reactive +and unstable compound. + +And the other thing that the +cell has succeeded in doing by + +all of these transformations +is it's got these two + +phosphates with all their +negative charges in. + +So this is a compound that would +very much like to move + +to a lower energy. + +So you can get rid of this +phosphate and move to an + +energy level, use that +energy to make ATP. + +And there's a similar kind of +logic that explains why you + +get energy out of the final +step when you look at it. + +So there's several points, I +guess, to make out of this. + +One is its pathway. + +None of these reactions make +any particular sense by + +themselves. + +You could have a cell that knew +how to do one of them and + +it would gain nothing. + +Unless you wanted to use the +product to make something. + +This thing only makes sense, +these reactions only make + +sense in the context of +this 10 step pathway. + +And each step in that pathway +we were looking at is + +catalyzed by a different +enzyme. + +So for an organism to pull this +off, the first one that + +did it had to collect in one +cell all 10 of those enzymes. + +And probably there is the reason +that this is such a + +complicated system. + +If you were sitting as a +designer you might be able to + +come up now with a more +efficient way to get ATP out. + +But what happened evolutionarily +was some bug + +somewhere got all of these +things together, and now + +suddenly it could make energy. + +So it had a huge advantage +over everybody else. + +And once it took over, that +system took over, then it + +became universal. + +Whether it was the best that +ever could be designed, it + +doesn't matter, because it +had an evolutionary edge. + +And that's so, to some extent, +we're looking at a living + +fossil, biochemical. + +But it's in bacteria, it's in +yeast, and it's going on + +inside of our body. + +Another principle that I think +you can see here, which I've + +been trying to say, is in this +case, the energy consuming + +reactions are driven by +coupling them to the + +hydrolysis of ATP. + +The cell spends a bit of its +energy money to get these + +intermediates, knowing +that it's invest-- + +well not knowing, but at least +conceptually anyway, knowing + +that it's going to get +its investment back. + +And then the reactions that +release energy are used to + +drive the synthesis of ATP. + +And you'll begin to see, we're +going to just talk about some + +other aspects of this +in just a minute. + +So, what do you think? + +You're the first bug and you've +got this and nobody + +else can do it, so you can +start charging away. + +What do we need to do? + +We just let this thing +cycle away? + +The stuff that I had up there, +is it going to work? + +There's a problem. + +Anybody see what +the problem is? + +We're making two molecules of +ATP and two molecules of NADH. + +Talk to the person beside you. + +Figure out why something +else has to happen. + +Go ahead. + +See if you've got any ideas. + +We're going to keep doing +this, over and + +over and over again. + +AUDIENCE: [INAUDIBLE]. + +Where's the first ATP? + +Where's the first ATP? + +PROFESSOR: OK, let's +imagine for the-- + +I don't think this process could +have invented ATP, it + +had to have been around, +because many of the + +enzymes used it. + +What else is being used +in this thing though? + +Did I hear NAD? + +To make this thing work, I have +to keep taking NADs out + +of my pocket and putting it in +the reaction, or it isn't + +going to go anywhere. + +So this isn't such a great +invention at the moment. + +We have to do something to get +the NADH back to NAD+ so we + +can do another molecule +of glucose. + +You guys see? + +Do you see this? + +This is really, really an +important consideration. + +So in order for cells to make +energy using glycolysis in the + +absence of oxygen, which is when +it evolved, they have to + +do something with that NADH or +it's only going to use up the + +few molecules of NAD+ in the +cell, and then it stops. + +And so there are two ways +that nature's figured. + +Major ways nature had figured +out how to do that. + +So here's a molecule +of pyruvate. + +I got an extra. + +Something was nagging at me +when I did this here. + +Sorry about that. + +It's always hard to see things +when you're up at the board. + +OK. + +Molecule of pyruvate. + +There's a couple of solutions +that have been arrived at. + +One is to take NADH, +2NADH, this is 2H+. + +Convert, make these back into +2NAD+, and to take those + +electrons and put them on the +pyruvate to give this + +molecule, which is +lactic acid. + +So by parking the electrons +there, the cell is able to + +recycle the NADH. + +And lactic acid, we've +run into that. + +That's why I showed you this +picture of yogurt. + +The lactobacilli that make +yogurt take the sugars that + +are present in milk and make +them into lactic acid. + +And what's interesting in +their case is they, even + +though there's oxygen around, +they don't do respiration, + +which you'll see you can +get more energy. + +They want it to get very acidic +because that prevents + +their competitors +from growing. + +And that's why you can leave +yogurt sitting out on the + +tabletop and it'll be OK +for quite a while. + +Whereas if you left some milk +or something it'll go bad + +almost right away. + +Here's another example of +when we run into it. + +When we do hard aerobic +exercise, when you're running + +or skating really hard, things +you see in the Olympics all + +the time, you deplete the oxygen +supply in your blood + +when you do hard anaerobic +exercise. + +And so the cells have the same +problem of regenerating NADH. + +The way they solve it is they +make the lactic acid. + +And that contributes to the sore +muscles you feel after + +you've done hard anaerobic +training. + +The other way of handling this +is to take the 2NADH plus two + +hydrogen ions to make it +into acetaldehyde, two + +acetaldehydes. + +Plus two CO2s. + +Oops, excuse me. + +Let's do this first. + +And then take the 2NADH +plus the 2H+. + +Convert this to 2NAD+, and what +we get out of this are + +two molecules of ethanol plus +two molecules of CO2. + +Again, a process that's very +similar to you, familiar to + +you, when I was showing +you yeast growing. + +What yeast is doing is it's +carrying out glycolysis and + +then it's taking those extra +electrons, putting them on the + +pyruvate and making ethanol +and carbon dioxide. + +I think there's a fermentation +with what we call a + +fermentation with yeast. + +I think in that case they're +making bourbon whiskey. + +Wine making, beer making, +it's all the same thing. + +You have yeast, you're +converting the sugars first to + +pyruvate, and then making +ethanol and carboxylic acid. + +So anyway. + +There's no energy gain out +of this, but these + +are important processes. + +They're called fermentation. + +And they can happen when there's +no oxygen around. + +If you recall, there's a version +of photosynthesis, + +what I called the second release +of photosynthesis that + +began to evolve oxygen +as a waste product. + +And then over the next ensuing +millennia, the levels of + +oxygen slowly, slowly began +to rise on earth. + +And as oxygen levels got to +higher levels, and recall the + +Cambrian period, which +is down on the fourth + +blackboard down there. + +We were only still even there +half a billion years ago. + +We were only about 5% the +present oxygen levels. + +But as oxygen levels arose, new +metabolic opportunities + +became available. + +And in particular, cells were +able to get at that energy + +which is stored in NADH. + +In the absence of oxygen, +NADH is just a nuisance. + +You've got to get rid of it. + +But as you'll see in a minute, +you can do something + +interesting if you have +oxygen around. + +So just to look at this from a +broad perspective, if we have + +glucose and we have all these +little steps going along to + +give the two pyruvate, if +there's, in the absence of + +oxygen, they get 2 lactate or +we can get 2 ethanol, 2CO2. + +And in both cases, 2ATP. + +2ATP. + +These processes happening in the +absence of oxygen to get + +rid of the, or at least not +requiring oxygen in any case + +called fermentations. + +However, when oxygen is +available, it became possible + +to evolve a new system for +handling these pyruvates. + +We go into a biochemical +cycle known as + +the citric acid cycle. + +And I'll say a word about +this in a minute. + +Plus something else that's +known as oxidative + +phosphorylation. + +This is also referred to as +the respiratory chain. + +And what these two sets of +processes together, enable the + +cell to take these two 3-carbon +compounds and take + +them all the way down to six +molecules of carbon dioxide, + +six molecules of water. + +And to make a net yield of +36 molecules of ATP. + +So if you go by fermentation +a molecule of sugar + +gives you two ATPs. + +If you go by glycolysis and then +follow it by respiration, + +you get 36. + +So respiration using oxygen, 18 +times more efficient than + +by glycolysis. + +So in order to understand how +this works though, we have to + +talk more about how you +change from one form + +of energy to another. + +And it's interesting, although +this process had to have + +evolved billions of years ago, +it was only relatively + +recently that we understood +the principal that was + +necessary for this kind +of thing to happen. + +It's known as the Chemiosmotic +Hypothesis. + +It was proposed by Peter +Mitchell in 1961. + +He eventually got a Nobel +Prize for it. + +It took quite a long time, it +took more than 10 years for it + +to be accepted. + +In fact when I was in grad +school in the mid '70s, people + +were still arguing whether +this made sense or not. + +So here's the way it works. + +And we have to consider first +three different forms of + +chemical energy that can +be all interconverted. + +One of them is familiar to you, +we've been talking about + +it all along. + +It's a chemical bond. + +Energy can be stored in +a high energy bond. + +And if we break it to get ADP, +an inorganic phosphate, we can + +release energy. + +However there's another way +of storing energy as a + +concentration gradient. + +The principal here would be to +have a barrier, which in this + +case is the cell membrane, and +to have a high concentration + +of whatever it is on one side, +and a low concentration on the + +other side. + +And there's energy +stored in that. + +If you give it a chance it'll +get to be the same + +concentration on both sides. + +And the trick is to have +whatever the substance is, is + +to have a protein in the +membrane that can permit this + +thing to go across in a +controlled fashion. + +The third form is electrical +potential. + +Again, the membrane actually +acts as an insulator, and all + +cells, if this is the inside, +and this is the outside, + +there's a gradient of hydrogen +ions, so there are more + +hydrogen ions outside the cell +than there are inside. + +So it creates an electrical +potential. + +And these can't cross the +membrane unless, guess what? + +There's a protein in the +membrane that's able to permit + +their passage under controlled +circumstances. + +So there's basically three +different forms of energy that + +can be interconverted. + +And Peter Mitchell's great +insight, which I will say was + +not intuitive for many people, +was the combination, so the + +combo of this proton +concentration gradient plus + +the electrical potential, could +be used to drive the + +synthesis of ATP. + +And let me just say +a couple of words. + +Because this may feel, +how could this be? + +Could you really have energy? + +Well the potential across a cell +is about 70 millivolts. + +May not seem all that much. + +But remember the membrane is +about three nanometers thick. + +So that's about 200,000 +volts per centimeter. + +High tension wires are 200,000 +volts per mile or something. + +There's a lot of +power in there. + +And furthermore, let's see +if I can bring this up. + +I've been showing +you this little + +movie a couple of times. + +The bacteria with these little +nanomotors are spinning those + +flagella, and we saw how there's +this machinery that's + +a little nanomotor. + +You know how it's powered? + +It's powered by the +proton gradient. + +A proton trickles its way +through this apparatus from + +the outside to the inside. + +It's coming down the gradient. + +That's the source +of the power. + +And as I showed you, it's +a pretty powerful motor. + +You can basically glue the +propeller to a slide and it + +can twirl the bacteria +all around. + +In fact, one of my favorite +demos is, years ago people + +took a bacterium, and they +managed to pop it open. + +So all the cytoplasm, all of the +stuff on the inside came + +out of the cell, and you just +got buffer on the inside. + +But it had these flagella. + +So you had just shells of +bacteria with nothing really + +inside them. + +But, if you add a drop of acid +to this media, now you've + +created a proton gradient with +more protons on the outside + +than are on the inside, and +guess what happens? + +The flagella motor starts +working, and the bacteria + +start swimming, even though all +the air, talk about dead + +man walking or something +like that. + +It gives you an idea of the +power that's in this + +combination of the proton +gradient and + +the electric potential. + +The combination of this is +often referred to as the + +proton motive force. + +So here's the principle +of how the cell is + +able to exploit that. + +And this is what underlies +respiration. + +There are two stages. + +Stage one, there's a membrane +with some kind of membrane + +protein in it, which is actually +a protein, functions + +as a proton pump. + +So it's a protein that's +designed to be embedded into a + +membrane and to work there. + +This part here is the +membrane itself. + +The proton gets transported from +the inside to the outside + +when energy is put into +this proton pump. + +So in response to some energy +producing event, the cell + +pumps protons from its inside to +its outside, and this then + +establishes the proton +gradient. + +The second phase, then, is to +take advantage of that proton + +gradient, and there's a +different protein embedded in + +the membrane. + +It's known as an ATP synthase. + +And it permits a proton to come +down the gradient, which + +you would want to do. + +But if that's all that happened, +all you'd do is + +you'd just dissipate +your gradient. + +So the key here is that this +proton is only allowed to come + +down the gradient to the +energetically more favorable + +side if ADP and inorganic +phosphate are bound to this + +ATP synthase. + +And the dropping of the proton +down the gradient's passage + +through this ATP synthase, which +is an energy favorable + +reaction, drives the +synthesis of ATP. + +So much energy is basically +given off with this, you can + +make an ATP and the thing +will still go. + +Now interestingly, this ATP +synthase, which really lies at + +the heart of our energetics for +how we function as human + +beings, is derived from it's +crystal structure. + +But in fact, evolutionarily, +it's related to + +that flagella motor. + +And as that proton comes down +the gradient, or actually this + +is presented upside down, so +there's the outside as it goes + +through in this direction, the +ATP synthase, which is known + +as the F1F0 ATP synthase +rotates. + +And probably this came first. + +It's a little hard in this one +because you don't have the + +flagella, so what scientists +have done is they've been able + +to attach something like an +actin filament onto this F1 + +ATP synthase, and show +that as a proton + +passages the thing rotates. + +So in all likelihood what +happened in evolution was this + +came first, and then later the +machinery got duplicated and + +evolved to become a nanomotor. + +And as I told you the other day, +that apparatus for the + +flagella motor got evolved again +into becoming a little + +syringe that bacteria like +ursinia are able to use to + +pump or to squeeze proteins or +squirt proteins from inside + +them into inside of +a mammalian cell. + +OK, well. + +Thanks to this work by Peter +Mitchell then, we can now + +understand how cells were able +to take advantage of that + +energy that was in the NADH. + +So this process is known +as respiration. + +And basically it's +taking the 2NADH. + +I'm supposed to see the physical +therapist today, so I + +hope we're going to begin to +make progress to lecturing on + +two feet sooner or later. + +Plus 2NAD+ plus two water. + +So as I said earlier, +NADH and protons, + +it's basically hydrogen. + +It's the equivalent of having +hydrogen gas and adding + +oxygen, and we're burning the +hydrogen gas down to water. + +So there's a lot +to yield water. + +So there's a lot of energy +potentially can be given off. + +That's the 50 kcals per mole. + +Now if you recall when we talked +about thermodynamics, + +so the NADH is up here, by the +time we get down to the 2NAD+ + +plus the water, the two waters, + +energetically we're down here. + +And this is about a free energy +changed of about 50 + +kcals per mole. + +In physiological terms, that's +a huge amount of energy. + +And I think some of the +textbooks compare it to + +letting a stick of dynamite +off inside of a cell. + +So it's really more than biology +figured out how to + +handle this in a single step. + +But do you remember that +important principle about a + +thermodynamic property, +when I had the little + +picture of the skier? + +It doesn't matter which +pathway you take. + +You get the same amount of +energy released whether you go + +down the black diamond +slope or you go + +down the bunny slope. + +So in fact, the way biology has +learned, life has learned + +to control this amount of energy +is basically taking the + +bunny slope. + +And so the energy drop occurs +in a series of stages, where + +you have the transfer of two +electrons to a lower state + +intermediate, transfer of two +electrons to another one, + +transfer of two electrons +to another one. + +And where this connects with +the stuff that I just told + +you, is as these two electrons +are coming down, what's + +happening is a proton is +being pumped from the + +inside to the outside. + +As it moves to the next lower +energy state, another proton + +gets pumped from the inside, +the outside. + +And the same thing +happens here. + +So at the end, you get the two +hydrogens plus the half of an + +oxygen and we get +a water molecule + +from these two electrons. + +But what's happened is these +three protons have changed + +from inside to outside. + +That enables the cell +to make three ATPs. + +So now instead of throwing away +all that energy, losing + +the NADH as in the +fermentations, the cell is + +extracting energy out of it by +taking advantage of this + +principle of the proton +gradient. + +So the game changes +if you're this + +evolutionary designer or something. + +If you were trying to design +life from first principles + +now, you could take +advantage of this. + +Well of course it doesn't +happen that way. + +Experiments happen all the time +in nature and something + +happens and sometimes +it's very efficient, + +sometimes it isn't. + +But if it's there first +it gets going. + +In this case, the need now, or +the opportunity was that if an + +organism could get more NADH out +of that original molecule + +of glucose, it could make more +energy than somebody else. + +And so the ultimate way to take +a molecule of glucose is + +if you burn it with, oxygen +you end up with six carbon + +dioxides and water. + +You burn it all away. + +So there's a system that, +in essence, does that. + +It's known as the citric +acid cycle. + +So you have the pyruvate that +comes from glycolysis. + +And the way it's processed is +first, one of the carboxyl + +group on the pyruvate +is released, and + +this produces acetyl. + +You can look to see +what CoA is. + +At the moment, it +doesn't matter. + +What does matter is this +is a 3-carbon compound. + +Acetyl, as you probably know, +is a two-carbon compound. + +And when you look in your +textbooks at the citric acid + +cycle, you'll see this very +confusing circle with lots of + +compounds and enzymes +and stuff. + +But I want you just keep your +eye on the ball here. + +If you'll notice, the compound +over here is in the cycle, is + +four carbons. + +And what happens is this +2-carbon compound that was + +derived from pyruvate gets +added to this to give a + +6-carbon compound. + +And then that gets converted to +a 5-carbon compound with a + +molecule of CO2 being +given off. + +That in turn gets converted to +a 4-carbon compound with + +another molecule of +CO2 given off. + +And then there's some molecular +gymnastics here that + +change the nature of the four +carbon compound a bit so you + +can get back into the cycle. + +But look what's happened to +those three carbons that were + +in the pyruvate. + +There's one of them, there's +the other one, + +there's the other one. + +So this citric acid cycle +produces, it actually makes + +some ATP, but it makes +quite a bit of NADH. + +And it also makes another, one +more reduced electron carrier. + +It's not NADH, it's another one +that's used in the cell. + +But anyway, the cell is then +able to take all of this NADH + +and this electron carrier plus +these to give you, what I'd + +said, the net yield you +get from respiration. + +36 ATPs from a single +molecule of glucose. + +So sort of quite remarkable +to some extent. + +We're looking at evolution, +through, if you will, almost + +like looking at biochemical +fossils and then when + +something works, it's a living +fossil, we still + +find it in our cells. \ No newline at end of file diff --git a/0h3ShhOQ6zI.txt b/0h3ShhOQ6zI.txt new file mode 100644 index 0000000000000000000000000000000000000000..8b13ad839deb950d256f6e556cb9e89fdf4bdb97 --- /dev/null +++ b/0h3ShhOQ6zI.txt @@ -0,0 +1,10709 @@ +align:start position:0% + +and um you'll remember probably it's all + + align:start position:0% +and um you'll remember probably it's all + + + align:start position:0% +and um you'll remember probably it's all +gone because it's like what a week ago + + align:start position:0% +gone because it's like what a week ago + + + align:start position:0% +gone because it's like what a week ago +uh P at 4 was mostly about the topic of + + align:start position:0% +uh P at 4 was mostly about the topic of + + + align:start position:0% +uh P at 4 was mostly about the topic of +equivalence classes + + align:start position:0% +equivalence classes + + + align:start position:0% +equivalence classes +equivalence in + + align:start position:0% + + + + align:start position:0% + +music what were some of the things that + + align:start position:0% +music what were some of the things that + + + align:start position:0% +music what were some of the things that +we were talking about back then cuz this + + align:start position:0% +we were talking about back then cuz this + + + align:start position:0% +we were talking about back then cuz this +is just going to keep coming up all + + align:start position:0% +is just going to keep coming up all + + + align:start position:0% +is just going to keep coming up all +semester what are some things that we + + align:start position:0% +semester what are some things that we + + + align:start position:0% +semester what are some things that we +could say in some context that two notes + + align:start position:0% +could say in some context that two notes + + + align:start position:0% +could say in some context that two notes +or two pitches are different but in + + align:start position:0% +or two pitches are different but in + + + align:start position:0% +or two pitches are different but in +another context we might say they're + + align:start position:0% +another context we might say they're + + + align:start position:0% +another context we might say they're +equivalent to each other yeah OCT + + align:start position:0% +equivalent to each other yeah OCT + + + align:start position:0% +equivalent to each other yeah OCT +octaves great let's just let's just + + align:start position:0% +octaves great let's just let's just + + + align:start position:0% +octaves great let's just let's just +shoot out perut + + align:start position:0% +shoot out perut + + + align:start position:0% +shoot out perut +permutation + + align:start position:0% +permutation + + + align:start position:0% +permutation +cardinality transposition inversion and + + align:start position:0% +cardinality transposition inversion and + + + align:start position:0% +cardinality transposition inversion and +the one that's not part of the optic + + align:start position:0% +the one that's not part of the optic + + + align:start position:0% +the one that's not part of the optic +spelling good good where uh just while I + + align:start position:0% +spelling good good where uh just while I + + + align:start position:0% +spelling good good where uh just while I +put some things on the board shout out + + align:start position:0% +put some things on the board shout out + + + align:start position:0% +put some things on the board shout out +some more things we talked about in + + align:start position:0% +some more things we talked about in + + + align:start position:0% +some more things we talked about in +class that we didn't put on the problem + + align:start position:0% +class that we didn't put on the problem + + + align:start position:0% +class that we didn't put on the problem +set what were some other things that we + + align:start position:0% +set what were some other things that we + + + align:start position:0% +set what were some other things that we +s say things are the same even though + + align:start position:0% +s say things are the same even though + + + align:start position:0% +s say things are the same even though +they might sound + + align:start position:0% +they might sound + + + align:start position:0% +they might sound +different instrumentation + + align:start position:0% +different instrumentation + + + align:start position:0% +different instrumentation +instrumentation yeah we s say hey that + + align:start position:0% +instrumentation yeah we s say hey that + + + align:start position:0% +instrumentation yeah we s say hey that +note's a c and it's like no that note + + align:start position:0% +note's a c and it's like no that note + + + align:start position:0% +note's a c and it's like no that note +was on a on a piano and this one was on + + align:start position:0% +was on a on a piano and this one was on + + + align:start position:0% +was on a on a piano and this one was on +a trumpet good other + + align:start position:0% +a trumpet good other + + + align:start position:0% +a trumpet good other +things and harmonics and harmonics yep + + align:start position:0% +things and harmonics and harmonics yep + + + align:start position:0% +things and harmonics and harmonics yep +that goes with as a special class of + + align:start position:0% +that goes with as a special class of + + + align:start position:0% +that goes with as a special class of +spelling good good but it's good to use + + align:start position:0% +spelling good good but it's good to use + + + align:start position:0% +spelling good good but it's good to use +that term else + + align:start position:0% +that term else + + + align:start position:0% +that term else +so I said it doesn't matter how long the + + align:start position:0% +so I said it doesn't matter how long the + + + align:start position:0% +so I said it doesn't matter how long the +note is it's still a c right yeah so + + align:start position:0% +note is it's still a c right yeah so + + + align:start position:0% +note is it's still a c right yeah so +duration when we're talking about notes + + align:start position:0% +duration when we're talking about notes + + + align:start position:0% +duration when we're talking about notes +good good so uh I can't apparently lead + + align:start position:0% +good good so uh I can't apparently lead + + + align:start position:0% +good good so uh I can't apparently lead +a discussion and write things on the + + align:start position:0% +a discussion and write things on the + + + align:start position:0% +a discussion and write things on the +board but I want to talk about two + + align:start position:0% +board but I want to talk about two + + + align:start position:0% +board but I want to talk about two +things that uh came up a lot um one of + + align:start position:0% +things that uh came up a lot um one of + + + align:start position:0% +things that uh came up a lot um one of +them I don't need notation for and one + + align:start position:0% +them I don't need notation for and one + + + align:start position:0% +them I don't need notation for and one +of them I do one of them is much better + + align:start position:0% +of them I do one of them is much better + + + align:start position:0% +of them I do one of them is much better +B Sharp for to I don't know it doesn't + + align:start position:0% +B Sharp for to I don't know it doesn't + + + align:start position:0% +B Sharp for to I don't know it doesn't +really matter but it's FP 5 you were + + align:start position:0% +really matter but it's FP 5 you were + + + align:start position:0% +really matter but it's FP 5 you were +asked to write a pro prr to + + align:start position:0% +asked to write a pro prr to + + + align:start position:0% +asked to write a pro prr to +automatically generate the interval um + + align:start position:0% +automatically generate the interval um + + + align:start position:0% +automatically generate the interval um +on well sorry you were asked to write a + + align:start position:0% +on well sorry you were asked to write a + + + align:start position:0% +on well sorry you were asked to write a +program to automatically generate the + + align:start position:0% +program to automatically generate the + + + align:start position:0% +program to automatically generate the +interval of anything and this was one of + + align:start position:0% +interval of anything and this was one of + + + align:start position:0% +interval of anything and this was one of +my hidden test cases that um I think + + align:start position:0% +my hidden test cases that um I think + + + align:start position:0% +my hidden test cases that um I think +it's the only problem that over half + + align:start position:0% +it's the only problem that over half + + + align:start position:0% +it's the only problem that over half +maybe three qus of the class uh the + + align:start position:0% +maybe three qus of the class uh the + + + align:start position:0% +maybe three qus of the class uh the +problem uh came up with what's which one + + align:start position:0% +problem uh came up with what's which one + + + align:start position:0% +problem uh came up with what's which one +of these two notes is the problematic + + align:start position:0% +of these two notes is the problematic + + + align:start position:0% +of these two notes is the problematic +one take a guess B good good now BP is a + + align:start position:0% +one take a guess B good good now BP is a + + + align:start position:0% +one take a guess B good good now BP is a +problematic note the way Esh is right + + align:start position:0% +problematic note the way Esh is right + + + align:start position:0% +problematic note the way Esh is right +but it also has its own special + + align:start position:0% +but it also has its own special + + + align:start position:0% +but it also has its own special +problematic things what what's bsharp 4 + + align:start position:0% +problematic things what what's bsharp 4 + + + align:start position:0% +problematic things what what's bsharp 4 +what note does that sound + + align:start position:0% +what note does that sound + + + align:start position:0% +what note does that sound +like C5 + + align:start position:0% +like C5 + + + align:start position:0% +like C5 +good + + align:start position:0% +good + + + align:start position:0% +good +so the issue that came up a lot um is + + align:start position:0% +so the issue that came up a lot um is + + + align:start position:0% +so the issue that came up a lot um is +the only thing what what should this + + align:start position:0% +the only thing what what should this + + + align:start position:0% +the only thing what what should this +interval be let's let's think about that + + align:start position:0% +interval be let's let's think about that + + + align:start position:0% +interval be let's let's think about that +first what should the interval + + align:start position:0% +first what should the interval + + + align:start position:0% +first what should the interval +be yeah diminished fifth diminished + + align:start position:0% +be yeah diminished fifth diminished + + + align:start position:0% +be yeah diminished fifth diminished +fifth so let's think about that + + align:start position:0% +fifth so let's think about that + + + align:start position:0% +fifth so let's think about that +diminished fifth good yeah what's what + + align:start position:0% +diminished fifth good yeah what's what + + + align:start position:0% +diminished fifth good yeah what's what +would be the interval if it was C5 to + + align:start position:0% +would be the interval if it was C5 to + + + align:start position:0% +would be the interval if it was C5 to +F + + align:start position:0% +F + + + align:start position:0% +F + + align:start position:0% + + + align:start position:0% +anybody augment + + align:start position:0% +anybody augment + + + align:start position:0% +anybody augment +augmented fourth good so the four and + + align:start position:0% +augmented fourth good so the four and + + + align:start position:0% +augmented fourth good so the four and +the five are changed around based on uh + + align:start position:0% +the five are changed around based on uh + + + align:start position:0% +the five are changed around based on uh +the number of distances in the step + + align:start position:0% +the number of distances in the step + + + align:start position:0% +the number of distances in the step +spacing which you all did great on um + + align:start position:0% +spacing which you all did great on um + + + align:start position:0% +spacing which you all did great on um +but now we have a different problem and + + align:start position:0% +but now we have a different problem and + + + align:start position:0% +but now we have a different problem and +so what came up a lot um from various + + align:start position:0% +so what came up a lot um from various + + + align:start position:0% +so what came up a lot um from various +things I saw a lot of um D D D D D D D D + + align:start position:0% +things I saw a lot of um D D D D D D D D + + + align:start position:0% +things I saw a lot of um D D D D D D D D +D is that the right number D D D um + + align:start position:0% +D is that the right number D D D um + + + align:start position:0% +D is that the right number D D D um +12th I think that might that might not + + align:start position:0% +12th I think that might that might not + + + align:start position:0% +12th I think that might that might not +be enough D's because the issue is that + + align:start position:0% +be enough D's because the issue is that + + + align:start position:0% +be enough D's because the issue is that +the BP is something that sounds in kind + + align:start position:0% +the BP is something that sounds in kind + + + align:start position:0% +the BP is something that sounds in kind +of octave five but it's not so always + + align:start position:0% +of octave five but it's not so always + + + align:start position:0% +of octave five but it's not so always +when you're thinking of you know how's + + align:start position:0% +when you're thinking of you know how's + + + align:start position:0% +when you're thinking of you know how's +your screwy Prof going to try to screw + + align:start position:0% +your screwy Prof going to try to screw + + + align:start position:0% +your screwy Prof going to try to screw +you up think about these things that + + align:start position:0% +you up think about these things that + + + align:start position:0% +you up think about these things that +cross over the boundaries between + + align:start position:0% +cross over the boundaries between + + + align:start position:0% +cross over the boundaries between +octaves or sound like one thing not the + + align:start position:0% +octaves or sound like one thing not the + + + align:start position:0% +octaves or sound like one thing not the +other um a lot of a lot of times what + + align:start position:0% +other um a lot of a lot of times what + + + align:start position:0% +other um a lot of a lot of times what +what happened was you needed to do + + align:start position:0% +what happened was you needed to do + + + align:start position:0% +what happened was you needed to do +something mod 12 at a certain point add + + align:start position:0% +something mod 12 at a certain point add + + + align:start position:0% +something mod 12 at a certain point add +an offset depending on how your + + align:start position:0% +an offset depending on how your + + + align:start position:0% +an offset depending on how your +algorithm works and then mod 12 it again + + align:start position:0% +algorithm works and then mod 12 it again + + + align:start position:0% +algorithm works and then mod 12 it again +so this sort of double mod 12 at this + + align:start position:0% +so this sort of double mod 12 at this + + + align:start position:0% +so this sort of double mod 12 at this +point we're we're going to be working + + align:start position:0% +point we're we're going to be working + + + align:start position:0% +point we're we're going to be working +for algorithms that get things right we + + align:start position:0% +for algorithms that get things right we + + + align:start position:0% +for algorithms that get things right we +can work on efficient algorithms as sort + + align:start position:0% +can work on efficient algorithms as sort + + + align:start position:0% +can work on efficient algorithms as sort +of um you know more efficient ones as + + align:start position:0% +of um you know more efficient ones as + + + align:start position:0% +of um you know more efficient ones as +kind of a project later good the second + + align:start position:0% +kind of a project later good the second + + + align:start position:0% +kind of a project later good the second +one that came up um had to do with + + align:start position:0% +one that came up um had to do with + + + align:start position:0% +one that came up um had to do with +asking you to uh This was done by hand + + align:start position:0% +asking you to uh This was done by hand + + + align:start position:0% +asking you to uh This was done by hand +um to come up with a pitch set that was + + align:start position:0% +um to come up with a pitch set that was + + + align:start position:0% +um to come up with a pitch set that was +equivalent to the one I gave you using p + + align:start position:0% +equivalent to the one I gave you using p + + + align:start position:0% +equivalent to the one I gave you using p +permutation and T transposition but + + align:start position:0% +permutation and T transposition but + + + align:start position:0% +permutation and T transposition but +without octave inversion or cardinality + + align:start position:0% +without octave inversion or cardinality + + + align:start position:0% +without octave inversion or cardinality +um equivalence and most of you are like + + align:start position:0% +um equivalence and most of you are like + + + align:start position:0% +um equivalence and most of you are like +I don't even want to think about + + align:start position:0% +I don't even want to think about + + + align:start position:0% +I don't even want to think about +inversional um you know equivalent so + + align:start position:0% +inversional um you know equivalent so + + + align:start position:0% +inversional um you know equivalent so +that's good and cardinality equivalence + + align:start position:0% +that's good and cardinality equivalence + + + align:start position:0% +that's good and cardinality equivalence +just means that I gave you three notes + + align:start position:0% +just means that I gave you three notes + + + align:start position:0% +just means that I gave you three notes +how many notes should you have three + + align:start position:0% +how many notes should you have three + + + align:start position:0% +how many notes should you have three +three good good so the hard part so this + + align:start position:0% +three good good so the hard part so this + + + align:start position:0% +three good good so the hard part so this +was A4 E5 C + + align:start position:0% +was A4 E5 C + + + align:start position:0% +was A4 E5 C +4 what I'd like you to do when you have + + align:start position:0% +4 what I'd like you to do when you have + + + align:start position:0% +4 what I'd like you to do when you have +a problem like this is go back to do it + + align:start position:0% +a problem like this is go back to do it + + + align:start position:0% +a problem like this is go back to do it +the oldfashioned way first get out staff + + align:start position:0% +the oldfashioned way first get out staff + + + align:start position:0% +the oldfashioned way first get out staff +paper or use finale Muse score whatever + + align:start position:0% +paper or use finale Muse score whatever + + + align:start position:0% +paper or use finale Muse score whatever +you're using and try to make sure that + + align:start position:0% +you're using and try to make sure that + + + align:start position:0% +you're using and try to make sure that +you're seeing what the notes are so + + align:start position:0% +you're seeing what the notes are so + + + align:start position:0% +you're seeing what the notes are so +where's A4 + + align:start position:0% +where's A4 + + + align:start position:0% +where's A4 +go stop two stop stop okay good + + align:start position:0% +go stop two stop stop okay good + + + align:start position:0% +go stop two stop stop okay good +A4 what's the next one + + align:start position:0% + + + + align:start position:0% + +E5 stop okay good go slower puff right + + align:start position:0% +E5 stop okay good go slower puff right + + + align:start position:0% +E5 stop okay good go slower puff right +and then what's the next + + align:start position:0% +and then what's the next + + + align:start position:0% +and then what's the next +one + + align:start position:0% +one + + + align:start position:0% +one +C four + + align:start position:0% +C four + + + align:start position:0% +C four +right stop + + align:start position:0% +right stop + + + align:start position:0% +right stop +what's the common name we would call to + + align:start position:0% +what's the common name we would call to + + + align:start position:0% +what's the common name we would call to +this If This Were a + + align:start position:0% +this If This Were a + + + align:start position:0% +this If This Were a +chord A major first inversion in first + + align:start position:0% +chord A major first inversion in first + + + align:start position:0% +chord A major first inversion in first +inversion yeah so oops I got to jle this + + align:start position:0% +inversion yeah so oops I got to jle this + + + align:start position:0% +inversion yeah so oops I got to jle this +otherwise was blood red yes first + + align:start position:0% +otherwise was blood red yes first + + + align:start position:0% +otherwise was blood red yes first +inversion um okay so then what you need + + align:start position:0% +inversion um okay so then what you need + + + align:start position:0% +inversion um okay so then what you need +to do you want to do is something + + align:start position:0% +to do you want to do is something + + + align:start position:0% +to do you want to do is something +that and it had to use both now you I + + align:start position:0% +that and it had to use both now you I + + + align:start position:0% +that and it had to use both now you I +think I tried to say it in such a way + + align:start position:0% +think I tried to say it in such a way + + + align:start position:0% +think I tried to say it in such a way +that even an MIT student wouldn't be + + align:start position:0% +that even an MIT student wouldn't be + + + align:start position:0% +that even an MIT student wouldn't be +allowed to say well you know uh not + + align:start position:0% +allowed to say well you know uh not + + + align:start position:0% +allowed to say well you know uh not +arranging anything is not rearranging + + align:start position:0% +arranging anything is not rearranging + + + align:start position:0% +arranging anything is not rearranging +anything is a permutation and + + align:start position:0% +anything is a permutation and + + + align:start position:0% +anything is a permutation and +transposition by Perfect Unison is a + + align:start position:0% +transposition by Perfect Unison is a + + + align:start position:0% +transposition by Perfect Unison is a +transposition but you needed to change + + align:start position:0% +transposition but you needed to change + + + align:start position:0% +transposition but you needed to change +them in some way so one of the things + + align:start position:0% +them in some way so one of the things + + + align:start position:0% +them in some way so one of the things +you could do uh so one of the things + + align:start position:0% +you could do uh so one of the things + + + align:start position:0% +you could do uh so one of the things +that happened a lot was that the octaves + + align:start position:0% +that happened a lot was that the octaves + + + align:start position:0% +that happened a lot was that the octaves +got changed and so that ended up being + + align:start position:0% +got changed and so that ended up being + + + align:start position:0% +got changed and so that ended up being +about 40% of the errors that we saw so + + align:start position:0% +about 40% of the errors that we saw so + + + align:start position:0% +about 40% of the errors that we saw so +you can do is you could first re permute + + align:start position:0% +you can do is you could first re permute + + + align:start position:0% +you can do is you could first re permute +things and probably the rep permutation + + align:start position:0% +things and probably the rep permutation + + + align:start position:0% +things and probably the rep permutation +that I would do first is let's just put + + align:start position:0% +that I would do first is let's just put + + + align:start position:0% +that I would do first is let's just put +it in ascending order so that's probably + + align:start position:0% +it in ascending order so that's probably + + + align:start position:0% +it in ascending order so that's probably +the permutation you'd like to um have + + align:start position:0% +the permutation you'd like to um have + + + align:start position:0% +the permutation you'd like to um have +your computer do + + align:start position:0% +your computer do + + + align:start position:0% +your computer do +anyhow and then let's just shift + + align:start position:0% +anyhow and then let's just shift + + + align:start position:0% +anyhow and then let's just shift +everything up um one way you can do it + + align:start position:0% +everything up um one way you can do it + + + align:start position:0% +everything up um one way you can do it +well in this one you I was going to say + + align:start position:0% +well in this one you I was going to say + + + align:start position:0% +well in this one you I was going to say +shift everything up a space or a line + + align:start position:0% +shift everything up a space or a line + + + align:start position:0% +shift everything up a space or a line +but the E is the problem so let's just + + align:start position:0% +but the E is the problem so let's just + + + align:start position:0% +but the E is the problem so let's just +transpose up a a major second what are + + align:start position:0% +transpose up a a major second what are + + + align:start position:0% +transpose up a a major second what are +we going to get + + align:start position:0% +we going to get + + + align:start position:0% +we going to get +here dsharp + + align:start position:0% + + + + align:start position:0% + +B FP good not um because well no this + + align:start position:0% +B FP good not um because well no this + + + align:start position:0% +B FP good not um because well no this +one we had implicitly because everything + + align:start position:0% +one we had implicitly because everything + + + align:start position:0% +one we had implicitly because everything +on this we had spelling or and that's an + + align:start position:0% +on this we had spelling or and that's an + + + align:start position:0% +on this we had spelling or and that's an +S not a five a spelling equivalent so + + align:start position:0% +S not a five a spelling equivalent so + + + align:start position:0% +S not a five a spelling equivalent so +yeah so D Shar 4 + + align:start position:0% +yeah so D Shar 4 + + + align:start position:0% +yeah so D Shar 4 +B4 and F five so um when you get that + + align:start position:0% +B4 and F five so um when you get that + + + align:start position:0% +B4 and F five so um when you get that +back that's there any other questions on + + align:start position:0% +back that's there any other questions on + + + align:start position:0% +back that's there any other questions on +problem set + + align:start position:0% + + + + align:start position:0% + +four hardest programming problem set so + + align:start position:0% +four hardest programming problem set so + + + align:start position:0% +four hardest programming problem set so +far no no two two was harder for some + + align:start position:0% +far no no two two was harder for some + + + align:start position:0% +far no no two two was harder for some +people anyone vote for one no okay if if + + align:start position:0% +people anyone vote for one no okay if if + + + align:start position:0% +people anyone vote for one no okay if if +if one was the hardest uh probably + + align:start position:0% +if one was the hardest uh probably + + + align:start position:0% +if one was the hardest uh probably +you're not here uh now um but sorry I + + align:start position:0% +you're not here uh now um but sorry I + + + align:start position:0% +you're not here uh now um but sorry I +shouldn't yeah um but yeah so prom set + + align:start position:0% +shouldn't yeah um but yeah so prom set + + + align:start position:0% +shouldn't yeah um but yeah so prom set +six will be announcing today it is also + + align:start position:0% +six will be announcing today it is also + + + align:start position:0% +six will be announcing today it is also +a slight programming one uh it's + + align:start position:0% +a slight programming one uh it's + + + align:start position:0% +a slight programming one uh it's +designed to give you a little bit of a + + align:start position:0% +designed to give you a little bit of a + + + align:start position:0% +designed to give you a little bit of a +break and it you'll I'll talk about it + + align:start position:0% +break and it you'll I'll talk about it + + + align:start position:0% +break and it you'll I'll talk about it +in a bit but it's uh more of a um the + + align:start position:0% +in a bit but it's uh more of a um the + + + align:start position:0% +in a bit but it's uh more of a um the +only sort of participation grade type of + + align:start position:0% +only sort of participation grade type of + + + align:start position:0% +only sort of participation grade type of +problem set than uh trying to get the + + align:start position:0% +problem set than uh trying to get the + + + align:start position:0% +problem set than uh trying to get the +exact results so we're going to have a + + align:start position:0% +exact results so we're going to have a + + + align:start position:0% +exact results so we're going to have a +little bit of a break um coming up for + + align:start position:0% +little bit of a break um coming up for + + + align:start position:0% +little bit of a break um coming up for +things somebody want to volunteer what + + align:start position:0% +things somebody want to volunteer what + + + align:start position:0% +things somebody want to volunteer what +electronic corpora did you find + + align:start position:0% +electronic corpora did you find + + + align:start position:0% +electronic corpora did you find +online Adam yeah we did musipedia + + align:start position:0% +online Adam yeah we did musipedia + + + align:start position:0% +online Adam yeah we did musipedia +musipedia great what's what is that it's + + align:start position:0% +musipedia great what's what is that it's + + + align:start position:0% +musipedia great what's what is that it's +a dual database and search query + + align:start position:0% +a dual database and search query + + + align:start position:0% +a dual database and search query +data cor cool great another another + + align:start position:0% +data cor cool great another another + + + align:start position:0% +data cor cool great another another +group yeah uh we did ultimate guitar + + align:start position:0% +group yeah uh we did ultimate guitar + + + align:start position:0% +group yeah uh we did ultimate guitar +ultimate guitar great how's how's that + + align:start position:0% +ultimate guitar great how's how's that + + + align:start position:0% +ultimate guitar great how's how's that +that encoded um I mean they started off + + align:start position:0% +that encoded um I mean they started off + + + align:start position:0% +that encoded um I mean they started off +with just like text um ask key guitar + + align:start position:0% +with just like text um ask key guitar + + + align:start position:0% +with just like text um ask key guitar +tab but then they kind of expanded and + + align:start position:0% +tab but then they kind of expanded and + + + align:start position:0% +tab but then they kind of expanded and +Incorporated more advanced software oh + + align:start position:0% +Incorporated more advanced software oh + + + align:start position:0% +Incorporated more advanced software oh +cool yeah I remember when it was a lot + + align:start position:0% +cool yeah I remember when it was a lot + + + align:start position:0% +cool yeah I remember when it was a lot +of asky guitar tabs I think everybody + + align:start position:0% +of asky guitar tabs I think everybody + + + align:start position:0% +of asky guitar tabs I think everybody +had their own parser for the ultimate + + align:start position:0% +had their own parser for the ultimate + + + align:start position:0% +had their own parser for the ultimate +guitar at some point uh good uh anybody + + align:start position:0% +guitar at some point uh good uh anybody + + + align:start position:0% +guitar at some point uh good uh anybody +else + + align:start position:0% +else + + + align:start position:0% +else +Vanessa video game music database video + + align:start position:0% +Vanessa video game music database video + + + align:start position:0% +Vanessa video game music database video +game music database fantastic great + + align:start position:0% +game music database fantastic great + + + align:start position:0% +game music database fantastic great +great repository what's what were things + + align:start position:0% +great repository what's what were things + + + align:start position:0% +great repository what's what were things +mostly encoded for that almost + + align:start position:0% +mostly encoded for that almost + + + align:start position:0% +mostly encoded for that almost +everything was in min5 almost everything + + align:start position:0% +everything was in min5 almost everything + + + align:start position:0% +everything was in min5 almost everything +was in mini files why why do you think + + align:start position:0% +was in mini files why why do you think + + + align:start position:0% +was in mini files why why do you think +that was I think it's like generally a + + align:start position:0% +that was I think it's like generally a + + + align:start position:0% +that was I think it's like generally a +standard and it's relatively small file + + align:start position:0% +standard and it's relatively small file + + + align:start position:0% +standard and it's relatively small file +sizes so it's easier to like Mass pop a + + align:start position:0% +sizes so it's easier to like Mass pop a + + + align:start position:0% +sizes so it's easier to like Mass pop a +whole bunch of different it is also + + align:start position:0% +whole bunch of different it is also + + + align:start position:0% +whole bunch of different it is also +that's probably how they were encoded in + + align:start position:0% +that's probably how they were encoded in + + + align:start position:0% +that's probably how they were encoded in +a lot of especially the early video + + align:start position:0% +a lot of especially the early video + + + align:start position:0% +a lot of especially the early video +games they were encoded so when you're + + align:start position:0% +games they were encoded so when you're + + + align:start position:0% +games they were encoded so when you're +ripping from or something like that uh + + align:start position:0% +ripping from or something like that uh + + + align:start position:0% +ripping from or something like that uh +but definitely not encoding Sharps and + + align:start position:0% +but definitely not encoding Sharps and + + + align:start position:0% +but definitely not encoding Sharps and +flats good one last one Su your group oh + + align:start position:0% +flats good one last one Su your group oh + + + align:start position:0% +flats good one last one Su your group oh +um we did a jazz it was a jazz database + + align:start position:0% +um we did a jazz it was a jazz database + + + align:start position:0% +um we did a jazz it was a jazz database +a jazz database fantastic fantastic what + + align:start position:0% +a jazz database fantastic fantastic what + + + align:start position:0% +a jazz database fantastic fantastic what +werein coding for that um they had a + + align:start position:0% +werein coding for that um they had a + + + align:start position:0% +werein coding for that um they had a +variety they had like the transcribed + + align:start position:0% +variety they had like the transcribed + + + align:start position:0% +variety they had like the transcribed +sheet music for a lot of jazz solos and + + align:start position:0% +sheet music for a lot of jazz solos and + + + align:start position:0% +sheet music for a lot of jazz solos and +then also a CSV file that just had every + + align:start position:0% +then also a CSV file that just had every + + + align:start position:0% +then also a CSV file that just had every +notes offset from the very beginning and + + align:start position:0% +notes offset from the very beginning and + + + align:start position:0% +notes offset from the very beginning and +its pitch as a number cool uh what + + align:start position:0% +its pitch as a number cool uh what + + + align:start position:0% +its pitch as a number cool uh what +you'll find is a lot of um a lot of + + align:start position:0% +you'll find is a lot of um a lot of + + + align:start position:0% +you'll find is a lot of um a lot of +these data sets they really have their + + align:start position:0% +these data sets they really have their + + + align:start position:0% +these data sets they really have their +own sort of oneoff make your own format + + align:start position:0% +own sort of oneoff make your own format + + + align:start position:0% +own sort of oneoff make your own format +because like I I don't think that that + + align:start position:0% +because like I I don't think that that + + + align:start position:0% +because like I I don't think that that +one's a standard but I've seen lots of + + align:start position:0% +one's a standard but I've seen lots of + + + align:start position:0% +one's a standard but I've seen lots of +these because um that's how uh things + + align:start position:0% +these because um that's how uh things + + + align:start position:0% +these because um that's how uh things +things uh you know tend to tend to go + + align:start position:0% +things uh you know tend to tend to go + + + align:start position:0% +things uh you know tend to tend to go +great uh where we're going to get to + + align:start position:0% +great uh where we're going to get to + + + align:start position:0% +great uh where we're going to get to +right back to + + align:start position:0% +right back to + + + align:start position:0% +right back to +representation uh in just a bit uh we' a + + align:start position:0% +representation uh in just a bit uh we' a + + + align:start position:0% +representation uh in just a bit uh we' a +special guest Michael good who knows a + + align:start position:0% +special guest Michael good who knows a + + + align:start position:0% +special guest Michael good who knows a +little something about representations + + align:start position:0% +little something about representations + + + align:start position:0% +little something about representations +being the creator of Music XML and uh + + align:start position:0% +being the creator of Music XML and uh + + + align:start position:0% +being the creator of Music XML and uh +sort of uh found and BR Bell also from + + align:start position:0% +sort of uh found and BR Bell also from + + + align:start position:0% +sort of uh found and BR Bell also from +the Dean's office um and um and so if if + + align:start position:0% +the Dean's office um and um and so if if + + + align:start position:0% +the Dean's office um and um and so if if +you guys can stick around for 10 minutes + + align:start position:0% +you guys can stick around for 10 minutes + + + align:start position:0% +you guys can stick around for 10 minutes +we're I'd like to before we do that + + align:start position:0% +we're I'd like to before we do that + + + align:start position:0% +we're I'd like to before we do that +let's get sort of warmed up for probably + + align:start position:0% +let's get sort of warmed up for probably + + + align:start position:0% +let's get sort of warmed up for probably +the thing that are on some people's mind + + align:start position:0% +the thing that are on some people's mind + + + align:start position:0% +the thing that are on some people's mind +right the downgraded midterm which is + + align:start position:0% +right the downgraded midterm which is + + + align:start position:0% +right the downgraded midterm which is +now I'm calling quiz because I'd like to + + align:start position:0% +now I'm calling quiz because I'd like to + + + align:start position:0% +now I'm calling quiz because I'd like to +divide this into two smaller low lower + + align:start position:0% +divide this into two smaller low lower + + + align:start position:0% +divide this into two smaller low lower +stress things and that will be on + + align:start position:0% +stress things and that will be on + + + align:start position:0% +stress things and that will be on +Wednesday uh we'll start recording about + + align:start position:0% +Wednesday uh we'll start recording about + + + align:start position:0% +Wednesday uh we'll start recording about +uh 30 40 minutes in I'm designing it to + + align:start position:0% +uh 30 40 minutes in I'm designing it to + + + align:start position:0% +uh 30 40 minutes in I'm designing it to +take 30 minutes if we take a little bit + + align:start position:0% +take 30 minutes if we take a little bit + + + align:start position:0% +take 30 minutes if we take a little bit +longer that's okay it's not all about + + align:start position:0% +longer that's okay it's not all about + + + align:start position:0% +longer that's okay it's not all about +the rush but we will do one type of + + align:start position:0% +the rush but we will do one type of + + + align:start position:0% +the rush but we will do one type of +thing um that uh is about sort of recall + + align:start position:0% +thing um that uh is about sort of recall + + + align:start position:0% +thing um that uh is about sort of recall +so the um the the the quiz will be not + + align:start position:0% +so the um the the the quiz will be not + + + align:start position:0% +so the um the the the quiz will be not +about your programming skills but about + + align:start position:0% +about your programming skills but about + + + align:start position:0% +about your programming skills but about +the reading and we want I want the + + align:start position:0% +the reading and we want I want the + + + align:start position:0% +the reading and we want I want the +quizzes to be more about the readings so + + align:start position:0% +quizzes to be more about the readings so + + + align:start position:0% +quizzes to be more about the readings so +that you keep thinking about ideas that + + align:start position:0% +that you keep thinking about ideas that + + + align:start position:0% +that you keep thinking about ideas that +you're going to be doing in your + + align:start position:0% +you're going to be doing in your + + + align:start position:0% +you're going to be doing in your +projects as we uh keep going with uh + + align:start position:0% +projects as we uh keep going with uh + + + align:start position:0% +projects as we uh keep going with uh +further um with further problem sets + + align:start position:0% +further um with further problem sets + + + align:start position:0% +further um with further problem sets +each one of them will start having a + + align:start position:0% +each one of them will start having a + + + align:start position:0% +each one of them will start having a +little bit of uh what do we call it uh + + align:start position:0% +little bit of uh what do we call it uh + + + align:start position:0% +little bit of uh what do we call it uh +sort of assign yourself your own um your + + align:start position:0% +sort of assign yourself your own um your + + + align:start position:0% +sort of assign yourself your own um your +own problem and start it okay we got + + align:start position:0% +own problem and start it okay we got + + + align:start position:0% +own problem and start it okay we got +some sound going we don't really need + + align:start position:0% +some sound going we don't really need + + + align:start position:0% +some sound going we don't really need +that but we can turn that down for a bit + + align:start position:0% +that but we can turn that down for a bit + + + align:start position:0% +that but we can turn that down for a bit +who's done cahoot + + align:start position:0% +who's done cahoot + + + align:start position:0% +who's done cahoot +before okay who knew that MIT apparently + + align:start position:0% +before okay who knew that MIT apparently + + + align:start position:0% +before okay who knew that MIT apparently +let their cahoot subscription uh lapse + + align:start position:0% +let their cahoot subscription uh lapse + + + align:start position:0% +let their cahoot subscription uh lapse +uh sometime between the last time I'm in + + align:start position:0% +uh sometime between the last time I'm in + + + align:start position:0% +uh sometime between the last time I'm in +here so I'm only able to do 10 players + + align:start position:0% +here so I'm only able to do 10 players + + + align:start position:0% +here so I'm only able to do 10 players +so can you all uh can you all pair up + + align:start position:0% +so can you all uh can you all pair up + + + align:start position:0% +so can you all uh can you all pair up +and do in teams with the other I know I + + align:start position:0% +and do in teams with the other I know I + + + align:start position:0% +and do in teams with the other I know I +know I I I was trying to fill out the + + align:start position:0% +know I I I was trying to fill out the + + + align:start position:0% +know I I I was trying to fill out the +subscription form right behind class so + + align:start position:0% +subscription form right behind class so + + + align:start position:0% +subscription form right behind class so +can you team up one two three three + + align:start position:0% +can you team up one two three three + + + align:start position:0% +can you team up one two three three +three four five six seven eight actually + + align:start position:0% +three four five six seven eight actually + + + align:start position:0% +three four five six seven eight actually +you can be your own team n or do you + + align:start position:0% +you can be your own team n or do you + + + align:start position:0% +you can be your own team n or do you +want to do it with Michael stu okay we + + align:start position:0% +want to do it with Michael stu okay we + + + align:start position:0% +want to do it with Michael stu okay we +might have one more thing do it okay oh + + align:start position:0% +might have one more thing do it okay oh + + + align:start position:0% +might have one more thing do it okay oh +yeah uh use any nickname you want just + + align:start position:0% +yeah uh use any nickname you want just + + + align:start position:0% +yeah uh use any nickname you want just +make it family + + align:start position:0% + + + + align:start position:0% + +safe oh you can you can decide if you + + align:start position:0% +safe oh you can you can decide if you + + + align:start position:0% +safe oh you can you can decide if you +want to + + align:start position:0% + + + + align:start position:0% + +be + + align:start position:0% +be + + + align:start position:0% +be +okay so this is ju this is just to judge + + align:start position:0% +okay so this is ju this is just to judge + + + align:start position:0% +okay so this is ju this is just to judge +how much time you feel like you might + + align:start position:0% +how much time you feel like you might + + + align:start position:0% +how much time you feel like you might +need to spend reviewing uh the things + + align:start position:0% +need to spend reviewing uh the things + + + align:start position:0% +need to spend reviewing uh the things +okay we have 1 two 3 four we have + + align:start position:0% +okay we have 1 two 3 four we have + + + align:start position:0% +okay we have 1 two 3 four we have +nickname nickname too great + + align:start position:0% +nickname nickname too great + + + align:start position:0% +nickname nickname too great +um five + + align:start position:0% + + + + align:start position:0% + +six okay we'll do a little bit of the + + align:start position:0% +six okay we'll do a little bit of the + + + align:start position:0% +six okay we'll do a little bit of the +background music but although + + align:start position:0% + + + + align:start position:0% + +maybe okay we have eight anybody anybody + + align:start position:0% +maybe okay we have eight anybody anybody + + + align:start position:0% +maybe okay we have eight anybody anybody +waiting on two more people want to be + + align:start position:0% +waiting on two more people want to be + + + align:start position:0% +waiting on two more people want to be +loners go on their own okay now that's + + align:start position:0% +loners go on their own okay now that's + + + align:start position:0% +loners go on their own okay now that's +good we're going to get + + align:start position:0% +good we're going to get + + + align:start position:0% +good we're going to get +started oh we got winners okay + + align:start position:0% +started oh we got winners okay + + + align:start position:0% +started oh we got winners okay +oh and okay great super um here we go so + + align:start position:0% +oh and okay great super um here we go so + + + align:start position:0% +oh and okay great super um here we go so +about 20 or 30 seconds on each one + + align:start position:0% +about 20 or 30 seconds on each one + + + align:start position:0% +about 20 or 30 seconds on each one +there's uh 11 questions I think 13 + + align:start position:0% +there's uh 11 questions I think 13 + + + align:start position:0% +there's uh 11 questions I think 13 +questions + + align:start position:0% + + + + align:start position:0% + +maybe which of the following is a binary + + align:start position:0% +maybe which of the following is a binary + + + align:start position:0% +maybe which of the following is a binary +music representation + + align:start position:0% + + + + align:start position:0% + +so this is your time if you haven't done + + align:start position:0% +so this is your time if you haven't done + + + align:start position:0% +so this is your time if you haven't done +this before lock in something no points + + align:start position:0% +this before lock in something no points + + + align:start position:0% +this before lock in something no points +for + + align:start position:0% + + + + align:start position:0% + +wrong three + + align:start position:0% + + + + align:start position:0% + +two what do we have midi mid is the only + + align:start position:0% +two what do we have midi mid is the only + + + align:start position:0% +two what do we have midi mid is the only +one that is typically represented in + + align:start position:0% +one that is typically represented in + + + align:start position:0% +one that is typically represented in +binary code and not in + + align:start position:0% +binary code and not in + + + align:start position:0% +binary code and not in +text okay okay I know you you would have + + align:start position:0% +text okay okay I know you you would have + + + align:start position:0% +text okay okay I know you you would have +thought I would have made the answer + + align:start position:0% +thought I would have made the answer + + + align:start position:0% +thought I would have made the answer +music XML to honor our guest but you + + align:start position:0% +music XML to honor our guest but you + + + align:start position:0% +music XML to honor our guest but you +didn't you knew it wasn't music XML you + + align:start position:0% +didn't you knew it wasn't music XML you + + + align:start position:0% +didn't you knew it wasn't music XML you +knew it wasn't music XML because you + + align:start position:0% +knew it wasn't music XML because you + + + align:start position:0% +knew it wasn't music XML because you +studied that well enough good let's keep + + align:start position:0% +studied that well enough good let's keep + + + align:start position:0% +studied that well enough good let's keep +going okay hey Nick the creative + + align:start position:0% +going okay hey Nick the creative + + + align:start position:0% +going okay hey Nick the creative +nicknames are up top according to cook + + align:start position:0% +nicknames are up top according to cook + + + align:start position:0% +nicknames are up top according to cook +what is ironic about the timing of the + + align:start position:0% +what is ironic about the timing of the + + + align:start position:0% +what is ironic about the timing of the +rise and fall of comparative and + + align:start position:0% +rise and fall of comparative and + + + align:start position:0% +rise and fall of comparative and +computational musicology + + align:start position:0% + + + + align:start position:0% + +hey most we got it comparative + + align:start position:0% +hey most we got it comparative + + + align:start position:0% +hey most we got it comparative +musicology which is kind of designed + + align:start position:0% +musicology which is kind of designed + + + align:start position:0% +musicology which is kind of designed +well for computers declined at the time + + align:start position:0% +well for computers declined at the time + + + align:start position:0% +well for computers declined at the time +computers came + + align:start position:0% +computers came + + + align:start position:0% +computers came +up okay that's Nicholas Cook's + + align:start position:0% +up okay that's Nicholas Cook's + + + align:start position:0% +up okay that's Nicholas Cook's +comparative and computational musicology + + align:start position:0% +comparative and computational musicology + + + align:start position:0% +comparative and computational musicology +to review if that one wasn't obvious + + align:start position:0% +to review if that one wasn't obvious + + + align:start position:0% +to review if that one wasn't obvious +we'll keep going okay we got much more + + align:start position:0% +we'll keep going okay we got much more + + + align:start position:0% +we'll keep going okay we got much more +on the board + + align:start position:0% + + + + align:start position:0% + +who was not a composer whose music was + + align:start position:0% +who was not a composer whose music was + + + align:start position:0% +who was not a composer whose music was +discussed by cook who was not in + + align:start position:0% + + + + align:start position:0% + +there this is a hard one this is about + + align:start position:0% +there this is a hard one this is about + + + align:start position:0% +there this is a hard one this is about +as hard + + align:start position:0% + + + + align:start position:0% + +as 3 + + align:start position:0% + + + + align:start position:0% + +seconds oh most people got it voger no + + align:start position:0% +seconds oh most people got it voger no + + + align:start position:0% +seconds oh most people got it voger no +liity was the one with all the graphs + + align:start position:0% +liity was the one with all the graphs + + + align:start position:0% +liity was the one with all the graphs +showing when things come in and out and + + align:start position:0% +showing when things come in and out and + + + align:start position:0% +showing when things come in and out and +the hideen one heyen was used as the + + align:start position:0% +the hideen one heyen was used as the + + + align:start position:0% +the hideen one heyen was used as the +example for um for the German + + align:start position:0% +example for um for the German + + + align:start position:0% +example for um for the German +nationalist song he was the composer of + + align:start position:0% +nationalist song he was the composer of + + + align:start position:0% +nationalist song he was the composer of +the music but not the + + align:start position:0% + + + + align:start position:0% + +lyrics okay we got one + + align:start position:0% +lyrics okay we got one + + + align:start position:0% +lyrics okay we got one +fire fu + + align:start position:0% +fire fu + + + align:start position:0% +fire fu +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +fu the music 21 iterator talking about + + align:start position:0% +fu the music 21 iterator talking about + + + align:start position:0% +fu the music 21 iterator talking about +my own stuff that returns offsets from + + align:start position:0% +my own stuff that returns offsets from + + + align:start position:0% +my own stuff that returns offsets from +the start of the part is + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +you got one more + + align:start position:0% + + + + align:start position:0% + +person two + + align:start position:0% +person two + + + align:start position:0% +person two +seconds hey almost everybody got + + align:start position:0% +seconds hey almost everybody got + + + align:start position:0% +seconds hey almost everybody got +flattened I know you know that we Cur + + align:start position:0% +flattened I know you know that we Cur + + + align:start position:0% +flattened I know you know that we Cur +somebody was trying to trying to do the + + align:start position:0% +somebody was trying to trying to do the + + + align:start position:0% +somebody was trying to trying to do the +the thought experiment that I like + + align:start position:0% +the thought experiment that I like + + + align:start position:0% +the thought experiment that I like +recurse better I keep telling you use + + align:start position:0% +recurse better I keep telling you use + + + align:start position:0% +recurse better I keep telling you use +recurse but in this case flatten is the + + align:start position:0% +recurse but in this case flatten is the + + + align:start position:0% +recurse but in this case flatten is the +better + + align:start position:0% +better + + + align:start position:0% +better +one + + align:start position:0% + + + + align:start position:0% + +oops + + align:start position:0% + + + + align:start position:0% + +okay who wrote about musical codes in + + align:start position:0% +okay who wrote about musical codes in + + + align:start position:0% +okay who wrote about musical codes in +the introduction to Beyond MIDI + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +oh done + + align:start position:0% +oh done + + + align:start position:0% +oh done +done M Michael good does have an article + + align:start position:0% +done M Michael good does have an article + + + align:start position:0% +done M Michael good does have an article +in that book but no you don't know that + + align:start position:0% +in that book but no you don't know that + + + align:start position:0% +in that book but no you don't know that +was the next virtual score what I wrote + + align:start position:0% +was the next virtual score what I wrote + + + align:start position:0% +was the next virtual score what I wrote +before starting + + align:start position:0% + + + + align:start position:0% + +okay getting + + align:start position:0% + + + + align:start position:0% + +close Dimitri tasko criticized me for + + align:start position:0% +close Dimitri tasko criticized me for + + + align:start position:0% +close Dimitri tasko criticized me for +all of these things about music 21 + + align:start position:0% +all of these things about music 21 + + + align:start position:0% +all of these things about music 21 +except what this is hard + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +and oh no the one thing he didn't + + align:start position:0% +and oh no the one thing he didn't + + + align:start position:0% +and oh no the one thing he didn't +criticize me for is the worst feature on + + align:start position:0% +criticize me for is the worst feature on + + + align:start position:0% +criticize me for is the worst feature on +it it is really hard to install but + + align:start position:0% +it it is really hard to install but + + + align:start position:0% +it it is really hard to install but +somehow he already got it installed so + + align:start position:0% +somehow he already got it installed so + + + align:start position:0% +somehow he already got it installed so +he didn't care about + + align:start position:0% +he didn't care about + + + align:start position:0% +he didn't care about +that okay so that was that was one that + + align:start position:0% +that okay so that was that was one that + + + align:start position:0% +that okay so that was that was one that +shook shook things up the + + align:start position:0% +shook shook things up the + + + align:start position:0% +shook shook things up the +Snowman here we go um we're half over + + align:start position:0% +Snowman here we go um we're half over + + + align:start position:0% +Snowman here we go um we're half over +halfway there this is an extra credit + + align:start position:0% +halfway there this is an extra credit + + + align:start position:0% +halfway there this is an extra credit +from an optional reading so don't worry + + align:start position:0% +from an optional reading so don't worry + + + align:start position:0% +from an optional reading so don't worry +but take a guess on this one Donald bird + + align:start position:0% +but take a guess on this one Donald bird + + + align:start position:0% +but take a guess on this one Donald bird +created his extremes of music notation + + align:start position:0% +created his extremes of music notation + + + align:start position:0% +created his extremes of music notation +uh thing to show that notation + + align:start position:0% + + + + align:start position:0% + +what yeah good good good okay we don't + + align:start position:0% +what yeah good good good okay we don't + + + align:start position:0% +what yeah good good good okay we don't +need to discuss that even if you didn't + + align:start position:0% +need to discuss that even if you didn't + + + align:start position:0% +need to discuss that even if you didn't +do the reading it's really cool article + + align:start position:0% +do the reading it's really cool article + + + align:start position:0% +do the reading it's really cool article +if you haven't had a chance to flip + + align:start position:0% +if you haven't had a chance to flip + + + align:start position:0% +if you haven't had a chance to flip +through it some weird things in there + + align:start position:0% +through it some weird things in there + + + align:start position:0% +through it some weird things in there +Craig Sap's name good guy good guy + + align:start position:0% +Craig Sap's name good guy good guy + + + align:start position:0% +Craig Sap's name good guy good guy +appeared in this class for his creation + + align:start position:0% +appeared in this class for his creation + + + align:start position:0% +appeared in this class for his creation +of + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +what okay what do we get yes the + + align:start position:0% +what okay what do we get yes the + + + align:start position:0% +what okay what do we get yes the +illustration of the same passage of + + align:start position:0% +illustration of the same passage of + + + align:start position:0% +illustration of the same passage of +Music in dozens of encodings also known + + align:start position:0% +Music in dozens of encodings also known + + + align:start position:0% +Music in dozens of encodings also known +allowing you to translate from one + + align:start position:0% +allowing you to translate from one + + + align:start position:0% +allowing you to translate from one +coding to another called the Rosetta + + align:start position:0% +coding to another called the Rosetta + + + align:start position:0% +coding to another called the Rosetta +Stone yep um we got um he now runs the + + align:start position:0% +Stone yep um we got um he now runs the + + + align:start position:0% +Stone yep um we got um he now runs the +hum drum thing but it was David here on + + align:start position:0% +hum drum thing but it was David here on + + + align:start position:0% +hum drum thing but it was David here on +here um nobody did this one and uh yeah + + align:start position:0% +here um nobody did this one and uh yeah + + + align:start position:0% +here um nobody did this one and uh yeah +I don't know the answer to the + + align:start position:0% +I don't know the answer to the + + + align:start position:0% +I don't know the answer to the +red yellow exist um yes I believe so + + align:start position:0% +red yellow exist um yes I believe so + + + align:start position:0% +red yellow exist um yes I believe so +somewhere I this is from the reading for + + align:start position:0% +somewhere I this is from the reading for + + + align:start position:0% +somewhere I this is from the reading for +today so we'll see if we got today's + + align:start position:0% +today so we'll see if we got today's + + + align:start position:0% +today so we'll see if we got today's +reading what do David Luen call his + + align:start position:0% +reading what do David Luen call his + + + align:start position:0% +reading what do David Luen call his +unifying rule for species + + align:start position:0% + + + + align:start position:0% + +Counterpoint okay a lot of people gold R + + align:start position:0% +Counterpoint okay a lot of people gold R + + + align:start position:0% +Counterpoint okay a lot of people gold R +those who said Golden Rule by the way I + + align:start position:0% +those who said Golden Rule by the way I + + + align:start position:0% +those who said Golden Rule by the way I +am going to misspeak and call it the + + align:start position:0% +am going to misspeak and call it the + + + align:start position:0% +am going to misspeak and call it the +Golden Rule a lot because I do that but + + align:start position:0% +Golden Rule a lot because I do that but + + + align:start position:0% +Golden Rule a lot because I do that but +um yep we'll talk about it a little bit + + align:start position:0% +um yep we'll talk about it a little bit + + + align:start position:0% +um yep we'll talk about it a little bit +more the end of class + + align:start position:0% + + + + align:start position:0% + +today common or conventional music + + align:start position:0% +today common or conventional music + + + align:start position:0% +today common or conventional music +notation also CW MN consists of + + align:start position:0% + + + + align:start position:0% + +what Seven Answers + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah it's I know all of the above is + + align:start position:0% +yeah it's I know all of the above is + + + align:start position:0% +yeah it's I know all of the above is +almost always the right answer when you + + align:start position:0% +almost always the right answer when you + + + align:start position:0% +almost always the right answer when you +take a guess but no in this case it was + + align:start position:0% +take a guess but no in this case it was + + + align:start position:0% +take a guess but no in this case it was +just um things that traditional western + + align:start position:0% +just um things that traditional western + + + align:start position:0% +just um things that traditional western +music notation in some way so that you + + align:start position:0% +music notation in some way so that you + + + align:start position:0% +music notation in some way so that you +can write down non-western and you can + + align:start position:0% +can write down non-western and you can + + + align:start position:0% +can write down non-western and you can +ENC as you all know you can encode many + + align:start position:0% +ENC as you all know you can encode many + + + align:start position:0% +ENC as you all know you can encode many +things into the computer that are not + + align:start position:0% +things into the computer that are not + + + align:start position:0% +things into the computer that are not +that so great we're doing we're doing + + align:start position:0% +that so great we're doing we're doing + + + align:start position:0% +that so great we're doing we're doing +well + + align:start position:0% + + + + align:start position:0% + +now okay three + + align:start position:0% + + + + align:start position:0% + +more oh + + align:start position:0% +more oh + + + align:start position:0% +more oh +wow nice we don't need to do that + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +anymore Arden and hon showed how + + align:start position:0% +anymore Arden and hon showed how + + + align:start position:0% +anymore Arden and hon showed how +European folk song varied across genre + + align:start position:0% +European folk song varied across genre + + + align:start position:0% +European folk song varied across genre +times locations + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +functions hey yep we almost always got + + align:start position:0% +functions hey yep we almost always got + + + align:start position:0% +functions hey yep we almost always got +that this was the article that showed + + align:start position:0% +that this was the article that showed + + + align:start position:0% +that this was the article that showed +the geographic information systems back + + align:start position:0% +the geographic information systems back + + + align:start position:0% +the geographic information systems back +when that was very very hard to do we + + align:start position:0% +when that was very very hard to do we + + + align:start position:0% +when that was very very hard to do we +should be able to do this more easily + + align:start position:0% +should be able to do this more easily + + + align:start position:0% +should be able to do this more easily +with Google Maps and + + align:start position:0% +with Google Maps and + + + align:start position:0% +with Google Maps and +things + + align:start position:0% +things + + + align:start position:0% +things +okay before we do the last one uh before + + align:start position:0% +okay before we do the last one uh before + + + align:start position:0% +okay before we do the last one uh before +we do the last one just to know the quiz + + align:start position:0% +we do the last one just to know the quiz + + + align:start position:0% +we do the last one just to know the quiz +will not be a bunch of these little + + align:start position:0% +will not be a bunch of these little + + + align:start position:0% +will not be a bunch of these little +factoid things that's just all I can + + align:start position:0% +factoid things that's just all I can + + + align:start position:0% +factoid things that's just all I can +figure out to do on cahoot it will be + + align:start position:0% +figure out to do on cahoot it will be + + + align:start position:0% +figure out to do on cahoot it will be +actually about conceptual issues and + + align:start position:0% +actually about conceptual issues and + + + align:start position:0% +actually about conceptual issues and +ability to apply these ideas but um + + align:start position:0% +ability to apply these ideas but um + + + align:start position:0% +ability to apply these ideas but um +let's finish this oh it's about uh + + align:start position:0% +let's finish this oh it's about uh + + + align:start position:0% +let's finish this oh it's about uh +Sophia son and me showed connections + + align:start position:0% +Sophia son and me showed connections + + + align:start position:0% +Sophia son and me showed connections +between music and emotion using what + + align:start position:0% +between music and emotion using what + + + align:start position:0% +between music and emotion using what +types of musical scores + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +answer oh no I know I do too many V + + align:start position:0% +answer oh no I know I do too many V + + + align:start position:0% +answer oh no I know I do too many V +crows and I do medieval music but it was + + align:start position:0% +crows and I do medieval music but it was + + + align:start position:0% +crows and I do medieval music but it was +lead sheets uh so yep oh yeah read great + + align:start position:0% +lead sheets uh so yep oh yeah read great + + + align:start position:0% +lead sheets uh so yep oh yeah read great +so we have on the + + align:start position:0% +so we have on the + + + align:start position:0% +so we have on the +podium third place nickname three + + align:start position:0% +podium third place nickname three + + + align:start position:0% +podium third place nickname three +anybody want to claim their Podium + + align:start position:0% +anybody want to claim their Podium + + + align:start position:0% +anybody want to claim their Podium +nicely done nickname too yep and + + align:start position:0% + + + + align:start position:0% + +top I guess this shows that some people + + align:start position:0% +top I guess this shows that some people + + + align:start position:0% +top I guess this shows that some people +spend their time not thinking of + + align:start position:0% +spend their time not thinking of + + + align:start position:0% +spend their time not thinking of +creative names but just reading the + + align:start position:0% +creative names but just reading the + + + align:start position:0% +creative names but just reading the +Articles congrats everybody so we've + + align:start position:0% +Articles congrats everybody so we've + + + align:start position:0% +Articles congrats everybody so we've +been talking a lot about encodings and + + align:start position:0% +been talking a lot about encodings and + + + align:start position:0% +been talking a lot about encodings and +what you'll be doing over the course of + + align:start position:0% +what you'll be doing over the course of + + + align:start position:0% +what you'll be doing over the course of +the semester sometimes is working with + + align:start position:0% +the semester sometimes is working with + + + align:start position:0% +the semester sometimes is working with +these strange encodings and maybe as + + align:start position:0% +these strange encodings and maybe as + + + align:start position:0% +these strange encodings and maybe as +we're starting to get well let me say + + align:start position:0% +we're starting to get well let me say + + + align:start position:0% +we're starting to get well let me say +you've had some problem sets where I've + + align:start position:0% +you've had some problem sets where I've + + + align:start position:0% +you've had some problem sets where I've +given you questions and you've given + + align:start position:0% +given you questions and you've given + + + align:start position:0% +given you questions and you've given +answers right and now you've given two + + align:start position:0% +answers right and now you've given two + + + align:start position:0% +answers right and now you've given two +problem sets that encoding one and uh + + align:start position:0% +problem sets that encoding one and uh + + + align:start position:0% +problem sets that encoding one and uh +this corpor one where you've been doing + + align:start position:0% +this corpor one where you've been doing + + + align:start position:0% +this corpor one where you've been doing +the research to find interesting + + align:start position:0% +the research to find interesting + + + align:start position:0% +the research to find interesting +problems but I haven't been asking you + + align:start position:0% +problems but I haven't been asking you + + + align:start position:0% +problems but I haven't been asking you +to actually get an answer you didn't + + align:start position:0% +to actually get an answer you didn't + + + align:start position:0% +to actually get an answer you didn't +need to make a corpus a par parser for + + align:start position:0% +need to make a corpus a par parser for + + + align:start position:0% +need to make a corpus a par parser for +guitar um ultimate guitar in order to + + align:start position:0% +guitar um ultimate guitar in order to + + + align:start position:0% +guitar um ultimate guitar in order to +answer any questions so we're getting to + + align:start position:0% +answer any questions so we're getting to + + + align:start position:0% +answer any questions so we're getting to +the end of the semester we'll be + + align:start position:0% +the end of the semester we'll be + + + align:start position:0% +the end of the semester we'll be +bringing those two things colliding + + align:start position:0% +bringing those two things colliding + + + align:start position:0% +bringing those two things colliding +together and doing more um on how you + + align:start position:0% +together and doing more um on how you + + + align:start position:0% +together and doing more um on how you +can come up with your own problems and + + align:start position:0% +can come up with your own problems and + + + align:start position:0% +can come up with your own problems and +come up with your own Solutions Michael + + align:start position:0% +come up with your own Solutions Michael + + + align:start position:0% +come up with your own Solutions Michael +would you like to come up and talk for + + align:start position:0% +would you like to come up and talk for + + + align:start position:0% +would you like to come up and talk for +just a little bit I'd like to introduce + + align:start position:0% +just a little bit I'd like to introduce + + + align:start position:0% +just a little bit I'd like to introduce +Michael good who's uh MIT grad and the + + align:start position:0% +Michael good who's uh MIT grad and the + + + align:start position:0% +Michael good who's uh MIT grad and the +inventor of Music XML up here who's + + align:start position:0% +inventor of Music XML up here who's + + + align:start position:0% +inventor of Music XML up here who's +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Vis you all have seen an interview with + + align:start position:0% +Vis you all have seen an interview with + + + align:start position:0% +Vis you all have seen an interview with +Michael right so just wanted to to talk + + align:start position:0% +Michael right so just wanted to to talk + + + align:start position:0% +Michael right so just wanted to to talk +the interview is a couple couple years + + align:start position:0% +the interview is a couple couple years + + + align:start position:0% +the interview is a couple couple years +old now I think we did it during covid + + align:start position:0% +old now I think we did it during covid + + + align:start position:0% +old now I think we did it during covid +um yeah so what's what's been up and + + align:start position:0% +um yeah so what's what's been up and + + + align:start position:0% +um yeah so what's what's been up and +interesting in the world of anything + + align:start position:0% +interesting in the world of anything + + + align:start position:0% +interesting in the world of anything +with computer music but especially you + + align:start position:0% +with computer music but especially you + + + align:start position:0% +with computer music but especially you +know music the encoding anything that + + align:start position:0% +know music the encoding anything that + + + align:start position:0% +know music the encoding anything that +you've been finding or oh that's I I + + align:start position:0% +you've been finding or oh that's I I + + + align:start position:0% +you've been finding or oh that's I I +retired um in January so my mind has + + align:start position:0% +retired um in January so my mind has + + + align:start position:0% +retired um in January so my mind has +sort of gone out of the music notation + + align:start position:0% +sort of gone out of the music notation + + + align:start position:0% +sort of gone out of the music notation +area + + align:start position:0% +area + + + align:start position:0% +area +CL I mean some of the things that were + + align:start position:0% +CL I mean some of the things that were + + + align:start position:0% +CL I mean some of the things that were +in these projects were really cool the + + align:start position:0% +in these projects were really cool the + + + align:start position:0% +in these projects were really cool the +uh the body percussion en coding stuff + + align:start position:0% +uh the body percussion en coding stuff + + + align:start position:0% +uh the body percussion en coding stuff +and I was like oh pretty pretty great + + align:start position:0% +and I was like oh pretty pretty great + + + align:start position:0% +and I was like oh pretty pretty great +yeah do you do you feel like like now + + align:start position:0% +yeah do you do you feel like like now + + + align:start position:0% +yeah do you do you feel like like now +now you got to come out of retirement + + align:start position:0% +now you got to come out of retirement + + + align:start position:0% +now you got to come out of retirement +and find a way to put all these things + + align:start position:0% +and find a way to put all these things + + + align:start position:0% +and find a way to put all these things +into music XML not yet + + align:start position:0% +into music XML not yet + + + align:start position:0% +into music XML not yet +okay so but in the future but what what + + align:start position:0% +okay so but in the future but what what + + + align:start position:0% +okay so but in the future but what what +are some ways that somebody could get um + + align:start position:0% +are some ways that somebody could get um + + + align:start position:0% +are some ways that somebody could get um +you know a particular musical project if + + align:start position:0% +you know a particular musical project if + + + align:start position:0% +you know a particular musical project if +they're interested in you know + + align:start position:0% +they're interested in you know + + + align:start position:0% +they're interested in you know +non-western music or something else and + + align:start position:0% +non-western music or something else and + + + align:start position:0% +non-western music or something else and +get get such a standard um sort of + + align:start position:0% +get get such a standard um sort of + + + align:start position:0% +get get such a standard um sort of +musical encoding as as you've created + + align:start position:0% +musical encoding as as you've created + + + align:start position:0% +musical encoding as as you've created +what what kind of advice would you give + + align:start position:0% +what what kind of advice would you give + + + align:start position:0% +what what kind of advice would you give +for that well + + align:start position:0% +for that well + + + align:start position:0% +for that well +you to develop a standard for a music + + align:start position:0% +you to develop a standard for a music + + + align:start position:0% +you to develop a standard for a music +representation you need to have multiple + + align:start position:0% +representation you need to have multiple + + + align:start position:0% +representation you need to have multiple +people who are using it right and you + + align:start position:0% +people who are using it right and you + + + align:start position:0% +people who are using it right and you +need to have I think tools that that + + align:start position:0% +need to have I think tools that that + + + align:start position:0% +need to have I think tools that that +support it so that becomes if it's non + + align:start position:0% +support it so that becomes if it's non + + + align:start position:0% +support it so that becomes if it's non +standard that becomes more of a you know + + align:start position:0% +standard that becomes more of a you know + + + align:start position:0% +standard that becomes more of a you know +less common repertoire that becomes more + + align:start position:0% +less common repertoire that becomes more + + + align:start position:0% +less common repertoire that becomes more +of a chicken and an egg problem so look + + align:start position:0% +of a chicken and an egg problem so look + + + align:start position:0% +of a chicken and an egg problem so look +for something that has at least two + + align:start position:0% +for something that has at least two + + + align:start position:0% +for something that has at least two +applications that are doing that type of + + align:start position:0% +applications that are doing that type of + + + align:start position:0% +applications that are doing that type of +music and see if you can do maybe there + + align:start position:0% +music and see if you can do maybe there + + + align:start position:0% +music and see if you can do maybe there +one's an application you wrote and one's + + align:start position:0% +one's an application you wrote and one's + + + align:start position:0% +one's an application you wrote and one's +an application somebody else wrote and + + align:start position:0% +an application somebody else wrote and + + + align:start position:0% +an application somebody else wrote and +tried to put something in between I mean + + align:start position:0% +tried to put something in between I mean + + + align:start position:0% +tried to put something in between I mean +when I was starting music XML a lot of + + align:start position:0% +when I was starting music XML a lot of + + + align:start position:0% +when I was starting music XML a lot of +people had tried to do a standard common + + align:start position:0% +people had tried to do a standard common + + + align:start position:0% +people had tried to do a standard common +western music notation format and I knew + + align:start position:0% +western music notation format and I knew + + + align:start position:0% +western music notation format and I knew +that if it was if it didn't work with + + align:start position:0% +that if it was if it didn't work with + + + align:start position:0% +that if it was if it didn't work with +either finale or cilus because those are + + align:start position:0% +either finale or cilus because those are + + + align:start position:0% +either finale or cilus because those are +the two programs people cared about then + + align:start position:0% +the two programs people cared about then + + + align:start position:0% +the two programs people cared about then +if it didn't work with at least one of + + align:start position:0% +if it didn't work with at least one of + + + align:start position:0% +if it didn't work with at least one of +those two programs I was just going to + + align:start position:0% +those two programs I was just going to + + + align:start position:0% +those two programs I was just going to +give up go home and find something else + + align:start position:0% +give up go home and find something else + + + align:start position:0% +give up go home and find something else +to do because nobody would care about + + align:start position:0% +to do because nobody would care about + + + align:start position:0% +to do because nobody would care about +music XML if it didn't work with one of + + align:start position:0% +music XML if it didn't work with one of + + + align:start position:0% +music XML if it didn't work with one of +those programs nowaday be M score Oro or + + align:start position:0% +those programs nowaday be M score Oro or + + + align:start position:0% +those programs nowaday be M score Oro or +things like + + align:start position:0% +things like + + + align:start position:0% +things like +that so if you're trying to do a + + align:start position:0% +that so if you're trying to do a + + + align:start position:0% +that so if you're trying to do a +standard music representation then you + + align:start position:0% +standard music representation then you + + + align:start position:0% +standard music representation then you +need to have a community of people who + + align:start position:0% +need to have a community of people who + + + align:start position:0% +need to have a community of people who +are using it and applications that use + + align:start position:0% +are using it and applications that use + + + align:start position:0% +are using it and applications that use +it um maybe more interesting is just to + + align:start position:0% +it um maybe more interesting is just to + + + align:start position:0% +it um maybe more interesting is just to +you know at this point is to come up + + align:start position:0% +you know at this point is to come up + + + align:start position:0% +you know at this point is to come up +with cool things that could be + + align:start position:0% +with cool things that could be + + + align:start position:0% +with cool things that could be +represented and and and do some analysis + + align:start position:0% +represented and and and do some analysis + + + align:start position:0% +represented and and and do some analysis +there and and try to figure out ways + + align:start position:0% +there and and try to figure out ways + + + align:start position:0% +there and and try to figure out ways +that these representations could be + + align:start position:0% +that these representations could be + + + align:start position:0% +that these representations could be +useful for the musicians + + align:start position:0% +useful for the musicians + + + align:start position:0% +useful for the musicians +uh who are doing these type of + + align:start position:0% +uh who are doing these type of + + + align:start position:0% +uh who are doing these type of +repertoire great so Michael was um you + + align:start position:0% +repertoire great so Michael was um you + + + align:start position:0% +repertoire great so Michael was um you +did music when you were at MIT oh yeah + + align:start position:0% +did music when you were at MIT oh yeah + + + align:start position:0% +did music when you were at MIT oh yeah +what what kinds of things well I was a + + align:start position:0% +what what kinds of things well I was a + + + align:start position:0% +what what kinds of things well I was a +trumpet player nowadays I sing my wife + + align:start position:0% +trumpet player nowadays I sing my wife + + + align:start position:0% +trumpet player nowadays I sing my wife +my wife my wife and I met in the MIT + + align:start position:0% +my wife my wife and I met in the MIT + + + align:start position:0% +my wife my wife and I met in the MIT +concert band she's an electrical + + align:start position:0% +concert band she's an electrical + + + align:start position:0% +concert band she's an electrical +engineer right she's she's uh the one of + + align:start position:0% +engineer right she's she's uh the one of + + + align:start position:0% +engineer right she's she's uh the one of +the 40 top engineers at Analog Devices + + align:start position:0% +the 40 top engineers at Analog Devices + + + align:start position:0% +the 40 top engineers at Analog Devices +so she just was talking with race dat at + + align:start position:0% +so she just was talking with race dat at + + + align:start position:0% +so she just was talking with race dat at +her company + + align:start position:0% +her company + + + align:start position:0% +her company +conference a couple days ago so she's 61 + + align:start position:0% +conference a couple days ago so she's 61 + + + align:start position:0% +conference a couple days ago so she's 61 +I'm 63 uh I'm class of 79 she's class of + + align:start position:0% +I'm 63 uh I'm class of 79 she's class of + + + align:start position:0% +I'm 63 uh I'm class of 79 she's class of +82 and she played Piccolo I played + + align:start position:0% +82 and she played Piccolo I played + + + align:start position:0% +82 and she played Piccolo I played +trumpet and I played trumpet in the band + + align:start position:0% +trumpet and I played trumpet in the band + + + align:start position:0% +trumpet and I played trumpet in the band +The Orchestra Festival Jazz Ensemble + + align:start position:0% +The Orchestra Festival Jazz Ensemble + + + align:start position:0% +The Orchestra Festival Jazz Ensemble +chamber music Society musical you know + + align:start position:0% +chamber music Society musical you know + + + align:start position:0% +chamber music Society musical you know +anything that needed a trumpet laptop + + align:start position:0% +anything that needed a trumpet laptop + + + align:start position:0% +anything that needed a trumpet laptop +Ensemble played it there was no there + + align:start position:0% +Ensemble played it there was no there + + + align:start position:0% +Ensemble played it there was no there +was no laptop laptops were not + + align:start position:0% +was no laptop laptops were not + + + align:start position:0% +was no laptop laptops were not +invented I was I ter the the coolest + + align:start position:0% +invented I was I ter the the coolest + + + align:start position:0% +invented I was I ter the the coolest +thing I did my my thesis in the + + align:start position:0% +thing I did my my thesis in the + + + align:start position:0% +thing I did my my thesis in the +experimental music studio with Professor + + align:start position:0% +experimental music studio with Professor + + + align:start position:0% +experimental music studio with Professor +Barry burko which is now the media lab + + align:start position:0% +Barry burko which is now the media lab + + + align:start position:0% +Barry burko which is now the media lab +one of the groups that became part of + + align:start position:0% +one of the groups that became part of + + + align:start position:0% +one of the groups that became part of +the media lab and the coolest thing was + + align:start position:0% +the media lab and the coolest thing was + + + align:start position:0% +the media lab and the coolest thing was +we got to use t52 terminals instead you + + align:start position:0% +we got to use t52 terminals instead you + + + align:start position:0% +we got to use t52 terminals instead you +know video terminals instead of the you + + align:start position:0% +know video terminals instead of the you + + + align:start position:0% +know video terminals instead of the you +know paper terminals that I was using + + align:start position:0% +know paper terminals that I was using + + + align:start position:0% +know paper terminals that I was using +for all my other classes so I got to use + + align:start position:0% +for all my other classes so I got to use + + + align:start position:0% +for all my other classes so I got to use +the coolest computer technology that I + + align:start position:0% +the coolest computer technology that I + + + align:start position:0% +the coolest computer technology that I +had seen at that point in my computer + + align:start position:0% +had seen at that point in my computer + + + align:start position:0% +had seen at that point in my computer +music class so that was awesome so + + align:start position:0% +music class so that was awesome so + + + align:start position:0% +music class so that was awesome so +Michael here's a a question I haven't I + + align:start position:0% +Michael here's a a question I haven't I + + + align:start position:0% +Michael here's a a question I haven't I +I don't think I've ever asked you so so + + align:start position:0% +I don't think I've ever asked you so so + + + align:start position:0% +I don't think I've ever asked you so so +you did music while you were at MIT and + + align:start position:0% +you did music while you were at MIT and + + + align:start position:0% +you did music while you were at MIT and +you did other things and then um but + + align:start position:0% +you did other things and then um but + + + align:start position:0% +you did other things and then um but +music wasn't your primary um sort of you + + align:start position:0% +music wasn't your primary um sort of you + + + align:start position:0% +music wasn't your primary um sort of you +know putting money in you're in a bank + + align:start position:0% +know putting money in you're in a bank + + + align:start position:0% +know putting money in you're in a bank +for a bit um you could ask a little bit + + align:start position:0% +for a bit um you could ask a little bit + + + align:start position:0% +for a bit um you could ask a little bit +about what that was but what made you + + align:start position:0% +about what that was but what made you + + + align:start position:0% +about what that was but what made you +want to come back and do it and is there + + align:start position:0% +want to come back and do it and is there + + + align:start position:0% +want to come back and do it and is there +anything for anybody who's not thinking + + align:start position:0% +anything for anybody who's not thinking + + + align:start position:0% +anything for anybody who's not thinking +of graduating this year next year + + align:start position:0% +of graduating this year next year + + + align:start position:0% +of graduating this year next year +whatever and doing music but might + + align:start position:0% +whatever and doing music but might + + + align:start position:0% +whatever and doing music but might +follow a career like years well yeah + + align:start position:0% +follow a career like years well yeah + + + align:start position:0% +follow a career like years well yeah +following a career like line is kind of + + align:start position:0% +following a career like line is kind of + + + align:start position:0% +following a career like line is kind of +I mean it's a whole different time now + + align:start position:0% +I mean it's a whole different time now + + + align:start position:0% +I mean it's a whole different time now +when I I was doing my bachelor's thesis + + align:start position:0% +when I I was doing my bachelor's thesis + + + align:start position:0% +when I I was doing my bachelor's thesis +at the experimental music studio was on + + align:start position:0% +at the experimental music studio was on + + + align:start position:0% +at the experimental music studio was on +one of these alpha alpha numeric + + align:start position:0% +one of these alpha alpha numeric + + + align:start position:0% +one of these alpha alpha numeric +encodings um which is now called Scott + + align:start position:0% +encodings um which is now called Scott + + + align:start position:0% +encodings um which is now called Scott +it's actually still still shipped I + + align:start position:0% +it's actually still still shipped I + + + align:start position:0% +it's actually still still shipped I +think as part of sees sound and I was + + align:start position:0% +think as part of sees sound and I was + + + align:start position:0% +think as part of sees sound and I was +rewriting it from an earlier version + + align:start position:0% +rewriting it from an earlier version + + + align:start position:0% +rewriting it from an earlier version +called Soo but this was in 1979 so there + + align:start position:0% +called Soo but this was in 1979 so there + + + align:start position:0% +called Soo but this was in 1979 so there +was no midi right there was no computer + + align:start position:0% +was no midi right there was no computer + + + align:start position:0% +was no midi right there was no computer +music technology industry okay New + + align:start position:0% +music technology industry okay New + + + align:start position:0% +music technology industry okay New +England digital was doing some clavet + + align:start position:0% +England digital was doing some clavet + + + align:start position:0% +England digital was doing some clavet +but you know that was know one tiny + + align:start position:0% +but you know that was know one tiny + + + align:start position:0% +but you know that was know one tiny +company so there wasn't any industry to + + align:start position:0% +company so there wasn't any industry to + + + align:start position:0% +company so there wasn't any industry to +go to for a job so I started to do + + align:start position:0% +go to for a job so I started to do + + + align:start position:0% +go to for a job so I started to do +usability work as for my grad school I I + + align:start position:0% +usability work as for my grad school I I + + + align:start position:0% +usability work as for my grad school I I +got my masters here too and I did + + align:start position:0% +got my masters here too and I did + + + align:start position:0% +got my masters here too and I did +usability work until 2000 when it you + + align:start position:0% +usability work until 2000 when it you + + + align:start position:0% +usability work until 2000 when it you +could see that everything was going to + + align:start position:0% +could see that everything was going to + + + align:start position:0% +could see that everything was going to +this is when the web was coming up and + + align:start position:0% +this is when the web was coming up and + + + align:start position:0% +this is when the web was coming up and +you know everything was going to be + + align:start position:0% +you know everything was going to be + + + align:start position:0% +you know everything was going to be +moved this app over to the web from from + + align:start position:0% +moved this app over to the web from from + + + align:start position:0% +moved this app over to the web from from +from Au GOI and the first time I did + + align:start position:0% +from Au GOI and the first time I did + + + align:start position:0% +from Au GOI and the first time I did +that it was a lot of fun and but doing + + align:start position:0% +that it was a lot of fun and but doing + + + align:start position:0% +that it was a lot of fun and but doing +it a thousand times was going to be + + align:start position:0% +it a thousand times was going to be + + + align:start position:0% +it a thousand times was going to be +really boring so I looked at you know + + align:start position:0% +really boring so I looked at you know + + + align:start position:0% +really boring so I looked at you know +there was an opportunity to do a + + align:start position:0% +there was an opportunity to do a + + + align:start position:0% +there was an opportunity to do a +standard music notation format there was + + align:start position:0% +standard music notation format there was + + + align:start position:0% +standard music notation format there was +downloadable sheet music starting to + + align:start position:0% +downloadable sheet music starting to + + + align:start position:0% +downloadable sheet music starting to +happen it was IND decent uh thing so + + align:start position:0% +happen it was IND decent uh thing so + + + align:start position:0% +happen it was IND decent uh thing so +there was obviously a demand for uh a + + align:start position:0% +there was obviously a demand for uh a + + + align:start position:0% +there was obviously a demand for uh a +standard computer music because it was + + align:start position:0% +standard computer music because it was + + + align:start position:0% +standard computer music because it was +silly you could download the music and + + align:start position:0% +silly you could download the music and + + + align:start position:0% +silly you could download the music and +all you could do was use it in the + + align:start position:0% +all you could do was use it in the + + + align:start position:0% +all you could do was use it in the +player or print it out and it's was like + + align:start position:0% +player or print it out and it's was like + + + align:start position:0% +player or print it out and it's was like +you should be able to share it back and + + align:start position:0% +you should be able to share it back and + + + align:start position:0% +you should be able to share it back and +forth between programs like HTML and + + align:start position:0% +forth between programs like HTML and + + + align:start position:0% +forth between programs like HTML and +midi you know if you don't have a + + align:start position:0% +midi you know if you don't have a + + + align:start position:0% +midi you know if you don't have a +standard it's it's nothing for for that + + align:start position:0% +standard it's it's nothing for for that + + + align:start position:0% +standard it's it's nothing for for that +type of common things + + align:start position:0% +type of common things + + + align:start position:0% +type of common things +so that was the motivation to do it you + + align:start position:0% +so that was the motivation to do it you + + + align:start position:0% +so that was the motivation to do it you +know that I I wanted to use downloadable + + align:start position:0% +know that I I wanted to use downloadable + + + align:start position:0% +know that I I wanted to use downloadable +music in any + + align:start position:0% +music in any + + + align:start position:0% +music in any +application and I but I had the + + align:start position:0% +application and I but I had the + + + align:start position:0% +application and I but I had the +financial uh ability to do that because + + align:start position:0% +financial uh ability to do that because + + + align:start position:0% +financial uh ability to do that because +my wife worked for Analog Devices and + + align:start position:0% +my wife worked for Analog Devices and + + + align:start position:0% +my wife worked for Analog Devices and +elect engineer and their company did + + align:start position:0% +elect engineer and their company did + + + align:start position:0% +elect engineer and their company did +really well and so if I totally failed + + align:start position:0% +really well and so if I totally failed + + + align:start position:0% +really well and so if I totally failed +it didn't matter financially so I mean I + + align:start position:0% +it didn't matter financially so I mean I + + + align:start position:0% +it didn't matter financially so I mean I +was in extremely lucky position there I + + align:start position:0% +was in extremely lucky position there I + + + align:start position:0% +was in extremely lucky position there I +me nowadays though you can you know you + + align:start position:0% +me nowadays though you can you know you + + + align:start position:0% +me nowadays though you can you know you +got each other all interested in music + + align:start position:0% +got each other all interested in music + + + align:start position:0% +got each other all interested in music +technology and there's all sort I + + align:start position:0% +technology and there's all sort I + + + align:start position:0% +technology and there's all sort I +mean to go through I mean if IID had a + + align:start position:0% +mean to go through I mean if IID had a + + + align:start position:0% +mean to go through I mean if IID had a +class like this I wouldn't have had a + + align:start position:0% +class like this I wouldn't have had a + + + align:start position:0% +class like this I wouldn't have had a +class like this because you didn't I had + + align:start position:0% +class like this because you didn't I had + + + align:start position:0% +class like this because you didn't I had +to spend all my time like building + + align:start position:0% +to spend all my time like building + + + align:start position:0% +to spend all my time like building +infrastructure now you can do the cool + + align:start position:0% +infrastructure now you can do the cool + + + align:start position:0% +infrastructure now you can do the cool +things on top of you know the cool + + align:start position:0% +things on top of you know the cool + + + align:start position:0% +things on top of you know the cool +problems on top of it so find find cool + + align:start position:0% +problems on top of it so find find cool + + + align:start position:0% +problems on top of it so find find cool +problems that people are interested in + + align:start position:0% +problems that people are interested in + + + align:start position:0% +problems that people are interested in +uh I mean if you want to make a career + + align:start position:0% +uh I mean if you want to make a career + + + align:start position:0% +uh I mean if you want to make a career +if you if you're just studying you know + + align:start position:0% +if you if you're just studying you know + + + align:start position:0% +if you if you're just studying you know +find a cool problem that you're + + align:start position:0% +find a cool problem that you're + + + align:start position:0% +find a cool problem that you're +interested in well that's I guess the + + align:start position:0% +interested in well that's I guess the + + + align:start position:0% +interested in well that's I guess the +starting point anyway find a cool + + align:start position:0% +starting point anyway find a cool + + + align:start position:0% +starting point anyway find a cool +problem that you're interested in + + align:start position:0% +problem that you're interested in + + + align:start position:0% +problem that you're interested in +because if you're not interested in it + + align:start position:0% +because if you're not interested in it + + + align:start position:0% +because if you're not interested in it +you won't be able to make a living at it + + align:start position:0% +you won't be able to make a living at it + + + align:start position:0% +you won't be able to make a living at it +you'll just be terribly bored and then + + align:start position:0% +you'll just be terribly bored and then + + + align:start position:0% +you'll just be terribly bored and then +find if somebody else is interested in + + align:start position:0% +find if somebody else is interested in + + + align:start position:0% +find if somebody else is interested in +that or something + + align:start position:0% +that or something + + + align:start position:0% +that or something +adjacent one last question before I let + + align:start position:0% +adjacent one last question before I let + + + align:start position:0% +adjacent one last question before I let +you go if that's if that's okay um you + + align:start position:0% +you go if that's if that's okay um you + + + align:start position:0% +you go if that's if that's okay um you +know it's hard for us to think of you + + align:start position:0% +know it's hard for us to think of you + + + align:start position:0% +know it's hard for us to think of you +know that that you went from the + + align:start position:0% +know that that you went from the + + + align:start position:0% +know that that you went from the +essentially teletype era things you + + align:start position:0% +essentially teletype era things you + + + align:start position:0% +essentially teletype era things you +don't see things on screen you have to + + align:start position:0% +don't see things on screen you have to + + + align:start position:0% +don't see things on screen you have to +type it onto and then it all comes out + + align:start position:0% +type it onto and then it all comes out + + + align:start position:0% +type it onto and then it all comes out +on paper and stuff in of what 30 uh + + align:start position:0% +on paper and stuff in of what 30 uh + + + align:start position:0% +on paper and stuff in of what 30 uh +bytes per second uh modems and and and + + align:start position:0% +bytes per second uh modems and and and + + + align:start position:0% +bytes per second uh modems and and and +things like that to I mean until two + + align:start position:0% +things like that to I mean until two + + + align:start position:0% +things like that to I mean until two +months ago when you retired you were + + align:start position:0% +months ago when you retired you were + + + align:start position:0% +months ago when you retired you were +still totally on top of of like 99% as + + align:start position:0% +still totally on top of of like 99% as + + + align:start position:0% +still totally on top of of like 99% as +many percent of the new technologies as + + align:start position:0% +many percent of the new technologies as + + + align:start position:0% +many percent of the new technologies as +anybody can do and things and someday + + align:start position:0% +anybody can do and things and someday + + + align:start position:0% +anybody can do and things and someday +it's hard for us to think but these will + + align:start position:0% +it's hard for us to think but these will + + + align:start position:0% +it's hard for us to think but these will +seem as outrageous as a teletype or a + + align:start position:0% +seem as outrageous as a teletype or a + + + align:start position:0% +seem as outrageous as a teletype or a +horse and buggy and stuff what not just + + align:start position:0% +horse and buggy and stuff what not just + + + align:start position:0% +horse and buggy and stuff what not just +for music people but how do we keep up + + align:start position:0% +for music people but how do we keep up + + + align:start position:0% +for music people but how do we keep up +how do we keep up like you with all the + + align:start position:0% +how do we keep up like you with all the + + + align:start position:0% +how do we keep up like you with all the +changing + + align:start position:0% +changing + + + align:start position:0% +changing +technology if you're a tech person like + + align:start position:0% +technology if you're a tech person like + + + align:start position:0% +technology if you're a tech person like +I think you you kind of do + + align:start position:0% +I think you you kind of do + + + align:start position:0% +I think you you kind of do +that live in Silicon Valley you gota but + + align:start position:0% +that live in Silicon Valley you gota but + + + align:start position:0% +that live in Silicon Valley you gota but +stay with you know what's going I mean I + + align:start position:0% +stay with you know what's going I mean I + + + align:start position:0% +stay with you know what's going I mean I +have this usability background so I was + + align:start position:0% +have this usability background so I was + + + align:start position:0% +have this usability background so I was +always interested in user interface + + align:start position:0% +always interested in user interface + + + align:start position:0% +always interested in user interface +Technologies but I mean I don't know + + align:start position:0% +Technologies but I mean I don't know + + + align:start position:0% +Technologies but I mean I don't know +anything about machine learning + + align:start position:0% +anything about machine learning + + + align:start position:0% +anything about machine learning +outside of applications for it I mean in + + align:start position:0% +outside of applications for it I mean in + + + align:start position:0% +outside of applications for it I mean in +the music space I'm excited to see what + + align:start position:0% +the music space I'm excited to see what + + + align:start position:0% +the music space I'm excited to see what +sound slice is doing for using machine + + align:start position:0% +sound slice is doing for using machine + + + align:start position:0% +sound slice is doing for using machine +learning for optical music recognition + + align:start position:0% +learning for optical music recognition + + + align:start position:0% +learning for optical music recognition +What audio Shake is doing for Source + + align:start position:0% +What audio Shake is doing for Source + + + align:start position:0% +What audio Shake is doing for Source +separation of of audio which everybody + + align:start position:0% +separation of of audio which everybody + + + align:start position:0% +separation of of audio which everybody +tried to do and nobody would they're the + + align:start position:0% +tried to do and nobody would they're the + + + align:start position:0% +tried to do and nobody would they're the +first ones who are able to do it and + + align:start position:0% +first ones who are able to do it and + + + align:start position:0% +first ones who are able to do it and +they're very clear about which problems + + align:start position:0% +they're very clear about which problems + + + align:start position:0% +they're very clear about which problems +they can handle and which problems they + + align:start position:0% +they can handle and which problems they + + + align:start position:0% +they can handle and which problems they +can't and why it's a good market and why + + align:start position:0% +can't and why it's a good market and why + + + align:start position:0% +can't and why it's a good market and why +it's supporting musicians so we were + + align:start position:0% +it's supporting musicians so we were + + + align:start position:0% +it's supporting musicians so we were +talking a little earlier about with + + align:start position:0% +talking a little earlier about with + + + align:start position:0% +talking a little earlier about with +generative music things sort of to sum + + align:start position:0% +generative music things sort of to sum + + + align:start position:0% +generative music things sort of to sum +up what you're saying is make make sure + + align:start position:0% +up what you're saying is make make sure + + + align:start position:0% +up what you're saying is make make sure +that there's a problem that you're + + align:start position:0% +that there's a problem that you're + + + align:start position:0% +that there's a problem that you're +trying to solve yeah a problem that + + align:start position:0% +trying to solve yeah a problem that + + + align:start position:0% +trying to solve yeah a problem that +you're trying to solve that isn't + + align:start position:0% +you're trying to solve that isn't + + + align:start position:0% +you're trying to solve that isn't +putting musicians out of work would + + align:start position:0% + + + + align:start position:0% + +be well thanks Michael for I wish we + + align:start position:0% +be well thanks Michael for I wish we + + + align:start position:0% +be well thanks Michael for I wish we +could have had you earlier when we were + + align:start position:0% +could have had you earlier when we were + + + align:start position:0% +could have had you earlier when we were +specifically talking music XML but we + + align:start position:0% +specifically talking music XML but we + + + align:start position:0% +specifically talking music XML but we +can't go you can't go six weeks into the + + align:start position:0% +can't go you can't go six weeks into the + + + align:start position:0% +can't go you can't go six weeks into the +semester without knowing music XML so + + align:start position:0% +semester without knowing music XML so + + + align:start position:0% +semester without knowing music XML so +even knowing you're coming now uh it's + + align:start position:0% +even knowing you're coming now uh it's + + + align:start position:0% +even knowing you're coming now uh it's +still it's so great so thanks and + + align:start position:0% + + + + align:start position:0% + +and feel free to stay feel free to move + + align:start position:0% +and feel free to stay feel free to move + + + align:start position:0% +and feel free to stay feel free to move +on we're going to uh unlock intervals + + align:start position:0% +on we're going to uh unlock intervals + + + align:start position:0% +on we're going to uh unlock intervals +we're going to be moving on to the + + align:start position:0% +we're going to be moving on to the + + + align:start position:0% +we're going to be moving on to the +shortest topic of the semester and that + + align:start position:0% +shortest topic of the semester and that + + + align:start position:0% +shortest topic of the semester and that +is a voice leading you're going to get + + align:start position:0% +is a voice leading you're going to get + + + align:start position:0% +is a voice leading you're going to get +just a little bit for me today you're + + align:start position:0% +just a little bit for me today you're + + + align:start position:0% +just a little bit for me today you're +going to have the world's shortest um + + align:start position:0% +going to have the world's shortest um + + + align:start position:0% +going to have the world's shortest um +not the world's shortest but a pretty + + align:start position:0% +not the world's shortest but a pretty + + + align:start position:0% +not the world's shortest but a pretty +short problem set and then we'll do talk + + align:start position:0% +short problem set and then we'll do talk + + + align:start position:0% +short problem set and then we'll do talk +about it a little bit after um after the + + align:start position:0% +about it a little bit after um after the + + + align:start position:0% +about it a little bit after um after the +midterm on Wednesday and that will be it + + align:start position:0% +midterm on Wednesday and that will be it + + + align:start position:0% +midterm on Wednesday and that will be it +uh it's very important topic we're going + + align:start position:0% +uh it's very important topic we're going + + + align:start position:0% +uh it's very important topic we're going +to keep working on it it's why it + + align:start position:0% +to keep working on it it's why it + + + align:start position:0% +to keep working on it it's why it +deserves to have its own number um but + + align:start position:0% +deserves to have its own number um but + + + align:start position:0% +deserves to have its own number um but +uh what um when we're talking about + + align:start position:0% +uh what um when we're talking about + + + align:start position:0% +uh what um when we're talking about +voice leading we're generally talking + + align:start position:0% +voice leading we're generally talking + + + align:start position:0% +voice leading we're generally talking +about how yeah we just need one staff + + align:start position:0% +about how yeah we just need one staff + + + align:start position:0% +about how yeah we just need one staff +for + + align:start position:0% +for + + + align:start position:0% +for +this how + + align:start position:0% +this how + + + align:start position:0% +this how +multiple parts are moving at the same + + align:start position:0% +multiple parts are moving at the same + + + align:start position:0% +multiple parts are moving at the same +time + + align:start position:0% +time + + + align:start position:0% +time +so this would be pretty bad voice + + align:start position:0% +so this would be pretty bad voice + + + align:start position:0% +so this would be pretty bad voice +leaning maybe very dissonant but + + align:start position:0% +leaning maybe very dissonant but + + + align:start position:0% +leaning maybe very dissonant but +something we're talking about not what's + + align:start position:0% +something we're talking about not what's + + + align:start position:0% +something we're talking about not what's +happening + + align:start position:0% + + + + align:start position:0% + +here and not what's happening that one's + + align:start position:0% +here and not what's happening that one's + + + align:start position:0% +here and not what's happening that one's +hard to do + + align:start position:0% + + + + align:start position:0% + +here but the combination of the two and + + align:start position:0% +here but the combination of the two and + + + align:start position:0% +here but the combination of the two and +why voice leading becomes a particularly + + align:start position:0% +why voice leading becomes a particularly + + + align:start position:0% +why voice leading becomes a particularly +interesting problem for computers is + + align:start position:0% +interesting problem for computers is + + + align:start position:0% +interesting problem for computers is +there's two general ways of inter of + + align:start position:0% +there's two general ways of inter of + + + align:start position:0% +there's two general ways of inter of +iterating um both and both um + + align:start position:0% +iterating um both and both um + + + align:start position:0% +iterating um both and both um +both flatten and recurse are in some + + align:start position:0% +both flatten and recurse are in some + + + align:start position:0% +both flatten and recurse are in some +ways well no sorry uh recurse is sort of + + align:start position:0% +ways well no sorry uh recurse is sort of + + + align:start position:0% +ways well no sorry uh recurse is sort of +the you go through one part or one voice + + align:start position:0% +the you go through one part or one voice + + + align:start position:0% +the you go through one part or one voice +and you go through everything and you go + + align:start position:0% +and you go through everything and you go + + + align:start position:0% +and you go through everything and you go +through the other part and the other + + align:start position:0% +through the other part and the other + + + align:start position:0% +through the other part and the other +voice and you go through everything and + + align:start position:0% +voice and you go through everything and + + + align:start position:0% +voice and you go through everything and +then you have something like flatten + + align:start position:0% +then you have something like flatten + + + align:start position:0% +then you have something like flatten +which in the + + align:start position:0% +which in the + + + align:start position:0% +which in the +end especially if everything is just + + align:start position:0% +end especially if everything is just + + + align:start position:0% +end especially if everything is just +quarter notes you're going through one + + align:start position:0% +quarter notes you're going through one + + + align:start position:0% +quarter notes you're going through one +slice going to the next and going to the + + align:start position:0% +slice going to the next and going to the + + + align:start position:0% +slice going to the next and going to the +next + + align:start position:0% +next + + + align:start position:0% +next +slice so voice leading is a particular + + align:start position:0% +slice so voice leading is a particular + + + align:start position:0% +slice so voice leading is a particular +problem requires you to be constantly + + align:start position:0% +problem requires you to be constantly + + + align:start position:0% +problem requires you to be constantly +moving back and forth between I'm moving + + align:start position:0% +moving back and forth between I'm moving + + + align:start position:0% +moving back and forth between I'm moving +according to Voice or according to part + + align:start position:0% +according to Voice or according to part + + + align:start position:0% +according to Voice or according to part +and I'm looking at what's happening at + + align:start position:0% +and I'm looking at what's happening at + + + align:start position:0% +and I'm looking at what's happening at +one time or + + align:start position:0% +one time or + + + align:start position:0% +one time or +another um one of the classic + + align:start position:0% +another um one of the classic + + + align:start position:0% +another um one of the classic +applications for uh sort of starting off + + align:start position:0% +applications for uh sort of starting off + + + align:start position:0% +applications for uh sort of starting off +computational voice leading is to work + + align:start position:0% +computational voice leading is to work + + + align:start position:0% +computational voice leading is to work +on a topic called species Counterpoint + + align:start position:0% +on a topic called species Counterpoint + + + align:start position:0% +on a topic called species Counterpoint +has anybody who has done species + + align:start position:0% +has anybody who has done species + + + align:start position:0% +has anybody who has done species +CounterPoint in one of their classes + + align:start position:0% +CounterPoint in one of their classes + + + align:start position:0% +CounterPoint in one of their classes +some instructors do it some don't not + + align:start position:0% +some instructors do it some don't not + + + align:start position:0% +some instructors do it some don't not +everybody has so there's it's a um I + + align:start position:0% +everybody has so there's it's a um I + + + align:start position:0% +everybody has so there's it's a um I +think it's invented it's an 18th century + + align:start position:0% +think it's invented it's an 18th century + + + align:start position:0% +think it's invented it's an 18th century +way of learning to write music like they + + align:start position:0% +way of learning to write music like they + + + align:start position:0% +way of learning to write music like they +wrote it in the 16th century so not 100% + + align:start position:0% +wrote it in the 16th century so not 100% + + + align:start position:0% +wrote it in the 16th century so not 100% +relevant to um to music composition + + align:start position:0% +relevant to um to music composition + + + align:start position:0% +relevant to um to music composition +today but still sort of a fundamental + + align:start position:0% +today but still sort of a fundamental + + + align:start position:0% +today but still sort of a fundamental +skill like um you practicing your scales + + align:start position:0% +skill like um you practicing your scales + + + align:start position:0% +skill like um you practicing your scales +or something Mozart and Brahms uh + + align:start position:0% +or something Mozart and Brahms uh + + + align:start position:0% +or something Mozart and Brahms uh +practiced species Counterpoint uh every + + align:start position:0% +practiced species Counterpoint uh every + + + align:start position:0% +practiced species Counterpoint uh every +day sort of keep up their chops um the + + align:start position:0% +day sort of keep up their chops um the + + + align:start position:0% +day sort of keep up their chops um the +earliest the first species that we tend + + align:start position:0% +earliest the first species that we tend + + + align:start position:0% +earliest the first species that we tend +to call it is something is all in whole + + align:start position:0% +to call it is something is all in whole + + + align:start position:0% +to call it is something is all in whole +notes let me see if I can compose one um + + align:start position:0% +notes let me see if I can compose one um + + + align:start position:0% +notes let me see if I can compose one um +while + + align:start position:0% +while + + + align:start position:0% +while +we're + + align:start position:0% +we're + + + align:start position:0% +we're +um how many notes I write 1 2 3 4 5 6 7 + + align:start position:0% +um how many notes I write 1 2 3 4 5 6 7 + + + align:start position:0% +um how many notes I write 1 2 3 4 5 6 7 +8 nine good classic ones tend to be + + align:start position:0% +8 nine good classic ones tend to be + + + align:start position:0% +8 nine good classic ones tend to be +around nine notes long and then against + + align:start position:0% +around nine notes long and then against + + + align:start position:0% +around nine notes long and then against +this in first species you're going to + + align:start position:0% +this in first species you're going to + + + align:start position:0% +this in first species you're going to +write one whole note for every + + align:start position:0% +write one whole note for every + + + align:start position:0% +write one whole note for every +note with particular conditions and some + + align:start position:0% +note with particular conditions and some + + + align:start position:0% +note with particular conditions and some +of these conditions will be horizontally + + align:start position:0% +of these conditions will be horizontally + + + align:start position:0% +of these conditions will be horizontally +constraining like for + + align:start position:0% + + + + align:start position:0% + +instance uh yeah now this that + + align:start position:0% +instance uh yeah now this that + + + align:start position:0% +instance uh yeah now this that +particular one + + align:start position:0% + + + + align:start position:0% + +don't do that why + + align:start position:0% +don't do that why + + + align:start position:0% +don't do that why +not trone Yep this case augmented fourth + + align:start position:0% +not trone Yep this case augmented fourth + + + align:start position:0% +not trone Yep this case augmented fourth +um or diminished fifth usually not + + align:start position:0% +um or diminished fifth usually not + + + align:start position:0% +um or diminished fifth usually not +allowed also especially in this context + + align:start position:0% +allowed also especially in this context + + + align:start position:0% +allowed also especially in this context +good so some of these things are going + + align:start position:0% +good so some of these things are going + + + align:start position:0% +good so some of these things are going +to be based on that and on on one case + + align:start position:0% +to be based on that and on on one case + + + align:start position:0% +to be based on that and on on one case +and some of them are going to be based + + align:start position:0% +and some of them are going to be based + + + align:start position:0% +and some of them are going to be based +on vertical things this would not be + + align:start position:0% +on vertical things this would not be + + + align:start position:0% +on vertical things this would not be +allowed why + + align:start position:0% + + + + align:start position:0% + +not sorry I need to two + + align:start position:0% +not sorry I need to two + + + align:start position:0% +not sorry I need to two +colors what's what somebody said it I + + align:start position:0% +colors what's what somebody said it I + + + align:start position:0% +colors what's what somebody said it I +just didn't + + align:start position:0% +just didn't + + + align:start position:0% +just didn't +hear no no I think I think I heard it + + align:start position:0% +hear no no I think I think I heard it + + + align:start position:0% +hear no no I think I think I heard it +properly seventh yeah so um in first + + align:start position:0% +properly seventh yeah so um in first + + + align:start position:0% +properly seventh yeah so um in first +species the rule is all horizontal + + align:start position:0% +species the rule is all horizontal + + + align:start position:0% +species the rule is all horizontal +vertical intervals must be consonant and + + align:start position:0% +vertical intervals must be consonant and + + + align:start position:0% +vertical intervals must be consonant and +all vertical intervals must be + + align:start position:0% +all vertical intervals must be + + + align:start position:0% +all vertical intervals must be +consonant but then there are other + + align:start position:0% +consonant but then there are other + + + align:start position:0% +consonant but then there are other +strange little + + align:start position:0% +strange little + + + align:start position:0% +strange little +rules + + align:start position:0% + + + + align:start position:0% + +like this is a consonant + + align:start position:0% +like this is a consonant + + + align:start position:0% +like this is a consonant +interval this is a consonant interval + + align:start position:0% +interval this is a consonant interval + + + align:start position:0% +interval this is a consonant interval +this is a con I I was going to do red + + align:start position:0% +this is a con I I was going to do red + + + align:start position:0% +this is a con I I was going to do red +this is a constant interval all these + + align:start position:0% +this is a constant interval all these + + + align:start position:0% +this is a constant interval all these +intervals are consonant what's the + + align:start position:0% +intervals are consonant what's the + + + align:start position:0% +intervals are consonant what's the +problem here with these + + align:start position:0% +problem here with these + + + align:start position:0% +problem here with these +two for anybody who's done this yeah so + + align:start position:0% +two for anybody who's done this yeah so + + + align:start position:0% +two for anybody who's done this yeah so +parallel fifth so what's the interval G + + align:start position:0% +parallel fifth so what's the interval G + + + align:start position:0% +parallel fifth so what's the interval G +to D perfect fifth e to B perfect fifth + + align:start position:0% +to D perfect fifth e to B perfect fifth + + + align:start position:0% +to D perfect fifth e to B perfect fifth +so two perfect fifths in a row um so I + + align:start position:0% +so two perfect fifths in a row um so I + + + align:start position:0% +so two perfect fifths in a row um so I +just want to give uh there for anybody + + align:start position:0% +just want to give uh there for anybody + + + align:start position:0% +just want to give uh there for anybody +who wants to um I don't have a + + align:start position:0% +who wants to um I don't have a + + + align:start position:0% +who wants to um I don't have a +formalized extra credit for this but um + + align:start position:0% +formalized extra credit for this but um + + + align:start position:0% +formalized extra credit for this but um +if you can writing + + align:start position:0% +if you can writing + + + align:start position:0% +if you can writing +software that can solve any given what + + align:start position:0% +software that can solve any given what + + + align:start position:0% +software that can solve any given what +we call the this is the part that's + + align:start position:0% +we call the this is the part that's + + + align:start position:0% +we call the this is the part that's +given to you there's always one part + + align:start position:0% +given to you there's always one part + + + align:start position:0% +given to you there's always one part +that's given to you it's called the Kus + + align:start position:0% +that's given to you it's called the Kus + + + align:start position:0% +that's given to you it's called the Kus +fmis or the fixed song in Latin and so + + align:start position:0% +fmis or the fixed song in Latin and so + + + align:start position:0% +fmis or the fixed song in Latin and so +you fixed you can't change it and one of + + align:start position:0% +you fixed you can't change it and one of + + + align:start position:0% +you fixed you can't change it and one of +the classic things is to write um + + align:start position:0% +the classic things is to write um + + + align:start position:0% +the classic things is to write um +nowadays in computers is to write + + align:start position:0% +nowadays in computers is to write + + + align:start position:0% +nowadays in computers is to write +software that can solve the other part + + align:start position:0% +software that can solve the other part + + + align:start position:0% +software that can solve the other part +that can give you the other part there + + align:start position:0% +that can give you the other part there + + + align:start position:0% +that can give you the other part there +and that's one of the ones if you're + + align:start position:0% +and that's one of the ones if you're + + + align:start position:0% +and that's one of the ones if you're +interested in in optimization and + + align:start position:0% +interested in in optimization and + + + align:start position:0% +interested in in optimization and +algorithmic things that this is one of + + align:start position:0% +algorithmic things that this is one of + + + align:start position:0% +algorithmic things that this is one of +the cases the first cases in this class + + align:start position:0% +the cases the first cases in this class + + + align:start position:0% +the cases the first cases in this class +where it is easy to write something that + + align:start position:0% +where it is easy to write something that + + + align:start position:0% +where it is easy to write something that +will do it properly but for a 20 note or + + align:start position:0% +will do it properly but for a 20 note or + + + align:start position:0% +will do it properly but for a 20 note or +40 Note One won't be able to generate it + + align:start position:0% +40 Note One won't be able to generate it + + + align:start position:0% +40 Note One won't be able to generate it +in the time that the Universe um before + + align:start position:0% +in the time that the Universe um before + + + align:start position:0% +in the time that the Universe um before +the heat death of the universe so it's + + align:start position:0% +the heat death of the universe so it's + + + align:start position:0% +the heat death of the universe so it's +something where uh algorithmic + + align:start position:0% +something where uh algorithmic + + + align:start position:0% +something where uh algorithmic +complexity comes in you are not going to + + align:start position:0% +complexity comes in you are not going to + + + align:start position:0% +complexity comes in you are not going to +be given that assignment this year um + + align:start position:0% +be given that assignment this year um + + + align:start position:0% +be given that assignment this year um +you all have worked pretty hard right + + align:start position:0% +you all have worked pretty hard right + + + align:start position:0% +you all have worked pretty hard right +this this class is yeah okay so not + + align:start position:0% +this this class is yeah okay so not + + + align:start position:0% +this this class is yeah okay so not +doing that seems like a good thing but + + align:start position:0% +doing that seems like a good thing but + + + align:start position:0% +doing that seems like a good thing but +instead we're going to be + + align:start position:0% +instead we're going to be + + + align:start position:0% +instead we're going to be +what you're going to be asked to do uh + + align:start position:0% +what you're going to be asked to do uh + + + align:start position:0% +what you're going to be asked to do uh +over between now and next Friday is to + + align:start position:0% +over between now and next Friday is to + + + align:start position:0% +over between now and next Friday is to +um come up and encode some of the basic + + align:start position:0% +um come up and encode some of the basic + + + align:start position:0% +um come up and encode some of the basic +features underlying how you might solve + + align:start position:0% +features underlying how you might solve + + + align:start position:0% +features underlying how you might solve +a problem like this and specifically how + + align:start position:0% +a problem like this and specifically how + + + align:start position:0% +a problem like this and specifically how +you might avoid things like this uh + + align:start position:0% +you might avoid things like this uh + + + align:start position:0% +you might avoid things like this uh +there's one or two uh things on this the + + align:start position:0% +there's one or two uh things on this the + + + align:start position:0% +there's one or two uh things on this the +this is not get an everything correct + + align:start position:0% +this is not get an everything correct + + + align:start position:0% +this is not get an everything correct +problem set but um looking quite down + + align:start position:0% +problem set but um looking quite down + + + align:start position:0% +problem set but um looking quite down +the road to the second probably the + + align:start position:0% +the road to the second probably the + + + align:start position:0% +the road to the second probably the +second to last problem set in this class + + align:start position:0% +second to last problem set in this class + + + align:start position:0% +second to last problem set in this class +problem set nine will this will be + + align:start position:0% +problem set nine will this will be + + + align:start position:0% +problem set nine will this will be +foundational knowledge on it and that + + align:start position:0% +foundational knowledge on it and that + + + align:start position:0% +foundational knowledge on it and that +one problem set nine you're going to be + + align:start position:0% +one problem set nine you're going to be + + + align:start position:0% +one problem set nine you're going to be +given a piece and you're going to be + + align:start position:0% +given a piece and you're going to be + + + align:start position:0% +given a piece and you're going to be +asked to remove all the passing tones + + align:start position:0% +asked to remove all the passing tones + + + align:start position:0% +asked to remove all the passing tones +and all the ornaments and leave it just + + align:start position:0% +and all the ornaments and leave it just + + + align:start position:0% +and all the ornaments and leave it just +with the block chords and so being able + + align:start position:0% +with the block chords and so being able + + + align:start position:0% +with the block chords and so being able +to identify voice leading moments is + + align:start position:0% +to identify voice leading moments is + + + align:start position:0% +to identify voice leading moments is +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +important okay so let's unlock intervals + + align:start position:0% +important okay so let's unlock intervals + + + align:start position:0% +important okay so let's unlock intervals +you've been working a lot on them + + align:start position:0% +you've been working a lot on them + + + align:start position:0% +you've been working a lot on them +so unlocking + + align:start position:0% +so unlocking + + + align:start position:0% +so unlocking +interval let's go ahead and from music + + align:start position:0% +interval let's go ahead and from music + + + align:start position:0% +interval let's go ahead and from music +21 import uh Corpus which we'll use just + + align:start position:0% +21 import uh Corpus which we'll use just + + + align:start position:0% +21 import uh Corpus which we'll use just +at the very end if we have time note + + align:start position:0% +at the very end if we have time note + + + align:start position:0% +at the very end if we have time note +pitch and the brand new interval + + align:start position:0% +pitch and the brand new interval + + + align:start position:0% +pitch and the brand new interval +module is that big enough bigger + + align:start position:0% + + + + align:start position:0% + +better okay um we'll start with the wor + + align:start position:0% +better okay um we'll start with the wor + + + align:start position:0% +better okay um we'll start with the wor +worst variable name ever I equals the + + align:start position:0% +worst variable name ever I equals the + + + align:start position:0% +worst variable name ever I equals the +interval module so it's + + align:start position:0% +interval module so it's + + + align:start position:0% +interval module so it's +lowercase and the + + align:start position:0% +lowercase and the + + + align:start position:0% +lowercase and the +interval class in there P5 let's start + + align:start position:0% +interval class in there P5 let's start + + + align:start position:0% +interval class in there P5 let's start +with a perfect fifth these are all + + align:start position:0% +with a perfect fifth these are all + + + align:start position:0% +with a perfect fifth these are all +things that you've been + + align:start position:0% +things that you've been + + + align:start position:0% +things that you've been +doing within the interval module by the + + align:start position:0% +doing within the interval module by the + + + align:start position:0% +doing within the interval module by the +way there are interval classes called + + align:start position:0% +way there are interval classes called + + + align:start position:0% +way there are interval classes called +chromatic interval diatonic interval + + align:start position:0% +chromatic interval diatonic interval + + + align:start position:0% +chromatic interval diatonic interval +generic interval all these things but + + align:start position:0% +generic interval all these things but + + + align:start position:0% +generic interval all these things but +the interval class will let you do + + align:start position:0% +the interval class will let you do + + + align:start position:0% +the interval class will let you do +basically almost anything in there great + + align:start position:0% +basically almost anything in there great + + + align:start position:0% +basically almost anything in there great +so now you've created a P5 interval you + + align:start position:0% +so now you've created a P5 interval you + + + align:start position:0% +so now you've created a P5 interval you +can get its name which is very unhelpful + + align:start position:0% +can get its name which is very unhelpful + + + align:start position:0% +can get its name which is very unhelpful +it just tells you what you just put in + + align:start position:0% +it just tells you what you just put in + + + align:start position:0% +it just tells you what you just put in +but you can get its nice name uh with a + + align:start position:0% +but you can get its nice name uh with a + + + align:start position:0% +but you can get its nice name uh with a +capital N in the + + align:start position:0% +capital N in the + + + align:start position:0% +capital N in the +middle perfect fifth um so it's just a + + align:start position:0% +middle perfect fifth um so it's just a + + + align:start position:0% +middle perfect fifth um so it's just a +little bit more helpful Let's uh keep + + align:start position:0% +little bit more helpful Let's uh keep + + + align:start position:0% +little bit more helpful Let's uh keep +going we can get its directed nice name + + align:start position:0% +going we can get its directed nice name + + + align:start position:0% +going we can get its directed nice name +so this is Allin snake case or camel + + align:start position:0% +so this is Allin snake case or camel + + + align:start position:0% +so this is Allin snake case or camel +case whatever you want to call it + + align:start position:0% +case whatever you want to call it + + + align:start position:0% +case whatever you want to call it +directed nice with a capital N name with + + align:start position:0% +directed nice with a capital N name with + + + align:start position:0% +directed nice with a capital N name with +a capital m and + + align:start position:0% +a capital m and + + + align:start position:0% +a capital m and +get us sending perfect fifth so there's + + align:start position:0% +get us sending perfect fifth so there's + + + align:start position:0% +get us sending perfect fifth so there's +sometimes we care about what direction + + align:start position:0% +sometimes we care about what direction + + + align:start position:0% +sometimes we care about what direction +the interval is and sometimes we don't + + align:start position:0% +the interval is and sometimes we don't + + + align:start position:0% +the interval is and sometimes we don't +uh in Melodies we care or don't + + align:start position:0% +uh in Melodies we care or don't + + + align:start position:0% +uh in Melodies we care or don't +care take a guess when you're talking + + align:start position:0% +care take a guess when you're talking + + + align:start position:0% +care take a guess when you're talking +about Melodies do we care which + + align:start position:0% +about Melodies do we care which + + + align:start position:0% +about Melodies do we care which +direction the interval + + align:start position:0% +direction the interval + + + align:start position:0% +direction the interval +is yes when we're talking about the + + align:start position:0% +is yes when we're talking about the + + + align:start position:0% +is yes when we're talking about the +notes of a chord do we care no not + + align:start position:0% +notes of a chord do we care no not + + + align:start position:0% +notes of a chord do we care no not +usually right because we're just talking + + align:start position:0% +usually right because we're just talking + + + align:start position:0% +usually right because we're just talking +about uh what things are great so if we + + align:start position:0% +about uh what things are great so if we + + + align:start position:0% +about uh what things are great so if we +want to create um a descending interval + + align:start position:0% +want to create um a descending interval + + + align:start position:0% +want to create um a descending interval +we can create interval. + + align:start position:0% +we can create interval. + + + align:start position:0% +we can create interval. +interval + + align:start position:0% + + + + align:start position:0% + +P5 and get its directed nice name you + + align:start position:0% +P5 and get its directed nice name you + + + align:start position:0% +P5 and get its directed nice name you +don't have to type all things I'll put + + align:start position:0% +don't have to type all things I'll put + + + align:start position:0% +don't have to type all things I'll put +this up later if you're not a fast + + align:start position:0% +this up later if you're not a fast + + + align:start position:0% +this up later if you're not a fast +typist but you can do that um also + + align:start position:0% +typist but you can do that um also + + + align:start position:0% +typist but you can do that um also +because I can never remember which one + + align:start position:0% +because I can never remember which one + + + align:start position:0% +because I can never remember which one +we prefer uh you can do negative P5 + + align:start position:0% +we prefer uh you can do negative P5 + + + align:start position:0% +we prefer uh you can do negative P5 +because I I don't know which one of + + align:start position:0% +because I I don't know which one of + + + align:start position:0% +because I I don't know which one of +those is actually + + align:start position:0% +those is actually + + + align:start position:0% +those is actually +better okay so that the most basic way + + align:start position:0% +better okay so that the most basic way + + + align:start position:0% +better okay so that the most basic way +of doing things um + + align:start position:0% +of doing things um + + + align:start position:0% +of doing things um +let's try to get the intervals um from + + align:start position:0% +let's try to get the intervals um from + + + align:start position:0% +let's try to get the intervals um from +pitches first off so let's create two + + align:start position:0% +pitches first off so let's create two + + + align:start position:0% +pitches first off so let's create two +pitches we'll create um pitch. Pitch + + align:start position:0% +pitches we'll create um pitch. Pitch + + + align:start position:0% +pitches we'll create um pitch. Pitch +B3 P2 pitch. + + align:start position:0% +B3 P2 pitch. + + + align:start position:0% +B3 P2 pitch. +pitch C5 so not little hard but not too + + align:start position:0% +pitch C5 so not little hard but not too + + + align:start position:0% +pitch C5 so not little hard but not too +hard and you don't need to type the + + align:start position:0% +hard and you don't need to type the + + + align:start position:0% +hard and you don't need to type the +question marks we're going to get the + + align:start position:0% +question marks we're going to get the + + + align:start position:0% +question marks we're going to get the +interval interval. + + align:start position:0% +interval interval. + + + align:start position:0% +interval interval. +interval + + align:start position:0% +interval + + + align:start position:0% +interval +interval between P1 and P2 so you can + + align:start position:0% +interval between P1 and P2 so you can + + + align:start position:0% +interval between P1 and P2 so you can +instead of putting in a string you can + + align:start position:0% +instead of putting in a string you can + + + align:start position:0% +instead of putting in a string you can +give it two pitches or something and I'm + + align:start position:0% +give it two pitches or something and I'm + + + align:start position:0% +give it two pitches or something and I'm +going to name this variable after what + + align:start position:0% +going to name this variable after what + + + align:start position:0% +going to name this variable after what +the name should be the interval between + + align:start position:0% +the name should be the interval between + + + align:start position:0% +the name should be the interval between +B3 and C5 what should I call that + + align:start position:0% +B3 and C5 what should I call that + + + align:start position:0% +B3 and C5 what should I call that +somebody who hasn't already gotten ahead + + align:start position:0% +somebody who hasn't already gotten ahead + + + align:start position:0% +somebody who hasn't already gotten ahead +in the computer what is that interv + + align:start position:0% +in the computer what is that interv + + + align:start position:0% +in the computer what is that interv +always try to do things in your head the + + align:start position:0% +always try to do things in your head the + + + align:start position:0% +always try to do things in your head the +first time + + align:start position:0% +first time + + + align:start position:0% +first time +nth minor 9th so I'll do lowercase m n u + + align:start position:0% +nth minor 9th so I'll do lowercase m n u + + + align:start position:0% +nth minor 9th so I'll do lowercase m n u +I do like naming things according to + + align:start position:0% +I do like naming things according to + + + align:start position:0% +I do like naming things according to +their interval or according to what + + align:start position:0% +their interval or according to what + + + align:start position:0% +their interval or according to what +they're representing it does hit my anal + + align:start position:0% +they're representing it does hit my anal + + + align:start position:0% +they're representing it does hit my anal +retentive uh like must be everything + + align:start position:0% +retentive uh like must be everything + + + align:start position:0% +retentive uh like must be everything +must be in order streak that when we do + + align:start position:0% +must be in order streak that when we do + + + align:start position:0% +must be in order streak that when we do +have something that should be a major + + align:start position:0% +have something that should be a major + + + align:start position:0% +have something that should be a major +third it's capital M but then I go + + align:start position:0% +third it's capital M but then I go + + + align:start position:0% +third it's capital M but then I go +Capital should only be used for classes + + align:start position:0% +Capital should only be used for classes + + + align:start position:0% +Capital should only be used for classes +and you know um but SI we have to do + + align:start position:0% +and you know um but SI we have to do + + + align:start position:0% +and you know um but SI we have to do +that okay so we have do we get + + align:start position:0% +that okay so we have do we get + + + align:start position:0% +that okay so we have do we get +yep minor ninth how many semitones in a + + align:start position:0% +yep minor ninth how many semitones in a + + + align:start position:0% +yep minor ninth how many semitones in a +minor + + align:start position:0% + + + + align:start position:0% + +ninth uh 13 13 13 so dot semitones will + + align:start position:0% +ninth uh 13 13 13 so dot semitones will + + + align:start position:0% +ninth uh 13 13 13 so dot semitones will +give you the number of semmit tones in + + align:start position:0% +give you the number of semmit tones in + + + align:start position:0% +give you the number of semmit tones in +an interval which is often quite helpful + + align:start position:0% +an interval which is often quite helpful + + + align:start position:0% +an interval which is often quite helpful +um obviously m9n name will give + + align:start position:0% +um obviously m9n name will give + + + align:start position:0% +um obviously m9n name will give +youname will give you M9 but M9 dos + + align:start position:0% +youname will give you M9 but M9 dos + + + align:start position:0% +youname will give you M9 but M9 dos +simple name also in C snake case + + align:start position:0% + + + + align:start position:0% + +so when you're dealing with compound + + align:start position:0% +so when you're dealing with compound + + + align:start position:0% +so when you're dealing with compound +intervals there is something called + + align:start position:0% +intervals there is something called + + + align:start position:0% +intervals there is something called +Simple name that would be very helpful + + align:start position:0% +Simple name that would be very helpful + + + align:start position:0% +Simple name that would be very helpful +for working through things + + align:start position:0% +for working through things + + + align:start position:0% +for working through things +um there's um now there's there's some + + align:start position:0% +um there's um now there's there's some + + + align:start position:0% +um there's um now there's there's some +some slight difference let's um let's + + align:start position:0% +some slight difference let's um let's + + + align:start position:0% +some slight difference let's um let's +come up with another interval this one + + align:start position:0% +come up with another interval this one + + + align:start position:0% +come up with another interval this one +I'll call + + align:start position:0% +I'll call + + + align:start position:0% +I'll call +p8 and I'll just show so you can do some + + align:start position:0% +p8 and I'll just show so you can do some + + + align:start position:0% +p8 and I'll just show so you can do some +of these things here we can also create + + align:start position:0% +of these things here we can also create + + + align:start position:0% +of these things here we can also create +an interval from notes not just from + + align:start position:0% +an interval from notes not just from + + + align:start position:0% +an interval from notes not just from +pitches uh that's probably a mistake in + + align:start position:0% +pitches uh that's probably a mistake in + + + align:start position:0% +pitches uh that's probably a mistake in +my taxonomy morony whatever it is but um + + align:start position:0% +my taxonomy morony whatever it is but um + + + align:start position:0% +my taxonomy morony whatever it is but um +it's been there for a while so p8 should + + align:start position:0% +it's been there for a while so p8 should + + + align:start position:0% +it's been there for a while so p8 should +be C4 to C five good the only difference + + align:start position:0% +be C4 to C five good the only difference + + + align:start position:0% +be C4 to C five good the only difference +why I'm creating a octave I should have + + align:start position:0% +why I'm creating a octave I should have + + + align:start position:0% +why I'm creating a octave I should have +just call it octave right um is that + + align:start position:0% +just call it octave right um is that + + + align:start position:0% +just call it octave right um is that +sometimes that the octave simple name is + + align:start position:0% +sometimes that the octave simple name is + + + align:start position:0% +sometimes that the octave simple name is +perfect Unis P1 right but um sometimes + + align:start position:0% +perfect Unis P1 right but um sometimes + + + align:start position:0% +perfect Unis P1 right but um sometimes +we care about the difference between + + align:start position:0% +we care about the difference between + + + align:start position:0% +we care about the difference between +octaves and Unison in a way that we + + align:start position:0% +octaves and Unison in a way that we + + + align:start position:0% +octaves and Unison in a way that we +don't care about uh seconds and nins so + + align:start position:0% +don't care about uh seconds and nins so + + + align:start position:0% +don't care about uh seconds and nins so +there is something called p8 dosi Simple + + align:start position:0% +there is something called p8 dosi Simple + + + align:start position:0% +there is something called p8 dosi Simple +name I wish I had spent some more time + + align:start position:0% +name I wish I had spent some more time + + + align:start position:0% +name I wish I had spent some more time +coming up with it which basically is + + align:start position:0% +coming up with it which basically is + + + align:start position:0% +coming up with it which basically is +exactly the same as a simple name except + + align:start position:0% +exactly the same as a simple name except + + + align:start position:0% +exactly the same as a simple name except +that things that are multiples of + + align:start position:0% +that things that are multiples of + + + align:start position:0% +that things that are multiples of +octaves get squished down to an octave + + align:start position:0% +octaves get squished down to an octave + + + align:start position:0% +octaves get squished down to an octave +so a double octave also becomes an + + align:start position:0% +so a double octave also becomes an + + + align:start position:0% +so a double octave also becomes an +octave in the semi-simple name whereas + + align:start position:0% +octave in the semi-simple name whereas + + + align:start position:0% +octave in the semi-simple name whereas +the 9th's semisimple name is my minor + + align:start position:0% +the 9th's semisimple name is my minor + + + align:start position:0% +the 9th's semisimple name is my minor +second I think there's also things see + + align:start position:0% +second I think there's also things see + + + align:start position:0% +second I think there's also things see +if I still have all these in here semi + + align:start position:0% +if I still have all these in here semi + + + align:start position:0% +if I still have all these in here semi +simple nice name yeah okay so there's + + align:start position:0% +simple nice name yeah okay so there's + + + align:start position:0% +simple nice name yeah okay so there's +there are all of these things in there + + align:start position:0% +there are all of these things in there + + + align:start position:0% +there are all of these things in there +great um + + align:start position:0% +great um + + + align:start position:0% +great um +let's let's stop typing so much and + + align:start position:0% +let's let's stop typing so much and + + + align:start position:0% +let's let's stop typing so much and +let's create some aliases Alias um we's + + align:start position:0% +let's create some aliases Alias um we's + + + align:start position:0% +let's create some aliases Alias um we's +just capital I is the interval. interval + + align:start position:0% +just capital I is the interval. interval + + + align:start position:0% +just capital I is the interval. interval +class so now we can call I and get new + + align:start position:0% +class so now we can call I and get new + + + align:start position:0% +class so now we can call I and get new +interval and P the pitch. pitch class + + align:start position:0% +interval and P the pitch. pitch class + + + align:start position:0% +interval and P the pitch. pitch class +not a pitch class the class pitch inside + + align:start position:0% +not a pitch class the class pitch inside + + + align:start position:0% +not a pitch class the class pitch inside +the module pitch right is that able to + + align:start position:0% +the module pitch right is that able to + + + align:start position:0% +the module pitch right is that able to +be + + align:start position:0% +be + + + align:start position:0% +be +seen great so now we can create like + + align:start position:0% +seen great so now we can create like + + + align:start position:0% +seen great so now we can create like +minor + + align:start position:0% +minor + + + align:start position:0% +minor +third just like that just a capital I + + align:start position:0% +third just like that just a capital I + + + align:start position:0% +third just like that just a capital I +parentheses and slow down okay slow down + + align:start position:0% +parentheses and slow down okay slow down + + + align:start position:0% +parentheses and slow down okay slow down +slow down yes a little bit okay good + + align:start position:0% +slow down yes a little bit okay good + + + align:start position:0% +slow down yes a little bit okay good +great pause for a second on this + + align:start position:0% +great pause for a second on this + + + align:start position:0% +great pause for a second on this +so far so far this is great uh except + + align:start position:0% +so far so far this is great uh except + + + align:start position:0% +so far so far this is great uh except +for being able to get the interval from + + align:start position:0% +for being able to get the interval from + + + align:start position:0% +for being able to get the interval from +two pitches which will probably be very + + align:start position:0% +two pitches which will probably be very + + + align:start position:0% +two pitches which will probably be very +helpful for you uh there's not too much + + align:start position:0% +helpful for you uh there's not too much + + + align:start position:0% +helpful for you uh there's not too much +you can do once you have an interval + + align:start position:0% +you can do once you have an interval + + + align:start position:0% +you can do once you have an interval +object so let's start creating some + + align:start position:0% +object so let's start creating some + + + align:start position:0% +object so let's start creating some +things that um might like so don't have + + align:start position:0% +things that um might like so don't have + + + align:start position:0% +things that um might like so don't have +to type all these things but this is + + align:start position:0% +to type all these things but this is + + + align:start position:0% +to type all these things but this is +probably a nice one to do the interval + + align:start position:0% +probably a nice one to do the interval + + + align:start position:0% +probably a nice one to do the interval +of a minor third is consonant now this + + align:start position:0% +of a minor third is consonant now this + + + align:start position:0% +of a minor third is consonant now this +is probably a mistaken term before I hit + + align:start position:0% +is probably a mistaken term before I hit + + + align:start position:0% +is probably a mistaken term before I hit +enter Because all of these things are + + align:start position:0% +enter Because all of these things are + + + align:start position:0% +enter Because all of these things are +consonant in some of the world's + + align:start position:0% +consonant in some of the world's + + + align:start position:0% +consonant in some of the world's +traditions and some not in some of the + + align:start position:0% +traditions and some not in some of the + + + align:start position:0% +traditions and some not in some of the +other world's traditions in fact um some + + align:start position:0% +other world's traditions in fact um some + + + align:start position:0% +other world's traditions in fact um some +of the early proposals of Music 21 said + + align:start position:0% +of the early proposals of Music 21 said + + + align:start position:0% +of the early proposals of Music 21 said +oh and then you'll be able to have a + + align:start position:0% +oh and then you'll be able to have a + + + align:start position:0% +oh and then you'll be able to have a +context objects which will be able to + + align:start position:0% +context objects which will be able to + + + align:start position:0% +context objects which will be able to +affect how these things are so if you're + + align:start position:0% +affect how these things are so if you're + + + align:start position:0% +affect how these things are so if you're +in 14th century Europe This will be + + align:start position:0% +in 14th century Europe This will be + + + align:start position:0% +in 14th century Europe This will be +false and if you're in some part if + + align:start position:0% +false and if you're in some part if + + + align:start position:0% +false and if you're in some part if +you're giving it a southern uh Southern + + align:start position:0% +you're giving it a southern uh Southern + + + align:start position:0% +you're giving it a southern uh Southern +Indian context it might be fals or you + + align:start position:0% +Indian context it might be fals or you + + + align:start position:0% +Indian context it might be fals or you +depending on what the time is and I've + + align:start position:0% +depending on what the time is and I've + + + align:start position:0% +depending on what the time is and I've +never actually fully implemented that so + + align:start position:0% +never actually fully implemented that so + + + align:start position:0% +never actually fully implemented that so +right now unfortunately this privileges + + align:start position:0% +right now unfortunately this privileges + + + align:start position:0% +right now unfortunately this privileges +the Western um sort of classical music + + align:start position:0% +the Western um sort of classical music + + + align:start position:0% +the Western um sort of classical music +context what should this be if it's in a + + align:start position:0% +context what should this be if it's in a + + + align:start position:0% +context what should this be if it's in a +western classical music context minor + + align:start position:0% +western classical music context minor + + + align:start position:0% +western classical music context minor +thirds are constant or dissonant con + + align:start position:0% +thirds are constant or dissonant con + + + align:start position:0% +thirds are constant or dissonant con +Conant good I programmed something right + + align:start position:0% +Conant good I programmed something right + + + align:start position:0% +Conant good I programmed something right +um now let's try something else a major + + align:start position:0% +um now let's try something else a major + + + align:start position:0% +um now let's try something else a major +sixth consonant or dissonant consonant + + align:start position:0% +sixth consonant or dissonant consonant + + + align:start position:0% +sixth consonant or dissonant consonant +consonant + + align:start position:0% +consonant + + + align:start position:0% +consonant +good and um + + align:start position:0% +good and um + + + align:start position:0% +good and um +sorry I'm just going to I'm typing a lot + + align:start position:0% +sorry I'm just going to I'm typing a lot + + + align:start position:0% +sorry I'm just going to I'm typing a lot +here you can probably assign things + + align:start position:0% +here you can probably assign things + + + align:start position:0% +here you can probably assign things +variables uh the number of semitones in + + align:start position:0% +variables uh the number of semitones in + + + align:start position:0% +variables uh the number of semitones in +a major + + align:start position:0% +a major + + + align:start position:0% +a major + + align:start position:0% + + + align:start position:0% +nine nine good now I'm going to create a + + align:start position:0% +nine nine good now I'm going to create a + + + align:start position:0% +nine nine good now I'm going to create a +diminish sth I lowercase + + align:start position:0% +diminish sth I lowercase + + + align:start position:0% +diminish sth I lowercase +D7 and number of semmit tones in a + + align:start position:0% +D7 and number of semmit tones in a + + + align:start position:0% +D7 and number of semmit tones in a +diminished + + align:start position:0% +diminished + + + align:start position:0% +diminished +7th + + align:start position:0% +7th + + + align:start position:0% +7th +11 one guess another guess n + + align:start position:0% +11 one guess another guess n + + + align:start position:0% +11 one guess another guess n +nine so diminish seventh is + + align:start position:0% + + + + align:start position:0% + +consonant false so one of the things + + align:start position:0% +consonant false so one of the things + + + align:start position:0% +consonant false so one of the things +built into the music 21 ontology that's + + align:start position:0% +built into the music 21 ontology that's + + + align:start position:0% +built into the music 21 ontology that's +different from um so Dimitri Chacho's + + align:start position:0% +different from um so Dimitri Chacho's + + + align:start position:0% +different from um so Dimitri Chacho's +optic default ontology is that spelling + + align:start position:0% +optic default ontology is that spelling + + + align:start position:0% +optic default ontology is that spelling +matters this case so diminish 7th sounds + + align:start position:0% +matters this case so diminish 7th sounds + + + align:start position:0% +matters this case so diminish 7th sounds +the same as a major sixth in isolation + + align:start position:0% +the same as a major sixth in isolation + + + align:start position:0% +the same as a major sixth in isolation +but it's not considered + + align:start position:0% +but it's not considered + + + align:start position:0% +but it's not considered +consonant that's important to know and + + align:start position:0% +consonant that's important to know and + + + align:start position:0% +consonant that's important to know and +uh I think uh I think last year there + + align:start position:0% +uh I think uh I think last year there + + + align:start position:0% +uh I think uh I think last year there +was a month that went by without + + align:start position:0% +was a month that went by without + + + align:start position:0% +was a month that went by without +somebody reporting this as a bug to the + + align:start position:0% +somebody reporting this as a bug to the + + + align:start position:0% +somebody reporting this as a bug to the +music 21 list but most most months one + + align:start position:0% +music 21 list but most most months one + + + align:start position:0% +music 21 list but most most months one +to two people um put that in not see + + align:start position:0% +to two people um put that in not see + + + align:start position:0% +to two people um put that in not see +that so it definitely means that you + + align:start position:0% +that so it definitely means that you + + + align:start position:0% +that so it definitely means that you +know um you uh I don't know an augmented + + align:start position:0% +know um you uh I don't know an augmented + + + align:start position:0% +know um you uh I don't know an augmented +sth is not consonant either even though + + align:start position:0% +sth is not consonant either even though + + + align:start position:0% +sth is not consonant either even though +an augmented second seventh is another + + align:start position:0% +an augmented second seventh is another + + + align:start position:0% +an augmented second seventh is another +way of + + align:start position:0% +way of + + + align:start position:0% +way of +saying octave perfect octave great super + + align:start position:0% +saying octave perfect octave great super + + + align:start position:0% +saying octave perfect octave great super +um basically anything in traditional + + align:start position:0% +um basically anything in traditional + + + align:start position:0% +um basically anything in traditional +theory in traditional tonal Theory + + align:start position:0% +theory in traditional tonal Theory + + + align:start position:0% +theory in traditional tonal Theory +anything that is marked as diminished or + + align:start position:0% +anything that is marked as diminished or + + + align:start position:0% +anything that is marked as diminished or +augmented or doubly diminished or doubly + + align:start position:0% +augmented or doubly diminished or doubly + + + align:start position:0% +augmented or doubly diminished or doubly +augmented or whatever is considered + + align:start position:0% +augmented or whatever is considered + + + align:start position:0% +augmented or whatever is considered +dissonant now the weird + + align:start position:0% +dissonant now the weird + + + align:start position:0% +dissonant now the weird +one um that we can always debate is the + + align:start position:0% +one um that we can always debate is the + + + align:start position:0% +one um that we can always debate is the +perfect forth who thinks it's + + align:start position:0% +perfect forth who thinks it's + + + align:start position:0% +perfect forth who thinks it's +consonants who thinks it's a + + align:start position:0% +consonants who thinks it's a + + + align:start position:0% +consonants who thinks it's a +dissonance a lot of people not voting + + align:start position:0% +dissonance a lot of people not voting + + + align:start position:0% +dissonance a lot of people not voting +I'm glad for either way people voted um + + align:start position:0% +I'm glad for either way people voted um + + + align:start position:0% +I'm glad for either way people voted um +in this case music 21 regards it as not + + align:start position:0% +in this case music 21 regards it as not + + + align:start position:0% +in this case music 21 regards it as not +a consonants perfect forths are + + align:start position:0% +a consonants perfect forths are + + + align:start position:0% +a consonants perfect forths are +generally they're the one weird interval + + align:start position:0% +generally they're the one weird interval + + + align:start position:0% +generally they're the one weird interval +they're generally considered consonant + + align:start position:0% +they're generally considered consonant + + + align:start position:0% +they're generally considered consonant +when they are melodic but dissonant when + + align:start position:0% +when they are melodic but dissonant when + + + align:start position:0% +when they are melodic but dissonant when +they're harmonic and above the + + align:start position:0% +they're harmonic and above the + + + align:start position:0% +they're harmonic and above the +base so it's take take Medieval music + + align:start position:0% +base so it's take take Medieval music + + + align:start position:0% +base so it's take take Medieval music +with me or speo um you can figure out + + align:start position:0% +with me or speo um you can figure out + + + align:start position:0% +with me or speo um you can figure out +the whole history of how this happened + + align:start position:0% +the whole history of how this happened + + + align:start position:0% +the whole history of how this happened +and why it's in the one weird double + + align:start position:0% +and why it's in the one weird double + + + align:start position:0% +and why it's in the one weird double +position but it's the only perfect thing + + align:start position:0% +position but it's the only perfect thing + + + align:start position:0% +position but it's the only perfect thing +that is not um consonant in some + + align:start position:0% +that is not um consonant in some + + + align:start position:0% +that is not um consonant in some +circumstances + + align:start position:0% +circumstances + + + align:start position:0% +circumstances +okay um what are some of the things you + + align:start position:0% +okay um what are some of the things you + + + align:start position:0% +okay um what are some of the things you +might do with interval uh class well + + align:start position:0% +might do with interval uh class well + + + align:start position:0% +might do with interval uh class well +let's start with let's create the + + align:start position:0% +let's start with let's create the + + + align:start position:0% +let's start with let's create the +perfect fifth one + + align:start position:0% +perfect fifth one + + + align:start position:0% +perfect fifth one +P5 hopefully I've created that good um + + align:start position:0% +P5 hopefully I've created that good um + + + align:start position:0% +P5 hopefully I've created that good um +and what we can do is let's say uh C4 + + align:start position:0% +and what we can do is let's say uh C4 + + + align:start position:0% +and what we can do is let's say uh C4 +we'll just C this equals P + + align:start position:0% +we'll just C this equals P + + + align:start position:0% +we'll just C this equals P +C4 and now P5 can + + align:start position:0% +C4 and now P5 can + + + align:start position:0% +C4 and now P5 can +transpose pitch + + align:start position:0% + + + + align:start position:0% + +C4 so you have a perfect fifth creating + + align:start position:0% +C4 so you have a perfect fifth creating + + + align:start position:0% +C4 so you have a perfect fifth creating +that as an interval object storing as P5 + + align:start position:0% +that as an interval object storing as P5 + + + align:start position:0% +that as an interval object storing as P5 +we can create a pitch object these just + + align:start position:0% +we can create a pitch object these just + + + align:start position:0% +we can create a pitch object these just +because of my aliases C4 start C4 then + + align:start position:0% +because of my aliases C4 start C4 then + + + align:start position:0% +because of my aliases C4 start C4 then +P5 can transpose the C4 transpose pitch + + align:start position:0% +P5 can transpose the C4 transpose pitch + + + align:start position:0% +P5 can transpose the C4 transpose pitch +on C4 and gets an a pitch object that's + + align:start position:0% +on C4 and gets an a pitch object that's + + + align:start position:0% +on C4 and gets an a pitch object that's +G4 + + align:start position:0% +G4 + + + align:start position:0% +G4 +now once you've done that if we look at + + align:start position:0% +now once you've done that if we look at + + + align:start position:0% +now once you've done that if we look at +C4 that object is + + align:start position:0% +C4 that object is + + + align:start position:0% +C4 that object is +unchanged so transpose pitch creates a + + align:start position:0% +unchanged so transpose pitch creates a + + + align:start position:0% +unchanged so transpose pitch creates a +new pitch that is not uh that is not the + + align:start position:0% +new pitch that is not uh that is not the + + + align:start position:0% +new pitch that is not uh that is not the +same pitch so if you wanted to do + + align:start position:0% +same pitch so if you wanted to do + + + align:start position:0% +same pitch so if you wanted to do +something useful with this you would + + align:start position:0% +something useful with this you would + + + align:start position:0% +something useful with this you would +probably store it as G4 equals this and + + align:start position:0% +probably store it as G4 equals this and + + + align:start position:0% +probably store it as G4 equals this and +then you can do something with + + align:start position:0% +then you can do something with + + + align:start position:0% +then you can do something with +with your new pitch obviously if you + + align:start position:0% +with your new pitch obviously if you + + + align:start position:0% +with your new pitch obviously if you +knew what the pitch was going to be + + align:start position:0% +knew what the pitch was going to be + + + align:start position:0% +knew what the pitch was going to be +coming in and what the pitch was going + + align:start position:0% +coming in and what the pitch was going + + + align:start position:0% +coming in and what the pitch was going +to be coming out you wouldn't need to do + + align:start position:0% +to be coming out you wouldn't need to do + + + align:start position:0% +to be coming out you wouldn't need to do +this right you can just create your own + + align:start position:0% +this right you can just create your own + + + align:start position:0% +this right you can just create your own +damn G4 but um but this would work sort + + align:start position:0% +damn G4 but um but this would work sort + + + align:start position:0% +damn G4 but um but this would work sort +of in general if you do want to + + align:start position:0% +of in general if you do want to + + + align:start position:0% +of in general if you do want to +transpose in place um and I don't think + + align:start position:0% +transpose in place um and I don't think + + + align:start position:0% +transpose in place um and I don't think +we've seen this in music 21 but you're + + align:start position:0% +we've seen this in music 21 but you're + + + align:start position:0% +we've seen this in music 21 but you're +going to start seeing it all over the + + align:start position:0% +going to start seeing it all over the + + + align:start position:0% +going to start seeing it all over the +place there is a keyword only argument + + align:start position:0% +place there is a keyword only argument + + + align:start position:0% +place there is a keyword only argument +that means you must type this as a + + align:start position:0% +that means you must type this as a + + + align:start position:0% +that means you must type this as a +keyword in place equals so C4 will now + + align:start position:0% +keyword in place equals so C4 will now + + + align:start position:0% +keyword in place equals so C4 will now +be transposed + + align:start position:0% +be transposed + + + align:start position:0% +be transposed +and nothing will be returned we run it + + align:start position:0% +and nothing will be returned we run it + + + align:start position:0% +and nothing will be returned we run it +but now + + align:start position:0% +but now + + + align:start position:0% +but now +c4 is a really terribly named variable + + align:start position:0% +c4 is a really terribly named variable + + + align:start position:0% +c4 is a really terribly named variable +right C4 is now a + + align:start position:0% +right C4 is now a + + + align:start position:0% +right C4 is now a +G4 um if you're ever doing a demo you + + align:start position:0% +G4 um if you're ever doing a demo you + + + align:start position:0% +G4 um if you're ever doing a demo you +all remember when we took two notes we + + align:start position:0% +all remember when we took two notes we + + + align:start position:0% +all remember when we took two notes we +inserted two notes or we removed them + + align:start position:0% +inserted two notes or we removed them + + + align:start position:0% +inserted two notes or we removed them +from the stream and then everything was + + align:start position:0% +from the stream and then everything was + + + align:start position:0% +from the stream and then everything was +screwed up uh so I always I'm going to + + align:start position:0% +screwed up uh so I always I'm going to + + + align:start position:0% +screwed up uh so I always I'm going to +remember learned from that experience + + align:start position:0% +remember learned from that experience + + + align:start position:0% +remember learned from that experience +and make C4 uh equals C4 right + + align:start position:0% +and make C4 uh equals C4 right + + + align:start position:0% +and make C4 uh equals C4 right +again but sometimes we want to just have + + align:start position:0% +again but sometimes we want to just have + + + align:start position:0% +again but sometimes we want to just have +a generic P equals um here this time + + align:start position:0% +a generic P equals um here this time + + + align:start position:0% +a generic P equals um here this time +I'll write it out so that we can copy + + align:start position:0% +I'll write it out so that we can copy + + + align:start position:0% +I'll write it out so that we can copy +and paste this pitch. pitch + + align:start position:0% +and paste this pitch. pitch + + + align:start position:0% +and paste this pitch. pitch +C4 and uh we still have P5 let's just do + + align:start position:0% +C4 and uh we still have P5 let's just do + + + align:start position:0% +C4 and uh we still have P5 let's just do +this for I in range 13 we don't actually + + align:start position:0% +this for I in range 13 we don't actually + + + align:start position:0% +this for I in range 13 we don't actually +need I you can some people like to have + + align:start position:0% +need I you can some people like to have + + + align:start position:0% +need I you can some people like to have +underscore as a dummy variable but we're + + align:start position:0% +underscore as a dummy variable but we're + + + align:start position:0% +underscore as a dummy variable but we're +just going to for 13 times let's take + + align:start position:0% +just going to for 13 times let's take + + + align:start position:0% +just going to for 13 times let's take +the pitch and + + align:start position:0% +the pitch and + + + align:start position:0% +the pitch and +then uh we can no since we just done it + + align:start position:0% +then uh we can no since we just done it + + + align:start position:0% +then uh we can no since we just done it +P5 transpose pitch p in place equals + + align:start position:0% + + + + align:start position:0% + +true so we create a + + align:start position:0% +true so we create a + + + align:start position:0% +true so we create a +C4 13 times we're going to go through + + align:start position:0% +C4 13 times we're going to go through + + + align:start position:0% +C4 13 times we're going to go through +and um transpose + + align:start position:0% +and um transpose + + + align:start position:0% +and um transpose +it so what is p + + align:start position:0% +it so what is p + + + align:start position:0% +it so what is p +now C + + align:start position:0% +now C + + + align:start position:0% +now C +B + + align:start position:0% +B + + + align:start position:0% +B +10 is that what it + + align:start position:0% + + + + align:start position:0% + +is oops not c um what do you call it + + align:start position:0% +is oops not c um what do you call it + + + align:start position:0% +is oops not c um what do you call it +P F double sharp 11 because if you + + align:start position:0% +P F double sharp 11 because if you + + + align:start position:0% +P F double sharp 11 because if you +notice we were Printing and then + + align:start position:0% +notice we were Printing and then + + + align:start position:0% +notice we were Printing and then +transposing was my little uh little + + align:start position:0% +transposing was my little uh little + + + align:start position:0% +transposing was my little uh little +trick thing just to just to make sure + + align:start position:0% +trick thing just to just to make sure + + + align:start position:0% +trick thing just to just to make sure +that we're all following things yeah so + + align:start position:0% +that we're all following things yeah so + + + align:start position:0% +that we're all following things yeah so +by the way this is one of the weird + + align:start position:0% +by the way this is one of the weird + + + align:start position:0% +by the way this is one of the weird +reasons why um why I wanted you to work + + align:start position:0% +reasons why um why I wanted you to work + + + align:start position:0% +reasons why um why I wanted you to work +early on with weird octave numbers like + + align:start position:0% +early on with weird octave numbers like + + + align:start position:0% +early on with weird octave numbers like +10 and 11 and -2 and things like that + + align:start position:0% +10 and 11 and -2 and things like that + + + align:start position:0% +10 and 11 and -2 and things like that +because quite often it is simpler to do + + align:start position:0% +because quite often it is simpler to do + + + align:start position:0% +because quite often it is simpler to do +an operation like this like let's all go + + align:start position:0% +an operation like this like let's all go + + + align:start position:0% +an operation like this like let's all go +around the circle of fifths and then + + align:start position:0% +around the circle of fifths and then + + + align:start position:0% +around the circle of fifths and then +we'll just print the step of it and not + + align:start position:0% +we'll just print the step of it and not + + + align:start position:0% +we'll just print the step of it and not +care about the octave number and then we + + align:start position:0% +care about the octave number and then we + + + align:start position:0% +care about the octave number and then we +in the end we can bring it back down a + + align:start position:0% +in the end we can bring it back down a + + + align:start position:0% +in the end we can bring it back down a +bunch of octaves later but sometimes + + align:start position:0% +bunch of octaves later but sometimes + + + align:start position:0% +bunch of octaves later but sometimes +you're going to end up in there and + + align:start position:0% +you're going to end up in there and + + + align:start position:0% +you're going to end up in there and +sometimes you're going to end up in in + + align:start position:0% +sometimes you're going to end up in in + + + align:start position:0% +sometimes you're going to end up in in +double sharp territory triple sharp + + align:start position:0% +double sharp territory triple sharp + + + align:start position:0% +double sharp territory triple sharp +territory before then transposing down + + align:start position:0% +territory before then transposing down + + + align:start position:0% +territory before then transposing down +back the other way or doing some other + + align:start position:0% +back the other way or doing some other + + + align:start position:0% +back the other way or doing some other +path so some so almost never is + + align:start position:0% +path so some so almost never is + + + align:start position:0% +path so some so almost never is +um is you know F quadruple sharp 22 + + align:start position:0% +um is you know F quadruple sharp 22 + + + align:start position:0% +um is you know F quadruple sharp 22 +going to be a useful thing to think + + align:start position:0% +going to be a useful thing to think + + + align:start position:0% +going to be a useful thing to think +about musically but sometimes it's a + + align:start position:0% +about musically but sometimes it's a + + + align:start position:0% +about musically but sometimes it's a +useful point in the mid in the midpoint + + align:start position:0% +useful point in the mid in the midpoint + + + align:start position:0% +useful point in the mid in the midpoint +of your work and by the way that's how + + align:start position:0% +of your work and by the way that's how + + + align:start position:0% +of your work and by the way that's how +imaginary numbers came out first that + + align:start position:0% +imaginary numbers came out first that + + + align:start position:0% +imaginary numbers came out first that +they were first used to solve I believe + + align:start position:0% +they were first used to solve I believe + + + align:start position:0% +they were first used to solve I believe +Quint equations in a way that U made it + + align:start position:0% +Quint equations in a way that U made it + + + align:start position:0% +Quint equations in a way that U made it +very easy even though they were NE in + + align:start position:0% +very easy even though they were NE in + + + align:start position:0% +very easy even though they were NE in +the intermediate stages even though they + + align:start position:0% +the intermediate stages even though they + + + align:start position:0% +the intermediate stages even though they +were never the answer at the end um so + + align:start position:0% +were never the answer at the end um so + + + align:start position:0% +were never the answer at the end um so +think of quadruple Sharps and octave 22s + + align:start position:0% +think of quadruple Sharps and octave 22s + + + align:start position:0% +think of quadruple Sharps and octave 22s +and stuff as like that okay + + align:start position:0% +and stuff as like that okay + + + align:start position:0% +and stuff as like that okay +um so a couple couple things is C4 still + + align:start position:0% +um so a couple couple things is C4 still + + + align:start position:0% +um so a couple couple things is C4 still +C4 yep good um you can also + + align:start position:0% +C4 yep good um you can also + + + align:start position:0% +C4 yep good um you can also +transpose uh do the opposite way way and + + align:start position:0% +transpose uh do the opposite way way and + + + align:start position:0% +transpose uh do the opposite way way and +this is a this is a real something that + + align:start position:0% +this is a this is a real something that + + + align:start position:0% +this is a this is a real something that +python allows that other languages I + + align:start position:0% +python allows that other languages I + + + align:start position:0% +python allows that other languages I +haven't been able to do it in so instead + + align:start position:0% +haven't been able to do it in so instead + + + align:start position:0% +haven't been able to do it in so instead +of taking the interval and saying tr. + + align:start position:0% +of taking the interval and saying tr. + + + align:start position:0% +of taking the interval and saying tr. +transpose pitch and the pitch you can + + align:start position:0% +transpose pitch and the pitch you can + + + align:start position:0% +transpose pitch and the pitch you can +take the pitch and say transpose that by + + align:start position:0% +take the pitch and say transpose that by + + + align:start position:0% +take the pitch and say transpose that by +the interval and that's sometimes pretty + + align:start position:0% +the interval and that's sometimes pretty + + + align:start position:0% +the interval and that's sometimes pretty +helpful so music 21 object. transpose by + + align:start position:0% +helpful so music 21 object. transpose by + + + align:start position:0% +helpful so music 21 object. transpose by +an interval class and um if you don't + + align:start position:0% +an interval class and um if you don't + + + align:start position:0% +an interval class and um if you don't +care about efficiency you can always um + + align:start position:0% +care about efficiency you can always um + + + align:start position:0% +care about efficiency you can always um +put in um just a string and it will + + align:start position:0% +put in um just a string and it will + + + align:start position:0% +put in um just a string and it will +create a interval for you and so + + align:start position:0% +create a interval for you and so + + + align:start position:0% +create a interval for you and so +transposing up an augmented 223rd gets + + align:start position:0% +transposing up an augmented 223rd gets + + + align:start position:0% +transposing up an augmented 223rd gets +you g Shar 35 is that right doesn't + + align:start position:0% +you g Shar 35 is that right doesn't + + + align:start position:0% +you g Shar 35 is that right doesn't +matter okay um by the way um okay uh + + align:start position:0% +matter okay um by the way um okay uh + + + align:start position:0% +matter okay um by the way um okay uh +looking at the time one or two last + + align:start position:0% +looking at the time one or two last + + + align:start position:0% +looking at the time one or two last +things uh if you ever + + align:start position:0% +things uh if you ever + + + align:start position:0% +things uh if you ever +want something when you um when you're + + align:start position:0% +want something when you um when you're + + + align:start position:0% +want something when you um when you're +working with the this is the interval + + align:start position:0% +working with the this is the interval + + + align:start position:0% +working with the this is the interval +object again perfect fifth there are + + align:start position:0% +object again perfect fifth there are + + + align:start position:0% +object again perfect fifth there are +things like specifier in here and you'll + + align:start position:0% +things like specifier in here and you'll + + + align:start position:0% +things like specifier in here and you'll +be able to um do a you know how to do + + align:start position:0% +be able to um do a you know how to do + + + align:start position:0% +be able to um do a you know how to do +dur on a um uh what do you call it on a + + align:start position:0% +dur on a um uh what do you call it on a + + + align:start position:0% +dur on a um uh what do you call it on a +object to see everything um that's in it + + align:start position:0% +object to see everything um that's in it + + + align:start position:0% +object to see everything um that's in it +but these are probably the most useful + + align:start position:0% +but these are probably the most useful + + + align:start position:0% +but these are probably the most useful +things you'll see so how many scents how + + align:start position:0% +things you'll see so how many scents how + + + align:start position:0% +things you'll see so how many scents how +many hundredths of a semitone is it and + + align:start position:0% +many hundredths of a semitone is it and + + + align:start position:0% +many hundredths of a semitone is it and +yes you can do microtonal intervals if + + align:start position:0% +yes you can do microtonal intervals if + + + align:start position:0% +yes you can do microtonal intervals if +you care about such things uh what's the + + align:start position:0% +you care about such things uh what's the + + + align:start position:0% +you care about such things uh what's the +chromatic interval what's the complement + + align:start position:0% +chromatic interval what's the complement + + + align:start position:0% +chromatic interval what's the complement +if you have a major sixth the complement + + align:start position:0% +if you have a major sixth the complement + + + align:start position:0% +if you have a major sixth the complement +is + + align:start position:0% +is + + + align:start position:0% +is +a remember it's minor thir it's the + + align:start position:0% +a remember it's minor thir it's the + + + align:start position:0% +a remember it's minor thir it's the +thing that fills out the octave dionic + + align:start position:0% +thing that fills out the octave dionic + + + align:start position:0% +thing that fills out the octave dionic +is it a skip is it a step can we reverse + + align:start position:0% +is it a skip is it a step can we reverse + + + align:start position:0% +is it a skip is it a step can we reverse +the interval all these things so you'll + + align:start position:0% +the interval all these things so you'll + + + align:start position:0% +the interval all these things so you'll +find some of these things in here um but + + align:start position:0% +find some of these things in here um but + + + align:start position:0% +find some of these things in here um but +the last thing I'm want to do is to + + align:start position:0% +the last thing I'm want to do is to + + + align:start position:0% +the last thing I'm want to do is to +think about uh this spelling non-s + + align:start position:0% +think about uh this spelling non-s + + + align:start position:0% +think about uh this spelling non-s +spelling thing so implicit dionic we'll + + align:start position:0% +spelling thing so implicit dionic we'll + + + align:start position:0% +spelling thing so implicit dionic we'll +say um let's create the interval of four + + align:start position:0% +say um let's create the interval of four + + + align:start position:0% +say um let's create the interval of four +semitones so all I car is that it's an + + align:start position:0% +semitones so all I car is that it's an + + + align:start position:0% +semitones so all I car is that it's an +interval of four semit tones and here's + + align:start position:0% +interval of four semit tones and here's + + + align:start position:0% +interval of four semit tones and here's +where um what do we call it polyvalent + + align:start position:0% +where um what do we call it polyvalent + + + align:start position:0% +where um what do we call it polyvalent +um polygamus whatever whatever we call + + align:start position:0% +um polygamus whatever whatever we call + + + align:start position:0% +um polygamus whatever whatever we call +the interval it will take um I that was + + align:start position:0% +the interval it will take um I that was + + + align:start position:0% +the interval it will take um I that was +a joke um it will take an integer + + align:start position:0% +a joke um it will take an integer + + + align:start position:0% +a joke um it will take an integer +instead of a string so we can say the + + align:start position:0% +instead of a string so we can say the + + + align:start position:0% +instead of a string so we can say the +int four and if I just look at this I4 + + align:start position:0% +int four and if I just look at this I4 + + + align:start position:0% +int four and if I just look at this I4 +right now it looks like hey it's just a + + align:start position:0% +right now it looks like hey it's just a + + + align:start position:0% +right now it looks like hey it's just a +cheap way of saying major third but it's + + align:start position:0% +cheap way of saying major third but it's + + + align:start position:0% +cheap way of saying major third but it's +actually a little bit different from + + align:start position:0% +actually a little bit different from + + + align:start position:0% +actually a little bit different from +that so if I take the pitch C double + + align:start position:0% +that so if I take the pitch C double + + + align:start position:0% +that so if I take the pitch C double +flat + + align:start position:0% +flat + + + align:start position:0% +flat +um so pitch C flat + + align:start position:0% +um so pitch C flat + + + align:start position:0% +um so pitch C flat +4 and i' say I4 + + align:start position:0% +4 and i' say I4 + + + align:start position:0% +4 and i' say I4 +transpose that pitch so take cou flat 4 + + align:start position:0% +transpose that pitch so take cou flat 4 + + + align:start position:0% +transpose that pitch so take cou flat 4 +and take it up a major third I don't + + align:start position:0% +and take it up a major third I don't + + + align:start position:0% +and take it up a major third I don't +care about the accidental but what's the + + align:start position:0% +care about the accidental but what's the + + + align:start position:0% +care about the accidental but what's the +F what's the step have to be if you're + + align:start position:0% +F what's the step have to be if you're + + + align:start position:0% +F what's the step have to be if you're +going up a third from C + + align:start position:0% +going up a third from C + + + align:start position:0% +going up a third from C +something e e so it should be uh what is + + align:start position:0% +something e e so it should be uh what is + + + align:start position:0% +something e e so it should be uh what is +that e double flat 4 + + align:start position:0% + + + + align:start position:0% + +and instead you get a D4 so there's + + align:start position:0% +and instead you get a D4 so there's + + + align:start position:0% +and instead you get a D4 so there's +something where if you initiate an + + align:start position:0% +something where if you initiate an + + + align:start position:0% +something where if you initiate an +interval just by saying the number of + + align:start position:0% +interval just by saying the number of + + + align:start position:0% +interval just by saying the number of +semones you're telling that interval + + align:start position:0% +semones you're telling that interval + + + align:start position:0% +semones you're telling that interval +that the dionic interval the minor major + + align:start position:0% +that the dionic interval the minor major + + + align:start position:0% +that the dionic interval the minor major +uh the major third is implicit that is + + align:start position:0% +uh the major third is implicit that is + + + align:start position:0% +uh the major third is implicit that is +to say um when you want to know if it's + + align:start position:0% +to say um when you want to know if it's + + + align:start position:0% +to say um when you want to know if it's +a major third yeah it'll be a major + + align:start position:0% +a major third yeah it'll be a major + + + align:start position:0% +a major third yeah it'll be a major +third but I4 will say no feel free to + + align:start position:0% +third but I4 will say no feel free to + + + align:start position:0% +third but I4 will say no feel free to +change this to anything that is for sem + + align:start position:0% +change this to anything that is for sem + + + align:start position:0% +change this to anything that is for sem +tones up that is logical um and easy to + + align:start position:0% +tones up that is logical um and easy to + + + align:start position:0% +tones up that is logical um and easy to +use so that's something that people will + + align:start position:0% +use so that's something that people will + + + align:start position:0% +use so that's something that people will +um see in there whereas if we take the + + align:start position:0% +um see in there whereas if we take the + + + align:start position:0% +um see in there whereas if we take the +perfect fifth and see which we created + + align:start position:0% +perfect fifth and see which we created + + + align:start position:0% +perfect fifth and see which we created +it with the P5 thing and see if it's an + + align:start position:0% +it with the P5 thing and see if it's an + + + align:start position:0% +it with the P5 thing and see if it's an +implicit + + align:start position:0% +implicit + + + align:start position:0% +implicit +dionic false perfect fifth will always + + align:start position:0% +dionic false perfect fifth will always + + + align:start position:0% +dionic false perfect fifth will always +take the one that we created with the + + align:start position:0% +take the one that we created with the + + + align:start position:0% +take the one that we created with the +string P5 will always make sure that + + align:start position:0% +string P5 will always make sure that + + + align:start position:0% +string P5 will always make sure that +something is a P5 uh I'm looking at the + + align:start position:0% +something is a P5 uh I'm looking at the + + + align:start position:0% +something is a P5 uh I'm looking at the +time so I won't demonstrate last thing + + align:start position:0% +time so I won't demonstrate last thing + + + align:start position:0% +time so I won't demonstrate last thing +which is music 21 still has a + + align:start position:0% +which is music 21 still has a + + + align:start position:0% +which is music 21 still has a +restriction that it won't go above + + align:start position:0% +restriction that it won't go above + + + align:start position:0% +restriction that it won't go above +quadruple sharps or quadruple Flats so + + align:start position:0% +quadruple sharps or quadruple Flats so + + + align:start position:0% +quadruple sharps or quadruple Flats so +at that point even the dionic one will + + align:start position:0% +at that point even the dionic one will + + + align:start position:0% +at that point even the dionic one will +say uh forget what I said let's make it + + align:start position:0% +say uh forget what I said let's make it + + + align:start position:0% +say uh forget what I said let's make it +work and round + + align:start position:0% +work and round + + + align:start position:0% +work and round +things uh great I'm um that's that's all + + align:start position:0% +things uh great I'm um that's that's all + + + align:start position:0% +things uh great I'm um that's that's all +the time that I have if you transpose a + + align:start position:0% +the time that I have if you transpose a + + + align:start position:0% +the time that I have if you transpose a +whole score uh you'll see that the key + + align:start position:0% +whole score uh you'll see that the key + + + align:start position:0% +whole score uh you'll see that the key +signature is transpose with you which + + align:start position:0% +signature is transpose with you which + + + align:start position:0% +signature is transpose with you which +can be kind of helpful and I'll I'll + + align:start position:0% +can be kind of helpful and I'll I'll + + + align:start position:0% +can be kind of helpful and I'll I'll +post my um I'll post my what do you call + + align:start position:0% +post my um I'll post my what do you call + + + align:start position:0% +post my um I'll post my what do you call +it uh the the thing where where I have + + align:start position:0% +it uh the the thing where where I have + + + align:start position:0% +it uh the the thing where where I have +that demo to the class right \ No newline at end of file diff --git a/0xjqZ8sutzA.txt b/0xjqZ8sutzA.txt new file mode 100644 index 0000000000000000000000000000000000000000..71986bdab44f7806d593ef41ff039603aed74bf5 --- /dev/null +++ b/0xjqZ8sutzA.txt @@ -0,0 +1,619 @@ +align:start position:0% + +well you made it this far how are you + + align:start position:0% +well you made it this far how are you + + + align:start position:0% +well you made it this far how are you +feeling um we're feeling actually pretty + + align:start position:0% +feeling um we're feeling actually pretty + + + align:start position:0% +feeling um we're feeling actually pretty +good we had a test earlier today so + + align:start position:0% +good we had a test earlier today so + + + align:start position:0% +good we had a test earlier today so +we're all kind of a little tired and a + + align:start position:0% +we're all kind of a little tired and a + + + align:start position:0% +we're all kind of a little tired and a +little nervous from the doing the test + + align:start position:0% +little nervous from the doing the test + + + align:start position:0% +little nervous from the doing the test +earlier but we feel good right now yeah + + align:start position:0% +earlier but we feel good right now yeah + + + align:start position:0% +earlier but we feel good right now yeah +so you're confident uh what's your + + align:start position:0% +so you're confident uh what's your + + + align:start position:0% +so you're confident uh what's your +strategy for winning today well pretty + + align:start position:0% +strategy for winning today well pretty + + + align:start position:0% +strategy for winning today well pretty +much our strategy is rather simple we're + + align:start position:0% +much our strategy is rather simple we're + + + align:start position:0% +much our strategy is rather simple we're +going to fly um really there's no we we + + align:start position:0% +going to fly um really there's no we we + + + align:start position:0% +going to fly um really there's no we we +are already did our little planning and + + align:start position:0% +are already did our little planning and + + + align:start position:0% +are already did our little planning and +um did the cost effectiveness of + + align:start position:0% +um did the cost effectiveness of + + + align:start position:0% +um did the cost effectiveness of +carrying one egg or two eggs and four + + align:start position:0% +carrying one egg or two eggs and four + + + align:start position:0% +carrying one egg or two eggs and four +eggs so that's already done all all we + + align:start position:0% +eggs so that's already done all all we + + + align:start position:0% +eggs so that's already done all all we +need to do now is just go up there and + + align:start position:0% +need to do now is just go up there and + + + align:start position:0% +need to do now is just go up there and +go in the air so getting off the ground + + align:start position:0% +go in the air so getting off the ground + + + align:start position:0% +go in the air so getting off the ground +is your goal today that is our primary + + align:start position:0% +is your goal today that is our primary + + + align:start position:0% +is your goal today that is our primary +goal uh so what is the most notable + + align:start position:0% +goal uh so what is the most notable + + + align:start position:0% +goal uh so what is the most notable +feature of your aircraft what what + + align:start position:0% +feature of your aircraft what what + + + align:start position:0% +feature of your aircraft what what +advantage do you have over the other + + align:start position:0% +advantage do you have over the other + + + align:start position:0% +advantage do you have over the other +teams um I I feel we we were one of the + + align:start position:0% +teams um I I feel we we were one of the + + + align:start position:0% +teams um I I feel we we were one of the +few teams that actually uh looked + + align:start position:0% +few teams that actually uh looked + + + align:start position:0% +few teams that actually uh looked +throughout the the spectrum of what + + align:start position:0% +throughout the the spectrum of what + + + align:start position:0% +throughout the the spectrum of what +would be the most effective way of + + align:start position:0% +would be the most effective way of + + + align:start position:0% +would be the most effective way of +carrying eggs cuz in this competition + + align:start position:0% +carrying eggs cuz in this competition + + + align:start position:0% +carrying eggs cuz in this competition +it's not just time endurance but how + + align:start position:0% +it's not just time endurance but how + + + align:start position:0% +it's not just time endurance but how +much how many eggs you carry per per how + + align:start position:0% +much how many eggs you carry per per how + + + align:start position:0% +much how many eggs you carry per per how +how much time so if you carried four + + align:start position:0% +how much time so if you carried four + + + align:start position:0% +how much time so if you carried four +eggs for 2 minutes that would be eight + + align:start position:0% +eggs for 2 minutes that would be eight + + + align:start position:0% +eggs for 2 minutes that would be eight +points carrying but if you carried two + + align:start position:0% +points carrying but if you carried two + + + align:start position:0% +points carrying but if you carried two +eggs for 4 minutes that would also be + + align:start position:0% +eggs for 4 minutes that would also be + + + align:start position:0% +eggs for 4 minutes that would also be +eight points and I feel we one of the + + align:start position:0% +eight points and I feel we one of the + + + align:start position:0% +eight points and I feel we one of the +few teams that actually did that so what + + align:start position:0% +few teams that actually did that so what + + + align:start position:0% +few teams that actually did that so what +configuration did you did you choose um + + align:start position:0% +configuration did you did you choose um + + + align:start position:0% +configuration did you did you choose um +we chose to uh have two eggs U towards + + align:start position:0% +we chose to uh have two eggs U towards + + + align:start position:0% +we chose to uh have two eggs U towards +the towards the have a underneath the + + align:start position:0% +the towards the have a underneath the + + + align:start position:0% +the towards the have a underneath the +center of gravity of the center of mass + + align:start position:0% +center of gravity of the center of mass + + + align:start position:0% +center of gravity of the center of mass +of the plane we feel that would be + + align:start position:0% +of the plane we feel that would be + + + align:start position:0% +of the plane we feel that would be +best so you've been working uh on this + + align:start position:0% +best so you've been working uh on this + + + align:start position:0% +best so you've been working uh on this +project as a team for most of the + + align:start position:0% +project as a team for most of the + + + align:start position:0% +project as a team for most of the +semester the rest of your team is + + align:start position:0% +semester the rest of your team is + + + align:start position:0% +semester the rest of your team is +currently uh loading up your eggs uh + + align:start position:0% +currently uh loading up your eggs uh + + + align:start position:0% +currently uh loading up your eggs uh +what what do you think was the most + + align:start position:0% +what what do you think was the most + + + align:start position:0% +what what do you think was the most +enjoyable part of the process uh the + + align:start position:0% +enjoyable part of the process uh the + + + align:start position:0% +enjoyable part of the process uh the +most enjoyable part I think is just us + + align:start position:0% +most enjoyable part I think is just us + + + align:start position:0% +most enjoyable part I think is just us +coming together and just talking cuz + + align:start position:0% +coming together and just talking cuz + + + align:start position:0% +coming together and just talking cuz +like our our meetings weren't as + + align:start position:0% +like our our meetings weren't as + + + align:start position:0% +like our our meetings weren't as +efficient as they could have been but uh + + align:start position:0% +efficient as they could have been but uh + + + align:start position:0% +efficient as they could have been but uh +we still we had a lot of fun like um I + + align:start position:0% +we still we had a lot of fun like um I + + + align:start position:0% +we still we had a lot of fun like um I +got to learn uh some of the people in my + + align:start position:0% +got to learn uh some of the people in my + + + align:start position:0% +got to learn uh some of the people in my +class from like on a more intimate level + + align:start position:0% +class from like on a more intimate level + + + align:start position:0% +class from like on a more intimate level +um I can call them friends I could just + + align:start position:0% +um I can call them friends I could just + + + align:start position:0% +um I can call them friends I could just +like hang out with them in fact me and + + align:start position:0% +like hang out with them in fact me and + + + align:start position:0% +like hang out with them in fact me and +uh uh Lynn the um the girl over there + + align:start position:0% +uh uh Lynn the um the girl over there + + + align:start position:0% +uh uh Lynn the um the girl over there +she's we're going to go to the mall + + align:start position:0% +she's we're going to go to the mall + + + align:start position:0% +she's we're going to go to the mall +either this week this weekend or next + + align:start position:0% +either this week this weekend or next + + + align:start position:0% +either this week this weekend or next +weekend to um go shopping + + align:start position:0% +weekend to um go shopping + + + align:start position:0% +weekend to um go shopping +together great uh what was the toughest + + align:start position:0% +together great uh what was the toughest + + + align:start position:0% +together great uh what was the toughest +part about engineering this system um I + + align:start position:0% +part about engineering this system um I + + + align:start position:0% +part about engineering this system um I +think it was the wings because at + + align:start position:0% +think it was the wings because at + + + align:start position:0% +think it was the wings because at +first we we designed something we + + align:start position:0% +first we we designed something we + + + align:start position:0% +first we we designed something we +designed a wing that seemed in theory + + align:start position:0% +designed a wing that seemed in theory + + + align:start position:0% +designed a wing that seemed in theory +was correct but seemed that in practice + + align:start position:0% +was correct but seemed that in practice + + + align:start position:0% +was correct but seemed that in practice +it was harder it was it was a correct uh + + align:start position:0% +it was harder it was it was a correct uh + + + align:start position:0% +it was harder it was it was a correct uh +thing in theory but when we actually + + align:start position:0% +thing in theory but when we actually + + + align:start position:0% +thing in theory but when we actually +tried to fly it it was in like it was to + + align:start position:0% +tried to fly it it was in like it was to + + + align:start position:0% +tried to fly it it was in like it was to +different ult for us to fly so we uh we + + align:start position:0% +different ult for us to fly so we uh we + + + align:start position:0% +different ult for us to fly so we uh we +had to change it and so there is this + + align:start position:0% +had to change it and so there is this + + + align:start position:0% +had to change it and so there is this +whole thing of theory like in theory + + align:start position:0% +whole thing of theory like in theory + + + align:start position:0% +whole thing of theory like in theory +this would be the best way but then in + + align:start position:0% +this would be the best way but then in + + + align:start position:0% +this would be the best way but then in +practicality we can't fly this we just + + align:start position:0% +practicality we can't fly this we just + + + align:start position:0% +practicality we can't fly this we just +we're not that good we don't have the + + align:start position:0% +we're not that good we don't have the + + + align:start position:0% +we're not that good we don't have the +240 hours or whatever amount of hours it + + align:start position:0% +240 hours or whatever amount of hours it + + + align:start position:0% +240 hours or whatever amount of hours it +takes to learn how to fly things like + + align:start position:0% +takes to learn how to fly things like + + + align:start position:0% +takes to learn how to fly things like +this sounds like a valuable lesson well + + align:start position:0% +this sounds like a valuable lesson well + + + align:start position:0% +this sounds like a valuable lesson well +good luck with the flight thanks very + + align:start position:0% +good luck with the flight thanks very + + + align:start position:0% +good luck with the flight thanks very +much for talking about this thank + + align:start position:0% +much for talking about this thank + + + align:start position:0% +much for talking about this thank +you \ No newline at end of file diff --git a/14m9MW-qMhg.txt b/14m9MW-qMhg.txt new file mode 100644 index 0000000000000000000000000000000000000000..cc5e0e1bece40036ed041d66cea878b675e7dd31 --- /dev/null +++ b/14m9MW-qMhg.txt @@ -0,0 +1,4333 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Why don't +we get started? + +So today we're going to talk +about comparative genomics. + +And first, a brief review +of what we did last time. + +So last time we talked +about global alignment + +of protein sequences, +including the Needleman-Wunsch + +and Smith-Waterman algorithms. + +And we talked about gap +penalties a little bit + +and started to introduce the +PAM series of matrices which + +are well described in the text. + +So what I wanted to +do is just briefly + +go over what I started to +talk about at the end, about + +Markov models of evolution. + +Because they're relevant, +not only for the PAM series, + +but also for some other +topics in the course. + +A short unit on +molecular evolution + +we're going to do today. + +And then they also introduce +hidden Markov models + +that will come up +later in the course. + +So the example that we gave of +a Markov model was DNA sequence + +evolution in successive +generations where + +the observation here is that the +base at a particular position + +at generation n+1 here depends +on the base at that generation + +and the base at generation n. + +But conditional on knowing +the base at generation n, + +you don't learn +anything from knowing + +what that base was +at generation n-1. + +That's the essence of +the Markov properties. + +So here's the formal +definition, as we saw before. + +Any questions on this? + +And I asked you to review +your conditional probability + +if it was rusty, because +that's very relevant. + +OK so in this example you might, +if you had a random variable x + +that represented the genotype +at a particular locus, + +let's say the +apolipoprotein locus, + +and it had alleles +A and a, then you + +might write something +like the probability + +that Bart's genotype +is a homozygous given + +his grandfather's genotype +and his dad's genotype + +is equal to just the conditional +probability given his father's + +genotype. + +So those are the sorts +of things that you + +can do with Markov chains + +So when you're working +with Markov chains + +matrices are extremely useful. + +So another thing that will +be helpful in this part + +of the course and then again +in Professor Fraenkel's + +part, where he's +talking-- he'll use also + +some ideas from +linear algebra-- is + +to review your basics +of matrices and vector + +multiplication. + +OK so, if you now make a +model of molecular evolution + +where sn is-- so s +is this variable that + +represents a particular +base in the genome + +and is the generation. + +And then to describe +the evolution + +of this base over +time, we're going + +to imagine that its evolution +is described by a Markov chain. + +And a Markov chain can be +described by, in this case, a 4 + +by 4 matrix, since there are +four possible nucleotides + +at generation i, for example, +and four possible at generation + +i plus one. + +And you simply need +to specify what + +the conditional probability +that the base will + +be, of any possible base, at +the next generation, given what + +it is at the current generation. + +So here's the matrix up here. + +And it describes, for +example, the probability + +of going from a c to an a. + +So then in general +you might know + +that that base is a g +at the first generation. + +But in general you +won't necessarily + +know what base it is if +you're modeling events that + +may happen in the future. + +So the most general +way of describing + +what's happening at +that base is a vector + +of probabilities of the +four possible bases-- + +so qa, qc, qg, qt, with those +probabilities summing up to 1. + +And so then it turns out +that with this notation + +that the content of the +vector at generation n plus 1 + +is equal to simply the +vector at generation n + +multiplied on the +right by the matrix, + +just using the standard +vector matrix multiplication. + +So for example, +if we have vectors + +with four things in +them, and we have + +a 4 by 4 matrix, then to get +this term here in this vector + +you multiply-- you basically +take the dot product + +of this vector times +this first column. + +The vector times +the first column + +will give you that entry. + +And this times this +column will give you + +that entry in the +vector, and so forth. + +And you can see that the +way this makes sense, + +the way the matrix is defined, +that first column tells you + +the probability that you'll have +an a at the next generation, + +conditional on each +of the four bases + +at the previous generation. + +And so you just multiply by +the probabilities of those four + +bases times the appropriate +conditional probability here. + +And those are all +the ways that you + +can be an a +generation, n plus 1. + +And so it's also true that if +you want to go further in time, + +so from generation +n to generation n + +plus k-- k is some integer-- +then this just corresponds + +to sequential multiplication +by the matrix k-- + +I'm sorry, by the matrix p. + +So qn plus 1 equals q times p. + +And then qn plus 2 will +equal q-- I'm sorry. + +That's a really bad q, +but-- qn plus 1 times p, + +which will equal q times p +squared, where p squared means + +matrix multiplication, again +using the standard rules + +of matrix multiplication +that you can look up. + +So one of the things you +might think about here + +is what happens +after a long time? + +If you start from some vector +q-- for example, q is 0010. + +That is, it's 100% chance of g. + +What would happen if +you run this matrix + +on that over a long +period of time. + +And we'll come back to that +question a little bit later. + +So thinking about the +Dayhoff matrices-- and again, + +I'm not going to go +into detail here, + +because it's well +described in the text. + +Dayhoff looked at these highly +identical alignments, these 85% + +identical alignments, and +calculated the mutability + +of each residue and these +mutation probabilities + +for how often each residue +changes into each other one + +and then scaled them so that on +average the chance of mutating + +is 1% and then took +these probabilities, + +these frequencies, +of mutation m, a, b, + +divided by the frequency of +the residue b, took the log, + +and then just multiplied by +two just for scaling purposes, + +and came up with a-- and then +rounded to the nearest integer, + +again for practical purposes. + +And that's how she came +up with her PAM 1 matrix. + +And then you can use +matrix multiplication + +to derive all the +successive PAM series. + +Just multiply the PAM1 matrix +times itself to get the PAM2 + +and recalculate the scores. + +So if you actually use +PAM matrices in practice + +there are some issues. + +And these are also well +described in the text. + +And the fundamental +problem seems + +to be that the way the +proteins evolve over + +short periods of time and +the way they evolve over + +long periods of time +is somewhat different. + +And basically this model, this +Markov model of evolution, + +is not quite right, that things +don't-- what you see in a short + +periods of time-- it does not +match long periods of time. + +And why is that? + +A number of possible reasons. + +But keep in mind that +in addition to proteins + +simply changing their +amino acid sequence, + +other things can +happen in evolution. + +You can have insertions +and deletions + +that are not captured +by this Markov model. + +And you can also have birth +and death of proteins. + +A protein can evolve according +to this model for millions + +of years. + +And then it can become unneeded, +and just be lost, for example. + +So real protein evolution +is more complicated. + +And so about 20 years ago +or so Henikoff and Henikoff + +decided to develop a +new type of matrix. + +And the way they did it was +to identify these things + +called blocks, which are regions +of reasonably high similarity, + +but not as high as +Dayhoff required. + +So there were many more-- +Dayhoff was working the '70s. + +They were working in the '90s. + +So there were many more +proteins available. + +And they could identify, +with confidence, basically + +a much larger data +set, including + +more distantly related, but +still confidently alignable, + +protein sequences. + +And they derived new parameters. + +And in the end this matrix they +came up with called BLOSUM62 + +seems to work well in +a variety of contexts + +when comparing moderately +distantly related + +proteins or quite +distantly related proteins. + +If you're comparing +very similar proteins + +it almost doesn't matter. + +Any reasonable +matrix will probably + +give you the right answer. + +But when you're comparing +the more distant ones, + +that's where it +becomes challenging. + +And so this is the +BLOSUM62 matrix here. + +And you can see it's similar +to the PAM matrices in that-- I + +think we showed PAM 250 +last time-- in that you have + +a diagonal with all +positive numbers. + +And it's also similar in +that, for example, trytophan + +down here has a higher +positive score than others. + +It's plus 9. + +And cysteine is also +one of the higher ones. + +But those are less extreme. + +And basically, maybe over short +periods of evolutionary time, + +you don't change your cysteine. + +But over longer periods +there is some rewiring + +of disulfide bonding, and +so cysteines can change. + +Something like that +may be going on. + +So we've just talked about +pairwise sequence alignments. + +But in practice you +often have, especially + +these days you often have, +many proteins though. + +So you want to align three or +five or 10 different proteins + +together to find +out which residues + +are most conserved, for example. + +And so basically +the principles are + +similar to pairwise alignment. + +But now you want +to find alignments + +that bring the greatest +number of single characters + +into register. + +So if you're aligning +three proteins, + +you really want to have +columns where all three are + +the same residue, or +very similar residues. + +And you need to then +define scoring systems, + +define gap penalties, +and so forth. + +This is also reasonably +well described in the text. + +I just wanted to +make one comment + +about the sort of computational +complexity of multiple sequence + +alignment. + +So if you think about +pairwise sequence alignment, + +say with Needleman-Wunsch +or Smith-Waterman, + +with a sequence +of length-- let's + +say you're aligning one +protein of sequence length n + +to another of life n, what is +the computational complexity + +of that calculation in using +this big O notation that we've + +talked about? + +Let's just say +standard gap penalties, + +linear gap penalties. + +Anyone? + +Or does it matter? + +Yeah, go ahead. + +STUDENT: n squared. + +PROFESSOR: It's n squared. + +So even though this has gaps, +with local-- with ungapped + +it was also n +squared, or n times n, + +So why is it that gaps +don't make it worse? + +Or do they? + +Any thoughts on that? + +STUDENT: You put a constant +number of gaps in the sequence. + +So it's just stating the +essence of the complexity + +should still be n squared. + +PROFESSOR: You put a +constant number of gaps? + +The-- I mean, yeah-- let's just +hear a few different comments. + +And then we'll try to summarize. + +Go ahead. + +STUDENT: So we're +still only filling out + +an n by n matrix +at any given time. + +PROFESSOR: You're still filling +out an n by n matrix, right. + +There happen to be +a few more things. + +The recursion is slightly +more complicated. + +But there's a few +more things you + +have to calculate +to fill in each. + +But it's like three +things, or four things. + +It's not-- so it doesn't +grow with the size. + +So it's just still n squared, +but with a larger constant. + +OK, good. + +And then if you did +affine gap penalty, + +remember where you +had a gap opening + +penalty and a gap +extension, what then? + +Does that make it worse? + +Or is it still n squared? + +STUDENT: I think +it's still n squared. + +PROFESSOR: Why is that? + +STUDENT: Computing the affine +gap penalty is no more than o + +of n, right? + +PROFESSOR: Yeah, +basically with the affine + +you have to keep track of +two things at each place. + +So yeah, it is. + +You're right. + +It's still n squared. + +It's just you got to keep track +of two numbers in each place + +there. + +OK, good. + +And so what about when +we go to three proteins? + +So how would you +generalize, let's say, + +the Needleman-Wunsch algorithm +to align three proteins? + +Any ideas? + +What structure would +you use, or what-- + +analogous to a matrix-- +yeah, in the back. + +STUDENT: Another way to do +this would be have a 3D matrix. + +PROFESSOR: OK, a 3D +matrix, like a cube. + +And can everyone visualize that? + +So yeah, basically +you could have + +a version of Needleman-Wunsch +that was on a cube. + +And it started in +the 0, 0, 0 corner + +and went down to the n, n, +n corner, filling in in 3D. + +OK so what kind of +computational complexity + +do you think that +algorithm would have? + +STUDENT: n cubed? + +PROFESSOR: n cubed. + +Yeah, makes sense. + +There would be a similar +number, a few operations + +to fill in each +element in the cube. + +And there's n cubed. + +So the way that the problem +grows with n is as n cubed. + +And what about in general, +if you have k sequences? + +STUDENT: n to the k? + +PROFESSOR: n to the k. + +So is this practical? + +With three proteins and modern +computers you could do it. + +You could implement +Needleman-Wunsch on a cube. + +But what about with 20 proteins? + +Is that practical? + +So it's really not. + +So if proteins are 500 +residues long and there's + +500 to the 20th, right. + +It starts to explode. + +So that approach +really only works + +in two dimensions and a little +bit in three dimensions. + +And it becomes impractical. + +So you need to use a +variety of shortcuts. + +And so this is, again, +described pretty well + +in chapter six of the text. + +And a commonly used-- if +you're looking for a default + +multiple sequence aligner, +CLUSTALW is a common one. + +There's a web +interface if you just + +need to do one or +two alignments. + +That works fine. + +You can also download a +version called CLUSTALX + +and run it locally. + +And it does a lot of things +with pairwise alignments + +and then combining the +pairwise alignments. + +It aligns the two +closest things first + +and then brings in the +next closest, and so forth. + +And it does a lot of +tricks that are-- they're + +basically heuristics. + +They're things +that usually work, + +give you a reasonable +answer, but don't necessarily + +guarantee that you will find the +optimal alignment if you were + +to do it on a 20 dimensional +cube, for example. + +So they work reasonably +well in practice. + +And then there's a variety +of other algorithms. + +OK, good. + +So that's a review of what +we've mostly been talking about. + +And now I want to introduce +a couple of new topics. + +So we're going to briefly +talk a little bit more + +about Markov models +of sequence evolution. + +And these are closely related +to some classic evolutionary + +theory from +Jukes-Cantor and Kimura. + +So we'll just +briefly mention that. + +And we'll talk a little +bit about different types + +of selection that sequences can +undergo-- so neutral, negative, + +and positive-- and how +you might distinguish + +among those for protein +coding sequences. + +And this will basically +serve as an intro + +into the main topic today, +which is comparative genomics. + +And comparative genomics-- it's +not really a field, exactly. + +It's more of an approach. + +But I wanted to give you +some actual concrete examples + +of computational biology +research, successful research + +that has led to various types of +insights into gene regulation, + +in this case, +mostly to emphasize + +that computational biology +is not just a bag of tools. + +We've mostly been +talking about tools. + +We introduced tools +for local alignment + +and multiple alignment and +statistics and so forth. + +But really it's a +living, breathing field + +with active research. + +And even using-- +comparative genomics + +is one of my favorite +areas within this field. + +Because it's very powerful. + +And you can often use +very simple ideas. + +And simple algorithms +can sometimes + +give you a really interesting +biological result, + +if you have the right +sequences and ask the question + +the right way. + +So I have posted a dozen of my +favorite comparative genomics + +papers in a special +section on the website. + +Obviously I'm not asking +you to read all of these. + +But I'm going to give you a few +insights and approaches that + +were used in each of +these papers here, + +just to give you a flavor +of some of the things + +that you can do with +comparative genomics, + +in the hopes that this might +inspire some of your projects. + +So hopefully you're +going to start + +thinking about finding teammates +and thinking about projects. + +And this will hopefully +help in that direction. + +Of course, they don't have to be +comparative genomics projects. + +You could do anything +in computational biology + +or systems biology +in this class. + +But that's just one area +to start thinking about. + +Yeah, I'll also-- +I'm sorry, I think + +I haven't posted this yet. + +But I will also post +this review by Sabeti + +that has a good discussion of +positive selection a little bit + +later. + +Again, not required. + +All right, so let's go +back to this question + +that I posed earlier. + +We have a Markov model of +DNA sequence evolution. + +And we-- sn is the +base at generation n. + +And then what happens +after a long time? + +If you take any vector-- +q, to start with, + +might be a known +base, for example-- + +and apply that +matrix many times, + +what happens as n +goes to infinity. + +And so it turns out that +there's fairly classical theory + +here that gives us an answer. + +This is not all the +theory that exists, + +but this describes +the typical case. + +So the theory says that if all +of the elements in the matrix + +are greater than 0, +and then of course + +all of the-- pij's, when you sum +over j, they have to equal 1. + +That's just for it to be a +well-defined Markov chain. + +Because you're +going from i to j. + +And so from any base +you have to go-- + +the probability of going +to one of those four bases + +has to sum to 1. + +And so if those conditions +hold, then there + +is a unique vector r such +that r equals r times p. + +And the limit of +q times p to the n + +equals r, independent +of what q was. + +So basically, wherever +you were starting + +from-- you could +have been starting + +from 100% g, or 50% +a, 50% g, or 100% + +c-- you apply this +matrix many, many times, + +you will eventually +approach this vector r. + +And the theory doesn't +say what r is, exactly. + +But it says that r +equals r times p. + +And that turns out to basically +implicitly define what r is. + +That is, you can solve +for r using that equation. + +And r, for this reason, because +the matrix doesn't move r, + +r is called the +stationary distribution. + +And it's often also called +the limiting distribution, + +for obvious reasons. + +And if you want to read more, +like where this theory comes + +from, here's a +reasonable reference. + +So any questions +about this theory? + +All the elements +in the matrix have + +to be strictly greater +than 1-- I'm sorry, + +strictly greater than 0. + +Otherwise, really no conditions. + +All right, question? + +Yeah, go ahead. + +STUDENT: Does the [INAUDIBLE] +distribution ever change, + +based on the sequence, or are +we assuming that it doesn't? + +PROFESSOR: The theory +says it only depends on p. + +It doesn't depend on q. + +So it depends on the model +of how the changes happen, + +the conditional probability +of what the base will + +be at the next +generation given what + +it is at the current generation. + +It doesn't depend +where you start. + +q is what your +starting point is, + +what base you're initially at. + +Does that make sense? + +And this is obviously +a very simplified case, + +where we're just modeling +evolution of one base, + +and we're not thinking +about whether the rates vary + +at different positions +or within-- this + +is the simplest case. + +But it's important to +understand the simplest case + +before you start +to generalize that. + +OK, so let's do +some examples here. + +So here are some matrices. + +So it turns out the math is +a lot easier if you limit + +yourself to a two-letter +alphabet instead of four. + +So that's what I've done here. + +So let's look at these matrices +and think about what they mean. + +So we have two-letter alphabet. + +R is purine. + +Y is pyrimidine. + +These matrices describe +the conditional probability + +that, at the next generation, +you'll be, for example-- oops, + +here we go. + +That, for example, if +you start at purine, + +that you'll remain purine +at the next generation. + +That would be 1 minus P. And +the probability that you'll + +change to pyrimidine is P. And +the probability of pyrimidine + +will remain as a +pyrimidine is 1 minus P. + +So what is the stationary +distribution of this matrix? + +OK, so if p is small, this +describes a typical model, + +where most of the +time you remain-- + +DNA replication and +repair is faithful. + +You maintain the same base. + +But occasionally a mutation +happens with probability p. + +Anyone want to guess what the +stationary distribution is + +or describe a strategy +for finding it? + +Like what do we know +about this distribution? + +Or imagine you +start with a purine + +and then you apply +this matrix many times + +to that vector that's 1 +comma 0, what will happen? + +Yeah, Levi. + +STUDENT: Probably 50-50 because +any other that way you skew it + +it would be pushed +towards the center + +because there's more +[INAUDIBLE] the other. + +PROFESSOR: OK, +everyone get that? + +So Levi's comment was +that it's probably 50-50. + +Because mutation +probabilities are symmetrical. + +Purine-pyrimidine and +pyrimidine-purine are the same. + +So if you were to start +with say, lots of purine, + +then there will be more +mutation toward pyrimidine + +in a given generation. + +So if you think about this +is your population of R + +and that's your population +of Y, then if this is bigger + +than that, you'll tend +to push it more that way. + +And there will be less +mutation coming this way, + +until they're equal. + +And then you'll have equal +flux going both directions. + +So that's a good way +to think about it. + +And that's correct. + +Can you think of how +would you show that? + +What's a way of solving for +the stationary distribution? + +Anyone? + +So remember, we'll +just get back one. + +The theory says +that R equals RP. + +That's the key. + +R equals RP. + +So what is R? + +Well we don't know R. So we +let that be a general vector. + +So notice there's only +one free parameter. + +Because the two components +have to sum to 1. + +It's a frequency vector, +so x and 1 minus x. + +And we just multiply +this times the matrix. + +So you take x comma 1 minus x. + +And you multiply +it by this matrix. + +The matrix is 1 minus P P. +I'm using too much space here. + +I'll just make it a little +smaller-- P 1 minus P. + +And that's going +to equal R. And so + +we'll get x times 1 +minus P plus-- remember, + +it's dot product of this +times this column, right? + +So x times 1 minus P +plus 1 minus x times P. + +That's the first component. + +And the second +component will be xp + +plus 1 minus x times 1 minus p. + +OK, everyone got that? + +So now what do we do? + +STUDENT: r. + +PROFESSOR: What's that? + +STUDENT: Make that +equal to the initial r. + +PROFESSOR: Yeah, make that +equal to the initial r. + +So it's two equations +and-- well, you really + +only need one equation here. + +Because we've already +simplified it. + +In general there will +be two equations. + +There will be one +equation that says + +that the components of +the vector sum to 1. + +And there will be another +equation coming from here. + +But we can just use +either one, either term. + +So we know that +the first component + +of a vector-- if this vector +is equal to that vector, then + +the first components +have to be equal, right? + +So x equals x +times-- times what? + +Times 1 minus p, just +combining these two. + +And then plus what are all the-- +I'm sorry, that's 1 minus p-- 1 + +minus p here. + +And then there's another +term here, minus another p. + +And then there's a +term that's just p. + +And so then what do you do? + +You just solve for x. + +And I think when +you work this out + +you'll get two p x equals +p, so x equals 1/2. + +Right, everyone got that? + +OK, so yeah. + +So if x is 1/2, then the +vector is 1/2 comma 1/2, + +which is the unbiased. + +All right, what about +this next matrix, + +right below-- 1 +minus p 1 minus q. + +p and q are two positive +numbers that are different. + +So now there's actually +a different probability + +of mutating purine to pyrimidine +and pyrimidine to purine. + +So Levi, can we +apply your approach + +to see what the answer is? + +STUDENT: Not exactly. + +PROFESSOR: Not exactly? + +OK, yeah, it's not as obvious. + +It's not symmetrical anymore. + +But can anyone guess +what the answer might be? + +Yeah, go ahead Diego. + +STUDENT: It'll go either +all the way to one side + +or depending on q and d. + +PROFESSOR: All the way to +one side or all the way + +to the other? + +So meaning it'll be all purine +or all pyrimidine again. + +STUDENT: Yeah, +depending on which-- + +PROFESSOR: Which is bigger? + +OK, anyone else have +an alternative theory? + +Yeah, go ahead. + +What was your name again? + +STUDENT: Daniel. + +PROFESSOR: Sorry, Daniel? + +STUDENT: Daniel, yeah. + +PROFESSOR: Daniel. + +OK, go ahead. + +STUDENT: It'll reach some +intermediate equilibrium + +once they balance +each other out. + +And that would be exactly-- +I'm not sure-- some ratio of q + +to p. + +PROFESSOR: OK. + +How many people think +that might happen? + +OK, some people. + +OK Daniel has maybe +slightly more supporters. + +So let's see. + +So how are we going +to solve this? + +How do we figure out what the +stationary distribution is? + +You just use that same approach. + +So you can do-- you +have x 1 minus x + +times that matrix, which is got +the 1 minus p p q 1 minus q. + +OK, and so now you'll +get x 1 minus p. + +Anyway, go through +the same operations. + +Solve for x. + +And you will get-- I think I put +the answer on the slide here. + +You will get q over p plus q. + +So as Danny predicted, some +ratio involving q's and p's. + +And does this make sense? + +Seeing what the +answer is, can you + +rationalize why that's true? + +STUDENT: It's like a +kind of equilibrium. + +You have one mode of +force play pushing + +one way and another +different one + +in this case pushing the other. + +PROFESSOR: Yeah, that's +basically the same idea. + +And so they have +to be in balance. + +So the one that has less, where +the mutation rate is a lower, + +will end up being bigger, so +that the amount that flows out + +will be the same as the +amount that flows in. + +You can apply Levi's +idea of thinking + +about how much flux +is going in each way. + +So there's going to be some +flux p in one direction, q + +in the other direction. + +And you want x times p to +equal 1 minus x times q. + +And this is the +value of that works. + +OK, good? + +What about this guy down here? + +So this is a very special matrix +called the identity matrix. + +And what kind of model +of evolution is this? + +STUDENT: There's no mutation. + +PROFESSOR: There's no evolution. + +This is like a perfect +replication repair system. + +The base never changes. + +So what's a stationary +distribution? + +STUDENT: It's all-- + +PROFESSOR: What's that? + +STUDENT: It'll just +stay where it is. + +PROFESSOR: It'll +stay where it is. + +That's right. + +So any vector is +stationary for this matrix. + +Remember that the +theory said there's + +a unique stationary +distribution. + +This seems to be inconsistent. + +Why is it not inconsistent? + +Sally? + +STUDENT: We defined all of the +variables to be greater than 0. + +So when you have anything that's +[INAUDIBLE] that is equal to 0. + +PROFESSOR: Right, so a +condition of the theorem + +is that all the entries be +strictly greater than 0. + +And this is why. + +If you have 0s, in there +then crazy things can happen. + +Wherever you start, that's where +you end up with this matrix. + +So every vector is stationary. + +And what about this crazy +matrix over here, matrix q? + +What does it do? + +Joe. + +STUDENT: It's going to +swap them back and forth. + +PROFESSOR: It swaps +them back and forth. + +So this is like a +hyper mutable organism + +that has such a high +mutation rate that it always + +mutates every base +to the other kind. + +It's never happy +with its genome. + +It always wants to switch +it, get something better. + +And so what can you say about +the stationary distribution + +for this matrix? + +Jeff? + +STUDENT: There isn't +going to be one. + +PROFESSOR: There +isn't going to be one? + +Anyone else? + +STUDENT: Well, actually, I +guess 1, 1, like 0.5, 0.5. + +PROFESSOR: 0.5, 0.5 +would be stationary. + +Because you're-- + +STUDENT: But you +won't converge to it. + +PROFESSOR: But you +won't converge to it. + +That's right. it's +stationary, but not limiting. + +And again, the +theory doesn't apply. + +Because there's some +0s in this matrix. + +But you can still +think about that. + +OK, everyone got that? + +All right, good. + +OK so let's talk now +about Jukes-Cantor. + +So Jukes-Cantor is very +much a Markov model + +of DNA sequence evolution. + +And it simply has-- now +we've got four bases. + +It's got probability alpha +of mutating from each base + +to any other base. + +And so the overall mutation +rate, or probability + +of substitution, at one +generation is three alpha. + +Because from the base G there's +an alpha probability mutate + +to A, an alpha probability +to C, an alpha to T, + +so the three alpha. + +And you can basically +write a recursion + +that describes +what's going on here. + +So if you start +with a G at time 0, + +the probability of a G at +time 1 is 1 minus 3 alpha. + +It's a probability +that you didn't mutate. + +But then, at generation +two, you have + +to consider two cases really. + +First of all, if you +didn't mutate, that's PG1. + +Then you have a 1 +minus alpha probability + +of not mutating +again, so remaining G. + +But you might have mutated. + +With probability 1 +minus PG 1 you mutated. + +And then whatever +you were-- might + +be a C-- you have +an alpha probably + +of mutating back to G. +Does that make sense? + +Everyone clear why there's a 3 +in one place and only a 1 alpha + +in the other? + +All right, so you can +actually solve this recursion. + +And you get this +expression here, P G of t + +equals 1/4 plus 3/4 E +to the minus 4 alpha t. + +OK so what does that +tell you about-- we + +know from our +previous discussion + +what the stationary distribution +of this Markov chain + +is going to be. + +What will it be? + +What's the stationary +distribution? + +STUDENT: 1/4 of each. + +PROFESSOR: 1/4 of each. + +And why, Daniel, is that? + +STUDENT: Because the probability +of them moving to any base + +is the same? + +PROFESSOR: Right, it's +totally symmetrical. + +So that has to be the +answer by symmetry. + +And you could solve it. + +You could use this same +approach with defining + +a value-- the theory applies +if alpha is greater than 0 + +and less than 1-- or +less than-- I think + +it has to be less than +a quarter, actually, + +or something like that. + +And you can apply the theory. + +So there will be a +stationary distribution. + +You can set up a vector. + +Now you have to have four +terms in it and multiplication. + +And then you'll get a +system of basically four + +equations and four unknowns. + +And you can solve that +system using linear algebra + +and get the answer. + +And yeah, the answer will +be 1/4, as you guessed. + +And so what this +Jukes-Cantor expression + +tells you is how quickly does +it get to that equilibrium. + +We're thinking about G. +You can start at 100% G. + +And it will then approach 1/4. + +You can see 1/4 +is clearly what's + +going to happen in the limit. + +Because as t gets big that +second term is going to 0. + +And so what does the +distribution look like? + +How rapidly do you approach 1/4? + +You approach it exponentially. + +So you start at 1 here. + +And this is 0. + +This is 1/4. + +You'll start here. + +And you'll go like that. + +You go rapidly at the beginning. + +And then you get just +very gradual approach 1/4. + +So you can do a little bit more +algebra with this expression. + +And here's where the really +useful part comes in. + +And you can show +that K, which we'll + +define as the true number +of substitutions that + +have occurred at this particular +base that we're considering, + +is related to D, where D is +the fraction of positions that + +differ when you just take +say the parental sequence + +and the daughter sequence, +the eventual sequence + +that you get to. + +You just match those two. + +And you count up +the differences. + +That's D. And then K +is the actual number + +of substitutions +that have occurred. + +And those are related by this +equation, K equals minus 3/4, + +natural log, 1 minus 4/3 d. + +So let's try to +think about, first + +of all, what is the +shape of that curve? + +What does that look like? + +Here's 0. + +I'll put 1 over here. + +So we all know that log-- +if it was just simply + +log of something +between 0 and 1, + +it would look like +what-- look like that. + +Starts from negative infinity +and comes up to 0 at 1. + +But it's actually not log +of D. It's log of 1 minus D, + +or 1 minus a constant times +D. So that will flip it. + +So the minus infinity +will be there. + +It will come in like that. + +And then we also have minus 3/4. + +There's a minus in front +of this whole thing. + +So all these logs are of +numbers that are less than 1. + +So they're all negative. + +But then it'll get flipped. + +So it'll actually +look like that. + +And it will go to +infinity where? + +Where does this go to infinity? + +So if this is now +K is on this axis. + +And yeah, sorry if +that wasn't clear. + +D is here. + +So this is just +again, this is if we + +did log of D it +would look like this. + +If we do log of 1 minus +something times D, + +that'll flip it. + +And then if we do minus that, +it'll flip it again that way. + +OK so now K, as a function of +D, is going to look like this. + +Sometimes people +like to put-- anyway, + +but let's just think about this. + +So it's going to go to +up to infinity somewhere. + +And where is that? + +STUDENT: 3/4. + +PROFESSOR: 3/4. + +So does that make sense? + +Can someone tell +us what's going on + +and what is the use of +this whole thing here? + +Yeah, in the back. + +What's your name? + +STUDENT: Julianne. + +PROFESSOR: Yeah, Julianne. + +Go ahead. + +STUDENT: [INAUDIBLE] 0. + +So part, it would give +you negative infinite. + +And so you just +solve for D in there. + +PROFESSOR: OK, so when D is +3/4 you'll get 1 minus 1. + +You get 0. + +That'll be negative infinity. + +And then there's +a minus in front, + +so it'll be constant infinity. + +So that's true. + +And does that intuitively +make sense to you? + +We have a sequence. + +It's evolving randomly, +according to this model. + +And then we have that +ancestral sequence. + +And then we have a modern +descendant of that sequence, + +millions of generations-- or +maybe thousands of generations, + +or some large number +of generations away. + +We line up those two sequences. + +We count how many matches +and how many mismatches. + +What's the fraction +of mismatches, + +of differences we have? + +Basically if that-- let's +look at a different case. + +What if d is very small? + +What if it's like 1%. + +Then what happens? + +If d is small, turns out +k is pretty much like d. + +It grows linearly with +d in the beginning. + +So does that make sense? + +That makes sense. + +Because k is the true number +of substitutions that happen. + +When you go one +generation, the true number + +of substitutions and +the measured number + +of substitutions is the same. + +Because there's +no back mutations. + +But when you go further, +there's an increasing chance + +of a back-- there's +an increasing chance + +of a mutation, therefore +increasing chance + +that you also have +a back mutation. + +And so this is what +happens at long time. + +So basically this is linear +here and then goes up like that. + +And so what this +allows you to do + +is d something that +you can measure. + +And then k is something +that you want to know. + +The point is, if I measure +the difference between human + +and chimp sequence, it +might be only 1% different. + +And if I have an idea of +mutation rate per generation, + +I configure out how +many generations apart, + +or how much time has passed, +since humans split from chimp. + +But if I go to mouse, where the +average base might be-- there + +might be only a 50% +matching-- if that's true, + +there have been a +lot of changes there. + +There will be a lot of bases +that have changed once, + +as well as a lot that +may have changed twice, + +and may have actually +changed back. + +And so that let's say human +and mouse are 50% identical. + +That 50% identical-- +I can't just + +compare it to let's +say the 1% with chimp + +and say it's 50 times longer. + +That 50% will be +an underestimate + +of the true difference. + +Because there's been some +back mutations as well. + +And so you have to +use this formula + +to figure out what the +true evolutionary time is, + +the true number of +changes that happened. + +Yeah, go ahead. + +STUDENT: Does simple count +refer to just the difference + +in the amount of mutations? + +Or what's-- + +PROFESSOR: The simple count +is what you actually observe. + +So you have a +stretch of sequence-- + +let's say the beta globin +genomic locus in human. + +You line it up to the beta +globin locus in chimp. + +You count what fraction +of positions differ? + +What fractions are different? + +That's d. + +And then k is-- actually, it's +slightly complicated here. + +Because if this is +human and that's chimp, + +then k is more like-- +because you don't actually + +observe the ancestor. + +You observe chimp. + +So you have to go back to the +ancestor and then forward. + +So that's the relevant +number of generations. + +And so k will tell +you how many changes + +must have occurred to +give you that observed + +fraction of differences. + +And for short +distances, it's linear. + +And then for long, it's +logarithmic, basically. + +Yeah, question. + +STUDENT: So I'm guessing all +of [INAUDIBLE] that selection + +is absent. + +PROFESSOR: Right, right. + +This is ignoring selection. + +That's a good point. + +So think about this. + +And let me if other +questions come up. + +So this actually +came up the other day + +when we were talking about +DNA substitution models. + +So Kimura and +others have observed + +that transitions occur much +more often than transversions, + +maybe two to three +times as often, + +and so proposed a +matrix like this. + +And now you can +use what you know + +about stationary +distributions to solve + +for the limiting or stationary +distribution of this matrix. + +And actually, you will find +it's still symmetrical. + +It's a little bit +more complicated now, + +but you'll still +get that 1/4, 1/4. + +But then more +recently others have + +observed that +really, dinucleotides + +matter in terms +of mutation rates, + +particularly in +vertebrates So what's + +special about vertebrates is +that they have methylation + +machinery that methylates +CPG dinucleotides on the C. + +And that makes those +C's hypermutable. + +They mutate at about 10 times +the rate of any other base. + +And so you can give a +higher mutation rate to C, + +but that doesn't +really capture it. + +It's really a higher mutation +rate of C's that are next + +to G's. + +And so you can +define a model that's + +16 by 16, which has +dinucleotide mutation rates. + +And that's actually +a better model + +of DNA sequence evolution. + +And it's just the math +gets a little hairier + +if you want to calculate +stationary distribution. + +But again, it can be done. + +And it's actually +pretty easy to simulate. + +Knowing that it will +converge to the stationary, + +you can just run the +thing many times. + +And you'll get to the answer. + +And there's even been +strand-specific models + +proposed, where there are +some differences between how + +the repair machinery treats +the two DNA strands that + +are related to transcription +coupled repair. + +So you actually get +some asymmetries there. + +And this is a +reasonably rich area. + +And you can look at some +of these references. + +All right, so one more +topic, while we're on + +evolution-- this +is very classical. + +But I just wanted to make sure +that everyone has seen it. + +If you are looking specifically +at protein coding sequences, + +exons, and you know the reading +frame, you can just align them. + +And then you can look +at two different types + +of substitutions. + +You can look at what are +called the nonsynonymous + +substitutions, so changes +to the codons that change + +the underlying amino acid, +the encoded amino acid. + +And you define +often a term that's + +either called Ka or dN, +depending who you read, + +that is the fraction of +nonsynonymous substitutions + +divided by nonsynonymous sites. + +And in this case let's +do synonymous first. + +So you can also look +at the other changes. + +So these are now +synonymous changes + +which are base +changes to triplets + +that do not change the +encoded amino acid. + +So in this case, there +are three of those. + +And a lot of +evolutionary approaches + +are just based on calculating +these two numbers. + +You count synonymous changes. + +You divide by +synonymous sites, count + +non-synonymous substitutions, +divide by non-synonymous sites. + +And so what do we +mean synonymous site? + +Well if you have only amino +acids that are fourfold, + +that have fourfold +degenerate codons, + +which is all of them are +like that in this case, + +then for example GG-- or +let's see what's up here. + +Yeah, CC anything +codes for proline. + +Do we have any of those? + +Actually, these are not +all fourfold degenerate. + +I apologize. + +But glycine, for example-- +so GG anything is glycine. + +So in this triplet, +this triplet here, + +there's one synonymous site. + +The third side is +a synonymous site. + +You can change that without +changing the amino acid. + +But the other two +are non-synonymous. + +So to do first +approximation, you + +take non-synonymous +substitutions + +and divide by the number +of codons-- I'm sorry, + +the number of codons +times 2, since there + +are two non-synonymous +positions in each codon. + +And you take synonymous +substitutions, + +divide by the number of codons. + +OK, does that make sense? + +One per codon. + +OK and so what do you +then do with this? + +You can correct this +value using-- basically + +this is the +Jukes-Cantor correction + +that we just calculated, +this 3/4 log 1 minus 4/3. + +That applies to codon evolution +as well as individual base + +evolution. + +And what people +often do with this + +is they calculate Ka +and Ks for a whole gene. + +Let's say you have +alignments of all human genes + +to their orthologs +in mouse-- that + +is, the corresponding +homologous gene in mouse. + +And you calculate Ka Ks. + +And then you can +look at those genes + +where this ratio is +significantly less than 1, + +or around 1, or greater than 1. + +And that actually +tells you something + +about how that-- the +type of selection + +that that gene is experiencing. + +So what would you +expect to see-- + +or if I told you +we've got two genes + +and the Ka/Ks ratio +is much less than 1. + +It's like 0.2. + +What would that tell you? + +Or what could you infer +about the selection + +that's happening to that gene? + +Ka/Ks is much less than 1. + +Any ideas? + +Julianne, yeah. + +STUDENT: The protein +sequence is important-- + +or the amino acid sequence. + +PROFESSOR: Yeah, exactly. + +The amino acid +sequence is important. + +Because you assume +that those synonymous + +sites and non-synonymous +sites-- they're + +going to mutate at +the same rate, right? + +The mutation processes don't +know about protein coding. + +So what you're seeing +is an absence, a loss, + +of the non-synonymous changes. + +80% of those +non-synonymous changes + +have been kicked +out by evolution. + +You're only seeing 20%. + +And you're using, assuming +the non-synonymous are + +neutral-- I'm sorry. + +I seem to have trouble +with these words today. + +But you assume that the +synonymous ones are neutral. + +And then that's +calibrates everything. + +And then you see that the +non-synonymous are much lower. + +Therefore you must have +lost-- these ones must + +have been kicked +out by evolution. + +So the amino acid +sequence is important. + +And it's optimal in some sense. + +The protein works-- the organism +does not want to change it. + +Or changes to that +protein sequence + +make the protein worse. + +And so you don't see them. + +And that's what you see +for most protein coding + +genes in the genome-- a Ka/Ks +ratio that's well below one. + +It says we care +what the protein is. + +And it's pretty good already. + +And we don't want to change it. + +All right, what +about a gene that + +has a Ka/Ks ratio of around 1? + +Anyone have an idea what would +that tell you about that gene? + +There are some-- Daniel? + +STUDENT: The sequence is-- it +doesn't particularly matter. + +Maybe it's a non-coding, +non-regulatory patch of DNA. + +I assume there +must be something. + +PROFESSOR: Yeah, so it could +be that it's not really + +protein coding after all. + +It's non-coding. + +Then this whole triplet thing we +were doing to it is arbitrary. + +So you don't expect any +particular distribution. + +That's true. + +Any other possibilities? + +Yeah, Tim. + +STUDENT: Could be that there +are opposite forces that + +are equilibrating. + +For example, we're +taking the unit of the G. + +But maybe in one +half of the G there's + +a strong selective +pressure for non-synonymous + +and in the other half it's +strong selective pressure + +for synonymous. + +Alternatively, it could be +in the same par of the gene, + +but it's involved in +two different processes. + +It's diatropic. + +So in one process it's +selecting this one thing. + +PROFESSOR: Yeah, or +one period of time, + +if you're looking at 10 +million years of evolution, + +it could have been for this +first five million years it was + +under negative selection, and +then it was under positive. + +And it averages out. + +Yes, all those things are +possible, but kind of unusual. + +And so maybe if +you saw that the-- + +if you plotted +Ka/Ks along the gene + +and you saw that it was high +in one area and low in another, + +then that would tell +you that you probably + +shouldn't be taking the +average across the gene. + +And that would be a +good thing to look for. + +But what if-- again, so +we said if Ka/Ks is near 1 + +it could be that it's not really +a protein coding gene at all. + +That's certainly possible. + +It could also be though +that it's a pseudogene. + +Or it's a gene that is no +longer needed by the organism. + +It still codes for protein, +but the organism just + +could care less +about its function. + +It's something that maybe +evolved in some other time. + +It helps you adapt to +when the temperature gets + +below minus 20. + +But it never gets +below minus 20 anymore. + +And so there's no selection +on it, or something like that. + +So neutral indicates-- this +is called neutral evolution. + +And then what about a gene which +has a Ka/Ks ratio significantly + +greater than 1? + +Any thoughts on what that might +mean and what kind of genes + +might happen to-- +yes, what's your name? + +STUDENT: Simona. + +PROFESSOR: Simona, go ahead. + +STUDENT: It might be a gene +that's selected against, + +so something that's detrimental +to the cell or the organism. + +PROFESSOR: It's detrimental-- +so the existing protein is + +bad for you, so you +want to change it. + +So it's better to change +it to something else. + +That's true. + +Can you think of an example +where that might be the case? + +STUDENT: A gene that +produces a toxin. + +PROFESSOR: A gene +that produces toxin. + +You might just lose +the gene completely + +if it produced a toxin. + +Any other examples you can +think of or other people? + +Yeah, Jeff. + +STUDENT: Maybe a +pigment that makes + +the organism more susceptible +to being eaten by a predator. + +PROFESSOR: OK, yeah if +it was a polar organism + +and it happened to have this +gene that made the fur dark + +and it showed up against the +snow, or something like that. + +And you can imagine that. + +Or a very common +case is, for example, + +a receptor that's used by +a virus to enter the cell. + +It probably had +some other purpose. + +But if the virus +is very virulent, + +you really just want +to change that receptor + +so that the virus can't +attack it anymore. + +So you see this kind +of thing is much rarer. + +It's only less than +1% of genes probably + +are under positive selection, +depending on how you measure it + +and what time +period you look at. + +But it tends to be really +recent, really strong selection + +for changing the +protein sequence. + +And the most common-- well, +probably the most common-- + +is these immune arms races +between a host and a pathogen. + +But there are other cases too. + +You can have very +strong selection + +where-- well, I don't +want to-- basically where + +a protein is maladapted, like +the organism moves from a very + +cold environment to a +very warm environment. + +And you just need to +change a lot of stuff + +to make those proteins +better adapted. + +Occasionally you can get +positive selection there. + +Yeah, go ahead. + +STUDENT: So the situation +where K or Ks is 1-- + +could it be possible that +the mRNA is under selection? + +PROFESSOR: Yeah, so that +basically we have always + +been implicitly assuming that +the synonymous substitution + +rate was neutral. + +But it could actually +be it's not neutral. + +That's under negative +selection too. + +And it happens +that they balance. + +That's also possible. + +So for that, to +assess that, you might + +want to compare the synonymous +substitution rate of that gene + +to neighboring genes. + +And if you find it's +much lower, that + +could indicate that +the coding sequences-- + +the third base of codons +is under selection-- + +could be for splicing, maybe. + +It could be for RNA secondary +structure, translation, + +different other-- +that's a good point. + +So yeah, you guys have +already poked holes in this. + +This is a method. + +It gives you something. + +You'll see it used. + +It gives you some inferences. + +But there are cases where +it doesn't fully work. + +OK, good. + +So in the remaining +time I wanted + +to do some examples of +comparative genomics. + +So as I mentioned +before, these are + +chosen to just give you some +examples of types of things + +you can learn about +gene regulation + +by comparing genomes again, +often by using really + +simple methods, +just blasting all + +the genes against each +other or things like this. + +And also, if you do choose +to read some of these papers, + +it can give you some +experience looking + +at this literature in +regulatory genomics. + +So the papers I've chosen-- +we'll start with Bejerano et al + +from 2002, who basically sought +to identify regulatory elements + +that are things that are +under evolutionary constraint. + +That's all he was +trying to find. + +Didn't know what +their functions were. + +But they turned out to be +interesting nonetheless, + +which is maybe a +little surprising. + +And then this other work from +Eddy Rubin's lab and others-- + +Steve Brenner's lab-- +actually characterized + +some of these extremely +conserved regions + +and assessed their function. + +And then Bejerano came +back a few years later + +and actually had a paper about +where these extremely conserved + +regions actually came from. + +So we'll talk about those. + +Then we'll look at +some papers that + +have to do with inferring +the regulatory targets + +of a transacting factor. + +And the factors that +we'll consider here + +will be microRNAs, +mostly, Either trying + +to understand what the +rules are for microRNA + +targeting and these +Lewis et al papers, + +or trying to identify +the regulatory targets + +in the genome. + +And then, time permitting, we'll +talk about a few other examples + +of slightly more exotic things. + +Graveley identified +a pair-- or pairs-- + +of interacting +regulatory elements + +through a clever comparative +genomic approach. + +And then I'll talk about +these two examples at the end + +if there's time, where a new +class of transacting factors + +was inferred from the +locations of the encoded genes + +in the genome. + +And also an inference was +made about the functions + +of some repetitive +elements from, again, + +looking at the matching +between these elements + +and another genome. + +All right, so first +example-- Bejerano + +"Ultraconserved elements." + +So they defined, in a fairly +arbitrary way, ultraconserved + +elements as unusually +long segments + +that 100% identical between +human, mouse, and rat. + +This was in 2000-- +I'm sorry, I might + +have the wrong-- it's +either 2004 or 2002. + +I forget. + +This was basically when the +first three mammalian genomes + +had been sequenced, which +were human, mouse, and rat. + +And there were whole +genome alignments. + +So they basically said let's +try to use these whole genome + +alignments to find +what's the most + +conserved thing in mammals. + +So they wanted to see if +there's anything 100% conserved. + +And so they did +statistics to say + +what's an unusually long +region of 100% identity. + +Any ideas how you would do +that calculation, what kind + +of statistics you would use? + +They used a really +simple approach. + +What they did was they +took one megabase segments + +of the genome, assuming it +might vary across the genome. + +They took ancestral repetitive +elements-- so repetitive + +elements that were +inserted, that + +were present in mouse, +rat, and human-- + +and assumed that they +were neutrally evolving, + +they were not under selection. + +And then therefor you could look +at the number of differences + +and get an idea what the +background rate of mutation is. + +And they use that. + +And they found that +that rate was-- + +this is from their supplementary +data-- that was never greater + +than 0.68. + +And so they just said well, if +we have a probability of-- I'm + +sorry. + +One is heads. + +So if they're all +three the same-- yeah, + +so if we have a probability +of 0.7 of heads, + +meaning that they're +all three the same, + +then the chance that you +have 200 heads in a row + +would be 1 minus P P to the 200, +just like [INAUDIBLE] trials. + +And you can just multiply that +times the size of the genome. + +And you say it's extremely +unlikely that you'll ever + +see anything where there's 200 +identical nucleotides in a row. + +So that's what they defined +as an ultraconserved element. + +So it all seems +very silly for now, + +until you actually +get to what they find. + +So they looked at where +are these elements + +around the genome. + +They found about 100 overlapped +exons of known protein coding + +genes, 100 are in +introns, and the remainder + +are in intergenic regions. + +So then they looked at +well what kind of genes + +contain exons with +overlapping-- or contain + +ultraconserved elements +that overlap exons? + +Those are type 1 genes. + +And what kind of +genes are next to + +the intergenic +ultraconserved elements, + +to try to get some clues about +the function of these elements. + +And so they did this early +gene ontology analysis. + +And what they found was that +the ultraconserved elements that + +overlapped exons +tended to fall in genes + +that encoded RNA-binding +proteins, particular splicing + +factors, by an order of +magnitude more frequent. + +And then the type 2 +genes, the ones that + +were next to these intergenic +ultraconserved regions, + +tended to be +transcription factors. + +In particular, homeobox +transcription factors + +were the most enriched class. + +So this gave them some clues +about what might be going on. + +Particularly the second +class was followed up + +by Eddy Rubins's +lab at Berkeley. + +And they tested 167 extremely +conserved sequences. + +So some of them were these +ultraconserved elements. + +And some of them were +just highly conserved, + +but not quite 100% conserved. + +And they had an assay +where they have a reporter. + +It's a lacZ with a-- you +take a minimal promoter, fuse + +in to lacZ, and then +you take your element + +of interest and +fuse it upstream. + +And then you do staining +of whole mount embryos. + +And you say what pattern +of gene expression + +does this element +drive, or does it + +drive a pattern of +gene expression? + +And so 45% of the time it +drove a particular pattern + +of gene expression. + +So it functioned as an enhancer. + +And these are the types +of patterns that they saw. + +So they saw often +forebrain, sometimes + +midbrain, neural +tube, lim, et cetera. + +So many of these +things are enhancers + +that drive particular +developmental patterns of gene + +expression. + +So that out to be actually-- +that was a pretty good way + +to identify +developmental enhancers. + +So they wondered, is +there anything special + +about these ultraconserved +regions, these 100% + +identical regions, versus +others that are 95% identical. + +And so they tested +a bunch of each. + +And they found absolutely +no difference there. + +They drive similar +types of expression. + +And you can even find +individual instances of them + +that drive pretty much exactly +the same pattern of expression. + +So this whole 100% +identical thing + +was just a purely-- it +was purely arbitrary. + +But still, it's useful. + +These things are among the +most interesting enhancers + +that have been identified. + +So what about the-- oh yeah, +so where did they come from? + +OK, so this is totally +from left field. + +Bejerano was looking at some of +these ultraconserved elements, + +probably just blasting them +against different genomes + +as they came out, and noticed +something very, very strange. + +And that was there +had recently been + +some sequencing from coelacanth. + +So for those of you who +aren't fish experts, + +this is a lobed fin fish, +where they found fossils + +from dating back to +400 million years. + +And they noticed that these +fossils-- the morphology never + +changed. + +From 400 million, 300 million +years, you could see this fish. + +It was exactly like this. + +And it has lobed fins. + +That was why they're +interested in it. + +Because the fins-- they +have a round structure. + +They look almost like +limbs, like maybe this guy + +could have evolved into +something that would eventually + +live on land. + +Anyway, but they +thought it was extinct. + +And then somebody caught one. + +In the '70s, in the West Indian +Ocean, from deep water fishing, + +they pulled one up, +and it looked exactly + +like these fossils from +400 million years before. + +And so then of course +somebody took some DNA + +and did some sequencing. + +And what Bejerano noticed is +that this one megabase or so + +coelacanth sequence had a +very common repeat in it that + +was around 500 bases or so, +that looked like a SINE element. + +SINE elements-- short, +interspersed nuclear element, + +like Alus, if you're +familiar with those, so + +some sort of repetitive element. + +And this repetitive +element was very + +similar to these ultraconserved +enhancers in mammals. + +So something that +we normally think + +of as the least +conserved of all, + +like a repetitive element +that inserts itself randomly + +in the genome, had become-- +some of these elements + +had become among the +most conserved sequences + +later in evolution. + +So how does that make +any sense at all? + +Anyone have a theory on that? + +I can tell you how +they interpreted it. + +So their theory-- here's some +text from their-- anyway, + +you can look at the paper +for the details here. + +But their theory is basically +that once you have a repetitive + +element-- initially it's +a parasitic element, + +inserts itself +randomly in the genome, + +doesn't actually do anything. + +But once you have hundreds +of them, by chance + +there will be perhaps +a set of genes + +that have this +element next to them, + +where you'd like to +control them coordinately. + +You'd like to turn all those +genes on or all those genes off + +in a particular circumstance-- +a stress response, + +during development, +something like that. + +And so then it's relatively +easy to evolve a transcription + +factor, for example, +that will bind + +to some sequence +in that element. + +And then it'll turn +on all those genes. + +Of course, it'll turn +out all the genes + +that have the +elements near them. + +So it'll probably turn +on some extra genes + +that you don't want. + +But you can then-- selection +will then tune these elements. + +It gives you a quick way of +generating a large-scale gene + +expression response. + +Because you've got so many +of these things scattered + +across the genome. + +And so this-- that's as good +as an explanation as we have, + +I would say, for what +is going on here. + +And there's been some +theories about this. + +And they point out +that actually something + +like 50% of our genome actually +comes from transposons, + +if you go back far enough. + +Some are recent, +some are ancient. + +And that maybe a lot of the +regulatory elements-- not just + +these ultraconserved +enhancers, but others-- + +may have evolved in this way. + +So basically you insert a bunch +of random junk throughout. + +And then the fact that +it's all identical, + +because it derived +from a common source, + +you use-- that fact +actually turns it + +into something that's useful, +a useful regulatory element. + +All right, just wanted +to throw that out. + +So what about the exonic +ultraconserved elements? + +So here's one. + +This is a 600 18 +nucleotide region + +that's 10% identical between +human, mouse, and rat. + +It's one of the +longest in the genome. + +And where is it? + +It's in a splicing +factor gene called SRp20. + +And it's actually not in +the protein coding part. + +It's in a essentially non-coding +exon of this splicing factor. + +So it's this yellow exon here. + +And what you'll notice is +there's this little red thing + +here. + +That's a stop codon. + +So this gene is +spliced-- produces + +two different isoforms. + +The full length is the +blue, when you just + +use all the blue exons. + +But when you include +this yellow exon, + +there's a premature +termination codon that you hit. + +So you don't make +full-length protein. + +Instead, that mRNA is +degraded in a pathway called + +nonsense mediated mRNA decay. + +So the purpose of +this exon appears + +to be so that this gene +can regulate expression + +of the protein at the +level of splicing. + +And others have shown that this +protein, the protein product, + +actually binds to +that exon and promotes + +the splicing of that exon. + +So it's basically a form of +negative auto regulation. + +The gene-- when the +protein gets high, + +it comes back and shifts the +splicing of its own transcripts + +to produce a non-functional +form of the message + +and reduce the +protein expression. + +So the theory is that this +helps to keep this splicing + +factor at a constant +level throughout time + +and between different +cells, which + +might be important for splicing. + +But that's only a theory. + +It could be something else. + +And it does not explain why you +need 600 nucleotides perfectly + +conserved in order to +have this function. + +So I think these exonic +ones are still fairly + +mysterious and +worth investigating. + +A couple examples +from microRNAs-- + +you probably it's just a +brief review on microRNAs. + +They are these small, +non-coding RNAs, + +typically 20 to 22 +nucleotides or so. + +They have a characteristic +RNA secondary structure + +in their precursor, +often called miRNAs. + +And they're produced from +primary transcripts typically, + +or introns, or +protein coding genes, + +which are then processed in +the nucleus of an enzyme called + +drosha into a hairpin +structure, like so. + +And then that is exported +to the cytoplasm, + +where it's further processed +by an enzyme called dicer + +to produce the mature microRNA, +which enters the risk complex, + +and which then pairs the +microRNA with mRNA targets, + +usually in the 3'-UTR. + +And that either inhibits +their translation + +or triggers the decay +of those messages. + +So microRNAs can do-- they +can be really important. + +Weird animation-- +but for example, + +this bantam microRNA in flies +inhibits a proapoptotic gene + +hid. + +If you delete bantam, +apoptosis goes crazy. + +And you can see this +is a normal fly. + +There's a little fly in there +with red eyes and so forth. + +In this guy there's +just a sack of mush. + +All the cells-- most of +the cells actually died. + +So microRNAs play +important roles + +in developmental pathways. + +And so we wanted to figure out +the rules for their targeting. + +And so this was an early +study from Ben Lewis, + +where he looked for conserved +instances of segments, + +short oligonucleotides, +that match perfectly + +to different parts +of the microRNA, + +using again these human, +mouse, rat alignments, + +which were what was +available at the time. + +And what he found was that if +you took the set of microRNAs + +which were known, and you +identified targets of these + +defined as 7-mers that +are perfectly conserved + +in 3'-UTRs of +mammalian messages, + +and then you looked at how many +you got and you compared that + +to the number of targets +of shuffled microRNA-- + +so where you take the +whole set of microRNAs, + +randomly permute their sequences +so you generate random stuff, + +look at how many conserve +targets they have-- + +that there was a significant +signal above background, + +in the sense of real +conserved targets, + +specifically only for the +5'-end of the microRNA. + +Especially, bases 2 to 8 of +the microRNA gave a signal. + +And no other positions +in the microRNA + +gave a significant +signal above background. + +And so that led to the inference +that the 5'-end of the microRNA + +is what matters, +specifically these bases. + +And then later, +alignments of actually + +paralogous microRNA +genes, shown here-- + +so these are +different let-7 genes. + +You can actually see that +the 5'-end of the microRNA, + +which the microRNA's +shown here in blue-- + +this is the fold-back. + +So you get conservation of the +microRNA and of the other arm + +of the fold-back, +which is complimentary. + +Little conservation of the loop, +but the most conserved part + +of the microRNA is the very +5'-end, consistent with that + +idea. + +Just one more example, +because it's so cool-- + +so this is the dscam +gene in drosophila. + +And this gene has four different +alternative spliced regions + +which are each spliced by +mutually exclusive splicing. + +So there are actually +12 copies of exon 4 + +and 48 different +copies of exon 6. + +And messages from this +gene only ever contain + +one of those particular exons. + +And so Brent Graveley asked +how does this gene get spliced + +in a mutually exclusive way? + +How do you only choose one of +those 48 different versions + +of exon 6? + +And so what he did was did some +sequencing from various fly + +and other insect species of +this locus, did some alignments. + +And he noticed that there was +this very conserved sequence + +just stream of exon 5, right +upstream of this cluster. + +And then, looking +more carefully, + +he saw that there is another +sequence, just immediately + +upstream of each of +the alternative exons, + +that was very similar +between all those exons, + +and also conserved +across the insects. + +And then he started +at these for a while, + +and recognized that +actually this sequence up + +at the 5'-end is-- its consensus +is perfectly complimentary + +to the sequence that's found +upstream of all of the other + +exons. + +And so what that +suggested, immediately, + +is that splicing +requires the pairing + +of this sequence +from exon 5 to one + +of those downstream sequences. + +And then you'll splice +to the next exons that's + +immediately downstream and +skip out all of the others. + +And that's been +subsequently confirmed, + +that that's the mechanism. + +So this just shows you +that to figure this out + +by molecular genetics would +have been extremely difficult. + +But sometimes +comparative genomics, + +when you ask the right question, +you get a really clear-- + +you can actually get mechanistic +insights from sequences. + +So that's it. + +And I'm actually passing +the baton over to David, + +who will be-- take +over next week. \ No newline at end of file diff --git a/1KRy9nUmzfM.txt b/1KRy9nUmzfM.txt new file mode 100644 index 0000000000000000000000000000000000000000..4ffb84e78be05ed524f72beada0e87b4b08d31c1 --- /dev/null +++ b/1KRy9nUmzfM.txt @@ -0,0 +1,8395 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a creative commons license + + align:start position:0% +a creative commons license + + + align:start position:0% +a creative commons license +your support will help mit + + align:start position:0% +your support will help mit + + + align:start position:0% +your support will help mit +opencourseware continue to offer high + + align:start position:0% +opencourseware continue to offer high + + + align:start position:0% +opencourseware continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of mit courses + + align:start position:0% +materials from hundreds of mit courses + + + align:start position:0% +materials from hundreds of mit courses +visit mit opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +i want to focus on the american city + + align:start position:0% +i want to focus on the american city + + + align:start position:0% +i want to focus on the american city +the contemporary american city + + align:start position:0% +the contemporary american city + + + align:start position:0% +the contemporary american city +and the enormous controversies + + align:start position:0% +and the enormous controversies + + + align:start position:0% +and the enormous controversies +which + + align:start position:0% +which + + + align:start position:0% +which +rage both in the profession + + align:start position:0% +rage both in the profession + + + align:start position:0% +rage both in the profession +and + + align:start position:0% +and + + + align:start position:0% +and +outside the profession as to + + align:start position:0% +outside the profession as to + + + align:start position:0% +outside the profession as to +what the condition of the american + + align:start position:0% +what the condition of the american + + + align:start position:0% +what the condition of the american +contemporary city is + + align:start position:0% +contemporary city is + + + align:start position:0% +contemporary city is +including everything from smart growth + + align:start position:0% +including everything from smart growth + + + align:start position:0% +including everything from smart growth +to + + align:start position:0% +to + + + align:start position:0% +to +new urbanism to + + align:start position:0% +new urbanism to + + + align:start position:0% +new urbanism to +the spray + + align:start position:0% +the spray + + + align:start position:0% +the spray +melville weapons sprayed city and so on + + align:start position:0% +melville weapons sprayed city and so on + + + align:start position:0% +melville weapons sprayed city and so on +what i'm going to do is i'm going to + + align:start position:0% +what i'm going to do is i'm going to + + + align:start position:0% +what i'm going to do is i'm going to +give you a number of inputs + + align:start position:0% +give you a number of inputs + + + align:start position:0% +give you a number of inputs +you some of them + + align:start position:0% +you some of them + + + align:start position:0% +you some of them +you will disagree with completely some + + align:start position:0% +you will disagree with completely some + + + align:start position:0% +you will disagree with completely some +of them you will agree with depending on + + align:start position:0% +of them you will agree with depending on + + + align:start position:0% +of them you will agree with depending on +your position + + align:start position:0% + + + + align:start position:0% + +i'd like you to + + align:start position:0% +i'd like you to + + + align:start position:0% +i'd like you to +listen to these + + align:start position:0% +listen to these + + + align:start position:0% +listen to these +comments if you want to + + align:start position:0% +comments if you want to + + + align:start position:0% +comments if you want to +but + + align:start position:0% +but + + + align:start position:0% +but +i will continue this on thursday + + align:start position:0% +i will continue this on thursday + + + align:start position:0% +i will continue this on thursday +first focusing a little more on + + align:start position:0% +first focusing a little more on + + + align:start position:0% +first focusing a little more on +uh + + align:start position:0% +uh + + + align:start position:0% +uh +decentralization technologies and + + align:start position:0% +decentralization technologies and + + + align:start position:0% +decentralization technologies and +climate change + + align:start position:0% +climate change + + + align:start position:0% +climate change +i want to switch to another + + align:start position:0% +i want to switch to another + + + align:start position:0% +i want to switch to another +complicated project + + align:start position:0% +complicated project + + + align:start position:0% +complicated project +that is the contemporary american city + + align:start position:0% + + + + align:start position:0% + +it is + + align:start position:0% + + + + align:start position:0% + +again a + + align:start position:0% +again a + + + align:start position:0% +again a +project which about which there's very + + align:start position:0% +project which about which there's very + + + align:start position:0% +project which about which there's very +little + + align:start position:0% +little + + + align:start position:0% +little +agreement except by cultural groups + + align:start position:0% +agreement except by cultural groups + + + align:start position:0% +agreement except by cultural groups +who have + + align:start position:0% +who have + + + align:start position:0% +who have +vested interests in believing that one + + align:start position:0% +vested interests in believing that one + + + align:start position:0% +vested interests in believing that one +form is superior to the other + + align:start position:0% +form is superior to the other + + + align:start position:0% +form is superior to the other +cities have always expanded when they + + align:start position:0% +cities have always expanded when they + + + align:start position:0% +cities have always expanded when they +could + + align:start position:0% +could + + + align:start position:0% +could +horizontal land is cheap to build on + + align:start position:0% +horizontal land is cheap to build on + + + align:start position:0% +horizontal land is cheap to build on +provided you can get there provided you + + align:start position:0% +provided you can get there provided you + + + align:start position:0% +provided you can get there provided you +don't have obstacles like defense + + align:start position:0% +don't have obstacles like defense + + + align:start position:0% +don't have obstacles like defense +fortresses or topography + + align:start position:0% +fortresses or topography + + + align:start position:0% +fortresses or topography +or anything else + + align:start position:0% + + + + align:start position:0% + +assisi was built on the slope of a hill + + align:start position:0% +assisi was built on the slope of a hill + + + align:start position:0% +assisi was built on the slope of a hill +in order that the + + align:start position:0% +in order that the + + + align:start position:0% +in order that the +the valley land + + align:start position:0% +the valley land + + + align:start position:0% +the valley land +could be used for agriculture + + align:start position:0% +could be used for agriculture + + + align:start position:0% +could be used for agriculture +it was a very smart move it also + + align:start position:0% +it was a very smart move it also + + + align:start position:0% +it was a very smart move it also +provided better climate our high up in + + align:start position:0% +provided better climate our high up in + + + align:start position:0% +provided better climate our high up in +the valley and also provided protection + + align:start position:0% +the valley and also provided protection + + + align:start position:0% +the valley and also provided protection +if necessary there was water on the city + + align:start position:0% +if necessary there was water on the city + + + align:start position:0% +if necessary there was water on the city +these are all logical decisions + + align:start position:0% + + + + align:start position:0% + +the american city was relatively + + align:start position:0% +the american city was relatively + + + align:start position:0% +the american city was relatively +contained + + align:start position:0% + + + + align:start position:0% + +until + + align:start position:0% +until + + + align:start position:0% +until +relatively recent times i'm just going + + align:start position:0% +relatively recent times i'm just going + + + align:start position:0% +relatively recent times i'm just going +to go through + + align:start position:0% +to go through + + + align:start position:0% +to go through +give you a sketch of the + + align:start position:0% +give you a sketch of the + + + align:start position:0% +give you a sketch of the +history of the american city + + align:start position:0% + + + + align:start position:0% + +cities have always expanded horizontally + + align:start position:0% +cities have always expanded horizontally + + + align:start position:0% +cities have always expanded horizontally +and is curved by wars natural barriers + + align:start position:0% +and is curved by wars natural barriers + + + align:start position:0% +and is curved by wars natural barriers +or the inability to communicate over + + align:start position:0% +or the inability to communicate over + + + align:start position:0% +or the inability to communicate over +distance + + align:start position:0% +distance + + + align:start position:0% +distance +policies such as green belts or the + + align:start position:0% +policies such as green belts or the + + + align:start position:0% +policies such as green belts or the +exclusion of immigrants + + align:start position:0% + + + + align:start position:0% + +the 16th and 17th century + + align:start position:0% +the 16th and 17th century + + + align:start position:0% +the 16th and 17th century +attempts to restrain the growth of + + align:start position:0% +attempts to restrain the growth of + + + align:start position:0% +attempts to restrain the growth of +london to exclude include the poor + + align:start position:0% +london to exclude include the poor + + + align:start position:0% +london to exclude include the poor +or the apartheid restrictions on black + + align:start position:0% +or the apartheid restrictions on black + + + align:start position:0% +or the apartheid restrictions on black +immigration in south africa have not + + align:start position:0% +immigration in south africa have not + + + align:start position:0% +immigration in south africa have not +been able to maintain themselves over + + align:start position:0% +been able to maintain themselves over + + + align:start position:0% +been able to maintain themselves over +time + + align:start position:0% + + + + align:start position:0% + +recent urban policies included either + + align:start position:0% +recent urban policies included either + + + align:start position:0% +recent urban policies included either +allowing low-density suburban expansion + + align:start position:0% +allowing low-density suburban expansion + + + align:start position:0% +allowing low-density suburban expansion +building dense public housing on the + + align:start position:0% +building dense public housing on the + + + align:start position:0% +building dense public housing on the +periphery establishing new towns or + + align:start position:0% +periphery establishing new towns or + + + align:start position:0% +periphery establishing new towns or +allowing poor immigrants to squat in + + align:start position:0% +allowing poor immigrants to squat in + + + align:start position:0% +allowing poor immigrants to squat in +minimally controlled settlements + + align:start position:0% +minimally controlled settlements + + + align:start position:0% +minimally controlled settlements +american city was chosen the first of + + align:start position:0% +american city was chosen the first of + + + align:start position:0% +american city was chosen the first of +these models + + align:start position:0% +these models + + + align:start position:0% +these models +the suburbs in the early years of the + + align:start position:0% +the suburbs in the early years of the + + + align:start position:0% +the suburbs in the early years of the +20th century were made up of large lots + + align:start position:0% +20th century were made up of large lots + + + align:start position:0% +20th century were made up of large lots +and made possible by the invention of + + align:start position:0% +and made possible by the invention of + + + align:start position:0% +and made possible by the invention of +the telephone + + align:start position:0% +the telephone + + + align:start position:0% +the telephone +in pre + + align:start position:0% +in pre + + + align:start position:0% +in pre +and pre-automobile + + align:start position:0% +and pre-automobile + + + align:start position:0% +and pre-automobile +street cars + + align:start position:0% + + + + align:start position:0% + +the telephone + + align:start position:0% +the telephone + + + align:start position:0% +the telephone +the social history of the television is + + align:start position:0% +the social history of the television is + + + align:start position:0% +the social history of the television is +a book that you should read + + align:start position:0% +a book that you should read + + + align:start position:0% +a book that you should read +i'll talk about it more + + align:start position:0% +i'll talk about it more + + + align:start position:0% +i'll talk about it more +on thursday's class + + align:start position:0% + + + + align:start position:0% + +but the telephone was introduced largely + + align:start position:0% +but the telephone was introduced largely + + + align:start position:0% +but the telephone was introduced largely +for rural populations + + align:start position:0% +for rural populations + + + align:start position:0% +for rural populations +to feel less + + align:start position:0% +to feel less + + + align:start position:0% +to feel less +distant + + align:start position:0% +distant + + + align:start position:0% +distant +from the rest of the world + + align:start position:0% + + + + align:start position:0% + +before world war ii less than half the + + align:start position:0% +before world war ii less than half the + + + align:start position:0% +before world war ii less than half the +nation + + align:start position:0% +nation + + + align:start position:0% +nation +owned their homes in less than half the + + align:start position:0% +owned their homes in less than half the + + + align:start position:0% +owned their homes in less than half the +housing stock was in single family homes + + align:start position:0% +housing stock was in single family homes + + + align:start position:0% +housing stock was in single family homes +after the war the percentage of families + + align:start position:0% +after the war the percentage of families + + + align:start position:0% +after the war the percentage of families +earning their + + align:start position:0% +earning their + + + align:start position:0% +earning their +owning their own homes jumped from + + align:start position:0% +owning their own homes jumped from + + + align:start position:0% +owning their own homes jumped from +nearly 40 percent in 1940 + + align:start position:0% +nearly 40 percent in 1940 + + + align:start position:0% +nearly 40 percent in 1940 +to 60 percent in 1960 due to a number of + + align:start position:0% +to 60 percent in 1960 due to a number of + + + align:start position:0% +to 60 percent in 1960 due to a number of +things higher incomes + + align:start position:0% +things higher incomes + + + align:start position:0% +things higher incomes +the federal highway program + + align:start position:0% +the federal highway program + + + align:start position:0% +the federal highway program +incentives for home ownership is a + + align:start position:0% +incentives for home ownership is a + + + align:start position:0% +incentives for home ownership is a +stabilizing social force + + align:start position:0% +stabilizing social force + + + align:start position:0% +stabilizing social force +federal housing association veterans + + align:start position:0% +federal housing association veterans + + + align:start position:0% +federal housing association veterans +association financing + + align:start position:0% +association financing + + + align:start position:0% +association financing +and other factors + + align:start position:0% + + + + align:start position:0% + +it's this combination of factors which + + align:start position:0% +it's this combination of factors which + + + align:start position:0% +it's this combination of factors which +created and still create suburbia + + align:start position:0% +created and still create suburbia + + + align:start position:0% +created and still create suburbia +it's not due to technology + + align:start position:0% + + + + align:start position:0% + +i'll give you a piece that i wrote + + align:start position:0% +i'll give you a piece that i wrote + + + align:start position:0% +i'll give you a piece that i wrote +attacking + + align:start position:0% +attacking + + + align:start position:0% +attacking +my neil castells + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% +for + + + align:start position:0% +for +for some of the stuff that he was + + align:start position:0% +for some of the stuff that he was + + + align:start position:0% +for some of the stuff that he was +advocating + + align:start position:0% +advocating + + + align:start position:0% +advocating +um + + align:start position:0% + + + + align:start position:0% + +what is the cell phone + + align:start position:0% +what is the cell phone + + + align:start position:0% +what is the cell phone +done to the use of public space + + align:start position:0% + + + + align:start position:0% + +bill mitchell unfortunately deceased now + + align:start position:0% +bill mitchell unfortunately deceased now + + + align:start position:0% +bill mitchell unfortunately deceased now +was senior + + align:start position:0% +was senior + + + align:start position:0% +was senior +and wrote + + align:start position:0% +and wrote + + + align:start position:0% +and wrote +books about + + align:start position:0% + + + + align:start position:0% + +virtual technology affecting space + + align:start position:0% +virtual technology affecting space + + + align:start position:0% +virtual technology affecting space +was wrong + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +what has happened is that people can + + align:start position:0% +what has happened is that people can + + + align:start position:0% +what has happened is that people can +communicate with each other + + align:start position:0% +communicate with each other + + + align:start position:0% +communicate with each other +much better and much faster and much + + align:start position:0% +much better and much faster and much + + + align:start position:0% +much better and much faster and much +more frequently but it doesn't matter + + align:start position:0% +more frequently but it doesn't matter + + + align:start position:0% +more frequently but it doesn't matter +where they are + + align:start position:0% +where they are + + + align:start position:0% +where they are +you don't have to go into the piazza to + + align:start position:0% +you don't have to go into the piazza to + + + align:start position:0% +you don't have to go into the piazza to +call somebody + + align:start position:0% + + + + align:start position:0% + +it is + + align:start position:0% +it is + + + align:start position:0% +it is +it is a form of ubiquity + + align:start position:0% +it is a form of ubiquity + + + align:start position:0% +it is a form of ubiquity +rather than a form of concentration but + + align:start position:0% +rather than a form of concentration but + + + align:start position:0% +rather than a form of concentration but +there are some activities + + align:start position:0% +there are some activities + + + align:start position:0% +there are some activities +that + + align:start position:0% +that + + + align:start position:0% +that +before that technology + + align:start position:0% + + + + align:start position:0% + +there were activities that were + + align:start position:0% +there were activities that were + + + align:start position:0% +there were activities that were +heavily linked to a place they had to be + + align:start position:0% +heavily linked to a place they had to be + + + align:start position:0% +heavily linked to a place they had to be +done there + + align:start position:0% +done there + + + align:start position:0% +done there +and and now you're not forced to do so + + align:start position:0% +and and now you're not forced to do so + + + align:start position:0% +and and now you're not forced to do so +exactly you + + align:start position:0% +exactly you + + + align:start position:0% +exactly you +you agreeing with me + + align:start position:0% +you agreeing with me + + + align:start position:0% +you agreeing with me +i asked you what is what the cell phone + + align:start position:0% +i asked you what is what the cell phone + + + align:start position:0% +i asked you what is what the cell phone +has contributed to the increase in use + + align:start position:0% +has contributed to the increase in use + + + align:start position:0% +has contributed to the increase in use +of public space + + align:start position:0% +of public space + + + align:start position:0% +of public space +in what form i don't understand the + + align:start position:0% +in what form i don't understand the + + + align:start position:0% +in what form i don't understand the +answer + + align:start position:0% + + + + align:start position:0% + +i can call you from here or i can call + + align:start position:0% +i can call you from here or i can call + + + align:start position:0% +i can call you from here or i can call +you in an office down there and say + + align:start position:0% +you in an office down there and say + + + align:start position:0% +you in an office down there and say +let's meet it let's meet for drink in + + align:start position:0% +let's meet it let's meet for drink in + + + align:start position:0% +let's meet it let's meet for drink in +the ayat hotel at eight o'clock tonight + + align:start position:0% + + + + align:start position:0% + +what's different + + align:start position:0% +what's different + + + align:start position:0% +what's different +only the speed is different from me + + align:start position:0% +only the speed is different from me + + + align:start position:0% +only the speed is different from me +telephoning you in the morning or + + align:start position:0% +telephoning you in the morning or + + + align:start position:0% +telephoning you in the morning or +sending you a letter or + + align:start position:0% +sending you a letter or + + + align:start position:0% +sending you a letter or +sending you a message by pigeon + + align:start position:0% +sending you a message by pigeon + + + align:start position:0% +sending you a message by pigeon +whatever form of communication we used + + align:start position:0% +whatever form of communication we used + + + align:start position:0% +whatever form of communication we used +prior to cell phones + + align:start position:0% +prior to cell phones + + + align:start position:0% +prior to cell phones +but + + align:start position:0% +but + + + align:start position:0% +but +the density of + + align:start position:0% +the density of + + + align:start position:0% +the density of +rockefeller center doesn't depend on the + + align:start position:0% +rockefeller center doesn't depend on the + + + align:start position:0% +rockefeller center doesn't depend on the +advent of the cell phone + + align:start position:0% +advent of the cell phone + + + align:start position:0% +advent of the cell phone +the cell phone is more likely to be + + align:start position:0% +the cell phone is more likely to be + + + align:start position:0% +the cell phone is more likely to be +you'll be ubiquitous distributor + + align:start position:0% +you'll be ubiquitous distributor + + + align:start position:0% +you'll be ubiquitous distributor +of your space use + + align:start position:0% +of your space use + + + align:start position:0% +of your space use +than a concentrator + + align:start position:0% + + + + align:start position:0% + +the same argument goes for computation + + align:start position:0% + + + + align:start position:0% + +the number of people in the united + + align:start position:0% +the number of people in the united + + + align:start position:0% +the number of people in the united +states who work at home + + align:start position:0% +states who work at home + + + align:start position:0% +states who work at home +is + + align:start position:0% +is + + + align:start position:0% +is +measured in a number of different ways + + align:start position:0% +measured in a number of different ways + + + align:start position:0% +measured in a number of different ways +if you have a cupboard and you have a + + align:start position:0% +if you have a cupboard and you have a + + + align:start position:0% +if you have a cupboard and you have a +computer in your cupboard you work at + + align:start position:0% +computer in your cupboard you work at + + + align:start position:0% +computer in your cupboard you work at +home + + align:start position:0% +home + + + align:start position:0% +home +whereas in fact all you do is you + + align:start position:0% +whereas in fact all you do is you + + + align:start position:0% +whereas in fact all you do is you +most of the time play + + align:start position:0% +most of the time play + + + align:start position:0% +most of the time play +games on your computer and don't do any + + align:start position:0% +games on your computer and don't do any + + + align:start position:0% +games on your computer and don't do any +work + + align:start position:0% +work + + + align:start position:0% +work +at all but you can't you measured as + + align:start position:0% +at all but you can't you measured as + + + align:start position:0% +at all but you can't you measured as +working at home + + align:start position:0% + + + + align:start position:0% + +the number of people working at home is + + align:start position:0% +the number of people working at home is + + + align:start position:0% +the number of people working at home is +a + + align:start position:0% +a + + + align:start position:0% +a +uneven commodity i was in a conference + + align:start position:0% +uneven commodity i was in a conference + + + align:start position:0% +uneven commodity i was in a conference +in texas + + align:start position:0% +in texas + + + align:start position:0% +in texas +where they were discussing this + + align:start position:0% +where they were discussing this + + + align:start position:0% +where they were discussing this +phenomenon and the real estate people + + align:start position:0% +phenomenon and the real estate people + + + align:start position:0% +phenomenon and the real estate people +were advocating all kinds of things + + align:start position:0% +were advocating all kinds of things + + + align:start position:0% +were advocating all kinds of things +um + + align:start position:0% + + + + align:start position:0% + +let me just finish this because i forgot + + align:start position:0% +let me just finish this because i forgot + + + align:start position:0% +let me just finish this because i forgot +to go through the reading list with you + + align:start position:0% +to go through the reading list with you + + + align:start position:0% +to go through the reading list with you +at least the + + align:start position:0% +at least the + + + align:start position:0% +at least the +handout with you + + align:start position:0% + + + + align:start position:0% + +livertown built 150 standard 25 foot by + + align:start position:0% +livertown built 150 standard 25 foot by + + + align:start position:0% +livertown built 150 standard 25 foot by +30 foot cottages a week each costing + + align:start position:0% +30 foot cottages a week each costing + + + align:start position:0% +30 foot cottages a week each costing +seven thousand nine hundred dollars + + align:start position:0% +seven thousand nine hundred dollars + + + align:start position:0% +seven thousand nine hundred dollars +requiring with a government subsidised + + align:start position:0% +requiring with a government subsidised + + + align:start position:0% +requiring with a government subsidised +loan a monthly of payment of 58 dollars + + align:start position:0% +loan a monthly of payment of 58 dollars + + + align:start position:0% +loan a monthly of payment of 58 dollars +for 25 years + + align:start position:0% + + + + align:start position:0% + +these + + align:start position:0% +these + + + align:start position:0% +these +these suburbs attracted the planned + + align:start position:0% +these suburbs attracted the planned + + + align:start position:0% +these suburbs attracted the planned +shopping centre an architectural unified + + align:start position:0% +shopping centre an architectural unified + + + align:start position:0% +shopping centre an architectural unified +development with large amounts of off + + align:start position:0% +development with large amounts of off + + + align:start position:0% +development with large amounts of off +street parking + + align:start position:0% + + + + align:start position:0% + +suburban growth has broken the link + + align:start position:0% +suburban growth has broken the link + + + align:start position:0% +suburban growth has broken the link +between city centre and its outskirts + + align:start position:0% +between city centre and its outskirts + + + align:start position:0% +between city centre and its outskirts +in 1975 + + align:start position:0% +in 1975 + + + align:start position:0% +in 1975 +people who commuted from home to work in + + align:start position:0% +people who commuted from home to work in + + + align:start position:0% +people who commuted from home to work in +the suburbs outnumbered people who + + align:start position:0% +the suburbs outnumbered people who + + + align:start position:0% +the suburbs outnumbered people who +commuted to the century + + align:start position:0% +commuted to the century + + + align:start position:0% +commuted to the century +central city were almost two to one + + align:start position:0% + + + + align:start position:0% + +i wonder if i should take a break + + align:start position:0% + + + + align:start position:0% + +outlying suburbs + + align:start position:0% +outlying suburbs + + + align:start position:0% +outlying suburbs +now called urban villages or eight + + align:start position:0% +now called urban villages or eight + + + align:start position:0% +now called urban villages or eight +cities are more diverse in land use have + + align:start position:0% +cities are more diverse in land use have + + + align:start position:0% +cities are more diverse in land use have +larger houses + + align:start position:0% +larger houses + + + align:start position:0% +larger houses +in 2000 the american house averaged over + + align:start position:0% +in 2000 the american house averaged over + + + align:start position:0% +in 2000 the american house averaged over +2 000 square feet twice as large as it + + align:start position:0% +2 000 square feet twice as large as it + + + align:start position:0% +2 000 square feet twice as large as it +was in 1970 + + align:start position:0% +was in 1970 + + + align:start position:0% +was in 1970 +and they have become different cultural + + align:start position:0% +and they have become different cultural + + + align:start position:0% +and they have become different cultural +enterprises than the post-world war ii + + align:start position:0% +enterprises than the post-world war ii + + + align:start position:0% +enterprises than the post-world war ii +suburbs + + align:start position:0% + + + + align:start position:0% + +i'll go into that a little while later + + align:start position:0% + + + + align:start position:0% + +private automill traffic continues to + + align:start position:0% +private automill traffic continues to + + + align:start position:0% +private automill traffic continues to +increase + + align:start position:0% +increase + + + align:start position:0% +increase +from 1 + + align:start position:0% +from 1 + + + align:start position:0% +from 1 +to 1 billion miles in 1970 to 1.5 + + align:start position:0% +to 1 billion miles in 1970 to 1.5 + + + align:start position:0% +to 1 billion miles in 1970 to 1.5 +billion miles in 1987 + + align:start position:0% +billion miles in 1987 + + + align:start position:0% +billion miles in 1987 +and road space over the same time + + align:start position:0% +and road space over the same time + + + align:start position:0% +and road space over the same time +decreased from 61 yards per vehicle to + + align:start position:0% +decreased from 61 yards per vehicle to + + + align:start position:0% +decreased from 61 yards per vehicle to +only 31 + + align:start position:0% +only 31 + + + align:start position:0% +only 31 +to only 39 + + align:start position:0% +to only 39 + + + align:start position:0% +to only 39 +while new cars are cleaner the condition + + align:start position:0% +while new cars are cleaner the condition + + + align:start position:0% +while new cars are cleaner the condition +of the air is worse in part because of + + align:start position:0% +of the air is worse in part because of + + + align:start position:0% +of the air is worse in part because of +the increase in car use + + align:start position:0% +the increase in car use + + + align:start position:0% +the increase in car use +now these figures are not + + align:start position:0% +now these figures are not + + + align:start position:0% +now these figures are not +updated to 2000 + + align:start position:0% +updated to 2000 + + + align:start position:0% +updated to 2000 +laura i want you to + + align:start position:0% +laura i want you to + + + align:start position:0% +laura i want you to +tell me what the recent figures are + + align:start position:0% + + + + align:start position:0% + +you are only a you're any transportation + + align:start position:0% +you are only a you're any transportation + + + align:start position:0% +you are only a you're any transportation +consultant here + + align:start position:0% + + + + align:start position:0% + +these figures don't include for the + + align:start position:0% +these figures don't include for the + + + align:start position:0% +these figures don't include for the +increase in the purchase of smaller cars + + align:start position:0% +increase in the purchase of smaller cars + + + align:start position:0% +increase in the purchase of smaller cars +hybrid cars and so on + + align:start position:0% + + + + align:start position:0% + +but recent calculations of + + align:start position:0% +but recent calculations of + + + align:start position:0% +but recent calculations of +uh + + align:start position:0% +uh + + + align:start position:0% +uh +automobile distance traveled + + align:start position:0% +automobile distance traveled + + + align:start position:0% +automobile distance traveled +largely on social trips + + align:start position:0% +largely on social trips + + + align:start position:0% +largely on social trips +large not so much on journey to work + + align:start position:0% +large not so much on journey to work + + + align:start position:0% +large not so much on journey to work +trips because journey to work is not + + align:start position:0% +trips because journey to work is not + + + align:start position:0% +trips because journey to work is not +very + + align:start position:0% + + + + align:start position:0% + +easily served by transportation + + align:start position:0% +easily served by transportation + + + align:start position:0% +easily served by transportation +there's a + + align:start position:0% +there's a + + + align:start position:0% +there's a +diagram in what are the package i gave + + align:start position:0% +diagram in what are the package i gave + + + align:start position:0% +diagram in what are the package i gave +you by robert severow the author of + + align:start position:0% +you by robert severow the author of + + + align:start position:0% +you by robert severow the author of +transit metropolis + + align:start position:0% + + + + align:start position:0% + +when a city had this form + + align:start position:0% +when a city had 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later on the + + align:start position:0% +be it a streetcar server or later on the + + + align:start position:0% +be it a streetcar server or later on the +subway + + align:start position:0% +subway + + + align:start position:0% +subway +the line hall depends on + + align:start position:0% +the line hall depends on + + + align:start position:0% +the line hall depends on +accumulating people + + align:start position:0% + + + + align:start position:0% + +from either space + + align:start position:0% +from either space + + + align:start position:0% +from either space +in between the + + align:start position:0% +in between the + + + align:start position:0% +in between the +the various line order + + align:start position:0% +the various line order + + + align:start position:0% +the various line order +let me get along + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% + + + + align:start position:0% + +the problem once the generation of trips + + align:start position:0% +the problem once the generation of trips + + + align:start position:0% +the problem once the generation of trips +starts being + + align:start position:0% +starts being + + + align:start position:0% +starts being +this + + align:start position:0% + + + + align:start position:0% + +to work centers which now + + align:start position:0% +to work centers which now + + + align:start position:0% +to work centers which now +proliferate outside the center of the + + align:start position:0% +proliferate outside the center of the + + + align:start position:0% +proliferate outside the center of the +city + + align:start position:0% +city + + + align:start position:0% +city +and form a random pattern + + align:start position:0% + + + + align:start position:0% + +you get the problem of how to + + align:start position:0% +you get the problem of how to + + + align:start position:0% +you get the problem of how to +introduce public translation into the + + align:start position:0% +introduce public translation into the + + + align:start position:0% +introduce public translation into the +distributive system + + align:start position:0% +distributive system + + + align:start position:0% +distributive system +which is much more difficult than the + + align:start position:0% +which is much more difficult than the + + + align:start position:0% +which is much more difficult than the +lionwall system + + align:start position:0% +lionwall system + + + align:start position:0% +lionwall system +we did a project + + align:start position:0% +we did a project + + + align:start position:0% +we did a project +when i came to mit + + align:start position:0% + + + + align:start position:0% + +trying to + + align:start position:0% +trying to + + + align:start position:0% +trying to +use dual mode technology + + align:start position:0% +use dual mode technology + + + align:start position:0% +use dual mode technology +to have the same vehicle which operated + + align:start position:0% +to have the same vehicle which operated + + + align:start position:0% +to have the same vehicle which operated +on the line all leave the line all + + align:start position:0% +on the line all leave the line all + + + align:start position:0% +on the line all leave the line all +system + + align:start position:0% +system + + + align:start position:0% +system +operate on the distributor system + + align:start position:0% +operate on the distributor system + + + align:start position:0% +operate on the distributor system +and then join the line all system again + + align:start position:0% +and then join the line all system again + + + align:start position:0% +and then join the line all system again +it involved a small vehicle + + align:start position:0% + + + + align:start position:0% + +which had the capacity to run on the + + align:start position:0% +which had the capacity to run on the + + + align:start position:0% +which had the capacity to run on the +rail + + align:start position:0% +rail + + + align:start position:0% +rail +and also to leave the rail and run on + + align:start position:0% +and also to leave the rail and run on + + + align:start position:0% +and also to leave the rail and run on +the land + + align:start position:0% +the land + + + align:start position:0% +the land +the distributor system would be + + align:start position:0% +the distributor system would be + + + align:start position:0% +the distributor system would be +serviced by the telephone in other words + + align:start position:0% +serviced by the telephone in other words + + + align:start position:0% +serviced by the telephone in other words +you would call and say i want to go to + + align:start position:0% +you would call and say i want to go to + + + align:start position:0% +you would call and say i want to go to +downtown boston + + align:start position:0% +downtown boston + + + align:start position:0% +downtown boston +and it would say + + align:start position:0% +and it would say + + + align:start position:0% +and it would say +wait in 2.6 minutes time + + align:start position:0% +wait in 2.6 minutes time + + + align:start position:0% +wait in 2.6 minutes time +you'll be picked up + + align:start position:0% +you'll be picked up + + + align:start position:0% +you'll be picked up +and it will + + align:start position:0% +and it will + + + align:start position:0% +and it will +you'll be in boston in seven minutes + + align:start position:0% + + + + align:start position:0% + +this project to link the + + align:start position:0% +this project to link the + + + align:start position:0% +this project to link the +distributor and lionwall system to make + + align:start position:0% +distributor and lionwall system to make + + + align:start position:0% +distributor and lionwall system to make +one + + align:start position:0% +one + + + align:start position:0% +one +has hasn't been applied anywhere in the + + align:start position:0% +has 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and + + + align:start position:0% +can move much more speedily and +accurately + + align:start position:0% + + + + align:start position:0% + +i think after + + align:start position:0% +i think after + + + align:start position:0% +i think after +x number of years of the london + + align:start position:0% +x number of years of the london + + + align:start position:0% +x number of years of the london +congestion pricing system + + align:start position:0% +congestion pricing system + + + align:start position:0% +congestion pricing system +they've introduced something like 100 + + align:start position:0% +they've introduced something like 100 + + + align:start position:0% +they've introduced something like 100 +new buses + + align:start position:0% +new buses + + + align:start position:0% +new buses +running + + align:start position:0% +running + + + align:start position:0% +running +on time and + + align:start position:0% +on time and + + + align:start position:0% +on time and +with air conditioning and all kinds of + + align:start position:0% +with air conditioning and all kinds of + + + align:start position:0% +with air conditioning and all kinds of +conveniences + + align:start position:0% +conveniences + + + align:start position:0% +conveniences +thinking + + align:start position:0% +thinking + + + align:start position:0% +thinking +sixteen percent of carbon emissions have + + align:start position:0% +sixteen percent of carbon emissions have + + + align:start position:0% +sixteen percent of carbon emissions have +also been reduced as a result of + + align:start position:0% +also been reduced as a result of + + + align:start position:0% +also been reduced as a result of +condition pricing + + align:start position:0% +condition pricing + + + align:start position:0% +condition pricing +congestion pricing is one of the new + + align:start position:0% +congestion pricing is one of the new + + + align:start position:0% +congestion pricing is one of the new +artifacts of the large metropolitan area + + align:start position:0% +artifacts of the large metropolitan area + + + align:start position:0% +artifacts of the large metropolitan area +it hasn't been applied in + + align:start position:0% +it hasn't been applied in + + + align:start position:0% +it hasn't been applied in +new york because of + + align:start position:0% +new york because of + + + align:start position:0% +new york because of +the conflict between the city and the + + align:start position:0% +the conflict between the city and the + + + align:start position:0% +the conflict between the city and the +rural + + align:start position:0% +rural + + + align:start position:0% +rural +rest of the state a basic conflict in + + align:start position:0% +rest of the state a basic conflict in + + + align:start position:0% +rest of the state a basic conflict in +the united states system of government + + align:start position:0% +the united states system of government + + + align:start position:0% +the united states system of government +we still depend in the senate on votes + + align:start position:0% +we still depend in the senate on votes + + + align:start position:0% +we still depend in the senate on votes +of people in idaho + + align:start position:0% +of people in idaho + + + align:start position:0% +of people in idaho +whereas + + align:start position:0% +whereas + + + align:start position:0% +whereas +i was just thinking + + align:start position:0% + + + + align:start position:0% + +you know we're talking about cities and + + align:start position:0% +you know we're talking about cities and + + + align:start position:0% +you know we're talking about cities and +having problems + + align:start position:0% +having problems + + + align:start position:0% +having problems +how long have cities existed + + align:start position:0% +how long have cities existed + + + align:start position:0% +how long have cities existed +including the first settlement permanent + + align:start 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align:start position:0% +ten thousand years +it took two point six million years for + + align:start position:0% +it took two point six million years for + + + align:start position:0% +it took two point six million years for +human beings to develop a brain large + + align:start position:0% +human beings to develop a brain large + + + align:start position:0% +human beings to develop a brain large +enough to + + align:start position:0% +enough to + + + align:start position:0% +enough to +to think + + align:start position:0% + + + + align:start position:0% + +and we're talking about + + align:start position:0% +and we're talking about + + + align:start position:0% +and we're talking about +twelve thousand years which + + align:start position:0% + + + + align:start position:0% + +which was nothing in time + + align:start position:0% +which was nothing in time + + + align:start position:0% +which was nothing in time +and we're expecting perfect answers to + + align:start position:0% +and we're expecting perfect answers to + + + align:start position:0% +and we're expecting perfect answers to +communal settlements + + align:start position:0% + + + + align:start position:0% + +so relax + + align:start position:0% + + + + align:start position:0% + +we + + align:start position:0% +we + + + align:start position:0% +we +teach + + align:start position:0% +teach + + + align:start position:0% +teach +i say this because i'm an architect and + + align:start position:0% +i say this because i'm an architect and + + + align:start position:0% +i say this because i'm an architect and +have taught design studios endlessly + + align:start position:0% +have taught design studios endlessly + + + align:start position:0% +have taught design studios endlessly +we tend to idealize the world that we + + align:start position:0% +we tend to idealize the world that we + + + align:start position:0% +we tend to idealize the world that we +and smooth the world around + + align:start position:0% + + + + align:start position:0% + +i remember when i worked for on the + + align:start position:0% +i remember when i worked for on the + + + align:start position:0% +i remember when i worked for on the +image of the city's research book with + + align:start position:0% +image of the city's research book with + + + align:start position:0% +image of the city's research book with +kevin lynch + + align:start position:0% +kevin lynch + + + align:start position:0% +kevin lynch +okay jerry cappish + + align:start position:0% +okay jerry cappish + + + align:start position:0% +okay jerry cappish +he's comparative asked me to take a walk + + align:start position:0% +he's comparative asked me to take a walk + + + align:start position:0% +he's comparative asked me to take a walk +down washington street on a busy day and + + align:start position:0% +down washington street on a busy day and + + + align:start position:0% +down washington street on a busy day and +now just note all the things that i saw + + align:start position:0% + + + + align:start position:0% + +i made this tabulation of all the things + + align:start position:0% +i made this tabulation of all the things + + + align:start position:0% +i made this tabulation of all the things +that i saw + + align:start position:0% +that i saw + + + align:start position:0% +that i saw +where the sun was shining what noise + + align:start position:0% +where the sun was shining what noise + + + align:start position:0% +where the sun was shining what noise +there was what signs they were and so on + + align:start position:0% +there was what signs they were and so on + + + align:start position:0% +there was what signs they were and so on +and i came up and presented my work + + align:start position:0% +and i came up and presented my work + + + align:start position:0% +and i came up and presented my work +and said this is such an unbelievably + + align:start position:0% +and said this is such an unbelievably + + + align:start position:0% +and said this is such an unbelievably +confused + + align:start position:0% +confused + + + align:start position:0% +confused +washington street + + align:start position:0% +washington street + + + align:start position:0% +washington street +i don't know anybody makes sense to it + + align:start position:0% +i don't know anybody makes sense to it + + + align:start position:0% +i don't know anybody makes sense to it +because at that time all urban design + + align:start position:0% +because at that time all urban design + + + align:start position:0% +because at that time all urban design +was + + align:start position:0% +was + + + align:start position:0% +was +was victor gruen's work + + align:start position:0% +was victor gruen's work + + + align:start position:0% +was victor gruen's work +and how to + + align:start position:0% +and how to + + + align:start position:0% +and how to +use modernism to cleans up + + align:start position:0% +use modernism to cleans up + + + align:start position:0% +use modernism to cleans up +conflict + + align:start position:0% +conflict + + + align:start position:0% +conflict +shopping centers had unified signpost + + align:start position:0% +shopping centers had unified signpost + + + align:start position:0% +shopping centers had unified signpost +control + + align:start position:0% +control + + + align:start position:0% +control +and + + align:start position:0% +and + + + align:start position:0% +and +here i was trying to say the real world + + align:start position:0% +here i was trying to say the real world + + + align:start position:0% +here i was trying to say the real world +is infinitely complex and yet + + align:start position:0% +is infinitely complex and yet + + + align:start position:0% +is infinitely complex and yet +because we have 10 to the 12 neurons + + align:start position:0% +because we have 10 to the 12 neurons + + + align:start position:0% +because we have 10 to the 12 neurons +in our brain + + align:start position:0% +in our brain + + + align:start position:0% +in our brain +each connecting to 5000 other sites + + align:start position:0% +each connecting to 5000 other sites + + + align:start position:0% +each connecting to 5000 other sites +we have the electricity + + align:start position:0% +we have the electricity + + + align:start position:0% +we have the electricity +electronic system which can manage such + + align:start position:0% +electronic system which can manage such + + + align:start position:0% +electronic system which can manage such +complexity + + align:start position:0% + + + + align:start position:0% + +i think it's a message + + align:start position:0% +i think it's a message + + + align:start position:0% +i think it's a message +worth remembering + + align:start position:0% + + + + align:start position:0% + +maybe + + align:start position:0% + + + + align:start position:0% + +it'll become much clearer + + align:start position:0% +it'll become much clearer + + + align:start position:0% +it'll become much clearer +but i think working as you do as an + + align:start position:0% +but i think working as you do as an + + + align:start position:0% +but i think working as you do as an +urban designer in the midst of a + + align:start position:0% +urban designer in the midst of a + + + align:start position:0% +urban designer in the midst of a +dialectic of + + align:start position:0% +dialectic of + + + align:start position:0% +dialectic of +opposites + + align:start position:0% +opposites + + + align:start position:0% +opposites +is an intelligent place to be + + align:start position:0% +is an intelligent place to be + + + align:start position:0% +is an intelligent place to be +i don't know + + align:start position:0% +i don't know + + + align:start position:0% +i don't know +the resolution + + align:start position:0% +the resolution + + + align:start position:0% +the resolution +in the world's global economy between + + align:start position:0% +in the world's global economy between + + + align:start position:0% +in the world's global economy between +the idea that what is yours is yours + + align:start position:0% +the idea that what is yours is yours + + + align:start position:0% +the idea that what is yours is yours +and what is yours belongs partly to a + + align:start position:0% +and what is yours belongs partly to a + + + align:start position:0% +and what is yours belongs partly to a +group of people + + align:start position:0% +group of people + + + align:start position:0% +group of people +as andrew george would have liked to + + align:start position:0% +as andrew george would have liked to + + + align:start position:0% +as andrew george would have liked to +have argued + + align:start position:0% +have argued + + + align:start position:0% +have argued +between socialism in my in my life the + + align:start position:0% +between socialism in my in my life the + + + align:start position:0% +between socialism in my in my life the +debate between socialism and capitalism + + align:start position:0% +debate between socialism and capitalism + + + align:start position:0% +debate between socialism and capitalism +is not abated they've been modifications + + align:start position:0% +is not abated they've been modifications + + + align:start position:0% +is not abated they've been modifications +and conjunctions and attempts to develop + + align:start position:0% +and conjunctions and attempts to develop + + + align:start position:0% +and conjunctions and attempts to develop +alternative models + + align:start position:0% +alternative models + + + align:start position:0% +alternative models +but essentially + + align:start position:0% +but essentially + + + align:start position:0% +but essentially +most of you live in the in the + + align:start position:0% +most of you live in the in the + + + align:start position:0% +most of you live in the in the +capitalist world + + align:start position:0% +capitalist world + + + align:start position:0% +capitalist world +you will be struck between + + align:start position:0% + + + + align:start position:0% + +the premise + + align:start position:0% +the premise + + + align:start position:0% +the premise +that you live in a liberal state + + align:start position:0% +that you live in a liberal state + + + align:start position:0% +that you live in a liberal state +you allowed in the liberal state to + + align:start position:0% +you allowed in the liberal state to + + + align:start position:0% +you allowed in the liberal state to +choose what system of communication you + + align:start position:0% +choose what system of communication you + + + align:start position:0% +choose what system of communication you +wish + + align:start position:0% +wish + + + align:start position:0% +wish +in this case you will choose an + + align:start position:0% +in this case you will choose an + + + align:start position:0% +in this case you will choose an +automobile + + align:start position:0% +automobile + + + align:start position:0% +automobile +there will be no taxation on your + + align:start position:0% +there will be no taxation on your + + + align:start position:0% +there will be no taxation on your +automobile use of streets + + align:start position:0% +automobile use of streets + + + align:start position:0% +automobile use of streets +except what you pay for gas + + align:start position:0% +except what you pay for gas + + + align:start position:0% +except what you pay for gas +and gasoline taxation + + align:start position:0% +and gasoline taxation + + + align:start position:0% +and gasoline taxation +for the use of the roads is + + align:start position:0% +for the use of the roads is + + + align:start position:0% +for the use of the roads is +minimal + + align:start position:0% + + + + align:start position:0% + +so what do you do + + align:start position:0% + + + + align:start position:0% + +i'm just arguing you've got a + + align:start 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align:start position:0% +downtown +and the suburban world + + align:start position:0% +and the suburban world + + + align:start position:0% +and the suburban world +american downtown is now increasing in + + align:start position:0% +american downtown is now increasing in + + + align:start position:0% +american downtown is now increasing in +value + + align:start position:0% +value + + + align:start position:0% +value +and attracting more and more people + + align:start position:0% +and attracting more and more people + + + align:start position:0% +and attracting more and more people +if only people + + align:start position:0% +if only people + + + align:start position:0% +if only people +only 17 + + align:start position:0% +only 17 + + + align:start position:0% +only 17 +of people in american downtown are under + + align:start position:0% +of people in american downtown are under + + + align:start position:0% +of people in american downtown are under +20. + + align:start position:0% + + + + align:start position:0% + +so the world is still one in which most + + align:start position:0% +so the world is still one in which most + + + align:start position:0% +so the world is still one in which most +people in the american city + + align:start position:0% +people in the american city + + + align:start position:0% +people in the american city +seeking to educate their children will + + align:start position:0% +seeking to educate their children will + + + align:start position:0% +seeking to educate their children will +move to suburbia + + align:start position:0% +move to suburbia + + + align:start position:0% +move to suburbia +often in the direction of places where + + align:start position:0% +often in the direction of places where + + + align:start position:0% +often in the direction of places where +suburban because of + + align:start position:0% +suburban because of + + + align:start position:0% +suburban because of +residential real estate taxes + + align:start 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+ + + align:start position:0% +so if you live in the back bay in boston +you don't rely on the state to educate + + align:start position:0% +you don't rely on the state to educate + + + align:start position:0% +you don't rely on the state to educate +your children + + align:start position:0% +your children + + + align:start position:0% +your children +you pay enormous subsidies + + align:start position:0% +you pay enormous subsidies + + + align:start position:0% +you pay enormous subsidies +to educate your children + + align:start position:0% + + + + align:start position:0% + +it's all crazy + + align:start position:0% +it's all crazy + + + align:start position:0% +it's all crazy +it means that the incentives for living + + align:start position:0% +it means that the incentives for living + + + align:start position:0% +it means that the incentives for living +in suburbia + + align:start position:0% +in suburbia + + + align:start position:0% +in suburbia +are established very quickly + + align:start position:0% +are established very quickly + + + align:start position:0% +are established very quickly +and + + align:start position:0% + + + + align:start position:0% + +very difficult to dislodge in a free + + align:start position:0% +very difficult to dislodge in a free + + + align:start position:0% +very difficult to dislodge in a free +society + + align:start position:0% +society + + + align:start position:0% +society +i don't foresee + + align:start position:0% +i don't foresee + + + align:start position:0% +i don't foresee +the american city + + align:start position:0% +the american city + + + align:start position:0% +the american city +changing its shape significantly + + align:start position:0% +changing its shape significantly + + + align:start position:0% +changing its shape significantly +i think it's i mean i lived in dc for + + align:start position:0% +i think it's i mean i lived in dc for + + + align:start position:0% +i think it's i mean i lived in dc for 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a really fast +play well + + align:start position:0% +play well + + + align:start position:0% +play well +one of the arguments + + align:start position:0% +one of the arguments + + + align:start position:0% +one of the arguments +that i would have gotten to + + align:start position:0% +that i would have gotten to + + + align:start position:0% +that i would have gotten to +if we can get through all of this stuff + + align:start position:0% +if we can get through all of this stuff + + + align:start position:0% +if we can get through all of this stuff +which is just + + align:start position:0% +which is just + + + align:start position:0% +which is just +stories about + + align:start position:0% +stories about + + + align:start position:0% +stories about +the situation + + align:start position:0% +the situation + + + align:start position:0% +the situation +is that + + align:start position:0% +is that + + + align:start position:0% +is that +the fetish with home ownership in this + + align:start position:0% +the fetish with home ownership in this + + + align:start position:0% +the fetish with home ownership in this +country has reduced the capacity for + + align:start position:0% +country has reduced the capacity for + + + align:start position:0% +country has reduced the capacity for +people to rent + + align:start position:0% +people to rent + + + align:start position:0% +people to rent +and rentership allows much greater + + align:start position:0% +and rentership allows much greater + + + align:start position:0% +and rentership allows much greater +mobility than home ownership + + align:start position:0% +mobility than home ownership + + + align:start position:0% +mobility than home ownership +home ownership creates conservative + + align:start position:0% +home ownership creates conservative + + + align:start position:0% +home ownership creates conservative +investments + + align:start position:0% +investments + + + align:start position:0% +investments +in which you don't want new people to + + align:start position:0% +in which you don't want new people to + + + align:start position:0% +in which you don't want new people to +come in so you limit the building of new + + align:start position:0% +come in so you limit the building of new + + + align:start position:0% +come in so you limit the building of new +housing especially affordable housing + + align:start position:0% +housing especially affordable housing + + + align:start position:0% +housing especially affordable housing +because + + align:start position:0% +because + + + align:start position:0% +because +the great virtue that herbert huber and + + align:start position:0% +the great virtue that herbert huber and + + + align:start position:0% +the great virtue that herbert huber and +frank nadilla roosevelt + + align:start position:0% +frank nadilla roosevelt + + + align:start position:0% +frank nadilla roosevelt +felt in stabilizing society through home + + align:start position:0% +felt in stabilizing society through home + + + align:start position:0% +felt in stabilizing society through home +ownership + + align:start position:0% +ownership + + + align:start position:0% +ownership +is + + align:start position:0% +is + + + align:start position:0% +is +producing a + + align:start position:0% +producing a + + + align:start position:0% +producing a +model + + align:start position:0% +model + + + align:start position:0% +model +whereby + + align:start position:0% +whereby + + + align:start position:0% +whereby +the largest savings you can make in your + + align:start position:0% +the largest savings you can make in your + + + align:start position:0% +the largest savings you can make in your +life + + align:start position:0% +life + + + align:start position:0% +life +are the profits between the cost of your + + align:start position:0% +are the profits between the cost of your + + + align:start position:0% +are the profits between the cost of your +house on purchase and its sale + + align:start position:0% +house on purchase and its sale + + + align:start position:0% +house on purchase and its sale +and that becomes an enormously + + align:start position:0% +and that becomes an enormously + + + align:start position:0% +and that becomes an enormously +conservative commodity that you have to + + align:start position:0% +conservative commodity that you have to + + + align:start position:0% +conservative commodity that you have to +maintain do you want a black family + + align:start position:0% +maintain do you want a black family + + + align:start position:0% +maintain do you want a black family +moving into + + align:start position:0% +moving into + + + align:start position:0% +moving into +next year house in newton + + align:start position:0% +next year house in newton + + + align:start position:0% +next year house in newton +or newton's liberal suburbs it wouldn't + + align:start position:0% +or newton's liberal suburbs it wouldn't + + + align:start position:0% +or newton's liberal suburbs it wouldn't +matter but in des moines iowa + + align:start position:0% + + + + align:start position:0% + +they've been + + align:start position:0% + + + + align:start position:0% + +number of pieces written on the + + align:start position:0% + + + + align:start position:0% + +difficulty now for young families to + + align:start position:0% +difficulty now for young families to + + + align:start position:0% +difficulty now for young families to +move into certain suburban sectors + + align:start position:0% +move into certain suburban sectors + + + align:start position:0% +move into certain suburban sectors +where the suburban tax base doesn't want + + align:start position:0% +where the suburban tax base doesn't want + + + align:start position:0% +where the suburban tax base doesn't want +to spend money on building schools + + align:start position:0% +to spend money on building schools + + + align:start position:0% +to spend money on building schools +for young immigrant families + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +this + + align:start position:0% +this + + + align:start position:0% +this +decentralized what melvin webber called + + align:start position:0% +decentralized what melvin webber called + + + align:start position:0% +decentralized what melvin webber called +the spread city + + align:start position:0% +the spread city + + + align:start position:0% +the spread city +is not + + align:start position:0% +is not + + + align:start position:0% +is not +a simple + + align:start position:0% +a simple + + + align:start position:0% +a simple +proposition about having free space + + align:start position:0% +proposition about having free space + + + align:start position:0% +proposition about having free space +and the unlimited auto autorelaxes + + align:start position:0% + + + + align:start position:0% + +let me just + + align:start position:0% +let me just + + + align:start position:0% +let me just +go through this + + align:start position:0% +go through this + + + align:start position:0% +go through this +sheet of stuff that i gave you + + align:start position:0% + + + + align:start position:0% + +the first is a controversial + + align:start position:0% +the first is a controversial + + + align:start position:0% +the first is a controversial +piece called prove it + + align:start position:0% +piece called prove it + + + align:start position:0% +piece called prove it +the costs and benefits of straw + + align:start position:0% +the costs and benefits of straw + + + align:start position:0% +the costs and benefits of straw +it's by two + + align:start position:0% +it's by two + + + align:start position:0% +it's by two +university of southern california + + align:start position:0% +university of southern california + + + align:start position:0% +university of southern california +economists who contend + + align:start position:0% + + + + align:start position:0% + +some of the premises + + align:start position:0% +some of the premises + + + align:start position:0% +some of the premises +of densifying the american city + + align:start position:0% + + + + align:start position:0% + +and so on you + + align:start position:0% +and so on you + + + align:start position:0% +and so on you +i'm not going to go through it in detail + + align:start position:0% +i'm not going to go through it in detail + + + align:start position:0% +i'm not going to go through it in detail +you can read it it's + + align:start position:0% +you can read it it's + + + align:start position:0% +you can read it it's +very well established as the + + align:start position:0% +very well established as the + + + align:start position:0% +very well established as the +counterpoint + + align:start position:0% +counterpoint + + + align:start position:0% +counterpoint +the pro sprawl argument + + align:start position:0% + + + + align:start position:0% + +after that + + align:start position:0% + + + + align:start position:0% + +are just some newspaper + + align:start position:0% + + + + align:start position:0% + +cuttings + + align:start position:0% +cuttings + + + align:start position:0% +cuttings +they now be dated + + align:start position:0% +they now be dated + + + align:start position:0% +they now be dated +but he + + align:start position:0% +but he + + + align:start position:0% +but he +argues that the american house has + + align:start position:0% +argues that the american house has + + + align:start position:0% +argues that the american house has +doubled in size + + align:start position:0% + + + + align:start position:0% + +the automobile + + align:start position:0% + + + + align:start position:0% + +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +have increased + + align:start position:0% +have increased + + + align:start position:0% +have increased +and whilst the emission control + + align:start position:0% +and whilst the emission control + + + align:start position:0% +and whilst the emission control +legislation + + align:start position:0% +legislation + + + align:start position:0% +legislation +is worse + + align:start position:0% + + + + align:start position:0% + +lester thoreau's next piece on the next + + align:start position:0% +lester thoreau's next piece on the next + + + align:start position:0% +lester thoreau's next piece on the next +page + + align:start position:0% +page + + + align:start position:0% +page +is an antidote to + + align:start position:0% +is an antidote to + + + align:start position:0% +is an antidote to +electronic commerce the spread of + + align:start position:0% +electronic commerce the spread of + + + align:start position:0% +electronic commerce the spread of +electronic commerce arguing that it's + + align:start position:0% +electronic commerce arguing that it's + + + align:start position:0% +electronic commerce arguing that it's +been counted by diversification + + align:start position:0% + + + + align:start position:0% + +you go to a bookstore now and it's a + + align:start position:0% +you go to a bookstore now and it's a + + + align:start position:0% +you go to a bookstore now and it's a +restaurant as well + + align:start position:0% +restaurant as well + + + align:start position:0% +restaurant as well +one of the unresolved + + align:start position:0% +one of the unresolved + + + align:start position:0% +one of the unresolved +pieces of the soul puzzle + + align:start position:0% +pieces of the soul puzzle + + + align:start position:0% +pieces of the soul puzzle +is how human beings value face to face + + align:start position:0% +is how human beings value face to face + + + align:start position:0% +is how human beings value face to face +contact as opposed to machine interposed + + align:start position:0% +contact as opposed to machine interposed + + + align:start position:0% +contact as opposed to machine interposed +contact + + align:start position:0% + + + + align:start position:0% + +melvin weber + + align:start position:0% +melvin weber + + + align:start position:0% +melvin weber +peace + + align:start position:0% +peace + + + align:start position:0% +peace +community without propinquity which + + align:start position:0% +community without propinquity which + + + align:start position:0% +community without propinquity which +i'll give you on thursday + + align:start position:0% +i'll give you on thursday + + + align:start position:0% +i'll give you on thursday +is one of the classic pieces of writing + + align:start position:0% +is one of the classic pieces of writing + + + align:start position:0% +is one of the classic pieces of writing +which argues that in the modern city you + + align:start position:0% +which argues that in the modern city you + + + align:start position:0% +which argues that in the modern city you +can maintain community + + align:start position:0% +can maintain community + + + align:start position:0% +can maintain community +would despite distant geography + + align:start position:0% + + + + align:start position:0% + +the next tisma and the last piece is a + + align:start position:0% +the next tisma and the last piece is a + + + align:start position:0% +the next tisma and the last piece is a +polemic from the new urbanist + + align:start position:0% +polemic from the new urbanist + + + align:start position:0% +polemic from the new urbanist +now given what i said + + align:start position:0% +now given what i said + + + align:start position:0% +now given what i said +are some of the problems of the + + align:start position:0% +are some of the problems of the + + + align:start position:0% +are some of the problems of the +decentralized city + + align:start position:0% +decentralized city + + + align:start position:0% +decentralized city +let's look at what they offer + + align:start position:0% + + + + align:start position:0% + +half of this is untrue + + align:start position:0% +half of this is untrue + + + align:start position:0% +half of this is untrue +it's just lies + + align:start position:0% +it's just lies + + + align:start position:0% +it's just lies +but in the traditional architectural + + align:start position:0% +but in the traditional architectural + + + align:start position:0% +but in the traditional architectural +pamphleteering + + align:start position:0% +pamphleteering + + + align:start position:0% +pamphleteering +is common to make statements which if + + align:start position:0% +is common to make statements which if + + + align:start position:0% +is common to make statements which if +you say them aggressively enough + + align:start position:0% +you say them aggressively enough + + + align:start position:0% +you say them aggressively enough +people will believe them to be true + + align:start position:0% +people will believe them to be true + + + align:start position:0% +people will believe them to be true +kobisi was a master using words + + align:start position:0% + + + + align:start position:0% + +by bringing most of the activities of + + align:start position:0% +by bringing most of the activities of + + + align:start position:0% +by bringing most of the activities of +dating living into walking distance + + align:start position:0% +dating living into walking distance + + + align:start position:0% +dating living into walking distance +everyone but especially the elder gain + + align:start position:0% +everyone but especially the elder gain + + + align:start position:0% +everyone but especially the elder gain +independence and movement + + align:start position:0% +independence and movement + + + align:start position:0% +independence and movement +what are we talking about + + align:start position:0% +what are we talking about + + + align:start position:0% +what are we talking about +the densities + + align:start position:0% +the densities + + + align:start position:0% +the densities +that + + align:start position:0% +that + + + align:start position:0% +that +the urbanists propose + + align:start position:0% +the urbanists propose + + + align:start position:0% +the urbanists propose +or the developers will maxima will + + align:start position:0% +or the developers will maxima will + + + align:start position:0% +or the developers will maxima will +minimize + + align:start position:0% + + + + align:start position:0% + +argue that you americans will walk seven + + align:start position:0% +argue that you americans will walk seven + + + align:start position:0% +argue that you americans will walk seven +minutes + + align:start position:0% +minutes + + + align:start position:0% +minutes +at most + + align:start position:0% +at most + + + align:start position:0% +at most +to + + align:start position:0% +to + + + align:start position:0% +to +another to a destination + + align:start position:0% +another to a destination + + + align:start position:0% +another to a destination +within you at the densities that + + align:start position:0% +within you at the densities that + + + align:start position:0% +within you at the densities that +you build + + align:start position:0% +you build + + + align:start position:0% +you build +in a decentralized american suburban + + align:start position:0% +in a decentralized american suburban + + + align:start position:0% +in a decentralized american suburban +situation + + align:start position:0% +situation + + + align:start position:0% +situation +admittedly there are + + align:start position:0% +admittedly there are + + + align:start position:0% +admittedly there are +as many attached houses in the united + + align:start position:0% +as many attached houses in the united + + + align:start position:0% +as many attached houses in the united +states as they are single hours + + align:start position:0% + + + + align:start position:0% + +you can probably + + align:start position:0% +you can probably + + + align:start position:0% +you can probably +develop a market for + + align:start position:0% +develop a market for + + + align:start position:0% +develop a market for +a video store and uh + + align:start position:0% +a video store and uh + + + align:start position:0% +a video store and uh +7-eleven + + align:start position:0% +7-eleven + + + align:start position:0% +7-eleven +so the notion that you can wander all + + align:start position:0% +so the notion that you can wander all + + + align:start position:0% +so the notion that you can wander all +over the place + + align:start position:0% +over the place + + + align:start position:0% +over the place +purchasing whatever you want to + + align:start position:0% +purchasing whatever you want to + + + align:start position:0% +purchasing whatever you want to +is rubbish + + align:start position:0% +is rubbish + + + align:start position:0% +is rubbish +it's nonsense it's just + + align:start position:0% +it's nonsense it's just + + + align:start position:0% +it's nonsense it's just +pamphleteering it should be stopped + + align:start position:0% + + + + align:start position:0% + +by reducing the number and length of + + align:start position:0% +by reducing the number and length of + + + align:start position:0% +by reducing the number and length of +autumn wheel drip + + align:start position:0% +autumn wheel drip + + + align:start position:0% +autumn wheel drip +how do you reduce the number length of + + align:start position:0% +how do you reduce the number length of + + + align:start position:0% +how do you reduce the number length of +watermale troops + + align:start position:0% +watermale troops + + + align:start position:0% +watermale troops +if it were easy to do we'd all be + + align:start position:0% +if it were easy to do we'd all be + + + align:start position:0% +if it were easy to do we'd all be +advocating it + + align:start position:0% + + + + align:start position:0% + +will give me an example + + align:start position:0% + + + + align:start position:0% + +were you going to say something + + align:start position:0% + + + + align:start position:0% + +by providing streets and squares of + + align:start position:0% +by providing streets and squares of + + + align:start position:0% +by providing streets and squares of +pedestrians and neighbors walking come + + align:start position:0% +pedestrians and neighbors walking come + + + align:start position:0% +pedestrians and neighbors walking come +to know each other + + align:start position:0% + + + + align:start position:0% + +these events from putnam's work + + align:start position:0% +these events from putnam's work + + + align:start position:0% +these events from putnam's work +in voting alone + + align:start position:0% +in voting alone + + + align:start position:0% +in voting alone +that + + align:start position:0% +that + + + align:start position:0% +that +americans who live in apartments get to + + align:start position:0% +americans who live in apartments get to + + + align:start position:0% +americans who live in apartments get to +know each other as well as people living + + align:start position:0% +know each other as well as people living + + + align:start position:0% +know each other as well as people living +in houses + + align:start position:0% +in houses + + + align:start position:0% +in houses +that neighborly relationships are the + + align:start position:0% +that neighborly relationships are the + + + align:start position:0% +that neighborly relationships are the +same + + align:start position:0% +same + + + align:start position:0% +same +independent of the + + align:start position:0% +independent of the + + + align:start position:0% +independent of the +condition of the + + align:start position:0% +condition of the + + + align:start position:0% +condition of the +block that you live in it's probably + + align:start position:0% +block that you live in it's probably + + + align:start position:0% +block that you live in it's probably +true that the poorer you are the more + + align:start position:0% +true that the poorer you are the more + + + align:start position:0% +true that the poorer you are the more +you depend on your neighbors + + align:start position:0% + + + + align:start position:0% + +so this is nonsense + + align:start position:0% + + + + align:start position:0% + +by providing appropriate building + + align:start position:0% +by providing appropriate building + + + align:start position:0% +by providing appropriate building +concentrations at easy walking distance + + align:start position:0% +concentrations at easy walking distance + + + align:start position:0% +concentrations at easy walking distance +from bus shops + + align:start position:0% +from bus shops + + + align:start position:0% +from bus shops +public transit becomes a viable + + align:start position:0% +public transit becomes a viable + + + align:start position:0% +public transit becomes a viable +alternative to the autumn bureau + + align:start position:0% +alternative to the autumn bureau + + + align:start position:0% +alternative to the autumn bureau +we can't finance in the mbta in boston + + align:start position:0% +we can't finance in the mbta in boston + + + align:start position:0% +we can't finance in the mbta in boston +unless we pay enormous shares of money + + align:start position:0% +unless we pay enormous shares of money + + + align:start position:0% +unless we pay enormous shares of money +to + + align:start position:0% +to + + + align:start position:0% +to +which probably would be justified in a + + align:start position:0% +which probably would be justified in a + + + align:start position:0% +which probably would be justified in a +decent economy + + align:start position:0% +decent economy + + + align:start position:0% +decent economy +but we're not doing it so what is + + align:start position:0% +but we're not doing it so what is + + + align:start position:0% +but we're not doing it so what is +the new uranus project for doing this + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +but you need enough people to do it + + align:start position:0% +but you need enough people to do it + + + align:start position:0% +but you need enough people to do it +to pay for the cost of doing it + + align:start position:0% +to pay for the cost of doing it + + + align:start position:0% +to pay for the cost of doing it +you can't run a public transportation + + align:start position:0% +you can't run a public transportation + + + align:start position:0% +you can't run a public transportation +system with six people in it + + align:start position:0% + + + + align:start position:0% + +it's unfortunately true it's as true as + + align:start position:0% +it's unfortunately true it's as true as + + + align:start position:0% +it's unfortunately true it's as true as +eating carrots + + align:start position:0% + + + + align:start position:0% + +it's true as eating carrots are healthy + + align:start position:0% +it's true as eating carrots are healthy + + + align:start position:0% +it's true as eating carrots are healthy +for you + + align:start position:0% +for you + + + align:start position:0% +for you +which i don't know i don't eat carrots + + align:start position:0% + + + + align:start position:0% + +but the cost of public transportation + + align:start position:0% +but the cost of public transportation + + + align:start position:0% +but the cost of public transportation +can only be justified by seeing it as a + + align:start position:0% +can only be justified by seeing it as a + + + align:start position:0% +can only be justified by seeing it as a +socially important act + + align:start position:0% +socially important act + + + align:start position:0% +socially important act +keeping the air cleaner + + align:start position:0% +keeping the air cleaner + + + align:start position:0% +keeping the air cleaner +having a much greater sense of belonging + + align:start position:0% +having a much greater sense of belonging + + + align:start position:0% +having a much greater sense of belonging +to a public and so many positive + + align:start position:0% +to a public and so many positive + + + align:start position:0% +to a public and so many positive +attributes but you can't do it + + align:start position:0% +attributes but you can't do it + + + align:start position:0% +attributes but you can't do it +at 10 people per acre + + align:start position:0% +at 10 people per acre + + + align:start position:0% +at 10 people per acre +10 people per acre + + align:start position:0% +10 people per acre + + + align:start position:0% +10 people per acre +is a tenth of an acre lot + + align:start position:0% +is a tenth of an acre lot + + + align:start position:0% +is a tenth of an acre lot +if your family size is three it's 30 + + align:start position:0% +if your family size is three it's 30 + + + align:start position:0% +if your family size is three it's 30 +people + + align:start position:0% +people + + + align:start position:0% +people +per acre + + align:start position:0% +per acre + + + align:start position:0% +per acre +30 people per acre generate one trip + + align:start position:0% +30 people per acre generate one trip + + + align:start position:0% +30 people per acre generate one trip +if your school happens to be on a subway + + align:start position:0% +if your school happens to be on a subway + + + align:start position:0% +if your school happens to be on a subway +line + + align:start position:0% +line + + + align:start position:0% +line +or you're close enough + + align:start position:0% +or you're close enough + + + align:start position:0% +or you're close enough +to walk + + align:start position:0% +to walk + + + align:start position:0% +to walk +give me a break + + align:start position:0% + + + + align:start position:0% + +now you're trying to say something tell + + align:start position:0% +now you're trying to say something tell + + + align:start position:0% +now you're trying to say something tell +me what you're trying to say + + align:start position:0% + + + + align:start position:0% + +but what i want to say is that + + align:start position:0% + + + + align:start position:0% + +when when there is also easy way uh for + + align:start position:0% +when when there is also easy way uh for + + + align:start position:0% +when when there is also easy way uh for +cars accessibility or moving by cars + + align:start position:0% +cars accessibility or moving by cars + + + align:start position:0% +cars accessibility or moving by cars +which is i think it's the case of boston + + align:start position:0% +which is i think it's the case of boston + + + align:start position:0% +which is i think it's the case of boston +then if you can choose and it comes it's + + align:start position:0% +then if you can choose and it comes it's + + + align:start position:0% +then if you can choose and it comes it's +as easy to move around with your car and + + align:start position:0% +as easy to move around with your car and + + + align:start position:0% +as easy to move around with your car and +park and go on these super highways that + + align:start position:0% +park and go on these super highways that + + + align:start position:0% +park and go on these super highways that +take you everywhere + + align:start position:0% +take you everywhere + + + align:start position:0% +take you everywhere +of course + + align:start position:0% +of course + + + align:start position:0% +of course +you know it's hard to decide to take the + + align:start position:0% +you know it's hard to decide to take the + + + align:start position:0% +you know it's hard to decide to take the +subway but if you're in new york where + + align:start position:0% +subway but if you're in new york where + + + align:start position:0% +subway but if you're in new york where +parking is such a hassle + + align:start position:0% +parking is such a hassle + + + align:start position:0% +parking is such a hassle +then of course it's a hassle in boston + + align:start position:0% +then of course it's a hassle in boston + + + align:start position:0% +then of course it's a hassle in boston +as well + + align:start position:0% + + + + align:start position:0% + +in manhattan yes people + + align:start position:0% +in manhattan yes people + + + align:start position:0% +in manhattan yes people +per capita walk in manhattan more than + + align:start position:0% +per capita walk in manhattan more than + + + align:start position:0% +per capita walk in manhattan more than +they do in any city in the world + + align:start position:0% +they do in any city in the world + + + align:start position:0% +they do in any city in the world +because of the restrictions + + align:start position:0% +because of the restrictions + + + align:start position:0% +because of the restrictions +on other forms of access although + + align:start position:0% +on other forms of access although + + + align:start position:0% +on other forms of access although +manhattan has a very good public + + align:start position:0% +manhattan has a very good public + + + align:start position:0% +manhattan has a very good public +transportation system + + align:start position:0% +transportation system + + + align:start position:0% +transportation system +but he improved with the second avenue + + align:start position:0% +but he improved with the second avenue + + + align:start position:0% +but he improved with the second avenue +extension + + align:start position:0% +extension + + + align:start position:0% +extension +um + + align:start position:0% +um + + + align:start position:0% +um +why is it does + + align:start position:0% +why is it does + + + align:start position:0% +why is it does +manhattan have a good subway system + + align:start position:0% +manhattan have a good subway system + + + align:start position:0% +manhattan have a good subway system +london has the best subway system in the + + align:start position:0% +london has the best subway system in the + + + align:start position:0% +london has the best subway system in the +world why + + align:start position:0% + + + + align:start position:0% + +yes correct in london's case it was + + align:start position:0% +yes correct in london's case it was + + + align:start position:0% +yes correct in london's case it was +developed early + + align:start position:0% +developed early + + + align:start position:0% +developed early +no country in the world can afford to + + align:start position:0% +no country in the world can afford to + + + align:start position:0% +no country in the world can afford to +build a london transportation system + + align:start position:0% +build a london transportation system + + + align:start position:0% +build a london transportation system +today + + align:start position:0% +today + + + align:start position:0% +today +it's where predictability + + align:start position:0% + + + + align:start position:0% + +saved the society enormous amount of + + align:start position:0% +saved the society enormous amount of + + + align:start position:0% +saved the society enormous amount of +money + + align:start position:0% + + + + align:start position:0% + +the subway system and the bus system in + + align:start position:0% +the subway system and the bus system in + + + align:start position:0% +the subway system and the bus system in +london cover almost every + + align:start position:0% +london cover almost every + + + align:start position:0% +london cover almost every +i think the distances every distance i + + align:start position:0% +i think the distances every distance i + + + align:start position:0% +i think the distances every distance i +remember saying it when we talked about + + align:start position:0% +remember saying it when we talked about + + + align:start position:0% +remember saying it when we talked about +london + + align:start position:0% +london + + + align:start position:0% +london +is very small + + align:start position:0% + + + + align:start position:0% + +density is one of the + + align:start position:0% +density is one of the + + + align:start position:0% +density is one of the +argued solutions if you put more people + + align:start position:0% +argued solutions if you put more people + + + align:start position:0% +argued solutions if you put more people +into space the more of them will likely + + align:start position:0% +into space the more of them will likely + + + align:start position:0% +into space the more of them will likely +be clients for using public + + align:start position:0% +be clients for using public + + + align:start position:0% +be clients for using public +transportation there's nothing that + + align:start position:0% +transportation there's nothing that + + + align:start position:0% +transportation there's nothing that +helps public transportation more than + + align:start position:0% +helps public transportation more than + + + align:start position:0% +helps public transportation more than +clients + + align:start position:0% + + + + align:start position:0% + +it's it's such an obvious + + align:start position:0% +it's it's such an obvious + + + align:start position:0% +it's it's such an obvious +algorithm that + + align:start position:0% +algorithm that + + + align:start position:0% +algorithm that +the difficulty is knowing what to do + + align:start position:0% +the difficulty is knowing what to do + + + align:start position:0% +the difficulty is knowing what to do +with it + + align:start position:0% +with it + + + align:start position:0% +with it +and that's where + + align:start position:0% +and that's where + + + align:start position:0% +and that's where +next the class on thursday is going to + + align:start position:0% +next the class on thursday is going to + + + align:start position:0% +next the class on thursday is going to +ask you to come up with some solutions + + align:start position:0% +ask you to come up with some solutions + + + align:start position:0% +ask you to come up with some solutions +let's say the following + + align:start position:0% +let's say the following + + + align:start position:0% +let's say the following +american cities that are going to remain + + align:start position:0% +american cities that are going to remain + + + align:start position:0% +american cities that are going to remain +largely automobile + + align:start position:0% + + + + align:start position:0% + +cities the rest of the world + + align:start position:0% +cities the rest of the world + + + align:start position:0% +cities the rest of the world +will follow + + align:start position:0% + + + + align:start position:0% + +to the extent that it can + + align:start position:0% +to the extent that it can + + + align:start position:0% +to the extent that it can +because gasoline prices in the united + + align:start position:0% +because gasoline prices in the united + + + align:start position:0% +because gasoline prices in the united +states are a fraction of gasoline prices + + align:start position:0% +states are a fraction of gasoline prices + + + align:start position:0% +states are a fraction of gasoline prices +in other parts of the world + + align:start position:0% +in other parts of the world + + + align:start position:0% +in other parts of the world +and the automobile highway system has + + align:start position:0% +and the automobile highway system has + + + align:start position:0% +and the automobile highway system has +been subsidized by the state + + align:start position:0% +been subsidized by the state + + + align:start position:0% +been subsidized by the state +to an enormous degree under eyes and our + + align:start position:0% +to an enormous degree under eyes and our + + + align:start position:0% +to an enormous degree under eyes and our +starting with eisenhower and so on + + align:start position:0% +starting with eisenhower and so on + + + align:start position:0% +starting with eisenhower and so on +we don't pay for the roads that we use + + align:start position:0% + + + + align:start position:0% + +a commuter living in + + align:start position:0% +a commuter living in + + + align:start position:0% +a commuter living in +lexington passing through cambridge + + align:start position:0% +lexington passing through cambridge + + + align:start position:0% +lexington passing through cambridge +every morning passed my house + + align:start position:0% +every morning passed my house + + + align:start position:0% +every morning passed my house +doesn't pay for the cost of maintaining + + align:start position:0% +doesn't pay for the cost of maintaining + + + align:start position:0% +doesn't pay for the cost of maintaining +the the street in cambridge it's free + + align:start position:0% + + + + align:start position:0% + +we've gotten used to + + align:start position:0% +we've gotten used to + + + align:start position:0% +we've gotten used to +having free + + align:start position:0% +having free + + + align:start position:0% +having free +waterville + + align:start position:0% + + + + align:start position:0% + +but to get agreement in the country as + + align:start position:0% +but to get agreement in the country as + + + align:start position:0% +but to get agreement in the country as +large as this + + align:start position:0% +large as this + + + align:start position:0% +large as this +takes a lot of can you imagine the + + align:start position:0% +takes a lot of can you imagine the + + + align:start position:0% +takes a lot of can you imagine the +opposition + + align:start position:0% +opposition + + + align:start position:0% +opposition +i don't know what the senators from + + align:start position:0% +i don't know what the senators from + + + align:start position:0% +i don't know what the senators from +texas would vote + + align:start position:0% +texas would vote + + + align:start position:0% +texas would vote +in favor of against + + align:start position:0% +in favor of against + + + align:start position:0% +in favor of against +taxation on automobile + + align:start position:0% +taxation on automobile + + + align:start position:0% +taxation on automobile +use + + align:start position:0% + + + + align:start position:0% + +because we're using fuel produced in + + align:start position:0% +because we're using fuel produced in + + + align:start position:0% +because we're using fuel produced in +texas + + align:start position:0% +texas + + + align:start position:0% +texas +and automobile + + align:start position:0% +and automobile + + + align:start position:0% +and automobile +gives an enormous amount of fuel + + align:start position:0% +gives an enormous amount of fuel + + + align:start position:0% +gives an enormous amount of fuel +so does most of the transportation + + align:start position:0% +so does most of the transportation + + + align:start position:0% +so does most of the transportation +system in the united states + + align:start position:0% +system in the united states + + + align:start position:0% +system in the united states +we service most of our delivery by truck + + align:start position:0% +we service most of our delivery by truck + + + align:start position:0% +we service most of our delivery by truck +not by rail + + align:start position:0% + + + + align:start position:0% + +we have enormous difficulty in building + + align:start position:0% +we have enormous difficulty in building + + + align:start position:0% +we have enormous difficulty in building +rail + + align:start position:0% + + + + align:start position:0% + +you just need to read about the + + align:start position:0% +you just need to read about the + + + align:start position:0% +you just need to read about the +controversies in california at the + + align:start position:0% +controversies in california at the + + + align:start position:0% +controversies in california at the +moment + + align:start position:0% +moment + + + align:start position:0% +moment +by trying to link + + align:start position:0% +by trying to link + + + align:start position:0% +by trying to link +san francisco and scala and sacramento + + align:start position:0% +san francisco and scala and sacramento + + + align:start position:0% +san francisco and scala and sacramento +on the way to los angeles + + align:start position:0% + + + + align:start position:0% + +it passes through palo alto and there's + + align:start position:0% +it passes through palo alto and there's + + + align:start position:0% +it passes through palo alto and there's +no place to put it in palo alto + + align:start position:0% + + + + align:start position:0% + +and land values are so high in palo alto + + align:start position:0% +and land values are so high in palo alto + + + align:start position:0% +and land values are so high in palo alto +that you can't + + align:start position:0% +that you can't + + + align:start position:0% +that you can't +do anything politically about + + align:start position:0% +do anything politically about + + + align:start position:0% +do anything politically about +how it's going to be resolved + + align:start position:0% + + + + align:start position:0% + +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +there are different kinds of suburbs the + + align:start position:0% +there are different kinds of suburbs the + + + align:start position:0% +there are different kinds of suburbs the +suburbs that originally that levittown + + align:start position:0% +suburbs that originally that levittown + + + align:start position:0% +suburbs that originally that levittown +was built on + + align:start position:0% +was built on + + + align:start position:0% +was built on +had a daily population of women + + align:start position:0% + + + + align:start position:0% + +a single car + + align:start position:0% +a single car + + + align:start position:0% +a single car +station wagon chevrolet station wagons + + align:start position:0% +station wagon chevrolet station wagons + + + align:start position:0% +station wagon chevrolet station wagons +what people had they had meat loaf for + + align:start position:0% +what people had they had meat loaf for + + + align:start position:0% +what people had they had meat loaf for +dinner there were no restaurants and so + + align:start position:0% +dinner there were no restaurants and so + + + align:start position:0% +dinner there were no restaurants and so +on + + align:start position:0% +on + + + align:start position:0% +on +this is + + align:start position:0% +this is + + + align:start position:0% +this is +the organization man the book by william + + align:start position:0% +the organization man the book by william + + + align:start position:0% +the organization man the book by william +white describes the conditions in park + + align:start position:0% +white describes the conditions in park + + + align:start position:0% +white describes the conditions in park +hill + + align:start position:0% +hill + + + align:start position:0% +hill +not park hill + + align:start position:0% +not park hill + + + align:start position:0% +not park hill +i forget the name of the suburb of + + align:start position:0% +i forget the name of the suburb of + + + align:start position:0% +i forget the name of the suburb of +chicago + + align:start position:0% +chicago + + + align:start position:0% +chicago +he's in a + + align:start position:0% +he's in a + + + align:start position:0% +he's in a +this piece by in your reading list + + align:start position:0% +this piece by in your reading list + + + align:start position:0% +this piece by in your reading list +called stressed out in suburbia + + align:start position:0% +called stressed out in suburbia + + + align:start position:0% +called stressed out in suburbia +writes a description of the suburb + + align:start position:0% + + + + align:start position:0% + +the new suburb of napierville just + + align:start position:0% +the new suburb of napierville just + + + align:start position:0% +the new suburb of napierville just +further away from chicago + + align:start position:0% +further away from chicago + + + align:start position:0% +further away from chicago +where + + align:start position:0% +where + + + align:start position:0% +where +all the restaurants are ethnic + + align:start position:0% +all the restaurants are ethnic + + + align:start position:0% +all the restaurants are ethnic +restaurants + + align:start position:0% +restaurants + + + align:start position:0% +restaurants +all the + + align:start position:0% +all the + + + align:start position:0% +all the +stress in the community is on children + + align:start position:0% +stress in the community is on children + + + align:start position:0% +stress in the community is on children +getting higher grades + + align:start position:0% + + + + align:start position:0% + +so american suburbs have + + align:start position:0% + + + + align:start position:0% + +grown in wealth + + align:start position:0% +grown in wealth + + + align:start position:0% +grown in wealth +houses are given french names the + + align:start position:0% +houses are given french names the + + + align:start position:0% +houses are given french names the +neighborhoods all given foreign names + + align:start position:0% +neighborhoods all given foreign names + + + align:start position:0% +neighborhoods all given foreign names +and so on it's quite amusing + + align:start position:0% +and so on it's quite amusing + + + align:start position:0% +and so on it's quite amusing +let me just pick up some other things + + align:start position:0% + + + + align:start position:0% + +robert putnam + + align:start position:0% +robert putnam + + + align:start position:0% +robert putnam +from harvard has written a book called + + align:start position:0% +from harvard has written a book called + + + align:start position:0% +from harvard has written a book called +bowling alone which caused a big + + align:start position:0% +bowling alone which caused a big + + + align:start position:0% +bowling alone which caused a big +surge of interest in social science + + align:start position:0% +surge of interest in social science + + + align:start position:0% +surge of interest in social science +timmy + + align:start position:0% +timmy + + + align:start position:0% +timmy +he + + align:start position:0% + + + + align:start position:0% + +he claims that + + align:start position:0% +he claims that + + + align:start position:0% +he claims that +what has happened in the united states + + align:start position:0% +what has happened in the united states + + + align:start position:0% +what has happened in the united states +and he's not blaming suburbia for it + + align:start position:0% +and he's not blaming suburbia for it + + + align:start position:0% +and he's not blaming suburbia for it +is that there's been a much + + align:start position:0% +is that there's been a much + + + align:start position:0% +is that there's been a much +strong tendency + + align:start position:0% +strong tendency + + + align:start position:0% +strong tendency +towards + + align:start position:0% +towards + + + align:start position:0% +towards +individualism + + align:start position:0% +individualism + + + align:start position:0% +individualism +as opposed to belonging to community or + + align:start position:0% +as opposed to belonging to community or + + + align:start position:0% +as opposed to belonging to community or +sharing + + align:start position:0% +sharing + + + align:start position:0% +sharing +he quotes endlessly + + align:start position:0% +he quotes endlessly + + + align:start position:0% +he quotes endlessly +um religious affiliation has dropped + + align:start position:0% + + + + align:start position:0% + +the united states has more houses + + align:start position:0% +the united states has more houses + + + align:start position:0% +the united states has more houses +worship per capita than any other nation + + align:start position:0% +worship per capita than any other nation + + + align:start position:0% +worship per capita than any other nation +on earth + + align:start position:0% + + + + align:start position:0% + +it's been a modest decline in all + + align:start position:0% +it's been a modest decline in all + + + align:start position:0% +it's been a modest decline in all +church-related groups over the past 20 + + align:start position:0% +church-related groups over the past 20 + + + align:start position:0% +church-related groups over the past 20 +years + + align:start position:0% +years + + + align:start position:0% +years +union membership has been falling for + + align:start position:0% +union membership has been falling for + + + align:start position:0% +union membership has been falling for +nearly four decades + + align:start position:0% +nearly four decades + + + align:start position:0% +nearly four decades +the peter the parent teacher association + + align:start position:0% +the peter the parent teacher association + + + align:start position:0% +the peter the parent teacher association +has become + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +which has always been an important form + + align:start position:0% +which has always been an important form + + + align:start position:0% +which has always been an important form +of civic engagement in 20th century + + align:start position:0% +of civic engagement in 20th century + + + align:start position:0% +of civic engagement in 20th century +america + + align:start position:0% +america + + + align:start position:0% +america +has declined from 12 million in 1964 to + + align:start position:0% +has declined from 12 million in 1964 to + + + align:start position:0% +has declined from 12 million in 1964 to +barely 5 million in 1982. + + align:start position:0% +barely 5 million in 1982. + + + align:start position:0% +barely 5 million in 1982. +volunteering + + align:start position:0% +volunteering + + + align:start position:0% +volunteering +for + + align:start position:0% +for + + + align:start position:0% +for +traditional women's groups + + align:start position:0% +traditional women's groups + + + align:start position:0% +traditional women's groups +the league of women voters the red cross + + align:start position:0% +the league of women voters the red cross + + + align:start position:0% +the league of women voters the red cross +boy scouts all have dropped in + + align:start position:0% +boy scouts all have dropped in + + + align:start position:0% +boy scouts all have dropped in +attendance + + align:start position:0% + + + + align:start position:0% + +he counters that by talking about + + align:start position:0% +he counters that by talking about + + + align:start position:0% +he counters that by talking about +groups that have increased in size + + align:start position:0% +groups that have increased in size + + + align:start position:0% +groups that have increased in size +i didn't know this but the american + + align:start position:0% +i didn't know this but the american + + + align:start position:0% +i didn't know this but the american +association of retired persons aarp + + align:start position:0% +association of retired persons aarp + + + align:start position:0% +association of retired persons aarp +has grown exponentially from 400 000 + + align:start position:0% +has grown exponentially from 400 000 + + + align:start position:0% +has grown exponentially from 400 000 +card carrying members in 1960 + + align:start position:0% +card carrying members in 1960 + + + align:start position:0% +card carrying members in 1960 +to 30 million 33 million in 1933 + + align:start position:0% +to 30 million 33 million in 1933 + + + align:start position:0% +to 30 million 33 million in 1933 +becoming + + align:start position:0% +becoming + + + align:start position:0% +becoming +after the catholic church the largest + + align:start position:0% +after the catholic church the largest + + + align:start position:0% +after the catholic church the largest +private organization in the world + + align:start position:0% + + + + align:start position:0% + +when i when he asked in his social + + align:start position:0% +when i when he asked in his social + + + align:start position:0% +when i when he asked in his social +survey in 1974 how often do you spend a + + align:start position:0% +survey in 1974 how often do you spend a + + + align:start position:0% +survey in 1974 how often do you spend a +social evening with a neighbor + + align:start position:0% +social evening with a neighbor + + + align:start position:0% +social evening with a neighbor +the proportion of americans who + + align:start position:0% +the proportion of americans who + + + align:start position:0% +the proportion of americans who +socialize with their neighbors more than + + align:start position:0% +socialize with their neighbors more than + + + align:start position:0% +socialize with their neighbors more than +once a year has slowly but steadily + + align:start position:0% +once a year has slowly but steadily + + + align:start position:0% +once a year has slowly but steadily +declined over the past + + align:start position:0% +declined over the past + + + align:start position:0% +declined over the past +year two decades from 72 to 61 + + align:start position:0% +year two decades from 72 to 61 + + + align:start position:0% +year two decades from 72 to 61 +whereas friends who do not live in your + + align:start position:0% +whereas friends who do not live in your + + + align:start position:0% +whereas friends who do not live in your +neighborhood appears to be on the + + align:start position:0% +neighborhood appears to be on the + + + align:start position:0% +neighborhood appears to be on the +increase + + align:start position:0% + + + + align:start position:0% + +it's + + align:start position:0% +it's + + + align:start position:0% +it's +oh we have some time i looked at the + + align:start position:0% +oh we have some time i looked at the + + + align:start position:0% +oh we have some time i looked at the +wrong thing or what + + align:start position:0% + + + + align:start position:0% + +the use of the automobile in + + align:start position:0% +the use of the automobile in + + + align:start position:0% +the use of the automobile in +metropolitan terms is is interesting in + + align:start position:0% +metropolitan terms is is interesting in + + + align:start position:0% +metropolitan terms is is interesting in +another respect + + align:start position:0% + + + + align:start position:0% + +what's + + align:start position:0% + + + + align:start position:0% + +oh it's two o'clock i'm sorry i've got a + + align:start position:0% +oh it's two o'clock i'm sorry i've got a + + + align:start position:0% +oh it's two o'clock i'm sorry i've got a +dull watch + + align:start position:0% + + + + align:start position:0% + +i'll continue with + + align:start position:0% +i'll continue with + + + align:start position:0% +i'll continue with +some more evidence for you to put into + + align:start position:0% +some more evidence for you to put into + + + align:start position:0% +some more evidence for you to put into +your + + align:start position:0% +your + + + align:start position:0% +your +mincing machine + + align:start position:0% +mincing machine + + + align:start position:0% +mincing machine +but i expect + + align:start position:0% +but i expect + + + align:start position:0% +but i expect +some feedback + + align:start position:0% +some feedback + + + align:start position:0% +some feedback +as to what you + + align:start position:0% +as to what you + + + align:start position:0% +as to what you +where you stand + + align:start position:0% +where you stand + + + align:start position:0% +where you stand +in the end maybe it's simply where you + + align:start position:0% +in the end maybe it's simply where you + + + align:start position:0% +in the end maybe it's simply where you +stand that matters + + align:start position:0% +stand that matters + + + align:start position:0% +stand that matters +many of you architects will favor + + align:start position:0% +many of you architects will favor + + + align:start position:0% +many of you architects will favor +densification of the city despite any + + align:start position:0% +densification of the city despite any + + + align:start position:0% +densification of the city despite any +notion of how it can be achieved in the + + align:start position:0% +notion of how it can be achieved in the + + + align:start position:0% +notion of how it can be achieved in the +liberal society + + align:start position:0% + + + + align:start position:0% + +maybe maybe the american city is just + + align:start position:0% +maybe maybe the american city is just + + + align:start position:0% +maybe maybe the american city is just +like american democracy + + align:start position:0% +like american democracy + + + align:start position:0% +like american democracy +slow and full of pitfalls not doing + + align:start position:0% +slow and full of pitfalls not doing + + + align:start position:0% +slow and full of pitfalls not doing +anything about gun control + + align:start position:0% +anything about gun control + + + align:start position:0% +anything about gun control +when it's obvious that it should + + align:start position:0% +when it's obvious that it should + + + align:start position:0% +when it's obvious that it should +and yet it survives \ No newline at end of file diff --git a/2IQxigpPMns.txt b/2IQxigpPMns.txt new file mode 100644 index 0000000000000000000000000000000000000000..7c1623c632dcb156745d7ef2518e47d602b4e6ff --- /dev/null +++ b/2IQxigpPMns.txt @@ -0,0 +1,1003 @@ +align:start position:0% + +we will now review a problem on error + + align:start position:0% +we will now review a problem on error + + + align:start position:0% +we will now review a problem on error +correction and detection in order to + + align:start position:0% +correction and detection in order to + + + align:start position:0% +correction and detection in order to +better understand how the selected + + align:start position:0% +better understand how the selected + + + align:start position:0% +better understand how the selected +encoding of a message can help both + + align:start position:0% +encoding of a message can help both + + + align:start position:0% +encoding of a message can help both +detect and correct transmission errors + + align:start position:0% +detect and correct transmission errors + + + align:start position:0% +detect and correct transmission errors +in this problem messages consist of nine + + align:start position:0% +in this problem messages consist of nine + + + align:start position:0% +in this problem messages consist of nine +data bits and seven parity bits each dij + + align:start position:0% +data bits and seven parity bits each dij + + + align:start position:0% +data bits and seven parity bits each dij +represents a data bit which belongs to + + align:start position:0% +represents a data bit which belongs to + + + align:start position:0% +represents a data bit which belongs to +row I and column J the pIJ bits are used + + align:start position:0% +row I and column J the pIJ bits are used + + + align:start position:0% +row I and column J the pIJ bits are used +to make the parity of each row and + + align:start position:0% +to make the parity of each row and + + + align:start position:0% +to make the parity of each row and +column B odd the pxx box which is in the + + align:start position:0% +column B odd the pxx box which is in the + + + align:start position:0% +column B odd the pxx box which is in the +bottom right corner is used to make the + + align:start position:0% +bottom right corner is used to make the + + + align:start position:0% +bottom right corner is used to make the +parity of the entire message odd in + + align:start position:0% +parity of the entire message odd in + + + align:start position:0% +parity of the entire message odd in +other words it makes a total number of + + align:start position:0% +other words it makes a total number of + + + align:start position:0% +other words it makes a total number of +ones be odd the first question we want + + align:start position:0% +ones be odd the first question we want + + + align:start position:0% +ones be odd the first question we want +to ask ourselves is what is the minimum + + align:start position:0% +to ask ourselves is what is the minimum + + + align:start position:0% +to ask ourselves is what is the minimum +Hamming distance between valid code + + align:start position:0% +Hamming distance between valid code + + + align:start position:0% +Hamming distance between valid code +words using this encoding in order to + + align:start position:0% +words using this encoding in order to + + + align:start position:0% +words using this encoding in order to +figure that out we need to think about + + align:start position:0% +figure that out we need to think about + + + align:start position:0% +figure that out we need to think about +how many bits of the encoding are + + align:start position:0% +how many bits of the encoding are + + + align:start position:0% +how many bits of the encoding are +changed if I want to change one of the + + align:start position:0% +changed if I want to change one of the + + + align:start position:0% +changed if I want to change one of the +data bits the easiest way to see this is + + align:start position:0% +data bits the easiest way to see this is + + + align:start position:0% +data bits the easiest way to see this is +through an example suppose that I want + + align:start position:0% +through an example suppose that I want + + + align:start position:0% +through an example suppose that I want +to change D zero one from a zero to a + + align:start position:0% +to change D zero one from a zero to a + + + align:start position:0% +to change D zero one from a zero to a +one + + align:start position:0% +one + + + align:start position:0% +one +the first thing changing is my data bit + + align:start position:0% +the first thing changing is my data bit + + + align:start position:0% +the first thing changing is my data bit +itself then p0x would get flipped + + align:start position:0% +itself then p0x would get flipped + + + align:start position:0% +itself then p0x would get flipped +because I just added another one to my + + align:start position:0% +because I just added another one to my + + + align:start position:0% +because I just added another one to my +row which means that I need to flips a + + align:start position:0% +row which means that I need to flips a + + + align:start position:0% +row which means that I need to flips a +parity bit in order for the total number + + align:start position:0% +parity bit in order for the total number + + + align:start position:0% +parity bit in order for the total number +of ones in my row to remain odd the next + + align:start position:0% +of ones in my row to remain odd the next + + + align:start position:0% +of ones in my row to remain odd the next +change is that px1 needs to get flipped + + align:start position:0% +change is that px1 needs to get flipped + + + align:start position:0% +change is that px1 needs to get flipped +in order to maintain an odd parity in my + + align:start position:0% +in order to maintain an odd parity in my + + + align:start position:0% +in order to maintain an odd parity in my +column so far three entries have changed + + align:start position:0% +column so far three entries have changed + + + align:start position:0% +column so far three entries have changed +which implies that the parity of the + + align:start position:0% +which implies that the parity of the + + + align:start position:0% +which implies that the parity of the +entire message flipped in order to keep + + align:start position:0% +entire message flipped in order to keep + + + align:start position:0% +entire message flipped in order to keep +the parity of the entire message odd pxx + + align:start position:0% +the parity of the entire message odd pxx + + + align:start position:0% +the parity of the entire message odd pxx +needs to be flipped as well so that + + align:start position:0% +needs to be flipped as well so that + + + align:start position:0% +needs to be flipped as well so that +there are a total of four entries being + + align:start position:0% +there are a total of four entries being + + + align:start position:0% +there are a total of four entries being +flipped which will cause the odd parity + + align:start position:0% +flipped which will cause the odd parity + + + align:start position:0% +flipped which will cause the odd parity +of the entire message to remain + + align:start position:0% +of the entire message to remain + + + align:start position:0% +of the entire message to remain +unchanged this means that our minimum + + align:start position:0% +unchanged this means that our minimum + + + align:start position:0% +unchanged this means that our minimum +Hamming distance for this encoding + + align:start position:0% +Hamming distance for this encoding + + + align:start position:0% +Hamming distance for this encoding +equals four because anytime we flip a + + align:start position:0% +equals four because anytime we flip a + + + align:start position:0% +equals four because anytime we flip a +data bit a total of four entries need to + + align:start position:0% +data bit a total of four entries need to + + + align:start position:0% +data bit a total of four entries need to +change to maintain our encoding we know + + align:start position:0% +change to maintain our encoding we know + + + align:start position:0% +change to maintain our encoding we know +that to detect an e bit error the + + align:start position:0% +that to detect an e bit error the + + + align:start position:0% +that to detect an e bit error the +hamming distance has to be greater than + + align:start position:0% +hamming distance has to be greater than + + + align:start position:0% +hamming distance has to be greater than +e or in other words the hamming distance + + align:start position:0% +e or in other words the hamming distance + + + align:start position:0% +e or in other words the hamming distance +has to be greater than or + + align:start position:0% +has to be greater than or + + + align:start position:0% +has to be greater than or +equal to e plus one so to detect a one + + align:start position:0% +equal to e plus one so to detect a one + + + align:start position:0% +equal to e plus one so to detect a one +bit error + + align:start position:0% +bit error + + + align:start position:0% +bit error +one needs a Hamming distance greater + + align:start position:0% +one needs a Hamming distance greater + + + align:start position:0% +one needs a Hamming distance greater +than or equal to two we also know that + + align:start position:0% +than or equal to two we also know that + + + align:start position:0% +than or equal to two we also know that +two correct and a bit error the Hamming + + align:start position:0% +two correct and a bit error the Hamming + + + align:start position:0% +two correct and a bit error the Hamming +distance has to be greater than two e or + + align:start position:0% +distance has to be greater than two e or + + + align:start position:0% +distance has to be greater than two e or +the Hamming distance has to be greater + + align:start position:0% +the Hamming distance has to be greater + + + align:start position:0% +the Hamming distance has to be greater +than or equal to 2 e plus one so it's a + + align:start position:0% +than or equal to 2 e plus one so it's a + + + align:start position:0% +than or equal to 2 e plus one so it's a +correct a one bit error one needs to + + align:start position:0% +correct a one bit error one needs to + + + align:start position:0% +correct a one bit error one needs to +have a Hamming distance greater than or + + align:start position:0% +have a Hamming distance greater than or + + + align:start position:0% +have a Hamming distance greater than or +equal to three for this encoding since + + align:start position:0% +equal to three for this encoding since + + + align:start position:0% +equal to three for this encoding since +our hamming distance equals four that + + align:start position:0% +our hamming distance equals four that + + + align:start position:0% +our hamming distance equals four that +means we should be able to both detect + + align:start position:0% +means we should be able to both detect + + + align:start position:0% +means we should be able to both detect +and correct one bit errors taking a look + + align:start position:0% +and correct one bit errors taking a look + + + align:start position:0% +and correct one bit errors taking a look +at this message if we check the parity + + align:start position:0% +at this message if we check the parity + + + align:start position:0% +at this message if we check the parity +of each row column and full message we + + align:start position:0% +of each row column and full message we + + + align:start position:0% +of each row column and full message we +see that in all cases our parity is odd + + align:start position:0% +see that in all cases our parity is odd + + + align:start position:0% +see that in all cases our parity is odd +since odd parity indicates a valid + + align:start position:0% +since odd parity indicates a valid + + + align:start position:0% +since odd parity indicates a valid +message there are no errors in this + + align:start position:0% +message there are no errors in this + + + align:start position:0% +message there are no errors in this +message looking at this message we see + + align:start position:0% +message looking at this message we see + + + align:start position:0% +message looking at this message we see +that all the row parodies are odd but + + align:start position:0% +that all the row parodies are odd but + + + align:start position:0% +that all the row parodies are odd but +the parity of column one is even this + + align:start position:0% +the parity of column one is even this + + + align:start position:0% +the parity of column one is even this +means that there is an error in column + + align:start position:0% +means that there is an error in column + + + align:start position:0% +means that there is an error in column +one however since there were no errors + + align:start position:0% +one however since there were no errors + + + align:start position:0% +one however since there were no errors +in the parity of the rows this means + + align:start position:0% +in the parity of the rows this means + + + align:start position:0% +in the parity of the rows this means +that the bit in error is the parity bit + + align:start position:0% +that the bit in error is the parity bit + + + align:start position:0% +that the bit in error is the parity bit +itself if we flip px one from a zero to + + align:start position:0% +itself if we flip px one from a zero to + + + align:start position:0% +itself if we flip px one from a zero to +a one we now have a valid message again + + align:start position:0% +a one we now have a valid message again + + + align:start position:0% +a one we now have a valid message again +looking at the parody of each row and + + align:start position:0% +looking at the parody of each row and + + + align:start position:0% +looking at the parody of each row and +column in this message we see that row + + align:start position:0% +column in this message we see that row + + + align:start position:0% +column in this message we see that row +zero has an even parity and column zero + + align:start position:0% +zero has an even parity and column zero + + + align:start position:0% +zero has an even parity and column zero +has an even parity this means that the + + align:start position:0% +has an even parity this means that the + + + align:start position:0% +has an even parity this means that the +database + + align:start position:0% +database + + + align:start position:0% +database +colum 0 is wrong if we flip this bit we + + align:start position:0% +colum 0 is wrong if we flip this bit we + + + align:start position:0% +colum 0 is wrong if we flip this bit we +now see that all of our row and column + + align:start position:0% +now see that all of our row and column + + + align:start position:0% +now see that all of our row and column +parodies are correct and our total + + align:start position:0% +parodies are correct and our total + + + align:start position:0% +parodies are correct and our total +message parity is correct as well so we + + align:start position:0% +message parity is correct as well so we + + + align:start position:0% +message parity is correct as well so we +have restored our message by identifying + + align:start position:0% +have restored our message by identifying + + + align:start position:0% +have restored our message by identifying +the bit and error in this example all of + + align:start position:0% +the bit and error in this example all of + + + align:start position:0% +the bit and error in this example all of +the row parodies and column parodies are + + align:start position:0% +the row parodies and column parodies are + + + align:start position:0% +the row parodies and column parodies are +odd however the parity of the entire + + align:start position:0% +odd however the parity of the entire + + + align:start position:0% +odd however the parity of the entire +message is even this means that the bit + + align:start position:0% +message is even this means that the bit + + + align:start position:0% +message is even this means that the bit +and error in this message is the pxx bit + + align:start position:0% +and error in this message is the pxx bit + + + align:start position:0% +and error in this message is the pxx bit +itself flipping that bottom-right bit + + align:start position:0% +itself flipping that bottom-right bit + + + align:start position:0% +itself flipping that bottom-right bit +results in a valid message once again + + align:start position:0% +results in a valid message once again + + + align:start position:0% +results in a valid message once again +now let's go back to our + + align:start position:0% +now let's go back to our + + + align:start position:0% +now let's go back to our +valid message and see if we can correct + + align:start position:0% +valid message and see if we can correct + + + align:start position:0% +valid message and see if we can correct +two-bit errors suppose we flip D 1 1 to + + align:start position:0% +two-bit errors suppose we flip D 1 1 to + + + align:start position:0% +two-bit errors suppose we flip D 1 1 to +0 and D 2 to 2 1 to create a 2 bit error + + align:start position:0% +0 and D 2 to 2 1 to create a 2 bit error + + + align:start position:0% +0 and D 2 to 2 1 to create a 2 bit error +now when we look at the parity of each + + align:start position:0% +now when we look at the parity of each + + + align:start position:0% +now when we look at the parity of each +row we find that both Row 1 and 2 have a + + align:start position:0% +row we find that both Row 1 and 2 have a + + + align:start position:0% +row we find that both Row 1 and 2 have a +parity error + + align:start position:0% +parity error + + + align:start position:0% +parity error +similarly columns 1 and 2 have a parity + + align:start position:0% +similarly columns 1 and 2 have a parity + + + align:start position:0% +similarly columns 1 and 2 have a parity +error the total message parity remains + + align:start position:0% +error the total message parity remains + + + align:start position:0% +error the total message parity remains +correct given this information we know + + align:start position:0% +correct given this information we know + + + align:start position:0% +correct given this information we know +that an error occurred in the + + align:start position:0% +that an error occurred in the + + + align:start position:0% +that an error occurred in the +transmission of this message but we + + align:start position:0% +transmission of this message but we + + + align:start position:0% +transmission of this message but we +cannot identify exactly which bits are + + align:start position:0% +cannot identify exactly which bits are + + + align:start position:0% +cannot identify exactly which bits are +an error because there is more than one + + align:start position:0% +an error because there is more than one + + + align:start position:0% +an error because there is more than one +possible way to alter two bits and + + align:start position:0% +possible way to alter two bits and + + + align:start position:0% +possible way to alter two bits and +arrive at a valid message this + + align:start position:0% +arrive at a valid message this + + + align:start position:0% +arrive at a valid message this +demonstrates that we can detect a two + + align:start position:0% +demonstrates that we can detect a two + + + align:start position:0% +demonstrates that we can detect a two +bit error but we can't correct a two bit + + align:start position:0% +bit error but we can't correct a two bit + + + align:start position:0% +bit error but we can't correct a two bit +error going back to our original claims + + align:start position:0% +error going back to our original claims + + + align:start position:0% +error going back to our original claims +about having distances this is in line + + align:start position:0% +about having distances this is in line + + + align:start position:0% +about having distances this is in line +with our expectations + + align:start position:0% +with our expectations + + + align:start position:0% +with our expectations +if e equals 2 meaning that we want to + + align:start position:0% +if e equals 2 meaning that we want to + + + align:start position:0% +if e equals 2 meaning that we want to +detect a 2 bit error then the Hamming + + align:start position:0% +detect a 2 bit error then the Hamming + + + align:start position:0% +detect a 2 bit error then the Hamming +distance must be greater than or equal + + align:start position:0% +distance must be greater than or equal + + + align:start position:0% +distance must be greater than or equal +to e plus 1 which equals 3 to correct + + align:start position:0% +to e plus 1 which equals 3 to correct + + + align:start position:0% +to e plus 1 which equals 3 to correct +the 2 bit error the Hamming distance + + align:start position:0% +the 2 bit error the Hamming distance + + + align:start position:0% +the 2 bit error the Hamming distance +must be greater than or equal to 2 e + + align:start position:0% +must be greater than or equal to 2 e + + + align:start position:0% +must be greater than or equal to 2 e +plus 1 which equals 5 since our Hamming + + align:start position:0% +plus 1 which equals 5 since our Hamming + + + align:start position:0% +plus 1 which equals 5 since our Hamming +distance in this problem is 4 we can + + align:start position:0% +distance in this problem is 4 we can + + + align:start position:0% +distance in this problem is 4 we can +only detect two bit errors but not + + align:start position:0% +only detect two bit errors but not + + + align:start position:0% +only detect two bit errors but not +correct them \ No newline at end of file diff --git a/2Q1GUhhc9is.txt b/2Q1GUhhc9is.txt new file mode 100644 index 0000000000000000000000000000000000000000..2d5597e782825e21e5f49cc74a999be97e91433d --- /dev/null +++ b/2Q1GUhhc9is.txt @@ -0,0 +1,16103 @@ +align:start position:0% + +last time + + align:start position:0% +last time + + + align:start position:0% +last time +we discussed standard reduction + + align:start position:0% +we discussed standard reduction + + + align:start position:0% +we discussed standard reduction +potential this e naught prime + + align:start position:0% +potential this e naught prime + + + align:start position:0% +potential this e naught prime +value that really is a way to quantitate + + align:start position:0% +value that really is a way to quantitate + + + align:start position:0% +value that really is a way to quantitate +the propensity of a molecule + + align:start position:0% +the propensity of a molecule + + + align:start position:0% +the propensity of a molecule +to accept or donate electrons + + align:start position:0% +to accept or donate electrons + + + align:start position:0% +to accept or donate electrons +and this is useful to think about + + align:start position:0% +and this is useful to think about + + + align:start position:0% +and this is useful to think about +how energy is transduced in biological + + align:start position:0% +how energy is transduced in biological + + + align:start position:0% +how energy is transduced in biological +systems because + + align:start position:0% +systems because + + + align:start position:0% +systems because +remember as i have now tried to + + align:start position:0% +remember as i have now tried to + + + align:start position:0% +remember as i have now tried to +stress many times how energy + + align:start position:0% +stress many times how energy + + + align:start position:0% +stress many times how energy +is moved through biology is largely + + align:start position:0% +is moved through biology is largely + + + align:start position:0% +is moved through biology is largely +about + + align:start position:0% +about + + + align:start position:0% +about +oxidation and reduction reactions + + align:start position:0% +oxidation and reduction reactions + + + align:start position:0% +oxidation and reduction reactions +involving + + align:start position:0% +involving + + + align:start position:0% +involving +carbon and ultimately oxygen and so + + align:start position:0% +carbon and ultimately oxygen and so + + + align:start position:0% +carbon and ultimately oxygen and so +remember that oxidation of carbon + + align:start position:0% +remember that oxidation of carbon + + + align:start position:0% +remember that oxidation of carbon +is favorable that is removing electrons + + align:start position:0% +is favorable that is removing electrons + + + align:start position:0% +is favorable that is removing electrons +from the carbon + + align:start position:0% +from the carbon + + + align:start position:0% +from the carbon +and giving them to oxygen exactly what + + align:start position:0% +and giving them to oxygen exactly what + + + align:start position:0% +and giving them to oxygen exactly what +we described for burning wood or burning + + align:start position:0% +we described for burning wood or burning + + + align:start position:0% +we described for burning wood or burning +gasoline + + align:start position:0% +gasoline + + + align:start position:0% +gasoline +and so that's why coming from the most + + align:start position:0% +and so that's why coming from the most + + + align:start position:0% +and so that's why coming from the most +reduced carbon like fatty acids or + + align:start position:0% +reduced carbon like fatty acids or + + + align:start position:0% +reduced carbon like fatty acids or +other reduced carbon like carbohydrates + + align:start position:0% +other reduced carbon like carbohydrates + + + align:start position:0% +other reduced carbon like carbohydrates +not as reduced as fatty acids + + align:start position:0% +not as reduced as fatty acids + + + align:start position:0% +not as reduced as fatty acids +that oxidizing that carbon + + align:start position:0% +that oxidizing that carbon + + + align:start position:0% +that oxidizing that carbon +releases energy and of course it means + + align:start position:0% +releases energy and of course it means + + + align:start position:0% +releases energy and of course it means +that + + align:start position:0% +that + + + align:start position:0% +that +storing carbon as reduced carbon either + + align:start position:0% +storing carbon as reduced carbon either + + + align:start position:0% +storing carbon as reduced carbon either +as carbohydrates or fatty acids + + align:start position:0% +as carbohydrates or fatty acids + + + align:start position:0% +as carbohydrates or fatty acids +is a way to store energy for later + + align:start position:0% +is a way to store energy for later + + + align:start position:0% +is a way to store energy for later +and so moving from left to right + + align:start position:0% +and so moving from left to right + + + align:start position:0% +and so moving from left to right +equilibrium strongly favors moving to + + align:start position:0% +equilibrium strongly favors moving to + + + align:start position:0% +equilibrium strongly favors moving to +the right that means that + + align:start position:0% +the right that means that + + + align:start position:0% +the right that means that +delta g is less than zero for the + + align:start position:0% +delta g is less than zero for the + + + align:start position:0% +delta g is less than zero for the +oxidation of carbon + + align:start position:0% +oxidation of carbon + + + align:start position:0% +oxidation of carbon +or we can describe this as moving from a + + align:start position:0% +or we can describe this as moving from a + + + align:start position:0% +or we can describe this as moving from a +smaller standard reduction potential to + + align:start position:0% +smaller standard reduction potential to + + + align:start position:0% +smaller standard reduction potential to +a larger standard reduction potential + + align:start position:0% +a larger standard reduction potential + + + align:start position:0% +a larger standard reduction potential +because remember the relationship + + align:start position:0% +because remember the relationship + + + align:start position:0% +because remember the relationship +between the change in standard reduction + + align:start position:0% +between the change in standard reduction + + + align:start position:0% +between the change in standard reduction +potential + + align:start position:0% +potential + + + align:start position:0% +potential +is related to um the equilibrium + + align:start position:0% +is related to um the equilibrium + + + align:start position:0% +is related to um the equilibrium +constant or delta g + + align:start position:0% +constant or delta g + + + align:start position:0% +constant or delta g +not prime um which is also related to + + align:start position:0% +not prime um which is also related to + + + align:start position:0% +not prime um which is also related to +the equilibrium constant + + align:start position:0% +the equilibrium constant + + + align:start position:0% +the equilibrium constant +by the above formula + + align:start position:0% +by the above formula + + + align:start position:0% +by the above formula +and so we closed last time + + align:start position:0% +and so we closed last time + + + align:start position:0% +and so we closed last time +by saying that with this formula we know + + align:start position:0% +by saying that with this formula we know + + + align:start position:0% +by saying that with this formula we know +that if we move from a smaller standard + + align:start position:0% +that if we move from a smaller standard + + + align:start position:0% +that if we move from a smaller standard +reduction potential + + align:start position:0% +reduction potential + + + align:start position:0% +reduction potential +that is donate electrons from a smaller + + align:start position:0% +that is donate electrons from a smaller + + + align:start position:0% +that is donate electrons from a smaller +standard reduction potential + + align:start position:0% +standard reduction potential + + + align:start position:0% +standard reduction potential +to a larger standard reduction potential + + align:start position:0% +to a larger standard reduction potential + + + align:start position:0% +to a larger standard reduction potential +that + + align:start position:0% +that + + + align:start position:0% +that +that number that difference will then be + + align:start position:0% +that number that difference will then be + + + align:start position:0% +that number that difference will then be +um positive which is the opposite of + + align:start position:0% +um positive which is the opposite of + + + align:start position:0% +um positive which is the opposite of +delta g because of that formula and so a + + align:start position:0% +delta g because of that formula and so a + + + align:start position:0% +delta g because of that formula and so a +positive change in standard reduction + + align:start position:0% +positive change in standard reduction + + + align:start position:0% +positive change in standard reduction +potential + + align:start position:0% +potential + + + align:start position:0% +potential +moving from lower to higher is going to + + align:start position:0% +moving from lower to higher is going to + + + align:start position:0% +moving from lower to higher is going to +be + + align:start position:0% +be + + + align:start position:0% +be +equilibrium is going to favor that + + align:start position:0% +equilibrium is going to favor that + + + align:start position:0% +equilibrium is going to favor that +direction + + align:start position:0% +direction + + + align:start position:0% +direction +okay should make sense from everything + + align:start position:0% +okay should make sense from everything + + + align:start position:0% +okay should make sense from everything +we + + align:start position:0% +we + + + align:start position:0% +we +discussed before and of course that + + align:start position:0% +discussed before and of course that + + + align:start position:0% +discussed before and of course that +change + + align:start position:0% +change + + + align:start position:0% +change +tells you the propensity of electron + + align:start position:0% +tells you the propensity of electron + + + align:start position:0% +tells you the propensity of electron +transfer that + + align:start position:0% +transfer that + + + align:start position:0% +transfer that +ultimately is going to be favorable at + + align:start position:0% +ultimately is going to be favorable at + + + align:start position:0% +ultimately is going to be favorable at +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +however exactly as we discussed for + + align:start position:0% +however exactly as we discussed for + + + align:start position:0% +however exactly as we discussed for +delta g whether an exact reaction is + + align:start position:0% +delta g whether an exact reaction is + + + align:start position:0% +delta g whether an exact reaction is +favorable + + align:start position:0% +favorable + + + align:start position:0% +favorable +is still going to be dependent on delta + + align:start position:0% +is still going to be dependent on delta + + + align:start position:0% +is still going to be dependent on delta +g and so + + align:start position:0% +g and so + + + align:start position:0% +g and so +the change in standard reduction + + align:start position:0% +the change in standard reduction + + + align:start position:0% +the change in standard reduction +potential tells you about the + + align:start position:0% +potential tells you about the + + + align:start position:0% +potential tells you about the +equilibrium constant + + align:start position:0% +equilibrium constant + + + align:start position:0% +equilibrium constant +and so which direction is going to be + + align:start position:0% +and so which direction is going to be + + + align:start position:0% +and so which direction is going to be +net favorable at equilibrium + + align:start position:0% +net favorable at equilibrium + + + align:start position:0% +net favorable at equilibrium +however what actually happens is still + + align:start position:0% +however what actually happens is still + + + align:start position:0% +however what actually happens is still +going to depend on conditions + + align:start position:0% +going to depend on conditions + + + align:start position:0% +going to depend on conditions +for all the reasons we talked about + + align:start position:0% +for all the reasons we talked about + + + align:start position:0% +for all the reasons we talked about +previously + + align:start position:0% +previously + + + align:start position:0% +previously +still this change in standard reduction + + align:start position:0% +still this change in standard reduction + + + align:start position:0% +still this change in standard reduction +potential is still + + align:start position:0% +potential is still + + + align:start position:0% +potential is still +a useful concept to think about + + align:start position:0% +a useful concept to think about + + + align:start position:0% +a useful concept to think about +because it tells us about how energy + + align:start position:0% +because it tells us about how energy + + + align:start position:0% +because it tells us about how energy +transfer can occur across + + align:start position:0% +transfer can occur across + + + align:start position:0% +transfer can occur across +redox pairs and that will be useful + + align:start position:0% +redox pairs and that will be useful + + + align:start position:0% +redox pairs and that will be useful +in thinking about this process of + + align:start position:0% +in thinking about this process of + + + align:start position:0% +in thinking about this process of +oxidative phosphorylation and how + + align:start position:0% +oxidative phosphorylation and how + + + align:start position:0% +oxidative phosphorylation and how +cells really couple electron transfer + + align:start position:0% +cells really couple electron transfer + + + align:start position:0% +cells really couple electron transfer +to oxygen as a way to do + + align:start position:0% +to oxygen as a way to do + + + align:start position:0% +to oxygen as a way to do +lots of useful things in cells including + + align:start position:0% +lots of useful things in cells including + + + align:start position:0% +lots of useful things in cells including +making atp now one point i want to + + align:start position:0% +making atp now one point i want to + + + align:start position:0% +making atp now one point i want to +come back to again which we discussed at + + align:start position:0% +come back to again which we discussed at + + + align:start position:0% +come back to again which we discussed at +length when we talked about + + align:start position:0% +length when we talked about + + + align:start position:0% +length when we talked about +uh changes in free energy and how that + + align:start position:0% +uh changes in free energy and how that + + + align:start position:0% +uh changes in free energy and how that +worked for + + align:start position:0% +worked for + + + align:start position:0% +worked for +pathways is that you know remember we + + align:start position:0% +pathways is that you know remember we + + + align:start position:0% +pathways is that you know remember we +discussed that if we start + + align:start position:0% +discussed that if we start + + + align:start position:0% +discussed that if we start +with wood or oil and all in one step + + align:start position:0% +with wood or oil and all in one step + + + align:start position:0% +with wood or oil and all in one step +burn it to co2 + + align:start position:0% +burn it to co2 + + + align:start position:0% +burn it to co2 +it releases a certain amount of energy + + align:start position:0% +it releases a certain amount of energy + + + align:start position:0% +it releases a certain amount of energy +or + + align:start position:0% +or + + + align:start position:0% +or +we can break that into individual steps + + align:start position:0% +we can break that into individual steps + + + align:start position:0% +we can break that into individual steps +as we did + + align:start position:0% +as we did + + + align:start position:0% +as we did +in glycolysis the same amount of energy + + align:start position:0% +in glycolysis the same amount of energy + + + align:start position:0% +in glycolysis the same amount of energy +is released but by breaking it into + + align:start position:0% +is released but by breaking it into + + + align:start position:0% +is released but by breaking it into +individual steps + + align:start position:0% +individual steps + + + align:start position:0% +individual steps +we can now capture that energy as + + align:start position:0% +we can now capture that energy as + + + align:start position:0% +we can now capture that energy as +intermediates such that we can + + align:start position:0% +intermediates such that we can + + + align:start position:0% +intermediates such that we can +say favorably synthesize atp at a high + + align:start position:0% +say favorably synthesize atp at a high + + + align:start position:0% +say favorably synthesize atp at a high +atp adp ratio in cells + + align:start position:0% +atp adp ratio in cells + + + align:start position:0% +atp adp ratio in cells +the exact same thing is true about any + + align:start position:0% +the exact same thing is true about any + + + align:start position:0% +the exact same thing is true about any +of these electron transfers + + align:start position:0% +of these electron transfers + + + align:start position:0% +of these electron transfers +there is the change in standard + + align:start position:0% +there is the change in standard + + + align:start position:0% +there is the change in standard +reduction potential or the change in + + align:start position:0% +reduction potential or the change in + + + align:start position:0% +reduction potential or the change in +free energy as one moves from electron + + align:start position:0% +free energy as one moves from electron + + + align:start position:0% +free energy as one moves from electron +transfer from + + align:start position:0% +transfer from + + + align:start position:0% +transfer from +one acceptor to one donor is the same if + + align:start position:0% +one acceptor to one donor is the same if + + + align:start position:0% +one acceptor to one donor is the same if +you go in one step + + align:start position:0% +you go in one step + + + align:start position:0% +you go in one step +or in many different steps and so by + + align:start position:0% +or in many different steps and so by + + + align:start position:0% +or in many different steps and so by +doing these stepwise + + align:start position:0% +doing these stepwise + + + align:start position:0% +doing these stepwise +electron transfers in exactly the same + + align:start position:0% +electron transfers in exactly the same + + + align:start position:0% +electron transfers in exactly the same +way we discussed + + align:start position:0% +way we discussed + + + align:start position:0% +way we discussed +about for glycolysis we can capture that + + align:start position:0% +about for glycolysis we can capture that + + + align:start position:0% +about for glycolysis we can capture that +energy release in smaller packets + + align:start position:0% +energy release in smaller packets + + + align:start position:0% +energy release in smaller packets +and this is a way to basically better + + align:start position:0% +and this is a way to basically better + + + align:start position:0% +and this is a way to basically better +harness this energy release + + align:start position:0% +harness this energy release + + + align:start position:0% +harness this energy release +to do useful things for cells ultimately + + align:start position:0% +to do useful things for cells ultimately + + + align:start position:0% +to do useful things for cells ultimately +you'll see it's how you make atp but it + + align:start position:0% +you'll see it's how you make atp but it + + + align:start position:0% +you'll see it's how you make atp but it +can do other work as well + + align:start position:0% +can do other work as well + + + align:start position:0% +can do other work as well +generate heat move ions etc + + align:start position:0% +generate heat move ions etc + + + align:start position:0% +generate heat move ions etc +and so this is really + + align:start position:0% +and so this is really + + + align:start position:0% +and so this is really +what i want to discuss today but it's + + align:start position:0% +what i want to discuss today but it's + + + align:start position:0% +what i want to discuss today but it's +important to remember + + align:start position:0% +important to remember + + + align:start position:0% +important to remember +these concepts um when we think through + + align:start position:0% +these concepts um when we think through + + + align:start position:0% +these concepts um when we think through +how these systems work and so we've now + + align:start position:0% +how these systems work and so we've now + + + align:start position:0% +how these systems work and so we've now +spent several lectures discussing the + + align:start position:0% +spent several lectures discussing the + + + align:start position:0% +spent several lectures discussing the +chemical details of how we can oxidize + + align:start position:0% +chemical details of how we can oxidize + + + align:start position:0% +chemical details of how we can oxidize +first we discuss carbohydrates then we + + align:start position:0% +first we discuss carbohydrates then we + + + align:start position:0% +first we discuss carbohydrates then we +discuss fatty acids + + align:start position:0% +discuss fatty acids + + + align:start position:0% +discuss fatty acids +and what we saw is that many of the + + align:start position:0% +and what we saw is that many of the + + + align:start position:0% +and what we saw is that many of the +electrons that are lost from the carbon + + align:start position:0% +electrons that are lost from the carbon + + + align:start position:0% +electrons that are lost from the carbon +oxidation + + align:start position:0% +oxidation + + + align:start position:0% +oxidation +are used to generate + + align:start position:0% +are used to generate + + + align:start position:0% +are used to generate +molecules such as nadh + + align:start position:0% +molecules such as nadh + + + align:start position:0% +molecules such as nadh +or fadh2 and effectively + + align:start position:0% +or fadh2 and effectively + + + align:start position:0% +or fadh2 and effectively +charge up a ratio if you will + + align:start position:0% +charge up a ratio if you will + + + align:start position:0% +charge up a ratio if you will +of reduced oxidized cofactors + + align:start position:0% +of reduced oxidized cofactors + + + align:start position:0% +of reduced oxidized cofactors +and these molecules then donate those + + align:start position:0% +and these molecules then donate those + + + align:start position:0% +and these molecules then donate those +electrons + + align:start position:0% +electrons + + + align:start position:0% +electrons +ultimately to oxygen and it's that + + align:start position:0% +ultimately to oxygen and it's that + + + align:start position:0% +ultimately to oxygen and it's that +how you couple those electron transfers + + align:start position:0% +how you couple those electron transfers + + + align:start position:0% +how you couple those electron transfers +from these carriers to oxygen + + align:start position:0% +from these carriers to oxygen + + + align:start position:0% +from these carriers to oxygen +ultimately is what oxidative + + align:start position:0% +ultimately is what oxidative + + + align:start position:0% +ultimately is what oxidative +phosphorylation is about + + align:start position:0% +phosphorylation is about + + + align:start position:0% +phosphorylation is about +as a way to um allow cells to + + align:start position:0% +as a way to um allow cells to + + + align:start position:0% +as a way to um allow cells to +convert this energy released into a + + align:start position:0% +convert this energy released into a + + + align:start position:0% +convert this energy released into a +biologically + + align:start position:0% +biologically + + + align:start position:0% +biologically +useful form now effectively the way + + align:start position:0% +useful form now effectively the way + + + align:start position:0% +useful form now effectively the way +biology does this + + align:start position:0% +biology does this + + + align:start position:0% +biology does this +is by using that favorable electron + + align:start position:0% +is by using that favorable electron + + + align:start position:0% +is by using that favorable electron +transfer + + align:start position:0% +transfer + + + align:start position:0% +transfer +to oxygen to charge a battery + + align:start position:0% +to oxygen to charge a battery + + + align:start position:0% +to oxygen to charge a battery +so really oxidative phosphorylation if + + align:start position:0% +so really oxidative phosphorylation if + + + align:start position:0% +so really oxidative phosphorylation if +you will + + align:start position:0% +you will + + + align:start position:0% +you will +is about a biological battery and it's + + align:start position:0% +is about a biological battery and it's + + + align:start position:0% +is about a biological battery and it's +really the same concepts that you may + + align:start position:0% +really the same concepts that you may + + + align:start position:0% +really the same concepts that you may +have learned in other courses about how + + align:start position:0% +have learned in other courses about how + + + align:start position:0% +have learned in other courses about how +chemical batteries work + + align:start position:0% +chemical batteries work + + + align:start position:0% +chemical batteries work +and so let's just think about that what + + align:start position:0% +and so let's just think about that what + + + align:start position:0% +and so let's just think about that what +is a battery well a battery is + + align:start position:0% +is a battery well a battery is + + + align:start position:0% +is a battery well a battery is +two different solutions of ions usually + + align:start position:0% +two different solutions of ions usually + + + align:start position:0% +two different solutions of ions usually +that is separated into two compartments + + align:start position:0% + + + + align:start position:0% + +it has a unit of + + align:start position:0% +it has a unit of + + + align:start position:0% +it has a unit of +volts that's exactly what the units are + + align:start position:0% +volts that's exactly what the units are + + + align:start position:0% +volts that's exactly what the units are +for this change in standard reduction + + align:start position:0% +for this change in standard reduction + + + align:start position:0% +for this change in standard reduction +potential + + align:start position:0% +potential + + + align:start position:0% +potential +is volts by + + align:start position:0% +is volts by + + + align:start position:0% +is volts by +using that voltage to run a current + + align:start position:0% +using that voltage to run a current + + + align:start position:0% +using that voltage to run a current +between the two + + align:start position:0% +between the two + + + align:start position:0% +between the two +compartments you can do work and + + align:start position:0% +compartments you can do work and + + + align:start position:0% +compartments you can do work and +if you short circuit a battery of course + + align:start position:0% +if you short circuit a battery of course + + + align:start position:0% +if you short circuit a battery of course +you can get some + + align:start position:0% +you can get some + + + align:start position:0% +you can get some +heat and so how are these really + + align:start position:0% +heat and so how are these really + + + align:start position:0% +heat and so how are these really +made well you basically just need + + align:start position:0% +made well you basically just need + + + align:start position:0% +made well you basically just need +to get that voltage you need to have + + align:start position:0% +to get that voltage you need to have + + + align:start position:0% +to get that voltage you need to have +some thing that insulates between those + + align:start position:0% +some thing that insulates between those + + + align:start position:0% +some thing that insulates between those +two compartments so you can then + + align:start position:0% +two compartments so you can then + + + align:start position:0% +two compartments so you can then +control electron flow from one side of + + align:start position:0% +control electron flow from one side of + + + align:start position:0% +control electron flow from one side of +the circuit to the other + + align:start position:0% +the circuit to the other + + + align:start position:0% +the circuit to the other +and it's exactly the same issue that + + align:start position:0% +and it's exactly the same issue that + + + align:start position:0% +and it's exactly the same issue that +happens + + align:start position:0% +happens + + + align:start position:0% +happens +in biology except biology needs some + + align:start position:0% +in biology except biology needs some + + + align:start position:0% +in biology except biology needs some +insulator between two compartments how + + align:start position:0% +insulator between two compartments how + + + align:start position:0% +insulator between two compartments how +do we create different compartments and + + align:start position:0% +do we create different compartments and + + + align:start position:0% +do we create different compartments and +cells + + align:start position:0% +cells + + + align:start position:0% +cells +well we create them with membranes and + + align:start position:0% +well we create them with membranes and + + + align:start position:0% +well we create them with membranes and +so + + align:start position:0% +so + + + align:start position:0% +so +an important function of membranes in + + align:start position:0% +an important function of membranes in + + + align:start position:0% +an important function of membranes in +cells + + align:start position:0% +cells + + + align:start position:0% +cells +other than things like separating + + align:start position:0% +other than things like separating + + + align:start position:0% +other than things like separating +cellular contents from the outside world + + align:start position:0% +cellular contents from the outside world + + + align:start position:0% +cellular contents from the outside world +or breaking up different organelles is + + align:start position:0% +or breaking up different organelles is + + + align:start position:0% +or breaking up different organelles is +that + + align:start position:0% +that + + + align:start position:0% +that +cells actually require a membrane + + align:start position:0% +cells actually require a membrane + + + align:start position:0% +cells actually require a membrane +they're essential for life + + align:start position:0% +they're essential for life + + + align:start position:0% +they're essential for life +because they are what allows + + align:start position:0% +because they are what allows + + + align:start position:0% +because they are what allows +an insulation between two aqueous + + align:start position:0% +an insulation between two aqueous + + + align:start position:0% +an insulation between two aqueous +compartments in a way + + align:start position:0% +compartments in a way + + + align:start position:0% +compartments in a way +that you can build a biological battery + + align:start position:0% +that you can build a biological battery + + + align:start position:0% +that you can build a biological battery +that is really central to how + + align:start position:0% +that is really central to how + + + align:start position:0% +that is really central to how +life uses energy as a way to do + + align:start position:0% +life uses energy as a way to do + + + align:start position:0% +life uses energy as a way to do +work and so life creates + + align:start position:0% +work and so life creates + + + align:start position:0% +work and so life creates +a voltage which i'm going to call delta + + align:start position:0% +a voltage which i'm going to call delta + + + align:start position:0% +a voltage which i'm going to call delta +psi delta ph we'll come back to that in + + align:start position:0% +psi delta ph we'll come back to that in + + + align:start position:0% +psi delta ph we'll come back to that in +a little bit + + align:start position:0% +a little bit + + + align:start position:0% +a little bit +to basically couple + + align:start position:0% + + + + align:start position:0% + +favorable electron transfer + + align:start position:0% +favorable electron transfer + + + align:start position:0% +favorable electron transfer +from say an electron carrier like + + align:start position:0% +from say an electron carrier like + + + align:start position:0% +from say an electron carrier like +nadnadh + + align:start position:0% + + + + align:start position:0% + +to oxygen so re-oxidizing + + align:start position:0% +to oxygen so re-oxidizing + + + align:start position:0% +to oxygen so re-oxidizing +nadh to reduce oxygen + + align:start position:0% +nadh to reduce oxygen + + + align:start position:0% +nadh to reduce oxygen +to water that + + align:start position:0% +to water that + + + align:start position:0% +to water that +is uh moving from a lower to a higher + + align:start position:0% +is uh moving from a lower to a higher + + + align:start position:0% +is uh moving from a lower to a higher +standard reduction potential + + align:start position:0% +standard reduction potential + + + align:start position:0% +standard reduction potential +that's favorable delta g dot prime is + + align:start position:0% +that's favorable delta g dot prime is + + + align:start position:0% +that's favorable delta g dot prime is +negative + + align:start position:0% +negative + + + align:start position:0% +negative +net transfer is favorable this + + align:start position:0% +net transfer is favorable this + + + align:start position:0% +net transfer is favorable this +can be coupled to + + align:start position:0% +can be coupled to + + + align:start position:0% +can be coupled to +doing some work that otherwise would be + + align:start position:0% +doing some work that otherwise would be + + + align:start position:0% +doing some work that otherwise would be +unfavorable in this case + + align:start position:0% +unfavorable in this case + + + align:start position:0% +unfavorable in this case +pumping protons from one side of the + + align:start position:0% +pumping protons from one side of the + + + align:start position:0% +pumping protons from one side of the +membrane to another + + align:start position:0% +membrane to another + + + align:start position:0% +membrane to another +by pumping protons to one side of a + + align:start position:0% +by pumping protons to one side of a + + + align:start position:0% +by pumping protons to one side of a +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +or the other you create a voltage + + align:start position:0% +or the other you create a voltage + + + align:start position:0% +or the other you create a voltage +membrane potential often abbreviated + + align:start position:0% +membrane potential often abbreviated + + + align:start position:0% +membrane potential often abbreviated +delta psi + + align:start position:0% +delta psi + + + align:start position:0% +delta psi +it's also a ph gradient so + + align:start position:0% +it's also a ph gradient so + + + align:start position:0% +it's also a ph gradient so +delta ph move protons have + + align:start position:0% +delta ph move protons have + + + align:start position:0% +delta ph move protons have +lower ph on one side of the membrane + + align:start position:0% +lower ph on one side of the membrane + + + align:start position:0% +lower ph on one side of the membrane +than the other + + align:start position:0% +than the other + + + align:start position:0% +than the other +and it's this charging of a battery at a + + align:start position:0% +and it's this charging of a battery at a + + + align:start position:0% +and it's this charging of a battery at a +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +that is what is captured by oxidative + + align:start position:0% +that is what is captured by oxidative + + + align:start position:0% +that is what is captured by oxidative +phosphorylation the + + align:start position:0% +phosphorylation the + + + align:start position:0% +phosphorylation the +what's typically referred to as that + + align:start position:0% +what's typically referred to as that + + + align:start position:0% +what's typically referred to as that +process as a way + + align:start position:0% +process as a way + + + align:start position:0% +process as a way +to make atp but of course this is a + + align:start position:0% +to make atp but of course this is a + + + align:start position:0% +to make atp but of course this is a +useful + + align:start position:0% +useful + + + align:start position:0% +useful +thing it's a battery and so it can also + + align:start position:0% +thing it's a battery and so it can also + + + align:start position:0% +thing it's a battery and so it can also +do + + align:start position:0% +do + + + align:start position:0% +do +other work for cells + + align:start position:0% + + + + align:start position:0% + +now i just want to say + + align:start position:0% +now i just want to say + + + align:start position:0% +now i just want to say +and really stress that this is really + + align:start position:0% +and really stress that this is really + + + align:start position:0% +and really stress that this is really +critical this process and it's really + + align:start position:0% +critical this process and it's really + + + align:start position:0% +critical this process and it's really +central to + + align:start position:0% +central to + + + align:start position:0% +central to +how energy works for cells + + align:start position:0% +how energy works for cells + + + align:start position:0% +how energy works for cells +you will see that effectively this + + align:start position:0% +you will see that effectively this + + + align:start position:0% +you will see that effectively this +is the key steps in photosynthesis do + + align:start position:0% +is the key steps in photosynthesis do + + + align:start position:0% +is the key steps in photosynthesis do +exactly the same thing + + align:start position:0% +exactly the same thing + + + align:start position:0% +exactly the same thing +it's how mitochondria work it's also how + + align:start position:0% +it's how mitochondria work it's also how + + + align:start position:0% +it's how mitochondria work it's also how +bacteria work and + + align:start position:0% +bacteria work and + + + align:start position:0% +bacteria work and +really prokaryotes end up doing this + + align:start position:0% +really prokaryotes end up doing this + + + align:start position:0% +really prokaryotes end up doing this +at their plasma membranes whereas + + align:start position:0% +at their plasma membranes whereas + + + align:start position:0% +at their plasma membranes whereas +mitochondria + + align:start position:0% +mitochondria + + + align:start position:0% +mitochondria +and chloroplasts end up doing this at + + align:start position:0% +and chloroplasts end up doing this at + + + align:start position:0% +and chloroplasts end up doing this at +intracellular membranes in eukaryotes + + align:start position:0% +intracellular membranes in eukaryotes + + + align:start position:0% +intracellular membranes in eukaryotes +but ultimately it's the same idea + + align:start position:0% +but ultimately it's the same idea + + + align:start position:0% +but ultimately it's the same idea +of charging this biological battery that + + align:start position:0% +of charging this biological battery that + + + align:start position:0% +of charging this biological battery that +really allows + + align:start position:0% +really allows + + + align:start position:0% +really allows +um cells to convert uh + + align:start position:0% +um cells to convert uh + + + align:start position:0% +um cells to convert uh +do energy conversions in a way that's + + align:start position:0% +do energy conversions in a way that's + + + align:start position:0% +do energy conversions in a way that's +useful for them + + align:start position:0% +useful for them + + + align:start position:0% +useful for them +to to uh to do their + + align:start position:0% +to to uh to do their + + + align:start position:0% +to to uh to do their +you know allow otherwise unfavorable + + align:start position:0% +you know allow otherwise unfavorable + + + align:start position:0% +you know allow otherwise unfavorable +things to happen + + align:start position:0% +things to happen + + + align:start position:0% +things to happen +um in cells now + + align:start position:0% +um in cells now + + + align:start position:0% +um in cells now +this works largely because you have this + + align:start position:0% +this works largely because you have this + + + align:start position:0% +this works largely because you have this +insulating membrane system which is + + align:start position:0% +insulating membrane system which is + + + align:start position:0% +insulating membrane system which is +of course made of lipids lipids are what + + align:start position:0% +of course made of lipids lipids are what + + + align:start position:0% +of course made of lipids lipids are what +separates the two compartments remember + + align:start position:0% +separates the two compartments remember + + + align:start position:0% +separates the two compartments remember +we discussed earlier that + + align:start position:0% +we discussed earlier that + + + align:start position:0% +we discussed earlier that +these lipid bilayers are useful because + + align:start position:0% +these lipid bilayers are useful because + + + align:start position:0% +these lipid bilayers are useful because +they create a + + align:start position:0% +they create a + + + align:start position:0% +they create a +hydrophobic interface between two + + align:start position:0% +hydrophobic interface between two + + + align:start position:0% +hydrophobic interface between two +aqueous + + align:start position:0% +aqueous + + + align:start position:0% +aqueous +compartments it's also useful because + + align:start position:0% +compartments it's also useful because + + + align:start position:0% +compartments it's also useful because +lipids are + + align:start position:0% +lipids are + + + align:start position:0% +lipids are +poor conductors of electrons + + align:start position:0% +poor conductors of electrons + + + align:start position:0% +poor conductors of electrons +and so this really ends up being the + + align:start position:0% +and so this really ends up being the + + + align:start position:0% +and so this really ends up being the +insulating system that makes this work + + align:start position:0% +insulating system that makes this work + + + align:start position:0% +insulating system that makes this work +now in the previous lecture we discussed + + align:start position:0% + + + + align:start position:0% + +a lot about the polar and nonpolar + + align:start position:0% +a lot about the polar and nonpolar + + + align:start position:0% +a lot about the polar and nonpolar +properties of phospholipids really allow + + align:start position:0% +properties of phospholipids really allow + + + align:start position:0% +properties of phospholipids really allow +them to assemble + + align:start position:0% +them to assemble + + + align:start position:0% +them to assemble +into these membrane barriers and i just + + align:start position:0% +into these membrane barriers and i just + + + align:start position:0% +into these membrane barriers and i just +want to do a + + align:start position:0% +want to do a + + + align:start position:0% +want to do a +slight diversion to revisit this in the + + align:start position:0% +slight diversion to revisit this in the + + + align:start position:0% +slight diversion to revisit this in the +context of + + align:start position:0% +context of + + + align:start position:0% +context of +how this works for bioenergetics + + align:start position:0% +how this works for bioenergetics + + + align:start position:0% +how this works for bioenergetics +so remember you have this lipid bilayer + + align:start position:0% +so remember you have this lipid bilayer + + + align:start position:0% +so remember you have this lipid bilayer +where you separate + + align:start position:0% + + + + align:start position:0% + +two + + align:start position:0% + + + + align:start position:0% + +aqueous compartments + + align:start position:0% +aqueous compartments + + + align:start position:0% +aqueous compartments +with this hydrophobic membrane in this + + align:start position:0% +with this hydrophobic membrane in this + + + align:start position:0% +with this hydrophobic membrane in this +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +are these phospholipids + + align:start position:0% +are these phospholipids + + + align:start position:0% +are these phospholipids +where you have these polar head groups + + align:start position:0% +where you have these polar head groups + + + align:start position:0% +where you have these polar head groups +with + + align:start position:0% +with + + + align:start position:0% +with +two lipid tails you can look back to a + + align:start position:0% +two lipid tails you can look back to a + + + align:start position:0% +two lipid tails you can look back to a +former + + align:start position:0% +former + + + align:start position:0% +former +lecture where i drew and we disguised + + align:start position:0% +lecture where i drew and we disguised + + + align:start position:0% +lecture where i drew and we disguised +that you know discuss what those + + align:start position:0% +that you know discuss what those + + + align:start position:0% +that you know discuss what those +phospholipids are in great detail + + align:start position:0% +phospholipids are in great detail + + + align:start position:0% +phospholipids are in great detail +but it's really having that polar + + align:start position:0% +but it's really having that polar + + + align:start position:0% +but it's really having that polar +non-polar interface that allows you to + + align:start position:0% +non-polar interface that allows you to + + + align:start position:0% +non-polar interface that allows you to +form these bilayers + + align:start position:0% +form these bilayers + + + align:start position:0% +form these bilayers +that's creating this separation between + + align:start position:0% +that's creating this separation between + + + align:start position:0% +that's creating this separation between +the aqueous compartments but also + + align:start position:0% +the aqueous compartments but also + + + align:start position:0% +the aqueous compartments but also +this insulator that allows a battery to + + align:start position:0% +this insulator that allows a battery to + + + align:start position:0% +this insulator that allows a battery to +be built + + align:start position:0% +be built + + + align:start position:0% +be built +across the membrane + + align:start position:0% +across the membrane + + + align:start position:0% +across the membrane +now there are several consequences + + align:start position:0% +now there are several consequences + + + align:start position:0% +now there are several consequences +though + + align:start position:0% +though + + + align:start position:0% +though +to this system that is worth thinking + + align:start position:0% +to this system that is worth thinking + + + align:start position:0% +to this system that is worth thinking +about + + align:start position:0% +about + + + align:start position:0% +about +at least in terms of how lipids and + + align:start position:0% +at least in terms of how lipids and + + + align:start position:0% +at least in terms of how lipids and +membranes + + align:start position:0% +membranes + + + align:start position:0% +membranes +work now a consequence of this is that + + align:start position:0% +work now a consequence of this is that + + + align:start position:0% +work now a consequence of this is that +if we're going to create this system + + align:start position:0% +if we're going to create this system + + + align:start position:0% +if we're going to create this system +now we create a system where we have + + align:start position:0% +now we create a system where we have + + + align:start position:0% +now we create a system where we have +issues + + align:start position:0% +issues + + + align:start position:0% +issues +with transport + + align:start position:0% + + + + align:start position:0% + +across the from one compartment to + + align:start position:0% +across the from one compartment to + + + align:start position:0% +across the from one compartment to +another + + align:start position:0% +another + + + align:start position:0% +another +now this of course is an opportunity for + + align:start position:0% +now this of course is an opportunity for + + + align:start position:0% +now this of course is an opportunity for +a layer of regulation + + align:start position:0% +a layer of regulation + + + align:start position:0% +a layer of regulation +because it also allows then these + + align:start position:0% +because it also allows then these + + + align:start position:0% +because it also allows then these +conditions where you can have + + align:start position:0% +conditions where you can have + + + align:start position:0% +conditions where you can have +different chemical conditions say + + align:start position:0% +different chemical conditions say + + + align:start position:0% +different chemical conditions say +different atp adp ratios nad nadh ratios + + align:start position:0% +different atp adp ratios nad nadh ratios + + + align:start position:0% +different atp adp ratios nad nadh ratios +in the different compartments which of + + align:start position:0% +in the different compartments which of + + + align:start position:0% +in the different compartments which of +course for all the thermodynamic reasons + + align:start position:0% +course for all the thermodynamic reasons + + + align:start position:0% +course for all the thermodynamic reasons +we've already discussed can + + align:start position:0% +we've already discussed can + + + align:start position:0% +we've already discussed can +make things more or less favorable to + + align:start position:0% +make things more or less favorable to + + + align:start position:0% +make things more or less favorable to +occur in different compartments + + align:start position:0% +occur in different compartments + + + align:start position:0% +occur in different compartments +in cells but it also means metabolism + + align:start position:0% +in cells but it also means metabolism + + + align:start position:0% +in cells but it also means metabolism +then has to have ways to + + align:start position:0% +then has to have ways to + + + align:start position:0% +then has to have ways to +transport stuff across these membranes + + align:start position:0% +transport stuff across these membranes + + + align:start position:0% +transport stuff across these membranes +and we've discussed this a couple times + + align:start position:0% +and we've discussed this a couple times + + + align:start position:0% +and we've discussed this a couple times +a few examples i talked briefly about + + align:start position:0% +a few examples i talked briefly about + + + align:start position:0% +a few examples i talked briefly about +the pyruvate carrier + + align:start position:0% +the pyruvate carrier + + + align:start position:0% +the pyruvate carrier +that is if glycolysis is happening in + + align:start position:0% +that is if glycolysis is happening in + + + align:start position:0% +that is if glycolysis is happening in +this compartment in the cytosol + + align:start position:0% +this compartment in the cytosol + + + align:start position:0% +this compartment in the cytosol +and we need to get the pyruvate inside + + align:start position:0% +and we need to get the pyruvate inside + + + align:start position:0% +and we need to get the pyruvate inside +the mitochondria + + align:start position:0% +the mitochondria + + + align:start position:0% +the mitochondria +across a membrane to for the pyruvate + + align:start position:0% +across a membrane to for the pyruvate + + + align:start position:0% +across a membrane to for the pyruvate +dehydrogenase reaction now you needed + + align:start position:0% +dehydrogenase reaction now you needed + + + align:start position:0% +dehydrogenase reaction now you needed +this pyruvate carrier molecule and it + + align:start position:0% +this pyruvate carrier molecule and it + + + align:start position:0% +this pyruvate carrier molecule and it +turns out that that transport process is + + align:start position:0% +turns out that that transport process is + + + align:start position:0% +turns out that that transport process is +an opportunity for regulation + + align:start position:0% +an opportunity for regulation + + + align:start position:0% +an opportunity for regulation +but it still needs to occur we discussed + + align:start position:0% +but it still needs to occur we discussed + + + align:start position:0% +but it still needs to occur we discussed +the carnitine + + align:start position:0% +the carnitine + + + align:start position:0% +the carnitine +shuttle right fatty acid + + align:start position:0% +shuttle right fatty acid + + + align:start position:0% +shuttle right fatty acid +are we generate fatty acyl coas from + + align:start position:0% +are we generate fatty acyl coas from + + + align:start position:0% +are we generate fatty acyl coas from +breakdown of lipids in one side and the + + align:start position:0% +breakdown of lipids in one side and the + + + align:start position:0% +breakdown of lipids in one side and the +cytosolic compartment + + align:start position:0% +cytosolic compartment + + + align:start position:0% +cytosolic compartment +need to get those fatty acyl coas into + + align:start position:0% +need to get those fatty acyl coas into + + + align:start position:0% +need to get those fatty acyl coas into +the mitochondria + + align:start position:0% +the mitochondria + + + align:start position:0% +the mitochondria +where they can be oxidized by fatty acid + + align:start position:0% +where they can be oxidized by fatty acid + + + align:start position:0% +where they can be oxidized by fatty acid +oxidation and that required that + + align:start position:0% +oxidation and that required that + + + align:start position:0% +oxidation and that required that +carnitine shuttle system now ultimately + + align:start position:0% +carnitine shuttle system now ultimately + + + align:start position:0% +carnitine shuttle system now ultimately +what mediates this transport is of + + align:start position:0% +what mediates this transport is of + + + align:start position:0% +what mediates this transport is of +course + + align:start position:0% +course + + + align:start position:0% +course +proteins that can sit within + + align:start position:0% +proteins that can sit within + + + align:start position:0% +proteins that can sit within +this membrane bilayer you can imagine + + align:start position:0% +this membrane bilayer you can imagine + + + align:start position:0% +this membrane bilayer you can imagine +you can have proteins that span the + + align:start position:0% +you can have proteins that span the + + + align:start position:0% +you can have proteins that span the +membrane bilayer such that there's + + align:start position:0% +membrane bilayer such that there's + + + align:start position:0% +membrane bilayer such that there's +hydrophilic surfaces that are on either + + align:start position:0% +hydrophilic surfaces that are on either + + + align:start position:0% +hydrophilic surfaces that are on either +face of the membrane and hydrophobic + + align:start position:0% +face of the membrane and hydrophobic + + + align:start position:0% +face of the membrane and hydrophobic +residues in the middle + + align:start position:0% +residues in the middle + + + align:start position:0% +residues in the middle +with various ways to make channels and + + align:start position:0% +with various ways to make channels and + + + align:start position:0% +with various ways to make channels and +other transport mechanisms to get things + + align:start position:0% +other transport mechanisms to get things + + + align:start position:0% +other transport mechanisms to get things +from one side of the membrane to the + + align:start position:0% +from one side of the membrane to the + + + align:start position:0% +from one side of the membrane to the +other + + align:start position:0% +other + + + align:start position:0% +other +all right or you could have complexes + + align:start position:0% +all right or you could have complexes + + + align:start position:0% +all right or you could have complexes +that float freely + + align:start position:0% +that float freely + + + align:start position:0% +that float freely +within the lipid bilayer such that + + align:start position:0% +within the lipid bilayer such that + + + align:start position:0% +within the lipid bilayer such that +there's a hydrophilic surface + + align:start position:0% +there's a hydrophilic surface + + + align:start position:0% +there's a hydrophilic surface +that faces one compartment and a + + align:start position:0% +that faces one compartment and a + + + align:start position:0% +that faces one compartment and a +hydrophobic surface + + align:start position:0% +hydrophobic surface + + + align:start position:0% +hydrophobic surface +that faces the inside of the membrane + + align:start position:0% +that faces the inside of the membrane + + + align:start position:0% +that faces the inside of the membrane +now having these complexes + + align:start position:0% +now having these complexes + + + align:start position:0% +now having these complexes +will become very important for ways in + + align:start position:0% +will become very important for ways in + + + align:start position:0% +will become very important for ways in +which + + align:start position:0% +which + + + align:start position:0% +which +one can regulate processes that occur + + align:start position:0% +one can regulate processes that occur + + + align:start position:0% +one can regulate processes that occur +either within the membrane or by moving + + align:start position:0% +either within the membrane or by moving + + + align:start position:0% +either within the membrane or by moving +things across membranes like + + align:start position:0% +things across membranes like + + + align:start position:0% +things across membranes like +generating moving protons and generating + + align:start position:0% +generating moving protons and generating + + + align:start position:0% +generating moving protons and generating +a voltage + + align:start position:0% +a voltage + + + align:start position:0% +a voltage +but it has additional consequences + + align:start position:0% +but it has additional consequences + + + align:start position:0% +but it has additional consequences +or even move large things like proteins + + align:start position:0% +or even move large things like proteins + + + align:start position:0% +or even move large things like proteins +across the membrane + + align:start position:0% +across the membrane + + + align:start position:0% +across the membrane +but it has additional consequences + + align:start position:0% +but it has additional consequences + + + align:start position:0% +but it has additional consequences +because it now means that the properties + + align:start position:0% +because it now means that the properties + + + align:start position:0% +because it now means that the properties +of the membrane + + align:start position:0% +of the membrane + + + align:start position:0% +of the membrane +also matter somewhat as well and this + + align:start position:0% +also matter somewhat as well and this + + + align:start position:0% +also matter somewhat as well and this +brings us back to the other discussion + + align:start position:0% +brings us back to the other discussion + + + align:start position:0% +brings us back to the other discussion +we had in the last lecture + + align:start position:0% +we had in the last lecture + + + align:start position:0% +we had in the last lecture +and that is how the various properties + + align:start position:0% +and that is how the various properties + + + align:start position:0% +and that is how the various properties +of the fatty acids that exist + + align:start position:0% +of the fatty acids that exist + + + align:start position:0% +of the fatty acids that exist +within this hydrophobic membrane + + align:start position:0% +within this hydrophobic membrane + + + align:start position:0% +within this hydrophobic membrane +area also now can really + + align:start position:0% +area also now can really + + + align:start position:0% +area also now can really +matter because they're going to affect + + align:start position:0% +matter because they're going to affect + + + align:start position:0% +matter because they're going to affect +things about + + align:start position:0% +things about + + + align:start position:0% +things about +how leaky this is as an insulator + + align:start position:0% +how leaky this is as an insulator + + + align:start position:0% +how leaky this is as an insulator +between the two compartments + + align:start position:0% +between the two compartments + + + align:start position:0% +between the two compartments +as well as how fluid the membrane is + + align:start position:0% +as well as how fluid the membrane is + + + align:start position:0% +as well as how fluid the membrane is +such that things like these proteins + + align:start position:0% +such that things like these proteins + + + align:start position:0% +such that things like these proteins +can actually move within this + + align:start position:0% +can actually move within this + + + align:start position:0% +can actually move within this +hydrophobic + + align:start position:0% +hydrophobic + + + align:start position:0% +hydrophobic +barrier between the two compartments + + align:start position:0% +barrier between the two compartments + + + align:start position:0% +barrier between the two compartments +in other words the fatty acid + + align:start position:0% +in other words the fatty acid + + + align:start position:0% +in other words the fatty acid +composition + + align:start position:0% + + + + align:start position:0% + +as well as the lipid species + + align:start position:0% +as well as the lipid species + + + align:start position:0% +as well as the lipid species +themselves that is which phospholipid + + align:start position:0% +themselves that is which phospholipid + + + align:start position:0% +themselves that is which phospholipid +other + + align:start position:0% +other + + + align:start position:0% +other +polar lipid species other polar + + align:start position:0% +polar lipid species other polar + + + align:start position:0% +polar lipid species other polar +hydrophobic lipid species + + align:start position:0% +hydrophobic lipid species + + + align:start position:0% +hydrophobic lipid species +analogous to phospholipids that form up + + align:start position:0% +analogous to phospholipids that form up + + + align:start position:0% +analogous to phospholipids that form up +membranes can change + + align:start position:0% +membranes can change + + + align:start position:0% +membranes can change +properties such as how leaky the + + align:start position:0% +properties such as how leaky the + + + align:start position:0% +properties such as how leaky the +membrane is + + align:start position:0% +membrane is + + + align:start position:0% +membrane is +or how fluid the membrane is + + align:start position:0% +or how fluid the membrane is + + + align:start position:0% +or how fluid the membrane is +you can imagine if you have a really + + align:start position:0% +you can imagine if you have a really + + + align:start position:0% +you can imagine if you have a really +rigid membrane surface + + align:start position:0% +rigid membrane surface + + + align:start position:0% +rigid membrane surface +you're not going to get any flow of + + align:start position:0% +you're not going to get any flow of + + + align:start position:0% +you're not going to get any flow of +materials it's not going to be very + + align:start position:0% +materials it's not going to be very + + + align:start position:0% +materials it's not going to be very +leaky + + align:start position:0% +leaky + + + align:start position:0% +leaky +which might be great if you want to + + align:start position:0% +which might be great if you want to + + + align:start position:0% +which might be great if you want to +build an insulator between the two + + align:start position:0% +build an insulator between the two + + + align:start position:0% +build an insulator between the two +compartments + + align:start position:0% +compartments + + + align:start position:0% +compartments +but it's going to be very difficult to + + align:start position:0% +but it's going to be very difficult to + + + align:start position:0% +but it's going to be very difficult to +regulate transport + + align:start position:0% +regulate transport + + + align:start position:0% +regulate transport +across that compartment and so nature + + align:start position:0% +across that compartment and so nature + + + align:start position:0% +across that compartment and so nature +has come up with a bunch of different + + align:start position:0% +has come up with a bunch of different + + + align:start position:0% +has come up with a bunch of different +solutions for how to play with fatty + + align:start position:0% +solutions for how to play with fatty + + + align:start position:0% +solutions for how to play with fatty +acid + + align:start position:0% +acid + + + align:start position:0% +acid +and other lipid composition to change + + align:start position:0% +and other lipid composition to change + + + align:start position:0% +and other lipid composition to change +the properties of membranes + + align:start position:0% +the properties of membranes + + + align:start position:0% +the properties of membranes +we don't have time to get into that in + + align:start position:0% +we don't have time to get into that in + + + align:start position:0% +we don't have time to get into that in +great detail in this course but i want + + align:start position:0% +great detail in this course but i want + + + align:start position:0% +great detail in this course but i want +you to appreciate that these things + + align:start position:0% +you to appreciate that these things + + + align:start position:0% +you to appreciate that these things +exist but one thing i want to discuss is + + align:start position:0% +exist but one thing i want to discuss is + + + align:start position:0% +exist but one thing i want to discuss is +that often when you see + + align:start position:0% +that often when you see + + + align:start position:0% +that often when you see +phospholipids drawn like this they're + + align:start position:0% +phospholipids drawn like this they're + + + align:start position:0% +phospholipids drawn like this they're +drawn in this way where the polar head + + align:start position:0% +drawn in this way where the polar head + + + align:start position:0% +drawn in this way where the polar head +group is a circle + + align:start position:0% +group is a circle + + + align:start position:0% +group is a circle +and then they'll draw the two lipid + + align:start position:0% +and then they'll draw the two lipid + + + align:start position:0% +and then they'll draw the two lipid +tails + + align:start position:0% +tails + + + align:start position:0% +tails +often with a kink in one of the lipid + + align:start position:0% +often with a kink in one of the lipid + + + align:start position:0% +often with a kink in one of the lipid +tails that's because many times + + align:start position:0% +tails that's because many times + + + align:start position:0% +tails that's because many times +phospholipids + + align:start position:0% +phospholipids + + + align:start position:0% +phospholipids +of the two lipid tails one is saturated + + align:start position:0% +of the two lipid tails one is saturated + + + align:start position:0% +of the two lipid tails one is saturated +and one is has a mono unsaturation + + align:start position:0% +and one is has a mono unsaturation + + + align:start position:0% +and one is has a mono unsaturation +in it and i just want to go back to the + + align:start position:0% +in it and i just want to go back to the + + + align:start position:0% +in it and i just want to go back to the +models here remember + + align:start position:0% +models here remember + + + align:start position:0% +models here remember +the mono unsaturated the double bond + + align:start position:0% +the mono unsaturated the double bond + + + align:start position:0% +the mono unsaturated the double bond +ends up being this + + align:start position:0% +ends up being this + + + align:start position:0% +ends up being this +cis double bond and so here's two + + align:start position:0% +cis double bond and so here's two + + + align:start position:0% +cis double bond and so here's two +fatty acids if you put these here in + + align:start position:0% +fatty acids if you put these here in + + + align:start position:0% +fatty acids if you put these here in +with the head groups on one side so this + + align:start position:0% +with the head groups on one side so this + + + align:start position:0% +with the head groups on one side so this +would be esterified to the glycerol the + + align:start position:0% +would be esterified to the glycerol the + + + align:start position:0% +would be esterified to the glycerol the +phospholipid + + align:start position:0% +phospholipid + + + align:start position:0% +phospholipid +you end up getting this kink in the + + align:start position:0% +you end up getting this kink in the + + + align:start position:0% +you end up getting this kink in the +membrane which is much different than + + align:start position:0% +membrane which is much different than + + + align:start position:0% +membrane which is much different than +two + + align:start position:0% +two + + + align:start position:0% +two +straight chains you can imagine that + + align:start position:0% +straight chains you can imagine that + + + align:start position:0% +straight chains you can imagine that +within the membrane itself + + align:start position:0% +within the membrane itself + + + align:start position:0% +within the membrane itself +this ends up basically not letting + + align:start position:0% +this ends up basically not letting + + + align:start position:0% +this ends up basically not letting +those lipid tails pack quite so tightly + + align:start position:0% +those lipid tails pack quite so tightly + + + align:start position:0% +those lipid tails pack quite so tightly +in the membrane + + align:start position:0% +in the membrane + + + align:start position:0% +in the membrane +which certainly contributes to um + + align:start position:0% +which certainly contributes to um + + + align:start position:0% +which certainly contributes to um +an ability to have space to put other + + align:start position:0% +an ability to have space to put other + + + align:start position:0% +an ability to have space to put other +stuff in the membrane + + align:start position:0% +stuff in the membrane + + + align:start position:0% +stuff in the membrane +to allow other processes to happen + + align:start position:0% +to allow other processes to happen + + + align:start position:0% +to allow other processes to happen +now recall that there's other ways we + + align:start position:0% +now recall that there's other ways we + + + align:start position:0% +now recall that there's other ways we +can + + align:start position:0% +can + + + align:start position:0% +can +modulate the properties of + + align:start position:0% +modulate the properties of + + + align:start position:0% +modulate the properties of +fatty acids introduce more double bonds + + align:start position:0% +fatty acids introduce more double bonds + + + align:start position:0% +fatty acids introduce more double bonds +chain length etc and + + align:start position:0% +chain length etc and + + + align:start position:0% +chain length etc and +different organisms use different + + align:start position:0% +different organisms use different + + + align:start position:0% +different organisms use different +strategies + + align:start position:0% +strategies + + + align:start position:0% +strategies +to deal with this and so plants + + align:start position:0% +to deal with this and so plants + + + align:start position:0% +to deal with this and so plants +remember have all kinds of + + align:start position:0% +remember have all kinds of + + + align:start position:0% +remember have all kinds of +polyunsaturated fatty acids just like we + + align:start position:0% +polyunsaturated fatty acids just like we + + + align:start position:0% +polyunsaturated fatty acids just like we +talked about with + + align:start position:0% +talked about with + + + align:start position:0% +talked about with +plant oils being liquid at room + + align:start position:0% +plant oils being liquid at room + + + align:start position:0% +plant oils being liquid at room +temperature having more + + align:start position:0% +temperature having more + + + align:start position:0% +temperature having more +polyunsaturated fatty acids in their + + align:start position:0% +polyunsaturated fatty acids in their + + + align:start position:0% +polyunsaturated fatty acids in their +lipid tails is one way plants use + + align:start position:0% +lipid tails is one way plants use + + + align:start position:0% +lipid tails is one way plants use +to keep their membranes more fluid + + align:start position:0% +to keep their membranes more fluid + + + align:start position:0% +to keep their membranes more fluid +animals remember have more saturated + + align:start position:0% +animals remember have more saturated + + + align:start position:0% +animals remember have more saturated +fatty acids + + align:start position:0% +fatty acids + + + align:start position:0% +fatty acids +all right those saturated fatty acids + + align:start position:0% +all right those saturated fatty acids + + + align:start position:0% +all right those saturated fatty acids +higher + + align:start position:0% +higher + + + align:start position:0% +higher +less double bonds going to be higher + + align:start position:0% +less double bonds going to be higher + + + align:start position:0% +less double bonds going to be higher +melting temperature more likely to be + + align:start position:0% +melting temperature more likely to be + + + align:start position:0% +melting temperature more likely to be +solid at room temperature + + align:start position:0% +solid at room temperature + + + align:start position:0% +solid at room temperature +so that's not going to be very good for + + align:start position:0% +so that's not going to be very good for + + + align:start position:0% +so that's not going to be very good for +membrane fluidity and it turns out + + align:start position:0% +membrane fluidity and it turns out + + + align:start position:0% +membrane fluidity and it turns out +animals use a different strategy to keep + + align:start position:0% +animals use a different strategy to keep + + + align:start position:0% +animals use a different strategy to keep +membrane fluidity that's not + + align:start position:0% +membrane fluidity that's not + + + align:start position:0% +membrane fluidity that's not +polyunsaturated fatty acids and that is + + align:start position:0% +polyunsaturated fatty acids and that is + + + align:start position:0% +polyunsaturated fatty acids and that is +that they incorporate + + align:start position:0% +that they incorporate + + + align:start position:0% +that they incorporate +this molecule shown here on the slide + + align:start position:0% +this molecule shown here on the slide + + + align:start position:0% +this molecule shown here on the slide +which is + + align:start position:0% +which is + + + align:start position:0% +which is +cholesterol which you're well aware of + + align:start position:0% +cholesterol which you're well aware of + + + align:start position:0% +cholesterol which you're well aware of +and so animals use + + align:start position:0% +and so animals use + + + align:start position:0% +and so animals use +use sterols like cholesterol as a way to + + align:start position:0% +use sterols like cholesterol as a way to + + + align:start position:0% +use sterols like cholesterol as a way to +keep their membranes more fluid and so + + align:start position:0% +keep their membranes more fluid and so + + + align:start position:0% +keep their membranes more fluid and so +that cholesterol + + align:start position:0% +that cholesterol + + + align:start position:0% +that cholesterol +that is present in animal products + + align:start position:0% +that is present in animal products + + + align:start position:0% +that is present in animal products +is not there to give you heart attacks + + align:start position:0% +is not there to give you heart attacks + + + align:start position:0% +is not there to give you heart attacks +it's really there + + align:start position:0% +it's really there + + + align:start position:0% +it's really there +as a way animals use to keep their + + align:start position:0% +as a way animals use to keep their + + + align:start position:0% +as a way animals use to keep their +membranes fluid + + align:start position:0% +membranes fluid + + + align:start position:0% +membranes fluid +and this is really at heart why plants + + align:start position:0% +and this is really at heart why plants + + + align:start position:0% +and this is really at heart why plants +are cholesterol free foods + + align:start position:0% +are cholesterol free foods + + + align:start position:0% +are cholesterol free foods +and animals have cholesterol and it's + + align:start position:0% +and animals have cholesterol and it's + + + align:start position:0% +and animals have cholesterol and it's +because + + align:start position:0% +because + + + align:start position:0% +because +animals use cholesterol as a way to keep + + align:start position:0% +animals use cholesterol as a way to keep + + + align:start position:0% +animals use cholesterol as a way to keep +their membranes fluid + + align:start position:0% +their membranes fluid + + + align:start position:0% +their membranes fluid +whereas plants use a different strategy + + align:start position:0% +whereas plants use a different strategy + + + align:start position:0% +whereas plants use a different strategy +polyunsaturated + + align:start position:0% +polyunsaturated + + + align:start position:0% +polyunsaturated +fatty acids all right + + align:start position:0% +fatty acids all right + + + align:start position:0% +fatty acids all right +now ultimately setting up the system + + align:start position:0% +now ultimately setting up the system + + + align:start position:0% +now ultimately setting up the system +this way + + align:start position:0% +this way + + + align:start position:0% +this way +is important because it allows for these + + align:start position:0% +is important because it allows for these + + + align:start position:0% +is important because it allows for these +flexible membranes that can + + align:start position:0% +flexible membranes that can + + + align:start position:0% +flexible membranes that can +enable ion and other transport between + + align:start position:0% +enable ion and other transport between + + + align:start position:0% +enable ion and other transport between +compartments + + align:start position:0% +compartments + + + align:start position:0% +compartments +as well as hold the charge so that you + + align:start position:0% +as well as hold the charge so that you + + + align:start position:0% +as well as hold the charge so that you +can form + + align:start position:0% +can form + + + align:start position:0% +can form +this battery which allows + + align:start position:0% +this battery which allows + + + align:start position:0% +this battery which allows +oxidative phosphorylation or other + + align:start position:0% +oxidative phosphorylation or other + + + align:start position:0% +oxidative phosphorylation or other +processes + + align:start position:0% +processes + + + align:start position:0% +processes +to occur where you can charge this + + align:start position:0% +to occur where you can charge this + + + align:start position:0% +to occur where you can charge this +membrane and + + align:start position:0% +membrane and + + + align:start position:0% +membrane and +ultimately use that voltage + + align:start position:0% +ultimately use that voltage + + + align:start position:0% +ultimately use that voltage +to do work like make atp + + align:start position:0% +to do work like make atp + + + align:start position:0% +to do work like make atp +all right now + + align:start position:0% +all right now + + + align:start position:0% +all right now +how this membrane charging occurs + + align:start position:0% +how this membrane charging occurs + + + align:start position:0% +how this membrane charging occurs +again is really taking advantage of + + align:start position:0% +again is really taking advantage of + + + align:start position:0% +again is really taking advantage of +favorable electron + + align:start position:0% +favorable electron + + + align:start position:0% +favorable electron +transfer across a series of + + align:start position:0% +transfer across a series of + + + align:start position:0% +transfer across a series of +redox pairs ultimately to + + align:start position:0% +redox pairs ultimately to + + + align:start position:0% +redox pairs ultimately to +oxygen or another good electron acceptor + + align:start position:0% +oxygen or another good electron acceptor + + + align:start position:0% +oxygen or another good electron acceptor +and it's really that + + align:start position:0% +and it's really that + + + align:start position:0% +and it's really that +favorable electron transfer that's being + + align:start position:0% +favorable electron transfer that's being + + + align:start position:0% +favorable electron transfer that's being +coupled + + align:start position:0% +coupled + + + align:start position:0% +coupled +to this pumping of proton ions to + + align:start position:0% +to this pumping of proton ions to + + + align:start position:0% +to this pumping of proton ions to +charge a battery that's the oxidation + + align:start position:0% +charge a battery that's the oxidation + + + align:start position:0% +charge a battery that's the oxidation +part + + align:start position:0% +part + + + align:start position:0% +part +and then that battery doing work + + align:start position:0% +and then that battery doing work + + + align:start position:0% +and then that battery doing work +such as driving favorable adp to atp + + align:start position:0% +such as driving favorable adp to atp + + + align:start position:0% +such as driving favorable adp to atp +conversion the phosphorylation part of + + align:start position:0% +conversion the phosphorylation part of + + + align:start position:0% +conversion the phosphorylation part of +oxidative phosphorylation + + align:start position:0% +oxidative phosphorylation + + + align:start position:0% +oxidative phosphorylation +is the type of work that you can then do + + align:start position:0% +is the type of work that you can then do + + + align:start position:0% +is the type of work that you can then do +once you generate this chemical battery + + align:start position:0% +once you generate this chemical battery + + + align:start position:0% +once you generate this chemical battery +although not the only work + + align:start position:0% +although not the only work + + + align:start position:0% +although not the only work +you can do with that battery and it's + + align:start position:0% +you can do with that battery and it's + + + align:start position:0% +you can do with that battery and it's +why this is so much more flexible + + align:start position:0% +why this is so much more flexible + + + align:start position:0% +why this is so much more flexible +than just making atp + + align:start position:0% +than just making atp + + + align:start position:0% +than just making atp +all right so ultimately + + align:start position:0% +all right so ultimately + + + align:start position:0% +all right so ultimately +this process by coupling + + align:start position:0% +this process by coupling + + + align:start position:0% +this process by coupling +transfer of electrons from favorable + + align:start position:0% +transfer of electrons from favorable + + + align:start position:0% +transfer of electrons from favorable +oxidation of carbon + + align:start position:0% +oxidation of carbon + + + align:start position:0% +oxidation of carbon +to charge up these other electron + + align:start position:0% +to charge up these other electron + + + align:start position:0% +to charge up these other electron +carriers + + align:start position:0% +carriers + + + align:start position:0% +carriers +that ultimately transfer to oxygen is + + align:start position:0% +that ultimately transfer to oxygen is + + + align:start position:0% +that ultimately transfer to oxygen is +a major way that life + + align:start position:0% +a major way that life + + + align:start position:0% +a major way that life +uses nutrient oxidation to + + align:start position:0% +uses nutrient oxidation to + + + align:start position:0% +uses nutrient oxidation to +convert it to biologically useful energy + + align:start position:0% +convert it to biologically useful energy + + + align:start position:0% +convert it to biologically useful energy +and this is where we get to this process + + align:start position:0% +and this is where we get to this process + + + align:start position:0% +and this is where we get to this process +of what is typically referred to as + + align:start position:0% +of what is typically referred to as + + + align:start position:0% +of what is typically referred to as +oxidative phosphorylation + + align:start position:0% + + + + align:start position:0% + +which is a concept or a process that was + + align:start position:0% +which is a concept or a process that was + + + align:start position:0% +which is a concept or a process that was +often abbreviated oxfos + + align:start position:0% +often abbreviated oxfos + + + align:start position:0% +often abbreviated oxfos +and it was discovered by or first + + align:start position:0% +and it was discovered by or first + + + align:start position:0% +and it was discovered by or first +described by a gentleman by the name of + + align:start position:0% +described by a gentleman by the name of + + + align:start position:0% +described by a gentleman by the name of +peter mitchell + + align:start position:0% + + + + align:start position:0% + +and like many novel or revolutionary + + align:start position:0% +and like many novel or revolutionary + + + align:start position:0% +and like many novel or revolutionary +ideas + + align:start position:0% +ideas + + + align:start position:0% +ideas +when peter mitchell first described or + + align:start position:0% +when peter mitchell first described or + + + align:start position:0% +when peter mitchell first described or +proposed + + align:start position:0% +proposed + + + align:start position:0% +proposed +the processes are about to tell you + + align:start position:0% +the processes are about to tell you + + + align:start position:0% +the processes are about to tell you +about his ideas were initially + + align:start position:0% +about his ideas were initially + + + align:start position:0% +about his ideas were initially +dismissed okay it was thought at the + + align:start position:0% +dismissed okay it was thought at the + + + align:start position:0% +dismissed okay it was thought at the +time + + align:start position:0% +time + + + align:start position:0% +time +when people were thinking about how do + + align:start position:0% +when people were thinking about how do + + + align:start position:0% +when people were thinking about how do +you couple metabolism to + + align:start position:0% +you couple metabolism to + + + align:start position:0% +you couple metabolism to +say charge up your atp adp ratio that + + align:start position:0% +say charge up your atp adp ratio that + + + align:start position:0% +say charge up your atp adp ratio that +that process would work via the + + align:start position:0% +that process would work via the + + + align:start position:0% +that process would work via the +oxidative phosphorylation + + align:start position:0% +oxidative phosphorylation + + + align:start position:0% +oxidative phosphorylation +type reactions that we otherwise + + align:start position:0% +type reactions that we otherwise + + + align:start position:0% +type reactions that we otherwise +described things like what happens at + + align:start position:0% +described things like what happens at + + + align:start position:0% +described things like what happens at +the gap dh step + + align:start position:0% +the gap dh step + + + align:start position:0% +the gap dh step +or the succinct thiokinase step in the + + align:start position:0% +or the succinct thiokinase step in the + + + align:start position:0% +or the succinct thiokinase step in the +tca cycle + + align:start position:0% +tca cycle + + + align:start position:0% +tca cycle +those are two examples where we could + + align:start position:0% +those are two examples where we could + + + align:start position:0% +those are two examples where we could +directly couple + + align:start position:0% +directly couple + + + align:start position:0% +directly couple +the oxidation of carbon + + align:start position:0% +the oxidation of carbon + + + align:start position:0% +the oxidation of carbon +to a phosphorylation event that + + align:start position:0% +to a phosphorylation event that + + + align:start position:0% +to a phosphorylation event that +ultimately allowed us + + align:start position:0% +ultimately allowed us + + + align:start position:0% +ultimately allowed us +to favorably produce atp + + align:start position:0% +to favorably produce atp + + + align:start position:0% +to favorably produce atp +to maintain an atp adp ratio that's high + + align:start position:0% +to maintain an atp adp ratio that's high + + + align:start position:0% +to maintain an atp adp ratio that's high +and is present in cells however + + align:start position:0% +and is present in cells however + + + align:start position:0% +and is present in cells however +what peter mitchell described was really + + align:start position:0% +what peter mitchell described was really + + + align:start position:0% +what peter mitchell described was really +this + + align:start position:0% +this + + + align:start position:0% +this +battery phenomena that we're talking + + align:start position:0% +battery phenomena that we're talking + + + align:start position:0% +battery phenomena that we're talking +about + + align:start position:0% +about + + + align:start position:0% +about +and it turned out to be largely right + + align:start position:0% +and it turned out to be largely right + + + align:start position:0% +and it turned out to be largely right +and + + align:start position:0% +and + + + align:start position:0% +and +represents something that's actually + + align:start position:0% +represents something that's actually + + + align:start position:0% +represents something that's actually +quite unique + + align:start position:0% +quite unique + + + align:start position:0% +quite unique +about biological processes even if you + + align:start position:0% +about biological processes even if you + + + align:start position:0% +about biological processes even if you +think about other biological processes + + align:start position:0% +think about other biological processes + + + align:start position:0% +think about other biological processes +that occur + + align:start position:0% +that occur + + + align:start position:0% +that occur +and that is what he proposed was + + align:start position:0% +and that is what he proposed was + + + align:start position:0% +and that is what he proposed was +is that the oxidation + + align:start position:0% +is that the oxidation + + + align:start position:0% +is that the oxidation +and phosphorylation + + align:start position:0% +and phosphorylation + + + align:start position:0% +and phosphorylation +events were actually separate + + align:start position:0% +events were actually separate + + + align:start position:0% +events were actually separate +processes + + align:start position:0% + + + + align:start position:0% + +that is nature does not have to have + + align:start position:0% +that is nature does not have to have + + + align:start position:0% +that is nature does not have to have +these two things + + align:start position:0% +these two things + + + align:start position:0% +these two things +touch in order for them to work that is + + align:start position:0% +touch in order for them to work that is + + + align:start position:0% +touch in order for them to work that is +that you + + align:start position:0% +that you + + + align:start position:0% +that you +use oxidation to create this battery + + align:start position:0% +use oxidation to create this battery + + + align:start position:0% +use oxidation to create this battery +as one event and then that battery + + align:start position:0% + + + + align:start position:0% + +so oxidation + + align:start position:0% + + + + align:start position:0% + +generates + + align:start position:0% + + + + align:start position:0% + +this potential across a membrane and + + align:start position:0% +this potential across a membrane and + + + align:start position:0% +this potential across a membrane and +then that + + align:start position:0% +then that + + + align:start position:0% +then that +potential across a membrane as a totally + + align:start position:0% +potential across a membrane as a totally + + + align:start position:0% +potential across a membrane as a totally +separate event + + align:start position:0% +separate event + + + align:start position:0% +separate event +can drive + + align:start position:0% +can drive + + + align:start position:0% +can drive +phosphorylation + + align:start position:0% + + + + align:start position:0% + +okay adp + + align:start position:0% + + + + align:start position:0% + +or do other work ultimately making this + + align:start position:0% +or do other work ultimately making this + + + align:start position:0% +or do other work ultimately making this +a more + + align:start position:0% +a more + + + align:start position:0% +a more +flexible system for biology + + align:start position:0% +flexible system for biology + + + align:start position:0% +flexible system for biology +and so turns out as i said before + + align:start position:0% +and so turns out as i said before + + + align:start position:0% +and so turns out as i said before +in a prokaryotic cell so this here is a + + align:start position:0% +in a prokaryotic cell so this here is a + + + align:start position:0% +in a prokaryotic cell so this here is a +some kind of prokaryote okay + + align:start position:0% +some kind of prokaryote okay + + + align:start position:0% +some kind of prokaryote okay +prokaryotes have a membrane that + + align:start position:0% +prokaryotes have a membrane that + + + align:start position:0% +prokaryotes have a membrane that +separates them from the outside world + + align:start position:0% +separates them from the outside world + + + align:start position:0% +separates them from the outside world +this cell membrane + + align:start position:0% +this cell membrane + + + align:start position:0% +this cell membrane +effectively couples that oxidation + + align:start position:0% +effectively couples that oxidation + + + align:start position:0% +effectively couples that oxidation +step to the pumping of protons that + + align:start position:0% +step to the pumping of protons that + + + align:start position:0% +step to the pumping of protons that +creates + + align:start position:0% +creates + + + align:start position:0% +creates +a + + align:start position:0% + + + + align:start position:0% + +battery at the cell membrane of the + + align:start position:0% +battery at the cell membrane of the + + + align:start position:0% +battery at the cell membrane of the +prokaryote + + align:start position:0% +prokaryote + + + align:start position:0% +prokaryote +and separate in space + + align:start position:0% +and separate in space + + + align:start position:0% +and separate in space +that can then be used to drive + + align:start position:0% +that can then be used to drive + + + align:start position:0% +that can then be used to drive +atp synthesis or do other work + + align:start position:0% +atp synthesis or do other work + + + align:start position:0% +atp synthesis or do other work +that's useful to maintain that + + align:start position:0% +that's useful to maintain that + + + align:start position:0% +that's useful to maintain that +prokaryotic cell now in + + align:start position:0% +prokaryotic cell now in + + + align:start position:0% +prokaryotic cell now in +eukaryotes + + align:start position:0% + + + + align:start position:0% + +this process occurs at membranes within + + align:start position:0% +this process occurs at membranes within + + + align:start position:0% +this process occurs at membranes within +the mitochondria so if this here is a + + align:start position:0% +the mitochondria so if this here is a + + + align:start position:0% +the mitochondria so if this here is a +mitochondria okay so just to remind + + align:start position:0% +mitochondria okay so just to remind + + + align:start position:0% +mitochondria okay so just to remind +you of some very basic + + align:start position:0% +you of some very basic + + + align:start position:0% +you of some very basic +cell biology and so remember + + align:start position:0% +cell biology and so remember + + + align:start position:0% +cell biology and so remember +mitochondria have + + align:start position:0% +mitochondria have + + + align:start position:0% +mitochondria have +two membranes so there's this outer + + align:start position:0% + + + + align:start position:0% + +mitochondrial membrane + + align:start position:0% + + + + align:start position:0% + +outer mitochondrial membrane and then + + align:start position:0% +outer mitochondrial membrane and then + + + align:start position:0% +outer mitochondrial membrane and then +there's this + + align:start position:0% +there's this + + + align:start position:0% +there's this +inner inner mitochondrial membrane + + align:start position:0% +inner inner mitochondrial membrane + + + align:start position:0% +inner inner mitochondrial membrane +okay so two membranes in the + + align:start position:0% +okay so two membranes in the + + + align:start position:0% +okay so two membranes in the +mitochondria + + align:start position:0% +mitochondria + + + align:start position:0% +mitochondria +remember there's this matrix + + align:start position:0% +remember there's this matrix + + + align:start position:0% +remember there's this matrix +space the cytosol + + align:start position:0% +space the cytosol + + + align:start position:0% +space the cytosol +would be out here and then there's this + + align:start position:0% +would be out here and then there's this + + + align:start position:0% +would be out here and then there's this +space between + + align:start position:0% +space between + + + align:start position:0% +space between +the two membranes called the + + align:start position:0% +the two membranes called the + + + align:start position:0% +the two membranes called the +inter membrane + + align:start position:0% + + + + align:start position:0% + +space inner + + align:start position:0% +space inner + + + align:start position:0% +space inner +mem inter membrane space between the two + + align:start position:0% +mem inter membrane space between the two + + + align:start position:0% +mem inter membrane space between the two +membranes + + align:start position:0% +membranes + + + align:start position:0% +membranes +if you'll recall many of these oxidation + + align:start position:0% +if you'll recall many of these oxidation + + + align:start position:0% +if you'll recall many of these oxidation +reactions the tca cycle + + align:start position:0% +reactions the tca cycle + + + align:start position:0% +reactions the tca cycle +fatty acid oxidation pyruvate + + align:start position:0% +fatty acid oxidation pyruvate + + + align:start position:0% +fatty acid oxidation pyruvate +dehydrogenase + + align:start position:0% +dehydrogenase + + + align:start position:0% +dehydrogenase +step all of those were happening in the + + align:start position:0% +step all of those were happening in the + + + align:start position:0% +step all of those were happening in the +matrix + + align:start position:0% +matrix + + + align:start position:0% +matrix +of the mitochondria remember glycolysis + + align:start position:0% +of the mitochondria remember glycolysis + + + align:start position:0% +of the mitochondria remember glycolysis +was in the cytosol + + align:start position:0% +was in the cytosol + + + align:start position:0% +was in the cytosol +but all these other processes were + + align:start position:0% +but all these other processes were + + + align:start position:0% +but all these other processes were +happening in the matrix of the + + align:start position:0% +happening in the matrix of the + + + align:start position:0% +happening in the matrix of the +mitochondria + + align:start position:0% +mitochondria + + + align:start position:0% +mitochondria +and really what's going on is that this + + align:start position:0% +and really what's going on is that this + + + align:start position:0% +and really what's going on is that this +battery + + align:start position:0% +battery + + + align:start position:0% +battery +is being charged across this inner + + align:start position:0% +is being charged across this inner + + + align:start position:0% +is being charged across this inner +mitochondrial membrane + + align:start position:0% +mitochondrial membrane + + + align:start position:0% +mitochondrial membrane +okay so protons are being pumped + + align:start position:0% +okay so protons are being pumped + + + align:start position:0% +okay so protons are being pumped +into the inner mitochondrial membrane + + align:start position:0% +into the inner mitochondrial membrane + + + align:start position:0% +into the inner mitochondrial membrane +into the inter membrane space of the + + align:start position:0% +into the inter membrane space of the + + + align:start position:0% +into the inter membrane space of the +mitochondria + + align:start position:0% +mitochondria + + + align:start position:0% +mitochondria +and then used to synthesize + + align:start position:0% +and then used to synthesize + + + align:start position:0% +and then used to synthesize +atp in the matrix of the mitochondria + + align:start position:0% +atp in the matrix of the mitochondria + + + align:start position:0% +atp in the matrix of the mitochondria +now part of this came many people know + + align:start position:0% +now part of this came many people know + + + align:start position:0% +now part of this came many people know +remember mitochondria have their own + + align:start position:0% +remember mitochondria have their own + + + align:start position:0% +remember mitochondria have their own +dna etc and so really + + align:start position:0% +dna etc and so really + + + align:start position:0% +dna etc and so really +where people thought eukaryotic + + align:start position:0% +where people thought eukaryotic + + + align:start position:0% +where people thought eukaryotic +eukaryotic cells came from + + align:start position:0% +eukaryotic cells came from + + + align:start position:0% +eukaryotic cells came from +is basically the mitochondria is an + + align:start position:0% +is basically the mitochondria is an + + + align:start position:0% +is basically the mitochondria is an +enslaved + + align:start position:0% +enslaved + + + align:start position:0% +enslaved +bacteria or a obligate captured symbiont + + align:start position:0% +bacteria or a obligate captured symbiont + + + align:start position:0% +bacteria or a obligate captured symbiont +if you will + + align:start position:0% +if you will + + + align:start position:0% +if you will +where one cell engulfed a different + + align:start position:0% +where one cell engulfed a different + + + align:start position:0% +where one cell engulfed a different +prokaryotic cell + + align:start position:0% +prokaryotic cell + + + align:start position:0% +prokaryotic cell +and if you track this + + align:start position:0% +and if you track this + + + align:start position:0% +and if you track this +think of the inner mitochondrial + + align:start position:0% +think of the inner mitochondrial + + + align:start position:0% +think of the inner mitochondrial +membrane as + + align:start position:0% +membrane as + + + align:start position:0% +membrane as +a enslaved prokaryotic cell you can see + + align:start position:0% +a enslaved prokaryotic cell you can see + + + align:start position:0% +a enslaved prokaryotic cell you can see +that you're generating + + align:start position:0% +that you're generating + + + align:start position:0% +that you're generating +this membrane potential + + align:start position:0% + + + + align:start position:0% + +across the inner mitochondrial membrane + + align:start position:0% +across the inner mitochondrial membrane + + + align:start position:0% +across the inner mitochondrial membrane +which is really equivalent + + align:start position:0% +which is really equivalent + + + align:start position:0% +which is really equivalent +to the bacterial membrane of the + + align:start position:0% +to the bacterial membrane of the + + + align:start position:0% +to the bacterial membrane of the +enslaved + + align:start position:0% +enslaved + + + align:start position:0% +enslaved +prokaryotic cell in both cases + + align:start position:0% +prokaryotic cell in both cases + + + align:start position:0% +prokaryotic cell in both cases +it's creating this battery at a membrane + + align:start position:0% +it's creating this battery at a membrane + + + align:start position:0% +it's creating this battery at a membrane +the inner mitochondrial membrane + + align:start position:0% +the inner mitochondrial membrane + + + align:start position:0% +the inner mitochondrial membrane +or the bacterial membrane of a + + align:start position:0% +or the bacterial membrane of a + + + align:start position:0% +or the bacterial membrane of a +prokaryote that is then being used + + align:start position:0% +prokaryote that is then being used + + + align:start position:0% +prokaryote that is then being used +to separately in space use that gradient + + align:start position:0% +to separately in space use that gradient + + + align:start position:0% +to separately in space use that gradient +to do work + + align:start position:0% +to do work + + + align:start position:0% +to do work +such as synthesize atp + + align:start position:0% + + + + align:start position:0% + +so if i draw this + + align:start position:0% +so if i draw this + + + align:start position:0% +so if i draw this +more explicitly is this here being + + align:start position:0% +more explicitly is this here being + + + align:start position:0% +more explicitly is this here being +the membrane so the inner mitochondrial + + align:start position:0% +the membrane so the inner mitochondrial + + + align:start position:0% +the membrane so the inner mitochondrial +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +of a mitochondria or + + align:start position:0% +of a mitochondria or + + + align:start position:0% +of a mitochondria or +the bacterial + + align:start position:0% + + + + align:start position:0% + +membrane of a prokaryotic cell such that + + align:start position:0% +membrane of a prokaryotic cell such that + + + align:start position:0% +membrane of a prokaryotic cell such that +this is outside the bacteria + + align:start position:0% +this is outside the bacteria + + + align:start position:0% +this is outside the bacteria +that's inside the bacteria this is the + + align:start position:0% +that's inside the bacteria this is the + + + align:start position:0% +that's inside the bacteria this is the +inner membrane space often referred to + + align:start position:0% +inner membrane space often referred to + + + align:start position:0% +inner membrane space often referred to +as the + + align:start position:0% +as the + + + align:start position:0% +as the +cytosol side of course there's another + + align:start position:0% +cytosol side of course there's another + + + align:start position:0% +cytosol side of course there's another +outer mitochondrial membrane here that + + align:start position:0% +outer mitochondrial membrane here that + + + align:start position:0% +outer mitochondrial membrane here that +for the + + align:start position:0% +for the + + + align:start position:0% +for the +sake of this class you can just think of + + align:start position:0% +sake of this class you can just think of + + + align:start position:0% +sake of this class you can just think of +as being generally permeable + + align:start position:0% +as being generally permeable + + + align:start position:0% +as being generally permeable +this would be the matrix side of the + + align:start position:0% +this would be the matrix side of the + + + align:start position:0% +this would be the matrix side of the +inner mitochondrial membrane + + align:start position:0% +inner mitochondrial membrane + + + align:start position:0% +inner mitochondrial membrane +and so all this + + align:start position:0% +and so all this + + + align:start position:0% +and so all this +nadh is being generated + + align:start position:0% +nadh is being generated + + + align:start position:0% +nadh is being generated +from nutrient oxidation tca cycle fatty + + align:start position:0% +from nutrient oxidation tca cycle fatty + + + align:start position:0% +from nutrient oxidation tca cycle fatty +acid oxidation pyruvate dehydrogenase + + align:start position:0% +acid oxidation pyruvate dehydrogenase + + + align:start position:0% +acid oxidation pyruvate dehydrogenase +whatever + + align:start position:0% +whatever + + + align:start position:0% +whatever +within the matrix or within the bacteria + + align:start position:0% + + + + align:start position:0% + +those electrons are ultimately being + + align:start position:0% +those electrons are ultimately being + + + align:start position:0% +those electrons are ultimately being +transferred + + align:start position:0% +transferred + + + align:start position:0% +transferred +from nadh re-oxidizing it to nad + + align:start position:0% +from nadh re-oxidizing it to nad + + + align:start position:0% +from nadh re-oxidizing it to nad +to reduce oxygen to water + + align:start position:0% +to reduce oxygen to water + + + align:start position:0% +to reduce oxygen to water +this is favorable this is + + align:start position:0% +this is favorable this is + + + align:start position:0% +this is favorable this is +therefore coupled to pumping protons + + align:start position:0% + + + + align:start position:0% + +that creates + + align:start position:0% + + + + align:start position:0% + +a membrane potential and ph gradient + + align:start position:0% +a membrane potential and ph gradient + + + align:start position:0% +a membrane potential and ph gradient +across this membrane which + + align:start position:0% +across this membrane which + + + align:start position:0% +across this membrane which +can be used to do + + align:start position:0% +can be used to do + + + align:start position:0% +can be used to do +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +work such as + + align:start position:0% + + + + align:start position:0% + +driving the synthesis of + + align:start position:0% +driving the synthesis of + + + align:start position:0% +driving the synthesis of +atp or other work so + + align:start position:0% +atp or other work so + + + align:start position:0% +atp or other work so +this all has to happen at the same + + align:start position:0% +this all has to happen at the same + + + align:start position:0% +this all has to happen at the same +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +but this process does not have to touch + + align:start position:0% +but this process does not have to touch + + + align:start position:0% +but this process does not have to touch +that process it's coupled because you + + align:start position:0% +that process it's coupled because you + + + align:start position:0% +that process it's coupled because you +create this battery + + align:start position:0% +create this battery + + + align:start position:0% +create this battery +this membrane potential and ph gradient + + align:start position:0% +this membrane potential and ph gradient + + + align:start position:0% +this membrane potential and ph gradient +that can be done that can be used + + align:start position:0% +that can be done that can be used + + + align:start position:0% +that can be done that can be used +elsewhere along the membrane to do some + + align:start position:0% +elsewhere along the membrane to do some + + + align:start position:0% +elsewhere along the membrane to do some +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +work now i draw this as delta psi delta + + align:start position:0% +work now i draw this as delta psi delta + + + align:start position:0% +work now i draw this as delta psi delta +ph you can imagine if you're moving + + align:start position:0% +ph you can imagine if you're moving + + + align:start position:0% +ph you can imagine if you're moving +protons you're going to create a voltage + + align:start position:0% +protons you're going to create a voltage + + + align:start position:0% +protons you're going to create a voltage +you're also going to create a ph + + align:start position:0% +you're also going to create a ph + + + align:start position:0% +you're also going to create a ph +gradient it turns out i don't have time + + align:start position:0% +gradient it turns out i don't have time + + + align:start position:0% +gradient it turns out i don't have time +to discuss this further in the class a + + align:start position:0% +to discuss this further in the class a + + + align:start position:0% +to discuss this further in the class a +lot is written about + + align:start position:0% +lot is written about + + + align:start position:0% +lot is written about +how to think about this membrane + + align:start position:0% +how to think about this membrane + + + align:start position:0% +how to think about this membrane +potential as either + + align:start position:0% +potential as either + + + align:start position:0% +potential as either +a true voltage or as a ph gradient + + align:start position:0% +a true voltage or as a ph gradient + + + align:start position:0% +a true voltage or as a ph gradient +it turns out that they're useful to + + align:start position:0% +it turns out that they're useful to + + + align:start position:0% +it turns out that they're useful to +think about in different ways for + + align:start position:0% +think about in different ways for + + + align:start position:0% +think about in different ways for +different processes + + align:start position:0% +different processes + + + align:start position:0% +different processes +but if you're interested in this there's + + align:start position:0% +but if you're interested in this there's + + + align:start position:0% +but if you're interested in this there's +certainly lots written about this on + + align:start position:0% +certainly lots written about this on + + + align:start position:0% +certainly lots written about this on +various um + + align:start position:0% +various um + + + align:start position:0% +various um +you know papers and texts on on on + + align:start position:0% +you know papers and texts on on on + + + align:start position:0% +you know papers and texts on on on +bioenergetics and i would encourage you + + align:start position:0% +bioenergetics and i would encourage you + + + align:start position:0% +bioenergetics and i would encourage you +to + + align:start position:0% +to + + + align:start position:0% +to +to read more about that okay + + align:start position:0% +to read more about that okay + + + align:start position:0% +to read more about that okay +all right what i want to do next then is + + align:start position:0% +all right what i want to do next then is + + + align:start position:0% +all right what i want to do next then is +discuss each of these processes in turn + + align:start position:0% +discuss each of these processes in turn + + + align:start position:0% +discuss each of these processes in turn +that is how does this work + + align:start position:0% +that is how does this work + + + align:start position:0% +that is how does this work +and how does that work um + + align:start position:0% +and how does that work um + + + align:start position:0% +and how does that work um +to really understand what's going on + + align:start position:0% +to really understand what's going on + + + align:start position:0% +to really understand what's going on +um in mitochondria and bacteria to + + align:start position:0% +um in mitochondria and bacteria to + + + align:start position:0% +um in mitochondria and bacteria to +to to carry out this process of + + align:start position:0% +to to carry out this process of + + + align:start position:0% +to to carry out this process of +oxidative phosphorylation + + align:start position:0% +oxidative phosphorylation + + + align:start position:0% +oxidative phosphorylation +so first let's talk here first how does + + align:start position:0% +so first let's talk here first how does + + + align:start position:0% +so first let's talk here first how does +one + + align:start position:0% + + + + align:start position:0% + +use favorable + + align:start position:0% +use favorable + + + align:start position:0% +use favorable +electron transfer to make + + align:start position:0% + + + + align:start position:0% + +this membrane potential + + align:start position:0% +this membrane potential + + + align:start position:0% +this membrane potential +obviously if we're going to pump protons + + align:start position:0% +obviously if we're going to pump protons + + + align:start position:0% +obviously if we're going to pump protons +against a gradient such that we have + + align:start position:0% +against a gradient such that we have + + + align:start position:0% +against a gradient such that we have +different proton gradient + + align:start position:0% +different proton gradient + + + align:start position:0% +different proton gradient +on different concentration of protons on + + align:start position:0% +on different concentration of protons on + + + align:start position:0% +on different concentration of protons on +either side of the membrane + + align:start position:0% +either side of the membrane + + + align:start position:0% +either side of the membrane +that's going to require energy input and + + align:start position:0% +that's going to require energy input and + + + align:start position:0% +that's going to require energy input and +that energy + + align:start position:0% +that energy + + + align:start position:0% +that energy +is going to come from favorable electron + + align:start position:0% +is going to come from favorable electron + + + align:start position:0% +is going to come from favorable electron +transfer + + align:start position:0% + + + + align:start position:0% + +and so really this process + + align:start position:0% +and so really this process + + + align:start position:0% +and so really this process +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +is + + align:start position:0% + + + + align:start position:0% + +taking electrons from say a cofactor + + align:start position:0% +taking electrons from say a cofactor + + + align:start position:0% +taking electrons from say a cofactor +like + + align:start position:0% +like + + + align:start position:0% +like +nadh and + + align:start position:0% + + + + align:start position:0% + +ultimately + + align:start position:0% +ultimately + + + align:start position:0% +ultimately +transferring those electrons to oxygen + + align:start position:0% +transferring those electrons to oxygen + + + align:start position:0% +transferring those electrons to oxygen +to get + + align:start position:0% +to get + + + align:start position:0% +to get +water the standard reduction potential + + align:start position:0% +water the standard reduction potential + + + align:start position:0% +water the standard reduction potential +of nadnadh is less + + align:start position:0% +of nadnadh is less + + + align:start position:0% +of nadnadh is less +than the standard reduction potential of + + align:start position:0% +than the standard reduction potential of + + + align:start position:0% +than the standard reduction potential of +oxygen in water + + align:start position:0% +oxygen in water + + + align:start position:0% +oxygen in water +that means that equilibrium is going to + + align:start position:0% +that means that equilibrium is going to + + + align:start position:0% +that means that equilibrium is going to +favor + + align:start position:0% +favor + + + align:start position:0% +favor +electron transport in this direction to + + align:start position:0% +electron transport in this direction to + + + align:start position:0% +electron transport in this direction to +say it another way + + align:start position:0% +say it another way + + + align:start position:0% +say it another way +and relative to oxygen water nadnadh is + + align:start position:0% +and relative to oxygen water nadnadh is + + + align:start position:0% +and relative to oxygen water nadnadh is +a better electron donor + + align:start position:0% +a better electron donor + + + align:start position:0% +a better electron donor +oxygen water is a better electron + + align:start position:0% +oxygen water is a better electron + + + align:start position:0% +oxygen water is a better electron +acceptor + + align:start position:0% +acceptor + + + align:start position:0% +acceptor +pair and so by + + align:start position:0% +pair and so by + + + align:start position:0% +pair and so by +this electron transfer being favorable + + align:start position:0% +this electron transfer being favorable + + + align:start position:0% +this electron transfer being favorable +it + + align:start position:0% +it + + + align:start position:0% +it +can be used then to release energy + + align:start position:0% +can be used then to release energy + + + align:start position:0% +can be used then to release energy +coupled to other processes such as + + align:start position:0% +coupled to other processes such as + + + align:start position:0% +coupled to other processes such as +moving protons + + align:start position:0% +moving protons + + + align:start position:0% +moving protons +and make that otherwise unfavorable + + align:start position:0% +and make that otherwise unfavorable + + + align:start position:0% +and make that otherwise unfavorable +process + + align:start position:0% +process + + + align:start position:0% +process +favorable now you'll note + + align:start position:0% +favorable now you'll note + + + align:start position:0% +favorable now you'll note +that in doing this we now regenerate + + align:start position:0% +that in doing this we now regenerate + + + align:start position:0% +that in doing this we now regenerate +the oxidized cofactor nad plus and so + + align:start position:0% +the oxidized cofactor nad plus and so + + + align:start position:0% +the oxidized cofactor nad plus and so +that solves our electron balance problem + + align:start position:0% +that solves our electron balance problem + + + align:start position:0% +that solves our electron balance problem +for glycolysis + + align:start position:0% +for glycolysis + + + align:start position:0% +for glycolysis +solves any electron balance problem that + + align:start position:0% +solves any electron balance problem that + + + align:start position:0% +solves any electron balance problem that +would exist for + + align:start position:0% +would exist for + + + align:start position:0% +would exist for +fatty acid oxidation or the tca cycle + + align:start position:0% +fatty acid oxidation or the tca cycle + + + align:start position:0% +fatty acid oxidation or the tca cycle +in the mitochondria because ultimately + + align:start position:0% +in the mitochondria because ultimately + + + align:start position:0% +in the mitochondria because ultimately +those electrons are being given + + align:start position:0% +those electrons are being given + + + align:start position:0% +those electrons are being given +to oxygen and so oxygen being this final + + align:start position:0% +to oxygen and so oxygen being this final + + + align:start position:0% +to oxygen and so oxygen being this final +electron acceptor being + + align:start position:0% +electron acceptor being + + + align:start position:0% +electron acceptor being +stoichiometrically + + align:start position:0% +stoichiometrically + + + align:start position:0% +stoichiometrically +produced to generate water is + + align:start position:0% +produced to generate water is + + + align:start position:0% +produced to generate water is +effectively water being the alternative + + align:start position:0% +effectively water being the alternative + + + align:start position:0% +effectively water being the alternative +waste product + + align:start position:0% +waste product + + + align:start position:0% +waste product +to say lactate or ethanol that we saw in + + align:start position:0% +to say lactate or ethanol that we saw in + + + align:start position:0% +to say lactate or ethanol that we saw in +fermentation all right now as + + align:start position:0% +fermentation all right now as + + + align:start position:0% +fermentation all right now as +we started the lecture with and + + align:start position:0% +we started the lecture with and + + + align:start position:0% +we started the lecture with and +discussed in glycolysis + + align:start position:0% +discussed in glycolysis + + + align:start position:0% +discussed in glycolysis +if we do this in one step it's favorable + + align:start position:0% +if we do this in one step it's favorable + + + align:start position:0% +if we do this in one step it's favorable +but it's also favorable + + align:start position:0% +but it's also favorable + + + align:start position:0% +but it's also favorable +if we do it in lots of little steps + + align:start position:0% +if we do it in lots of little steps + + + align:start position:0% +if we do it in lots of little steps +by doing it in lots of little steps just + + align:start position:0% +by doing it in lots of little steps just + + + align:start position:0% +by doing it in lots of little steps just +like we did in glycolysis + + align:start position:0% +like we did in glycolysis + + + align:start position:0% +like we did in glycolysis +we can break up that energy release in a + + align:start position:0% +we can break up that energy release in a + + + align:start position:0% +we can break up that energy release in a +way to allow us to do + + align:start position:0% +way to allow us to do + + + align:start position:0% +way to allow us to do +more work right so on glycolysis + + align:start position:0% +more work right so on glycolysis + + + align:start position:0% +more work right so on glycolysis +we could turn carbohydrate + + align:start position:0% +we could turn carbohydrate + + + align:start position:0% +we could turn carbohydrate +into co2 one step burning wood release a + + align:start position:0% +into co2 one step burning wood release a + + + align:start position:0% +into co2 one step burning wood release a +lot of light and heat + + align:start position:0% +lot of light and heat + + + align:start position:0% +lot of light and heat +all in one step that can be used to do + + align:start position:0% +all in one step that can be used to do + + + align:start position:0% +all in one step that can be used to do +work + + align:start position:0% +work + + + align:start position:0% +work +but it was more efficient to break it up + + align:start position:0% +but it was more efficient to break it up + + + align:start position:0% +but it was more efficient to break it up +into little steps where we could then + + align:start position:0% +into little steps where we could then + + + align:start position:0% +into little steps where we could then +capture intermediates that made atp + + align:start position:0% +capture intermediates that made atp + + + align:start position:0% +capture intermediates that made atp +synthesis favorable + + align:start position:0% +synthesis favorable + + + align:start position:0% +synthesis favorable +despite a high atp adp ratio same idea + + align:start position:0% +despite a high atp adp ratio same idea + + + align:start position:0% +despite a high atp adp ratio same idea +here we could transfer this all in one + + align:start position:0% +here we could transfer this all in one + + + align:start position:0% +here we could transfer this all in one +step + + align:start position:0% +step + + + align:start position:0% +step +but instead you break it up into a bunch + + align:start position:0% +but instead you break it up into a bunch + + + align:start position:0% +but instead you break it up into a bunch +of individual steps + + align:start position:0% +of individual steps + + + align:start position:0% +of individual steps +which can then be coupled individually + + align:start position:0% +which can then be coupled individually + + + align:start position:0% +which can then be coupled individually +to pumping protons across the membrane + + align:start position:0% +to pumping protons across the membrane + + + align:start position:0% +to pumping protons across the membrane +to generate more efficiently this uh + + align:start position:0% +to generate more efficiently this uh + + + align:start position:0% +to generate more efficiently this uh +delta psi delta ph charge this battery + + align:start position:0% +delta psi delta ph charge this battery + + + align:start position:0% +delta psi delta ph charge this battery +and so this occurs across + + align:start position:0% +and so this occurs across + + + align:start position:0% +and so this occurs across +a series of electron carriers + + align:start position:0% +a series of electron carriers + + + align:start position:0% +a series of electron carriers +multi-protein + + align:start position:0% +multi-protein + + + align:start position:0% +multi-protein +complexes electron carriers called the + + align:start position:0% +complexes electron carriers called the + + + align:start position:0% +complexes electron carriers called the +electron + + align:start position:0% +electron + + + align:start position:0% +electron +transport chain + + align:start position:0% +transport chain + + + align:start position:0% +transport chain +okay and you can think of this electron + + align:start position:0% +okay and you can think of this electron + + + align:start position:0% +okay and you can think of this electron +transport chain + + align:start position:0% +transport chain + + + align:start position:0% +transport chain +as being entirely analogous to what we + + align:start position:0% +as being entirely analogous to what we + + + align:start position:0% +as being entirely analogous to what we +already talked about + + align:start position:0% +already talked about + + + align:start position:0% +already talked about +when we talked about how pyruvate + + align:start position:0% +when we talked about how pyruvate + + + align:start position:0% +when we talked about how pyruvate +dehydrogenase or alpha-ketoglutarate + + align:start position:0% +dehydrogenase or alpha-ketoglutarate + + + align:start position:0% +dehydrogenase or alpha-ketoglutarate +dehydrogenase works when we talked about + + align:start position:0% +dehydrogenase works when we talked about + + + align:start position:0% +dehydrogenase works when we talked about +the tca cycle + + align:start position:0% +the tca cycle + + + align:start position:0% +the tca cycle +remember these have these different + + align:start position:0% +remember these have these different + + + align:start position:0% +remember these have these different +protein complexes this e1 e2 e3 + + align:start position:0% +protein complexes this e1 e2 e3 + + + align:start position:0% +protein complexes this e1 e2 e3 +where electrons were transferred across + + align:start position:0% +where electrons were transferred across + + + align:start position:0% +where electrons were transferred across +this chain it's exactly the same idea + + align:start position:0% +this chain it's exactly the same idea + + + align:start position:0% +this chain it's exactly the same idea +here + + align:start position:0% +here + + + align:start position:0% +here +a number of multi-polypeptide encoded + + align:start position:0% +a number of multi-polypeptide encoded + + + align:start position:0% +a number of multi-polypeptide encoded +protein complexes that come together + + align:start position:0% +protein complexes that come together + + + align:start position:0% +protein complexes that come together +to hold a bunch of electron carriers + + align:start position:0% +to hold a bunch of electron carriers + + + align:start position:0% +to hold a bunch of electron carriers +that break up the energy release if you + + align:start position:0% +that break up the energy release if you + + + align:start position:0% +that break up the energy release if you +will + + align:start position:0% +will + + + align:start position:0% +will +as we oxidize nadh and reduce + + align:start position:0% +as we oxidize nadh and reduce + + + align:start position:0% +as we oxidize nadh and reduce +oxygen and transfer those electrons + + align:start position:0% +oxygen and transfer those electrons + + + align:start position:0% +oxygen and transfer those electrons +along the chain + + align:start position:0% +along the chain + + + align:start position:0% +along the chain +with the complexes themselves coupling + + align:start position:0% +with the complexes themselves coupling + + + align:start position:0% +with the complexes themselves coupling +the favorable electron transfer + + align:start position:0% +the favorable electron transfer + + + align:start position:0% +the favorable electron transfer +to the moving of protons against a + + align:start position:0% +to the moving of protons against a + + + align:start position:0% +to the moving of protons against a +gradient + + align:start position:0% +gradient + + + align:start position:0% +gradient +across the membrane to work and so + + align:start position:0% +across the membrane to work and so + + + align:start position:0% +across the membrane to work and so +for this electron transport chain to + + align:start position:0% +for this electron transport chain to + + + align:start position:0% +for this electron transport chain to +work + + align:start position:0% +work + + + align:start position:0% +work +we obviously need a bunch of electron + + align:start position:0% +we obviously need a bunch of electron + + + align:start position:0% +we obviously need a bunch of electron +carriers + + align:start position:0% +carriers + + + align:start position:0% +carriers +and why you need more than one electron + + align:start position:0% +and why you need more than one electron + + + align:start position:0% +and why you need more than one electron +carrier should now be obvious + + align:start position:0% +carrier should now be obvious + + + align:start position:0% +carrier should now be obvious +because having different carriers at + + align:start position:0% +because having different carriers at + + + align:start position:0% +because having different carriers at +that sit at + + align:start position:0% +that sit at + + + align:start position:0% +that sit at +different standard reduction potentials + + align:start position:0% +different standard reduction potentials + + + align:start position:0% +different standard reduction potentials +is going to be + + align:start position:0% +is going to be + + + align:start position:0% +is going to be +useful if we want to build a change such + + align:start position:0% +useful if we want to build a change such + + + align:start position:0% +useful if we want to build a change such +that we can have + + align:start position:0% +that we can have + + + align:start position:0% +that we can have +favorable oxidation and reduction + + align:start position:0% +favorable oxidation and reduction + + + align:start position:0% +favorable oxidation and reduction +to move electrons in a favorable + + align:start position:0% +to move electrons in a favorable + + + align:start position:0% +to move electrons in a favorable +direction and + + align:start position:0% +direction and + + + align:start position:0% +direction and +couple that to processes that allow us + + align:start position:0% +couple that to processes that allow us + + + align:start position:0% +couple that to processes that allow us +to + + align:start position:0% +to + + + align:start position:0% +to +charge this battery and so it turns out + + align:start position:0% +charge this battery and so it turns out + + + align:start position:0% +charge this battery and so it turns out +that for this electron transport chain + + align:start position:0% +that for this electron transport chain + + + align:start position:0% +that for this electron transport chain +to work + + align:start position:0% +to work + + + align:start position:0% +to work +what we know about some of our electron + + align:start position:0% +what we know about some of our electron + + + align:start position:0% +what we know about some of our electron +carriers so we've discussed + + align:start position:0% +carriers so we've discussed + + + align:start position:0% +carriers so we've discussed +nad nadh there's fad + + align:start position:0% +nad nadh there's fad + + + align:start position:0% +nad nadh there's fad +fadh2 there is lipoic acid + + align:start position:0% + + + + align:start position:0% + +lipoic acid is not part of the electron + + align:start position:0% +lipoic acid is not part of the electron + + + align:start position:0% +lipoic acid is not part of the electron +transport chain + + align:start position:0% +transport chain + + + align:start position:0% +transport chain +nadnadh is a donor you'll see fad is + + align:start position:0% +nadnadh is a donor you'll see fad is + + + align:start position:0% +nadnadh is a donor you'll see fad is +can be part of the electron transport + + align:start position:0% +can be part of the electron transport + + + align:start position:0% +can be part of the electron transport +chain but there's a different + + align:start position:0% +chain but there's a different + + + align:start position:0% +chain but there's a different +there's additional electron carriers i + + align:start position:0% +there's additional electron carriers i + + + align:start position:0% +there's additional electron carriers i +want to discuss those + + align:start position:0% +want to discuss those + + + align:start position:0% +want to discuss those +now so another important one is + + align:start position:0% +now so another important one is + + + align:start position:0% +now so another important one is +something called + + align:start position:0% +something called + + + align:start position:0% +something called +fmn or flavin + + align:start position:0% + + + + align:start position:0% + +mono nucleotide + + align:start position:0% +mono nucleotide + + + align:start position:0% +mono nucleotide +what fmn or flavin mononucleotide is + + align:start position:0% +what fmn or flavin mononucleotide is + + + align:start position:0% +what fmn or flavin mononucleotide is +it's it's effectively fad + + align:start position:0% +it's it's effectively fad + + + align:start position:0% +it's it's effectively fad +but it's fad not in a dinucleotide state + + align:start position:0% +but it's fad not in a dinucleotide state + + + align:start position:0% +but it's fad not in a dinucleotide state +but + + align:start position:0% +but + + + align:start position:0% +but +a mononucleotide state so if you take + + align:start position:0% +a mononucleotide state so if you take + + + align:start position:0% +a mononucleotide state so if you take +fad + + align:start position:0% +fad + + + align:start position:0% +fad +and you remove an amp group from it what + + align:start position:0% +and you remove an amp group from it what + + + align:start position:0% +and you remove an amp group from it what +you're left with is + + align:start position:0% +you're left with is + + + align:start position:0% +you're left with is +fmn so just to remind you + + align:start position:0% +fmn so just to remind you + + + align:start position:0% +fmn so just to remind you +to be explicit about this so + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% + + + + align:start position:0% + +three four + + align:start position:0% +three four + + + align:start position:0% +three four +okay so you have this flavin group + + align:start position:0% +okay so you have this flavin group + + + align:start position:0% +okay so you have this flavin group +attached to this + + align:start position:0% +attached to this + + + align:start position:0% +attached to this +ribotol group with a phosphate on it + + align:start position:0% +ribotol group with a phosphate on it + + + align:start position:0% +ribotol group with a phosphate on it +if i put another phosphate and an + + align:start position:0% +if i put another phosphate and an + + + align:start position:0% +if i put another phosphate and an +adenine nucleotide here an amp + + align:start position:0% +adenine nucleotide here an amp + + + align:start position:0% +adenine nucleotide here an amp +group attached here that would be fad + + align:start position:0% +group attached here that would be fad + + + align:start position:0% +group attached here that would be fad +this would be + + align:start position:0% +this would be + + + align:start position:0% +this would be +fmn mononucleotide instead of a + + align:start position:0% +fmn mononucleotide instead of a + + + align:start position:0% +fmn mononucleotide instead of a +dinucleotide + + align:start position:0% +dinucleotide + + + align:start position:0% +dinucleotide +this is fmn in the + + align:start position:0% +this is fmn in the + + + align:start position:0% +this is fmn in the +oxidized form and just like + + align:start position:0% +oxidized form and just like + + + align:start position:0% +oxidized form and just like +fad it can accept + + align:start position:0% + + + + align:start position:0% + +an electron pair so here's our hydride + + align:start position:0% +an electron pair so here's our hydride + + + align:start position:0% +an electron pair so here's our hydride +ion + + align:start position:0% +ion + + + align:start position:0% +ion +two electrons we just draw here the + + align:start position:0% +two electrons we just draw here the + + + align:start position:0% +two electrons we just draw here the +middle part + + align:start position:0% +middle part + + + align:start position:0% +middle part +of the molecule + + align:start position:0% + + + + align:start position:0% + +and so this here would be fm + + align:start position:0% + + + + align:start position:0% + +fmnh2 + + align:start position:0% +fmnh2 + + + align:start position:0% +fmnh2 +or + + align:start position:0% + + + + align:start position:0% + +the reduced form of this electron + + align:start position:0% +the reduced form of this electron + + + align:start position:0% +the reduced form of this electron +carrier okay so flavin mononucleotide + + align:start position:0% +carrier okay so flavin mononucleotide + + + align:start position:0% +carrier okay so flavin mononucleotide +part of the electron transport chain now + + align:start position:0% +part of the electron transport chain now + + + align:start position:0% +part of the electron transport chain now +note fmn + + align:start position:0% +note fmn + + + align:start position:0% +note fmn +fad nad all of these things are + + align:start position:0% +fad nad all of these things are + + + align:start position:0% +fad nad all of these things are +two electron carriers right we disguised + + align:start position:0% +two electron carriers right we disguised + + + align:start position:0% +two electron carriers right we disguised +the mechanism of + + align:start position:0% +the mechanism of + + + align:start position:0% +the mechanism of +all of them just reminded you of it + + align:start position:0% +all of them just reminded you of it + + + align:start position:0% +all of them just reminded you of it +these hydride ion transfers + + align:start position:0% +these hydride ion transfers + + + align:start position:0% +these hydride ion transfers +two electron carriers turns out the + + align:start position:0% +two electron carriers turns out the + + + align:start position:0% +two electron carriers turns out the +electron transport chain + + align:start position:0% +electron transport chain + + + align:start position:0% +electron transport chain +also uses metal ions as electron + + align:start position:0% +also uses metal ions as electron + + + align:start position:0% +also uses metal ions as electron +carriers + + align:start position:0% +carriers + + + align:start position:0% +carriers +and so lots of minerals in our diet + + align:start position:0% +and so lots of minerals in our diet + + + align:start position:0% +and so lots of minerals in our diet +things like iron + + align:start position:0% +things like iron + + + align:start position:0% +things like iron +it turns out elemental iron is a great + + align:start position:0% +it turns out elemental iron is a great + + + align:start position:0% +it turns out elemental iron is a great +electron carrier and it's very important + + align:start position:0% +electron carrier and it's very important + + + align:start position:0% +electron carrier and it's very important +for + + align:start position:0% +for + + + align:start position:0% +for +this for electron transport chain now + + align:start position:0% +this for electron transport chain now + + + align:start position:0% +this for electron transport chain now +elemental metals are one electron + + align:start position:0% +elemental metals are one electron + + + align:start position:0% +elemental metals are one electron +carriers + + align:start position:0% +carriers + + + align:start position:0% +carriers +and so there's a few ways you + + align:start position:0% +and so there's a few ways you + + + align:start position:0% +and so there's a few ways you +incorporate iron + + align:start position:0% +incorporate iron + + + align:start position:0% +incorporate iron +one is something called iron sulfur + + align:start position:0% +one is something called iron sulfur + + + align:start position:0% +one is something called iron sulfur +clusters + + align:start position:0% +clusters + + + align:start position:0% +clusters +and so iron sulfur clusters is within a + + align:start position:0% +and so iron sulfur clusters is within a + + + align:start position:0% +and so iron sulfur clusters is within a +protein + + align:start position:0% +protein + + + align:start position:0% +protein +you have some cysteine residues + + align:start position:0% + + + + align:start position:0% + +and those cysteine residues can + + align:start position:0% +and those cysteine residues can + + + align:start position:0% +and those cysteine residues can +coordinate + + align:start position:0% +coordinate + + + align:start position:0% +coordinate +on iron atom and so that iron + + align:start position:0% +on iron atom and so that iron + + + align:start position:0% +on iron atom and so that iron +atom can sit in the three plus + + align:start position:0% +atom can sit in the three plus + + + align:start position:0% +atom can sit in the three plus +versus two plus state okay + + align:start position:0% +versus two plus state okay + + + align:start position:0% +versus two plus state okay +oxidized reduced + + align:start position:0% + + + + align:start position:0% + +so reduction of the iron oxidation + + align:start position:0% +so reduction of the iron oxidation + + + align:start position:0% +so reduction of the iron oxidation +of the iron okay so one electron + + align:start position:0% +of the iron okay so one electron + + + align:start position:0% +of the iron okay so one electron +carrier move one electron that way also + + align:start position:0% +carrier move one electron that way also + + + align:start position:0% +carrier move one electron that way also +iron sits within molecules called + + align:start position:0% +iron sits within molecules called + + + align:start position:0% +iron sits within molecules called +cytochromes so + + align:start position:0% +cytochromes so + + + align:start position:0% +cytochromes so +what are cytochromes this is a iron atom + + align:start position:0% +what are cytochromes this is a iron atom + + + align:start position:0% +what are cytochromes this is a iron atom +that's + + align:start position:0% +that's + + + align:start position:0% +that's +basically chelated into a porphyrin + + align:start position:0% +basically chelated into a porphyrin + + + align:start position:0% +basically chelated into a porphyrin +very similar to what you saw for + + align:start position:0% +very similar to what you saw for + + + align:start position:0% +very similar to what you saw for +hemoglobin and so + + align:start position:0% + + + + align:start position:0% + +you have an iron two plus or three plus + + align:start position:0% +you have an iron two plus or three plus + + + align:start position:0% +you have an iron two plus or three plus +that's chelated here into the + + align:start position:0% + + + + align:start position:0% + +this porphyrin ring structure + + align:start position:0% + + + + align:start position:0% + +okay lots of conjugated double bond + + align:start position:0% +okay lots of conjugated double bond + + + align:start position:0% +okay lots of conjugated double bond +systems in it + + align:start position:0% +systems in it + + + align:start position:0% +systems in it +this should look very similar porphyrin + + align:start position:0% +this should look very similar porphyrin + + + align:start position:0% +this should look very similar porphyrin +is the thing on the outside coordinates + + align:start position:0% +is the thing on the outside coordinates + + + align:start position:0% +is the thing on the outside coordinates +an iron atom in the middle + + align:start position:0% +an iron atom in the middle + + + align:start position:0% +an iron atom in the middle +that can move between the two plus and + + align:start position:0% +that can move between the two plus and + + + align:start position:0% +that can move between the two plus and +the three plus state just like we do for + + align:start position:0% +the three plus state just like we do for + + + align:start position:0% +the three plus state just like we do for +iron sulfur clusters + + align:start position:0% +iron sulfur clusters + + + align:start position:0% +iron sulfur clusters +so carry electrons be oxidized or + + align:start position:0% +so carry electrons be oxidized or + + + align:start position:0% +so carry electrons be oxidized or +reduced + + align:start position:0% +reduced + + + align:start position:0% +reduced +three plus or two plus and ultimately + + align:start position:0% +three plus or two plus and ultimately + + + align:start position:0% +three plus or two plus and ultimately +this porphyrin is + + align:start position:0% +this porphyrin is + + + align:start position:0% +this porphyrin is +can have some r groups added here + + align:start position:0% + + + + align:start position:0% + +can be associated with it or bound to + + align:start position:0% +can be associated with it or bound to + + + align:start position:0% +can be associated with it or bound to +cysteine residues within + + align:start position:0% +cysteine residues within + + + align:start position:0% +cysteine residues within +proteins effectively these molecules + + align:start position:0% +proteins effectively these molecules + + + align:start position:0% +proteins effectively these molecules +varying these r groups and how it's + + align:start position:0% +varying these r groups and how it's + + + align:start position:0% +varying these r groups and how it's +attached to proteins + + align:start position:0% +attached to proteins + + + align:start position:0% +attached to proteins +gives you different families of + + align:start position:0% +gives you different families of + + + align:start position:0% +gives you different families of +cytochromes + + align:start position:0% +cytochromes + + + align:start position:0% +cytochromes +referred to as cytochrome + + align:start position:0% +referred to as cytochrome + + + align:start position:0% +referred to as cytochrome +a the b type cytochromes and + + align:start position:0% +a the b type cytochromes and + + + align:start position:0% +a the b type cytochromes and +cytochrome c these are associated with + + align:start position:0% +cytochrome c these are associated with + + + align:start position:0% +cytochrome c these are associated with +enzyme complexes cytochrome c it's + + align:start position:0% +enzyme complexes cytochrome c it's + + + align:start position:0% +enzyme complexes cytochrome c it's +actually covalently bound + + align:start position:0% +actually covalently bound + + + align:start position:0% +actually covalently bound +to the polypeptide itself + + align:start position:0% +to the polypeptide itself + + + align:start position:0% +to the polypeptide itself +basically these are named because you + + align:start position:0% +basically these are named because you + + + align:start position:0% +basically these are named because you +have these different conjugated + + align:start position:0% +have these different conjugated + + + align:start position:0% +have these different conjugated +ring structures here that and how the r + + align:start position:0% +ring structures here that and how the r + + + align:start position:0% +ring structures here that and how the r +groups are will slightly + + align:start position:0% +groups are will slightly + + + align:start position:0% +groups are will slightly +change so this will absorb visible light + + align:start position:0% +change so this will absorb visible light + + + align:start position:0% +change so this will absorb visible light +that'll slightly change the absorption + + align:start position:0% +that'll slightly change the absorption + + + align:start position:0% +that'll slightly change the absorption +spectra + + align:start position:0% +spectra + + + align:start position:0% +spectra +and so classically based on absorption + + align:start position:0% +and so classically based on absorption + + + align:start position:0% +and so classically based on absorption +spectra these were classified into a b + + align:start position:0% +spectra these were classified into a b + + + align:start position:0% +spectra these were classified into a b +and c type cytochromes and you can + + align:start position:0% +and c type cytochromes and you can + + + align:start position:0% +and c type cytochromes and you can +imagine by + + align:start position:0% +imagine by + + + align:start position:0% +imagine by +these properties having slightly + + align:start position:0% +these properties having slightly + + + align:start position:0% +these properties having slightly +different um + + align:start position:0% +different um + + + align:start position:0% +different um +you know affecting the iron in ways that + + align:start position:0% +you know affecting the iron in ways that + + + align:start position:0% +you know affecting the iron in ways that +it slightly affects its electron + + align:start position:0% +it slightly affects its electron + + + align:start position:0% +it slightly affects its electron +transport + + align:start position:0% +transport + + + align:start position:0% +transport +properties of course hemoglobin + + align:start position:0% +properties of course hemoglobin + + + align:start position:0% +properties of course hemoglobin +almost certainly evolved from these + + align:start position:0% +almost certainly evolved from these + + + align:start position:0% +almost certainly evolved from these +molecules as oxygen carrying ways + + align:start position:0% +molecules as oxygen carrying ways + + + align:start position:0% +molecules as oxygen carrying ways +in multicellular life but of course the + + align:start position:0% +in multicellular life but of course the + + + align:start position:0% +in multicellular life but of course the +original use was as electron carriers + + align:start position:0% +original use was as electron carriers + + + align:start position:0% +original use was as electron carriers +for the processes here that we're going + + align:start position:0% +for the processes here that we're going + + + align:start position:0% +for the processes here that we're going +to talk about to hold that iron as a way + + align:start position:0% +to talk about to hold that iron as a way + + + align:start position:0% +to talk about to hold that iron as a way +to + + align:start position:0% +to + + + align:start position:0% +to +control electron transport across these + + align:start position:0% +control electron transport across these + + + align:start position:0% +control electron transport across these +electron transport chains + + align:start position:0% +electron transport chains + + + align:start position:0% +electron transport chains +all right so that's iron turns out + + align:start position:0% +all right so that's iron turns out + + + align:start position:0% +all right so that's iron turns out +iron's not the only metal + + align:start position:0% +iron's not the only metal + + + align:start position:0% +iron's not the only metal +that can be used to do this and so cells + + align:start position:0% +that can be used to do this and so cells + + + align:start position:0% +that can be used to do this and so cells +also use + + align:start position:0% +also use + + + align:start position:0% +also use +copper and so + + align:start position:0% +copper and so + + + align:start position:0% +copper and so +histidine can coordinate a copper + + align:start position:0% + + + + align:start position:0% + +that can move between an oxidized and + + align:start position:0% +that can move between an oxidized and + + + align:start position:0% +that can move between an oxidized and +reduced state so copper two plus + + align:start position:0% +reduced state so copper two plus + + + align:start position:0% +reduced state so copper two plus +reduced to copper plus copper plus to + + align:start position:0% +reduced to copper plus copper plus to + + + align:start position:0% +reduced to copper plus copper plus to +copper two plus + + align:start position:0% +copper two plus + + + align:start position:0% +copper two plus +or copper plus oxidized copper two plus + + align:start position:0% +or copper plus oxidized copper two plus + + + align:start position:0% +or copper plus oxidized copper two plus +another + + align:start position:0% +another + + + align:start position:0% +another +one electron carrier and so iron and + + align:start position:0% +one electron carrier and so iron and + + + align:start position:0% +one electron carrier and so iron and +copper + + align:start position:0% +copper + + + align:start position:0% +copper +can act as one electron carriers and so + + align:start position:0% +can act as one electron carriers and so + + + align:start position:0% +can act as one electron carriers and so +you have these two electron carriers + + align:start position:0% +you have these two electron carriers + + + align:start position:0% +you have these two electron carriers +here's a bunch of metals there's one + + align:start position:0% +here's a bunch of metals there's one + + + align:start position:0% +here's a bunch of metals there's one +electron carriers + + align:start position:0% +electron carriers + + + align:start position:0% +electron carriers +obviously you need ways to carry + + align:start position:0% +obviously you need ways to carry + + + align:start position:0% +obviously you need ways to carry +both one and two electrons if you're + + align:start position:0% +both one and two electrons if you're + + + align:start position:0% +both one and two electrons if you're +going to move electrons between these + + align:start position:0% +going to move electrons between these + + + align:start position:0% +going to move electrons between these +different + + align:start position:0% +different + + + align:start position:0% +different +carriers and an important molecule to do + + align:start position:0% +carriers and an important molecule to do + + + align:start position:0% +carriers and an important molecule to do +that is something called + + align:start position:0% +that is something called + + + align:start position:0% +that is something called +coenzyme + + align:start position:0% + + + + align:start position:0% + +q all right coenzyme q sometimes + + align:start position:0% +q all right coenzyme q sometimes + + + align:start position:0% +q all right coenzyme q sometimes +referred to + + align:start position:0% +referred to + + + align:start position:0% +referred to +as ubiquinone + + align:start position:0% + + + + align:start position:0% + +ubiquinol because it's ubiquitous + + align:start position:0% +ubiquinol because it's ubiquitous + + + align:start position:0% +ubiquinol because it's ubiquitous +um often abbreviated + + align:start position:0% +um often abbreviated + + + align:start position:0% +um often abbreviated +coq many of you have probably heard of + + align:start position:0% +coq many of you have probably heard of + + + align:start position:0% +coq many of you have probably heard of +the supplement coq10 + + align:start position:0% +the supplement coq10 + + + align:start position:0% +the supplement coq10 +okay very popular supplement out there + + align:start position:0% +okay very popular supplement out there + + + align:start position:0% +okay very popular supplement out there +coq10 + + align:start position:0% +coq10 + + + align:start position:0% +coq10 +is basically a version of coenzyme q + + align:start position:0% +is basically a version of coenzyme q + + + align:start position:0% +is basically a version of coenzyme q +ubiquinone ubiquinol + + align:start position:0% +ubiquinone ubiquinol + + + align:start position:0% +ubiquinone ubiquinol +what this looks like is as follows + + align:start position:0% + + + + align:start position:0% + +so this here is ubiquinone + + align:start position:0% +so this here is ubiquinone + + + align:start position:0% +so this here is ubiquinone +the oxidized form okay + + align:start position:0% +the oxidized form okay + + + align:start position:0% +the oxidized form okay +so this middle part is the quinone + + align:start position:0% +so this middle part is the quinone + + + align:start position:0% +so this middle part is the quinone +and then you have these decorations on + + align:start position:0% +and then you have these decorations on + + + align:start position:0% +and then you have these decorations on +the outside including this r + + align:start position:0% +the outside including this r + + + align:start position:0% +the outside including this r +group this r group is typically a long + + align:start position:0% +group this r group is typically a long + + + align:start position:0% +group this r group is typically a long +acyl chain if it's 10 carbons long + + align:start position:0% +acyl chain if it's 10 carbons long + + + align:start position:0% +acyl chain if it's 10 carbons long +that's coq10 the supplement + + align:start position:0% +that's coq10 the supplement + + + align:start position:0% +that's coq10 the supplement +having this long acyl chain makes this a + + align:start position:0% +having this long acyl chain makes this a + + + align:start position:0% +having this long acyl chain makes this a +very hydrophobic molecule + + align:start position:0% +very hydrophobic molecule + + + align:start position:0% +very hydrophobic molecule +and it actually lives within the + + align:start position:0% +and it actually lives within the + + + align:start position:0% +and it actually lives within the +membrane itself + + align:start position:0% +membrane itself + + + align:start position:0% +membrane itself +as an electron carrier and so this + + align:start position:0% +as an electron carrier and so this + + + align:start position:0% +as an electron carrier and so this +ubiquin known can + + align:start position:0% +ubiquin known can + + + align:start position:0% +ubiquin known can +pick up an electron + + align:start position:0% +pick up an electron + + + align:start position:0% +pick up an electron +as well as a proton + + align:start position:0% + + + + align:start position:0% + +and so by picking up + + align:start position:0% + + + + align:start position:0% + +one electron it can then + + align:start position:0% +one electron it can then + + + align:start position:0% +one electron it can then +basically + + align:start position:0% + + + + align:start position:0% + +go here to this semi quinone + + align:start position:0% + + + + align:start position:0% + +stabilized free radical state and then + + align:start position:0% +stabilized free radical state and then + + + align:start position:0% +stabilized free radical state and then +pick up + + align:start position:0% +pick up + + + align:start position:0% +pick up +a second electron to go + + align:start position:0% +a second electron to go + + + align:start position:0% +a second electron to go +to the fully reduced form + + align:start position:0% + + + + align:start position:0% + +ubiquinol + + align:start position:0% +ubiquinol + + + align:start position:0% +ubiquinol +okay so one electron carrier and two + + align:start position:0% +okay so one electron carrier and two + + + align:start position:0% +okay so one electron carrier and two +electron carrier + + align:start position:0% +electron carrier + + + align:start position:0% +electron carrier +so basically can carry two electrons + + align:start position:0% +so basically can carry two electrons + + + align:start position:0% +so basically can carry two electrons +from the oxidized the reduced form but + + align:start position:0% +from the oxidized the reduced form but + + + align:start position:0% +from the oxidized the reduced form but +can transfer them as single electrons + + align:start position:0% +can transfer them as single electrons + + + align:start position:0% +can transfer them as single electrons +by going from through this stabilized + + align:start position:0% +by going from through this stabilized + + + align:start position:0% +by going from through this stabilized +free radical + + align:start position:0% +free radical + + + align:start position:0% +free radical +ubiquinone state and so basically + + align:start position:0% +ubiquinone state and so basically + + + align:start position:0% +ubiquinone state and so basically +these various electron carriers are + + align:start position:0% +these various electron carriers are + + + align:start position:0% +these various electron carriers are +associated with + + align:start position:0% +associated with + + + align:start position:0% +associated with +these protein complexes within this + + align:start position:0% +these protein complexes within this + + + align:start position:0% +these protein complexes within this +electron transport chain that ultimately + + align:start position:0% +electron transport chain that ultimately + + + align:start position:0% +electron transport chain that ultimately +works to couple + + align:start position:0% +works to couple + + + align:start position:0% +works to couple +favorable electron transport down the + + align:start position:0% +favorable electron transport down the + + + align:start position:0% +favorable electron transport down the +chain + + align:start position:0% +chain + + + align:start position:0% +chain +to pumping protons to generate this + + align:start position:0% +to pumping protons to generate this + + + align:start position:0% +to pumping protons to generate this +potential + + align:start position:0% +potential + + + align:start position:0% +potential +across the membrane all right + + align:start position:0% +across the membrane all right + + + align:start position:0% +across the membrane all right +so this process + + align:start position:0% +so this process + + + align:start position:0% +so this process +occurs + + align:start position:0% + + + + align:start position:0% + +this process occurs um again + + align:start position:0% +this process occurs um again + + + align:start position:0% +this process occurs um again +at the bacterial membrane or the inner + + align:start position:0% +at the bacterial membrane or the inner + + + align:start position:0% +at the bacterial membrane or the inner +mitochondrial membrane + + align:start position:0% +mitochondrial membrane + + + align:start position:0% +mitochondrial membrane +and in animals + + align:start position:0% +and in animals + + + align:start position:0% +and in animals +and most organisms + + align:start position:0% +and most organisms + + + align:start position:0% +and most organisms +operates with four + + align:start position:0% + + + + align:start position:0% + +large multi-subunit protein + + align:start position:0% +large multi-subunit protein + + + align:start position:0% +large multi-subunit protein +complexes all right each of these + + align:start position:0% +complexes all right each of these + + + align:start position:0% +complexes all right each of these +protein complexes is + + align:start position:0% +protein complexes is + + + align:start position:0% +protein complexes is +mostly has multiple polypeptides as i + + align:start position:0% +mostly has multiple polypeptides as i + + + align:start position:0% +mostly has multiple polypeptides as i +said coming together to form these + + align:start position:0% +said coming together to form these + + + align:start position:0% +said coming together to form these +complexes just like we described for + + align:start position:0% +complexes just like we described for + + + align:start position:0% +complexes just like we described for +pdh for instance most of the + + align:start position:0% +pdh for instance most of the + + + align:start position:0% +pdh for instance most of the +components of this are encoded in the + + align:start position:0% +components of this are encoded in the + + + align:start position:0% +components of this are encoded in the +nuclear genome + + align:start position:0% +nuclear genome + + + align:start position:0% +nuclear genome +but a subset of these are encoded in the + + align:start position:0% +but a subset of these are encoded in the + + + align:start position:0% +but a subset of these are encoded in the +mitochondrial genome + + align:start position:0% +mitochondrial genome + + + align:start position:0% +mitochondrial genome +now what exactly is encoded in different + + align:start position:0% +now what exactly is encoded in different + + + align:start position:0% +now what exactly is encoded in different +mitochondrial genomes varies + + align:start position:0% +mitochondrial genomes varies + + + align:start position:0% +mitochondrial genomes varies +by organisms but across organisms is + + align:start position:0% +by organisms but across organisms is + + + align:start position:0% +by organisms but across organisms is +basically + + align:start position:0% +basically + + + align:start position:0% +basically +mostly complex components of these + + align:start position:0% +mostly complex components of these + + + align:start position:0% +mostly complex components of these +protein complexes and so this is why + + align:start position:0% +protein complexes and so this is why + + + align:start position:0% +protein complexes and so this is why +mitochondrial dna is retained it's kind + + align:start position:0% +mitochondrial dna is retained it's kind + + + align:start position:0% +mitochondrial dna is retained it's kind +of this vestige + + align:start position:0% +of this vestige + + + align:start position:0% +of this vestige +of this symbiotic relationship the + + align:start position:0% +of this symbiotic relationship the + + + align:start position:0% +of this symbiotic relationship the +mitochondria have retained + + align:start position:0% +mitochondria have retained + + + align:start position:0% +mitochondria have retained +some of the ability to control their own + + align:start position:0% +some of the ability to control their own + + + align:start position:0% +some of the ability to control their own +energy + + align:start position:0% +energy + + + align:start position:0% +energy +transduction sort of core components of + + align:start position:0% +transduction sort of core components of + + + align:start position:0% +transduction sort of core components of +these complexes + + align:start position:0% +these complexes + + + align:start position:0% +these complexes +there is one soluble + + align:start position:0% +there is one soluble + + + align:start position:0% +there is one soluble +protein so these complexes are embedded + + align:start position:0% +protein so these complexes are embedded + + + align:start position:0% +protein so these complexes are embedded +within the membrane + + align:start position:0% +within the membrane + + + align:start position:0% +within the membrane +there's also one soluble protein that's + + align:start position:0% +there's also one soluble protein that's + + + align:start position:0% +there's also one soluble protein that's +associated with the membrane + + align:start position:0% +associated with the membrane + + + align:start position:0% +associated with the membrane +and then there's coenzyme q + + align:start position:0% +and then there's coenzyme q + + + align:start position:0% +and then there's coenzyme q +which also floats within the membrane + + align:start position:0% + + + + align:start position:0% + +so in the membrane + + align:start position:0% +so in the membrane + + + align:start position:0% +so in the membrane +these are embedded in the membrane + + align:start position:0% +these are embedded in the membrane + + + align:start position:0% +these are embedded in the membrane +and then there's a soluble protein + + align:start position:0% +and then there's a soluble protein + + + align:start position:0% +and then there's a soluble protein +that's associated with the membrane + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +okay now i want to discuss the details + + align:start position:0% +okay now i want to discuss the details + + + align:start position:0% +okay now i want to discuss the details +of what these protein complexes + + align:start position:0% +of what these protein complexes + + + align:start position:0% +of what these protein complexes +are and also + + align:start position:0% +are and also + + + align:start position:0% +are and also +a few comments about how they work + + align:start position:0% +a few comments about how they work + + + align:start position:0% +a few comments about how they work +so this is the inner membrane space and + + align:start position:0% +so this is the inner membrane space and + + + align:start position:0% +so this is the inner membrane space and +this is the matrix side + + align:start position:0% +this is the matrix side + + + align:start position:0% +this is the matrix side +be out or in + + align:start position:0% +be out or in + + + align:start position:0% +be out or in +if we're discussing a prokaryote okay + + align:start position:0% +if we're discussing a prokaryote okay + + + align:start position:0% +if we're discussing a prokaryote okay +the first is + + align:start position:0% +the first is + + + align:start position:0% +the first is +we have + + align:start position:0% + + + + align:start position:0% + +something called complex one + + align:start position:0% + + + + align:start position:0% + +complex one also referred to + + align:start position:0% +complex one also referred to + + + align:start position:0% +complex one also referred to +as nadh + + align:start position:0% + + + + align:start position:0% + +oxidase okay + + align:start position:0% +oxidase okay + + + align:start position:0% +oxidase okay +because it oxidizes nadh + + align:start position:0% +because it oxidizes nadh + + + align:start position:0% +because it oxidizes nadh +back to nad + + align:start position:0% + + + + align:start position:0% + +nadh oxidase is a + + align:start position:0% +nadh oxidase is a + + + align:start position:0% +nadh oxidase is a +giant complex greater than 900 + + align:start position:0% +giant complex greater than 900 + + + align:start position:0% +giant complex greater than 900 +kilodaltons in total has more than + + align:start position:0% +kilodaltons in total has more than + + + align:start position:0% +kilodaltons in total has more than + + align:start position:0% + + + + align:start position:0% + +individual protein subunits + + align:start position:0% +individual protein subunits + + + align:start position:0% +individual protein subunits +contains some flavin mononucleotides + + align:start position:0% +contains some flavin mononucleotides + + + align:start position:0% +contains some flavin mononucleotides +as well as some iron sulfur clusters + + align:start position:0% +as well as some iron sulfur clusters + + + align:start position:0% +as well as some iron sulfur clusters +as electron carriers and + + align:start position:0% +as electron carriers and + + + align:start position:0% +as electron carriers and +it is the least well understood + + align:start position:0% +it is the least well understood + + + align:start position:0% +it is the least well understood +of all of the protein complexes in fact + + align:start position:0% +of all of the protein complexes in fact + + + align:start position:0% +of all of the protein complexes in fact +it is still a major + + align:start position:0% +it is still a major + + + align:start position:0% +it is still a major +um field of study to try to understand + + align:start position:0% +um field of study to try to understand + + + align:start position:0% +um field of study to try to understand +how + + align:start position:0% +how + + + align:start position:0% +how +nadh oxidase really works but it + + align:start position:0% +nadh oxidase really works but it + + + align:start position:0% +nadh oxidase really works but it +effectively + + align:start position:0% +effectively + + + align:start position:0% +effectively +is one of the complexes that can pump + + align:start position:0% +is one of the complexes that can pump + + + align:start position:0% +is one of the complexes that can pump +protons + + align:start position:0% +protons + + + align:start position:0% +protons +across the membrane as those two + + align:start position:0% +across the membrane as those two + + + align:start position:0% +across the membrane as those two +electrons are transferred + + align:start position:0% +electrons are transferred + + + align:start position:0% +electrons are transferred +through the complex from nadh ultimately + + align:start position:0% +through the complex from nadh ultimately + + + align:start position:0% +through the complex from nadh ultimately +to coenzyme + + align:start position:0% +to coenzyme + + + align:start position:0% +to coenzyme +q that exists within + + align:start position:0% +q that exists within + + + align:start position:0% +q that exists within +the membrane okay + + align:start position:0% +the membrane okay + + + align:start position:0% +the membrane okay +the next complex is + + align:start position:0% + + + + align:start position:0% + +discuss is complex ii complex + + align:start position:0% +discuss is complex ii complex + + + align:start position:0% +discuss is complex ii complex +ii is succinate dehydrogenase + + align:start position:0% + + + + align:start position:0% + +the exact enzyme that we heard about + + align:start position:0% +the exact enzyme that we heard about + + + align:start position:0% +the exact enzyme that we heard about +from + + align:start position:0% +from + + + align:start position:0% +from +the tca cycle so what does succinate + + align:start position:0% +the tca cycle so what does succinate + + + align:start position:0% +the tca cycle so what does succinate +dehydrogenase do + + align:start position:0% +dehydrogenase do + + + align:start position:0% +dehydrogenase do +remember it converts fumarate to + + align:start position:0% +remember it converts fumarate to + + + align:start position:0% +remember it converts fumarate to +succinate + + align:start position:0% +succinate + + + align:start position:0% +succinate +it gave those electrons to fad + + align:start position:0% + + + + align:start position:0% + +to make fadh2 + + align:start position:0% +to make fadh2 + + + align:start position:0% +to make fadh2 +well that occurs within this complex + + align:start position:0% +well that occurs within this complex + + + align:start position:0% +well that occurs within this complex +which can also re-oxidize the fadh2 + + align:start position:0% +which can also re-oxidize the fadh2 + + + align:start position:0% +which can also re-oxidize the fadh2 +with those two electrons and give them + + align:start position:0% +with those two electrons and give them + + + align:start position:0% +with those two electrons and give them +also + + align:start position:0% +also + + + align:start position:0% +also +two coenzyme q that + + align:start position:0% +two coenzyme q that + + + align:start position:0% +two coenzyme q that +sits within the membrane so + + align:start position:0% +sits within the membrane so + + + align:start position:0% +sits within the membrane so +i want to point out that this + + align:start position:0% +i want to point out that this + + + align:start position:0% +i want to point out that this +ultimately you will see is why it is + + align:start position:0% +ultimately you will see is why it is + + + align:start position:0% +ultimately you will see is why it is +that electron transfer + + align:start position:0% +that electron transfer + + + align:start position:0% +that electron transfer +from nadh and fadh2 has different + + align:start position:0% +from nadh and fadh2 has different + + + align:start position:0% +from nadh and fadh2 has different +energy yields and so the electron + + align:start position:0% +energy yields and so the electron + + + align:start position:0% +energy yields and so the electron +transfer from nadh to + + align:start position:0% +transfer from nadh to + + + align:start position:0% +transfer from nadh to +ubiquinone is more of a change in + + align:start position:0% +ubiquinone is more of a change in + + + align:start position:0% +ubiquinone is more of a change in +standard reduction potential + + align:start position:0% +standard reduction potential + + + align:start position:0% +standard reduction potential +than from fadh2 to ubiquinone + + align:start position:0% +than from fadh2 to ubiquinone + + + align:start position:0% +than from fadh2 to ubiquinone +why use fadh2 well because remember + + align:start position:0% +why use fadh2 well because remember + + + align:start position:0% +why use fadh2 well because remember +when we did electron transfers we used + + align:start position:0% +when we did electron transfers we used + + + align:start position:0% +when we did electron transfers we used +when we oxidized a + + align:start position:0% +when we oxidized a + + + align:start position:0% +when we oxidized a +carbon okay say + + align:start position:0% +carbon okay say + + + align:start position:0% +carbon okay say +in a carbohydrate to a ketone + + align:start position:0% +in a carbohydrate to a ketone + + + align:start position:0% +in a carbohydrate to a ketone +all right we tended to use nad + + align:start position:0% +all right we tended to use nad + + + align:start position:0% +all right we tended to use nad +plus nadh as the + + align:start position:0% +plus nadh as the + + + align:start position:0% +plus nadh as the +electron transport pair so this change + + align:start position:0% +electron transport pair so this change + + + align:start position:0% +electron transport pair so this change +in standard reduction potential + + align:start position:0% +in standard reduction potential + + + align:start position:0% +in standard reduction potential +is such that we can make that reaction + + align:start position:0% +is such that we can make that reaction + + + align:start position:0% +is such that we can make that reaction +work + + align:start position:0% +work + + + align:start position:0% +work +and ultimately drive that it turns out + + align:start position:0% +and ultimately drive that it turns out + + + align:start position:0% +and ultimately drive that it turns out +that + + align:start position:0% +that + + + align:start position:0% +that +oxidizing a putting a double bond in + + align:start position:0% +oxidizing a putting a double bond in + + + align:start position:0% +oxidizing a putting a double bond in +okay this going from uh + + align:start position:0% +okay this going from uh + + + align:start position:0% +okay this going from uh +not oxidizing an alcohol to a ketone but + + align:start position:0% +not oxidizing an alcohol to a ketone but + + + align:start position:0% +not oxidizing an alcohol to a ketone but +oxidizing the carbon to a double bond + + align:start position:0% +oxidizing the carbon to a double bond + + + align:start position:0% +oxidizing the carbon to a double bond +that this is basically + + align:start position:0% +that this is basically + + + align:start position:0% +that this is basically +you need a different change + + align:start position:0% +you need a different change + + + align:start position:0% +you need a different change +in standard reduction potential to carry + + align:start position:0% +in standard reduction potential to carry + + + align:start position:0% +in standard reduction potential to carry +out + + align:start position:0% +out + + + align:start position:0% +out +that reaction and make it worse work + + align:start position:0% +that reaction and make it worse work + + + align:start position:0% +that reaction and make it worse work +fadh fadh2 sits at a + + align:start position:0% +fadh fadh2 sits at a + + + align:start position:0% +fadh fadh2 sits at a +higher standard reduction potential than + + align:start position:0% +higher standard reduction potential than + + + align:start position:0% +higher standard reduction potential than +nad nadh + + align:start position:0% +nad nadh + + + align:start position:0% +nad nadh +and so that means to further transfer + + align:start position:0% +and so that means to further transfer + + + align:start position:0% +and so that means to further transfer +them to + + align:start position:0% +them to + + + align:start position:0% +them to +something further downstream + + align:start position:0% +something further downstream + + + align:start position:0% +something further downstream +like coenzyme q there's a bigger change + + align:start position:0% +like coenzyme q there's a bigger change + + + align:start position:0% +like coenzyme q there's a bigger change +in standard reduction potential here + + align:start position:0% +in standard reduction potential here + + + align:start position:0% +in standard reduction potential here +that can be used to drive protons + + align:start position:0% +that can be used to drive protons + + + align:start position:0% +that can be used to drive protons +there's not enough of a change here + + align:start position:0% +there's not enough of a change here + + + align:start position:0% +there's not enough of a change here +can't use that to drive protons + + align:start position:0% +can't use that to drive protons + + + align:start position:0% +can't use that to drive protons +and it's because of these differences + + align:start position:0% +and it's because of these differences + + + align:start position:0% +and it's because of these differences +and what's actually being oxidized + + align:start position:0% +and what's actually being oxidized + + + align:start position:0% +and what's actually being oxidized +that ultimately leads to this + + align:start position:0% +that ultimately leads to this + + + align:start position:0% +that ultimately leads to this +difference in energetics when we think + + align:start position:0% +difference in energetics when we think + + + align:start position:0% +difference in energetics when we think +about + + align:start position:0% +about + + + align:start position:0% +about +fadh2 versus nadh and how much + + align:start position:0% +fadh2 versus nadh and how much + + + align:start position:0% +fadh2 versus nadh and how much +atp equivalents that they might have for + + align:start position:0% +atp equivalents that they might have for + + + align:start position:0% +atp equivalents that they might have for +cells + + align:start position:0% +cells + + + align:start position:0% +cells +all right once electrons are in the + + align:start position:0% +all right once electrons are in the + + + align:start position:0% +all right once electrons are in the +ubiquinone pool they can now be + + align:start position:0% +ubiquinone pool they can now be + + + align:start position:0% +ubiquinone pool they can now be +or coenzyme q pool they can now be + + align:start position:0% +or coenzyme q pool they can now be + + + align:start position:0% +or coenzyme q pool they can now be +transferred to complex + + align:start position:0% +transferred to complex + + + align:start position:0% +transferred to complex +three so oh complex + + align:start position:0% +three so oh complex + + + align:start position:0% +three so oh complex +three is + + align:start position:0% +three is + + + align:start position:0% +three is +also referred to as + + align:start position:0% +also referred to as + + + align:start position:0% +also referred to as +cytochrome c + + align:start position:0% +cytochrome c + + + align:start position:0% +cytochrome c +reductase you'll see why in a second + + align:start position:0% +reductase you'll see why in a second + + + align:start position:0% +reductase you'll see why in a second +it's a 250 kilodalton + + align:start position:0% +it's a 250 kilodalton + + + align:start position:0% +it's a 250 kilodalton +complex there are 10 subunits + + align:start position:0% +complex there are 10 subunits + + + align:start position:0% +complex there are 10 subunits +it has a bunch of b type + + align:start position:0% +it has a bunch of b type + + + align:start position:0% +it has a bunch of b type +and c type + + align:start position:0% +and c type + + + align:start position:0% +and c type +cytochromes + + align:start position:0% + + + + align:start position:0% + +as well as some iron sulfur clusters + + align:start position:0% +as well as some iron sulfur clusters + + + align:start position:0% +as well as some iron sulfur clusters +shown here on the slide from textbook is + + align:start position:0% +shown here on the slide from textbook is + + + align:start position:0% +shown here on the slide from textbook is +a picture + + align:start position:0% +a picture + + + align:start position:0% +a picture +of complex three and + + align:start position:0% +of complex three and + + + align:start position:0% +of complex three and +what it actually looks like + + align:start position:0% +what it actually looks like + + + align:start position:0% +what it actually looks like +fairly well understood how it works + + align:start position:0% +fairly well understood how it works + + + align:start position:0% +fairly well understood how it works +this coupling of basically electron + + align:start position:0% +this coupling of basically electron + + + align:start position:0% +this coupling of basically electron +transfer through the q pool + + align:start position:0% +transfer through the q pool + + + align:start position:0% +transfer through the q pool +can pump protons um + + align:start position:0% +can pump protons um + + + align:start position:0% +can pump protons um +and this ultimately allows + + align:start position:0% +and this ultimately allows + + + align:start position:0% +and this ultimately allows +transfer of electrons to this + + align:start position:0% +transfer of electrons to this + + + align:start position:0% +transfer of electrons to this +small soluble protein that lives in the + + align:start position:0% +small soluble protein that lives in the + + + align:start position:0% +small soluble protein that lives in the +inter-membrane space + + align:start position:0% +inter-membrane space + + + align:start position:0% +inter-membrane space +or associated with the outside of the + + align:start position:0% +or associated with the outside of the + + + align:start position:0% +or associated with the outside of the +bacteria called + + align:start position:0% +bacteria called + + + align:start position:0% +bacteria called +cytochrome c or outside in the inner + + align:start position:0% +cytochrome c or outside in the inner + + + align:start position:0% +cytochrome c or outside in the inner +membrane space called cytochrome c + + align:start position:0% +membrane space called cytochrome c + + + align:start position:0% +membrane space called cytochrome c +cytochrome c + + align:start position:0% + + + + align:start position:0% + +is a 13 kilodalton + + align:start position:0% +is a 13 kilodalton + + + align:start position:0% +is a 13 kilodalton +protein it's a very small + + align:start position:0% +protein it's a very small + + + align:start position:0% +protein it's a very small +highly conserved protein with a c-type + + align:start position:0% +highly conserved protein with a c-type + + + align:start position:0% +highly conserved protein with a c-type +cytochrome + + align:start position:0% +cytochrome + + + align:start position:0% +cytochrome +commonly used because it's found across + + align:start position:0% +commonly used because it's found across + + + align:start position:0% +commonly used because it's found across +many many different types of organisms + + align:start position:0% +many many different types of organisms + + + align:start position:0% +many many different types of organisms +and so it's been + + align:start position:0% +and so it's been + + + align:start position:0% +and so it's been +sequenced from many many organisms as a + + align:start position:0% +sequenced from many many organisms as a + + + align:start position:0% +sequenced from many many organisms as a +way to identify evolutionary + + align:start position:0% +way to identify evolutionary + + + align:start position:0% +way to identify evolutionary +relationships + + align:start position:0% +relationships + + + align:start position:0% +relationships +and then cytochrome c this is also why + + align:start position:0% +and then cytochrome c this is also why + + + align:start position:0% +and then cytochrome c this is also why +it's called cytochrome c reductase + + align:start position:0% +it's called cytochrome c reductase + + + align:start position:0% +it's called cytochrome c reductase +because it's reducing cytochrome c + + align:start position:0% +because it's reducing cytochrome c + + + align:start position:0% +because it's reducing cytochrome c +to transfer electrons along the chain + + align:start position:0% +to transfer electrons along the chain + + + align:start position:0% +to transfer electrons along the chain +ultimately + + align:start position:0% +ultimately + + + align:start position:0% +ultimately +to the final complex cyto complex four + + align:start position:0% +to the final complex cyto complex four + + + align:start position:0% +to the final complex cyto complex four +complex four also referred to as + + align:start position:0% +complex four also referred to as + + + align:start position:0% +complex four also referred to as +cytochrome c oxidase + + align:start position:0% +cytochrome c oxidase + + + align:start position:0% +cytochrome c oxidase +and this is ultimately + + align:start position:0% +and this is ultimately + + + align:start position:0% +and this is ultimately +the place where electrons are + + align:start position:0% +the place where electrons are + + + align:start position:0% +the place where electrons are +transferred + + align:start position:0% +transferred + + + align:start position:0% +transferred +to reduce oxygen to water + + align:start position:0% +to reduce oxygen to water + + + align:start position:0% +to reduce oxygen to water +so this is a 160 kilodalton + + align:start position:0% +so this is a 160 kilodalton + + + align:start position:0% +so this is a 160 kilodalton +protein complex with 13 + + align:start position:0% +protein complex with 13 + + + align:start position:0% +protein complex with 13 +subunits uses + + align:start position:0% +subunits uses + + + align:start position:0% +subunits uses +a type cytochromes + + align:start position:0% + + + + align:start position:0% + +and copper + + align:start position:0% + + + + align:start position:0% + +as electron carriers + + align:start position:0% +as electron carriers + + + align:start position:0% +as electron carriers +and ultimately allows you to get + + align:start position:0% +and ultimately allows you to get + + + align:start position:0% +and ultimately allows you to get +electrons from cytochrome c + + align:start position:0% +electrons from cytochrome c + + + align:start position:0% +electrons from cytochrome c +to oxygen and so here again from the + + align:start position:0% +to oxygen and so here again from the + + + align:start position:0% +to oxygen and so here again from the +textbook is a picture of + + align:start position:0% +textbook is a picture of + + + align:start position:0% +textbook is a picture of +complex four + + align:start position:0% +complex four + + + align:start position:0% +complex four +and what it looks like also fairly well + + align:start position:0% +and what it looks like also fairly well + + + align:start position:0% +and what it looks like also fairly well +understood + + align:start position:0% +understood + + + align:start position:0% +understood +also couples electron transport to + + align:start position:0% +also couples electron transport to + + + align:start position:0% +also couples electron transport to +proton pumping and so + + align:start position:0% + + + + align:start position:0% + +this is effectively the electron + + align:start position:0% +this is effectively the electron + + + align:start position:0% +this is effectively the electron +transport chain as it exists in + + align:start position:0% +transport chain as it exists in + + + align:start position:0% +transport chain as it exists in +mitochondria + + align:start position:0% +mitochondria + + + align:start position:0% +mitochondria +and you can draw it a different way + + align:start position:0% +and you can draw it a different way + + + align:start position:0% +and you can draw it a different way +as i will do here so here's + + align:start position:0% +as i will do here so here's + + + align:start position:0% +as i will do here so here's +complex one + + align:start position:0% + + + + align:start position:0% + +allows oxidation of nadh + + align:start position:0% +allows oxidation of nadh + + + align:start position:0% +allows oxidation of nadh +back to nad plus + + align:start position:0% +back to nad plus + + + align:start position:0% +back to nad plus +that oxidation can be coupled + + align:start position:0% +that oxidation can be coupled + + + align:start position:0% +that oxidation can be coupled +to reduction of fmn + + align:start position:0% +to reduction of fmn + + + align:start position:0% +to reduction of fmn +ultimately those are passed + + align:start position:0% + + + + align:start position:0% + +through some iron sulfur clusters + + align:start position:0% +through some iron sulfur clusters + + + align:start position:0% +through some iron sulfur clusters +leading to + + align:start position:0% +leading to + + + align:start position:0% +leading to +the reduction of ubric quinone + + align:start position:0% +the reduction of ubric quinone + + + align:start position:0% +the reduction of ubric quinone +and in the process this can + + align:start position:0% +and in the process this can + + + align:start position:0% +and in the process this can +electron transport can pump on the order + + align:start position:0% +electron transport can pump on the order + + + align:start position:0% +electron transport can pump on the order +of four + + align:start position:0% +of four + + + align:start position:0% +of four +protons or at least that's what's + + align:start position:0% +protons or at least that's what's + + + align:start position:0% +protons or at least that's what's +estimated + + align:start position:0% +estimated + + + align:start position:0% +estimated +complex ii which is + + align:start position:0% +complex ii which is + + + align:start position:0% +complex ii which is +succinate dehydrogenase from the tca + + align:start position:0% +succinate dehydrogenase from the tca + + + align:start position:0% +succinate dehydrogenase from the tca +cycle + + align:start position:0% +cycle + + + align:start position:0% +cycle +really converts succinate + + align:start position:0% +really converts succinate + + + align:start position:0% +really converts succinate +to fumarate that + + align:start position:0% +to fumarate that + + + align:start position:0% +to fumarate that +oxidation reaction + + align:start position:0% +oxidation reaction + + + align:start position:0% +oxidation reaction +within the complex leads to + + align:start position:0% +within the complex leads to + + + align:start position:0% +within the complex leads to +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the reduction of fad to fadh2 + + align:start position:0% +the reduction of fad to fadh2 + + + align:start position:0% +the reduction of fad to fadh2 +that can be re-oxidized + + align:start position:0% + + + + align:start position:0% + +through iron ultimately + + align:start position:0% +through iron ultimately + + + align:start position:0% +through iron ultimately +driving the reduction + + align:start position:0% + + + + align:start position:0% + +of coenzyme q from ubiquinone to + + align:start position:0% +of coenzyme q from ubiquinone to + + + align:start position:0% +of coenzyme q from ubiquinone to +ubiquinol + + align:start position:0% +ubiquinol + + + align:start position:0% +ubiquinol +that ubiquinone to ubiquinol + + align:start position:0% +that ubiquinone to ubiquinol + + + align:start position:0% +that ubiquinone to ubiquinol +in something called the q pool + + align:start position:0% +in something called the q pool + + + align:start position:0% +in something called the q pool +within the membrane can then + + align:start position:0% + + + + align:start position:0% + +be re-oxidized + + align:start position:0% +be re-oxidized + + + align:start position:0% +be re-oxidized +in complex + + align:start position:0% + + + + align:start position:0% + +3. that re-oxidized and complex 3 + + align:start position:0% +3. that re-oxidized and complex 3 + + + align:start position:0% +3. that re-oxidized and complex 3 +puts electrons + + align:start position:0% +puts electrons + + + align:start position:0% +puts electrons +through complex 3 that can be coupled to + + align:start position:0% +through complex 3 that can be coupled to + + + align:start position:0% +through complex 3 that can be coupled to +pumping on the order of + + align:start position:0% +pumping on the order of + + + align:start position:0% +pumping on the order of +two protons those electrons + + align:start position:0% +two protons those electrons + + + align:start position:0% +two protons those electrons +are transferred to cytochrome c + + align:start position:0% +are transferred to cytochrome c + + + align:start position:0% +are transferred to cytochrome c +ultimately those electrons are + + align:start position:0% +ultimately those electrons are + + + align:start position:0% +ultimately those electrons are +transferred to + + align:start position:0% +transferred to + + + align:start position:0% +transferred to +copper in + + align:start position:0% + + + + align:start position:0% + +complex 4 to cytochrome a + + align:start position:0% +complex 4 to cytochrome a + + + align:start position:0% +complex 4 to cytochrome a +and ultimately + + align:start position:0% + + + + align:start position:0% + +oxygen to water + + align:start position:0% +oxygen to water + + + align:start position:0% +oxygen to water +reducing oxygen to water and pumping on + + align:start position:0% +reducing oxygen to water and pumping on + + + align:start position:0% +reducing oxygen to water and pumping on +the order of + + align:start position:0% +the order of + + + align:start position:0% +the order of +four protons and so + + align:start position:0% +four protons and so + + + align:start position:0% +four protons and so +you can see here that + + align:start position:0% +you can see here that + + + align:start position:0% +you can see here that +basically this is a series of + + align:start position:0% +basically this is a series of + + + align:start position:0% +basically this is a series of +oxidation and reduction reactions that + + align:start position:0% +oxidation and reduction reactions that + + + align:start position:0% +oxidation and reduction reactions that +happens across these complexes + + align:start position:0% +happens across these complexes + + + align:start position:0% +happens across these complexes +such that complex 1 the + + align:start position:0% +such that complex 1 the + + + align:start position:0% +such that complex 1 the +transfer electrons from the q pool + + align:start position:0% +transfer electrons from the q pool + + + align:start position:0% +transfer electrons from the q pool +through complex 3 and complex 4 + + align:start position:0% +through complex 3 and complex 4 + + + align:start position:0% +through complex 3 and complex 4 +can pump protons across the membrane + + align:start position:0% +can pump protons across the membrane + + + align:start position:0% +can pump protons across the membrane +and generate this delta side delta ph + + align:start position:0% +and generate this delta side delta ph + + + align:start position:0% +and generate this delta side delta ph +that can be used to do work and it's + + align:start position:0% +that can be used to do work and it's + + + align:start position:0% +that can be used to do work and it's +really the favorable transfer of + + align:start position:0% +really the favorable transfer of + + + align:start position:0% +really the favorable transfer of +electrons either from nad nadh or the + + align:start position:0% +electrons either from nad nadh or the + + + align:start position:0% +electrons either from nad nadh or the +oxidation of the + + align:start position:0% +oxidation of the + + + align:start position:0% +oxidation of the +succinate to fumarate with those + + align:start position:0% +succinate to fumarate with those + + + align:start position:0% +succinate to fumarate with those +electrons being given to oxygen + + align:start position:0% +electrons being given to oxygen + + + align:start position:0% +electrons being given to oxygen +to drive this process + + align:start position:0% +to drive this process + + + align:start position:0% +to drive this process +and so really just to schematize + + align:start position:0% +and so really just to schematize + + + align:start position:0% +and so really just to schematize +this in a way + + align:start position:0% + + + + align:start position:0% + +is that if this is our membrane + + align:start position:0% + + + + align:start position:0% + +nad plus the nadh gives electrons to + + align:start position:0% +nad plus the nadh gives electrons to + + + align:start position:0% +nad plus the nadh gives electrons to +complex one + + align:start position:0% +complex one + + + align:start position:0% +complex one +which goes to coenzyme q which goes to + + align:start position:0% +which goes to coenzyme q which goes to + + + align:start position:0% +which goes to coenzyme q which goes to +complex three + + align:start position:0% +complex three + + + align:start position:0% +complex three +which grows to cytochrome c which goes + + align:start position:0% +which grows to cytochrome c which goes + + + align:start position:0% +which grows to cytochrome c which goes +to complex four + + align:start position:0% +to complex four + + + align:start position:0% +to complex four +and reduces oxygen + + align:start position:0% +and reduces oxygen + + + align:start position:0% +and reduces oxygen +to water that is one way to carry out + + align:start position:0% +to water that is one way to carry out + + + align:start position:0% +to water that is one way to carry out +this set of reactions the other way is + + align:start position:0% +this set of reactions the other way is + + + align:start position:0% +this set of reactions the other way is +we can + + align:start position:0% +we can + + + align:start position:0% +we can +convert fumarate + + align:start position:0% + + + + align:start position:0% + +sorry succinate to fumarate + + align:start position:0% +sorry succinate to fumarate + + + align:start position:0% +sorry succinate to fumarate +okay that's the fad that's complex two + + align:start position:0% +okay that's the fad that's complex two + + + align:start position:0% +okay that's the fad that's complex two +also gives it to the q pool and so you + + align:start position:0% +also gives it to the q pool and so you + + + align:start position:0% +also gives it to the q pool and so you +can see that the + + align:start position:0% +can see that the + + + align:start position:0% +can see that the +electron transport chain would be + + align:start position:0% +electron transport chain would be + + + align:start position:0% +electron transport chain would be +complex one q three c + + align:start position:0% +complex one q three c + + + align:start position:0% +complex one q three c +four or two q three c four + + align:start position:0% +four or two q three c four + + + align:start position:0% +four or two q three c four +it is not one two three four it is + + align:start position:0% +it is not one two three four it is + + + align:start position:0% +it is not one two three four it is +actually + + align:start position:0% +actually + + + align:start position:0% +actually +1 to q or 2 to q ultimately going + + align:start position:0% +1 to q or 2 to q ultimately going + + + align:start position:0% +1 to q or 2 to q ultimately going +to 3. now + + align:start position:0% +to 3. now + + + align:start position:0% +to 3. now +the way protons are pumped is a process + + align:start position:0% +the way protons are pumped is a process + + + align:start position:0% +the way protons are pumped is a process +that i don't have time + + align:start position:0% +that i don't have time + + + align:start position:0% +that i don't have time +this year to discuss in class i will + + align:start position:0% +this year to discuss in class i will + + + align:start position:0% +this year to discuss in class i will +post something on stellar that is just a + + align:start position:0% +post something on stellar that is just a + + + align:start position:0% +post something on stellar that is just a +short section from the textbook + + align:start position:0% +short section from the textbook + + + align:start position:0% +short section from the textbook +that describes at least what is known + + align:start position:0% +that describes at least what is known + + + align:start position:0% +that describes at least what is known +about how that process + + align:start position:0% +about how that process + + + align:start position:0% +about how that process +works such as the q cycle + + align:start position:0% +works such as the q cycle + + + align:start position:0% +works such as the q cycle +basically how oxidation and reduction of + + align:start position:0% +basically how oxidation and reduction of + + + align:start position:0% +basically how oxidation and reduction of +coenzyme q which will take protons on + + align:start position:0% +coenzyme q which will take protons on + + + align:start position:0% +coenzyme q which will take protons on +and off the molecule on either side of + + align:start position:0% +and off the molecule on either side of + + + align:start position:0% +and off the molecule on either side of +the membrane + + align:start position:0% +the membrane + + + align:start position:0% +the membrane +can be used to show how this can be + + align:start position:0% +can be used to show how this can be + + + align:start position:0% +can be used to show how this can be +coupled to + + align:start position:0% +coupled to + + + align:start position:0% +coupled to +proton pumping across the the membrane + + align:start position:0% +proton pumping across the the membrane + + + align:start position:0% +proton pumping across the the membrane +and you can read that + + align:start position:0% +and you can read that + + + align:start position:0% +and you can read that +if you're interested + + align:start position:0% +if you're interested + + + align:start position:0% +if you're interested +okay now couple other points + + align:start position:0% +okay now couple other points + + + align:start position:0% +okay now couple other points +about this this + + align:start position:0% +about this this + + + align:start position:0% +about this this +works because you're moving from a lower + + align:start position:0% +works because you're moving from a lower + + + align:start position:0% +works because you're moving from a lower +to a standard a higher lower to a higher + + align:start position:0% +to a standard a higher lower to a higher + + + align:start position:0% +to a standard a higher lower to a higher +standard reduction potential across + + align:start position:0% +standard reduction potential across + + + align:start position:0% +standard reduction potential across +the chain and it turns out oxygen + + align:start position:0% +the chain and it turns out oxygen + + + align:start position:0% +the chain and it turns out oxygen +is a particularly good electron acceptor + + align:start position:0% +is a particularly good electron acceptor + + + align:start position:0% +is a particularly good electron acceptor +and this is really why oxygen and + + align:start position:0% +and this is really why oxygen and + + + align:start position:0% +and this is really why oxygen and +respiration is really so + + align:start position:0% +respiration is really so + + + align:start position:0% +respiration is really so +vital to a lot of the way energy + + align:start position:0% +vital to a lot of the way energy + + + align:start position:0% +vital to a lot of the way energy +transduction works in metabolism + + align:start position:0% +transduction works in metabolism + + + align:start position:0% +transduction works in metabolism +oxygen is now abundant and being a great + + align:start position:0% +oxygen is now abundant and being a great + + + align:start position:0% +oxygen is now abundant and being a great +electron acceptor is why it's used but + + align:start position:0% +electron acceptor is why it's used but + + + align:start position:0% +electron acceptor is why it's used but +of course oxygen was not + + align:start position:0% +of course oxygen was not + + + align:start position:0% +of course oxygen was not +abundant two and a half billion years + + align:start position:0% +abundant two and a half billion years + + + align:start position:0% +abundant two and a half billion years +ago + + align:start position:0% +ago + + + align:start position:0% +ago +and it doesn't have to be oxygen for + + align:start position:0% +and it doesn't have to be oxygen for + + + align:start position:0% +and it doesn't have to be oxygen for +this to work + + align:start position:0% +this to work + + + align:start position:0% +this to work +if you have another electron acceptor + + align:start position:0% +if you have another electron acceptor + + + align:start position:0% +if you have another electron acceptor +that + + align:start position:0% +that + + + align:start position:0% +that +basically makes this process favorable + + align:start position:0% +basically makes this process favorable + + + align:start position:0% +basically makes this process favorable +that can work just as well and in fact + + align:start position:0% +that can work just as well and in fact + + + align:start position:0% +that can work just as well and in fact +that happens still + + align:start position:0% +that happens still + + + align:start position:0% +that happens still +in some very extreme environments okay + + align:start position:0% +in some very extreme environments okay + + + align:start position:0% +in some very extreme environments okay +this so-called chemosynthesis + + align:start position:0% +this so-called chemosynthesis + + + align:start position:0% +this so-called chemosynthesis +basically can use other electron + + align:start position:0% +basically can use other electron + + + align:start position:0% +basically can use other electron +acceptors + + align:start position:0% +acceptors + + + align:start position:0% +acceptors +to drive the energetics of cells + + align:start position:0% +to drive the energetics of cells + + + align:start position:0% +to drive the energetics of cells +and you really just need the right + + align:start position:0% +and you really just need the right + + + align:start position:0% +and you really just need the right +ways to build an electron transport + + align:start position:0% +ways to build an electron transport + + + align:start position:0% +ways to build an electron transport +chain to make this whole system work so + + align:start position:0% +chain to make this whole system work so + + + align:start position:0% +chain to make this whole system work so +that you can build a battery + + align:start position:0% +that you can build a battery + + + align:start position:0% +that you can build a battery +and use it to do work okay so oxygen + + align:start position:0% +and use it to do work okay so oxygen + + + align:start position:0% +and use it to do work okay so oxygen +commonly used because it's abundant and + + align:start position:0% +commonly used because it's abundant and + + + align:start position:0% +commonly used because it's abundant and +good + + align:start position:0% +good + + + align:start position:0% +good +at it but it's not the only way that + + align:start position:0% +at it but it's not the only way that + + + align:start position:0% +at it but it's not the only way that +this can work and there are examples in + + align:start position:0% +this can work and there are examples in + + + align:start position:0% +this can work and there are examples in +biology where + + align:start position:0% +biology where + + + align:start position:0% +biology where +oxygen is not used that there's other + + align:start position:0% +oxygen is not used that there's other + + + align:start position:0% +oxygen is not used that there's other +acceptors that are used + + align:start position:0% +acceptors that are used + + + align:start position:0% +acceptors that are used +instead i also want to note + + align:start position:0% +instead i also want to note + + + align:start position:0% +instead i also want to note +as i've alluded to in discussing complex + + align:start position:0% +as i've alluded to in discussing complex + + + align:start position:0% +as i've alluded to in discussing complex + + align:start position:0% + + + align:start position:0% +this fad fadh2 so when we talk about + + align:start position:0% +this fad fadh2 so when we talk about + + + align:start position:0% +this fad fadh2 so when we talk about +that + + align:start position:0% +that + + + align:start position:0% +that +in the tca cycle or in fatty acid + + align:start position:0% +in the tca cycle or in fatty acid + + + align:start position:0% +in the tca cycle or in fatty acid +oxidation + + align:start position:0% +oxidation + + + align:start position:0% +oxidation +we discuss it as if it's kind of like + + align:start position:0% +we discuss it as if it's kind of like + + + align:start position:0% +we discuss it as if it's kind of like +nadnadh + + align:start position:0% +nadnadh + + + align:start position:0% +nadnadh +but it's not nad nadh are + + align:start position:0% +but it's not nad nadh are + + + align:start position:0% +but it's not nad nadh are +basically cofactors that move around + + align:start position:0% +basically cofactors that move around + + + align:start position:0% +basically cofactors that move around +between enzymes + + align:start position:0% +between enzymes + + + align:start position:0% +between enzymes +fad fadh2 are not free + + align:start position:0% +fad fadh2 are not free + + + align:start position:0% +fad fadh2 are not free +these are really part of their electron + + align:start position:0% +these are really part of their electron + + + align:start position:0% +these are really part of their electron +carriers + + align:start position:0% +carriers + + + align:start position:0% +carriers +that are part of protein complexes like + + align:start position:0% +that are part of protein complexes like + + + align:start position:0% +that are part of protein complexes like +what we described up here + + align:start position:0% +what we described up here + + + align:start position:0% +what we described up here +okay and they're part of enzymes like + + align:start position:0% +okay and they're part of enzymes like + + + align:start position:0% +okay and they're part of enzymes like +succinate dehydrogenase so complex + + align:start position:0% +succinate dehydrogenase so complex + + + align:start position:0% +succinate dehydrogenase so complex +ii is just happens to be an + + align:start position:0% +ii is just happens to be an + + + align:start position:0% +ii is just happens to be an +fad fadh2 containing enzyme that's part + + align:start position:0% +fad fadh2 containing enzyme that's part + + + align:start position:0% +fad fadh2 containing enzyme that's part +of the tca cycle + + align:start position:0% +of the tca cycle + + + align:start position:0% +of the tca cycle +and part of the electron transport chain + + align:start position:0% +and part of the electron transport chain + + + align:start position:0% +and part of the electron transport chain +as a way to transfer electrons in the + + align:start position:0% +as a way to transfer electrons in the + + + align:start position:0% +as a way to transfer electrons in the +tca cycle into the + + align:start position:0% +tca cycle into the + + + align:start position:0% +tca cycle into the +q pool via this succinate to fumarate + + align:start position:0% +q pool via this succinate to fumarate + + + align:start position:0% +q pool via this succinate to fumarate +conversion acyl coa dehydrogenase the + + align:start position:0% +conversion acyl coa dehydrogenase the + + + align:start position:0% +conversion acyl coa dehydrogenase the +fad fadh2 enzyme we discussed in fatty + + align:start position:0% +fad fadh2 enzyme we discussed in fatty + + + align:start position:0% +fad fadh2 enzyme we discussed in fatty +acid oxidation + + align:start position:0% +acid oxidation + + + align:start position:0% +acid oxidation +could easily be drawn instead in an + + align:start position:0% +could easily be drawn instead in an + + + align:start position:0% +could easily be drawn instead in an +electron transport chain that goes acyl + + align:start position:0% +electron transport chain that goes acyl + + + align:start position:0% +electron transport chain that goes acyl +coa dehydrogenase + + align:start position:0% +coa dehydrogenase + + + align:start position:0% +coa dehydrogenase +complex coenzyme q3 c4 just like we can + + align:start position:0% +complex coenzyme q3 c4 just like we can + + + align:start position:0% +complex coenzyme q3 c4 just like we can +say succinate to fumarate is the same as + + align:start position:0% +say succinate to fumarate is the same as + + + align:start position:0% +say succinate to fumarate is the same as +complex 2 + + align:start position:0% +complex 2 + + + align:start position:0% +complex 2 +q3 c4 okay and so + + align:start position:0% +q3 c4 okay and so + + + align:start position:0% +q3 c4 okay and so +there's really lots of alternative + + align:start position:0% +there's really lots of alternative + + + align:start position:0% +there's really lots of alternative +electron transport chains + + align:start position:0% +electron transport chains + + + align:start position:0% +electron transport chains +that involve these fad fadh2 containing + + align:start position:0% +that involve these fad fadh2 containing + + + align:start position:0% +that involve these fad fadh2 containing +enzymes + + align:start position:0% +enzymes + + + align:start position:0% +enzymes +that really sit in the membrane and + + align:start position:0% +that really sit in the membrane and + + + align:start position:0% +that really sit in the membrane and +directly transfer + + align:start position:0% +directly transfer + + + align:start position:0% +directly transfer +electrons to the q pool + + align:start position:0% + + + + align:start position:0% + +ultimately the goal of all of this is of + + align:start position:0% +ultimately the goal of all of this is of + + + align:start position:0% +ultimately the goal of all of this is of +course to create this + + align:start position:0% +course to create this + + + align:start position:0% +course to create this +delta psi delta ph which can be used to + + align:start position:0% +delta psi delta ph which can be used to + + + align:start position:0% +delta psi delta ph which can be used to +charge this battery + + align:start position:0% +charge this battery + + + align:start position:0% +charge this battery +that thing can then be done to do work + + align:start position:0% +that thing can then be done to do work + + + align:start position:0% +that thing can then be done to do work +and so + + align:start position:0% +and so + + + align:start position:0% +and so +this work includes the phosphorylation + + align:start position:0% +this work includes the phosphorylation + + + align:start position:0% +this work includes the phosphorylation +of atp + + align:start position:0% +of atp + + + align:start position:0% +of atp +and so if we charge this battery + + align:start position:0% +and so if we charge this battery + + + align:start position:0% +and so if we charge this battery +we can now use + + align:start position:0% + + + + align:start position:0% + +this as a way to couple + + align:start position:0% + + + + align:start position:0% + +current in this battery to phosphorylate + + align:start position:0% +current in this battery to phosphorylate + + + align:start position:0% +current in this battery to phosphorylate +adp + + align:start position:0% +adp + + + align:start position:0% +adp +to make atp the phosphorylation part + + align:start position:0% +to make atp the phosphorylation part + + + align:start position:0% +to make atp the phosphorylation part +of oxidative phosphorylation + + align:start position:0% +of oxidative phosphorylation + + + align:start position:0% +of oxidative phosphorylation +now this occurs also by a large protein + + align:start position:0% +now this occurs also by a large protein + + + align:start position:0% +now this occurs also by a large protein +complex sometimes referred to as + + align:start position:0% +complex sometimes referred to as + + + align:start position:0% +complex sometimes referred to as +complex 5 but remember complex 5 or this + + align:start position:0% +complex 5 but remember complex 5 or this + + + align:start position:0% +complex 5 but remember complex 5 or this +atp synthesis machinery is not really + + align:start position:0% +atp synthesis machinery is not really + + + align:start position:0% +atp synthesis machinery is not really +part of the electron transport chain it + + align:start position:0% +part of the electron transport chain it + + + align:start position:0% +part of the electron transport chain it +is separate in space + + align:start position:0% +is separate in space + + + align:start position:0% +is separate in space +and is basically something a way to + + align:start position:0% +and is basically something a way to + + + align:start position:0% +and is basically something a way to +utilize + + align:start position:0% +utilize + + + align:start position:0% +utilize +this delta psi delta ph across the + + align:start position:0% +this delta psi delta ph across the + + + align:start position:0% +this delta psi delta ph across the +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +to drive atp synthesis + + align:start position:0% +to drive atp synthesis + + + align:start position:0% +to drive atp synthesis +all right how does + + align:start position:0% +all right how does + + + align:start position:0% +all right how does +this complex 5 or atp synthesis + + align:start position:0% +this complex 5 or atp synthesis + + + align:start position:0% +this complex 5 or atp synthesis +work + + align:start position:0% + + + + align:start position:0% + +so this is also + + align:start position:0% +so this is also + + + align:start position:0% +so this is also +a large protein complex sits within + + align:start position:0% +a large protein complex sits within + + + align:start position:0% +a large protein complex sits within +the same membrane of course because it + + align:start position:0% +the same membrane of course because it + + + align:start position:0% +the same membrane of course because it +has to utilize the + + align:start position:0% +has to utilize the + + + align:start position:0% +has to utilize the +membrane potential to function + + align:start position:0% + + + + align:start position:0% + +and this so-called + + align:start position:0% +and this so-called + + + align:start position:0% +and this so-called +complex 5 is also referred to + + align:start position:0% +complex 5 is also referred to + + + align:start position:0% +complex 5 is also referred to +as the atp synthase + + align:start position:0% + + + + align:start position:0% + +or the f0 f1 + + align:start position:0% +or the f0 f1 + + + align:start position:0% +or the f0 f1 +atp ace and basically + + align:start position:0% + + + + align:start position:0% + +if this is the inner membrane space + + align:start position:0% +if this is the inner membrane space + + + align:start position:0% +if this is the inner membrane space +this is the inner mitochondrial membrane + + align:start position:0% +this is the inner mitochondrial membrane + + + align:start position:0% +this is the inner mitochondrial membrane +this is the matrix you have + + align:start position:0% +this is the matrix you have + + + align:start position:0% +this is the matrix you have +a protein complex that sits within the + + align:start position:0% +a protein complex that sits within the + + + align:start position:0% +a protein complex that sits within the +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +called f zero it's actually f + + align:start position:0% +called f zero it's actually f + + + align:start position:0% +called f zero it's actually f +o the o stands for oligomycin + + align:start position:0% +o the o stands for oligomycin + + + align:start position:0% +o the o stands for oligomycin +because there's a drug called oligomycin + + align:start position:0% +because there's a drug called oligomycin + + + align:start position:0% +because there's a drug called oligomycin +that inhibits the + + align:start position:0% +that inhibits the + + + align:start position:0% +that inhibits the +f o or f zero part of the + + align:start position:0% +f o or f zero part of the + + + align:start position:0% +f o or f zero part of the +molecule and then there's this f1 + + align:start position:0% +molecule and then there's this f1 + + + align:start position:0% +molecule and then there's this f1 +component that is associated with the + + align:start position:0% +component that is associated with the + + + align:start position:0% +component that is associated with the +f-zero component + + align:start position:0% +f-zero component + + + align:start position:0% +f-zero component +that sits on the matrix side of the + + align:start position:0% +that sits on the matrix side of the + + + align:start position:0% +that sits on the matrix side of the +membrane and it is effectively + + align:start position:0% +membrane and it is effectively + + + align:start position:0% +membrane and it is effectively +the machine that + + align:start position:0% +the machine that + + + align:start position:0% +the machine that +phosphorylates + + align:start position:0% + + + + align:start position:0% + +or interconverts atp and + + align:start position:0% +or interconverts atp and + + + align:start position:0% +or interconverts atp and +adp on the matrix side of the membrane + + align:start position:0% +adp on the matrix side of the membrane + + + align:start position:0% +adp on the matrix side of the membrane +now it's pretty well understood how this + + align:start position:0% +now it's pretty well understood how this + + + align:start position:0% +now it's pretty well understood how this +system works + + align:start position:0% +system works + + + align:start position:0% +system works +and basically f1 works by a process + + align:start position:0% +and basically f1 works by a process + + + align:start position:0% +and basically f1 works by a process +called + + align:start position:0% +called + + + align:start position:0% +called +rotational catalysis how this works was + + align:start position:0% +rotational catalysis how this works was + + + align:start position:0% +rotational catalysis how this works was +awarded the nobel prize in 1997 + + align:start position:0% +awarded the nobel prize in 1997 + + + align:start position:0% +awarded the nobel prize in 1997 +figured out not all that long ago + + align:start position:0% +figured out not all that long ago + + + align:start position:0% +figured out not all that long ago +and basically this is f1 is a large + + align:start position:0% +and basically this is f1 is a large + + + align:start position:0% +and basically this is f1 is a large +protein + + align:start position:0% +protein + + + align:start position:0% +protein +complex where you have a gamma subunit + + align:start position:0% +complex where you have a gamma subunit + + + align:start position:0% +complex where you have a gamma subunit +that is attached to f0 that couples + + align:start position:0% +that is attached to f0 that couples + + + align:start position:0% +that is attached to f0 that couples +basically proton pumping + + align:start position:0% +basically proton pumping + + + align:start position:0% +basically proton pumping +to this gamma subunit to literally turn + + align:start position:0% +to this gamma subunit to literally turn + + + align:start position:0% +to this gamma subunit to literally turn +the f1 component + + align:start position:0% +the f1 component + + + align:start position:0% +the f1 component +and change the confirmation of attached + + align:start position:0% +and change the confirmation of attached + + + align:start position:0% +and change the confirmation of attached +regions parts of this f1 + + align:start position:0% +regions parts of this f1 + + + align:start position:0% +regions parts of this f1 +machine because it turns out you can + + align:start position:0% +machine because it turns out you can + + + align:start position:0% +machine because it turns out you can +have three different confirmations + + align:start position:0% +have three different confirmations + + + align:start position:0% +have three different confirmations +of the rest of f1 the so-called l + + align:start position:0% +of the rest of f1 the so-called l + + + align:start position:0% +of the rest of f1 the so-called l +or loose confirmation the t or tight + + align:start position:0% +or loose confirmation the t or tight + + + align:start position:0% +or loose confirmation the t or tight +confirmation + + align:start position:0% +confirmation + + + align:start position:0% +confirmation +or the o or open confirmation + + align:start position:0% +or the o or open confirmation + + + align:start position:0% +or the o or open confirmation +and so in the open conformation + + align:start position:0% +and so in the open conformation + + + align:start position:0% +and so in the open conformation +adp and phosphate + + align:start position:0% +adp and phosphate + + + align:start position:0% +adp and phosphate +or atp + + align:start position:0% +or atp + + + align:start position:0% +or atp +can exchange in and out of + + align:start position:0% +can exchange in and out of + + + align:start position:0% +can exchange in and out of +this complex all right + + align:start position:0% +this complex all right + + + align:start position:0% +this complex all right +in the loose conformation you basically + + align:start position:0% +in the loose conformation you basically + + + align:start position:0% +in the loose conformation you basically +have adp and phosphate bound + + align:start position:0% +have adp and phosphate bound + + + align:start position:0% +have adp and phosphate bound +and in the tight conformation + + align:start position:0% +and in the tight conformation + + + align:start position:0% +and in the tight conformation +this is favored + + align:start position:0% +this is favored + + + align:start position:0% +this is favored +to synthesize atp + + align:start position:0% +to synthesize atp + + + align:start position:0% +to synthesize atp +and so you can envision that what + + align:start position:0% +and so you can envision that what + + + align:start position:0% +and so you can envision that what +actually happens here is that you first + + align:start position:0% +actually happens here is that you first + + + align:start position:0% +actually happens here is that you first +have + + align:start position:0% +have + + + align:start position:0% +have +adp and atp bind + + align:start position:0% +adp and atp bind + + + align:start position:0% +adp and atp bind +in this open conformation + + align:start position:0% + + + + align:start position:0% + +okay protons are moved + + align:start position:0% +okay protons are moved + + + align:start position:0% +okay protons are moved +you get rotation around the gamma + + align:start position:0% +you get rotation around the gamma + + + align:start position:0% +you get rotation around the gamma +subunit + + align:start position:0% +subunit + + + align:start position:0% +subunit +that changes the conformation of the o + + align:start position:0% +that changes the conformation of the o + + + align:start position:0% +that changes the conformation of the o +subunit to the loose subunit so now you + + align:start position:0% +subunit to the loose subunit so now you + + + align:start position:0% +subunit to the loose subunit so now you +have adp + + align:start position:0% +have adp + + + align:start position:0% +have adp +plus pi bound another proton moves + + align:start position:0% +plus pi bound another proton moves + + + align:start position:0% +plus pi bound another proton moves +changes the confirmation of the loose + + align:start position:0% +changes the confirmation of the loose + + + align:start position:0% +changes the confirmation of the loose +subunit + + align:start position:0% +subunit + + + align:start position:0% +subunit +into the tight conformation + + align:start position:0% +into the tight conformation + + + align:start position:0% +into the tight conformation +now atp synthesis is + + align:start position:0% +now atp synthesis is + + + align:start position:0% +now atp synthesis is +favored another proton moves + + align:start position:0% +favored another proton moves + + + align:start position:0% +favored another proton moves +comes back to the open conformation + + align:start position:0% +comes back to the open conformation + + + align:start position:0% +comes back to the open conformation +and atp is released from the molecule + + align:start position:0% +and atp is released from the molecule + + + align:start position:0% +and atp is released from the molecule +and you can run another rotational + + align:start position:0% +and you can run another rotational + + + align:start position:0% +and you can run another rotational +catalysis cycle + + align:start position:0% +catalysis cycle + + + align:start position:0% +catalysis cycle +again to ultimately drive adp to atp + + align:start position:0% +again to ultimately drive adp to atp + + + align:start position:0% +again to ultimately drive adp to atp +synthesis + + align:start position:0% +synthesis + + + align:start position:0% +synthesis +using this transfer of protons + + align:start position:0% +using this transfer of protons + + + align:start position:0% +using this transfer of protons +across the f0 subunit to ultimately + + align:start position:0% +across the f0 subunit to ultimately + + + align:start position:0% +across the f0 subunit to ultimately +rotate this machine to synthesize + + align:start position:0% +rotate this machine to synthesize + + + align:start position:0% +rotate this machine to synthesize +atp now the way f0 works + + align:start position:0% +atp now the way f0 works + + + align:start position:0% +atp now the way f0 works +is within the membrane and this is + + align:start position:0% +is within the membrane and this is + + + align:start position:0% +is within the membrane and this is +always + + align:start position:0% +always + + + align:start position:0% +always +hard to draw you basically have + + align:start position:0% + + + + align:start position:0% + +a central piece + + align:start position:0% +a central piece + + + align:start position:0% +a central piece +with another uh central complex with + + align:start position:0% +with another uh central complex with + + + align:start position:0% +with another uh central complex with +another set of complexes around it + + align:start position:0% +another set of complexes around it + + + align:start position:0% +another set of complexes around it +that within that have two half channels + + align:start position:0% +that within that have two half channels + + + align:start position:0% +that within that have two half channels +that are open to either side of the + + align:start position:0% +that are open to either side of the + + + align:start position:0% +that are open to either side of the +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +and so if you look at this from the top + + align:start position:0% +and so if you look at this from the top + + + align:start position:0% +and so if you look at this from the top +view + + align:start position:0% +view + + + align:start position:0% +view +so looking at it straight down you'd + + align:start position:0% +so looking at it straight down you'd + + + align:start position:0% +so looking at it straight down you'd +have this central piece + + align:start position:0% +have this central piece + + + align:start position:0% +have this central piece +with this external piece with the two + + align:start position:0% +with this external piece with the two + + + align:start position:0% +with this external piece with the two +half channels + + align:start position:0% +half channels + + + align:start position:0% +half channels +that basically can rotate around + + align:start position:0% +that basically can rotate around + + + align:start position:0% +that basically can rotate around +the central stalk this is hooked up to + + align:start position:0% +the central stalk this is hooked up to + + + align:start position:0% +the central stalk this is hooked up to +the gamma subunit of f1 in which drives + + align:start position:0% +the gamma subunit of f1 in which drives + + + align:start position:0% +the gamma subunit of f1 in which drives +rotational catalysis + + align:start position:0% +rotational catalysis + + + align:start position:0% +rotational catalysis +and how this works is that attached to + + align:start position:0% +and how this works is that attached to + + + align:start position:0% +and how this works is that attached to +this + + align:start position:0% +this + + + align:start position:0% +this +inner piece that is open to the half + + align:start position:0% +inner piece that is open to the half + + + align:start position:0% +inner piece that is open to the half +channels is an aspartate + + align:start position:0% +channels is an aspartate + + + align:start position:0% +channels is an aspartate +residue okay so this is an aspartic acid + + align:start position:0% +residue okay so this is an aspartic acid + + + align:start position:0% +residue okay so this is an aspartic acid +residue that's there and + + align:start position:0% +residue that's there and + + + align:start position:0% +residue that's there and +recall that aspartic acid + + align:start position:0% +recall that aspartic acid + + + align:start position:0% +recall that aspartic acid +is an acid so it can pick up a proton + + align:start position:0% + + + + align:start position:0% + +or release a proton from its acid group + + align:start position:0% +or release a proton from its acid group + + + align:start position:0% +or release a proton from its acid group +depending on + + align:start position:0% +depending on + + + align:start position:0% +depending on +the ph on either side of the membrane + + align:start position:0% +the ph on either side of the membrane + + + align:start position:0% +the ph on either side of the membrane +and so remember there's a different ph + + align:start position:0% +and so remember there's a different ph + + + align:start position:0% +and so remember there's a different ph +on the two + + align:start position:0% +on the two + + + align:start position:0% +on the two +sides of the membrane okay + + align:start position:0% +sides of the membrane okay + + + align:start position:0% +sides of the membrane okay +and it's really that difference in + + align:start position:0% +and it's really that difference in + + + align:start position:0% +and it's really that difference in +ph that will allow + + align:start position:0% +ph that will allow + + + align:start position:0% +ph that will allow +favorable turning around this center + + align:start position:0% +favorable turning around this center + + + align:start position:0% +favorable turning around this center +stalk + + align:start position:0% +stalk + + + align:start position:0% +stalk +and so the ph in the inner membrane + + align:start position:0% +and so the ph in the inner membrane + + + align:start position:0% +and so the ph in the inner membrane +space is + + align:start position:0% +space is + + + align:start position:0% +space is +lower okay so that means you're more + + align:start position:0% +lower okay so that means you're more + + + align:start position:0% +lower okay so that means you're more +likely to favor + + align:start position:0% +likely to favor + + + align:start position:0% +likely to favor +protonation of the aspartate it can then + + align:start position:0% +protonation of the aspartate it can then + + + align:start position:0% +protonation of the aspartate it can then +rotate such that the channel that + + align:start position:0% +rotate such that the channel that + + + align:start position:0% +rotate such that the channel that +aspartate is now exposed to the other + + align:start position:0% +aspartate is now exposed to the other + + + align:start position:0% +aspartate is now exposed to the other +channel to the matrix side + + align:start position:0% +channel to the matrix side + + + align:start position:0% +channel to the matrix side +there the ph is higher so favors + + align:start position:0% +there the ph is higher so favors + + + align:start position:0% +there the ph is higher so favors +deprotonation + + align:start position:0% +deprotonation + + + align:start position:0% +deprotonation +and basically this will drive + + align:start position:0% +and basically this will drive + + + align:start position:0% +and basically this will drive +motion of this piece around the central + + align:start position:0% +motion of this piece around the central + + + align:start position:0% +motion of this piece around the central +stock + + align:start position:0% +stock + + + align:start position:0% +stock +that being coupled to the gamma subunit + + align:start position:0% +that being coupled to the gamma subunit + + + align:start position:0% +that being coupled to the gamma subunit +of f1 + + align:start position:0% +of f1 + + + align:start position:0% +of f1 +will cause rotation of the + + align:start position:0% +will cause rotation of the + + + align:start position:0% +will cause rotation of the +f1 subunit changing the attached + + align:start position:0% +f1 subunit changing the attached + + + align:start position:0% +f1 subunit changing the attached +conformation of the rest of the complex + + align:start position:0% +conformation of the rest of the complex + + + align:start position:0% +conformation of the rest of the complex +to favor atp synthesis and it's really + + align:start position:0% +to favor atp synthesis and it's really + + + align:start position:0% +to favor atp synthesis and it's really +this + + align:start position:0% +this + + + align:start position:0% +this +is how you have moving of protons back + + align:start position:0% +is how you have moving of protons back + + + align:start position:0% +is how you have moving of protons back +from the inner membrane space to the + + align:start position:0% +from the inner membrane space to the + + + align:start position:0% +from the inner membrane space to the +matrix can drive + + align:start position:0% +matrix can drive + + + align:start position:0% +matrix can drive +the synthesis of atp the phosphorylation + + align:start position:0% +the synthesis of atp the phosphorylation + + + align:start position:0% +the synthesis of atp the phosphorylation +part + + align:start position:0% +part + + + align:start position:0% +part +of this process + + align:start position:0% +of this process + + + align:start position:0% +of this process +and so now you have a full picture of + + align:start position:0% +and so now you have a full picture of + + + align:start position:0% +and so now you have a full picture of +how + + align:start position:0% +how + + + align:start position:0% +how +carbon oxidation really releases energy + + align:start position:0% +carbon oxidation really releases energy + + + align:start position:0% +carbon oxidation really releases energy +in a way that's coupled to do work in + + align:start position:0% +in a way that's coupled to do work in + + + align:start position:0% +in a way that's coupled to do work in +biology + + align:start position:0% +biology + + + align:start position:0% +biology +so we can of course couple this directly + + align:start position:0% +so we can of course couple this directly + + + align:start position:0% +so we can of course couple this directly +as we did + + align:start position:0% +as we did + + + align:start position:0% +as we did +at gap dh or succinct thiokinase but + + align:start position:0% +at gap dh or succinct thiokinase but + + + align:start position:0% +at gap dh or succinct thiokinase but +mostly it's captured to charge up + + align:start position:0% +mostly it's captured to charge up + + + align:start position:0% +mostly it's captured to charge up +these nad nadh ratios + + align:start position:0% +these nad nadh ratios + + + align:start position:0% +these nad nadh ratios +where favorable electron transport can + + align:start position:0% +where favorable electron transport can + + + align:start position:0% +where favorable electron transport can +be used to make this delta psi delta ph + + align:start position:0% +be used to make this delta psi delta ph + + + align:start position:0% +be used to make this delta psi delta ph +in a membrane + + align:start position:0% +in a membrane + + + align:start position:0% +in a membrane +that can be used also to synthesize atp + + align:start position:0% +that can be used also to synthesize atp + + + align:start position:0% +that can be used also to synthesize atp +despite a high atp adp ratio + + align:start position:0% +despite a high atp adp ratio + + + align:start position:0% +despite a high atp adp ratio +because electron trans because that + + align:start position:0% +because electron trans because that + + + align:start position:0% +because electron trans because that +battery + + align:start position:0% +battery + + + align:start position:0% +battery +can be used to drive this machine + + align:start position:0% +can be used to drive this machine + + + align:start position:0% +can be used to drive this machine +now i want to point out that the atp + + align:start position:0% +now i want to point out that the atp + + + align:start position:0% +now i want to point out that the atp +synthase is just like any other enzyme + + align:start position:0% +synthase is just like any other enzyme + + + align:start position:0% +synthase is just like any other enzyme +in any pathway + + align:start position:0% +in any pathway + + + align:start position:0% +in any pathway +and that is if conditions are right + + align:start position:0% +and that is if conditions are right + + + align:start position:0% +and that is if conditions are right +there's no reason + + align:start position:0% +there's no reason + + + align:start position:0% +there's no reason +that this machine has to drive atp + + align:start position:0% +that this machine has to drive atp + + + align:start position:0% +that this machine has to drive atp +synthesis + + align:start position:0% +synthesis + + + align:start position:0% +synthesis +it could also consume atp + + align:start position:0% +it could also consume atp + + + align:start position:0% +it could also consume atp +as a way to create a proton gradient + + align:start position:0% +as a way to create a proton gradient + + + align:start position:0% +as a way to create a proton gradient +that is use atp hydrolysis + + align:start position:0% +that is use atp hydrolysis + + + align:start position:0% +that is use atp hydrolysis +to pump protons in the opposite + + align:start position:0% +to pump protons in the opposite + + + align:start position:0% +to pump protons in the opposite +direction into the inner membrane space + + align:start position:0% +direction into the inner membrane space + + + align:start position:0% +direction into the inner membrane space +well why would you ever do that well you + + align:start position:0% +well why would you ever do that well you + + + align:start position:0% +well why would you ever do that well you +would do that because having this + + align:start position:0% +would do that because having this + + + align:start position:0% +would do that because having this +battery + + align:start position:0% +battery + + + align:start position:0% +battery +is useful because atp is not the only + + align:start position:0% +is useful because atp is not the only + + + align:start position:0% +is useful because atp is not the only +way that cells can use energy to do work + + align:start position:0% +way that cells can use energy to do work + + + align:start position:0% +way that cells can use energy to do work +it turns out that having a membrane + + align:start position:0% +it turns out that having a membrane + + + align:start position:0% +it turns out that having a membrane +potential is useful for other things so + + align:start position:0% +potential is useful for other things so + + + align:start position:0% +potential is useful for other things so +if you're in course nine you know + + align:start position:0% +if you're in course nine you know + + + align:start position:0% +if you're in course nine you know +that action potentials are carried + + align:start position:0% +that action potentials are carried + + + align:start position:0% +that action potentials are carried +basically electricity along + + align:start position:0% +basically electricity along + + + align:start position:0% +basically electricity along +cells what is that that is basically + + align:start position:0% +cells what is that that is basically + + + align:start position:0% +cells what is that that is basically +changing membrane potentials across + + align:start position:0% +changing membrane potentials across + + + align:start position:0% +changing membrane potentials across +cells more generally membrane potentials + + align:start position:0% +cells more generally membrane potentials + + + align:start position:0% +cells more generally membrane potentials +can be used to do lots of other + + align:start position:0% +can be used to do lots of other + + + align:start position:0% +can be used to do lots of other +types of work and so atp is only one way + + align:start position:0% +types of work and so atp is only one way + + + align:start position:0% +types of work and so atp is only one way +that cells can use + + align:start position:0% +that cells can use + + + align:start position:0% +that cells can use +biological energy because it can be + + align:start position:0% +biological energy because it can be + + + align:start position:0% +biological energy because it can be +coupled to otherwise unfavorable + + align:start position:0% +coupled to otherwise unfavorable + + + align:start position:0% +coupled to otherwise unfavorable +reactions + + align:start position:0% +reactions + + + align:start position:0% +reactions +but you can also couple ion gradients to + + align:start position:0% +but you can also couple ion gradients to + + + align:start position:0% +but you can also couple ion gradients to +unfavorable reactions and use that + + align:start position:0% +unfavorable reactions and use that + + + align:start position:0% +unfavorable reactions and use that +to do work and so lots of useful ways + + align:start position:0% +to do work and so lots of useful ways + + + align:start position:0% +to do work and so lots of useful ways +that delta psi delta ph + + align:start position:0% +that delta psi delta ph + + + align:start position:0% +that delta psi delta ph +can be used by cells + + align:start position:0% +can be used by cells + + + align:start position:0% +can be used by cells +and so what are some of these well the + + align:start position:0% +and so what are some of these well the + + + align:start position:0% +and so what are some of these well the +first one + + align:start position:0% +first one + + + align:start position:0% +first one +is this can be used to generate heat + + align:start position:0% +is this can be used to generate heat + + + align:start position:0% +is this can be used to generate heat +so if you're checking your phone right + + align:start position:0% +so if you're checking your phone right + + + align:start position:0% +so if you're checking your phone right +now your phone is obviously a very + + align:start position:0% +now your phone is obviously a very + + + align:start position:0% +now your phone is obviously a very +useful device to do all kinds of + + align:start position:0% +useful device to do all kinds of + + + align:start position:0% +useful device to do all kinds of +work for you you can read whatever you + + align:start position:0% +work for you you can read whatever you + + + align:start position:0% +work for you you can read whatever you +want on your phone + + align:start position:0% +want on your phone + + + align:start position:0% +want on your phone +use it to call people but what happens + + align:start position:0% +use it to call people but what happens + + + align:start position:0% +use it to call people but what happens +if you short circuit the battery in your + + align:start position:0% +if you short circuit the battery in your + + + align:start position:0% +if you short circuit the battery in your +phone + + align:start position:0% +phone + + + align:start position:0% +phone +well it'll get really hot and the same + + align:start position:0% +well it'll get really hot and the same + + + align:start position:0% +well it'll get really hot and the same +thing happens here + + align:start position:0% +thing happens here + + + align:start position:0% +thing happens here +if i rather than use this delta psi + + align:start position:0% +if i rather than use this delta psi + + + align:start position:0% +if i rather than use this delta psi +delta ph to generate atp + + align:start position:0% +delta ph to generate atp + + + align:start position:0% +delta ph to generate atp +if i just put a hole in the membrane + + align:start position:0% +if i just put a hole in the membrane + + + align:start position:0% +if i just put a hole in the membrane +something referred to as an uncoupling + + align:start position:0% +something referred to as an uncoupling + + + align:start position:0% +something referred to as an uncoupling +protein on + + align:start position:0% +protein on + + + align:start position:0% +protein on +ucp or uncoupling protein this will just + + align:start position:0% +ucp or uncoupling protein this will just + + + align:start position:0% +ucp or uncoupling protein this will just +allow + + align:start position:0% +allow + + + align:start position:0% +allow +the leak of protons back across the + + align:start position:0% +the leak of protons back across the + + + align:start position:0% +the leak of protons back across the +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +well that's short-circuiting the battery + + align:start position:0% +well that's short-circuiting the battery + + + align:start position:0% +well that's short-circuiting the battery +energy has to be dissipated somewhere + + align:start position:0% +energy has to be dissipated somewhere + + + align:start position:0% +energy has to be dissipated somewhere +and it's dissipated + + align:start position:0% +and it's dissipated + + + align:start position:0% +and it's dissipated +as heat and this is effectively + + align:start position:0% +as heat and this is effectively + + + align:start position:0% +as heat and this is effectively +ways in which biology can create heat + + align:start position:0% +ways in which biology can create heat + + + align:start position:0% +ways in which biology can create heat +and so uncoupling proteins are expressed + + align:start position:0% +and so uncoupling proteins are expressed + + + align:start position:0% +and so uncoupling proteins are expressed +in a tissue called brown fat + + align:start position:0% +in a tissue called brown fat + + + align:start position:0% +in a tissue called brown fat +in mammals brown fat is a way to + + align:start position:0% +in mammals brown fat is a way to + + + align:start position:0% +in mammals brown fat is a way to +generate heat and it's one way that we + + align:start position:0% +generate heat and it's one way that we + + + align:start position:0% +generate heat and it's one way that we +maintain our body temperatures + + align:start position:0% +maintain our body temperatures + + + align:start position:0% +maintain our body temperatures +now the system is imperfect and lots of + + align:start position:0% +now the system is imperfect and lots of + + + align:start position:0% +now the system is imperfect and lots of +cells + + align:start position:0% +cells + + + align:start position:0% +cells +all metabolism generates some heat if + + align:start position:0% +all metabolism generates some heat if + + + align:start position:0% +all metabolism generates some heat if +you've ever done composting you know + + align:start position:0% +you've ever done composting you know + + + align:start position:0% +you've ever done composting you know +your compost pile gets hot + + align:start position:0% +your compost pile gets hot + + + align:start position:0% +your compost pile gets hot +that's because the organisms there that + + align:start position:0% +that's because the organisms there that + + + align:start position:0% +that's because the organisms there that +are metabolizing the material in the + + align:start position:0% +are metabolizing the material in the + + + align:start position:0% +are metabolizing the material in the +compost pile + + align:start position:0% +compost pile + + + align:start position:0% +compost pile +are generating some heat and that's + + align:start position:0% +are generating some heat and that's + + + align:start position:0% +are generating some heat and that's +because membranes aren't perfect they're + + align:start position:0% +because membranes aren't perfect they're + + + align:start position:0% +because membranes aren't perfect they're +somewhat leaky + + align:start position:0% +somewhat leaky + + + align:start position:0% +somewhat leaky +now as humans we work hard to maintain a + + align:start position:0% +now as humans we work hard to maintain a + + + align:start position:0% +now as humans we work hard to maintain a +constant body temperature + + align:start position:0% +constant body temperature + + + align:start position:0% +constant body temperature +and there's actually a huge amount of + + align:start position:0% +and there's actually a huge amount of + + + align:start position:0% +and there's actually a huge amount of +energy that goes into just maintaining + + align:start position:0% +energy that goes into just maintaining + + + align:start position:0% +energy that goes into just maintaining +our body temperature but you can imagine + + align:start position:0% +our body temperature but you can imagine + + + align:start position:0% +our body temperature but you can imagine +how efficiently + + align:start position:0% +how efficiently + + + align:start position:0% +how efficiently +we couple these processes we'll + + align:start position:0% +we couple these processes we'll + + + align:start position:0% +we couple these processes we'll +determine how many calories we need + + align:start position:0% +determine how many calories we need + + + align:start position:0% +determine how many calories we need +to maintain heat and that's actually a + + align:start position:0% +to maintain heat and that's actually a + + + align:start position:0% +to maintain heat and that's actually a +theory of weight control + + align:start position:0% +theory of weight control + + + align:start position:0% +theory of weight control +that those of us out there who have less + + align:start position:0% +that those of us out there who have less + + + align:start position:0% +that those of us out there who have less +well-coupled mitochondria can eat more + + align:start position:0% +well-coupled mitochondria can eat more + + + align:start position:0% +well-coupled mitochondria can eat more +because they waste more energy in + + align:start position:0% +because they waste more energy in + + + align:start position:0% +because they waste more energy in +generating heat than those of us who are + + align:start position:0% +generating heat than those of us who are + + + align:start position:0% +generating heat than those of us who are +really efficient + + align:start position:0% +really efficient + + + align:start position:0% +really efficient +in doing this and in fact there's drugs + + align:start position:0% +in doing this and in fact there's drugs + + + align:start position:0% +in doing this and in fact there's drugs +that allow you to uncouple + + align:start position:0% +that allow you to uncouple + + + align:start position:0% +that allow you to uncouple +electron transport generation of delta + + align:start position:0% +electron transport generation of delta + + + align:start position:0% +electron transport generation of delta +psi delta ph + + align:start position:0% +psi delta ph + + + align:start position:0% +psi delta ph +from utilizing that membrane potential + + align:start position:0% +from utilizing that membrane potential + + + align:start position:0% +from utilizing that membrane potential +and these are great weight loss drugs + + align:start position:0% +and these are great weight loss drugs + + + align:start position:0% +and these are great weight loss drugs +dinitrophenol + + align:start position:0% +dinitrophenol + + + align:start position:0% +dinitrophenol +was used middle part of the last century + + align:start position:0% +was used middle part of the last century + + + align:start position:0% +was used middle part of the last century +as a weight loss agent was very + + align:start position:0% +as a weight loss agent was very + + + align:start position:0% +as a weight loss agent was very +effective the problem is it's also + + align:start position:0% +effective the problem is it's also + + + align:start position:0% +effective the problem is it's also +incredibly dangerous because people will + + align:start position:0% +incredibly dangerous because people will + + + align:start position:0% +incredibly dangerous because people will +die because it turns out + + align:start position:0% +die because it turns out + + + align:start position:0% +die because it turns out +if you uncouple this process and you + + align:start position:0% +if you uncouple this process and you + + + align:start position:0% +if you uncouple this process and you +don't have enough atp you die really + + align:start position:0% +don't have enough atp you die really + + + align:start position:0% +don't have enough atp you die really +fast + + align:start position:0% +fast + + + align:start position:0% +fast +and so don't use that drug but it + + align:start position:0% +and so don't use that drug but it + + + align:start position:0% +and so don't use that drug but it +illustrates + + align:start position:0% +illustrates + + + align:start position:0% +illustrates +how you can use this battery to generate + + align:start position:0% +how you can use this battery to generate + + + align:start position:0% +how you can use this battery to generate +heat another form of + + align:start position:0% +heat another form of + + + align:start position:0% +heat another form of +energy another big one is + + align:start position:0% +energy another big one is + + + align:start position:0% +energy another big one is +membrane transport + + align:start position:0% +membrane transport + + + align:start position:0% +membrane transport +so if i want to concentrate something + + align:start position:0% +so if i want to concentrate something + + + align:start position:0% +so if i want to concentrate something +and this could be + + align:start position:0% +and this could be + + + align:start position:0% +and this could be +moving proteins or it could be + + align:start position:0% +moving proteins or it could be + + + align:start position:0% +moving proteins or it could be +moving other ions like in an action + + align:start position:0% +moving other ions like in an action + + + align:start position:0% +moving other ions like in an action +potential + + align:start position:0% +potential + + + align:start position:0% +potential +all right those are unfavorable + + align:start position:0% +all right those are unfavorable + + + align:start position:0% +all right those are unfavorable +processes right i'm + + align:start position:0% +processes right i'm + + + align:start position:0% +processes right i'm +causing dissociation of ions across + + align:start position:0% +causing dissociation of ions across + + + align:start position:0% +causing dissociation of ions across +membranes okay + + align:start position:0% +membranes okay + + + align:start position:0% +membranes okay +or moving protein from one side of a + + align:start position:0% +or moving protein from one side of a + + + align:start position:0% +or moving protein from one side of a +membrane to another + + align:start position:0% +membrane to another + + + align:start position:0% +membrane to another +one can couple those transport processes + + align:start position:0% +one can couple those transport processes + + + align:start position:0% +one can couple those transport processes +to these + + align:start position:0% +to these + + + align:start position:0% +to these +delta side delta ph as well and in fact + + align:start position:0% +delta side delta ph as well and in fact + + + align:start position:0% +delta side delta ph as well and in fact +protein imported in the mitochondria + + align:start position:0% +protein imported in the mitochondria + + + align:start position:0% +protein imported in the mitochondria +depends very much on a membrane + + align:start position:0% +depends very much on a membrane + + + align:start position:0% +depends very much on a membrane +potential to get those proteins in + + align:start position:0% +potential to get those proteins in + + + align:start position:0% +potential to get those proteins in +the mitochondria is an important site of + + align:start position:0% +the mitochondria is an important site of + + + align:start position:0% +the mitochondria is an important site of +calcium storage for cells + + align:start position:0% +calcium storage for cells + + + align:start position:0% +calcium storage for cells +calcium is concentrated in the + + align:start position:0% +calcium is concentrated in the + + + align:start position:0% +calcium is concentrated in the +mitochondria and that concentration + + align:start position:0% +mitochondria and that concentration + + + align:start position:0% +mitochondria and that concentration +can be driven by this membrane potential + + align:start position:0% +can be driven by this membrane potential + + + align:start position:0% +can be driven by this membrane potential +and of course this potential can also + + align:start position:0% +and of course this potential can also + + + align:start position:0% +and of course this potential can also +use + + align:start position:0% +use + + + align:start position:0% +use +to power lots of shuttles like the + + align:start position:0% +to power lots of shuttles like the + + + align:start position:0% +to power lots of shuttles like the +carnitine shuttle + + align:start position:0% +carnitine shuttle + + + align:start position:0% +carnitine shuttle +and actually create situations where you + + align:start position:0% +and actually create situations where you + + + align:start position:0% +and actually create situations where you +have different conditions across + + align:start position:0% +have different conditions across + + + align:start position:0% +have different conditions across +membranes + + align:start position:0% +membranes + + + align:start position:0% +membranes +as a way to favor different chemistries + + align:start position:0% +as a way to favor different chemistries + + + align:start position:0% +as a way to favor different chemistries +and so the last thing i want to mention + + align:start position:0% +and so the last thing i want to mention + + + align:start position:0% +and so the last thing i want to mention +is in fact these shuttles + + align:start position:0% +is in fact these shuttles + + + align:start position:0% +is in fact these shuttles +which is just ways that one can couple + + align:start position:0% +which is just ways that one can couple + + + align:start position:0% +which is just ways that one can couple +membrane potential to drive other things + + align:start position:0% +membrane potential to drive other things + + + align:start position:0% +membrane potential to drive other things +can also be really important for how + + align:start position:0% +can also be really important for how + + + align:start position:0% +can also be really important for how +metabolism works + + align:start position:0% +metabolism works + + + align:start position:0% +metabolism works +and i just want to illustrate one aspect + + align:start position:0% +and i just want to illustrate one aspect + + + align:start position:0% +and i just want to illustrate one aspect +of this so if i draw here + + align:start position:0% +of this so if i draw here + + + align:start position:0% +of this so if i draw here +my mitochondr + + align:start position:0% + + + + align:start position:0% + +if i draw a mitochondria + + align:start position:0% + + + + align:start position:0% + +so here's all these processes are + + align:start position:0% +so here's all these processes are + + + align:start position:0% +so here's all these processes are +happening + + align:start position:0% +happening + + + align:start position:0% +happening +here where we have electron transport + + align:start position:0% +here where we have electron transport + + + align:start position:0% +here where we have electron transport +generating a potential across the inner + + align:start position:0% +generating a potential across the inner + + + align:start position:0% +generating a potential across the inner +mitochondrial membrane + + align:start position:0% +mitochondrial membrane + + + align:start position:0% +mitochondrial membrane +that can be used to synthesize + + align:start position:0% +that can be used to synthesize + + + align:start position:0% +that can be used to synthesize +atp well this synthesis is occurring + + align:start position:0% +atp well this synthesis is occurring + + + align:start position:0% +atp well this synthesis is occurring +in the mitochondria but ultimately + + align:start position:0% +in the mitochondria but ultimately + + + align:start position:0% +in the mitochondria but ultimately +i need to get that atp out into the + + align:start position:0% +i need to get that atp out into the + + + align:start position:0% +i need to get that atp out into the +cytosol + + align:start position:0% +cytosol + + + align:start position:0% +cytosol +for it to be useful for the cell + + align:start position:0% +for it to be useful for the cell + + + align:start position:0% +for it to be useful for the cell +to run otherwise unfavorable processes + + align:start position:0% +to run otherwise unfavorable processes + + + align:start position:0% +to run otherwise unfavorable processes +in the cytosol + + align:start position:0% +in the cytosol + + + align:start position:0% +in the cytosol +and so one needs a transporter for this + + align:start position:0% +and so one needs a transporter for this + + + align:start position:0% +and so one needs a transporter for this +some transporter called the adenine + + align:start position:0% +some transporter called the adenine + + + align:start position:0% +some transporter called the adenine +nucleotide transporter + + align:start position:0% +nucleotide transporter + + + align:start position:0% +nucleotide transporter +and this partially takes advantage of + + align:start position:0% +and this partially takes advantage of + + + align:start position:0% +and this partially takes advantage of +the fact that there's a charge + + align:start position:0% +the fact that there's a charge + + + align:start position:0% +the fact that there's a charge +difference between atp + + align:start position:0% +difference between atp + + + align:start position:0% +difference between atp +and adp to actually couple + + align:start position:0% +and adp to actually couple + + + align:start position:0% +and adp to actually couple +membrane potential to exchange of atp + + align:start position:0% +membrane potential to exchange of atp + + + align:start position:0% +membrane potential to exchange of atp +adp + + align:start position:0% +adp + + + align:start position:0% +adp +between the cytosol and the + + align:start position:0% +between the cytosol and the + + + align:start position:0% +between the cytosol and the +mitochondrial + + align:start position:0% +mitochondrial + + + align:start position:0% +mitochondrial +matrix now there's other issues we'll + + align:start position:0% +matrix now there's other issues we'll + + + align:start position:0% +matrix now there's other issues we'll +talk about next time as well + + align:start position:0% +talk about next time as well + + + align:start position:0% +talk about next time as well +and so remember some metabolism is + + align:start position:0% +and so remember some metabolism is + + + align:start position:0% +and so remember some metabolism is +happening + + align:start position:0% +happening + + + align:start position:0% +happening +in the cytosol so glycolysis + + align:start position:0% +in the cytosol so glycolysis + + + align:start position:0% +in the cytosol so glycolysis +turning glucose + + align:start position:0% +turning glucose + + + align:start position:0% +turning glucose +into pyruvate is occurring + + align:start position:0% +into pyruvate is occurring + + + align:start position:0% +into pyruvate is occurring +in the cytosol we've already discussed + + align:start position:0% +in the cytosol we've already discussed + + + align:start position:0% +in the cytosol we've already discussed +that means you got to get pyruvate in + + align:start position:0% +that means you got to get pyruvate in + + + align:start position:0% +that means you got to get pyruvate in +the mitochondria for the pdh reaction + + align:start position:0% +the mitochondria for the pdh reaction + + + align:start position:0% +the mitochondria for the pdh reaction +but this is also generating nadh in the + + align:start position:0% +but this is also generating nadh in the + + + align:start position:0% +but this is also generating nadh in the +cytosol and if that nadh + + align:start position:0% +cytosol and if that nadh + + + align:start position:0% +cytosol and if that nadh +needs to transfer its electrons to + + align:start position:0% +needs to transfer its electrons to + + + align:start position:0% +needs to transfer its electrons to +oxygen we also have to get that nadh + + align:start position:0% +oxygen we also have to get that nadh + + + align:start position:0% +oxygen we also have to get that nadh +into the mitochondrial matrix or more + + align:start position:0% +into the mitochondrial matrix or more + + + align:start position:0% +into the mitochondrial matrix or more +correctly transfer those electrons into + + align:start position:0% +correctly transfer those electrons into + + + align:start position:0% +correctly transfer those electrons into +the mitochondrial matrix + + align:start position:0% +the mitochondrial matrix + + + align:start position:0% +the mitochondrial matrix +turns out cells maintain distinct + + align:start position:0% +turns out cells maintain distinct + + + align:start position:0% +turns out cells maintain distinct +nadnadh pools and the mitochondria in + + align:start position:0% +nadnadh pools and the mitochondria in + + + align:start position:0% +nadnadh pools and the mitochondria in +the cytosol + + align:start position:0% +the cytosol + + + align:start position:0% +the cytosol +that's part of the conditions that make + + align:start position:0% +that's part of the conditions that make + + + align:start position:0% +that's part of the conditions that make +different + + align:start position:0% +different + + + align:start position:0% +different +reactions favorable in each compartment + + align:start position:0% +reactions favorable in each compartment + + + align:start position:0% +reactions favorable in each compartment +and how cells do that transfer those + + align:start position:0% +and how cells do that transfer those + + + align:start position:0% +and how cells do that transfer those +electrons into the mitochondria + + align:start position:0% +electrons into the mitochondria + + + align:start position:0% +electrons into the mitochondria +ends up being another important thing + + align:start position:0% +ends up being another important thing + + + align:start position:0% +ends up being another important thing +that has to be transport that's + + align:start position:0% +that has to be transport that's + + + align:start position:0% +that has to be transport that's +driven across these membranes where one + + align:start position:0% +driven across these membranes where one + + + align:start position:0% +driven across these membranes where one +can use delta psi delta ph + + align:start position:0% +can use delta psi delta ph + + + align:start position:0% +can use delta psi delta ph +and we'll talk about that at the start + + align:start position:0% +and we'll talk about that at the start + + + align:start position:0% +and we'll talk about that at the start +of the next lecture thanks \ No newline at end of file diff --git a/2SYV_b3OelQ.txt b/2SYV_b3OelQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..e696bc24e60a17d67837cfe498b13b94983631b6 --- /dev/null +++ b/2SYV_b3OelQ.txt @@ -0,0 +1,1493 @@ +PROFESSOR: OK. + +Before we get started, I'd +like to deal with a small + +matter of some unpleasantness. + +The class is sort of like +a football game. + +When there's two minutes to go, +you shoot off a pistol. + +But when there are two meetings +to go until we have + +the quiz, we shoot off a +pistol to wake you up. + +We're scheduled to have +a quiz on October 6. + +And even though October seems +far away when you're still in + +September, that is going +to be a week + +from this coming Thursday. + +So if you have problems that +you're working on, try to get + +them to me on Thursday, or just +come slide them under my + +office door, if I'm not in. + +And I'll have them back for you +on this coming Tuesday. + +The way the material has played +out is that we're + +really at a nice, convenient +juncture between one chunk of + +interconnected material +moving on to another. + +So I think the first quiz +we'll confine to + +two-dimensional symmetry. + +And beginning in about two +minutes flat, we'll begin to + +move into-- + +take the first small steps, +at any rate, into + +three-dimensional symmetries, +which will be much more + +complicated in which we +will not deal with the + +exhaustiveness that we have been +able to afford the luxury + +of in two dimensions. + +Before I begin, let me-- does +everybody remember their + +spherical trigonometry? + +Has anybody had spherical +trigonometry? + +OK. + +What I will then do is give a +short primer on some of the + +definitions and concepts in +spherical trigonometry. + +And then we shall immediately +use this to combine rotation + +axes in space. + +Pass those back. + +AUDIENCE: I had a quick +question on this. + +PROFESSOR: Oh, sure, please. + +AUDIENCE: With the limiting +possible-- + +PROFESSOR: Yep. + +AUDIENCE: --reflections and +conditions, that does say they + +have to be figured out? + +PROFESSOR: Actually, that was a +good question and something + +that we are not going to use at +all in the symmetry tables. + +Somebody asked what about this +notation in the far right-hand + +edge of all of the +plane groups-- + +conditions limiting possible +reflections. + +One usually doesn't put a +two-dimensional crystal in an + +x-ray beam fairly often, +although I suppose a thin film + +actually is almost a +two-dimensional crystal. + +But you've probably all heard +one way or another about the + +magic conditions relating the +Miller indices of a plane that + +will require that the intensity +diffracted from that + +set of planes is identically +zero. + +And they're linear combinations +of H, K, and L. + +And one of the rules is that if +H plus K plus L is even or + +not, the intensity +may be zero. + +These are rules for systematic +absences. + +And the corresponding +information is given for you + +here for these not terribly +realistic real + +two-dimensional crystals. + +So, for example, if you turn to +number seven, P2MG, it says + +conditions limiting possible +reflections + +for the general position. + +For H and K, there's +no condition. + +For H zero, H has to be even, +if the reflection is to have + +non-zero intensity. + +And for the last two, for the +general reflections, H, K, if + +there's an atom occupying the +position either zero, zero or + +the position zero, one half, +then for the general planes + +with indices H, K, you will +see intensity only if H is + +even, as well-- same as +the condition above. + +This is something that is not +generally known that everybody + +knows-- that if the crystal is +face-centered cubic, there is + +a pattern of absences. + +But there are additional +absences if the atom is in a + +special position. + +And this can very often be used +to advantage because you + +can single out certain classes +of Miller indices for which + +one atom in the structure will +not diffract or which another + +atom in the structure +will not diffract. + +And that can be of +great utility in + +unraveling a structure. + +We'll see some examples of this +in useful form when we + +deal with three-dimensional +space groups. + +And the corresponding sheets +for the three-dimensional + +symmetries will be handed +out to you-- some of + +them, not all of them. + +Let me take a little bit of time +to remind you, if you've + +forgotten them, but to inform +you of certain definitions and + +trigonometry in spherical +geometry. + +Spherical trigonometry differs +from plane geometry in that + +all of the action takes place +on the surface of a sphere. + +And it'd be nice if I had +a spherical blackboard. + +Actually there is one in the +x-ray laboratory that I can + +draw things right on that +spherical surface. + +But this is a sphere. + +We'll see directly that +the radius of the + +sphere is not important. + +So we'll take that as a unity, +which is a nice, even number. + +And as my dichotomy of the +afternoon, if we pass a plane + +through that sphere, if the +plane hits the sphere, it will + +intersect it in a circle. + +If the plane passes through +the center of the sphere-- + +and we've assigned the radius +of the sphere as unity, then + +this is a circle that's referred +to a great circle. + +Sounds like a value judgment, +but it's simply saying that's + +as large as the circle is going +to get is when it passes + +through the center of the +sphere., it would have unit + +radius, just as the +sphere does. + +So if you take any other plane +which intersects the sphere + +but doesn't pass through the +center, it's going to have a + +smaller radius. + +And this is something that's +called a small circle. + +OK, so if all of the action is +going to take place on the + +surface of the sphere, and we +have two points on the sphere, + +A and B, sitting on the surface +of the sphere, how do + +we measure the separation +of A and B? + +Well, if you think in terms of +a normal three-dimensional + +person, you say, zonk, connect +them by a line. + +And that's the distance between +A and B. Now, you + +can't do that because all the +action has to take place on + +the surface of the sphere. + +People who deal with spherical +trigonometry all the time are + +airplane pilots. + +And if your pilot is going to +take you from New York-- + +where would you like to go? + +Paris? + +That sounds like a nice place. + +But if you're going to go from +New York to Paris, you don't + +plow your way through the +intervening earth. + +You follow something that is at +a constant radius out from + +the center the Earth, at a +height of 5,000 feet above the + +surface of the Earth, an +additional radius. + +So the way we'll define distance +is to pass a great + +circle through A, B, pass a +plane through A, B in the + +center of the sphere. + +And then we will define distance +between A and B as + +the smaller of the two angles +subtended at the + +center of the sphere. + +So this is a more reasonable +looking great circle. + +If this is point A and this is +point B, pass a plane through + +the center of the sphere, O, and +through A and through B. + +And then we'll measure the +length of the arc AB in terms + +of the angle alpha subtended at +the center of the sphere. + +So it's a crazy notion. + +We're measuring distance +in terms of an angle. + +And if that's an angle, we can +take a trigonometric function + +of that angle, like +sine or cosine. + +And that blows the mind that +you can take trigonometric + +functions of a distance. + +But we can. + +We'll see it's going to +be useful to us, too. + +And then I emphasize again, +we'll take this + +as the smaller distance. + +It'll be 360 degrees +minus alpha. + +That would be the +long way around + +from A to B. All right. + +We've defined now +how we will draw + +distances between two points. + +Suppose I have three points on +the surface of the sphere-- + +A, B, and C. I can pass a great +circle through A and B. + +I know how to do that. + +I can pass a great circle +through A and C. I + +know how to do that. + +And I can pass a great circle +through B and C. + +So now I have defined something +that is referred to + +as a spherical triangle. + +We know how to measure +the length of + +the spherical triangle. + +Let's call the arc opposite the +point of intersection A as + +little a and the length of the +arc opposite B as a distance + +and angles little b, and +the distance from A + +to C as little c. + +But there's something in between +these arcs that looks + +like an angle analogous to the +angle in a planar triangle. + +And how can we define that? + +Well, the arc AB is defined by +a plane, a great circle. + +The arc AC is similarly defined +by a plane that passes + +through a, c in the center +of the sphere. + +And what we will define as the +spherical angle BAC is the + +angle between the great circles +that define the two + +different arcs. + +So if there's one great circle +that defines the arc from A to + +B and another plane that defines +the arc from A to C, + +we'll define as the spherical +angle between those two arcs + +the angle between the planes +that define the great circles. + +So we're going to call this +angle in here between these + +two planes as angle BAC. + +Another construct that +is a useful one-- + +suppose I look at the plane +that I've used to define a + +great circle and at the center +of the sphere construct a line + +that is perpendicular +to the great circle. + +And if I extend that line, +sooner or later it's going to + +poke out through the surface +of the sphere. + +And I will refer to this point +as the pole of arc AB, or the + +pole of the great circle that +we've used to define arc AB. + +So the North Pole is actually +the pole of the great circle + +that defines the equator. + +And clearly there +are two poles. + +There's one in either +direction. + +So there's a North Pole and a +South Pole to this arc AB and + +to the great circle +that defines it. + +AUDIENCE: I have a question. + +Why couldn't you define the +angle BAC as the angle + +[INAUDIBLE]? + +PROFESSOR: You want to +make a tangent here? + +AUDIENCE: Yeah. + +PROFESSOR: I don't know if +that's really defined. + +In other words, if I'm saying I +want a line that is tangent + +to the sphere, it doesn't +fix its orientation. + +AUDIENCE: In the plane +of the great circle. + +PROFESSOR: OK. + +In the plane of the +great circle. + +Suppose you could if +you wanted to. + +There are trigonometric +qualities to defining the + +angle in the way that we have. + +And the construct really is not +something confined to the + +surface of the sphere, and +everything else that + +we are doing is. + +OK? + +So it's sort of the non sequitur +because we started + +out by saying that everything +has to take place on the + +surface of the sphere. + +There's things that we would +do in our three-dimensional + +world, like defining distances +between points as the shortest + +straight line, that are ruled +out in spherical trigonometry. + +And I think something +similar could be + +levied at your proposal. + +And the answer is we just +don't do it that way. + +That's the real answer. + +OK. + +If I have not boggled your mind +so far, let me go a bit + +further with another +useful construct. + +We can see how we can define a +pole of a great circle or a + +pole on an arc that is a portion +of a great circle. + +Let me take a spherical +triangle, A, B, and C. And + +I've got three great circles +now, which have formed those + +arcs that make up the sides +of my triangle. + +Let me now find the +pole of arc CB. + +And that means we're going to +go out 90 degrees to that + +plane through the center +of the sphere. + +And that's going to define some +point that I'll call A + +prime, that is the +pole of arc BC. + +And I'm going to do the same +thing for the other arcs that + +are sides of my great circle +of my spherical triangle. + +I'll find the pole of arc AC. + +And I'm going to label that +point as B prime. + +And, finally, there'll be +another pole that is + +the pole of arc AB. + +And that's going to define +a point C prime. + +Now I've got three points, I can +connect these together and + +make another spherical +triangle. + +AUDIENCE: How do you know to +determine where the pole is? + +PROFESSOR: If you think of it +in three dimensions, I got + +three different arcs. + +And for each one of them I am +drawing a perpendicular to the + +plane of that great circle +and looking at the + +point where it emerges. + +OK. + +So now if there's another arc, +there'll be another great + +circle coming around +like this. + +And I look for the pole of it. + +And that would be another +one of the corners. + +This thing that I've constructed +is bizarre. + +But it's given a special name. + +This is called the +polar triangle. + +And it has some useful +properties. + +A property of the polar triangle +is that the two + +triangles, A, B, and C, and A +prime, B prime, and C prime + +are mutually polar. + +That is, if I use the spherical +triangle ABC to + +define and locate the +three points A + +prime, B prime, C prime-- + +now if I reverse the process +and find the whole of arc A + +prime C prime, that turns +out to be point B. + +And if I take the arc of A prime +B prime, that turns-- + +I'm sorry-- take the arc of B +prime C prime, that turns out + +to be point A. So the two +triangles are mutually polar. + +The polar triangle of the polar +triangle is the triangle + +that we started with. + +Yeah? + +AUDIENCE: I guess +I missed that. + +So if you take B prime +through C prime, then + +all of that is going-- + +PROFESSOR: Yeah, I'm saying that +the pole of this arc, A + +prime C prime, is +this point here. + +And the way I can show that +is to say that we got B by + +looking at the pole-- + +I'm sorry-- + +I got C by looking at the +pole of the arc AB. + +So B is 90 degrees away +from C prime. + +I found point A prime by finding +the pole of arc CB. + +So B is 90 degrees from +any point on that arc. + +So it's 90 degrees away +from A. So B is 90 + +degrees from A prime. + +B is 90 degrees C prime. + +And, therefore, it has to +be the pole of that arc. + +Now that was a little +too quick. + +That's written down +in the notes. + +And that's why I +wrote them out. + +One final thing and then we can +put circle trigonometry to + +one side, and this is something + +that is not all obvious. + +If we look at a spherical +triangle and simultaneously + +the polar triangle-- + +so let's say this is ABC. + +And here is the polar triangle +A prime, C prime, B prime. + +It turns out that the spherical +angle in one circle + +triangle and the length of the +arc opposite it, namely this + +arc B prime C prime, +are complementary-- + +supplementary, not +complementary. + +And the way one would do that is +to say that the measure of + +alpha is the length +of this arc here. + +And this total side, B prime C +prime, is equal to this arc + +plus this arc minus +this length. + +And these two arcs +are 90 degrees. + +So let me do as I've +done in the notes. + +Let me call this +point P prime. + +And I'll call this +point Q prime. + +So my argument, it says that B +prime is the pole of arc AC. + +And, therefore, B prime +Q prime equals + +90 degrees in length. + +And then I would say that C +prime is the pole of arc AB. + +And, therefore, the distance C +prime P prime is also exactly + +90 degrees. + +And that says that B prime Q +prime plus C prime P prime-- + +if I add those two together, +it has to be 180 degrees. + +But I can write B prime C prime +as B prime P prime plus + +P prime Q prime plus Q prime +C prime plus the + +side P prime Q prime. + +And that's 180 degrees. + +But these three things that I've +lumped together here are + +exactly the same as the length +of the spherical polar + +triangle A prime. + +So what we've shown then is +that A prime plus alpha is + +equal to 180 degrees-- + +QED. + +So this angle plus the side of +the polar triangle add up to + +180 degrees. + +And that is not obvious +at all. + +One final relation-- + +and this I will simply hand +to you on a platter. + +I'm not about to derive it. + +Sides and angles in planar +geometry are related. + +And there's a particularly +useful relation in plane + +geometry that's called +the Law of Cosines. + +So this is in plane geometry. + +And if you have a triangle +that has sides a, b, c-- + +a general oblique triangle-- + +and it has angles A, B, and C, +the Law of Cosines says that + +the side A is determined +by c and b and the + +angle between them. + +And that's clear. + +If I specify this length, +specify this length, specify + +that angle, things set up like +a bowl of supercooled jello. + +And the triangle's completely +specified. + +So a squared in the Law of +Cosines is b squared plus c + +squared minus 2bc times +the cosine of angle A. + +In a spherical triangle there +is a similar sort of + +constraint. + +If we have a spherical triangle +with sides a, b, and + +c, and spherical angles capital +A, capital B, capital + +C, in the same way as specifying +the spherical angle + +A and the lengths of the two +sides c and b, specifies and + +fixes the spherical +triangle entirely. + +This side must be determined by +the length of side c, the + +length of side b, and the +angle between them. + +And that, since everything +is in terms of angles, is + +something that doesn't +involve squares. + +It involves totally +trigonometric expressions. + +And it turns out the cosine of +this missing side a is given + +by the product of the cosines +of the two other sides. + +So as I said, you can take a +trigonometric function of a + +length, which sounds +like an oxymoron. + +And it's the product of the +cosines of the two known sides + +and times the sine of b sine of +c times the cosine of the + +spherical angle A. +And that is also + +called the Law of Cosines. + +And this is the corresponding +case in spherical geometry. + +OK. + +So there's some machinery-- + +yes, sir? + +AUDIENCE: What's the difference +between the sines + +of lowercase a and-- + +PROFESSOR: OK, the angles +are the capital letters. + +This would be the angle between +the great circles that + +defines the-- + +AUDIENCE: Since the radius is +one, there's no difference + +between the angles and the-- + +[INAUDIBLE]? + +PROFESSOR: No. + +This angle is something, for +example, we can choose. + +And depending on how long we +want this arc to be, we can + +put the arc BC anywhere +we like. + +AUDIENCE: Does that mean your +radius [INAUDIBLE]? + +PROFESSOR: No. + +This would be, say, two points +of the spherical triangle. + +Now we can pick any third point +on the surface of the + +sphere, connect that with great +circles, and here is a + +spherical triangle. + +OK? + +So I see. + +I think I see what +your problem is. + +Here are the two planes. + +We define the angle of the +spherical triangle as the + +angle subtended buy +the great circle. + +So this is the definition +of A. + +But now the other two points on +the spherical triangle can + +be any point on these +great circles. + +So this can be point B, and this +can be point C. And my + +spherical triangle can be +something like this. + +So the arc that defines the +spherical angle A is a value + +that is independent from the +length of the arc AC. + +That would be what is +subtended at the + +center of the sphere. + +I'm going to have time just to +set the stage for how we're + +going to use these relations. + +And the problem that I would +like to raise and then apply + +spherical trigonometry to is +the question if I go into + +three-dimensional space, there +is no longer any requirement + +that rotation axes be all + +parallel to the same direction. + +In two dimensions the rotation +points were really-- + +could be viewed as axes that +were always perpendicular to + +the plane of the blackboard, the +plane of the plane group. + +But now when I'm dealing with +three-dimensional spaces, this + +could be the operation +A alpha. + +And there is no reason +whatsoever why we should not + +try to combine with this +first operation a + +second rotation B beta-- + +a rotation through an angle beta +about this axis B and a + +rotation of angle alpha through +this axis A. If we're + +going to come up with a +crystallographic combination, + +the angles alpha and beta have +to be restricted to the + +angular rotations of either +a onefold, a twofold, a + +threefold, a fourfold, or +a sixfold axis, if the + +combination is going to +be crystallographic. + +Yes, sir? + +AUDIENCE: You're just rotating +around those lines? + +PROFESSOR: I'm rotating around +those lines, yeah. + +So I'm saying that we're going +to rotate an angle alpha about + +axis A. + +And now what I'm going +to raise as + +a rhetorical question-- + +what is the rotation A alpha +followed by B beta? + +So I rotate through the angle +alpha about A. So here's my + +first motif, right-handed. + +Then I'll rotate +alpha degrees. + +And this here's number two. + +And that will stay +right-handed. + +Now, I will place on axis +B the two constraints. + +These have to be +crystallographic rotation + +angles, namely 360, 180, +120, 90, or 60. + +And I'll also, since I would +like to obtain point group + +symmetries initially, I will +require that axis A and axis B + +intersect at some point. + +And one of the variables in the +combination will be this + +angle between the two +rotation axes. + +So let's complete our +combination of operations. + +I'll rotate from one +to two by A alpha. + +If the first one is +right-handed, the second motif + +is right-handed, as well. + +And then I will rotate beta +degrees about B. And here will + +sit number three. + +And it will stay right-handed. + +So, again, the $64 question that +we raise periodically-- + +what operation is the net +effect of two successive + +rotations about a point +of intersection? + +[INTERPOSING VOICES] + +PROFESSOR: Lots of opinions. + +Let's sort them out. + +I heard translation. + +Well, let's put down +what it could be. + +We know that only translation +and rotation leaves the + +chirality of the motif +unchanged. + +So it's got to be one +or the other. + +AUDIENCE: Since there's no +reason for the general + +orientation of the two to say +it has to be rotation around + +the third axis, so +the question is + +what angle and what-- + +PROFESSOR: OK. + +That is exactly the problem. + +Now that we know the problem, +we can go home early because + +we know what we're going +to do next time. + +Well, let me expand +a little bit. + +It can't be translation because +clearly the separation + +of number one and number three +depend on exactly where I + +place the first one. + +If I place it a little further +out from A, then it's going to + +rotate to here. + +And then B is going +to swing it off to + +some different location. + +So it can't be translation. + +And I don't think these guys, if +I rotate this way and then + +I rotate this way, are going to +be parallel to one another. + +I doubt that very much. + +So it's got to be a rotation. + +So without knowing how to find +it, let's say that we can get + +from number one to number three +in one shot through + +rotation of an angle gamma about +some third axis, C. So + +the answer, in general, without +being specific, is A + +alpha followed B beta has got +to be equal to a third + +rotation, C, about a direction +that has the same point of + +intersection with the +first two axes. + +Now we've got some really, +really tough constraints. + +Alpha is restricted to +one of five values. + +Beta is restricted to +one of five values. + +The third rotation, gamma, +jolly well better be a + +crystallographic rotation and +not something that is not a + +sub-multiple of 2 pi. + +And even if it is a sub-multiple +of 2 pi, it has + +to be either 0 degrees, +120, so on. + +It has to be one of the + +crystallographic rotation angles. + +So what sort of relation can +we get that would give us, + +first, the value of gamma in +terms of alpha, beta, and the + +angle at which we +combine them? + +So taking A and B as the five +crystallographic rotation axes + +two at a time, we want to put +them together, if we can, such + +that the angle makes the third +rotation axis also be + +crystallographic. + +And then we would have +to find its location. + +It looks like an impossible +constraint . + +It looks absolutely +impossible to do. + +We've got to put this first in +quantitative form and then + +simply put in the values for +alpha, beta, and gamma and + +find the angle that they have +to be combined on to make + +this, if possible, be one +of the crystallographics + +sub-multiples. + +That is not an easy problem +to formulate. + +And, as I said a couple of times +ago, the geometry that + +is the basis of this derivation +was originally + +proposed by Euler. + +And it's known as Euler's +Construction. + +I will have for you next time +my own set of notes on this. + +We have finished with +two-dimensional + +crystallography. + +So we are back to Buerger's +book again. + +We had that little interlude. + +Buerger deals with Euler's +Construction. + +But I don't think he's +at his best in + +this particular section. + +So we'll take it a little +more slowly. + +And next time we'll get around +to deriving Euler's + +Construction. \ No newline at end of file diff --git a/2fbrl6WoIyo.txt b/2fbrl6WoIyo.txt new file mode 100644 index 0000000000000000000000000000000000000000..4c341f9193ffb87d7849c8228dc18bc5aca45b99 --- /dev/null +++ b/2fbrl6WoIyo.txt @@ -0,0 +1,3066 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Good afternoon. + +Congratulations for braving it +through what's now become a + +weekly snow disaster. + +This week's maybe three +of them or something. + +My name's John Gabrieli. + +This is Introductory to +Psychology, 9.00. + +This is a course about you. + +The entire course is what do we +understand in a scientific + +way about human nature-- + +how people's minds work, how +people's brains work that + +supports their mind. + +This entire course is about +what's a scientific way to + +understanding how people feel, +think, and act in the world. + +And so we're trying to say that +we constantly think you + +must in your everyday life think +about why do you have + +your preferences, +your desires? + +What's easy for you? + +What's hard for you? + +What's delightful for you? + +Why do other people behave +the way they do? + +How do they think? + +How do they feel? + +And so there's a lot of realms +of this that are tough to get + +to by science. + +But what we're going to focus on +this semester is where the + +scientific approach has shed +light in the way that we used + +to think about experiments +and evidence, + +about how humans tick. + +And as we go through this +semester, we'll talk about the + +brain, we'll talk a fair bit +about chapters from this book, + +The Man Who Mistook His Wife for +a Hat, from Oliver Sacks. + +It was a bestseller even when it +wasn't [? a ScienceWare ?] + +course. + +It's a great book. + +You'll enjoy it. + +Short, really fun chapters. + +We'll talk about how we perceive +the world; how we + +see; especially, a little bit, +how we hear; how we think; how + +we feel; personality; how we +differ from one to the other; + +and what we're sort of like; +and how we behave in the + +world; development from +childhood and infancy through + +adolescence, through young +adulthood, where you are + +mostly, through getting older, +where I am; social + +interaction, how we behave in +groups and think about other + +people; and variation in +the mental health or + +psychopathology. + +And increasingly, we understand +that there's a huge + +number of people who, at some +moment in their life or + +another, struggle with some +aspect of mental health. + +And then we'll focus a lot on, +not only the psychological + +aspects of what we study in +terms of behavior, but also + +the brain basis of that, and +think a little bit about to + +what extent the mind is what the +brain does, to what extent + +the mind is what +the brain does. + +And so for every dimension of +being a human being that we'll + +talk about, we'll also talk +about what we understand + +currently from the +neurological and + +neuroscientific literature +about how the human brain + +supports and contributes +to different + +aspects of being a person. + +OK. + +So everybody who works in a +certain field thinks that + +their field is really, really, +really special, right? + +So here's why psychology +is really, + +really, really special. + +So it's really, really special, +I think, most of all, + +because every endeavor that we +undertake at a university or + +in society as a whole-- + +it's about people, right, except +for when we think about + +the rest of nature. + +But people study biology, +chemistry, and physics. + +And they think, right, that the +sun orbits the earth for + +some period of time. + +And then they think +it's the other way + +around currently, right? + +OK, so people come up with +these conclusions. + +Even though we're trying to +understand nature, it's people + +who make certain investments +in economics or behave in a + +certain way or vote +in a certain way. + +It's people who make music and +appreciate music, make art and + +appreciate art, read and write +literature, right? + +So in all these dimensions, +there's something very + +fundamental about what it is +about the human mind that + +gives birth to these areas of +inquiry and how those areas, + +domains of human experience, +are enacted. + +So my only goal today is to +try to convince you in a + +number of different ways that +we're not simple video camera + +in our minds between our ears, +recording the world in some + +objective, simple way, that +even the simplest, most + +obvious things are +interpretations of the world + +around us at many different +levels of thought and feeling + +and perception. + +And then our minds, the way +our minds are constructed, + +determines the world that we +experience, that we see, that + +we act upon. + +And even very simple things +that we think are pretty + +objective and simple, right +in front of our eyes, are + +determined by inferences and +deductions that our mind + +makes, weighing sources of +evidence in the world and + +coming to conclusions about +what's around us, what we + +hear, what we see, +and how we think. + +So let's start with seeing. + +If your vision is reasonable, +we say we see something, we + +believe it, right? + +So let's start with something +very simple-- + +these lines. + +So one of the tough things about +psychology is ever since + +the Internet came into +existence, people know every + +cool thing there is +to know, right? + +OK. + +I can tell you when I began +teaching, people said, oh my + +gosh, I've never seen +such a thing. + +It's unbelievable! + +And then now, it's like two +thirds of the class is like, + +yeah, I've got that on +my computer at home. + +We did that in third +grade or whatever. + +So all I'm saying is enjoy the +ones you haven't seen before, + +don't ruin it for your neighbors +today, because it's + +harder and harder to +surprise the world + +in a nice way, right? + +OK, but let's look at these +lines for a moment here. + +And perhaps you'll have the +sense, and maybe-- is it + +glaring up there, sir? + +Let's see. + +OK, is that better? + +OK. + +Maybe not. + +So you might have the sense that +this line is a different + +length than this line. + +And this might be somewhere +intermediate, right? + +Now you know, because of +psychology, it's all a trick. + +But what's simpler than +the length of a line? + +What's more objective +in some sense than + +the length of a line? + +But if we look at the actual +lengths, they're + +all literally identical. + +But that center part +looks different. + +So what does it mean for +it to look different? + +It means our minds are +determining as simple a thing + +as how long a line is depending +on the other + +information surrounding it. + +It's an interpretation +in context. + +If we're simply looking, the +lines will look the same. + +Let's try another one. + +It's remarkable that those two +lines are identical in length. + +[LAUGHTER] + +PROFESSOR: OK, all right. + +It's OK to test the limits +of the credibility of the + +audience, right? + +All right. + +Yeah. + +Of course, if our visual system +were ludicrously off, + +we'd be constantly walking into +walls and falling out + +windows and things like that, +right, if we were + +misestimating at that length. + +So the idea where we have visual +illusions-- and I'll + +show you some more that I think +you'll be impressed by-- + +it's not that our visual system +is messed up or that + +psychologists think it's +hilarious to trick us. + +It's that lots of things our +visual system is a brilliant + +at, but it's brilliant by +having certain laws or + +principles that it follows. + +And we can show this following +those principles by seeing + +that when we mess with the +typical circumstances, those + +principles calculate +the wrong answer. + +So here's another one. + +So, to most people, which line +looks bigger, the one in the + +middle or the one on the side? + +I know you know it's +all a trick, right? + +OK. + +What could be more obvious +than that this is longer? + +It's just a simple line, but if +we draw red lines on top of + +it then move them over here, +they're dead identical. + +The central circle-- + +does one of them, the +middle circle, look + +larger than the other? + +Now you already know, +intellectually, that it will + +turn out those two circles in +the middle will be the same. + +But you have to convince +yourself that it still looks + +like they're different. + +Here there in red. + +Here they are next +to each other. + +They're identical. + +Again, this is evidence that, +even for a simple thing like + +the size of a circle, your mind +is making inferences. + +And there are principles and +laws that it's following that + +determine what it is you +think that you see. + +Here is two monsters +chasing each other. + +But in fact, they're +identical in size. + +The perspective cues make +the more distant + +one look much bigger. + +This is from Ted Adelson. + +This is a beautiful +demonstration of an illusion. + +Ted Adelson's in the psychology +department. + +There's a letter A here. + +And believe it or not, there's +a letter B there. + +Let's see if this looks any +better when it goes like this. + +It doesn't. + +All right. + +So one of the important things +about illusions, + +demonstrations in this class-- +and you will learn this as we + +go along-- is occasionally they +fail, and we come back + +and discover what the +lesson of that is. + +So I'm just telling you +it's showing you on my + +monitor much brighter. + +It always has before. + +We'll adjust that. + +So I'm going to skip this, but +I'll show you another time, + +because it's so good. + +And I'm going to feel +bad about this. + +OK. + +Now, let's see. + +This'll work. + +All the same shade +of grey, right? + +[LAUGHTER] + +PROFESSOR: Did that work +reasonably from where you sat? + +We'll try a few more. + +Maybe. + +For some reason, +my connection's + +always like this, sorry. + +Does that one look lighter +than that one that way? + +Yeah. + +Now they look radically +different, right? + +It's the same grey constantly. + +But again, the context is hugely +determining how to + +bright you see that grey. + +There it is. + +Two boxes equal grey. + +So things as simple as how +bright something is or how + +long something is depend +on interpretation. + +Here's an illusion from +Roger Shepard. + +It's kind of great. + +So here's two kind of different + +looking tables, right? + +But they're not that +different. + +And watch. + +There goes one tabletop. + +You're not impressed that those +are identical tables? + +OK. + +Want me to do it again? + +That's the identical tabletop. + +To me, the one on the left looks +pretty rectangular and + +the one on the right looks +pretty square-ish. + +You're not easy to +impress, are you? + +[LAUGHTER] + +PROFESSOR: You see that those +two bars are moving together + +at the same time. + +Does it look like they're +little steps? + +It'll show you. + +All right, fine. + +It's just like that, but +now you add those bars. + +Does it look like little steps? + +[LAUGHTER] + +PROFESSOR: One more +of this kind. + +This is kind of fun. + +You see the way that the +mask is turning? + +It always looks like it's +towards you, even though I'm-- + +one of the rotations-- it's +because of the way you're + +interpreting the light is +influencing how you + +interpreting what's-- + +OK. + +So that's simply a consequence, +as far as people + +understand that, that the source +of the illumination is + +not where you're used to, so +you're misinterpreting where + +the illumination is coming +from for the depth of the + +face, what's front and what's +back, whether the nose is + +sticking in or sticking out. + +OK. + +So again, the point in these +illusions is, even for very + +simple things our, minds make +certain assumptions about how + +we interpret the world. + +And that drives everything that +we see and how we act + +upon what we see. + +So at a slightly higher +or more conceptual + +level, I need your help. + +Now, there's lots of these +things we'll do this semester + +where you get to participate. + +The fun thing about-- + +I said this course was about +you-- when you could have + +thought that was a bit +rhetorical, it's not. + +It's truly about you. + +So you get to be your +own laboratory. + +We get to share a laboratory +sitting here. + +And what I'm going to do is ask +for you to participate. + +You don't have to do any of +these things sitting at your + +seat, but I think it's usually +fun to do them. + +So what's going to happen +is I'm going + +to show you a drawing. + +If the people to my left-- + +so about in the middle, but you +can decide for yourself-- + +about this way, let's have you +be Group A if you're willing + +to be that way. + +All right. + +Because of that, I +can't call you-- + +I was going to call you guys +Group B, but I already see + +that's getting me in trouble. + +So we'll call it Group B, but +that really means equals A. + +But I'll just call it B, OK? + +So A and B, OK? + +So what I need is Group B-- + +B for best, A for awesome, OK. + +[LAUGHTER] + +PROFESSOR: --Group B to close +your eyes for a moment. + +Group B, if you want to have fun +with this, close your eyes + +for a moment. + +Group A, you're gonna see some +instructions, and read them + +silently to yourself. + +And then I'll ask you a question +about the picture. + +OK, Group A, you're +now reading. + +Group B has your eyes closed. + +So read the instructions +silently to yourself. + +OK? + +Now Group A, close your eyes. + +Everybody has their eyes +closed for a moment. + +Everybody has their +eyes closed. + +Now Group B, look at +your instructions. + +So A has their eyes closed, +B is reading instructions. + +OK? + +Everybody's eyes are open now. + +Everybody's eyes are open. + +Here's your picture. + +Take it in and I'm going +to ask you a few + +questions about it. + +Look at it for a moment +and inspect it. + +OK, here we go, ready? + +So just out loud-- + +was there an automobile +in the picture? + +AUDIENCE: No. + +PROFESSOR: OK. + +See, this is a smart class. + +We're gonna have a-- + +Was there a man in +the picture? + +AUDIENCE: Yes. + +PROFESSOR: Was there a +woman in the picture? + +AUDIENCE: Yes. + +AUDIENCE: No. + +PROFESSOR: OK. + +This side again, woman +in the picture? + +AUDIENCE: No. + +PROFESSOR: All right, +all right. + +OK, a child? + +AUDIENCE: No. + +PROFESSOR: An animal? + +AUDIENCE: No. + +AUDIENCE: Yes. + +PROFESSOR: Ah. + +OK. + +And now it gets a little wild. + +OK? + +A whip? + +AUDIENCE: Yes. + +PROFESSOR: OK. + +A sword? + +AUDIENCE: Yes. + +PROFESSOR: All right, +a man's hat? + +AUDIENCE: Yes. + +PROFESSOR: A ball? + +AUDIENCE: Yes. + +AUDIENCE: No. + +PROFESSOR: A fish? + +AUDIENCE: Yes. + +PROFESSOR: All right, so +there's disagreement. + +And that's-- + +we're a democracy, right? + +So all these things are +big setups, right? + +So here's what happened. + +Group A was told they were gonna +look at a picture of a + +trained seal act. + +And Group B got the identical +instructions, but they were + +told you're gonna look +at a costume ball. + +So you had an expectation of +what you were going to see. + +That expectation drives your +interpretation of the very + +thing you see next, which +is this picture. + +OK? + +[LAUGHTER] + +[CHATTER] + +PROFESSOR: OK, is +that all right? + +All right. + +And this is just +for fun, right? + +It's a set up. + +You're participating nicely. + +But in the world, when groups +that are arguing with each + +other about things like peace +settlements, read a document, + +or make a statement, how much +do you think the perspective + +they start with guides the +interpretation of what they + +read or what they hear? + +Because you didn't have +big stakes in this. + +You weren't going, I believe in +fish and if I don't see a + +fish, I know things aren't just +and my group will be not + +treated fairly. + +You're not emotionally invested +in, probably, whether + +there was a fish present. + +So your interpretation, your +beliefs guide tremendously + +what you think you see and how +you interpret the situation-- + +for complicated things +or even easy things + +like lines or squares. + +And here's another kind of an +example where you would + +interpret that as a +B for "baker" or + +13 if it's in numbers. + +Again, the context is driving +a lot of the interpretation. + +OK. + +Now this is one of those +examples that, again, when-- + +some number of years ago, +it was a huge hit. + +And now, mostly people say, +can't you come up with + +something better +that we haven't + +all seen on the internet? + +So if you know this, don't +ruin it for the other + +individuals. + +But what I need is a +few volunteers-- + +you'll be facing me +this way-- who are + +willing to count something. + +And it's MIT, we're pretty +good at counting. + +So what's the message of that? + +The message is-- + +we've talked about what we +perceive, what we see by + +expectations in context. + +But it's also we have very +limited what psychologists + +call attentional resources. + +We can pay attention +to a limited number + +of things at a time. + +And even when those things can +be right in front of us, if + +our attention is focused or +occupied by something else, + +like counting the passes +in a difficult scene-- + +it wouldn't work if there was +one or two passes only, + +because you would notice it. + +But when your mind is focused on +identifying all the passes + +among the players-- and the +white shirts are moving, + +they're weaving with the other +players and so on-- + +then your attention is absorbed +by that, and some of + +it is not left over to notice +what's right in front of you. + +And we'll talk more +about that. + +But it's a huge thing with +humans that we can pay + +attention pretty well, on +average, to a thing at a time + +under many circumstances. + +And the other things escape us +completely, even if they're + +obviously present if we were +looking at them or paying + +attention to them. + +So here's another example of how +our minds make our world-- + +what we see and what we don't +see, what we pay attention to + +and what we don't pay +attention to. + +And that's something to +do with how we hear. + +OK, so I'm going +to replay this. + +So listen to what the +guy is saying. + +Take a look, and +just tell he-- + +he's saying some letters, +OK, just not a word. + +What is it? + +OK, most people think he's +saying "da." "Da da, da da, da + +da." Now let's try that again. + +I'm going to turn off the +sound and I'm going to + +run the same film. + +What does his mouth look +like it's saying? + +"Ga ga." OK? + +But now we'll do one more thing, +which is turn the sound + +back on, have you close +your eyes, and listen + +to what he's saying. + +What's he saying? + +AUDIENCE: "Ba." + +PROFESSOR: Yeah. + +So it doesn't work for +everybody every time. + +But the basic idea is most +people think they hear the + +word "da" coming from +the speaker. + +And in fact, in their mind they +do because that's how + +they interpret what +they're hearing. + +But in reality, the film clip +is a film clip of the person + +saying "ba ba ba." And then an +audio recording of the person + +saying "ga ga ga." Your mind +intertwines across modalities + +what you hear and what you see, +integrates them in some + +way below your level +of consciousness. + +You're not thinking about it. + +And you come up with a different +interpretation of + +what you hear. + +Right? + +So what you see would +be this one thing. + +What you hear is +another thing. + +When your eyes are open and your +ears are open, they meld + +together and produce +something-- + +a third thing that's +entirely different. + +Again, your mind interpreted +what you hear, not your ear + +interpreting what you hear, +in a simple sense. + +OK. + +How about things that we know? + +So let's think about this. + +If somebody were to ask you +which is farther east, closer + +to the Atlantic-- + +San Diego, California, +or Reno, Nevada? + +Who likes San Diego as +being farther east? + +A few hands. + +Who likes Reno as being +farther east? + +OK. + +So, here's the mental map most +people have-- the mental map-- + +which is we know California's +right next to the ocean with + +Arnold Schwarzenegger protecting +us on that side of + +the country, right? + +And then Nevada's a little bit +more towards Boston, right? + +OK. + +That's a mental map that +most people have. + +And that's how the +hands went up. + +This is the actual map. + +And the only actual map you've +ever seen, ever-- on a globe, + +on a map, anything. + +Because California takes a big +turn on the south, San Diego's + +further east than Reno. + +Why do we imagine, and most +people do, that Reno is + +further east, when you've never +seen a map or globe + +that's shown you that? + +Never ever, ever. + +Yeah. + +PROFESSOR: Because it's farther +from the ocean, + +because in our mind we go, +California's way out there. + +There's nothing-- + +Hawaii is the only one out there +further west, right? + +So our mind makes this +answer despite that. + +And that's what we think +we might know. + +Now, we might not be +totally certain. + +We might not bet the +farm on that. + +Which is farther north-- + +Philadelphia, Pennsylvania, +or Rome, Italy? + +So start to think-- how would +you think about that? + +It's not something you know. + +Nobody memorizes it, right? + +But how would you begin +to think which is + +probably more northern? + +What's your first gut? + +How many people like +Philadelphia being more north? + +How many people like Rome +being more north? + +There's kind of a mixture +of hands. + +The answer is that Rome is +north of Philadelphia. + +Mostly people will answer that +Philadelphia is north. + +Why they do that is they think +the US and Europe, they're + +both sort of above the equator, +below Antarctica, + +kind of a aligned, even +historically, culturally. + +So they think, well, Rome is +pretty south in Europe. + +And it is. + +It's in Italy. + +Philadelphia's reasonably +north in the US. + +It gets winters and all +that kinds of stuff. + +So a northern city in the US +has got to be north of a + +southern city in Europe. + +But in fact, Europe is-- the +whole continent is shifted up + +compared to the US. + +So you won't-- wait until get +your mind around this. + +Which is further north, +Atlanta or Chicago? + +[LAUGHTER] + +PROFESSOR: All right, +all right. + +Sorry. + +It's sort of a joke. + +Because sometimes when you do +this, people go like, wait a + +minute, all my assumptions +are off. + +Like, where am I? + +What's reality? + +[LAUGHTER] + +PROFESSOR: OK. + +Here's one more-- two more. + +Which is further north, +Portland or Toronto? + +Now you are already learning +the lesson go opposite. + +Whatever I thought, go +opposite, right? + +But why do you think most +people will answer that + +Toronto is further north? + +Canada is up there, US is +below it, but in fact-- + +that's the mental map +in the colors. + +But in fact, Portland +in Oregon is + +actually north of Toronto. + +We'll do one last one. + +Which is further west? + +Which is further west, Miami, +Florida-- which that's all the + +way towards the Atlantic +Ocean-- + +or Santiago, Chili-- which is +towards the Pacific Ocean. + +Further west. + +So most people have a mental +map that North America and + +South America are kind of +lined up like that. + +And so you say well, Miami is +further east and Santiago's + +farther west. + +But in fact, South America is +fairly shifted compared to + +North America. + +And Santiago is actually more +eastern or Miami is more + +western, one relative +to the other. + +Because in our head, we kind +of think, North and South + +America-- they're kind of lined +up even though we never + +saw a global map like that. + +So again, some of our knowledge +guides how we think + +about the world and what +we believe we know. + +So what's the point of this? + +It's what used to be called +telephone, right? + +Their story keeps changing. + +And it's hard to remember +details in a story. + +People remember a nugget, or +what we call a gist in + +psychology, a little point. + +And second, what you take as a +point is how you then tell the + +next person, the way you +interpret the story, + +something like that. + +Thanks very much, +that was good. + +[APPLAUSE] + +PROFESSOR: Again, two things-- +our memory for precise details + +is surprisingly modest. + +And how we interpret things +matter changes things a lot. + +So now, you had four brave +students demonstrating some of + +the limits and properties +of memory. + +So now, here's an exercise you +can do in your own seat. + +OK, you're just knowing +yourself how you + +did, but here we go. + +I'm going to read +you some words. + +And then just give you-- don't +have to write anything down. + +If you write it down, +it's no good. + +And then I'm going to ask you on +a recognition test, whether + +you heard a word or not. + +Ready? + +So here's the list. + +So just listen and then +I'll test your memory + +for it right after. + +Here's the list. + +Sour, candy, sugar, bitter, +good, taste, tooth, nice, + +honey, soda, chocolate, heart, +cake, tart, pie. + +OK? + +All right, how many +people heard the + +word "sour?" All right. + +Yeah, excellent, thank you. + +"Chair." "Candy." Hey. + +"Honey." "Building." "Sweet." +Every hand up there, you have + +a false memory. + +[LAUGHTER] + +PROFESSOR: Now, it's +a set up OK? + +Because here's the way they make +these lists, it's a set + +up, but there's a huge lesson. + +And in fact, you may hear +debates about what are real + +memories, what are false +memories, in court cases, in + +clinical cases. + +This is a laboratory experiment +that's been the + +testing ground for lots of ideas +about how we make real + +memories and how we end up +with false memories. + +So here's the way they +made the list. + +They took the word "sour." And +they took a lot of students + +basically like you and said, +what's the first word you + +think of that goes with sour? + +And people came up with +this kind of a list. + +Candy, sugar, bitter, good, +taste, tooth, nice, honey, + +soda, chocolate, heart, +cake, tart, pie. + +But they left out one +word that people + +came up with a lot. + +The word "sweet." OK? + +So your mind interpreted +the list. + +You said, hey, this is all about +things that are related + +to sweet things in one way or +another-- sweet sugar, sweet + +candy, sweet and sour, honey is +sweet, chocolate is sweet. + +So your mind imagined it heard +the word "sweet." And the + +majority of you put your hand up +that you actually heard the + +word "sweet." Your mind imagined +it was there because + +that was generally what +was going on. + +That was the gist of +the experience, OK? + +So this idea is it's very +easy, because of the way + +memory works, we remember the +gist of things because that's + +what's the important part. + +It's hard to remember +the details. + +But that gist is an +interpreted gist. + +The gist was it's +sweet things. + +So the word "sweet" feels like +it was part of the memory. + +And we'll come back to that +later on in the course. + +So one of the themes we'll talk +about a lot in the course + +is both an amazing power of the +human mind and an amazing + +peril of the human mind. + +And it's what psychologists +call automaticity. + +It's that our mind, in order +to be efficient and quick, + +does things automatically +without thought, without + +consciousness. + +It lets us walk without +thinking a lot about + +where our feet are. + +It lets us speak quickly without +thinking about the + +syntax and the vocabulary, +right? + +It lets us do a lot of things. + +So that's the power of it. + +The peril is when something +becomes automatic, we lose + +control of it within +ourselves. + +So I need somebody at their +seat who's willing to read + +aloud something as fast as they +can when they see it on + +the computer monitor. + +If I can get a volunteer +at your seat. + +OK, all the way back +there, OK. + +And then I'll come to you +for the second one. + +Ready? + +Here it comes. + +As fast as you can, go. + +AUDIENCE: One way +not do enter. + +PROFESSOR: OK, then, +you got it. + +I couldn't trick you. + +OK. + +But you might imagine a person +might mistake that, right? + +Was there another one? + +Was it you? + +OK, ready? + +Here we go. + +Go. + +AUDIENCE: Paris in spring. + +PROFESSOR: Ah. + +I got you on that. + +[LAUGHTER] + +PROFESSOR: Because your mind +is automatically reading. + +We have lots of evidence in +psychology that you're barely + +looking at words like +"the." You're + +assuming over those things. + +They're almost invisible to you +there even though they're + +physically present, because your +mind is looking for the + +big content, right? + +Who cares about the word "the?" +Your mind is going for + +the essential information, and +it becomes literally blind to + +what's in front of you, because +it knows what it's + +looking for. + +Here's a fun one. + +You've seen things like +this before, but it's + +always fun to try. + +It's the same principle. + +How many letter F's do you +find in this display? + +Can I get some numbers? + +AUDIENCE: 6. + +AUDIENCE: 4. + +AUDIENCE: 5. + +PROFESSOR: 4, 5, 6. + +Those are all good. + +We're not an exact science. + +[CLAMORING] + +PROFESSOR: Some of you may have +missed one or two F's. + +Again, it's because your +mind is automatically-- + +typical readers read at +spectacular speeds. + +And the way you read at a +spectacular speed is you don't + +look for little details. + +You get the big words and the +big ideas and you zoom through + +for the big meaning. + +And you're leaving behind what +you consider to be details. + +Yeah. + +AUDIENCE: So if you ask this +question to a society that + +pronounces "of" just +like "off," + +would that change anything? + +PROFESSOR: The question was if +we asked a society that didn't + +pronounce F's or something +like that. + +AUDIENCE: That didn't pronounce +F's as F's. + +In America, we pronounce +it "of." + +PROFESSOR: "Of," you mean +like a "v" sound or + +something like that. + +Does that matter for this? + +Yes. + +It also matters a lot that words +like "of" are little + +preposition words that we +don't think much about. + +So this is a set up. + +Like "finish," most +people get. + +Or the beginning of a word +you're more likely to get. + +I think the pronunciation +probably matters. + +I don't know that for sure. + +That's a very good thought. + +And certainly, hiding it in +words that seem low in content + +for interpreting a sentence is +about the best way we did it. + +That's why the second "the" +disappeared too. + +It's sort of a low +content word for + +processing a sentence. + +OK. + +This is an example that you +know, but it's a nice example + +and we can come back to +it a couple times. + +So let me think about +this for one second. + +Maybe we'll do it this way-- +that we'll ask somebody at + +their seat who has typical +color vision. + +If you're color blind, this one +is not a good one for you. + +Some percentage are. + +Is somebody willing at their +seat to read aloud stuff they + +see on a monitor? + +OK, thank you. + +Here we go. + +So you're gonna see words +that are printed + +in different colors. + +Your job is to name aloud the +color of the ink that it's + +printed in. + +Does that make sense? + +So like on this F, you +would say it's red on + +that F. Is that OK? + +Here we go. + +So start here and just go. + +AUDIENCE: Red, orange. + +PROFESSOR: As fast as you +can, just keep going. + +AUDIENCE: Green, brown, pink, +green, blue, yellow, red. + +PROFESSOR: Great, excellent. + +Same thing. + +Read the color of the ink +exactly like you were doing. + +Go. + +AUDIENCE: Green, blue, red, +blue, red, yellow, red. + +PROFESSOR: Ah, you're +pretty good. + +OK. + +It's supposed to slow you down +when you get the ink in the + +wrong colors. + +And it usually does. + +But you were very good. + +All right. + +Again, if you know this from +courses and the internet, + +don't ruin it for others, but +think about it for yourself. + +So now we're gonna +turn to thought. + +There's 30 people in a room. + +Just imagine you sat-- there' +just groups of 30 here. + +You get the month and date of +each person's birthday. + +So it's not the year they were +born, but it could be December + +1 or February 5 or something +like that. + +What is the approximate +probability that two people + +will have the exact +same birthday? + +I can tell you the vast majority +of people under + +slightly less suspicious +circumstances of this will + +answer about 10%. + +That's the vast majority. + +The correct answer is-- + +OK? + +Why do you think-- + +this is work from Kahneman +and Tversky. + +We'll come back to this. + +Why do you think people tend +to answer 10%, some 30%? + +Very few people give you +the mathematically + +correct answer of 70%. + +Why do they do that? + +Because they tend to think, how +often have I met somebody + +who has my exact birthday? + +And you go, not that often. + +It's not like every 30 people +I meet, somebody says, you + +were born on March 3. + +I was born in March 3. + +And then you go have lunch +and you go, hey, I was + +born on March 3. + +And you go have dinner with +another group and they go, I + +was born on March 3. + +It's not something that +happens a lot, right? + +So you go, well, in real +life it doesn't seem + +to happen very often. + +That's what we call a +heuristic-- a simple way to + +think about it. + +Because your experience +is kind of like that. + +But why is that incorrect + +mathematically for this question? + +Because the math depends on +not that's exactly your + +birthday, but any pair of +birthdays among the 30 people. + +And then it goes way up. + +In fact, it goes to 70%. + +And if it's 24 people, +it's 50%. + +If you're a group of 36 people, +there's a 90% chance, + +just mathematically, that +two people will + +share the same birthday. + +Because when we face things that +are hard to think about, + +because there's no easy answer, +humans tend to take + +shortcuts and say, what's the +gist of my experience, and + +that's what I think +the answer is. + +Even when a calculable +answer is available. + +It's human nature to make a +shortcut based on your sense + +of your experience. + +So there's a very interesting +line of work-- + +Dan Gilbert of Harvard +is a leading figure-- + +about this idea of thinking +about your future. + +Now, thinking about our future +is a big thing, right? + +We're thinking about what's it +like in this course, what's it + +like in college, what's our +friendship like, relations + +with parents, what's our future +career paths, what kind + +of life will we lead, right? + +Our future is something that's +hugely on our mind, I think, + +very powerfully when you're +a college student + +or a graduate student. + +What's my future? + +And a big question that people +have is what will make me + +happy in a deep sense? + +What will make me happy +in a deep sense? + +Because that's the life +I want to lead-- + +the values I want to have, the +kind of career choices and + +personal choices I want to make, +where I will devote my + +time on this earth. + +So most people, first of all, +tend to think about good + +things, positive things. + +Actually, I can tell you what +comes later in the course. + +It's good to think that lots of + +positive things are happening. + +It's kind of a nice place +to be in terms of + +being a happy person. + +But it turns out that people +have done studies like this. + +So now this is particularly +sensitive for a faculty + +member, but it could work for +any sports team you've tried + +out or anything you've tried +out for in your life. + +So what happens when we get +reviewed for tenure? + +And you hear a bit about that. + +This was an easy study for +a psychologist to do. + +What they did is they called up +people in the fall who were + +being reviewed for tenure. + +And you get tenure +or you don't. + +And it's a bit of a sad process +if you don't, right, + +because you don't get tenure, +and then you don't feel happy + +about that. + +And you have to call your +parents and say, I didn't get + +tenure, and your parents go, +come on, if you just slept + +better, you would've +gotten tenure. + +[LAUGHTER] + +PROFESSOR: Remember the piano +lessons you didn't take. + +So it's a bit of a +nuisance, right? + +On top of that-- + +because weirdly, in academics, +we tend to be super + +specialized-- you have +to move out of town. + +You don't have to, but +typically, a person who + +doesn't get tenure will get +a job somewhere else. + +There's plenty of stories of +people who don't get tenure at + +awesome places who were +geniuses in history. + +The tenure decisions +are often wrong. + +But still, you'd rather +get it than not. + +You'd rather get into the +medical school than not. + +You'd rather make a sports +team you want + +to be on than not. + +So here's what they found out. + +If they asked them what happens +if you don't get + +tenure, everybody says, oh, +it's gonna be awful. + +It's gonna be miserable. + +I'm gonna be such an +unhappy person. + +Two years later, the average +happiness of people who didn't + +get tenure was equal to the +average happiness of people + +who did get tenure. + +So you can say, well, +tenure-- only + +professors care about tenure. + +Well, how about winning +the lottery? + +What if I won hundreds of +thousands of dollars? + +There' been a lot of psychology +on this, actually. + +In about a year to two, the +average happiness of a lottery + +winner who won a substantial +amount of money is rated the + +same by him or her as it was +the population as a whole. + +Yeah? + +AUDIENCE: How did they go about + +measuring average happiness? + +PROFESSOR: Yeah, so we'll +come back to this, + +but I'll tell you. + +You can like this or +not like this. + +In some parts of psychology, +we measure things like + +reaction time to the +millisecond. + +That's good data, right? + +Our brain activation, +that's good data. + +When you ask a person how happy +they are, the only thing + +we can do is have you basically +fill a scale from + +one to seven. + +How happy are you? + +And you could go, well I'm a +little worried about that, + +because sometimes people say, I +hope that it makes you happy + +or something. + +So you could say, how +much can we trust + +subjective reports of happiness? + +And that's a very +good question. + +On the other hand, it's hard +to know what would + +be better than that. + +If we measure your +pulse, is that a + +better measure of happiness? + +Your pulse could be racing +because you're sad or happy, + +scared or enthusiastic. + +So we don't have a better one +that we can think of. + +But psychologists do worry that +sometimes people will + +just say what they're +supposed to say. + +Or they'll pretend they're happy +or things like that. + +We have to worry about +those things. + +So you could worry deep down, +but a year or two later, + +people who win huge amounts of +money don't report themselves + +as any happier than people +around them. + +And kind of amazingly-- + +but I think it's deep +about life-- + +accidents leading to +quadriplegia or paraplegia, + +accidents that, before you had +such an accident you would + +imagine that it would be +something extremely difficult. + +And it can be in many ways. + +But by self report, ratings of +happiness return to typical + +average populations +of the same age + +in about three months. + +So what's a huge lesson here +in happiness research-- + +a huge surprise. + +It's two things. + +We're kind of bad at predicting +what will make us + +happy or sad, which is +kind of weird, right? + +We're kind of bad at +predicting it. + +Here's all these things where +we think they would make us + +happy or make us not so happy. + +It turns out we're wrong when +this is studied at all + +scientifically. + +So we'll come back to that later +on, because it's a very + +deep thing about +being a human-- + +what makes you happy and +your wrong guesses + +sometimes about what does. + +So let me end with a +last experiment. + +So we've really haven't done +experiments until right now. + +And this is now a sensitive and +difficult issue, which is + +problems we have in dealing +with racism. + +And here's a study that +did the following. + +It said, well, in North America, +certainly, Canada, + +the US-- a study was +done in Canada-- + +racism is widely condemned, +as I think most of us + +believe it should be. + +But examples of blatant +racism still occurred. + +One recent poll said that +about a third of white + +individuals reported hearing +anti-black slurs in the + +workplace in the last +couple years-- + +to pick one thing. + +So how does this happen in a +society that speaks so much + +about not being racist, about +treating everybody equally and + +fairly and kindly? + +How does it happen that +we still struggle. + +And it's such a very deep, +difficult question about human + +nature and the world +we live in. + +But here's something again +that's a hint about why it's + +hard to get society to change +some of its behaviors. + +So here's the experiment-- + +so it's an actual experiment. + +So they took two groups of +college undergraduates and + +randomly assigned one to be +in the forecaster group. + +That's a group that tells you +how they think they would feel + +and how they think they would +act under certain + +circumstances. + +And then an experiencer +group-- + +that's a group who actually +undergoes an experience, and + +I'll tell you what +that is now. + +So in the experiencer group, +pretend you were their + +research participant. + +You walk into a room, and you +see in that room a black male + +and a white male. + +Now those two are what +psychologists, for some + +reason, have called +confederates. + +Those are role players. + +They know what they're doing. + +They have a plan of what +they're going to do. + +They're going to put on +a little show for you. + +But you don't know that. + +And the black male stands up and +leaves the room to get his + +cell phone, and he gently bumps +the white male's knee. + +This is all set up. + +You're just sitting there and +you see that little bump. + +And now, there's three +different groups. + +One group, that's it. + +Nothing else happens-- + +A small bump, and the +person leaves. + +A second group-- + +as you sit there, the black +individual leaves the room and + +the white individual says, +quote, "Typical, I hate it + +when black people do that." +It's meant to be obviously + +provocative and racist. + +And then what they consider +an extreme slur-- + +the white person in the room +playing this role uses the + +derogatory word that's meant +to be an extreme slur. + +So there's one more thing +you need to know. + +Now, you're sitting there, and +you're either in the control + +group where there's been the +slight bump, or there's been a + +moderate slur, or an extreme +slur in their words. + +The black male returns. + +Don't forget, he's in on it, +and so is that white male. + +But you're not in on it. + +You just think there was a bump, +and something else may + +have happened, depending on +which condition you're in. + +And the experimenter then gives +you a survey about how + +you feel right now. + +Sort of like the happiness, +but it's not that. + +It's like, how do you +feel right now? + +And then asks you to pick +between those two people a + +partner for an anagram +experiment that + +you're about to do. + +So they're going to ask you-- + +this is sort of this +question you have. + +What's the difference or +similarity between what you + +say you're feeling is and +what you really do? + +Both things are important, +but do they line up, do + +they not line up? + +So here's the results. + +Here's a graph. + +And here's how this works. + +Negative emotional distress the +higher the bar, the more + +you say, I feel really bad about +what's just happened. + +I just heard this comment +or no comment. + +So let's take a look, +the higher the bar. + +If you heard no comment, +here's how you begin. + +So let's start with +the forecasters. + +All of you are forecasters, +because you're pretending + +you're in the situation +but you're not in it. + +So here is there was +no comments. + +That's sort of average +or something. + +And then you said if you +heard a racial slur + +you would feel terrible. + +You would feel terrible. + +But look at the other students +who are randomly picked. + +So we don't think it's a +difference among students. + +Look at these grey bars. + +They're pretty flat. + +The person on the spot is +somehow not processing this. + +And they're filling out, +I feel average. + +You see the split-- + +the split between the values +that the person thinks they + +would have, and the values that +are responded to on the + +spot in the moment. + +And what we'll talk about later +on in social psychology + +is there's a tough gap, often, +between the values we espouse + +and how we act when there's +especially unexpected, + +difficult things. + +And very often-- + +if you've had any experience +like this-- afterwards, you + +go, oh, what I should +have done is this. + +Or I wish I would've +said that. + +But that moment is not happening +at that moment, + +probably because you're +kind of weirded out + +by the whole thing. + +What's going on? + +Why would the person say this? + +Something doesn't seem right. + +I can't sort it out. + +And so people tend to shrink +in terms of making a strong + +conclusion of what's going on +if something seems unusually + +provocative. + +And you could say, well, OK, +that's their attitudes. + +But how about their action? + +Who do they pick to +be their partner? + +And again, the people +forecasting said, if I was in + +this situation, I would never +pick that racist white person + +to be my partner, because +that person stinks-- + +if I was in that situation. + +But if the people are +in the situation-- + +look at the grey bars-- + +pretty flat. + +It's a if on the spot, in the +moment, they can't quite + +process the values they +feel and the action + +they're going to take. + +And we'll talk about that. + +And it's very hard, often, +in part, to be brave + +and stand up to things. + +It turns out there's a lot +of evidence for this. + +It's a human nature thing. + +It's very hard to be brave and +stand up to things when things + +are kind of weird, because +almost everybody at first + +thinks, I don't want to +make a fool of myself. + +I don't want make trouble. + +Maybe I'm not getting the +whole picture on this. + +And we shrink back from acting +in a way that aligns with the + +values that are clearly +shown here. + +So this, again, is something +about human + +nature that's very weird. + +And it's powerful to come +into social psychology. + +And that's why it's very hard +to stand up to things like + +oppression and bias. + +It's very hard to do, because +we tend to not act on our + +values when we're +in complicated + +situations on the spot. + +And there's a tremendous amount +of evidence for that. + +So again, how we interpret +the situation-- + +very different in our mind when +we imagine we're there, + +and when we actually +sit there. + +And so what these researchers +say is this is partly why it's + +been hard to eradicate some +vestiges of stereotypes and + +racism, because people have a +hard time clamping down on it + +in the moment. + +So that's a tough topic, but we +know we want to deal both + +with things that are less +controversial but also things + +that touch people's lives +in the real world + +that we live in. + +So we talked about a +scientific study + +of the human nature-- + +mind and behavior-- + +how what we see and hear is +determined so much but how our + +mind interprets the world around +us; how we remember + +things like word lists or +stories, that's hugely + +influenced by what we expect to +see, like in the picture; + +how we think we know things like +where Reno is compared to + +San Francisco; how we think +about things like the + +probability that somebody else +will have the same birthday, + +that somebody else will in a +group; and the relationship + +between how we feel +and how we act. + +The very feelings we have are +often disconnected for actions + +in the moment. + +And sometimes that has a sort +of a difficult consequence. + +And so we'll explore all these +things through the semester, + +all the different facets that we +could possibly get through + +in one semester of what it is to +be human, and where science + +has showed us something about +human nature, the + +mind, and the brain. \ No newline at end of file diff --git a/37CbZdeh_lU.txt b/37CbZdeh_lU.txt new file mode 100644 index 0000000000000000000000000000000000000000..5c05ffbacd11659e0c90d74d3a37d93955322798 --- /dev/null +++ b/37CbZdeh_lU.txt @@ -0,0 +1,235 @@ +align:start position:0% + +the researcher sent me a very wonderful + + align:start position:0% +the researcher sent me a very wonderful + + + align:start position:0% +the researcher sent me a very wonderful +microscopic picture of these micro + + align:start position:0% +microscopic picture of these micro + + + align:start position:0% +microscopic picture of these micro +needles and he really wanted to try to + + align:start position:0% +needles and he really wanted to try to + + + align:start position:0% +needles and he really wanted to try to +get a cover and although this course is + + align:start position:0% +get a cover and although this course is + + + align:start position:0% +get a cover and although this course is +about a camera and a lens I thought it'd + + align:start position:0% +about a camera and a lens I thought it'd + + + align:start position:0% +about a camera and a lens I thought it'd +be interesting for you to see the + + align:start position:0% +be interesting for you to see the + + + align:start position:0% +be interesting for you to see the +possibility of creating a potential + + align:start position:0% +possibility of creating a potential + + + align:start position:0% +possibility of creating a potential +cover submission from a horizontal + + align:start position:0% +cover submission from a horizontal + + + align:start position:0% +cover submission from a horizontal +picture so here's the picture that he + + align:start position:0% +picture so here's the picture that he + + + align:start position:0% +picture so here's the picture that he +made and what I decided to do was I was + + align:start position:0% +made and what I decided to do was I was + + + align:start position:0% +made and what I decided to do was I was +thinking ahead and cropped it imagining + + align:start position:0% +thinking ahead and cropped it imagining + + + align:start position:0% +thinking ahead and cropped it imagining +what the image would look like becoming + + align:start position:0% +what the image would look like becoming + + + align:start position:0% +what the image would look like becoming +a vertical shot there I did crop it and + + align:start position:0% +a vertical shot there I did crop it and + + + align:start position:0% +a vertical shot there I did crop it and +then what we have to do is make sure + + align:start position:0% +then what we have to do is make sure + + + align:start position:0% +then what we have to do is make sure +when we're looking for cover to make the + + align:start position:0% +when we're looking for cover to make the + + + align:start position:0% +when we're looking for cover to make the +DPI setting right which is 300 DPI the + + align:start position:0% +DPI setting right which is 300 DPI the + + + align:start position:0% +DPI setting right which is 300 DPI the +width of the image needs to be + + align:start position:0% +width of the image needs to be + + + align:start position:0% +width of the image needs to be +8.5 and we have to increase the canvas + + align:start position:0% +8.5 and we have to increase the canvas + + + align:start position:0% +8.5 and we have to increase the canvas +size to make the vertical Dimension 11 I + + align:start position:0% +size to make the vertical Dimension 11 I + + + align:start position:0% +size to make the vertical Dimension 11 I +then selected a piece of the background + + align:start position:0% +then selected a piece of the background + + + align:start position:0% +then selected a piece of the background +and distorted it to make up for the + + align:start position:0% +and distorted it to make up for the + + + align:start position:0% +and distorted it to make up for the +empty space and I also you could see + + align:start position:0% +empty space and I also you could see + + + align:start position:0% +empty space and I also you could see +that I I made a mistake and I I needed + + align:start position:0% +that I I made a mistake and I I needed + + + align:start position:0% +that I I made a mistake and I I needed +to fill in uh the side that I didn't get + + align:start position:0% +to fill in uh the side that I didn't get + + + align:start position:0% +to fill in uh the side that I didn't get +a hold of eventually I really do + + align:start position:0% +a hold of eventually I really do + + + align:start position:0% +a hold of eventually I really do +encourage enage you to consider doing + + align:start position:0% +encourage enage you to consider doing + + + align:start position:0% +encourage enage you to consider doing +these kinds of things we're not changing + + align:start position:0% +these kinds of things we're not changing + + + align:start position:0% +these kinds of things we're not changing +the micro needles we're just changing + + align:start position:0% +the micro needles we're just changing + + + align:start position:0% +the micro needles we're just changing +the background of the micro + + align:start position:0% +the background of the micro + + + align:start position:0% +the background of the micro +needles \ No newline at end of file diff --git a/3TnQSVytQ8A.txt b/3TnQSVytQ8A.txt new file mode 100644 index 0000000000000000000000000000000000000000..ac35ac14f257eed4d5dd2614826405819b9e505f --- /dev/null +++ b/3TnQSVytQ8A.txt @@ -0,0 +1,14616 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +opencourseware under a Creative Commons + + align:start position:0% +opencourseware under a Creative Commons + + + align:start position:0% +opencourseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +good afternoon + + align:start position:0% +good afternoon + + + align:start position:0% +good afternoon +when uh + + align:start position:0% +when uh + + + align:start position:0% +when uh +when we parted last time I was uh + + align:start position:0% +when we parted last time I was uh + + + align:start position:0% +when we parted last time I was uh +you you just did that demo with uh Sam + + align:start position:0% +you you just did that demo with uh Sam + + + align:start position:0% +you you just did that demo with uh Sam +who was either collecting um + + align:start position:0% +who was either collecting um + + + align:start position:0% +who was either collecting um +stamps or ladies undergarments depending + + align:start position:0% +stamps or ladies undergarments depending + + + align:start position:0% +stamps or ladies undergarments depending +and the point there was to + + align:start position:0% + + + + align:start position:0% + +describe the fact that + + align:start position:0% +describe the fact that + + + align:start position:0% +describe the fact that +any behavior is going to um is going to + + align:start position:0% +any behavior is going to um is going to + + + align:start position:0% +any behavior is going to um is going to +be distributed across the population in + + align:start position:0% +be distributed across the population in + + + align:start position:0% +be distributed across the population in +some fashion it may well be that the + + align:start position:0% +some fashion it may well be that the + + + align:start position:0% +some fashion it may well be that the +extreme of the population is abnormal in + + align:start position:0% +extreme of the population is abnormal in + + + align:start position:0% +extreme of the population is abnormal in +some meaningful sense + + align:start position:0% +some meaningful sense + + + align:start position:0% +some meaningful sense +maybe even pathological in some sense + + align:start position:0% +maybe even pathological in some sense + + + align:start position:0% +maybe even pathological in some sense +but that the border between what is + + align:start position:0% +but that the border between what is + + + align:start position:0% +but that the border between what is +normal and what is abnormal is going to + + align:start position:0% +normal and what is abnormal is going to + + + align:start position:0% +normal and what is abnormal is going to +be + + align:start position:0% +be + + + align:start position:0% +be +necessarily uh ambiguous there's not + + align:start position:0% +necessarily uh ambiguous there's not + + + align:start position:0% +necessarily uh ambiguous there's not +going to be some nice neat line that can + + align:start position:0% +going to be some nice neat line that can + + + align:start position:0% +going to be some nice neat line that can +be drawn in um + + align:start position:0% +be drawn in um + + + align:start position:0% +be drawn in um +in all cases I was arguing that + + align:start position:0% +in all cases I was arguing that + + + align:start position:0% +in all cases I was arguing that +something like schizophrenia + + align:start position:0% +something like schizophrenia + + + align:start position:0% +something like schizophrenia +is a bit more like that where the + + align:start position:0% +is a bit more like that where the + + + align:start position:0% +is a bit more like that where the +abnormal State really does look quite + + align:start position:0% +abnormal State really does look quite + + + align:start position:0% +abnormal State really does look quite +different from the from the normal State + + align:start position:0% +different from the from the normal State + + + align:start position:0% +different from the from the normal State +and and less likely less like that it's + + align:start position:0% +and and less likely less like that it's + + + align:start position:0% +and and less likely less like that it's +on a Continuum + + align:start position:0% +on a Continuum + + + align:start position:0% +on a Continuum +um oh you will notice on your handout + + align:start position:0% +um oh you will notice on your handout + + + align:start position:0% +um oh you will notice on your handout +that it says lecture 20 and and those of + + align:start position:0% +that it says lecture 20 and and those of + + + align:start position:0% +that it says lecture 20 and and those of +you who are particularly observant will + + align:start position:0% +you who are particularly observant will + + + align:start position:0% +you who are particularly observant will +say last one was called lecture 20. + + align:start position:0% +say last one was called lecture 20. + + + align:start position:0% +say last one was called lecture 20. +that's true + + align:start position:0% +that's true + + + align:start position:0% +that's true +I just liked 20. + + align:start position:0% +I just liked 20. + + + align:start position:0% +I just liked 20. +now if this is this is really 21. + + align:start position:0% +now if this is this is really 21. + + + align:start position:0% +now if this is this is really 21. +um and if I'm with a bit of luck I'll + + align:start position:0% +um and if I'm with a bit of luck I'll + + + align:start position:0% +um and if I'm with a bit of luck I'll +label the next one 22 otherwise it'll + + align:start position:0% +label the next one 22 otherwise it'll + + + align:start position:0% +label the next one 22 otherwise it'll +just turn out that there's 20 a and 20 b + + align:start position:0% +just turn out that there's 20 a and 20 b + + + align:start position:0% +just turn out that there's 20 a and 20 b +or something like that anyway it really + + align:start position:0% +or something like that anyway it really + + + align:start position:0% +or something like that anyway it really +is the right handout you'll discover + + align:start position:0% +is the right handout you'll discover + + + align:start position:0% +is the right handout you'll discover +that it is closely related + + align:start position:0% +that it is closely related + + + align:start position:0% +that it is closely related +to the um later pages of the of the last + + align:start position:0% +to the um later pages of the of the last + + + align:start position:0% +to the um later pages of the of the last +handout that we didn't get to last time + + align:start position:0% +handout that we didn't get to last time + + + align:start position:0% +handout that we didn't get to last time +um yeah it's kind of the same as is what + + align:start position:0% +um yeah it's kind of the same as is what + + + align:start position:0% +um yeah it's kind of the same as is what +people are noting but I didn't have any + + align:start position:0% +people are noting but I didn't have any + + + align:start position:0% +people are noting but I didn't have any +faith that people would remember to + + align:start position:0% +faith that people would remember to + + + align:start position:0% +faith that people would remember to +bring the real lecture 20-handed anyway + + align:start position:0% +bring the real lecture 20-handed anyway + + + align:start position:0% +bring the real lecture 20-handed anyway +what I want to talk about + + align:start position:0% + + + + align:start position:0% + +at least initially here is to talk a bit + + align:start position:0% +at least initially here is to talk a bit + + + align:start position:0% +at least initially here is to talk a bit +about how you would end up in this + + align:start position:0% +about how you would end up in this + + + align:start position:0% +about how you would end up in this +abnormal bin of uh of schizophrenia and + + align:start position:0% +abnormal bin of uh of schizophrenia and + + + align:start position:0% +abnormal bin of uh of schizophrenia and +one reasonable question to ask is uh + + align:start position:0% +one reasonable question to ask is uh + + + align:start position:0% +one reasonable question to ask is uh +well it's on the handout it says is + + align:start position:0% +well it's on the handout it says is + + + align:start position:0% +well it's on the handout it says is +there evidence for genetic component + + align:start position:0% +there evidence for genetic component + + + align:start position:0% +there evidence for genetic component +and the answer is yes and the way you + + align:start position:0% +and the answer is yes and the way you + + + align:start position:0% +and the answer is yes and the way you +get a one of the important sources of + + align:start position:0% +get a one of the important sources of + + + align:start position:0% +get a one of the important sources of +that information is similar to the data + + align:start position:0% +that information is similar to the data + + + align:start position:0% +that information is similar to the data +that we were talking about + + align:start position:0% +that we were talking about + + + align:start position:0% +that we were talking about +um in intelligence testing take a look + + align:start position:0% +um in intelligence testing take a look + + + align:start position:0% +um in intelligence testing take a look +at at + + align:start position:0% +at at + + + align:start position:0% +at at +um people who vary in the amount that + + align:start position:0% +um people who vary in the amount that + + + align:start position:0% +um people who vary in the amount that +they are genetically related to each + + align:start position:0% +they are genetically related to each + + + align:start position:0% +they are genetically related to each +other notably here MZ stands for + + align:start position:0% +other notably here MZ stands for + + + align:start position:0% +other notably here MZ stands for +monozygotic or identical single egg + + align:start position:0% +monozygotic or identical single egg + + + align:start position:0% +monozygotic or identical single egg +Twins and DZ stands for dizygotic uh two + + align:start position:0% +Twins and DZ stands for dizygotic uh two + + + align:start position:0% +Twins and DZ stands for dizygotic uh two +egg twins who are no more similar than + + align:start position:0% +egg twins who are no more similar than + + + align:start position:0% +egg twins who are no more similar than +than siblings + + align:start position:0% +than siblings + + + align:start position:0% +than siblings +um concordance means + + align:start position:0% +um concordance means + + + align:start position:0% +um concordance means +um + + align:start position:0% +um + + + align:start position:0% +um +what the chance is of Twin Two having + + align:start position:0% +what the chance is of Twin Two having + + + align:start position:0% +what the chance is of Twin Two having +the disease if twin one has it and so + + align:start position:0% +the disease if twin one has it and so + + + align:start position:0% +the disease if twin one has it and so +what you can see is that for monozygotic + + align:start position:0% +what you can see is that for monozygotic + + + align:start position:0% +what you can see is that for monozygotic +twins if one of a pair of identical + + align:start position:0% +twins if one of a pair of identical + + + align:start position:0% +twins if one of a pair of identical +twins becomes schizophrenic there's a 50 + + align:start position:0% +twins becomes schizophrenic there's a 50 + + + align:start position:0% +twins becomes schizophrenic there's a 50 +chance that the other one will too + + align:start position:0% +chance that the other one will too + + + align:start position:0% +chance that the other one will too +that tells you two things well well it + + align:start position:0% +that tells you two things well well it + + + align:start position:0% +that tells you two things well well it +only tells you two things if you look at + + align:start position:0% +only tells you two things if you look at + + + align:start position:0% +only tells you two things if you look at +the die zygotic the dizygotic twins have + + align:start position:0% +the die zygotic the dizygotic twins have + + + align:start position:0% +the die zygotic the dizygotic twins have +a much lower concordance rate of about + + align:start position:0% +a much lower concordance rate of about + + + align:start position:0% +a much lower concordance rate of about + + align:start position:0% + + + align:start position:0% +um so that tells you first of all that + + align:start position:0% +um so that tells you first of all that + + + align:start position:0% +um so that tells you first of all that +there's a probable genetic component + + align:start position:0% +there's a probable genetic component + + + align:start position:0% +there's a probable genetic component +there and second of all that it's not + + align:start position:0% +there and second of all that it's not + + + align:start position:0% +there and second of all that it's not +absolute if you have the genetic + + align:start position:0% +absolute if you have the genetic + + + align:start position:0% +absolute if you have the genetic +mutation + + align:start position:0% +mutation + + + align:start position:0% +mutation +um that makes you colorblind + + align:start position:0% +um that makes you colorblind + + + align:start position:0% +um that makes you colorblind +um or or color anomalous you'll be color + + align:start position:0% +um or or color anomalous you'll be color + + + align:start position:0% +um or or color anomalous you'll be color +anomalous there's no big mystery at this + + align:start position:0% +anomalous there's no big mystery at this + + + align:start position:0% +anomalous there's no big mystery at this +point about that if you have whatever + + align:start position:0% +point about that if you have whatever + + + align:start position:0% +point about that if you have whatever +the genetic predisposition is + + align:start position:0% +the genetic predisposition is + + + align:start position:0% +the genetic predisposition is +um for schizophrenia something else has + + align:start position:0% +um for schizophrenia something else has + + + align:start position:0% +um for schizophrenia something else has +to happen before uh before you would end + + align:start position:0% +to happen before uh before you would end + + + align:start position:0% +to happen before uh before you would end +up showing the disorder now um + + align:start position:0% +up showing the disorder now um + + + align:start position:0% +up showing the disorder now um +these these twin studies run into the + + align:start position:0% +these these twin studies run into the + + + align:start position:0% +these these twin studies run into the +same problem that the intelligence + + align:start position:0% +same problem that the intelligence + + + align:start position:0% +same problem that the intelligence +testing twin studies did which is that + + align:start position:0% +testing twin studies did which is that + + + align:start position:0% +testing twin studies did which is that +monozygotic twins are simply more + + align:start position:0% +monozygotic twins are simply more + + + align:start position:0% +monozygotic twins are simply more +similar on all sorts of things you know + + align:start position:0% +similar on all sorts of things you know + + + align:start position:0% +similar on all sorts of things you know +they're treated more similarly and so on + + align:start position:0% +they're treated more similarly and so on + + + align:start position:0% +they're treated more similarly and so on +one way to look at whether or not + + align:start position:0% +one way to look at whether or not + + + align:start position:0% +one way to look at whether or not +um there is a uh you know to try + + align:start position:0% +um there is a uh you know to try + + + align:start position:0% +um there is a uh you know to try +parceling this out is this third line + + align:start position:0% +parceling this out is this third line + + + align:start position:0% +parceling this out is this third line +here + + align:start position:0% +here + + + align:start position:0% +here +um this was a population of dizygotic + + align:start position:0% +um this was a population of dizygotic + + + align:start position:0% +um this was a population of dizygotic +twins who thought they were identical + + align:start position:0% +twins who thought they were identical + + + align:start position:0% +twins who thought they were identical +now they looked alike presumably that + + align:start position:0% +now they looked alike presumably that + + + align:start position:0% +now they looked alike presumably that +the same sex and stuff like that + + align:start position:0% +the same sex and stuff like that + + + align:start position:0% +the same sex and stuff like that +um thought they were identical + + align:start position:0% +um thought they were identical + + + align:start position:0% +um thought they were identical +um you'll see that their concordance + + align:start position:0% +um you'll see that their concordance + + + align:start position:0% +um you'll see that their concordance +rate was less than the 50 percent that + + align:start position:0% +rate was less than the 50 percent that + + + align:start position:0% +rate was less than the 50 percent that +the uh the true monozygotic twins had so + + align:start position:0% +the uh the true monozygotic twins had so + + + align:start position:0% +the uh the true monozygotic twins had so +there does seem to be something to be + + align:start position:0% +there does seem to be something to be + + + align:start position:0% +there does seem to be something to be +really genetically identical you can + + align:start position:0% +really genetically identical you can + + + align:start position:0% +really genetically identical you can +also do twins reared apart store uh + + align:start position:0% +also do twins reared apart store uh + + + align:start position:0% +also do twins reared apart store uh +things but look if you have a set of + + align:start position:0% +things but look if you have a set of + + + align:start position:0% +things but look if you have a set of +twins twins reared apart not common but + + align:start position:0% +twins twins reared apart not common but + + + align:start position:0% +twins twins reared apart not common but +all those twins have IQs you can always + + align:start position:0% +all those twins have IQs you can always + + + align:start position:0% +all those twins have IQs you can always +measure their IQs + + align:start position:0% +measure their IQs + + + align:start position:0% +measure their IQs +um if you take twins weird apart and + + align:start position:0% +um if you take twins weird apart and + + + align:start position:0% +um if you take twins weird apart and +then take + + align:start position:0% +then take + + + align:start position:0% +then take +the cases where one of them has a um it + + align:start position:0% +the cases where one of them has a um it + + + align:start position:0% +the cases where one of them has a um it +has schizophrenia and asks what the + + align:start position:0% +has schizophrenia and asks what the + + + align:start position:0% +has schizophrenia and asks what the +concordance rate is the answer is it's + + align:start position:0% +concordance rate is the answer is it's + + + align:start position:0% +concordance rate is the answer is it's +quite elevated but you know it's a + + align:start position:0% +quite elevated but you know it's a + + + align:start position:0% +quite elevated but you know it's a +really small population of people you + + align:start position:0% +really small population of people you + + + align:start position:0% +really small population of people you +know twin reared apart and schizophrenic + + align:start position:0% +know twin reared apart and schizophrenic + + + align:start position:0% +know twin reared apart and schizophrenic +it's not a big crowd + + align:start position:0% +it's not a big crowd + + + align:start position:0% +it's not a big crowd +um + + align:start position:0% +um + + + align:start position:0% +um +now when you go look for + + align:start position:0% +now when you go look for + + + align:start position:0% +now when you go look for +the genetic marker + + align:start position:0% +the genetic marker + + + align:start position:0% +the genetic marker +since the late 80s there have been a + + align:start position:0% +since the late 80s there have been a + + + align:start position:0% +since the late 80s there have been a +slew of papers on genetic markers for + + align:start position:0% +slew of papers on genetic markers for + + + align:start position:0% +slew of papers on genetic markers for +schizophrenia the way you look for this + + align:start position:0% +schizophrenia the way you look for this + + + align:start position:0% +schizophrenia the way you look for this +one of the typical ways to look for this + + align:start position:0% +one of the typical ways to look for this + + + align:start position:0% +one of the typical ways to look for this +is that schizophrenia runs in families + + align:start position:0% +is that schizophrenia runs in families + + + align:start position:0% +is that schizophrenia runs in families +um and if you go and analyze the uh the + + align:start position:0% +um and if you go and analyze the uh the + + + align:start position:0% +um and if you go and analyze the uh the +genetics of families you can find + + align:start position:0% +genetics of families you can find + + + align:start position:0% +genetics of families you can find +specific loci that seem to be abnormal + + align:start position:0% +specific loci that seem to be abnormal + + + align:start position:0% +specific loci that seem to be abnormal +in the schizophrenic members of the + + align:start position:0% +in the schizophrenic members of the + + + align:start position:0% +in the schizophrenic members of the +family the the the the difficulty or the + + align:start position:0% +family the the the the difficulty or the + + + align:start position:0% +family the the the the difficulty or the +interesting aspect of this genetic story + + align:start position:0% +interesting aspect of this genetic story + + + align:start position:0% +interesting aspect of this genetic story +is that the story that works for this + + align:start position:0% +is that the story that works for this + + + align:start position:0% +is that the story that works for this +family doesn't necessarily work for this + + align:start position:0% +family doesn't necessarily work for this + + + align:start position:0% +family doesn't necessarily work for this +family so in in the early days of this + + align:start position:0% +family so in in the early days of this + + + align:start position:0% +family so in in the early days of this +there'd be some big article in science + + align:start position:0% +there'd be some big article in science + + + align:start position:0% +there'd be some big article in science +or nature or something saying Gene Locus + + align:start position:0% +or nature or something saying Gene Locus + + + align:start position:0% +or nature or something saying Gene Locus +on chromosome 8 + + align:start position:0% +on chromosome 8 + + + align:start position:0% +on chromosome 8 +for uh you know for schizophrenia or + + align:start position:0% +for uh you know for schizophrenia or + + + align:start position:0% +for uh you know for schizophrenia or +whatever I'm making it up and then you + + align:start position:0% +whatever I'm making it up and then you + + + align:start position:0% +whatever I'm making it up and then you +know either in the same issue or on the + + align:start position:0% +know either in the same issue or on the + + + align:start position:0% +know either in the same issue or on the +next uh you know next week there'd be + + align:start position:0% +next uh you know next week there'd be + + + align:start position:0% +next uh you know next week there'd be +another thing saying but not in this + + align:start position:0% +another thing saying but not in this + + + align:start position:0% +another thing saying but not in this +family + + align:start position:0% +family + + + align:start position:0% +family +um clearly schizophrenic but not clearly + + align:start position:0% +um clearly schizophrenic but not clearly + + + align:start position:0% +um clearly schizophrenic but not clearly +having the same defect it suggests that + + align:start position:0% +having the same defect it suggests that + + + align:start position:0% +having the same defect it suggests that +there are multiple + + align:start position:0% +there are multiple + + + align:start position:0% +there are multiple +Roots genetic predispositions to + + align:start position:0% +Roots genetic predispositions to + + + align:start position:0% +Roots genetic predispositions to +schizophrenia it's also possible that + + align:start position:0% +schizophrenia it's also possible that + + + align:start position:0% +schizophrenia it's also possible that +you need more than one genetic insult if + + align:start position:0% +you need more than one genetic insult if + + + align:start position:0% +you need more than one genetic insult if +that's jargon not not you don't say you + + align:start position:0% +that's jargon not not you don't say you + + + align:start position:0% +that's jargon not not you don't say you +got an ugly gene + + align:start position:0% +got an ugly gene + + + align:start position:0% +got an ugly gene +um you know you need to have perhaps + + align:start position:0% +um you know you need to have perhaps + + + align:start position:0% +um you know you need to have perhaps +more than one defect in order to um have + + align:start position:0% +more than one defect in order to um have + + + align:start position:0% +more than one defect in order to um have +the susceptibility to + + align:start position:0% +the susceptibility to + + + align:start position:0% +the susceptibility to +um uh to schizophrenia one of the + + align:start position:0% +um uh to schizophrenia one of the + + + align:start position:0% +um uh to schizophrenia one of the +curious little wrinkles that I dug up in + + align:start position:0% +curious little wrinkles that I dug up in + + + align:start position:0% +curious little wrinkles that I dug up in +my reading on this and I've been I I've + + align:start position:0% +my reading on this and I've been I I've + + + align:start position:0% +my reading on this and I've been I I've +only read this in a secondary source I + + align:start position:0% +only read this in a secondary source I + + + align:start position:0% +only read this in a secondary source I +have been unsuccessful in tracking down + + align:start position:0% +have been unsuccessful in tracking down + + + align:start position:0% +have been unsuccessful in tracking down +the primary source but I'll tell you + + align:start position:0% +the primary source but I'll tell you + + + align:start position:0% +the primary source but I'll tell you +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +um is a a study that turns out that + + align:start position:0% +um is a a study that turns out that + + + align:start position:0% +um is a a study that turns out that +there are two types of identical twins + + align:start position:0% +there are two types of identical twins + + + align:start position:0% +there are two types of identical twins +there are sort of plain vanilla + + align:start position:0% +there are sort of plain vanilla + + + align:start position:0% +there are sort of plain vanilla +identical twins you know twin one is + + align:start position:0% +identical twins you know twin one is + + + align:start position:0% +identical twins you know twin one is +right-handed Twin Two is right-handed + + align:start position:0% +right-handed Twin Two is right-handed + + + align:start position:0% +right-handed Twin Two is right-handed +and so on and then there are so-called + + align:start position:0% +and so on and then there are so-called + + + align:start position:0% +and so on and then there are so-called +mirror twins they're genetically + + align:start position:0% +mirror twins they're genetically + + + align:start position:0% +mirror twins they're genetically +identical but the phenotype the actual + + align:start position:0% +identical but the phenotype the actual + + + align:start position:0% +identical but the phenotype the actual +uh organism is mirrored rather than than + + align:start position:0% +uh organism is mirrored rather than than + + + align:start position:0% +uh organism is mirrored rather than than +mirrored rather than identical or + + align:start position:0% +mirrored rather than identical or + + + align:start position:0% +mirrored rather than identical or +something like that so if one's + + align:start position:0% +something like that so if one's + + + align:start position:0% +something like that so if one's +right-handed the other's left-handed you + + align:start position:0% +right-handed the other's left-handed you + + + align:start position:0% +right-handed the other's left-handed you +know swirl on the top of your head if if + + align:start position:0% +know swirl on the top of your head if if + + + align:start position:0% +know swirl on the top of your head if if +it swirls clockwise for uh one twin it + + align:start position:0% +it swirls clockwise for uh one twin it + + + align:start position:0% +it swirls clockwise for uh one twin it +swirls the other way for the other twin + + align:start position:0% +swirls the other way for the other twin + + + align:start position:0% +swirls the other way for the other twin +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +um and the Curious finding reported in + + align:start position:0% +um and the Curious finding reported in + + + align:start position:0% +um and the Curious finding reported in +this one uh relatively small study I + + align:start position:0% +this one uh relatively small study I + + + align:start position:0% +this one uh relatively small study I +think + + align:start position:0% +think + + + align:start position:0% +think +um is that the concordance rates for + + align:start position:0% +um is that the concordance rates for + + + align:start position:0% +um is that the concordance rates for +identical identical twins the right hand + + align:start position:0% +identical identical twins the right hand + + + align:start position:0% +identical identical twins the right hand +right hand identical twins very high in + + align:start position:0% +right hand identical twins very high in + + + align:start position:0% +right hand identical twins very high in +this study like over 90 if you had if + + align:start position:0% +this study like over 90 if you had if + + + align:start position:0% +this study like over 90 if you had if +one twin was schizophrenic the other was + + align:start position:0% +one twin was schizophrenic the other was + + + align:start position:0% +one twin was schizophrenic the other was +schizophrenic + + align:start position:0% +schizophrenic + + + align:start position:0% +schizophrenic +um the mirrored twins + + align:start position:0% +um the mirrored twins + + + align:start position:0% +um the mirrored twins +to the left right ones were concordance + + align:start position:0% +to the left right ones were concordance + + + align:start position:0% +to the left right ones were concordance +rate down at about 25 both of these are + + align:start position:0% +rate down at about 25 both of these are + + + align:start position:0% +rate down at about 25 both of these are +genetically identical pairs of of twins + + align:start position:0% +genetically identical pairs of of twins + + + align:start position:0% +genetically identical pairs of of twins +it's + + align:start position:0% +it's + + + align:start position:0% +it's +abundantly unclear what it is that makes + + align:start position:0% +abundantly unclear what it is that makes + + + align:start position:0% +abundantly unclear what it is that makes +these two groups different if indeed + + align:start position:0% +these two groups different if indeed + + + align:start position:0% +these two groups different if indeed +that turns out to be a reliable result + + align:start position:0% +that turns out to be a reliable result + + + align:start position:0% +that turns out to be a reliable result +I'm I I went hunting in the databases + + align:start position:0% +I'm I I went hunting in the databases + + + align:start position:0% +I'm I I went hunting in the databases +and I think I found the guy who did it + + align:start position:0% +and I think I found the guy who did it + + + align:start position:0% +and I think I found the guy who did it +so I sent him an email but he didn't get + + align:start position:0% +so I sent him an email but he didn't get + + + align:start position:0% +so I sent him an email but he didn't get +back to me in time + + align:start position:0% +back to me in time + + + align:start position:0% +back to me in time +um but oh that reminds me it's a little + + align:start position:0% +um but oh that reminds me it's a little + + + align:start position:0% +um but oh that reminds me it's a little +late in the day to tell you this but uh + + align:start position:0% +late in the day to tell you this but uh + + + align:start position:0% +late in the day to tell you this but uh +um if you discover that something that + + align:start position:0% +um if you discover that something that + + + align:start position:0% +um if you discover that something that +you're looking for in in primary source + + align:start position:0% +you're looking for in in primary source + + + align:start position:0% +you're looking for in in primary source +land you know you you're looking for the + + align:start position:0% +land you know you you're looking for the + + + align:start position:0% +land you know you you're looking for the +Journal of who's he fousey results or + + align:start position:0% +Journal of who's he fousey results or + + + align:start position:0% +Journal of who's he fousey results or +whatever and and oh my God MIT doesn't + + align:start position:0% +whatever and and oh my God MIT doesn't + + + align:start position:0% +whatever and and oh my God MIT doesn't +carry it so you don't have access to it + + align:start position:0% +carry it so you don't have access to it + + + align:start position:0% +carry it so you don't have access to it +it's often very useful to go and see if + + align:start position:0% +it's often very useful to go and see if + + + align:start position:0% +it's often very useful to go and see if +you can find the website for the lab + + align:start position:0% +you can find the website for the lab + + + align:start position:0% +you can find the website for the lab +where the work was done because + + align:start position:0% +where the work was done because + + + align:start position:0% +where the work was done because +um many many of us post all of our + + align:start position:0% +um many many of us post all of our + + + align:start position:0% +um many many of us post all of our +Publications or as many as we have PDFs + + align:start position:0% +Publications or as many as we have PDFs + + + align:start position:0% +Publications or as many as we have PDFs +for on the website to be downloaded and + + align:start position:0% +for on the website to be downloaded and + + + align:start position:0% +for on the website to be downloaded and +so you can dig things up + + align:start position:0% +so you can dig things up + + + align:start position:0% +so you can dig things up +um + + align:start position:0% +um + + + align:start position:0% +um +we can dig things up that way so anyway + + align:start position:0% +we can dig things up that way so anyway + + + align:start position:0% +we can dig things up that way so anyway +there's there's pretty strong evidence + + align:start position:0% +there's there's pretty strong evidence + + + align:start position:0% +there's there's pretty strong evidence +for a genetic component + + align:start position:0% +for a genetic component + + + align:start position:0% +for a genetic component +um and then there's pretty strong + + align:start position:0% +um and then there's pretty strong + + + align:start position:0% +um and then there's pretty strong +evidence that that by itself is not + + align:start position:0% +evidence that that by itself is not + + + align:start position:0% +evidence that that by itself is not +enough unlike a variety of other + + align:start position:0% +enough unlike a variety of other + + + align:start position:0% +enough unlike a variety of other +neurological uh disorders there are + + align:start position:0% +neurological uh disorders there are + + + align:start position:0% +neurological uh disorders there are +plenty of neurological disorders where + + align:start position:0% +plenty of neurological disorders where + + + align:start position:0% +plenty of neurological disorders where +if you've got this problem with your uh + + align:start position:0% +if you've got this problem with your uh + + + align:start position:0% +if you've got this problem with your uh +your genome it's going to munch up your + + align:start position:0% +your genome it's going to munch up your + + + align:start position:0% +your genome it's going to munch up your +brain in the following fashion you're + + align:start position:0% +brain in the following fashion you're + + + align:start position:0% +brain in the following fashion you're +going to have this problem and you know + + align:start position:0% +going to have this problem and you know + + + align:start position:0% +going to have this problem and you know +it's it's fortunately most of these are + + align:start position:0% +it's it's fortunately most of these are + + + align:start position:0% +it's it's fortunately most of these are +very rare but these they're they're + + align:start position:0% +very rare but these they're they're + + + align:start position:0% +very rare but these they're they're +straightforward genetic stories in + + align:start position:0% +straightforward genetic stories in + + + align:start position:0% +straightforward genetic stories in +schizophrenia something about the + + align:start position:0% +schizophrenia something about the + + + align:start position:0% +schizophrenia something about the +environment seems to be important to + + align:start position:0% +environment seems to be important to + + + align:start position:0% +environment seems to be important to +trip it off the leading notion is stress + + align:start position:0% +trip it off the leading notion is stress + + + align:start position:0% +trip it off the leading notion is stress +um so actually does anybody remember + + align:start position:0% +um so actually does anybody remember + + + align:start position:0% +um so actually does anybody remember +does the is the the book used to go on + + align:start position:0% +does the is the the book used to go on + + + align:start position:0% +does the is the the book used to go on +at vast lengths about uh the stress + + align:start position:0% +at vast lengths about uh the stress + + + align:start position:0% +at vast lengths about uh the stress +diastesis model of uh schizophrenia does + + align:start position:0% +diastesis model of uh schizophrenia does + + + align:start position:0% +diastesis model of uh schizophrenia does +this sound familiar to anybody + + align:start position:0% +this sound familiar to anybody + + + align:start position:0% +this sound familiar to anybody +has anybody looked at the + + align:start position:0% +has anybody looked at the + + + align:start position:0% +has anybody looked at the +relevant parts of the book yet nobody + + align:start position:0% +relevant parts of the book yet nobody + + + align:start position:0% +relevant parts of the book yet nobody +knows all right well anyway + + align:start position:0% +knows all right well anyway + + + align:start position:0% +knows all right well anyway +one of the leading Notions about + + align:start position:0% +one of the leading Notions about + + + align:start position:0% +one of the leading Notions about +um what it is that that actually + + align:start position:0% +um what it is that that actually + + + align:start position:0% +um what it is that that actually +produces the Florence disease is that + + align:start position:0% +produces the Florence disease is that + + + align:start position:0% +produces the Florence disease is that +you need to have some genetic + + align:start position:0% +you need to have some genetic + + + align:start position:0% +you need to have some genetic +predisposition and then you need + + align:start position:0% +predisposition and then you need + + + align:start position:0% +predisposition and then you need +something like stress to drop kick you + + align:start position:0% +something like stress to drop kick you + + + align:start position:0% +something like stress to drop kick you +into pathology now this is an + + align:start position:0% +into pathology now this is an + + + align:start position:0% +into pathology now this is an +interesting this this raises + + align:start position:0% +interesting this this raises + + + align:start position:0% +interesting this this raises +um interesting problems for Public + + align:start position:0% +um interesting problems for Public + + + align:start position:0% +um interesting problems for Public +Policy I think we talked last time about + + align:start position:0% +Policy I think we talked last time about + + + align:start position:0% +Policy I think we talked last time about +you know when is it okay to force + + align:start position:0% +you know when is it okay to force + + + align:start position:0% +you know when is it okay to force +somebody to be medicated right + + align:start position:0% +somebody to be medicated right + + + align:start position:0% +somebody to be medicated right +um + + align:start position:0% +um + + + align:start position:0% +um +this is a similar sort of problem + + align:start position:0% +this is a similar sort of problem + + + align:start position:0% +this is a similar sort of problem +um so + + align:start position:0% +um so + + + align:start position:0% +um so +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +well + + align:start position:0% +well + + + align:start position:0% +well +suppose you were applying to MIT this + + align:start position:0% +suppose you were applying to MIT this + + + align:start position:0% +suppose you were applying to MIT this +year + + align:start position:0% +year + + + align:start position:0% +year +should I be able to should I go and + + align:start position:0% +should I be able to should I go and + + + align:start position:0% +should I be able to should I go and +suggest to the head of admissions that + + align:start position:0% +suggest to the head of admissions that + + + align:start position:0% +suggest to the head of admissions that +we really should get little tubes of + + align:start position:0% +we really should get little tubes of + + + align:start position:0% +we really should get little tubes of +blood from everybody + + align:start position:0% +blood from everybody + + + align:start position:0% +blood from everybody +because if we got little tubes of blood + + align:start position:0% +because if we got little tubes of blood + + + align:start position:0% +because if we got little tubes of blood +from everybody we could genetically + + align:start position:0% +from everybody we could genetically + + + align:start position:0% +from everybody we could genetically +screen them and we know where uh we know + + align:start position:0% +screen them and we know where uh we know + + + align:start position:0% +screen them and we know where uh we know +we don't know exactly which loci are + + align:start position:0% +we don't know exactly which loci are + + + align:start position:0% +we don't know exactly which loci are +critical but we know a bunch of loci + + align:start position:0% +critical but we know a bunch of loci + + + align:start position:0% +critical but we know a bunch of loci +that seem to be related to family + + align:start position:0% +that seem to be related to family + + + align:start position:0% +that seem to be related to family +histories of schizophrenia and anyway + + align:start position:0% +histories of schizophrenia and anyway + + + align:start position:0% +histories of schizophrenia and anyway +there's all sorts of other interesting + + align:start position:0% +there's all sorts of other interesting + + + align:start position:0% +there's all sorts of other interesting +genetic markers out there at this point + + align:start position:0% +genetic markers out there at this point + + + align:start position:0% +genetic markers out there at this point +we could screen the incoming population + + align:start position:0% +we could screen the incoming population + + + align:start position:0% +we could screen the incoming population +or the population of applicants and + + align:start position:0% +or the population of applicants and + + + align:start position:0% +or the population of applicants and +systematically decide not to admit + + align:start position:0% +systematically decide not to admit + + + align:start position:0% +systematically decide not to admit +people who had the genetic marker for + + align:start position:0% +people who had the genetic marker for + + + align:start position:0% +people who had the genetic marker for +schizophrenia or for some other well + + align:start position:0% +schizophrenia or for some other well + + + align:start position:0% +schizophrenia or for some other well +schizophrenia is a good example why in + + align:start position:0% +schizophrenia is a good example why in + + + align:start position:0% +schizophrenia is a good example why in +the world would we do this well + + align:start position:0% +the world would we do this well + + + align:start position:0% +the world would we do this well +um is there anybody currently present + + align:start position:0% +um is there anybody currently present + + + align:start position:0% +um is there anybody currently present +who believes that MIT is a at least + + align:start position:0% +who believes that MIT is a at least + + + align:start position:0% +who believes that MIT is a at least +modestly stressful environment + + align:start position:0% +modestly stressful environment + + + align:start position:0% +modestly stressful environment +yeah all right you know short of + + align:start position:0% +yeah all right you know short of + + + align:start position:0% +yeah all right you know short of +Guantanamo Bay or something you know + + align:start position:0% +Guantanamo Bay or something you know + + + align:start position:0% +Guantanamo Bay or something you know +it's right up there + + align:start position:0% +it's right up there + + + align:start position:0% +it's right up there +um + + align:start position:0% +um + + + align:start position:0% +um +all right + + align:start position:0% +all right + + + align:start position:0% +all right +we know the state of the art is that we + + align:start position:0% +we know the state of the art is that we + + + align:start position:0% +we know the state of the art is that we +know that stress is a contributing + + align:start position:0% +know that stress is a contributing + + + align:start position:0% +know that stress is a contributing +factor to a variety of mental illness + + align:start position:0% +factor to a variety of mental illness + + + align:start position:0% +factor to a variety of mental illness +this is notably in this example + + align:start position:0% +this is notably in this example + + + align:start position:0% +this is notably in this example +schizophrenia if we admit people to a a + + align:start position:0% +schizophrenia if we admit people to a a + + + align:start position:0% +schizophrenia if we admit people to a a +a an environment that we know is highly + + align:start position:0% +a an environment that we know is highly + + + align:start position:0% +a an environment that we know is highly +stressful we are asking for a certain + + align:start position:0% +stressful we are asking for a certain + + + align:start position:0% +stressful we are asking for a certain +number of um of of psychiatric problems + + align:start position:0% +number of um of of psychiatric problems + + + align:start position:0% +number of um of of psychiatric problems +isn't it our responsibility + + align:start position:0% +isn't it our responsibility + + + align:start position:0% +isn't it our responsibility +to prevent that from happening well now + + align:start position:0% +to prevent that from happening well now + + + align:start position:0% +to prevent that from happening well now +typically the uh I won't take a poll but + + align:start position:0% +typically the uh I won't take a poll but + + + align:start position:0% +typically the uh I won't take a poll but +the typical answer is no that doesn't + + align:start position:0% +the typical answer is no that doesn't + + + align:start position:0% +the typical answer is no that doesn't +sound right + + align:start position:0% +sound right + + + align:start position:0% +sound right +um you know that somehow that sounds a + + align:start position:0% +um you know that somehow that sounds a + + + align:start position:0% +um you know that somehow that sounds a +little too paternalistic too invasive + + align:start position:0% +little too paternalistic too invasive + + + align:start position:0% +little too paternalistic too invasive +for me to be screening your genes and + + align:start position:0% +for me to be screening your genes and + + + align:start position:0% +for me to be screening your genes and +you know who knows down the line we take + + align:start position:0% +you know who knows down the line we take + + + align:start position:0% +you know who knows down the line we take +a look at this hunk of the genome and we + + align:start position:0% +a look at this hunk of the genome and we + + + align:start position:0% +a look at this hunk of the genome and we +say you know sorry you're just never + + align:start position:0% +say you know sorry you're just never + + + align:start position:0% +say you know sorry you're just never +passing 1803. + + align:start position:0% +passing 1803. + + + align:start position:0% +passing 1803. +um + + align:start position:0% +um + + + align:start position:0% +um +you know what what what would we ever do + + align:start position:0% +you know what what what would we ever do + + + align:start position:0% +you know what what what would we ever do +with information + + align:start position:0% +with information + + + align:start position:0% +with information +um like that but but the disease case + + align:start position:0% +um like that but but the disease case + + + align:start position:0% +um like that but but the disease case +it doesn't feel right typically to to + + align:start position:0% +it doesn't feel right typically to to + + + align:start position:0% +it doesn't feel right typically to to +people but on the other hand + + align:start position:0% +people but on the other hand + + + align:start position:0% +people but on the other hand +um we spend a lot of time worrying + + align:start position:0% +um we spend a lot of time worrying + + + align:start position:0% +um we spend a lot of time worrying +believe it or not about your mental + + align:start position:0% +believe it or not about your mental + + + align:start position:0% +believe it or not about your mental +health right the the the the Dean's + + align:start position:0% +health right the the the the Dean's + + + align:start position:0% +health right the the the the Dean's +office + + align:start position:0% +office + + + align:start position:0% +office +um has substantial branches devoted to + + align:start position:0% +um has substantial branches devoted to + + + align:start position:0% +um has substantial branches devoted to +um mental health issues as does the + + align:start position:0% +um mental health issues as does the + + + align:start position:0% +um mental health issues as does the +medical Department we know that um + + align:start position:0% +medical Department we know that um + + + align:start position:0% +medical Department we know that um +university environments kick up a + + align:start position:0% +university environments kick up a + + + align:start position:0% +university environments kick up a +certain amount of + + align:start position:0% +certain amount of + + + align:start position:0% +certain amount of +um a psychiatric problems and we know + + align:start position:0% +um a psychiatric problems and we know + + + align:start position:0% +um a psychiatric problems and we know +that that can be catastrophically bad + + align:start position:0% +that that can be catastrophically bad + + + align:start position:0% +that that can be catastrophically bad +for for the the person and and for + + align:start position:0% +for for the the person and and for + + + align:start position:0% +for for the the person and and for +people around them + + align:start position:0% +people around them + + + align:start position:0% +people around them +wouldn't it be our responsibility to do + + align:start position:0% +wouldn't it be our responsibility to do + + + align:start position:0% +wouldn't it be our responsibility to do +something about that well look I'm not + + align:start position:0% +something about that well look I'm not + + + align:start position:0% +something about that well look I'm not +going to give you an answer to that and + + align:start position:0% +going to give you an answer to that and + + + align:start position:0% +going to give you an answer to that and +I promise not to ask on the exam you + + align:start position:0% +I promise not to ask on the exam you + + + align:start position:0% +I promise not to ask on the exam you +know should we get blood samples from + + align:start position:0% +know should we get blood samples from + + + align:start position:0% +know should we get blood samples from +everybody and you know the choices are + + align:start position:0% +everybody and you know the choices are + + + align:start position:0% +everybody and you know the choices are +yes no all of the above or something + + align:start position:0% +yes no all of the above or something + + + align:start position:0% +yes no all of the above or something +like that I raised that as an issue to + + align:start position:0% +like that I raised that as an issue to + + + align:start position:0% +like that I raised that as an issue to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um to to think about + + align:start position:0% +um to to think about + + + align:start position:0% +um to to think about +um oh when you take a look at the brains + + align:start position:0% +um oh when you take a look at the brains + + + align:start position:0% +um oh when you take a look at the brains +of schizophrenics by the way they don't + + align:start position:0% +of schizophrenics by the way they don't + + + align:start position:0% +of schizophrenics by the way they don't +look like the brains of + + align:start position:0% +look like the brains of + + + align:start position:0% +look like the brains of +um uh of healthy normal individuals so + + align:start position:0% +um uh of healthy normal individuals so + + + align:start position:0% +um uh of healthy normal individuals so +you get things like shrinkage of uh of + + align:start position:0% +you get things like shrinkage of uh of + + + align:start position:0% +you get things like shrinkage of uh of +gray matter you get + + align:start position:0% +gray matter you get + + + align:start position:0% +gray matter you get +enlargement of the the ventricles the + + align:start position:0% +enlargement of the the ventricles the + + + align:start position:0% +enlargement of the the ventricles the +ventricles or those nice empty + + align:start position:0% +ventricles or those nice empty + + + align:start position:0% +ventricles or those nice empty +fluid-filled spaces in your brain great + + align:start position:0% +fluid-filled spaces in your brain great + + + align:start position:0% +fluid-filled spaces in your brain great +answer for a uh if you if you're looking + + align:start position:0% +answer for a uh if you if you're looking + + + align:start position:0% +answer for a uh if you if you're looking +at the multiple choice question on the + + align:start position:0% +at the multiple choice question on the + + + align:start position:0% +at the multiple choice question on the +final and you're thinking I'm gonna go + + align:start position:0% +final and you're thinking I'm gonna go + + + align:start position:0% +final and you're thinking I'm gonna go +for you know the third ventricle as the + + align:start position:0% +for you know the third ventricle as the + + + align:start position:0% +for you know the third ventricle as the +answer you're probably getting suckered + + align:start position:0% +answer you're probably getting suckered + + + align:start position:0% +answer you're probably getting suckered +here right because the ventricles are + + align:start position:0% +here right because the ventricles are + + + align:start position:0% +here right because the ventricles are +empty fluid-filled spaces it's not where + + align:start position:0% +empty fluid-filled spaces it's not where + + + align:start position:0% +empty fluid-filled spaces it's not where +any of the more important mental + + align:start position:0% +any of the more important mental + + + align:start position:0% +any of the more important mental +functions are thoughts to be localized + + align:start position:0% +functions are thoughts to be localized + + + align:start position:0% +functions are thoughts to be localized +at least not since the Middle Ages where + + align:start position:0% +at least not since the Middle Ages where + + + align:start position:0% +at least not since the Middle Ages where +people did think that that memories were + + align:start position:0% +people did think that that memories were + + + align:start position:0% +people did think that that memories were +stored in the ventricles because after + + align:start position:0% +stored in the ventricles because after + + + align:start position:0% +stored in the ventricles because after +all they look like storerooms + + align:start position:0% +all they look like storerooms + + + align:start position:0% +all they look like storerooms +um anyway the ventricles get bigger + + align:start position:0% +um anyway the ventricles get bigger + + + align:start position:0% +um anyway the ventricles get bigger +that's presumably not a good thing + + align:start position:0% +that's presumably not a good thing + + + align:start position:0% +that's presumably not a good thing +because it's reflecting loss of of brain + + align:start position:0% +because it's reflecting loss of of brain + + + align:start position:0% +because it's reflecting loss of of brain +tissue + + align:start position:0% +tissue + + + align:start position:0% +tissue +um what's not absolutely clear is + + align:start position:0% +um what's not absolutely clear is + + + align:start position:0% +um what's not absolutely clear is +whether or not abnormalities in brain + + align:start position:0% +whether or not abnormalities in brain + + + align:start position:0% +whether or not abnormalities in brain +structure precede disease you know are + + align:start position:0% +structure precede disease you know are + + + align:start position:0% +structure precede disease you know are +they there somehow from birth is part of + + align:start position:0% +they there somehow from birth is part of + + + align:start position:0% +they there somehow from birth is part of +what the gene is doing somehow changing + + align:start position:0% +what the gene is doing somehow changing + + + align:start position:0% +what the gene is doing somehow changing +the structure of the brain in such a way + + align:start position:0% +the structure of the brain in such a way + + + align:start position:0% +the structure of the brain in such a way +that it makes it vulnerable or is it + + align:start position:0% +that it makes it vulnerable or is it + + + align:start position:0% +that it makes it vulnerable or is it +that having the disease itself is uh is + + align:start position:0% +that having the disease itself is uh is + + + align:start position:0% +that having the disease itself is uh is +is bad for the brain + + align:start position:0% +is bad for the brain + + + align:start position:0% +is bad for the brain +case + + align:start position:0% +case + + + align:start position:0% +case +the point to take away + + align:start position:0% +the point to take away + + + align:start position:0% +the point to take away +there are lots + + align:start position:0% +there are lots + + + align:start position:0% +there are lots +a lot of boots into + + align:start position:0% +a lot of boots into + + + align:start position:0% +a lot of boots into +the kingdom of schizophrenia it's not a + + align:start position:0% +the kingdom of schizophrenia it's not a + + + align:start position:0% +the kingdom of schizophrenia it's not a +nice clean simple diagnosis where you + + align:start position:0% +nice clean simple diagnosis where you + + + align:start position:0% +nice clean simple diagnosis where you +say you get this bacterium you get this + + align:start position:0% +say you get this bacterium you get this + + + align:start position:0% +say you get this bacterium you get this +disease we give you this um uh you know + + align:start position:0% +disease we give you this um uh you know + + + align:start position:0% +disease we give you this um uh you know +we give you this antibiotic and you're + + align:start position:0% +we give you this antibiotic and you're + + + align:start position:0% +we give you this antibiotic and you're +okay multiple roots in + + align:start position:0% +okay multiple roots in + + + align:start position:0% +okay multiple roots in +um and and treatment options are are you + + align:start position:0% +um and and treatment options are are you + + + align:start position:0% +um and and treatment options are are you +know getting better but but are but + + align:start position:0% +know getting better but but are but + + + align:start position:0% +know getting better but but are but +remain difficult + + align:start position:0% +remain difficult + + + align:start position:0% +remain difficult +um what I let's see here oh yes what I + + align:start position:0% +um what I let's see here oh yes what I + + + align:start position:0% +um what I let's see here oh yes what I +think I will do is uh switch gears and + + align:start position:0% +think I will do is uh switch gears and + + + align:start position:0% +think I will do is uh switch gears and +talk a bit about depression + + align:start position:0% +talk a bit about depression + + + align:start position:0% +talk a bit about depression +um but in order to talk about depression + + align:start position:0% +um but in order to talk about depression + + + align:start position:0% +um but in order to talk about depression +what I want you to do is to decide how + + align:start position:0% +what I want you to do is to decide how + + + align:start position:0% +what I want you to do is to decide how +you want to treat my three invented + + align:start position:0% +you want to treat my three invented + + + align:start position:0% +you want to treat my three invented +patients on the handout + + align:start position:0% +patients on the handout + + + align:start position:0% +patients on the handout +the second one the third one's on the + + align:start position:0% +the second one the third one's on the + + + align:start position:0% +the second one the third one's on the +back of the page + + align:start position:0% +back of the page + + + align:start position:0% +back of the page +so play with that for a second Kristen + + align:start position:0% +so play with that for a second Kristen + + + align:start position:0% +so play with that for a second Kristen +can you do me a favor go find me a + + align:start position:0% +can you do me a favor go find me a + + + align:start position:0% +can you do me a favor go find me a +bottle of water I'm gonna expire today + + align:start position:0% +bottle of water I'm gonna expire today + + + align:start position:0% +bottle of water I'm gonna expire today +otherwise + + align:start position:0% +otherwise + + + align:start position:0% +otherwise +I don't know do you got any interesting + + align:start position:0% +I don't know do you got any interesting + + + align:start position:0% +I don't know do you got any interesting +diseases + + align:start position:0% + + + + align:start position:0% + +steal me find me something somewhere + + align:start position:0% +steal me find me something somewhere + + + align:start position:0% +steal me find me something somewhere +thank you + + align:start position:0% + + + + align:start position:0% + +I'm still + + align:start position:0% +I'm still + + + align:start position:0% +I'm still +I'm I'm recovering from a cold still and + + align:start position:0% +I'm I'm recovering from a cold still and + + + align:start position:0% +I'm I'm recovering from a cold still and +I can feel that I've got the run out of + + align:start position:0% +I can feel that I've got the run out of + + + align:start position:0% +I can feel that I've got the run out of +moisture + + align:start position:0% +moisture + + + align:start position:0% +moisture +and my tongue is going to get all big in + + align:start position:0% +and my tongue is going to get all big in + + + align:start position:0% +and my tongue is going to get all big in +like a parrot or something I won't be + + align:start position:0% +like a parrot or something I won't be + + + align:start position:0% +like a parrot or something I won't be +able to talk all right have you managed + + align:start position:0% +able to talk all right have you managed + + + align:start position:0% +able to talk all right have you managed +to do this + + align:start position:0% +to do this + + + align:start position:0% +to do this +still working on it all right don't + + align:start position:0% +still working on it all right don't + + + align:start position:0% +still working on it all right don't +cheat off your neighbors but I promise + + align:start position:0% +cheat off your neighbors but I promise + + + align:start position:0% +cheat off your neighbors but I promise +you this time none of these guys are + + align:start position:0% +you this time none of these guys are + + + align:start position:0% +you this time none of these guys are +dealing in ladies undergarments + + align:start position:0% + + + + align:start position:0% + +uh here let's let's collect some + + align:start position:0% + + + + align:start position:0% + +all right let's collect us + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +everybody pretty much done here + + align:start position:0% +everybody pretty much done here + + + align:start position:0% +everybody pretty much done here +yeah make ascending noises or something + + align:start position:0% +yeah make ascending noises or something + + + align:start position:0% +yeah make ascending noises or something +oh okay that's good + + align:start position:0% +oh okay that's good + + + align:start position:0% +oh okay that's good +um that sounded very extenting okay so + + align:start position:0% +um that sounded very extenting okay so + + + align:start position:0% +um that sounded very extenting okay so +Sarah had a bad day + + align:start position:0% +Sarah had a bad day + + + align:start position:0% +Sarah had a bad day +um how many people would uh let's see so + + align:start position:0% +um how many people would uh let's see so + + + align:start position:0% +um how many people would uh let's see so +that that the low numbers are the no way + + align:start position:0% +that that the low numbers are the no way + + + align:start position:0% +that that the low numbers are the no way +we're not going to medicate this + + align:start position:0% +we're not going to medicate this + + + align:start position:0% +we're not going to medicate this +depression uh how many people oh that + + align:start position:0% +depression uh how many people oh that + + + align:start position:0% +depression uh how many people oh that +was quick that was good thank you + + align:start position:0% +was quick that was good thank you + + + align:start position:0% +was quick that was good thank you +um how many people are going to give her + + align:start position:0% +um how many people are going to give her + + + align:start position:0% +um how many people are going to give her +nomads + + align:start position:0% +nomads + + + align:start position:0% +nomads +oh okay so the answer is everybody more + + align:start position:0% +oh okay so the answer is everybody more + + + align:start position:0% +oh okay so the answer is everybody more +or less I'm sure and don't worry if you + + align:start position:0% +or less I'm sure and don't worry if you + + + align:start position:0% +or less I'm sure and don't worry if you +said I'll give her a little bit of Med + + align:start position:0% +said I'll give her a little bit of Med + + + align:start position:0% +said I'll give her a little bit of Med +that's okay too but I won't bother + + align:start position:0% +that's okay too but I won't bother + + + align:start position:0% +that's okay too but I won't bother +asking about it + + align:start position:0% +asking about it + + + align:start position:0% +asking about it +um these really are all the same by the + + align:start position:0% +um these really are all the same by the + + + align:start position:0% +um these really are all the same by the +way there's no 50 50 split this is just + + align:start position:0% +way there's no 50 50 split this is just + + + align:start position:0% +way there's no 50 50 split this is just +straight up + + align:start position:0% +straight up + + + align:start position:0% +straight up +normal I'm not tricking it this time + + align:start position:0% +normal I'm not tricking it this time + + + align:start position:0% +normal I'm not tricking it this time +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +um + + align:start position:0% +um + + + align:start position:0% +um +and by contrast if we look at Sam Sam's + + align:start position:0% +and by contrast if we look at Sam Sam's + + + align:start position:0% +and by contrast if we look at Sam Sam's +depressed no particular reason just + + align:start position:0% +depressed no particular reason just + + + align:start position:0% +depressed no particular reason just +happens and he oscillates between + + align:start position:0% +happens and he oscillates between + + + align:start position:0% +happens and he oscillates between +mannequin and and uh and depressed + + align:start position:0% +mannequin and and uh and depressed + + + align:start position:0% +mannequin and and uh and depressed +States + + align:start position:0% +States + + + align:start position:0% +States +um how many people think + + align:start position:0% +um how many people think + + + align:start position:0% +um how many people think +um no treatment or you know or unlikely + + align:start position:0% +um no treatment or you know or unlikely + + + align:start position:0% +um no treatment or you know or unlikely +to medicate + + align:start position:0% +to medicate + + + align:start position:0% +to medicate +uh how many moderately like you know I + + align:start position:0% +uh how many moderately like you know I + + + align:start position:0% +uh how many moderately like you know I +mean somewhere in the four to seven + + align:start position:0% +mean somewhere in the four to seven + + + align:start position:0% +mean somewhere in the four to seven +Department well a few people in there + + align:start position:0% +Department well a few people in there + + + align:start position:0% +Department well a few people in there +and and and you have all embodied the uh + + align:start position:0% +and and and you have all embodied the uh + + + align:start position:0% +and and and you have all embodied the uh +the ethos of the yeah yeah okay good + + align:start position:0% +the ethos of the yeah yeah okay good + + + align:start position:0% +the ethos of the yeah yeah okay good +I mean I don't know if it's good or not + + align:start position:0% +I mean I don't know if it's good or not + + + align:start position:0% +I mean I don't know if it's good or not +but it's it's clearly it's it's clearly + + align:start position:0% +but it's it's clearly it's it's clearly + + + align:start position:0% +but it's it's clearly it's it's clearly +where where uh + + align:start position:0% +where where uh + + + align:start position:0% +where where uh +um + + align:start position:0% +um + + + align:start position:0% +um +Medical Science I suppose is these days + + align:start position:0% +Medical Science I suppose is these days + + + align:start position:0% +Medical Science I suppose is these days +which is that that he would be a + + align:start position:0% +which is that that he would be a + + + align:start position:0% +which is that that he would be a +candidate for an antidepressant in a way + + align:start position:0% +candidate for an antidepressant in a way + + + align:start position:0% +candidate for an antidepressant in a way +that that she wouldn't uh why not what's + + align:start position:0% +that that she wouldn't uh why not what's + + + align:start position:0% +that that she wouldn't uh why not what's +why wouldn't you give her a an + + align:start position:0% +why wouldn't you give her a an + + + align:start position:0% +why wouldn't you give her a an +antidepressant she's depressed + + align:start position:0% + + + + align:start position:0% + +professional + + align:start position:0% +professional + + + align:start position:0% +professional +[Music] + + align:start position:0% + + + + align:start position:0% + +ism + + align:start position:0% + + + + align:start position:0% + +um okay there's a couple of things that + + align:start position:0% +um okay there's a couple of things that + + + align:start position:0% +um okay there's a couple of things that +are worth picking up on here one one is + + align:start position:0% +are worth picking up on here one one is + + + align:start position:0% +are worth picking up on here one one is +that I + + align:start position:0% +that I + + + align:start position:0% +that I +mentioned last time that the exact + + align:start position:0% +mentioned last time that the exact + + + align:start position:0% +mentioned last time that the exact +mapping between cause and treatment + + align:start position:0% +mapping between cause and treatment + + + align:start position:0% +mapping between cause and treatment +um + + align:start position:0% +um + + + align:start position:0% +um +shouldn't be seen as one to one so even + + align:start position:0% +shouldn't be seen as one to one so even + + + align:start position:0% +shouldn't be seen as one to one so even +if we take uh even if we take as uh + + align:start position:0% +if we take uh even if we take as uh + + + align:start position:0% +if we take uh even if we take as uh +correct for present purposes that uh + + align:start position:0% +correct for present purposes that uh + + + align:start position:0% +correct for present purposes that uh +that that Sam's got something + + align:start position:0% +that that Sam's got something + + + align:start position:0% +that that Sam's got something +biochemical wrong with him it wouldn't + + align:start position:0% +biochemical wrong with him it wouldn't + + + align:start position:0% +biochemical wrong with him it wouldn't +necessarily be the case that the only + + align:start position:0% +necessarily be the case that the only + + + align:start position:0% +necessarily be the case that the only +way to deal with this would be by uh by + + align:start position:0% +way to deal with this would be by uh by + + + align:start position:0% +way to deal with this would be by uh by +a biochemical kind of treatment there + + align:start position:0% +a biochemical kind of treatment there + + + align:start position:0% +a biochemical kind of treatment there +isn't that necessary one-to-one mapping + + align:start position:0% +isn't that necessary one-to-one mapping + + + align:start position:0% +isn't that necessary one-to-one mapping +but it's not an unreasonable + + align:start position:0% +but it's not an unreasonable + + + align:start position:0% +but it's not an unreasonable +um it's not an unreasonable thought and + + align:start position:0% +um it's not an unreasonable thought and + + + align:start position:0% +um it's not an unreasonable thought and +the other part of that thought was + + align:start position:0% +the other part of that thought was + + + align:start position:0% +the other part of that thought was +um you know she's depressed for a reason + + align:start position:0% +um you know she's depressed for a reason + + + align:start position:0% +um you know she's depressed for a reason +and and we don't want to + + align:start position:0% +and and we don't want to + + + align:start position:0% +and and we don't want to +Shield her + + align:start position:0% +Shield her + + + align:start position:0% +Shield her +necessarily from that depression though + + align:start position:0% +necessarily from that depression though + + + align:start position:0% +necessarily from that depression though +this gets raised as an issue too now + + align:start position:0% +this gets raised as an issue too now + + + align:start position:0% +this gets raised as an issue too now +um there I I talked last time about + + align:start position:0% +um there I I talked last time about + + + align:start position:0% +um there I I talked last time about +treatments for post-traumatic stress + + align:start position:0% +treatments for post-traumatic stress + + + align:start position:0% +treatments for post-traumatic stress +disorder + + align:start position:0% +disorder + + + align:start position:0% +disorder +um one of the uh Notions is that you + + align:start position:0% +um one of the uh Notions is that you + + + align:start position:0% +um one of the uh Notions is that you +could give people medications that would + + align:start position:0% +could give people medications that would + + + align:start position:0% +could give people medications that would +in a sense prevent them from feeling as + + align:start position:0% +in a sense prevent them from feeling as + + + align:start position:0% +in a sense prevent them from feeling as +bad about something horrible + + align:start position:0% +bad about something horrible + + + align:start position:0% +bad about something horrible +as + + align:start position:0% +as + + + align:start position:0% +as +um + + align:start position:0% +um + + + align:start position:0% +um +as they normally would I mean this is a + + align:start position:0% +as they normally would I mean this is a + + + align:start position:0% +as they normally would I mean this is a +real something horrible now you + + align:start position:0% +real something horrible now you + + + align:start position:0% +real something horrible now you +understand but we're gonna get you so + + align:start position:0% +understand but we're gonna get you so + + + align:start position:0% +understand but we're gonna get you so +you you've some audibles happen we're + + align:start position:0% +you you've some audibles happen we're + + + align:start position:0% +you you've some audibles happen we're +going to give you a pill that is going + + align:start position:0% +going to give you a pill that is going + + + align:start position:0% +going to give you a pill that is going +to + + align:start position:0% +to + + + align:start position:0% +to +um decrease we hope the chance of you + + align:start position:0% +um decrease we hope the chance of you + + + align:start position:0% +um decrease we hope the chance of you +having a post-traumatic stress disorder + + align:start position:0% +having a post-traumatic stress disorder + + + align:start position:0% +having a post-traumatic stress disorder +but it's going to do that by blunting + + align:start position:0% +but it's going to do that by blunting + + + align:start position:0% +but it's going to do that by blunting +your emotional response and your memory + + align:start position:0% +your emotional response and your memory + + + align:start position:0% +your emotional response and your memory +for that event + + align:start position:0% +for that event + + + align:start position:0% +for that event +is that is that something that uh um + + align:start position:0% +is that is that something that uh um + + + align:start position:0% +is that is that something that uh um +that we want to get into now uh Sam Sam + + align:start position:0% +that we want to get into now uh Sam Sam + + + align:start position:0% +that we want to get into now uh Sam Sam +I described as + + align:start position:0% +I described as + + + align:start position:0% +I described as +um having this if this if this is now + + align:start position:0% +um having this if this if this is now + + + align:start position:0% +um having this if this if this is now +um oh I suppose mood + + align:start position:0% +um oh I suppose mood + + + align:start position:0% +um oh I suppose mood +Sam I described as having one of these + + align:start position:0% +Sam I described as having one of these + + + align:start position:0% +Sam I described as having one of these +oscillatory or bipolar conditions where + + align:start position:0% +oscillatory or bipolar conditions where + + + align:start position:0% +oscillatory or bipolar conditions where +he bounces back and forth between oh + + align:start position:0% +he bounces back and forth between oh + + + align:start position:0% +he bounces back and forth between oh +let's see which end is this this can be + + align:start position:0% +let's see which end is this this can be + + + align:start position:0% +let's see which end is this this can be +the manic end + + align:start position:0% + + + + align:start position:0% + +and the uh depressed end + + align:start position:0% +and the uh depressed end + + + align:start position:0% +and the uh depressed end +um + + align:start position:0% +um + + + align:start position:0% +um +the um + + align:start position:0% + + + + align:start position:0% + +you sometimes think that it might kind + + align:start position:0% +you sometimes think that it might kind + + + align:start position:0% +you sometimes think that it might kind +of be worth it right because you have to + + align:start position:0% +of be worth it right because you have to + + + align:start position:0% +of be worth it right because you have to +put up with the depression but but but + + align:start position:0% +put up with the depression but but but + + + align:start position:0% +put up with the depression but but but +the the manic energy thing would be good + + align:start position:0% +the the manic energy thing would be good + + + align:start position:0% +the the manic energy thing would be good +well the the manic energy thing is kind + + align:start position:0% +well the the manic energy thing is kind + + + align:start position:0% +well the the manic energy thing is kind +of good here maybe you know you get all + + align:start position:0% +of good here maybe you know you get all + + + align:start position:0% +of good here maybe you know you get all +your problem sets done in in 10 minutes + + align:start position:0% +your problem sets done in in 10 minutes + + + align:start position:0% +your problem sets done in in 10 minutes +or something + + align:start position:0% +or something + + + align:start position:0% +or something +um and but by the time + + align:start position:0% + + + + align:start position:0% + +you are just + + align:start position:0% +you are just + + + align:start position:0% +you are just +Al if you like or just as crazy if we + + align:start position:0% +Al if you like or just as crazy if we + + + align:start position:0% +Al if you like or just as crazy if we +want to be colloquial about this out + + align:start position:0% +want to be colloquial about this out + + + align:start position:0% +want to be colloquial about this out +here as you are + + align:start position:0% +here as you are + + + align:start position:0% +here as you are +um down here + + align:start position:0% +um down here + + + align:start position:0% +um down here +and you can be pretty hard on your + + align:start position:0% +and you can be pretty hard on your + + + align:start position:0% +and you can be pretty hard on your +friends and neighbors + + align:start position:0% +friends and neighbors + + + align:start position:0% +friends and neighbors +um and yourself in fact if you you I + + align:start position:0% +um and yourself in fact if you you I + + + align:start position:0% +um and yourself in fact if you you I +don't need I'm necessary MIT right I + + align:start position:0% +don't need I'm necessary MIT right I + + + align:start position:0% +don't need I'm necessary MIT right I +don't need to sleep anymore I can talk + + align:start position:0% +don't need to sleep anymore I can talk + + + align:start position:0% +don't need to sleep anymore I can talk +all night + + align:start position:0% +all night + + + align:start position:0% +all night +you don't want to listen to me well I'll + + align:start position:0% +you don't want to listen to me well I'll + + + align:start position:0% +you don't want to listen to me well I'll +talk anyway + + align:start position:0% +talk anyway + + + align:start position:0% +talk anyway +um and and or I remember reading a a + + align:start position:0% +um and and or I remember reading a a + + + align:start position:0% +um and and or I remember reading a a +memoir by the uh the child of a manic + + align:start position:0% +memoir by the uh the child of a manic + + + align:start position:0% +memoir by the uh the child of a manic +depressive mother + + align:start position:0% +depressive mother + + + align:start position:0% +depressive mother +um who is I recall comes home the child + + align:start position:0% +um who is I recall comes home the child + + + align:start position:0% +um who is I recall comes home the child +comes home from school one day discovers + + align:start position:0% +comes home from school one day discovers + + + align:start position:0% +comes home from school one day discovers +mom has decided we're gonna have a great + + align:start position:0% +mom has decided we're gonna have a great + + + align:start position:0% +mom has decided we're gonna have a great +old-fashioned Christmas this year so she + + align:start position:0% +old-fashioned Christmas this year so she + + + align:start position:0% +old-fashioned Christmas this year so she +went out and bought like 35 Christmas + + align:start position:0% +went out and bought like 35 Christmas + + + align:start position:0% +went out and bought like 35 Christmas +trees and and you walk into the living + + align:start position:0% +trees and and you walk into the living + + + align:start position:0% +trees and and you walk into the living +room and it's just you know forest in + + align:start position:0% +room and it's just you know forest in + + + align:start position:0% +room and it's just you know forest in +there she's stuffed the Christmas trees + + align:start position:0% +there she's stuffed the Christmas trees + + + align:start position:0% +there she's stuffed the Christmas trees +all over them yeah and and you know this + + align:start position:0% +all over them yeah and and you know this + + + align:start position:0% +all over them yeah and and you know this +is I'm sorry I'm glad you're feeling + + align:start position:0% +is I'm sorry I'm glad you're feeling + + + align:start position:0% +is I'm sorry I'm glad you're feeling +really up but this is nuts too + + align:start position:0% +really up but this is nuts too + + + align:start position:0% +really up but this is nuts too +um it's not it it's not working + + align:start position:0% +um it's not it it's not working + + + align:start position:0% +um it's not it it's not working +um + + align:start position:0% +um + + + align:start position:0% +um +it is + + align:start position:0% +it is + + + align:start position:0% +it is +um + + align:start position:0% +um + + + align:start position:0% +um +it's an interesting observation there + + align:start position:0% +it's an interesting observation there + + + align:start position:0% +it's an interesting observation there +are interesting data suggesting + + align:start position:0% +are interesting data suggesting + + + align:start position:0% +are interesting data suggesting +um that this sort of bipolar disorder + + align:start position:0% +um that this sort of bipolar disorder + + + align:start position:0% +um that this sort of bipolar disorder +this oscillation between deep depression + + align:start position:0% +this oscillation between deep depression + + + align:start position:0% +this oscillation between deep depression +and and this wild Mania + + align:start position:0% +and and this wild Mania + + + align:start position:0% +and and this wild Mania +um that that's over represented in in at + + align:start position:0% +um that that's over represented in in at + + + align:start position:0% +um that that's over represented in in at +least some creative populations the uh + + align:start position:0% +least some creative populations the uh + + + align:start position:0% +least some creative populations the uh +the notable one is is poets + + align:start position:0% +the notable one is is poets + + + align:start position:0% +the notable one is is poets +um it's notable because a woman named + + align:start position:0% +um it's notable because a woman named + + + align:start position:0% +um it's notable because a woman named +what is her full name well anyway + + align:start position:0% +what is her full name well anyway + + + align:start position:0% +what is her full name well anyway +Jameson is her last name + + align:start position:0% +Jameson is her last name + + + align:start position:0% +Jameson is her last name +um + + align:start position:0% +um + + + align:start position:0% +um +Jane + + align:start position:0% +Jane + + + align:start position:0% +Jane +I think it's spelled like this anyway + + align:start position:0% +I think it's spelled like this anyway + + + align:start position:0% +I think it's spelled like this anyway +she wrote a book called Touched By Fire + + align:start position:0% +she wrote a book called Touched By Fire + + + align:start position:0% +she wrote a book called Touched By Fire +where what she did was she went and + + align:start position:0% +where what she did was she went and + + + align:start position:0% +where what she did was she went and +looked at the biographies of in + + align:start position:0% +looked at the biographies of in + + + align:start position:0% +looked at the biographies of in +particular sort of the the the the Run + + align:start position:0% +particular sort of the the the the Run + + + align:start position:0% +particular sort of the the the the Run +of famous English poets and over and + + align:start position:0% +of famous English poets and over and + + + align:start position:0% +of famous English poets and over and +over in their biographies you get these + + align:start position:0% +over in their biographies you get these + + + align:start position:0% +over in their biographies you get these +descriptions that you know they didn't + + align:start position:0% +descriptions that you know they didn't + + + align:start position:0% +descriptions that you know they didn't +have the diagnosis in in 18th century + + align:start position:0% +have the diagnosis in in 18th century + + + align:start position:0% +have the diagnosis in in 18th century +England but it sure sounds like a manic + + align:start position:0% +England but it sure sounds like a manic + + + align:start position:0% +England but it sure sounds like a manic +depressive disorder you know Shelly or + + align:start position:0% +depressive disorder you know Shelly or + + + align:start position:0% +depressive disorder you know Shelly or +keeps or somebody writes eight million + + align:start position:0% +keeps or somebody writes eight million + + + align:start position:0% +keeps or somebody writes eight million +poems and and and then lies in bed for a + + align:start position:0% +poems and and and then lies in bed for a + + + align:start position:0% +poems and and and then lies in bed for a +month + + align:start position:0% +month + + + align:start position:0% +month +um + + align:start position:0% +um + + + align:start position:0% +um +it's that that sort of thing now + + align:start position:0% +it's that that sort of thing now + + + align:start position:0% +it's that that sort of thing now +um great you know I can be a famous poet + + align:start position:0% +um great you know I can be a famous poet + + + align:start position:0% +um great you know I can be a famous poet +all I have to do is put up with this the + + align:start position:0% +all I have to do is put up with this the + + + align:start position:0% +all I have to do is put up with this the +problem well there's a number of + + align:start position:0% +problem well there's a number of + + + align:start position:0% +problem well there's a number of +problems with this first of all you + + align:start position:0% +problems with this first of all you + + + align:start position:0% +problems with this first of all you +become a little intolerable to your + + align:start position:0% +become a little intolerable to your + + + align:start position:0% +become a little intolerable to your +um immediate surroundings + + align:start position:0% +um immediate surroundings + + + align:start position:0% +um immediate surroundings +um the other thing is that a a very + + align:start position:0% +um the other thing is that a a very + + + align:start position:0% +um the other thing is that a a very +serious consequence of deep depression + + align:start position:0% +serious consequence of deep depression + + + align:start position:0% +serious consequence of deep depression +um is the threat of suicide + + align:start position:0% +um is the threat of suicide + + + align:start position:0% +um is the threat of suicide +um interestingly + + align:start position:0% +um interestingly + + + align:start position:0% +um interestingly +you would think you would think that + + align:start position:0% +you would think you would think that + + + align:start position:0% +you would think you would think that +this was a continuum thing right that + + align:start position:0% +this was a continuum thing right that + + + align:start position:0% +this was a continuum thing right that +you go way way down here and if you get + + align:start position:0% +you go way way down here and if you get + + + align:start position:0% +you go way way down here and if you get +this far down into depression + + align:start position:0% +this far down into depression + + + align:start position:0% +this far down into depression +um that's when people commit suicide + + align:start position:0% +um that's when people commit suicide + + + align:start position:0% +um that's when people commit suicide +turns out not to be the case when people + + align:start position:0% +turns out not to be the case when people + + + align:start position:0% +turns out not to be the case when people +describe their really deep view there's + + align:start position:0% +describe their really deep view there's + + + align:start position:0% +describe their really deep view there's +a huge genre here it's a very popular + + align:start position:0% +a huge genre here it's a very popular + + + align:start position:0% +a huge genre here it's a very popular +genre at the moment if you're if you're + + align:start position:0% +genre at the moment if you're if you're + + + align:start position:0% +genre at the moment if you're if you're +into depression + + align:start position:0% +into depression + + + align:start position:0% +into depression +um you can you're you're you know + + align:start position:0% +um you can you're you're you know + + + align:start position:0% +um you can you're you're you know +Christmas reading list can be all set + + align:start position:0% +Christmas reading list can be all set + + + align:start position:0% +Christmas reading list can be all set +out because there's all sorts of people + + align:start position:0% +out because there's all sorts of people + + + align:start position:0% +out because there's all sorts of people +who are happy to describe happy to + + align:start position:0% +who are happy to describe happy to + + + align:start position:0% +who are happy to describe happy to +describe the depression anyway + + align:start position:0% +describe the depression anyway + + + align:start position:0% +describe the depression anyway +more than willing to describe their + + align:start position:0% +more than willing to describe their + + + align:start position:0% +more than willing to describe their +depression in uh in volumes thin or + + align:start position:0% +depression in uh in volumes thin or + + + align:start position:0% +depression in uh in volumes thin or +thick Jameson actually has a volume of + + align:start position:0% +thick Jameson actually has a volume of + + + align:start position:0% +thick Jameson actually has a volume of +her she got interested in this because + + align:start position:0% +her she got interested in this because + + + align:start position:0% +her she got interested in this because +she was a manic depressive + + align:start position:0% +she was a manic depressive + + + align:start position:0% +she was a manic depressive +um and and trained in Psychiatry so + + align:start position:0% +um and and trained in Psychiatry so + + + align:start position:0% +um and and trained in Psychiatry so +she's coming at it from every which way + + align:start position:0% +she's coming at it from every which way + + + align:start position:0% +she's coming at it from every which way +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +um she has a memoir I don't remember the + + align:start position:0% +um she has a memoir I don't remember the + + + align:start position:0% +um she has a memoir I don't remember the +title of it but uh about her own + + align:start position:0% +title of it but uh about her own + + + align:start position:0% +title of it but uh about her own +um + + align:start position:0% +um + + + align:start position:0% +um +and depression that's actually nice and + + align:start position:0% +and depression that's actually nice and + + + align:start position:0% +and depression that's actually nice and +slim it's not a bad read + + align:start position:0% +slim it's not a bad read + + + align:start position:0% +slim it's not a bad read +um but what what all these what the + + align:start position:0% +um but what what all these what the + + + align:start position:0% +um but what what all these what the +descriptions sound like is that when + + align:start position:0% +descriptions sound like is that when + + + align:start position:0% +descriptions sound like is that when +you're really really deeply depressed + + align:start position:0% +you're really really deeply depressed + + + align:start position:0% +you're really really deeply depressed +you just don't do anything even though + + align:start position:0% +you just don't do anything even though + + + align:start position:0% +you just don't do anything even though +you might in some sense want to be dead + + align:start position:0% +you might in some sense want to be dead + + + align:start position:0% +you might in some sense want to be dead +but that's just too much effort to do + + align:start position:0% +but that's just too much effort to do + + + align:start position:0% +but that's just too much effort to do +anything about that the the the danger + + align:start position:0% +anything about that the the the danger + + + align:start position:0% +anything about that the the the danger +for suicide in in um in bipolar + + align:start position:0% +for suicide in in um in bipolar + + + align:start position:0% +for suicide in in um in bipolar +disorders turns out to be well let's get + + align:start position:0% +disorders turns out to be well let's get + + + align:start position:0% +disorders turns out to be well let's get +rid of this turns out to be when you're + + align:start position:0% +rid of this turns out to be when you're + + + align:start position:0% +rid of this turns out to be when you're +on your way back out + + align:start position:0% +on your way back out + + + align:start position:0% +on your way back out +um still depressed + + align:start position:0% +um still depressed + + + align:start position:0% +um still depressed +but but um and you know maybe but but + + align:start position:0% +but but um and you know maybe but but + + + align:start position:0% +but but um and you know maybe but but +now you're activated enough that you can + + align:start position:0% +now you're activated enough that you can + + + align:start position:0% +now you're activated enough that you can +do stuff and you but you're not + + align:start position:0% +do stuff and you but you're not + + + align:start position:0% +do stuff and you but you're not +convinced you're ever really going to + + align:start position:0% +convinced you're ever really going to + + + align:start position:0% +convinced you're ever really going to +get better I mean look most of us have + + align:start position:0% +get better I mean look most of us have + + + align:start position:0% +get better I mean look most of us have +not been really clinically depressed but + + align:start position:0% +not been really clinically depressed but + + + align:start position:0% +not been really clinically depressed but +many of us can tap into this uh in in + + align:start position:0% +many of us can tap into this uh in in + + + align:start position:0% +many of us can tap into this uh in in +into this aspect in the sense of have + + align:start position:0% +into this aspect in the sense of have + + + align:start position:0% +into this aspect in the sense of have +you had like + + align:start position:0% +you had like + + + align:start position:0% +you had like +the flu or some you know relatively + + align:start position:0% +the flu or some you know relatively + + + align:start position:0% +the flu or some you know relatively +disgusting disorder of some variety + + align:start position:0% +disgusting disorder of some variety + + + align:start position:0% +disgusting disorder of some variety +where you're sitting there thinking + + align:start position:0% +where you're sitting there thinking + + + align:start position:0% +where you're sitting there thinking +I know rationally that I'm gonna get + + align:start position:0% +I know rationally that I'm gonna get + + + align:start position:0% +I know rationally that I'm gonna get +better but am I Really Gonna Get Better + + align:start position:0% +better but am I Really Gonna Get Better + + + align:start position:0% +better but am I Really Gonna Get Better +or am I just gonna be barfing forever + + align:start position:0% +or am I just gonna be barfing forever + + + align:start position:0% +or am I just gonna be barfing forever +you know and and I think that so coming + + align:start position:0% +you know and and I think that so coming + + + align:start position:0% +you know and and I think that so coming +on you're coming on your way out and and + + align:start position:0% +on you're coming on your way out and and + + + align:start position:0% +on you're coming on your way out and and +that's where the suicide risk is high + + align:start position:0% +that's where the suicide risk is high + + + align:start position:0% +that's where the suicide risk is high +now + + align:start position:0% +now + + + align:start position:0% +now +um that phenomenon + + align:start position:0% +um that phenomenon + + + align:start position:0% +um that phenomenon +may be related to something that that + + align:start position:0% +may be related to something that that + + + align:start position:0% +may be related to something that that +hit the news a lot + + align:start position:0% +hit the news a lot + + + align:start position:0% +hit the news a lot +um + + align:start position:0% +um + + + align:start position:0% +um +this year which was + + align:start position:0% +this year which was + + + align:start position:0% +this year which was +um concerns about giving antidepressants + + align:start position:0% +um concerns about giving antidepressants + + + align:start position:0% +um concerns about giving antidepressants +to uh children and adolescents because + + align:start position:0% +to uh children and adolescents because + + + align:start position:0% +to uh children and adolescents because +there are data out there that say that + + align:start position:0% +there are data out there that say that + + + align:start position:0% +there are data out there that say that +the suicide risk in um depressed + + align:start position:0% +the suicide risk in um depressed + + + align:start position:0% +the suicide risk in um depressed +adolescents taking antidepressants is + + align:start position:0% +adolescents taking antidepressants is + + + align:start position:0% +adolescents taking antidepressants is +elevated exactly what you don't want to + + align:start position:0% +elevated exactly what you don't want to + + + align:start position:0% +elevated exactly what you don't want to +have happen right what you really want + + align:start position:0% +have happen right what you really want + + + align:start position:0% +have happen right what you really want +to not have happen is people commit + + align:start position:0% +to not have happen is people commit + + + align:start position:0% +to not have happen is people commit +suicide when they're depressed what is + + align:start position:0% +suicide when they're depressed what is + + + align:start position:0% +suicide when they're depressed what is +the cause of this well we don't actually + + align:start position:0% +the cause of this well we don't actually + + + align:start position:0% +the cause of this well we don't actually +know I don't think at least I haven't + + align:start position:0% +know I don't think at least I haven't + + + align:start position:0% +know I don't think at least I haven't +seen anything definitive but there are a + + align:start position:0% +seen anything definitive but there are a + + + align:start position:0% +seen anything definitive but there are a +number of one theory is that + + align:start position:0% +number of one theory is that + + + align:start position:0% +number of one theory is that +antidepressants work differently in + + align:start position:0% +antidepressants work differently in + + + align:start position:0% +antidepressants work differently in +young brains than in older brains that's + + align:start position:0% +young brains than in older brains that's + + + align:start position:0% +young brains than in older brains that's +one possibility but the other + + align:start position:0% +one possibility but the other + + + align:start position:0% +one possibility but the other +possibility is that what the + + align:start position:0% +possibility is that what the + + + align:start position:0% +possibility is that what the +antidepressant did was it sort of moved + + align:start position:0% +antidepressant did was it sort of moved + + + align:start position:0% +antidepressant did was it sort of moved +the uh the patient along to a point + + align:start position:0% +the uh the patient along to a point + + + align:start position:0% +the uh the patient along to a point +where they weren't so paralyzed by the + + align:start position:0% +where they weren't so paralyzed by the + + + align:start position:0% +where they weren't so paralyzed by the +depression that suicide became an option + + align:start position:0% +depression that suicide became an option + + + align:start position:0% +depression that suicide became an option +it sounds weird and disturbing but that + + align:start position:0% +it sounds weird and disturbing but that + + + align:start position:0% +it sounds weird and disturbing but that +is one possibility for where this + + align:start position:0% +is one possibility for where this + + + align:start position:0% +is one possibility for where this +elevated rate of of suicide in an + + align:start position:0% +elevated rate of of suicide in an + + + align:start position:0% +elevated rate of of suicide in an +antidepressant treated young young + + align:start position:0% +antidepressant treated young young + + + align:start position:0% +antidepressant treated young young +patients + + align:start position:0% +patients + + + align:start position:0% +patients +came from + + align:start position:0% +came from + + + align:start position:0% +came from +the um let's see what else do I want to + + align:start position:0% +the um let's see what else do I want to + + + align:start position:0% +the um let's see what else do I want to +say about Sam and and uh + + align:start position:0% + + + + align:start position:0% + +and and Emma here oh well we got it we + + align:start position:0% +and and Emma here oh well we got it we + + + align:start position:0% +and and Emma here oh well we got it we +got it oh Emma Emma's the one on the + + align:start position:0% +got it oh Emma Emma's the one on the + + + align:start position:0% +got it oh Emma Emma's the one on the +back + + align:start position:0% +back + + + align:start position:0% +back +all right so how about Emma we need to + + align:start position:0% +all right so how about Emma we need to + + + align:start position:0% +all right so how about Emma we need to +collect some data on uh + + align:start position:0% +collect some data on uh + + + align:start position:0% +collect some data on uh +on Emma Emma did I describe Emma as + + align:start position:0% +on Emma Emma did I describe Emma as + + + align:start position:0% +on Emma Emma did I describe Emma as +dysphoric yes Emma is a dysphoric that's + + align:start position:0% +dysphoric yes Emma is a dysphoric that's + + + align:start position:0% +dysphoric yes Emma is a dysphoric that's +the opposite of euphoric so it's not + + align:start position:0% +the opposite of euphoric so it's not + + + align:start position:0% +the opposite of euphoric so it's not +depressed it'd be sort of lying around + + align:start position:0% +depressed it'd be sort of lying around + + + align:start position:0% +depressed it'd be sort of lying around +here somewhere just kind of flat + + align:start position:0% +here somewhere just kind of flat + + + align:start position:0% +here somewhere just kind of flat +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so + + align:start position:0% +so + + + align:start position:0% +so +um how many people voted that we uh + + align:start position:0% +um how many people voted that we uh + + + align:start position:0% +um how many people voted that we uh +we'll we'll leave her be + + align:start position:0% +we'll we'll leave her be + + + align:start position:0% +we'll we'll leave her be +okay how many people voted where Maybe + + align:start position:0% +okay how many people voted where Maybe + + + align:start position:0% +okay how many people voted where Maybe +and how many uh people voted sure + + align:start position:0% +and how many uh people voted sure + + + align:start position:0% +and how many uh people voted sure +so well okay we got we got a normal + + align:start position:0% +so well okay we got we got a normal + + + align:start position:0% +so well okay we got we got a normal +curve out of that + + align:start position:0% +curve out of that + + + align:start position:0% +curve out of that +um well I could have gotten it's look + + align:start position:0% +um well I could have gotten it's look + + + align:start position:0% +um well I could have gotten it's look +looked sort of like this to me + + align:start position:0% + + + + align:start position:0% + +so people are sort of unsure about oops + + align:start position:0% +so people are sort of unsure about oops + + + align:start position:0% +so people are sort of unsure about oops +well I guess it's going over there now + + align:start position:0% +well I guess it's going over there now + + + align:start position:0% +well I guess it's going over there now +people are sort of unsure about it um + + align:start position:0% +people are sort of unsure about it um + + + align:start position:0% +people are sort of unsure about it um +what so what are the issues here + + align:start position:0% +what so what are the issues here + + + align:start position:0% +what so what are the issues here +why wouldn't you give it to her + + align:start position:0% +why wouldn't you give it to her + + + align:start position:0% +why wouldn't you give it to her +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +oh yes yes well that's a separate issue + + align:start position:0% +oh yes yes well that's a separate issue + + + align:start position:0% +oh yes yes well that's a separate issue +did I did that did I say anything about + + align:start position:0% +did I did that did I say anything about + + + align:start position:0% +did I did that did I say anything about +it + + align:start position:0% +it + + + align:start position:0% +it +no no no this is just well actually + + align:start position:0% +no no no this is just well actually + + + align:start position:0% +no no no this is just well actually +we'll come back to that that's an + + align:start position:0% +we'll come back to that that's an + + + align:start position:0% +we'll come back to that that's an +interesting that's an interesting + + align:start position:0% +interesting that's an interesting + + + align:start position:0% +interesting that's an interesting +problem but yes I was not suggesting + + align:start position:0% +problem but yes I was not suggesting + + + align:start position:0% +problem but yes I was not suggesting +that we jam it down her throat + + align:start position:0% +that we jam it down her throat + + + align:start position:0% +that we jam it down her throat +um which is by the way not the problem + + align:start position:0% +um which is by the way not the problem + + + align:start position:0% +um which is by the way not the problem +with Prozac the problem oh uh + + align:start position:0% +with Prozac the problem oh uh + + + align:start position:0% +with Prozac the problem oh uh +let's imagine that the antidepressant is + + align:start position:0% +let's imagine that the antidepressant is + + + align:start position:0% +let's imagine that the antidepressant is +Prozac here because that got uh or one + + align:start position:0% +Prozac here because that got uh or one + + + align:start position:0% +Prozac here because that got uh or one +of its one of its newer friends + + align:start position:0% +of its one of its newer friends + + + align:start position:0% +of its one of its newer friends +um Prozac got a lot of uh uh that gets a + + align:start position:0% +um Prozac got a lot of uh uh that gets a + + + align:start position:0% +um Prozac got a lot of uh uh that gets a +lot of play in the in the in the public + + align:start position:0% +lot of play in the in the in the public + + + align:start position:0% +lot of play in the in the in the public +here + + align:start position:0% +here + + + align:start position:0% +here +um whoops well I'll put a p there now + + align:start position:0% + + + + align:start position:0% + +uh-oh C or k + + align:start position:0% +uh-oh C or k + + + align:start position:0% +uh-oh C or k +C yes thank you um okay Prozac is a uh + + align:start position:0% +C yes thank you um okay Prozac is a uh + + + align:start position:0% +C yes thank you um okay Prozac is a uh +Sarah + + align:start position:0% +Sarah + + + align:start position:0% +Sarah +tone in that's a neurotransmitter + + align:start position:0% +tone in that's a neurotransmitter + + + align:start position:0% +tone in that's a neurotransmitter +um + + align:start position:0% +um + + + align:start position:0% +um +selective thank you where was that + + align:start position:0% +selective thank you where was that + + + align:start position:0% +selective thank you where was that +coming oh it's a selective serotonin not + + align:start position:0% +coming oh it's a selective serotonin not + + + align:start position:0% +coming oh it's a selective serotonin not +certain serotonin selective it's SS all + + align:start position:0% +certain serotonin selective it's SS all + + + align:start position:0% +certain serotonin selective it's SS all +right + + align:start position:0% +right + + + align:start position:0% +right +all right it's a serotonin selective + + align:start position:0% +all right it's a serotonin selective + + + align:start position:0% +all right it's a serotonin selective +reavers + + align:start position:0% + + + + align:start position:0% + +uh uptake reuptake can I do re-uptake + + align:start position:0% +uh uptake reuptake can I do re-uptake + + + align:start position:0% +uh uptake reuptake can I do re-uptake +yeah okay re-uptake + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% +in + + + align:start position:0% +in +Hibbett R + + align:start position:0% +Hibbett R + + + align:start position:0% +Hibbett R +um or an SSRI which makes it + + align:start position:0% +um or an SSRI which makes it + + + align:start position:0% +um or an SSRI which makes it +understandable how I would have thought + + align:start position:0% +understandable how I would have thought + + + align:start position:0% +understandable how I would have thought +it might have been an SSRI rather than + + align:start position:0% +it might have been an SSRI rather than + + + align:start position:0% +it might have been an SSRI rather than +an SSRI + + align:start position:0% +an SSRI + + + align:start position:0% +an SSRI +um but let me let me uh explain what + + align:start position:0% +um but let me let me uh explain what + + + align:start position:0% +um but let me let me uh explain what +this is doing actually + + align:start position:0% +this is doing actually + + + align:start position:0% +this is doing actually +um + + align:start position:0% +um + + + align:start position:0% +um +so remember that in in schizophrenia the + + align:start position:0% +so remember that in in schizophrenia the + + + align:start position:0% +so remember that in in schizophrenia the +first big + + align:start position:0% +first big + + + align:start position:0% +first big +psychopharmacological breakthrough was + + align:start position:0% +psychopharmacological breakthrough was + + + align:start position:0% +psychopharmacological breakthrough was +the discovery there's too much dopamine + + align:start position:0% +the discovery there's too much dopamine + + + align:start position:0% +the discovery there's too much dopamine +in bits of the brain if we block uh some + + align:start position:0% +in bits of the brain if we block uh some + + + align:start position:0% +in bits of the brain if we block uh some +dopamine receptors we reduce the um + + align:start position:0% +dopamine receptors we reduce the um + + + align:start position:0% +dopamine receptors we reduce the um +we reduce the symptoms in the case of uh + + align:start position:0% +we reduce the symptoms in the case of uh + + + align:start position:0% +we reduce the symptoms in the case of uh +at least some forms of depression the + + align:start position:0% +at least some forms of depression the + + + align:start position:0% +at least some forms of depression the +problem seems to be too little serotonin + + align:start position:0% +problem seems to be too little serotonin + + + align:start position:0% +problem seems to be too little serotonin +or a problem seems to be too little + + align:start position:0% +or a problem seems to be too little + + + align:start position:0% +or a problem seems to be too little +serotonin in some parts of the brain and + + align:start position:0% +serotonin in some parts of the brain and + + + align:start position:0% +serotonin in some parts of the brain and +so here's what you you got a synapse + + align:start position:0% +so here's what you you got a synapse + + + align:start position:0% +so here's what you you got a synapse +foreign + + align:start position:0% + + + + align:start position:0% + +ton is being released here and binding + + align:start position:0% +ton is being released here and binding + + + align:start position:0% +ton is being released here and binding +to the other side + + align:start position:0% + + + + align:start position:0% + +but now in order to have this uh synapse + + align:start position:0% +but now in order to have this uh synapse + + + align:start position:0% +but now in order to have this uh synapse +be reusable once you've released some + + align:start position:0% +be reusable once you've released some + + + align:start position:0% +be reusable once you've released some +some serotonin you got to get rid of it + + align:start position:0% +some serotonin you got to get rid of it + + + align:start position:0% +some serotonin you got to get rid of it +you got to get it out of the synapse so + + align:start position:0% +you got to get it out of the synapse so + + + align:start position:0% +you got to get it out of the synapse so +you can do it again and again and again + + align:start position:0% +you can do it again and again and again + + + align:start position:0% +you can do it again and again and again +one of the techniques is to take the + + align:start position:0% +one of the techniques is to take the + + + align:start position:0% +one of the techniques is to take the +molecules and suck them back into + + align:start position:0% +molecules and suck them back into + + + align:start position:0% +molecules and suck them back into +um the uh the originating + + align:start position:0% +um the uh the originating + + + align:start position:0% +um the uh the originating +neuron that's called reuptake now if you + + align:start position:0% +neuron that's called reuptake now if you + + + align:start position:0% +neuron that's called reuptake now if you +don't have enough serotonin here to do + + align:start position:0% +don't have enough serotonin here to do + + + align:start position:0% +don't have enough serotonin here to do +the job one thing to do is to slow down + + align:start position:0% +the job one thing to do is to slow down + + + align:start position:0% +the job one thing to do is to slow down +this reuptake so that the serotonin + + align:start position:0% +this reuptake so that the serotonin + + + align:start position:0% +this reuptake so that the serotonin +hangs around here longer and that way + + align:start position:0% +hangs around here longer and that way + + + align:start position:0% +hangs around here longer and that way +you get more bang for your molecular + + align:start position:0% +you get more bang for your molecular + + + align:start position:0% +you get more bang for your molecular +Buck + + align:start position:0% +Buck + + + align:start position:0% +Buck +um + + align:start position:0% +um + + + align:start position:0% +um +and and and so that that's that's what + + align:start position:0% +and and and so that that's that's what + + + align:start position:0% +and and and so that that's that's what +uh that's what Prozac is doing + + align:start position:0% +uh that's what Prozac is doing + + + align:start position:0% +uh that's what Prozac is doing +um the reason I put Emma on here is that + + align:start position:0% +um the reason I put Emma on here is that + + + align:start position:0% +um the reason I put Emma on here is that +uh Prozac seemed to do good things for + + align:start position:0% +uh Prozac seemed to do good things for + + + align:start position:0% +uh Prozac seemed to do good things for +uh dysphoric patients patients who did + + align:start position:0% +uh dysphoric patients patients who did + + + align:start position:0% +uh dysphoric patients patients who did +not meet a clinical Criterion for + + align:start position:0% +not meet a clinical Criterion for + + + align:start position:0% +not meet a clinical Criterion for +depression + + align:start position:0% +depression + + + align:start position:0% +depression +um but who found + + align:start position:0% + + + + align:start position:0% + +I think in part because uh the the drug + + align:start position:0% +I think in part because uh the the drug + + + align:start position:0% +I think in part because uh the the drug +manufacturer gave the + + align:start position:0% +manufacturer gave the + + + align:start position:0% +manufacturer gave the +the docks piles of free Prozac your + + align:start position:0% +the docks piles of free Prozac your + + + align:start position:0% +the docks piles of free Prozac your +patient comes through and says oh fuel + + align:start position:0% +patient comes through and says oh fuel + + + align:start position:0% +patient comes through and says oh fuel +kind of down + + align:start position:0% +kind of down + + + align:start position:0% +kind of down +so all right I try this this is new + + align:start position:0% +so all right I try this this is new + + + align:start position:0% +so all right I try this this is new +yeah all right hey I feel better + + align:start position:0% +yeah all right hey I feel better + + + align:start position:0% +yeah all right hey I feel better +I feel a bunch better I'm not clinically + + align:start position:0% +I feel a bunch better I'm not clinically + + + align:start position:0% +I feel a bunch better I'm not clinically +depressed but I really like this stuff + + align:start position:0% +depressed but I really like this stuff + + + align:start position:0% +depressed but I really like this stuff +um + + align:start position:0% +um + + + align:start position:0% +um +and + + align:start position:0% +and + + + align:start position:0% +and +not only that if I go off it I go back + + align:start position:0% +not only that if I go off it I go back + + + align:start position:0% +not only that if I go off it I go back +to my dysphoric State I go back to it's + + align:start position:0% +to my dysphoric State I go back to it's + + + align:start position:0% +to my dysphoric State I go back to it's +just the other side why the example says + + align:start position:0% +just the other side why the example says + + + align:start position:0% +just the other side why the example says +something to the effect of that's just + + align:start position:0% +something to the effect of that's just + + + align:start position:0% +something to the effect of that's just +the way she is if she goes back if she + + align:start position:0% +the way she is if she goes back if she + + + align:start position:0% +the way she is if she goes back if she +goes off Prozac + + align:start position:0% +goes off Prozac + + + align:start position:0% +goes off Prozac +uh there are lots of of reports in uh + + align:start position:0% +uh there are lots of of reports in uh + + + align:start position:0% +uh there are lots of of reports in uh +even in the popular literature of this + + align:start position:0% +even in the popular literature of this + + + align:start position:0% +even in the popular literature of this +of people who said you know if I'm off + + align:start position:0% +of people who said you know if I'm off + + + align:start position:0% +of people who said you know if I'm off +Prozac I'm just uh but if I'm on Prozac + + align:start position:0% +Prozac I'm just uh but if I'm on Prozac + + + align:start position:0% +Prozac I'm just uh but if I'm on Prozac +I I'm I'm just a better me + + align:start position:0% +I I'm I'm just a better me + + + align:start position:0% +I I'm I'm just a better me +well to give them the drug + + align:start position:0% +well to give them the drug + + + align:start position:0% +well to give them the drug +do you give them the drug do you allow + + align:start position:0% +do you give them the drug do you allow + + + align:start position:0% +do you give them the drug do you allow +them to continue taking the drug for the + + align:start position:0% +them to continue taking the drug for the + + + align:start position:0% +them to continue taking the drug for the +rest of their natural born days + + align:start position:0% +rest of their natural born days + + + align:start position:0% +rest of their natural born days +particularly since we have no idea since + + align:start position:0% +particularly since we have no idea since + + + align:start position:0% +particularly since we have no idea since +it's a new drug well now it's a couple + + align:start position:0% +it's a new drug well now it's a couple + + + align:start position:0% +it's a new drug well now it's a couple +over a decade old but you know we don't + + align:start position:0% +over a decade old but you know we don't + + + align:start position:0% +over a decade old but you know we don't +know what happens if you take this for + + align:start position:0% +know what happens if you take this for + + + align:start position:0% +know what happens if you take this for +20 30 40 years + + align:start position:0% +20 30 40 years + + + align:start position:0% +20 30 40 years +um who should pay for it + + align:start position:0% +um who should pay for it + + + align:start position:0% +um who should pay for it +you know if you think that this drug + + align:start position:0% +you know if you think that this drug + + + align:start position:0% +you know if you think that this drug +makes you feel better that's lovely + + align:start position:0% +makes you feel better that's lovely + + + align:start position:0% +makes you feel better that's lovely +should should your insurance company pay + + align:start position:0% +should should your insurance company pay + + + align:start position:0% +should should your insurance company pay +for it on a + + align:start position:0% +for it on a + + + align:start position:0% +for it on a +on a continuing basis + + align:start position:0% +on a continuing basis + + + align:start position:0% +on a continuing basis +so those those are the sort of those are + + align:start position:0% +so those those are the sort of those are + + + align:start position:0% +so those those are the sort of those are +the Emma issues here the issues about + + align:start position:0% +the Emma issues here the issues about + + + align:start position:0% +the Emma issues here the issues about +whether or not it's okay to + + align:start position:0% +whether or not it's okay to + + + align:start position:0% +whether or not it's okay to +um to to make somebody better than they + + align:start position:0% +um to to make somebody better than they + + + align:start position:0% +um to to make somebody better than they +in some sense better than they were + + align:start position:0% +in some sense better than they were + + + align:start position:0% +in some sense better than they were +um are you the same person + + align:start position:0% +um are you the same person + + + align:start position:0% +um are you the same person +is this you know is this the real Emma + + align:start position:0% +is this you know is this the real Emma + + + align:start position:0% +is this you know is this the real Emma +or is this some medicated Emma + + align:start position:0% +or is this some medicated Emma + + + align:start position:0% +or is this some medicated Emma +and + + align:start position:0% +and + + + align:start position:0% +and +um well all right now let's all right + + align:start position:0% +um well all right now let's all right + + + align:start position:0% +um well all right now let's all right +I'll loop back to the the comment about + + align:start position:0% +I'll loop back to the the comment about + + + align:start position:0% +I'll loop back to the the comment about +forcing them well you know what it works + + align:start position:0% +forcing them well you know what it works + + + align:start position:0% +forcing them well you know what it works +on kids too + + align:start position:0% +on kids too + + + align:start position:0% +on kids too +and + + align:start position:0% +and + + + align:start position:0% +and +um yeah you know that there's a a fairly + + align:start position:0% +um yeah you know that there's a a fairly + + + align:start position:0% +um yeah you know that there's a a fairly +substantial + + align:start position:0% +substantial + + + align:start position:0% +substantial +industry in in feeding uh + + align:start position:0% +industry in in feeding uh + + + align:start position:0% +industry in in feeding uh +um psychiatric drugs to to kids for + + align:start position:0% +um psychiatric drugs to to kids for + + + align:start position:0% +um psychiatric drugs to to kids for +various and Sundry problems + + align:start position:0% +various and Sundry problems + + + align:start position:0% +various and Sundry problems +um suppose what we know that shy what + + align:start position:0% +um suppose what we know that shy what + + + align:start position:0% +um suppose what we know that shy what +how did I describe Old Emma here + + align:start position:0% +how did I describe Old Emma here + + + align:start position:0% +how did I describe Old Emma here +is she signed withdrawn no that was + + align:start position:0% +is she signed withdrawn no that was + + + align:start position:0% +is she signed withdrawn no that was +what's his name collecting the underwear + + align:start position:0% +what's his name collecting the underwear + + + align:start position:0% +what's his name collecting the underwear +wasn't it + + align:start position:0% +wasn't it + + + align:start position:0% +wasn't it +oh well + + align:start position:0% +oh well + + + align:start position:0% +oh well +but we know + + align:start position:0% +but we know + + + align:start position:0% +but we know +that if we I could have described Emma + + align:start position:0% +that if we I could have described Emma + + + align:start position:0% +that if we I could have described Emma +as as shy and quiet we know that the kid + + align:start position:0% +as as shy and quiet we know that the kid + + + align:start position:0% +as as shy and quiet we know that the kid +who shy and quiet in + + align:start position:0% +who shy and quiet in + + + align:start position:0% +who shy and quiet in +first grade doesn't get the same amount + + align:start position:0% +first grade doesn't get the same amount + + + align:start position:0% +first grade doesn't get the same amount +of attention + + align:start position:0% +of attention + + + align:start position:0% +of attention +that the bouncy active kid go gets and + + align:start position:0% +that the bouncy active kid go gets and + + + align:start position:0% +that the bouncy active kid go gets and +in fact + + align:start position:0% +in fact + + + align:start position:0% +in fact +um + + align:start position:0% +um + + + align:start position:0% +um +there's some evidence that if you feed + + align:start position:0% +there's some evidence that if you feed + + + align:start position:0% +there's some evidence that if you feed +something like Prozac to this kid + + align:start position:0% +something like Prozac to this kid + + + align:start position:0% +something like Prozac to this kid +the kid will move from + + align:start position:0% +the kid will move from + + + align:start position:0% +the kid will move from +here in the well we're going to change + + align:start position:0% +here in the well we're going to change + + + align:start position:0% +here in the well we're going to change +the axis again you know I don't know + + align:start position:0% +the axis again you know I don't know + + + align:start position:0% +the axis again you know I don't know +what's the axis here bounciness + + align:start position:0% +what's the axis here bounciness + + + align:start position:0% +what's the axis here bounciness +technical term + + align:start position:0% +technical term + + + align:start position:0% +technical term +you know so the kid's going to move from + + align:start position:0% +you know so the kid's going to move from + + + align:start position:0% +you know so the kid's going to move from +being uh unbouncy to you know Tigger is + + align:start position:0% +being uh unbouncy to you know Tigger is + + + align:start position:0% +being uh unbouncy to you know Tigger is +up here somewhere I mean and and oh + + align:start position:0% +up here somewhere I mean and and oh + + + align:start position:0% +up here somewhere I mean and and oh +as well + + align:start position:0% +as well + + + align:start position:0% +as well +as are several couple of people out + + align:start position:0% +as are several couple of people out + + + align:start position:0% +as are several couple of people out +there halfway up there + + align:start position:0% +there halfway up there + + + align:start position:0% +there halfway up there +but it's yeah no this is so there's this + + align:start position:0% +but it's yeah no this is so there's this + + + align:start position:0% +but it's yeah no this is so there's this +Tigger I guess and uh + + align:start position:0% +Tigger I guess and uh + + + align:start position:0% +Tigger I guess and uh +um but you know I'm gonna move them up + + align:start position:0% +um but you know I'm gonna move them up + + + align:start position:0% +um but you know I'm gonna move them up +here let's say get them above average + + align:start position:0% +here let's say get them above average + + + align:start position:0% +here let's say get them above average +and the teachers are going to pay more + + align:start position:0% +and the teachers are going to pay more + + + align:start position:0% +and the teachers are going to pay more +attention to them is it okay to medicate + + align:start position:0% +attention to them is it okay to medicate + + + align:start position:0% +attention to them is it okay to medicate +your kid + + align:start position:0% + + + + align:start position:0% + +if it's all right man it's not okay to + + align:start position:0% +if it's all right man it's not okay to + + + align:start position:0% +if it's all right man it's not okay to +medicate your kid I'm not gonna medicate + + align:start position:0% +medicate your kid I'm not gonna medicate + + + align:start position:0% +medicate your kid I'm not gonna medicate +my kid + + align:start position:0% +my kid + + + align:start position:0% +my kid +the neighbors + + align:start position:0% +the neighbors + + + align:start position:0% +the neighbors +they're medicating their kids + + align:start position:0% +they're medicating their kids + + + align:start position:0% +they're medicating their kids +so what they've done my kid was right + + align:start position:0% +so what they've done my kid was right + + + align:start position:0% +so what they've done my kid was right +here he was like average right + + align:start position:0% +here he was like average right + + + align:start position:0% +here he was like average right +all right now with the neighbors and the + + align:start position:0% +all right now with the neighbors and the + + + align:start position:0% +all right now with the neighbors and the +the population as a whole is done is + + align:start position:0% +the population as a whole is done is + + + align:start position:0% +the population as a whole is done is +they move the whole distribution over + + align:start position:0% +they move the whole distribution over + + + align:start position:0% +they move the whole distribution over +because they you know they're they're + + align:start position:0% +because they you know they're they're + + + align:start position:0% +because they you know they're they're +all handing out Prozac in The Lunchbox + + align:start position:0% +all handing out Prozac in The Lunchbox + + + align:start position:0% +all handing out Prozac in The Lunchbox +now is it fair to my kid this is a + + align:start position:0% +now is it fair to my kid this is a + + + align:start position:0% +now is it fair to my kid this is a +hypothetical my kid this is not a real + + align:start position:0% +hypothetical my kid this is not a real + + + align:start position:0% +hypothetical my kid this is not a real +issue on my street in case you're + + align:start position:0% +issue on my street in case you're + + + align:start position:0% +issue on my street in case you're +wondering but is it fair to my kid to + + align:start position:0% +wondering but is it fair to my kid to + + + align:start position:0% +wondering but is it fair to my kid to +not medicate him + + align:start position:0% +not medicate him + + + align:start position:0% +not medicate him +right he's gonna fall behind + + align:start position:0% +right he's gonna fall behind + + + align:start position:0% +right he's gonna fall behind +Is this systematically different + + align:start position:0% +Is this systematically different + + + align:start position:0% +Is this systematically different +um you know is is this sort of morally + + align:start position:0% +um you know is is this sort of morally + + + align:start position:0% +um you know is is this sort of morally +or ethically different than the uh + + align:start position:0% +or ethically different than the uh + + + align:start position:0% +or ethically different than the uh +um the Kaplan or Princeton Review + + align:start position:0% +um the Kaplan or Princeton Review + + + align:start position:0% +um the Kaplan or Princeton Review +approach to sat tests + + align:start position:0% +approach to sat tests + + + align:start position:0% +approach to sat tests +um + + align:start position:0% +um + + + align:start position:0% +um +you know what that's what the what what + + align:start position:0% +you know what that's what the what what + + + align:start position:0% +you know what that's what the what what +Princeton Review and stuff does is it + + align:start position:0% +Princeton Review and stuff does is it + + + align:start position:0% +Princeton Review and stuff does is it +takes the population and it shoves it on + + align:start position:0% +takes the population and it shoves it on + + + align:start position:0% +takes the population and it shoves it on +you know everybody gets to gain those + + align:start position:0% +you know everybody gets to gain those + + + align:start position:0% +you know everybody gets to gain those +hundred points or whatever + + align:start position:0% +hundred points or whatever + + + align:start position:0% +hundred points or whatever +so is it okay for you to say my kid + + align:start position:0% +so is it okay for you to say my kid + + + align:start position:0% +so is it okay for you to say my kid +doesn't need to do that I didn't do that + + align:start position:0% +doesn't need to do that I didn't do that + + + align:start position:0% +doesn't need to do that I didn't do that +when I was a kid and then and my no kid + + align:start position:0% +when I was a kid and then and my no kid + + + align:start position:0% +when I was a kid and then and my no kid +of mine's gonna go off and get tutored + + align:start position:0% +of mine's gonna go off and get tutored + + + align:start position:0% +of mine's gonna go off and get tutored +it'll do it on his own Brains it's an + + align:start position:0% +it'll do it on his own Brains it's an + + + align:start position:0% +it'll do it on his own Brains it's an +aptitude test after all right uh + + align:start position:0% +aptitude test after all right uh + + + align:start position:0% +aptitude test after all right uh +um you know is there a difference + + align:start position:0% +um you know is there a difference + + + align:start position:0% +um you know is there a difference +between everybody being signed up for + + align:start position:0% +between everybody being signed up for + + + align:start position:0% +between everybody being signed up for +Princeton Review versus everybody being + + align:start position:0% +Princeton Review versus everybody being + + + align:start position:0% +Princeton Review versus everybody being +signed up you know going down to the + + align:start position:0% +signed up you know going down to the + + + align:start position:0% +signed up you know going down to the +nurse's office for the daily Prozac dose + + align:start position:0% +nurse's office for the daily Prozac dose + + + align:start position:0% +nurse's office for the daily Prozac dose +or is there a difference between oh + + align:start position:0% +or is there a difference between oh + + + align:start position:0% +or is there a difference between oh +you're sitting there saying I'm not + + align:start position:0% +you're sitting there saying I'm not + + + align:start position:0% +you're sitting there saying I'm not +gonna go in and make myself into a + + align:start position:0% +gonna go in and make myself into a + + + align:start position:0% +gonna go in and make myself into a +better meet by + + align:start position:0% +better meet by + + + align:start position:0% +better meet by +um uh by by popping Prozac all the time + + align:start position:0% +um uh by by popping Prozac all the time + + + align:start position:0% +um uh by by popping Prozac all the time +I'll stick with what is that Mountain + + align:start position:0% +I'll stick with what is that Mountain + + + align:start position:0% +I'll stick with what is that Mountain +Dew + + align:start position:0% +Dew + + + align:start position:0% +Dew +yeah yeah you know twice the caffeine of + + align:start position:0% +yeah yeah you know twice the caffeine of + + + align:start position:0% +yeah yeah you know twice the caffeine of +whatever right you know we hmm + + align:start position:0% +whatever right you know we hmm + + + align:start position:0% +whatever right you know we hmm +yeah okay that's good you're you're + + align:start position:0% +yeah okay that's good you're you're + + + align:start position:0% +yeah okay that's good you're you're +you're you're vertical that's that's + + align:start position:0% +you're you're vertical that's that's + + + align:start position:0% +you're you're vertical that's that's +encouraging get some to the guy next to + + align:start position:0% +encouraging get some to the guy next to + + + align:start position:0% +encouraging get some to the guy next to +you today he's he's gone + + align:start position:0% + + + + align:start position:0% + +um I shouldn't have said that + + align:start position:0% +um I shouldn't have said that + + + align:start position:0% +um I shouldn't have said that +um + + align:start position:0% + + + + align:start position:0% + +anyway we do this all the time right we + + align:start position:0% +anyway we do this all the time right we + + + align:start position:0% +anyway we do this all the time right we +self-medicate + + align:start position:0% +self-medicate + + + align:start position:0% +self-medicate +we self-medicate particularly with + + align:start position:0% +we self-medicate particularly with + + + align:start position:0% +we self-medicate particularly with +caffeine + + align:start position:0% +caffeine + + + align:start position:0% +caffeine +um but perhaps with a variety of of + + align:start position:0% +um but perhaps with a variety of of + + + align:start position:0% +um but perhaps with a variety of of +other things the use of alcohol is an + + align:start position:0% +other things the use of alcohol is an + + + align:start position:0% +other things the use of alcohol is an +antidepressant is probably a mistake but + + align:start position:0% +antidepressant is probably a mistake but + + + align:start position:0% +antidepressant is probably a mistake but +but it's not uncommon + + align:start position:0% +but it's not uncommon + + + align:start position:0% +but it's not uncommon +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +when is this a sort of an unwarranted + + align:start position:0% +when is this a sort of an unwarranted + + + align:start position:0% +when is this a sort of an unwarranted +medicalization of your life and when is + + align:start position:0% +medicalization of your life and when is + + + align:start position:0% +medicalization of your life and when is +it you know a lifestyle Choice + + align:start position:0% +it you know a lifestyle Choice + + + align:start position:0% +it you know a lifestyle Choice +um again there's not going to be a + + align:start position:0% +um again there's not going to be a + + + align:start position:0% +um again there's not going to be a +question on the final that says it's + + align:start position:0% +question on the final that says it's + + + align:start position:0% +question on the final that says it's +okay to drink Mountain Dew yes no only + + align:start position:0% +okay to drink Mountain Dew yes no only + + + align:start position:0% +okay to drink Mountain Dew yes no only +if it was a late night yeah it's but you + + align:start position:0% +if it was a late night yeah it's but you + + + align:start position:0% +if it was a late night yeah it's but you +can see that there there are um + + align:start position:0% +can see that there there are um + + + align:start position:0% +can see that there there are um +there are issues to to wrestle with and + + align:start position:0% +there are issues to to wrestle with and + + + align:start position:0% +there are issues to to wrestle with and +the doctors + + align:start position:0% +the doctors + + + align:start position:0% +the doctors +um + + align:start position:0% +um + + + align:start position:0% +um +ended up with or have ended up with a + + align:start position:0% +ended up with or have ended up with a + + + align:start position:0% +ended up with or have ended up with a +serious problem which is what you do + + align:start position:0% +serious problem which is what you do + + + align:start position:0% +serious problem which is what you do +with these patients who you cannot in + + align:start position:0% +with these patients who you cannot in + + + align:start position:0% +with these patients who you cannot in +good conscience give a clinical + + align:start position:0% +good conscience give a clinical + + + align:start position:0% +good conscience give a clinical +diagnosis of of clinical depression too + + align:start position:0% +diagnosis of of clinical depression too + + + align:start position:0% +diagnosis of of clinical depression too +um but who say you know if you don't + + align:start position:0% +um but who say you know if you don't + + + align:start position:0% +um but who say you know if you don't +give me my Prozac I'm gonna just be so + + align:start position:0% +give me my Prozac I'm gonna just be so + + + align:start position:0% +give me my Prozac I'm gonna just be so +depressed + + align:start position:0% +depressed + + + align:start position:0% +depressed +um yeah they who really need that or who + + align:start position:0% +um yeah they who really need that or who + + + align:start position:0% +um yeah they who really need that or who +think that they really um who think that + + align:start position:0% +think that they really um who think that + + + align:start position:0% +think that they really um who think that +they really need that oh by the way + + align:start position:0% +they really need that oh by the way + + + align:start position:0% +they really need that oh by the way +um okay well sure + + align:start position:0% +um okay well sure + + + align:start position:0% +um okay well sure +want to make sure that I do what it says + + align:start position:0% +want to make sure that I do what it says + + + align:start position:0% +want to make sure that I do what it says +oh okay let's say something about how um + + align:start position:0% +oh okay let's say something about how um + + + align:start position:0% +oh okay let's say something about how um +antidepressants work + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +a mystery + + align:start position:0% +a mystery + + + align:start position:0% +a mystery +here's here here's here's a mystery for + + align:start position:0% +here's here here's here's a mystery for + + + align:start position:0% +here's here here's here's a mystery for +you + + align:start position:0% +you + + + align:start position:0% +you +take Prozac + + align:start position:0% +take Prozac + + + align:start position:0% +take Prozac +it blocks your uh the the re-uptake + + align:start position:0% +it blocks your uh the the re-uptake + + + align:start position:0% +it blocks your uh the the re-uptake +pathway within hours it doesn't take + + align:start position:0% +pathway within hours it doesn't take + + + align:start position:0% +pathway within hours it doesn't take +much time at all okay so you are + + align:start position:0% +much time at all okay so you are + + + align:start position:0% +much time at all okay so you are +down here + + align:start position:0% +down here + + + align:start position:0% +down here +clinically depressed you come into the + + align:start position:0% +clinically depressed you come into the + + + align:start position:0% +clinically depressed you come into the +doctor's office he says here's your + + align:start position:0% +doctor's office he says here's your + + + align:start position:0% +doctor's office he says here's your +Prozac you take the Prozac few hours + + align:start position:0% +Prozac you take the Prozac few hours + + + align:start position:0% +Prozac you take the Prozac few hours +later more more serotonin at all those + + align:start position:0% +later more more serotonin at all those + + + align:start position:0% +later more more serotonin at all those +synapses how do you feel + + align:start position:0% +synapses how do you feel + + + align:start position:0% +synapses how do you feel +before I feel depressed actually + + align:start position:0% +before I feel depressed actually + + + align:start position:0% +before I feel depressed actually +um it takes typically + + align:start position:0% +um it takes typically + + + align:start position:0% +um it takes typically +um at least days more like several weeks + + align:start position:0% +um at least days more like several weeks + + + align:start position:0% +um at least days more like several weeks +before an antidepressant of this sort + + align:start position:0% +before an antidepressant of this sort + + + align:start position:0% +before an antidepressant of this sort +has an effect + + align:start position:0% +has an effect + + + align:start position:0% +has an effect +um Beyond perhaps Placebo effects there + + align:start position:0% +um Beyond perhaps Placebo effects there + + + align:start position:0% +um Beyond perhaps Placebo effects there +are Placebo effects where you take you + + align:start position:0% +are Placebo effects where you take you + + + align:start position:0% +are Placebo effects where you take you +know you can take any old damn thing and + + align:start position:0% +know you can take any old damn thing and + + + align:start position:0% +know you can take any old damn thing and +you feel a little better if you're + + align:start position:0% +you feel a little better if you're + + + align:start position:0% +you feel a little better if you're +convinced that it's going to work but + + align:start position:0% +convinced that it's going to work but + + + align:start position:0% +convinced that it's going to work but +the the main effect of of uh of + + align:start position:0% +the the main effect of of uh of + + + align:start position:0% +the the main effect of of uh of +antidepressants seems to take a long + + align:start position:0% +antidepressants seems to take a long + + + align:start position:0% +antidepressants seems to take a long +time that's a mystery at least as far as + + align:start position:0% +time that's a mystery at least as far as + + + align:start position:0% +time that's a mystery at least as far as +I know there's no neat clean answer to + + align:start position:0% +I know there's no neat clean answer to + + + align:start position:0% +I know there's no neat clean answer to +why it should be the case that the that + + align:start position:0% +why it should be the case that the that + + + align:start position:0% +why it should be the case that the that +the pharmacological EV um + + align:start position:0% +the pharmacological EV um + + + align:start position:0% +the pharmacological EV um +effect is there instantly almost and the + + align:start position:0% +effect is there instantly almost and the + + + align:start position:0% +effect is there instantly almost and the +psychological effect takes a vastly + + align:start position:0% +psychological effect takes a vastly + + + align:start position:0% +psychological effect takes a vastly +longer time the reference that I put on + + align:start position:0% +longer time the reference that I put on + + + align:start position:0% +longer time the reference that I put on +the handout is a theory it's not proven + + align:start position:0% +the handout is a theory it's not proven + + + align:start position:0% +the handout is a theory it's not proven +but it's an interesting theory about + + align:start position:0% +but it's an interesting theory about + + + align:start position:0% +but it's an interesting theory about +what might be going on + + align:start position:0% +what might be going on + + + align:start position:0% +what might be going on +um as I think I mentioned earlier in the + + align:start position:0% +um as I think I mentioned earlier in the + + + align:start position:0% +um as I think I mentioned earlier in the +course + + align:start position:0% +course + + + align:start position:0% +course +one of the interesting new findings in + + align:start position:0% +one of the interesting new findings in + + + align:start position:0% +one of the interesting new findings in +Neuroscience is that we grow new neurons + + align:start position:0% +Neuroscience is that we grow new neurons + + + align:start position:0% +Neuroscience is that we grow new neurons +we didn't used to think we grew new + + align:start position:0% +we didn't used to think we grew new + + + align:start position:0% +we didn't used to think we grew new +neurons but now it's pretty clear that + + align:start position:0% +neurons but now it's pretty clear that + + + align:start position:0% +neurons but now it's pretty clear that +you grow um you grow new neurons + + align:start position:0% +you grow um you grow new neurons + + + align:start position:0% +you grow um you grow new neurons +um and there's a pretty strong + + align:start position:0% +um and there's a pretty strong + + + align:start position:0% +um and there's a pretty strong +suggestion that that uh this + + align:start position:0% +suggestion that that uh this + + + align:start position:0% +suggestion that that uh this +neurogenesis as it's called is depressed + + align:start position:0% +neurogenesis as it's called is depressed + + + align:start position:0% +neurogenesis as it's called is depressed +in depression you're not making those + + align:start position:0% +in depression you're not making those + + + align:start position:0% +in depression you're not making those +new neurons and one theory is that when + + align:start position:0% +new neurons and one theory is that when + + + align:start position:0% +new neurons and one theory is that when +an antidepressant is doing is + + align:start position:0% +an antidepressant is doing is + + + align:start position:0% +an antidepressant is doing is +um is jump starting the neurogenesis + + align:start position:0% +um is jump starting the neurogenesis + + + align:start position:0% +um is jump starting the neurogenesis +that this is the beginning of a Cascade + + align:start position:0% +that this is the beginning of a Cascade + + + align:start position:0% +that this is the beginning of a Cascade +of events that leads eventually to the + + align:start position:0% +of events that leads eventually to the + + + align:start position:0% +of events that leads eventually to the +birth of new cells new neurons and only + + align:start position:0% +birth of new cells new neurons and only + + + align:start position:0% +birth of new cells new neurons and only +when you manage to sort of grow yourself + + align:start position:0% +when you manage to sort of grow yourself + + + align:start position:0% +when you manage to sort of grow yourself +a new bit of brain in a sense do you uh + + align:start position:0% +a new bit of brain in a sense do you uh + + + align:start position:0% +a new bit of brain in a sense do you uh +break out that does it help you to break + + align:start position:0% +break out that does it help you to break + + + align:start position:0% +break out that does it help you to break +out of the + + align:start position:0% +out of the + + + align:start position:0% +out of the +um to break out of the depression + + align:start position:0% +um to break out of the depression + + + align:start position:0% +um to break out of the depression +um this also it the the data on how well + + align:start position:0% +um this also it the the data on how well + + + align:start position:0% +um this also it the the data on how well +these things work is a little depressing + + align:start position:0% +these things work is a little depressing + + + align:start position:0% +these things work is a little depressing +in its own right it's not clear + + align:start position:0% +in its own right it's not clear + + + align:start position:0% +in its own right it's not clear +um + + align:start position:0% +um + + + align:start position:0% +um +that uh antidepressants like a lot of + + align:start position:0% +that uh antidepressants like a lot of + + + align:start position:0% +that uh antidepressants like a lot of +these meta antidepressants don't work as + + align:start position:0% +these meta antidepressants don't work as + + + align:start position:0% +these meta antidepressants don't work as +well once they go off patent + + align:start position:0% +well once they go off patent + + + align:start position:0% +well once they go off patent +it's a mysterious thing + + align:start position:0% +it's a mysterious thing + + + align:start position:0% +it's a mysterious thing +this is uh you you want to worry about + + align:start position:0% +this is uh you you want to worry about + + + align:start position:0% +this is uh you you want to worry about +this this over and over again you get + + align:start position:0% +this this over and over again you get + + + align:start position:0% +this this over and over again you get +some cool new drug like Prozac it's got + + align:start position:0% +some cool new drug like Prozac it's got + + + align:start position:0% +some cool new drug like Prozac it's got +no After Effects it cures the disease + + align:start position:0% +no After Effects it cures the disease + + + align:start position:0% +no After Effects it cures the disease +like that and everybody is better and + + align:start position:0% +like that and everybody is better and + + + align:start position:0% +like that and everybody is better and +and and and it's it's a miracle drug + + align:start position:0% +and and and it's it's a miracle drug + + + align:start position:0% +and and and it's it's a miracle drug +amazingly by the time you know Eli Lilly + + align:start position:0% +amazingly by the time you know Eli Lilly + + + align:start position:0% +amazingly by the time you know Eli Lilly +or whoever is his patent is worn off it + + align:start position:0% +or whoever is his patent is worn off it + + + align:start position:0% +or whoever is his patent is worn off it +now has side effects doesn't work all + + align:start position:0% +now has side effects doesn't work all + + + align:start position:0% +now has side effects doesn't work all +that well but you want to try my new + + align:start position:0% +that well but you want to try my new + + + align:start position:0% +that well but you want to try my new +amazing wonder drug + + align:start position:0% +amazing wonder drug + + + align:start position:0% +amazing wonder drug +um so the last few reviews I've read of + + align:start position:0% +um so the last few reviews I've read of + + + align:start position:0% +um so the last few reviews I've read of +of the effectiveness of antidepressants + + align:start position:0% +of the effectiveness of antidepressants + + + align:start position:0% +of the effectiveness of antidepressants +have been well they've been sort of + + align:start position:0% +have been well they've been sort of + + + align:start position:0% +have been well they've been sort of +depressing actually + + align:start position:0% +depressing actually + + + align:start position:0% +depressing actually +um that they're they're they're they're + + align:start position:0% +um that they're they're they're they're + + + align:start position:0% +um that they're they're they're they're +not Magic Bullets now there are several + + align:start position:0% +not Magic Bullets now there are several + + + align:start position:0% +not Magic Bullets now there are several +ways to treat depression + + align:start position:0% +ways to treat depression + + + align:start position:0% +ways to treat depression +um and and and how you treat it uh + + align:start position:0% +um and and and how you treat it uh + + + align:start position:0% +um and and and how you treat it uh +depends in there are also several + + align:start position:0% +depends in there are also several + + + align:start position:0% +depends in there are also several +flavors of depression + + align:start position:0% +flavors of depression + + + align:start position:0% +flavors of depression +um not not all not all depressions well + + align:start position:0% +um not not all not all depressions well + + + align:start position:0% +um not not all not all depressions well +certainly not all are bipolar and + + align:start position:0% +certainly not all are bipolar and + + + align:start position:0% +certainly not all are bipolar and +there's evidence that they differ both + + align:start position:0% +there's evidence that they differ both + + + align:start position:0% +there's evidence that they differ both +in their symptoms and in um in their + + align:start position:0% +in their symptoms and in um in their + + + align:start position:0% +in their symptoms and in um in their +neurochemistry so for instance let's say + + align:start position:0% +neurochemistry so for instance let's say + + + align:start position:0% +neurochemistry so for instance let's say +oh I think it says on the handout yeah + + align:start position:0% +oh I think it says on the handout yeah + + + align:start position:0% +oh I think it says on the handout yeah +typical versus atypical depression I'm + + align:start position:0% +typical versus atypical depression I'm + + + align:start position:0% +typical versus atypical depression I'm +sure if I rummaged around I'd remember + + align:start position:0% +sure if I rummaged around I'd remember + + + align:start position:0% +sure if I rummaged around I'd remember +which was which + + align:start position:0% +which was which + + + align:start position:0% +which was which +um but uh in some forms of depression + + align:start position:0% +um but uh in some forms of depression + + + align:start position:0% +um but uh in some forms of depression +people + + align:start position:0% +people + + + align:start position:0% +people +um sleep too much and eat too much + + align:start position:0% +um sleep too much and eat too much + + + align:start position:0% +um sleep too much and eat too much +in other forms of depression they sleep + + align:start position:0% +in other forms of depression they sleep + + + align:start position:0% +in other forms of depression they sleep +too little and eat too little + + align:start position:0% +too little and eat too little + + + align:start position:0% +too little and eat too little +um they're both depressions + + align:start position:0% +um they're both depressions + + + align:start position:0% +um they're both depressions +um in in terms of the mood + + align:start position:0% +um in in terms of the mood + + + align:start position:0% +um in in terms of the mood +but they are clinically distinct and + + align:start position:0% +but they are clinically distinct and + + + align:start position:0% +but they are clinically distinct and +psychopharmacologically uh distinct + + align:start position:0% +psychopharmacologically uh distinct + + + align:start position:0% +psychopharmacologically uh distinct +actually + + align:start position:0% +actually + + + align:start position:0% +actually +um + + align:start position:0% +um + + + align:start position:0% +um +bipolar + + align:start position:0% +bipolar + + + align:start position:0% +bipolar +disorders + + align:start position:0% +disorders + + + align:start position:0% +disorders +the the treatment of choice for long + + align:start position:0% +the the treatment of choice for long + + + align:start position:0% +the the treatment of choice for long +before there was long before Prozac came + + align:start position:0% +before there was long before Prozac came + + + align:start position:0% +before there was long before Prozac came +on on the scene was of all things + + align:start position:0% +on on the scene was of all things + + + align:start position:0% +on on the scene was of all things +lithium chloride it's just the salt of + + align:start position:0% +lithium chloride it's just the salt of + + + align:start position:0% +lithium chloride it's just the salt of +lithium + + align:start position:0% +lithium + + + align:start position:0% +lithium +um you know just move right up from + + align:start position:0% +um you know just move right up from + + + align:start position:0% +um you know just move right up from +sodium chloride + + align:start position:0% +sodium chloride + + + align:start position:0% +sodium chloride +um and that that that's Jameson credits + + align:start position:0% +um and that that that's Jameson credits + + + align:start position:0% +um and that that that's Jameson credits +lithium uh with keeping her alive that + + align:start position:0% +lithium uh with keeping her alive that + + + align:start position:0% +lithium uh with keeping her alive that +if she had not been put on on uh on on + + align:start position:0% +if she had not been put on on uh on on + + + align:start position:0% +if she had not been put on on uh on on +lithium as a treatment for her bipolar + + align:start position:0% +lithium as a treatment for her bipolar + + + align:start position:0% +lithium as a treatment for her bipolar +disorder that she thinks she probably + + align:start position:0% +disorder that she thinks she probably + + + align:start position:0% +disorder that she thinks she probably +would have ended up + + align:start position:0% +would have ended up + + + align:start position:0% +would have ended up +um committing suicide any anybody an + + align:start position:0% +um committing suicide any anybody an + + + align:start position:0% +um committing suicide any anybody an +expert on how lithium works + + align:start position:0% +expert on how lithium works + + + align:start position:0% +expert on how lithium works +no I think I don't know the answer to + + align:start position:0% +no I think I don't know the answer to + + + align:start position:0% +no I think I don't know the answer to +this I'm not sure it's known the last + + align:start position:0% +this I'm not sure it's known the last + + + align:start position:0% +this I'm not sure it's known the last +time I checked on it we didn't know how + + align:start position:0% +time I checked on it we didn't know how + + + align:start position:0% +time I checked on it we didn't know how +it worked it was just how was it + + align:start position:0% +it worked it was just how was it + + + align:start position:0% +it worked it was just how was it +discovered it was discovered in some + + align:start position:0% +discovered it was discovered in some + + + align:start position:0% +discovered it was discovered in some +Bizarro fashion + + align:start position:0% +Bizarro fashion + + + align:start position:0% +Bizarro fashion +you know where do you find lithium + + align:start position:0% +you know where do you find lithium + + + align:start position:0% +you know where do you find lithium +like a salt you know I don't know I I + + align:start position:0% +like a salt you know I don't know I I + + + align:start position:0% +like a salt you know I don't know I I +I'm remembering some odd story about you + + align:start position:0% +I'm remembering some odd story about you + + + align:start position:0% +I'm remembering some odd story about you +know + + align:start position:0% +know + + + align:start position:0% +know +find batteries that people + + align:start position:0% +find batteries that people + + + align:start position:0% +find batteries that people +that's it seven up + + align:start position:0% +that's it seven up + + + align:start position:0% +that's it seven up +okay if you dissolve your battery in + + align:start position:0% +okay if you dissolve your battery in + + + align:start position:0% +okay if you dissolve your battery in +seven up I don't know what happens but I + + align:start position:0% +seven up I don't know what happens but I + + + align:start position:0% +seven up I don't know what happens but I +don't imagine it's good because the + + align:start position:0% +don't imagine it's good because the + + + align:start position:0% +don't imagine it's good because the +Mercury and the rest of it probably + + align:start position:0% +Mercury and the rest of it probably + + + align:start position:0% +Mercury and the rest of it probably +isn't really good for you + + align:start position:0% +isn't really good for you + + + align:start position:0% +isn't really good for you +um + + align:start position:0% +um + + + align:start position:0% +um +the other treatment for + + align:start position:0% +the other treatment for + + + align:start position:0% +the other treatment for +now the the + + align:start position:0% +now the the + + + align:start position:0% +now the the +sadly + + align:start position:0% +sadly + + + align:start position:0% +sadly +not all depressions are + + align:start position:0% +not all depressions are + + + align:start position:0% +not all depressions are +um amenable to the pharmacology oh first + + align:start position:0% +um amenable to the pharmacology oh first + + + align:start position:0% +um amenable to the pharmacology oh first +of all + + align:start position:0% +of all + + + align:start position:0% +of all +the big mistake which I think the uh the + + align:start position:0% +the big mistake which I think the uh the + + + align:start position:0% +the big mistake which I think the uh the +insurance people are growing out of was + + align:start position:0% +insurance people are growing out of was + + + align:start position:0% +insurance people are growing out of was +the notion okay we'll now that we've got + + align:start position:0% +the notion okay we'll now that we've got + + + align:start position:0% +the notion okay we'll now that we've got +these cool pills we'll pay for the pills + + align:start position:0% +these cool pills we'll pay for the pills + + + align:start position:0% +these cool pills we'll pay for the pills +but that's it + + align:start position:0% +but that's it + + + align:start position:0% +but that's it +so + + align:start position:0% +so + + + align:start position:0% +so +um it's if it's going to take you + + align:start position:0% +um it's if it's going to take you + + + align:start position:0% +um it's if it's going to take you +several weeks for the medicine to work + + align:start position:0% +several weeks for the medicine to work + + + align:start position:0% +several weeks for the medicine to work +it turns out to be very helpful if + + align:start position:0% +it turns out to be very helpful if + + + align:start position:0% +it turns out to be very helpful if +you're actually talking to somebody + + align:start position:0% +you're actually talking to somebody + + + align:start position:0% +you're actually talking to somebody +during this time if there's some + + align:start position:0% +during this time if there's some + + + align:start position:0% +during this time if there's some +Psychotherapy of some sort + + align:start position:0% +Psychotherapy of some sort + + + align:start position:0% +Psychotherapy of some sort +going on because if you're down here in + + align:start position:0% +going on because if you're down here in + + + align:start position:0% +going on because if you're down here in +the depths of the depression and some + + align:start position:0% +the depths of the depression and some + + + align:start position:0% +the depths of the depression and some +genius hands you a pill and says go away + + align:start position:0% +genius hands you a pill and says go away + + + align:start position:0% +genius hands you a pill and says go away +don't bother me no more you know if if + + align:start position:0% +don't bother me no more you know if if + + + align:start position:0% +don't bother me no more you know if if +it's true that as you're coming out as + + align:start position:0% +it's true that as you're coming out as + + + align:start position:0% +it's true that as you're coming out as +slowly coming out of the depression + + align:start position:0% +slowly coming out of the depression + + + align:start position:0% +slowly coming out of the depression +that's when the suicides take place you + + align:start position:0% +that's when the suicides take place you + + + align:start position:0% +that's when the suicides take place you +know this is a recipe for disaster and + + align:start position:0% +know this is a recipe for disaster and + + + align:start position:0% +know this is a recipe for disaster and +if it takes a long time to work you know + + align:start position:0% +if it takes a long time to work you know + + + align:start position:0% +if it takes a long time to work you know +if you take a medicine and nothing + + align:start position:0% +if you take a medicine and nothing + + + align:start position:0% +if you take a medicine and nothing +happens for weeks what do you do + + align:start position:0% +happens for weeks what do you do + + + align:start position:0% +happens for weeks what do you do +is stopped taking the medicine and so + + align:start position:0% +is stopped taking the medicine and so + + + align:start position:0% +is stopped taking the medicine and so +what you really need + + align:start position:0% +what you really need + + + align:start position:0% +what you really need +typically as part of of a sensible + + align:start position:0% +typically as part of of a sensible + + + align:start position:0% +typically as part of of a sensible +treatment for a depression is not only + + align:start position:0% +treatment for a depression is not only + + + align:start position:0% +treatment for a depression is not only +somebody who'll give you the medicine + + align:start position:0% +somebody who'll give you the medicine + + + align:start position:0% +somebody who'll give you the medicine +but somebody will talk to you about it + + align:start position:0% +but somebody will talk to you about it + + + align:start position:0% +but somebody will talk to you about it +two + + align:start position:0% +two + + + align:start position:0% +two +um but even so there are there are + + align:start position:0% +um but even so there are there are + + + align:start position:0% +um but even so there are there are +depressions that are not amenable or + + align:start position:0% +depressions that are not amenable or + + + align:start position:0% +depressions that are not amenable or +don't seem to respond well to uh to any + + align:start position:0% +don't seem to respond well to uh to any + + + align:start position:0% +don't seem to respond well to uh to any +of the medicines that we have at the + + align:start position:0% +of the medicines that we have at the + + + align:start position:0% +of the medicines that we have at the +moment and + + align:start position:0% +moment and + + + align:start position:0% +moment and +um under the heading of even more + + align:start position:0% +um under the heading of even more + + + align:start position:0% +um under the heading of even more +unlikely treatments that really turn out + + align:start position:0% +unlikely treatments that really turn out + + + align:start position:0% +unlikely treatments that really turn out +to work + + align:start position:0% +to work + + + align:start position:0% +to work +um more unlikely than feeding them at a + + align:start position:0% +um more unlikely than feeding them at a + + + align:start position:0% +um more unlikely than feeding them at a +lithium salts is what's known as ECT for + + align:start position:0% +lithium salts is what's known as ECT for + + + align:start position:0% +lithium salts is what's known as ECT for +electroconvulsive therapy I talked about + + align:start position:0% +electroconvulsive therapy I talked about + + + align:start position:0% +electroconvulsive therapy I talked about +this a bit when we were talking about + + align:start position:0% +this a bit when we were talking about + + + align:start position:0% +this a bit when we were talking about +memory remember this is little rats they + + align:start position:0% +memory remember this is little rats they + + + align:start position:0% +memory remember this is little rats they +step down you run electrical current + + align:start position:0% +step down you run electrical current + + + align:start position:0% +step down you run electrical current +through their heads they shock their + + align:start position:0% +through their heads they shock their + + + align:start position:0% +through their heads they shock their +little feet you run electrical current + + align:start position:0% +little feet you run electrical current + + + align:start position:0% +little feet you run electrical current +through their brains they don't remember + + align:start position:0% +through their brains they don't remember + + + align:start position:0% +through their brains they don't remember +that you shocked their feet so they step + + align:start position:0% +that you shocked their feet so they step + + + align:start position:0% +that you shocked their feet so they step +down again you know sound familiar yeah + + align:start position:0% +down again you know sound familiar yeah + + + align:start position:0% +down again you know sound familiar yeah +okay good + + align:start position:0% +okay good + + + align:start position:0% +okay good +um + + align:start position:0% +um + + + align:start position:0% +um +well this is a treatment for depression + + align:start position:0% +well this is a treatment for depression + + + align:start position:0% +well this is a treatment for depression +not abundantly clear why it works + + align:start position:0% +not abundantly clear why it works + + + align:start position:0% +not abundantly clear why it works +um but it in in uh in in my in in my + + align:start position:0% +um but it in in uh in in my in in my + + + align:start position:0% +um but it in in uh in in my in in my +circle of friends I have a uh + + align:start position:0% +circle of friends I have a uh + + + align:start position:0% +circle of friends I have a uh +friend who actually went back to uh + + align:start position:0% +friend who actually went back to uh + + + align:start position:0% +friend who actually went back to uh +um graduated college went off did a + + align:start position:0% +um graduated college went off did a + + + align:start position:0% +um graduated college went off did a +whole bunch of stuff then went back to + + align:start position:0% +whole bunch of stuff then went back to + + + align:start position:0% +whole bunch of stuff then went back to +med school then became desperately + + align:start position:0% +med school then became desperately + + + align:start position:0% +med school then became desperately +clinically depressed and had to be + + align:start position:0% +clinically depressed and had to be + + + align:start position:0% +clinically depressed and had to be +hospitalized + + align:start position:0% +hospitalized + + + align:start position:0% +hospitalized +um and um and what got her through it + + align:start position:0% +um and um and what got her through it + + + align:start position:0% +um and um and what got her through it +was uh was electroconvulsive therapy + + align:start position:0% +was uh was electroconvulsive therapy + + + align:start position:0% +was uh was electroconvulsive therapy +um not an entirely benign procedure it + + align:start position:0% +um not an entirely benign procedure it + + + align:start position:0% +um not an entirely benign procedure it +really does it does have memory side + + align:start position:0% +really does it does have memory side + + + align:start position:0% +really does it does have memory side +effects but well it used to be that + + align:start position:0% +effects but well it used to be that + + + align:start position:0% +effects but well it used to be that +nobody in an intro psych class thought + + align:start position:0% +nobody in an intro psych class thought + + + align:start position:0% +nobody in an intro psych class thought +this was a good idea at all because + + align:start position:0% +this was a good idea at all because + + + align:start position:0% +this was a good idea at all because +everybody had seen One Flew Over the + + align:start position:0% +everybody had seen One Flew Over the + + + align:start position:0% +everybody had seen One Flew Over the +Cuckoo's Nest how many people have seen + + align:start position:0% +Cuckoo's Nest how many people have seen + + + align:start position:0% +Cuckoo's Nest how many people have seen +that movie + + align:start position:0% +that movie + + + align:start position:0% +that movie +also a fair number of people have seen + + align:start position:0% +also a fair number of people have seen + + + align:start position:0% +also a fair number of people have seen +it uh that that's a movie that does + + align:start position:0% +it uh that that's a movie that does + + + align:start position:0% +it uh that that's a movie that does +nothing good for the reputation of + + align:start position:0% +nothing good for the reputation of + + + align:start position:0% +nothing good for the reputation of +electroconvulsive therapy + + align:start position:0% +electroconvulsive therapy + + + align:start position:0% +electroconvulsive therapy +electroconvulsive therapy these days is + + align:start position:0% +electroconvulsive therapy these days is + + + align:start position:0% +electroconvulsive therapy these days is +um uh you know you give somebody a + + align:start position:0% +um uh you know you give somebody a + + + align:start position:0% +um uh you know you give somebody a +sedative they don't thrash around they + + align:start position:0% +sedative they don't thrash around they + + + align:start position:0% +sedative they don't thrash around they +don't hurt themselves it still has + + align:start position:0% +don't hurt themselves it still has + + + align:start position:0% +don't hurt themselves it still has +memory consequences consolidation of + + align:start position:0% +memory consequences consolidation of + + + align:start position:0% +memory consequences consolidation of +memory consequences but it really does + + align:start position:0% +memory consequences but it really does + + + align:start position:0% +memory consequences but it really does +seem to mysteriously break up + + align:start position:0% +seem to mysteriously break up + + + align:start position:0% +seem to mysteriously break up +um + + align:start position:0% +um + + + align:start position:0% +um +uh depressions now the latest wrinkle on + + align:start position:0% +uh depressions now the latest wrinkle on + + + align:start position:0% +uh depressions now the latest wrinkle on +this + + align:start position:0% +this + + + align:start position:0% +this +um + + align:start position:0% +um + + + align:start position:0% +um +you know what boils down to smack him up + + align:start position:0% +you know what boils down to smack him up + + + align:start position:0% +you know what boils down to smack him up +the side of the head treatments of of + + align:start position:0% +the side of the head treatments of of + + + align:start position:0% +the side of the head treatments of of +depression + + align:start position:0% +depression + + + align:start position:0% +depression +um is the use of uh it's very new is the + + align:start position:0% +um is the use of uh it's very new is the + + + align:start position:0% +um is the use of uh it's very new is the +use of transcranial magnetic stimulation + + align:start position:0% +use of transcranial magnetic stimulation + + + align:start position:0% +use of transcranial magnetic stimulation +um which I think I also talked about + + align:start position:0% +um which I think I also talked about + + + align:start position:0% +um which I think I also talked about +earlier but basically what you do is you + + align:start position:0% +earlier but basically what you do is you + + + align:start position:0% +earlier but basically what you do is you +put a giant electromagnet or a strong + + align:start position:0% +put a giant electromagnet or a strong + + + align:start position:0% +put a giant electromagnet or a strong +electromagnet next to the uh skull you + + align:start position:0% +electromagnet next to the uh skull you + + + align:start position:0% +electromagnet next to the uh skull you +fire off a big pulse of of a big + + align:start position:0% +fire off a big pulse of of a big + + + align:start position:0% +fire off a big pulse of of a big +magnetic field that induces an + + align:start position:0% +magnetic field that induces an + + + align:start position:0% +magnetic field that induces an +electrical field locally + + align:start position:0% +electrical field locally + + + align:start position:0% +electrical field locally +and uh and knocks out uh the neural + + align:start position:0% +and uh and knocks out uh the neural + + + align:start position:0% +and uh and knocks out uh the neural +activity locally and there's some + + align:start position:0% +activity locally and there's some + + + align:start position:0% +activity locally and there's some +evidence that properly applied that this + + align:start position:0% +evidence that properly applied that this + + + align:start position:0% +evidence that properly applied that this +is a sort of a Kinder gentler version of + + align:start position:0% +is a sort of a Kinder gentler version of + + + align:start position:0% +is a sort of a Kinder gentler version of +of ECT that it acts to break up + + align:start position:0% +of ECT that it acts to break up + + + align:start position:0% +of ECT that it acts to break up +depressions I don't anybody knows + + align:start position:0% +depressions I don't anybody knows + + + align:start position:0% +depressions I don't anybody knows +there's a brilliant theory for how that + + align:start position:0% +there's a brilliant theory for how that + + + align:start position:0% +there's a brilliant theory for how that +works uh who knows but it's uh it's it's + + align:start position:0% +works uh who knows but it's uh it's it's + + + align:start position:0% +works uh who knows but it's uh it's it's +very new but uh but but expect I I + + align:start position:0% +very new but uh but but expect I I + + + align:start position:0% +very new but uh but but expect I I +expect that in a few years I'll be + + align:start position:0% +expect that in a few years I'll be + + + align:start position:0% +expect that in a few years I'll be +lecturing more about that because it's + + align:start position:0% +lecturing more about that because it's + + + align:start position:0% +lecturing more about that because it's +at least initially sounds + + align:start position:0% +at least initially sounds + + + align:start position:0% +at least initially sounds +um + + align:start position:0% +um + + + align:start position:0% +um +sounds rather promising + + align:start position:0% +sounds rather promising + + + align:start position:0% +sounds rather promising +um all right I think this would be + + align:start position:0% +um all right I think this would be + + + align:start position:0% +um all right I think this would be +a good time to take a break + + align:start position:0% +a good time to take a break + + + align:start position:0% +a good time to take a break +let's take + + align:start position:0% +let's take + + + align:start position:0% +let's take +unless you're too depressed to get up + + align:start position:0% +unless you're too depressed to get up + + + align:start position:0% +unless you're too depressed to get up +take a break + + align:start position:0% +take a break + + + align:start position:0% +take a break +[Music] + + align:start position:0% + + + + align:start position:0% + +which one Prozac Nation no Prozac Nation + + align:start position:0% +which one Prozac Nation no Prozac Nation + + + align:start position:0% +which one Prozac Nation no Prozac Nation +somebody else's book no Jameson no + + align:start position:0% +somebody else's book no Jameson no + + + align:start position:0% +somebody else's book no Jameson no +that's somebody else I can't remember + + align:start position:0% +that's somebody else I can't remember + + + align:start position:0% +that's somebody else I can't remember +who wrote it but yes that's a cool book + + align:start position:0% +who wrote it but yes that's a cool book + + + align:start position:0% +who wrote it but yes that's a cool book +too yeah + + align:start position:0% +too yeah + + + align:start position:0% +too yeah +nope nope but you'll come back and tell + + align:start position:0% +nope nope but you'll come back and tell + + + align:start position:0% +nope nope but you'll come back and tell +me who wrote it because that we're both + + align:start position:0% +me who wrote it because that we're both + + + align:start position:0% +me who wrote it because that we're both +forgetting who ready have they ever done + + align:start position:0% + + + + align:start position:0% + +hand imaginations + + align:start position:0% + + + + align:start position:0% + +it's a big problem in mental illness in + + align:start position:0% +it's a big problem in mental illness in + + + align:start position:0% +it's a big problem in mental illness in +general and certainly in depression + + align:start position:0% +general and certainly in depression + + + align:start position:0% +general and certainly in depression +which is particularly if you've got a + + align:start position:0% +which is particularly if you've got a + + + align:start position:0% +which is particularly if you've got a +cycling depression this is going to get + + align:start position:0% +cycling depression this is going to get + + + align:start position:0% +cycling depression this is going to get +better right and and um and yeah the the + + align:start position:0% +better right and and um and yeah the the + + + align:start position:0% +better right and and um and yeah the the +difference between placebo and Prozac is + + align:start position:0% +difference between placebo and Prozac is + + + align:start position:0% +difference between placebo and Prozac is +at least in some of the studies that + + align:start position:0% +at least in some of the studies that + + + align:start position:0% +at least in some of the studies that +I've read a lot less dramatic than you + + align:start position:0% +I've read a lot less dramatic than you + + + align:start position:0% +I've read a lot less dramatic than you +would think that and and the problem + + align:start position:0% +would think that and and the problem + + + align:start position:0% +would think that and and the problem +with a population like us is that we're + + align:start position:0% +with a population like us is that we're + + + align:start position:0% +with a population like us is that we're +too well informed in the good old days + + align:start position:0% +too well informed in the good old days + + + align:start position:0% +too well informed in the good old days +placebos are great you know the side + + align:start position:0% +placebos are great you know the side + + + align:start position:0% +placebos are great you know the side +effects are really Limited in the good + + align:start position:0% +effects are really Limited in the good + + + align:start position:0% +effects are really Limited in the good +old days your doctor would come around + + align:start position:0% +old days your doctor would come around + + + align:start position:0% +old days your doctor would come around +have no clue what the hell he would say + + align:start position:0% +have no clue what the hell he would say + + + align:start position:0% +have no clue what the hell he would say +you know how to treat you but give you + + align:start position:0% +you know how to treat you but give you + + + align:start position:0% +you know how to treat you but give you +you know Dr housie's magic Elixir and + + align:start position:0% +you know Dr housie's magic Elixir and + + + align:start position:0% +you know Dr housie's magic Elixir and +you'd feel better + + align:start position:0% +you'd feel better + + + align:start position:0% +you'd feel better +um and and it's a great pity that now if + + align:start position:0% +um and and it's a great pity that now if + + + align:start position:0% +um and and it's a great pity that now if +I fed you Doctor Who's these Elixir the + + align:start position:0% +I fed you Doctor Who's these Elixir the + + + align:start position:0% +I fed you Doctor Who's these Elixir the +first thing you do is Google it discover + + align:start position:0% +first thing you do is Google it discover + + + align:start position:0% +first thing you do is Google it discover +that it's snake oil and feel worse than + + align:start position:0% +that it's snake oil and feel worse than + + + align:start position:0% +that it's snake oil and feel worse than +Sue me so yeah it is I can if you turn + + align:start position:0% +Sue me so yeah it is I can if you turn + + + align:start position:0% +Sue me so yeah it is I can if you turn +out to be um + + align:start position:0% +out to be um + + + align:start position:0% +out to be um +particularly interested send me an email + + align:start position:0% +particularly interested send me an email + + + align:start position:0% +particularly interested send me an email +and I can send you a couple of the + + align:start position:0% +and I can send you a couple of the + + + align:start position:0% +and I can send you a couple of the +references of things that depressed me + + align:start position:0% +references of things that depressed me + + + align:start position:0% +references of things that depressed me +when I read them because it's doing that + + align:start position:0% +when I read them because it's doing that + + + align:start position:0% +when I read them because it's doing that +much good + + align:start position:0% +much good + + + align:start position:0% +much good +on the other hand my mother absolutely + + align:start position:0% +on the other hand my mother absolutely + + + align:start position:0% +on the other hand my mother absolutely +swears by the stuff she was saying she's + + align:start position:0% +swears by the stuff she was saying she's + + + align:start position:0% +swears by the stuff she was saying she's +had her own issues with depression and + + align:start position:0% +had her own issues with depression and + + + align:start position:0% +had her own issues with depression and +and thinks that Prozac is wonderful + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +you have to drill what + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +I'm not entirely sure what's happening + + align:start position:0% +I'm not entirely sure what's happening + + + align:start position:0% +I'm not entirely sure what's happening +here but uh + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +that's uh well that's very that's very + + align:start position:0% +that's uh well that's very that's very + + + align:start position:0% +that's uh well that's very that's very +sad in several ways um but + + align:start position:0% +sad in several ways um but + + + align:start position:0% +sad in several ways um but +however I would suggest that that uh you + + align:start position:0% +however I would suggest that that uh you + + + align:start position:0% +however I would suggest that that uh you +you she's got a great future because her + + align:start position:0% +you she's got a great future because her + + + align:start position:0% +you she's got a great future because her +artistic abilities are at least the + + align:start position:0% +artistic abilities are at least the + + + align:start position:0% +artistic abilities are at least the +equivalent of mine so you know I'll come + + align:start position:0% +equivalent of mine so you know I'll come + + + align:start position:0% +equivalent of mine so you know I'll come +back in 20 years she'll be teaching the + + align:start position:0% +back in 20 years she'll be teaching the + + + align:start position:0% +back in 20 years she'll be teaching the +course + + align:start position:0% +course + + + align:start position:0% +course +um + + align:start position:0% +um + + + align:start position:0% +um +I want to talk about a a couple of other + + align:start position:0% +I want to talk about a a couple of other + + + align:start position:0% +I want to talk about a a couple of other +disease you know mental illness States + + align:start position:0% +disease you know mental illness States + + + align:start position:0% +disease you know mental illness States +um + + align:start position:0% +um + + + align:start position:0% +um +in part as a way of + + align:start position:0% +in part as a way of + + + align:start position:0% +in part as a way of +um + + align:start position:0% +um + + + align:start position:0% +um +illustrating I I guess what I really + + align:start position:0% +illustrating I I guess what I really + + + align:start position:0% +illustrating I I guess what I really +want to illustrate in the last bit of + + align:start position:0% +want to illustrate in the last bit of + + + align:start position:0% +want to illustrate in the last bit of +this lecture is is the sort of mind and + + align:start position:0% +this lecture is is the sort of mind and + + + align:start position:0% +this lecture is is the sort of mind and +brain links we tend to like to make up + + align:start position:0% +brain links we tend to like to make up + + + align:start position:0% +brain links we tend to like to make up +theories that are one or the other and + + align:start position:0% +theories that are one or the other and + + + align:start position:0% +theories that are one or the other and +the current popular trend is towards + + align:start position:0% +the current popular trend is towards + + + align:start position:0% +the current popular trend is towards +brain explanations oh you're depressed + + align:start position:0% +brain explanations oh you're depressed + + + align:start position:0% +brain explanations oh you're depressed +because you don't have enough serotonin + + align:start position:0% +because you don't have enough serotonin + + + align:start position:0% +because you don't have enough serotonin +happening for you will boost up your + + align:start position:0% +happening for you will boost up your + + + align:start position:0% +happening for you will boost up your +serotonin you'll be fine it's a very + + align:start position:0% +serotonin you'll be fine it's a very + + + align:start position:0% +serotonin you'll be fine it's a very +brain kind of uh thing Freudian theories + + align:start position:0% +brain kind of uh thing Freudian theories + + + align:start position:0% +brain kind of uh thing Freudian theories +we're very mind kinds of things but + + align:start position:0% +we're very mind kinds of things but + + + align:start position:0% +we're very mind kinds of things but +there are some + + align:start position:0% +there are some + + + align:start position:0% +there are some +a number of cases that really illustrate + + align:start position:0% +a number of cases that really illustrate + + + align:start position:0% +a number of cases that really illustrate +I think + + align:start position:0% +I think + + + align:start position:0% +I think +um the + + align:start position:0% +um the + + + align:start position:0% +um the +the well what you sort of know + + align:start position:0% +the well what you sort of know + + + align:start position:0% +the well what you sort of know +intuitively right the brain isn't here + + align:start position:0% +intuitively right the brain isn't here + + + align:start position:0% +intuitively right the brain isn't here +and the mind is here they're they're + + align:start position:0% +and the mind is here they're they're + + + align:start position:0% +and the mind is here they're they're +they're it's you know waves and + + align:start position:0% +they're it's you know waves and + + + align:start position:0% +they're it's you know waves and +particles they're they're two + + align:start position:0% +particles they're they're two + + + align:start position:0% +particles they're they're two +manifestations of the same thing and + + align:start position:0% +manifestations of the same thing and + + + align:start position:0% +manifestations of the same thing and +brain stuff and mind stuff bounce back + + align:start position:0% +brain stuff and mind stuff bounce back + + + align:start position:0% +brain stuff and mind stuff bounce back +and forth here all the time so let's + + align:start position:0% +and forth here all the time so let's + + + align:start position:0% +and forth here all the time so let's +think for example of panic attacks + + align:start position:0% +think for example of panic attacks + + + align:start position:0% +think for example of panic attacks +um which I didn't put on the handout at + + align:start position:0% +um which I didn't put on the handout at + + + align:start position:0% +um which I didn't put on the handout at +all I see but I suddenly developed a + + align:start position:0% +all I see but I suddenly developed a + + + align:start position:0% +all I see but I suddenly developed a +need to talk about because I was feeling + + align:start position:0% +need to talk about because I was feeling + + + align:start position:0% +need to talk about because I was feeling +really anxious and and and and and no + + align:start position:0% +really anxious and and and and and no + + + align:start position:0% +really anxious and and and and and no +um so panic attack is is this feeling of + + align:start position:0% +um so panic attack is is this feeling of + + + align:start position:0% +um so panic attack is is this feeling of +anxiety + + align:start position:0% +anxiety + + + align:start position:0% +anxiety +out of the blue + + align:start position:0% +out of the blue + + + align:start position:0% +out of the blue +um that uh um you know the the people + + align:start position:0% +um that uh um you know the the people + + + align:start position:0% +um that uh um you know the the people +report that they just suddenly feel very + + align:start position:0% +report that they just suddenly feel very + + + align:start position:0% +report that they just suddenly feel very +very very fearful and anxious + + align:start position:0% +very very fearful and anxious + + + align:start position:0% +very very fearful and anxious +um and and it's scary and it's + + align:start position:0% +um and and it's scary and it's + + + align:start position:0% +um and and it's scary and it's +unpleasant and and and and so on + + align:start position:0% +unpleasant and and and and so on + + + align:start position:0% +unpleasant and and and and so on +um you may recall that that uh Freud and + + align:start position:0% +um you may recall that that uh Freud and + + + align:start position:0% +um you may recall that that uh Freud and +his followers had a perfectly nice + + align:start position:0% +his followers had a perfectly nice + + + align:start position:0% +his followers had a perfectly nice +notion about this which was that anxiety + + align:start position:0% +notion about this which was that anxiety + + + align:start position:0% +notion about this which was that anxiety +was warning you + + align:start position:0% +was warning you + + + align:start position:0% +was warning you +um that uh uh that you were about to + + align:start position:0% +um that uh uh that you were about to + + + align:start position:0% +um that uh uh that you were about to +tread on the super ego and uh it was the + + align:start position:0% +tread on the super ego and uh it was the + + + align:start position:0% +tread on the super ego and uh it was the +warning sign of the ego that that was + + align:start position:0% +warning sign of the ego that that was + + + align:start position:0% +warning sign of the ego that that was +saying don't go and do that but that + + align:start position:0% +saying don't go and do that but that + + + align:start position:0% +saying don't go and do that but that +doesn't work that well + + align:start position:0% + + + + align:start position:0% + +um more modern + + align:start position:0% +um more modern + + + align:start position:0% +um more modern +Notions tend to focus on the idea that + + align:start position:0% +Notions tend to focus on the idea that + + + align:start position:0% +Notions tend to focus on the idea that +it's essentially neurochemical right + + align:start position:0% +it's essentially neurochemical right + + + align:start position:0% +it's essentially neurochemical right +something + + align:start position:0% +something + + + align:start position:0% +something +you get too much of some + + align:start position:0% +you get too much of some + + + align:start position:0% +you get too much of some +juice some neurotransmitter it fires off + + align:start position:0% +juice some neurotransmitter it fires off + + + align:start position:0% +juice some neurotransmitter it fires off +the bits of your brain that are + + align:start position:0% +the bits of your brain that are + + + align:start position:0% +the bits of your brain that are +responsible for the experience of + + align:start position:0% +responsible for the experience of + + + align:start position:0% +responsible for the experience of +anxiety and you feel this anxiety oh you + + align:start position:0% +anxiety and you feel this anxiety oh you + + + align:start position:0% +anxiety and you feel this anxiety oh you +can and this is a lovely case of looping + + align:start position:0% +can and this is a lovely case of looping + + + align:start position:0% +can and this is a lovely case of looping +back to a a a prior mode of uh of + + align:start position:0% +back to a a a prior mode of uh of + + + align:start position:0% +back to a a a prior mode of uh of +understanding the notion that you feel + + align:start position:0% +understanding the notion that you feel + + + align:start position:0% +understanding the notion that you feel +too anxious because you have too much of + + align:start position:0% +too anxious because you have too much of + + + align:start position:0% +too anxious because you have too much of +this fluid it's an awful lot like the + + align:start position:0% +this fluid it's an awful lot like the + + + align:start position:0% +this fluid it's an awful lot like the +notion that you feel melancholic because + + align:start position:0% +notion that you feel melancholic because + + + align:start position:0% +notion that you feel melancholic because +you have too much black bile the + + align:start position:0% +you have too much black bile the + + + align:start position:0% +you have too much black bile the +difference of course is that we think + + align:start position:0% +difference of course is that we think + + + align:start position:0% +difference of course is that we think +we've got a better scientific grounding + + align:start position:0% +we've got a better scientific grounding + + + align:start position:0% +we've got a better scientific grounding +than we had but the form of the argument + + align:start position:0% +than we had but the form of the argument + + + align:start position:0% +than we had but the form of the argument +is um + + align:start position:0% +is um + + + align:start position:0% +is um +is rather similar + + align:start position:0% +is rather similar + + + align:start position:0% +is rather similar +um but so is it the case that panic + + align:start position:0% +um but so is it the case that panic + + + align:start position:0% +um but so is it the case that panic +attacks that the clinical condition of a + + align:start position:0% +attacks that the clinical condition of a + + + align:start position:0% +attacks that the clinical condition of a +panic attack is just + + align:start position:0% +panic attack is just + + + align:start position:0% +panic attack is just +um too much of some some juice it's + + align:start position:0% +um too much of some some juice it's + + + align:start position:0% +um too much of some some juice it's +possible to think about it as as being + + align:start position:0% +possible to think about it as as being + + + align:start position:0% +possible to think about it as as being +uh somewhat more complicated than that + + align:start position:0% +uh somewhat more complicated than that + + + align:start position:0% +uh somewhat more complicated than that +and well I didn't put the reference on + + align:start position:0% +and well I didn't put the reference on + + + align:start position:0% +and well I didn't put the reference on +the handout + + align:start position:0% +the handout + + + align:start position:0% +the handout +um because I didn't and but here here's + + align:start position:0% +um because I didn't and but here here's + + + align:start position:0% +um because I didn't and but here here's +I'm stealing a story from who am I + + align:start position:0% +I'm stealing a story from who am I + + + align:start position:0% +I'm stealing a story from who am I +stealing it from uh oh uh Dave Barlow + + align:start position:0% +stealing it from uh oh uh Dave Barlow + + + align:start position:0% +stealing it from uh oh uh Dave Barlow +over at uh who's over at bu + + align:start position:0% +over at uh who's over at bu + + + align:start position:0% +over at uh who's over at bu +this is a a three-step route into panic + + align:start position:0% +this is a a three-step route into panic + + + align:start position:0% +this is a a three-step route into panic +attack + + align:start position:0% +attack + + + align:start position:0% +attack +um and the the first part of it is that + + align:start position:0% +um and the the first part of it is that + + + align:start position:0% +um and the the first part of it is that +um you feel the visceral symptoms of + + align:start position:0% +um you feel the visceral symptoms of + + + align:start position:0% +um you feel the visceral symptoms of +anxiety what's you know let your heart + + align:start position:0% +anxiety what's you know let your heart + + + align:start position:0% +anxiety what's you know let your heart +starts right remember this remember the + + align:start position:0% +starts right remember this remember the + + + align:start position:0% +starts right remember this remember the +uh the shaky Bridge experiment + + align:start position:0% +uh the shaky Bridge experiment + + + align:start position:0% +uh the shaky Bridge experiment +shaky Bridge experiment it's all about + + align:start position:0% +shaky Bridge experiment it's all about + + + align:start position:0% +shaky Bridge experiment it's all about +misattribution of arousal + + align:start position:0% +misattribution of arousal + + + align:start position:0% +misattribution of arousal +um you're feeling and you see her and + + align:start position:0% +um you're feeling and you see her and + + + align:start position:0% +um you're feeling and you see her and +you just you think you're feeling right + + align:start position:0% +you just you think you're feeling right + + + align:start position:0% +you just you think you're feeling right +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so that can work in all sorts of ways + + align:start position:0% +so that can work in all sorts of ways + + + align:start position:0% +so that can work in all sorts of ways +suppose that your your your heart is + + align:start position:0% +suppose that your your your heart is + + + align:start position:0% +suppose that your your your heart is +going through there are a variety of + + align:start position:0% +going through there are a variety of + + + align:start position:0% +going through there are a variety of +things that cause your heart to to go + + align:start position:0% +things that cause your heart to to go + + + align:start position:0% +things that cause your heart to to go +pitter Pat + + align:start position:0% +pitter Pat + + + align:start position:0% +pitter Pat +um suppose that you get the um these + + align:start position:0% +um suppose that you get the um these + + + align:start position:0% +um suppose that you get the um these +sort of symptoms and you don't interpret + + align:start position:0% +sort of symptoms and you don't interpret + + + align:start position:0% +sort of symptoms and you don't interpret +it as love you interpret it as I I feel + + align:start position:0% +it as love you interpret it as I I feel + + + align:start position:0% +it as love you interpret it as I I feel +nervous about something I can't quite + + align:start position:0% +nervous about something I can't quite + + + align:start position:0% +nervous about something I can't quite +tell + + align:start position:0% +tell + + + align:start position:0% +tell +um exactly what it is but but I don't + + align:start position:0% +um exactly what it is but but I don't + + + align:start position:0% +um exactly what it is but but I don't +people don't have panic attacks by the + + align:start position:0% +people don't have panic attacks by the + + + align:start position:0% +people don't have panic attacks by the +way typically when they're exercising + + align:start position:0% +way typically when they're exercising + + + align:start position:0% +way typically when they're exercising +vigorously because they've got a good + + align:start position:0% +vigorously because they've got a good + + + align:start position:0% +vigorously because they've got a good +account of where that that symptom is + + align:start position:0% +account of where that that symptom is + + + align:start position:0% +account of where that that symptom is +coming from your heart's pounding you're + + align:start position:0% +coming from your heart's pounding you're + + + align:start position:0% +coming from your heart's pounding you're +sweating and stuff like that yeah all + + align:start position:0% +sweating and stuff like that yeah all + + + align:start position:0% +sweating and stuff like that yeah all +right fine if you're walking down the + + align:start position:0% +right fine if you're walking down the + + + align:start position:0% +right fine if you're walking down the +street and your heart's pounding and + + align:start position:0% +street and your heart's pounding and + + + align:start position:0% +street and your heart's pounding and +you're you're sweating you need a + + align:start position:0% +you're you're sweating you need a + + + align:start position:0% +you're you're sweating you need a +different uh you need a different + + align:start position:0% +different uh you need a different + + + align:start position:0% +different uh you need a different +interpretation + + align:start position:0% +interpretation + + + align:start position:0% +interpretation +um now this is unpleasant + + align:start position:0% +um now this is unpleasant + + + align:start position:0% +um now this is unpleasant +so you develop + + align:start position:0% +so you develop + + + align:start position:0% +so you develop +um flipping back to an earlier piece of + + align:start position:0% +um flipping back to an earlier piece of + + + align:start position:0% +um flipping back to an earlier piece of +the course you can you develop a + + align:start position:0% +the course you can you develop a + + + align:start position:0% +the course you can you develop a +conditioned fear of + + align:start position:0% +conditioned fear of + + + align:start position:0% +conditioned fear of +um these symptoms so you start avoiding + + align:start position:0% +um these symptoms so you start avoiding + + + align:start position:0% +um these symptoms so you start avoiding +situations that would produce the um + + align:start position:0% +situations that would produce the um + + + align:start position:0% +situations that would produce the um +uh the the the the situation the uh the + + align:start position:0% +uh the the the the situation the uh the + + + align:start position:0% +uh the the the the situation the uh the +symptoms or that you think might produce + + align:start position:0% +symptoms or that you think might produce + + + align:start position:0% +symptoms or that you think might produce +these symptoms + + align:start position:0% +these symptoms + + + align:start position:0% +these symptoms +um and this can be quite unconscious + + align:start position:0% +um and this can be quite unconscious + + + align:start position:0% +um and this can be quite unconscious +right this is this this is good + + align:start position:0% +right this is this this is good + + + align:start position:0% +right this is this this is good +classical Association uh learning or + + align:start position:0% +classical Association uh learning or + + + align:start position:0% +classical Association uh learning or +something of that sort + + align:start position:0% +something of that sort + + + align:start position:0% +something of that sort +um and that in turns that sort of step + + align:start position:0% +um and that in turns that sort of step + + + align:start position:0% +um and that in turns that sort of step +two is is sort of a learning story that + + align:start position:0% +two is is sort of a learning story that + + + align:start position:0% +two is is sort of a learning story that +is going to cause you to + + align:start position:0% +is going to cause you to + + + align:start position:0% +is going to cause you to +um + + align:start position:0% +um + + + align:start position:0% +um +start uh you're going to act to avoid + + align:start position:0% +start uh you're going to act to avoid + + + align:start position:0% +start uh you're going to act to avoid +situations that that make you feel + + align:start position:0% +situations that that make you feel + + + align:start position:0% +situations that that make you feel +um nervous + + align:start position:0% +um nervous + + + align:start position:0% +um nervous +um but all right remember remember + + align:start position:0% +um but all right remember remember + + + align:start position:0% +um but all right remember remember +Pavlov + + align:start position:0% +Pavlov + + + align:start position:0% +Pavlov +Beltone Beltone bell tone now I ring the + + align:start position:0% +Beltone Beltone bell tone now I ring the + + + align:start position:0% +Beltone Beltone bell tone now I ring the +bell by itself no bell tone that's + + align:start position:0% +bell by itself no bell tone that's + + + align:start position:0% +bell by itself no bell tone that's +stupid + + align:start position:0% + + + + align:start position:0% + +I'm not supposed to be the one who + + align:start position:0% +I'm not supposed to be the one who + + + align:start position:0% +I'm not supposed to be the one who +notices that first guys you're supposed + + align:start position:0% +notices that first guys you're supposed + + + align:start position:0% +notices that first guys you're supposed +to what's he talking about anyway Bell + + align:start position:0% +to what's he talking about anyway Bell + + + align:start position:0% +to what's he talking about anyway Bell +food Bell food Bell food eventually the + + align:start position:0% +food Bell food Bell food eventually the + + + align:start position:0% +food Bell food Bell food eventually the +Bell by itself produces salivation so + + align:start position:0% +Bell by itself produces salivation so + + + align:start position:0% +Bell by itself produces salivation so +you make this Association in your own + + align:start position:0% +you make this Association in your own + + + align:start position:0% +you make this Association in your own +mind + + align:start position:0% +mind + + + align:start position:0% +mind +um so outside I went when did this + + align:start position:0% +um so outside I went when did this + + + align:start position:0% +um so outside I went when did this +happen to me I was outside okay so now + + align:start position:0% +happen to me I was outside okay so now + + + align:start position:0% +happen to me I was outside okay so now +I'm outside it doesn't happen to me but + + align:start position:0% +I'm outside it doesn't happen to me but + + + align:start position:0% +I'm outside it doesn't happen to me but +I feel I get the the conditioned + + align:start position:0% +I feel I get the the conditioned + + + align:start position:0% +I feel I get the the conditioned +response in effect so now something else + + align:start position:0% +response in effect so now something else + + + align:start position:0% +response in effect so now something else +acts as a trigger for the Panic the + + align:start position:0% +acts as a trigger for the Panic the + + + align:start position:0% +acts as a trigger for the Panic the +initial Panic feeling of panic might + + align:start position:0% +initial Panic feeling of panic might + + + align:start position:0% +initial Panic feeling of panic might +have been I don't know too many uh the + + align:start position:0% +have been I don't know too many uh the + + + align:start position:0% +have been I don't know too many uh the +bottles of of Mountain Dew right you + + align:start position:0% +bottles of of Mountain Dew right you + + + align:start position:0% +bottles of of Mountain Dew right you +drink enough caffeine and you'll get + + align:start position:0% +drink enough caffeine and you'll get + + + align:start position:0% +drink enough caffeine and you'll get +forget that you drank the cat yeah so + + align:start position:0% +forget that you drank the cat yeah so + + + align:start position:0% +forget that you drank the cat yeah so +sometimes your brain doesn't remember + + align:start position:0% +sometimes your brain doesn't remember + + + align:start position:0% +sometimes your brain doesn't remember +the caffeine part of the story and + + align:start position:0% +the caffeine part of the story and + + + align:start position:0% +the caffeine part of the story and +you're going and you say oh I'm having a + + align:start position:0% +you're going and you say oh I'm having a + + + align:start position:0% +you're going and you say oh I'm having a +panic attack then + + align:start position:0% +panic attack then + + + align:start position:0% +panic attack then +you don't want that to happen this is an + + align:start position:0% +you don't want that to happen this is an + + + align:start position:0% +you don't want that to happen this is an +aversive event just just like the + + align:start position:0% +aversive event just just like the + + + align:start position:0% +aversive event just just like the +business of the Rat stepping down right + + align:start position:0% +business of the Rat stepping down right + + + align:start position:0% +business of the Rat stepping down right +the rat steps down + + align:start position:0% +the rat steps down + + + align:start position:0% +the rat steps down +up all right rats up here rat steps down + + align:start position:0% +up all right rats up here rat steps down + + + align:start position:0% +up all right rats up here rat steps down +gets his little feet shocked + + align:start position:0% +gets his little feet shocked + + + align:start position:0% +gets his little feet shocked +that's unpleasant rats put back up here + + align:start position:0% +that's unpleasant rats put back up here + + + align:start position:0% +that's unpleasant rats put back up here +does the rats step down again no why + + align:start position:0% +does the rats step down again no why + + + align:start position:0% +does the rats step down again no why +because he's got this anticipatory fear + + align:start position:0% +because he's got this anticipatory fear + + + align:start position:0% +because he's got this anticipatory fear +you can actually measure Theory + + align:start position:0% +you can actually measure Theory + + + align:start position:0% +you can actually measure Theory +physiologically all right so yeah yeah + + align:start position:0% +physiologically all right so yeah yeah + + + align:start position:0% +physiologically all right so yeah yeah +yeah caffeine overdose or whatever you + + align:start position:0% +yeah caffeine overdose or whatever you + + + align:start position:0% +yeah caffeine overdose or whatever you +have this unpleasant experience now + + align:start position:0% +have this unpleasant experience now + + + align:start position:0% +have this unpleasant experience now +you're in that environment again + + align:start position:0% +you're in that environment again + + + align:start position:0% +you're in that environment again +sometime later and you have the + + align:start position:0% +sometime later and you have the + + + align:start position:0% +sometime later and you have the +experience again because it's a + + align:start position:0% +experience again because it's a + + + align:start position:0% +experience again because it's a +conditioned response now no caffeine + + align:start position:0% +conditioned response now no caffeine + + + align:start position:0% +conditioned response now no caffeine +involved you come to the reasonable uh + + align:start position:0% +involved you come to the reasonable uh + + + align:start position:0% +involved you come to the reasonable uh +if perhaps unconscious conclusion that + + align:start position:0% +if perhaps unconscious conclusion that + + + align:start position:0% +if perhaps unconscious conclusion that +what makes me nervous is is is being + + align:start position:0% +what makes me nervous is is is being + + + align:start position:0% +what makes me nervous is is is being +outside in public and or being on shaky + + align:start position:0% +outside in public and or being on shaky + + + align:start position:0% +outside in public and or being on shaky +Bridges or or whatever then you get step + + align:start position:0% +Bridges or or whatever then you get step + + + align:start position:0% +Bridges or or whatever then you get step +three which is again learning theory + + align:start position:0% +three which is again learning theory + + + align:start position:0% +three which is again learning theory +kind of stuff like thorndike's law of + + align:start position:0% +kind of stuff like thorndike's law of + + + align:start position:0% +kind of stuff like thorndike's law of +effect you start doing things to avoid + + align:start position:0% +effect you start doing things to avoid + + + align:start position:0% +effect you start doing things to avoid +this + + align:start position:0% +this + + + align:start position:0% +this +um uh this punishment + + align:start position:0% +um uh this punishment + + + align:start position:0% +um uh this punishment +right you're going to avoid the aversive + + align:start position:0% +right you're going to avoid the aversive + + + align:start position:0% +right you're going to avoid the aversive +stimulus so you can get secondary + + align:start position:0% +stimulus so you can get secondary + + + align:start position:0% +stimulus so you can get secondary +symptoms to the Panic like a fear of + + align:start position:0% +symptoms to the Panic like a fear of + + + align:start position:0% +symptoms to the Panic like a fear of +Open Spaces let's say because you've now + + align:start position:0% +Open Spaces let's say because you've now + + + align:start position:0% +Open Spaces let's say because you've now +perhaps completely unconsciously + + align:start position:0% +perhaps completely unconsciously + + + align:start position:0% +perhaps completely unconsciously +concluded if I go out in public you know + + align:start position:0% +concluded if I go out in public you know + + + align:start position:0% +concluded if I go out in public you know +with the sky is so big I feel so small I + + align:start position:0% +with the sky is so big I feel so small I + + + align:start position:0% +with the sky is so big I feel so small I +get panicky and and and so I'm not gonna + + align:start position:0% +get panicky and and and so I'm not gonna + + + align:start position:0% +get panicky and and and so I'm not gonna +go outside and so what you end up with + + align:start position:0% +go outside and so what you end up with + + + align:start position:0% +go outside and so what you end up with +is the possibility that the clinical + + align:start position:0% +is the possibility that the clinical + + + align:start position:0% +is the possibility that the clinical +thing that you see what you get in your + + align:start position:0% +thing that you see what you get in your + + + align:start position:0% +thing that you see what you get in your +office if you're the clinician is + + align:start position:0% +office if you're the clinician is + + + align:start position:0% +office if you're the clinician is +somebody who says I have you know I I + + align:start position:0% +somebody who says I have you know I I + + + align:start position:0% +somebody who says I have you know I I +have uncontrollable panic when I'm out + + align:start position:0% +have uncontrollable panic when I'm out + + + align:start position:0% +have uncontrollable panic when I'm out +Outdoors this is this is crippling my + + align:start position:0% +Outdoors this is this is crippling my + + + align:start position:0% +Outdoors this is this is crippling my +life because I don't go out anymore and + + align:start position:0% +life because I don't go out anymore and + + + align:start position:0% +life because I don't go out anymore and +what this may be is a Cascade of events + + align:start position:0% +what this may be is a Cascade of events + + + align:start position:0% +what this may be is a Cascade of events +coming from some sort of an initial + + align:start position:0% +coming from some sort of an initial + + + align:start position:0% +coming from some sort of an initial +physiological issue that you then + + align:start position:0% +physiological issue that you then + + + align:start position:0% +physiological issue that you then +learned about if you like in the using + + align:start position:0% +learned about if you like in the using + + + align:start position:0% +learned about if you like in the using +the laws of sort of animal learning in + + align:start position:0% +the laws of sort of animal learning in + + + align:start position:0% +the laws of sort of animal learning in +ways that uh that that don't work well + + align:start position:0% +ways that uh that that don't work well + + + align:start position:0% +ways that uh that that don't work well +well what are you gonna do about it well + + align:start position:0% +well what are you gonna do about it well + + + align:start position:0% +well what are you gonna do about it well +one thing you might do about it if you + + align:start position:0% +one thing you might do about it if you + + + align:start position:0% +one thing you might do about it if you +believed that there was a significant + + align:start position:0% +believed that there was a significant + + + align:start position:0% +believed that there was a significant +learning component here + + align:start position:0% +learning component here + + + align:start position:0% +learning component here +is to use learning theory kinds of + + align:start position:0% +is to use learning theory kinds of + + + align:start position:0% +is to use learning theory kinds of +things to treat it + + align:start position:0% +things to treat it + + + align:start position:0% +things to treat it +now if it turns out that that there + + align:start position:0% +now if it turns out that that there + + + align:start position:0% +now if it turns out that that there +really is a chemical imbalance and every + + align:start position:0% +really is a chemical imbalance and every + + + align:start position:0% +really is a chemical imbalance and every +time the chemicals go out of whack + + align:start position:0% +time the chemicals go out of whack + + + align:start position:0% +time the chemicals go out of whack +um you feel panicked you might want to + + align:start position:0% +um you feel panicked you might want to + + + align:start position:0% +um you feel panicked you might want to +do something about the chemicals but if + + align:start position:0% +do something about the chemicals but if + + + align:start position:0% +do something about the chemicals but if +you've got one of these situations where + + align:start position:0% +you've got one of these situations where + + + align:start position:0% +you've got one of these situations where +the person has basically scared + + align:start position:0% +the person has basically scared + + + align:start position:0% +the person has basically scared +themselves into maladaptive Behavior + + align:start position:0% +themselves into maladaptive Behavior + + + align:start position:0% +themselves into maladaptive Behavior +you've now got to unscare them so what + + align:start position:0% +you've now got to unscare them so what + + + align:start position:0% +you've now got to unscare them so what +are you going to do one of the standard + + align:start position:0% +are you going to do one of the standard + + + align:start position:0% +are you going to do one of the standard +techniques for these sort of disorders + + align:start position:0% +techniques for these sort of disorders + + + align:start position:0% +techniques for these sort of disorders +would be + + align:start position:0% +would be + + + align:start position:0% +would be +desensitization methods said Barlow who + + align:start position:0% +desensitization methods said Barlow who + + + align:start position:0% +desensitization methods said Barlow who +was doing this + + align:start position:0% + + + + align:start position:0% + +people those are one of the versions you + + align:start position:0% +people those are one of the versions you + + + align:start position:0% +people those are one of the versions you +can imagine I I did a version where you + + align:start position:0% +can imagine I I did a version where you + + + align:start position:0% +can imagine I I did a version where you +became scared at the outside and other + + align:start position:0% +became scared at the outside and other + + + align:start position:0% +became scared at the outside and other +versions you have a a panic attack in an + + align:start position:0% +versions you have a a panic attack in an + + + align:start position:0% +versions you have a a panic attack in an +enclosed space and you become very + + align:start position:0% +enclosed space and you become very + + + align:start position:0% +enclosed space and you become very +nervous about enclosed spaces you won't + + align:start position:0% +nervous about enclosed spaces you won't + + + align:start position:0% +nervous about enclosed spaces you won't +go into elevators and stuff like that + + align:start position:0% +go into elevators and stuff like that + + + align:start position:0% +go into elevators and stuff like that +I'm not I can't remember if it was + + align:start position:0% +I'm not I can't remember if it was + + + align:start position:0% +I'm not I can't remember if it was +Barlow + + align:start position:0% +Barlow + + + align:start position:0% +Barlow +I got a feeling it was whose technique + + align:start position:0% +I got a feeling it was whose technique + + + align:start position:0% +I got a feeling it was whose technique +for the the so there are a variety of + + align:start position:0% +for the the so there are a variety of + + + align:start position:0% +for the the so there are a variety of +ways of of using learning theory to to + + align:start position:0% +ways of of using learning theory to to + + + align:start position:0% +ways of of using learning theory to to +to get around this one is to sort of the + + align:start position:0% +to get around this one is to sort of the + + + align:start position:0% +to get around this one is to sort of the +Kinder gentler one so you come to me you + + align:start position:0% +Kinder gentler one so you come to me you + + + align:start position:0% +Kinder gentler one so you come to me you +say I'm really afraid of being in + + align:start position:0% +say I'm really afraid of being in + + + align:start position:0% +say I'm really afraid of being in +enclosed spaces you say okay let's we'll + + align:start position:0% +enclosed spaces you say okay let's we'll + + + align:start position:0% +enclosed spaces you say okay let's we'll +we'll we'll we'll we'll first hear and + + align:start position:0% +we'll we'll we'll we'll first hear and + + + align:start position:0% +we'll we'll we'll we'll first hear and +out in this field that you've come to + + align:start position:0% +out in this field that you've come to + + + align:start position:0% +out in this field that you've come to +and that I'm using for my doctor's + + align:start position:0% +and that I'm using for my doctor's + + + align:start position:0% +and that I'm using for my doctor's +office at the moment + + align:start position:0% +office at the moment + + + align:start position:0% +office at the moment +um imagine that you're in a space can + + align:start position:0% +um imagine that you're in a space can + + + align:start position:0% +um imagine that you're in a space can +you deal with that uh oh it's making me + + align:start position:0% +you deal with that uh oh it's making me + + + align:start position:0% +you deal with that uh oh it's making me +nervous but but yeah okay I can deal + + align:start position:0% +nervous but but yeah okay I can deal + + + align:start position:0% +nervous but but yeah okay I can deal +with that okay now we'll go to 10 to 50. + + align:start position:0% +with that okay now we'll go to 10 to 50. + + + align:start position:0% +with that okay now we'll go to 10 to 50. +it's a big enclosed space and then we'll + + align:start position:0% +it's a big enclosed space and then we'll + + + align:start position:0% +it's a big enclosed space and then we'll +go to a smaller room in a small room and + + align:start position:0% +go to a smaller room in a small room and + + + align:start position:0% +go to a smaller room in a small room and +eventually we'll we'll put you in in a + + align:start position:0% +eventually we'll we'll put you in in a + + + align:start position:0% +eventually we'll we'll put you in in a +uh a closet for a while and you'll + + align:start position:0% +uh a closet for a while and you'll + + + align:start position:0% +uh a closet for a while and you'll +discover what you'll do is unlearn the + + align:start position:0% +discover what you'll do is unlearn the + + + align:start position:0% +discover what you'll do is unlearn the +response in effect you'll learn nothing + + align:start position:0% +response in effect you'll learn nothing + + + align:start position:0% +response in effect you'll learn nothing +bad happened to me + + align:start position:0% +bad happened to me + + + align:start position:0% +bad happened to me +and this this behaviorist sort of + + align:start position:0% +and this this behaviorist sort of + + + align:start position:0% +and this this behaviorist sort of +therapy does work to break up these + + align:start position:0% +therapy does work to break up these + + + align:start position:0% +therapy does work to break up these +sorts of behaviors in in many cases + + align:start position:0% +sorts of behaviors in in many cases + + + align:start position:0% +sorts of behaviors in in many cases +um I think it's Barlow who uh has been + + align:start position:0% +um I think it's Barlow who uh has been + + + align:start position:0% +um I think it's Barlow who uh has been +advocating a much less Kinder gentler + + align:start position:0% +advocating a much less Kinder gentler + + + align:start position:0% +advocating a much less Kinder gentler +version which is to shut people in car + + align:start position:0% +version which is to shut people in car + + + align:start position:0% +version which is to shut people in car +trunks + + align:start position:0% +trunks + + + align:start position:0% +trunks +um that uh right so none of this + + align:start position:0% +um that uh right so none of this + + + align:start position:0% +um that uh right so none of this +business of doing it gradually this is + + align:start position:0% +business of doing it gradually this is + + + align:start position:0% +business of doing it gradually this is +known in the trade as flooding you just + + align:start position:0% +known in the trade as flooding you just + + + align:start position:0% +known in the trade as flooding you just +take the pre the guy says you know I I + + align:start position:0% +take the pre the guy says you know I I + + + align:start position:0% +take the pre the guy says you know I I +think if if I'm in an enclosed space I'm + + align:start position:0% +think if if I'm in an enclosed space I'm + + + align:start position:0% +think if if I'm in an enclosed space I'm +gonna die all right + + align:start position:0% +gonna die all right + + + align:start position:0% +gonna die all right +you dead yet no okay you're cured good + + align:start position:0% +you dead yet no okay you're cured good + + + align:start position:0% +you dead yet no okay you're cured good +out well it's not quite that simple but + + align:start position:0% +out well it's not quite that simple but + + + align:start position:0% +out well it's not quite that simple but +the the basic idea is that um + + align:start position:0% +the the basic idea is that um + + + align:start position:0% +the the basic idea is that um +if you have a patient who can actually + + align:start position:0% +if you have a patient who can actually + + + align:start position:0% +if you have a patient who can actually +deal with this that that you can + + align:start position:0% +deal with this that that you can + + + align:start position:0% +deal with this that that you can +um basically speed up the therapy rather + + align:start position:0% +um basically speed up the therapy rather + + + align:start position:0% +um basically speed up the therapy rather +dramatically by not moving gradually to + + align:start position:0% +dramatically by not moving gradually to + + + align:start position:0% +dramatically by not moving gradually to +uh this is this is used for all sorts of + + align:start position:0% +uh this is this is used for all sorts of + + + align:start position:0% +uh this is this is used for all sorts of +uh phobias so uh scared of snakes you + + align:start position:0% +uh phobias so uh scared of snakes you + + + align:start position:0% +uh phobias so uh scared of snakes you +know you're pathologically scared of + + align:start position:0% +know you're pathologically scared of + + + align:start position:0% +know you're pathologically scared of +snakes Okay what we'll do is first we'll + + align:start position:0% +snakes Okay what we'll do is first we'll + + + align:start position:0% +snakes Okay what we'll do is first we'll +show you so the two versions are + + align:start position:0% +show you so the two versions are + + + align:start position:0% +show you so the two versions are +desensitization and flooding the + + align:start position:0% +desensitization and flooding the + + + align:start position:0% +desensitization and flooding the +desensitization story would be we'll + + align:start position:0% +desensitization story would be we'll + + + align:start position:0% +desensitization story would be we'll +show you pictures of snakes are you dead + + align:start position:0% +show you pictures of snakes are you dead + + + align:start position:0% +show you pictures of snakes are you dead +no okay + + align:start position:0% +no okay + + + align:start position:0% +no okay +um so now now we'll uh now we'll go to + + align:start position:0% +um so now now we'll uh now we'll go to + + + align:start position:0% +um so now now we'll uh now we'll go to +the zoo and see that snake age way over + + align:start position:0% +the zoo and see that snake age way over + + + align:start position:0% +the zoo and see that snake age way over +there you dead yet no okay let's get + + align:start position:0% +there you dead yet no okay let's get + + + align:start position:0% +there you dead yet no okay let's get +closer okay that's a snake right okay + + align:start position:0% +closer okay that's a snake right okay + + + align:start position:0% +closer okay that's a snake right okay +now you're gonna get in with them yeah + + align:start position:0% +now you're gonna get in with them yeah + + + align:start position:0% +now you're gonna get in with them yeah +oh all right but I'm not dead + + align:start position:0% +oh all right but I'm not dead + + + align:start position:0% +oh all right but I'm not dead +um and and the flooding technique is + + align:start position:0% +um and and the flooding technique is + + + align:start position:0% +um and and the flooding technique is +you're afraid of snakes + + align:start position:0% +you're afraid of snakes + + + align:start position:0% +you're afraid of snakes +see those bullets are you dead Yes + + align:start position:0% +see those bullets are you dead Yes + + + align:start position:0% +see those bullets are you dead Yes +actually + + align:start position:0% + + + + align:start position:0% + +um so anyway + + align:start position:0% + + + + align:start position:0% + +that the the point from the panic attack + + align:start position:0% +that the the point from the panic attack + + + align:start position:0% +that the the point from the panic attack +example is that it's possible that what + + align:start position:0% +example is that it's possible that what + + + align:start position:0% +example is that it's possible that what +you're seeing is the clinical entity is + + align:start position:0% +you're seeing is the clinical entity is + + + align:start position:0% +you're seeing is the clinical entity is +a dance between physiology and + + align:start position:0% +a dance between physiology and + + + align:start position:0% +a dance between physiology and +um uh and learning in effect and that + + align:start position:0% +um uh and learning in effect and that + + + align:start position:0% +um uh and learning in effect and that +what you learn uh and and that emotive + + align:start position:0% +what you learn uh and and that emotive + + + align:start position:0% +what you learn uh and and that emotive +treatment would be to unlearn + + align:start position:0% +treatment would be to unlearn + + + align:start position:0% +treatment would be to unlearn +um + + align:start position:0% +um + + + align:start position:0% +um +now let's take another example which I + + align:start position:0% +now let's take another example which I + + + align:start position:0% +now let's take another example which I +did put on the handout which is + + align:start position:0% +did put on the handout which is + + + align:start position:0% +did put on the handout which is +obsessive compulsive disorders + + align:start position:0% +obsessive compulsive disorders + + + align:start position:0% +obsessive compulsive disorders +um + + align:start position:0% +um + + + align:start position:0% +um +obsessive-compulsive disorders are um + + align:start position:0% +obsessive-compulsive disorders are um + + + align:start position:0% +obsessive-compulsive disorders are um +are are well there's the obsessive part + + align:start position:0% +are are well there's the obsessive part + + + align:start position:0% +are are well there's the obsessive part +and there's uh the the compulsive part + + align:start position:0% +and there's uh the the compulsive part + + + align:start position:0% +and there's uh the the compulsive part +obsessive the obsessive part refers to + + align:start position:0% +obsessive the obsessive part refers to + + + align:start position:0% +obsessive the obsessive part refers to +obsessive thoughts if you what gets you + + align:start position:0% +obsessive thoughts if you what gets you + + + align:start position:0% +obsessive thoughts if you what gets you +into uh + + align:start position:0% +into uh + + + align:start position:0% +into uh +um treatment is not some sort of + + align:start position:0% +um treatment is not some sort of + + + align:start position:0% +um treatment is not some sort of +obsessive thought that + + align:start position:0% +obsessive thought that + + + align:start position:0% +obsessive thought that +I love him I really love him oh I love + + align:start position:0% +I love him I really love him oh I love + + + align:start position:0% +I love him I really love him oh I love +him a lot oh yeah yeah yeah I can't help + + align:start position:0% +him a lot oh yeah yeah yeah I can't help + + + align:start position:0% +him a lot oh yeah yeah yeah I can't help +but think about him yeah it's a little + + align:start position:0% +but think about him yeah it's a little + + + align:start position:0% +but think about him yeah it's a little +obsessive but tough + + align:start position:0% +obsessive but tough + + + align:start position:0% +obsessive but tough +um it's every time I look at him I want + + align:start position:0% +um it's every time I look at him I want + + + align:start position:0% +um it's every time I look at him I want +to rip his guts out I'm imagining the + + align:start position:0% +to rip his guts out I'm imagining the + + + align:start position:0% +to rip his guts out I'm imagining the +knife you know or something yeah and + + align:start position:0% +knife you know or something yeah and + + + align:start position:0% +knife you know or something yeah and +yeah it's disturbing thoughts that + + align:start position:0% +yeah it's disturbing thoughts that + + + align:start position:0% +yeah it's disturbing thoughts that +somehow won't get out of your brain + + align:start position:0% +somehow won't get out of your brain + + + align:start position:0% +somehow won't get out of your brain +that's the that's the sort of obsession + + align:start position:0% +that's the that's the sort of obsession + + + align:start position:0% +that's the that's the sort of obsession +that people uh seek treatment for and + + align:start position:0% +that people uh seek treatment for and + + + align:start position:0% +that people uh seek treatment for and +compulsive behaviors are + + align:start position:0% +compulsive behaviors are + + + align:start position:0% +compulsive behaviors are +um behaviors where well everybody has + + align:start position:0% +um behaviors where well everybody has + + + align:start position:0% +um behaviors where well everybody has +some degree of this how many people here + + align:start position:0% +some degree of this how many people here + + + align:start position:0% +some degree of this how many people here +have left their uh their room gotten + + align:start position:0% +have left their uh their room gotten + + + align:start position:0% +have left their uh their room gotten +halfway down the hall said did I really + + align:start position:0% +halfway down the hall said did I really + + + align:start position:0% +halfway down the hall said did I really +lock it + + align:start position:0% +lock it + + + align:start position:0% +lock it +and gone back to check + + align:start position:0% +and gone back to check + + + align:start position:0% +and gone back to check +everybody does that sometime or did I + + align:start position:0% +everybody does that sometime or did I + + + align:start position:0% +everybody does that sometime or did I +turn the stove off or something like + + align:start position:0% +turn the stove off or something like + + + align:start position:0% +turn the stove off or something like +that that's you know okay that's normal + + align:start position:0% +that that's you know okay that's normal + + + align:start position:0% +that that's you know okay that's normal +on compulsion land and and almost always + + align:start position:0% +on compulsion land and and almost always + + + align:start position:0% +on compulsion land and and almost always +you have locked it right because the + + align:start position:0% +you have locked it right because the + + + align:start position:0% +you have locked it right because the +time you didn't lock it is the time you + + align:start position:0% +time you didn't lock it is the time you + + + align:start position:0% +time you didn't lock it is the time you +don't go back to check and somebody + + align:start position:0% +don't go back to check and somebody + + + align:start position:0% +don't go back to check and somebody +steals all your stuff very annoying I + + align:start position:0% +steals all your stuff very annoying I + + + align:start position:0% +steals all your stuff very annoying I +donated a laptop to the criminal + + align:start position:0% +donated a laptop to the criminal + + + align:start position:0% +donated a laptop to the criminal +elements + + align:start position:0% +elements + + + align:start position:0% +elements +um doing exactly that very annoying um + + align:start position:0% +um doing exactly that very annoying um + + + align:start position:0% +um doing exactly that very annoying um +but anyway if you have to go if you get + + align:start position:0% +but anyway if you have to go if you get + + + align:start position:0% +but anyway if you have to go if you get +if you have to go and + + align:start position:0% +if you have to go and + + + align:start position:0% +if you have to go and +um + + align:start position:0% +um + + + align:start position:0% +um +you know get down the hall did I lock it + + align:start position:0% +you know get down the hall did I lock it + + + align:start position:0% +you know get down the hall did I lock it +yeah yep it's locked + + align:start position:0% +yeah yep it's locked + + + align:start position:0% +yeah yep it's locked +did I lock it + + align:start position:0% +did I lock it + + + align:start position:0% +did I lock it +you got to do that 40 or 50 times + + align:start position:0% +you got to do that 40 or 50 times + + + align:start position:0% +you got to do that 40 or 50 times +and you're you know you can't get on + + align:start position:0% +and you're you know you can't get on + + + align:start position:0% +and you're you know you can't get on +with your light literally you can't get + + align:start position:0% +with your light literally you can't get + + + align:start position:0% +with your light literally you can't get +to the next event in your life that's a + + align:start position:0% +to the next event in your life that's a + + + align:start position:0% +to the next event in your life that's a +compulsion that that is likely to lead + + align:start position:0% +compulsion that that is likely to lead + + + align:start position:0% +compulsion that that is likely to lead +you to to uh want to do something about + + align:start position:0% +you to to uh want to do something about + + + align:start position:0% +you to to uh want to do something about +it + + align:start position:0% +it + + + align:start position:0% +it +um it's interesting that the + + align:start position:0% + + + + align:start position:0% + +SE in people's uh narrative dreams that + + align:start position:0% +SE in people's uh narrative dreams that + + + align:start position:0% +SE in people's uh narrative dreams that +that compulsions seem to be drawn from a + + align:start position:0% +that compulsions seem to be drawn from a + + + align:start position:0% +that compulsions seem to be drawn from a +limited uh vocabulary of candidate + + align:start position:0% +limited uh vocabulary of candidate + + + align:start position:0% +limited uh vocabulary of candidate +compulsions I mean I'm sure there's one + + align:start position:0% +compulsions I mean I'm sure there's one + + + align:start position:0% +compulsions I mean I'm sure there's one +of everything out there but there's lots + + align:start position:0% +of everything out there but there's lots + + + align:start position:0% +of everything out there but there's lots +of hand washers + + align:start position:0% +of hand washers + + + align:start position:0% +of hand washers +right that you know my hand actually I + + align:start position:0% +right that you know my hand actually I + + + align:start position:0% +right that you know my hand actually I +can see my hands are covered in in chalk + + align:start position:0% +can see my hands are covered in in chalk + + + align:start position:0% +can see my hands are covered in in chalk +at the moment I should go watch them but + + align:start position:0% +at the moment I should go watch them but + + + align:start position:0% +at the moment I should go watch them but +you know why do you wash your hands + + align:start position:0% + + + + align:start position:0% + +because your mother said so right and + + align:start position:0% +because your mother said so right and + + + align:start position:0% +because your mother said so right and +because there's germs on them can you + + align:start position:0% +because there's germs on them can you + + + align:start position:0% +because there's germs on them can you +see the germs + + align:start position:0% +see the germs + + + align:start position:0% +see the germs +no so you got to do the act and convince + + align:start position:0% +no so you got to do the act and convince + + + align:start position:0% +no so you got to do the act and convince +yourself that you've done it + + align:start position:0% +yourself that you've done it + + + align:start position:0% +yourself that you've done it +yeah okay + + align:start position:0% + + + + align:start position:0% + +they're really clean + + align:start position:0% +they're really clean + + + align:start position:0% +they're really clean +I can't tell because there might be + + align:start position:0% +I can't tell because there might be + + + align:start position:0% +I can't tell because there might be +germs there aren't going to get sick + + align:start position:0% +germs there aren't going to get sick + + + align:start position:0% +germs there aren't going to get sick +I'll wash them again if you have to do + + align:start position:0% +I'll wash them again if you have to do + + + align:start position:0% +I'll wash them again if you have to do +this so often that your hands are + + align:start position:0% +this so often that your hands are + + + align:start position:0% +this so often that your hands are +getting red and raw + + align:start position:0% +getting red and raw + + + align:start position:0% +getting red and raw +you're probably + + align:start position:0% +you're probably + + + align:start position:0% +you're probably +um yeah that that that's that's a a + + align:start position:0% +um yeah that that that's that's a a + + + align:start position:0% +um yeah that that that's that's a a +compulsion + + align:start position:0% +compulsion + + + align:start position:0% +compulsion +of some sort now you can treat + + align:start position:0% +of some sort now you can treat + + + align:start position:0% +of some sort now you can treat +uh OCD as it's known in the trade in + + align:start position:0% +uh OCD as it's known in the trade in + + + align:start position:0% +uh OCD as it's known in the trade in +another + + align:start position:0% +another + + + align:start position:0% +another +for example that Prozac + + align:start position:0% +for example that Prozac + + + align:start position:0% +for example that Prozac +um is is good against + + align:start position:0% +um is is good against + + + align:start position:0% +um is is good against +um obsessive compulsive disorders it + + align:start position:0% +um obsessive compulsive disorders it + + + align:start position:0% +um obsessive compulsive disorders it +breaks up the obsession you know the + + align:start position:0% +breaks up the obsession you know the + + + align:start position:0% +breaks up the obsession you know the +obsessive quality here of of this sort + + align:start position:0% +obsessive quality here of of this sort + + + align:start position:0% +obsessive quality here of of this sort +of thought that doesn't that doesn't + + align:start position:0% +of thought that doesn't that doesn't + + + align:start position:0% +of thought that doesn't that doesn't +quite work for you you can imagine that + + align:start position:0% +quite work for you you can imagine that + + + align:start position:0% +quite work for you you can imagine that +you've got some little circuit in the + + align:start position:0% +you've got some little circuit in the + + + align:start position:0% +you've got some little circuit in the +brain somewhere that's that that's + + align:start position:0% +brain somewhere that's that that's + + + align:start position:0% +brain somewhere that's that that's +checked you know it is a little Checker + + align:start position:0% +checked you know it is a little Checker + + + align:start position:0% +checked you know it is a little Checker +you know did I do what I was supposed to + + align:start position:0% +you know did I do what I was supposed to + + + align:start position:0% +you know did I do what I was supposed to +do and if that goes a little wacko on + + align:start position:0% +do and if that goes a little wacko on + + + align:start position:0% +do and if that goes a little wacko on +you if that's got too much serotonin or + + align:start position:0% +you if that's got too much serotonin or + + + align:start position:0% +you if that's got too much serotonin or +too little serotonin I suppose or + + align:start position:0% +too little serotonin I suppose or + + + align:start position:0% +too little serotonin I suppose or +whatever you know you might end up in a + + align:start position:0% +whatever you know you might end up in a + + + align:start position:0% +whatever you know you might end up in a +sort of an infinite Loop where gotta + + align:start position:0% +sort of an infinite Loop where gotta + + + align:start position:0% +sort of an infinite Loop where gotta +check gotta check gotta check gotta + + align:start position:0% +check gotta check gotta check gotta + + + align:start position:0% +check gotta check gotta check gotta +check and something chemical that gives + + align:start position:0% +check and something chemical that gives + + + align:start position:0% +check and something chemical that gives +it a a a kick will help + + align:start position:0% +it a a a kick will help + + + align:start position:0% +it a a a kick will help +um okay you can treat it that way you + + align:start position:0% +um okay you can treat it that way you + + + align:start position:0% +um okay you can treat it that way you +can also treat it + + align:start position:0% +can also treat it + + + align:start position:0% +can also treat it +um using the same sort of Behavioral + + align:start position:0% +um using the same sort of Behavioral + + + align:start position:0% +um using the same sort of Behavioral +techniques that I was just talking about + + align:start position:0% +techniques that I was just talking about + + + align:start position:0% +techniques that I was just talking about +for phobias so let's do it for for uh + + align:start position:0% +for phobias so let's do it for for uh + + + align:start position:0% +for phobias so let's do it for for uh +hand washing all right patience so and + + align:start position:0% +hand washing all right patience so and + + + align:start position:0% +hand washing all right patience so and +so why do you have to watch it well I + + align:start position:0% +so why do you have to watch it well I + + + align:start position:0% +so why do you have to watch it well I +I'm just like really concerned that my + + align:start position:0% +I'm just like really concerned that my + + + align:start position:0% +I'm just like really concerned that my +hands are dirty + + align:start position:0% +hands are dirty + + + align:start position:0% +hands are dirty +uh I mean I you know right it just when + + align:start position:0% +uh I mean I you know right it just when + + + align:start position:0% +uh I mean I you know right it just when +I get dirt on my hands it can kind of I + + align:start position:0% +I get dirt on my hands it can kind of I + + + align:start position:0% +I get dirt on my hands it can kind of I +get all excited and uh right all right + + align:start position:0% +get all excited and uh right all right + + + align:start position:0% +get all excited and uh right all right +so we can do the desensitization + + align:start position:0% +so we can do the desensitization + + + align:start position:0% +so we can do the desensitization +business or we can do the flooding + + align:start position:0% +business or we can do the flooding + + + align:start position:0% +business or we can do the flooding +business in the interest of time we'll + + align:start position:0% +business in the interest of time we'll + + + align:start position:0% +business in the interest of time we'll +do flooding all right see this this is + + align:start position:0% +do flooding all right see this this is + + + align:start position:0% +do flooding all right see this this is +dirt put your hands in it + + align:start position:0% +dirt put your hands in it + + + align:start position:0% +dirt put your hands in it +right are you dead yet no all right how + + align:start position:0% +right are you dead yet no all right how + + + align:start position:0% +right are you dead yet no all right how +long can you leave them there + + align:start position:0% +long can you leave them there + + + align:start position:0% +long can you leave them there +all right and and you can basically + + align:start position:0% +all right and and you can basically + + + align:start position:0% +all right and and you can basically +desensitize this this feeling of deep + + align:start position:0% +desensitize this this feeling of deep + + + align:start position:0% +desensitize this this feeling of deep +anxiety about not um uh not not cleaning + + align:start position:0% +anxiety about not um uh not not cleaning + + + align:start position:0% +anxiety about not um uh not not cleaning +your hands all right so that's mildly + + align:start position:0% +your hands all right so that's mildly + + + align:start position:0% +your hands all right so that's mildly +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +um what's interesting the reason for + + align:start position:0% +um what's interesting the reason for + + + align:start position:0% +um what's interesting the reason for +raising this uh + + align:start position:0% +raising this uh + + + align:start position:0% +raising this uh +question + + align:start position:0% +question + + + align:start position:0% +question +um or this example comes from this uh a + + align:start position:0% +um or this example comes from this uh a + + + align:start position:0% +um or this example comes from this uh a +nice article now more than a decade old + + align:start position:0% +nice article now more than a decade old + + + align:start position:0% +nice article now more than a decade old +by Baxter + + align:start position:0% +by Baxter + + + align:start position:0% +by Baxter +um you can see obsessive compulsive + + align:start position:0% +um you can see obsessive compulsive + + + align:start position:0% +um you can see obsessive compulsive +um States in in uh in brain Imaging + + align:start position:0% +um States in in uh in brain Imaging + + + align:start position:0% +um States in in uh in brain Imaging +um there are little bits of brain uh + + align:start position:0% +um there are little bits of brain uh + + + align:start position:0% +um there are little bits of brain uh +specifically in the chaudate doesn't + + align:start position:0% +specifically in the chaudate doesn't + + + align:start position:0% +specifically in the chaudate doesn't +particularly matter for present purposes + + align:start position:0% +particularly matter for present purposes + + + align:start position:0% +particularly matter for present purposes +where that might be but it's overactive + + align:start position:0% +where that might be but it's overactive + + + align:start position:0% +where that might be but it's overactive +you know you look at the brain of an + + align:start position:0% +you know you look at the brain of an + + + align:start position:0% +you know you look at the brain of an +obsessive-compulsive sort and and this + + align:start position:0% +obsessive-compulsive sort and and this + + + align:start position:0% +obsessive-compulsive sort and and this +little chunk of brain is is busy uh you + + align:start position:0% +little chunk of brain is is busy uh you + + + align:start position:0% +little chunk of brain is is busy uh you +know just going nuts + + align:start position:0% +know just going nuts + + + align:start position:0% +know just going nuts +if you give the patient Prozac + + align:start position:0% +if you give the patient Prozac + + + align:start position:0% +if you give the patient Prozac +there that that chunk of brain now + + align:start position:0% +there that that chunk of brain now + + + align:start position:0% +there that that chunk of brain now +doesn't look weird anymore it comes into + + align:start position:0% +doesn't look weird anymore it comes into + + + align:start position:0% +doesn't look weird anymore it comes into +the normal range + + align:start position:0% +the normal range + + + align:start position:0% +the normal range +if you go and do behavioral therapy on + + align:start position:0% +if you go and do behavioral therapy on + + + align:start position:0% +if you go and do behavioral therapy on +on a patient with the same story + + align:start position:0% +on a patient with the same story + + + align:start position:0% +on a patient with the same story +the same piece of brain comes to look + + align:start position:0% +the same piece of brain comes to look + + + align:start position:0% +the same piece of brain comes to look +normal the point here is that you can + + align:start position:0% +normal the point here is that you can + + + align:start position:0% +normal the point here is that you can +reach this chunk of the brain if you + + align:start position:0% +reach this chunk of the brain if you + + + align:start position:0% +reach this chunk of the brain if you +like either through the brain sort of + + align:start position:0% +like either through the brain sort of + + + align:start position:0% +like either through the brain sort of +neurochemical root or through the psych + + align:start position:0% +neurochemical root or through the psych + + + align:start position:0% +neurochemical root or through the psych +behavioral route they're not necessarily + + align:start position:0% +behavioral route they're not necessarily + + + align:start position:0% +behavioral route they're not necessarily +either mutually exclusive or or you know + + align:start position:0% +either mutually exclusive or or you know + + + align:start position:0% +either mutually exclusive or or you know +one works in the other doesn't or + + align:start position:0% +one works in the other doesn't or + + + align:start position:0% +one works in the other doesn't or +something like that this is a case where + + align:start position:0% +something like that this is a case where + + + align:start position:0% +something like that this is a case where +you can get to the source of the problem + + align:start position:0% +you can get to the source of the problem + + + align:start position:0% +you can get to the source of the problem +at least in in a low you know a neural + + align:start position:0% +at least in in a low you know a neural + + + align:start position:0% +at least in in a low you know a neural +localization kind of a way you can get + + align:start position:0% +localization kind of a way you can get + + + align:start position:0% +localization kind of a way you can get +to the source of the problem + + align:start position:0% +to the source of the problem + + + align:start position:0% +to the source of the problem +um through either of these roots + + align:start position:0% +um through either of these roots + + + align:start position:0% +um through either of these roots +um + + align:start position:0% +um + + + align:start position:0% +um +and the uh and I I suppose the bottom + + align:start position:0% +and the uh and I I suppose the bottom + + + align:start position:0% +and the uh and I I suppose the bottom +line here is that in + + align:start position:0% +line here is that in + + + align:start position:0% +line here is that in +disorder after disorder + + align:start position:0% +disorder after disorder + + + align:start position:0% +disorder after disorder +what you find is that there isn't just + + align:start position:0% +what you find is that there isn't just + + + align:start position:0% +what you find is that there isn't just +one way of treating one problem is that + + align:start position:0% +one way of treating one problem is that + + + align:start position:0% +one way of treating one problem is that +in in most mental illness situations + + align:start position:0% +in in most mental illness situations + + + align:start position:0% +in in most mental illness situations +there isn't one Magic Bullet treatment + + align:start position:0% +there isn't one Magic Bullet treatment + + + align:start position:0% +there isn't one Magic Bullet treatment +that automatically works for you + + align:start position:0% +that automatically works for you + + + align:start position:0% +that automatically works for you +um and then in all of these in many of + + align:start position:0% +um and then in all of these in many of + + + align:start position:0% +um and then in all of these in many of +these cases there are both brain and + + align:start position:0% +these cases there are both brain and + + + align:start position:0% +these cases there are both brain and +mind roots to therapy so when you're + + align:start position:0% +mind roots to therapy so when you're + + + align:start position:0% +mind roots to therapy so when you're +asking + + align:start position:0% +asking + + + align:start position:0% +asking +um when when you have like these these + + align:start position:0% +um when when you have like these these + + + align:start position:0% +um when when you have like these these +patients we were cooking up when you + + align:start position:0% +patients we were cooking up when you + + + align:start position:0% +patients we were cooking up when you +have a particular patient + + align:start position:0% +have a particular patient + + + align:start position:0% +have a particular patient +um the uh there's there's a spectrum + + align:start position:0% +um the uh there's there's a spectrum + + + align:start position:0% +um the uh there's there's a spectrum +of choices that might potentially be of + + align:start position:0% +of choices that might potentially be of + + + align:start position:0% +of choices that might potentially be of +some use + + align:start position:0% +some use + + + align:start position:0% +some use +um it says on the handout what happens + + align:start position:0% +um it says on the handout what happens + + + align:start position:0% +um it says on the handout what happens +when drugs make us better than we ever + + align:start position:0% +when drugs make us better than we ever + + + align:start position:0% +when drugs make us better than we ever +were that was the example I was talking + + align:start position:0% +were that was the example I was talking + + + align:start position:0% +were that was the example I was talking +about before of of Emma who uh + + align:start position:0% +about before of of Emma who uh + + + align:start position:0% +about before of of Emma who uh +um you know who who feels better on + + align:start position:0% +um you know who who feels better on + + + align:start position:0% +um you know who who feels better on +Prozac even though she wasn't + + align:start position:0% +Prozac even though she wasn't + + + align:start position:0% +Prozac even though she wasn't +technically + + align:start position:0% +technically + + + align:start position:0% +technically +um + + align:start position:0% +um + + + align:start position:0% +um +in in uh it didn't have a reasonable + + align:start position:0% +in in uh it didn't have a reasonable + + + align:start position:0% +in in uh it didn't have a reasonable +diagnosis of something being wrong with + + align:start position:0% +diagnosis of something being wrong with + + + align:start position:0% +diagnosis of something being wrong with +her so we've already talked about that + + align:start position:0% +her so we've already talked about that + + + align:start position:0% +her so we've already talked about that +so I think I'll quit + + align:start position:0% +so I think I'll quit + + + align:start position:0% +so I think I'll quit +see ya next week + + align:start position:0% +see ya next week + + + align:start position:0% +see ya next week +[Music] \ No newline at end of file diff --git a/3_qvO8bKGus.txt b/3_qvO8bKGus.txt new file mode 100644 index 0000000000000000000000000000000000000000..f53c34200574695d8eda50fec75dd9d41cc516c8 --- /dev/null +++ b/3_qvO8bKGus.txt @@ -0,0 +1,1376 @@ +align:start position:0% + +we've talked a lot about the broley + + align:start position:0% +we've talked a lot about the broley + + + align:start position:0% +we've talked a lot about the broley +saying that the wavelength is given by H + + align:start position:0% +saying that the wavelength is given by H + + + align:start position:0% +saying that the wavelength is given by H +over P but we have not said much yet + + align:start position:0% +over P but we have not said much yet + + + align:start position:0% +over P but we have not said much yet +about the frequency of the Waves so what + + align:start position:0% +about the frequency of the Waves so what + + + align:start position:0% +about the frequency of the Waves so what +is the frequency of those matter + + align:start position:0% +is the frequency of those matter + + + align:start position:0% +is the frequency of those matter +waves so what is the + + align:start position:0% + + + + align:start position:0% + +frequency + + align:start position:0% + + + + align:start position:0% + +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +of the matter + + align:start position:0% + + + + align:start position:0% + +waves so the broley did answer that same + + align:start position:0% +waves so the broley did answer that same + + + align:start position:0% +waves so the broley did answer that same +question and the answer was obtained by + + align:start position:0% +question and the answer was obtained by + + + align:start position:0% +question and the answer was obtained by +analogy we have P equal H bar + + align:start position:0% + + + + align:start position:0% + +K and he said well just like the + + align:start position:0% +K and he said well just like the + + + align:start position:0% +K and he said well just like the +wavelength determined by the momentum + + align:start position:0% +wavelength determined by the momentum + + + align:start position:0% +wavelength determined by the momentum +will have + + align:start position:0% +will have + + + align:start position:0% +will have +e equal H + + align:start position:0% +e equal H + + + align:start position:0% +e equal H +bar Omega so the frequency so this + + align:start position:0% +bar Omega so the frequency so this + + + align:start position:0% +bar Omega so the frequency so this +equation is the one that now completes + + align:start position:0% +equation is the one that now completes + + + align:start position:0% +equation is the one that now completes +the story Omega is equal to e over H + + align:start position:0% + + + + align:start position:0% + +bar fixes Omega in terms of the + + align:start position:0% +bar fixes Omega in terms of the + + + align:start position:0% +bar fixes Omega in terms of the +energy and we're going to say a few + + align:start position:0% +energy and we're going to say a few + + + align:start position:0% +energy and we're going to say a few +things uh in fact this will be an + + align:start position:0% +things uh in fact this will be an + + + align:start position:0% +things uh in fact this will be an +interesting degression into an important + + align:start position:0% +interesting degression into an important + + + align:start position:0% +interesting degression into an important +subject about waves that illustrates why + + align:start position:0% +subject about waves that illustrates why + + + align:start position:0% +subject about waves that illustrates why +this uh answer makes a lot of + + align:start position:0% +this uh answer makes a lot of + + + align:start position:0% +this uh answer makes a lot of +sense and uh that's really all you can + + align:start position:0% +sense and uh that's really all you can + + + align:start position:0% +sense and uh that's really all you can +do at this moment this is a postulate of + + align:start position:0% +do at this moment this is a postulate of + + + align:start position:0% +do at this moment this is a postulate of +quantum mechanics that you do this thing + + align:start position:0% +quantum mechanics that you do this thing + + + align:start position:0% +quantum mechanics that you do this thing +and with this you get Quant mechanics so + + align:start position:0% +and with this you get Quant mechanics so + + + align:start position:0% +and with this you get Quant mechanics so +the best thing we can do is explain why + + align:start position:0% +the best thing we can do is explain why + + + align:start position:0% +the best thing we can do is explain why +it makes sense in a number of ways and + + align:start position:0% +it makes sense in a number of ways and + + + align:start position:0% +it makes sense in a number of ways and +then hope that the theory that you build + + align:start position:0% +then hope that the theory that you build + + + align:start position:0% +then hope that the theory that you build +makes full + + align:start position:0% +makes full + + + align:start position:0% +makes full +sense so I want to remind you about + + align:start position:0% +sense so I want to remind you about + + + align:start position:0% +sense so I want to remind you about +velocities of + + align:start position:0% +velocities of + + + align:start position:0% +velocities of +waves so if you have a wave now that it + + align:start position:0% +waves so if you have a wave now that it + + + align:start position:0% +waves so if you have a wave now that it +has K and Omega you have this thing K + + align:start position:0% +has K and Omega you have this thing K + + + align:start position:0% +has K and Omega you have this thing K +minus Omega wave with a + + align:start position:0% + + + + align:start position:0% + +face + + align:start position:0% +face + + + align:start position:0% +face +KX - Omega + + align:start position:0% +KX - Omega + + + align:start position:0% +KX - Omega +T then there is something called the + + align:start position:0% +T then there is something called the + + + align:start position:0% +T then there is something called the +phase + + align:start position:0% + + + + align:start position:0% + +velocity and it's given by Omega over + + align:start position:0% + + + + align:start position:0% + +K it's the Velocity in which the nodes + + align:start position:0% +K it's the Velocity in which the nodes + + + align:start position:0% +K it's the Velocity in which the nodes +and Max Maxima of this plane wave + + align:start position:0% +and Max Maxima of this plane wave + + + align:start position:0% +and Max Maxima of this plane wave +move so let's see if this makes some + + align:start position:0% +move so let's see if this makes some + + + align:start position:0% +move so let's see if this makes some +sense um Omega over K is the same thing + + align:start position:0% +sense um Omega over K is the same thing + + + align:start position:0% +sense um Omega over K is the same thing +as e over + + align:start position:0% +as e over + + + align:start position:0% +as e over +P we're nonrelativistic so let's + + align:start position:0% +P we're nonrelativistic so let's + + + align:start position:0% +P we're nonrelativistic so let's +continue 12 MV SAR over + + align:start position:0% +continue 12 MV SAR over + + + align:start position:0% +continue 12 MV SAR over +MV and this seems a little strange + + align:start position:0% +MV and this seems a little strange + + + align:start position:0% +MV and this seems a little strange + + align:start position:0% + + + align:start position:0% +V so if I have a particle you see this + + align:start position:0% +V so if I have a particle you see this + + + align:start position:0% +V so if I have a particle you see this +is matter waves of energy e and momentum + + align:start position:0% +is matter waves of energy e and momentum + + + align:start position:0% +is matter waves of energy e and momentum +p and E is 12 MV SED the velocity of the + + align:start position:0% +p and E is 12 MV SED the velocity of the + + + align:start position:0% +p and E is 12 MV SED the velocity of the +particle p is equal to MV and now + + align:start position:0% +particle p is equal to MV and now + + + align:start position:0% +particle p is equal to MV and now +somehow this wave seems to be moving + + align:start position:0% +somehow this wave seems to be moving + + + align:start position:0% +somehow this wave seems to be moving +with half the speed of the particle and + + align:start position:0% +with half the speed of the particle and + + + align:start position:0% +with half the speed of the particle and +that looks pretty + + align:start position:0% +that looks pretty + + + align:start position:0% +that looks pretty +bad what's going on + + align:start position:0% + + + + align:start position:0% + +well U this is the usual story with + + align:start position:0% +well U this is the usual story with + + + align:start position:0% +well U this is the usual story with +waves if the wave itself doesn't a wave + + align:start position:0% +waves if the wave itself doesn't a wave + + + align:start position:0% +waves if the wave itself doesn't a wave +a plain wave carries no real information + + align:start position:0% +a plain wave carries no real information + + + align:start position:0% +a plain wave carries no real information +it's not a signal so many times when you + + align:start position:0% +it's not a signal so many times when you + + + align:start position:0% +it's not a signal so many times when you +try to represent a particle or a a + + align:start position:0% +try to represent a particle or a a + + + align:start position:0% +try to represent a particle or a a +little bit of information traveling + + align:start position:0% +little bit of information traveling + + + align:start position:0% +little bit of information traveling +representing it with a plane wave is + + align:start position:0% +representing it with a plane wave is + + + align:start position:0% +representing it with a plane wave is +actually quite wrong you have to + + align:start position:0% +actually quite wrong you have to + + + align:start position:0% +actually quite wrong you have to +represent it with a wave packet + + align:start position:0% +represent it with a wave packet + + + align:start position:0% +represent it with a wave packet +and uh therefore this face wave velocity + + align:start position:0% +and uh therefore this face wave velocity + + + align:start position:0% +and uh therefore this face wave velocity +being 1/ half of the velocity of the + + align:start position:0% +being 1/ half of the velocity of the + + + align:start position:0% +being 1/ half of the velocity of the +particles seems to just confirm the idea + + align:start position:0% +particles seems to just confirm the idea + + + align:start position:0% +particles seems to just confirm the idea +that first these waves are a little + + align:start position:0% +that first these waves are a little + + + align:start position:0% +that first these waves are a little +strange and second um phase velocity is + + align:start position:0% +strange and second um phase velocity is + + + align:start position:0% +strange and second um phase velocity is +not very meaningful + + align:start position:0% +not very meaningful + + + align:start position:0% +not very meaningful +physically the velocity that is more + + align:start position:0% +physically the velocity that is more + + + align:start position:0% +physically the velocity that is more +meaningful is vrp + + align:start position:0% + + + + align:start position:0% + +velocity and it's + + align:start position:0% +velocity and it's + + + align:start position:0% +velocity and it's +D + + align:start position:0% +D + + + align:start position:0% +D +Omega d + + align:start position:0% +Omega d + + + align:start position:0% +Omega d +k + + align:start position:0% +k + + + align:start position:0% +k +evaluated + + align:start position:0% +evaluated + + + align:start position:0% +evaluated +at the value K that you're using + + align:start position:0% +at the value K that you're using + + + align:start position:0% +at the value K that you're using +remember K is a proxy for momentum so + + align:start position:0% +remember K is a proxy for momentum so + + + align:start position:0% +remember K is a proxy for momentum so +you know the Omega d k may depend on K + + align:start position:0% +you know the Omega d k may depend on K + + + align:start position:0% +you know the Omega d k may depend on K +and Omega so if it's the Omega DK is a + + align:start position:0% +and Omega so if it's the Omega DK is a + + + align:start position:0% +and Omega so if it's the Omega DK is a +function which value should you use well + + align:start position:0% +function which value should you use well + + + align:start position:0% +function which value should you use well +the value at the K that you're + + align:start position:0% +the value at the K that you're + + + align:start position:0% +the value at the K that you're +propagating + + align:start position:0% +propagating + + + align:start position:0% +propagating +and this would be the same as D Omega + + align:start position:0% + + + + align:start position:0% + +DK is because of the constant separating + + align:start position:0% +DK is because of the constant separating + + + align:start position:0% +DK is because of the constant separating +the same as D + + align:start position:0% + + + + align:start position:0% + +DP but what is the kinetic energy in + + align:start position:0% +DP but what is the kinetic energy in + + + align:start position:0% +DP but what is the kinetic energy in +terms of the momentum we wrote it last + + align:start position:0% +terms of the momentum we wrote it last + + + align:start position:0% +terms of the momentum we wrote it last +time p^ 2 over 2 + + align:start position:0% +time p^ 2 over 2 + + + align:start position:0% +time p^ 2 over 2 +m that's the kinetic energy Express in + + align:start position:0% +m that's the kinetic energy Express in + + + align:start position:0% +m that's the kinetic energy Express in +terms of momentum so this is D + + align:start position:0% +terms of momentum so this is D + + + align:start position:0% +terms of momentum so this is D +DP of p^2 / 2 + + align:start position:0% + + + + align:start position:0% + +m write P equal MV and you recover the + + align:start position:0% +m write P equal MV and you recover the + + + align:start position:0% +m write P equal MV and you recover the +kinetic energy and this is just because + + align:start position:0% +kinetic energy and this is just because + + + align:start position:0% +kinetic energy and this is just because +of the two p/ M which is the velocity of + + align:start position:0% +of the two p/ M which is the velocity of + + + align:start position:0% +of the two p/ M which is the velocity of +the + + align:start position:0% +the + + + align:start position:0% +the +particle and this is the reason people + + align:start position:0% +particle and this is the reason people + + + align:start position:0% +particle and this is the reason people +believe the + + align:start position:0% +believe the + + + align:start position:0% +believe the +brole the brole made + + align:start position:0% +brole the brole made + + + align:start position:0% +brole the brole made +sense because the group velocity of this + + align:start position:0% +sense because the group velocity of this + + + align:start position:0% +sense because the group velocity of this +packets would be correct and that's a + + align:start position:0% +packets would be correct and that's a + + + align:start position:0% +packets would be correct and that's a +very beautiful result actually it's true + + align:start position:0% +very beautiful result actually it's true + + + align:start position:0% +very beautiful result actually it's true +relativistically as well if you put the + + align:start position:0% +relativistically as well if you put the + + + align:start position:0% +relativistically as well if you put the +energy and the momentum in relativity + + align:start position:0% +energy and the momentum in relativity + + + align:start position:0% +energy and the momentum in relativity +this answer comes out exactly the same + + align:start position:0% +this answer comes out exactly the same + + + align:start position:0% +this answer comes out exactly the same +perfectly well so to a large degree + + align:start position:0% +perfectly well so to a large degree + + + align:start position:0% +perfectly well so to a large degree +since it also works works for energy and + + align:start position:0% +since it also works works for energy and + + + align:start position:0% +since it also works works for energy and +momentum in relativity there was a + + align:start position:0% +momentum in relativity there was a + + + align:start position:0% +momentum in relativity there was a +motivation from relativity that I want + + align:start position:0% +motivation from relativity that I want + + + align:start position:0% +motivation from relativity that I want +to + + align:start position:0% +to + + + align:start position:0% +to +quote although not elaborate on it too + + align:start position:0% +quote although not elaborate on it too + + + align:start position:0% +quote although not elaborate on it too +much + + align:start position:0% + + + + align:start position:0% + +so the + + align:start position:0% + + + + align:start position:0% + +motivation is that um in special + + align:start position:0% + + + + align:start position:0% + +relativity + + align:start position:0% +relativity + + + align:start position:0% +relativity +relativity + + align:start position:0% +relativity + + + align:start position:0% +relativity +the components of the energy divided by + + align:start position:0% +the components of the energy divided by + + + align:start position:0% +the components of the energy divided by +C and the + + align:start position:0% +C and the + + + align:start position:0% +C and the +momentum form a four + + align:start position:0% + + + + align:start position:0% + +Vector just like position and time forms + + align:start position:0% +Vector just like position and time forms + + + align:start position:0% +Vector just like position and time forms +a four vector and transform nicely about + + align:start position:0% +a four vector and transform nicely about + + + align:start position:0% +a four vector and transform nicely about +with theen transformation e and P form a + + align:start position:0% +with theen transformation e and P form a + + + align:start position:0% +with theen transformation e and P form a +four Vector nevertheless when you + + align:start position:0% +four Vector nevertheless when you + + + align:start position:0% +four Vector nevertheless when you +consider + + align:start position:0% +consider + + + align:start position:0% +consider +faces + + align:start position:0% +faces + + + align:start position:0% +faces +like this and you have x and t that form + + align:start position:0% +like this and you have x and t that form + + + align:start position:0% +like this and you have x and t that form +a four Vector the good behavior of faces + + align:start position:0% +a four Vector the good behavior of faces + + + align:start position:0% +a four Vector the good behavior of faces +also imply that K and Omega form for + + align:start position:0% +also imply that K and Omega form for + + + align:start position:0% +also imply that K and Omega form for +Vector in fact Omega in relativity Omega + + align:start position:0% +Vector in fact Omega in relativity Omega + + + align:start position:0% +Vector in fact Omega in relativity Omega +over C and the K + + align:start position:0% +over C and the K + + + align:start position:0% +over C and the K +Vector form a four Vector you see in all + + align:start position:0% +Vector form a four Vector you see in all + + + align:start position:0% +Vector form a four Vector you see in all +the equations we've written and the + + align:start position:0% +the equations we've written and the + + + align:start position:0% +the equations we've written and the +Broly the Broly in three dimensions or + + align:start position:0% +Broly the Broly in three dimensions or + + + align:start position:0% +Broly the Broly in three dimensions or +more really is p Vector equal H bar k + + align:start position:0% +more really is p Vector equal H bar k + + + align:start position:0% +more really is p Vector equal H bar k +vector and K is usually used for the + + align:start position:0% +vector and K is usually used for the + + + align:start position:0% +vector and K is usually used for the +magnitude of this uh K Vector so this is + + align:start position:0% +magnitude of this uh K Vector so this is + + + align:start position:0% +magnitude of this uh K Vector so this is +also for Vector in special relativity + + align:start position:0% +also for Vector in special relativity + + + align:start position:0% +also for Vector in special relativity +and + + align:start position:0% +and + + + align:start position:0% +and +therefore vectors are things that + + align:start position:0% +therefore vectors are things that + + + align:start position:0% +therefore vectors are things that +transform + + align:start position:0% +transform + + + align:start position:0% +transform +nicely so it makes sense to say that one + + align:start position:0% +nicely so it makes sense to say that one + + + align:start position:0% +nicely so it makes sense to say that one +for Vector is equal to another for + + align:start position:0% +for Vector is equal to another for + + + align:start position:0% +for Vector is equal to another for +Vector because if it's true in one + + align:start position:0% +Vector because if it's true in one + + + align:start position:0% +Vector because if it's true in one +reference frame it will be true in every + + align:start position:0% +reference frame it will be true in every + + + align:start position:0% +reference frame it will be true in every +reference frame so it's almost + + align:start position:0% +reference frame so it's almost + + + align:start position:0% +reference frame so it's almost +irresistible to make them equal and the + + align:start position:0% +irresistible to make them equal and the + + + align:start position:0% +irresistible to make them equal and the +Broly in some sense said this is equal + + align:start position:0% +Broly in some sense said this is equal + + + align:start position:0% +Broly in some sense said this is equal +to H bar * that that's the + + align:start position:0% + + + + align:start position:0% + +Broly the interesting thing is that this + + align:start position:0% +Broly the interesting thing is that this + + + align:start position:0% +Broly the interesting thing is that this +is true relativistically but actually + + align:start position:0% +is true relativistically but actually + + + align:start position:0% +is true relativistically but actually +nonrelativistically you can make sense + + align:start position:0% +nonrelativistically you can make sense + + + align:start position:0% +nonrelativistically you can make sense +of this and set it equal to be the same + + align:start position:0% +of this and set it equal to be the same + + + align:start position:0% +of this and set it equal to be the same +things and the phase velocities group + + align:start position:0% +things and the phase velocities group + + + align:start position:0% +things and the phase velocities group +velocities all make sense um certainly + + align:start position:0% +velocities all make sense um certainly + + + align:start position:0% +velocities all make sense um certainly +you know we've now set for mod particles + + align:start position:0% +you know we've now set for mod particles + + + align:start position:0% +you know we've now set for mod particles +that e is equal to H bar Omega but + + align:start position:0% +that e is equal to H bar Omega but + + + align:start position:0% +that e is equal to H bar Omega but +another statement would be that yes + + align:start position:0% +another statement would be that yes + + + align:start position:0% +another statement would be that yes +indeed Einstein said that that for + + align:start position:0% +indeed Einstein said that that for + + + align:start position:0% +indeed Einstein said that that for +photons e was equal to H Omega or H new + + align:start position:0% +photons e was equal to H Omega or H new + + + align:start position:0% +photons e was equal to H Omega or H new +and therefore yes whatever happens for + + align:start position:0% +and therefore yes whatever happens for + + + align:start position:0% +and therefore yes whatever happens for +photons happen for this waves and so + + align:start position:0% +photons happen for this waves and so + + + align:start position:0% +photons happen for this waves and so +also so this is another argument group + + align:start position:0% +also so this is another argument group + + + align:start position:0% +also so this is another argument group +velocities is one special relativity is + + align:start position:0% +velocities is one special relativity is + + + align:start position:0% +velocities is one special relativity is +another reason and of course + + align:start position:0% +another reason and of course + + + align:start position:0% +another reason and of course +photons or + + align:start position:0% + + + + align:start position:0% + +Einstein said that e is equal H new + + align:start position:0% +Einstein said that e is equal H new + + + align:start position:0% +Einstein said that e is equal H new +which is equal to H bar Omega \ No newline at end of file diff --git a/3eQh_W8YF_g.txt b/3eQh_W8YF_g.txt new file mode 100644 index 0000000000000000000000000000000000000000..3f4c4bf9ce1f3ece592eaa4e3d5fe6fef5bcaa03 --- /dev/null +++ b/3eQh_W8YF_g.txt @@ -0,0 +1,311 @@ +The problem we need to solve is where to store +the values needed by procedure: its arguments, + +its return address, its return value. + +The procedure may also need storage for its +local variables and space to save the values + +of the caller's registers before they get +overwritten by the procedure. + +We'd like to avoid any limitations on the +number of arguments, the number of local variables, + +etc. + +So we'll need a block of storage for each +active procedure call, what we'll call the + +"activation record". + +As we saw in the factorial example, we can't +statically allocate a single block of storage + +for a particular procedure since recursive +calls mean we'll have many active calls to + +that procedure at points during the execution. + +What we need is a way to dynamically allocate +storage for an activation record when the + +procedure is called, which can then be reclaimed +when the procedure returns. + +Let's see how activation records come and +go as execution proceeds. + +The first activation record is for the call +fact(3). + +It's created at the beginning of the procedure +and holds, among other things, the value of + +the argument n and the return address where +execution should resume after the fact(3) + +computation is complete. + +During the execution of fact(3), we need to +make a recursive call to compute fact(2). + +So that procedure call also gets an activation +record with the appropriate values for the + +argument and return address. + +Note that the original activation record is +kept since it contains information needed + +to complete the computation of fact(3) after +the call to fact(2) returns. + +So now we have two active procedure calls +and hence two activation records. + +fact(2) requires computing fact(1), which, +in turn, requires computing fact(0). + +At this point there are four active procedure +calls and hence four activation records. + +The recursion terminates with fact(0), which +returns the value 1 to its caller. + +At this point we've finished execution of +fact(0) and so its activation record is no + +longer needed and can be discarded. + +fact(1) now finishes its computation returning +1 to its caller. + +We no longer need its activation record. + +Then fact(2) completes, returning 2 to its +caller and its activation record can be discarded. + +And so on… + +Note that the activation record of a nested +procedure call is always discarded before + +the activation record of the caller. + +That makes sense: the execution of the caller +can't complete until the nested procedure + +call returns. + +What we need is a storage scheme that efficiently +supports the allocation and deallocation of + +activation records as shown here. + +Early compiler writers recognized that activation +records are allocated and deallocated in last-in + +first-out (LIFO) order. + +So they invented the "stack", a data structure +that implements a PUSH operation to add a + +record to the top of the stack and a POP operation +to remove the top element. + +New activation records are PUSHed onto the +stack during procedure calls and the POPed + +from the stack when the procedure call returns. + +Note that stack operations affect the top +(i.e., most recent) record on the stack. + +C procedures only need to access the top activation +record on the stack. + +Other programming languages, e.g. Java, support +accesses to other active activation records. + +The stack supports both modes of operation. + +One final technical note: some programming +languages support closures (e.g., Javascript) + +or continuations (e.g., Python's yield statement), +where the activation records need to be preserved + +even after the procedure returns. + +In these cases, the simple LIFO behavior of +the stack is no longer sufficient and we'll + +need another scheme for allocating and deallocating +activation records. + +But that's a topic for another course! + +Here's how we'll implement the stack on the +Beta: + +We'll dedicate one of the Beta registers, +R29, to be the "stack pointer" that will be + +used to manage stack operations. + +When we PUSH a word onto the stack, we'll +increment the stack pointer. + +So the stack grows to successively higher +addresses as words are PUSHed onto the stack. + +We'll adopt the convention that SP points +to (i.e., its value is the address of) the + +first unused stack location, the location +that will be filled by next PUSH. + +So locations with addresses lower than the +value in SP correspond to words that have + +been previously allocated. + +Words can be PUSHed to or POPed from the stack +at any point in execution, but we'll impose + +the rule that code sequences that PUSH words +onto the stack must POP those words at the + +end of execution. + +So when a code sequence finishes execution, +SP will have the same value as it had before + +the sequence started. + +This is called the "stack discipline" and +ensures that intervening uses of the stack + +don't affect later stack references. + +We'll allocate a large region of memory to +hold the stack located so that the stack can + +grow without overwriting other program storage. + +Most systems require that you specify a maximum +stack size when running a program and will + +signal an execution error if the program attempts +to PUSH too many items onto the stack. + +For our Beta stack implementation, we'll use +existing instructions to implement stack operations, + +so for us the stack is strictly a set of software +conventions. + +Other ISAs provide instructions specifically +for stack operations. + +There are many other sensible stack conventions, +so you'll need to read up on the conventions + +adopted by the particular ISA or programming +language you'll be using. + +We've added some convenience macros to UASM +to support stacks. + +The PUSH macro expands into two instructions. + +The ADDC increments the stack pointer, allocating +a new word at the top of stack, and then initializes + +the new top-of-stack from a specified register +value with a ST instruction. + +The POP macro LDs the value at the top of +the stack into the specified register, then + +uses a SUBC instruction to decrement the stack +pointer, deallocating that word from the stack. + +Note that the order of the instructions in +the PUSH and POP macro is very important. + +As we'll see in the next lecture, interrupts +can cause the Beta hardware to stop executing + +the current program between any two instructions, +so we have to be careful about the order of + +operations. + +So for PUSH, we first allocate the word on +the stack, then initialize it. + +If we did it the other way around and execution +was interrupted between the initialization + +and allocation, code run during the interrupt +which uses the stack might unintentionally + +overwrite the initialized value. + +But, assuming all code follows stack discipline, +allocation followed by initialization is always + +safe. + +The same reasoning applies to the order of +the POP instructions. + +We first access the top-of-stack one last +time to retrieve its value, then we deallocate + +that location. + +We can use the ALLOCATE macro to reserve a +number of stack locations for later use. + +Sort of like PUSH but without the initialization. + +DEALLOCATE performs the opposite operation, +removing N words from the stack. + +In general, if we see a PUSH or ALLOCATE in +an assembly language program, we should be + +able to find the corresponding POP or DEALLOCATE, +which would indicate that stack discipline + +is maintained. + +We'll use stacks to save values we'll need +later. + +For example, if we need to use some registers +for a computation but don't know if the register's + +current values are needed later in the program, +we can PUSH their current values onto the + +stack and then are free to use the registers +in our code. + +After we're done, we can use POP to restore +the saved values. + +Note that we POP data off the stack in the +opposite order that the data was PUSHed, i.e., + +we need to follow the last-in first-out discipline +imposed by the stack operations. + +Now that we have the stack data structure, +we'll use it to solve our problems with allocating + +and deallocating activation records during +procedure calls. \ No newline at end of file diff --git a/4H0GXzQ41t0.txt b/4H0GXzQ41t0.txt new file mode 100644 index 0000000000000000000000000000000000000000..c1ef6f94252249f9b562739e9991e0713c632725 --- /dev/null +++ b/4H0GXzQ41t0.txt @@ -0,0 +1,13528 @@ +align:start position:0% + +so welcome to the last class please + + align:start position:0% +so welcome to the last class please + + + align:start position:0% +so welcome to the last class please +don't come on Wednesday I will not be + + align:start position:0% +don't come on Wednesday I will not be + + + align:start position:0% +don't come on Wednesday I will not be +here uh today we will just be uh tying + + align:start position:0% +here uh today we will just be uh tying + + + align:start position:0% +here uh today we will just be uh tying +up some loose ends regarding some topics + + align:start position:0% +up some loose ends regarding some topics + + + align:start position:0% +up some loose ends regarding some topics +that we've seen throughout the course + + align:start position:0% +that we've seen throughout the course + + + align:start position:0% +that we've seen throughout the course +and then I'm going to do just a wrap up + + align:start position:0% +and then I'm going to do just a wrap up + + + align:start position:0% +and then I'm going to do just a wrap up +of things we've learned and potential uh + + align:start position:0% +of things we've learned and potential uh + + + align:start position:0% +of things we've learned and potential uh +uh courses that you might want to take + + align:start position:0% +uh courses that you might want to take + + + align:start position:0% +uh courses that you might want to take +after this okay so today uh as I + + align:start position:0% +after this okay so today uh as I + + + align:start position:0% +after this okay so today uh as I +mentioned we're going to tie up some + + align:start position:0% +mentioned we're going to tie up some + + + align:start position:0% +mentioned we're going to tie up some +loose ends regarding lists dictionaries + + align:start position:0% +loose ends regarding lists dictionaries + + + align:start position:0% +loose ends regarding lists dictionaries +so those two topics are kind of going to + + align:start position:0% +so those two topics are kind of going to + + + align:start position:0% +so those two topics are kind of going to +be combined into uh one sort of kind of + + align:start position:0% +be combined into uh one sort of kind of + + + align:start position:0% +be combined into uh one sort of kind of +uh one part of this lecture um it's + + align:start position:0% +uh one part of this lecture um it's + + + align:start position:0% +uh one part of this lecture um it's +going to also include a little bit about + + align:start position:0% +going to also include a little bit about + + + align:start position:0% +going to also include a little bit about +complexity so just some things that + + align:start position:0% +complexity so just some things that + + + align:start position:0% +complexity so just some things that +we've learned kind of demystifying some + + align:start position:0% +we've learned kind of demystifying some + + + align:start position:0% +we've learned kind of demystifying some +details that I kind of ski throughout uh + + align:start position:0% +details that I kind of ski throughout uh + + + align:start position:0% +details that I kind of ski throughout uh +the past few lectures and then we're + + align:start position:0% +the past few lectures and then we're + + + align:start position:0% +the past few lectures and then we're +going to talk about simulations so + + align:start position:0% +going to talk about simulations so + + + align:start position:0% +going to talk about simulations so +simulations are very very useful is a + + align:start position:0% +simulations are very very useful is a + + + align:start position:0% +simulations are very very useful is a +very useful idea that you can already do + + align:start position:0% +very useful idea that you can already do + + + align:start position:0% +very useful idea that you can already do +with what you've learned in this class + + align:start position:0% +with what you've learned in this class + + + align:start position:0% +with what you've learned in this class +and I'll show you some uh useful places + + align:start position:0% +and I'll show you some uh useful places + + + align:start position:0% +and I'll show you some uh useful places +where you can apply computation and + + align:start position:0% +where you can apply computation and + + + align:start position:0% +where you can apply computation and +simulation to do some interesting uh + + align:start position:0% +simulation to do some interesting uh + + + align:start position:0% +simulation to do some interesting uh +some interesting things and then we'll + + align:start position:0% +some interesting things and then we'll + + + align:start position:0% +some interesting things and then we'll +do the wrap up so let's first uh start + + align:start position:0% +do the wrap up so let's first uh start + + + align:start position:0% +do the wrap up so let's first uh start +talking about lists so lists were the + + align:start position:0% +talking about lists so lists were the + + + align:start position:0% +talking about lists so lists were the +first data structure that we encountered + + align:start position:0% +first data structure that we encountered + + + align:start position:0% +first data structure that we encountered +that was really useful right like we did + + align:start position:0% +that was really useful right like we did + + + align:start position:0% +that was really useful right like we did +see strings and we did see tupal and + + align:start position:0% +see strings and we did see tupal and + + + align:start position:0% +see strings and we did see tupal and +things like that but once we saw lists + + align:start position:0% +things like that but once we saw lists + + + align:start position:0% +things like that but once we saw lists +it opened up a whole new world of + + align:start position:0% +it opened up a whole new world of + + + align:start position:0% +it opened up a whole new world of +possibilities for how we can manipulate + + align:start position:0% +possibilities for how we can manipulate + + + align:start position:0% +possibilities for how we can manipulate +data right so lists are sequences of + + align:start position:0% +data right so lists are sequences of + + + align:start position:0% +data right so lists are sequences of +objects I kind of skipped past how + + align:start position:0% +objects I kind of skipped past how + + + align:start position:0% +objects I kind of skipped past how +they're actually implemented in memory + + align:start position:0% +they're actually implemented in memory + + + align:start position:0% +they're actually implemented in memory +so I do want to talk about that a little + + align:start position:0% +so I do want to talk about that a little + + + align:start position:0% +so I do want to talk about that a little +bit but what we did talk about was the + + align:start position:0% +bit but what we did talk about was the + + + align:start position:0% +bit but what we did talk about was the +uh complexity the the ASM totic + + align:start position:0% +uh complexity the the ASM totic + + + align:start position:0% +uh complexity the the ASM totic +complexity of list operations okay so + + align:start position:0% +complexity of list operations okay so + + + align:start position:0% +complexity of list operations okay so +some of these are were pretty obvious so + + align:start position:0% +some of these are were pretty obvious so + + + align:start position:0% +some of these are were pretty obvious so +the ones that are Theta of n down here + + align:start position:0% +the ones that are Theta of n down here + + + align:start position:0% +the ones that are Theta of n down here +were obvious because well to check for + + align:start position:0% +were obvious because well to check for + + + align:start position:0% +were obvious because well to check for +equality between two lists you of course + + align:start position:0% +equality between two lists you of course + + + align:start position:0% +equality between two lists you of course +have to look at each element in the list + + align:start position:0% +have to look at each element in the list + + + align:start position:0% +have to look at each element in the list +right so that's sta of the length of the + + align:start position:0% +right so that's sta of the length of the + + + align:start position:0% +right so that's sta of the length of the +list to check whether an item is in a + + align:start position:0% +list to check whether an item is in a + + + align:start position:0% +list to check whether an item is in a +list or to iterate over a list obviously + + align:start position:0% +list or to iterate over a list obviously + + + align:start position:0% +list or to iterate over a list obviously +it's Theta of n because you have to look + + align:start position:0% +it's Theta of n because you have to look + + + align:start position:0% +it's Theta of n because you have to look +at each element in the list but we + + align:start position:0% +at each element in the list but we + + + align:start position:0% +at each element in the list but we +didn't really talk about the uh + + align:start position:0% +didn't really talk about the uh + + + align:start position:0% +didn't really talk about the uh +complexities up here so accessing an + + align:start position:0% +complexities up here so accessing an + + + align:start position:0% +complexities up here so accessing an +item in the list specifically is Theta + + align:start position:0% +item in the list specifically is Theta + + + align:start position:0% +item in the list specifically is Theta +of one so that means if you have a list + + align:start position:0% +of one so that means if you have a list + + + align:start position:0% +of one so that means if you have a list +with a whole bunch of elements in it to + + align:start position:0% +with a whole bunch of elements in it to + + + align:start position:0% +with a whole bunch of elements in it to +grab the element at a specific memory + + align:start position:0% +grab the element at a specific memory + + + align:start position:0% +grab the element at a specific memory +location it's Conant time complexity + + align:start position:0% +location it's Conant time complexity + + + align:start position:0% +location it's Conant time complexity +right so it's basically doesn't depend + + align:start position:0% +right so it's basically doesn't depend + + + align:start position:0% +right so it's basically doesn't depend +on the length of the list it's instant + + align:start position:0% +on the length of the list it's instant + + + align:start position:0% +on the length of the list it's instant +so we're going to see why that is let's + + align:start position:0% +so we're going to see why that is let's + + + align:start position:0% +so we're going to see why that is let's +first for Simplicity St sake assume that + + align:start position:0% +first for Simplicity St sake assume that + + + align:start position:0% +first for Simplicity St sake assume that +we're storing a list in memory of just + + align:start position:0% +we're storing a list in memory of just + + + align:start position:0% +we're storing a list in memory of just +integers right so I know lists can store + + align:start position:0% +integers right so I know lists can store + + + align:start position:0% +integers right so I know lists can store +other lists and dictionaries and things + + align:start position:0% +other lists and dictionaries and things + + + align:start position:0% +other lists and dictionaries and things +like that but just for the this first + + align:start position:0% +like that but just for the this first + + + align:start position:0% +like that but just for the this first +slide let's assume all we're doing is + + align:start position:0% +slide let's assume all we're doing is + + + align:start position:0% +slide let's assume all we're doing is +storing integers so the way python does + + align:start position:0% +storing integers so the way python does + + + align:start position:0% +storing integers so the way python does +this is uh when you create a list let's + + align:start position:0% +this is uh when you create a list let's + + + align:start position:0% +this is uh when you create a list let's +say you're initially populated with + + align:start position:0% +say you're initially populated with + + + align:start position:0% +say you're initially populated with +length L python initially allocates a + + align:start position:0% +length L python initially allocates a + + + align:start position:0% +length L python initially allocates a +contiguous memory block with uh with + + align:start position:0% +contiguous memory block with uh with + + + align:start position:0% +contiguous memory block with uh with +length L memory locations okay so if you + + align:start position:0% +length L memory locations okay so if you + + + align:start position:0% +length L memory locations okay so if you +have a list with 100 elements in it + + align:start position:0% +have a list with 100 elements in it + + + align:start position:0% +have a list with 100 elements in it +initially populated with 100 elements in + + align:start position:0% +initially populated with 100 elements in + + + align:start position:0% +initially populated with 100 elements in +it python will initially create for you + + align:start position:0% +it python will initially create for you + + + align:start position:0% +it python will initially create for you +a sequence of memory locations that are + + align:start position:0% +a sequence of memory locations that are + + + align:start position:0% +a sequence of memory locations that are +reserved for this list then it says well + + align:start position:0% +reserved for this list then it says well + + + align:start position:0% +reserved for this list then it says well +if this is going to contain just + + align:start position:0% +if this is going to contain just + + + align:start position:0% +if this is going to contain just +integers I'm going to say each one of + + align:start position:0% +integers I'm going to say each one of + + + align:start position:0% +integers I'm going to say each one of +these memory locations will hold four + + align:start position:0% +these memory locations will hold four + + + align:start position:0% +these memory locations will hold four +bytes for that integer that's kind of + + align:start position:0% +bytes for that integer that's kind of + + + align:start position:0% +bytes for that integer that's kind of +how we represent an integer right and it + + align:start position:0% +how we represent an integer right and it + + + align:start position:0% +how we represent an integer right and it +could be you know eight bytes something + + align:start position:0% +could be you know eight bytes something + + + align:start position:0% +could be you know eight bytes something +else for different machines but in this + + align:start position:0% +else for different machines but in this + + + align:start position:0% +else for different machines but in this +particular example let's just say each + + align:start position:0% +particular example let's just say each + + + align:start position:0% +particular example let's just say each +one of those memory locations will store + + align:start position:0% +one of those memory locations will store + + + align:start position:0% +one of those memory locations will store +an integer and that's four bytes long + + align:start position:0% +an integer and that's four bytes long + + + align:start position:0% +an integer and that's four bytes long +well if this list is contiguous right a + + align:start position:0% +well if this list is contiguous right a + + + align:start position:0% +well if this list is contiguous right a +bunch of blocks of memory in all in + + align:start position:0% +bunch of blocks of memory in all in + + + align:start position:0% +bunch of blocks of memory in all in +order then to access the I element all + + align:start position:0% +order then to access the I element all + + + align:start position:0% +order then to access the I element all +you need to do is a little bit of math + + align:start position:0% +you need to do is a little bit of math + + + align:start position:0% +you need to do is a little bit of math +right so here I've got an integer in one + + align:start position:0% +right so here I've got an integer in one + + + align:start position:0% +right so here I've got an integer in one +uh position in my contiguous block then + + align:start position:0% +uh position in my contiguous block then + + + align:start position:0% +uh position in my contiguous block then +I have maybe another integer at the next + + align:start position:0% +I have maybe another integer at the next + + + align:start position:0% +I have maybe another integer at the next +position and so on and so on until I + + align:start position:0% +position and so on and so on until I + + + align:start position:0% +position and so on and so on until I +have another integer at the I position + + align:start position:0% +have another integer at the I position + + + align:start position:0% +have another integer at the I position +so since these are consecutive to access + + align:start position:0% +so since these are consecutive to access + + + align:start position:0% +so since these are consecutive to access +the location of the of the element in + + align:start position:0% +the location of the of the element in + + + align:start position:0% +the location of the of the element in +this I spot all I need to do is look up + + align:start position:0% +this I spot all I need to do is look up + + + align:start position:0% +this I spot all I need to do is look up +that many memory locations from the + + align:start position:0% +that many memory locations from the + + + align:start position:0% +that many memory locations from the +start of my list okay so that's just + + align:start position:0% +start of my list okay so that's just + + + align:start position:0% +start of my list okay so that's just +pure math so one bite is eight bits so + + align:start position:0% +pure math so one bite is eight bits so + + + align:start position:0% +pure math so one bite is eight bits so +if I have have 4 + + align:start position:0% +if I have have 4 + + + align:start position:0% +if I have have 4 +* uh 4 * 8 Bits multiplied I plus the + + align:start position:0% +* uh 4 * 8 Bits multiplied I plus the + + + align:start position:0% +* uh 4 * 8 Bits multiplied I plus the +first location that will tell me exactly + + align:start position:0% +first location that will tell me exactly + + + align:start position:0% +first location that will tell me exactly +the location of the I integer + + align:start position:0% +the location of the I integer + + + align:start position:0% +the location of the I integer +okay so this is all made possible + + align:start position:0% +okay so this is all made possible + + + align:start position:0% +okay so this is all made possible +because these memory uh these memory + + align:start position:0% +because these memory uh these memory + + + align:start position:0% +because these memory uh these memory +locations are allocated in order if they + + align:start position:0% +locations are allocated in order if they + + + align:start position:0% +locations are allocated in order if they +were allocated not in in order then + + align:start position:0% +were allocated not in in order then + + + align:start position:0% +were allocated not in in order then +maybe this would not be uh as as easy + + align:start position:0% +maybe this would not be uh as as easy + + + align:start position:0% +maybe this would not be uh as as easy +yeah is it 32 um 32 because uh so if I + + align:start position:0% +yeah is it 32 um 32 because uh so if I + + + align:start position:0% +yeah is it 32 um 32 because uh so if I +say an integer is stored as four bytes + + align:start position:0% +say an integer is stored as four bytes + + + align:start position:0% +say an integer is stored as four bytes +um in bits that's 4 * 8 because eight + + align:start position:0% +um in bits that's 4 * 8 because eight + + + align:start position:0% +um in bits that's 4 * 8 because eight +bits is in one bite so eight Time 4 is + + align:start position:0% +bits is in one bite so eight Time 4 is + + + align:start position:0% +bits is in one bite so eight Time 4 is +32 bits for one bite + + align:start position:0% +32 bits for one bite + + + align:start position:0% +32 bits for one bite +yeah all right but this is assuming that + + align:start position:0% +yeah all right but this is assuming that + + + align:start position:0% +yeah all right but this is assuming that +I'm storing integers and obviously lists + + align:start position:0% +I'm storing integers and obviously lists + + + align:start position:0% +I'm storing integers and obviously lists +can contain other lists they can contain + + align:start position:0% +can contain other lists they can contain + + + align:start position:0% +can contain other lists they can contain +tupal they can contain dictionaries and + + align:start position:0% +tupal they can contain dictionaries and + + + align:start position:0% +tupal they can contain dictionaries and +some of those objects might not fit + + align:start position:0% +some of those objects might not fit + + + align:start position:0% +some of those objects might not fit +within this set number of bytes right + + align:start position:0% +within this set number of bytes right + + + align:start position:0% +within this set number of bytes right +within four bytes because some of those + + align:start position:0% +within four bytes because some of those + + + align:start position:0% +within four bytes because some of those +objects might be very very large + + align:start position:0% +objects might be very very large + + + align:start position:0% +objects might be very very large +themselves so in that particular case + + align:start position:0% +themselves so in that particular case + + + align:start position:0% +themselves so in that particular case +let's say the list is + + align:start position:0% +let's say the list is + + + align:start position:0% +let's say the list is +heterogeneous that doesn't phase us + + align:start position:0% +heterogeneous that doesn't phase us + + + align:start position:0% +heterogeneous that doesn't phase us +because we can say well instead of + + align:start position:0% +because we can say well instead of + + + align:start position:0% +because we can say well instead of +storing the object itself at each memory + + align:start position:0% +storing the object itself at each memory + + + align:start position:0% +storing the object itself at each memory +location that worked for integers but + + align:start position:0% +location that worked for integers but + + + align:start position:0% +location that worked for integers but +not might not work when we have to store + + align:start position:0% +not might not work when we have to store + + + align:start position:0% +not might not work when we have to store +a list of you know a thousand elements + + align:start position:0% +a list of you know a thousand elements + + + align:start position:0% +a list of you know a thousand elements +at a particular memory + + align:start position:0% +at a particular memory + + + align:start position:0% +at a particular memory +location let's instead instead of + + align:start position:0% +location let's instead instead of + + + align:start position:0% +location let's instead instead of +storing the element itself let's store a + + align:start position:0% +storing the element itself let's store a + + + align:start position:0% +storing the element itself let's store a +pointer and a pointer is just a number + + align:start position:0% +pointer and a pointer is just a number + + + align:start position:0% +pointer and a pointer is just a number +that tells you which memory location + + align:start position:0% +that tells you which memory location + + + align:start position:0% +that tells you which memory location +that list might be stored at or that + + align:start position:0% +that list might be stored at or that + + + align:start position:0% +that list might be stored at or that +dictionary might be stored at right so + + align:start position:0% +dictionary might be stored at right so + + + align:start position:0% +dictionary might be stored at right so +if we store a pointer at a particular + + align:start position:0% +if we store a pointer at a particular + + + align:start position:0% +if we store a pointer at a particular +memory location then that means that + + align:start position:0% +memory location then that means that + + + align:start position:0% +memory location then that means that +this is my again contiguous memory + + align:start position:0% +this is my again contiguous memory + + + align:start position:0% +this is my again contiguous memory +allocated for a list of length l or + + align:start position:0% +allocated for a list of length l or + + + align:start position:0% +allocated for a list of length l or +something like that then here I'm + + align:start position:0% +something like that then here I'm + + + align:start position:0% +something like that then here I'm +storing still an integer and that + + align:start position:0% +storing still an integer and that + + + align:start position:0% +storing still an integer and that +integer tells python + + align:start position:0% +integer tells python + + + align:start position:0% +integer tells python +which memory location to jump to to grab + + align:start position:0% +which memory location to jump to to grab + + + align:start position:0% +which memory location to jump to to grab +the integer that's stored there or + + align:start position:0% +the integer that's stored there or + + + align:start position:0% +the integer that's stored there or +something like that okay and here I + + align:start position:0% +something like that okay and here I + + + align:start position:0% +something like that okay and here I +might have another list that I'm storing + + align:start position:0% +might have another list that I'm storing + + + align:start position:0% +might have another list that I'm storing +but I'm not storing it exactly in that + + align:start position:0% +but I'm not storing it exactly in that + + + align:start position:0% +but I'm not storing it exactly in that +memory location it's pointed to by uh by + + align:start position:0% +memory location it's pointed to by uh by + + + align:start position:0% +memory location it's pointed to by uh by +this pointer that tells python again to + + align:start position:0% +this pointer that tells python again to + + + align:start position:0% +this pointer that tells python again to +jump to a different memory location + + align:start position:0% +jump to a different memory location + + + align:start position:0% +jump to a different memory location +where that list might be continuously + + align:start position:0% +where that list might be continuously + + + align:start position:0% +where that list might be continuously +stored itself right so here in this in + + align:start position:0% +stored itself right so here in this in + + + align:start position:0% +stored itself right so here in this in +this example I'm still + + align:start position:0% +this example I'm still + + + align:start position:0% +this example I'm still +storing um numbers it's just that these + + align:start position:0% +storing um numbers it's just that these + + + align:start position:0% +storing um numbers it's just that these +numbers correspond to a memory location + + align:start position:0% +numbers correspond to a memory location + + + align:start position:0% +numbers correspond to a memory location +that tells python where to go to get my + + align:start position:0% +that tells python where to go to get my + + + align:start position:0% +that tells python where to go to get my +element in that list right so in terms + + align:start position:0% +element in that list right so in terms + + + align:start position:0% +element in that list right so in terms +of the computation to get the I element + + align:start position:0% +of the computation to get the I element + + + align:start position:0% +of the computation to get the I element +in the list it's going to be the same + + align:start position:0% +in the list it's going to be the same + + + align:start position:0% +in the list it's going to be the same +I'm still allocating in my original list + + align:start position:0% +I'm still allocating in my original list + + + align:start position:0% +I'm still allocating in my original list +four bytes to store my pointer again + + align:start position:0% +four bytes to store my pointer again + + + align:start position:0% +four bytes to store my pointer again +just a number and so to get the I + + align:start position:0% +just a number and so to get the I + + + align:start position:0% +just a number and so to get the I +location all I need to do is tell python + + align:start position:0% +location all I need to do is tell python + + + align:start position:0% +location all I need to do is tell python +to go the start of this list plus 32 * I + + align:start position:0% +to go the start of this list plus 32 * I + + + align:start position:0% +to go the start of this list plus 32 * I +locations down to get to that + + align:start position:0% +locations down to get to that + + + align:start position:0% +locations down to get to that +element okay so this formula here right + + align:start position:0% +element okay so this formula here right + + + align:start position:0% +element okay so this formula here right +adding the start of this memory location + + align:start position:0% +adding the start of this memory location + + + align:start position:0% +adding the start of this memory location +of the list plus 32 * I is just math + + align:start position:0% +of the list plus 32 * I is just math + + + align:start position:0% +of the list plus 32 * I is just math +there's nothing here that depends on the + + align:start position:0% +there's nothing here that depends on the + + + align:start position:0% +there's nothing here that depends on the +length of the list right so to grab the + + align:start position:0% +length of the list right so to grab the + + + align:start position:0% +length of the list right so to grab the +element at the I location right + + align:start position:0% +element at the I location right + + + align:start position:0% +element at the I location right +somewhere within here all we're doing is + + align:start position:0% +somewhere within here all we're doing is + + + align:start position:0% +somewhere within here all we're doing is +some math right an addition and a + + align:start position:0% +some math right an addition and a + + + align:start position:0% +some math right an addition and a +multiplication and since that is just + + align:start position:0% +multiplication and since that is just + + + align:start position:0% +multiplication and since that is just +you know that none none of that depends + + align:start position:0% +you know that none none of that depends + + + align:start position:0% +you know that none none of that depends +on the length of the list the complexity + + align:start position:0% +on the length of the list the complexity + + + align:start position:0% +on the length of the list the complexity +to access the I element in the list is + + align:start position:0% +to access the I element in the list is + + + align:start position:0% +to access the I element in the list is +constant right just math and we're using + + align:start position:0% +constant right just math and we're using + + + align:start position:0% +constant right just math and we're using +this idea that we are we know exactly + + align:start position:0% +this idea that we are we know exactly + + + align:start position:0% +this idea that we are we know exactly +how many uh memory locations we need to + + align:start position:0% +how many uh memory locations we need to + + + align:start position:0% +how many uh memory locations we need to +jump to get to the I location does that + + align:start position:0% +jump to get to the I location does that + + + align:start position:0% +jump to get to the I location does that +make + + align:start position:0% +make + + + align:start position:0% +make +sense okay so that leads us to uh the + + align:start position:0% +sense okay so that leads us to uh the + + + align:start position:0% +sense okay so that leads us to uh the +question well okay we're storing a list + + align:start position:0% +question well okay we're storing a list + + + align:start position:0% +question well okay we're storing a list +of elements and we're using the idea + + align:start position:0% +of elements and we're using the idea + + + align:start position:0% +of elements and we're using the idea +that a list has indices right to tell us + + align:start position:0% +that a list has indices right to tell us + + + align:start position:0% +that a list has indices right to tell us +the value there's an element at index + + align:start position:0% +the value there's an element at index + + + align:start position:0% +the value there's an element at index +zero a an element at index one an + + align:start position:0% +zero a an element at index one an + + + align:start position:0% +zero a an element at index one an +element at index two and so on so + + align:start position:0% +element at index two and so on so + + + align:start position:0% +element at index two and so on so +there's an order to the lists right and + + align:start position:0% +there's an order to the lists right and + + + align:start position:0% +there's an order to the lists right and +because of that order we're able to + + align:start position:0% +because of that order we're able to + + + align:start position:0% +because of that order we're able to +index an element at the I location in + + align:start position:0% +index an element at the I location in + + + align:start position:0% +index an element at the I location in +constant time but let's say we wanted to + + align:start position:0% +constant time but let's say we wanted to + + + align:start position:0% +constant time but let's say we wanted to +store a DI + + align:start position:0% +store a DI + + + align:start position:0% +store a DI +dictionary a dictionary does not have an + + align:start position:0% +dictionary a dictionary does not have an + + + align:start position:0% +dictionary a dictionary does not have an +order to it right and what does a + + align:start position:0% +order to it right and what does a + + + align:start position:0% +order to it right and what does a +dictionary store it stores a key value + + align:start position:0% +dictionary store it stores a key value + + + align:start position:0% +dictionary store it stores a key value +pair in a list you could think of the + + align:start position:0% +pair in a list you could think of the + + + align:start position:0% +pair in a list you could think of the +quote unquote key as the index 0 1 2 3 + + align:start position:0% +quote unquote key as the index 0 1 2 3 + + + align:start position:0% +quote unquote key as the index 0 1 2 3 +four and so on and the value was the + + align:start position:0% +four and so on and the value was the + + + align:start position:0% +four and so on and the value was the +element at that index but in a + + align:start position:0% +element at that index but in a + + + align:start position:0% +element at that index but in a +dictionary the key is not ordered right + + align:start position:0% +dictionary the key is not ordered right + + + align:start position:0% +dictionary the key is not ordered right +the key can be anything so here I've got + + align:start position:0% +the key can be anything so here I've got + + + align:start position:0% +the key can be anything so here I've got +a dictionary that Maps maybe a name to a + + align:start position:0% +a dictionary that Maps maybe a name to a + + + align:start position:0% +a dictionary that Maps maybe a name to a +Boolean Maybe you know this student is + + align:start position:0% +Boolean Maybe you know this student is + + + align:start position:0% +Boolean Maybe you know this student is +in this class true or false so a naive + + align:start position:0% +in this class true or false so a naive + + + align:start position:0% +in this class true or false so a naive +implementation of a dictionary could be + + align:start position:0% +implementation of a dictionary could be + + + align:start position:0% +implementation of a dictionary could be +to say well let's Implement elements of + + align:start position:0% +to say well let's Implement elements of + + + align:start position:0% +to say well let's Implement elements of +the dictionary so a key value pair as a + + align:start position:0% +the dictionary so a key value pair as a + + + align:start position:0% +the dictionary so a key value pair as a +list so just two elements the first + + align:start position:0% +list so just two elements the first + + + align:start position:0% +list so just two elements the first +element in that list is my key and the + + align:start position:0% +element in that list is my key and the + + + align:start position:0% +element in that list is my key and the +second element in my list is my value + + align:start position:0% +second element in my list is my value + + + align:start position:0% +second element in my list is my value +right so here really naive + + align:start position:0% +right so here really naive + + + align:start position:0% +right so here really naive +implementation uses the list and I've + + align:start position:0% +implementation uses the list and I've + + + align:start position:0% +implementation uses the list and I've +got four entries in my dictionary the + + align:start position:0% +got four entries in my dictionary the + + + align:start position:0% +got four entries in my dictionary the +element at index zero are all stri + + align:start position:0% +element at index zero are all stri + + + align:start position:0% +element at index zero are all stri +strings the element at index one in each + + align:start position:0% +strings the element at index one in each + + + align:start position:0% +strings the element at index one in each +location is my value associated with + + align:start position:0% +location is my value associated with + + + align:start position:0% +location is my value associated with +that + + align:start position:0% +that + + + align:start position:0% +that +key well if I were to index into this + + align:start position:0% +key well if I were to index into this + + + align:start position:0% +key well if I were to index into this +list right to grab the value associated + + align:start position:0% +list right to grab the value associated + + + align:start position:0% +list right to grab the value associated +with Eric for example can I do that in + + align:start position:0% +with Eric for example can I do that in + + + align:start position:0% +with Eric for example can I do that in +constant + + align:start position:0% +constant + + + align:start position:0% +constant +time no right because there's no + + align:start position:0% +time no right because there's no + + + align:start position:0% +time no right because there's no +numerical index here there's no order to + + align:start position:0% +numerical index here there's no order to + + + align:start position:0% +numerical index here there's no order to +this set of values right + + align:start position:0% +this set of values right + + + align:start position:0% +this set of values right +um it's not even an alphabetical order + + align:start position:0% +um it's not even an alphabetical order + + + align:start position:0% +um it's not even an alphabetical order +right so a then J then e then s and + + align:start position:0% +right so a then J then e then s and + + + align:start position:0% +right so a then J then e then s and +there's no order guaranteed for + + align:start position:0% +there's no order guaranteed for + + + align:start position:0% +there's no order guaranteed for +dictionaries anyway so in order to look + + align:start position:0% +dictionaries anyway so in order to look + + + align:start position:0% +dictionaries anyway so in order to look +up an item in this naive implementation + + align:start position:0% +up an item in this naive implementation + + + align:start position:0% +up an item in this naive implementation +of a dictionary where you're just + + align:start position:0% +of a dictionary where you're just + + + align:start position:0% +of a dictionary where you're just +putting all the elements in order in a + + align:start position:0% +putting all the elements in order in a + + + align:start position:0% +putting all the elements in order in a +list it's Theta of n where n is the + + align:start position:0% +list it's Theta of n where n is the + + + align:start position:0% +list it's Theta of n where n is the +length of our list right and + + align:start position:0% +length of our list right and + + + align:start position:0% +length of our list right and +so this implementation of a dictionary + + align:start position:0% +so this implementation of a dictionary + + + align:start position:0% +so this implementation of a dictionary +doesn't + + align:start position:0% +doesn't + + + align:start position:0% +doesn't +work and yet when I showed you this + + align:start position:0% +work and yet when I showed you this + + + align:start position:0% +work and yet when I showed you this +slide a few a few uh a few lect lectures + + align:start position:0% +slide a few a few uh a few lect lectures + + + align:start position:0% +slide a few a few uh a few lect lectures +ago we saw something interesting so this + + align:start position:0% +ago we saw something interesting so this + + + align:start position:0% +ago we saw something interesting so this +is what we just uh what we just kind of + + align:start position:0% +is what we just uh what we just kind of + + + align:start position:0% +is what we just uh what we just kind of +proved quote unquote um the access time + + align:start position:0% +proved quote unquote um the access time + + + align:start position:0% +proved quote unquote um the access time +in a list is + + align:start position:0% +in a list is + + + align:start position:0% +in a list is +constant but the access time in a + + align:start position:0% +constant but the access time in a + + + align:start position:0% +constant but the access time in a +dictionary is uh is constant as well in + + align:start position:0% +dictionary is uh is constant as well in + + + align:start position:0% +dictionary is uh is constant as well in +the average case in the worst case it is + + align:start position:0% +the average case in the worst case it is + + + align:start position:0% +the average case in the worst case it is +Theta of n right accessing an item in a + + align:start position:0% +Theta of n right accessing an item in a + + + align:start position:0% +Theta of n right accessing an item in a +dictionary is Theta of V because in the + + align:start position:0% +dictionary is Theta of V because in the + + + align:start position:0% +dictionary is Theta of V because in the +worst case we might store the dictionary + + align:start position:0% +worst case we might store the dictionary + + + align:start position:0% +worst case we might store the dictionary +like this right it's just a list of all + + align:start position:0% +like this right it's just a list of all + + + align:start position:0% +like this right it's just a list of all +of our dictionary entries all in order + + align:start position:0% +of our dictionary entries all in order + + + align:start position:0% +of our dictionary entries all in order +so to look up one index we'd have to go + + align:start position:0% +so to look up one index we'd have to go + + + align:start position:0% +so to look up one index we'd have to go +through the entire list and check if the + + align:start position:0% +through the entire list and check if the + + + align:start position:0% +through the entire list and check if the +element at index zero is the one we're + + align:start position:0% +element at index zero is the one we're + + + align:start position:0% +element at index zero is the one we're +looking for and then grab the element at + + align:start position:0% +looking for and then grab the element at + + + align:start position:0% +looking for and then grab the element at +index one as its value but in the + + align:start position:0% +index one as its value but in the + + + align:start position:0% +index one as its value but in the +average case and this is what we're + + align:start position:0% +average case and this is what we're + + + align:start position:0% +average case and this is what we're +going to see next in the average case + + align:start position:0% +going to see next in the average case + + + align:start position:0% +going to see next in the average case +the access the time it takes to do a + + align:start position:0% +the access the time it takes to do a + + + align:start position:0% +the access the time it takes to do a +lookup for a key uh in a dictionary is + + align:start position:0% +lookup for a key uh in a dictionary is + + + align:start position:0% +lookup for a key uh in a dictionary is +constant it's actually Theta of one + + align:start position:0% +constant it's actually Theta of one + + + align:start position:0% +constant it's actually Theta of one +which makes dictionary really powerful + + align:start position:0% +which makes dictionary really powerful + + + align:start position:0% +which makes dictionary really powerful +data structures to use in a lot of + + align:start position:0% +data structures to use in a lot of + + + align:start position:0% +data structures to use in a lot of +situations so why is this well it has to + + align:start position:0% +situations so why is this well it has to + + + align:start position:0% +situations so why is this well it has to +do with the idea of hashing okay so the + + align:start position:0% +do with the idea of hashing okay so the + + + align:start position:0% +do with the idea of hashing okay so the +way that dictionaries are actually + + align:start position:0% +way that dictionaries are actually + + + align:start position:0% +way that dictionaries are actually +stored in memory is not as a list of a + + align:start position:0% +stored in memory is not as a list of a + + + align:start position:0% +stored in memory is not as a list of a +bunch of entries right we just showed + + align:start position:0% +bunch of entries right we just showed + + + align:start position:0% +bunch of entries right we just showed +that that is not feasible that leads to + + align:start position:0% +that that is not feasible that leads to + + + align:start position:0% +that that is not feasible that leads to +a Theta of n lookup time so instead they + + align:start position:0% +a Theta of n lookup time so instead they + + + align:start position:0% +a Theta of n lookup time so instead they +use something called a hash table we + + align:start position:0% +use something called a hash table we + + + align:start position:0% +use something called a hash table we +briefly spoke about + + align:start position:0% +briefly spoke about + + + align:start position:0% +briefly spoke about +this a hash table is just like a long + + align:start position:0% +this a hash table is just like a long + + + align:start position:0% +this a hash table is just like a long +list uh and the indices of the hash + + align:start position:0% +list uh and the indices of the hash + + + align:start position:0% +list uh and the indices of the hash +table are actually things that you look + + align:start position:0% +table are actually things that you look + + + align:start position:0% +table are actually things that you look +up using a hash function okay so how + + align:start position:0% +up using a hash function okay so how + + + align:start position:0% +up using a hash function okay so how +does this work well any key that you'd + + align:start position:0% +does this work well any key that you'd + + + align:start position:0% +does this work well any key that you'd +like to add to a + + align:start position:0% +like to add to a + + + align:start position:0% +like to add to a +dictionary can actually actually has a + + align:start position:0% +dictionary can actually actually has a + + + align:start position:0% +dictionary can actually actually has a +hash function run on it and this hash + + align:start position:0% +hash function run on it and this hash + + + align:start position:0% +hash function run on it and this hash +function takes in maybe an integer maybe + + align:start position:0% +function takes in maybe an integer maybe + + + align:start position:0% +function takes in maybe an integer maybe +a float maybe a string maybe a tupal any + + align:start position:0% +a float maybe a string maybe a tupal any + + + align:start position:0% +a float maybe a string maybe a tupal any +sort of any any hashable object hashes + + align:start position:0% +sort of any any hashable object hashes + + + align:start position:0% +sort of any any hashable object hashes +it which means it takes that object if + + align:start position:0% +it which means it takes that object if + + + align:start position:0% +it which means it takes that object if +it's a string it'll give us an integer + + align:start position:0% +it's a string it'll give us an integer + + + align:start position:0% +it's a string it'll give us an integer +if it's a tuple it'll give us an integer + + align:start position:0% +if it's a tuple it'll give us an integer + + + align:start position:0% +if it's a tuple it'll give us an integer +so if it hashes it that means it takes + + align:start position:0% +so if it hashes it that means it takes + + + align:start position:0% +so if it hashes it that means it takes +it in as an input and gives us back a + + align:start position:0% +it in as an input and gives us back a + + + align:start position:0% +it in as an input and gives us back a +number an + + align:start position:0% +number an + + + align:start position:0% +number an +integer and that integer is what is used + + align:start position:0% +integer and that integer is what is used + + + align:start position:0% +integer and that integer is what is used +as the index to look it up in the hash + + align:start position:0% +as the index to look it up in the hash + + + align:start position:0% +as the index to look it up in the hash +table to look up the value associated + + align:start position:0% +table to look up the value associated + + + align:start position:0% +table to look up the value associated +with it in a hash table so in that sense + + align:start position:0% +with it in a hash table so in that sense + + + align:start position:0% +with it in a hash table so in that sense +the lookup itself is constant time + + align:start position:0% +the lookup itself is constant time + + + align:start position:0% +the lookup itself is constant time +because we just showed looking up an + + align:start position:0% +because we just showed looking up an + + + align:start position:0% +because we just showed looking up an +item in a AR using the index is constant + + align:start position:0% +item in a AR using the index is constant + + + align:start position:0% +item in a AR using the index is constant +time and if that hash function is also + + align:start position:0% +time and if that hash function is also + + + align:start position:0% +time and if that hash function is also +constant time then the time it takes to + + align:start position:0% +constant time then the time it takes to + + + align:start position:0% +constant time then the time it takes to +uh look up an item in a dictionary is + + align:start position:0% +uh look up an item in a dictionary is + + + align:start position:0% +uh look up an item in a dictionary is +also constant + + align:start position:0% +also constant + + + align:start position:0% +also constant +time so here are some examples of the + + align:start position:0% +time so here are some examples of the + + + align:start position:0% +time so here are some examples of the +Python hash function actually being run + + align:start position:0% +Python hash function actually being run + + + align:start position:0% +Python hash function actually being run +on different objects so up here if I run + + align:start position:0% +on different objects so up here if I run + + + align:start position:0% +on different objects so up here if I run +it's it's literally a function in Python + + align:start position:0% +it's it's literally a function in Python + + + align:start position:0% +it's it's literally a function in Python +hash of some parameter so in this case + + align:start position:0% +hash of some parameter so in this case + + + align:start position:0% +hash of some parameter so in this case +123 it just gives me the value back so + + align:start position:0% +123 it just gives me the value back so + + + align:start position:0% +123 it just gives me the value back so +the hash of some number is the number + + align:start position:0% +the hash of some number is the number + + + align:start position:0% +the hash of some number is the number +itself itself um we can hash a + + align:start position:0% +itself itself um we can hash a + + + align:start position:0% +itself itself um we can hash a +string uh that'll give us you know this + + align:start position:0% +string uh that'll give us you know this + + + align:start position:0% +string uh that'll give us you know this +particular number so again an integer + + align:start position:0% +particular number so again an integer + + + align:start position:0% +particular number so again an integer +the hash of a tuple also gives us some + + align:start position:0% +the hash of a tuple also gives us some + + + align:start position:0% +the hash of a tuple also gives us some +number back so these are all this these + + align:start position:0% +number back so these are all this these + + + align:start position:0% +number back so these are all this these +are all just some function running + + align:start position:0% +are all just some function running + + + align:start position:0% +are all just some function running +behind the scenes that takes in this + + align:start position:0% +behind the scenes that takes in this + + + align:start position:0% +behind the scenes that takes in this +hashable object and gives us back a + + align:start position:0% +hashable object and gives us back a + + + align:start position:0% +hashable object and gives us back a +number that's it now we can't run a hash + + align:start position:0% +number that's it now we can't run a hash + + + align:start position:0% +number that's it now we can't run a hash +function on a list because a list is + + align:start position:0% +function on a list because a list is + + + align:start position:0% +function on a list because a list is +mutable and therefore unhashable right + + align:start position:0% +mutable and therefore unhashable right + + + align:start position:0% +mutable and therefore unhashable right +if the object changes then the hash + + align:start position:0% +if the object changes then the hash + + + align:start position:0% +if the object changes then the hash +function run on this object will give us + + align:start position:0% +function run on this object will give us + + + align:start position:0% +function run on this object will give us +a different value + + align:start position:0% +a different value + + + align:start position:0% +a different value +okay okay so if you actually run this on + + align:start position:0% +okay okay so if you actually run this on + + + align:start position:0% +okay okay so if you actually run this on +your own computer you might get + + align:start position:0% +your own computer you might get + + + align:start position:0% +your own computer you might get +different answers or if you run it at + + align:start position:0% +different answers or if you run it at + + + align:start position:0% +different answers or if you run it at +different times you might get different + + align:start position:0% +different times you might get different + + + align:start position:0% +different times you might get different +answers because python adds a little bit + + align:start position:0% +answers because python adds a little bit + + + align:start position:0% +answers because python adds a little bit +of Randomness to the uh the hash values + + align:start position:0% +of Randomness to the uh the hash values + + + align:start position:0% +of Randomness to the uh the hash values +just in case you want to encrypt data + + align:start position:0% +just in case you want to encrypt data + + + align:start position:0% +just in case you want to encrypt data +and things like that but generally you + + align:start position:0% +and things like that but generally you + + + align:start position:0% +and things like that but generally you +will always get some integer back if you + + align:start position:0% +will always get some integer back if you + + + align:start position:0% +will always get some integer back if you +run the hash function on a mut uh on a + + align:start position:0% +run the hash function on a mut uh on a + + + align:start position:0% +run the hash function on a mut uh on a +immutable object + + align:start position:0% +immutable object + + + align:start position:0% +immutable object +okay so then that begs the question how + + align:start position:0% +okay so then that begs the question how + + + align:start position:0% +okay so then that begs the question how +big should a hash table be right so if a + + align:start position:0% +big should a hash table be right so if a + + + align:start position:0% +big should a hash table be right so if a +hash table is basically just a long list + + align:start position:0% +hash table is basically just a long list + + + align:start position:0% +hash table is basically just a long list +and if I run a function on some object + + align:start position:0% +and if I run a function on some object + + + align:start position:0% +and if I run a function on some object +to give me the value of an index within + + align:start position:0% +to give me the value of an index within + + + align:start position:0% +to give me the value of an index within +that list how big should this table be + + align:start position:0% +that list how big should this table be + + + align:start position:0% +that list how big should this table be +how many indices should I have a + + align:start position:0% +how many indices should I have a + + + align:start position:0% +how many indices should I have a +thousand a million 10 million right + + align:start position:0% +thousand a million 10 million right + + + align:start position:0% +thousand a million 10 million right +what's a good + + align:start position:0% +what's a good + + + align:start position:0% +what's a good +number well let's take a example of a + + align:start position:0% +number well let's take a example of a + + + align:start position:0% +number well let's take a example of a +string okay so for a string what we can + + align:start position:0% +string okay so for a string what we can + + + align:start position:0% +string okay so for a string what we can +do is and we can use my name as an + + align:start position:0% +do is and we can use my name as an + + + align:start position:0% +do is and we can use my name as an +example if we want to Hash uh my name + + align:start position:0% +example if we want to Hash uh my name + + + align:start position:0% +example if we want to Hash uh my name +such that every single name hashes to + + align:start position:0% +such that every single name hashes to + + + align:start position:0% +such that every single name hashes to +something unique what we can do is the + + align:start position:0% +something unique what we can do is the + + + align:start position:0% +something unique what we can do is the +following so we can take each character + + align:start position:0% +following so we can take each character + + + align:start position:0% +following so we can take each character +in somebody's name and behind the scenes + + align:start position:0% +in somebody's name and behind the scenes + + + align:start position:0% +in somebody's name and behind the scenes +each one of these uh uh characters + + align:start position:0% +each one of these uh uh characters + + + align:start position:0% +each one of these uh uh characters +actually has uh an integer uh sorry an + + align:start position:0% +actually has uh an integer uh sorry an + + + align:start position:0% +actually has uh an integer uh sorry an +asky code associated with it which is + + align:start position:0% +asky code associated with it which is + + + align:start position:0% +asky code associated with it which is +something numeric and what we can do is + + align:start position:0% +something numeric and what we can do is + + + align:start position:0% +something numeric and what we can do is +just conver convert that number to + + align:start position:0% +just conver convert that number to + + + align:start position:0% +just conver convert that number to +Binary so the letter capital A happens + + align:start position:0% +Binary so the letter capital A happens + + + align:start position:0% +Binary so the letter capital A happens +to be uh this binary value right 0 1 0 0 + + align:start position:0% +to be uh this binary value right 0 1 0 0 + + + align:start position:0% +to be uh this binary value right 0 1 0 0 +z001 the lowercase n is this value the + + align:start position:0% +z001 the lowercase n is this value the + + + align:start position:0% +z001 the lowercase n is this value the +lowercase a is this value and so on + + align:start position:0% +lowercase a is this value and so on + + + align:start position:0% +lowercase a is this value and so on +right so I've got seven different sort + + align:start position:0% +right so I've got seven different sort + + + align:start position:0% +right so I've got seven different sort +of groups of eight bits here for + + align:start position:0% +of groups of eight bits here for + + + align:start position:0% +of groups of eight bits here for +corresponding to each letter in my name + + align:start position:0% +corresponding to each letter in my name + + + align:start position:0% +corresponding to each letter in my name +now if I take those bits and now just + + align:start position:0% +now if I take those bits and now just + + + align:start position:0% +now if I take those bits and now just +smush them together concatenate them to + + align:start position:0% +smush them together concatenate them to + + + align:start position:0% +smush them together concatenate them to +give me one really really big number + + align:start position:0% +give me one really really big number + + + align:start position:0% +give me one really really big number +right so this is all going to be one + + align:start position:0% +right so this is all going to be one + + + align:start position:0% +right so this is all going to be one +really big + + align:start position:0% +really big + + + align:start position:0% +really big +number the corresponding number in base + + align:start position:0% +number the corresponding number in base + + + align:start position:0% +number the corresponding number in base +10 is this really long + + align:start position:0% +10 is this really long + + + align:start position:0% +10 is this really long +thing okay and so if I do this as long + + align:start position:0% +thing okay and so if I do this as long + + + align:start position:0% +thing okay and so if I do this as long +as someone's name is unique they will + + align:start position:0% +as someone's name is unique they will + + + align:start position:0% +as someone's name is unique they will +end up with a unique number associated + + align:start position:0% +end up with a unique number associated + + + align:start position:0% +end up with a unique number associated +with their name right and therefore that + + align:start position:0% +with their name right and therefore that + + + align:start position:0% +with their name right and therefore that +unique number can be used as a unique + + align:start position:0% +unique number can be used as a unique + + + align:start position:0% +unique number can be used as a unique +index into a really big hash + + align:start position:0% +index into a really big hash + + + align:start position:0% +index into a really big hash +table so let's think about how hashing + + align:start position:0% +table so let's think about how hashing + + + align:start position:0% +table so let's think about how hashing +the names of mit's 4,000 undergrads + + align:start position:0% +the names of mit's 4,000 undergrads + + + align:start position:0% +the names of mit's 4,000 undergrads +right let's assume that the longest name + + align:start position:0% +right let's assume that the longest name + + + align:start position:0% +right let's assume that the longest name +is 20 characters long right so there's + + align:start position:0% +is 20 characters long right so there's + + + align:start position:0% +is 20 characters long right so there's +going to be 20 of these different uh + + align:start position:0% +going to be 20 of these different uh + + + align:start position:0% +going to be 20 of these different uh +letters that we need to Hash so we use + + align:start position:0% +letters that we need to Hash so we use + + + align:start position:0% +letters that we need to Hash so we use +the same process here each one of those + + align:start position:0% +the same process here each one of those + + + align:start position:0% +the same process here each one of those +20 characters gets its own eight bit + + align:start position:0% +20 characters gets its own eight bit + + + align:start position:0% +20 characters gets its own eight bit +representation so in total the number of + + align:start position:0% +representation so in total the number of + + + align:start position:0% +representation so in total the number of +bits that I'm going to use to represent + + align:start position:0% +bits that I'm going to use to represent + + + align:start position:0% +bits that I'm going to use to represent +that 20 long character + + align:start position:0% +that 20 long character + + + align:start position:0% +that 20 long character +is going to be 8 * 20 so 160 different + + align:start position:0% +is going to be 8 * 20 so 160 different + + + align:start position:0% +is going to be 8 * 20 so 160 different +bits okay that's a lot of Bits And if I + + align:start position:0% +bits okay that's a lot of Bits And if I + + + align:start position:0% +bits okay that's a lot of Bits And if I +concatenate all those together the + + align:start position:0% +concatenate all those together the + + + align:start position:0% +concatenate all those together the +number that that corresponds to is 2 to + + align:start position:0% +number that that corresponds to is 2 to + + + align:start position:0% +number that that corresponds to is 2 to +the 160 which is this thing here okay so + + align:start position:0% +the 160 which is this thing here okay so + + + align:start position:0% +the 160 which is this thing here okay so +if I want every single combination of + + align:start position:0% +if I want every single combination of + + + align:start position:0% +if I want every single combination of +letters in the alphabet to be a unique + + align:start position:0% +letters in the alphabet to be a unique + + + align:start position:0% +letters in the alphabet to be a unique +value in this long list then I will need + + align:start position:0% +value in this long list then I will need + + + align:start position:0% +value in this long list then I will need +to have a list that is this long I'm not + + align:start position:0% +to have a list that is this long I'm not + + + align:start position:0% +to have a list that is this long I'm not +even going to try to figure out or to + + align:start position:0% +even going to try to figure out or to + + + align:start position:0% +even going to try to figure out or to +say how big this number is but it's + + align:start position:0% +say how big this number is but it's + + + align:start position:0% +say how big this number is but it's +really really + + align:start position:0% +really really + + + align:start position:0% +really really +big and having a list AKA hashtable that + + align:start position:0% +big and having a list AKA hashtable that + + + align:start position:0% +big and having a list AKA hashtable that +has this many entries will guarantee for + + align:start position:0% +has this many entries will guarantee for + + + align:start position:0% +has this many entries will guarantee for +me that names that are 20 characters + + align:start position:0% +me that names that are 20 characters + + + align:start position:0% +me that names that are 20 characters +long will each hash to something + + align:start position:0% +long will each hash to something + + + align:start position:0% +long will each hash to something +unique but I only have 4,000 names that + + align:start position:0% +unique but I only have 4,000 names that + + + align:start position:0% +unique but I only have 4,000 names that +I'd like to put in my + + align:start position:0% +I'd like to put in my + + + align:start position:0% +I'd like to put in my +table so I have 4 th000 names that I'd + + align:start position:0% +table so I have 4 th000 names that I'd + + + align:start position:0% +table so I have 4 th000 names that I'd +like to put in a table that has this + + align:start position:0% +like to put in a table that has this + + + align:start position:0% +like to put in a table that has this +many spots right so that's a lot of + + align:start position:0% +many spots right so that's a lot of + + + align:start position:0% +many spots right so that's a lot of +wasted space yeah is it 160 because he + + align:start position:0% +wasted space yeah is it 160 because he + + + align:start position:0% +wasted space yeah is it 160 because he +put it to Binary yeah so exactly so uh + + align:start position:0% +put it to Binary yeah so exactly so uh + + + align:start position:0% +put it to Binary yeah so exactly so uh +each one of the characters has eight + + align:start position:0% +each one of the characters has eight + + + align:start position:0% +each one of the characters has eight +bits associated with it right so there's + + align:start position:0% +bits associated with it right so there's + + + align:start position:0% +bits associated with it right so there's +going to be 160 of these zeros or ones + + align:start position:0% +going to be 160 of these zeros or ones + + + align:start position:0% +going to be 160 of these zeros or ones +in a row so to tell the number that that + + align:start position:0% +in a row so to tell the number that that + + + align:start position:0% +in a row so to tell the number that that +is that's associated with we basically + + align:start position:0% +is that's associated with we basically + + + align:start position:0% +is that's associated with we basically +say uh uh we basically calculate at + + align:start position:0% +say uh uh we basically calculate at + + + align:start position:0% +say uh uh we basically calculate at +1 20 with 20 zeros at the end and that + + align:start position:0% +1 20 with 20 zeros at the end and that + + + align:start position:0% +1 20 with 20 zeros at the end and that +gives me 2 to the 160 right that's going + + align:start position:0% +gives me 2 to the 160 right that's going + + + align:start position:0% +gives me 2 to the 160 right that's going +to be how big my number + + align:start position:0% +to be how big my number + + + align:start position:0% +to be how big my number +is that is uh going to be uh that's + + align:start position:0% +is that is uh going to be uh that's + + + align:start position:0% +is that is uh going to be uh that's +going to be for one for one not that's + + align:start position:0% +going to be for one for one not that's + + + align:start position:0% +going to be for one for one not that's +going to be how many slots I'll need in + + align:start position:0% +going to be how many slots I'll need in + + + align:start position:0% +going to be how many slots I'll need in +order to have unique combinations of + + align:start position:0% +order to have unique combinations of + + + align:start position:0% +order to have unique combinations of +letters be mapped to one slot right so 0 + + align:start position:0% +letters be mapped to one slot right so 0 + + + align:start position:0% +letters be mapped to one slot right so 0 +one will map to one thing 00 1 0 will + + align:start position:0% +one will map to one thing 00 1 0 will + + + align:start position:0% +one will map to one thing 00 1 0 will +map to another thing 0011 will map to + + align:start position:0% +map to another thing 0011 will map to + + + align:start position:0% +map to another thing 0011 will map to +another thing so like all these + + align:start position:0% +another thing so like all these + + + align:start position:0% +another thing so like all these +combinations of letters will each map to + + align:start position:0% +combinations of letters will each map to + + + align:start position:0% +combinations of letters will each map to +something unique and I in order to + + align:start position:0% +something unique and I in order to + + + align:start position:0% +something unique and I in order to +guarantee that I need this many slots + + align:start position:0% +guarantee that I need this many slots + + + align:start position:0% +guarantee that I need this many slots +but since again since I only have 4,000 + + align:start position:0% +but since again since I only have 4,000 + + + align:start position:0% +but since again since I only have 4,000 +undergrads well that's a lot of wasted + + align:start position:0% +undergrads well that's a lot of wasted + + + align:start position:0% +undergrads well that's a lot of wasted +space right I'm only using 4,000 of + + align:start position:0% +space right I'm only using 4,000 of + + + align:start position:0% +space right I'm only using 4,000 of +these slots to hold students names and + + align:start position:0% +these slots to hold students names and + + + align:start position:0% +these slots to hold students names and +that's because a lot of those + + align:start position:0% +that's because a lot of those + + + align:start position:0% +that's because a lot of those +combinations of letters aren't really + + align:start position:0% +combinations of letters aren't really + + + align:start position:0% +combinations of letters aren't really +valid + + align:start position:0% +valid + + + align:start position:0% +valid +right so what's the solution + + align:start position:0% +right so what's the solution + + + align:start position:0% +right so what's the solution +there's a lot of wasted space there so + + align:start position:0% +there's a lot of wasted space there so + + + align:start position:0% +there's a lot of wasted space there so +the solution would be to say well you + + align:start position:0% +the solution would be to say well you + + + align:start position:0% +the solution would be to say well you +know what I would be fine with having a + + align:start position:0% +know what I would be fine with having a + + + align:start position:0% +know what I would be fine with having a +smaller hash table I don't need that + + align:start position:0% +smaller hash table I don't need that + + + align:start position:0% +smaller hash table I don't need that +giant number of entries in my hash table + + align:start position:0% +giant number of entries in my hash table + + + align:start position:0% +giant number of entries in my hash table +I would be fine with maybe having you + + align:start position:0% +I would be fine with maybe having you + + + align:start position:0% +I would be fine with maybe having you +know 10,000 spots and then having some + + align:start position:0% +know 10,000 spots and then having some + + + align:start position:0% +know 10,000 spots and then having some +names that happen to Hash to the same + + align:start position:0% +names that happen to Hash to the same + + + align:start position:0% +names that happen to Hash to the same +thing or saying I'm fine with having a + + align:start position:0% +thing or saying I'm fine with having a + + + align:start position:0% +thing or saying I'm fine with having a +hash table that has a million spots and + + align:start position:0% +hash table that has a million spots and + + + align:start position:0% +hash table that has a million spots and +you know out of those 4,000 some will be + + align:start position:0% +you know out of those 4,000 some will be + + + align:start position:0% +you know out of those 4,000 some will be +used some will be unused and some might + + align:start position:0% +used some will be unused and some might + + + align:start position:0% +used some will be unused and some might +Collide to the same hash value and + + align:start position:0% +Collide to the same hash value and + + + align:start position:0% +Collide to the same hash value and +that's totally + + align:start position:0% +that's totally + + + align:start position:0% +that's totally +okay okay so if we allow collisions what + + align:start position:0% +okay okay so if we allow collisions what + + + align:start position:0% +okay okay so if we allow collisions what +is this going to look like so here's a + + align:start position:0% +is this going to look like so here's a + + + align:start position:0% +is this going to look like so here's a +visualization of our hash + + align:start position:0% +visualization of our hash + + + align:start position:0% +visualization of our hash +table so think of the hash table like a + + align:start position:0% +table so think of the hash table like a + + + align:start position:0% +table so think of the hash table like a +list the reason why we think of it as a + + align:start position:0% +list the reason why we think of it as a + + + align:start position:0% +list the reason why we think of it as a +list is because indexing into a list is + + align:start position:0% +list is because indexing into a list is + + + align:start position:0% +list is because indexing into a list is +constant time right we're taking + + align:start position:0% +constant time right we're taking + + + align:start position:0% +constant time right we're taking +advantage of the idea that if we index + + align:start position:0% +advantage of the idea that if we index + + + align:start position:0% +advantage of the idea that if we index +into a list that's going to be + + align:start position:0% +into a list that's going to be + + + align:start position:0% +into a list that's going to be +constant so let's say we're adding some + + align:start position:0% +constant so let's say we're adding some + + + align:start position:0% +constant so let's say we're adding some +names and grades into our hash table + + align:start position:0% +names and grades into our hash table + + + align:start position:0% +names and grades into our hash table +right so this is our representation of a + + align:start position:0% +right so this is our representation of a + + + align:start position:0% +right so this is our representation of a +dictionary the values here uh says that + + align:start position:0% +dictionary the values here uh says that + + + align:start position:0% +dictionary the values here uh says that +I have a hash table that has 16 + + align:start position:0% +I have a hash table that has 16 + + + align:start position:0% +I have a hash table that has 16 +different entries right 0 to 15 and 0 to + + align:start position:0% +different entries right 0 to 15 and 0 to + + + align:start position:0% +different entries right 0 to 15 and 0 to +15 corresponds to like the list + + align:start position:0% +15 corresponds to like the list + + + align:start position:0% +15 corresponds to like the list +index okay so if I have a name and a + + align:start position:0% +index okay so if I have a name and a + + + align:start position:0% +index okay so if I have a name and a +grade that I'd like to add to my hash + + align:start position:0% +grade that I'd like to add to my hash + + + align:start position:0% +grade that I'd like to add to my hash +table I need to run a hash function on + + align:start position:0% +table I need to run a hash function on + + + align:start position:0% +table I need to run a hash function on +the key so the key is the name and the + + align:start position:0% +the key so the key is the name and the + + + align:start position:0% +the key so the key is the name and the +grade is the uh uh the value associated + + align:start position:0% +grade is the uh uh the value associated + + + align:start position:0% +grade is the uh uh the value associated +with the name so to add Anna with the + + align:start position:0% +with the name so to add Anna with the + + + align:start position:0% +with the name so to add Anna with the +grade of C to my hash table I need to + + align:start position:0% +grade of C to my hash table I need to + + + align:start position:0% +grade of C to my hash table I need to +take my Anna which is the key and run a + + align:start position:0% +take my Anna which is the key and run a + + + align:start position:0% +take my Anna which is the key and run a +hash function on it such that when I run + + align:start position:0% +hash function on it such that when I run + + + align:start position:0% +hash function on it such that when I run +the hash function on this name a Anda + + align:start position:0% +the hash function on this name a Anda + + + align:start position:0% +the hash function on this name a Anda +it'll give me a number an integer + + align:start position:0% +it'll give me a number an integer + + + align:start position:0% +it'll give me a number an integer +between zero and 15 okay and if I can do + + align:start position:0% +between zero and 15 okay and if I can do + + + align:start position:0% +between zero and 15 okay and if I can do +that then I know I've added my uh my + + align:start position:0% +that then I know I've added my uh my + + + align:start position:0% +that then I know I've added my uh my +entry here into into one of these + + align:start position:0% +entry here into into one of these + + + align:start position:0% +entry here into into one of these +buckets so a reasonable hash function to + + align:start position:0% +buckets so a reasonable hash function to + + + align:start position:0% +buckets so a reasonable hash function to +run on the name and we saw this in the + + align:start position:0% +run on the name and we saw this in the + + + align:start position:0% +run on the name and we saw this in the +dictionary lecture is to say well let's + + align:start position:0% +dictionary lecture is to say well let's + + + align:start position:0% +dictionary lecture is to say well let's +have a ma to one B ma to two c ma to + + align:start position:0% +have a ma to one B ma to two c ma to + + + align:start position:0% +have a ma to one B ma to two c ma to +three and so on so in for my name I've + + align:start position:0% +three and so on so in for my name I've + + + align:start position:0% +three and so on so in for my name I've +got 1 + 14 + 1al 16 but since I want to + + align:start position:0% +got 1 + 14 + 1al 16 but since I want to + + + align:start position:0% +got 1 + 14 + 1al 16 but since I want to +ensure that this hash function gives me + + align:start position:0% +ensure that this hash function gives me + + + align:start position:0% +ensure that this hash function gives me +a number between 0o and 15 let's mod + + align:start position:0% +a number between 0o and 15 let's mod + + + align:start position:0% +a number between 0o and 15 let's mod +that with 16 right so I can sum all the + + align:start position:0% +that with 16 right so I can sum all the + + + align:start position:0% +that with 16 right so I can sum all the +letters in my name just fine and then + + align:start position:0% +letters in my name just fine and then + + + align:start position:0% +letters in my name just fine and then +let's finalize it by saying mod 16 to + + align:start position:0% +let's finalize it by saying mod 16 to + + + align:start position:0% +let's finalize it by saying mod 16 to +give me the remainder either 0 one two + + align:start position:0% +give me the remainder either 0 one two + + + align:start position:0% +give me the remainder either 0 one two +or 15 and if I do that I'm ensured that + + align:start position:0% +or 15 and if I do that I'm ensured that + + + align:start position:0% +or 15 and if I do that I'm ensured that +this key value pair will be added to one + + align:start position:0% +this key value pair will be added to one + + + align:start position:0% +this key value pair will be added to one +of these buckets from 0 to 50 okay so in + + align:start position:0% +of these buckets from 0 to 50 okay so in + + + align:start position:0% +of these buckets from 0 to 50 okay so in +this particular case Anna with a grade + + align:start position:0% +this particular case Anna with a grade + + + align:start position:0% +this particular case Anna with a grade +of c maps to zero right that's what the + + align:start position:0% +of c maps to zero right that's what the + + + align:start position:0% +of c maps to zero right that's what the +hash function on my name uh told me to + + align:start position:0% +hash function on my name uh told me to + + + align:start position:0% +hash function on my name uh told me to +add uh the the location that the hash + + align:start position:0% +add uh the the location that the hash + + + align:start position:0% +add uh the the location that the hash +function on my name told me to add to so + + align:start position:0% +function on my name told me to add to so + + + align:start position:0% +function on my name told me to add to so +there I am putting my name in there + + align:start position:0% +there I am putting my name in there + + + align:start position:0% +there I am putting my name in there +let's add a couple more people so here's + + align:start position:0% +let's add a couple more people so here's + + + align:start position:0% +let's add a couple more people so here's +Eric um his name hashes to 35 mod 16 so + + align:start position:0% +Eric um his name hashes to 35 mod 16 so + + + align:start position:0% +Eric um his name hashes to 35 mod 16 so +that's three so I'm going to add Eric + + align:start position:0% +that's three so I'm going to add Eric + + + align:start position:0% +that's three so I'm going to add Eric +and his grade to bucket number three + + align:start position:0% +and his grade to bucket number three + + + align:start position:0% +and his grade to bucket number three +then we can add John with a grade of B + + align:start position:0% +then we can add John with a grade of B + + + align:start position:0% +then we can add John with a grade of B +his name hashes to 47 mod 16 so that's + + align:start position:0% +his name hashes to 47 mod 16 so that's + + + align:start position:0% +his name hashes to 47 mod 16 so that's +15 so we can add John down in bucket 15 + + align:start position:0% +15 so we can add John down in bucket 15 + + + align:start position:0% +15 so we can add John down in bucket 15 +okay and then let's add Eve with a grade + + align:start position:0% +okay and then let's add Eve with a grade + + + align:start position:0% +okay and then let's add Eve with a grade +of B so she uh hashes to 32 mod 16 which + + align:start position:0% +of B so she uh hashes to 32 mod 16 which + + + align:start position:0% +of B so she uh hashes to 32 mod 16 which +is also zero and you know what Anna was + + align:start position:0% +is also zero and you know what Anna was + + + align:start position:0% +is also zero and you know what Anna was +already in the bucket zero but that's + + align:start position:0% +already in the bucket zero but that's + + + align:start position:0% +already in the bucket zero but that's +fine because you know what I have four + + align:start position:0% +fine because you know what I have four + + + align:start position:0% +fine because you know what I have four +number four names here so four entries + + align:start position:0% +number four names here so four entries + + + align:start position:0% +number four names here so four entries +that I want to add to my hash table + + align:start position:0% +that I want to add to my hash table + + + align:start position:0% +that I want to add to my hash table +dictionary and two of them + + align:start position:0% +dictionary and two of them + + + align:start position:0% +dictionary and two of them +collided that's fine I still have many + + align:start position:0% +collided that's fine I still have many + + + align:start position:0% +collided that's fine I still have many +other buckets that are empty here so if + + align:start position:0% +other buckets that are empty here so if + + + align:start position:0% +other buckets that are empty here so if +I have you know uh you know 10 students + + align:start position:0% +I have you know uh you know 10 students + + + align:start position:0% +I have you know uh you know 10 students +in my class probably they won't all hash + + align:start position:0% +in my class probably they won't all hash + + + align:start position:0% +in my class probably they won't all hash +to zero they'll probably hash you know + + align:start position:0% +to zero they'll probably hash you know + + + align:start position:0% +to zero they'll probably hash you know +somewhere within here so that it's + + align:start position:0% +somewhere within here so that it's + + + align:start position:0% +somewhere within here so that it's +nicely balanced and so maybe out of 10 + + align:start position:0% +nicely balanced and so maybe out of 10 + + + align:start position:0% +nicely balanced and so maybe out of 10 +students in my class only two collided + + align:start position:0% +students in my class only two collided + + + align:start position:0% +students in my class only two collided +and that's way better than having all of + + align:start position:0% +and that's way better than having all of + + + align:start position:0% +and that's way better than having all of +the students in the class be you know + + align:start position:0% +the students in the class be you know + + + align:start position:0% +the students in the class be you know +enumerated in one long list right so + + align:start position:0% +enumerated in one long list right so + + + align:start position:0% +enumerated in one long list right so +when I look up Anna the way that this + + align:start position:0% +when I look up Anna the way that this + + + align:start position:0% +when I look up Anna the way that this +works is you hash the name Anna against + + align:start position:0% +works is you hash the name Anna against + + + align:start position:0% +works is you hash the name Anna against +right so when you want to look up the + + align:start position:0% +right so when you want to look up the + + + align:start position:0% +right so when you want to look up the +grade of Anna you that's the key you + + align:start position:0% +grade of Anna you that's the key you + + + align:start position:0% +grade of Anna you that's the key you +hash the value again you say hey Anna + + align:start position:0% +hash the value again you say hey Anna + + + align:start position:0% +hash the value again you say hey Anna +hash to zero so then I'm going to look + + align:start position:0% +hash to zero so then I'm going to look + + + align:start position:0% +hash to zero so then I'm going to look +in bucket zero and say all right let me + + align:start position:0% +in bucket zero and say all right let me + + + align:start position:0% +in bucket zero and say all right let me +enumerate everybody who's in bucket zero + + align:start position:0% +enumerate everybody who's in bucket zero + + + align:start position:0% +enumerate everybody who's in bucket zero +and see if I can find Anna with her + + align:start position:0% +and see if I can find Anna with her + + + align:start position:0% +and see if I can find Anna with her +grade happens to be the first one but + + align:start position:0% +grade happens to be the first one but + + + align:start position:0% +grade happens to be the first one but +you know if it was later on then I'd + + align:start position:0% +you know if it was later on then I'd + + + align:start position:0% +you know if it was later on then I'd +still be able to grab it much faster + + align:start position:0% +still be able to grab it much faster + + + align:start position:0% +still be able to grab it much faster +than if I had everybody in one long list + + align:start position:0% +than if I had everybody in one long list + + + align:start position:0% +than if I had everybody in one long list +does that make sense like the idea of + + align:start position:0% +does that make sense like the idea of + + + align:start position:0% +does that make sense like the idea of +yeah go ahead so you can still like + + align:start position:0% +yeah go ahead so you can still like + + + align:start position:0% +yeah go ahead so you can still like +access them just that like you might get + + align:start position:0% +access them just that like you might get + + + align:start position:0% +access them just that like you might get +two answers instead of exactly yeah you + + align:start position:0% +two answers instead of exactly yeah you + + + align:start position:0% +two answers instead of exactly yeah you +can still access them you just might + + align:start position:0% +can still access them you just might + + + align:start position:0% +can still access them you just might +have to look through a list of two right + + align:start position:0% +have to look through a list of two right + + + align:start position:0% +have to look through a list of two right +so here at bucket zero I'm effectively + + align:start position:0% +so here at bucket zero I'm effectively + + + align:start position:0% +so here at bucket zero I'm effectively +storing a list of these everything that + + align:start position:0% +storing a list of these everything that + + + align:start position:0% +storing a list of these everything that +hashed to a zero right which is it's + + align:start position:0% +hashed to a zero right which is it's + + + align:start position:0% +hashed to a zero right which is it's +fine yes that's that's two that I have + + align:start position:0% +fine yes that's that's two that I have + + + align:start position:0% +fine yes that's that's two that I have +to look through it's not four it's not + + align:start position:0% +to look through it's not four it's not + + + align:start position:0% +to look through it's not four it's not +10 it's not you know 100 it's not + + align:start position:0% +10 it's not you know 100 it's not + + + align:start position:0% +10 it's not you know 100 it's not +everybody all in a + + align:start position:0% +everybody all in a + + + align:start position:0% +everybody all in a +row right yeah is the complexity that so + + align:start position:0% +row right yeah is the complexity that so + + + align:start position:0% +row right yeah is the complexity that so +the complexity of this is actually going + + align:start position:0% +the complexity of this is actually going + + + align:start position:0% +the complexity of this is actually going +to be smaller than Theta of n right and + + align:start position:0% +to be smaller than Theta of n right and + + + align:start position:0% +to be smaller than Theta of n right and +it it'll depend on on the hash function + + align:start position:0% +it it'll depend on on the hash function + + + align:start position:0% +it it'll depend on on the hash function +that we use right this hash function + + align:start position:0% +that we use right this hash function + + + align:start position:0% +that we use right this hash function +needs to be nicely balanced it shouldn't + + align:start position:0% +needs to be nicely balanced it shouldn't + + + align:start position:0% +needs to be nicely balanced it shouldn't +put everyone in bucket zero right then + + align:start position:0% +put everyone in bucket zero right then + + + align:start position:0% +put everyone in bucket zero right then +that's a useless hash function um and it + + align:start position:0% +that's a useless hash function um and it + + + align:start position:0% +that's a useless hash function um and it +depends on the size of the hash table + + align:start position:0% +depends on the size of the hash table + + + align:start position:0% +depends on the size of the hash table +right if I have maybe you know a + + align:start position:0% +right if I have maybe you know a + + + align:start position:0% +right if I have maybe you know a +thousand people that I'm storing in 15 + + align:start position:0% +thousand people that I'm storing in 15 + + + align:start position:0% +thousand people that I'm storing in 15 +buckets I'm going to have a lot of + + align:start position:0% +buckets I'm going to have a lot of + + + align:start position:0% +buckets I'm going to have a lot of +collisions right but if I'm only storing + + align:start position:0% +collisions right but if I'm only storing + + + align:start position:0% +collisions right but if I'm only storing +these four or maybe you know eight or 10 + + align:start position:0% +these four or maybe you know eight or 10 + + + align:start position:0% +these four or maybe you know eight or 10 +or something smaller than the size of my + + align:start position:0% +or something smaller than the size of my + + + align:start position:0% +or something smaller than the size of my +table then there will be far fewer + + align:start position:0% +table then there will be far fewer + + + align:start position:0% +table then there will be far fewer +collisions it'll be more nicely balanced + + align:start position:0% +collisions it'll be more nicely balanced + + + align:start position:0% +collisions it'll be more nicely balanced +yeah I bet likea n like things in zero + + align:start position:0% +yeah I bet likea n like things in zero + + + align:start position:0% +yeah I bet likea n like things in zero +oh Theta of n for the things in zero yes + + align:start position:0% +oh Theta of n for the things in zero yes + + + align:start position:0% +oh Theta of n for the things in zero yes +and that's fine because usually what we + + align:start position:0% +and that's fine because usually what we + + + align:start position:0% +and that's fine because usually what we +care about is Theta of the length of the + + align:start position:0% +care about is Theta of the length of the + + + align:start position:0% +care about is Theta of the length of the +input right so in this case it's Theta + + align:start position:0% +input right so in this case it's Theta + + + align:start position:0% +input right so in this case it's Theta +of if I have four students in my class + + align:start position:0% +of if I have four students in my class + + + align:start position:0% +of if I have four students in my class +right I've got only two + + align:start position:0% +right I've got only two + + + align:start position:0% +right I've got only two +that uh that mapped to zero so here it's + + align:start position:0% +that uh that mapped to zero so here it's + + + align:start position:0% +that uh that mapped to zero so here it's +you know length over two but if I had + + align:start position:0% +you know length over two but if I had + + + align:start position:0% +you know length over two but if I had +more students then it would be far fewer + + align:start position:0% +more students then it would be far fewer + + + align:start position:0% +more students then it would be far fewer +right it would be two out of 10 or maybe + + align:start position:0% +right it would be two out of 10 or maybe + + + align:start position:0% +right it would be two out of 10 or maybe +two out of 15 that to the same thing + + align:start position:0% + + + + align:start position:0% + +yeah so yeah so as as the question said + + align:start position:0% +yeah so yeah so as as the question said + + + align:start position:0% +yeah so yeah so as as the question said +what makes a good hash table and hash + + align:start position:0% +what makes a good hash table and hash + + + align:start position:0% +what makes a good hash table and hash +function uh pair right because this only + + align:start position:0% +function uh pair right because this only + + + align:start position:0% +function uh pair right because this only +works if you have a really good hash + + align:start position:0% +works if you have a really good hash + + + align:start position:0% +works if you have a really good hash +function and a nice hash table to go + + align:start position:0% +function and a nice hash table to go + + + align:start position:0% +function and a nice hash table to go +along with it so this is actually a + + align:start position:0% +along with it so this is actually a + + + align:start position:0% +along with it so this is actually a +problem in computer science you know a + + align:start position:0% +problem in computer science you know a + + + align:start position:0% +problem in computer science you know a +research problem all by itself so people + + align:start position:0% +research problem all by itself so people + + + align:start position:0% +research problem all by itself so people +actually study this for their um for + + align:start position:0% +actually study this for their um for + + + align:start position:0% +actually study this for their um for +their lives coming up with good hash + + align:start position:0% +their lives coming up with good hash + + + align:start position:0% +their lives coming up with good hash +functions and and hash tables so some + + align:start position:0% +functions and and hash tables so some + + + align:start position:0% +functions and and hash tables so some +some base rules uh you want to have uh + + align:start position:0% +some base rules uh you want to have uh + + + align:start position:0% +some base rules uh you want to have uh +the domain of Interest so in this + + align:start position:0% +the domain of Interest so in this + + + align:start position:0% +the domain of Interest so in this +particular case you know a tupal or a + + align:start position:0% +particular case you know a tupal or a + + + align:start position:0% +particular case you know a tupal or a +string or whatever it is um map to + + align:start position:0% +string or whatever it is um map to + + + align:start position:0% +string or whatever it is um map to +integers between zero and the size of + + align:start position:0% +integers between zero and the size of + + + align:start position:0% +integers between zero and the size of +the hash table so in the previous + + align:start position:0% +the hash table so in the previous + + + align:start position:0% +the hash table so in the previous +example we don't want to have a hash + + align:start position:0% +example we don't want to have a hash + + + align:start position:0% +example we don't want to have a hash +function that mods two because then + + align:start position:0% +function that mods two because then + + + align:start position:0% +function that mods two because then +everything will either hash to zero or + + align:start position:0% +everything will either hash to zero or + + + align:start position:0% +everything will either hash to zero or +one right if our hash table has 15 + + align:start position:0% +one right if our hash table has 15 + + + align:start position:0% +one right if our hash table has 15 +things well we better make sure that our + + align:start position:0% +things well we better make sure that our + + + align:start position:0% +things well we better make sure that our +hash function is going to give us a + + align:start position:0% +hash function is going to give us a + + + align:start position:0% +hash function is going to give us a +number between 0 and + + align:start position:0% +number between 0 and + + + align:start position:0% +number between 0 and +15 second you want the hash uh the hash + + align:start position:0% +15 second you want the hash uh the hash + + + align:start position:0% +15 second you want the hash uh the hash +value to be fully determined by the + + align:start position:0% +value to be fully determined by the + + + align:start position:0% +value to be fully determined by the +value being hashed so in this case we + + align:start position:0% +value being hashed so in this case we + + + align:start position:0% +value being hashed so in this case we +don't want any sort of Randomness to go + + align:start position:0% +don't want any sort of Randomness to go + + + align:start position:0% +don't want any sort of Randomness to go +on for the reason that well if I want to + + align:start position:0% +on for the reason that well if I want to + + + align:start position:0% +on for the reason that well if I want to +look up Eve's + + align:start position:0% +look up Eve's + + + align:start position:0% +look up Eve's +grade later on in you know in in the + + align:start position:0% +grade later on in you know in in the + + + align:start position:0% +grade later on in you know in in the +code or whatever then I need to run the + + align:start position:0% +code or whatever then I need to run the + + + align:start position:0% +code or whatever then I need to run the +exact same hash function on her name to + + align:start position:0% +exact same hash function on her name to + + + align:start position:0% +exact same hash function on her name to +determine the grade + + align:start position:0% +determine the grade + + + align:start position:0% +determine the grade +so if there's Randomness involved in + + align:start position:0% +so if there's Randomness involved in + + + align:start position:0% +so if there's Randomness involved in +this hash function then you might not + + align:start position:0% +this hash function then you might not + + + align:start position:0% +this hash function then you might not +get back the same value that it hashed + + align:start position:0% +get back the same value that it hashed + + + align:start position:0% +get back the same value that it hashed +to originally right so you'll be looking + + align:start position:0% +to originally right so you'll be looking + + + align:start position:0% +to originally right so you'll be looking +in the wrong bucket and you'll uh you + + align:start position:0% +in the wrong bucket and you'll uh you + + + align:start position:0% +in the wrong bucket and you'll uh you +know incorrectly say she doesn't have a + + align:start position:0% +know incorrectly say she doesn't have a + + + align:start position:0% +know incorrectly say she doesn't have a +value or she's not + + align:start position:0% +value or she's not + + + align:start position:0% +value or she's not +there um third you want to use the whole + + align:start position:0% +there um third you want to use the whole + + + align:start position:0% +there um third you want to use the whole +input to Hash the uh uh the function + + align:start position:0% +input to Hash the uh uh the function + + + align:start position:0% +input to Hash the uh uh the function +should use the whole input to to run the + + align:start position:0% +should use the whole input to to run the + + + align:start position:0% +should use the whole input to to run the +hash + + align:start position:0% +hash + + + align:start position:0% +hash +function so again in this example we + + align:start position:0% +function so again in this example we + + + align:start position:0% +function so again in this example we +don't just want to use the first letters + + align:start position:0% +don't just want to use the first letters + + + align:start position:0% +don't just want to use the first letters +of people's names because then that will + + align:start position:0% +of people's names because then that will + + + align:start position:0% +of people's names because then that will +lead to a lot more collisions than if we + + align:start position:0% +lead to a lot more collisions than if we + + + align:start position:0% +lead to a lot more collisions than if we +use the entire you know the sum of all + + align:start position:0% +use the entire you know the sum of all + + + align:start position:0% +use the entire you know the sum of all +the letters in the alphabet or all the + + align:start position:0% +the letters in the alphabet or all the + + + align:start position:0% +the letters in the alphabet or all the +letters in their name + + align:start position:0% +letters in their name + + + align:start position:0% +letters in their name +right um okay so those are really big + + align:start position:0% +right um okay so those are really big + + + align:start position:0% +right um okay so those are really big +ideas and then uh what we want out of + + align:start position:0% +ideas and then uh what we want out of + + + align:start position:0% +ideas and then uh what we want out of +our hash function is all the values + + align:start position:0% +our hash function is all the values + + + align:start position:0% +our hash function is all the values +right if you run this hash function on a + + align:start position:0% +right if you run this hash function on a + + + align:start position:0% +right if you run this hash function on a +bunch of different inputs for you're + + align:start position:0% +bunch of different inputs for you're + + + align:start position:0% +bunch of different inputs for you're +storing names or you're storing I don't + + align:start position:0% +storing names or you're storing I don't + + + align:start position:0% +storing names or you're storing I don't +know tupal or whatever you're storing + + align:start position:0% +know tupal or whatever you're storing + + + align:start position:0% +know tupal or whatever you're storing +you you want this function to give you a + + align:start position:0% +you you want this function to give you a + + + align:start position:0% +you you want this function to give you a +nice uniform distribution of values + + align:start position:0% +nice uniform distribution of values + + + align:start position:0% +nice uniform distribution of values +right so in our hash table previously + + align:start position:0% +right so in our hash table previously + + + align:start position:0% +right so in our hash table previously +here if I add more names to my hash + + align:start position:0% +here if I add more names to my hash + + + align:start position:0% +here if I add more names to my hash +table I want to ensure that they're + + align:start position:0% +table I want to ensure that they're + + + align:start position:0% +table I want to ensure that they're +going to land in buckets you know 2 5 6 + + align:start position:0% +going to land in buckets you know 2 5 6 + + + align:start position:0% +going to land in buckets you know 2 5 6 +7 8 9 10 11 12 133 14 I don't want + + align:start position:0% +7 8 9 10 11 12 133 14 I don't want + + + align:start position:0% +7 8 9 10 11 12 133 14 I don't want +everything to Hash to number zero right + + align:start position:0% +everything to Hash to number zero right + + + align:start position:0% +everything to Hash to number zero right +that would be very + + align:start position:0% +that would be very + + + align:start position:0% +that would be very +bad so as a side reminder back in the + + align:start position:0% +bad so as a side reminder back in the + + + align:start position:0% +bad so as a side reminder back in the +lecture on dictionaries I actually said + + align:start position:0% +lecture on dictionaries I actually said + + + align:start position:0% +lecture on dictionaries I actually said +something like + + align:start position:0% +something like + + + align:start position:0% +something like +um uh for now think of the objects that + + align:start position:0% +um uh for now think of the objects that + + + align:start position:0% +um uh for now think of the objects that +can be Keys uh to a dictionary as + + align:start position:0% +can be Keys uh to a dictionary as + + + align:start position:0% +can be Keys uh to a dictionary as +immutable objects right and I said + + align:start position:0% +immutable objects right and I said + + + align:start position:0% +immutable objects right and I said +technically hashable but we don't need + + align:start position:0% +technically hashable but we don't need + + + align:start position:0% +technically hashable but we don't need +to know what that is well hashable means + + align:start position:0% +to know what that is well hashable means + + + align:start position:0% +to know what that is well hashable means +just this you can run a hash function on + + align:start position:0% +just this you can run a hash function on + + + align:start position:0% +just this you can run a hash function on +the object and you'll get the same value + + align:start position:0% +the object and you'll get the same value + + + align:start position:0% +the object and you'll get the same value +back no matter how many times you run + + align:start position:0% +back no matter how many times you run + + + align:start position:0% +back no matter how many times you run +the hash function on that object right + + align:start position:0% +the hash function on that object right + + + align:start position:0% +the hash function on that object right +so we looked at this example what + + align:start position:0% +so we looked at this example what + + + align:start position:0% +so we looked at this example what +happens if we add a student whose name + + align:start position:0% +happens if we add a student whose name + + + align:start position:0% +happens if we add a student whose name +is not immutable not hashable so lists + + align:start position:0% +is not immutable not hashable so lists + + + align:start position:0% +is not immutable not hashable so lists +are mutable objects so as such they are + + align:start position:0% +are mutable objects so as such they are + + + align:start position:0% +are mutable objects so as such they are +not hashable that means if we run a hash + + align:start position:0% +not hashable that means if we run a hash + + + align:start position:0% +not hashable that means if we run a hash +function on a list today and then we + + align:start position:0% +function on a list today and then we + + + align:start position:0% +function on a list today and then we +potentially mutate the list tomorrow + + align:start position:0% +potentially mutate the list tomorrow + + + align:start position:0% +potentially mutate the list tomorrow +that list will not hash to the same + + align:start position:0% +that list will not hash to the same + + + align:start position:0% +that list will not hash to the same +thing right so we saw this example let's + + align:start position:0% +thing right so we saw this example let's + + + align:start position:0% +thing right so we saw this example let's +say Kate with a K uh is added to our + + align:start position:0% +say Kate with a K uh is added to our + + + align:start position:0% +say Kate with a K uh is added to our +hash table so her name currently hashes + + align:start position:0% +hash table so her name currently hashes + + + align:start position:0% +hash table so her name currently hashes +to 37 mod 16 which is a five right so we + + align:start position:0% +to 37 mod 16 which is a five right so we + + + align:start position:0% +to 37 mod 16 which is a five right so we +added her there now let's say you know + + align:start position:0% +added her there now let's say you know + + + align:start position:0% +added her there now let's say you know +tomorrow we want to look up her grade to + + align:start position:0% +tomorrow we want to look up her grade to + + + align:start position:0% +tomorrow we want to look up her grade to +you know do whatever to integrate it + + align:start position:0% +you know do whatever to integrate it + + + align:start position:0% +you know do whatever to integrate it +into a bigger spreadsheet she had + + align:start position:0% +into a bigger spreadsheet she had + + + align:start position:0% +into a bigger spreadsheet she had +changed her name between yesterday and + + align:start position:0% +changed her name between yesterday and + + + align:start position:0% +changed her name between yesterday and +today now she's Kate with a c if we run + + align:start position:0% +today now she's Kate with a c if we run + + + align:start position:0% +today now she's Kate with a c if we run +the same hash function again on her name + + align:start position:0% +the same hash function again on her name + + + align:start position:0% +the same hash function again on her name +that leads us to look in a different + + align:start position:0% +that leads us to look in a different + + + align:start position:0% +that leads us to look in a different +bucket right she's still there she's + + align:start position:0% +bucket right she's still there she's + + + align:start position:0% +bucket right she's still there she's +Kate with a K as we had originally added + + align:start position:0% +Kate with a K as we had originally added + + + align:start position:0% +Kate with a K as we had originally added +her but now her name is Kate with a c we + + align:start position:0% +her but now her name is Kate with a c we + + + align:start position:0% +her but now her name is Kate with a c we +run the same hash function tells us to + + align:start position:0% +run the same hash function tells us to + + + align:start position:0% +run the same hash function tells us to +look bucket 13 and she's not there right + + align:start position:0% +look bucket 13 and she's not there right + + + align:start position:0% +look bucket 13 and she's not there right +so that's why we only want uh hashable + + align:start position:0% +so that's why we only want uh hashable + + + align:start position:0% +so that's why we only want uh hashable +objects to be added to be uh keys to the + + align:start position:0% +objects to be added to be uh keys to the + + + align:start position:0% +objects to be added to be uh keys to the +dictionary because we want the same + + align:start position:0% +dictionary because we want the same + + + align:start position:0% +dictionary because we want the same +value to come back to us when we run the + + align:start position:0% +value to come back to us when we run the + + + align:start position:0% +value to come back to us when we run the +hash function on them + + align:start position:0% +hash function on them + + + align:start position:0% +hash function on them +right okay so now we can see in the + + align:start position:0% +right okay so now we can see in the + + + align:start position:0% +right okay so now we can see in the +worst case + + align:start position:0% +worst case + + + align:start position:0% +worst case +scenario everything maps to the same + + align:start position:0% +scenario everything maps to the same + + + align:start position:0% +scenario everything maps to the same +bucket in my hash table my list right + + align:start position:0% +bucket in my hash table my list right + + + align:start position:0% +bucket in my hash table my list right +every single thing I add is has a really + + align:start position:0% +every single thing I add is has a really + + + align:start position:0% +every single thing I add is has a really +bad hash function on it let's say the + + align:start position:0% +bad hash function on it let's say the + + + align:start position:0% +bad hash function on it let's say the +hash function always returns three right + + align:start position:0% +hash function always returns three right + + + align:start position:0% +hash function always returns three right +if my hash function always returns three + + align:start position:0% +if my hash function always returns three + + + align:start position:0% +if my hash function always returns three +no matter what I'm adding to my uh + + align:start position:0% +no matter what I'm adding to my uh + + + align:start position:0% +no matter what I'm adding to my uh +diction no matter what I'm hashing then + + align:start position:0% +diction no matter what I'm hashing then + + + align:start position:0% +diction no matter what I'm hashing then +every single item essentially gets put + + align:start position:0% +every single item essentially gets put + + + align:start position:0% +every single item essentially gets put +in a really long list at bucket number + + align:start position:0% +in a really long list at bucket number + + + align:start position:0% +in a really long list at bucket number +three so when I look up a value well + + align:start position:0% +three so when I look up a value well + + + align:start position:0% +three so when I look up a value well +surprise it hashes to three and now I + + align:start position:0% +surprise it hashes to three and now I + + + align:start position:0% +surprise it hashes to three and now I +need to look through every single thing + + align:start position:0% +need to look through every single thing + + + align:start position:0% +need to look through every single thing +in that bucket number three to find the + + align:start position:0% +in that bucket number three to find the + + + align:start position:0% +in that bucket number three to find the +one I'm looking for right so it's just + + align:start position:0% +one I'm looking for right so it's just + + + align:start position:0% +one I'm looking for right so it's just +very very bad and in the worst case + + align:start position:0% +very very bad and in the worst case + + + align:start position:0% +very very bad and in the worst case +scenario this is is the complexity it's + + align:start position:0% +scenario this is is the complexity it's + + + align:start position:0% +scenario this is is the complexity it's +Theta of n where n is the length of + + align:start position:0% +Theta of n where n is the length of + + + align:start position:0% +Theta of n where n is the length of +whatever items we have that we're adding + + align:start position:0% +whatever items we have that we're adding + + + align:start position:0% +whatever items we have that we're adding +to our buckets to our hash table but in + + align:start position:0% +to our buckets to our hash table but in + + + align:start position:0% +to our buckets to our hash table but in +the average case and this is only when + + align:start position:0% +the average case and this is only when + + + align:start position:0% +the average case and this is only when +we have a hash table that's pretty big + + align:start position:0% +we have a hash table that's pretty big + + + align:start position:0% +we have a hash table that's pretty big +relative to the things that we're adding + + align:start position:0% +relative to the things that we're adding + + + align:start position:0% +relative to the things that we're adding +to it and when we have a hash function + + align:start position:0% +to it and when we have a hash function + + + align:start position:0% +to it and when we have a hash function +that's good enough right that has a nice + + align:start position:0% +that's good enough right that has a nice + + + align:start position:0% +that's good enough right that has a nice +uniform distribution of values only in + + align:start position:0% +uniform distribution of values only in + + + align:start position:0% +uniform distribution of values only in +that case in the average uh in the + + align:start position:0% +that case in the average uh in the + + + align:start position:0% +that case in the average uh in the +average case the time it takes for us to + + align:start position:0% +average case the time it takes for us to + + + align:start position:0% +average case the time it takes for us to +grab a value from uh a dictionary is + + align:start position:0% +grab a value from uh a dictionary is + + + align:start position:0% +grab a value from uh a dictionary is +Theta of one constant right and so + + align:start position:0% +Theta of one constant right and so + + + align:start position:0% +Theta of one constant right and so +that's why dictionaries are really + + align:start position:0% +that's why dictionaries are really + + + align:start position:0% +that's why dictionaries are really +really useful data structures to store + + align:start position:0% +really useful data structures to store + + + align:start position:0% +really useful data structures to store +things and to retrieve things from um + + align:start position:0% +things and to retrieve things from um + + + align:start position:0% +things and to retrieve things from um +back in uh back when I was doing a + + align:start position:0% +back in uh back when I was doing a + + + align:start position:0% +back in uh back when I was doing a +little project I didn't know about + + align:start position:0% +little project I didn't know about + + + align:start position:0% +little project I didn't know about +python dictionaries I had just learned + + align:start position:0% +python dictionaries I had just learned + + + align:start position:0% +python dictionaries I had just learned +about the language and I was actually + + align:start position:0% +about the language and I was actually + + + align:start position:0% +about the language and I was actually +using lists to read in um genomic data + + align:start position:0% +using lists to read in um genomic data + + + align:start position:0% +using lists to read in um genomic data +files and I was storing everything in + + align:start position:0% +files and I was storing everything in + + + align:start position:0% +files and I was storing everything in +lists like jom names and things like + + align:start position:0% +lists like jom names and things like + + + align:start position:0% +lists like jom names and things like +that and um it was really slow like you + + align:start position:0% +that and um it was really slow like you + + + align:start position:0% +that and um it was really slow like you +know my advisor would be like you know + + align:start position:0% +know my advisor would be like you know + + + align:start position:0% +know my advisor would be like you know +uh is your code done yet I'm like no + + align:start position:0% +uh is your code done yet I'm like no + + + align:start position:0% +uh is your code done yet I'm like no +it's been a couple days still waiting + + align:start position:0% +it's been a couple days still waiting + + + align:start position:0% +it's been a couple days still waiting +and then you know someone told me hey + + align:start position:0% +and then you know someone told me hey + + + align:start position:0% +and then you know someone told me hey +just use a dictionary to store the + + align:start position:0% +just use a dictionary to store the + + + align:start position:0% +just use a dictionary to store the +values and then the lookup is going to + + align:start position:0% +values and then the lookup is going to + + + align:start position:0% +values and then the lookup is going to +be a lot faster it was done you know + + align:start position:0% +be a lot faster it was done you know + + + align:start position:0% +be a lot faster it was done you know +within a couple seconds so very very + + align:start position:0% +within a couple seconds so very very + + + align:start position:0% +within a couple seconds so very very +useful the time complex because it's + + align:start position:0% +useful the time complex because it's + + + align:start position:0% +useful the time complex because it's +genomic data it's huge amounts of data + + align:start position:0% +genomic data it's huge amounts of data + + + align:start position:0% +genomic data it's huge amounts of data +right so the the the Theta of n versus + + align:start position:0% +right so the the the Theta of n versus + + + align:start position:0% +right so the the the Theta of n versus +Theta of one is really it makes a really + + align:start position:0% +Theta of one is really it makes a really + + + align:start position:0% +Theta of one is really it makes a really +big difference when you deal with large + + align:start position:0% +big difference when you deal with large + + + align:start position:0% +big difference when you deal with large +data sets right it's not just on paper + + align:start position:0% +data sets right it's not just on paper + + + align:start position:0% +data sets right it's not just on paper +it's it actually makes a big + + align:start position:0% +it's it actually makes a big + + + align:start position:0% +it's it actually makes a big +difference okay questions about this I + + align:start position:0% +difference okay questions about this I + + + align:start position:0% +difference okay questions about this I +hope this ties in uh yeah so Pyon uses a + + align:start position:0% +hope this ties in uh yeah so Pyon uses a + + + align:start position:0% +hope this ties in uh yeah so Pyon uses a +specific cash function yeah if python + + align:start position:0% +specific cash function yeah if python + + + align:start position:0% +specific cash function yeah if python +updates or anything can they change that + + align:start position:0% +updates or anything can they change that + + + align:start position:0% +updates or anything can they change that +function and nothing would change or is + + align:start position:0% +function and nothing would change or is + + + align:start position:0% +function and nothing would change or is +it so you don't yeah so python right now + + align:start position:0% +it so you don't yeah so python right now + + + align:start position:0% +it so you don't yeah so python right now +uses a specific hash function in a + + align:start position:0% +uses a specific hash function in a + + + align:start position:0% +uses a specific hash function in a +future version they might use a + + align:start position:0% +future version they might use a + + + align:start position:0% +future version they might use a +different hash function we don't really + + align:start position:0% +different hash function we don't really + + + align:start position:0% +different hash function we don't really +use the numbers associated with the hash + + align:start position:0% +use the numbers associated with the hash + + + align:start position:0% +use the numbers associated with the hash +functions I mean you could for your + + align:start position:0% +functions I mean you could for your + + + align:start position:0% +functions I mean you could for your +programs but it would be I guess + + align:start position:0% +programs but it would be I guess + + + align:start position:0% +programs but it would be I guess +relative to whatever value you get right + + align:start position:0% +relative to whatever value you get right + + + align:start position:0% +relative to whatever value you get right +so you wouldn't kind of hardcode the + + align:start position:0% +so you wouldn't kind of hardcode the + + + align:start position:0% +so you wouldn't kind of hardcode the +value for you know the the tle one two + + align:start position:0% +value for you know the the tle one two + + + align:start position:0% +value for you know the the tle one two +three as something right you just get + + align:start position:0% +three as something right you just get + + + align:start position:0% +three as something right you just get +what you get and and and that's what it + + align:start position:0% +what you get and and and that's what it + + + align:start position:0% +what you get and and and that's what it +is right but it it could give you a + + align:start position:0% +is right but it it could give you a + + + align:start position:0% +is right but it it could give you a +different hash function if you ran out + + align:start position:0% +different hash function if you ran out + + + align:start position:0% +different hash function if you ran out +of your computer actually you might get + + align:start position:0% +of your computer actually you might get + + + align:start position:0% +of your computer actually you might get +a different hash value than mine + + align:start position:0% +a different hash value than mine + + + align:start position:0% +a different hash value than mine +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um so this topic kind of ties in data + + align:start position:0% +um so this topic kind of ties in data + + + align:start position:0% +um so this topic kind of ties in data +structures we've seen lists and + + align:start position:0% +structures we've seen lists and + + + align:start position:0% +structures we've seen lists and +dictionaries um some of the behind the + + align:start position:0% +dictionaries um some of the behind the + + + align:start position:0% +dictionaries um some of the behind the +scenes look at how things are stored + + align:start position:0% +scenes look at how things are stored + + + align:start position:0% +scenes look at how things are stored +puts a little complexity in there + + align:start position:0% +puts a little complexity in there + + + align:start position:0% +puts a little complexity in there +talking about algorithms and and runtime + + align:start position:0% +talking about algorithms and and runtime + + + align:start position:0% +talking about algorithms and and runtime +so it ties in a bunch of the topics that + + align:start position:0% +so it ties in a bunch of the topics that + + + align:start position:0% +so it ties in a bunch of the topics that +we've seen in this class really really + + align:start position:0% +we've seen in this class really really + + + align:start position:0% +we've seen in this class really really +nicely so one other thing that I'd like + + align:start position:0% +nicely so one other thing that I'd like + + + align:start position:0% +nicely so one other thing that I'd like +to now talk about is the idea of a + + align:start position:0% +to now talk about is the idea of a + + + align:start position:0% +to now talk about is the idea of a +simulation okay and this hopefully is + + align:start position:0% +simulation okay and this hopefully is + + + align:start position:0% +simulation okay and this hopefully is +going to be a little bit more useful to + + align:start position:0% +going to be a little bit more useful to + + + align:start position:0% +going to be a little bit more useful to +you if you decide to take another uh + + align:start position:0% +you if you decide to take another uh + + + align:start position:0% +you if you decide to take another uh +computer science course or computation + + align:start position:0% +computer science course or computation + + + align:start position:0% +computer science course or computation +course in a different field you know + + align:start position:0% +course in a different field you know + + + align:start position:0% +course in a different field you know +whatever you'd like computation uh + + align:start position:0% +whatever you'd like computation uh + + + align:start position:0% +whatever you'd like computation uh +simulations are very useful tools in + + align:start position:0% +simulations are very useful tools in + + + align:start position:0% +simulations are very useful tools in +computer science so it allows you to + + align:start position:0% +computer science so it allows you to + + + align:start position:0% +computer science so it allows you to +computationally describe the world so if + + align:start position:0% +computationally describe the world so if + + + align:start position:0% +computationally describe the world so if +you see an event in the world you can + + align:start position:0% +you see an event in the world you can + + + align:start position:0% +you see an event in the world you can +actually simulate it computationally + + align:start position:0% +actually simulate it computationally + + + align:start position:0% +actually simulate it computationally +what you've learned so with what you've + + align:start position:0% +what you've learned so with what you've + + + align:start position:0% +what you've learned so with what you've +learned so far you can totally simulate + + align:start position:0% +learned so far you can totally simulate + + + align:start position:0% +learned so far you can totally simulate +a whole bunch of things um and we're + + align:start position:0% +a whole bunch of things um and we're + + + align:start position:0% +a whole bunch of things um and we're +using Randomness to simulate the these + + align:start position:0% +using Randomness to simulate the these + + + align:start position:0% +using Randomness to simulate the these +events that you might see in the real + + align:start position:0% +events that you might see in the real + + + align:start position:0% +events that you might see in the real +world so for example you might have seen + + align:start position:0% +world so for example you might have seen + + + align:start position:0% +world so for example you might have seen +sort of um the the hurricane paths right + + align:start position:0% +sort of um the the hurricane paths right + + + align:start position:0% +sort of um the the hurricane paths right +when you see on the on on in the news or + + align:start position:0% +when you see on the on on in the news or + + + align:start position:0% +when you see on the on on in the news or +whatever the the most likely path right + + align:start position:0% +whatever the the most likely path right + + + align:start position:0% +whatever the the most likely path right +that a hurricane might take but then + + align:start position:0% +that a hurricane might take but then + + + align:start position:0% +that a hurricane might take but then +they also have the little models that + + align:start position:0% +they also have the little models that + + + align:start position:0% +they also have the little models that +show you know other likely paths they + + align:start position:0% +show you know other likely paths they + + + align:start position:0% +show you know other likely paths they +simulated right using a bunch of uh uh + + align:start position:0% +simulated right using a bunch of uh uh + + + align:start position:0% +simulated right using a bunch of uh uh +data that they have the most likely path + + align:start position:0% +data that they have the most likely path + + + align:start position:0% +data that they have the most likely path +for that hurricane right um another + + align:start position:0% +for that hurricane right um another + + + align:start position:0% +for that hurricane right um another +place where simulation where where + + align:start position:0% +place where simulation where where + + + align:start position:0% +place where simulation where where +simulation is useful is if if you see a + + align:start position:0% +simulation is useful is if if you see a + + + align:start position:0% +simulation is useful is if if you see a +real world event that's actually kind of + + align:start position:0% +real world event that's actually kind of + + + align:start position:0% +real world event that's actually kind of +complex you can take a a simpler set of + + align:start position:0% +complex you can take a a simpler set of + + + align:start position:0% +complex you can take a a simpler set of +rules and simulate those and then add in + + align:start position:0% +rules and simulate those and then add in + + + align:start position:0% +rules and simulate those and then add in +more rules you know to make it closer + + align:start position:0% +more rules you know to make it closer + + + align:start position:0% +more rules you know to make it closer +and closer to the thing that you + + align:start position:0% +and closer to the thing that you + + + align:start position:0% +and closer to the thing that you +actually observe in the real world okay + + align:start position:0% +actually observe in the real world okay + + + align:start position:0% +actually observe in the real world okay +so the idea of a simulation is that you + + align:start position:0% +so the idea of a simulation is that you + + + align:start position:0% +so the idea of a simulation is that you +have some event in the real world and + + align:start position:0% +have some event in the real world and + + + align:start position:0% +have some event in the real world and +you want to calculate something about it + + align:start position:0% +you want to calculate something about it + + + align:start position:0% +you want to calculate something about it +we're going to use uh computation to + + align:start position:0% +we're going to use uh computation to + + + align:start position:0% +we're going to use uh computation to +design an experiment right and we're + + align:start position:0% +design an experiment right and we're + + + align:start position:0% +design an experiment right and we're +going to do R use Randomness for that + + align:start position:0% +going to do R use Randomness for that + + + align:start position:0% +going to do R use Randomness for that +once we've done that we're going to + + align:start position:0% +once we've done that we're going to + + + align:start position:0% +once we've done that we're going to +repeat the experiment a whole bunch of + + align:start position:0% +repeat the experiment a whole bunch of + + + align:start position:0% +repeat the experiment a whole bunch of +times computationally and that just + + align:start position:0% +times computationally and that just + + + align:start position:0% +times computationally and that just +means we're going to put a for loop + + align:start position:0% +means we're going to put a for loop + + + align:start position:0% +means we're going to put a for loop +around whatever experiment we've + + align:start position:0% +around whatever experiment we've + + + align:start position:0% +around whatever experiment we've +designed + + align:start position:0% +designed + + + align:start position:0% +designed +computationally and if you're interested + + align:start position:0% +computationally and if you're interested + + + align:start position:0% +computationally and if you're interested +in some outcome some particular outcome + + align:start position:0% +in some outcome some particular outcome + + + align:start position:0% +in some outcome some particular outcome +like uh as we're going to see we're + + align:start position:0% +like uh as we're going to see we're + + + align:start position:0% +like uh as we're going to see we're +going to roll a die when we're + + align:start position:0% +going to roll a die when we're + + + align:start position:0% +going to roll a die when we're +interested in how many times you know a + + align:start position:0% +interested in how many times you know a + + + align:start position:0% +interested in how many times you know a +four comes up then we're going to keep + + align:start position:0% +four comes up then we're going to keep + + + align:start position:0% +four comes up then we're going to keep +track of that outcome okay and you keep + + align:start position:0% +track of that outcome okay and you keep + + + align:start position:0% +track of that outcome okay and you keep +track of it however many times that + + align:start position:0% +track of it however many times that + + + align:start position:0% +track of it however many times that +outcome happened in in your whole bunch + + align:start position:0% +outcome happened in in your whole bunch + + + align:start position:0% +outcome happened in in your whole bunch +of repetitions and then after the end of + + align:start position:0% +of repetitions and then after the end of + + + align:start position:0% +of repetitions and then after the end of +the repetitions you can report some + + align:start position:0% +the repetitions you can report some + + + align:start position:0% +the repetitions you can report some +value of Interest maybe the probability + + align:start position:0% +value of Interest maybe the probability + + + align:start position:0% +value of Interest maybe the probability +that a four comes up on a DI + + align:start position:0% +that a four comes up on a DI + + + align:start position:0% +that a four comes up on a DI +roll so here's the example it's going to + + align:start position:0% +roll so here's the example it's going to + + + align:start position:0% +roll so here's the example it's going to +be very simple because it's something we + + align:start position:0% +be very simple because it's something we + + + align:start position:0% +be very simple because it's something we +can calculate already right off the bat + + align:start position:0% +can calculate already right off the bat + + + align:start position:0% +can calculate already right off the bat +but it'll give you a sense of how you + + align:start position:0% +but it'll give you a sense of how you + + + align:start position:0% +but it'll give you a sense of how you +can write code around uh such a real + + align:start position:0% +can write code around uh such a real + + + align:start position:0% +can write code around uh such a real +world event so here we're interested in + + align:start position:0% +world event so here we're interested in + + + align:start position:0% +world event so here we're interested in +just rolling a dice and seeing the + + align:start position:0% +just rolling a dice and seeing the + + + align:start position:0% +just rolling a dice and seeing the +probability to get a dot dot dot dot + + align:start position:0% +probability to get a dot dot dot dot + + + align:start position:0% +probability to get a dot dot dot dot +right to get a four on on the dice uh on + + align:start position:0% +right to get a four on on the dice uh on + + + align:start position:0% +right to get a four on on the dice uh on +on on one of the dice rolls or the + + align:start position:0% +on on one of the dice rolls or the + + + align:start position:0% +on on one of the dice rolls or the +probability to get a DOT + + align:start position:0% +probability to get a DOT + + + align:start position:0% +probability to get a DOT +whichever so here the event is that + + align:start position:0% +whichever so here the event is that + + + align:start position:0% +whichever so here the event is that +we're rolling a dice and then we're + + align:start position:0% +we're rolling a dice and then we're + + + align:start position:0% +we're rolling a dice and then we're +interested in getting the probability of + + align:start position:0% +interested in getting the probability of + + + align:start position:0% +interested in getting the probability of +some uh face so we're going to design an + + align:start position:0% +some uh face so we're going to design an + + + align:start position:0% +some uh face so we're going to design an +experiment for that dice roll and this + + align:start position:0% +experiment for that dice roll and this + + + align:start position:0% +experiment for that dice roll and this +is just one way to design the experiment + + align:start position:0% +is just one way to design the experiment + + + align:start position:0% +is just one way to design the experiment +there are a whole other many many other + + align:start position:0% +there are a whole other many many other + + + align:start position:0% +there are a whole other many many other +ways to design it this is just one that + + align:start position:0% +ways to design it this is just one that + + + align:start position:0% +ways to design it this is just one that +I chose that felt Illustrated uh most + + align:start position:0% +I chose that felt Illustrated uh most + + + align:start position:0% +I chose that felt Illustrated uh most +how we can uh uh take a real world + + align:start position:0% +how we can uh uh take a real world + + + align:start position:0% +how we can uh uh take a real world +example and put it into code so a d has + + align:start position:0% +example and put it into code so a d has + + + align:start position:0% +example and put it into code so a d has +six faces so what I have done here is + + align:start position:0% +six faces so what I have done here is + + + align:start position:0% +six faces so what I have done here is +I've created a list of each one of those + + align:start position:0% +I've created a list of each one of those + + + align:start position:0% +I've created a list of each one of those +faces right you could have used numbers + + align:start position:0% +faces right you could have used numbers + + + align:start position:0% +faces right you could have used numbers +as the elements in the list in this case + + align:start position:0% +as the elements in the list in this case + + + align:start position:0% +as the elements in the list in this case +I just use strings to be a little bit + + align:start position:0% +I just use strings to be a little bit + + + align:start position:0% +I just use strings to be a little bit +cuter or cuter but you know whatever + + align:start position:0% +cuter or cuter but you know whatever + + + align:start position:0% +cuter or cuter but you know whatever +however you'd like to represent each one + + align:start position:0% +however you'd like to represent each one + + + align:start position:0% +however you'd like to represent each one +of those die faces here's a list of six + + align:start position:0% +of those die faces here's a list of six + + + align:start position:0% +of those die faces here's a list of six +things in it and then I'm using using + + align:start position:0% +things in it and then I'm using using + + + align:start position:0% +things in it and then I'm using using +this Choice function from this random + + align:start position:0% +this Choice function from this random + + + align:start position:0% +this Choice function from this random +Library again the random Library super + + align:start position:0% +Library again the random Library super + + + align:start position:0% +Library again the random Library super +duper useful Library random. choice will + + align:start position:0% +duper useful Library random. choice will + + + align:start position:0% +duper useful Library random. choice will +effectively select one of the elements + + align:start position:0% +effectively select one of the elements + + + align:start position:0% +effectively select one of the elements +in this list for me so if I type in + + align:start position:0% +in this list for me so if I type in + + + align:start position:0% +in this list for me so if I type in +random. choice in the console now it + + align:start position:0% +random. choice in the console now it + + + align:start position:0% +random. choice in the console now it +might give me the dot dot if I type it + + align:start position:0% +might give me the dot dot if I type it + + + align:start position:0% +might give me the dot dot if I type it +in right after it might give me the dot + + align:start position:0% +in right after it might give me the dot + + + align:start position:0% +in right after it might give me the dot +dot dot dot whatever it's going to be + + align:start position:0% +dot dot dot whatever it's going to be + + + align:start position:0% +dot dot dot whatever it's going to be +random each time I run this + + align:start position:0% +random each time I run this + + + align:start position:0% +random each time I run this +function but this line of code + + align:start position:0% +function but this line of code + + + align:start position:0% +function but this line of code +effectively simulates me taking a dice + + align:start position:0% +effectively simulates me taking a dice + + + align:start position:0% +effectively simulates me taking a dice +and rolling it + + align:start position:0% +and rolling it + + + align:start position:0% +and rolling it +and then we can repeat this experiment a + + align:start position:0% +and then we can repeat this experiment a + + + align:start position:0% +and then we can repeat this experiment a +whole lot of times right if I'm taking a + + align:start position:0% +whole lot of times right if I'm taking a + + + align:start position:0% +whole lot of times right if I'm taking a +dice and rolling it that's like what one + + align:start position:0% +dice and rolling it that's like what one + + + align:start position:0% +dice and rolling it that's like what one +or two seconds per roll I don't think I + + align:start position:0% +or two seconds per roll I don't think I + + + align:start position:0% +or two seconds per roll I don't think I +have time to repeat that experiment + + align:start position:0% +have time to repeat that experiment + + + align:start position:0% +have time to repeat that experiment +10,000 times but with simulation with + + align:start position:0% +10,000 times but with simulation with + + + align:start position:0% +10,000 times but with simulation with +computation right with programming we + + align:start position:0% +computation right with programming we + + + align:start position:0% +computation right with programming we +can simulate it 10,000 times or a + + align:start position:0% +can simulate it 10,000 times or a + + + align:start position:0% +can simulate it 10,000 times or a +million times and then just wait a + + align:start position:0% +million times and then just wait a + + + align:start position:0% +million times and then just wait a +couple seconds right so very very useful + + align:start position:0% +couple seconds right so very very useful + + + align:start position:0% +couple seconds right so very very useful +um application of programming so so how + + align:start position:0% +um application of programming so so how + + + align:start position:0% +um application of programming so so how +do you simulate this dial 10,000 times + + align:start position:0% +do you simulate this dial 10,000 times + + + align:start position:0% +do you simulate this dial 10,000 times +just slap a for loop around that line of + + align:start position:0% +just slap a for loop around that line of + + + align:start position:0% +just slap a for loop around that line of +code right so for some number in range + + align:start position:0% +code right so for some number in range + + + align:start position:0% +code right so for some number in range +10,000 that means I'm going to get this + + align:start position:0% +10,000 that means I'm going to get this + + + align:start position:0% +10,000 that means I'm going to get this +run this line of code 10,000 times all + + align:start position:0% +run this line of code 10,000 times all + + + align:start position:0% +run this line of code 10,000 times all +of a sudden I've just rolled a dice + + align:start position:0% +of a sudden I've just rolled a dice + + + align:start position:0% +of a sudden I've just rolled a dice +10,000 + + align:start position:0% +10,000 + + + align:start position:0% +10,000 +times as I'm doing so I'm interested in + + align:start position:0% +times as I'm doing so I'm interested in + + + align:start position:0% +times as I'm doing so I'm interested in +the outcome of some event so let's say + + align:start position:0% +the outcome of some event so let's say + + + align:start position:0% +the outcome of some event so let's say +how many times did a dot dot dot dot + + align:start position:0% +how many times did a dot dot dot dot + + + align:start position:0% +how many times did a dot dot dot dot +come up right a four well each time in + + align:start position:0% +come up right a four well each time in + + + align:start position:0% +come up right a four well each time in +my for loop I can keep track of the + + align:start position:0% +my for loop I can keep track of the + + + align:start position:0% +my for loop I can keep track of the +value of roll if it was a four increment + + align:start position:0% +value of roll if it was a four increment + + + align:start position:0% +value of roll if it was a four increment +a counter if it was not a four I don't + + align:start position:0% +a counter if it was not a four I don't + + + align:start position:0% +a counter if it was not a four I don't +care do + + align:start position:0% +care do + + + align:start position:0% +care do +nothing so each time I have a counter + + align:start position:0% +nothing so each time I have a counter + + + align:start position:0% +nothing so each time I have a counter +that tells me how many times a four came + + align:start position:0% +that tells me how many times a four came + + + align:start position:0% +that tells me how many times a four came +up and then after the for Loop is done + + align:start position:0% +up and then after the for Loop is done + + + align:start position:0% +up and then after the for Loop is done +I've repeated my experiment 10,000 times + + align:start position:0% +I've repeated my experiment 10,000 times + + + align:start position:0% +I've repeated my experiment 10,000 times +and I can report the probability to get + + align:start position:0% +and I can report the probability to get + + + align:start position:0% +and I can report the probability to get +a four right so the counter divided by + + align:start position:0% +a four right so the counter divided by + + + align:start position:0% +a four right so the counter divided by +10,000 so this is the code code that's + + align:start position:0% +10,000 so this is the code code that's + + + align:start position:0% +10,000 so this is the code code that's +it it's super + + align:start position:0% +it it's super + + + align:start position:0% +it it's super +simple uh I wrote a function and it + + align:start position:0% +simple uh I wrote a function and it + + + align:start position:0% +simple uh I wrote a function and it +actually takes in a parameter so if + + align:start position:0% +actually takes in a parameter so if + + + align:start position:0% +actually takes in a parameter so if +we're interested in the probability for + + align:start position:0% +we're interested in the probability for + + + align:start position:0% +we're interested in the probability for +a you know a dot dot dot dot to come up + + align:start position:0% +a you know a dot dot dot dot to come up + + + align:start position:0% +a you know a dot dot dot dot to come up +then we pass in the value of that + + align:start position:0% +then we pass in the value of that + + + align:start position:0% +then we pass in the value of that +particular uh of that side if I'm + + align:start position:0% +particular uh of that side if I'm + + + align:start position:0% +particular uh of that side if I'm +interested in the probability that a DOT + + align:start position:0% +interested in the probability that a DOT + + + align:start position:0% +interested in the probability that a DOT +comes up then I pass in the dot as a + + align:start position:0% +comes up then I pass in the dot as a + + + align:start position:0% +comes up then I pass in the dot as a +string okay so what does it do well just + + align:start position:0% +string okay so what does it do well just + + + align:start position:0% +string okay so what does it do well just +like in the previous slide I've got this + + align:start position:0% +like in the previous slide I've got this + + + align:start position:0% +like in the previous slide I've got this +for Loop here that tells tells uh python + + align:start position:0% +for Loop here that tells tells uh python + + + align:start position:0% +for Loop here that tells tells uh python +how many times to repeat the experiment + + align:start position:0% +how many times to repeat the experiment + + + align:start position:0% +how many times to repeat the experiment +I have the experiment number here as a + + align:start position:0% +I have the experiment number here as a + + + align:start position:0% +I have the experiment number here as a +variable so I can easily just change it + + align:start position:0% +variable so I can easily just change it + + + align:start position:0% +variable so I can easily just change it +to be something else and then I've got + + align:start position:0% +to be something else and then I've got + + + align:start position:0% +to be something else and then I've got +my roll here so this is me actually + + align:start position:0% +my roll here so this is me actually + + + align:start position:0% +my roll here so this is me actually +doing the experiment so just here's me + + align:start position:0% +doing the experiment so just here's me + + + align:start position:0% +doing the experiment so just here's me +rolling the dice here's roll value and + + align:start position:0% +rolling the dice here's roll value and + + + align:start position:0% +rolling the dice here's roll value and +then I check what the value of the Roll + + align:start position:0% +then I check what the value of the Roll + + + align:start position:0% +then I check what the value of the Roll +was and increment the counter if it was + + align:start position:0% +was and increment the counter if it was + + + align:start position:0% +was and increment the counter if it was +the side of Interest right the thing + + align:start position:0% +the side of Interest right the thing + + + align:start position:0% +the side of Interest right the thing +I've passed in as a parameter and then + + align:start position:0% +I've passed in as a parameter and then + + + align:start position:0% +I've passed in as a parameter and then +at the end I just do a print but you + + align:start position:0% +at the end I just do a print but you + + + align:start position:0% +at the end I just do a print but you +could imagine doing a return or + + align:start position:0% +could imagine doing a return or + + + align:start position:0% +could imagine doing a return or +something something like that so if I + + align:start position:0% +something something like that so if I + + + align:start position:0% +something something like that so if I +run it uh we're going to get the + + align:start position:0% +run it uh we're going to get the + + + align:start position:0% +run it uh we're going to get the +probability that the side dot came up + + align:start position:0% +probability that the side dot came up + + + align:start position:0% +probability that the side dot came up +was 0.167 and the probability that dot + + align:start position:0% +was 0.167 and the probability that dot + + + align:start position:0% +was 0.167 and the probability that dot +dot dot dot came up was + + align:start position:0% +dot dot dot came up was + + + align:start position:0% +dot dot dot came up was +1602 intuition says they should be the + + align:start position:0% +1602 intuition says they should be the + + + align:start position:0% +1602 intuition says they should be the +same but you know what that's that's + + align:start position:0% +same but you know what that's that's + + + align:start position:0% +same but you know what that's that's +that's our intuition right we already + + align:start position:0% +that's our intuition right we already + + + align:start position:0% +that's our intuition right we already +know the problem if we didn't know how + + align:start position:0% +know the problem if we didn't know how + + + align:start position:0% +know the problem if we didn't know how +to calculate the probability of you know + + align:start position:0% +to calculate the probability of you know + + + align:start position:0% +to calculate the probability of you know +one of these uh sides coming up this + + align:start position:0% +one of these uh sides coming up this + + + align:start position:0% +one of these uh sides coming up this +would be pretty good right the the + + align:start position:0% +would be pretty good right the the + + + align:start position:0% +would be pretty good right the the +beauty of computation is we can just add + + align:start position:0% +beauty of computation is we can just add + + + align:start position:0% +beauty of computation is we can just add +two more zeros on there run it right and + + align:start position:0% +two more zeros on there run it right and + + + align:start position:0% +two more zeros on there run it right and +maybe uncomment it so we actually see + + align:start position:0% +maybe uncomment it so we actually see + + + align:start position:0% +maybe uncomment it so we actually see +the values run it we wait a couple + + align:start position:0% +the values run it we wait a couple + + + align:start position:0% +the values run it we wait a couple +seconds but now the probability is + + align:start position:0% +seconds but now the probability is + + + align:start position:0% +seconds but now the probability is +getting closer and closer to the true + + align:start position:0% +getting closer and closer to the true + + + align:start position:0% +getting closer and closer to the true +probability right so the more + + align:start position:0% +probability right so the more + + + align:start position:0% +probability right so the more +experiments I do the better my answer + + align:start position:0% +experiments I do the better my answer + + + align:start position:0% +experiments I do the better my answer +becomes and I just had to wait a couple + + align:start position:0% +becomes and I just had to wait a couple + + + align:start position:0% +becomes and I just had to wait a couple +seconds if I increase it by 10 more I + + align:start position:0% +seconds if I increase it by 10 more I + + + align:start position:0% +seconds if I increase it by 10 more I +would have to wait 10 more times right + + align:start position:0% +would have to wait 10 more times right + + + align:start position:0% +would have to wait 10 more times right +10 times as long so maybe 20 seconds I'm + + align:start position:0% +10 times as long so maybe 20 seconds I'm + + + align:start position:0% +10 times as long so maybe 20 seconds I'm +not going to do + + align:start position:0% +not going to do + + + align:start position:0% +not going to do +it so it's still a guesstimate but it's + + align:start position:0% +it so it's still a guesstimate but it's + + + align:start position:0% +it so it's still a guesstimate but it's +a pretty close + + align:start position:0% +a pretty close + + + align:start position:0% +a pretty close +guesstimate now the other beauty of + + align:start position:0% +guesstimate now the other beauty of + + + align:start position:0% +guesstimate now the other beauty of +writing code is that we can now ask well + + align:start position:0% +writing code is that we can now ask well + + + align:start position:0% +writing code is that we can now ask well +this is a fair die right every single + + align:start position:0% +this is a fair die right every single + + + align:start position:0% +this is a fair die right every single +one of these sides comes up with an + + align:start position:0% +one of these sides comes up with an + + + align:start position:0% +one of these sides comes up with an +equal probability what do you guys think + + align:start position:0% +equal probability what do you guys think + + + align:start position:0% +equal probability what do you guys think +the change I should make to uh to make + + align:start position:0% +the change I should make to uh to make + + + align:start position:0% +the change I should make to uh to make +an unfair die let's say it's weighted + + align:start position:0% +an unfair die let's say it's weighted + + + align:start position:0% +an unfair die let's say it's weighted +unfairly towards uh the the the the the + + align:start position:0% +unfairly towards uh the the the the the + + + align:start position:0% +unfairly towards uh the the the the the +do dot right the one yeah add the dot + + align:start position:0% +do dot right the one yeah add the dot + + + align:start position:0% +do dot right the one yeah add the dot +yeah exactly let me just add another dot + + align:start position:0% +yeah exactly let me just add another dot + + + align:start position:0% +yeah exactly let me just add another dot +here here uh I've got another Dot and + + align:start position:0% +here here uh I've got another Dot and + + + align:start position:0% +here here uh I've got another Dot and +now the die is weighted unfairly right + + align:start position:0% +now the die is weighted unfairly right + + + align:start position:0% +now the die is weighted unfairly right +it comes up more times on the one than + + align:start position:0% +it comes up more times on the one than + + + align:start position:0% +it comes up more times on the one than +on anything else so if I run the code + + align:start position:0% +on anything else so if I run the code + + + align:start position:0% +on anything else so if I run the code +again wait a couple seconds probability + + align:start position:0% +again wait a couple seconds probability + + + align:start position:0% +again wait a couple seconds probability +to get a one twice as high as + + align:start position:0% +to get a one twice as high as + + + align:start position:0% +to get a one twice as high as +probability to get a four right so a + + align:start position:0% +probability to get a four right so a + + + align:start position:0% +probability to get a four right so a +really easy change it helped me answer + + align:start position:0% +really easy change it helped me answer + + + align:start position:0% +really easy change it helped me answer +another question a small variation of my + + align:start position:0% +another question a small variation of my + + + align:start position:0% +another question a small variation of my +original problem and I didn't have to + + align:start position:0% +original problem and I didn't have to + + + align:start position:0% +original problem and I didn't have to +you know roll it dice 10,000 times in in + + align:start position:0% +you know roll it dice 10,000 times in in + + + align:start position:0% +you know roll it dice 10,000 times in in +the real + + align:start position:0% + + + + align:start position:0% + +world + + align:start position:0% + + + + align:start position:0% + +okay so that was really easy simulation + + align:start position:0% +okay so that was really easy simulation + + + align:start position:0% +okay so that was really easy simulation +right the probability of getting one d + + align:start position:0% +right the probability of getting one d + + + align:start position:0% +right the probability of getting one d +uh of calculating uh uh sides of dies + + align:start position:0% +uh of calculating uh uh sides of dies + + + align:start position:0% +uh of calculating uh uh sides of dies +coming up is is pretty simple so why did + + align:start position:0% +coming up is is pretty simple so why did + + + align:start position:0% +coming up is is pretty simple so why did +we bother with the code right because we + + align:start position:0% +we bother with the code right because we + + + align:start position:0% +we bother with the code right because we +could just do it mathematically the side + + align:start position:0% +could just do it mathematically the side + + + align:start position:0% +could just do it mathematically the side +question that I asked was also kind of + + align:start position:0% +question that I asked was also kind of + + + align:start position:0% +question that I asked was also kind of +simple to figure out because we can + + align:start position:0% +simple to figure out because we can + + + align:start position:0% +simple to figure out because we can +actually ask harder questions and harder + + align:start position:0% +actually ask harder questions and harder + + + align:start position:0% +actually ask harder questions and harder +variations of our original problem we + + align:start position:0% +variations of our original problem we + + + align:start position:0% +variations of our original problem we +could certainly come up with + + align:start position:0% +could certainly come up with + + + align:start position:0% +could certainly come up with +mathematical solutions to these harder + + align:start position:0% +mathematical solutions to these harder + + + align:start position:0% +mathematical solutions to these harder +problems as well but I wouldn't be as + + align:start position:0% +problems as well but I wouldn't be as + + + align:start position:0% +problems as well but I wouldn't be as +certain about though my answers to those + + align:start position:0% +certain about though my answers to those + + + align:start position:0% +certain about though my answers to those +um as I would be just writing code for + + align:start position:0% +um as I would be just writing code for + + + align:start position:0% +um as I would be just writing code for +me it would be a little bit easier to + + align:start position:0% +me it would be a little bit easier to + + + align:start position:0% +me it would be a little bit easier to +debug code than it would be to answer to + + align:start position:0% +debug code than it would be to answer to + + + align:start position:0% +debug code than it would be to answer to +uh to mathematically write probabilities + + align:start position:0% +uh to mathematically write probabilities + + + align:start position:0% +uh to mathematically write probabilities +to much harder questions and you can see + + align:start position:0% +to much harder questions and you can see + + + align:start position:0% +to much harder questions and you can see +once you've written the code right once + + align:start position:0% +once you've written the code right once + + + align:start position:0% +once you've written the code right once +you've kind of framed your experiment in + + align:start position:0% +you've kind of framed your experiment in + + + align:start position:0% +you've kind of framed your experiment in +this way it's really easy e to just go + + align:start position:0% +this way it's really easy e to just go + + + align:start position:0% +this way it's really easy e to just go +ahead and change it a little bit right + + align:start position:0% +ahead and change it a little bit right + + + align:start position:0% +ahead and change it a little bit right +so the code is easy to change once it's + + align:start position:0% +so the code is easy to change once it's + + + align:start position:0% +so the code is easy to change once it's +written so let's look at a new question + + align:start position:0% +written so let's look at a new question + + + align:start position:0% +written so let's look at a new question +this one + + align:start position:0% +this one + + + align:start position:0% +this one +says um one experiment is no longer to + + align:start position:0% +says um one experiment is no longer to + + + align:start position:0% +says um one experiment is no longer to +just roll a die once one experiment is + + align:start position:0% +just roll a die once one experiment is + + + align:start position:0% +just roll a die once one experiment is +now that we're rolling a die seven times + + align:start position:0% +now that we're rolling a die seven times + + + align:start position:0% +now that we're rolling a die seven times +and I'm interested to know the + + align:start position:0% +and I'm interested to know the + + + align:start position:0% +and I'm interested to know the +probability to get the dot dot dot dot + + align:start position:0% +probability to get the dot dot dot dot + + + align:start position:0% +probability to get the dot dot dot dot +at least three times out of those seven + + align:start position:0% +at least three times out of those seven + + + align:start position:0% +at least three times out of those seven +rolles + + align:start position:0% +rolles + + + align:start position:0% +rolles +much harder question right than before + + align:start position:0% +much harder question right than before + + + align:start position:0% +much harder question right than before +it would require a little bit of + + align:start position:0% +it would require a little bit of + + + align:start position:0% +it would require a little bit of +thinking some paper right to figure out + + align:start position:0% +thinking some paper right to figure out + + + align:start position:0% +thinking some paper right to figure out +but in terms of code it's going to be + + align:start position:0% +but in terms of code it's going to be + + + align:start position:0% +but in terms of code it's going to be +really simple so now one experiment is + + align:start position:0% +really simple so now one experiment is + + + align:start position:0% +really simple so now one experiment is +no longer just one choice from my list + + align:start position:0% +no longer just one choice from my list + + + align:start position:0% +no longer just one choice from my list +of of dice faces but it's going to be + + align:start position:0% +of of dice faces but it's going to be + + + align:start position:0% +of of dice faces but it's going to be +seven choices from my list of dieces + + align:start position:0% +seven choices from my list of dieces + + + align:start position:0% +seven choices from my list of dieces +right representing the seven roles that + + align:start position:0% +right representing the seven roles that + + + align:start position:0% +right representing the seven roles that +I have for one experiment right + + align:start position:0% +I have for one experiment right + + + align:start position:0% +I have for one experiment right +and out of those seven roles what I'm + + align:start position:0% +and out of those seven roles what I'm + + + align:start position:0% +and out of those seven roles what I'm +interested to do is keeping track of + + align:start position:0% +interested to do is keeping track of + + + align:start position:0% +interested to do is keeping track of +right incrementing a counter whenever I + + align:start position:0% +right incrementing a counter whenever I + + + align:start position:0% +right incrementing a counter whenever I +see a four dot dot dot + + align:start position:0% +see a four dot dot dot + + + align:start position:0% +see a four dot dot dot +dot and then just like before slap a + + align:start position:0% +dot and then just like before slap a + + + align:start position:0% +dot and then just like before slap a +four loop around it repeat that + + align:start position:0% +four loop around it repeat that + + + align:start position:0% +four loop around it repeat that +experiment 10,000 a million times + + align:start position:0% +experiment 10,000 a million times + + + align:start position:0% +experiment 10,000 a million times +however many times you'd like and then + + align:start position:0% +however many times you'd like and then + + + align:start position:0% +however many times you'd like and then +keep track of how many times that four + + align:start position:0% +keep track of how many times that four + + + align:start position:0% +keep track of how many times that four +came up uh three or more times out of + + align:start position:0% +came up uh three or more times out of + + + align:start position:0% +came up uh three or more times out of +the seven rules okay so this is our + + align:start position:0% +the seven rules okay so this is our + + + align:start position:0% +the seven rules okay so this is our +event count how many times out of of the + + align:start position:0% +event count how many times out of of the + + + align:start position:0% +event count how many times out of of the +10,000 in that case but it could be a + + align:start position:0% +10,000 in that case but it could be a + + + align:start position:0% +10,000 in that case but it could be a +million whatever it is the um we + + align:start position:0% +million whatever it is the um we + + + align:start position:0% +million whatever it is the um we +incremented our counter to be uh more + + align:start position:0% +incremented our counter to be uh more + + + align:start position:0% +incremented our counter to be uh more +than three more than or equal to three + + align:start position:0% +than three more than or equal to three + + + align:start position:0% +than three more than or equal to three +okay and then our value of interest is + + align:start position:0% +okay and then our value of interest is + + + align:start position:0% +okay and then our value of interest is +the probability of that happening so + + align:start position:0% +the probability of that happening so + + + align:start position:0% +the probability of that happening so +take that counter and divide by 10,000 + + align:start position:0% +take that counter and divide by 10,000 + + + align:start position:0% +take that counter and divide by 10,000 +because that's how many times we + + align:start position:0% +because that's how many times we + + + align:start position:0% +because that's how many times we +repeated our experiment okay so this is + + align:start position:0% +repeated our experiment okay so this is + + + align:start position:0% +repeated our experiment okay so this is +the code slightly longer and I've + + align:start position:0% +the code slightly longer and I've + + + align:start position:0% +the code slightly longer and I've +actually divided it into two parts this + + align:start position:0% +actually divided it into two parts this + + + align:start position:0% +actually divided it into two parts this +one up here and then this one down here + + align:start position:0% +one up here and then this one down here + + + align:start position:0% +one up here and then this one down here +so so the code up here is going to uh do + + align:start position:0% +so so the code up here is going to uh do + + + align:start position:0% +so so the code up here is going to uh do +the simulation 10,000 times so I've got + + align:start position:0% +the simulation 10,000 times so I've got + + + align:start position:0% +the simulation 10,000 times so I've got +one for Loop here that goes through + + align:start position:0% +one for Loop here that goes through + + + align:start position:0% +one for Loop here that goes through +10,000 or a million however many times + + align:start position:0% +10,000 or a million however many times + + + align:start position:0% +10,000 or a million however many times +you want to repeat the the + + align:start position:0% +you want to repeat the the + + + align:start position:0% +you want to repeat the the +experiment within here sorry uh and I + + align:start position:0% +experiment within here sorry uh and I + + + align:start position:0% +experiment within here sorry uh and I +sorry I forgot to mention that here I + + align:start position:0% +sorry I forgot to mention that here I + + + align:start position:0% +sorry I forgot to mention that here I +have a function where I've kind of + + align:start position:0% +have a function where I've kind of + + + align:start position:0% +have a function where I've kind of +generalized a bunch of stuff so we could + + align:start position:0% +generalized a bunch of stuff so we could + + + align:start position:0% +generalized a bunch of stuff so we could +run it with different values so instead + + align:start position:0% +run it with different values so instead + + + align:start position:0% +run it with different values so instead +of SE three times out of seven Rolls we + + align:start position:0% +of SE three times out of seven Rolls we + + + align:start position:0% +of SE three times out of seven Rolls we +could have 15 times out of 3,000 rolls + + align:start position:0% +could have 15 times out of 3,000 rolls + + + align:start position:0% +could have 15 times out of 3,000 rolls +right so we can generalize this um so + + align:start position:0% +right so we can generalize this um so + + + align:start position:0% +right so we can generalize this um so +here um inside this for Loop I've got + + align:start position:0% +here um inside this for Loop I've got + + + align:start position:0% +here um inside this for Loop I've got +the simulation of rolling seven times + + align:start position:0% +the simulation of rolling seven times + + + align:start position:0% +the simulation of rolling seven times +right so here I've got range of n rolls + + align:start position:0% +right so here I've got range of n rolls + + + align:start position:0% +right so here I've got range of n rolls +in the previous slide I said it's seven + + align:start position:0% +in the previous slide I said it's seven + + + align:start position:0% +in the previous slide I said it's seven +but it could be anything you'd like and + + align:start position:0% +but it could be anything you'd like and + + + align:start position:0% +but it could be anything you'd like and +then I've got choosing one of the faces + + align:start position:0% +then I've got choosing one of the faces + + + align:start position:0% +then I've got choosing one of the faces +seven times and keeping track of how + + align:start position:0% +seven times and keeping track of how + + + align:start position:0% +seven times and keeping track of how +many times out of those seven I got a + + align:start position:0% +many times out of those seven I got a + + + align:start position:0% +many times out of those seven I got a +dot dot dot + + align:start position:0% +dot dot dot + + + align:start position:0% +dot dot dot +dot + + align:start position:0% + + + + align:start position:0% + +okay so at the end of this for Loop here + + align:start position:0% +okay so at the end of this for Loop here + + + align:start position:0% +okay so at the end of this for Loop here +I've counted how many times I got a dot + + align:start position:0% +I've counted how many times I got a dot + + + align:start position:0% +I've counted how many times I got a dot +dot dot dot and then I'm going to keep + + align:start position:0% +dot dot dot and then I'm going to keep + + + align:start position:0% +dot dot dot and then I'm going to keep +track of that number in this list how + + align:start position:0% +track of that number in this list how + + + align:start position:0% +track of that number in this list how +many matched so how many matched will be + + align:start position:0% +many matched so how many matched will be + + + align:start position:0% +many matched so how many matched will be +a list of 10,000 elements right 10,000 + + align:start position:0% +a list of 10,000 elements right 10,000 + + + align:start position:0% +a list of 10,000 elements right 10,000 +elements one element for each one of my + + align:start position:0% +elements one element for each one of my + + + align:start position:0% +elements one element for each one of my +experiments so the first time may be + + align:start position:0% +experiments so the first time may be + + + align:start position:0% +experiments so the first time may be +three dot dot dot dot dots came up out + + align:start position:0% +three dot dot dot dot dots came up out + + + align:start position:0% +three dot dot dot dot dots came up out +of seven then the next time one then the + + align:start position:0% +of seven then the next time one then the + + + align:start position:0% +of seven then the next time one then the +next time five then the next time four + + align:start position:0% +next time five then the next time four + + + align:start position:0% +next time five then the next time four +however many right so now I've got a + + align:start position:0% +however many right so now I've got a + + + align:start position:0% +however many right so now I've got a +list of how many times the dot dot dot + + align:start position:0% +list of how many times the dot dot dot + + + align:start position:0% +list of how many times the dot dot dot +dot came up out of seven rows so the + + align:start position:0% +dot came up out of seven rows so the + + + align:start position:0% +dot came up out of seven rows so the +code down here that's why I split it up + + align:start position:0% +code down here that's why I split it up + + + align:start position:0% +code down here that's why I split it up +because it's a little bit easier for me + + align:start position:0% +because it's a little bit easier for me + + + align:start position:0% +because it's a little bit easier for me +to think about it the code down here is + + align:start position:0% +to think about it the code down here is + + + align:start position:0% +to think about it the code down here is +now going to iterate through this list + + align:start position:0% +now going to iterate through this list + + + align:start position:0% +now going to iterate through this list +of 10,000 experiments and say which one + + align:start position:0% +of 10,000 experiments and say which one + + + align:start position:0% +of 10,000 experiments and say which one +of these is greater or equal to three + + align:start position:0% +of these is greater or equal to three + + + align:start position:0% +of these is greater or equal to three +this one this one this one so I'm + + align:start position:0% +this one this one this one so I'm + + + align:start position:0% +this one this one this one so I'm +incrementing a counter anytime that is + + align:start position:0% +incrementing a counter anytime that is + + + align:start position:0% +incrementing a counter anytime that is +true and at the end of this Loop down + + align:start position:0% +true and at the end of this Loop down + + + align:start position:0% +true and at the end of this Loop down +there I'm going to know how many times + + align:start position:0% +there I'm going to know how many times + + + align:start position:0% +there I'm going to know how many times +out of those 10,000 trials I had uh + + align:start position:0% +out of those 10,000 trials I had uh + + + align:start position:0% +out of those 10,000 trials I had uh +three or more times out of seven come up + + align:start position:0% +three or more times out of seven come up + + + align:start position:0% +three or more times out of seven come up +uh on the dot dot dot dot okay so I can + + align:start position:0% +uh on the dot dot dot dot okay so I can + + + align:start position:0% +uh on the dot dot dot dot okay so I can +run the code and here I've got the exact + + align:start position:0% +run the code and here I've got the exact + + + align:start position:0% +run the code and here I've got the exact +problem on the previous slide so if I'm + + align:start position:0% +problem on the previous slide so if I'm + + + align:start position:0% +problem on the previous slide so if I'm +interested in the probability of the + + align:start position:0% +interested in the probability of the + + + align:start position:0% +interested in the probability of the +four coming up at least three or more + + align:start position:0% +four coming up at least three or more + + + align:start position:0% +four coming up at least three or more +times out of seven rols that's + + align:start position:0% +times out of seven rols that's + + + align:start position:0% +times out of seven rols that's + + align:start position:0% + + + align:start position:0% +and then I also down here wrote it like + + align:start position:0% +and then I also down here wrote it like + + + align:start position:0% +and then I also down here wrote it like +this and this probability + + align:start position:0% +this and this probability + + + align:start position:0% +this and this probability +is16 what is this problem down here does + + align:start position:0% +is16 what is this problem down here does + + + align:start position:0% +is16 what is this problem down here does +it look + + align:start position:0% +it look + + + align:start position:0% +it look +familiar so the probability of a dot dot + + align:start position:0% +familiar so the probability of a dot dot + + + align:start position:0% +familiar so the probability of a dot dot +dot dot coming up at least once out of + + align:start position:0% +dot dot coming up at least once out of + + + align:start position:0% +dot dot coming up at least once out of +one + + align:start position:0% + + + + align:start position:0% + +roll that's just the previous problem + + align:start position:0% +roll that's just the previous problem + + + align:start position:0% +roll that's just the previous problem +right on the previous slide I just have + + align:start position:0% +right on the previous slide I just have + + + align:start position:0% +right on the previous slide I just have +one roll and I count the probability to + + align:start position:0% +one roll and I count the probability to + + + align:start position:0% +one roll and I count the probability to +get the four okay so this matches what I + + align:start position:0% +get the four okay so this matches what I + + + align:start position:0% +get the four okay so this matches what I +got with my the previous function that I + + align:start position:0% +got with my the previous function that I + + + align:start position:0% +got with my the previous function that I +wrote but hey now I wrote a better + + align:start position:0% +wrote but hey now I wrote a better + + + align:start position:0% +wrote but hey now I wrote a better +function that can actually that's more + + align:start position:0% +function that can actually that's more + + + align:start position:0% +function that can actually that's more +General and I can also run it to get the + + align:start position:0% +General and I can also run it to get the + + + align:start position:0% +General and I can also run it to get the +probability that I from the previous + + align:start position:0% +probability that I from the previous + + + align:start position:0% +probability that I from the previous +code right so this is actually a much + + align:start position:0% +code right so this is actually a much + + + align:start position:0% +code right so this is actually a much +better code to + + align:start position:0% + + + + align:start position:0% + +run okay questions about this + + align:start position:0% +run okay questions about this + + + align:start position:0% +run okay questions about this +interesting I mean it's dice rolls how + + align:start position:0% +interesting I mean it's dice rolls how + + + align:start position:0% +interesting I mean it's dice rolls how +interesting can it be but yeah so let's + + align:start position:0% +interesting can it be but yeah so let's + + + align:start position:0% +interesting can it be but yeah so let's +look at a more uh interesting problem + + align:start position:0% +look at a more uh interesting problem + + + align:start position:0% +look at a more uh interesting problem +something that you might apply uh to you + + align:start position:0% +something that you might apply uh to you + + + align:start position:0% +something that you might apply uh to you +know to the real + + align:start position:0% +know to the real + + + align:start position:0% +know to the real +world so you might see this in a + + align:start position:0% +world so you might see this in a + + + align:start position:0% +world so you might see this in a +calculus course might not um but it is + + align:start position:0% +calculus course might not um but it is + + + align:start position:0% +calculus course might not um but it is +more of a calculus problem so I've got + + align:start position:0% +more of a calculus problem so I've got + + + align:start position:0% +more of a calculus problem so I've got +water that runs through a + + align:start position:0% +water that runs through a + + + align:start position:0% +water that runs through a +faucet at random somewhere between one + + align:start position:0% +faucet at random somewhere between one + + + align:start position:0% +faucet at random somewhere between one +gallons per minute and three gallons per + + align:start position:0% +gallons per minute and three gallons per + + + align:start position:0% +gallons per minute and three gallons per +minute this is the + + align:start position:0% +minute this is the + + + align:start position:0% +minute this is the +setup what is the time it takes to fill + + align:start position:0% +setup what is the time it takes to fill + + + align:start position:0% +setup what is the time it takes to fill +the 600g pool does anyone have an + + align:start position:0% +the 600g pool does anyone have an + + + align:start position:0% +the 600g pool does anyone have an +intuition for how we could solve + + align:start position:0% +intuition for how we could solve + + + align:start position:0% +intuition for how we could solve +this if not I can just click + + align:start position:0% + + + + align:start position:0% + +next yeah definitely between the lowest + + align:start position:0% +next yeah definitely between the lowest + + + align:start position:0% +next yeah definitely between the lowest +rate and the highest rate right so + + align:start position:0% +rate and the highest rate right so + + + align:start position:0% +rate and the highest rate right so +between 200 gallons per minute sorry + + align:start position:0% +between 200 gallons per minute sorry + + + align:start position:0% +between 200 gallons per minute sorry +between 200 minutes and 600 minutes + + align:start position:0% +between 200 minutes and 600 minutes + + + align:start position:0% +between 200 minutes and 600 minutes +right 200 at best if the water flows at + + align:start position:0% +right 200 at best if the water flows at + + + align:start position:0% +right 200 at best if the water flows at +three Gall per minute and uh 600 minutes + + align:start position:0% +three Gall per minute and uh 600 minutes + + + align:start position:0% +three Gall per minute and uh 600 minutes +at worst if the water flows super slowly + + align:start position:0% +at worst if the water flows super slowly + + + align:start position:0% +at worst if the water flows super slowly +one gallon per minute + + align:start position:0% +one gallon per minute + + + align:start position:0% +one gallon per minute +so we could say well let's take the + + align:start position:0% +so we could say well let's take the + + + align:start position:0% +so we could say well let's take the +average of the flow one the average + + align:start position:0% +average of the flow one the average + + + align:start position:0% +average of the flow one the average +between one and three gallons is two + + align:start position:0% +between one and three gallons is two + + + align:start position:0% +between one and three gallons is two +right so if we take 600 gallons divided + + align:start position:0% +right so if we take 600 gallons divided + + + align:start position:0% +right so if we take 600 gallons divided +by two gallons per minute that would + + align:start position:0% +by two gallons per minute that would + + + align:start position:0% +by two gallons per minute that would +give us 300 + + align:start position:0% +give us 300 + + + align:start position:0% +give us 300 +minutes it's a reasonable guess but + + align:start position:0% +minutes it's a reasonable guess but + + + align:start position:0% +minutes it's a reasonable guess but +that's not actually the right + + align:start position:0% +that's not actually the right + + + align:start position:0% +that's not actually the right +answer another way we could say is well + + align:start position:0% +answer another way we could say is well + + + align:start position:0% +answer another way we could say is well +let's uh take the slowest and the + + align:start position:0% +let's uh take the slowest and the + + + align:start position:0% +let's uh take the slowest and the +fastest it could run right so it could + + align:start position:0% +fastest it could run right so it could + + + align:start position:0% +fastest it could run right so it could +take so here I've got 600 minutes and + + align:start position:0% +take so here I've got 600 minutes and + + + align:start position:0% +take so here I've got 600 minutes and +200 minutes and average those numbers + + align:start position:0% +200 minutes and average those numbers + + + align:start position:0% +200 minutes and average those numbers +out right divide by two so that's 400 + + align:start position:0% +out right divide by two so that's 400 + + + align:start position:0% +out right divide by two so that's 400 +minutes but that's actually not right + + align:start position:0% +minutes but that's actually not right + + + align:start position:0% +minutes but that's actually not right +either + + align:start position:0% + + + + align:start position:0% + +yeah you could yeah I don't want to do + + align:start position:0% +yeah you could yeah I don't want to do + + + align:start position:0% +yeah you could yeah I don't want to do +integrals + + align:start position:0% +integrals + + + align:start position:0% +integrals +though yeah but that's exactly the right + + align:start position:0% +though yeah but that's exactly the right + + + align:start position:0% +though yeah but that's exactly the right +answer yeah you have to do an + + align:start position:0% +answer yeah you have to do an + + + align:start position:0% +answer yeah you have to do an +integral and yeah I I I yeah we yeah + + align:start position:0% +integral and yeah I I I yeah we yeah + + + align:start position:0% +integral and yeah I I I yeah we yeah +we're teaching computer science + + align:start position:0% +we're teaching computer science + + + align:start position:0% +we're teaching computer science +here so we're not going to do integrals + + align:start position:0% +here so we're not going to do integrals + + + align:start position:0% +here so we're not going to do integrals +in this class instead we're going to do + + align:start position:0% +in this class instead we're going to do + + + align:start position:0% +in this class instead we're going to do +code and the code is going to be like + + align:start position:0% +code and the code is going to be like + + + align:start position:0% +code and the code is going to be like +five lines okay to do the to find the + + align:start position:0% +five lines okay to do the to find the + + + align:start position:0% +five lines okay to do the to find the +answer to this so all we're going to do + + align:start position:0% +answer to this so all we're going to do + + + align:start position:0% +answer to this so all we're going to do +is grab a whole bunch of numbers between + + align:start position:0% +is grab a whole bunch of numbers between + + + align:start position:0% +is grab a whole bunch of numbers between +one and three a million of them if you + + align:start position:0% +one and three a million of them if you + + + align:start position:0% +one and three a million of them if you +want these will represent a bunch of + + align:start position:0% +want these will represent a bunch of + + + align:start position:0% +want these will represent a bunch of +random values you could have the water + + align:start position:0% +random values you could have the water + + + align:start position:0% +random values you could have the water +flow right + + align:start position:0% +flow right + + + align:start position:0% +flow right +be and then we're going to say for each + + align:start position:0% +be and then we're going to say for each + + + align:start position:0% +be and then we're going to say for each +one of these numbers chosen at random + + align:start position:0% +one of these numbers chosen at random + + + align:start position:0% +one of these numbers chosen at random +how long would it take to fill the pool + + align:start position:0% +how long would it take to fill the pool + + + align:start position:0% +how long would it take to fill the pool +so you do 600 divided by that rate right + + align:start position:0% +so you do 600 divided by that rate right + + + align:start position:0% +so you do 600 divided by that rate right +just just just how long it takes and + + align:start position:0% +just just just how long it takes and + + + align:start position:0% +just just just how long it takes and +then we're going to average all of these + + align:start position:0% +then we're going to average all of these + + + align:start position:0% +then we're going to average all of these +rates right so we have a million of + + align:start position:0% +rates right so we have a million of + + + align:start position:0% +rates right so we have a million of +these numbers potential times that it + + align:start position:0% +these numbers potential times that it + + + align:start position:0% +these numbers potential times that it +could take to fill the pool sum them all + + align:start position:0% +could take to fill the pool sum them all + + + align:start position:0% +could take to fill the pool sum them all +average + + align:start position:0% +average + + + align:start position:0% +average +them this is the code it looks like a + + align:start position:0% +them this is the code it looks like a + + + align:start position:0% +them this is the code it looks like a +lot but down here the bottom half of + + align:start position:0% +lot but down here the bottom half of + + + align:start position:0% +lot but down here the bottom half of +this is just us reporting the results + + align:start position:0% +this is just us reporting the results + + + align:start position:0% +this is just us reporting the results +this is you know here's two print + + align:start position:0% +this is you know here's two print + + + align:start position:0% +this is you know here's two print +statements and here I'm actually also + + align:start position:0% +statements and here I'm actually also + + + align:start position:0% +statements and here I'm actually also +plotting what the what the uh what the + + align:start position:0% +plotting what the what the uh what the + + + align:start position:0% +plotting what the what the uh what the +dots look like right all the flow rates + + align:start position:0% +dots look like right all the flow rates + + + align:start position:0% +dots look like right all the flow rates +the actual code to do the simulation is + + align:start position:0% +the actual code to do the simulation is + + + align:start position:0% +the actual code to do the simulation is +these Okay I lied seven lines of code + + align:start position:0% +these Okay I lied seven lines of code + + + align:start position:0% +these Okay I lied seven lines of code +not + + align:start position:0% +not + + + align:start position:0% +not +five so I've got a function Phill pool + + align:start position:0% +five so I've got a function Phill pool + + + align:start position:0% +five so I've got a function Phill pool +it can take in a size parameter we could + + align:start position:0% +it can take in a size parameter we could + + + align:start position:0% +it can take in a size parameter we could +even do a lower range and an upper range + + align:start position:0% +even do a lower range and an upper range + + + align:start position:0% +even do a lower range and an upper range +if we wanted to for the flow rate for + + align:start position:0% +if we wanted to for the flow rate for + + + align:start position:0% +if we wanted to for the flow rate for +now we'll just hardcode it to be between + + align:start position:0% +now we'll just hardcode it to be between + + + align:start position:0% +now we'll just hardcode it to be between +one and three I've got two lists that + + align:start position:0% +one and three I've got two lists that + + + align:start position:0% +one and three I've got two lists that +I'm going to populate with a bunch of + + align:start position:0% +I'm going to populate with a bunch of + + + align:start position:0% +I'm going to populate with a bunch of +different random numbers so the flow + + align:start position:0% +different random numbers so the flow + + + align:start position:0% +different random numbers so the flow +rate R will be chosen between one and + + align:start position:0% +rate R will be chosen between one and + + + align:start position:0% +rate R will be chosen between one and +three so here I've got um random. random + + align:start position:0% +three so here I've got um random. random + + + align:start position:0% +three so here I've got um random. random +is another useful random function from + + align:start position:0% +is another useful random function from + + + align:start position:0% +is another useful random function from +the random library that uh gives me a + + align:start position:0% +the random library that uh gives me a + + + align:start position:0% +the random library that uh gives me a +number between zero and one so to get a + + align:start position:0% +number between zero and one so to get a + + + align:start position:0% +number between zero and one so to get a +number between one and three at random + + align:start position:0% +number between one and three at random + + + align:start position:0% +number between one and three at random +I'll just multiply by two and add one + + align:start position:0% +I'll just multiply by two and add one + + + align:start position:0% +I'll just multiply by two and add one +right so bottom case it'll be one top + + align:start position:0% +right so bottom case it'll be one top + + + align:start position:0% +right so bottom case it'll be one top +case will be 2 * 1 + 1 + + align:start position:0% +case will be 2 * 1 + 1 + + + align:start position:0% +case will be 2 * 1 + 1 +three right so R all we need to know + + align:start position:0% +three right so R all we need to know + + + align:start position:0% +three right so R all we need to know +will be a random number between one and + + align:start position:0% +will be a random number between one and + + + align:start position:0% +will be a random number between one and +three a float right so could be anything + + align:start position:0% +three a float right so could be anything + + + align:start position:0% +three a float right so could be anything +um append that random number to our list + + align:start position:0% +um append that random number to our list + + + align:start position:0% +um append that random number to our list +of of flow rates and then using that + + align:start position:0% +of of flow rates and then using that + + + align:start position:0% +of of flow rates and then using that +flow rate that we just randomly chose + + align:start position:0% +flow rate that we just randomly chose + + + align:start position:0% +flow rate that we just randomly chose +figure out how long it takes to fill the + + align:start position:0% +figure out how long it takes to fill the + + + align:start position:0% +figure out how long it takes to fill the +pool SI the pool of size size so size + + align:start position:0% +pool SI the pool of size size so size + + + align:start position:0% +pool SI the pool of size size so size +divided by the rate + + align:start position:0% +divided by the rate + + + align:start position:0% +divided by the rate +right just very simple math and then we + + align:start position:0% +right just very simple math and then we + + + align:start position:0% +right just very simple math and then we +now have a list uh that's populated with + + align:start position:0% +now have a list uh that's populated with + + + align:start position:0% +now have a list uh that's populated with +all of these times that it takes to fill + + align:start position:0% +all of these times that it takes to fill + + + align:start position:0% +all of these times that it takes to fill +the + + align:start position:0% +the + + + align:start position:0% +the +pool okay and that's the stuff inside + + align:start position:0% +pool okay and that's the stuff inside + + + align:start position:0% +pool okay and that's the stuff inside +the loop the for Loop here is one + + align:start position:0% +the loop the for Loop here is one + + + align:start position:0% +the loop the for Loop here is one +experiment right so I grabbed one random + + align:start position:0% +experiment right so I grabbed one random + + + align:start position:0% +experiment right so I grabbed one random +number I figured out how long it takes + + align:start position:0% +number I figured out how long it takes + + + align:start position:0% +number I figured out how long it takes +for me to fill my pool and then I + + align:start position:0% +for me to fill my pool and then I + + + align:start position:0% +for me to fill my pool and then I +repeated that 10,000 times + + align:start position:0% +repeated that 10,000 times + + + align:start position:0% +repeated that 10,000 times +right okay so down here I'm going to + + align:start position:0% +right okay so down here I'm going to + + + align:start position:0% +right okay so down here I'm going to +report the average flow rate which + + align:start position:0% +report the average flow rate which + + + align:start position:0% +report the average flow rate which +should be two right because if we're + + align:start position:0% +should be two right because if we're + + + align:start position:0% +should be two right because if we're +choosing a random number between one and + + align:start position:0% +choosing a random number between one and + + + align:start position:0% +choosing a random number between one and +three the average of those numbers + + align:start position:0% +three the average of those numbers + + + align:start position:0% +three the average of those numbers +better be two and then I'm reporting the + + align:start position:0% +better be two and then I'm reporting the + + + align:start position:0% +better be two and then I'm reporting the +thing that we're actually interested in + + align:start position:0% +thing that we're actually interested in + + + align:start position:0% +thing that we're actually interested in +which is the average fill time right + + align:start position:0% +which is the average fill time right + + + align:start position:0% +which is the average fill time right +which was not either of those two things + + align:start position:0% +which was not either of those two things + + + align:start position:0% +which was not either of those two things +we had the intuition for but it is the + + align:start position:0% +we had the intuition for but it is the + + + align:start position:0% +we had the intuition for but it is the +integral and down here I'm doing some + + align:start position:0% +integral and down here I'm doing some + + + align:start position:0% +integral and down here I'm doing some +plots so these are the things that I've + + align:start position:0% +plots so these are the things that I've + + + align:start position:0% +plots so these are the things that I've +plotted so on the left side I've got on + + align:start position:0% +plotted so on the left side I've got on + + + align:start position:0% +plotted so on the left side I've got on +the x- axis apologies I forgot to label + + align:start position:0% +the x- axis apologies I forgot to label + + + align:start position:0% +the x- axis apologies I forgot to label +my axes and put a title on this so I'm + + align:start position:0% +my axes and put a title on this so I'm + + + align:start position:0% +my axes and put a title on this so I'm +just going to uh talk about it so the x + + align:start position:0% +just going to uh talk about it so the x + + + align:start position:0% +just going to uh talk about it so the x +axis is numbers zero through 10,000 + + align:start position:0% +axis is numbers zero through 10,000 + + + align:start position:0% +axis is numbers zero through 10,000 +representing each basically like you + + align:start position:0% +representing each basically like you + + + align:start position:0% +representing each basically like you +know 0 1 two 3 four represents one of my + + align:start position:0% +know 0 1 two 3 four represents one of my + + + align:start position:0% +know 0 1 two 3 four represents one of my +experiments right choosing a random + + align:start position:0% +experiments right choosing a random + + + align:start position:0% +experiments right choosing a random +number and the y- axis is the random + + align:start position:0% +number and the y- axis is the random + + + align:start position:0% +number and the y- axis is the random +number that was chosen right so this is + + align:start position:0% +number that was chosen right so this is + + + align:start position:0% +number that was chosen right so this is +uh looks like a a nice smattering of + + align:start position:0% +uh looks like a a nice smattering of + + + align:start position:0% +uh looks like a a nice smattering of +Randomness here which is what we wanted + + align:start position:0% +Randomness here which is what we wanted + + + align:start position:0% +Randomness here which is what we wanted +and then for each one of these values + + align:start position:0% +and then for each one of these values + + + align:start position:0% +and then for each one of these values +I'm going to have a corresponding fill + + align:start position:0% +I'm going to have a corresponding fill + + + align:start position:0% +I'm going to have a corresponding fill +rate right so for example here if at + + align:start position:0% +rate right so for example here if at + + + align:start position:0% +rate right so for example here if at +Point z uh the fill rate happened to be + + align:start position:0% +Point z uh the fill rate happened to be + + + align:start position:0% +Point z uh the fill rate happened to be +uh one right + + align:start position:0% +uh one right + + + align:start position:0% +uh one right +then that means the time it took for me + + align:start position:0% +then that means the time it took for me + + + align:start position:0% +then that means the time it took for me +to fill the pool should be up there at + + align:start position:0% +to fill the pool should be up there at + + + align:start position:0% +to fill the pool should be up there at +about 600 right it could be that little + + align:start position:0% +about 600 right it could be that little + + + align:start position:0% +about 600 right it could be that little +point right there + + align:start position:0% +point right there + + + align:start position:0% +point right there +maybe okay so this is a graph of random + + align:start position:0% +maybe okay so this is a graph of random + + + align:start position:0% +maybe okay so this is a graph of random +numbers between one and three 10,000 of + + align:start position:0% +numbers between one and three 10,000 of + + + align:start position:0% +numbers between one and three 10,000 of +them Chosen and this is the graph of the + + align:start position:0% +them Chosen and this is the graph of the + + + align:start position:0% +them Chosen and this is the graph of the +corresponding times it took for me to + + align:start position:0% +corresponding times it took for me to + + + align:start position:0% +corresponding times it took for me to +fill the pool with each one of these + + align:start position:0% +fill the pool with each one of these + + + align:start position:0% +fill the pool with each one of these +dots that we randomly chose we + + align:start position:0% +dots that we randomly chose we + + + align:start position:0% +dots that we randomly chose we +notice that the plot on the right is not + + align:start position:0% +notice that the plot on the right is not + + + align:start position:0% +notice that the plot on the right is not +uniformly scattered right in fact it's + + align:start position:0% +uniformly scattered right in fact it's + + + align:start position:0% +uniformly scattered right in fact it's +more kind of densely populated down + + align:start position:0% +more kind of densely populated down + + + align:start position:0% +more kind of densely populated down +towards the + + align:start position:0% +towards the + + + align:start position:0% +towards the +bottom + + align:start position:0% +bottom + + + align:start position:0% +bottom +right so our two guesses were that the + + align:start position:0% +right so our two guesses were that the + + + align:start position:0% +right so our two guesses were that the +fill rate was either 300 or 400 on + + align:start position:0% +fill rate was either 300 or 400 on + + + align:start position:0% +fill rate was either 300 or 400 on +average right and neither of those were + + align:start position:0% +average right and neither of those were + + + align:start position:0% +average right and neither of those were +right um let's view these graphs in a + + align:start position:0% +right um let's view these graphs in a + + + align:start position:0% +right um let's view these graphs in a +slightly different way I'm actually + + align:start position:0% +slightly different way I'm actually + + + align:start position:0% +slightly different way I'm actually +going to sort the values so right now + + align:start position:0% +going to sort the values so right now + + + align:start position:0% +going to sort the values so right now +right it was just a random uh number + + align:start position:0% +right it was just a random uh number + + + align:start position:0% +right it was just a random uh number +gotten between uh one and three but I + + align:start position:0% +gotten between uh one and three but I + + + align:start position:0% +gotten between uh one and three but I +can sort them it doesn't matter the + + align:start position:0% +can sort them it doesn't matter the + + + align:start position:0% +can sort them it doesn't matter the +order that I got these random numbers I + + align:start position:0% +order that I got these random numbers I + + + align:start position:0% +order that I got these random numbers I +can sort them and if I sort them I get + + align:start position:0% +can sort them and if I sort them I get + + + align:start position:0% +can sort them and if I sort them I get +something that looks like this so again + + align:start position:0% +something that looks like this so again + + + align:start position:0% +something that looks like this so again +I've got randomly chosen numbers 10,000 + + align:start position:0% +I've got randomly chosen numbers 10,000 + + + align:start position:0% +I've got randomly chosen numbers 10,000 +of + + align:start position:0% +of + + + align:start position:0% +of +them and with equal probability right + + align:start position:0% +them and with equal probability right + + + align:start position:0% +them and with equal probability right +that's why we see this nice line I chose + + align:start position:0% +that's why we see this nice line I chose + + + align:start position:0% +that's why we see this nice line I chose +a number between one and + + align:start position:0% +a number between one and + + + align:start position:0% +a number between one and +three does that make sense okay and so + + align:start position:0% +three does that make sense okay and so + + + align:start position:0% +three does that make sense okay and so +then the corresponding time it took for + + align:start position:0% +then the corresponding time it took for + + + align:start position:0% +then the corresponding time it took for +me to fill my pool for each one of these + + align:start position:0% +me to fill my pool for each one of these + + + align:start position:0% +me to fill my pool for each one of these +numbers right is a number between uh 200 + + align:start position:0% +numbers right is a number between uh 200 + + + align:start position:0% +numbers right is a number between uh 200 +and 600 as we had + + align:start position:0% +and 600 as we had + + + align:start position:0% +and 600 as we had +guessed now the average of the time it + + align:start position:0% +guessed now the average of the time it + + + align:start position:0% +guessed now the average of the time it +takes uh of the fill rate is + + align:start position:0% +takes uh of the fill rate is + + + align:start position:0% +takes uh of the fill rate is +two which is true right that is not a + + align:start position:0% +two which is true right that is not a + + + align:start position:0% +two which is true right that is not a +surprise for us because it's a random + + align:start position:0% +surprise for us because it's a random + + + align:start position:0% +surprise for us because it's a random +number between one and three but the + + align:start position:0% +number between one and three but the + + + align:start position:0% +number between one and three but the +actual average time it takes to fill my + + align:start position:0% +actual average time it takes to fill my + + + align:start position:0% +actual average time it takes to fill my +pool is down here if I were to average + + align:start position:0% +pool is down here if I were to average + + + align:start position:0% +pool is down here if I were to average +every single one of these values it's + + align:start position:0% +every single one of these values it's + + + align:start position:0% +every single one of these values it's +down down here at around + + align:start position:0% +down down here at around + + + align:start position:0% +down down here at around +330 so it's not 300 it's not 400 it's + + align:start position:0% +330 so it's not 300 it's not 400 it's + + + align:start position:0% +330 so it's not 300 it's not 400 it's +definitely between you know between + + align:start position:0% +definitely between you know between + + + align:start position:0% +definitely between you know between +those two but it's not really close to + + align:start position:0% +those two but it's not really close to + + + align:start position:0% +those two but it's not really close to +one or the other that's because I've got + + align:start position:0% +one or the other that's because I've got + + + align:start position:0% +one or the other that's because I've got +more points kind of dense more densely + + align:start position:0% +more points kind of dense more densely + + + align:start position:0% +more points kind of dense more densely +populated down towards the bottom than + + align:start position:0% +populated down towards the bottom than + + + align:start position:0% +populated down towards the bottom than +the top okay so the actual values that I + + align:start position:0% +the top okay so the actual values that I + + + align:start position:0% +the top okay so the actual values that I +got for 10,000 different randomly chosen + + align:start position:0% +got for 10,000 different randomly chosen + + + align:start position:0% +got for 10,000 different randomly chosen +numbers is + + align:start position:0% +numbers is + + + align:start position:0% +numbers is +331 I think the actual value if we do + + align:start position:0% +331 I think the actual value if we do + + + align:start position:0% +331 I think the actual value if we do +the integral is like + + align:start position:0% +the integral is like + + + align:start position:0% +the integral is like +329 something or rather so we're pretty + + align:start position:0% +329 something or rather so we're pretty + + + align:start position:0% +329 something or rather so we're pretty +close but then again we only did 10,000 + + align:start position:0% +close but then again we only did 10,000 + + + align:start position:0% +close but then again we only did 10,000 +we could do a million and we would get + + align:start position:0% +we could do a million and we would get + + + align:start position:0% +we could do a million and we would get +pretty close to the actual value right + + align:start position:0% +pretty close to the actual value right + + + align:start position:0% +pretty close to the actual value right +so it's not 300 or 400 and that's + + align:start position:0% +so it's not 300 or 400 and that's + + + align:start position:0% +so it's not 300 or 400 and that's +because as was mentioned from uh from + + align:start position:0% +because as was mentioned from uh from + + + align:start position:0% +because as was mentioned from uh from +one of your uh uh from fellow students + + align:start position:0% +one of your uh uh from fellow students + + + align:start position:0% +one of your uh uh from fellow students +there is an inverse relationship between + + align:start position:0% +there is an inverse relationship between + + + align:start position:0% +there is an inverse relationship between +the fill time right and the uh and the + + align:start position:0% +the fill time right and the uh and the + + + align:start position:0% +the fill time right and the uh and the +pool rate right so it's the size of the + + align:start position:0% +pool rate right so it's the size of the + + + align:start position:0% +pool rate right so it's the size of the +pool divided by the rate so what we + + align:start position:0% +pool divided by the rate so what we + + + align:start position:0% +pool divided by the rate so what we +actually need to do if we wanted to + + align:start position:0% +actually need to do if we wanted to + + + align:start position:0% +actually need to do if we wanted to +figure out the the value is to solve the + + align:start position:0% +figure out the the value is to solve the + + + align:start position:0% +figure out the the value is to solve the +integral between one and three of you + + align:start position:0% +integral between one and three of you + + + align:start position:0% +integral between one and three of you +know D DX overx whatever that would be + + align:start position:0% +know D DX overx whatever that would be + + + align:start position:0% +know D DX overx whatever that would be +right so I don't want to bother with + + align:start position:0% +right so I don't want to bother with + + + align:start position:0% +right so I don't want to bother with +that but I will bother with seven lines + + align:start position:0% +that but I will bother with seven lines + + + align:start position:0% +that but I will bother with seven lines +of code and then just wait you know wait + + align:start position:0% +of code and then just wait you know wait + + + align:start position:0% +of code and then just wait you know wait +five seconds for that code to repeat you + + align:start position:0% +five seconds for that code to repeat you + + + align:start position:0% +five seconds for that code to repeat you +know five million times or a million + + align:start position:0% +know five million times or a million + + + align:start position:0% +know five million times or a million +times or 10 million times + + align:start position:0% +times or 10 million times + + + align:start position:0% +times or 10 million times +right is that + + align:start position:0% +right is that + + + align:start position:0% +right is that +cool and this is totally within your + + align:start position:0% +cool and this is totally within your + + + align:start position:0% +cool and this is totally within your +reach right it's it's not hard code to + + align:start position:0% +reach right it's it's not hard code to + + + align:start position:0% +reach right it's it's not hard code to +do it's just for Loops it's using a a + + align:start position:0% +do it's just for Loops it's using a a + + + align:start position:0% +do it's just for Loops it's using a a +random library right to just randomly + + align:start position:0% +random library right to just randomly + + + align:start position:0% +random library right to just randomly +grab a whole bunch of numbers and then + + align:start position:0% +grab a whole bunch of numbers and then + + + align:start position:0% +grab a whole bunch of numbers and then +just knowing the problem at hand filling + + align:start position:0% +just knowing the problem at hand filling + + + align:start position:0% +just knowing the problem at hand filling +a pool you know at a certain rate um + + align:start position:0% +a pool you know at a certain rate um + + + align:start position:0% +a pool you know at a certain rate um +simple math and then you get a nice a + + align:start position:0% +simple math and then you get a nice a + + + align:start position:0% +simple math and then you get a nice a +nice answer a nice approximation but + + align:start position:0% +nice answer a nice approximation but + + + align:start position:0% +nice answer a nice approximation but +still an answer to the + + align:start position:0% +still an answer to the + + + align:start position:0% +still an answer to the +question so hopefully this shows you how + + align:start position:0% +question so hopefully this shows you how + + + align:start position:0% +question so hopefully this shows you how +powerful computation can be this is just + + align:start position:0% +powerful computation can be this is just + + + align:start position:0% +powerful computation can be this is just +another example of how you can just + + align:start position:0% +another example of how you can just + + + align:start position:0% +another example of how you can just +apply computation programming to a + + align:start position:0% +apply computation programming to a + + + align:start position:0% +apply computation programming to a +problem that you see in real life um if + + align:start position:0% +problem that you see in real life um if + + + align:start position:0% +problem that you see in real life um if +if you choose to do like a you know a + + align:start position:0% +if you choose to do like a you know a + + + align:start position:0% +if you choose to do like a you know a +europ or uh take future courses in in + + align:start position:0% +europ or uh take future courses in in + + + align:start position:0% +europ or uh take future courses in in +you know a different field maybe not in + + align:start position:0% +you know a different field maybe not in + + + align:start position:0% +you know a different field maybe not in +CS uh you will probably apply + + align:start position:0% +CS uh you will probably apply + + + align:start position:0% +CS uh you will probably apply +computation to uh uh Concepts and ideas + + align:start position:0% +computation to uh uh Concepts and ideas + + + align:start position:0% +computation to uh uh Concepts and ideas +and problems in those fields and it'll + + align:start position:0% +and problems in those fields and it'll + + + align:start position:0% +and problems in those fields and it'll +be something similar to this You observe + + align:start position:0% +be something similar to this You observe + + + align:start position:0% +be something similar to this You observe +something you try to think of it + + align:start position:0% +something you try to think of it + + + align:start position:0% +something you try to think of it +computationally model it with a bunch of + + align:start position:0% +computationally model it with a bunch of + + + align:start position:0% +computationally model it with a bunch of +uh you know Randomness and then uh + + align:start position:0% +uh you know Randomness and then uh + + + align:start position:0% +uh you know Randomness and then uh +calculate an idea uh something of + + align:start position:0% +calculate an idea uh something of + + + align:start position:0% +calculate an idea uh something of +Interest okay so that's the end uh of + + align:start position:0% +Interest okay so that's the end uh of + + + align:start position:0% +Interest okay so that's the end uh of +6100 L I've got a little wrap up to uh + + align:start position:0% +6100 L I've got a little wrap up to uh + + + align:start position:0% +6100 L I've got a little wrap up to uh +remind ourselves where we've been and + + align:start position:0% +remind ourselves where we've been and + + + align:start position:0% +remind ourselves where we've been and +where we will go um so what did we learn + + align:start position:0% +where we will go um so what did we learn + + + align:start position:0% +where we will go um so what did we learn +oh also this is also these slides will + + align:start position:0% +oh also this is also these slides will + + + align:start position:0% +oh also this is also these slides will +be kind of like a meme dump of every + + align:start position:0% +be kind of like a meme dump of every + + + align:start position:0% +be kind of like a meme dump of every +remaining meme that I have okay so this + + align:start position:0% +remaining meme that I have okay so this + + + align:start position:0% +remaining meme that I have okay so this +is going to be very meme heavy uh okay + + align:start position:0% +is going to be very meme heavy uh okay + + + align:start position:0% +is going to be very meme heavy uh okay +so what did we learn we've got of course + + align:start position:0% +so what did we learn we've got of course + + + align:start position:0% +so what did we learn we've got of course +we learned Python Programming right we + + align:start position:0% +we learned Python Programming right we + + + align:start position:0% +we learned Python Programming right we +learned a lot of python syntax some + + align:start position:0% +learned a lot of python syntax some + + + align:start position:0% +learned a lot of python syntax some +lectures were heavier on python syntax + + align:start position:0% +lectures were heavier on python syntax + + + align:start position:0% +lectures were heavier on python syntax +than others but hopefully you've got a a + + align:start position:0% +than others but hopefully you've got a a + + + align:start position:0% +than others but hopefully you've got a a +handle on that we learned of course flow + + align:start position:0% +handle on that we learned of course flow + + + align:start position:0% +handle on that we learned of course flow +of control right with branches if + + align:start position:0% +of control right with branches if + + + align:start position:0% +of control right with branches if +statements L Lis L sorry L ifs L + + align:start position:0% +statements L Lis L sorry L ifs L + + + align:start position:0% +statements L Lis L sorry L ifs L +statements right allow us to either do + + align:start position:0% +statements right allow us to either do + + + align:start position:0% +statements right allow us to either do +one thing or another in the code make a + + align:start position:0% +one thing or another in the code make a + + + align:start position:0% +one thing or another in the code make a +decision Point um Loops four loops and + + align:start position:0% +decision Point um Loops four loops and + + + align:start position:0% +decision Point um Loops four loops and +while Loops as well as exceptions as a + + align:start position:0% +while Loops as well as exceptions as a + + + align:start position:0% +while Loops as well as exceptions as a +way for us to deal with unexpected + + align:start position:0% +way for us to deal with unexpected + + + align:start position:0% +way for us to deal with unexpected +things coming up in the course the ideas + + align:start position:0% +things coming up in the course the ideas + + + align:start position:0% +things coming up in the course the ideas +here flow of control + + align:start position:0% +here flow of control + + + align:start position:0% +here flow of control +um are actually transferable to any + + align:start position:0% +um are actually transferable to any + + + align:start position:0% +um are actually transferable to any +other programming language so you know + + align:start position:0% +other programming language so you know + + + align:start position:0% +other programming language so you know +if you know the ideas if you have the + + align:start position:0% +if you know the ideas if you have the + + + align:start position:0% +if you know the ideas if you have the +intuition for what kind of flow of + + align:start position:0% +intuition for what kind of flow of + + + align:start position:0% +intuition for what kind of flow of +control you'd like to use all you'd have + + align:start position:0% +control you'd like to use all you'd have + + + align:start position:0% +control you'd like to use all you'd have +to do is change the syntax and then + + align:start position:0% +to do is change the syntax and then + + + align:start position:0% +to do is change the syntax and then +suddenly you can write some code in + + align:start position:0% +suddenly you can write some code in + + + align:start position:0% +suddenly you can write some code in +another + + align:start position:0% +another + + + align:start position:0% +another +language of course we learned about data + + align:start position:0% +language of course we learned about data + + + align:start position:0% +language of course we learned about data +structures so we did lists right really + + align:start position:0% +structures so we did lists right really + + + align:start position:0% +structures so we did lists right really +useful data structures dictionaries + + align:start position:0% +useful data structures dictionaries + + + align:start position:0% +useful data structures dictionaries +super useful data structures tupal + + align:start position:0% +super useful data structures tupal + + + align:start position:0% +super useful data structures tupal +things like that so uh you can learn + + align:start position:0% +things like that so uh you can learn + + + align:start position:0% +things like that so uh you can learn +about more advanced data structures in a + + align:start position:0% +about more advanced data structures in a + + + align:start position:0% +about more advanced data structures in a +future course if you'd like but those + + align:start position:0% +future course if you'd like but those + + + align:start position:0% +future course if you'd like but those +are really the the top you know two or + + align:start position:0% +are really the the top you know two or + + + align:start position:0% +are really the the top you know two or +three most useful data + + align:start position:0% +three most useful data + + + align:start position:0% +three most useful data +structures um we talked a lot actually + + align:start position:0% +structures um we talked a lot actually + + + align:start position:0% +structures um we talked a lot actually +it was a common we didn't talk a lot + + align:start position:0% +it was a common we didn't talk a lot + + + align:start position:0% +it was a common we didn't talk a lot +specifically but it was a common theme + + align:start position:0% +specifically but it was a common theme + + + align:start position:0% +specifically but it was a common theme +in this class organization of code right + + align:start position:0% +in this class organization of code right + + + align:start position:0% +in this class organization of code right +so these ideas of decomposition and + + align:start position:0% +so these ideas of decomposition and + + + align:start position:0% +so these ideas of decomposition and +abstraction they came up a lot when we + + align:start position:0% +abstraction they came up a lot when we + + + align:start position:0% +abstraction they came up a lot when we +talked about functions that's our first + + align:start position:0% +talked about functions that's our first + + + align:start position:0% +talked about functions that's our first +introduction uh so functions helped us + + align:start position:0% +introduction uh so functions helped us + + + align:start position:0% +introduction uh so functions helped us +take uh some functional piece of code + + align:start position:0% +take uh some functional piece of code + + + align:start position:0% +take uh some functional piece of code +like some code that does something + + align:start position:0% +like some code that does something + + + align:start position:0% +like some code that does something +abstract it away into a nice little + + align:start position:0% +abstract it away into a nice little + + + align:start position:0% +abstract it away into a nice little +module right decompose it into one + + align:start position:0% +module right decompose it into one + + + align:start position:0% +module right decompose it into one +little module you have to write it one + + align:start position:0% +little module you have to write it one + + + align:start position:0% +little module you have to write it one +maybe write it a few times but debug it + + align:start position:0% +maybe write it a few times but debug it + + + align:start position:0% +maybe write it a few times but debug it +a few times um and then use it a whole + + align:start position:0% +a few times um and then use it a whole + + + align:start position:0% +a few times um and then use it a whole +bunch of times uh you know without + + align:start position:0% +bunch of times uh you know without + + + align:start position:0% +bunch of times uh you know without +worrying that it's going to change so + + align:start position:0% +worrying that it's going to change so + + + align:start position:0% +worrying that it's going to change so +it's just a very nice way for us to + + align:start position:0% +it's just a very nice way for us to + + + align:start position:0% +it's just a very nice way for us to +decompose functional pieces of code and + + align:start position:0% +decompose functional pieces of code and + + + align:start position:0% +decompose functional pieces of code and +then we saw it come up again when we did + + align:start position:0% +then we saw it come up again when we did + + + align:start position:0% +then we saw it come up again when we did +classes object-oriented programming + + align:start position:0% +classes object-oriented programming + + + align:start position:0% +classes object-oriented programming +right we were able to bundle behaviors + + align:start position:0% +right we were able to bundle behaviors + + + align:start position:0% +right we were able to bundle behaviors +and data together into one nice little + + align:start position:0% +and data together into one nice little + + + align:start position:0% +and data together into one nice little +object right that we could then create + + align:start position:0% +object right that we could then create + + + align:start position:0% +object right that we could then create +many of in many different parts of the + + align:start position:0% +many of in many different parts of the + + + align:start position:0% +many of in many different parts of the +code and then manipulate + + align:start position:0% +code and then manipulate + + + align:start position:0% +code and then manipulate +individually another common theme + + align:start position:0% +individually another common theme + + + align:start position:0% +individually another common theme +throughout this class was algorithms so + + align:start position:0% +throughout this class was algorithms so + + + align:start position:0% +throughout this class was algorithms so +we talked about B section search + + align:start position:0% +we talked about B section search + + + align:start position:0% +we talked about B section search +algorithm way at the beginning of the + + align:start position:0% +algorithm way at the beginning of the + + + align:start position:0% +algorithm way at the beginning of the +lectures right we talked about it in pet + + align:start position:0% +lectures right we talked about it in pet + + + align:start position:0% +lectures right we talked about it in pet +one and it came up again towards the end + + align:start position:0% +one and it came up again towards the end + + + align:start position:0% +one and it came up again towards the end +when we talked about complexity and + + align:start position:0% +when we talked about complexity and + + + align:start position:0% +when we talked about complexity and +searching and sorting algorithms things + + align:start position:0% +searching and sorting algorithms things + + + align:start position:0% +searching and sorting algorithms things +like that so that was kind of your own + + align:start position:0% +like that so that was kind of your own + + + align:start position:0% +like that so that was kind of your own +a big algorithm that you saw in this + + align:start position:0% +a big algorithm that you saw in this + + + align:start position:0% +a big algorithm that you saw in this +class but it shows you just how you can + + align:start position:0% +class but it shows you just how you can + + + align:start position:0% +class but it shows you just how you can +Implement you know some code in a + + align:start position:0% +Implement you know some code in a + + + align:start position:0% +Implement you know some code in a +completely different way to behave in + + align:start position:0% +completely different way to behave in + + + align:start position:0% +completely different way to behave in +completely different way right to be a + + align:start position:0% +completely different way right to be a + + + align:start position:0% +completely different way right to be a +lot faster you know with some conditions + + align:start position:0% +lot faster you know with some conditions + + + align:start position:0% +lot faster you know with some conditions +like being sorted things like that and + + align:start position:0% +like being sorted things like that and + + + align:start position:0% +like being sorted things like that and +then lastly the last part of the class + + align:start position:0% +then lastly the last part of the class + + + align:start position:0% +then lastly the last part of the class +was a little bit more Theory heavy we + + align:start position:0% +was a little bit more Theory heavy we + + + align:start position:0% +was a little bit more Theory heavy we +talked about computational complexity + + align:start position:0% +talked about computational complexity + + + align:start position:0% +talked about computational complexity +and that big Theta notation um so that + + align:start position:0% +and that big Theta notation um so that + + + align:start position:0% +and that big Theta notation um so that +gave you a sense of how to maybe design + + align:start position:0% +gave you a sense of how to maybe design + + + align:start position:0% +gave you a sense of how to maybe design +algorithms right so if you have a first + + align:start position:0% +algorithms right so if you have a first + + + align:start position:0% +algorithms right so if you have a first +crack of pseudo code on piece of paper + + align:start position:0% +crack of pseudo code on piece of paper + + + align:start position:0% +crack of pseudo code on piece of paper +you can see well H if I need to run this + + align:start position:0% +you can see well H if I need to run this + + + align:start position:0% +you can see well H if I need to run this +code on a really large data set it's not + + align:start position:0% +code on a really large data set it's not + + + align:start position:0% +code on a really large data set it's not +going to work because it's too slow + + align:start position:0% +going to work because it's too slow + + + align:start position:0% +going to work because it's too slow +right you've got three nested Loops or + + align:start position:0% +right you've got three nested Loops or + + + align:start position:0% +right you've got three nested Loops or +something like that so it might force + + align:start position:0% +something like that so it might force + + + align:start position:0% +something like that so it might force +you to rethink the design of the + + align:start position:0% +you to rethink the design of the + + + align:start position:0% +you to rethink the design of the +algorithm sooner than you know having + + align:start position:0% +algorithm sooner than you know having + + + align:start position:0% +algorithm sooner than you know having +already implemented it um but you know + + align:start position:0% +already implemented it um but you know + + + align:start position:0% +already implemented it um but you know +if you're dealing with small data sets + + align:start position:0% +if you're dealing with small data sets + + + align:start position:0% +if you're dealing with small data sets +maybe you wouldn't care that you've got + + align:start position:0% +maybe you wouldn't care that you've got + + + align:start position:0% +maybe you wouldn't care that you've got +three nested four Loops or you know a + + align:start position:0% +three nested four Loops or you know a + + + align:start position:0% +three nested four Loops or you know a +really inefficient recursion + + align:start position:0% +really inefficient recursion + + + align:start position:0% +really inefficient recursion +algorithm so that's those are the big uh + + align:start position:0% +algorithm so that's those are the big uh + + + align:start position:0% +algorithm so that's those are the big uh +the big things that we learned in this + + align:start position:0% +the big things that we learned in this + + + align:start position:0% +the big things that we learned in this +class your experience I kind of + + align:start position:0% +class your experience I kind of + + + align:start position:0% +class your experience I kind of +categorize in three different uh three + + align:start position:0% +categorize in three different uh three + + + align:start position:0% +categorize in three different uh three +different ways so you might have been a + + align:start position:0% +different ways so you might have been a + + + align:start position:0% +different ways so you might have been a +natural if you kind of joined this class + + align:start position:0% +natural if you kind of joined this class + + + align:start position:0% +natural if you kind of joined this class +and immediately got logic immediately + + align:start position:0% +and immediately got logic immediately + + + align:start position:0% +and immediately got logic immediately +learned you know knew how to do the + + align:start position:0% +learned you know knew how to do the + + + align:start position:0% +learned you know knew how to do the +problem sets that's totally fine I still + + align:start position:0% +problem sets that's totally fine I still + + + align:start position:0% +problem sets that's totally fine I still +hope you got something out of this class + + align:start position:0% +hope you got something out of this class + + + align:start position:0% +hope you got something out of this class +and you learned some some something you + + align:start position:0% +and you learned some some something you + + + align:start position:0% +and you learned some some something you +might have joined the class late right + + align:start position:0% +might have joined the class late right + + + align:start position:0% +might have joined the class late right +if you uh found 61008 to be too fast or + + align:start position:0% +if you uh found 61008 to be too fast or + + + align:start position:0% +if you uh found 61008 to be too fast or +uh too challenging you might have joined + + align:start position:0% +uh too challenging you might have joined + + + align:start position:0% +uh too challenging you might have joined +it uh joined it late kicked it to the + + align:start position:0% +it uh joined it late kicked it to the + + + align:start position:0% +it uh joined it late kicked it to the +curb and said let me join 100 L I + + align:start position:0% +curb and said let me join 100 L I + + + align:start position:0% +curb and said let me join 100 L I +welcomed you um we did a little bit of + + align:start position:0% +welcomed you um we did a little bit of + + + align:start position:0% +welcomed you um we did a little bit of +research and found that even if you join + + align:start position:0% +research and found that even if you join + + + align:start position:0% +research and found that even if you join +late it does not actually hinder your + + align:start position:0% +late it does not actually hinder your + + + align:start position:0% +late it does not actually hinder your +performance in the class so hopefully + + align:start position:0% +performance in the class so hopefully + + + align:start position:0% +performance in the class so hopefully +that was your + + align:start position:0% +that was your + + + align:start position:0% +that was your +experience + + align:start position:0% +experience + + + align:start position:0% +experience +um did you work hard so maybe you didn't + + align:start position:0% +um did you work hard so maybe you didn't + + + align:start position:0% +um did you work hard so maybe you didn't +get all the concepts right away maybe + + align:start position:0% +get all the concepts right away maybe + + + align:start position:0% +get all the concepts right away maybe +you struggled a little bit with the + + align:start position:0% +you struggled a little bit with the + + + align:start position:0% +you struggled a little bit with the +problem sets maybe you struggled a + + align:start position:0% +problem sets maybe you struggled a + + + align:start position:0% +problem sets maybe you struggled a +little bit on the pet uh or on the + + align:start position:0% +little bit on the pet uh or on the + + + align:start position:0% +little bit on the pet uh or on the +quizzes but I still think that you + + align:start position:0% +quizzes but I still think that you + + + align:start position:0% +quizzes but I still think that you +learned a lot and the test is always to + + align:start position:0% +learned a lot and the test is always to + + + align:start position:0% +learned a lot and the test is always to +go back and look at the first problem + + align:start position:0% +go back and look at the first problem + + + align:start position:0% +go back and look at the first problem +set so if you do that when you go home + + align:start position:0% +set so if you do that when you go home + + + align:start position:0% +set so if you do that when you go home +tonight you look back at the first + + align:start position:0% +tonight you look back at the first + + + align:start position:0% +tonight you look back at the first +problem set in this class you look back + + align:start position:0% +problem set in this class you look back + + + align:start position:0% +problem set in this class you look back +at the code that you wrote it will seem + + align:start position:0% +at the code that you wrote it will seem + + + align:start position:0% +at the code that you wrote it will seem +so easy I I promise you this and that's + + align:start position:0% +so easy I I promise you this and that's + + + align:start position:0% +so easy I I promise you this and that's +because I think you all did such a good + + align:start position:0% +because I think you all did such a good + + + align:start position:0% +because I think you all did such a good +job you tried your your hardest in this + + align:start position:0% +job you tried your your hardest in this + + + align:start position:0% +job you tried your your hardest in this +class I know it's not easy um I know + + align:start position:0% +class I know it's not easy um I know + + + align:start position:0% +class I know it's not easy um I know +it's slower paced but it's still not you + + align:start position:0% +it's slower paced but it's still not you + + + align:start position:0% +it's slower paced but it's still not you +know not not an easy easy class and I + + align:start position:0% +know not not an easy easy class and I + + + align:start position:0% +know not not an easy easy class and I +think you've learned a lot looking back + + align:start position:0% +think you've learned a lot looking back + + + align:start position:0% +think you've learned a lot looking back +at the first problem set we'll just + + align:start position:0% +at the first problem set we'll just + + + align:start position:0% +at the first problem set we'll just +we'll show you that for + + align:start position:0% +we'll show you that for + + + align:start position:0% +we'll show you that for +sure so what's next uh there have been + + align:start position:0% +sure so what's next uh there have been + + + align:start position:0% +sure so what's next uh there have been +some questions about what are some + + align:start position:0% +some questions about what are some + + + align:start position:0% +some questions about what are some +future classes that you might want to + + align:start position:0% +future classes that you might want to + + + align:start position:0% +future classes that you might want to +take or what can you do once you've you + + align:start position:0% +take or what can you do once you've you + + + align:start position:0% +take or what can you do once you've you +know once You' finished here here we go + + align:start position:0% +know once You' finished here here we go + + + align:start position:0% +know once You' finished here here we go +so we've got + + align:start position:0% +so we've got + + + align:start position:0% +so we've got +600b is kind of the most natural Next + + align:start position:0% +600b is kind of the most natural Next + + + align:start position:0% +600b is kind of the most natural Next +Step it's a half semester class in the + + align:start position:0% +Step it's a half semester class in the + + + align:start position:0% +Step it's a half semester class in the +second half of the semester so there + + align:start position:0% +second half of the semester so there + + + align:start position:0% +second half of the semester so there +finishing up right now basically um it's + + align:start position:0% +finishing up right now basically um it's + + + align:start position:0% +finishing up right now basically um it's +an overview of really interesting topics + + align:start position:0% +an overview of really interesting topics + + + align:start position:0% +an overview of really interesting topics +in computer science and with a focus on + + align:start position:0% +in computer science and with a focus on + + + align:start position:0% +in computer science and with a focus on +data science though so what we talk and + + align:start position:0% +data science though so what we talk and + + + align:start position:0% +data science though so what we talk and +I actually run that class as well so + + align:start position:0% +I actually run that class as well so + + + align:start position:0% +I actually run that class as well so +what we talk about there is optimization + + align:start position:0% +what we talk about there is optimization + + + align:start position:0% +what we talk about there is optimization +algorithms so for example let's say you + + align:start position:0% +algorithms so for example let's say you + + + align:start position:0% +algorithms so for example let's say you +want to um create a schedule for your + + align:start position:0% +want to um create a schedule for your + + + align:start position:0% +want to um create a schedule for your +classes next semester and you will have + + align:start position:0% +classes next semester and you will have + + + align:start position:0% +classes next semester and you will have +some constraints right like you don't + + align:start position:0% +some constraints right like you don't + + + align:start position:0% +some constraints right like you don't +want to have classes at 8:00 a.m. or + + align:start position:0% +want to have classes at 8:00 a.m. or + + + align:start position:0% +want to have classes at 8:00 a.m. or +9:00 a.m. or 10: a.m. or 11:00 a.m. and + + align:start position:0% +9:00 a.m. or 10: a.m. or 11:00 a.m. and + + + align:start position:0% +9:00 a.m. or 10: a.m. or 11:00 a.m. and +you want it to all be within you know + + align:start position:0% +you want it to all be within you know + + + align:start position:0% +you want it to all be within you know +some time limit or things like that + + align:start position:0% +some time limit or things like that + + + align:start position:0% +some time limit or things like that +optimization algorithm could be + + align:start position:0% +optimization algorithm could be + + + align:start position:0% +optimization algorithm could be +something that you write and you could + + align:start position:0% +something that you write and you could + + + align:start position:0% +something that you write and you could +just apply it to something that you have + + align:start position:0% +just apply it to something that you have + + + align:start position:0% +just apply it to something that you have +simulations uh exactly what we saw today + + align:start position:0% +simulations uh exactly what we saw today + + + align:start position:0% +simulations uh exactly what we saw today +of the you know the physics filling the + + align:start position:0% +of the you know the physics filling the + + + align:start position:0% +of the you know the physics filling the +pool thing uh you'll see + + align:start position:0% +pool thing uh you'll see + + + align:start position:0% +pool thing uh you'll see +more uh examples of that and ask + + align:start position:0% +more uh examples of that and ask + + + align:start position:0% +more uh examples of that and ask +different questions about it as well so + + align:start position:0% +different questions about it as well so + + + align:start position:0% +different questions about it as well so +you'll see things like + + align:start position:0% +you'll see things like + + + align:start position:0% +you'll see things like +um um you'll calculate you know things + + align:start position:0% +um um you'll calculate you know things + + + align:start position:0% +um um you'll calculate you know things +like standard deviations how many times + + align:start position:0% +like standard deviations how many times + + + align:start position:0% +like standard deviations how many times +do we need to repeat this experiment in + + align:start position:0% +do we need to repeat this experiment in + + + align:start position:0% +do we need to repeat this experiment in +order to be within some confidence + + align:start position:0% +order to be within some confidence + + + align:start position:0% +order to be within some confidence +interval right so how confident are you + + align:start position:0% +interval right so how confident are you + + + align:start position:0% +interval right so how confident are you +about your answers so we'll be doing + + align:start position:0% +about your answers so we'll be doing + + + align:start position:0% +about your answers so we'll be doing +more things like that and then there's + + align:start position:0% +more things like that and then there's + + + align:start position:0% +more things like that and then there's +of course the uh machine learning aspect + + align:start position:0% +of course the uh machine learning aspect + + + align:start position:0% +of course the uh machine learning aspect +of it so if you have uh a bunch of + + align:start position:0% +of it so if you have uh a bunch of + + + align:start position:0% +of it so if you have uh a bunch of +experiments that you do that you get a + + align:start position:0% +experiments that you do that you get a + + + align:start position:0% +experiments that you do that you get a +whole bunch of data + + align:start position:0% +whole bunch of data + + + align:start position:0% +whole bunch of data +from how can you fit a curve to those + + align:start position:0% +from how can you fit a curve to those + + + align:start position:0% +from how can you fit a curve to those +experiments and then you know for a + + align:start position:0% +experiments and then you know for a + + + align:start position:0% +experiments and then you know for a +future experiment what's the expected + + align:start position:0% +future experiment what's the expected + + + align:start position:0% +future experiment what's the expected +value right so that's a little bit of + + align:start position:0% +value right so that's a little bit of + + + align:start position:0% +value right so that's a little bit of +machine learning uh on experimental data + + align:start position:0% +machine learning uh on experimental data + + + align:start position:0% +machine learning uh on experimental data +and then some more machine learning in + + align:start position:0% +and then some more machine learning in + + + align:start position:0% +and then some more machine learning in +sort of a more classical sense is uh + + align:start position:0% +sort of a more classical sense is uh + + + align:start position:0% +sort of a more classical sense is uh +dealing with clustering algorithms and + + align:start position:0% +dealing with clustering algorithms and + + + align:start position:0% +dealing with clustering algorithms and +classification of of data and things + + align:start position:0% +classification of of data and things + + + align:start position:0% +classification of of data and things +like that okay so 6100b I know a lot + + align:start position:0% +like that okay so 6100b I know a lot + + + align:start position:0% +like that okay so 6100b I know a lot +about because right it's I also teach it + + align:start position:0% +about because right it's I also teach it + + + align:start position:0% +about because right it's I also teach it +it's a really good next class if if you + + align:start position:0% +it's a really good next class if if you + + + align:start position:0% +it's a really good next class if if you +want to kind of be employable for an + + align:start position:0% +want to kind of be employable for an + + + align:start position:0% +want to kind of be employable for an +internship if you take this I think + + align:start position:0% +internship if you take this I think + + + align:start position:0% +internship if you take this I think +you'll be good to + + align:start position:0% +you'll be good to + + + align:start position:0% +you'll be good to +go um 6101 is also a really nice class + + align:start position:0% +go um 6101 is also a really nice class + + + align:start position:0% +go um 6101 is also a really nice class +to take next if you really enjoyed the + + align:start position:0% +to take next if you really enjoyed the + + + align:start position:0% +to take next if you really enjoyed the +programming in this class 61 one will be + + align:start position:0% +programming in this class 61 one will be + + + align:start position:0% +programming in this class 61 one will be +your next step it's called fundamentals + + align:start position:0% +your next step it's called fundamentals + + + align:start position:0% +your next step it's called fundamentals +of programming and it is in Python that + + align:start position:0% +of programming and it is in Python that + + + align:start position:0% +of programming and it is in Python that +one has um it's it's pretty fastpaced so + + align:start position:0% +one has um it's it's pretty fastpaced so + + + align:start position:0% +one has um it's it's pretty fastpaced so +there will be problem sets every week + + align:start position:0% +there will be problem sets every week + + + align:start position:0% +there will be problem sets every week +and they're going to be pretty uh + + align:start position:0% +and they're going to be pretty uh + + + align:start position:0% +and they're going to be pretty uh +hardcore um there's going to be a lot of + + align:start position:0% +hardcore um there's going to be a lot of + + + align:start position:0% +hardcore um there's going to be a lot of +debugging involved in those problem sets + + align:start position:0% +debugging involved in those problem sets + + + align:start position:0% +debugging involved in those problem sets +and uh I actually was a recitation + + align:start position:0% +and uh I actually was a recitation + + + align:start position:0% +and uh I actually was a recitation +instructor for that class and to get a + + align:start position:0% +instructor for that class and to get a + + + align:start position:0% +instructor for that class and to get a +first um for the problem sets at least + + align:start position:0% +first um for the problem sets at least + + + align:start position:0% +first um for the problem sets at least +to get something working doesn't take + + align:start position:0% +to get something working doesn't take + + + align:start position:0% +to get something working doesn't take +that long but to make it work according + + align:start position:0% +that long but to make it work according + + + align:start position:0% +that long but to make it work according +to the + + align:start position:0% +to the + + + align:start position:0% +to the +specifications that they have will take + + align:start position:0% +specifications that they have will take + + + align:start position:0% +specifications that they have will take +a little bit of debugging and reworking + + align:start position:0% +a little bit of debugging and reworking + + + align:start position:0% +a little bit of debugging and reworking +that's because they deal with a lot of + + align:start position:0% +that's because they deal with a lot of + + + align:start position:0% +that's because they deal with a lot of +real world data so writing code that's + + align:start position:0% +real world data so writing code that's + + + align:start position:0% +real world data so writing code that's +really efficient is very important right + + align:start position:0% +really efficient is very important right + + + align:start position:0% +really efficient is very important right +so again writing you know nested for + + align:start position:0% +so again writing you know nested for + + + align:start position:0% +so again writing you know nested for +Loops of course we can totally do that + + align:start position:0% +Loops of course we can totally do that + + + align:start position:0% +Loops of course we can totally do that +but making it efficient using data + + align:start position:0% +but making it efficient using data + + + align:start position:0% +but making it efficient using data +structures like sets uh to make the code + + align:start position:0% +structures like sets uh to make the code + + + align:start position:0% +structures like sets uh to make the code +efficient using you know proper uh + + align:start position:0% +efficient using you know proper uh + + + align:start position:0% +efficient using you know proper uh +algorithms that are efficient is is very + + align:start position:0% +algorithms that are efficient is is very + + + align:start position:0% +algorithms that are efficient is is very +important part of this class but you'll + + align:start position:0% +important part of this class but you'll + + + align:start position:0% +important part of this class but you'll +learn a lot if you take this class + + align:start position:0% +learn a lot if you take this class + + + align:start position:0% +learn a lot if you take this class +you'll be very employable for an + + align:start position:0% +you'll be very employable for an + + + align:start position:0% +you'll be very employable for an +internship in some uh you know some some + + align:start position:0% +internship in some uh you know some some + + + align:start position:0% +internship in some uh you know some some +computer science or some computer + + align:start position:0% +computer science or some computer + + + align:start position:0% +computer science or some computer +science + + align:start position:0% +science + + + align:start position:0% +science +company um 6102 is also a nice next + + align:start position:0% +company um 6102 is also a nice next + + + align:start position:0% +company um 6102 is also a nice next +class if you're interested in software + + align:start position:0% +class if you're interested in software + + + align:start position:0% +class if you're interested in software +construction um it is actually in a + + align:start position:0% +construction um it is actually in a + + + align:start position:0% +construction um it is actually in a +different language it's in typescript + + align:start position:0% +different language it's in typescript + + + align:start position:0% +different language it's in typescript +these days used to be in Java um you can + + align:start position:0% +these days used to be in Java um you can + + + align:start position:0% +these days used to be in Java um you can +take what you've learned here and if + + align:start position:0% +take what you've learned here and if + + + align:start position:0% +take what you've learned here and if +you're interested in you know learning a + + align:start position:0% +you're interested in you know learning a + + + align:start position:0% +you're interested in you know learning a +different language this is a nice one to + + align:start position:0% +different language this is a nice one to + + + align:start position:0% +different language this is a nice one to +try it's their their their motto is + + align:start position:0% +try it's their their their motto is + + + align:start position:0% +try it's their their their motto is +you're writing code that is safe from + + align:start position:0% +you're writing code that is safe from + + + align:start position:0% +you're writing code that is safe from +bugs easy to understand and ready for + + align:start position:0% +bugs easy to understand and ready for + + + align:start position:0% +bugs easy to understand and ready for +change so they have also lots of problem + + align:start position:0% +change so they have also lots of problem + + + align:start position:0% +change so they have also lots of problem +sets but you're also working in a team + + align:start position:0% +sets but you're also working in a team + + + align:start position:0% +sets but you're also working in a team +so you get to learn how to work in a + + align:start position:0% +so you get to learn how to work in a + + + align:start position:0% +so you get to learn how to work in a +team um well with with other students + + align:start position:0% +team um well with with other students + + + align:start position:0% +team um well with with other students +how to code together um how to write + + align:start position:0% +how to code together um how to write + + + align:start position:0% +how to code together um how to write +code that has you know nice + + align:start position:0% +code that has you know nice + + + align:start position:0% +code that has you know nice +documentation is you know lots of + + align:start position:0% +documentation is you know lots of + + + align:start position:0% +documentation is you know lots of +debugging things like that so more of + + align:start position:0% +debugging things like that so more of + + + align:start position:0% +debugging things like that so more of +that those ideas of decomposition + + align:start position:0% +that those ideas of decomposition + + + align:start position:0% +that those ideas of decomposition +abstraction that we learned in this + + align:start position:0% +abstraction that we learned in this + + + align:start position:0% +abstraction that we learned in this +class will definitely be uh prominent in + + align:start position:0% +class will definitely be uh prominent in + + + align:start position:0% +class will definitely be uh prominent in +this class in + + align:start position:0% +this class in + + + align:start position:0% +this class in +6102 and then of course we've got other + + align:start position:0% +6102 and then of course we've got other + + + align:start position:0% +6102 and then of course we've got other +classes I'm happy to chat about uh so + + align:start position:0% +classes I'm happy to chat about uh so + + + align:start position:0% +classes I'm happy to chat about uh so +machine learning is a a nice one if + + align:start position:0% +machine learning is a a nice one if + + + align:start position:0% +machine learning is a a nice one if +again if you have a handle on + + align:start position:0% +again if you have a handle on + + + align:start position:0% +again if you have a handle on +programming really well and want to try + + align:start position:0% +programming really well and want to try + + + align:start position:0% +programming really well and want to try +uh some just applying programming to + + align:start position:0% +uh some just applying programming to + + + align:start position:0% +uh some just applying programming to +machine learning an algorithms class is + + align:start position:0% +machine learning an algorithms class is + + + align:start position:0% +machine learning an algorithms class is +also a fine next step if you're more + + align:start position:0% +also a fine next step if you're more + + + align:start position:0% +also a fine next step if you're more +interested in the complexity part of + + align:start position:0% +interested in the complexity part of + + + align:start position:0% +interested in the complexity part of +this class that we saw um also very very + + align:start position:0% +this class that we saw um also very very + + + align:start position:0% +this class that we saw um also very very +reasonable things to try to to do next + + align:start position:0% +reasonable things to try to to do next + + + align:start position:0% +reasonable things to try to to do next +after this class + + align:start position:0% +after this class + + + align:start position:0% +after this class +okay um yes last slide if you're not + + align:start position:0% +okay um yes last slide if you're not + + + align:start position:0% +okay um yes last slide if you're not +going to code for a while but think you + + align:start position:0% +going to code for a while but think you + + + align:start position:0% +going to code for a while but think you +might code in a couple semesters or + + align:start position:0% +might code in a couple semesters or + + + align:start position:0% +might code in a couple semesters or +something like that uh like you know you + + align:start position:0% +something like that uh like you know you + + + align:start position:0% +something like that uh like you know you +want to take a more computational class + + align:start position:0% +want to take a more computational class + + + align:start position:0% +want to take a more computational class +in some desired field I would + + align:start position:0% +in some desired field I would + + + align:start position:0% +in some desired field I would +say that you should try to practice + + align:start position:0% +say that you should try to practice + + + align:start position:0% +say that you should try to practice +coding at least once a week so in our + + align:start position:0% +coding at least once a week so in our + + + align:start position:0% +coding at least once a week so in our +website we've got a little help um menu + + align:start position:0% +website we've got a little help um menu + + + align:start position:0% +website we've got a little help um menu +where you can go to we we've listed some + + align:start position:0% +where you can go to we we've listed some + + + align:start position:0% +where you can go to we we've listed some +other websites there's a little bit of + + align:start position:0% +other websites there's a little bit of + + + align:start position:0% +other websites there's a little bit of +coding practice you can do it doesn't + + align:start position:0% +coding practice you can do it doesn't + + + align:start position:0% +coding practice you can do it doesn't +need to be a lot 30 minutes you know + + align:start position:0% +need to be a lot 30 minutes you know + + + align:start position:0% +need to be a lot 30 minutes you know +once a week something like that just so + + align:start position:0% +once a week something like that just so + + + align:start position:0% +once a week something like that just so +you don't forget to code um can go a + + align:start position:0% +you don't forget to code um can go a + + + align:start position:0% +you don't forget to code um can go a +really long way because I know you know + + align:start position:0% +really long way because I know you know + + + align:start position:0% +really long way because I know you know +over the summer sometimes I don't code + + align:start position:0% +over the summer sometimes I don't code + + + align:start position:0% +over the summer sometimes I don't code +for a month or so um because I do other + + align:start position:0% +for a month or so um because I do other + + + align:start position:0% +for a month or so um because I do other +stuff besides coding in my life and um + + align:start position:0% +stuff besides coding in my life and um + + + align:start position:0% +stuff besides coding in my life and um +you know coming back into it takes a + + align:start position:0% +you know coming back into it takes a + + + align:start position:0% +you know coming back into it takes a +little bit of time and it's just without + + align:start position:0% +little bit of time and it's just without + + + align:start position:0% +little bit of time and it's just without +practice like with anything else it's + + align:start position:0% +practice like with anything else it's + + + align:start position:0% +practice like with anything else it's +just easy to forget and it's hard to get + + align:start position:0% +just easy to forget and it's hard to get + + + align:start position:0% +just easy to forget and it's hard to get +back into it so even if you just do a + + align:start position:0% +back into it so even if you just do a + + + align:start position:0% +back into it so even if you just do a +little bit of coding write a really + + align:start position:0% +little bit of coding write a really + + + align:start position:0% +little bit of coding write a really +simple program you know once a week it's + + align:start position:0% +simple program you know once a week it's + + + align:start position:0% +simple program you know once a week it's +it's going to go a long way right so + + align:start position:0% +it's going to go a long way right so + + + align:start position:0% +it's going to go a long way right so +that's that's it I want to thank you all + + align:start position:0% +that's that's it I want to thank you all + + + align:start position:0% +that's that's it I want to thank you all +for being in this class and thank you + + align:start position:0% +for being in this class and thank you + + + align:start position:0% +for being in this class and thank you +for coming to this last lecture I know + + align:start position:0% +for coming to this last lecture I know + + + align:start position:0% +for coming to this last lecture I know +you didn't have to but I I do appreciate + + align:start position:0% +you didn't have to but I I do appreciate + + + align:start position:0% +you didn't have to but I I do appreciate +it um happy coding and you know good + + align:start position:0% +it um happy coding and you know good + + + align:start position:0% +it um happy coding and you know good +luck with exams and have a good break + + align:start position:0% +luck with exams and have a good break + + + align:start position:0% +luck with exams and have a good break +everyone thank + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/4MhGi6JSGbA.txt b/4MhGi6JSGbA.txt new file mode 100644 index 0000000000000000000000000000000000000000..687ec9b89769d842065f6f96102e8d0004c3962e --- /dev/null +++ b/4MhGi6JSGbA.txt @@ -0,0 +1,1219 @@ +align:start position:0% + +in this video we'll create a basic line + + align:start position:0% +in this video we'll create a basic line + + + align:start position:0% +in this video we'll create a basic line +plot to visualize crime trends let's + + align:start position:0% +plot to visualize crime trends let's + + + align:start position:0% +plot to visualize crime trends let's +start by reading in our data we'll call + + align:start position:0% +start by reading in our data we'll call + + + align:start position:0% +start by reading in our data we'll call +it m VT for motor vehicle thefts and use + + align:start position:0% +it m VT for motor vehicle thefts and use + + + align:start position:0% +it m VT for motor vehicle thefts and use +the read CSV function to read in the + + align:start position:0% +the read CSV function to read in the + + + align:start position:0% +the read CSV function to read in the +file m VT dot CSV well add the argument + + align:start position:0% +file m VT dot CSV well add the argument + + + align:start position:0% +file m VT dot CSV well add the argument +strings as factors equals false since we + + align:start position:0% +strings as factors equals false since we + + + align:start position:0% +strings as factors equals false since we +have a text field and we want to make + + align:start position:0% +have a text field and we want to make + + + align:start position:0% +have a text field and we want to make +sure it's read improperly let's take a + + align:start position:0% +sure it's read improperly let's take a + + + align:start position:0% +sure it's read improperly let's take a +look at the structure of our data using + + align:start position:0% +look at the structure of our data using + + + align:start position:0% +look at the structure of our data using +the STR function we have over 190,000 + + align:start position:0% +the STR function we have over 190,000 + + + align:start position:0% +the STR function we have over 190,000 +observations of three different + + align:start position:0% +observations of three different + + + align:start position:0% +observations of three different +variables the date of the crime and the + + align:start position:0% +variables the date of the crime and the + + + align:start position:0% +variables the date of the crime and the +location of the crime in terms of + + align:start position:0% +location of the crime in terms of + + + align:start position:0% +location of the crime in terms of +latitude and longitude we want to first + + align:start position:0% +latitude and longitude we want to first + + + align:start position:0% +latitude and longitude we want to first +convert the date variable to a format + + align:start position:0% +convert the date variable to a format + + + align:start position:0% +convert the date variable to a format +that our will recognize so that we can + + align:start position:0% +that our will recognize so that we can + + + align:start position:0% +that our will recognize so that we can +extract the day of the week and the hour + + align:start position:0% +extract the day of the week and the hour + + + align:start position:0% +extract the day of the week and the hour +of the day we can do this using the STRP + + align:start position:0% +of the day we can do this using the STRP + + + align:start position:0% +of the day we can do this using the STRP +time function so we want to replace our + + align:start position:0% +time function so we want to replace our + + + align:start position:0% +time function so we want to replace our +variable date with the output of the STR + + align:start position:0% +variable date with the output of the STR + + + align:start position:0% +variable date with the output of the STR +P time function which takes as a first + + align:start position:0% +P time function which takes as a first + + + align:start position:0% +P time function which takes as a first +argument our variable date and then as a + + align:start position:0% +argument our variable date and then as a + + + align:start position:0% +argument our variable date and then as a +second argument the format that the date + + align:start position:0% +second argument the format that the date + + + align:start position:0% +second argument the format that the date +is in here we can see in the output from + + align:start position:0% +is in here we can see in the output from + + + align:start position:0% +is in here we can see in the output from +the STR function that our format is the + + align:start position:0% +the STR function that our format is the + + + align:start position:0% +the STR function that our format is the +month slash the day slash the year and + + align:start position:0% +month slash the day slash the year and + + + align:start position:0% +month slash the day slash the year and +then the hour + + align:start position:0% +then the hour + + + align:start position:0% +then the hour +colon minutes so our format equals and + + align:start position:0% +colon minutes so our format equals and + + + align:start position:0% +colon minutes so our format equals and +in quotes a percentage sign and a little + + align:start position:0% +in quotes a percentage sign and a little + + + align:start position:0% +in quotes a percentage sign and a little +M for month + + align:start position:0% +M for month + + + align:start position:0% +M for month +slash percentage sign and a little d for + + align:start position:0% +slash percentage sign and a little d for + + + align:start position:0% +slash percentage sign and a little d for +day slash percentage sign and the little + + align:start position:0% +day slash percentage sign and the little + + + align:start position:0% +day slash percentage sign and the little +Y for year and then a space and a + + align:start position:0% +Y for year and then a space and a + + + align:start position:0% +Y for year and then a space and a +percentage sign capital H for our colon + + align:start position:0% +percentage sign capital H for our colon + + + align:start position:0% +percentage sign capital H for our colon +and then a percentage sign and capital M + + align:start position:0% +and then a percentage sign and capital M + + + align:start position:0% +and then a percentage sign and capital M +for minutes then just close the quotes + + align:start position:0% +for minutes then just close the quotes + + + align:start position:0% +for minutes then just close the quotes +close the parentheses and hit enter in + + align:start position:0% +close the parentheses and hit enter in + + + align:start position:0% +close the parentheses and hit enter in +this format we can extract the hour in + + align:start position:0% +this format we can extract the hour in + + + align:start position:0% +this format we can extract the hour in +the day of the week from the date + + align:start position:0% +the day of the week from the date + + + align:start position:0% +the day of the week from the date +variable and we can add these as new + + align:start position:0% +variable and we can add these as new + + + align:start position:0% +variable and we can add these as new +variables to our data frame we can do + + align:start position:0% +variables to our data frame we can do + + + align:start position:0% +variables to our data frame we can do +this by first defining our new variable + + align:start position:0% +this by first defining our new variable + + + align:start position:0% +this by first defining our new variable +mvt dollar sign weekday to be equal to + + align:start position:0% +mvt dollar sign weekday to be equal to + + + align:start position:0% +mvt dollar sign weekday to be equal to +the weekdays function run on the MBT + + align:start position:0% +the weekdays function run on the MBT + + + align:start position:0% +the weekdays function run on the MBT +date variable then to add the hour which + + align:start position:0% +date variable then to add the hour which + + + align:start position:0% +date variable then to add the hour which +we'll call em bt hour we just take the + + align:start position:0% +we'll call em bt hour we just take the + + + align:start position:0% +we'll call em bt hour we just take the +hour variable out of the date variable + + align:start position:0% +hour variable out of the date variable + + + align:start position:0% +hour variable out of the date variable +this only exists because we converted + + align:start position:0% +this only exists because we converted + + + align:start position:0% +this only exists because we converted +the date variable let's take a look at + + align:start position:0% +the date variable let's take a look at + + + align:start position:0% +the date variable let's take a look at +the structure of our data again to see + + align:start position:0% +the structure of our data again to see + + + align:start position:0% +the structure of our data again to see +what it looks like now we have two more + + align:start position:0% +what it looks like now we have two more + + + align:start position:0% +what it looks like now we have two more +variables weekday which gives the day of + + align:start position:0% +variables weekday which gives the day of + + + align:start position:0% +variables weekday which gives the day of +the week an hour which gives the hour of + + align:start position:0% +the week an hour which gives the hour of + + + align:start position:0% +the week an hour which gives the hour of +the day now we're ready to make some + + align:start position:0% +the day now we're ready to make some + + + align:start position:0% +the day now we're ready to make some +line plots let's start by creating the + + align:start position:0% +line plots let's start by creating the + + + align:start position:0% +line plots let's start by creating the +line plot we saw in the previous video + + align:start position:0% +line plot we saw in the previous video + + + align:start position:0% +line plot we saw in the previous video +with just one line and a value for every + + align:start position:0% +with just one line and a value for every + + + align:start position:0% +with just one line and a value for every +day of the week + + align:start position:0% +day of the week + + + align:start position:0% +day of the week +we wanna plot as that value the total + + align:start position:0% +we wanna plot as that value the total + + + align:start position:0% +we wanna plot as that value the total +number of crimes on each day of the week + + align:start position:0% +number of crimes on each day of the week + + + align:start position:0% +number of crimes on each day of the week +we can get this information by creating + + align:start position:0% +we can get this information by creating + + + align:start position:0% +we can get this information by creating +a table of the weekday variable this + + align:start position:0% +a table of the weekday variable this + + + align:start position:0% +a table of the weekday variable this +gives the total amount of crime on each + + align:start position:0% +gives the total amount of crime on each + + + align:start position:0% +gives the total amount of crime on each +day of the week let's save this table as + + align:start position:0% +day of the week let's save this table as + + + align:start position:0% +day of the week let's save this table as +a data frame so that we can pass it to + + align:start position:0% +a data frame so that we can pass it to + + + align:start position:0% +a data frame so that we can pass it to +ggplot as our data we'll call it weekday + + align:start position:0% +ggplot as our data we'll call it weekday + + + align:start position:0% +ggplot as our data we'll call it weekday +counts and use the AAS data frame + + align:start position:0% +counts and use the AAS data frame + + + align:start position:0% +counts and use the AAS data frame +function to convert our table to a data + + align:start position:0% +function to convert our table to a data + + + align:start position:0% +function to convert our table to a data +frame let's see what this looks like + + align:start position:0% +frame let's see what this looks like + + + align:start position:0% +frame let's see what this looks like +with the STR function we can see that + + align:start position:0% +with the STR function we can see that + + + align:start position:0% +with the STR function we can see that +our data frame has seven observations + + align:start position:0% +our data frame has seven observations + + + align:start position:0% +our data frame has seven observations +one for each day of the week and two + + align:start position:0% +one for each day of the week and two + + + align:start position:0% +one for each day of the week and two +different variables the first variable + + align:start position:0% +different variables the first variable + + + align:start position:0% +different variables the first variable +card called var one gives the name of + + align:start position:0% +card called var one gives the name of + + + align:start position:0% +card called var one gives the name of +the day of the week and the second + + align:start position:0% +the day of the week and the second + + + align:start position:0% +the day of the week and the second +variable called F req for frequency it + + align:start position:0% +variable called F req for frequency it + + + align:start position:0% +variable called F req for frequency it +gives the total amount of crime on that + + align:start position:0% +gives the total amount of crime on that + + + align:start position:0% +gives the total amount of crime on that +day of the week now we're ready to make + + align:start position:0% +day of the week now we're ready to make + + + align:start position:0% +day of the week now we're ready to make +our plot first we need to load the + + align:start position:0% +our plot first we need to load the + + + align:start position:0% +our plot first we need to load the +ggplot2 package so we'll type library + + align:start position:0% +ggplot2 package so we'll type library + + + align:start position:0% +ggplot2 package so we'll type library +and then in parentheses ggplot2 now + + align:start position:0% +and then in parentheses ggplot2 now + + + align:start position:0% +and then in parentheses ggplot2 now +we'll create our plot using the GG plot + + align:start position:0% +we'll create our plot using the GG plot + + + align:start position:0% +we'll create our plot using the GG plot +function so type GG plot and then we + + align:start position:0% +function so type GG plot and then we + + + align:start position:0% +function so type GG plot and then we +need to give the name of our data which + + align:start position:0% +need to give the name of our data which + + + align:start position:0% +need to give the name of our data which +is weekday counts and then we need to + + align:start position:0% +is weekday counts and then we need to + + + align:start position:0% +is weekday counts and then we need to +define our aesthetic so our aesthetic + + align:start position:0% +define our aesthetic so our aesthetic + + + align:start position:0% +define our aesthetic so our aesthetic +should have x equals var one since we + + align:start position:0% +should have x equals var one since we + + + align:start position:0% +should have x equals var one since we +want the day of the week on the x axis + + align:start position:0% +want the day of the week on the x axis + + + align:start position:0% +want the day of the week on the x axis +and y equals F req since we want the + + align:start position:0% +and y equals F req since we want the + + + align:start position:0% +and y equals F req since we want the +frequency the number of crimes on the y + + align:start position:0% +frequency the number of crimes on the y + + + align:start position:0% +frequency the number of crimes on the y +axis now we just need to add G our + + align:start position:0% +axis now we just need to add G our + + + align:start position:0% +axis now we just need to add G our +Munder score line since we want a line + + align:start position:0% +Munder score line since we want a line + + + align:start position:0% +Munder score line since we want a line +plot and in the parentheses type a es + + align:start position:0% +plot and in the parentheses type a es + + + align:start position:0% +plot and in the parentheses type a es +for aesthetic and then in parenthesis + + align:start position:0% +for aesthetic and then in parenthesis + + + align:start position:0% +for aesthetic and then in parenthesis +group equals one this just groups all of + + align:start position:0% +group equals one this just groups all of + + + align:start position:0% +group equals one this just groups all of +our data into one line since we want one + + align:start position:0% +our data into one line since we want one + + + align:start position:0% +our data into one line since we want one +line in our plot go ahead and hit enter + + align:start position:0% +line in our plot go ahead and hit enter + + + align:start position:0% +line in our plot go ahead and hit enter +we can see that this is very close to + + align:start position:0% +we can see that this is very close to + + + align:start position:0% +we can see that this is very close to +the plot we want we have the total + + align:start position:0% +the plot we want we have the total + + + align:start position:0% +the plot we want we have the total +number of crime plotted by day of the + + align:start position:0% +number of crime plotted by day of the + + + align:start position:0% +number of crime plotted by day of the +week but our days of the week are a + + align:start position:0% +week but our days of the week are a + + + align:start position:0% +week but our days of the week are a +little bit out of order + + align:start position:0% +little bit out of order + + + align:start position:0% +little bit out of order +we have Friday first then Monday than + + align:start position:0% +we have Friday first then Monday than + + + align:start position:0% +we have Friday first then Monday than +Saturday than Sunday etc what ggplot did + + align:start position:0% +Saturday than Sunday etc what ggplot did + + + align:start position:0% +Saturday than Sunday etc what ggplot did +was it put the days of the week in + + align:start position:0% +was it put the days of the week in + + + align:start position:0% +was it put the days of the week in +alphabetical order but we actually want + + align:start position:0% +alphabetical order but we actually want + + + align:start position:0% +alphabetical order but we actually want +the days of the week in chronological + + align:start position:0% +the days of the week in chronological + + + align:start position:0% +the days of the week in chronological +order to make this plot a bit easier to + + align:start position:0% +order to make this plot a bit easier to + + + align:start position:0% +order to make this plot a bit easier to +read we can do this by making the VAR + + align:start position:0% +read we can do this by making the VAR + + + align:start position:0% +read we can do this by making the VAR +one variable an ordered factor variable + + align:start position:0% +one variable an ordered factor variable + + + align:start position:0% +one variable an ordered factor variable +this signals to ggplot that the ordering + + align:start position:0% +this signals to ggplot that the ordering + + + align:start position:0% +this signals to ggplot that the ordering +is meaningful we can do this by using + + align:start position:0% +is meaningful we can do this by using + + + align:start position:0% +is meaningful we can do this by using +the factor function so let's start by + + align:start position:0% +the factor function so let's start by + + + align:start position:0% +the factor function so let's start by +typing + + align:start position:0% +typing + + + align:start position:0% +typing +weekday counts the name of our data + + align:start position:0% +weekday counts the name of our data + + + align:start position:0% +weekday counts the name of our data +frame dollar sign var one the variable + + align:start position:0% +frame dollar sign var one the variable + + + align:start position:0% +frame dollar sign var one the variable +we want to convert and set that equal to + + align:start position:0% +we want to convert and set that equal to + + + align:start position:0% +we want to convert and set that equal to +the output of the factor function where + + align:start position:0% +the output of the factor function where + + + align:start position:0% +the output of the factor function where +the first argument is our variable + + align:start position:0% +the first argument is our variable + + + align:start position:0% +the first argument is our variable +weekday counts dollar sign var 1 the + + align:start position:0% +weekday counts dollar sign var 1 the + + + align:start position:0% +weekday counts dollar sign var 1 the +second argument is ordered equals true + + align:start position:0% +second argument is ordered equals true + + + align:start position:0% +second argument is ordered equals true +this says that we want an ordered factor + + align:start position:0% +this says that we want an ordered factor + + + align:start position:0% +this says that we want an ordered factor +and the third argument which is levels + + align:start position:0% +and the third argument which is levels + + + align:start position:0% +and the third argument which is levels +should be equal to a vector of the days + + align:start position:0% +should be equal to a vector of the days + + + align:start position:0% +should be equal to a vector of the days +of the week in the order we want them to + + align:start position:0% +of the week in the order we want them to + + + align:start position:0% +of the week in the order we want them to +be in we'll use the C function to do + + align:start position:0% +be in we'll use the C function to do + + + align:start position:0% +be in we'll use the C function to do +this so first in quotes type Sunday + + align:start position:0% +this so first in quotes type Sunday + + + align:start position:0% +this so first in quotes type Sunday +we want Sunday first and then Monday + + align:start position:0% +we want Sunday first and then Monday + + + align:start position:0% +we want Sunday first and then Monday +Tuesday Wednesday Thursday Friday and + + align:start position:0% +Tuesday Wednesday Thursday Friday and + + + align:start position:0% +Tuesday Wednesday Thursday Friday and +Saturday go ahead and close both + + align:start position:0% +Saturday go ahead and close both + + + align:start position:0% +Saturday go ahead and close both +parentheses and hit enter now let's try + + align:start position:0% +parentheses and hit enter now let's try + + + align:start position:0% +parentheses and hit enter now let's try +our plot again by just hitting the up + + align:start position:0% +our plot again by just hitting the up + + + align:start position:0% +our plot again by just hitting the up +arrow twice and hitting Enter + + align:start position:0% +arrow twice and hitting Enter + + + align:start position:0% +arrow twice and hitting Enter +now this is the plot we want we have the + + align:start position:0% +now this is the plot we want we have the + + + align:start position:0% +now this is the plot we want we have the +total crime by day of the week with the + + align:start position:0% +total crime by day of the week with the + + + align:start position:0% +total crime by day of the week with the +days of the week in chronological order + + align:start position:0% +days of the week in chronological order + + + align:start position:0% +days of the week in chronological order +the last thing we'll want to do to our + + align:start position:0% +the last thing we'll want to do to our + + + align:start position:0% +the last thing we'll want to do to our +plot is just change the x and y axis + + align:start position:0% +plot is just change the x and y axis + + + align:start position:0% +plot is just change the x and y axis +labels since they're not very helpful as + + align:start position:0% +labels since they're not very helpful as + + + align:start position:0% +labels since they're not very helpful as +they are now to do this back in the our + + align:start position:0% +they are now to do this back in the our + + + align:start position:0% +they are now to do this back in the our +console just hit the up arrow to get + + align:start position:0% +console just hit the up arrow to get + + + align:start position:0% +console just hit the up arrow to get +back to our plotting line and then we'll + + align:start position:0% +back to our plotting line and then we'll + + + align:start position:0% +back to our plotting line and then we'll +add X lab for X label and in parenthesis + + align:start position:0% +add X lab for X label and in parenthesis + + + align:start position:0% +add X lab for X label and in parenthesis +in quotes we'll call it day of the week + + align:start position:0% +in quotes we'll call it day of the week + + + align:start position:0% +in quotes we'll call it day of the week +and then we'll add Y lab for Y label and + + align:start position:0% +and then we'll add Y lab for Y label and + + + align:start position:0% +and then we'll add Y lab for Y label and +in parenthesis in quotes will say total + + align:start position:0% +in parenthesis in quotes will say total + + + align:start position:0% +in parenthesis in quotes will say total +motor vehicle thefts now this is the + + align:start position:0% +motor vehicle thefts now this is the + + + align:start position:0% +motor vehicle thefts now this is the +plot we were trying to generate with + + align:start position:0% +plot we were trying to generate with + + + align:start position:0% +plot we were trying to generate with +descriptive labels on the x and y axis + + align:start position:0% +descriptive labels on the x and y axis + + + align:start position:0% +descriptive labels on the x and y axis +in the next video we'll add the hour of + + align:start position:0% +in the next video we'll add the hour of + + + align:start position:0% +in the next video we'll add the hour of +the day to our line plot and then create + + align:start position:0% +the day to our line plot and then create + + + align:start position:0% +the day to our line plot and then create +a heat map \ No newline at end of file diff --git a/4Q1fWMxVDZY.txt b/4Q1fWMxVDZY.txt new file mode 100644 index 0000000000000000000000000000000000000000..e5ab001e96925a11d182b6f4d349b7715997abac --- /dev/null +++ b/4Q1fWMxVDZY.txt @@ -0,0 +1,1796 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +ALAN V. OPPENHEIM: Last time, +we introduced the notion of + +mapping continuous time filters +to discrete time + +filters, and we developed +impulse invariance as one + +useful technique for carrying +out that type of mapping. + +What I'd like to do in this +lecture is illustrate impulse + +invariance as a design procedure +in the context of + +one specific class of filters, +namely Butterworth filters. + +And then following that, we'll +proceed on to discuss another + +very important and useful +mapping or design procedure + +referred to as the bilinear +transformation. + +So to begin, let me just discuss +briefly what the class + +of Butterworth filters is. + +And specifically, the +Butterworth filters are + +defined through their frequency + +response or transfer function. + +And I'm using capital B to +denote a Butterworth filter. + +And by definition, the magnitude +squared of the + +frequency response of a +Butterworth filter is given by + +this expression. + +And for example, if N were equal +to 1, then this would + +simply correspond to the +magnitude squared of the + +frequency response for a first +order differential equation. + +Now if you look at the frequency +response, B of omega + +for this class of filters-- + +I've illustrated that below-- + +and what we see is that the +frequency response starts at + +unity, because that's the way +that it's normalized, and it + +has a monotonic characteristic +in the pass band + +and in the stop band. + +At a frequency equal to the +parameter omega sub c, up + +here, which is referred to as +the cutoff frequency, the + +Butterworth filter frequency +response always goes through + +the same point, namely 0.707. + +And as the order of the +Butterworth filter, capital N, + +increases, the transition from +the pass band to the stop band + +becomes sharper and sharper. + +So for higher order filters, +then, the frequency response + +is flatter in the pass band and +drops off more quickly, + +and attenuates more +in the stop band. + +Now in designing Butterworth +filters, what we want to look + +at is the location of the poles +of the system function. + +And we can infer those from +our definition of what the + +frequency response for the +Butterworth filter is. + +In particular, we have this +expression for the magnitude + +squared of the frequency +response. + +And we recognize that, of +course, as B of j omega times + +B of minus j omega, that's what +the magnitude squared + +will be equal to. + +And in order to convert this +to an expression describing + +the system function, or in +terms of the more general + +Laplace transform variable s, +what we recognize is that j + +omega, in the more general +setting, simply corresponds to + +the Laplace transform +variable s. + +So this product, in fact, is +the Laplace transform for s + +equal to j omega. + +More generally, then, this is +the result of evaluating B of + +s times B of minus s at +s equals j omega. + +Consequently, comparing this +expression with this statement + +leads us to the conclusion that +the transfer function B + +of s of the Butterworth filter, +times B of minus s, is + +given by the expression that +I indicate here, simply + +replacing j omega by s. + +Now what we want to look at +are the poles of B of s. + +That's what we'll want +to get as we design + +a Butterworth filter. + +And we can recognize the poles +of this product simply by + +looking at the roots of the +denominative polynomial. + +And those roots are-- + +just taking account of +this factor 2N-- + +those roots are at j omega +sub c times the 2N + +roots of minus 1. + +Those roots, in fact, all +lie on a circle, and the + +consequence of that is that the +poles of this expression + +are on a circle. + +The circle is of radius omega +sub c, and the poles are + +distributed around the circle. + +So here I've illustrated the +poles of B of s times B of + +minus s, for this specific +case where capital + +N is equal to 3. + +So there are a total of six +poles around this circle. + +And then for this specific case, +the poles are spaced by + +60 degrees. + +Now we have B of s times +B of minus s. + +To get the system function for +the Butterworth filter, we'd + +like to get B of s, and +the question now is + +how do we get that? + +Well, the thing to recognize is +that wherever this factor + +has a root, this factor +has to have a root at + +the negative location. + +So in fact, when we look at +these poles, we compare them + +with this, for example, +associated with B of s, this + +associated with B of minus s. + +And likewise, we compare these +two together, likewise we + +compare these two together. + +And so we can extract B of s +from this product, simply by + +taking one pole out of +each of those pairs. + +Now a question, of course, is +out of each pair, which one do + +we associate with B of s, and +which do we associate with B + +of minus s? + +And the answer drops out fairly +simply if we recognize + +that if we want to design +filters that are stable, then + +B of s, the transfer function +that we're designing, must + +have all its poles in the left +half of the s plane. + +So in fact, out of each of these +pairs we would associate + +the left half plane pole with +B of s, and so the transfer + +function for the Butterworth +filter for this particular + +case, where the this designates +the parameter omega + +sub c and capital N is 3, +namely a third order + +Butterworth filter, is this +set of pole locations. + +Given those, of course, we can +figure out, simply through + +Algebraic means, what the +transfer function B of s is. + +All right, so that's what +Butterworth filters are. + +And now what I'd like to do is +talk about the design of a + +digital Butterworth filter using +the design technique + +that we introduced last time, +namely impulse invariance. + +And the context in which I will +phrase the design is the + +context of mapping a continuous +time signal to a + +discrete time signal, carrying +out filtering using the + +discrete time filter that we're +designing, and then + +mapping back. + +So we're talking about now a +discrete time filter that we + +want to design through impulse +invariance from continuous + +time Butterworth filters, and +we're going to get our design + +specifications in the context of +having considered discrete + +time processing of continuous +time signals, where we will + +map from a continuous time +signal to a sequence, carry + +out the filtering with the +discrete time filter that + +we're going to design. + +And then we will take the +resulting filtered output and + +map it back to the continuous +time signal. + +But this discrete time filter is +the one that we're talking + +about designing. + +And for a choice of parameter, +there's a sampling frequency, + +of course, involved +in this process. + +And the value that I'll pick for +the sampling frequency is + +10 kilohertz. + +OK, all fairly straightforward +so far. + +And so since we have a sampling +rate of 10 kilohertz, + +we want to first look at our +specifications on the desired + +continuous time filter and then +map those to appropriate + +specifications on the discrete +time filter. + +And what I'll pick for the +desired specifications on the + +continuous time filter is that +at 1 kilohertz, I will ask + +that the continuous time +frequency response be down by + +no more than 1 db in comparison +with its value at + +omega equals 0. + +So that, in effect, specifies +the behavior in the pass band, + +or the specifications +on the pass band. + +And for the stop band, I'll +specify that the filter is + +down by 15 db by the time we've +gotten to 1.5 kilohertz. + +So we have, essentially, the +beginning of the transition + +band-- the end of the pass +band--at 1 kilohertz, and the + +beginning of the stop band +at 1.5 kilohertz. + +And since we're talking about +designing a Butterworth + +filter, we know that the +Butterworth filter is + +monotonic in the pass band and +stop band, and so we'll have a + +filter specification, something +as I show here. + +This represents the allowable +pass band tolerance. + +This is the allowable +stop band tolerance. + +And if I can draw this without +getting myself into trouble, + +essentially we're looking for +a filter, then, that always + +stays between the specified +boundaries here. + +Now what we have to figure out +is what the corresponding + +specifications are for +the digital filter. + +And the strategy, let me +emphasize, is that we have a + +situation where we're doing +discrete time processing of + +continuous time signals, +and we have a set of + +specifications associated +with that. + +That imposes specifications on +our discrete time filter, and + +then we want to design the +discrete time filter using + +impulse invariance, and that's +the discrete time filter that + +we'll use in the +overall system. + +All right, now we want +specifications on the discrete + +time filter, and we want the +continuous overall equivalent + +system to meet certain +specifications at certain + +frequencies related to +continuous time frequencies. + +Recall that when we sample +a continuous time signal, + +there's a very specific mapping +from the continuous + +time frequency axis to the +discrete time frequency axis. + +In particular, the sampling +frequency gets mapped to 2 pi. + +Well, that means that our other +critical frequencies get + +mapped in proportion to that. + +So 1 kilohertz, which is +a 1/10 of the sampling + +frequency, would then convert +to a discrete time + +frequency of 0.2 pi. + +And 1.5 kilohertz will convert +to a discrete time + +frequency of 0.3 pi. + +So what this says is that for +the discrete time filter, we + +would like the same behavior, +but at frequencies-- + +or the same specifications, but +at frequencies normalized + +to the discrete time +frequency axis. + +That means that we want the +discrete time frequency + +response magnitude to be greater +than or equal to minus + +1 db at 2/10 pi-- + +corresponding to the 1 kilohertz +in continuous time-- + +and for the beginning of the +stop band, that would occur at + +0.3 pi, at which point we +want this less than or + +equal to minus 15. + +So those are our discrete +time specifications. + +And we now want to design the +discrete time filter using + +impulse invariance. + +Now in impulse invariance, as +you recall, it corresponds to + +generating an impulse response +which is a sampled version of + +the continuous time impulse +response, and there is a + +temptation naturally to think +all of this parameter, capital + +T, as necessarily identical to +the sampling in the system in + +which the filter is +going to be used. + +Now this is a fairly subtle, +complicated, tongue twisting + +issue, but the bottom line on +it, the essential point, is + +that the parameter capital +T that we use in impulse + +invariant design is a totally +different, unrelated, and in + +fact, as it turns out, arbitrary +parameter, which is + +not necessarily pegged to +the sampling frequency. + +And I think it would be +difficult for me to totally + +clarify that during +the lecture. + +It's discussed more in the +book, and certainly, you + +should take plenty of time +to reflect on it. + +All right, but let's now look, +then, at where we are in our + +design procedure, and +specifically, what it is that + +we need to do in order +to design the + +digital Butterworth filter. + +Now we have a set of +specifications that we've + +generated relating, essentially, +to how we want + +the pass band of the digital +filter and the stop band of + +the digital filter to behave. + +Of course, since this isn't an +ideal filter, it has some + +transition from pass band to +stop band, and as we discussed + +last time, there is aliasing, +which we need to at + +least be aware of. + +We specified certain frequencies +along this axis + +which are easily converted by +relating to the two axes + +through this mapping, are easily +related back to the + +continuous time frequency +axis, as we have here. + +And in particular, now if we +were to simply pick that + +parameter in the impulse +invariant design, capital T, + +as equal to unity, and I +indicated just a minute ago + +that we can pick it arbitrarily, +if I pick it as + +unity, then the procedure would +consist of designing the + +continuous time Butterworth +filter with meeting or + +exceeding the appropriate +specifications and then going + +through the impulse invariant +procedure. + +All right, so let's +do that then. + +We want the discrete time +impulse response to be the + +continuous time impulse response +sampled, and for + +convenience, I'm going to +pick this parameter + +capital T equal to 1. + +That means that the frequency +normalization between the + +discrete time frequency axis +and the continuous time + +frequency axis in fact is-- + +those axes are scaled +identically, because capital T + +is equal to 1. + +And so now we want the analog, +or continuous time, + +specifications. + +And so what we need to +do then is design + +a Butterworth filter. + +I'm using capital B here again +to denote the frequency + +response of the Butterworth +filter. + +The Butterworth filter to have +a magnitude which is greater + +than or equal to minus 1 db +prior to the frequency 0.2 pi, + +and less than or equal +to minus 15 at a + +frequency beyond 0.3 pi. + +And so now what we need to do +is determine capital N and + +omega sub c in order to +meet or exceed those + +specifications. + +Now if you go through the +associated algebra in doing + +that, let's say that you decide +that you want to pick + +capital N and omega sub c +to exactly meet those + +inequalities at the two +frequencies, 0.2 pi and 0.3 + +pi, what you'll find after going +through the algebra is + +that they're exactly met if +capital N is 5.88 and omega + +sub c is 0.7047. + +And this obviously isn't +satisfactory as parameters for + +the Butterworth filter. + +Why is that? + +The reason is that capital N +isn't an integer, and in the + +class of Butterworth filters, +to generate a rational + +transfer function, +capital N, this + +parameter, must be an integer. + +So since it can't be 5.88, the +natural thing to do is to move + +it up to the next closest +integer, namely 6. + +And that means that we'll end +up with a filter that does + +even better than the +specifications. + +On the other hand, there's +something kind of underneath + +the surface that is inherent +in the impulse invariant + +design procedure, namely the +fact that there will always be + +some aliasing. + +So one strategy, and a natural +one, often, in impulse + +invariant design, is to choose +N as the next highest integer + +as I've done, and then choose +the parameter omega sub c so + +that the pass band +specifications are exactly + +met, and the stop band +specifications are then + +slightly exceeded, and +that will leave + +some margin for aliasing. + +All right, now continuing this +example, then, how would we + +complete the design? + +Well, we know what our two +parameters, capital N and + +omega sub c are. + +That means that we can +determine B of s + +times B of minus s. + +Those poles are located on a +circle in the complex s plane. + +And the poles on that circle +are paired, some being + +associated with B of s and +some with B of minus s. + +And in particular, to determine +B of s, we would + +simply take the poles on the +portion of the circle that's + +in the left half +of the s plane. + +Now what that gives us is a +Butterworth continuous time + +filter, which we are then +mapping through impulse + +invariance with capital +T equal to 1 to a + +discrete time filter. + +That discrete time filter to be +used in a system which has + +an associated sampling + +frequency which is 10 kilohertz. + +So to get the discrete time +filter, then, we first + +determine B of s, +as we just did-- + +or at least I indicated +how to do it. + +We would then expand that out +in a partial fraction + +expansion, and then apply the +impulse invariant procedure, + +which consists of mapping the +poles in the s plane to poles + +in the z plane at locations e +to the s of k, capital T, + +capital T is equal to 1. + +And retaining the +residue, or the + +coefficient, in the expansion. + +And this, then, will give us the +transfer function for the + +discrete time filter. + +So if in fact we did that, then +the resulting frequency + +response that we would get is +what I've indicated here. + +And I indicated first on a +magnitude scale, linear + +magnitude scale, and second +on a logarithmic scale. + +And as we had originally +specified, the digital filter + +is supposed to be greater than +or equal to minus 1 db at + +point 2 pi, and less than +or equal to minus + +15 db at 0.3 pi. + +And in fact, this slightly +exceeds those specifications + +since we had purposely allowed +some margin in the stop band. + +Now this is an illustration +of the impulse invariant + +procedure, and it has a number +of very nice properties, one + +of which is that it takes +a continuous time filter + +frequency response and it +converts it to a discrete time + +frequency response, which in the +absence of aliasing, looks + +identical, except for a linear +frequency scale change. + +And in fact, if we picked +capital T equal to 1, then + +there is no scale change. + +It has the major disadvantage +that there is always aliasing, + +and for some problems, for +example, if the filter that + +we're trying to design is not +band limited or low pass, then + +the aliasing will naturally +become intolerable. + +Well, there's another design +procedure which I now want to + +introduce, which totally +avoids the problems of + +aliasing, but, obviously, +then has its own costs + +associated with it. + +And that's procedure is referred +to as the bilinear + +transformation. + +The bilinear transformation, +which I won't try to derive + +here in any detail, is a mapping +of continuous time + +filters to discrete time +filters, corresponding to + +taking the Laplace transform +variable s in the continuous + +time filter and replacing it +by what is referred to as a + +bilinear function of z. + +And so if I substitute this in +here, that will give me the + +discrete time frequency +response. + +Again in this procedure, there's +a parameter capital T, + +which again is totally +irrelevant given the approach + +that we're taking, and which +we will generally tend to + +normalize out to unity. + +And let me just say quickly and +in passing that although + +we won't go through this, the +notion that the bilinear + +transformation can be tied to +the concept of taking the + +differential equation for the +continuous time filter, + +converting it to an integral +equation by integrating enough + +times on both sides, and then +converting that to a + +difference equation by +approximating the integrals + +with the trapezoidal rule. + +And that, in effect, will +correspond to mapping the + +continuous time filter to a +discrete time filter with the + +bilinear transformation. + +Well, we'll just focus on the +properties of the mapping. + +And in particular, if we were +to substitute into the + +expression z equal to e to the +j omega corresponding to the + +unit circle, we would find +that the unit circle in + +discrete time corresponds to +mapping the j omega axis in + +continuous time, which is +exactly what we want. + +Now the mapping between the +continuous time frequency and + +the discrete time frequency is +a nonlinear mapping, which is + +given by the algebraic +expression + +that I indicate here. + +And if we plot this mapping, +what we have is this curve. + +And what this corresponds to, +then, is a mapping of the j + +omega axis, or continuous +time frequency, to + +discrete time frequency. + +And if we think more generally +of the mapping represented by + +the bilinear transformation in +the context of the s-plane and + +the z-plane, it corresponds to +mapping the j omega axis in + +the s-plane to once around the +unit circle in the z-plane. + +And you could also convince +yourself that the left half of + +the s-plane maps to the inside +of the unit circle. + +And so that means that stable +continuous time filters will + +always map to stable discrete +time filters, which is exactly + +what we desire. + +Now notice in this that there's +no issue of aliasing. + +What's happened is that we've +replaced s by a function of z, + +and it corresponds to mapping +the s-plane to the z-plane. + +In fact, the whole j omega axis +has mapped to once around + +the unit circle, which obviously +requires some type + +of nonlinear mapping, because, +look, the j omega axis is + +infinitely long. + +The unit circle has +a finite radius. + +And so essentially, what has to +happen is if you think of + +walking along the continuous +time frequency axis, and + +simultaneously walking around +the unit circle, if you walk + +at a constant rate around the +unit circle and you're + +simultaneously walking up the +j omega axis, if you want to + +get around to pi by the time, +here, you've gotten to + +infinity along the continuous +time frequency axis, you + +better start walking faster, +and faster, and faster, + +because you've got an infinite +distance to cover while you + +just go over a finite +distance here. + +Well, what all that says, +really, is that that's why, in + +fact, we're taking +the entire-- + +or we're able to take the entire +omega axis and just map + +it into an interval +of length pi. + +All right, now that means that +there is a nonlinear + +distortion of the frequency +axis if we were to take a + +continuous time filter and +convert it to a discrete time + +filter with the bilinear +transformation. + +How do we account for that, or +for that matter, when can we + +really use it? + +And we can see how to both take +account of it, and what + +its limitations are, by +recognizing the following. + +Suppose that I want to design +a discrete time filter and + +what is going to happen is that +it will be mapped to a + +continuous time filter, or the +relationship between the two + +frequency axes will be +given by this curve. + +So let's suppose that the +continuous time frequency + +response looks as I've shown +here, with a pass band cutoff + +frequency and a stop band +cutoff frequency. + +If this were mapped through the +bilinear transformation to + +a discrete time filter, then +this cutoff frequency would + +fall over here, which is related +through this curve, + +and this cutoff frequency, the +stop band edge would be here. + +Again, it's these frequencies +reflected through this curve. + +So let's suppose now that what +I'd like to do is design a + +discrete time filter, where the +discrete time filter has + +certain frequency +specifications, which is what + +our previous example has. + +It has, let's say, a specified +stop band edge and a specified + +pass band edge, and a specified +stop band edge. + +The design procedure would then +correspond to mapping + +those frequencies to the +corresponding continuous time + +frequencies, designing the +continuous time filter to meet + +the specifications based on +those critical frequencies, + +then taking the continuous time +design and mapping it + +back to a discrete time filter +through the bilinear + +transformation. + +All right, now what we want to +do is again map a Butterworth + +filter, continuous time +Butterworth filter to a + +digital filter in such a way +that the digital filter + +approximately meets the + +specifications that we had before. + +And let me just remind +you of where we were. + +The critical frequencies were +at 0.2 pi and 0.3 pi. + +And what we had asked for is +that the frequency response be + +down by no more than 1 db up +to 0.2 pi, and down by at + +least 15 db at 0.3 pi. + +So we want to design the same +discrete time filter as we did + +before with impulse +invariance. + +We now want to do it with the +bilinear transformation + +applied to an appropriate +Butterworth design. + +OK, well, let's see what kind +of specifications we have. + +We know that the frequency, the +critical frequencies, are + +mapped through this curve, +or this equation. + +And I indicated again that this +parameter capital T is + +arbitrary in the design +procedure. + +That may seem confusing, +initially, but there's some + +further discussion of it in the +book, and it's true and + +important to sort out. + +So we're going to pick capital +T equal to unity. + +And that means then that the +corresponding critical + +frequencies of the continuous +time filter are at twice the + +tangent of 0.2 pi over 2, +and twice the tangent + +of 0.3 pi over 2. + +So that means then that the +specifications on our + +continuous time filter are given +by this, essentially + +pass band and stop band +edges warped through + +that nonlinear curve-- + +this nonlinear curve. + +And I'm using capital G here to +denote the system function + +for the resulting continuous +time filter. + +And so now we could think of +designing a Butterworth filter + +that, let's say, exactly meets +these specifications. + +Well, if you do that, what +you'll find is that you get + +exact equality here if you pick +capital N equal to 5.3. + +And again, we have the issue +that if we want to meet or + +exceed the specifications, we +can't make the filter order + +lower, we have to +make it higher. + +And so we would make it, instead +of 5.3, we would make + +the filter order equal to 6. + +And now, again, we have several + +options and trade offs. + +Before, with impulse invariance, +we essentially + +decided to meet the pass band +specifications and exceed the + +stop band specifications +to provide + +some margin for aliasing. + +Here, we don't have any +aliasing, and we can trade + +things off anyway we'd like. + +The way that I've chosen to do +it is to exactly meet the stop + +band cut off, and exceed the +pass band specifications. + +And the result of doing that +is to choose a filter order + +capital N equal to 6, and the +parameter omega sub c in the + +Butterworth filter is +given by 0.76622. + +All right, so now we have the +parameters for the continuous + +time Butterworth filter, which +when mapped to the discrete + +time filter through the bilinear +transformation, will + +exceed our requirements in the +pass band and just meet the + +stop band cutoff. + +And so now we want to complete +the design procedure. + +And given the parameters of the +Butterworth filter, we can + +draw our appropriate circle in +the s-plane, which happens to + +be the same circle as before, +but with a different radius. + +And then associate poles on this +circle with B of s and B + +of minus s. + +In particular, take +the ones in the + +left half of the s-plane-- + +same ones we had before except +we have a different value for + +omega sub c-- + +and those, then, represent +B of s. + +So we can now determine +B of s. + +And once we have the transfer +function B of s, we then map + +that to a discrete time filter +by mapping through the + +bilinear transformation. + +And that then is the design +procedure which we would + +follow this example. + +All right, well, let's just see +what the result looks like + +when we're done. + +Here I show, again, on both a +linear magnitude scale and on + +a logarithmic or DB scale, the +frequency response of the + +resulting filter. + +And recall that the +specifications were that at + +0.2 pi, we should be down by no +more than 1 db, and clearly + +we've exceeded that +considerably. + +And at 0.3 pi, we should be down +by at least 15 db, and we + +chose the design so that we +would exactly meet that edge. + +So we've met this point and +exceeded this point, and this + +is our design. + +Now let's just compare this +with the impulse invariant + +design that we saw a +few minutes ago. + +The impulse invariant design +is what I indicate here. + +The bilinear transformation +design is now + +overlaid on top of it. + +It's hard to see much difference +on a linear + +magnitude scale, but let's look +on a logarithmic scale. + +And this one that I'm lifting +is the bilinear + +transformation, and this +is impulse invariance. + +And notice, in fact, something +very interesting, which is + +that the filter that we obtained +by mapping the + +Butterworth filter to a digital +filter through the + +bilinear transformation in fact +falls off in frequency + +much more rapidly than the one +that we got through impulse + +invariance. + +The question is why? + +Now one thought that might come +to mind is, well, impulse + +invariance has aliasing, the +bilinear transformation + +doesn't have aliasing, +that must be a + +consequence of aliasing. + +In fact, that's not +the reason. + +Aliasing, as it turns out in +this particular design, was + +relatively minimal in the +impulse invariant design. + +The reason has to do with this +nonlinear mapping in the + +bilinear transformation from the +continuous time frequency + +to the discrete time +frequency. + +Keep in mind that through that +mapping, as you start walking + +around the unit circle and +moving up to j omega axis, as + +you move up the j omega axis, +you have to move faster, and + +faster, and faster, +and faster. + +And what's in continuous time +frequency at infinity is what + +you get to in the discrete time +frequency by the time you + +get around to pi. + +So in fact, what we're looking +at as we look out along this + +frequency axis is we're seeing +higher, and higher, and higher + +frequencies in the continuous +time filter. + +By the time we get to pi, we +should in fact be in the + +continuous time filter +equivalently off to infinity, + +which sounds like a pretty +uncomfortable place to be. + +OK, now this was a fairly rapid +trip through a number of + +issues, in particular, some of +the issues associated with the + +bilinear transformation, and +also this issue of how you + +pick this parameter capital T, +and how it might be associated + +with a sampling frequency if +you're doing discrete time + +processing of continuous +time signals. + +And we don't have time to +explore some of those issues + +more fully in this lecture. + +But I'd like to conclude by +making a couple of comments. + +One comment is that the two +techniques that we've talked + +about, impulse invariance and +the bilinear transformation, + +are the two techniques that are +principally used when one + +thinks of mapping continuous +time filters to discrete time + +filters for whatever +application. + +And I stress again that you may +want to do that mapping + +whether or not the discrete +time filter is eventually + +going to be used for processing + +continuous time signals. + +Now impulse invariance had the +very nice characteristic that + +it corresponds to a linear +mapping between the two + +frequency axes, except for the +issue of aliasing, and that's + +a problem with it, and in +particular, limits its + +usefulness to filter designs, or +for mapping continuous time + +filters that are band limited. + +On the other hand, we have the +bilinear transformation as a + +design procedure, which totally +avoids aliasing, but + +has the disadvantage or +difficulty that it represents + +a nonlinear mapping from the +continuous time filter to the + +discrete time filter. + +Now this nonlinear distortion +is perfectly acceptable if + +we're designing or attempting +to design filters that have + +flat frequency characteristics. + +It's not acceptable if, for +example, we had a linear + +frequency characteristic that we +wanted to map to a discrete + +time filter and end up with +a linear frequency + +characteristic. + +It won't come out to be linear +because of this nonlinear + +mapping of the frequency axis. + +Now there are also a number of +other design procedures, which + +we won't go into, for designing +discrete time + +filters, and among them are +a variety of techniques, + +including, for example, +computer aided design + +procedures. + +And I invite you, if you're +interested and want to dig + +into that in more detail and +more deeply, to explore that + +topic by making reference to +various of the books listed in + +the bibliography in the text. + +Thank you. \ No newline at end of file diff --git a/4zpQwirFsbk.txt b/4zpQwirFsbk.txt new file mode 100644 index 0000000000000000000000000000000000000000..e6a8f5b2533a527443a550da958dda9ff4ca5ed4 --- /dev/null +++ b/4zpQwirFsbk.txt @@ -0,0 +1,10439 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu um okay so we should + + align:start position:0% +ocw.mit.edu um okay so we should + + + align:start position:0% +ocw.mit.edu um okay so we should +probably start um so last time we + + align:start position:0% +probably start um so last time we + + + align:start position:0% +probably start um so last time we +finished up talking about energy + + align:start position:0% +finished up talking about energy + + + align:start position:0% +finished up talking about energy +absorption in Foy cellular materials and + + align:start position:0% +absorption in Foy cellular materials and + + + align:start position:0% +absorption in Foy cellular materials and +today I wanted to start a new topic + + align:start position:0% +today I wanted to start a new topic + + + align:start position:0% +today I wanted to start a new topic +we're going to talk about sandwich + + align:start position:0% +we're going to talk about sandwich + + + align:start position:0% +we're going to talk about sandwich +panels so sandwich panels have two stiff + + align:start position:0% +panels so sandwich panels have two stiff + + + align:start position:0% +panels so sandwich panels have two stiff +strong skins that are separated by some + + align:start position:0% +strong skins that are separated by some + + + align:start position:0% +strong skins that are separated by some +sort of lightweight core so the Skins + + align:start position:0% +sort of lightweight core so the Skins + + + align:start position:0% +sort of lightweight core so the Skins +are typically say a metal like aluminum + + align:start position:0% +are typically say a metal like aluminum + + + align:start position:0% +are typically say a metal like aluminum +or some sort of fiber composite and the + + align:start position:0% +or some sort of fiber composite and the + + + align:start position:0% +or some sort of fiber composite and the +core is usually some sort of cellular + + align:start position:0% +core is usually some sort of cellular + + + align:start position:0% +core is usually some sort of cellular +material sometimes it's a engineering + + align:start position:0% +material sometimes it's a engineering + + + align:start position:0% +material sometimes it's a engineering +honeycomb sometimes it's a foam + + align:start position:0% +honeycomb sometimes it's a foam + + + align:start position:0% +honeycomb sometimes it's a foam +sometimes it's balls of wood and the + + align:start position:0% +sometimes it's balls of wood and the + + + align:start position:0% +sometimes it's balls of wood and the +idea is is that what you're doing with + + align:start position:0% +idea is is that what you're doing with + + + align:start position:0% +idea is is that what you're doing with +the core is you're using a light + + align:start position:0% +the core is you're using a light + + + align:start position:0% +the core is you're using a light +material to separate the faces and if + + align:start position:0% +material to separate the faces and if + + + align:start position:0% +material to separate the faces and if +you think about an ie beam so remember + + align:start position:0% +you think about an ie beam so remember + + + align:start position:0% +you think about an ie beam so remember +when we talk about bending and we talk + + align:start position:0% +when we talk about bending and we talk + + + align:start position:0% +when we talk about bending and we talk +about eye beams the whole idea is that + + align:start position:0% +about eye beams the whole idea is that + + + align:start position:0% +about eye beams the whole idea is that +in bending you want to increase the + + align:start position:0% +in bending you want to increase the + + + align:start position:0% +in bending you want to increase the +moment of inertia so you want to um make + + align:start position:0% +moment of inertia so you want to um make + + + align:start position:0% +moment of inertia so you want to um make +as much material as far away from the + + align:start position:0% +as much material as far away from the + + + align:start position:0% +as much material as far away from the +middle of the beam as possible to + + align:start position:0% +middle of the beam as possible to + + + align:start position:0% +middle of the beam as possible to +increase the moment of inertia so if you + + align:start position:0% +increase the moment of inertia so if you + + + align:start position:0% +increase the moment of inertia so if you +think about an ibeam you put the flanges + + align:start position:0% +think about an ibeam you put the flanges + + + align:start position:0% +think about an ibeam you put the flanges +far apart with the web and that + + align:start position:0% +far apart with the web and that + + + align:start position:0% +far apart with the web and that +increases the moment of inertia and the + + align:start position:0% +increases the moment of inertia and the + + + align:start position:0% +increases the moment of inertia and the +sandwich panels and the sandwich beams + + align:start position:0% +sandwich panels and the sandwich beams + + + align:start position:0% +sandwich panels and the sandwich beams +essentially do the same thing but + + align:start position:0% +essentially do the same thing but + + + align:start position:0% +essentially do the same thing but +they're using a lightweight core instead + + align:start position:0% +they're using a lightweight core instead + + + align:start position:0% +they're using a lightweight core instead +of a web and so the idea is you use a + + align:start position:0% +of a web and so the idea is you use a + + + align:start position:0% +of a web and so the idea is you use a +lightweight core it separates the faces + + align:start position:0% +lightweight core it separates the faces + + + align:start position:0% +lightweight core it separates the faces +it increases the moment of inertia but + + align:start position:0% +it increases the moment of inertia but + + + align:start position:0% +it increases the moment of inertia but +you don't add a whole lot of weight + + align:start position:0% +you don't add a whole lot of weight + + + align:start position:0% +you don't add a whole lot of weight +because you've got this lightweight core + + align:start position:0% +because you've got this lightweight core + + + align:start position:0% +because you've got this lightweight core +in the middle so I brought some examples + + align:start position:0% +in the middle so I brought some examples + + + align:start position:0% +in the middle so I brought some examples +I'll pass around and we can play with so + + align:start position:0% +I'll pass around and we can play with so + + + align:start position:0% +I'll pass around and we can play with so +these are some examples um up on the + + align:start position:0% +these are some examples um up on the + + + align:start position:0% +these are some examples um up on the +screen and and some of those I have down + + align:start position:0% +screen and and some of those I have down + + + align:start position:0% +screen and and some of those I have down +here so for instance the top uh turn my + + align:start position:0% +here so for instance the top uh turn my + + + align:start position:0% +here so for instance the top uh turn my +little Gizmo on the top uh left here + + align:start position:0% +little Gizmo on the top uh left here + + + align:start position:0% +little Gizmo on the top uh left here +this is a helicopter rotor blade and + + align:start position:0% +this is a helicopter rotor blade and + + + align:start position:0% +this is a helicopter rotor blade and +that has a Honeycomb Core in it this is + + align:start position:0% +that has a Honeycomb Core in it this is + + + align:start position:0% +that has a Honeycomb Core in it this is +a aircraft flooring panel that has a + + align:start position:0% +a aircraft flooring panel that has a + + + align:start position:0% +a aircraft flooring panel that has a +Honeycomb Core and has carbon fiber + + align:start position:0% +Honeycomb Core and has carbon fiber + + + align:start position:0% +Honeycomb Core and has carbon fiber +faces so that's this thing here I'll + + align:start position:0% +faces so that's this thing here I'll + + + align:start position:0% +faces so that's this thing here I'll +pass that around in a middle minute this + + align:start position:0% +pass that around in a middle minute this + + + align:start position:0% +pass that around in a middle minute this +is a downhill ski this has aluminum + + align:start position:0% +is a downhill ski this has aluminum + + + align:start position:0% +is a downhill ski this has aluminum +faces and a polyurethane foam core and + + align:start position:0% +faces and a polyurethane foam core and + + + align:start position:0% +faces and a polyurethane foam core and +that's the ski here and it's quite + + align:start position:0% +that's the ski here and it's quite + + + align:start position:0% +that's the ski here and it's quite +common in skis now to have these + + align:start position:0% +common in skis now to have these + + + align:start position:0% +common in skis now to have these +sandwich panels This is a little piece + + align:start position:0% +sandwich panels This is a little piece + + + align:start position:0% +sandwich panels This is a little piece +of a a small Sailing Boat it had I think + + align:start position:0% +of a a small Sailing Boat it had I think + + + align:start position:0% +of a a small Sailing Boat it had I think +glass fiber faces and a balsa wood core + + align:start position:0% +glass fiber faces and a balsa wood core + + + align:start position:0% +glass fiber faces and a balsa wood core +and I don't know if any of you sail but + + align:start position:0% +and I don't know if any of you sail but + + + align:start position:0% +and I don't know if any of you sail but +MIT has new sailing boats do you sail + + align:start position:0% +MIT has new sailing boats do you sail + + + align:start position:0% +MIT has new sailing boats do you sail +not much okay but those little Tech + + align:start position:0% +not much okay but those little Tech + + + align:start position:0% +not much okay but those little Tech +dingies that you see out in the river + + align:start position:0% +dingies that you see out in the river + + + align:start position:0% +dingies that you see out in the river +those have sandwich panel hulls to them + + align:start position:0% +those have sandwich panel hulls to them + + + align:start position:0% +those have sandwich panel hulls to them +so those are little sandwich panels uh + + align:start position:0% +so those are little sandwich panels uh + + + align:start position:0% +so those are little sandwich panels uh +this is an example from a building + + align:start position:0% +this is an example from a building + + + align:start position:0% +this is an example from a building +panel uh this has a a drywall face and a + + align:start position:0% +panel uh this has a a drywall face and a + + + align:start position:0% +panel uh this has a a drywall face and a +plywood face and a foam core and the + + align:start position:0% +plywood face and a foam core and the + + + align:start position:0% +plywood face and a foam core and the +idea with uh panels for buildings is + + align:start position:0% +idea with uh panels for buildings is + + + align:start position:0% +idea with uh panels for buildings is +that usually they use a a foam core uh + + align:start position:0% +that usually they use a a foam core uh + + + align:start position:0% +that usually they use a a foam core uh +because the foam has some thermal + + align:start position:0% +because the foam has some thermal + + + align:start position:0% +because the foam has some thermal +insulation so as well as sort of + + align:start position:0% +insulation so as well as sort of + + + align:start position:0% +insulation so as well as sort of +separating the faces and having a + + align:start position:0% +separating the faces and having a + + + align:start position:0% +separating the faces and having a +structural role it has a a role in + + align:start position:0% +structural role it has a a role in + + + align:start position:0% +structural role it has a a role in +thermally insulating the building the + + align:start position:0% +thermally insulating the building the + + + align:start position:0% +thermally insulating the building the +Foams are a little less efficient than + + align:start position:0% +Foams are a little less efficient than + + + align:start position:0% +Foams are a little less efficient than +using a Honeycomb Core so for the same + + align:start position:0% +using a Honeycomb Core so for the same + + + align:start position:0% +using a Honeycomb Core so for the same +weight you get a stiffer structure with + + align:start position:0% +weight you get a stiffer structure with + + + align:start position:0% +weight you get a stiffer structure with +a Honeycomb Core than a foam core but if + + align:start position:0% +a Honeycomb Core than a foam core but if + + + align:start position:0% +a Honeycomb Core than a foam core but if +you want thermal insulation as well as a + + align:start position:0% +you want thermal insulation as well as a + + + align:start position:0% +you want thermal insulation as well as a +structural requirement then the foam + + align:start position:0% +structural requirement then the foam + + + align:start position:0% +structural requirement then the foam +cores are good and these are a couple + + align:start position:0% +cores are good and these are a couple + + + align:start position:0% +cores are good and these are a couple +examples of sandwiches in nature this is + + align:start position:0% +examples of sandwiches in nature this is + + + align:start position:0% +examples of sandwiches in nature this is +the human skull and your skull is a + + align:start position:0% +the human skull and your skull is a + + + align:start position:0% +the human skull and your skull is a +sandwich of two dense layers of the + + align:start position:0% +sandwich of two dense layers of the + + + align:start position:0% +sandwich of two dense layers of the +compact bone and you can see there's a + + align:start position:0% +compact bone and you can see there's a + + + align:start position:0% +compact bone and you can see there's a +little thin layer of the uh tacular bone + + align:start position:0% +little thin layer of the uh tacular bone + + + align:start position:0% +little thin layer of the uh tacular bone +in between so your your head is like a + + align:start position:0% +in between so your your head is like a + + + align:start position:0% +in between so your your head is like a +sandwich your skull is like a sandwich + + align:start position:0% +sandwich your skull is like a sandwich + + + align:start position:0% +sandwich your skull is like a sandwich +and um I don't know if I'll get to it + + align:start position:0% +and um I don't know if I'll get to it + + + align:start position:0% +and um I don't know if I'll get to it +next time but in the next couple of + + align:start position:0% +next time but in the next couple of + + + align:start position:0% +next time but in the next couple of +lectures I'm going to talk a little bit + + align:start position:0% +lectures I'm going to talk a little bit + + + align:start position:0% +lectures I'm going to talk a little bit +about sandwich panels in nature or + + align:start position:0% +about sandwich panels in nature or + + + align:start position:0% +about sandwich panels in nature or +sandwich shells in nature you see this + + align:start position:0% +sandwich shells in nature you see this + + + align:start position:0% +sandwich shells in nature you see this +all the time and this is a Birdwing here + + align:start position:0% +all the time and this is a Birdwing here + + + align:start position:0% +all the time and this is a Birdwing here +and so you can see there's got the dense + + align:start position:0% +and so you can see there's got the dense + + + align:start position:0% +and so you can see there's got the dense +bone on the top and the bottom and it's + + align:start position:0% +bone on the top and the bottom and it's + + + align:start position:0% +bone on the top and the bottom and it's +got this kind of almost truss-like + + align:start position:0% +got this kind of almost truss-like + + + align:start position:0% +got this kind of almost truss-like +structure in the middle and obviously + + align:start position:0% +structure in the middle and obviously + + + align:start position:0% +structure in the middle and obviously +Birds want to reduce their weight + + align:start position:0% +Birds want to reduce their weight + + + align:start position:0% +Birds want to reduce their weight +because they want to fly so reducing the + + align:start position:0% +because they want to fly so reducing the + + + align:start position:0% +because they want to fly so reducing the +weight is very important uh and so the + + align:start position:0% +weight is very important uh and so the + + + align:start position:0% +weight is very important uh and so the +this is one of the ways that birds + + align:start position:0% +this is one of the ways that birds + + + align:start position:0% +this is one of the ways that birds +reduce their weight is by having this + + align:start position:0% +reduce their weight is by having this + + + align:start position:0% +reduce their weight is by having this +sandwich kind of structure so I have a + + align:start position:0% +sandwich kind of structure so I have a + + + align:start position:0% +sandwich kind of structure so I have a +couple of things here these are the two + + align:start position:0% +couple of things here these are the two + + + align:start position:0% +couple of things here these are the two +panels at the top there this is the ski + + align:start position:0% +panels at the top there this is the ski + + + align:start position:0% +panels at the top there this is the ski +and you can you know yank those + + align:start position:0% +and you can you know yank those + + + align:start position:0% +and you can you know yank those +around + + align:start position:0% +around + + + align:start position:0% +around +um I also have a few panels that people + + align:start position:0% +um I also have a few panels that people + + + align:start position:0% +um I also have a few panels that people +at MIT have made and I have the pieces + + align:start position:0% +at MIT have made and I have the pieces + + + align:start position:0% +at MIT have made and I have the pieces +that they're made from so you can see + + align:start position:0% +that they're made from so you can see + + + align:start position:0% +that they're made from so you can see +how effective the sandwich thing is so + + align:start position:0% +how effective the sandwich thing is so + + + align:start position:0% +how effective the sandwich thing is so +this was made by a guy called Dirk Moore + + align:start position:0% +this was made by a guy called Dirk Moore + + + align:start position:0% +this was made by a guy called Dirk Moore +he was a graduate student in Ocean + + align:start position:0% +he was a graduate student in Ocean + + + align:start position:0% +he was a graduate student in Ocean +engineering and it has aluminum faces + + align:start position:0% +engineering and it has aluminum faces + + + align:start position:0% +engineering and it has aluminum faces +and a little thin aluminum core so you + + align:start position:0% +and a little thin aluminum core so you + + + align:start position:0% +and a little thin aluminum core so you +can see if you try and bend that with + + align:start position:0% +can see if you try and bend that with + + + align:start position:0% +can see if you try and bend that with +your fingers you really can't bend it + + align:start position:0% +your fingers you really can't bend it + + + align:start position:0% +your fingers you really can't bend it +any noticeable amount and this panel + + align:start position:0% +any noticeable amount and this panel + + + align:start position:0% +any noticeable amount and this panel +here is roughly the same thickness of + + align:start position:0% +here is roughly the same thickness of + + + align:start position:0% +here is roughly the same thickness of +the face on that and you can see how + + align:start position:0% +the face on that and you can see how + + + align:start position:0% +the face on that and you can see how +easy it is for me to bend that very + + align:start position:0% +easy it is for me to bend that very + + + align:start position:0% +easy it is for me to bend that very +easy and this is the same kind of thing + + align:start position:0% +easy and this is the same kind of thing + + + align:start position:0% +easy and this is the same kind of thing +as the core it's thicker than that core + + align:start position:0% +as the core it's thicker than that core + + + align:start position:0% +as the core it's thicker than that core +but you can see how easy it is for me to + + align:start position:0% +but you can see how easy it is for me to + + + align:start position:0% +but you can see how easy it is for me to +bend this too so each of the pieces is + + align:start position:0% +bend this too so each of the pieces is + + + align:start position:0% +bend this too so each of the pieces is +not very stiff at all but when you put + + align:start position:0% +not very stiff at all but when you put + + + align:start position:0% +not very stiff at all but when you put +them all together it's very stiff so so + + align:start position:0% +them all together it's very stiff so so + + + align:start position:0% +them all together it's very stiff so so +that's really the the beauty of this you + + align:start position:0% +that's really the the beauty of this you + + + align:start position:0% +that's really the the beauty of this you +can have lightweight components and by + + align:start position:0% +can have lightweight components and by + + + align:start position:0% +can have lightweight components and by +putting them together in the right way + + align:start position:0% +putting them together in the right way + + + align:start position:0% +putting them together in the right way +they're quite stiff so here's another + + align:start position:0% +they're quite stiff so here's another + + + align:start position:0% +they're quite stiff so here's another +example here this is a panel that one of + + align:start position:0% +example here this is a panel that one of + + + align:start position:0% +example here this is a panel that one of +my students Kevin Chen Chang made and + + align:start position:0% +my students Kevin Chen Chang made and + + + align:start position:0% +my students Kevin Chen Chang made and +this is actually already been broken a + + align:start position:0% +this is actually already been broken a + + + align:start position:0% +this is actually already been broken a +little bit so it's not quite as stiff as + + align:start position:0% +little bit so it's not quite as stiff as + + + align:start position:0% +little bit so it's not quite as stiff as +it used to be and you can kind of hear + + align:start position:0% +it used to be and you can kind of hear + + + align:start position:0% +it used to be and you can kind of hear +it squeaks um but you can feel that and + + align:start position:0% +it squeaks um but you can feel that and + + + align:start position:0% +it squeaks um but you can feel that and +see how stiff that is and this is the + + align:start position:0% +see how stiff that is and this is the + + + align:start position:0% +see how stiff that is and this is the +this is the face panel here and you can + + align:start position:0% +this is the face panel here and you can + + + align:start position:0% +this is the face panel here and you can +see I can bend that quite easily with my + + align:start position:0% +see I can bend that quite easily with my + + + align:start position:0% +see I can bend that quite easily with my +hands + + align:start position:0% +hands + + + align:start position:0% +hands +and then this is the core piece here and + + align:start position:0% +and then this is the core piece here and + + + align:start position:0% +and then this is the core piece here and +again this is you know very flexible so + + align:start position:0% +again this is you know very flexible so + + + align:start position:0% +again this is you know very flexible so +it's really like putting all those + + align:start position:0% +it's really like putting all those + + + align:start position:0% +it's really like putting all those +pieces together you get this sandwich + + align:start position:0% +pieces together you get this sandwich + + + align:start position:0% +pieces together you get this sandwich +construction and you get that effect + + align:start position:0% +construction and you get that effect + + + align:start position:0% +construction and you get that effect +okay + + align:start position:0% +okay + + + align:start position:0% +okay +hello all right so what we're going to + + align:start position:0% +hello all right so what we're going to + + + align:start position:0% +hello all right so what we're going to +do is first of all look at the stiffness + + align:start position:0% +do is first of all look at the stiffness + + + align:start position:0% +do is first of all look at the stiffness +of these panels calculate their + + align:start position:0% +of these panels calculate their + + + align:start position:0% +of these panels calculate their +deflection we're going to look at the + + align:start position:0% +deflection we're going to look at the + + + align:start position:0% +deflection we're going to look at the +minimum weight design of them so we're + + align:start position:0% +minimum weight design of them so we're + + + align:start position:0% +minimum weight design of them so we're +going to look at how for say given + + align:start position:0% +going to look at how for say given + + + align:start position:0% +going to look at how for say given +materials in a given span how do we + + align:start position:0% +materials in a given span how do we + + + align:start position:0% +materials in a given span how do we +minim + + align:start position:0% +minim + + + align:start position:0% +minim +weight of the beam for a given stiffness + + align:start position:0% +weight of the beam for a given stiffness + + + align:start position:0% +weight of the beam for a given stiffness +and then we're going to look at the + + align:start position:0% +and then we're going to look at the + + + align:start position:0% +and then we're going to look at the +stresses in the sandwich beam so there's + + align:start position:0% +stresses in the sandwich beam so there's + + + align:start position:0% +stresses in the sandwich beam so there's +going to be one set of stresses in the + + align:start position:0% +going to be one set of stresses in the + + + align:start position:0% +going to be one set of stresses in the +faces and a different kind of stress + + align:start position:0% +faces and a different kind of stress + + + align:start position:0% +faces and a different kind of stress +distribution in the core so we'll look + + align:start position:0% +distribution in the core so we'll look + + + align:start position:0% +distribution in the core so we'll look +at the stress distribution and then + + align:start position:0% +at the stress distribution and then + + + align:start position:0% +at the stress distribution and then +we'll talk about failure modes how these + + align:start position:0% +we'll talk about failure modes how these + + + align:start position:0% +we'll talk about failure modes how these +things can fail and then how to figure + + align:start position:0% +things can fail and then how to figure + + + align:start position:0% +things can fail and then how to figure +out which failure mode is dominant which + + align:start position:0% +out which failure mode is dominant which + + + align:start position:0% +out which failure mode is dominant which +one occurs at the lowest load and then + + align:start position:0% +one occurs at the lowest load and then + + + align:start position:0% +one occurs at the lowest load and then +we'll look at optimizing the design + + align:start position:0% +we'll look at optimizing the design + + + align:start position:0% +we'll look at optimizing the design +minimizing the design uh for a certain + + align:start position:0% +minimizing the design uh for a certain + + + align:start position:0% +minimizing the design uh for a certain +strength and stiffness so we're not + + align:start position:0% +strength and stiffness so we're not + + + align:start position:0% +strength and stiffness so we're not +going to get all that way through + + align:start position:0% +going to get all that way through + + + align:start position:0% +going to get all that way through +everything today but we'll we'll kind of + + align:start position:0% +everything today but we'll we'll kind of + + + align:start position:0% +everything today but we'll we'll kind of +make a start on + + align:start position:0% +make a start on + + + align:start position:0% +make a start on +that okay so let me let me start so the + + align:start position:0% +that okay so let me let me start so the + + + align:start position:0% +that okay so let me let me start so the +idea here is we have two stiff strong + + align:start position:0% +idea here is we have two stiff strong + + + align:start position:0% +idea here is we have two stiff strong +skins or faces separated by a + + align:start position:0% +skins or faces separated by a + + + align:start position:0% +skins or faces separated by a +lightweight + + align:start position:0% + + + + align:start position:0% + +core + + align:start position:0% + + + + align:start position:0% + +and the idea is that by separating the + + align:start position:0% +and the idea is that by separating the + + + align:start position:0% +and the idea is that by separating the +faces you increase the moment of inertia + + align:start position:0% +faces you increase the moment of inertia + + + align:start position:0% +faces you increase the moment of inertia +with little increase in + + align:start position:0% + + + + align:start position:0% + +weight + + align:start position:0% + + + + align:start position:0% + +so these are particularly good if you + + align:start position:0% +so these are particularly good if you + + + align:start position:0% +so these are particularly good if you +want to resist bending or if you want to + + align:start position:0% +want to resist bending or if you want to + + + align:start position:0% +want to resist bending or if you want to +resist buckling because both of those + + align:start position:0% +resist buckling because both of those + + + align:start position:0% +resist buckling because both of those +involve the moment of + + align:start position:0% + + + + align:start position:0% + +inertia + + align:start position:0% + + + + align:start position:0% + +and they work like an + + align:start position:0% + + + + align:start position:0% + +ibeam so the faces of the sandwich are + + align:start position:0% +ibeam so the faces of the sandwich are + + + align:start position:0% +ibeam so the faces of the sandwich are +like the flanges of the ibeam and the + + align:start position:0% +like the flanges of the ibeam and the + + + align:start position:0% +like the flanges of the ibeam and the +core is like the + + align:start position:0% + + + + align:start position:0% + +web + + align:start position:0% + + + + align:start position:0% + +the faces are typically made of either + + align:start position:0% +the faces are typically made of either + + + align:start position:0% +the faces are typically made of either +fiber reinforced + + align:start position:0% +fiber reinforced + + + align:start position:0% +fiber reinforced +Composites or + + align:start position:0% + + + + align:start position:0% + +Metals so typically something like + + align:start position:0% +Metals so typically something like + + + align:start position:0% +Metals so typically something like +aluminum usually you're trying to reduce + + align:start position:0% +aluminum usually you're trying to reduce + + + align:start position:0% +aluminum usually you're trying to reduce +the weight if you use these things so a + + align:start position:0% +the weight if you use these things so a + + + align:start position:0% +the weight if you use these things so a +lightweight metal like aluminum is + + align:start position:0% +lightweight metal like aluminum is + + + align:start position:0% +lightweight metal like aluminum is +sometimes + + align:start position:0% +sometimes + + + align:start position:0% +sometimes +used and the + + align:start position:0% +used and the + + + align:start position:0% +used and the +cores are usually + + align:start position:0% + + + + align:start position:0% + +Honeycombs or foams + + align:start position:0% + + + + align:start position:0% + +or Balsa and when they use balsa wood + + align:start position:0% +or Balsa and when they use balsa wood + + + align:start position:0% +or Balsa and when they use balsa wood +what they do is I I brought a piece of + + align:start position:0% +what they do is I I brought a piece of + + + align:start position:0% +what they do is I I brought a piece of +Balsa here what they do is they would + + align:start position:0% +Balsa here what they do is they would + + + align:start position:0% +Balsa here what they do is they would +take a block like this and chop it into + + align:start position:0% +take a block like this and chop it into + + + align:start position:0% +take a block like this and chop it into +pieces you know around here and then + + align:start position:0% +pieces you know around here and then + + + align:start position:0% +pieces you know around here and then +they would lay those pieces on a cloth + + align:start position:0% +they would lay those pieces on a cloth + + + align:start position:0% +they would lay those pieces on a cloth +mat so typically the pieces are maybe 2 + + align:start position:0% +mat so typically the pieces are maybe 2 + + + align:start position:0% +mat so typically the pieces are maybe 2 +in by 2 inch they lay them on a cloth + + align:start position:0% +in by 2 inch they lay them on a cloth + + + align:start position:0% +in by 2 inch they lay them on a cloth +mat and because they're not one + + align:start position:0% +mat and because they're not one + + + align:start position:0% +mat and because they're not one +monolithic piece they can then shape + + align:start position:0% +monolithic piece they can then shape + + + align:start position:0% +monolithic piece they can then shape +that mat to curved shape so they you + + align:start position:0% +that mat to curved shape so they you + + + align:start position:0% +that mat to curved shape so they you +know it doesn't have to be just a flat + + align:start position:0% +know it doesn't have to be just a flat + + + align:start position:0% +know it doesn't have to be just a flat +panel they can curve it around to curve + + align:start position:0% +panel they can curve it around to curve + + + align:start position:0% +panel they can curve it around to curve +surface if they + + align:start position:0% + + + + align:start position:0% + +want so we'll say the Honeycombs are + + align:start position:0% +want so we'll say the Honeycombs are + + + align:start position:0% +want so we'll say the Honeycombs are +lighter than the Foams for a given + + align:start position:0% +lighter than the Foams for a given + + + align:start position:0% +lighter than the Foams for a given +stiffness or + + align:start position:0% + + + + align:start position:0% + +strength + + align:start position:0% + + + + align:start position:0% + +but the Foams provide thermal insulation + + align:start position:0% +but the Foams provide thermal insulation + + + align:start position:0% +but the Foams provide thermal insulation +as well as a mechanical + + align:start position:0% + + + + align:start position:0% + +support + + align:start position:0% + + + + align:start position:0% + +and the overall mechanical properties of + + align:start position:0% +and the overall mechanical properties of + + + align:start position:0% +and the overall mechanical properties of +the honeycomb depend on the properties + + align:start position:0% +the honeycomb depend on the properties + + + align:start position:0% +the honeycomb depend on the properties +of each of the two parts of the faces + + align:start position:0% +of each of the two parts of the faces + + + align:start position:0% +of each of the two parts of the faces +and the core and also the geometry of + + align:start position:0% +and the core and also the geometry of + + + align:start position:0% +and the core and also the geometry of +the whole thing how Thick's the core how + + align:start position:0% +the whole thing how Thick's the core how + + + align:start position:0% +the whole thing how Thick's the core how +Thick's the face how dense is the core + + align:start position:0% +Thick's the face how dense is the core + + + align:start position:0% +Thick's the face how dense is the core +that kind of + + align:start position:0% + + + + align:start position:0% + +thing + + align:start position:0% + + + + align:start position:0% + +and typically the panel has to have some + + align:start position:0% +and typically the panel has to have some + + + align:start position:0% +and typically the panel has to have some +required stiffness or strength and often + + align:start position:0% +required stiffness or strength and often + + + align:start position:0% +required stiffness or strength and often +what you want to do is minimize the + + align:start position:0% +what you want to do is minimize the + + + align:start position:0% +what you want to do is minimize the +weight for that required stiffness or + + align:start position:0% + + + + align:start position:0% + +strength + + align:start position:0% + + + + align:start position:0% + +so often these panels are used in in + + align:start position:0% +so often these panels are used in in + + + align:start position:0% +so often these panels are used in in +some sort of vehicle like we talked + + align:start position:0% +some sort of vehicle like we talked + + + align:start position:0% +some sort of vehicle like we talked +about the sailboat or like a helicopter + + align:start position:0% +about the sailboat or like a helicopter + + + align:start position:0% +about the sailboat or like a helicopter +or like an airplane uh they also used in + + align:start position:0% +or like an airplane uh they also used in + + + align:start position:0% +or like an airplane uh they also used in +like refrigerated trucks they would have + + align:start position:0% +like refrigerated trucks they would have + + + align:start position:0% +like refrigerated trucks they would have +a foam core because they'd want the + + align:start position:0% +a foam core because they'd want the + + + align:start position:0% +a foam core because they'd want the +thermal insulation so if you're going to + + align:start position:0% +thermal insulation so if you're going to + + + align:start position:0% +thermal insulation so if you're going to +use it in some sort of a vehicle you + + align:start position:0% +use it in some sort of a vehicle you + + + align:start position:0% +use it in some sort of a vehicle you +want to reduce the mass of the vehicle + + align:start position:0% +want to reduce the mass of the vehicle + + + align:start position:0% +want to reduce the mass of the vehicle +and you want to have the lightest panel + + align:start position:0% +and you want to have the lightest panel + + + align:start position:0% +and you want to have the lightest panel +that you + + align:start position:0% + + + + align:start position:0% + +can yep use the face material and you + + align:start position:0% +can yep use the face material and you + + + align:start position:0% +can yep use the face material and you +have the thickness of U the the sandwich + + align:start position:0% +have the thickness of U the the sandwich + + + align:start position:0% +have the thickness of U the the sandwich +panel that be differ than the sandwich + + align:start position:0% +panel that be differ than the sandwich + + + align:start position:0% +panel that be differ than the sandwich +panel with something sof in the middle + + align:start position:0% +panel with something sof in the middle + + + align:start position:0% +panel with something sof in the middle +um well you um you have like one of the + + align:start position:0% +um well you um you have like one of the + + + align:start position:0% +um well you um you have like one of the +aluminum pieces that was as thick as a 7 + + align:start position:0% +aluminum pieces that was as thick as a 7 + + + align:start position:0% +aluminum pieces that was as thick as a 7 +in panel yeah compare to oh well if you + + align:start position:0% +in panel yeah compare to oh well if you + + + align:start position:0% +in panel yeah compare to oh well if you +had a solid aluminum piece that was as + + align:start position:0% +had a solid aluminum piece that was as + + + align:start position:0% +had a solid aluminum piece that was as +thick as the sandwi it's going to be + + align:start position:0% +thick as the sandwi it's going to be + + + align:start position:0% +thick as the sandwi it's going to be +stiffer but it's going to be a lot lot + + align:start position:0% +stiffer but it's going to be a lot lot + + + align:start position:0% +stiffer but it's going to be a lot lot +heavier so the stiffness per unit weight + + align:start position:0% +heavier so the stiffness per unit weight + + + align:start position:0% +heavier so the stiffness per unit weight +would not be as good okay so we're going + + align:start position:0% +would not be as good okay so we're going + + + align:start position:0% +would not be as good okay so we're going +to we're going to calculate the + + align:start position:0% +to we're going to calculate the + + + align:start position:0% +to we're going to calculate the +stiffness in just one minute and then + + align:start position:0% +stiffness in just one minute and then + + + align:start position:0% +stiffness in just one minute and then +we're going to look at how we minimize + + align:start position:0% +we're going to look at how we minimize + + + align:start position:0% +we're going to look at how we minimize +the weight + + align:start position:0% +the weight + + + align:start position:0% +the weight +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so what I'm going to do is set this + + align:start position:0% +okay so what I'm going to do is set this + + + align:start position:0% +okay so what I'm going to do is set this +up as kind of a general thing we're just + + align:start position:0% +up as kind of a general thing we're just + + + align:start position:0% +up as kind of a general thing we're just +going to look at Sandwich beams rather + + align:start position:0% +going to look at Sandwich beams rather + + + align:start position:0% +going to look at Sandwich beams rather +than plates just because it's simpler + + align:start position:0% +than plates just because it's simpler + + + align:start position:0% +than plates just because it's simpler +but the plates everything we say for the + + align:start position:0% +but the plates everything we say for the + + + align:start position:0% +but the plates everything we say for the +beams basically applies to the plates + + align:start position:0% +beams basically applies to the plates + + + align:start position:0% +beams basically applies to the plates +the equation just a little bit more + + align:start position:0% +the equation just a little bit more + + + align:start position:0% +the equation just a little bit more +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +so we're going to start with analyzing + + align:start position:0% + + + + align:start position:0% + +beams and I'm just going to start with a + + align:start position:0% +beams and I'm just going to start with a + + + align:start position:0% +beams and I'm just going to start with a +beam saying three-point + + align:start position:0% +beam saying three-point + + + align:start position:0% +beam saying three-point +bending so there's my faces + + align:start position:0% + + + + align:start position:0% + +there and I've made it kind of more + + align:start position:0% +there and I've made it kind of more + + + align:start position:0% +there and I've made it kind of more +Stumpy than it would be in real life + + align:start position:0% +Stumpy than it would be in real life + + + align:start position:0% +Stumpy than it would be in real life +just cuz it's makes it easier to draw it + + align:start position:0% +just cuz it's makes it easier to draw it + + + align:start position:0% +just cuz it's makes it easier to draw it +and then if I look at it the other way + + align:start position:0% +and then if I look at it the other way + + + align:start position:0% +and then if I look at it the other way +on it would look something like that so + + align:start position:0% +on it would look something like that so + + + align:start position:0% +on it would look something like that so +say there's some load P + + align:start position:0% +say there's some load P + + + align:start position:0% +say there's some load P +here say the span of the beam is l + + align:start position:0% +here say the span of the beam is l + + + align:start position:0% +here say the span of the beam is l +say the loads in the middle so each of + + align:start position:0% +say the loads in the middle so each of + + + align:start position:0% +say the loads in the middle so each of +the supports just sees a load of p over + + align:start position:0% +the supports just sees a load of p over + + + align:start position:0% +the supports just sees a load of p over +two and then let me just Define some + + align:start position:0% +two and then let me just Define some + + + align:start position:0% +two and then let me just Define some +geometrical parameters here I'm going to + + align:start position:0% +geometrical parameters here I'm going to + + + align:start position:0% +geometrical parameters here I'm going to +say the width of the beam is B and I'm + + align:start position:0% +say the width of the beam is B and I'm + + + align:start position:0% +say the width of the beam is B and I'm +going to say the face thicknesses are + + align:start position:0% +going to say the face thicknesses are + + + align:start position:0% +going to say the face thicknesses are +each + + align:start position:0% +each + + + align:start position:0% +each +T so the thickness of each face is T and + + align:start position:0% +T so the thickness of each face is T and + + + align:start position:0% +T so the thickness of each face is T and +the thickness of the core is C + + align:start position:0% +the thickness of the core is C + + + align:start position:0% +the thickness of the core is C +okay so that's just sort of + + align:start position:0% +okay so that's just sort of + + + align:start position:0% +okay so that's just sort of +definitions and I'm going to say the + + align:start position:0% +definitions and I'm going to say the + + + align:start position:0% +definitions and I'm going to say the +face has a set of properties the core + + align:start position:0% +face has a set of properties the core + + + align:start position:0% +face has a set of properties the core +has a set of properties and then the + + align:start position:0% +has a set of properties and then the + + + align:start position:0% +has a set of properties and then the +solid from which the core is made has + + align:start position:0% +solid from which the core is made has + + + align:start position:0% +solid from which the core is made has +another set of + + align:start position:0% +another set of + + + align:start position:0% +another set of +properties so the face properties that + + align:start position:0% +properties so the face properties that + + + align:start position:0% +properties so the face properties that +we're going to use are a density of the + + align:start position:0% +we're going to use are a density of the + + + align:start position:0% +we're going to use are a density of the +face I'll call that row F A modulus of + + align:start position:0% +face I'll call that row F A modulus of + + + align:start position:0% +face I'll call that row F A modulus of +the face EF and some sort of strength of + + align:start position:0% +the face EF and some sort of strength of + + + align:start position:0% +the face EF and some sort of strength of +the face let's imagine it's Alum + + align:start position:0% +the face let's imagine it's Alum + + + align:start position:0% +the face let's imagine it's Alum +aluminum and it yields that would be + + align:start position:0% +aluminum and it yields that would be + + + align:start position:0% +aluminum and it yields that would be +Sigma y of the face and then the + + align:start position:0% +Sigma y of the face and then the + + + align:start position:0% +Sigma y of the face and then the +core similarly is going to have a + + align:start position:0% +core similarly is going to have a + + + align:start position:0% +core similarly is going to have a +density rowar C it's going to have a + + align:start position:0% +density rowar C it's going to have a + + + align:start position:0% +density rowar C it's going to have a +modulus e c and it's going to have some + + align:start position:0% +modulus e c and it's going to have some + + + align:start position:0% +modulus e c and it's going to have some +strength I'm going to call Sigma star + + align:start position:0% +strength I'm going to call Sigma star + + + align:start position:0% +strength I'm going to call Sigma star +C and then the solid from which the core + + align:start position:0% +C and then the solid from which the core + + + align:start position:0% +C and then the solid from which the core +is made is going to have a density row S + + align:start position:0% +is made is going to have a density row S + + + align:start position:0% +is made is going to have a density row S +A modulus + + align:start position:0% +A modulus + + + align:start position:0% +A modulus +es and some strength Sigma Ys + + align:start position:0% + + + + align:start position:0% + +okay so the core is going to be some + + align:start position:0% +okay so the core is going to be some + + + align:start position:0% +okay so the core is going to be some +kind of cellular material a honeycomb or + + align:start position:0% +kind of cellular material a honeycomb or + + + align:start position:0% +kind of cellular material a honeycomb or +a foam or Balsa and typically the + + align:start position:0% +a foam or Balsa and typically the + + + align:start position:0% +a foam or Balsa and typically the +modulus of the core is going to be a lot + + align:start position:0% +modulus of the core is going to be a lot + + + align:start position:0% +modulus of the core is going to be a lot +less than the modulus of the + + align:start position:0% + + + + align:start position:0% + +face so I'm just going to say here that + + align:start position:0% +face so I'm just going to say here that + + + align:start position:0% +face so I'm just going to say here that +the e c is typically much greater than + + align:start position:0% +the e c is typically much greater than + + + align:start position:0% +the e c is typically much greater than +EF and we're going to use that later + + align:start position:0% + + + + align:start position:0% + +on so we're going to derive some + + align:start position:0% +on so we're going to derive some + + + align:start position:0% +on so we're going to derive some +equations for example for an equivalent + + align:start position:0% +equations for example for an equivalent + + + align:start position:0% +equations for example for an equivalent +flexural rigidity for the section an EI + + align:start position:0% +flexural rigidity for the section an EI + + + align:start position:0% +flexural rigidity for the section an EI +equivalent and that has several terms + + align:start position:0% +equivalent and that has several terms + + + align:start position:0% +equivalent and that has several terms +but if we can say the core stiffness is + + align:start position:0% +but if we can say the core stiffness is + + + align:start position:0% +but if we can say the core stiffness is +much less than the face thickness and + + align:start position:0% +much less than the face thickness and + + + align:start position:0% +much less than the face thickness and +also if we can say the core um or the + + align:start position:0% +also if we can say the core um or the + + + align:start position:0% +also if we can say the core um or the +stiffness is less and also the thickness + + align:start position:0% +stiffness is less and also the thickness + + + align:start position:0% +stiffness is less and also the thickness +of the core is much greater than the + + align:start position:0% +of the core is much greater than the + + + align:start position:0% +of the core is much greater than the +thickness of the face a lot of the + + align:start position:0% +thickness of the face a lot of the + + + align:start position:0% +thickness of the face a lot of the +Expressions we're going to use simplify + + align:start position:0% +Expressions we're going to use simplify + + + align:start position:0% +Expressions we're going to use simplify +so we're going to make those + + align:start position:0% +so we're going to make those + + + align:start position:0% +so we're going to make those +assumptions + + align:start position:0% +assumptions + + + align:start position:0% +assumptions +so let me just draw the sheer diagram + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +so V is shear that's the shear diagram + + align:start position:0% +so V is shear that's the shear diagram + + + align:start position:0% +so V is shear that's the shear diagram +we have some load P over2 at the support + + align:start position:0% +we have some load P over2 at the support + + + align:start position:0% +we have some load P over2 at the support +it doesn't there's no other load applied + + align:start position:0% +it doesn't there's no other load applied + + + align:start position:0% +it doesn't there's no other load applied +until we get to here then the shear + + align:start position:0% +until we get to here then the shear + + + align:start position:0% +until we get to here then the shear +diagram goes down by P so we're at minus + + align:start position:0% +diagram goes down by P so we're at minus + + + align:start position:0% +diagram goes down by P so we're at minus +P over2 then there's no load here so + + align:start position:0% +P over2 then there's no load here so + + + align:start position:0% +P over2 then there's no load here so +this just stays constant and then we go + + align:start position:0% +this just stays constant and then we go + + + align:start position:0% +this just stays constant and then we go +back up to zero and then let me just + + align:start position:0% +back up to zero and then let me just + + + align:start position:0% +back up to zero and then let me just +draw the bending moment + + align:start position:0% + + + + align:start position:0% + +diagram bending moment Di diagram for + + align:start position:0% +diagram bending moment Di diagram for + + + align:start position:0% +diagram bending moment Di diagram for +this is just going to look like a + + align:start position:0% +this is just going to look like a + + + align:start position:0% +this is just going to look like a +triangle remember if we integrate the + + align:start position:0% +triangle remember if we integrate the + + + align:start position:0% +triangle remember if we integrate the +shear diagram we get the bending moment + + align:start position:0% +shear diagram we get the bending moment + + + align:start position:0% +shear diagram we get the bending moment +diagram and that maximum moment there is + + align:start position:0% +diagram and that maximum moment there is + + + align:start position:0% +diagram and that maximum moment there is +going to be PL over + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +okay so initially I'm going to calculate + + align:start position:0% +okay so initially I'm going to calculate + + + align:start position:0% +okay so initially I'm going to calculate +the + + align:start position:0% +the + + + align:start position:0% +the +deflections and I don't really need + + align:start position:0% +deflections and I don't really need + + + align:start position:0% +deflections and I don't really need +those diagrams for that but then I'm + + align:start position:0% +those diagrams for that but then I'm + + + align:start position:0% +those diagrams for that but then I'm +going to calculate the stresses that I'm + + align:start position:0% +going to calculate the stresses that I'm + + + align:start position:0% +going to calculate the stresses that I'm +going to need those diagrams for the + + align:start position:0% +going to need those diagrams for the + + + align:start position:0% +going to need those diagrams for the +stresses so just kind of keep those in + + align:start position:0% +stresses so just kind of keep those in + + + align:start position:0% +stresses so just kind of keep those in +mind for now so to calculate the + + align:start position:0% + + + + align:start position:0% + +deflections sandwich panels are a little + + align:start position:0% +deflections sandwich panels are a little + + + align:start position:0% +deflections sandwich panels are a little +bit different from + + align:start position:0% +bit different from + + + align:start position:0% +bit different from +homogeneous beams in a sandwich panel + + align:start position:0% +homogeneous beams in a sandwich panel + + + align:start position:0% +homogeneous beams in a sandwich panel +the core is not very stiff compared to + + align:start position:0% +the core is not very stiff compared to + + + align:start position:0% +the core is not very stiff compared to +the faces and we've got some sheer + + align:start position:0% +the faces and we've got some sheer + + + align:start position:0% +the faces and we've got some sheer +stresses acting on the thing and the + + align:start position:0% +stresses acting on the thing and the + + + align:start position:0% +stresses acting on the thing and the +shear stresses are largely carried by + + align:start position:0% +shear stresses are largely carried by + + + align:start position:0% +shear stresses are largely carried by +the core so the core is actually going + + align:start position:0% +the core so the core is actually going + + + align:start position:0% +the core so the core is actually going +to shear and there's going to be a + + align:start position:0% +to shear and there's going to be a + + + align:start position:0% +to shear and there's going to be a +significant deflection of the core and + + align:start position:0% +significant deflection of the core and + + + align:start position:0% +significant deflection of the core and +Shear as well as the overall bending of + + align:start position:0% +Shear as well as the overall bending of + + + align:start position:0% +Shear as well as the overall bending of +the whole panel so you have to count for + + align:start position:0% +the whole panel so you have to count for + + + align:start position:0% +the whole panel so you have to count for +that so we're going to have a a bending + + align:start position:0% +that so we're going to have a a bending + + + align:start position:0% +that so we're going to have a a bending +term and a sheer term that's what those + + align:start position:0% +term and a sheer term that's what those + + + align:start position:0% +term and a sheer term that's what those +two terms are there so we're going to + + align:start position:0% +two terms are there so we're going to + + + align:start position:0% +two terms are there so we're going to +say there's a bending + + align:start position:0% + + + + align:start position:0% + +deflection and a + + align:start position:0% +deflection and a + + + align:start position:0% +deflection and a +sheer + + align:start position:0% + + + + align:start position:0% + +deflection and that shearing deflection + + align:start position:0% + + + + align:start position:0% + +arises from the core being + + align:start position:0% + + + + align:start position:0% + +sheared and the fact that the core say + + align:start position:0% +sheared and the fact that the core say + + + align:start position:0% +sheared and the fact that the core say +Young's modulus or also the sheer + + align:start position:0% +Young's modulus or also the sheer + + + align:start position:0% +Young's modulus or also the sheer +modulus is quite a bit less than the + + align:start position:0% +modulus is quite a bit less than the + + + align:start position:0% +modulus is quite a bit less than the +face modulus so if you think of the core + + align:start position:0% +face modulus so if you think of the core + + + align:start position:0% +face modulus so if you think of the core +is being much more compliant than the + + align:start position:0% +is being much more compliant than the + + + align:start position:0% +is being much more compliant than the +face then the core is going to have some + + align:start position:0% +face then the core is going to have some + + + align:start position:0% +face then the core is going to have some +deflection from that sheer um + + align:start position:0% +deflection from that sheer um + + + align:start position:0% +deflection from that sheer um +stress okay so we're going to start out + + align:start position:0% +stress okay so we're going to start out + + + align:start position:0% +stress okay so we're going to start out +with this term here with the bending + + align:start position:0% +with this term here with the bending + + + align:start position:0% +with this term here with the bending +term and and if I just had a homogeneous + + align:start position:0% +term and and if I just had a homogeneous + + + align:start position:0% +term and and if I just had a homogeneous +beam in three-point + + align:start position:0% +beam in three-point + + + align:start position:0% +beam in three-point +bending the central deflection so these + + align:start position:0% +bending the central deflection so these + + + align:start position:0% +bending the central deflection so these +are all the central deflections I'm + + align:start position:0% +are all the central deflections I'm + + + align:start position:0% +are all the central deflections I'm +calculating here would be PL cubed over + + align:start position:0% +calculating here would be PL cubed over + + + align:start position:0% +calculating here would be PL cubed over +it turns out to be 48 is the number and + + align:start position:0% +it turns out to be 48 is the number and + + + align:start position:0% +it turns out to be 48 is the number and +divided by EI and because we don't have + + align:start position:0% +divided by EI and because we don't have + + + align:start position:0% +divided by EI and because we don't have +a homogeneous beam here I'm going to + + align:start position:0% +a homogeneous beam here I'm going to + + + align:start position:0% +a homogeneous beam here I'm going to +call that equivalent EI and to make it a + + align:start position:0% +call that equivalent EI and to make it a + + + align:start position:0% +call that equivalent EI and to make it a +little bit more General instead of + + align:start position:0% +little bit more General instead of + + + align:start position:0% +little bit more General instead of +putting 48 that number I'm just going to + + align:start position:0% +putting 48 that number I'm just going to + + + align:start position:0% +putting 48 that number I'm just going to +put a constant B1 and that B1 constant + + align:start position:0% +put a constant B1 and that B1 constant + + + align:start position:0% +put a constant B1 and that B1 constant +is just going to depend on the loading + + align:start position:0% +is just going to depend on the loading + + + align:start position:0% +is just going to depend on the loading +geometry so anytime I have a + + align:start position:0% +geometry so anytime I have a + + + align:start position:0% +geometry so anytime I have a +concentrated load on a beam the + + align:start position:0% +concentrated load on a beam the + + + align:start position:0% +concentrated load on a beam the +deflection is always PL cubed over EI + + align:start position:0% +deflection is always PL cubed over EI + + + align:start position:0% +deflection is always PL cubed over EI +and then there's some number in the + + align:start position:0% +and then there's some number in the + + + align:start position:0% +and then there's some number in the +denominator and that number just depends + + align:start position:0% +denominator and that number just depends + + + align:start position:0% +denominator and that number just depends +on the loading configuration so for + + align:start position:0% +on the loading configuration so for + + + align:start position:0% +on the loading configuration so for +three-point bending it's 48 for for the + + align:start position:0% +three-point bending it's 48 for for the + + + align:start position:0% +three-point bending it's 48 for for the +end the flection of a can lever B1 would + + align:start position:0% +end the flection of a can lever B1 would + + + align:start position:0% +end the flection of a can lever B1 would +be three so think of that as just a + + align:start position:0% +be three so think of that as just a + + + align:start position:0% +be three so think of that as just a +number that you can work out for the + + align:start position:0% +number that you can work out for the + + + align:start position:0% +number that you can work out for the +particular loading configuration so here + + align:start position:0% +particular loading configuration so here + + + align:start position:0% +particular loading configuration so here +we'll say + + align:start position:0% +we'll say + + + align:start position:0% +we'll say +B1 is just a constant + + align:start position:0% +B1 is just a constant + + + align:start position:0% +B1 is just a constant +that depends on the loading + + align:start position:0% + + + + align:start position:0% + +configuration and I'll say for for + + align:start position:0% +configuration and I'll say for for + + + align:start position:0% +configuration and I'll say for for +example for three-point + + align:start position:0% + + + + align:start position:0% + +bending that B1 is 48 for a can + + align:start position:0% + + + + align:start position:0% + +lever + + align:start position:0% + + + + align:start position:0% + +for a can't leave n deflection then B1 + + align:start position:0% +for a can't leave n deflection then B1 + + + align:start position:0% +for a can't leave n deflection then B1 +would be three so it's just some + + align:start position:0% +would be three so it's just some + + + align:start position:0% +would be three so it's just some +number so the next thing we have to + + align:start position:0% +number so the next thing we have to + + + align:start position:0% +number so the next thing we have to +figure out is what's the EI + + align:start position:0% + + + + align:start position:0% + +equivalent so if this was just a + + align:start position:0% +equivalent so if this was just a + + + align:start position:0% +equivalent so if this was just a +homogeneous beam and it was rectangular + + align:start position:0% +homogeneous beam and it was rectangular + + + align:start position:0% +homogeneous beam and it was rectangular +e would just be e of the material and I + + align:start position:0% +e would just be e of the material and I + + + align:start position:0% +e would just be e of the material and I +would be the width B * the H time the + + align:start position:0% +would be the width B * the H time the + + + align:start position:0% +would be the width B * the H time the +height H cubed / 12 okay so here we + + align:start position:0% +height H cubed / 12 okay so here we + + + align:start position:0% +height H cubed / 12 okay so here we +don't quite have that cuz we have two + + align:start position:0% +don't quite have that cuz we have two + + + align:start position:0% +don't quite have that cuz we have two +different materials so here we have to + + align:start position:0% +different materials so here we have to + + + align:start position:0% +different materials so here we have to +use something called The Parallel axis + + align:start position:0% +use something called The Parallel axis + + + align:start position:0% +use something called The Parallel axis +theorem which I'm hoping you may have + + align:start position:0% +theorem which I'm hoping you may have + + + align:start position:0% +theorem which I'm hoping you may have +seen somewhere in calculous maybe but + + align:start position:0% +seen somewhere in calculous maybe but + + + align:start position:0% +seen somewhere in calculous maybe but +I'll no somebody's nodding yes okay so + + align:start position:0% +I'll no somebody's nodding yes okay so + + + align:start position:0% +I'll no somebody's nodding yes okay so +what we + + align:start position:0% +what we + + + align:start position:0% +what we +do what we want to do is get the + + align:start position:0% +do what we want to do is get the + + + align:start position:0% +do what we want to do is get the +equivalent EI I'm going to put it back + + align:start position:0% +equivalent EI I'm going to put it back + + + align:start position:0% +equivalent EI I'm going to put it back +up Don't Panic of this thing here right + + align:start position:0% +up Don't Panic of this thing here right + + + align:start position:0% +up Don't Panic of this thing here right +so I want this is the neutral axis + + align:start position:0% +so I want this is the neutral axis + + + align:start position:0% +so I want this is the neutral axis +here and I want the EI about that + + align:start position:0% +here and I want the EI about that + + + align:start position:0% +here and I want the EI about that +neutral axis there + + align:start position:0% +neutral axis there + + + align:start position:0% +neutral axis there +so okay are you happy there okay so I've + + align:start position:0% +so okay are you happy there okay so I've + + + align:start position:0% +so okay are you happy there okay so I've +got a term for the + + align:start position:0% + + + + align:start position:0% + +core okay the core that is the middle of + + align:start position:0% +core okay the core that is the middle of + + + align:start position:0% +core okay the core that is the middle of +the core right so for the core it's just + + align:start position:0% +the core right so for the core it's just + + + align:start position:0% +the core right so for the core it's just +going to be e of the + + align:start position:0% +going to be e of the + + + align:start position:0% +going to be e of the +core time b c Cub over 12 remember for a + + align:start position:0% +core time b c Cub over 12 remember for a + + + align:start position:0% +core time b c Cub over 12 remember for a +rectangular section it's BH cubed over + + align:start position:0% +rectangular section it's BH cubed over + + + align:start position:0% +rectangular section it's BH cubed over +12 is the moment of inertia and here our + + align:start position:0% +12 is the moment of inertia and here our + + + align:start position:0% +12 is the moment of inertia and here our +height for the core is just C okay and + + align:start position:0% +height for the core is just C okay and + + + align:start position:0% +height for the core is just C okay and +then if I took the moment of inertia for + + align:start position:0% +then if I took the moment of inertia for + + + align:start position:0% +then if I took the moment of inertia for +say one face about its own centroidal + + align:start position:0% +say one face about its own centroidal + + + align:start position:0% +say one face about its own centroidal +axis I would get e of the face now * b t + + align:start position:0% +axis I would get e of the face now * b t + + + align:start position:0% +axis I would get e of the face now * b t +cubed over 12 so that's taking the + + align:start position:0% +cubed over 12 so that's taking the + + + align:start position:0% +cubed over 12 so that's taking the +moment of inertia of one face about the + + align:start position:0% +moment of inertia of one face about the + + + align:start position:0% +moment of inertia of one face about the +middle of the face and I have two of + + align:start position:0% +middle of the face and I have two of + + + align:start position:0% +middle of the face and I have two of +those right so I have two + + align:start position:0% +those right so I have two + + + align:start position:0% +those right so I have two +faces and the parallel axis theorem + + align:start position:0% +faces and the parallel axis theorem + + + align:start position:0% +faces and the parallel axis theorem +tells you what the moment of inertia is + + align:start position:0% +tells you what the moment of inertia is + + + align:start position:0% +tells you what the moment of inertia is +going to be if you move it not to the + + align:start position:0% +going to be if you move it not to the + + + align:start position:0% +going to be if you move it not to the +um you don't use the centroid of the uh + + align:start position:0% +um you don't use the centroid of the uh + + + align:start position:0% +um you don't use the centroid of the uh +area but you use some other parallel + + align:start position:0% +area but you use some other parallel + + + align:start position:0% +area but you use some other parallel +axis and what that tells you to do is + + align:start position:0% +axis and what that tells you to do is + + + align:start position:0% +axis and what that tells you to do is +take the area that you're interested in + + align:start position:0% +take the area that you're interested in + + + align:start position:0% +take the area that you're interested in +so the area of the face is BT and you + + align:start position:0% +so the area of the face is BT and you + + + align:start position:0% +so the area of the face is BT and you +multiply by the square of the distance + + align:start position:0% +multiply by the square of the distance + + + align:start position:0% +multiply by the square of the distance +between the two axes that you're + + align:start position:0% +between the two axes that you're + + + align:start position:0% +between the two axes that you're +interested + + align:start position:0% + + + + align:start position:0% + +in let me change my little + + align:start position:0% + + + + align:start position:0% + +brackets + + align:start position:0% +brackets + + + align:start position:0% +brackets +so maybe I'll stick this make a little + + align:start position:0% +so maybe I'll stick this make a little + + + align:start position:0% +so maybe I'll stick this make a little +sketch over here + + align:start position:0% + + + + align:start position:0% + +again + + align:start position:0% + + + + align:start position:0% + +okay all right so this term here e fbt + + align:start position:0% +okay all right so this term here e fbt + + + align:start position:0% +okay all right so this term here e fbt +cubed over 12 that would be the moment + + align:start position:0% +cubed over 12 that would be the moment + + + align:start position:0% +cubed over 12 that would be the moment +of inertia of this piece + + align:start position:0% +of inertia of this piece + + + align:start position:0% +of inertia of this piece +here about the AIS that goes through the + + align:start position:0% +here about the AIS that goes through the + + + align:start position:0% +here about the AIS that goes through the +middle of that right its own centroidal + + align:start position:0% +middle of that right its own centroidal + + + align:start position:0% +middle of that right its own centroidal +axis but what I want to do is I want to + + align:start position:0% +axis but what I want to do is I want to + + + align:start position:0% +axis but what I want to do is I want to +know what the moment of inertia of this + + align:start position:0% +know what the moment of inertia of this + + + align:start position:0% +know what the moment of inertia of this +piece is about this axis here this is + + align:start position:0% +piece is about this axis here this is + + + align:start position:0% +piece is about this axis here this is +the neutral + + align:start position:0% +the neutral + + + align:start position:0% +the neutral +axis so let's call this the centroidal + + align:start position:0% + + + + align:start position:0% + +axis and the parallel axis theorem tells + + align:start position:0% +axis and the parallel axis theorem tells + + + align:start position:0% +axis and the parallel axis theorem tells +me what I do is I take the area of this + + align:start position:0% +me what I do is I take the area of this + + + align:start position:0% +me what I do is I take the area of this +little thing here so that's B * T and I + + align:start position:0% +little thing here so that's B * T and I + + + align:start position:0% +little thing here so that's B * T and I +multiply by the square of the distance + + align:start position:0% +multiply by the square of the distance + + + align:start position:0% +multiply by the square of the distance +between those two axes so the distance + + align:start position:0% +between those two axes so the distance + + + align:start position:0% +between those two axes so the distance +between those axes is just C + t/ 2 and + + align:start position:0% +between those axes is just C + t/ 2 and + + + align:start position:0% +between those axes is just C + t/ 2 and +I Square it okay and then I multiply + + align:start position:0% +I Square it okay and then I multiply + + + align:start position:0% +I Square it okay and then I multiply +that whole thing by two because I've got + + align:start position:0% +that whole thing by two because I've got + + + align:start position:0% +that whole thing by two because I've got +two + + align:start position:0% +two + + + align:start position:0% +two +faces are we + + align:start position:0% +faces are we + + + align:start position:0% +faces are we +good + + align:start position:0% + + + + align:start position:0% + +Yeahs or EFS these are EFS because this + + align:start position:0% +Yeahs or EFS these are EFS because this + + + align:start position:0% +Yeahs or EFS these are EFS because this +is the face now right right so this term + + align:start position:0% +is the face now right right so this term + + + align:start position:0% +is the face now right right so this term +here is for the core so here the + + align:start position:0% +here is for the core so here the + + + align:start position:0% +here is for the core so here the +core has e star C and these two EFS are + + align:start position:0% +core has e star C and these two EFS are + + + align:start position:0% +core has e star C and these two EFS are +for the face up there okay because you + + align:start position:0% +for the face up there okay because you + + + align:start position:0% +for the face up there okay because you +have to account for the modulus of the + + align:start position:0% +have to account for the modulus of the + + + align:start position:0% +have to account for the modulus of the +material of the bit that you're getting + + align:start position:0% +material of the bit that you're getting + + + align:start position:0% +material of the bit that you're getting +the moment of inertia for are we + + align:start position:0% +the moment of inertia for are we + + + align:start position:0% +the moment of inertia for are we +good okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so now I'm just going to simplify these + + align:start position:0% +so now I'm just going to simplify these + + + align:start position:0% +so now I'm just going to simplify these +guys a little + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +bit + + align:start position:0% +bit + + + align:start position:0% +bit +okay so I've just multiplied the + + align:start position:0% +okay so I've just multiplied the + + + align:start position:0% +okay so I've just multiplied the +twos maybe I'll just write down here + + align:start position:0% +twos maybe I'll just write down here + + + align:start position:0% +twos maybe I'll just write down here +this is the parallel axis + + align:start position:0% + + + + align:start position:0% + +theorem + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +sorry ah because I'm taking what I'm + + align:start position:0% +sorry ah because I'm taking what I'm + + + align:start position:0% +sorry ah because I'm taking what I'm +looking at so the very first term this + + align:start position:0% +looking at so the very first term this + + + align:start position:0% +looking at so the very first term this +guy here accounts for this right and + + align:start position:0% +guy here accounts for this right and + + + align:start position:0% +guy here accounts for this right and +these two terms both account for the + + align:start position:0% +these two terms both account for the + + + align:start position:0% +these two terms both account for the +face oh okay so the face acting about + + align:start position:0% +face oh okay so the face acting about + + + align:start position:0% +face oh okay so the face acting about +this axis so the parallel axis theorem + + align:start position:0% +this axis so the parallel axis theorem + + + align:start position:0% +this axis so the parallel axis theorem +says you take you know the moment of + + align:start position:0% +says you take you know the moment of + + + align:start position:0% +says you take you know the moment of +inertia of your area about its own + + align:start position:0% +inertia of your area about its own + + + align:start position:0% +inertia of your area about its own +centroidal axis and then you add this + + align:start position:0% +centroidal axis and then you add this + + + align:start position:0% +centroidal axis and then you add this +term here but it's it's really referring + + align:start position:0% +term here but it's it's really referring + + + align:start position:0% +term here but it's it's really referring +to that face + + align:start position:0% +to that face + + + align:start position:0% +to that face +okay um so let + + align:start position:0% +okay um so let + + + align:start position:0% +okay um so let +me let me scoot that down and then scoot + + align:start position:0% +me let me scoot that down and then scoot + + + align:start position:0% +me let me scoot that down and then scoot +over + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% +here + + + align:start position:0% +here +[Applause] + + align:start position:0% + + + + align:start position:0% + +and this is where we get to say the + + align:start position:0% +and this is where we get to say the + + + align:start position:0% +and this is where we get to say the +modulus of the face is much greater than + + align:start position:0% +modulus of the face is much greater than + + + align:start position:0% +modulus of the face is much greater than +the modulus of the core and also + + align:start position:0% +the modulus of the core and also + + + align:start position:0% +the modulus of the core and also +typically C the core thickness is much + + align:start position:0% +typically C the core thickness is much + + + align:start position:0% +typically C the core thickness is much +greater than T the face + + align:start position:0% +greater than T the face + + + align:start position:0% +greater than T the face +thickness so if that's true then it + + align:start position:0% +thickness so if that's true then it + + + align:start position:0% +thickness so if that's true then it +turns out this term is small compared to + + align:start position:0% +turns out this term is small compared to + + + align:start position:0% +turns out this term is small compared to +that one and also this term is small + + align:start position:0% +that one and also this term is small + + + align:start position:0% +that one and also this term is small +compared to this one and also this term + + align:start position:0% +compared to this one and also this term + + + align:start position:0% +compared to this one and also this term +instead of having C plus t^2 if C is Big + + align:start position:0% +instead of having C plus t^2 if C is Big + + + align:start position:0% +instead of having C plus t^2 if C is Big +compared to T then I can just call it + + align:start position:0% +compared to T then I can just call it + + + align:start position:0% +compared to T then I can just call it +c^2 okay so you can see here if EC is + + align:start position:0% +c^2 okay so you can see here if EC is + + + align:start position:0% +c^2 okay so you can see here if EC is +small then this is going to be small + + align:start position:0% +small then this is going to be small + + + align:start position:0% +small then this is going to be small +compared to these if T is small then + + align:start position:0% +compared to these if T is small then + + + align:start position:0% +compared to these if T is small then +this guy is going to be small so even + + align:start position:0% +this guy is going to be small so even + + + align:start position:0% +this guy is going to be small so even +though it looks ugly many times we can + + align:start position:0% +though it looks ugly many times we can + + + align:start position:0% +though it looks ugly many times we can +make this simpler + + align:start position:0% + + + + align:start position:0% + +approximation okay so we can just + + align:start position:0% +approximation okay so we can just + + + align:start position:0% +approximation okay so we can just +approximate it as EF * BT c^2 over + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +so then this bending term here we've got + + align:start position:0% +so then this bending term here we've got + + + align:start position:0% +so then this bending term here we've got +everything we need now to get that bit + + align:start position:0% +everything we need now to get that bit + + + align:start position:0% +everything we need now to get that bit +there so the next bit we want to get is + + align:start position:0% +there so the next bit we want to get is + + + align:start position:0% +there so the next bit we want to get is +the shearing + + align:start position:0% + + + + align:start position:0% + +deflection so what's the shearing + + align:start position:0% +deflection so what's the shearing + + + align:start position:0% +deflection so what's the shearing +deflection equal to so say we just + + align:start position:0% +deflection equal to so say we just + + + align:start position:0% +deflection equal to so say we just +thought about the core and all we're + + align:start position:0% +thought about the core and all we're + + + align:start position:0% +thought about the core and all we're +interested in here is what's the + + align:start position:0% +interested in here is what's the + + + align:start position:0% +interested in here is what's the +deflection of the core in shear and so + + align:start position:0% +deflection of the core in shear and so + + + align:start position:0% +deflection of the core in shear and so +say that's P + + align:start position:0% +say that's P + + + align:start position:0% +say that's P +over2 that's p over2 that's L + + align:start position:0% +over2 that's p over2 that's L + + + align:start position:0% +over2 that's p over2 that's L +over2 we'll say that's + + align:start position:0% +over2 we'll say that's + + + align:start position:0% +over2 we'll say that's +oops that's our shearing deflection + + align:start position:0% +oops that's our shearing deflection + + + align:start position:0% +oops that's our shearing deflection +there we can say the shear stress in the + + align:start position:0% +there we can say the shear stress in the + + + align:start position:0% +there we can say the shear stress in the +core is going to equal the sheer modulus + + align:start position:0% +core is going to equal the sheer modulus + + + align:start position:0% +core is going to equal the sheer modulus +times the sheer + + align:start position:0% +times the sheer + + + align:start position:0% +times the sheer +strain so we can say p over the area of + + align:start position:0% +strain so we can say p over the area of + + + align:start position:0% +strain so we can say p over the area of +the core is going to be proportional to + + align:start position:0% +the core is going to be proportional to + + + align:start position:0% +the core is going to be proportional to +the young modulus + + align:start position:0% +the young modulus + + + align:start position:0% +the young modulus +time Delta s over + + align:start position:0% +time Delta s over + + + align:start position:0% +time Delta s over +L and what's not worry about the + + align:start position:0% +L and what's not worry about the + + + align:start position:0% +L and what's not worry about the +constant just + + align:start position:0% + + + + align:start position:0% + +yet so Delta s is going to be + + align:start position:0% +yet so Delta s is going to be + + + align:start position:0% +yet so Delta s is going to be +proportional to well let me get R the + + align:start position:0% +proportional to well let me get R the + + + align:start position:0% +proportional to well let me get R the +proportional at this point Delta s is + + align:start position:0% +proportional at this point Delta s is + + + align:start position:0% +proportional at this point Delta s is +going to + + align:start position:0% + + + + align:start position:0% + +equal + + align:start position:0% +equal + + + align:start position:0% +equal +PL divided by some other constant that + + align:start position:0% +PL divided by some other constant that + + + align:start position:0% +PL divided by some other constant that +I'm going to call B2 and divided by the + + align:start position:0% +I'm going to call B2 and divided by the + + + align:start position:0% +I'm going to call B2 and divided by the +sheer modulus of the core and the + + align:start position:0% +sheer modulus of the core and the + + + align:start position:0% +sheer modulus of the core and the +essentially the area of the + + align:start position:0% +essentially the area of the + + + align:start position:0% +essentially the area of the +core um and here B2 is another + + align:start position:0% + + + + align:start position:0% + +constant so again B2 just depends on the + + align:start position:0% +constant so again B2 just depends on the + + + align:start position:0% +constant so again B2 just depends on the +loading + + align:start position:0% + + + + align:start position:0% + +configuration + + align:start position:0% + + + + align:start position:0% + +yeah this is a little bit of an + + align:start position:0% +yeah this is a little bit of an + + + align:start position:0% +yeah this is a little bit of an +approximation here but I'm just going to + + align:start position:0% +approximation here but I'm just going to + + + align:start position:0% +approximation here but I'm just going to +leave it at that um okay so then we have + + align:start position:0% +leave it at that um okay so then we have + + + align:start position:0% +leave it at that um okay so then we have +these two terms and we just add them up + + align:start position:0% +these two terms and we just add them up + + + align:start position:0% +these two terms and we just add them up +to get the final + + align:start position:0% +to get the final + + + align:start position:0% +to get the final +thing + + align:start position:0% + + + + align:start position:0% + +board + + align:start position:0% + + + + align:start position:0% + +okay so that would give us an equation + + align:start position:0% +okay so that would give us an equation + + + align:start position:0% +okay so that would give us an equation +for the + + align:start position:0% +for the + + + align:start position:0% +for the +deflection and one thing to note here is + + align:start position:0% +deflection and one thing to note here is + + + align:start position:0% +deflection and one thing to note here is +that this sheer modulus of the core if + + align:start position:0% +that this sheer modulus of the core if + + + align:start position:0% +that this sheer modulus of the core if +the core is a foam then we have an + + align:start position:0% +the core is a foam then we have an + + + align:start position:0% +the core is a foam then we have an +equation for that we also could use an + + align:start position:0% +equation for that we also could use an + + + align:start position:0% +equation for that we also could use an +equation if it's it's a honeycomb so but + + align:start position:0% +equation if it's it's a honeycomb so but + + + align:start position:0% +equation if it's it's a honeycomb so but +I'm just going to write for foam cor + + align:start position:0% +I'm just going to write for foam cor + + + align:start position:0% +I'm just going to write for foam cor +is + + align:start position:0% + + + + align:start position:0% + +oops and this is + + align:start position:0% + + + + align:start position:0% + +for that will be for open cell foam + + align:start position:0% +for that will be for open cell foam + + + align:start position:0% +for that will be for open cell foam +cores + + align:start position:0% + + + + align:start position:0% + +oops don't want + + align:start position:0% +oops don't want + + + align:start position:0% +oops don't want +to get rid of + + align:start position:0% +to get rid of + + + align:start position:0% +to get rid of +that we won't update just now thank + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +go + + align:start position:0% + + + + align:start position:0% + +okay so the next thing I want to think + + align:start position:0% +okay so the next thing I want to think + + + align:start position:0% +okay so the next thing I want to think +about is how we would minimize the + + align:start position:0% +about is how we would minimize the + + + align:start position:0% +about is how we would minimize the +weight for a given stiffness so say if + + align:start position:0% +weight for a given stiffness so say if + + + align:start position:0% +weight for a given stiffness so say if +we're given a stiffness we're given p + + align:start position:0% +we're given a stiffness we're given p + + + align:start position:0% +we're given a stiffness we're given p +over Delta so I could take out the two + + align:start position:0% +over Delta so I could take out the two + + + align:start position:0% +over Delta so I could take out the two +PS here if I divide it through by P + + align:start position:0% +PS here if I divide it through by P + + + align:start position:0% +PS here if I divide it through by P +Delta over P would be the compliance p + + align:start position:0% +Delta over P would be the compliance p + + + align:start position:0% +Delta over P would be the compliance p +over Delta would be the stiffness so + + align:start position:0% +over Delta would be the stiffness so + + + align:start position:0% +over Delta would be the stiffness so +imagine that you're given the face and + + align:start position:0% +imagine that you're given the face and + + + align:start position:0% +imagine that you're given the face and +core material s and you're told how long + + align:start position:0% +core material s and you're told how long + + + align:start position:0% +core material s and you're told how long +the span has to be you're told how width + + align:start position:0% +the span has to be you're told how width + + + align:start position:0% +the span has to be you're told how width +how wide the beam's going to be and + + align:start position:0% +how wide the beam's going to be and + + + align:start position:0% +how wide the beam's going to be and +you're told the loading configuration so + + align:start position:0% +you're told the loading configuration so + + + align:start position:0% +you're told the loading configuration so +you know if it's three-point bending or + + align:start position:0% +you know if it's three-point bending or + + + align:start position:0% +you know if it's three-point bending or +fourpoint bending or a c leave or + + align:start position:0% +fourpoint bending or a c leave or + + + align:start position:0% +fourpoint bending or a c leave or +whatever it is and you might be asked to + + align:start position:0% +whatever it is and you might be asked to + + + align:start position:0% +whatever it is and you might be asked to +find the core thickness the face + + align:start position:0% +find the core thickness the face + + + align:start position:0% +find the core thickness the face +thickness and the core density that + + align:start position:0% +thickness and the core density that + + + align:start position:0% +thickness and the core density that +would minimize the weight so I have a + + align:start position:0% +would minimize the weight so I have a + + + align:start position:0% +would minimize the weight so I have a +little schematic here I don't know if + + align:start position:0% +little schematic here I don't know if + + + align:start position:0% +little schematic here I don't know if +you're going to be able to read it so + + align:start position:0% +you're going to be able to read it so + + + align:start position:0% +you're going to be able to read it so +I'm going to walk through it and then + + align:start position:0% +I'm going to walk through it and then + + + align:start position:0% +I'm going to walk through it and then +I'll write things on the + + align:start position:0% +I'll write things on the + + + align:start position:0% +I'll write things on the +board oops hit the wrong button + + align:start position:0% + + + + align:start position:0% + +okay so we start with the weight + + align:start position:0% +okay so we start with the weight + + + align:start position:0% +okay so we start with the weight +equation here the weight's obviously the + + align:start position:0% +equation here the weight's obviously the + + + align:start position:0% +equation here the weight's obviously the +sum of the weight of the faces the + + align:start position:0% +sum of the weight of the faces the + + + align:start position:0% +sum of the weight of the faces the +weight of the core so there's two terms + + align:start position:0% +weight of the core so there's two terms + + + align:start position:0% +weight of the core so there's two terms +there um so I'll write that down in a + + align:start position:0% +there um so I'll write that down in a + + + align:start position:0% +there um so I'll write that down in a +minute then we have the stiffness + + align:start position:0% +minute then we have the stiffness + + + align:start position:0% +minute then we have the stiffness +constraint here so this equation here is + + align:start position:0% +constraint here so this equation here is + + + align:start position:0% +constraint here so this equation here is +just this equation that I have down here + + align:start position:0% +just this equation that I have down here + + + align:start position:0% +just this equation that I have down here +on the board okay then what you do is + + align:start position:0% +on the board okay then what you do is + + + align:start position:0% +on the board okay then what you do is +you solve that stiffness constraint for + + align:start position:0% +you solve that stiffness constraint for + + + align:start position:0% +you solve that stiffness constraint for +the density of the core so this equation + + align:start position:0% +the density of the core so this equation + + + align:start position:0% +the density of the core so this equation +here just solves uh we're solving this + + align:start position:0% +here just solves uh we're solving this + + + align:start position:0% +here just solves uh we're solving this +equation here in terms of the density + + align:start position:0% +equation here in terms of the density + + + align:start position:0% +equation here in terms of the density +and we get the density by substituting + + align:start position:0% +and we get the density by substituting + + + align:start position:0% +and we get the density by substituting +in this equation here for the sheer + + align:start position:0% +in this equation here for the sheer + + + align:start position:0% +in this equation here for the sheer +modulus of the core so you substitute + + align:start position:0% +modulus of the core so you substitute + + + align:start position:0% +modulus of the core so you substitute +that there you it's kind of a messy + + align:start position:0% +that there you it's kind of a messy + + + align:start position:0% +that there you it's kind of a messy +thing but you solve that in terms of the + + align:start position:0% +thing but you solve that in terms of the + + + align:start position:0% +thing but you solve that in terms of the +density then you put that version of the + + align:start position:0% +density then you put that version of the + + + align:start position:0% +density then you put that version of the +density here in terms of this weight + + align:start position:0% +density here in terms of this weight + + + align:start position:0% +density here in terms of this weight +equation up here so then you've + + align:start position:0% +equation up here so then you've + + + align:start position:0% +equation up here so then you've +eliminated the density out of the weight + + align:start position:0% +eliminated the density out of the weight + + + align:start position:0% +eliminated the density out of the weight +equation now you've just got it in terms + + align:start position:0% +equation now you've just got it in terms + + + align:start position:0% +equation now you've just got it in terms +of the other variables and then you take + + align:start position:0% +of the other variables and then you take + + + align:start position:0% +of the other variables and then you take +the partial derivative of the weight + + align:start position:0% +the partial derivative of the weight + + + align:start position:0% +the partial derivative of the weight +with respect to the core thickness C set + + align:start position:0% +with respect to the core thickness C set + + + align:start position:0% +with respect to the core thickness C set +that equal to zero and you take the + + align:start position:0% +that equal to zero and you take the + + + align:start position:0% +that equal to zero and you take the +partial derivative of the weight with + + align:start position:0% +partial derivative of the weight with + + + align:start position:0% +partial derivative of the weight with +respect to the face thickness T and you + + align:start position:0% +respect to the face thickness T and you + + + align:start position:0% +respect to the face thickness T and you +set that equal to zero and that then + + align:start position:0% +set that equal to zero and that then + + + align:start position:0% +set that equal to zero and that then +gives you two equations in two unknowns + + align:start position:0% +gives you two equations in two unknowns + + + align:start position:0% +gives you two equations in two unknowns +you've got the core thickness and the + + align:start position:0% +you've got the core thickness and the + + + align:start position:0% +you've got the core thickness and the +face thickness of the two unknowns and + + align:start position:0% +face thickness of the two unknowns and + + + align:start position:0% +face thickness of the two unknowns and +you got the two equations so then you + + align:start position:0% +you got the two equations so then you + + + align:start position:0% +you got the two equations so then you +solve those so the value you get for the + + align:start position:0% +solve those so the value you get for the + + + align:start position:0% +solve those so the value you get for the +core thickness is then the optimum so + + align:start position:0% +core thickness is then the optimum so + + + align:start position:0% +core thickness is then the optimum so +it's going to be some function of the + + align:start position:0% +it's going to be some function of the + + + align:start position:0% +it's going to be some function of the +stiffness the material properties you + + align:start position:0% +stiffness the material properties you + + + align:start position:0% +stiffness the material properties you +started with in the beam geometry and + + align:start position:0% +started with in the beam geometry and + + + align:start position:0% +started with in the beam geometry and +similarly you get some equation for the + + align:start position:0% +similarly you get some equation for the + + + align:start position:0% +similarly you get some equation for the +optimum face thickness T and again again + + align:start position:0% +optimum face thickness T and again again + + + align:start position:0% +optimum face thickness T and again again +it's uh function of the stiffness and + + align:start position:0% +it's uh function of the stiffness and + + + align:start position:0% +it's uh function of the stiffness and +the material properties in the beam + + align:start position:0% +the material properties in the beam + + + align:start position:0% +the material properties in the beam +geometry then you take those two values + + align:start position:0% +geometry then you take those two values + + + align:start position:0% +geometry then you take those two values +for C and T those two Optimum values and + + align:start position:0% +for C and T those two Optimum values and + + + align:start position:0% +for C and T those two Optimum values and +plug it back into this equation here and + + align:start position:0% +plug it back into this equation here and + + + align:start position:0% +plug it back into this equation here and +get the optimum value of the core + + align:start position:0% +get the optimum value of the core + + + align:start position:0% +get the optimum value of the core +density and so what you end up are three + + align:start position:0% +density and so what you end up are three + + + align:start position:0% +density and so what you end up are three +equations for the optimum values of the + + align:start position:0% +equations for the optimum values of the + + + align:start position:0% +equations for the optimum values of the +core thickness the face thickness and + + align:start position:0% +core thickness the face thickness and + + + align:start position:0% +core thickness the face thickness and +the core density in terms of the + + align:start position:0% +the core density in terms of the + + + align:start position:0% +the core density in terms of the +required stiffness the material + + align:start position:0% +required stiffness the material + + + align:start position:0% +required stiffness the material +properties and then the loading + + align:start position:0% +properties and then the loading + + + align:start position:0% +properties and then the loading +geometry so I'm going to write down some + + align:start position:0% +geometry so I'm going to write down some + + + align:start position:0% +geometry so I'm going to write down some +more notes cuz I'll put the on the + + align:start position:0% +more notes cuz I'll put the on the + + + align:start position:0% +more notes cuz I'll put the on the +Stellar site but um it's hard to read + + align:start position:0% +Stellar site but um it's hard to read + + + align:start position:0% +Stellar site but um it's hard to read +just here so let me write it down and + + align:start position:0% +just here so let me write it down and + + + align:start position:0% +just here so let me write it down and +I'll also write out the equations so you + + align:start position:0% +I'll also write out the equations so you + + + align:start position:0% +I'll also write out the equations so you +have the equations for calculating those + + align:start position:0% +have the equations for calculating those + + + align:start position:0% +have the equations for calculating those +Optimum values so one before I do that + + align:start position:0% +Optimum values so one before I do that + + + align:start position:0% +Optimum values so one before I do that +though one of the interesting things + + align:start position:0% +though one of the interesting things + + + align:start position:0% +though one of the interesting things +though is if you figure out the optimum + + align:start position:0% +though is if you figure out the optimum + + + align:start position:0% +though is if you figure out the optimum +values of the core thickness and the + + align:start position:0% +values of the core thickness and the + + + align:start position:0% +values of the core thickness and the +face thickness and the core density um + + align:start position:0% +face thickness and the core density um + + + align:start position:0% +face thickness and the core density um +and you substitute it back into the + + align:start position:0% +and you substitute it back into the + + + align:start position:0% +and you substitute it back into the +weight and you calculate this is the + + align:start position:0% +weight and you calculate this is the + + + align:start position:0% +weight and you calculate this is the +weight of the face relative to the + + align:start position:0% +weight of the face relative to the + + + align:start position:0% +weight of the face relative to the +weight of the core no matter what the + + align:start position:0% +weight of the core no matter what the + + + align:start position:0% +weight of the core no matter what the +geometry is and what the loading + + align:start position:0% +geometry is and what the loading + + + align:start position:0% +geometry is and what the loading +configuration is the weight of the face + + align:start position:0% +configuration is the weight of the face + + + align:start position:0% +configuration is the weight of the face +is always a quarter of the weight of the + + align:start position:0% +is always a quarter of the weight of the + + + align:start position:0% +is always a quarter of the weight of the +core so the ratio of how much materials + + align:start position:0% +core so the ratio of how much materials + + + align:start position:0% +core so the ratio of how much materials +in the core and the face is constant + + align:start position:0% +in the core and the face is constant + + + align:start position:0% +in the core and the face is constant +regardless of the core uh of the loading + + align:start position:0% +regardless of the core uh of the loading + + + align:start position:0% +regardless of the core uh of the loading +configuration and this is the the + + align:start position:0% +configuration and this is the the + + + align:start position:0% +configuration and this is the the +bending deflection relative to the the + + align:start position:0% +bending deflection relative to the the + + + align:start position:0% +bending deflection relative to the the +total deflection it's always a third and + + align:start position:0% +total deflection it's always a third and + + + align:start position:0% +total deflection it's always a third and +the shearing deflection relative to the + + align:start position:0% +the shearing deflection relative to the + + + align:start position:0% +the shearing deflection relative to the +total deflection is always 2/3 so + + align:start position:0% +total deflection is always 2/3 so + + + align:start position:0% +total deflection is always 2/3 so +regardless of um you know how you set + + align:start position:0% +regardless of um you know how you set + + + align:start position:0% +regardless of um you know how you set +things up the ratio of what weight the + + align:start position:0% +things up the ratio of what weight the + + + align:start position:0% +things up the ratio of what weight the +face is relative to the core and the + + align:start position:0% +face is relative to the core and the + + + align:start position:0% +face is relative to the core and the +amount of shearing and and bending to + + align:start position:0% +amount of shearing and and bending to + + + align:start position:0% +amount of shearing and and bending to +deflections is always a constant at the + + align:start position:0% +deflections is always a constant at the + + + align:start position:0% +deflections is always a constant at the +optimum okay so let's say we're + + align:start position:0% +optimum okay so let's say we're + + + align:start position:0% +optimum okay so let's say we're +given the face and the core + + align:start position:0% + + + + align:start position:0% + +materials so that means we're given + + align:start position:0% +materials so that means we're given + + + align:start position:0% +materials so that means we're given +their material property + + align:start position:0% +their material property + + + align:start position:0% +their material property +to and say we're + + align:start position:0% +to and say we're + + + align:start position:0% +to and say we're +given the beam length and + + align:start position:0% + + + + align:start position:0% + +width and the loading + + align:start position:0% +width and the loading + + + align:start position:0% +width and the loading +configuration + + align:start position:0% + + + + align:start position:0% + +so that means we're given those + + align:start position:0% +so that means we're given those + + + align:start position:0% +so that means we're given those +constants B1 and B2 if I told you it was + + align:start position:0% +constants B1 and B2 if I told you it was + + + align:start position:0% +constants B1 and B2 if I told you it was +three-point bending you would know what + + align:start position:0% +three-point bending you would know what + + + align:start position:0% +three-point bending you would know what +B1 and B2 + + align:start position:0% + + + + align:start position:0% + +are so then what you need to do is find + + align:start position:0% +are so then what you need to do is find + + + align:start position:0% +are so then what you need to do is find +the core thickness + + align:start position:0% +the core thickness + + + align:start position:0% +the core thickness +C the face thickness + + align:start position:0% + + + + align:start position:0% + +t + + align:start position:0% +t + + + align:start position:0% +t +and the core + + align:start position:0% + + + + align:start position:0% + +density row C to minimize the + + align:start position:0% +density row C to minimize the + + + align:start position:0% +density row C to minimize the +weight of the + + align:start position:0% + + + + align:start position:0% + +beam so there's two faces so the weight + + align:start position:0% +beam so there's two faces so the weight + + + align:start position:0% +beam so there's two faces so the weight +of the face is two row FG times + + align:start position:0% + + + + align:start position:0% + +BTL and then the weight of the + + align:start position:0% +BTL and then the weight of the + + + align:start position:0% +BTL and then the weight of the +um core is row C G * + + align:start position:0% + + + + align:start position:0% + +BCL so I'm going to write down the steps + + align:start position:0% +BCL so I'm going to write down the steps + + + align:start position:0% +BCL so I'm going to write down the steps +and then I'll write down the + + align:start position:0% + + + + align:start position:0% + +solution + + align:start position:0% + + + + align:start position:0% + +so you + + align:start position:0% +so you + + + align:start position:0% +so you +solve so you put this equation for the + + align:start position:0% +solve so you put this equation for the + + + align:start position:0% +solve so you put this equation for the +sheer modulus of the core into here and + + align:start position:0% +sheer modulus of the core into here and + + + align:start position:0% +sheer modulus of the core into here and +then you arrange rearrange this equation + + align:start position:0% +then you arrange rearrange this equation + + + align:start position:0% +then you arrange rearrange this equation +in terms of the density of the core + + align:start position:0% +in terms of the density of the core + + + align:start position:0% +in terms of the density of the core +here so you have an equation for the + + align:start position:0% +here so you have an equation for the + + + align:start position:0% +here so you have an equation for the +core density in terms of that + + align:start position:0% + + + + align:start position:0% + +stiffness + + align:start position:0% +stiffness + + + align:start position:0% +stiffness +and then you solve the + + align:start position:0% +and then you solve the + + + align:start position:0% +and then you solve the +partial derivatives of the weight + + align:start position:0% +partial derivatives of the weight + + + align:start position:0% +partial derivatives of the weight +equation with respect to the core + + align:start position:0% +equation with respect to the core + + + align:start position:0% +equation with respect to the core +thickness C and put that equal to + + align:start position:0% + + + + align:start position:0% + +zero and then the partial of DW by DT + + align:start position:0% +zero and then the partial of DW by DT + + + align:start position:0% +zero and then the partial of DW by DT +and set that to + + align:start position:0% + + + + align:start position:0% + +zero and if you do that you can then + + align:start position:0% +zero and if you do that you can then + + + align:start position:0% +zero and if you do that you can then +solve for the optimum values of the face + + align:start position:0% +solve for the optimum values of the face + + + align:start position:0% +solve for the optimum values of the face +and core thicknesses + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +gravity just so density is mass mass + + align:start position:0% +gravity just so density is mass mass + + + align:start position:0% +gravity just so density is mass mass +times gravity weight that's all it + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +and then you've got a version of this + + align:start position:0% +and then you've got a version of this + + + align:start position:0% +and then you've got a version of this +that's in terms of the the core density + + align:start position:0% +that's in terms of the the core density + + + align:start position:0% +that's in terms of the the core density +you can substitute those values of the + + align:start position:0% +you can substitute those values of the + + + align:start position:0% +you can substitute those values of the +optimum face and core thicknesses into + + align:start position:0% +optimum face and core thicknesses into + + + align:start position:0% +optimum face and core thicknesses into +that equation and get the optimum core + + align:start position:0% +that equation and get the optimum core + + + align:start position:0% +that equation and get the optimum core +density + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% +and then + + + align:start position:0% +and then +the the final equations you get when you + + align:start position:0% +the the final equations you get when you + + + align:start position:0% +the the final equations you get when you +do all that and I'm I'm going to make + + align:start position:0% +do all that and I'm I'm going to make + + + align:start position:0% +do all that and I'm I'm going to make +them all dimensionless so this is the + + align:start position:0% +them all dimensionless so this is the + + + align:start position:0% +them all dimensionless so this is the +core thickness normalized by the span of + + align:start position:0% +core thickness normalized by the span of + + + align:start position:0% +core thickness normalized by the span of +the + + align:start position:0% +the + + + align:start position:0% +the +beam is equal to this thing + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +o + + align:start position:0% + + + + align:start position:0% + +come on on + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so you can see each of these parameters + + align:start position:0% +so you can see each of these parameters + + + align:start position:0% +so you can see each of these parameters +here the design parameters that we're + + align:start position:0% +here the design parameters that we're + + + align:start position:0% +here the design parameters that we're +calculating the optimum of I've grouped + + align:start position:0% +calculating the optimum of I've grouped + + + align:start position:0% +calculating the optimum of I've grouped +the constants B1 and B2 together that + + align:start position:0% +the constants B1 and B2 together that + + + align:start position:0% +the constants B1 and B2 together that +describ the loading configuration so + + align:start position:0% +describ the loading configuration so + + + align:start position:0% +describ the loading configuration so +you'd be given those C2 is this constant + + align:start position:0% +you'd be given those C2 is this constant + + + align:start position:0% +you'd be given those C2 is this constant +oop which I just ripped off that relates + + align:start position:0% +oop which I just ripped off that relates + + + align:start position:0% +oop which I just ripped off that relates +the sheer modulus of the foam core so + + align:start position:0% +the sheer modulus of the foam core so + + + align:start position:0% +the sheer modulus of the foam core so +you'd be given that these are the + + align:start position:0% +you'd be given that these are the + + + align:start position:0% +you'd be given that these are the +material properties of the this you know + + align:start position:0% +material properties of the this you know + + + align:start position:0% +material properties of the this you know +say it's a polyurethane foam core this + + align:start position:0% +say it's a polyurethane foam core this + + + align:start position:0% +say it's a polyurethane foam core this +would be the density of the polyurethane + + align:start position:0% +would be the density of the polyurethane + + + align:start position:0% +would be the density of the polyurethane +say it's aluminum faces that would be + + align:start position:0% +say it's aluminum faces that would be + + + align:start position:0% +say it's aluminum faces that would be +the density of the aluminum so you'd be + + align:start position:0% +the density of the aluminum so you'd be + + + align:start position:0% +the density of the aluminum so you'd be +given that you'd be given the um this + + align:start position:0% +given that you'd be given the um this + + + align:start position:0% +given that you'd be given the um this +the stiffnesses of the two materials the + + align:start position:0% +the stiffnesses of the two materials the + + + align:start position:0% +the stiffnesses of the two materials the +solid from which the core is made and + + align:start position:0% +solid from which the core is made and + + + align:start position:0% +solid from which the core is made and +the the face material and then this is + + align:start position:0% +the the face material and then this is + + + align:start position:0% +the the face material and then this is +the stiffness here that you're given + + align:start position:0% +the stiffness here that you're given + + + align:start position:0% +the stiffness here that you're given +just divided by the width of the beam B + + align:start position:0% +just divided by the width of the beam B + + + align:start position:0% +just divided by the width of the beam B +so this stiffness you'd be given the + + align:start position:0% +so this stiffness you'd be given the + + + align:start position:0% +so this stiffness you'd be given the +width B so you're given all those things + + align:start position:0% +width B so you're given all those things + + + align:start position:0% +width B so you're given all those things +and you could calculate what that + + align:start position:0% +and you could calculate what that + + + align:start position:0% +and you could calculate what that +Optimum design would be + + align:start position:0% +Optimum design would be + + + align:start position:0% +Optimum design would be +okay so the next slide here just shows + + align:start position:0% +okay so the next slide here just shows + + + align:start position:0% +okay so the next slide here just shows +some experiments and these were done on + + align:start position:0% +some experiments and these were done on + + + align:start position:0% +some experiments and these were done on +sandwiches with aluminum faces and a + + align:start position:0% +sandwiches with aluminum faces and a + + + align:start position:0% +sandwiches with aluminum faces and a +rigid polyurethane foam core and here we + + align:start position:0% +rigid polyurethane foam core and here we + + + align:start position:0% +rigid polyurethane foam core and here we +knew what the relationship was for the + + align:start position:0% +knew what the relationship was for the + + + align:start position:0% +knew what the relationship was for the +sheer modulus we we measured that and + + align:start position:0% +sheer modulus we we measured that and + + + align:start position:0% +sheer modulus we we measured that and +what we did here was we designed the + + align:start position:0% +what we did here was we designed the + + + align:start position:0% +what we did here was we designed the +beams to all have the same stiffness and + + align:start position:0% +beams to all have the same stiffness and + + + align:start position:0% +beams to all have the same stiffness and +they all had the same span and the and + + align:start position:0% +they all had the same span and the and + + + align:start position:0% +they all had the same span and the and +the width B and then we we kept one + + align:start position:0% +the width B and then we we kept one + + + align:start position:0% +the width B and then we we kept one +parameter at the optimum value and we + + align:start position:0% +parameter at the optimum value and we + + + align:start position:0% +parameter at the optimum value and we +varied the other ones so here on this + + align:start position:0% +varied the other ones so here on this + + + align:start position:0% +varied the other ones so here on this +beam this set of beams here the density + + align:start position:0% +beam this set of beams here the density + + + align:start position:0% +beam this set of beams here the density +was at the optimum and we varied the + + align:start position:0% +was at the optimum and we varied the + + + align:start position:0% +was at the optimum and we varied the +core thickness and we varied the face + + align:start position:0% +core thickness and we varied the face + + + align:start position:0% +core thickness and we varied the face +thickness and the solid line was our + + align:start position:0% +thickness and the solid line was our + + + align:start position:0% +thickness and the solid line was our +model or our sort of optimization and + + align:start position:0% +model or our sort of optimization and + + + align:start position:0% +model or our sort of optimization and +the um little X's were the experiments + + align:start position:0% +the um little X's were the experiments + + + align:start position:0% +the um little X's were the experiments +so you can see there's pretty good + + align:start position:0% +so you can see there's pretty good + + + align:start position:0% +so you can see there's pretty good +agreement there then this second set + + align:start position:0% +agreement there then this second set + + + align:start position:0% +agreement there then this second set +here we kept the face thickness at the + + align:start position:0% +here we kept the face thickness at the + + + align:start position:0% +here we kept the face thickness at the +optimum value and we varied the core + + align:start position:0% +optimum value and we varied the core + + + align:start position:0% +optimum value and we varied the core +thickness and we varied the core density + + align:start position:0% +thickness and we varied the core density + + + align:start position:0% +thickness and we varied the core density +so the same thing the solid line is the + + align:start position:0% +so the same thing the solid line is the + + + align:start position:0% +so the same thing the solid line is the +um the sort of theory and the X's are + + align:start position:0% +um the sort of theory and the X's are + + + align:start position:0% +um the sort of theory and the X's are +the experiments and here we had the core + + align:start position:0% +the experiments and here we had the core + + + align:start position:0% +the experiments and here we had the core +thickness at the optimum value and we + + align:start position:0% +thickness at the optimum value and we + + + align:start position:0% +thickness at the optimum value and we +varied the face thickness and the core + + align:start position:0% +varied the face thickness and the core + + + align:start position:0% +varied the face thickness and the core +density okay so you can kind of see how + + align:start position:0% +density okay so you can kind of see how + + + align:start position:0% +density okay so you can kind of see how +how you can see this here and over here + + align:start position:0% +how you can see this here and over here + + + align:start position:0% +how you can see this here and over here +just because I forgot to say it this is + + align:start position:0% +just because I forgot to say it this is + + + align:start position:0% +just because I forgot to say it this is +the stiffness per unit weight over here + + align:start position:0% +the stiffness per unit weight over here + + + align:start position:0% +the stiffness per unit weight over here +okay so these are the optimum designs + + align:start position:0% +okay so these are the optimum designs + + + align:start position:0% +okay so these are the optimum designs +here all right so there was pretty good + + align:start position:0% +here all right so there was pretty good + + + align:start position:0% +here all right so there was pretty good +agreement between these calculations and + + align:start position:0% +agreement between these calculations and + + + align:start position:0% +agreement between these calculations and +what we measured on some + + align:start position:0% +what we measured on some + + + align:start position:0% +what we measured on some +beams do I need to write anything down + + align:start position:0% +beams do I need to write anything down + + + align:start position:0% +beams do I need to write anything down +you think you've got that yeah + + align:start position:0% +you think you've got that yeah + + + align:start position:0% +you think you've got that yeah +ask colum that you have there do those + + align:start position:0% +ask colum that you have there do those + + + align:start position:0% +ask colum that you have there do those +numbers like fall out of these equations + + align:start position:0% +numbers like fall out of these equations + + + align:start position:0% +numbers like fall out of these equations +if you do the math just did it for us I + + align:start position:0% +if you do the math just did it for us I + + + align:start position:0% +if you do the math just did it for us I +mean it's yeah exactly so so if you + + align:start position:0% +mean it's yeah exactly so so if you + + + align:start position:0% +mean it's yeah exactly so so if you +remember the equation we had for the + + align:start position:0% +remember the equation we had for the + + + align:start position:0% +remember the equation we had for the +weight uh so the weight is equal to two + + align:start position:0% +weight uh so the weight is equal to two + + + align:start position:0% +weight uh so the weight is equal to two +row F GB + + align:start position:0% +row F GB + + + align:start position:0% +row F GB +TL plus the density of the core b c so + + align:start position:0% +TL plus the density of the core b c so + + + align:start position:0% +TL plus the density of the core b c so +if you plug these things into there then + + align:start position:0% +if you plug these things into there then + + + align:start position:0% +if you plug these things into there then +uh so this is the weight of the face + + align:start position:0% +uh so this is the weight of the face + + + align:start position:0% +uh so this is the weight of the face +that's the weight of the core then it + + align:start position:0% +that's the weight of the core then it + + + align:start position:0% +that's the weight of the core then it +drops out to be a quarter so it's kind + + align:start position:0% +drops out to be a quarter so it's kind + + + align:start position:0% +drops out to be a quarter so it's kind +of magical I mean you have this big long + + align:start position:0% +of magical I mean you have this big long + + + align:start position:0% +of magical I mean you have this big long +complicated gory thing and then poof + + align:start position:0% +complicated gory thing and then poof + + + align:start position:0% +complicated gory thing and then poof +everything disappears except a factor of + + align:start position:0% +everything disappears except a factor of + + + align:start position:0% +everything disappears except a factor of +14 and the same for the bending + + align:start position:0% +14 and the same for the bending + + + align:start position:0% +14 and the same for the bending +deflection so we had those two terms so + + align:start position:0% +deflection so we had those two terms so + + + align:start position:0% +deflection so we had those two terms so +it was the bending and the shear if you + + align:start position:0% +it was the bending and the shear if you + + + align:start position:0% +it was the bending and the shear if you +just calculate each of those terms and + + align:start position:0% +just calculate each of those terms and + + + align:start position:0% +just calculate each of those terms and +take the ratio of one over the total or + + align:start position:0% +take the ratio of one over the total or + + + align:start position:0% +take the ratio of one over the total or +the one over the other everything drops + + align:start position:0% +the one over the other everything drops + + + align:start position:0% +the one over the other everything drops +out except that number so that's why I + + align:start position:0% +out except that number so that's why I + + + align:start position:0% +out except that number so that's why I +pointed it out because it seemed kind of + + align:start position:0% +pointed it out because it seemed kind of + + + align:start position:0% +pointed it out because it seemed kind of +amazing that everything would drop out + + align:start position:0% +amazing that everything would drop out + + + align:start position:0% +amazing that everything would drop out +except for that one + + align:start position:0% +except for that one + + + align:start position:0% +except for that one +thing okay so then the next thing so + + align:start position:0% +thing okay so then the next thing so + + + align:start position:0% +thing okay so then the next thing so +that's the stiffness and optimizing the + + align:start position:0% +that's the stiffness and optimizing the + + + align:start position:0% +that's the stiffness and optimizing the +stiffness are we happyish yeah okay so + + align:start position:0% +stiffness are we happyish yeah okay so + + + align:start position:0% +stiffness are we happyish yeah okay so +the next thing oh well let's see um I + + align:start position:0% +the next thing oh well let's see um I + + + align:start position:0% +the next thing oh well let's see um I +don't think I need to write any I think + + align:start position:0% +don't think I need to write any I think + + + align:start position:0% +don't think I need to write any I think +if you have that graph I don't really + + align:start position:0% +if you have that graph I don't really + + + align:start position:0% +if you have that graph I don't really +need to write much down um so the next + + align:start position:0% +need to write much down um so the next + + + align:start position:0% +need to write much down um so the next +thing then is the strength of the + + align:start position:0% +thing then is the strength of the + + + align:start position:0% +thing then is the strength of the +sandwich beams so let me get rid of + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +you guys + + align:start position:0% +you guys + + + align:start position:0% +you guys +okay yeah yeah yeah but you're shaking + + align:start position:0% +okay yeah yeah yeah but you're shaking + + + align:start position:0% +okay yeah yeah yeah but you're shaking +your head like this it's very it's very + + align:start position:0% +your head like this it's very it's very + + + align:start position:0% +your head like this it's very it's very +helpful for + + align:start position:0% +helpful for + + + align:start position:0% +helpful for +me oh okay that's + + align:start position:0% +me oh okay that's + + + align:start position:0% +me oh okay that's +okay that's okay you can do that I don't + + align:start position:0% +okay that's okay you can do that I don't + + + align:start position:0% +okay that's okay you can do that I don't +mind but as long as you don't have + + align:start position:0% +mind but as long as you don't have + + + align:start position:0% +mind but as long as you don't have +questions for me okay so the first step + + align:start position:0% +questions for me okay so the first step + + + align:start position:0% +questions for me okay so the first step +in trying to figure out about the + + align:start position:0% +in trying to figure out about the + + + align:start position:0% +in trying to figure out about the +strength is we need to figure out the + + align:start position:0% +strength is we need to figure out the + + + align:start position:0% +strength is we need to figure out the +stresses in the beams + + align:start position:0% + + + + align:start position:0% + +so so we need to find out about the + + align:start position:0% +so so we need to find out about the + + + align:start position:0% +so so we need to find out about the +stress + + align:start position:0% +stress + + + align:start position:0% +stress +and we're going to have normal stresses + + align:start position:0% +and we're going to have normal stresses + + + align:start position:0% +and we're going to have normal stresses +and we're going to have sheer + + align:start position:0% +and we're going to have sheer + + + align:start position:0% +and we're going to have sheer +stresses so I'm going to do the normal + + align:start position:0% +stresses so I'm going to do the normal + + + align:start position:0% +stresses so I'm going to do the normal +stresses first and then we'll do the + + align:start position:0% +stresses first and then we'll do the + + + align:start position:0% +stresses first and then we'll do the +sheer stresses so you do this in a way + + align:start position:0% +sheer stresses so you do this in a way + + + align:start position:0% +sheer stresses so you do this in a way +that's just analogous to how you figure + + align:start position:0% +that's just analogous to how you figure + + + align:start position:0% +that's just analogous to how you figure +out the stresses in a homogeneous beam + + align:start position:0% +out the stresses in a homogeneous beam + + + align:start position:0% +out the stresses in a homogeneous beam +so we'll say the stress is in the face + + align:start position:0% +so we'll say the stress is in the face + + + align:start position:0% +so we'll say the stress is in the face +normally it would be m y over I M's the + + align:start position:0% +normally it would be m y over I M's the + + + align:start position:0% +normally it would be m y over I M's the +moment Y is the distance from the + + align:start position:0% +moment Y is the distance from the + + + align:start position:0% +moment Y is the distance from the +neutral axis I is the moment of inertia + + align:start position:0% +neutral axis I is the moment of inertia + + + align:start position:0% +neutral axis I is the moment of inertia +so this time instead of having a moment + + align:start position:0% +so this time instead of having a moment + + + align:start position:0% +so this time instead of having a moment +of inertia we have this equivalent + + align:start position:0% +of inertia we have this equivalent + + + align:start position:0% +of inertia we have this equivalent +moment of + + align:start position:0% +moment of + + + align:start position:0% +moment of +inertia and we multiply by E of the + + align:start position:0% +inertia and we multiply by E of the + + + align:start position:0% +inertia and we multiply by E of the +face so you can think of this as being + + align:start position:0% +face so you can think of this as being + + + align:start position:0% +face so you can think of this as being +the strain essentially and then you + + align:start position:0% +the strain essentially and then you + + + align:start position:0% +the strain essentially and then you +multiply by E of the face to get the + + align:start position:0% + + + + align:start position:0% + +stress the the maximum distance from the + + align:start position:0% +stress the the maximum distance from the + + + align:start position:0% +stress the the maximum distance from the +neutral axis we can call C + + align:start position:0% +neutral axis we can call C + + + align:start position:0% +neutral axis we can call C +over2 so that's y then e equivalent we + + align:start position:0% +over2 so that's y then e equivalent we + + + align:start position:0% +over2 so that's y then e equivalent we +had EF BT + + align:start position:0% +had EF BT + + + align:start position:0% +had EF BT +c^2 over two and then I have a term of + + align:start position:0% +c^2 over two and then I have a term of + + + align:start position:0% +c^2 over two and then I have a term of +EF + + align:start position:0% +EF + + + align:start position:0% +EF +here c^ squar so one of the C's goes the + + align:start position:0% +here c^ squar so one of the C's goes the + + + align:start position:0% +here c^ squar so one of the C's goes the +twos go the EFS + + align:start position:0% + + + + align:start position:0% + +go and you just get that the normal + + align:start position:0% +go and you just get that the normal + + + align:start position:0% +go and you just get that the normal +stress in the face is the moment at that + + align:start position:0% +stress in the face is the moment at that + + + align:start position:0% +stress in the face is the moment at that +section divided by the width B the face + + align:start position:0% +section divided by the width B the face + + + align:start position:0% +section divided by the width B the face +thickness T the core thickness + + align:start position:0% + + + + align:start position:0% + +C I can do the same kind of thing for + + align:start position:0% +C I can do the same kind of thing for + + + align:start position:0% +C I can do the same kind of thing for +the stress in the core except now I + + align:start position:0% +the stress in the core except now I + + + align:start position:0% +the stress in the core except now I +multiply by the core + + align:start position:0% + + + + align:start position:0% + +modulus so if I go through the + + align:start position:0% +modulus so if I go through the + + + align:start position:0% +modulus so if I go through the +same kind of + + align:start position:0% + + + + align:start position:0% + +thing it's the same fact of M over BTC + + align:start position:0% +thing it's the same fact of M over BTC + + + align:start position:0% +thing it's the same fact of M over BTC +but now I multiply times e of the core + + align:start position:0% +but now I multiply times e of the core + + + align:start position:0% +but now I multiply times e of the core +over e of the + + align:start position:0% +over e of the + + + align:start position:0% +over e of the +face and since e of the core is a lot + + align:start position:0% +face and since e of the core is a lot + + + align:start position:0% +face and since e of the core is a lot +smaller than e of the face typically + + align:start position:0% +smaller than e of the face typically + + + align:start position:0% +smaller than e of the face typically +these normal stresses in the core are + + align:start position:0% +these normal stresses in the core are + + + align:start position:0% +these normal stresses in the core are +much smaller than the normal stresses in + + align:start position:0% +much smaller than the normal stresses in + + + align:start position:0% +much smaller than the normal stresses in +the + + align:start position:0% + + + + align:start position:0% + +face + + align:start position:0% + + + + align:start position:0% + +so the faces carry almost all of the + + align:start position:0% +so the faces carry almost all of the + + + align:start position:0% +so the faces carry almost all of the +normal + + align:start position:0% + + + + align:start position:0% + +stresses and if you look at an ie beam + + align:start position:0% +stresses and if you look at an ie beam + + + align:start position:0% +stresses and if you look at an ie beam +the flanges of the eyebeam carry almost + + align:start position:0% +the flanges of the eyebeam carry almost + + + align:start position:0% +the flanges of the eyebeam carry almost +all the normal + + align:start position:0% +all the normal + + + align:start position:0% +all the normal +[Applause] + + align:start position:0% + + + + align:start position:0% + +stresses + + align:start position:0% +stresses + + + align:start position:0% +stresses +so I want to do one more thing here I + + align:start position:0% +so I want to do one more thing here I + + + align:start position:0% +so I want to do one more thing here I +want to relate the moment to some + + align:start position:0% +want to relate the moment to some + + + align:start position:0% +want to relate the moment to some +concentrated load so let's say we have a + + align:start position:0% + + + + align:start position:0% + +beam with a concentrated load + + align:start position:0% + + + + align:start position:0% + +P so for example something in + + align:start position:0% +P so for example something in + + + align:start position:0% +P so for example something in +three-point + + align:start position:0% +three-point + + + align:start position:0% +three-point +bending typically we're interested in + + align:start position:0% +bending typically we're interested in + + + align:start position:0% +bending typically we're interested in +the maximum stresses so we want the + + align:start position:0% +the maximum stresses so we want the + + + align:start position:0% +the maximum stresses so we want the +maximum moment so ma Max it's going to + + align:start position:0% +maximum moment so ma Max it's going to + + + align:start position:0% +maximum moment so ma Max it's going to +be P * L over some number and this B3 is + + align:start position:0% +be P * L over some number and this B3 is + + + align:start position:0% +be P * L over some number and this B3 is +another constant that depends on the + + align:start position:0% +another constant that depends on the + + + align:start position:0% +another constant that depends on the +loading + + align:start position:0% + + + + align:start position:0% + +configuration + + align:start position:0% +configuration + + + align:start position:0% +configuration +so if it was three-point bending B3 + + align:start position:0% +so if it was three-point bending B3 + + + align:start position:0% +so if it was three-point bending B3 +would be four if it was a can't lever B3 + + align:start position:0% +would be four if it was a can't lever B3 + + + align:start position:0% +would be four if it was a can't lever B3 +would be + + align:start position:0% + + + + align:start position:0% + +one so if I put those things together + + align:start position:0% +one so if I put those things together + + + align:start position:0% +one so if I put those things together +the normal stress in the face is + + align:start position:0% +the normal stress in the face is + + + align:start position:0% +the normal stress in the face is +PL over + + align:start position:0% +PL over + + + align:start position:0% +PL over +B3 * BT or divided by + + align:start position:0% + + + + align:start position:0% + +BTC + + align:start position:0% + + + + align:start position:0% + +okay so that's the normal + + align:start position:0% +okay so that's the normal + + + align:start position:0% +okay so that's the normal +stresses and then the next thing is the + + align:start position:0% +stresses and then the next thing is the + + + align:start position:0% +stresses and then the next thing is the +sheer stresses and the sheer stresses + + align:start position:0% +sheer stresses and the sheer stresses + + + align:start position:0% +sheer stresses and the sheer stresses +are going to be carried largely by the + + align:start position:0% +are going to be carried largely by the + + + align:start position:0% +are going to be carried largely by the +core and if you do all the exact + + align:start position:0% +core and if you do all the exact + + + align:start position:0% +core and if you do all the exact +calculations they vary parabolically + + align:start position:0% +calculations they vary parabolically + + + align:start position:0% +calculations they vary parabolically +through the core but if we make those + + align:start position:0% +through the core but if we make those + + + align:start position:0% +through the core but if we make those +same approximations that the face is + + align:start position:0% +same approximations that the face is + + + align:start position:0% +same approximations that the face is +stiff compared to the core and that the + + align:start position:0% +stiff compared to the core and that the + + + align:start position:0% +stiff compared to the core and that the +face is thin compared to the core then + + align:start position:0% +face is thin compared to the core then + + + align:start position:0% +face is thin compared to the core then +you can say that the sheer stress is + + align:start position:0% +you can say that the sheer stress is + + + align:start position:0% +you can say that the sheer stress is +just constant through the + + align:start position:0% + + + + align:start position:0% + +core so we'll say the shear stress is + + align:start position:0% +core so we'll say the shear stress is + + + align:start position:0% +core so we'll say the shear stress is +very + + align:start position:0% + + + + align:start position:0% + +parabolically through the + + align:start position:0% + + + + align:start position:0% + +core but if the face is much stiffer + + align:start position:0% +core but if the face is much stiffer + + + align:start position:0% +core but if the face is much stiffer +than the core and the core is much + + align:start position:0% +than the core and the core is much + + + align:start position:0% +than the core and the core is much +thicker than the + + align:start position:0% +thicker than the + + + align:start position:0% +thicker than the +face then you can say that the shear + + align:start position:0% +face then you can say that the shear + + + align:start position:0% +face then you can say that the shear +stress in the core is just equal to the + + align:start position:0% +stress in the core is just equal to the + + + align:start position:0% +stress in the core is just equal to the +sheer force over the area of the core BC + + align:start position:0% +sheer force over the area of the core BC + + + align:start position:0% +sheer force over the area of the core BC +so here V is the sheer force of the + + align:start position:0% +so here V is the sheer force of the + + + align:start position:0% +so here V is the sheer force of the +crosssection you're interested + + align:start position:0% + + + + align:start position:0% + +in BC is just the area of the + + align:start position:0% +in BC is just the area of the + + + align:start position:0% +in BC is just the area of the +core and we could say the maximum sheer + + align:start position:0% +core and we could say the maximum sheer + + + align:start position:0% +core and we could say the maximum sheer +force is just going to be V + + align:start position:0% +force is just going to be V + + + align:start position:0% +force is just going to be V +over um actually let's make it + + align:start position:0% +over um actually let's make it + + + align:start position:0% +over um actually let's make it +p p over yet another + + align:start position:0% +p p over yet another + + + align:start position:0% +p p over yet another +constant and B4 also depends on the + + align:start position:0% +constant and B4 also depends on the + + + align:start position:0% +constant and B4 also depends on the +loading + + align:start position:0% + + + + align:start position:0% + +configuration so if I was giving you a + + align:start position:0% +configuration so if I was giving you a + + + align:start position:0% +configuration so if I was giving you a +problem I would give you all these B1 B2 + + align:start position:0% +problem I would give you all these B1 B2 + + + align:start position:0% +problem I would give you all these B1 B2 +B3 b4s and + + align:start position:0% +B3 b4s and + + + align:start position:0% +B3 b4s and +everything + + align:start position:0% + + + + align:start position:0% + +so the maximum sheer stress in the core + + align:start position:0% +so the maximum sheer stress in the core + + + align:start position:0% +so the maximum sheer stress in the core +is then just the applied load P divided + + align:start position:0% +is then just the applied load P divided + + + align:start position:0% +is then just the applied load P divided +by this B4 and divided by the area of + + align:start position:0% +by this B4 and divided by the area of + + + align:start position:0% +by this B4 and divided by the area of +the + + align:start position:0% + + + + align:start position:0% + +core + + align:start position:0% + + + + align:start position:0% + +okay so this next figure up here just + + align:start position:0% +okay so this next figure up here just + + + align:start position:0% +okay so this next figure up here just +shows those stress distributions so + + align:start position:0% +shows those stress distributions so + + + align:start position:0% +shows those stress distributions so +here's a piece of the uh cross-section + + align:start position:0% +here's a piece of the uh cross-section + + + align:start position:0% +here's a piece of the uh cross-section +here so there's the face thickness and + + align:start position:0% +here so there's the face thickness and + + + align:start position:0% +here so there's the face thickness and +the core thickness you can think of that + + align:start position:0% +the core thickness you can think of that + + + align:start position:0% +the core thickness you can think of that +as a piece along the length if you want + + align:start position:0% +as a piece along the length if you want + + + align:start position:0% +as a piece along the length if you want +this is the normal stress distribution + + align:start position:0% +this is the normal stress distribution + + + align:start position:0% +this is the normal stress distribution +here so this is all really from saying + + align:start position:0% +here so this is all really from saying + + + align:start position:0% +here so this is all really from saying +plain sections remain plain these are + + align:start position:0% +plain sections remain plain these are + + + align:start position:0% +plain sections remain plain these are +the stresses the normal stresses in the + + align:start position:0% +the stresses the normal stresses in the + + + align:start position:0% +the stresses the normal stresses in the +core and you can see they're a lot + + align:start position:0% +core and you can see they're a lot + + + align:start position:0% +core and you can see they're a lot +smaller in this schematic than the ones + + align:start position:0% +smaller in this schematic than the ones + + + align:start position:0% +smaller in this schematic than the ones +in the face um and then this is the + + align:start position:0% +in the face um and then this is the + + + align:start position:0% +in the face um and then this is the +parabolic stress in the core and + + align:start position:0% +parabolic stress in the core and + + + align:start position:0% +parabolic stress in the core and +similarly there'd be a different + + align:start position:0% +similarly there'd be a different + + + align:start position:0% +similarly there'd be a different +Parabola in the face and these are the + + align:start position:0% +Parabola in the face and these are the + + + align:start position:0% +Parabola in the face and these are the +approximations typically these + + align:start position:0% +approximations typically these + + + align:start position:0% +approximations typically these +approximations are made so the normal + + align:start position:0% +approximations are made so the normal + + + align:start position:0% +approximations are made so the normal +stress in the face is just taken as a + + align:start position:0% +stress in the face is just taken as a + + + align:start position:0% +stress in the face is just taken as a +constant the normal stress in the core + + align:start position:0% +constant the normal stress in the core + + + align:start position:0% +constant the normal stress in the core +is often neglected and here the sheer + + align:start position:0% +is often neglected and here the sheer + + + align:start position:0% +is often neglected and here the sheer +stress in the core is just a constant + + align:start position:0% +stress in the core is just a constant + + + align:start position:0% +stress in the core is just a constant +here so the the the two things you need + + align:start position:0% +here so the the the two things you need + + + align:start position:0% +here so the the the two things you need +to worry about are the normal stress for + + align:start position:0% +to worry about are the normal stress for + + + align:start position:0% +to worry about are the normal stress for +the face and the sheer stress for the + + align:start position:0% +the face and the sheer stress for the + + + align:start position:0% +the face and the sheer stress for the +core okay are we good we're good yeah + + align:start position:0% +core okay are we good we're good yeah + + + align:start position:0% +core okay are we good we're good yeah +good good + + align:start position:0% +good good + + + align:start position:0% +good good +goodish okay so if we want to talk about + + align:start position:0% +goodish okay so if we want to talk about + + + align:start position:0% +goodish okay so if we want to talk about +the strength of the beam we now have to + + align:start position:0% +the strength of the beam we now have to + + + align:start position:0% +the strength of the beam we now have to +talk about different failure + + align:start position:0% +talk about different failure + + + align:start position:0% +talk about different failure +modes and the next slide just shows some + + align:start position:0% +modes and the next slide just shows some + + + align:start position:0% +modes and the next slide just shows some +schematics of the failure modes so + + align:start position:0% +schematics of the failure modes so + + + align:start position:0% +schematics of the failure modes so +there's different ways the beam can fail + + align:start position:0% +there's different ways the beam can fail + + + align:start position:0% +there's different ways the beam can fail +say it's in three-point bending just for + + align:start position:0% +say it's in three-point bending just for + + + align:start position:0% +say it's in three-point bending just for +the sake of convenience one way it can + + align:start position:0% +the sake of convenience one way it can + + + align:start position:0% +the sake of convenience one way it can +fail is say it had aluminum faces this + + align:start position:0% +fail is say it had aluminum faces this + + + align:start position:0% +fail is say it had aluminum faces this +face here would be in tension and the + + align:start position:0% +face here would be in tension and the + + + align:start position:0% +face here would be in tension and the +face could just yield so you can just + + align:start position:0% +face could just yield so you can just + + + align:start position:0% +face could just yield so you can just +get yielding of the aluminum that would + + align:start position:0% +get yielding of the aluminum that would + + + align:start position:0% +get yielding of the aluminum that would +be one way it could be a composite face + + align:start position:0% +be one way it could be a composite face + + + align:start position:0% +be one way it could be a composite face +and you could have some sort of + + align:start position:0% +and you could have some sort of + + + align:start position:0% +and you could have some sort of +composite failure mode you get more + + align:start position:0% +composite failure mode you get more + + + align:start position:0% +composite failure mode you get more +complicated failure modes for Composites + + align:start position:0% +complicated failure modes for Composites + + + align:start position:0% +complicated failure modes for Composites +but there could be some sort of failure + + align:start position:0% +but there could be some sort of failure + + + align:start position:0% +but there could be some sort of failure +mode this face up here is in + + align:start position:0% +mode this face up here is in + + + align:start position:0% +mode this face up here is in +compression and if you compress that + + align:start position:0% +compression and if you compress that + + + align:start position:0% +compression and if you compress that +face you can get something called face + + align:start position:0% +face you can get something called face + + + align:start position:0% +face you can get something called face +wrinkling you get sort of a local + + align:start position:0% +wrinkling you get sort of a local + + + align:start position:0% +wrinkling you get sort of a local +buckling mode so imagine you have the + + align:start position:0% +buckling mode so imagine you have the + + + align:start position:0% +buckling mode so imagine you have the +face that you're pressing on it but the + + align:start position:0% +face that you're pressing on it but the + + + align:start position:0% +face that you're pressing on it but the +core is kind of acting like an elastic + + align:start position:0% +core is kind of acting like an elastic + + + align:start position:0% +core is kind of acting like an elastic +Foundation underneath it and you can get + + align:start position:0% +Foundation underneath it and you can get + + + align:start position:0% +Foundation underneath it and you can get +this kind of local buckling that's + + align:start position:0% +this kind of local buckling that's + + + align:start position:0% +this kind of local buckling that's +called + + align:start position:0% +called + + + align:start position:0% +called +wrinkling that's another mode of failure + + align:start position:0% +wrinkling that's another mode of failure + + + align:start position:0% +wrinkling that's another mode of failure +you can also get the core failing in + + align:start position:0% +you can also get the core failing in + + + align:start position:0% +you can also get the core failing in +shear so here's these two little cracks + + align:start position:0% +shear so here's these two little cracks + + + align:start position:0% +shear so here's these two little cracks +um denoting sheer failure in the core + + align:start position:0% +um denoting sheer failure in the core + + + align:start position:0% +um denoting sheer failure in the core +and there's a couple of other modes you + + align:start position:0% +and there's a couple of other modes you + + + align:start position:0% +and there's a couple of other modes you +can get but we're going to not pay much + + align:start position:0% +can get but we're going to not pay much + + + align:start position:0% +can get but we're going to not pay much +attention to those the whole thing can + + align:start position:0% +attention to those the whole thing can + + + align:start position:0% +attention to those the whole thing can +delaminate and as you might guess if the + + align:start position:0% +delaminate and as you might guess if the + + + align:start position:0% +delaminate and as you might guess if the +whole thing delaminates you're in deep + + align:start position:0% +whole thing delaminates you're in deep + + + align:start position:0% +whole thing delaminates you're in deep +doooo because remember when I passed + + align:start position:0% +doooo because remember when I passed + + + align:start position:0% +doooo because remember when I passed +those samples around how flexible the + + align:start position:0% +those samples around how flexible the + + + align:start position:0% +those samples around how flexible the +face was by itself and how flexible the + + align:start position:0% +face was by itself and how flexible the + + + align:start position:0% +face was by itself and how flexible the +core is by itself if the whole thing + + align:start position:0% +core is by itself if the whole thing + + + align:start position:0% +core is by itself if the whole thing +delaminates you lose that whole sandwich + + align:start position:0% +delaminates you lose that whole sandwich + + + align:start position:0% +delaminates you lose that whole sandwich +effect and the whole thing kind of falls + + align:start position:0% +effect and the whole thing kind of falls + + + align:start position:0% +effect and the whole thing kind of falls +apart we're going to assume we have a + + align:start position:0% +apart we're going to assume we have a + + + align:start position:0% +apart we're going to assume we have a +perfect Bond and that we don't have to + + align:start position:0% +perfect Bond and that we don't have to + + + align:start position:0% +perfect Bond and that we don't have to +worry about that the other sort of + + align:start position:0% +worry about that the other sort of + + + align:start position:0% +worry about that the other sort of +failure mode you you can get is called + + align:start position:0% +failure mode you you can get is called + + + align:start position:0% +failure mode you you can get is called +indentation so imagine that you apply + + align:start position:0% +indentation so imagine that you apply + + + align:start position:0% +indentation so imagine that you apply +this load here over a very small area it + + align:start position:0% +this load here over a very small area it + + + align:start position:0% +this load here over a very small area it +the load can just transfer straight + + align:start position:0% +the load can just transfer straight + + + align:start position:0% +the load can just transfer straight +through the face and just kind of indent + + align:start position:0% +through the face and just kind of indent + + + align:start position:0% +through the face and just kind of indent +the core underneath it we're going to + + align:start position:0% +the core underneath it we're going to + + + align:start position:0% +the core underneath it we're going to +assume that you distribute this load + + align:start position:0% +assume that you distribute this load + + + align:start position:0% +assume that you distribute this load +over a big enough area here that you + + align:start position:0% +over a big enough area here that you + + + align:start position:0% +over a big enough area here that you +don't indent the core so we're going to + + align:start position:0% +don't indent the core so we're going to + + + align:start position:0% +don't indent the core so we're going to +worry about these three failure modes + + align:start position:0% +worry about these three failure modes + + + align:start position:0% +worry about these three failure modes +here the face yielding the face + + align:start position:0% +here the face yielding the face + + + align:start position:0% +here the face yielding the face +wrinkling and the core failing in sheer + + align:start position:0% +wrinkling and the core failing in sheer + + + align:start position:0% +wrinkling and the core failing in sheer +okay so let me just write that down + + align:start position:0% + + + + align:start position:0% + +h + + align:start position:0% + + + + align:start position:0% + +and then you also can have + + align:start position:0% + + + + align:start position:0% + +debonding or + + align:start position:0% +debonding or + + + align:start position:0% +debonding or +delamination and we're going to assume + + align:start position:0% +delamination and we're going to assume + + + align:start position:0% +delamination and we're going to assume +perfect + + align:start position:0% + + + + align:start position:0% + +Bond and then you can have indentation + + align:start position:0% +Bond and then you can have indentation + + + align:start position:0% +Bond and then you can have indentation +and we're going to assume the loads are + + align:start position:0% +and we're going to assume the loads are + + + align:start position:0% +and we're going to assume the loads are +applied over a large enough area that + + align:start position:0% +applied over a large enough area that + + + align:start position:0% +applied over a large enough area that +you don't + + align:start position:0% + + + + align:start position:0% + +get + + align:start position:0% + + + + align:start position:0% + +so you can have different modes of + + align:start position:0% +so you can have different modes of + + + align:start position:0% +so you can have different modes of +failure and the the question becomes + + align:start position:0% +failure and the the question becomes + + + align:start position:0% +failure and the the question becomes +which mode is going to be dominant so + + align:start position:0% +which mode is going to be dominant so + + + align:start position:0% +which mode is going to be dominant so +whichever one occurs at the lowest load + + align:start position:0% +whichever one occurs at the lowest load + + + align:start position:0% +whichever one occurs at the lowest load +is going to be the dominant failure mode + + align:start position:0% +is going to be the dominant failure mode + + + align:start position:0% +is going to be the dominant failure mode +so you'd like to know what that lowest + + align:start position:0% +so you'd like to know what that lowest + + + align:start position:0% +so you'd like to know what that lowest +failure mode is so we want to write + + align:start position:0% +failure mode is so we want to write + + + align:start position:0% +failure mode is so we want to write +equations for each of these failure + + align:start position:0% +equations for each of these failure + + + align:start position:0% +equations for each of these failure +modes and then U figure out which one + + align:start position:0% +modes and then U figure out which one + + + align:start position:0% +modes and then U figure out which one +occurs + + align:start position:0% + + + + align:start position:0% + +first so we'll look at the face yielding + + align:start position:0% +first so we'll look at the face yielding + + + align:start position:0% +first so we'll look at the face yielding +here and face yielding is going to occur + + align:start position:0% +here and face yielding is going to occur + + + align:start position:0% +here and face yielding is going to occur +just when the normal stress in the face + + align:start position:0% +just when the normal stress in the face + + + align:start position:0% +just when the normal stress in the face +is equal to the yield stress of the face + + align:start position:0% +is equal to the yield stress of the face + + + align:start position:0% +is equal to the yield stress of the face +so this is fairly + + align:start position:0% + + + + align:start position:0% + +straightforward + + align:start position:0% +straightforward + + + align:start position:0% +straightforward +okay so this was our equation for the + + align:start position:0% +okay so this was our equation for the + + + align:start position:0% +okay so this was our equation for the +stress in the face and when that's equal + + align:start position:0% +stress in the face and when that's equal + + + align:start position:0% +stress in the face and when that's equal +to the face yield strength then you'll + + align:start position:0% +to the face yield strength then you'll + + + align:start position:0% +to the face yield strength then you'll +get + + align:start position:0% + + + + align:start position:0% + +failure the face wrinkling occurs when + + align:start position:0% +failure the face wrinkling occurs when + + + align:start position:0% +failure the face wrinkling occurs when +the normal compressive face in the + + align:start position:0% +the normal compressive face in the + + + align:start position:0% +the normal compressive face in the +normal compressive stress in the face + + align:start position:0% +normal compressive stress in the face + + + align:start position:0% +normal compressive stress in the face +equals a local buckling + + align:start position:0% + + + + align:start position:0% + +stress + + align:start position:0% +stress + + + align:start position:0% +stress +and people have worked that out by + + align:start position:0% +and people have worked that out by + + + align:start position:0% +and people have worked that out by +looking at what's called buckling on an + + align:start position:0% +looking at what's called buckling on an + + + align:start position:0% +looking at what's called buckling on an +elastic foundation so the core acts as + + align:start position:0% +elastic foundation so the core acts as + + + align:start position:0% +elastic foundation so the core acts as +elastic support you can think that as + + align:start position:0% +elastic support you can think that as + + + align:start position:0% +elastic support you can think that as +the as the face is trying to buckle into + + align:start position:0% +the as the face is trying to buckle into + + + align:start position:0% +the as the face is trying to buckle into +the core the core is pushing back on the + + align:start position:0% +the core the core is pushing back on the + + + align:start position:0% +the core the core is pushing back on the +face and so the face is acting like a or + + align:start position:0% +face and so the face is acting like a or + + + align:start position:0% +face and so the face is acting like a or +the core is acting like a spring that + + align:start position:0% +the core is acting like a spring that + + + align:start position:0% +the core is acting like a spring that +pushes back and that's called an elastic + + align:start position:0% +pushes back and that's called an elastic + + + align:start position:0% +pushes back and that's called an elastic +foundation so people have calculated + + align:start position:0% +foundation so people have calculated + + + align:start position:0% +foundation so people have calculated +this local + + align:start position:0% +this local + + + align:start position:0% +this local +buckling + + align:start position:0% +buckling + + + align:start position:0% +buckling +stress and they found that's equal to + + align:start position:0% +stress and they found that's equal to + + + align:start position:0% +stress and they found that's equal to +0.57 time + + align:start position:0% +0.57 time + + + align:start position:0% +0.57 time +the modulus of the face to the 1/3 power + + align:start position:0% +the modulus of the face to the 1/3 power + + + align:start position:0% +the modulus of the face to the 1/3 power +time the modulus of the core to the 2/3 + + align:start position:0% + + + + align:start position:0% + +power and here if we use our model for + + align:start position:0% +power and here if we use our model for + + + align:start position:0% +power and here if we use our model for +open cell foams + + align:start position:0% + + + + align:start position:0% + +we can say the core modulus goes as the + + align:start position:0% +we can say the core modulus goes as the + + + align:start position:0% +we can say the core modulus goes as the +relative density squared times the solid + + align:start position:0% +relative density squared times the solid + + + align:start position:0% +relative density squared times the solid +modulus and so you can plug that in + + align:start position:0% + + + + align:start position:0% + +there + + align:start position:0% + + + + align:start position:0% + +so then the wrinkling occurs when the + + align:start position:0% +so then the wrinkling occurs when the + + + align:start position:0% +so then the wrinkling occurs when the +stress in the face the pl over the B3 + + align:start position:0% +stress in the face the pl over the B3 + + + align:start position:0% +stress in the face the pl over the B3 +BTC is equal to this thing here + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +okay so one more failure mode that's + + align:start position:0% + + + + align:start position:0% + +corer + + align:start position:0% + + + + align:start position:0% + +and that's going to occur when the shear + + align:start position:0% +and that's going to occur when the shear + + + align:start position:0% +and that's going to occur when the shear +stress in the core is just equal to the + + align:start position:0% +stress in the core is just equal to the + + + align:start position:0% +stress in the core is just equal to the +sheer strength of the core so the sheer + + align:start position:0% +sheer strength of the core so the sheer + + + align:start position:0% +sheer strength of the core so the sheer +stress is + + align:start position:0% +stress is + + + align:start position:0% +stress is +p over B4 * BC and the sheer strength is + + align:start position:0% +p over B4 * BC and the sheer strength is + + + align:start position:0% +p over B4 * BC and the sheer strength is +some constant I think it's + + align:start position:0% +some constant I think it's + + + align:start position:0% +some constant I think it's +C11 times the relative density of the + + align:start position:0% +C11 times the relative density of the + + + align:start position:0% +C11 times the relative density of the +core to the 3es power times the yield + + align:start position:0% +core to the 3es power times the yield + + + align:start position:0% +core to the 3es power times the yield +strength of the solid and here this + + align:start position:0% +strength of the solid and here this + + + align:start position:0% +strength of the solid and here this +constant is about equal + + align:start position:0% +constant is about equal + + + align:start position:0% +constant is about equal +to5 something like + + align:start position:0% + + + + align:start position:0% + +that so now we have a set of equations + + align:start position:0% +that so now we have a set of equations + + + align:start position:0% +that so now we have a set of equations +for the different failure modes and we + + align:start position:0% +for the different failure modes and we + + + align:start position:0% +for the different failure modes and we +could solve each of them not in terms of + + align:start position:0% +could solve each of them not in terms of + + + align:start position:0% +could solve each of them not in terms of +a stress but in terms of a load P the + + align:start position:0% +a stress but in terms of a load P the + + + align:start position:0% +a stress but in terms of a load P the +load p is what's applied to the beam + + align:start position:0% +load p is what's applied to the beam + + + align:start position:0% +load p is what's applied to the beam +right so we could solve each of these in + + align:start position:0% +right so we could solve each of these in + + + align:start position:0% +right so we could solve each of these in +terms of the load p and then we could + + align:start position:0% +terms of the load p and then we could + + + align:start position:0% +terms of the load p and then we could +see which one occurs at the lowest load + + align:start position:0% +see which one occurs at the lowest load + + + align:start position:0% +see which one occurs at the lowest load +p and that's going to be the dominant + + align:start position:0% +p and that's going to be the dominant + + + align:start position:0% +p and that's going to be the dominant +failure mode so one way to do it would + + align:start position:0% +failure mode so one way to do it would + + + align:start position:0% +failure mode so one way to do it would +be to for every time you wanted to do + + align:start position:0% +be to for every time you wanted to do + + + align:start position:0% +be to for every time you wanted to do +this to work out all these three + + align:start position:0% +this to work out all these three + + + align:start position:0% +this to work out all these three +equations and figure out which one's the + + align:start position:0% +equations and figure out which one's the + + + align:start position:0% +equations and figure out which one's the +lowest load but there's actually + + align:start position:0% +lowest load but there's actually + + + align:start position:0% +lowest load but there's actually +something called a failure mode map + + align:start position:0% +something called a failure mode map + + + align:start position:0% +something called a failure mode map +which we're going to talk about so let + + align:start position:0% +which we're going to talk about so let + + + align:start position:0% +which we're going to talk about so let +me just show you it and we'll start now + + align:start position:0% +me just show you it and we'll start now + + + align:start position:0% +me just show you it and we'll start now +I don't know if we'll get to finish this + + align:start position:0% +I don't know if we'll get to finish this + + + align:start position:0% +I don't know if we'll get to finish this +but there's a way that you can + + align:start position:0% +but there's a way that you can + + + align:start position:0% +but there's a way that you can +manipulate these equations and plot the + + align:start position:0% +manipulate these equations and plot the + + + align:start position:0% +manipulate these equations and plot the +results as this failure mode map and + + align:start position:0% +results as this failure mode map and + + + align:start position:0% +results as this failure mode map and +you'll end up plotting the core density + + align:start position:0% +you'll end up plotting the core density + + + align:start position:0% +you'll end up plotting the core density +on this plot on this axis here and the + + align:start position:0% +on this plot on this axis here and the + + + align:start position:0% +on this plot on this axis here and the +face thickness to span ratio here and so + + align:start position:0% +face thickness to span ratio here and so + + + align:start position:0% +face thickness to span ratio here and so +this will kind of tell you um for + + align:start position:0% +this will kind of tell you um for + + + align:start position:0% +this will kind of tell you um for +different configurations of the beam + + align:start position:0% +different configurations of the beam + + + align:start position:0% +different configurations of the beam +different designs you know for these + + align:start position:0% +different designs you know for these + + + align:start position:0% +different designs you know for these +ones here the face is going to wrinkle + + align:start position:0% +ones here the face is going to wrinkle + + + align:start position:0% +ones here the face is going to wrinkle +for those ones there the face is going + + align:start position:0% +for those ones there the face is going + + + align:start position:0% +for those ones there the face is going +to yield and for these ones here the + + align:start position:0% +to yield and for these ones here the + + + align:start position:0% +to yield and for these ones here the +core is going to Shear so I'm going to + + align:start position:0% +core is going to Shear so I'm going to + + + align:start position:0% +core is going to Shear so I'm going to +work through these equations but I don't + + align:start position:0% +work through these equations but I don't + + + align:start position:0% +work through these equations but I don't +think we're going to finish it uh today + + align:start position:0% +think we're going to finish it uh today + + + align:start position:0% +think we're going to finish it uh today +so this is just kind of where we're + + align:start position:0% +so this is just kind of where we're + + + align:start position:0% +so this is just kind of where we're +headed to get is to getting this + + align:start position:0% + + + + align:start position:0% + +map so we'll say the dominant failure + + align:start position:0% +map so we'll say the dominant failure + + + align:start position:0% +map so we'll say the dominant failure +mode + + align:start position:0% +mode + + + align:start position:0% +mode +is the one that occurs at the lowest + + align:start position:0% + + + + align:start position:0% + +load so the question we're going to + + align:start position:0% +load so the question we're going to + + + align:start position:0% +load so the question we're going to +answer is how does the failure mode + + align:start position:0% +answer is how does the failure mode + + + align:start position:0% +answer is how does the failure mode +depend on the beam design + + align:start position:0% + + + + align:start position:0% + +and we're going to do this by looking at + + align:start position:0% +and we're going to do this by looking at + + + align:start position:0% +and we're going to do this by looking at +the transition from one failure mode to + + align:start position:0% + + + + align:start position:0% + +another + + align:start position:0% + + + + align:start position:0% + +so at the transition from one mode to + + align:start position:0% +so at the transition from one mode to + + + align:start position:0% +so at the transition from one mode to +another the two modes occur at the same + + align:start position:0% + + + + align:start position:0% + +load + + align:start position:0% +load + + + align:start position:0% +load +so I'm going to take those equations I + + align:start position:0% +so I'm going to take those equations I + + + align:start position:0% +so I'm going to take those equations I +had for each of the failure modes and + + align:start position:0% +had for each of the failure modes and + + + align:start position:0% +had for each of the failure modes and +instead of writing this in terms of say + + align:start position:0% +instead of writing this in terms of say + + + align:start position:0% +instead of writing this in terms of say +the stress in the face I'm going to + + align:start position:0% +the stress in the face I'm going to + + + align:start position:0% +the stress in the face I'm going to +write it in terms of the load + + align:start position:0% + + + + align:start position:0% + +P so using that first one over there the + + align:start position:0% +P so using that first one over there the + + + align:start position:0% +P so using that first one over there the +load for face yielding I'm just + + align:start position:0% +load for face yielding I'm just + + + align:start position:0% +load for face yielding I'm just +rearranging that it's + + align:start position:0% +rearranging that it's + + + align:start position:0% +rearranging that it's +B3 * + + align:start position:0% + + + + align:start position:0% + +BC * t l * the Y strength of the + + align:start position:0% + + + + align:start position:0% + +face and similarly for face wrinkling I + + align:start position:0% +face and similarly for face wrinkling I + + + align:start position:0% +face and similarly for face wrinkling I +can take this equation down here and + + align:start position:0% +can take this equation down here and + + + align:start position:0% +can take this equation down here and +solve it for this P here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +then I can take that equation at the top + + align:start position:0% +then I can take that equation at the top + + + align:start position:0% +then I can take that equation at the top +and solve that for P2 for the cord sheer + + align:start position:0% +and solve that for P2 for the cord sheer + + + align:start position:0% +and solve that for P2 for the cord sheer +and that's equal to + + align:start position:0% +and that's equal to + + + align:start position:0% +and that's equal to +C11 * B4 * BC * Sigma + + align:start position:0% +C11 * B4 * BC * Sigma + + + align:start position:0% +C11 * B4 * BC * Sigma +Ys times oops wrong thing times the + + align:start position:0% +Ys times oops wrong thing times the + + + align:start position:0% +Ys times oops wrong thing times the +relative density to the 2/3 + + align:start position:0% + + + + align:start position:0% + +power + + align:start position:0% + + + + align:start position:0% + +okay and then the next step is to equate + + align:start position:0% +okay and then the next step is to equate + + + align:start position:0% +okay and then the next step is to equate +these guys so you get a transition from + + align:start position:0% +these guys so you get a transition from + + + align:start position:0% +these guys so you get a transition from +one mode to the other when two of these + + align:start position:0% +one mode to the other when two of these + + + align:start position:0% +one mode to the other when two of these +guys are equal to each other right so + + align:start position:0% +guys are equal to each other right so + + + align:start position:0% +guys are equal to each other right so +there's going to be a transition from + + align:start position:0% +there's going to be a transition from + + + align:start position:0% +there's going to be a transition from +face yielding to face wrinkling when + + align:start position:0% +face yielding to face wrinkling when + + + align:start position:0% +face yielding to face wrinkling when +these guys are equal and I'm not going + + align:start position:0% +these guys are equal and I'm not going + + + align:start position:0% +these guys are equal and I'm not going +to start that because we're going to run + + align:start position:0% +to start that because we're going to run + + + align:start position:0% +to start that because we're going to run +out of time but let me just say that I + + align:start position:0% +out of time but let me just say that I + + + align:start position:0% +out of time but let me just say that I +can pair these two up and say there's a + + align:start position:0% +can pair these two up and say there's a + + + align:start position:0% +can pair these two up and say there's a +transition between those two and that + + align:start position:0% +transition between those two and that + + + align:start position:0% +transition between those two and that +transition is going to correspond to + + align:start position:0% +transition is going to correspond to + + + align:start position:0% +transition is going to correspond to +this line here okay so at this line here + + align:start position:0% +this line here okay so at this line here + + + align:start position:0% +this line here okay so at this line here +that means you get face yielding and + + align:start position:0% +that means you get face yielding and + + + align:start position:0% +that means you get face yielding and +face ring L at the same load okay and + + align:start position:0% +face ring L at the same load okay and + + + align:start position:0% +face ring L at the same load okay and +then if I paired + + align:start position:0% +then if I paired + + + align:start position:0% +then if I paired +up uh let's see here if I paired up face + + align:start position:0% +up uh let's see here if I paired up face + + + align:start position:0% +up uh let's see here if I paired up face +wrinkling and corer these two guys here + + align:start position:0% +wrinkling and corer these two guys here + + + align:start position:0% +wrinkling and corer these two guys here +I'm going to get this equation here on + + align:start position:0% +I'm going to get this equation here on + + + align:start position:0% +I'm going to get this equation here on +that plot and then if I paired up these + + align:start position:0% +that plot and then if I paired up these + + + align:start position:0% +that plot and then if I paired up these +two guys here the face yielding in the + + align:start position:0% +two guys here the face yielding in the + + + align:start position:0% +two guys here the face yielding in the +corer I would get that line there okay + + align:start position:0% +corer I would get that line there okay + + + align:start position:0% +corer I would get that line there okay +so once I have those lines that tells me + + align:start position:0% +so once I have those lines that tells me + + + align:start position:0% +so once I have those lines that tells me +you know anything with a lower density + + align:start position:0% +you know anything with a lower density + + + align:start position:0% +you know anything with a lower density +core and smaller face thickness is going + + align:start position:0% +core and smaller face thickness is going + + + align:start position:0% +core and smaller face thickness is going +to fail by face ring sprinkling anything + + align:start position:0% +to fail by face ring sprinkling anything + + + align:start position:0% +to fail by face ring sprinkling anything +with a bigger density is going to fail + + align:start position:0% +with a bigger density is going to fail + + + align:start position:0% +with a bigger density is going to fail +by face yielding and anything with a + + align:start position:0% +by face yielding and anything with a + + + align:start position:0% +by face yielding and anything with a +larger face thickness and a larger uh + + align:start position:0% +larger face thickness and a larger uh + + + align:start position:0% +larger face thickness and a larger uh +density is going to fail by core + + align:start position:0% +density is going to fail by core + + + align:start position:0% +density is going to fail by core +shearing and sort of you can start to + + align:start position:0% +shearing and sort of you can start to + + + align:start position:0% +shearing and sort of you can start to +see that it um I'll work out the + + align:start position:0% +see that it um I'll work out the + + + align:start position:0% +see that it um I'll work out the +equations next time but you can start to + + align:start position:0% +equations next time but you can start to + + + align:start position:0% +equations next time but you can start to +see that it kind of physically makes + + align:start position:0% +see that it kind of physically makes + + + align:start position:0% +see that it kind of physically makes +sense intuitively this face wrinkling + + align:start position:0% +sense intuitively this face wrinkling + + + align:start position:0% +sense intuitively this face wrinkling +depends on a normal stress in the in the + + align:start position:0% +depends on a normal stress in the in the + + + align:start position:0% +depends on a normal stress in the in the +face in compression so obviously the + + align:start position:0% +face in compression so obviously the + + + align:start position:0% +face in compression so obviously the +thinner the face gets the more likely + + align:start position:0% +thinner the face gets the more likely + + + align:start position:0% +thinner the face gets the more likely +that's going to be to happen so it's + + align:start position:0% +that's going to be to happen so it's + + + align:start position:0% +that's going to be to happen so it's +going to happen at this end of the + + align:start position:0% +going to happen at this end of the + + + align:start position:0% +going to happen at this end of the +diagram and it also depends on that + + align:start position:0% +diagram and it also depends on that + + + align:start position:0% +diagram and it also depends on that +elastic foundation on how much spring + + align:start position:0% +elastic foundation on how much spring + + + align:start position:0% +elastic foundation on how much spring +support the foundation has right so the + + align:start position:0% +support the foundation has right so the + + + align:start position:0% +support the foundation has right so the +lower the core density the more likely + + align:start position:0% +lower the core density the more likely + + + align:start position:0% +lower the core density the more likely +that is to happen then if you say you + + align:start position:0% +that is to happen then if you say you + + + align:start position:0% +that is to happen then if you say you +have small T so that the face is going + + align:start position:0% +have small T so that the face is going + + + align:start position:0% +have small T so that the face is going +to fail before the core as you increase + + align:start position:0% +to fail before the core as you increase + + + align:start position:0% +to fail before the core as you increase +the core density you're making that + + align:start position:0% +the core density you're making that + + + align:start position:0% +the core density you're making that +elastic Foundation stiffer and stiffer + + align:start position:0% +elastic Foundation stiffer and stiffer + + + align:start position:0% +elastic Foundation stiffer and stiffer +and you're making it harder for the + + align:start position:0% +and you're making it harder for the + + + align:start position:0% +and you're making it harder for the +buckling to occur it can't Buckle into + + align:start position:0% +buckling to occur it can't Buckle into + + + align:start position:0% +buckling to occur it can't Buckle into +the elastic foundation so then you're + + align:start position:0% +the elastic foundation so then you're + + + align:start position:0% +the elastic foundation so then you're +going to push it up to the yielding and + + align:start position:0% +going to push it up to the yielding and + + + align:start position:0% +going to push it up to the yielding and +then as you make the face thickness + + align:start position:0% +then as you make the face thickness + + + align:start position:0% +then as you make the face thickness +bigger as T gets bigger then the face + + align:start position:0% +bigger as T gets bigger then the face + + + align:start position:0% +bigger as T gets bigger then the face +isn't going to fail and the core is + + align:start position:0% +isn't going to fail and the core is + + + align:start position:0% +isn't going to fail and the core is +going to fail so you can kind of see + + align:start position:0% +going to fail so you can kind of see + + + align:start position:0% +going to fail so you can kind of see +just looking at the relative position of + + align:start position:0% +just looking at the relative position of + + + align:start position:0% +just looking at the relative position of +those things they all kind of make + + align:start position:0% +those things they all kind of make + + + align:start position:0% +those things they all kind of make +physical sense so I'm going to stop + + align:start position:0% +physical sense so I'm going to stop + + + align:start position:0% +physical sense so I'm going to stop +there for today and I'll finish the + + align:start position:0% +there for today and I'll finish the + + + align:start position:0% +there for today and I'll finish the +equations for that next time and we'll + + align:start position:0% +equations for that next time and we'll + + + align:start position:0% +equations for that next time and we'll +also talk about how to optimize for + + align:start position:0% +also talk about how to optimize for + + + align:start position:0% +also talk about how to optimize for +strength next time and we'll we'll talk + + align:start position:0% +strength next time and we'll we'll talk + + + align:start position:0% +strength next time and we'll we'll talk +about a few other things on sandwich + + align:start position:0% + + + + align:start position:0% + +panels \ No newline at end of file diff --git a/55OXxe_ix2o.txt b/55OXxe_ix2o.txt new file mode 100644 index 0000000000000000000000000000000000000000..814ba49ae8301c4807fa2377ffcb025cc78f5fbc --- /dev/null +++ b/55OXxe_ix2o.txt @@ -0,0 +1,16843 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu guess we can get started + + align:start position:0% +ocw.mit.edu guess we can get started + + + align:start position:0% +ocw.mit.edu guess we can get started +anyway welcome today uh Stefan andreev + + align:start position:0% +anyway welcome today uh Stefan andreev + + + align:start position:0% +anyway welcome today uh Stefan andreev +is our guest speaker from Morgan Stanley + + align:start position:0% +is our guest speaker from Morgan Stanley + + + align:start position:0% +is our guest speaker from Morgan Stanley +and as I understand you have a degree + + align:start position:0% +and as I understand you have a degree + + + align:start position:0% +and as I understand you have a degree +PhD degree in chemical physics in + + align:start position:0% +PhD degree in chemical physics in + + + align:start position:0% +PhD degree in chemical physics in +chemical physics yes maybe I should go + + align:start position:0% +chemical physics yes maybe I should go + + + align:start position:0% +chemical physics yes maybe I should go +here + + align:start position:0% +here + + + align:start position:0% +here +and okay and now he's in the world of + + align:start position:0% +and okay and now he's in the world of + + + align:start position:0% +and okay and now he's in the world of +Finance uh and we're here to benefit + + align:start position:0% +Finance uh and we're here to benefit + + + align:start position:0% +Finance uh and we're here to benefit +from your experience thank you thank you + + align:start position:0% +from your experience thank you thank you + + + align:start position:0% +from your experience thank you thank you +very much for the + + align:start position:0% +very much for the + + + align:start position:0% +very much for the +introduction U yeah I went to um went to + + align:start position:0% +introduction U yeah I went to um went to + + + align:start position:0% +introduction U yeah I went to um went to +school at darmouth College undergrad and + + align:start position:0% +school at darmouth College undergrad and + + + align:start position:0% +school at darmouth College undergrad and +then up the street at Harvard for my + + align:start position:0% +then up the street at Harvard for my + + + align:start position:0% +then up the street at Harvard for my +PhD and then I transitioned from from + + align:start position:0% +PhD and then I transitioned from from + + + align:start position:0% +PhD and then I transitioned from from +science to + + align:start position:0% +science to + + + align:start position:0% +science to +finance and for the last eight years + + align:start position:0% +finance and for the last eight years + + + align:start position:0% +finance and for the last eight years +I've been working K Morgan Stanley + + align:start position:0% +I've been working K Morgan Stanley + + + align:start position:0% +I've been working K Morgan Stanley +working with vasil Estrella the + + align:start position:0% +working with vasil Estrella the + + + align:start position:0% +working with vasil Estrella the +instructor in the + + align:start position:0% +instructor in the + + + align:start position:0% +instructor in the +course + + align:start position:0% +course + + + align:start position:0% +course +um so today what are we going to be + + align:start position:0% +um so today what are we going to be + + + align:start position:0% +um so today what are we going to be +talking about well to give you a a big + + align:start position:0% +talking about well to give you a a big + + + align:start position:0% +talking about well to give you a a big +picture view of where our topic fits + + align:start position:0% +picture view of where our topic fits + + + align:start position:0% +picture view of where our topic fits +within the grant scheme of Finance in + + align:start position:0% +within the grant scheme of Finance in + + + align:start position:0% +within the grant scheme of Finance in +general there really two big areas in my + + align:start position:0% +general there really two big areas in my + + + align:start position:0% +general there really two big areas in my +my view were where well there's probably + + align:start position:0% +my view were where well there's probably + + + align:start position:0% +my view were where well there's probably +more but these are kind of most famous I + + align:start position:0% +more but these are kind of most famous I + + + align:start position:0% +more but these are kind of most famous I +would say areas where + + align:start position:0% +would say areas where + + + align:start position:0% +would say areas where +quantitative uh skills can be are very + + align:start position:0% +quantitative uh skills can be are very + + + align:start position:0% +quantitative uh skills can be are very +valuable in finance and the two areas + + align:start position:0% +valuable in finance and the two areas + + + align:start position:0% +valuable in finance and the two areas +are one one area is is statistics + + align:start position:0% +are one one area is is statistics + + + align:start position:0% +are one one area is is statistics +predictions which is uh essentially said + + align:start position:0% +predictions which is uh essentially said + + + align:start position:0% +predictions which is uh essentially said +given some historical behavior in the + + align:start position:0% +given some historical behavior in the + + + align:start position:0% +given some historical behavior in the +market how do we predict what will + + align:start position:0% +market how do we predict what will + + + align:start position:0% +market how do we predict what will +happen in the + + align:start position:0% +happen in the + + + align:start position:0% +happen in the +future and that's that's certainly a + + align:start position:0% +future and that's that's certainly a + + + align:start position:0% +future and that's that's certainly a +huge industry people have made a ton of + + align:start position:0% +huge industry people have made a ton of + + + align:start position:0% +huge industry people have made a ton of +money applying Cor ative Concepts to + + align:start position:0% +money applying Cor ative Concepts to + + + align:start position:0% +money applying Cor ative Concepts to +that and um but that's not what we're + + align:start position:0% +that and um but that's not what we're + + + align:start position:0% +that and um but that's not what we're +going to talk about today what we're + + align:start position:0% +going to talk about today what we're + + + align:start position:0% +going to talk about today what we're +going to talk about is another very big + + align:start position:0% +going to talk about is another very big + + + align:start position:0% +going to talk about is another very big +area called pricing which is pricing and + + align:start position:0% +area called pricing which is pricing and + + + align:start position:0% +area called pricing which is pricing and +hedging of complex instruments and that + + align:start position:0% +hedging of complex instruments and that + + + align:start position:0% +hedging of complex instruments and that +area is really it's really about + + align:start position:0% +area is really it's really about + + + align:start position:0% +area is really it's really about +um essentially when you have a a complex + + align:start position:0% +um essentially when you have a a complex + + + align:start position:0% +um essentially when you have a a complex +product that you don't really know the + + align:start position:0% +product that you don't really know the + + + align:start position:0% +product that you don't really know the +price of but you do know the prices of + + align:start position:0% +price of but you do know the prices of + + + align:start position:0% +price of but you do know the prices of +other products and then you can know you + + align:start position:0% +other products and then you can know you + + + align:start position:0% +other products and then you can know you +can use the other products to + + align:start position:0% +can use the other products to + + + align:start position:0% +can use the other products to +essentially replicate the payoff of your + + align:start position:0% +essentially replicate the payoff of your + + + align:start position:0% +essentially replicate the payoff of your +complex product then you can use + + align:start position:0% +complex product then you can use + + + align:start position:0% +complex product then you can use +mathematical techniques to essentially + + align:start position:0% +mathematical techniques to essentially + + + align:start position:0% +mathematical techniques to essentially +say look um the main statement is hey + + align:start position:0% +say look um the main statement is hey + + + align:start position:0% +say look um the main statement is hey +because I can replicate my payoff and I + + align:start position:0% +because I can replicate my payoff and I + + + align:start position:0% +because I can replicate my payoff and I +because using products that I know the + + align:start position:0% +because using products that I know the + + + align:start position:0% +because using products that I know the +price of then that means that I I can + + align:start position:0% +price of then that means that I I can + + + align:start position:0% +price of then that means that I I can +say something about the price of my + + align:start position:0% +say something about the price of my + + + align:start position:0% +say something about the price of my +complex product I can basically price it + + align:start position:0% +complex product I can basically price it + + + align:start position:0% +complex product I can basically price it +and not only can I price it but I can + + align:start position:0% +and not only can I price it but I can + + + align:start position:0% +and not only can I price it but I can +also um when I give the price I know + + align:start position:0% +also um when I give the price I know + + + align:start position:0% +also um when I give the price I know +that I can eliminate minate any + + align:start position:0% +that I can eliminate minate any + + + align:start position:0% +that I can eliminate minate any +uncertainty from owning the product by + + align:start position:0% +uncertainty from owning the product by + + + align:start position:0% +uncertainty from owning the product by +by executing a hedging replication + + align:start position:0% +by executing a hedging replication + + + align:start position:0% +by executing a hedging replication +strategy at least theoretically speaking + + align:start position:0% +strategy at least theoretically speaking + + + align:start position:0% +strategy at least theoretically speaking +right so that's the area we're going to + + align:start position:0% +right so that's the area we're going to + + + align:start position:0% +right so that's the area we're going to +focus today and our our main main focus + + align:start position:0% +focus today and our our main main focus + + + align:start position:0% +focus today and our our main main focus +is going to be on FX a foreign exchange + + align:start position:0% +is going to be on FX a foreign exchange + + + align:start position:0% +is going to be on FX a foreign exchange +interest rates in credit and it's + + align:start position:0% +interest rates in credit and it's + + + align:start position:0% +interest rates in credit and it's +particular about credit effects Hybrid + + align:start position:0% +particular about credit effects Hybrid + + + align:start position:0% +particular about credit effects Hybrid +models we're going to be talking about + + align:start position:0% +models we're going to be talking about + + + align:start position:0% +models we're going to be talking about +essenti what happens why do we need Crea + + align:start position:0% +essenti what happens why do we need Crea + + + align:start position:0% +essenti what happens why do we need Crea +effects Hybrid models and go going + + align:start position:0% +effects Hybrid models and go going + + + align:start position:0% +effects Hybrid models and go going +through an example of a simple one and + + align:start position:0% +through an example of a simple one and + + + align:start position:0% +through an example of a simple one and +how to apply it in particular in terms + + align:start position:0% +how to apply it in particular in terms + + + align:start position:0% +how to apply it in particular in terms +of mathematical techniques we're going + + align:start position:0% +of mathematical techniques we're going + + + align:start position:0% +of mathematical techniques we're going +to be using uh as I said we're going to + + align:start position:0% +to be using uh as I said we're going to + + + align:start position:0% +to be using uh as I said we're going to +be talking about risk neutral pricing + + align:start position:0% +be talking about risk neutral pricing + + + align:start position:0% +be talking about risk neutral pricing +which is essentially + + align:start position:0% +which is essentially + + + align:start position:0% +which is essentially +replication and we're going to talk + + align:start position:0% +replication and we're going to talk + + + align:start position:0% +replication and we're going to talk +about how to use jump + + align:start position:0% +about how to use jump + + + align:start position:0% +about how to use jump +processes which is um you might have + + align:start position:0% +processes which is um you might have + + + align:start position:0% +processes which is um you might have +seen in other parts of your studies as + + align:start position:0% +seen in other parts of your studies as + + + align:start position:0% +seen in other parts of your studies as +Pon + + align:start position:0% +Pon + + + align:start position:0% +Pon +processes to to describe certain + + align:start position:0% +processes to to describe certain + + + align:start position:0% +processes to to describe certain +behaviors of um price behavior that that + + align:start position:0% +behaviors of um price behavior that that + + + align:start position:0% +behaviors of um price behavior that that +you cannot really describe very easily + + align:start position:0% +you cannot really describe very easily + + + align:start position:0% +you cannot really describe very easily +using pure diffusion Brown emotions that + + align:start position:0% +using pure diffusion Brown emotions that + + + align:start position:0% +using pure diffusion Brown emotions that +you probably have so have seen so far in + + align:start position:0% +you probably have so have seen so far in + + + align:start position:0% +you probably have so have seen so far in +the + + align:start position:0% +the + + + align:start position:0% +the +course and why do we care about that + + align:start position:0% +course and why do we care about that + + + align:start position:0% +course and why do we care about that +well there are certain Financial + + align:start position:0% +well there are certain Financial + + + align:start position:0% +well there are certain Financial +applications where this is important and + + align:start position:0% +applications where this is important and + + + align:start position:0% +applications where this is important and +in + + align:start position:0% +in + + + align:start position:0% +in +particular something that happened in + + align:start position:0% +particular something that happened in + + + align:start position:0% +particular something that happened in +the last few years this The Sovereign + + align:start position:0% +the last few years this The Sovereign + + + align:start position:0% +the last few years this The Sovereign +crisis in Europe and also it has + + align:start position:0% +crisis in Europe and also it has + + + align:start position:0% +crisis in Europe and also it has +happened not just last year this + + align:start position:0% +happened not just last year this + + + align:start position:0% +happened not just last year this +happened many times in other parts of + + align:start position:0% +happened many times in other parts of + + + align:start position:0% +happened many times in other parts of +emerging markets and given the Market is + + align:start position:0% +emerging markets and given the Market is + + + align:start position:0% +emerging markets and given the Market is +my background I've worked on these kind + + align:start position:0% +my background I've worked on these kind + + + align:start position:0% +my background I've worked on these kind +of models and this is when you have Bond + + align:start position:0% +of models and this is when you have Bond + + + align:start position:0% +of models and this is when you have Bond +Greek Bonds in euros and and there is a + + align:start position:0% +Greek Bonds in euros and and there is a + + + align:start position:0% +Greek Bonds in euros and and there is a +potential for Greek default and as we + + align:start position:0% +potential for Greek default and as we + + + align:start position:0% +potential for Greek default and as we +know as we as you might have um read in + + align:start position:0% +know as we as you might have um read in + + + align:start position:0% +know as we as you might have um read in +the + + align:start position:0% +the + + + align:start position:0% +the +news there was a really a big worry + + align:start position:0% +news there was a really a big worry + + + align:start position:0% +news there was a really a big worry +about what will happen to the + + align:start position:0% +about what will happen to the + + + align:start position:0% +about what will happen to the +eurocurrency if there is a Spate of + + align:start position:0% +eurocurrency if there is a Spate of + + + align:start position:0% +eurocurrency if there is a Spate of +sovereign defaults and in fact + + align:start position:0% +sovereign defaults and in fact + + + align:start position:0% +sovereign defaults and in fact +eurocurrency did in anticipation of + + align:start position:0% +eurocurrency did in anticipation of + + + align:start position:0% +eurocurrency did in anticipation of +possibility of default it actually did + + align:start position:0% +possibility of default it actually did + + + align:start position:0% +possibility of default it actually did +depreciate for a while + + align:start position:0% +depreciate for a while + + + align:start position:0% +depreciate for a while +back in 201 um 2011 and and 2012 now + + align:start position:0% +back in 201 um 2011 and and 2012 now + + + align:start position:0% +back in 201 um 2011 and and 2012 now +it's pretty much back where where it was + + align:start position:0% +it's pretty much back where where it was + + + align:start position:0% +it's pretty much back where where it was +before that but it certainly there was a + + align:start position:0% +before that but it certainly there was a + + + align:start position:0% +before that but it certainly there was a +there was a fear in the market which was + + align:start position:0% +there was a fear in the market which was + + + align:start position:0% +there was a fear in the market which was +also very very obvious in in terms of + + align:start position:0% +also very very obvious in in terms of + + + align:start position:0% +also very very obvious in in terms of +option prices + + align:start position:0% +option prices + + + align:start position:0% +option prices +that eurocurrency could depreciate + + align:start position:0% +that eurocurrency could depreciate + + + align:start position:0% +that eurocurrency could depreciate +significantly if in fact a disorderly + + align:start position:0% +significantly if in fact a disorderly + + + align:start position:0% +significantly if in fact a disorderly +default happened now it didn't happen so + + align:start position:0% +default happened now it didn't happen so + + + align:start position:0% +default happened now it didn't happen so +that's kind of that's good but in other + + align:start position:0% +that's kind of that's good but in other + + + align:start position:0% +that's kind of that's good but in other +emerging markets in history it has + + align:start position:0% +emerging markets in history it has + + + align:start position:0% +emerging markets in history it has +happened before + + align:start position:0% +happened before + + + align:start position:0% +happened before +so it's not it's not really a kind of an + + align:start position:0% +so it's not it's not really a kind of an + + + align:start position:0% +so it's not it's not really a kind of an +empty question so foreign exchange how + + align:start position:0% +empty question so foreign exchange how + + + align:start position:0% +empty question so foreign exchange how +do we describe it in math Finance what + + align:start position:0% +do we describe it in math Finance what + + + align:start position:0% +do we describe it in math Finance what +we think of it is the price of a unit of + + align:start position:0% +we think of it is the price of a unit of + + + align:start position:0% +we think of it is the price of a unit of +foreign currency in dollars we in our + + align:start position:0% +foreign currency in dollars we in our + + + align:start position:0% +foreign currency in dollars we in our +presentation we're going to denote the + + align:start position:0% +presentation we're going to denote the + + + align:start position:0% +presentation we're going to denote the +spot FX rate which is the current rate + + align:start position:0% +spot FX rate which is the current rate + + + align:start position:0% +spot FX rate which is the current rate +of exchange by S and here is a sample + + align:start position:0% +of exchange by S and here is a sample + + + align:start position:0% +of exchange by S and here is a sample +graph of f USD FX rate you can see it + + align:start position:0% +graph of f USD FX rate you can see it + + + align:start position:0% +graph of f USD FX rate you can see it +looks like a random walk um it's very + + align:start position:0% +looks like a random walk um it's very + + + align:start position:0% +looks like a random walk um it's very +very well described in normal + + align:start position:0% +very well described in normal + + + align:start position:0% +very well described in normal +circumstances a random walk + + align:start position:0% + + + + align:start position:0% + +walk so one um kind of very fundamental + + align:start position:0% +walk so one um kind of very fundamental + + + align:start position:0% +walk so one um kind of very fundamental +property that connects FX and interest + + align:start position:0% +property that connects FX and interest + + + align:start position:0% +property that connects FX and interest +rate interest rates is the so-called FX + + align:start position:0% +rate interest rates is the so-called FX + + + align:start position:0% +rate interest rates is the so-called FX +forwards interest rate + + align:start position:0% +forwards interest rate + + + align:start position:0% +forwards interest rate +parity which + + align:start position:0% +parity which + + + align:start position:0% +parity which +says if uh if I have a certain amount of + + align:start position:0% +says if uh if I have a certain amount of + + + align:start position:0% +says if uh if I have a certain amount of +money in this example $5 + + align:start position:0% +money in this example $5 + + + align:start position:0% +money in this example $5 +million I really have + + align:start position:0% +million I really have + + + align:start position:0% +million I really have +um if if I and I can invest it there's + + align:start position:0% +um if if I and I can invest it there's + + + align:start position:0% +um if if I and I can invest it there's +two ways that I can utilize this money + + align:start position:0% +two ways that I can utilize this money + + + align:start position:0% +two ways that I can utilize this money +to one way is to just invest at a dollar + + align:start position:0% +to one way is to just invest at a dollar + + + align:start position:0% +to one way is to just invest at a dollar +kind of risk-free rate and we're + + align:start position:0% +kind of risk-free rate and we're + + + align:start position:0% +kind of risk-free rate and we're +assuming here we have a risk-free rate + + align:start position:0% +assuming here we have a risk-free rate + + + align:start position:0% +assuming here we have a risk-free rate +so that standard assumption or we can do + + align:start position:0% +so that standard assumption or we can do + + + align:start position:0% +so that standard assumption or we can do +something like we can take the money + + align:start position:0% +something like we can take the money + + + align:start position:0% +something like we can take the money +exchange it into into say Euros invest + + align:start position:0% +exchange it into into say Euros invest + + + align:start position:0% +exchange it into into say Euros invest +it using the euro risk-free rate and + + align:start position:0% +it using the euro risk-free rate and + + + align:start position:0% +it using the euro risk-free rate and +then exchange it back into + + align:start position:0% +then exchange it back into + + + align:start position:0% +then exchange it back into +dollars and if we're and this is + + align:start position:0% +dollars and if we're and this is + + + align:start position:0% +dollars and if we're and this is +essentially used to to replic to price + + align:start position:0% +essentially used to to replic to price + + + align:start position:0% +essentially used to to replic to price +FX forward contracts so FX forward + + align:start position:0% +FX forward contracts so FX forward + + + align:start position:0% +FX forward contracts so FX forward +contracts are cont ract that allow you + + align:start position:0% +contracts are cont ract that allow you + + + align:start position:0% +contracts are cont ract that allow you +to say look I'm going to agree with you + + align:start position:0% +to say look I'm going to agree with you + + + align:start position:0% +to say look I'm going to agree with you +then in one month's time I'm going to + + align:start position:0% +then in one month's time I'm going to + + + align:start position:0% +then in one month's time I'm going to +say give you um 4 4,8 and 45 and you're + + align:start position:0% +say give you um 4 4,8 and 45 and you're + + + align:start position:0% +say give you um 4 4,8 and 45 and you're +going to give me back $ 5,870 + + align:start position:0% +going to give me back $ 5,870 + + + align:start position:0% +going to give me back $ 5,870 +th000 it's a it's essentially an + + align:start position:0% +th000 it's a it's essentially an + + + align:start position:0% +th000 it's a it's essentially an +agreement it's a derivative contract and + + align:start position:0% +agreement it's a derivative contract and + + + align:start position:0% +agreement it's a derivative contract and +if you see the if you have this forward + + align:start position:0% +if you see the if you have this forward + + + align:start position:0% +if you see the if you have this forward +contract you can lock in essentially + + align:start position:0% +contract you can lock in essentially + + + align:start position:0% +contract you can lock in essentially +through conversion in Euros so you can + + align:start position:0% +through conversion in Euros so you can + + + align:start position:0% +through conversion in Euros so you can +lock in an effective dollar interest + + align:start position:0% +lock in an effective dollar interest + + + align:start position:0% +lock in an effective dollar interest +rate so FX forwards can be be + + align:start position:0% +rate so FX forwards can be be + + + align:start position:0% +rate so FX forwards can be be +essentially described fully by knowing + + align:start position:0% +essentially described fully by knowing + + + align:start position:0% +essentially described fully by knowing +the interest rates in each currency and + + align:start position:0% +the interest rates in each currency and + + + align:start position:0% +the interest rates in each currency and +the spot effects rate conversely you can + + align:start position:0% +the spot effects rate conversely you can + + + align:start position:0% +the spot effects rate conversely you can +infer foreign interest rates knowing the + + align:start position:0% +infer foreign interest rates knowing the + + + align:start position:0% +infer foreign interest rates knowing the +effect forwards + + align:start position:0% +effect forwards + + + align:start position:0% +effect forwards +they're they're very + + align:start position:0% + + + + align:start position:0% + +connected yes in this example there's no + + align:start position:0% +connected yes in this example there's no + + + align:start position:0% +connected yes in this example there's no +mispricing so you get back the same + + align:start position:0% +mispricing so you get back the same + + + align:start position:0% +mispricing so you get back the same +amount is that the idea in this example + + align:start position:0% +amount is that the idea in this example + + + align:start position:0% +amount is that the idea in this example +there is no mispricing you get back the + + align:start position:0% +there is no mispricing you get back the + + + align:start position:0% +there is no mispricing you get back the +same amount so we're assuming + + align:start position:0% +same amount so we're assuming + + + align:start position:0% +same amount so we're assuming +essentially that there's no Arbitrage uh + + align:start position:0% +essentially that there's no Arbitrage uh + + + align:start position:0% +essentially that there's no Arbitrage uh +we're not assuming but we're given if + + align:start position:0% +we're not assuming but we're given if + + + align:start position:0% +we're not assuming but we're given if +the prices were indeed if this interest + + align:start position:0% +the prices were indeed if this interest + + + align:start position:0% +the prices were indeed if this interest +rate 4.6% in Euros interest rate was 4.6 + + align:start position:0% +rate 4.6% in Euros interest rate was 4.6 + + + align:start position:0% +rate 4.6% in Euros interest rate was 4.6 +and in dollars is 3.4 and here are the + + align:start position:0% +and in dollars is 3.4 and here are the + + + align:start position:0% +and in dollars is 3.4 and here are the +current spots which is 127 and the + + align:start position:0% +current spots which is 127 and the + + + align:start position:0% +current spots which is 127 and the +forward + + align:start position:0% +forward + + + align:start position:0% +forward +125 if these were in fact the the + + align:start position:0% +125 if these were in fact the the + + + align:start position:0% +125 if these were in fact the the +observable Mark quantities in the market + + align:start position:0% +observable Mark quantities in the market + + + align:start position:0% +observable Mark quantities in the market +then there would be no + + align:start position:0% +then there would be no + + + align:start position:0% +then there would be no +Arbitrage and there is you're basically + + align:start position:0% +Arbitrage and there is you're basically + + + align:start position:0% +Arbitrage and there is you're basically +indifferent whether you invest the money + + align:start position:0% +indifferent whether you invest the money + + + align:start position:0% +indifferent whether you invest the money +in dollars or you go the way of + + align:start position:0% +in dollars or you go the way of + + + align:start position:0% +in dollars or you go the way of +exchanging into euros and invest in + + align:start position:0% +exchanging into euros and invest in + + + align:start position:0% +exchanging into euros and invest in +euros and then back into dollar + + align:start position:0% +euros and then back into dollar + + + align:start position:0% +euros and then back into dollar +so in this example the way I've I've + + align:start position:0% +so in this example the way I've I've + + + align:start position:0% +so in this example the way I've I've +presented worked it out there is no + + align:start position:0% +presented worked it out there is no + + + align:start position:0% +presented worked it out there is no +Arbitrage now if some of these numbers + + align:start position:0% +Arbitrage now if some of these numbers + + + align:start position:0% +Arbitrage now if some of these numbers +say if the interest rate in Euros were + + align:start position:0% +say if the interest rate in Euros were + + + align:start position:0% +say if the interest rate in Euros were +4% instead of 4.6 and all the other + + align:start position:0% +4% instead of 4.6 and all the other + + + align:start position:0% +4% instead of 4.6 and all the other +quantities were the same then in fact + + align:start position:0% +quantities were the same then in fact + + + align:start position:0% +quantities were the same then in fact +there would be + + align:start position:0% +there would be + + + align:start position:0% +there would be +Arbitrage and you could make money by + + align:start position:0% +Arbitrage and you could make money by + + + align:start position:0% +Arbitrage and you could make money by +borrowing money in dollars + + align:start position:0% +borrowing money in dollars + + + align:start position:0% +borrowing money in dollars +and you know + + align:start position:0% + + + + align:start position:0% + +investing I mean this the purpose of + + align:start position:0% +investing I mean this the purpose of + + + align:start position:0% +investing I mean this the purpose of +this slide is really to illustrate kind + + align:start position:0% +this slide is really to illustrate kind + + + align:start position:0% +this slide is really to illustrate kind +of hey if there's no Arbitrage how how + + align:start position:0% +of hey if there's no Arbitrage how how + + + align:start position:0% +of hey if there's no Arbitrage how how +one would actually compare how one would + + align:start position:0% +one would actually compare how one would + + + align:start position:0% +one would actually compare how one would +actually look for Arbitrage in this + + align:start position:0% +actually look for Arbitrage in this + + + align:start position:0% +actually look for Arbitrage in this +example uh this is again this is a + + align:start position:0% +example uh this is again this is a + + + align:start position:0% +example uh this is again this is a +little bit of definition what are um + + align:start position:0% +little bit of definition what are um + + + align:start position:0% +little bit of definition what are um +interest compound interest interest + + align:start position:0% +interest compound interest interest + + + align:start position:0% +interest compound interest interest +rates we um we're talking we're going to + + align:start position:0% +rates we um we're talking we're going to + + + align:start position:0% +rates we um we're talking we're going to +talk about instantaneous risk-free rates + + align:start position:0% +talk about instantaneous risk-free rates + + + align:start position:0% +talk about instantaneous risk-free rates +we're going to again say they're + + align:start position:0% +we're going to again say they're + + + align:start position:0% +we're going to again say they're +risk-free so we're not basically we know + + align:start position:0% +risk-free so we're not basically we know + + + align:start position:0% +risk-free so we're not basically we know +for sure that we're going to get our + + align:start position:0% +for sure that we're going to get our + + + align:start position:0% +for sure that we're going to get our +money back you can think of risk-free + + align:start position:0% +money back you can think of risk-free + + + align:start position:0% +money back you can think of risk-free +rates as as the one that uh treasuries + + align:start position:0% +rates as as the one that uh treasuries + + + align:start position:0% +rates as as the one that uh treasuries +pay or in real life or the one that + + align:start position:0% +pay or in real life or the one that + + + align:start position:0% +pay or in real life or the one that +Federal Reserve guarantees on deposits + + align:start position:0% +Federal Reserve guarantees on deposits + + + align:start position:0% +Federal Reserve guarantees on deposits +there are various uh various example of + + align:start position:0% +there are various uh various example of + + + align:start position:0% +there are various uh various example of +risk-free rates and while in practice + + align:start position:0% +risk-free rates and while in practice + + + align:start position:0% +risk-free rates and while in practice +different risk rates can actually be + + align:start position:0% +different risk rates can actually be + + + align:start position:0% +different risk rates can actually be +different so they're not really risk- + + align:start position:0% +different so they're not really risk- + + + align:start position:0% +different so they're not really risk- +free but in our in our world right now + + align:start position:0% +free but in our in our world right now + + + align:start position:0% +free but in our in our world right now +in our model we're going to assume that + + align:start position:0% +in our model we're going to assume that + + + align:start position:0% +in our model we're going to assume that +there is such a thing as a risk- free + + align:start position:0% +there is such a thing as a risk- free + + + align:start position:0% +there is such a thing as a risk- free +risk-free rate for every currency and + + align:start position:0% +risk-free rate for every currency and + + + align:start position:0% +risk-free rate for every currency and +it's + + align:start position:0% +it's + + + align:start position:0% +it's +Unique and now as we talk about our + + align:start position:0% +Unique and now as we talk about our + + + align:start position:0% +Unique and now as we talk about our +dynamics of the interest rate of the + + align:start position:0% +dynamics of the interest rate of the + + + align:start position:0% +dynamics of the interest rate of the +sorry the effect process what we really + + align:start position:0% +sorry the effect process what we really + + + align:start position:0% +sorry the effect process what we really +focused on here is is an effect we're + + align:start position:0% +focused on here is is an effect we're + + + align:start position:0% +focused on here is is an effect we're +making an fx model and we want to see in + + align:start position:0% +making an fx model and we want to see in + + + align:start position:0% +making an fx model and we want to see in +the previous example we saw hey here + + align:start position:0% +the previous example we saw hey here + + + align:start position:0% +the previous example we saw hey here +given an fx rate and given some interest + + align:start position:0% +given an fx rate and given some interest + + + align:start position:0% +given an fx rate and given some interest +rates here is what the FX forward really + + align:start position:0% +rates here is what the FX forward really + + + align:start position:0% +rates here is what the FX forward really +has to be in order to have no + + align:start position:0% +has to be in order to have no + + + align:start position:0% +has to be in order to have no +Arbitrage well now we're trying to + + align:start position:0% +Arbitrage well now we're trying to + + + align:start position:0% +Arbitrage well now we're trying to +describe when we try to describe a + + align:start position:0% +describe when we try to describe a + + + align:start position:0% +describe when we try to describe a +Define a process for the FX + + align:start position:0% + + + + align:start position:0% + +currency essentially this kind of no + + align:start position:0% +currency essentially this kind of no + + + align:start position:0% +currency essentially this kind of no +Arbitrage condition leads to having a + + align:start position:0% +Arbitrage condition leads to having a + + + align:start position:0% +Arbitrage condition leads to having a +certain + + align:start position:0% +certain + + + align:start position:0% +certain +um have leads to having a certain + + align:start position:0% +um have leads to having a certain + + + align:start position:0% +um have leads to having a certain +constraints on what the stochastic + + align:start position:0% +constraints on what the stochastic + + + align:start position:0% +constraints on what the stochastic +differential equation has to be so in + + align:start position:0% +differential equation has to be so in + + + align:start position:0% +differential equation has to be so in +this particular case the constraint is + + align:start position:0% +this particular case the constraint is + + + align:start position:0% +this particular case the constraint is +that um the drift of the process has to + + align:start position:0% +that um the drift of the process has to + + + align:start position:0% +that um the drift of the process has to +be the differential in interest + + align:start position:0% +be the differential in interest + + + align:start position:0% +be the differential in interest +rates so if one currency pays more than + + align:start position:0% +rates so if one currency pays more than + + + align:start position:0% +rates so if one currency pays more than +the other + + align:start position:0% +the other + + + align:start position:0% +the other +currency obviously people would want to + + align:start position:0% +currency obviously people would want to + + + align:start position:0% +currency obviously people would want to +invest in that currency so that in order + + align:start position:0% +invest in that currency so that in order + + + align:start position:0% +invest in that currency so that in order +for no Arbitrage to exist there has to + + align:start position:0% +for no Arbitrage to exist there has to + + + align:start position:0% +for no Arbitrage to exist there has to +be an expectation that currency would + + align:start position:0% +be an expectation that currency would + + + align:start position:0% +be an expectation that currency would +the currency that pays more would + + align:start position:0% +the currency that pays more would + + + align:start position:0% +the currency that pays more would +depreciate in the future otherwise it + + align:start position:0% +depreciate in the future otherwise it + + + align:start position:0% +depreciate in the future otherwise it +would be an + + align:start position:0% +would be an + + + align:start position:0% +would be an +Arbitrage so if it doesn't depreciate if + + align:start position:0% +Arbitrage so if it doesn't depreciate if + + + align:start position:0% +Arbitrage so if it doesn't depreciate if +if you if you can sign of say hey this + + align:start position:0% +if you if you can sign of say hey this + + + align:start position:0% +if you if you can sign of say hey this +currency w't depreciate then you can + + align:start position:0% +currency w't depreciate then you can + + + align:start position:0% +currency w't depreciate then you can +just always invest in that currency that + + align:start position:0% +just always invest in that currency that + + + align:start position:0% +just always invest in that currency that +pays higher interest rates and make + + align:start position:0% +pays higher interest rates and make + + + align:start position:0% +pays higher interest rates and make +money which in fact many people do but + + align:start position:0% +money which in fact many people do but + + + align:start position:0% +money which in fact many people do but +again that's a they're taking a certain + + align:start position:0% +again that's a they're taking a certain + + + align:start position:0% +again that's a they're taking a certain +risk they're taking the risk that the + + align:start position:0% +risk they're taking the risk that the + + + align:start position:0% +risk they're taking the risk that the +currency will + + align:start position:0% +currency will + + + align:start position:0% +currency will +depreciate so what do we actually want + + align:start position:0% +depreciate so what do we actually want + + + align:start position:0% +depreciate so what do we actually want +uh what we want is to say + + align:start position:0% +uh what we want is to say + + + align:start position:0% +uh what we want is to say +we want to + + align:start position:0% +we want to + + + align:start position:0% +we want to +essentially enforce this Arbitrage + + align:start position:0% +essentially enforce this Arbitrage + + + align:start position:0% +essentially enforce this Arbitrage +conditions from before which is to say + + align:start position:0% +conditions from before which is to say + + + align:start position:0% +conditions from before which is to say +that my forward rate has to be + + align:start position:0% +that my forward rate has to be + + + align:start position:0% +that my forward rate has to be +essentially the spot + + align:start position:0% +essentially the spot + + + align:start position:0% +essentially the spot +rate + + align:start position:0% +rate + + + align:start position:0% +rate +um has has to be the spot rate time well + + align:start position:0% +um has has to be the spot rate time well + + + align:start position:0% +um has has to be the spot rate time well +this condition here has to be observed + + align:start position:0% +this condition here has to be observed + + + align:start position:0% +this condition here has to be observed +essentially and what does that mean it + + align:start position:0% +essentially and what does that mean it + + + align:start position:0% +essentially and what does that mean it +means that my forward + + align:start position:0% +means that my forward + + + align:start position:0% +means that my forward +rate has to be my SP what did you + + align:start position:0% +rate has to be my SP what did you + + + align:start position:0% +rate has to be my SP what did you +sayal to each other yes yeah my spot + + align:start position:0% +sayal to each other yes yeah my spot + + + align:start position:0% +sayal to each other yes yeah my spot +rate has to my forward rate has to be + + align:start position:0% +rate has to my forward rate has to be + + + align:start position:0% +rate has to my forward rate has to be +equal to the spot rate times um times + + align:start position:0% +equal to the spot rate times um times + + + align:start position:0% +equal to the spot rate times um times +essentially the interest rate + + align:start position:0% +essentially the interest rate + + + align:start position:0% +essentially the interest rate +differential if that is true then then + + align:start position:0% +differential if that is true then then + + + align:start position:0% +differential if that is true then then +uh this previous condition previous uh + + align:start position:0% +uh this previous condition previous uh + + + align:start position:0% +uh this previous condition previous uh +risk the AR in the previous setup there + + align:start position:0% +risk the AR in the previous setup there + + + align:start position:0% +risk the AR in the previous setup there +will be no + + align:start position:0% +will be no + + + align:start position:0% +will be no +Arbitrage and why is that well that's + + align:start position:0% +Arbitrage and why is that well that's + + + align:start position:0% +Arbitrage and why is that well that's +because you know the am the amount of + + align:start position:0% +because you know the am the amount of + + + align:start position:0% +because you know the am the amount of +money I earn on the on the domestic leg + + align:start position:0% +money I earn on the on the domestic leg + + + align:start position:0% +money I earn on the on the domestic leg +is um e to the Rd the amount of money I + + align:start position:0% +is um e to the Rd the amount of money I + + + align:start position:0% +is um e to the Rd the amount of money I +earn on the foreign leg is e to the RF + + align:start position:0% +earn on the foreign leg is e to the RF + + + align:start position:0% +earn on the foreign leg is e to the RF +but then I multiply by by the forward + + align:start position:0% +but then I multiply by by the forward + + + align:start position:0% +but then I multiply by by the forward +and that has to equal to the e to the + + align:start position:0% +and that has to equal to the e to the + + + align:start position:0% +and that has to equal to the e to the +Rd + + align:start position:0% +Rd + + + align:start position:0% +Rd +so + + align:start position:0% +so + + + align:start position:0% +so +um this is a standard this is a very + + align:start position:0% +um this is a standard this is a very + + + align:start position:0% +um this is a standard this is a very +based this is the most basic + + align:start position:0% +based this is the most basic + + + align:start position:0% +based this is the most basic +Dynamic FX model that um that people use + + align:start position:0% +Dynamic FX model that um that people use + + + align:start position:0% +Dynamic FX model that um that people use +in industry it's kind of referred to as + + align:start position:0% +in industry it's kind of referred to as + + + align:start position:0% +in industry it's kind of referred to as +the black Shaws FX model and in the + + align:start position:0% +the black Shaws FX model and in the + + + align:start position:0% +the black Shaws FX model and in the +stock price you've you've seen + + align:start position:0% +stock price you've you've seen + + + align:start position:0% +stock price you've you've seen +stochastic models before usually as is a + + align:start position:0% +stochastic models before usually as is a + + + align:start position:0% +stochastic models before usually as is a +stock price when people talk about + + align:start position:0% +stock price when people talk about + + + align:start position:0% +stock price when people talk about +options in uh in that case this um this + + align:start position:0% +options in uh in that case this um this + + + align:start position:0% +options in uh in that case this um this +drift is just um it's just a risk-free + + align:start position:0% +drift is just um it's just a risk-free + + + align:start position:0% +drift is just um it's just a risk-free +interest rate well here in F it's it's a + + align:start position:0% +interest rate well here in F it's it's a + + + align:start position:0% +interest rate well here in F it's it's a +differential of interest + + align:start position:0% +differential of interest + + + align:start position:0% +differential of interest +rates otherwise it's very + + align:start position:0% +rates otherwise it's very + + + align:start position:0% +rates otherwise it's very +similar + + align:start position:0% +similar + + + align:start position:0% +similar +so it has some FX has some interesting + + align:start position:0% +so it has some FX has some interesting + + + align:start position:0% +so it has some FX has some interesting +property + + align:start position:0% +property + + + align:start position:0% +property +so we're going to talk about the game + + align:start position:0% +so we're going to talk about the game + + + align:start position:0% +so we're going to talk about the game +and before we go to that game one + + align:start position:0% +and before we go to that game one + + + align:start position:0% +and before we go to that game one +question can FX exchange rate can ever + + align:start position:0% +question can FX exchange rate can ever + + + align:start position:0% +question can FX exchange rate can ever +be is can it ever be + + align:start position:0% +be is can it ever be + + + align:start position:0% +be is can it ever be +negative what do you guys + + align:start position:0% +negative what do you guys + + + align:start position:0% +negative what do you guys +think can dollar year exchange rate be + + align:start position:0% + + + + align:start position:0% + +negative any + + align:start position:0% +negative any + + + align:start position:0% +negative any +ideas no it's hard what does it negative + + align:start position:0% +ideas no it's hard what does it negative + + + align:start position:0% +ideas no it's hard what does it negative +mean + + align:start position:0% +mean + + + align:start position:0% +mean +means um I have to pay you money to give + + align:start position:0% +means um I have to pay you money to give + + + align:start position:0% +means um I have to pay you money to give +you Euros why why would you have that or + + align:start position:0% +you Euros why why would you have that or + + + align:start position:0% +you Euros why why would you have that or +you have to pay me money to give me + + align:start position:0% +you have to pay me money to give me + + + align:start position:0% +you have to pay me money to give me +Euros nobody would do that it can be + + align:start position:0% +Euros nobody would do that it can be + + + align:start position:0% +Euros nobody would do that it can be +zero potentially if + + align:start position:0% +zero potentially if + + + align:start position:0% +zero potentially if +you say dollars the worthless or + + align:start position:0% +you say dollars the worthless or + + + align:start position:0% +you say dollars the worthless or +something but you can but it's really it + + align:start position:0% +something but you can but it's really it + + + align:start position:0% +something but you can but it's really it +cannot really be negative so that's one + + align:start position:0% +cannot really be negative so that's one + + + align:start position:0% +cannot really be negative so that's one +reason why I wrote um my SD is a is a + + align:start position:0% +reason why I wrote um my SD is a is a + + + align:start position:0% +reason why I wrote um my SD is a is a +kind of a log normal process you + + align:start position:0% +kind of a log normal process you + + + align:start position:0% +kind of a log normal process you +recognize this by by the form DS over s + + align:start position:0% +recognize this by by the form DS over s + + + align:start position:0% +recognize this by by the form DS over s +so the changes in in the FX are + + align:start position:0% +so the changes in in the FX are + + + align:start position:0% +so the changes in in the FX are +proportional to the value of the effect + + align:start position:0% +proportional to the value of the effect + + + align:start position:0% +proportional to the value of the effect +so the the process can never become + + align:start position:0% +so the the process can never become + + + align:start position:0% +so the the process can never become +negative okay so it can it can never be + + align:start position:0% +negative okay so it can it can never be + + + align:start position:0% +negative okay so it can it can never be +become negative but how big can it + + align:start position:0% + + + + align:start position:0% + +get and the answer is it can get very + + align:start position:0% +get and the answer is it can get very + + + align:start position:0% +get and the answer is it can get very +big I mean we have currencies um notably + + align:start position:0% +big I mean we have currencies um notably + + + align:start position:0% +big I mean we have currencies um notably +some currencies like Zimbabwe and + + align:start position:0% +some currencies like Zimbabwe and + + + align:start position:0% +some currencies like Zimbabwe and +dollars that traded I don't know I mean + + align:start position:0% +dollars that traded I don't know I mean + + + align:start position:0% +dollars that traded I don't know I mean +I actually don't know where Zimbabwe and + + align:start position:0% +I actually don't know where Zimbabwe and + + + align:start position:0% +I actually don't know where Zimbabwe and +dollars trade at but I I think it's + + align:start position:0% +dollars trade at but I I think it's + + + align:start position:0% +dollars trade at but I I think it's +somewhere in the billions of Zimbabwean + + align:start position:0% +somewhere in the billions of Zimbabwean + + + align:start position:0% +somewhere in the billions of Zimbabwean +dollars per per dollar or something like + + align:start position:0% +dollars per per dollar or something like + + + align:start position:0% +dollars per per dollar or something like +it's some really extreme examples it can + + align:start position:0% +it's some really extreme examples it can + + + align:start position:0% +it's some really extreme examples it can +really get extremely big so there is no + + align:start position:0% +really get extremely big so there is no + + + align:start position:0% +really get extremely big so there is no +really upper bound while there is a + + align:start position:0% +really upper bound while there is a + + + align:start position:0% +really upper bound while there is a +lower bound so distribution as you can + + align:start position:0% +lower bound so distribution as you can + + + align:start position:0% +lower bound so distribution as you can +imagine has a SK it's not symmetric + + align:start position:0% +imagine has a SK it's not symmetric + + + align:start position:0% +imagine has a SK it's not symmetric +around the around the average it's it's + + align:start position:0% +around the around the average it's it's + + + align:start position:0% +around the around the average it's it's +limited on the on the lower side it's + + align:start position:0% +limited on the on the lower side it's + + + align:start position:0% +limited on the on the lower side it's +can go very high on the high side log + + align:start position:0% +can go very high on the high side log + + + align:start position:0% +can go very high on the high side log +normal distribution has that property + + align:start position:0% +normal distribution has that property + + + align:start position:0% +normal distribution has that property +have you guys seen log normal + + align:start position:0% +have you guys seen log normal + + + align:start position:0% +have you guys seen log normal +distribution you've talked about that + + align:start position:0% +distribution you've talked about that + + + align:start position:0% +distribution you've talked about that +stuff in the course before + + align:start position:0% +stuff in the course before + + + align:start position:0% +stuff in the course before +right so let's go back to our game + + align:start position:0% +right so let's go back to our game + + + align:start position:0% +right so let's go back to our game +um so our game is we have assumptions + + align:start position:0% +um so our game is we have assumptions + + + align:start position:0% +um so our game is we have assumptions +our and my assumptions are not to be + + align:start position:0% +our and my assumptions are not to be + + + align:start position:0% +our and my assumptions are not to be +realistic but to make it simple let's + + align:start position:0% +realistic but to make it simple let's + + + align:start position:0% +realistic but to make it simple let's +assume that our dollars and euros + + align:start position:0% +assume that our dollars and euros + + + align:start position:0% +assume that our dollars and euros +exchange rate is one so we can exchange + + align:start position:0% +exchange rate is one so we can exchange + + + align:start position:0% +exchange rate is one so we can exchange +one Euro for one dollar clearly not + + align:start position:0% +one Euro for one dollar clearly not + + + align:start position:0% +one Euro for one dollar clearly not +exactly the case but let's make that + + align:start position:0% +exactly the case but let's make that + + + align:start position:0% +exactly the case but let's make that +assumption and we also assume that the + + align:start position:0% +assumption and we also assume that the + + + align:start position:0% +assumption and we also assume that the +FX forward is one which basically means + + align:start position:0% +FX forward is one which basically means + + + align:start position:0% +FX forward is one which basically means +that the interest rates in both + + align:start position:0% +that the interest rates in both + + + align:start position:0% +that the interest rates in both +currencies are the + + align:start position:0% +currencies are the + + + align:start position:0% +currencies are the +same and now let's + + align:start position:0% +same and now let's + + + align:start position:0% +same and now let's +say I'm going to make you a bet + + align:start position:0% +say I'm going to make you a bet + + + align:start position:0% +say I'm going to make you a bet +that now dollars and Euros is a is a + + align:start position:0% +that now dollars and Euros is a is a + + + align:start position:0% +that now dollars and Euros is a is a +volatile process it can right now it's + + align:start position:0% +volatile process it can right now it's + + + align:start position:0% +volatile process it can right now it's +one but in the future it could be + + align:start position:0% +one but in the future it could be + + + align:start position:0% +one but in the future it could be +different from one it could be higher or + + align:start position:0% +different from one it could be higher or + + + align:start position:0% +different from one it could be higher or +lower so if dollar euro FX process is + + align:start position:0% +lower so if dollar euro FX process is + + + align:start position:0% +lower so if dollar euro FX process is +more than one in one month then um you + + align:start position:0% +more than one in one month then um you + + + align:start position:0% +more than one in one month then um you +give me money and then if it's uh less + + align:start position:0% +give me money and then if it's uh less + + + align:start position:0% +give me money and then if it's uh less +than one in one months then I give you + + align:start position:0% +than one in one months then I give you + + + align:start position:0% +than one in one months then I give you +money and we're going to have two + + align:start position:0% +money and we're going to have two + + + align:start position:0% +money and we're going to have two +payoffs so two two + + align:start position:0% +payoffs so two two + + + align:start position:0% +payoffs so two two +games I don't know why it says bet Beach + + align:start position:0% +games I don't know why it says bet Beach + + + align:start position:0% +games I don't know why it says bet Beach +say just bet I'm sorry about that um + + align:start position:0% +say just bet I'm sorry about that um + + + align:start position:0% +say just bet I'm sorry about that um +that + + align:start position:0% +that + + + align:start position:0% +that +in the payoff + + align:start position:0% +in the payoff + + + align:start position:0% +in the payoff +a basically you're going to give me + + align:start position:0% +a basically you're going to give me + + + align:start position:0% +a basically you're going to give me +$100 if I win and I'm going to give you + + align:start position:0% +$100 if I win and I'm going to give you + + + align:start position:0% +$100 if I win and I'm going to give you +$100 if you win and in Pay of B you're + + align:start position:0% +$100 if you win and in Pay of B you're + + + align:start position:0% +$100 if you win and in Pay of B you're +going to give + + align:start position:0% +going to give + + + align:start position:0% +going to give +me100 if I win and I'll give + + align:start position:0% +me100 if I win and I'll give + + + align:start position:0% +me100 if I win and I'll give +you 100 if you win and the question + + align:start position:0% +you 100 if you win and the question + + + align:start position:0% +you 100 if you win and the question +is which game would you prefer to play + + align:start position:0% +is which game would you prefer to play + + + align:start position:0% +is which game would you prefer to play +or do you not + + align:start position:0% +or do you not + + + align:start position:0% +or do you not +care so in each case you kind of win and + + align:start position:0% +care so in each case you kind of win and + + + align:start position:0% +care so in each case you kind of win and +lose + + align:start position:0% +lose + + + align:start position:0% +lose +same + + align:start position:0% +same + + + align:start position:0% +same +number so I want to see uh hands who + + align:start position:0% +number so I want to see uh hands who + + + align:start position:0% +number so I want to see uh hands who +wants to play game + + align:start position:0% + + + + align:start position:0% + +a come on guys wake up who wants to play + + align:start position:0% +a come on guys wake up who wants to play + + + align:start position:0% +a come on guys wake up who wants to play +game a I mean if you don't know you you + + align:start position:0% +game a I mean if you don't know you you + + + align:start position:0% +game a I mean if you don't know you you +just let's say you like Euros better you + + align:start position:0% +just let's say you like Euros better you + + + align:start position:0% +just let's say you like Euros better you +can say this is not really graded so + + align:start position:0% +can say this is not really graded so + + + align:start position:0% +can say this is not really graded so +it's + + align:start position:0% + + + + align:start position:0% + +okay okay nobody really knows what to + + align:start position:0% +okay okay nobody really knows what to + + + align:start position:0% +okay okay nobody really knows what to +play like how about game B anybody wants + + align:start position:0% +play like how about game B anybody wants + + + align:start position:0% +play like how about game B anybody wants +to play game B okay you guys want to + + align:start position:0% +to play game B okay you guys want to + + + align:start position:0% +to play game B okay you guys want to +play three three people for game four + + align:start position:0% +play three three people for game four + + + align:start position:0% +play three three people for game four +game a nobody + + align:start position:0% +game a nobody + + + align:start position:0% +game a nobody +still same person for game A and B all + + align:start position:0% +still same person for game A and B all + + + align:start position:0% +still same person for game A and B all +right okay two people so now behav says + + align:start position:0% +right okay two people so now behav says + + + align:start position:0% +right okay two people so now behav says +people are reluctant to lose more + + align:start position:0% +people are reluctant to lose more + + + align:start position:0% +people are reluctant to lose more +reluctant to + + align:start position:0% +reluctant to + + + align:start position:0% +reluctant to +lose that's true that's true that is + + align:start position:0% +lose that's true that's true that is + + + align:start position:0% +lose that's true that's true that is +true however like um so people are + + align:start position:0% +true however like um so people are + + + align:start position:0% +true however like um so people are +reluctant to lose and I said look the + + align:start position:0% +reluctant to lose and I said look the + + + align:start position:0% +reluctant to lose and I said look the +the FX forward in one month is one so + + align:start position:0% +the FX forward in one month is one so + + + align:start position:0% +the FX forward in one month is one so +that's kind of you can actually that's + + align:start position:0% +that's kind of you can actually that's + + + align:start position:0% +that's kind of you can actually that's +the market price that in one month FX + + align:start position:0% +the market price that in one month FX + + + align:start position:0% +the market price that in one month FX +forward is one and this our bet is kind + + align:start position:0% +forward is one and this our bet is kind + + + align:start position:0% +forward is one and this our bet is kind +of the strike is one so our bet level is + + align:start position:0% +of the strike is one so our bet level is + + + align:start position:0% +of the strike is one so our bet level is +one so you can kind of say well this + + align:start position:0% +one so you can kind of say well this + + + align:start position:0% +one so you can kind of say well this +looks like kind of a fair + + align:start position:0% +looks like kind of a fair + + + align:start position:0% +looks like kind of a fair +game um so I don't expect to win or lose + + align:start position:0% +game um so I don't expect to win or lose + + + align:start position:0% +game um so I don't expect to win or lose +much but I'm just reluctant to do it and + + align:start position:0% +much but I'm just reluctant to do it and + + + align:start position:0% +much but I'm just reluctant to do it and +I can get that feeling that's the risk + + align:start position:0% +I can get that feeling that's the risk + + + align:start position:0% +I can get that feeling that's the risk +aversion aspect of it but if you were + + align:start position:0% +aversion aspect of it but if you were + + + align:start position:0% +aversion aspect of it but if you were +forced to make a bet question is which + + align:start position:0% +forced to make a bet question is which + + + align:start position:0% +forced to make a bet question is which +one would you + + align:start position:0% +one would you + + + align:start position:0% +one would you +prefer um so I understand you might not + + align:start position:0% +prefer um so I understand you might not + + + align:start position:0% +prefer um so I understand you might not +want to play + + align:start position:0% +want to play + + + align:start position:0% +want to play +but I would say okay + + align:start position:0% +but I would say okay + + + align:start position:0% +but I would say okay +so you guys don't seem to be in the mood + + align:start position:0% +so you guys don't seem to be in the mood + + + align:start position:0% +so you guys don't seem to be in the mood +to play that's fine we can uh we can + + align:start position:0% +to play that's fine we can uh we can + + + align:start position:0% +to play that's fine we can uh we can +let's look at some um let's look at some + + align:start position:0% +let's look at some um let's look at some + + + align:start position:0% +let's look at some um let's look at some +scenarios so let's say in one month + + align:start position:0% +scenarios so let's say in one month + + + align:start position:0% +scenarios so let's say in one month +dollar euro goes to + + align:start position:0% +dollar euro goes to + + + align:start position:0% +dollar euro goes to +1.25 in bet a I lose $100 in bet b i + + align:start position:0% +1.25 in bet a I lose $100 in bet b i + + + align:start position:0% +1.25 in bet a I lose $100 in bet b i +lose1 + + align:start position:0% +lose1 + + + align:start position:0% +lose1 +so bet a + + align:start position:0% +so bet a + + + align:start position:0% +so bet a +for actually you lose1 not not so bet a + + align:start position:0% +for actually you lose1 not not so bet a + + + align:start position:0% +for actually you lose1 not not so bet a +for you you're + + align:start position:0% +for you you're + + + align:start position:0% +for you you're +$25 better than bet b and in the second + + align:start position:0% +$25 better than bet b and in the second + + + align:start position:0% +$25 better than bet b and in the second +case if dollar EUR + + align:start position:0% +case if dollar EUR + + + align:start position:0% +case if dollar EUR +is75 you make + + align:start position:0% +is75 you make + + + align:start position:0% +is75 you make +$100 and or you make1 EUR in bet b in + + align:start position:0% +$100 and or you make1 EUR in bet b in + + + align:start position:0% +$100 and or you make1 EUR in bet b in +that case you're also bet a is $25 + + align:start position:0% +that case you're also bet a is $25 + + + align:start position:0% +that case you're also bet a is $25 +better so it doesn't matter what + + align:start position:0% +better so it doesn't matter what + + + align:start position:0% +better so it doesn't matter what +happens bet a seems to be the better + + align:start position:0% +happens bet a seems to be the better + + + align:start position:0% +happens bet a seems to be the better +case so if you're like uh our Dear + + align:start position:0% +case so if you're like uh our Dear + + + align:start position:0% +case so if you're like uh our Dear +Professor here then you're you don't + + align:start position:0% +Professor here then you're you don't + + + align:start position:0% +Professor here then you're you don't +like to lose then you're probably gonna + + align:start position:0% +like to lose then you're probably gonna + + + align:start position:0% +like to lose then you're probably gonna +choose bet a I assume right it's a + + align:start position:0% +choose bet a I assume right it's a + + + align:start position:0% +choose bet a I assume right it's a +better + + align:start position:0% +better + + + align:start position:0% +better +deal but and that's kind of strange + + align:start position:0% +deal but and that's kind of strange + + + align:start position:0% +deal but and that's kind of strange +though I mean like you you know this + + align:start position:0% +though I mean like you you know this + + + align:start position:0% +though I mean like you you know this +both both payoffs were symmetric so you + + align:start position:0% +both both payoffs were symmetric so you + + + align:start position:0% +both both payoffs were symmetric so you +know it's 100100 $100 + + align:start position:0% +know it's 100100 $100 + + + align:start position:0% +know it's 100100 $100 +$100 why is it if one is better than the + + align:start position:0% +$100 why is it if one is better than the + + + align:start position:0% +$100 why is it if one is better than the +other + + align:start position:0% + + + + align:start position:0% + +well it's like what what really happens + + align:start position:0% +well it's like what what really happens + + + align:start position:0% +well it's like what what really happens +is well the the units of the bed the + + align:start position:0% +is well the the units of the bed the + + + align:start position:0% +is well the the units of the bed the +value of those units depend on whether + + align:start position:0% +value of those units depend on whether + + + align:start position:0% +value of those units depend on whether +you win or lose so it's not like if I + + align:start position:0% +you win or lose so it's not like if I + + + align:start position:0% +you win or lose so it's not like if I +was betting using + + align:start position:0% +was betting using + + + align:start position:0% +was betting using +acorns then like you get two acorns or I + + align:start position:0% +acorns then like you get two acorns or I + + + align:start position:0% +acorns then like you get two acorns or I +get two acorns then then actually it + + align:start position:0% +get two acorns then then actually it + + + align:start position:0% +get two acorns then then actually it +might be a fair bet but because I'm + + align:start position:0% +might be a fair bet but because I'm + + + align:start position:0% +might be a fair bet but because I'm +betting in euros and dollars and the + + align:start position:0% +betting in euros and dollars and the + + + align:start position:0% +betting in euros and dollars and the +value of these things the relative value + + align:start position:0% +value of these things the relative value + + + align:start position:0% +value of these things the relative value +changes compared based on based on the + + align:start position:0% +changes compared based on based on the + + + align:start position:0% +changes compared based on based on the +actual whether you win or lose then then + + align:start position:0% +actual whether you win or lose then then + + + align:start position:0% +actual whether you win or lose then then +it's not then the game is not symmetric + + align:start position:0% +it's not then the game is not symmetric + + + align:start position:0% +it's not then the game is not symmetric +anymore so this is um + + align:start position:0% +anymore so this is um + + + align:start position:0% +anymore so this is um +the reason I wanted to take you through + + align:start position:0% +the reason I wanted to take you through + + + align:start position:0% +the reason I wanted to take you through +this game is because there is a lot of + + align:start position:0% +this game is because there is a lot of + + + align:start position:0% +this game is because there is a lot of +cases in finance where people make beds + + align:start position:0% +cases in finance where people make beds + + + align:start position:0% +cases in finance where people make beds +but then the value of what you get + + align:start position:0% +but then the value of what you get + + + align:start position:0% +but then the value of what you get +depends on whether you win or you lose + + align:start position:0% +depends on whether you win or you lose + + + align:start position:0% +depends on whether you win or you lose +and that has a that has an effect on the + + align:start position:0% +and that has a that has an effect on the + + + align:start position:0% +and that has a that has an effect on the +value of the + + align:start position:0% +value of the + + + align:start position:0% +value of the +bed and in particular the case we're + + align:start position:0% +bed and in particular the case we're + + + align:start position:0% +bed and in particular the case we're +going to talk about today is one of + + align:start position:0% +going to talk about today is one of + + + align:start position:0% +going to talk about today is one of +these cases which is the credit effects + + align:start position:0% +these cases which is the credit effects + + + align:start position:0% +these cases which is the credit effects +um that's why we need Creed effects + + align:start position:0% +um that's why we need Creed effects + + + align:start position:0% +um that's why we need Creed effects +Quantum + + align:start position:0% +Quantum + + + align:start position:0% +Quantum +models to give you an illustration from + + align:start position:0% +models to give you an illustration from + + + align:start position:0% +models to give you an illustration from +from Finance like let's take Italy bonds + + align:start position:0% +from Finance like let's take Italy bonds + + + align:start position:0% +from Finance like let's take Italy bonds +so Italy issues bonds both in dollars + + align:start position:0% +so Italy issues bonds both in dollars + + + align:start position:0% +so Italy issues bonds both in dollars +and in + + align:start position:0% +and in + + + align:start position:0% +and in +Euros why does it issue in both + + align:start position:0% +Euros why does it issue in both + + + align:start position:0% +Euros why does it issue in both +currencies because Italy has to issue a + + align:start position:0% +currencies because Italy has to issue a + + + align:start position:0% +currencies because Italy has to issue a +lot of bonds + + align:start position:0% +lot of bonds + + + align:start position:0% +lot of bonds +and they uh they need to find as many + + align:start position:0% +and they uh they need to find as many + + + align:start position:0% +and they uh they need to find as many +investors as they as they can and some + + align:start position:0% +investors as they as they can and some + + + align:start position:0% +investors as they as they can and some +investors want to buy euro bonds and + + align:start position:0% +investors want to buy euro bonds and + + + align:start position:0% +investors want to buy euro bonds and +some investors want to buy dollar bonds + + align:start position:0% +some investors want to buy dollar bonds + + + align:start position:0% +some investors want to buy dollar bonds +and they want to access both bases of + + align:start position:0% +and they want to access both bases of + + + align:start position:0% +and they want to access both bases of +investors now these bonds um they they + + align:start position:0% +investors now these bonds um they they + + + align:start position:0% +investors now these bonds um they they +cross default meaning if they if ital + + align:start position:0% +cross default meaning if they if ital + + + align:start position:0% +cross default meaning if they if ital +defaults on one Bond + + align:start position:0% +defaults on one Bond + + + align:start position:0% +defaults on one Bond +all of its bonds default together + + align:start position:0% +all of its bonds default together + + + align:start position:0% +all of its bonds default together +including the euros and the dollar + + align:start position:0% +including the euros and the dollar + + + align:start position:0% +including the euros and the dollar +bonds so + + align:start position:0% +bonds so + + + align:start position:0% +bonds so +then you know the there is a there is + + align:start position:0% +then you know the there is a there is + + + align:start position:0% +then you know the there is a there is +the notion of credit spread which is the + + align:start position:0% +the notion of credit spread which is the + + + align:start position:0% +the notion of credit spread which is the +measure of how risky Italy is so you can + + align:start position:0% +measure of how risky Italy is so you can + + + align:start position:0% +measure of how risky Italy is so you can +take Euro bonds and you can say well how + + align:start position:0% +take Euro bonds and you can say well how + + + align:start position:0% +take Euro bonds and you can say well how +much premium does Italy pay over German + + align:start position:0% +much premium does Italy pay over German + + + align:start position:0% +much premium does Italy pay over German +bonds let's assume that German bonds are + + align:start position:0% +bonds let's assume that German bonds are + + + align:start position:0% +bonds let's assume that German bonds are +risk-free which is kind of the standard + + align:start position:0% +risk-free which is kind of the standard + + + align:start position:0% +risk-free which is kind of the standard +assumption for euros that the German + + align:start position:0% +assumption for euros that the German + + + align:start position:0% +assumption for euros that the German +bonds Germany is the uh is the main + + align:start position:0% +bonds Germany is the uh is the main + + + align:start position:0% +bonds Germany is the uh is the main +under + + align:start position:0% +under + + + align:start position:0% +under +lying economic Force for the Euro they + + align:start position:0% +lying economic Force for the Euro they + + + align:start position:0% +lying economic Force for the Euro they +they are kind of risk-free bonds and + + align:start position:0% +they are kind of risk-free bonds and + + + align:start position:0% +they are kind of risk-free bonds and +Italy pays a certain spread over Euros + + align:start position:0% +Italy pays a certain spread over Euros + + + align:start position:0% +Italy pays a certain spread over Euros +same same thing for dollars it pays a + + align:start position:0% +same same thing for dollars it pays a + + + align:start position:0% +same same thing for dollars it pays a +certain spread over over USA so if Italy + + align:start position:0% +certain spread over over USA so if Italy + + + align:start position:0% +certain spread over over USA so if Italy +wants to borrow money they have to pay a + + align:start position:0% +wants to borrow money they have to pay a + + + align:start position:0% +wants to borrow money they have to pay a +higher interest rate just like if you + + align:start position:0% +higher interest rate just like if you + + + align:start position:0% +higher interest rate just like if you +want to borrow money for student loans + + align:start position:0% +want to borrow money for student loans + + + align:start position:0% +want to borrow money for student loans +you have to pay higher interest rates in + + align:start position:0% +you have to pay higher interest rates in + + + align:start position:0% +you have to pay higher interest rates in +the + + align:start position:0% +the + + + align:start position:0% +the +FED it's uh and the size of that spread + + align:start position:0% +FED it's uh and the size of that spread + + + align:start position:0% +FED it's uh and the size of that spread +is uh in the market it determines on how + + align:start position:0% +is uh in the market it determines on how + + + align:start position:0% +is uh in the market it determines on how +risky of a borrower you are + + align:start position:0% +risky of a borrower you are + + + align:start position:0% +risky of a borrower you are +well it turns out that these spreads are + + align:start position:0% +well it turns out that these spreads are + + + align:start position:0% +well it turns out that these spreads are +not not the same in both currencies + + align:start position:0% +not not the same in both currencies + + + align:start position:0% +not not the same in both currencies +there's some one currency has a higher + + align:start position:0% +there's some one currency has a higher + + + align:start position:0% +there's some one currency has a higher +spread than other + + align:start position:0% +spread than other + + + align:start position:0% +spread than other +currencies that's kind of an interesting + + align:start position:0% +currencies that's kind of an interesting + + + align:start position:0% +currencies that's kind of an interesting +thing so there is two questions really + + align:start position:0% +thing so there is two questions really + + + align:start position:0% +thing so there is two questions really +when the spreads are not the same which + + align:start position:0% +when the spreads are not the same which + + + align:start position:0% +when the spreads are not the same which +which currency would itally prefer to + + align:start position:0% +which currency would itally prefer to + + + align:start position:0% +which currency would itally prefer to +issue bonds Bonds in and which currency + + align:start position:0% +issue bonds Bonds in and which currency + + + align:start position:0% +issue bonds Bonds in and which currency +do investors prefer to buy Bonds + + align:start position:0% + + + + align:start position:0% + +in so this is kind of similar if you + + align:start position:0% +in so this is kind of similar if you + + + align:start position:0% +in so this is kind of similar if you +think then um to the previous this game + + align:start position:0% +think then um to the previous this game + + + align:start position:0% +think then um to the previous this game +we played because if you're an investor + + align:start position:0% +we played because if you're an investor + + + align:start position:0% +we played because if you're an investor +trying to buy + + align:start position:0% +trying to buy + + + align:start position:0% +trying to buy +bonds well if itally defaults then + + align:start position:0% +bonds well if itally defaults then + + + align:start position:0% +bonds well if itally defaults then +chances are euro is not doing so + + align:start position:0% +chances are euro is not doing so + + + align:start position:0% +chances are euro is not doing so +well so you would lose money and if you + + align:start position:0% +well so you would lose money and if you + + + align:start position:0% +well so you would lose money and if you +have Euro bonds you would lose Euros if + + align:start position:0% +have Euro bonds you would lose Euros if + + + align:start position:0% +have Euro bonds you would lose Euros if +you lose if you have dollar bonds you + + align:start position:0% +you lose if you have dollar bonds you + + + align:start position:0% +you lose if you have dollar bonds you +lose dollars on the other hand if it + + align:start position:0% +lose dollars on the other hand if it + + + align:start position:0% +lose dollars on the other hand if it +does not default and pays you back then + + align:start position:0% +does not default and pays you back then + + + align:start position:0% +does not default and pays you back then +then chances are EUR is not doing that + + align:start position:0% +then chances are EUR is not doing that + + + align:start position:0% +then chances are EUR is not doing that +bad so you would actually be making + + align:start position:0% +bad so you would actually be making + + + align:start position:0% +bad so you would actually be making +euros and dollars so it's um it's an + + align:start position:0% +euros and dollars so it's um it's an + + + align:start position:0% +euros and dollars so it's um it's an +interesting uh it's kind of a similar + + align:start position:0% +interesting uh it's kind of a similar + + + align:start position:0% +interesting uh it's kind of a similar +similar Dynamic going + + align:start position:0% + + + + align:start position:0% + +on so there's the same kind of question + + align:start position:0% +on so there's the same kind of question + + + align:start position:0% +on so there's the same kind of question +that I asked before USD Euros or equal + + align:start position:0% +that I asked before USD Euros or equal + + + align:start position:0% +that I asked before USD Euros or equal +in both so what do you what do you think + + align:start position:0% +in both so what do you what do you think + + + align:start position:0% +in both so what do you what do you think +now now that we've gone through that + + align:start position:0% +now now that we've gone through that + + + align:start position:0% +now now that we've gone through that +example maybe we'll have a higher + + align:start position:0% +example maybe we'll have a higher + + + align:start position:0% +example maybe we'll have a higher +participation in my in my pub quiz uh + + align:start position:0% +participation in my in my pub quiz uh + + + align:start position:0% +participation in my in my pub quiz uh +who thinks that + + align:start position:0% +who thinks that + + + align:start position:0% +who thinks that +um who thinks that USD bonds have a + + align:start position:0% +um who thinks that USD bonds have a + + + align:start position:0% +um who thinks that USD bonds have a +higher credit spread and who thinks so a + + align:start position:0% +higher credit spread and who thinks so a + + + align:start position:0% +higher credit spread and who thinks so a +votes for + + align:start position:0% +votes for + + + align:start position:0% +votes for +a + + align:start position:0% +a + + + align:start position:0% +a +one + + align:start position:0% +one + + + align:start position:0% +one +two so and who thinks that Euro bonds + + align:start position:0% +two so and who thinks that Euro bonds + + + align:start position:0% +two so and who thinks that Euro bonds +will have a higher credit + + align:start position:0% +will have a higher credit + + + align:start position:0% +will have a higher credit +spread okay + + align:start position:0% +spread okay + + + align:start position:0% +spread okay +one all + + align:start position:0% +one all + + + align:start position:0% +one all +right so 2 to + + align:start position:0% +right so 2 to + + + align:start position:0% +right so 2 to +one I think the two two guy the two to + + align:start position:0% +one I think the two two guy the two to + + + align:start position:0% +one I think the two two guy the two to +one wins all right I must say um you + + align:start position:0% +one wins all right I must say um you + + + align:start position:0% +one wins all right I must say um you +guys are seems that maybe it's the + + align:start position:0% +guys are seems that maybe it's the + + + align:start position:0% +guys are seems that maybe it's the +format of the auditorium people don't + + align:start position:0% +format of the auditorium people don't + + + align:start position:0% +format of the auditorium people don't +like to raise their hands too much or + + align:start position:0% +like to raise their hands too much or + + + align:start position:0% +like to raise their hands too much or +maybe the the afid that they're being + + align:start position:0% +maybe the the afid that they're being + + + align:start position:0% +maybe the the afid that they're being +filmed I don't + + align:start position:0% +filmed I don't + + + align:start position:0% +filmed I don't +know + + align:start position:0% +know + + + align:start position:0% +know +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well how are we going to um how are we + + align:start position:0% +well how are we going to um how are we + + + align:start position:0% +well how are we going to um how are we +going to to do this be um how are we + + align:start position:0% +going to to do this be um how are we + + + align:start position:0% +going to to do this be um how are we +going to answer this + + align:start position:0% +going to answer this + + + align:start position:0% +going to answer this +question before I give you the answer + + align:start position:0% +question before I give you the answer + + + align:start position:0% +question before I give you the answer +we're going to go through the slide well + + align:start position:0% +we're going to go through the slide well + + + align:start position:0% +we're going to go through the slide well +first we're going to say well FX rates + + align:start position:0% +first we're going to say well FX rates + + + align:start position:0% +first we're going to say well FX rates +are volatile there is volatility as we + + align:start position:0% +are volatile there is volatility as we + + + align:start position:0% +are volatile there is volatility as we +said before so now we're going to there + + align:start position:0% +said before so now we're going to there + + + align:start position:0% +said before so now we're going to there +is a in order to compare Euro Dons to + + align:start position:0% +is a in order to compare Euro Dons to + + + align:start position:0% +is a in order to compare Euro Dons to +Dollar bonds we need to really come up + + align:start position:0% +Dollar bonds we need to really come up + + + align:start position:0% +Dollar bonds we need to really come up +with a strategy to replicate one with + + align:start position:0% +with a strategy to replicate one with + + + align:start position:0% +with a strategy to replicate one with +the other and then look at the price + + align:start position:0% +the other and then look at the price + + + align:start position:0% +the other and then look at the price +look at the uh how much do we need to + + align:start position:0% +look at the uh how much do we need to + + + align:start position:0% +look at the uh how much do we need to +buy one to replicate the other if you if + + align:start position:0% +buy one to replicate the other if you if + + + align:start position:0% +buy one to replicate the other if you if +we're able to come up with such a + + align:start position:0% +we're able to come up with such a + + + align:start position:0% +we're able to come up with such a +replication strategy then we can + + align:start position:0% +replication strategy then we can + + + align:start position:0% +replication strategy then we can +immediately say hey if you need like 150 + + align:start position:0% +immediately say hey if you need like 150 + + + align:start position:0% +immediately say hey if you need like 150 +bonds to of Euro bonds to replicate $100 + + align:start position:0% +bonds to of Euro bonds to replicate $100 + + + align:start position:0% +bonds to of Euro bonds to replicate $100 +bonds then then that means that the the + + align:start position:0% +bonds then then that means that the the + + + align:start position:0% +bonds then then that means that the the +Euro bonds have to be cheaper right + + align:start position:0% +Euro bonds have to be cheaper right + + + align:start position:0% +Euro bonds have to be cheaper right +that's that's basically the replication + + align:start position:0% +that's that's basically the replication + + + align:start position:0% +that's that's basically the replication +argument so you you can kind of try to + + align:start position:0% +argument so you you can kind of try to + + + align:start position:0% +argument so you you can kind of try to +do that by piecing together bonds or you + + align:start position:0% +do that by piecing together bonds or you + + + align:start position:0% +do that by piecing together bonds or you +can use the powerful tools of + + align:start position:0% +can use the powerful tools of + + + align:start position:0% +can use the powerful tools of +mathematical finance that you've been + + align:start position:0% +mathematical finance that you've been + + + align:start position:0% +mathematical finance that you've been +learning about which is all about + + align:start position:0% +learning about which is all about + + + align:start position:0% +learning about which is all about +replication and pricing and the three + + align:start position:0% +replication and pricing and the three + + + align:start position:0% +replication and pricing and the three +steps are you know we're going to + + align:start position:0% +steps are you know we're going to + + + align:start position:0% +steps are you know we're going to +analyze the payoffs of the instruments + + align:start position:0% +analyze the payoffs of the instruments + + + align:start position:0% +analyze the payoffs of the instruments +and we're going to write some um model + + align:start position:0% +and we're going to write some um model + + + align:start position:0% +and we're going to write some um model +my model for FX and for credit and we're + + align:start position:0% +my model for FX and for credit and we're + + + align:start position:0% +my model for FX and for credit and we're +going to price those bonds and then + + align:start position:0% +going to price those bonds and then + + + align:start position:0% +going to price those bonds and then +we're going to look at the results and + + align:start position:0% +we're going to look at the results and + + + align:start position:0% +we're going to look at the results and +try to understand the problem + + align:start position:0% +try to understand the problem + + + align:start position:0% +try to understand the problem +intuitively and that's basically what we + + align:start position:0% +intuitively and that's basically what we + + + align:start position:0% +intuitively and that's basically what we +do pretty much um that's what option + + align:start position:0% +do pretty much um that's what option + + + align:start position:0% +do pretty much um that's what option +option quants do in Wall Street all the + + align:start position:0% +option quants do in Wall Street all the + + + align:start position:0% +option quants do in Wall Street all the +time so here is the + + align:start position:0% +time so here is the + + + align:start position:0% +time so here is the +answer uh dollar versus Euro spreads + + align:start position:0% +answer uh dollar versus Euro spreads + + + align:start position:0% +answer uh dollar versus Euro spreads +from the marketplace so you usually what + + align:start position:0% +from the marketplace so you usually what + + + align:start position:0% +from the marketplace so you usually what +happens in in this kind of questions in + + align:start position:0% +happens in in this kind of questions in + + + align:start position:0% +happens in in this kind of questions in +finance is you kind of you kind of have + + align:start position:0% +finance is you kind of you kind of have + + + align:start position:0% +finance is you kind of you kind of have +an answer and then you try to come with + + align:start position:0% +an answer and then you try to come with + + + align:start position:0% +an answer and then you try to come with +a model that explains the difference so + + align:start position:0% +a model that explains the difference so + + + align:start position:0% +a model that explains the difference so +that's kind of what we're going to do + + align:start position:0% +that's kind of what we're going to do + + + align:start position:0% +that's kind of what we're going to do +now um while the um the USD spreads are + + align:start position:0% +now um while the um the USD spreads are + + + align:start position:0% +now um while the um the USD spreads are +actually + + align:start position:0% +actually + + + align:start position:0% +actually +lower USD USD Bond spreads are actually + + align:start position:0% +lower USD USD Bond spreads are actually + + + align:start position:0% +lower USD USD Bond spreads are actually +lower + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now so there is really um when we're + + align:start position:0% +now so there is really um when we're + + + align:start position:0% +now so there is really um when we're +talking about bonds risky + + align:start position:0% +talking about bonds risky + + + align:start position:0% +talking about bonds risky +bonds there's two states they're either + + align:start position:0% +bonds there's two states they're either + + + align:start position:0% +bonds there's two states they're either +performing or they are or they are which + + align:start position:0% +performing or they are or they are which + + + align:start position:0% +performing or they are or they are which +is non-performing in default + + align:start position:0% +is non-performing in default + + + align:start position:0% +is non-performing in default +and we're going to go here through an + + align:start position:0% +and we're going to go here through an + + + align:start position:0% +and we're going to go here through an +example of uh of two bonds and we're + + align:start position:0% +example of uh of two bonds and we're + + + align:start position:0% +example of uh of two bonds and we're +going to use two zero coupon + + align:start position:0% +going to use two zero coupon + + + align:start position:0% +going to use two zero coupon +bonds which essentially have zero + + align:start position:0% +bonds which essentially have zero + + + align:start position:0% +bonds which essentially have zero +recovery um it's and the idea there is + + align:start position:0% +recovery um it's and the idea there is + + + align:start position:0% +recovery um it's and the idea there is +um really to to make it to make the + + align:start position:0% +um really to to make it to make the + + + align:start position:0% +um really to to make it to make the +question simple so we can analyze it + + align:start position:0% +question simple so we can analyze it + + + align:start position:0% +question simple so we can analyze it +better but uh you don't lose a lot of + + align:start position:0% +better but uh you don't lose a lot of + + + align:start position:0% +better but uh you don't lose a lot of +generality by saying zero coupon versus + + align:start position:0% +generality by saying zero coupon versus + + + align:start position:0% +generality by saying zero coupon versus +coupon it's it's not the the answer the + + align:start position:0% +coupon it's it's not the the answer the + + + align:start position:0% +coupon it's it's not the the answer the +the intuition would be exactly the same + + align:start position:0% +the intuition would be exactly the same + + + align:start position:0% +the intuition would be exactly the same +so let's say we have two zero coupon + + align:start position:0% +so let's say we have two zero coupon + + + align:start position:0% +so let's say we have two zero coupon +bonds same maturity they pay 100 + + align:start position:0% +bonds same maturity they pay 100 + + + align:start position:0% +bonds same maturity they pay 100 +maturities and by the way bonds I don't + + align:start position:0% +maturities and by the way bonds I don't + + + align:start position:0% +maturities and by the way bonds I don't +know how much you guys have this I say + + align:start position:0% +know how much you guys have this I say + + + align:start position:0% +know how much you guys have this I say +these things I'm very familiar with them + + align:start position:0% +these things I'm very familiar with them + + + align:start position:0% +these things I'm very familiar with them +bonds are nothing more than loans so + + align:start position:0% +bonds are nothing more than loans so + + + align:start position:0% +bonds are nothing more than loans so +zero coupon Bond means I give you some + + align:start position:0% +zero coupon Bond means I give you some + + + align:start position:0% +zero coupon Bond means I give you some +amount of money and at at at some M + + align:start position:0% +amount of money and at at at some M + + + align:start position:0% +amount of money and at at at some M +pre-agreed maturity you're going to pay + + align:start position:0% +pre-agreed maturity you're going to pay + + + align:start position:0% +pre-agreed maturity you're going to pay +me 100 so let's say I give you 80 cents + + align:start position:0% +me 100 so let's say I give you 80 cents + + + align:start position:0% +me 100 so let's say I give you 80 cents +one year from now you pay me 100 + + align:start position:0% +one year from now you pay me 100 + + + align:start position:0% +one year from now you pay me 100 +and I call this a zero coupon Bond + + align:start position:0% +and I call this a zero coupon Bond + + + align:start position:0% +and I call this a zero coupon Bond +because you don't pay me any + + align:start position:0% +because you don't pay me any + + + align:start position:0% +because you don't pay me any +intermediate coupons there's no interest + + align:start position:0% +intermediate coupons there's no interest + + + align:start position:0% +intermediate coupons there's no interest +payments but just I pay you less money + + align:start position:0% +payments but just I pay you less money + + + align:start position:0% +payments but just I pay you less money +now and you pay me more at + + align:start position:0% + + + + align:start position:0% + +maturity okay so um we know that Bond U + + align:start position:0% +maturity okay so um we know that Bond U + + + align:start position:0% +maturity okay so um we know that Bond U +pays $100 Bond e pays 10000 and let's + + align:start position:0% +pays $100 Bond e pays 10000 and let's + + + align:start position:0% +pays $100 Bond e pays 10000 and let's +say there's we Den note the prices of + + align:start position:0% +say there's we Den note the prices of + + + align:start position:0% +say there's we Den note the prices of +price of U is PU price of e is p our + + align:start position:0% +price of U is PU price of e is p our + + + align:start position:0% +price of U is PU price of e is p our +spot FX rate we're going to call it St + + align:start position:0% +spot FX rate we're going to call it St + + + align:start position:0% +spot FX rate we're going to call it St +our FX forward + + align:start position:0% +our FX forward + + + align:start position:0% +our FX forward +ft now um we can have kind of a simple + + align:start position:0% +ft now um we can have kind of a simple + + + align:start position:0% +ft now um we can have kind of a simple +arbitrage strategy well let's say if we + + align:start position:0% +arbitrage strategy well let's say if we + + + align:start position:0% +arbitrage strategy well let's say if we +we can sell 100 times ft dollar bonds + + align:start position:0% +we can sell 100 times ft dollar bonds + + + align:start position:0% +we can sell 100 times ft dollar bonds +and with the proceeds by 100 + + align:start position:0% +and with the proceeds by 100 + + + align:start position:0% +and with the proceeds by 100 +ft uh 100 we're going to get if we sell + + align:start position:0% +ft uh 100 we're going to get if we sell + + + align:start position:0% +ft uh 100 we're going to get if we sell +a th sorry $1,000 bonds we're going to + + align:start position:0% +a th sorry $1,000 bonds we're going to + + + align:start position:0% +a th sorry $1,000 bonds we're going to +get this much proceed that's the + + align:start position:0% +get this much proceed that's the + + + align:start position:0% +get this much proceed that's the +price and if we buy a 100 euro bonds and + + align:start position:0% +price and if we buy a 100 euro bonds and + + + align:start position:0% +price and if we buy a 100 euro bonds and +a th000 sorry Euro + + align:start position:0% +a th000 sorry Euro + + + align:start position:0% +a th000 sorry Euro +bonds + + align:start position:0% +bonds + + + align:start position:0% +bonds +so um we can enter into into an fx + + align:start position:0% +so um we can enter into into an fx + + + align:start position:0% +so um we can enter into into an fx +forward contract + + align:start position:0% +forward contract + + + align:start position:0% +forward contract +for €100,000 for maturity T at zero cost + + align:start position:0% +for €100,000 for maturity T at zero cost + + + align:start position:0% +for €100,000 for maturity T at zero cost +all right so let's see how um how this + + align:start position:0% +all right so let's see how um how this + + + align:start position:0% +all right so let's see how um how this +uh strategy actually pays out + + align:start position:0% + + + + align:start position:0% + +well what happens is you get you get um + + align:start position:0% +well what happens is you get you get um + + + align:start position:0% +well what happens is you get you get um +you pay + + align:start position:0% +you pay + + + align:start position:0% +you pay +100,000 like you there's + + align:start position:0% +100,000 like you there's + + + align:start position:0% +100,000 like you there's +$100,000 you get $100,000 EUR for + + align:start position:0% +$100,000 you get $100,000 EUR for + + + align:start position:0% +$100,000 you get $100,000 EUR for +selling the Euro Bond you pay 100,000 + + align:start position:0% +selling the Euro Bond you pay 100,000 + + + align:start position:0% +selling the Euro Bond you pay 100,000 +times ft doll say the dollar Bond there + + align:start position:0% +times ft doll say the dollar Bond there + + + align:start position:0% +times ft doll say the dollar Bond there +is a FX forward contract and at + + align:start position:0% +is a FX forward contract and at + + + align:start position:0% +is a FX forward contract and at +maturity you can exchange this + + align:start position:0% +maturity you can exchange this + + + align:start position:0% +maturity you can exchange this +$100,000 for €100,000 using the FX + + align:start position:0% +$100,000 for €100,000 using the FX + + + align:start position:0% +$100,000 for €100,000 using the FX +forward contract you've already + + align:start position:0% +forward contract you've already + + + align:start position:0% +forward contract you've already +pre-agreed to do that so your FX forward + + align:start position:0% +pre-agreed to do that so your FX forward + + + align:start position:0% +pre-agreed to do that so your FX forward +actually exactly Hedges you can + + align:start position:0% +actually exactly Hedges you can + + + align:start position:0% +actually exactly Hedges you can +basically use the proceeds of these + + align:start position:0% +basically use the proceeds of these + + + align:start position:0% +basically use the proceeds of these +months to to you can exchange the + + align:start position:0% +months to to you can exchange the + + + align:start position:0% +months to to you can exchange the +proceeds at zero cost at at maturity + + align:start position:0% +proceeds at zero cost at at maturity + + + align:start position:0% +proceeds at zero cost at at maturity +because you have entered into the FX FX + + align:start position:0% +because you have entered into the FX FX + + + align:start position:0% +because you have entered into the FX FX +forward contract so your net payoff is + + align:start position:0% +forward contract so your net payoff is + + + align:start position:0% +forward contract so your net payoff is +zero so that means that the prices of + + align:start position:0% +zero so that means that the prices of + + + align:start position:0% +zero so that means that the prices of +these bonds have to be the same but what + + align:start position:0% +these bonds have to be the same but what + + + align:start position:0% +these bonds have to be the same but what +if they're not what if FT which is the + + align:start position:0% +if they're not what if FT which is the + + + align:start position:0% +if they're not what if FT which is the +Ft in this case is one for contract what + + align:start position:0% +Ft in this case is one for contract what + + + align:start position:0% +Ft in this case is one for contract what +if the price in dollars is different + + align:start position:0% +if the price in dollars is different + + + align:start position:0% +if the price in dollars is different +from exchange rate times the price in + + align:start position:0% +from exchange rate times the price in + + + align:start position:0% +from exchange rate times the price in +Euros well in that case you can say well + + align:start position:0% +Euros well in that case you can say well + + + align:start position:0% +Euros well in that case you can say well +there is an + + align:start position:0% +there is an + + + align:start position:0% +there is an +Arbitrage and You' be right if uh you + + align:start position:0% +Arbitrage and You' be right if uh you + + + align:start position:0% +Arbitrage and You' be right if uh you +kind of make you you would be able to + + align:start position:0% +kind of make you you would be able to + + + align:start position:0% +kind of make you you would be able to +make or make money if in fact the bonds + + align:start position:0% +make or make money if in fact the bonds + + + align:start position:0% +make or make money if in fact the bonds +performed but what if what if happens if + + align:start position:0% +performed but what if what if happens if + + + align:start position:0% +performed but what if what if happens if +there is a default or if there is a + + align:start position:0% + + + + align:start position:0% + +default um if there is a default that + + align:start position:0% +default um if there is a default that + + + align:start position:0% +default um if there is a default that +wouldn't really necessarily be the case + + align:start position:0% +wouldn't really necessarily be the case + + + align:start position:0% +wouldn't really necessarily be the case +because there's default these bonds + + align:start position:0% +because there's default these bonds + + + align:start position:0% +because there's default these bonds +don't pay anything and you just have an + + align:start position:0% +don't pay anything and you just have an + + + align:start position:0% +don't pay anything and you just have an +fx forward contract and this FX forward + + align:start position:0% +fx forward contract and this FX forward + + + align:start position:0% +fx forward contract and this FX forward +contract is going to be worth something + + align:start position:0% +contract is going to be worth something + + + align:start position:0% +contract is going to be worth something +after theault especially if FX the FX + + align:start position:0% +after theault especially if FX the FX + + + align:start position:0% +after theault especially if FX the FX +rate depends like jumps upon the + + align:start position:0% +rate depends like jumps upon the + + + align:start position:0% +rate depends like jumps upon the +fault + + align:start position:0% +fault + + + align:start position:0% +fault +so Arbitrage again is you start with + + align:start position:0% +so Arbitrage again is you start with + + + align:start position:0% +so Arbitrage again is you start with +zero money you make money if there's non + + align:start position:0% +zero money you make money if there's non + + + align:start position:0% +zero money you make money if there's non +zero + + align:start position:0% +zero + + + align:start position:0% +zero +probability and + + align:start position:0% +probability and + + + align:start position:0% +probability and +um let's say in this particular case the + + align:start position:0% +um let's say in this particular case the + + + align:start position:0% +um let's say in this particular case the +strategy payoff in case of the Fall with + + align:start position:0% +strategy payoff in case of the Fall with + + + align:start position:0% +strategy payoff in case of the Fall with +25% recovery rate is you actually have + + align:start position:0% +25% recovery rate is you actually have + + + align:start position:0% +25% recovery rate is you actually have +only 25% means you only have a quarter + + align:start position:0% +only 25% means you only have a quarter + + + align:start position:0% +only 25% means you only have a quarter +of theay payoff now at maturity if + + align:start position:0% +of theay payoff now at maturity if + + + align:start position:0% +of theay payoff now at maturity if +default occurs but you have a hedge for + + align:start position:0% +default occurs but you have a hedge for + + + align:start position:0% +default occurs but you have a hedge for +the full 100,000 your FX forward is for + + align:start position:0% +the full 100,000 your FX forward is for + + + align:start position:0% +the full 100,000 your FX forward is for +a full 100,000 so the 20 for 25,000 of + + align:start position:0% +a full 100,000 so the 20 for 25,000 of + + + align:start position:0% +a full 100,000 so the 20 for 25,000 of +it you can use the FX forward to + + align:start position:0% +it you can use the FX forward to + + + align:start position:0% +it you can use the FX forward to +exchange money for the remaining + + align:start position:0% +exchange money for the remaining + + + align:start position:0% +exchange money for the remaining +75,000 you just have an fx forward out + + align:start position:0% +75,000 you just have an fx forward out + + + align:start position:0% +75,000 you just have an fx forward out +right so if FX moved against you you + + align:start position:0% +right so if FX moved against you you + + + align:start position:0% +right so if FX moved against you you +would lose + + align:start position:0% +would lose + + + align:start position:0% +would lose +money so that's why the strategy is not + + align:start position:0% +money so that's why the strategy is not + + + align:start position:0% +money so that's why the strategy is not +necessarily an Arbitrage and that's why + + align:start position:0% +necessarily an Arbitrage and that's why + + + align:start position:0% +necessarily an Arbitrage and that's why +the two prices of the dollar and Euro + + align:start position:0% +the two prices of the dollar and Euro + + + align:start position:0% +the two prices of the dollar and Euro +Bond are not necessarily related + + align:start position:0% +Bond are not necessarily related + + + align:start position:0% +Bond are not necessarily related +to each other they don't have to be + + align:start position:0% +to each other they don't have to be + + + align:start position:0% +to each other they don't have to be +equal because in fact um there there is + + align:start position:0% +equal because in fact um there there is + + + align:start position:0% +equal because in fact um there there is +a possibility of default and you cannot + + align:start position:0% +a possibility of default and you cannot + + + align:start position:0% +a possibility of default and you cannot +really directly hedge um you cannot + + align:start position:0% +really directly hedge um you cannot + + + align:start position:0% +really directly hedge um you cannot +really construct an arbitr strategy by + + align:start position:0% +really construct an arbitr strategy by + + + align:start position:0% +really construct an arbitr strategy by +using FX forwards and the bonds + + align:start position:0% +using FX forwards and the bonds + + + align:start position:0% +using FX forwards and the bonds +together so easily you have to take into + + align:start position:0% +together so easily you have to take into + + + align:start position:0% +together so easily you have to take into +account what happens if theault + + align:start position:0% + + + + align:start position:0% + +occurs okay so give you an example what + + align:start position:0% +occurs okay so give you an example what + + + align:start position:0% +occurs okay so give you an example what +happens upon F when default occurs well + + align:start position:0% +happens upon F when default occurs well + + + align:start position:0% +happens upon F when default occurs well +one of the most recent defaults of a + + align:start position:0% +one of the most recent defaults of a + + + align:start position:0% +one of the most recent defaults of a +country of a big country that has its + + align:start position:0% +country of a big country that has its + + + align:start position:0% +country of a big country that has its +own currency is Argentina + + align:start position:0% +own currency is Argentina + + + align:start position:0% +own currency is Argentina +2001 and when it + + align:start position:0% +2001 and when it + + + align:start position:0% +2001 and when it +defaulted the Argentinian peso + + align:start position:0% +defaulted the Argentinian peso + + + align:start position:0% +defaulted the Argentinian peso +skyrocketed here's the graph of of the + + align:start position:0% +skyrocketed here's the graph of of the + + + align:start position:0% +skyrocketed here's the graph of of the +of the price Series + + align:start position:0% +of the price Series + + + align:start position:0% +of the price Series +so if you had Argentinian if you had an + + align:start position:0% +so if you had Argentinian if you had an + + + align:start position:0% +so if you had Argentinian if you had an +fx forward + + align:start position:0% +fx forward + + + align:start position:0% +fx forward +contract that essentially if you had a + + align:start position:0% +contract that essentially if you had a + + + align:start position:0% +contract that essentially if you had a +position where you were left with a + + align:start position:0% +position where you were left with a + + + align:start position:0% +position where you were left with a +naked FX forward contract where you were + + align:start position:0% +naked FX forward contract where you were + + + align:start position:0% +naked FX forward contract where you were +receiving pesos and paying dollars in + + align:start position:0% +receiving pesos and paying dollars in + + + align:start position:0% +receiving pesos and paying dollars in +the event of theault you would have lost + + align:start position:0% +the event of theault you would have lost + + + align:start position:0% +the event of theault you would have lost +a lot of money when that happened it + + align:start position:0% +a lot of money when that happened it + + + align:start position:0% +a lot of money when that happened it +would have really gone against you and + + align:start position:0% +would have really gone against you and + + + align:start position:0% +would have really gone against you and +this is by the way this is this is a + + align:start position:0% +this is by the way this is this is a + + + align:start position:0% +this is by the way this is this is a +massive move and there's an TM PES still + + align:start position:0% +massive move and there's an TM PES still + + + align:start position:0% +massive move and there's an TM PES still +is not recovered from from that + + align:start position:0% +is not recovered from from that + + + align:start position:0% +is not recovered from from that +default so can we do better what what do + + align:start position:0% +default so can we do better what what do + + + align:start position:0% +default so can we do better what what do +we actually what should we be doing when + + align:start position:0% +we actually what should we be doing when + + + align:start position:0% +we actually what should we be doing when +we're hedging this and the answer is + + align:start position:0% +we're hedging this and the answer is + + + align:start position:0% +we're hedging this and the answer is +again we have to + + align:start position:0% +again we have to + + + align:start position:0% +again we have to +apply mathematical models uh to really + + align:start position:0% +apply mathematical models uh to really + + + align:start position:0% +apply mathematical models uh to really +try to come up with a replication + + align:start position:0% +try to come up with a replication + + + align:start position:0% +try to come up with a replication +strategy so what is the main features of + + align:start position:0% +strategy so what is the main features of + + + align:start position:0% +strategy so what is the main features of +a model that would help me do this well + + align:start position:0% +a model that would help me do this well + + + align:start position:0% +a model that would help me do this well +first I need to model a credit default + + align:start position:0% +first I need to model a credit default + + + align:start position:0% +first I need to model a credit default +the credit default event I need to have + + align:start position:0% +the credit default event I need to have + + + align:start position:0% +the credit default event I need to have +this in my model and I need to have + + align:start position:0% +this in my model and I need to have + + + align:start position:0% +this in my model and I need to have +something which says FX has to move upon + + align:start position:0% + + + + align:start position:0% + +theault and then we're going to + + align:start position:0% +theault and then we're going to + + + align:start position:0% +theault and then we're going to +construct a complete market then we're + + align:start position:0% +construct a complete market then we're + + + align:start position:0% +construct a complete market then we're +going to Define some simple Dynamics on + + align:start position:0% +going to Define some simple Dynamics on + + + align:start position:0% +going to Define some simple Dynamics on +our exchange rate and on our on our + + align:start position:0% +our exchange rate and on our on our + + + align:start position:0% +our exchange rate and on our on our +defaults and and we're going to try to + + align:start position:0% +defaults and and we're going to try to + + + align:start position:0% +defaults and and we're going to try to +price for + + align:start position:0% +price for + + + align:start position:0% +price for +bonds so + + align:start position:0% +bonds so + + + align:start position:0% +bonds so +um how do we do + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +well what we generally again how are we + + align:start position:0% +well what we generally again how are we + + + align:start position:0% +well what we generally again how are we +going to use the + + align:start position:0% +going to use the + + + align:start position:0% +going to use the +models we're going to Define an SD just + + align:start position:0% +models we're going to Define an SD just + + + align:start position:0% +models we're going to Define an SD just +like I defined initially a DS over s is + + align:start position:0% +like I defined initially a DS over s is + + + align:start position:0% +like I defined initially a DS over s is +something then I'm going to solve this + + align:start position:0% +something then I'm going to solve this + + + align:start position:0% +something then I'm going to solve this +sde using IAL ically or numerically and + + align:start position:0% +sde using IAL ically or numerically and + + + align:start position:0% +sde using IAL ically or numerically and +um what's what's important the way we + + align:start position:0% +um what's what's important the way we + + + align:start position:0% +um what's what's important the way we +actually use these models in trading + + align:start position:0% +actually use these models in trading + + + align:start position:0% +actually use these models in trading +we're going to look at how the price of + + align:start position:0% +we're going to look at how the price of + + + align:start position:0% +we're going to look at how the price of +each of each instrument depends on on + + align:start position:0% +each of each instrument depends on on + + + align:start position:0% +each of each instrument depends on on +the hedging instrument and that's going + + align:start position:0% +the hedging instrument and that's going + + + align:start position:0% +the hedging instrument and that's going +to Define my hedge Ratio or my + + align:start position:0% +to Define my hedge Ratio or my + + + align:start position:0% +to Define my hedge Ratio or my +replicating strategy that's really the + + align:start position:0% +replicating strategy that's really the + + + align:start position:0% +replicating strategy that's really the +kind of the main part it it's really + + align:start position:0% +kind of the main part it it's really + + + align:start position:0% +kind of the main part it it's really +hedging and valuation and pricing are + + align:start position:0% +hedging and valuation and pricing are + + + align:start position:0% +hedging and valuation and pricing are +really the same right and left hand is + + align:start position:0% +really the same right and left hand is + + + align:start position:0% +really the same right and left hand is +really talking about the same thing you + + align:start position:0% +really talking about the same thing you + + + align:start position:0% +really talking about the same thing you +cannot really price without hedging and + + align:start position:0% +cannot really price without hedging and + + + align:start position:0% +cannot really price without hedging and +pricing without hedging is kind of + + align:start position:0% +pricing without hedging is kind of + + + align:start position:0% +pricing without hedging is kind of +meaningless in some sense pricing + + align:start position:0% +meaningless in some sense pricing + + + align:start position:0% +meaningless in some sense pricing +represents the price of a hedging + + align:start position:0% + + + + align:start position:0% + +strategy okay so uh how do we a basic + + align:start position:0% +strategy okay so uh how do we a basic + + + align:start position:0% +strategy okay so uh how do we a basic +credit model how do we model default + + align:start position:0% +credit model how do we model default + + + align:start position:0% +credit model how do we model default +well the standard model in finance for + + align:start position:0% +well the standard model in finance for + + + align:start position:0% +well the standard model in finance for +default is to define the default + + align:start position:0% +default is to define the default + + + align:start position:0% +default is to define the default +events and we say well this default + + align:start position:0% +events and we say well this default + + + align:start position:0% +events and we say well this default +event arrives is a is a discrete event + + align:start position:0% +event arrives is a is a discrete event + + + align:start position:0% +event arrives is a is a discrete event +and it arrives at at the time tow which + + align:start position:0% +and it arrives at at the time tow which + + + align:start position:0% +and it arrives at at the time tow which +is a random + + align:start position:0% +is a random + + + align:start position:0% +is a random +time and um we're going to model that to + + align:start position:0% +time and um we're going to model that to + + + align:start position:0% +time and um we're going to model that to +the time is a PO some + + align:start position:0% +the time is a PO some + + + align:start position:0% +the time is a PO some +process which means that we don't know + + align:start position:0% +process which means that we don't know + + + align:start position:0% +process which means that we don't know +when it's going to come but we know + + align:start position:0% +when it's going to come but we know + + + align:start position:0% +when it's going to come but we know +something about the probabilities of + + align:start position:0% +something about the probabilities of + + + align:start position:0% +something about the probabilities of +when it's + + align:start position:0% +when it's + + + align:start position:0% +when it's +coming and the prome process has an + + align:start position:0% +coming and the prome process has an + + + align:start position:0% +coming and the prome process has an +intensity the intensity in this case is + + align:start position:0% +intensity the intensity in this case is + + + align:start position:0% +intensity the intensity in this case is +H and basically the mean the the meaning + + align:start position:0% +H and basically the mean the the meaning + + + align:start position:0% +H and basically the mean the the meaning +of intensity means the probability of + + align:start position:0% +of intensity means the probability of + + + align:start position:0% +of intensity means the probability of +the default time not arriving by time + + align:start position:0% +the default time not arriving by time + + + align:start position:0% +the default time not arriving by time +capital t + + align:start position:0% +capital t + + + align:start position:0% +capital t +is is um e to the minus H * capital T + + align:start position:0% +is is um e to the minus H * capital T + + + align:start position:0% +is is um e to the minus H * capital T +minus Little T little t means your + + align:start position:0% +minus Little T little t means your + + + align:start position:0% +minus Little T little t means your +little T is now let's say we're saying + + align:start position:0% +little T is now let's say we're saying + + + align:start position:0% +little T is now let's say we're saying +at time Little T we know default has not + + align:start position:0% +at time Little T we know default has not + + + align:start position:0% +at time Little T we know default has not +arrived here's the probability that + + align:start position:0% +arrived here's the probability that + + + align:start position:0% +arrived here's the probability that +default would not arrive by some time T + + align:start position:0% +default would not arrive by some time T + + + align:start position:0% +default would not arrive by some time T +later so in our model we're going to + + align:start position:0% +later so in our model we're going to + + + align:start position:0% +later so in our model we're going to +make a simple assumption let's say + + align:start position:0% +make a simple assumption let's say + + + align:start position:0% +make a simple assumption let's say +constant Hazard rate and we can uh since + + align:start position:0% +constant Hazard rate and we can uh since + + + align:start position:0% +constant Hazard rate and we can uh since +we know the probability of default time + + align:start position:0% +we know the probability of default time + + + align:start position:0% +we know the probability of default time +not arri arriving after certain time + + align:start position:0% +not arri arriving after certain time + + + align:start position:0% +not arri arriving after certain time +capital T that's like a cumulative + + align:start position:0% +capital T that's like a cumulative + + + align:start position:0% +capital T that's like a cumulative +distribution we can also look find the + + align:start position:0% +distribution we can also look find the + + + align:start position:0% +distribution we can also look find the +probability density the default time + + align:start position:0% +probability density the default time + + + align:start position:0% +probability density the default time +happens at some time capital T or like + + align:start position:0% +happens at some time capital T or like + + + align:start position:0% +happens at some time capital T or like +around sometime Epsilon around around + + align:start position:0% +around sometime Epsilon around around + + + align:start position:0% +around sometime Epsilon around around +capital T it's just a derivative of the + + align:start position:0% +capital T it's just a derivative of the + + + align:start position:0% +capital T it's just a derivative of the +um of the cumulative + + align:start position:0% + + + + align:start position:0% + +distribution and corly is that the the + + align:start position:0% +distribution and corly is that the the + + + align:start position:0% +distribution and corly is that the the +probability density of theault at any + + align:start position:0% +probability density of theault at any + + + align:start position:0% +probability density of theault at any +given time is + + align:start position:0% + + + + align:start position:0% + +H which is essentially the limit of + + align:start position:0% +H which is essentially the limit of + + + align:start position:0% +H which is essentially the limit of +capital T going to Little + + align:start position:0% + + + + align:start position:0% + +T so now what happens to in our model + + align:start position:0% +T so now what happens to in our model + + + align:start position:0% +T so now what happens to in our model +what happens to FX rate well FX rate is + + align:start position:0% +what happens to FX rate well FX rate is + + + align:start position:0% +what happens to FX rate well FX rate is +going to be denoted by S and FX rate + + align:start position:0% +going to be denoted by S and FX rate + + + align:start position:0% +going to be denoted by S and FX rate +right after theault would equal to FX + + align:start position:0% +right after theault would equal to FX + + + align:start position:0% +right after theault would equal to FX +rate before theault times um e to the um + + align:start position:0% +rate before theault times um e to the um + + + align:start position:0% +rate before theault times um e to the um +e to the power J and J essentially is + + align:start position:0% +e to the power J and J essentially is + + + align:start position:0% +e to the power J and J essentially is +our kind of percent devaluation you can + + align:start position:0% +our kind of percent devaluation you can + + + align:start position:0% +our kind of percent devaluation you can +think of it so if um you can it's kind + + align:start position:0% +think of it so if um you can it's kind + + + align:start position:0% +think of it so if um you can it's kind +of like a percent evaluation so if J can + + align:start position:0% +of like a percent evaluation so if J can + + + align:start position:0% +of like a percent evaluation so if J can +go from minus infinity to Infinity if J + + align:start position:0% +go from minus infinity to Infinity if J + + + align:start position:0% +go from minus infinity to Infinity if J +is zero then that means that there's no + + align:start position:0% +is zero then that means that there's no + + + align:start position:0% +is zero then that means that there's no +devaluation so you can see the log of s + + align:start position:0% +devaluation so you can see the log of s + + + align:start position:0% +devaluation so you can see the log of s +of St basically jumps by by + + align:start position:0% +of St basically jumps by by + + + align:start position:0% +of St basically jumps by by +J so in a log normal in a log normal + + align:start position:0% +J so in a log normal in a log normal + + + align:start position:0% +J so in a log normal in a log normal +process a log of St is normal and + + align:start position:0% +process a log of St is normal and + + + align:start position:0% +process a log of St is normal and +essentially it's just a a shift of the + + align:start position:0% +essentially it's just a a shift of the + + + align:start position:0% +essentially it's just a a shift of the +normal + + align:start position:0% +normal + + + align:start position:0% +normal +distribution okay + + align:start position:0% +distribution okay + + + align:start position:0% +distribution okay +so how do we describe this we Define a + + align:start position:0% +so how do we describe this we Define a + + + align:start position:0% +so how do we describe this we Define a +jump from default for some process with + + align:start position:0% +jump from default for some process with + + + align:start position:0% +jump from default for some process with +intensity + + align:start position:0% +intensity + + + align:start position:0% +intensity +H as on the + + align:start position:0% +H as on the + + + align:start position:0% +H as on the +board and um our FX Dynamics and I + + align:start position:0% +board and um our FX Dynamics and I + + + align:start position:0% +board and um our FX Dynamics and I +apologize for the small small script is + + align:start position:0% +apologize for the small small script is + + + align:start position:0% +apologize for the small small script is +that + + align:start position:0% +that + + + align:start position:0% +that +um our D log of s would have some uh + + align:start position:0% +um our D log of s would have some uh + + + align:start position:0% +um our D log of s would have some uh +some drift + + align:start position:0% +some drift + + + align:start position:0% +some drift +mtdt and then a jump process + + align:start position:0% +mtdt and then a jump process + + + align:start position:0% +mtdt and then a jump process +jdn so this is slightly different from + + align:start position:0% +jdn so this is slightly different from + + + align:start position:0% +jdn so this is slightly different from +what you've seen so far so far you've + + align:start position:0% +what you've seen so far so far you've + + + align:start position:0% +what you've seen so far so far you've +seen um brownan motions this is uh + + align:start position:0% +seen um brownan motions this is uh + + + align:start position:0% +seen um brownan motions this is uh +jdn this is now a jump process now what + + align:start position:0% +jdn this is now a jump process now what + + + align:start position:0% +jdn this is now a jump process now what +we want again is um you know what we + + align:start position:0% +we want again is um you know what we + + + align:start position:0% +we want again is um you know what we +want is uh from our we want still our + + align:start position:0% +want is uh from our we want still our + + + align:start position:0% +want is uh from our we want still our +standard no Arbitrage condition to + + align:start position:0% +standard no Arbitrage condition to + + + align:start position:0% +standard no Arbitrage condition to +remain constant and from before we had a + + align:start position:0% +remain constant and from before we had a + + + align:start position:0% +remain constant and from before we had a +condition that expected value + + align:start position:0% +condition that expected value + + + align:start position:0% +condition that expected value +of s of + + align:start position:0% +of s of + + + align:start position:0% +of s of +T has to be S of0 time e to the + + align:start position:0% +T has to be S of0 time e to the + + + align:start position:0% +T has to be S of0 time e to the +um RF minus + + align:start position:0% +um RF minus + + + align:start position:0% +um RF minus +Rd times + + align:start position:0% +Rd times + + + align:start position:0% +Rd times +um time + + align:start position:0% +um time + + + align:start position:0% +um time +T right so that that still has to be the + + align:start position:0% +T right so that that still has to be the + + + align:start position:0% +T right so that that still has to be the +case um and in our case we're going to + + align:start position:0% +case um and in our case we're going to + + + align:start position:0% +case um and in our case we're going to +assume that RF and RD are both + + align:start position:0% +assume that RF and RD are both + + + align:start position:0% +assume that RF and RD are both +um are both um zero so in our case we're + + align:start position:0% +um are both um zero so in our case we're + + + align:start position:0% +um are both um zero so in our case we're +going to ask basically zero interest + + align:start position:0% +going to ask basically zero interest + + + align:start position:0% +going to ask basically zero interest +rate environment to make again the model + + align:start position:0% +rate environment to make again the model + + + align:start position:0% +rate environment to make again the model +simple then we just want the expected + + align:start position:0% +simple then we just want the expected + + + align:start position:0% +simple then we just want the expected +value of St to be s0o so how do we + + align:start position:0% +value of St to be s0o so how do we + + + align:start position:0% +value of St to be s0o so how do we +achieve that well we need to show + + align:start position:0% +achieve that well we need to show + + + align:start position:0% +achieve that well we need to show +essentially that this uh this mu the + + align:start position:0% +essentially that this uh this mu the + + + align:start position:0% +essentially that this uh this mu the +drift has to equal to um this expression + + align:start position:0% +drift has to equal to um this expression + + + align:start position:0% +drift has to equal to um this expression +here H * 1 e to the + + align:start position:0% +here H * 1 e to the + + + align:start position:0% +here H * 1 e to the +J that's known as the compensator term + + align:start position:0% +J that's known as the compensator term + + + align:start position:0% +J that's known as the compensator term +and you can think you can imagine this + + align:start position:0% +and you can think you can imagine this + + + align:start position:0% +and you can think you can imagine this +is the formula like if if I have a Pon + + align:start position:0% +is the formula like if if I have a Pon + + + align:start position:0% +is the formula like if if I have a Pon +process that has a possibility of + + align:start position:0% +process that has a possibility of + + + align:start position:0% +process that has a possibility of +jumping up then in order for that Pon + + align:start position:0% +jumping up then in order for that Pon + + + align:start position:0% +jumping up then in order for that Pon +process to be on + + align:start position:0% +process to be on + + + align:start position:0% +process to be on +average to be equal to the initial value + + align:start position:0% +average to be equal to the initial value + + + align:start position:0% +average to be equal to the initial value +it has to be like kind of trending down + + align:start position:0% +it has to be like kind of trending down + + + align:start position:0% +it has to be like kind of trending down +most of the time and then um and then so + + align:start position:0% +most of the time and then um and then so + + + align:start position:0% +most of the time and then um and then so +that when the possibility of jump is + + align:start position:0% +that when the possibility of jump is + + + align:start position:0% +that when the possibility of jump is +there the average of the two can be can + + align:start position:0% +there the average of the two can be can + + + align:start position:0% +there the average of the two can be can +be zero so that's that's known as a + + align:start position:0% +be zero so that's that's known as a + + + align:start position:0% +be zero so that's that's known as a +compensator term of the posan process + + align:start position:0% +compensator term of the posan process + + + align:start position:0% +compensator term of the posan process +okay so we can go through and um and + + align:start position:0% +okay so we can go through and um and + + + align:start position:0% +okay so we can go through and um and +derive how that's um how do we get we + + align:start position:0% +derive how that's um how do we get we + + + align:start position:0% +derive how that's um how do we get we +not what we're going to do is we're + + align:start position:0% +not what we're going to do is we're + + + align:start position:0% +not what we're going to do is we're +going to we're going to check that this + + align:start position:0% +going to we're going to check that this + + + align:start position:0% +going to we're going to check that this +form actually does indeed give you um + + align:start position:0% +form actually does indeed give you um + + + align:start position:0% +form actually does indeed give you um +that expectation that satisfy the the + + align:start position:0% +that expectation that satisfy the the + + + align:start position:0% +that expectation that satisfy the the +condition for the + + align:start position:0% +condition for the + + + align:start position:0% +condition for the +expectation okay so again we start with + + align:start position:0% +expectation okay so again we start with + + + align:start position:0% +expectation okay so again we start with +um the St + + align:start position:0% +um the St + + + align:start position:0% +um the St +is is um M to T so it's going to be in + + align:start position:0% +is is um M to T so it's going to be in + + + align:start position:0% +is is um M to T so it's going to be in +our case is going to + + align:start position:0% +our case is going to + + + align:start position:0% +our case is going to +be um H * 1 I + + align:start position:0% + + + + align:start position:0% + +CJ time the indicator function of to + + align:start position:0% +CJ time the indicator function of to + + + align:start position:0% +CJ time the indicator function of to +bigger than + + align:start position:0% +bigger than + + + align:start position:0% +bigger than +t plus J + + align:start position:0% +t plus J + + + align:start position:0% +t plus J +DN T + + align:start position:0% +DN T + + + align:start position:0% +DN T +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um + + align:start position:0% + + + + align:start position:0% + +we and we're we're not not D St sorry + + align:start position:0% +we and we're we're not not D St sorry + + + align:start position:0% +we and we're we're not not D St sorry +this is D of log of St okay so now U + + align:start position:0% +this is D of log of St okay so now U + + + align:start position:0% +this is D of log of St okay so now U +what do we want to do we want to + + align:start position:0% +what do we want to do we want to + + + align:start position:0% +what do we want to do we want to +integrate this this equation so we + + align:start position:0% +integrate this this equation so we + + + align:start position:0% +integrate this this equation so we +essentially what we're going to do we're + + align:start position:0% +essentially what we're going to do we're + + + align:start position:0% +essentially what we're going to do we're +going to WR + + align:start position:0% +going to WR + + + align:start position:0% +going to WR +integral from 0 to capital T of D of log + + align:start position:0% +integral from 0 to capital T of D of log + + + align:start position:0% +integral from 0 to capital T of D of log +s t we integrate both sides integral + + align:start position:0% +s t we integrate both sides integral + + + align:start position:0% +s t we integrate both sides integral +from 0 to capital t h 1 minus E to the + + align:start position:0% +from 0 to capital t h 1 minus E to the + + + align:start position:0% +from 0 to capital t h 1 minus E to the +J T is um bigger than + + align:start position:0% +J T is um bigger than + + + align:start position:0% +J T is um bigger than +T + + align:start position:0% +T + + + align:start position:0% +T +times here has a DT in here times the + + align:start position:0% +times here has a DT in here times the + + + align:start position:0% +times here has a DT in here times the +t plus um integral from 0 to T of J D + + align:start position:0% + + + + align:start position:0% + +nt Okay so + + align:start position:0% +nt Okay so + + + align:start position:0% +nt Okay so +um + + align:start position:0% +um + + + align:start position:0% +um +then this side just gives me essentially + + align:start position:0% +then this side just gives me essentially + + + align:start position:0% +then this side just gives me essentially +the um log of + + align:start position:0% +the um log of + + + align:start position:0% +the um log of +St over s0 this is + + align:start position:0% +St over s0 this is + + + align:start position:0% +St over s0 this is +just basic calculus and + + align:start position:0% +just basic calculus and + + + align:start position:0% +just basic calculus and +then here we have + + align:start position:0% +then here we have + + + align:start position:0% +then here we have +um we can this indicator + + align:start position:0% +um we can this indicator + + + align:start position:0% +um we can this indicator +function just says um + + align:start position:0% +function just says um + + + align:start position:0% +function just says um +if T is bigger than T it's one if T is + + align:start position:0% +if T is bigger than T it's one if T is + + + align:start position:0% +if T is bigger than T it's one if T is +less than T then it's zero + + align:start position:0% +less than T then it's zero + + + align:start position:0% +less than T then it's zero +that's that's basically what it is so I + + align:start position:0% +that's that's basically what it is so I + + + align:start position:0% +that's that's basically what it is so I +know that essentially when T this is + + align:start position:0% +know that essentially when T this is + + + align:start position:0% +know that essentially when T this is +this is only one when T is less than T + + align:start position:0% +this is only one when T is less than T + + + align:start position:0% +this is only one when T is less than T +so I can my integral goes from0 to to + + align:start position:0% +so I can my integral goes from0 to to + + + align:start position:0% +so I can my integral goes from0 to to +now I can replace this from an integral + + align:start position:0% +now I can replace this from an integral + + + align:start position:0% +now I can replace this from an integral +from zero to to and I can take out the + + align:start position:0% +from zero to to and I can take out the + + + align:start position:0% +from zero to to and I can take out the +indicator function + + align:start position:0% + + + + align:start position:0% + +now of H 1 minus E to the J + + align:start position:0% +now of H 1 minus E to the J + + + align:start position:0% +now of H 1 minus E to the J +DT and + + align:start position:0% + + + + align:start position:0% + +um then I can say well what if + + align:start position:0% +um then I can say well what if + + + align:start position:0% +um then I can say well what if +uh what if towel is um bigger + + align:start position:0% +uh what if towel is um bigger + + + align:start position:0% +uh what if towel is um bigger +than there is there is also + + align:start position:0% +than there is there is also + + + align:start position:0% +than there is there is also +the there is a possibility here that to + + align:start position:0% +the there is a possibility here that to + + + align:start position:0% +the there is a possibility here that to +is + + align:start position:0% + + + + align:start position:0% + +um this is I would say this is + + align:start position:0% +um this is I would say this is + + + align:start position:0% +um this is I would say this is +possibility this is T is less than + + align:start position:0% +possibility this is T is less than + + + align:start position:0% +possibility this is T is less than +capital + + align:start position:0% +capital + + + align:start position:0% +capital +T and there's also a possibility that t + + align:start position:0% +T and there's also a possibility that t + + + align:start position:0% +T and there's also a possibility that t +is greater than capital T right in which + + align:start position:0% +is greater than capital T right in which + + + align:start position:0% +is greater than capital T right in which +case if T is greater than capital T this + + align:start position:0% +case if T is greater than capital T this + + + align:start position:0% +case if T is greater than capital T this +integral is there without any indicator + + align:start position:0% +integral is there without any indicator + + + align:start position:0% +integral is there without any indicator +functions right so again integral from 0 + + align:start position:0% +functions right so again integral from 0 + + + align:start position:0% +functions right so again integral from 0 +to capital T of h 1us e to the J DT + + align:start position:0% +to capital T of h 1us e to the J DT + + + align:start position:0% +to capital T of h 1us e to the J DT +times indicator function to being + + align:start position:0% +times indicator function to being + + + align:start position:0% +times indicator function to being +greater than capital T so I kind of + + align:start position:0% +greater than capital T so I kind of + + + align:start position:0% +greater than capital T so I kind of +divided + + align:start position:0% +divided + + + align:start position:0% +divided +um divided this in + + align:start position:0% +um divided this in + + + align:start position:0% +um divided this in +this counting both possibilities + + align:start position:0% +this counting both possibilities + + + align:start position:0% +this counting both possibilities +separately + + align:start position:0% +separately + + + align:start position:0% +separately +essentially and now the second part + + align:start position:0% +essentially and now the second part + + + align:start position:0% +essentially and now the second part +integral from 0 to capital T of JD NT + + align:start position:0% +integral from 0 to capital T of JD NT + + + align:start position:0% +integral from 0 to capital T of JD NT +now n is uh + + align:start position:0% +now n is uh + + + align:start position:0% +now n is uh +is what was n well n of + + align:start position:0% +is what was n well n of + + + align:start position:0% +is what was n well n of +T is + + align:start position:0% +T is + + + align:start position:0% +T is +essentially um it starts out at well it + + align:start position:0% +essentially um it starts out at well it + + + align:start position:0% +essentially um it starts out at well it +starts out as as zero for t + + align:start position:0% +starts out as as zero for t + + + align:start position:0% +starts out as as zero for t +less than T less than to and then + + align:start position:0% +less than T less than to and then + + + align:start position:0% +less than T less than to and then +becomes one for T bigger than + + align:start position:0% + + + + align:start position:0% + +T + + align:start position:0% + + + + align:start position:0% + +So this integral is Just J is a constant + + align:start position:0% +So this integral is Just J is a constant + + + align:start position:0% +So this integral is Just J is a constant +so it's just J * n of + + align:start position:0% + + + + align:start position:0% + +T and this is capital TQ and by the way + + align:start position:0% +T and this is capital TQ and by the way + + + align:start position:0% +T and this is capital TQ and by the way +all these um all these derivation is + + align:start position:0% +all these um all these derivation is + + + align:start position:0% +all these um all these derivation is +posted on the note so you don't + + align:start position:0% +posted on the note so you don't + + + align:start position:0% +posted on the note so you don't +necessarily have to + + align:start position:0% +necessarily have to + + + align:start position:0% +necessarily have to +worry if you can't + + align:start position:0% + + + + align:start position:0% + +um can I move this board up not + + align:start position:0% +um can I move this board up not + + + align:start position:0% +um can I move this board up not +really how does it + + align:start position:0% + + + + align:start position:0% + +work okay so I'm going to do one more + + align:start position:0% +work okay so I'm going to do one more + + + align:start position:0% +work okay so I'm going to do one more +line I'm going to erase this top + + align:start position:0% + + + + align:start position:0% + +line so we got to here and there's one + + align:start position:0% +line so we got to here and there's one + + + align:start position:0% +line so we got to here and there's one +more step which is now to actually do + + align:start position:0% +more step which is now to actually do + + + align:start position:0% +more step which is now to actually do +the + + align:start position:0% +the + + + align:start position:0% +the +integration um we're going to have log + + align:start position:0% +integration um we're going to have log + + + align:start position:0% +integration um we're going to have log +of St over + + align:start position:0% +of St over + + + align:start position:0% +of St over +s0 + + align:start position:0% +s0 + + + align:start position:0% +s0 +well + + align:start position:0% +well + + + align:start position:0% +well +uh two things now if to is less than T + + align:start position:0% +uh two things now if to is less than T + + + align:start position:0% +uh two things now if to is less than T +So default happened before capital T + + align:start position:0% +So default happened before capital T + + + align:start position:0% +So default happened before capital T +then what is NT NT is going to be + + align:start position:0% +then what is NT NT is going to be + + + align:start position:0% +then what is NT NT is going to be +one so I can say this equals to + + align:start position:0% + + + + align:start position:0% + +H to * 1 minus E to the J this is the + + align:start position:0% +H to * 1 minus E to the J this is the + + + align:start position:0% +H to * 1 minus E to the J this is the +first this integral + + align:start position:0% +first this integral + + + align:start position:0% +first this integral +now + + align:start position:0% +now + + + align:start position:0% +now +um plus + + align:start position:0% +um plus + + + align:start position:0% +um plus +J so this is this this is if um ta is + + align:start position:0% +J so this is this this is if um ta is + + + align:start position:0% +J so this is this this is if um ta is +less than T and then if T is bigger than + + align:start position:0% +less than T and then if T is bigger than + + + align:start position:0% +less than T and then if T is bigger than +T then um this term is zero this is the + + align:start position:0% +T then um this term is zero this is the + + + align:start position:0% +T then um this term is zero this is the +term that's for T bigger than T this is + + align:start position:0% +term that's for T bigger than T this is + + + align:start position:0% +term that's for T bigger than T this is +just a constant so it just becomes H * + + align:start position:0% +just a constant so it just becomes H * + + + align:start position:0% +just a constant so it just becomes H * +capital T 1 - e to the + + align:start position:0% +capital T 1 - e to the + + + align:start position:0% +capital T 1 - e to the +J time indicator function of to bigger + + align:start position:0% +J time indicator function of to bigger + + + align:start position:0% +J time indicator function of to bigger +than T bigger bigger than equal + + align:start position:0% +than T bigger bigger than equal + + + align:start position:0% +than T bigger bigger than equal +T and we can then exponentiate both + + align:start position:0% +T and we can then exponentiate both + + + align:start position:0% +T and we can then exponentiate both +sides and it becomes um here's the magic + + align:start position:0% +sides and it becomes um here's the magic + + + align:start position:0% +sides and it becomes um here's the magic +of the Blackboard you can erase St + + align:start position:0% +of the Blackboard you can erase St + + + align:start position:0% +of the Blackboard you can erase St +equals s0 times the + + align:start position:0% +equals s0 times the + + + align:start position:0% +equals s0 times the +exponential of + + align:start position:0% +exponential of + + + align:start position:0% +exponential of +this + + align:start position:0% +this + + + align:start position:0% +this +so I've kind + + align:start position:0% +so I've kind + + + align:start position:0% +so I've kind +of here is my um this is my exchange + + align:start position:0% +of here is my um this is my exchange + + + align:start position:0% +of here is my um this is my exchange +this is what my exchange rate is going + + align:start position:0% +this is what my exchange rate is going + + + align:start position:0% +this is what my exchange rate is going +to + + align:start position:0% +to + + + align:start position:0% +to +be + + align:start position:0% +be + + + align:start position:0% +be +essentially at at time capital T now + + align:start position:0% +essentially at at time capital T now + + + align:start position:0% +essentially at at time capital T now +what was I trying to do I was trying to + + align:start position:0% +what was I trying to do I was trying to + + + align:start position:0% +what was I trying to do I was trying to +do this right to compute this + + align:start position:0% +do this right to compute this + + + align:start position:0% +do this right to compute this +expectation but to compute expectation + + align:start position:0% +expectation but to compute expectation + + + align:start position:0% +expectation but to compute expectation +now I have to integrate over the + + align:start position:0% +now I have to integrate over the + + + align:start position:0% +now I have to integrate over the +probability distribution of tow now + + align:start position:0% +probability distribution of tow now + + + align:start position:0% +probability distribution of tow now +remember probability distribution of tow + + align:start position:0% +remember probability distribution of tow + + + align:start position:0% +remember probability distribution of tow +is a pum process + + align:start position:0% + + + + align:start position:0% + +so we have essentially um I'll write it + + align:start position:0% +so we have essentially um I'll write it + + + align:start position:0% +so we have essentially um I'll write it +here F of + + align:start position:0% +here F of + + + align:start position:0% +here F of +um 0 t is just a h * + + align:start position:0% +um 0 t is just a h * + + + align:start position:0% +um 0 t is just a h * +eus h t that's the um kind of the + + align:start position:0% +eus h t that's the um kind of the + + + align:start position:0% +eus h t that's the um kind of the +probability density of to so now what I + + align:start position:0% +probability density of to so now what I + + + align:start position:0% +probability density of to so now what I +need to do is essentially the + + align:start position:0% +need to do is essentially the + + + align:start position:0% +need to do is essentially the +expectation of St is just integral + + align:start position:0% +expectation of St is just integral + + + align:start position:0% +expectation of St is just integral +from 0 to Infinity of s of T * 5 0 t d + + align:start position:0% +from 0 to Infinity of s of T * 5 0 t d + + + align:start position:0% +from 0 to Infinity of s of T * 5 0 t d +to so here is my S of T you can think of + + align:start position:0% +to so here is my S of T you can think of + + + align:start position:0% +to so here is my S of T you can think of +this s of T of + + align:start position:0% + + + + align:start position:0% + +to for time to so this is for a given + + align:start position:0% +to for time to so this is for a given + + + align:start position:0% +to for time to so this is for a given +time to I know what my what my value of + + align:start position:0% +time to I know what my what my value of + + + align:start position:0% +time to I know what my what my value of +s oft is so I can do this integral and + + align:start position:0% +s oft is so I can do this integral and + + + align:start position:0% +s oft is so I can do this integral and +now we're going to do + + align:start position:0% +now we're going to do + + + align:start position:0% +now we're going to do +it um so what is going to be the first + + align:start position:0% +it um so what is going to be the first + + + align:start position:0% +it um so what is going to be the first +term so the + + align:start position:0% +term so the + + + align:start position:0% +term so the +exponential of s of of St + + align:start position:0% +exponential of s of of St + + + align:start position:0% +exponential of s of of St +T not exponential but the expectation of + + align:start position:0% +T not exponential but the expectation of + + + align:start position:0% +T not exponential but the expectation of +St is going to + + align:start position:0% +St is going to + + + align:start position:0% +St is going to +be + + align:start position:0% +be + + + align:start position:0% +be +um first so it's going to + + align:start position:0% +um first so it's going to + + + align:start position:0% +um first so it's going to +be integral from zero to capital t is + + align:start position:0% +be integral from zero to capital t is + + + align:start position:0% +be integral from zero to capital t is +going to have two terms first I'm going + + align:start position:0% +going to have two terms first I'm going + + + align:start position:0% +going to have two terms first I'm going +to integrate from zero to capital T and + + align:start position:0% +to integrate from zero to capital T and + + + align:start position:0% +to integrate from zero to capital T and +then I'm going to integrate from capital + + align:start position:0% +then I'm going to integrate from capital + + + align:start position:0% +then I'm going to integrate from capital +T to to Infinity so I'll split this + + align:start position:0% +T to to Infinity so I'll split this + + + align:start position:0% +T to to Infinity so I'll split this +integral into two parts and from 0 to + + align:start position:0% +integral into two parts and from 0 to + + + align:start position:0% +integral into two parts and from 0 to +capital T I have essentially um so H * e + + align:start position:0% +capital T I have essentially um so H * e + + + align:start position:0% +capital T I have essentially um so H * e +to the minus H + + align:start position:0% +to the minus H + + + align:start position:0% +to the minus H +to and this is my density function and + + align:start position:0% +to and this is my density function and + + + align:start position:0% +to and this is my density function and +then I'm going to plug that in here so + + align:start position:0% +then I'm going to plug that in here so + + + align:start position:0% +then I'm going to plug that in here so +this is for to being less than T so it's + + align:start position:0% +this is for to being less than T so it's + + + align:start position:0% +this is for to being less than T so it's +basically this first + + align:start position:0% +basically this first + + + align:start position:0% +basically this first +term I'm going to divide this by s0 here + + align:start position:0% +term I'm going to divide this by s0 here + + + align:start position:0% +term I'm going to divide this by s0 here +going to to make it easy so first term + + align:start position:0% +going to to make it easy so first term + + + align:start position:0% +going to to make it easy so first term +is going to be e to the H to * 1- a to + + align:start position:0% +is going to be e to the H to * 1- a to + + + align:start position:0% +is going to be e to the H to * 1- a to +the J + + + align:start position:0% +the J + + + + align:start position:0% +the J + +J + + align:start position:0% +J + + + align:start position:0% +J +okay and + + align:start position:0% + + + + align:start position:0% + +um so this is + + align:start position:0% +um so this is + + + align:start position:0% +um so this is +the to so this is the first part from0 + + align:start position:0% +the to so this is the first part from0 + + + align:start position:0% +the to so this is the first part from0 +to T and the second part is essentially + + align:start position:0% +to T and the second part is essentially + + + align:start position:0% +to T and the second part is essentially +the integral from + + align:start position:0% +the integral from + + + align:start position:0% +the integral from +capital T to + + align:start position:0% +capital T to + + + align:start position:0% +capital T to +Infinity for um for to being bigger than + + align:start position:0% +Infinity for um for to being bigger than + + + align:start position:0% +Infinity for um for to being bigger than +capital T now that's actually this part + + align:start position:0% +capital T now that's actually this part + + + align:start position:0% +capital T now that's actually this part +here does not depend on to it's a + + align:start position:0% +here does not depend on to it's a + + + align:start position:0% +here does not depend on to it's a +constant so it would be just h capital T + + align:start position:0% +constant so it would be just h capital T + + + align:start position:0% +constant so it would be just h capital T +1us C to the J times what the + + align:start position:0% +1us C to the J times what the + + + align:start position:0% +1us C to the J times what the +probability of uh of to being bigger + + align:start position:0% +probability of uh of to being bigger + + + align:start position:0% +probability of uh of to being bigger +than capital T well it's just uh that's + + align:start position:0% +than capital T well it's just uh that's + + + align:start position:0% +than capital T well it's just uh that's +the cumulative probability distribution + + align:start position:0% +the cumulative probability distribution + + + align:start position:0% +the cumulative probability distribution +we saw before just e to the minus + + align:start position:0% +we saw before just e to the minus + + + align:start position:0% +we saw before just e to the minus +HT that's the probability that t is + + align:start position:0% +HT that's the probability that t is + + + align:start position:0% +HT that's the probability that t is +bigger than + + align:start position:0% +bigger than + + + align:start position:0% +bigger than +t Okay + + align:start position:0% +t Okay + + + align:start position:0% +t Okay +so and what I should really it's e to + + align:start position:0% +so and what I should really it's e to + + + align:start position:0% +so and what I should really it's e to +the HT 1 minus E to the J okay time e to + + align:start position:0% +the HT 1 minus E to the J okay time e to + + + align:start position:0% +the HT 1 minus E to the J okay time e to +the minus HT so I can now + + align:start position:0% +the minus HT so I can now + + + align:start position:0% +the minus HT so I can now +simplify this expression + + align:start position:0% +simplify this expression + + + align:start position:0% +simplify this expression +somewhat uh you can see that say this + + align:start position:0% +somewhat uh you can see that say this + + + align:start position:0% +somewhat uh you can see that say this +term and this + + align:start position:0% +term and this + + + align:start position:0% +term and this +term this term and this term go away + + align:start position:0% +term this term and this term go away + + + align:start position:0% +term this term and this term go away +and um also this term and this go away + + align:start position:0% +and um also this term and this go away + + + align:start position:0% +and um also this term and this go away +so I'm left with um integral from 0 to + + align:start position:0% +so I'm left with um integral from 0 to + + + align:start position:0% +so I'm left with um integral from 0 to +T of + + align:start position:0% +T of + + + align:start position:0% +T of +um + + align:start position:0% +um + + + align:start position:0% +um +essentially + + align:start position:0% + + + + align:start position:0% + +um H * e + + align:start position:0% +um H * e + + + align:start position:0% +um H * e +to H + + align:start position:0% +to H + + + align:start position:0% +to H +to minus H to e to the J + + align:start position:0% +to minus H to e to the J + + + align:start position:0% +to minus H to e to the J +time e to the + + align:start position:0% +time e to the + + + align:start position:0% +time e to the +J right so you can think of this as H * + + align:start position:0% +J right so you can think of this as H * + + + align:start position:0% +J right so you can think of this as H * +e to the J * eus H to e to the J D + + align:start position:0% +e to the J * eus H to e to the J D + + + align:start position:0% +e to the J * eus H to e to the J D +to plus e to the minus h capital T * C + + align:start position:0% +to plus e to the minus h capital T * C + + + align:start position:0% +to plus e to the minus h capital T * C +to the + + align:start position:0% +to the + + + align:start position:0% +to the +J so this is if I think of h e to the J + + align:start position:0% +J so this is if I think of h e to the J + + + align:start position:0% +J so this is if I think of h e to the J +is this is the constant in front of to + + align:start position:0% +is this is the constant in front of to + + + align:start position:0% +is this is the constant in front of to +this is just a normal this is a standard + + align:start position:0% +this is just a normal this is a standard + + + align:start position:0% +this is just a normal this is a standard +um integral of + + align:start position:0% +um integral of + + + align:start position:0% +um integral of +exponential so this just becomes + + align:start position:0% +exponential so this just becomes + + + align:start position:0% +exponential so this just becomes +essentially e to the + + align:start position:0% +essentially e to the + + + align:start position:0% +essentially e to the +um e to the minus HT e to the + + align:start position:0% +um e to the minus HT e to the + + + align:start position:0% +um e to the minus HT e to the +J minus + + align:start position:0% +J minus + + + align:start position:0% +J minus +one plus I the minus HT a to the + + align:start position:0% +one plus I the minus HT a to the + + + align:start position:0% +one plus I the minus HT a to the +J and um these two terms are going to + + align:start position:0% +J and um these two terms are going to + + + align:start position:0% +J and um these two terms are going to +cancel out and I'm going to have one so + + align:start position:0% +cancel out and I'm going to have one so + + + align:start position:0% +cancel out and I'm going to have one so +again the ratio of e the St over s z + + align:start position:0% +again the ratio of e the St over s z + + + align:start position:0% +again the ratio of e the St over s z +just gives you one so all this is just + + align:start position:0% +just gives you one so all this is just + + + align:start position:0% +just gives you one so all this is just +to kind of show you a little bit how you + + align:start position:0% +to kind of show you a little bit how you + + + align:start position:0% +to kind of show you a little bit how you +work with uh jump processes and you take + + align:start position:0% +work with uh jump processes and you take + + + align:start position:0% +work with uh jump processes and you take +expectations it's not nothing really you + + align:start position:0% +expectations it's not nothing really you + + + align:start position:0% +expectations it's not nothing really you +haven't seen in terms of math it just + + align:start position:0% +haven't seen in terms of math it just + + + align:start position:0% +haven't seen in terms of math it just +slightly different from Brown emotions + + align:start position:0% +slightly different from Brown emotions + + + align:start position:0% +slightly different from Brown emotions +but still the same idea you have DN and + + align:start position:0% +but still the same idea you have DN and + + + align:start position:0% +but still the same idea you have DN and +you have a compensator + + align:start position:0% +you have a compensator + + + align:start position:0% +you have a compensator +term so this here proves that + + align:start position:0% +term so this here proves that + + + align:start position:0% +term so this here proves that +essentially my drift guess that I + + align:start position:0% +essentially my drift guess that I + + + align:start position:0% +essentially my drift guess that I +started with in fact does PR use does + + align:start position:0% +started with in fact does PR use does + + + align:start position:0% +started with in fact does PR use does +make my expectation + + align:start position:0% + + + + align:start position:0% + +zero okay so what have we done so far + + align:start position:0% +zero okay so what have we done so far + + + align:start position:0% +zero okay so what have we done so far +we've D defined the Dynamics for log of + + align:start position:0% +we've D defined the Dynamics for log of + + + align:start position:0% +we've D defined the Dynamics for log of +s we jump on default defined probability + + align:start position:0% +s we jump on default defined probability + + + align:start position:0% +s we jump on default defined probability +density and + + align:start position:0% +density and + + + align:start position:0% +density and +now we have to derive kind of dynamics + + align:start position:0% +now we have to derive kind of dynamics + + + align:start position:0% +now we have to derive kind of dynamics +of S price Euro bonds hedge ratios and + + align:start position:0% +of S price Euro bonds hedge ratios and + + + align:start position:0% +of S price Euro bonds hedge ratios and +so + + align:start position:0% +so + + + align:start position:0% +so +on okay so + + align:start position:0% + + + + align:start position:0% + +um log of s Dynamics we and I apologize + + align:start position:0% +um log of s Dynamics we and I apologize + + + align:start position:0% +um log of s Dynamics we and I apologize +again for the small + + align:start position:0% +again for the small + + + align:start position:0% +again for the small +font we have here we have the log ass + + align:start position:0% +font we have here we have the log ass + + + align:start position:0% +font we have here we have the log ass +Dynamics um applying applying itos + + align:start position:0% +Dynamics um applying applying itos + + + align:start position:0% +Dynamics um applying applying itos +lama itos lama there is a there is an + + align:start position:0% +lama itos lama there is a there is an + + + align:start position:0% +lama itos lama there is a there is an +equivalent + + align:start position:0% +equivalent + + + align:start position:0% +equivalent +um it was Lemo you know from Brown and + + align:start position:0% +um it was Lemo you know from Brown and + + + align:start position:0% +um it was Lemo you know from Brown and +motion but there is another one + + align:start position:0% +motion but there is another one + + + align:start position:0% +motion but there is another one +for for some processes as well and that + + align:start position:0% +for for some processes as well and that + + + align:start position:0% +for for some processes as well and that +is it Lam is like the chain rule so if + + align:start position:0% +is it Lam is like the chain rule so if + + + align:start position:0% +is it Lam is like the chain rule so if +you know the process for for some for + + align:start position:0% +you know the process for for some for + + + align:start position:0% +you know the process for for some for +some um say log of s how do you find the + + align:start position:0% +some um say log of s how do you find the + + + align:start position:0% +some um say log of s how do you find the +process for S + + align:start position:0% +process for S + + + align:start position:0% +process for S +itself well in uh in this case um what's + + align:start position:0% +itself well in uh in this case um what's + + + align:start position:0% +itself well in uh in this case um what's +going to happen is our DS over + + align:start position:0% +going to happen is our DS over + + + align:start position:0% +going to happen is our DS over +s is going to be um yeah the same drift + + align:start position:0% +s is going to be um yeah the same drift + + + align:start position:0% +s is going to be um yeah the same drift +H * 1 the minus + + align:start position:0% +H * 1 the minus + + + align:start position:0% +H * 1 the minus +J th less than T DT sorry T less than + + align:start position:0% +J th less than T DT sorry T less than + + + align:start position:0% +J th less than T DT sorry T less than +to + + align:start position:0% +to + + + align:start position:0% +to +plus um the e to the J minus + + align:start position:0% +plus um the e to the J minus + + + align:start position:0% +plus um the e to the J minus +one the J minus one + + align:start position:0% +one the J minus one + + + align:start position:0% +one the J minus one +DN + + align:start position:0% +DN + + + align:start position:0% +DN +okay D NT so that's the uh that's that's + + align:start position:0% +okay D NT so that's the uh that's that's + + + align:start position:0% +okay D NT so that's the uh that's that's +really the uh the derivation of + + align:start position:0% +really the uh the derivation of + + + align:start position:0% +really the uh the derivation of +um that's derivation of um of the um + + align:start position:0% +um that's derivation of um of the um + + + align:start position:0% +um that's derivation of um of the um +that that's the final result for for S + + align:start position:0% +that that's the final result for for S + + + align:start position:0% +that that's the final result for for S +now how do we get to this + + align:start position:0% +now how do we get to this + + + align:start position:0% +now how do we get to this +well maybe I should I can write ital + + align:start position:0% +well maybe I should I can write ital + + + align:start position:0% +well maybe I should I can write ital +lamb what does it say it l basically + + align:start position:0% +lamb what does it say it l basically + + + align:start position:0% +lamb what does it say it l basically +says that if we have the XT is equal + + align:start position:0% +says that if we have the XT is equal + + + align:start position:0% +says that if we have the XT is equal +Mt plus + + align:start position:0% +Mt plus + + + align:start position:0% +Mt plus +jdn then and you have a function y of T + + align:start position:0% +jdn then and you have a function y of T + + + align:start position:0% +jdn then and you have a function y of T +which is f of + + align:start position:0% +which is f of + + + align:start position:0% +which is f of +XT then + + align:start position:0% + + + + align:start position:0% + +Dy is + + align:start position:0% +Dy is + + + align:start position:0% +Dy is +um + + align:start position:0% +um + + + align:start position:0% +um +DF DX mu + + align:start position:0% +DF DX mu + + + align:start position:0% +DF DX mu +DT + + align:start position:0% + + + + align:start position:0% + +plus F of xt+ + + align:start position:0% + + + + align:start position:0% + +J minus F of + + align:start position:0% + + + + align:start position:0% + +XT D + + align:start position:0% + + + + align:start position:0% + +NT + + align:start position:0% +NT + + + align:start position:0% +NT +so you can it's it's um + + align:start position:0% + + + + align:start position:0% + +this is the kind of the term that the + + align:start position:0% +this is the kind of the term that the + + + align:start position:0% +this is the kind of the term that the +kind of the analog analog of the + + align:start position:0% +kind of the analog analog of the + + + align:start position:0% +kind of the analog analog of the +convexity term in uh in your brownan + + align:start position:0% +convexity term in uh in your brownan + + + align:start position:0% +convexity term in uh in your brownan +motion it was + + align:start position:0% +motion it was + + + align:start position:0% +motion it was +Lama but it's now for jump processes so + + align:start position:0% +Lama but it's now for jump processes so + + + align:start position:0% +Lama but it's now for jump processes so +this F of XT plus J and F of XT so what + + align:start position:0% +this F of XT plus J and F of XT so what + + + align:start position:0% +this F of XT plus J and F of XT so what +happens essentially to so you have some + + align:start position:0% +happens essentially to so you have some + + + align:start position:0% +happens essentially to so you have some +function + + align:start position:0% +function + + + align:start position:0% +function +f and XT plus J is what happens if a + + align:start position:0% +f and XT plus J is what happens if a + + + align:start position:0% +f and XT plus J is what happens if a +jump happens and XT is before the jump + + align:start position:0% +jump happens and XT is before the jump + + + align:start position:0% +jump happens and XT is before the jump +so kind of the effect of the jump on the + + align:start position:0% +so kind of the effect of the jump on the + + + align:start position:0% +so kind of the effect of the jump on the +function that's that's what this term + + align:start position:0% +function that's that's what this term + + + align:start position:0% +function that's that's what this term +yes that's like the convexity + + align:start position:0% +yes that's like the convexity + + + align:start position:0% +yes that's like the convexity +term I think of it as a convexity term I + + align:start position:0% +term I think of it as a convexity term I + + + align:start position:0% +term I think of it as a convexity term I +don't know how it's called maybe more + + align:start position:0% +don't know how it's called maybe more + + + align:start position:0% +don't know how it's called maybe more +mathematical Minds + + align:start position:0% +mathematical Minds + + + align:start position:0% +mathematical Minds +here um so in our case if you look at + + align:start position:0% +here um so in our case if you look at + + + align:start position:0% +here um so in our case if you look at +the top equation um our function is just + + align:start position:0% +the top equation um our function is just + + + align:start position:0% +the top equation um our function is just +uh essentially the + + align:start position:0% +uh essentially the + + + align:start position:0% +uh essentially the +exponent and um what happens is when + + align:start position:0% +exponent and um what happens is when + + + align:start position:0% +exponent and um what happens is when +when the function goes up by J is that + + align:start position:0% +when the function goes up by J is that + + + align:start position:0% +when the function goes up by J is that +exponent goes C to the J minus C to Z + + align:start position:0% +exponent goes C to the J minus C to Z + + + align:start position:0% +exponent goes C to the J minus C to Z +that's that's what this + + align:start position:0% +that's that's what this + + + align:start position:0% +that's that's what this +terms + + align:start position:0% +terms + + + align:start position:0% +terms +okay so that's how you um that's how you + + align:start position:0% +okay so that's how you um that's how you + + + align:start position:0% +okay so that's how you um that's how you +write the equation and now the SD + + align:start position:0% +write the equation and now the SD + + + align:start position:0% +write the equation and now the SD +solving the + + align:start position:0% + + + + align:start position:0% + +SD solving the SD generally means like + + align:start position:0% +SD solving the SD generally means like + + + align:start position:0% +SD solving the SD generally means like +write down what s is so we have S of T + + align:start position:0% +write down what s is so we have S of T + + + align:start position:0% +write down what s is so we have S of T +in our case it's going to be + + align:start position:0% +in our case it's going to be + + + align:start position:0% +in our case it's going to be +um s of little + + align:start position:0% +um s of little + + + align:start position:0% +um s of little +T well I'm I'm not going to write it you + + align:start position:0% +T well I'm I'm not going to write it you + + + align:start position:0% +T well I'm I'm not going to write it you +can have it on the board cuz I think + + align:start position:0% +can have it on the board cuz I think + + + align:start position:0% +can have it on the board cuz I think +we're getting we're going to get late so + + align:start position:0% +we're getting we're going to get late so + + + align:start position:0% +we're getting we're going to get late so +hurry up a little + + align:start position:0% +hurry up a little + + + align:start position:0% +hurry up a little +bit we're going on to the next part + + align:start position:0% +bit we're going on to the next part + + + align:start position:0% +bit we're going on to the next part +which is the um pricing exercise so we + + align:start position:0% +which is the um pricing exercise so we + + + align:start position:0% +which is the um pricing exercise so we +have two bonds zero coupon zero recovery + + align:start position:0% +have two bonds zero coupon zero recovery + + + align:start position:0% +have two bonds zero coupon zero recovery +bonds one pays $1 one the other pays + + align:start position:0% +bonds one pays $1 one the other pays + + + align:start position:0% +bonds one pays $1 one the other pays +one1 e so + + align:start position:0% +one1 e so + + + align:start position:0% +one1 e so +um how are we going to price this we + + align:start position:0% +um how are we going to price this we + + + align:start position:0% +um how are we going to price this we +have to use our model we have a model + + align:start position:0% +have to use our model we have a model + + + align:start position:0% +have to use our model we have a model +for the FX rate we have a model for + + align:start position:0% +for the FX rate we have a model for + + + align:start position:0% +for the FX rate we have a model for +credit so we can price both Bonds in + + align:start position:0% +credit so we can price both Bonds in + + + align:start position:0% +credit so we can price both Bonds in +dollars uh what is the price in dollars + + align:start position:0% +dollars uh what is the price in dollars + + + align:start position:0% +dollars uh what is the price in dollars +for each Bond and the ratio of prices + + align:start position:0% +for each Bond and the ratio of prices + + + align:start position:0% +for each Bond and the ratio of prices +kind of gives you the ratio of the + + align:start position:0% +kind of gives you the ratio of the + + + align:start position:0% +kind of gives you the ratio of the +notional in your hedge portfolio if you + + align:start position:0% +notional in your hedge portfolio if you + + + align:start position:0% +notional in your hedge portfolio if you +want to hedge one against the + + align:start position:0% +want to hedge one against the + + + align:start position:0% +want to hedge one against the +other + + align:start position:0% +other + + + align:start position:0% +other +so it's a zero coupon + + align:start position:0% + + + + align:start position:0% + +Bond so I wrote here the bond dollar + + align:start position:0% +Bond so I wrote here the bond dollar + + + align:start position:0% +Bond so I wrote here the bond dollar +bond price is this why is that why do I + + align:start position:0% +bond price is this why is that why do I + + + align:start position:0% +bond price is this why is that why do I +write it like that well + + align:start position:0% +write it like that well + + + align:start position:0% +write it like that well +it's it's a zero coupon Bond + + align:start position:0% +it's it's a zero coupon Bond + + + align:start position:0% +it's it's a zero coupon Bond +so what does zero coupon Bond say say it + + align:start position:0% +so what does zero coupon Bond say say it + + + align:start position:0% +so what does zero coupon Bond say say it +maturity it pays + + align:start position:0% +maturity it pays + + + align:start position:0% +maturity it pays +one so we have something where the + + align:start position:0% +one so we have something where the + + + align:start position:0% +one so we have something where the +payoff at time T is either one + + align:start position:0% +payoff at time T is either one + + + align:start position:0% +payoff at time T is either one +if if ta is um bigger than t or zero if + + align:start position:0% +if if ta is um bigger than t or zero if + + + align:start position:0% +if if ta is um bigger than t or zero if +to is um less than + + align:start position:0% + + + + align:start position:0% + +T okay so + + align:start position:0% +T okay so + + + align:start position:0% +T okay so +now what is my price well I know that um + + align:start position:0% +now what is my price well I know that um + + + align:start position:0% +now what is my price well I know that um +standard pricing Theory tells me that I + + align:start position:0% +standard pricing Theory tells me that I + + + align:start position:0% +standard pricing Theory tells me that I +I kind of my the price at time A Time + + align:start position:0% +I kind of my the price at time A Time + + + align:start position:0% +I kind of my the price at time A Time +Little + + align:start position:0% +Little + + + align:start position:0% +Little +T is equal to there is a to to + + align:start position:0% +T is equal to there is a to to + + + align:start position:0% +T is equal to there is a to to +expectation of a price at time Big + + align:start position:0% +expectation of a price at time Big + + + align:start position:0% +expectation of a price at time Big +T and you can kind of say there is a + + align:start position:0% +T and you can kind of say there is a + + + align:start position:0% +T and you can kind of say there is a +money market account but money market + + align:start position:0% +money market account but money market + + + align:start position:0% +money market account but money market +accounts in our cases just one because + + align:start position:0% +accounts in our cases just one because + + + align:start position:0% +accounts in our cases just one because +interest rates are zero so so you can + + align:start position:0% +interest rates are zero so so you can + + + align:start position:0% +interest rates are zero so so you can +just that that's really just the case + + align:start position:0% +just that that's really just the case + + + align:start position:0% +just that that's really just the case +that's just true so now the expectation + + align:start position:0% +that's just true so now the expectation + + + align:start position:0% +that's just true so now the expectation +of this well that's just equal to the + + align:start position:0% +of this well that's just equal to the + + + align:start position:0% +of this well that's just equal to the +expectation of an indicator + + align:start position:0% +expectation of an indicator + + + align:start position:0% +expectation of an indicator +function of to bigger than T which just + + align:start position:0% +function of to bigger than T which just + + + align:start position:0% +function of to bigger than T which just +equals to the + + align:start position:0% +equals to the + + + align:start position:0% +equals to the +probability of to bigger than + + align:start position:0% +probability of to bigger than + + + align:start position:0% +probability of to bigger than +T so if that's + + align:start position:0% +T so if that's + + + align:start position:0% +T so if that's +true uh that we know what that is that's + + align:start position:0% +true uh that we know what that is that's + + + align:start position:0% +true uh that we know what that is that's +just the probability that's the + + align:start position:0% +just the probability that's the + + + align:start position:0% +just the probability that's the +cumulative probability function e to the + + align:start position:0% +cumulative probability function e to the + + + align:start position:0% +cumulative probability function e to the +minus + + align:start position:0% +minus + + + align:start position:0% +minus +HT that's why the price of the bond in + + align:start position:0% +HT that's why the price of the bond in + + + align:start position:0% +HT that's why the price of the bond in +dollars has to be 8 the minus + + align:start position:0% +dollars has to be 8 the minus + + + align:start position:0% +dollars has to be 8 the minus +HT + + align:start position:0% +HT + + + align:start position:0% +HT +um Euro bond + + align:start position:0% +um Euro bond + + + align:start position:0% +um Euro bond +price same idea except + + align:start position:0% +price same idea except + + + align:start position:0% +price same idea except +um so Euro Euro bond price in + + align:start position:0% +um so Euro Euro bond price in + + + align:start position:0% +um so Euro Euro bond price in +dollars is that so why why why is the + + align:start position:0% +dollars is that so why why why is the + + + align:start position:0% +dollars is that so why why why is the +Euro Bond bond price in dollars like + + align:start position:0% +Euro Bond bond price in dollars like + + + align:start position:0% +Euro Bond bond price in dollars like +that + + align:start position:0% +that + + + align:start position:0% +that +well uh + + align:start position:0% + + + + align:start position:0% + +um the Euro bond price in dollars again + + align:start position:0% +um the Euro bond price in dollars again + + + align:start position:0% +um the Euro bond price in dollars again +what is the payoff same payoff except + + align:start position:0% +what is the payoff same payoff except + + + align:start position:0% +what is the payoff same payoff except +the payoff is in Euros right so if I + + align:start position:0% +the payoff is in Euros right so if I + + + align:start position:0% +the payoff is in Euros right so if I +want to do the payoff of my bond in + + align:start position:0% +want to do the payoff of my bond in + + + align:start position:0% +want to do the payoff of my bond in +dollars so this is I'm going to call + + align:start position:0% +dollars so this is I'm going to call + + + align:start position:0% +dollars so this is I'm going to call +this the the Euro Bond but the payoff + + align:start position:0% +this the the Euro Bond but the payoff + + + align:start position:0% +this the the Euro Bond but the payoff +now if I want to do it in dollars is not + + align:start position:0% +now if I want to do it in dollars is not + + + align:start position:0% +now if I want to do it in dollars is not +really one it's it's one times um s of + + align:start position:0% +really one it's it's one times um s of + + + align:start position:0% +really one it's it's one times um s of +T and zero Time s of t + + align:start position:0% +T and zero Time s of t + + + align:start position:0% +T and zero Time s of t +that's really my payoff so my so then + + align:start position:0% +that's really my payoff so my so then + + + align:start position:0% +that's really my payoff so my so then +the expectation here is not just one but + + align:start position:0% +the expectation here is not just one but + + + align:start position:0% +the expectation here is not just one but +actually s of T so now I have something + + align:start position:0% +actually s of T so now I have something + + + align:start position:0% +actually s of T so now I have something +where I have to take the + + align:start position:0% +where I have to take the + + + align:start position:0% +where I have to take the +expectation of s of + + align:start position:0% +expectation of s of + + + align:start position:0% +expectation of s of +T essentially at + + align:start position:0% +T essentially at + + + align:start position:0% +T essentially at +maturity that's my my my little my bond + + align:start position:0% +maturity that's my my my little my bond + + + align:start position:0% +maturity that's my my my little my bond +price in + + align:start position:0% +price in + + + align:start position:0% +price in +Euros is equal to the expectation of s + + align:start position:0% +Euros is equal to the expectation of s + + + align:start position:0% +Euros is equal to the expectation of s +of + + align:start position:0% +of + + + align:start position:0% +of +T and what is my expectation of s of t + + align:start position:0% +T and what is my expectation of s of t + + + align:start position:0% +T and what is my expectation of s of t +well it's um it's um eus HT * e the + + align:start position:0% +well it's um it's um eus HT * e the + + + align:start position:0% +well it's um it's um eus HT * e the +J and that's the expectation of s of + + align:start position:0% +J and that's the expectation of s of + + + align:start position:0% +J and that's the expectation of s of +T indicator function of to bigger than T + + align:start position:0% +T indicator function of to bigger than T + + + align:start position:0% +T indicator function of to bigger than T +right so not just expectation of s of T + + align:start position:0% +right so not just expectation of s of T + + + align:start position:0% +right so not just expectation of s of T +is s of zero but expectation of s of T + + align:start position:0% +is s of zero but expectation of s of T + + + align:start position:0% +is s of zero but expectation of s of T +times indicator function only if the cas + + align:start position:0% +times indicator function only if the cas + + + align:start position:0% +times indicator function only if the cas +is of to bigger than capital T now + + align:start position:0% +is of to bigger than capital T now + + + align:start position:0% +is of to bigger than capital T now +that's not S zero that's s that's + + align:start position:0% +that's not S zero that's s that's + + + align:start position:0% +that's not S zero that's s that's +basically this e to Theus HT * e + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so what can we do well we construct a + + align:start position:0% +so what can we do well we construct a + + + align:start position:0% +so what can we do well we construct a +what we should do is uh we construct a + + align:start position:0% +what we should do is uh we construct a + + + align:start position:0% +what we should do is uh we construct a +portfolio at time equals zero which is + + align:start position:0% +portfolio at time equals zero which is + + + align:start position:0% +portfolio at time equals zero which is +we sell one1 doll Bond and we buy this + + align:start position:0% +we sell one1 doll Bond and we buy this + + + align:start position:0% +we sell one1 doll Bond and we buy this +much amount here of Euro bonds and the + + align:start position:0% +much amount here of Euro bonds and the + + + align:start position:0% +much amount here of Euro bonds and the +portfolio value at time equals T equals + + align:start position:0% +portfolio value at time equals T equals + + + align:start position:0% +portfolio value at time equals T equals +z is + + align:start position:0% +z is + + + align:start position:0% +z is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +um basically you can take so e to the HD + + align:start position:0% +um basically you can take so e to the HD + + + align:start position:0% +um basically you can take so e to the HD +the first Bond you would get e to the + + align:start position:0% +the first Bond you would get e to the + + + align:start position:0% +the first Bond you would get e to the +minus HD and from the second amount + + align:start position:0% +minus HD and from the second amount + + + align:start position:0% +minus HD and from the second amount +would cost you e to the minus HD to buy + + align:start position:0% +would cost you e to the minus HD to buy + + + align:start position:0% +would cost you e to the minus HD to buy +that's how I've chosen this uh scaling + + align:start position:0% +that's how I've chosen this uh scaling + + + align:start position:0% +that's how I've chosen this uh scaling +factors we have started a portfolio + + align:start position:0% +factors we have started a portfolio + + + align:start position:0% +factors we have started a portfolio +which cost + + align:start position:0% +which cost + + + align:start position:0% +which cost +zero and um I should probably I'm going + + align:start position:0% +zero and um I should probably I'm going + + + align:start position:0% +zero and um I should probably I'm going +to go back here and and + + align:start position:0% +to go back here and and + + + align:start position:0% +to go back here and and +um I'm going to write down the notional + + align:start position:0% +um I'm going to write down the notional + + + align:start position:0% +um I'm going to write down the notional +because we lost + + align:start position:0% + + + + align:start position:0% + +them so how many dollar bonds do we + + align:start position:0% +them so how many dollar bonds do we + + + align:start position:0% +them so how many dollar bonds do we +have we have minus one and how many Euro + + align:start position:0% +have we have minus one and how many Euro + + + align:start position:0% +have we have minus one and how many Euro +bonds do we + + align:start position:0% +bonds do we + + + align:start position:0% +bonds do we +have we have + + align:start position:0% + + + + align:start position:0% + +um e to the minus HT time um 1 + + align:start position:0% +um e to the minus HT time um 1 + + + align:start position:0% +um e to the minus HT time um 1 +minus E to the J this is how many bonds + + align:start position:0% +minus E to the J this is how many bonds + + + align:start position:0% +minus E to the J this is how many bonds +we have how many Bond we have okay so + + align:start position:0% +we have how many Bond we have okay so + + + align:start position:0% +we have how many Bond we have okay so +sometime delta T + + align:start position:0% +sometime delta T + + + align:start position:0% +sometime delta T +later what happens to our bond prices + + align:start position:0% +later what happens to our bond prices + + + align:start position:0% +later what happens to our bond prices +well we know what the bond prices are + + align:start position:0% +well we know what the bond prices are + + + align:start position:0% +well we know what the bond prices are +the only thing that changed was that + + align:start position:0% +the only thing that changed was that + + + align:start position:0% +the only thing that changed was that +time some time + + align:start position:0% +time some time + + + align:start position:0% +time some time +expired so now instead of capital T we + + align:start position:0% +expired so now instead of capital T we + + + align:start position:0% +expired so now instead of capital T we +have T minus delta T to + + align:start position:0% +have T minus delta T to + + + align:start position:0% +have T minus delta T to +expiration so these are the bond prices + + align:start position:0% +expiration so these are the bond prices + + + align:start position:0% +expiration so these are the bond prices +if we didn't default of course if we + + align:start position:0% +if we didn't default of course if we + + + align:start position:0% +if we didn't default of course if we +defaulted then the bond prices are + + align:start position:0% +defaulted then the bond prices are + + + align:start position:0% +defaulted then the bond prices are +zero so obviously if we default it since + + align:start position:0% +zero so obviously if we default it since + + + align:start position:0% +zero so obviously if we default it since +Bond both bond prices are Z we started + + align:start position:0% +Bond both bond prices are Z we started + + + align:start position:0% +Bond both bond prices are Z we started +with a portfolio for zero if theault + + align:start position:0% +with a portfolio for zero if theault + + + align:start position:0% +with a portfolio for zero if theault +happened now we have a portfolio for + + align:start position:0% +happened now we have a portfolio for + + + align:start position:0% +happened now we have a portfolio for +zero so nothing changed right so the key + + align:start position:0% +zero so nothing changed right so the key + + + align:start position:0% +zero so nothing changed right so the key +part is okay now what if theault didn't + + align:start position:0% +part is okay now what if theault didn't + + + align:start position:0% +part is okay now what if theault didn't +happen would we have the same price as + + align:start position:0% +happen would we have the same price as + + + align:start position:0% +happen would we have the same price as +well that's what we want to check so and + + align:start position:0% +well that's what we want to check so and + + + align:start position:0% +well that's what we want to check so and +if we have the same price both in the + + align:start position:0% +if we have the same price both in the + + + align:start position:0% +if we have the same price both in the +case of default and in the case of no + + align:start position:0% +case of default and in the case of no + + + align:start position:0% +case of default and in the case of no +default then that means we have + + align:start position:0% +default then that means we have + + + align:start position:0% +default then that means we have +essentially a a u a replicated portfolio + + align:start position:0% +essentially a a u a replicated portfolio + + + align:start position:0% +essentially a a u a replicated portfolio +a hedge + + align:start position:0% + + + + align:start position:0% + +portfolio + + align:start position:0% +portfolio + + + align:start position:0% +portfolio +okay so what is the value of the bonds + + align:start position:0% +okay so what is the value of the bonds + + + align:start position:0% +okay so what is the value of the bonds +if theault did not happen again we have + + align:start position:0% +if theault did not happen again we have + + + align:start position:0% +if theault did not happen again we have +um this is the dollar bonds here and + + align:start position:0% +um this is the dollar bonds here and + + + align:start position:0% +um this is the dollar bonds here and +these are the Euro bonds and this is my + + align:start position:0% +these are the Euro bonds and this is my + + + align:start position:0% +these are the Euro bonds and this is my +effect rate why did my effect rate move + + align:start position:0% +effect rate why did my effect rate move + + + align:start position:0% +effect rate why did my effect rate move +well because theault did not happen so + + align:start position:0% +well because theault did not happen so + + + align:start position:0% +well because theault did not happen so +jump did not happen but still I have my + + align:start position:0% +jump did not happen but still I have my + + + align:start position:0% +jump did not happen but still I have my +drift a compensator drift so FX drifts + + align:start position:0% +drift a compensator drift so FX drifts + + + align:start position:0% +drift a compensator drift so FX drifts +in in the opposite + + align:start position:0% +in in the opposite + + + align:start position:0% +in in the opposite +direction okay + + align:start position:0% +direction okay + + + align:start position:0% +direction okay +so um + + align:start position:0% +so um + + + align:start position:0% +so um +this is so the dollar + + align:start position:0% +this is so the dollar + + + align:start position:0% +this is so the dollar +Bond dollar Bond there was there was one + + align:start position:0% +Bond dollar Bond there was there was one + + + align:start position:0% +Bond dollar Bond there was there was one +Bond minus one Bond and the price so the + + align:start position:0% +Bond minus one Bond and the price so the + + + align:start position:0% +Bond minus one Bond and the price so the +value of the dollar bond is just um + + align:start position:0% +value of the dollar bond is just um + + + align:start position:0% +value of the dollar bond is just um +minus E minus h t minus delta + + align:start position:0% +minus E minus h t minus delta + + + align:start position:0% +minus E minus h t minus delta +T what about the Euro bonds well the + + align:start position:0% +T what about the Euro bonds well the + + + align:start position:0% +T what about the Euro bonds well the +Euro bonds here is the number of bonds + + align:start position:0% +Euro bonds here is the number of bonds + + + align:start position:0% +Euro bonds here is the number of bonds +we + + align:start position:0% +we + + + align:start position:0% +we +have this is this divided by a zero by + + align:start position:0% +have this is this divided by a zero by + + + align:start position:0% +have this is this divided by a zero by +the way + + align:start position:0% +the way + + + align:start position:0% +the way +yeah in our case as zero is one so + + align:start position:0% +yeah in our case as zero is one so + + + align:start position:0% +yeah in our case as zero is one so +doesn't matter + + align:start position:0% +doesn't matter + + + align:start position:0% +doesn't matter +but price of each Bond + + align:start position:0% +but price of each Bond + + + align:start position:0% +but price of each Bond +again we we take that from um the price + + align:start position:0% +again we we take that from um the price + + + align:start position:0% +again we we take that from um the price +of each Bond comes from comes from this + + align:start position:0% +of each Bond comes from comes from this + + + align:start position:0% +of each Bond comes from comes from this +formula and then the FX rate multiply by + + align:start position:0% +formula and then the FX rate multiply by + + + align:start position:0% +formula and then the FX rate multiply by +the FX rate and then when you actually + + align:start position:0% +the FX rate and then when you actually + + + align:start position:0% +the FX rate and then when you actually +multiply all these guys out you end up + + align:start position:0% +multiply all these guys out you end up + + + align:start position:0% +multiply all these guys out you end up +with + + align:start position:0% +with + + + align:start position:0% +with +um with essentially the value in dollars + + align:start position:0% +um with essentially the value in dollars + + + align:start position:0% +um with essentially the value in dollars +of your Euro bonds equals again the + + align:start position:0% +of your Euro bonds equals again the + + + align:start position:0% +of your Euro bonds equals again the +value of your dollar bonds so we started + + align:start position:0% +value of your dollar bonds so we started + + + align:start position:0% +value of your dollar bonds so we started +out with a portfolio that was worth zero + + align:start position:0% +out with a portfolio that was worth zero + + + align:start position:0% +out with a portfolio that was worth zero +and then some time delta T later it's + + align:start position:0% +and then some time delta T later it's + + + align:start position:0% +and then some time delta T later it's +worth zero again both in the case of um + + align:start position:0% +worth zero again both in the case of um + + + align:start position:0% +worth zero again both in the case of um +in the case of default and in the case + + align:start position:0% +in the case of default and in the case + + + align:start position:0% +in the case of default and in the case +of no default so there's no Arbitrage in + + align:start position:0% +of no default so there's no Arbitrage in + + + align:start position:0% +of no default so there's no Arbitrage in +some sense not terribly surprising + + align:start position:0% +some sense not terribly surprising + + + align:start position:0% +some sense not terribly surprising +because we actually derive these prices + + align:start position:0% +because we actually derive these prices + + + align:start position:0% +because we actually derive these prices +based on the Assumption of no Arbitrage + + align:start position:0% +based on the Assumption of no Arbitrage + + + align:start position:0% +based on the Assumption of no Arbitrage +but it's a good check it kind of tells + + align:start position:0% +but it's a good check it kind of tells + + + align:start position:0% +but it's a good check it kind of tells +you hey if I actually follow this model + + align:start position:0% +you hey if I actually follow this model + + + align:start position:0% +you hey if I actually follow this model +to hedge I'm really going to be hedged + + align:start position:0% +to hedge I'm really going to be hedged + + + align:start position:0% +to hedge I'm really going to be hedged +and I'm going to be hedged not just when + + align:start position:0% +and I'm going to be hedged not just when + + + align:start position:0% +and I'm going to be hedged not just when +theault occurs or only if theault does + + align:start position:0% +theault occurs or only if theault does + + + align:start position:0% +theault occurs or only if theault does +not occur but I'm in both situations if + + align:start position:0% +not occur but I'm in both situations if + + + align:start position:0% +not occur but I'm in both situations if +default occurs and default does not + + align:start position:0% +default occurs and default does not + + + align:start position:0% +default occurs and default does not +occur and you can't really do that + + align:start position:0% +occur and you can't really do that + + + align:start position:0% +occur and you can't really do that +unless you have models that actually + + align:start position:0% +unless you have models that actually + + + align:start position:0% +unless you have models that actually +um that are that are Hybrid models that + + align:start position:0% +um that are that are Hybrid models that + + + align:start position:0% +um that are that are Hybrid models that +that allow you to to mix and match to + + align:start position:0% +that allow you to to mix and match to + + + align:start position:0% +that allow you to to mix and match to +basically describe both the create + + align:start position:0% +basically describe both the create + + + align:start position:0% +basically describe both the create +events and the FX + + align:start position:0% + + + + align:start position:0% + +process so that's um that's kind of the + + align:start position:0% +process so that's um that's kind of the + + + align:start position:0% +process so that's um that's kind of the +the usefulness now and the hedging + + align:start position:0% +the usefulness now and the hedging + + + align:start position:0% +the usefulness now and the hedging +strategy you can + + align:start position:0% +strategy you can + + + align:start position:0% +strategy you can +see it's it's interesting that the + + align:start position:0% +see it's it's interesting that the + + + align:start position:0% +see it's it's interesting that the +hedging strategy + + align:start position:0% +hedging strategy + + + align:start position:0% +hedging strategy +a the Hedge ratio depends on the credit + + align:start position:0% +a the Hedge ratio depends on the credit + + + align:start position:0% +a the Hedge ratio depends on the credit +riskiness so how much bonds we bought + + align:start position:0% +riskiness so how much bonds we bought + + + align:start position:0% +riskiness so how much bonds we bought +depends on J for first depends on age + + align:start position:0% +depends on J for first depends on age + + + align:start position:0% +depends on J for first depends on age +the CR riskiness and it also depends on + + align:start position:0% +the CR riskiness and it also depends on + + + align:start position:0% +the CR riskiness and it also depends on +J the jump + + align:start position:0% +J the jump + + + align:start position:0% +J the jump +size so it really depends how many bonds + + align:start position:0% +size so it really depends how many bonds + + + align:start position:0% +size so it really depends how many bonds +you use how many Euro bonds you buy to + + align:start position:0% +you use how many Euro bonds you buy to + + + align:start position:0% +you use how many Euro bonds you buy to +hge your dollar bonds it depends on both + + align:start position:0% +hge your dollar bonds it depends on both + + + align:start position:0% +hge your dollar bonds it depends on both +the probability of theault and on the + + align:start position:0% +the probability of theault and on the + + + align:start position:0% +the probability of theault and on the +jump + + align:start position:0% +jump + + + align:start position:0% +jump +size so that's that's what I mean by + + align:start position:0% +size so that's that's what I mean by + + + align:start position:0% +size so that's that's what I mean by +that it's um that it depends on credit + + align:start position:0% +that it's um that it depends on credit + + + align:start position:0% +that it's um that it depends on credit +riskiness it's also dynamic in the sense + + align:start position:0% +riskiness it's also dynamic in the sense + + + align:start position:0% +riskiness it's also dynamic in the sense +that for given amount of dollar bonds + + align:start position:0% +that for given amount of dollar bonds + + + align:start position:0% +that for given amount of dollar bonds +the amount of Euro bonds you need to + + align:start position:0% +the amount of Euro bonds you need to + + + align:start position:0% +the amount of Euro bonds you need to +sell is going to + + align:start position:0% +sell is going to + + + align:start position:0% +sell is going to +vary as as in as effects and and uh and + + align:start position:0% +vary as as in as effects and and uh and + + + align:start position:0% +vary as as in as effects and and uh and +the time goes goes forward as you can + + align:start position:0% +the time goes goes forward as you can + + + align:start position:0% +the time goes goes forward as you can +see like if you have like one day before + + align:start position:0% +see like if you have like one day before + + + align:start position:0% +see like if you have like one day before +before + + align:start position:0% +before + + + align:start position:0% +before +expiration the Hedge ratio of the two + + align:start position:0% +expiration the Hedge ratio of the two + + + align:start position:0% +expiration the Hedge ratio of the two +are going to be different than the than + + align:start position:0% +are going to be different than the than + + + align:start position:0% +are going to be different than the than +one year before eration so You' have to + + align:start position:0% +one year before eration so You' have to + + + align:start position:0% +one year before eration so You' have to +be rebalancing your portfolio + + align:start position:0% +be rebalancing your portfolio + + + align:start position:0% +be rebalancing your portfolio +continuously which is not again Not + + align:start position:0% +continuously which is not again Not + + + align:start position:0% +continuously which is not again Not +Unusual like if you're hedging an option + + align:start position:0% +Unusual like if you're hedging an option + + + align:start position:0% +Unusual like if you're hedging an option +you always have to also have to + + align:start position:0% +you always have to also have to + + + align:start position:0% +you always have to also have to +rebalance but it's not it's different + + align:start position:0% +rebalance but it's not it's different + + + align:start position:0% +rebalance but it's not it's different +from say a static model a static + + align:start position:0% +from say a static model a static + + + align:start position:0% +from say a static model a static +replication strategy where you say oh + + align:start position:0% +replication strategy where you say oh + + + align:start position:0% +replication strategy where you say oh +I'm going to buy x amount of Euro bonds + + align:start position:0% +I'm going to buy x amount of Euro bonds + + + align:start position:0% +I'm going to buy x amount of Euro bonds +x amount of dollar bonds and I won't + + align:start position:0% +x amount of dollar bonds and I won't + + + align:start position:0% +x amount of dollar bonds and I won't +have to ever worry about it it's not + + align:start position:0% +have to ever worry about it it's not + + + align:start position:0% +have to ever worry about it it's not +really the case here you're saying well + + align:start position:0% +really the case here you're saying well + + + align:start position:0% +really the case here you're saying well +I buy these ratio bonds and if theault + + align:start position:0% +I buy these ratio bonds and if theault + + + align:start position:0% +I buy these ratio bonds and if theault +does not happen I'm going to have to + + align:start position:0% +does not happen I'm going to have to + + + align:start position:0% +does not happen I'm going to have to +readjust my ratio because the original + + align:start position:0% +readjust my ratio because the original + + + align:start position:0% +readjust my ratio because the original +ratio took took to account the + + align:start position:0% +ratio took took to account the + + + align:start position:0% +ratio took took to account the +probability of default happening and if + + align:start position:0% +probability of default happening and if + + + align:start position:0% +probability of default happening and if +theault did not happen now I have some + + align:start position:0% +theault did not happen now I have some + + + align:start position:0% +theault did not happen now I have some +information extra information and that + + align:start position:0% +information extra information and that + + + align:start position:0% +information extra information and that +now I have to readjust my ratio to + + align:start position:0% +now I have to readjust my ratio to + + + align:start position:0% +now I have to readjust my ratio to +reflect + + align:start position:0% +reflect + + + align:start position:0% +reflect +that + + align:start position:0% +that + + + align:start position:0% +that +so what happens if + + align:start position:0% +so what happens if + + + align:start position:0% +so what happens if +recovery is bigger than zero and by the + + align:start position:0% +recovery is bigger than zero and by the + + + align:start position:0% +recovery is bigger than zero and by the +way how much time do we have just quick + + align:start position:0% +way how much time do we have just quick + + + align:start position:0% +way how much time do we have just quick +check have four o00 okay so we have + + align:start position:0% +check have four o00 okay so we have + + + align:start position:0% +check have four o00 okay so we have +about like 12 minutes 10 10 minutes okay + + align:start position:0% +about like 12 minutes 10 10 minutes okay + + + align:start position:0% +about like 12 minutes 10 10 minutes okay +good so what happens is in case recovery + + align:start position:0% +good so what happens is in case recovery + + + align:start position:0% +good so what happens is in case recovery +is bigger than + + align:start position:0% +is bigger than + + + align:start position:0% +is bigger than +zero + + align:start position:0% +zero + + + align:start position:0% +zero +um well if recovery is bigger than + + align:start position:0% +um well if recovery is bigger than + + + align:start position:0% +um well if recovery is bigger than +zero we can go through this exercise + + align:start position:0% +zero we can go through this exercise + + + align:start position:0% +zero we can go through this exercise +that that we did again the pricing + + align:start position:0% +that that we did again the pricing + + + align:start position:0% +that that we did again the pricing +exercise and see what happens to um what + + align:start position:0% +exercise and see what happens to um what + + + align:start position:0% +exercise and see what happens to um what +happens to our bond + + align:start position:0% +happens to our bond + + + align:start position:0% +happens to our bond +prices so let's + + align:start position:0% +prices so let's + + + align:start position:0% +prices so let's +say let's do this for for dollars and + + align:start position:0% +say let's do this for for dollars and + + + align:start position:0% +say let's do this for for dollars and +Euro + + align:start position:0% +Euro + + + align:start position:0% +Euro +bonds just to give an example of some of + + align:start position:0% +bonds just to give an example of some of + + + align:start position:0% +bonds just to give an example of some of +the complexity that can arise when you + + align:start position:0% +the complexity that can arise when you + + + align:start position:0% +the complexity that can arise when you +start making the model more realistic + + align:start position:0% +start making the model more realistic + + + align:start position:0% +start making the model more realistic +because usually bonds do not have zero + + align:start position:0% +because usually bonds do not have zero + + + align:start position:0% +because usually bonds do not have zero +recovery so then we assume that our + + align:start position:0% +recovery so then we assume that our + + + align:start position:0% +recovery so then we assume that our +payoff of the zero coupon zero recovery + + align:start position:0% +payoff of the zero coupon zero recovery + + + align:start position:0% +payoff of the zero coupon zero recovery +bonds was one if theault doesn't happen + + align:start position:0% +bonds was one if theault doesn't happen + + + align:start position:0% +bonds was one if theault doesn't happen +zero if theault happens now it's going + + align:start position:0% +zero if theault happens now it's going + + + align:start position:0% +zero if theault happens now it's going +to be the payoff of dollar + + align:start position:0% +to be the payoff of dollar + + + align:start position:0% +to be the payoff of dollar +Bond at time T is going to be + + align:start position:0% +Bond at time T is going to be + + + align:start position:0% +Bond at time T is going to be +one + + align:start position:0% +one + + + align:start position:0% +one +if default is uh default did not happen + + align:start position:0% +if default is uh default did not happen + + + align:start position:0% +if default is uh default did not happen +so if T is bigger than T and R if um + + align:start position:0% +so if T is bigger than T and R if um + + + align:start position:0% +so if T is bigger than T and R if um +default was less than + + align:start position:0% + + + + align:start position:0% + +T okay so now when we price our + + align:start position:0% +T okay so now when we price our + + + align:start position:0% +T okay so now when we price our +expectation it's um you know it's going + + align:start position:0% +expectation it's um you know it's going + + + align:start position:0% +expectation it's um you know it's going +to be like this our + + align:start position:0% +to be like this our + + + align:start position:0% +to be like this our +my P of little T would be just the + + align:start position:0% +my P of little T would be just the + + + align:start position:0% +my P of little T would be just the +expectation time Little T of um or let's + + align:start position:0% +expectation time Little T of um or let's + + + align:start position:0% +expectation time Little T of um or let's +say in this case uh + + align:start position:0% +say in this case uh + + + align:start position:0% +say in this case uh +going to call expectation the initial + + align:start position:0% +going to call expectation the initial + + + align:start position:0% +going to call expectation the initial +price is zero the expectation of P of + + align:start position:0% +price is zero the expectation of P of + + + align:start position:0% +price is zero the expectation of P of +capital + + align:start position:0% +capital + + + align:start position:0% +capital +T times um yeah which is equal to + + align:start position:0% +T times um yeah which is equal to + + + align:start position:0% +T times um yeah which is equal to +expectation + + align:start position:0% +expectation + + + align:start position:0% +expectation +of essentially one of to bigger than t + + align:start position:0% +of essentially one of to bigger than t + + + align:start position:0% +of essentially one of to bigger than t +plus r one of to less than + + align:start position:0% + + + + align:start position:0% + +T well a + + align:start position:0% + + + + align:start position:0% + +what we have here is uh essentially so + + align:start position:0% +what we have here is uh essentially so + + + align:start position:0% +what we have here is uh essentially so +you can + + align:start position:0% +you can + + + align:start position:0% +you can +think we have uh this first guy is going + + align:start position:0% +think we have uh this first guy is going + + + align:start position:0% +think we have uh this first guy is going +to + + align:start position:0% +to + + + align:start position:0% +to +be SEC first guy is going to be e to the + + align:start position:0% +be SEC first guy is going to be e to the + + + align:start position:0% +be SEC first guy is going to be e to the +if T bigger than T is e to the minus + + align:start position:0% +if T bigger than T is e to the minus + + + align:start position:0% +if T bigger than T is e to the minus +HT and the second guy plus + + align:start position:0% +HT and the second guy plus + + + align:start position:0% +HT and the second guy plus +r times probability of T being less than + + align:start position:0% +r times probability of T being less than + + + align:start position:0% +r times probability of T being less than +T is just 1 minus probability of T + + align:start position:0% +T is just 1 minus probability of T + + + align:start position:0% +T is just 1 minus probability of T +bigger than T So 1 minus E Theus + + align:start position:0% +bigger than T So 1 minus E Theus + + + align:start position:0% +bigger than T So 1 minus E Theus +HT which + + align:start position:0% +HT which + + + align:start position:0% +HT which +essentially gives you R is it R + + align:start position:0% +essentially gives you R is it R + + + align:start position:0% +essentially gives you R is it R +plus + + align:start position:0% +plus + + + align:start position:0% +plus +um e to the + + align:start position:0% +um e to the + + + align:start position:0% +um e to the +minus HT * 1 - R + + align:start position:0% +minus HT * 1 - R + + + align:start position:0% +minus HT * 1 - R +yeah so that's how you derive uh the + + align:start position:0% +yeah so that's how you derive uh the + + + align:start position:0% +yeah so that's how you derive uh the +dollar bond price + + align:start position:0% +dollar bond price + + + align:start position:0% +dollar bond price +and for the Euro bond price you will do + + align:start position:0% +and for the Euro bond price you will do + + + align:start position:0% +and for the Euro bond price you will do +the same thing except now this will be + + align:start position:0% +the same thing except now this will be + + + align:start position:0% +the same thing except now this will be +multiplied by by the effect rate and now + + align:start position:0% +multiplied by by the effect rate and now + + + align:start position:0% +multiplied by by the effect rate and now +the effect + + align:start position:0% + + + + align:start position:0% + +rate the tricky thing about the effect + + align:start position:0% +rate the tricky thing about the effect + + + align:start position:0% +rate the tricky thing about the effect +rate is that FX rate jumps on default so + + align:start position:0% +rate is that FX rate jumps on default so + + + align:start position:0% +rate is that FX rate jumps on default so +it's not going to be the same same + + align:start position:0% +it's not going to be the same same + + + align:start position:0% +it's not going to be the same same +number so in this case PT this is for + + align:start position:0% +number so in this case PT this is for + + + align:start position:0% +number so in this case PT this is for +for one kind of dollar unit it's 1 * s + + align:start position:0% +for one kind of dollar unit it's 1 * s + + + align:start position:0% +for one kind of dollar unit it's 1 * s +of T and R * s of T so now we + + align:start position:0% +of T and R * s of T so now we + + + align:start position:0% +of T and R * s of T so now we +have P Little T this is for + + align:start position:0% + + + + align:start position:0% + +euros the price a Time Zero of the Euro + + align:start position:0% +euros the price a Time Zero of the Euro + + + align:start position:0% +euros the price a Time Zero of the Euro +Bond divided by + + align:start position:0% +Bond divided by + + + align:start position:0% +Bond divided by +s0 that equals to expected value Time + + align:start position:0% +s0 that equals to expected value Time + + + align:start position:0% +s0 that equals to expected value Time +Zero + + align:start position:0% +Zero + + + align:start position:0% +Zero +of s of T of T bigger than t + + align:start position:0% +of s of T of T bigger than t + + + align:start position:0% +of s of T of T bigger than t +plus r s of + + align:start position:0% +plus r s of + + + align:start position:0% +plus r s of +T times to less than + + align:start position:0% +T times to less than + + + align:start position:0% +T times to less than +T + + align:start position:0% +T + + + align:start position:0% +T +well okay + + align:start position:0% + + + + align:start position:0% + +so first part s of T to bigger than T + + align:start position:0% +so first part s of T to bigger than T + + + align:start position:0% +so first part s of T to bigger than T +that was like the zero coupon bond price + + align:start position:0% +that was like the zero coupon bond price + + + align:start position:0% +that was like the zero coupon bond price +so that's just + + align:start position:0% +so that's just + + + align:start position:0% +so that's just +um that's just essentially the um the in + + align:start position:0% +um that's just essentially the um the in + + + align:start position:0% +um that's just essentially the um the in +order to + + align:start position:0% +order to + + + align:start position:0% +order to +really I would + + align:start position:0% +really I would + + + align:start position:0% +really I would +say guess this well right we we have to + + align:start position:0% +say guess this well right we we have to + + + align:start position:0% +say guess this well right we we have to +go back to what was s of T so let's say + + align:start position:0% +go back to what was s of T so let's say + + + align:start position:0% +go back to what was s of T so let's say +if we go back to the equation for S of + + align:start position:0% +if we go back to the equation for S of + + + align:start position:0% +if we go back to the equation for S of +T to + + align:start position:0% + + + + align:start position:0% + +um write that so s of + + align:start position:0% +um write that so s of + + + align:start position:0% +um write that so s of +T is s of little T time e to the + + align:start position:0% +T is s of little T time e to the + + + align:start position:0% +T is s of little T time e to the +um can't even yeah e to the + + align:start position:0% + + + + align:start position:0% + +h + + align:start position:0% +h + + + align:start position:0% +h +t 1 minus t to + + align:start position:0% + + + + align:start position:0% + +J times um plus + + align:start position:0% + + + + align:start position:0% + +J + + align:start position:0% +J + + + align:start position:0% +J +times + + align:start position:0% + + + + align:start position:0% + +one t bigger + + align:start position:0% + + + + align:start position:0% + +t + + align:start position:0% +t + + + align:start position:0% +t +plus um + + align:start position:0% +plus um + + + align:start position:0% +plus um +now + + align:start position:0% + + + + align:start position:0% + +times e to the + + align:start position:0% + + + + align:start position:0% + +HT this is H + + align:start position:0% + + + + align:start position:0% + +to to less than T and this is if to is + + align:start position:0% +to to less than T and this is if to is + + + align:start position:0% +to to less than T and this is if to is +less than T and then times e to the uh + + align:start position:0% +less than T and then times e to the uh + + + align:start position:0% +less than T and then times e to the uh +HD 1 minus h HT * 1 minus C to J + + align:start position:0% + + + + align:start position:0% + +yeah t bigger than + + align:start position:0% +yeah t bigger than + + + align:start position:0% +yeah t bigger than +T so if T if T if if theault has not + + align:start position:0% +T so if T if T if if theault has not + + + align:start position:0% +T so if T if T if if theault has not +occurred s of T is is s of + + align:start position:0% +occurred s of T is is s of + + + align:start position:0% +occurred s of T is is s of +um s of um s of zero in this + + align:start position:0% +um s of um s of zero in this + + + align:start position:0% +um s of um s of zero in this +case s of T is s of Z times this term + + align:start position:0% +case s of T is s of Z times this term + + + align:start position:0% +case s of T is s of Z times this term +and if default has occurred then it's SI + + align:start position:0% +and if default has occurred then it's SI + + + align:start position:0% +and if default has occurred then it's SI +of zero times this term so the two terms + + align:start position:0% +of zero times this term so the two terms + + + align:start position:0% +of zero times this term so the two terms +are the same except for the + + align:start position:0% +are the same except for the + + + align:start position:0% +are the same except for the +for the J J + + align:start position:0% +for the J J + + + align:start position:0% +for the J J +part okay so now when we try to do this + + align:start position:0% +part okay so now when we try to do this + + + align:start position:0% +part okay so now when we try to do this +expectation here we're in the situation + + align:start position:0% +expectation here we're in the situation + + + align:start position:0% +expectation here we're in the situation +where t with default has not occurred so + + align:start position:0% +where t with default has not occurred so + + + align:start position:0% +where t with default has not occurred so +our FX rate is essentially s0 times the + + align:start position:0% +our FX rate is essentially s0 times the + + + align:start position:0% +our FX rate is essentially s0 times the +second term so we + + align:start position:0% +second term so we + + + align:start position:0% +second term so we +have expectation of + + align:start position:0% +have expectation of + + + align:start position:0% +have expectation of +um s0 times um well and we're kind of + + align:start position:0% +um s0 times um well and we're kind of + + + align:start position:0% +um s0 times um well and we're kind of +dividing by s0 so say zero drops + + align:start position:0% +dividing by s0 so say zero drops + + + align:start position:0% +dividing by s0 so say zero drops +out um e + + align:start position:0% + + + + align:start position:0% + +Tod HD * 1 - e to the + + align:start position:0% + + + + align:start position:0% + +J + + align:start position:0% +J + + + align:start position:0% +J +okay and + + align:start position:0% + + + + align:start position:0% + +um one to bigger than T that's the first + + align:start position:0% +um one to bigger than T that's the first + + + align:start position:0% +um one to bigger than T that's the first +the first expectation and the second + + align:start position:0% +the first expectation and the second + + + align:start position:0% +the first expectation and the second +one the expectation + + align:start position:0% +one the expectation + + + align:start position:0% +one the expectation +of cannot raise this expectation of um + + align:start position:0% +of cannot raise this expectation of um + + + align:start position:0% +of cannot raise this expectation of um +so we put this R times the + + align:start position:0% +so we put this R times the + + + align:start position:0% +so we put this R times the +expectation of now here we have t is + + align:start position:0% +expectation of now here we have t is + + + align:start position:0% +expectation of now here we have t is +less than T so we're going to have it's + + align:start position:0% +less than T so we're going to have it's + + + align:start position:0% +less than T so we're going to have it's +our s of T is the first + + align:start position:0% +our s of T is the first + + + align:start position:0% +our s of T is the first +part only would be true second part + + align:start position:0% +part only would be true second part + + + align:start position:0% +part only would be true second part +would be would be one so that will be + + align:start position:0% +would be would be one so that will be + + + align:start position:0% +would be would be one so that will be +the + + align:start position:0% +the + + + align:start position:0% +the +formula e to the um e to the H to + + align:start position:0% + + + + align:start position:0% + +1 - e to + + align:start position:0% +1 - e to + + + align:start position:0% +1 - e to +J + + + align:start position:0% +J + + + + align:start position:0% +J + +J time one t less than + + align:start position:0% + + + + align:start position:0% + +T + + align:start position:0% +T + + + align:start position:0% +T +So this e to the J Term that you see + + align:start position:0% + + + + align:start position:0% + +um is a to the J Term you see you see + + align:start position:0% +um is a to the J Term you see you see + + + align:start position:0% +um is a to the J Term you see you see +here in the Euro price that comes from + + align:start position:0% +here in the Euro price that comes from + + + align:start position:0% +here in the Euro price that comes from +from this term + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% +here + + + align:start position:0% +here +so how do I do this expectation well to + + align:start position:0% +so how do I do this expectation well to + + + align:start position:0% +so how do I do this expectation well to +do this expectation + + align:start position:0% +do this expectation + + + align:start position:0% +do this expectation +again you have to you do an integral + + align:start position:0% +again you have to you do an integral + + + align:start position:0% +again you have to you do an integral +essentially using times over the + + align:start position:0% +essentially using times over the + + + align:start position:0% +essentially using times over the +integral from 0 to Infinity of the + + align:start position:0% +integral from 0 to Infinity of the + + + align:start position:0% +integral from 0 to Infinity of the +probability + + align:start position:0% +probability + + + align:start position:0% +probability +density since T here is bigger than T + + align:start position:0% +density since T here is bigger than T + + + align:start position:0% +density since T here is bigger than T +I'm really integrating from T to + + align:start position:0% +I'm really integrating from T to + + + align:start position:0% +I'm really integrating from T to +Infinity so um and this really here is + + align:start position:0% +Infinity so um and this really here is + + + align:start position:0% +Infinity so um and this really here is +um + + align:start position:0% +um + + + align:start position:0% +um +this is just a + + align:start position:0% +this is just a + + + align:start position:0% +this is just a +constant so um this this first + + align:start position:0% +constant so um this this first + + + align:start position:0% +constant so um this this first +term I'll write it here so you + + align:start position:0% +term I'll write it here so you + + + align:start position:0% +term I'll write it here so you +have p 0 over + + align:start position:0% +have p 0 over + + + align:start position:0% +have p 0 over +St over S zero sorry zero that would be + + align:start position:0% +St over S zero sorry zero that would be + + + align:start position:0% +St over S zero sorry zero that would be +first term would be again e to the + + align:start position:0% +first term would be again e to the + + + align:start position:0% +first term would be again e to the +HT 1 - U to the + + align:start position:0% +HT 1 - U to the + + + align:start position:0% +HT 1 - U to the +J and it's going to be integral from PT + + align:start position:0% +J and it's going to be integral from PT + + + align:start position:0% +J and it's going to be integral from PT +to Infinity of the partial differential + + align:start position:0% +to Infinity of the partial differential + + + align:start position:0% +to Infinity of the partial differential +function so that's just e to the minus + + align:start position:0% +function so that's just e to the minus + + + align:start position:0% +function so that's just e to the minus +HT so this looks like something we've + + align:start position:0% +HT so this looks like something we've + + + align:start position:0% +HT so this looks like something we've +already done before in the previous + + align:start position:0% +already done before in the previous + + + align:start position:0% +already done before in the previous +calculation so that and then the second + + align:start position:0% + + + + align:start position:0% + +term is um R + + align:start position:0% +term is um R + + + align:start position:0% +term is um R +times now we're integrating from0 to + + align:start position:0% +times now we're integrating from0 to + + + align:start position:0% +times now we're integrating from0 to +T of uh so this would be integrate from + + align:start position:0% +T of uh so this would be integrate from + + + align:start position:0% +T of uh so this would be integrate from +0 to + + align:start position:0% + + + + align:start position:0% + +t e to the H to 1 minus E to the J plus + + align:start position:0% +t e to the H to 1 minus E to the J plus + + + align:start position:0% +t e to the H to 1 minus E to the J plus +J well I can do it like this time e to + + align:start position:0% +J well I can do it like this time e to + + + align:start position:0% +J well I can do it like this time e to +the J let's put it like that and um + + align:start position:0% +the J let's put it like that and um + + + align:start position:0% +the J let's put it like that and um +times H * + + align:start position:0% +times H * + + + align:start position:0% +times H * +cus H to to this part + + align:start position:0% +cus H to to this part + + + align:start position:0% +cus H to to this part +being the + + align:start position:0% +being the + + + align:start position:0% +being the +um distribu function probability + + align:start position:0% +um distribu function probability + + + align:start position:0% +um distribu function probability +distribution function so again we have + + align:start position:0% +distribution function so again we have + + + align:start position:0% +distribution function so again we have +like this guy cancels + + align:start position:0% +like this guy cancels + + + align:start position:0% +like this guy cancels +this and what we're left with first term + + align:start position:0% +this and what we're left with first term + + + align:start position:0% +this and what we're left with first term +gives us e Tod + + align:start position:0% +gives us e Tod + + + align:start position:0% +gives us e Tod +minus HT J plus + + align:start position:0% +minus HT J plus + + + align:start position:0% +minus HT J plus +r + + align:start position:0% +r + + + align:start position:0% +r +times + + align:start position:0% +times + + + align:start position:0% +times +um H * e to J * to this is again + + align:start position:0% +um H * e to J * to this is again + + + align:start position:0% +um H * e to J * to this is again +exponent function so + + align:start position:0% +exponent function so + + + align:start position:0% +exponent function so +we + + align:start position:0% +we + + + align:start position:0% +we +have e to the h t e to the J minus + + align:start position:0% + + + + align:start position:0% + +one is that that's true + + align:start position:0% +one is that that's true + + + align:start position:0% +one is that that's true +right right + + align:start position:0% + + + + align:start position:0% + +so or + + align:start position:0% +so or + + + align:start position:0% +so or +sorry it's there's a minus sign here in + + align:start position:0% +sorry it's there's a minus sign here in + + + align:start position:0% +sorry it's there's a minus sign here in +front of + + align:start position:0% +front of + + + align:start position:0% +front of +this the reason there's a minus sign is + + align:start position:0% +this the reason there's a minus sign is + + + align:start position:0% +this the reason there's a minus sign is +um we have minus h e to the J * T and so + + align:start position:0% +um we have minus h e to the J * T and so + + + align:start position:0% +um we have minus h e to the J * T and so +we have to put a minus here in front we + + align:start position:0% +we have to put a minus here in front we + + + align:start position:0% +we have to put a minus here in front we +do the integral so there is a minus here + + align:start position:0% +do the integral so there is a minus here + + + align:start position:0% +do the integral so there is a minus here +in front + + align:start position:0% +in front + + + align:start position:0% +in front +so this thing is um just + + align:start position:0% +so this thing is um just + + + align:start position:0% +so this thing is um just +a it it basically reduces to that + + align:start position:0% +a it it basically reduces to that + + + align:start position:0% +a it it basically reduces to that +expression on the + + align:start position:0% +expression on the + + + align:start position:0% +expression on the +board so that's kind of + + align:start position:0% +board so that's kind of + + + align:start position:0% +board so that's kind of +um that's basically um so this is how + + align:start position:0% +um that's basically um so this is how + + + align:start position:0% +um that's basically um so this is how +you extend the problem to having non + + align:start position:0% +you extend the problem to having non + + + align:start position:0% +you extend the problem to having non +zero + + align:start position:0% + + + + align:start position:0% + +recoveries what you could do for um your + + align:start position:0% +recoveries what you could do for um your + + + align:start position:0% +recoveries what you could do for um your +final paper if you decide to do final + + align:start position:0% +final paper if you decide to do final + + + align:start position:0% +final paper if you decide to do final +paper on this + + align:start position:0% +paper on this + + + align:start position:0% +paper on this +topic is to um extend the model one step + + align:start position:0% +topic is to um extend the model one step + + + align:start position:0% +topic is to um extend the model one step +further and say in our model um our FX + + align:start position:0% +further and say in our model um our FX + + + align:start position:0% +further and say in our model um our FX +rat jumped but did not have any + + align:start position:0% +rat jumped but did not have any + + + align:start position:0% +rat jumped but did not have any +diffusive elements right it was + + align:start position:0% +diffusive elements right it was + + + align:start position:0% +diffusive elements right it was +just our you know our equation was the + + align:start position:0% +just our you know our equation was the + + + align:start position:0% +just our you know our equation was the +log of + + align:start position:0% +log of + + + align:start position:0% +log of +s was uh + + align:start position:0% +s was uh + + + align:start position:0% +s was uh +mu log of s oh sorry mu to t plus um JD + + align:start position:0% +mu log of s oh sorry mu to t plus um JD + + + align:start position:0% +mu log of s oh sorry mu to t plus um JD +NT that was our SD for log of s so next + + align:start position:0% +NT that was our SD for log of s so next + + + align:start position:0% +NT that was our SD for log of s so next +step would be hey why don't we just add + + align:start position:0% +step would be hey why don't we just add + + + align:start position:0% +step would be hey why don't we just add +a another term plus Sigma d + + align:start position:0% + + + + align:start position:0% + +w + + align:start position:0% +w + + + align:start position:0% +w +so without this jump this is just a + + align:start position:0% +so without this jump this is just a + + + align:start position:0% +so without this jump this is just a +standard kind of L normal process that + + align:start position:0% +standard kind of L normal process that + + + align:start position:0% +standard kind of L normal process that +that you know how to + + align:start position:0% +that you know how to + + + align:start position:0% +that you know how to +do now we add jump essentially so you + + align:start position:0% +do now we add jump essentially so you + + + align:start position:0% +do now we add jump essentially so you +take a log normal process you add a jump + + align:start position:0% +take a log normal process you add a jump + + + align:start position:0% +take a log normal process you add a jump +process to it and you and then repeat + + align:start position:0% +process to it and you and then repeat + + + align:start position:0% +process to it and you and then repeat +the same things that we we were going + + align:start position:0% +the same things that we we were going + + + align:start position:0% +the same things that we we were going +through so far pricing European pricing + + align:start position:0% +through so far pricing European pricing + + + align:start position:0% +through so far pricing European pricing +Euro bonds dollar + + align:start position:0% +Euro bonds dollar + + + align:start position:0% +Euro bonds dollar +bonds and coming up with a replication + + align:start position:0% + + + + align:start position:0% + +strategy this is for example a model + + align:start position:0% +strategy this is for example a model + + + align:start position:0% +strategy this is for example a model +that um + + align:start position:0% +that um + + + align:start position:0% +that um +we're currently working to implement a a + + align:start position:0% +we're currently working to implement a a + + + align:start position:0% +we're currently working to implement a a +model like that at Morgan Stanley um our + + align:start position:0% +model like that at Morgan Stanley um our + + + align:start position:0% +model like that at Morgan Stanley um our +model has you know nonzero interest + + align:start position:0% +model has you know nonzero interest + + + align:start position:0% +model has you know nonzero interest +rates it has like Dynamic interest + + align:start position:0% +rates it has like Dynamic interest + + + align:start position:0% +rates it has like Dynamic interest +rates but um so it makes it that makes + + align:start position:0% +rates but um so it makes it that makes + + + align:start position:0% +rates but um so it makes it that makes +it a little bit more complex but overall + + align:start position:0% +it a little bit more complex but overall + + + align:start position:0% +it a little bit more complex but overall +it doesn't make it too much more complex + + align:start position:0% +it doesn't make it too much more complex + + + align:start position:0% +it doesn't make it too much more complex +adding extra having nonzero interest + + align:start position:0% +adding extra having nonzero interest + + + align:start position:0% +adding extra having nonzero interest +rates just kind of has an EXT extra + + align:start position:0% +rates just kind of has an EXT extra + + + align:start position:0% +rates just kind of has an EXT extra +drift term that doesn't really change + + align:start position:0% +drift term that doesn't really change + + + align:start position:0% +drift term that doesn't really change +that much the mathematics of it + + align:start position:0% + + + + align:start position:0% + +and reason why we want to do that is + + align:start position:0% +and reason why we want to do that is + + + align:start position:0% +and reason why we want to do that is +because we want to be able to price + + align:start position:0% +because we want to be able to price + + + align:start position:0% +because we want to be able to price +essentially contracts where which are + + align:start position:0% +essentially contracts where which are + + + align:start position:0% +essentially contracts where which are +credit contingent meaning the payoff + + align:start position:0% +credit contingent meaning the payoff + + + align:start position:0% +credit contingent meaning the payoff +depends on the whether something has + + align:start position:0% +depends on the whether something has + + + align:start position:0% +depends on the whether something has +survived or not whether credit default + + align:start position:0% +survived or not whether credit default + + + align:start position:0% +survived or not whether credit default +has occurred or not and the payoff is in + + align:start position:0% +has occurred or not and the payoff is in + + + align:start position:0% +has occurred or not and the payoff is in +units is in like foreign currency + + align:start position:0% +units is in like foreign currency + + + align:start position:0% +units is in like foreign currency +typical example would be a credit + + align:start position:0% +typical example would be a credit + + + align:start position:0% +typical example would be a credit +default swap denominated in Brazilian + + align:start position:0% +default swap denominated in Brazilian + + + align:start position:0% +default swap denominated in Brazilian +re or that that happens a bra create + + align:start position:0% +re or that that happens a bra create + + + align:start position:0% +re or that that happens a bra create +default swap on Brazil denominated on + + align:start position:0% +default swap on Brazil denominated on + + + align:start position:0% +default swap on Brazil denominated on +Brazilian re now common sense is that + + align:start position:0% +Brazilian re now common sense is that + + + align:start position:0% +Brazilian re now common sense is that +when Brazil defaults Brazil R is not + + align:start position:0% +when Brazil defaults Brazil R is not + + + align:start position:0% +when Brazil defaults Brazil R is not +going to cost very much it's not going + + align:start position:0% +going to cost very much it's not going + + + align:start position:0% +going to cost very much it's not going +to be very valuable just like as we saw + + align:start position:0% +to be very valuable just like as we saw + + + align:start position:0% +to be very valuable just like as we saw +on the graph with Argentinian peso which + + align:start position:0% +on the graph with Argentinian peso which + + + align:start position:0% +on the graph with Argentinian peso which +totally devalued it would value as well + + align:start position:0% +totally devalued it would value as well + + + align:start position:0% +totally devalued it would value as well +now Brazil is a very big economy strong + + align:start position:0% +now Brazil is a very big economy strong + + + align:start position:0% +now Brazil is a very big economy strong +country so right now people are buying a + + align:start position:0% +country so right now people are buying a + + + align:start position:0% +country so right now people are buying a +lot of their bonds people investing in + + align:start position:0% +lot of their bonds people investing in + + + align:start position:0% +lot of their bonds people investing in +it um still it has greater risk and you + + align:start position:0% +it um still it has greater risk and you + + + align:start position:0% +it um still it has greater risk and you +can you you can buy you can trade the + + align:start position:0% +can you you can buy you can trade the + + + align:start position:0% +can you you can buy you can trade the +cred risk you can trade cred default + + align:start position:0% +cred risk you can trade cred default + + + align:start position:0% +cred risk you can trade cred default +swaps in dollars and you can also enter + + align:start position:0% +swaps in dollars and you can also enter + + + align:start position:0% +swaps in dollars and you can also enter +into contracts that + + align:start position:0% +into contracts that + + + align:start position:0% +into contracts that +essentially Quanto the credit risk into + + align:start position:0% +essentially Quanto the credit risk into + + + align:start position:0% +essentially Quanto the credit risk into +into Brazilian currency itself and to be + + align:start position:0% +into Brazilian currency itself and to be + + + align:start position:0% +into Brazilian currency itself and to be +able to really price + + align:start position:0% +able to really price + + + align:start position:0% +able to really price +this we you can do it we've done it for + + align:start position:0% +this we you can do it we've done it for + + + align:start position:0% +this we you can do it we've done it for +many years without having a jump model + + align:start position:0% +many years without having a jump model + + + align:start position:0% +many years without having a jump model +but then your hedge ratios are not very + + align:start position:0% +but then your hedge ratios are not very + + + align:start position:0% +but then your hedge ratios are not very +good and you cannot really you cannot + + align:start position:0% +good and you cannot really you cannot + + + align:start position:0% +good and you cannot really you cannot +really explain the prices you see in the + + align:start position:0% +really explain the prices you see in the + + + align:start position:0% +really explain the prices you see in the +market so we're essentially implementing + + align:start position:0% +market so we're essentially implementing + + + align:start position:0% +market so we're essentially implementing +uh infrastructure to we've already + + align:start position:0% +uh infrastructure to we've already + + + align:start position:0% +uh infrastructure to we've already +implemented this model or a version of + + align:start position:0% +implemented this model or a version of + + + align:start position:0% +implemented this model or a version of +this model but we're implementing + + align:start position:0% +this model but we're implementing + + + align:start position:0% +this model but we're implementing +infrastructure to kind of really put it + + align:start position:0% +infrastructure to kind of really put it + + + align:start position:0% +infrastructure to kind of really put it +in production as you can see in this + + align:start position:0% +in production as you can see in this + + + align:start position:0% +in production as you can see in this +model now your FX process depends on + + align:start position:0% +model now your FX process depends on + + + align:start position:0% +model now your FX process depends on +credit so actually calibration and all + + align:start position:0% +credit so actually calibration and all + + + align:start position:0% +credit so actually calibration and all +these things become a little bit more + + align:start position:0% +these things become a little bit more + + + align:start position:0% +these things become a little bit more +tricky so which I don't want you to + + align:start position:0% +tricky so which I don't want you to + + + align:start position:0% +tricky so which I don't want you to +worry about for your final project but I + + align:start position:0% +worry about for your final project but I + + + align:start position:0% +worry about for your final project but I +think it's a it would be a very + + align:start position:0% +think it's a it would be a very + + + align:start position:0% +think it's a it would be a very +interesting exercise to take something + + align:start position:0% +interesting exercise to take something + + + align:start position:0% +interesting exercise to take something +like that + + align:start position:0% +like that + + + align:start position:0% +like that +and + + align:start position:0% +and + + + align:start position:0% +and +um and basically um work out all the all + + align:start position:0% +um and basically um work out all the all + + + align:start position:0% +um and basically um work out all the all +the steps it does get a little bit more + + align:start position:0% +the steps it does get a little bit more + + + align:start position:0% +the steps it does get a little bit more +complicated because now you have to when + + align:start position:0% +complicated because now you have to when + + + align:start position:0% +complicated because now you have to when +you're doing it was LMA you got to do it + + align:start position:0% +you're doing it was LMA you got to do it + + + align:start position:0% +you're doing it was LMA you got to do it +both for diffusive processes and for for + + align:start position:0% +both for diffusive processes and for for + + + align:start position:0% +both for diffusive processes and for for +the jump process so you're going to have + + align:start position:0% +the jump process so you're going to have + + + align:start position:0% +the jump process so you're going to have +two terms in your Rus Lama but you've + + align:start position:0% +two terms in your Rus Lama but you've + + + align:start position:0% +two terms in your Rus Lama but you've +seen them both they're in the class + + align:start position:0% +seen them both they're in the class + + + align:start position:0% +seen them both they're in the class +notes so if you're so inclined you can + + align:start position:0% +notes so if you're so inclined you can + + + align:start position:0% +notes so if you're so inclined you can +do + + align:start position:0% + + + + align:start position:0% + +it and + + align:start position:0% +it and + + + align:start position:0% +it and +um you can once you solve the model then + + align:start position:0% +um you can once you solve the model then + + + align:start position:0% +um you can once you solve the model then +you can do you can you can kind of check + + align:start position:0% +you can do you can you can kind of check + + + align:start position:0% +you can do you can you can kind of check +your results you can actually build a + + align:start position:0% +your results you can actually build a + + + align:start position:0% +your results you can actually build a +Monte Carlo simulation or essentially + + align:start position:0% +Monte Carlo simulation or essentially + + + align:start position:0% +Monte Carlo simulation or essentially +run a bunch of paths where you simulate + + align:start position:0% +run a bunch of paths where you simulate + + + align:start position:0% +run a bunch of paths where you simulate +both the default and the um diffusive + + align:start position:0% +both the default and the um diffusive + + + align:start position:0% +both the default and the um diffusive +part and see if your if your prices + + align:start position:0% +part and see if your if your prices + + + align:start position:0% +part and see if your if your prices +derive analytically match with your + + align:start position:0% +derive analytically match with your + + + align:start position:0% +derive analytically match with your +expectations computed by Monte Carlo + + align:start position:0% +expectations computed by Monte Carlo + + + align:start position:0% +expectations computed by Monte Carlo +this will be a good examp a good it's + + align:start position:0% +this will be a good examp a good it's + + + align:start position:0% +this will be a good examp a good it's +always a very good check to see if um + + align:start position:0% +always a very good check to see if um + + + align:start position:0% +always a very good check to see if um +usually usually we do this exercise to + + align:start position:0% +usually usually we do this exercise to + + + align:start position:0% +usually usually we do this exercise to +check if our Monte Carlo simulation is + + align:start position:0% +check if our Monte Carlo simulation is + + + align:start position:0% +check if our Monte Carlo simulation is +correct because we we know that our math + + align:start position:0% +correct because we we know that our math + + + align:start position:0% +correct because we we know that our math +is + + align:start position:0% +is + + + align:start position:0% +is +right but you can also do it for uh you + + align:start position:0% +right but you can also do it for uh you + + + align:start position:0% +right but you can also do it for uh you +know to check the other way + + align:start position:0% + + + + align:start position:0% + +around okay so + + align:start position:0% +around okay so + + + align:start position:0% +around okay so +um in real life as uh as we went over I + + align:start position:0% +um in real life as uh as we went over I + + + align:start position:0% +um in real life as uh as we went over I +mentioned a couple of times during the + + align:start position:0% +mentioned a couple of times during the + + + align:start position:0% +mentioned a couple of times during the +lecture our models are more complicated + + align:start position:0% +lecture our models are more complicated + + + align:start position:0% +lecture our models are more complicated +we have stochastic interest rates + + align:start position:0% +we have stochastic interest rates + + + align:start position:0% +we have stochastic interest rates +stochastic Hazard rates So currently we + + align:start position:0% +stochastic Hazard rates So currently we + + + align:start position:0% +stochastic Hazard rates So currently we +assume that our Hazard rate H is a fixed + + align:start position:0% +assume that our Hazard rate H is a fixed + + + align:start position:0% +assume that our Hazard rate H is a fixed +number H can be stochastic as well it + + align:start position:0% +number H can be stochastic as well it + + + align:start position:0% +number H can be stochastic as well it +can have its own distribution and + + align:start position:0% +can have its own distribution and + + + align:start position:0% +can have its own distribution and +typically that's what we use model in + + align:start position:0% +typically that's what we use model in + + + align:start position:0% +typically that's what we use model in +our + + align:start position:0% +our + + + align:start position:0% +our +models um stochastic in effects so say + + align:start position:0% +models um stochastic in effects so say + + + align:start position:0% +models um stochastic in effects so say +stochastic both jump and diffusion + + align:start position:0% +stochastic both jump and diffusion + + + align:start position:0% +stochastic both jump and diffusion +processes and then + + align:start position:0% +processes and then + + + align:start position:0% +processes and then +um if you get really fancy then you can + + align:start position:0% +um if you get really fancy then you can + + + align:start position:0% +um if you get really fancy then you can +start putting correlations between + + align:start position:0% +start putting correlations between + + + align:start position:0% +start putting correlations between +interest rates FX and and Hazard rates + + align:start position:0% +interest rates FX and and Hazard rates + + + align:start position:0% +interest rates FX and and Hazard rates +so in + + align:start position:0% +so in + + + align:start position:0% +so in +particular um having a jump of FX on + + align:start position:0% +particular um having a jump of FX on + + + align:start position:0% +particular um having a jump of FX on +default naturally introduces a + + align:start position:0% +default naturally introduces a + + + align:start position:0% +default naturally introduces a +correlation between credit and interest + + align:start position:0% +correlation between credit and interest + + + align:start position:0% +correlation between credit and interest +rate so sorry and FX when F when credit + + align:start position:0% +rate so sorry and FX when F when credit + + + align:start position:0% +rate so sorry and FX when F when credit +occurs FX The the value so clearly + + align:start position:0% +occurs FX The the value so clearly + + + align:start position:0% +occurs FX The the value so clearly +there's going to be a correlation but + + align:start position:0% +there's going to be a correlation but + + + align:start position:0% +there's going to be a correlation but +there also could be a correlation + + align:start position:0% +there also could be a correlation + + + align:start position:0% +there also could be a correlation +between the hazard rates themselves and + + align:start position:0% +between the hazard rates themselves and + + + align:start position:0% +between the hazard rates themselves and +effects so it's another source of + + align:start position:0% +effects so it's another source of + + + align:start position:0% +effects so it's another source of +correlation and these correlations would + + align:start position:0% +correlation and these correlations would + + + align:start position:0% +correlation and these correlations would +produce different effects in the market + + align:start position:0% +produce different effects in the market + + + align:start position:0% +produce different effects in the market +so + + align:start position:0% +so + + + align:start position:0% +so +um basically you can you can um by if + + align:start position:0% +um basically you can you can um by if + + + align:start position:0% +um basically you can you can um by if +you have enough data points you would be + + align:start position:0% +you have enough data points you would be + + + align:start position:0% +you have enough data points you would be +able to say well this model seems like + + align:start position:0% +able to say well this model seems like + + + align:start position:0% +able to say well this model seems like +it describes the market better than that + + align:start position:0% +it describes the market better than that + + + align:start position:0% +it describes the market better than that +model both of them produce Quanto + + align:start position:0% +model both of them produce Quanto + + + align:start position:0% +model both of them produce Quanto +effects + + align:start position:0% + + + + align:start position:0% + +though and U in our in + + align:start position:0% +though and U in our in + + + align:start position:0% +though and U in our in +um it's whether we use analytic + + align:start position:0% +um it's whether we use analytic + + + align:start position:0% +um it's whether we use analytic +Solutions or or Monte Carlo there are + + align:start position:0% +Solutions or or Monte Carlo there are + + + align:start position:0% +Solutions or or Monte Carlo there are +different approaches to price + + align:start position:0% +different approaches to price + + + align:start position:0% +different approaches to price +derivatives in computer risk + + align:start position:0% +derivatives in computer risk + + + align:start position:0% +derivatives in computer risk +it depends really on how complex your + + align:start position:0% +it depends really on how complex your + + + align:start position:0% +it depends really on how complex your +model is certain in for certain markets + + align:start position:0% +model is certain in for certain markets + + + align:start position:0% +model is certain in for certain markets +you you'd rather have a more complex + + align:start position:0% +you you'd rather have a more complex + + + align:start position:0% +you you'd rather have a more complex +model that is slower and requires Monte + + align:start position:0% +model that is slower and requires Monte + + + align:start position:0% +model that is slower and requires Monte +Carlo so and in other places You' want + + align:start position:0% +Carlo so and in other places You' want + + + align:start position:0% +Carlo so and in other places You' want +to have faster more tractable models + + align:start position:0% +to have faster more tractable models + + + align:start position:0% +to have faster more tractable models +that can be PRI you can price your + + align:start position:0% +that can be PRI you can price your + + + align:start position:0% +that can be PRI you can price your +derivatives + + align:start position:0% +derivatives + + + align:start position:0% +derivatives +analytically but maybe your models are + + align:start position:0% +analytically but maybe your models are + + + align:start position:0% +analytically but maybe your models are +not uh they don't have as many features + + align:start position:0% +not uh they don't have as many features + + + align:start position:0% +not uh they don't have as many features +in them so there's a a whole range of + + align:start position:0% +in them so there's a a whole range of + + + align:start position:0% +in them so there's a a whole range of +models implemented for various markets + + align:start position:0% +models implemented for various markets + + + align:start position:0% +models implemented for various markets +in in Morgan Stanley so it's a very it's + + align:start position:0% +in in Morgan Stanley so it's a very it's + + + align:start position:0% +in in Morgan Stanley so it's a very it's +a very big area of expertise for + + align:start position:0% +a very big area of expertise for + + + align:start position:0% +a very big area of expertise for +us so um I think that's it um I think I + + align:start position:0% +us so um I think that's it um I think I + + + align:start position:0% +us so um I think that's it um I think I +ran a little bit over time apologize + + align:start position:0% +ran a little bit over time apologize + + + align:start position:0% +ran a little bit over time apologize +five minutes thank thank you very very + + align:start position:0% +five minutes thank thank you very very + + + align:start position:0% +five minutes thank thank you very very +much and uh why don't we just have a + + align:start position:0% +much and uh why don't we just have a + + + align:start position:0% +much and uh why don't we just have a +well thank our speaker first I + + align:start position:0% +well thank our speaker first I + + + align:start position:0% +well thank our speaker first I +guess but also I think there probably a + + align:start position:0% +guess but also I think there probably a + + + align:start position:0% +guess but also I think there probably a +question or two that uh people might + + align:start position:0% +question or two that uh people might + + + align:start position:0% +question or two that uh people might +have but I was wondering if we could now + + align:start position:0% +have but I was wondering if we could now + + + align:start position:0% +have but I was wondering if we could now +answer which of the Italian bets was + + align:start position:0% +answer which of the Italian bets was + + + align:start position:0% +answer which of the Italian bets was +better which what which was the which of + + align:start position:0% +better which what which was the which of + + + align:start position:0% +better which what which was the which of +the bets that we initially were + + align:start position:0% +the bets that we initially were + + + align:start position:0% +the bets that we initially were +considering on the Italian bonds was + + align:start position:0% +considering on the Italian bonds was + + + align:start position:0% +considering on the Italian bonds was +better could we answer that + + align:start position:0% +better could we answer that + + + align:start position:0% +better could we answer that +now we haven't I think yeah yeah let's + + align:start position:0% +now we haven't I think yeah yeah let's + + + align:start position:0% +now we haven't I think yeah yeah let's +go + + align:start position:0% +go + + + align:start position:0% +go +back which Italian bonds was + + align:start position:0% +back which Italian bonds was + + + align:start position:0% +back which Italian bonds was +better what was + + align:start position:0% +better what was + + + align:start position:0% +better what was +that yeah okay so let's try to answer + + align:start position:0% +that yeah okay so let's try to answer + + + align:start position:0% +that yeah okay so let's try to answer +that together right + + align:start position:0% +that together right + + + align:start position:0% +that together right +um and when we we can answer it within + + align:start position:0% +um and when we we can answer it within + + + align:start position:0% +um and when we we can answer it within +our model right so in reality + + align:start position:0% +our model right so in reality + + + align:start position:0% +our model right so in reality +there's all kinds of factors going into + + align:start position:0% +there's all kinds of factors going into + + + align:start position:0% +there's all kinds of factors going into +into the price so there's supply and + + align:start position:0% +into the price so there's supply and + + + align:start position:0% +into the price so there's supply and +demand liquidity in Euros liquidities in + + align:start position:0% +demand liquidity in Euros liquidities in + + + align:start position:0% +demand liquidity in Euros liquidities in +dollars but let's say if you're trying + + align:start position:0% +dollars but let's say if you're trying + + + align:start position:0% +dollars but let's say if you're trying +to invest in Euros or trying to invest + + align:start position:0% +to invest in Euros or trying to invest + + + align:start position:0% +to invest in Euros or trying to invest +in dollars + + align:start position:0% +in dollars + + + align:start position:0% +in dollars +um if I invest in dollars + + align:start position:0% +um if I invest in dollars + + + align:start position:0% +um if I invest in dollars +right if a default happens I lose + + align:start position:0% +right if a default happens I lose + + + align:start position:0% +right if a default happens I lose +essentially let's say the recovery was + + align:start position:0% +essentially let's say the recovery was + + + align:start position:0% +essentially let's say the recovery was +zero so I lose all my money in dollars + + align:start position:0% +zero so I lose all my money in dollars + + + align:start position:0% +zero so I lose all my money in dollars +so I I thought I had some amount of + + align:start position:0% +so I I thought I had some amount of + + + align:start position:0% +so I I thought I had some amount of +dollars default + + align:start position:0% +dollars default + + + align:start position:0% +dollars default +occurs I lost my + + align:start position:0% +occurs I lost my + + + align:start position:0% +occurs I lost my +dollars same thing in Euros if I invest + + align:start position:0% +dollars same thing in Euros if I invest + + + align:start position:0% +dollars same thing in Euros if I invest +in Euros if default occurs I lost my + + align:start position:0% +in Euros if default occurs I lost my + + + align:start position:0% +in Euros if default occurs I lost my +Euros so how much did I + + align:start position:0% +Euros so how much did I + + + align:start position:0% +Euros so how much did I +lose in a case of euros and in the case + + align:start position:0% +lose in a case of euros and in the case + + + align:start position:0% +lose in a case of euros and in the case +of dollars so if I invested + + align:start position:0% +of dollars so if I invested + + + align:start position:0% +of dollars so if I invested +Euros you can say well if default + + align:start position:0% +Euros you can say well if default + + + align:start position:0% +Euros you can say well if default +happens my Euros are not maybe not as + + align:start position:0% +happens my Euros are not maybe not as + + + align:start position:0% +happens my Euros are not maybe not as +valuable + + align:start position:0% +valuable + + + align:start position:0% +valuable +so Euros are not as valuable so I I I + + align:start position:0% +so Euros are not as valuable so I I I + + + align:start position:0% +so Euros are not as valuable so I I I +lost my Euros but what I lost was not as + + align:start position:0% +lost my Euros but what I lost was not as + + + align:start position:0% +lost my Euros but what I lost was not as +much because already is also devalued a + + align:start position:0% +much because already is also devalued a + + + align:start position:0% +much because already is also devalued a +lot conversely as we saw because of the + + align:start position:0% +lot conversely as we saw because of the + + + align:start position:0% +lot conversely as we saw because of the +because of the compensator drift + + align:start position:0% +because of the compensator drift + + + align:start position:0% +because of the compensator drift +remember + + align:start position:0% +remember + + + align:start position:0% +remember +um when the if you have a jump that + + align:start position:0% +um when the if you have a jump that + + + align:start position:0% +um when the if you have a jump that +makes the currency the value upon the + + align:start position:0% +makes the currency the value upon the + + + align:start position:0% +makes the currency the value upon the +fault the currency will tend to + + align:start position:0% +fault the currency will tend to + + + align:start position:0% +fault the currency will tend to +appreciate if the fault doesn't happen + + align:start position:0% +appreciate if the fault doesn't happen + + + align:start position:0% +appreciate if the fault doesn't happen +because we want the the expected value + + align:start position:0% +because we want the the expected value + + + align:start position:0% +because we want the the expected value +of the currency has to be that's + + align:start position:0% +of the currency has to be that's + + + align:start position:0% +of the currency has to be that's +determined by interest rate parity the + + align:start position:0% +determined by interest rate parity the + + + align:start position:0% +determined by interest rate parity the +first thing we talked about + + align:start position:0% +first thing we talked about + + + align:start position:0% +first thing we talked about +the interest rate differential so that + + align:start position:0% +the interest rate differential so that + + + align:start position:0% +the interest rate differential so that +that is kind of an + + align:start position:0% +that is kind of an + + + align:start position:0% +that is kind of an +ironclad Arbitrage condition that you + + align:start position:0% +ironclad Arbitrage condition that you + + + align:start position:0% +ironclad Arbitrage condition that you +have to follow so if you want your FX + + align:start position:0% +have to follow so if you want your FX + + + align:start position:0% +have to follow so if you want your FX +forward to really to the expected value + + align:start position:0% +forward to really to the expected value + + + align:start position:0% +forward to really to the expected value +of your FX to to remain fixed by the + + align:start position:0% +of your FX to to remain fixed by the + + + align:start position:0% +of your FX to to remain fixed by the +interest rate differential and you know + + align:start position:0% +interest rate differential and you know + + + align:start position:0% +interest rate differential and you know +that upon default your currency will + + align:start position:0% +that upon default your currency will + + + align:start position:0% +that upon default your currency will +devalue that means that if the currency + + align:start position:0% +devalue that means that if the currency + + + align:start position:0% +devalue that means that if the currency +does not devalue it's going to + + align:start position:0% +does not devalue it's going to + + + align:start position:0% +does not devalue it's going to +appreciate mean if default does not + + align:start position:0% +appreciate mean if default does not + + + align:start position:0% +appreciate mean if default does not +happen the currency would appreciate + + align:start position:0% +happen the currency would appreciate + + + align:start position:0% +happen the currency would appreciate +relatively speaking + + align:start position:0% +relatively speaking + + + align:start position:0% +relatively speaking +so in our case when we're buying bonds + + align:start position:0% +so in our case when we're buying bonds + + + align:start position:0% +so in our case when we're buying bonds +we only get paid if the default does not + + align:start position:0% +we only get paid if the default does not + + + align:start position:0% +we only get paid if the default does not +occur so you'd + + align:start position:0% +occur so you'd + + + align:start position:0% +occur so you'd +rather you would rather essentially buy + + align:start position:0% +rather you would rather essentially buy + + + align:start position:0% +rather you would rather essentially buy +the bonds in the currency that's going + + align:start position:0% +the bonds in the currency that's going + + + align:start position:0% +the bonds in the currency that's going +to relatively appreciate essentially + + align:start position:0% +to relatively appreciate essentially + + + align:start position:0% +to relatively appreciate essentially +suppose interest rates were zero in both + + align:start position:0% +suppose interest rates were zero in both + + + align:start position:0% +suppose interest rates were zero in both +cases you would rather buy the bond + + align:start position:0% +cases you would rather buy the bond + + + align:start position:0% +cases you would rather buy the bond +where interest where FX would appreciate + + align:start position:0% +where interest where FX would appreciate + + + align:start position:0% +where interest where FX would appreciate +if if the fult does not occur because if + + align:start position:0% +if if the fult does not occur because if + + + align:start position:0% +if if the fult does not occur because if +it occurs you get nothing in any case + + align:start position:0% +it occurs you get nothing in any case + + + align:start position:0% +it occurs you get nothing in any case +right but if it doesn't occur when you + + align:start position:0% +right but if it doesn't occur when you + + + align:start position:0% +right but if it doesn't occur when you +get paid you want something that would + + align:start position:0% +get paid you want something that would + + + align:start position:0% +get paid you want something that would +appreciate versus something that would + + align:start position:0% +appreciate versus something that would + + + align:start position:0% +appreciate versus something that would +not like the dollar for example let's + + align:start position:0% +not like the dollar for example let's + + + align:start position:0% +not like the dollar for example let's +say the dollar doesn't move versus other + + align:start position:0% +say the dollar doesn't move versus other + + + align:start position:0% +say the dollar doesn't move versus other +currencies when when the Euro default + + align:start position:0% +currencies when when the Euro default + + + align:start position:0% +currencies when when the Euro default +happens so you you'd rather get the U + + align:start position:0% +happens so you you'd rather get the U + + + align:start position:0% +happens so you you'd rather get the U +Euro bonds y do you want to estimate + + align:start position:0% +Euro bonds y do you want to estimate + + + align:start position:0% +Euro bonds y do you want to estimate +recovery right um can you use a bunch I + + align:start position:0% +recovery right um can you use a bunch I + + + align:start position:0% +recovery right um can you use a bunch I +mean not necessarily factors already in + + align:start position:0% +mean not necessarily factors already in + + + align:start position:0% +mean not necessarily factors already in +the model but outside factors like uh um + + align:start position:0% +the model but outside factors like uh um + + + align:start position:0% +the model but outside factors like uh um +like macroeconomic factors to predict + + align:start position:0% +like macroeconomic factors to predict + + + align:start position:0% +like macroeconomic factors to predict +the expected value of recovery + + align:start position:0% +the expected value of recovery + + + align:start position:0% +the expected value of recovery +absolutely yeah recovery is something + + align:start position:0% +absolutely yeah recovery is something + + + align:start position:0% +absolutely yeah recovery is something +that we cannot really price + + align:start position:0% +that we cannot really price + + + align:start position:0% +that we cannot really price +necessarily uh because we usually + + align:start position:0% +necessarily uh because we usually + + + align:start position:0% +necessarily uh because we usually +usually we have bonds and the bond price + + align:start position:0% +usually we have bonds and the bond price + + + align:start position:0% +usually we have bonds and the bond price +there is you know bond price you can say + + align:start position:0% +there is you know bond price you can say + + + align:start position:0% +there is you know bond price you can say +we model default probability of default + + align:start position:0% +we model default probability of default + + + align:start position:0% +we model default probability of default +versus probability of non- default but + + align:start position:0% +versus probability of non- default but + + + align:start position:0% +versus probability of non- default but +now if you introduce a second variable + + align:start position:0% +now if you introduce a second variable + + + align:start position:0% +now if you introduce a second variable +which is the recovery now you have + + align:start position:0% +which is the recovery now you have + + + align:start position:0% +which is the recovery now you have +essentially both probability of defaults + + align:start position:0% +essentially both probability of defaults + + + align:start position:0% +essentially both probability of defaults +and Recovery amount as variables and you + + align:start position:0% +and Recovery amount as variables and you + + + align:start position:0% +and Recovery amount as variables and you +only have price as as your data point + + align:start position:0% +only have price as as your data point + + + align:start position:0% +only have price as as your data point +and you you can have infinitely many + + align:start position:0% +and you you can have infinitely many + + + align:start position:0% +and you you can have infinitely many +solutions so typically what happens is + + align:start position:0% +solutions so typically what happens is + + + align:start position:0% +solutions so typically what happens is +you kind of um fix the recovery at + + align:start position:0% +you kind of um fix the recovery at + + + align:start position:0% +you kind of um fix the recovery at +something now what do we use to fix the + + align:start position:0% +something now what do we use to fix the + + + align:start position:0% +something now what do we use to fix the +recovery well for Sovereign countries we + + align:start position:0% +recovery well for Sovereign countries we + + + align:start position:0% +recovery well for Sovereign countries we +use + + align:start position:0% +use + + + align:start position:0% +use +25% and for corporates uh we use 40% but + + align:start position:0% +25% and for corporates uh we use 40% but + + + align:start position:0% +25% and for corporates uh we use 40% but +these numbers everybody knows that + + align:start position:0% +these numbers everybody knows that + + + align:start position:0% +these numbers everybody knows that +they're kind of just conventions really + + align:start position:0% +they're kind of just conventions really + + + align:start position:0% +they're kind of just conventions really +more than anything no we don't we don't + + align:start position:0% +more than anything no we don't we don't + + + align:start position:0% +more than anything no we don't we don't +really believe that recovery is really + + align:start position:0% +really believe that recovery is really + + + align:start position:0% +really believe that recovery is really +40% or + + align:start position:0% +40% or + + + align:start position:0% +40% or +25% it varies a lot by corporations and + + align:start position:0% +25% it varies a lot by corporations and + + + align:start position:0% +25% it varies a lot by corporations and +there are Studies by Credit Agencies + + align:start position:0% +there are Studies by Credit Agencies + + + align:start position:0% +there are Studies by Credit Agencies +about how much + + align:start position:0% +about how much + + + align:start position:0% +about how much +recoveries um what are the recoveries + + align:start position:0% +recoveries um what are the recoveries + + + align:start position:0% +recoveries um what are the recoveries +for for various um various bonds and + + align:start position:0% +for for various um various bonds and + + + align:start position:0% +for for various um various bonds and +this 25% for Sovereign is based on some + + align:start position:0% +this 25% for Sovereign is based on some + + + align:start position:0% +this 25% for Sovereign is based on some +study like that that like went over the + + align:start position:0% +study like that that like went over the + + + align:start position:0% +study like that that like went over the +last 50 years looked at the recoveries + + align:start position:0% +last 50 years looked at the recoveries + + + align:start position:0% +last 50 years looked at the recoveries +of sovereigns of which they're they're + + align:start position:0% +of sovereigns of which they're they're + + + align:start position:0% +of sovereigns of which they're they're +not that many every year but if you look + + align:start position:0% +not that many every year but if you look + + + align:start position:0% +not that many every year but if you look +50 years there's quite a few and then it + + align:start position:0% +50 years there's quite a few and then it + + + align:start position:0% +50 years there's quite a few and then it +made some statement say oh they some + + align:start position:0% +made some statement say oh they some + + + align:start position:0% +made some statement say oh they some +recover higher some recover lower but on + + align:start position:0% +recover higher some recover lower but on + + + align:start position:0% +recover higher some recover lower but on +average they recover + + align:start position:0% +average they recover + + + align:start position:0% +average they recover +25% now if you remember what Greece what + + align:start position:0% +25% now if you remember what Greece what + + + align:start position:0% +25% now if you remember what Greece what +happened in Greece how much did Bond + + align:start position:0% +happened in Greece how much did Bond + + + align:start position:0% +happened in Greece how much did Bond +holders grease got for their bonds now + + align:start position:0% +holders grease got for their bonds now + + + align:start position:0% +holders grease got for their bonds now +they didn't really default technically + + align:start position:0% +they didn't really default technically + + + align:start position:0% +they didn't really default technically +they did default technically but it was + + align:start position:0% +they did default technically but it was + + + align:start position:0% +they did default technically but it was +it's a very managed process + + align:start position:0% +it's a very managed process + + + align:start position:0% +it's a very managed process +but they got definitely less than 25% I + + align:start position:0% +but they got definitely less than 25% I + + + align:start position:0% +but they got definitely less than 25% I +think they got something on the over 15 + + align:start position:0% +think they got something on the over 15 + + + align:start position:0% +think they got something on the over 15 +cents on the dollar so recovery there + + align:start position:0% +cents on the dollar so recovery there + + + align:start position:0% +cents on the dollar so recovery there +was can say it was less + + align:start position:0% +was can say it was less + + + align:start position:0% +was can say it was less +than less than + + align:start position:0% +than less than + + + align:start position:0% +than less than +25% same for uh same this Argentinian + + align:start position:0% +25% same for uh same this Argentinian + + + align:start position:0% +25% same for uh same this Argentinian +default that I'm talking about the + + align:start position:0% +default that I'm talking about the + + + align:start position:0% +default that I'm talking about the +2001 um Argentina is still being sued by + + align:start position:0% +2001 um Argentina is still being sued by + + + align:start position:0% +2001 um Argentina is still being sued by +creditors trying to get money + + align:start position:0% +creditors trying to get money + + + align:start position:0% +creditors trying to get money +back from this and it's like a big thing + + align:start position:0% +back from this and it's like a big thing + + + align:start position:0% +back from this and it's like a big thing +in the + + align:start position:0% +in the + + + align:start position:0% +in the +news you have a plane from Argentina and + + align:start position:0% +news you have a plane from Argentina and + + + align:start position:0% +news you have a plane from Argentina and +they fly over it can be seized by + + align:start position:0% +they fly over it can be seized by + + + align:start position:0% +they fly over it can be seized by +exactly headphones exactly yeah they try + + align:start position:0% +exactly headphones exactly yeah they try + + + align:start position:0% +exactly headphones exactly yeah they try +to do some settlements so how much did + + align:start position:0% +to do some settlements so how much did + + + align:start position:0% +to do some settlements so how much did +people recover well depends who you are + + align:start position:0% +people recover well depends who you are + + + align:start position:0% +people recover well depends who you are +if you took the original deal maybe you + + align:start position:0% +if you took the original deal maybe you + + + align:start position:0% +if you took the original deal maybe you +got 20 25 30 cents on a dollar maybe you + + align:start position:0% +got 20 25 30 cents on a dollar maybe you + + + align:start position:0% +got 20 25 30 cents on a dollar maybe you +got 20 cents on a dollar but now if you + + align:start position:0% +got 20 cents on a dollar but now if you + + + align:start position:0% +got 20 cents on a dollar but now if you +hold out if you held out apparently you + + align:start position:0% +hold out if you held out apparently you + + + align:start position:0% +hold out if you held out apparently you +got a little bit more eventually so it's + + align:start position:0% +got a little bit more eventually so it's + + + align:start position:0% +got a little bit more eventually so it's +a little bit of a fuzzy concept it but + + align:start position:0% +a little bit of a fuzzy concept it but + + + align:start position:0% +a little bit of a fuzzy concept it but +it's not something you usually you make + + align:start position:0% +it's not something you usually you make + + + align:start position:0% +it's not something you usually you make +an assumption of what it + + align:start position:0% +an assumption of what it + + + align:start position:0% +an assumption of what it +is and related question so how how would + + align:start position:0% +is and related question so how how would + + + align:start position:0% +is and related question so how how would +we also estimate uh the other constants + + align:start position:0% +we also estimate uh the other constants + + + align:start position:0% +we also estimate uh the other constants +like the the hazard rate and and the J + + align:start position:0% +like the the hazard rate and and the J + + + align:start position:0% +like the the hazard rate and and the J +so once you fix R once you fix the + + align:start position:0% +so once you fix R once you fix the + + + align:start position:0% +so once you fix R once you fix the +recovery rate then you can take the bond + + align:start position:0% +recovery rate then you can take the bond + + + align:start position:0% +recovery rate then you can take the bond +price and because bond price + + align:start position:0% +price and because bond price + + + align:start position:0% +price and because bond price +theoretically is e to the minus HT you + + align:start position:0% +theoretically is e to the minus HT you + + + align:start position:0% +theoretically is e to the minus HT you +can estimate H from the bond price so + + align:start position:0% +can estimate H from the bond price so + + + align:start position:0% +can estimate H from the bond price so +like if You observe a bond price in the + + align:start position:0% +like if You observe a bond price in the + + + align:start position:0% +like if You observe a bond price in the +market you can say I'm going to estimate + + align:start position:0% +market you can say I'm going to estimate + + + align:start position:0% +market you can say I'm going to estimate +H so like say I'm going to take some + + align:start position:0% +H so like say I'm going to take some + + + align:start position:0% +H so like say I'm going to take some +Benchmark bonds which I know the price + + align:start position:0% +Benchmark bonds which I know the price + + + align:start position:0% +Benchmark bonds which I know the price +of and I'm going to estimate H for each + + align:start position:0% +of and I'm going to estimate H for each + + + align:start position:0% +of and I'm going to estimate H for each +of these bond prices and I'm going to + + align:start position:0% +of these bond prices and I'm going to + + + align:start position:0% +of these bond prices and I'm going to +create a + + align:start position:0% +create a + + + align:start position:0% +create a +curve which is going to be my hazard + + align:start position:0% +curve which is going to be my hazard + + + align:start position:0% +curve which is going to be my hazard +curve and then I take another derivative + + align:start position:0% +curve and then I take another derivative + + + align:start position:0% +curve and then I take another derivative +bond that I don't know the price of and + + align:start position:0% +bond that I don't know the price of and + + + align:start position:0% +bond that I don't know the price of and +I can use that same curve to price it so + + align:start position:0% +I can use that same curve to price it so + + + align:start position:0% +I can use that same curve to price it so +essentially what I'm by doing this what + + align:start position:0% +essentially what I'm by doing this what + + + align:start position:0% +essentially what I'm by doing this what +I'm saying is I'm going to replicate my + + align:start position:0% +I'm saying is I'm going to replicate my + + + align:start position:0% +I'm saying is I'm going to replicate my +derivative using these Benchmark bonds + + align:start position:0% +derivative using these Benchmark bonds + + + align:start position:0% +derivative using these Benchmark bonds +as much as I + + align:start position:0% +as much as I + + + align:start position:0% +as much as I +can that's the assumption that I'm + + align:start position:0% + + + + align:start position:0% + +making + + align:start position:0% +making + + + align:start position:0% +making +how if um multiple currencies are + + align:start position:0% +how if um multiple currencies are + + + align:start position:0% +how if um multiple currencies are +involved if we are trying to trade with + + align:start position:0% +involved if we are trying to trade with + + + align:start position:0% +involved if we are trying to trade with +multiple different currencies how does + + align:start position:0% +multiple different currencies how does + + + align:start position:0% +multiple different currencies how does +the M the whole model differ if multiple + + align:start position:0% +the M the whole model differ if multiple + + + align:start position:0% +the M the whole model differ if multiple +currencies are involved you can first + + align:start position:0% +currencies are involved you can first + + + align:start position:0% +currencies are involved you can first +you can Define like um it becomes tricky + + align:start position:0% +you can Define like um it becomes tricky + + + align:start position:0% +you can Define like um it becomes tricky +like you can say each currency can + + align:start position:0% +like you can say each currency can + + + align:start position:0% +like you can say each currency can +devalue x amount like if theault happens + + align:start position:0% +devalue x amount like if theault happens + + + align:start position:0% +devalue x amount like if theault happens +you can have more than one currency + + align:start position:0% +you can have more than one currency + + + align:start position:0% +you can have more than one currency +being devalued + + align:start position:0% +being devalued + + + align:start position:0% +being devalued +uh if you have more than one currency if + + align:start position:0% +uh if you have more than one currency if + + + align:start position:0% +uh if you have more than one currency if +you have if you have more than two + + align:start position:0% +you have if you have more than two + + + align:start position:0% +you have if you have more than two +currencies like three currencies there's + + align:start position:0% +currencies like three currencies there's + + + align:start position:0% +currencies like three currencies there's +other identities you have + + align:start position:0% +other identities you have + + + align:start position:0% +other identities you have +to take care like you you really + + align:start position:0% +to take care like you you really + + + align:start position:0% +to take care like you you really +simulate if you have three currencies + + align:start position:0% +simulate if you have three currencies + + + align:start position:0% +simulate if you have three currencies +there is a triangle identity that say + + align:start position:0% +there is a triangle identity that say + + + align:start position:0% +there is a triangle identity that say +dollar Euros times Euro n exchange rate + + align:start position:0% +dollar Euros times Euro n exchange rate + + + align:start position:0% +dollar Euros times Euro n exchange rate +has to equal to dollar yen exchange rate + + align:start position:0% +has to equal to dollar yen exchange rate + + + align:start position:0% +has to equal to dollar yen exchange rate +that's kind of an Arbitrage + + align:start position:0% +that's kind of an Arbitrage + + + align:start position:0% +that's kind of an Arbitrage +condition um just like interest rates FX + + align:start position:0% +condition um just like interest rates FX + + + align:start position:0% +condition um just like interest rates FX +forward parody even stronger in some + + align:start position:0% +forward parody even stronger in some + + + align:start position:0% +forward parody even stronger in some +sense and so you you just you can + + align:start position:0% +sense and so you you just you can + + + align:start position:0% +sense and so you you just you can +basically you can say multip you can + + align:start position:0% +basically you can say multip you can + + + align:start position:0% +basically you can say multip you can +write down multiple processes and price + + align:start position:0% + + + + align:start position:0% + +stuff how much equations change when you + + align:start position:0% +stuff how much equations change when you + + + align:start position:0% +stuff how much equations change when you +add in bonds that are paying coupons and + + align:start position:0% +add in bonds that are paying coupons and + + + align:start position:0% +add in bonds that are paying coupons and +how do you factor in like duration and + + align:start position:0% +how do you factor in like duration and + + + align:start position:0% +how do you factor in like duration and +all that well you know you just uh you + + align:start position:0% +all that well you know you just uh you + + + align:start position:0% +all that well you know you just uh you +just uh it's not hard really you just + + align:start position:0% +just uh it's not hard really you just + + + align:start position:0% +just uh it's not hard really you just +instead of having this you just write + + align:start position:0% +instead of having this you just write + + + align:start position:0% +instead of having this you just write +down all the coupon payments when you + + align:start position:0% +down all the coupon payments when you + + + align:start position:0% +down all the coupon payments when you +pay them and then you just take an + + align:start position:0% +pay them and then you just take an + + + align:start position:0% +pay them and then you just take an +expectation all the coupon payments so + + align:start position:0% +expectation all the coupon payments so + + + align:start position:0% +expectation all the coupon payments so +it's uh really the same process you just + + align:start position:0% +it's uh really the same process you just + + + align:start position:0% +it's uh really the same process you just +repeated it for every coupon + + align:start position:0% + + + + align:start position:0% + +why don't we shut the formal class over + + align:start position:0% +why don't we shut the formal class over + + + align:start position:0% +why don't we shut the formal class over +now but people have questions afterwards + + align:start position:0% +now but people have questions afterwards + + + align:start position:0% +now but people have questions afterwards +we'll uh yeah I'm certainly around to + + align:start position:0% +we'll uh yeah I'm certainly around to + + + align:start position:0% +we'll uh yeah I'm certainly around to +answer question anybody want thank you + + align:start position:0% +answer question anybody want thank you + + + align:start position:0% +answer question anybody want thank you +can pick up your \ No newline at end of file diff --git a/5An3DOfA0Zk.txt b/5An3DOfA0Zk.txt new file mode 100644 index 0000000000000000000000000000000000000000..e83b363ae3ac34d810eca7f2e283f56c3a5daa60 --- /dev/null +++ b/5An3DOfA0Zk.txt @@ -0,0 +1,19 @@ +align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/5CExAUWzHEQ.txt b/5CExAUWzHEQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..95372e922028ad4a851030425b183efc8f8875a2 --- /dev/null +++ b/5CExAUWzHEQ.txt @@ -0,0 +1,491 @@ +align:start position:0% + +the CP parameter C P stands for + + align:start position:0% +the CP parameter C P stands for + + + align:start position:0% +the CP parameter C P stands for +complexity parameter recall that the + + align:start position:0% +complexity parameter recall that the + + + align:start position:0% +complexity parameter recall that the +first tree we made using latitude and + + align:start position:0% +first tree we made using latitude and + + + align:start position:0% +first tree we made using latitude and +longitude only had many splits that we + + align:start position:0% +longitude only had many splits that we + + + align:start position:0% +longitude only had many splits that we +were able to trim it without losing much + + align:start position:0% +were able to trim it without losing much + + + align:start position:0% +were able to trim it without losing much +accuracy the intuition we gain is having + + align:start position:0% +accuracy the intuition we gain is having + + + align:start position:0% +accuracy the intuition we gain is having +too many splits is bad for + + align:start position:0% +too many splits is bad for + + + align:start position:0% +too many splits is bad for +generalization that is performance on + + align:start position:0% +generalization that is performance on + + + align:start position:0% +generalization that is performance on +the test set so we should penalize the + + align:start position:0% +the test set so we should penalize the + + + align:start position:0% +the test set so we should penalize the +complexity let us define our SS to be + + align:start position:0% +complexity let us define our SS to be + + + align:start position:0% +complexity let us define our SS to be +the residual sum of squares also known + + align:start position:0% +the residual sum of squares also known + + + align:start position:0% +the residual sum of squares also known +as the sum of square differences our + + align:start position:0% +as the sum of square differences our + + + align:start position:0% +as the sum of square differences our +goal when building the tree is to + + align:start position:0% +goal when building the tree is to + + + align:start position:0% +goal when building the tree is to +minimize our SS by making splits we want + + align:start position:0% +minimize our SS by making splits we want + + + align:start position:0% +minimize our SS by making splits we want +to penalize having too many splits now + + align:start position:0% +to penalize having too many splits now + + + align:start position:0% +to penalize having too many splits now +define s to be the number of splits and + + align:start position:0% +define s to be the number of splits and + + + align:start position:0% +define s to be the number of splits and +lambda to be our penalty our new goal is + + align:start position:0% +lambda to be our penalty our new goal is + + + align:start position:0% +lambda to be our penalty our new goal is +to find a tree that minimizes the sum of + + align:start position:0% +to find a tree that minimizes the sum of + + + align:start position:0% +to find a tree that minimizes the sum of +the RSS at each leaf plus lambda times s + + align:start position:0% +the RSS at each leaf plus lambda times s + + + align:start position:0% +the RSS at each leaf plus lambda times s +the number of splits let us consider + + align:start position:0% +the number of splits let us consider + + + align:start position:0% +the number of splits let us consider +this follow example owing example here + + align:start position:0% +this follow example owing example here + + + align:start position:0% +this follow example owing example here +we have set lambda to be equal to 0.5 + + align:start position:0% +we have set lambda to be equal to 0.5 + + + align:start position:0% +we have set lambda to be equal to 0.5 +initially we have a tree with no splits + + align:start position:0% +initially we have a tree with no splits + + + align:start position:0% +initially we have a tree with no splits +we simply take the average of the data + + align:start position:0% +we simply take the average of the data + + + align:start position:0% +we simply take the average of the data +the RSS in this case is 5 thus our total + + align:start position:0% +the RSS in this case is 5 thus our total + + + align:start position:0% +the RSS in this case is 5 thus our total +penalty is also 5 if we make one split + + align:start position:0% +penalty is also 5 if we make one split + + + align:start position:0% +penalty is also 5 if we make one split +we now have two leaves at each of these + + align:start position:0% +we now have two leaves at each of these + + + align:start position:0% +we now have two leaves at each of these +leaves say we have an error or RSS of 2 + + align:start position:0% +leaves say we have an error or RSS of 2 + + + align:start position:0% +leaves say we have an error or RSS of 2 +the total RSS error is then 2 plus 2 is + + align:start position:0% +the total RSS error is then 2 plus 2 is + + + align:start position:0% +the total RSS error is then 2 plus 2 is +4 and the total penalty is 4 plus 0.5 + + align:start position:0% +4 and the total penalty is 4 plus 0.5 + + + align:start position:0% +4 and the total penalty is 4 plus 0.5 +times 1 the number of splits a total + + align:start position:0% +times 1 the number of splits a total + + + align:start position:0% +times 1 the number of splits a total +penalty in this case is 4.5 if we split + + align:start position:0% +penalty in this case is 4.5 if we split + + + align:start position:0% +penalty in this case is 4.5 if we split +a game on one of our leaves we now have + + align:start position:0% +a game on one of our leaves we now have + + + align:start position:0% +a game on one of our leaves we now have +a total of 3 leaves for 2 splits the + + align:start position:0% +a total of 3 leaves for 2 splits the + + + align:start position:0% +a total of 3 leaves for 2 splits the +error at our left most leaf is 1 the + + align:start position:0% +error at our left most leaf is 1 the + + + align:start position:0% +error at our left most leaf is 1 the +next leaf has an error of 0.8 and the + + align:start position:0% +next leaf has an error of 0.8 and the + + + align:start position:0% +next leaf has an error of 0.8 and the +next leaf has an error of 2 for a total + + align:start position:0% +next leaf has an error of 2 for a total + + + align:start position:0% +next leaf has an error of 2 for a total +error of 3.8 the total penalty is thus + + align:start position:0% +error of 3.8 the total penalty is thus + + + align:start position:0% +error of 3.8 the total penalty is thus +3.8 plus 0.5 times 2 for a total penalty + + align:start position:0% +3.8 plus 0.5 times 2 for a total penalty + + + align:start position:0% +3.8 plus 0.5 times 2 for a total penalty +of 4.8 notice that if we pick a large + + align:start position:0% +of 4.8 notice that if we pick a large + + + align:start position:0% +of 4.8 notice that if we pick a large +value of lambda we won't + + align:start position:0% +value of lambda we won't + + + align:start position:0% +value of lambda we won't +make many splits because you pay a big + + align:start position:0% +make many splits because you pay a big + + + align:start position:0% +make many splits because you pay a big +price for every additional split that + + align:start position:0% +price for every additional split that + + + align:start position:0% +price for every additional split that +will outweigh the decrease in error if + + align:start position:0% +will outweigh the decrease in error if + + + align:start position:0% +will outweigh the decrease in error if +we pick a small zero value of lambda + + align:start position:0% +we pick a small zero value of lambda + + + align:start position:0% +we pick a small zero value of lambda +will make splits until it no longer + + align:start position:0% +will make splits until it no longer + + + align:start position:0% +will make splits until it no longer +decreases the error you may be wondering + + align:start position:0% +decreases the error you may be wondering + + + align:start position:0% +decreases the error you may be wondering +at this point the definition of CP is + + align:start position:0% +at this point the definition of CP is + + + align:start position:0% +at this point the definition of CP is +what exactly well it's very closely + + align:start position:0% +what exactly well it's very closely + + + align:start position:0% +what exactly well it's very closely +related to lambda considering a tree + + align:start position:0% +related to lambda considering a tree + + + align:start position:0% +related to lambda considering a tree +with no splits we simply take the + + align:start position:0% +with no splits we simply take the + + + align:start position:0% +with no splits we simply take the +average of a data calculate our assists + + align:start position:0% +average of a data calculate our assists + + + align:start position:0% +average of a data calculate our assists +for that so-called tree and let us call + + align:start position:0% +for that so-called tree and let us call + + + align:start position:0% +for that so-called tree and let us call +that RSS for no splits then we can + + align:start position:0% +that RSS for no splits then we can + + + align:start position:0% +that RSS for no splits then we can +define CP as lambda over RSS no splits + + align:start position:0% +define CP as lambda over RSS no splits + + + align:start position:0% +define CP as lambda over RSS no splits +when you're actually using CP in your + + align:start position:0% +when you're actually using CP in your + + + align:start position:0% +when you're actually using CP in your +our code you don't need to think exactly + + align:start position:0% +our code you don't need to think exactly + + + align:start position:0% +our code you don't need to think exactly +what it means just that small numbers of + + align:start position:0% +what it means just that small numbers of + + + align:start position:0% +what it means just that small numbers of +CP encourage large trees and large + + align:start position:0% +CP encourage large trees and large + + + align:start position:0% +CP encourage large trees and large +values of CP encourage small trees let's + + align:start position:0% +values of CP encourage small trees let's + + + align:start position:0% +values of CP encourage small trees let's +go back to our now and apply + + align:start position:0% +go back to our now and apply + + + align:start position:0% +go back to our now and apply +cross-validation to our training data \ No newline at end of file diff --git a/5QHc0RK0FxA.txt b/5QHc0RK0FxA.txt new file mode 100644 index 0000000000000000000000000000000000000000..e2cc88198cab8a9f082c6e78a983b66e9a173b8a --- /dev/null +++ b/5QHc0RK0FxA.txt @@ -0,0 +1,547 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu as an overall uh statement + + align:start position:0% +ocw.mit.edu as an overall uh statement + + + align:start position:0% +ocw.mit.edu as an overall uh statement +about the course it is uh the aim is to + + align:start position:0% +about the course it is uh the aim is to + + + align:start position:0% +about the course it is uh the aim is to +bring the Learned discipline called + + align:start position:0% +bring the Learned discipline called + + + align:start position:0% +bring the Learned discipline called +engineering ethics + + align:start position:0% +engineering ethics + + + align:start position:0% +engineering ethics +to the students uh and my goal is to get + + align:start position:0% +to the students uh and my goal is to get + + + align:start position:0% +to the students uh and my goal is to get +them to um talk in ethical categories + + align:start position:0% +them to um talk in ethical categories + + + align:start position:0% +them to um talk in ethical categories +and to be able to understand engineering + + align:start position:0% +and to be able to understand engineering + + + align:start position:0% +and to be able to understand engineering +at a philosophical level uh and my uh + + align:start position:0% +at a philosophical level uh and my uh + + + align:start position:0% +at a philosophical level uh and my uh +approach to doing that is to treat the + + align:start position:0% +approach to doing that is to treat the + + + align:start position:0% +approach to doing that is to treat the +course or engineering ethics as a uh an + + align:start position:0% +course or engineering ethics as a uh an + + + align:start position:0% +course or engineering ethics as a uh an +engagement of two other learnning + + align:start position:0% +engagement of two other learnning + + + align:start position:0% +engagement of two other learnning +disciplines in this class what seemed to + + align:start position:0% +disciplines in this class what seemed to + + + align:start position:0% +disciplines in this class what seemed to +work was the approach of being many + + align:start position:0% +work was the approach of being many + + + align:start position:0% +work was the approach of being many +discipline of many disciplines I brought + + align:start position:0% +discipline of many disciplines I brought + + + align:start position:0% +discipline of many disciplines I brought +uh the great pieces of art into this + + align:start position:0% +uh the great pieces of art into this + + + align:start position:0% +uh the great pieces of art into this +class and I talked about how + + align:start position:0% +class and I talked about how + + + align:start position:0% +class and I talked about how +Raphael's um um uh mass at bosina gave a + + align:start position:0% +Raphael's um um uh mass at bosina gave a + + + align:start position:0% +Raphael's um um uh mass at bosina gave a +picture of what engineering really is as + + align:start position:0% +picture of what engineering really is as + + + align:start position:0% +picture of what engineering really is as +distinct from uh mathematics for example + + align:start position:0% +distinct from uh mathematics for example + + + align:start position:0% +distinct from uh mathematics for example +when you look at Raphael's uh the school + + align:start position:0% +when you look at Raphael's uh the school + + + align:start position:0% +when you look at Raphael's uh the school +at Athens so I brought the high arts in + + align:start position:0% +at Athens so I brought the high arts in + + + align:start position:0% +at Athens so I brought the high arts in +uh we talked about literature + + align:start position:0% +uh we talked about literature + + + align:start position:0% +uh we talked about literature +uh one part of talking one way to talk + + align:start position:0% +uh one part of talking one way to talk + + + align:start position:0% +uh one part of talking one way to talk +about literature is to talk about + + align:start position:0% +about literature is to talk about + + + align:start position:0% +about literature is to talk about +literature is presented in in in the + + align:start position:0% +literature is presented in in in the + + + align:start position:0% +literature is presented in in in the +cinema students go to movies they like + + align:start position:0% +cinema students go to movies they like + + + align:start position:0% +cinema students go to movies they like +the movies and what worked in the class + + align:start position:0% +the movies and what worked in the class + + + align:start position:0% +the movies and what worked in the class +was that the students today young people + + align:start position:0% +was that the students today young people + + + align:start position:0% +was that the students today young people +today are very good at critiquing a film + + align:start position:0% +today are very good at critiquing a film + + + align:start position:0% +today are very good at critiquing a film +so I was able to bring out ethical + + align:start position:0% +so I was able to bring out ethical + + + align:start position:0% +so I was able to bring out ethical +points by way of of of of + + align:start position:0% +points by way of of of of + + + align:start position:0% +points by way of of of of +film uh the third part was that I had no + + align:start position:0% +film uh the third part was that I had no + + + align:start position:0% +film uh the third part was that I had no +hesitation in the class or or as I do it + + align:start position:0% +hesitation in the class or or as I do it + + + align:start position:0% +hesitation in the class or or as I do it +in my writing to talk about experiences + + align:start position:0% +in my writing to talk about experiences + + + align:start position:0% +in my writing to talk about experiences +that I've had in my personal life with + + align:start position:0% +that I've had in my personal life with + + + align:start position:0% +that I've had in my personal life with +my family + + align:start position:0% +my family + + + align:start position:0% +my family +ethics as it seems at first to be very + + align:start position:0% +ethics as it seems at first to be very + + + align:start position:0% +ethics as it seems at first to be very +amorphous kind of uh subject but it can + + align:start position:0% +amorphous kind of uh subject but it can + + + align:start position:0% +amorphous kind of uh subject but it can +be approached + + align:start position:0% +be approached + + + align:start position:0% +be approached +systematically that not everything that + + align:start position:0% +systematically that not everything that + + + align:start position:0% +systematically that not everything that +everybody says is right uh if they come + + align:start position:0% +everybody says is right uh if they come + + + align:start position:0% +everybody says is right uh if they come +up to a conclusion not every way they + + align:start position:0% +up to a conclusion not every way they + + + align:start position:0% +up to a conclusion not every way they +try to justify it uh uh is something + + align:start position:0% +try to justify it uh uh is something + + + align:start position:0% +try to justify it uh uh is something +that is defensible uh so being + + align:start position:0% +that is defensible uh so being + + + align:start position:0% +that is defensible uh so being +engineering students they were very + + align:start position:0% +engineering students they were very + + + align:start position:0% +engineering students they were very +happy to see that uh ethics is just as + + align:start position:0% +happy to see that uh ethics is just as + + + align:start position:0% +happy to see that uh ethics is just as +rigorous as science mathematics and + + align:start position:0% +rigorous as science mathematics and + + + align:start position:0% +rigorous as science mathematics and +Engineering the engineering faculty + + align:start position:0% +Engineering the engineering faculty + + + align:start position:0% +Engineering the engineering faculty +here + + align:start position:0% +here + + + align:start position:0% +here +um are skeptical about a course on + + align:start position:0% +um are skeptical about a course on + + + align:start position:0% +um are skeptical about a course on +engineering + + align:start position:0% +engineering + + + align:start position:0% +engineering +ethics uh because many of them don't see + + align:start position:0% +ethics uh because many of them don't see + + + align:start position:0% +ethics uh because many of them don't see +how they can use it in their + + align:start position:0% +how they can use it in their + + + align:start position:0% +how they can use it in their +classes uh but there's a large + + align:start position:0% +classes uh but there's a large + + + align:start position:0% +classes uh but there's a large +literature on how to use engineering + + align:start position:0% +literature on how to use engineering + + + align:start position:0% +literature on how to use engineering +ethics in engineering + + align:start position:0% +ethics in engineering + + + align:start position:0% +ethics in engineering +problems uh and um I think that their + + align:start position:0% +problems uh and um I think that their + + + align:start position:0% +problems uh and um I think that their +attitudes about how to fit this course + + align:start position:0% +attitudes about how to fit this course + + + align:start position:0% +attitudes about how to fit this course +into an already busy schedule uh will + + align:start position:0% +into an already busy schedule uh will + + + align:start position:0% +into an already busy schedule uh will +change once they see how to make an + + align:start position:0% +change once they see how to make an + + + align:start position:0% +change once they see how to make an +ordinary engineering problem an ethical + + align:start position:0% +ordinary engineering problem an ethical + + + align:start position:0% +ordinary engineering problem an ethical +problem \ No newline at end of file diff --git a/5QV8Gr1z16E.txt b/5QV8Gr1z16E.txt new file mode 100644 index 0000000000000000000000000000000000000000..de5a6a4b887cb55027595d2e167d7a0a89f0acfa --- /dev/null +++ b/5QV8Gr1z16E.txt @@ -0,0 +1,11491 @@ +align:start position:0% + +Okay, today is our second and probably + + align:start position:0% +Okay, today is our second and probably + + + align:start position:0% +Okay, today is our second and probably +last day of homogeneous dynamics and + + align:start position:0% +last day of homogeneous dynamics and + + + align:start position:0% +last day of homogeneous dynamics and +projection theory. Um, let's remember + + align:start position:0% +projection theory. Um, let's remember + + + align:start position:0% +projection theory. Um, let's remember +where we are and then we're going to uh + + align:start position:0% +where we are and then we're going to uh + + + align:start position:0% +where we are and then we're going to uh +try to use the the things we learned + + align:start position:0% +try to use the the things we learned + + + align:start position:0% +try to use the the things we learned +about last time to say something about + + align:start position:0% +about last time to say something about + + + align:start position:0% +about last time to say something about +dynamics. + + align:start position:0% +dynamics. + + + align:start position:0% +dynamics. +Okay. Um, so we'll have a league group + + align:start position:0% +Okay. Um, so we'll have a league group + + + align:start position:0% +Okay. Um, so we'll have a league group +G, which so far is SL2R, and we have a + + align:start position:0% +G, which so far is SL2R, and we have a + + + align:start position:0% +G, which so far is SL2R, and we have a +discrete subgroup, which so far has been + + align:start position:0% +discrete subgroup, which so far has been + + + align:start position:0% +discrete subgroup, which so far has been +SL2Z, + + align:start position:0% +SL2Z, + + + align:start position:0% +SL2Z, +and we're interested in GOD gamma. + + align:start position:0% +and we're interested in GOD gamma. + + + align:start position:0% +and we're interested in GOD gamma. +Um, we have a metric M, which is a right + + align:start position:0% +Um, we have a metric M, which is a right + + + align:start position:0% +Um, we have a metric M, which is a right +invariant + + align:start position:0% +invariant + + + align:start position:0% +invariant +metric + + align:start position:0% +metric + + + align:start position:0% +metric +on G. and then + + align:start position:0% +on G. and then + + + align:start position:0% +on G. and then +we get it leads to a metric that I also + + align:start position:0% +we get it leads to a metric that I also + + + align:start position:0% +we get it leads to a metric that I also +call M and G mod gamma. + + align:start position:0% +call M and G mod gamma. + + + align:start position:0% +call M and G mod gamma. +Okay. So now G also has a left action + + align:start position:0% + + + + align:start position:0% + +on G mod gamma + + align:start position:0% +on G mod gamma + + + align:start position:0% +on G mod gamma +and this left this left action does not + + align:start position:0% +and this left this left action does not + + + align:start position:0% +and this left this left action does not +preserve the metric because the metric + + align:start position:0% +preserve the metric because the metric + + + align:start position:0% +preserve the metric because the metric +is not left invariant. So this left + + align:start position:0% +is not left invariant. So this left + + + align:start position:0% +is not left invariant. So this left +action distorts the metric and we + + align:start position:0% +action distorts the metric and we + + + align:start position:0% +action distorts the metric and we +started to study that last time and it's + + align:start position:0% +started to study that last time and it's + + + align:start position:0% +started to study that last time and it's +going to continue to be crucial how it + + align:start position:0% +going to continue to be crucial how it + + + align:start position:0% +going to continue to be crucial how it +distorts the metric. Um but it preserves + + align:start position:0% +distorts the metric. Um but it preserves + + + align:start position:0% +distorts the metric. Um but it preserves +the volume. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um + + align:start position:0% + + + + align:start position:0% + +cool. Okay. Now uh inside of this group + + align:start position:0% +cool. Okay. Now uh inside of this group + + + align:start position:0% +cool. Okay. Now uh inside of this group +we have the uh unitary group + + align:start position:0% +we have the uh unitary group + + + align:start position:0% +we have the uh unitary group +uh sorry the unipotent group + + align:start position:0% + + + + align:start position:0% + +let's say UT is one t and our goal is to + + align:start position:0% +let's say UT is one t and our goal is to + + + align:start position:0% +let's say UT is one t and our goal is to +understand what how the unipotent orbits + + align:start position:0% +understand what how the unipotent orbits + + + align:start position:0% +understand what how the unipotent orbits +in gamma look. So we're going to study + + align:start position:0% +in gamma look. So we're going to study + + + align:start position:0% +in gamma look. So we're going to study +u dox + + align:start position:0% +u dox + + + align:start position:0% +u dox +in gamma. So x is a gamma + + align:start position:0% + + + + align:start position:0% + +and there's an an old theorem of + + align:start position:0% +and there's an an old theorem of + + + align:start position:0% +and there's an an old theorem of +headland from the 30s + + align:start position:0% +headland from the 30s + + + align:start position:0% +headland from the 30s +which is the the kind of thing about + + align:start position:0% +which is the the kind of thing about + + + align:start position:0% +which is the the kind of thing about +about this orbit that we're interested + + align:start position:0% +about this orbit that we're interested + + + align:start position:0% +about this orbit that we're interested +in that + + align:start position:0% +in that + + + align:start position:0% +in that +u dox is either periodic + + align:start position:0% +u dox is either periodic + + + align:start position:0% +u dox is either periodic +or dense. + + align:start position:0% +or dense. + + + align:start position:0% +or dense. +We won't exactly prove that but we'll + + align:start position:0% +We won't exactly prove that but we'll + + + align:start position:0% +We won't exactly prove that but we'll +prove some things that are a little bit + + align:start position:0% +prove some things that are a little bit + + + align:start position:0% +prove some things that are a little bit +related. + + align:start position:0% +related. + + + align:start position:0% +related. +Okay. Um, now the unipotent group is + + align:start position:0% +Okay. Um, now the unipotent group is + + + align:start position:0% +Okay. Um, now the unipotent group is +special and the one way of getting our + + align:start position:0% +special and the one way of getting our + + + align:start position:0% +special and the one way of getting our +hands on something special about it is + + align:start position:0% +hands on something special about it is + + + align:start position:0% +hands on something special about it is +to see how it relates to diagonal + + align:start position:0% +to see how it relates to diagonal + + + align:start position:0% +to see how it relates to diagonal +matrices. So let's say this + + align:start position:0% +matrices. So let's say this + + + align:start position:0% +matrices. So let's say this +a sub is that matrix that diagonal + + align:start position:0% +a sub is that matrix that diagonal + + + align:start position:0% +a sub is that matrix that diagonal +matrix in SL2R. And then acute + + align:start position:0% +matrix in SL2R. And then acute + + + align:start position:0% +matrix in SL2R. And then acute +observation is that a subr u t a subr + + align:start position:0% +observation is that a subr u t a subr + + + align:start position:0% +observation is that a subr u t a subr +inverse is u e to the 2r t. + + align:start position:0% +inverse is u e to the 2r t. + + + align:start position:0% +inverse is u e to the 2r t. +Um it's just a computation with + + align:start position:0% +Um it's just a computation with + + + align:start position:0% +Um it's just a computation with +matrices. Uh I've done it a couple times + + align:start position:0% +matrices. Uh I've done it a couple times + + + align:start position:0% +matrices. Uh I've done it a couple times +and I start to sort of anyway doing it + + align:start position:0% +and I start to sort of anyway doing it + + + align:start position:0% +and I start to sort of anyway doing it +in front of you I think is not very + + align:start position:0% +in front of you I think is not very + + + align:start position:0% +in front of you I think is not very +useful but if you are interested in this + + align:start position:0% +useful but if you are interested in this + + + align:start position:0% +useful but if you are interested in this +it's if you do it yourself it starts to + + align:start position:0% +it's if you do it yourself it starts to + + + align:start position:0% +it's if you do it yourself it starts to +make sense. Uh okay. + + align:start position:0% +make sense. Uh okay. + + + align:start position:0% +make sense. Uh okay. +So now let's say that u 0 t of x that + + align:start position:0% +So now let's say that u 0 t of x that + + + align:start position:0% +So now let's say that u 0 t of x that +means the set of u t of x t is a zero t. + + align:start position:0% +means the set of u t of x t is a zero t. + + + align:start position:0% +means the set of u t of x t is a zero t. +So if capital t is large this is a big + + align:start position:0% +So if capital t is large this is a big + + + align:start position:0% +So if capital t is large this is a big +piece of an orbit and that's more or + + align:start position:0% +piece of an orbit and that's more or + + + align:start position:0% +piece of an orbit and that's more or +less what we'd like to study. What is + + align:start position:0% +less what we'd like to study. What is + + + align:start position:0% +less what we'd like to study. What is +the shape of a big piece of the orbit? + + align:start position:0% +the shape of a big piece of the orbit? + + + align:start position:0% +the shape of a big piece of the orbit? +And this observation tells us that + + align:start position:0% +And this observation tells us that + + + align:start position:0% +And this observation tells us that +um u0 t of x is a r + + align:start position:0% +um u0 t of x is a r + + + align:start position:0% +um u0 t of x is a r +u01 + + align:start position:0% +u01 + + + align:start position:0% +u01 +a r inverse of x. + + align:start position:0% +a r inverse of x. + + + align:start position:0% +a r inverse of x. +Okay. And this is helpful because this + + align:start position:0% +Okay. And this is helpful because this + + + align:start position:0% +Okay. And this is helpful because this +this u01 is much less intimidating than + + align:start position:0% +this u01 is much less intimidating than + + + align:start position:0% +this u01 is much less intimidating than +u t. So this here is just a little piece + + align:start position:0% +u t. So this here is just a little piece + + + align:start position:0% +u t. So this here is just a little piece +of the orbit. Um and so to understand a + + align:start position:0% +of the orbit. Um and so to understand a + + + align:start position:0% +of the orbit. Um and so to understand a +big orbit we have to understand how this + + align:start position:0% +big orbit we have to understand how this + + + align:start position:0% +big orbit we have to understand how this +a sub rar acts on a little orbit. + + align:start position:0% +a sub rar acts on a little orbit. + + + align:start position:0% +a sub rar acts on a little orbit. +Um okay and another simple observation + + align:start position:0% +Um okay and another simple observation + + + align:start position:0% +Um okay and another simple observation +is that a r is like a + + align:start position:0% +is that a r is like a + + + align:start position:0% +is that a r is like a +little r to the j. So if big R is big J + + align:start position:0% +little r to the j. So if big R is big J + + + align:start position:0% +little r to the j. So if big R is big J +* little R then we have this. Oh and in + + align:start position:0% +* little R then we have this. Oh and in + + + align:start position:0% +* little R then we have this. Oh and in +in this equation by the way um E to the + + align:start position:0% +in this equation by the way um E to the + + + align:start position:0% +in this equation by the way um E to the +2 big R is T. + + align:start position:0% +2 big R is T. + + + align:start position:0% +2 big R is T. +Okay. So this a a r we can think of it + + align:start position:0% +Okay. So this a a r we can think of it + + + align:start position:0% +Okay. So this a a r we can think of it +as a little r applied many times. Okay. + + align:start position:0% +as a little r applied many times. Okay. + + + align:start position:0% +as a little r applied many times. Okay. +So therefore it makes sense that we + + align:start position:0% +So therefore it makes sense that we + + + align:start position:0% +So therefore it makes sense that we +could just try to understand + + align:start position:0% + + + + align:start position:0% + +how a little r acts on unipotent orbits. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, we made a picture of this at the end + + align:start position:0% +So, we made a picture of this at the end + + + align:start position:0% +So, we made a picture of this at the end +of class last time with models and props + + align:start position:0% +of class last time with models and props + + + align:start position:0% +of class last time with models and props +and everything. And uh and this picture + + align:start position:0% +and everything. And uh and this picture + + + align:start position:0% +and everything. And uh and this picture +is is is uh the the the main tool that + + align:start position:0% +is is is uh the the the main tool that + + + align:start position:0% +is is is uh the the the main tool that +we're going to think about for + + align:start position:0% +we're going to think about for + + + align:start position:0% +we're going to think about for +homogeneous dynamics. So, I'm going to + + align:start position:0% +homogeneous dynamics. So, I'm going to + + + align:start position:0% +homogeneous dynamics. So, I'm going to +draw this picture again and then we're + + align:start position:0% +draw this picture again and then we're + + + align:start position:0% +draw this picture again and then we're +going to talk about why it why it is the + + align:start position:0% +going to talk about why it why it is the + + + align:start position:0% +going to talk about why it why it is the +way we drew it. Um okay. So, + + align:start position:0% +way we drew it. Um okay. So, + + + align:start position:0% +way we drew it. Um okay. So, +over here something a shape that I'll + + align:start position:0% +over here something a shape that I'll + + + align:start position:0% +over here something a shape that I'll +draw as being kind of a cylinder. And + + align:start position:0% +draw as being kind of a cylinder. And + + + align:start position:0% +draw as being kind of a cylinder. And +this is a fundamental domain. Um so so + + align:start position:0% +this is a fundamental domain. Um so so + + + align:start position:0% +this is a fundamental domain. Um so so +this is either the whole fundamental + + align:start position:0% +this is either the whole fundamental + + + align:start position:0% +this is either the whole fundamental +domain or maybe a tube in + + align:start position:0% + + + + align:start position:0% + +in f. So f is sitting in the group g and + + align:start position:0% +in f. So f is sitting in the group g and + + + align:start position:0% +in f. So f is sitting in the group g and +it's a fundamental domain + + align:start position:0% + + + + align:start position:0% + +for g mod gap. + + align:start position:0% +for g mod gap. + + + align:start position:0% +for g mod gap. +Okay. And so this length scale is one. + + align:start position:0% +Okay. And so this length scale is one. + + + align:start position:0% +Okay. And so this length scale is one. +And this length scale um is also one. Or + + align:start position:0% +And this length scale um is also one. Or + + + align:start position:0% +And this length scale um is also one. Or +we could also make it smaller if we'd + + align:start position:0% +we could also make it smaller if we'd + + + align:start position:0% +we could also make it smaller if we'd +like to have a thinner tube. + + align:start position:0% +like to have a thinner tube. + + + align:start position:0% +like to have a thinner tube. +All right. And now inside of this tube + + align:start position:0% +All right. And now inside of this tube + + + align:start position:0% +All right. And now inside of this tube +are a bunch of pieces of unipotent orbit + + align:start position:0% +are a bunch of pieces of unipotent orbit + + + align:start position:0% +are a bunch of pieces of unipotent orbit +that I'll draw like this. + + align:start position:0% + + + + align:start position:0% + +Okay. So each of those is a piece of + + align:start position:0% +Okay. So each of those is a piece of + + + align:start position:0% +Okay. So each of those is a piece of +unipotent orbit. + + align:start position:0% +unipotent orbit. + + + align:start position:0% +unipotent orbit. +Um here is t = 0 and here is t = 1. + + align:start position:0% +Um here is t = 0 and here is t = 1. + + + align:start position:0% +Um here is t = 0 and here is t = 1. +Okay. And now understand what is going + + align:start position:0% +Okay. And now understand what is going + + + align:start position:0% +Okay. And now understand what is going +to happen to this picture when we apply + + align:start position:0% +to happen to this picture when we apply + + + align:start position:0% +to happen to this picture when we apply +a subr. + + align:start position:0% +a subr. + + + align:start position:0% +a subr. +So what we're going we're going to apply + + align:start position:0% +So what we're going we're going to apply + + + align:start position:0% +So what we're going we're going to apply +um I guess strictly speaking l the the + + align:start position:0% +um I guess strictly speaking l the the + + + align:start position:0% +um I guess strictly speaking l the the +we're going to apply it on the left. + + align:start position:0% +we're going to apply it on the left. + + + align:start position:0% +we're going to apply it on the left. +We're going to multiply by a subar on + + align:start position:0% +We're going to multiply by a subar on + + + align:start position:0% +We're going to multiply by a subar on +the left. + + align:start position:0% +the left. + + + align:start position:0% +the left. +Okay. So what's going to happen? Um + + align:start position:0% +Okay. So what's going to happen? Um + + + align:start position:0% +Okay. So what's going to happen? Um +first of all the unipotent orbits are + + align:start position:0% +first of all the unipotent orbits are + + + align:start position:0% +first of all the unipotent orbits are +going to stretch that way. + + align:start position:0% +going to stretch that way. + + + align:start position:0% +going to stretch that way. +Then second of all, okay, so so so you + + align:start position:0% +Then second of all, okay, so so so you + + + align:start position:0% +Then second of all, okay, so so so you +just think about what happens to the + + align:start position:0% +just think about what happens to the + + + align:start position:0% +just think about what happens to the +cylinder. There's going to be a + + align:start position:0% +cylinder. There's going to be a + + + align:start position:0% +cylinder. There's going to be a +direction where it stretches. There's + + align:start position:0% +direction where it stretches. There's + + + align:start position:0% +direction where it stretches. There's +going to be a direction that compresses. + + align:start position:0% +going to be a direction that compresses. + + + align:start position:0% +going to be a direction that compresses. +And there's going to be a direction that + + align:start position:0% +And there's going to be a direction that + + + align:start position:0% +And there's going to be a direction that +stays the same. That will be true at + + align:start position:0% +stays the same. That will be true at + + + align:start position:0% +stays the same. That will be true at +every point. Um, but what's important is + + align:start position:0% +every point. Um, but what's important is + + + align:start position:0% +every point. Um, but what's important is +that the direction that compresses is + + align:start position:0% +that the direction that compresses is + + + align:start position:0% +that the direction that compresses is +kind of not the same everywhere in this + + align:start position:0% +kind of not the same everywhere in this + + + align:start position:0% +kind of not the same everywhere in this +picture. And so to illustrate that, I'm + + align:start position:0% +picture. And so to illustrate that, I'm + + + align:start position:0% +picture. And so to illustrate that, I'm +going to draw what happens at at a + + align:start position:0% +going to draw what happens at at a + + + align:start position:0% +going to draw what happens at at a +couple of different heights. + + align:start position:0% +couple of different heights. + + + align:start position:0% +couple of different heights. +So at t = 1 + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +um and there'll be some direction that + + align:start position:0% +um and there'll be some direction that + + + align:start position:0% +um and there'll be some direction that +compresses maybe it's that direction and + + align:start position:0% +compresses maybe it's that direction and + + + align:start position:0% +compresses maybe it's that direction and +so when we apply l a r inverse this disc + + align:start position:0% +so when we apply l a r inverse this disc + + + align:start position:0% +so when we apply l a r inverse this disc +is going to be squished vertically + + align:start position:0% +is going to be squished vertically + + + align:start position:0% +is going to be squished vertically +and when it's squished vertically + + align:start position:0% +and when it's squished vertically + + + align:start position:0% +and when it's squished vertically +then we'll have a triangle that looks + + align:start position:0% +then we'll have a triangle that looks + + + align:start position:0% +then we'll have a triangle that looks +sort of like so. + + align:start position:0% + + + + align:start position:0% + +Okay. And also at t equals z we have the + + align:start position:0% +Okay. And also at t equals z we have the + + + align:start position:0% +Okay. And also at t equals z we have the +same disc with the same triangle in it + + align:start position:0% + + + + align:start position:0% + +but there's a compression direction + + align:start position:0% +but there's a compression direction + + + align:start position:0% +but there's a compression direction +which is different. So maybe down here + + align:start position:0% +which is different. So maybe down here + + + align:start position:0% +which is different. So maybe down here +it's this direction. + + align:start position:0% +it's this direction. + + + align:start position:0% +it's this direction. +So when we apply + + align:start position:0% +So when we apply + + + align:start position:0% +So when we apply +LA subar inverse um then we will get a + + align:start position:0% +LA subar inverse um then we will get a + + + align:start position:0% +LA subar inverse um then we will get a +pancake who gets squished this way and + + align:start position:0% +pancake who gets squished this way and + + + align:start position:0% +pancake who gets squished this way and +that will affect these points + + align:start position:0% +that will affect these points + + + align:start position:0% +that will affect these points +differently. + + align:start position:0% +differently. + + + align:start position:0% +differently. +This after squishing the green point and + + align:start position:0% +This after squishing the green point and + + + align:start position:0% +This after squishing the green point and +the orange point will be quite close + + align:start position:0% +the orange point will be quite close + + + align:start position:0% +the orange point will be quite close +together. + + align:start position:0% +together. + + + align:start position:0% +together. +All right. So that's the picture that we + + align:start position:0% +All right. So that's the picture that we + + + align:start position:0% +All right. So that's the picture that we +ended with last time. + + align:start position:0% + + + + align:start position:0% + +And what is important here + + align:start position:0% +And what is important here + + + align:start position:0% +And what is important here +key point + + align:start position:0% +key point + + + align:start position:0% +key point +is that the compression direction + + align:start position:0% + + + + align:start position:0% + +is twisting + + align:start position:0% + + + + align:start position:0% + +relative to + + align:start position:0% +relative to + + + align:start position:0% +relative to +the unipotent orbits. + + align:start position:0% + + + + align:start position:0% + +Meaning that if at a given height two + + align:start position:0% +Meaning that if at a given height two + + + align:start position:0% +Meaning that if at a given height two +unipotent orbits are being compressed + + align:start position:0% +unipotent orbits are being compressed + + + align:start position:0% +unipotent orbits are being compressed +towards each other then at most other + + align:start position:0% +towards each other then at most other + + + align:start position:0% +towards each other then at most other +heights uh they won't be. + + align:start position:0% + + + + align:start position:0% + +All right. So this is where we left off + + align:start position:0% +All right. So this is where we left off + + + align:start position:0% +All right. So this is where we left off +last time. Um are there questions or + + align:start position:0% +last time. Um are there questions or + + + align:start position:0% +last time. Um are there questions or +comments about this picture? + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +>> So in the picture you had last week, + + align:start position:0% +>> So in the picture you had last week, + + + align:start position:0% +>> So in the picture you had last week, +these after things are all kind of + + align:start position:0% +these after things are all kind of + + + align:start position:0% +these after things are all kind of +stretched out and compressed, they're + + align:start position:0% +stretched out and compressed, they're + + + align:start position:0% +stretched out and compressed, they're +then mapped back onto the fundamental + + align:start position:0% +then mapped back onto the fundamental + + + align:start position:0% +then mapped back onto the fundamental +domain half. But if they've been twisted + + align:start position:0% +domain half. But if they've been twisted + + + align:start position:0% +domain half. But if they've been twisted +around, like is there some are they kind + + align:start position:0% +around, like is there some are they kind + + + align:start position:0% +around, like is there some are they kind +of mapped back onto F without twisting + + align:start position:0% +of mapped back onto F without twisting + + + align:start position:0% +of mapped back onto F without twisting +in some way to make it all perfectly + + align:start position:0% +in some way to make it all perfectly + + + align:start position:0% +in some way to make it all perfectly +line up or is there kind of some other + + align:start position:0% +line up or is there kind of some other + + + align:start position:0% +line up or is there kind of some other +twisting that happens again as they get + + align:start position:0% +twisting that happens again as they get + + + align:start position:0% +twisting that happens again as they get +back back on F? + + align:start position:0% +back back on F? + + + align:start position:0% +back back on F? +>> Yeah. Yeah. Okay, that's a good + + align:start position:0% +>> Yeah. Yeah. Okay, that's a good + + + align:start position:0% +>> Yeah. Yeah. Okay, that's a good +question. Let's So the question is about + + align:start position:0% +question. Let's So the question is about + + + align:start position:0% +question. Let's So the question is about +um how this gets mapped back into the + + align:start position:0% +um how this gets mapped back into the + + + align:start position:0% +um how this gets mapped back into the +fundamental domain. Let's try to draw + + align:start position:0% +fundamental domain. Let's try to draw + + + align:start position:0% +fundamental domain. Let's try to draw +that also. + + align:start position:0% + + + + align:start position:0% + +So here + + align:start position:0% +So here + + + align:start position:0% +So here +here's our fundamental domain. + + align:start position:0% +here's our fundamental domain. + + + align:start position:0% +here's our fundamental domain. +First we apply this map just in our + + align:start position:0% +First we apply this map just in our + + + align:start position:0% +First we apply this map just in our +group and we get something which is tall + + align:start position:0% +group and we get something which is tall + + + align:start position:0% +group and we get something which is tall +and flat + + align:start position:0% + + + + align:start position:0% + +and perhaps it is twisted a little bit + + align:start position:0% +and perhaps it is twisted a little bit + + + align:start position:0% +and perhaps it is twisted a little bit +between the bottom and the top. Um + + align:start position:0% +between the bottom and the top. Um + + + align:start position:0% +between the bottom and the top. Um +um + + align:start position:0% +um + + + align:start position:0% +um +okay anyway then that is going to get + + align:start position:0% +okay anyway then that is going to get + + + align:start position:0% +okay anyway then that is going to get +mapped back into our domain. So pi is + + align:start position:0% +mapped back into our domain. So pi is + + + align:start position:0% +mapped back into our domain. So pi is +the projection from g to gm mod gamma + + align:start position:0% +the projection from g to gm mod gamma + + + align:start position:0% +the projection from g to gm mod gamma +and which gamma will identify with our + + align:start position:0% +and which gamma will identify with our + + + align:start position:0% +and which gamma will identify with our +fundamental domain. So this thing is + + align:start position:0% +fundamental domain. So this thing is + + + align:start position:0% +fundamental domain. So this thing is +going to get mapped back into the + + align:start position:0% +going to get mapped back into the + + + align:start position:0% +going to get mapped back into the +fundamental domain. What does that look + + align:start position:0% +fundamental domain. What does that look + + + align:start position:0% +fundamental domain. What does that look +like? Um, so the fundamental domain is + + align:start position:0% +like? Um, so the fundamental domain is + + + align:start position:0% +like? Um, so the fundamental domain is +kind of sort of a unit cube, + + align:start position:0% +kind of sort of a unit cube, + + + align:start position:0% +kind of sort of a unit cube, +but this thing is way taller than a unit + + align:start position:0% +but this thing is way taller than a unit + + + align:start position:0% +but this thing is way taller than a unit +cube. So imagine cutting it into pieces + + align:start position:0% +cube. So imagine cutting it into pieces + + + align:start position:0% +cube. So imagine cutting it into pieces +whose height is only around one. + + align:start position:0% +whose height is only around one. + + + align:start position:0% +whose height is only around one. +Okay? And this was only ever around one. + + align:start position:0% +Okay? And this was only ever around one. + + + align:start position:0% +Okay? And this was only ever around one. +So each of those pieces now is small + + align:start position:0% +So each of those pieces now is small + + + align:start position:0% +So each of those pieces now is small +enough to fit in the fundamental domain. + + align:start position:0% +enough to fit in the fundamental domain. + + + align:start position:0% +enough to fit in the fundamental domain. +Um, and um + + align:start position:0% +Um, and um + + + align:start position:0% +Um, and um +um let me call it piece one, piece two, + + align:start position:0% +um let me call it piece one, piece two, + + + align:start position:0% +um let me call it piece one, piece two, +piece three, and piece four. + + align:start position:0% +piece three, and piece four. + + + align:start position:0% +piece three, and piece four. +All right. Now, those are going to sort + + align:start position:0% +All right. Now, those are going to sort + + + align:start position:0% +All right. Now, those are going to sort +of fold back into the fundamental + + align:start position:0% +of fold back into the fundamental + + + align:start position:0% +of fold back into the fundamental +domain. + + align:start position:0% +domain. + + + align:start position:0% +domain. +And at least roughly, I think it's good + + align:start position:0% +And at least roughly, I think it's good + + + align:start position:0% +And at least roughly, I think it's good +to imagine it like this. + + align:start position:0% + + + + align:start position:0% + +So each one of of these guys is + + align:start position:0% +So each one of of these guys is + + + align:start position:0% +So each one of of these guys is +corresponds to one of those guys, + + align:start position:0% +corresponds to one of those guys, + + + align:start position:0% +corresponds to one of those guys, +right? Okay. But they are not in order. + + align:start position:0% +right? Okay. But they are not in order. + + + align:start position:0% +right? Okay. But they are not in order. +So it's not like they go 1 2 3 4. + + align:start position:0% +So it's not like they go 1 2 3 4. + + + align:start position:0% +So it's not like they go 1 2 3 4. +They're in some um they're in some + + align:start position:0% +They're in some um they're in some + + + align:start position:0% +They're in some um they're in some +order. uh one two three um so uh I don't + + align:start position:0% +order. uh one two three um so uh I don't + + + align:start position:0% +order. uh one two three um so uh I don't +know much about about this order. I + + align:start position:0% +know much about about this order. I + + + align:start position:0% +know much about about this order. I +personally don't know anything about + + align:start position:0% +personally don't know anything about + + + align:start position:0% +personally don't know anything about +this order. + + align:start position:0% +this order. + + + align:start position:0% +this order. +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. So now I think the question was + + align:start position:0% +Okay. So now I think the question was + + + align:start position:0% +Okay. So now I think the question was +how would this picture look if this + + align:start position:0% +how would this picture look if this + + + align:start position:0% +how would this picture look if this +thing were twisted a little bit. Um so + + align:start position:0% +thing were twisted a little bit. Um so + + + align:start position:0% +thing were twisted a little bit. Um so +first of all you know when we say that + + align:start position:0% +first of all you know when we say that + + + align:start position:0% +first of all you know when we say that +this thing is twisted a little bit it's + + align:start position:0% +this thing is twisted a little bit it's + + + align:start position:0% +this thing is twisted a little bit it's +a change sort something like a change of + + align:start position:0% +a change sort something like a change of + + + align:start position:0% +a change sort something like a change of +90 degrees or 180 degrees between the + + align:start position:0% +90 degrees or 180 degrees between the + + + align:start position:0% +90 degrees or 180 degrees between the +bottom and the top and there are many + + align:start position:0% +bottom and the top and there are many + + + align:start position:0% +bottom and the top and there are many +steps between the bottom and the top. So + + align:start position:0% +steps between the bottom and the top. So + + + align:start position:0% +steps between the bottom and the top. So +that means if you just look at one of + + align:start position:0% +that means if you just look at one of + + + align:start position:0% +that means if you just look at one of +these guys you don't notice or barely + + align:start position:0% +these guys you don't notice or barely + + + align:start position:0% +these guys you don't notice or barely +notice any twisting. This thing is + + align:start position:0% +notice any twisting. This thing is + + + align:start position:0% +notice any twisting. This thing is +basically a planer slab. Um, and then + + align:start position:0% +basically a planer slab. Um, and then + + + align:start position:0% +basically a planer slab. Um, and then +these planer slabs are at slightly + + align:start position:0% +these planer slabs are at slightly + + + align:start position:0% +these planer slabs are at slightly +different angles, but this map pi, it it + + align:start position:0% +different angles, but this map pi, it it + + + align:start position:0% +different angles, but this map pi, it it +doesn't it doesn't exactly preserve. I + + align:start position:0% +doesn't it doesn't exactly preserve. I + + + align:start position:0% +doesn't it doesn't exactly preserve. I +mean, those angles aren't exactly well + + align:start position:0% +mean, those angles aren't exactly well + + + align:start position:0% +mean, those angles aren't exactly well +defined because this this is not living + + align:start position:0% +defined because this this is not living + + + align:start position:0% +defined because this this is not living +in R3. So, it's actually not it's not + + align:start position:0% +in R3. So, it's actually not it's not + + + align:start position:0% +in R3. So, it's actually not it's not +clear exactly what we mean when we say + + align:start position:0% +clear exactly what we mean when we say + + + align:start position:0% +clear exactly what we mean when we say +that this slab and this slab are they + + align:start position:0% +that this slab and this slab are they + + + align:start position:0% +that this slab and this slab are they +parallel or are they twisted compared to + + align:start position:0% +parallel or are they twisted compared to + + + align:start position:0% +parallel or are they twisted compared to +each other? + + align:start position:0% +each other? + + + align:start position:0% +each other? +Anyway, when they get mapped back in, + + align:start position:0% +Anyway, when they get mapped back in, + + + align:start position:0% +Anyway, when they get mapped back in, +it's not I + + align:start position:0% +it's not I + + + align:start position:0% +it's not I +I think that imagining this is is + + align:start position:0% +I think that imagining this is is + + + align:start position:0% +I think that imagining this is is +reasonable. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um, + + align:start position:0% + + + + align:start position:0% + +okay. Now, that raises a bit of a + + align:start position:0% +okay. Now, that raises a bit of a + + + align:start position:0% +okay. Now, that raises a bit of a +question coming back to this picture + + align:start position:0% +question coming back to this picture + + + align:start position:0% +question coming back to this picture +that people that that that we we were + + align:start position:0% +that people that that that we we were + + + align:start position:0% +that people that that that we we were +trying to digest last time, like what + + align:start position:0% +trying to digest last time, like what + + + align:start position:0% +trying to digest last time, like what +exactly do we mean when we say that the + + align:start position:0% +exactly do we mean when we say that the + + + align:start position:0% +exactly do we mean when we say that the +compression angle is twisting? + + align:start position:0% +compression angle is twisting? + + + align:start position:0% +compression angle is twisting? +Because the compression angle here lives + + align:start position:0% +Because the compression angle here lives + + + align:start position:0% +Because the compression angle here lives +at one height, it lives over here, and + + align:start position:0% +at one height, it lives over here, and + + + align:start position:0% +at one height, it lives over here, and +the compression angle there lives over + + align:start position:0% +the compression angle there lives over + + + align:start position:0% +the compression angle there lives over +there. How do we compare an angle over + + align:start position:0% +there. How do we compare an angle over + + + align:start position:0% +there. How do we compare an angle over +here with an angle over here? Uh given + + align:start position:0% +here with an angle over here? Uh given + + + align:start position:0% +here with an angle over here? Uh given +that this is not R3, this is living in a + + align:start position:0% +that this is not R3, this is living in a + + + align:start position:0% +that this is not R3, this is living in a +curved thing. Right? So I actually + + align:start position:0% +curved thing. Right? So I actually + + + align:start position:0% +curved thing. Right? So I actually +rethought how to state it and I added + + align:start position:0% +rethought how to state it and I added + + + align:start position:0% +rethought how to state it and I added +some words that I don't think I + + align:start position:0% +some words that I don't think I + + + align:start position:0% +some words that I don't think I +mentioned last time. + + align:start position:0% +mentioned last time. + + + align:start position:0% +mentioned last time. +I think when we talk about this + + align:start position:0% +I think when we talk about this + + + align:start position:0% +I think when we talk about this +twisting, we need to include these words + + align:start position:0% +twisting, we need to include these words + + + align:start position:0% +twisting, we need to include these words +relative to the unipotent orbits. + + align:start position:0% +relative to the unipotent orbits. + + + align:start position:0% +relative to the unipotent orbits. +Okay. So let me try to make a more + + align:start position:0% +Okay. So let me try to make a more + + + align:start position:0% +Okay. So let me try to make a more +precise statement about what this + + align:start position:0% +precise statement about what this + + + align:start position:0% +precise statement about what this +twisting means and then we'll see how we + + align:start position:0% +twisting means and then we'll see how we + + + align:start position:0% +twisting means and then we'll see how we +can do some computations in the league + + align:start position:0% +can do some computations in the league + + + align:start position:0% +can do some computations in the league +group with matrices and and see that it + + align:start position:0% +group with matrices and and see that it + + + align:start position:0% +group with matrices and and see that it +happens + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +All right. So, um, + + align:start position:0% +All right. So, um, + + + align:start position:0% +All right. So, um, +okay. So, precise + + align:start position:0% +okay. So, precise + + + align:start position:0% +okay. So, precise +statement + + align:start position:0% +statement + + + align:start position:0% +statement +about what is twisting. + + align:start position:0% + + + + align:start position:0% + +What is twisting? + + align:start position:0% + + + + align:start position:0% + +Okay. So suppose I have a piece of + + align:start position:0% +Okay. So suppose I have a piece of + + + align:start position:0% +Okay. So suppose I have a piece of +unipotent orbit in my fundamental domain + + align:start position:0% +unipotent orbit in my fundamental domain + + + align:start position:0% +unipotent orbit in my fundamental domain +starts at G knot that's over there some + + align:start position:0% +starts at G knot that's over there some + + + align:start position:0% +starts at G knot that's over there some +group element in my fundamental domain + + align:start position:0% +group element in my fundamental domain + + + align:start position:0% +group element in my fundamental domain +and then over here I have UT of G KN and + + align:start position:0% +and then over here I have UT of G KN and + + + align:start position:0% +and then over here I have UT of G KN and +T goes say from 0 to one. + + align:start position:0% +T goes say from 0 to one. + + + align:start position:0% +T goes say from 0 to one. +Okay. Now at each point here there's + + align:start position:0% +Okay. Now at each point here there's + + + align:start position:0% +Okay. Now at each point here there's +going to be a vector that compresses + + align:start position:0% +going to be a vector that compresses + + + align:start position:0% +going to be a vector that compresses +when I perform ar. + + align:start position:0% +when I perform ar. + + + align:start position:0% +when I perform ar. +So let's say v compression of t. This is + + align:start position:0% +So let's say v compression of t. This is + + + align:start position:0% +So let's say v compression of t. This is +a a vector uh and this is the direction + + align:start position:0% +a a vector uh and this is the direction + + + align:start position:0% +a a vector uh and this is the direction +that compresses + + align:start position:0% + + + + align:start position:0% + +when we apply + + align:start position:0% + + + + align:start position:0% + +left arce. + + align:start position:0% +left arce. + + + align:start position:0% +left arce. +So it's the um so it's a it's a vector. + + align:start position:0% +So it's the um so it's a it's a vector. + + + align:start position:0% +So it's the um so it's a it's a vector. +It lives in the tangent space of our + + align:start position:0% +It lives in the tangent space of our + + + align:start position:0% +It lives in the tangent space of our +group at the given point. + + align:start position:0% +group at the given point. + + + align:start position:0% +group at the given point. +and it's the smallest singular vector + + align:start position:0% + + + + align:start position:0% + +for the derivative of this map. + + align:start position:0% + + + + align:start position:0% + +Okay, so that's what we mean by the + + align:start position:0% +Okay, so that's what we mean by the + + + align:start position:0% +Okay, so that's what we mean by the +compression direction. + + align:start position:0% +compression direction. + + + align:start position:0% +compression direction. +Now, what does it mean relative to the + + align:start position:0% +Now, what does it mean relative to the + + + align:start position:0% +Now, what does it mean relative to the +unipotent orbits? + + align:start position:0% +unipotent orbits? + + + align:start position:0% +unipotent orbits? +So suppose that over here I have another + + align:start position:0% +So suppose that over here I have another + + + align:start position:0% +So suppose that over here I have another +unipotent orbit + + align:start position:0% +unipotent orbit + + + align:start position:0% +unipotent orbit +and it's this is like a nearby unipotent + + align:start position:0% +and it's this is like a nearby unipotent + + + align:start position:0% +and it's this is like a nearby unipotent +orbit. + + align:start position:0% + + + + align:start position:0% + +Okay. So this might be g plus epsilon * + + align:start position:0% +Okay. So this might be g plus epsilon * + + + align:start position:0% +Okay. So this might be g plus epsilon * +v kn. epsilon * v is a little vector + + align:start position:0% +v kn. epsilon * v is a little vector + + + align:start position:0% +v kn. epsilon * v is a little vector +that goes between these + + align:start position:0% +that goes between these + + + align:start position:0% +that goes between these +starting points of these two nearby + + align:start position:0% +starting points of these two nearby + + + align:start position:0% +starting points of these two nearby +unipotent orbits. + + align:start position:0% +unipotent orbits. + + + align:start position:0% +unipotent orbits. +And up here or maybe here is ut of g + + align:start position:0% +And up here or maybe here is ut of g + + + align:start position:0% +And up here or maybe here is ut of g +plus epsilon v kn. And here there's a + + align:start position:0% +plus epsilon v kn. And here there's a + + + align:start position:0% +plus epsilon v kn. And here there's a +vector that goes between them. I guess + + align:start position:0% +vector that goes between them. I guess + + + align:start position:0% +vector that goes between them. I guess +epsilon times + + align:start position:0% +epsilon times + + + align:start position:0% +epsilon times +v orbit of t. So V orbit of T is going + + align:start position:0% +v orbit of t. So V orbit of T is going + + + align:start position:0% +v orbit of t. So V orbit of T is going +in the direction of the from the red + + align:start position:0% +in the direction of the from the red + + + align:start position:0% +in the direction of the from the red +orbit to the orange orbit. + + align:start position:0% + + + + align:start position:0% + +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +so the the thing that is twisting is V + + align:start position:0% +so the the thing that is twisting is V + + + align:start position:0% +so the the thing that is twisting is V +compression of T relative to V orbit of + + align:start position:0% +compression of T relative to V orbit of + + + align:start position:0% +compression of T relative to V orbit of +T is twisting. The angle between those + + align:start position:0% +T is twisting. The angle between those + + + align:start position:0% +T is twisting. The angle between those +two vectors is changing. That's the + + align:start position:0% +two vectors is changing. That's the + + + align:start position:0% +two vectors is changing. That's the +precise statement of what is twisting. + + align:start position:0% +precise statement of what is twisting. + + + align:start position:0% +precise statement of what is twisting. +And we can we can check what it's + + align:start position:0% +And we can we can check what it's + + + align:start position:0% +And we can we can check what it's +happening by computing these two + + align:start position:0% +happening by computing these two + + + align:start position:0% +happening by computing these two +vectors. Yeah, + + align:start position:0% +vectors. Yeah, + + + align:start position:0% +vectors. Yeah, +>> you're conjugating technically, right? + + align:start position:0% +>> you're conjugating technically, right? + + + align:start position:0% +>> you're conjugating technically, right? +Not just applying action. You're + + align:start position:0% +Not just applying action. You're + + + align:start position:0% +Not just applying action. You're +conjugating, but when you say twisting, + + align:start position:0% +conjugating, but when you say twisting, + + + align:start position:0% +conjugating, but when you say twisting, +you need to compare that some + + align:start position:0% +you need to compare that some + + + align:start position:0% +you need to compare that some +if you apply the + + align:start position:0% + + + + align:start position:0% + +apply the the gemic + + align:start position:0% +apply the the gemic + + + align:start position:0% +apply the the gemic +you end up somewhere else. + + align:start position:0% +you end up somewhere else. + + + align:start position:0% +you end up somewhere else. +I'm not sure if I understand comparison + + align:start position:0% +I'm not sure if I understand comparison + + + align:start position:0% +I'm not sure if I understand comparison +twist. + + align:start position:0% +twist. + + + align:start position:0% +twist. +>> Well, are you also following the body + + align:start position:0% +>> Well, are you also following the body + + + align:start position:0% +>> Well, are you also following the body +orbit too? + + align:start position:0% +orbit too? + + + align:start position:0% +orbit too? +>> Um, + + align:start position:0% + + + + align:start position:0% + +right. So, the question has to do with + + align:start position:0% +right. So, the question has to do with + + + align:start position:0% +right. So, the question has to do with +keeping track of things given that they + + align:start position:0% +keeping track of things given that they + + + align:start position:0% +keeping track of things given that they +live in different tangent spaces. So, + + align:start position:0% +live in different tangent spaces. So, + + + align:start position:0% +live in different tangent spaces. So, +okay. So, the compression direction is a + + align:start position:0% +okay. So, the compression direction is a + + + align:start position:0% +okay. So, the compression direction is a +vector in the tangent space at the given + + align:start position:0% +vector in the tangent space at the given + + + align:start position:0% +vector in the tangent space at the given +point along the orbit. Does that is that + + align:start position:0% +point along the orbit. Does that is that + + + align:start position:0% +point along the orbit. Does that is that +okay so far? + + align:start position:0% +okay so far? + + + align:start position:0% +okay so far? +>> Uh + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah. + + align:start position:0% +yeah yeah yeah. + + + align:start position:0% +yeah yeah yeah. +>> Okay. Um but then the comment is + + align:start position:0% +>> Okay. Um but then the comment is + + + align:start position:0% +>> Okay. Um but then the comment is +you know if if I have a family of + + align:start position:0% +you know if if I have a family of + + + align:start position:0% +you know if if I have a family of +vectors in one vector space then I can + + align:start position:0% +vectors in one vector space then I can + + + align:start position:0% +vectors in one vector space then I can +say that they're twisted. But here I + + align:start position:0% +say that they're twisted. But here I + + + align:start position:0% +say that they're twisted. But here I +have a family of vectors in a family of + + align:start position:0% +have a family of vectors in a family of + + + align:start position:0% +have a family of vectors in a family of +vector spaces. And so it's not so clear + + align:start position:0% +vector spaces. And so it's not so clear + + + align:start position:0% +vector spaces. And so it's not so clear +what it means that they're twisted. Um, + + align:start position:0% +what it means that they're twisted. Um, + + + align:start position:0% +what it means that they're twisted. Um, +so I need to I need one way to do it is + + align:start position:0% +so I need to I need one way to do it is + + + align:start position:0% +so I need to I need one way to do it is +to pick a reference vector to compare + + align:start position:0% +to pick a reference vector to compare + + + align:start position:0% +to pick a reference vector to compare +them with. And so that's the job of the + + align:start position:0% +them with. And so that's the job of the + + + align:start position:0% +them with. And so that's the job of the +of this V orbit vector which goes from + + align:start position:0% +of this V orbit vector which goes from + + + align:start position:0% +of this V orbit vector which goes from +the red vector to this from the red + + align:start position:0% +the red vector to this from the red + + + align:start position:0% +the red vector to this from the red +orbit to this orange orbit. And that's + + align:start position:0% +orbit to this orange orbit. And that's + + + align:start position:0% +orbit to this orange orbit. And that's +like a a reference vector. + + align:start position:0% +like a a reference vector. + + + align:start position:0% +like a a reference vector. +Um and then we'll see that so at each t + + align:start position:0% +Um and then we'll see that so at each t + + + align:start position:0% +Um and then we'll see that so at each t +there's there's a orbit vector and a + + align:start position:0% +there's there's a orbit vector and a + + + align:start position:0% +there's there's a orbit vector and a +compression vector and um the angle + + align:start position:0% +compression vector and um the angle + + + align:start position:0% +compression vector and um the angle +between them is changing. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um cool. So, so there was a question + + align:start position:0% +Um cool. So, so there was a question + + + align:start position:0% +Um cool. So, so there was a question +last class that basically was like + + align:start position:0% +last class that basically was like + + + align:start position:0% +last class that basically was like +how are we sure that this is happening + + align:start position:0% +how are we sure that this is happening + + + align:start position:0% +how are we sure that this is happening +this picture and the one way to be sure + + align:start position:0% +this picture and the one way to be sure + + + align:start position:0% +this picture and the one way to be sure +is to compute these two vectors and then + + align:start position:0% +is to compute these two vectors and then + + + align:start position:0% +is to compute these two vectors and then +and see that that they're not the same. + + align:start position:0% +and see that that they're not the same. + + + align:start position:0% +and see that that they're not the same. +Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. So, let's compute them. + + align:start position:0% + + + + align:start position:0% + +actually one of them we can comput. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +ut is a matrix. So when we can we can + + align:start position:0% +ut is a matrix. So when we can we can + + + align:start position:0% +ut is a matrix. So when we can we can +just multiply this through. This is ut + + align:start position:0% +just multiply this through. This is ut + + + align:start position:0% +just multiply this through. This is ut +plus epsilon ut of v kn. And if we + + align:start position:0% +plus epsilon ut of v kn. And if we + + + align:start position:0% +plus epsilon ut of v kn. And if we +compare sides we see that v orbit of t + + align:start position:0% +compare sides we see that v orbit of t + + + align:start position:0% +compare sides we see that v orbit of t +is u subt. + + align:start position:0% + + + + align:start position:0% + +Okay. Now let's figure out what v + + align:start position:0% +Okay. Now let's figure out what v + + + align:start position:0% +Okay. Now let's figure out what v +compression of t is. + + align:start position:0% +compression of t is. + + + align:start position:0% +compression of t is. +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. Um, + + align:start position:0% + + + + align:start position:0% + +cool. So say we have some G knot and um + + align:start position:0% +cool. So say we have some G knot and um + + + align:start position:0% +cool. So say we have some G knot and um +we're going to apply the left action of + + align:start position:0% +we're going to apply the left action of + + + align:start position:0% +we're going to apply the left action of +a R inverse and that will move us to to + + align:start position:0% +a R inverse and that will move us to to + + + align:start position:0% +a R inverse and that will move us to to +um a subr G. + + align:start position:0% +um a subr G. + + + align:start position:0% +um a subr G. +And we want to understand how this map + + align:start position:0% +And we want to understand how this map + + + align:start position:0% +And we want to understand how this map +is distorting the geometry of G knot, + + align:start position:0% +is distorting the geometry of G knot, + + + align:start position:0% +is distorting the geometry of G knot, +the geometry near GN, and in particular + + align:start position:0% +the geometry near GN, and in particular + + + align:start position:0% +the geometry near GN, and in particular +figure out which direction is being + + align:start position:0% +figure out which direction is being + + + align:start position:0% +figure out which direction is being +compressed. + + align:start position:0% +compressed. + + + align:start position:0% +compressed. +Okay. Um, so I think the best the best + + align:start position:0% +Okay. Um, so I think the best the best + + + align:start position:0% +Okay. Um, so I think the best the best +way I could figure out to understand + + align:start position:0% +way I could figure out to understand + + + align:start position:0% +way I could figure out to understand +this is to put it in a picture uh with + + align:start position:0% +this is to put it in a picture uh with + + + align:start position:0% +this is to put it in a picture uh with +connecting this thing that I don't + + align:start position:0% +connecting this thing that I don't + + + align:start position:0% +connecting this thing that I don't +understand yet to some maps that are + + align:start position:0% +understand yet to some maps that are + + + align:start position:0% +understand yet to some maps that are +easier to understand. + + align:start position:0% +easier to understand. + + + align:start position:0% +easier to understand. +So here's the identity and from here to + + align:start position:0% +So here's the identity and from here to + + + align:start position:0% +So here's the identity and from here to +here I could apply a right + + align:start position:0% +here I could apply a right + + + align:start position:0% +here I could apply a right +multiplication by GMAT and right + + align:start position:0% +multiplication by GMAT and right + + + align:start position:0% +multiplication by GMAT and right +multiplication is much easier to + + align:start position:0% +multiplication is much easier to + + + align:start position:0% +multiplication is much easier to +understand because that's an isometry + + align:start position:0% +understand because that's an isometry + + + align:start position:0% +understand because that's an isometry +and the identity also is kind of nicer + + align:start position:0% +and the identity also is kind of nicer + + + align:start position:0% +and the identity also is kind of nicer +than other matrices. + + align:start position:0% +than other matrices. + + + align:start position:0% +than other matrices. +Okay. And then I'm going to go back to + + align:start position:0% +Okay. And then I'm going to go back to + + + align:start position:0% +Okay. And then I'm going to go back to +the identity. + + align:start position:0% +the identity. + + + align:start position:0% +the identity. +So this is right multiplication by a r g + + align:start position:0% +So this is right multiplication by a r g + + + align:start position:0% +So this is right multiplication by a r g +all inverse which is also an isometry. + + align:start position:0% +all inverse which is also an isometry. + + + align:start position:0% +all inverse which is also an isometry. +So if you put this all together, I'm + + align:start position:0% +So if you put this all together, I'm + + + align:start position:0% +So if you put this all together, I'm +going to have a map from the tangent + + align:start position:0% +going to have a map from the tangent + + + align:start position:0% +going to have a map from the tangent +space of the identity to itself. + + align:start position:0% +space of the identity to itself. + + + align:start position:0% +space of the identity to itself. +And that map is an isometry times the + + align:start position:0% +And that map is an isometry times the + + + align:start position:0% +And that map is an isometry times the +map I want to understand times an + + align:start position:0% +map I want to understand times an + + + align:start position:0% +map I want to understand times an +isometry. So that all of the metric + + align:start position:0% +isometry. So that all of the metric + + + align:start position:0% +isometry. So that all of the metric +distortion is going to come from here. + + align:start position:0% +distortion is going to come from here. + + + align:start position:0% +distortion is going to come from here. +Okay, now this map is not so hard to + + align:start position:0% +Okay, now this map is not so hard to + + + align:start position:0% +Okay, now this map is not so hard to +understand. So if I apply what am I + + align:start position:0% +understand. So if I apply what am I + + + align:start position:0% +understand. So if I apply what am I +doing? So I I start with some matrix H. + + align:start position:0% +doing? So I I start with some matrix H. + + + align:start position:0% +doing? So I I start with some matrix H. +I right multiply by G knot. Then I left + + align:start position:0% +I right multiply by G knot. Then I left + + + align:start position:0% +I right multiply by G knot. Then I left +multiply by A R then I right multiply by + + align:start position:0% +multiply by A R then I right multiply by + + + align:start position:0% +multiply by A R then I right multiply by +the inverse of A R G KN. What do I get? + + align:start position:0% +the inverse of A R G KN. What do I get? + + + align:start position:0% +the inverse of A R G KN. What do I get? +Well have h I might I multiply on the + + align:start position:0% +Well have h I might I multiply on the + + + align:start position:0% +Well have h I might I multiply on the +right by G knot. Now I multiply on the + + align:start position:0% +right by G knot. Now I multiply on the + + + align:start position:0% +right by G knot. Now I multiply on the +left by a r. Now I multiply on the right + + align:start position:0% +left by a r. Now I multiply on the right + + + align:start position:0% +left by a r. Now I multiply on the right +by this. + + align:start position:0% +by this. + + + align:start position:0% +by this. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay. When I invert this I switch those. + + align:start position:0% +Okay. When I invert this I switch those. + + + align:start position:0% +Okay. When I invert this I switch those. +I get a g not inverse and they cancel. + + align:start position:0% + + + + align:start position:0% + +So this operation is none other than + + align:start position:0% +So this operation is none other than + + + align:start position:0% +So this operation is none other than +conjugating by a r. Right? So this is + + align:start position:0% +conjugating by a r. Right? So this is + + + align:start position:0% +conjugating by a r. Right? So this is +the conjugation by ar. + + align:start position:0% +the conjugation by ar. + + + align:start position:0% +the conjugation by ar. +Okay. So conjugation by a r is a map + + align:start position:0% +Okay. So conjugation by a r is a map + + + align:start position:0% +Okay. So conjugation by a r is a map +from our new group to itself takes the + + align:start position:0% +from our new group to itself takes the + + + align:start position:0% +from our new group to itself takes the +identity to the identity and therefore + + align:start position:0% +identity to the identity and therefore + + + align:start position:0% +identity to the identity and therefore +this map or really its derivative takes + + align:start position:0% +this map or really its derivative takes + + + align:start position:0% +this map or really its derivative takes +the tangent space of the identity to + + align:start position:0% +the tangent space of the identity to + + + align:start position:0% +the tangent space of the identity to +itself. + + align:start position:0% +itself. + + + align:start position:0% +itself. +All right and now you can write this + + align:start position:0% +All right and now you can write this + + + align:start position:0% +All right and now you can write this +down. This a r is an explicit matrix uh + + align:start position:0% +down. This a r is an explicit matrix uh + + + align:start position:0% +down. This a r is an explicit matrix uh +tangent a tangent vector here is a + + align:start position:0% +tangent a tangent vector here is a + + + align:start position:0% +tangent a tangent vector here is a +matrix abcd. + + align:start position:0% +matrix abcd. + + + align:start position:0% +matrix abcd. +So this is just a b c d goes to or d c a + + align:start position:0% +So this is just a b c d goes to or d c a + + + align:start position:0% +So this is just a b c d goes to or d c a +r of this is + + align:start position:0% +r of this is + + + align:start position:0% +r of this is +e r e minus r ab c d e minus r e + + align:start position:0% +e r e minus r ab c d e minus r e + + + align:start position:0% +e r e minus r ab c d e minus r e +so this is a thing you can write down + + align:start position:0% +so this is a thing you can write down + + + align:start position:0% +so this is a thing you can write down +it's not that scary and we worked out + + align:start position:0% +it's not that scary and we worked out + + + align:start position:0% +it's not that scary and we worked out +last time uh what it does so recall from + + align:start position:0% +last time uh what it does so recall from + + + align:start position:0% +last time uh what it does so recall from +last time + + align:start position:0% +last time + + + align:start position:0% +last time +that we have first of all we have an + + align:start position:0% +that we have first of all we have an + + + align:start position:0% +that we have first of all we have an +orthonormal basis of TE of G which are + + align:start position:0% +orthonormal basis of TE of G which are + + + align:start position:0% +orthonormal basis of TE of G which are +there's a basis vector N 0 1 0 0. Last + + align:start position:0% +there's a basis vector N 0 1 0 0. Last + + + align:start position:0% +there's a basis vector N 0 1 0 0. Last +time I called this U, but there were so + + align:start position:0% +time I called this U, but there were so + + + align:start position:0% +time I called this U, but there were so +many U's on the blackboard that I was + + align:start position:0% +many U's on the blackboard that I was + + + align:start position:0% +many U's on the blackboard that I was +worried it was not a great idea. So I'm + + align:start position:0% +worried it was not a great idea. So I'm + + + align:start position:0% +worried it was not a great idea. So I'm +going to call it N. N for nil potent + + align:start position:0% +going to call it N. N for nil potent + + + align:start position:0% +going to call it N. N for nil potent +which is also true. + + align:start position:0% +which is also true. + + + align:start position:0% +which is also true. +Um there's N tilda which is 0 1 0 0. And + + align:start position:0% +Um there's N tilda which is 0 1 0 0. And + + + align:start position:0% +Um there's N tilda which is 0 1 0 0. And +there's a diagonal guy which looks like + + align:start position:0% +there's a diagonal guy which looks like + + + align:start position:0% +there's a diagonal guy which looks like +this. + + align:start position:0% +this. + + + align:start position:0% +this. +Okay. So what we figured out is that + + align:start position:0% +Okay. So what we figured out is that + + + align:start position:0% +Okay. So what we figured out is that +the conjugation + + align:start position:0% +the conjugation + + + align:start position:0% +the conjugation +makes n way bigger. + + align:start position:0% +makes n way bigger. + + + align:start position:0% +makes n way bigger. +It makes n tilda way smaller + + align:start position:0% +It makes n tilda way smaller + + + align:start position:0% +It makes n tilda way smaller +and it leaves the diagonal fixed. + + align:start position:0% + + + + align:start position:0% + +Okay. So if I start at the identity and + + align:start position:0% +Okay. So if I start at the identity and + + + align:start position:0% +Okay. So if I start at the identity and +I go all the way around, I'm doing this + + align:start position:0% +I go all the way around, I'm doing this + + + align:start position:0% +I go all the way around, I'm doing this +conjugation and n tilda is the vector + + align:start position:0% +conjugation and n tilda is the vector + + + align:start position:0% +conjugation and n tilda is the vector +that's going to get compressed. + + align:start position:0% + + + + align:start position:0% + +But now if I want to know what vector + + align:start position:0% +But now if I want to know what vector + + + align:start position:0% +But now if I want to know what vector +over here is going to get compressed, + + align:start position:0% +over here is going to get compressed, + + + align:start position:0% +over here is going to get compressed, +well I start with antilda. I map it over + + align:start position:0% +well I start with antilda. I map it over + + + align:start position:0% +well I start with antilda. I map it over +here. It hasn't gotten any shorter yet + + align:start position:0% +here. It hasn't gotten any shorter yet + + + align:start position:0% +here. It hasn't gotten any shorter yet +because this is an isometry. That's the + + align:start position:0% +because this is an isometry. That's the + + + align:start position:0% +because this is an isometry. That's the +vector that's going to be compressed in + + align:start position:0% +vector that's going to be compressed in + + + align:start position:0% +vector that's going to be compressed in +this set. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So it's the + + align:start position:0% +So it's the + + + align:start position:0% +So it's the +right action by g of n tilda. This is + + align:start position:0% +right action by g of n tilda. This is + + + align:start position:0% +right action by g of n tilda. This is +the singular vector + + align:start position:0% +the singular vector + + + align:start position:0% +the singular vector +of d l a r inverse + + align:start position:0% +of d l a r inverse + + + align:start position:0% +of d l a r inverse +with singular value + + align:start position:0% +with singular value + + + align:start position:0% +with singular value +e to the minus 2r. + + align:start position:0% + + + + align:start position:0% + +Okay. So that's basically the answer to + + align:start position:0% +Okay. So that's basically the answer to + + + align:start position:0% +Okay. So that's basically the answer to +our question. So the V compress the + + align:start position:0% +our question. So the V compress the + + + align:start position:0% +our question. So the V compress the +compression vector at T + + align:start position:0% +compression vector at T + + + align:start position:0% +compression vector at T +that's R at so now I'm not necessarily + + align:start position:0% +that's R at so now I'm not necessarily + + + align:start position:0% +that's R at so now I'm not necessarily +at the point GN but I'm at the point ut + + align:start position:0% + + + + align:start position:0% + +of N tilda. + + align:start position:0% +of N tilda. + + + align:start position:0% +of N tilda. +So that's n tilda ut g. + + align:start position:0% + + + + align:start position:0% + +Okay. So now if you compare how these + + align:start position:0% +Okay. So now if you compare how these + + + align:start position:0% +Okay. So now if you compare how these +two things are changing with T, you see + + align:start position:0% +two things are changing with T, you see + + + align:start position:0% +two things are changing with T, you see +it is not the same because our group is + + align:start position:0% +it is not the same because our group is + + + align:start position:0% +it is not the same because our group is +not commutative + + align:start position:0% +not commutative + + + align:start position:0% +not commutative +because when you changing the orbit of + + align:start position:0% +because when you changing the orbit of + + + align:start position:0% +because when you changing the orbit of +T, you're multiplying by UT on the left. + + align:start position:0% +T, you're multiplying by UT on the left. + + + align:start position:0% +T, you're multiplying by UT on the left. +But when you're changing the compression + + align:start position:0% +But when you're changing the compression + + + align:start position:0% +But when you're changing the compression +direction, you're multiplying by UT over + + align:start position:0% +direction, you're multiplying by UT over + + + align:start position:0% +direction, you're multiplying by UT over +here in the middle. And it's a + + align:start position:0% +here in the middle. And it's a + + + align:start position:0% +here in the middle. And it's a +non-commutative group. So those two + + align:start position:0% +non-commutative group. So those two + + + align:start position:0% +non-commutative group. So those two +operations are not the same as each + + align:start position:0% +operations are not the same as each + + + align:start position:0% +operations are not the same as each +other. + + align:start position:0% + + + + align:start position:0% + +Oh um so I don't necessarily + + align:start position:0% +Oh um so I don't necessarily + + + align:start position:0% +Oh um so I don't necessarily +think it will be helpful to do more + + align:start position:0% +think it will be helpful to do more + + + align:start position:0% +think it will be helpful to do more +computations but I did some at home to + + align:start position:0% +computations but I did some at home to + + + align:start position:0% +computations but I did some at home to +be sure and you know if if you imagined + + align:start position:0% +be sure and you know if if you imagined + + + align:start position:0% +be sure and you know if if you imagined +that at time zero + + align:start position:0% +that at time zero + + + align:start position:0% +that at time zero +the these two directions coincided and + + align:start position:0% +the these two directions coincided and + + + align:start position:0% +the these two directions coincided and +then you see what happens as t changes. + + align:start position:0% +then you see what happens as t changes. + + + align:start position:0% +then you see what happens as t changes. +You'll see that they stop coinciding. + + align:start position:0% +You'll see that they stop coinciding. + + + align:start position:0% +You'll see that they stop coinciding. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> So picking the inner product of the + + align:start position:0% +>> So picking the inner product of the + + + align:start position:0% +>> So picking the inner product of the +vectors it makes sense as an operation + + align:start position:0% +vectors it makes sense as an operation + + + align:start position:0% +vectors it makes sense as an operation +to do it to compare the angles in the + + align:start position:0% +to do it to compare the angles in the + + + align:start position:0% +to do it to compare the angles in the +tangent space. + + align:start position:0% +tangent space. + + + align:start position:0% +tangent space. +>> Yeah. Um that's right. So these are + + align:start position:0% +>> Yeah. Um that's right. So these are + + + align:start position:0% +>> Yeah. Um that's right. So these are +vectors in a Romanian + + align:start position:0% +vectors in a Romanian + + + align:start position:0% +vectors in a Romanian +manifold. um and so they have a well- + + align:start position:0% +manifold. um and so they have a well- + + + align:start position:0% +manifold. um and so they have a well- +definfined angle and we can compute it + + align:start position:0% +definfined angle and we can compute it + + + align:start position:0% +definfined angle and we can compute it +by taking inner products and and then um + + align:start position:0% +by taking inner products and and then um + + + align:start position:0% +by taking inner products and and then um +uh right so I guess I guess we could say + + align:start position:0% +uh right so I guess I guess we could say + + + align:start position:0% +uh right so I guess I guess we could say +that the coine of + + align:start position:0% +that the coine of + + + align:start position:0% +that the coine of +uh + + align:start position:0% +uh + + + align:start position:0% +uh +of the angle + + align:start position:0% +of the angle + + + align:start position:0% +of the angle +between v of t and w of t + + align:start position:0% +between v of t and w of t + + + align:start position:0% +between v of t and w of t +would be um + + align:start position:0% +would be um + + + align:start position:0% +would be um +V.W + + align:start position:0% +V.W + + + align:start position:0% +V.W +over norm of V norm of W. + + align:start position:0% + + + + align:start position:0% + +I used to teach this a lot in 1802. I + + align:start position:0% +I used to teach this a lot in 1802. I + + + align:start position:0% +I used to teach this a lot in 1802. I +think that's right. Um so we have + + align:start position:0% +think that's right. Um so we have + + + align:start position:0% +think that's right. Um so we have +formulas for V and W. So we can compute + + align:start position:0% +formulas for V and W. So we can compute + + + align:start position:0% +formulas for V and W. So we can compute +this and um it'll be a little messy but + + align:start position:0% +this and um it'll be a little messy but + + + align:start position:0% +this and um it'll be a little messy but +we'll see that it is not constant in T. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Other questions or comments? + + align:start position:0% + + + + align:start position:0% + +Okay, so the first big goal that was the + + align:start position:0% +Okay, so the first big goal that was the + + + align:start position:0% +Okay, so the first big goal that was the +first chunk of the class, the first big + + align:start position:0% +first chunk of the class, the first big + + + align:start position:0% +first chunk of the class, the first big +goal of the class was to um check that + + align:start position:0% +goal of the class was to um check that + + + align:start position:0% +goal of the class was to um check that +this picture happens + + align:start position:0% +this picture happens + + + align:start position:0% +this picture happens +and then the second part of the class we + + align:start position:0% +and then the second part of the class we + + + align:start position:0% +and then the second part of the class we +will uh discuss how to use this picture + + align:start position:0% +will uh discuss how to use this picture + + + align:start position:0% +will uh discuss how to use this picture +to figure out stuff about a long + + align:start position:0% +to figure out stuff about a long + + + align:start position:0% +to figure out stuff about a long +unipotent orbit. + + align:start position:0% +unipotent orbit. + + + align:start position:0% +unipotent orbit. +Okay. So, let's switch gears. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. So, let's call this tracking + + align:start position:0% +Okay. So, let's call this tracking + + + align:start position:0% +Okay. So, let's call this tracking +the spread + + align:start position:0% +the spread + + + align:start position:0% +the spread +of an orbit. + + align:start position:0% + + + + align:start position:0% + +All right. So remember that we had this + + align:start position:0% +All right. So remember that we had this + + + align:start position:0% +All right. So remember that we had this +u 0 t of x is a r + + align:start position:0% +u 0 t of x is a r + + + align:start position:0% +u 0 t of x is a r +u01 + + align:start position:0% +u01 + + + align:start position:0% +u01 +a r inverse x. Let's call this guy x + + align:start position:0% +a r inverse x. Let's call this guy x + + + align:start position:0% +a r inverse x. Let's call this guy x +tilda. + + align:start position:0% +tilda. + + + align:start position:0% +tilda. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +now this uh there was a discussion last + + align:start position:0% +now this uh there was a discussion last + + + align:start position:0% +now this uh there was a discussion last +time you know what happens if this orbit + + align:start position:0% +time you know what happens if this orbit + + + align:start position:0% +time you know what happens if this orbit +here is periodic + + align:start position:0% +here is periodic + + + align:start position:0% +here is periodic +if this orbit here is periodic the + + align:start position:0% +if this orbit here is periodic the + + + align:start position:0% +if this orbit here is periodic the +special thing that happens is that this + + align:start position:0% +special thing that happens is that this + + + align:start position:0% +special thing that happens is that this +point X tilda will be deep in the cusp + + align:start position:0% +point X tilda will be deep in the cusp + + + align:start position:0% +point X tilda will be deep in the cusp +and the deep in the cusp is sort of a + + align:start position:0% +and the deep in the cusp is sort of a + + + align:start position:0% +and the deep in the cusp is sort of a +special case because we were imagining + + align:start position:0% +special case because we were imagining + + + align:start position:0% +special case because we were imagining +that this was like a regular nice orbit + + align:start position:0% +that this was like a regular nice orbit + + + align:start position:0% +that this was like a regular nice orbit +of length one but if it's deep in the + + align:start position:0% +of length one but if it's deep in the + + + align:start position:0% +of length one but if it's deep in the +cusp it's sort of different. + + align:start position:0% +cusp it's sort of different. + + + align:start position:0% +cusp it's sort of different. +So let's assume that X tilda is not deep + + align:start position:0% +So let's assume that X tilda is not deep + + + align:start position:0% +So let's assume that X tilda is not deep +in the custom + + align:start position:0% + + + + align:start position:0% + +and that's equivalent to saying that UX + + align:start position:0% +and that's equivalent to saying that UX + + + align:start position:0% +and that's equivalent to saying that UX +is not close to periodic. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay. And let's break up R as capital J + + align:start position:0% +Okay. And let's break up R as capital J + + + align:start position:0% +Okay. And let's break up R as capital J +times little R. + + align:start position:0% +times little R. + + + align:start position:0% +times little R. +And uh so then I'm going to say that U.j + + align:start position:0% +And uh so then I'm going to say that U.j + + + align:start position:0% +And uh so then I'm going to say that U.j +J is a little R to the J of U01 of X to + + align:start position:0% + + + + align:start position:0% + +Okay. And I want to track how this thing + + align:start position:0% +Okay. And I want to track how this thing + + + align:start position:0% +Okay. And I want to track how this thing +is spreading out through my homogeneous + + align:start position:0% +is spreading out through my homogeneous + + + align:start position:0% +is spreading out through my homogeneous +space GM mod gamma. And we'll we're + + align:start position:0% +space GM mod gamma. And we'll we're + + + align:start position:0% +space GM mod gamma. And we'll we're +going to track it by noticing how many + + align:start position:0% +going to track it by noticing how many + + + align:start position:0% +going to track it by noticing how many +delta balls it takes to cover it. So + + align:start position:0% +delta balls it takes to cover it. So + + + align:start position:0% +delta balls it takes to cover it. So +recall that X delta + + align:start position:0% +recall that X delta + + + align:start position:0% +recall that X delta +is the minimum number of delta balls + + align:start position:0% +is the minimum number of delta balls + + + align:start position:0% +is the minimum number of delta balls +needed + + align:start position:0% +needed + + + align:start position:0% +needed +to cover X. + + align:start position:0% + + + + align:start position:0% + +So our goal is going to be to estimate + + align:start position:0% + + + + align:start position:0% + +U.j J delta um + + align:start position:0% +U.j J delta um + + + align:start position:0% +U.j J delta um +in terms of J + + align:start position:0% +in terms of J + + + align:start position:0% +in terms of J +delta and R. + + align:start position:0% + + + + align:start position:0% + +Okay. And for for context for reference + + align:start position:0% +Okay. And for for context for reference + + + align:start position:0% +Okay. And for for context for reference +um the we have a three-dimensional + + align:start position:0% +um the we have a three-dimensional + + + align:start position:0% +um the we have a three-dimensional +space. So for the whole space the number + + align:start position:0% +space. So for the whole space the number + + + align:start position:0% +space. So for the whole space the number +of delta balls that we need to cover it + + align:start position:0% +of delta balls that we need to cover it + + + align:start position:0% +of delta balls that we need to cover it +is delta to the minus 3. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +All right. So, next of all, + + align:start position:0% +All right. So, next of all, + + + align:start position:0% +All right. So, next of all, +our U.J is like a bunch of these + + align:start position:0% +our U.J is like a bunch of these + + + align:start position:0% +our U.J is like a bunch of these +unipotent orbits. + + align:start position:0% + + + + align:start position:0% + +Looks like that. And so, you might + + align:start position:0% +Looks like that. And so, you might + + + align:start position:0% +Looks like that. And so, you might +notice that + + align:start position:0% +notice that + + + align:start position:0% +notice that +it only really matters what the top + + align:start position:0% +it only really matters what the top + + + align:start position:0% +it only really matters what the top +cross-section looks like. All the other + + align:start position:0% +cross-section looks like. All the other + + + align:start position:0% +cross-section looks like. All the other +cross-sections are similar. So let's + + align:start position:0% +cross-sections are similar. So let's + + + align:start position:0% +cross-sections are similar. So let's +take that top part down. Inside of + + align:start position:0% +take that top part down. Inside of + + + align:start position:0% +take that top part down. Inside of +there, we see this. So let's call that + + align:start position:0% +there, we see this. So let's call that + + + align:start position:0% +there, we see this. So let's call that +XJ. That's the top cross-section + + align:start position:0% + + + + align:start position:0% + +of U.J. + + align:start position:0% +of U.J. + + + align:start position:0% +of U.J. +And um then it's not hard to check that + + align:start position:0% +And um then it's not hard to check that + + + align:start position:0% +And um then it's not hard to check that +U.j delta is like delta inverse time XJ + + align:start position:0% +U.j delta is like delta inverse time XJ + + + align:start position:0% +U.j delta is like delta inverse time XJ +delta. + + align:start position:0% +delta. + + + align:start position:0% +delta. +have uh + + align:start position:0% +have uh + + + align:start position:0% +have uh +cut it into slabs of thickness delta. + + align:start position:0% +cut it into slabs of thickness delta. + + + align:start position:0% +cut it into slabs of thickness delta. +For each thickness, the number of delta + + align:start position:0% +For each thickness, the number of delta + + + align:start position:0% +For each thickness, the number of delta +balls that we need to cover that slab is + + align:start position:0% +balls that we need to cover that slab is + + + align:start position:0% +balls that we need to cover that slab is +xj delta. This is the number of slabs. + + align:start position:0% +xj delta. This is the number of slabs. + + + align:start position:0% +xj delta. This is the number of slabs. +Okay. So, so basically we want to track + + align:start position:0% +Okay. So, so basically we want to track + + + align:start position:0% +Okay. So, so basically we want to track +how xj delta depends on delta. + + align:start position:0% +how xj delta depends on delta. + + + align:start position:0% +how xj delta depends on delta. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +so fully spread + + align:start position:0% + + + + align:start position:0% + +or maybe I'll say very spread. + + align:start position:0% +or maybe I'll say very spread. + + + align:start position:0% +or maybe I'll say very spread. +Um, that means that + + align:start position:0% +Um, that means that + + + align:start position:0% +Um, that means that +u.j delta is like delta to the minus3. + + align:start position:0% +u.j delta is like delta to the minus3. + + + align:start position:0% +u.j delta is like delta to the minus3. +That would be like saying xj delta is + + align:start position:0% +That would be like saying xj delta is + + + align:start position:0% +That would be like saying xj delta is +like delta to the minus 2. That xj + + align:start position:0% +like delta to the minus 2. That xj + + + align:start position:0% +like delta to the minus 2. That xj +really fills a lot of the disc. + + align:start position:0% +really fills a lot of the disc. + + + align:start position:0% +really fills a lot of the disc. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So now + + align:start position:0% +So now + + + align:start position:0% +So now +how does this picture help us to study + + align:start position:0% +how does this picture help us to study + + + align:start position:0% +how does this picture help us to study +XJ? + + align:start position:0% + + + + align:start position:0% + +So using the key picture. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +So um + + align:start position:0% + + + + align:start position:0% + +so let me label these maps pi 1 and pi 0 + + align:start position:0% +so let me label these maps pi 1 and pi 0 + + + align:start position:0% +so let me label these maps pi 1 and pi 0 +and somewhere in the middle we would + + align:start position:0% +and somewhere in the middle we would + + + align:start position:0% +and somewhere in the middle we would +have pi t. Pi t is what our map ar is + + align:start position:0% +have pi t. Pi t is what our map ar is + + + align:start position:0% +have pi t. Pi t is what our map ar is +doing to the slice at height t. + + align:start position:0% + + + + align:start position:0% + +Okay, using the key picture + + align:start position:0% +Okay, using the key picture + + + align:start position:0% +Okay, using the key picture +have a lama. + + align:start position:0% +have a lama. + + + align:start position:0% +have a lama. +So if + + align:start position:0% +So if + + + align:start position:0% +So if +e to the minus 2r is delta + + align:start position:0% +e to the minus 2r is delta + + + align:start position:0% +e to the minus 2r is delta +then + + align:start position:0% +then + + + align:start position:0% +then +um + + align:start position:0% +um + + + align:start position:0% +um +xj + 1 delta is around a sum over t of + + align:start position:0% +xj + 1 delta is around a sum over t of + + + align:start position:0% +xj + 1 delta is around a sum over t of +pi t of xj delta. + + align:start position:0% + + + + align:start position:0% + +And which t's do we sum over? The t's + + align:start position:0% +And which t's do we sum over? The t's + + + align:start position:0% +And which t's do we sum over? The t's +are in delta z and t goes from zero to + + align:start position:0% +are in delta z and t goes from zero to + + + align:start position:0% +are in delta z and t goes from zero to +one. + + align:start position:0% + + + + align:start position:0% + +Um this is al we can also write this as + + align:start position:0% +Um this is al we can also write this as + + + align:start position:0% +Um this is al we can also write this as +delta inverse times the average + + align:start position:0% +delta inverse times the average + + + align:start position:0% +delta inverse times the average +t between zero and one + + align:start position:0% +t between zero and one + + + align:start position:0% +t between zero and one +of pi t of xj delta. + + align:start position:0% + + + + align:start position:0% + +Okay. So, proof sketch. + + align:start position:0% + + + + align:start position:0% + +Um, + + align:start position:0% + + + + align:start position:0% + +okay. + + align:start position:0% + + + + align:start position:0% + +So, here is our fundamental domain. Cut + + align:start position:0% +So, here is our fundamental domain. Cut + + + align:start position:0% +So, here is our fundamental domain. Cut +it into slices of thickness delta. + + align:start position:0% + + + + align:start position:0% + +So here's a slice at height t with + + align:start position:0% +So here's a slice at height t with + + + align:start position:0% +So here's a slice at height t with +thickness delta. + + align:start position:0% +thickness delta. + + + align:start position:0% +thickness delta. +Okay. Now when we apply l, we uh stretch + + align:start position:0% +Okay. Now when we apply l, we uh stretch + + + align:start position:0% +Okay. Now when we apply l, we uh stretch +it up vertically + + align:start position:0% + + + + align:start position:0% + +and we compress it in some other + + align:start position:0% +and we compress it in some other + + + align:start position:0% +and we compress it in some other +direction. We get something like this. + + align:start position:0% +direction. We get something like this. + + + align:start position:0% +direction. We get something like this. +And then we divide this into pieces at + + align:start position:0% +And then we divide this into pieces at + + + align:start position:0% +And then we divide this into pieces at +different heights. + + align:start position:0% +different heights. + + + align:start position:0% +different heights. +And let me color this particular + + align:start position:0% +And let me color this particular + + + align:start position:0% +And let me color this particular +slab in red. + + align:start position:0% +slab in red. + + + align:start position:0% +slab in red. +So that red one is one of them over + + align:start position:0% +So that red one is one of them over + + + align:start position:0% +So that red one is one of them over +here. + + align:start position:0% + + + + align:start position:0% + +So this these are each of height one. + + align:start position:0% + + + + align:start position:0% + +Okay. Um + + align:start position:0% + + + + align:start position:0% + +right. + + align:start position:0% + + + + align:start position:0% + +So in this new picture there will be so + + align:start position:0% +So in this new picture there will be so + + + align:start position:0% +So in this new picture there will be so +in the in the old picture there were + + align:start position:0% +in the in the old picture there were + + + align:start position:0% +in the in the old picture there were +some unipotent orbits + + align:start position:0% + + + + align:start position:0% + +that went through our slab. + + align:start position:0% + + + + align:start position:0% + +Um so x describes where the unipotent + + align:start position:0% +Um so x describes where the unipotent + + + align:start position:0% +Um so x describes where the unipotent +orbits hit the top of our slab. And now + + align:start position:0% +orbits hit the top of our slab. And now + + + align:start position:0% +orbits hit the top of our slab. And now +we apply this map and now there will be + + align:start position:0% +we apply this map and now there will be + + + align:start position:0% +we apply this map and now there will be +some points over here in the top of this + + align:start position:0% +some points over here in the top of this + + + align:start position:0% +some points over here in the top of this +slab. And who will they be? Those points + + align:start position:0% +slab. And who will they be? Those points + + + align:start position:0% +slab. And who will they be? Those points +over there would be pi t of x. + + align:start position:0% + + + + align:start position:0% + +Okay. Now we want to cover things with + + align:start position:0% +Okay. Now we want to cover things with + + + align:start position:0% +Okay. Now we want to cover things with +delta balls. So this distance here is e + + align:start position:0% +delta balls. So this distance here is e + + + align:start position:0% +delta balls. So this distance here is e +to the minus 2r. So that's delta. So we + + align:start position:0% +to the minus 2r. So that's delta. So we + + + align:start position:0% +to the minus 2r. So that's delta. So we +want to know how many delta balls does + + align:start position:0% +want to know how many delta balls does + + + align:start position:0% +want to know how many delta balls does +it take to cover + + align:start position:0% +it take to cover + + + align:start position:0% +it take to cover +that. + + align:start position:0% +that. + + + align:start position:0% +that. +So that number there is delta covering + + align:start position:0% +So that number there is delta covering + + + align:start position:0% +So that number there is delta covering +number of pi t of xj. + + align:start position:0% + + + + align:start position:0% + +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +So over over here we started with xj. + + align:start position:0% +So over over here we started with xj. + + + align:start position:0% +So over over here we started with xj. +Now what happens when we apply pi? + + align:start position:0% +Now what happens when we apply pi? + + + align:start position:0% +Now what happens when we apply pi? +Each of these slabs gets folded back in. + + align:start position:0% + + + + align:start position:0% + +Okay. Um and um the red one went + + align:start position:0% +Okay. Um and um the red one went + + + align:start position:0% +Okay. Um and um the red one went +somewhere. I don't really know where, + + align:start position:0% +somewhere. I don't really know where, + + + align:start position:0% +somewhere. I don't really know where, +but maybe it went over here. + + align:start position:0% + + + + align:start position:0% + +And here in the top of it is pi t of xj + + align:start position:0% +And here in the top of it is pi t of xj + + + align:start position:0% +And here in the top of it is pi t of xj +and it's delta covering number. + + align:start position:0% +and it's delta covering number. + + + align:start position:0% +and it's delta covering number. +So the number of delta balls + + align:start position:0% +So the number of delta balls + + + align:start position:0% +So the number of delta balls +in this strip + + align:start position:0% +in this strip + + + align:start position:0% +in this strip +that would be um pi t of xj. + + align:start position:0% + + + + align:start position:0% + +Okay. And now the uh this thing these + + align:start position:0% +Okay. And now the uh this thing these + + + align:start position:0% +Okay. And now the uh this thing these +dots up here are are xj + one. It's the + + align:start position:0% +dots up here are are xj + one. It's the + + + align:start position:0% +dots up here are are xj + one. It's the +set of set of dots on the top face. And + + align:start position:0% +set of set of dots on the top face. And + + + align:start position:0% +set of set of dots on the top face. And +so how many delta balls do we need to + + align:start position:0% +so how many delta balls do we need to + + + align:start position:0% +so how many delta balls do we need to +cover them? Well, for these ones we + + align:start position:0% +cover them? Well, for these ones we + + + align:start position:0% +cover them? Well, for these ones we +needed pixj delta covering number and + + align:start position:0% +needed pixj delta covering number and + + + align:start position:0% +needed pixj delta covering number and +and these other guys those corresponded + + align:start position:0% +and these other guys those corresponded + + + align:start position:0% +and these other guys those corresponded +to different um slabs here. So there are + + align:start position:0% +to different um slabs here. So there are + + + align:start position:0% +to different um slabs here. So there are +different terms in this. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um so now + + align:start position:0% +Um so now + + + align:start position:0% +Um so now +we can try to use projection theory to + + align:start position:0% +we can try to use projection theory to + + + align:start position:0% +we can try to use projection theory to +study this thing and it will tell us how + + align:start position:0% +study this thing and it will tell us how + + + align:start position:0% +study this thing and it will tell us how +the covering number XJ + 1 delta evolves + + align:start position:0% +the covering number XJ + 1 delta evolves + + + align:start position:0% +the covering number XJ + 1 delta evolves +as we increase J. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Any + + align:start position:0% + + + + align:start position:0% + +question? Yeah. + + align:start position:0% +question? Yeah. + + + align:start position:0% +question? Yeah. +>> Why do + + align:start position:0% +>> Why do + + + align:start position:0% +>> Why do +the delta balls start to overlap when J + + align:start position:0% +the delta balls start to overlap when J + + + align:start position:0% +the delta balls start to overlap when J +is large enough and kind of the + + align:start position:0% +is large enough and kind of the + + + align:start position:0% +is large enough and kind of the +compression is more than delta? Because + + align:start position:0% +compression is more than delta? Because + + + align:start position:0% +compression is more than delta? Because +delta is kind of the size of one round + + align:start position:0% +delta is kind of the size of one round + + + align:start position:0% +delta is kind of the size of one round +of compression. If you do multiple, why + + align:start position:0% +of compression. If you do multiple, why + + + align:start position:0% +of compression. If you do multiple, why +would it be for that? + + align:start position:0% +would it be for that? + + + align:start position:0% +would it be for that? +Um + + align:start position:0% + + + + align:start position:0% + +so I think the question is suppose at + + align:start position:0% +so I think the question is suppose at + + + align:start position:0% +so I think the question is suppose at +the beginning that there happened to be + + align:start position:0% +the beginning that there happened to be + + + align:start position:0% +the beginning that there happened to be +two guys here in X whose distance was + + align:start position:0% +two guys here in X whose distance was + + + align:start position:0% +two guys here in X whose distance was +less than delta which might happen + + align:start position:0% +less than delta which might happen + + + align:start position:0% +less than delta which might happen +>> then um what would happen to them? + + align:start position:0% +>> then um what would happen to them? + + + align:start position:0% +>> then um what would happen to them? +Um + + align:start position:0% +Um + + + align:start position:0% +Um +>> well + + align:start position:0% +>> well + + + align:start position:0% +>> well +>> not that they're less than delta + + align:start position:0% +>> not that they're less than delta + + + align:start position:0% +>> not that they're less than delta +slightly more than delta + + align:start position:0% +slightly more than delta + + + align:start position:0% +slightly more than delta +but less than + + align:start position:0% +but less than + + + align:start position:0% +but less than +eus 2r or e to the 2 r delta so that in + + align:start position:0% +eus 2r or e to the 2 r delta so that in + + + align:start position:0% +eus 2r or e to the 2 r delta so that in +the in f they're in the same delta b + + align:start position:0% +the in f they're in the same delta b + + + align:start position:0% +the in f they're in the same delta b +then applying the transformation + + align:start position:0% +then applying the transformation + + + align:start position:0% +then applying the transformation +diagonal transformation that they're + + align:start position:0% +diagonal transformation that they're + + + align:start position:0% +diagonal transformation that they're +then then they become in a delta + + align:start position:0% + + + + align:start position:0% + +But before they're not in before they're + + align:start position:0% +But before they're not in before they're + + + align:start position:0% +But before they're not in before they're +in two separate delta balls after the + + align:start position:0% +in two separate delta balls after the + + + align:start position:0% +in two separate delta balls after the +transformation of one delta ball. + + align:start position:0% +transformation of one delta ball. + + + align:start position:0% +transformation of one delta ball. +>> Right. Right. Okay. So it could happen + + align:start position:0% +>> Right. Right. Okay. So it could happen + + + align:start position:0% +>> Right. Right. Okay. So it could happen +that we have two guys like maybe these + + align:start position:0% +that we have two guys like maybe these + + + align:start position:0% +that we have two guys like maybe these +two guys are pretty far apart but after + + align:start position:0% +two guys are pretty far apart but after + + + align:start position:0% +two guys are pretty far apart but after +we perform um pi t they got squished + + align:start position:0% +we perform um pi t they got squished + + + align:start position:0% +we perform um pi t they got squished +together and they're now in the same + + align:start position:0% +together and they're now in the same + + + align:start position:0% +together and they're now in the same +delta ball over here. Yeah that could + + align:start position:0% +delta ball over here. Yeah that could + + + align:start position:0% +delta ball over here. Yeah that could +that could happen. And the the main + + align:start position:0% +that could happen. And the the main + + + align:start position:0% +that could happen. And the the main +thing we have to study is how often that + + align:start position:0% +thing we have to study is how often that + + + align:start position:0% +thing we have to study is how often that +happens. + + align:start position:0% +happens. + + + align:start position:0% +happens. +Um but um + + align:start position:0% +Um but um + + + align:start position:0% +Um but um +this lema is still true. Um + + align:start position:0% +this lema is still true. Um + + + align:start position:0% +this lema is still true. Um +this might be a lot smaller than xj + + align:start position:0% +this might be a lot smaller than xj + + + align:start position:0% +this might be a lot smaller than xj +delta because many many uh points that + + align:start position:0% +delta because many many uh points that + + + align:start position:0% +delta because many many uh points that +were far apart in xj may have gotten + + align:start position:0% +were far apart in xj may have gotten + + + align:start position:0% +were far apart in xj may have gotten +squished together in pi t of xj. + + align:start position:0% +squished together in pi t of xj. + + + align:start position:0% +squished together in pi t of xj. +But this is just the number of delta + + align:start position:0% +But this is just the number of delta + + + align:start position:0% +But this is just the number of delta +balls that it takes to cover um + + align:start position:0% +balls that it takes to cover um + + + align:start position:0% +balls that it takes to cover um +the the image there. + + align:start position:0% + + + + align:start position:0% + +>> Does that answer your question? + + align:start position:0% +>> Does that answer your question? + + + align:start position:0% +>> Does that answer your question? +>> Yeah. I guess also like in the third + + align:start position:0% +>> Yeah. I guess also like in the third + + + align:start position:0% +>> Yeah. I guess also like in the third +image like why is each delta ball + + align:start position:0% +image like why is each delta ball + + + align:start position:0% +image like why is each delta ball +contained in only the size of one of + + align:start position:0% +contained in only the size of one of + + + align:start position:0% +contained in only the size of one of +those kind of strips? + + align:start position:0% +those kind of strips? + + + align:start position:0% +those kind of strips? +>> Ah okay. So we we tuned delta and r to + + align:start position:0% +>> Ah okay. So we we tuned delta and r to + + + align:start position:0% +>> Ah okay. So we we tuned delta and r to +play together so that we picked r so the + + align:start position:0% +play together so that we picked r so the + + + align:start position:0% +play together so that we picked r so the +thickness of this strip is delta. I + + align:start position:0% +thickness of this strip is delta. I + + + align:start position:0% +thickness of this strip is delta. I +thought if the transformation is applied + + align:start position:0% +thought if the transformation is applied + + + align:start position:0% +thought if the transformation is applied +multiple times then you get multiple + + align:start position:0% +multiple times then you get multiple + + + align:start position:0% +multiple times then you get multiple +like e to the minus 2 r j scaling. + + align:start position:0% +like e to the minus 2 r j scaling. + + + align:start position:0% +like e to the minus 2 r j scaling. +>> Um that's not wrong but when we apply it + + align:start position:0% +>> Um that's not wrong but when we apply it + + + align:start position:0% +>> Um that's not wrong but when we apply it +multiple times we're not changing little + + align:start position:0% +multiple times we're not changing little + + + align:start position:0% +multiple times we're not changing little +r we're just applying a subr a sub + + align:start position:0% +r we're just applying a subr a sub + + + align:start position:0% +r we're just applying a subr a sub +little r multiple times. So so this + + align:start position:0% +little r multiple times. So so this + + + align:start position:0% +little r multiple times. So so this +picture is describing what happens in in + + align:start position:0% +picture is describing what happens in in + + + align:start position:0% +picture is describing what happens in in +one time + + align:start position:0% +one time + + + align:start position:0% +one time +>> and then you could use this in many + + align:start position:0% +>> and then you could use this in many + + + align:start position:0% +>> and then you could use this in many +rounds. So you could use this lama over + + align:start position:0% +rounds. So you could use this lama over + + + align:start position:0% +rounds. So you could use this lama over +and over again. + + align:start position:0% +and over again. + + + align:start position:0% +and over again. +>> Okay, + + align:start position:0% +>> Okay, + + + align:start position:0% +>> Okay, +>> which which is what we'll do. + + align:start position:0% +>> which which is what we'll do. + + + align:start position:0% +>> which which is what we'll do. +Okay. + + align:start position:0% + + + + align:start position:0% + +Um, + + align:start position:0% + + + + align:start position:0% + +let me change my notation a little bit. + + align:start position:0% +let me change my notation a little bit. + + + align:start position:0% +let me change my notation a little bit. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +so I was using the letter pi for this + + align:start position:0% +so I was using the letter pi for this + + + align:start position:0% +so I was using the letter pi for this +maybe a little bit prematurely. What's + + align:start position:0% +maybe a little bit prematurely. What's + + + align:start position:0% +maybe a little bit prematurely. What's +clear so far is that this is a map. So + + align:start position:0% +clear so far is that this is a map. So + + + align:start position:0% +clear so far is that this is a map. So +I'm going to call it f_sub_1, f_t, and + + align:start position:0% +I'm going to call it f_sub_1, f_t, and + + + align:start position:0% +I'm going to call it f_sub_1, f_t, and +f0. And so then I'll change this. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay. So now the next remark is that + + align:start position:0% +Okay. So now the next remark is that + + + align:start position:0% +Okay. So now the next remark is that +these maps look a lot like linear + + align:start position:0% +these maps look a lot like linear + + + align:start position:0% +these maps look a lot like linear +projections. So remark + + align:start position:0% +projections. So remark + + + align:start position:0% +projections. So remark +ft is kind of approximately an + + align:start position:0% +ft is kind of approximately an + + + align:start position:0% +ft is kind of approximately an +orthogonal projection + + align:start position:0% +orthogonal projection + + + align:start position:0% +orthogonal projection +um pi t. So let me make a picture. So ft + + align:start position:0% +um pi t. So let me make a picture. So ft + + + align:start position:0% +um pi t. So let me make a picture. So ft +does something like this. + + align:start position:0% +does something like this. + + + align:start position:0% +does something like this. +And this thickness is delta. This is + + align:start position:0% +And this thickness is delta. This is + + + align:start position:0% +And this thickness is delta. This is +one. Um and then pi t would just be an + + align:start position:0% +one. Um and then pi t would just be an + + + align:start position:0% +one. Um and then pi t would just be an +actual orthogonal projection. + + align:start position:0% + + + + align:start position:0% + +Okay. Um + + align:start position:0% +Okay. Um + + + align:start position:0% +Okay. Um +so + + align:start position:0% +so + + + align:start position:0% +so +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +uh ft is not not perfectly linear + + align:start position:0% + + + + align:start position:0% + +uh but it is smooth. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So now here is a proposition or exercise + + align:start position:0% +So now here is a proposition or exercise + + + align:start position:0% +So now here is a proposition or exercise +about projections + + align:start position:0% +about projections + + + align:start position:0% +about projections +says that if x is in the unit ball in + + align:start position:0% +says that if x is in the unit ball in + + + align:start position:0% +says that if x is in the unit ball in +the plane. + + align:start position:0% +the plane. + + + align:start position:0% +the plane. +Then if you take the average overall + + align:start position:0% +Then if you take the average overall + + + align:start position:0% +Then if you take the average overall +directions theta and s1 + + align:start position:0% +directions theta and s1 + + + align:start position:0% +directions theta and s1 +of um pi theta of x delta + + align:start position:0% +of um pi theta of x delta + + + align:start position:0% +of um pi theta of x delta +is at least as big as x delta to the 12. + + align:start position:0% + + + + align:start position:0% + +Here's an example that shows where the x + + align:start position:0% +Here's an example that shows where the x + + + align:start position:0% +Here's an example that shows where the x +delta to the 1/2 comes from. + + align:start position:0% + + + + align:start position:0% + +So here's the unit ball and then inside + + align:start position:0% +So here's the unit ball and then inside + + + align:start position:0% +So here's the unit ball and then inside +of it I take a smaller ball and I call + + align:start position:0% +of it I take a smaller ball and I call + + + align:start position:0% +of it I take a smaller ball and I call +that X. + + align:start position:0% + + + + align:start position:0% + +So X is the ball of some small radius + + align:start position:0% +So X is the ball of some small radius + + + align:start position:0% +So X is the ball of some small radius +row inside of the ball of radius one. + + align:start position:0% +row inside of the ball of radius one. + + + align:start position:0% +row inside of the ball of radius one. +Um okay then when I perform an + + align:start position:0% +Um okay then when I perform an + + + align:start position:0% +Um okay then when I perform an +orthogonal projection + + align:start position:0% + + + + align:start position:0% + +there's pi theta of X in any direction + + align:start position:0% +there's pi theta of X in any direction + + + align:start position:0% +there's pi theta of X in any direction +I'll get a line of length row. + + align:start position:0% +I'll get a line of length row. + + + align:start position:0% +I'll get a line of length row. +So I see that x delta is like row over + + align:start position:0% +So I see that x delta is like row over + + + align:start position:0% +So I see that x delta is like row over +delta squared + + align:start position:0% +delta squared + + + align:start position:0% +delta squared +and pi theta of x delta covering up is + + align:start position:0% +and pi theta of x delta covering up is + + + align:start position:0% +and pi theta of x delta covering up is +like row over delta. So this is the + + align:start position:0% +like row over delta. So this is the + + + align:start position:0% +like row over delta. So this is the +square root of that. + + align:start position:0% +square root of that. + + + align:start position:0% +square root of that. +Okay. And this is the best thing to do. + + align:start position:0% +Okay. And this is the best thing to do. + + + align:start position:0% +Okay. And this is the best thing to do. +Um you could devise an example where in + + align:start position:0% +Um you could devise an example where in + + + align:start position:0% +Um you could devise an example where in +one particular direction the compression + + align:start position:0% +one particular direction the compression + + + align:start position:0% +one particular direction the compression +is much smaller than the square root. + + align:start position:0% +is much smaller than the square root. + + + align:start position:0% +is much smaller than the square root. +Um, here's an example like that. + + align:start position:0% +Um, here's an example like that. + + + align:start position:0% +Um, here's an example like that. +B1, + + align:start position:0% +B1, + + + align:start position:0% +B1, +here's X, + + align:start position:0% +here's X, + + + align:start position:0% +here's X, +here's theta. Okay, in this example, pi + + align:start position:0% +here's theta. Okay, in this example, pi + + + align:start position:0% +here's theta. Okay, in this example, pi +theta of X delta is much smaller. I'll + + align:start position:0% +theta of X delta is much smaller. I'll + + + align:start position:0% +theta of X delta is much smaller. I'll +call this theta KN much smaller than X + + align:start position:0% +call this theta KN much smaller than X + + + align:start position:0% +call this theta KN much smaller than X +delta to the 12 for one theta KN. + + align:start position:0% + + + + align:start position:0% + +But at least in this picture, the most + + align:start position:0% +But at least in this picture, the most + + + align:start position:0% +But at least in this picture, the most +of the projections are way bigger. + + align:start position:0% +of the projections are way bigger. + + + align:start position:0% +of the projections are way bigger. +Okay, so it's not not super difficult uh + + align:start position:0% +Okay, so it's not not super difficult uh + + + align:start position:0% +Okay, so it's not not super difficult uh +to check this proposition. And I'm going + + align:start position:0% +to check this proposition. And I'm going + + + align:start position:0% +to check this proposition. And I'm going +to make it an exercise. I think we're + + align:start position:0% +to make it an exercise. I think we're + + + align:start position:0% +to make it an exercise. I think we're +out of problem sets, but if we weren't, + + align:start position:0% +out of problem sets, but if we weren't, + + + align:start position:0% +out of problem sets, but if we weren't, +this is a a nice one to review the + + align:start position:0% +this is a a nice one to review the + + + align:start position:0% +this is a a nice one to review the +class. + + align:start position:0% + + + + align:start position:0% + +Okay. And another comment is even though + + align:start position:0% +Okay. And another comment is even though + + + align:start position:0% +Okay. And another comment is even though +these FTs are not exactly linear maps so + + align:start position:0% +these FTs are not exactly linear maps so + + + align:start position:0% +these FTs are not exactly linear maps so +that we cannot just literally apply this + + align:start position:0% +that we cannot just literally apply this + + + align:start position:0% +that we cannot just literally apply this +proposition they're close enough that by + + align:start position:0% +proposition they're close enough that by + + + align:start position:0% +proposition they're close enough that by +using the proof of this you you can get + + align:start position:0% +using the proof of this you you can get + + + align:start position:0% +using the proof of this you you can get +it for FT2. + + align:start position:0% +it for FT2. + + + align:start position:0% +it for FT2. +So remark + + align:start position:0% +So remark + + + align:start position:0% +So remark +the proof applies + + align:start position:0% +the proof applies + + + align:start position:0% +the proof applies +to FT also. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So if we put together this lema and this + + align:start position:0% +So if we put together this lema and this + + + align:start position:0% +So if we put together this lema and this +proposition, we'll get an estimate about + + align:start position:0% +proposition, we'll get an estimate about + + + align:start position:0% +proposition, we'll get an estimate about +the delta covering number of XJ. + + align:start position:0% + + + + align:start position:0% + +Okay. So correlary if we put these + + align:start position:0% +Okay. So correlary if we put these + + + align:start position:0% +Okay. So correlary if we put these +together xj + 1 delta covering number is + + align:start position:0% +together xj + 1 delta covering number is + + + align:start position:0% +together xj + 1 delta covering number is +at least around um delta inverse time xj + + align:start position:0% +at least around um delta inverse time xj + + + align:start position:0% +at least around um delta inverse time xj +delta to the 12 + + align:start position:0% + + + + align:start position:0% + +um proof. + + align:start position:0% +um proof. + + + align:start position:0% +um proof. +So xj + 1 delta is + + align:start position:0% +So xj + 1 delta is + + + align:start position:0% +So xj + 1 delta is +uh is at least by our lema delta inverse + + align:start position:0% +uh is at least by our lema delta inverse + + + align:start position:0% +uh is at least by our lema delta inverse +times the average over t of xj + + align:start position:0% +times the average over t of xj + + + align:start position:0% +times the average over t of xj +of um ft of xj delta + + align:start position:0% +of um ft of xj delta + + + align:start position:0% +of um ft of xj delta +and then by our proposition that's at + + align:start position:0% +and then by our proposition that's at + + + align:start position:0% +and then by our proposition that's at +least delta inverse time xj delta to the + + align:start position:0% +least delta inverse time xj delta to the + + + align:start position:0% +least delta inverse time xj delta to the +on half and that's the proof. + + align:start position:0% + + + + align:start position:0% + +Okay. So then let's just track what this + + align:start position:0% +Okay. So then let's just track what this + + + align:start position:0% +Okay. So then let's just track what this +means. So x0 delta would be one. Think + + align:start position:0% +means. So x0 delta would be one. Think + + + align:start position:0% +means. So x0 delta would be one. Think +about what x0 delta means. It's one + + align:start position:0% +about what x0 delta means. It's one + + + align:start position:0% +about what x0 delta means. It's one +unipotent orbit. There's okay. So + + align:start position:0% +unipotent orbit. There's okay. So + + + align:start position:0% +unipotent orbit. There's okay. So +therefore + + align:start position:0% +therefore + + + align:start position:0% +therefore +x1 delta would be at least around delta + + align:start position:0% +x1 delta would be at least around delta + + + align:start position:0% +x1 delta would be at least around delta +inverse. + + align:start position:0% +inverse. + + + align:start position:0% +inverse. +x2 delta would be at least around delta + + align:start position:0% +x2 delta would be at least around delta + + + align:start position:0% +x2 delta would be at least around delta +to the minus3s. + + align:start position:0% + + + + align:start position:0% + +X3 delta be at least around delta to the + + align:start position:0% +X3 delta be at least around delta to the + + + align:start position:0% +X3 delta be at least around delta to the +minus1 and 3/4 + + align:start position:0% +minus1 and 3/4 + + + align:start position:0% +minus1 and 3/4 +and so on and you'd get pretty close to + + align:start position:0% +and so on and you'd get pretty close to + + + align:start position:0% +and so on and you'd get pretty close to +delta to the minus2. + + align:start position:0% + + + + align:start position:0% + +Okay. And delta to the minus2 would be + + align:start position:0% +Okay. And delta to the minus2 would be + + + align:start position:0% +Okay. And delta to the minus2 would be +like a definite fraction of the whole + + align:start position:0% +like a definite fraction of the whole + + + align:start position:0% +like a definite fraction of the whole +space. + + align:start position:0% + + + + align:start position:0% + +All right. Um, so this proves that a + + align:start position:0% +All right. Um, so this proves that a + + + align:start position:0% +All right. Um, so this proves that a +unipotent orbit that's not close to + + align:start position:0% +unipotent orbit that's not close to + + + align:start position:0% +unipotent orbit that's not close to +periodic, + + align:start position:0% +periodic, + + + align:start position:0% +periodic, +it proves that it fills up a lot of the + + align:start position:0% +it proves that it fills up a lot of the + + + align:start position:0% +it proves that it fills up a lot of the +homogeneous space. + + align:start position:0% +homogeneous space. + + + align:start position:0% +homogeneous space. +It's not Headland's theorem. Um, hold on + + align:start position:0% +It's not Headland's theorem. Um, hold on + + + align:start position:0% +It's not Headland's theorem. Um, hold on +a second. So, we didn't prove yet that + + align:start position:0% +a second. So, we didn't prove yet that + + + align:start position:0% +a second. So, we didn't prove yet that +the orbit is dense. The orbit could be + + align:start position:0% +the orbit is dense. The orbit could be + + + align:start position:0% +the orbit is dense. The orbit could be +missing an entire ball that's like half + + align:start position:0% +missing an entire ball that's like half + + + align:start position:0% +missing an entire ball that's like half +the size of the space, and this could + + align:start position:0% +the size of the space, and this could + + + align:start position:0% +the size of the space, and this could +still be true, but we did prove that the + + align:start position:0% +still be true, but we did prove that the + + + align:start position:0% +still be true, but we did prove that the +orbit goes a lot of places. Yeah. Um and + + align:start position:0% +orbit goes a lot of places. Yeah. Um and + + + align:start position:0% +orbit goes a lot of places. Yeah. Um and +this proof like does apply since + + align:start position:0% +this proof like does apply since + + + align:start position:0% +this proof like does apply since +applying it each time loses some sort of + + align:start position:0% +applying it each time loses some sort of + + + align:start position:0% +applying it each time loses some sort of +implicit constant like how do we know + + align:start position:0% +implicit constant like how do we know + + + align:start position:0% +implicit constant like how do we know +that it's not becoming dense and just + + align:start position:0% +that it's not becoming dense and just + + + align:start position:0% +that it's not becoming dense and just +like kind of an infinite decimally small + + align:start position:0% +like kind of an infinite decimally small + + + align:start position:0% +like kind of an infinite decimally small +region of this full space. + + align:start position:0% +region of this full space. + + + align:start position:0% +region of this full space. +Um + + align:start position:0% + + + + align:start position:0% + +right so I think the question is like we + + align:start position:0% +right so I think the question is like we + + + align:start position:0% +right so I think the question is like we +we didn't actually get to a constant + + align:start position:0% +we didn't actually get to a constant + + + align:start position:0% +we didn't actually get to a constant +times delta to the minus 2 and if I + + align:start position:0% +times delta to the minus 2 and if I + + + align:start position:0% +times delta to the minus 2 and if I +tried to do this sort of infinitely many + + align:start position:0% +tried to do this sort of infinitely many + + + align:start position:0% +tried to do this sort of infinitely many +times I would be losing a constant each + + align:start position:0% +times I would be losing a constant each + + + align:start position:0% +times I would be losing a constant each +time. Yeah, that's right. So, you know, + + align:start position:0% +time. Yeah, that's right. So, you know, + + + align:start position:0% +time. Yeah, that's right. So, you know, +imagine doing this 10 times and we get + + align:start position:0% +imagine doing this 10 times and we get + + + align:start position:0% +imagine doing this 10 times and we get +delta to the minus 1.99 + + align:start position:0% +delta to the minus 1.99 + + + align:start position:0% +delta to the minus 1.99 +and and that's what the method uh proves + + align:start position:0% +and and that's what the method uh proves + + + align:start position:0% +and and that's what the method uh proves +so far. So, stronger things are true, + + align:start position:0% +so far. So, stronger things are true, + + + align:start position:0% +so far. So, stronger things are true, +but but this method doesn't prove them + + align:start position:0% +but but this method doesn't prove them + + + align:start position:0% +but but this method doesn't prove them +yet. + + align:start position:0% +yet. + + + align:start position:0% +yet. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +so remark + + align:start position:0% +so remark + + + align:start position:0% +so remark +um this doesn't show + + align:start position:0% + + + + align:start position:0% + +that the orbit is uh is actually dense + + align:start position:0% +that the orbit is uh is actually dense + + + align:start position:0% +that the orbit is uh is actually dense +and so + + align:start position:0% +and so + + + align:start position:0% +and so +uh so maybe a question you know could + + align:start position:0% +uh so maybe a question you know could + + + align:start position:0% +uh so maybe a question you know could +the orbit + + align:start position:0% +the orbit + + + align:start position:0% +the orbit +do this + + align:start position:0% +do this + + + align:start position:0% +do this +so here's our homogeneous space there's + + align:start position:0% +so here's our homogeneous space there's + + + align:start position:0% +so here's our homogeneous space there's +a cusp but it's not that important + + align:start position:0% +a cusp but it's not that important + + + align:start position:0% +a cusp but it's not that important +and and the orbit like goes around a + + align:start position:0% +and and the orbit like goes around a + + + align:start position:0% +and and the orbit like goes around a +good bit, but it only ever goes around + + align:start position:0% +good bit, but it only ever goes around + + + align:start position:0% +good bit, but it only ever goes around +over here and it never goes over there. + + align:start position:0% +over here and it never goes over there. + + + align:start position:0% +over here and it never goes over there. +So, this proof doesn't say anything + + align:start position:0% +So, this proof doesn't say anything + + + align:start position:0% +So, this proof doesn't say anything +about that. + + align:start position:0% +about that. + + + align:start position:0% +about that. +Um, okay. So, as far as I know, the to + + align:start position:0% +Um, okay. So, as far as I know, the to + + + align:start position:0% +Um, okay. So, as far as I know, the to +finish Headland's theorem requires + + align:start position:0% +finish Headland's theorem requires + + + align:start position:0% +finish Headland's theorem requires +another step uh that is based on + + align:start position:0% +another step uh that is based on + + + align:start position:0% +another step uh that is based on +different ideas from these ideas. Um, so + + align:start position:0% +different ideas from these ideas. Um, so + + + align:start position:0% +different ideas from these ideas. Um, so +there's more to homogeneous dynamics + + align:start position:0% +there's more to homogeneous dynamics + + + align:start position:0% +there's more to homogeneous dynamics +than than this story. Uh but this we did + + align:start position:0% +than than this story. Uh but this we did + + + align:start position:0% +than than this story. Uh but this we did +still learn something interesting. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Do you know like how close it's possible + + align:start position:0% +>> Do you know like how close it's possible + + + align:start position:0% +>> Do you know like how close it's possible +to get to the full theorem by trying to + + align:start position:0% +to get to the full theorem by trying to + + + align:start position:0% +to get to the full theorem by trying to +optimize all the constants in this term? + + align:start position:0% + + + + align:start position:0% + +>> Um okay. So there are two things that we + + align:start position:0% +>> Um okay. So there are two things that we + + + align:start position:0% +>> Um okay. So there are two things that we +might like to improve here. So the + + align:start position:0% +might like to improve here. So the + + + align:start position:0% +might like to improve here. So the +question is how how close can we get to + + align:start position:0% +question is how how close can we get to + + + align:start position:0% +question is how how close can we get to +the full theorem by optimizing the + + align:start position:0% +the full theorem by optimizing the + + + align:start position:0% +the full theorem by optimizing the +argument that we've been talking about. + + align:start position:0% +argument that we've been talking about. + + + align:start position:0% +argument that we've been talking about. +So one thing that you might like is you + + align:start position:0% +So one thing that you might like is you + + + align:start position:0% +So one thing that you might like is you +might like to actually get to delta to + + align:start position:0% +might like to actually get to delta to + + + align:start position:0% +might like to actually get to delta to +the minus2. + + align:start position:0% +the minus2. + + + align:start position:0% +the minus2. +Um that still wouldn't necessarily rule + + align:start position:0% +Um that still wouldn't necessarily rule + + + align:start position:0% +Um that still wouldn't necessarily rule +out this possibility but it would be + + align:start position:0% +out this possibility but it would be + + + align:start position:0% +out this possibility but it would be +interesting. + + align:start position:0% +interesting. + + + align:start position:0% +interesting. +And um if you look + + align:start position:0% +And um if you look + + + align:start position:0% +And um if you look +if you look at this proposition, + + align:start position:0% +if you look at this proposition, + + + align:start position:0% +if you look at this proposition, +one thing that you you sort of notice + + align:start position:0% +one thing that you you sort of notice + + + align:start position:0% +one thing that you you sort of notice +that this proposition is sharp in this + + align:start position:0% +that this proposition is sharp in this + + + align:start position:0% +that this proposition is sharp in this +very clumped case. And if you remember + + align:start position:0% +very clumped case. And if you remember + + + align:start position:0% +very clumped case. And if you remember +back to the early months of our class, + + align:start position:0% +back to the early months of our class, + + + align:start position:0% +back to the early months of our class, +if X was not so compressed, then there + + align:start position:0% +if X was not so compressed, then there + + + align:start position:0% +if X was not so compressed, then there +would be even better estimates. So if if + + align:start position:0% +would be even better estimates. So if if + + + align:start position:0% +would be even better estimates. So if if +you knew as an input that X is not too + + align:start position:0% +you knew as an input that X is not too + + + align:start position:0% +you knew as an input that X is not too +clustered, then you could get all the + + align:start position:0% +clustered, then you could get all the + + + align:start position:0% +clustered, then you could get all the +way to delta to the minus 2 in one step + + align:start position:0% +way to delta to the minus 2 in one step + + + align:start position:0% +way to delta to the minus 2 in one step +or or two steps or something. Um and so + + align:start position:0% +or or two steps or something. Um and so + + + align:start position:0% +or or two steps or something. Um and so +you might try to track that. You might + + align:start position:0% +you might try to track that. You might + + + align:start position:0% +you might try to track that. You might +try to track not just the delta covering + + align:start position:0% +try to track not just the delta covering + + + align:start position:0% +try to track not just the delta covering +number but also the row covering number + + align:start position:0% +number but also the row covering number + + + align:start position:0% +number but also the row covering number +for different delta and row. And then + + align:start position:0% +for different delta and row. And then + + + align:start position:0% +for different delta and row. And then +you could take advantage of this + + align:start position:0% +you could take advantage of this + + + align:start position:0% +you could take advantage of this +clustering. And um I am not positive but + + align:start position:0% +clustering. And um I am not positive but + + + align:start position:0% +clustering. And um I am not positive but +I think it is a reasonable 18156 project + + align:start position:0% +I think it is a reasonable 18156 project + + + align:start position:0% +I think it is a reasonable 18156 project +uh to you try to use that to get all the + + align:start position:0% +uh to you try to use that to get all the + + + align:start position:0% +uh to you try to use that to get all the +way to delta to the minus 2. + + align:start position:0% +way to delta to the minus 2. + + + align:start position:0% +way to delta to the minus 2. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Even if you got a constant times delta + + align:start position:0% +Even if you got a constant times delta + + + align:start position:0% +Even if you got a constant times delta +to the minus 2, it would + + align:start position:0% +to the minus 2, it would + + + align:start position:0% +to the minus 2, it would +still not be obvious to me that you + + align:start position:0% +still not be obvious to me that you + + + align:start position:0% +still not be obvious to me that you +filled the entire manifold and that + + align:start position:0% +filled the entire manifold and that + + + align:start position:0% +filled the entire manifold and that +you're not missing a ball. And um I I + + align:start position:0% +you're not missing a ball. And um I I + + + align:start position:0% +you're not missing a ball. And um I I +thought about it yesterday and today and + + align:start position:0% +thought about it yesterday and today and + + + align:start position:0% +thought about it yesterday and today and +I I don't have I don't have a good + + align:start position:0% +I I don't have I don't have a good + + + align:start position:0% +I I don't have I don't have a good +understanding yet of what you need to to + + align:start position:0% +understanding yet of what you need to to + + + align:start position:0% +understanding yet of what you need to to +to get everywhere. Um so I would be + + align:start position:0% +to get everywhere. Um so I would be + + + align:start position:0% +to get everywhere. Um so I would be +interested to learn if people have + + align:start position:0% +interested to learn if people have + + + align:start position:0% +interested to learn if people have +thoughts about it or know about it. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +cool. Um so I think that there actually + + align:start position:0% +cool. Um so I think that there actually + + + align:start position:0% +cool. Um so I think that there actually +are a bunch of ways to prove Headlland's + + align:start position:0% +are a bunch of ways to prove Headlland's + + + align:start position:0% +are a bunch of ways to prove Headlland's +theorem and this is not one that I have + + align:start position:0% +theorem and this is not one that I have + + + align:start position:0% +theorem and this is not one that I have +seen in the literature. Um and + + align:start position:0% +seen in the literature. Um and + + + align:start position:0% +seen in the literature. Um and +all all of these problems become more + + align:start position:0% +all all of these problems become more + + + align:start position:0% +all all of these problems become more +difficult and maybe more interesting + + align:start position:0% +difficult and maybe more interesting + + + align:start position:0% +difficult and maybe more interesting +when you go to higher dimensions. Um so + + align:start position:0% +when you go to higher dimensions. Um so + + + align:start position:0% +when you go to higher dimensions. Um so +the projection theory also becomes more + + align:start position:0% +the projection theory also becomes more + + + align:start position:0% +the projection theory also becomes more +difficult and more interesting in higher + + align:start position:0% +difficult and more interesting in higher + + + align:start position:0% +difficult and more interesting in higher +dimensions. And I wanted in the last + + align:start position:0% +dimensions. And I wanted in the last + + + align:start position:0% +dimensions. And I wanted in the last +part of the class to just show you what + + align:start position:0% +part of the class to just show you what + + + align:start position:0% +part of the class to just show you what +happens. Um and in particular we will + + align:start position:0% +happens. Um and in particular we will + + + align:start position:0% +happens. Um and in particular we will +see a new question about projection + + align:start position:0% +see a new question about projection + + + align:start position:0% +see a new question about projection +theory that we haven't mentioned so far + + align:start position:0% +theory that we haven't mentioned so far + + + align:start position:0% +theory that we haven't mentioned so far +in this class but which I think is a + + align:start position:0% +in this class but which I think is a + + + align:start position:0% +in this class but which I think is a +really cool question. + + align:start position:0% +really cool question. + + + align:start position:0% +really cool question. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +okay. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So that I'm going to put this way. What + + align:start position:0% +So that I'm going to put this way. What + + + align:start position:0% +So that I'm going to put this way. What +about + + align:start position:0% + + + + align:start position:0% + +SLNR? + + align:start position:0% + + + + align:start position:0% + +Right. + + align:start position:0% +Right. + + + align:start position:0% +Right. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um so I'm going to take a somewhat + + align:start position:0% +Um so I'm going to take a somewhat + + + align:start position:0% +Um so I'm going to take a somewhat +specific example although I think most + + align:start position:0% +specific example although I think most + + + align:start position:0% +specific example although I think most +of what we'll say then would work for + + align:start position:0% +of what we'll say then would work for + + + align:start position:0% +of what we'll say then would work for +any N. So for example, we could have + + align:start position:0% +any N. So for example, we could have + + + align:start position:0% +any N. So for example, we could have +SL3R + + align:start position:0% +SL3R + + + align:start position:0% +SL3R +for our G. Gamma could be SL3 Z. And U + + align:start position:0% +for our G. Gamma could be SL3 Z. And U + + + align:start position:0% +for our G. Gamma could be SL3 Z. And U +could be the unipotent group of matrices + + align:start position:0% +could be the unipotent group of matrices + + + align:start position:0% +could be the unipotent group of matrices +that look like this. + + align:start position:0% + + + + align:start position:0% + +So the so from what I understand there + + align:start position:0% +So the so from what I understand there + + + align:start position:0% +So the so from what I understand there +are several different one parameter + + align:start position:0% +are several different one parameter + + + align:start position:0% +are several different one parameter +unipotent subgroups of SL3R. They're + + align:start position:0% +unipotent subgroups of SL3R. They're + + + align:start position:0% +unipotent subgroups of SL3R. They're +slightly different from each other. And + + align:start position:0% +slightly different from each other. And + + + align:start position:0% +slightly different from each other. And +this one is sort of particularly well + + align:start position:0% +this one is sort of particularly well + + + align:start position:0% +this one is sort of particularly well +studied in the homogeneous dynamics + + align:start position:0% +studied in the homogeneous dynamics + + + align:start position:0% +studied in the homogeneous dynamics +community because it's the one that + + align:start position:0% +community because it's the one that + + + align:start position:0% +community because it's the one that +comes up in the Oppenheim conjecture + + align:start position:0% +comes up in the Oppenheim conjecture + + + align:start position:0% +comes up in the Oppenheim conjecture +about quadratic forms. + + align:start position:0% +about quadratic forms. + + + align:start position:0% +about quadratic forms. +Um, okay. But anyway, so we have this + + align:start position:0% +Um, okay. But anyway, so we have this + + + align:start position:0% +Um, okay. But anyway, so we have this +one parameter subgroup. And so let's + + align:start position:0% +one parameter subgroup. And so let's + + + align:start position:0% +one parameter subgroup. And so let's +call this u subt. + + align:start position:0% +call this u subt. + + + align:start position:0% +call this u subt. +Okay. So our basic setup with like + + align:start position:0% +Okay. So our basic setup with like + + + align:start position:0% +Okay. So our basic setup with like +conjugating by a diagonal matrix that + + align:start position:0% +conjugating by a diagonal matrix that + + + align:start position:0% +conjugating by a diagonal matrix that +works. And the relevant diagonal matrix + + align:start position:0% +works. And the relevant diagonal matrix + + + align:start position:0% +works. And the relevant diagonal matrix +is this matrix. + + align:start position:0% +is this matrix. + + + align:start position:0% +is this matrix. +Okay. And then you can check that a subr + + align:start position:0% +Okay. And then you can check that a subr + + + align:start position:0% +Okay. And then you can check that a subr +u subt a sub r inverse is u sub e to the + + align:start position:0% +u subt a sub r inverse is u sub e to the + + + align:start position:0% +u subt a sub r inverse is u sub e to the +rt turns out to be e to the rt not e to + + align:start position:0% +rt turns out to be e to the rt not e to + + + align:start position:0% +rt turns out to be e to the rt not e to +the 2 rt but that's not too big a deal. + + align:start position:0% +the 2 rt but that's not too big a deal. + + + align:start position:0% +the 2 rt but that's not too big a deal. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So now um + + align:start position:0% + + + + align:start position:0% + +we have a bunch of unipotent orbits like + + align:start position:0% +we have a bunch of unipotent orbits like + + + align:start position:0% +we have a bunch of unipotent orbits like +before. + + align:start position:0% + + + + align:start position:0% + +There's a bunch of unit potent orbits, + + align:start position:0% +There's a bunch of unit potent orbits, + + + align:start position:0% +There's a bunch of unit potent orbits, +but um the dimension of our group is + + align:start position:0% +but um the dimension of our group is + + + align:start position:0% +but um the dimension of our group is +eight instead of three. And so we have + + align:start position:0% +eight instead of three. And so we have + + + align:start position:0% +eight instead of three. And so we have +the direction along the orbits t = 0 up + + align:start position:0% +the direction along the orbits t = 0 up + + + align:start position:0% +the direction along the orbits t = 0 up +to t= 1. That's still onedimensional. So + + align:start position:0% +to t= 1. That's still onedimensional. So + + + align:start position:0% +to t= 1. That's still onedimensional. So +this thing here is a seven-dimensional + + align:start position:0% +this thing here is a seven-dimensional + + + align:start position:0% +this thing here is a seven-dimensional +ball instead of a disc. + + align:start position:0% +ball instead of a disc. + + + align:start position:0% +ball instead of a disc. +Okay. So now we apply uh we study + + align:start position:0% +Okay. So now we apply uh we study + + + align:start position:0% +Okay. So now we apply uh we study +the action + + align:start position:0% +the action + + + align:start position:0% +the action +of L a r inverse and we'll have a + + align:start position:0% +of L a r inverse and we'll have a + + + align:start position:0% +of L a r inverse and we'll have a +picture like this + + align:start position:0% +picture like this + + + align:start position:0% +picture like this +f1 + + align:start position:0% + + + + align:start position:0% + +f0 + + align:start position:0% +f0 + + + align:start position:0% +f0 +um and okay something here will happen + + align:start position:0% +um and okay something here will happen + + + align:start position:0% +um and okay something here will happen +and something different here will + + align:start position:0% + + + + align:start position:0% + +Um okay. So you can study the singular + + align:start position:0% +Um okay. So you can study the singular + + + align:start position:0% +Um okay. So you can study the singular +values + + align:start position:0% + + + + align:start position:0% + +the singular values + + align:start position:0% +the singular values + + + align:start position:0% +the singular values +of l a r inverse and those are equal to + + align:start position:0% +of l a r inverse and those are equal to + + + align:start position:0% +of l a r inverse and those are equal to +the singular values + + align:start position:0% +the singular values + + + align:start position:0% +the singular values +of conjugation by a r. So conjugation by + + align:start position:0% +of conjugation by a r. So conjugation by + + + align:start position:0% +of conjugation by a r. So conjugation by +a r is is a very nice operation on + + align:start position:0% +a r is is a very nice operation on + + + align:start position:0% +a r is is a very nice operation on +matrices. You can write it down and see + + align:start position:0% +matrices. You can write it down and see + + + align:start position:0% +matrices. You can write it down and see +what happens. And you can compute these + + align:start position:0% +what happens. And you can compute these + + + align:start position:0% +what happens. And you can compute these +singular values and they are as follows. + + align:start position:0% +singular values and they are as follows. + + + align:start position:0% +singular values and they are as follows. +Um eus 2r eus r eus r 1 1 e to the r e + + align:start position:0% +Um eus 2r eus r eus r 1 1 e to the r e + + + align:start position:0% +Um eus 2r eus r eus r 1 1 e to the r e +to the r e 2 r. + + align:start position:0% +to the r e 2 r. + + + align:start position:0% +to the r e 2 r. +I won't do it on the board but I promise + + align:start position:0% +I won't do it on the board but I promise + + + align:start position:0% +I won't do it on the board but I promise +it's not hard. + + align:start position:0% +it's not hard. + + + align:start position:0% +it's not hard. +Okay. Now one of these singular values + + align:start position:0% +Okay. Now one of these singular values + + + align:start position:0% +Okay. Now one of these singular values +corresponds to the u direction. + + align:start position:0% +corresponds to the u direction. + + + align:start position:0% +corresponds to the u direction. +So little n is the vector that's the + + align:start position:0% +So little n is the vector that's the + + + align:start position:0% +So little n is the vector that's the +tangent vector + + align:start position:0% +tangent vector + + + align:start position:0% +tangent vector +to the group u at the identity. + + align:start position:0% +to the group u at the identity. + + + align:start position:0% +to the group u at the identity. +Um and so little n is it's not super + + align:start position:0% +Um and so little n is it's not super + + + align:start position:0% +Um and so little n is it's not super +important what the formula is but if you + + align:start position:0% +important what the formula is but if you + + + align:start position:0% +important what the formula is but if you +differentiate that you'll see that the + + align:start position:0% +differentiate that you'll see that the + + + align:start position:0% +differentiate that you'll see that the +tangent vector is that and that's one of + + align:start position:0% +tangent vector is that and that's one of + + + align:start position:0% +tangent vector is that and that's one of +these guys. + + align:start position:0% +these guys. + + + align:start position:0% +these guys. +So as before the direction of the orbits + + align:start position:0% +So as before the direction of the orbits + + + align:start position:0% +So as before the direction of the orbits +is expanding and then on the B7 we have + + align:start position:0% +is expanding and then on the B7 we have + + + align:start position:0% +is expanding and then on the B7 we have +the other seven uh directions. So this + + align:start position:0% +the other seven uh directions. So this + + + align:start position:0% +the other seven uh directions. So this +thing over here is an ellypoid + + align:start position:0% +thing over here is an ellypoid + + + align:start position:0% +thing over here is an ellypoid +with axes eus 2 r eus r eus r 1 1 e to + + align:start position:0% +with axes eus 2 r eus r eus r 1 1 e to + + + align:start position:0% +with axes eus 2 r eus r eus r 1 1 e to +the r e 2 r + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so as we go from here to here these fs + + align:start position:0% +so as we go from here to here these fs + + + align:start position:0% +so as we go from here to here these fs +are not exactly linear but they're close + + align:start position:0% +are not exactly linear but they're close + + + align:start position:0% +are not exactly linear but they're close +to linear they're close to linear maps + + align:start position:0% +to linear they're close to linear maps + + + align:start position:0% +to linear they're close to linear maps +and they stretch some directions and + + align:start position:0% +and they stretch some directions and + + + align:start position:0% +and they stretch some directions and +they compress other directions by these + + align:start position:0% +they compress other directions by these + + + align:start position:0% +they compress other directions by these +amount + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So what is different from before? + + align:start position:0% + + + + align:start position:0% + +Okay. One difference is that this thing + + align:start position:0% +Okay. One difference is that this thing + + + align:start position:0% +Okay. One difference is that this thing +is not exactly a projection. + + align:start position:0% +is not exactly a projection. + + + align:start position:0% +is not exactly a projection. +Um + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +but that's not the most important + + align:start position:0% +but that's not the most important + + + align:start position:0% +but that's not the most important +difference. + + align:start position:0% + + + + align:start position:0% + +Um so differences from last time + + align:start position:0% + + + + align:start position:0% + +Right? So if we had like an approximate + + align:start position:0% +Right? So if we had like an approximate + + + align:start position:0% +Right? So if we had like an approximate +projection + + align:start position:0% +projection + + + align:start position:0% +projection +that went from the seven ball to some + + align:start position:0% +that went from the seven ball to some + + + align:start position:0% +that went from the seven ball to some +vector space V of dimension three say so + + align:start position:0% +vector space V of dimension three say so + + + align:start position:0% +vector space V of dimension three say so +four dimensions are getting squished and + + align:start position:0% +four dimensions are getting squished and + + + align:start position:0% +four dimensions are getting squished and +three dimensions are staying as they + + align:start position:0% +three dimensions are staying as they + + + align:start position:0% +three dimensions are staying as they +are. That would sort of be approximately + + align:start position:0% +are. That would sort of be approximately + + + align:start position:0% +are. That would sort of be approximately +a linear map with singular values + + align:start position:0% +a linear map with singular values + + + align:start position:0% +a linear map with singular values +e to the minus r e to the minus r eus r + + align:start position:0% +e to the minus r e to the minus r eus r + + + align:start position:0% +e to the minus r e to the minus r eus r +e the minus r 1 one one right if I had a + + align:start position:0% +e the minus r 1 one one right if I had a + + + align:start position:0% +e the minus r 1 one one right if I had a +linear map like that these guys are + + align:start position:0% +linear map like that these guys are + + + align:start position:0% +linear map like that these guys are +almost zero so these are the four + + align:start position:0% +almost zero so these are the four + + + align:start position:0% +almost zero so these are the four +directions that are being squished these + + align:start position:0% +directions that are being squished these + + + align:start position:0% +directions that are being squished these +are the three directions that are + + align:start position:0% +are the three directions that are + + + align:start position:0% +are the three directions that are +staying the same the sing list of + + align:start position:0% +staying the same the sing list of + + + align:start position:0% +staying the same the sing list of +singular values here is not quite like + + align:start position:0% +singular values here is not quite like + + + align:start position:0% +singular values here is not quite like +that some of them are bigger than one we + + align:start position:0% +that some of them are bigger than one we + + + align:start position:0% +that some of them are bigger than one we +didn't have that before and the ones + + align:start position:0% +didn't have that before and the ones + + + align:start position:0% +didn't have that before and the ones +that are some of them are equal to one + + align:start position:0% +that are some of them are equal to one + + + align:start position:0% +that are some of them are equal to one +the ones that are smaller than one have + + align:start position:0% +the ones that are smaller than one have + + + align:start position:0% +the ones that are smaller than one have +two different scales. So that's a little + + align:start position:0% +two different scales. So that's a little + + + align:start position:0% +two different scales. So that's a little +bit more complicated but I don't want to + + align:start position:0% +bit more complicated but I don't want to + + + align:start position:0% +bit more complicated but I don't want to +focus on it. + + align:start position:0% +focus on it. + + + align:start position:0% +focus on it. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +so + + align:start position:0% +so + + + align:start position:0% +so +our singular values are a little more + + align:start position:0% +our singular values are a little more + + + align:start position:0% +our singular values are a little more +complicated. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay let's ignore that. Suppose each of + + align:start position:0% +Okay let's ignore that. Suppose each of + + + align:start position:0% +Okay let's ignore that. Suppose each of +these linear maps actually had those + + align:start position:0% +these linear maps actually had those + + + align:start position:0% +these linear maps actually had those +singular values. So it was more like + + align:start position:0% +singular values. So it was more like + + + align:start position:0% +singular values. So it was more like +what we were used to in projection + + align:start position:0% +what we were used to in projection + + + align:start position:0% +what we were used to in projection +theory. There would be a different there + + align:start position:0% +theory. There would be a different there + + + align:start position:0% +theory. There would be a different there +would be another difference from before + + align:start position:0% +would be another difference from before + + + align:start position:0% +would be another difference from before +which is more important. + + align:start position:0% +which is more important. + + + align:start position:0% +which is more important. +So number one number two we still have + + align:start position:0% +So number one number two we still have + + + align:start position:0% +So number one number two we still have +only a one parameter family + + align:start position:0% +only a one parameter family + + + align:start position:0% +only a one parameter family +of linear maps. + + align:start position:0% + + + + align:start position:0% + +All right. So before when we talked + + align:start position:0% +All right. So before when we talked + + + align:start position:0% +All right. So before when we talked +about projections from B7 to V to + + align:start position:0% +about projections from B7 to V to + + + align:start position:0% +about projections from B7 to V to +threedimensional vector space, we talked + + align:start position:0% +threedimensional vector space, we talked + + + align:start position:0% +threedimensional vector space, we talked +about like all of them. If you look at + + align:start position:0% +about like all of them. If you look at + + + align:start position:0% +about like all of them. If you look at +all of the projections from B7 to + + align:start position:0% +all of the projections from B7 to + + + align:start position:0% +all of the projections from B7 to +threedimensional vector spaces, then + + align:start position:0% +threedimensional vector spaces, then + + + align:start position:0% +threedimensional vector spaces, then +something nice happens most of the time. + + align:start position:0% +something nice happens most of the time. + + + align:start position:0% +something nice happens most of the time. +But we don't have all of them. We just + + align:start position:0% +But we don't have all of them. We just + + + align:start position:0% +But we don't have all of them. We just +have a very thin subf family. + + align:start position:0% +have a very thin subf family. + + + align:start position:0% +have a very thin subf family. +So this is not all of the projections. + + align:start position:0% +So this is not all of the projections. + + + align:start position:0% +So this is not all of the projections. +Cool. + + align:start position:0% + + + + align:start position:0% + +Okay. So, um there's also a cosmetic + + align:start position:0% +Okay. So, um there's also a cosmetic + + + align:start position:0% +Okay. So, um there's also a cosmetic +complication that seven is a lot of + + align:start position:0% +complication that seven is a lot of + + + align:start position:0% +complication that seven is a lot of +dimensions and there are a lot of + + align:start position:0% +dimensions and there are a lot of + + + align:start position:0% +dimensions and there are a lot of +numbers. Um that but that that's not + + align:start position:0% +numbers. Um that but that that's not + + + align:start position:0% +numbers. Um that but that that's not +that important. It's just a pain. But + + align:start position:0% +that important. It's just a pain. But + + + align:start position:0% +that important. It's just a pain. But +but but these are this to some extent + + align:start position:0% +but but these are this to some extent + + + align:start position:0% +but but these are this to some extent +and this is a really fundamental + + align:start position:0% +and this is a really fundamental + + + align:start position:0% +and this is a really fundamental +conceptual difference. + + align:start position:0% +conceptual difference. + + + align:start position:0% +conceptual difference. +Um so I wanted to show you not this + + align:start position:0% +Um so I wanted to show you not this + + + align:start position:0% +Um so I wanted to show you not this +problem but the simplest problem of this + + align:start position:0% +problem but the simplest problem of this + + + align:start position:0% +problem but the simplest problem of this +type + + align:start position:0% +type + + + align:start position:0% +type +which is called the restricted + + align:start position:0% +which is called the restricted + + + align:start position:0% +which is called the restricted +projection problem. + + align:start position:0% +projection problem. + + + align:start position:0% +projection problem. +[Applause] + + align:start position:0% + + + + align:start position:0% + +All + + align:start position:0% + + + + align:start position:0% + +right. So this question which I think is + + align:start position:0% +right. So this question which I think is + + + align:start position:0% +right. So this question which I think is +is is a cool question was raised by Fler + + align:start position:0% +is is a cool question was raised by Fler + + + align:start position:0% +is is a cool question was raised by Fler +Katrine Fler and Thomas Orpinan in 2013 + + align:start position:0% +Katrine Fler and Thomas Orpinan in 2013 + + + align:start position:0% +Katrine Fler and Thomas Orpinan in 2013 +and the question is like this. So here's + + align:start position:0% +and the question is like this. So here's + + + align:start position:0% +and the question is like this. So here's +the two sphere. + + align:start position:0% +the two sphere. + + + align:start position:0% +the two sphere. +So we're going to be doing projection + + align:start position:0% +So we're going to be doing projection + + + align:start position:0% +So we're going to be doing projection +theory in three dimensions in R3. So the + + align:start position:0% +theory in three dimensions in R3. So the + + + align:start position:0% +theory in three dimensions in R3. So the +different directions are parameterized + + align:start position:0% +different directions are parameterized + + + align:start position:0% +different directions are parameterized +by the two sphere. But we're not going + + align:start position:0% +by the two sphere. But we're not going + + + align:start position:0% +by the two sphere. But we're not going +to project in all of them. We're just + + align:start position:0% +to project in all of them. We're just + + + align:start position:0% +to project in all of them. We're just +going to pick some curve gamma and + + align:start position:0% +going to pick some curve gamma and + + + align:start position:0% +going to pick some curve gamma and +project in the directions of gamma. So + + align:start position:0% +project in the directions of gamma. So + + + align:start position:0% +project in the directions of gamma. So +gamma contained in s2 is a curve. + + align:start position:0% +gamma contained in s2 is a curve. + + + align:start position:0% +gamma contained in s2 is a curve. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +the question is like this. um if X is + + align:start position:0% +the question is like this. um if X is + + + align:start position:0% +the question is like this. um if X is +contained in the unit three ball and + + align:start position:0% +contained in the unit three ball and + + + align:start position:0% +contained in the unit three ball and +let's say X is a delta SC set we'll put + + align:start position:0% +let's say X is a delta SC set we'll put + + + align:start position:0% +let's say X is a delta SC set we'll put +to make it interesting we put some kind + + align:start position:0% +to make it interesting we put some kind + + + align:start position:0% +to make it interesting we put some kind +of non-conentration condition and this + + align:start position:0% +of non-conentration condition and this + + + align:start position:0% +of non-conentration condition and this +is the one that they had in their paper + + align:start position:0% +is the one that they had in their paper + + + align:start position:0% +is the one that they had in their paper +basically + + align:start position:0% +basically + + + align:start position:0% +basically +okay then estimate + + align:start position:0% + + + + align:start position:0% + +the average + + align:start position:0% +the average + + + align:start position:0% +the average +over all the directions in gamma + + align:start position:0% +over all the directions in gamma + + + align:start position:0% +over all the directions in gamma +of the of pi theta of x delta cover + + align:start position:0% +of the of pi theta of x delta cover + + + align:start position:0% +of the of pi theta of x delta cover +remember okay so pi so theta is a + + align:start position:0% +remember okay so pi so theta is a + + + align:start position:0% +remember okay so pi so theta is a +direction an element of s2 and pi theta + + align:start position:0% +direction an element of s2 and pi theta + + + align:start position:0% +direction an element of s2 and pi theta +is the orthogonal projection from r3 to + + align:start position:0% +is the orthogonal projection from r3 to + + + align:start position:0% +is the orthogonal projection from r3 to +theta per so from three dimensions to + + align:start position:0% +theta per so from three dimensions to + + + align:start position:0% +theta per so from three dimensions to +two dimensions + + align:start position:0% + + + + align:start position:0% + +so estimate the average of that + + align:start position:0% +so estimate the average of that + + + align:start position:0% +so estimate the average of that +seeh + + align:start position:0% +seeh + + + align:start position:0% +seeh +I erased the wrong thing okay on this + + align:start position:0% +I erased the wrong thing okay on this + + + align:start position:0% +I erased the wrong thing okay on this +very boring. Not two minutes ago, there + + align:start position:0% +very boring. Not two minutes ago, there + + + align:start position:0% +very boring. Not two minutes ago, there +was a proposition. It said if you had a + + align:start position:0% +was a proposition. It said if you had a + + + align:start position:0% +was a proposition. It said if you had a +set in R2 and you projected it in all + + align:start position:0% +set in R2 and you projected it in all + + + align:start position:0% +set in R2 and you projected it in all +the different angles, then on average + + align:start position:0% +the different angles, then on average + + + align:start position:0% +the different angles, then on average +the delta covering number of the + + align:start position:0% +the delta covering number of the + + + align:start position:0% +the delta covering number of the +projection was at least something or + + align:start position:0% +projection was at least something or + + + align:start position:0% +projection was at least something or +another. So this is like an analog of + + align:start position:0% +another. So this is like an analog of + + + align:start position:0% +another. So this is like an analog of +that in three dimensions for a set with + + align:start position:0% +that in three dimensions for a set with + + + align:start position:0% +that in three dimensions for a set with +the spacing condition, but with the key + + align:start position:0% +the spacing condition, but with the key + + + align:start position:0% +the spacing condition, but with the key +difference that we're not averaging over + + align:start position:0% +difference that we're not averaging over + + + align:start position:0% +difference that we're not averaging over +all of them. We're only averaging over + + align:start position:0% +all of them. We're only averaging over + + + align:start position:0% +all of them. We're only averaging over +the ones in a particular curve gamma. + + align:start position:0% +the ones in a particular curve gamma. + + + align:start position:0% +the ones in a particular curve gamma. +Okay. Now an interesting thing about + + align:start position:0% +Okay. Now an interesting thing about + + + align:start position:0% +Okay. Now an interesting thing about +this question is that it matters what + + align:start position:0% +this question is that it matters what + + + align:start position:0% +this question is that it matters what +the curved gamma is. And in particular + + align:start position:0% +the curved gamma is. And in particular + + + align:start position:0% +the curved gamma is. And in particular +there's a big difference between an + + align:start position:0% +there's a big difference between an + + + align:start position:0% +there's a big difference between an +equator which is sort of like a straight + + align:start position:0% +equator which is sort of like a straight + + + align:start position:0% +equator which is sort of like a straight +line on the sphere and a non- degenerate + + align:start position:0% +line on the sphere and a non- degenerate + + + align:start position:0% +line on the sphere and a non- degenerate +or curved gamma. + + align:start position:0% +or curved gamma. + + + align:start position:0% +or curved gamma. +So the answer + + align:start position:0% +So the answer + + + align:start position:0% +So the answer +depends + + align:start position:0% +depends + + + align:start position:0% +depends +on whether gamma gamma is the equator is + + align:start position:0% +on whether gamma gamma is the equator is + + + align:start position:0% +on whether gamma gamma is the equator is +one extreme or gamma non- degenerate + + align:start position:0% +one extreme or gamma non- degenerate + + + align:start position:0% +one extreme or gamma non- degenerate +is another extreme. + + align:start position:0% +is another extreme. + + + align:start position:0% +is another extreme. +Um instead of writing the definition of + + align:start position:0% +Um instead of writing the definition of + + + align:start position:0% +Um instead of writing the definition of +non- degenerate let me just give you one + + align:start position:0% +non- degenerate let me just give you one + + + align:start position:0% +non- degenerate let me just give you one +example of a non- degenerate curve. So + + align:start position:0% +example of a non- degenerate curve. So + + + align:start position:0% +example of a non- degenerate curve. So +an example of a non- degenerate curve is + + align:start position:0% +an example of a non- degenerate curve is + + + align:start position:0% +an example of a non- degenerate curve is +gamma is equal to the set of theta in + + align:start position:0% +gamma is equal to the set of theta in + + + align:start position:0% +gamma is equal to the set of theta in +s2. So that the third component of theta + + align:start position:0% +s2. So that the third component of theta + + + align:start position:0% +s2. So that the third component of theta +is a half. + + align:start position:0% + + + + align:start position:0% + +So it looks like a the boundary of a + + align:start position:0% +So it looks like a the boundary of a + + + align:start position:0% +So it looks like a the boundary of a +spherical cap like that. + + align:start position:0% +spherical cap like that. + + + align:start position:0% +spherical cap like that. +Okay. So let me show you how these are + + align:start position:0% +Okay. So let me show you how these are + + + align:start position:0% +Okay. So let me show you how these are +different from each other. + + align:start position:0% +different from each other. + + + align:start position:0% +different from each other. +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. So, example + + align:start position:0% +Okay. So, example + + + align:start position:0% +Okay. So, example +say gamma is the equator and s is two. + + align:start position:0% +say gamma is the equator and s is two. + + + align:start position:0% +say gamma is the equator and s is two. +So, we have a sort of a quote unquote + + align:start position:0% +So, we have a sort of a quote unquote + + + align:start position:0% +So, we have a sort of a quote unquote +two-dimensional set a delta 2 set. Okay. + + align:start position:0% +two-dimensional set a delta 2 set. Okay. + + + align:start position:0% +two-dimensional set a delta 2 set. Okay. +So, our set x is going to be a delta by + + align:start position:0% +So, our set x is going to be a delta by + + + align:start position:0% +So, our set x is going to be a delta by +one by one slab. + + align:start position:0% + + + + align:start position:0% + +So that looks + + align:start position:0% + + + + align:start position:0% + +okay. And so imagine that the the um the + + align:start position:0% +okay. And so imagine that the the um the + + + align:start position:0% +okay. And so imagine that the the um the +two big directions are in the plane of + + align:start position:0% +two big directions are in the plane of + + + align:start position:0% +two big directions are in the plane of +the blackboard and the slab is sticking + + align:start position:0% +the blackboard and the slab is sticking + + + align:start position:0% +the blackboard and the slab is sticking +out of the blackboard by a little bit + + align:start position:0% +out of the blackboard by a little bit + + + align:start position:0% +out of the blackboard by a little bit +delta. Okay. Now there's an equator of + + align:start position:0% +delta. Okay. Now there's an equator of + + + align:start position:0% +delta. Okay. Now there's an equator of +directions that we're going to project + + align:start position:0% +directions that we're going to project + + + align:start position:0% +directions that we're going to project +in. And think of that as the equator + + align:start position:0% +in. And think of that as the equator + + + align:start position:0% +in. And think of that as the equator +that's like uh the sphere was centered + + align:start position:0% +that's like uh the sphere was centered + + + align:start position:0% +that's like uh the sphere was centered +at the blackboard. You intersected the + + align:start position:0% +at the blackboard. You intersected the + + + align:start position:0% +at the blackboard. You intersected the +sphere with the blackboard you would get + + align:start position:0% +sphere with the blackboard you would get + + + align:start position:0% +sphere with the blackboard you would get +a circle. + + align:start position:0% +a circle. + + + align:start position:0% +a circle. +So + + align:start position:0% +So + + + align:start position:0% +So +here's gamma. So now if theta is in + + align:start position:0% +here's gamma. So now if theta is in + + + align:start position:0% +here's gamma. So now if theta is in +gamma + + align:start position:0% +gamma + + + align:start position:0% +gamma +then the projection of x is a delta by + + align:start position:0% +then the projection of x is a delta by + + + align:start position:0% +then the projection of x is a delta by +one rectangle. + + align:start position:0% +one rectangle. + + + align:start position:0% +one rectangle. +So there's a circle of directions where + + align:start position:0% +So there's a circle of directions where + + + align:start position:0% +So there's a circle of directions where +if you project this slab you just get a + + align:start position:0% +if you project this slab you just get a + + + align:start position:0% +if you project this slab you just get a +delta by one rectangle. + + align:start position:0% + + + + align:start position:0% + +Okay. So then we see that the average + + align:start position:0% +Okay. So then we see that the average + + + align:start position:0% +Okay. So then we see that the average +uh pi theta of x delta is like delta + + align:start position:0% +uh pi theta of x delta is like delta + + + align:start position:0% +uh pi theta of x delta is like delta +inverse. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. Now, there's no obvious version of + + align:start position:0% +Okay. Now, there's no obvious version of + + + align:start position:0% +Okay. Now, there's no obvious version of +this example where where gamma is that + + align:start position:0% +this example where where gamma is that + + + align:start position:0% +this example where where gamma is that +curve that's up nearer the top. + + align:start position:0% +curve that's up nearer the top. + + + align:start position:0% +curve that's up nearer the top. +And the difference is so you know if + + align:start position:0% +And the difference is so you know if + + + align:start position:0% +And the difference is so you know if +you're if you're projecting in in a + + align:start position:0% +you're if you're projecting in in a + + + align:start position:0% +you're if you're projecting in in a +certain direction then the fibers are + + align:start position:0% +certain direction then the fibers are + + + align:start position:0% +certain direction then the fibers are +like lines in that direction. And so + + align:start position:0% +like lines in that direction. And so + + + align:start position:0% +like lines in that direction. And so +what's special here is that all of these + + align:start position:0% +what's special here is that all of these + + + align:start position:0% +what's special here is that all of these +lines are co-planer. And so you could + + align:start position:0% +lines are co-planer. And so you could + + + align:start position:0% +lines are co-planer. And so you could +have a kind of planer object that has a + + align:start position:0% +have a kind of planer object that has a + + + align:start position:0% +have a kind of planer object that has a +lot that that p where these lines + + align:start position:0% +lot that that p where these lines + + + align:start position:0% +lot that that p where these lines +intersected a lot. And instead, when we + + align:start position:0% +intersected a lot. And instead, when we + + + align:start position:0% +intersected a lot. And instead, when we +have those directions, then all of our + + align:start position:0% +have those directions, then all of our + + + align:start position:0% +have those directions, then all of our +lines make an angle of 45 degrees with + + align:start position:0% +lines make an angle of 45 degrees with + + + align:start position:0% +lines make an angle of 45 degrees with +the horizontal. They're like light + + align:start position:0% +the horizontal. They're like light + + + align:start position:0% +the horizontal. They're like light +cones. + + align:start position:0% +cones. + + + align:start position:0% +cones. +And these just don't fit together in the + + align:start position:0% +And these just don't fit together in the + + + align:start position:0% +And these just don't fit together in the +same nice way that co-planer lines fit + + align:start position:0% +same nice way that co-planer lines fit + + + align:start position:0% +same nice way that co-planer lines fit +together. So, it makes a difference. And + + align:start position:0% +together. So, it makes a difference. And + + + align:start position:0% +together. So, it makes a difference. And +Fler and and Orpin, they they proved + + align:start position:0% +Fler and and Orpin, they they proved + + + align:start position:0% +Fler and and Orpin, they they proved +that it makes a difference. So, they + + align:start position:0% +that it makes a difference. So, they + + + align:start position:0% +that it makes a difference. So, they +proved some bounds for that thing that + + align:start position:0% +proved some bounds for that thing that + + + align:start position:0% +proved some bounds for that thing that +are strictly bigger than this thing. But + + align:start position:0% +are strictly bigger than this thing. But + + + align:start position:0% +are strictly bigger than this thing. But +it took a while to figure out what is + + align:start position:0% +it took a while to figure out what is + + + align:start position:0% +it took a while to figure out what is +the sharpest bound. Um and that was + + align:start position:0% +the sharpest bound. Um and that was + + + align:start position:0% +the sharpest bound. Um and that was +figured out sometime later in a paper of + + align:start position:0% +figured out sometime later in a paper of + + + align:start position:0% +figured out sometime later in a paper of +six authors. Um Shang Wang Gan Shia Guo + + align:start position:0% +six authors. Um Shang Wang Gan Shia Guo + + + align:start position:0% +six authors. Um Shang Wang Gan Shia Guo +me Terrence Harris Dominique Mald and + + align:start position:0% +me Terrence Harris Dominique Mald and + + + align:start position:0% +me Terrence Harris Dominique Mald and +Hang Wa many of whom were here working + + align:start position:0% +Hang Wa many of whom were here working + + + align:start position:0% +Hang Wa many of whom were here working +on it at various times. Okay. And we + + align:start position:0% +on it at various times. Okay. And we + + + align:start position:0% +on it at various times. Okay. And we +approved um I'll just do a special case. + + align:start position:0% +approved um I'll just do a special case. + + + align:start position:0% +approved um I'll just do a special case. +So if uh x and b3 is a delta 2c set + + align:start position:0% +So if uh x and b3 is a delta 2c set + + + align:start position:0% +So if uh x and b3 is a delta 2c set +um and gamma is non- degenerate like + + align:start position:0% +um and gamma is non- degenerate like + + + align:start position:0% +um and gamma is non- degenerate like +this example above then the average + + align:start position:0% +this example above then the average + + + align:start position:0% +this example above then the average +theta in gamma of pi theta of x delta + + align:start position:0% +theta in gamma of pi theta of x delta + + + align:start position:0% +theta in gamma of pi theta of x delta +covering number is bigger than cepsilon + + align:start position:0% +covering number is bigger than cepsilon + + + align:start position:0% +covering number is bigger than cepsilon +delta to the -2 plus epsilon + + align:start position:0% + + + + align:start position:0% + +Okay. And the best thing you could hope + + align:start position:0% +Okay. And the best thing you could hope + + + align:start position:0% +Okay. And the best thing you could hope +for here is delta to the minus2 because + + align:start position:0% +for here is delta to the minus2 because + + + align:start position:0% +for here is delta to the minus2 because +x itself probably has delta covering + + align:start position:0% +x itself probably has delta covering + + + align:start position:0% +x itself probably has delta covering +number delta to the minus 2. So up to + + align:start position:0% +number delta to the minus 2. So up to + + + align:start position:0% +number delta to the minus 2. So up to +small issues that this is the sharp + + align:start position:0% +small issues that this is the sharp + + + align:start position:0% +small issues that this is the sharp +theorem. + + align:start position:0% + + + + align:start position:0% + +Okay. Um this proof is based on some + + align:start position:0% +Okay. Um this proof is based on some + + + align:start position:0% +Okay. Um this proof is based on some +version of the fora analysis method. Uh + + align:start position:0% +version of the fora analysis method. Uh + + + align:start position:0% +version of the fora analysis method. Uh +but it's a more difficult version that + + align:start position:0% +but it's a more difficult version that + + + align:start position:0% +but it's a more difficult version that +involves decoupling. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +cool. So this connection between + + align:start position:0% +cool. So this connection between + + + align:start position:0% +cool. So this connection between +projection theory and uh between + + align:start position:0% +projection theory and uh between + + + align:start position:0% +projection theory and uh between +homogeneous dynamics and projection + + align:start position:0% +homogeneous dynamics and projection + + + align:start position:0% +homogeneous dynamics and projection +theory was discovered by Alan Linden + + align:start position:0% +theory was discovered by Alan Linden + + + align:start position:0% +theory was discovered by Alan Linden +Strauss and Amir Mohammadi who were + + align:start position:0% +Strauss and Amir Mohammadi who were + + + align:start position:0% +Strauss and Amir Mohammadi who were +working on uh quantitative estimates for + + align:start position:0% +working on uh quantitative estimates for + + + align:start position:0% +working on uh quantitative estimates for +how how unipotent orbits become dense in + + align:start position:0% +how how unipotent orbits become dense in + + + align:start position:0% +how how unipotent orbits become dense in +this setup and they realized this + + align:start position:0% +this setup and they realized this + + + align:start position:0% +this setup and they realized this +connection with projection theory and + + align:start position:0% +connection with projection theory and + + + align:start position:0% +connection with projection theory and +they found the literature they found the + + align:start position:0% +they found the literature they found the + + + align:start position:0% +they found the literature they found the +paper by Fler and Orpin and and all the + + align:start position:0% +paper by Fler and Orpin and and all the + + + align:start position:0% +paper by Fler and Orpin and and all the +follow-up papers and they used those + + align:start position:0% +follow-up papers and they used those + + + align:start position:0% +follow-up papers and they used those +tools to prove of quantitative estimates + + align:start position:0% +tools to prove of quantitative estimates + + + align:start position:0% +tools to prove of quantitative estimates +about how these unipotent orbits mix. + + align:start position:0% +about how these unipotent orbits mix. + + + align:start position:0% +about how these unipotent orbits mix. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> The question of projection theory where + + align:start position:0% +>> The question of projection theory where + + + align:start position:0% +>> The question of projection theory where +kind of each unipotent filament kind of + + align:start position:0% +kind of each unipotent filament kind of + + + align:start position:0% +kind of each unipotent filament kind of +reduces a different projection. Is that + + align:start position:0% +reduces a different projection. Is that + + + align:start position:0% +reduces a different projection. Is that +set of projections dense in kind of the + + align:start position:0% +set of projections dense in kind of the + + + align:start position:0% +set of projections dense in kind of the +whole space of projections or is it some + + align:start position:0% +whole space of projections or is it some + + + align:start position:0% +whole space of projections or is it some +non-dense subset? + + align:start position:0% +non-dense subset? + + + align:start position:0% +non-dense subset? +>> No, it's some non-dense subset. Yeah. So + + align:start position:0% +>> No, it's some non-dense subset. Yeah. So + + + align:start position:0% +>> No, it's some non-dense subset. Yeah. So +here t is going from zero to one. For + + align:start position:0% +here t is going from zero to one. For + + + align:start position:0% +here t is going from zero to one. For +each t we have more or less a + + align:start position:0% +each t we have more or less a + + + align:start position:0% +each t we have more or less a +projection. Um and so we have a smooth + + align:start position:0% +projection. Um and so we have a smooth + + + align:start position:0% +projection. Um and so we have a smooth +curve of length length one in the space + + align:start position:0% +curve of length length one in the space + + + align:start position:0% +curve of length length one in the space +of pro of not exactly projections but + + align:start position:0% +of pro of not exactly projections but + + + align:start position:0% +of pro of not exactly projections but +the space of linear maps. + + align:start position:0% +the space of linear maps. + + + align:start position:0% +the space of linear maps. +Um and so it it is not in any sense + + align:start position:0% +Um and so it it is not in any sense + + + align:start position:0% +Um and so it it is not in any sense +becoming dense in the space of linear + + align:start position:0% +becoming dense in the space of linear + + + align:start position:0% +becoming dense in the space of linear +maps. is really just a few special ones. + + align:start position:0% +maps. is really just a few special ones. + + + align:start position:0% +maps. is really just a few special ones. +And um and this is a a reasonable model + + align:start position:0% +And um and this is a a reasonable model + + + align:start position:0% +And um and this is a a reasonable model +to picture in your mind like that that + + align:start position:0% +to picture in your mind like that that + + + align:start position:0% +to picture in your mind like that that +sphere is like all of the projections or + + align:start position:0% +sphere is like all of the projections or + + + align:start position:0% +sphere is like all of the projections or +all of the linear maps and that orange + + align:start position:0% +all of the linear maps and that orange + + + align:start position:0% +all of the linear maps and that orange +circle is the ones that come up in the + + align:start position:0% +circle is the ones that come up in the + + + align:start position:0% +circle is the ones that come up in the +in homogeneous dynamics. + + align:start position:0% +in homogeneous dynamics. + + + align:start position:0% +in homogeneous dynamics. +Yeah. Okay. So in the last two minutes I + + align:start position:0% +Yeah. Okay. So in the last two minutes I + + + align:start position:0% +Yeah. Okay. So in the last two minutes I +will write down a theorem that they + + align:start position:0% +will write down a theorem that they + + + align:start position:0% +will write down a theorem that they +proved. + + align:start position:0% + + + + align:start position:0% + +uh at least approximately. + + align:start position:0% +uh at least approximately. + + + align:start position:0% +uh at least approximately. +Okay. So this is Linton Strauss, + + align:start position:0% +Okay. So this is Linton Strauss, + + + align:start position:0% +Okay. So this is Linton Strauss, +Mahmadi, Wang and Yang. + + align:start position:0% +Mahmadi, Wang and Yang. + + + align:start position:0% +Mahmadi, Wang and Yang. +Um so setup is on that board. So if G is + + align:start position:0% +Um so setup is on that board. So if G is + + + align:start position:0% +Um so setup is on that board. So if G is +SL3R, + + align:start position:0% +SL3R, + + + align:start position:0% +SL3R, +gamma is S L + + align:start position:0% +gamma is S L + + + align:start position:0% +gamma is S L +3 Z U as above. + + align:start position:0% +3 Z U as above. + + + align:start position:0% +3 Z U as above. +Okay, we take X um and we suppose U dox + + align:start position:0% +Okay, we take X um and we suppose U dox + + + align:start position:0% +Okay, we take X um and we suppose U dox +is not close + + align:start position:0% +is not close + + + align:start position:0% +is not close +to a proper homogeneous subspace. + + align:start position:0% + + + + align:start position:0% + +So it's some analog of being not close + + align:start position:0% +So it's some analog of being not close + + + align:start position:0% +So it's some analog of being not close +to periodic. + + align:start position:0% +to periodic. + + + align:start position:0% +to periodic. +Okay. Then the conclusion is that + + align:start position:0% +Okay. Then the conclusion is that + + + align:start position:0% +Okay. Then the conclusion is that +u 0t of x is delta dense + + align:start position:0% +u 0t of x is delta dense + + + align:start position:0% +u 0t of x is delta dense +in um in the homogeneous space. But so + + align:start position:0% +in um in the homogeneous space. But so + + + align:start position:0% +in um in the homogeneous space. But so +the homogeneous space has infinite + + align:start position:0% +the homogeneous space has infinite + + + align:start position:0% +the homogeneous space has infinite +diameter. So this can't quite be true. + + align:start position:0% +diameter. So this can't quite be true. + + + align:start position:0% +diameter. So this can't quite be true. +But in the if you cut off the cusp. + + align:start position:0% +But in the if you cut off the cusp. + + + align:start position:0% +But in the if you cut off the cusp. +So you cut off the cusp. So you have a + + align:start position:0% +So you cut off the cusp. So you have a + + + align:start position:0% +So you cut off the cusp. So you have a +compact piece of this. Um and delta is t + + align:start position:0% +compact piece of this. Um and delta is t + + + align:start position:0% +compact piece of this. Um and delta is t +to the minus c. C greater than zero is a + + align:start position:0% +to the minus c. C greater than zero is a + + + align:start position:0% +to the minus c. C greater than zero is a +universal constant. + + align:start position:0% + + + + align:start position:0% + +Okay. And a key step in the proof is to + + align:start position:0% +Okay. And a key step in the proof is to + + + align:start position:0% +Okay. And a key step in the proof is to +first show an estimate of the kind that + + align:start position:0% +first show an estimate of the kind that + + + align:start position:0% +first show an estimate of the kind that +we were talking about that the delta + + align:start position:0% +we were talking about that the delta + + + align:start position:0% +we were talking about that the delta +covering number of this orbit is is + + align:start position:0% +covering number of this orbit is is + + + align:start position:0% +covering number of this orbit is is +pretty big. + + align:start position:0% + + + + align:start position:0% + +Right? So the biggest it could possibly + + align:start position:0% +Right? So the biggest it could possibly + + + align:start position:0% +Right? So the biggest it could possibly +be would be delta to minus the dimension + + align:start position:0% +be would be delta to minus the dimension + + + align:start position:0% +be would be delta to minus the dimension +of the group. That's the delta covering + + align:start position:0% +of the group. That's the delta covering + + + align:start position:0% +of the group. That's the delta covering +number of the whole space. And it's + + align:start position:0% +number of the whole space. And it's + + + align:start position:0% +number of the whole space. And it's +quite close to that. That's a key step. + + align:start position:0% +quite close to that. That's a key step. + + + align:start position:0% +quite close to that. That's a key step. +It's analogous to the proof that we + + align:start position:0% +It's analogous to the proof that we + + + align:start position:0% +It's analogous to the proof that we +sketched for the simpler SL2R case. Um, + + align:start position:0% +sketched for the simpler SL2R case. Um, + + + align:start position:0% +sketched for the simpler SL2R case. Um, +and there is an additional argument, but + + align:start position:0% +and there is an additional argument, but + + + align:start position:0% +and there is an additional argument, but +it seems like the most novel and + + align:start position:0% +it seems like the most novel and + + + align:start position:0% +it seems like the most novel and +important part of of this paper was + + align:start position:0% +important part of of this paper was + + + align:start position:0% +important part of of this paper was +using projection theory, using those + + align:start position:0% +using projection theory, using those + + + align:start position:0% +using projection theory, using those +kind of theorems + + align:start position:0% +kind of theorems + + + align:start position:0% +kind of theorems +plus some other smart stuff uh to show + + align:start position:0% +plus some other smart stuff uh to show + + + align:start position:0% +plus some other smart stuff uh to show +that the orbit covers a lot of ground. + + align:start position:0% + + + + align:start position:0% + +Okay. Um Okay. So homogeneous dynamics + + align:start position:0% +Okay. Um Okay. So homogeneous dynamics + + + align:start position:0% +Okay. Um Okay. So homogeneous dynamics +is a big subject and there are different + + align:start position:0% +is a big subject and there are different + + + align:start position:0% +is a big subject and there are different +techniques but in this course I wanted + + align:start position:0% +techniques but in this course I wanted + + + align:start position:0% +techniques but in this course I wanted +to show that there's a connection to + + align:start position:0% +to show that there's a connection to + + + align:start position:0% +to show that there's a connection to +projection theory which is one set of + + align:start position:0% +projection theory which is one set of + + + align:start position:0% +projection theory which is one set of +techniques and which helps to say some + + align:start position:0% +techniques and which helps to say some + + + align:start position:0% +techniques and which helps to say some +some interesting \ No newline at end of file diff --git a/5W4EnYzNRdA.txt b/5W4EnYzNRdA.txt new file mode 100644 index 0000000000000000000000000000000000000000..b99e03ee47ff3d9c168f7044fbd75c45a5047d06 --- /dev/null +++ b/5W4EnYzNRdA.txt @@ -0,0 +1,6923 @@ +align:start position:0% + +so I just want to back up a couple + + align:start position:0% +so I just want to back up a couple + + + align:start position:0% +so I just want to back up a couple +because I think uh there's still some + + align:start position:0% +because I think uh there's still some + + + align:start position:0% +because I think uh there's still some +confusion about what a restriction + + align:start position:0% +confusion about what a restriction + + + align:start position:0% +confusion about what a restriction +enzyme is and exactly what it + + align:start position:0% +enzyme is and exactly what it + + + align:start position:0% +enzyme is and exactly what it +does and although I indicated a thre + + align:start position:0% +does and although I indicated a thre + + + align:start position:0% +does and although I indicated a thre +Prime hydroxy and a five Prime phosphate + + align:start position:0% +Prime hydroxy and a five Prime phosphate + + + align:start position:0% +Prime hydroxy and a five Prime phosphate +let me show you this is the way a lot at + + align:start position:0% +let me show you this is the way a lot at + + + align:start position:0% +let me show you this is the way a lot at +least a large class of restriction + + align:start position:0% +least a large class of restriction + + + align:start position:0% +least a large class of restriction +enzymes went we've + + align:start position:0% +enzymes went we've + + + align:start position:0% +enzymes went we've +seen uh + + align:start position:0% +seen uh + + + align:start position:0% +seen uh +a deoxy ribos + + align:start position:0% +a deoxy ribos + + + align:start position:0% +a deoxy ribos +backbone before with a + + align:start position:0% +backbone before with a + + + align:start position:0% +backbone before with a +phosphate backbone going on up to the + + align:start position:0% +phosphate backbone going on up to the + + + align:start position:0% +phosphate backbone going on up to the +next nucleotide this is the five Prime + + align:start position:0% +next nucleotide this is the five Prime + + + align:start position:0% +next nucleotide this is the five Prime +position this is the three prime + + align:start position:0% +position this is the three prime + + + align:start position:0% +position this is the three prime +position there's a + + align:start position:0% +position there's a + + + align:start position:0% +position there's a +phosphate here it goes down to + + align:start position:0% + + + + align:start position:0% + +the the next one it goes down like this + + align:start position:0% +the the next one it goes down like this + + + align:start position:0% +the the next one it goes down like this +so when I'm showing you GA a t t c five + + align:start position:0% +so when I'm showing you GA a t t c five + + + align:start position:0% +so when I'm showing you GA a t t c five +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +to three prime here's the first here's + + align:start position:0% +to three prime here's the first here's + + + align:start position:0% +to three prime here's the first here's +where I indicated the + + align:start position:0% + + + + align:start position:0% + +first cut comes from and I indicated + + align:start position:0% +first cut comes from and I indicated + + + align:start position:0% +first cut comes from and I indicated +that the cleavage generates a g with a + + align:start position:0% +that the cleavage generates a g with a + + + align:start position:0% +that the cleavage generates a g with a +thre + + align:start position:0% +thre + + + align:start position:0% +thre +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +hydroxy and the g ends up with a five + + align:start position:0% +hydroxy and the g ends up with a five + + + align:start position:0% +hydroxy and the g ends up with a five +Prime phosphate so that means is that + + align:start position:0% +Prime phosphate so that means is that + + + align:start position:0% +Prime phosphate so that means is that +the + + align:start position:0% +the + + + align:start position:0% +the +hydrolysis happens right there so that + + align:start position:0% +hydrolysis happens right there so that + + + align:start position:0% +hydrolysis happens right there so that +after cleavage what you end up + + align:start position:0% + + + + align:start position:0% + +with there a five Prime phosphate and a + + align:start position:0% +with there a five Prime phosphate and a + + + align:start position:0% +with there a five Prime phosphate and a +thre Prime hydroxy this is paired with a + + align:start position:0% +thre Prime hydroxy this is paired with a + + + align:start position:0% +thre Prime hydroxy this is paired with a +with a c on the opposite strand it makes + + align:start position:0% +with a c on the opposite strand it makes + + + align:start position:0% +with a c on the opposite strand it makes +one cut here and then it would make the + + align:start position:0% +one cut here and then it would make the + + + align:start position:0% +one cut here and then it would make the +identical cut on the on the opposite + + align:start position:0% +identical cut on the on the opposite + + + align:start position:0% +identical cut on the on the opposite +strand so if we were to pull those apart + + align:start position:0% +strand so if we were to pull those apart + + + align:start position:0% +strand so if we were to pull those apart +this strand here would would have + + align:start position:0% +this strand here would would have + + + align:start position:0% +this strand here would would have +G with this three prime o and the the + + align:start position:0% +G with this three prime o and the the + + + align:start position:0% +G with this three prime o and the the +other strand would be + + align:start position:0% +other strand would be + + + align:start position:0% +other strand would be +TT a a and if we were to pull this one + + align:start position:0% +TT a a and if we were to pull this one + + + align:start position:0% +TT a a and if we were to pull this one +apart we'd have a a t t c the + + align:start position:0% +apart we'd have a a t t c the + + + align:start position:0% +apart we'd have a a t t c the +g a three prime o + + align:start position:0% +g a three prime o + + + align:start position:0% +g a three prime o +here a five Prime phosphate there a five + + align:start position:0% +here a five Prime phosphate there a five + + + align:start position:0% +here a five Prime phosphate there a five +Prime phosphate there again you have to + + align:start position:0% +Prime phosphate there again you have to + + + align:start position:0% +Prime phosphate there again you have to +remember this strand is going five + + align:start position:0% +remember this strand is going five + + + align:start position:0% +remember this strand is going five +Prime three Prime in that direction this + + align:start position:0% +Prime three Prime in that direction this + + + align:start position:0% +Prime three Prime in that direction this +one is going five Prime three Prime in + + align:start position:0% +one is going five Prime three Prime in + + + align:start position:0% +one is going five Prime three Prime in +the end and the beauty of of this of + + align:start position:0% +the end and the beauty of of this of + + + align:start position:0% +the end and the beauty of of this of +these restriction enzymes at least it's + + align:start position:0% +these restriction enzymes at least it's + + + align:start position:0% +these restriction enzymes at least it's +not true of all of them but it's true of + + align:start position:0% +not true of all of them but it's true of + + + align:start position:0% +not true of all of them but it's true of +a lot of them is they generate these + + align:start position:0% +a lot of them is they generate these + + + align:start position:0% +a lot of them is they generate these +what are called sticky ends you can pull + + align:start position:0% +what are called sticky ends you can pull + + + align:start position:0% +what are called sticky ends you can pull +them apart and it's a little they come + + align:start position:0% +them apart and it's a little they come + + + align:start position:0% +them apart and it's a little they come +back together they'll reform those base + + align:start position:0% +back together they'll reform those base + + + align:start position:0% +back together they'll reform those base +pairs it's almost like having little + + align:start position:0% +pairs it's almost like having little + + + align:start position:0% +pairs it's almost like having little +bits of velcro at the end and and when + + align:start position:0% +bits of velcro at the end and and when + + + align:start position:0% +bits of velcro at the end and and when +this end is looking for a complimentary + + align:start position:0% +this end is looking for a complimentary + + + align:start position:0% +this end is looking for a complimentary +sequence to pair with it doesn't know + + align:start position:0% +sequence to pair with it doesn't know + + + align:start position:0% +sequence to pair with it doesn't know +what's out here or it doesn't know what + + align:start position:0% +what's out here or it doesn't know what + + + align:start position:0% +what's out here or it doesn't know what +what's out there all it sees is this so + + align:start position:0% +what's out there all it sees is this so + + + align:start position:0% +what's out there all it sees is this so +I can cut this and rejoin it or I can + + align:start position:0% +I can cut this and rejoin it or I can + + + align:start position:0% +I can cut this and rejoin it or I can +cut them pull it apart take another + + align:start position:0% +cut them pull it apart take another + + + align:start position:0% +cut them pull it apart take another +piece of DNA it's been cut with the same + + align:start position:0% +piece of DNA it's been cut with the same + + + align:start position:0% +piece of DNA it's been cut with the same +enzyme and therefore has the same + + align:start position:0% +enzyme and therefore has the same + + + align:start position:0% +enzyme and therefore has the same +corresponding little sticky ends on each + + align:start position:0% +corresponding little sticky ends on each + + + align:start position:0% +corresponding little sticky ends on each +end and it could insert right in the + + align:start position:0% +end and it could insert right in the + + + align:start position:0% +end and it could insert right in the +middle and that's the principle of of um + + align:start position:0% +middle and that's the principle of of um + + + align:start position:0% +middle and that's the principle of of um +of cloning it was the development of + + align:start position:0% +of cloning it was the development of + + + align:start position:0% +of cloning it was the development of +these if you will magic scissors that uh + + align:start position:0% +these if you will magic scissors that uh + + + align:start position:0% +these if you will magic scissors that uh +made possible made it possible to take + + align:start position:0% +made possible made it possible to take + + + align:start position:0% +made possible made it possible to take +this DNA which looked so homogeneous + + align:start position:0% +this DNA which looked so homogeneous + + + align:start position:0% +this DNA which looked so homogeneous +nothing but gaas T's and C's uh and then + + align:start position:0% +nothing but gaas T's and C's uh and then + + + align:start position:0% +nothing but gaas T's and C's uh and then +cut it up into find ways when I uh I + + align:start position:0% +cut it up into find ways when I uh I + + + align:start position:0% +cut it up into find ways when I uh I +told you when I was a uh postto a friend + + align:start position:0% +told you when I was a uh postto a friend + + + align:start position:0% +told you when I was a uh postto a friend +of mine had just purified $2 million + + align:start position:0% +of mine had just purified $2 million + + + align:start position:0% +of mine had just purified $2 million +worth of Eco R1 because he he purified + + align:start position:0% +worth of Eco R1 because he he purified + + + align:start position:0% +worth of Eco R1 because he he purified +some of this enzyme at that point the + + align:start position:0% +some of this enzyme at that point the + + + align:start position:0% +some of this enzyme at that point the +only way to get these things was to to + + align:start position:0% +only way to get these things was to to + + + align:start position:0% +only way to get these things was to to +produce them yourself and purify them + + align:start position:0% +produce them yourself and purify them + + + align:start position:0% +produce them yourself and purify them +now there are literally hundreds of + + align:start position:0% +now there are literally hundreds of + + + align:start position:0% +now there are literally hundreds of +these and they recognize different + + align:start position:0% +these and they recognize different + + + align:start position:0% +these and they recognize different +sequences and what people once people + + align:start position:0% +sequences and what people once people + + + align:start position:0% +sequences and what people once people +understood that they existed then they + + align:start position:0% +understood that they existed then they + + + align:start position:0% +understood that they existed then they +just started to look in different + + align:start position:0% +just started to look in different + + + align:start position:0% +just started to look in different +usually they're from bacteria and they + + align:start position:0% +usually they're from bacteria and they + + + align:start position:0% +usually they're from bacteria and they +just looked in different bacteria and uh + + align:start position:0% +just looked in different bacteria and uh + + + align:start position:0% +just looked in different bacteria and uh +until they found another one and then + + align:start position:0% +until they found another one and then + + + align:start position:0% +until they found another one and then +they purify it so um if you go to uh say + + align:start position:0% +they purify it so um if you go to uh say + + + align:start position:0% +they purify it so um if you go to uh say +any of the the companies that uh do + + align:start position:0% +any of the the companies that uh do + + + align:start position:0% +any of the the companies that uh do +stuff for recombinant DNA you'll find + + align:start position:0% +stuff for recombinant DNA you'll find + + + align:start position:0% +stuff for recombinant DNA you'll find +list like this uh you you could the + + align:start position:0% +list like this uh you you could the + + + align:start position:0% +list like this uh you you could the +funny little abbreviations sort of like + + align:start position:0% +funny little abbreviations sort of like + + + align:start position:0% +funny little abbreviations sort of like +the eco1 usually have something that + + align:start position:0% +the eco1 usually have something that + + + align:start position:0% +the eco1 usually have something that +tells you some abbreviation related to + + align:start position:0% +tells you some abbreviation related to + + + align:start position:0% +tells you some abbreviation related to +the organism uh from which the + + align:start position:0% +the organism uh from which the + + + align:start position:0% +the organism uh from which the +Restriction enzyme was isolated and you + + align:start position:0% +Restriction enzyme was isolated and you + + + align:start position:0% +Restriction enzyme was isolated and you +can find things that will cut I won't + + align:start position:0% +can find things that will cut I won't + + + align:start position:0% +can find things that will cut I won't +say every sequence but very very uh many + + align:start position:0% +say every sequence but very very uh many + + + align:start position:0% +say every sequence but very very uh many +sequences there are literally hundreds + + align:start position:0% +sequences there are literally hundreds + + + align:start position:0% +sequences there are literally hundreds +of these and you just order them and the + + align:start position:0% +of these and you just order them and the + + + align:start position:0% +of these and you just order them and the +next day a FedEx package arrives with a + + align:start position:0% +next day a FedEx package arrives with a + + + align:start position:0% +next day a FedEx package arrives with a +little bit of the enzyme that will cut + + align:start position:0% +little bit of the enzyme that will cut + + + align:start position:0% +little bit of the enzyme that will cut +it that cut at that + + align:start position:0% + + + + align:start position:0% + +sequence the another concept that seemed + + align:start position:0% +sequence the another concept that seemed + + + align:start position:0% +sequence the another concept that seemed +to be problem was what + + align:start position:0% + + + + align:start position:0% + +was what's a + + align:start position:0% +was what's a + + + align:start position:0% +was what's a +vector so if you understand that there + + align:start position:0% +vector so if you understand that there + + + align:start position:0% +vector so if you understand that there +are sequence + + align:start position:0% +are sequence + + + align:start position:0% +are sequence +specific molecular scissors then if we + + align:start position:0% +specific molecular scissors then if we + + + align:start position:0% +specific molecular scissors then if we +have a piece of DNA and there's an Eco + + align:start position:0% +have a piece of DNA and there's an Eco + + + align:start position:0% +have a piece of DNA and there's an Eco +R1 site here would sort of be kind of + + align:start position:0% +R1 site here would sort of be kind of + + + align:start position:0% +R1 site here would sort of be kind of +think of it like that because it's going + + align:start position:0% +think of it like that because it's going + + + align:start position:0% +think of it like that because it's going +to cut in this slightly skewed + + align:start position:0% + + + + align:start position:0% + +way maybe there's another one right + + align:start position:0% + + + + align:start position:0% + +here another one over + + align:start position:0% +here another one over + + + align:start position:0% +here another one over +here if we take this DNA and cut it with + + align:start position:0% +here if we take this DNA and cut it with + + + align:start position:0% +here if we take this DNA and cut it with +this uh particular enzyme we're going to + + align:start position:0% +this uh particular enzyme we're going to + + + align:start position:0% +this uh particular enzyme we're going to +get a break here then this we'll get + + align:start position:0% +get a break here then this we'll get + + + align:start position:0% +get a break here then this we'll get +this piece running from here to here + + align:start position:0% +this piece running from here to here + + + align:start position:0% +this piece running from here to here +we'll get this little piece here + + align:start position:0% +we'll get this little piece here + + + align:start position:0% +we'll get this little piece here +we'll get this piece here and we'll get + + align:start position:0% +we'll get this piece here and we'll get + + + align:start position:0% +we'll get this piece here and we'll get +whatever goes off on those sides so + + align:start position:0% +whatever goes off on those sides so + + + align:start position:0% +whatever goes off on those sides so +that's + + align:start position:0% +that's + + + align:start position:0% +that's +naked in a test + + align:start position:0% +naked in a test + + + align:start position:0% +naked in a test +tube if so I could cut any piece of + + align:start position:0% +tube if so I could cut any piece of + + + align:start position:0% +tube if so I could cut any piece of +DNA at some sites generating a bunch of + + align:start position:0% +DNA at some sites generating a bunch of + + + align:start position:0% +DNA at some sites generating a bunch of +fragments now if I just took those + + align:start position:0% +fragments now if I just took those + + + align:start position:0% +fragments now if I just took those +fragments and transformed them into e + + align:start position:0% +fragments and transformed them into e + + + align:start position:0% +fragments and transformed them into e +Cola I took naked DNA took it from the + + align:start position:0% +Cola I took naked DNA took it from the + + + align:start position:0% +Cola I took naked DNA took it from the +outside put it + + align:start position:0% +outside put it + + + align:start position:0% +outside put it +inside is it going to replicate + + align:start position:0% + + + + align:start position:0% + +no why not because there's a special + + align:start position:0% +no why not because there's a special + + + align:start position:0% +no why not because there's a special +signal called the origin replication + + align:start position:0% +signal called the origin replication + + + align:start position:0% +signal called the origin replication +that says start replicating DNA here + + align:start position:0% +that says start replicating DNA here + + + align:start position:0% +that says start replicating DNA here +this came from a piece of human let's + + align:start position:0% +this came from a piece of human let's + + + align:start position:0% +this came from a piece of human let's +say some of my DNA it would not have a + + align:start position:0% +say some of my DNA it would not have a + + + align:start position:0% +say some of my DNA it would not have a +signal in it that said to the coli + + align:start position:0% +signal in it that said to the coli + + + align:start position:0% +signal in it that said to the coli +replication Machinery start start + + align:start position:0% +replication Machinery start start + + + align:start position:0% +replication Machinery start start +copying DNA right here so the sort of + + align:start position:0% +copying DNA right here so the sort of + + + align:start position:0% +copying DNA right here so the sort of +principle of apart from being able to + + align:start position:0% +principle of apart from being able to + + + align:start position:0% +principle of apart from being able to +cut DNA into fragments is you have to to + + align:start position:0% +cut DNA into fragments is you have to to + + + align:start position:0% +cut DNA into fragments is you have to to +get it to replicate so you can make lots + + align:start position:0% +get it to replicate so you can make lots + + + align:start position:0% +get it to replicate so you can make lots +and lots of copies so the trick is to + + align:start position:0% +and lots of copies so the trick is to + + + align:start position:0% +and lots of copies so the trick is to +attach the DNA at least a widely used + + align:start position:0% +attach the DNA at least a widely used + + + align:start position:0% +attach the DNA at least a widely used +trick is to attach the DNA to something + + align:start position:0% +trick is to attach the DNA to something + + + align:start position:0% +trick is to attach the DNA to something +that has an origin of replication that + + align:start position:0% +that has an origin of replication that + + + align:start position:0% +that has an origin of replication that +will work in the organism in question + + align:start position:0% +will work in the organism in question + + + align:start position:0% +will work in the organism in question +and that was what we call a + + align:start position:0% + + + + align:start position:0% + +vector so this is a this is an eoli cell + + align:start position:0% +vector so this is a this is an eoli cell + + + align:start position:0% +vector so this is a this is an eoli cell +another thing is very confusing is all + + align:start position:0% +another thing is very confusing is all + + + align:start position:0% +another thing is very confusing is all +the circles that show up in this course + + align:start position:0% +the circles that show up in this course + + + align:start position:0% +the circles that show up in this course +this is huge the vector was + + align:start position:0% +this is huge the vector was + + + align:start position:0% +this is huge the vector was +double stranded + + align:start position:0% + + + + align:start position:0% + +DNA that maybe let's say had a unique E1 + + align:start position:0% +DNA that maybe let's say had a unique E1 + + + align:start position:0% +DNA that maybe let's say had a unique E1 +restriction site in it that's the only + + align:start position:0% +restriction site in it that's the only + + + align:start position:0% +restriction site in it that's the only +eco1 restriction site the other thing it + + align:start position:0% +eco1 restriction site the other thing it + + + align:start position:0% +eco1 restriction site the other thing it +would need to have is an origin of + + align:start position:0% +would need to have is an origin of + + + align:start position:0% +would need to have is an origin of +replic DNA + + align:start position:0% +replic DNA + + + align:start position:0% +replic DNA +replication so that's why this plasma is + + align:start position:0% +replication so that's why this plasma is + + + align:start position:0% +replication so that's why this plasma is +able to propagate itself this little + + align:start position:0% +able to propagate itself this little + + + align:start position:0% +able to propagate itself this little +circle of DNA is able to propagate + + align:start position:0% +circle of DNA is able to propagate + + + align:start position:0% +circle of DNA is able to propagate +itself and then some kind of selectable + + align:start position:0% +itself and then some kind of selectable + + + align:start position:0% +itself and then some kind of selectable +marker and most of the time that's a + + align:start position:0% +marker and most of the time that's a + + + align:start position:0% +marker and most of the time that's a +drug res consistent so though it doesn't + + align:start position:0% +drug res consistent so though it doesn't + + + align:start position:0% +drug res consistent so though it doesn't +have to be and if we cut that here + + align:start position:0% +have to be and if we cut that here + + + align:start position:0% +have to be and if we cut that here +generate sticky ends then we could take + + align:start position:0% +generate sticky ends then we could take + + + align:start position:0% +generate sticky ends then we could take +this fragment and stick it in here to + + align:start position:0% +this fragment and stick it in here to + + + align:start position:0% +this fragment and stick it in here to +give this piece + + align:start position:0% + + + + align:start position:0% + +here joined to the vector so that's + + align:start position:0% + + + + align:start position:0% + +vector and that's an + + align:start position:0% +vector and that's an + + + align:start position:0% +vector and that's an +insert let's say it was that piece that + + align:start position:0% +insert let's say it was that piece that + + + align:start position:0% +insert let's say it was that piece that +piece there in fact if you wanted to + + align:start position:0% +piece there in fact if you wanted to + + + align:start position:0% +piece there in fact if you wanted to +clone D DNA in eoli and then have it + + align:start position:0% +clone D DNA in eoli and then have it + + + align:start position:0% +clone D DNA in eoli and then have it +have the plasma work in uh in yeast if + + align:start position:0% +have the plasma work in uh in yeast if + + + align:start position:0% +have the plasma work in uh in yeast if +you just take that plasma that works in + + align:start position:0% +you just take that plasma that works in + + + align:start position:0% +you just take that plasma that works in +the vector with its insert that works in + + align:start position:0% +the vector with its insert that works in + + + align:start position:0% +the vector with its insert that works in +ecoli and put it in yeast it won't + + align:start position:0% +ecoli and put it in yeast it won't + + + align:start position:0% +ecoli and put it in yeast it won't +replicate either and that's because + + align:start position:0% +replicate either and that's because + + + align:start position:0% +replicate either and that's because +these other languages other than the + + align:start position:0% +these other languages other than the + + + align:start position:0% +these other languages other than the +genetic code are not Universal so you'd + + align:start position:0% +genetic code are not Universal so you'd + + + align:start position:0% +genetic code are not Universal so you'd +have to put also in a sequence that's + + align:start position:0% +have to put also in a sequence that's + + + align:start position:0% +have to put also in a sequence that's +said to the yeast replication Machinery + + align:start position:0% +said to the yeast replication Machinery + + + align:start position:0% +said to the yeast replication Machinery +start something here people call that a + + align:start position:0% +start something here people call that a + + + align:start position:0% +start something here people call that a +shuttle Vector something that will + + align:start position:0% +shuttle Vector something that will + + + align:start position:0% +shuttle Vector something that will +replicate in Inc coli or replicate in ye + + align:start position:0% +replicate in Inc coli or replicate in ye + + + align:start position:0% +replicate in Inc coli or replicate in ye +East and the same principle applies to + + align:start position:0% +East and the same principle applies to + + + align:start position:0% +East and the same principle applies to +other + + align:start position:0% +other + + + align:start position:0% +other +organisms okay now probably the + + align:start position:0% +organisms okay now probably the + + + align:start position:0% +organisms okay now probably the +trickiest thing the thing where I sort + + align:start position:0% +trickiest thing the thing where I sort + + + align:start position:0% +trickiest thing the thing where I sort +of muddled it yes on Friday and I + + align:start position:0% +of muddled it yes on Friday and I + + + align:start position:0% +of muddled it yes on Friday and I +apologized for that was this discovery + + align:start position:0% +apologized for that was this discovery + + + align:start position:0% +apologized for that was this discovery +of of restriction enzymes and again some + + align:start position:0% +of of restriction enzymes and again some + + + align:start position:0% +of of restriction enzymes and again some +of you are frustrated you said how could + + align:start position:0% +of you are frustrated you said how could + + + align:start position:0% +of you are frustrated you said how could +this why do I waste time why don't just + + align:start position:0% +this why do I waste time why don't just + + + align:start position:0% +this why do I waste time why don't just +tell you stuff that's on the exam okay + + align:start position:0% +tell you stuff that's on the exam okay + + + align:start position:0% +tell you stuff that's on the exam okay +again people were talking about + + align:start position:0% +again people were talking about + + + align:start position:0% +again people were talking about +molecular scissors when I was uh an + + align:start position:0% +molecular scissors when I was uh an + + + align:start position:0% +molecular scissors when I was uh an +undergrad and a grad student and + + align:start position:0% +undergrad and a grad student and + + + align:start position:0% +undergrad and a grad student and +chemists were trying to think of they if + + align:start position:0% +chemists were trying to think of they if + + + align:start position:0% +chemists were trying to think of they if +they could come up with some way where + + align:start position:0% +they could come up with some way where + + + align:start position:0% +they could come up with some way where +you could get some specificity into how + + align:start position:0% +you could get some specificity into how + + + align:start position:0% +you could get some specificity into how +to cutting DNA and the answer the + + align:start position:0% +to cutting DNA and the answer the + + + align:start position:0% +to cutting DNA and the answer the +discovery of restriction enzymes didn't + + align:start position:0% +discovery of restriction enzymes didn't + + + align:start position:0% +discovery of restriction enzymes didn't +come from that kind of experiment it + + align:start position:0% +come from that kind of experiment it + + + align:start position:0% +come from that kind of experiment it +came from somebody trying to understand + + align:start position:0% +came from somebody trying to understand + + + align:start position:0% +came from somebody trying to understand +what seemed to be a really obscure piece + + align:start position:0% +what seemed to be a really obscure piece + + + align:start position:0% +what seemed to be a really obscure piece +of biology and I'm just going to Julia + + align:start position:0% +of biology and I'm just going to Julia + + + align:start position:0% +of biology and I'm just going to Julia +made up a lovely little slide what I + + align:start position:0% +made up a lovely little slide what I + + + align:start position:0% +made up a lovely little slide what I +think what basically I did was I left + + align:start position:0% +think what basically I did was I left + + + align:start position:0% +think what basically I did was I left +out one of the little layers that I + + align:start position:0% +out one of the little layers that I + + + align:start position:0% +out one of the little layers that I +usually show so let me just talk here's + + align:start position:0% +usually show so let me just talk here's + + + align:start position:0% +usually show so let me just talk here's +what again what um + + align:start position:0% +what again what um + + + align:start position:0% +what again what um +Lura saw when he was doing these + + align:start position:0% +Lura saw when he was doing these + + + align:start position:0% +Lura saw when he was doing these +experiments so I'm going to tell you + + align:start position:0% +experiments so I'm going to tell you + + + align:start position:0% +experiments so I'm going to tell you +now what was in strain A and B and maybe + + align:start position:0% +now what was in strain A and B and maybe + + + align:start position:0% +now what was in strain A and B and maybe +that will help + + align:start position:0% +that will help + + + align:start position:0% +that will help +now but I wanted you at first to see it + + align:start position:0% +now but I wanted you at first to see it + + + align:start position:0% +now but I wanted you at first to see it +without knowing what anything beyond + + align:start position:0% +without knowing what anything beyond + + + align:start position:0% +without knowing what anything beyond +what luran + + align:start position:0% +what luran + + + align:start position:0% +what luran +knew okay strain a has no restriction + + align:start position:0% + + + + align:start position:0% + +enzyme + + align:start position:0% + + + + align:start position:0% + +and no modification enzyme and although + + align:start position:0% +and no modification enzyme and although + + + align:start position:0% +and no modification enzyme and although +there are different types of Ed + + align:start position:0% +there are different types of Ed + + + align:start position:0% +there are different types of Ed +modification + + align:start position:0% +modification + + + align:start position:0% +modification +enzymes there are are two um most of + + align:start position:0% +enzymes there are are two um most of + + + align:start position:0% +enzymes there are are two um most of +many of them are methylases so we'll + + align:start position:0% +many of them are methylases so we'll + + + align:start position:0% +many of them are methylases so we'll +call that and this one + + align:start position:0% +call that and this one + + + align:start position:0% +call that and this one +has a restriction + + align:start position:0% + + + + align:start position:0% + +enzyme + + align:start position:0% + + + + align:start position:0% + +um and it + + align:start position:0% + + + + align:start position:0% + +has it has a corresponding + + align:start position:0% +has it has a corresponding + + + align:start position:0% +has it has a corresponding +methylase just to review that again if + + align:start position:0% +methylase just to review that again if + + + align:start position:0% +methylase just to review that again if +you can figure this pretty much out from + + align:start position:0% +you can figure this pretty much out from + + + align:start position:0% +you can figure this pretty much out from +first principles that if you were an + + align:start position:0% +first principles that if you were an + + + align:start position:0% +first principles that if you were an +organism and you had a restriction + + align:start position:0% +organism and you had a restriction + + + align:start position:0% +organism and you had a restriction +enzyme that would cut this there are two + + align:start position:0% +enzyme that would cut this there are two + + + align:start position:0% +enzyme that would cut this there are two +things you can possibly do to keep from + + align:start position:0% +things you can possibly do to keep from + + + align:start position:0% +things you can possibly do to keep from +cutting up your own DNA one is to NE + + align:start position:0% +cutting up your own DNA one is to NE + + + align:start position:0% +cutting up your own DNA one is to NE +never have that sequence appear in your + + align:start position:0% +never have that sequence appear in your + + + align:start position:0% +never have that sequence appear in your +DNA that would prevent you from cutting + + align:start position:0% +DNA that would prevent you from cutting + + + align:start position:0% +DNA that would prevent you from cutting +up your own DNA even though it has it + + align:start position:0% +up your own DNA even though it has it + + + align:start position:0% +up your own DNA even though it has it +becomes pretty constraining now because + + align:start position:0% +becomes pretty constraining now because + + + align:start position:0% +becomes pretty constraining now because +it's somewhere in a particular protein + + align:start position:0% +it's somewhere in a particular protein + + + align:start position:0% +it's somewhere in a particular protein +you might need that little bit of + + align:start position:0% +you might need that little bit of + + + align:start position:0% +you might need that little bit of +sequence to encode something that you + + align:start position:0% +sequence to encode something that you + + + align:start position:0% +sequence to encode something that you +need to make a critical protein so + + align:start position:0% +need to make a critical protein so + + + align:start position:0% +need to make a critical protein so +instead what you find is organisms that + + align:start position:0% +instead what you find is organisms that + + + align:start position:0% +instead what you find is organisms that +have a restriction enzyme have those + + align:start position:0% +have a restriction enzyme have those + + + align:start position:0% +have a restriction enzyme have those +sequences but they don't cut up their + + align:start position:0% +sequences but they don't cut up their + + + align:start position:0% +sequences but they don't cut up their +own DNA because they modify their own + + align:start position:0% +own DNA because they modify their own + + + align:start position:0% +own DNA because they modify their own +DNA by putting in this in the case of + + align:start position:0% +DNA by putting in this in the case of + + + align:start position:0% +DNA by putting in this in the case of +this one they put a methyl group here + + align:start position:0% +this one they put a methyl group here + + + align:start position:0% +this one they put a methyl group here +and I drew that out the other day you + + align:start position:0% +and I drew that out the other day you + + + align:start position:0% +and I drew that out the other day you +can see you can put a methyl group on + + align:start position:0% +can see you can put a methyl group on + + + align:start position:0% +can see you can put a methyl group on +the on on um the ex exocyclic amino + + align:start position:0% +the on on um the ex exocyclic amino + + + align:start position:0% +the on on um the ex exocyclic amino +group of adenine and not interfere with + + align:start position:0% +group of adenine and not interfere with + + + align:start position:0% +group of adenine and not interfere with +base pairing but what you can do is + + align:start position:0% +base pairing but what you can do is + + + align:start position:0% +base pairing but what you can do is +interfere with the way that the + + align:start position:0% +interfere with the way that the + + + align:start position:0% +interfere with the way that the +Restriction enzyme sees that sequence + + align:start position:0% +Restriction enzyme sees that sequence + + + align:start position:0% +Restriction enzyme sees that sequence +and when the cell pulls the DNA apart + + align:start position:0% +and when the cell pulls the DNA apart + + + align:start position:0% +and when the cell pulls the DNA apart +each of the old strands is methylated + + align:start position:0% +each of the old strands is methylated + + + align:start position:0% +each of the old strands is methylated +and the New Strand is initially not + + align:start position:0% +and the New Strand is initially not + + + align:start position:0% +and the New Strand is initially not +methylated but that's enough to keep the + + align:start position:0% +methylated but that's enough to keep the + + + align:start position:0% +methylated but that's enough to keep the +Restriction enzyme from doing its thing + + align:start position:0% +Restriction enzyme from doing its thing + + + align:start position:0% +Restriction enzyme from doing its thing +and then the methylase will come along + + align:start position:0% +and then the methylase will come along + + + align:start position:0% +and then the methylase will come along +find the sequence and then the progyny + + align:start position:0% +find the sequence and then the progyny + + + align:start position:0% +find the sequence and then the progyny +Strand the daughter strand will DNA up + + align:start position:0% +Strand the daughter strand will DNA up + + + align:start position:0% +Strand the daughter strand will DNA up +methylated so once you get DNA + + align:start position:0% +methylated so once you get DNA + + + align:start position:0% +methylated so once you get DNA +methylated you can propagate it as long + + align:start position:0% +methylated you can propagate it as long + + + align:start position:0% +methylated you can propagate it as long +as you have the methyl group so that was + + align:start position:0% +as you have the methyl group so that was + + + align:start position:0% +as you have the methyl group so that was +this was what was really underlying what + + align:start position:0% +this was what was really underlying what + + + align:start position:0% +this was what was really underlying what +Lura did but he didn't know that so let + + align:start position:0% +Lura did but he didn't know that so let + + + align:start position:0% +Lura did but he didn't know that so let +me just quickly go through this again so + + align:start position:0% +me just quickly go through this again so + + + align:start position:0% +me just quickly go through this again so +he took he grew the strain the Fage + + align:start position:0% +he took he grew the strain the Fage + + + align:start position:0% +he took he grew the strain the Fage +unstrain a okay no restriction enzyme no + + align:start position:0% +unstrain a okay no restriction enzyme no + + + align:start position:0% +unstrain a okay no restriction enzyme no +it's just plain old DNA and if he plates + + align:start position:0% +it's just plain old DNA and if he plates + + + align:start position:0% +it's just plain old DNA and if he plates +so he picks a plaque that's probably + + align:start position:0% +so he picks a plaque that's probably + + + align:start position:0% +so he picks a plaque that's probably +about a a + + align:start position:0% +about a a + + + align:start position:0% +about a a +billion yeah a billion Fage in in a + + align:start position:0% +billion yeah a billion Fage in in a + + + align:start position:0% +billion yeah a billion Fage in in a +plaque somewhere around 10 to the eth 10 + + align:start position:0% +plaque somewhere around 10 to the eth 10 + + + align:start position:0% +plaque somewhere around 10 to the eth 10 +to the 9th Fage probably in a in a uh no + + align:start position:0% +to the 9th Fage probably in a in a uh no + + + align:start position:0% +to the 9th Fage probably in a in a uh no +that's probably not true a little a + + align:start position:0% +that's probably not true a little a + + + align:start position:0% +that's probably not true a little a +little bit less than that but somewhat + + align:start position:0% +little bit less than that but somewhat + + + align:start position:0% +little bit less than that but somewhat +less than that but lots and lots of Fage + + align:start position:0% +less than that but lots and lots of Fage + + + align:start position:0% +less than that but lots and lots of Fage +particles in that plaque so we just + + align:start position:0% +particles in that plaque so we just + + + align:start position:0% +particles in that plaque so we just +resuspend them and then plate them out + + align:start position:0% +resuspend them and then plate them out + + + align:start position:0% +resuspend them and then plate them out +and of course it grew on strain a that's + + align:start position:0% +and of course it grew on strain a that's + + + align:start position:0% +and of course it grew on strain a that's +what it was growing on that wouldn't + + align:start position:0% +what it was growing on that wouldn't + + + align:start position:0% +what it was growing on that wouldn't +surprise you at all the surprise was + + align:start position:0% +surprise you at all the surprise was + + + align:start position:0% +surprise you at all the surprise was +even though he knew he had lots and lots + + align:start position:0% +even though he knew he had lots and lots + + + align:start position:0% +even though he knew he had lots and lots +of Fage hardly any of them grew on + + align:start position:0% +of Fage hardly any of them grew on + + + align:start position:0% +of Fage hardly any of them grew on +strain B but he found a rare plaque that + + align:start position:0% +strain B but he found a rare plaque that + + + align:start position:0% +strain B but he found a rare plaque that +had learned to + + align:start position:0% +had learned to + + + align:start position:0% +had learned to +grow and he tested then and this + + align:start position:0% +grow and he tested then and this + + + align:start position:0% +grow and he tested then and this +thing grows on strain B that was not a + + align:start position:0% +thing grows on strain B that was not a + + + align:start position:0% +thing grows on strain B that was not a +surprise cuz it had to grow in strain B + + align:start position:0% +surprise cuz it had to grow in strain B + + + align:start position:0% +surprise cuz it had to grow in strain B +to be up there and he tested and it's + + align:start position:0% +to be up there and he tested and it's + + + align:start position:0% +to be up there and he tested and it's +still grew on strain a so up till now + + align:start position:0% +still grew on strain a so up till now + + + align:start position:0% +still grew on strain a so up till now +everything you knew everything we've + + align:start position:0% +everything you knew everything we've + + + align:start position:0% +everything you knew everything we've +talked about in that course you think + + align:start position:0% +talked about in that course you think + + + align:start position:0% +talked about in that course you think +aha this original Fage couldn't grow on + + align:start position:0% +aha this original Fage couldn't grow on + + + align:start position:0% +aha this original Fage couldn't grow on +strain B but it's mutated somehow it's + + align:start position:0% +strain B but it's mutated somehow it's + + + align:start position:0% +strain B but it's mutated somehow it's +learned to grow on strain B because of a + + align:start position:0% + + + + align:start position:0% + +mutation okay that would be a perfectly + + align:start position:0% +mutation okay that would be a perfectly + + + align:start position:0% +mutation okay that would be a perfectly +reasonable explanation but if that were + + align:start position:0% +reasonable explanation but if that were + + + align:start position:0% +reasonable explanation but if that were +the case what would have happened well + + align:start position:0% +the case what would have happened well + + + align:start position:0% +the case what would have happened well +it was growing on those Fades you pick + + align:start position:0% +it was growing on those Fades you pick + + + align:start position:0% +it was growing on those Fades you pick +them again they should still grow on On + + align:start position:0% +them again they should still grow on On + + + align:start position:0% +them again they should still grow on On +A and B ones from here and they still do + + align:start position:0% +A and B ones from here and they still do + + + align:start position:0% +A and B ones from here and they still do +the problem with that model + + align:start position:0% +the problem with that model + + + align:start position:0% +the problem with that model +was they grew in strain a we had trouble + + align:start position:0% +was they grew in strain a we had trouble + + + align:start position:0% +was they grew in strain a we had trouble +growing in strain B now you learned to + + align:start position:0% +growing in strain B now you learned to + + + align:start position:0% +growing in strain B now you learned to +grow in strain B but you hadn't + + align:start position:0% +grow in strain B but you hadn't + + + align:start position:0% +grow in strain B but you hadn't +forgotten how to grow on strain a but if + + align:start position:0% +forgotten how to grow on strain a but if + + + align:start position:0% +forgotten how to grow on strain a but if +you take the ones that were going on + + align:start position:0% +you take the ones that were going on + + + align:start position:0% +you take the ones that were going on +strain + + align:start position:0% +strain + + + align:start position:0% +strain +a they grow in strain a not a surprise + + align:start position:0% +a they grow in strain a not a surprise + + + align:start position:0% +a they grow in strain a not a surprise +that's what they're growing in here this + + align:start position:0% +that's what they're growing in here this + + + align:start position:0% +that's what they're growing in here this +is the problem right here + + align:start position:0% +is the problem right here + + + align:start position:0% +is the problem right here +if this was a mutant and a permanent + + align:start position:0% +if this was a mutant and a permanent + + + align:start position:0% +if this was a mutant and a permanent +change then we should have been able to + + align:start position:0% +change then we should have been able to + + + align:start position:0% +change then we should have been able to +have it grow on strain a as well so what + + align:start position:0% +have it grow on strain a as well so what + + + align:start position:0% +have it grow on strain a as well so what +was really happening in there well at + + align:start position:0% +was really happening in there well at + + + align:start position:0% +was really happening in there well at +the beginning the Fage DNA was lacking + + align:start position:0% +the beginning the Fage DNA was lacking + + + align:start position:0% +the beginning the Fage DNA was lacking +any kind of + + align:start position:0% +any kind of + + + align:start position:0% +any kind of +modification grew fine in strain a + + align:start position:0% +modification grew fine in strain a + + + align:start position:0% +modification grew fine in strain a +because it was no restriction enzyme + + align:start position:0% +because it was no restriction enzyme + + + align:start position:0% +because it was no restriction enzyme +when it went into strain B that now had + + align:start position:0% +when it went into strain B that now had + + + align:start position:0% +when it went into strain B that now had +a an enzyme a restriction enzyme that + + align:start position:0% +a an enzyme a restriction enzyme that + + + align:start position:0% +a an enzyme a restriction enzyme that +cut up anytime it found that sequence + + align:start position:0% +cut up anytime it found that sequence + + + align:start position:0% +cut up anytime it found that sequence +and so most of the Fage that injected + + align:start position:0% +and so most of the Fage that injected + + + align:start position:0% +and so most of the Fage that injected +their DNA those dnas were Trashed by the + + align:start position:0% +their DNA those dnas were Trashed by the + + + align:start position:0% +their DNA those dnas were Trashed by the +Restriction enzyme but there is a a + + align:start position:0% +Restriction enzyme but there is a a + + + align:start position:0% +Restriction enzyme but there is a a +methylase in there that's also able to + + align:start position:0% +methylase in there that's also able to + + + align:start position:0% +methylase in there that's also able to +methylate those sequences and what + + align:start position:0% +methylate those sequences and what + + + align:start position:0% +methylate those sequences and what +happened somewhere along the way was + + align:start position:0% +happened somewhere along the way was + + + align:start position:0% +happened somewhere along the way was +that there was the methyl one on one + + align:start position:0% +that there was the methyl one on one + + + align:start position:0% +that there was the methyl one on one +phage DNA and got enough methyls on + + align:start position:0% +phage DNA and got enough methyls on + + + align:start position:0% +phage DNA and got enough methyls on +there that the Fage could be replicated + + align:start position:0% +there that the Fage could be replicated + + + align:start position:0% +there that the Fage could be replicated +before it got cut up by the Restriction + + align:start position:0% +before it got cut up by the Restriction + + + align:start position:0% +before it got cut up by the Restriction +enzyme once the Fage molecule has + + align:start position:0% +enzyme once the Fage molecule has + + + align:start position:0% +enzyme once the Fage molecule has +methylations on the site it's a ble to + + align:start position:0% +methylations on the site it's a ble to + + + align:start position:0% +methylations on the site it's a ble to +grow just fine in strain B and it'll be + + align:start position:0% +grow just fine in strain B and it'll be + + + align:start position:0% +grow just fine in strain B and it'll be +able to do it + + align:start position:0% +able to do it + + + align:start position:0% +able to do it +forever um however if you take that meth + + align:start position:0% +forever um however if you take that meth + + + align:start position:0% +forever um however if you take that meth +that DNA with the methyls on it and we + + align:start position:0% +that DNA with the methyls on it and we + + + align:start position:0% +that DNA with the methyls on it and we +put it back in strain a well it still + + align:start position:0% +put it back in strain a well it still + + + align:start position:0% +put it back in strain a well it still +grows this one doesn't have any kind of + + align:start position:0% +grows this one doesn't have any kind of + + + align:start position:0% +grows this one doesn't have any kind of +restriction enzyme but while it's + + align:start position:0% +restriction enzyme but while it's + + + align:start position:0% +restriction enzyme but while it's +growing it's busy losing all the methyls + + align:start position:0% +growing it's busy losing all the methyls + + + align:start position:0% +growing it's busy losing all the methyls +again and we're right back to where we + + align:start position:0% +again and we're right back to where we + + + align:start position:0% +again and we're right back to where we +started + + align:start position:0% +started + + + align:start position:0% +started +from okay an + + align:start position:0% +from okay an + + + align:start position:0% +from okay an +obscure experiment probably one of the + + align:start position:0% +obscure experiment probably one of the + + + align:start position:0% +obscure experiment probably one of the +most obscure you could get many people + + align:start position:0% +most obscure you could get many people + + + align:start position:0% +most obscure you could get many people +would have paid no attention this does + + align:start position:0% +would have paid no attention this does + + + align:start position:0% +would have paid no attention this does +not seem worth it but neverthe so the + + align:start position:0% +not seem worth it but neverthe so the + + + align:start position:0% +not seem worth it but neverthe so the +phenomenon was called restriction they + + align:start position:0% +phenomenon was called restriction they + + + align:start position:0% +phenomenon was called restriction they +had to give it a name it wasn't mutation + + align:start position:0% +had to give it a name it wasn't mutation + + + align:start position:0% +had to give it a name it wasn't mutation +they said this phage DNA was being + + align:start position:0% +they said this phage DNA was being + + + align:start position:0% +they said this phage DNA was being +restricted somehow when it grew on + + align:start position:0% +restricted somehow when it grew on + + + align:start position:0% +restricted somehow when it grew on +strain B people called then postulated + + align:start position:0% +strain B people called then postulated + + + align:start position:0% +strain B people called then postulated +there must be a restriction enzyme that + + align:start position:0% +there must be a restriction enzyme that + + + align:start position:0% +there must be a restriction enzyme that +was doing this restricting of phage + + align:start position:0% +was doing this restricting of phage + + + align:start position:0% +was doing this restricting of phage +growth when they found out what was + + align:start position:0% +growth when they found out what was + + + align:start position:0% +growth when they found out what was +doing it they had discovered magic + + align:start position:0% +doing it they had discovered magic + + + align:start position:0% +doing it they had discovered magic +scissors that would cut DNA at + + align:start position:0% +scissors that would cut DNA at + + + align:start position:0% +scissors that would cut DNA at +particular sequences so + + align:start position:0% +particular sequences so + + + align:start position:0% +particular sequences so +and the point here again to try and go + + align:start position:0% +and the point here again to try and go + + + align:start position:0% +and the point here again to try and go +back and do this I hope some of you will + + align:start position:0% +back and do this I hope some of you will + + + align:start position:0% +back and do this I hope some of you will +get this anyway that many of the really + + align:start position:0% +get this anyway that many of the really + + + align:start position:0% +get this anyway that many of the really +important discoveries come out of basic + + align:start position:0% +important discoveries come out of basic + + + align:start position:0% +important discoveries come out of basic +research they're easy to ridicule why + + align:start position:0% +research they're easy to ridicule why + + + align:start position:0% +research they're easy to ridicule why +would I spend money on cancer human + + align:start position:0% +would I spend money on cancer human + + + align:start position:0% +would I spend money on cancer human +disease or something for somebody + + align:start position:0% +disease or something for somebody + + + align:start position:0% +disease or something for somebody +studying some little weird phenomenon + + align:start position:0% +studying some little weird phenomenon + + + align:start position:0% +studying some little weird phenomenon +about Fage but if you want to trace back + + align:start position:0% +about Fage but if you want to trace back + + + align:start position:0% +about Fage but if you want to trace back +to the experiment that sort of started + + align:start position:0% +to the experiment that sort of started + + + align:start position:0% +to the experiment that sort of started +the Biotech Industry it was the + + align:start position:0% +the Biotech Industry it was the + + + align:start position:0% +the Biotech Industry it was the +discovery of restriction enzymes it took + + align:start position:0% +discovery of restriction enzymes it took + + + align:start position:0% +discovery of restriction enzymes it took +a little while to discover what it was + + align:start position:0% +a little while to discover what it was + + + align:start position:0% +a little while to discover what it was +but the reason they were discovered + + align:start position:0% +but the reason they were discovered + + + align:start position:0% +but the reason they were discovered +where people were trying to understand + + align:start position:0% +where people were trying to understand + + + align:start position:0% +where people were trying to understand +that phenomenology once we got + + align:start position:0% +that phenomenology once we got + + + align:start position:0% +that phenomenology once we got +restriction enzymes we already had + + align:start position:0% +restriction enzymes we already had + + + align:start position:0% +restriction enzymes we already had +ligase which is sort of the tape we'd + + align:start position:0% +ligase which is sort of the tape we'd + + + align:start position:0% +ligase which is sort of the tape we'd +need and just to show you here when we + + align:start position:0% +need and just to show you here when we + + + align:start position:0% +need and just to show you here when we +go + + align:start position:0% +go + + + align:start position:0% +go +back this one you can see if we put + + align:start position:0% +back this one you can see if we put + + + align:start position:0% +back this one you can see if we put +these together again we have a three + + align:start position:0% +these together again we have a three + + + align:start position:0% +these together again we have a three +prime hydroxy and a five Prime phosphate + + align:start position:0% +prime hydroxy and a five Prime phosphate + + + align:start position:0% +prime hydroxy and a five Prime phosphate +that's what DNA ligase knows how to do + + align:start position:0% +that's what DNA ligase knows how to do + + + align:start position:0% +that's what DNA ligase knows how to do +because that's how you seal up the end + + align:start position:0% +because that's how you seal up the end + + + align:start position:0% +because that's how you seal up the end +of a okazaki fragment so that particular + + align:start position:0% +of a okazaki fragment so that particular + + + align:start position:0% +of a okazaki fragment so that particular +part of the of the molecular biology + + align:start position:0% +part of the of the molecular biology + + + align:start position:0% +part of the of the molecular biology +toolkit was already known to molecular + + align:start position:0% +toolkit was already known to molecular + + + align:start position:0% +toolkit was already known to molecular +biologists who'd been studying DNA + + align:start position:0% +biologists who'd been studying DNA + + + align:start position:0% +biologists who'd been studying DNA +replication okay + + align:start position:0% + + + + align:start position:0% + +so if we took some DNA from anything and + + align:start position:0% +so if we took some DNA from anything and + + + align:start position:0% +so if we took some DNA from anything and +we cut it + + align:start position:0% +we cut it + + + align:start position:0% +we cut it +up uh into pieces like this and then we + + align:start position:0% +up uh into pieces like this and then we + + + align:start position:0% +up uh into pieces like this and then we +joined them with a vector that had been + + align:start position:0% +joined them with a vector that had been + + + align:start position:0% +joined them with a vector that had been +cut so that it let's just sort of open + + align:start position:0% +cut so that it let's just sort of open + + + align:start position:0% +cut so that it let's just sort of open +it up a little bit and then this + + align:start position:0% +it up a little bit and then this + + + align:start position:0% +it up a little bit and then this +fragment would go in here into one + + align:start position:0% +fragment would go in here into one + + + align:start position:0% +fragment would go in here into one +vector molecule this fragment would + + align:start position:0% +vector molecule this fragment would + + + align:start position:0% +vector molecule this fragment would +insert into another Vector molecule and + + align:start position:0% +insert into another Vector molecule and + + + align:start position:0% +insert into another Vector molecule and +so on and so forth then we would have + + align:start position:0% +so on and so forth then we would have + + + align:start position:0% +so on and so forth then we would have +what I said was a library and uh the + + align:start position:0% +what I said was a library and uh the + + + align:start position:0% +what I said was a library and uh the +problem at this point is you if you + + align:start position:0% +problem at this point is you if you + + + align:start position:0% +problem at this point is you if you +trans so you transform those into eoli + + align:start position:0% +trans so you transform those into eoli + + + align:start position:0% +trans so you transform those into eoli +and now we have a whole series + + align:start position:0% +and now we have a whole series + + + align:start position:0% +and now we have a whole series +of eoli they have their their own + + align:start position:0% +of eoli they have their their own + + + align:start position:0% +of eoli they have their their own +chromosome every one of them because + + align:start position:0% +chromosome every one of them because + + + align:start position:0% +chromosome every one of them because +they have they still have to be a + + align:start position:0% + + + + align:start position:0% + +bacterium let's say let's take three + + align:start position:0% +bacterium let's say let's take three + + + align:start position:0% +bacterium let's say let's take three +members of eoli from this this + + align:start position:0% +members of eoli from this this + + + align:start position:0% +members of eoli from this this +library and they'll all have this this + + align:start position:0% +library and they'll all have this this + + + align:start position:0% +library and they'll all have this this +Vector but they'll have let's say insert + + align:start position:0% +Vector but they'll have let's say insert + + + align:start position:0% +Vector but they'll have let's say insert +number + + align:start position:0% + + + + align:start position:0% + +one number + + align:start position:0% +one number + + + align:start position:0% +one number +two number + + align:start position:0% +two number + + + align:start position:0% +two number +three this this insert is + + align:start position:0% +three this this insert is + + + align:start position:0% +three this this insert is +little this insert is + + align:start position:0% + + + + align:start position:0% + +bigger and so on if we did it right we'd + + align:start position:0% +bigger and so on if we did it right we'd + + + align:start position:0% +bigger and so on if we did it right we'd +have every possible fragment of DNA from + + align:start position:0% +have every possible fragment of DNA from + + + align:start position:0% +have every possible fragment of DNA from +that original Source sitting in its own + + align:start position:0% +that original Source sitting in its own + + + align:start position:0% +that original Source sitting in its own +vector and the whole collection of eoli + + align:start position:0% +vector and the whole collection of eoli + + + align:start position:0% +vector and the whole collection of eoli +in this uh + + align:start position:0% +in this uh + + + align:start position:0% +in this uh +population um and this turned to library + + align:start position:0% +population um and this turned to library + + + align:start position:0% +population um and this turned to library +and the next part of the trick was how + + align:start position:0% +and the next part of the trick was how + + + align:start position:0% +and the next part of the trick was how +do you find the thing you want + + align:start position:0% +do you find the thing you want + + + align:start position:0% +do you find the thing you want +especially if you take my DNA with three + + align:start position:0% +especially if you take my DNA with three + + + align:start position:0% +especially if you take my DNA with three +billion d uh base pairs that's an awful + + align:start position:0% +billion d uh base pairs that's an awful + + + align:start position:0% +billion d uh base pairs that's an awful +lot of restriction fragments no matter + + align:start position:0% +lot of restriction fragments no matter + + + align:start position:0% +lot of restriction fragments no matter +what I do it how do you go about doing + + align:start position:0% +what I do it how do you go about doing + + + align:start position:0% +what I do it how do you go about doing +it so the experiment that I showed you + + align:start position:0% +it so the experiment that I showed you + + + align:start position:0% +it so the experiment that I showed you +at the end the the lecture cloning by + + align:start position:0% +at the end the the lecture cloning by + + + align:start position:0% +at the end the the lecture cloning by +complementation uh is fairly simple and + + align:start position:0% +complementation uh is fairly simple and + + + align:start position:0% +complementation uh is fairly simple and +it was one of it's basically the first + + align:start position:0% +it was one of it's basically the first + + + align:start position:0% +it was one of it's basically the first +method that was used to find genes in + + align:start position:0% +method that was used to find genes in + + + align:start position:0% +method that was used to find genes in +recombinant library and that would be + + align:start position:0% +recombinant library and that would be + + + align:start position:0% +recombinant library and that would be +for example to take something that had a + + align:start position:0% +for example to take something that had a + + + align:start position:0% +for example to take something that had a +hist G mutation in the chromosomal DNA + + align:start position:0% +hist G mutation in the chromosomal DNA + + + align:start position:0% +hist G mutation in the chromosomal DNA +this is what the situation I described + + align:start position:0% +this is what the situation I described + + + align:start position:0% +this is what the situation I described +the other day and so if we put the + + align:start position:0% +the other day and so if we put the + + + align:start position:0% +the other day and so if we put the +library into + + align:start position:0% +library into + + + align:start position:0% +library into +every such that the the bacterium we + + align:start position:0% +every such that the the bacterium we + + + align:start position:0% +every such that the the bacterium we +transformed the library into was broken + + align:start position:0% +transformed the library into was broken + + + align:start position:0% +transformed the library into was broken +for its his G Gene then that mutant + + align:start position:0% +for its his G Gene then that mutant + + + align:start position:0% +for its his G Gene then that mutant +couldn't grow on minimal medium unless + + align:start position:0% +couldn't grow on minimal medium unless + + + align:start position:0% +couldn't grow on minimal medium unless +we put in added + + align:start position:0% +we put in added + + + align:start position:0% +we put in added +histadine but if one member of of that + + align:start position:0% +histadine but if one member of of that + + + align:start position:0% +histadine but if one member of of that +Library had the wild type his G Gene + + align:start position:0% +Library had the wild type his G Gene + + + align:start position:0% +Library had the wild type his G Gene +let's say it was this this one here + + align:start position:0% +let's say it was this this one here + + + align:start position:0% +let's say it was this this one here +maybe it had several genes on it but + + align:start position:0% +maybe it had several genes on it but + + + align:start position:0% +maybe it had several genes on it but +let's say over + + align:start position:0% +let's say over + + + align:start position:0% +let's say over +here we + + align:start position:0% +here we + + + align:start position:0% +here we +had his gen + + align:start position:0% +had his gen + + + align:start position:0% +had his gen +plus then this strain is back to being + + align:start position:0% +plus then this strain is back to being + + + align:start position:0% +plus then this strain is back to being +able to synthesize histadine because + + align:start position:0% +able to synthesize histadine because + + + align:start position:0% +able to synthesize histadine because +it's got all the enzymes and what I was + + align:start position:0% +it's got all the enzymes and what I was + + + align:start position:0% +it's got all the enzymes and what I was +pointing out was this really is + + align:start position:0% +pointing out was this really is + + + align:start position:0% +pointing out was this really is +complementation just like we did in that + + align:start position:0% +complementation just like we did in that + + + align:start position:0% +complementation just like we did in that +Fage Cron + + align:start position:0% +Fage Cron + + + align:start position:0% +Fage Cron +we've got one broken copy of the gene + + align:start position:0% +we've got one broken copy of the gene + + + align:start position:0% +we've got one broken copy of the gene +you got a good copy and all you need is + + align:start position:0% +you got a good copy and all you need is + + + align:start position:0% +you got a good copy and all you need is +one good copy in your back in + + align:start position:0% +one good copy in your back in + + + align:start position:0% +one good copy in your back in +business and what I was saying at the + + align:start position:0% +business and what I was saying at the + + + align:start position:0% +business and what I was saying at the +end of the lecture was this is not a + + align:start position:0% +end of the lecture was this is not a + + + align:start position:0% +end of the lecture was this is not a +general solution though if I wanted to + + align:start position:0% +general solution though if I wanted to + + + align:start position:0% +general solution though if I wanted to +find the corresponding histadine Gene + + align:start position:0% +find the corresponding histadine Gene + + + align:start position:0% +find the corresponding histadine Gene +from my my DNA and all these + + align:start position:0% +from my my DNA and all these + + + align:start position:0% +from my my DNA and all these +biosynthetic Pathways pretty much they + + align:start position:0% +biosynthetic Pathways pretty much they + + + align:start position:0% +biosynthetic Pathways pretty much they +AR Rose so so early in evolution the + + align:start position:0% +AR Rose so so early in evolution the + + + align:start position:0% +AR Rose so so early in evolution the +biochemistry is essentially identical in + + align:start position:0% +biochemistry is essentially identical in + + + align:start position:0% +biochemistry is essentially identical in +all cells + + align:start position:0% +all cells + + + align:start position:0% +all cells +could I use this + + align:start position:0% +could I use this + + + align:start position:0% +could I use this +approach to find the same gene from my + + align:start position:0% +approach to find the same gene from my + + + align:start position:0% +approach to find the same gene from my +DNA what do you + + align:start position:0% +DNA what do you + + + align:start position:0% +DNA what do you +think let you turn to somebody beside + + align:start position:0% +think let you turn to somebody beside + + + align:start position:0% +think let you turn to somebody beside +you and see if you can talk for a minute + + align:start position:0% +you and see if you can talk for a minute + + + align:start position:0% +you and see if you can talk for a minute +and then let's see if I can think of at + + align:start position:0% +and then let's see if I can think of at + + + align:start position:0% +and then let's see if I can think of at +least a couple of problems see if you + + align:start position:0% +least a couple of problems see if you + + + align:start position:0% +least a couple of problems see if you +can come up with one or two I'm talk for + + align:start position:0% +can come up with one or two I'm talk for + + + align:start position:0% +can come up with one or two I'm talk for +a minute somebody find somebody near you + + align:start position:0% +a minute somebody find somebody near you + + + align:start position:0% +a minute somebody find somebody near you +and see what you can come up with + + align:start position:0% + + + + align:start position:0% + +anything + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% + + + + align:start position:0% + +we got any anybody want to + + align:start position:0% +we got any anybody want to + + + align:start position:0% +we got any anybody want to +volunteer uh an idea why it wouldn't + + align:start position:0% +volunteer uh an idea why it wouldn't + + + align:start position:0% +volunteer uh an idea why it wouldn't +work or do somebody think it + + align:start position:0% + + + + align:start position:0% + +would no + + align:start position:0% + + + + align:start position:0% + +ideas + + align:start position:0% + + + + align:start position:0% + +anyone God it's + + align:start position:0% +anyone God it's + + + align:start position:0% +anyone God it's +Monday I feel like most of you guys + + align:start position:0% +Monday I feel like most of you guys + + + align:start position:0% +Monday I feel like most of you guys +somebody come + + align:start position:0% +somebody come + + + align:start position:0% +somebody come +on what do you + + align:start position:0% +on what do you + + + align:start position:0% +on what do you +think going to + + align:start position:0% +think going to + + + align:start position:0% +think going to +work no idea what has to happen for it + + align:start position:0% +work no idea what has to happen for it + + + align:start position:0% +work no idea what has to happen for it +to work what has to happen to work I'll + + align:start position:0% +to work what has to happen to work I'll + + + align:start position:0% +to work what has to happen to work I'll +give you a vector that has my Gene + + align:start position:0% +give you a vector that has my Gene + + + align:start position:0% +give you a vector that has my Gene +corresponding to that enzyme it's + + align:start position:0% +corresponding to that enzyme it's + + + align:start position:0% +corresponding to that enzyme it's +anyoli I need to make the + + align:start position:0% +anyoli I need to make the + + + align:start position:0% +anyoli I need to make the +protein + + align:start position:0% +protein + + + align:start position:0% +protein +yeah no it's in Vector the vector has + + align:start position:0% +yeah no it's in Vector the vector has + + + align:start position:0% +yeah no it's in Vector the vector has +we've cloned it into any + + align:start position:0% +we've cloned it into any + + + align:start position:0% +we've cloned it into any +coli um vectors that's got it + + align:start position:0% + + + + align:start position:0% + +yeah well it'll have a language that'll + + align:start position:0% +yeah well it'll have a language that'll + + + align:start position:0% +yeah well it'll have a language that'll +say start transcription but whose + + align:start position:0% +say start transcription but whose + + + align:start position:0% +say start transcription but whose +language is it going to have it's going + + align:start position:0% +language is it going to have it's going + + + align:start position:0% +language is it going to have it's going +to have human my transcriptional stuff + + align:start position:0% +to have human my transcriptional stuff + + + align:start position:0% +to have human my transcriptional stuff +will that work in E Coline no it's not + + align:start position:0% +will that work in E Coline no it's not + + + align:start position:0% +will that work in E Coline no it's not +Universal even though the open reading + + align:start position:0% +Universal even though the open reading + + + align:start position:0% +Universal even though the open reading +frame is fine that's + + align:start position:0% +frame is fine that's + + + align:start position:0% +frame is fine that's +good how about translation I didn't even + + align:start position:0% +good how about translation I didn't even + + + align:start position:0% +good how about translation I didn't even +tell you but that but there's actually + + align:start position:0% +tell you but that but there's actually + + + align:start position:0% +tell you but that but there's actually +some specific stuff needed that's not + + align:start position:0% +some specific stuff needed that's not + + + align:start position:0% +some specific stuff needed that's not +Universal either so when you get the RNA + + align:start position:0% +Universal either so when you get the RNA + + + align:start position:0% +Universal either so when you get the RNA +you still have to translate it there's + + align:start position:0% +you still have to translate it there's + + + align:start position:0% +you still have to translate it there's +another thing that might mess us up do + + align:start position:0% +another thing that might mess us up do + + + align:start position:0% +another thing that might mess us up do +you remember anything else about G yeah + + align:start position:0% +you remember anything else about G yeah + + + align:start position:0% +you remember anything else about G yeah +introns and + + align:start position:0% +introns and + + + align:start position:0% +introns and +exons what if my Gene has introns in it + + align:start position:0% +exons what if my Gene has introns in it + + + align:start position:0% +exons what if my Gene has introns in it +which it almost surely has you have to + + align:start position:0% +which it almost surely has you have to + + + align:start position:0% +which it almost surely has you have to +get rid of those Cola doesn't know what + + align:start position:0% +get rid of those Cola doesn't know what + + + align:start position:0% +get rid of those Cola doesn't know what +they are it's not used to taking them + + align:start position:0% +they are it's not used to taking them + + + align:start position:0% +they are it's not used to taking them +out you see the you see the issues so + + align:start position:0% +out you see the you see the issues so + + + align:start position:0% +out you see the you see the issues so +this is although that's a cute thing and + + align:start position:0% +this is although that's a cute thing and + + + align:start position:0% +this is although that's a cute thing and +that helped you find a gene from eoli by + + align:start position:0% +that helped you find a gene from eoli by + + + align:start position:0% +that helped you find a gene from eoli by +complimenting an eoli mutant or maybe + + align:start position:0% +complimenting an eoli mutant or maybe + + + align:start position:0% +complimenting an eoli mutant or maybe +you could do it with yeast if you had a + + align:start position:0% +you could do it with yeast if you had a + + + align:start position:0% +you could do it with yeast if you had a +vector that would replicate in yeast it + + align:start position:0% +vector that would replicate in yeast it + + + align:start position:0% +vector that would replicate in yeast it +wasn't a general solution so people have + + align:start position:0% +wasn't a general solution so people have + + + align:start position:0% +wasn't a general solution so people have +had to use a whole variety of different + + align:start position:0% +had to use a whole variety of different + + + align:start position:0% +had to use a whole variety of different +ways here's another way now you you know + + align:start position:0% +ways here's another way now you you know + + + align:start position:0% +ways here's another way now you you know +that um genetic you have that genetic + + align:start position:0% +that um genetic you have that genetic + + + align:start position:0% +that um genetic you have that genetic +code that was worked out years ago so + + align:start position:0% +code that was worked out years ago so + + + align:start position:0% +code that was worked out years ago so +let's say I was a biochemist and I'd + + align:start position:0% +let's say I was a biochemist and I'd + + + align:start position:0% +let's say I was a biochemist and I'd +Found A protein that I was interested in + + align:start position:0% +Found A protein that I was interested in + + + align:start position:0% +Found A protein that I was interested in +and I purified it and I got it out to a + + align:start position:0% +and I purified it and I got it out to a + + + align:start position:0% +and I purified it and I got it out to a +single protein and then I could cut it + + align:start position:0% +single protein and then I could cut it + + + align:start position:0% +single protein and then I could cut it +up with things that that proteases that + + align:start position:0% +up with things that that proteases that + + + align:start position:0% +up with things that that proteases that +will cut the protein into pieces and + + align:start position:0% +will cut the protein into pieces and + + + align:start position:0% +will cut the protein into pieces and +their ways of sequencing protein I'm not + + align:start position:0% +their ways of sequencing protein I'm not + + + align:start position:0% +their ways of sequencing protein I'm not +going to tell you how it works in this + + align:start position:0% +going to tell you how it works in this + + + align:start position:0% +going to tell you how it works in this +in this course we just don't have time + + align:start position:0% +in this course we just don't have time + + + align:start position:0% +in this course we just don't have time +but you can get a sequence of little + + align:start position:0% +but you can get a sequence of little + + + align:start position:0% +but you can get a sequence of little +pieces of protein and let's imagine that + + align:start position:0% +pieces of protein and let's imagine that + + + align:start position:0% +pieces of protein and let's imagine that +this was the sequence of part of the + + align:start position:0% +this was the sequence of part of the + + + align:start position:0% +this was the sequence of part of the +protein that I purified it's one of my + + align:start position:0% +protein that I purified it's one of my + + + align:start position:0% +protein that I purified it's one of my +inzy and I'd like to I'd like to find + + align:start position:0% +inzy and I'd like to I'd like to find + + + align:start position:0% +inzy and I'd like to I'd like to find +the gene how could I use that add + + align:start position:0% +the gene how could I use that add + + + align:start position:0% +the gene how could I use that add +information to uh to figure out uh where + + align:start position:0% +information to uh to figure out uh where + + + align:start position:0% +information to uh to figure out uh where +the gene is in this Library so here's + + align:start position:0% +the gene is in this Library so here's + + + align:start position:0% +the gene is in this Library so here's +the strategy we get out the genetic code + + align:start position:0% +the strategy we get out the genetic code + + + align:start position:0% +the strategy we get out the genetic code +which Goin kurana and and Marshall + + align:start position:0% +which Goin kurana and and Marshall + + + align:start position:0% +which Goin kurana and and Marshall +nernberg help work out uh and we say + + align:start position:0% +nernberg help work out uh and we say + + + align:start position:0% +nernberg help work out uh and we say +okay alanine and if you look it up what + + align:start position:0% +okay alanine and if you look it up what + + + align:start position:0% +okay alanine and if you look it up what +you'll find is that it's g c and then it + + align:start position:0% +you'll find is that it's g c and then it + + + align:start position:0% +you'll find is that it's g c and then it +can be a t c or G it can be any of + + align:start position:0% +can be a t c or G it can be any of + + + align:start position:0% +can be a t c or G it can be any of +those if we look up what's the code on + + align:start position:0% +those if we look up what's the code on + + + align:start position:0% +those if we look up what's the code on +for a Spate we'll find there's a g or an + + align:start position:0% +for a Spate we'll find there's a g or an + + + align:start position:0% +for a Spate we'll find there's a g or an +A but it could be t or it could be C if + + align:start position:0% +A but it could be t or it could be C if + + + align:start position:0% +A but it could be t or it could be C if +we look up line we'll see be a but it + + align:start position:0% +we look up line we'll see be a but it + + + align:start position:0% +we look up line we'll see be a but it +could be a or G you'll notice the + + align:start position:0% +could be a or G you'll notice the + + + align:start position:0% +could be a or G you'll notice the +variation of these things is almost the + + align:start position:0% +variation of these things is almost the + + + align:start position:0% +variation of these things is almost the +third codeon if that hadn't struck you + + align:start position:0% +third codeon if that hadn't struck you + + + align:start position:0% +third codeon if that hadn't struck you +same thing with three a c and then this + + align:start position:0% +same thing with three a c and then this + + + align:start position:0% +same thing with three a c and then this +is another one there are four codons + + align:start position:0% +is another one there are four codons + + + align:start position:0% +is another one there are four codons +that that encode this and this one uh + + align:start position:0% +that that encode this and this one uh + + + align:start position:0% +that that encode this and this one uh +asparagine is + + align:start position:0% +asparagine is + + + align:start position:0% +asparagine is +uh is that so knowing that piece of the + + align:start position:0% +uh is that so knowing that piece of the + + + align:start position:0% +uh is that so knowing that piece of the +protein doesn't Define a unique sequence + + align:start position:0% +protein doesn't Define a unique sequence + + + align:start position:0% +protein doesn't Define a unique sequence +but what we could do is we could + + align:start position:0% + + + + align:start position:0% + +synthesize what's + + align:start position:0% + + + + align:start position:0% + +called a mixed probe and that would mean + + align:start position:0% +called a mixed probe and that would mean + + + align:start position:0% +called a mixed probe and that would mean +when we were going to synthesize this + + align:start position:0% +when we were going to synthesize this + + + align:start position:0% +when we were going to synthesize this +DNA we'd start with the G building block + + align:start position:0% +DNA we'd start with the G building block + + + align:start position:0% +DNA we'd start with the G building block +and then we'd add a c building block so + + align:start position:0% +and then we'd add a c building block so + + + align:start position:0% +and then we'd add a c building block so +now we made G and c and at the next step + + align:start position:0% +now we made G and c and at the next step + + + align:start position:0% +now we made G and c and at the next step +we'd add an equal mixture of a g and C + + align:start position:0% +we'd add an equal mixture of a g and C + + + align:start position:0% +we'd add an equal mixture of a g and C +so what we would get out of that would + + align:start position:0% +so what we would get out of that would + + + align:start position:0% +so what we would get out of that would +be we'd be getting G and then the next + + align:start position:0% +be we'd be getting G and then the next + + + align:start position:0% +be we'd be getting G and then the next +biosynthetic step would give us g c and + + align:start position:0% +biosynthetic step would give us g c and + + + align:start position:0% +biosynthetic step would give us g c and +then the next biochemical step would + + align:start position:0% +then the next biochemical step would + + + align:start position:0% +then the next biochemical step would +give us + + align:start position:0% +give us + + + align:start position:0% +give us +GCT or let's say a g c t g c c and g c + + align:start position:0% +GCT or let's say a g c t g c c and g c + + + align:start position:0% +GCT or let's say a g c t g c c and g c +g at the next step we'd add uh a g so + + align:start position:0% +g at the next step we'd add uh a g so + + + align:start position:0% +g at the next step we'd add uh a g so +every one of these would get a g + + align:start position:0% +every one of these would get a g + + + align:start position:0% +every one of these would get a g +everyone would get an A and then the + + align:start position:0% +everyone would get an A and then the + + + align:start position:0% +everyone would get an A and then the +next step they would branch and if you + + align:start position:0% +next step they would branch and if you + + + align:start position:0% +next step they would branch and if you +follow that out you'll see by the end + + align:start position:0% +follow that out you'll see by the end + + + align:start position:0% +follow that out you'll see by the end +you have a mixture of probes one of them + + align:start position:0% +you have a mixture of probes one of them + + + align:start position:0% +you have a mixture of probes one of them +is going to be the + + align:start position:0% +is going to be the + + + align:start position:0% +is going to be the +right uh the right one that you find in + + align:start position:0% +right uh the right one that you find in + + + align:start position:0% +right uh the right one that you find in +the + + align:start position:0% +the + + + align:start position:0% +the +DNA now if you work out the number of + + align:start position:0% +DNA now if you work out the number of + + + align:start position:0% +DNA now if you work out the number of +possibilities you'll discover that most + + align:start position:0% +possibilities you'll discover that most + + + align:start position:0% +possibilities you'll discover that most +of the time there's only going to be one + + align:start position:0% +of the time there's only going to be one + + + align:start position:0% +of the time there's only going to be one +probe that's that's unique once you get + + align:start position:0% +probe that's that's unique once you get + + + align:start position:0% +probe that's that's unique once you get +to about 20 nucleotides any sequence on + + align:start position:0% +to about 20 nucleotides any sequence on + + + align:start position:0% +to about 20 nucleotides any sequence on +average is you know represented once in + + align:start position:0% +average is you know represented once in + + + align:start position:0% +average is you know represented once in +the human genome so as long as you make + + align:start position:0% +the human genome so as long as you make + + + align:start position:0% +the human genome so as long as you make +the probe long enough you'll find + + align:start position:0% +the probe long enough you'll find + + + align:start position:0% +the probe long enough you'll find +usually you'll one of one of the things + + align:start position:0% +usually you'll one of one of the things + + + align:start position:0% +usually you'll one of one of the things +in your mixture will be a defined probe + + align:start position:0% +in your mixture will be a defined probe + + + align:start position:0% +in your mixture will be a defined probe +so what we' then take is we'd have all + + align:start position:0% +so what we' then take is we'd have all + + + align:start position:0% +so what we' then take is we'd have all +these different pieces of DNA that are + + align:start position:0% +these different pieces of DNA that are + + + align:start position:0% +these different pieces of DNA that are +the the The Logical variants you can see + + align:start position:0% +the the The Logical variants you can see + + + align:start position:0% +the the The Logical variants you can see +here and then we would + + align:start position:0% +here and then we would + + + align:start position:0% +here and then we would +label the + + align:start position:0% +label the + + + align:start position:0% +label the +probe with p32 it's a radioactive + + align:start position:0% +probe with p32 it's a radioactive + + + align:start position:0% +probe with p32 it's a radioactive +isotope and it's uh very easy you can + + align:start position:0% +isotope and it's uh very easy you can + + + align:start position:0% +isotope and it's uh very easy you can +add + + align:start position:0% + + + + align:start position:0% + +it to a five Prime hydroxy there's a + + align:start position:0% +it to a five Prime hydroxy there's a + + + align:start position:0% +it to a five Prime hydroxy there's a +special enzyme that will very easily + + align:start position:0% +special enzyme that will very easily + + + align:start position:0% +special enzyme that will very easily +take the terminal phosphate from ATP and + + align:start position:0% +take the terminal phosphate from ATP and + + + align:start position:0% +take the terminal phosphate from ATP and +put it over we don't doesn't really for + + align:start position:0% +put it over we don't doesn't really for + + + align:start position:0% +put it over we don't doesn't really for +this course how we get it there but what + + align:start position:0% +this course how we get it there but what + + + align:start position:0% +this course how we get it there but what +we can do is Radio Active label the + + align:start position:0% +we can do is Radio Active label the + + + align:start position:0% +we can do is Radio Active label the +probe so now we got this mixture and + + align:start position:0% +probe so now we got this mixture and + + + align:start position:0% +probe so now we got this mixture and +somewhere in this library is a piece of + + align:start position:0% +somewhere in this library is a piece of + + + align:start position:0% +somewhere in this library is a piece of +DNA that's going to have the gene that's + + align:start position:0% +DNA that's going to have the gene that's + + + align:start position:0% +DNA that's going to have the gene that's +encoding the protein that we're + + align:start position:0% +encoding the protein that we're + + + align:start position:0% +encoding the protein that we're +interested in so how do you go about + + align:start position:0% +interested in so how do you go about + + + align:start position:0% +interested in so how do you go about +trying to to deal with that + + align:start position:0% +trying to to deal with that + + + align:start position:0% +trying to to deal with that +so we'll do is our plate our eoli + + align:start position:0% +so we'll do is our plate our eoli + + + align:start position:0% +so we'll do is our plate our eoli +library onto a + + align:start position:0% +library onto a + + + align:start position:0% +library onto a +bunch of Petri plates so we'll + + align:start position:0% +bunch of Petri plates so we'll + + + align:start position:0% +bunch of Petri plates so we'll +get I won't put too many colonies on + + align:start position:0% +get I won't put too many colonies on + + + align:start position:0% +get I won't put too many colonies on +here so we can sort + + align:start position:0% +here so we can sort + + + align:start position:0% +here so we can sort +of see see a pattern um but we'd have + + align:start position:0% +of see see a pattern um but we'd have + + + align:start position:0% +of see see a pattern um but we'd have +probably a lot of them and we'd have a + + align:start position:0% +probably a lot of them and we'd have a + + + align:start position:0% +probably a lot of them and we'd have a +bunch of plates uh you can work out + + align:start position:0% +bunch of plates uh you can work out + + + align:start position:0% +bunch of plates uh you can work out +statistically how many plates you have + + align:start position:0% +statistically how many plates you have + + + align:start position:0% +statistically how many plates you have +to have to have a chance of finding your + + align:start position:0% +to have to have a chance of finding your + + + align:start position:0% +to have to have a chance of finding your +your Gene of of Interest then what we + + align:start position:0% + + + + align:start position:0% + +do lay a + + align:start position:0% + + + + align:start position:0% + +membrane on the plate it's particular + + align:start position:0% +membrane on the plate it's particular + + + align:start position:0% +membrane on the plate it's particular +type of of of membrane and what will + + align:start position:0% +type of of of membrane and what will + + + align:start position:0% +type of of of membrane and what will +that will do is it'll make a copy of + + align:start position:0% +that will do is it'll make a copy of + + + align:start position:0% +that will do is it'll make a copy of +everything that's there and we're going + + align:start position:0% +everything that's there and we're going + + + align:start position:0% +everything that's there and we're going +to save the + + align:start position:0% + + + + align:start position:0% + +plate and then we're going to treat the + + align:start position:0% +plate and then we're going to treat the + + + align:start position:0% +plate and then we're going to treat the +membrane okay we've got now for we've + + align:start position:0% +membrane okay we've got now for we've + + + align:start position:0% +membrane okay we've got now for we've +got a membrane that's + + align:start position:0% + + + + align:start position:0% + +got an identic + + align:start position:0% +got an identic + + + align:start position:0% +got an identic +pattern + + align:start position:0% + + + + align:start position:0% + +of of they've got some of the bacteria + + align:start position:0% +of of they've got some of the bacteria + + + align:start position:0% +of of they've got some of the bacteria +from the colonies stuck at the + + align:start position:0% +from the colonies stuck at the + + + align:start position:0% +from the colonies stuck at the +corresponding parts on the + + align:start position:0% + + + + align:start position:0% + +membrane we're going to lice the back + + align:start position:0% +membrane we're going to lice the back + + + align:start position:0% +membrane we're going to lice the back +the + + align:start position:0% +the + + + align:start position:0% +the +ecoli that means break them open so all + + align:start position:0% +ecoli that means break them open so all + + + align:start position:0% +ecoli that means break them open so all +their insides spill + + align:start position:0% +their insides spill + + + align:start position:0% +their insides spill +out and we will denature the DNA by + + align:start position:0% +out and we will denature the DNA by + + + align:start position:0% +out and we will denature the DNA by +treating with a condition you can for + + align:start position:0% +treating with a condition you can for + + + align:start position:0% +treating with a condition you can for +example vary the ph and then make the + + align:start position:0% +example vary the ph and then make the + + + align:start position:0% +example vary the ph and then make the +strands come + + align:start position:0% + + + + align:start position:0% + +apart that gives single stranded + + align:start position:0% + + + + align:start position:0% + +DNA SS I'm using as an abbreviation for + + align:start position:0% +DNA SS I'm using as an abbreviation for + + + align:start position:0% +DNA SS I'm using as an abbreviation for +single stranded the strands are pulled + + align:start position:0% +single stranded the strands are pulled + + + align:start position:0% +single stranded the strands are pulled +apart and this + + align:start position:0% + + + + align:start position:0% + +sticks to the + + align:start position:0% + + + + align:start position:0% + +membrane so now we've got at every one + + align:start position:0% +membrane so now we've got at every one + + + align:start position:0% +membrane so now we've got at every one +of + + align:start position:0% +of + + + align:start position:0% +of +these little position on the membrane is + + align:start position:0% +these little position on the membrane is + + + align:start position:0% +these little position on the membrane is +something that looks like this here's + + align:start position:0% +something that looks like this here's + + + align:start position:0% +something that looks like this here's +the membrane and there's some sort + + align:start position:0% +the membrane and there's some sort + + + align:start position:0% +the membrane and there's some sort +of uh single + + align:start position:0% +of uh single + + + align:start position:0% +of uh single +stranded + + align:start position:0% + + + + align:start position:0% + +DNA that's stuck to the membrane in that + + align:start position:0% +DNA that's stuck to the membrane in that + + + align:start position:0% +DNA that's stuck to the membrane in that +fashion the DNA that's stuck here came + + align:start position:0% +fashion the DNA that's stuck here came + + + align:start position:0% +fashion the DNA that's stuck here came +from the bacterium here that had a + + align:start position:0% +from the bacterium here that had a + + + align:start position:0% +from the bacterium here that had a +particular + + align:start position:0% +particular + + + align:start position:0% +particular +insert over here we have all the coli + + align:start position:0% +insert over here we have all the coli + + + align:start position:0% +insert over here we have all the coli +DNA and the vector d DNA but it will + + align:start position:0% +DNA and the vector d DNA but it will + + + align:start position:0% +DNA and the vector d DNA but it will +have a different piece of DNA in the + + align:start position:0% +have a different piece of DNA in the + + + align:start position:0% +have a different piece of DNA in the +vector everybody with me okay so if we + + align:start position:0% +vector everybody with me okay so if we + + + align:start position:0% +vector everybody with me okay so if we +were now to take + + align:start position:0% +were now to take + + + align:start position:0% +were now to take +our um radioactive probe that we made up + + align:start position:0% +our um radioactive probe that we made up + + + align:start position:0% +our um radioactive probe that we made up +there and get the conditions just right + + align:start position:0% +there and get the conditions just right + + + align:start position:0% +there and get the conditions just right +that single stranded probe will come in + + align:start position:0% +that single stranded probe will come in + + + align:start position:0% +that single stranded probe will come in +and it will try and find its complement + + align:start position:0% +and it will try and find its complement + + + align:start position:0% +and it will try and find its complement +it'll form hydrogen bonds because that's + + align:start position:0% +it'll form hydrogen bonds because that's + + + align:start position:0% +it'll form hydrogen bonds because that's +the lowest energy well in the we think + + align:start position:0% +the lowest energy well in the we think + + + align:start position:0% +the lowest energy well in the we think +about it thermodynamically and if we can + + align:start position:0% +about it thermodynamically and if we can + + + align:start position:0% +about it thermodynamically and if we can +get it right the temperature and the + + align:start position:0% +get it right the temperature and the + + + align:start position:0% +get it right the temperature and the +conditions right nothing will stick + + align:start position:0% +conditions right nothing will stick + + + align:start position:0% +conditions right nothing will stick +unless it's an exact match to the + + align:start position:0% +unless it's an exact match to the + + + align:start position:0% +unless it's an exact match to the +sequence and if we get the + + align:start position:0% +sequence and if we get the + + + align:start position:0% +sequence and if we get the +right probe that can + + align:start position:0% +right probe that can + + + align:start position:0% +right probe that can +form hydrogen + + align:start position:0% +form hydrogen + + + align:start position:0% +form hydrogen +bonds with with everything along here + + align:start position:0% +bonds with with everything along here + + + align:start position:0% +bonds with with everything along here +and it's got p32 at this point what will + + align:start position:0% +and it's got p32 at this point what will + + + align:start position:0% +and it's got p32 at this point what will +happen is we'll have now the probe will + + align:start position:0% +happen is we'll have now the probe will + + + align:start position:0% +happen is we'll have now the probe will +stick let's say to this + + align:start position:0% +stick let's say to this + + + align:start position:0% +stick let's say to this +particular uh colony and now we have + + align:start position:0% +particular uh colony and now we have + + + align:start position:0% +particular uh colony and now we have +radioactivity right there + + align:start position:0% + + + + align:start position:0% + +so put some photographic + + align:start position:0% + + + + align:start position:0% + +film over the + + align:start position:0% + + + + align:start position:0% + +membrane and right here there's p32 and + + align:start position:0% +membrane and right here there's p32 and + + + align:start position:0% +membrane and right here there's p32 and +that'll expose the film and nowhere else + + align:start position:0% +that'll expose the film and nowhere else + + + align:start position:0% +that'll expose the film and nowhere else +and then when we develop but what we'll + + align:start position:0% +and then when we develop but what we'll + + + align:start position:0% +and then when we develop but what we'll +find is + + align:start position:0% +find is + + + align:start position:0% +find is +one if this works well anyway one spot + + align:start position:0% +one if this works well anyway one spot + + + align:start position:0% +one if this works well anyway one spot +so now we know that that piece that + + align:start position:0% +so now we know that that piece that + + + align:start position:0% +so now we know that that piece that +colony had a piece of human DNA in it + + align:start position:0% +colony had a piece of human DNA in it + + + align:start position:0% +colony had a piece of human DNA in it +that was uh related to the the sequence + + align:start position:0% +that was uh related to the the sequence + + + align:start position:0% +that was uh related to the the sequence +that from the protein that I purified so + + align:start position:0% +that from the protein that I purified so + + + align:start position:0% +that from the protein that I purified so +we go back to this Colony I think I + + align:start position:0% +we go back to this Colony I think I + + + align:start position:0% +we go back to this Colony I think I +think that probably migrated around a + + align:start position:0% +think that probably migrated around a + + + align:start position:0% +think that probably migrated around a +little bit here but let's move this up + + align:start position:0% +little bit here but let's move this up + + + align:start position:0% +little bit here but let's move this up +just a little bit make it look a little + + align:start position:0% +just a little bit make it look a little + + + align:start position:0% +just a little bit make it look a little +better so this one + + align:start position:0% +better so this one + + + align:start position:0% +better so this one +is this one is this one so now I can go + + align:start position:0% +is this one is this one so now I can go + + + align:start position:0% +is this one is this one so now I can go +back to this Colony pick it out and + + align:start position:0% +back to this Colony pick it out and + + + align:start position:0% +back to this Colony pick it out and +let's say it's this insert so now I've + + align:start position:0% +let's say it's this insert so now I've + + + align:start position:0% +let's say it's this insert so now I've +found I can sequence the rest of that + + align:start position:0% +found I can sequence the rest of that + + + align:start position:0% +found I can sequence the rest of that +that piece of DNA we'll talk about how + + align:start position:0% +that piece of DNA we'll talk about how + + + align:start position:0% +that piece of DNA we'll talk about how +we sequence DNA in the next next lecture + + align:start position:0% +we sequence DNA in the next next lecture + + + align:start position:0% +we sequence DNA in the next next lecture +so that's an alternative way of of uh + + align:start position:0% +so that's an alternative way of of uh + + + align:start position:0% +so that's an alternative way of of uh +sequencing of identifying a clone of + + align:start position:0% +sequencing of identifying a clone of + + + align:start position:0% +sequencing of identifying a clone of +interest there was a particularly + + align:start position:0% +interest there was a particularly + + + align:start position:0% +interest there was a particularly +painful way + + align:start position:0% +painful way + + + align:start position:0% +painful way +of sequencing Gene uh finding a gene in + + align:start position:0% +of sequencing Gene uh finding a gene in + + + align:start position:0% +of sequencing Gene uh finding a gene in +a library that we for the most part do + + align:start position:0% +a library that we for the most part do + + + align:start position:0% +a library that we for the most part do +not have to do anymore it was called + + align:start position:0% +not have to do anymore it was called + + + align:start position:0% +not have to do anymore it was called +positional + + align:start position:0% + + + + align:start position:0% + +cloning and for example the gene for the + + align:start position:0% +cloning and for example the gene for the + + + align:start position:0% +cloning and for example the gene for the +gene that when it's broken causes Cystic + + align:start position:0% + + + + align:start position:0% + +Fibrosis uh f + + align:start position:0% +Fibrosis uh f + + + align:start position:0% +Fibrosis uh f +iosis it's a very difficult disease the + + align:start position:0% +iosis it's a very difficult disease the + + + align:start position:0% +iosis it's a very difficult disease the +humans who who have cystic fibrosis have + + align:start position:0% +humans who who have cystic fibrosis have + + + align:start position:0% +humans who who have cystic fibrosis have +very very tough time and so there was a + + align:start position:0% +very very tough time and so there was a + + + align:start position:0% +very very tough time and so there was a +great deal of interest in finding the + + align:start position:0% +great deal of interest in finding the + + + align:start position:0% +great deal of interest in finding the +gene that was broken in these patients + + align:start position:0% +gene that was broken in these patients + + + align:start position:0% +gene that was broken in these patients +now what you had human geneticists I + + align:start position:0% +now what you had human geneticists I + + + align:start position:0% +now what you had human geneticists I +showed you something about pedigrees + + align:start position:0% +showed you something about pedigrees + + + align:start position:0% +showed you something about pedigrees +they would have a a + + align:start position:0% +they would have a a + + + align:start position:0% +they would have a a +chromosome they might have banding + + align:start position:0% +chromosome they might have banding + + + align:start position:0% +chromosome they might have banding +patterns and they would have figured out + + align:start position:0% +patterns and they would have figured out + + + align:start position:0% +patterns and they would have figured out +that + + align:start position:0% +that + + + align:start position:0% +that +somewhere along this Chromo + + align:start position:0% +somewhere along this Chromo + + + align:start position:0% +somewhere along this Chromo +chromosome that the gene for Cystic F + + align:start position:0% +chromosome that the gene for Cystic F + + + align:start position:0% +chromosome that the gene for Cystic F +fibrosis lay somewhere between two + + align:start position:0% +fibrosis lay somewhere between two + + + align:start position:0% +fibrosis lay somewhere between two +genetic markers that they had identified + + align:start position:0% +genetic markers that they had identified + + + align:start position:0% +genetic markers that they had identified +now the amount of DNA between something + + align:start position:0% +now the amount of DNA between something + + + align:start position:0% +now the amount of DNA between something +that you knew what the gene was here and + + align:start position:0% +that you knew what the gene was here and + + + align:start position:0% +that you knew what the gene was here and +something you knew what the gene was + + align:start position:0% +something you knew what the gene was + + + align:start position:0% +something you knew what the gene was +there could be huge it could be many + + align:start position:0% +there could be huge it could be many + + + align:start position:0% +there could be huge it could be many +many many times the size of thecoli + + align:start position:0% +many many times the size of thecoli + + + align:start position:0% +many many times the size of thecoli +chromosome so what people would do is + + align:start position:0% +chromosome so what people would do is + + + align:start position:0% +chromosome so what people would do is +they get they clone something from here + + align:start position:0% +they get they clone something from here + + + align:start position:0% +they get they clone something from here +a little piece of DNA from there and + + align:start position:0% +a little piece of DNA from there and + + + align:start position:0% +a little piece of DNA from there and +also clone something and they get a + + align:start position:0% +also clone something and they get a + + + align:start position:0% +also clone something and they get a +little piece of DNA from there and then + + align:start position:0% +little piece of DNA from there and then + + + align:start position:0% +little piece of DNA from there and then +theyd go into the library and they try + + align:start position:0% +theyd go into the library and they try + + + align:start position:0% +theyd go into the library and they try +and find something that had this DNA and + + align:start position:0% +and find something that had this DNA and + + + align:start position:0% +and find something that had this DNA and +it and something that + + align:start position:0% +it and something that + + + align:start position:0% +it and something that +extended in this direction a little bit + + align:start position:0% +extended in this direction a little bit + + + align:start position:0% +extended in this direction a little bit +so by this sort + + align:start position:0% +so by this sort + + + align:start position:0% +so by this sort +of thing you'd have marker a somewhere + + align:start position:0% +of thing you'd have marker a somewhere + + + align:start position:0% +of thing you'd have marker a somewhere +in the middle with cystic fibrosis Gene + + align:start position:0% +in the middle with cystic fibrosis Gene + + + align:start position:0% +in the middle with cystic fibrosis Gene +but you didn't know exactly where You' + + align:start position:0% +but you didn't know exactly where You' + + + align:start position:0% +but you didn't know exactly where You' +clone a little piece of DNA and youd use + + align:start position:0% +clone a little piece of DNA and youd use + + + align:start position:0% +clone a little piece of DNA and youd use +that to find another one that overlap + + align:start position:0% +that to find another one that overlap + + + align:start position:0% +that to find another one that overlap +with it and then you'd find use that to + + align:start position:0% +with it and then you'd find use that to + + + align:start position:0% +with it and then you'd find use that to +find another piece of DNA you kind of + + align:start position:0% +find another piece of DNA you kind of + + + align:start position:0% +find another piece of DNA you kind of +walk your way over this way and youd + + align:start position:0% +walk your way over this way and youd + + + align:start position:0% +walk your way over this way and youd +start the same process at the other + + align:start position:0% +start the same process at the other + + + align:start position:0% +start the same process at the other +end and every one of + + align:start position:0% +end and every one of + + + align:start position:0% +end and every one of +these things was the same kind of + + align:start position:0% +these things was the same kind of + + + align:start position:0% +these things was the same kind of +operation that we've got here so cycles + + align:start position:0% +operation that we've got here so cycles + + + align:start position:0% +operation that we've got here so cycles +and cycles and cycles of acquiring the + + align:start position:0% +and cycles and cycles of acquiring the + + + align:start position:0% +and cycles and cycles of acquiring the +next adjacent piece of DNA and working + + align:start position:0% +next adjacent piece of DNA and working + + + align:start position:0% +next adjacent piece of DNA and working +your way along here and you had to use + + align:start position:0% +your way along here and you had to use + + + align:start position:0% +your way along here and you had to use +more than one different restrict + + align:start position:0% +more than one different restrict + + + align:start position:0% +more than one different restrict +different restriction enzymes otherwise + + align:start position:0% +different restriction enzymes otherwise + + + align:start position:0% +different restriction enzymes otherwise +you wouldn't be able to get these + + align:start position:0% +you wouldn't be able to get these + + + align:start position:0% +you wouldn't be able to get these +overlaps and by doing that eventually + + align:start position:0% +overlaps and by doing that eventually + + + align:start position:0% +overlaps and by doing that eventually +they were able to get all the DNA that + + align:start position:0% +they were able to get all the DNA that + + + align:start position:0% +they were able to get all the DNA that +was between these markers they knew the + + align:start position:0% +was between these markers they knew the + + + align:start position:0% +was between these markers they knew the +cystic fibrosis Gene was there from + + align:start position:0% +cystic fibrosis Gene was there from + + + align:start position:0% +cystic fibrosis Gene was there from +their the recombinant the maps they had + + align:start position:0% +their the recombinant the maps they had + + + align:start position:0% +their the recombinant the maps they had +made by studying human + + align:start position:0% +made by studying human + + + align:start position:0% +made by studying human +pedigrees and that was uh and then you'd + + align:start position:0% +pedigrees and that was uh and then you'd + + + align:start position:0% +pedigrees and that was uh and then you'd +start once you knew the sequence then + + align:start position:0% +start once you knew the sequence then + + + align:start position:0% +start once you knew the sequence then +You' take candidate genes and you take a + + align:start position:0% +You' take candidate genes and you take a + + + align:start position:0% +You' take candidate genes and you take a +bunch of cystic fibrosis patients and + + align:start position:0% +bunch of cystic fibrosis patients and + + + align:start position:0% +bunch of cystic fibrosis patients and +you start to see if every person who had + + align:start position:0% +you start to see if every person who had + + + align:start position:0% +you start to see if every person who had +cystic fibrosis had a mutation in that + + align:start position:0% +cystic fibrosis had a mutation in that + + + align:start position:0% +cystic fibrosis had a mutation in that +Gene and eventually they got it that + + align:start position:0% +Gene and eventually they got it that + + + align:start position:0% +Gene and eventually they got it that +process in the case of cystic + + align:start position:0% +process in the case of cystic + + + align:start position:0% +process in the case of cystic +fibrosis uh took something like it took + + align:start position:0% +fibrosis uh took something like it took + + + align:start position:0% +fibrosis uh took something like it took +five years to do that with a huge team + + align:start position:0% +five years to do that with a huge team + + + align:start position:0% +five years to do that with a huge team +of + + align:start position:0% +of + + + align:start position:0% +of +people uh and I guess it was from 1985 + + align:start position:0% +people uh and I guess it was from 1985 + + + align:start position:0% +people uh and I guess it was from 1985 +to + + align:start position:0% +to + + + align:start position:0% +to +1990 if you wanted to do that experiment + + align:start position:0% +1990 if you wanted to do that experiment + + + align:start position:0% +1990 if you wanted to do that experiment +today today we come now to probably one + + align:start position:0% +today today we come now to probably one + + + align:start position:0% +today today we come now to probably one +of the most widely used ways of finding + + align:start position:0% +of the most widely used ways of finding + + + align:start position:0% +of the most widely used ways of finding +uh a gen of interest and that is you go + + align:start position:0% +uh a gen of interest and that is you go + + + align:start position:0% +uh a gen of interest and that is you go +to your computer the whole Human Genome + + align:start position:0% +to your computer the whole Human Genome + + + align:start position:0% +to your computer the whole Human Genome +sequence is in there if we were to do + + align:start position:0% +sequence is in there if we were to do + + + align:start position:0% +sequence is in there if we were to do +that experiment today we'd say well I + + align:start position:0% +that experiment today we'd say well I + + + align:start position:0% +that experiment today we'd say well I +know what this Gene is you'd look that + + align:start position:0% +know what this Gene is you'd look that + + + align:start position:0% +know what this Gene is you'd look that +Gene up in the in the database and you + + align:start position:0% +Gene up in the in the database and you + + + align:start position:0% +Gene up in the in the database and you +knew what this Gene was you look it up + + align:start position:0% +knew what this Gene was you look it up + + + align:start position:0% +knew what this Gene was you look it up +in the database and you just look at all + + align:start position:0% +in the database and you just look at all + + + align:start position:0% +in the database and you just look at all +the the DNA that's in the middle and + + align:start position:0% +the the DNA that's in the middle and + + + align:start position:0% +the the DNA that's in the middle and +you'd see a whole series of open reading + + align:start position:0% +you'd see a whole series of open reading + + + align:start position:0% +you'd see a whole series of open reading +frames and you'd probably say well what + + align:start position:0% +frames and you'd probably say well what + + + align:start position:0% +frames and you'd probably say well what +do I know about the the co about the + + align:start position:0% +do I know about the the co about the + + + align:start position:0% +do I know about the the co about the +biology of cystic fibrosis says could I + + align:start position:0% +biology of cystic fibrosis says could I + + + align:start position:0% +biology of cystic fibrosis says could I +make a guess is it a membrane protein is + + align:start position:0% +make a guess is it a membrane protein is + + + align:start position:0% +make a guess is it a membrane protein is +it not a membrane protein and you there + + align:start position:0% +it not a membrane protein and you there + + + align:start position:0% +it not a membrane protein and you there +are certain characteristics would + + align:start position:0% +are certain characteristics would + + + align:start position:0% +are certain characteristics would +probably allow you to make a guess and + + align:start position:0% +probably allow you to make a guess and + + + align:start position:0% +probably allow you to make a guess and +then you could jump right in and start + + align:start position:0% +then you could jump right in and start + + + align:start position:0% +then you could jump right in and start +sequencing DNA a person you could do the + + align:start position:0% +sequencing DNA a person you could do the + + + align:start position:0% +sequencing DNA a person you could do the +start the experiment practically that + + align:start position:0% +start the experiment practically that + + + align:start position:0% +start the experiment practically that +afternoon instead of five years later so + + align:start position:0% +afternoon instead of five years later so + + + align:start position:0% +afternoon instead of five years later so +if you look back in the literature + + align:start position:0% +if you look back in the literature + + + align:start position:0% +if you look back in the literature +you'll find some of the key genes in in + + align:start position:0% +you'll find some of the key genes in in + + + align:start position:0% +you'll find some of the key genes in in +human fact in human biology were + + align:start position:0% +human fact in human biology were + + + align:start position:0% +human fact in human biology were +isolated by this very painful process of + + align:start position:0% +isolated by this very painful process of + + + align:start position:0% +isolated by this very painful process of +positional cloning and it's sort of you + + align:start position:0% +positional cloning and it's sort of you + + + align:start position:0% +positional cloning and it's sort of you +hardly ever have to do that now there + + align:start position:0% +hardly ever have to do that now there + + + align:start position:0% +hardly ever have to do that now there +may be the odd case where something's + + align:start position:0% +may be the odd case where something's + + + align:start position:0% +may be the odd case where something's +needed but most of the stuff now there + + align:start position:0% +needed but most of the stuff now there + + + align:start position:0% +needed but most of the stuff now there +are these amazing databases um and I'll + + align:start position:0% +are these amazing databases um and I'll + + + align:start position:0% +are these amazing databases um and I'll +give you the the open the um URL for at + + align:start position:0% +give you the the open the um URL for at + + + align:start position:0% +give you the the open the um URL for at +the beginning of of next + + align:start position:0% +the beginning of of next + + + align:start position:0% +the beginning of of next +lecture and I'll show you when I had the + + align:start position:0% +lecture and I'll show you when I had the + + + align:start position:0% +lecture and I'll show you when I had the +uh if you this is some an experiment in + + align:start position:0% +uh if you this is some an experiment in + + + align:start position:0% +uh if you this is some an experiment in +which someone took this Gene for Cystic + + align:start position:0% +which someone took this Gene for Cystic + + + align:start position:0% +which someone took this Gene for Cystic +Fibrosis it is a membrane protein and + + align:start position:0% +Fibrosis it is a membrane protein and + + + align:start position:0% +Fibrosis it is a membrane protein and +it's one of those proteins that mediates + + align:start position:0% +it's one of those proteins that mediates + + + align:start position:0% +it's one of those proteins that mediates +the passage of I across a a channel CH + + align:start position:0% +the passage of I across a a channel CH + + + align:start position:0% +the passage of I across a a channel CH +chloride ions across the uh across the + + align:start position:0% +chloride ions across the uh across the + + + align:start position:0% +chloride ions across the uh across the +membrane and if you if that gets broken + + align:start position:0% +membrane and if you if that gets broken + + + align:start position:0% +membrane and if you if that gets broken +you end up cystic fibrosis what someone + + align:start position:0% +you end up cystic fibrosis what someone + + + align:start position:0% +you end up cystic fibrosis what someone +done has done here is they've taken that + + align:start position:0% +done has done here is they've taken that + + + align:start position:0% +done has done here is they've taken that +green fuorescent protein Gene and they + + align:start position:0% +green fuorescent protein Gene and they + + + align:start position:0% +green fuorescent protein Gene and they +fused it to the end of the cystic + + align:start position:0% +fused it to the end of the cystic + + + align:start position:0% +fused it to the end of the cystic +fibrosis Gene so you can tell where the + + align:start position:0% +fibrosis Gene so you can tell where the + + + align:start position:0% +fibrosis Gene so you can tell where the +cystic fibrosis Gene is localized in a + + align:start position:0% +cystic fibrosis Gene is localized in a + + + align:start position:0% +cystic fibrosis Gene is localized in a +lung cell by looking to see where the + + align:start position:0% +lung cell by looking to see where the + + + align:start position:0% +lung cell by looking to see where the +fluoresence is and I think you can see + + align:start position:0% +fluoresence is and I think you can see + + + align:start position:0% +fluoresence is and I think you can see +that the fluoresence is out there along + + align:start position:0% +that the fluoresence is out there along + + + align:start position:0% +that the fluoresence is out there along +the um + + align:start position:0% +the um + + + align:start position:0% +the um +along the uh + + align:start position:0% +along the uh + + + align:start position:0% +along the uh +membrane okay so uh at the beginning of + + align:start position:0% +membrane okay so uh at the beginning of + + + align:start position:0% +membrane okay so uh at the beginning of +uh next lecture I'll introduce you to + + align:start position:0% +uh next lecture I'll introduce you to + + + align:start position:0% +uh next lecture I'll introduce you to +how we take one of these recombinant uh + + align:start position:0% +how we take one of these recombinant uh + + + align:start position:0% +how we take one of these recombinant uh +plasmids and make what's called a + + align:start position:0% +plasmids and make what's called a + + + align:start position:0% +plasmids and make what's called a +restriction map it's using a very simple + + align:start position:0% +restriction map it's using a very simple + + + align:start position:0% +restriction map it's using a very simple +little piece of apparatus like that and + + align:start position:0% +little piece of apparatus like that and + + + align:start position:0% +little piece of apparatus like that and +we'll go in and tell you about DNA + + align:start position:0% +we'll go in and tell you about DNA + + + align:start position:0% +we'll go in and tell you about DNA +sequencing and this PCR technique you've + + align:start position:0% +sequencing and this PCR technique you've + + + align:start position:0% +sequencing and this PCR technique you've +heard pmer Chain Reaction you've heard + + align:start position:0% +heard pmer Chain Reaction you've heard + + + align:start position:0% +heard pmer Chain Reaction you've heard +so much about + + align:start position:0% +so much about + + + align:start position:0% +so much about +okay \ No newline at end of file diff --git a/5hUX2Z5ffF0.txt b/5hUX2Z5ffF0.txt new file mode 100644 index 0000000000000000000000000000000000000000..14ca47604e4a27b7559dfb852d32086658642023 --- /dev/null +++ b/5hUX2Z5ffF0.txt @@ -0,0 +1,123 @@ +At one point, I realized that I was teaching +the course in a way that was sort of timeless. + +And it's really about, I really wanted to +think about it much more in a way that was + +set in context - of today and the history +of education in the past. + +And I wanted to do that in a way that felt +like, again I was embodying the constructivist + +principles that I really think are important +to learning. + +And so the first thing I brought in was Current +Events. + +I wanted students to bring in, to understand +what's going on in the world of education + +today because it's changing very rapidly in +terms of what we know about teaching and learning, + +what technologies we're using for teaching +and learning, and the policies surrounding + +all this, and people's attitudes towards it. + +So rather than sort of me... sort of telling +them about this, I wanted the students to + +take some ownership over that, and we brought +in Current Events. + +And so students... + +investigate current events, choose things +that are important and meaningful to them, + +and bring it into the classroom for discussion. + +And then, over time, we've sort of changed +the way that we do that, so that we think + +about the ways that - can we use the online +components more effectively so that students + +are doing some of the... thinking about the +issues before they get to class, and then + +use the class time for something that's unique? + +For the Current Events, we actually think +that there's enough that you can get out of + +an article and some questions online and some +online forums so that actually some of that + +conversation can happen before they even get +to class. + +So, in those cases, there's a current events +article that goes up - usually relatively + +short - and some questions that are posed +with it, and students need to read the article + +and respond to those questions. + +And then what happens in class is a follow-up +to that. + +So sometimes there's themes that happened +in student responses. + +Sometimes there's an issue raised that was, +that maybe the people who were responsible + +for the Current Events that week didn't think +of in advance. + +And that's a chance to kind of follow up on +some of that. + +And this year actually for the first time +we were actually saw, started seeing some + +groups do some interesting activities that +were follow-ups to those as well. + +Not just pure discussion, but activities that +sort of brought out some of the big issues, + +or sort of pointed out some similar thinking +or dissimilar thinking that was happening + +in the class. + +There was some that were sort of like voting +with your feet. + +So it was a matter of like looking at distributions +on... in terms of viewpoints on issues, where, + +you know, people who thought like "Yes" about +one issue and "No" about one issue went to + +different sides of the room. + +And then there was some debate around the +issues around there. + +So it was a nice way to sort of call out, +"OK, there's distributions on issues. + +There's people that think different things +about this, but there's reasons for that, + +and let's have some dialogue within people +that have common thoughts, and people who + +have disparate thoughts as well." \ No newline at end of file diff --git a/5oLLnCGStUc.txt b/5oLLnCGStUc.txt new file mode 100644 index 0000000000000000000000000000000000000000..f1562e141d2a4691fd867055b0299765d3c1b259 --- /dev/null +++ b/5oLLnCGStUc.txt @@ -0,0 +1,2179 @@ +align:start position:0% + +now we've been discussing steady uniform + + align:start position:0% +now we've been discussing steady uniform + + + align:start position:0% +now we've been discussing steady uniform +procession which is the simplest + + align:start position:0% +procession which is the simplest + + + align:start position:0% +procession which is the simplest +possible case of a phenomenon that can + + align:start position:0% +possible case of a phenomenon that can + + + align:start position:0% +possible case of a phenomenon that can +be much more complicated as an example + + align:start position:0% +be much more complicated as an example + + + align:start position:0% +be much more complicated as an example +in the case we've been discussing so far + + align:start position:0% +in the case we've been discussing so far + + + align:start position:0% +in the case we've been discussing so far +where we release a gyroscope from rest + + align:start position:0% +where we release a gyroscope from rest + + + align:start position:0% +where we release a gyroscope from rest +uh when it's horizontal very careful + + align:start position:0% +uh when it's horizontal very careful + + + align:start position:0% +uh when it's horizontal very careful +measurements would show that the initial + + align:start position:0% +measurements would show that the initial + + + align:start position:0% +measurements would show that the initial +motion isn't just steady procession but + + align:start position:0% +motion isn't just steady procession but + + + align:start position:0% +motion isn't just steady procession but +has some additional motion superimposed + + align:start position:0% +has some additional motion superimposed + + + align:start position:0% +has some additional motion superimposed +on it um the spin axis sort of bounces + + align:start position:0% +on it um the spin axis sort of bounces + + + align:start position:0% +on it um the spin axis sort of bounces +or nods up and down as it processes + + align:start position:0% +or nods up and down as it processes + + + align:start position:0% +or nods up and down as it processes +however friction at the Pivot Point + + align:start position:0% +however friction at the Pivot Point + + + align:start position:0% +however friction at the Pivot Point +causes the amplitude of the nodding to + + align:start position:0% +causes the amplitude of the nodding to + + + align:start position:0% +causes the amplitude of the nodding to +rapidly Decay until it settles into + + align:start position:0% +rapidly Decay until it settles into + + + align:start position:0% +rapidly Decay until it settles into +steady procession this nodding motion is + + align:start position:0% +steady procession this nodding motion is + + + align:start position:0% +steady procession this nodding motion is +called mutation in our example it decays + + align:start position:0% +called mutation in our example it decays + + + align:start position:0% +called mutation in our example it decays +so quickly that we don't even notice it + + align:start position:0% +so quickly that we don't even notice it + + + align:start position:0% +so quickly that we don't even notice it +but if you had a perfectly frictionless + + align:start position:0% +but if you had a perfectly frictionless + + + align:start position:0% +but if you had a perfectly frictionless +pivot point it would be it would be a + + align:start position:0% +pivot point it would be it would be a + + + align:start position:0% +pivot point it would be it would be a +more noticeable effect and it would + + align:start position:0% +more noticeable effect and it would + + + align:start position:0% +more noticeable effect and it would +persist for much + + align:start position:0% +persist for much + + + align:start position:0% +persist for much +longer now there's an interesting point + + align:start position:0% +longer now there's an interesting point + + + align:start position:0% +longer now there's an interesting point +about our horizontal gyroscope that I'd + + align:start position:0% +about our horizontal gyroscope that I'd + + + align:start position:0% +about our horizontal gyroscope that I'd +like to point + + align:start position:0% + + + + align:start position:0% + +out so here's my rod of length D this is + + align:start position:0% +out so here's my rod of length D this is + + + align:start position:0% +out so here's my rod of length D this is +my point + + align:start position:0% +my point + + + align:start position:0% +my point +s here's my wheel that's rotating with + + align:start position:0% +s here's my wheel that's rotating with + + + align:start position:0% +s here's my wheel that's rotating with +some angular + + align:start position:0% +some angular + + + align:start position:0% +some angular +velocity and + + align:start position:0% +velocity and + + + align:start position:0% +velocity and +again there's the r hat Direction that's + + align:start position:0% +again there's the r hat Direction that's + + + align:start position:0% +again there's the r hat Direction that's +the direction that little Omega Vector + + align:start position:0% +the direction that little Omega Vector + + + align:start position:0% +the direction that little Omega Vector +is pointing in that's the K hat + + align:start position:0% +is pointing in that's the K hat + + + align:start position:0% +is pointing in that's the K hat +Direction + + align:start position:0% +Direction + + + align:start position:0% +Direction +and that's the Theta hat + + align:start position:0% +and that's the Theta hat + + + align:start position:0% +and that's the Theta hat +Direction now before I release it before + + align:start position:0% +Direction now before I release it before + + + align:start position:0% +Direction now before I release it before +I release this jcope from rest the + + align:start position:0% +I release this jcope from rest the + + + align:start position:0% +I release this jcope from rest the +angular of momentum Vector points in the + + align:start position:0% +angular of momentum Vector points in the + + + align:start position:0% +angular of momentum Vector points in the +r hat direction as drawn at this + + align:start position:0% +r hat direction as drawn at this + + + align:start position:0% +r hat direction as drawn at this +instant when I release it from rest + + align:start position:0% +instant when I release it from rest + + + align:start position:0% +instant when I release it from rest +there is a torque acting in the Theta + + align:start position:0% +there is a torque acting in the Theta + + + align:start position:0% +there is a torque acting in the Theta +hat direction that causes the angular + + align:start position:0% +hat direction that causes the angular + + + align:start position:0% +hat direction that causes the angular +momentum Vector to rotate and we've seen + + align:start position:0% +momentum Vector to rotate and we've seen + + + align:start position:0% +momentum Vector to rotate and we've seen +this in some + + align:start position:0% +this in some + + + align:start position:0% +this in some +detail but there's something else to + + align:start position:0% +detail but there's something else to + + + align:start position:0% +detail but there's something else to +keep in mind which is that now when the + + align:start position:0% +keep in mind which is that now when the + + + align:start position:0% +keep in mind which is that now when the +system is processing that means that the + + align:start position:0% +system is processing that means that the + + + align:start position:0% +system is processing that means that the +center of mass of the wheel is orbiting + + align:start position:0% +center of mass of the wheel is orbiting + + + align:start position:0% +center of mass of the wheel is orbiting +around the z-axis the vertical axis + + align:start position:0% +around the z-axis the vertical axis + + + align:start position:0% +around the z-axis the vertical axis +through this Pivot + + align:start position:0% +through this Pivot + + + align:start position:0% +through this Pivot +Point okay so you can think of that as a + + align:start position:0% +Point okay so you can think of that as a + + + align:start position:0% +Point okay so you can think of that as a +point Mass with the full mass of + + align:start position:0% +point Mass with the full mass of + + + align:start position:0% +point Mass with the full mass of +the gyroscope moving in a circular path + + align:start position:0% +the gyroscope moving in a circular path + + + align:start position:0% +the gyroscope moving in a circular path +around Point s with a radius + + align:start position:0% +around Point s with a radius + + + align:start position:0% +around Point s with a radius +D that implies that there must be a + + align:start position:0% +D that implies that there must be a + + + align:start position:0% +D that implies that there must be a +component of angular + + align:start position:0% +component of angular + + + align:start position:0% +component of angular +momentum pointing in the K hat Direction + + align:start position:0% +momentum pointing in the K hat Direction + + + align:start position:0% +momentum pointing in the K hat Direction +pointing along the z-axis corresponding + + align:start position:0% +pointing along the z-axis corresponding + + + align:start position:0% +pointing along the z-axis corresponding +to the translational motion of the + + align:start position:0% +to the translational motion of the + + + align:start position:0% +to the translational motion of the +center of mass a circular translational + + align:start position:0% +center of mass a circular translational + + + align:start position:0% +center of mass a circular translational +motion of the center of mass of the + + align:start position:0% +motion of the center of mass of the + + + align:start position:0% +motion of the center of mass of the +gyroscope around the + + align:start position:0% +gyroscope around the + + + align:start position:0% +gyroscope around the +z-axis but where did that K component + + align:start position:0% +z-axis but where did that K component + + + align:start position:0% +z-axis but where did that K component +come from there was no initial Z + + align:start position:0% +come from there was no initial Z + + + align:start position:0% +come from there was no initial Z +component of the angular momentum we + + align:start position:0% +component of the angular momentum we + + + align:start position:0% +component of the angular momentum we +said that initially the angular momentum + + align:start position:0% +said that initially the angular momentum + + + align:start position:0% +said that initially the angular momentum +just pointed in the r hat Direction and + + align:start position:0% +just pointed in the r hat Direction and + + + align:start position:0% +just pointed in the r hat Direction and +there's no torque in the K hat Direction + + align:start position:0% +there's no torque in the K hat Direction + + + align:start position:0% +there's no torque in the K hat Direction +the only torque is in the Theta hat + + align:start position:0% +the only torque is in the Theta hat + + + align:start position:0% +the only torque is in the Theta hat +Direction so how do we end up with some + + align:start position:0% +Direction so how do we end up with some + + + align:start position:0% +Direction so how do we end up with some +angular momentum pointing in the K hat + + align:start position:0% +angular momentum pointing in the K hat + + + align:start position:0% +angular momentum pointing in the K hat +Direction this seems to violate the + + align:start position:0% +Direction this seems to violate the + + + align:start position:0% +Direction this seems to violate the +conservation of angular + + align:start position:0% +conservation of angular + + + align:start position:0% +conservation of angular +momentum the solution to this puzzle is + + align:start position:0% +momentum the solution to this puzzle is + + + align:start position:0% +momentum the solution to this puzzle is +that in fact the gyroscope doesn't + + align:start position:0% +that in fact the gyroscope doesn't + + + align:start position:0% +that in fact the gyroscope doesn't +remain precisely horizontal when I + + align:start position:0% +remain precisely horizontal when I + + + align:start position:0% +remain precisely horizontal when I +release it instead + + align:start position:0% +release it instead + + + align:start position:0% +release it instead +it dips by a very small angle so that's + + align:start position:0% +it dips by a very small angle so that's + + + align:start position:0% +it dips by a very small angle so that's +the horizontal after I release it the + + align:start position:0% +the horizontal after I release it the + + + align:start position:0% +the horizontal after I release it the +gyroscopes actually dipped downward by a + + align:start position:0% +gyroscopes actually dipped downward by a + + + align:start position:0% +gyroscopes actually dipped downward by a +small amount I've exaggerated it + + align:start position:0% +small amount I've exaggerated it + + + align:start position:0% +small amount I've exaggerated it +considerably in this drawing call that + + align:start position:0% +considerably in this drawing call that + + + align:start position:0% +considerably in this drawing call that +angle Delta + + align:start position:0% + + + + align:start position:0% + +Theta that small dip gives a small + + align:start position:0% +Theta that small dip gives a small + + + align:start position:0% +Theta that small dip gives a small +negative component of the spin angular + + align:start position:0% +negative component of the spin angular + + + align:start position:0% +negative component of the spin angular +momentum that's able to balance the plus + + align:start position:0% +momentum that's able to balance the plus + + + align:start position:0% +momentum that's able to balance the plus +Z angular momentum due to the motion of + + align:start position:0% +Z angular momentum due to the motion of + + + align:start position:0% +Z angular momentum due to the motion of +the center of mass now because the spin + + align:start position:0% +the center of mass now because the spin + + + align:start position:0% +the center of mass now because the spin +angular momentum Vector has such a large + + align:start position:0% + + + + align:start position:0% + +magnitude that's my spin angular + + align:start position:0% +magnitude that's my spin angular + + + align:start position:0% +magnitude that's my spin angular +momentum + + align:start position:0% + + + + align:start position:0% + +Vector only a small angle is necessary + + align:start position:0% +Vector only a small angle is necessary + + + align:start position:0% +Vector only a small angle is necessary +in order to get enough of a negative LZ + + align:start position:0% +in order to get enough of a negative LZ + + + align:start position:0% +in order to get enough of a negative LZ +component to balance out the LZ + + align:start position:0% +component to balance out the LZ + + + align:start position:0% +component to balance out the LZ +corresponding to the center of mass + + align:start position:0% +corresponding to the center of mass + + + align:start position:0% +corresponding to the center of mass +motion + + align:start position:0% +motion + + + align:start position:0% +motion +okay but what we see is that although + + align:start position:0% +okay but what we see is that although + + + align:start position:0% +okay but what we see is that although +gyroscopes seem like a + + align:start position:0% +gyroscopes seem like a + + + align:start position:0% +gyroscopes seem like a +remarkable system they're not magic and + + align:start position:0% +remarkable system they're not magic and + + + align:start position:0% +remarkable system they're not magic and +in fact angular momentum is + + align:start position:0% + + + + align:start position:0% + +conserved the faster little Omega the + + align:start position:0% +conserved the faster little Omega the + + + align:start position:0% +conserved the faster little Omega the +larger little Omega is the faster the + + align:start position:0% +larger little Omega is the faster the + + + align:start position:0% +larger little Omega is the faster the +spin angular momentum uh spin angular + + align:start position:0% +spin angular momentum uh spin angular + + + align:start position:0% +spin angular momentum uh spin angular +velocity is and therefore the larger the + + align:start position:0% +velocity is and therefore the larger the + + + align:start position:0% +velocity is and therefore the larger the +vector L is the smaller that angle is + + align:start position:0% +vector L is the smaller that angle is + + + align:start position:0% +vector L is the smaller that angle is +and the L of a dip that you + + align:start position:0% +and the L of a dip that you + + + align:start position:0% +and the L of a dip that you +get so now we can write the exact + + align:start position:0% +get so now we can write the exact + + + align:start position:0% +get so now we can write the exact +angular momentum for the + + align:start position:0% + + + + align:start position:0% + +gyroscope this is my distance D this is + + align:start position:0% +gyroscope this is my distance D this is + + + align:start position:0% +gyroscope this is my distance D this is +my Pivot Point + + align:start position:0% + + + + align:start position:0% + +s my spin angular velocity looks like + + align:start position:0% +s my spin angular velocity looks like + + + align:start position:0% +s my spin angular velocity looks like +that here's the r hat Direction + + align:start position:0% + + + + align:start position:0% + +the K hat Direction and The Theta hat + + align:start position:0% +the K hat Direction and The Theta hat + + + align:start position:0% +the K hat Direction and The Theta hat +Direction into the + + align:start position:0% +Direction into the + + + align:start position:0% +Direction into the +screen and we're + + align:start position:0% +screen and we're + + + align:start position:0% +screen and we're +orbiting the procession is around the + + align:start position:0% +orbiting the procession is around the + + + align:start position:0% +orbiting the procession is around the +z-axis with an angular speed Capital + + align:start position:0% +z-axis with an angular speed Capital + + + align:start position:0% +z-axis with an angular speed Capital +Omega now recall + + align:start position:0% +Omega now recall + + + align:start position:0% +Omega now recall +that the total angular momentum with + + align:start position:0% +that the total angular momentum with + + + align:start position:0% +that the total angular momentum with +respect to point s can be + + align:start position:0% +respect to point s can be + + + align:start position:0% +respect to point s can be +written in two + + align:start position:0% +written in two + + + align:start position:0% +written in two +parts there's the the angular momentum + + align:start position:0% +parts there's the the angular momentum + + + align:start position:0% +parts there's the the angular momentum +due to the translational motion of the + + align:start position:0% +due to the translational motion of the + + + align:start position:0% +due to the translational motion of the +center of mass now we know the center of + + align:start position:0% +center of mass now we know the center of + + + align:start position:0% +center of mass now we know the center of +mass is just orbiting around the z-axis + + align:start position:0% +mass is just orbiting around the z-axis + + + align:start position:0% +mass is just orbiting around the z-axis +so I'll call that in + + align:start position:0% +so I'll call that in + + + align:start position:0% +so I'll call that in +fact the orbital angular + + align:start position:0% +fact the orbital angular + + + align:start position:0% +fact the orbital angular +momentum so this is due to the + + align:start position:0% +momentum so this is due to the + + + align:start position:0% +momentum so this is due to the +translation of the center of mass with + + align:start position:0% +translation of the center of mass with + + + align:start position:0% +translation of the center of mass with +respect to point s and then the second + + align:start position:0% +respect to point s and then the second + + + align:start position:0% +respect to point s and then the second +term + + align:start position:0% + + + + align:start position:0% + +is due to the rotational angular + + align:start position:0% +is due to the rotational angular + + + align:start position:0% +is due to the rotational angular +momentum or spin angular + + align:start position:0% + + + + align:start position:0% + +momentum relative to the center of mass + + align:start position:0% +momentum relative to the center of mass + + + align:start position:0% +momentum relative to the center of mass +so this is due + + align:start position:0% + + + + align:start position:0% + +to rotation + + align:start position:0% +to rotation + + + align:start position:0% +to rotation +about the center of mass so again the + + align:start position:0% +about the center of mass so again the + + + align:start position:0% +about the center of mass so again the +general angular momentum of a rigid body + + align:start position:0% +general angular momentum of a rigid body + + + align:start position:0% +general angular momentum of a rigid body +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +the center of mass translational angular + + align:start position:0% +the center of mass translational angular + + + align:start position:0% +the center of mass translational angular +momentum + + align:start position:0% +momentum + + + align:start position:0% +momentum +plus the angular momentum due to + + align:start position:0% +plus the angular momentum due to + + + align:start position:0% +plus the angular momentum due to +rotation a pure rotation about the + + align:start position:0% +rotation a pure rotation about the + + + align:start position:0% +rotation a pure rotation about the +center of mass so let's write each of + + align:start position:0% +center of mass so let's write each of + + + align:start position:0% +center of mass so let's write each of +these + + align:start position:0% +these + + + align:start position:0% +these +terms the orbital angular + + align:start position:0% + + + + align:start position:0% + +momentum that is the translational + + align:start position:0% +momentum that is the translational + + + align:start position:0% +momentum that is the translational +angular momentum and the center of mass + + align:start position:0% +angular momentum and the center of mass + + + align:start position:0% +angular momentum and the center of mass +is just due to the motion of the center + + align:start position:0% +is just due to the motion of the center + + + align:start position:0% +is just due to the motion of the center +of mass of the + + align:start position:0% +of mass of the + + + align:start position:0% +of mass of the +gyroscope which is at radius D with + + align:start position:0% +gyroscope which is at radius D with + + + align:start position:0% +gyroscope which is at radius D with +respect to point s moving in a circle + + align:start position:0% +respect to point s moving in a circle + + + align:start position:0% +respect to point s moving in a circle +with angular speed Capital + + align:start position:0% +with angular speed Capital + + + align:start position:0% +with angular speed Capital +Omega okay so that's equal + + align:start position:0% +Omega okay so that's equal + + + align:start position:0% +Omega okay so that's equal +to the + + align:start position:0% +to the + + + align:start position:0% +to the +masstimes the center of mass + + align:start position:0% +masstimes the center of mass + + + align:start position:0% +masstimes the center of mass +velocity times the radius of the + + align:start position:0% +velocity times the radius of the + + + align:start position:0% +velocity times the radius of the +circle and that angular momentum is in + + align:start position:0% +circle and that angular momentum is in + + + align:start position:0% +circle and that angular momentum is in +the K hat Direction but the center of + + align:start position:0% +the K hat Direction but the center of + + + align:start position:0% +the K hat Direction but the center of +mass velocity is just equal to since + + align:start position:0% +mass velocity is just equal to since + + + align:start position:0% +mass velocity is just equal to since +it's a circular motion is just equal to + + align:start position:0% +it's a circular motion is just equal to + + + align:start position:0% +it's a circular motion is just equal to +the radius of the circle D times the + + align:start position:0% +the radius of the circle D times the + + + align:start position:0% +the radius of the circle D times the +angular speed of the circle motion of + + align:start position:0% +angular speed of the circle motion of + + + align:start position:0% +angular speed of the circle motion of +the center of mass which is capital + + align:start position:0% +the center of mass which is capital + + + align:start position:0% +the center of mass which is capital +Omega so I can write + + align:start position:0% +Omega so I can write + + + align:start position:0% +Omega so I can write +this + + align:start position:0% +this + + + align:start position:0% +this +as + + align:start position:0% +as + + + align:start position:0% +as +m capital Omega + + align:start position:0% +m capital Omega + + + align:start position:0% +m capital Omega +d^2 in the K hat Direction so that's the + + align:start position:0% +d^2 in the K hat Direction so that's the + + + align:start position:0% +d^2 in the K hat Direction so that's the +angular momentum due to the + + align:start position:0% +angular momentum due to the + + + align:start position:0% +angular momentum due to the +translational motion of the center of + + align:start position:0% +translational motion of the center of + + + align:start position:0% +translational motion of the center of +mass around Point s what I'm calling the + + align:start position:0% +mass around Point s what I'm calling the + + + align:start position:0% +mass around Point s what I'm calling the +orbital angular + + align:start position:0% +orbital angular + + + align:start position:0% +orbital angular +momentum now the spin angular momentum + + align:start position:0% + + + + align:start position:0% + +we've been talking about the rapid spin + + align:start position:0% +we've been talking about the rapid spin + + + align:start position:0% +we've been talking about the rapid spin +of the wheel around its + + align:start position:0% +of the wheel around its + + + align:start position:0% +of the wheel around its +axis so that's given + + align:start position:0% +axis so that's given + + + align:start position:0% +axis so that's given +by the moment of inertia about that axis + + align:start position:0% +by the moment of inertia about that axis + + + align:start position:0% +by the moment of inertia about that axis +times the spin angular velocity and + + align:start position:0% +times the spin angular velocity and + + + align:start position:0% +times the spin angular velocity and +that's pointing in the r hat + + align:start position:0% +that's pointing in the r hat + + + align:start position:0% +that's pointing in the r hat +Direction but there's a subtlety here it + + align:start position:0% +Direction but there's a subtlety here it + + + align:start position:0% +Direction but there's a subtlety here it +points out it turns out that that is not + + align:start position:0% +points out it turns out that that is not + + + align:start position:0% +points out it turns out that that is not +the only rotation about the center of + + align:start position:0% +the only rotation about the center of + + + align:start position:0% +the only rotation about the center of +mass that this wheel is undergoing and + + align:start position:0% +mass that this wheel is undergoing and + + + align:start position:0% +mass that this wheel is undergoing and +actually because of that I'm going to + + align:start position:0% +actually because of that I'm going to + + + align:start position:0% +actually because of that I'm going to +call this + + align:start position:0% +call this + + + align:start position:0% +call this +i1 and let me just draw a picture here + + align:start position:0% +i1 and let me just draw a picture here + + + align:start position:0% +i1 and let me just draw a picture here +so + + align:start position:0% + + + + align:start position:0% + +for my + + align:start position:0% +for my + + + align:start position:0% +for my +dis rotating + + align:start position:0% + + + + align:start position:0% + +around this axis the relevant moment of + + align:start position:0% +around this axis the relevant moment of + + + align:start position:0% +around this axis the relevant moment of +inertia is what I'll call i1 and for a + + align:start position:0% +inertia is what I'll call i1 and for a + + + align:start position:0% +inertia is what I'll call i1 and for a +disc we know that would be 12 m r + + align:start position:0% + + + + align:start position:0% + +2 the other + + align:start position:0% +2 the other + + + align:start position:0% +2 the other +rotation is a subtle one notice in this + + align:start position:0% +rotation is a subtle one notice in this + + + align:start position:0% +rotation is a subtle one notice in this +drawing suppose I were to draw a DOT on + + align:start position:0% +drawing suppose I were to draw a DOT on + + + align:start position:0% +drawing suppose I were to draw a DOT on +the outside + + align:start position:0% +the outside + + + align:start position:0% +the outside +face of the + + align:start position:0% + + + + align:start position:0% + +wheel when this wheel processed around + + align:start position:0% +wheel when this wheel processed around + + + align:start position:0% +wheel when this wheel processed around +180° to the other + + align:start position:0% +180° to the other + + + align:start position:0% +180° to the other +side that out that dot on the outside + + align:start position:0% +side that out that dot on the outside + + + align:start position:0% +side that out that dot on the outside +would be facing in the minus r hat + + align:start position:0% +would be facing in the minus r hat + + + align:start position:0% +would be facing in the minus r hat +Direction now or would be pointing in to + + align:start position:0% +Direction now or would be pointing in to + + + align:start position:0% +Direction now or would be pointing in to +the left rather than to the + + align:start position:0% +the left rather than to the + + + align:start position:0% +the left rather than to the +right and what that means is that this + + align:start position:0% +right and what that means is that this + + + align:start position:0% +right and what that means is that this +disc has actually rotated about its + + align:start position:0% +disc has actually rotated about its + + + align:start position:0% +disc has actually rotated about its +diameter so this + + align:start position:0% + + + + align:start position:0% + +dis has + + align:start position:0% +dis has + + + align:start position:0% +dis has +rotated around a diameter like this and + + align:start position:0% +rotated around a diameter like this and + + + align:start position:0% +rotated around a diameter like this and +that rotation is at the slower angular + + align:start position:0% +that rotation is at the slower angular + + + align:start position:0% +that rotation is at the slower angular +speed Capital Omega + + align:start position:0% +speed Capital Omega + + + align:start position:0% +speed Capital Omega +okay and it takes one full orbit for it + + align:start position:0% +okay and it takes one full orbit for it + + + align:start position:0% +okay and it takes one full orbit for it +to rotate entirely around if that + + align:start position:0% +to rotate entirely around if that + + + align:start position:0% +to rotate entirely around if that +rotation weren't + + align:start position:0% +rotation weren't + + + align:start position:0% +rotation weren't +happening it wouldn't this wouldn't make + + align:start position:0% +happening it wouldn't this wouldn't make + + + align:start position:0% +happening it wouldn't this wouldn't make +sense physically the way I have the set + + align:start position:0% +sense physically the way I have the set + + + align:start position:0% +sense physically the way I have the set +up but as an object if that rotation + + align:start position:0% +up but as an object if that rotation + + + align:start position:0% +up but as an object if that rotation +weren't happening what that would mean + + align:start position:0% +weren't happening what that would mean + + + align:start position:0% +weren't happening what that would mean +is + + align:start position:0% +is + + + align:start position:0% +is +that this face with the dot on it would + + align:start position:0% +that this face with the dot on it would + + + align:start position:0% +that this face with the dot on it would +always be pointing to the right as the + + align:start position:0% +always be pointing to the right as the + + + align:start position:0% +always be pointing to the right as the +dis moved around if it had an + + align:start position:0% +dis moved around if it had an + + + align:start position:0% +dis moved around if it had an +independent Pivot Point right at the + + align:start position:0% +independent Pivot Point right at the + + + align:start position:0% +independent Pivot Point right at the +center it would be physically possible + + align:start position:0% +center it would be physically possible + + + align:start position:0% +center it would be physically possible +for it to do that that's not what's + + align:start position:0% +for it to do that that's not what's + + + align:start position:0% +for it to do that that's not what's +happening in this case in this case this + + align:start position:0% +happening in this case in this case this + + + align:start position:0% +happening in this case in this case this +face is always pointing outward radially + + align:start position:0% +face is always pointing outward radially + + + align:start position:0% +face is always pointing outward radially +away from the pivot point and that + + align:start position:0% +away from the pivot point and that + + + align:start position:0% +away from the pivot point and that +results in a rotation around this + + align:start position:0% +results in a rotation around this + + + align:start position:0% +results in a rotation around this +diameter now turns out that moment of + + align:start position:0% +diameter now turns out that moment of + + + align:start position:0% +diameter now turns out that moment of +inertia which I'll call + + align:start position:0% +inertia which I'll call + + + align:start position:0% +inertia which I'll call +I2 happens to be half the moment of + + align:start position:0% +I2 happens to be half the moment of + + + align:start position:0% +I2 happens to be half the moment of +inertia for this axis so in this case + + align:start position:0% +inertia for this axis so in this case + + + align:start position:0% +inertia for this axis so in this case +it's + + align:start position:0% + + + + align:start position:0% + +1/4 Mr + + align:start position:0% +1/4 Mr + + + align:start position:0% +1/4 Mr +squ okay so that is another kind of + + align:start position:0% +squ okay so that is another kind of + + + align:start position:0% +squ okay so that is another kind of +rotation + + align:start position:0% +rotation + + + align:start position:0% +rotation +that's happening about Center of mass + + align:start position:0% +that's happening about Center of mass + + + align:start position:0% +that's happening about Center of mass +and so there's an additional angular + + align:start position:0% +and so there's an additional angular + + + align:start position:0% +and so there's an additional angular +momentum + + align:start position:0% +momentum + + + align:start position:0% +momentum +term arising from that + + align:start position:0% +term arising from that + + + align:start position:0% +term arising from that +rotation and that's equal + + align:start position:0% +rotation and that's equal + + + align:start position:0% +rotation and that's equal +to I2 time the angular velocity of that + + align:start position:0% +to I2 time the angular velocity of that + + + align:start position:0% +to I2 time the angular velocity of that +rotation which is capital + + align:start position:0% +rotation which is capital + + + align:start position:0% +rotation which is capital +Omega and because the axis there is the + + align:start position:0% +Omega and because the axis there is the + + + align:start position:0% +Omega and because the axis there is the +z-axis this is + + align:start position:0% +z-axis this is + + + align:start position:0% +z-axis this is +pointing in the K hat + + align:start position:0% +pointing in the K hat + + + align:start position:0% +pointing in the K hat +Direction so the total angular + + align:start position:0% + + + + align:start position:0% + +momentum of the + + align:start position:0% +momentum of the + + + align:start position:0% +momentum of the +gyroscope is + + align:start position:0% +gyroscope is + + + align:start position:0% +gyroscope is +i1 * Omega in the r hat + + align:start position:0% +i1 * Omega in the r hat + + + align:start position:0% +i1 * Omega in the r hat +Direction plus I2 * Capital Omega in the + + align:start position:0% +Direction plus I2 * Capital Omega in the + + + align:start position:0% +Direction plus I2 * Capital Omega in the +Kat + + align:start position:0% +Kat + + + align:start position:0% +Kat +Direction + + align:start position:0% +Direction + + + align:start position:0% +Direction +plus + + align:start position:0% +plus + + + align:start position:0% +plus +M Omega Capital Omega d^2 + + align:start position:0% +M Omega Capital Omega d^2 + + + align:start position:0% +M Omega Capital Omega d^2 +in the K hat + + align:start position:0% +in the K hat + + + align:start position:0% +in the K hat +Direction the first term the r hat + + align:start position:0% +Direction the first term the r hat + + + align:start position:0% +Direction the first term the r hat +component is the only part that's + + align:start position:0% +component is the only part that's + + + align:start position:0% +component is the only part that's +rotating so + + align:start position:0% +rotating so + + + align:start position:0% +rotating so +this is a rotating + + align:start position:0% +this is a rotating + + + align:start position:0% +this is a rotating +Vector the K hat terms are + + align:start position:0% + + + + align:start position:0% + +constant this is the exact expression + + align:start position:0% +constant this is the exact expression + + + align:start position:0% +constant this is the exact expression +for the angular momentum of a gyroscope + + align:start position:0% +for the angular momentum of a gyroscope + + + align:start position:0% +for the angular momentum of a gyroscope +and now we see the roscopic + + align:start position:0% +and now we see the roscopic + + + align:start position:0% +and now we see the roscopic +approximation more precisely is saying + + align:start position:0% +approximation more precisely is saying + + + align:start position:0% +approximation more precisely is saying +that this rotating term dominates over + + align:start position:0% +that this rotating term dominates over + + + align:start position:0% +that this rotating term dominates over +the other two terms so it's actually + + align:start position:0% +the other two terms so it's actually + + + align:start position:0% +the other two terms so it's actually +that this term is very large compared to + + align:start position:0% +that this term is very large compared to + + + align:start position:0% +that this term is very large compared to +either of these two terms which as we + + align:start position:0% +either of these two terms which as we + + + align:start position:0% +either of these two terms which as we +can see is roughly equivalent to saying + + align:start position:0% +can see is roughly equivalent to saying + + + align:start position:0% +can see is roughly equivalent to saying +that little Omega is very large compared + + align:start position:0% +that little Omega is very large compared + + + align:start position:0% +that little Omega is very large compared +to big Omega \ No newline at end of file diff --git a/6LOwPhPDwVc.txt b/6LOwPhPDwVc.txt new file mode 100644 index 0000000000000000000000000000000000000000..c4467863875c9573b0bbb76d2ab7041bf4a8884c --- /dev/null +++ b/6LOwPhPDwVc.txt @@ -0,0 +1,9544 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu + + align:start position:0% +ocw.mit.edu + + + align:start position:0% +ocw.mit.edu +so for the last two lectures we've been + + align:start position:0% +so for the last two lectures we've been + + + align:start position:0% +so for the last two lectures we've been +talking about analyzing algorithms + + align:start position:0% +talking about analyzing algorithms + + + align:start position:0% +talking about analyzing algorithms +complexity orders of growth how do we + + align:start position:0% +complexity orders of growth how do we + + + align:start position:0% +complexity orders of growth how do we +estimate the cost of an algorithm as the + + align:start position:0% +estimate the cost of an algorithm as the + + + align:start position:0% +estimate the cost of an algorithm as the +size of the input grows and as I've said + + align:start position:0% +size of the input grows and as I've said + + + align:start position:0% +size of the input grows and as I've said +several times I'll say at least once + + align:start position:0% +several times I'll say at least once + + + align:start position:0% +several times I'll say at least once +more how do we also turn it the other + + align:start position:0% +more how do we also turn it the other + + + align:start position:0% +more how do we also turn it the other +direction how do we use thoughts about + + align:start position:0% +direction how do we use thoughts about + + + align:start position:0% +direction how do we use thoughts about +choices of pieces of algorithm in terms + + align:start position:0% +choices of pieces of algorithm in terms + + + align:start position:0% +choices of pieces of algorithm in terms +of implications on the cost it's going + + align:start position:0% +of implications on the cost it's going + + + align:start position:0% +of implications on the cost it's going +to take us to + + align:start position:0% +to take us to + + + align:start position:0% +to take us to +compute we saw last time a set of + + align:start position:0% +compute we saw last time a set of + + + align:start position:0% +compute we saw last time a set of +examples constant algorithms linear + + align:start position:0% +examples constant algorithms linear + + + align:start position:0% +examples constant algorithms linear +algorithms sorry constant algorithms + + align:start position:0% +algorithms sorry constant algorithms + + + align:start position:0% +algorithms sorry constant algorithms +logarithmic algorithms linear algorithms + + align:start position:0% +logarithmic algorithms linear algorithms + + + align:start position:0% +logarithmic algorithms linear algorithms +quadratic algorithms exponential + + align:start position:0% +quadratic algorithms exponential + + + align:start position:0% +quadratic algorithms exponential +algorithms today what I'm going to do is + + align:start position:0% +algorithms today what I'm going to do is + + + align:start position:0% +algorithms today what I'm going to do is +fill in one more piece a log linear + + align:start position:0% +fill in one more piece a log linear + + + align:start position:0% +fill in one more piece a log linear +algorithm something that's really a nice + + align:start position:0% +algorithm something that's really a nice + + + align:start position:0% +algorithm something that's really a nice +kind of algorithm to have and use it to + + align:start position:0% +kind of algorithm to have and use it to + + + align:start position:0% +kind of algorithm to have and use it to +talk about one last class of algorithms + + align:start position:0% +talk about one last class of algorithms + + + align:start position:0% +talk about one last class of algorithms +that are really valuable and those are + + align:start position:0% +that are really valuable and those are + + + align:start position:0% +that are really valuable and those are +searching and sorting + + align:start position:0% +searching and sorting + + + align:start position:0% +searching and sorting +algorithms so a search algorithm kind of + + align:start position:0% +algorithms so a search algorithm kind of + + + align:start position:0% +algorithms so a search algorithm kind of +an obvious statement you use them all + + align:start position:0% +an obvious statement you use them all + + + align:start position:0% +an obvious statement you use them all +all the time when you go to to Google or + + align:start position:0% +all the time when you go to to Google or + + + align:start position:0% +all the time when you go to to Google or +Bing or whatever your favorite search + + align:start position:0% +Bing or whatever your favorite search + + + align:start position:0% +Bing or whatever your favorite search +mechanism on the web is it's just a way + + align:start position:0% +mechanism on the web is it's just a way + + + align:start position:0% +mechanism on the web is it's just a way +to find an item or a group of items from + + align:start position:0% +to find an item or a group of items from + + + align:start position:0% +to find an item or a group of items from +a + + align:start position:0% +a + + + align:start position:0% +a +collection if you think about it that + + align:start position:0% +collection if you think about it that + + + align:start position:0% +collection if you think about it that +collection could be either implicit or + + align:start position:0% +collection could be either implicit or + + + align:start position:0% +collection could be either implicit or +explicit so way back at the beginning of + + align:start position:0% +explicit so way back at the beginning of + + + align:start position:0% +explicit so way back at the beginning of +the term we saw an example of a search + + align:start position:0% +the term we saw an example of a search + + + align:start position:0% +the term we saw an example of a search +algorithm when you were looking for + + align:start position:0% +algorithm when you were looking for + + + align:start position:0% +algorithm when you were looking for +square roots and we saw simple things + + align:start position:0% +square roots and we saw simple things + + + align:start position:0% +square roots and we saw simple things +like en or exhaustive enumeration we'd + + align:start position:0% +like en or exhaustive enumeration we'd + + + align:start position:0% +like en or exhaustive enumeration we'd +go through all the possibilities we saw + + align:start position:0% +go through all the possibilities we saw + + + align:start position:0% +go through all the possibilities we saw +our first version of section search + + align:start position:0% +our first version of section search + + + align:start position:0% +our first version of section search +there where you would do approximations + + align:start position:0% +there where you would do approximations + + + align:start position:0% +there where you would do approximations +Newton RS and these are all examples of + + align:start position:0% +Newton RS and these are all examples of + + + align:start position:0% +Newton RS and these are all examples of +a search algorithm where the collection + + align:start position:0% +a search algorithm where the collection + + + align:start position:0% +a search algorithm where the collection +is implicit it's all the numbers between + + align:start position:0% +is implicit it's all the numbers between + + + align:start position:0% +is implicit it's all the numbers between +some point and some other point more + + align:start position:0% +some point and some other point more + + + align:start position:0% +some point and some other point more +common is a search algorithm where the + + align:start position:0% +common is a search algorithm where the + + + align:start position:0% +common is a search algorithm where the +collection is + + align:start position:0% +collection is + + + align:start position:0% +collection is +explicit I don't know for example I've + + align:start position:0% +explicit I don't know for example I've + + + align:start position:0% +explicit I don't know for example I've +got all the data records of students and + + align:start position:0% +got all the data records of students and + + + align:start position:0% +got all the data records of students and +I want to know how do I find a + + align:start position:0% +I want to know how do I find a + + + align:start position:0% +I want to know how do I find a +particular student so I can record that + + align:start position:0% +particular student so I can record that + + + align:start position:0% +particular student so I can record that +A+ that everybody in this room is going + + align:start position:0% +A+ that everybody in this room is going + + + align:start position:0% +A+ that everybody in this room is going +to get next Tuesday on that exam that's + + align:start position:0% +to get next Tuesday on that exam that's + + + align:start position:0% +to get next Tuesday on that exam that's +not a promise sorry but we'll work on it + + align:start position:0% +not a promise sorry but we'll work on it + + + align:start position:0% +not a promise sorry but we'll work on it +so could do it implicit could do it + + align:start position:0% +so could do it implicit could do it + + + align:start position:0% +so could do it implicit could do it +explicit today I want to focus on doing + + align:start position:0% +explicit today I want to focus on doing + + + align:start position:0% +explicit today I want to focus on doing +search explicitly and it could be on + + align:start position:0% +search explicitly and it could be on + + + align:start position:0% +search explicitly and it could be on +different kinds of collections but I'm + + align:start position:0% +different kinds of collections but I'm + + + align:start position:0% +different kinds of collections but I'm +going to focus just as an example on + + align:start position:0% +going to focus just as an example on + + + align:start position:0% +going to focus just as an example on +search over lists and to make it a + + align:start position:0% +search over lists and to make it a + + + align:start position:0% +search over lists and to make it a +little easier let's just do search over + + align:start position:0% +little easier let's just do search over + + + align:start position:0% +little easier let's just do search over +lists of numbers but it could obviously + + align:start position:0% +lists of numbers but it could obviously + + + align:start position:0% +lists of numbers but it could obviously +be other kinds of + + align:start position:0% +be other kinds of + + + align:start position:0% +be other kinds of +elements now you've already seen some of + + align:start position:0% +elements now you've already seen some of + + + align:start position:0% +elements now you've already seen some of +this right we did search where we said + + align:start position:0% +this right we did search where we said + + + align:start position:0% +this right we did search where we said +we could do linear search Brute Force + + align:start position:0% +we could do linear search Brute Force + + + align:start position:0% +we could do linear search Brute Force +just walk down the list looking at + + align:start position:0% +just walk down the list looking at + + + align:start position:0% +just walk down the list looking at +everything till we either find the thing + + align:start position:0% +everything till we either find the thing + + + align:start position:0% +everything till we either find the thing +we're looking for or we get to the end + + align:start position:0% +we're looking for or we get to the end + + + align:start position:0% +we're looking for or we get to the end +of the list sometimes also called + + align:start position:0% +of the list sometimes also called + + + align:start position:0% +of the list sometimes also called +British museum algorithm or exhaustive + + align:start position:0% +British museum algorithm or exhaustive + + + align:start position:0% +British museum algorithm or exhaustive +enumeration I go through everything in + + align:start position:0% +enumeration I go through everything in + + + align:start position:0% +enumeration I go through everything in +the list nice news is the list doesn't + + align:start position:0% +the list nice news is the list doesn't + + + align:start position:0% +the list nice news is the list doesn't +have to be sorted it could be just an + + align:start position:0% +have to be sorted it could be just an + + + align:start position:0% +have to be sorted it could be just an +arbitrary order what we saw is that the + + align:start position:0% +arbitrary order what we saw is that the + + + align:start position:0% +arbitrary order what we saw is that the +expected sorry not expected the worst + + align:start position:0% +expected sorry not expected the worst + + + align:start position:0% +expected sorry not expected the worst +case behavior is linear in the worst + + align:start position:0% +case behavior is linear in the worst + + + align:start position:0% +case behavior is linear in the worst +case the elements not on the list I got + + align:start position:0% +case the elements not on the list I got + + + align:start position:0% +case the elements not on the list I got +to look at everything so it's going to + + align:start position:0% +to look at everything so it's going to + + + align:start position:0% +to look at everything so it's going to +be linear in terms of + + align:start position:0% +be linear in terms of + + + align:start position:0% +be linear in terms of +complexity and then we looked at + + align:start position:0% +complexity and then we looked at + + + align:start position:0% +complexity and then we looked at +bsection search where we said the list + + align:start position:0% +bsection search where we said the list + + + align:start position:0% +bsection search where we said the list +needs to be sorted but if it is we can + + align:start position:0% +needs to be sorted but if it is we can + + + align:start position:0% +needs to be sorted but if it is we can +actually be much more efficient because + + align:start position:0% +actually be much more efficient because + + + align:start position:0% +actually be much more efficient because +we can take advantage of the Sorting to + + align:start position:0% +we can take advantage of the Sorting to + + + align:start position:0% +we can take advantage of the Sorting to +cut down the size of the problem and + + align:start position:0% +cut down the size of the problem and + + + align:start position:0% +cut down the size of the problem and +I'll remind you about both of those + + align:start position:0% +I'll remind you about both of those + + + align:start position:0% +I'll remind you about both of those +there was our simple little linear + + align:start position:0% +there was our simple little linear + + + align:start position:0% +there was our simple little linear +search right set a flag that says I + + align:start position:0% +search right set a flag that says I + + + align:start position:0% +search right set a flag that says I +haven't yet found it and then just Loop + + align:start position:0% +haven't yet found it and then just Loop + + + align:start position:0% +haven't yet found it and then just Loop +over the indices into the list I could + + align:start position:0% +over the indices into the list I could + + + align:start position:0% +over the indices into the list I could +have also just Loop directly over the + + align:start position:0% +have also just Loop directly over the + + + align:start position:0% +have also just Loop directly over the +list itself checking to see if the I + + align:start position:0% +list itself checking to see if the I + + + align:start position:0% +list itself checking to see if the I +member of the list is a thing I'm + + align:start position:0% +member of the list is a thing I'm + + + align:start position:0% +member of the list is a thing I'm +looking for if it is change the flag to + + align:start position:0% +looking for if it is change the flag to + + + align:start position:0% +looking for if it is change the flag to +tr so that when I come out of all of + + align:start position:0% +tr so that when I come out of all of + + + align:start position:0% +tr so that when I come out of all of +this I'll return the flag either false + + align:start position:0% +this I'll return the flag either false + + + align:start position:0% +this I'll return the flag either false +because it was set that way initially or + + align:start position:0% +because it was set that way initially or + + + align:start position:0% +because it was set that way initially or +true because I found it and of course + + align:start position:0% +true because I found it and of course + + + align:start position:0% +true because I found it and of course +what we knew is we have to look at + + align:start position:0% +what we knew is we have to look at + + + align:start position:0% +what we knew is we have to look at +everything to see if it's there or not I + + align:start position:0% +everything to see if it's there or not I + + + align:start position:0% +everything to see if it's there or not I +could speed this up by just returning + + align:start position:0% +could speed this up by just returning + + + align:start position:0% +could speed this up by just returning +true at this point well that would + + align:start position:0% +true at this point well that would + + + align:start position:0% +true at this point well that would +improve the average case doesn't improve + + align:start position:0% +improve the average case doesn't improve + + + align:start position:0% +improve the average case doesn't improve +the worst case and that's the thing we + + align:start position:0% +the worst case and that's the thing we + + + align:start position:0% +the worst case and that's the thing we +usually are concerned about because in + + align:start position:0% +usually are concerned about because in + + + align:start position:0% +usually are concerned about because in +the worst case I got to go through + + align:start position:0% +the worst case I got to go through + + + align:start position:0% +the worst case I got to go through +everything and just to remind you we + + align:start position:0% +everything and just to remind you we + + + align:start position:0% +everything and just to remind you we +said this is order length of the list to + + align:start position:0% +said this is order length of the list to + + + align:start position:0% +said this is order length of the list to +go around this part the loop right here + + align:start position:0% +go around this part the loop right here + + + align:start position:0% +go around this part the loop right here +and inside the loop it's constant work + + align:start position:0% +and inside the loop it's constant work + + + align:start position:0% +and inside the loop it's constant work +I'm doing the same number of things each + + align:start position:0% +I'm doing the same number of things each + + + align:start position:0% +I'm doing the same number of things each +time that's order n * order 1 and by our + + align:start position:0% +time that's order n * order 1 and by our + + + align:start position:0% +time that's order n * order 1 and by our +rules that's just order n so it's linear + + align:start position:0% +rules that's just order n so it's linear + + + align:start position:0% +rules that's just order n so it's linear +in the size of the + + align:start position:0% +in the size of the + + + align:start position:0% +in the size of the +problem + + align:start position:0% +problem + + + align:start position:0% +problem +okay we said we could do it on sorted + + align:start position:0% +okay we said we could do it on sorted + + + align:start position:0% +okay we said we could do it on sorted +lists but just again walk down the list + + align:start position:0% +lists but just again walk down the list + + + align:start position:0% +lists but just again walk down the list +again here I could Loop over everything + + align:start position:0% +again here I could Loop over everything + + + align:start position:0% +again here I could Loop over everything +in the list checking to see if it's a + + align:start position:0% +in the list checking to see if it's a + + + align:start position:0% +in the list checking to see if it's a +thing I want return true and if I ever + + align:start position:0% +thing I want return true and if I ever + + + align:start position:0% +thing I want return true and if I ever +get to a point where the element of the + + align:start position:0% +get to a point where the element of the + + + align:start position:0% +get to a point where the element of the +list is bigger than the thing I'm + + align:start position:0% +list is bigger than the thing I'm + + + align:start position:0% +list is bigger than the thing I'm +looking for I know it can't be in the + + align:start position:0% +looking for I know it can't be in the + + + align:start position:0% +looking for I know it can't be in the +rest of the list cuz all the things to + + align:start position:0% +rest of the list cuz all the things to + + + align:start position:0% +rest of the list cuz all the things to +the right are bigger yet I could just + + align:start position:0% +the right are bigger yet I could just + + + align:start position:0% +the right are bigger yet I could just +return fults and drop + + align:start position:0% +return fults and drop + + + align:start position:0% +return fults and drop +out in terms of average Behavior this is + + align:start position:0% +out in terms of average Behavior this is + + + align:start position:0% +out in terms of average Behavior this is +better because it's going to stop as + + align:start position:0% +better because it's going to stop as + + + align:start position:0% +better because it's going to stop as +soon as it gets to a point where it can + + align:start position:0% +soon as it gets to a point where it can + + + align:start position:0% +soon as it gets to a point where it can +rule everything else out but in terms of + + align:start position:0% +rule everything else out but in terms of + + + align:start position:0% +rule everything else out but in terms of +complexity it's still order n because I + + align:start position:0% +complexity it's still order n because I + + + align:start position:0% +complexity it's still order n because I +still on average have to not average in + + align:start position:0% +still on average have to not average in + + + align:start position:0% +still on average have to not average in +the worst case I'm still going to be + + align:start position:0% +the worst case I'm still going to be + + + align:start position:0% +the worst case I'm still going to be +looking end times through the loop + + align:start position:0% +looking end times through the loop + + + align:start position:0% +looking end times through the loop +before I get to a point where I can + + align:start position:0% +before I get to a point where I can + + + align:start position:0% +before I get to a point where I can +decide to bail out of it so order in and + + align:start position:0% +decide to bail out of it so order in and + + + align:start position:0% +decide to bail out of it so order in and +then finally last piece of recap + + align:start position:0% +then finally last piece of recap + + + align:start position:0% +then finally last piece of recap +bsection + + align:start position:0% +bsection + + + align:start position:0% +bsection +search repeat again the idea here is + + align:start position:0% +search repeat again the idea here is + + + align:start position:0% +search repeat again the idea here is +take the midpoint of the list look at + + align:start position:0% +take the midpoint of the list look at + + + align:start position:0% +take the midpoint of the list look at +that element if it's the thing I'm + + align:start position:0% +that element if it's the thing I'm + + + align:start position:0% +that element if it's the thing I'm +looking for great I just won the lottery + + align:start position:0% +looking for great I just won the lottery + + + align:start position:0% +looking for great I just won the lottery +if it isn't decide is the thing I'm + + align:start position:0% +if it isn't decide is the thing I'm + + + align:start position:0% +if it isn't decide is the thing I'm +looking for bigger or less than that + + align:start position:0% +looking for bigger or less than that + + + align:start position:0% +looking for bigger or less than that +middle point if it's bigger than that I + + align:start position:0% +middle point if it's bigger than that I + + + align:start position:0% +middle point if it's bigger than that I +only use the upper half of the list if + + align:start position:0% +only use the upper half of the list if + + + align:start position:0% +only use the upper half of the list if +it's less than that I only use the lower + + align:start position:0% +it's less than that I only use the lower + + + align:start position:0% +it's less than that I only use the lower +half of the list and the characteristic + + align:start position:0% +half of the list and the characteristic + + + align:start position:0% +half of the list and the characteristic +here was at each step I'm reducing the + + align:start position:0% +here was at each step I'm reducing the + + + align:start position:0% +here was at each step I'm reducing the +size of the problem in half I'm throwing + + align:start position:0% +size of the problem in half I'm throwing + + + align:start position:0% +size of the problem in half I'm throwing +away half of the remaining list at each + + align:start position:0% +away half of the remaining list at each + + + align:start position:0% +away half of the remaining list at each +step and I'll just remind you of that + + align:start position:0% +step and I'll just remind you of that + + + align:start position:0% +step and I'll just remind you of that +code I know it's a lot here but just to + + align:start position:0% +code I know it's a lot here but just to + + + align:start position:0% +code I know it's a lot here but just to +remind you it said down here if I've got + + align:start position:0% +remind you it said down here if I've got + + + align:start position:0% +remind you it said down here if I've got +an empty list can't be there I'm going + + align:start position:0% +an empty list can't be there I'm going + + + align:start position:0% +an empty list can't be there I'm going +to return faults otherwise call this + + align:start position:0% +to return faults otherwise call this + + + align:start position:0% +to return faults otherwise call this +little helper function with the list the + + align:start position:0% +little helper function with the list the + + + align:start position:0% +little helper function with the list the +thing for which I'm searching and the + + align:start position:0% +thing for which I'm searching and the + + + align:start position:0% +thing for which I'm searching and the +beginning and end point indices into the + + align:start position:0% +beginning and end point indices into the + + + align:start position:0% +beginning and end point indices into the +list initially the start and the very + + align:start position:0% +list initially the start and the very + + + align:start position:0% +list initially the start and the very +end and this code up here B basically + + align:start position:0% +end and this code up here B basically + + + align:start position:0% +end and this code up here B basically +says if those two numbers are the same + + align:start position:0% +says if those two numbers are the same + + + align:start position:0% +says if those two numbers are the same +I'm down to a list of one just check to + + align:start position:0% +I'm down to a list of one just check to + + + align:start position:0% +I'm down to a list of one just check to +see if it's the thing I'm looking for + + align:start position:0% +see if it's the thing I'm looking for + + + align:start position:0% +see if it's the thing I'm looking for +otherwise pick something halfway in + + align:start position:0% +otherwise pick something halfway in + + + align:start position:0% +otherwise pick something halfway in +between and ignore this case for the + + align:start position:0% +between and ignore this case for the + + + align:start position:0% +between and ignore this case for the +moment basically then check to see is + + align:start position:0% +moment basically then check to see is + + + align:start position:0% +moment basically then check to see is +the thing at that point bigger than e in + + align:start position:0% +the thing at that point bigger than e in + + + align:start position:0% +the thing at that point bigger than e in +which case I'm in general going to call + + align:start position:0% +which case I'm in general going to call + + + align:start position:0% +which case I'm in general going to call +this only with from the low point to the + + align:start position:0% +this only with from the low point to the + + + align:start position:0% +this only with from the low point to the +midpoint otherwise I'm going to call + + align:start position:0% +midpoint otherwise I'm going to call + + + align:start position:0% +midpoint otherwise I'm going to call +this with the midpoint to high and that + + align:start position:0% +this with the midpoint to high and that + + + align:start position:0% +this with the midpoint to high and that +was just this idea of keep cutting down + + align:start position:0% +was just this idea of keep cutting down + + + align:start position:0% +was just this idea of keep cutting down +in half the size of the list + + align:start position:0% +in half the size of the list + + + align:start position:0% +in half the size of the list +last piece of the recap the thing we + + align:start position:0% +last piece of the recap the thing we + + + align:start position:0% +last piece of the recap the thing we +wanted you to see here is there are the + + align:start position:0% +wanted you to see here is there are the + + + align:start position:0% +wanted you to see here is there are the +two recursive calls I'm going to only + + align:start position:0% +two recursive calls I'm going to only + + + align:start position:0% +two recursive calls I'm going to only +going to do one because I'm making a + + align:start position:0% +going to do one because I'm making a + + + align:start position:0% +going to do one because I'm making a +decision at each step I'm cutting down + + align:start position:0% +decision at each step I'm cutting down + + + align:start position:0% +decision at each step I'm cutting down +the problem by half and that says the + + align:start position:0% +the problem by half and that says the + + + align:start position:0% +the problem by half and that says the +number of steps the number of times I'm + + align:start position:0% +number of steps the number of times I'm + + + align:start position:0% +number of steps the number of times I'm +going to iterate through here will be + + align:start position:0% +going to iterate through here will be + + + align:start position:0% +going to iterate through here will be +log in the length of the list and if + + align:start position:0% +log in the length of the list and if + + + align:start position:0% +log in the length of the list and if +that still doesn't make sense to you it + + align:start position:0% +that still doesn't make sense to you it + + + align:start position:0% +that still doesn't make sense to you it +says I need to know when 1 over two to + + align:start position:0% +says I need to know when 1 over two to + + + align:start position:0% +says I need to know when 1 over two to +the K where K is the number of steps is + + align:start position:0% +the K where K is the number of steps is + + + align:start position:0% +the K where K is the number of steps is +equal to one because on each step I'm + + align:start position:0% +equal to one because on each step I'm + + + align:start position:0% +equal to one because on each step I'm +reducing by half and that's when K is + + align:start position:0% +reducing by half and that's when K is + + + align:start position:0% +reducing by half and that's when K is +log base 2 of n so that's why it's log + + align:start position:0% +log base 2 of n so that's why it's log + + + align:start position:0% +log base 2 of n so that's why it's log +linear and so this just reminds you + + align:start position:0% +linear and so this just reminds you + + + align:start position:0% +linear and so this just reminds you +again that recap number of calls redu or + + align:start position:0% +again that recap number of calls redu or + + + align:start position:0% +again that recap number of calls redu or +sorry the call gets reduced by factor of + + align:start position:0% +sorry the call gets reduced by factor of + + + align:start position:0% +sorry the call gets reduced by factor of +two each time I'm going to have log in + + align:start position:0% +two each time I'm going to have log in + + + align:start position:0% +two each time I'm going to have log in +work going around it and inside it's + + align:start position:0% +work going around it and inside it's + + + align:start position:0% +work going around it and inside it's +constant amount of work because I'm just + + align:start position:0% +constant amount of work because I'm just + + + align:start position:0% +constant amount of work because I'm just +passing the pointers not actually + + align:start position:0% +passing the pointers not actually + + + align:start position:0% +passing the pointers not actually +copying the list and that's a nice state + + align:start position:0% +copying the list and that's a nice state + + + align:start position:0% +copying the list and that's a nice state +to + + align:start position:0% +to + + + align:start position:0% +to +be okay + + align:start position:0% +be okay + + + align:start position:0% +be okay +so sounds good could just use linear + + align:start position:0% +so sounds good could just use linear + + + align:start position:0% +so sounds good could just use linear +search it's going to be linear when you + + align:start position:0% +search it's going to be linear when you + + + align:start position:0% +search it's going to be linear when you +use binary search or bsection search um + + align:start position:0% +use binary search or bsection search um + + + align:start position:0% +use binary search or bsection search um +we can do it in log time that's great we + + align:start position:0% +we can do it in log time that's great we + + + align:start position:0% +we can do it in log time that's great we +assumed the list was sorted but all + + align:start position:0% +assumed the list was sorted but all + + + align:start position:0% +assumed the list was sorted but all +right + + align:start position:0% +right + + + align:start position:0% +right +so that Les basically says okay so when + + align:start position:0% +so that Les basically says okay so when + + + align:start position:0% +so that Les basically says okay so when +does it make sense to sort the list and + + align:start position:0% +does it make sense to sort the list and + + + align:start position:0% +does it make sense to sort the list and +then do the search right because if I + + align:start position:0% +then do the search right because if I + + + align:start position:0% +then do the search right because if I +can sort the list cheaply then the + + align:start position:0% +can sort the list cheaply then the + + + align:start position:0% +can sort the list cheaply then the +search is going to be logarithmic that's + + align:start position:0% +search is going to be logarithmic that's + + + align:start position:0% +search is going to be logarithmic that's +really what I would + + align:start position:0% +really what I would + + + align:start position:0% +really what I would +like this little expression basically + + align:start position:0% +like this little expression basically + + + align:start position:0% +like this little expression basically +says let's let sort be the cost of + + align:start position:0% +says let's let sort be the cost of + + + align:start position:0% +says let's let sort be the cost of +sorting the list + + align:start position:0% +sorting the list + + + align:start position:0% +sorting the list +I want to know when that cost plus + + align:start position:0% +I want to know when that cost plus + + + align:start position:0% +I want to know when that cost plus +something that's order log in which is + + align:start position:0% +something that's order log in which is + + + align:start position:0% +something that's order log in which is +what it's going to cost me to do the + + align:start position:0% +what it's going to cost me to do the + + + align:start position:0% +what it's going to cost me to do the +search when is that less than something + + align:start position:0% +search when is that less than something + + + align:start position:0% +search when is that less than something +that's order n because then it's going + + align:start position:0% +that's order n because then it's going + + + align:start position:0% +that's order n because then it's going +to be better to do the sort first and do + + align:start position:0% +to be better to do the sort first and do + + + align:start position:0% +to be better to do the sort first and do +the search and so I can just rearrange + + align:start position:0% +the search and so I can just rearrange + + + align:start position:0% +the search and so I can just rearrange +it it needs to be when does the cost of + + align:start position:0% +it it needs to be when does the cost of + + + align:start position:0% +it it needs to be when does the cost of +sorting when is it less than this + + align:start position:0% +sorting when is it less than this + + + align:start position:0% +sorting when is it less than this +expression which basically says when is + + align:start position:0% +expression which basically says when is + + + align:start position:0% +expression which basically says when is +sorting going to be less expensive than + + align:start position:0% +sorting going to be less expensive than + + + align:start position:0% +sorting going to be less expensive than +the linear + + align:start position:0% + + + + align:start position:0% + +cost + + align:start position:0% +cost + + + align:start position:0% +cost +crud actually good news for you right + + align:start position:0% +crud actually good news for you right + + + align:start position:0% +crud actually good news for you right +this is a really short lecture because + + align:start position:0% +this is a really short lecture because + + + align:start position:0% +this is a really short lecture because +it says it's never true ouch don't worry + + align:start position:0% +it says it's never true ouch don't worry + + + align:start position:0% +it says it's never true ouch don't worry +we got more to go in the lecture the + + align:start position:0% +we got more to go in the lecture the + + + align:start position:0% +we got more to go in the lecture the +reason it can't be true if you think + + align:start position:0% +reason it can't be true if you think + + + align:start position:0% +reason it can't be true if you think +about it just informally is if I've got + + align:start position:0% +about it just informally is if I've got + + + align:start position:0% +about it just informally is if I've got +a collection of n elements and I want to + + align:start position:0% +a collection of n elements and I want to + + + align:start position:0% +a collection of n elements and I want to +sort it I've got to look at Le each one + + align:start position:0% +sort it I've got to look at Le each one + + + align:start position:0% +sort it I've got to look at Le each one +of those elements at least once right I + + align:start position:0% +of those elements at least once right I + + + align:start position:0% +of those elements at least once right I +have to look at them to decide where + + align:start position:0% +have to look at them to decide where + + + align:start position:0% +have to look at them to decide where +they go oh that's n elements so sorting + + align:start position:0% +they go oh that's n elements so sorting + + + align:start position:0% +they go oh that's n elements so sorting +must be at least order n because I got + + align:start position:0% +must be at least order n because I got + + + align:start position:0% +must be at least order n because I got +to look at everything and in fact as it + + align:start position:0% +to look at everything and in fact as it + + + align:start position:0% +to look at everything and in fact as it +says there I'm going to have to use at + + align:start position:0% +says there I'm going to have to use at + + + align:start position:0% +says there I'm going to have to use at +least linear time to do the + + align:start position:0% +least linear time to do the + + + align:start position:0% +least linear time to do the +sort sounds like we're stuck but we're + + align:start position:0% +sort sounds like we're stuck but we're + + + align:start position:0% +sort sounds like we're stuck but we're +not and the reason is often when I want + + align:start position:0% +not and the reason is often when I want + + + align:start position:0% +not and the reason is often when I want +to search something I'm going to do + + align:start position:0% +to search something I'm going to do + + + align:start position:0% +to search something I'm going to do +multiple searches but I may only want to + + align:start position:0% +multiple searches but I may only want to + + + align:start position:0% +multiple searches but I may only want to +sort the list once in fact I probably + + align:start position:0% +sort the list once in fact I probably + + + align:start position:0% +sort the list once in fact I probably +only want to sort the list once so in + + align:start position:0% +only want to sort the list once so in + + + align:start position:0% +only want to sort the list once so in +that case I'm spreading out the cost I'm + + align:start position:0% +that case I'm spreading out the cost I'm + + + align:start position:0% +that case I'm spreading out the cost I'm +amortising the expense of the sort and + + align:start position:0% +amortising the expense of the sort and + + + align:start position:0% +amortising the expense of the sort and +now what I want to know is if I'm going + + align:start position:0% +now what I want to know is if I'm going + + + align:start position:0% +now what I want to know is if I'm going +to do K searches the cost of those K + + align:start position:0% +to do K searches the cost of those K + + + align:start position:0% +to do K searches the cost of those K +searches I know is going to be K log in + + align:start position:0% +searches I know is going to be K log in + + + align:start position:0% +searches I know is going to be K log in +because it's loged to do the search and + + align:start position:0% +because it's loged to do the search and + + + align:start position:0% +because it's loged to do the search and +I simply need to know is the cost of + + align:start position:0% +I simply need to know is the cost of + + + align:start position:0% +I simply need to know is the cost of +sorting plus this can I have something + + align:start position:0% +sorting plus this can I have something + + + align:start position:0% +sorting plus this can I have something +where it's less than case searches just + + align:start position:0% +where it's less than case searches just + + + align:start position:0% +where it's less than case searches just +using linear search and the answer is + + align:start position:0% +using linear search and the answer is + + + align:start position:0% +using linear search and the answer is +yes there are going to be for large case + + align:start position:0% +yes there are going to be for large case + + + align:start position:0% +yes there are going to be for large case +ways in which we can do the sort where + + align:start position:0% +ways in which we can do the sort where + + + align:start position:0% +ways in which we can do the sort where +the sort time becomes irrelevant that + + align:start position:0% +the sort time becomes irrelevant that + + + align:start position:0% +the sort time becomes irrelevant that +the cost is really dominated by the + + align:start position:0% +the cost is really dominated by the + + + align:start position:0% +the cost is really dominated by the +search and so what I want want to do now + + align:start position:0% +search and so what I want want to do now + + + align:start position:0% +search and so what I want want to do now +is look at all right how could we do the + + align:start position:0% +is look at all right how could we do the + + + align:start position:0% +is look at all right how could we do the +sort reasonably efficiently it's going + + align:start position:0% +sort reasonably efficiently it's going + + + align:start position:0% +sort reasonably efficiently it's going +to have to be at least linear we're + + align:start position:0% +to have to be at least linear we're + + + align:start position:0% +to have to be at least linear we're +going to see it's going to be a little + + align:start position:0% +going to see it's going to be a little + + + align:start position:0% +going to see it's going to be a little +more than linear but if I could do it + + align:start position:0% +more than linear but if I could do it + + + align:start position:0% +more than linear but if I could do it +reasonably I'm going to be in good shape + + align:start position:0% +reasonably I'm going to be in good shape + + + align:start position:0% +reasonably I'm going to be in good shape +here so what I want to do is show you a + + align:start position:0% +here so what I want to do is show you a + + + align:start position:0% +here so what I want to do is show you a +number of ways in which we can do + + align:start position:0% +number of ways in which we can do + + + align:start position:0% +number of ways in which we can do +sorting take a list of elements and sort + + align:start position:0% +sorting take a list of elements and sort + + + align:start position:0% +sorting take a list of elements and sort +them from in this case smaller to higher + + align:start position:0% +them from in this case smaller to higher + + + align:start position:0% +them from in this case smaller to higher +or in in increasing + + align:start position:0% +or in in increasing + + + align:start position:0% +or in in increasing +order so here's my goal I want to + + align:start position:0% +order so here's my goal I want to + + + align:start position:0% +order so here's my goal I want to +efficiently sort a list I want to see if + + align:start position:0% +efficiently sort a list I want to see if + + + align:start position:0% +efficiently sort a list I want to see if +we can do this as efficiently as + + align:start position:0% +we can do this as efficiently as + + + align:start position:0% +we can do this as efficiently as +possible + + align:start position:0% +possible + + + align:start position:0% +possible +I'm going to + + align:start position:0% +I'm going to + + + align:start position:0% +I'm going to +start I'm going to say with a humorous + + align:start position:0% +start I'm going to say with a humorous + + + align:start position:0% +start I'm going to say with a humorous +version of sort you've all convinced + + align:start position:0% +version of sort you've all convinced + + + align:start position:0% +version of sort you've all convinced +that my humor is non-existent you're + + align:start position:0% +that my humor is non-existent you're + + + align:start position:0% +that my humor is non-existent you're +right but it sets the stage for this is + + align:start position:0% +right but it sets the stage for this is + + + align:start position:0% +right but it sets the stage for this is +a sort you can look it up it's called + + align:start position:0% +a sort you can look it up it's called + + + align:start position:0% +a sort you can look it up it's called +monkey sort BOGO sort stupid sort slow + + align:start position:0% +monkey sort BOGO sort stupid sort slow + + + align:start position:0% +monkey sort BOGO sort stupid sort slow +sort permutation sort shotgun sort and + + align:start position:0% +sort permutation sort shotgun sort and + + + align:start position:0% +sort permutation sort shotgun sort and +here's how it works Anna has nicely + + align:start position:0% +here's how it works Anna has nicely + + + align:start position:0% +here's how it works Anna has nicely +given me a set of numbers on cards here + + align:start position:0% +given me a set of numbers on cards here + + + align:start position:0% +given me a set of numbers on cards here +here's how you do BOGO + + align:start position:0% +here's how you do BOGO + + + align:start position:0% +here's how you do BOGO +sort I got to do that better I got to + + align:start position:0% +sort I got to do that better I got to + + + align:start position:0% +sort I got to do that better I got to +spread them out randomly like this oh + + align:start position:0% +spread them out randomly like this oh + + + align:start position:0% +spread them out randomly like this oh +good I'm going to have to sorry Tom I'm + + align:start position:0% +good I'm going to have to sorry Tom I'm + + + align:start position:0% +good I'm going to have to sorry Tom I'm +now walking and now I picked them up + + align:start position:0% +now walking and now I picked them up + + + align:start position:0% +now walking and now I picked them up +saying is that less than this Which is + + align:start position:0% +saying is that less than this Which is + + + align:start position:0% +saying is that less than this Which is +less than o crud they're not sorted all + + align:start position:0% +less than o crud they're not sorted all + + + align:start position:0% +less than o crud they're not sorted all +right I pick them all + + align:start position:0% +right I pick them all + + + align:start position:0% +right I pick them all +up and I do it again a little brain + + align:start position:0% +up and I do it again a little brain + + + align:start position:0% +up and I do it again a little brain +damage right now it's intended to get + + align:start position:0% +damage right now it's intended to get + + + align:start position:0% +damage right now it's intended to get +your attention I did I heard a couple of + + align:start position:0% +your attention I did I heard a couple of + + + align:start position:0% +your attention I did I heard a couple of +Chuckles those are a students by the way + + align:start position:0% +Chuckles those are a students by the way + + + align:start position:0% +Chuckles those are a students by the way +I heard a couple of Chuckles + + align:start position:0% +I heard a couple of Chuckles + + + align:start position:0% +I heard a couple of Chuckles +here we could actually do this + + align:start position:0% +here we could actually do this + + + align:start position:0% +here we could actually do this +exhaustively basically it's called + + align:start position:0% +exhaustively basically it's called + + + align:start position:0% +exhaustively basically it's called +permutation sort because you could + + align:start position:0% +permutation sort because you could + + + align:start position:0% +permutation sort because you could +search through all possible permutations + + align:start position:0% +search through all possible permutations + + + align:start position:0% +search through all possible permutations +to see if you find something that's + + align:start position:0% +to see if you find something that's + + + align:start position:0% +to see if you find something that's +sorted that by the way the complexity of + + align:start position:0% +sorted that by the way the complexity of + + + align:start position:0% +sorted that by the way the complexity of +that is something like n factorial which + + align:start position:0% +that is something like n factorial which + + + align:start position:0% +that is something like n factorial which +for large n is n to the nth + + align:start position:0% +for large n is n to the nth + + + align:start position:0% +for large n is n to the nth +power and if 's anything bigger than + + align:start position:0% +power and if 's anything bigger than + + + align:start position:0% +power and if 's anything bigger than +about two don't do it all right but it + + align:start position:0% +about two don't do it all right but it + + + align:start position:0% +about two don't do it all right but it +would be a way to think about doing this + + align:start position:0% +would be a way to think about doing this + + + align:start position:0% +would be a way to think about doing this +all right now having caught in the + + align:start position:0% +all right now having caught in the + + + align:start position:0% +all right now having caught in the +humorous version of this how could we do + + align:start position:0% +humorous version of this how could we do + + + align:start position:0% +humorous version of this how could we do +this a little bit + + align:start position:0% +this a little bit + + + align:start position:0% +this a little bit +better oh sorry I should say What's the + + align:start position:0% +better oh sorry I should say What's the + + + align:start position:0% +better oh sorry I should say What's the +complexity there is a nice crisp + + align:start position:0% +complexity there is a nice crisp + + + align:start position:0% +complexity there is a nice crisp +definition of BOGO + + align:start position:0% +definition of BOGO + + + align:start position:0% +definition of BOGO +sort its best case is order n because I + + align:start position:0% +sort its best case is order n because I + + + align:start position:0% +sort its best case is order n because I +just need to check it sorted its average + + align:start position:0% +just need to check it sorted its average + + + align:start position:0% +just need to check it sorted its average +case is n factorial and its worst case + + align:start position:0% +case is n factorial and its worst case + + + align:start position:0% +case is n factorial and its worst case +if I'm just doing it randomly as God + + align:start position:0% +if I'm just doing it randomly as God + + + align:start position:0% +if I'm just doing it randomly as God +knows because I could be doing it here + + align:start position:0% +knows because I could be doing it here + + + align:start position:0% +knows because I could be doing it here +forever so we're going to move + + align:start position:0% +forever so we're going to move + + + align:start position:0% +forever so we're going to move +on here's a second way to do it called + + align:start position:0% +on here's a second way to do it called + + + align:start position:0% +on here's a second way to do it called +Bubble sword I'm going to do this with a + + align:start position:0% +Bubble sword I'm going to do this with a + + + align:start position:0% +Bubble sword I'm going to do this with a +small version of this I'm going to put + + align:start position:0% +small version of this I'm going to put + + + align:start position:0% +small version of this I'm going to put +out a set I'll turn these up so you can + + align:start position:0% +out a set I'll turn these up so you can + + + align:start position:0% +out a set I'll turn these up so you can +see them in a + + align:start position:0% +see them in a + + + align:start position:0% +see them in a +second the idea of bubble sword is I'm + + align:start position:0% +second the idea of bubble sword is I'm + + + align:start position:0% +second the idea of bubble sword is I'm +I'm going to start at I'm going to call + + align:start position:0% +I'm going to start at I'm going to call + + + align:start position:0% +I'm going to start at I'm going to call +this the front end of the list and I'm + + align:start position:0% +this the front end of the list and I'm + + + align:start position:0% +this the front end of the list and I'm +going to walk down comparing elements + + align:start position:0% +going to walk down comparing elements + + + align:start position:0% +going to walk down comparing elements +one pairwise and I'm always going to + + align:start position:0% +one pairwise and I'm always going to + + + align:start position:0% +one pairwise and I'm always going to +move the larger one over so I start here + + align:start position:0% +move the larger one over so I start here + + + align:start position:0% +move the larger one over so I start here +and I say one's less than 11 I'm okay + + align:start position:0% +and I say one's less than 11 I'm okay + + + align:start position:0% +and I say one's less than 11 I'm okay +11's bigger than five I'm going to + + align:start position:0% +11's bigger than five I'm going to + + + align:start position:0% +11's bigger than five I'm going to +bubble that up 11's bigger than six I'm + + align:start position:0% +bubble that up 11's bigger than six I'm + + + align:start position:0% +bubble that up 11's bigger than six I'm +going to bubble that up 11's bigger than + + align:start position:0% +going to bubble that up 11's bigger than + + + align:start position:0% +going to bubble that up 11's bigger than +two I've basically bubbled 11 to the end + + align:start position:0% +two I've basically bubbled 11 to the end + + + align:start position:0% +two I've basically bubbled 11 to the end +now I go back here I say one is less + + align:start position:0% +now I go back here I say one is less + + + align:start position:0% +now I go back here I say one is less +than five that's good five is less than + + align:start position:0% +than five that's good five is less than + + + align:start position:0% +than five that's good five is less than +six that's good ah six is bigger than + + align:start position:0% +six that's good ah six is bigger than + + + align:start position:0% +six that's good ah six is bigger than +two two bubble that six is less than 11 + + align:start position:0% +two two bubble that six is less than 11 + + + align:start position:0% +two two bubble that six is less than 11 +you get the idea comparison comparison + + align:start position:0% +you get the idea comparison comparison + + + align:start position:0% +you get the idea comparison comparison +and swap comparison comparison and now + + align:start position:0% +and swap comparison comparison and now + + + align:start position:0% +and swap comparison comparison and now +if I go back to this part and do it + + align:start position:0% +if I go back to this part and do it + + + align:start position:0% +if I go back to this part and do it +you'll notice that's in the right order + + align:start position:0% +you'll notice that's in the right order + + + align:start position:0% +you'll notice that's in the right order +that's in the right order that's in the + + align:start position:0% +that's in the right order that's in the + + + align:start position:0% +that's in the right order that's in the +right order that's in the right order + + align:start position:0% +right order that's in the right order + + + align:start position:0% +right order that's in the right order +I'm + + align:start position:0% +I'm + + + align:start position:0% +I'm +done small round of applause please I + + align:start position:0% +done small round of applause please I + + + align:start position:0% +done small round of applause please I +was able to sort five elements thank + + align:start position:0% +was able to sort five elements thank + + + align:start position:0% +was able to sort five elements thank +you the little video was sort of showing + + align:start position:0% +you the little video was sort of showing + + + align:start position:0% +you the little video was sort of showing +the same thing you can see the idea here + + align:start position:0% +the same thing you can see the idea here + + + align:start position:0% +the same thing you can see the idea here +it's called bubble sort because you're + + align:start position:0% +it's called bubble sort because you're + + + align:start position:0% +it's called bubble sort because you're +literally bubbling things up uh to the + + align:start position:0% +literally bubbling things up uh to the + + + align:start position:0% +literally bubbling things up uh to the +end of the list it's pretty simple to do + + align:start position:0% +end of the list it's pretty simple to do + + + align:start position:0% +end of the list it's pretty simple to do +you're just swapping Pairs and as you + + align:start position:0% +you're just swapping Pairs and as you + + + align:start position:0% +you're just swapping Pairs and as you +saw when I get to the end of the list I + + align:start position:0% +saw when I get to the end of the list I + + + align:start position:0% +saw when I get to the end of the list I +go back and do it until I have a pass + + align:start position:0% +go back and do it until I have a pass + + + align:start position:0% +go back and do it until I have a pass +where I go all the way through the list + + align:start position:0% +where I go all the way through the list + + + align:start position:0% +where I go all the way through the list +and I don't do any swaps and in that + + align:start position:0% +and I don't do any swaps and in that + + + align:start position:0% +and I don't do any swaps and in that +case I know I'm done because + + align:start position:0% +case I know I'm done because + + + align:start position:0% +case I know I'm done because +everything's in order and I can stop one + + align:start position:0% +everything's in order and I can stop one + + + align:start position:0% +everything's in order and I can stop one +of the properties of it is that the + + align:start position:0% +of the properties of it is that the + + + align:start position:0% +of the properties of it is that the +largest unsorted element is always at + + align:start position:0% +largest unsorted element is always at + + + align:start position:0% +largest unsorted element is always at +the end after the pass in other words + + align:start position:0% +the end after the pass in other words + + + align:start position:0% +the end after the pass in other words +after the first one I know that the + + align:start position:0% +after the first one I know that the + + + align:start position:0% +after the first one I know that the +largest elements at the end after the + + align:start position:0% +largest elements at the end after the + + + align:start position:0% +largest elements at the end after the +the second one the largest thing left is + + align:start position:0% +the second one the largest thing left is + + + align:start position:0% +the second one the largest thing left is +going to be in the next place and that + + align:start position:0% +going to be in the next place and that + + + align:start position:0% +going to be in the next place and that +tells me among other things that this is + + align:start position:0% +tells me among other things that this is + + + align:start position:0% +tells me among other things that this is +going to take no more than n times + + align:start position:0% +going to take no more than n times + + + align:start position:0% +going to take no more than n times +through the list to succeed might + + align:start position:0% +through the list to succeed might + + + align:start position:0% +through the list to succeed might +actually take fewer than + + align:start position:0% +actually take fewer than + + + align:start position:0% +actually take fewer than +that + + align:start position:0% +that + + + align:start position:0% +that +okay again let's look at some code for + + align:start position:0% +okay again let's look at some code for + + + align:start position:0% +okay again let's look at some code for +it let's look at its complexity and + + align:start position:0% +it let's look at its complexity and + + + align:start position:0% +it let's look at its complexity and +let's actually run this so here is a + + align:start position:0% +let's actually run this so here is a + + + align:start position:0% +let's actually run this so here is a +little simple version of bubble sort I'm + + align:start position:0% +little simple version of bubble sort I'm + + + align:start position:0% +little simple version of bubble sort I'm +going to set a flag up here I'm going to + + align:start position:0% +going to set a flag up here I'm going to + + + align:start position:0% +going to set a flag up here I'm going to +call it swap initially to false that's + + align:start position:0% +call it swap initially to false that's + + + align:start position:0% +call it swap initially to false that's +going to let me tell when I'm done when + + align:start position:0% +going to let me tell when I'm done when + + + align:start position:0% +going to let me tell when I'm done when +I'm gone through everything in the list + + align:start position:0% +I'm gone through everything in the list + + + align:start position:0% +I'm gone through everything in the list +without doing a swap and then I'm going + + align:start position:0% +without doing a swap and then I'm going + + + align:start position:0% +without doing a swap and then I'm going +to loop as long as swap is false so the + + align:start position:0% +to loop as long as swap is false so the + + + align:start position:0% +to loop as long as swap is false so the +first time through it's going to do that + + align:start position:0% +first time through it's going to do that + + + align:start position:0% +first time through it's going to do that +loop I set swap initially to true and + + align:start position:0% +loop I set swap initially to true and + + + align:start position:0% +loop I set swap initially to true and +notice what I then do I let J range from + + align:start position:0% +notice what I then do I let J range from + + + align:start position:0% +notice what I then do I let J range from +one up to the length of the list and I + + align:start position:0% +one up to the length of the list and I + + + align:start position:0% +one up to the length of the list and I +look at the jth element and the previous + + align:start position:0% +look at the jth element and the previous + + + align:start position:0% +look at the jth element and the previous +element If the previous element is + + align:start position:0% +element If the previous element is + + + align:start position:0% +element If the previous element is +bigger I'm going to flip them right + + align:start position:0% +bigger I'm going to flip them right + + + align:start position:0% +bigger I'm going to flip them right +there and that's just doing that swap + + align:start position:0% +there and that's just doing that swap + + + align:start position:0% +there and that's just doing that swap +what I just did down here and if that's + + align:start position:0% +what I just did down here and if that's + + + align:start position:0% +what I just did down here and if that's +the case I'm going to set the flag to + + align:start position:0% +the case I'm going to set the flag to + + + align:start position:0% +the case I'm going to set the flag to +false which says I've done at least one + + align:start position:0% +false which says I've done at least one + + + align:start position:0% +false which says I've done at least one +bubble as part of this which means when + + align:start position:0% +bubble as part of this which means when + + + align:start position:0% +bubble as part of this which means when +I come out of here and go back around to + + align:start position:0% +I come out of here and go back around to + + + align:start position:0% +I come out of here and go back around to +the loop it's going to do it again and + + align:start position:0% +the loop it's going to do it again and + + + align:start position:0% +the loop it's going to do it again and +it will do it until all of this succeeds + + align:start position:0% +it will do it until all of this succeeds + + + align:start position:0% +it will do it until all of this succeeds +without this ever being true in which + + align:start position:0% +without this ever being true in which + + + align:start position:0% +without this ever being true in which +case that's true which makes that false + + align:start position:0% +case that's true which makes that false + + + align:start position:0% +case that's true which makes that false +and it will drop + + align:start position:0% +and it will drop + + + align:start position:0% +and it will drop +out + + align:start position:0% +out + + + align:start position:0% +out +okay let's look at an example of this + + align:start position:0% +okay let's look at an example of this + + + align:start position:0% +okay let's look at an example of this +running it's just to give you a sense of + + align:start position:0% +running it's just to give you a sense of + + + align:start position:0% +running it's just to give you a sense of +that assuming I can find the right place + + align:start position:0% +that assuming I can find the right place + + + align:start position:0% +that assuming I can find the right place +here so there's again a version of sort + + align:start position:0% +here so there's again a version of sort + + + align:start position:0% +here so there's again a version of sort +um on the side and I'm going to bring + + align:start position:0% +um on the side and I'm going to bring + + + align:start position:0% +um on the side and I'm going to bring +this down to the bottom I've got a + + align:start position:0% +this down to the bottom I've got a + + + align:start position:0% +this down to the bottom I've got a +little test list there and I'm just I've + + align:start position:0% +little test list there and I'm just I've + + + align:start position:0% +little test list there and I'm just I've +put a a print statement in it so you can + + align:start position:0% +put a a print statement in it so you can + + + align:start position:0% +put a a print statement in it so you can +see each time through the loop what's + + align:start position:0% +see each time through the loop what's + + + align:start position:0% +see each time through the loop what's +the form of the list as it starts and + + align:start position:0% +the form of the list as it starts and + + + align:start position:0% +the form of the list as it starts and +assuming I've done this + + align:start position:0% +assuming I've done this + + + align:start position:0% +assuming I've done this +right there you + + align:start position:0% +right there you + + + align:start position:0% +right there you +go there's the list the first time + + align:start position:0% +go there's the list the first time + + + align:start position:0% +go there's the list the first time +through notice after one pass 25's at + + align:start position:0% +through notice after one pass 25's at + + + align:start position:0% +through notice after one pass 25's at +the end of the list the biggest element + + align:start position:0% +the end of the list the biggest element + + + align:start position:0% +the end of the list the biggest element +exactly what I like but you can also see + + align:start position:0% +exactly what I like but you can also see + + + align:start position:0% +exactly what I like but you can also see +a few other things have flipped right + + align:start position:0% +a few other things have flipped right + + + align:start position:0% +a few other things have flipped right +right in there there have been some + + align:start position:0% +right in there there have been some + + + align:start position:0% +right in there there have been some +other swaps as it bubbled through and in + + align:start position:0% +other swaps as it bubbled through and in + + + align:start position:0% +other swaps as it bubbled through and in +fact uh you can see uh it's well you can + + align:start position:0% +fact uh you can see uh it's well you can + + + align:start position:0% +fact uh you can see uh it's well you can +see that idea you can see 25 moving + + align:start position:0% +see that idea you can see 25 moving + + + align:start position:0% +see that idea you can see 25 moving +through notice on the next step a whole + + align:start position:0% +through notice on the next step a whole + + + align:start position:0% +through notice on the next step a whole +bunch of the list is actually in the + + align:start position:0% +bunch of the list is actually in the + + + align:start position:0% +bunch of the list is actually in the +right order it's just because I got + + align:start position:0% +right order it's just because I got + + + align:start position:0% +right order it's just because I got +lucky all I can guarantee is that the + + align:start position:0% +lucky all I can guarantee is that the + + + align:start position:0% +lucky all I can guarantee is that the +second largest element is at the second + + align:start position:0% +second largest element is at the second + + + align:start position:0% +second largest element is at the second +and or the second from the end at the + + align:start position:0% +and or the second from the end at the + + + align:start position:0% +and or the second from the end at the +list but you can see here even though + + align:start position:0% +list but you can see here even though + + + align:start position:0% +list but you can see here even though +the list is I think nine long it only + + align:start position:0% +the list is I think nine long it only + + + align:start position:0% +the list is I think nine long it only +took us four passes through so this is + + align:start position:0% +took us four passes through so this is + + + align:start position:0% +took us four passes through so this is +nice it says at most end times through + + align:start position:0% +nice it says at most end times through + + + align:start position:0% +nice it says at most end times through +the list and at the end we actually get + + align:start position:0% +the list and at the end we actually get + + + align:start position:0% +the list and at the end we actually get +out something that's in the right + + align:start position:0% +out something that's in the right + + + align:start position:0% +out something that's in the right +form okay so let's go back to this and + + align:start position:0% +form okay so let's go back to this and + + + align:start position:0% +form okay so let's go back to this and +basically say what's the + + align:start position:0% + + + + align:start position:0% + +complexity well that's length n right + + align:start position:0% +complexity well that's length n right + + + align:start position:0% +complexity well that's length n right +has to be I'm going through the entire + + align:start position:0% +has to be I'm going through the entire + + + align:start position:0% +has to be I'm going through the entire +list + + align:start position:0% +list + + + align:start position:0% +list +and inside of there is just constant + + align:start position:0% +and inside of there is just constant + + + align:start position:0% +and inside of there is just constant +work four operations I'm doing a test + + align:start position:0% +work four operations I'm doing a test + + + align:start position:0% +work four operations I'm doing a test +sorry five I'm doing a test and + + align:start position:0% +sorry five I'm doing a test and + + + align:start position:0% +sorry five I'm doing a test and +depending whether that test is true or + + align:start position:0% +depending whether that test is true or + + + align:start position:0% +depending whether that test is true or +not I'm setting a flag and doing some + + align:start position:0% +not I'm setting a flag and doing some + + + align:start position:0% +not I'm setting a flag and doing some +movement of things around but it's just + + align:start position:0% +movement of things around but it's just + + + align:start position:0% +movement of things around but it's just +const I don't care about the + + align:start position:0% +const I don't care about the + + + align:start position:0% +const I don't care about the +five and there how many times do I go + + align:start position:0% +five and there how many times do I go + + + align:start position:0% +five and there how many times do I go +around the loop in the worst case n all + + align:start position:0% +around the loop in the worst case n all + + + align:start position:0% +around the loop in the worst case n all +I can guarantee is after the first pass + + align:start position:0% +I can guarantee is after the first pass + + + align:start position:0% +I can guarantee is after the first pass +biggest thing is here after the second + + align:start position:0% +biggest thing is here after the second + + + align:start position:0% +biggest thing is here after the second +pass the second biggest thing is there + + align:start position:0% +pass the second biggest thing is there + + + align:start position:0% +pass the second biggest thing is there +after the third pass you get the idea so + + align:start position:0% +after the third pass you get the idea so + + + align:start position:0% +after the third pass you get the idea so +I've got order and things inside the + + align:start position:0% +I've got order and things inside the + + + align:start position:0% +I've got order and things inside the +loop and I'm doing that Loop end times + + align:start position:0% +loop and I'm doing that Loop end times + + + align:start position:0% +loop and I'm doing that Loop end times +and I hope that looks familiar we've + + align:start position:0% +and I hope that looks familiar we've + + + align:start position:0% +and I hope that looks familiar we've +talked about this right this is nested + + align:start position:0% +talked about this right this is nested + + + align:start position:0% +talked about this right this is nested +Loops what's this + + align:start position:0% +Loops what's this + + + align:start position:0% +Loops what's this +quadratic so it's order n squ where n is + + align:start position:0% +quadratic so it's order n squ where n is + + + align:start position:0% +quadratic so it's order n squ where n is +the length of the list now as you also + + align:start position:0% +the length of the list now as you also + + + align:start position:0% +the length of the list now as you also +saw on average it could be less than + + align:start position:0% +saw on average it could be less than + + + align:start position:0% +saw on average it could be less than +that but it's going to be order n + + align:start position:0% +that but it's going to be order n + + + align:start position:0% +that but it's going to be order n +squ + + align:start position:0% +squ + + + align:start position:0% +squ +okay that's one + + align:start position:0% +okay that's one + + + align:start position:0% +okay that's one +possibility here's the second nice + + align:start position:0% +possibility here's the second nice + + + align:start position:0% +possibility here's the second nice +simple sord algorithm it's called + + align:start position:0% +simple sord algorithm it's called + + + align:start position:0% +simple sord algorithm it's called +selection + + align:start position:0% +selection + + + align:start position:0% +selection +sort you can kind of think of this as + + align:start position:0% +sort you can kind of think of this as + + + align:start position:0% +sort you can kind of think of this as +going the other way not completely but + + align:start position:0% +going the other way not completely but + + + align:start position:0% +going the other way not completely but +going the other way when I say going the + + align:start position:0% +going the other way when I say going the + + + align:start position:0% +going the other way when I say going the +other way the idea here is that I'm + + align:start position:0% +other way the idea here is that I'm + + + align:start position:0% +other way the idea here is that I'm +going to find the smallest element in + + align:start position:0% +going to find the smallest element in + + + align:start position:0% +going to find the smallest element in +the list and I'm going to stick it at + + align:start position:0% +the list and I'm going to stick it at + + + align:start position:0% +the list and I'm going to stick it at +the front of the list when I'm done and + + align:start position:0% +the front of the list when I'm done and + + + align:start position:0% +the front of the list when I'm done and +simply swap that place with whatever was + + align:start position:0% +simply swap that place with whatever was + + + align:start position:0% +simply swap that place with whatever was +there flip them I might do a few other + + align:start position:0% +there flip them I might do a few other + + + align:start position:0% +there flip them I might do a few other +flips along the way depending how I + + align:start position:0% +flips along the way depending how I + + + align:start position:0% +flips along the way depending how I +implement this next pass I'm just going + + align:start position:0% +implement this next pass I'm just going + + + align:start position:0% +implement this next pass I'm just going +to look at everything but the first + + align:start position:0% +to look at everything but the first + + + align:start position:0% +to look at everything but the first +element because I know that one's done + + align:start position:0% +element because I know that one's done + + + align:start position:0% +element because I know that one's done +I'm going to do the same thing find the + + align:start position:0% +I'm going to do the same thing find the + + + align:start position:0% +I'm going to do the same thing find the +smallest element remaining in the list + + align:start position:0% +smallest element remaining in the list + + + align:start position:0% +smallest element remaining in the list +put it in the second spot and keep doing + + align:start position:0% +put it in the second spot and keep doing + + + align:start position:0% +put it in the second spot and keep doing +that what I know is if I imp this + + align:start position:0% +that what I know is if I imp this + + + align:start position:0% +that what I know is if I imp this +correctly after I steps the first I + + align:start position:0% +correctly after I steps the first I + + + align:start position:0% +correctly after I steps the first I +elements of the list will be sorted and + + align:start position:0% +elements of the list will be sorted and + + + align:start position:0% +elements of the list will be sorted and +everything in the rest of the list has + + align:start position:0% +everything in the rest of the list has + + + align:start position:0% +everything in the rest of the list has +to be bigger than the largest thing in + + align:start position:0% +to be bigger than the largest thing in + + + align:start position:0% +to be bigger than the largest thing in +the first part of the + + align:start position:0% +the first part of the + + + align:start position:0% +the first part of the +list okay so we could build that before + + align:start position:0% +list okay so we could build that before + + + align:start position:0% +list okay so we could build that before +we do it I'm going to show you a little + + align:start position:0% +we do it I'm going to show you a little + + + align:start position:0% +we do it I'm going to show you a little +video starring Professor gag this is his + + align:start position:0% +video starring Professor gag this is his + + + align:start position:0% +video starring Professor gag this is his +Cameo per performance here but I want to + + align:start position:0% +Cameo per performance here but I want to + + + align:start position:0% +Cameo per performance here but I want to +just show you an example of this using + + align:start position:0% +just show you an example of this using + + + align:start position:0% +just show you an example of this using +not numbers but people all right so now + + align:start position:0% +not numbers but people all right so now + + + align:start position:0% +not numbers but people all right so now +we're going to do selection sort the + + align:start position:0% +we're going to do selection sort the + + + align:start position:0% +we're going to do selection sort the +idea here is at each step we're going to + + align:start position:0% +idea here is at each step we're going to + + + align:start position:0% +idea here is at each step we're going to +select the shortest person and put them + + align:start position:0% +select the shortest person and put them + + + align:start position:0% +select the shortest person and put them +next in line of the sorted + + align:start position:0% +next in line of the sorted + + + align:start position:0% +next in line of the sorted +group so we'll bring the leftmost person + + align:start position:0% +group so we'll bring the leftmost person + + + align:start position:0% +group so we'll bring the leftmost person +forward and we will compare her to + + align:start position:0% +forward and we will compare her to + + + align:start position:0% +forward and we will compare her to +everybody else so one at a time step + + align:start position:0% +everybody else so one at a time step + + + align:start position:0% +everybody else so one at a time step +forward you're still the winner you go + + align:start position:0% +forward you're still the winner you go + + + align:start position:0% +forward you're still the winner you go +back please step + + align:start position:0% +back please step + + + align:start position:0% +back please step +forward and watch the number of + + align:start position:0% +forward and watch the number of + + + align:start position:0% +forward and watch the number of +comparisons that go on by the way we're + + align:start position:0% +comparisons that go on by the way we're + + + align:start position:0% +comparisons that go on by the way we're +going to go back to + + align:start position:0% +going to go back to + + + align:start position:0% +going to go back to +that + + align:start position:0% +that + + + align:start position:0% +that +still the + + align:start position:0% +still the + + + align:start position:0% +still the +winner + + align:start position:0% +winner + + + align:start position:0% +winner +next ah a new winner all right so you + + align:start position:0% +next ah a new winner all right so you + + + align:start position:0% +next ah a new winner all right so you +can take her place so here we're + + align:start position:0% +can take her place so here we're + + + align:start position:0% +can take her place so here we're +choosing to actually insert into the + + align:start position:0% +choosing to actually insert into the + + + align:start position:0% +choosing to actually insert into the +spot in the line we could have put her + + align:start position:0% +spot in the line we could have put her + + + align:start position:0% +spot in the line we could have put her +back at the front but this + + align:start position:0% +back at the front but this + + + align:start position:0% +back at the front but this +compare same old + + align:start position:0% + + + + align:start position:0% + +winner same + + align:start position:0% + + + + align:start position:0% + +winner no change + + align:start position:0% +winner no change + + + align:start position:0% +winner no change +it's getting kind of + + align:start position:0% +it's getting kind of + + + align:start position:0% +it's getting kind of +boring don't fall that we same + + align:start position:0% +boring don't fall that we same + + + align:start position:0% +boring don't fall that we same +winner + + align:start position:0% +winner + + + align:start position:0% +winner +please this is a tough + + align:start position:0% +please this is a tough + + + align:start position:0% +please this is a tough +one oh close but I think you're still + + align:start position:0% +one oh close but I think you're still + + + align:start position:0% +one oh close but I think you're still +shorter all right + + align:start position:0% + + + + align:start position:0% + +next no change which means you are the + + align:start position:0% +next no change which means you are the + + + align:start position:0% +next no change which means you are the +first in line congratulations so + + align:start position:0% +first in line congratulations so + + + align:start position:0% +first in line congratulations so +smallest element now guarant the first + + align:start position:0% +smallest element now guarant the first + + + align:start position:0% +smallest element now guarant the first +now you step forward and we'll compare + + align:start position:0% +now you step forward and we'll compare + + + align:start position:0% +now you step forward and we'll compare +are + + align:start position:0% + + + + align:start position:0% + +you and I would invite you to watch the + + align:start position:0% +you and I would invite you to watch the + + + align:start position:0% +you and I would invite you to watch the +left hand of the list notice how it is + + align:start position:0% +left hand of the list notice how it is + + + align:start position:0% +left hand of the list notice how it is +slowly building up at each stage to have + + align:start position:0% +slowly building up at each stage to have + + + align:start position:0% +slowly building up at each stage to have +that portion + + align:start position:0% + + + + align:start position:0% + +sorted and we deliberately admit + + align:start position:0% +sorted and we deliberately admit + + + align:start position:0% +sorted and we deliberately admit +students to be of different heights so + + align:start position:0% +students to be of different heights so + + + align:start position:0% +students to be of different heights so +John can do this + + align:start position:0% +John can do this + + + align:start position:0% +John can do this +demo you are the winner take your place + + align:start position:0% +demo you are the winner take your place + + + align:start position:0% +demo you are the winner take your place +in line + + align:start position:0% +in line + + + align:start position:0% +in line +next it's + + align:start position:0% + + + + align:start position:0% + +you and once again we have a lovely + + align:start position:0% +you and once again we have a lovely + + + align:start position:0% +you and once again we have a lovely +group of students sorted in height + + align:start position:0% +group of students sorted in height + + + align:start position:0% +group of students sorted in height +order and check out I want you to + + align:start position:0% +order and check out I want you to + + + align:start position:0% +order and check out I want you to +remember number of comparisons 55 not + + align:start position:0% +remember number of comparisons 55 not + + + align:start position:0% +remember number of comparisons 55 not +that the 50 but I want you to see a + + align:start position:0% +that the 50 but I want you to see a + + + align:start position:0% +that the 50 but I want you to see a +comparison as we go on in a second so + + align:start position:0% +comparison as we go on in a second so + + + align:start position:0% +comparison as we go on in a second so +again selection sort this is this idea + + align:start position:0% +again selection sort this is this idea + + + align:start position:0% +again selection sort this is this idea +of find the smallest element put it at + + align:start position:0% +of find the smallest element put it at + + + align:start position:0% +of find the smallest element put it at +the front and I might do a little number + + align:start position:0% +the front and I might do a little number + + + align:start position:0% +the front and I might do a little number +of flips as you can see here along the + + align:start position:0% +of flips as you can see here along the + + + align:start position:0% +of flips as you can see here along the +way but this is the same sort of + + align:start position:0% +way but this is the same sort of + + + align:start position:0% +way but this is the same sort of +animation of that so let's first of all + + align:start position:0% +animation of that so let's first of all + + + align:start position:0% +animation of that so let's first of all +convince ourselves it will do the right + + align:start position:0% +convince ourselves it will do the right + + + align:start position:0% +convince ourselves it will do the right +thing and then look at some code and + + align:start position:0% +thing and then look at some code and + + + align:start position:0% +thing and then look at some code and +then run the + + align:start position:0% +then run the + + + align:start position:0% +then run the +code so to convince ourselves that this + + align:start position:0% +code so to convince ourselves that this + + + align:start position:0% +code so to convince ourselves that this +is going to do the right thing we could + + align:start position:0% +is going to do the right thing we could + + + align:start position:0% +is going to do the right thing we could +talk about something that we often refer + + align:start position:0% +talk about something that we often refer + + + align:start position:0% +talk about something that we often refer +to as a loop invariant we're going to + + align:start position:0% +to as a loop invariant we're going to + + + align:start position:0% +to as a loop invariant we're going to +write a loop where we're going to walk + + align:start position:0% +write a loop where we're going to walk + + + align:start position:0% +write a loop where we're going to walk +through this and the invariant here we + + align:start position:0% +through this and the invariant here we + + + align:start position:0% +through this and the invariant here we +want to just demonstrate if it's true at + + align:start position:0% +want to just demonstrate if it's true at + + + align:start position:0% +want to just demonstrate if it's true at +the beginning and it's true at each step + + align:start position:0% +the beginning and it's true at each step + + + align:start position:0% +the beginning and it's true at each step +therefore by induction as we did earlier + + align:start position:0% +therefore by induction as we did earlier + + + align:start position:0% +therefore by induction as we did earlier +I can conclude it's true always is that + + align:start position:0% +I can conclude it's true always is that + + + align:start position:0% +I can conclude it's true always is that +if I'm given the prefix or the first + + align:start position:0% +if I'm given the prefix or the first + + + align:start position:0% +if I'm given the prefix or the first +part of a list from zero up to I and a + + align:start position:0% +part of a list from zero up to I and a + + + align:start position:0% +part of a list from zero up to I and a +suffix or a second part of the list from + + align:start position:0% +suffix or a second part of the list from + + + align:start position:0% +suffix or a second part of the list from +i+ one up to the end of the overall list + + align:start position:0% +i+ one up to the end of the overall list + + + align:start position:0% +i+ one up to the end of the overall list +given that then I'm going to assert that + + align:start position:0% +given that then I'm going to assert that + + + align:start position:0% +given that then I'm going to assert that +the invariant is that the prefix is + + align:start position:0% +the invariant is that the prefix is + + + align:start position:0% +the invariant is that the prefix is +sorted and no element of the prefix is + + align:start position:0% +sorted and no element of the prefix is + + + align:start position:0% +sorted and no element of the prefix is +larger than the smallest element of the + + align:start position:0% +larger than the smallest element of the + + + align:start position:0% +larger than the smallest element of the +suffix just what I said earlier says at + + align:start position:0% +suffix just what I said earlier says at + + + align:start position:0% +suffix just what I said earlier says at +any stage here if this is the amount of + + align:start position:0% +any stage here if this is the amount of + + + align:start position:0% +any stage here if this is the amount of +sort I've done so far I can guarantee + + align:start position:0% +sort I've done so far I can guarantee + + + align:start position:0% +sort I've done so far I can guarantee +I'm going to claim this will be sorted + + align:start position:0% +I'm going to claim this will be sorted + + + align:start position:0% +I'm going to claim this will be sorted +and everything here is bigger than that + + align:start position:0% +and everything here is bigger than that + + + align:start position:0% +and everything here is bigger than that +thing + + align:start position:0% +thing + + + align:start position:0% +thing +there how do I prove + + align:start position:0% +there how do I prove + + + align:start position:0% +there how do I prove +it the base case is really easy in the + + align:start position:0% +it the base case is really easy in the + + + align:start position:0% +it the base case is really easy in the +base case the prefix is empty I don't + + align:start position:0% +base case the prefix is empty I don't + + + align:start position:0% +base case the prefix is empty I don't +have anything so it's obviously sorted + + align:start position:0% +have anything so it's obviously sorted + + + align:start position:0% +have anything so it's obviously sorted +and everything in the suffix is bigger + + align:start position:0% +and everything in the suffix is bigger + + + align:start position:0% +and everything in the suffix is bigger +than anything in the prefix so I'm fine + + align:start position:0% +than anything in the prefix so I'm fine + + + align:start position:0% +than anything in the prefix so I'm fine +and then I just want to say as long as I + + align:start position:0% +and then I just want to say as long as I + + + align:start position:0% +and then I just want to say as long as I +write my code so that this step is true + + align:start position:0% +write my code so that this step is true + + + align:start position:0% +write my code so that this step is true +then I'm going to move the smallest + + align:start position:0% +then I'm going to move the smallest + + + align:start position:0% +then I'm going to move the smallest +element from the suffix the second part + + align:start position:0% +element from the suffix the second part + + + align:start position:0% +element from the suffix the second part +of the list to the end of the prefix + + align:start position:0% +of the list to the end of the prefix + + + align:start position:0% +of the list to the end of the prefix +since the prefix was sorted this is now + + align:start position:0% +since the prefix was sorted this is now + + + align:start position:0% +since the prefix was sorted this is now +sorted and everything in the suffix is + + align:start position:0% +sorted and everything in the suffix is + + + align:start position:0% +sorted and everything in the suffix is +still going to be bigger than everything + + align:start position:0% +still going to be bigger than everything + + + align:start position:0% +still going to be bigger than everything +in the prefix and as a consequence by + + align:start position:0% +in the prefix and as a consequence by + + + align:start position:0% +in the prefix and as a consequence by +induction this is going to give me + + align:start position:0% +induction this is going to give me + + + align:start position:0% +induction this is going to give me +something that says it's always going to + + align:start position:0% +something that says it's always going to + + + align:start position:0% +something that says it's always going to +be + + align:start position:0% +be + + + align:start position:0% +be +correct so here's code that would do + + align:start position:0% +correct so here's code that would do + + + align:start position:0% +correct so here's code that would do +that here I'm just going to set a little + + align:start position:0% +that here I'm just going to set a little + + + align:start position:0% +that here I'm just going to set a little +thing called the start of suffix or + + align:start position:0% +thing called the start of suffix or + + + align:start position:0% +thing called the start of suffix or +suffix start initially it's going to + + align:start position:0% +suffix start initially it's going to + + + align:start position:0% +suffix start initially it's going to +point to to the beginning of the list + + align:start position:0% +point to to the beginning of the list + + + align:start position:0% +point to to the beginning of the list +and then I'm going to run a loop and as + + align:start position:0% +and then I'm going to run a loop and as + + + align:start position:0% +and then I'm going to run a loop and as +long as I still have things to search in + + align:start position:0% +long as I still have things to search in + + + align:start position:0% +long as I still have things to search in +the list that that pointer doesn't point + + align:start position:0% +the list that that pointer doesn't point + + + align:start position:0% +the list that that pointer doesn't point +to the end of the list what am I going + + align:start position:0% +to the end of the list what am I going + + + align:start position:0% +to the end of the list what am I going +to do I'm going to Loop over everything + + align:start position:0% +to do I'm going to Loop over everything + + + align:start position:0% +to do I'm going to Loop over everything +from that point to the end of the list + + align:start position:0% +from that point to the end of the list + + + align:start position:0% +from that point to the end of the list +comparing it to the thing at that + + align:start position:0% +comparing it to the thing at that + + + align:start position:0% +comparing it to the thing at that +point if it's less than I'm going to do + + align:start position:0% +point if it's less than I'm going to do + + + align:start position:0% +point if it's less than I'm going to do +a swap because I want it to move it up + + align:start position:0% +a swap because I want it to move it up + + + align:start position:0% +a swap because I want it to move it up +and you can see by the time I get + + align:start position:0% +and you can see by the time I get + + + align:start position:0% +and you can see by the time I get +through this loop I will have found the + + align:start position:0% +through this loop I will have found the + + + align:start position:0% +through this loop I will have found the +smallest element in the remainder of the + + align:start position:0% +smallest element in the remainder of the + + + align:start position:0% +smallest element in the remainder of the +list and I would have put it at that + + align:start position:0% +list and I would have put it at that + + + align:start position:0% +list and I would have put it at that +spot whatever suffix start points to and + + align:start position:0% +spot whatever suffix start points to and + + + align:start position:0% +spot whatever suffix start points to and +when I'm done all of that I just change + + align:start position:0% +when I'm done all of that I just change + + + align:start position:0% +when I'm done all of that I just change +this by one having found the smallest + + align:start position:0% +this by one having found the smallest + + + align:start position:0% +this by one having found the smallest +element I've stuck it at spot zero I'll + + align:start position:0% +element I've stuck it at spot zero I'll + + + align:start position:0% +element I've stuck it at spot zero I'll +do the same thing having found the next + + align:start position:0% +do the same thing having found the next + + + align:start position:0% +do the same thing having found the next +smallest element I know it's at 0.1 and + + align:start position:0% +smallest element I know it's at 0.1 and + + + align:start position:0% +smallest element I know it's at 0.1 and +I'll just continue + + align:start position:0% +I'll just continue + + + align:start position:0% +I'll just continue +around one of the things you can see + + align:start position:0% +around one of the things you can see + + + align:start position:0% +around one of the things you can see +here is as opposed to bubble + + align:start position:0% +here is as opposed to bubble + + + align:start position:0% +here is as opposed to bubble +sort this one is going to take n times + + align:start position:0% +sort this one is going to take n times + + + align:start position:0% +sort this one is going to take n times +around the loop because I'm only moving + + align:start position:0% +around the loop because I'm only moving + + + align:start position:0% +around the loop because I'm only moving +this pointer by one so it starts at zero + + align:start position:0% +this pointer by one so it starts at zero + + + align:start position:0% +this pointer by one so it starts at zero +and then one and then two all the way up + + align:start position:0% +and then one and then two all the way up + + + align:start position:0% +and then one and then two all the way up +to n minus one you can also see in this + + align:start position:0% +to n minus one you can also see in this + + + align:start position:0% +to n minus one you can also see in this +particular implementation while I'm + + align:start position:0% +particular implementation while I'm + + + align:start position:0% +particular implementation while I'm +certainly ensuring that the smallest + + align:start position:0% +certainly ensuring that the smallest + + + align:start position:0% +certainly ensuring that the smallest +element goes into that spot I may do a a + + align:start position:0% +element goes into that spot I may do a a + + + align:start position:0% +element goes into that spot I may do a a +few other flips along the way I'm going + + align:start position:0% +few other flips along the way I'm going + + + align:start position:0% +few other flips along the way I'm going +to find something I think is the + + align:start position:0% +to find something I think is the + + + align:start position:0% +to find something I think is the +smallest element put it there and put + + align:start position:0% +smallest element put it there and put + + + align:start position:0% +smallest element put it there and put +that element here and then when I find + + align:start position:0% +that element here and then when I find + + + align:start position:0% +that element here and then when I find +another smaller element I may do that + + align:start position:0% +another smaller element I may do that + + + align:start position:0% +another smaller element I may do that +flip I could have implemented this where + + align:start position:0% +flip I could have implemented this where + + + align:start position:0% +flip I could have implemented this where +I literally search for the smallest + + align:start position:0% +I literally search for the smallest + + + align:start position:0% +I literally search for the smallest +element and only move that doesn't make + + align:start position:0% +element and only move that doesn't make + + + align:start position:0% +element and only move that doesn't make +any difference in terms of the + + align:start position:0% +any difference in terms of the + + + align:start position:0% +any difference in terms of the +complexity all right what's the + + align:start position:0% +complexity all right what's the + + + align:start position:0% +complexity all right what's the +complexity here already said this part I + + align:start position:0% +complexity here already said this part I + + + align:start position:0% +complexity here already said this part I +will Loop end times because I start at + + align:start position:0% +will Loop end times because I start at + + + align:start position:0% +will Loop end times because I start at +zero and then one you get the idea + + align:start position:0% +zero and then one you get the idea + + + align:start position:0% +zero and then one you get the idea +inside of the + + align:start position:0% +inside of the + + + align:start position:0% +inside of the +loop I'm going to walk down the + + align:start position:0% +loop I'm going to walk down the + + + align:start position:0% +loop I'm going to walk down the +remainder of the list which is initially + + align:start position:0% +remainder of the list which is initially + + + align:start position:0% +remainder of the list which is initially +n and then n minus one and then n minus + + align:start position:0% +n and then n minus one and then n minus + + + align:start position:0% +n and then n minus one and then n minus + + align:start position:0% + + + align:start position:0% +times but we've seen that before as well + + align:start position:0% +times but we've seen that before as well + + + align:start position:0% +times but we've seen that before as well +while it gets shorter that complexity is + + align:start position:0% +while it gets shorter that complexity is + + + align:start position:0% +while it gets shorter that complexity is +still + + align:start position:0% +still + + + align:start position:0% +still +quadratic order and times going through + + align:start position:0% +quadratic order and times going through + + + align:start position:0% +quadratic order and times going through +this process within the process order + + align:start position:0% +this process within the process order + + + align:start position:0% +this process within the process order +and things that I have to compare and + + align:start position:0% +and things that I have to compare and + + + align:start position:0% +and things that I have to compare and +yes n gets smaller but we know that that + + align:start position:0% +yes n gets smaller but we know that that + + + align:start position:0% +yes n gets smaller but we know that that +that that n term if you like dominate so + + align:start position:0% +that that n term if you like dominate so + + + align:start position:0% +that that n term if you like dominate so +again this is + + align:start position:0% +again this is + + + align:start position:0% +again this is +quadratic okay before you believe that + + align:start position:0% +quadratic okay before you believe that + + + align:start position:0% +quadratic okay before you believe that +all sorting algorithms are quadratic I + + align:start position:0% +all sorting algorithms are quadratic I + + + align:start position:0% +all sorting algorithms are quadratic I +want to show you the last one the one + + align:start position:0% +want to show you the last one the one + + + align:start position:0% +want to show you the last one the one +that actually is is one of the I think + + align:start position:0% +that actually is is one of the I think + + + align:start position:0% +that actually is is one of the I think +the the prettiest algorithms around in a + + align:start position:0% +the the prettiest algorithms around in a + + + align:start position:0% +the the prettiest algorithms around in a +great example of a more efficient + + align:start position:0% +great example of a more efficient + + + align:start position:0% +great example of a more efficient +algorithm is called merge + + align:start position:0% +algorithm is called merge + + + align:start position:0% +algorithm is called merge +sort merge sort takes an approach we've + + align:start position:0% +sort merge sort takes an approach we've + + + align:start position:0% +sort merge sort takes an approach we've +seen before talked about divide and + + align:start position:0% +seen before talked about divide and + + + align:start position:0% +seen before talked about divide and +conquer break the problem down into + + align:start position:0% +conquer break the problem down into + + + align:start position:0% +conquer break the problem down into +smaller versions of the same problem and + + align:start position:0% +smaller versions of the same problem and + + + align:start position:0% +smaller versions of the same problem and +once you've got those Solutions bring + + align:start position:0% +once you've got those Solutions bring + + + align:start position:0% +once you've got those Solutions bring +the answer back together for merge sort + + align:start position:0% +the answer back together for merge sort + + + align:start position:0% +the answer back together for merge sort +that's pretty easy it says if I've got a + + align:start position:0% +that's pretty easy it says if I've got a + + + align:start position:0% +that's pretty easy it says if I've got a +list of zero or one elements it's sorted + + align:start position:0% +list of zero or one elements it's sorted + + + align:start position:0% +list of zero or one elements it's sorted +duh okay if I got a list of more more + + align:start position:0% +duh okay if I got a list of more more + + + align:start position:0% +duh okay if I got a list of more more +than one element here's my trick going + + align:start position:0% +than one element here's my trick going + + + align:start position:0% +than one element here's my trick going +to split it into two lists I'm going to + + align:start position:0% +to split it into two lists I'm going to + + + align:start position:0% +to split it into two lists I'm going to +sort them and when I'm done I'm just + + align:start position:0% +sort them and when I'm done I'm just + + + align:start position:0% +sort them and when I'm done I'm just +going to merge those two lists into one + + align:start position:0% +going to merge those two lists into one + + + align:start position:0% +going to merge those two lists into one +list and the merge is easy because if + + align:start position:0% +list and the merge is easy because if + + + align:start position:0% +list and the merge is easy because if +I've got two lists that are sorted I + + align:start position:0% +I've got two lists that are sorted I + + + align:start position:0% +I've got two lists that are sorted I +just need to look at the first element + + align:start position:0% +just need to look at the first element + + + align:start position:0% +just need to look at the first element +of each take the one that's smaller add + + align:start position:0% +of each take the one that's smaller add + + + align:start position:0% +of each take the one that's smaller add +it to my result and keep doing that + + align:start position:0% +it to my result and keep doing that + + + align:start position:0% +it to my result and keep doing that +until one of the lists is empty and then + + align:start position:0% +until one of the lists is empty and then + + + align:start position:0% +until one of the lists is empty and then +just copy the remainder of the other + + align:start position:0% +just copy the remainder of the other + + + align:start position:0% +just copy the remainder of the other +list you can probably already get a + + align:start position:0% +list you can probably already get a + + + align:start position:0% +list you can probably already get a +sense of what the cost is going to to be + + align:start position:0% +sense of what the cost is going to to be + + + align:start position:0% +sense of what the cost is going to to be +here because this is cutting the problem + + align:start position:0% +here because this is cutting the problem + + + align:start position:0% +here because this is cutting the problem +in half now I've got two pieces so I + + align:start position:0% +in half now I've got two pieces so I + + + align:start position:0% +in half now I've got two pieces so I +need to think about both of them I want + + align:start position:0% +need to think about both of them I want + + + align:start position:0% +need to think about both of them I want +to give you a couple of visualizations + + align:start position:0% +to give you a couple of visualizations + + + align:start position:0% +to give you a couple of visualizations +of this here's the first one it says + + align:start position:0% +of this here's the first one it says + + + align:start position:0% +of this here's the first one it says +basically I've got a big unsorted list + + align:start position:0% +basically I've got a big unsorted list + + + align:start position:0% +basically I've got a big unsorted list +I'm going to split it and I'm going to + + align:start position:0% +I'm going to split it and I'm going to + + + align:start position:0% +I'm going to split it and I'm going to +split it and I'm going to split it until + + align:start position:0% +split it and I'm going to split it until + + + align:start position:0% +split it and I'm going to split it until +I get down to just lists that are either + + align:start position:0% +I get down to just lists that are either + + + align:start position:0% +I get down to just lists that are either +zero or one which by definition are + + align:start position:0% +zero or one which by definition are + + + align:start position:0% +zero or one which by definition are +sorted and once I'm at that level then I + + align:start position:0% +sorted and once I'm at that level then I + + + align:start position:0% +sorted and once I'm at that level then I +just have to merge them into a sorted + + align:start position:0% +just have to merge them into a sorted + + + align:start position:0% +just have to merge them into a sorted +list and then merge them pairwise into a + + align:start position:0% +list and then merge them pairwise into a + + + align:start position:0% +list and then merge them pairwise into a +sorted list and you get the + + align:start position:0% +sorted list and you get the + + + align:start position:0% +sorted list and you get the +idea so it's divide and conquer the + + align:start position:0% +idea so it's divide and conquer the + + + align:start position:0% +idea so it's divide and conquer the +Divide is dividing it up into smaller + + align:start position:0% +Divide is dividing it up into smaller + + + align:start position:0% +Divide is dividing it up into smaller +pieces the conquer is merging them back + + align:start position:0% +pieces the conquer is merging them back + + + align:start position:0% +pieces the conquer is merging them back +together and we have Professor good tag + + align:start position:0% +together and we have Professor good tag + + + align:start position:0% +together and we have Professor good tag +back for an encore together with his + + align:start position:0% +back for an encore together with his + + + align:start position:0% +back for an encore together with his +students so let's show you an example of + + align:start position:0% +students so let's show you an example of + + + align:start position:0% +students so let's show you an example of +merge sort so we're about to demonstrate + + align:start position:0% +merge sort so we're about to demonstrate + + + align:start position:0% +merge sort so we're about to demonstrate +merge sort and we're going to sort this + + align:start position:0% +merge sort and we're going to sort this + + + align:start position:0% +merge sort and we're going to sort this +rather mly collection of MIT students by + + align:start position:0% +rather mly collection of MIT students by + + + align:start position:0% +rather mly collection of MIT students by +height + + align:start position:0% +height + + + align:start position:0% +height +so the first thing we need to do is + + align:start position:0% +so the first thing we need to do is + + + align:start position:0% +so the first thing we need to do is +we're going to ask everyone to split + + align:start position:0% +we're going to ask everyone to split + + + align:start position:0% +we're going to ask everyone to split +into a group of two so you split a + + align:start position:0% +into a group of two so you split a + + + align:start position:0% +into a group of two so you split a +little bit you two are together you two + + align:start position:0% +little bit you two are together you two + + + align:start position:0% +little bit you two are together you two +are together you two are together you + + align:start position:0% +are together you two are together you + + + align:start position:0% +are together you two are together you +two are together and you are all by + + align:start position:0% +two are together and you are all by + + + align:start position:0% +two are together and you are all by +yourself I'm + + align:start position:0% +yourself I'm + + + align:start position:0% +yourself I'm +sorry all right forna so now let's take + + align:start position:0% +sorry all right forna so now let's take + + + align:start position:0% +sorry all right forna so now let's take +the first group take a step down and + + align:start position:0% +the first group take a step down and + + + align:start position:0% +the first group take a step down and +what we do is we sort this group by + + align:start position:0% +what we do is we sort this group by + + + align:start position:0% +what we do is we sort this group by +with the shortest on the left and look + + align:start position:0% +with the shortest on the left and look + + + align:start position:0% +with the shortest on the left and look +at this we don't have to do anything + + align:start position:0% +at this we don't have to do anything + + + align:start position:0% +at this we don't have to do anything +thank you feel free to go back + + align:start position:0% +thank you feel free to go back + + + align:start position:0% +thank you feel free to go back +up we then sort the next pair please and + + align:start position:0% +up we then sort the next pair please and + + + align:start position:0% +up we then sort the next pair please and +it looks to me like we need to + + align:start position:0% +it looks to me like we need to + + + align:start position:0% +it looks to me like we need to +switch all right take a step + + align:start position:0% +switch all right take a step + + + align:start position:0% +switch all right take a step +back + + align:start position:0% + + + + align:start position:0% + +ladies + + align:start position:0% +ladies + + + align:start position:0% +ladies +okay ladies gentlemen + + align:start position:0% +okay ladies gentlemen + + + align:start position:0% +okay ladies gentlemen +also + + align:start position:0% + + + + align:start position:0% + +okay and again + + align:start position:0% +okay and again + + + align:start position:0% +okay and again +okay notice each subgroup is now which + + align:start position:0% +okay notice each subgroup is now which + + + align:start position:0% +okay notice each subgroup is now which +is + + align:start position:0% +is + + + align:start position:0% +is +great now what we do is we take these + + align:start position:0% +great now what we do is we take these + + + align:start position:0% +great now what we do is we take these +groups and merge the groups so let's + + align:start position:0% +groups and merge the groups so let's + + + align:start position:0% +groups and merge the groups so let's +have these two going to sort these + + align:start position:0% +have these two going to sort these + + + align:start position:0% +have these two going to sort these +groups have them step + + align:start position:0% +groups have them step + + + align:start position:0% +groups have them step +forward and now what we're doing is + + align:start position:0% +forward and now what we're doing is + + + align:start position:0% +forward and now what we're doing is +we're doing a merge of the the two + + align:start position:0% +we're doing a merge of the the two + + + align:start position:0% +we're doing a merge of the the two +sorted groups so we start by merging + + align:start position:0% +sorted groups so we start by merging + + + align:start position:0% +sorted groups so we start by merging +them we'll take the leftmost person in + + align:start position:0% +them we'll take the leftmost person in + + + align:start position:0% +them we'll take the leftmost person in +this group and compare her to the first + + align:start position:0% +this group and compare her to the first + + + align:start position:0% +this group and compare her to the first +person in this group and decide she's + + align:start position:0% +person in this group and decide she's + + + align:start position:0% +person in this group and decide she's +still the shortest take a step + + align:start position:0% + + + + align:start position:0% + +back now we're going to look at you and + + align:start position:0% +back now we're going to look at you and + + + align:start position:0% +back now we're going to look at you and +say you're actually taller than this + + align:start position:0% +say you're actually taller than this + + + align:start position:0% +say you're actually taller than this +fellow so you now step up + + align:start position:0% +fellow so you now step up + + + align:start position:0% +fellow so you now step up +there + + align:start position:0% +there + + + align:start position:0% +there +and we're good here both of you take a + + align:start position:0% +and we're good here both of you take a + + + align:start position:0% +and we're good here both of you take a +step + + align:start position:0% + + + + align:start position:0% + +back now we'll take these two groups and + + align:start position:0% +back now we'll take these two groups and + + + align:start position:0% +back now we'll take these two groups and +follow the same procedure we'll merge + + align:start position:0% +follow the same procedure we'll merge + + + align:start position:0% +follow the same procedure we'll merge +them let's see we'll compare you the + + align:start position:0% +them let's see we'll compare you the + + + align:start position:0% +them let's see we'll compare you the +first person in this group to the first + + align:start position:0% +first person in this group to the first + + + align:start position:0% +first person in this group to the first +person in this group now it's a little + + align:start position:0% +person in this group now it's a little + + + align:start position:0% +person in this group now it's a little +tricky so let's see the two of you + + align:start position:0% +tricky so let's see the two of you + + + align:start position:0% +tricky so let's see the two of you +compare let's see back to + + align:start position:0% +compare let's see back to + + + align:start position:0% +compare let's see back to +back we have a + + align:start position:0% +back we have a + + + align:start position:0% +back we have a +winner set back and now we need to + + align:start position:0% +winner set back and now we need to + + + align:start position:0% +winner set back and now we need to +compare the shortest person in this + + align:start position:0% +compare the shortest person in this + + + align:start position:0% +compare the shortest person in this +group to the shortest person in this + + align:start position:0% +group to the shortest person in this + + + align:start position:0% +group to the shortest person in this +group we have a winner it's + + align:start position:0% +group we have a winner it's + + + align:start position:0% +group we have a winner it's +you I'm sorry and now we just we're okay + + align:start position:0% +you I'm sorry and now we just we're okay + + + align:start position:0% +you I'm sorry and now we just we're okay +please step + + align:start position:0% + + + + align:start position:0% + +back now we'll have these two groups + + align:start position:0% +back now we'll have these two groups + + + align:start position:0% +back now we'll have these two groups +come forward we'll compare the shortest + + align:start position:0% +come forward we'll compare the shortest + + + align:start position:0% +come forward we'll compare the shortest +person in this group to the shortest + + align:start position:0% +person in this group to the shortest + + + align:start position:0% +person in this group to the shortest +person in that group I actually need you + + align:start position:0% +person in that group I actually need you + + + align:start position:0% +person in that group I actually need you +guys to get back to back here + + align:start position:0% + + + + align:start position:0% + +you are the + + align:start position:0% +you are the + + + align:start position:0% +you are the +winner and it's pretty clear that the + + align:start position:0% +winner and it's pretty clear that the + + + align:start position:0% +winner and it's pretty clear that the +shortest person in this group is shorter + + align:start position:0% +shortest person in this group is shorter + + + align:start position:0% +shortest person in this group is shorter +than the shortest person in that group + + align:start position:0% +than the shortest person in that group + + + align:start position:0% +than the shortest person in that group +so you go there and you step back notice + + align:start position:0% +so you go there and you step back notice + + + align:start position:0% +so you go there and you step back notice +the groups sorted now we repeat the same + + align:start position:0% + + + + align:start position:0% + +process and notice how the whole + + align:start position:0% +process and notice how the whole + + + align:start position:0% +process and notice how the whole +subgroup now goes up once we know that + + align:start position:0% +subgroup now goes up once we know that + + + align:start position:0% +subgroup now goes up once we know that +one group is + + align:start position:0% +one group is + + + align:start position:0% +one group is +empty + + align:start position:0% + + + + align:start position:0% + +and you can see that we have a group of + + align:start position:0% +and you can see that we have a group of + + + align:start position:0% +and you can see that we have a group of +students sorted in order by + + align:start position:0% + + + + align:start position:0% + +height remember the first number right + + align:start position:0% +height remember the first number right + + + align:start position:0% +height remember the first number right +55 28 now this just numbers but you can + + align:start position:0% +55 28 now this just numbers but you can + + + align:start position:0% +55 28 now this just numbers but you can +see the expectation is this is going to + + align:start position:0% +see the expectation is this is going to + + + align:start position:0% +see the expectation is this is going to +take less time and it certainly did + + align:start position:0% +take less time and it certainly did + + + align:start position:0% +take less time and it certainly did +there so getting just the demo another + + align:start position:0% +there so getting just the demo another + + + align:start position:0% +there so getting just the demo another +way visually I'm sorting sorry I'm + + align:start position:0% +way visually I'm sorting sorry I'm + + + align:start position:0% +way visually I'm sorting sorry I'm +splitting down until I get small things + + align:start position:0% +splitting down until I get small things + + + align:start position:0% +splitting down until I get small things +and then just merging them up I may have + + align:start position:0% +and then just merging them up I may have + + + align:start position:0% +and then just merging them up I may have +to do multiple passes through here but + + align:start position:0% +to do multiple passes through here but + + + align:start position:0% +to do multiple passes through here but +it's going to be hopefully faster than + + align:start position:0% +it's going to be hopefully faster than + + + align:start position:0% +it's going to be hopefully faster than +the other methods we looked + + align:start position:0% +the other methods we looked + + + align:start position:0% +the other methods we looked +at I'm going to show you code in a + + align:start position:0% +at I'm going to show you code in a + + + align:start position:0% +at I'm going to show you code in a +second and then we're going to run it + + align:start position:0% +second and then we're going to run it + + + align:start position:0% +second and then we're going to run it +just to see it but let me stress one + + align:start position:0% +just to see it but let me stress one + + + align:start position:0% +just to see it but let me stress one +more time just the idea of + + align:start position:0% +more time just the idea of + + + align:start position:0% +more time just the idea of +merging you can see the idea I keep + + align:start position:0% +merging you can see the idea I keep + + + align:start position:0% +merging you can see the idea I keep +splitting down till I got something + + align:start position:0% +splitting down till I got something + + + align:start position:0% +splitting down till I got something +small enough I want to merge them back + + align:start position:0% +small enough I want to merge them back + + + align:start position:0% +small enough I want to merge them back +the idea of merging you've seen it from + + align:start position:0% +the idea of merging you've seen it from + + + align:start position:0% +the idea of merging you've seen it from +Prof from Professor good tag but I just + + align:start position:0% +Prof from Professor good tag but I just + + + align:start position:0% +Prof from Professor good tag but I just +want to highlight why this is going to + + align:start position:0% +want to highlight why this is going to + + + align:start position:0% +want to highlight why this is going to +be efficient if I've got two lists + + align:start position:0% + + + + align:start position:0% + +comparisons I'm only comparing the ends + + align:start position:0% +comparisons I'm only comparing the ends + + + align:start position:0% +comparisons I'm only comparing the ends +of the list I only therefore look at + + align:start position:0% +of the list I only therefore look at + + + align:start position:0% +of the list I only therefore look at +each element or the number of + + align:start position:0% +each element or the number of + + + align:start position:0% +each element or the number of +comparisons rather I should say I do I + + align:start position:0% +comparisons rather I should say I do I + + + align:start position:0% +comparisons rather I should say I do I +may look at each element more than once + + align:start position:0% +may look at each element more than once + + + align:start position:0% +may look at each element more than once +the number of comparisons is going to be + + align:start position:0% +the number of comparisons is going to be + + + align:start position:0% +the number of comparisons is going to be +at most the number of elements in both + + align:start position:0% +at most the number of elements in both + + + align:start position:0% +at most the number of elements in both +lists and that's going to be a nice cue + + align:start position:0% +lists and that's going to be a nice cue + + + align:start position:0% +lists and that's going to be a nice cue +as we think about how to solve + + align:start position:0% +as we think about how to solve + + + align:start position:0% +as we think about how to solve +it so here's the code to merge and then + + align:start position:0% +it so here's the code to merge and then + + + align:start position:0% +it so here's the code to merge and then +we'll write merge sort and I know + + align:start position:0% +we'll write merge sort and I know + + + align:start position:0% +we'll write merge sort and I know +there's a lot of code here but we can + + align:start position:0% +there's a lot of code here but we can + + + align:start position:0% +there's a lot of code here but we can +walk through it and get a good sense of + + align:start position:0% +walk through it and get a good sense of + + + align:start position:0% +walk through it and get a good sense of +it I'm going to set up variable called + + align:start position:0% +it I'm going to set up variable called + + + align:start position:0% +it I'm going to set up variable called +result that's going to hold my answer + + align:start position:0% +result that's going to hold my answer + + + align:start position:0% +result that's going to hold my answer +and I'm going to set up two indices I + + align:start position:0% +and I'm going to set up two indices I + + + align:start position:0% +and I'm going to set up two indices I +and J that are initially zero they're + + align:start position:0% +and J that are initially zero they're + + + align:start position:0% +and J that are initially zero they're +pointing to the beginning and remember + + align:start position:0% +pointing to the beginning and remember + + + align:start position:0% +pointing to the beginning and remember +the input here is two lists that we know + + align:start position:0% +the input here is two lists that we know + + + align:start position:0% +the input here is two lists that we know +are sorted or should be sorted or we + + align:start position:0% +are sorted or should be sorted or we + + + align:start position:0% +are sorted or should be sorted or we +screwed up in some way so initially I + + align:start position:0% +screwed up in some way so initially I + + + align:start position:0% +screwed up in some way so initially I +and J are both pointing to the beginning + + align:start position:0% +and J are both pointing to the beginning + + + align:start position:0% +and J are both pointing to the beginning +of the left and right list and look at + + align:start position:0% +of the left and right list and look at + + + align:start position:0% +of the left and right list and look at +what we do we say as long as there's + + align:start position:0% +what we do we say as long as there's + + + align:start position:0% +what we do we say as long as there's +still something in the left list and + + align:start position:0% +still something in the left list and + + + align:start position:0% +still something in the left list and +still something in the right list I is + + align:start position:0% +still something in the right list I is + + + align:start position:0% +still something in the right list I is +less than the length of left J is less + + align:start position:0% +less than the length of left J is less + + + align:start position:0% +less than the length of left J is less +than the length of right do the + + align:start position:0% +than the length of right do the + + + align:start position:0% +than the length of right do the +comparison if the left one's smaller + + align:start position:0% +comparison if the left one's smaller + + + align:start position:0% +comparison if the left one's smaller +add it to the end of result to the end + + align:start position:0% +add it to the end of result to the end + + + align:start position:0% +add it to the end of result to the end +of result right I'm appending it because + + align:start position:0% +of result right I'm appending it because + + + align:start position:0% +of result right I'm appending it because +I want it to be in that sorted order and + + align:start position:0% +I want it to be in that sorted order and + + + align:start position:0% +I want it to be in that sorted order and +increase I if it's not add the right one + + align:start position:0% +increase I if it's not add the right one + + + align:start position:0% +increase I if it's not add the right one +to the end of result and increase J and + + align:start position:0% +to the end of result and increase J and + + + align:start position:0% +to the end of result and increase J and +I'll just keep doing that until I + + align:start position:0% +I'll just keep doing that until I + + + align:start position:0% +I'll just keep doing that until I +exhaust one of the lists and when I do I + + align:start position:0% +exhaust one of the lists and when I do I + + + align:start position:0% +exhaust one of the lists and when I do I +can basically say if the right list is + + align:start position:0% +can basically say if the right list is + + + align:start position:0% +can basically say if the right list is +empty I know if I get out of here they + + align:start position:0% +empty I know if I get out of here they + + + align:start position:0% +empty I know if I get out of here they +can't both be true in other words if + + align:start position:0% +can't both be true in other words if + + + align:start position:0% +can't both be true in other words if +there's still something in the left list + + align:start position:0% +there's still something in the left list + + + align:start position:0% +there's still something in the left list +just put it on the end otherwise if the + + align:start position:0% +just put it on the end otherwise if the + + + align:start position:0% +just put it on the end otherwise if the +only things left in the right list just + + align:start position:0% +only things left in the right list just + + + align:start position:0% +only things left in the right list just +put them on the + + align:start position:0% +put them on the + + + align:start position:0% +put them on the +end so I'm just walking down the list + + align:start position:0% +end so I'm just walking down the list + + + align:start position:0% +end so I'm just walking down the list +doing the comparison adding the smallest + + align:start position:0% +doing the comparison adding the smallest + + + align:start position:0% +doing the comparison adding the smallest +element to my result and when I'm done I + + align:start position:0% +element to my result and when I'm done I + + + align:start position:0% +element to my result and when I'm done I +just return + + align:start position:0% +just return + + + align:start position:0% +just return +result complexity we can already begin + + align:start position:0% +result complexity we can already begin + + + align:start position:0% +result complexity we can already begin +to see here right this says the left and + + align:start position:0% +to see here right this says the left and + + + align:start position:0% +to see here right this says the left and +right sublists are order so I'm just + + align:start position:0% +right sublists are order so I'm just + + + align:start position:0% +right sublists are order so I'm just +moving the indices depending on which + + align:start position:0% +moving the indices depending on which + + + align:start position:0% +moving the indices depending on which +one holds the smaller element and when I + + align:start position:0% +one holds the smaller element and when I + + + align:start position:0% +one holds the smaller element and when I +get done I'm just returning the rest of + + align:start position:0% +get done I'm just returning the rest of + + + align:start position:0% +get done I'm just returning the rest of +the + + align:start position:0% +the + + + align:start position:0% +the +list so what's the complex + + align:start position:0% +list so what's the complex + + + align:start position:0% +list so what's the complex +here I'm going to do this a little more + + align:start position:0% +here I'm going to do this a little more + + + align:start position:0% +here I'm going to do this a little more +informally you could actually do that + + align:start position:0% +informally you could actually do that + + + align:start position:0% +informally you could actually do that +kind of relationship I did last time but + + align:start position:0% +kind of relationship I did last time but + + + align:start position:0% +kind of relationship I did last time but +what am I doing I'm going through the + + align:start position:0% +what am I doing I'm going through the + + + align:start position:0% +what am I doing I'm going through the +two lists but only one time through each + + align:start position:0% +two lists but only one time through each + + + align:start position:0% +two lists but only one time through each +of those two lists I'm only comparing + + align:start position:0% +of those two lists I'm only comparing + + + align:start position:0% +of those two lists I'm only comparing +the smallest elements so as I already + + align:start position:0% +the smallest elements so as I already + + + align:start position:0% +the smallest elements so as I already +said this says that the number of + + align:start position:0% +said this says that the number of + + + align:start position:0% +said this says that the number of +elements I copy will be everything in + + align:start position:0% +elements I copy will be everything in + + + align:start position:0% +elements I copy will be everything in +the left list and everything in the + + align:start position:0% +the left list and everything in the + + + align:start position:0% +the left list and everything in the +right list so that order is just the + + align:start position:0% +right list so that order is just the + + + align:start position:0% +right list so that order is just the +length of left plus the length of right + + align:start position:0% +length of left plus the length of right + + + align:start position:0% +length of left plus the length of right +and how many comparisons do I do the + + align:start position:0% +and how many comparisons do I do the + + + align:start position:0% +and how many comparisons do I do the +most I have to do is however many are in + + align:start position:0% +most I have to do is however many are in + + + align:start position:0% +most I have to do is however many are in +the longer list right that's the maximum + + align:start position:0% +the longer list right that's the maximum + + + align:start position:0% +the longer list right that's the maximum +number I need to have oh that's nice + + align:start position:0% +number I need to have oh that's nice + + + align:start position:0% +number I need to have oh that's nice +that says if the lists are of order n + + align:start position:0% +that says if the lists are of order n + + + align:start position:0% +that says if the lists are of order n +I'm doing order n copies because order n + + align:start position:0% +I'm doing order n copies because order n + + + align:start position:0% +I'm doing order n copies because order n +plus order n is just 2 N which is order + + align:start position:0% +plus order n is just 2 N which is order + + + align:start position:0% +plus order n is just 2 N which is order +n and I'm doing order n comparisons so + + align:start position:0% +n and I'm doing order n comparisons so + + + align:start position:0% +n and I'm doing order n comparisons so +it's linear in the length of the list + + align:start position:0% +it's linear in the length of the list + + + align:start position:0% +it's linear in the length of the list +okay sounds + + align:start position:0% +okay sounds + + + align:start position:0% +okay sounds +good that just does the merge how do I + + align:start position:0% +good that just does the merge how do I + + + align:start position:0% +good that just does the merge how do I +do merge sort well we set it break the + + align:start position:0% +do merge sort well we set it break the + + + align:start position:0% +do merge sort well we set it break the +problem in half keep doing it until + + align:start position:0% +problem in half keep doing it until + + + align:start position:0% +problem in half keep doing it until +until I get sorted lists and then grow + + align:start position:0% +until I get sorted lists and then grow + + + align:start position:0% +until I get sorted lists and then grow +them back up so there's merge sort it + + align:start position:0% +them back up so there's merge sort it + + + align:start position:0% +them back up so there's merge sort it +says if the list is either empty or of + + align:start position:0% +says if the list is either empty or of + + + align:start position:0% +says if the list is either empty or of +length one just return a copy of the + + align:start position:0% +length one just return a copy of the + + + align:start position:0% +length one just return a copy of the +list it's + + align:start position:0% +list it's + + + align:start position:0% +list it's +sorted otherwise find the Middle Point + + align:start position:0% +sorted otherwise find the Middle Point + + + align:start position:0% +sorted otherwise find the Middle Point +there's that integer Division and split + + align:start position:0% +there's that integer Division and split + + + align:start position:0% +there's that integer Division and split +split the list everything up to the + + align:start position:0% +split the list everything up to the + + + align:start position:0% +split the list everything up to the +middle point and do merge sord on that + + align:start position:0% +middle point and do merge sord on that + + + align:start position:0% +middle point and do merge sord on that +split everything in the list from the + + align:start position:0% +split everything in the list from the + + + align:start position:0% +split everything in the list from the +Middle Point on do merge merge sord on + + align:start position:0% +Middle Point on do merge merge sord on + + + align:start position:0% +Middle Point on do merge merge sord on +that and when I get back those two + + align:start position:0% +that and when I get back those two + + + align:start position:0% +that and when I get back those two +sorted lists just merge + + align:start position:0% +sorted lists just merge + + + align:start position:0% +sorted lists just merge +them + + align:start position:0% +them + + + align:start position:0% +them +again I hope you can see what the order + + align:start position:0% +again I hope you can see what the order + + + align:start position:0% +again I hope you can see what the order +of growth should be here cutting the + + align:start position:0% +of growth should be here cutting the + + + align:start position:0% +of growth should be here cutting the +problem down in half at each step so the + + align:start position:0% +problem down in half at each step so the + + + align:start position:0% +problem down in half at each step so the +number of times I should have to go + + align:start position:0% +number of times I should have to go + + + align:start position:0% +number of times I should have to go +through this should be log in the size + + align:start position:0% +through this should be log in the size + + + align:start position:0% +through this should be log in the size +of the original list and you can see why + + align:start position:0% +of the original list and you can see why + + + align:start position:0% +of the original list and you can see why +we call it divide and conquer I'm + + align:start position:0% +we call it divide and conquer I'm + + + align:start position:0% +we call it divide and conquer I'm +dividing it down into small pieces until + + align:start position:0% +dividing it down into small pieces until + + + align:start position:0% +dividing it down into small pieces until +I have a simple solution and then I'm + + align:start position:0% +I have a simple solution and then I'm + + + align:start position:0% +I have a simple solution and then I'm +growing that solution back + + align:start position:0% +growing that solution back + + + align:start position:0% +growing that solution back +up so there's the base case there's the + + align:start position:0% +up so there's the base case there's the + + + align:start position:0% +up so there's the base case there's the +divide and there's the nice conquer + + align:start position:0% +divide and there's the nice conquer + + + align:start position:0% +divide and there's the nice conquer +piece of this + + align:start position:0% +piece of this + + + align:start position:0% +piece of this +okay I'm going to show you an example of + + align:start position:0% +okay I'm going to show you an example of + + + align:start position:0% +okay I'm going to show you an example of +that but let's actually look at some + + align:start position:0% +that but let's actually look at some + + + align:start position:0% +that but let's actually look at some +code sorry about that let's look at some + + align:start position:0% +code sorry about that let's look at some + + + align:start position:0% +code sorry about that let's look at some +code to do this and in fact I meant to + + align:start position:0% +code to do this and in fact I meant to + + + align:start position:0% +code to do this and in fact I meant to +do this earlier and didn't I also have a + + align:start position:0% +do this earlier and didn't I also have a + + + align:start position:0% +do this earlier and didn't I also have a +version of bubble sort + + align:start position:0% +version of bubble sort + + + align:start position:0% +version of bubble sort +here sorry selection sort I've already + + align:start position:0% +here sorry selection sort I've already + + + align:start position:0% +here sorry selection sort I've already +done bubble sort there's selection sort + + align:start position:0% +done bubble sort there's selection sort + + + align:start position:0% +done bubble sort there's selection sort +let's uncomment + + align:start position:0% +let's uncomment + + + align:start position:0% +let's uncomment +this and let's run both of those and + + align:start position:0% +this and let's run both of those and + + + align:start position:0% +this and let's run both of those and +just see the comparison between them and + + align:start position:0% +just see the comparison between them and + + + align:start position:0% +just see the comparison between them and +sorry just to make that a little easier + + align:start position:0% +sorry just to make that a little easier + + + align:start position:0% +sorry just to make that a little easier +to read indeed there we + + align:start position:0% +to read indeed there we + + + align:start position:0% +to read indeed there we +go so we saw bubble sort it only went + + align:start position:0% +go so we saw bubble sort it only went + + + align:start position:0% +go so we saw bubble sort it only went +through four times so less than n times + + align:start position:0% +through four times so less than n times + + + align:start position:0% +through four times so less than n times +there's selection sort and as I said to + + align:start position:0% +there's selection sort and as I said to + + + align:start position:0% +there's selection sort and as I said to +you it has to do n passes because it can + + align:start position:0% +you it has to do n passes because it can + + + align:start position:0% +you it has to do n passes because it can +only ever guarantee that it gets one + + align:start position:0% +only ever guarantee that it gets one + + + align:start position:0% +only ever guarantee that it gets one +element at the beginning so you can in + + align:start position:0% +element at the beginning so you can in + + + align:start position:0% +element at the beginning so you can in +fact see in this case from the first or + + align:start position:0% +fact see in this case from the first or + + + align:start position:0% +fact see in this case from the first or +after the initial input until the end of + + align:start position:0% +after the initial input until the end of + + + align:start position:0% +after the initial input until the end of +the first step it looks like it didn't + + align:start position:0% +the first step it looks like it didn't + + + align:start position:0% +the first step it looks like it didn't +do anything because it determined + + align:start position:0% +do anything because it determined + + + align:start position:0% +do anything because it determined +eventually that one was in the right + + align:start position:0% +eventually that one was in the right + + + align:start position:0% +eventually that one was in the right +spot and similarly I think there's + + align:start position:0% +spot and similarly I think there's + + + align:start position:0% +spot and similarly I think there's +another one right there where it doesn't + + align:start position:0% +another one right there where it doesn't + + + align:start position:0% +another one right there where it doesn't +do any or appears not to do anything all + + align:start position:0% +do any or appears not to do anything all + + + align:start position:0% +do any or appears not to do anything all +it's guaranteeing is that the next + + align:start position:0% +it's guaranteeing is that the next + + + align:start position:0% +it's guaranteeing is that the next +smallest element is in the right spot as + + align:start position:0% +smallest element is in the right spot as + + + align:start position:0% +smallest element is in the right spot as +we get to to the end of it and in fact + + align:start position:0% +we get to to the end of it and in fact + + + align:start position:0% +we get to to the end of it and in fact +ends up in the right place and then + + align:start position:0% +ends up in the right place and then + + + align:start position:0% +ends up in the right place and then +let's look at merge sort and do one more + + align:start position:0% +let's look at merge sort and do one more + + + align:start position:0% +let's look at merge sort and do one more +visualization of + + align:start position:0% +visualization of + + + align:start position:0% +visualization of +this so again let me remove + + align:start position:0% +this so again let me remove + + + align:start position:0% +this so again let me remove +that and if we run + + align:start position:0% + + + + align:start position:0% + +it again I've just put some print + + align:start position:0% +it again I've just put some print + + + align:start position:0% +it again I've just put some print +statements in there here you can see a + + align:start position:0% +statements in there here you can see a + + + align:start position:0% +statements in there here you can see a +nice behavior + + align:start position:0% +nice behavior + + + align:start position:0% +nice behavior +I start off calling merge sort with that + + align:start position:0% +I start off calling merge sort with that + + + align:start position:0% +I start off calling merge sort with that +which splits down into doing merge sort + + align:start position:0% +which splits down into doing merge sort + + + align:start position:0% +which splits down into doing merge sort +of this portion eventually it's going to + + align:start position:0% +of this portion eventually it's going to + + + align:start position:0% +of this portion eventually it's going to +come back down there and do the second + + align:start position:0% +come back down there and do the second + + + align:start position:0% +come back down there and do the second +one it keeps doing it until it gets down + + align:start position:0% +one it keeps doing it until it gets down + + + align:start position:0% +one it keeps doing it until it gets down +to simple list that it knows or sorted + + align:start position:0% +to simple list that it knows or sorted + + + align:start position:0% +to simple list that it knows or sorted +and then it merges it does the smaller + + align:start position:0% +and then it merges it does the smaller + + + align:start position:0% +and then it merges it does the smaller +pieces and then merges it and having now + + align:start position:0% +pieces and then merges it and having now + + + align:start position:0% +pieces and then merges it and having now +two merged things it can do the next + + align:start position:0% +two merged things it can do the next + + + align:start position:0% +two merged things it can do the next +level of + + align:start position:0% +level of + + + align:start position:0% +level of +merge so you can see that it gets this + + align:start position:0% +merge so you can see that it gets this + + + align:start position:0% +merge so you can see that it gets this +nice reduction of problems until it gets + + align:start position:0% +nice reduction of problems until it gets + + + align:start position:0% +nice reduction of problems until it gets +down to the smallest + + align:start position:0% +down to the smallest + + + align:start position:0% +down to the smallest +size so let's just look at one more + + align:start position:0% +size so let's just look at one more + + + align:start position:0% +size so let's just look at one more +visualization of that and then get the + + align:start position:0% +visualization of that and then get the + + + align:start position:0% +visualization of that and then get the +complexity so if I start out with this + + align:start position:0% +complexity so if I start out with this + + + align:start position:0% +complexity so if I start out with this +list sorry about that what I need to do + + align:start position:0% +list sorry about that what I need to do + + + align:start position:0% +list sorry about that what I need to do +is split it take the first one split it + + align:start position:0% +is split it take the first one split it + + + align:start position:0% +is split it take the first one split it +keep doing that until I get down to a + + align:start position:0% +keep doing that until I get down to a + + + align:start position:0% +keep doing that until I get down to a +base case where I know what those are + + align:start position:0% +base case where I know what those are + + + align:start position:0% +base case where I know what those are +and I simply merge them pass it back up + + align:start position:0% +and I simply merge them pass it back up + + + align:start position:0% +and I simply merge them pass it back up +take the second piece split it until I + + align:start position:0% +take the second piece split it until I + + + align:start position:0% +take the second piece split it until I +get down to base cases do the merge + + align:start position:0% +get down to base cases do the merge + + + align:start position:0% +get down to base cases do the merge +which is nice and linear pass that back + + align:start position:0% +which is nice and linear pass that back + + + align:start position:0% +which is nice and linear pass that back +up having done those two pieces I do one + + align:start position:0% +up having done those two pieces I do one + + + align:start position:0% +up having done those two pieces I do one +more merge and I do the same + + align:start position:0% + + + + align:start position:0% + +thing I want you to see this because + + align:start position:0% +thing I want you to see this because + + + align:start position:0% +thing I want you to see this because +again you can notice how many levels in + + align:start position:0% +again you can notice how many levels in + + + align:start position:0% +again you can notice how many levels in +this tree log log in the size because at + + align:start position:0% +this tree log log in the size because at + + + align:start position:0% +this tree log log in the size because at +each stage here I went from a problem of + + align:start position:0% +each stage here I went from a problem of + + + align:start position:0% +each stage here I went from a problem of +eight to two problems of four each of + + align:start position:0% +eight to two problems of four each of + + + align:start position:0% +eight to two problems of four each of +those went to two problems of two and + + align:start position:0% +those went to two problems of two and + + + align:start position:0% +those went to two problems of two and +each of those went to two problems of + + align:start position:0% +each of those went to two problems of + + + align:start position:0% +each of those went to two problems of +size + + align:start position:0% +size + + + align:start position:0% +size +one all right so the last piece is + + align:start position:0% +one all right so the last piece is + + + align:start position:0% +one all right so the last piece is +what's the + + align:start position:0% +what's the + + + align:start position:0% +what's the +complexity + + align:start position:0% +complexity + + + align:start position:0% +complexity +here's a simple way to think about it at + + align:start position:0% +here's a simple way to think about it at + + + align:start position:0% +here's a simple way to think about it at +the top level I've got I start off with + + align:start position:0% +the top level I've got I start off with + + + align:start position:0% +the top level I've got I start off with +n elements I've got two sorted lists of + + align:start position:0% +n elements I've got two sorted lists of + + + align:start position:0% +n elements I've got two sorted lists of +size n over two and to merge them + + align:start position:0% +size n over two and to merge them + + + align:start position:0% +size n over two and to merge them +together I need to do order and work + + align:start position:0% +together I need to do order and work + + + align:start position:0% +together I need to do order and work +because as I said I've got to do at + + align:start position:0% +because as I said I've got to do at + + + align:start position:0% +because as I said I've got to do at +least n comparisons where n is the + + align:start position:0% +least n comparisons where n is the + + + align:start position:0% +least n comparisons where n is the +length of the list and then I got to do + + align:start position:0% +length of the list and then I got to do + + + align:start position:0% +length of the list and then I got to do +n plus n copies which is just order and + + align:start position:0% +n plus n copies which is just order and + + + align:start position:0% +n plus n copies which is just order and +so I'm doing order n work at the second + + align:start position:0% +so I'm doing order n work at the second + + + align:start position:0% +so I'm doing order n work at the second +level gets a little more complicated now + + align:start position:0% +level gets a little more complicated now + + + align:start position:0% +level gets a little more complicated now +I've got problems of size n + + align:start position:0% +I've got problems of size n + + + align:start position:0% +I've got problems of size n +over4 but how many of them do I have + + align:start position:0% +over4 but how many of them do I have + + + align:start position:0% +over4 but how many of them do I have +four oh that's nice because what do I + + align:start position:0% +four oh that's nice because what do I + + + align:start position:0% +four oh that's nice because what do I +know about this I know that I have to + + align:start position:0% +know about this I know that I have to + + + align:start position:0% +know about this I know that I have to +copy each element at least once so not + + align:start position:0% +copy each element at least once so not + + + align:start position:0% +copy each element at least once so not +at least once I will copy each element + + align:start position:0% +at least once I will copy each element + + + align:start position:0% +at least once I will copy each element +exactly once and I'll do comparisons + + align:start position:0% +exactly once and I'll do comparisons + + + align:start position:0% +exactly once and I'll do comparisons +that are equal to the length of the + + align:start position:0% +that are equal to the length of the + + + align:start position:0% +that are equal to the length of the +longer list so I've got four subl lists + + align:start position:0% +longer list so I've got four subl lists + + + align:start position:0% +longer list so I've got four subl lists +of length n over 4 that says n elements + + align:start position:0% +of length n over 4 that says n elements + + + align:start position:0% +of length n over 4 that says n elements +oh that's nice order n at each step sub + + align:start position:0% +oh that's nice order n at each step sub + + + align:start position:0% +oh that's nice order n at each step sub +problems get smaller but I have more of + + align:start position:0% +problems get smaller but I have more of + + + align:start position:0% +problems get smaller but I have more of +them but the total size of the problem + + align:start position:0% +them but the total size of the problem + + + align:start position:0% +them but the total size of the problem +is n so the cost at each step is order + + align:start position:0% +is n so the cost at each step is order + + + align:start position:0% +is n so the cost at each step is order +n how many times do I do it log n so + + align:start position:0% +n how many times do I do it log n so + + + align:start position:0% +n how many times do I do it log n so +this is log n iterations with order and + + align:start position:0% +this is log n iterations with order and + + + align:start position:0% +this is log n iterations with order and +work at each step and this is a + + align:start position:0% +work at each step and this is a + + + align:start position:0% +work at each step and this is a +wonderful example of a log linear + + align:start position:0% +wonderful example of a log linear + + + align:start position:0% +wonderful example of a log linear +algorithm it's n log n where n is the + + align:start position:0% +algorithm it's n log n where n is the + + + align:start position:0% +algorithm it's n log n where n is the +length of the + + align:start position:0% +length of the + + + align:start position:0% +length of the +list so what you end up with then is + + align:start position:0% +list so what you end up with then is + + + align:start position:0% +list so what you end up with then is +all right a joke version some reasonable + + align:start position:0% +all right a joke version some reasonable + + + align:start position:0% +all right a joke version some reasonable +ways of doing sort that are quick and + + align:start position:0% +ways of doing sort that are quick and + + + align:start position:0% +ways of doing sort that are quick and +easy to implement but are quadratic and + + align:start position:0% +easy to implement but are quadratic and + + + align:start position:0% +easy to implement but are quadratic and +then an elegant way of doing the search + + align:start position:0% +then an elegant way of doing the search + + + align:start position:0% +then an elegant way of doing the search +that's end log in and I'll remind you I + + align:start position:0% +that's end log in and I'll remind you I + + + align:start position:0% +that's end log in and I'll remind you I +started by saying as long as I can make + + align:start position:0% +started by saying as long as I can make + + + align:start position:0% +started by saying as long as I can make +the cost of sorting small enough I can + + align:start position:0% +the cost of sorting small enough I can + + + align:start position:0% +the cost of sorting small enough I can +amortise that cost and if you go back + + align:start position:0% +amortise that cost and if you go back + + + align:start position:0% +amortise that cost and if you go back +and look at last lecture's notes you'll + + align:start position:0% +and look at last lecture's notes you'll + + + align:start position:0% +and look at last lecture's notes you'll +see n log n grows pretty slowly and it's + + align:start position:0% +see n log n grows pretty slowly and it's + + + align:start position:0% +see n log n grows pretty slowly and it's +actually a nice thing to do it makes it + + align:start position:0% +actually a nice thing to do it makes it + + + align:start position:0% +actually a nice thing to do it makes it +reasonable to do the sort and then I can + + align:start position:0% +reasonable to do the sort and then I can + + + align:start position:0% +reasonable to do the sort and then I can +do the search in order and time and + + align:start position:0% +do the search in order and time and + + + align:start position:0% +do the search in order and time and +here's the last + + align:start position:0% +here's the last + + + align:start position:0% +here's the last +punchline it's the fastest we can do I'm + + align:start position:0% +punchline it's the fastest we can do I'm + + + align:start position:0% +punchline it's the fastest we can do I'm +going to look at John again I don't + + align:start position:0% +going to look at John again I don't + + + align:start position:0% +going to look at John again I don't +think anybody has found a faster um + + align:start position:0% +think anybody has found a faster um + + + align:start position:0% +think anybody has found a faster um +sword algorithm right this is the best + + align:start position:0% +sword algorithm right this is the best + + + align:start position:0% +sword algorithm right this is the best +one can do unless you + + align:start position:0% +one can do unless you + + + align:start position:0% +one can do unless you +do sorry the best worst case absolutely + + align:start position:0% +do sorry the best worst case absolutely + + + align:start position:0% +do sorry the best worst case absolutely +John is absolutely right there are + + align:start position:0% +John is absolutely right there are + + + align:start position:0% +John is absolutely right there are +better average cases again our concern + + align:start position:0% +better average cases again our concern + + + align:start position:0% +better average cases again our concern +is worst case so this is as good as + + align:start position:0% +is worst case so this is as good as + + + align:start position:0% +is worst case so this is as good as +we're going to do in terms of a worst + + align:start position:0% +we're going to do in terms of a worst + + + align:start position:0% +we're going to do in terms of a worst +case algorithm so there you now have + + align:start position:0% +case algorithm so there you now have + + + align:start position:0% +case algorithm so there you now have +sorting algorithms and searching + + align:start position:0% +sorting algorithms and searching + + + align:start position:0% +sorting algorithms and searching +algorithms and you've now seen excuse me + + align:start position:0% +algorithms and you've now seen excuse me + + + align:start position:0% +algorithms and you've now seen excuse me +sorry constant log linear log linear + + align:start position:0% +sorry constant log linear log linear + + + align:start position:0% +sorry constant log linear log linear +quadratic and exponential algorithms I + + align:start position:0% +quadratic and exponential algorithms I + + + align:start position:0% +quadratic and exponential algorithms I +remind you we want things as high up in + + align:start position:0% +remind you we want things as high up in + + + align:start position:0% +remind you we want things as high up in +that hierarchy as + + align:start position:0% +that hierarchy as + + + align:start position:0% +that hierarchy as +possible all right I have six minutes + + align:start position:0% +possible all right I have six minutes + + + align:start position:0% +possible all right I have six minutes +left some of you are going to leave us + + align:start position:0% +left some of you are going to leave us + + + align:start position:0% +left some of you are going to leave us +we're going to miss you but that's okay + + align:start position:0% +we're going to miss you but that's okay + + + align:start position:0% +we're going to miss you but that's okay +I'm sure we'll see you later on for + + align:start position:0% +I'm sure we'll see you later on for + + + align:start position:0% +I'm sure we'll see you later on for +those of you hanging around this isn't a + + align:start position:0% +those of you hanging around this isn't a + + + align:start position:0% +those of you hanging around this isn't a +bad time just to step back and say so + + align:start position:0% +bad time just to step back and say so + + + align:start position:0% +bad time just to step back and say so +what have we seen and I want to do this + + align:start position:0% +what have we seen and I want to do this + + + align:start position:0% +what have we seen and I want to do this +just very + + align:start position:0% +just very + + + align:start position:0% +just very +quickly sorry I'm remind you we started + + align:start position:0% +quickly sorry I'm remind you we started + + + align:start position:0% +quickly sorry I'm remind you we started +by in some sense giving you a little bit + + align:start position:0% +by in some sense giving you a little bit + + + align:start position:0% +by in some sense giving you a little bit +of a contract of things we were going to + + align:start position:0% +of a contract of things we were going to + + + align:start position:0% +of a contract of things we were going to +show you and I would simply suggest to + + align:start position:0% +show you and I would simply suggest to + + + align:start position:0% +show you and I would simply suggest to +you what have we + + align:start position:0% +you what have we + + + align:start position:0% +you what have we +done we given you a sense of how to + + align:start position:0% +done we given you a sense of how to + + + align:start position:0% +done we given you a sense of how to +represent knowledge with data structures + + align:start position:0% +represent knowledge with data structures + + + align:start position:0% +represent knowledge with data structures +tupal lists dictionaries more + + align:start position:0% +tupal lists dictionaries more + + + align:start position:0% +tupal lists dictionaries more +complicated structures we've shown you + + align:start position:0% +complicated structures we've shown you + + + align:start position:0% +complicated structures we've shown you +some good computational metaphors + + align:start position:0% +some good computational metaphors + + + align:start position:0% +some good computational metaphors +iteration and Loops recursion as a great + + align:start position:0% +iteration and Loops recursion as a great + + + align:start position:0% +iteration and Loops recursion as a great +way of breaking problems down into + + align:start position:0% +way of breaking problems down into + + + align:start position:0% +way of breaking problems down into +simpler versions of the same problem and + + align:start position:0% +simpler versions of the same problem and + + + align:start position:0% +simpler versions of the same problem and +there really are metaphors there ways of + + align:start position:0% +there really are metaphors there ways of + + + align:start position:0% +there really are metaphors there ways of +thinking about problems + + align:start position:0% +thinking about problems + + + align:start position:0% +thinking about problems +we've given you + + align:start position:0% +we've given you + + + align:start position:0% +we've given you +abstraction the idea of capture a + + align:start position:0% +abstraction the idea of capture a + + + align:start position:0% +abstraction the idea of capture a +computation bury it in a procedure you + + align:start position:0% +computation bury it in a procedure you + + + align:start position:0% +computation bury it in a procedure you +now have a contract you don't need to + + align:start position:0% +now have a contract you don't need to + + + align:start position:0% +now have a contract you don't need to +know what happens inside the procedure + + align:start position:0% +know what happens inside the procedure + + + align:start position:0% +know what happens inside the procedure +as long as it delivers the answer it + + align:start position:0% +as long as it delivers the answer it + + + align:start position:0% +as long as it delivers the answer it +says it would or another way of saying + + align:start position:0% +says it would or another way of saying + + + align:start position:0% +says it would or another way of saying +it you can delegate it to somebody and + + align:start position:0% +it you can delegate it to somebody and + + + align:start position:0% +it you can delegate it to somebody and +trust it you're going to get what you + + align:start position:0% +trust it you're going to get what you + + + align:start position:0% +trust it you're going to get what you +like out of it we've seen classes and + + align:start position:0% +like out of it we've seen classes and + + + align:start position:0% +like out of it we've seen classes and +methods as a wonderful way to modularize + + align:start position:0% +methods as a wonderful way to modularize + + + align:start position:0% +methods as a wonderful way to modularize +systems to capture combinations of data + + align:start position:0% +systems to capture combinations of data + + + align:start position:0% +systems to capture combinations of data +and things that operate on them in a + + align:start position:0% +and things that operate on them in a + + + align:start position:0% +and things that operate on them in a +nice elegant way and we just spent a + + align:start position:0% +nice elegant way and we just spent a + + + align:start position:0% +nice elegant way and we just spent a +week and a half talking about classes of + + align:start position:0% +week and a half talking about classes of + + + align:start position:0% +week and a half talking about classes of +algorithms and their + + align:start position:0% +algorithms and their + + + align:start position:0% +algorithms and their +complexity if you step up a + + align:start position:0% +complexity if you step up a + + + align:start position:0% +complexity if you step up a +level what we hope you've gotten out of + + align:start position:0% +level what we hope you've gotten out of + + + align:start position:0% +level what we hope you've gotten out of +this are a couple of things you've begun + + align:start position:0% +this are a couple of things you've begun + + + align:start position:0% +this are a couple of things you've begun +to learn computational modes of thinking + + align:start position:0% +to learn computational modes of thinking + + + align:start position:0% +to learn computational modes of thinking +how do I tackle a problem in divide and + + align:start position:0% +how do I tackle a problem in divide and + + + align:start position:0% +how do I tackle a problem in divide and +conquer how do I think about recursion + + align:start position:0% +conquer how do I think about recursion + + + align:start position:0% +conquer how do I think about recursion +as a tool in dealing with something + + align:start position:0% +as a tool in dealing with something + + + align:start position:0% +as a tool in dealing with something +you've begun to begun I will use that + + align:start position:0% +you've begun to begun I will use that + + + align:start position:0% +you've begun to begun I will use that +word deliberately to master the art of + + align:start position:0% +word deliberately to master the art of + + + align:start position:0% +word deliberately to master the art of +computational problem solving how can + + align:start position:0% +computational problem solving how can + + + align:start position:0% +computational problem solving how can +you take a problem and turn it into an + + align:start position:0% +you take a problem and turn it into an + + + align:start position:0% +you take a problem and turn it into an +algorithm and especially You' begun to + + align:start position:0% +algorithm and especially You' begun to + + + align:start position:0% +algorithm and especially You' begun to +have the ability to make the computer do + + align:start position:0% +have the ability to make the computer do + + + align:start position:0% +have the ability to make the computer do +what you want it to to say if I've got a + + align:start position:0% +what you want it to to say if I've got a + + + align:start position:0% +what you want it to to say if I've got a +problem from biology or chemistry or + + align:start position:0% +problem from biology or chemistry or + + + align:start position:0% +problem from biology or chemistry or +math or physics or chemical engineering + + align:start position:0% +math or physics or chemical engineering + + + align:start position:0% +math or physics or chemical engineering +or mechanical engineering how do I take + + align:start position:0% +or mechanical engineering how do I take + + + align:start position:0% +or mechanical engineering how do I take +that problem and say Here's how I would + + align:start position:0% +that problem and say Here's how I would + + + align:start position:0% +that problem and say Here's how I would +design an algorithm to give me a + + align:start position:0% +design an algorithm to give me a + + + align:start position:0% +design an algorithm to give me a +simulation a way of evaluating what it + + align:start position:0% +simulation a way of evaluating what it + + + align:start position:0% +simulation a way of evaluating what it +does and so what we hope we've done is + + align:start position:0% +does and so what we hope we've done is + + + align:start position:0% +does and so what we hope we've done is +we started you down the path to being + + align:start position:0% +we started you down the path to being + + + align:start position:0% +we started you down the path to being +able to think and act like a computer + + align:start position:0% +able to think and act like a computer + + + align:start position:0% +able to think and act like a computer +scientist all right don't panic that + + align:start position:0% +scientist all right don't panic that + + + align:start position:0% +scientist all right don't panic that +doesn't mean you stare at people's shoes + + align:start position:0% +doesn't mean you stare at people's shoes + + + align:start position:0% +doesn't mean you stare at people's shoes +when you talk to them not all computer + + align:start position:0% +when you talk to them not all computer + + + align:start position:0% +when you talk to them not all computer +scientists do that just + + align:start position:0% +scientists do that just + + + align:start position:0% +scientists do that just +faculty sorry John so what do computer + + align:start position:0% +faculty sorry John so what do computer + + + align:start position:0% +faculty sorry John so what do computer +scientists do and this is actually meant + + align:start position:0% +scientists do and this is actually meant + + + align:start position:0% +scientists do and this is actually meant +to be serious and I've put up two of my + + align:start position:0% +to be serious and I've put up two of my + + + align:start position:0% +to be serious and I've put up two of my +famous historical figures that computer + + align:start position:0% +famous historical figures that computer + + + align:start position:0% +famous historical figures that computer +scientists they do think computationally + + align:start position:0% +scientists they do think computationally + + + align:start position:0% +scientists they do think computationally +they think about abstractions about + + align:start position:0% +they think about abstractions about + + + align:start position:0% +they think about abstractions about +algorithms about automated execution so + + align:start position:0% +algorithms about automated execution so + + + align:start position:0% +algorithms about automated execution so +the three a of computational sying and + + align:start position:0% +the three a of computational sying and + + + align:start position:0% +the three a of computational sying and +in the same way that traditionally you + + align:start position:0% +in the same way that traditionally you + + + align:start position:0% +in the same way that traditionally you +had the three Rs of Reading Writing and + + align:start position:0% +had the three Rs of Reading Writing and + + + align:start position:0% +had the three Rs of Reading Writing and +arithmetic computational thinking we + + align:start position:0% +arithmetic computational thinking we + + + align:start position:0% +arithmetic computational thinking we +hope is becoming a fundamental that + + align:start position:0% +hope is becoming a fundamental that + + + align:start position:0% +hope is becoming a fundamental that +every well-educated person is going to + + align:start position:0% +every well-educated person is going to + + + align:start position:0% +every well-educated person is going to +need and that says you think about the + + align:start position:0% +need and that says you think about the + + + align:start position:0% +need and that says you think about the +right + + align:start position:0% +right + + + align:start position:0% +right +abstraction when you have a problem in + + align:start position:0% +abstraction when you have a problem in + + + align:start position:0% +abstraction when you have a problem in +your europ what's the right abstraction + + align:start position:0% +your europ what's the right abstraction + + + align:start position:0% +your europ what's the right abstraction +how do I pull apart the pieces how do I + + align:start position:0% +how do I pull apart the pieces how do I + + + align:start position:0% +how do I pull apart the pieces how do I +think about that in in terms of of + + align:start position:0% +think about that in in terms of of + + + align:start position:0% +think about that in in terms of of +decomposing things into a relationship + + align:start position:0% +decomposing things into a relationship + + + align:start position:0% +decomposing things into a relationship +that I can use to solve problems how do + + align:start position:0% +that I can use to solve problems how do + + + align:start position:0% +that I can use to solve problems how do +I automate how do I mechanize that + + align:start position:0% +I automate how do I mechanize that + + + align:start position:0% +I automate how do I mechanize that +abstraction how do I use what I know + + align:start position:0% +abstraction how do I use what I know + + + align:start position:0% +abstraction how do I use what I know +happens inside of the machine to write a + + align:start position:0% +happens inside of the machine to write a + + + align:start position:0% +happens inside of the machine to write a +sequence of steps in a language I'm + + align:start position:0% +sequence of steps in a language I'm + + + align:start position:0% +sequence of steps in a language I'm +using to capture that process and then + + align:start position:0% +using to capture that process and then + + + align:start position:0% +using to capture that process and then +finally how do I turn that into an + + align:start position:0% +finally how do I turn that into an + + + align:start position:0% +finally how do I turn that into an +algorithm and that not only means I need + + align:start position:0% +algorithm and that not only means I need + + + align:start position:0% +algorithm and that not only means I need +a language for describing those + + align:start position:0% +a language for describing those + + + align:start position:0% +a language for describing those +automated processes and and if you like + + align:start position:0% +automated processes and and if you like + + + align:start position:0% +automated processes and and if you like +allowing the abstraction of details but + + align:start position:0% +allowing the abstraction of details but + + + align:start position:0% +allowing the abstraction of details but +frankly also a way to communicate if you + + align:start position:0% +frankly also a way to communicate if you + + + align:start position:0% +frankly also a way to communicate if you +have to think crisply about how do I + + align:start position:0% +have to think crisply about how do I + + + align:start position:0% +have to think crisply about how do I +describe an algorithm it's actually + + align:start position:0% +describe an algorithm it's actually + + + align:start position:0% +describe an algorithm it's actually +giving you a way to crystallize or + + align:start position:0% +giving you a way to crystallize or + + + align:start position:0% +giving you a way to crystallize or +clarify your thinking about a problem + + align:start position:0% +clarify your thinking about a problem + + + align:start position:0% +clarify your thinking about a problem +this is not to say you should talk to + + align:start position:0% +this is not to say you should talk to + + + align:start position:0% +this is not to say you should talk to +your friends in Python I don't recommend + + align:start position:0% +your friends in Python I don't recommend + + + align:start position:0% +your friends in Python I don't recommend +it + + align:start position:0% +it + + + align:start position:0% +it +but it does say you should use that + + align:start position:0% +but it does say you should use that + + + align:start position:0% +but it does say you should use that +thinking as a way of capturing your + + align:start position:0% +thinking as a way of capturing your + + + align:start position:0% +thinking as a way of capturing your +ideas of what you're going to do and + + align:start position:0% +ideas of what you're going to do and + + + align:start position:0% +ideas of what you're going to do and +that leads then to this idea of how + + align:start position:0% +that leads then to this idea of how + + + align:start position:0% +that leads then to this idea of how +difficult is a problem how best can I + + align:start position:0% +difficult is a problem how best can I + + + align:start position:0% +difficult is a problem how best can I +solve it we've shown you these + + align:start position:0% +solve it we've shown you these + + + align:start position:0% +solve it we've shown you these +complexity classes and we've hinted at + + align:start position:0% +complexity classes and we've hinted at + + + align:start position:0% +complexity classes and we've hinted at +the idea that in fact some problems are + + align:start position:0% +the idea that in fact some problems are + + + align:start position:0% +the idea that in fact some problems are +inherently more difficult than others + + align:start position:0% +inherently more difficult than others + + + align:start position:0% +inherently more difficult than others +that's something I hope you come back to + + align:start position:0% +that's something I hope you come back to + + + align:start position:0% +that's something I hope you come back to +as you go along and especially we want + + align:start position:0% +as you go along and especially we want + + + align:start position:0% +as you go along and especially we want +you to start thinking recursively we + + align:start position:0% +you to start thinking recursively we + + + align:start position:0% +you to start thinking recursively we +want you to think about how do I take a + + align:start position:0% +want you to think about how do I take a + + + align:start position:0% +want you to think about how do I take a +hard problem break it up into simpler + + align:start position:0% +hard problem break it up into simpler + + + align:start position:0% +hard problem break it up into simpler +versions of the same problem and then + + align:start position:0% +versions of the same problem and then + + + align:start position:0% +versions of the same problem and then +construct the + + align:start position:0% +construct the + + + align:start position:0% +construct the +solution and that shows up lots of + + align:start position:0% +solution and that shows up lots of + + + align:start position:0% +solution and that shows up lots of +places right recursion is in all sorts + + align:start position:0% +places right recursion is in all sorts + + + align:start position:0% +places right recursion is in all sorts +of wonderful places so just to give you + + align:start position:0% +of wonderful places so just to give you + + + align:start position:0% +of wonderful places so just to give you +an example I could say to you + + align:start position:0% +an example I could say to you + + + align:start position:0% +an example I could say to you +recursively this lecture will end when + + align:start position:0% +recursively this lecture will end when + + + align:start position:0% +recursively this lecture will end when +I'm done talking about this lecture + + align:start position:0% +I'm done talking about this lecture + + + align:start position:0% +I'm done talking about this lecture +which will end when I'm done talking + + align:start position:0% +which will end when I'm done talking + + + align:start position:0% +which will end when I'm done talking +about this lecture which will end when + + align:start position:0% +about this lecture which will end when + + + align:start position:0% +about this lecture which will end when +I'm done all right you don't like + + align:start position:0% +I'm done all right you don't like + + + align:start position:0% +I'm done all right you don't like +infinite recursion good luck on the + + align:start position:0% + + + + align:start position:0% + +exam \ No newline at end of file diff --git a/6MffbP5O2v0.txt b/6MffbP5O2v0.txt new file mode 100644 index 0000000000000000000000000000000000000000..7bf47e3a85a95ed621539e16bc23355b6aef234a --- /dev/null +++ b/6MffbP5O2v0.txt @@ -0,0 +1,713 @@ +Hi. + +Today we're going to do another +fun problem that + +involves rolling two dice. + +So if you guys happen to +frequent casinos, this problem + +might be really useful +for you. + +I'm just kidding. + +But in all seriousness, this +problem is a good problem, + +because it's going to remind +us how and when to use the + +discrete uniform law. + +Don't worry, I'll review +what that says. + +And it's also going to exercise +your understanding of + +conditional probability. + +So quick recap. + +The discrete uniform law says +that when your sample space is + +discrete, and when the outcomes +in your sample space + +are equally likely, then to +compute the probability of any + +event A, you can simply count +the number of outcomes in A + +and divide it by the total +number of possible outcomes. + +OK, so coming back +to our problem. + +The problem statement tells +us that we roll two fair + +six-sided die. + +And it also tells us that each +one of the 36 possible + +outcomes is assumed to +be equally likely. + +So you know alarm bell should +be going off in your head. + +Our sample space is +clearly discrete. + +And it says explicitly that all + +outcomes are equally likely. + +So clearly, we can use the +discrete uniform law. + +And again, this is helpful +because it reduces a problem + +of computing probabilities +to a problem of counting. + +OK, and before we go any +further, I just want to review + +what this graph is plotting. + +You've seen it a few times, but +just to clarify, on one + +axis, we're plotting the outcome +of the first die roll, + +and on the second axis, we're +plotting the outcome of the + +second die roll. + +So if you got a 4 on your first +die, and you get a 1 on + +your second die, that +corresponds to this point over + +4 and up 1. + +OK, so part a asks us to +find the probability + +that doubles our rolls. + +So let's use some shorthand. + +We're going to let D be the +event that doubles are rolled. + +And we want to compute +the probability of D. + +I argue before we can use the +discrete uniform law. + +So if we apply that, we just +get the number of outcomes + +that comprise the event "doubles +rolled" divided by + +36, because there are 36 +possible outcomes, which you + +can see just by counting +the dots in this graph. + +Six possible outcomes for the +first die, six possible + +outcomes for the second die. + +That's how you-- + +6 times 6 is 36. + +So I've been assuming this +entire time that you know what + +doubles are. + +For those of you who don't know, +doubles is essentially + +when that number on the first +die matches the number on the + +second die. + +So this outcome here 1-1 is +part of the event "doubles + +rolled." Similarly, 2-2, 3-3, +4-4, 5-5, and 6-6-- + +these six points comprise the +event "doubles rolled." + +So we can go ahead and +put 6 over 36, + +which is equal to 1/6. + +So we're done with part a. + +We haven't seen any +conditioning yet. + +The conditioning comes +in part b. + +So in part b we're still +interested in the event D, in + +the event that "doubles are +rolled." But now we want to + +compute this probability +conditioned on the event that + +the sum of the results is +less than or equal to 4. + +So I'm going to use this +shorthand sum less than or + +equal to 4 to denote the event +that the role results in the + +sum of 4 or smaller. + +So there's two ways we're +going to go about + +solving part b. + +Let's just jump right +into the first way. + +The first way is applying the +definition of conditional + +probability. + +So hopefully you remember that +this is just probability of D + +intersect sum less than or +equal to 4, divided by + +probability of sum less +than or equal to 4. + +Now, sum less than or equal to +4 and D intersect sum less + +than or equal to 4 are +just two events. + +And so we can apply the discrete +uniform law to + +calculate both the numerator +and the denominator. + +So let's start with the +denominator first because it + +seems a little bit easier. + +So sum less than or equal to +4, let's figure this out. + +Well, 1-1 gives us a sum +of 2, that's less + +than or equal to 4. + +2-1 gives us 3. + +3-1 gives us 4. + +4-1 gives us 5, so we don't want +to include this or this, + +or this point. + +And you can sort of convince +yourself that the next point + +we want to include +is this one. + +That corresponds to 2-2, which +is 4, so it makes sense that + +these guys should form the +boundary, because all dots + +sort of up and to the right +will have a bigger sum. + +3-1 gives us 4. + +And 1-2 gives us 3. + +So these six points-- + +1, 2, 3, 4, 5, 6-- + +are the outcomes that comprise +the event sum less than or + +equal to 4. + +So we can go ahead and write in +the denominator, 6 over 36, + +because we just counted the +outcomes in sum less than or + +equal to, 4 and divided +it by the number + +of outcomes in omega. + +Now, let's compute +the numerator. + +D intersect sum less +than or equal to 4. + +So we already found the +blue check marks. + +Those correspond to sum less +than or equal to 4. + +Out of the points that have blue +check marks, which one + +correspond to doubles? + +Well, they're actually +already circled. + +It's just these two points. + +So we don't even need to circle +those, so we get 2 over + +36, using the discrete +uniform law. + +And you see that these two +36s cancel each other. + +So you just get 2/6 or 1/3. + +So that is one way of solving +part b, but I want to take + +you, guys, through a different +way, which I think is + +important, and that make sure +you really understand what + +conditioning means. + +So another way that you can +solve part b is to say, OK, we + +are now in the universe, we +are in the conditional + +universe, where we know +the sum of our + +results is 4 or smaller. + +And so that means our new sample +space is really just + +this set of six points. + + + +And one thing that it's worth +noting is that conditioning + +never changes the relative +frequencies or relative + +likelihoods of the different +outcomes. + +So because all outcomes were +equally likely in our original + +sample space omega, in the +conditional worlds the + +outcomes are also +equally likely. + +So using that argument, we could +say that in our sort of + +blue conditional universe +all of the + +outcomes are equally likely. + +And therefore, we can apply a +conditional version of the + +discrete uniform law. + +So namely, to compute the +probability of some event in + +that conditional world. + +So the conditional probability +that "doubles are rolled", we + +need only count the number of +outcomes in that event and + +divide it by the total +number of outcomes. + +So in the conditional world, +there's only two outcomes that + +comprise the event "doubles +rolled." These are the only + +two circles in the blue +region, right? + +So applying the conditional +version number + +law, we have two. + +And then we need to divide +by the size of omega. + +So our conditional universe, +we've already said, has six + +possible dots. + +So we just divide by 6, and you +see that we get the same + +answer of 1/3. + +And so again, we used two +different strategies. + +I happen to prefer the second +one, because it's slightly + +faster and it makes you think +about what does conditioning + +really mean. + +Conditioning means you're now +restricting your attention to + +a conditional universe. + +And given that you're in this +conditional universe where the + +sum was less than or equal +to 4, what is then the + +probability that doubles +also happened? + +OK, hopefully you, guys, +are following. + +Let's move on to part c. + +So part c asks for the +probability that at least one + +die roll is a 6. + +So I'm going to use the letter +S to denote this, the + +probability that at least +one die roll is a 6. + +So let's go back to +our picture and + +we'll use a green marker. + +So hopefully you agree that +anything in this column + +corresponds to at least one 6. + +So this point, this point, this +point, this point, this + +point, and this point your first +die landed on a 6, so at + +least one 6 is satisfied. + +Similarly, if your second die +has a 6, then we're also OK. + +So I claim we want to look +at these 11 points. + +Let me just check that, +yeah, 6 plus 5-- + +11. + +So using the discrete uniform +law again, we get + +11 divided by 36. + + + +OK, last problem, we're +almost done. + +So again, we're interested in +the event S again, so the + +event that at least one +die roll is a 6. + +But now we want to compute the +probability of that event in + +the conditional world where +the two dice land + +on different numbers. + + + +So I'm going to call this +probability of S. Let's see, + +I'm running out of letters. + +Let's for lack of a better +letter, my name is Katie, so + +we'll just use a K. We want to +compute the probability of S + +given K. And instead of using +the definition of conditional + +probability, like we did back in +part b, we're going to use + +the faster route. + +So essentially, we're going to +find the number of outcomes in + +the conditional world. + + + +And then we're also going to +compute the number of outcomes + +that comprise S in the +conditional world. + +So let's take a look at this. + +We are conditioning on the event +that the two dice land + +on different numbers. + +So hopefully you agree with me +that every single dot that is + +not on the diagonal, so every +single dot that doesn't + +correspond to doubles, is a +dot that we care about. + +So our conditional universe of +that the two dice land on + +"different numbers", that +corresponds to these dots. + + + +And it corresponds +to these dots. + +I don't want to get this one. + +OK, that's good. + +So let's see, how many outcomes +do we have in our + +conditional world? + +And I'm sorry I don't know why +I didn't include this. + +This is absolutely included. + +I'm just testing to see if you, + +guys, are paying attention. + +So we counted before that there +are six dots on the + +diagonal, and we know that +there are 36 dots total. + +So the number of dots, or +outcomes to use the proper + +word, in our conditional world +is 36 minus 6, or 30. + +So we get a 30 on +the denominator. + +And now we're sort of using a +conditional version of our + +discrete uniform law, again. + +And the reason why we can do +this is, as I argued before, + +that conditioning doesn't change +the relative frequency + +of the outcomes. + +So in this conditional world, +all of the outcomes are still + +equally likely, hence we can +apply this law again. + +So now we need to count the +number of outcomes that are in + +the orange conditional world, +but that also satisfy at least + +one die roll is a 6. + +So you can see-- + +1-- we just need to count the +green circles that are also in + +the orange. + +So that's 1, 2, 3, 4, +5, 6, 7, 8, 9, 10. + +So we get a 10, so our answer +is 10 over 30, or 1/3. + +So now we're done with +this problem. + +As you see, hopefully, it +wasn't too painful. + +And what are the important +takeaways + +here for this problem? + +Well, one is that whenever you +have a discrete sample space, + +in which all of outcomes are +equally likely, you should + +think about using the discrete +uniform law, because this law + +lets you reduce the problem from +computing probabilities + +to just counting outcomes +within events. + +And the second takeaway is +the way we thought about + +conditioning. + +So we talked about one thing, +which is that in your + +conditional world, when you +condition, the relative + +likelihoods of the various +outcomes don't change. + +So in our original universe, +all of the outcomes were + +equally likely. + +So in our conditional universe, +all of the outcomes + +are equally likely. + +And we saw it was much faster to +apply a conditional version + +of the discrete uniform law. + +So that's it for today. + +And we'll do more problems +next time. \ No newline at end of file diff --git a/6O9D6am_RK4.txt b/6O9D6am_RK4.txt new file mode 100644 index 0000000000000000000000000000000000000000..c23d20763263ad5aad3f0b89401130fbbf2f1433 --- /dev/null +++ b/6O9D6am_RK4.txt @@ -0,0 +1,619 @@ +align:start position:0% + +very important property of a numerical + + align:start position:0% +very important property of a numerical + + + align:start position:0% +very important property of a numerical +method is its border the accuracy of a + + align:start position:0% +method is its border the accuracy of a + + + align:start position:0% +method is its border the accuracy of a +method is proportional to a power of the + + align:start position:0% +method is proportional to a power of the + + + align:start position:0% +method is proportional to a power of the +step size and that power is called the + + align:start position:0% +step size and that power is called the + + + align:start position:0% +step size and that power is called the +order if H is the step size and P is the + + align:start position:0% +order if H is the step size and P is the + + + align:start position:0% +order if H is the step size and P is the +order then the error made in one step is + + align:start position:0% +order then the error made in one step is + + + align:start position:0% +order then the error made in one step is +proportional to H to the P plus one and + + align:start position:0% +proportional to H to the P plus one and + + + align:start position:0% +proportional to H to the P plus one and +the error made in traversing an entire + + align:start position:0% +the error made in traversing an entire + + + align:start position:0% +the error made in traversing an entire +interval is proportional to H to the P + + align:start position:0% +interval is proportional to H to the P + + + align:start position:0% +interval is proportional to H to the P +so this means if you're using a method + + align:start position:0% +so this means if you're using a method + + + align:start position:0% +so this means if you're using a method +order P and to cut these step size in + + align:start position:0% +order P and to cut these step size in + + + align:start position:0% +order P and to cut these step size in +half you can expect the overall error to + + align:start position:0% +half you can expect the overall error to + + + align:start position:0% +half you can expect the overall error to +be reduced by a factor of two to the P + + align:start position:0% + + + + align:start position:0% + +the order of a numerical method is + + align:start position:0% +the order of a numerical method is + + + align:start position:0% +the order of a numerical method is +determined by an analysis involving + + align:start position:0% +determined by an analysis involving + + + align:start position:0% +determined by an analysis involving +Taylor series during the derivation of + + align:start position:0% +Taylor series during the derivation of + + + align:start position:0% +Taylor series during the derivation of +the method but we can also do an + + align:start position:0% +the method but we can also do an + + + align:start position:0% +the method but we can also do an +experiment to determine the order that's + + align:start position:0% +experiment to determine the order that's + + + align:start position:0% +experiment to determine the order that's +what this program does the input is the + + align:start position:0% +what this program does the input is the + + + align:start position:0% +what this program does the input is the +name of a know de solver and then it's + + align:start position:0% +name of a know de solver and then it's + + + align:start position:0% +name of a know de solver and then it's +going to do a numerical integration of + + align:start position:0% +going to do a numerical integration of + + + align:start position:0% +going to do a numerical integration of +an ordinary differential equation just + + align:start position:0% +an ordinary differential equation just + + + align:start position:0% +an ordinary differential equation just +involving T so the result is the value + + align:start position:0% +involving T so the result is the value + + + align:start position:0% +involving T so the result is the value +of an integral the integral from of 1 + + align:start position:0% +of an integral the integral from of 1 + + + align:start position:0% +of an integral the integral from of 1 +over 1 plus T squared from 0 to 1 we + + align:start position:0% +over 1 plus T squared from 0 to 1 we + + + align:start position:0% +over 1 plus T squared from 0 to 1 we +know the exact answer is 1/2 so we do + + align:start position:0% +know the exact answer is 1/2 so we do + + + align:start position:0% +know the exact answer is 1/2 so we do +that integrate that differential + + align:start position:0% +that integrate that differential + + + align:start position:0% +that integrate that differential +equation twice once with a step size of + + align:start position:0% +equation twice once with a step size of + + + align:start position:0% +equation twice once with a step size of +point 1 and then with a step size of 1/2 + + align:start position:0% +point 1 and then with a step size of 1/2 + + + align:start position:0% +point 1 and then with a step size of 1/2 +of 1/2 that we integrate the + + align:start position:0% +of 1/2 that we integrate the + + + align:start position:0% +of 1/2 that we integrate the +differential equation take the final + + align:start position:0% +differential equation take the final + + + align:start position:0% +differential equation take the final +value of y for each of those two + + align:start position:0% +value of y for each of those two + + + align:start position:0% +value of y for each of those two +integrations compare those values with + + align:start position:0% +integrations compare those values with + + + align:start position:0% +integrations compare those values with +the exact answer take the ratio of those + + align:start position:0% +the exact answer take the ratio of those + + + align:start position:0% +the exact answer take the ratio of those +two values that shows how much the error + + align:start position:0% +two values that shows how much the error + + + align:start position:0% +two values that shows how much the error +is decreased when we cut the step size + + align:start position:0% +is decreased when we cut the step size + + + align:start position:0% +is decreased when we cut the step size +in half + + align:start position:0% +in half + + + align:start position:0% +in half +the log base 2 of that ratio is the + + align:start position:0% +the log base 2 of that ratio is the + + + align:start position:0% +the log base 2 of that ratio is the +order it should be an integer so we can + + align:start position:0% +order it should be an integer so we can + + + align:start position:0% +order it should be an integer so we can +round it to the nearest integer and + + align:start position:0% +round it to the nearest integer and + + + align:start position:0% +round it to the nearest integer and +return that value as the value of this + + align:start position:0% +return that value as the value of this + + + align:start position:0% +return that value as the value of this +function let's run our experiment first + + align:start position:0% +function let's run our experiment first + + + align:start position:0% +function let's run our experiment first +on OD e1 with step size of point 1 this + + align:start position:0% +on OD e1 with step size of point 1 this + + + align:start position:0% +on OD e1 with step size of point 1 this +method gets the integral as point 5 3 8 + + align:start position:0% +method gets the integral as point 5 3 8 + + + align:start position:0% +method gets the integral as point 5 3 8 +9 not very accurate cut the step size in + + align:start position:0% +9 not very accurate cut the step size in + + + align:start position:0% +9 not very accurate cut the step size in +half + + align:start position:0% +half + + + align:start position:0% +half +it gets point 5 1 9 1 the ratio of those + + align:start position:0% +it gets point 5 1 9 1 the ratio of those + + + align:start position:0% +it gets point 5 1 9 1 the ratio of those +is 2 logarithm base 2 is 1 so OD e1 has + + align:start position:0% +is 2 logarithm base 2 is 1 so OD e1 has + + + align:start position:0% +is 2 logarithm base 2 is 1 so OD e1 has +order 1 now OD e 2 step size point 1 + + align:start position:0% +order 1 now OD e 2 step size point 1 + + + align:start position:0% +order 1 now OD e 2 step size point 1 +point 4 9 9 cut it in half point 4 9 9 8 + + align:start position:0% +point 4 9 9 cut it in half point 4 9 9 8 + + + align:start position:0% +point 4 9 9 cut it in half point 4 9 9 8 +the ratio of those is close to 4 and so + + align:start position:0% +the ratio of those is close to 4 and so + + + align:start position:0% +the ratio of those is close to 4 and so +de 2 we find it with this experiment as + + align:start position:0% +de 2 we find it with this experiment as + + + align:start position:0% +de 2 we find it with this experiment as +a getting order 2 + + align:start position:0% + + + + align:start position:0% + +now let's try classical Runge Kutta this + + align:start position:0% +now let's try classical Runge Kutta this + + + align:start position:0% +now let's try classical Runge Kutta this +is why it's so popular it's very + + align:start position:0% +is why it's so popular it's very + + + align:start position:0% +is why it's so popular it's very +accurate with step size 0.1 we get close + + align:start position:0% +accurate with step size 0.1 we get close + + + align:start position:0% +accurate with step size 0.1 we get close +to 1/2 cut the step size and a half we + + align:start position:0% +to 1/2 cut the step size and a half we + + + align:start position:0% +to 1/2 cut the step size and a half we +get even closer the ratio of these two + + align:start position:0% +get even closer the ratio of these two + + + align:start position:0% +get even closer the ratio of these two +is close to 16 and the log base 2 is 4 + + align:start position:0% +is close to 16 and the log base 2 is 4 + + + align:start position:0% +is close to 16 and the log base 2 is 4 +so OBE for has experimentally order 4 so + + align:start position:0% +so OBE for has experimentally order 4 so + + + align:start position:0% +so OBE for has experimentally order 4 so +we found that at least with this single + + align:start position:0% +we found that at least with this single + + + align:start position:0% +we found that at least with this single +experiment that OD e solvers 1 2 & 4 + + align:start position:0% +experiment that OD e solvers 1 2 & 4 + + + align:start position:0% +experiment that OD e solvers 1 2 & 4 +have orders 1 2 & 4 so as you probably + + align:start position:0% +have orders 1 2 & 4 so as you probably + + + align:start position:0% +have orders 1 2 & 4 so as you probably +realized this is why we named them OD e + + align:start position:0% +realized this is why we named them OD e + + + align:start position:0% +realized this is why we named them OD e +1 2 & 4 + + align:start position:0% + + + + align:start position:0% + +this brings us to the naming conventions + + align:start position:0% +this brings us to the naming conventions + + + align:start position:0% +this brings us to the naming conventions +in the functions in the MATLAB Oh de + + align:start position:0% +in the functions in the MATLAB Oh de + + + align:start position:0% +in the functions in the MATLAB Oh de +suite all of the functions have names + + align:start position:0% +suite all of the functions have names + + + align:start position:0% +suite all of the functions have names +that are variations on the theme + + align:start position:0% +that are variations on the theme + + + align:start position:0% +that are variations on the theme +OD e PQ that means that the method OD e + + align:start position:0% +OD e PQ that means that the method OD e + + + align:start position:0% +OD e PQ that means that the method OD e +PQ uses methods of order P and Q so + + align:start position:0% +PQ uses methods of order P and Q so + + + align:start position:0% +PQ uses methods of order P and Q so +we've been getting a glimpse of that + + align:start position:0% +we've been getting a glimpse of that + + + align:start position:0% +we've been getting a glimpse of that +with our names Oh de 1 2 & 4 there's an + + align:start position:0% +with our names Oh de 1 2 & 4 there's an + + + align:start position:0% +with our names Oh de 1 2 & 4 there's an +exercise modify order X to do further + + align:start position:0% +exercise modify order X to do further + + + align:start position:0% +exercise modify order X to do further +experiments involving the order of our + + align:start position:0% +experiments involving the order of our + + + align:start position:0% +experiments involving the order of our +ODS offers change it to do other + + align:start position:0% +ODS offers change it to do other + + + align:start position:0% +ODS offers change it to do other +integrals and check out the order of our + + align:start position:0% +integrals and check out the order of our + + + align:start position:0% +integrals and check out the order of our +three vodi e 1 2 & 4 \ No newline at end of file diff --git a/6oV3pKLgW2I.txt b/6oV3pKLgW2I.txt new file mode 100644 index 0000000000000000000000000000000000000000..0da82fc36947ee49d5b9e435709d6598b96b84a3 --- /dev/null +++ b/6oV3pKLgW2I.txt @@ -0,0 +1,2360 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation, or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK. + +So today's lecture will be on +the subject of counting. + +So counting, I guess, is +a pretty simple affair + +conceptually, but it's a +topic that can also get + +to be pretty tricky. + +The reason we're going to talk +about counting is that there's + +a lot of probability problems +whose solution actually + +reduces to successfully counting +the cardinalities of + +various sets. + +So we're going to see the basic, +simplest methods that + +one can use to count +systematically in various + +situations. + +So in contrast to previous +lectures, we're not going to + +introduce any significant +new concepts of a + +probabilistic nature. + +We're just going to use the +probability tools that we + +already know. + +And we're going to apply them +in situations where there's + +also some counting involved. + +Now, today we're going +to just touch the + +surface of this subject. + +There's a whole field of +mathematics called + +combinatorics who are people who +actually spend their whole + +lives counting more and +more complicated sets. + +We were not going to get +anywhere close to the full + +complexity of the field, but +we'll get just enough tools + +that allow us to address +problems of the type that one + +encounters in most common +situations. + +So the basic idea, the basic +principle is something that + +we've already discussed. + +So counting methods apply in +situations where we have + +probabilistic experiments with +a finite number of outcomes + +and where every outcome-- + +every possible outcome-- + +has the same probability +of occurring. + +So we have our sample space, +omega, and it's got a bunch of + +discrete points in there. + +And the cardinality of the set +omega is some capital N. So, + +in particular, we assume that +the sample points are equally + +likely, which means that every +element of the sample space + +has the same probability +equal to 1 over N. + +And then we are interested in a +subset of the sample space, + +call it A. And that +subset consists + +of a number of elements. + +Let the cardinality of that +subset be equal to little n. + +And then to find the probability +of that set, all + +we need to do is to add the +probabilities of the + +individual elements. + +There's little n elements, and +each one has probability one + +over capital N. And +that's the answer. + +So this means that to solve +problems in this context, all + +that we need to be able to do +is to figure out the number + +capital N and to figure out +the number little n. + +Now, if somebody gives you a set +by just giving you a list + +and gives you another set, +again, giving you a list, it's + +easy to count there element. + +You just count how much +there is on the list. + +But sometimes the sets are +described in some more + +implicit way, and we may have to +do a little bit more work. + +There's various tricks that are + +involved in counting properly. + +And the most common +one is to-- + +when you consider a set of +possible outcomes, to describe + +the construction of those +possible outcomes through a + +sequential process. + +So think of a probabilistic +experiment that involves a + +number of stages, and in each +one of the stages there's a + +number of possible choices +that there may be. + +The overall experiment consists +of carrying out all + +the stages to the end. + +And the number of points in the +sample space is how many + +final outcomes there can be in +this multi-stage experiment. + +So in this picture we have an +experiment in which of the + +first stage we have +four choices. + +In the second stage, no matter +what happened in the first + +stage, the way this is drawn +we have three choices. + +No matter whether we ended up +here, there, or there, we have + +three choices in the +second stage. + +And then there's a third stage +and at least in this picture, + +no matter what happened in the +first two stages, in the third + +stage we're going to have +two possible choices. + +So how many leaves are there +at the end of this tree? + +That's simple. + +It's just the product of +these three numbers. + +The number of possible leaves +that we have out there is 4 + +times 3 times 2. + +Number of choices at each stage +gets multiplied, and + +that gives us the number +of overall choices. + +So this is the general rule, the +general trick that we are + +going to use over and over. + +So let's apply it to some very +simple problems as a warm up. + +How many license plates can you +make if you're allowed to + +use three letters and then +followed by four digits? + +At least if you're dealing with +the English alphabet, you + +have 26 choices for +the first letter. + +Then you have 26 choices +for the second letter. + +And then 26 choices for +the third letter. + +And then we start the digits. + +We have 10 choices for the first +digit, 10 choices for + +the second digit, 10 choices for +the third, 10 choices for + +the last one. + +Let's make it a little more +complicated, suppose that + +we're interested in license +plates where no letter can be + +repeated and no digit +can be repeated. + +So you have to use different +letters, different digits. + +How many license plates +can you make? + +OK, let's choose the +first letter, + +and we have 26 choices. + +Now, I'm ready to choose my +second letter, how many + +choices do I have? + +I have 25, because I already +used one letter. + +I have the 25 remaining letters +to choose from. + +For the next letter, +how many choices? + +Well, I used up two of +my letters, so I + +only have 24 available. + +And then we start with the +digits, 10 choices for the + +first digit, 9 choices for the +second, 8 for the third, 7 for + +the last one. + +All right. + +So, now, let's bring some +symbols in a related problem. + +You are given a set that +consists of n elements and + +you're supposed to take +those n elements and + +put them in a sequence. + +That is to order them. + +Any possible ordering of those +elements is called a + +permutation. + +So for example, if we have the +set 1, 2, 3, 4, a possible + +permutation is the +list 2, 3, 4, 1. + +That's one possible +permutation. + +And there's lots of possible +permutations, of course, the + +question is how many +are there. + +OK, let's think about building +this permutation by choosing + +one at a time. + +Which of these elements goes +into each one of these slots? + +How many choices for the number +that goes into the + +first slot or the elements? + +Well, we can choose any one of +the available elements, so we + +have n choices. + +Let's say this element goes +here, having used up that + +element, we're left with n minus +1 elements and we can + +pick any one of these and bring +it into the second slot. + +So here we have n choices, here +we're going to have n + +minus 1 choices, then how +many we put there will + +have n minus 2 choices. + +And you go down until the end. + +What happens at this point +when you are to + +pick the last element? + +Well, you've used n minus of +them, there's only one + +left in your bag. + +You're forced to use that one. + +So the last stage, you're going +to have only one choice. + +So, basically, the number of +possible permutations is the + +product of all integers +from n down to one, or + +from one up to n. + +And there's a symbol that we +use for this number, it's + +called n factorial. + +So n factorial is the number of +permutations of n objects. + +The number of ways that you can +order n objects that are + +given to you. + +Now, a different equation. + +We have n elements. + +Let's say the elements +are 1, 1,2, up to n. + +And it's a set. + +And we want to create +a subset. + +How many possible subsets +are there? + +So speaking of subsets means +looking at each one of the + +elements and deciding whether +you're going to put it in to + +subsets or not. + +For example, I could choose +to put 1 in, but 2 I'm not + +putting it in, 3 I'm not putting +it in, 4 I'm putting + +it, and so on. + +So that's how you +create a subset. + +You look at each one of the +elements and you say, OK, I'm + +going to put it in the subset, +or I'm not going to put it. + +So think of these as consisting +of stages. + +At each stage you look at +one element, and you + +make a binary decision. + +Do I put it in the +subset, or not? + +So therefore, how many +subsets are there? + +Well, I have two choices +for the first element. + +Am I going to put in +the subset, or not? + +I have two choices for the +next element, and so on. + +For each one of the elements, +we have two choices. + +So the overall number of choices +is 2 to the power n. + +So, conclusion-- + +the number of subsets, often n +element set, is 2 to the n. + +So in particular, if we take n +equal to 1, let's check that + +our answer makes sense. + +If we have n equal to one, how +many subsets does it have? + +So we're dealing with +a set of just one. + +What are the subsets? + +One subset is this one. + +Do we have other subsets +of the one element set? + +Yes, we have the empty set. + +That's the second one. + +These are the two possible +subsets of + +this particular set. + +So 2 subsets when n is equal to +1, that checks the answer. + +All right. + +OK, so having gone so far, we +can do our first example now. + +So we are given a die +and we're going + +to roll it 6 times. + +OK, let's make some assumptions +about the rolls. + +Let's assume that the rolls are +independent, and that the + +die is also fair. + +So this means that the +probability of any particular + +outcome of the die rolls-- + +for example, so we have 6 rolls, +one particular outcome + +could be 3,3,1,6,5. + +So that's one possible +outcome. + +What's the probability +of this outcome? + +There's probability 1/6 that +this happens, 1/6 that this + +happens, 1/6 that this +happens, and so on. + +So the probability that +the outcome is this + +is 1/6 to the sixth. + +What did I use to come +up with this answer? + +I used independence, so I +multiplied the probability of + +the first roll gives me a 2, +times the probability that the + +second roll gives me +a 3, and so on. + +And then I used the assumption +that the die is fair, so that + +the probability of 2 is +1/6, the probably of 3 + +is 1/6, and so on. + +So if I were to spell it out, +it's the probability that we + +get the 2 in the first roll, +times the probability of 3 in + +the second roll, times the +probability of the + +5 in the last roll. + +So by independence, I can +multiply probabilities. + +And because the die is fair, +each one of these numbers is + +1/6 to the sixth. + +And so the same calculation +would apply no matter what + +numbers I would put in here. + +So all possible outcomes +are equally likely. + +Let's start with this. + +So since all possible outcomes +are equally likely to find an + +answer to a probability +question, if we're dealing + +with some particular event, so +the event is that all rolls + +give different numbers. + +That's our event A. And our +sample space is some set + +capital omega. + +We know that the answer is going +to be the cardinality of + +the set A, divided by the +cardinality of the set omega. + +So let's deal with the +easy one first. + +How many elements are there +in the sample space? + +How many possible outcomes +are there when you + +roll a dice 6 times? + +You have 6 choices for +the first roll. + +You have 6 choices for the +second roll and so on. + +So the overall number +of outcomes is going + +to be 6 to the sixth. + +So number of elements in +the sample space is 6 + +to the sixth power. + +And I guess this checks +with this. + +We have 6 to the sixth outcomes, +each one has this + +much probability, +so the overall + +probability is equal to one. + +Right? + +So the probability of an +individual outcome is one over + +how many possible outcomes +we have, which is this. + +All right. + +So how about the numerator? + +We are interested in outcomes +in which the numbers that we + +get are all different. + +So what is an outcome in which +the numbers are all different? + +So the die has 6 faces. + +We roll it 6 times. + +We're going to get 6 +different numbers. + +This means that we're going to +exhaust all the possible + +numbers, but they can appear +in any possible sequence. + +So an outcome that makes this +event happen is a list of the + +numbers from 1 to 6, +but arranged in + +some arbitrary order. + +So the possible outcomes that +make event A happen are just + +the permutations of the +numbers from 1 to 6. + +One possible outcome that makes +our events to happen-- + +it would be this. + +Here we have 6 possible numbers, +but any other list of + +this kind in which none +of the numbers is + +repeated would also do. + +So number of outcomes that make +the event happen is the + +number of permutations +of 6 elements. + +So it's 6 factorial. + +And so the final answer is +going to be 6 factorial + +divided by 6 to the sixth. + +All right, so that's a typical +way that's one solves problems + +of this kind. + +We know how to count +certain things. + +For example, here we knew how to +count permutations, and we + +used our knowledge to count the +elements of the set that + +we need to deal with. + +So now let's get to a slightly +more difficult problem. + +We're given once more a +set with n elements. + +We already know how many subsets +that set has, but now + +we would be interested in +subsets that have exactly k + +elements in them. + +So we start with our big set +that has n elements, and we + +want to construct a subset +that has k elements. + +Out of those n I'm +going to choose k + +and put them in there. + +In how many ways +can I do this? + +More concrete way of thinking +about this problem-- + +you have n people in some group +and you want to form a + +committee by picking people from +that group, and you want + +to form a committee +with k people. + +Where k is a given number. + +For example, a 5 person +committee. + +How many 5 person committees +are possible if you're + +starting with 100 people? + +So that's what we +want to count. + +How many k element subsets +are there? + +We don't yet know the answer, +but let's give a name to it. + +And the name is going to be this +particular symbol, which + +we read as n choose k. + +Out of n elements, we want +to choose k of them. + +OK. + +That may be a little tricky. + +So what we're going to do is +to instead figure out a + +somewhat easier problem, +which is going to be-- + +in how many ways can I pick k +out of these people and puts + +them in a particular order? + +So how many possible ordered +lists can I make that consist + +of k people? + +By ordered, I mean that we take +those k people and we say + +this is the first person +in the community. + +That's the second person +in the committee. + +That's the third person in +the committee and so on. + +So in how many ways +can we do this? + +Out of these n, we want to +choose just k of them and put + +them in slots. + +One after the other. + +So this is pretty much like the +license plate problem we + +solved just a little earlier. + +So we have n choices for who +we put as the top person in + +the community. + +We can pick anyone and have +them be the first person. + +Then I'm going to choose +the second + +person in the committee. + +I've used up 1 person. + +So I'm going to have n +minus 1 choices here. + +And now, at this stage I've used +up 2 people, so I have n + +minus 2 choices here. + +And this keeps going on. + +Well, what is going to +be the last number? + +Is it's n minus k? + +Well, not really. + +I'm starting subtracting numbers +after the second one, + +so by the end I will have +subtracted k minus 1. + +So that's how many choices I +will have for the last person. + +So this is the number +of ways-- + +the product of these numbers +there gives me the number of + +ways that I can create ordered +lists consisting of k people + +out of the n that +we started with. + +Now, you can do a little bit of +algebra and check that this + +expression here is the same +as that expression. + +Why is this? + +This factorial has all the +products from 1 up to n. + +This factorial has all +the products from 1 + +up to n minus k. + +So you get cancellations. + +And what's left is all the +products starting from the + +next number after here, which +is this particular number. + +So the number of possible ways +of creating such ordered lists + +is n factorial divided by +n minus k factorial. + +Now, a different way that I +could make an ordered list-- + +instead of picking the people +one at a time, I could first + +choose my k people who are going +to be in the committee, + +and then put them in order. + +And tell them out of these k, +you are the first, you are the + +second, you are the third. + +Starting with this k +people, in how many + +ways can I order them? + +That's the number +of permutations. + +Starting with a set with k +objects, in how many ways can + +I put them in a specific +order? + +How many specific orders +are there? + +That's basically the question. + +In how many ways can +I permute these k + +people and arrange them. + +So the number of ways +that you can do + +this step is k factorial. + +So in how many ways can I +start with a set with n + +elements, go through this +process, and end up with a + +sorted list with k elements? + +By the rule that-- + +when we have stages, the total +number of stages is how many + +choices we had in the first +stage, times how many choices + +we had in the second stage. + +The number of ways that this +process can happen is this + +times that. + +This is a different way that +that process could happen. + +And the number of possible +of ways is this number. + +No matter which way we carry out +that process, in the end + +we have the possible ways of +arranging k people out of the + +n that we started with. + +So the final answer that we get +when we count should be + +either this, or this +times that. + +Both are equally valid ways of +counting, so both should give + +us the same answer. + +So we get this equality here. + +So these two expressions +corresponds to two different + +ways of constructing ordered +lists of k people starting + +with n people initially. + +And now that we have this +relation, we can send the k + +factorial to the denominator. + +And that tells us what +that number, n choose + +k, is going to be. + +So this formula-- it's written +here in red, because you're + +going to see it a zillion +times until + +the end of the semester-- + +they are called the binomial +coefficients. + +And they tell us the number of +possible ways that we can + +create a k element subset, +starting with a + +set that has n elements. + +It's always good to do a sanity +check to formulas by + +considering extreme cases. + +So let's take the case where +k is equal to n. + +What's the right answer +in this case? + +How many n elements subsets +are there out + +of an element set? + +Well, your subset needs +to include every one. + +You don't have any choices. + +There's only one choice. + +It's the set itself. + +So the answer should +be equal to 1. + +That's the number of n element +subsets, starting with a set + +with n elements. + +Let's see if the formula gives +us the right answer. + +We have n factorial divided by +k, which is n in our case-- + +n factorial. + +And then n minus k +is 0 factorial. + +So if our formula is correct, we +should have this equality. + +And what's the way to +make that correct? + +Well, it depends what kind +of meaning do we + +give to this symbol? + +How do we define +zero factorial? + +I guess in some ways +it's arbitrary. + +We're going to define it +in a way that makes + +this formula right. + +So the definition that we will +be using is that whenever you + +have 0 factorial, it's going +to stand for the number 1. + +So let's check that this is +also correct, at the other + +extreme case. + +If we let k equal to 0, what +does the formula give us? + +It gives us, again, n factorial +divided by 0 + +factorial times n factorial. + +According to our convention, +this again is equal to 1. + +So there is one subset of our +set that we started with that + +has zero elements. + +Which subset is it? + +It's the empty set. + +So the empty set is the single +subset of the set that we + +started with that happens to +have exactly zero elements. + +So the formula checks in this +extreme case as well. + +So we're comfortable using it. + +Now these factorials and these +coefficients are really messy + +algebraic objects. + +There's lots of beautiful +identities that they satisfy, + +which you can prove +algebraically sometimes by + +using induction and having +cancellations happen + +all over the place. + +But it's really messy. + +Sometimes you can bypass those +calculations by being clever + +and using your understanding +of what these + +coefficients stand for. + +So here's a typical example. + +What is the sum of those +binomial coefficients? + +I fix n, and sum over +all possible cases. + +So if you're an algebra genius, +you're going to take + +this expression here, plug it in +here, and then start doing + +algebra furiously. + +And half an hour later, you +may get the right answer. + +But now let's try +to be clever. + +What does this really do? + +What does that formula count? + +We're considering k +element subsets. + +That's this number. + +And we're considering the number +of k element subsets + +for different choices of k. + +The first term in this sum +counts how many 0-element + +subsets we have. + +The next term in this sum counts +how many 1-element + +subsets we have. + +The next term counts how many +2-element subsets we have. + +So in the end, what +have we counted? + +We've counted the total +number of subsets. + +We've considered all possible +cardinalities. + +We've counted the number +of subsets of size k. + +We've considered all +possible sizes k. + +The overall count is +going to be the + +total number of subsets. + +And we know what this is. + +A couple of slides ago, we +discussed that this number is + +equal to 2 to the n. + +So, nice, clean and simple +answer, which is easy to guess + +once you give an interpretation +to the + +algebraic expression that you +have in front of you. + +All right. + +So let's move again to sort of +an example in which those + +binomial coefficients are +going to show up. + +So here's the setting-- + +n independent coin tosses, +and each coin toss has a + +probability, P, of resulting +in heads. + +So this is our probabilistic +experiment. + +Suppose we do 6 tosses. + +What's the probability that we +get this particular sequence + +of outcomes? + +Because of independence, we +can multiply probability. + +So it's going to be the +probability that the first + +toss results in heads, times +the probability that the + +second toss results in tails, +times the probability that the + +third one results in tails, +times probability of heads, + +times probability of heads, +times probability of heads, + +which is just P to the fourth +times (1 minus P) squared. + +So that's the probability of +this particular sequence. + +How about a different +sequence? + +If I had 4 tails and 2 heads, +but in a different order-- + +let's say if we considered +this particular outcome-- + +would the answer be different? + +We would still have P, times P, +times P, times P, times (1 + +minus P), times (1 minus P). + +We would get again, +the same answer. + +So what you observe from just +this example is that, more + +generally, the probability +of obtaining a particular + +sequence of heads and tails is +P to a power, equal to the + +number of heads. + +So here we had 4 heads. + +So there's P to the +fourth showing up. + +And then (1 minus P) to the +power number of tails. + +So every k head sequence-- + +every outcome in which we have +exactly k heads, has the same + +probability, which is going to +be P to the k, (1 minus p), to + +the (n minus k). + +This is the probability of any +particular sequence that has + +exactly k heads. + +So that's the probability +of a particular + +sequence with k heads. + +So now let's ask the question, +what is the probability that + +my experiment results in exactly +k heads, but in some + +arbitrary order? + +So the heads could +show up anywhere. + +So there's a number +of different ways + +that this can happen. + +What's the overall probability +that this event takes place? + +So the probability of an event +taking place is the sum of the + +probabilities of all the +individual ways that + +the event can occur. + +So it's the sum of the +probabilities of all the + +outcomes that make +the event happen. + +The different ways that we can +obtain k heads are the number + +of different sequences that +contain exactly k heads. + +We just figured out that any +sequence with exactly k heads + +has this probability. + +So to do this summation, we just +need to take the common + +probability of each individual +k head sequence, times how + +many terms we have +in this sum. + +So what we're left to do now +is to figure out how many k + +head sequences are there. + +How many outcomes are there in +which we have exactly k heads. + +OK. + +So what are the ways that I can +describe to you a sequence + +with k heads? + +I can take my n slots +that corresponds to + +the different tosses. + +I'm interested in particular +sequences that + +have exactly k heads. + +So what I need to do is to +choose k slots and assign + +heads to them. + +So to specify a sequence that +has exactly k heads is the + +same thing as drawing this +picture and telling you which + +are the k slots that happened +to have heads. + +So I need to choose out of those +n slots, k of them, and + +assign them heads. + +In how many ways can I +choose this k slots? + +Well, it's the question of +starting with a set of n slots + +and choosing k slots out +of the n available. + +So the number of k head +sequences is the same as the + +number of k element subsets of +the set of slots that we + +started with, which are +the n slots 1 up to n. + +We know what that number is. + +We counted, before, the number +of k element subsets, starting + +with a set with n elements. + +And we gave a symbol to that +number, which is that + +thing, n choose k. + +So this is the final answer +that we obtain. + +So these are the so-called +binomial probabilities. + +And they gave us the +probabilities for different + +numbers of heads starting with +a fair coin that's being + +tossed a number of times. + +This formula is correct, of +course, for reasonable values + +of k, meaning its correct for +k equals 0, 1, up to n. + +If k is bigger than n, what's +the probability of k heads? + +If k is bigger than n, there's +no way to obtain k heads, so + +that probability is, +of course, zero. + +So these probabilities only +makes sense for the numbers k + +that are possible, given +that we have n tosses. + +And now a question similar +to the one we had in + +the previous slide. + +If I write down this +summation-- + +even worse algebra than the one +in the previous slide-- + +what do you think this number +will turn out to be? + +It should be 1 because this +is the probability + +of obtaining k heads. + +When we do the summation, what +we're doing is we're + +considering the probability of +0 heads, plus the probability + +of 1 head, plus the probability +of 2 heads, plus + +the probability of n heads. + +We've exhausted all the +possibilities in our + +experiment. + +So the overall probability, +when you exhaust all + +possibilities, must +be equal to 1. + +So that's yet another beautiful +formula that + +evaluates into something +really simple. + +And if you tried to prove this +identity algebraically, of + +course, you would have to +suffer quite a bit. + +So now armed with the binomial +probabilities, we can do the + +harder problems. + +So let's take the same +experiment again. + +We flip a coin independently +10 times. + +So these 10 tosses +are independent. + +We flip it 10 times. + +We don't see the result, but +somebody comes and tells us, + +you know, there were exactly +3 heads in the 10 + +tosses that you had. + +OK? + +So a certain event happened. + +And now you're asked to find +the probability of another + +event, which is that the first +2 tosses were heads. + +Let's call that event A. OK. + +So are we in the setting +of discrete + +uniform probability laws? + +When we toss a coin multiple +times, is it the case that all + +outcomes are equally likely? + +All sequences are +equally likely? + +That's the case if you +have a fair coin-- + +that all sequences are +equally likely. + +But if your coin is not fair, +of course, heads/heads is + +going to have a different +probability than tails/tails. + +If your coin is biased towards +heads, then heads/heads is + +going to be more likely. + +So we're not quite in +the uniform setting. + +Our overall sample space, omega, +does not have equally + +likely elements. + +Do we care about that? + +Not necessarily. + +All the action now happens +inside the event B that we are + +told has occurred. + +So we have our big sample +space, omega. + +Elements of that sample space +are not equally likely. + +We are told that a certain +event B occurred. + +And inside that event B, we're +asked to find the conditional + +probability that A has +also occurred. + +Now here's the lucky thing, +inside the event B, all + +outcomes are equally likely. + +The outcomes inside B are the +sequences of 10 tosses that + +have exactly 3 heads. + +Every 3-head sequence has +this probability. + +So the elements of +B are equally + +likely with each other. + +Once we condition on the event +B having occurred, what + +happens to the probabilities +of the different outcomes + +inside here? + +Well, conditional probability +laws keep the same proportions + +as the unconditional ones. + +The elements of B were equally +likely when we started, so + +they're equally likely once we +are told that B has occurred. + +So to do with this problem, we +need to just transport us to + +this smaller universe and think +about what's happening + +in that little universe. + +In that little universe, +all elements of + +B are equally likely. + +So to find the probability of +some subset of that set, we + +only need to count the +cardinality of B, and count + +the cardinality of A. +So let's do that. + +Number of outcomes in B-- + +in how many ways can we get +3 heads out of 10 tosses? + +That's the number we considered +before, and + +it's 10 choose 3. + +This is the number of +3-head sequences + +when you have 10 tosses. + +Now let's look at the event A. +The event A is that the first + +2 tosses where heads, but we're +living now inside this + +universe B. Given that B +occurred, how many elements + +does A have in there? + +In how many ways can A happen +inside the B universe. + +If you're told that the +first 2 were heads-- + +sorry. + +So out of the outcomes in B that +have 3 heads, how many + +start with heads/heads? + +Well, if it starts with +heads/heads, then the only + +uncertainty is the location +of the third head. + +So we started with heads/heads, +we're going to + +have three heads, the question +is, where is that third head + +going to be. + +It has eight possibilities. + +So slot 1 is heads, slot 2 is +heads, the third heads can be + +anywhere else. + +So there's 8 possibilities +for where the third + +head is going to be. + +OK. + +So what we have counted here is +really the cardinality of A + +intersection B, which is out of +the elements in B, how many + +of them make A happen, divided +by the cardinality of B. And + +that gives us the answer, which +is going to be 10 choose + +3, divided by 8. + +And I should probably redraw a +little bit of the picture that + +they have here. + +The set A is not necessarily +contained in B. It could also + +have stuff outside B. So the +event that the first 2 tosses + +are heads can happen with a +total of 3 heads, but it can + +also happen with a different +total number of heads. + +But once we are transported +inside the set B, what we need + +to count is just this part of +A. It's A intersection B and + +compare it with the total number +of elements in the set + +B. Did I write it the +opposite way? + +Yes. + +So this is 8 over 10 choose 3. + +OK. + +So we're going to close with a +more difficult problem now. + +OK. + +This business of n choose k has +to do with starting with a + +set and picking a subset +of k elements. + +Another way of thinking of that +is that we start with a + +set with n elements and you +choose a subset that has k, + +which means that there's n +minus k that are left. + +Picking a subset is the same as +partitioning our set into + +two pieces. + +Now let's generalize this +question and start counting + +partitions in general. + +Somebody gives you a set +that has n elements. + +Somebody gives you also +certain numbers-- + +n1, n2, n3, let's say, +n4, where these + +numbers add up to n. + +And you're asked to partition +this set into four subsets + +where each one of the subsets +has this particular + +cardinality. + +So you're asking to cut it into +four pieces, each one + +having the prescribed +cardinality. + +In how many ways can we +do this partitioning? + +n choose k was the answer when +we partitioned in two pieces, + +what's the answer +more generally? + +For a concrete example of a +partition, you have your 52 + +card deck and you deal, as in +bridge, by giving 13 cards to + +each one of the players. + +Assuming that the dealing is +done fairly and with a well + +shuffled deck of cards, every +particular partition of the 52 + +cards into four hands, that is +four subsets of 13 each, + +should be equally likely. + +So we take the 52 cards and we +partition them into subsets of + +13, 13, 13, and 13. + +And we assume that all possible +partitions, all + +possible ways of dealing the +cards are equally likely. + +So we are again in a setting +where we can use counting, + +because all the possible +outcomes are equally likely. + +So an outcome of the experiment +is the hands that + +each player ends up getting. + +And when you get the cards in +your hands, it doesn't matter + +in which order that +you got them. + +It only matters what cards +you have on you. + +So it only matters which subset +of the cards you got. + +All right. + +So what's the cardinality of +the sample space in this + +experiment? + +So let's do it for the concrete +numbers that we have + +for the problem of partitioning +52 cards. + +So think of dealing as follows-- +you shuffle the deck + +perfectly, and then you take the +top 13 cards and give them + +to one person. + +In how many possible hands are +there for that person? + +Out of the 52 cards, I choose 13 +at random and give them to + +the first person. + +Having done that, what +happens next? + +I'm left with 39 cards. + +And out of those 39 cards, I +pick 13 of them and give them + +to the second person. + +Now I'm left with 26 cards. + +Out of those 26, I choose 13, +give them to the third person. + +And for the last person there +isn't really any choice. + +Out of the 13, I have to give +that person all 13. + +And that number is +just equal to 1. + +So we don't care about it. + +All right. + +So next thing you do is to write +down the formulas for + +these numbers. + +So, for example, here you +would have 52 factorial, + +divided by 13 factorial, +times 39 + +factorial, and you continue. + +And then there are nice +cancellations that happen. + +This 39 factorial is going to +cancel the 39 factorial that + +comes from there, and so on. + +After you do the cancellations +and all the algebra, you're + +left with this particular +answer, which is the number of + +possible partitions of 52 cards +into four players where + +each player gets exactly +13 hands. + +If you were to generalize this +formula to the setting that we + +have here, the more general +formula is-- + +you have n factorial, where n is +the number of objects that + +you are distributing, divided +by the product of the + +factorials of the-- + +OK, here I'm doing it for +the case where we split + +it into four sets. + +So that would be the answer when +we partition a set into + +four subsets of prescribed +cardinalities. + +And you can guess how that +formula would generalize if + +you want to split it into +five sets or six sets. + +OK. + +So far we just figured out the +size of the sample space. + +Now we need to look at our +event, which is the event that + +each player gets an ace, let's +call that event A. In how many + +ways can that event happens? + +How many possible hands are +there in which every player + +has exactly one ace? + +So I need to think about the +sequential process by which I + +distribute the cards so that +everybody gets exactly one + +ace, and then try to think +in how many ways can that + +sequential process happen. + +So one way of making sure that +everybody gets exactly one ace + +is the following-- + +I take the four aces and I +distribute them randomly to + +the four players, but making +sure that each one gets + +exactly one ace. + +In how many ways can +that happen? + +I take the ace of spades and I +send it to a random person out + +of the four. + +So there's 4 choices for this. + +Then I'm left with 3 +aces to distribute. + +That person already +gotten an ace. + +I take the next ace, and +I give it to one of + +the 3 people remaining. + +So there's 3 choices +for how to do that. + +And then for the next ace, +there's 2 people who have not + +yet gotten an ace, +and they give it + +randomly to one of them. + +So these are the possible ways +of distributing for the 4 + +aces, so that each person +gets exactly one. + +It's actually the same +as this problem. + +Starting with a set of four +things, in how many ways can I + +partition them into four subsets +where the first set + +has one element, the second has +one element, the third one + +has another element, +and so on. + +So it agrees with that formula +by giving us 4 factorial. + +OK. + +So there are different ways +of distributing the aces. + +And then there's different +ways of distributing the + +remaining 48 cards. + +How many ways are there? + +Well, I have 48 cards that I'm +going to distribute to four + +players by giving 12 +cards to each one. + +It's exactly the same question +as the one we had here, except + +that now it's 48 cards, +12 to each person. + +And that gives us this +particular count. + +So putting all that together +gives us the different ways + +that we can distribute the cards +to the four players so + +that each one gets +exactly one ace. + +The number of possible ways +is going to be this four + +factorial, coming from here, +times this number-- + +this gives us the number of +ways that the event of + +interest can happen-- + +and then the denominator is the +cardinality of our sample + +space, which is this number. + +So this looks like +a horrible mess. + +It turns out that this +expression does simplify to + +something really, +really simple. + +And if you look at the textbook +for this problem, you + +will see an alternative +derivation that gives you a + +short cut to the same +numerical answer. + +All right. + +So that basically concludes +chapter one. + +From next time we're going to +consider introducing random + +variables and make the subject +even more interesting. \ No newline at end of file diff --git a/6stYmO_N7LI.txt b/6stYmO_N7LI.txt new file mode 100644 index 0000000000000000000000000000000000000000..5e0919e9097c543f63f8e875ceb8e958cd4faf2a --- /dev/null +++ b/6stYmO_N7LI.txt @@ -0,0 +1,1787 @@ +align:start position:0% + +we now follow a program that parallels + + align:start position:0% +we now follow a program that parallels + + + align:start position:0% +we now follow a program that parallels +our development for the case of the + + align:start position:0% +our development for the case of the + + + align:start position:0% +our development for the case of the +Bernoulli process we will study the time + + align:start position:0% +Bernoulli process we will study the time + + + align:start position:0% +Bernoulli process we will study the time +until the first arrival a random + + align:start position:0% +until the first arrival a random + + + align:start position:0% +until the first arrival a random +variable that we denote by t1 we are + + align:start position:0% +variable that we denote by t1 we are + + + align:start position:0% +variable that we denote by t1 we are +interested in finding the probability + + align:start position:0% +interested in finding the probability + + + align:start position:0% +interested in finding the probability +distribution of this random variable and + + align:start position:0% +distribution of this random variable and + + + align:start position:0% +distribution of this random variable and +later on we will continue and try to + + align:start position:0% +later on we will continue and try to + + + align:start position:0% +later on we will continue and try to +study the time until the case arrival + + align:start position:0% +study the time until the case arrival + + + align:start position:0% +study the time until the case arrival +now T 1 is a continuous random variable + + align:start position:0% +now T 1 is a continuous random variable + + + align:start position:0% +now T 1 is a continuous random variable +because the Poisson process runs in + + align:start position:0% +because the Poisson process runs in + + + align:start position:0% +because the Poisson process runs in +continuous time and therefore it has a + + align:start position:0% +continuous time and therefore it has a + + + align:start position:0% +continuous time and therefore it has a +PDF but instead of finding the PDF + + align:start position:0% +PDF but instead of finding the PDF + + + align:start position:0% +PDF but instead of finding the PDF +directly we will first find the cdf of + + align:start position:0% +directly we will first find the cdf of + + + align:start position:0% +directly we will first find the cdf of +this random variable so we fix a certain + + align:start position:0% +this random variable so we fix a certain + + + align:start position:0% +this random variable so we fix a certain +time T and we're asking for the + + align:start position:0% +time T and we're asking for the + + + align:start position:0% +time T and we're asking for the +probability that the first arrival + + align:start position:0% +probability that the first arrival + + + align:start position:0% +probability that the first arrival +happens during this interval now this is + + align:start position:0% +happens during this interval now this is + + + align:start position:0% +happens during this interval now this is +1 minus the probability that the first + + align:start position:0% +1 minus the probability that the first + + + align:start position:0% +1 minus the probability that the first +arrival happens outside this interval so + + align:start position:0% +arrival happens outside this interval so + + + align:start position:0% +arrival happens outside this interval so +we can write this probability as 1 minus + + align:start position:0% +we can write this probability as 1 minus + + + align:start position:0% +we can write this probability as 1 minus +the probability that t1 is bigger than T + + align:start position:0% +the probability that t1 is bigger than T + + + align:start position:0% +the probability that t1 is bigger than T +but what is this event the first arrival + + align:start position:0% +but what is this event the first arrival + + + align:start position:0% +but what is this event the first arrival +occurring after time little T is the + + align:start position:0% +occurring after time little T is the + + + align:start position:0% +occurring after time little T is the +same as saying that there were no + + align:start position:0% +same as saying that there were no + + + align:start position:0% +same as saying that there were no +arrivals in the time interval from 0 to + + align:start position:0% +arrivals in the time interval from 0 to + + + align:start position:0% +arrivals in the time interval from 0 to +little T and this probability of zero + + align:start position:0% +little T and this probability of zero + + + align:start position:0% +little T and this probability of zero +arrivals in a time interval of length T + + align:start position:0% +arrivals in a time interval of length T + + + align:start position:0% +arrivals in a time interval of length T +is something for which we already have a + + align:start position:0% +is something for which we already have a + + + align:start position:0% +is something for which we already have a +formula take this formula and replace K + + align:start position:0% +formula take this formula and replace K + + + align:start position:0% +formula take this formula and replace K +by 0 tau by T when K is equal to 0 this + + align:start position:0% +by 0 tau by T when K is equal to 0 this + + + align:start position:0% +by 0 tau by T when K is equal to 0 this +term is something to the zeroth power + + align:start position:0% +term is something to the zeroth power + + + align:start position:0% +term is something to the zeroth power +equal to 1 using our convention that 0 + + align:start position:0% +equal to 1 using our convention that 0 + + + align:start position:0% +equal to 1 using our convention that 0 +factorial is equal to 1 we're left just + + align:start position:0% +factorial is equal to 1 we're left just + + + align:start position:0% +factorial is equal to 1 we're left just +with e to the minus lambda T and this is + + align:start position:0% +with e to the minus lambda T and this is + + + align:start position:0% +with e to the minus lambda T and this is +the answer for the CDF of the time until + + align:start position:0% +the answer for the CDF of the time until + + + align:start position:0% +the answer for the CDF of the time until +the first arrival we then take a + + align:start position:0% +the first arrival we then take a + + + align:start position:0% +the first arrival we then take a +derivative and we find that the PDF of + + align:start position:0% +derivative and we find that the PDF of + + + align:start position:0% +derivative and we find that the PDF of +the time until the first arrival has + + align:start position:0% +the time until the first arrival has + + + align:start position:0% +the time until the first arrival has +this form which is the PDF of an + + align:start position:0% +this form which is the PDF of an + + + align:start position:0% +this form which is the PDF of an +exponential random variable of course + + align:start position:0% +exponential random variable of course + + + align:start position:0% +exponential random variable of course +this calculation here is only valid for + + align:start position:0% +this calculation here is only valid for + + + align:start position:0% +this calculation here is only valid for +T's that are non negative for negative + + align:start position:0% +T's that are non negative for negative + + + align:start position:0% +T's that are non negative for negative +T's the PDF of T 1 is of course 0 for + + align:start position:0% +T's the PDF of T 1 is of course 0 for + + + align:start position:0% +T's the PDF of T 1 is of course 0 for +the exponential random variable we have + + align:start position:0% +the exponential random variable we have + + + align:start position:0% +the exponential random variable we have +seen that it has certain memory less + + align:start position:0% +seen that it has certain memory less + + + align:start position:0% +seen that it has certain memory less +properties namely if I condition on the + + align:start position:0% +properties namely if I condition on the + + + align:start position:0% +properties namely if I condition on the +event that nothing has occurred until at + + align:start position:0% +event that nothing has occurred until at + + + align:start position:0% +event that nothing has occurred until at +certain time T and I'm interested in the + + align:start position:0% +certain time T and I'm interested in the + + + align:start position:0% +certain time T and I'm interested in the +time from now until the first arrival + + align:start position:0% +time from now until the first arrival + + + align:start position:0% +time from now until the first arrival +occurs this remaining time until the + + align:start position:0% +occurs this remaining time until the + + + align:start position:0% +occurs this remaining time until the +first arrival is again an exponential + + align:start position:0% +first arrival is again an exponential + + + align:start position:0% +first arrival is again an exponential +distribution that is looking ahead from + + align:start position:0% +distribution that is looking ahead from + + + align:start position:0% +distribution that is looking ahead from +this time I will still wait and + + align:start position:0% +this time I will still wait and + + + align:start position:0% +this time I will still wait and +exponentially distributed the amount of + + align:start position:0% +exponentially distributed the amount of + + + align:start position:0% +exponentially distributed the amount of +time until I see the first arrival + + align:start position:0% +time until I see the first arrival + + + align:start position:0% +time until I see the first arrival +whatever happened in the past and how + + align:start position:0% +whatever happened in the past and how + + + align:start position:0% +whatever happened in the past and how +long I have been waiting doesn't matter + + align:start position:0% +long I have been waiting doesn't matter + + + align:start position:0% +long I have been waiting doesn't matter +starting from this time I will still + + align:start position:0% +starting from this time I will still + + + align:start position:0% +starting from this time I will still +wait and exponentially distributed + + align:start position:0% +wait and exponentially distributed + + + align:start position:0% +wait and exponentially distributed +amount of time this is essentially an + + align:start position:0% +amount of time this is essentially an + + + align:start position:0% +amount of time this is essentially an +expression of a fresh start property of + + align:start position:0% +expression of a fresh start property of + + + align:start position:0% +expression of a fresh start property of +the Poisson process which is analogous + + align:start position:0% +the Poisson process which is analogous + + + align:start position:0% +the Poisson process which is analogous +to the fresh start properties for the + + align:start position:0% +to the fresh start properties for the + + + align:start position:0% +to the fresh start properties for the +Bernoulli process and we will be + + align:start position:0% +Bernoulli process and we will be + + + align:start position:0% +Bernoulli process and we will be +discussing this fresh start property a + + align:start position:0% +discussing this fresh start property a + + + align:start position:0% +discussing this fresh start property a +lot more having figured out the + + align:start position:0% +lot more having figured out the + + + align:start position:0% +lot more having figured out the +distribution of the time of the first + + align:start position:0% +distribution of the time of the first + + + align:start position:0% +distribution of the time of the first +arrival let us now study the time of the + + align:start position:0% +arrival let us now study the time of the + + + align:start position:0% +arrival let us now study the time of the +caithe arrival a random variable that we + + align:start position:0% +caithe arrival a random variable that we + + + align:start position:0% +caithe arrival a random variable that we +denote by y sub k similar to the case of + + align:start position:0% +denote by y sub k similar to the case of + + + align:start position:0% +denote by y sub k similar to the case of +the Bernoulli process this random + + align:start position:0% +the Bernoulli process this random + + + align:start position:0% +the Bernoulli process this random +variable is a continuous one because + + align:start position:0% +variable is a continuous one because + + + align:start position:0% +variable is a continuous one because +arrivals happen in continuous time so it + + align:start position:0% +arrivals happen in continuous time so it + + + align:start position:0% +arrivals happen in continuous time so it +takes continuous values and therefore it + + align:start position:0% +takes continuous values and therefore it + + + align:start position:0% +takes continuous values and therefore it +will be described by a PDF and this is + + align:start position:0% +will be described by a PDF and this is + + + align:start position:0% +will be described by a PDF and this is +what we want to find in order to find it + + align:start position:0% +what we want to find in order to find it + + + align:start position:0% +what we want to find in order to find it +we will make use of the Poisson PMF that + + align:start position:0% +we will make use of the Poisson PMF that + + + align:start position:0% +we will make use of the Poisson PMF that +we have already derived for the number + + align:start position:0% +we have already derived for the number + + + align:start position:0% +we have already derived for the number +of arrivals during an interval of a + + align:start position:0% +of arrivals during an interval of a + + + align:start position:0% +of arrivals during an interval of a +fixed length one approach to finding the + + align:start position:0% +fixed length one approach to finding the + + + align:start position:0% +fixed length one approach to finding the +PDF of YJ is the usual program similar + + align:start position:0% +PDF of YJ is the usual program similar + + + align:start position:0% +PDF of YJ is the usual program similar +again to what we did for the case of the + + align:start position:0% +again to what we did for the case of the + + + align:start position:0% +again to what we did for the case of the +first arrival time we can first find the + + align:start position:0% +first arrival time we can first find the + + + align:start position:0% +first arrival time we can first find the +CDF and then differentiate to find the + + align:start position:0% +CDF and then differentiate to find the + + + align:start position:0% +CDF and then differentiate to find the +PDF so what is the CDF we want to + + align:start position:0% +PDF so what is the CDF we want to + + + align:start position:0% +PDF so what is the CDF we want to +calculate the probability that y K is + + align:start position:0% +calculate the probability that y K is + + + align:start position:0% +calculate the probability that y K is +less than or equal to some number little + + align:start position:0% +less than or equal to some number little + + + align:start position:0% +less than or equal to some number little +Y now what is this event the caithe + + align:start position:0% +Y now what is this event the caithe + + + align:start position:0% +Y now what is this event the caithe +arrival occurs by time Y this means that + + align:start position:0% +arrival occurs by time Y this means that + + + align:start position:0% +arrival occurs by time Y this means that +by time Y we've had at least K arrivals + + align:start position:0% +by time Y we've had at least K arrivals + + + align:start position:0% +by time Y we've had at least K arrivals +we've had J arrivals or maybe K plus 1 + + align:start position:0% +we've had J arrivals or maybe K plus 1 + + + align:start position:0% +we've had J arrivals or maybe K plus 1 +or maybe k plus 2 we've had some number + + align:start position:0% +or maybe k plus 2 we've had some number + + + align:start position:0% +or maybe k plus 2 we've had some number +of + + align:start position:0% +of + + + align:start position:0% +of +rivals and in an interval of length why + + align:start position:0% +rivals and in an interval of length why + + + align:start position:0% +rivals and in an interval of length why +and this is an event that happens with + + align:start position:0% +and this is an event that happens with + + + align:start position:0% +and this is an event that happens with +this probability but we need to take + + align:start position:0% +this probability but we need to take + + + align:start position:0% +this probability but we need to take +into account all the possible values of + + align:start position:0% +into account all the possible values of + + + align:start position:0% +into account all the possible values of +n that are at least as large as K now we + + align:start position:0% +n that are at least as large as K now we + + + align:start position:0% +n that are at least as large as K now we +have a formula for this probability the + + align:start position:0% +have a formula for this probability the + + + align:start position:0% +have a formula for this probability the +probability of n arrivals in an interval + + align:start position:0% +probability of n arrivals in an interval + + + align:start position:0% +probability of n arrivals in an interval +of given length this is the Poisson PMF + + align:start position:0% +of given length this is the Poisson PMF + + + align:start position:0% +of given length this is the Poisson PMF +with appropriate changes of symbols so + + align:start position:0% +with appropriate changes of symbols so + + + align:start position:0% +with appropriate changes of symbols so +we can take this expression substitute + + align:start position:0% +we can take this expression substitute + + + align:start position:0% +we can take this expression substitute +it here and then differentiate do some + + align:start position:0% +it here and then differentiate do some + + + align:start position:0% +it here and then differentiate do some +algebra and find the answer instead of + + align:start position:0% +algebra and find the answer instead of + + + align:start position:0% +algebra and find the answer instead of +carrying out this algebra + + align:start position:0% +carrying out this algebra + + + align:start position:0% +carrying out this algebra +however we will proceed in a more + + align:start position:0% +however we will proceed in a more + + + align:start position:0% +however we will proceed in a more +intuitive way that will get us there + + align:start position:0% +intuitive way that will get us there + + + align:start position:0% +intuitive way that will get us there +perhaps faster and the derivation that + + align:start position:0% +perhaps faster and the derivation that + + + align:start position:0% +perhaps faster and the derivation that +we will follow actually parallels the + + align:start position:0% +we will follow actually parallels the + + + align:start position:0% +we will follow actually parallels the +one that we went through in the case of + + align:start position:0% +one that we went through in the case of + + + align:start position:0% +one that we went through in the case of +the Bernoulli process the intuitive + + align:start position:0% +the Bernoulli process the intuitive + + + align:start position:0% +the Bernoulli process the intuitive +argument that we will use will rest on + + align:start position:0% +argument that we will use will rest on + + + align:start position:0% +argument that we will use will rest on +the interpretation of a PDF in terms of + + align:start position:0% +the interpretation of a PDF in terms of + + + align:start position:0% +the interpretation of a PDF in terms of +probabilities of small intervals so the + + align:start position:0% +probabilities of small intervals so the + + + align:start position:0% +probabilities of small intervals so the +PDF evaluated at some particular point Y + + align:start position:0% +PDF evaluated at some particular point Y + + + align:start position:0% +PDF evaluated at some particular point Y +times Delta is approximately the + + align:start position:0% +times Delta is approximately the + + + align:start position:0% +times Delta is approximately the +probability that our random variable + + align:start position:0% +probability that our random variable + + + align:start position:0% +probability that our random variable +falls within a delta interval from this + + align:start position:0% +falls within a delta interval from this + + + align:start position:0% +falls within a delta interval from this +number little Y that we are considering + + align:start position:0% +number little Y that we are considering + + + align:start position:0% +number little Y that we are considering +so here x 0 here's time Y and here's + + align:start position:0% +so here x 0 here's time Y and here's + + + align:start position:0% +so here x 0 here's time Y and here's +time y plus Delta we want to find or to + + align:start position:0% +time y plus Delta we want to find or to + + + align:start position:0% +time y plus Delta we want to find or to +say something about the probability of + + align:start position:0% +say something about the probability of + + + align:start position:0% +say something about the probability of +falling inside this small interval now + + align:start position:0% +falling inside this small interval now + + + align:start position:0% +falling inside this small interval now +what does it mean + + align:start position:0% +what does it mean + + + align:start position:0% +what does it mean +for the case arrival to fall inside this + + align:start position:0% +for the case arrival to fall inside this + + + align:start position:0% +for the case arrival to fall inside this +interval this is an event that can + + align:start position:0% +interval this is an event that can + + + align:start position:0% +interval this is an event that can +happen as follows the case arrival Falls + + align:start position:0% +happen as follows the case arrival Falls + + + align:start position:0% +happen as follows the case arrival Falls +in this interval and we have K minus 1 + + align:start position:0% +in this interval and we have K minus 1 + + + align:start position:0% +in this interval and we have K minus 1 +arrivals during the previous interval + + align:start position:0% +arrivals during the previous interval + + + align:start position:0% +arrivals during the previous interval +what is the probability of this event a + + align:start position:0% +what is the probability of this event a + + + align:start position:0% +what is the probability of this event a +basic assumption about the Poisson + + align:start position:0% +basic assumption about the Poisson + + + align:start position:0% +basic assumption about the Poisson +process is the independence assumption + + align:start position:0% +process is the independence assumption + + + align:start position:0% +process is the independence assumption +therefore having K minus 1 arrivals in + + align:start position:0% +therefore having K minus 1 arrivals in + + + align:start position:0% +therefore having K minus 1 arrivals in +this interval and having one arrival in + + align:start position:0% +this interval and having one arrival in + + + align:start position:0% +this interval and having one arrival in +this interval are independent events + + align:start position:0% +this interval are independent events + + + align:start position:0% +this interval are independent events +therefore the probability of this + + align:start position:0% +therefore the probability of this + + + align:start position:0% +therefore the probability of this +scenario is the product of the + + align:start position:0% +scenario is the product of the + + + align:start position:0% +scenario is the product of the +probabilities that + + align:start position:0% +probabilities that + + + align:start position:0% +probabilities that +had K minus 1 arrivals in an interval of + + align:start position:0% +had K minus 1 arrivals in an interval of + + + align:start position:0% +had K minus 1 arrivals in an interval of +length y times the probability that + + align:start position:0% +length y times the probability that + + + align:start position:0% +length y times the probability that +we've had one arrival in an interval of + + align:start position:0% +we've had one arrival in an interval of + + + align:start position:0% +we've had one arrival in an interval of +length Delta and that latter probability + + align:start position:0% +length Delta and that latter probability + + + align:start position:0% +length Delta and that latter probability +is approximately equal to lambda times + + align:start position:0% +is approximately equal to lambda times + + + align:start position:0% +is approximately equal to lambda times +Delta so I should write here an + + align:start position:0% +Delta so I should write here an + + + align:start position:0% +Delta so I should write here an +approximate equality instead of an exact + + align:start position:0% +approximate equality instead of an exact + + + align:start position:0% +approximate equality instead of an exact +equality to indicate that there are + + align:start position:0% +equality to indicate that there are + + + align:start position:0% +equality to indicate that there are +other terms order of Delta square for + + align:start position:0% +other terms order of Delta square for + + + align:start position:0% +other terms order of Delta square for +example but which are much smaller + + align:start position:0% +example but which are much smaller + + + align:start position:0% +example but which are much smaller +compared to Delta however this is not + + align:start position:0% +compared to Delta however this is not + + + align:start position:0% +compared to Delta however this is not +the only way that we can get the case + + align:start position:0% +the only way that we can get the case + + + align:start position:0% +the only way that we can get the case +arrival in this interval there's an + + align:start position:0% +arrival in this interval there's an + + + align:start position:0% +arrival in this interval there's an +alternative scenario we might have had K + + align:start position:0% +alternative scenario we might have had K + + + align:start position:0% +alternative scenario we might have had K +minus 2 arrivals during this interval + + align:start position:0% +minus 2 arrivals during this interval + + + align:start position:0% +minus 2 arrivals during this interval +and then two arrivals during that little + + align:start position:0% +and then two arrivals during that little + + + align:start position:0% +and then two arrivals during that little +interval in this case the K arrival + + align:start position:0% +interval in this case the K arrival + + + align:start position:0% +interval in this case the K arrival +again occurs within that little interval + + align:start position:0% +again occurs within that little interval + + + align:start position:0% +again occurs within that little interval +so we need to also calculate the + + align:start position:0% +so we need to also calculate the + + + align:start position:0% +so we need to also calculate the +probability of this scenario the + + align:start position:0% +probability of this scenario the + + + align:start position:0% +probability of this scenario the +probability of that scenario is the + + align:start position:0% +probability of that scenario is the + + + align:start position:0% +probability of that scenario is the +probability of K minus 2 arrivals in an + + align:start position:0% +probability of K minus 2 arrivals in an + + + align:start position:0% +probability of K minus 2 arrivals in an +interval of length y times the + + align:start position:0% +interval of length y times the + + + align:start position:0% +interval of length y times the +probability of two arrivals but the + + align:start position:0% +probability of two arrivals but the + + + align:start position:0% +probability of two arrivals but the +probability of two arrivals is something + + align:start position:0% +probability of two arrivals is something + + + align:start position:0% +probability of two arrivals is something +that's order of Delta squared and order + + align:start position:0% +that's order of Delta squared and order + + + align:start position:0% +that's order of Delta squared and order +of Delta squared is much smaller than + + align:start position:0% +of Delta squared is much smaller than + + + align:start position:0% +of Delta squared is much smaller than +this term which is linear in Delta and + + align:start position:0% +this term which is linear in Delta and + + + align:start position:0% +this term which is linear in Delta and +so this term can be ignored as long as + + align:start position:0% +so this term can be ignored as long as + + + align:start position:0% +so this term can be ignored as long as +we're just keeping track of the dominant + + align:start position:0% +we're just keeping track of the dominant + + + align:start position:0% +we're just keeping track of the dominant +terms those that are linear in Delta and + + align:start position:0% +terms those that are linear in Delta and + + + align:start position:0% +terms those that are linear in Delta and +then they would be similar expressions + + align:start position:0% +then they would be similar expressions + + + align:start position:0% +then they would be similar expressions +for example the scenario that we have + + align:start position:0% +for example the scenario that we have + + + align:start position:0% +for example the scenario that we have +three arrivals up to time Y and then + + align:start position:0% +three arrivals up to time Y and then + + + align:start position:0% +three arrivals up to time Y and then +three more arrivals during that little + + align:start position:0% +three more arrivals during that little + + + align:start position:0% +three more arrivals during that little +interval which is again an event of + + align:start position:0% +interval which is again an event of + + + align:start position:0% +interval which is again an event of +probability order of Delta square that + + align:start position:0% +probability order of Delta square that + + + align:start position:0% +probability order of Delta square that +we get three arrivals there and all of + + align:start position:0% +we get three arrivals there and all of + + + align:start position:0% +we get three arrivals there and all of +those terms are insignificant and we can + + align:start position:0% +those terms are insignificant and we can + + + align:start position:0% +those terms are insignificant and we can +ignore them and we end up with an + + align:start position:0% +ignore them and we end up with an + + + align:start position:0% +ignore them and we end up with an +approximate equality between this term + + align:start position:0% +approximate equality between this term + + + align:start position:0% +approximate equality between this term +and this expression here Delta shows up + + align:start position:0% +and this expression here Delta shows up + + + align:start position:0% +and this expression here Delta shows up +on both sides so we can cancel Delta and + + align:start position:0% +on both sides so we can cancel Delta and + + + align:start position:0% +on both sides so we can cancel Delta and +therefore we have ended up with a + + align:start position:0% +therefore we have ended up with a + + + align:start position:0% +therefore we have ended up with a +formula for the PDF in particular the + + align:start position:0% +formula for the PDF in particular the + + + align:start position:0% +formula for the PDF in particular the +PDF is equal to this probability times + + align:start position:0% +PDF is equal to this probability times + + + align:start position:0% +PDF is equal to this probability times +lambda + + align:start position:0% +lambda + + + align:start position:0% +lambda +what is this probably + + align:start position:0% +what is this probably + + + align:start position:0% +what is this probably +we have a formula for it but we just + + align:start position:0% +we have a formula for it but we just + + + align:start position:0% +we have a formula for it but we just +need to substitute put K minus 1 in the + + align:start position:0% +need to substitute put K minus 1 in the + + + align:start position:0% +need to substitute put K minus 1 in the +place of K and put a Y in the place of + + align:start position:0% +place of K and put a Y in the place of + + + align:start position:0% +place of K and put a Y in the place of +tau this gives us lambda Y to the power + + align:start position:0% +tau this gives us lambda Y to the power + + + align:start position:0% +tau this gives us lambda Y to the power +K minus 1 e to the minus lambda Y + + align:start position:0% +K minus 1 e to the minus lambda Y + + + align:start position:0% +K minus 1 e to the minus lambda Y +divided by K minus 1 factorial and then + + align:start position:0% +divided by K minus 1 factorial and then + + + align:start position:0% +divided by K minus 1 factorial and then +we have the extra factor of lambda which + + align:start position:0% +we have the extra factor of lambda which + + + align:start position:0% +we have the extra factor of lambda which +can be put together with this lambda to + + align:start position:0% +can be put together with this lambda to + + + align:start position:0% +can be put together with this lambda to +the K minus 1 here and we end up with + + align:start position:0% +the K minus 1 here and we end up with + + + align:start position:0% +the K minus 1 here and we end up with +this final formula for the PDF of YK the + + align:start position:0% +this final formula for the PDF of YK the + + + align:start position:0% +this final formula for the PDF of YK the +distribution that we have here is called + + align:start position:0% +distribution that we have here is called + + + align:start position:0% +distribution that we have here is called +an Erlang distribution but actually it's + + align:start position:0% +an Erlang distribution but actually it's + + + align:start position:0% +an Erlang distribution but actually it's +not just one distribution we have + + align:start position:0% +not just one distribution we have + + + align:start position:0% +not just one distribution we have +different distributions depending on + + align:start position:0% +different distributions depending on + + + align:start position:0% +different distributions depending on +what K were considering the distribution + + align:start position:0% +what K were considering the distribution + + + align:start position:0% +what K were considering the distribution +of the time of the third arrival is + + align:start position:0% +of the time of the third arrival is + + + align:start position:0% +of the time of the third arrival is +different from the distribution of the + + align:start position:0% +different from the distribution of the + + + align:start position:0% +different from the distribution of the +tenth arrival so if we fix a particular + + align:start position:0% +tenth arrival so if we fix a particular + + + align:start position:0% +tenth arrival so if we fix a particular +k then we say that we have an earlier + + align:start position:0% +k then we say that we have an earlier + + + align:start position:0% +k then we say that we have an earlier +distribution of order k for the case + + align:start position:0% +distribution of order k for the case + + + align:start position:0% +distribution of order k for the case +where k is equal to 1 this term here + + align:start position:0% +where k is equal to 1 this term here + + + align:start position:0% +where k is equal to 1 this term here +disappears k minus 1 is equal to 0 and + + align:start position:0% +disappears k minus 1 is equal to 0 and + + + align:start position:0% +disappears k minus 1 is equal to 0 and +the denominator term disappears and we + + align:start position:0% +the denominator term disappears and we + + + align:start position:0% +the denominator term disappears and we +end up with lambda times e to the minus + + align:start position:0% +end up with lambda times e to the minus + + + align:start position:0% +end up with lambda times e to the minus +lambda Y but this is the exponential + + align:start position:0% +lambda Y but this is the exponential + + + align:start position:0% +lambda Y but this is the exponential +distribution that we had already derived + + align:start position:0% +distribution that we had already derived + + + align:start position:0% +distribution that we had already derived +with a different method earlier as you + + align:start position:0% +with a different method earlier as you + + + align:start position:0% +with a different method earlier as you +increase K of course you get different + + align:start position:0% +increase K of course you get different + + + align:start position:0% +increase K of course you get different +distributions and these tend to shift + + align:start position:0% +distributions and these tend to shift + + + align:start position:0% +distributions and these tend to shift +towards the right this makes sense the + + align:start position:0% +towards the right this makes sense the + + + align:start position:0% +towards the right this makes sense the +time of the second arrival is likely to + + align:start position:0% +time of the second arrival is likely to + + + align:start position:0% +time of the second arrival is likely to +take certain values the time of the + + align:start position:0% +take certain values the time of the + + + align:start position:0% +take certain values the time of the +third arrival is likely to take values + + align:start position:0% +third arrival is likely to take values + + + align:start position:0% +third arrival is likely to take values +that are higher and the more you + + align:start position:0% +that are higher and the more you + + + align:start position:0% +that are higher and the more you +increase K the more the distribution + + align:start position:0% +increase K the more the distribution + + + align:start position:0% +increase K the more the distribution +will be shifting towards the right \ No newline at end of file diff --git a/6wUD_gp5WeE.txt b/6wUD_gp5WeE.txt new file mode 100644 index 0000000000000000000000000000000000000000..097687864cd632bc081c0ab734b427e0db5dfc3c --- /dev/null +++ b/6wUD_gp5WeE.txt @@ -0,0 +1,7922 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer high quality educational + + align:start position:0% +to offer high quality educational + + + align:start position:0% +to offer high quality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right um today we're + + align:start position:0% +ocw.mit.edu all right um today we're + + + align:start position:0% +ocw.mit.edu all right um today we're +we're starting a a new topic but is of + + align:start position:0% +we're starting a a new topic but is of + + + align:start position:0% +we're starting a a new topic but is of +course related to previous + + align:start position:0% +course related to previous + + + align:start position:0% +course related to previous +topics + + align:start position:0% +topics + + + align:start position:0% +topics +um as usual if you go to the either the + + align:start position:0% +um as usual if you go to the either the + + + align:start position:0% +um as usual if you go to the either the +602 or the 600 website you'll find both + + align:start position:0% +602 or the 600 website you'll find both + + + align:start position:0% +602 or the 600 website you'll find both +today's PowerPoint and today's python uh + + align:start position:0% +today's PowerPoint and today's python uh + + + align:start position:0% +today's PowerPoint and today's python uh +you'll discover if you look at the + + align:start position:0% +you'll discover if you look at the + + + align:start position:0% +you'll discover if you look at the +python file that there's quite a lot of + + align:start position:0% +python file that there's quite a lot of + + + align:start position:0% +python file that there's quite a lot of +code in there and I'll be talking only + + align:start position:0% +code in there and I'll be talking only + + + align:start position:0% +code in there and I'll be talking only +about some of it but it's probably all + + align:start position:0% +about some of it but it's probably all + + + align:start position:0% +about some of it but it's probably all +worth looking at and uh a fair amount of + + align:start position:0% +worth looking at and uh a fair amount of + + + align:start position:0% +worth looking at and uh a fair amount of +reading associated with uh this + + align:start position:0% +reading associated with uh this + + + align:start position:0% +reading associated with uh this +week all right why are we looking at + + align:start position:0% +week all right why are we looking at + + + align:start position:0% +week all right why are we looking at +random walks see a picture here of uh + + align:start position:0% +random walks see a picture here of uh + + + align:start position:0% +random walks see a picture here of uh +think of them as molecules just bouncing + + align:start position:0% +think of them as molecules just bouncing + + + align:start position:0% +think of them as molecules just bouncing +around uh this actually a picture of + + align:start position:0% +around uh this actually a picture of + + + align:start position:0% +around uh this actually a picture of +what's called brownie in motion though + + align:start position:0% +what's called brownie in motion though + + + align:start position:0% +what's called brownie in motion though +Robert Brown probably did not Discover + + align:start position:0% +Robert Brown probably did not Discover + + + align:start position:0% +Robert Brown probably did not Discover +it um we're looking at random walks + + align:start position:0% +it um we're looking at random walks + + + align:start position:0% +it um we're looking at random walks +because well first of all they're + + align:start position:0% +because well first of all they're + + + align:start position:0% +because well first of all they're +important uh in many domains there are + + align:start position:0% +important uh in many domains there are + + + align:start position:0% +important uh in many domains there are +people who will argue for example that + + align:start position:0% +people who will argue for example that + + + align:start position:0% +people who will argue for example that +the movement of prices in the stock + + align:start position:0% +the movement of prices in the stock + + + align:start position:0% +the movement of prices in the stock +market is best modeled as a random walk + + align:start position:0% +market is best modeled as a random walk + + + align:start position:0% +market is best modeled as a random walk +uh there was a very popular book called + + align:start position:0% +uh there was a very popular book called + + + align:start position:0% +uh there was a very popular book called +a random walk down Wall Street that made + + align:start position:0% +a random walk down Wall Street that made + + + align:start position:0% +a random walk down Wall Street that made +this argument uh and a lot of modern + + align:start position:0% +this argument uh and a lot of modern + + + align:start position:0% +this argument uh and a lot of modern +portfolio analysis is based upon + + align:start position:0% +portfolio analysis is based upon + + + align:start position:0% +portfolio analysis is based upon +that um those of you who are not + + align:start position:0% +that um those of you who are not + + + align:start position:0% +that um those of you who are not +interested in making money and I presume + + align:start position:0% +interested in making money and I presume + + + align:start position:0% +interested in making money and I presume +that's most of you + + align:start position:0% +that's most of you + + + align:start position:0% +that's most of you +um it's also very important in many + + align:start position:0% +um it's also very important in many + + + align:start position:0% +um it's also very important in many +physical processes we use random walk + + align:start position:0% +physical processes we use random walk + + + align:start position:0% +physical processes we use random walk +say to model diffusion heat diffusion or + + align:start position:0% +say to model diffusion heat diffusion or + + + align:start position:0% +say to model diffusion heat diffusion or +the diffusion of + + align:start position:0% +the diffusion of + + + align:start position:0% +the diffusion of +molecules uh in suspension Etc so + + align:start position:0% +molecules uh in suspension Etc so + + + align:start position:0% +molecules uh in suspension Etc so +they're very important in a lot of + + align:start position:0% +they're very important in a lot of + + + align:start position:0% +they're very important in a lot of +scientific and indeed social + + align:start position:0% +scientific and indeed social + + + align:start position:0% +scientific and indeed social +disciplines that's they're not the only + + align:start position:0% +disciplines that's they're not the only + + + align:start position:0% +disciplines that's they're not the only +important thing so why are we looking at + + align:start position:0% +important thing so why are we looking at + + + align:start position:0% +important thing so why are we looking at +those uh because I think it provides a + + align:start position:0% +those uh because I think it provides a + + + align:start position:0% +those uh because I think it provides a +really good illustration of how we can + + align:start position:0% +really good illustration of how we can + + + align:start position:0% +really good illustration of how we can +use simulation to understand the world + + align:start position:0% +use simulation to understand the world + + + align:start position:0% +use simulation to understand the world +around + + align:start position:0% +around + + + align:start position:0% +around +us and it does give me an excuse to + + align:start position:0% +us and it does give me an excuse to + + + align:start position:0% +us and it does give me an excuse to +cover some important topics related to + + align:start position:0% +cover some important topics related to + + + align:start position:0% +cover some important topics related to +programming you'll remember that one of + + align:start position:0% +programming you'll remember that one of + + + align:start position:0% +programming you'll remember that one of +the subtexts of the course is while I'm + + align:start position:0% +the subtexts of the course is while I'm + + + align:start position:0% +the subtexts of the course is while I'm +covering a lot of what you might think + + align:start position:0% +covering a lot of what you might think + + + align:start position:0% +covering a lot of what you might think +of as abstract + + align:start position:0% +of as abstract + + + align:start position:0% +of as abstract +material we're using it as an excuse to + + align:start position:0% +material we're using it as an excuse to + + + align:start position:0% +material we're using it as an excuse to +teach more about programming and + + align:start position:0% +teach more about programming and + + + align:start position:0% +teach more about programming and +software engineering a little practice + + align:start position:0% +software engineering a little practice + + + align:start position:0% +software engineering a little practice +with classes and subclassing and we're + + align:start position:0% +with classes and subclassing and we're + + + align:start position:0% +with classes and subclassing and we're +going to also look at producing + + align:start position:0% +going to also look at producing + + + align:start position:0% +going to also look at producing +plots all right so the first random walk + + align:start position:0% +plots all right so the first random walk + + + align:start position:0% +plots all right so the first random walk +I want to look at is actually not a + + align:start position:0% +I want to look at is actually not a + + + align:start position:0% +I want to look at is actually not a +diffusion process of the stock market + + align:start position:0% +diffusion process of the stock market + + + align:start position:0% +diffusion process of the stock market +but an actual walk so imagine that + + align:start position:0% +but an actual walk so imagine that + + + align:start position:0% +but an actual walk so imagine that +you've got a field which is somehow + + align:start position:0% +you've got a field which is somehow + + + align:start position:0% +you've got a field which is somehow +inexplicably been moaned to look like a + + align:start position:0% +inexplicably been moaned to look like a + + + align:start position:0% +inexplicably been moaned to look like a +piece of graph paper and you've got a + + align:start position:0% +piece of graph paper and you've got a + + + align:start position:0% +piece of graph paper and you've got a +drunk sort of wandering around the field + + align:start position:0% +drunk sort of wandering around the field + + + align:start position:0% +drunk sort of wandering around the field +taking the step every once in a while in + + align:start position:0% +taking the step every once in a while in + + + align:start position:0% +taking the step every once in a while in +some random + + align:start position:0% +some random + + + align:start position:0% +some random +direction we can then ask the question + + align:start position:0% +direction we can then ask the question + + + align:start position:0% +direction we can then ask the question +is there an interesting relationship + + align:start position:0% +is there an interesting relationship + + + align:start position:0% +is there an interesting relationship +between the number of steps the drum + + align:start position:0% +between the number of steps the drum + + + align:start position:0% +between the number of steps the drum +takes and how far the drunk is from the + + align:start position:0% +takes and how far the drunk is from the + + + align:start position:0% +takes and how far the drunk is from the +origin at the end of those + + align:start position:0% +origin at the end of those + + + align:start position:0% +origin at the end of those +steps you could imagine that if the + + align:start position:0% +steps you could imagine that if the + + + align:start position:0% +steps you could imagine that if the +drunk takes more steps he's ever further + + align:start position:0% +drunk takes more steps he's ever further + + + align:start position:0% +drunk takes more steps he's ever further +from the origin or maybe you could + + align:start position:0% +from the origin or maybe you could + + + align:start position:0% +from the origin or maybe you could +imagine since it's random that he just + + align:start position:0% +imagine since it's random that he just + + + align:start position:0% +imagine since it's random that he just +wanders away and he wanders back and all + + align:start position:0% +wanders away and he wanders back and all + + + align:start position:0% +wanders away and he wanders back and all +directions and more or less never gets + + align:start position:0% +directions and more or less never gets + + + align:start position:0% +directions and more or less never gets +very far so just out of curiosity I'll + + align:start position:0% +very far so just out of curiosity I'll + + + align:start position:0% +very far so just out of curiosity I'll +take a poll who thinks that the drunk + + align:start position:0% +take a poll who thinks that the drunk + + + align:start position:0% +take a poll who thinks that the drunk +doesn't doesn't much matter how many + + align:start position:0% +doesn't doesn't much matter how many + + + align:start position:0% +doesn't doesn't much matter how many +steps he takes he'll be more or less the + + align:start position:0% +steps he takes he'll be more or less the + + + align:start position:0% +steps he takes he'll be more or less the +same distance + + align:start position:0% +same distance + + + align:start position:0% +same distance +away and who thinks the more steps he + + align:start position:0% +away and who thinks the more steps he + + + align:start position:0% +away and who thinks the more steps he +takes the further away he's likely to be + + align:start position:0% +takes the further away he's likely to be + + + align:start position:0% +takes the further away he's likely to be +all right it seems to be a season where + + align:start position:0% +all right it seems to be a season where + + + align:start position:0% +all right it seems to be a season where +when you take polls they come out almost + + align:start position:0% +when you take polls they come out almost + + + align:start position:0% +when you take polls they come out almost +tied all right so let + + align:start position:0% +tied all right so let + + + align:start position:0% +tied all right so let +let let's look at a small example + + align:start position:0% +let let's look at a small example + + + align:start position:0% +let let's look at a small example +suppose he takes one step only well if + + align:start position:0% +suppose he takes one step only well if + + + align:start position:0% +suppose he takes one step only well if +he takes one step he could and we assume + + align:start position:0% +he takes one step he could and we assume + + + align:start position:0% +he takes one step he could and we assume +for Simplicity that he's not so drunk + + align:start position:0% +for Simplicity that he's not so drunk + + + align:start position:0% +for Simplicity that he's not so drunk +that he moves at random either moves + + align:start position:0% +that he moves at random either moves + + + align:start position:0% +that he moves at random either moves +north or south east or + + align:start position:0% +north or south east or + + + align:start position:0% +north or south east or +west these are all the places he can get + + align:start position:0% +west these are all the places he can get + + + align:start position:0% +west these are all the places he can get +to in one step what they have in common + + align:start position:0% +to in one step what they have in common + + + align:start position:0% +to in one step what they have in common +is that after one step the drunk is + + align:start position:0% +is that after one step the drunk is + + + align:start position:0% +is that after one step the drunk is +always exactly one unit away from the + + align:start position:0% +always exactly one unit away from the + + + align:start position:0% +always exactly one unit away from the +origin well how about after two steps so + + align:start position:0% +origin well how about after two steps so + + + align:start position:0% +origin well how about after two steps so +without loss of generality let's assume + + align:start position:0% +without loss of generality let's assume + + + align:start position:0% +without loss of generality let's assume +that the first step let me use the pen + + align:start position:0% +that the first step let me use the pen + + + align:start position:0% +that the first step let me use the pen +that you're supposed to use to write on + + align:start position:0% +that you're supposed to use to write on + + + align:start position:0% +that you're supposed to use to write on +this rather than than this pen which + + align:start position:0% +this rather than than this pen which + + + align:start position:0% +this rather than than this pen which +would make a real mess on my + + align:start position:0% + + + + align:start position:0% + +screen um what did I do with it all + + align:start position:0% +screen um what did I do with it all + + + align:start position:0% +screen um what did I do with it all +right well I won't write on it so + + align:start position:0% +right well I won't write on it so + + + align:start position:0% +right well I won't write on it so +without loss of generality we'll assume + + align:start position:0% +without loss of generality we'll assume + + + align:start position:0% +without loss of generality we'll assume +that the drunk + + align:start position:0% +that the drunk + + + align:start position:0% +that the drunk +is there after one step took one step to + + align:start position:0% +is there after one step took one step to + + + align:start position:0% +is there after one step took one step to +the east well after two steps those are + + align:start position:0% +the east well after two steps those are + + + align:start position:0% +the east well after two steps those are +all the possible places he could be so + + align:start position:0% +all the possible places he could be so + + + align:start position:0% +all the possible places he could be so +on average how far is the drunk from the + + align:start position:0% +on average how far is the drunk from the + + + align:start position:0% +on average how far is the drunk from the +origin + + align:start position:0% +origin + + + align:start position:0% +origin +well if we look he could either be uh + + align:start position:0% +well if we look he could either be uh + + + align:start position:0% +well if we look he could either be uh +two steps away if he took another step + + align:start position:0% +two steps away if he took another step + + + align:start position:0% +two steps away if he took another step +East zero steps away if he took a step + + align:start position:0% +East zero steps away if he took a step + + + align:start position:0% +East zero steps away if he took a step +West or what do we see for the top two + + align:start position:0% +West or what do we see for the top two + + + align:start position:0% +West or what do we see for the top two +well the top and the bottom one we can + + align:start position:0% +well the top and the bottom one we can + + + align:start position:0% +well the top and the bottom one we can +go back and use the Pythagorean + + align:start position:0% +go back and use the Pythagorean + + + align:start position:0% +go back and use the Pythagorean +theorem + + align:start position:0% + + + + align:start position:0% + +um c^2 = a a 2 + b^ + + align:start position:0% + + + + align:start position:0% + +2 and that will tell us that it'll be + + align:start position:0% +2 and that will tell us that it'll be + + + align:start position:0% +2 and that will tell us that it'll be +the square root of a S Plus + + align:start position:0% +the square root of a S Plus + + + align:start position:0% +the square root of a S Plus +b^2 + + align:start position:0% +b^2 + + + align:start position:0% +b^2 +and that will tell us how far away the + + align:start position:0% +and that will tell us how far away the + + + align:start position:0% +and that will tell us how far away the +upper two are and then we can just + + align:start position:0% +upper two are and then we can just + + + align:start position:0% +upper two are and then we can just +average them and get a distance and as + + align:start position:0% +average them and get a distance and as + + + align:start position:0% +average them and get a distance and as +we can + + align:start position:0% +we can + + + align:start position:0% +we can +see on average the drunk will be a + + align:start position:0% +see on average the drunk will be a + + + align:start position:0% +see on average the drunk will be a +little bit further away after two steps + + align:start position:0% +little bit further away after two steps + + + align:start position:0% +little bit further away after two steps +than after one + + align:start position:0% +than after one + + + align:start position:0% +than after one +step well how about after after 100,000 + + align:start position:0% +step well how about after after 100,000 + + + align:start position:0% +step well how about after after 100,000 +steps it would be a little bit tedious + + align:start position:0% +steps it would be a little bit tedious + + + align:start position:0% +steps it would be a little bit tedious +to go through the case analysis I just + + align:start position:0% +to go through the case analysis I just + + + align:start position:0% +to go through the case analysis I just +did right there are a lot of cases after + + align:start position:0% +did right there are a lot of cases after + + + align:start position:0% +did right there are a lot of cases after +100,000 steps so we end up resorting to + + align:start position:0% +100,000 steps so we end up resorting to + + + align:start position:0% +100,000 steps so we end up resorting to +a + + align:start position:0% + + + + align:start position:0% + +simulation so we'll structure it exactly + + align:start position:0% +simulation so we'll structure it exactly + + + align:start position:0% +simulation so we'll structure it exactly +the same way we've been structuring our + + align:start position:0% +the same way we've been structuring our + + + align:start position:0% +the same way we've been structuring our +other + + align:start position:0% +other + + + align:start position:0% +other +simulations we're going to simulate one + + align:start position:0% +simulations we're going to simulate one + + + align:start position:0% +simulations we're going to simulate one +walk of K steps end such walks and then + + align:start position:0% +walk of K steps end such walks and then + + + align:start position:0% +walk of K steps end such walks and then +report the average distance from the + + align:start position:0% +report the average distance from the + + + align:start position:0% +report the average distance from the +origin of the N + + align:start position:0% + + + + align:start position:0% + +walks before we do that in line with the + + align:start position:0% +walks before we do that in line with the + + + align:start position:0% +walks before we do that in line with the +software engineering theme of the course + + align:start position:0% +software engineering theme of the course + + + align:start position:0% +software engineering theme of the course +we'll start by defining some useful + + align:start position:0% +we'll start by defining some useful + + + align:start position:0% +we'll start by defining some useful +abstractions the three of them I want to + + align:start position:0% +abstractions the three of them I want to + + + align:start position:0% +abstractions the three of them I want to +look at + + align:start position:0% +look at + + + align:start position:0% +look at +location the field that the drunk is in + + align:start position:0% +location the field that the drunk is in + + + align:start position:0% +location the field that the drunk is in +and the drunk him or + + align:start position:0% +and the drunk him or + + + align:start position:0% +and the drunk him or +herself all right so let's first look at + + align:start position:0% +herself all right so let's first look at + + + align:start position:0% +herself all right so let's first look at +location this is going to be an + + align:start position:0% +location this is going to be an + + + align:start position:0% +location this is going to be an +immutable type + + align:start position:0% +immutable type + + + align:start position:0% +immutable type +so what we see here as long as I can't + + align:start position:0% +so what we see here as long as I can't + + + align:start position:0% +so what we see here as long as I can't +point on the screen I'll point with a + + align:start position:0% +point on the screen I'll point with a + + + align:start position:0% +point on the screen I'll point with a +pointer is that we'll initiate it we'll + + align:start position:0% +pointer is that we'll initiate it we'll + + + align:start position:0% +pointer is that we'll initiate it we'll +initialize it to with an X and Y value + + align:start position:0% +initialize it to with an X and Y value + + + align:start position:0% +initialize it to with an X and Y value +that makes sense we'll be able to have + + align:start position:0% +that makes sense we'll be able to have + + + align:start position:0% +that makes sense we'll be able to have +two Getters get X and get + + align:start position:0% +two Getters get X and get + + + align:start position:0% +two Getters get X and get +Y and here's how we see it's immutable + + align:start position:0% +Y and here's how we see it's immutable + + + align:start position:0% +Y and here's how we see it's immutable +what move is doing is it's not changing + + align:start position:0% +what move is doing is it's not changing + + + align:start position:0% +what move is doing is it's not changing +the location it's returning a new + + align:start position:0% +the location it's returning a new + + + align:start position:0% +the location it's returning a new +location perhaps move is poor choice of + + align:start position:0% +location perhaps move is poor choice of + + + align:start position:0% +location perhaps move is poor choice of +name for that but that is what it's + + align:start position:0% +name for that but that is what it's + + + align:start position:0% +name for that but that is what it's +doing it's just returning a new location + + align:start position:0% +doing it's just returning a new location + + + align:start position:0% +doing it's just returning a new location +where it adds the change in X and the + + align:start position:0% +where it adds the change in X and the + + + align:start position:0% +where it adds the change in X and the +change in y to get two new XY + + align:start position:0% +change in y to get two new XY + + + align:start position:0% +change in y to get two new XY +values notice by the way that I'm not + + align:start position:0% +values notice by the way that I'm not + + + align:start position:0% +values notice by the way that I'm not +restricting these to be integers or one + + align:start position:0% +restricting these to be integers or one + + + align:start position:0% +restricting these to be integers or one +or anything like that so this would work + + align:start position:0% +or anything like that so this would work + + + align:start position:0% +or anything like that so this would work +even if I did not want to take those + + align:start position:0% +even if I did not want to take those + + + align:start position:0% +even if I did not want to take those +nice little east west north south + + align:start position:0% + + + + align:start position:0% + +steps I've got a under bar underbar + + align:start position:0% +steps I've got a under bar underbar + + + align:start position:0% +steps I've got a under bar underbar +string Str Str and then here's my + + align:start position:0% +string Str Str and then here's my + + + align:start position:0% +string Str Str and then here's my +implementation you can see it's very + + align:start position:0% +implementation you can see it's very + + + align:start position:0% +implementation you can see it's very +sophisticated of the Pythagorean + + align:start position:0% + + + + align:start position:0% + +theorem so I just do it that way and + + align:start position:0% +theorem so I just do it that way and + + + align:start position:0% +theorem so I just do it that way and +that will get me the distance between + + align:start position:0% +that will get me the distance between + + + align:start position:0% +that will get me the distance between +two things it's one of the annoying + + align:start position:0% +two things it's one of the annoying + + + align:start position:0% +two things it's one of the annoying +things about classes in actually all + + align:start position:0% +things about classes in actually all + + + align:start position:0% +things about classes in actually all +languages I know with classes is you + + align:start position:0% +languages I know with classes is you + + + align:start position:0% +languages I know with classes is you +would like to think that self and other + + align:start position:0% +would like to think that self and other + + + align:start position:0% +would like to think that self and other +there's a symmetry here + + align:start position:0% +there's a symmetry here + + + align:start position:0% +there's a symmetry here +the distance from self to other is the + + align:start position:0% +the distance from self to other is the + + + align:start position:0% +the distance from self to other is the +same as from other to self but + + align:start position:0% +same as from other to self but + + + align:start position:0% +same as from other to self but +syntactically because of the way the + + align:start position:0% +syntactically because of the way the + + + align:start position:0% +syntactically because of the way the +language is structured we treat them a + + align:start position:0% +language is structured we treat them a + + + align:start position:0% +language is structured we treat them a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +differently all + + align:start position:0% +differently all + + + align:start position:0% +differently all +right how about class + + align:start position:0% +right how about class + + + align:start position:0% +right how about class +drunk well this is kind of + + align:start position:0% +drunk well this is kind of + + + align:start position:0% +drunk well this is kind of +boring drunk has a name and a + + align:start position:0% +boring drunk has a name and a + + + align:start position:0% +boring drunk has a name and a +string uh and that's + + align:start position:0% +string uh and that's + + + align:start position:0% +string uh and that's +all + + align:start position:0% +all + + + align:start position:0% +all +well the point of this and I don't think + + align:start position:0% +well the point of this and I don't think + + + align:start position:0% +well the point of this and I don't think +we've looked at this before is this is + + align:start position:0% +we've looked at this before is this is + + + align:start position:0% +we've looked at this before is this is +not intended to be a useful class on its + + align:start position:0% +not intended to be a useful class on its + + + align:start position:0% +not intended to be a useful class on its +own it's what we call a base + + align:start position:0% +own it's what we call a base + + + align:start position:0% +own it's what we call a base +class the notion here is its only + + align:start position:0% +class the notion here is its only + + + align:start position:0% +class the notion here is its only +purposes to be + + align:start position:0% +purposes to be + + + align:start position:0% +purposes to be +inherited okay it's not supposed to be + + align:start position:0% +inherited okay it's not supposed to be + + + align:start position:0% +inherited okay it's not supposed to be +useful on itself but it does give me + + align:start position:0% +useful on itself but it does give me + + + align:start position:0% +useful on itself but it does give me +something that will be used for the two + + align:start position:0% +something that will be used for the two + + + align:start position:0% +something that will be used for the two +super class or + + align:start position:0% +super class or + + + align:start position:0% +super class or +subclasses and we'll look at two + + align:start position:0% +subclasses and we'll look at two + + + align:start position:0% +subclasses and we'll look at two +subclasses the so-called usual drunk the + + align:start position:0% +subclasses the so-called usual drunk the + + + align:start position:0% +subclasses the so-called usual drunk the +one I tried to simulate when I was + + align:start position:0% +one I tried to simulate when I was + + + align:start position:0% +one I tried to simulate when I was +wandering around who wanders around at + + align:start position:0% +wandering around who wanders around at + + + align:start position:0% +wandering around who wanders around at +random and a drunk I like to think of as + + align:start position:0% +random and a drunk I like to think of as + + + align:start position:0% +random and a drunk I like to think of as +a New Englander or a masochistic drunk + + align:start position:0% +a New Englander or a masochistic drunk + + + align:start position:0% +a New Englander or a masochistic drunk +who uh tries forever to move ever + + align:start position:0% +who uh tries forever to move ever + + + align:start position:0% +who uh tries forever to move ever +northward because he or she wants to be + + align:start position:0% +northward because he or she wants to be + + + align:start position:0% +northward because he or she wants to be +Frozen um I do like this picture of + + align:start position:0% +Frozen um I do like this picture of + + + align:start position:0% +Frozen um I do like this picture of +entering the state of Maine in the + + align:start position:0% +entering the state of Maine in the + + + align:start position:0% +entering the state of Maine in the +winter all right so here's the usual + + align:start position:0% +winter all right so here's the usual + + + align:start position:0% +winter all right so here's the usual +drunk subclass of drunk and it can take + + align:start position:0% +drunk subclass of drunk and it can take + + + align:start position:0% +drunk subclass of drunk and it can take +steps at random One Step either + + align:start position:0% +steps at random One Step either + + + align:start position:0% +steps at random One Step either +increasing y a step North decreasing y a + + align:start position:0% +increasing y a step North decreasing y a + + + align:start position:0% +increasing y a step North decreasing y a +step + + align:start position:0% +step + + + align:start position:0% +step +South increasing x a step East or + + align:start position:0% +South increasing x a step East or + + + align:start position:0% +South increasing x a step East or +decreasing x a step y + + align:start position:0% +decreasing x a step y + + + align:start position:0% +decreasing x a step y +West so those are the choices and it's + + align:start position:0% +West so those are the choices and it's + + + align:start position:0% +West so those are the choices and it's +going to return one of those at random I + + align:start position:0% +going to return one of those at random I + + + align:start position:0% +going to return one of those at random I +think we saw random. choice in the last + + align:start position:0% +think we saw random. choice in the last + + + align:start position:0% +think we saw random. choice in the last +lecture and then our masochistic drunk + + align:start position:0% +lecture and then our masochistic drunk + + + align:start position:0% +lecture and then our masochistic drunk +it's almost the same except the choices + + align:start position:0% +it's almost the same except the choices + + + align:start position:0% +it's almost the same except the choices +are slight complely different if he + + align:start position:0% +are slight complely different if he + + + align:start position:0% +are slight complely different if he +chooses to head north he doesn't go one + + align:start position:0% +chooses to head north he doesn't go one + + + align:start position:0% +chooses to head north he doesn't go one +step he goes 1.1 steps + + align:start position:0% +step he goes 1.1 steps + + + align:start position:0% +step he goes 1.1 steps +North and if he chooses to go south he + + align:start position:0% +North and if he chooses to go south he + + + align:start position:0% +North and if he chooses to go south he +only goes 9/10 of a step so what we're + + align:start position:0% +only goes 9/10 of a step so what we're + + + align:start position:0% +only goes 9/10 of a step so what we're +seeing here is what's called a bias + + align:start position:0% +seeing here is what's called a bias + + + align:start position:0% +seeing here is what's called a bias +random walk and the bias here is the + + align:start position:0% +random walk and the bias here is the + + + align:start position:0% +random walk and the bias here is the +direction of the + + align:start position:0% +direction of the + + + align:start position:0% +direction of the +Walk that is moving either up or + + align:start position:0% +Walk that is moving either up or + + + align:start position:0% +Walk that is moving either up or +down + + align:start position:0% +down + + + align:start position:0% +down +okay pretty simple + + align:start position:0% +okay pretty simple + + + align:start position:0% +okay pretty simple +how about just for to test things out + + align:start position:0% +how about just for to test things out + + + align:start position:0% +how about just for to test things out +we'll ask the question is this an + + align:start position:0% +we'll ask the question is this an + + + align:start position:0% +we'll ask the question is this an +immutable or a mutable + + align:start position:0% + + + + align:start position:0% + +type are these are drunks mutable or + + align:start position:0% +type are these are drunks mutable or + + + align:start position:0% +type are these are drunks mutable or +immutable this is sort of a deep + + align:start position:0% +immutable this is sort of a deep + + + align:start position:0% +immutable this is sort of a deep +philosophical question right but if we + + align:start position:0% +philosophical question right but if we + + + align:start position:0% +philosophical question right but if we +ignore the philos philosophical + + align:start position:0% +ignore the philos philosophical + + + align:start position:0% +ignore the philos philosophical +underpinnings of that question what + + align:start position:0% +underpinnings of that question what + + + align:start position:0% +underpinnings of that question what +about the two types + + align:start position:0% + + + + align:start position:0% + +here who thinks it's + + align:start position:0% +here who thinks it's + + + align:start position:0% +here who thinks it's +immutable + + align:start position:0% +immutable + + + align:start position:0% +immutable +who thinks it's + + align:start position:0% +who thinks it's + + + align:start position:0% +who thinks it's +mutable all right why what's why do you + + align:start position:0% +mutable all right why what's why do you + + + align:start position:0% +mutable all right why what's why do you +think it's mutable what's getting + + align:start position:0% + + + + align:start position:0% + +changed the answer is nothing + + align:start position:0% +changed the answer is nothing + + + align:start position:0% +changed the answer is nothing +right it gets + + align:start position:0% + + + + align:start position:0% + +created and then it's + + align:start position:0% +created and then it's + + + align:start position:0% +created and then it's +returning the step but it's not actually + + align:start position:0% +returning the step but it's not actually + + + align:start position:0% +returning the step but it's not actually +changing the drunk so so far we have two + + align:start position:0% +changing the drunk so so far we have two + + + align:start position:0% +changing the drunk so so far we have two +things that are immutable drunk Trunks + + align:start position:0% +things that are immutable drunk Trunks + + + align:start position:0% +things that are immutable drunk Trunks +and + + align:start position:0% +and + + + align:start position:0% +and +locations let's look at Fields fields + + align:start position:0% +locations let's look at Fields fields + + + align:start position:0% +locations let's look at Fields fields +are a little bit more + + align:start position:0% +are a little bit more + + + align:start position:0% +are a little bit more +complicated so we field will be a + + align:start position:0% +complicated so we field will be a + + + align:start position:0% +complicated so we field will be a +dictionary and the dictionary is going + + align:start position:0% +dictionary and the dictionary is going + + + align:start position:0% +dictionary and the dictionary is going +to map a drunk to his or her location in + + align:start position:0% +to map a drunk to his or her location in + + + align:start position:0% +to map a drunk to his or her location in +the + + align:start position:0% +the + + + align:start position:0% +the +field so we can add a drunk at some + + align:start position:0% +field so we can add a drunk at some + + + align:start position:0% +field so we can add a drunk at some +location and we're going to check and if + + align:start position:0% +location and we're going to check and if + + + align:start position:0% +location and we're going to check and if +the drunk is already there we're not + + align:start position:0% +the drunk is already there we're not + + + align:start position:0% +the drunk is already there we're not +going to put the drunk in we're going to + + align:start position:0% +going to put the drunk in we're going to + + + align:start position:0% +going to put the drunk in we're going to +raise a value error duplicate drunks + + align:start position:0% +raise a value error duplicate drunks + + + align:start position:0% +raise a value error duplicate drunks +otherwise we're going to set the value + + align:start position:0% +otherwise we're going to set the value + + + align:start position:0% +otherwise we're going to set the value +of Drunk In This mapping to L and now + + align:start position:0% +of Drunk In This mapping to L and now + + + align:start position:0% +of Drunk In This mapping to L and now +you see by the way why I wanted drunks + + align:start position:0% +you see by the way why I wanted drunks + + + align:start position:0% +you see by the way why I wanted drunks +to be immutable because I want to they + + align:start position:0% +to be immutable because I want to they + + + align:start position:0% +to be immutable because I want to they +have to be hashable so I can use them as + + align:start position:0% +have to be hashable so I can use them as + + + align:start position:0% +have to be hashable so I can use them as +a key in a + + align:start position:0% +a key in a + + + align:start position:0% +a key in a +dictionary so it was not an idle + + align:start position:0% +dictionary so it was not an idle + + + align:start position:0% +dictionary so it was not an idle +question whether they were immutable it + + align:start position:0% +question whether they were immutable it + + + align:start position:0% +question whether they were immutable it +was an important + + align:start position:0% +was an important + + + align:start position:0% +was an important +question I can get the location of a + + align:start position:0% +question I can get the location of a + + + align:start position:0% +question I can get the location of a +drunk if the drunk is not in there then + + align:start position:0% +drunk if the drunk is not in there then + + + align:start position:0% +drunk if the drunk is not in there then +I'll raise a different value error drunk + + align:start position:0% +I'll raise a different value error drunk + + + align:start position:0% +I'll raise a different value error drunk +not in field otherwise I'll return the + + align:start position:0% +not in field otherwise I'll return the + + + align:start position:0% +not in field otherwise I'll return the +location associated with that + + align:start position:0% + + + + align:start position:0% + +drunk and finally we're going to have + + align:start position:0% +drunk and finally we're going to have + + + align:start position:0% +drunk and finally we're going to have +move + + align:start position:0% +move + + + align:start position:0% +move +drunk again I'll check whether the drunk + + align:start position:0% +drunk again I'll check whether the drunk + + + align:start position:0% +drunk again I'll check whether the drunk +is + + align:start position:0% +is + + + align:start position:0% +is +there if the drunk is there I'm going to + + align:start position:0% +there if the drunk is there I'm going to + + + align:start position:0% +there if the drunk is there I'm going to +get the distance on X and the distance + + align:start position:0% +get the distance on X and the distance + + + align:start position:0% +get the distance on X and the distance +in y by calling drunk do + + align:start position:0% +in y by calling drunk do + + + align:start position:0% +in y by calling drunk do +takep all right so we saw a take step + + align:start position:0% +takep all right so we saw a take step + + + align:start position:0% +takep all right so we saw a take step +for a drunk didn't move the drunk + + align:start position:0% +for a drunk didn't move the drunk + + + align:start position:0% +for a drunk didn't move the drunk +anywhere because the drunks were + + align:start position:0% +anywhere because the drunks were + + + align:start position:0% +anywhere because the drunks were +immutable but return new locations a new + + align:start position:0% +immutable but return new locations a new + + + align:start position:0% +immutable but return new locations a new +X and new values and then I'm going to + + align:start position:0% +X and new values and then I'm going to + + + align:start position:0% +X and new values and then I'm going to +use + + align:start position:0% +use + + + align:start position:0% +use +that to + + align:start position:0% +that to + + + align:start position:0% +that to +move the drunk in the field + + align:start position:0% +move the drunk in the field + + + align:start position:0% +move the drunk in the field +okay so I'll set self-d drunk sub drunk + + align:start position:0% +okay so I'll set self-d drunk sub drunk + + + align:start position:0% +okay so I'll set self-d drunk sub drunk +to move X distance and Y + + align:start position:0% +to move X distance and Y + + + align:start position:0% +to move X distance and Y +distance + + align:start position:0% + + + + align:start position:0% + +all right so it's very simple but having + + align:start position:0% +all right so it's very simple but having + + + align:start position:0% +all right so it's very simple but having +built these this set of classes we can + + align:start position:0% +built these this set of classes we can + + + align:start position:0% +built these this set of classes we can +now actually write the simulation oh + + align:start position:0% +now actually write the simulation oh + + + align:start position:0% +now actually write the simulation oh +what about classes are they mutable or + + align:start position:0% +what about classes are they mutable or + + + align:start position:0% +what about classes are they mutable or +immutable not classes what about + + align:start position:0% + + + + align:start position:0% + +Fields any votes for + + align:start position:0% +Fields any votes for + + + align:start position:0% +Fields any votes for +mutable yeah + + align:start position:0% +mutable yeah + + + align:start position:0% +mutable yeah +exactly because you can see I'm I'm + + align:start position:0% +exactly because you can see I'm I'm + + + align:start position:0% +exactly because you can see I'm I'm +mutating it right right here I'm + + align:start position:0% +mutating it right right here I'm + + + align:start position:0% +mutating it right right here I'm +changing the value of the dictionary and + + align:start position:0% +changing the value of the dictionary and + + + align:start position:0% +changing the value of the dictionary and +in fact every time I add a drunk to the + + align:start position:0% +in fact every time I add a drunk to the + + + align:start position:0% +in fact every time I add a drunk to the +field I'm changing the value of the + + align:start position:0% +field I'm changing the value of the + + + align:start position:0% +field I'm changing the value of the +dictionary which is to say mutating the + + align:start position:0% +dictionary which is to say mutating the + + + align:start position:0% +dictionary which is to say mutating the +field so I'll have a bunch of locations + + align:start position:0% +field so I'll have a bunch of locations + + + align:start position:0% +field so I'll have a bunch of locations +which are immutable objects makes sense + + align:start position:0% +which are immutable objects makes sense + + + align:start position:0% +which are immutable objects makes sense +that a location is immutable a bunch of + + align:start position:0% +that a location is immutable a bunch of + + + align:start position:0% +that a location is immutable a bunch of +drunks and the thing I'm going to change + + align:start position:0% +drunks and the thing I'm going to change + + + align:start position:0% +drunks and the thing I'm going to change +is where the drunks are in the + + align:start position:0% + + + + align:start position:0% + +field all right I said we'd start by + + align:start position:0% +field all right I said we'd start by + + + align:start position:0% +field all right I said we'd start by +simulating a single + + align:start position:0% +simulating a single + + + align:start position:0% +simulating a single +walk so here it is a walk in a + + align:start position:0% +walk so here it is a walk in a + + + align:start position:0% +walk so here it is a walk in a +field with a drunk and that drunk will + + align:start position:0% +field with a drunk and that drunk will + + + align:start position:0% +field with a drunk and that drunk will +take some number of steps in the + + align:start position:0% + + + + align:start position:0% + +field and you can see this it's very + + align:start position:0% +field and you can see this it's very + + + align:start position:0% +field and you can see this it's very +simple I just have a loop I drunk takes + + align:start position:0% +simple I just have a loop I drunk takes + + + align:start position:0% +simple I just have a loop I drunk takes +some number of random steps and I'm + + align:start position:0% +some number of random steps and I'm + + + align:start position:0% +some number of random steps and I'm +going to return the distance from the + + align:start position:0% +going to return the distance from the + + + align:start position:0% +going to return the distance from the +start to the final location of the + + align:start position:0% +start to the final location of the + + + align:start position:0% +start to the final location of the +drunk all right so how far is the drunk + + align:start position:0% +drunk all right so how far is the drunk + + + align:start position:0% +drunk all right so how far is the drunk +from the + + align:start position:0% +from the + + + align:start position:0% +from the +origin I then need to simulate multiple + + align:start position:0% +origin I then need to simulate multiple + + + align:start position:0% +origin I then need to simulate multiple +walks + + align:start position:0% +walks + + + align:start position:0% +walks +um notice here that I've got the number + + align:start position:0% +um notice here that I've got the number + + + align:start position:0% +um notice here that I've got the number +of steps the number of + + align:start position:0% +of steps the number of + + + align:start position:0% +of steps the number of +Trials and D class stands for class of + + align:start position:0% +Trials and D class stands for class of + + + align:start position:0% +Trials and D class stands for class of +the drunk and that's because I want to + + align:start position:0% +the drunk and that's because I want to + + + align:start position:0% +the drunk and that's because I want to +use the same function to simulate as + + align:start position:0% +use the same function to simulate as + + + align:start position:0% +use the same function to simulate as +many different kinds of drunk I care + + align:start position:0% +many different kinds of drunk I care + + + align:start position:0% +many different kinds of drunk I care +about we've only seen two here the + + align:start position:0% +about we've only seen two here the + + + align:start position:0% +about we've only seen two here the +masochistic drunk and the usual drunk + + align:start position:0% +masochistic drunk and the usual drunk + + + align:start position:0% +masochistic drunk and the usual drunk +but you can imagine many other kinds as + + align:start position:0% +but you can imagine many other kinds as + + + align:start position:0% +but you can imagine many other kinds as +well + + align:start position:0% +well + + + align:start position:0% +well +um so let's do it so here I'm going to + + align:start position:0% +um so let's do it so here I'm going to + + + align:start position:0% +um so let's do it so here I'm going to +simulate a walk for one drunk homer so + + align:start position:0% +simulate a walk for one drunk homer so + + + align:start position:0% +simulate a walk for one drunk homer so +we'll create a drunk named Homer or the + + align:start position:0% +we'll create a drunk named Homer or the + + + align:start position:0% +we'll create a drunk named Homer or the +variable homer which is the drunk + + align:start position:0% +variable homer which is the drunk + + + align:start position:0% +variable homer which is the drunk +class then the + + align:start position:0% +class then the + + + align:start position:0% +class then the +origin + + align:start position:0% +origin + + + align:start position:0% +origin +distances and for in range number of + + align:start position:0% +distances and for in range number of + + + align:start position:0% +distances and for in range number of +Trials we'll just do it and then we'll + + align:start position:0% +Trials we'll just do it and then we'll + + + align:start position:0% +Trials we'll just do it and then we'll +return the distances so it's initialized + + align:start position:0% +return the distances so it's initialized + + + align:start position:0% +return the distances so it's initialized +to the empty list so we're going to + + align:start position:0% +to the empty list so we're going to + + + align:start position:0% +to the empty list so we're going to +return a list of for however many trials + + align:start position:0% +return a list of for however many trials + + + align:start position:0% +return a list of for however many trials +we do how far the drunk ended up from + + align:start position:0% +we do how far the drunk ended up from + + + align:start position:0% +we do how far the drunk ended up from +the + + align:start position:0% +the + + + align:start position:0% +the +origin then we can average that and we + + align:start position:0% +origin then we can average that and we + + + align:start position:0% +origin then we can average that and we +look at the mean maybe we'll look at the + + align:start position:0% +look at the mean maybe we'll look at the + + + align:start position:0% +look at the mean maybe we'll look at the +Min or the max lots of different + + align:start position:0% +Min or the max lots of different + + + align:start position:0% +Min or the max lots of different +questions we could ask about the + + align:start position:0% +questions we could ask about the + + + align:start position:0% +questions we could ask about the +behavior and now we can put it all + + align:start position:0% +behavior and now we can put it all + + + align:start position:0% +behavior and now we can put it all +together here + + align:start position:0% +together here + + + align:start position:0% +together here +so drunk test will take the length a set + + align:start position:0% +so drunk test will take the length a set + + + align:start position:0% +so drunk test will take the length a set +of different walk lengths a list of + + align:start position:0% +of different walk lengths a list of + + + align:start position:0% +of different walk lengths a list of +different walk lengths the number of + + align:start position:0% +different walk lengths the number of + + + align:start position:0% +different walk lengths the number of +Trials and the + + align:start position:0% +Trials and the + + + align:start position:0% +Trials and the +class and for number of steps and walk + + align:start position:0% +class and for number of steps and walk + + + align:start position:0% +class and for number of steps and walk +lengths distances will be Sim walks of + + align:start position:0% +lengths distances will be Sim walks of + + + align:start position:0% +lengths distances will be Sim walks of +number of steps numb trials + + align:start position:0% +number of steps numb trials + + + align:start position:0% +number of steps numb trials +declass and then I'm going to just print + + align:start position:0% +declass and then I'm going to just print + + + align:start position:0% +declass and then I'm going to just print +some + + align:start position:0% + + + + align:start position:0% + +statistics you may or may not have seen + + align:start position:0% +statistics you may or may not have seen + + + align:start position:0% +statistics you may or may not have seen +this this is something that's sort of + + align:start position:0% +this this is something that's sort of + + + align:start position:0% +this this is something that's sort of +built in to + + align:start position:0% +built in to + + + align:start position:0% +built in to +python I + + align:start position:0% +python I + + + align:start position:0% +python I +can ask for the name of a + + align:start position:0% +can ask for the name of a + + + align:start position:0% +can ask for the name of a +class so DCL class to remember is a + + align:start position:0% +class so DCL class to remember is a + + + align:start position:0% +class so DCL class to remember is a +class and underbar underbar name will + + align:start position:0% +class and underbar underbar name will + + + align:start position:0% +class and underbar underbar name will +give me the name of the class might be + + align:start position:0% +give me the name of the class might be + + + align:start position:0% +give me the name of the class might be +usual it might be drunk in this case + + align:start position:0% + + + + align:start position:0% + +Okay so let's try + + align:start position:0% + + + + align:start position:0% + +it all right so the code we've looked + + align:start position:0% +it all right so the code we've looked + + + align:start position:0% +it all right so the code we've looked +looked + + align:start position:0% + + + + align:start position:0% + +at so let's go down here and we'll run + + align:start position:0% +at so let's go down here and we'll run + + + align:start position:0% +at so let's go down here and we'll run +it and we'll try it for walks of 10 100 + + align:start position:0% +it and we'll try it for walks of 10 100 + + + align:start position:0% +it and we'll try it for walks of 10 100 +a th000 and 10,000 steps and we'll do a + + align:start position:0% +a th000 and 10,000 steps and we'll do a + + + align:start position:0% +a th000 and 10,000 steps and we'll do a + + align:start position:0% + + + + align:start position:0% + +trials all right here's what we + + align:start position:0% +trials all right here's what we + + + align:start position:0% +trials all right here's what we +got so my question to you is does this + + align:start position:0% +got so my question to you is does this + + + align:start position:0% +got so my question to you is does this +look + + align:start position:0% + + + + align:start position:0% + +plausible does + + align:start position:0% +plausible does + + + align:start position:0% +plausible does +this what is it telling us here well + + align:start position:0% +this what is it telling us here well + + + align:start position:0% +this what is it telling us here well +it's telling us here that the length of + + align:start position:0% +it's telling us here that the length of + + + align:start position:0% +it's telling us here that the length of +the Walk actually doesn't really affect + + align:start position:0% +the Walk actually doesn't really affect + + + align:start position:0% +the Walk actually doesn't really affect +the number of steps doesn't affect how + + align:start position:0% +the number of steps doesn't affect how + + + align:start position:0% +the number of steps doesn't affect how +far the drunk + + align:start position:0% +far the drunk + + + align:start position:0% +far the drunk +gets you know there's some Randomness + + align:start position:0% +gets you know there's some Randomness + + + align:start position:0% +gets you know there's some Randomness +8.6 8.57 9.2 + + align:start position:0% +8.6 8.57 9.2 + + + align:start position:0% +8.6 8.57 9.2 +8.7 not much variance + + align:start position:0% +8.7 not much variance + + + align:start position:0% +8.7 not much variance +so we've done the simulation and we've + + align:start position:0% +so we've done the simulation and we've + + + align:start position:0% +so we've done the simulation and we've +learned something + + align:start position:0% +learned something + + + align:start position:0% +learned something +maybe so does this look + + align:start position:0% + + + + align:start position:0% + +plausible we can look at it + + align:start position:0% +plausible we can look at it + + + align:start position:0% +plausible we can look at it +here I've just transcribed + + align:start position:0% + + + + align:start position:0% + +it what do you + + align:start position:0% +it what do you + + + align:start position:0% +it what do you +think well go ahead I to say seems + + align:start position:0% +think well go ahead I to say seems + + + align:start position:0% +think well go ahead I to say seems +because after the first two steps + + align:start position:0% + + + + align:start position:0% + +% + + align:start position:0% +% + + + align:start position:0% +% +right so we have at least one vote for + + align:start position:0% +right so we have at least one vote for + + + align:start position:0% +right so we have at least one vote for +plausible and it's certainly a plausible + + align:start position:0% +plausible and it's certainly a plausible + + + align:start position:0% +plausible and it's certainly a plausible +argument well one of the things we need + + align:start position:0% +argument well one of the things we need + + + align:start position:0% +argument well one of the things we need +to learn to do is whenever we build a + + align:start position:0% +to learn to do is whenever we build a + + + align:start position:0% +to learn to do is whenever we build a +simulation we need to do what I call a + + align:start position:0% +simulation we need to do what I call a + + + align:start position:0% +simulation we need to do what I call a +sanity check to see whether or not the + + align:start position:0% +sanity check to see whether or not the + + + align:start position:0% +sanity check to see whether or not the +the simulation actually makes sense + + align:start position:0% +the simulation actually makes sense + + + align:start position:0% +the simulation actually makes sense +so if we're going to do a sanity check + + align:start position:0% +so if we're going to do a sanity check + + + align:start position:0% +so if we're going to do a sanity check +what might we do in this + + align:start position:0% +what might we do in this + + + align:start position:0% +what might we do in this +case we should try it on cases where we + + align:start position:0% +case we should try it on cases where we + + + align:start position:0% +case we should try it on cases where we +think we know the + + align:start position:0% +think we know the + + + align:start position:0% +think we know the +answer right so we say all right let's + + align:start position:0% +answer right so we say all right let's + + + align:start position:0% +answer right so we say all right let's +take a really simple case where we're + + align:start position:0% +take a really simple case where we're + + + align:start position:0% +take a really simple case where we're +pretty sure we know what the answer is + + align:start position:0% +pretty sure we know what the answer is + + + align:start position:0% +pretty sure we know what the answer is +let's run our simulation and make sure + + align:start position:0% +let's run our simulation and make sure + + + align:start position:0% +let's run our simulation and make sure +it gives us the right answer for this + + align:start position:0% +it gives us the right answer for this + + + align:start position:0% +it gives us the right answer for this +simple + + align:start position:0% +simple + + + align:start position:0% +simple +case so if we think of a sanity check + + align:start position:0% +case so if we think of a sanity check + + + align:start position:0% +case so if we think of a sanity check +here here maybe we should look at these + + align:start position:0% +here here maybe we should look at these + + + align:start position:0% +here here maybe we should look at these +numbers we just did it we know how far + + align:start position:0% +numbers we just did it we know how far + + + align:start position:0% +numbers we just did it we know how far +the drunk should get in zero + + align:start position:0% +the drunk should get in zero + + + align:start position:0% +the drunk should get in zero +steps right how far should the drunk + + align:start position:0% +steps right how far should the drunk + + + align:start position:0% +steps right how far should the drunk +move in zero steps zero how far should + + align:start position:0% +move in zero steps zero how far should + + + align:start position:0% +move in zero steps zero how far should +the drunk move in one steps we know that + + align:start position:0% +the drunk move in one steps we know that + + + align:start position:0% +the drunk move in one steps we know that +should be one two steps well we knew + + align:start position:0% +should be one two steps well we knew + + + align:start position:0% +should be one two steps well we knew +what that should be well if I run this + + align:start position:0% +what that should be well if I run this + + + align:start position:0% +what that should be well if I run this +sanity check these are the numbers I + + align:start position:0% + + + + align:start position:0% + +get I should be pretty + + align:start position:0% +get I should be pretty + + + align:start position:0% +get I should be pretty +suspicious I should also be suspicious + + align:start position:0% +suspicious I should also be suspicious + + + align:start position:0% +suspicious I should also be suspicious +they're kind of the same numbers I got + + align:start position:0% +they're kind of the same numbers I got + + + align:start position:0% +they're kind of the same numbers I got +for like 10,000 + + align:start position:0% +for like 10,000 + + + align:start position:0% +for like 10,000 +steps what should I think about I should + + align:start position:0% +steps what should I think about I should + + + align:start position:0% +steps what should I think about I should +think that maybe there's a bug in my + + align:start position:0% + + + + align:start position:0% + +code so if we now go back and look at + + align:start position:0% +code so if we now go back and look at + + + align:start position:0% +code so if we now go back and look at +the code yes this is fails the pants on + + align:start position:0% +the code yes this is fails the pants on + + + align:start position:0% +the code yes this is fails the pants on +fire + + align:start position:0% +fire + + + align:start position:0% +fire +test that there's clearly something + + align:start position:0% +test that there's clearly something + + + align:start position:0% +test that there's clearly something +wrong with these + + align:start position:0% + + + + align:start position:0% + +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +what we were appending is walk of Homer + + align:start position:0% +what we were appending is walk of Homer + + + align:start position:0% +what we were appending is walk of Homer +num Tri one well numb trials is a + + align:start position:0% +num Tri one well numb trials is a + + + align:start position:0% +num Tri one well numb trials is a +constant it's always a + + align:start position:0% +constant it's always a + + + align:start position:0% +constant it's always a +100 what I intended to write here was + + align:start position:0% +100 what I intended to write here was + + + align:start position:0% +100 what I intended to write here was +not numb trials but numb + + align:start position:0% +not numb trials but numb + + + align:start position:0% +not numb trials but numb +steps but it was you know I actually did + + align:start position:0% +steps but it was you know I actually did + + + align:start position:0% +steps but it was you know I actually did +this the first time I wrote this + + align:start position:0% +this the first time I wrote this + + + align:start position:0% +this the first time I wrote this +simulation many years ago I made this + + align:start position:0% +simulation many years ago I made this + + + align:start position:0% +simulation many years ago I made this +typo if you will and I got these bizarre + + align:start position:0% +typo if you will and I got these bizarre + + + align:start position:0% +typo if you will and I got these bizarre +answers + + align:start position:0% +answers + + + align:start position:0% +answers +so I looked at the code and I said well + + align:start position:0% +so I looked at the code and I said well + + + align:start position:0% +so I looked at the code and I said well +that's actually wrong no wonder it's + + align:start position:0% +that's actually wrong no wonder it's + + + align:start position:0% +that's actually wrong no wonder it's +always the same number I'm calling it + + align:start position:0% +always the same number I'm calling it + + + align:start position:0% +always the same number I'm calling it +with a constant the constant happens to + + align:start position:0% +with a constant the constant happens to + + + align:start position:0% +with a constant the constant happens to +be 100 so let's go fix the + + align:start position:0% + + + + align:start position:0% + +simulation so this should have B numb + + align:start position:0% + + + + align:start position:0% + +steps now let's run it + + align:start position:0% + + + + align:start position:0% + +again well these results are pretty + + align:start position:0% +again well these results are pretty + + + align:start position:0% +again well these results are pretty +different now we see that in fact + + align:start position:0% +different now we see that in fact + + + align:start position:0% +different now we see that in fact +they're + + align:start position:0% + + + + align:start position:0% + +increasing should I just look at this + + align:start position:0% +increasing should I just look at this + + + align:start position:0% +increasing should I just look at this +and be + + align:start position:0% +and be + + + align:start position:0% +and be +happy probably not right I should run my + + align:start position:0% +happy probably not right I should run my + + + align:start position:0% +happy probably not right I should run my +sanity check again and make sure I get + + align:start position:0% +sanity check again and make sure I get + + + align:start position:0% +sanity check again and make sure I get +the right results for 0 one and + + align:start position:0% +the right results for 0 one and + + + align:start position:0% +the right results for 0 one and +two so let's go back and do that just to + + align:start position:0% +two so let's go back and do that just to + + + align:start position:0% +two so let's go back and do that just to +be a little bit + + align:start position:0% + + + + align:start position:0% + +safe so so I'll just change this tupal + + align:start position:0% +safe so so I'll just change this tupal + + + align:start position:0% +safe so so I'll just change this tupal +of values to + + align:start position:0% + + + + align:start position:0% + +be and I should feel a lot better about + + align:start position:0% +be and I should feel a lot better about + + + align:start position:0% +be and I should feel a lot better about +this right all + + align:start position:0% +this right all + + + align:start position:0% +this right all +right the mean the Max and the Min are + + align:start position:0% +right the mean the Max and the Min are + + + align:start position:0% +right the mean the Max and the Min are +all zero when he doesn't take any + + align:start position:0% +all zero when he doesn't take any + + + align:start position:0% +all zero when he doesn't take any +steps one is exactly what we should + + align:start position:0% +steps one is exactly what we should + + + align:start position:0% +steps one is exactly what we should +expect and two is also the mean is where + + align:start position:0% +expect and two is also the mean is where + + + align:start position:0% +expect and two is also the mean is where +we would guess it to be and the max is + + align:start position:0% +we would guess it to be and the max is + + + align:start position:0% +we would guess it to be and the max is +two happen to take two steps in the same + + align:start position:0% +two happen to take two steps in the same + + + align:start position:0% +two happen to take two steps in the same +direction and the Min is zero happened + + align:start position:0% +direction and the Min is zero happened + + + align:start position:0% +direction and the Min is zero happened +to end up where he started so I've + + align:start position:0% +to end up where he started so I've + + + align:start position:0% +to end up where he started so I've +passed my sanity check doesn't mean my + + align:start position:0% +passed my sanity check doesn't mean my + + + align:start position:0% +passed my sanity check doesn't mean my +simulation is right but at least I have + + align:start position:0% +simulation is right but at least I have + + + align:start position:0% +simulation is right but at least I have +reason to be + + align:start position:0% + + + + align:start position:0% + +hopeful so all right getting + + align:start position:0% + + + + align:start position:0% + +back + + align:start position:0% + + + + align:start position:0% + +so we saw these results and now we're + + align:start position:0% +so we saw these results and now we're + + + align:start position:0% +so we saw these results and now we're +getting the indication that in fact + + align:start position:0% +getting the indication that in fact + + + align:start position:0% +getting the indication that in fact +contrary to what we might have thought + + align:start position:0% +contrary to what we might have thought + + + align:start position:0% +contrary to what we might have thought +it does appear to be that the more steps + + align:start position:0% +it does appear to be that the more steps + + + align:start position:0% +it does appear to be that the more steps +the drunk takes the further away the + + align:start position:0% +the drunk takes the further away the + + + align:start position:0% +the drunk takes the further away the +drunk ends + + align:start position:0% + + + + align:start position:0% + +up and that was the usual drunk we can + + align:start position:0% +up and that was the usual drunk we can + + + align:start position:0% +up and that was the usual drunk we can +try the masochistic drunk and then we + + align:start position:0% +try the masochistic drunk and then we + + + align:start position:0% +try the masochistic drunk and then we +see something pretty + + align:start position:0% +see something pretty + + + align:start position:0% +see something pretty +interesting I won't make you sit through + + align:start position:0% +interesting I won't make you sit through + + + align:start position:0% +interesting I won't make you sit through +it but when we run it here are the usual + + align:start position:0% +it but when we run it here are the usual + + + align:start position:0% +it but when we run it here are the usual +drunks the numbers and I just looked at + + align:start position:0% +drunks the numbers and I just looked at + + + align:start position:0% +drunks the numbers and I just looked at +it for a thousand and 10,000 so it would + + align:start position:0% +it for a thousand and 10,000 so it would + + + align:start position:0% +it for a thousand and 10,000 so it would +fit on the screen you see for the usual + + align:start position:0% +fit on the screen you see for the usual + + + align:start position:0% +fit on the screen you see for the usual +drunk it's 26.8 90 roughly 90 Fair + + align:start position:0% +drunk it's 26.8 90 roughly 90 Fair + + + align:start position:0% +drunk it's 26.8 90 roughly 90 Fair +dispersion in the men in the Max and the + + align:start position:0% +dispersion in the men in the Max and the + + + align:start position:0% +dispersion in the men in the Max and the +masochistic drunk seems to be making + + align:start position:0% +masochistic drunk seems to be making + + + align:start position:0% +masochistic drunk seems to be making +considerably more + + align:start position:0% +considerably more + + + align:start position:0% +considerably more +progress than the usual drunk so what we + + align:start position:0% +progress than the usual drunk so what we + + + align:start position:0% +progress than the usual drunk so what we +see is this bias actually appear appears + + align:start position:0% +see is this bias actually appear appears + + + align:start position:0% +see is this bias actually appear appears +to be changing the + + align:start position:0% + + + + align:start position:0% + +distance well that's kind of + + align:start position:0% +distance well that's kind of + + + align:start position:0% +distance well that's kind of +interesting now we could ask the + + align:start position:0% +interesting now we could ask the + + + align:start position:0% +interesting now we could ask the +question why what's going + + align:start position:0% +question why what's going + + + align:start position:0% +question why what's going +on and to do that I want to go and start + + align:start position:0% +on and to do that I want to go and start + + + align:start position:0% +on and to do that I want to go and start +visualizing what's the trend so rather + + align:start position:0% +visualizing what's the trend so rather + + + align:start position:0% +visualizing what's the trend so rather +than just looking at two numbers or n + + align:start position:0% +than just looking at two numbers or n + + + align:start position:0% +than just looking at two numbers or n +three numbers as we've been doing I'm + + align:start position:0% +three numbers as we've been doing I'm + + + align:start position:0% +three numbers as we've been doing I'm +going to draw a pretty picture actually + + align:start position:0% +going to draw a pretty picture actually + + + align:start position:0% +going to draw a pretty picture actually +I'm not going to draw I'm a terrible + + align:start position:0% +I'm not going to draw I'm a terrible + + + align:start position:0% +I'm not going to draw I'm a terrible +artist but py will draw some pretty + + align:start position:0% +artist but py will draw some pretty + + + align:start position:0% +artist but py will draw some pretty +pictures we're going to simulate walks + + align:start position:0% +pictures we're going to simulate walks + + + align:start position:0% +pictures we're going to simulate walks +of multiple lengths for each kind of + + align:start position:0% +of multiple lengths for each kind of + + + align:start position:0% +of multiple lengths for each kind of +drunk and then plot the distance at the + + align:start position:0% +drunk and then plot the distance at the + + + align:start position:0% +drunk and then plot the distance at the +end of each length walk for each kind of + + align:start position:0% +end of each length walk for each kind of + + + align:start position:0% +end of each length walk for each kind of +drunk all right I now digress for a + + align:start position:0% +drunk all right I now digress for a + + + align:start position:0% +drunk all right I now digress for a +moment to talk about how we do + + align:start position:0% +moment to talk about how we do + + + align:start position:0% +moment to talk about how we do +plotting um so we're going to use + + align:start position:0% +plotting um so we're going to use + + + align:start position:0% +plotting um so we're going to use +something called pylab I've listed here + + align:start position:0% +something called pylab I've listed here + + + align:start position:0% +something called pylab I've listed here +four really important + + align:start position:0% +four really important + + + align:start position:0% +four really important +libraries that you will surely end up + + align:start position:0% +libraries that you will surely end up + + + align:start position:0% +libraries that you will surely end up +using extensively in uh if you continue + + align:start position:0% +using extensively in uh if you continue + + + align:start position:0% +using extensively in uh if you continue +to use Python for for research purposes + + align:start position:0% +to use Python for for research purposes + + + align:start position:0% +to use Python for for research purposes +uh numi adds vectors matrices and many + + align:start position:0% +uh numi adds vectors matrices and many + + + align:start position:0% +uh numi adds vectors matrices and many +highlevel mathematical functions + + align:start position:0% +highlevel mathematical functions + + + align:start position:0% +highlevel mathematical functions +actually it might be numpy it might be + + align:start position:0% +actually it might be numpy it might be + + + align:start position:0% +actually it might be numpy it might be +num I'm not sure how to pronounce it but + + align:start position:0% +num I'm not sure how to pronounce it but + + + align:start position:0% +num I'm not sure how to pronounce it but +we'll call it numpy so these are really + + align:start position:0% +we'll call it numpy so these are really + + + align:start position:0% +we'll call it numpy so these are really +useful + + align:start position:0% +useful + + + align:start position:0% +useful +things + + align:start position:0% +things + + + align:start position:0% +things +scipi adds on top of that a bunch of + + align:start position:0% +scipi adds on top of that a bunch of + + + align:start position:0% +scipi adds on top of that a bunch of +mathematical classes and functions + + align:start position:0% +mathematical classes and functions + + + align:start position:0% +mathematical classes and functions +useful to + + align:start position:0% +useful to + + + align:start position:0% +useful to +scientists things like uh well we'll + + align:start position:0% +scientists things like uh well we'll + + + align:start position:0% +scientists things like uh well we'll +look at some of them as we go on through + + align:start position:0% +look at some of them as we go on through + + + align:start position:0% +look at some of them as we go on through +the term Matt plot lib adds an + + align:start position:0% +the term Matt plot lib adds an + + + align:start position:0% +the term Matt plot lib adds an +objectoriented programming interface for + + align:start position:0% +objectoriented programming interface for + + + align:start position:0% +objectoriented programming interface for +plotting anybody here used + + align:start position:0% +plotting anybody here used + + + align:start position:0% +plotting anybody here used +matlb great well you'll find that + + align:start position:0% +matlb great well you'll find that + + + align:start position:0% +matlb great well you'll find that +matplot lib is the Matt think mat + + align:start position:0% +matplot lib is the Matt think mat + + + align:start position:0% +matplot lib is the Matt think mat +lab uh let you in Python use all the + + align:start position:0% +lab uh let you in Python use all the + + + align:start position:0% +lab uh let you in Python use all the +plotting stuff that you've come to + + align:start position:0% +plotting stuff that you've come to + + + align:start position:0% +plotting stuff that you've come to +either like or hate in in mat + + align:start position:0% +either like or hate in in mat + + + align:start position:0% +either like or hate in in mat +lab so it's really convenient if you + + align:start position:0% +lab so it's really convenient if you + + + align:start position:0% +lab so it's really convenient if you +know how to do plots in mat lab you'll + + align:start position:0% +know how to do plots in mat lab you'll + + + align:start position:0% +know how to do plots in mat lab you'll +know how to do it in Python pylab + + align:start position:0% +know how to do it in Python pylab + + + align:start position:0% +know how to do it in Python pylab +combines all of these to give you a mat + + align:start position:0% +combines all of these to give you a mat + + + align:start position:0% +combines all of these to give you a mat +laab like interface to + + align:start position:0% +laab like interface to + + + align:start position:0% +laab like interface to +python so once you have pylab you can do + + align:start position:0% +python so once you have pylab you can do + + + align:start position:0% +python so once you have pylab you can do +a lot of things that you would normally + + align:start position:0% +a lot of things that you would normally + + + align:start position:0% +a lot of things that you would normally +want to do in mat lab for example + + align:start position:0% +want to do in mat lab for example + + + align:start position:0% +want to do in mat lab for example +produce weird looking plots like this + + align:start position:0% +produce weird looking plots like this + + + align:start position:0% +produce weird looking plots like this +one all right I'm going to show you one + + align:start position:0% +one all right I'm going to show you one + + + align:start position:0% +one all right I'm going to show you one +of the many many plotting commands + + align:start position:0% +of the many many plotting commands + + + align:start position:0% +of the many many plotting commands +uh it is called plot it takes two + + align:start position:0% +uh it is called plot it takes two + + + align:start position:0% +uh it is called plot it takes two +arguments which must be sequences of the + + align:start position:0% +arguments which must be sequences of the + + + align:start position:0% +arguments which must be sequences of the +same + + align:start position:0% + + + + align:start position:0% + +length the first argument is the x + + align:start position:0% +length the first argument is the x + + + align:start position:0% +length the first argument is the x +coordinates the second argument is the + + align:start position:0% +coordinates the second argument is the + + + align:start position:0% +coordinates the second argument is the +y-coordinates corresponding to the x1's + + align:start position:0% +y-coordinates corresponding to the x1's + + + align:start position:0% +y-coordinates corresponding to the x1's +there are roughly three zillion optional + + align:start position:0% +there are roughly three zillion optional + + + align:start position:0% +there are roughly three zillion optional +arguments um and you'll see me use only + + align:start position:0% +arguments um and you'll see me use only + + + align:start position:0% +arguments um and you'll see me use only +a small subset of them it plots the + + align:start position:0% +a small subset of them it plots the + + + align:start position:0% +a small subset of them it plots the +points in order first the first XY then + + align:start position:0% +points in order first the first XY then + + + align:start position:0% +points in order first the first XY then +the second XY than the third XY why is + + align:start position:0% +the second XY than the third XY why is + + + align:start position:0% +the second XY than the third XY why is +it important that I say it plots them in + + align:start position:0% +it important that I say it plots them in + + + align:start position:0% +it important that I say it plots them in +order because by + + align:start position:0% +order because by + + + align:start position:0% +order because by +default as each point is plotted it + + align:start position:0% +default as each point is plotted it + + + align:start position:0% +default as each point is plotted it +connects it draws a line connecting one + + align:start position:0% +connects it draws a line connecting one + + + align:start position:0% +connects it draws a line connecting one +point to the next point to the next + + align:start position:0% +point to the next point to the next + + + align:start position:0% +point to the next point to the next +point and so the order in which they're + + align:start position:0% +point and so the order in which they're + + + align:start position:0% +point and so the order in which they're +plotted will determine where the lines + + align:start position:0% +plotted will determine where the lines + + + align:start position:0% +plotted will determine where the lines +go now we'll see as we go on that we + + align:start position:0% +go now we'll see as we go on that we + + + align:start position:0% +go now we'll see as we go on that we +often don't draw the lines but by + + align:start position:0% +often don't draw the lines but by + + + align:start position:0% +often don't draw the lines but by +default they are + + align:start position:0% +default they are + + + align:start position:0% +default they are +drawn here's an + + align:start position:0% +drawn here's an + + + align:start position:0% +drawn here's an +example you start by importing + + align:start position:0% +example you start by importing + + + align:start position:0% +example you start by importing +PAB then I've given X vals and Y vales + + align:start position:0% +PAB then I've given X vals and Y vales + + + align:start position:0% +PAB then I've given X vals and Y vales +one and if I call pylab the plot of X + + align:start position:0% +one and if I call pylab the plot of X + + + align:start position:0% +one and if I call pylab the plot of X +vales y vales one here is one of the + + align:start position:0% +vales y vales one here is one of the + + + align:start position:0% +vales y vales one here is one of the +arguments I can give it I'm saying I'd + + align:start position:0% +arguments I can give it I'm saying I'd + + + align:start position:0% +arguments I can give it I'm saying I'd +like this to be plotted in blue b for + + align:start position:0% +like this to be plotted in blue b for + + + align:start position:0% +like this to be plotted in blue b for +blue and I'd like it to be plotted as a + + align:start position:0% +blue and I'd like it to be plotted as a + + + align:start position:0% +blue and I'd like it to be plotted as a +solid line a single Dash and I want to + + align:start position:0% +solid line a single Dash and I want to + + + align:start position:0% +solid line a single Dash and I want to +give that line a a label which I've said + + align:start position:0% +give that line a a label which I've said + + + align:start position:0% +give that line a a label which I've said +is + + align:start position:0% +is + + + align:start position:0% +is +first y vales 2 is a different list I'll + + align:start position:0% +first y vales 2 is a different list I'll + + + align:start position:0% +first y vales 2 is a different list I'll +plot it again here I'm going to say I + + align:start position:0% +plot it again here I'm going to say I + + + align:start position:0% +plot it again here I'm going to say I +want a red dotted + + align:start position:0% +want a red dotted + + + align:start position:0% +want a red dotted +line and the label will be second and + + align:start position:0% +line and the label will be second and + + + align:start position:0% +line and the label will be second and +then after plotting it I'm going to + + align:start position:0% +then after plotting it I'm going to + + + align:start position:0% +then after plotting it I'm going to +invoke py. Legend which puts this nice + + align:start position:0% +invoke py. Legend which puts this nice + + + align:start position:0% +invoke py. Legend which puts this nice +little box up here in the corner in this + + align:start position:0% +little box up here in the corner in this + + + align:start position:0% +little box up here in the corner in this +case saying that first is a solid blue + + align:start position:0% +case saying that first is a solid blue + + + align:start position:0% +case saying that first is a solid blue +line and second + + align:start position:0% +line and second + + + align:start position:0% +line and second +a dotted red line or dashed red line I + + align:start position:0% +a dotted red line or dashed red line I + + + align:start position:0% +a dotted red line or dashed red line I +should + + align:start position:0% +should + + + align:start position:0% +should +say now now again there are lots of + + align:start position:0% +say now now again there are lots of + + + align:start position:0% +say now now again there are lots of +arguments lots of other arguments I + + align:start position:0% +arguments lots of other arguments I + + + align:start position:0% +arguments lots of other arguments I +could have given plot also Legend I can + + align:start position:0% +could have given plot also Legend I can + + + align:start position:0% +could have given plot also Legend I can +tell it where to put the legend if I so + + align:start position:0% +tell it where to put the legend if I so + + + align:start position:0% +tell it where to put the legend if I so +choose here I've just said put it + + align:start position:0% +choose here I've just said put it + + + align:start position:0% +choose here I've just said put it +wherever you happen to want to put it or + + align:start position:0% +wherever you happen to want to put it or + + + align:start position:0% +wherever you happen to want to put it or +pylab wants to put it all right so very + + align:start position:0% +pylab wants to put it all right so very + + + align:start position:0% +pylab wants to put it all right so very +simple way to produce a + + align:start position:0% + + + + align:start position:0% + +plot um there are lots of details and + + align:start position:0% +plot um there are lots of details and + + + align:start position:0% +plot um there are lots of details and +many more examples about plotting in the + + align:start position:0% +many more examples about plotting in the + + + align:start position:0% +many more examples about plotting in the +assigned reading uh we posted a video + + align:start position:0% +assigned reading uh we posted a video + + + align:start position:0% +assigned reading uh we posted a video +that Professor Grimson produced for uh + + align:start position:0% +that Professor Grimson produced for uh + + + align:start position:0% +that Professor Grimson produced for uh +the an online course 600.1 X it's about + + align:start position:0% +the an online course 600.1 X it's about + + + align:start position:0% +the an online course 600.1 X it's about +a 50 minute video broken into multiple + + align:start position:0% +a 50 minute video broken into multiple + + + align:start position:0% +a 50 minute video broken into multiple +segments about how to use plotting and + + align:start position:0% +segments about how to use plotting and + + + align:start position:0% +segments about how to use plotting and +pylab with a lot more detail than I've + + align:start position:0% +pylab with a lot more detail than I've + + + align:start position:0% +pylab with a lot more detail than I've +given you uh you'll see if you read the + + align:start position:0% +given you uh you'll see if you read the + + + align:start position:0% +given you uh you'll see if you read the +code for this lecture and as you see + + align:start position:0% +code for this lecture and as you see + + + align:start position:0% +code for this lecture and as you see +this lecture there'll be lots of other + + align:start position:0% +this lecture there'll be lots of other + + + align:start position:0% +this lecture there'll be lots of other +plots showing up of different kinds + + align:start position:0% +plots showing up of different kinds + + + align:start position:0% +plots showing up of different kinds +these are the my two favorite online + + align:start position:0% +these are the my two favorite online + + + align:start position:0% +these are the my two favorite online +sites for finding out what to to do and + + align:start position:0% +sites for finding out what to to do and + + + align:start position:0% +sites for finding out what to to do and +of course you can Google all sorts of + + align:start position:0% +of course you can Google all sorts of + + + align:start position:0% +of course you can Google all sorts of +things uh that's all I'm going to tell + + align:start position:0% +things uh that's all I'm going to tell + + + align:start position:0% +things uh that's all I'm going to tell +you about how to produce plots in class + + align:start position:0% +you about how to produce plots in class + + + align:start position:0% +you about how to produce plots in class +but we're going to expect you to learn a + + align:start position:0% +but we're going to expect you to learn a + + + align:start position:0% +but we're going to expect you to learn a +lot about it because I think it's a + + align:start position:0% +lot about it because I think it's a + + + align:start position:0% +lot about it because I think it's a +really useful skill and at the very + + align:start position:0% +really useful skill and at the very + + + align:start position:0% +really useful skill and at the very +least you should feel comfortable that + + align:start position:0% +least you should feel comfortable that + + + align:start position:0% +least you should feel comfortable that +any plot I show you you now obviously + + align:start position:0% +any plot I show you you now obviously + + + align:start position:0% +any plot I show you you now obviously +not right now but you will eventually + + align:start position:0% +not right now but you will eventually + + + align:start position:0% +not right now but you will eventually +know how to produce so if you do these + + align:start position:0% +know how to produce so if you do these + + + align:start position:0% +know how to produce so if you do these +things you'll you'll be more than up to + + align:start position:0% +things you'll you'll be more than up to + + + align:start position:0% +things you'll you'll be more than up to +speed all right so I started by saying I + + align:start position:0% +speed all right so I started by saying I + + + align:start position:0% +speed all right so I started by saying I +wanted to plot the trends in + + align:start position:0% +wanted to plot the trends in + + + align:start position:0% +wanted to plot the trends in +distance and they're kind of interesting + + align:start position:0% +distance and they're kind of interesting + + + align:start position:0% +distance and they're kind of interesting +so here's the usual drunk and the + + align:start position:0% +so here's the usual drunk and the + + + align:start position:0% +so here's the usual drunk and the +masochistic drunk so you can see sure + + align:start position:0% +masochistic drunk so you can see sure + + + align:start position:0% +masochistic drunk so you can see sure +enough the usual drunk this fuchal line + + align:start position:0% +enough the usual drunk this fuchal line + + + align:start position:0% +enough the usual drunk this fuchal line +is progressing very slowly and the + + align:start position:0% +is progressing very slowly and the + + + align:start position:0% +is progressing very slowly and the +masochistic drunk considerably + + align:start position:0% +masochistic drunk considerably + + + align:start position:0% +masochistic drunk considerably +faster I looked at these and after + + align:start position:0% +faster I looked at these and after + + + align:start position:0% +faster I looked at these and after +looking at those to I tried to figure + + align:start position:0% +looking at those to I tried to figure + + + align:start position:0% +looking at those to I tried to figure +out whether there was some mathematical + + align:start position:0% +out whether there was some mathematical + + + align:start position:0% +out whether there was some mathematical +explanation of what was going on and + + align:start position:0% +explanation of what was going on and + + + align:start position:0% +explanation of what was going on and +decided Well it looked to me like the + + align:start position:0% +decided Well it looked to me like the + + + align:start position:0% +decided Well it looked to me like the +usual drunk was moving at about the + + align:start position:0% +usual drunk was moving at about the + + + align:start position:0% +usual drunk was moving at about the +square root of the number of + + align:start position:0% + + + + align:start position:0% + +steps not so odd to think about it if + + align:start position:0% +steps not so odd to think about it if + + + align:start position:0% +steps not so odd to think about it if +you go back to Old Pythagoras + + align:start position:0% +you go back to Old Pythagoras + + + align:start position:0% +you go back to Old Pythagoras +here and sure enough when I plot I ran + + align:start position:0% +here and sure enough when I plot I ran + + + align:start position:0% +here and sure enough when I plot I ran +this simulation up to 100,000 steps when + + align:start position:0% +this simulation up to 100,000 steps when + + + align:start position:0% +this simulation up to 100,000 steps when +I plot the square root of the number of + + align:start position:0% +I plot the square root of the number of + + + align:start position:0% +I plot the square root of the number of +steps it's not identical but it's pretty + + align:start position:0% +steps it's not identical but it's pretty + + + align:start position:0% +steps it's not identical but it's pretty +darn + + align:start position:0% +darn + + + align:start position:0% +darn +close seems to be moving just a tad + + align:start position:0% +close seems to be moving just a tad + + + align:start position:0% +close seems to be moving just a tad +faster than the square root but not much + + align:start position:0% +faster than the square root but not much + + + align:start position:0% +faster than the square root but not much +but who knows exactly but pretty good + + align:start position:0% +but who knows exactly but pretty good + + + align:start position:0% +but who knows exactly but pretty good +and + + align:start position:0% +and + + + align:start position:0% +and +then the masochistic drunk seems to be + + align:start position:0% +then the masochistic drunk seems to be + + + align:start position:0% +then the masochistic drunk seems to be +moving at a rate of num steps times + + align:start position:0% + + + + align:start position:0% + +0.05 kind of a less intuitive answer + + align:start position:0% +0.05 kind of a less intuitive answer + + + align:start position:0% +0.05 kind of a less intuitive answer +than the square + + align:start position:0% +than the square + + + align:start position:0% +than the square +root why do think it might be doing + + align:start position:0% + + + + align:start position:0% + +that well what we notice is that and + + align:start position:0% +that well what we notice is that and + + + align:start position:0% +that well what we notice is that and +we'll look at this maybe there's not + + align:start position:0% +we'll look at this maybe there's not + + + align:start position:0% +we'll look at this maybe there's not +much difference between what the + + align:start position:0% +much difference between what the + + + align:start position:0% +much difference between what the +masochistic drunk and the usual drunk do + + align:start position:0% +masochistic drunk and the usual drunk do + + + align:start position:0% +masochistic drunk and the usual drunk do +on the x axis East and West in fact + + align:start position:0% +on the x axis East and West in fact + + + align:start position:0% +on the x axis East and West in fact +there shouldn't be but there should be a + + align:start position:0% +there shouldn't be but there should be a + + + align:start position:0% +there shouldn't be but there should be a +difference on the Y AIS because every + + align:start position:0% +difference on the Y AIS because every + + + align:start position:0% +difference on the Y AIS because every +time one quarter of the time the drunk + + align:start position:0% +time one quarter of the time the drunk + + + align:start position:0% +time one quarter of the time the drunk +is taking a step north of 1.1 units and + + align:start position:0% +is taking a step north of 1.1 units and + + + align:start position:0% +is taking a step north of 1.1 units and +one quarter of the time is taking a step + + align:start position:0% +one quarter of the time is taking a step + + + align:start position:0% +one quarter of the time is taking a step +south of 0.9 + + align:start position:0% +south of 0.9 + + + align:start position:0% +south of 0.9 +units and so half the time the steps are + + align:start position:0% +units and so half the time the steps are + + + align:start position:0% +units and so half the time the steps are +diverging by a small + + align:start position:0% +diverging by a small + + + align:start position:0% +diverging by a small +fraction and if we think about it 0. one + + align:start position:0% +fraction and if we think about it 0. one + + + align:start position:0% +fraction and if we think about it 0. one +half the + + align:start position:0% +half the + + + align:start position:0% +half the +time + + align:start position:0% +time + + + align:start position:0% +time +we divide it we get + + align:start position:0% +we divide it we get + + + align:start position:0% +we divide it we get +0.05 okay so there's at least we need to + + align:start position:0% +0.05 okay so there's at least we need to + + + align:start position:0% +0.05 okay so there's at least we need to +do some more analysis but the data is + + align:start position:0% +do some more analysis but the data is + + + align:start position:0% +do some more analysis but the data is +pretty compelling here that it's a very + + align:start position:0% +pretty compelling here that it's a very + + + align:start position:0% +pretty compelling here that it's a very +good + + align:start position:0% + + + + align:start position:0% + +fit well let's look at the ending + + align:start position:0% +fit well let's look at the ending + + + align:start position:0% +fit well let's look at the ending +location so here you see a rather + + align:start position:0% +location so here you see a rather + + + align:start position:0% +location so here you see a rather +different kind of + + align:start position:0% +different kind of + + + align:start position:0% +different kind of +plot here I'm showing that you can plot + + align:start position:0% +plot here I'm showing that you can plot + + + align:start position:0% +plot here I'm showing that you can plot +these things without connecting them by + + align:start position:0% +these things without connecting them by + + + align:start position:0% +these things without connecting them by +lines + + align:start position:0% + + + + align:start position:0% + +so and giving them different + + align:start position:0% +so and giving them different + + + align:start position:0% +so and giving them different +shapes so what here I've said is that + + align:start position:0% +shapes so what here I've said is that + + + align:start position:0% +shapes so what here I've said is that +the masochistic drunk we're going to + + align:start position:0% +the masochistic drunk we're going to + + + align:start position:0% +the masochistic drunk we're going to +plot using red + + align:start position:0% + + + + align:start position:0% + +triangles and the usual drunk I'm going + + align:start position:0% +triangles and the usual drunk I'm going + + + align:start position:0% +triangles and the usual drunk I'm going +to plot + + align:start position:0% +to plot + + + align:start position:0% +to plot +using black plus + + align:start position:0% + + + + align:start position:0% + +signs and since I'm going to plot the + + align:start position:0% +signs and since I'm going to plot the + + + align:start position:0% +signs and since I'm going to plot the +location at the end of many + + align:start position:0% +location at the end of many + + + align:start position:0% +location at the end of many +walks it doesn't make sense to draw + + align:start position:0% +walks it doesn't make sense to draw + + + align:start position:0% +walks it doesn't make sense to draw +lines connecting everything because all + + align:start position:0% +lines connecting everything because all + + + align:start position:0% +lines connecting everything because all +we're caring about here is the end + + align:start position:0% +we're caring about here is the end + + + align:start position:0% +we're caring about here is the end +points so since I only want the end + + align:start position:0% +points so since I only want the end + + + align:start position:0% +points so since I only want the end +points I'm plotting them a different way + + align:start position:0% +points I'm plotting them a different way + + + align:start position:0% +points I'm plotting them a different way +so for + + align:start position:0% +so for + + + align:start position:0% +so for +example I can write something like + + align:start position:0% + + + + align:start position:0% + +plot X + + align:start position:0% +plot X + + + align:start position:0% +plot X +valve y valve + + align:start position:0% + + + + align:start position:0% + +and then if I do something + + align:start position:0% +and then if I do something + + + align:start position:0% +and then if I do something +like + + align:start position:0% +like + + + align:start position:0% +like +uh let's see Dash + + align:start position:0% + + + + align:start position:0% + +b0 or just b0 in + + align:start position:0% +b0 or just b0 in + + + align:start position:0% +b0 or just b0 in +fact what that says is plot blue + + align:start position:0% + + + + align:start position:0% + +circles I could have + + align:start position:0% + + + + align:start position:0% + +written in fact I did WR write K plus + + align:start position:0% +written in fact I did WR write K plus + + + align:start position:0% +written in fact I did WR write K plus +and that says black plus + + align:start position:0% +and that says black plus + + + align:start position:0% +and that says black plus +signs and I don't actually remember what + + align:start position:0% +signs and I don't actually remember what + + + align:start position:0% +signs and I don't actually remember what +I did to get the triangles but it's in + + align:start position:0% +I did to get the triangles but it's in + + + align:start position:0% +I did to get the triangles but it's in +the + + align:start position:0% + + + + align:start position:0% + +code and so that's very flexible what + + align:start position:0% +code and so that's very flexible what + + + align:start position:0% +code and so that's very flexible what +you do and as you can see here we get + + align:start position:0% +you do and as you can see here we get + + + align:start position:0% +you do and as you can see here we get +the inside I communicated earlier that + + align:start position:0% +the inside I communicated earlier that + + + align:start position:0% +the inside I communicated earlier that +if you look at East and + + align:start position:0% +if you look at East and + + + align:start position:0% +if you look at East and +West not much difference between this + + align:start position:0% +West not much difference between this + + + align:start position:0% +West not much difference between this +ball and that ball right they seem to be + + align:start position:0% +ball and that ball right they seem to be + + + align:start position:0% +ball and that ball right they seem to be +moving about the same spread the same + + align:start position:0% +moving about the same spread the same + + + align:start position:0% +moving about the same spread the same +outliers but this ball is displaced + + align:start position:0% + + + + align:start position:0% + +North and not surprisingly after 10,000 + + align:start position:0% +North and not surprisingly after 10,000 + + + align:start position:0% +North and not surprisingly after 10,000 +steps you would not expect any of these + + align:start position:0% +steps you would not expect any of these + + + align:start position:0% +steps you would not expect any of these +points to be below + + align:start position:0% +points to be below + + + align:start position:0% +points to be below +zero where you'd expect roughly half of + + align:start position:0% +zero where you'd expect roughly half of + + + align:start position:0% +zero where you'd expect roughly half of +these points to be below + + align:start position:0% + + + + align:start position:0% + +zero and indeed that's about + + align:start position:0% +zero and indeed that's about + + + align:start position:0% +zero and indeed that's about +true and we see here what's going on + + align:start position:0% +true and we see here what's going on + + + align:start position:0% +true and we see here what's going on +that if we look at the mean absolute + + align:start position:0% +that if we look at the mean absolute + + + align:start position:0% +that if we look at the mean absolute +difference in X and Y we see that not a + + align:start position:0% +difference in X and Y we see that not a + + + align:start position:0% +difference in X and Y we see that not a +huge difference between the usual drunk + + align:start position:0% +huge difference between the usual drunk + + + align:start position:0% +huge difference between the usual drunk +and the masochistic drunk there happens + + align:start position:0% +and the masochistic drunk there happens + + + align:start position:0% +and the masochistic drunk there happens +to be a distance but a huge + + align:start position:0% +to be a distance but a huge + + + align:start position:0% +to be a distance but a huge +difference sorry x and x the comparing + + align:start position:0% +difference sorry x and x the comparing + + + align:start position:0% +difference sorry x and x the comparing +the two y values there's a big + + align:start position:0% +the two y values there's a big + + + align:start position:0% +the two y values there's a big +difference as you see here so what's the + + align:start position:0% +difference as you see here so what's the + + + align:start position:0% +difference as you see here so what's the +point of all this it's not to learn + + align:start position:0% +point of all this it's not to learn + + + align:start position:0% +point of all this it's not to learn +about different kinds of drunks it's to + + align:start position:0% +about different kinds of drunks it's to + + + align:start position:0% +about different kinds of drunks it's to +show how by visualization we can get + + align:start position:0% +show how by visualization we can get + + + align:start position:0% +show how by visualization we can get +insight into our data that if I just + + align:start position:0% +insight into our data that if I just + + + align:start position:0% +insight into our data that if I just +printed spreadsheets showing you all of + + align:start position:0% +printed spreadsheets showing you all of + + + align:start position:0% +printed spreadsheets showing you all of +these end points it would be hard to + + align:start position:0% +these end points it would be hard to + + + align:start position:0% +these end points it would be hard to +make sense of what was there so get + + align:start position:0% +make sense of what was there so get + + + align:start position:0% +make sense of what was there so get +accustomed to using plotting to help you + + align:start position:0% +accustomed to using plotting to help you + + + align:start position:0% +accustomed to using plotting to help you +understand + + align:start position:0% +understand + + + align:start position:0% +understand +data all right now let's play a little + + align:start position:0% +data all right now let's play a little + + + align:start position:0% +data all right now let's play a little +bit more with the simul + + align:start position:0% +bit more with the simul + + + align:start position:0% +bit more with the simul +simulation uh we looked at different + + align:start position:0% +simulation uh we looked at different + + + align:start position:0% +simulation uh we looked at different +kinds of drunks let's look at different + + align:start position:0% +kinds of drunks let's look at different + + + align:start position:0% +kinds of drunks let's look at different +kinds of + + align:start position:0% +kinds of + + + align:start position:0% +kinds of +fields so I want to look at a field with + + align:start position:0% +fields so I want to look at a field with + + + align:start position:0% +fields so I want to look at a field with +what we'll call a wormhole in + + align:start position:0% +what we'll call a wormhole in + + + align:start position:0% +what we'll call a wormhole in +it + + align:start position:0% +it + + + align:start position:0% +it +um for those of you of a certain + + align:start position:0% +um for those of you of a certain + + + align:start position:0% +um for those of you of a certain +generation you will recognize the + + align:start position:0% +generation you will recognize the + + + align:start position:0% +generation you will recognize the +Taris so the idea here is that the field + + align:start position:0% +Taris so the idea here is that the field + + + align:start position:0% +Taris so the idea here is that the field +is such that as you wander around it + + align:start position:0% +is such that as you wander around it + + + align:start position:0% +is such that as you wander around it +everything is normal but every once in a + + align:start position:0% +everything is normal but every once in a + + + align:start position:0% +everything is normal but every once in a +while you hit a place where you're + + align:start position:0% +while you hit a place where you're + + + align:start position:0% +while you hit a place where you're +magically transported to a different + + align:start position:0% +magically transported to a different + + + align:start position:0% +magically transported to a different +place so it behaves very + + align:start position:0% +place so it behaves very + + + align:start position:0% +place so it behaves very +peculiarly so let's call this an odd + + align:start position:0% +peculiarly so let's call this an odd + + + align:start position:0% +peculiarly so let's call this an odd +field + + align:start position:0% +field + + + align:start position:0% +field +not odd numbers but odd is in + + align:start position:0% +not odd numbers but odd is in + + + align:start position:0% +not odd numbers but odd is in +strange so it's going to be a subclass + + align:start position:0% +strange so it's going to be a subclass + + + align:start position:0% +strange so it's going to be a subclass +of + + align:start position:0% +of + + + align:start position:0% +of +field uh we're going to have a parameter + + align:start position:0% +field uh we're going to have a parameter + + + align:start position:0% +field uh we're going to have a parameter +that tells us how many wormholes it has + + align:start position:0% +that tells us how many wormholes it has + + + align:start position:0% +that tells us how many wormholes it has +default value of a + + align:start position:0% +default value of a + + + align:start position:0% +default value of a +thousand um and we'll see how we use x + + align:start position:0% +thousand um and we'll see how we use x + + + align:start position:0% +thousand um and we'll see how we use x +range and Y range + + align:start position:0% +range and Y range + + + align:start position:0% +range and Y range +shortly so what are the first thing we + + align:start position:0% +shortly so what are the first thing we + + + align:start position:0% +shortly so what are the first thing we +do well we'll call field underbar and it + + align:start position:0% +do well we'll call field underbar and it + + + align:start position:0% +do well we'll call field underbar and it +to initialize the field in the usual way + + align:start position:0% +to initialize the field in the usual way + + + align:start position:0% +to initialize the field in the usual way +and then we're going to create a + + align:start position:0% +and then we're going to create a + + + align:start position:0% +and then we're going to create a +dictionary of + + align:start position:0% +dictionary of + + + align:start position:0% +dictionary of +wormholes so for w in the range number + + align:start position:0% +wormholes so for w in the range number + + + align:start position:0% +wormholes so for w in the range number +of + + align:start position:0% +of + + + align:start position:0% +of +wormholes I'm going to choose a random X + + align:start position:0% +wormholes I'm going to choose a random X + + + align:start position:0% +wormholes I'm going to choose a random X +and a random + + align:start position:0% +and a random + + + align:start position:0% +and a random +Y in X range minus X range to plus X + + align:start position:0% +Y in X range minus X range to plus X + + + align:start position:0% +Y in X range minus X range to plus X +range minus y range to Y + + align:start position:0% +range minus y range to Y + + + align:start position:0% +range minus y range to Y +range so this is going to be where the + + align:start position:0% +range so this is going to be where the + + + align:start position:0% +range so this is going to be where the +wormholes are located and then for each + + align:start position:0% +wormholes are located and then for each + + + align:start position:0% +wormholes are located and then for each +of those I'm going to get a random + + align:start position:0% +of those I'm going to get a random + + + align:start position:0% +of those I'm going to get a random +location where you're in some sense + + align:start position:0% +location where you're in some sense + + + align:start position:0% +location where you're in some sense +teleported to if you enter the + + align:start position:0% +teleported to if you enter the + + + align:start position:0% +teleported to if you enter the +Wormhole so here we're using random to + + align:start position:0% +Wormhole so here we're using random to + + + align:start position:0% +Wormhole so here we're using random to +get random integers we've seen that + + align:start position:0% +get random integers we've seen that + + + align:start position:0% +get random integers we've seen that +before and so the new location will be + + align:start position:0% +before and so the new location will be + + + align:start position:0% +before and so the new location will be +the location of the new X and the new + + align:start position:0% +the location of the new X and the new + + + align:start position:0% +the location of the new X and the new +Y and we're going to update this + + align:start position:0% +Y and we're going to update this + + + align:start position:0% +Y and we're going to update this +dictionary of wormholes to say that + + align:start position:0% +dictionary of wormholes to say that + + + align:start position:0% +dictionary of wormholes to say that +paired with the location + + align:start position:0% +paired with the location + + + align:start position:0% +paired with the location +XY is new + + align:start position:0% + + + + align:start position:0% + +Lo + + align:start position:0% + + + + align:start position:0% + +now when we move the drunk and again + + align:start position:0% +now when we move the drunk and again + + + align:start position:0% +now when we move the drunk and again +this is just changing we're overriding + + align:start position:0% +this is just changing we're overriding + + + align:start position:0% +this is just changing we're overriding +move drunk so we're overriding one of + + align:start position:0% +move drunk so we're overriding one of + + + align:start position:0% +move drunk so we're overriding one of +the methods in + + align:start position:0% +the methods in + + + align:start position:0% +the methods in +field so field. mov + + align:start position:0% +field so field. mov + + + align:start position:0% +field so field. mov +drunk will take a self and a + + align:start position:0% + + + + align:start position:0% + +drunk it's going to get the x value the + + align:start position:0% +drunk it's going to get the x value the + + + align:start position:0% +drunk it's going to get the x value the +yalue and if that is in the + + align:start position:0% +yalue and if that is in the + + + align:start position:0% +yalue and if that is in the +wormholes it's going to move the drunk + + align:start position:0% +wormholes it's going to move the drunk + + + align:start position:0% +wormholes it's going to move the drunk +to the location of associated with that + + align:start position:0% +to the location of associated with that + + + align:start position:0% +to the location of associated with that +Wormhole so we move a drunk and if the + + align:start position:0% +Wormhole so we move a drunk and if the + + + align:start position:0% +Wormhole so we move a drunk and if the +drunk ends up being in the + + align:start position:0% +drunk ends up being in the + + + align:start position:0% +drunk ends up being in the +Wormhole he gets transported so we're + + align:start position:0% +Wormhole he gets transported so we're + + + align:start position:0% +Wormhole he gets transported so we're +using field. mov drunk so notice that + + align:start position:0% +using field. mov drunk so notice that + + + align:start position:0% +using field. mov drunk so notice that +we're using the move drunk of the super + + align:start position:0% +we're using the move drunk of the super + + + align:start position:0% +we're using the move drunk of the super +class even though we're overriding it + + align:start position:0% +class even though we're overriding it + + + align:start position:0% +class even though we're overriding it +here because we've overridden it here I + + align:start position:0% +here because we've overridden it here I + + + align:start position:0% +here because we've overridden it here I +have to say field dot to indicate I want + + align:start position:0% +have to say field dot to indicate I want + + + align:start position:0% +have to say field dot to indicate I want +the one from the super class not the + + align:start position:0% +the one from the super class not the + + + align:start position:0% +the one from the super class not the +subass and then we're doing something + + align:start position:0% +subass and then we're doing something + + + align:start position:0% +subass and then we're doing something +peculiar after the + + align:start position:0% + + + + align:start position:0% + +move so interestingly here I've taken I + + align:start position:0% +move so interestingly here I've taken I + + + align:start position:0% +move so interestingly here I've taken I +think a usual drunk and plotted the + + align:start position:0% +think a usual drunk and plotted the + + + align:start position:0% +think a usual drunk and plotted the +usual drunk on a + + align:start position:0% +usual drunk on a + + + align:start position:0% +usual drunk on a +walk of 500 steps one walk and shown all + + align:start position:0% +walk of 500 steps one walk and shown all + + + align:start position:0% +walk of 500 steps one walk and shown all +the places the drunk + + align:start position:0% +the places the drunk + + + align:start position:0% +the places the drunk +visited so we've seen three kinds of + + align:start position:0% +visited so we've seen three kinds of + + + align:start position:0% +visited so we've seen three kinds of +plots one showing how far the drunk + + align:start position:0% +plots one showing how far the drunk + + + align:start position:0% +plots one showing how far the drunk +would get at different length walks + + align:start position:0% +would get at different length walks + + + align:start position:0% +would get at different length walks +one + + align:start position:0% +one + + + align:start position:0% +one +showing um all the places the drunk + + align:start position:0% +showing um all the places the drunk + + + align:start position:0% +showing um all the places the drunk +would end up with with many walks of the + + align:start position:0% +would end up with with many walks of the + + + align:start position:0% +would end up with with many walks of the +same length and here a single walk all + + align:start position:0% +same length and here a single walk all + + + align:start position:0% +same length and here a single walk all +the places the drunk + + align:start position:0% +the places the drunk + + + align:start position:0% +the places the drunk +visits and as you can see the wormholes + + align:start position:0% +visits and as you can see the wormholes + + + align:start position:0% +visits and as you can see the wormholes +produce a profound + + align:start position:0% +produce a profound + + + align:start position:0% +produce a profound +effect in this case on on where the + + align:start position:0% +effect in this case on on where the + + + align:start position:0% +effect in this case on on where the +drunks end + + align:start position:0% +drunks end + + + align:start position:0% +drunks end +up and again you have the code you can + + align:start position:0% +up and again you have the code you can + + + align:start position:0% +up and again you have the code you can +run this yourself and simulate it and + + align:start position:0% +run this yourself and simulate it and + + + align:start position:0% +run this yourself and simulate it and +see what you go and I think set random. + + align:start position:0% +see what you go and I think set random. + + + align:start position:0% +see what you go and I think set random. +seed to zero in each of the simulations + + align:start position:0% +seed to zero in each of the simulations + + + align:start position:0% +seed to zero in each of the simulations +in the code but you should have play + + align:start position:0% +in the code but you should have play + + + align:start position:0% +in the code but you should have play +with it change it to just see that + + align:start position:0% +with it change it to just see that + + + align:start position:0% +with it change it to just see that +you'll actually get different results + + align:start position:0% +you'll actually get different results + + + align:start position:0% +you'll actually get different results +with different + + align:start position:0% +with different + + + align:start position:0% +with different +seeds all + + align:start position:0% +seeds all + + + align:start position:0% +seeds all +right let me summarize + + align:start position:0% +right let me summarize + + + align:start position:0% +right let me summarize +here and say the point of going through + + align:start position:0% +here and say the point of going through + + + align:start position:0% +here and say the point of going through +these random walks is not the + + align:start position:0% +these random walks is not the + + + align:start position:0% +these random walks is not the +simulations themselves but how we built + + align:start position:0% +simulations themselves but how we built + + + align:start position:0% +simulations themselves but how we built +them + + align:start position:0% +them + + + align:start position:0% +them +that we started by defining the + + align:start position:0% +that we started by defining the + + + align:start position:0% +that we started by defining the +classes we then built functions + + align:start position:0% +classes we then built functions + + + align:start position:0% +classes we then built functions +corresponding to one trial multiple + + align:start position:0% +corresponding to one trial multiple + + + align:start position:0% +corresponding to one trial multiple +trials and reported the + + align:start position:0% +trials and reported the + + + align:start position:0% +trials and reported the +results and then made a set of + + align:start position:0% +results and then made a set of + + + align:start position:0% +results and then made a set of +incremental changes to the simulation so + + align:start position:0% +incremental changes to the simulation so + + + align:start position:0% +incremental changes to the simulation so +that we could investigate different + + align:start position:0% +that we could investigate different + + + align:start position:0% +that we could investigate different +questions um so we started with a simple + + align:start position:0% +questions um so we started with a simple + + + align:start position:0% +questions um so we started with a simple +simulation with just the usual drunk and + + align:start position:0% +simulation with just the usual drunk and + + + align:start position:0% +simulation with just the usual drunk and +the simple field + + align:start position:0% +the simple field + + + align:start position:0% +the simple field +and we noticed it didn't + + align:start position:0% +and we noticed it didn't + + + align:start position:0% +and we noticed it didn't +work how did we know it well not because + + align:start position:0% +work how did we know it well not because + + + align:start position:0% +work how did we know it well not because +when we did the full simulation we had + + align:start position:0% +when we did the full simulation we had + + + align:start position:0% +when we did the full simulation we had +great Insight right I probably could + + align:start position:0% +great Insight right I probably could + + + align:start position:0% +great Insight right I probably could +have fooled half of you and convinced + + align:start position:0% +have fooled half of you and convinced + + + align:start position:0% +have fooled half of you and convinced +you that that was a reasonable answer + + align:start position:0% +you that that was a reasonable answer + + + align:start position:0% +you that that was a reasonable answer +but as soon as we went into the sanity + + align:start position:0% +but as soon as we went into the sanity + + + align:start position:0% +but as soon as we went into the sanity +check where we knew the answer we could + + align:start position:0% +check where we knew the answer we could + + + align:start position:0% +check where we knew the answer we could +know something was + + align:start position:0% +know something was + + + align:start position:0% +know something was +wrong and then we went and we fixed it + + align:start position:0% +wrong and then we went and we fixed it + + + align:start position:0% +wrong and then we went and we fixed it +and then we went and we elaborated it at + + align:start position:0% +and then we went and we elaborated it at + + + align:start position:0% +and then we went and we elaborated it at +a step of of a time I first got a more + + align:start position:0% +a step of of a time I first got a more + + + align:start position:0% +a step of of a time I first got a more +sophistic I shouldn't say sophisticated + + align:start position:0% +sophistic I shouldn't say sophisticated + + + align:start position:0% +sophistic I shouldn't say sophisticated +a different kind of + + align:start position:0% +a different kind of + + + align:start position:0% +a different kind of +drunk and then we went to a different + + align:start position:0% +drunk and then we went to a different + + + align:start position:0% +drunk and then we went to a different +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +field + + align:start position:0% +field + + + align:start position:0% +field +finally we spent time showing how to use + + align:start position:0% +finally we spent time showing how to use + + + align:start position:0% +finally we spent time showing how to use +plots to get an insight and in the + + align:start position:0% +plots to get an insight and in the + + + align:start position:0% +plots to get an insight and in the +remaining few minutes of the class I + + align:start position:0% +remaining few minutes of the class I + + + align:start position:0% +remaining few minutes of the class I +want to go back and and show you some of + + align:start position:0% +want to go back and and show you some of + + + align:start position:0% +want to go back and and show you some of +the plotting + + align:start position:0% + + + + align:start position:0% + +commands to show you how these plots + + align:start position:0% +commands to show you how these plots + + + align:start position:0% +commands to show you how these plots +were + + align:start position:0% +were + + + align:start position:0% +were +produced + + align:start position:0% + + + + align:start position:0% + +so one of the things I did since I knew + + align:start position:0% +so one of the things I did since I knew + + + align:start position:0% +so one of the things I did since I knew +I was going to be producing a lot of + + align:start position:0% +I was going to be producing a lot of + + + align:start position:0% +I was going to be producing a lot of +different plots I decided I would + + align:start position:0% +different plots I decided I would + + + align:start position:0% +different plots I decided I would +actually not spend time worrying about + + align:start position:0% +actually not spend time worrying about + + + align:start position:0% +actually not spend time worrying about +what kind of markers the those are the + + align:start position:0% +what kind of markers the those are the + + + align:start position:0% +what kind of markers the those are the +things like the triangles and the plus + + align:start position:0% +things like the triangles and the plus + + + align:start position:0% +things like the triangles and the plus +sign or what colors for each one + + align:start position:0% +sign or what colors for each one + + + align:start position:0% +sign or what colors for each one +individually but instead I'd set up a + + align:start position:0% +individually but instead I'd set up a + + + align:start position:0% +individually but instead I'd set up a +style iterator that would just return a + + align:start position:0% +style iterator that would just return a + + + align:start position:0% +style iterator that would just return a +bunch of different styles so once and + + align:start position:0% +bunch of different styles so once and + + + align:start position:0% +bunch of different styles so once and +for all I could Define n + + align:start position:0% +for all I could Define n + + + align:start position:0% +for all I could Define n +Styles and then when I want to plot a + + align:start position:0% +Styles and then when I want to plot a + + + align:start position:0% +Styles and then when I want to plot a +new kind of drunk I would just call the + + align:start position:0% +new kind of drunk I would just call the + + + align:start position:0% +new kind of drunk I would just call the +style iterator to get the next + + align:start position:0% +style iterator to get the next + + + align:start position:0% +style iterator to get the next +style so this is a fairly common kind of + + align:start position:0% +style so this is a fairly common kind of + + + align:start position:0% +style so this is a fairly common kind of +Paradigm to say that I just want to do + + align:start position:0% +Paradigm to say that I just want to do + + + align:start position:0% +Paradigm to say that I just want to do +this one once and for all I don't want + + align:start position:0% +this one once and for all I don't want + + + align:start position:0% +this one once and for all I don't want +to have to go through each time I do + + align:start position:0% + + + + align:start position:0% + +this so what do the Styles look + + align:start position:0% + + + + align:start position:0% + +like let me + + align:start position:0% +like let me + + + align:start position:0% +like let me +just get this window + + align:start position:0% + + + + align:start position:0% + +oh so + + align:start position:0% +oh so + + + align:start position:0% +oh so +here it + + align:start position:0% + + + + align:start position:0% + +is I said there going to be three styles + + align:start position:0% +is I said there going to be three styles + + + align:start position:0% +is I said there going to be three styles +that I'm going to iterate through style + + align:start position:0% +that I'm going to iterate through style + + + align:start position:0% +that I'm going to iterate through style +one is going to be a uh an M I guess + + align:start position:0% +one is going to be a uh an M I guess + + + align:start position:0% +one is going to be a uh an M I guess +that's maroon with a line a blue with a + + align:start position:0% +that's maroon with a line a blue with a + + + align:start position:0% +that's maroon with a line a blue with a +uh dashed line and green with a line + + align:start position:0% +uh dashed line and green with a line + + + align:start position:0% +uh dashed line and green with a line +with a comma and a + + align:start position:0% +with a comma and a + + + align:start position:0% +with a comma and a +minus + + align:start position:0% +minus + + + align:start position:0% +minus +sign so these are called the Styles and + + align:start position:0% +sign so these are called the Styles and + + + align:start position:0% +sign so these are called the Styles and +you can control the marker if you have a + + align:start position:0% +you can control the marker if you have a + + + align:start position:0% +you can control the marker if you have a +marker uh you can control the line you + + align:start position:0% +marker uh you can control the line you + + + align:start position:0% +marker uh you can control the line you +can control the + + align:start position:0% +can control the + + + align:start position:0% +can control the +color also you can control the size you + + align:start position:0% +color also you can control the size you + + + align:start position:0% +color also you can control the size you +can give the sizes of all these things + + align:start position:0% +can give the sizes of all these things + + + align:start position:0% +can give the sizes of all these things +what you'll see is when you look at the + + align:start position:0% +what you'll see is when you look at the + + + align:start position:0% +what you'll see is when you look at the +code is I don't like the default + + align:start position:0% +code is I don't like the default + + + align:start position:0% +code is I don't like the default +Styles things because when they show up + + align:start position:0% +Styles things because when they show up + + + align:start position:0% +Styles things because when they show up +on the screen they're too small so + + align:start position:0% +on the screen they're too small so + + + align:start position:0% +on the screen they're too small so +there's something called RC + + align:start position:0% +there's something called RC + + + align:start position:0% +there's something called RC +params those of you who are Unix hackers + + align:start position:0% +params those of you who are Unix hackers + + + align:start position:0% +params those of you who are Unix hackers +can maybe guess where that name come + + align:start position:0% +can maybe guess where that name come + + + align:start position:0% +can maybe guess where that name come +came from and I've just said a bunch of + + align:start position:0% +came from and I've just said a bunch of + + + align:start position:0% +came from and I've just said a bunch of +things like my default line width will + + align:start position:0% +things like my default line width will + + + align:start position:0% +things like my default line width will +be four points the size for the titles + + align:start position:0% +be four points the size for the titles + + + align:start position:0% +be four points the size for the titles +will be 20 you can put titles on the + + align:start position:0% +will be 20 you can put titles on the + + + align:start position:0% +will be 20 you can put titles on the +graphs + + align:start position:0% +graphs + + + align:start position:0% +graphs +um various kinds of things again once + + align:start position:0% +um various kinds of things again once + + + align:start position:0% +um various kinds of things again once +and for all trying to set some of these + + align:start position:0% +and for all trying to set some of these + + + align:start position:0% +and for all trying to set some of these +parameters so they get used over and + + align:start position:0% +parameters so they get used over and + + + align:start position:0% +parameters so they get used over and +over + + align:start position:0% + + + + align:start position:0% + +again and then finally down + + align:start position:0% +again and then finally down + + + align:start position:0% +again and then finally down +here you'll see that I did things like + + align:start position:0% +here you'll see that I did things like + + + align:start position:0% +here you'll see that I did things like +you want to put titles on the + + align:start position:0% +you want to put titles on the + + + align:start position:0% +you want to put titles on the +slides so on the graph so here's the + + align:start position:0% +slides so on the graph so here's the + + + align:start position:0% +slides so on the graph so here's the +location at end of walk title is just a + + align:start position:0% +location at end of walk title is just a + + + align:start position:0% +location at end of walk title is just a +string you want to label your X and Y + + align:start position:0% +string you want to label your X and Y + + + align:start position:0% +string you want to label your X and Y +axis so I've labeled labeled them here + + align:start position:0% +axis so I've labeled labeled them here + + + align:start position:0% +axis so I've labeled labeled them here +and here I've said where I want the + + align:start position:0% +and here I've said where I want the + + + align:start position:0% +and here I've said where I want the +legend to appear in the lower + + align:start position:0% +legend to appear in the lower + + + align:start position:0% +legend to appear in the lower +Center um I've also set the Y limits and + + align:start position:0% +Center um I've also set the Y limits and + + + align:start position:0% +Center um I've also set the Y limits and +the X limits on the axis because I + + align:start position:0% +the X limits on the axis because I + + + align:start position:0% +the X limits on the axis because I +wanted a little extra room otherwise by + + align:start position:0% +wanted a little extra room otherwise by + + + align:start position:0% +wanted a little extra room otherwise by +default it will plant put points right + + align:start position:0% +default it will plant put points right + + + align:start position:0% +default it will plant put points right +on the axes which I find hard to + + align:start position:0% +on the axes which I find hard to + + + align:start position:0% +on the axes which I find hard to +read anyway I don't the point here is + + align:start position:0% +read anyway I don't the point here is + + + align:start position:0% +read anyway I don't the point here is +not that you understand all of this + + align:start position:0% +not that you understand all of this + + + align:start position:0% +not that you understand all of this +instantaneously the point I want to + + align:start position:0% +instantaneously the point I want to + + + align:start position:0% +instantaneously the point I want to +communicate is that it's very flexible + + align:start position:0% +communicate is that it's very flexible + + + align:start position:0% +communicate is that it's very flexible +and so if you decide you don't like the + + align:start position:0% +and so if you decide you don't like the + + + align:start position:0% +and so if you decide you don't like the +way a plot looks and you want to change + + align:start position:0% +way a plot looks and you want to change + + + align:start position:0% +way a plot looks and you want to change +it and you know what you want it to look + + align:start position:0% +it and you know what you want it to look + + + align:start position:0% +it and you know what you want it to look +like there's almost surely a way to make + + align:start position:0% +like there's almost surely a way to make + + + align:start position:0% +like there's almost surely a way to make +it do that so don't don't despair you + + align:start position:0% +it do that so don't don't despair you + + + align:start position:0% +it do that so don't don't despair you +can look at the references I gave + + align:start position:0% +can look at the references I gave + + + align:start position:0% +can look at the references I gave +earlier and figure that + + align:start position:0% +earlier and figure that + + + align:start position:0% +earlier and figure that +out okay next lecture we're going to + + align:start position:0% +out okay next lecture we're going to + + + align:start position:0% +out okay next lecture we're going to +move on no more random walks we'll look + + align:start position:0% +move on no more random walks we'll look + + + align:start position:0% +move on no more random walks we'll look +at simulating other things and in + + align:start position:0% +at simulating other things and in + + + align:start position:0% +at simulating other things and in +particular we'll look at the question of + + align:start position:0% +particular we'll look at the question of + + + align:start position:0% +particular we'll look at the question of +how believable is a + + align:start position:0% +how believable is a + + + align:start position:0% +how believable is a +simulation see you Wednesday if the + + align:start position:0% +simulation see you Wednesday if the + + + align:start position:0% +simulation see you Wednesday if the +world do not come to an + + align:start position:0% + + + + align:start position:0% + +end \ No newline at end of file diff --git a/7ZlzvS7YoSM.txt b/7ZlzvS7YoSM.txt new file mode 100644 index 0000000000000000000000000000000000000000..d65f12db5a73453d2ef9e6ed6851608e7efac4aa --- /dev/null +++ b/7ZlzvS7YoSM.txt @@ -0,0 +1,8851 @@ +align:start position:0% + +so let's get started um so I'm going to + + align:start position:0% +so let's get started um so I'm going to + + + align:start position:0% +so let's get started um so I'm going to +finish up um energy today and then we're + + align:start position:0% +finish up um energy today and then we're + + + align:start position:0% +finish up um energy today and then we're +going to begin sort of + + align:start position:0% +going to begin sort of + + + align:start position:0% +going to begin sort of +section more or less we'll call it + + align:start position:0% +section more or less we'll call it + + + align:start position:0% +section more or less we'll call it +molecular biology but it's sort of + + align:start position:0% +molecular biology but it's sort of + + + align:start position:0% +molecular biology but it's sort of +dealing with the issues that revolve + + align:start position:0% +dealing with the issues that revolve + + + align:start position:0% +dealing with the issues that revolve +around the discovery that DNA was the + + align:start position:0% +around the discovery that DNA was the + + + align:start position:0% +around the discovery that DNA was the +genetic material and then working + + align:start position:0% +genetic material and then working + + + align:start position:0% +genetic material and then working +through how people understood how + + align:start position:0% +through how people understood how + + + align:start position:0% +through how people understood how +information got from the DNA into + + align:start position:0% +information got from the DNA into + + + align:start position:0% +information got from the DNA into +everything else how things were + + align:start position:0% +everything else how things were + + + align:start position:0% +everything else how things were +regulated there were incredible + + align:start position:0% +regulated there were incredible + + + align:start position:0% +regulated there were incredible +large number of important discoveries uh + + align:start position:0% +large number of important discoveries uh + + + align:start position:0% +large number of important discoveries uh +that form the foundation of how we think + + align:start position:0% +that form the foundation of how we think + + + align:start position:0% +that form the foundation of how we think +about biology that are going to come out + + align:start position:0% +about biology that are going to come out + + + align:start position:0% +about biology that are going to come out +in this next section but before I do + + align:start position:0% +in this next section but before I do + + + align:start position:0% +in this next section but before I do +that I just want to I want to finish up + + align:start position:0% +that I just want to I want to finish up + + + align:start position:0% +that I just want to I want to finish up +this this section that uh I'd uh talk to + + align:start position:0% +this this section that uh I'd uh talk to + + + align:start position:0% +this this section that uh I'd uh talk to +you about uh about energy and I hope as + + align:start position:0% +you about uh about energy and I hope as + + + align:start position:0% +you about uh about energy and I hope as +we go along here you're going to see how + + align:start position:0% +we go along here you're going to see how + + + align:start position:0% +we go along here you're going to see how +some of these sort of disperate parts of + + align:start position:0% +some of these sort of disperate parts of + + + align:start position:0% +some of these sort of disperate parts of +the course begin to come together almost + + align:start position:0% +the course begin to come together almost + + + align:start position:0% +the course begin to come together almost +everything we're going to be talking + + align:start position:0% +everything we're going to be talking + + + align:start position:0% +everything we're going to be talking +about now is going to be needing energy + + align:start position:0% +about now is going to be needing energy + + + align:start position:0% +about now is going to be needing energy +such as replicating DNA or making + + align:start position:0% +such as replicating DNA or making + + + align:start position:0% +such as replicating DNA or making +proteins and all sorts of things and + + align:start position:0% +proteins and all sorts of things and + + + align:start position:0% +proteins and all sorts of things and +those are driven by ultimately by ATP + + align:start position:0% +those are driven by ultimately by ATP + + + align:start position:0% +those are driven by ultimately by ATP +and what I've been trying to talk to you + + align:start position:0% +and what I've been trying to talk to you + + + align:start position:0% +and what I've been trying to talk to you +about the last lecture or two is how the + + align:start position:0% +about the last lecture or two is how the + + + align:start position:0% +about the last lecture or two is how the +cell gets the ATP that the energy money + + align:start position:0% +cell gets the ATP that the energy money + + + align:start position:0% +cell gets the ATP that the energy money +that it needs to make things we talked + + align:start position:0% +that it needs to make things we talked + + + align:start position:0% +that it needs to make things we talked +through glycolosis this Ancient Ancient + + align:start position:0% +through glycolosis this Ancient Ancient + + + align:start position:0% +through glycolosis this Ancient Ancient +way of getting a couple of atps out of a + + align:start position:0% +way of getting a couple of atps out of a + + + align:start position:0% +way of getting a couple of atps out of a +molecule of sugar so well embedded in in + + align:start position:0% +molecule of sugar so well embedded in in + + + align:start position:0% +molecule of sugar so well embedded in in +uh our genetic makeup it's in almost all + + align:start position:0% +uh our genetic makeup it's in almost all + + + align:start position:0% +uh our genetic makeup it's in almost all +organisms and then I talked last lecture + + align:start position:0% +organisms and then I talked last lecture + + + align:start position:0% +organisms and then I talked last lecture +about this other principle which must + + align:start position:0% +about this other principle which must + + + align:start position:0% +about this other principle which must +have come up very very early in + + align:start position:0% +have come up very very early in + + + align:start position:0% +have come up very very early in +evolution again it's used by all + + align:start position:0% +evolution again it's used by all + + + align:start position:0% +evolution again it's used by all +organisms and that's the principle of + + align:start position:0% +organisms and that's the principle of + + + align:start position:0% +organisms and that's the principle of +capturing the energy that's inherent in + + align:start position:0% +capturing the energy that's inherent in + + + align:start position:0% +capturing the energy that's inherent in +a proton gradient across a membrane and + + align:start position:0% +a proton gradient across a membrane and + + + align:start position:0% +a proton gradient across a membrane and +I talked to you then about a couple of + + align:start position:0% +I talked to you then about a couple of + + + align:start position:0% +I talked to you then about a couple of +uh the idea then the way it worked was + + align:start position:0% +uh the idea then the way it worked was + + + align:start position:0% +uh the idea then the way it worked was +that the cell would have something in + + align:start position:0% +that the cell would have something in + + + align:start position:0% +that the cell would have something in +its me membrane that would be a proton + + align:start position:0% +its me membrane that would be a proton + + + align:start position:0% +its me membrane that would be a proton +pump and it would pump the the proton + + align:start position:0% +pump and it would pump the the proton + + + align:start position:0% +pump and it would pump the the proton +from one side of the membrane to the + + align:start position:0% +from one side of the membrane to the + + + align:start position:0% +from one side of the membrane to the +other if it's so it's working against + + align:start position:0% +other if it's so it's working against + + + align:start position:0% +other if it's so it's working against +the gradient so it's doing energy so + + align:start position:0% +the gradient so it's doing energy so + + + align:start position:0% +the gradient so it's doing energy so +there's a couple of different so the + + align:start position:0% +there's a couple of different so the + + + align:start position:0% +there's a couple of different so the +energy needs to be provided it could be + + align:start position:0% +energy needs to be provided it could be + + + align:start position:0% +energy needs to be provided it could be +provided + + align:start position:0% +provided + + + align:start position:0% +provided +by by some kind of light energy and + + align:start position:0% +by by some kind of light energy and + + + align:start position:0% +by by some kind of light energy and +that's what drives photosynthesis I'll + + align:start position:0% +that's what drives photosynthesis I'll + + + align:start position:0% +that's what drives photosynthesis I'll +say a few words about that or in the + + align:start position:0% +say a few words about that or in the + + + align:start position:0% +say a few words about that or in the +case of uh of + + align:start position:0% + + + + align:start position:0% + +respiration with the oxidative + + align:start position:0% +respiration with the oxidative + + + align:start position:0% +respiration with the oxidative +phosphorilation I showed you how is the + + align:start position:0% +phosphorilation I showed you how is the + + + align:start position:0% +phosphorilation I showed you how is the +electrons sort of descend in stepwise + + align:start position:0% +electrons sort of descend in stepwise + + + align:start position:0% +electrons sort of descend in stepwise +fashion uh down + + align:start position:0% +fashion uh down + + + align:start position:0% +fashion uh down +um uh from one state to another they + + align:start position:0% +um uh from one state to another they + + + align:start position:0% +um uh from one state to another they +there's energy given off free energy is + + align:start position:0% +there's energy given off free energy is + + + align:start position:0% +there's energy given off free energy is +is available and that can be used to + + align:start position:0% +is available and that can be used to + + + align:start position:0% +is available and that can be used to +power the pump and once the proton + + align:start position:0% +power the pump and once the proton + + + align:start position:0% +power the pump and once the proton +gradient is is uh made then the cells + + align:start position:0% +gradient is is uh made then the cells + + + align:start position:0% +gradient is is uh made then the cells +can turn it around and make use that the + + align:start position:0% +can turn it around and make use that the + + + align:start position:0% +can turn it around and make use that the +energy that's in that proton uh gradient + + align:start position:0% +energy that's in that proton uh gradient + + + align:start position:0% +energy that's in that proton uh gradient +to make ATP so in respir ation remember + + align:start position:0% +to make ATP so in respir ation remember + + + align:start position:0% +to make ATP so in respir ation remember +the trick was then to take those two + + align:start position:0% +the trick was then to take those two + + + align:start position:0% +the trick was then to take those two +pyrates burn them as far as all the way + + align:start position:0% +pyrates burn them as far as all the way + + + align:start position:0% +pyrates burn them as far as all the way +down to carbon dioxide and water make as + + align:start position:0% +down to carbon dioxide and water make as + + + align:start position:0% +down to carbon dioxide and water make as +many atps and nadhs as you could then + + align:start position:0% +many atps and nadhs as you could then + + + align:start position:0% +many atps and nadhs as you could then +take the nadh's use them to make a + + align:start position:0% +take the nadh's use them to make a + + + align:start position:0% +take the nadh's use them to make a +proton gradient and eventually if you + + align:start position:0% +proton gradient and eventually if you + + + align:start position:0% +proton gradient and eventually if you +will convert everything into ATP so + + align:start position:0% +will convert everything into ATP so + + + align:start position:0% +will convert everything into ATP so +you've got it as energy + + align:start position:0% +you've got it as energy + + + align:start position:0% +you've got it as energy +um our our cells do it that part + + align:start position:0% +um our our cells do it that part + + + align:start position:0% +um our our cells do it that part +respiration and the oxidative + + align:start position:0% +respiration and the oxidative + + + align:start position:0% +respiration and the oxidative +phosphorilation is done in mitochondria + + align:start position:0% +phosphorilation is done in mitochondria + + + align:start position:0% +phosphorilation is done in mitochondria +when said was um were sort of came from + + align:start position:0% +when said was um were sort of came from + + + align:start position:0% +when said was um were sort of came from +bacteria that were captured at some + + align:start position:0% +bacteria that were captured at some + + + align:start position:0% +bacteria that were captured at some +point here's a picture of a + + align:start position:0% +point here's a picture of a + + + align:start position:0% +point here's a picture of a +mitochondrian still looks more or less + + align:start position:0% +mitochondrian still looks more or less + + + align:start position:0% +mitochondrian still looks more or less +like a bacterium and I showed you the + + align:start position:0% +like a bacterium and I showed you the + + + align:start position:0% +like a bacterium and I showed you the +little Parts um that are in there it was + + align:start position:0% +little Parts um that are in there it was + + + align:start position:0% +little Parts um that are in there it was +funny right after lecture I went back to + + align:start position:0% +funny right after lecture I went back to + + + align:start position:0% +funny right after lecture I went back to +my lab I picked up a recent issue of + + align:start position:0% +my lab I picked up a recent issue of + + + align:start position:0% +my lab I picked up a recent issue of +Science and I opened up uh to a page + + align:start position:0% +Science and I opened up uh to a page + + + align:start position:0% +Science and I opened up uh to a page +that said something about rats that had + + align:start position:0% +that said something about rats that had + + + align:start position:0% +that said something about rats that had +been uh bred uh to be very very poor at + + align:start position:0% +been uh bred uh to be very very poor at + + + align:start position:0% +been uh bred uh to be very very poor at +aerobic exercise size and it went on to + + align:start position:0% +aerobic exercise size and it went on to + + + align:start position:0% +aerobic exercise size and it went on to +talk about all the health problems they + + align:start position:0% +talk about all the health problems they + + + align:start position:0% +talk about all the health problems they +had and the sentence then there's a + + align:start position:0% +had and the sentence then there's a + + + align:start position:0% +had and the sentence then there's a +sentence in there that they think the + + align:start position:0% +sentence in there that they think the + + + align:start position:0% +sentence in there that they think the +underlying cause is by breeding these + + align:start position:0% +underlying cause is by breeding these + + + align:start position:0% +underlying cause is by breeding these +rats and selecting for rats that are + + align:start position:0% +rats and selecting for rats that are + + + align:start position:0% +rats and selecting for rats that are +poor at uh doing aerobic exercise what + + align:start position:0% +poor at uh doing aerobic exercise what + + + align:start position:0% +poor at uh doing aerobic exercise what +they think it all stems from is is + + align:start position:0% +they think it all stems from is is + + + align:start position:0% +they think it all stems from is is +having very inefficient mitochondria + + align:start position:0% +having very inefficient mitochondria + + + align:start position:0% +having very inefficient mitochondria +that don't work nearly as well and that + + align:start position:0% +that don't work nearly as well and that + + + align:start position:0% +that don't work nearly as well and that +would make a lot of sense I was going to + + align:start position:0% +would make a lot of sense I was going to + + + align:start position:0% +would make a lot of sense I was going to +scan that article but it didn't quite we + + align:start position:0% +scan that article but it didn't quite we + + + align:start position:0% +scan that article but it didn't quite we +had some technical issues this morning + + align:start position:0% +had some technical issues this morning + + + align:start position:0% +had some technical issues this morning +maybe I can show it to you next lecture + + align:start position:0% +maybe I can show it to you next lecture + + + align:start position:0% +maybe I can show it to you next lecture +okay so the one last thing then that I + + align:start position:0% +okay so the one last thing then that I + + + align:start position:0% +okay so the one last thing then that I +want to do is I want to say a few words + + align:start position:0% +want to do is I want to say a few words + + + align:start position:0% +want to do is I want to say a few words +about um the photosynthesis because that + + align:start position:0% +about um the photosynthesis because that + + + align:start position:0% +about um the photosynthesis because that +actually preceded respiration + + align:start position:0% +actually preceded respiration + + + align:start position:0% +actually preceded respiration +respiration couldn't evolve until there + + align:start position:0% +respiration couldn't evolve until there + + + align:start position:0% +respiration couldn't evolve until there +was oxygen in the atmosphere so probably + + align:start position:0% +was oxygen in the atmosphere so probably + + + align:start position:0% +was oxygen in the atmosphere so probably +the first use or one of certainly one of + + align:start position:0% +the first use or one of certainly one of + + + align:start position:0% +the first use or one of certainly one of +the first uses of the of of the proton + + align:start position:0% +the first uses of the of of the proton + + + align:start position:0% +the first uses of the of of the proton +gradient happened in this scale of of + + align:start position:0% +gradient happened in this scale of of + + + align:start position:0% +gradient happened in this scale of of +evolution in put here somewhere maybe + + align:start position:0% +evolution in put here somewhere maybe + + + align:start position:0% +evolution in put here somewhere maybe +3.4 billion years ago or so when what I + + align:start position:0% +3.4 billion years ago or so when what I + + + align:start position:0% +3.4 billion years ago or so when what I +had called uh + + align:start position:0% + + + + align:start position:0% + +photosynthesis + + align:start position:0% + + + + align:start position:0% + +release one on on day one in a sort of + + align:start position:0% +release one on on day one in a sort of + + + align:start position:0% +release one on on day one in a sort of +trivial fashion this is known as uh + + align:start position:0% + + + + align:start position:0% + +cyclic photo + + align:start position:0% + + + + align:start position:0% + +phosphorilation and the the principle is + + align:start position:0% +phosphorilation and the the principle is + + + align:start position:0% +phosphorilation and the the principle is +is relatively simple it's to + + align:start position:0% +is relatively simple it's to + + + align:start position:0% +is relatively simple it's to +capture the energy in sunlight + + align:start position:0% + + + + align:start position:0% + +to make a proton + + align:start position:0% + + + + align:start position:0% + +gradient and that then can be used as + + align:start position:0% +gradient and that then can be used as + + + align:start position:0% +gradient and that then can be used as +you now know to make uh ATP + + align:start position:0% +you now know to make uh ATP + + + align:start position:0% +you now know to make uh ATP +so in order to capture energy from uh + + align:start position:0% +so in order to capture energy from uh + + + align:start position:0% +so in order to capture energy from uh +sunlight uh nature head to evolve + + align:start position:0% +sunlight uh nature head to evolve + + + align:start position:0% +sunlight uh nature head to evolve +molecules are able to absorb in the + + align:start position:0% +molecules are able to absorb in the + + + align:start position:0% +molecules are able to absorb in the +appropriate uh wavelength range + + align:start position:0% +appropriate uh wavelength range + + + align:start position:0% +appropriate uh wavelength range +you know the names of those molecules + + align:start position:0% +you know the names of those molecules + + + align:start position:0% +you know the names of those molecules +chlorophyll they come in two principal + + align:start position:0% +chlorophyll they come in two principal + + + align:start position:0% +chlorophyll they come in two principal +species you don't have to remember the + + align:start position:0% +species you don't have to remember the + + + align:start position:0% +species you don't have to remember the +structure which you can see a lot of + + align:start position:0% +structure which you can see a lot of + + + align:start position:0% +structure which you can see a lot of +conjugated double bonds that's how you + + align:start position:0% +conjugated double bonds that's how you + + + align:start position:0% +conjugated double bonds that's how you +sort of tune the absorption of a + + align:start position:0% +sort of tune the absorption of a + + + align:start position:0% +sort of tune the absorption of a +molecule if you want to make it absorb + + align:start position:0% +molecule if you want to make it absorb + + + align:start position:0% +molecule if you want to make it absorb +it longer and longer wavelength you + + align:start position:0% +it longer and longer wavelength you + + + align:start position:0% +it longer and longer wavelength you +start hooking together double double + + align:start position:0% +start hooking together double double + + + align:start position:0% +start hooking together double double +bonds and you can set it up sort of you + + align:start position:0% +bonds and you can set it up sort of you + + + align:start position:0% +bonds and you can set it up sort of you +can get a molecule to absorb it just + + align:start position:0% +can get a molecule to absorb it just + + + align:start position:0% +can get a molecule to absorb it just +about any maximum maximum absorption any + + align:start position:0% +about any maximum maximum absorption any + + + align:start position:0% +about any maximum maximum absorption any +wavelength you want so chlorop + + align:start position:0% +wavelength you want so chlorop + + + align:start position:0% +wavelength you want so chlorop +chlorophyll is able to absorb this this + + align:start position:0% +chlorophyll is able to absorb this this + + + align:start position:0% +chlorophyll is able to absorb this this +energy and the principle of this is what + + align:start position:0% +energy and the principle of this is what + + + align:start position:0% +energy and the principle of this is what +happens is you have this chlorophyll and + + align:start position:0% +happens is you have this chlorophyll and + + + align:start position:0% +happens is you have this chlorophyll and +it gets it absorbs a photon and the + + align:start position:0% +it gets it absorbs a photon and the + + + align:start position:0% +it gets it absorbs a photon and the +electrons an electron this gets + + align:start position:0% +electrons an electron this gets + + + align:start position:0% +electrons an electron this gets +excited so it's basically moves to an + + align:start position:0% +excited so it's basically moves to an + + + align:start position:0% +excited so it's basically moves to an +outer orbital it's farther away from the + + align:start position:0% +outer orbital it's farther away from the + + + align:start position:0% +outer orbital it's farther away from the +nucleus it's easy easier now for that + + align:start position:0% +nucleus it's easy easier now for that + + + align:start position:0% +nucleus it's easy easier now for that +electron to get lost than it was before + + align:start position:0% +electron to get lost than it was before + + + align:start position:0% +electron to get lost than it was before +now if nothing was happening that that + + align:start position:0% +now if nothing was happening that that + + + align:start position:0% +now if nothing was happening that that +electron would eventually just fall down + + align:start position:0% +electron would eventually just fall down + + + align:start position:0% +electron would eventually just fall down +to its ground state you'd lose all the + + align:start position:0% +to its ground state you'd lose all the + + + align:start position:0% +to its ground state you'd lose all the +energy as heat so what happens in in + + align:start position:0% +energy as heat so what happens in in + + + align:start position:0% +energy as heat so what happens in in +photosynthesis though is that the + + align:start position:0% +photosynthesis though is that the + + + align:start position:0% +photosynthesis though is that the +electron falls back down to the the + + align:start position:0% +electron falls back down to the the + + + align:start position:0% +electron falls back down to the the +ground state again in a series of steps + + align:start position:0% +ground state again in a series of steps + + + align:start position:0% +ground state again in a series of steps +and how this happens that electrons are + + align:start position:0% +and how this happens that electrons are + + + align:start position:0% +and how this happens that electrons are +basically getting passed from one + + align:start position:0% +basically getting passed from one + + + align:start position:0% +basically getting passed from one +carrier to + + align:start position:0% +carrier to + + + align:start position:0% +carrier to +another and the same Principle as we saw + + align:start position:0% +another and the same Principle as we saw + + + align:start position:0% +another and the same Principle as we saw +in respiration applies in that at each + + align:start position:0% +in respiration applies in that at each + + + align:start position:0% +in respiration applies in that at each +phase in here a proton is + + align:start position:0% +phase in here a proton is + + + align:start position:0% +phase in here a proton is +pumped now the out and + + align:start position:0% +pumped now the out and + + + align:start position:0% +pumped now the out and +the + + align:start position:0% +the + + + align:start position:0% +the +um the out and the + + align:start position:0% +um the out and the + + + align:start position:0% +um the out and the +in are reversed from um what it says in + + align:start position:0% +in are reversed from um what it says in + + + align:start position:0% +in are reversed from um what it says in +respiration uh in the not your notes in + + align:start position:0% +respiration uh in the not your notes in + + + align:start position:0% +respiration uh in the not your notes in +respiration or it should be anyway + + align:start position:0% +respiration or it should be anyway + + + align:start position:0% +respiration or it should be anyway +um but the in and the out is as you'll + + align:start position:0% +um but the in and the out is as you'll + + + align:start position:0% +um but the in and the out is as you'll +see it's sort of an arbitrary you have + + align:start position:0% +see it's sort of an arbitrary you have + + + align:start position:0% +see it's sort of an arbitrary you have +to you take a fix a frame of reference + + align:start position:0% +to you take a fix a frame of reference + + + align:start position:0% +to you take a fix a frame of reference +and then something's in and something's + + align:start position:0% +and then something's in and something's + + + align:start position:0% +and then something's in and something's +out the point is that in in both of them + + align:start position:0% +out the point is that in in both of them + + + align:start position:0% +out the point is that in in both of them +protons go from one side of the membrane + + align:start position:0% +protons go from one side of the membrane + + + align:start position:0% +protons go from one side of the membrane +to the other and you get more on one + + align:start position:0% +to the other and you get more on one + + + align:start position:0% +to the other and you get more on one +side you pump them in One Direction you + + align:start position:0% +side you pump them in One Direction you + + + align:start position:0% +side you pump them in One Direction you +let them flow back in the other and the + + align:start position:0% +let them flow back in the other and the + + + align:start position:0% +let them flow back in the other and the +in and the out is sort of an arbitrary + + align:start position:0% +in and the out is sort of an arbitrary + + + align:start position:0% +in and the out is sort of an arbitrary +way of describing what's happening but + + align:start position:0% +way of describing what's happening but + + + align:start position:0% +way of describing what's happening but +in both both cases the key thing is that + + align:start position:0% +in both both cases the key thing is that + + + align:start position:0% +in both both cases the key thing is that +you're you're pumping electrons out and + + align:start position:0% +you're you're pumping electrons out and + + + align:start position:0% +you're you're pumping electrons out and +then these can be + + align:start position:0% +then these can be + + + align:start position:0% +then these can be +used to make ATP as we talked about with + + align:start position:0% +used to make ATP as we talked about with + + + align:start position:0% +used to make ATP as we talked about with +ATP synthesis in this case the electrons + + align:start position:0% +ATP synthesis in this case the electrons + + + align:start position:0% +ATP synthesis in this case the electrons +eventually end up back on the uh back on + + align:start position:0% +eventually end up back on the uh back on + + + align:start position:0% +eventually end up back on the uh back on +the chlorophyll and so that's why it's + + align:start position:0% +the chlorophyll and so that's why it's + + + align:start position:0% +the chlorophyll and so that's why it's +called cyclic phosphorilation what it + + align:start position:0% +called cyclic phosphorilation what it + + + align:start position:0% +called cyclic phosphorilation what it +does what you get out of this as you can + + align:start position:0% +does what you get out of this as you can + + + align:start position:0% +does what you get out of this as you can +see is ATP so this was probably a really + + align:start position:0% +see is ATP so this was probably a really + + + align:start position:0% +see is ATP so this was probably a really +big deal in evolution because the + + align:start position:0% +big deal in evolution because the + + + align:start position:0% +big deal in evolution because the +current thinking is perhaps there was an + + align:start position:0% +current thinking is perhaps there was an + + + align:start position:0% +current thinking is perhaps there was an +RNA world that's still sort of being + + align:start position:0% +RNA world that's still sort of being + + + align:start position:0% +RNA world that's still sort of being +debated at some point it's clear that + + align:start position:0% +debated at some point it's clear that + + + align:start position:0% +debated at some point it's clear that +somewhere around 3.8 billion years or so + + align:start position:0% +somewhere around 3.8 billion years or so + + + align:start position:0% +somewhere around 3.8 billion years or so +something that looks sort of like a + + align:start position:0% +something that looks sort of like a + + + align:start position:0% +something that looks sort of like a +present day bacterium arose probably + + align:start position:0% +present day bacterium arose probably + + + align:start position:0% +present day bacterium arose probably +eight molecules that had already been + + align:start position:0% +eight molecules that had already been + + + align:start position:0% +eight molecules that had already been +made in the sort of primordial soup but + + align:start position:0% +made in the sort of primordial soup but + + + align:start position:0% +made in the sort of primordial soup but +when those started to run out out then + + align:start position:0% +when those started to run out out then + + + align:start position:0% +when those started to run out out then +you needed other ways of making energy + + align:start position:0% +you needed other ways of making energy + + + align:start position:0% +you needed other ways of making energy +needed other ways of making carbon + + align:start position:0% +needed other ways of making carbon + + + align:start position:0% +needed other ways of making carbon +here's a way of getting energy but + + align:start position:0% +here's a way of getting energy but + + + align:start position:0% +here's a way of getting energy but +what's available to make more organic + + align:start position:0% +what's available to make more organic + + + align:start position:0% +what's available to make more organic +molecules is only carbon dioxide and if + + align:start position:0% +molecules is only carbon dioxide and if + + + align:start position:0% +molecules is only carbon dioxide and if +you remember that little thing I showed + + align:start position:0% +you remember that little thing I showed + + + align:start position:0% +you remember that little thing I showed +you of if we're going increasing going + + align:start position:0% +you of if we're going increasing going + + + align:start position:0% +you of if we're going increasing going +from a + + align:start position:0% +from a + + + align:start position:0% +from a +methyl to hydroxy to a + + align:start position:0% +methyl to hydroxy to a + + + align:start position:0% +methyl to hydroxy to a +alahh to an + + align:start position:0% + + + + align:start position:0% + +acid to + + align:start position:0% +acid to + + + align:start position:0% +acid to +CO2 that + + align:start position:0% +CO2 that + + + align:start position:0% +CO2 that +direction is oxidation and that + + align:start position:0% +direction is oxidation and that + + + align:start position:0% +direction is oxidation and that +direction is reduction so if we go in + + align:start position:0% +direction is reduction so if we go in + + + align:start position:0% +direction is reduction so if we go in +that direction and + + align:start position:0% +that direction and + + + align:start position:0% +that direction and +we we end up generating nadh a red + + align:start position:0% +we we end up generating nadh a red + + + align:start position:0% +we we end up generating nadh a red +because we're taking the electrons and + + align:start position:0% +because we're taking the electrons and + + + align:start position:0% +because we're taking the electrons and +giving them to something else if we want + + align:start position:0% +giving them to something else if we want + + + align:start position:0% +giving them to something else if we want +to go the other way what we have to if + + align:start position:0% +to go the other way what we have to if + + + align:start position:0% +to go the other way what we have to if +we're starting with CO2 what we need to + + align:start position:0% +we're starting with CO2 what we need to + + + align:start position:0% +we're starting with CO2 what we need to +do is we need to have a supply of + + align:start position:0% +do is we need to have a supply of + + + align:start position:0% +do is we need to have a supply of +reducing power so we can take the CO2 + + align:start position:0% +reducing power so we can take the CO2 + + + align:start position:0% +reducing power so we can take the CO2 +and get it down to all the less oxidized + + align:start position:0% +and get it down to all the less oxidized + + + align:start position:0% +and get it down to all the less oxidized +states that are necessary for building + + align:start position:0% +states that are necessary for building + + + align:start position:0% +states that are necessary for building +all the molecules that we've been we've + + align:start position:0% +all the molecules that we've been we've + + + align:start position:0% +all the molecules that we've been we've +been talking about so making ATP was a + + align:start position:0% +been talking about so making ATP was a + + + align:start position:0% +been talking about so making ATP was a +great idea but the cell still needed to + + align:start position:0% +great idea but the cell still needed to + + + align:start position:0% +great idea but the cell still needed to +have some form of reducing agent and + + align:start position:0% +have some form of reducing agent and + + + align:start position:0% +have some form of reducing agent and +what they used was they used hydrogen + + align:start position:0% +what they used was they used hydrogen + + + align:start position:0% +what they used was they used hydrogen +sulfide this is one of at least one of + + align:start position:0% +sulfide this is one of at least one of + + + align:start position:0% +sulfide this is one of at least one of +the major ways that it was done and so + + align:start position:0% +the major ways that it was done and so + + + align:start position:0% +the major ways that it was done and so +they take na D know there's a very + + align:start position:0% +they take na D know there's a very + + + align:start position:0% +they take na D know there's a very +slight twist here this is nadp it's the + + align:start position:0% +slight twist here this is nadp it's the + + + align:start position:0% +slight twist here this is nadp it's the +same molecule as NAD except there's an + + align:start position:0% +same molecule as NAD except there's an + + + align:start position:0% +same molecule as NAD except there's an +extra phosphorilation and the one with + + align:start position:0% +extra phosphorilation and the one with + + + align:start position:0% +extra phosphorilation and the one with +the phosphate on it tends to be used in + + align:start position:0% +the phosphate on it tends to be used in + + + align:start position:0% +the phosphate on it tends to be used in +biosynthetic reactions but otherwise + + align:start position:0% +biosynthetic reactions but otherwise + + + align:start position:0% +biosynthetic reactions but otherwise +it's exactly the same thing it's + + align:start position:0% +it's exactly the same thing it's + + + align:start position:0% +it's exactly the same thing it's +electron banking thing and what this + + align:start position:0% +electron banking thing and what this + + + align:start position:0% +electron banking thing and what this +gave was + + align:start position:0% +gave was + + + align:start position:0% +gave was +NAD pH plus + + align:start position:0% +NAD pH plus + + + align:start position:0% +NAD pH plus +sulfur a hydrogen so sulfur is a waste + + align:start position:0% +sulfur a hydrogen so sulfur is a waste + + + align:start position:0% +sulfur a hydrogen so sulfur is a waste +product here's the reducing power here's + + align:start position:0% +product here's the reducing power here's + + + align:start position:0% +product here's the reducing power here's +the ATP that's what those organisms need + + align:start position:0% +the ATP that's what those organisms need + + + align:start position:0% +the ATP that's what those organisms need +to be able to synthesize uh new organic + + align:start position:0% +to be able to synthesize uh new organic + + + align:start position:0% +to be able to synthesize uh new organic +material without having to have it + + align:start position:0% +material without having to have it + + + align:start position:0% +material without having to have it +pre-made molecules a really big deal in + + align:start position:0% +pre-made molecules a really big deal in + + + align:start position:0% +pre-made molecules a really big deal in +evolution and it's based on the for Mak + + align:start position:0% +evolution and it's based on the for Mak + + + align:start position:0% +evolution and it's based on the for Mak +the idea for making the ATP is based on + + align:start position:0% +the idea for making the ATP is based on + + + align:start position:0% +the idea for making the ATP is based on +this use of establishing a proton + + align:start position:0% +this use of establishing a proton + + + align:start position:0% +this use of establishing a proton +gradient the same principle we've seen + + align:start position:0% +gradient the same principle we've seen + + + align:start position:0% +gradient the same principle we've seen +again now there's another possible + + align:start position:0% +again now there's another possible + + + align:start position:0% +again now there's another possible +source of reducing + + align:start position:0% + + + + align:start position:0% + +power and that would be to use water as + + align:start position:0% +power and that would be to use water as + + + align:start position:0% +power and that would be to use water as +the source of the the reducing power but + + align:start position:0% +the source of the the reducing power but + + + align:start position:0% +the source of the the reducing power but +in order to do that you got to you got + + align:start position:0% +in order to do that you got to you got + + + align:start position:0% +in order to do that you got to you got +to put more energy into it and this + + align:start position:0% +to put more energy into it and this + + + align:start position:0% +to put more energy into it and this +system wasn't able to handle it but that + + align:start position:0% +system wasn't able to handle it but that + + + align:start position:0% +system wasn't able to handle it but that +happened soon enough + + align:start position:0% +happened soon enough + + + align:start position:0% +happened soon enough +um + + align:start position:0% + + + + align:start position:0% + +with the development of what I called on + + align:start position:0% +with the development of what I called on + + + align:start position:0% +with the development of what I called on +the first day photosynthesis release + + align:start position:0% + + + + align:start position:0% + +2 which is technically known as + + align:start position:0% + + + + align:start position:0% + +noncyclic uh + + align:start position:0% + + + + align:start position:0% + +photo + + align:start position:0% + + + + align:start position:0% + +phosphorilation again it uses the energy + + align:start position:0% +phosphorilation again it uses the energy + + + align:start position:0% +phosphorilation again it uses the energy +of + + align:start position:0% + + + + align:start position:0% + +sunlight but the twist this time it not + + align:start position:0% +sunlight but the twist this time it not + + + align:start position:0% +sunlight but the twist this time it not +only makes ATP it also makes + + align:start position:0% +only makes ATP it also makes + + + align:start position:0% +only makes ATP it also makes +nadph it makes reducing power at the + + align:start position:0% +nadph it makes reducing power at the + + + align:start position:0% +nadph it makes reducing power at the +same time so you could see that is a + + align:start position:0% +same time so you could see that is a + + + align:start position:0% +same time so you could see that is a +really major Advance if you can use + + align:start position:0% +really major Advance if you can use + + + align:start position:0% +really major Advance if you can use +sunlight to make both of them now you're + + align:start position:0% +sunlight to make both of them now you're + + + align:start position:0% +sunlight to make both of them now you're +really uh efficient and so this is how + + align:start position:0% +really uh efficient and so this is how + + + align:start position:0% +really uh efficient and so this is how +this one works it's related to the other + + align:start position:0% +this one works it's related to the other + + + align:start position:0% +this one works it's related to the other +one the first part is more or less the + + align:start position:0% +one the first part is more or less the + + + align:start position:0% +one the first part is more or less the +same idea photon is absorbed by a + + align:start position:0% +same idea photon is absorbed by a + + + align:start position:0% +same idea photon is absorbed by a +molecule of chlorophyll it kicks the + + align:start position:0% +molecule of chlorophyll it kicks the + + + align:start position:0% +molecule of chlorophyll it kicks the +chlorophyll up to an activated state + + align:start position:0% +chlorophyll up to an activated state + + + align:start position:0% +chlorophyll up to an activated state +where the electrons uh at a higher + + align:start position:0% +where the electrons uh at a higher + + + align:start position:0% +where the electrons uh at a higher +orbital further away it wants to come + + align:start position:0% +orbital further away it wants to come + + + align:start position:0% +orbital further away it wants to come +back down energyy is going to be + + align:start position:0% +back down energyy is going to be + + + align:start position:0% +back down energyy is going to be +released so electrons get + + align:start position:0% + + + + align:start position:0% + +passed protons get pumped from one side + + align:start position:0% +passed protons get pumped from one side + + + align:start position:0% +passed protons get pumped from one side +of a of a of a membrane + + align:start position:0% +of a of a of a membrane + + + align:start position:0% +of a of a of a membrane +to another except this time instead of + + align:start position:0% +to another except this time instead of + + + align:start position:0% +to another except this time instead of +coming back the chlorophyll this lands + + align:start position:0% +coming back the chlorophyll this lands + + + align:start position:0% +coming back the chlorophyll this lands +in a different chlorophyll that has just + + align:start position:0% +in a different chlorophyll that has just + + + align:start position:0% +in a different chlorophyll that has just +recently lost a pair of electrons + + align:start position:0% +recently lost a pair of electrons + + + align:start position:0% +recently lost a pair of electrons +there's a there's a new energy input + + align:start position:0% +there's a there's a new energy input + + + align:start position:0% +there's a there's a new energy input +here that kicks this + + align:start position:0% +here that kicks this + + + align:start position:0% +here that kicks this +chlorophyll up to an even higher energy + + align:start position:0% +chlorophyll up to an even higher energy + + + align:start position:0% +chlorophyll up to an even higher energy +State than this one and as these + + align:start position:0% +State than this one and as these + + + align:start position:0% +State than this one and as these +electrons start to come down the energy + + align:start position:0% +electrons start to come down the energy + + + align:start position:0% +electrons start to come down the energy +Hill there's enough energy here to take + + align:start position:0% +Hill there's enough energy here to take + + + align:start position:0% +Hill there's enough energy here to take +a molecule of any D p+ plus a hydrogen + + align:start position:0% +a molecule of any D p+ plus a hydrogen + + + align:start position:0% +a molecule of any D p+ plus a hydrogen +ion and give na + + align:start position:0% +ion and give na + + + align:start position:0% +ion and give na +D + + align:start position:0% +D + + + align:start position:0% +D +pH there's one thing that this isn't + + align:start position:0% +pH there's one thing that this isn't + + + align:start position:0% +pH there's one thing that this isn't +going to work like a cycle or machine + + align:start position:0% +going to work like a cycle or machine + + + align:start position:0% +going to work like a cycle or machine +yet anybody see what's hasn't been taken + + align:start position:0% +yet anybody see what's hasn't been taken + + + align:start position:0% +yet anybody see what's hasn't been taken +care of + + align:start position:0% + + + + align:start position:0% + +yet say again send the electrons back + + align:start position:0% +yet say again send the electrons back + + + align:start position:0% +yet say again send the electrons back +send the electrons back to this + + align:start position:0% +send the electrons back to this + + + align:start position:0% +send the electrons back to this +chlorophyll exactly so + + align:start position:0% +chlorophyll exactly so + + + align:start position:0% +chlorophyll exactly so +however now the way the energetics is + + align:start position:0% +however now the way the energetics is + + + align:start position:0% +however now the way the energetics is +structured now they're able the cells + + align:start position:0% +structured now they're able the cells + + + align:start position:0% +structured now they're able the cells +were able to take reducing power from + + align:start position:0% +were able to take reducing power from + + + align:start position:0% +were able to take reducing power from +here and generate 2 H+ plus a half of an + + align:start position:0% +here and generate 2 H+ plus a half of an + + + align:start position:0% +here and generate 2 H+ plus a half of an +oxygen + + align:start position:0% +oxygen + + + align:start position:0% +oxygen +molecule and so two this would really be + + align:start position:0% +molecule and so two this would really be + + + align:start position:0% +molecule and so two this would really be +two waters giving four hydrogens and one + + align:start position:0% +two waters giving four hydrogens and one + + + align:start position:0% +two waters giving four hydrogens and one +oxygen molecule so what you can see here + + align:start position:0% +oxygen molecule so what you can see here + + + align:start position:0% +oxygen molecule so what you can see here +now there's a couple of really important + + align:start position:0% +now there's a couple of really important + + + align:start position:0% +now there's a couple of really important +things about this it needs more + + align:start position:0% +things about this it needs more + + + align:start position:0% +things about this it needs more +energy + + align:start position:0% + + + + align:start position:0% + +it makes + + align:start position:0% +it makes + + + align:start position:0% +it makes +ATP and + + align:start position:0% +ATP and + + + align:start position:0% +ATP and +nadh + + align:start position:0% +nadh + + + align:start position:0% +nadh +NPH which leaves the + + align:start position:0% +NPH which leaves the + + + align:start position:0% +NPH which leaves the +cell able to carry out biosynthesis and + + align:start position:0% +cell able to carry out biosynthesis and + + + align:start position:0% +cell able to carry out biosynthesis and +the third thing which is an incredible + + align:start position:0% +the third thing which is an incredible + + + align:start position:0% +the third thing which is an incredible +influence on our planet it started to + + align:start position:0% +influence on our planet it started to + + + align:start position:0% +influence on our planet it started to +generate + + align:start position:0% +generate + + + align:start position:0% +generate +oxygen as a waste + + align:start position:0% + + + + align:start position:0% + +product and it's really a mixed blessing + + align:start position:0% +product and it's really a mixed blessing + + + align:start position:0% +product and it's really a mixed blessing +i me we it oxy oygen very reactive it + + align:start position:0% +i me we it oxy oygen very reactive it + + + align:start position:0% +i me we it oxy oygen very reactive it +damages our DNA it damages our proteins + + align:start position:0% +damages our DNA it damages our proteins + + + align:start position:0% +damages our DNA it damages our proteins +we have an amazing number of defenses + + align:start position:0% +we have an amazing number of defenses + + + align:start position:0% +we have an amazing number of defenses +against oxygen U but on the other hand + + align:start position:0% +against oxygen U but on the other hand + + + align:start position:0% +against oxygen U but on the other hand +is it accumulate in the atmosphere and + + align:start position:0% +is it accumulate in the atmosphere and + + + align:start position:0% +is it accumulate in the atmosphere and +organisms slowly over revolutionary time + + align:start position:0% +organisms slowly over revolutionary time + + + align:start position:0% +organisms slowly over revolutionary time +learn to deal with it it then set us up + + align:start position:0% +learn to deal with it it then set us up + + + align:start position:0% +learn to deal with it it then set us up +for the possibility of respiration which + + align:start position:0% +for the possibility of respiration which + + + align:start position:0% +for the possibility of respiration which +as you could see is 18 times more + + align:start position:0% +as you could see is 18 times more + + + align:start position:0% +as you could see is 18 times more +efficient than in that ancient way of + + align:start position:0% +efficient than in that ancient way of + + + align:start position:0% +efficient than in that ancient way of +using glycolysis to make energy out of + + align:start position:0% +using glycolysis to make energy out of + + + align:start position:0% +using glycolysis to make energy out of +sugars so um that's more or less uh the + + align:start position:0% +sugars so um that's more or less uh the + + + align:start position:0% +sugars so um that's more or less uh the +the story this is this part is called + + align:start position:0% + + + + align:start position:0% + +photosystem uh two this this assembly of + + align:start position:0% +photosystem uh two this this assembly of + + + align:start position:0% +photosystem uh two this this assembly of +stuff is + + align:start position:0% +stuff is + + + align:start position:0% +stuff is +photosystem one and I just wanted to + + align:start position:0% +photosystem one and I just wanted to + + + align:start position:0% +photosystem one and I just wanted to +show you this next slide because I mean + + align:start position:0% +show you this next slide because I mean + + + align:start position:0% +show you this next slide because I mean +chlorophyll isn't just floating around + + align:start position:0% +chlorophyll isn't just floating around + + + align:start position:0% +chlorophyll isn't just floating around +like this as you might guess it's bound + + align:start position:0% +like this as you might guess it's bound + + + align:start position:0% +like this as you might guess it's bound +into proteins and things and someone has + + align:start position:0% +into proteins and things and someone has + + + align:start position:0% +into proteins and things and someone has +figured out the structure of photosynth + + align:start position:0% +figured out the structure of photosynth + + + align:start position:0% +figured out the structure of photosynth +photosystem one consists of 12 proteins + + align:start position:0% +photosystem one consists of 12 proteins + + + align:start position:0% +photosystem one consists of 12 proteins +96 chlorophylls and about 30 other + + align:start position:0% +96 chlorophylls and about 30 other + + + align:start position:0% +96 chlorophylls and about 30 other +molecules and what it really does is it + + align:start position:0% +molecules and what it really does is it + + + align:start position:0% +molecules and what it really does is it +functions as an antenna some of the + + align:start position:0% +functions as an antenna some of the + + + align:start position:0% +functions as an antenna some of the +other molecules can absorb it at + + align:start position:0% +other molecules can absorb it at + + + align:start position:0% +other molecules can absorb it at +wavelengths that are that are different + + align:start position:0% +wavelengths that are that are different + + + align:start position:0% +wavelengths that are that are different +from chlorophyll and all the energy gets + + align:start position:0% +from chlorophyll and all the energy gets + + + align:start position:0% +from chlorophyll and all the energy gets +funnel into the chlorophyll and into + + align:start position:0% +funnel into the chlorophyll and into + + + align:start position:0% +funnel into the chlorophyll and into +this this process and you'll you'll + + align:start position:0% +this this process and you'll you'll + + + align:start position:0% +this this process and you'll you'll +probably recognize by now proteins here + + align:start position:0% +probably recognize by now proteins here + + + align:start position:0% +probably recognize by now proteins here +we're seeing Alpha helices and beta + + align:start position:0% +we're seeing Alpha helices and beta + + + align:start position:0% +we're seeing Alpha helices and beta +sheets in here as part of this as part + + align:start position:0% +sheets in here as part of this as part + + + align:start position:0% +sheets in here as part of this as part +of this structure so the first organisms + + align:start position:0% +of this structure so the first organisms + + + align:start position:0% +of this structure so the first organisms +that learned how to do this were + + align:start position:0% +that learned how to do this were + + + align:start position:0% +that learned how to do this were +organisms we now know as + + align:start position:0% +organisms we now know as + + + align:start position:0% +organisms we now know as +cyanobacteria + + align:start position:0% + + + + align:start position:0% + +they're kind of bacteria that has two + + align:start position:0% +they're kind of bacteria that has two + + + align:start position:0% +they're kind of bacteria that has two +membranes like eoli and like the other + + align:start position:0% +membranes like eoli and like the other + + + align:start position:0% +membranes like eoli and like the other +ones that we've talked about you're + + align:start position:0% +ones that we've talked about you're + + + align:start position:0% +ones that we've talked about you're +familiar with these there's the green + + align:start position:0% +familiar with these there's the green + + + align:start position:0% +familiar with these there's the green +scum you see on on ponds here's a + + align:start position:0% +scum you see on on ponds here's a + + + align:start position:0% +scum you see on on ponds here's a +closeup sometimes they grow as filaments + + align:start position:0% +closeup sometimes they grow as filaments + + + align:start position:0% +closeup sometimes they grow as filaments +the cells in a chain you notice they're + + align:start position:0% +the cells in a chain you notice they're + + + align:start position:0% +the cells in a chain you notice they're +green they're making chlorophyll and + + align:start position:0% +green they're making chlorophyll and + + + align:start position:0% +green they're making chlorophyll and +what happened in Plants was that + + align:start position:0% +what happened in Plants was that + + + align:start position:0% +what happened in Plants was that +apparently something probably one + + align:start position:0% +apparently something probably one + + + align:start position:0% +apparently something probably one +something related to the present day + + align:start position:0% +something related to the present day + + + align:start position:0% +something related to the present day +cyano bacteria got trapped inside some + + align:start position:0% +cyano bacteria got trapped inside some + + + align:start position:0% +cyano bacteria got trapped inside some +early progenitor of uh what we now know + + align:start position:0% +early progenitor of uh what we now know + + + align:start position:0% +early progenitor of uh what we now know +as as uh plants and green algae and this + + align:start position:0% +as as uh plants and green algae and this + + + align:start position:0% +as as uh plants and green algae and this +trapped bacterium became a + + align:start position:0% + + + + align:start position:0% + +chloroplast and it had all the uh + + align:start position:0% +chloroplast and it had all the uh + + + align:start position:0% +chloroplast and it had all the uh +Machinery necessary to carry out this uh + + align:start position:0% +Machinery necessary to carry out this uh + + + align:start position:0% +Machinery necessary to carry out this uh +noncyclic photo + + align:start position:0% +noncyclic photo + + + align:start position:0% +noncyclic photo +phosphorilation the structure of these + + align:start position:0% +phosphorilation the structure of these + + + align:start position:0% +phosphorilation the structure of these +things there's + + align:start position:0% +things there's + + + align:start position:0% +things there's +an outer + + align:start position:0% +an outer + + + align:start position:0% +an outer +membrane just similar to what I told you + + align:start position:0% +membrane just similar to what I told you + + + align:start position:0% +membrane just similar to what I told you +for the mitochondria there's an inner + + align:start position:0% + + + + align:start position:0% + +membrane and what's special about the + + align:start position:0% +membrane and what's special about the + + + align:start position:0% +membrane and what's special about the +mitochondrian then there's another + + align:start position:0% +mitochondrian then there's another + + + align:start position:0% +mitochondrian then there's another +membrane inside that's known as the + + align:start position:0% + + + + align:start position:0% + +phylloid and that's where all the that's + + align:start position:0% +phylloid and that's where all the that's + + + align:start position:0% +phylloid and that's where all the that's +where all the chlorophyll + + align:start position:0% +where all the chlorophyll + + + align:start position:0% +where all the chlorophyll +is + + align:start position:0% + + + + align:start position:0% + +and the reason the out and the in is a + + align:start position:0% +and the reason the out and the in is a + + + align:start position:0% +and the reason the out and the in is a +little bit confusing in here is this + + align:start position:0% +little bit confusing in here is this + + + align:start position:0% +little bit confusing in here is this +part which is probably the cytoplasm of + + align:start position:0% +part which is probably the cytoplasm of + + + align:start position:0% +part which is probably the cytoplasm of +the old + + align:start position:0% +the old + + + align:start position:0% +the old +bacterium is pumped from what's known as + + align:start position:0% +bacterium is pumped from what's known as + + + align:start position:0% +bacterium is pumped from what's known as +the + + align:start position:0% + + + + align:start position:0% + +stroma the Strom of a chloroplast which + + align:start position:0% +stroma the Strom of a chloroplast which + + + align:start position:0% +stroma the Strom of a chloroplast which +is equivalent to the cytoplasm of the + + align:start position:0% +is equivalent to the cytoplasm of the + + + align:start position:0% +is equivalent to the cytoplasm of the +original + + align:start position:0% +original + + + align:start position:0% +original +bacteria into the Lumen so the + + align:start position:0% +bacteria into the Lumen so the + + + align:start position:0% +bacteria into the Lumen so the +chlorophyll that's in this membrane + + align:start position:0% +chlorophyll that's in this membrane + + + align:start position:0% +chlorophyll that's in this membrane +absorbs the light pumps protons into the + + align:start position:0% +absorbs the light pumps protons into the + + + align:start position:0% +absorbs the light pumps protons into the +Lumen building up a proton gradient and + + align:start position:0% +Lumen building up a proton gradient and + + + align:start position:0% +Lumen building up a proton gradient and +then they flow back out in the other + + align:start position:0% +then they flow back out in the other + + + align:start position:0% +then they flow back out in the other +direction uh and make ATP here's a + + align:start position:0% +direction uh and make ATP here's a + + + align:start position:0% +direction uh and make ATP here's a +picture of a chloroplast once again + + align:start position:0% +picture of a chloroplast once again + + + align:start position:0% +picture of a chloroplast once again +looks an awful lot like the bacterium + + align:start position:0% +looks an awful lot like the bacterium + + + align:start position:0% +looks an awful lot like the bacterium +still that that got captured all this + + align:start position:0% +still that that got captured all this + + + align:start position:0% +still that that got captured all this +stuff in the inside those are the thilo + + align:start position:0% +stuff in the inside those are the thilo + + + align:start position:0% +stuff in the inside those are the thilo +covid membranes that + + align:start position:0% +covid membranes that + + + align:start position:0% +covid membranes that +um that uh carry out this specialized + + align:start position:0% +um that uh carry out this specialized + + + align:start position:0% +um that uh carry out this specialized +stuff so there you have it + + align:start position:0% +stuff so there you have it + + + align:start position:0% +stuff so there you have it +uh that's how cells how life the major + + align:start position:0% +uh that's how cells how life the major + + + align:start position:0% +uh that's how cells how life the major +ways that life has figured out how to uh + + align:start position:0% +ways that life has figured out how to uh + + + align:start position:0% +ways that life has figured out how to uh +make energy when Penny Chism starts to + + align:start position:0% +make energy when Penny Chism starts to + + + align:start position:0% +make energy when Penny Chism starts to +talk to you she'll talk to you about how + + align:start position:0% +talk to you she'll talk to you about how + + + align:start position:0% +talk to you she'll talk to you about how +organisms adapt to various niches things + + align:start position:0% +organisms adapt to various niches things + + + align:start position:0% +organisms adapt to various niches things +that live in the bottom of the ocean + + align:start position:0% +that live in the bottom of the ocean + + + align:start position:0% +that live in the bottom of the ocean +things that live in various places they + + align:start position:0% +things that live in various places they + + + align:start position:0% +things that live in various places they +all have to make energy they all use + + align:start position:0% +all have to make energy they all use + + + align:start position:0% +all have to make energy they all use +some variation on these principles I've + + align:start position:0% +some variation on these principles I've + + + align:start position:0% +some variation on these principles I've +talked to you and she'll then show you + + align:start position:0% +talked to you and she'll then show you + + + align:start position:0% +talked to you and she'll then show you +how by they've got very clever at + + align:start position:0% +how by they've got very clever at + + + align:start position:0% +how by they've got very clever at +extracting energy out of all sorts of + + align:start position:0% +extracting energy out of all sorts of + + + align:start position:0% +extracting energy out of all sorts of +things by applying these principles in + + align:start position:0% +things by applying these principles in + + + align:start position:0% +things by applying these principles in +different ways + + align:start position:0% +different ways + + + align:start position:0% +different ways +okay so what we're going to start doing + + align:start position:0% +okay so what we're going to start doing + + + align:start position:0% +okay so what we're going to start doing +now is we're going to start talking + + align:start position:0% +now is we're going to start talking + + + align:start position:0% +now is we're going to start talking +about um DNA is it certainly a molecule + + align:start position:0% +about um DNA is it certainly a molecule + + + align:start position:0% +about um DNA is it certainly a molecule +that's fascinated me all my life you + + align:start position:0% +that's fascinated me all my life you + + + align:start position:0% +that's fascinated me all my life you +should know from the first part uh that + + align:start position:0% +should know from the first part uh that + + + align:start position:0% +should know from the first part uh that +it's built up of units known as + + align:start position:0% +it's built up of units known as + + + align:start position:0% +it's built up of units known as +nucleotides that have a sugar it's a + + align:start position:0% +nucleotides that have a sugar it's a + + + align:start position:0% +nucleotides that have a sugar it's a +ribos sugar that's missing one hydroxy + + align:start position:0% +ribos sugar that's missing one hydroxy + + + align:start position:0% +ribos sugar that's missing one hydroxy +so it's a deoxy ribos the sugars are + + align:start position:0% +so it's a deoxy ribos the sugars are + + + align:start position:0% +so it's a deoxy ribos the sugars are +numbered uh 1 2 3 4 5 I showed you that + + align:start position:0% +numbered uh 1 2 3 4 5 I showed you that + + + align:start position:0% +numbered uh 1 2 3 4 5 I showed you that +uh they be a a phosphate and then one of + + align:start position:0% +uh they be a a phosphate and then one of + + + align:start position:0% +uh they be a a phosphate and then one of +these nucleic acid bases either a pine + + align:start position:0% +these nucleic acid bases either a pine + + + align:start position:0% +these nucleic acid bases either a pine +or a purine and the in DNA you find the + + align:start position:0% +or a purine and the in DNA you find the + + + align:start position:0% +or a purine and the in DNA you find the +perine bases are cytosine and thyine and + + align:start position:0% +perine bases are cytosine and thyine and + + + align:start position:0% +perine bases are cytosine and thyine and +in uh DNA the purine bases are adenine + + align:start position:0% +in uh DNA the purine bases are adenine + + + align:start position:0% +in uh DNA the purine bases are adenine +and and guanine and then these subunits + + align:start position:0% +and and guanine and then these subunits + + + align:start position:0% +and and guanine and then these subunits +are polymerized together in essence + + align:start position:0% +are polymerized together in essence + + + align:start position:0% +are polymerized together in essence +splitting out water to give you a + + align:start position:0% +splitting out water to give you a + + + align:start position:0% +splitting out water to give you a +polymer and uh there's a I didn't + + align:start position:0% +polymer and uh there's a I didn't + + + align:start position:0% +polymer and uh there's a I didn't +emphasize this too strongly the first + + align:start position:0% +emphasize this too strongly the first + + + align:start position:0% +emphasize this too strongly the first +time I showed it to you it's going to + + align:start position:0% +time I showed it to you it's going to + + + align:start position:0% +time I showed it to you it's going to +become a very big deal over the next few + + align:start position:0% +become a very big deal over the next few + + + align:start position:0% +become a very big deal over the next few +we uh few lectures as we begin to + + align:start position:0% +we uh few lectures as we begin to + + + align:start position:0% +we uh few lectures as we begin to +consider how uh nature had to figure out + + align:start position:0% +consider how uh nature had to figure out + + + align:start position:0% +consider how uh nature had to figure out +how to replicate DNA and all sorts of + + align:start position:0% +how to replicate DNA and all sorts of + + + align:start position:0% +how to replicate DNA and all sorts of +implications go along with this but + + align:start position:0% +implications go along with this but + + + align:start position:0% +implications go along with this but +there's a polarity to a strand of DNA + + align:start position:0% +there's a polarity to a strand of DNA + + + align:start position:0% +there's a polarity to a strand of DNA +the this is the five What's called the + + align:start position:0% +the this is the five What's called the + + + align:start position:0% +the this is the five What's called the +five Prime sugar the primes indicate the + + align:start position:0% +five Prime sugar the primes indicate the + + + align:start position:0% +five Prime sugar the primes indicate the +numbers referring to the sugar and the + + align:start position:0% +numbers referring to the sugar and the + + + align:start position:0% +numbers referring to the sugar and the +ones without primes are referring to + + align:start position:0% +ones without primes are referring to + + + align:start position:0% +ones without primes are referring to +numbers of of uh atoms that make up part + + align:start position:0% +numbers of of uh atoms that make up part + + + align:start position:0% +numbers of of uh atoms that make up part +of the nucleic acid base so if we're + + align:start position:0% +of the nucleic acid base so if we're + + + align:start position:0% +of the nucleic acid base so if we're +looking at a chain this is a five Prime + + align:start position:0% +looking at a chain this is a five Prime + + + align:start position:0% +looking at a chain this is a five Prime +carbon of the sugar that's the thre + + align:start position:0% +carbon of the sugar that's the thre + + + align:start position:0% +carbon of the sugar that's the thre +Prime and + + align:start position:0% +Prime and + + + align:start position:0% +Prime and +so um what you can see is this bond + + align:start position:0% +so um what you can see is this bond + + + align:start position:0% +so um what you can see is this bond +which is really a phosphodiester bond + + align:start position:0% +which is really a phosphodiester bond + + + align:start position:0% +which is really a phosphodiester bond +the phosphate group is formed an Esther + + align:start position:0% +the phosphate group is formed an Esther + + + align:start position:0% +the phosphate group is formed an Esther +with this hydroxy and with the hydroxy + + align:start position:0% +with this hydroxy and with the hydroxy + + + align:start position:0% +with this hydroxy and with the hydroxy +that used to be here so it's a phosphor + + align:start position:0% +that used to be here so it's a phosphor + + + align:start position:0% +that used to be here so it's a phosphor +phosphodiester bond and it runs uh it + + align:start position:0% +phosphodiester bond and it runs uh it + + + align:start position:0% +phosphodiester bond and it runs uh it +it's a five Prime three prime Bond it + + align:start position:0% +it's a five Prime three prime Bond it + + + align:start position:0% +it's a five Prime three prime Bond it +joins the five Prime carbon to the three + + align:start position:0% +joins the five Prime carbon to the three + + + align:start position:0% +joins the five Prime carbon to the three +three the five Prime carbon to the three + + align:start position:0% +three the five Prime carbon to the three + + + align:start position:0% +three the five Prime carbon to the three +prime carbon up here so that means if + + align:start position:0% +prime carbon up here so that means if + + + align:start position:0% +prime carbon up here so that means if +you're looking at a chain of DNA if you + + align:start position:0% +you're looking at a chain of DNA if you + + + align:start position:0% +you're looking at a chain of DNA if you +come down this way you're coming in the + + align:start position:0% +come down this way you're coming in the + + + align:start position:0% +come down this way you're coming in the +five to three prime direction if we come + + align:start position:0% +five to three prime direction if we come + + + align:start position:0% +five to three prime direction if we come +up the other way we're coming from the + + align:start position:0% +up the other way we're coming from the + + + align:start position:0% +up the other way we're coming from the +three prime end heading towards the five + + align:start position:0% +three prime end heading towards the five + + + align:start position:0% +three prime end heading towards the five +Prime end so you'll see me saying five + + align:start position:0% +Prime end so you'll see me saying five + + + align:start position:0% +Prime end so you'll see me saying five +Prime 3 Prime now as well the as I told + + align:start position:0% +Prime 3 Prime now as well the as I told + + + align:start position:0% +Prime 3 Prime now as well the as I told +you the principal force that holds the + + align:start position:0% +you the principal force that holds the + + + align:start position:0% +you the principal force that holds the +strands of the DNA together are hydrogen + + align:start position:0% +strands of the DNA together are hydrogen + + + align:start position:0% +strands of the DNA together are hydrogen +bonds three of them between a g and a c + + align:start position:0% +bonds three of them between a g and a c + + + align:start position:0% +bonds three of them between a g and a c +and two of them between uh an A and A T + + align:start position:0% +and two of them between uh an A and A T + + + align:start position:0% +and two of them between uh an A and A T +and + + align:start position:0% +and + + + align:start position:0% +and +then the their pair of strands and + + align:start position:0% +then the their pair of strands and + + + align:start position:0% +then the their pair of strands and +they're actually running in opposite + + align:start position:0% +they're actually running in opposite + + + align:start position:0% +they're actually running in opposite +polarities this is something we to + + align:start position:0% +polarities this is something we to + + + align:start position:0% +polarities this is something we to +contend with when you think about + + align:start position:0% +contend with when you think about + + + align:start position:0% +contend with when you think about +replication five Prime to three Prime in + + align:start position:0% +replication five Prime to three Prime in + + + align:start position:0% +replication five Prime to three Prime in +One Direction and five Prime to three + + align:start position:0% +One Direction and five Prime to three + + + align:start position:0% +One Direction and five Prime to three +prime going the opposite way here and + + align:start position:0% +prime going the opposite way here and + + + align:start position:0% +prime going the opposite way here and +then as all you you all know it's called + + align:start position:0% +then as all you you all know it's called + + + align:start position:0% +then as all you you all know it's called +the double helix so it's actually not + + align:start position:0% +the double helix so it's actually not + + + align:start position:0% +the double helix so it's actually not +flat like this in space it's in a + + align:start position:0% +flat like this in space it's in a + + + align:start position:0% +flat like this in space it's in a +three-dimensional um uh Twisted into a + + align:start position:0% +three-dimensional um uh Twisted into a + + + align:start position:0% +three-dimensional um uh Twisted into a +double helix and the base pairs are held + + align:start position:0% +double helix and the base pairs are held + + + align:start position:0% +double helix and the base pairs are held +together by hydrogen bonds between these + + align:start position:0% +together by hydrogen bonds between these + + + align:start position:0% +together by hydrogen bonds between these +the bases on the opposite strands down + + align:start position:0% +the bases on the opposite strands down + + + align:start position:0% +the bases on the opposite strands down +the middle of the molecule and I like + + align:start position:0% +the middle of the molecule and I like + + + align:start position:0% +the middle of the molecule and I like +this little movie I showed you because + + align:start position:0% +this little movie I showed you because + + + align:start position:0% +this little movie I showed you because +you can see it pretty well the the + + align:start position:0% +you can see it pretty well the the + + + align:start position:0% +you can see it pretty well the the +nitrogens are blue it's easy to see the + + align:start position:0% +nitrogens are blue it's easy to see the + + + align:start position:0% +nitrogens are blue it's easy to see the +bases and the hydrogen bonds are right + + align:start position:0% +bases and the hydrogen bonds are right + + + align:start position:0% +bases and the hydrogen bonds are right +in the middle and there's another Force + + align:start position:0% +in the middle and there's another Force + + + align:start position:0% +in the middle and there's another Force +I didn't me didn't me mention it doesn't + + align:start position:0% +I didn't me didn't me mention it doesn't + + + align:start position:0% +I didn't me didn't me mention it doesn't +matter for this course but when the + + align:start position:0% +matter for this course but when the + + + align:start position:0% +matter for this course but when the +bases sort of stack on top of each other + + align:start position:0% +bases sort of stack on top of each other + + + align:start position:0% +bases sort of stack on top of each other +there's actually a kind of an extra + + align:start position:0% +there's actually a kind of an extra + + + align:start position:0% +there's actually a kind of an extra +stabilization that that comes comes from + + align:start position:0% +stabilization that that comes comes from + + + align:start position:0% +stabilization that that comes comes from +that it's a gorgeous molecule you all + + align:start position:0% +that it's a gorgeous molecule you all + + + align:start position:0% +that it's a gorgeous molecule you all +know it encodes uh the genetic + + align:start position:0% +know it encodes uh the genetic + + + align:start position:0% +know it encodes uh the genetic +information we're going to be talking + + align:start position:0% +information we're going to be talking + + + align:start position:0% +information we're going to be talking +about it a lot but + + align:start position:0% +about it a lot but + + + align:start position:0% +about it a lot but +um first thing I really wanted I want to + + align:start position:0% +um first thing I really wanted I want to + + + align:start position:0% +um first thing I really wanted I want to +you know I could just tell you it's the + + align:start position:0% +you know I could just tell you it's the + + + align:start position:0% +you know I could just tell you it's the +genetic information but one of the + + align:start position:0% +genetic information but one of the + + + align:start position:0% +genetic information but one of the +really big discoveries in biology was + + align:start position:0% +really big discoveries in biology was + + + align:start position:0% +really big discoveries in biology was +that DNA is the genetic information and + + align:start position:0% +that DNA is the genetic information and + + + align:start position:0% +that DNA is the genetic information and +a point I'm trying to help you learn + + align:start position:0% +a point I'm trying to help you learn + + + align:start position:0% +a point I'm trying to help you learn +here A Part you know I'm trying to teach + + align:start position:0% +here A Part you know I'm trying to teach + + + align:start position:0% +here A Part you know I'm trying to teach +you more than just facts and I hope some + + align:start position:0% +you more than just facts and I hope some + + + align:start position:0% +you more than just facts and I hope some +of you at least will catch that I'm + + align:start position:0% +of you at least will catch that I'm + + + align:start position:0% +of you at least will catch that I'm +trying to show you how biology is done + + align:start position:0% +trying to show you how biology is done + + + align:start position:0% +trying to show you how biology is done +it's experimental scientist you don't + + align:start position:0% +it's experimental scientist you don't + + + align:start position:0% +it's experimental scientist you don't +sit down usually and figure it out + + align:start position:0% +sit down usually and figure it out + + + align:start position:0% +sit down usually and figure it out +instead you start doing experiments and + + align:start position:0% +instead you start doing experiments and + + + align:start position:0% +instead you start doing experiments and +you get all kinds of unexpected + + align:start position:0% +you get all kinds of unexpected + + + align:start position:0% +you get all kinds of unexpected +discoveries and in general as people + + align:start position:0% +discoveries and in general as people + + + align:start position:0% +discoveries and in general as people +work in these unexpected discoveries + + align:start position:0% +work in these unexpected discoveries + + + align:start position:0% +work in these unexpected discoveries +ultimately they come to these Grand new + + align:start position:0% +ultimately they come to these Grand new + + + align:start position:0% +ultimately they come to these Grand new +insights that we you know sometimes + + align:start position:0% +insights that we you know sometimes + + + align:start position:0% +insights that we you know sometimes +would have been very hard to predict so + + align:start position:0% +would have been very hard to predict so + + + align:start position:0% +would have been very hard to predict so +the um the real question that people + + align:start position:0% +the um the real question that people + + + align:start position:0% +the um the real question that people +wondered for a long time was they we'll + + align:start position:0% +wondered for a long time was they we'll + + + align:start position:0% +wondered for a long time was they we'll +talk more about the history of genetics + + align:start position:0% +talk more about the history of genetics + + + align:start position:0% +talk more about the history of genetics +but people knew that we clearly had + + align:start position:0% +but people knew that we clearly had + + + align:start position:0% +but people knew that we clearly had +inheritable traits you could see it in + + align:start position:0% +inheritable traits you could see it in + + + align:start position:0% +inheritable traits you could see it in +your in your kids you could people had + + align:start position:0% +your in your kids you could people had + + + align:start position:0% +your in your kids you could people had +been breeding plants and all sorts of + + align:start position:0% +been breeding plants and all sorts of + + + align:start position:0% +been breeding plants and all sorts of +things breeding domestic animals they + + align:start position:0% +things breeding domestic animals they + + + align:start position:0% +things breeding domestic animals they +sort of understood the principle of of + + align:start position:0% +sort of understood the principle of of + + + align:start position:0% +sort of understood the principle of of +of inheritance when I tell you about + + align:start position:0% +of inheritance when I tell you about + + + align:start position:0% +of inheritance when I tell you about +menle we'll begin to see how his + + align:start position:0% +menle we'll begin to see how his + + + align:start position:0% +menle we'll begin to see how his +thinking led to the idea that the + + align:start position:0% +thinking led to the idea that the + + + align:start position:0% +thinking led to the idea that the +inheritance wasn't just like a sort of + + align:start position:0% +inheritance wasn't just like a sort of + + + align:start position:0% +inheritance wasn't just like a sort of +like a liquid where everything mixed + + align:start position:0% +like a liquid where everything mixed + + + align:start position:0% +like a liquid where everything mixed +together it came in units or particles + + align:start position:0% +together it came in units or particles + + + align:start position:0% +together it came in units or particles +which we know is of as genes and so the + + align:start position:0% +which we know is of as genes and so the + + + align:start position:0% +which we know is of as genes and so the +idea that there were genes + + align:start position:0% +idea that there were genes + + + align:start position:0% +idea that there were genes +um had been + + align:start position:0% +um had been + + + align:start position:0% +um had been +accepted by uh certainly by the + + align:start position:0% +accepted by uh certainly by the + + + align:start position:0% +accepted by uh certainly by the +beginning of this Century anyway but + + align:start position:0% +beginning of this Century anyway but + + + align:start position:0% +beginning of this Century anyway but +nobody knew what they were made of they + + align:start position:0% +nobody knew what they were made of they + + + align:start position:0% +nobody knew what they were made of they +were made of what what property the + + align:start position:0% +were made of what what property the + + + align:start position:0% +were made of what what property the +major properties uh that they they had + + align:start position:0% +major properties uh that they they had + + + align:start position:0% +major properties uh that they they had +was they encoded they clearly encoded + + align:start position:0% +was they encoded they clearly encoded + + + align:start position:0% +was they encoded they clearly encoded +information in some + + align:start position:0% + + + + align:start position:0% + +way they must replicate because one cell + + align:start position:0% +way they must replicate because one cell + + + align:start position:0% +way they must replicate because one cell +could give two and on and on and on so + + align:start position:0% +could give two and on and on and on so + + + align:start position:0% +could give two and on and on and on so +if you're going to pass it down in an + + align:start position:0% +if you're going to pass it down in an + + + align:start position:0% +if you're going to pass it down in an +inherited way it they have to be + + align:start position:0% +inherited way it they have to be + + + align:start position:0% +inherited way it they have to be +replicated and the third thing uh was + + align:start position:0% +replicated and the third thing uh was + + + align:start position:0% +replicated and the third thing uh was +that people knew they somehow they could + + align:start position:0% +that people knew they somehow they could + + + align:start position:0% +that people knew they somehow they could +mutate or the information content that + + align:start position:0% +mutate or the information content that + + + align:start position:0% +mutate or the information content that +they encoded could be changed you again + + align:start position:0% +they encoded could be changed you again + + + align:start position:0% +they encoded could be changed you again +you could see that that you get a uh + + align:start position:0% +you could see that that you get a uh + + + align:start position:0% +you could see that that you get a uh +something and altered characteristic and + + align:start position:0% +something and altered characteristic and + + + align:start position:0% +something and altered characteristic and +then it would be propagated down through + + align:start position:0% +then it would be propagated down through + + + align:start position:0% +then it would be propagated down through +that line that was the principle + + align:start position:0% +that line that was the principle + + + align:start position:0% +that line that was the principle +breeding that people had done for ages + + align:start position:0% +breeding that people had done for ages + + + align:start position:0% +breeding that people had done for ages +and uh so they understood that there was + + align:start position:0% +and uh so they understood that there was + + + align:start position:0% +and uh so they understood that there was +one other key thing then you they knew + + align:start position:0% +one other key thing then you they knew + + + align:start position:0% +one other key thing then you they knew +that it was in that these genes were in + + align:start position:0% +that it was in that these genes were in + + + align:start position:0% +that it was in that these genes were in +the nucleus and I'll tell you the full + + align:start position:0% +the nucleus and I'll tell you the full + + + align:start position:0% +the nucleus and I'll tell you the full +story of how even that insight + + align:start position:0% +story of how even that insight + + + align:start position:0% +story of how even that insight +was uh was arrived at but I'll just show + + align:start position:0% +was uh was arrived at but I'll just show + + + align:start position:0% +was uh was arrived at but I'll just show +you for the moment this little movie + + align:start position:0% +you for the moment this little movie + + + align:start position:0% +you for the moment this little movie +this shows some chromosomes that are all + + align:start position:0% +this shows some chromosomes that are all + + + align:start position:0% +this shows some chromosomes that are all +bunched up and are just pulled apart at + + align:start position:0% +bunched up and are just pulled apart at + + + align:start position:0% +bunched up and are just pulled apart at +the time of a cell division those + + align:start position:0% +the time of a cell division those + + + align:start position:0% +the time of a cell division those +chromosomes are as we now know are made + + align:start position:0% +chromosomes are as we now know are made + + + align:start position:0% +chromosomes are as we now know are made +of of DNA but in essence what people had + + align:start position:0% +of of DNA but in essence what people had + + + align:start position:0% +of of DNA but in essence what people had +seen through the microscope was these + + align:start position:0% +seen through the microscope was these + + + align:start position:0% +seen through the microscope was these +chromosomes or colored things that they + + align:start position:0% +chromosomes or colored things that they + + + align:start position:0% +chromosomes or colored things that they +could stain they could sort of see + + align:start position:0% +could stain they could sort of see + + + align:start position:0% +could stain they could sort of see +something had doubled and just before + + align:start position:0% +something had doubled and just before + + + align:start position:0% +something had doubled and just before +the cell + + align:start position:0% +the cell + + + align:start position:0% +the cell +divided the two sets separate ated and + + align:start position:0% +divided the two sets separate ated and + + + align:start position:0% +divided the two sets separate ated and +each cell got a new set so that's about + + align:start position:0% +each cell got a new set so that's about + + + align:start position:0% +each cell got a new set so that's about +what people + + align:start position:0% +what people + + + align:start position:0% +what people +knew they had those properties they were + + align:start position:0% +knew they had those properties they were + + + align:start position:0% +knew they had those properties they were +in the + + align:start position:0% +in the + + + align:start position:0% +in the +nucleus they knew about as much as you + + align:start position:0% +nucleus they knew about as much as you + + + align:start position:0% +nucleus they knew about as much as you +do they knew the major classes of + + align:start position:0% +do they knew the major classes of + + + align:start position:0% +do they knew the major classes of +biomolecules in a + + align:start position:0% +biomolecules in a + + + align:start position:0% +biomolecules in a +Cell so what do you + + align:start position:0% +Cell so what do you + + + align:start position:0% +Cell so what do you +think you would need to do to show that + + align:start position:0% +think you would need to do to show that + + + align:start position:0% +think you would need to do to show that +DNA encodes the is the genetic material + + align:start position:0% +DNA encodes the is the genetic material + + + align:start position:0% +DNA encodes the is the genetic material +encodes genes find somebody near you + + align:start position:0% +encodes genes find somebody near you + + + align:start position:0% +encodes genes find somebody near you +give them you a minute or so just see + + align:start position:0% +give them you a minute or so just see + + + align:start position:0% +give them you a minute or so just see +what kind I'd like to hear what kind of + + align:start position:0% +what kind I'd like to hear what kind of + + + align:start position:0% +what kind I'd like to hear what kind of +ideas you come up with then I'm gonna + + align:start position:0% +ideas you come up with then I'm gonna + + + align:start position:0% +ideas you come up with then I'm gonna +I'll tell you how it happened but I want + + align:start position:0% +I'll tell you how it happened but I want + + + align:start position:0% +I'll tell you how it happened but I want +to hear on you think about it just see + + align:start position:0% +to hear on you think about it just see + + + align:start position:0% +to hear on you think about it just see +you can come up with a couple ideas for + + align:start position:0% +you can come up with a couple ideas for + + + align:start position:0% +you can come up with a couple ideas for +me what you need to figure + + align:start position:0% + + + + align:start position:0% + +out + + align:start position:0% + + + + align:start position:0% + +okay well let's let's just see see what + + align:start position:0% +okay well let's let's just see see what + + + align:start position:0% +okay well let's let's just see see what +sort of thing so anybody what kind of + + align:start position:0% +sort of thing so anybody what kind of + + + align:start position:0% +sort of thing so anybody what kind of +ideas anybody got what would you want to + + align:start position:0% +ideas anybody got what would you want to + + + align:start position:0% +ideas anybody got what would you want to +make me believe + + align:start position:0% +make me believe + + + align:start position:0% +make me believe +that DNA is doing that I think it's a + + align:start position:0% +that DNA is doing that I think it's a + + + align:start position:0% +that DNA is doing that I think it's a +protein for the moment that's what I + + align:start position:0% +protein for the moment that's what I + + + align:start position:0% +protein for the moment that's what I +think is most likely what do you think + + align:start position:0% +think is most likely what do you think + + + align:start position:0% +think is most likely what do you think +anybody got an + + align:start position:0% +anybody got an + + + align:start position:0% +anybody got an +idea the + + align:start position:0% + + + + align:start position:0% + +DNA mess up the DNA and see if we mess + + align:start position:0% +DNA mess up the DNA and see if we mess + + + align:start position:0% +DNA mess up the DNA and see if we mess +up the + + align:start position:0% + + + + align:start position:0% + +cell how we can do + + align:start position:0% + + + + align:start position:0% + +that I I can break a cell open and I can + + align:start position:0% +that I I can break a cell open and I can + + + align:start position:0% +that I I can break a cell open and I can +I guess I can purify DNA and I can + + align:start position:0% +I guess I can purify DNA and I can + + + align:start position:0% +I guess I can purify DNA and I can +analyze it and it's got four bases in it + + align:start position:0% +analyze it and it's got four bases in it + + + align:start position:0% +analyze it and it's got four bases in it +and it's got a sugars and phosphates at + + align:start position:0% +and it's got a sugars and phosphates at + + + align:start position:0% +and it's got a sugars and phosphates at +that point nobody could see DNA we + + align:start position:0% +that point nobody could see DNA we + + + align:start position:0% +that point nobody could see DNA we +didn't even know the + + align:start position:0% +didn't even know the + + + align:start position:0% +didn't even know the +structure yeah take it out of one + + align:start position:0% +structure yeah take it out of one + + + align:start position:0% +structure yeah take it out of one +cell take it out of one cell put it into + + align:start position:0% +cell take it out of one cell put it into + + + align:start position:0% +cell take it out of one cell put it into +another and what would you expect to + + align:start position:0% +another and what would you expect to + + + align:start position:0% +another and what would you expect to +happen + + align:start position:0% + + + + align:start position:0% + +then okay so some that's that's that's a + + align:start position:0% +then okay so some that's that's that's a + + + align:start position:0% +then okay so some that's that's that's a +really nice idea so somehow the if you + + align:start position:0% +really nice idea so somehow the if you + + + align:start position:0% +really nice idea so somehow the if you +took the DNA and moved it from one cell + + align:start position:0% +took the DNA and moved it from one cell + + + align:start position:0% +took the DNA and moved it from one cell +to another that the characteristic of + + align:start position:0% +to another that the characteristic of + + + align:start position:0% +to another that the characteristic of +this cell would be somehow carried over + + align:start position:0% +this cell would be somehow carried over + + + align:start position:0% +this cell would be somehow carried over +okay that's in fact the way it happened + + align:start position:0% +okay that's in fact the way it happened + + + align:start position:0% +okay that's in fact the way it happened +but not as simply as as that as I'll + + align:start position:0% +but not as simply as as that as I'll + + + align:start position:0% +but not as simply as as that as I'll +tell you but that's that exactly the + + align:start position:0% +tell you but that's that exactly the + + + align:start position:0% +tell you but that's that exactly the +essence of it one little problem maybe + + align:start position:0% +essence of it one little problem maybe + + + align:start position:0% +essence of it one little problem maybe +see if anybody has a thought on this if + + align:start position:0% +see if anybody has a thought on this if + + + align:start position:0% +see if anybody has a thought on this if +I purify DNA I mean nothing's ever + + align:start position:0% +I purify DNA I mean nothing's ever + + + align:start position:0% +I purify DNA I mean nothing's ever +really pure right you get it out and + + align:start position:0% +really pure right you get it out and + + + align:start position:0% +really pure right you get it out and +there's always little bits of stuff and + + align:start position:0% +there's always little bits of stuff and + + + align:start position:0% +there's always little bits of stuff and +someone can always argue well it yeah + + align:start position:0% +someone can always argue well it yeah + + + align:start position:0% +someone can always argue well it yeah +it's 99% DNA but it's the other bits you + + align:start position:0% +it's 99% DNA but it's the other bits you + + + align:start position:0% +it's 99% DNA but it's the other bits you +can't get rid of yeah what if we use + + align:start position:0% +can't get rid of yeah what if we use + + + align:start position:0% +can't get rid of yeah what if we use +radioactive + + align:start position:0% + + + + align:start position:0% + +we use radioactive material how's that + + align:start position:0% +we use radioactive material how's that + + + align:start position:0% +we use radioactive material how's that +going to help us for + + align:start position:0% +going to help us for + + + align:start position:0% +going to help us for +example so like DNA contain doesn't + + align:start position:0% +example so like DNA contain doesn't + + + align:start position:0% +example so like DNA contain doesn't +contain uh nitrogen right it does + + align:start position:0% +contain uh nitrogen right it does + + + align:start position:0% +contain uh nitrogen right it does +contain + + align:start position:0% +contain + + + align:start position:0% +contain +nitrogen for example like find any at + + align:start position:0% +nitrogen for example like find any at + + + align:start position:0% +nitrogen for example like find any at +that only DNA + + align:start position:0% +that only DNA + + + align:start position:0% +that only DNA +contain uh don't + + align:start position:0% +contain uh don't + + + align:start position:0% +contain uh don't +contain well it gets it gets a little + + align:start position:0% +contain well it gets it gets a little + + + align:start position:0% +contain well it gets it gets a little +comp you can label certainly nucleic + + align:start position:0% +comp you can label certainly nucleic + + + align:start position:0% +comp you can label certainly nucleic +acids have like phosphate in them but so + + align:start position:0% +acids have like phosphate in them but so + + + align:start position:0% +acids have like phosphate in them but so +does + + align:start position:0% +does + + + align:start position:0% +does +RNA that's that's going to be hard any + + align:start position:0% +RNA that's that's going to be hard any + + + align:start position:0% +RNA that's that's going to be hard any +we got if I if I had a mixture of things + + align:start position:0% +we got if I if I had a mixture of things + + + align:start position:0% +we got if I if I had a mixture of things +and and I wanted to prove whether + + align:start position:0% +and and I wanted to prove whether + + + align:start position:0% +and and I wanted to prove whether +something was DNA let's say DNA a + + align:start position:0% +something was DNA let's say DNA a + + + align:start position:0% +something was DNA let's say DNA a +protein or something need some some + + align:start position:0% +protein or something need some some + + + align:start position:0% +protein or something need some some +really specific way of saying I did + + align:start position:0% +really specific way of saying I did + + + align:start position:0% +really specific way of saying I did +something to the DNA and not to the + + align:start position:0% +something to the DNA and not to the + + + align:start position:0% +something to the DNA and not to the +protein or something like that you heard + + align:start position:0% +protein or something like that you heard + + + align:start position:0% +protein or something like that you heard +anything in this course that is really + + align:start position:0% + + + + align:start position:0% + +specific and enzymes do you think that + + align:start position:0% +specific and enzymes do you think that + + + align:start position:0% +specific and enzymes do you think that +give you an idea for how you might do + + align:start position:0% +give you an idea for how you might do + + + align:start position:0% +give you an idea for how you might do +it if I've got a tube and it's mostly + + align:start position:0% +it if I've got a tube and it's mostly + + + align:start position:0% +it if I've got a tube and it's mostly +DNA and maybe a bit of protein and + + align:start position:0% +DNA and maybe a bit of protein and + + + align:start position:0% +DNA and maybe a bit of protein and +something and let's say his idea is + + align:start position:0% +something and let's say his idea is + + + align:start position:0% +something and let's say his idea is +working that we can take the DNA from + + align:start position:0% +working that we can take the DNA from + + + align:start position:0% +working that we can take the DNA from +this cell and put it over in that into + + align:start position:0% +this cell and put it over in that into + + + align:start position:0% +this cell and put it over in that into +the second cell and see the + + align:start position:0% +the second cell and see the + + + align:start position:0% +the second cell and see the +characteristic + + align:start position:0% +characteristic + + + align:start position:0% +characteristic +changed if I wanted to do something to + + align:start position:0% +changed if I wanted to do something to + + + align:start position:0% +changed if I wanted to do something to +show that it was the DNA in the in the + + align:start position:0% +show that it was the DNA in the in the + + + align:start position:0% +show that it was the DNA in the in the +tube that was responsible could you use + + align:start position:0% +tube that was responsible could you use + + + align:start position:0% +tube that was responsible could you use +an + + align:start position:0% +an + + + align:start position:0% +an +enzyme and what kind of enzyme would you + + align:start position:0% +enzyme and what kind of enzyme would you + + + align:start position:0% +enzyme and what kind of enzyme would you +want just make what characteristics + + align:start position:0% +want just make what characteristics + + + align:start position:0% +want just make what characteristics +would you like it to + + align:start position:0% +would you like it to + + + align:start position:0% +would you like it to +have Nature's probably made it for you + + align:start position:0% + + + + align:start position:0% + +already like something that synthesizes + + align:start position:0% +already like something that synthesizes + + + align:start position:0% +already like something that synthesizes +DNA something that breaks down + + align:start position:0% +DNA something that breaks down + + + align:start position:0% +DNA something that breaks down +DNA + + align:start position:0% +DNA + + + align:start position:0% +DNA +any say I treated this tube with some + + align:start position:0% +any say I treated this tube with some + + + align:start position:0% +any say I treated this tube with some +kind of enzyme what would we and then I + + align:start position:0% +kind of enzyme what would we and then I + + + align:start position:0% +kind of enzyme what would we and then I +wanted to see the outcome what would we + + align:start position:0% +wanted to see the outcome what would we + + + align:start position:0% +wanted to see the outcome what would we +want an enzyme that did what anybody + + align:start position:0% +want an enzyme that did what anybody + + + align:start position:0% +want an enzyme that did what anybody +else got an + + align:start position:0% + + + + align:start position:0% + +idea + + align:start position:0% +idea + + + align:start position:0% +idea +we're you're saying asserting that it's + + align:start position:0% +we're you're saying asserting that it's + + + align:start position:0% +we're you're saying asserting that it's +the DNA in my prep I like your idea but + + align:start position:0% +the DNA in my prep I like your idea but + + + align:start position:0% +the DNA in my prep I like your idea but +I need to prove it so I need to do + + align:start position:0% +I need to prove it so I need to do + + + align:start position:0% +I need to prove it so I need to do +something to show that it's actually the + + align:start position:0% +something to show that it's actually the + + + align:start position:0% +something to show that it's actually the +DNA not the other stuff so I had an + + align:start position:0% +DNA not the other stuff so I had an + + + align:start position:0% +DNA not the other stuff so I had an +enzyme that did what to the + + align:start position:0% +enzyme that did what to the + + + align:start position:0% +enzyme that did what to the +DNA if it broke it down yeah we could + + align:start position:0% +DNA if it broke it down yeah we could + + + align:start position:0% +DNA if it broke it down yeah we could +treat it and if your idea is right if we + + align:start position:0% +treat it and if your idea is right if we + + + align:start position:0% +treat it and if your idea is right if we +treat the stuff with with something that + + align:start position:0% +treat the stuff with with something that + + + align:start position:0% +treat the stuff with with something that +specifically breaks down DNA it won't + + align:start position:0% +specifically breaks down DNA it won't + + + align:start position:0% +specifically breaks down DNA it won't +get + + align:start position:0% +get + + + align:start position:0% +get +transferred that make sense okay I mean + + align:start position:0% +transferred that make sense okay I mean + + + align:start position:0% +transferred that make sense okay I mean +that's a way you could go out a proof of + + align:start position:0% +that's a way you could go out a proof of + + + align:start position:0% +that's a way you could go out a proof of +this and in fact that's what happened + + align:start position:0% +this and in fact that's what happened + + + align:start position:0% +this and in fact that's what happened +but I'm going to quickly tell you how it + + align:start position:0% +but I'm going to quickly tell you how it + + + align:start position:0% +but I'm going to quickly tell you how it +actually + + align:start position:0% +actually + + + align:start position:0% +actually +happened and again you know as I say I'm + + align:start position:0% +happened and again you know as I say I'm + + + align:start position:0% +happened and again you know as I say I'm +trying to tell you a few things there + + align:start position:0% +trying to tell you a few things there + + + align:start position:0% +trying to tell you a few things there +besides here's the facts that you have + + align:start position:0% +besides here's the facts that you have + + + align:start position:0% +besides here's the facts that you have +to need to know an exam there's a bigger + + align:start position:0% +to need to know an exam there's a bigger + + + align:start position:0% +to need to know an exam there's a bigger +picture here and this is how research + + align:start position:0% +picture here and this is how research + + + align:start position:0% +picture here and this is how research +goes and particularly in an experimental + + align:start position:0% +goes and particularly in an experimental + + + align:start position:0% +goes and particularly in an experimental +science such as biology the important + + align:start position:0% +science such as biology the important + + + align:start position:0% +science such as biology the important +early work on this came from a guy who + + align:start position:0% +early work on this came from a guy who + + + align:start position:0% +early work on this came from a guy who +was known as Frederick his name was + + align:start position:0% +was known as Frederick his name was + + + align:start position:0% +was known as Frederick his name was +Frederick + + align:start position:0% + + + + align:start position:0% + +Griffith he was in London he was a + + align:start position:0% +Griffith he was in London he was a + + + align:start position:0% +Griffith he was in London he was a +physician he was working in the + + align:start position:0% + + + + align:start position:0% + +1920s and he was studying + + align:start position:0% + + + + align:start position:0% + +pneumonia that's an infection of the + + align:start position:0% + + + + align:start position:0% + +lungs by + + align:start position:0% +lungs by + + + align:start position:0% +lungs by +bacteria there's there's one there's + + align:start position:0% +bacteria there's there's one there's + + + align:start position:0% +bacteria there's there's one there's +more than one kind of bacterium will + + align:start position:0% +more than one kind of bacterium will + + + align:start position:0% +more than one kind of bacterium will +cause pneumonia but one of the really + + align:start position:0% +cause pneumonia but one of the really + + + align:start position:0% +cause pneumonia but one of the really +important on clinically was + + align:start position:0% +important on clinically was + + + align:start position:0% +important on clinically was +streptococus + + align:start position:0% + + + + align:start position:0% + +um pneumoni so it was a bacterium it was + + align:start position:0% +um pneumoni so it was a bacterium it was + + + align:start position:0% +um pneumoni so it was a bacterium it was +uh it was given that uh that name it's a + + align:start position:0% +uh it was given that uh that name it's a + + + align:start position:0% +uh it was given that uh that name it's a +common we all have bacteria on us we I + + align:start position:0% +common we all have bacteria on us we I + + + align:start position:0% +common we all have bacteria on us we I +think I told you we have about 10 to the + + align:start position:0% +think I told you we have about 10 to the + + + align:start position:0% +think I told you we have about 10 to the +12th on our skin for example and if + + align:start position:0% +12th on our skin for example and if + + + align:start position:0% +12th on our skin for example and if +pseudomonas excuse me if strepto oxus is + + align:start position:0% +pseudomonas excuse me if strepto oxus is + + + align:start position:0% +pseudomonas excuse me if strepto oxus is +on your skin it's not a problem but if + + align:start position:0% +on your skin it's not a problem but if + + + align:start position:0% +on your skin it's not a problem but if +it gets into your lungs it's a problem + + align:start position:0% +it gets into your lungs it's a problem + + + align:start position:0% +it gets into your lungs it's a problem +and so to live with all all these um + + align:start position:0% +and so to live with all all these um + + + align:start position:0% +and so to live with all all these um +bacteria um they with us our bodies have + + align:start position:0% +bacteria um they with us our bodies have + + + align:start position:0% +bacteria um they with us our bodies have +defenses so that we have uh this immune + + align:start position:0% +defenses so that we have uh this immune + + + align:start position:0% +defenses so that we have uh this immune +system we'll talk about more in a bunch + + align:start position:0% +system we'll talk about more in a bunch + + + align:start position:0% +system we'll talk about more in a bunch +of Defender cells things that you know + + align:start position:0% +of Defender cells things that you know + + + align:start position:0% +of Defender cells things that you know +is white blood cells are Defenders um + + align:start position:0% +is white blood cells are Defenders um + + + align:start position:0% +is white blood cells are Defenders um +let's just see here I'm going to show + + align:start position:0% +let's just see here I'm going to show + + + align:start position:0% +let's just see here I'm going to show +you this little movie this is one of + + align:start position:0% +you this little movie this is one of + + + align:start position:0% +you this little movie this is one of +your white blood cells a special kind of + + align:start position:0% +your white blood cells a special kind of + + + align:start position:0% +your white blood cells a special kind of +white blood cell that little thing it's + + align:start position:0% +white blood cell that little thing it's + + + align:start position:0% +white blood cell that little thing it's +chasing is a bacterium these round + + align:start position:0% +chasing is a bacterium these round + + + align:start position:0% +chasing is a bacterium these round +things are red blood cells I mean + + align:start position:0% +things are red blood cells I mean + + + align:start position:0% +things are red blood cells I mean +doesn't look like a dog going after a + + align:start position:0% +doesn't look like a dog going after a + + + align:start position:0% +doesn't look like a dog going after a +mouse or a cat going something it's + + align:start position:0% +mouse or a cat going something it's + + + align:start position:0% +mouse or a cat going something it's +chasing it it can tell it's there this + + align:start position:0% +chasing it it can tell it's there this + + + align:start position:0% +chasing it it can tell it's there this +is remarkable it's a little pixelated + + align:start position:0% +is remarkable it's a little pixelated + + + align:start position:0% +is remarkable it's a little pixelated +but this is real it's going to catch it + + align:start position:0% +but this is real it's going to catch it + + + align:start position:0% +but this is real it's going to catch it +right about + + align:start position:0% +right about + + + align:start position:0% +right about +there and it eats + + align:start position:0% +there and it eats + + + align:start position:0% +there and it eats +it I mean we have these cells in inside + + align:start position:0% +it I mean we have these cells in inside + + + align:start position:0% +it I mean we have these cells in inside +us that's why you don't die even though + + align:start position:0% +us that's why you don't die even though + + + align:start position:0% +us that's why you don't die even though +we live in a world that's surrounded by + + align:start position:0% +we live in a world that's surrounded by + + + align:start position:0% +we live in a world that's surrounded by +uh by uh + + align:start position:0% +uh by uh + + + align:start position:0% +uh by uh +bacteria okay so we'll go on um so + + align:start position:0% +bacteria okay so we'll go on um so + + + align:start position:0% +bacteria okay so we'll go on um so +getting pneumonia in the in the old days + + align:start position:0% +getting pneumonia in the in the old days + + + align:start position:0% +getting pneumonia in the in the old days +was in those days was a really bad uh uh + + align:start position:0% +was in those days was a really bad uh uh + + + align:start position:0% +was in those days was a really bad uh uh +thing you you get + + align:start position:0% +thing you you get + + + align:start position:0% +thing you you get +infected get this uh in in your lungs + + align:start position:0% +infected get this uh in in your lungs + + + align:start position:0% +infected get this uh in in your lungs +and then you'd have four to six days of + + align:start position:0% +and then you'd have four to six days of + + + align:start position:0% +and then you'd have four to six days of +high + + align:start position:0% + + + + align:start position:0% + +fever and then the patient would go + + align:start position:0% +fever and then the patient would go + + + align:start position:0% +fever and then the patient would go +would reach what's termed as a crisis + + align:start position:0% +would reach what's termed as a crisis + + + align:start position:0% +would reach what's termed as a crisis +and one of two things would happen + + align:start position:0% +and one of two things would happen + + + align:start position:0% +and one of two things would happen +they'd either + + align:start position:0% +they'd either + + + align:start position:0% +they'd either +live or they' + + align:start position:0% + + + + align:start position:0% + +die and that was it I mean this was no + + align:start position:0% +die and that was it I mean this was no + + + align:start position:0% +die and that was it I mean this was no +fun if somebody you knew had it because + + align:start position:0% +fun if somebody you knew had it because + + + align:start position:0% +fun if somebody you knew had it because +you didn't know the outcome and the + + align:start position:0% +you didn't know the outcome and the + + + align:start position:0% +you didn't know the outcome and the +outcome wasn't necessarily very good now + + align:start position:0% +outcome wasn't necessarily very good now + + + align:start position:0% +outcome wasn't necessarily very good now +you call up the doctor and they pump you + + align:start position:0% +you call up the doctor and they pump you + + + align:start position:0% +you call up the doctor and they pump you +full of antibiotics but antibiotics + + align:start position:0% +full of antibiotics but antibiotics + + + align:start position:0% +full of antibiotics but antibiotics +hadn't been discovered yet so this was + + align:start position:0% +hadn't been discovered yet so this was + + + align:start position:0% +hadn't been discovered yet so this was +pretty serious business and people were + + align:start position:0% +pretty serious business and people were + + + align:start position:0% +pretty serious business and people were +trying uh to understand what was + + align:start position:0% +trying uh to understand what was + + + align:start position:0% +trying uh to understand what was +happening well what was what goes on + + align:start position:0% +happening well what was what goes on + + + align:start position:0% +happening well what was what goes on +what was going on during those uh during + + align:start position:0% +what was going on during those uh during + + + align:start position:0% +what was going on during those uh during +these four to six days that then led to + + align:start position:0% +these four to six days that then led to + + + align:start position:0% +these four to six days that then led to +one of these two outcomes well it turns + + align:start position:0% +one of these two outcomes well it turns + + + align:start position:0% +one of these two outcomes well it turns +out that uh strepto Co is is a bacterium + + align:start position:0% +out that uh strepto Co is is a bacterium + + + align:start position:0% +out that uh strepto Co is is a bacterium +like this that has around it so that's + + align:start position:0% +like this that has around it so that's + + + align:start position:0% +like this that has around it so that's +the + + align:start position:0% + + + + align:start position:0% + +bacterium and it has around it something + + align:start position:0% +bacterium and it has around it something + + + align:start position:0% +bacterium and it has around it something +known as a + + align:start position:0% +known as a + + + align:start position:0% +known as a +capsule and what that capsule is is + + align:start position:0% + + + + align:start position:0% + +polysaccharide remember back to the + + align:start position:0% +polysaccharide remember back to the + + + align:start position:0% +polysaccharide remember back to the +second lecture when I was confusing you + + align:start position:0% +second lecture when I was confusing you + + + align:start position:0% +second lecture when I was confusing you +all by showing you how sugars could hook + + align:start position:0% +all by showing you how sugars could hook + + + align:start position:0% +all by showing you how sugars could hook +together in all manner of different ways + + align:start position:0% +together in all manner of different ways + + + align:start position:0% +together in all manner of different ways +well that's what polysaccharides are you + + align:start position:0% +well that's what polysaccharides are you + + + align:start position:0% +well that's what polysaccharides are you +just hook a bunch of sugars together and + + align:start position:0% +just hook a bunch of sugars together and + + + align:start position:0% +just hook a bunch of sugars together and +you for this course you don't have to + + align:start position:0% +you for this course you don't have to + + + align:start position:0% +you for this course you don't have to +remember link the linkages particular + + align:start position:0% +remember link the linkages particular + + + align:start position:0% +remember link the linkages particular +you just have to understand that there + + align:start position:0% +you just have to understand that there + + + align:start position:0% +you just have to understand that there +are different kinds of linkages and + + align:start position:0% +are different kinds of linkages and + + + align:start position:0% +are different kinds of linkages and +every time you hook at it in a different + + align:start position:0% +every time you hook at it in a different + + + align:start position:0% +every time you hook at it in a different +way you get a different kind of of + + align:start position:0% +way you get a different kind of of + + + align:start position:0% +way you get a different kind of of +polysaccharide out of it but anyway the + + align:start position:0% +polysaccharide out of it but anyway the + + + align:start position:0% +polysaccharide out of it but anyway the +uh the bacteria make these this capsule + + align:start position:0% +uh the bacteria make these this capsule + + + align:start position:0% +uh the bacteria make these this capsule +of polysaccharide and it's full of + + align:start position:0% +of polysaccharide and it's full of + + + align:start position:0% +of polysaccharide and it's full of +hydroxy groups from all those sugars so + + align:start position:0% +hydroxy groups from all those sugars so + + + align:start position:0% +hydroxy groups from all those sugars so +it attracts a lot of water around it and + + align:start position:0% +it attracts a lot of water around it and + + + align:start position:0% +it attracts a lot of water around it and +what it does is it causes a problem for + + align:start position:0% +what it does is it causes a problem for + + + align:start position:0% +what it does is it causes a problem for +those Defender cells that we just saw + + align:start position:0% +those Defender cells that we just saw + + + align:start position:0% +those Defender cells that we just saw +those would be for example a macro Fage + + align:start position:0% +those would be for example a macro Fage + + + align:start position:0% +those would be for example a macro Fage +a kind of white blood cell and it can't + + align:start position:0% +a kind of white blood cell and it can't + + + align:start position:0% +a kind of white blood cell and it can't +eat something that's got the capsule now + + align:start position:0% +eat something that's got the capsule now + + + align:start position:0% +eat something that's got the capsule now +this is uh here's a picture of one of + + align:start position:0% +this is uh here's a picture of one of + + + align:start position:0% +this is uh here's a picture of one of +these capsules and one of these kinds of + + align:start position:0% +these capsules and one of these kinds of + + + align:start position:0% +these capsules and one of these kinds of +bacteria you can sort of see it out here + + align:start position:0% +bacteria you can sort of see it out here + + + align:start position:0% +bacteria you can sort of see it out here +it's polysaccharide that's the main part + + align:start position:0% +it's polysaccharide that's the main part + + + align:start position:0% +it's polysaccharide that's the main part +of the bacterium and here's a another + + align:start position:0% +of the bacterium and here's a another + + + align:start position:0% +of the bacterium and here's a another +pixelated thing of of one of these white + + align:start position:0% +pixelated thing of of one of these white + + + align:start position:0% +pixelated thing of of one of these white +blood cells eating a a bacterium that + + align:start position:0% +blood cells eating a a bacterium that + + + align:start position:0% +blood cells eating a a bacterium that +doesn't have a capsule but Watch What + + align:start position:0% +doesn't have a capsule but Watch What + + + align:start position:0% +doesn't have a capsule but Watch What +Happens the bacterium has a + + align:start position:0% +Happens the bacterium has a + + + align:start position:0% +Happens the bacterium has a +capsule it can't get hold of it it just + + align:start position:0% +capsule it can't get hold of it it just + + + align:start position:0% +capsule it can't get hold of it it just +can't quite grab hold of it so what what + + align:start position:0% +can't quite grab hold of it so what what + + + align:start position:0% +can't quite grab hold of it so what what +happened during those those days though + + align:start position:0% +happened during those those days though + + + align:start position:0% +happened during those those days though +was this capsule which is a foreign + + align:start position:0% +was this capsule which is a foreign + + + align:start position:0% +was this capsule which is a foreign +um um entity to your body gets + + align:start position:0% +um um entity to your body gets + + + align:start position:0% +um um entity to your body gets +recognized by your immune system and + + align:start position:0% +recognized by your immune system and + + + align:start position:0% +recognized by your immune system and +they your immune system made antibodies + + align:start position:0% +they your immune system made antibodies + + + align:start position:0% +they your immune system made antibodies +that could recognize that we'll talk + + align:start position:0% +that could recognize that we'll talk + + + align:start position:0% +that could recognize that we'll talk +about what these + + align:start position:0% +about what these + + + align:start position:0% +about what these +are but what you all you need to know + + align:start position:0% +are but what you all you need to know + + + align:start position:0% +are but what you all you need to know +for the moment is that they're proteins + + align:start position:0% +for the moment is that they're proteins + + + align:start position:0% +for the moment is that they're proteins +and they have a they can be tuned to + + align:start position:0% +and they have a they can be tuned to + + + align:start position:0% +and they have a they can be tuned to +recognize some chemical entity with a + + align:start position:0% +recognize some chemical entity with a + + + align:start position:0% +recognize some chemical entity with a +very very high degree of specificity so + + align:start position:0% +very very high degree of specificity so + + + align:start position:0% +very very high degree of specificity so +what the body was doing during this + + align:start position:0% +what the body was doing during this + + + align:start position:0% +what the body was doing during this +thing was trying to make antibodies that + + align:start position:0% +thing was trying to make antibodies that + + + align:start position:0% +thing was trying to make antibodies that +would help it Rec that would + + align:start position:0% +would help it Rec that would + + + align:start position:0% +would help it Rec that would +recognize this capsule and then it + + align:start position:0% +recognize this capsule and then it + + + align:start position:0% +recognize this capsule and then it +decorates the capsule with these things + + align:start position:0% +decorates the capsule with these things + + + align:start position:0% +decorates the capsule with these things +and once it puts anybody stuck all over + + align:start position:0% +and once it puts anybody stuck all over + + + align:start position:0% +and once it puts anybody stuck all over +the surface now it can get hold of it + + align:start position:0% +the surface now it can get hold of it + + + align:start position:0% +the surface now it can get hold of it +and again in a fact you don't have to + + align:start position:0% +and again in a fact you don't have to + + + align:start position:0% +and again in a fact you don't have to +know these These are turn this whole + + align:start position:0% +know these These are turn this whole + + + align:start position:0% +know these These are turn this whole +process is called opsonization or these + + align:start position:0% +process is called opsonization or these + + + align:start position:0% +process is called opsonization or these +things the reason they use the word + + align:start position:0% +things the reason they use the word + + + align:start position:0% +things the reason they use the word +opson because opson is the Greek word + + align:start position:0% +opson because opson is the Greek word + + + align:start position:0% +opson because opson is the Greek word +for seasoning and it was as if these + + align:start position:0% +for seasoning and it was as if these + + + align:start position:0% +for seasoning and it was as if these +white blood cells like to have their + + align:start position:0% +white blood cells like to have their + + + align:start position:0% +white blood cells like to have their +bacteria seasoned correctly before they + + align:start position:0% +bacteria seasoned correctly before they + + + align:start position:0% +bacteria seasoned correctly before they +can eat them and what's really going on + + align:start position:0% +can eat them and what's really going on + + + align:start position:0% +can eat them and what's really going on +is that they're decorating them with + + align:start position:0% +is that they're decorating them with + + + align:start position:0% +is that they're decorating them with +anbody so what was going on after a + + align:start position:0% +anbody so what was going on after a + + + align:start position:0% +anbody so what was going on after a +person got sick it was a race between + + align:start position:0% +person got sick it was a race between + + + align:start position:0% +person got sick it was a race between +their immune system trying to make + + align:start position:0% +their immune system trying to make + + + align:start position:0% +their immune system trying to make +antibodies which would let their immune + + align:start position:0% +antibodies which would let their immune + + + align:start position:0% +antibodies which would let their immune +system suppress the infection and the + + align:start position:0% +system suppress the infection and the + + + align:start position:0% +system suppress the infection and the +bacterium which is replicating unchecked + + align:start position:0% +bacterium which is replicating unchecked + + + align:start position:0% +bacterium which is replicating unchecked +for the first few days and that's why uh + + align:start position:0% +for the first few days and that's why uh + + + align:start position:0% +for the first few days and that's why uh +it was such a scary business CU you + + align:start position:0% +it was such a scary business CU you + + + align:start position:0% +it was such a scary business CU you +didn't know what the outcome was and + + align:start position:0% +didn't know what the outcome was and + + + align:start position:0% +didn't know what the outcome was and +things could tip it one way or the other + + align:start position:0% +things could tip it one way or the other + + + align:start position:0% +things could tip it one way or the other +well this did suggest a kind of therapy + + align:start position:0% +well this did suggest a kind of therapy + + + align:start position:0% +well this did suggest a kind of therapy +uh the kind of therapy would be to + + align:start position:0% + + + + align:start position:0% + +isolate isolate a + + align:start position:0% +isolate isolate a + + + align:start position:0% +isolate isolate a +capsule to inject a + + align:start position:0% + + + + align:start position:0% + +horse get the antibodies from the horse + + align:start position:0% +horse get the antibodies from the horse + + + align:start position:0% +horse get the antibodies from the horse +while horse a horse is huge right makes + + align:start position:0% +while horse a horse is huge right makes + + + align:start position:0% +while horse a horse is huge right makes +a lot of a lot of antibodies a lot + + align:start position:0% +a lot of a lot of antibodies a lot + + + align:start position:0% +a lot of a lot of antibodies a lot +better than injecting a mouse if you + + align:start position:0% +better than injecting a mouse if you + + + align:start position:0% +better than injecting a mouse if you +want to get antibodies um so get any + + align:start position:0% +want to get antibodies um so get any + + + align:start position:0% +want to get antibodies um so get any +bodies and then + + align:start position:0% +bodies and then + + + align:start position:0% +bodies and then +inject the + + align:start position:0% + + + + align:start position:0% + +patient it's a good idea in principle + + align:start position:0% +patient it's a good idea in principle + + + align:start position:0% +patient it's a good idea in principle +see what you do you're sort of short + + align:start position:0% +see what you do you're sort of short + + + align:start position:0% +see what you do you're sort of short +circuiting this whole process problem + + align:start position:0% +circuiting this whole process problem + + + align:start position:0% +circuiting this whole process problem +was uh there were + + align:start position:0% +was uh there were + + + align:start position:0% +was uh there were +20 more than 20 kinds of + + align:start position:0% +20 more than 20 kinds of + + + align:start position:0% +20 more than 20 kinds of +capsules + + align:start position:0% + + + + align:start position:0% + +and so what uh people had to + + align:start position:0% +and so what uh people had to + + + align:start position:0% +and so what uh people had to +um uh people had to do was they had to + + align:start position:0% +um uh people had to do was they had to + + + align:start position:0% +um uh people had to do was they had to +isolate the + + align:start position:0% + + + + align:start position:0% + +bacterium from from the + + align:start position:0% + + + + align:start position:0% + +patient + + align:start position:0% + + + + align:start position:0% + +determine the type of capsule + + align:start position:0% + + + + align:start position:0% + +let's say it's sort of from capsule one + + align:start position:0% +let's say it's sort of from capsule one + + + align:start position:0% +let's say it's sort of from capsule one +up + + align:start position:0% +up + + + align:start position:0% +up +to capsule type 20 which one it was and + + align:start position:0% +to capsule type 20 which one it was and + + + align:start position:0% +to capsule type 20 which one it was and +then + + align:start position:0% +then + + + align:start position:0% +then +inject the correct + + align:start position:0% + + + + align:start position:0% + +antibody so this was nerve-wracking + + align:start position:0% +antibody so this was nerve-wracking + + + align:start position:0% +antibody so this was nerve-wracking +because it took a while for the bacteria + + align:start position:0% +because it took a while for the bacteria + + + align:start position:0% +because it took a while for the bacteria +to grow so it was pretty tight time + + align:start position:0% +to grow so it was pretty tight time + + + align:start position:0% +to grow so it was pretty tight time +window if you saw the patient right away + + align:start position:0% +window if you saw the patient right away + + + align:start position:0% +window if you saw the patient right away +that's good but if they were partway + + align:start position:0% +that's good but if they were partway + + + align:start position:0% +that's good but if they were partway +down infection not so good um so the one + + align:start position:0% +down infection not so good um so the one + + + align:start position:0% +down infection not so good um so the one +other thing when they didn't actually to + + align:start position:0% +other thing when they didn't actually to + + + align:start position:0% +other thing when they didn't actually to +do this they didn't bother all the way + + align:start position:0% +do this they didn't bother all the way + + + align:start position:0% +do this they didn't bother all the way +to isolate the capsule what they would + + align:start position:0% +to isolate the capsule what they would + + + align:start position:0% +to isolate the capsule what they would +usually do is used heat + + align:start position:0% +usually do is used heat + + + align:start position:0% +usually do is used heat +killed + + align:start position:0% + + + + align:start position:0% + +bacteria and that would then you'd have + + align:start position:0% +bacteria and that would then you'd have + + + align:start position:0% +bacteria and that would then you'd have +the capsule and everything the + + align:start position:0% +the capsule and everything the + + + align:start position:0% +the capsule and everything the +bacterium's dead it can't do anything + + align:start position:0% +bacterium's dead it can't do anything + + + align:start position:0% +bacterium's dead it can't do anything +they'd inject the horse with that and + + align:start position:0% +they'd inject the horse with that and + + + align:start position:0% +they'd inject the horse with that and +that would get you the antibodies to the + + align:start position:0% +that would get you the antibodies to the + + + align:start position:0% +that would get you the antibodies to the +capsule so what + + align:start position:0% +capsule so what + + + align:start position:0% +capsule so what +um Griffith was doing was he was + + align:start position:0% +um Griffith was doing was he was + + + align:start position:0% +um Griffith was doing was he was +fiddling around with uh with this system + + align:start position:0% +fiddling around with uh with this system + + + align:start position:0% +fiddling around with uh with this system +and there was one other Discovery they + + align:start position:0% +and there was one other Discovery they + + + align:start position:0% +and there was one other Discovery they +made perhaps wouldn't surprise you that + + align:start position:0% +made perhaps wouldn't surprise you that + + + align:start position:0% +made perhaps wouldn't surprise you that +since the bacteria surrounded by a + + align:start position:0% +since the bacteria surrounded by a + + + align:start position:0% +since the bacteria surrounded by a +molecule absorbs water that the capsules + + align:start position:0% +molecule absorbs water that the capsules + + + align:start position:0% +molecule absorbs water that the capsules +would look sort of glistening they + + align:start position:0% +would look sort of glistening they + + + align:start position:0% +would look sort of glistening they +absorb a lot of water you can see they + + align:start position:0% +absorb a lot of water you can see they + + + align:start position:0% +absorb a lot of water you can see they +look here so what they discover so if + + align:start position:0% +look here so what they discover so if + + + align:start position:0% +look here so what they discover so if +they if they have a + + align:start position:0% + + + + align:start position:0% + +capsule you get what are called + + align:start position:0% +capsule you get what are called + + + align:start position:0% +capsule you get what are called +Smooth colonies and the word col + + align:start position:0% +Smooth colonies and the word col + + + align:start position:0% +Smooth colonies and the word col +in this thing just refers to started out + + align:start position:0% +in this thing just refers to started out + + + align:start position:0% +in this thing just refers to started out +as one back Criterium and it kept + + align:start position:0% +as one back Criterium and it kept + + + align:start position:0% +as one back Criterium and it kept +dividing and dividing and dividing and + + align:start position:0% +dividing and dividing and dividing and + + + align:start position:0% +dividing and dividing and dividing and +maybe there's 10 to the eth or 10 the + + align:start position:0% +maybe there's 10 to the eth or 10 the + + + align:start position:0% +maybe there's 10 to the eth or 10 the +9th bacteria in that little Colony but + + align:start position:0% +9th bacteria in that little Colony but + + + align:start position:0% +9th bacteria in that little Colony but +you can see it they've all got capsules + + align:start position:0% +you can see it they've all got capsules + + + align:start position:0% +you can see it they've all got capsules +on the outside so attracts a lot of + + align:start position:0% +on the outside so attracts a lot of + + + align:start position:0% +on the outside so attracts a lot of +water and it looks wet and those are + + align:start position:0% +water and it looks wet and those are + + + align:start position:0% +water and it looks wet and those are +what you saw but what they found if you + + align:start position:0% +what you saw but what they found if you + + + align:start position:0% +what you saw but what they found if you +waited or grew the cultures up that you + + align:start position:0% +waited or grew the cultures up that you + + + align:start position:0% +waited or grew the cultures up that you +would see some things that look dry or + + align:start position:0% +would see some things that look dry or + + + align:start position:0% +would see some things that look dry or +they called them + + align:start position:0% +they called them + + + align:start position:0% +they called them +rough and these turned out to be + + align:start position:0% +rough and these turned out to be + + + align:start position:0% +rough and these turned out to be +bacteria that lacked a + + align:start position:0% + + + + align:start position:0% + +capsule and so if you might start with a + + align:start position:0% +capsule and so if you might start with a + + + align:start position:0% +capsule and so if you might start with a +smooth + + align:start position:0% +smooth + + + align:start position:0% +smooth +strain um s + + align:start position:0% +strain um s + + + align:start position:0% +strain um s +here and a and then isolate from it a + + align:start position:0% +here and a and then isolate from it a + + + align:start position:0% +here and a and then isolate from it a +rough strain might designate it in that + + align:start position:0% +rough strain might designate it in that + + + align:start position:0% +rough strain might designate it in that +kind of way so this is the sort of thing + + align:start position:0% +kind of way so this is the sort of thing + + + align:start position:0% +kind of way so this is the sort of thing +that uh Griffith was fooling around with + + align:start position:0% +that uh Griffith was fooling around with + + + align:start position:0% +that uh Griffith was fooling around with +so um he started with doing this kind of + + align:start position:0% +so um he started with doing this kind of + + + align:start position:0% +so um he started with doing this kind of +experiment he took a smooth strain + + align:start position:0% +experiment he took a smooth strain + + + align:start position:0% +experiment he took a smooth strain +making a capsule of capsule type two + + align:start position:0% +making a capsule of capsule type two + + + align:start position:0% +making a capsule of capsule type two +okay so he was injecting a + + align:start position:0% +okay so he was injecting a + + + align:start position:0% +okay so he was injecting a +mouse with this and what + + align:start position:0% +mouse with this and what + + + align:start position:0% +mouse with this and what +happened mouse was + + align:start position:0% +happened mouse was + + + align:start position:0% +happened mouse was +dead this was a virulent form of the of + + align:start position:0% +dead this was a virulent form of the of + + + align:start position:0% +dead this was a virulent form of the of +the bacterium so he took if he took the + + align:start position:0% +the bacterium so he took if he took the + + + align:start position:0% +the bacterium so he took if he took the +the rough + + align:start position:0% +the rough + + + align:start position:0% +the rough +mutant injected the + + align:start position:0% +mutant injected the + + + align:start position:0% +mutant injected the +mouse MOS is + + align:start position:0% +mouse MOS is + + + align:start position:0% +mouse MOS is +alive and you saw why if it doesn't have + + align:start position:0% +alive and you saw why if it doesn't have + + + align:start position:0% +alive and you saw why if it doesn't have +the capsule your the Moses Defender + + align:start position:0% +the capsule your the Moses Defender + + + align:start position:0% +the capsule your the Moses Defender +cells white blood cells could eat it + + align:start position:0% +cells white blood cells could eat it + + + align:start position:0% +cells white blood cells could eat it +then he + + align:start position:0% +then he + + + align:start position:0% +then he +had heat + + align:start position:0% +had heat + + + align:start position:0% +had heat +killed S3 so this was a strain of uh + + align:start position:0% +killed S3 so this was a strain of uh + + + align:start position:0% +killed S3 so this was a strain of uh +streptococus that + + align:start position:0% +streptococus that + + + align:start position:0% +streptococus that +was uh had a different capsule a Type 3 + + align:start position:0% +was uh had a different capsule a Type 3 + + + align:start position:0% +was uh had a different capsule a Type 3 +capsule but he was heat killed why was + + align:start position:0% +capsule but he was heat killed why was + + + align:start position:0% +capsule but he was heat killed why was +he working with heat killed stuff cuz + + align:start position:0% +he working with heat killed stuff cuz + + + align:start position:0% +he working with heat killed stuff cuz +that's what you injected the horses with + + align:start position:0% +that's what you injected the horses with + + + align:start position:0% +that's what you injected the horses with +to get it so + + align:start position:0% +to get it so + + + align:start position:0% +to get it so +uh what do you think would happen here + + align:start position:0% +uh what do you think would happen here + + + align:start position:0% +uh what do you think would happen here +since the bacteria dead probably not a + + align:start position:0% +since the bacteria dead probably not a + + + align:start position:0% +since the bacteria dead probably not a +big + + align:start position:0% +big + + + align:start position:0% +big +surprise Mouse is alive now I don't know + + align:start position:0% +surprise Mouse is alive now I don't know + + + align:start position:0% +surprise Mouse is alive now I don't know +whether he did this on purpose or he did + + align:start position:0% +whether he did this on purpose or he did + + + align:start position:0% +whether he did this on purpose or he did +it as a control but what he did was he + + align:start position:0% +it as a control but what he did was he + + + align:start position:0% +it as a control but what he did was he +injected at the same time then R2 plus + + align:start position:0% +injected at the same time then R2 plus + + + align:start position:0% +injected at the same time then R2 plus +heat + + align:start position:0% +heat + + + align:start position:0% +heat +killed uh + + align:start position:0% +killed uh + + + align:start position:0% +killed uh +S3 so he's got two things that don't do + + align:start position:0% +S3 so he's got two things that don't do + + + align:start position:0% +S3 so he's got two things that don't do +anything he injects the mouse and + + align:start position:0% +anything he injects the mouse and + + + align:start position:0% +anything he injects the mouse and +uhoh mouse + + align:start position:0% + + + + align:start position:0% + +dies that is a weird + + align:start position:0% +dies that is a weird + + + align:start position:0% +dies that is a weird +result that is actually also though the + + align:start position:0% +result that is actually also though the + + + align:start position:0% +result that is actually also though the +first really key step to understanding + + align:start position:0% +first really key step to understanding + + + align:start position:0% +first really key step to understanding +that DNA is a genetic + + align:start position:0% +that DNA is a genetic + + + align:start position:0% +that DNA is a genetic +material doesn't look like it at this + + align:start position:0% +material doesn't look like it at this + + + align:start position:0% +material doesn't look like it at this +point probably but it was this is where + + align:start position:0% +point probably but it was this is where + + + align:start position:0% +point probably but it was this is where +this is how we learned this really + + align:start position:0% +this is how we learned this really + + + align:start position:0% +this is how we learned this really +enormous fact from these experiments he + + align:start position:0% +enormous fact from these experiments he + + + align:start position:0% +enormous fact from these experiments he +wasn't trying to figure it out he was + + align:start position:0% +wasn't trying to figure it out he was + + + align:start position:0% +wasn't trying to figure it out he was +trying to work out something else as you + + align:start position:0% +trying to work out something else as you + + + align:start position:0% +trying to work out something else as you +can see but it was a bizarre finding so + + align:start position:0% +can see but it was a bizarre finding so + + + align:start position:0% +can see but it was a bizarre finding so +what would you think I put in something + + align:start position:0% +what would you think I put in something + + + align:start position:0% +what would you think I put in something +used to have an R2 capsule so did it get + + align:start position:0% +used to have an R2 capsule so did it get + + + align:start position:0% +used to have an R2 capsule so did it get +rejuvenated somehow by this heat killed + + align:start position:0% +rejuvenated somehow by this heat killed + + + align:start position:0% +rejuvenated somehow by this heat killed +thing or as had you suggested did some + + align:start position:0% +thing or as had you suggested did some + + + align:start position:0% +thing or as had you suggested did some +characteristic get transferred from here + + align:start position:0% +characteristic get transferred from here + + + align:start position:0% +characteristic get transferred from here +whatever so he isolated the bacteria out + + align:start position:0% +whatever so he isolated the bacteria out + + + align:start position:0% +whatever so he isolated the bacteria out +of this and what he found now was he had + + align:start position:0% +of this and what he found now was he had + + + align:start position:0% +of this and what he found now was he had +alive bacteria that were making + + align:start position:0% +alive bacteria that were making + + + align:start position:0% +alive bacteria that were making +S3 so something had been transferred + + align:start position:0% +S3 so something had been transferred + + + align:start position:0% +S3 so something had been transferred +from this set of dead bacteria into the + + align:start position:0% +from this set of dead bacteria into the + + + align:start position:0% +from this set of dead bacteria into the +bacteria that were alive and the + + align:start position:0% +bacteria that were alive and the + + + align:start position:0% +bacteria that were alive and the +characteristic had been passed from the + + align:start position:0% +characteristic had been passed from the + + + align:start position:0% +characteristic had been passed from the +dead bacterium to the new bacterium the + + align:start position:0% +dead bacterium to the new bacterium the + + + align:start position:0% +dead bacterium to the new bacterium the +other bacterium so this is uh about what + + align:start position:0% +other bacterium so this is uh about what + + + align:start position:0% +other bacterium so this is uh about what +Griffith did but this problem was picked + + align:start position:0% +Griffith did but this problem was picked + + + align:start position:0% +Griffith did but this problem was picked +up by + + align:start position:0% +up by + + + align:start position:0% +up by +uh a scientist at at Rockefeller + + align:start position:0% +uh a scientist at at Rockefeller + + + align:start position:0% +uh a scientist at at Rockefeller +uh um + + align:start position:0% +uh um + + + align:start position:0% +uh um +Avery Oswalt Avery who worked with um + + align:start position:0% +Avery Oswalt Avery who worked with um + + + align:start position:0% +Avery Oswalt Avery who worked with um +with uh is as part of a a team and he + + align:start position:0% +with uh is as part of a a team and he + + + align:start position:0% +with uh is as part of a a team and he +took this finding uh and started to work + + align:start position:0% +took this finding uh and started to work + + + align:start position:0% +took this finding uh and started to work +on it and tried to figure out because he + + align:start position:0% +on it and tried to figure out because he + + + align:start position:0% +on it and tried to figure out because he +saw in this + + align:start position:0% +saw in this + + + align:start position:0% +saw in this +um uh in this result a way of finding + + align:start position:0% +um uh in this result a way of finding + + + align:start position:0% +um uh in this result a way of finding +out what was the genetic material + + align:start position:0% +out what was the genetic material + + + align:start position:0% +out what was the genetic material +because somehow what was in that heat + + align:start position:0% +because somehow what was in that heat + + + align:start position:0% +because somehow what was in that heat +killed S3 was the stuff that would trans + + align:start position:0% +killed S3 was the stuff that would trans + + + align:start position:0% +killed S3 was the stuff that would trans +transfer genetic information to another + + align:start position:0% +transfer genetic information to another + + + align:start position:0% +transfer genetic information to another +bacterium so so he did one he made one + + align:start position:0% +bacterium so so he did one he made one + + + align:start position:0% +bacterium so so he did one he made one +really big Discovery and that was you + + align:start position:0% +really big Discovery and that was you + + + align:start position:0% +really big Discovery and that was you +didn't need the mouse at all all that + + align:start position:0% +didn't need the mouse at all all that + + + align:start position:0% +didn't need the mouse at all all that +was happening was the mouse was by dying + + align:start position:0% +was happening was the mouse was by dying + + + align:start position:0% +was happening was the mouse was by dying +was in essence selecting for smooth + + align:start position:0% +was in essence selecting for smooth + + + align:start position:0% +was in essence selecting for smooth +bacteria so he could simplify things by + + align:start position:0% +bacteria so he could simplify things by + + + align:start position:0% +bacteria so he could simplify things by +just taking a rough bacteria taking the + + align:start position:0% +just taking a rough bacteria taking the + + + align:start position:0% +just taking a rough bacteria taking the +heat killed extract putting it in and + + align:start position:0% +heat killed extract putting it in and + + + align:start position:0% +heat killed extract putting it in and +now he just looked for smooth colonies + + align:start position:0% +now he just looked for smooth colonies + + + align:start position:0% +now he just looked for smooth colonies +didn't need any mice at all so he was + + align:start position:0% +didn't need any mice at all so he was + + + align:start position:0% +didn't need any mice at all so he was +able to to see the characteristic of the + + align:start position:0% +able to to see the characteristic of the + + + align:start position:0% +able to to see the characteristic of the +capsule being transferred from some kind + + align:start position:0% +capsule being transferred from some kind + + + align:start position:0% +capsule being transferred from some kind +of heat killed mess of things into a + + align:start position:0% +of heat killed mess of things into a + + + align:start position:0% +of heat killed mess of things into a +rough bacterium changing it into a live + + align:start position:0% +rough bacterium changing it into a live + + + align:start position:0% +rough bacterium changing it into a live +bacterium so he started fractionating + + align:start position:0% +bacterium so he started fractionating + + + align:start position:0% +bacterium so he started fractionating +and he did exactly what uh the kind of + + align:start position:0% +and he did exactly what uh the kind of + + + align:start position:0% +and he did exactly what uh the kind of +approach that you suggested and he + + align:start position:0% +approach that you suggested and he + + + align:start position:0% +approach that you suggested and he +purified and he purified and he purified + + align:start position:0% +purified and he purified and he purified + + + align:start position:0% +purified and he purified and he purified +using as his assay this ability to pass + + align:start position:0% +using as his assay this ability to pass + + + align:start position:0% +using as his assay this ability to pass +on this smooth characteristic and what + + align:start position:0% +on this smooth characteristic and what + + + align:start position:0% +on this smooth characteristic and what +he ended up with was virtually pure + + align:start position:0% +he ended up with was virtually pure + + + align:start position:0% +he ended up with was virtually pure +DNA but as I said you know it's always + + align:start position:0% +DNA but as I said you know it's always + + + align:start position:0% +DNA but as I said you know it's always +never quite pure and somebody can always + + align:start position:0% +never quite pure and somebody can always + + + align:start position:0% +never quite pure and somebody can always +argue oh you got a little bit of + + align:start position:0% +argue oh you got a little bit of + + + align:start position:0% +argue oh you got a little bit of +something else in there so he did a + + align:start position:0% +something else in there so he did a + + + align:start position:0% +something else in there so he did a +really key + + align:start position:0% +really key + + + align:start position:0% +really key +experiment and he treated with DNA your + + align:start position:0% +experiment and he treated with DNA your + + + align:start position:0% +experiment and he treated with DNA your +experiment and it lost the + + align:start position:0% +experiment and it lost the + + + align:start position:0% +experiment and it lost the +transforming activity this process that + + align:start position:0% +transforming activity this process that + + + align:start position:0% +transforming activity this process that +uh of doing this was called + + align:start position:0% + + + + align:start position:0% + +transformation initially it described + + align:start position:0% +transformation initially it described + + + align:start position:0% +transformation initially it described +that phenomenon now that we know what + + align:start position:0% +that phenomenon now that we know what + + + align:start position:0% +that phenomenon now that we know what +what matters uh in the thing was taking + + align:start position:0% +what matters uh in the thing was taking + + + align:start position:0% +what matters uh in the thing was taking +DNA and putting it in so if you do a + + align:start position:0% +DNA and putting it in so if you do a + + + align:start position:0% +DNA and putting it in so if you do a +europ somewhere here you clone a piece + + align:start position:0% +europ somewhere here you clone a piece + + + align:start position:0% +europ somewhere here you clone a piece +of DNA into a plasma and you stick it + + align:start position:0% +of DNA into a plasma and you stick it + + + align:start position:0% +of DNA into a plasma and you stick it +into eoline so you can grow it up + + align:start position:0% +into eoline so you can grow it up + + + align:start position:0% +into eoline so you can grow it up +everybody will you'll call that process + + align:start position:0% +everybody will you'll call that process + + + align:start position:0% +everybody will you'll call that process +of taking the naked DNA and putting + + align:start position:0% +of taking the naked DNA and putting + + + align:start position:0% +of taking the naked DNA and putting +inside the bacterium you'll call it + + align:start position:0% +inside the bacterium you'll call it + + + align:start position:0% +inside the bacterium you'll call it +transformation now in fact it wasn't + + align:start position:0% +transformation now in fact it wasn't + + + align:start position:0% +transformation now in fact it wasn't +this result wasn't accepted right away + + align:start position:0% +this result wasn't accepted right away + + + align:start position:0% +this result wasn't accepted right away +this was published in think + + align:start position:0% +this was published in think + + + align:start position:0% +this was published in think +1944 and the general realization that + + align:start position:0% +1944 and the general realization that + + + align:start position:0% +1944 and the general realization that +DNA uh was the genetic material really + + align:start position:0% +DNA uh was the genetic material really + + + align:start position:0% +DNA uh was the genetic material really +didn't come to the 50s yet this result + + align:start position:0% +didn't come to the 50s yet this result + + + align:start position:0% +didn't come to the 50s yet this result +proved it if you will + + align:start position:0% +proved it if you will + + + align:start position:0% +proved it if you will +but part of the problem was the world + + align:start position:0% +but part of the problem was the world + + + align:start position:0% +but part of the problem was the world +wasn't yet ready to accept that DNA was + + align:start position:0% +wasn't yet ready to accept that DNA was + + + align:start position:0% +wasn't yet ready to accept that DNA was +a genetic material and maybe you can see + + align:start position:0% +a genetic material and maybe you can see + + + align:start position:0% +a genetic material and maybe you can see +the problem it looked like a monotonous + + align:start position:0% +the problem it looked like a monotonous + + + align:start position:0% +the problem it looked like a monotonous +molecule it only had four different + + align:start position:0% +molecule it only had four different + + + align:start position:0% +molecule it only had four different +things things that were different in it + + align:start position:0% +things things that were different in it + + + align:start position:0% +things things that were different in it +if you isolated they were all often kind + + align:start position:0% +if you isolated they were all often kind + + + align:start position:0% +if you isolated they were all often kind +of there about the same amount people + + align:start position:0% +of there about the same amount people + + + align:start position:0% +of there about the same amount people +thought it was just an analyst gatc it + + align:start position:0% +thought it was just an analyst gatc it + + + align:start position:0% +thought it was just an analyst gatc it +didn't sound like anything could encode + + align:start position:0% +didn't sound like anything could encode + + + align:start position:0% +didn't sound like anything could encode +information whereas proteins looked + + align:start position:0% +information whereas proteins looked + + + align:start position:0% +information whereas proteins looked +really attractive 20 different amino + + align:start position:0% +really attractive 20 different amino + + + align:start position:0% +really attractive 20 different amino +acids they all had different + + align:start position:0% +acids they all had different + + + align:start position:0% +acids they all had different +characteristics there was a great place + + align:start position:0% +characteristics there was a great place + + + align:start position:0% +characteristics there was a great place +for storing information so the world + + align:start position:0% +for storing information so the world + + + align:start position:0% +for storing information so the world +wasn't quite ready to to accept it even + + align:start position:0% +wasn't quite ready to to accept it even + + + align:start position:0% +wasn't quite ready to to accept it even +though the experiment evidence was there + + align:start position:0% +though the experiment evidence was there + + + align:start position:0% +though the experiment evidence was there +and so the result came later now the + + align:start position:0% +and so the result came later now the + + + align:start position:0% +and so the result came later now the +last thing I just want to show you is + + align:start position:0% +last thing I just want to show you is + + + align:start position:0% +last thing I just want to show you is +because there's a kind of direct link + + align:start position:0% +because there's a kind of direct link + + + align:start position:0% +because there's a kind of direct link +from that Avery experiment to you guys + + align:start position:0% +from that Avery experiment to you guys + + + align:start position:0% +from that Avery experiment to you guys +because in a year or two ago it was the + + align:start position:0% +because in a year or two ago it was the + + + align:start position:0% +because in a year or two ago it was the +50th Anniversary the discovery of DNA + + align:start position:0% +50th Anniversary the discovery of DNA + + + align:start position:0% +50th Anniversary the discovery of DNA +and uh Avery worked with a team of + + align:start position:0% +and uh Avery worked with a team of + + + align:start position:0% +and uh Avery worked with a team of +um uh two other people called McLoud and + + align:start position:0% +um uh two other people called McLoud and + + + align:start position:0% +um uh two other people called McLoud and +mccardy this uh this was at the 50th an + + align:start position:0% +mccardy this uh this was at the 50th an + + + align:start position:0% +mccardy this uh this was at the 50th an +iversary the meeting down at Colt Spring + + align:start position:0% +iversary the meeting down at Colt Spring + + + align:start position:0% +iversary the meeting down at Colt Spring +Harbor celebrating it uh mccardy is the + + align:start position:0% +Harbor celebrating it uh mccardy is the + + + align:start position:0% +Harbor celebrating it uh mccardy is the +only was the only member of the team + + align:start position:0% +only was the only member of the team + + + align:start position:0% +only was the only member of the team +alive there he was I asked them to + + align:start position:0% +alive there he was I asked them to + + + align:start position:0% +alive there he was I asked them to +autograph my program there was a + + align:start position:0% +autograph my program there was a + + + align:start position:0% +autograph my program there was a +signature he just died uh a little while + + align:start position:0% +signature he just died uh a little while + + + align:start position:0% +signature he just died uh a little while +ago and so there's no living connection + + align:start position:0% +ago and so there's no living connection + + + align:start position:0% +ago and so there's no living connection +to that anymore but I have a picture to + + align:start position:0% +to that anymore but I have a picture to + + + align:start position:0% +to that anymore but I have a picture to +show you guys that takes you back from + + align:start position:0% +show you guys that takes you back from + + + align:start position:0% +show you guys that takes you back from +that experiment to his signature right + + align:start position:0% +that experiment to his signature right + + + align:start position:0% +that experiment to his signature right +there okay so I'll tell you some more + + align:start position:0% +there okay so I'll tell you some more + + + align:start position:0% +there okay so I'll tell you some more +stuff next lecture have a good + + align:start position:0% + + + + align:start position:0% + +weekend + + align:start position:0% + + + + align:start position:0% + +for \ No newline at end of file diff --git a/7ciUw92IGs4.txt b/7ciUw92IGs4.txt new file mode 100644 index 0000000000000000000000000000000000000000..f21890b7b8bccbd371933402bb3f7b6e82bbb530 --- /dev/null +++ b/7ciUw92IGs4.txt @@ -0,0 +1,7467 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open coreware under a Creative Commons + + align:start position:0% +open coreware under a Creative Commons + + + align:start position:0% +open coreware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu we also + + align:start position:0% +ocw.mit.edu we also + + + align:start position:0% +ocw.mit.edu we also +saw or we tried to understand what the + + align:start position:0% +saw or we tried to understand what the + + + align:start position:0% +saw or we tried to understand what the +free energy actually was and we said + + align:start position:0% +free energy actually was and we said + + + align:start position:0% +free energy actually was and we said +that when you have for example an + + align:start position:0% +that when you have for example an + + + align:start position:0% +that when you have for example an +exothermic reaction + + align:start position:0% +exothermic reaction + + + align:start position:0% +exothermic reaction +that not all of that energy + + align:start position:0% +that not all of that energy + + + align:start position:0% +that not all of that energy +released is going to be released in a + + align:start position:0% +released is going to be released in a + + + align:start position:0% +released is going to be released in a +form that can do useful + + align:start position:0% +form that can do useful + + + align:start position:0% +form that can do useful +work some of that energy that's released + + align:start position:0% +work some of that energy that's released + + + align:start position:0% +work some of that energy that's released +some of that Delta H for + + align:start position:0% +some of that Delta H for + + + align:start position:0% +some of that Delta H for +example goes into or can go into the + + align:start position:0% +example goes into or can go into the + + + align:start position:0% +example goes into or can go into the +vibrations and rotations of the product + + align:start position:0% +vibrations and rotations of the product + + + align:start position:0% +vibrations and rotations of the product +molecules which that energy of which is + + align:start position:0% +molecules which that energy of which is + + + align:start position:0% +molecules which that energy of which is +not able to do useful work and so the + + align:start position:0% +not able to do useful work and so the + + + align:start position:0% +not able to do useful work and so the +amount of energy that we can actually + + align:start position:0% +amount of energy that we can actually + + + align:start position:0% +amount of energy that we can actually +use to do work is this free energy is + + align:start position:0% +use to do work is this free energy is + + + align:start position:0% +use to do work is this free energy is +Delta G right here so it's something it + + align:start position:0% +Delta G right here so it's something it + + + align:start position:0% +Delta G right here so it's something it +can be something less than Delta H we + + align:start position:0% +can be something less than Delta H we + + + align:start position:0% +can be something less than Delta H we +also saw a condition which was the + + align:start position:0% +also saw a condition which was the + + + align:start position:0% +also saw a condition which was the +oxidation of glucose where Delta G was + + align:start position:0% +oxidation of glucose where Delta G was + + + align:start position:0% +oxidation of glucose where Delta G was +actually greater than Delta H and that's + + align:start position:0% +actually greater than Delta H and that's + + + align:start position:0% +actually greater than Delta H and that's +the case where we have some of that + + align:start position:0% +the case where we have some of that + + + align:start position:0% +the case where we have some of that +internal energy lock locked up in the + + align:start position:0% +internal energy lock locked up in the + + + align:start position:0% +internal energy lock locked up in the +reactants which now is released in the + + align:start position:0% +reactants which now is released in the + + + align:start position:0% +reactants which now is released in the +form of this useful work Delta + + align:start position:0% +form of this useful work Delta + + + align:start position:0% +form of this useful work Delta +G and I think we had just started to + + align:start position:0% +G and I think we had just started to + + + align:start position:0% +G and I think we had just started to +talk about this term Delta s which is + + align:start position:0% +talk about this term Delta s which is + + + align:start position:0% +talk about this term Delta s which is +the change in the entropy for the + + align:start position:0% +the change in the entropy for the + + + align:start position:0% +the change in the entropy for the +reaction and we talked about how to + + align:start position:0% +reaction and we talked about how to + + + align:start position:0% +reaction and we talked about how to +calculate it we calculate it from the + + align:start position:0% +calculate it we calculate it from the + + + align:start position:0% +calculate it we calculate it from the +absolute entropies of the reactants in + + align:start position:0% +absolute entropies of the reactants in + + + align:start position:0% +absolute entropies of the reactants in +the + + align:start position:0% +the + + + align:start position:0% +the +products so Delta's s for a reaction + + align:start position:0% +products so Delta's s for a reaction + + + align:start position:0% +products so Delta's s for a reaction +then is the absolute ropy of each one of + + align:start position:0% +then is the absolute ropy of each one of + + + align:start position:0% +then is the absolute ropy of each one of +the product times the appropriate + + align:start position:0% +the product times the appropriate + + + align:start position:0% +the product times the appropriate +stochiometric number summed over all the + + align:start position:0% +stochiometric number summed over all the + + + align:start position:0% +stochiometric number summed over all the +products and then minus the absolute + + align:start position:0% +products and then minus the absolute + + + align:start position:0% +products and then minus the absolute +entropy of each one of the reactants + + align:start position:0% +entropy of each one of the reactants + + + align:start position:0% +entropy of each one of the reactants +times that appropriate stochiometric + + align:start position:0% +times that appropriate stochiometric + + + align:start position:0% +times that appropriate stochiometric +number summed overall the reactants and + + align:start position:0% +number summed overall the reactants and + + + align:start position:0% +number summed overall the reactants and +it's the difference between the two is + + align:start position:0% +it's the difference between the two is + + + align:start position:0% +it's the difference between the two is +Delta s for the chemical + + align:start position:0% +Delta s for the chemical + + + align:start position:0% +Delta s for the chemical +reaction and S is an absolute entropy + + align:start position:0% +reaction and S is an absolute entropy + + + align:start position:0% +reaction and S is an absolute entropy +that is a result of the third law of + + align:start position:0% +that is a result of the third law of + + + align:start position:0% +that is a result of the third law of +thermodynamics which uh I mentioned I + + align:start position:0% +thermodynamics which uh I mentioned I + + + align:start position:0% +thermodynamics which uh I mentioned I +think last time you will talk about a + + align:start position:0% +think last time you will talk about a + + + align:start position:0% +think last time you will talk about a +lot in detail in + + align:start position:0% +lot in detail in + + + align:start position:0% +lot in detail in +560 all + + align:start position:0% +560 all + + + align:start position:0% +560 all +right but uh let's look at an example + + align:start position:0% +right but uh let's look at an example + + + align:start position:0% +right but uh let's look at an example +here of the change in + + align:start position:0% +here of the change in + + + align:start position:0% +here of the change in +entropy because I want to show you that + + align:start position:0% +entropy because I want to show you that + + + align:start position:0% +entropy because I want to show you that +you can have a change in entropy that's + + align:start position:0% +you can have a change in entropy that's + + + align:start position:0% +you can have a change in entropy that's +large enough to make an endothermic + + align:start position:0% +large enough to make an endothermic + + + align:start position:0% +large enough to make an endothermic +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +spontaneous you can have what we call an + + align:start position:0% +spontaneous you can have what we call an + + + align:start position:0% +spontaneous you can have what we call an +entropy driven reaction for example the + + align:start position:0% +entropy driven reaction for example the + + + align:start position:0% +entropy driven reaction for example the +melting of ice to melt ice to go from + + align:start position:0% +melting of ice to melt ice to go from + + + align:start position:0% +melting of ice to melt ice to go from +the solid form of water to the liquid + + align:start position:0% +the solid form of water to the liquid + + + align:start position:0% +the solid form of water to the liquid +form well that is an endothermic + + align:start position:0% +form well that is an endothermic + + + align:start position:0% +form well that is an endothermic +reaction 6.95 KJ per + + align:start position:0% +reaction 6.95 KJ per + + + align:start position:0% +reaction 6.95 KJ per +mole however going from the solid form + + align:start position:0% +mole however going from the solid form + + + align:start position:0% +mole however going from the solid form +of water to the liquid form there's a + + align:start position:0% +of water to the liquid form there's a + + + align:start position:0% +of water to the liquid form there's a +great increase there in the entropy in + + align:start position:0% +great increase there in the entropy in + + + align:start position:0% +great increase there in the entropy in +the + + align:start position:0% +the + + + align:start position:0% +the +disorder and it's that increase in the + + align:start position:0% +disorder and it's that increase in the + + + align:start position:0% +disorder and it's that increase in the +disorder that allows that reaction to be + + align:start position:0% +disorder that allows that reaction to be + + + align:start position:0% +disorder that allows that reaction to be +spontaneous so we can calculate the + + align:start position:0% +spontaneous so we can calculate the + + + align:start position:0% +spontaneous so we can calculate the +entropy change for that reaction that + + align:start position:0% +entropy change for that reaction that + + + align:start position:0% +entropy change for that reaction that +entropy change then is the absolute + + align:start position:0% +entropy change then is the absolute + + + align:start position:0% +entropy change then is the absolute +entropy of the product which is liquid + + align:start position:0% +entropy of the product which is liquid + + + align:start position:0% +entropy of the product which is liquid +water minus the absolute entropy of the + + align:start position:0% +water minus the absolute entropy of the + + + align:start position:0% +water minus the absolute entropy of the +reactant which is solid water and you + + align:start position:0% +reactant which is solid water and you + + + align:start position:0% +reactant which is solid water and you +can see that Delta s here is positive we + + align:start position:0% +can see that Delta s here is positive we + + + align:start position:0% +can see that Delta s here is positive we +increased is there a question that I can + + align:start position:0% +increased is there a question that I can + + + align:start position:0% +increased is there a question that I can +help you out + + align:start position:0% + + + + align:start position:0% + +with did you have a question can I help + + align:start position:0% +with did you have a question can I help + + + align:start position:0% +with did you have a question can I help +you out + + align:start position:0% +you out + + + align:start position:0% +you out +okay um that Delta s here is positive we + + align:start position:0% +okay um that Delta s here is positive we + + + align:start position:0% +okay um that Delta s here is positive we +increase the disorder of the + + align:start position:0% +increase the disorder of the + + + align:start position:0% +increase the disorder of the +system and it is that positive Delta s + + align:start position:0% +system and it is that positive Delta s + + + align:start position:0% +system and it is that positive Delta s +then that gives us a Delta G that's + + align:start position:0% +then that gives us a Delta G that's + + + align:start position:0% +then that gives us a Delta G that's +negative meaning our reaction in this + + align:start position:0% +negative meaning our reaction in this + + + align:start position:0% +negative meaning our reaction in this +direction from solid to the liquid is a + + align:start position:0% +direction from solid to the liquid is a + + + align:start position:0% +direction from solid to the liquid is a +spontaneous reaction so Delta G here is + + align:start position:0% +spontaneous reaction so Delta G here is + + + align:start position:0% +spontaneous reaction so Delta G here is +Delta H + + align:start position:0% +Delta H + + + align:start position:0% +Delta H +6.95 times or minus the the temperature + + align:start position:0% +6.95 times or minus the the temperature + + + align:start position:0% +6.95 times or minus the the temperature +at which the reaction is preceding times + + align:start position:0% +at which the reaction is preceding times + + + align:start position:0% +at which the reaction is preceding times +that change in the entropy and in this + + align:start position:0% +that change in the entropy and in this + + + align:start position:0% +that change in the entropy and in this +case here Delta G now is minus 1.57 K + + align:start position:0% +case here Delta G now is minus 1.57 K + + + align:start position:0% +case here Delta G now is minus 1.57 K +that reaction is spontaneous even though + + align:start position:0% +that reaction is spontaneous even though + + + align:start position:0% +that reaction is spontaneous even though +it is endothermic and it's that increase + + align:start position:0% +it is endothermic and it's that increase + + + align:start position:0% +it is endothermic and it's that increase +in the entropy that is driving this + + align:start position:0% +in the entropy that is driving this + + + align:start position:0% +in the entropy that is driving this +reaction here all right now I want you + + align:start position:0% +reaction here all right now I want you + + + align:start position:0% +reaction here all right now I want you +also to notice something right here and + + align:start position:0% +also to notice something right here and + + + align:start position:0% +also to notice something right here and +that is that the change in the + + align:start position:0% +that is that the change in the + + + align:start position:0% +that is that the change in the +entropy usually is in units of jewels + + align:start position:0% +entropy usually is in units of jewels + + + align:start position:0% +entropy usually is in units of jewels +per degree Kelvin + + align:start position:0% +per degree Kelvin + + + align:start position:0% +per degree Kelvin +mole Delta H just about always is in + + align:start position:0% +mole Delta H just about always is in + + + align:start position:0% +mole Delta H just about always is in +units of kles per uh mole so remember + + align:start position:0% +units of kles per uh mole so remember + + + align:start position:0% +units of kles per uh mole so remember +when you're working with Delta H Bells + + align:start position:0% +when you're working with Delta H Bells + + + align:start position:0% +when you're working with Delta H Bells +ought to go off in your + + align:start position:0% +ought to go off in your + + + align:start position:0% +ought to go off in your +head you know remember that you probably + + align:start position:0% +head you know remember that you probably + + + align:start position:0% +head you know remember that you probably +have to do a unit conversion here from + + align:start position:0% +have to do a unit conversion here from + + + align:start position:0% +have to do a unit conversion here from +jewels to koges all right this catches a + + align:start position:0% +jewels to koges all right this catches a + + + align:start position:0% +jewels to koges all right this catches a +lot of students on an exam so I'm trying + + align:start position:0% +lot of students on an exam so I'm trying + + + align:start position:0% +lot of students on an exam so I'm trying +to give you some fear warning about this + + align:start position:0% +to give you some fear warning about this + + + align:start position:0% +to give you some fear warning about this +all + + align:start position:0% +all + + + align:start position:0% +all +right + + align:start position:0% +right + + + align:start position:0% +right +okay now um what I want to talk about is + + align:start position:0% +okay now um what I want to talk about is + + + align:start position:0% +okay now um what I want to talk about is +this free energy of formation Delta G + + align:start position:0% +this free energy of formation Delta G + + + align:start position:0% +this free energy of formation Delta G +subf + + align:start position:0% +subf + + + align:start position:0% +subf +knot the Gibs free energy of + + align:start position:0% +knot the Gibs free energy of + + + align:start position:0% +knot the Gibs free energy of +formation is analogous to the enthalpy + + align:start position:0% +formation is analogous to the enthalpy + + + align:start position:0% +formation is analogous to the enthalpy +of formation this is what we looked at + + align:start position:0% +of formation this is what we looked at + + + align:start position:0% +of formation this is what we looked at +the last time + + align:start position:0% +the last time + + + align:start position:0% +the last time +right the Gibs freey energy of formation + + align:start position:0% +right the Gibs freey energy of formation + + + align:start position:0% +right the Gibs freey energy of formation +Delta G subf are not for our standard + + align:start position:0% +Delta G subf are not for our standard + + + align:start position:0% +Delta G subf are not for our standard +state which is one by pressure the Gibs + + align:start position:0% +state which is one by pressure the Gibs + + + align:start position:0% +state which is one by pressure the Gibs +free energy of + + align:start position:0% +free energy of + + + align:start position:0% +free energy of +formation is the free energy formation + + align:start position:0% +formation is the free energy formation + + + align:start position:0% +formation is the free energy formation +of one mole of a compound from the + + align:start position:0% +of one mole of a compound from the + + + align:start position:0% +of one mole of a compound from the +elements from its elements in their most + + align:start position:0% +elements from its elements in their most + + + align:start position:0% +elements from its elements in their most +stable form at the uh standard State all + + align:start position:0% +stable form at the uh standard State all + + + align:start position:0% +stable form at the uh standard State all +right so it's analogous to the heat of + + align:start position:0% +right so it's analogous to the heat of + + + align:start position:0% +right so it's analogous to the heat of +formation only it's the free energy of + + align:start position:0% +formation only it's the free energy of + + + align:start position:0% +formation only it's the free energy of +formation it is tabulated for you just + + align:start position:0% +formation it is tabulated for you just + + + align:start position:0% +formation it is tabulated for you just +like the enthalpy of formation is so you + + align:start position:0% +like the enthalpy of formation is so you + + + align:start position:0% +like the enthalpy of formation is so you +can look up the free energy of formation + + align:start position:0% +can look up the free energy of formation + + + align:start position:0% +can look up the free energy of formation +for uh every compound that is is + + align:start position:0% +for uh every compound that is is + + + align:start position:0% +for uh every compound that is is +known however unlike the enthalpy of + + align:start position:0% +known however unlike the enthalpy of + + + align:start position:0% +known however unlike the enthalpy of +formation here the free energy of + + align:start position:0% +formation here the free energy of + + + align:start position:0% +formation here the free energy of +formation you can also calculate you can + + align:start position:0% +formation you can also calculate you can + + + align:start position:0% +formation you can also calculate you can +calculate from this expression right + + align:start position:0% +calculate from this expression right + + + align:start position:0% +calculate from this expression right +Delta G equal Delta H minus t Delta s so + + align:start position:0% +Delta G equal Delta H minus t Delta s so + + + align:start position:0% +Delta G equal Delta H minus t Delta s so +if you've got a reaction for which you + + align:start position:0% +if you've got a reaction for which you + + + align:start position:0% +if you've got a reaction for which you +um you've defined the free energy of + + align:start position:0% +um you've defined the free energy of + + + align:start position:0% +um you've defined the free energy of +formation so if you know the free energy + + align:start position:0% +formation so if you know the free energy + + + align:start position:0% +formation so if you know the free energy +of formation of a + + align:start position:0% +of formation of a + + + align:start position:0% +of formation of a +molecule and you know the Delta s for + + align:start position:0% +molecule and you know the Delta s for + + + align:start position:0% +molecule and you know the Delta s for +the reaction that defines that uh uh + + align:start position:0% +the reaction that defines that uh uh + + + align:start position:0% +the reaction that defines that uh uh +enthalpy of + + align:start position:0% +enthalpy of + + + align:start position:0% +enthalpy of +formation then you can calculate the + + align:start position:0% +formation then you can calculate the + + + align:start position:0% +formation then you can calculate the +free energy of formation for every + + align:start position:0% +free energy of formation for every + + + align:start position:0% +free energy of formation for every +molecule all right which is different + + align:start position:0% +molecule all right which is different + + + align:start position:0% +molecule all right which is different +from the enthalpy of formation that you + + align:start position:0% +from the enthalpy of formation that you + + + align:start position:0% +from the enthalpy of formation that you +do have to look up but you can actually + + align:start position:0% +do have to look up but you can actually + + + align:start position:0% +do have to look up but you can actually +calculate the free energy of formation + + align:start position:0% +calculate the free energy of formation + + + align:start position:0% +calculate the free energy of formation +given that you know the enthalpy of + + align:start position:0% +given that you know the enthalpy of + + + align:start position:0% +given that you know the enthalpy of +formation and given that you know Delta + + align:start position:0% +formation and given that you know Delta + + + align:start position:0% +formation and given that you know Delta +s for the + + align:start position:0% +s for the + + + align:start position:0% +s for the +reaction that defines that en enthalpy + + align:start position:0% +reaction that defines that en enthalpy + + + align:start position:0% +reaction that defines that en enthalpy +of formation all right questions on + + align:start position:0% +of formation all right questions on + + + align:start position:0% +of formation all right questions on +that + + align:start position:0% +that + + + align:start position:0% +that +okay but why is this free energy of + + align:start position:0% +okay but why is this free energy of + + + align:start position:0% +okay but why is this free energy of +formation so important well that's what + + align:start position:0% +formation so important well that's what + + + align:start position:0% +formation so important well that's what +we got to look at right + + align:start position:0% +we got to look at right + + + align:start position:0% +we got to look at right +now here's a reaction uh that produces + + align:start position:0% +now here's a reaction uh that produces + + + align:start position:0% +now here's a reaction uh that produces +one mole of carbon + + align:start position:0% +one mole of carbon + + + align:start position:0% +one mole of carbon +dioxide the Delta G for this reaction is + + align:start position:0% +dioxide the Delta G for this reaction is + + + align:start position:0% +dioxide the Delta G for this reaction is +minus 394 K per mole the Delta G for + + align:start position:0% +minus 394 K per mole the Delta G for + + + align:start position:0% +minus 394 K per mole the Delta G for +this reaction is defined as the free + + align:start position:0% +this reaction is defined as the free + + + align:start position:0% +this reaction is defined as the free +energy of formation for + + align:start position:0% +energy of formation for + + + align:start position:0% +energy of formation for +CO2 why because this Rea reaction as + + align:start position:0% +CO2 why because this Rea reaction as + + + align:start position:0% +CO2 why because this Rea reaction as +written produce is one mole of + + align:start position:0% +written produce is one mole of + + + align:start position:0% +written produce is one mole of +CO2 from the elements that compose CO2 + + align:start position:0% +CO2 from the elements that compose CO2 + + + align:start position:0% +CO2 from the elements that compose CO2 +but the elements in their most stable + + align:start position:0% +but the elements in their most stable + + + align:start position:0% +but the elements in their most stable +form the elements are carbon and the + + align:start position:0% +form the elements are carbon and the + + + align:start position:0% +form the elements are carbon and the +most stable form of carbon is graphite + + align:start position:0% +most stable form of carbon is graphite + + + align:start position:0% +most stable form of carbon is graphite +and the element is oxygen and O2 is the + + align:start position:0% +and the element is oxygen and O2 is the + + + align:start position:0% +and the element is oxygen and O2 is the +most stable form of oxygen at one bar + + align:start position:0% +most stable form of oxygen at one bar + + + align:start position:0% +most stable form of oxygen at one bar +pressure and uh our room temperature + + align:start position:0% +pressure and uh our room temperature + + + align:start position:0% +pressure and uh our room temperature +which we're working with here all right + + align:start position:0% +which we're working with here all right + + + align:start position:0% +which we're working with here all right +so that's the free energy of formation + + align:start position:0% +so that's the free energy of formation + + + align:start position:0% +so that's the free energy of formation +of CO2 + + align:start position:0% +of CO2 + + + align:start position:0% +of CO2 +and um this is very important because + + align:start position:0% +and um this is very important because + + + align:start position:0% +and um this is very important because +that free energy of formation of a + + align:start position:0% +that free energy of formation of a + + + align:start position:0% +that free energy of formation of a +molecule defines the molecule stability + + align:start position:0% +molecule defines the molecule stability + + + align:start position:0% +molecule defines the molecule stability +relative to decomposition to its + + align:start position:0% +relative to decomposition to its + + + align:start position:0% +relative to decomposition to its +elements so for example here the forward + + align:start position:0% +elements so for example here the forward + + + align:start position:0% +elements so for example here the forward +Direction here this Delta G is negative + + align:start position:0% +Direction here this Delta G is negative + + + align:start position:0% +Direction here this Delta G is negative +it's spontaneous in the forward + + align:start position:0% +it's spontaneous in the forward + + + align:start position:0% +it's spontaneous in the forward +Direction when Delta G is negative Delta + + align:start position:0% +Direction when Delta G is negative Delta + + + align:start position:0% +Direction when Delta G is negative Delta +G of formation is negative for a + + align:start position:0% +G of formation is negative for a + + + align:start position:0% +G of formation is negative for a +molecule what we say is that that + + align:start position:0% +molecule what we say is that that + + + align:start position:0% +molecule what we say is that that +molecule is thermodynamically stable + + align:start position:0% +molecule is thermodynamically stable + + + align:start position:0% +molecule is thermodynamically stable +relative to its elements right because + + align:start position:0% +relative to its elements right because + + + align:start position:0% +relative to its elements right because +the formation of that + + align:start position:0% +the formation of that + + + align:start position:0% +the formation of that +molecule that Delta G is negative the + + align:start position:0% +molecule that Delta G is negative the + + + align:start position:0% +molecule that Delta G is negative the +reaction is spontaneous as written in + + align:start position:0% +reaction is spontaneous as written in + + + align:start position:0% +reaction is spontaneous as written in +the forward Direction it is not + + align:start position:0% +the forward Direction it is not + + + align:start position:0% +the forward Direction it is not +spontaneous in the reverse direction + + align:start position:0% +spontaneous in the reverse direction + + + align:start position:0% +spontaneous in the reverse direction +right the reverse Direction This Delta G + + align:start position:0% +right the reverse Direction This Delta G + + + align:start position:0% +right the reverse Direction This Delta G +would be positive + + align:start position:0% +would be positive + + + align:start position:0% +would be positive +so because the Delta G for this reaction + + align:start position:0% +so because the Delta G for this reaction + + + align:start position:0% +so because the Delta G for this reaction +is negative we say that CO2 is + + align:start position:0% +is negative we say that CO2 is + + + align:start position:0% +is negative we say that CO2 is +thermodynamically stable relative to + + align:start position:0% +thermodynamically stable relative to + + + align:start position:0% +thermodynamically stable relative to +decomposition to its elements carbon and + + align:start position:0% +decomposition to its elements carbon and + + + align:start position:0% +decomposition to its elements carbon and +oxygen so this is important the sign of + + align:start position:0% +oxygen so this is important the sign of + + + align:start position:0% +oxygen so this is important the sign of +the free energy of formation for a + + align:start position:0% +the free energy of formation for a + + + align:start position:0% +the free energy of formation for a +molecule is + + align:start position:0% +molecule is + + + align:start position:0% +molecule is +important had the free energy of + + align:start position:0% +important had the free energy of + + + align:start position:0% +important had the free energy of +formation of CO2 been + + align:start position:0% +formation of CO2 been + + + align:start position:0% +formation of CO2 been +positive we would have said that was + + align:start position:0% +positive we would have said that was + + + align:start position:0% +positive we would have said that was +thermody dynamically unstable relative + + align:start position:0% +thermody dynamically unstable relative + + + align:start position:0% +thermody dynamically unstable relative +to decomposition to its elements because + + align:start position:0% +to decomposition to its elements because + + + align:start position:0% +to decomposition to its elements because +this forward reaction Delta G would have + + align:start position:0% +this forward reaction Delta G would have + + + align:start position:0% +this forward reaction Delta G would have +been positive but the reverse reaction + + align:start position:0% +been positive but the reverse reaction + + + align:start position:0% +been positive but the reverse reaction +would have been negative the reverse + + align:start position:0% +would have been negative the reverse + + + align:start position:0% +would have been negative the reverse +reaction there would be a spontaneous + + align:start position:0% +reaction there would be a spontaneous + + + align:start position:0% +reaction there would be a spontaneous +tendency for CO2 to + + align:start position:0% +tendency for CO2 to + + + align:start position:0% +tendency for CO2 to +decompose all right all right but this + + align:start position:0% +decompose all right all right but this + + + align:start position:0% +decompose all right all right but this +is an example CO2 where CO2 is stable + + align:start position:0% +is an example CO2 where CO2 is stable + + + align:start position:0% +is an example CO2 where CO2 is stable +relative to decomposition to its + + align:start position:0% +relative to decomposition to its + + + align:start position:0% +relative to decomposition to its +elements here's an example of a + + align:start position:0% +elements here's an example of a + + + align:start position:0% +elements here's an example of a +molecule uh where uh it is + + align:start position:0% +molecule uh where uh it is + + + align:start position:0% +molecule uh where uh it is +thermodynamically unstable relative to + + align:start position:0% +thermodynamically unstable relative to + + + align:start position:0% +thermodynamically unstable relative to +decomposition to its elements Benzene + + align:start position:0% +decomposition to its elements Benzene + + + align:start position:0% +decomposition to its elements Benzene +right I write a reaction here that is + + align:start position:0% +right I write a reaction here that is + + + align:start position:0% +right I write a reaction here that is +the formation of one mole of benzene + + align:start position:0% +the formation of one mole of benzene + + + align:start position:0% +the formation of one mole of benzene +from the elements in the most stable + + align:start position:0% +from the elements in the most stable + + + align:start position:0% +from the elements in the most stable +form the free energy of formation of a + + align:start position:0% +form the free energy of formation of a + + + align:start position:0% +form the free energy of formation of a +mole of benzene here is positive 12 4 K + + align:start position:0% +mole of benzene here is positive 12 4 K + + + align:start position:0% +mole of benzene here is positive 12 4 K +per mole it's positive what does that + + align:start position:0% +per mole it's positive what does that + + + align:start position:0% +per mole it's positive what does that +mean well it means that the reverse + + align:start position:0% +mean well it means that the reverse + + + align:start position:0% +mean well it means that the reverse +reaction Delta G is negative it means + + align:start position:0% +reaction Delta G is negative it means + + + align:start position:0% +reaction Delta G is negative it means +that Benzene has a thermodynamic + + align:start position:0% +that Benzene has a thermodynamic + + + align:start position:0% +that Benzene has a thermodynamic +tendency to decompose into its elements + + align:start position:0% +tendency to decompose into its elements + + + align:start position:0% +tendency to decompose into its elements +right it's unstable relative to + + align:start position:0% +right it's unstable relative to + + + align:start position:0% +right it's unstable relative to +decomposition into its elements because + + align:start position:0% +decomposition into its elements because + + + align:start position:0% +decomposition into its elements because +it has a positive Delta G it's the + + align:start position:0% +it has a positive Delta G it's the + + + align:start position:0% +it has a positive Delta G it's the +reverse reaction that's spontaneous + + align:start position:0% +reverse reaction that's spontaneous + + + align:start position:0% +reverse reaction that's spontaneous +all right but even though a verse + + align:start position:0% +all right but even though a verse + + + align:start position:0% +all right but even though a verse +reaction may be + + align:start position:0% +reaction may be + + + align:start position:0% +reaction may be +spontaneous it can also be really pretty + + align:start position:0% +spontaneous it can also be really pretty + + + align:start position:0% +spontaneous it can also be really pretty +slow right when was the last time you + + align:start position:0% +slow right when was the last time you + + + align:start position:0% +slow right when was the last time you +saw a pint of benzene decomposed to + + align:start position:0% +saw a pint of benzene decomposed to + + + align:start position:0% +saw a pint of benzene decomposed to +graphite and + + align:start position:0% +graphite and + + + align:start position:0% +graphite and +hydrogen not recently + + align:start position:0% +hydrogen not recently + + + align:start position:0% +hydrogen not recently +right and so even though you have a + + align:start position:0% +right and so even though you have a + + + align:start position:0% +right and so even though you have a +thermodynamic tendency to + + align:start position:0% +thermodynamic tendency to + + + align:start position:0% +thermodynamic tendency to +decompose right it doesn't mean that the + + align:start position:0% +decompose right it doesn't mean that the + + + align:start position:0% +decompose right it doesn't mean that the +rate is going to be fast enough for you + + align:start position:0% +rate is going to be fast enough for you + + + align:start position:0% +rate is going to be fast enough for you +to see that in any reasonable amount of + + align:start position:0% +to see that in any reasonable amount of + + + align:start position:0% +to see that in any reasonable amount of +time so there's a thermodynamic effect + + align:start position:0% +time so there's a thermodynamic effect + + + align:start position:0% +time so there's a thermodynamic effect +and there's a kinetic effect and you're + + align:start position:0% +and there's a kinetic effect and you're + + + align:start position:0% +and there's a kinetic effect and you're +going to talk about the kinetic effect + + align:start position:0% +going to talk about the kinetic effect + + + align:start position:0% +going to talk about the kinetic effect +in much more detail with Professor + + align:start position:0% +in much more detail with Professor + + + align:start position:0% +in much more detail with Professor +drenon a few weeks from now but at the + + align:start position:0% +drenon a few weeks from now but at the + + + align:start position:0% +drenon a few weeks from now but at the +moment right here we've got two + + align:start position:0% +moment right here we've got two + + + align:start position:0% +moment right here we've got two +different names to talk about + + align:start position:0% +different names to talk about + + + align:start position:0% +different names to talk about +thermodynamic stability and kinetic + + align:start position:0% +thermodynamic stability and kinetic + + + align:start position:0% +thermodynamic stability and kinetic +stability so to speak and that is the + + align:start position:0% +stability so to speak and that is the + + + align:start position:0% +stability so to speak and that is the +following + + align:start position:0% +following + + + align:start position:0% +following +we call a molecule stable or + + align:start position:0% +we call a molecule stable or + + + align:start position:0% +we call a molecule stable or +unstable and when we use those terms + + align:start position:0% +unstable and when we use those terms + + + align:start position:0% +unstable and when we use those terms +stable or unstable we're referring to + + align:start position:0% +stable or unstable we're referring to + + + align:start position:0% +stable or unstable we're referring to +the Delta G of formation we're referring + + align:start position:0% +the Delta G of formation we're referring + + + align:start position:0% +the Delta G of formation we're referring +to the thermodynamic tendency of the + + align:start position:0% +to the thermodynamic tendency of the + + + align:start position:0% +to the thermodynamic tendency of the +molecule to + + align:start position:0% +molecule to + + + align:start position:0% +molecule to +decompose so Benzene here is + + align:start position:0% +decompose so Benzene here is + + + align:start position:0% +decompose so Benzene here is +thermodynamically unstable with respect + + align:start position:0% +thermodynamically unstable with respect + + + align:start position:0% +thermodynamically unstable with respect +to decomposition to its + + align:start position:0% +to decomposition to its + + + align:start position:0% +to decomposition to its +elements however Benzene is what we call + + align:start position:0% +elements however Benzene is what we call + + + align:start position:0% +elements however Benzene is what we call +non + + align:start position:0% +non + + + align:start position:0% +non +laile these terms labile and non labile + + align:start position:0% +laile these terms labile and non labile + + + align:start position:0% +laile these terms labile and non labile +refer to the + + align:start position:0% +refer to the + + + align:start position:0% +refer to the +rate with which that thermodynamic + + align:start position:0% +rate with which that thermodynamic + + + align:start position:0% +rate with which that thermodynamic +tendency is + + align:start position:0% +tendency is + + + align:start position:0% +tendency is +realized so + + align:start position:0% +realized so + + + align:start position:0% +realized so +Benzene because the rate of + + align:start position:0% +Benzene because the rate of + + + align:start position:0% +Benzene because the rate of +decomposition is so slow such that you + + align:start position:0% +decomposition is so slow such that you + + + align:start position:0% +decomposition is so slow such that you +never see it we say Benzene is non laile + + align:start position:0% +never see it we say Benzene is non laile + + + align:start position:0% +never see it we say Benzene is non laile +all right non labile means it's not + + align:start position:0% +all right non labile means it's not + + + align:start position:0% +all right non labile means it's not +going to decompose not because it + + align:start position:0% +going to decompose not because it + + + align:start position:0% +going to decompose not because it +doesn't have the thermodynamic tendency + + align:start position:0% +doesn't have the thermodynamic tendency + + + align:start position:0% +doesn't have the thermodynamic tendency +to but because the rate is just too + + align:start position:0% +to but because the rate is just too + + + align:start position:0% +to but because the rate is just too +slow all right + + align:start position:0% +slow all right + + + align:start position:0% +slow all right +however if benzene's rate for + + align:start position:0% +however if benzene's rate for + + + align:start position:0% +however if benzene's rate for +decomposition was very fast we'd call it + + align:start position:0% +decomposition was very fast we'd call it + + + align:start position:0% +decomposition was very fast we'd call it +a laile molecule but it's not it's + + align:start position:0% +a laile molecule but it's not it's + + + align:start position:0% +a laile molecule but it's not it's +non-l but it is unstable so unstable + + align:start position:0% +non-l but it is unstable so unstable + + + align:start position:0% +non-l but it is unstable so unstable +refers to the thermodynamic tendency + + align:start position:0% +refers to the thermodynamic tendency + + + align:start position:0% +refers to the thermodynamic tendency +Lile non-l bile refers to the kinetic + + align:start position:0% +Lile non-l bile refers to the kinetic + + + align:start position:0% +Lile non-l bile refers to the kinetic +the rates at which that thermodynamic + + align:start position:0% +the rates at which that thermodynamic + + + align:start position:0% +the rates at which that thermodynamic +tendency is + + align:start position:0% +tendency is + + + align:start position:0% +tendency is +realized + + align:start position:0% +realized + + + align:start position:0% +realized +okay okay so well like the free the + + align:start position:0% +okay okay so well like the free the + + + align:start position:0% +okay okay so well like the free the +enthalpy of formation Delta H + + align:start position:0% +enthalpy of formation Delta H + + + align:start position:0% +enthalpy of formation Delta H +subf like that Delta G subf the free + + align:start position:0% +subf like that Delta G subf the free + + + align:start position:0% +subf like that Delta G subf the free +energy of formation well that can also + + align:start position:0% +energy of formation well that can also + + + align:start position:0% +energy of formation well that can also +be zero right so for example for the + + align:start position:0% +be zero right so for example for the + + + align:start position:0% +be zero right so for example for the +elements hydrogen oxygen chlorine Xenon + + align:start position:0% +elements hydrogen oxygen chlorine Xenon + + + align:start position:0% +elements hydrogen oxygen chlorine Xenon +all those gases free energy of formation + + align:start position:0% +all those gases free energy of formation + + + align:start position:0% +all those gases free energy of formation +is zero all right just the same way in + + align:start position:0% +is zero all right just the same way in + + + align:start position:0% +is zero all right just the same way in +which we described it last time for the + + align:start position:0% +which we described it last time for the + + + align:start position:0% +which we described it last time for the +enthalpy of formation for the elements + + align:start position:0% +enthalpy of formation for the elements + + + align:start position:0% +enthalpy of formation for the elements +bromine here and mercury in the liquid + + align:start position:0% +bromine here and mercury in the liquid + + + align:start position:0% +bromine here and mercury in the liquid +form hey Delta G subf free energy of + + align:start position:0% +form hey Delta G subf free energy of + + + align:start position:0% +form hey Delta G subf free energy of +formation is equal to + + align:start position:0% +formation is equal to + + + align:start position:0% +formation is equal to +zero for the elements carbon in the form + + align:start position:0% +zero for the elements carbon in the form + + + align:start position:0% +zero for the elements carbon in the form +of graphite sodium iron iodine all + + align:start position:0% +of graphite sodium iron iodine all + + + align:start position:0% +of graphite sodium iron iodine all +solids they're free energy of formation + + align:start position:0% +solids they're free energy of formation + + + align:start position:0% +solids they're free energy of formation +is also equal to zero because those are + + align:start position:0% +is also equal to zero because those are + + + align:start position:0% +is also equal to zero because those are +the elements in their most stable form + + align:start position:0% +the elements in their most stable form + + + align:start position:0% +the elements in their most stable form +at our standard + + align:start position:0% +at our standard + + + align:start position:0% +at our standard +State however look at this the free + + align:start position:0% +State however look at this the free + + + align:start position:0% +State however look at this the free +energy of formation of bromine in the + + align:start position:0% +energy of formation of bromine in the + + + align:start position:0% +energy of formation of bromine in the +gas phase hey that's not equal to zero + + align:start position:0% +gas phase hey that's not equal to zero + + + align:start position:0% +gas phase hey that's not equal to zero +it's not equal to zero because bromine + + align:start position:0% +it's not equal to zero because bromine + + + align:start position:0% +it's not equal to zero because bromine +in the gas space is not the most stable + + align:start position:0% +in the gas space is not the most stable + + + align:start position:0% +in the gas space is not the most stable +form of bromine at our standard State + + align:start position:0% +form of bromine at our standard State + + + align:start position:0% +form of bromine at our standard State +liquid bromine is so it's so Delta g a + + align:start position:0% +liquid bromine is so it's so Delta g a + + + align:start position:0% +liquid bromine is so it's so Delta g a +formation of bromine in the gas phase is + + align:start position:0% +formation of bromine in the gas phase is + + + align:start position:0% +formation of bromine in the gas phase is +not zero likewise here the free energy + + align:start position:0% +not zero likewise here the free energy + + + align:start position:0% +not zero likewise here the free energy +of formation of diamond hey that's not + + align:start position:0% +of formation of diamond hey that's not + + + align:start position:0% +of formation of diamond hey that's not +zero because diamond is not the most + + align:start position:0% +zero because diamond is not the most + + + align:start position:0% +zero because diamond is not the most +stable form of the element carbon at one + + align:start position:0% +stable form of the element carbon at one + + + align:start position:0% +stable form of the element carbon at one +bar pressure and room temperature + + align:start position:0% +bar pressure and room temperature + + + align:start position:0% +bar pressure and room temperature +graphite is okay so you do have to look + + align:start position:0% +graphite is okay so you do have to look + + + align:start position:0% +graphite is okay so you do have to look +at the it's important to look at the + + align:start position:0% +at the it's important to look at the + + + align:start position:0% +at the it's important to look at the +form the phase of the elements that + + align:start position:0% +form the phase of the elements that + + + align:start position:0% +form the phase of the elements that +you're dealing + + align:start position:0% +you're dealing + + + align:start position:0% +you're dealing +with okay if you want to calculate Delta + + align:start position:0% +with okay if you want to calculate Delta + + + align:start position:0% +with okay if you want to calculate Delta +G for a reaction well just like + + align:start position:0% +G for a reaction well just like + + + align:start position:0% +G for a reaction well just like +calculating Delta H for the reaction you + + align:start position:0% +calculating Delta H for the reaction you + + + align:start position:0% +calculating Delta H for the reaction you +can use the free energy of formation you + + align:start position:0% +can use the free energy of formation you + + + align:start position:0% +can use the free energy of formation you +need to know the free energy of + + align:start position:0% +need to know the free energy of + + + align:start position:0% +need to know the free energy of +formation for every one of the + + align:start position:0% +formation for every one of the + + + align:start position:0% +formation for every one of the +products multiply that by the + + align:start position:0% +products multiply that by the + + + align:start position:0% +products multiply that by the +appropriate stochiometric + + align:start position:0% +appropriate stochiometric + + + align:start position:0% +appropriate stochiometric +number sum that all up right and then + + align:start position:0% +number sum that all up right and then + + + align:start position:0% +number sum that all up right and then +you do the same here for the reactants + + align:start position:0% +you do the same here for the reactants + + + align:start position:0% +you do the same here for the reactants +you need to know the free energy of + + align:start position:0% +you need to know the free energy of + + + align:start position:0% +you need to know the free energy of +formation for every single one of the + + align:start position:0% +formation for every single one of the + + + align:start position:0% +formation for every single one of the +reactants multiplied by the + + align:start position:0% +reactants multiplied by the + + + align:start position:0% +reactants multiplied by the +stochiometric number sum that all + + align:start position:0% + + + + align:start position:0% + +up and take the difference and you will + + align:start position:0% +up and take the difference and you will + + + align:start position:0% +up and take the difference and you will +have the free energy of the free energy + + align:start position:0% +have the free energy of the free energy + + + align:start position:0% +have the free energy of the free energy +for that chemical + + align:start position:0% +for that chemical + + + align:start position:0% +for that chemical +reaction okay notice this is products + + align:start position:0% +reaction okay notice this is products + + + align:start position:0% +reaction okay notice this is products +minus + + align:start position:0% +minus + + + align:start position:0% +minus +reactants right just like calculating + + align:start position:0% +reactants right just like calculating + + + align:start position:0% +reactants right just like calculating +enthalpies from the Heats of formation + + align:start position:0% +enthalpies from the Heats of formation + + + align:start position:0% +enthalpies from the Heats of formation +that was products minus + + align:start position:0% +that was products minus + + + align:start position:0% +that was products minus +reactants however when we calculated + + align:start position:0% +reactants however when we calculated + + + align:start position:0% +reactants however when we calculated +enthalpies from bond enthalpies that was + + align:start position:0% +enthalpies from bond enthalpies that was + + + align:start position:0% +enthalpies from bond enthalpies that was +reactants minus products all right + + align:start position:0% +reactants minus products all right + + + align:start position:0% +reactants minus products all right +that's something you do have to + + align:start position:0% +that's something you do have to + + + align:start position:0% +that's something you do have to +know likewise you can also calculate + + align:start position:0% +know likewise you can also calculate + + + align:start position:0% +know likewise you can also calculate +Delta G for a reaction now from knowing + + align:start position:0% +Delta G for a reaction now from knowing + + + align:start position:0% +Delta G for a reaction now from knowing +Delta H for that reaction and also + + align:start position:0% +Delta H for that reaction and also + + + align:start position:0% +Delta H for that reaction and also +knowing Delta s for that reaction so you + + align:start position:0% +knowing Delta s for that reaction so you + + + align:start position:0% +knowing Delta s for that reaction so you +got your choice to use the free energies + + align:start position:0% +got your choice to use the free energies + + + align:start position:0% +got your choice to use the free energies +of formation that you can look up or + + align:start position:0% +of formation that you can look up or + + + align:start position:0% +of formation that you can look up or +from knowing the enthalpy for a reaction + + align:start position:0% +from knowing the enthalpy for a reaction + + + align:start position:0% +from knowing the enthalpy for a reaction +and knowing the entropy for that + + align:start position:0% +and knowing the entropy for that + + + align:start position:0% +and knowing the entropy for that +reaction you can calculate Delta G all + + align:start position:0% +reaction you can calculate Delta G all + + + align:start position:0% +reaction you can calculate Delta G all +right so you got your choice with Delta + + align:start position:0% +right so you got your choice with Delta + + + align:start position:0% +right so you got your choice with Delta +G here depending on what information + + align:start position:0% +G here depending on what information + + + align:start position:0% +G here depending on what information +you're + + align:start position:0% +you're + + + align:start position:0% +you're +given or no + + align:start position:0% +given or no + + + align:start position:0% +given or no +okay so now what we want to talk about + + align:start position:0% +okay so now what we want to talk about + + + align:start position:0% +okay so now what we want to talk about +is uh our ability or + + align:start position:0% +is uh our ability or + + + align:start position:0% +is uh our ability or +inability to control the spontaneity of + + align:start position:0% +inability to control the spontaneity of + + + align:start position:0% +inability to control the spontaneity of +some uh chemical reaction to control it + + align:start position:0% +some uh chemical reaction to control it + + + align:start position:0% +some uh chemical reaction to control it +by virtue of adjusting the temperature + + align:start position:0% +by virtue of adjusting the temperature + + + align:start position:0% +by virtue of adjusting the temperature +all + + align:start position:0% +all + + + align:start position:0% +all +right all right so let's take uh this + + align:start position:0% +right all right so let's take uh this + + + align:start position:0% +right all right so let's take uh this +example here this is a sodium + + align:start position:0% +example here this is a sodium + + + align:start position:0% +example here this is a sodium +bicarbonate better known as as baking + + align:start position:0% +bicarbonate better known as as baking + + + align:start position:0% +bicarbonate better known as as baking +soda this is uh what you put into the + + align:start position:0% +soda this is uh what you put into the + + + align:start position:0% +soda this is uh what you put into the +dough of some kind of bake Goods that + + align:start position:0% +dough of some kind of bake Goods that + + + align:start position:0% +dough of some kind of bake Goods that +you want to make muffins or cakes you + + align:start position:0% +you want to make muffins or cakes you + + + align:start position:0% +you want to make muffins or cakes you +put it in there in order to lighten the + + align:start position:0% +put it in there in order to lighten the + + + align:start position:0% +put it in there in order to lighten the +batter and of course the way this works + + align:start position:0% +batter and of course the way this works + + + align:start position:0% +batter and of course the way this works +is that the sodium bicarbonate + + align:start position:0% +is that the sodium bicarbonate + + + align:start position:0% +is that the sodium bicarbonate +decomposes it decomposes to form CO2 and + + align:start position:0% +decomposes it decomposes to form CO2 and + + + align:start position:0% +decomposes it decomposes to form CO2 and +water + + align:start position:0% +water + + + align:start position:0% +water +and um when it decomposes it does so at + + align:start position:0% +and um when it decomposes it does so at + + + align:start position:0% +and um when it decomposes it does so at +um in the oven and the CO2 and the water + + align:start position:0% +um in the oven and the CO2 and the water + + + align:start position:0% +um in the oven and the CO2 and the water +then expand right they + + align:start position:0% +then expand right they + + + align:start position:0% +then expand right they +evaporate but they in that dough they + + align:start position:0% +evaporate but they in that dough they + + + align:start position:0% +evaporate but they in that dough they +kind of make bubbles right before they + + align:start position:0% +kind of make bubbles right before they + + + align:start position:0% +kind of make bubbles right before they +totally evaporate and around those gas + + align:start position:0% +totally evaporate and around those gas + + + align:start position:0% +totally evaporate and around those gas +bubbles the dough kind of hardens a + + align:start position:0% +bubbles the dough kind of hardens a + + + align:start position:0% +bubbles the dough kind of hardens a +little + + align:start position:0% +little + + + align:start position:0% +little +bit and um eventually the CO2 and water + + align:start position:0% +bit and um eventually the CO2 and water + + + align:start position:0% +bit and um eventually the CO2 and water +are driven off but what it leaves behind + + align:start position:0% +are driven off but what it leaves behind + + + align:start position:0% +are driven off but what it leaves behind +is a very porous structure in the in the + + align:start position:0% +is a very porous structure in the in the + + + align:start position:0% +is a very porous structure in the in the +dough so uh it leaves you something that + + align:start position:0% +dough so uh it leaves you something that + + + align:start position:0% +dough so uh it leaves you something that +you can actually put your teeth + + align:start position:0% +you can actually put your teeth + + + align:start position:0% +you can actually put your teeth +into have you ever tried putting your + + align:start position:0% +into have you ever tried putting your + + + align:start position:0% +into have you ever tried putting your +teeth into some cake where somebody left + + align:start position:0% +teeth into some cake where somebody left + + + align:start position:0% +teeth into some cake where somebody left +out the sodium bicarbonate it's an + + align:start position:0% +out the sodium bicarbonate it's an + + + align:start position:0% +out the sodium bicarbonate it's an +interesting experience I've done it okay + + align:start position:0% +interesting experience I've done it okay + + + align:start position:0% +interesting experience I've done it okay +so important here but this is a + + align:start position:0% +so important here but this is a + + + align:start position:0% +so important here but this is a +reaction that is very endo ermic plus + + align:start position:0% +reaction that is very endo ermic plus + + + align:start position:0% +reaction that is very endo ermic plus +136 K per mole it is however a reaction + + align:start position:0% +136 K per mole it is however a reaction + + + align:start position:0% +136 K per mole it is however a reaction +where there's an increase in the entropy + + align:start position:0% +where there's an increase in the entropy + + + align:start position:0% +where there's an increase in the entropy +right we're increasing the entropy a lot + + align:start position:0% +right we're increasing the entropy a lot + + + align:start position:0% +right we're increasing the entropy a lot +here increasing the + + align:start position:0% +here increasing the + + + align:start position:0% +here increasing the +disorder and let's calculate Delta G for + + align:start position:0% +disorder and let's calculate Delta G for + + + align:start position:0% +disorder and let's calculate Delta G for +this + + align:start position:0% +this + + + align:start position:0% +this +reaction well Delta G for this reaction + + align:start position:0% +reaction well Delta G for this reaction + + + align:start position:0% +reaction well Delta G for this reaction +at room + + align:start position:0% +at room + + + align:start position:0% +at room +temperature is plus 36 K per mole it is + + align:start position:0% +temperature is plus 36 K per mole it is + + + align:start position:0% +temperature is plus 36 K per mole it is +nons spontan aneous you know what that's + + align:start position:0% +nons spontan aneous you know what that's + + + align:start position:0% +nons spontan aneous you know what that's +good because you don't want that + + align:start position:0% +good because you don't want that + + + align:start position:0% +good because you don't want that +reaction to start when the dough batter + + align:start position:0% +reaction to start when the dough batter + + + align:start position:0% +reaction to start when the dough batter +is still sitting on the kitchen counter + + align:start position:0% +is still sitting on the kitchen counter + + + align:start position:0% +is still sitting on the kitchen counter +right because at that point you're not + + align:start position:0% +right because at that point you're not + + + align:start position:0% +right because at that point you're not +going to be able to harden the dough in + + align:start position:0% +going to be able to harden the dough in + + + align:start position:0% +going to be able to harden the dough in +any + + align:start position:0% +any + + + align:start position:0% +any +way and but let's try to make this + + align:start position:0% +way and but let's try to make this + + + align:start position:0% +way and but let's try to make this +reaction now spontaneous by increasing + + align:start position:0% +reaction now spontaneous by increasing + + + align:start position:0% +reaction now spontaneous by increasing +the temperature let's make this term + + align:start position:0% +the temperature let's make this term + + + align:start position:0% +the temperature let's make this term +here negative more in absolute value we + + align:start position:0% +here negative more in absolute value we + + + align:start position:0% +here negative more in absolute value we +want to make this term larger than Delta + + align:start position:0% +want to make this term larger than Delta + + + align:start position:0% +want to make this term larger than Delta +H so that we can have a negative Delta + + align:start position:0% +H so that we can have a negative Delta + + + align:start position:0% +H so that we can have a negative Delta +G well we can do + + align:start position:0% +G well we can do + + + align:start position:0% +G well we can do +that by raising the temperature to a + + align:start position:0% +that by raising the temperature to a + + + align:start position:0% +that by raising the temperature to a +baking temperature + + align:start position:0% +baking temperature + + + align:start position:0% +baking temperature +350 Fahrenheit which is about + + align:start position:0% +350 Fahrenheit which is about + + + align:start position:0% +350 Fahrenheit which is about +450° + + align:start position:0% +450° + + + align:start position:0% +450° +Kelvin and now when we calculate Delta G + + align:start position:0% +Kelvin and now when we calculate Delta G + + + align:start position:0% +Kelvin and now when we calculate Delta G +at + + align:start position:0% +at + + + align:start position:0% +at +450° Kelvin what we find is that Delta G + + align:start position:0% +450° Kelvin what we find is that Delta G + + + align:start position:0% +450° Kelvin what we find is that Delta G +is now negative + + align:start position:0% +is now negative + + + align:start position:0% +is now negative +and now we've got a spontaneous reaction + + align:start position:0% +and now we've got a spontaneous reaction + + + align:start position:0% +and now we've got a spontaneous reaction +now when you get up to this baking + + align:start position:0% +now when you get up to this baking + + + align:start position:0% +now when you get up to this baking +temperature this reaction proceeds + + align:start position:0% +temperature this reaction proceeds + + + align:start position:0% +temperature this reaction proceeds +readily in the forward direction we have + + align:start position:0% +readily in the forward direction we have + + + align:start position:0% +readily in the forward direction we have +adjusted the spontaneity of this + + align:start position:0% +adjusted the spontaneity of this + + + align:start position:0% +adjusted the spontaneity of this +particular reaction by increasing the + + align:start position:0% +particular reaction by increasing the + + + align:start position:0% +particular reaction by increasing the +temperature by making this term this + + align:start position:0% +temperature by making this term this + + + align:start position:0% +temperature by making this term this +second term the T times Delta s by + + align:start position:0% +second term the T times Delta s by + + + align:start position:0% +second term the T times Delta s by +making that larger in absolute magnitude + + align:start position:0% +making that larger in absolute magnitude + + + align:start position:0% +making that larger in absolute magnitude +than Delta h + + align:start position:0% +than Delta h + + + align:start position:0% +than Delta h +we've made that reaction + + align:start position:0% +we've made that reaction + + + align:start position:0% +we've made that reaction +spontaneous so there are reactions for + + align:start position:0% +spontaneous so there are reactions for + + + align:start position:0% +spontaneous so there are reactions for +which we can control the spontaneity by + + align:start position:0% +which we can control the spontaneity by + + + align:start position:0% +which we can control the spontaneity by +adjusting the temperature and let's take + + align:start position:0% +adjusting the temperature and let's take + + + align:start position:0% +adjusting the temperature and let's take +a look at + + align:start position:0% +a look at + + + align:start position:0% +a look at +that well as you know here Delta G is + + align:start position:0% +that well as you know here Delta G is + + + align:start position:0% +that well as you know here Delta G is +the linear function of the temperature + + align:start position:0% +the linear function of the temperature + + + align:start position:0% +the linear function of the temperature +so let me draw just a dependence and + + align:start position:0% +so let me draw just a dependence and + + + align:start position:0% +so let me draw just a dependence and +actually this is for the decomposition + + align:start position:0% +actually this is for the decomposition + + + align:start position:0% +actually this is for the decomposition +of sodium bicarbonate + + align:start position:0% +of sodium bicarbonate + + + align:start position:0% +of sodium bicarbonate +let me just draw Delta G as a function + + align:start position:0% +let me just draw Delta G as a function + + + align:start position:0% +let me just draw Delta G as a function +of the + + align:start position:0% +of the + + + align:start position:0% +of the +temperature the slope of this line here + + align:start position:0% +temperature the slope of this line here + + + align:start position:0% +temperature the slope of this line here +the slope of that line is minus Delta s + + align:start position:0% +the slope of that line is minus Delta s + + + align:start position:0% +the slope of that line is minus Delta s +for that reaction right you can see that + + align:start position:0% +for that reaction right you can see that + + + align:start position:0% +for that reaction right you can see that +this is going to be the slope I'm + + align:start position:0% +this is going to be the slope I'm + + + align:start position:0% +this is going to be the slope I'm +plotting it versus + + align:start position:0% +plotting it versus + + + align:start position:0% +plotting it versus +T The Intercept is Delta H it's the + + align:start position:0% +T The Intercept is Delta H it's the + + + align:start position:0% +T The Intercept is Delta H it's the +enthalpy change for this + + align:start position:0% +enthalpy change for this + + + align:start position:0% +enthalpy change for this +reaction and now let me just draw a zero + + align:start position:0% +reaction and now let me just draw a zero + + + align:start position:0% +reaction and now let me just draw a zero +here dotted line all right I drew that + + align:start position:0% +here dotted line all right I drew that + + + align:start position:0% +here dotted line all right I drew that +zero because I want you to see that at + + align:start position:0% +zero because I want you to see that at + + + align:start position:0% +zero because I want you to see that at +some temperature right here that I'm + + align:start position:0% +some temperature right here that I'm + + + align:start position:0% +some temperature right here that I'm +going to label + + align:start position:0% +going to label + + + align:start position:0% +going to label +tar at some temperature that Delta G is + + align:start position:0% +tar at some temperature that Delta G is + + + align:start position:0% +tar at some temperature that Delta G is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +zero what that means is that at this + + align:start position:0% +zero what that means is that at this + + + align:start position:0% +zero what that means is that at this +temperature the sign of Delta G is + + align:start position:0% +temperature the sign of Delta G is + + + align:start position:0% +temperature the sign of Delta G is +changing you can see that for + + align:start position:0% +changing you can see that for + + + align:start position:0% +changing you can see that for +temperatures less than + + align:start position:0% +temperatures less than + + + align:start position:0% +temperatures less than +tar the value of delta G KN here is + + align:start position:0% +tar the value of delta G KN here is + + + align:start position:0% +tar the value of delta G KN here is +greater than + + align:start position:0% +greater than + + + align:start position:0% +greater than +zero meaning the reaction is + + align:start position:0% +zero meaning the reaction is + + + align:start position:0% +zero meaning the reaction is +non-spontaneous + + align:start position:0% +non-spontaneous + + + align:start position:0% +non-spontaneous +for temperatures greater than T Star + + align:start position:0% +for temperatures greater than T Star + + + align:start position:0% +for temperatures greater than T Star +right in here you see that Delta G KN is + + align:start position:0% +right in here you see that Delta G KN is + + + align:start position:0% +right in here you see that Delta G KN is +less than zero means we have a + + align:start position:0% +less than zero means we have a + + + align:start position:0% +less than zero means we have a +spontaneous + + align:start position:0% +spontaneous + + + align:start position:0% +spontaneous +reaction right we've controlled the + + align:start position:0% +reaction right we've controlled the + + + align:start position:0% +reaction right we've controlled the +spontaneity of this reaction by the use + + align:start position:0% +spontaneity of this reaction by the use + + + align:start position:0% +spontaneity of this reaction by the use +of + + align:start position:0% +of + + + align:start position:0% +of +temperature let's calculate the value of + + align:start position:0% +temperature let's calculate the value of + + + align:start position:0% +temperature let's calculate the value of +the temperature at which the spontaneity + + align:start position:0% +the temperature at which the spontaneity + + + align:start position:0% +the temperature at which the spontaneity +of this reaction changes let's do that + + align:start position:0% +of this reaction changes let's do that + + + align:start position:0% +of this reaction changes let's do that +all right to do that we're going to set + + align:start position:0% +all right to do that we're going to set + + + align:start position:0% +all right to do that we're going to set +Delta G not here equal to + + align:start position:0% +Delta G not here equal to + + + align:start position:0% +Delta G not here equal to +zero and then we're just going to solve + + align:start position:0% +zero and then we're just going to solve + + + align:start position:0% +zero and then we're just going to solve +for T star we're going to solve for that + + align:start position:0% +for T star we're going to solve for that + + + align:start position:0% +for T star we're going to solve for that +value of T star that for this Delta H + + align:start position:0% +value of T star that for this Delta H + + + align:start position:0% +value of T star that for this Delta H +and that Delta s will make Delta G equal + + align:start position:0% +and that Delta s will make Delta G equal + + + align:start position:0% +and that Delta s will make Delta G equal +to + + align:start position:0% +to + + + align:start position:0% +to +Z let's do that well then T star is + + align:start position:0% +Z let's do that well then T star is + + + align:start position:0% +Z let's do that well then T star is +Delta H over Delta s if I plug in for + + align:start position:0% +Delta H over Delta s if I plug in for + + + align:start position:0% +Delta H over Delta s if I plug in for +the decomposition of sodium bicarbonate + + align:start position:0% +the decomposition of sodium bicarbonate + + + align:start position:0% +the decomposition of sodium bicarbonate +the Delta H and the Delta s then tar is + + align:start position:0% +the Delta H and the Delta s then tar is + + + align:start position:0% +the Delta H and the Delta s then tar is +406 Dees Kelvin all right so your sodium + + align:start position:0% +406 Dees Kelvin all right so your sodium + + + align:start position:0% +406 Dees Kelvin all right so your sodium +bicarbonate isn't going to decompose + + align:start position:0% +bicarbonate isn't going to decompose + + + align:start position:0% +bicarbonate isn't going to decompose +until you get to this temperature + + align:start position:0% + + + + align:start position:0% + +right okay so at least for this reaction + + align:start position:0% +right okay so at least for this reaction + + + align:start position:0% +right okay so at least for this reaction +it appears we can control the + + align:start position:0% +it appears we can control the + + + align:start position:0% +it appears we can control the +spontaneity of this chemical reaction + + align:start position:0% +spontaneity of this chemical reaction + + + align:start position:0% +spontaneity of this chemical reaction +reaction and that is the case in + + align:start position:0% +reaction and that is the case in + + + align:start position:0% +reaction and that is the case in +general if you have a reaction that is + + align:start position:0% +general if you have a reaction that is + + + align:start position:0% +general if you have a reaction that is +endothermic that is Delta H is greater + + align:start position:0% +endothermic that is Delta H is greater + + + align:start position:0% +endothermic that is Delta H is greater +than zero and if that reaction increases + + align:start position:0% +than zero and if that reaction increases + + + align:start position:0% +than zero and if that reaction increases +in entropy Delta s is greater than + + align:start position:0% +in entropy Delta s is greater than + + + align:start position:0% +in entropy Delta s is greater than +zero you can that reaction will be + + align:start position:0% +zero you can that reaction will be + + + align:start position:0% +zero you can that reaction will be +spontaneous for temperatures greater + + align:start position:0% +spontaneous for temperatures greater + + + align:start position:0% +spontaneous for temperatures greater +than some temperature T star you can see + + align:start position:0% +than some temperature T star you can see + + + align:start position:0% +than some temperature T star you can see +that by the signs of the reactions here + + align:start position:0% +that by the signs of the reactions here + + + align:start position:0% +that by the signs of the reactions here +if Delta H up here is positive and Delta + + align:start position:0% +if Delta H up here is positive and Delta + + + align:start position:0% +if Delta H up here is positive and Delta +s is positive then you've got to + + align:start position:0% +s is positive then you've got to + + + align:start position:0% +s is positive then you've got to +increase this second term T Delta s the + + align:start position:0% +increase this second term T Delta s the + + + align:start position:0% +increase this second term T Delta s the +absolute magnitude of it + + align:start position:0% +absolute magnitude of it + + + align:start position:0% +absolute magnitude of it +enough so that it is larger than Delta H + + align:start position:0% +enough so that it is larger than Delta H + + + align:start position:0% +enough so that it is larger than Delta H +and you're subtracting the two well + + align:start position:0% +and you're subtracting the two well + + + align:start position:0% +and you're subtracting the two well +that's when you're going to get the + + align:start position:0% +that's when you're going to get the + + + align:start position:0% +that's when you're going to get the +Delta G negative all right for large + + align:start position:0% +Delta G negative all right for large + + + align:start position:0% +Delta G negative all right for large +enough temperatures the Delta G will be + + align:start position:0% +enough temperatures the Delta G will be + + + align:start position:0% +enough temperatures the Delta G will be +negative + + align:start position:0% +negative + + + align:start position:0% +negative +okay but suppose we have a reaction + + align:start position:0% +okay but suppose we have a reaction + + + align:start position:0% +okay but suppose we have a reaction +that's + + align:start position:0% +that's + + + align:start position:0% +that's +exothermic Delta H is less than + + align:start position:0% +exothermic Delta H is less than + + + align:start position:0% +exothermic Delta H is less than +zero and a reaction that decreases the + + align:start position:0% +zero and a reaction that decreases the + + + align:start position:0% +zero and a reaction that decreases the +entropy Delta s is less than + + align:start position:0% +entropy Delta s is less than + + + align:start position:0% +entropy Delta s is less than +zero I plotted that now as a function of + + align:start position:0% +zero I plotted that now as a function of + + + align:start position:0% +zero I plotted that now as a function of +the temperature and you can see that the + + align:start position:0% +the temperature and you can see that the + + + align:start position:0% +the temperature and you can see that the +slope of this line has changed we now + + align:start position:0% +slope of this line has changed we now + + + align:start position:0% +slope of this line has changed we now +have this positive + + align:start position:0% +have this positive + + + align:start position:0% +have this positive +slope all right well in this particular + + align:start position:0% +slope all right well in this particular + + + align:start position:0% +slope all right well in this particular +case you're going to have a spontaneous + + align:start position:0% +case you're going to have a spontaneous + + + align:start position:0% +case you're going to have a spontaneous +reaction whenever the temperature is + + align:start position:0% +reaction whenever the temperature is + + + align:start position:0% +reaction whenever the temperature is +less than some temperature + + align:start position:0% +less than some temperature + + + align:start position:0% +less than some temperature +tar right because right here that's our + + align:start position:0% +tar right because right here that's our + + + align:start position:0% +tar right because right here that's our +T star and so for temperatures less than + + align:start position:0% +T star and so for temperatures less than + + + align:start position:0% +T star and so for temperatures less than +that Delta G is negative for temperatur + + align:start position:0% +that Delta G is negative for temperatur + + + align:start position:0% +that Delta G is negative for temperatur +is greater than that Delta G is + + align:start position:0% +is greater than that Delta G is + + + align:start position:0% +is greater than that Delta G is +positive all right and again you can see + + align:start position:0% +positive all right and again you can see + + + align:start position:0% +positive all right and again you can see +that if Delta H is less than zero this + + align:start position:0% +that if Delta H is less than zero this + + + align:start position:0% +that if Delta H is less than zero this +Delta H will be negative and Delta s + + align:start position:0% +Delta H will be negative and Delta s + + + align:start position:0% +Delta H will be negative and Delta s +here is going to be a negative we're + + align:start position:0% +here is going to be a negative we're + + + align:start position:0% +here is going to be a negative we're +going to have a negative times a + + align:start position:0% +going to have a negative times a + + + align:start position:0% +going to have a negative times a +negative that's a + + align:start position:0% +negative that's a + + + align:start position:0% +negative that's a +positive and so since Delta H is + + align:start position:0% +positive and so since Delta H is + + + align:start position:0% +positive and so since Delta H is +negative T is going to have to be small + + align:start position:0% +negative T is going to have to be small + + + align:start position:0% +negative T is going to have to be small +this is going to be a positive term T is + + align:start position:0% +this is going to be a positive term T is + + + align:start position:0% +this is going to be a positive term T is +going to have to be small so that an + + align:start position:0% +going to have to be small so that an + + + align:start position:0% +going to have to be small so that an +absolute value right it is not larger + + align:start position:0% +absolute value right it is not larger + + + align:start position:0% +absolute value right it is not larger +than Delta a in order to get a negative + + align:start position:0% +than Delta a in order to get a negative + + + align:start position:0% +than Delta a in order to get a negative +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +G + + align:start position:0% +G + + + align:start position:0% +G +okay however suppose we have a reaction + + align:start position:0% +okay however suppose we have a reaction + + + align:start position:0% +okay however suppose we have a reaction +that's n exothermic Delta h less than + + align:start position:0% +that's n exothermic Delta h less than + + + align:start position:0% +that's n exothermic Delta h less than +zero and Delta s is greater than zero + + align:start position:0% +zero and Delta s is greater than zero + + + align:start position:0% +zero and Delta s is greater than zero +we're increasing the entropy here well + + align:start position:0% +we're increasing the entropy here well + + + align:start position:0% +we're increasing the entropy here well +this is the best of all worlds when Del + + align:start position:0% +this is the best of all worlds when Del + + + align:start position:0% +this is the best of all worlds when Del +when you have an exothermic reaction + + align:start position:0% +when you have an exothermic reaction + + + align:start position:0% +when you have an exothermic reaction +that increases the entropy hey this + + align:start position:0% +that increases the entropy hey this + + + align:start position:0% +that increases the entropy hey this +reaction is spontaneous at all + + align:start position:0% +reaction is spontaneous at all + + + align:start position:0% +reaction is spontaneous at all +temperatures Delta G is going to be z uh + + align:start position:0% +temperatures Delta G is going to be z uh + + + align:start position:0% +temperatures Delta G is going to be z uh +negative for all temperatures because + + align:start position:0% +negative for all temperatures because + + + align:start position:0% +negative for all temperatures because +Delta H is + + align:start position:0% +Delta H is + + + align:start position:0% +Delta H is +negative and then you have minus t Delta + + align:start position:0% +negative and then you have minus t Delta + + + align:start position:0% +negative and then you have minus t Delta +s well Delta s is positive so you have a + + align:start position:0% +s well Delta s is positive so you have a + + + align:start position:0% +s well Delta s is positive so you have a +negative number plus a negative number + + align:start position:0% +negative number plus a negative number + + + align:start position:0% +negative number plus a negative number +or a negative number minus a positive + + align:start position:0% +or a negative number minus a positive + + + align:start position:0% +or a negative number minus a positive +number Delta G is always negative + + align:start position:0% +number Delta G is always negative + + + align:start position:0% +number Delta G is always negative +spontaneous at every temperature for + + align:start position:0% +spontaneous at every temperature for + + + align:start position:0% +spontaneous at every temperature for +those reactions you can't control the + + align:start position:0% +those reactions you can't control the + + + align:start position:0% +those reactions you can't control the +spontaneity of the + + align:start position:0% +spontaneity of the + + + align:start position:0% +spontaneity of the +reaction and then + + align:start position:0% +reaction and then + + + align:start position:0% +reaction and then +finally you can have a situation where + + align:start position:0% +finally you can have a situation where + + + align:start position:0% +finally you can have a situation where +you have an endo mic reaction Delta H + + align:start position:0% +you have an endo mic reaction Delta H + + + align:start position:0% +you have an endo mic reaction Delta H +greater than zero and the worst of all + + align:start position:0% +greater than zero and the worst of all + + + align:start position:0% +greater than zero and the worst of all +cases Delta s less than zero you're + + align:start position:0% +cases Delta s less than zero you're + + + align:start position:0% +cases Delta s less than zero you're +decreasing the entropy you're making the + + align:start position:0% +decreasing the entropy you're making the + + + align:start position:0% +decreasing the entropy you're making the +system more ordered in that case you + + align:start position:0% +system more ordered in that case you + + + align:start position:0% +system more ordered in that case you +have a reaction that's never spontaneous + + align:start position:0% +have a reaction that's never spontaneous + + + align:start position:0% +have a reaction that's never spontaneous +again you can see it from the sign if + + align:start position:0% +again you can see it from the sign if + + + align:start position:0% +again you can see it from the sign if +Delta H is positive and Delta s here is + + align:start position:0% +Delta H is positive and Delta s here is + + + align:start position:0% +Delta H is positive and Delta s here is +negative a negative times a negative is + + align:start position:0% +negative a negative times a negative is + + + align:start position:0% +negative a negative times a negative is +a positive so we have a positive number + + align:start position:0% +a positive so we have a positive number + + + align:start position:0% +a positive so we have a positive number +plus a positive number hey Delta G's + + align:start position:0% +plus a positive number hey Delta G's + + + align:start position:0% +plus a positive number hey Delta G's +positive all temperatures okay so with + + align:start position:0% +positive all temperatures okay so with + + + align:start position:0% +positive all temperatures okay so with +temperature there we also can't adjust + + align:start position:0% +temperature there we also can't adjust + + + align:start position:0% +temperature there we also can't adjust +the + + align:start position:0% + + + + align:start position:0% + +spontaneity + + align:start position:0% +spontaneity + + + align:start position:0% +spontaneity +okay so this is uh very important here + + align:start position:0% +okay so this is uh very important here + + + align:start position:0% +okay so this is uh very important here +to uh + + align:start position:0% + + + + align:start position:0% + +understand all + + align:start position:0% +understand all + + + align:start position:0% +understand all +right so + + align:start position:0% +right so + + + align:start position:0% +right so +now what we've been talking about so far + + align:start position:0% +now what we've been talking about so far + + + align:start position:0% +now what we've been talking about so far +is uh Delta + + align:start position:0% +is uh Delta + + + align:start position:0% +is uh Delta +G's that uh have been Delta G knots + + align:start position:0% +G's that uh have been Delta G knots + + + align:start position:0% +G's that uh have been Delta G knots +we've been talking about Delta G's free + + align:start position:0% +we've been talking about Delta G's free + + + align:start position:0% +we've been talking about Delta G's free +energies of formation in our standard + + align:start position:0% +energies of formation in our standard + + + align:start position:0% +energies of formation in our standard +state of one bar + + align:start position:0% +state of one bar + + + align:start position:0% +state of one bar +pressure what that means for Delta G not + + align:start position:0% +pressure what that means for Delta G not + + + align:start position:0% +pressure what that means for Delta G not +what that + + align:start position:0% +what that + + + align:start position:0% +what that +means is that the partial pressures of + + align:start position:0% +means is that the partial pressures of + + + align:start position:0% +means is that the partial pressures of +your reactants and your products they + + align:start position:0% +your reactants and your products they + + + align:start position:0% +your reactants and your products they +are all one + + align:start position:0% +are all one + + + align:start position:0% +are all one +bar so Delta G KN for for a + + align:start position:0% +bar so Delta G KN for for a + + + align:start position:0% +bar so Delta G KN for for a +reaction is the free energy change for + + align:start position:0% +reaction is the free energy change for + + + align:start position:0% +reaction is the free energy change for +that + + align:start position:0% +that + + + align:start position:0% +that +reaction when there's one + + align:start position:0% +reaction when there's one + + + align:start position:0% +reaction when there's one +atmosphere of each of or one bar of each + + align:start position:0% +atmosphere of each of or one bar of each + + + align:start position:0% +atmosphere of each of or one bar of each +of the products and the reactants so + + align:start position:0% +of the products and the reactants so + + + align:start position:0% +of the products and the reactants so +let's take this famous + + align:start position:0% +let's take this famous + + + align:start position:0% +let's take this famous +reaction argon plus Boron going to + + align:start position:0% +reaction argon plus Boron going to + + + align:start position:0% +reaction argon plus Boron going to +carbon plus detarium all right A plus b + + align:start position:0% +carbon plus detarium all right A plus b + + + align:start position:0% +carbon plus detarium all right A plus b +c to D all right this Delta G knot here + + align:start position:0% +c to D all right this Delta G knot here + + + align:start position:0% +c to D all right this Delta G knot here +that's a Delta G for a reaction + + align:start position:0% +that's a Delta G for a reaction + + + align:start position:0% +that's a Delta G for a reaction +under the conditions of one bar partial + + align:start position:0% +under the conditions of one bar partial + + + align:start position:0% +under the conditions of one bar partial +pressure for d one bar partial pressure + + align:start position:0% +pressure for d one bar partial pressure + + + align:start position:0% +pressure for d one bar partial pressure +for c one bar partial pressure for B one + + align:start position:0% +for c one bar partial pressure for B one + + + align:start position:0% +for c one bar partial pressure for B one +bar partial pressure for + + align:start position:0% +bar partial pressure for + + + align:start position:0% +bar partial pressure for +a that's what that + + align:start position:0% +a that's what that + + + align:start position:0% +a that's what that +means but you know what gee that's not + + align:start position:0% +means but you know what gee that's not + + + align:start position:0% +means but you know what gee that's not +the situation you usually have say for + + align:start position:0% +the situation you usually have say for + + + align:start position:0% +the situation you usually have say for +example you're going to start this + + align:start position:0% +example you're going to start this + + + align:start position:0% +example you're going to start this +reaction you start the reaction with one + + align:start position:0% +reaction you start the reaction with one + + + align:start position:0% +reaction you start the reaction with one +bar of a and one bar of + + align:start position:0% +bar of a and one bar of + + + align:start position:0% +bar of a and one bar of +B but of course you don't have any C or + + align:start position:0% +B but of course you don't have any C or + + + align:start position:0% +B but of course you don't have any C or +D yet right because you haven't run the + + align:start position:0% +D yet right because you haven't run the + + + align:start position:0% +D yet right because you haven't run the +reaction so what we've got to be able to + + align:start position:0% +reaction so what we've got to be able to + + + align:start position:0% +reaction so what we've got to be able to +do is to calculate Delta + + align:start position:0% +do is to calculate Delta + + + align:start position:0% +do is to calculate Delta +G for conditions which aren't at the + + align:start position:0% +G for conditions which aren't at the + + + align:start position:0% +G for conditions which aren't at the +standard state which aren't at one bar d + + align:start position:0% +standard state which aren't at one bar d + + + align:start position:0% +standard state which aren't at one bar d +one bar c one bar B one bar a all right + + align:start position:0% +one bar c one bar B one bar a all right + + + align:start position:0% +one bar c one bar B one bar a all right +we've got to be able to do + + align:start position:0% +we've got to be able to do + + + align:start position:0% +we've got to be able to do +that and the way you do that is + + align:start position:0% +that and the way you do that is + + + align:start position:0% +that and the way you do that is +represented here by this expression + + align:start position:0% +represented here by this expression + + + align:start position:0% +represented here by this expression +where this expression came from is again + + align:start position:0% +where this expression came from is again + + + align:start position:0% +where this expression came from is again +a subject of a great uh interest in 560 + + align:start position:0% +a subject of a great uh interest in 560 + + + align:start position:0% +a subject of a great uh interest in 560 +you'll see where this expression comes + + align:start position:0% +you'll see where this expression comes + + + align:start position:0% +you'll see where this expression comes +from when you take + + align:start position:0% +from when you take + + + align:start position:0% +from when you take +560 but right now we're going to use it + + align:start position:0% +560 but right now we're going to use it + + + align:start position:0% +560 but right now we're going to use it +this is going to allow us to calculate + + align:start position:0% +this is going to allow us to calculate + + + align:start position:0% +this is going to allow us to calculate +Delta G from knowing the standard State + + align:start position:0% +Delta G from knowing the standard State + + + align:start position:0% +Delta G from knowing the standard State +Delta G + + align:start position:0% +Delta G + + + align:start position:0% +Delta G +knot is going to allow us to calculate + + align:start position:0% +knot is going to allow us to calculate + + + align:start position:0% +knot is going to allow us to calculate +Delta G for the reactants and products + + align:start position:0% +Delta G for the reactants and products + + + align:start position:0% +Delta G for the reactants and products +at any given pressure all + + align:start position:0% +at any given pressure all + + + align:start position:0% +at any given pressure all +right okay so you see this is Delta G + + align:start position:0% +right okay so you see this is Delta G + + + align:start position:0% +right okay so you see this is Delta G +Delta equal Delta G Plus RT Ln of the + + align:start position:0% +Delta equal Delta G Plus RT Ln of the + + + align:start position:0% +Delta equal Delta G Plus RT Ln of the +following this has the partial pressure + + align:start position:0% +following this has the partial pressure + + + align:start position:0% +following this has the partial pressure +of product C divided by a reference + + align:start position:0% +of product C divided by a reference + + + align:start position:0% +of product C divided by a reference +refence pressure raised to the + + align:start position:0% +refence pressure raised to the + + + align:start position:0% +refence pressure raised to the +appropriate stochiometric + + align:start position:0% +appropriate stochiometric + + + align:start position:0% +appropriate stochiometric +number and that's multiplied by the + + align:start position:0% +number and that's multiplied by the + + + align:start position:0% +number and that's multiplied by the +partial pressure of the product D + + align:start position:0% +partial pressure of the product D + + + align:start position:0% +partial pressure of the product D +divided by a reference pressure raised + + align:start position:0% +divided by a reference pressure raised + + + align:start position:0% +divided by a reference pressure raised +to the appropriate stochiometric + + align:start position:0% +to the appropriate stochiometric + + + align:start position:0% +to the appropriate stochiometric +number and that's all over the partial + + align:start position:0% +number and that's all over the partial + + + align:start position:0% +number and that's all over the partial +pressure of a divided by a reference + + align:start position:0% +pressure of a divided by a reference + + + align:start position:0% +pressure of a divided by a reference +pressure raised to that appropriate + + align:start position:0% +pressure raised to that appropriate + + + align:start position:0% +pressure raised to that appropriate +stochiometric number times the partial + + align:start position:0% +stochiometric number times the partial + + + align:start position:0% +stochiometric number times the partial +pressure of the other reactant over some + + align:start position:0% +pressure of the other reactant over some + + + align:start position:0% +pressure of the other reactant over some +reference pressure raise to the uh + + align:start position:0% +reference pressure raise to the uh + + + align:start position:0% +reference pressure raise to the uh +appropriate stochiometric number that + + align:start position:0% +appropriate stochiometric number that + + + align:start position:0% +appropriate stochiometric number that +ratio is something that we call a + + align:start position:0% +ratio is something that we call a + + + align:start position:0% +ratio is something that we call a +reaction quotient we call it + + align:start position:0% +reaction quotient we call it + + + align:start position:0% +reaction quotient we call it +Q it is the ratio of instantaneous + + align:start position:0% +Q it is the ratio of instantaneous + + + align:start position:0% +Q it is the ratio of instantaneous +partial + + align:start position:0% +partial + + + align:start position:0% +partial +pressures so we might be running a + + align:start position:0% +pressures so we might be running a + + + align:start position:0% +pressures so we might be running a +reaction and uh at any time the reaction + + align:start position:0% +reaction and uh at any time the reaction + + + align:start position:0% +reaction and uh at any time the reaction +may not be complete at any time we can + + align:start position:0% +may not be complete at any time we can + + + align:start position:0% +may not be complete at any time we can +stop the reaction we can figure out or + + align:start position:0% +stop the reaction we can figure out or + + + align:start position:0% +stop the reaction we can figure out or +measure what the partial pressures of + + align:start position:0% +measure what the partial pressures of + + + align:start position:0% +measure what the partial pressures of +reactants and products + + align:start position:0% +reactants and products + + + align:start position:0% +reactants and products +are and we can calculate what this Q is + + align:start position:0% +are and we can calculate what this Q is + + + align:start position:0% +are and we can calculate what this Q is +Right knowing what those are from a + + align:start position:0% +Right knowing what those are from a + + + align:start position:0% +Right knowing what those are from a +measurement that's what the reaction + + align:start position:0% +measurement that's what the reaction + + + align:start position:0% +measurement that's what the reaction +quotient + + align:start position:0% +quotient + + + align:start position:0% +quotient +is now our reference pressure is going + + align:start position:0% +is now our reference pressure is going + + + align:start position:0% +is now our reference pressure is going +to be one + + align:start position:0% +to be one + + + align:start position:0% +to be one +bar so what I'm going to do and what you + + align:start position:0% +bar so what I'm going to do and what you + + + align:start position:0% +bar so what I'm going to do and what you +can do in this reaction quotient + + align:start position:0% +can do in this reaction quotient + + + align:start position:0% +can do in this reaction quotient +is that I'm going to put P RF the + + align:start position:0% +is that I'm going to put P RF the + + + align:start position:0% +is that I'm going to put P RF the +reference pressure as ones in here right + + align:start position:0% +reference pressure as ones in here right + + + align:start position:0% +reference pressure as ones in here right +and so I'm not going to explicitly write + + align:start position:0% +and so I'm not going to explicitly write + + + align:start position:0% +and so I'm not going to explicitly write +it out and that's just fine as long as + + align:start position:0% +it out and that's just fine as long as + + + align:start position:0% +it out and that's just fine as long as +you put the pressures then here in units + + align:start position:0% +you put the pressures then here in units + + + align:start position:0% +you put the pressures then here in units +of + + align:start position:0% +of + + + align:start position:0% +of +bar okay so this is the reaction + + align:start position:0% +bar okay so this is the reaction + + + align:start position:0% +bar okay so this is the reaction +quotient the form of it that we're going + + align:start position:0% +quotient the form of it that we're going + + + align:start position:0% +quotient the form of it that we're going +to use as long as you put the pressures + + align:start position:0% +to use as long as you put the pressures + + + align:start position:0% +to use as long as you put the pressures +here in units of bar + + align:start position:0% + + + + align:start position:0% + +okay so we got to remember this because + + align:start position:0% +okay so we got to remember this because + + + align:start position:0% +okay so we got to remember this because +I'm now going to use this in a very + + align:start position:0% +I'm now going to use this in a very + + + align:start position:0% +I'm now going to use this in a very +interesting way this is going to give me + + align:start position:0% +interesting way this is going to give me + + + align:start position:0% +interesting way this is going to give me +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +G at any arbitrary pressures of the + + align:start position:0% +G at any arbitrary pressures of the + + + align:start position:0% +G at any arbitrary pressures of the +reactants and the products okay all + + align:start position:0% +reactants and the products okay all + + + align:start position:0% +reactants and the products okay all +right so how am I going to use this I'm + + align:start position:0% +right so how am I going to use this I'm + + + align:start position:0% +right so how am I going to use this I'm +going to start to talk about the + + align:start position:0% +going to start to talk about the + + + align:start position:0% +going to start to talk about the +equilibrium constant for the + + align:start position:0% +equilibrium constant for the + + + align:start position:0% +equilibrium constant for the +reaction so I've got my famous a plus b + + align:start position:0% +reaction so I've got my famous a plus b + + + align:start position:0% +reaction so I've got my famous a plus b +going to C plus d + + align:start position:0% + + + + align:start position:0% + +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +and you already know that all reactions + + align:start position:0% +and you already know that all reactions + + + align:start position:0% +and you already know that all reactions +have some kind of + + align:start position:0% +have some kind of + + + align:start position:0% +have some kind of +equilibrium there's a forward reaction + + align:start position:0% +equilibrium there's a forward reaction + + + align:start position:0% +equilibrium there's a forward reaction +and there's a reverse + + align:start position:0% + + + + align:start position:0% + +reaction and we know that as we said + + align:start position:0% +reaction and we know that as we said + + + align:start position:0% +reaction and we know that as we said +Delta G is less than zero if Delta G + + align:start position:0% +Delta G is less than zero if Delta G + + + align:start position:0% +Delta G is less than zero if Delta G +were less than zero for this reaction is + + align:start position:0% +were less than zero for this reaction is + + + align:start position:0% +were less than zero for this reaction is +written then it is the forward reaction + + align:start position:0% +written then it is the forward reaction + + + align:start position:0% +written then it is the forward reaction +that's + + align:start position:0% +that's + + + align:start position:0% +that's +spontaneous if Delta G is is less than + + align:start position:0% +spontaneous if Delta G is is less than + + + align:start position:0% +spontaneous if Delta G is is less than +zero or is greater than zero sorry that + + align:start position:0% +zero or is greater than zero sorry that + + + align:start position:0% +zero or is greater than zero sorry that +for the reaction is written then it's + + align:start position:0% +for the reaction is written then it's + + + align:start position:0% +for the reaction is written then it's +the reverse reaction that's + + align:start position:0% +the reverse reaction that's + + + align:start position:0% +the reverse reaction that's +spontaneous and now here comes the + + align:start position:0% +spontaneous and now here comes the + + + align:start position:0% +spontaneous and now here comes the +really important + + align:start position:0% + + + + align:start position:0% + +point and that is if Delta G is equal to + + align:start position:0% +point and that is if Delta G is equal to + + + align:start position:0% +point and that is if Delta G is equal to +zero for that reaction as + + align:start position:0% +zero for that reaction as + + + align:start position:0% +zero for that reaction as +written then hey then we're at chemical + + align:start position:0% +written then hey then we're at chemical + + + align:start position:0% +written then hey then we're at chemical +equilibrium when Delta G is equal to + + align:start position:0% +equilibrium when Delta G is equal to + + + align:start position:0% +equilibrium when Delta G is equal to +zero then we're at equilibrium notice + + align:start position:0% +zero then we're at equilibrium notice + + + align:start position:0% +zero then we're at equilibrium notice +this is not Delta G not equals z this is + + align:start position:0% +this is not Delta G not equals z this is + + + align:start position:0% +this is not Delta G not equals z this is +Delta g equals z that's what defines + + align:start position:0% +Delta g equals z that's what defines + + + align:start position:0% +Delta g equals z that's what defines +chemical + + align:start position:0% +chemical + + + align:start position:0% +chemical +equilibrium when that Delta G that I + + align:start position:0% +equilibrium when that Delta G that I + + + align:start position:0% +equilibrium when that Delta G that I +just showed you is equal to + + align:start position:0% +just showed you is equal to + + + align:start position:0% +just showed you is equal to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay so here's that expression again + + align:start position:0% +okay so here's that expression again + + + align:start position:0% +okay so here's that expression again +that I showed you Delta G is Delta G + + align:start position:0% +that I showed you Delta G is Delta G + + + align:start position:0% +that I showed you Delta G is Delta G +Plus + + align:start position:0% +Plus + + + align:start position:0% +Plus +rtln of this reaction + + align:start position:0% +rtln of this reaction + + + align:start position:0% +rtln of this reaction +quotient what I'm saying is that we're + + align:start position:0% +quotient what I'm saying is that we're + + + align:start position:0% +quotient what I'm saying is that we're +at + + align:start position:0% +at + + + align:start position:0% +at +equilibrium when this Delta G here this + + align:start position:0% +equilibrium when this Delta G here this + + + align:start position:0% +equilibrium when this Delta G here this +one is equal to zero not that one this + + align:start position:0% +one is equal to zero not that one this + + + align:start position:0% +one is equal to zero not that one this +one + + align:start position:0% +one + + + align:start position:0% +one +okay all right right if that's the casee + + align:start position:0% +okay all right right if that's the casee + + + align:start position:0% +okay all right right if that's the casee +if you're at + + align:start position:0% +if you're at + + + align:start position:0% +if you're at +equilibrium then I can take this + + align:start position:0% +equilibrium then I can take this + + + align:start position:0% +equilibrium then I can take this +reaction or I can take this equation + + align:start position:0% +reaction or I can take this equation + + + align:start position:0% +reaction or I can take this equation +here and what I'm going to do is I'm + + align:start position:0% +here and what I'm going to do is I'm + + + align:start position:0% +here and what I'm going to do is I'm +going to move Delta G to this + + align:start position:0% +going to move Delta G to this + + + align:start position:0% +going to move Delta G to this +side and the result is Delta G KN is + + align:start position:0% +side and the result is Delta G KN is + + + align:start position:0% +side and the result is Delta G KN is +equal to minus RT Ln of this reaction + + align:start position:0% +equal to minus RT Ln of this reaction + + + align:start position:0% +equal to minus RT Ln of this reaction +quotient all right see where I'm going + + align:start position:0% +quotient all right see where I'm going + + + align:start position:0% +quotient all right see where I'm going +Delta G was equal to zero that l me then + + align:start position:0% +Delta G was equal to zero that l me then + + + align:start position:0% +Delta G was equal to zero that l me then +solve for Delta G is equal to minus RT + + align:start position:0% +solve for Delta G is equal to minus RT + + + align:start position:0% +solve for Delta G is equal to minus RT +Ln of this reaction + + align:start position:0% + + + + align:start position:0% + +quotient + + align:start position:0% +quotient + + + align:start position:0% +quotient +okay + + align:start position:0% + + + + align:start position:0% + +now under this condition when Delta G is + + align:start position:0% +now under this condition when Delta G is + + + align:start position:0% +now under this condition when Delta G is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +zero this reaction quotient Q has a + + align:start position:0% +zero this reaction quotient Q has a + + + align:start position:0% +zero this reaction quotient Q has a +special name and that special name is a + + align:start position:0% +special name and that special name is a + + + align:start position:0% +special name and that special name is a +thermodynamic equilibrium con constant + + align:start position:0% +thermodynamic equilibrium con constant + + + align:start position:0% +thermodynamic equilibrium con constant +right when we're at equilibrium this + + align:start position:0% +right when we're at equilibrium this + + + align:start position:0% +right when we're at equilibrium this +reaction quotient is that equilibrium + + align:start position:0% +reaction quotient is that equilibrium + + + align:start position:0% +reaction quotient is that equilibrium +constant K this defines the equilibrium + + align:start position:0% +constant K this defines the equilibrium + + + align:start position:0% +constant K this defines the equilibrium +constant what the equilibrium constant + + align:start position:0% +constant what the equilibrium constant + + + align:start position:0% +constant what the equilibrium constant +tells + + align:start position:0% +tells + + + align:start position:0% +tells +us is about the relative proportions + + align:start position:0% +us is about the relative proportions + + + align:start position:0% +us is about the relative proportions +here of the products to the + + align:start position:0% +here of the products to the + + + align:start position:0% +here of the products to the +reactants so if the equilibrium constant + + align:start position:0% +reactants so if the equilibrium constant + + + align:start position:0% +reactants so if the equilibrium constant +is large hey we got a lot of products + + align:start position:0% +is large hey we got a lot of products + + + align:start position:0% +is large hey we got a lot of products +the numerator got to be large relative + + align:start position:0% +the numerator got to be large relative + + + align:start position:0% +the numerator got to be large relative +to the + + align:start position:0% +to the + + + align:start position:0% +to the +reactants if the equilibrium constant is + + align:start position:0% +reactants if the equilibrium constant is + + + align:start position:0% +reactants if the equilibrium constant is +small well then we've got few products + + align:start position:0% +small well then we've got few products + + + align:start position:0% +small well then we've got few products +relative to the + + align:start position:0% +relative to the + + + align:start position:0% +relative to the +reactants okay so the quotient q that + + align:start position:0% +reactants okay so the quotient q that + + + align:start position:0% +reactants okay so the quotient q that +reaction quotient is equal to the + + align:start position:0% +reaction quotient is equal to the + + + align:start position:0% +reaction quotient is equal to the +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +constant when Delta G is equal to zero + + align:start position:0% +constant when Delta G is equal to zero + + + align:start position:0% +constant when Delta G is equal to zero +okay okay not Delta + + align:start position:0% + + + + align:start position:0% + +G all right and so that's where this + + align:start position:0% +G all right and so that's where this + + + align:start position:0% +G all right and so that's where this +expression comes from Delta G is equal + + align:start position:0% +expression comes from Delta G is equal + + + align:start position:0% +expression comes from Delta G is equal +to minus RT time the log of the + + align:start position:0% +to minus RT time the log of the + + + align:start position:0% +to minus RT time the log of the +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +constant okay so if you know Delta G KN + + align:start position:0% +constant okay so if you know Delta G KN + + + align:start position:0% +constant okay so if you know Delta G KN +for a reaction hey you can figure out + + align:start position:0% +for a reaction hey you can figure out + + + align:start position:0% +for a reaction hey you can figure out +the equilibrium constant if you know the + + align:start position:0% +the equilibrium constant if you know the + + + align:start position:0% +the equilibrium constant if you know the +equilibrium constant + + align:start position:0% +equilibrium constant + + + align:start position:0% +equilibrium constant +by knowing say the partial pressures + + align:start position:0% +by knowing say the partial pressures + + + align:start position:0% +by knowing say the partial pressures +present of the products and the + + align:start position:0% +present of the products and the + + + align:start position:0% +present of the products and the +reactants at equilibrium you can work + + align:start position:0% +reactants at equilibrium you can work + + + align:start position:0% +reactants at equilibrium you can work +backwards and get Delta G + + align:start position:0% +backwards and get Delta G + + + align:start position:0% +backwards and get Delta G +KN + + align:start position:0% +KN + + + align:start position:0% +KN +okay okay so + + align:start position:0% +okay okay so + + + align:start position:0% +okay okay so +now what we're going to do is we're + + align:start position:0% +now what we're going to do is we're + + + align:start position:0% +now what we're going to do is we're +going to rearrange these equations here + + align:start position:0% +going to rearrange these equations here + + + align:start position:0% +going to rearrange these equations here +a little + + align:start position:0% +a little + + + align:start position:0% +a little +bit we're going to rearrange them in a + + align:start position:0% +bit we're going to rearrange them in a + + + align:start position:0% +bit we're going to rearrange them in a +form so that it will be easy to + + align:start position:0% +form so that it will be easy to + + + align:start position:0% +form so that it will be easy to +tell whether or not you're at chemical + + align:start position:0% +tell whether or not you're at chemical + + + align:start position:0% +tell whether or not you're at chemical +equilibrium we're going to use this + + align:start position:0% +equilibrium we're going to use this + + + align:start position:0% +equilibrium we're going to use this +reaction quotient Q as a measure of + + align:start position:0% +reaction quotient Q as a measure of + + + align:start position:0% +reaction quotient Q as a measure of +whether or not we are at chemical + + align:start position:0% +whether or not we are at chemical + + + align:start position:0% +whether or not we are at chemical +equilibrium we're going to compare Q to + + align:start position:0% +equilibrium we're going to compare Q to + + + align:start position:0% +equilibrium we're going to compare Q to +K right when Q is equal to K we're at + + align:start position:0% +K right when Q is equal to K we're at + + + align:start position:0% +K right when Q is equal to K we're at +equilibrium remember what Q is Q is the + + align:start position:0% +equilibrium remember what Q is Q is the + + + align:start position:0% +equilibrium remember what Q is Q is the +in the ratio of the instantaneous + + align:start position:0% +in the ratio of the instantaneous + + + align:start position:0% +in the ratio of the instantaneous +partial pressures of the products to the + + align:start position:0% +partial pressures of the products to the + + + align:start position:0% +partial pressures of the products to the +reactants at any time during the + + align:start position:0% +reactants at any time during the + + + align:start position:0% +reactants at any time during the +reaction K is the ratio of the + + align:start position:0% +reaction K is the ratio of the + + + align:start position:0% +reaction K is the ratio of the +equilibrium partial pressures of the + + align:start position:0% +equilibrium partial pressures of the + + + align:start position:0% +equilibrium partial pressures of the +products to the + + align:start position:0% +products to the + + + align:start position:0% +products to the +reactants all right so now we're going + + align:start position:0% +reactants all right so now we're going + + + align:start position:0% +reactants all right so now we're going +to work on a + + align:start position:0% +to work on a + + + align:start position:0% +to work on a +formalism that's going to allow us to + + align:start position:0% +formalism that's going to allow us to + + + align:start position:0% +formalism that's going to allow us to +easily compare Q to K so that we can + + align:start position:0% +easily compare Q to K so that we can + + + align:start position:0% +easily compare Q to K so that we can +tell whether or not we're at chemical + + align:start position:0% +tell whether or not we're at chemical + + + align:start position:0% +tell whether or not we're at chemical +equilibrium all right let's do that so + + align:start position:0% +equilibrium all right let's do that so + + + align:start position:0% +equilibrium all right let's do that so +here's the expression that that I wrote + + align:start position:0% +here's the expression that that I wrote + + + align:start position:0% +here's the expression that that I wrote +earlier that allowed me to calculate + + align:start position:0% +earlier that allowed me to calculate + + + align:start position:0% +earlier that allowed me to calculate +Delta G at any arbitrary pressures for + + align:start position:0% +Delta G at any arbitrary pressures for + + + align:start position:0% +Delta G at any arbitrary pressures for +the products and the + + align:start position:0% +the products and the + + + align:start position:0% +the products and the +reactants here is the expression that I + + align:start position:0% +reactants here is the expression that I + + + align:start position:0% +reactants here is the expression that I +got when Delta G was Zero when we're at + + align:start position:0% +got when Delta G was Zero when we're at + + + align:start position:0% +got when Delta G was Zero when we're at +equilibrium right and then Delta G is + + align:start position:0% +equilibrium right and then Delta G is + + + align:start position:0% +equilibrium right and then Delta G is +equal to minus RTL + + align:start position:0% +equal to minus RTL + + + align:start position:0% +equal to minus RTL +nfk what I'm going to do right now is + + align:start position:0% +nfk what I'm going to do right now is + + + align:start position:0% +nfk what I'm going to do right now is +I'm going to take this and I'm going to + + align:start position:0% +I'm going to take this and I'm going to + + + align:start position:0% +I'm going to take this and I'm going to +substitute it in let's do that right I'm + + align:start position:0% +substitute it in let's do that right I'm + + + align:start position:0% +substitute it in let's do that right I'm +going to sub substitute this into this + + align:start position:0% +going to sub substitute this into this + + + align:start position:0% +going to sub substitute this into this +more general + + align:start position:0% +more general + + + align:start position:0% +more general +form when I do that I'm going to get + + align:start position:0% +form when I do that I'm going to get + + + align:start position:0% +form when I do that I'm going to get +minus rtln of + + align:start position:0% +minus rtln of + + + align:start position:0% +minus rtln of +K plus rtln of Q right this is just a + + align:start position:0% +K plus rtln of Q right this is just a + + + align:start position:0% +K plus rtln of Q right this is just a +simple + + align:start position:0% +simple + + + align:start position:0% +simple +substitution but now what do I got I + + align:start position:0% +substitution but now what do I got I + + + align:start position:0% +substitution but now what do I got I +have the difference between two logs I + + align:start position:0% +have the difference between two logs I + + + align:start position:0% +have the difference between two logs I +have a minus Ln K here plus an Ln Q here + + align:start position:0% +have a minus Ln K here plus an Ln Q here + + + align:start position:0% +have a minus Ln K here plus an Ln Q here +the difference between logs is the log + + align:start position:0% +the difference between logs is the log + + + align:start position:0% +the difference between logs is the log +of that quotient of the arguments of + + align:start position:0% +of that quotient of the arguments of + + + align:start position:0% +of that quotient of the arguments of +those + + align:start position:0% +those + + + align:start position:0% +those +logs so I have rt is equal RT * Ln of Q + + align:start position:0% +logs so I have rt is equal RT * Ln of Q + + + align:start position:0% +logs so I have rt is equal RT * Ln of Q +over K all right this is the difference + + align:start position:0% +over K all right this is the difference + + + align:start position:0% +over K all right this is the difference +in the logs that's then the uh log of + + align:start position:0% +in the logs that's then the uh log of + + + align:start position:0% +in the logs that's then the uh log of +the quotient of the arguments of those + + align:start position:0% +the quotient of the arguments of those + + + align:start position:0% +the quotient of the arguments of those +logs okay so this is going to be great + + align:start position:0% +logs okay so this is going to be great + + + align:start position:0% +logs okay so this is going to be great +here because look at what we're going to + + align:start position:0% +here because look at what we're going to + + + align:start position:0% +here because look at what we're going to +be able to + + align:start position:0% +be able to + + + align:start position:0% +be able to +do remember what Q is the ratio of + + align:start position:0% +do remember what Q is the ratio of + + + align:start position:0% +do remember what Q is the ratio of +instantaneous partial pressures + + align:start position:0% +instantaneous partial pressures + + + align:start position:0% +instantaneous partial pressures +right and you know what K is the ratio + + align:start position:0% +right and you know what K is the ratio + + + align:start position:0% +right and you know what K is the ratio +of partial pressures at + + align:start position:0% +of partial pressures at + + + align:start position:0% +of partial pressures at +equilibrium so bottom line here is the + + align:start position:0% +equilibrium so bottom line here is the + + + align:start position:0% +equilibrium so bottom line here is the +following if + + align:start position:0% +following if + + + align:start position:0% +following if +Q right is less than K if Q is less than + + align:start position:0% +Q right is less than K if Q is less than + + + align:start position:0% +Q right is less than K if Q is less than +K what that means is we don't have + + align:start position:0% +K what that means is we don't have + + + align:start position:0% +K what that means is we don't have +enough products formed compared to what + + align:start position:0% +enough products formed compared to what + + + align:start position:0% +enough products formed compared to what +we should have at + + align:start position:0% +we should have at + + + align:start position:0% +we should have at +equilibrium that's when Q is less than + + align:start position:0% +equilibrium that's when Q is less than + + + align:start position:0% +equilibrium that's when Q is less than +K we don't we haven't got enough + + align:start position:0% +K we don't we haven't got enough + + + align:start position:0% +K we don't we haven't got enough +products compared to what we need for + + align:start position:0% +products compared to what we need for + + + align:start position:0% +products compared to what we need for +chemical equilibrium if Q is less than K + + align:start position:0% +chemical equilibrium if Q is less than K + + + align:start position:0% +chemical equilibrium if Q is less than K +well then up here in + + align:start position:0% +well then up here in + + + align:start position:0% +well then up here in +this expression for Delta G we have the + + align:start position:0% +this expression for Delta G we have the + + + align:start position:0% +this expression for Delta G we have the +log of a number smaller than + + align:start position:0% +log of a number smaller than + + + align:start position:0% +log of a number smaller than +one the log of a number smaller than one + + align:start position:0% +one the log of a number smaller than one + + + align:start position:0% +one the log of a number smaller than one +is going to be negative so if Q is less + + align:start position:0% +is going to be negative so if Q is less + + + align:start position:0% +is going to be negative so if Q is less +than k then our Delta G is going to be + + align:start position:0% +than k then our Delta G is going to be + + + align:start position:0% +than k then our Delta G is going to be +negative if our Delta G and notice this + + align:start position:0% +negative if our Delta G and notice this + + + align:start position:0% +negative if our Delta G and notice this +is Delta G not Delta G KN if our Delta G + + align:start position:0% +is Delta G not Delta G KN if our Delta G + + + align:start position:0% +is Delta G not Delta G KN if our Delta G +is negative then the reaction is going + + align:start position:0% +is negative then the reaction is going + + + align:start position:0% +is negative then the reaction is going +to be spontaneous in that forward + + align:start position:0% + + + + align:start position:0% + +Direction on the other hand if we've got + + align:start position:0% +Direction on the other hand if we've got + + + align:start position:0% +Direction on the other hand if we've got +a situation + + align:start position:0% +a situation + + + align:start position:0% +a situation +where Q is greater than + + align:start position:0% +where Q is greater than + + + align:start position:0% +where Q is greater than +K that is where we have more + + align:start position:0% +K that is where we have more + + + align:start position:0% +K that is where we have more +products then what equilibrium says we + + align:start position:0% +products then what equilibrium says we + + + align:start position:0% +products then what equilibrium says we +should + + align:start position:0% +should + + + align:start position:0% +should +have well then in that case Q over K is + + align:start position:0% +have well then in that case Q over K is + + + align:start position:0% +have well then in that case Q over K is +going to be a number greater than one + + align:start position:0% +going to be a number greater than one + + + align:start position:0% +going to be a number greater than one +and the log of a number greater than one + + align:start position:0% +and the log of a number greater than one + + + align:start position:0% +and the log of a number greater than one +is always going to be positive and so + + align:start position:0% +is always going to be positive and so + + + align:start position:0% +is always going to be positive and so +our Delta G here our Delta G for the + + align:start position:0% +our Delta G here our Delta G for the + + + align:start position:0% +our Delta G here our Delta G for the +reaction as written + + align:start position:0% +reaction as written + + + align:start position:0% +reaction as written +that Delta G is going to be greater than + + align:start position:0% +that Delta G is going to be greater than + + + align:start position:0% +that Delta G is going to be greater than +zero and so the forward reaction is not + + align:start position:0% +zero and so the forward reaction is not + + + align:start position:0% +zero and so the forward reaction is not +spontaneous but the reverse reaction is + + align:start position:0% +spontaneous but the reverse reaction is + + + align:start position:0% +spontaneous but the reverse reaction is +spontaneous and what's going to happen + + align:start position:0% +spontaneous and what's going to happen + + + align:start position:0% +spontaneous and what's going to happen +is that the chemical reaction will + + align:start position:0% +is that the chemical reaction will + + + align:start position:0% +is that the chemical reaction will +proceed in the reverse Direction it will + + align:start position:0% +proceed in the reverse Direction it will + + + align:start position:0% +proceed in the reverse Direction it will +use up all of those extra products that + + align:start position:0% +use up all of those extra products that + + + align:start position:0% +use up all of those extra products that +we made for whatever or have for + + align:start position:0% +we made for whatever or have for + + + align:start position:0% +we made for whatever or have for +whatever reason to try to attain + + align:start position:0% +whatever reason to try to attain + + + align:start position:0% +whatever reason to try to attain +equilibrium here there's another way to + + align:start position:0% +equilibrium here there's another way to + + + align:start position:0% +equilibrium here there's another way to +look at + + align:start position:0% +look at + + + align:start position:0% +look at +it I'm going to plot + + align:start position:0% +it I'm going to plot + + + align:start position:0% +it I'm going to plot +here + + align:start position:0% +here + + + align:start position:0% +here +Q versus the time of a + + align:start position:0% +Q versus the time of a + + + align:start position:0% +Q versus the time of a +reaction and we know when Q is equal to + + align:start position:0% +reaction and we know when Q is equal to + + + align:start position:0% +reaction and we know when Q is equal to +K we're at chemical + + align:start position:0% +K we're at chemical + + + align:start position:0% +K we're at chemical +equilibrium so suppose we + + align:start position:0% +equilibrium so suppose we + + + align:start position:0% +equilibrium so suppose we +start in a condition sometime T equals z + + align:start position:0% +start in a condition sometime T equals z + + + align:start position:0% +start in a condition sometime T equals z +where Q is less than K all right if Q is + + align:start position:0% +where Q is less than K all right if Q is + + + align:start position:0% +where Q is less than K all right if Q is +less than + + align:start position:0% +less than + + + align:start position:0% +less than +K what that says is that we don't have + + align:start position:0% +K what that says is that we don't have + + + align:start position:0% +K what that says is that we don't have +enough products compared to what we need + + align:start position:0% +enough products compared to what we need + + + align:start position:0% +enough products compared to what we need +for chemical + + align:start position:0% +for chemical + + + align:start position:0% +for chemical +equilibrium so when Q is less than K the + + align:start position:0% +equilibrium so when Q is less than K the + + + align:start position:0% +equilibrium so when Q is less than K the +reaction is going to proceed in the + + align:start position:0% +reaction is going to proceed in the + + + align:start position:0% +reaction is going to proceed in the +forward Direction it is going to make + + align:start position:0% +forward Direction it is going to make + + + align:start position:0% +forward Direction it is going to make +the + + align:start position:0% +the + + + align:start position:0% +the +products so that we can attain + + align:start position:0% +products so that we can attain + + + align:start position:0% +products so that we can attain +equilibrium so we can make enough + + align:start position:0% +equilibrium so we can make enough + + + align:start position:0% +equilibrium so we can make enough +products so that we get Q is equal to K + + align:start position:0% +products so that we get Q is equal to K + + + align:start position:0% +products so that we get Q is equal to K +the reaction will proceed in the forward + + align:start position:0% +the reaction will proceed in the forward + + + align:start position:0% +the reaction will proceed in the forward +direction if however we start in a + + align:start position:0% +direction if however we start in a + + + align:start position:0% +direction if however we start in a +situation where Q is greater than + + align:start position:0% +situation where Q is greater than + + + align:start position:0% +situation where Q is greater than +K if Q is greater than K it means we've + + align:start position:0% +K if Q is greater than K it means we've + + + align:start position:0% +K if Q is greater than K it means we've +got too many products compared to what + + align:start position:0% +got too many products compared to what + + + align:start position:0% +got too many products compared to what +our chemical equilibrium says we should + + align:start position:0% +our chemical equilibrium says we should + + + align:start position:0% +our chemical equilibrium says we should +have and so what's going to happen is + + align:start position:0% +have and so what's going to happen is + + + align:start position:0% +have and so what's going to happen is +that the reverse reaction is is going to + + align:start position:0% +that the reverse reaction is is going to + + + align:start position:0% +that the reverse reaction is is going to +proceed it's going to use up those + + align:start position:0% +proceed it's going to use up those + + + align:start position:0% +proceed it's going to use up those +products and form more + + align:start position:0% +products and form more + + + align:start position:0% +products and form more +reactants so that it can attain the + + align:start position:0% +reactants so that it can attain the + + + align:start position:0% +reactants so that it can attain the +equilibrium value for the partial + + align:start position:0% +equilibrium value for the partial + + + align:start position:0% +equilibrium value for the partial +pressures of the products and the + + align:start position:0% +pressures of the products and the + + + align:start position:0% +pressures of the products and the +reactants + + align:start position:0% +reactants + + + align:start position:0% +reactants +okay so Q is going to be our measure of + + align:start position:0% +okay so Q is going to be our measure of + + + align:start position:0% +okay so Q is going to be our measure of +whether or not a reaction is at chemical + + align:start position:0% +whether or not a reaction is at chemical + + + align:start position:0% +whether or not a reaction is at chemical +equilibrium very + + align:start position:0% +equilibrium very + + + align:start position:0% +equilibrium very +important all right + + align:start position:0% +important all right + + + align:start position:0% +important all right +questions r r is the gas constant it is + + align:start position:0% +questions r r is the gas constant it is + + + align:start position:0% +questions r r is the gas constant it is +something that will be given to you you + + align:start position:0% +something that will be given to you you + + + align:start position:0% +something that will be given to you you +can look up other + + align:start position:0% + + + + align:start position:0% + +questions okay see you later this + + align:start position:0% + + + + align:start position:0% + +week \ No newline at end of file diff --git a/8FWfmvj3HYw.txt b/8FWfmvj3HYw.txt new file mode 100644 index 0000000000000000000000000000000000000000..f2c087a8b2a8a515d4aace1b994edeae42d3c6ca --- /dev/null +++ b/8FWfmvj3HYw.txt @@ -0,0 +1,585 @@ +PROFESSOR: Hi. + +Today I'd like to talk to you +about state machines. + +State machines are an incredibly +important concept, + +both in 6.01, and in the general +sense when you're + +going to be doing things like +control theory or artificial + +intelligence. + +Any further work you do in terms +of computability theory, + +state machines are +really important. + +So I'm going to review what +we've done so far and talk + +about why we now need state +machines to add additional + +complexity to the kinds of +models that we're going to + +build, and then talk a little +bit about how state machines + +are represented in different +domains, and then also talk + +about how we're going +to use state + +machines in the 6.01 software. + +First of all, let's review what +we've learned so far. + +We've talked, so far, about +functional, imperative and + +object-oriented programming +paradigms. + +In functional programming, +everything is a function. + +And in imperative programming, +we're allowed to use + +functions, but they're also +allowed to have side effects. + +And in object-oriented +programming, + +everything is an object. + +We can actually use the first +two to implement the last one, + +and use the first one plus +an idea of maintaining + +assignments to variables, +that sort of thing, to + +implement this one. + +So you can trace the progression +of different kinds + +of computer science language +along this paradigm. + +But the one thing that none of +these languages on their own + +allows us to do is keep a notion +of internal state. + +And what I mean by that is that +if we have a system that + +we want to model in terms of +the passage of time or keep + +track of the evolution of that +system or keep track of some + +of the data that has accumulated +over time in that + +system, then we certainly can't +do it with functional + +programming. + +Functional programming takes +one input, generates one + +output, and you could generate +a list of codes that took in + +every possible situation and +then generated the logical + +output, but that would +be a lot of code. + +Same thing for imperative and +object-oriented programming. + +They alone do not address +everything that we want to + +address, which is the ability to +look at everything that has + +happened as a consequence of the +passage of time and all of + +the data that we've looked at +as a consequence of the + +passage of time, synthesize it +in some way, and then generate + +whatever was supposed to come +out of that situation. + +That is the notion of +internal state. + +State machines have been +around for a while. + +You might see them refer to as +discrete finite automata. + +There are also such things as +continuous state machines, but + +we're not going to talk about +those in this course so much. + +So we're only talking about +discrete state machines. + +And when you see them referred +to as state machines or + +discrete finite automata in +literature, especially + +mathematics, you'll be looking +for this five set of things. + +One is a set of the possible +states you could be in, given + +a particular state machine. + +One is the set of inputs you +could possibly encounter while + +in that state machine. + +One is the set of outputs that +that state machine could + +possibly generate. + +One is a transition function +that looks at pairs of these + +values and tells you, based on +which state you're currently + +in, what state you will end up +in as a consequence of the + +current input, and then also +specify what the output will + +be as a consequence of +that transition. + +And finally, it'll tell you +where you start out. + +That's a lot to absorb. + +I'm going to show you a state +transition diagram, which many + +of you have probably seen +before, and map these values + +to this state transition diagram +in hopes of making + +this a little bit +more concrete. + +Hopefully at this point, all +of you who have interacted + +with an MBTA turnstile. + +This is a thing that opens and +closes, and you stick your + +RFID card on it, and then +Richard Stallman yells at you + +and possibly hands you more +Charlie tickets or + +something like that. + +It has four states. + +One of them is that this +turnstile could be closed, and + +it's waiting for people to +interact with it in some way. + +It could be open, and I +anthropomorphize the turnstile + +as being happy as a consequence +of you putting + +money in it. + +It could be open and quiet as a +consequence of usually some + +sort of other previous +interaction + +with another person. + +Or it could be open and angry +as a consequence of people + +interacting with it when +they should not. + +The vertices in this directed +graph are my set of states. + +So when you see something like +this, and you're asked to map + +it to the mathematical +construct, just grab the names + +and say this is my +set of states. + +Let's say I start +off in closed. + +And actually, it occurs to me +that the other thing that + +should be specified +is a start state. + +And it's not here. + +So let's say the turnstile +starts off as closed. + +Usually this is an arrow coming +out of nowhere that + +directs into one +of the states. + +Sometimes it will be explicitly +indicated by saying + +start state, but typically +you'll just see + +an arrow from nowhere. + +At this point, I don't have +any inputs or outputs. + +If I put money in the turnstile, +it constitutes + +input to my system. + +It's going to end up in my +set of inputs for math. + +My transition function looks at +the state I'm in and looks + +at the current input and +generates the output and the + +next state. + +So all of these arrows, in +addition to whatever + +information is contained in +the receiving vertex, + +specifies my transition +function. + +Any transition that's not +specified is not considered in + +the function. + +This was not part of our +original drawing. + +So if I was fed open angry, +there would be no way to get + +to open happy. + +Likewise, if I was in open angry +and fed money for this + +simple system, we're going to +say nothing would happen. + +I think at this point it's +become clear how to transform + +a state transition diagram +into the mathematical + +constructs. + +It's good to have the +mathematical constructs, + +because they end up being used +in software, which I'll talk + +about in a second. + +But the first thing I'm going to +do is just walk around the + +state transition diagram and +indicate what would be inputs, + +what would be outputs, +that sort of thing. + +So let's say I walk up to the +turnstile and somebody else + +interacts with the turnstile +by exiting. + +In this case, exit is the input, +none is the output, the + +turnstile doesn't make +any noise, and the + +turnstile is open. + +If at that point I interact +with the turnstile by + +entering, it's going to make +noise, which is the output. + +And then the new state is going +to be that the turnstile + +is open and angry. + +At that point, you and +I know that the + +turnstile is going to close. + +So this edge indicates that the +only available input at + +that point is to do nothing. + +Or independent of anything else, +it's going to squawk + +again and close. + +One more time, here +are the states. + +Inputs are the first +of these two pairs. + +Outputs, as a consequence of the +transition, is the second + +of these two pairs. + +And the transition function is +represented by the directed + +edge and the new state. + +Once you have all those sets +figured out, you can start + +talking about how to implement +state machines and software. + +We've actually abstracted +this away from you. + +You don't have to +deal with it. + +But as a consequence, you should +know how to interact + +with the 6.01 library. + +Let's look at an example of +the state machine class. + +I want to build an accumulator, +which at every + +time step we'll look at the +input, add it to every other + +example of input and output, and +output the new value and + +retain it as the new state. + +The first thing I need to do is +initialize the accumulator + +with a value. + +This is our start state, which +is the same as our start state + +from the MBTA turnstile, and +also the same as our start + +state from the mathematical +construct. + +I also want something called +getNext Values which is the + +functional equivalent +of the transitions. + +Here's our self again from +object oriented programming -- + +but we don't care about that. + +We're going to look at +the current state + +and the current input. + +Some getNext Values we'll do +some internal data munging, + +possibly multiplication by two +or comparing to the previous + +input and then having +some conditionals, + +that sort of thing. + +But there'll be some sort of +very simple function under + +getNext Values at least for +the first couple of weeks. + +And then we will return +the new state and + +the output into tuple. + +In this case, the new state +is going to be the linear + +combination of the current state +and the current input. + +And the output is going to be +the linear combination of the + +current state and the +current input. + +If I were to draw this +accumulator as a state + +transition diagram, +I would do this. + +My start state is the +initial value. + +If I pass in a new input-- + +we'll call it input 0 -- + +both my output and the new +state are going to be the + +linear combination of +these two values. + +If I made another transition, I +would take whatever my next + +input was and add it to the +current state value and return + +it out as the output, and +so on and so forth. + +I encourage you try this in +Python, or in IDLE and munge + +around with it and see what +you can get it to do. + +You might have to type add +lib6.01 in order to get the + +state machine class, or +initialize using lib6.01 in + +order to get the state +machine class. + +But otherwise, those should be +enough to get you started with + +an introduction to +state machines. + +If you're having trouble, I +highly recommend going through + +all the examples in +the readings. + +They're pretty comprehensive, +and it also includes the + +accumulator. + +That's all for now. + +Next time we'll talk about +linear time varying systems. \ No newline at end of file diff --git a/8bITVuu7-O8.txt b/8bITVuu7-O8.txt new file mode 100644 index 0000000000000000000000000000000000000000..3a880a023b71e59c837b066fed2dbc1b3e727484 --- /dev/null +++ b/8bITVuu7-O8.txt @@ -0,0 +1,259 @@ +align:start position:0% + +today + + align:start position:0% +today + + + align:start position:0% +today +we're going to sing the ingredients oh + + align:start position:0% + + + + align:start position:0% + +we have a new picture here gran is + + align:start position:0% +we have a new picture here gran is + + + align:start position:0% +we have a new picture here gran is +short and poetic for grande + + align:start position:0% + + + + align:start position:0% + +do you have a large kitchen here + + align:start position:0% +do you have a large kitchen here + + + align:start position:0% +do you have a large kitchen here +yeah + + align:start position:0% + + + + align:start position:0% + +so in the new big kitchen yeah + + align:start position:0% + + + + align:start position:0% + +so i can say + + align:start position:0% + + + + align:start position:0% + +it doesn't mean that i have a bag full + + align:start position:0% +it doesn't mean that i have a bag full + + + align:start position:0% +it doesn't mean that i have a bag full +of homework it means i have + + align:start position:0% +of homework it means i have + + + align:start position:0% +of homework it means i have +a lot of assignments + + align:start position:0% +a lot of assignments + + + align:start position:0% +a lot of assignments +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +and then well here we will have to + + align:start position:0% +and then well here we will have to + + + align:start position:0% +and then well here we will have to +decide we have a lot of ingredients and + + align:start position:0% +decide we have a lot of ingredients and + + + align:start position:0% +decide we have a lot of ingredients and +kitchen tools + + align:start position:0% +kitchen tools + + + align:start position:0% +kitchen tools +and you will have to decide whether you + + align:start position:0% +and you will have to decide whether you + + + align:start position:0% +and you will have to decide whether you +need to use chai which means there is + + align:start position:0% + + + + align:start position:0% + +guava + + align:start position:0% + + + + align:start position:0% + +wow + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% + + + + align:start position:0% + +hello + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +okay repeat one two three + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% + + + + align:start position:0% + +although they're different so we can say + + align:start position:0% +although they're different so we can say + + + align:start position:0% +although they're different so we can say +chisono + + align:start position:0% + + + + align:start position:0% + +vestali + + align:start position:0% +vestali + + + align:start position:0% +vestali +messness mexico + + align:start position:0% + + + + align:start position:0% + +day \ No newline at end of file diff --git a/91uxbd_QmUI.txt b/91uxbd_QmUI.txt new file mode 100644 index 0000000000000000000000000000000000000000..8435d8e7eb21035a6f58859ea806f8ad4e018c4f --- /dev/null +++ b/91uxbd_QmUI.txt @@ -0,0 +1,15035 @@ +align:start position:0% + +so connecting it to the course so far + + align:start position:0% +so connecting it to the course so far + + + align:start position:0% +so connecting it to the course so far +we've been talking a lot about planet + + align:start position:0% +we've been talking a lot about planet + + + align:start position:0% +we've been talking a lot about planet +and environmental and reducing energy + + align:start position:0% +and environmental and reducing energy + + + align:start position:0% +and environmental and reducing energy +for the sake of saving the planet and + + align:start position:0% +for the sake of saving the planet and + + + align:start position:0% +for the sake of saving the planet and +what we are going to talk about today is + + align:start position:0% +what we are going to talk about today is + + + align:start position:0% +what we are going to talk about today is +not talking about outside the building + + align:start position:0% +not talking about outside the building + + + align:start position:0% +not talking about outside the building +but talking inside the building so how + + align:start position:0% +but talking inside the building so how + + + align:start position:0% +but talking inside the building so how +can we actually think about the + + align:start position:0% +can we actually think about the + + + align:start position:0% +can we actually think about the +strategies of investing in buildings + + align:start position:0% +strategies of investing in buildings + + + align:start position:0% +strategies of investing in buildings +that will improve + + align:start position:0% +that will improve + + + align:start position:0% +that will improve +the lives of people in the building like + + align:start position:0% +the lives of people in the building like + + + align:start position:0% +the lives of people in the building like +us and we will talk a little bit about + + align:start position:0% +us and we will talk a little bit about + + + align:start position:0% +us and we will talk a little bit about +this classroom we have a a sensor over + + align:start position:0% +this classroom we have a a sensor over + + + align:start position:0% +this classroom we have a a sensor over +there that is monitoring the air quality + + align:start position:0% +there that is monitoring the air quality + + + align:start position:0% +there that is monitoring the air quality +in this classroom so we will see how + + align:start position:0% +in this classroom so we will see how + + + align:start position:0% +in this classroom so we will see how +good the CR is with us uh in terms of + + align:start position:0% +good the CR is with us uh in terms of + + + align:start position:0% +good the CR is with us uh in terms of +the places that they put it um here is + + align:start position:0% +the places that they put it um here is + + + align:start position:0% +the places that they put it um here is +the some of the key uh formulas and key + + align:start position:0% +the some of the key uh formulas and key + + + align:start position:0% +the some of the key uh formulas and key +uh diagrams that CG always uses for for + + align:start position:0% +uh diagrams that CG always uses for for + + + align:start position:0% +uh diagrams that CG always uses for for +the lecture so here is one of the key + + align:start position:0% +the lecture so here is one of the key + + + align:start position:0% +the lecture so here is one of the key +things of the the business case for for + + align:start position:0% +things of the the business case for for + + + align:start position:0% +things of the the business case for for +green buildings is that the tenants are + + align:start position:0% +green buildings is that the tenants are + + + align:start position:0% +green buildings is that the tenants are +going to be better off in a in a green + + align:start position:0% +going to be better off in a in a green + + + align:start position:0% +going to be better off in a in a green +building than in a non- green building + + align:start position:0% +building than in a non- green building + + + align:start position:0% +building than in a non- green building +and mainly because of you have on the + + align:start position:0% +and mainly because of you have on the + + + align:start position:0% +and mainly because of you have on the +one side energy cost environmental + + align:start position:0% +one side energy cost environmental + + + align:start position:0% +one side energy cost environmental +damages but especially and I will show + + align:start position:0% +damages but especially and I will show + + + align:start position:0% +damages but especially and I will show +that this is the largest part of the buy + + align:start position:0% +that this is the largest part of the buy + + + align:start position:0% +that this is the largest part of the buy +because employees are going to be more + + align:start position:0% +because employees are going to be more + + + align:start position:0% +because employees are going to be more +productive healthier more comfortable + + align:start position:0% +productive healthier more comfortable + + + align:start position:0% +productive healthier more comfortable +and they're going to choose to be in + + align:start position:0% +and they're going to choose to be in + + + align:start position:0% +and they're going to choose to be in +those buildings and therefore their + + align:start position:0% +those buildings and therefore their + + + align:start position:0% +those buildings and therefore their +corporate tenants are going to make + + align:start position:0% +corporate tenants are going to make + + + align:start position:0% +corporate tenants are going to make +larger bits for those buildings that's + + align:start position:0% +larger bits for those buildings that's + + + align:start position:0% +larger bits for those buildings that's +sort of the theoretical link and then we + + align:start position:0% +sort of the theoretical link and then we + + + align:start position:0% +sort of the theoretical link and then we +are going to talk about whether that + + align:start position:0% +are going to talk about whether that + + + align:start position:0% +are going to talk about whether that +happens in the market or not and also + + align:start position:0% +happens in the market or not and also + + + align:start position:0% +happens in the market or not and also +not only today but also on Tuesday we + + align:start position:0% +not only today but also on Tuesday we + + + align:start position:0% +not only today but also on Tuesday we +see that is there talking on the corner + + align:start position:0% +see that is there talking on the corner + + + align:start position:0% +see that is there talking on the corner +is going to happen also we're going to + + align:start position:0% +is going to happen also we're going to + + + align:start position:0% +is going to happen also we're going to +analyze that decision in one specific + + align:start position:0% +analyze that decision in one specific + + + align:start position:0% +analyze that decision in one specific +building in New York and we are going to + + align:start position:0% +building in New York and we are going to + + + align:start position:0% +building in New York and we are going to +have a lot of discussions about under + + align:start position:0% +have a lot of discussions about under + + + align:start position:0% +have a lot of discussions about under +which conditions this will be holding + + align:start position:0% +which conditions this will be holding + + + align:start position:0% +which conditions this will be holding +and under which conditions this not will + + align:start position:0% +and under which conditions this not will + + + align:start position:0% +and under which conditions this not will +holding because we have here people from + + align:start position:0% +holding because we have here people from + + + align:start position:0% +holding because we have here people from +Latin America Europe us different parts + + align:start position:0% +Latin America Europe us different parts + + + align:start position:0% +Latin America Europe us different parts +of the United States Asia is not going + + align:start position:0% +of the United States Asia is not going + + + align:start position:0% +of the United States Asia is not going +to apply to every Market but the + + align:start position:0% +to apply to every Market but the + + + align:start position:0% +to apply to every Market but the +fundamentals are going to be there + + align:start position:0% +fundamentals are going to be there + + + align:start position:0% +fundamentals are going to be there +whether the market is going to + + align:start position:0% +whether the market is going to + + + align:start position:0% +whether the market is going to +appreciate it or not that's a different + + align:start position:0% +appreciate it or not that's a different + + + align:start position:0% +appreciate it or not that's a different +story but the core technology is going + + align:start position:0% +story but the core technology is going + + + align:start position:0% +story but the core technology is going +to work in the same way the core idea of + + align:start position:0% +to work in the same way the core idea of + + + align:start position:0% +to work in the same way the core idea of +the engineers behind the design of those + + align:start position:0% +the engineers behind the design of those + + + align:start position:0% +the engineers behind the design of those +building is going to be very similar + + align:start position:0% +building is going to be very similar + + + align:start position:0% +building is going to be very similar +into why they are going to promote air + + align:start position:0% +into why they are going to promote air + + + align:start position:0% +into why they are going to promote air +quality in the building why are they + + align:start position:0% +quality in the building why are they + + + align:start position:0% +quality in the building why are they +going to upgrade the uh the hbac system + + align:start position:0% +going to upgrade the uh the hbac system + + + align:start position:0% +going to upgrade the uh the hbac system +in a building and so forth so the the + + align:start position:0% +in a building and so forth so the the + + + align:start position:0% +in a building and so forth so the the +fundamentals are there and now the key + + align:start position:0% +fundamentals are there and now the key + + + align:start position:0% +fundamentals are there and now the key +question afterwards and we are going to + + align:start position:0% +question afterwards and we are going to + + + align:start position:0% +question afterwards and we are going to +discuss a little bit later is whether + + align:start position:0% +discuss a little bit later is whether + + + align:start position:0% +discuss a little bit later is whether +the market is going to be ready or not + + align:start position:0% +the market is going to be ready or not + + + align:start position:0% +the market is going to be ready or not +okay but today we are going to learn + + align:start position:0% +okay but today we are going to learn + + + align:start position:0% +okay but today we are going to learn +about the fundamentals so forth why is + + align:start position:0% +about the fundamentals so forth why is + + + align:start position:0% +about the fundamentals so forth why is +also important for the general + + align:start position:0% +also important for the general + + + align:start position:0% +also important for the general +sustainability in the real estate uh + + align:start position:0% +sustainability in the real estate uh + + + align:start position:0% +sustainability in the real estate uh +sector is that if you see the evolution + + align:start position:0% +sector is that if you see the evolution + + + align:start position:0% +sector is that if you see the evolution +of the certificates are going is that at + + align:start position:0% +of the certificates are going is that at + + + align:start position:0% +of the certificates are going is that at +the beginning they were mainly mainly + + align:start position:0% +the beginning they were mainly mainly + + + align:start position:0% +the beginning they were mainly mainly +focusing on uh um on saving energy + + align:start position:0% +focusing on uh um on saving energy + + + align:start position:0% +focusing on uh um on saving energy +reducing emissions and so forth actually + + align:start position:0% +reducing emissions and so forth actually + + + align:start position:0% +reducing emissions and so forth actually +at the very beginning only saving energy + + align:start position:0% +at the very beginning only saving energy + + + align:start position:0% +at the very beginning only saving energy +because there was not even the Kyoto + + align:start position:0% +because there was not even the Kyoto + + + align:start position:0% +because there was not even the Kyoto +Protocol back then but really saving + + align:start position:0% +Protocol back then but really saving + + + align:start position:0% +Protocol back then but really saving +energy reducing the energy cost it was + + align:start position:0% +energy reducing the energy cost it was + + + align:start position:0% +energy reducing the energy cost it was +the beginning of the energy crisis in + + align:start position:0% +the beginning of the energy crisis in + + + align:start position:0% +the beginning of the energy crisis in +the 1970s and 80s in the United States + + align:start position:0% +the 1970s and 80s in the United States + + + align:start position:0% +the 1970s and 80s in the United States +and Europe and so forth so that was the + + align:start position:0% +and Europe and so forth so that was the + + + align:start position:0% +and Europe and so forth so that was the +focus of of uh Green Building + + align:start position:0% +focus of of uh Green Building + + + align:start position:0% +focus of of uh Green Building +certification as we move towards uh H + + align:start position:0% +certification as we move towards uh H + + + align:start position:0% +certification as we move towards uh H +the present you see that Health starts + + align:start position:0% +the present you see that Health starts + + + align:start position:0% +the present you see that Health starts +to appear more and more and you see that + + align:start position:0% +to appear more and more and you see that + + + align:start position:0% +to appear more and more and you see that +it takes more a larger role in The Green + + align:start position:0% +it takes more a larger role in The Green + + + align:start position:0% +it takes more a larger role in The Green +Building certification and you even have + + align:start position:0% +Building certification and you even have + + + align:start position:0% +Building certification and you even have +since five years ago certifications that + + align:start position:0% +since five years ago certifications that + + + align:start position:0% +since five years ago certifications that +are specifically focusing on health and + + align:start position:0% +are specifically focusing on health and + + + align:start position:0% +are specifically focusing on health and +well-being in the building so you see + + align:start position:0% +well-being in the building so you see + + + align:start position:0% +well-being in the building so you see +that in the in the Green Building market + + align:start position:0% +that in the in the Green Building market + + + align:start position:0% +that in the in the Green Building market +and the Green Building sector the role + + align:start position:0% +and the Green Building sector the role + + + align:start position:0% +and the Green Building sector the role +of health is going up more and more + + align:start position:0% +of health is going up more and more + + + align:start position:0% +of health is going up more and more +especially since the covid-19 David tell + + align:start position:0% +especially since the covid-19 David tell + + + align:start position:0% +especially since the covid-19 David tell +me um just a question I guess sure are + + align:start position:0% +me um just a question I guess sure are + + + align:start position:0% +me um just a question I guess sure are +there studies like longitudinal or like + + align:start position:0% +there studies like longitudinal or like + + + align:start position:0% +there studies like longitudinal or like +discontinuity studies done on like + + align:start position:0% +discontinuity studies done on like + + + align:start position:0% +discontinuity studies done on like +whether people are do take less sick + + align:start position:0% +whether people are do take less sick + + + align:start position:0% +whether people are do take less sick +days yeah we'll we'll we'll show you + + align:start position:0% +days yeah we'll we'll we'll show you + + + align:start position:0% +days yeah we'll we'll we'll show you +later actually I did one I'm very proud + + align:start position:0% +later actually I did one I'm very proud + + + align:start position:0% +later actually I did one I'm very proud +of it + + align:start position:0% +of it + + + align:start position:0% +of it +UHD disertation and and the work of a + + align:start position:0% +UHD disertation and and the work of a + + + align:start position:0% +UHD disertation and and the work of a +lot of people so there is a actually you + + align:start position:0% +lot of people so there is a actually you + + + align:start position:0% +lot of people so there is a actually you +are in a very good City uh for health + + align:start position:0% +are in a very good City uh for health + + + align:start position:0% +are in a very good City uh for health +and wellbe in the build environment so + + align:start position:0% +and wellbe in the build environment so + + + align:start position:0% +and wellbe in the build environment so +you have me that's great uh but beyond + + align:start position:0% +you have me that's great uh but beyond + + + align:start position:0% +you have me that's great uh but beyond +me you have the Harvard School of Public + + align:start position:0% +me you have the Harvard School of Public + + + align:start position:0% +me you have the Harvard School of Public +Health you have Joe Allen and the + + align:start position:0% +Health you have Joe Allen and the + + + align:start position:0% +Health you have Joe Allen and the +in HBS you also have John mccomber they + + align:start position:0% +in HBS you also have John mccomber they + + + align:start position:0% +in HBS you also have John mccomber they +both wrote the book on healthy buildings + + align:start position:0% +both wrote the book on healthy buildings + + + align:start position:0% +both wrote the book on healthy buildings +they are very uh big into understanding + + align:start position:0% +they are very uh big into understanding + + + align:start position:0% +they are very uh big into understanding +what is the business case and what are + + align:start position:0% +what is the business case and what are + + + align:start position:0% +what is the business case and what are +the effects of buildings on human health + + align:start position:0% +the effects of buildings on human health + + + align:start position:0% +the effects of buildings on human health +it's quite a lot Ariel what are you + + align:start position:0% +it's quite a lot Ariel what are you + + + align:start position:0% +it's quite a lot Ariel what are you +talking about in the 1990s like to + + align:start position:0% +talking about in the 1990s like to + + + align:start position:0% +talking about in the 1990s like to +Sol uh yeah so that is something that + + align:start position:0% +Sol uh yeah so that is something that + + + align:start position:0% +Sol uh yeah so that is something that +was a rebound in the in the way that we + + align:start position:0% +was a rebound in the in the way that we + + + align:start position:0% +was a rebound in the in the way that we +understood sustainable buildings in a + + align:start position:0% +understood sustainable buildings in a + + + align:start position:0% +understood sustainable buildings in a +way well not actually it was I don't + + align:start position:0% +way well not actually it was I don't + + + align:start position:0% +way well not actually it was I don't +think that they were talking about + + align:start position:0% +think that they were talking about + + + align:start position:0% +think that they were talking about +sustainability but anyways in the 1970s + + align:start position:0% +sustainability but anyways in the 1970s + + + align:start position:0% +sustainability but anyways in the 1970s +and ' 80s H they were experiencing this + + align:start position:0% +and ' 80s H they were experiencing this + + + align:start position:0% +and ' 80s H they were experiencing this +very similar environment as what we are + + align:start position:0% +very similar environment as what we are + + + align:start position:0% +very similar environment as what we are +experiencing now with the energy prices + + align:start position:0% +experiencing now with the energy prices + + + align:start position:0% +experiencing now with the energy prices +very expensive because of uh + + align:start position:0% +very expensive because of uh + + + align:start position:0% +very expensive because of uh +International conflicts and so forth the + + align:start position:0% +International conflicts and so forth the + + + align:start position:0% +International conflicts and so forth the +price of oil went up by a lot and then + + align:start position:0% +price of oil went up by a lot and then + + + align:start position:0% +price of oil went up by a lot and then +out of the sudden you went from almost + + align:start position:0% +out of the sudden you went from almost + + + align:start position:0% +out of the sudden you went from almost +paying nothing for energy and wasting a + + align:start position:0% +paying nothing for energy and wasting a + + + align:start position:0% +paying nothing for energy and wasting a +lot of energy not only in cars but also + + align:start position:0% +lot of energy not only in cars but also + + + align:start position:0% +lot of energy not only in cars but also +in heating to being actually paying a + + align:start position:0% +in heating to being actually paying a + + + align:start position:0% +in heating to being actually paying a +painful price for every uh degree that + + align:start position:0% +painful price for every uh degree that + + + align:start position:0% +painful price for every uh degree that +you put up in the heating in the in the + + align:start position:0% +you put up in the heating in the in the + + + align:start position:0% +you put up in the heating in the in the +heating in the building so one of the + + align:start position:0% +heating in the building so one of the + + + align:start position:0% +heating in the building so one of the +things that the physicist and the + + align:start position:0% +things that the physicist and the + + + align:start position:0% +things that the physicist and the +engineers figure out is that hey you + + align:start position:0% +engineers figure out is that hey you + + + align:start position:0% +engineers figure out is that hey you +know what one of the most expensive + + align:start position:0% +know what one of the most expensive + + + align:start position:0% +know what one of the most expensive +things that you can that you need to do + + align:start position:0% +things that you can that you need to do + + + align:start position:0% +things that you can that you need to do +in a building is to bring fresh air from + + align:start position:0% +in a building is to bring fresh air from + + + align:start position:0% +in a building is to bring fresh air from +the outside because every time that you + + align:start position:0% +the outside because every time that you + + + align:start position:0% +the outside because every time that you +bring some fresh air from the outside + + align:start position:0% +bring some fresh air from the outside + + + align:start position:0% +bring some fresh air from the outside +you have to bring it to the temperature + + align:start position:0% +you have to bring it to the temperature + + + align:start position:0% +you have to bring it to the temperature +that people inside the building want to + + align:start position:0% +that people inside the building want to + + + align:start position:0% +that people inside the building want to +have uh that means bringing from uh 0 + + align:start position:0% +have uh that means bringing from uh 0 + + + align:start position:0% +have uh that means bringing from uh 0 +degrees Celsius to 20 or from 90 degrees + + align:start position:0% +degrees Celsius to 20 or from 90 degrees + + + align:start position:0% +degrees Celsius to 20 or from 90 degrees +uh Fahrenheit to uh 60 or 80s I don't + + align:start position:0% +uh Fahrenheit to uh 60 or 80s I don't + + + align:start position:0% +uh Fahrenheit to uh 60 or 80s I don't +know like a Fahrenheit is something that + + align:start position:0% +know like a Fahrenheit is something that + + + align:start position:0% +know like a Fahrenheit is something that +I still have to work on but let's say + + align:start position:0% +I still have to work on but let's say + + + align:start position:0% +I still have to work on but let's say +from the '90s to the 80s anyways that is + + align:start position:0% +from the '90s to the 80s anyways that is + + + align:start position:0% +from the '90s to the 80s anyways that is +one of the most expensive things that + + align:start position:0% +one of the most expensive things that + + + align:start position:0% +one of the most expensive things that +you need to do in a building so what do + + align:start position:0% +you need to do in a building so what do + + + align:start position:0% +you need to do in a building so what do +you do let's reduce the amount of air + + align:start position:0% +you do let's reduce the amount of air + + + align:start position:0% +you do let's reduce the amount of air +that you bring to the building that + + align:start position:0% +that you bring to the building that + + + align:start position:0% +that you bring to the building that +comes with reducing ventilation rates + + align:start position:0% +comes with reducing ventilation rates + + + align:start position:0% +comes with reducing ventilation rates +but it also comes with designing + + align:start position:0% +but it also comes with designing + + + align:start position:0% +but it also comes with designing +buildings that are practically bunkers + + align:start position:0% +buildings that are practically bunkers + + + align:start position:0% +buildings that are practically bunkers +where there is no filtration of air from + + align:start position:0% +where there is no filtration of air from + + + align:start position:0% +where there is no filtration of air from +the + + align:start position:0% +the + + + align:start position:0% +the +outside that is great for reducing + + align:start position:0% +outside that is great for reducing + + + align:start position:0% +outside that is great for reducing +energy consumption but it creates a lot + + align:start position:0% +energy consumption but it creates a lot + + + align:start position:0% +energy consumption but it creates a lot +of problems with air quality so that was + + align:start position:0% +of problems with air quality so that was + + + align:start position:0% +of problems with air quality so that was +when the term of sick building synr + + align:start position:0% +when the term of sick building synr + + + align:start position:0% +when the term of sick building synr +syndrome was coined where people will + + align:start position:0% +syndrome was coined where people will + + + align:start position:0% +syndrome was coined where people will +get into their offices and will get uh + + align:start position:0% +get into their offices and will get uh + + + align:start position:0% +get into their offices and will get uh +headaches and they will get a lot of + + align:start position:0% +headaches and they will get a lot of + + + align:start position:0% +headaches and they will get a lot of +problems that are just purely related to + + align:start position:0% +problems that are just purely related to + + + align:start position:0% +problems that are just purely related to +the place where they were + + align:start position:0% +the place where they were + + + align:start position:0% +the place where they were +working and not to say the risk of uh + + align:start position:0% +working and not to say the risk of uh + + + align:start position:0% +working and not to say the risk of uh +infectious diseases like covid and so + + align:start position:0% +infectious diseases like covid and so + + + align:start position:0% +infectious diseases like covid and so +forth where basically we are all sharing + + align:start position:0% +forth where basically we are all sharing + + + align:start position:0% +forth where basically we are all sharing +our air I'm throwing a lot of droplets + + align:start position:0% +our air I'm throwing a lot of droplets + + + align:start position:0% +our air I'm throwing a lot of droplets +of you on you guys so the only ones that + + align:start position:0% +of you on you guys so the only ones that + + + align:start position:0% +of you on you guys so the only ones that +are preventing you from breathing what I + + align:start position:0% +are preventing you from breathing what I + + + align:start position:0% +are preventing you from breathing what I +am excelling is are these guys there + + align:start position:0% +am excelling is are these guys there + + + align:start position:0% +am excelling is are these guys there +that are trying to sack there faster + + align:start position:0% +that are trying to sack there faster + + + align:start position:0% +that are trying to sack there faster +than you guys than your Banks can Brea + + align:start position:0% +than you guys than your Banks can Brea + + + align:start position:0% +than you guys than your Banks can Brea +in so all of these problems were + + align:start position:0% +in so all of these problems were + + + align:start position:0% +in so all of these problems were +happening in the 70s and the 80s there + + align:start position:0% +happening in the 70s and the 80s there + + + align:start position:0% +happening in the 70s and the 80s there +were a lot of problems in the office + + align:start position:0% +were a lot of problems in the office + + + align:start position:0% +were a lot of problems in the office +sector especially and that was something + + align:start position:0% +sector especially and that was something + + + align:start position:0% +sector especially and that was something +that we're trying to remediate + + align:start position:0% +that we're trying to remediate + + + align:start position:0% +that we're trying to remediate +afterwards all right and to understand + + align:start position:0% +afterwards all right and to understand + + + align:start position:0% +afterwards all right and to understand +the role of buildings you have to + + align:start position:0% +the role of buildings you have to + + + align:start position:0% +the role of buildings you have to +understand the role of environment on on + + align:start position:0% +understand the role of environment on on + + + align:start position:0% +understand the role of environment on on +our health we have people from all over + + align:start position:0% +our health we have people from all over + + + align:start position:0% +our health we have people from all over +the world I think that H things like we + + align:start position:0% +the world I think that H things like we + + + align:start position:0% +the world I think that H things like we +have a lot of environmental threats but + + align:start position:0% +have a lot of environmental threats but + + + align:start position:0% +have a lot of environmental threats but +I'm going to show you the two most + + align:start position:0% +I'm going to show you the two most + + + align:start position:0% +I'm going to show you the two most +prominent this is a satellite image of + + align:start position:0% +prominent this is a satellite image of + + + align:start position:0% +prominent this is a satellite image of +the level of air pollution all over the + + align:start position:0% +the level of air pollution all over the + + + align:start position:0% +the level of air pollution all over the +world you see that almost in any you can + + align:start position:0% +world you see that almost in any you can + + + align:start position:0% +world you see that almost in any you can +find your city here you can see that + + align:start position:0% +find your city here you can see that + + + align:start position:0% +find your city here you can see that +anywhere where there is a city almost + + align:start position:0% +anywhere where there is a city almost + + + align:start position:0% +anywhere where there is a city almost +there is a red spot that means that + + align:start position:0% +there is a red spot that means that + + + align:start position:0% +there is a red spot that means that +there is a high level of air pollution + + align:start position:0% +there is a high level of air pollution + + + align:start position:0% +there is a high level of air pollution +so it's almost like pollution is the + + align:start position:0% +so it's almost like pollution is the + + + align:start position:0% +so it's almost like pollution is the +shadow of of of humankind so because the + + align:start position:0% +shadow of of of humankind so because the + + + align:start position:0% +shadow of of of humankind so because the +way that we move we generate pollution + + align:start position:0% +way that we move we generate pollution + + + align:start position:0% +way that we move we generate pollution +the way that we hit our buildings we + + align:start position:0% +the way that we hit our buildings we + + + align:start position:0% +the way that we hit our buildings we +generate pollution so forth and and we + + align:start position:0% +generate pollution so forth and and we + + + align:start position:0% +generate pollution so forth and and we +are trying to remediate that but that is + + align:start position:0% +are trying to remediate that but that is + + + align:start position:0% +are trying to remediate that but that is +now the reality for all places in the + + align:start position:0% +now the reality for all places in the + + + align:start position:0% +now the reality for all places in the +world um so and and what you see is that + + align:start position:0% +world um so and and what you see is that + + + align:start position:0% +world um so and and what you see is that +W considers that as one of the largest + + align:start position:0% +W considers that as one of the largest + + + align:start position:0% +W considers that as one of the largest +threats actually uh as you put you see + + align:start position:0% +threats actually uh as you put you see + + + align:start position:0% +threats actually uh as you put you see +here 4.2 million ion premature deaths + + align:start position:0% +here 4.2 million ion premature deaths + + + align:start position:0% +here 4.2 million ion premature deaths +due to inhaling air pollution across the + + align:start position:0% +due to inhaling air pollution across the + + + align:start position:0% +due to inhaling air pollution across the +wall that comes because when you inhale + + align:start position:0% +wall that comes because when you inhale + + + align:start position:0% +wall that comes because when you inhale +uh these little particles that come out + + align:start position:0% +uh these little particles that come out + + + align:start position:0% +uh these little particles that come out +of the exhausts of buildings and power + + align:start position:0% +of the exhausts of buildings and power + + + align:start position:0% +of the exhausts of buildings and power +plants and so forth into your lung that + + align:start position:0% +plants and so forth into your lung that + + + align:start position:0% +plants and so forth into your lung that +damages your lungs that gets into your + + align:start position:0% +damages your lungs that gets into your + + + align:start position:0% +damages your lungs that gets into your +blood flow that also hurt your your uh + + align:start position:0% +blood flow that also hurt your your uh + + + align:start position:0% +blood flow that also hurt your your uh +cardiovascular system and ultimately and + + align:start position:0% +cardiovascular system and ultimately and + + + align:start position:0% +cardiovascular system and ultimately and +that's also something that uh we've been + + align:start position:0% +that's also something that uh we've been + + + align:start position:0% +that's also something that uh we've been +discovering for the last years and now + + align:start position:0% +discovering for the last years and now + + + align:start position:0% +discovering for the last years and now +is one of the most uh serious threats it + + align:start position:0% +is one of the most uh serious threats it + + + align:start position:0% +is one of the most uh serious threats it +gets into your brain and it affects your + + align:start position:0% +gets into your brain and it affects your + + + align:start position:0% +gets into your brain and it affects your +cognitive performance + + align:start position:0% +cognitive performance + + + align:start position:0% +cognitive performance +so all of those things are things that + + align:start position:0% +so all of those things are things that + + + align:start position:0% +so all of those things are things that +are out there and you guys have been + + align:start position:0% +are out there and you guys have been + + + align:start position:0% +are out there and you guys have been +breathing quite a bit of it already on + + align:start position:0% +breathing quite a bit of it already on + + + align:start position:0% +breathing quite a bit of it already on +the way home to here all right so that's + + align:start position:0% +the way home to here all right so that's + + + align:start position:0% +the way home to here all right so that's +one of the things that the building is + + align:start position:0% +one of the things that the building is + + + align:start position:0% +one of the things that the building is +trying to prevent and I will talk a + + align:start position:0% +trying to prevent and I will talk a + + + align:start position:0% +trying to prevent and I will talk a +little bit about it because the the air + + align:start position:0% +little bit about it because the the air + + + align:start position:0% +little bit about it because the the air +that we are breathing here is being + + align:start position:0% +that we are breathing here is being + + + align:start position:0% +that we are breathing here is being +brought up by These Guys these systems + + align:start position:0% +brought up by These Guys these systems + + + align:start position:0% +brought up by These Guys these systems +so it's not we are not breathing through + + align:start position:0% +so it's not we are not breathing through + + + align:start position:0% +so it's not we are not breathing through +a window or anything so this building is + + align:start position:0% +a window or anything so this building is + + + align:start position:0% +a window or anything so this building is +between us and those red things that you + + align:start position:0% +between us and those red things that you + + + align:start position:0% +between us and those red things that you +see there is between us and those cars + + align:start position:0% +see there is between us and those cars + + + align:start position:0% +see there is between us and those cars +that are polluting and so forth so all + + align:start position:0% +that are polluting and so forth so all + + + align:start position:0% +that are polluting and so forth so all +the time that we are spending here is + + align:start position:0% +the time that we are spending here is + + + align:start position:0% +the time that we are spending here is +actually a time that the building can + + align:start position:0% +actually a time that the building can + + + align:start position:0% +actually a time that the building can +reduce our exposure to those things and + + align:start position:0% +reduce our exposure to those things and + + + align:start position:0% +reduce our exposure to those things and +make us breathing healthier air that we + + align:start position:0% +make us breathing healthier air that we + + + align:start position:0% +make us breathing healthier air that we +will have outdoor in the at the door of + + align:start position:0% +will have outdoor in the at the door of + + + align:start position:0% +will have outdoor in the at the door of +the SI so the question there will be + + align:start position:0% +the SI so the question there will be + + + align:start position:0% +the SI so the question there will be +some of the strategies that we can do to + + align:start position:0% +some of the strategies that we can do to + + + align:start position:0% +some of the strategies that we can do to +make that air as healthier as possible + + align:start position:0% +make that air as healthier as possible + + + align:start position:0% +make that air as healthier as possible +that will come with investments in the + + align:start position:0% +that will come with investments in the + + + align:start position:0% +that will come with investments in the +HB system and so forth this is one of + + align:start position:0% +HB system and so forth this is one of + + + align:start position:0% +HB system and so forth this is one of +the key things especially in areas like + + align:start position:0% +the key things especially in areas like + + + align:start position:0% +the key things especially in areas like +California where you have got wildfires + + align:start position:0% +California where you have got wildfires + + + align:start position:0% +California where you have got wildfires +but also Beijing Delhi and so forth + + align:start position:0% +but also Beijing Delhi and so forth + + + align:start position:0% +but also Beijing Delhi and so forth +where there's a lot of focus on how do + + align:start position:0% +where there's a lot of focus on how do + + + align:start position:0% +where there's a lot of focus on how do +do you filter the air in a way that you + + align:start position:0% +do you filter the air in a way that you + + + align:start position:0% +do you filter the air in a way that you +reduce as much as possible the level of + + align:start position:0% +reduce as much as possible the level of + + + align:start position:0% +reduce as much as possible the level of +particles that people will breathe in so + + align:start position:0% +particles that people will breathe in so + + + align:start position:0% +particles that people will breathe in so +that's one the second one is temperature + + align:start position:0% +that's one the second one is temperature + + + align:start position:0% +that's one the second one is temperature +we are talking a lot about not throwing + + align:start position:0% +we are talking a lot about not throwing + + + align:start position:0% +we are talking a lot about not throwing +CO2 to the atmosphere but we know that + + align:start position:0% +CO2 to the atmosphere but we know that + + + align:start position:0% +CO2 to the atmosphere but we know that +if you throw CO2 to the atmosphere the + + align:start position:0% +if you throw CO2 to the atmosphere the + + + align:start position:0% +if you throw CO2 to the atmosphere the +the whole planet will warm up and the + + align:start position:0% +the whole planet will warm up and the + + + align:start position:0% +the whole planet will warm up and the +the amount of heat waves and so forth + + align:start position:0% +the amount of heat waves and so forth + + + align:start position:0% +the amount of heat waves and so forth +will increase uh there are a lot of + + align:start position:0% +will increase uh there are a lot of + + + align:start position:0% +will increase uh there are a lot of +studies too to show that the effect of + + align:start position:0% +studies too to show that the effect of + + + align:start position:0% +studies too to show that the effect of +heat on uh on human health and cold on + + align:start position:0% +heat on uh on human health and cold on + + + align:start position:0% +heat on uh on human health and cold on +human health and there is around 5 + + align:start position:0% +human health and there is around 5 + + + align:start position:0% +human health and there is around 5 +million premature death every year due + + align:start position:0% +million premature death every year due + + + align:start position:0% +million premature death every year due +to being exposed to extremely cold + + align:start position:0% +to being exposed to extremely cold + + + align:start position:0% +to being exposed to extremely cold +extremely warm weather so again one of + + align:start position:0% +extremely warm weather so again one of + + + align:start position:0% +extremely warm weather so again one of +the things that our weather our building + + align:start position:0% +the things that our weather our building + + + align:start position:0% +the things that our weather our building +is doing is that we are not exposed to + + align:start position:0% +is doing is that we are not exposed to + + + align:start position:0% +is doing is that we are not exposed to +the cold weather outdoor in uh in the + + align:start position:0% +the cold weather outdoor in uh in the + + + align:start position:0% +the cold weather outdoor in uh in the +Boston in the city of Boston today and + + align:start position:0% +Boston in the city of Boston today and + + + align:start position:0% +Boston in the city of Boston today and +being freezing there being sitting down + + align:start position:0% +being freezing there being sitting down + + + align:start position:0% +being freezing there being sitting down +but actually we are in a very + + align:start position:0% +but actually we are in a very + + + align:start position:0% +but actually we are in a very +comfortable rather even warm uh room + + align:start position:0% +comfortable rather even warm uh room + + + align:start position:0% +comfortable rather even warm uh room +here uh that is trying to make our + + align:start position:0% +here uh that is trying to make our + + + align:start position:0% +here uh that is trying to make our +temperature exposure better than it is + + align:start position:0% +temperature exposure better than it is + + + align:start position:0% +temperature exposure better than it is +out there so buildings the way that we + + align:start position:0% +out there so buildings the way that we + + + align:start position:0% +out there so buildings the way that we +are conceptualizing in this uh and there + + align:start position:0% +are conceptualizing in this uh and there + + + align:start position:0% +are conceptualizing in this uh and there +are way more things that we can think + + align:start position:0% +are way more things that we can think + + + align:start position:0% +are way more things that we can think +about it but today what we are going to + + align:start position:0% +about it but today what we are going to + + + align:start position:0% +about it but today what we are going to +conceptualize is buildings that are + + align:start position:0% +conceptualize is buildings that are + + + align:start position:0% +conceptualize is buildings that are +going to generate an environment that is + + align:start position:0% +going to generate an environment that is + + + align:start position:0% +going to generate an environment that is +better than out there that's how we are + + align:start position:0% +better than out there that's how we are + + + align:start position:0% +better than out there that's how we are +going to think so we are not thinking of + + align:start position:0% +going to think so we are not thinking of + + + align:start position:0% +going to think so we are not thinking of +building generating Problems by + + align:start position:0% +building generating Problems by + + + align:start position:0% +building generating Problems by +themselves that there is also some + + align:start position:0% +themselves that there is also some + + + align:start position:0% +themselves that there is also some +things related to materials and so forth + + align:start position:0% +things related to materials and so forth + + + align:start position:0% +things related to materials and so forth +but mainly the way that a lot of people + + align:start position:0% +but mainly the way that a lot of people + + + align:start position:0% +but mainly the way that a lot of people +are conceptualizing healthy buildings + + align:start position:0% +are conceptualizing healthy buildings + + + align:start position:0% +are conceptualizing healthy buildings +are buildings that are creating a better + + align:start position:0% +are buildings that are creating a better + + + align:start position:0% +are buildings that are creating a better +environment and it can also be creating + + align:start position:0% +environment and it can also be creating + + + align:start position:0% +environment and it can also be creating +a better physical environment so they + + align:start position:0% +a better physical environment so they + + + align:start position:0% +a better physical environment so they +will make you move more that you will be + + align:start position:0% +will make you move more that you will be + + + align:start position:0% +will make you move more that you will be +moving out there with different + + align:start position:0% +moving out there with different + + + align:start position:0% +moving out there with different +staircases and so forth but basically + + align:start position:0% +staircases and so forth but basically + + + align:start position:0% +staircases and so forth but basically +buildings are trying to make better off + + align:start position:0% +buildings are trying to make better off + + + align:start position:0% +buildings are trying to make better off +than out there that's the definition of + + align:start position:0% +than out there that's the definition of + + + align:start position:0% +than out there that's the definition of +a healthy building very lemon terms + + align:start position:0% +a healthy building very lemon terms + + + align:start position:0% +a healthy building very lemon terms +okay and this is important because if + + align:start position:0% +okay and this is important because if + + + align:start position:0% +okay and this is important because if +you think about your daily life and this + + align:start position:0% +you think about your daily life and this + + + align:start position:0% +you think about your daily life and this +is the the is an old survey but it's + + align:start position:0% +is the the is an old survey but it's + + + align:start position:0% +is the the is an old survey but it's +still like the survey that everyone + + align:start position:0% +still like the survey that everyone + + + align:start position:0% +still like the survey that everyone +quotes we spend 90% of the time indoors + + align:start position:0% +quotes we spend 90% of the time indoors + + + align:start position:0% +quotes we spend 90% of the time indoors +this is something that they did the + + align:start position:0% +this is something that they did the + + + align:start position:0% +this is something that they did the +surveys about across the the United + + align:start position:0% +surveys about across the the United + + + align:start position:0% +surveys about across the the United +States H to show how many people will + + align:start position:0% +States H to show how many people will + + + align:start position:0% +States H to show how many people will +where will people spend time in and you + + align:start position:0% +where will people spend time in and you + + + align:start position:0% +where will people spend time in and you +see that if you sum all the indoor + + align:start position:0% +see that if you sum all the indoor + + + align:start position:0% +see that if you sum all the indoor +places in their in their home their + + align:start position:0% +places in their in their home their + + + align:start position:0% +places in their in their home their +Factory or a bar or restaurant uh most + + align:start position:0% +Factory or a bar or restaurant uh most + + + align:start position:0% +Factory or a bar or restaurant uh most +of it happens to be indoors and in a + + align:start position:0% +of it happens to be indoors and in a + + + align:start position:0% +of it happens to be indoors and in a +building actually except for the for the + + align:start position:0% +building actually except for the for the + + + align:start position:0% +building actually except for the for the +vehicle part so 90% of our time our air + + align:start position:0% +vehicle part so 90% of our time our air + + + align:start position:0% +vehicle part so 90% of our time our air +our temperature our movements our light + + align:start position:0% +our temperature our movements our light + + + align:start position:0% +our temperature our movements our light +is shaped by a building giving the + + align:start position:0% +is shaped by a building giving the + + + align:start position:0% +is shaped by a building giving the +building a very big role in our lives + + align:start position:0% +building a very big role in our lives + + + align:start position:0% +building a very big role in our lives +and therefore giving the building a very + + align:start position:0% +and therefore giving the building a very + + + align:start position:0% +and therefore giving the building a very +big exante power to shape our health + + align:start position:0% +big exante power to shape our health + + + align:start position:0% +big exante power to shape our health +shape our well-being and so + + align:start position:0% +shape our well-being and so + + + align:start position:0% +shape our well-being and so +forth and indoors is not always so great + + align:start position:0% +forth and indoors is not always so great + + + align:start position:0% +forth and indoors is not always so great +not not in Europe not in the US so you + + align:start position:0% +not not in Europe not in the US so you + + + align:start position:0% +not not in Europe not in the US so you +see around 5% of people in the United + + align:start position:0% +see around 5% of people in the United + + + align:start position:0% +see around 5% of people in the United +States live on average in a in a house + + align:start position:0% +States live on average in a in a house + + + align:start position:0% +States live on average in a in a house +that needs uh certain work uh that can + + align:start position:0% +that needs uh certain work uh that can + + + align:start position:0% +that needs uh certain work uh that can +be moderate it can be severe but 5% of + + align:start position:0% +be moderate it can be severe but 5% of + + + align:start position:0% +be moderate it can be severe but 5% of +people that need to live in a place + + align:start position:0% +people that need to live in a place + + + align:start position:0% +people that need to live in a place +better than they are doing now if you go + + align:start position:0% +better than they are doing now if you go + + + align:start position:0% +better than they are doing now if you go +to the renters this will be doubl so one + + align:start position:0% +to the renters this will be doubl so one + + + align:start position:0% +to the renters this will be doubl so one +out of 10 renters will actually be + + align:start position:0% +out of 10 renters will actually be + + + align:start position:0% +out of 10 renters will actually be +living in a place that needs some work + + align:start position:0% +living in a place that needs some work + + + align:start position:0% +living in a place that needs some work +uh if you go to the low income renters + + align:start position:0% +uh if you go to the low income renters + + + align:start position:0% +uh if you go to the low income renters +that will be way more more so it will be + + align:start position:0% +that will be way more more so it will be + + + align:start position:0% +that will be way more more so it will be +15% of the population will be there so + + align:start position:0% +15% of the population will be there so + + + align:start position:0% +15% of the population will be there so +if you especially dig into the + + align:start position:0% +if you especially dig into the + + + align:start position:0% +if you especially dig into the +subpopulations that will need more + + align:start position:0% +subpopulations that will need more + + + align:start position:0% +subpopulations that will need more +support and actually the ones that are + + align:start position:0% +support and actually the ones that are + + + align:start position:0% +support and actually the ones that are +probably suffering for the ER with the + + align:start position:0% +probably suffering for the ER with the + + + align:start position:0% +probably suffering for the ER with the +most severe health problems then this is + + align:start position:0% +most severe health problems then this is + + + align:start position:0% +most severe health problems then this is +actually worse than than the graph that + + align:start position:0% +actually worse than than the graph that + + + align:start position:0% +actually worse than than the graph that +you see for the entire population and + + align:start position:0% +you see for the entire population and + + + align:start position:0% +you see for the entire population and +the same for for Europe but we are going + + align:start position:0% +the same for for Europe but we are going + + + align:start position:0% +the same for for Europe but we are going +to talk about not uh not so much about + + align:start position:0% +to talk about not uh not so much about + + + align:start position:0% +to talk about not uh not so much about +the people that are uh about the + + align:start position:0% +the people that are uh about the + + + align:start position:0% +the people that are uh about the +buildings that make an six but we are + + align:start position:0% +buildings that make an six but we are + + + align:start position:0% +buildings that make an six but we are +going to talk about investment + + align:start position:0% +going to talk about investment + + + align:start position:0% +going to talk about investment +strategies that will actually try to + + align:start position:0% +strategies that will actually try to + + + align:start position:0% +strategies that will actually try to +promote health and make us healthier in + + align:start position:0% +promote health and make us healthier in + + + align:start position:0% +promote health and make us healthier in +a way all right so this is whole the + + align:start position:0% +a way all right so this is whole the + + + align:start position:0% +a way all right so this is whole the +whole lecture today how can we invest in + + align:start position:0% +whole lecture today how can we invest in + + + align:start position:0% +whole lecture today how can we invest in +a building to make it to make us + + align:start position:0% +a building to make it to make us + + + align:start position:0% +a building to make it to make us +healthier how can we actually think + + align:start position:0% +healthier how can we actually think + + + align:start position:0% +healthier how can we actually think +about the health implications of + + align:start position:0% +about the health implications of + + + align:start position:0% +about the health implications of +investing investing in any of those + + align:start position:0% +investing investing in any of those + + + align:start position:0% +investing investing in any of those +Technologies and this is important for + + align:start position:0% +Technologies and this is important for + + + align:start position:0% +Technologies and this is important for +both I know that the before the uh there + + align:start position:0% +both I know that the before the uh there + + + align:start position:0% +both I know that the before the uh there +was not a lot of reactions from the + + align:start position:0% +was not a lot of reactions from the + + + align:start position:0% +was not a lot of reactions from the +public sector but if you really look at + + align:start position:0% +public sector but if you really look at + + + align:start position:0% +public sector but if you really look at +the the amount of money that governments + + align:start position:0% +the the amount of money that governments + + + align:start position:0% +the the amount of money that governments +spend in health is around in a normal + + align:start position:0% +spend in health is around in a normal + + + align:start position:0% +spend in health is around in a normal +year for a lot of countries almost one + + align:start position:0% +year for a lot of countries almost one + + + align:start position:0% +year for a lot of countries almost one +out of uh 10 uh dollars that we generate + + align:start position:0% +out of uh 10 uh dollars that we generate + + + align:start position:0% +out of uh 10 uh dollars that we generate +goes to to pay in healthcare and to make + + align:start position:0% +goes to to pay in healthcare and to make + + + align:start position:0% +goes to to pay in healthcare and to make +us uh avoid from dying or or make us + + align:start position:0% +us uh avoid from dying or or make us + + + align:start position:0% +us uh avoid from dying or or make us +less sick than than we are basically a + + align:start position:0% +less sick than than we are basically a + + + align:start position:0% +less sick than than we are basically a +one out of 10 and if you see the what + + align:start position:0% +one out of 10 and if you see the what + + + align:start position:0% +one out of 10 and if you see the what +happened after covid you see that in + + align:start position:0% +happened after covid you see that in + + + align:start position:0% +happened after covid you see that in +places like the United States things get + + align:start position:0% +places like the United States things get + + + align:start position:0% +places like the United States things get +rock so it's a substantial amount of all + + align:start position:0% +rock so it's a substantial amount of all + + + align:start position:0% +rock so it's a substantial amount of all +the money that we generate in a country + + align:start position:0% +the money that we generate in a country + + + align:start position:0% +the money that we generate in a country +going to healthare and also from the um + + align:start position:0% +going to healthare and also from the um + + + align:start position:0% +going to healthare and also from the um +there are a lot of estimates of cost of + + align:start position:0% +there are a lot of estimates of cost of + + + align:start position:0% +there are a lot of estimates of cost of +unhealthy + + align:start position:0% +unhealthy + + + align:start position:0% +unhealthy +workers for for aiv sector this is one + + align:start position:0% +workers for for aiv sector this is one + + + align:start position:0% +workers for for aiv sector this is one +of the most famous articles from The + + align:start position:0% +of the most famous articles from The + + + align:start position:0% +of the most famous articles from The +harbard Business Review that estimate + + align:start position:0% +harbard Business Review that estimate + + + align:start position:0% +harbard Business Review that estimate +that + + align:start position:0% +that + + + align:start position:0% +that +one50 billion dollar per year in in the + + align:start position:0% +one50 billion dollar per year in in the + + + align:start position:0% +one50 billion dollar per year in in the +US sector office sector goes to pay ER + + align:start position:0% +US sector office sector goes to pay ER + + + align:start position:0% +US sector office sector goes to pay ER +workers that are not fully fit so they + + align:start position:0% +workers that are not fully fit so they + + + align:start position:0% +workers that are not fully fit so they +are going there with burnout problems + + align:start position:0% +are going there with burnout problems + + + align:start position:0% +are going there with burnout problems +they are going there with some physical + + align:start position:0% +they are going there with some physical + + + align:start position:0% +they are going there with some physical +problems and so forth they still earn + + align:start position:0% +problems and so forth they still earn + + + align:start position:0% +problems and so forth they still earn +the full salary because they show up in + + align:start position:0% +the full salary because they show up in + + + align:start position:0% +the full salary because they show up in +the office but they are not uh + + align:start position:0% +the office but they are not uh + + + align:start position:0% +the office but they are not uh +performing at it best and that goes back + + align:start position:0% +performing at it best and that goes back + + + align:start position:0% +performing at it best and that goes back +to things like the sick building + + align:start position:0% +to things like the sick building + + + align:start position:0% +to things like the sick building +syndrome where you know you make someone + + align:start position:0% +syndrome where you know you make someone + + + align:start position:0% +syndrome where you know you make someone +work in a place that make them miserable + + align:start position:0% +work in a place that make them miserable + + + align:start position:0% +work in a place that make them miserable +and then they therefore cannot exert the + + align:start position:0% +and then they therefore cannot exert the + + + align:start position:0% +and then they therefore cannot exert the +full potential and I will also show you + + align:start position:0% +full potential and I will also show you + + + align:start position:0% +full potential and I will also show you +that you know there are some things that + + align:start position:0% +that you know there are some things that + + + align:start position:0% +that you know there are some things that +you can think about compensating right + + align:start position:0% +you can think about compensating right + + + align:start position:0% +you can think about compensating right +like kind of oh I have low concentration + + align:start position:0% +like kind of oh I have low concentration + + + align:start position:0% +like kind of oh I have low concentration +but I stay extra hours so you know I + + align:start position:0% +but I stay extra hours so you know I + + + align:start position:0% +but I stay extra hours so you know I +bear the cost as an employee I I get + + align:start position:0% +bear the cost as an employee I I get + + + align:start position:0% +bear the cost as an employee I I get +some extra coffee and you know I still + + align:start position:0% +some extra coffee and you know I still + + + align:start position:0% +some extra coffee and you know I still +even if I feel a little bit DIY or + + align:start position:0% +even if I feel a little bit DIY or + + + align:start position:0% +even if I feel a little bit DIY or +whatever I'll just get the job done but + + align:start position:0% +whatever I'll just get the job done but + + + align:start position:0% +whatever I'll just get the job done but +when it comes to decision making when + + align:start position:0% +when it comes to decision making when + + + align:start position:0% +when it comes to decision making when +you when it comes to negotiations when + + align:start position:0% +you when it comes to negotiations when + + + align:start position:0% +you when it comes to negotiations when +it comes to being a boardroom and you + + align:start position:0% +it comes to being a boardroom and you + + + align:start position:0% +it comes to being a boardroom and you +need to make a sharp decision that + + align:start position:0% +need to make a sharp decision that + + + align:start position:0% +need to make a sharp decision that +cannot be compensated if you make a mad + + align:start position:0% +cannot be compensated if you make a mad + + + align:start position:0% +cannot be compensated if you make a mad +bad decision in an strategic meeting + + align:start position:0% +bad decision in an strategic meeting + + + align:start position:0% +bad decision in an strategic meeting +that is going to handt you for the rest + + align:start position:0% +that is going to handt you for the rest + + + align:start position:0% +that is going to handt you for the rest +of the quarter at least so if that is + + align:start position:0% +of the quarter at least so if that is + + + align:start position:0% +of the quarter at least so if that is +affected by the place where we are + + align:start position:0% +affected by the place where we are + + + align:start position:0% +affected by the place where we are +making those decision even at the very + + align:start position:0% +making those decision even at the very + + + align:start position:0% +making those decision even at the very +low margin you will see big consequences + + align:start position:0% +low margin you will see big consequences + + + align:start position:0% +low margin you will see big consequences +because these are big numbers right the + + align:start position:0% +because these are big numbers right the + + + align:start position:0% +because these are big numbers right the +10 the 10% of the GDP of the United + + align:start position:0% +10 the 10% of the GDP of the United + + + align:start position:0% +10 the 10% of the GDP of the United +States is a big number so even if you do + + align:start position:0% +States is a big number so even if you do + + + align:start position:0% +States is a big number so even if you do +a + + align:start position:0% +a + + + align:start position:0% +a +0.5% change on these number is going to + + align:start position:0% +0.5% change on these number is going to + + + align:start position:0% +0.5% change on these number is going to +be a big change for for um for the for + + align:start position:0% +be a big change for for um for the for + + + align:start position:0% +be a big change for for um for the for +the whole country the same for $150 + + align:start position:0% +the whole country the same for $150 + + + align:start position:0% +the whole country the same for $150 +billion for the US sector so we are we + + align:start position:0% +billion for the US sector so we are we + + + align:start position:0% +billion for the US sector so we are we +are going to be moving in those margins + + align:start position:0% +are going to be moving in those margins + + + align:start position:0% +are going to be moving in those margins +small impacts but hopefully credible but + + align:start position:0% +small impacts but hopefully credible but + + + align:start position:0% +small impacts but hopefully credible but +if you make a small impact in a big part + + align:start position:0% +if you make a small impact in a big part + + + align:start position:0% +if you make a small impact in a big part +of the pie is going to generate a big + + align:start position:0% +of the pie is going to generate a big + + + align:start position:0% +of the pie is going to generate a big +impact after all and that's different + + align:start position:0% +impact after all and that's different + + + align:start position:0% +impact after all and that's different +from the from the Energy Efficiency + + align:start position:0% +from the from the Energy Efficiency + + + align:start position:0% +from the from the Energy Efficiency +where utilities as we will show in the + + align:start position:0% +where utilities as we will show in the + + + align:start position:0% +where utilities as we will show in the +Inon statements from tenants utilit has + + align:start position:0% +Inon statements from tenants utilit has + + + align:start position:0% +Inon statements from tenants utilit has +to be relatively a small part but we can + + align:start position:0% +to be relatively a small part but we can + + + align:start position:0% +to be relatively a small part but we can +actually make a big impact with with + + align:start position:0% +actually make a big impact with with + + + align:start position:0% +actually make a big impact with with +energy efficient Investments but you + + align:start position:0% +energy efficient Investments but you + + + align:start position:0% +energy efficient Investments but you +need to make a big impact because + + align:start position:0% +need to make a big impact because + + + align:start position:0% +need to make a big impact because +otherwise it will not make a meaningful + + align:start position:0% +otherwise it will not make a meaningful + + + align:start position:0% +otherwise it will not make a meaningful +change in the in the income statements + + align:start position:0% +change in the in the income statements + + + align:start position:0% +change in the in the income statements +of of tenants but here it is you have a + + align:start position:0% +of of tenants but here it is you have a + + + align:start position:0% +of of tenants but here it is you have a +large set of the P it's very difficult + + align:start position:0% +large set of the P it's very difficult + + + align:start position:0% +large set of the P it's very difficult +to make even any small impact but if you + + align:start position:0% +to make even any small impact but if you + + + align:start position:0% +to make even any small impact but if you +do you have very big numbers that will + + align:start position:0% +do you have very big numbers that will + + + align:start position:0% +do you have very big numbers that will +actually make a very big impact after + + align:start position:0% +actually make a very big impact after + + + align:start position:0% +actually make a very big impact after +all when you compute that any + + align:start position:0% +all when you compute that any + + + align:start position:0% +all when you compute that any +Reflections ich yeah that's why the C we + + align:start position:0% +Reflections ich yeah that's why the C we + + + align:start position:0% +Reflections ich yeah that's why the C we +are committed to make this place a very + + align:start position:0% +are committed to make this place a very + + + align:start position:0% +are committed to make this place a very +healthy amen we are going to run away to + + align:start position:0% +healthy amen we are going to run away to + + + align:start position:0% +healthy amen we are going to run away to +this natural Hall to make them + + align:start position:0% + + + + align:start position:0% + +healthier understand the S exactly so if + + align:start position:0% +healthier understand the S exactly so if + + + align:start position:0% +healthier understand the S exactly so if +you want if you have any requests please + + align:start position:0% +you want if you have any requests please + + + align:start position:0% +you want if you have any requests please +send an email to CI with a nice sofa or + + align:start position:0% +send an email to CI with a nice sofa or + + + align:start position:0% +send an email to CI with a nice sofa or +something I already doing so yeah but + + align:start position:0% +something I already doing so yeah but + + + align:start position:0% +something I already doing so yeah but +after you + + align:start position:0% + + + + align:start position:0% + +graduate I must business but they you + + align:start position:0% +graduate I must business but they you + + + align:start position:0% +graduate I must business but they you +can always come you will anyways come + + align:start position:0% +can always come you will anyways come + + + align:start position:0% +can always come you will anyways come +for the commencement so imagine being + + align:start position:0% +for the commencement so imagine being + + + align:start position:0% +for the commencement so imagine being +here with a nice sofa and I think that + + align:start position:0% +here with a nice sofa and I think that + + + align:start position:0% +here with a nice sofa and I think that +would be nice great okay okay so now + + align:start position:0% +would be nice great okay okay so now + + + align:start position:0% +would be nice great okay okay so now +that we understand the science and what + + align:start position:0% +that we understand the science and what + + + align:start position:0% +that we understand the science and what +buildings do to inject what the + + align:start position:0% +buildings do to inject what the + + + align:start position:0% +buildings do to inject what the +environment makes to to us and sort of + + align:start position:0% +environment makes to to us and sort of + + + align:start position:0% +environment makes to to us and sort of +like the the prospects of of making a + + align:start position:0% +like the the prospects of of making a + + + align:start position:0% +like the the prospects of of making a +lot money let me go really into uh first + + align:start position:0% +lot money let me go really into uh first + + + align:start position:0% +lot money let me go really into uh first +the impact of of buildings or The Proven + + align:start position:0% +the impact of of buildings or The Proven + + + align:start position:0% +the impact of of buildings or The Proven +impact in the research of buildings on + + align:start position:0% +impact in the research of buildings on + + + align:start position:0% +impact in the research of buildings on +on human health by me but also by others + + align:start position:0% +on human health by me but also by others + + + align:start position:0% +on human health by me but also by others +uh and then also you know not only on + + align:start position:0% +uh and then also you know not only on + + + align:start position:0% +uh and then also you know not only on +the occupants and the people the users + + align:start position:0% +the occupants and the people the users + + + align:start position:0% +the occupants and the people the users +of those buildings but also how that + + align:start position:0% +of those buildings but also how that + + + align:start position:0% +of those buildings but also how that +scales up all the way to an investment + + align:start position:0% +scales up all the way to an investment + + + align:start position:0% +scales up all the way to an investment +valuable decision right so how the + + align:start position:0% +valuable decision right so how the + + + align:start position:0% +valuable decision right so how the +tenants will actually be able to pay for + + align:start position:0% +tenants will actually be able to pay for + + + align:start position:0% +tenants will actually be able to pay for +this or not and why would they pay so + + align:start position:0% +this or not and why would they pay so + + + align:start position:0% +this or not and why would they pay so +basically thinking about the accounting + + align:start position:0% +basically thinking about the accounting + + + align:start position:0% +basically thinking about the accounting +of those so my employees are healthier + + align:start position:0% +of those so my employees are healthier + + + align:start position:0% +of those so my employees are healthier +but that doesn't mean that I care uh but + + align:start position:0% +but that doesn't mean that I care uh but + + + align:start position:0% +but that doesn't mean that I care uh but +actually if that means money for me then + + align:start position:0% +actually if that means money for me then + + + align:start position:0% +actually if that means money for me then +I will care and I will actually make + + align:start position:0% +I will care and I will actually make + + + align:start position:0% +I will care and I will actually make +sure that I'm in the best office or that + + align:start position:0% +sure that I'm in the best office or that + + + align:start position:0% +sure that I'm in the best office or that +the that office is at the best + + align:start position:0% +the that office is at the best + + + align:start position:0% +the that office is at the best +performance that can be but then also of + + align:start position:0% +performance that can be but then also of + + + align:start position:0% +performance that can be but then also of +course talking about when you when we + + align:start position:0% +course talking about when you when we + + + align:start position:0% +course talking about when you when we +climb the leather also some uh barriers + + align:start position:0% +climb the leather also some uh barriers + + + align:start position:0% +climb the leather also some uh barriers +to adoption right so so even if we prove + + align:start position:0% +to adoption right so so even if we prove + + + align:start position:0% +to adoption right so so even if we prove +that these buildings make people + + align:start position:0% +that these buildings make people + + + align:start position:0% +that these buildings make people +healthier even if we prove that these + + align:start position:0% +healthier even if we prove that these + + + align:start position:0% +healthier even if we prove that these +build + + align:start position:0% +build + + + align:start position:0% +build +uh will make people more + + align:start position:0% +uh will make people more + + + align:start position:0% +uh will make people more +productive is this going to scale up to + + align:start position:0% +productive is this going to scale up to + + + align:start position:0% +productive is this going to scale up to +the final decision maker that is able to + + align:start position:0% +the final decision maker that is able to + + + align:start position:0% +the final decision maker that is able to +actually put the money to make that + + align:start position:0% +actually put the money to make that + + + align:start position:0% +actually put the money to make that +investment and we were talking before + + align:start position:0% +investment and we were talking before + + + align:start position:0% +investment and we were talking before +with with Willian about the fact that + + align:start position:0% +with with Willian about the fact that + + + align:start position:0% +with with Willian about the fact that +sometimes these split incentives are not + + align:start position:0% +sometimes these split incentives are not + + + align:start position:0% +sometimes these split incentives are not +easy to solve and we will have them here + + align:start position:0% +easy to solve and we will have them here + + + align:start position:0% +easy to solve and we will have them here +again and actually you will have a + + align:start position:0% +again and actually you will have a + + + align:start position:0% +again and actually you will have a +little bit more um a more complex flavor + + align:start position:0% +little bit more um a more complex flavor + + + align:start position:0% +little bit more um a more complex flavor +than even the Energy Efficiency for + + align:start position:0% +than even the Energy Efficiency for + + + align:start position:0% +than even the Energy Efficiency for +certain reasons so we need to understand + + align:start position:0% +certain reasons so we need to understand + + + align:start position:0% +certain reasons so we need to understand +both we need to understand what is the + + align:start position:0% +both we need to understand what is the + + + align:start position:0% +both we need to understand what is the +potential of this Investments but but we + + align:start position:0% +potential of this Investments but but we + + + align:start position:0% +potential of this Investments but but we +also need to understand very clearly + + align:start position:0% +also need to understand very clearly + + + align:start position:0% +also need to understand very clearly +what are the barriers and also start the + + align:start position:0% +what are the barriers and also start the + + + align:start position:0% +what are the barriers and also start the +conversation about what are the + + align:start position:0% +conversation about what are the + + + align:start position:0% +conversation about what are the +solutions so this is the the whole + + align:start position:0% +solutions so this is the the whole + + + align:start position:0% +solutions so this is the the whole +purpose of the conver of the uh of the + + align:start position:0% +purpose of the conver of the uh of the + + + align:start position:0% +purpose of the conver of the uh of the +conversation today and finally you know + + align:start position:0% +conversation today and finally you know + + + align:start position:0% +conversation today and finally you know +to to wrap up to connect to to the first + + align:start position:0% +to to wrap up to connect to to the first + + + align:start position:0% +to to wrap up to connect to to the first +two lectures of the course including + + align:start position:0% +two lectures of the course including + + + align:start position:0% +two lectures of the course including +also the the introductory lecture the + + align:start position:0% +also the the introductory lecture the + + + align:start position:0% +also the the introductory lecture the +three first lecture of the course + + align:start position:0% +three first lecture of the course + + + align:start position:0% +three first lecture of the course +connecting healthy and green and is + + align:start position:0% +connecting healthy and green and is + + + align:start position:0% +connecting healthy and green and is +there a trade-off or not and so forth + + align:start position:0% +there a trade-off or not and so forth + + + align:start position:0% +there a trade-off or not and so forth +and if we have time given the H + + align:start position:0% +and if we have time given the H + + + align:start position:0% +and if we have time given the H +projector part I can also give you a + + align:start position:0% +projector part I can also give you a + + + align:start position:0% +projector part I can also give you a +glimpse of how covid is going to shift + + align:start position:0% +glimpse of how covid is going to shift + + + align:start position:0% +glimpse of how covid is going to shift +or is Shifting this uh all of these + + align:start position:0% +or is Shifting this uh all of these + + + align:start position:0% +or is Shifting this uh all of these +things all + + align:start position:0% +things all + + + align:start position:0% +things all +right + + align:start position:0% +right + + + align:start position:0% +right +Jason + + align:start position:0% + + + + align:start position:0% + +do because often healthy buildings green + + align:start position:0% +do because often healthy buildings green + + + align:start position:0% +do because often healthy buildings green +buildings are also just like newer + + align:start position:0% +buildings are also just like newer + + + align:start position:0% +buildings are also just like newer +buildings like maybe with a better + + align:start position:0% +buildings like maybe with a better + + + align:start position:0% +buildings like maybe with a better +layout or like more economic Furniture + + align:start position:0% +layout or like more economic Furniture + + + align:start position:0% +layout or like more economic Furniture +better lighting like how do you control + + align:start position:0% +better lighting like how do you control + + + align:start position:0% +better lighting like how do you control +for the fact that it's the healthiness + + align:start position:0% +for the fact that it's the healthiness + + + align:start position:0% +for the fact that it's the healthiness +or the greenness that is what's causing + + align:start position:0% +or the greenness that is what's causing + + + align:start position:0% +or the greenness that is what's causing +prod + + align:start position:0% +prod + + + align:start position:0% +prod +can you hold on that for like five + + align:start position:0% +can you hold on that for like five + + + align:start position:0% +can you hold on that for like five +minutes I have like three or four or + + align:start position:0% +minutes I have like three or four or + + + align:start position:0% +minutes I have like three or four or +five slides for that for you then you + + align:start position:0% +five slides for that for you then you + + + align:start position:0% +five slides for that for you then you +throw all of those comments to me but + + align:start position:0% +throw all of those comments to me but + + + align:start position:0% +throw all of those comments to me but +that is going to be an important part of + + align:start position:0% +that is going to be an important part of + + + align:start position:0% +that is going to be an important part of +the lecture so that's exactly that's + + align:start position:0% +the lecture so that's exactly that's + + + align:start position:0% +the lecture so that's exactly that's +exactly what we are here actually one of + + align:start position:0% +exactly what we are here actually one of + + + align:start position:0% +exactly what we are here actually one of +the main purposes of of uh of c and me + + align:start position:0% +the main purposes of of uh of c and me + + + align:start position:0% +the main purposes of of uh of c and me +in this course is actually to giving you + + align:start position:0% +in this course is actually to giving you + + + align:start position:0% +in this course is actually to giving you +the right Thinking Tools to evaluate + + align:start position:0% +the right Thinking Tools to evaluate + + + align:start position:0% +the right Thinking Tools to evaluate +those in a way that is H it's a fair + + align:start position:0% +those in a way that is H it's a fair + + + align:start position:0% +those in a way that is H it's a fair +assessment and it's an actual assessment + + align:start position:0% +assessment and it's an actual assessment + + + align:start position:0% +assessment and it's an actual assessment +of the feature that you want to evaluate + + align:start position:0% +of the feature that you want to evaluate + + + align:start position:0% +of the feature that you want to evaluate +and not something else because that's + + align:start position:0% +and not something else because that's + + + align:start position:0% +and not something else because that's +something that you can carry for + + align:start position:0% +something that you can carry for + + + align:start position:0% +something that you can carry for +anything that you will do in your job + + align:start position:0% +anything that you will do in your job + + + align:start position:0% +anything that you will do in your job +afterwards like I can teach you + + align:start position:0% +afterwards like I can teach you + + + align:start position:0% +afterwards like I can teach you +everything from the car technology now + + align:start position:0% +everything from the car technology now + + + align:start position:0% +everything from the car technology now +but if it changes in five + + align:start position:0% +but if it changes in five + + + align:start position:0% +but if it changes in five +years you are not going to be in a very + + align:start position:0% +years you are not going to be in a very + + + align:start position:0% +years you are not going to be in a very +good position but if I teach you how to + + align:start position:0% +good position but if I teach you how to + + + align:start position:0% +good position but if I teach you how to +think about any evaluation of the + + align:start position:0% +think about any evaluation of the + + + align:start position:0% +think about any evaluation of the +technology you can carry it for green + + align:start position:0% +technology you can carry it for green + + + align:start position:0% +technology you can carry it for green +healthy smart heat pumps hydrogen + + align:start position:0% +healthy smart heat pumps hydrogen + + + align:start position:0% +healthy smart heat pumps hydrogen +whatever it is you will think about the + + align:start position:0% +whatever it is you will think about the + + + align:start position:0% +whatever it is you will think about the +exact same uh in the exact same way so + + align:start position:0% +exact same uh in the exact same way so + + + align:start position:0% +exact same uh in the exact same way so +we are going to do that today we're are + + align:start position:0% +we are going to do that today we're are + + + align:start position:0% +we are going to do that today we're are +going to do it tomorrow we are not + + align:start position:0% +going to do it tomorrow we are not + + + align:start position:0% +going to do it tomorrow we are not +tomorrow sorry next well actually maybe + + align:start position:0% +tomorrow sorry next well actually maybe + + + align:start position:0% +tomorrow sorry next well actually maybe +tomorrow in nakot Taco I can also give + + align:start position:0% +tomorrow in nakot Taco I can also give + + + align:start position:0% +tomorrow in nakot Taco I can also give +some of those um but next week with the + + align:start position:0% +some of those um but next week with the + + + align:start position:0% +some of those um but next week with the +green uh C's lecture there will be a lot + + align:start position:0% +green uh C's lecture there will be a lot + + + align:start position:0% +green uh C's lecture there will be a lot +of it we call it Apple to Apple + + align:start position:0% +of it we call it Apple to Apple + + + align:start position:0% +of it we call it Apple to Apple +comparison right so you really want to + + align:start position:0% +comparison right so you really want to + + + align:start position:0% +comparison right so you really want to +compare things that are exactly the same + + align:start position:0% +compare things that are exactly the same + + + align:start position:0% +compare things that are exactly the same +except for the fact that that specific + + align:start position:0% +except for the fact that that specific + + + align:start position:0% +except for the fact that that specific +feature that you are looking at is + + align:start position:0% +feature that you are looking at is + + + align:start position:0% +feature that you are looking at is +changing all right so in terms of what + + align:start position:0% +changing all right so in terms of what + + + align:start position:0% +changing all right so in terms of what +we can do in the building and given that + + align:start position:0% +we can do in the building and given that + + + align:start position:0% +we can do in the building and given that +c is going to put unlock a lot of money + + align:start position:0% +c is going to put unlock a lot of money + + + align:start position:0% +c is going to put unlock a lot of money +uh what can we do to this lecture hall + + align:start position:0% +uh what can we do to this lecture hall + + + align:start position:0% +uh what can we do to this lecture hall +to make it there you go we have an an + + align:start position:0% +to make it there you go we have an an + + + align:start position:0% +to make it there you go we have an an +inquiry already always + + align:start position:0% +inquiry already always + + + align:start position:0% +inquiry already always +leure outdo no wait wait one second take + + align:start position:0% +leure outdo no wait wait one second take + + + align:start position:0% +leure outdo no wait wait one second take +not okay + + align:start position:0% +not okay + + + align:start position:0% +not okay +yes very important there's no there's no + + align:start position:0% +yes very important there's no there's no + + + align:start position:0% +yes very important there's no there's no +outdoor light and so hard to see the one + + align:start position:0% +outdoor light and so hard to see the one + + + align:start position:0% +outdoor light and so hard to see the one +you don't get uh the health benefits + + align:start position:0% +you don't get uh the health benefits + + + align:start position:0% +you don't get uh the health benefits +from it and also you don't see the time + + align:start position:0% +from it and also you don't see the time + + + align:start position:0% +from it and also you don't see the time +pass and so like you're just like I've + + align:start position:0% +pass and so like you're just like I've + + + align:start position:0% +pass and so like you're just like I've +been in here for so + + align:start position:0% +been in here for so + + + align:start position:0% +been in here for so +long like what happen to the day that's + + align:start position:0% +long like what happen to the day that's + + + align:start position:0% +long like what happen to the day that's +my biggest complaint with this this room + + align:start position:0% +my biggest complaint with this this room + + + align:start position:0% +my biggest complaint with this this room +can we test that how long do you think + + align:start position:0% +can we test that how long do you think + + + align:start position:0% +can we test that how long do you think +that you've been today here + + align:start position:0% +that you've been today here + + + align:start position:0% +that you've been today here +uh six hours eight + + align:start position:0% +uh six hours eight + + + align:start position:0% +uh six hours eight +hours I don't know uh 25 minutes so no + + align:start position:0% +hours I don't know uh 25 minutes so no + + + align:start position:0% +hours I don't know uh 25 minutes so no +actually today it feels shorter than it + + align:start position:0% +actually today it feels shorter than it + + + align:start position:0% +actually today it feels shorter than it +is it's H you've been here 40 minutes + + align:start position:0% +is it's H you've been here 40 minutes + + + align:start position:0% +is it's H you've been here 40 minutes +okay it's a compliment I'll take it as a + + align:start position:0% +okay it's a compliment I'll take it as a + + + align:start position:0% +okay it's a compliment I'll take it as a +compliment let's let's slow down time + + align:start position:0% +compliment let's let's slow down time + + + align:start position:0% +compliment let's let's slow down time +for now anyone else any inquiry how so + + align:start position:0% +for now anyone else any inquiry how so + + + align:start position:0% +for now anyone else any inquiry how so +we have okay let's bring it back to here + + align:start position:0% +we have okay let's bring it back to here + + + align:start position:0% +we have okay let's bring it back to here +lighting and Views I will I will call + + align:start position:0% +lighting and Views I will I will call + + + align:start position:0% +lighting and Views I will I will call +that one lighting and Views any anything + + align:start position:0% +that one lighting and Views any anything + + + align:start position:0% +that one lighting and Views any anything +else ergonomic these chairs are designed + + align:start position:0% +else ergonomic these chairs are designed + + + align:start position:0% +else ergonomic these chairs are designed +to like stay in place so we're always + + align:start position:0% +to like stay in place so we're always + + + align:start position:0% +to like stay in place so we're always +kind of like portioning our spine like + + align:start position:0% +kind of like portioning our spine like + + + align:start position:0% +kind of like portioning our spine like +after like after like Ventures it's like + + align:start position:0% +after like after like Ventures it's like + + + align:start position:0% +after like after like Ventures it's like +three hours we kind of walk like + + align:start position:0% +three hours we kind of walk like + + + align:start position:0% +three hours we kind of walk like +this no it's very important ergonomics + + align:start position:0% +this no it's very important ergonomics + + + align:start position:0% +this no it's very important ergonomics +anyone else we'll fix + + align:start position:0% +anyone else we'll fix + + + align:start position:0% +anyone else we'll fix +that we'll change all + + align:start position:0% +that we'll change all + + + align:start position:0% +that we'll change all +the Vicky was Rel to the chair I I like + + align:start position:0% +the Vicky was Rel to the chair I I like + + + align:start position:0% +the Vicky was Rel to the chair I I like +to know if there's like any in + + align:start position:0% +to know if there's like any in + + + align:start position:0% +to know if there's like any in +like these Fabrics because they like + + align:start position:0% +like these Fabrics because they like + + + align:start position:0% +like these Fabrics because they like +haard materials and so yeah like if like + + align:start position:0% +haard materials and so yeah like if like + + + align:start position:0% +haard materials and so yeah like if like +this like coating of the materials like + + align:start position:0% +this like coating of the materials like + + + align:start position:0% +this like coating of the materials like +VCS or not correct yeah so very + + align:start position:0% +VCS or not correct yeah so very + + + align:start position:0% +VCS or not correct yeah so very +important materials carpets yeah yeah + + align:start position:0% +important materials carpets yeah yeah + + + align:start position:0% +important materials carpets yeah yeah +the V yeah V so we were talking about + + align:start position:0% +the V yeah V so we were talking about + + + align:start position:0% +the V yeah V so we were talking about +outdoor air quality like outo air + + align:start position:0% +outdoor air quality like outo air + + + align:start position:0% +outdoor air quality like outo air +quality problems with pollution and so + + align:start position:0% +quality problems with pollution and so + + + align:start position:0% +quality problems with pollution and so +forth but of course we deploy things in + + align:start position:0% +forth but of course we deploy things in + + + align:start position:0% +forth but of course we deploy things in +buildings that are a lot of times + + align:start position:0% +buildings that are a lot of times + + + align:start position:0% +buildings that are a lot of times +poisoned and poisoning us so that's + + align:start position:0% +poisoned and poisoning us so that's + + + align:start position:0% +poisoned and poisoning us so that's +important and that's something that the + + align:start position:0% +important and that's something that the + + + align:start position:0% +important and that's something that the +science is getting there but there's a + + align:start position:0% +science is getting there but there's a + + + align:start position:0% +science is getting there but there's a +lot of information symmetries there's a + + align:start position:0% +lot of information symmetries there's a + + + align:start position:0% +lot of information symmetries there's a +lot of capacity on what is what each of + + align:start position:0% +lot of capacity on what is what each of + + + align:start position:0% +lot of capacity on what is what each of +these materials have have in them that + + align:start position:0% +these materials have have in them that + + + align:start position:0% +these materials have have in them that +can actually affect us in one way or + + align:start position:0% +can actually affect us in one way or + + + align:start position:0% +can actually affect us in one way or +another uh it's too small to so that if + + align:start position:0% +another uh it's too small to so that if + + + align:start position:0% +another uh it's too small to so that if +you skip class it's very easy to get + + align:start position:0% + + + + align:start position:0% + +car that I don't know where we will fix + + align:start position:0% +car that I don't know where we will fix + + + align:start position:0% +car that I don't know where we will fix +but uh valid concern anyone so we have + + align:start position:0% +but uh valid concern anyone so we have + + + align:start position:0% +but uh valid concern anyone so we have +we have materials we have ergonomics we + + align:start position:0% +we have materials we have ergonomics we + + + align:start position:0% +we have materials we have ergonomics we +have lights and view anyone SE I don't + + align:start position:0% +have lights and view anyone SE I don't + + + align:start position:0% +have lights and view anyone SE I don't +know Sy + + align:start position:0% + + + + align:start position:0% + +ventilation so here we are testing it + + align:start position:0% +ventilation so here we are testing it + + + align:start position:0% +ventilation so here we are testing it +this guy I don't know why you guys can + + align:start position:0% +this guy I don't know why you guys can + + + align:start position:0% +this guy I don't know why you guys can +read it he says + + align:start position:0% +read it he says + + + align:start position:0% +read it he says +700 when it will get to 1, or 900 then + + align:start position:0% +700 when it will get to 1, or 900 then + + + align:start position:0% +700 when it will get to 1, or 900 then +these things will actually start + + align:start position:0% +these things will actually start + + + align:start position:0% +these things will actually start +consider as not healthy we are we are + + align:start position:0% +consider as not healthy we are we are + + + align:start position:0% +consider as not healthy we are we are +keeping it below uh but we will show you + + align:start position:0% +keeping it below uh but we will show you + + + align:start position:0% +keeping it below uh but we will show you +that even going from these levels all + + align:start position:0% +that even going from these levels all + + + align:start position:0% +that even going from these levels all +the way to 500 can actually have a + + align:start position:0% +the way to 500 can actually have a + + + align:start position:0% +the way to 500 can actually have a +benefit from concentration and so forth + + align:start position:0% +benefit from concentration and so forth + + + align:start position:0% +benefit from concentration and so forth +but that is definitely one of the key + + align:start position:0% +but that is definitely one of the key + + + align:start position:0% +but that is definitely one of the key +things that at the moment because of + + align:start position:0% +things that at the moment because of + + + align:start position:0% +things that at the moment because of +covid but also beforehand like + + align:start position:0% +covid but also beforehand like + + + align:start position:0% +covid but also beforehand like +ventilation is being considered sort of + + align:start position:0% +ventilation is being considered sort of + + + align:start position:0% +ventilation is being considered sort of +like the flagship of uh of healthy + + align:start position:0% +like the flagship of uh of healthy + + + align:start position:0% +like the flagship of uh of healthy +buildings so if you are in a in a + + align:start position:0% +buildings so if you are in a in a + + + align:start position:0% +buildings so if you are in a in a +building that is not good in terms of + + align:start position:0% +building that is not good in terms of + + + align:start position:0% +building that is not good in terms of +air quality it's very hard to argue that + + align:start position:0% +air quality it's very hard to argue that + + + align:start position:0% +air quality it's very hard to argue that +it's healthy um anything else one more + + align:start position:0% +it's healthy um anything else one more + + + align:start position:0% +it's healthy um anything else one more +give me one more we talk about vus we + + align:start position:0% +give me one more we talk about vus we + + + align:start position:0% +give me one more we talk about vus we +talk about ergonomics we talk about v's + + align:start position:0% +talk about ergonomics we talk about v's + + + align:start position:0% +talk about ergonomics we talk about v's +and materials we talk about ventilation + + align:start position:0% +and materials we talk about ventilation + + + align:start position:0% +and materials we talk about ventilation +we talk about Tamar lights lights + + align:start position:0% +we talk about Tamar lights lights + + + align:start position:0% +we talk about Tamar lights lights +artificial lighting yeah + + align:start position:0% + + + + align:start position:0% + +thisone + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +imitates yeah that's important one I you + + align:start position:0% +imitates yeah that's important one I you + + + align:start position:0% +imitates yeah that's important one I you +know that I have a joint position with + + align:start position:0% +know that I have a joint position with + + + align:start position:0% +know that I have a joint position with +the University of mas there you have + + align:start position:0% +the University of mas there you have + + + align:start position:0% +the University of mas there you have +Phillips and Phillips is developing a + + align:start position:0% +Phillips and Phillips is developing a + + + align:start position:0% +Phillips and Phillips is developing a +lot of work into trying to mimic natural + + align:start position:0% +lot of work into trying to mimic natural + + + align:start position:0% +lot of work into trying to mimic natural +light the the reality is that you look + + align:start position:0% +light the the reality is that you look + + + align:start position:0% +light the the reality is that you look +at the science is very hard to mimic it + + align:start position:0% +at the science is very hard to mimic it + + + align:start position:0% +at the science is very hard to mimic it +but it's definitely there is definitely + + align:start position:0% +but it's definitely there is definitely + + + align:start position:0% +but it's definitely there is definitely +a room for improvement uh in terms of we + + align:start position:0% +a room for improvement uh in terms of we + + + align:start position:0% +a room for improvement uh in terms of we +have here and what we could have but is + + align:start position:0% +have here and what we could have but is + + + align:start position:0% +have here and what we could have but is +very hard to mimic any effects that the + + align:start position:0% +very hard to mimic any effects that the + + + align:start position:0% +very hard to mimic any effects that the +Sun have on us in our C circulan rhythms + + align:start position:0% +Sun have on us in our C circulan rhythms + + + align:start position:0% +Sun have on us in our C circulan rhythms +and so forth but we can make our life + + align:start position:0% +and so forth but we can make our life + + + align:start position:0% +and so forth but we can make our life +lives less miserable by being here yeah + + align:start position:0% +lives less miserable by being here yeah + + + align:start position:0% +lives less miserable by being here yeah +yeah those two + + align:start position:0% +yeah those two + + + align:start position:0% +yeah those two +lights that I can fix right oh can I fix + + align:start position:0% +lights that I can fix right oh can I fix + + + align:start position:0% +lights that I can fix right oh can I fix +it can I don't know you every single one + + align:start position:0% +it can I don't know you every single one + + + align:start position:0% +it can I don't know you every single one +of that's great sometimes actually just + + align:start position:0% +of that's great sometimes actually just + + + align:start position:0% +of that's great sometimes actually just +about asking the right question + + align:start position:0% +about asking the right question + + + align:start position:0% +about asking the right question +and also I noticed um something about me + + align:start position:0% +and also I noticed um something about me + + + align:start position:0% +and also I noticed um something about me +my + + align:start position:0% +my + + + align:start position:0% +my +perfume the T the T slots works for + + align:start position:0% +perfume the T the T slots works for + + + align:start position:0% +perfume the T the T slots works for +hours but if it's if a student from Stow + + align:start position:0% +hours but if it's if a student from Stow + + + align:start position:0% +hours but if it's if a student from Stow +or Harvard doesn't + + align:start position:0% +or Harvard doesn't + + + align:start position:0% +or Harvard doesn't +work that's an easy fix too much bigger + + align:start position:0% + + + + align:start position:0% + +oh we are not + + align:start position:0% +oh we are not + + + align:start position:0% +oh we are not +inclusive all right guys but these are + + align:start position:0% +inclusive all right guys but these are + + + align:start position:0% +inclusive all right guys but these are +let me like I I put it also in the + + align:start position:0% +let me like I I put it also in the + + + align:start position:0% +let me like I I put it also in the +reading notes but these are pretty much + + align:start position:0% +reading notes but these are pretty much + + + align:start position:0% +reading notes but these are pretty much +we hit into everything that that is + + align:start position:0% +we hit into everything that that is + + + align:start position:0% +we hit into everything that that is +there we we missed noise these are this + + align:start position:0% +there we we missed noise these are this + + + align:start position:0% +there we we missed noise these are this +is sort of a bunker so we don't really + + align:start position:0% +is sort of a bunker so we don't really + + + align:start position:0% +is sort of a bunker so we don't really +have a lot of noise that is good but of + + align:start position:0% +have a lot of noise that is good but of + + + align:start position:0% +have a lot of noise that is good but of +course comes at the cost of not having + + align:start position:0% +course comes at the cost of not having + + + align:start position:0% +course comes at the cost of not having +any views or anything like that plants + + align:start position:0% +any views or anything like that plants + + + align:start position:0% +any views or anything like that plants +we don't have any plant here SII has the + + align:start position:0% +we don't have any plant here SII has the + + + align:start position:0% +we don't have any plant here SII has the +the office full of plants but she didn't + + align:start position:0% +the office full of plants but she didn't + + + align:start position:0% +the office full of plants but she didn't +dare to bring anyone here uh and then as + + align:start position:0% +dare to bring anyone here uh and then as + + + align:start position:0% +dare to bring anyone here uh and then as +we say design and and so forth and of + + align:start position:0% +we say design and and so forth and of + + + align:start position:0% +we say design and and so forth and of +course there's a lot of work into uh the + + align:start position:0% +course there's a lot of work into uh the + + + align:start position:0% +course there's a lot of work into uh the +access and the design or something of + + align:start position:0% +access and the design or something of + + + align:start position:0% +access and the design or something of +how how you make people move in a + + align:start position:0% +how how you make people move in a + + + align:start position:0% +how how you make people move in a +building right so you see that in a lot + + align:start position:0% +building right so you see that in a lot + + + align:start position:0% +building right so you see that in a lot +of these healthy buildings what when you + + align:start position:0% +of these healthy buildings what when you + + + align:start position:0% +of these healthy buildings what when you +enter the most prominent thing that you + + align:start position:0% +enter the most prominent thing that you + + + align:start position:0% +enter the most prominent thing that you +have is the staircase to make you go up + + align:start position:0% +have is the staircase to make you go up + + + align:start position:0% +have is the staircase to make you go up +and move and exercise and in some others + + align:start position:0% +and move and exercise and in some others + + + align:start position:0% +and move and exercise and in some others +what you see most prominent is is an + + align:start position:0% +what you see most prominent is is an + + + align:start position:0% +what you see most prominent is is an +elevator uh and we are not talking about + + align:start position:0% +elevator uh and we are not talking about + + + align:start position:0% +elevator uh and we are not talking about +the high-rise buildings where you don't + + align:start position:0% +the high-rise buildings where you don't + + + align:start position:0% +the high-rise buildings where you don't +have any alternative there but we are + + align:start position:0% +have any alternative there but we are + + + align:start position:0% +have any alternative there but we are +talking also about like a four five + + align:start position:0% +talking also about like a four five + + + align:start position:0% +talking also about like a four five +story office building where you could + + align:start position:0% +story office building where you could + + + align:start position:0% +story office building where you could +definitely walk upstairs and you still + + align:start position:0% +definitely walk upstairs and you still + + + align:start position:0% +definitely walk upstairs and you still +make people the default and Notch them + + align:start position:0% +make people the default and Notch them + + + align:start position:0% +make people the default and Notch them +to go to to an elevator all right so but + + align:start position:0% +to go to to an elevator all right so but + + + align:start position:0% +to go to to an elevator all right so but +what I like is that almost I saw you the + + align:start position:0% +what I like is that almost I saw you the + + + align:start position:0% +what I like is that almost I saw you the +what I like is that almost + + align:start position:0% +what I like is that almost + + + align:start position:0% +what I like is that almost +in any class I always come to the + + align:start position:0% +in any class I always come to the + + + align:start position:0% +in any class I always come to the +conclusion that this graph is sort of + + align:start position:0% +conclusion that this graph is sort of + + + align:start position:0% +conclusion that this graph is sort of +intuitive for everyone like kind of we + + align:start position:0% +intuitive for everyone like kind of we + + + align:start position:0% +intuitive for everyone like kind of we +all think that there is a better way to + + align:start position:0% +all think that there is a better way to + + + align:start position:0% +all think that there is a better way to +to design buildings and along the same + + align:start position:0% +to design buildings and along the same + + + align:start position:0% +to design buildings and along the same +Dimension so this is nothing that is + + align:start position:0% +Dimension so this is nothing that is + + + align:start position:0% +Dimension so this is nothing that is +rocket science is not that I'm asking + + align:start position:0% +rocket science is not that I'm asking + + + align:start position:0% +rocket science is not that I'm asking +you how an mRNA uh vaccine works this is + + align:start position:0% +you how an mRNA uh vaccine works this is + + + align:start position:0% +you how an mRNA uh vaccine works this is +something that if you give people the + + align:start position:0% +something that if you give people the + + + align:start position:0% +something that if you give people the +the opportunity to talk they will always + + align:start position:0% +the opportunity to talk they will always + + + align:start position:0% +the opportunity to talk they will always +point out the same problems + + align:start position:0% +point out the same problems + + + align:start position:0% +point out the same problems +Tamar are these meas are these being + + align:start position:0% +Tamar are these meas are these being + + + align:start position:0% +Tamar are these meas are these being +measured to uh um so a lot of the top + + align:start position:0% +measured to uh um so a lot of the top + + + align:start position:0% +measured to uh um so a lot of the top +part are measured at a continuous basis + + align:start position:0% +part are measured at a continuous basis + + + align:start position:0% +part are measured at a continuous basis +so this guy is measuring uh is a chip + + align:start position:0% +so this guy is measuring uh is a chip + + + align:start position:0% +so this guy is measuring uh is a chip +sensor and it already measures thermal + + align:start position:0% +sensor and it already measures thermal + + + align:start position:0% +sensor and it already measures thermal +Comfort it's already measur indoor air + + align:start position:0% +Comfort it's already measur indoor air + + + align:start position:0% +Comfort it's already measur indoor air +quality and ventilation not very + + align:start position:0% +quality and ventilation not very + + + align:start position:0% +quality and ventilation not very +difficult to measure the uh the tones + + align:start position:0% +difficult to measure the uh the tones + + + align:start position:0% +difficult to measure the uh the tones +and the intensity especially the + + align:start position:0% +and the intensity especially the + + + align:start position:0% +and the intensity especially the +intensity of light and noise and + + align:start position:0% +intensity of light and noise and + + + align:start position:0% +intensity of light and noise and +Acoustics also very easy to measure a + + align:start position:0% +Acoustics also very easy to measure a + + + align:start position:0% +Acoustics also very easy to measure a +lot of these guys will be way more + + align:start position:0% +lot of these guys will be way more + + + align:start position:0% +lot of these guys will be way more +qualitative to measure and will be the + + align:start position:0% +qualitative to measure and will be the + + + align:start position:0% +qualitative to measure and will be the +studies will be a little bit less strong + + align:start position:0% +studies will be a little bit less strong + + + align:start position:0% +studies will be a little bit less strong +than what you have up there because also + + align:start position:0% +than what you have up there because also + + + align:start position:0% +than what you have up there because also +this comes from environmental science + + align:start position:0% +this comes from environmental science + + + align:start position:0% +this comes from environmental science +this comes from more the psychology and + + align:start position:0% +this comes from more the psychology and + + + align:start position:0% +this comes from more the psychology and +softer part of the scientific world + + align:start position:0% +softer part of the scientific world + + + align:start position:0% +softer part of the scientific world +don't need the bottom parts to be + + align:start position:0% +don't need the bottom parts to be + + + align:start position:0% +don't need the bottom parts to be +included in order to determine the of + + align:start position:0% +included in order to determine the of + + + align:start position:0% +included in order to determine the of +yeah I mean to be comprehensive but I + + align:start position:0% +yeah I mean to be comprehensive but I + + + align:start position:0% +yeah I mean to be comprehensive but I +mean it definitely there is definitely + + align:start position:0% +mean it definitely there is definitely + + + align:start position:0% +mean it definitely there is definitely +studies that would say that makes a + + align:start position:0% +studies that would say that makes a + + + align:start position:0% +studies that would say that makes a +difference and so forth with this one + + align:start position:0% +difference and so forth with this one + + + align:start position:0% +difference and so forth with this one +you can actually almost pinpoint like uh + + align:start position:0% +you can actually almost pinpoint like uh + + + align:start position:0% +you can actually almost pinpoint like uh +what you will do in in a basic real + + align:start position:0% +what you will do in in a basic real + + + align:start position:0% +what you will do in in a basic real +estate economics like elasticities and + + align:start position:0% +estate economics like elasticities and + + + align:start position:0% +estate economics like elasticities and +so forth like for every unit increase + + align:start position:0% +so forth like for every unit increase + + + align:start position:0% +so forth like for every unit increase +that you will have in indoor air quality + + align:start position:0% +that you will have in indoor air quality + + + align:start position:0% +that you will have in indoor air quality +how much you would expect in of the + + align:start position:0% +how much you would expect in of the + + + align:start position:0% +how much you would expect in of the +outcomes and so forth here there's no + + align:start position:0% +outcomes and so forth here there's no + + + align:start position:0% +outcomes and so forth here there's no +unit increase in in biophilia and views + + align:start position:0% +unit increase in in biophilia and views + + + align:start position:0% +unit increase in in biophilia and views +right either you have them or not and + + align:start position:0% +right either you have them or not and + + + align:start position:0% +right either you have them or not and +it's also very complex so what do you + + align:start position:0% +it's also very complex so what do you + + + align:start position:0% +it's also very complex so what do you +see outdoors and so forth but there's a + + align:start position:0% +see outdoors and so forth but there's a + + + align:start position:0% +see outdoors and so forth but there's a +lot of studies especially in hospitals + + align:start position:0% +lot of studies especially in hospitals + + + align:start position:0% +lot of studies especially in hospitals +about recovery times and so forth of + + align:start position:0% +about recovery times and so forth of + + + align:start position:0% +about recovery times and so forth of +patients when they are having natural + + align:start position:0% +patients when they are having natural + + + align:start position:0% +patients when they are having natural +light when they're having certain views + + align:start position:0% +light when they're having certain views + + + align:start position:0% +light when they're having certain views +when they have wooden rooms instead of + + align:start position:0% +when they have wooden rooms instead of + + + align:start position:0% +when they have wooden rooms instead of +just this whitish room and so forth + + align:start position:0% +just this whitish room and so forth + + + align:start position:0% +just this whitish room and so forth +actually the hospital is there are few + + align:start position:0% +actually the hospital is there are few + + + align:start position:0% +actually the hospital is there are few +podcasts I'm happy to put in in the + + align:start position:0% +podcasts I'm happy to put in in the + + + align:start position:0% +podcasts I'm happy to put in in the +canvas if you find it interesting but + + align:start position:0% +canvas if you find it interesting but + + + align:start position:0% +canvas if you find it interesting but +this is a place where we will really + + align:start position:0% +this is a place where we will really + + + align:start position:0% +this is a place where we will really +need all of these Technologies to be the + + align:start position:0% +need all of these Technologies to be the + + + align:start position:0% +need all of these Technologies to be the +best and unfortunately this is where we + + align:start position:0% +best and unfortunately this is where we + + + align:start position:0% +best and unfortunately this is where we +make the worst design options that is + + align:start position:0% +make the worst design options that is + + + align:start position:0% +make the worst design options that is +actually very very sad that we actually + + align:start position:0% +actually very very sad that we actually + + + align:start position:0% +actually very very sad that we actually +make people going through one of the + + align:start position:0% +make people going through one of the + + + align:start position:0% +make people going through one of the +most difficult moments in their life + + align:start position:0% +most difficult moments in their life + + + align:start position:0% +most difficult moments in their life +from the family side or from the patient + + align:start position:0% +from the family side or from the patient + + + align:start position:0% +from the family side or from the patient +side in the rooms that are actually wide + + align:start position:0% +side in the rooms that are actually wide + + + align:start position:0% +side in the rooms that are actually wide +with no consideration for design and + + align:start position:0% +with no consideration for design and + + + align:start position:0% +with no consideration for design and +making them more miserable than their + + align:start position:0% +making them more miserable than their + + + align:start position:0% +making them more miserable than their +disease will actually even make them so + + align:start position:0% +disease will actually even make them so + + + align:start position:0% +disease will actually even make them so +there's a lot of there very interesting + + align:start position:0% +there's a lot of there very interesting + + + align:start position:0% +there's a lot of there very interesting +topics Yeah question um heard of any + + align:start position:0% +topics Yeah question um heard of any + + + align:start position:0% +topics Yeah question um heard of any +research based on like carpets and + + align:start position:0% +research based on like carpets and + + + align:start position:0% +research based on like carpets and +allergens I know as walk + + align:start position:0% +allergens I know as walk + + + align:start position:0% +allergens I know as walk +lot in there but seems like builds + + align:start position:0% + + + + align:start position:0% + +don't + + align:start position:0% +don't + + + align:start position:0% +don't +Comfort yeah there are quite a lot of + + align:start position:0% +Comfort yeah there are quite a lot of + + + align:start position:0% +Comfort yeah there are quite a lot of +these things uh out there of like the + + align:start position:0% +these things uh out there of like the + + + align:start position:0% +these things uh out there of like the +the risk like the the problems with uh + + align:start position:0% +the risk like the the problems with uh + + + align:start position:0% +the risk like the the problems with uh +carpets and voc's and and so forth and + + align:start position:0% +carpets and voc's and and so forth and + + + align:start position:0% +carpets and voc's and and so forth and +the D that will make people uh less + + align:start position:0% +the D that will make people uh less + + + align:start position:0% +the D that will make people uh less +healthy or in the schools make Asma + + align:start position:0% +healthy or in the schools make Asma + + + align:start position:0% +healthy or in the schools make Asma +asthma attacks and so forth more likely + + align:start position:0% +asthma attacks and so forth more likely + + + align:start position:0% +asthma attacks and so forth more likely +and so forth like there are a lot of + + align:start position:0% +and so forth like there are a lot of + + + align:start position:0% +and so forth like there are a lot of +these things but the problem is that + + align:start position:0% +these things but the problem is that + + + align:start position:0% +these things but the problem is that +when it comes to + + align:start position:0% +when it comes to + + + align:start position:0% +when it comes to +uh when it comes to materials the + + align:start position:0% +uh when it comes to materials the + + + align:start position:0% +uh when it comes to materials the +problem of thinking about it in a + + align:start position:0% +problem of thinking about it in a + + + align:start position:0% +problem of thinking about it in a +systematic way is that when it comes to + + align:start position:0% +systematic way is that when it comes to + + + align:start position:0% +systematic way is that when it comes to +make decisions for your own building on + + align:start position:0% +make decisions for your own building on + + + align:start position:0% +make decisions for your own building on +how do you upgrade them there is not a + + align:start position:0% +how do you upgrade them there is not a + + + align:start position:0% +how do you upgrade them there is not a +lot of information about any of these + + align:start position:0% +lot of information about any of these + + + align:start position:0% +lot of information about any of these +things composition and treatment along + + align:start position:0% +things composition and treatment along + + + align:start position:0% +things composition and treatment along +the way right so we don't know where + + align:start position:0% +the way right so we don't know where + + + align:start position:0% +the way right so we don't know where +this what kind of pain they put in this + + align:start position:0% +this what kind of pain they put in this + + + align:start position:0% +this what kind of pain they put in this +wood to make it more resistant to + + align:start position:0% +wood to make it more resistant to + + + align:start position:0% +wood to make it more resistant to +different things and so forth it's very + + align:start position:0% +different things and so forth it's very + + + align:start position:0% +different things and so forth it's very +hard to understand the chemical + + align:start position:0% +hard to understand the chemical + + + align:start position:0% +hard to understand the chemical +composition of anything like that you + + align:start position:0% +composition of anything like that you + + + align:start position:0% +composition of anything like that you +will expect that and that's s of one of + + align:start position:0% +will expect that and that's s of one of + + + align:start position:0% +will expect that and that's s of one of +the the discussion points of the healthy + + align:start position:0% +the the discussion points of the healthy + + + align:start position:0% +the the discussion points of the healthy +buildings book of these Harvard + + align:start position:0% +buildings book of these Harvard + + + align:start position:0% +buildings book of these Harvard +professors you will they put it in a + + align:start position:0% +professors you will they put it in a + + + align:start position:0% +professors you will they put it in a +very nice way you will find it crazy + + align:start position:0% +very nice way you will find it crazy + + + align:start position:0% +very nice way you will find it crazy +nowadays if you will buy any can I take + + align:start position:0% +nowadays if you will buy any can I take + + + align:start position:0% +nowadays if you will buy any can I take +this you will buy any drink or any U any + + align:start position:0% +this you will buy any drink or any U any + + + align:start position:0% +this you will buy any drink or any U any +food item and you will not see the + + align:start position:0% +food item and you will not see the + + + align:start position:0% +food item and you will not see the +composition of every single thing that + + align:start position:0% +composition of every single thing that + + + align:start position:0% +composition of every single thing that +came into the production of these guys + + align:start position:0% +came into the production of these guys + + + align:start position:0% +came into the production of these guys +but you cannot see anything at all when + + align:start position:0% +but you cannot see anything at all when + + + align:start position:0% +but you cannot see anything at all when +you buy any building or almost any + + align:start position:0% +you buy any building or almost any + + + align:start position:0% +you buy any building or almost any +building component that you want to + + align:start position:0% +building component that you want to + + + align:start position:0% +building component that you want to +deploy in a building so to have this + + align:start position:0% +deploy in a building so to have this + + + align:start position:0% +deploy in a building so to have this +strategy in a systematic way we are a + + align:start position:0% +strategy in a systematic way we are a + + + align:start position:0% +strategy in a systematic way we are a +long way down the road to to go and that + + align:start position:0% +long way down the road to to go and that + + + align:start position:0% +long way down the road to to go and that +also affects by the way a lot of the + + align:start position:0% +also affects by the way a lot of the + + + align:start position:0% +also affects by the way a lot of the +problems when it comes to Energy + + align:start position:0% +problems when it comes to Energy + + + align:start position:0% +problems when it comes to Energy +Efficiency that we don't have these + + align:start position:0% +Efficiency that we don't have these + + + align:start position:0% +Efficiency that we don't have these +building passports that we actually + + align:start position:0% +building passports that we actually + + + align:start position:0% +building passports that we actually +understand let us understand what is all + + align:start position:0% +understand let us understand what is all + + + align:start position:0% +understand let us understand what is all +the elements and the characteristics and + + align:start position:0% +the elements and the characteristics and + + + align:start position:0% +the elements and the characteristics and +the efficiency and so forth so then we + + align:start position:0% +the efficiency and so forth so then we + + + align:start position:0% +the efficiency and so forth so then we +could actually as as a almost like a + + align:start position:0% +could actually as as a almost like a + + + align:start position:0% +could actually as as a almost like a +Lego type of of work from a engineering + + align:start position:0% +Lego type of of work from a engineering + + + align:start position:0% +Lego type of of work from a engineering +perspective see what type of elements do + + align:start position:0% +perspective see what type of elements do + + + align:start position:0% +perspective see what type of elements do +we need to upgrade to have the biggest + + align:start position:0% +we need to upgrade to have the biggest + + + align:start position:0% +we need to upgrade to have the biggest +impact because we bought something that + + align:start position:0% +impact because we bought something that + + + align:start position:0% +impact because we bought something that +we don't know what has on and we have to + + align:start position:0% +we don't know what has on and we have to + + + align:start position:0% +we don't know what has on and we have to +even like break the roofs and so forth + + align:start position:0% +even like break the roofs and so forth + + + align:start position:0% +even like break the roofs and so forth +to understand what is really in there or + + align:start position:0% +to understand what is really in there or + + + align:start position:0% +to understand what is really in there or +get into the the machines and so forth + + align:start position:0% +get into the the machines and so forth + + + align:start position:0% +get into the the machines and so forth +so it's is very hard we don't have a + + align:start position:0% +so it's is very hard we don't have a + + + align:start position:0% +so it's is very hard we don't have a +systematic information system on + + align:start position:0% +systematic information system on + + + align:start position:0% +systematic information system on +components in buildings and that's + + align:start position:0% +components in buildings and that's + + + align:start position:0% +components in buildings and that's +something that will require those type + + align:start position:0% +something that will require those type + + + align:start position:0% +something that will require those type +of strategies to to + + align:start position:0% +of strategies to to + + + align:start position:0% +of strategies to to +flourish yes so the light system and the + + align:start position:0% + + + + align:start position:0% + +planting to the house building because + + align:start position:0% +planting to the house building because + + + align:start position:0% +planting to the house building because +before IED in the headquarter about the + + align:start position:0% +before IED in the headquarter about the + + + align:start position:0% +before IED in the headquarter about the +house building and prity standard prity + + align:start position:0% +house building and prity standard prity + + + align:start position:0% +house building and prity standard prity +High about the W certificate so planting + + align:start position:0% +High about the W certificate so planting + + + align:start position:0% +High about the W certificate so planting +is everywhere in our office and control + + align:start position:0% +is everywhere in our office and control + + + align:start position:0% +is everywhere in our office and control +the life system M so is important + + align:start position:0% +the life system M so is important + + + align:start position:0% +the life system M so is important +yeah yeah very important yeah yeah yeah + + align:start position:0% +yeah yeah very important yeah yeah yeah + + + align:start position:0% +yeah yeah very important yeah yeah yeah +I mean lighting is something that is + + align:start position:0% +I mean lighting is something that is + + + align:start position:0% +I mean lighting is something that is +definitely affecting a lot of our bio + + align:start position:0% +definitely affecting a lot of our bio + + + align:start position:0% +definitely affecting a lot of our bio +rhythms and so forth and then you can + + align:start position:0% +rhythms and so forth and then you can + + + align:start position:0% +rhythms and so forth and then you can +sort of go against the clock and the day + + align:start position:0% +sort of go against the clock and the day + + + align:start position:0% +sort of go against the clock and the day +if you flatten it out over the entire + + align:start position:0% +if you flatten it out over the entire + + + align:start position:0% +if you flatten it out over the entire +day all right today we are going to talk + + align:start position:0% +day all right today we are going to talk + + + align:start position:0% +day all right today we are going to talk +about mainly for the the sake of time + + align:start position:0% +about mainly for the the sake of time + + + align:start position:0% +about mainly for the the sake of time +because otherwise we will have to be + + align:start position:0% +because otherwise we will have to be + + + align:start position:0% +because otherwise we will have to be +here as long as the studio class the + + align:start position:0% +here as long as the studio class the + + + align:start position:0% +here as long as the studio class the +other day or Ventures and it's really + + align:start position:0% +other day or Ventures and it's really + + + align:start position:0% +other day or Ventures and it's really +not the purpose to lock you up here for + + align:start position:0% +not the purpose to lock you up here for + + + align:start position:0% +not the purpose to lock you up here for +for five six hours today so I'm going to + + align:start position:0% +for five six hours today so I'm going to + + + align:start position:0% +for five six hours today so I'm going to +give you we are going to walk through + + align:start position:0% +give you we are going to walk through + + + align:start position:0% +give you we are going to walk through +the the whole value chain of ventilation + + align:start position:0% +the the whole value chain of ventilation + + + align:start position:0% +the the whole value chain of ventilation +and air quality just to show how to + + align:start position:0% +and air quality just to show how to + + + align:start position:0% +and air quality just to show how to +think about it how to be critical about + + align:start position:0% +think about it how to be critical about + + + align:start position:0% +think about it how to be critical about +the the science how to be uh + + align:start position:0% +the the science how to be uh + + + align:start position:0% +the the science how to be uh +knowledgeable about how tenants will + + align:start position:0% +knowledgeable about how tenants will + + + align:start position:0% +knowledgeable about how tenants will +think about it and also how to discuss + + align:start position:0% +think about it and also how to discuss + + + align:start position:0% +think about it and also how to discuss +what are the barriers to to it right so + + align:start position:0% +what are the barriers to to it right so + + + align:start position:0% +what are the barriers to to it right so +let's go through two basic and then + + align:start position:0% +let's go through two basic and then + + + align:start position:0% +let's go through two basic and then +climb from the very bottom all the way + + align:start position:0% +climb from the very bottom all the way + + + align:start position:0% +climb from the very bottom all the way +to the very up and you will tell me when + + align:start position:0% +to the very up and you will tell me when + + + align:start position:0% +to the very up and you will tell me when +you have any questions and comments and + + align:start position:0% +you have any questions and comments and + + + align:start position:0% +you have any questions and comments and +so forth okay I like this Lively + + align:start position:0% +so forth okay I like this Lively + + + align:start position:0% +so forth okay I like this Lively +discussion so I'm very happy today I + + align:start position:0% +discussion so I'm very happy today I + + + align:start position:0% +discussion so I'm very happy today I +think that we are beating the the + + align:start position:0% +think that we are beating the the + + + align:start position:0% +think that we are beating the the +previous class last year it was very + + align:start position:0% +previous class last year it was very + + + align:start position:0% +previous class last year it was very +Lively yeah you remember IIs you were + + align:start position:0% +Lively yeah you remember IIs you were + + + align:start position:0% +Lively yeah you remember IIs you were +always a quiet guy though + + align:start position:0% +always a quiet guy though + + + align:start position:0% +always a quiet guy though +but very very smart that's why we picked + + align:start position:0% +but very very smart that's why we picked + + + align:start position:0% +but very very smart that's why we picked +him to TA and I actually even his thesis + + align:start position:0% +him to TA and I actually even his thesis + + + align:start position:0% +him to TA and I actually even his thesis +adviser but quiet you're are quiet by + + align:start position:0% +adviser but quiet you're are quiet by + + + align:start position:0% +adviser but quiet you're are quiet by +nakot Taco he talks tomorrow you can + + align:start position:0% +nakot Taco he talks tomorrow you can + + + align:start position:0% +nakot Taco he talks tomorrow you can +come you do do do you you see you put + + align:start position:0% +come you do do do you you see you put + + + align:start position:0% +come you do do do you you see you put +him in nakot Taco he talks that's the + + align:start position:0% +him in nakot Taco he talks that's the + + + align:start position:0% +him in nakot Taco he talks that's the +the impact of buildings all right + + align:start position:0% +the impact of buildings all right + + + align:start position:0% +the impact of buildings all right +so the + + align:start position:0% +so the + + + align:start position:0% +so the +impact exactly more that I don't know I + + align:start position:0% +impact exactly more that I don't know I + + + align:start position:0% +impact exactly more that I don't know I +I haven't that I I cannot say that so H + + align:start position:0% +I haven't that I I cannot say that so H + + + align:start position:0% +I haven't that I I cannot say that so H +all right so first thing that we are + + align:start position:0% +all right so first thing that we are + + + align:start position:0% +all right so first thing that we are +going to do is how we are going to + + align:start position:0% +going to do is how we are going to + + + align:start position:0% +going to do is how we are going to +connect these different strategies how + + align:start position:0% +connect these different strategies how + + + align:start position:0% +connect these different strategies how +are we going to evaluate the impact so I + + align:start position:0% +are we going to evaluate the impact so I + + + align:start position:0% +are we going to evaluate the impact so I +don't know where you guys done any work + + align:start position:0% +don't know where you guys done any work + + + align:start position:0% +don't know where you guys done any work +on uh on funds but you have these impact + + align:start position:0% +on uh on funds but you have these impact + + + align:start position:0% +on uh on funds but you have these impact +funds what they do all the time is to + + align:start position:0% +funds what they do all the time is to + + + align:start position:0% +funds what they do all the time is to +one of the things that you need to do to + + align:start position:0% +one of the things that you need to do to + + + align:start position:0% +one of the things that you need to do to +create an impact fund is to show the + + align:start position:0% +create an impact fund is to show the + + + align:start position:0% +create an impact fund is to show the +impact that you do that you create with + + align:start position:0% +impact that you do that you create with + + + align:start position:0% +impact that you do that you create with +the Investments that you do with the + + align:start position:0% +the Investments that you do with the + + + align:start position:0% +the Investments that you do with the +money that you have in the fund so let's + + align:start position:0% +money that you have in the fund so let's + + + align:start position:0% +money that you have in the fund so let's +think about healthy building strategic + + align:start position:0% +think about healthy building strategic + + + align:start position:0% +think about healthy building strategic +from the impact fund perspective so how + + align:start position:0% +from the impact fund perspective so how + + + align:start position:0% +from the impact fund perspective so how +we actually can are able to evaluate + + align:start position:0% +we actually can are able to evaluate + + + align:start position:0% +we actually can are able to evaluate +impact in a way that we can go to + + align:start position:0% +impact in a way that we can go to + + + align:start position:0% +impact in a way that we can go to +investors developers and Pitch it to + + align:start position:0% +investors developers and Pitch it to + + + align:start position:0% +investors developers and Pitch it to +them in a way that say Hey you want to + + align:start position:0% +them in a way that say Hey you want to + + + align:start position:0% +them in a way that say Hey you want to +can generate a building that can promote + + align:start position:0% +can generate a building that can promote + + + align:start position:0% +can generate a building that can promote +X this is this is one technology that + + align:start position:0% +X this is this is one technology that + + + align:start position:0% +X this is this is one technology that +you need to deploy because I know what + + align:start position:0% +you need to deploy because I know what + + + align:start position:0% +you need to deploy because I know what +is the impact of that for that there are + + align:start position:0% +is the impact of that for that there are + + + align:start position:0% +is the impact of that for that there are +multiple ways to to think about it but + + align:start position:0% +multiple ways to to think about it but + + + align:start position:0% +multiple ways to to think about it but +one of the the most intuitive ones that + + align:start position:0% +one of the the most intuitive ones that + + + align:start position:0% +one of the the most intuitive ones that +I that I think especially when it comes + + align:start position:0% +I that I think especially when it comes + + + align:start position:0% +I that I think especially when it comes +to air quality is coming from the uh um + + align:start position:0% +to air quality is coming from the uh um + + + align:start position:0% +to air quality is coming from the uh um +environmental science and the and uh the + + align:start position:0% +environmental science and the and uh the + + + align:start position:0% +environmental science and the and uh the +environmental science literature where + + align:start position:0% +environmental science literature where + + + align:start position:0% +environmental science literature where +when you want to evaluate the impact of + + align:start position:0% +when you want to evaluate the impact of + + + align:start position:0% +when you want to evaluate the impact of +any threat any poisoning element you + + align:start position:0% +any threat any poisoning element you + + + align:start position:0% +any threat any poisoning element you +have different steps so you have first + + align:start position:0% +have different steps so you have first + + + align:start position:0% +have different steps so you have first +you need to understand what is the the + + align:start position:0% +you need to understand what is the the + + + align:start position:0% +you need to understand what is the the +concentration of that threat right so if + + align:start position:0% +concentration of that threat right so if + + + align:start position:0% +concentration of that threat right so if +you want to think about what is the + + align:start position:0% +you want to think about what is the + + + align:start position:0% +you want to think about what is the +impact of ozone or or voc's or PM 2.5 or + + align:start position:0% +impact of ozone or or voc's or PM 2.5 or + + + align:start position:0% +impact of ozone or or voc's or PM 2.5 or +something on someone in a given building + + align:start position:0% +something on someone in a given building + + + align:start position:0% +something on someone in a given building +or in a given part of the city you first + + align:start position:0% +or in a given part of the city you first + + + align:start position:0% +or in a given part of the city you first +need to know how high is the + + align:start position:0% +need to know how high is the + + + align:start position:0% +need to know how high is the +concentration of that pollutant or or + + align:start position:0% +concentration of that pollutant or or + + + align:start position:0% +concentration of that pollutant or or +chemical in that area so the first thing + + align:start position:0% +chemical in that area so the first thing + + + align:start position:0% +chemical in that area so the first thing +we need to do is assess how uh how large + + align:start position:0% +we need to do is assess how uh how large + + + align:start position:0% +we need to do is assess how uh how large +is the threat how much of that pollutant + + align:start position:0% +is the threat how much of that pollutant + + + align:start position:0% +is the threat how much of that pollutant +that we want to reduce with those + + align:start position:0% +that we want to reduce with those + + + align:start position:0% +that we want to reduce with those +Investments is and then we need to know + + align:start position:0% +Investments is and then we need to know + + + align:start position:0% +Investments is and then we need to know +because ultimately what we want to + + align:start position:0% +because ultimately what we want to + + + align:start position:0% +because ultimately what we want to +understand is the impact on people we + + align:start position:0% +understand is the impact on people we + + + align:start position:0% +understand is the impact on people we +need to understand for everyone that + + align:start position:0% +need to understand for everyone that + + + align:start position:0% +need to understand for everyone that +passes by or every one of the target uh + + align:start position:0% +passes by or every one of the target uh + + + align:start position:0% +passes by or every one of the target uh +group that we have the occupants the + + align:start position:0% +group that we have the occupants the + + + align:start position:0% +group that we have the occupants the +employees and so for how much exposure + + align:start position:0% +employees and so for how much exposure + + + align:start position:0% +employees and so for how much exposure +they get and that is break out in two + + align:start position:0% +they get and that is break out in two + + + align:start position:0% +they get and that is break out in two +parts how much they get exposed every + + align:start position:0% +parts how much they get exposed every + + + align:start position:0% +parts how much they get exposed every +time that they are exposed and how often + + align:start position:0% +time that they are exposed and how often + + + align:start position:0% +time that they are exposed and how often +they get Expose and let me give you an + + align:start position:0% +they get Expose and let me give you an + + + align:start position:0% +they get Expose and let me give you an +example for example we get this kitchen + + align:start position:0% +example for example we get this kitchen + + + align:start position:0% +example for example we get this kitchen +there that is locked up to almost + + align:start position:0% +there that is locked up to almost + + + align:start position:0% +there that is locked up to almost +everyone except for Chichi right your + + align:start position:0% +everyone except for Chichi right your + + + align:start position:0% +everyone except for Chichi right your +private kitchen no I I don't even have + + align:start position:0% +private kitchen no I I don't even have + + + align:start position:0% +private kitchen no I I don't even have +the researchers and the students if we + + align:start position:0% +the researchers and the students if we + + + align:start position:0% +the researchers and the students if we +want to use a kitchen become our + + align:start position:0% +want to use a kitchen become our + + + align:start position:0% +want to use a kitchen become our +researchers notching is always good uh + + align:start position:0% +researchers notching is always good uh + + + align:start position:0% +researchers notching is always good uh +so there there might be like a gas + + align:start position:0% +so there there might be like a gas + + + align:start position:0% +so there there might be like a gas +leakage and almost nobody will get a + + align:start position:0% +leakage and almost nobody will get a + + + align:start position:0% +leakage and almost nobody will get a +problem because nobody is there almost + + align:start position:0% +problem because nobody is there almost + + + align:start position:0% +problem because nobody is there almost +any time I've been there probably twice + + align:start position:0% +any time I've been there probably twice + + + align:start position:0% +any time I've been there probably twice +in four years um so that's one of the + + align:start position:0% +in four years um so that's one of the + + + align:start position:0% +in four years um so that's one of the +examples that if you really want to be a + + align:start position:0% +examples that if you really want to be a + + + align:start position:0% +examples that if you really want to be a +meaningful investment even if you have a + + align:start position:0% +meaningful investment even if you have a + + + align:start position:0% +meaningful investment even if you have a +high concentration of a problem there of + + align:start position:0% +high concentration of a problem there of + + + align:start position:0% +high concentration of a problem there of +a of a pollutant there you probably + + align:start position:0% +a of a pollutant there you probably + + + align:start position:0% +a of a pollutant there you probably +don't have the be the best investment in + + align:start position:0% +don't have the be the best investment in + + + align:start position:0% +don't have the be the best investment in +terms of improving health because nobody + + align:start position:0% +terms of improving health because nobody + + + align:start position:0% +terms of improving health because nobody +really gets exposed now a gas lick is + + align:start position:0% +really gets exposed now a gas lick is + + + align:start position:0% +really gets exposed now a gas lick is +very harmful right so if you spend there + + align:start position:0% +very harmful right so if you spend there + + + align:start position:0% +very harmful right so if you spend there +few minutes probably get passed out and + + align:start position:0% +few minutes probably get passed out and + + + align:start position:0% +few minutes probably get passed out and +you might actually die there are other + + align:start position:0% +you might actually die there are other + + + align:start position:0% +you might actually die there are other +things like poor ventilation that are + + align:start position:0% +things like poor ventilation that are + + + align:start position:0% +things like poor ventilation that are +definitely less harmful but everyone is + + align:start position:0% +definitely less harmful but everyone is + + + align:start position:0% +definitely less harmful but everyone is +exposed to for example in this room we + + align:start position:0% +exposed to for example in this room we + + + align:start position:0% +exposed to for example in this room we +keep climbing up not not yet there but + + align:start position:0% +keep climbing up not not yet there but + + + align:start position:0% +keep climbing up not not yet there but +imagine that that that guy goes double + + align:start position:0% +imagine that that that guy goes double + + + align:start position:0% +imagine that that that guy goes double +none of us will die maybe some of them + + align:start position:0% +none of us will die maybe some of them + + + align:start position:0% +none of us will die maybe some of them +some of us will get sleepy but all of us + + align:start position:0% +some of us will get sleepy but all of us + + + align:start position:0% +some of us will get sleepy but all of us +are exposed and for several hours during + + align:start position:0% +are exposed and for several hours during + + + align:start position:0% +are exposed and for several hours during +the day so then when it comes to + + align:start position:0% +the day so then when it comes to + + + align:start position:0% +the day so then when it comes to +improving that one it's much better + + align:start position:0% +improving that one it's much better + + + align:start position:0% +improving that one it's much better +because yeah the concentration or the + + align:start position:0% +because yeah the concentration or the + + + align:start position:0% +because yeah the concentration or the +harm of that concentration is much lower + + align:start position:0% +harm of that concentration is much lower + + + align:start position:0% +harm of that concentration is much lower +but the the exposure is much larger so + + align:start position:0% +but the the exposure is much larger so + + + align:start position:0% +but the the exposure is much larger so +this is what we need to to understand + + align:start position:0% +this is what we need to to understand + + + align:start position:0% +this is what we need to to understand +very well first how much we are exposed + + align:start position:0% +very well first how much we are exposed + + + align:start position:0% +very well first how much we are exposed +so what is the concentration of whatever + + align:start position:0% +so what is the concentration of whatever + + + align:start position:0% +so what is the concentration of whatever +Factor we want to improve how harmful it + + align:start position:0% +Factor we want to improve how harmful it + + + align:start position:0% +Factor we want to improve how harmful it +is and that will require to look into + + align:start position:0% +is and that will require to look into + + + align:start position:0% +is and that will require to look into +the the the literature and the standards + + align:start position:0% +the the the literature and the standards + + + align:start position:0% +the the the literature and the standards +from ashr from EPA and so forth to + + align:start position:0% +from ashr from EPA and so forth to + + + align:start position:0% +from ashr from EPA and so forth to +understand how harmful that is so it's + + align:start position:0% +understand how harmful that is so it's + + + align:start position:0% +understand how harmful that is so it's +not the same uh being exposed to uh C o + + align:start position:0% +not the same uh being exposed to uh C o + + + align:start position:0% +not the same uh being exposed to uh C o +or being exposed to nox or than being + + align:start position:0% +or being exposed to nox or than being + + + align:start position:0% +or being exposed to nox or than being +exposed to voccs or CO2 those things is + + align:start position:0% +exposed to voccs or CO2 those things is + + + align:start position:0% +exposed to voccs or CO2 those things is +something that you need to understand + + align:start position:0% +something that you need to understand + + + align:start position:0% +something that you need to understand +and that's why the public health + + align:start position:0% +and that's why the public health + + + align:start position:0% +and that's why the public health +literature epidemiologist and so forth + + align:start position:0% +literature epidemiologist and so forth + + + align:start position:0% +literature epidemiologist and so forth +earn their lives so we can break the + + align:start position:0% +earn their lives so we can break the + + + align:start position:0% +earn their lives so we can break the +process of understanding the impact of + + align:start position:0% +process of understanding the impact of + + + align:start position:0% +process of understanding the impact of +an investment in two side so + + align:start position:0% +an investment in two side so + + + align:start position:0% +an investment in two side so +understanding the Baseline concentration + + align:start position:0% +understanding the Baseline concentration + + + align:start position:0% +understanding the Baseline concentration +and how much we actually uh reduce the + + align:start position:0% +and how much we actually uh reduce the + + + align:start position:0% +and how much we actually uh reduce the +concentration and then understanding the + + align:start position:0% +concentration and then understanding the + + + align:start position:0% +concentration and then understanding the +actual exposure and the and the actual + + align:start position:0% +actual exposure and the and the actual + + + align:start position:0% +actual exposure and the and the actual +impact on on the people so there's going + + align:start position:0% +impact on on the people so there's going + + + align:start position:0% +impact on on the people so there's going +to be an assessment part and there's + + align:start position:0% +to be an assessment part and there's + + + align:start position:0% +to be an assessment part and there's +going to be an attribution part that + + align:start position:0% +going to be an attribution part that + + + align:start position:0% +going to be an attribution part that +that is going to ultimately connect to + + align:start position:0% +that is going to ultimately connect to + + + align:start position:0% +that is going to ultimately connect to +the health and wellbeing and performance + + align:start position:0% +the health and wellbeing and performance + + + align:start position:0% +the health and wellbeing and performance +of people so if we don't understand that + + align:start position:0% +of people so if we don't understand that + + + align:start position:0% +of people so if we don't understand that +black box on how people are exposed to + + align:start position:0% +black box on how people are exposed to + + + align:start position:0% +black box on how people are exposed to +that investment and how people are + + align:start position:0% +that investment and how people are + + + align:start position:0% +that investment and how people are +exposed to those threats then it doesn't + + align:start position:0% +exposed to those threats then it doesn't + + + align:start position:0% +exposed to those threats then it doesn't +matter whether we are measuring + + align:start position:0% +matter whether we are measuring + + + align:start position:0% +matter whether we are measuring +everything all the time we will not be + + align:start position:0% +everything all the time we will not be + + + align:start position:0% +everything all the time we will not be +able to connect an investment in the + + align:start position:0% +able to connect an investment in the + + + align:start position:0% +able to connect an investment in the +building to the people that are using + + align:start position:0% +building to the people that are using + + + align:start position:0% +building to the people that are using +that building is that clear enough or we + + align:start position:0% +that building is that clear enough or we + + + align:start position:0% +that building is that clear enough or we +make it more + + align:start position:0% +make it more + + + align:start position:0% +make it more +complicated clear enough Julio how can + + align:start position:0% +complicated clear enough Julio how can + + + align:start position:0% +complicated clear enough Julio how can +you compare the impact that a PO has + + align:start position:0% +you compare the impact that a PO has + + + align:start position:0% +you compare the impact that a PO has +that a + + align:start position:0% +that a + + + align:start position:0% +that a +PO how can you + + align:start position:0% + + + + align:start position:0% + +compare to kill you have to put it on a + + align:start position:0% +compare to kill you have to put it on a + + + align:start position:0% +compare to kill you have to put it on a +scale right well that is yes so there is + + align:start position:0% +scale right well that is yes so there is + + + align:start position:0% +scale right well that is yes so there is +one thing like kind know there's some uh + + align:start position:0% +one thing like kind know there's some uh + + + align:start position:0% +one thing like kind know there's some uh +basic uh tools of exposure science that + + align:start position:0% +basic uh tools of exposure science that + + + align:start position:0% +basic uh tools of exposure science that +is you have the dose response function + + align:start position:0% +is you have the dose response function + + + align:start position:0% +is you have the dose response function +so that's something that you can compare + + align:start position:0% +so that's something that you can compare + + + align:start position:0% +so that's something that you can compare +with the same outcome what will be the + + align:start position:0% +with the same outcome what will be the + + + align:start position:0% +with the same outcome what will be the +the impact of every unit of intake of + + align:start position:0% +the impact of every unit of intake of + + + align:start position:0% +the impact of every unit of intake of +that polutan on that given outcome when + + align:start position:0% +that polutan on that given outcome when + + + align:start position:0% +that polutan on that given outcome when +you want to compare across outcomes that + + align:start position:0% +you want to compare across outcomes that + + + align:start position:0% +you want to compare across outcomes that +is something that comes down to what do + + align:start position:0% +is something that comes down to what do + + + align:start position:0% +is something that comes down to what do +you value as a company or what do you + + align:start position:0% +you value as a company or what do you + + + align:start position:0% +you value as a company or what do you +value as a um as a country right so how + + align:start position:0% +value as a um as a country right so how + + + align:start position:0% +value as a um as a country right so how +much do you value uh one person dying + + align:start position:0% +much do you value uh one person dying + + + align:start position:0% +much do you value uh one person dying +versus 300 kids scoring lower in a in a + + align:start position:0% +versus 300 kids scoring lower in a in a + + + align:start position:0% +versus 300 kids scoring lower in a in a +in a test that will let them uh get a a + + align:start position:0% +in a test that will let them uh get a a + + + align:start position:0% +in a test that will let them uh get a a +worse job afterwards so there is some + + align:start position:0% +worse job afterwards so there is some + + + align:start position:0% +worse job afterwards so there is some +subjective part there that will come + + align:start position:0% +subjective part there that will come + + + align:start position:0% +subjective part there that will come +down to policymaking and and and + + align:start position:0% +down to policymaking and and and + + + align:start position:0% +down to policymaking and and and +preferences and so forth of people that + + align:start position:0% +preferences and so forth of people that + + + align:start position:0% +preferences and so forth of people that +are are just not objective like it's + + align:start position:0% +are are just not objective like it's + + + align:start position:0% +are are just not objective like it's +just like we have a lot of discussion + + align:start position:0% +just like we have a lot of discussion + + + align:start position:0% +just like we have a lot of discussion +about the the value of uh of a of a life + + align:start position:0% +about the the value of uh of a of a life + + + align:start position:0% +about the the value of uh of a of a life +the value of an statistical life that's + + align:start position:0% +the value of an statistical life that's + + + align:start position:0% +the value of an statistical life that's +how they call it in in that those are + + align:start position:0% +how they call it in in that those are + + + align:start position:0% +how they call it in in that those are +things very subjective at the end of the + + align:start position:0% +things very subjective at the end of the + + + align:start position:0% +things very subjective at the end of the +day it comes down to the priorities of + + align:start position:0% +day it comes down to the priorities of + + + align:start position:0% +day it comes down to the priorities of +your firm or your local government of + + align:start position:0% +your firm or your local government of + + + align:start position:0% +your firm or your local government of +yourself if you are thinking about how + + align:start position:0% +yourself if you are thinking about how + + + align:start position:0% +yourself if you are thinking about how +do you want to improve the family your + + align:start position:0% +do you want to improve the family your + + + align:start position:0% +do you want to improve the family your +your family's uh + + align:start position:0% +your family's uh + + + align:start position:0% +your family's uh +situation anything else yeah a very + + align:start position:0% +situation anything else yeah a very + + + align:start position:0% +situation anything else yeah a very +interesting phenomenon + + align:start position:0% +interesting phenomenon + + + align:start position:0% +interesting phenomenon +during uh + + align:start position:0% +during uh + + + align:start position:0% +during uh +2018 uh 2015 to + + align:start position:0% +2018 uh 2015 to + + + align:start position:0% +2018 uh 2015 to +2018 Bing uh polluted pollution is very + + align:start position:0% +2018 Bing uh polluted pollution is very + + + align:start position:0% +2018 Bing uh polluted pollution is very +serious and protect our house so + + align:start position:0% +serious and protect our house so + + + align:start position:0% +serious and protect our house so +developer who prefer to build the house + + align:start position:0% +developer who prefer to build the house + + + align:start position:0% +developer who prefer to build the house +house building but after that uh because + + align:start position:0% +house building but after that uh because + + + align:start position:0% +house building but after that uh because +the pollution Improvement and develop + + align:start position:0% +the pollution Improvement and develop + + + align:start position:0% +the pollution Improvement and develop +per now prer build the house building + + align:start position:0% +per now prer build the house building + + + align:start position:0% +per now prer build the house building +because it's pretty high cost and the + + align:start position:0% +because it's pretty high cost and the + + + align:start position:0% +because it's pretty high cost and the +rent May a little increase so yeah it's + + align:start position:0% +rent May a little increase so yeah it's + + + align:start position:0% +rent May a little increase so yeah it's +very interest yeah Beijing is also a + + align:start position:0% +very interest yeah Beijing is also a + + + align:start position:0% +very interest yeah Beijing is also a +good example right because Beijing you + + align:start position:0% +good example right because Beijing you + + + align:start position:0% +good example right because Beijing you +have two things going in parallel on the + + align:start position:0% +have two things going in parallel on the + + + align:start position:0% +have two things going in parallel on the +one side the local government uh and the + + align:start position:0% +one side the local government uh and the + + + align:start position:0% +one side the local government uh and the +same as the national government tries to + + align:start position:0% +same as the national government tries to + + + align:start position:0% +same as the national government tries to +put down pollution that she's a lot of + + align:start position:0% +put down pollution that she's a lot of + + + align:start position:0% +put down pollution that she's a lot of +work there she's the expert and then on + + align:start position:0% +work there she's the expert and then on + + + align:start position:0% +work there she's the expert and then on +the other side you get people exactly so + + align:start position:0% +the other side you get people exactly so + + + align:start position:0% +the other side you get people exactly so +so the the threat the outdoor threat is + + align:start position:0% +so the the threat the outdoor threat is + + + align:start position:0% +so the the threat the outdoor threat is +going down and therefore what you are + + align:start position:0% +going down and therefore what you are + + + align:start position:0% +going down and therefore what you are +preventing people from being exposed to + + align:start position:0% +preventing people from being exposed to + + + align:start position:0% +preventing people from being exposed to +is also going down so then the the the + + align:start position:0% +is also going down so then the the the + + + align:start position:0% +is also going down so then the the the +benefits of improving filtration in + + align:start position:0% +benefits of improving filtration in + + + align:start position:0% +benefits of improving filtration in +China is start to be less problematic + + align:start position:0% +China is start to be less problematic + + + align:start position:0% +China is start to be less problematic +than when you go back to 10 years ago + + align:start position:0% +than when you go back to 10 years ago + + + align:start position:0% +than when you go back to 10 years ago +when or 15 years ago when was the the + + align:start position:0% +when or 15 years ago when was the the + + + align:start position:0% +when or 15 years ago when was the the +the peak of pollution c yeah I think + + align:start position:0% +the peak of pollution c yeah I think + + + align:start position:0% +the peak of pollution c yeah I think +that's more nuanced because although the + + align:start position:0% +that's more nuanced because although the + + + align:start position:0% +that's more nuanced because although the +absolute level of the air pollution is + + align:start position:0% +absolute level of the air pollution is + + + align:start position:0% +absolute level of the air pollution is +going down maybe thanks to the + + align:start position:0% +going down maybe thanks to the + + + align:start position:0% +going down maybe thanks to the +government regulation but people's + + align:start position:0% +government regulation but people's + + + align:start position:0% +government regulation but people's +awareness is going up right so the + + align:start position:0% +awareness is going up right so the + + + align:start position:0% +awareness is going up right so the +awareness going up so they more and more + + align:start position:0% +awareness going up so they more and more + + + align:start position:0% +awareness going up so they more and more +people to pay higher PR higher price for + + align:start position:0% +people to pay higher PR higher price for + + + align:start position:0% +people to pay higher PR higher price for +lower uh lower air pollution so the + + align:start position:0% +lower uh lower air pollution so the + + + align:start position:0% +lower uh lower air pollution so the +absolute level may be down but now + + align:start position:0% +absolute level may be down but now + + + align:start position:0% +absolute level may be down but now +people are more and more worried about + + align:start position:0% +people are more and more worried about + + + align:start position:0% +people are more and more worried about +this and they care more so they still + + align:start position:0% +this and they care more so they still + + + align:start position:0% +this and they care more so they still +want healthy + + align:start position:0% +want healthy + + + align:start position:0% +want healthy +buildings and we know that because of + + align:start position:0% +buildings and we know that because of + + + align:start position:0% +buildings and we know that because of +your + + align:start position:0% +your + + + align:start position:0% +your +work it's true but actually developer + + align:start position:0% +work it's true but actually developer + + + align:start position:0% +work it's true but actually developer +and customer to prer the Green + + align:start position:0% +and customer to prer the Green + + + align:start position:0% +and customer to prer the Green +Building that house building is the cost + + align:start position:0% +Building that house building is the cost + + + align:start position:0% +Building that house building is the cost +is + + align:start position:0% +is + + + align:start position:0% +is +the great building yeah the features + + align:start position:0% +the great building yeah the features + + + align:start position:0% +the great building yeah the features +yeah it's not cheap that's why we are + + align:start position:0% +yeah it's not cheap that's why we are + + + align:start position:0% +yeah it's not cheap that's why we are +here um okay so in the in the assessment + + align:start position:0% +here um okay so in the in the assessment + + + align:start position:0% +here um okay so in the in the assessment +part into the detection of how big is + + align:start position:0% +part into the detection of how big is + + + align:start position:0% +part into the detection of how big is +the problem and how much actually we + + align:start position:0% +the problem and how much actually we + + + align:start position:0% +the problem and how much actually we +have do a threat in our building one of + + align:start position:0% +have do a threat in our building one of + + + align:start position:0% +have do a threat in our building one of +the things that is very uh powerful in + + align:start position:0% +the things that is very uh powerful in + + + align:start position:0% +the things that is very uh powerful in +the real estate industry and Engineering + + align:start position:0% +the real estate industry and Engineering + + + align:start position:0% +the real estate industry and Engineering +side is that the price of these guys of + + align:start position:0% +side is that the price of these guys of + + + align:start position:0% +side is that the price of these guys of +Those sensors is going down dramatically + + align:start position:0% +Those sensors is going down dramatically + + + align:start position:0% +Those sensors is going down dramatically +so it used to be that something that + + align:start position:0% +so it used to be that something that + + + align:start position:0% +so it used to be that something that +will measure CO2 with any + + align:start position:0% +will measure CO2 with any + + + align:start position:0% +will measure CO2 with any +ER trustworthy accuracy will cost like + + align:start position:0% +ER trustworthy accuracy will cost like + + + align:start position:0% +ER trustworthy accuracy will cost like +$10,000 and this guy cost me like2 + + align:start position:0% +$10,000 and this guy cost me like2 + + + align:start position:0% +$10,000 and this guy cost me like2 +200 uh so it's very big drop and also + + align:start position:0% +200 uh so it's very big drop and also + + + align:start position:0% +200 uh so it's very big drop and also +the the the connection to the internet + + align:start position:0% +the the the connection to the internet + + + align:start position:0% +the the the connection to the internet +also makes that the The Human Side of + + align:start position:0% +also makes that the The Human Side of + + + align:start position:0% +also makes that the The Human Side of +operating those devices is much much + + align:start position:0% +operating those devices is much much + + + align:start position:0% +operating those devices is much much +lower because beforehand I would have to + + align:start position:0% +lower because beforehand I would have to + + + align:start position:0% +lower because beforehand I would have to +have one person going with it all over + + align:start position:0% +have one person going with it all over + + + align:start position:0% +have one person going with it all over +the place and pay that salary to measure + + align:start position:0% +the place and pay that salary to measure + + + align:start position:0% +the place and pay that salary to measure +anything and to do an assessment while + + align:start position:0% +anything and to do an assessment while + + + align:start position:0% +anything and to do an assessment while +now I can just connect these guys to the + + align:start position:0% +now I can just connect these guys to the + + + align:start position:0% +now I can just connect these guys to the +internet they will be loading all the + + align:start position:0% +internet they will be loading all the + + + align:start position:0% +internet they will be loading all the +all the time data and that will + + align:start position:0% +all the time data and that will + + + align:start position:0% +all the time data and that will +ultimately uh generate give me the the + + align:start position:0% +ultimately uh generate give me the the + + + align:start position:0% +ultimately uh generate give me the the +answer of how big is the pollutant + + align:start position:0% +answer of how big is the pollutant + + + align:start position:0% +answer of how big is the pollutant +concentration and how big is the problem + + align:start position:0% +concentration and how big is the problem + + + align:start position:0% +concentration and how big is the problem +and so forth and on the other side the + + align:start position:0% +and so forth and on the other side the + + + align:start position:0% +and so forth and on the other side the +other sanana she's working on very + + align:start position:0% +other sanana she's working on very + + + align:start position:0% +other sanana she's working on very +exciting project downstairs your + + align:start position:0% +exciting project downstairs your + + + align:start position:0% +exciting project downstairs your +sensible City lab uh City scanner right + + align:start position:0% +sensible City lab uh City scanner right + + + align:start position:0% +sensible City lab uh City scanner right +do you want to say something about that + + align:start position:0% +do you want to say something about that + + + align:start position:0% +do you want to say something about that +how big is the pollution in this area + + align:start position:0% +how big is the pollution in this area + + + align:start position:0% +how big is the pollution in this area +yeah actually the pollution in cabridge + + align:start position:0% +yeah actually the pollution in cabridge + + + align:start position:0% +yeah actually the pollution in cabridge +compared to a lot of the rest of the + + align:start position:0% +compared to a lot of the rest of the + + + align:start position:0% +compared to a lot of the rest of the +world as you saw like 90% of the Worlds + + align:start position:0% +world as you saw like 90% of the Worlds + + + align:start position:0% +world as you saw like 90% of the Worlds +uh is is pretty decent here overall but + + align:start position:0% +uh is is pretty decent here overall but + + + align:start position:0% +uh is is pretty decent here overall but +there's High spao temporal variability + + align:start position:0% +there's High spao temporal variability + + + align:start position:0% +there's High spao temporal variability +so as C was saying even though absolute + + align:start position:0% +so as C was saying even though absolute + + + align:start position:0% +so as C was saying even though absolute +levels in some parts of the world are + + align:start position:0% +levels in some parts of the world are + + + align:start position:0% +levels in some parts of the world are +going down we're starting to understand + + align:start position:0% +going down we're starting to understand + + + align:start position:0% +going down we're starting to understand +more and more of it both in the + + align:start position:0% +more and more of it both in the + + + align:start position:0% +more and more of it both in the +scientific way and in the public + + align:start position:0% +scientific way and in the public + + + align:start position:0% +scientific way and in the public +perception way and also the World Health + + align:start position:0% +perception way and also the World Health + + + align:start position:0% +perception way and also the World Health +Organization is constantly reevaluating + + align:start position:0% +Organization is constantly reevaluating + + + align:start position:0% +Organization is constantly reevaluating +and understanding kind of how they + + align:start position:0% +and understanding kind of how they + + + align:start position:0% +and understanding kind of how they +recommend or how they make those + + align:start position:0% +recommend or how they make those + + + align:start position:0% +recommend or how they make those +guidelines on what safe exposure is and + + align:start position:0% +guidelines on what safe exposure is and + + + align:start position:0% +guidelines on what safe exposure is and +so I think with the latest round of + + align:start position:0% +so I think with the latest round of + + + align:start position:0% +so I think with the latest round of +revisions that's what kind of pushed you + + align:start position:0% +revisions that's what kind of pushed you + + + align:start position:0% +revisions that's what kind of pushed you +know this number up so high for us to + + align:start position:0% +know this number up so high for us to + + + align:start position:0% +know this number up so high for us to +understand that wow we are not doing so + + align:start position:0% +understand that wow we are not doing so + + + align:start position:0% +understand that wow we are not doing so +well in terms of mitigating a lot of the + + align:start position:0% +well in terms of mitigating a lot of the + + + align:start position:0% +well in terms of mitigating a lot of the +root causes of this work so there's a + + align:start position:0% +root causes of this work so there's a + + + align:start position:0% +root causes of this work so there's a +lot of interactions and there's a lot of + + align:start position:0% +lot of interactions and there's a lot of + + + align:start position:0% +lot of interactions and there's a lot of +um you know interplay between the built + + align:start position:0% +um you know interplay between the built + + + align:start position:0% +um you know interplay between the built +environment especially in urban areas + + align:start position:0% +environment especially in urban areas + + + align:start position:0% +environment especially in urban areas +Transportation air pollution and uh as V + + align:start position:0% +Transportation air pollution and uh as V + + + align:start position:0% +Transportation air pollution and uh as V +was talking about as well personal + + align:start position:0% +was talking about as well personal + + + align:start position:0% +was talking about as well personal +exposure different groups are exposed in + + align:start position:0% +exposure different groups are exposed in + + + align:start position:0% +exposure different groups are exposed in +different ways depending on what they do + + align:start position:0% +different ways depending on what they do + + + align:start position:0% +different ways depending on what they do +their incomes fortunately especially in + + align:start position:0% +their incomes fortunately especially in + + + align:start position:0% +their incomes fortunately especially in +the United States race is a very big + + align:start position:0% +the United States race is a very big + + + align:start position:0% +the United States race is a very big +indicator of exposure to air quality for + + align:start position:0% +indicator of exposure to air quality for + + + align:start position:0% +indicator of exposure to air quality for +environmental conditions so it's a very + + align:start position:0% +environmental conditions so it's a very + + + align:start position:0% +environmental conditions so it's a very +complex set of topics but as one showed + + align:start position:0% +complex set of topics but as one showed + + + align:start position:0% +complex set of topics but as one showed +us there's some really nice ways that we + + align:start position:0% +us there's some really nice ways that we + + + align:start position:0% +us there's some really nice ways that we +can combat it side exactly and I would + + align:start position:0% +can combat it side exactly and I would + + + align:start position:0% +can combat it side exactly and I would +say like kind of the wh puts the alarm + + align:start position:0% +say like kind of the wh puts the alarm + + + align:start position:0% +say like kind of the wh puts the alarm +up which means that puts the the level + + align:start position:0% +up which means that puts the the level + + + align:start position:0% +up which means that puts the the level +of acceptable exposure down every time + + align:start position:0% +of acceptable exposure down every time + + + align:start position:0% +of acceptable exposure down every time +so it goes like 40 25 10 and it seems + + align:start position:0% +so it goes like 40 25 10 and it seems + + + align:start position:0% +so it goes like 40 25 10 and it seems +that it will get to zero because any any + + align:start position:0% +that it will get to zero because any any + + + align:start position:0% +that it will get to zero because any any +particle that we will breathe will + + align:start position:0% +particle that we will breathe will + + + align:start position:0% +particle that we will breathe will +generate some somehow a damage and on + + align:start position:0% +generate some somehow a damage and on + + + align:start position:0% +generate some somehow a damage and on +the other side the data from people you + + align:start position:0% +the other side the data from people you + + + align:start position:0% +the other side the data from people you +know our phones are generating so much + + align:start position:0% +know our phones are generating so much + + + align:start position:0% +know our phones are generating so much +data of us and all the weable some + + align:start position:0% +data of us and all the weable some + + + align:start position:0% +data of us and all the weable some +people I can see here with apple watches + + align:start position:0% +people I can see here with apple watches + + + align:start position:0% +people I can see here with apple watches +and so forth so we now have access of H + + align:start position:0% +and so forth so we now have access of H + + + align:start position:0% +and so forth so we now have access of H +pools and and movement and so forth from + + align:start position:0% +pools and and movement and so forth from + + + align:start position:0% +pools and and movement and so forth from +a bunch of people that were actually + + align:start position:0% +a bunch of people that were actually + + + align:start position:0% +a bunch of people that were actually +very unaffordable again few years ago + + align:start position:0% +very unaffordable again few years ago + + + align:start position:0% +very unaffordable again few years ago +now uh when it comes to the attribution + + align:start position:0% +now uh when it comes to the attribution + + + align:start position:0% +now uh when it comes to the attribution +side so how do we connect these data + + align:start position:0% +side so how do we connect these data + + + align:start position:0% +side so how do we connect these data +together or how we do connect the data + + align:start position:0% +together or how we do connect the data + + + align:start position:0% +together or how we do connect the data +from buildings to any outcome of of + + align:start position:0% +from buildings to any outcome of of + + + align:start position:0% +from buildings to any outcome of of +people this is where where the where the + + align:start position:0% +people this is where where the where the + + + align:start position:0% +people this is where where the where the +diff the Striking difference comes with + + align:start position:0% +diff the Striking difference comes with + + + align:start position:0% +diff the Striking difference comes with +respect to evaluating Energy Efficiency + + align:start position:0% +respect to evaluating Energy Efficiency + + + align:start position:0% +respect to evaluating Energy Efficiency +Investments where everything is + + align:start position:0% +Investments where everything is + + + align:start position:0% +Investments where everything is +mechanical you know as a facilities + + align:start position:0% +mechanical you know as a facilities + + + align:start position:0% +mechanical you know as a facilities +manager at which level you running the + + align:start position:0% +manager at which level you running the + + + align:start position:0% +manager at which level you running the +engines of an hbac system and you can + + align:start position:0% +engines of an hbac system and you can + + + align:start position:0% +engines of an hbac system and you can +actually see very accurately what that + + align:start position:0% +actually see very accurately what that + + + align:start position:0% +actually see very accurately what that +will imply for the energy consumption of + + align:start position:0% +will imply for the energy consumption of + + + align:start position:0% +will imply for the energy consumption of +that building and the CO2 emissions and + + align:start position:0% +that building and the CO2 emissions and + + + align:start position:0% +that building and the CO2 emissions and +so forth you cannot do that with the + + align:start position:0% +so forth you cannot do that with the + + + align:start position:0% +so forth you cannot do that with the +health implications of that specific + + align:start position:0% +health implications of that specific + + + align:start position:0% +health implications of that specific +action you can put the HVAC system up + + align:start position:0% +action you can put the HVAC system up + + + align:start position:0% +action you can put the HVAC system up +but ultimately the health impact of that + + align:start position:0% +but ultimately the health impact of that + + + align:start position:0% +but ultimately the health impact of that +comes down + + align:start position:0% +comes down + + + align:start position:0% +comes down +like interacts with the with the + + align:start position:0% +like interacts with the with the + + + align:start position:0% +like interacts with the with the +behavioral and the people's layer and + + align:start position:0% +behavioral and the people's layer and + + + align:start position:0% +behavioral and the people's layer and +also with what happens in the city as a + + align:start position:0% +also with what happens in the city as a + + + align:start position:0% +also with what happens in the city as a +whole too right so if we are in a very + + align:start position:0% +whole too right so if we are in a very + + + align:start position:0% +whole too right so if we are in a very +severely polluted day as as Sana said + + align:start position:0% +severely polluted day as as Sana said + + + align:start position:0% +severely polluted day as as Sana said +there is a big spatial and temporal + + align:start position:0% +there is a big spatial and temporal + + + align:start position:0% +there is a big spatial and temporal +variation which means that some days we + + align:start position:0% +variation which means that some days we + + + align:start position:0% +variation which means that some days we +will be exposed to three times the level + + align:start position:0% +will be exposed to three times the level + + + align:start position:0% +will be exposed to three times the level +than another day and actually from my + + align:start position:0% +than another day and actually from my + + + align:start position:0% +than another day and actually from my +research I could see from the data + + align:start position:0% +research I could see from the data + + + align:start position:0% +research I could see from the data +always the case that it can change very + + align:start position:0% +always the case that it can change very + + + align:start position:0% +always the case that it can change very +rapidly from one day to the other + + align:start position:0% +rapidly from one day to the other + + + align:start position:0% +rapidly from one day to the other +because one of the things that brings + + align:start position:0% +because one of the things that brings + + + align:start position:0% +because one of the things that brings +pollution is wind so in the city like + + align:start position:0% +pollution is wind so in the city like + + + align:start position:0% +pollution is wind so in the city like +Boston if the wind is blowing from the + + align:start position:0% +Boston if the wind is blowing from the + + + align:start position:0% +Boston if the wind is blowing from the +sea very good if the wind is flow is is + + align:start position:0% +sea very good if the wind is flow is is + + + align:start position:0% +sea very good if the wind is flow is is +blowing from a city like New York and + + align:start position:0% +blowing from a city like New York and + + + align:start position:0% +blowing from a city like New York and +the power generation system of the state + + align:start position:0% +the power generation system of the state + + + align:start position:0% +the power generation system of the state +of New York very bad we have no control + + align:start position:0% +of New York very bad we have no control + + + align:start position:0% +of New York very bad we have no control +it can change very rapidly and it can be + + align:start position:0% +it can change very rapidly and it can be + + + align:start position:0% +it can change very rapidly and it can be +and it doesn't matter for our lungs + + align:start position:0% +and it doesn't matter for our lungs + + + align:start position:0% +and it doesn't matter for our lungs +because we are still breathing the the + + align:start position:0% +because we are still breathing the the + + + align:start position:0% +because we are still breathing the the +pollution no matter what the source is + + align:start position:0% +pollution no matter what the source is + + + align:start position:0% +pollution no matter what the source is +um so in that sense the same action that + + align:start position:0% +um so in that sense the same action that + + + align:start position:0% +um so in that sense the same action that +is improving the filters or improving + + align:start position:0% +is improving the filters or improving + + + align:start position:0% +is improving the filters or improving +the HVB system can have very different + + align:start position:0% +the HVB system can have very different + + + align:start position:0% +the HVB system can have very different +consequences on the health given the + + align:start position:0% +consequences on the health given the + + + align:start position:0% +consequences on the health given the +environment but also given the people if + + align:start position:0% +environment but also given the people if + + + align:start position:0% +environment but also given the people if +I make this lecture hall very + + align:start position:0% +I make this lecture hall very + + + align:start position:0% +I make this lecture hall very +healthy and nobody shows up we going + + align:start position:0% +healthy and nobody shows up we going + + + align:start position:0% +healthy and nobody shows up we going +back to the exposure part of the + + align:start position:0% +back to the exposure part of the + + + align:start position:0% +back to the exposure part of the +equation then it will have no impact on + + align:start position:0% +equation then it will have no impact on + + + align:start position:0% +equation then it will have no impact on +you if I want to see what is the impact + + align:start position:0% +you if I want to see what is the impact + + + align:start position:0% +you if I want to see what is the impact +of that investment on the great of you + + align:start position:0% +of that investment on the great of you + + + align:start position:0% +of that investment on the great of you +guys and everyone connects on + + align:start position:0% +guys and everyone connects on + + + align:start position:0% +guys and everyone connects on +Zoom yeah fantastic no impact on that we + + align:start position:0% +Zoom yeah fantastic no impact on that we + + + align:start position:0% +Zoom yeah fantastic no impact on that we +will have to put very large coaches for + + align:start position:0% +will have to put very large coaches for + + + align:start position:0% +will have to put very large coaches for +us to to just do napping here because + + align:start position:0% +us to to just do napping here because + + + align:start position:0% +us to to just do napping here because +that would be the only use of that + + align:start position:0% +that would be the only use of that + + + align:start position:0% +that would be the only use of that +lecture hall so all of these behavioral + + align:start position:0% +lecture hall so all of these behavioral + + + align:start position:0% +lecture hall so all of these behavioral +things make it very hard to assess but + + align:start position:0% +things make it very hard to assess but + + + align:start position:0% +things make it very hard to assess but +also very hard to just uh understand + + align:start position:0% +also very hard to just uh understand + + + align:start position:0% +also very hard to just uh understand +from a mechanical perspective what will + + align:start position:0% +from a mechanical perspective what will + + + align:start position:0% +from a mechanical perspective what will +be the consequence of that and what we + + align:start position:0% +be the consequence of that and what we + + + align:start position:0% +be the consequence of that and what we +are going to talk in the next five to 10 + + align:start position:0% +are going to talk in the next five to 10 + + + align:start position:0% +are going to talk in the next five to 10 +minutes is going to be about how do we + + align:start position:0% +minutes is going to be about how do we + + + align:start position:0% +minutes is going to be about how do we +design a studies or how do we design + + align:start position:0% +design a studies or how do we design + + + align:start position:0% +design a studies or how do we design +evaluation systems so then we can + + align:start position:0% +evaluation systems so then we can + + + align:start position:0% +evaluation systems so then we can +actually assess the health implications + + align:start position:0% +actually assess the health implications + + + align:start position:0% +actually assess the health implications +of those impacts taking into account + + align:start position:0% +of those impacts taking into account + + + align:start position:0% +of those impacts taking into account +that there will be Al always a + + align:start position:0% +that there will be Al always a + + + align:start position:0% +that there will be Al always a +behavioral layer in between the action + + align:start position:0% +behavioral layer in between the action + + + align:start position:0% +behavioral layer in between the action +of the facility manager pulling up the + + align:start position:0% +of the facility manager pulling up the + + + align:start position:0% +of the facility manager pulling up the +engines or the action of the developer + + align:start position:0% +engines or the action of the developer + + + align:start position:0% +engines or the action of the developer +upgrading a uh a system in a building + + align:start position:0% +upgrading a uh a system in a building + + + align:start position:0% +upgrading a uh a system in a building +and the ultimate consequences of of the + + align:start position:0% +and the ultimate consequences of of the + + + align:start position:0% +and the ultimate consequences of of the +people that we care about the residents + + align:start position:0% +people that we care about the residents + + + align:start position:0% +people that we care about the residents +the uh employees uh the clients whatever + + align:start position:0% +the uh employees uh the clients whatever + + + align:start position:0% +the uh employees uh the clients whatever +it is right if you go to the marketing + + align:start position:0% +it is right if you go to the marketing + + + align:start position:0% +it is right if you go to the marketing +literature there is also like we don't + + align:start position:0% +literature there is also like we don't + + + align:start position:0% +literature there is also like we don't +talk about it here but there is a lot of + + align:start position:0% +talk about it here but there is a lot of + + + align:start position:0% +talk about it here but there is a lot of +data on how people behave in a + + align:start position:0% +data on how people behave in a + + + align:start position:0% +data on how people behave in a +supermarket and there's a lot of tactics + + align:start position:0% +supermarket and there's a lot of tactics + + + align:start position:0% +supermarket and there's a lot of tactics +to try to get every penny from our + + align:start position:0% +to try to get every penny from our + + + align:start position:0% +to try to get every penny from our +pockets every time that we enter in a + + align:start position:0% +pockets every time that we enter in a + + + align:start position:0% +pockets every time that we enter in a +Walmart or in a Costco or in Prudential + + align:start position:0% +Walmart or in a Costco or in Prudential + + + align:start position:0% +Walmart or in a Costco or in Prudential +Center and so forth look at C she's + + align:start position:0% +Center and so forth look at C she's + + + align:start position:0% +Center and so forth look at C she's +always buying these necklace from from + + align:start position:0% +always buying these necklace from from + + + align:start position:0% +always buying these necklace from from +presential center it's all because of + + align:start position:0% +presential center it's all because of + + + align:start position:0% +presential center it's all because of +you're notched by the + + align:start position:0% +you're notched by the + + + align:start position:0% +you're notched by the +design um all right so going back to + + align:start position:0% +design um all right so going back to + + + align:start position:0% +design um all right so going back to +Jason this is your moment of Glory + + align:start position:0% +Jason this is your moment of Glory + + + align:start position:0% +Jason this is your moment of Glory +because I prepare this uh this lecture + + align:start position:0% +because I prepare this uh this lecture + + + align:start position:0% +because I prepare this uh this lecture +this slid exactly to tackle those + + align:start position:0% +this slid exactly to tackle those + + + align:start position:0% +this slid exactly to tackle those +questions so when it comes to + + align:start position:0% +questions so when it comes to + + + align:start position:0% +questions so when it comes to +understanding the impact as you said + + align:start position:0% +understanding the impact as you said + + + align:start position:0% +understanding the impact as you said +it's very hard because if you just + + align:start position:0% +it's very hard because if you just + + + align:start position:0% +it's very hard because if you just +whatever the difference between a + + align:start position:0% +whatever the difference between a + + + align:start position:0% +whatever the difference between a +healthy building and a non-healthy + + align:start position:0% +healthy building and a non-healthy + + + align:start position:0% +healthy building and a non-healthy +building comes in terms of health and + + align:start position:0% +building comes in terms of health and + + + align:start position:0% +building comes in terms of health and +performance let's say that we find that + + align:start position:0% +performance let's say that we find that + + + align:start position:0% +performance let's say that we find that +the the people living in this house are + + align:start position:0% +the the people living in this house are + + + align:start position:0% +the the people living in this house are +uh being 5% healthier and 5% more + + align:start position:0% +uh being 5% healthier and 5% more + + + align:start position:0% +uh being 5% healthier and 5% more +productive than the guys living in this + + align:start position:0% +productive than the guys living in this + + + align:start position:0% +productive than the guys living in this +house now the question is what generates + + align:start position:0% +house now the question is what generates + + + align:start position:0% +house now the question is what generates +those differences there could be some + + align:start position:0% +those differences there could be some + + + align:start position:0% +those differences there could be some +features there they could he like they + + align:start position:0% +features there they could he like they + + + align:start position:0% +features there they could he like they +might have better ventilation and so + + align:start position:0% +might have better ventilation and so + + + align:start position:0% +might have better ventilation and so +forth but the level of Health especially + + align:start position:0% +forth but the level of Health especially + + + align:start position:0% +forth but the level of Health especially +when it comes to air quality is very + + align:start position:0% +when it comes to air quality is very + + + align:start position:0% +when it comes to air quality is very +much shaped by the environment where + + align:start position:0% +much shaped by the environment where + + + align:start position:0% +much shaped by the environment where +these guys are so it's very hard right + + align:start position:0% +these guys are so it's very hard right + + + align:start position:0% +these guys are so it's very hard right +you have uh different things like uh + + align:start position:0% +you have uh different things like uh + + + align:start position:0% +you have uh different things like uh +green areas and so forth that will + + align:start position:0% +green areas and so forth that will + + + align:start position:0% +green areas and so forth that will +actually affect the ultimate level of + + align:start position:0% +actually affect the ultimate level of + + + align:start position:0% +actually affect the ultimate level of +environmental conditions in this house + + align:start position:0% +environmental conditions in this house + + + align:start position:0% +environmental conditions in this house +and that will actually be very different + + align:start position:0% +and that will actually be very different + + + align:start position:0% +and that will actually be very different +if we have in the other side factories + + align:start position:0% +if we have in the other side factories + + + align:start position:0% +if we have in the other side factories +and so forth so the outdoor factors + + align:start position:0% +and so forth so the outdoor factors + + + align:start position:0% +and so forth so the outdoor factors +change and we have to control for that + + align:start position:0% +change and we have to control for that + + + align:start position:0% +change and we have to control for that +in one way or another and also one of + + align:start position:0% +in one way or another and also one of + + + align:start position:0% +in one way or another and also one of +the important things that the occupants + + align:start position:0% +the important things that the occupants + + + align:start position:0% +the important things that the occupants +are also different because if you think + + align:start position:0% +are also different because if you think + + + align:start position:0% +are also different because if you think +about that area and if you think about + + align:start position:0% +about that area and if you think about + + + align:start position:0% +about that area and if you think about +that house and those two houses are put + + align:start position:0% +that house and those two houses are put + + + align:start position:0% +that house and those two houses are put +in the market then the question is why + + align:start position:0% +in the market then the question is why + + + align:start position:0% +in the market then the question is why +would you go to the one on the right why + + align:start position:0% +would you go to the one on the right why + + + align:start position:0% +would you go to the one on the right why +would you go to a house that is in the + + align:start position:0% +would you go to a house that is in the + + + align:start position:0% +would you go to a house that is in the +middle of an industrial area gray full + + align:start position:0% +middle of an industrial area gray full + + + align:start position:0% +middle of an industrial area gray full +of + + align:start position:0% +of + + + align:start position:0% +of +clouds not good right so the reason why + + align:start position:0% +clouds not good right so the reason why + + + align:start position:0% +clouds not good right so the reason why +you will go to that house is either + + align:start position:0% +you will go to that house is either + + + align:start position:0% +you will go to that house is either +Financial you can afford you cannot + + align:start position:0% +Financial you can afford you cannot + + + align:start position:0% +Financial you can afford you cannot +afford to go to the one on the left and + + align:start position:0% +afford to go to the one on the left and + + + align:start position:0% +afford to go to the one on the left and +that means that you probably cannot + + align:start position:0% +that means that you probably cannot + + + align:start position:0% +that means that you probably cannot +afford also other things related to your + + align:start position:0% +afford also other things related to your + + + align:start position:0% +afford also other things related to your +health you might actually not have the + + align:start position:0% +health you might actually not have the + + + align:start position:0% +health you might actually not have the +best health insurance you might not go + + align:start position:0% +best health insurance you might not go + + + align:start position:0% +best health insurance you might not go +to the gym you might not do all things + + align:start position:0% +to the gym you might not do all things + + + align:start position:0% +to the gym you might not do all things +or even if you have it it might be your + + align:start position:0% +or even if you have it it might be your + + + align:start position:0% +or even if you have it it might be your +choice not to uh pay the premium for + + align:start position:0% +choice not to uh pay the premium for + + + align:start position:0% +choice not to uh pay the premium for +this house and it might be your choice + + align:start position:0% +this house and it might be your choice + + + align:start position:0% +this house and it might be your choice +also therefore not to go to the gym + + align:start position:0% +also therefore not to go to the gym + + + align:start position:0% +also therefore not to go to the gym +because I just want to save all my money + + align:start position:0% +because I just want to save all my money + + + align:start position:0% +because I just want to save all my money +or whatever or I just enjoy doing other + + align:start position:0% +or whatever or I just enjoy doing other + + + align:start position:0% +or whatever or I just enjoy doing other +things enjoy going to the cinema and I + + align:start position:0% +things enjoy going to the cinema and I + + + align:start position:0% +things enjoy going to the cinema and I +don't enjoy to the G so your value of + + align:start position:0% +don't enjoy to the G so your value of + + + align:start position:0% +don't enjoy to the G so your value of +any health strategy that you have in + + align:start position:0% +any health strategy that you have in + + + align:start position:0% +any health strategy that you have in +your life not only the place where you + + align:start position:0% +your life not only the place where you + + + align:start position:0% +your life not only the place where you +live is probably much lower than the guy + + align:start position:0% +live is probably much lower than the guy + + + align:start position:0% +live is probably much lower than the guy +that lives in this house and that + + align:start position:0% +that lives in this house and that + + + align:start position:0% +that lives in this house and that +introduced a lot of problems because all + + align:start position:0% +introduced a lot of problems because all + + + align:start position:0% +introduced a lot of problems because all +the difference between these two guys + + align:start position:0% +the difference between these two guys + + + align:start position:0% +the difference between these two guys +are not related to this specific guy + + align:start position:0% +are not related to this specific guy + + + align:start position:0% +are not related to this specific guy +here but is related to this but also to + + align:start position:0% +here but is related to this but also to + + + align:start position:0% +here but is related to this but also to +the people that lived in there + + align:start position:0% +the people that lived in there + + + align:start position:0% +the people that lived in there +and therefore if we let people choose + + align:start position:0% +and therefore if we let people choose + + + align:start position:0% +and therefore if we let people choose +the environment where they live where + + align:start position:0% +the environment where they live where + + + align:start position:0% +the environment where they live where +they + + align:start position:0% +they + + + align:start position:0% +they +work then we will always have this + + align:start position:0% +work then we will always have this + + + align:start position:0% +work then we will always have this +problem confounding our studies and + + align:start position:0% +problem confounding our studies and + + + align:start position:0% +problem confounding our studies and +introducing and and basically inflating + + align:start position:0% +introducing and and basically inflating + + + align:start position:0% +introducing and and basically inflating +the difference between this building and + + align:start position:0% +the difference between this building and + + + align:start position:0% +the difference between this building and +this building because all of it is + + align:start position:0% +this building because all of it is + + + align:start position:0% +this building because all of it is +inflated by the outdoor environment and + + align:start position:0% +inflated by the outdoor environment and + + + align:start position:0% +inflated by the outdoor environment and +all of it is infed inflated by the + + align:start position:0% +all of it is infed inflated by the + + + align:start position:0% +all of it is infed inflated by the +people that live here versus the people + + align:start position:0% +people that live here versus the people + + + align:start position:0% +people that live here versus the people +that live + + align:start position:0% + + + + align:start position:0% + +here this kind of looks like a a picture + + align:start position:0% +here this kind of looks like a a picture + + + align:start position:0% +here this kind of looks like a a picture +of the suburbs versus the city how do + + align:start position:0% +of the suburbs versus the city how do + + + align:start position:0% +of the suburbs versus the city how do +you say I mean moving into the city + + align:start position:0% +you say I mean moving into the city + + + align:start position:0% +you say I mean moving into the city +isn't because you don't have the means + + align:start position:0% +isn't because you don't have the means + + + align:start position:0% +isn't because you don't have the means +to live in the suburb it's a it's a + + align:start position:0% +to live in the suburb it's a it's a + + + align:start position:0% +to live in the suburb it's a it's a +choice you know you want cut down Comm + + align:start position:0% +choice you know you want cut down Comm + + + align:start position:0% +choice you know you want cut down Comm +time you want to be closer to amenities + + align:start position:0% +time you want to be closer to amenities + + + align:start position:0% +time you want to be closer to amenities +you want to be closer to work it's I + + align:start position:0% +you want to be closer to work it's I + + + align:start position:0% +you want to be closer to work it's I +think it's just you have the means to to + + align:start position:0% +think it's just you have the means to to + + + align:start position:0% +think it's just you have the means to to +live here you know just City living + + align:start position:0% +live here you know just City living + + + align:start position:0% +live here you know just City living +versus suburb living correct so then + + align:start position:0% +versus suburb living correct so then + + + align:start position:0% +versus suburb living correct so then +that will also be like if you prefer to + + align:start position:0% +that will also be like if you prefer to + + + align:start position:0% +that will also be like if you prefer to +live in the subbs it's very hard to to + + align:start position:0% +live in the subbs it's very hard to to + + + align:start position:0% +live in the subbs it's very hard to to +to imagine that that's only thing that + + align:start position:0% +to imagine that that's only thing that + + + align:start position:0% +to imagine that that's only thing that +you differ from the person that want to + + align:start position:0% +you differ from the person that want to + + + align:start position:0% +you differ from the person that want to +live in the in the um in the center and + + align:start position:0% +live in the in the um in the center and + + + align:start position:0% +live in the in the um in the center and +then that those differences will be not + + align:start position:0% +then that those differences will be not + + + align:start position:0% +then that those differences will be not +uh will not be intertwin also with + + align:start position:0% +uh will not be intertwin also with + + + align:start position:0% +uh will not be intertwin also with +anything that affect your health because + + align:start position:0% +anything that affect your health because + + + align:start position:0% +anything that affect your health because +if you live in the S maybe you + + align:start position:0% +if you live in the S maybe you + + + align:start position:0% +if you live in the S maybe you +appreciate also some walks in the + + align:start position:0% +appreciate also some walks in the + + + align:start position:0% +appreciate also some walks in the +evening while the guy that lives in the + + align:start position:0% +evening while the guy that lives in the + + + align:start position:0% +evening while the guy that lives in the +city center they he just appreci to go + + align:start position:0% +city center they he just appreci to go + + + align:start position:0% +city center they he just appreci to go +to the bar and have some beers with the + + align:start position:0% +to the bar and have some beers with the + + + align:start position:0% +to the bar and have some beers with the +with the co-workers after after work + + align:start position:0% +with the co-workers after after work + + + align:start position:0% +with the co-workers after after work +alcohol versus active living very big + + align:start position:0% +alcohol versus active living very big + + + align:start position:0% +alcohol versus active living very big +for health so forth that's just one + + align:start position:0% +for health so forth that's just one + + + align:start position:0% +for health so forth that's just one +example right but basically once you + + align:start position:0% +example right but basically once you + + + align:start position:0% +example right but basically once you +introduce people sorting into places + + align:start position:0% +introduce people sorting into places + + + align:start position:0% +introduce people sorting into places +either within the same neighborhood or + + align:start position:0% +either within the same neighborhood or + + + align:start position:0% +either within the same neighborhood or +across neighborhoods then you always + + align:start position:0% +across neighborhoods then you always + + + align:start position:0% +across neighborhoods then you always +have the problem of if I attach any + + align:start position:0% +have the problem of if I attach any + + + align:start position:0% +have the problem of if I attach any +differences in your health or in your + + align:start position:0% +differences in your health or in your + + + align:start position:0% +differences in your health or in your +performance to the place where you live + + align:start position:0% +performance to the place where you live + + + align:start position:0% +performance to the place where you live +to the building that you leave is it + + align:start position:0% +to the building that you leave is it + + + align:start position:0% +to the building that you leave is it +really a fair comparison or you are + + align:start position:0% +really a fair comparison or you are + + + align:start position:0% +really a fair comparison or you are +actually blowing up these differences by + + align:start position:0% +actually blowing up these differences by + + + align:start position:0% +actually blowing up these differences by +all the other things that you are that + + align:start position:0% +all the other things that you are that + + + align:start position:0% +all the other things that you are that +so the challenge here is that because + + align:start position:0% +so the challenge here is that because + + + align:start position:0% +so the challenge here is that because +you have this human layer in between the + + align:start position:0% +you have this human layer in between the + + + align:start position:0% +you have this human layer in between the +actions of the facility manager or the + + align:start position:0% +actions of the facility manager or the + + + align:start position:0% +actions of the facility manager or the +architect or the the designer and the + + align:start position:0% +architect or the the designer and the + + + align:start position:0% +architect or the the designer and the +people that ultimately you care about + + align:start position:0% +people that ultimately you care about + + + align:start position:0% +people that ultimately you care about +you have to take those things into + + align:start position:0% +you have to take those things into + + + align:start position:0% +you have to take those things into +account very + + align:start position:0% +account very + + + align:start position:0% +account very +seriously and that's what we try to + + align:start position:0% +seriously and that's what we try to + + + align:start position:0% +seriously and that's what we try to +do the people that try to do these + + align:start position:0% +do the people that try to do these + + + align:start position:0% +do the people that try to do these +studies and I will show you a little bit + + align:start position:0% +studies and I will show you a little bit + + + align:start position:0% +studies and I will show you a little bit +few techniques that people use um there + + align:start position:0% +few techniques that people use um there + + + align:start position:0% +few techniques that people use um there +you go this is one one is uh we don't + + align:start position:0% +you go this is one one is uh we don't + + + align:start position:0% +you go this is one one is uh we don't +let people decide their exposure to + + align:start position:0% +let people decide their exposure to + + + align:start position:0% +let people decide their exposure to +something but we actually manipulate + + align:start position:0% +something but we actually manipulate + + + align:start position:0% +something but we actually manipulate +that exposure in an experiment so we + + align:start position:0% +that exposure in an experiment so we + + + align:start position:0% +that exposure in an experiment so we +invite people when we care about how + + align:start position:0% +invite people when we care about how + + + align:start position:0% +invite people when we care about how +ventilation affects people CO2 levels + + align:start position:0% +ventilation affects people CO2 levels + + + align:start position:0% +ventilation affects people CO2 levels +affect people so this guy is measuring + + align:start position:0% +affect people so this guy is measuring + + + align:start position:0% +affect people so this guy is measuring +in PPM the concentration of CO2 in the + + align:start position:0% +in PPM the concentration of CO2 in the + + + align:start position:0% +in PPM the concentration of CO2 in the +room so basics of CO2 when we breathe we + + align:start position:0% +room so basics of CO2 when we breathe we + + + align:start position:0% +room so basics of CO2 when we breathe we +take oxygen we exhale CO2 and then the + + align:start position:0% +take oxygen we exhale CO2 and then the + + + align:start position:0% +take oxygen we exhale CO2 and then the +concentration of CO2 in this room uh + + align:start position:0% +concentration of CO2 in this room uh + + + align:start position:0% +concentration of CO2 in this room uh +will be up uh or will be like the2 that + + align:start position:0% +will be up uh or will be like the2 that + + + align:start position:0% +will be up uh or will be like the2 that +I'm exceling will stay here until the + + align:start position:0% +I'm exceling will stay here until the + + + align:start position:0% +I'm exceling will stay here until the +the room refreshes the air with outdoor + + align:start position:0% +the room refreshes the air with outdoor + + + align:start position:0% +the room refreshes the air with outdoor +air and brings back oxygen right so if + + align:start position:0% +air and brings back oxygen right so if + + + align:start position:0% +air and brings back oxygen right so if +this room will be empty it will be + + align:start position:0% +this room will be empty it will be + + + align:start position:0% +this room will be empty it will be +around 450 that is the Outdoor levels + + align:start position:0% +around 450 that is the Outdoor levels + + + align:start position:0% +around 450 that is the Outdoor levels +when we come all in and we are + + align:start position:0% +when we come all in and we are + + + align:start position:0% +when we come all in and we are +generating CO2 the room goes the CO2 + + align:start position:0% +generating CO2 the room goes the CO2 + + + align:start position:0% +generating CO2 the room goes the CO2 +levels in the room goes up until these + + align:start position:0% +levels in the room goes up until these + + + align:start position:0% +levels in the room goes up until these +guys refresh there so uh one of the + + align:start position:0% +guys refresh there so uh one of the + + + align:start position:0% +guys refresh there so uh one of the +things that people do is that they bring + + align:start position:0% +things that people do is that they bring + + + align:start position:0% +things that people do is that they bring +people some of some of the techniques + + align:start position:0% +people some of some of the techniques + + + align:start position:0% +people some of some of the techniques +that people do in in research is that + + align:start position:0% +that people do in in research is that + + + align:start position:0% +that people do in in research is that +they bring people to a lab and they + + align:start position:0% +they bring people to a lab and they + + + align:start position:0% +they bring people to a lab and they +manipulate the environmental conditions + + align:start position:0% +manipulate the environmental conditions + + + align:start position:0% +manipulate the environmental conditions +where while they are doing a a task so + + align:start position:0% +where while they are doing a a task so + + + align:start position:0% +where while they are doing a a task so +they are interested in how cognitive + + align:start position:0% +they are interested in how cognitive + + + align:start position:0% +they are interested in how cognitive +performance is affected by levels of CO2 + + align:start position:0% +performance is affected by levels of CO2 + + + align:start position:0% +performance is affected by levels of CO2 +what they did was bringing uh around 24 + + align:start position:0% +what they did was bringing uh around 24 + + + align:start position:0% +what they did was bringing uh around 24 +people uh healthy o office workers to to + + align:start position:0% +people uh healthy o office workers to to + + + align:start position:0% +people uh healthy o office workers to to +a lab in syak Cruz and they will have to + + align:start position:0% +a lab in syak Cruz and they will have to + + + align:start position:0% +a lab in syak Cruz and they will have to +work in that lab for uh the whole for a + + align:start position:0% +work in that lab for uh the whole for a + + + align:start position:0% +work in that lab for uh the whole for a +whole week and every day the the + + align:start position:0% +whole week and every day the the + + + align:start position:0% +whole week and every day the the +scientist will manipulate the level of + + align:start position:0% +scientist will manipulate the level of + + + align:start position:0% +scientist will manipulate the level of +CO2 that these people will be working on + + align:start position:0% +CO2 that these people will be working on + + + align:start position:0% +CO2 that these people will be working on +for six hours and at the end of the day + + align:start position:0% +for six hours and at the end of the day + + + align:start position:0% +for six hours and at the end of the day +they will give in a cognitive task to + + align:start position:0% +they will give in a cognitive task to + + + align:start position:0% +they will give in a cognitive task to +see how their decision making is + + align:start position:0% +see how their decision making is + + + align:start position:0% +see how their decision making is +affected by the level of CO2 in the best + + align:start position:0% +affected by the level of CO2 in the best + + + align:start position:0% +affected by the level of CO2 in the best +day or in the best CO2 levels they will + + align:start position:0% +day or in the best CO2 levels they will + + + align:start position:0% +day or in the best CO2 levels they will +have around uh 550 BPM is almost outdoor + + align:start position:0% +have around uh 550 BPM is almost outdoor + + + align:start position:0% +have around uh 550 BPM is almost outdoor +levels it's the best that you can have + + align:start position:0% +levels it's the best that you can have + + + align:start position:0% +levels it's the best that you can have +um in the in the medium level so it's + + align:start position:0% +um in the in the medium level so it's + + + align:start position:0% +um in the in the medium level so it's +what they will say like a Green Building + + align:start position:0% +what they will say like a Green Building + + + align:start position:0% +what they will say like a Green Building +day it will be 945 almost double and in + + align:start position:0% +day it will be 945 almost double and in + + + align:start position:0% +day it will be 945 almost double and in +a conventional level it will be uh where + + align:start position:0% +a conventional level it will be uh where + + + align:start position:0% +a conventional level it will be uh where +where most of the people will be + + align:start position:0% +where most of the people will be + + + align:start position:0% +where most of the people will be +exposing a normal building it will be + + align:start position:0% +exposing a normal building it will be + + + align:start position:0% +exposing a normal building it will be +around 1400 these was these were the + + align:start position:0% +around 1400 these was these were the + + + align:start position:0% +around 1400 these was these were the +levels that actually we observe a lot of + + align:start position:0% +levels that actually we observe a lot of + + + align:start position:0% +levels that actually we observe a lot of +times around MIT before covid but this + + align:start position:0% +times around MIT before covid but this + + + align:start position:0% +times around MIT before covid but this +was sort of like the conventional level + + align:start position:0% +was sort of like the conventional level + + + align:start position:0% +was sort of like the conventional level +what you see is that in any level for + + align:start position:0% +what you see is that in any level for + + + align:start position:0% +what you see is that in any level for +the performance as you go to lower + + align:start position:0% +the performance as you go to lower + + + align:start position:0% +the performance as you go to lower +levels of CO2 the level of cognitive + + align:start position:0% +levels of CO2 the level of cognitive + + + align:start position:0% +levels of CO2 the level of cognitive +performance increases and what this + + align:start position:0% +performance increases and what this + + + align:start position:0% +performance increases and what this +means that people are better able to uh + + align:start position:0% +means that people are better able to uh + + + align:start position:0% +means that people are better able to uh +to process information and are better + + align:start position:0% +to process information and are better + + + align:start position:0% +to process information and are better +able to strategize with those they were + + align:start position:0% +able to strategize with those they were + + + align:start position:0% +able to strategize with those they were +having all of these complex uh cognitive + + align:start position:0% +having all of these complex uh cognitive + + + align:start position:0% +having all of these complex uh cognitive +tasks that I'm happy to talk about it + + align:start position:0% +tasks that I'm happy to talk about it + + + align:start position:0% +tasks that I'm happy to talk about it +more but they are developed by + + align:start position:0% +more but they are developed by + + + align:start position:0% +more but they are developed by +psychologist to understand how you your + + align:start position:0% +psychologist to understand how you your + + + align:start position:0% +psychologist to understand how you your +decision making is impaired by CO2 level + + align:start position:0% +decision making is impaired by CO2 level + + + align:start position:0% +decision making is impaired by CO2 level +this is their study that everyone quotes + + align:start position:0% +this is their study that everyone quotes + + + align:start position:0% +this is their study that everyone quotes +when they are thinking about ventilation + + align:start position:0% +when they are thinking about ventilation + + + align:start position:0% +when they are thinking about ventilation +and air quality in buildings this is by + + align:start position:0% +and air quality in buildings this is by + + + align:start position:0% +and air quality in buildings this is by +Joe Allen here uh the first author is + + align:start position:0% +Joe Allen here uh the first author is + + + align:start position:0% +Joe Allen here uh the first author is +this professor at Harvard Public Health + + align:start position:0% +this professor at Harvard Public Health + + + align:start position:0% +this professor at Harvard Public Health +School of Public Health he's the most + + align:start position:0% +School of Public Health he's the most + + + align:start position:0% +School of Public Health he's the most +famous guy doing these studies and this + + align:start position:0% +famous guy doing these studies and this + + + align:start position:0% +famous guy doing these studies and this +was the study that make him famous + + align:start position:0% +was the study that make him famous + + + align:start position:0% +was the study that make him famous +bringing 24 people into a lab and + + align:start position:0% +bringing 24 people into a lab and + + + align:start position:0% +bringing 24 people into a lab and +manipulating the levels of CO2 sometimes + + align:start position:0% +manipulating the levels of CO2 sometimes + + + align:start position:0% +manipulating the levels of CO2 sometimes +science can be simple powerful and if + + align:start position:0% +science can be simple powerful and if + + + align:start position:0% +science can be simple powerful and if +you're a Harvard Professor impactful + + align:start position:0% +you're a Harvard Professor impactful + + + align:start position:0% +you're a Harvard Professor impactful +too I got questions really interesting + + align:start position:0% +too I got questions really interesting + + + align:start position:0% +too I got questions really interesting +research never thank + + align:start position:0% +research never thank + + + align:start position:0% +research never thank +appreciate it so in this is that saying + + align:start position:0% +appreciate it so in this is that saying + + + align:start position:0% +appreciate it so in this is that saying +simply saying from your perspective is + + align:start position:0% +simply saying from your perspective is + + + align:start position:0% +simply saying from your perspective is +that saying that the high Concentra of + + align:start position:0% +that saying that the high Concentra of + + + align:start position:0% +that saying that the high Concentra of +carbon dioxygen yeah will decrease the + + align:start position:0% +carbon dioxygen yeah will decrease the + + + align:start position:0% +carbon dioxygen yeah will decrease the +concentration commity or simply saying + + align:start position:0% +concentration commity or simply saying + + + align:start position:0% +concentration commity or simply saying +because the level of carbon dioxygen is + + align:start position:0% +because the level of carbon dioxygen is + + + align:start position:0% +because the level of carbon dioxygen is +high it means there's less fresh and + + align:start position:0% +high it means there's less fresh and + + + align:start position:0% +high it means there's less fresh and +less oygen it's a better question yeah + + align:start position:0% +less oygen it's a better question yeah + + + align:start position:0% +less oygen it's a better question yeah +these two things are always convoluted + + align:start position:0% +these two things are always convoluted + + + align:start position:0% +these two things are always convoluted +but in this case the level of + + align:start position:0% +but in this case the level of + + + align:start position:0% +but in this case the level of +ventilation was keeping constant and + + align:start position:0% +ventilation was keeping constant and + + + align:start position:0% +ventilation was keeping constant and +they just artificially put CO2 in the + + align:start position:0% +they just artificially put CO2 in the + + + align:start position:0% +they just artificially put CO2 in the +room with a gas bottle + + align:start position:0% +room with a gas bottle + + + align:start position:0% +room with a gas bottle +so if this one is purely CO2 levels but + + align:start position:0% +so if this one is purely CO2 levels but + + + align:start position:0% +so if this one is purely CO2 levels but +in this in the in the real world so I + + align:start position:0% +in this in the in the real world so I + + + align:start position:0% +in this in the in the real world so I +did for example a study trying to + + align:start position:0% +did for example a study trying to + + + align:start position:0% +did for example a study trying to +measure with Those sensors uh the levels + + align:start position:0% +measure with Those sensors uh the levels + + + align:start position:0% +measure with Those sensors uh the levels +of CO2 in classrooms of the classrooms + + align:start position:0% +of CO2 in classrooms of the classrooms + + + align:start position:0% +of CO2 in classrooms of the classrooms +of 6 6,000 kids and I will get overtime + + align:start position:0% +of 6 6,000 kids and I will get overtime + + + align:start position:0% +of 6 6,000 kids and I will get overtime +changes in CO2 levels School term after + + align:start position:0% +changes in CO2 levels School term after + + + align:start position:0% +changes in CO2 levels School term after +school term three years and connected to + + align:start position:0% +school term three years and connected to + + + align:start position:0% +school term three years and connected to +a test score seeing that actually there + + align:start position:0% +a test score seeing that actually there + + + align:start position:0% +a test score seeing that actually there +are big differences when they are + + align:start position:0% +are big differences when they are + + + align:start position:0% +are big differences when they are +exposed that that is convoluted with + + align:start position:0% +exposed that that is convoluted with + + + align:start position:0% +exposed that that is convoluted with +ventilation so you are not only exposed + + align:start position:0% +ventilation so you are not only exposed + + + align:start position:0% +ventilation so you are not only exposed +to higher levels CO2 but also probably + + align:start position:0% +to higher levels CO2 but also probably + + + align:start position:0% +to higher levels CO2 but also probably +voccs and other things that are uh more + + align:start position:0% +voccs and other things that are uh more + + + align:start position:0% +voccs and other things that are uh more +prevalent in the room where the level of + + align:start position:0% +prevalent in the room where the level of + + + align:start position:0% +prevalent in the room where the level of +uh the ventilation rates are lower where + + align:start position:0% +uh the ventilation rates are lower where + + + align:start position:0% +uh the ventilation rates are lower where +you are putting flashing in less oxygen + + align:start position:0% +you are putting flashing in less oxygen + + + align:start position:0% +you are putting flashing in less oxygen +into it Le have you seen differ + + align:start position:0% + + + + align:start position:0% + +home gas oh yeah there's a very + + align:start position:0% +home gas oh yeah there's a very + + + align:start position:0% +home gas oh yeah there's a very +interesting study uh in so the + + align:start position:0% +interesting study uh in so the + + + align:start position:0% +interesting study uh in so the +the the exposure science studies in in + + align:start position:0% +the the exposure science studies in in + + + align:start position:0% +the the exposure science studies in in +homes are usually less prevalent because + + align:start position:0% +homes are usually less prevalent because + + + align:start position:0% +homes are usually less prevalent because +you have less ability to measure and so + + align:start position:0% +you have less ability to measure and so + + + align:start position:0% +you have less ability to measure and so +forth but there is one done by + + align:start position:0% +forth but there is one done by + + + align:start position:0% +forth but there is one done by +researches at MIT uh where they install + + align:start position:0% +researches at MIT uh where they install + + + align:start position:0% +researches at MIT uh where they install +all sort of sensors in in homes and + + align:start position:0% +all sort of sensors in in homes and + + + align:start position:0% +all sort of sensors in in homes and +there was sort of like the to your + + align:start position:0% +there was sort of like the to your + + + align:start position:0% +there was sort of like the to your +toaster is killing you is so that was + + align:start position:0% +toaster is killing you is so that was + + + align:start position:0% +toaster is killing you is so that was +the MIT news headline because when you + + align:start position:0% +the MIT news headline because when you + + + align:start position:0% +the MIT news headline because when you +switch on the the toaster there was a + + align:start position:0% +switch on the the toaster there was a + + + align:start position:0% +switch on the the toaster there was a +big spike in particles and so forth um I + + align:start position:0% +big spike in particles and so forth um I + + + align:start position:0% +big spike in particles and so forth um I +think that it depend this like one of + + align:start position:0% +think that it depend this like one of + + + align:start position:0% +think that it depend this like one of +the things that is important to to + + align:start position:0% +the things that is important to to + + + align:start position:0% +the things that is important to to +understand in all of these healthy + + align:start position:0% +understand in all of these healthy + + + align:start position:0% +understand in all of these healthy +buildings that there is no such a thing + + align:start position:0% +buildings that there is no such a thing + + + align:start position:0% +buildings that there is no such a thing +as one home genius one thing that is + + align:start position:0% +as one home genius one thing that is + + + align:start position:0% +as one home genius one thing that is +healthy buildings there is a + + align:start position:0% +healthy buildings there is a + + + align:start position:0% +healthy buildings there is a +multi-dimensional aspect so in some + + align:start position:0% +multi-dimensional aspect so in some + + + align:start position:0% +multi-dimensional aspect so in some +things some chemicals you will be more + + align:start position:0% +things some chemicals you will be more + + + align:start position:0% +things some chemicals you will be more +exposed in certain offices than at home + + align:start position:0% +exposed in certain offices than at home + + + align:start position:0% +exposed in certain offices than at home +because you know you use different + + align:start position:0% +because you know you use different + + + align:start position:0% +because you know you use different +cleaning products you also have + + align:start position:0% +cleaning products you also have + + + align:start position:0% +cleaning products you also have +different ventilation systems and so + + align:start position:0% +different ventilation systems and so + + + align:start position:0% +different ventilation systems and so +forth uh but some others you will have + + align:start position:0% +forth uh but some others you will have + + + align:start position:0% +forth uh but some others you will have +way more exposure at home uh and also + + align:start position:0% +way more exposure at home uh and also + + + align:start position:0% +way more exposure at home uh and also +depending on the neighborhood and so + + align:start position:0% +depending on the neighborhood and so + + + align:start position:0% +depending on the neighborhood and so +forth so it's very hard to say whether + + align:start position:0% +forth so it's very hard to say whether + + + align:start position:0% +forth so it's very hard to say whether +it's healthier at home than healthier at + + align:start position:0% +it's healthier at home than healthier at + + + align:start position:0% +it's healthier at home than healthier at +the office there are some chemicals that + + align:start position:0% +the office there are some chemicals that + + + align:start position:0% +the office there are some chemicals that +will be much more prevalent in at home + + align:start position:0% +will be much more prevalent in at home + + + align:start position:0% +will be much more prevalent in at home +than at the office uh and the other way + + align:start position:0% +than at the office uh and the other way + + + align:start position:0% +than at the office uh and the other way +around will also hold + + align:start position:0% +around will also hold + + + align:start position:0% +around will also hold +too + + align:start position:0% +too + + + align:start position:0% +too +Carlos question as as we looking into + + align:start position:0% +Carlos question as as we looking into + + + align:start position:0% +Carlos question as as we looking into +we're looking into real estate like + + align:start position:0% +we're looking into real estate like + + + align:start position:0% +we're looking into real estate like +office lab and all this stuff is being + + align:start position:0% +office lab and all this stuff is being + + + align:start position:0% +office lab and all this stuff is being +basically basically imposed by Public + + align:start position:0% +basically basically imposed by Public + + + align:start position:0% +basically basically imposed by Public +public policy at least in the states in + + align:start position:0% +public policy at least in the states in + + + align:start position:0% +public policy at least in the states in +Europe are there any studies and any + + align:start position:0% +Europe are there any studies and any + + + align:start position:0% +Europe are there any studies and any +actions being taken for + + align:start position:0% +actions being taken for + + + align:start position:0% +actions being taken for +examples at the school level School + + align:start position:0% +examples at the school level School + + + align:start position:0% +examples at the school level School +proper real estate and are publicly + + align:start position:0% +proper real estate and are publicly + + + align:start position:0% +proper real estate and are publicly +owned yeah it's the public policy is + + align:start position:0% +owned yeah it's the public policy is + + + align:start position:0% +owned yeah it's the public policy is +basically making mandatory for private + + align:start position:0% +basically making mandatory for private + + + align:start position:0% +basically making mandatory for private +investors to mutate or retrofit or + + align:start position:0% +investors to mutate or retrofit or + + + align:start position:0% +investors to mutate or retrofit or +whatever their assets into green assets + + align:start position:0% +whatever their assets into green assets + + + align:start position:0% +whatever their assets into green assets +because of being prone to uh environment + + align:start position:0% +because of being prone to uh environment + + + align:start position:0% +because of being prone to uh environment +and sustainability yeah are there are + + align:start position:0% +and sustainability yeah are there are + + + align:start position:0% +and sustainability yeah are there are +they doing something with their assets + + align:start position:0% +they doing something with their assets + + + align:start position:0% +they doing something with their assets +publicly owned assets to improve or like + + align:start position:0% +publicly owned assets to improve or like + + + align:start position:0% +publicly owned assets to improve or like +show yeah yeah some support yeah so for + + align:start position:0% +show yeah yeah some support yeah so for + + + align:start position:0% +show yeah yeah some support yeah so for +yeah more of the more of most of the + + align:start position:0% +yeah more of the more of most of the + + + align:start position:0% +yeah more of the more of most of the +Investments that you will see in the + + align:start position:0% +Investments that you will see in the + + + align:start position:0% +Investments that you will see in the +schools will be done by public + + align:start position:0% +schools will be done by public + + + align:start position:0% +schools will be done by public +governments or school districts in a way + + align:start position:0% +governments or school districts in a way + + + align:start position:0% +governments or school districts in a way +some sort of public or or or public good + + align:start position:0% +some sort of public or or or public good + + + align:start position:0% +some sort of public or or or public good +money uh there is a lot of money being + + align:start position:0% +money uh there is a lot of money being + + + align:start position:0% +money uh there is a lot of money being +pumped in since the covid because the + + align:start position:0% +pumped in since the covid because the + + + align:start position:0% +pumped in since the covid because the +schools closures was one of the key + + align:start position:0% +schools closures was one of the key + + + align:start position:0% +schools closures was one of the key +things that were happening because there + + align:start position:0% +things that were happening because there + + + align:start position:0% +things that were happening because there +were these buildings that were very + + align:start position:0% +were these buildings that were very + + + align:start position:0% +were these buildings that were very +poorly maintained especially the hbac + + align:start position:0% +poorly maintained especially the hbac + + + align:start position:0% +poorly maintained especially the hbac +systems in the in the US you will have + + align:start position:0% +systems in the in the US you will have + + + align:start position:0% +systems in the in the US you will have +one out of two schools that are not + + align:start position:0% +one out of two schools that are not + + + align:start position:0% +one out of two schools that are not +having the the HB system up to speed uh + + align:start position:0% +having the the HB system up to speed uh + + + align:start position:0% +having the the HB system up to speed uh +and they will need to modernize or or + + align:start position:0% +and they will need to modernize or or + + + align:start position:0% +and they will need to modernize or or +replace or even install so school + + align:start position:0% +replace or even install so school + + + align:start position:0% +replace or even install so school +systems are really bad school school + + align:start position:0% +systems are really bad school school + + + align:start position:0% +systems are really bad school school +buildings are really bad and now they + + align:start position:0% +buildings are really bad and now they + + + align:start position:0% +buildings are really bad and now they +they were also very densely populated so + + align:start position:0% +they were also very densely populated so + + + align:start position:0% +they were also very densely populated so +they were at the epicenter of this covid + + align:start position:0% +they were at the epicenter of this covid + + + align:start position:0% +they were at the epicenter of this covid +outbreak so now they are getting a lot + + align:start position:0% +outbreak so now they are getting a lot + + + align:start position:0% +outbreak so now they are getting a lot +of public money that's what they are + + align:start position:0% +of public money that's what they are + + + align:start position:0% +of public money that's what they are +having all right and the same happens + + align:start position:0% +having all right and the same happens + + + align:start position:0% +having all right and the same happens +with particles is one of my research we + + align:start position:0% +with particles is one of my research we + + + align:start position:0% +with particles is one of my research we +had it with the chess players so the + + align:start position:0% +had it with the chess players so the + + + align:start position:0% +had it with the chess players so the +Strategic decision making is also + + align:start position:0% +Strategic decision making is also + + + align:start position:0% +Strategic decision making is also +impaired so and again being back to the + + align:start position:0% +impaired so and again being back to the + + + align:start position:0% +impaired so and again being back to the +point right this is nothing that you can + + align:start position:0% +point right this is nothing that you can + + + align:start position:0% +point right this is nothing that you can +compensate if you are making a decision + + align:start position:0% +compensate if you are making a decision + + + align:start position:0% +compensate if you are making a decision +and you made that decision and it's wor + + align:start position:0% +and you made that decision and it's wor + + + align:start position:0% +and you made that decision and it's wor +off then you cannot just replace it by + + align:start position:0% +off then you cannot just replace it by + + + align:start position:0% +off then you cannot just replace it by +extra coffee and stay in extra hours you + + align:start position:0% +extra coffee and stay in extra hours you + + + align:start position:0% +extra coffee and stay in extra hours you +made that decision is going to handt you + + align:start position:0% +made that decision is going to handt you + + + align:start position:0% +made that decision is going to handt you +so if that decision making is impair you + + align:start position:0% +so if that decision making is impair you + + + align:start position:0% +so if that decision making is impair you +have very bad consequences one of the + + align:start position:0% +have very bad consequences one of the + + + align:start position:0% +have very bad consequences one of the +things that I am uh that it also happens + + align:start position:0% +things that I am uh that it also happens + + + align:start position:0% +things that I am uh that it also happens +in the office building with the respect + + align:start position:0% +in the office building with the respect + + + align:start position:0% +in the office building with the respect +to health there are several studies this + + align:start position:0% +to health there are several studies this + + + align:start position:0% +to health there are several studies this +is one that I did was basically + + align:start position:0% +is one that I did was basically + + + align:start position:0% +is one that I did was basically +understanding what are the impacts of + + align:start position:0% +understanding what are the impacts of + + + align:start position:0% +understanding what are the impacts of +moving from an normal office building to + + align:start position:0% +moving from an normal office building to + + + align:start position:0% +moving from an normal office building to +a healthy building basically a lot of + + align:start position:0% +a healthy building basically a lot of + + + align:start position:0% +a healthy building basically a lot of +stuff happening in here for the + + align:start position:0% +stuff happening in here for the + + + align:start position:0% +stuff happening in here for the +technology around ventilation uh they + + align:start position:0% +technology around ventilation uh they + + + align:start position:0% +technology around ventilation uh they +have natural ventilation principles + + align:start position:0% +have natural ventilation principles + + + align:start position:0% +have natural ventilation principles +where uh they don't rely a lot in in a + + align:start position:0% +where uh they don't rely a lot in in a + + + align:start position:0% +where uh they don't rely a lot in in a +mechanical ventilation system but what + + align:start position:0% +mechanical ventilation system but what + + + align:start position:0% +mechanical ventilation system but what +they have is a solar chimney that will + + align:start position:0% +they have is a solar chimney that will + + + align:start position:0% +they have is a solar chimney that will +actually make the air circulate it's + + align:start position:0% +actually make the air circulate it's + + + align:start position:0% +actually make the air circulate it's +very high ventilation rate in that one + + align:start position:0% +very high ventilation rate in that one + + + align:start position:0% +very high ventilation rate in that one +very good building and they actually + + align:start position:0% +very good building and they actually + + + align:start position:0% +very good building and they actually +work with me to understand what are the + + align:start position:0% +work with me to understand what are the + + + align:start position:0% +work with me to understand what are the +impacts of of this building on health so + + align:start position:0% +impacts of of this building on health so + + + align:start position:0% +impacts of of this building on health so +we work with them for over two years for + + align:start position:0% +we work with them for over two years for + + + align:start position:0% +we work with them for over two years for +three years so we were with them before + + align:start position:0% +three years so we were with them before + + + align:start position:0% +three years so we were with them before +everyone was moved and then 70% of the + + align:start position:0% +everyone was moved and then 70% of the + + + align:start position:0% +everyone was moved and then 70% of the +workforce of the municipality were moved + + align:start position:0% +workforce of the municipality were moved + + + align:start position:0% +workforce of the municipality were moved +to this healthy building and 30% was + + align:start position:0% +to this healthy building and 30% was + + + align:start position:0% +to this healthy building and 30% was +staying here and the reason why they + + align:start position:0% +staying here and the reason why they + + + align:start position:0% +staying here and the reason why they +stay here is mainly because they were + + align:start position:0% +stay here is mainly because they were + + + align:start position:0% +stay here is mainly because they were +not exposed to to the public very Wells + + align:start position:0% +not exposed to to the public very Wells + + + align:start position:0% +not exposed to to the public very Wells +if you didn't have a lot of meetings + + align:start position:0% +if you didn't have a lot of meetings + + + align:start position:0% +if you didn't have a lot of meetings +with external people if the citizens + + align:start position:0% +with external people if the citizens + + + align:start position:0% +with external people if the citizens +didn't have to meet you then they will + + align:start position:0% +didn't have to meet you then they will + + + align:start position:0% +didn't have to meet you then they will +not have you in the flagship building + + align:start position:0% +not have you in the flagship building + + + align:start position:0% +not have you in the flagship building +but they will give you where you are + + align:start position:0% +but they will give you where you are + + + align:start position:0% +but they will give you where you are +which means that it's also a very nice + + align:start position:0% +which means that it's also a very nice + + + align:start position:0% +which means that it's also a very nice +environment because it's actually not + + align:start position:0% +environment because it's actually not + + + align:start position:0% +environment because it's actually not +you again who decides where you want to + + align:start position:0% +you again who decides where you want to + + + align:start position:0% +you again who decides where you want to +go but it's actually the municipality + + align:start position:0% +go but it's actually the municipality + + + align:start position:0% +go but it's actually the municipality +very random decision it forces you to + + align:start position:0% +very random decision it forces you to + + + align:start position:0% +very random decision it forces you to +stay where you are it forces you to + + align:start position:0% +stay where you are it forces you to + + + align:start position:0% +stay where you are it forces you to +change actually this building is even + + align:start position:0% +change actually this building is even + + + align:start position:0% +change actually this building is even +put in a in an area where it's more + + align:start position:0% +put in a in an area where it's more + + + align:start position:0% +put in a in an area where it's more +polluted so it's actually you would + + align:start position:0% +polluted so it's actually you would + + + align:start position:0% +polluted so it's actually you would +expect in that one to backfire and they + + align:start position:0% +expect in that one to backfire and they + + + align:start position:0% +expect in that one to backfire and they +work with us to be able to assess the + + align:start position:0% +work with us to be able to assess the + + + align:start position:0% +work with us to be able to assess the +the um the health and wellbeing of + + align:start position:0% +the um the health and wellbeing of + + + align:start position:0% +the um the health and wellbeing of +people and also the sick Lees around uh + + align:start position:0% +people and also the sick Lees around uh + + + align:start position:0% +people and also the sick Lees around uh +the changes in sick leaf and what you + + align:start position:0% +the changes in sick leaf and what you + + + align:start position:0% +the changes in sick leaf and what you +see is that when you measure how these + + align:start position:0% +see is that when you measure how these + + + align:start position:0% +see is that when you measure how these +people feel the people we were seeing + + align:start position:0% +people feel the people we were seeing + + + align:start position:0% +people feel the people we were seeing +the the prevalence of sick building + + align:start position:0% +the the prevalence of sick building + + + align:start position:0% +the the prevalence of sick building +syndrome so the amount of people going + + align:start position:0% +syndrome so the amount of people going + + + align:start position:0% +syndrome so the amount of people going +there with fatigue and other symptoms uh + + align:start position:0% +there with fatigue and other symptoms uh + + + align:start position:0% +there with fatigue and other symptoms uh +and you will see that almost one out of + + align:start position:0% +and you will see that almost one out of + + + align:start position:0% +and you will see that almost one out of +two will be suffering from that before + + align:start position:0% +two will be suffering from that before + + + align:start position:0% +two will be suffering from that before +moving and then as they moved the people + + align:start position:0% +moving and then as they moved the people + + + align:start position:0% +moving and then as they moved the people +that were to a new building h went down + + align:start position:0% +that were to a new building h went down + + + align:start position:0% +that were to a new building h went down +by half the amount of people reporting + + align:start position:0% +by half the amount of people reporting + + + align:start position:0% +by half the amount of people reporting +SI building syndrome and the others stay + + align:start position:0% +SI building syndrome and the others stay + + + align:start position:0% +SI building syndrome and the others stay +where they are so this Gap here will + + align:start position:0% +where they are so this Gap here will + + + align:start position:0% +where they are so this Gap here will +tell you the difference uh in health + + align:start position:0% +tell you the difference uh in health + + + align:start position:0% +tell you the difference uh in health +associated with the building and if you + + align:start position:0% +associated with the building and if you + + + align:start position:0% +associated with the building and if you +will do the quantification and Link it + + align:start position:0% +will do the quantification and Link it + + + align:start position:0% +will do the quantification and Link it +to the sck Lea and so forth you will see + + align:start position:0% +to the sck Lea and so forth you will see + + + align:start position:0% +to the sck Lea and so forth you will see +that if you will capitalize that + + align:start position:0% +that if you will capitalize that + + + align:start position:0% +that if you will capitalize that +investment will be around 2.5 million + + align:start position:0% +investment will be around 2.5 million + + + align:start position:0% +investment will be around 2.5 million +euros that this municipality is actually + + align:start position:0% +euros that this municipality is actually + + + align:start position:0% +euros that this municipality is actually +getting by just having people taking + + align:start position:0% +getting by just having people taking + + + align:start position:0% +getting by just having people taking +just less days of sick Le so it was + + align:start position:0% +just less days of sick Le so it was + + + align:start position:0% +just less days of sick Le so it was +around one to two days uh less sick Le + + align:start position:0% +around one to two days uh less sick Le + + + align:start position:0% +around one to two days uh less sick Le +and that is what you will get there um + + align:start position:0% +and that is what you will get there um + + + align:start position:0% +and that is what you will get there um +now why is this important not only for + + align:start position:0% +now why is this important not only for + + + align:start position:0% +now why is this important not only for +the municipality but in general for + + align:start position:0% +the municipality but in general for + + + align:start position:0% +the municipality but in general for +corporate tenants is because if you look + + align:start position:0% +corporate tenants is because if you look + + + align:start position:0% +corporate tenants is because if you look +at the income statements of tenants you + + align:start position:0% +at the income statements of tenants you + + + align:start position:0% +at the income statements of tenants you +will see that most of the money of a + + align:start position:0% +will see that most of the money of a + + + align:start position:0% +will see that most of the money of a +corporate goes to pay employees so we + + align:start position:0% +corporate goes to pay employees so we + + + align:start position:0% +corporate goes to pay employees so we +were talking a lot over the first two + + align:start position:0% +were talking a lot over the first two + + + align:start position:0% +were talking a lot over the first two +lectures around the H not only because + + align:start position:0% +lectures around the H not only because + + + align:start position:0% +lectures around the H not only because +of the money but also the CO2 emissions + + align:start position:0% +of the money but also the CO2 emissions + + + align:start position:0% +of the money but also the CO2 emissions +uh uh involved in it but basically about + + align:start position:0% +uh uh involved in it but basically about + + + align:start position:0% +uh uh involved in it but basically about +this + + align:start position:0% +this + + + align:start position:0% +this +$3 uh part of the buy so basically this + + align:start position:0% +$3 uh part of the buy so basically this + + + align:start position:0% +$3 uh part of the buy so basically this +is the 330 300 rule is the proportion of + + align:start position:0% +is the 330 300 rule is the proportion of + + + align:start position:0% +is the 330 300 rule is the proportion of +money that goes to utilities rent + + align:start position:0% +money that goes to utilities rent + + + align:start position:0% +money that goes to utilities rent +and payroll we were talking about that + + align:start position:0% +and payroll we were talking about that + + + align:start position:0% +and payroll we were talking about that +part of the p and now we are talking + + align:start position:0% +part of the p and now we are talking + + + align:start position:0% +part of the p and now we are talking +about that part of the P so even one + + align:start position:0% +about that part of the P so even one + + + align:start position:0% +about that part of the P so even one +like very minor changes in here will + + align:start position:0% +like very minor changes in here will + + + align:start position:0% +like very minor changes in here will +generate ultimately a big impact in the + + align:start position:0% +generate ultimately a big impact in the + + + align:start position:0% +generate ultimately a big impact in the +in the income statements so we are going + + align:start position:0% +in the income statements so we are going + + + align:start position:0% +in the income statements so we are going +to talk now about how to quantify those + + align:start position:0% +to talk now about how to quantify those + + + align:start position:0% +to talk now about how to quantify those +you want to say something yeah uh I mean + + align:start position:0% +you want to say something yeah uh I mean + + + align:start position:0% +you want to say something yeah uh I mean +a good a good example to support the + + align:start position:0% +a good a good example to support the + + + align:start position:0% +a good a good example to support the +this hous building uh in China a very + + align:start position:0% +this hous building uh in China a very + + + align:start position:0% +this hous building uh in China a very +famous developer uh called B and another + + align:start position:0% +famous developer uh called B and another + + + align:start position:0% +famous developer uh called B and another +of + + align:start position:0% +of + + + align:start position:0% +of +is famous about the housing building and + + align:start position:0% +is famous about the housing building and + + + align:start position:0% +is famous about the housing building and +one the same location uh uh the gous + + align:start position:0% +one the same location uh uh the gous + + + align:start position:0% +one the same location uh uh the gous +projects always price higher than + + align:start position:0% +projects always price higher than + + + align:start position:0% +projects always price higher than +competitor and always uh always can + + align:start position:0% +competitor and always uh always can + + + align:start position:0% +competitor and always uh always can +higher than 10% to uh 15% have price + + align:start position:0% +higher than 10% to uh 15% have price + + + align:start position:0% +higher than 10% to uh 15% have price +than others competitor right so and + + align:start position:0% +than others competitor right so and + + + align:start position:0% +than others competitor right so and +always the consumer prefer to uh this + + align:start position:0% +always the consumer prefer to uh this + + + align:start position:0% +always the consumer prefer to uh this +higher price because + + align:start position:0% + + + + align:start position:0% + +also great that's liation about this + + align:start position:0% +also great that's liation about this + + + align:start position:0% +also great that's liation about this +only + + align:start position:0% +only + + + align:start position:0% +only +to + + align:start position:0% +to + + + align:start position:0% +to +building + + align:start position:0% +building + + + align:start position:0% +building +low yeah we'll talk more on uh on + + align:start position:0% +low yeah we'll talk more on uh on + + + align:start position:0% +low yeah we'll talk more on uh on +Tuesday also about these differences in + + align:start position:0% +Tuesday also about these differences in + + + align:start position:0% +Tuesday also about these differences in +market segments and so forth + + align:start position:0% +market segments and so forth + + + align:start position:0% +market segments and so forth +yeah people + + align:start position:0% + + + + align:start position:0% + +it be the that those + + align:start position:0% + + + + align:start position:0% + +people yeah well that would be the the + + align:start position:0% +people yeah well that would be the the + + + align:start position:0% +people yeah well that would be the the +reason why you will have a baseline + + align:start position:0% +reason why you will have a baseline + + + align:start position:0% +reason why you will have a baseline +right so we were with them before they + + align:start position:0% +right so we were with them before they + + + align:start position:0% +right so we were with them before they +were moved so if these people were just + + align:start position:0% +were moved so if these people were just + + + align:start position:0% +were moved so if these people were just +in general different they are right they + + align:start position:0% +in general different they are right they + + + align:start position:0% +in general different they are right they +are different people and so forth but + + align:start position:0% +are different people and so forth but + + + align:start position:0% +are different people and so forth but +basically what we are using is the + + align:start position:0% +basically what we are using is the + + + align:start position:0% +basically what we are using is the +differences in in health symptoms and + + align:start position:0% +differences in in health symptoms and + + + align:start position:0% +differences in in health symptoms and +sickly before and after they were moved + + align:start position:0% +sickly before and after they were moved + + + align:start position:0% +sickly before and after they were moved +for everyone so you're looking at within + + align:start position:0% +for everyone so you're looking at within + + + align:start position:0% +for everyone so you're looking at within +person variation so in that sense you + + align:start position:0% +person variation so in that sense you + + + align:start position:0% +person variation so in that sense you +are not comparing people to people you + + align:start position:0% +are not comparing people to people you + + + align:start position:0% +are not comparing people to people you +are comparing someone before and after + + align:start position:0% +are comparing someone before and after + + + align:start position:0% +are comparing someone before and after +the move uh for both groups and the + + align:start position:0% +the move uh for both groups and the + + + align:start position:0% +the move uh for both groups and the +difference in the in the Delta for the + + align:start position:0% +difference in the in the Delta for the + + + align:start position:0% +difference in the in the Delta for the +people that moved and the people that + + align:start position:0% +people that moved and the people that + + + align:start position:0% +people that moved and the people that +didn't move is what gives you the impact + + align:start position:0% +didn't move is what gives you the impact + + + align:start position:0% +didn't move is what gives you the impact +of the + + align:start position:0% +of the + + + align:start position:0% +of the +building um all right so if you think + + align:start position:0% +building um all right so if you think + + + align:start position:0% +building um all right so if you think +about the the translation of that into + + align:start position:0% +about the the translation of that into + + + align:start position:0% +about the the translation of that into +money for the average tenant you see + + align:start position:0% +money for the average tenant you see + + + align:start position:0% +money for the average tenant you see +that most of it like this a um a fake + + align:start position:0% +that most of it like this a um a fake + + + align:start position:0% +that most of it like this a um a fake +company a fake company that the income + + align:start position:0% +company a fake company that the income + + + align:start position:0% +company a fake company that the income +statements that the the professors at + + align:start position:0% +statements that the the professors at + + + align:start position:0% +statements that the the professors at +Harvard came up with to to show how to + + align:start position:0% +Harvard came up with to to show how to + + + align:start position:0% +Harvard came up with to to show how to +quantify those uh benefits for for + + align:start position:0% +quantify those uh benefits for for + + + align:start position:0% +quantify those uh benefits for for +teners see that that average tenner will + + align:start position:0% +teners see that that average tenner will + + + align:start position:0% +teners see that that average tenner will +have six million in Revenue three + + align:start position:0% +have six million in Revenue three + + + align:start position:0% +have six million in Revenue three +million in payroll that is sort of half + + align:start position:0% +million in payroll that is sort of half + + + align:start position:0% +million in payroll that is sort of half +of it uh and then you will pay 300,000 + + align:start position:0% +of it uh and then you will pay 300,000 + + + align:start position:0% +of it uh and then you will pay 300,000 +in in rent 30,000 in utility and so + + align:start position:0% +in in rent 30,000 in utility and so + + + align:start position:0% +in in rent 30,000 in utility and so +forth and you want to consider what will + + align:start position:0% +forth and you want to consider what will + + + align:start position:0% +forth and you want to consider what will +happen if you double the ventilation + + align:start position:0% +happen if you double the ventilation + + + align:start position:0% +happen if you double the ventilation +rate from 20 CPM per person to 40 CPM + + align:start position:0% +rate from 20 CPM per person to 40 CPM + + + align:start position:0% +rate from 20 CPM per person to 40 CPM +per person and see what will be the + + align:start position:0% +per person and see what will be the + + + align:start position:0% +per person and see what will be the +impact so if you bring the science into + + align:start position:0% +impact so if you bring the science into + + + align:start position:0% +impact so if you bring the science into +play you will be like okay the the cost + + align:start position:0% +play you will be like okay the the cost + + + align:start position:0% +play you will be like okay the the cost +will be around 1,600 that would be the + + align:start position:0% +will be around 1,600 that would be the + + + align:start position:0% +will be around 1,600 that would be the +the cost of of doubling the ventilation + + align:start position:0% +the cost of of doubling the ventilation + + + align:start position:0% +the cost of of doubling the ventilation +that is still a quite significant part + + align:start position:0% +that is still a quite significant part + + + align:start position:0% +that is still a quite significant part +of the utility but it is what it is and + + align:start position:0% +of the utility but it is what it is and + + + align:start position:0% +of the utility but it is what it is and +now if you get people less sick it means + + align:start position:0% +now if you get people less sick it means + + + align:start position:0% +now if you get people less sick it means +that basically the way that they + + align:start position:0% +that basically the way that they + + + align:start position:0% +that basically the way that they +conceptualize that you have to pay less + + align:start position:0% +conceptualize that you have to pay less + + + align:start position:0% +conceptualize that you have to pay less +number of people because now you are + + align:start position:0% +number of people because now you are + + + align:start position:0% +number of people because now you are +paying some people that will be sick or + + align:start position:0% +paying some people that will be sick or + + + align:start position:0% +paying some people that will be sick or +you have to pay less number of days per + + align:start position:0% +you have to pay less number of days per + + + align:start position:0% +you have to pay less number of days per +person because some days you are paying + + align:start position:0% +person because some days you are paying + + + align:start position:0% +person because some days you are paying +and these people are sick so you know + + align:start position:0% +and these people are sick so you know + + + align:start position:0% +and these people are sick so you know +you could just do the exact same Revenue + + align:start position:0% +you could just do the exact same Revenue + + + align:start position:0% +you could just do the exact same Revenue +with just less uh money because now + + align:start position:0% +with just less uh money because now + + + align:start position:0% +with just less uh money because now +these people are fully operational and + + align:start position:0% +these people are fully operational and + + + align:start position:0% +these people are fully operational and +they work all the time and they are also + + align:start position:0% +they work all the time and they are also + + + align:start position:0% +they work all the time and they are also +more productive so they are actually + + align:start position:0% +more productive so they are actually + + + align:start position:0% +more productive so they are actually +more able to produce whatever they are + + align:start position:0% +more able to produce whatever they are + + + align:start position:0% +more able to produce whatever they are +doing or better quality so that's how it + + align:start position:0% +doing or better quality so that's how it + + + align:start position:0% +doing or better quality so that's how it +is uh so in total this how this is the + + align:start position:0% +is uh so in total this how this is the + + + align:start position:0% +is uh so in total this how this is the +amount of of benefits so you see that + + align:start position:0% +amount of of benefits so you see that + + + align:start position:0% +amount of of benefits so you see that +anyways again small impacts on here and + + align:start position:0% +anyways again small impacts on here and + + + align:start position:0% +anyways again small impacts on here and +here will have a big impact on the + + align:start position:0% +here will have a big impact on the + + + align:start position:0% +here will have a big impact on the +ultimate bottom line and that's sort of + + align:start position:0% +ultimate bottom line and that's sort of + + + align:start position:0% +ultimate bottom line and that's sort of +the message here um even if you are very + + align:start position:0% +the message here um even if you are very + + + align:start position:0% +the message here um even if you are very +conservative you will have because you + + align:start position:0% +conservative you will have because you + + + align:start position:0% +conservative you will have because you +are chipping in this big big large + + align:start position:0% +are chipping in this big big large + + + align:start position:0% +are chipping in this big big large +shares of the buy it will be a very very + + align:start position:0% +shares of the buy it will be a very very + + + align:start position:0% +shares of the buy it will be a very very +powerful impact on your incon statements + + align:start position:0% +powerful impact on your incon statements + + + align:start position:0% +powerful impact on your incon statements +as a tenant so if you believe any impact + + align:start position:0% +as a tenant so if you believe any impact + + + align:start position:0% +as a tenant so if you believe any impact +then it's worth probably going for it + + align:start position:0% +then it's worth probably going for it + + + align:start position:0% +then it's worth probably going for it +because anything that will impact these + + align:start position:0% +because anything that will impact these + + + align:start position:0% +because anything that will impact these +large numbers will have a big impact + + align:start position:0% +large numbers will have a big impact + + + align:start position:0% +large numbers will have a big impact +here now uh and that will also for the + + align:start position:0% +here now uh and that will also for the + + + align:start position:0% +here now uh and that will also for the +split incentive type of bargain in + + align:start position:0% +split incentive type of bargain in + + + align:start position:0% +split incentive type of bargain in +William you can still because you you + + align:start position:0% +William you can still because you you + + + align:start position:0% +William you can still because you you +grow the pie so much the landlord can + + align:start position:0% +grow the pie so much the landlord can + + + align:start position:0% +grow the pie so much the landlord can +still say hey give me some part of this + + align:start position:0% +still say hey give me some part of this + + + align:start position:0% +still say hey give me some part of this +because I am the one making the + + align:start position:0% +because I am the one making the + + + align:start position:0% +because I am the one making the +investment and you still have a lot of + + align:start position:0% +investment and you still have a lot of + + + align:start position:0% +investment and you still have a lot of +margin to make both a win-win now you + + align:start position:0% +margin to make both a win-win now you + + + align:start position:0% +margin to make both a win-win now you +have to communicate and we will talk + + align:start position:0% +have to communicate and we will talk + + + align:start position:0% +have to communicate and we will talk +about it later CZ maybe I need to use + + align:start position:0% +about it later CZ maybe I need to use + + + align:start position:0% +about it later CZ maybe I need to use +five minutes of your lecture on + + align:start position:0% +five minutes of your lecture on + + + align:start position:0% +five minutes of your lecture on +Tuesday welcome how are you sure you + + align:start position:0% +Tuesday welcome how are you sure you + + + align:start position:0% +Tuesday welcome how are you sure you +enjoy it any time there you go anytime + + align:start position:0% +enjoy it any time there you go anytime + + + align:start position:0% +enjoy it any time there you go anytime +that's what I like uh let's bring the + + align:start position:0% +that's what I like uh let's bring the + + + align:start position:0% +that's what I like uh let's bring the +projector but uh I don't want to rush + + align:start position:0% +projector but uh I don't want to rush + + + align:start position:0% +projector but uh I don't want to rush +the the last wrap-up because actually + + align:start position:0% +the the last wrap-up because actually + + + align:start position:0% +the the last wrap-up because actually +it's connected to you uh but basically + + align:start position:0% +it's connected to you uh but basically + + + align:start position:0% +it's connected to you uh but basically +here you see the the idea also that we + + align:start position:0% +here you see the the idea also that we + + + align:start position:0% +here you see the the idea also that we +talk at the beginning you grow the pie + + align:start position:0% +talk at the beginning you grow the pie + + + align:start position:0% +talk at the beginning you grow the pie +and you have the negotiation how much + + align:start position:0% +and you have the negotiation how much + + + align:start position:0% +and you have the negotiation how much +you're going to give and so forth and + + align:start position:0% +you're going to give and so forth and + + + align:start position:0% +you're going to give and so forth and +what is the the approach do negotiation + + align:start position:0% +what is the the approach do negotiation + + + align:start position:0% +what is the the approach do negotiation +is something that is H for the next part + + align:start position:0% +is something that is H for the next part + + + align:start position:0% +is something that is H for the next part +I will Pro I promise that I will only + + align:start position:0% +I will Pro I promise that I will only + + + align:start position:0% +I will Pro I promise that I will only +take five minutes and in a way that is + + align:start position:0% +take five minutes and in a way that is + + + align:start position:0% +take five minutes and in a way that is +connected to your lecture but I don't + + align:start position:0% +connected to your lecture but I don't + + + align:start position:0% +connected to your lecture but I don't +want to keep you longer than we are + + align:start position:0% +want to keep you longer than we are + + + align:start position:0% +want to keep you longer than we are +supposed to I want to take some + + align:start position:0% +supposed to I want to take some + + + align:start position:0% +supposed to I want to take some +questions and then we are going to go up + + align:start position:0% +questions and then we are going to go up + + + align:start position:0% +questions and then we are going to go up +but one last slide this is just an + + align:start position:0% +but one last slide this is just an + + + align:start position:0% +but one last slide this is just an +hypothetical case but this is a slide + + align:start position:0% +hypothetical case but this is a slide + + + align:start position:0% +hypothetical case but this is a slide +that will show you what will be the + + align:start position:0% +that will show you what will be the + + + align:start position:0% +that will show you what will be the +numbers if you will use the best science + + align:start position:0% +numbers if you will use the best science + + + align:start position:0% +numbers if you will use the best science +that you have to understand what are the + + align:start position:0% +that you have to understand what are the + + + align:start position:0% +that you have to understand what are the +impacts of increasing ventilation rates + + align:start position:0% +impacts of increasing ventilation rates + + + align:start position:0% +impacts of increasing ventilation rates +either doubling or increasing by 20% uh + + align:start position:0% +either doubling or increasing by 20% uh + + + align:start position:0% +either doubling or increasing by 20% uh +in an average office building in the + + align:start position:0% +in an average office building in the + + + align:start position:0% +in an average office building in the +United States actually for the entire + + align:start position:0% +United States actually for the entire + + + align:start position:0% +United States actually for the entire +office building portfolio in the United + + align:start position:0% +office building portfolio in the United + + + align:start position:0% +office building portfolio in the United +States what will be the consequence for + + align:start position:0% +States what will be the consequence for + + + align:start position:0% +States what will be the consequence for +the energy cost the absentismo + + align:start position:0% +the energy cost the absentismo + + + align:start position:0% +the energy cost the absentismo +and therefore the the performance here + + align:start position:0% +and therefore the the performance here + + + align:start position:0% +and therefore the the performance here +and what will be the The Net Present + + align:start position:0% +and what will be the The Net Present + + + align:start position:0% +and what will be the The Net Present +Value impact of that you see that if you + + align:start position:0% +Value impact of that you see that if you + + + align:start position:0% +Value impact of that you see that if you +will double the ventilation rate even + + align:start position:0% +will double the ventilation rate even + + + align:start position:0% +will double the ventilation rate even +before covid this is a study of 2012 but + + align:start position:0% +before covid this is a study of 2012 but + + + align:start position:0% +before covid this is a study of 2012 but +is the most comprehensive one you have + + align:start position:0% +is the most comprehensive one you have + + + align:start position:0% +is the most comprehensive one you have +still 37 billion gains of doubling the + + align:start position:0% +still 37 billion gains of doubling the + + + align:start position:0% +still 37 billion gains of doubling the +ventilation rate and you will have 20% + + align:start position:0% +ventilation rate and you will have 20% + + + align:start position:0% +ventilation rate and you will have 20% +um if you will increase by 20% the + + align:start position:0% +um if you will increase by 20% the + + + align:start position:0% +um if you will increase by 20% the +ventilation rate you will still have 30 + + align:start position:0% +ventilation rate you will still have 30 + + + align:start position:0% +ventilation rate you will still have 30 +billion Gaines if you compare the cost + + align:start position:0% +billion Gaines if you compare the cost + + + align:start position:0% +billion Gaines if you compare the cost +versus the the benefits using the best + + align:start position:0% +versus the the benefits using the best + + + align:start position:0% +versus the the benefits using the best +science available + + align:start position:0% +science available + + + align:start position:0% +science available +now these numbers are big enough that + + align:start position:0% +now these numbers are big enough that + + + align:start position:0% +now these numbers are big enough that +even if you have a big margin of error + + align:start position:0% +even if you have a big margin of error + + + align:start position:0% +even if you have a big margin of error +big big big error bars there as you like + + align:start position:0% +big big big error bars there as you like + + + align:start position:0% +big big big error bars there as you like +to do in the in the in the science + + align:start position:0% +to do in the in the in the science + + + align:start position:0% +to do in the in the in the science +literature you will still have a + + align:start position:0% +literature you will still have a + + + align:start position:0% +literature you will still have a +positive number so I don't want you to + + align:start position:0% +positive number so I don't want you to + + + align:start position:0% +positive number so I don't want you to +kind of memorize 37 or 13 but I want you + + align:start position:0% +kind of memorize 37 or 13 but I want you + + + align:start position:0% +kind of memorize 37 or 13 but I want you +to walk through it when you have the + + align:start position:0% +to walk through it when you have the + + + align:start position:0% +to walk through it when you have the +time before the midterm to see the whole + + align:start position:0% +time before the midterm to see the whole + + + align:start position:0% +time before the midterm to see the whole +logic and you see and realize that even + + align:start position:0% +logic and you see and realize that even + + + align:start position:0% +logic and you see and realize that even +if you have some uncertainties in there + + align:start position:0% +if you have some uncertainties in there + + + align:start position:0% +if you have some uncertainties in there +the gains are so large that is worth + + align:start position:0% +the gains are so large that is worth + + + align:start position:0% +the gains are so large that is worth +considering and we will talk more later + + align:start position:0% +considering and we will talk more later + + + align:start position:0% +considering and we will talk more later +about the barriers that will be how + + align:start position:0% +about the barriers that will be how + + + align:start position:0% +about the barriers that will be how +we're going to grab up everything but + + align:start position:0% +we're going to grab up everything but + + + align:start position:0% +we're going to grab up everything but +just for you to go home saying there is + + align:start position:0% +just for you to go home saying there is + + + align:start position:0% +just for you to go home saying there is +something to gain and then maybe in + + align:start position:0% +something to gain and then maybe in + + + align:start position:0% +something to gain and then maybe in +nakoto we want talk about why wouldn't + + align:start position:0% +nakoto we want talk about why wouldn't + + + align:start position:0% +nakoto we want talk about why wouldn't +you do it and now I will take the last + + align:start position:0% +you do it and now I will take the last + + + align:start position:0% +you do it and now I will take the last +question I let you free roit + + align:start position:0% + + + + align:start position:0% + +yes at the + + align:start position:0% +yes at the + + + align:start position:0% +yes at the +surve think the costs were higher than + + align:start position:0% +surve think the costs were higher than + + + align:start position:0% +surve think the costs were higher than +the benefits right well the cost only + + align:start position:0% +the benefits right well the cost only + + + align:start position:0% +the benefits right well the cost only +for that part yes but the the marginal + + align:start position:0% +for that part yes but the the marginal + + + align:start position:0% +for that part yes but the the marginal +um this is the the marginal benefit of + + align:start position:0% +um this is the the marginal benefit of + + + align:start position:0% +um this is the the marginal benefit of +making the building sustainable not only + + align:start position:0% +making the building sustainable not only + + + align:start position:0% +making the building sustainable not only +healthy but also improving the Energy + + align:start position:0% +healthy but also improving the Energy + + + align:start position:0% +healthy but also improving the Energy +Efficiency and the circularity these are + + align:start position:0% +Efficiency and the circularity these are + + + align:start position:0% +Efficiency and the circularity these are +I can talk hours about this building + + align:start position:0% +I can talk hours about this building + + + align:start position:0% +I can talk hours about this building +it's a building that is also based on + + align:start position:0% +it's a building that is also based on + + + align:start position:0% +it's a building that is also based on +principles of circularity the building + + align:start position:0% +principles of circularity the building + + + align:start position:0% +principles of circularity the building +is made we actually brought the Misty + + align:start position:0% +is made we actually brought the Misty + + + align:start position:0% +is made we actually brought the Misty +Netherlands Fox there the building is + + align:start position:0% +Netherlands Fox there the building is + + + align:start position:0% +Netherlands Fox there the building is +made in a way that all materials can be + + align:start position:0% +made in a way that all materials can be + + + align:start position:0% +made in a way that all materials can be +upcycled from the tables to the concrete + + align:start position:0% +upcycled from the tables to the concrete + + + align:start position:0% +upcycled from the tables to the concrete +and so forth so that require also an + + align:start position:0% +and so forth so that require also an + + + align:start position:0% +and so forth so that require also an +extra uh amount of money to select those + + align:start position:0% +extra uh amount of money to select those + + + align:start position:0% +extra uh amount of money to select those +materials have the people that to make + + align:start position:0% +materials have the people that to make + + + align:start position:0% +materials have the people that to make +sure that they wouldn't treat it in a + + align:start position:0% +sure that they wouldn't treat it in a + + + align:start position:0% +sure that they wouldn't treat it in a +way that will make it less uh um less + + align:start position:0% +way that will make it less uh um less + + + align:start position:0% +way that will make it less uh um less +upsable and so forth so all of that is + + align:start position:0% +upsable and so forth so all of that is + + + align:start position:0% +upsable and so forth so all of that is +3.4 they didn't quantify how much it was + + align:start position:0% +3.4 they didn't quantify how much it was + + + align:start position:0% +3.4 they didn't quantify how much it was +exactly the healthy aspects everything + + align:start position:0% +exactly the healthy aspects everything + + + align:start position:0% +exactly the healthy aspects everything +was a bundle what they quantify here but + + align:start position:0% +was a bundle what they quantify here but + + + align:start position:0% +was a bundle what they quantify here but +this is only the healthy aspect that + + align:start position:0% +this is only the healthy aspect that + + + align:start position:0% +this is only the healthy aspect that +already will cover quite a big chunk of + + align:start position:0% +already will cover quite a big chunk of + + + align:start position:0% +already will cover quite a big chunk of +it and then if you put the changes in + + align:start position:0% +it and then if you put the changes in + + + align:start position:0% +it and then if you put the changes in +operation because you have a natural + + align:start position:0% +operation because you have a natural + + + align:start position:0% +operation because you have a natural +ventilation system instead of a + + align:start position:0% +ventilation system instead of a + + + align:start position:0% +ventilation system instead of a +mechanical ventilation system so you + + align:start position:0% +mechanical ventilation system so you + + + align:start position:0% +mechanical ventilation system so you +need less uh operational cost of + + align:start position:0% +need less uh operational cost of + + + align:start position:0% +need less uh operational cost of +maintaining that edge back system so for + + align:start position:0% +maintaining that edge back system so for + + + align:start position:0% +maintaining that edge back system so for +that cost will be much much higher 2.5 + + align:start position:0% +that cost will be much much higher 2.5 + + + align:start position:0% +that cost will be much much higher 2.5 +million per year all no it's capitalized + + align:start position:0% +million per year all no it's capitalized + + + align:start position:0% +million per year all no it's capitalized +capitalized yeah everything is + + align:start position:0% +capitalized yeah everything is + + + align:start position:0% +capitalized yeah everything is +capitalized good good question right + + align:start position:0% +capitalized good good question right + + + align:start position:0% +capitalized good good question right +thank you so much guys I'll see you + + align:start position:0% +thank you so much guys I'll see you + + + align:start position:0% +thank you so much guys I'll see you +tomorrow and on Tuesday we'll gra that + + align:start position:0% +tomorrow and on Tuesday we'll gra that + + + align:start position:0% +tomorrow and on Tuesday we'll gra that +thank you for all the questions + + align:start position:0% +thank you for all the questions + + + align:start position:0% +thank you for all the questions +appreciate it \ No newline at end of file diff --git a/9Cxa0c8P9Qc.txt b/9Cxa0c8P9Qc.txt new file mode 100644 index 0000000000000000000000000000000000000000..3e4da5d039c8af5be06d8ca922a79fa30403f462 --- /dev/null +++ b/9Cxa0c8P9Qc.txt @@ -0,0 +1,667 @@ +align:start position:0% + +hello I want to give a sense of how some + + align:start position:0% +hello I want to give a sense of how some + + + align:start position:0% +hello I want to give a sense of how some +problem sets are going to work or the + + align:start position:0% +problem sets are going to work or the + + + align:start position:0% +problem sets are going to work or the +majority of the time generally speaking + + align:start position:0% +majority of the time generally speaking + + + align:start position:0% +majority of the time generally speaking +you'll be given some instructions on + + align:start position:0% +you'll be given some instructions on + + + align:start position:0% +you'll be given some instructions on +what to do like write a routine that + + align:start position:0% +what to do like write a routine that + + + align:start position:0% +what to do like write a routine that +takes a string representing in harmonic + + align:start position:0% +takes a string representing in harmonic + + + align:start position:0% +takes a string representing in harmonic +with minus sign for Flats we'll talk + + align:start position:0% +with minus sign for Flats we'll talk + + + align:start position:0% +with minus sign for Flats we'll talk +about that in a bit and number sign for + + align:start position:0% +about that in a bit and number sign for + + + align:start position:0% +about that in a bit and number sign for +sharps and rning a new string that is an + + align:start position:0% +sharps and rning a new string that is an + + + align:start position:0% +sharps and rning a new string that is an +n and harmonic you're not allowed to + + align:start position:0% +n and harmonic you're not allowed to + + + align:start position:0% +n and harmonic you're not allowed to +change it but I can here that is an and + + align:start position:0% +change it but I can here that is an and + + + align:start position:0% +change it but I can here that is an and +harmonic of the pitch you will be given + + align:start position:0% +harmonic of the pitch you will be given + + + align:start position:0% +harmonic of the pitch you will be given +valid input only I will always tell you + + align:start position:0% +valid input only I will always tell you + + + align:start position:0% +valid input only I will always tell you +if you have to check for invalid input + + align:start position:0% +if you have to check for invalid input + + + align:start position:0% +if you have to check for invalid input +um if there's more than one valid + + align:start position:0% +um if there's more than one valid + + + align:start position:0% +um if there's more than one valid +inharmonic you can give any inharmonic + + align:start position:0% +inharmonic you can give any inharmonic + + + align:start position:0% +inharmonic you can give any inharmonic +up to double Flats of shuts then below + + align:start position:0% +up to double Flats of shuts then below + + + align:start position:0% +up to double Flats of shuts then below +you're going to be + + align:start position:0% +you're going to be + + + align:start position:0% +you're going to be +giving um the name of the routine that + + align:start position:0% +giving um the name of the routine that + + + align:start position:0% +giving um the name of the routine that +you're going to need write along with um + + align:start position:0% +you're going to need write along with um + + + align:start position:0% +you're going to need write along with um +usually the name of a variable that you + + align:start position:0% +usually the name of a variable that you + + + align:start position:0% +usually the name of a variable that you +should + + align:start position:0% +should + + + align:start position:0% +should +use and the type if you haven't looked + + align:start position:0% +use and the type if you haven't looked + + + align:start position:0% +use and the type if you haven't looked +at python typing this can be really + + align:start position:0% +at python typing this can be really + + + align:start position:0% +at python typing this can be really +exciting and what's + + align:start position:0% +exciting and what's + + + align:start position:0% +exciting and what's +output at this point you need to define + + align:start position:0% +output at this point you need to define + + + align:start position:0% +output at this point you need to define +the routine what often you can take some + + align:start position:0% +the routine what often you can take some + + + align:start position:0% +the routine what often you can take some +of the language from above but make it + + align:start position:0% +of the language from above but make it + + + align:start position:0% +of the language from above but make it +in your own words to see uh what + + align:start position:0% +in your own words to see uh what + + + align:start position:0% +in your own words to see uh what +happened but put it in the active uh + + align:start position:0% +happened but put it in the active uh + + + align:start position:0% +happened but put it in the active uh +voice takes in a string representing a + + align:start position:0% +voice takes in a string representing a + + + align:start position:0% +voice takes in a string representing a +pitch sorry I should say representing a + + align:start position:0% +pitch sorry I should say representing a + + + align:start position:0% +pitch sorry I should say representing a +pitch earlier U and returns a valid and + + align:start position:0% + + + + align:start position:0% + +harmonic for + + align:start position:0% +harmonic for + + + align:start position:0% +harmonic for +it um if there's specific things that + + align:start position:0% +it um if there's specific things that + + + align:start position:0% +it um if there's specific things that +constrain what the valid input might be + + align:start position:0% +constrain what the valid input might be + + + align:start position:0% +constrain what the valid input might be +I'll tend to write it here or you should + + align:start position:0% +I'll tend to write it here or you should + + + align:start position:0% +I'll tend to write it here or you should +be writing it in + + align:start position:0% +be writing it in + + + align:start position:0% +be writing it in +we write for humans to read not just for + + align:start position:0% +we write for humans to read not just for + + + align:start position:0% +we write for humans to read not just for +computers to process so it's always + + align:start position:0% +computers to process so it's always + + + align:start position:0% +computers to process so it's always +going to be important that uh that your + + align:start position:0% +going to be important that uh that your + + + align:start position:0% +going to be important that uh that your +code be documented and that your + + align:start position:0% +code be documented and that your + + + align:start position:0% +code be documented and that your +variable names be things that humans can + + align:start position:0% +variable names be things that humans can + + + align:start position:0% +variable names be things that humans can +understand okay so then you can go ahead + + align:start position:0% +understand okay so then you can go ahead + + + align:start position:0% +understand okay so then you can go ahead +and write your code and if you're uh not + + align:start position:0% +and write your code and if you're uh not + + + align:start position:0% +and write your code and if you're uh not +so great programmer maybe you'll start + + align:start position:0% +so great programmer maybe you'll start + + + align:start position:0% +so great programmer maybe you'll start +with if and harmonic in is + + align:start position:0% +with if and harmonic in is + + + align:start position:0% +with if and harmonic in is +the flat we then use minus signs for + + align:start position:0% +the flat we then use minus signs for + + + align:start position:0% +the flat we then use minus signs for +flat return + + align:start position:0% +flat return + + + align:start position:0% +flat return +DP otherwise return C Shar and at least + + align:start position:0% +DP otherwise return C Shar and at least + + + align:start position:0% +DP otherwise return C Shar and at least +maybe you'll get it right + + align:start position:0% +maybe you'll get it right + + + align:start position:0% +maybe you'll get it right +sometimes + + align:start position:0% +sometimes + + + align:start position:0% +sometimes +great now I will sometimes give you one + + align:start position:0% +great now I will sometimes give you one + + + align:start position:0% +great now I will sometimes give you one +or two test cases so maybe I'll say + + align:start position:0% +or two test cases so maybe I'll say + + + align:start position:0% +or two test cases so maybe I'll say +assert FP and + + align:start position:0% +assert FP and + + + align:start position:0% +assert FP and +harmonic E flat + + align:start position:0% +harmonic E flat + + + align:start position:0% +harmonic E flat +equals + + align:start position:0% +equals + + + align:start position:0% +equals +gar and can see that that + + align:start position:0% +gar and can see that that + + + align:start position:0% +gar and can see that that +works maybe if I'm very nice I'll give + + align:start position:0% +works maybe if I'm very nice I'll give + + + align:start position:0% +works maybe if I'm very nice I'll give +you two of them up and you can see that + + align:start position:0% +you two of them up and you can see that + + + align:start position:0% +you two of them up and you can see that +doesn't + + align:start position:0% +doesn't + + + align:start position:0% +doesn't +work I am not going to give you all of + + align:start position:0% +work I am not going to give you all of + + + align:start position:0% +work I am not going to give you all of +the interesting and + + align:start position:0% +the interesting and + + + align:start position:0% +the interesting and +fun test cases part of the thought + + align:start position:0% +fun test cases part of the thought + + + align:start position:0% +fun test cases part of the thought +process of this class part of why you + + align:start position:0% +process of this class part of why you + + + align:start position:0% +process of this class part of why you +get humani credit is is that you need to + + align:start position:0% +get humani credit is is that you need to + + + align:start position:0% +get humani credit is is that you need to +be thinking about well what are the + + align:start position:0% +be thinking about well what are the + + + align:start position:0% +be thinking about well what are the +weird cases okay uh I can put it if it + + align:start position:0% +weird cases okay uh I can put it if it + + + align:start position:0% +weird cases okay uh I can put it if it +this it's E flat and if it's dsharp it's + + align:start position:0% +this it's E flat and if it's dsharp it's + + + align:start position:0% +this it's E flat and if it's dsharp it's +E flat and so on oh + + align:start position:0% +E flat and so on oh + + + align:start position:0% +E flat and so on oh +but we going to need to make sure + + align:start position:0% +but we going to need to make sure + + + align:start position:0% +but we going to need to make sure +that this + + align:start position:0% + + + + align:start position:0% + +works or maybe I need to make sure + + align:start position:0% + + + + align:start position:0% + +that that + + align:start position:0% +that that + + + align:start position:0% +that that +works or at least that it's a valued + + align:start position:0% +works or at least that it's a valued + + + align:start position:0% +works or at least that it's a valued +answer + + align:start position:0% +answer + + + align:start position:0% +answer +ha and so part of what you need to do is + + align:start position:0% +ha and so part of what you need to do is + + + align:start position:0% +ha and so part of what you need to do is +be thinking about how do we write test + + align:start position:0% +be thinking about how do we write test + + + align:start position:0% +be thinking about how do we write test +code what are the test cases that + + align:start position:0% +code what are the test cases that + + + align:start position:0% +code what are the test cases that +Professor cord is going to be putting in + + align:start position:0% +Professor cord is going to be putting in + + + align:start position:0% +Professor cord is going to be putting in +such that it's going to challenge how I + + align:start position:0% +such that it's going to challenge how I + + + align:start position:0% +such that it's going to challenge how I +write you'll probably need to rewrite + + align:start position:0% +write you'll probably need to rewrite + + + align:start position:0% +write you'll probably need to rewrite +your code as you go great let's get + + align:start position:0% +your code as you go great let's get + + + align:start position:0% +your code as you go great let's get +started \ No newline at end of file diff --git a/9TQCKWWAVjM.txt b/9TQCKWWAVjM.txt new file mode 100644 index 0000000000000000000000000000000000000000..136af0276512c585665ca6a6958efe1ad56d1e43 --- /dev/null +++ b/9TQCKWWAVjM.txt @@ -0,0 +1,2115 @@ +align:start position:0% + +okay uh this video is about the third of + + align:start position:0% +okay uh this video is about the third of + + + align:start position:0% +okay uh this video is about the third of +the great Trio of partial differential + + align:start position:0% +the great Trio of partial differential + + + align:start position:0% +the great Trio of partial differential +equations ll's equation was number one + + align:start position:0% +equations ll's equation was number one + + + align:start position:0% +equations ll's equation was number one +that's called an elliptic equation the + + align:start position:0% +that's called an elliptic equation the + + + align:start position:0% +that's called an elliptic equation the +heat equation was number two that's + + align:start position:0% +heat equation was number two that's + + + align:start position:0% +heat equation was number two that's +called a parabolic equation now we reach + + align:start position:0% +called a parabolic equation now we reach + + + align:start position:0% +called a parabolic equation now we reach +the wave equation that's number three + + align:start position:0% +the wave equation that's number three + + + align:start position:0% +the wave equation that's number three +and it's called a hyperbolic equation so + + align:start position:0% +and it's called a hyperbolic equation so + + + align:start position:0% +and it's called a hyperbolic equation so +somehow the three equations remind us of + + align:start position:0% +somehow the three equations remind us of + + + align:start position:0% +somehow the three equations remind us of +ellipses parabas and hyperbolas there + + align:start position:0% +ellipses parabas and hyperbolas there + + + align:start position:0% +ellipses parabas and hyperbolas there +they have different types of solutions + + align:start position:0% +they have different types of solutions + + + align:start position:0% +they have different types of solutions +ll's equation you solve it inside a + + align:start position:0% +ll's equation you solve it inside a + + + align:start position:0% +ll's equation you solve it inside a +circle or inside some closed region the + + align:start position:0% +circle or inside some closed region the + + + align:start position:0% +circle or inside some closed region the +heat equation and the wave equation time + + align:start position:0% +heat equation and the wave equation time + + + align:start position:0% +heat equation and the wave equation time +enters and you're you're going forward + + align:start position:0% +enters and you're you're going forward + + + align:start position:0% +enters and you're you're going forward +in time the heat equation is first order + + align:start position:0% +in time the heat equation is first order + + + align:start position:0% +in time the heat equation is first order +in time + + align:start position:0% +in time + + + align:start position:0% +in time +dudt and the wave equation the full + + align:start position:0% +dudt and the wave equation the full + + + align:start position:0% +dudt and the wave equation the full +scale wave equation is second order in + + align:start position:0% +scale wave equation is second order in + + + align:start position:0% +scale wave equation is second order in +time that stands for the second + + align:start position:0% +time that stands for the second + + + align:start position:0% +time that stands for the second +derivative DC u dt^ 2 and it matches the + + align:start position:0% +derivative DC u dt^ 2 and it matches the + + + align:start position:0% +derivative DC u dt^ 2 and it matches the +second derivative in space with a + + align:start position:0% +second derivative in space with a + + + align:start position:0% +second derivative in space with a +velocity coefficient c^ + + align:start position:0% +velocity coefficient c^ + + + align:start position:0% +velocity coefficient c^ +2 it's I'm I'm in onedimensional space + + align:start position:0% +2 it's I'm I'm in onedimensional space + + + align:start position:0% +2 it's I'm I'm in onedimensional space +if if I were in three dimensions where + + align:start position:0% +if if I were in three dimensions where + + + align:start position:0% +if if I were in three dimensions where +we really have sound waves and light + + align:start position:0% +we really have sound waves and light + + + align:start position:0% +we really have sound waves and light +waves and all the most important things + + align:start position:0% +waves and all the most important things + + + align:start position:0% +waves and all the most important things +in life uh then there would be a uxx and + + align:start position:0% +in life uh then there would be a uxx and + + + align:start position:0% +in life uh then there would be a uxx and +a uy y and a u z Z second derivatives in + + align:start position:0% +a uy y and a u z Z second derivatives in + + + align:start position:0% +a uy y and a u z Z second derivatives in +all the space directions but let's good + + align:start position:0% +all the space directions but let's good + + + align:start position:0% +all the space directions but let's good +enough to do 1D so what are the + + align:start position:0% +enough to do 1D so what are the + + + align:start position:0% +enough to do 1D so what are the +differences first of all between the + + align:start position:0% +differences first of all between the + + + align:start position:0% +differences first of all between the +heat equation and wave equation so I'll + + align:start position:0% +heat equation and wave equation so I'll + + + align:start position:0% +heat equation and wave equation so I'll +say + + align:start position:0% + + + + align:start position:0% + +Heat versus + + align:start position:0% +Heat versus + + + align:start position:0% +Heat versus +wave equations what what are the sort of + + align:start position:0% +wave equations what what are the sort of + + + align:start position:0% +wave equations what what are the sort of +biggest differences the heat the + + align:start position:0% +biggest differences the heat the + + + align:start position:0% +biggest differences the heat the +signal + + align:start position:0% + + + + align:start position:0% + +travels infinitely + + align:start position:0% + + + + align:start position:0% + +fast and the wave equation the + + align:start position:0% +fast and the wave equation the + + + align:start position:0% +fast and the wave equation the +signal + + align:start position:0% + + + + align:start position:0% + +travels with finite velocity and that + + align:start position:0% +travels with finite velocity and that + + + align:start position:0% +travels with finite velocity and that +velocity is that number c with + + align:start position:0% + + + + align:start position:0% + +speed C + + align:start position:0% +speed C + + + align:start position:0% +speed C +so fortunately for sound waves the + + align:start position:0% +so fortunately for sound waves the + + + align:start position:0% +so fortunately for sound waves the +wave comes to us when I'm speaking into + + align:start position:0% +wave comes to us when I'm speaking into + + + align:start position:0% +wave comes to us when I'm speaking into +speaking to + + align:start position:0% +speaking to + + + align:start position:0% +speaking to +you my voice is my my voice is traveling + + align:start position:0% +you my voice is my my voice is traveling + + + align:start position:0% +you my voice is my my voice is traveling +out to the microphone at the speed of + + align:start position:0% +out to the microphone at the speed of + + + align:start position:0% +out to the microphone at the speed of +sound the speed + + align:start position:0% +sound the speed + + + align:start position:0% +sound the speed +C and actually another good thing is + + align:start position:0% +C and actually another good thing is + + + align:start position:0% +C and actually another good thing is +after it gets + + align:start position:0% +after it gets + + + align:start position:0% +after it gets +there it goes on and go goes by the + + align:start position:0% +there it goes on and go goes by the + + + align:start position:0% +there it goes on and go goes by the +point and doesn't just stay there + + align:start position:0% +point and doesn't just stay there + + + align:start position:0% +point and doesn't just stay there +messing up the The Future + + align:start position:0% +messing up the The Future + + + align:start position:0% +messing up the The Future +Sounds it travels it dies out + + align:start position:0% +Sounds it travels it dies out + + + align:start position:0% +Sounds it travels it dies out +whereas uh well the the heat uh so so + + align:start position:0% +whereas uh well the the heat uh so so + + + align:start position:0% +whereas uh well the the heat uh so so +let me try to give an example suppose + + align:start position:0% +let me try to give an example suppose + + + align:start position:0% +let me try to give an example suppose +the initial condition is a Delta + + align:start position:0% +the initial condition is a Delta + + + align:start position:0% +the initial condition is a Delta +function so + + align:start position:0% +function so + + + align:start position:0% +function so +if U equals a Delta function + + align:start position:0% +if U equals a Delta function + + + align:start position:0% +if U equals a Delta function +a point source which is quite normal a + + align:start position:0% +a point source which is quite normal a + + + align:start position:0% +a point source which is quite normal a +point source of + + align:start position:0% +point source of + + + align:start position:0% +point source of +heat something really hot or a point + + align:start position:0% +heat something really hot or a point + + + align:start position:0% +heat something really hot or a point +source of + + align:start position:0% +source of + + + align:start position:0% +source of +sound my voice so if is that at T equals + + align:start position:0% +sound my voice so if is that at T equals + + + align:start position:0% +sound my voice so if is that at T equals +z then for the heat + + align:start position:0% + + + + align:start position:0% + +equation there's a famous solution to + + align:start position:0% +equation there's a famous solution to + + + align:start position:0% +equation there's a famous solution to +the heat + + align:start position:0% +the heat + + + align:start position:0% +the heat +equation remember the heat equation is D + + align:start position:0% +equation remember the heat equation is D + + + align:start position:0% +equation remember the heat equation is D +DT equal + + align:start position:0% +DT equal + + + align:start position:0% +DT equal +uxa first derivative in time and the and + + align:start position:0% +uxa first derivative in time and the and + + + align:start position:0% +uxa first derivative in time and the and +the solution that starts from the Delta + + align:start position:0% +the solution that starts from the Delta + + + align:start position:0% +the solution that starts from the Delta +function oh do I know what it is I think + + align:start position:0% +function oh do I know what it is I think + + + align:start position:0% +function oh do I know what it is I think +there's a one over there's a s < TK of 4 + + align:start position:0% +there's a one over there's a s < TK of 4 + + + align:start position:0% +there's a one over there's a s < TK of 4 +piun T there's an e to the - x^2 over 4T + + align:start position:0% +piun T there's an e to the - x^2 over 4T + + + align:start position:0% +piun T there's an e to the - x^2 over 4T +I think perhaps that's it perhaps that's + + align:start position:0% +I think perhaps that's it perhaps that's + + + align:start position:0% +I think perhaps that's it perhaps that's +it so uh + + align:start position:0% +it so uh + + + align:start position:0% +it so uh +what do I see from that I see big + + align:start position:0% +what do I see from that I see big + + + align:start position:0% +what do I see from that I see big +damping out I see immediate travel as + + align:start position:0% +damping out I see immediate travel as + + + align:start position:0% +damping out I see immediate travel as +soon + + align:start position:0% +soon + + + align:start position:0% +soon +as time is just a little Beyond zero + + align:start position:0% +as time is just a little Beyond zero + + + align:start position:0% +as time is just a little Beyond zero +then for every X we get an answer but + + align:start position:0% +then for every X we get an answer but + + + align:start position:0% +then for every X we get an answer but +it's an extremely extremely small answer + + align:start position:0% +it's an extremely extremely small answer + + + align:start position:0% +it's an extremely extremely small answer +e Theus x^2 is is tailing off to zero + + align:start position:0% +e Theus x^2 is is tailing off to zero + + + align:start position:0% +e Theus x^2 is is tailing off to zero +incredibly fast so that's a very small + + align:start position:0% +incredibly fast so that's a very small + + + align:start position:0% +incredibly fast so that's a very small +answer very little of the heat + + align:start position:0% +answer very little of the heat + + + align:start position:0% +answer very little of the heat +immediately gets very very quickly to a + + align:start position:0% +immediately gets very very quickly to a + + + align:start position:0% +immediately gets very very quickly to a +across the ocean but in theory it little + + align:start position:0% +across the ocean but in theory it little + + + align:start position:0% +across the ocean but in theory it little +bit does whereas for the wave + + align:start position:0% +bit does whereas for the wave + + + align:start position:0% +bit does whereas for the wave +equation it takes time to cross the + + align:start position:0% +equation it takes time to cross the + + + align:start position:0% +equation it takes time to cross the +ocean we have a tsunami we have a wave + + align:start position:0% +ocean we have a tsunami we have a wave + + + align:start position:0% +ocean we have a tsunami we have a wave +it gets there it reaches the other side + + align:start position:0% +it gets there it reaches the other side + + + align:start position:0% +it gets there it reaches the other side +and and actually at the at the it's very + + align:start position:0% +and and actually at the at the it's very + + + align:start position:0% +and and actually at the at the it's very +important what is the speed of that wave + + align:start position:0% +important what is the speed of that wave + + + align:start position:0% +important what is the speed of that wave +to tell people about a tsunami that's + + align:start position:0% +to tell people about a tsunami that's + + + align:start position:0% +to tell people about a tsunami that's +coming and you can actually do it which + + align:start position:0% +coming and you can actually do it which + + + align:start position:0% +coming and you can actually do it which +you couldn't do for the heater equation + + align:start position:0% +you couldn't do for the heater equation + + + align:start position:0% +you couldn't do for the heater equation +so for the wave + + align:start position:0% +so for the wave + + + align:start position:0% +so for the wave +equation what do + + align:start position:0% +equation what do + + + align:start position:0% +equation what do +I what will + + align:start position:0% +I what will + + + align:start position:0% +I what will +I what comes out of a Delta function in + + align:start position:0% +I what comes out of a Delta function in + + + align:start position:0% +I what comes out of a Delta function in +1D well a wave goes to the right and a + + align:start position:0% +1D well a wave goes to the right and a + + + align:start position:0% +1D well a wave goes to the right and a +wave goes to the left that's what + + align:start position:0% +wave goes to the left that's what + + + align:start position:0% +wave goes to the left that's what +happens and those waves are half of a + + align:start position:0% +happens and those waves are half of a + + + align:start position:0% +happens and those waves are half of a +Delta function each way so the the + + align:start position:0% +Delta function each way so the the + + + align:start position:0% +Delta function each way so the the +solution is 1/2 of a Delta function + + align:start position:0% +solution is 1/2 of a Delta function + + + align:start position:0% +solution is 1/2 of a Delta function +that's + + align:start position:0% + + + + align:start position:0% + +traveling I see that and let me write + + align:start position:0% +traveling I see that and let me write + + + align:start position:0% +traveling I see that and let me write +down the other half that's traveling the + + align:start position:0% +down the other half that's traveling the + + + align:start position:0% +down the other half that's traveling the +other way + + align:start position:0% +other way + + + align:start position:0% +other way +Delta at x + + + align:start position:0% + + + + align:start position:0% + +CT that's a cool solution so that means + + align:start position:0% +CT that's a cool solution so that means + + + align:start position:0% +CT that's a cool solution so that means +the sound in 1 D the sound half of it + + align:start position:0% +the sound in 1 D the sound half of it + + + align:start position:0% +the sound in 1 D the sound half of it +takes off in One Direction half in the + + align:start position:0% +takes off in One Direction half in the + + + align:start position:0% +takes off in One Direction half in the +other direction + + align:start position:0% +other direction + + + align:start position:0% +other direction +and what happens in each direction is a + + align:start position:0% +and what happens in each direction is a + + + align:start position:0% +and what happens in each direction is a +spike of sound you don't hear anything + + align:start position:0% +spike of sound you don't hear anything + + + align:start position:0% +spike of sound you don't hear anything +then at a particular time depending on + + align:start position:0% +then at a particular time depending on + + + align:start position:0% +then at a particular time depending on +your position X there's a particular + + align:start position:0% +your position X there's a particular + + + align:start position:0% +your position X there's a particular +time when you get zero in there and you + + align:start position:0% +time when you get zero in there and you + + + align:start position:0% +time when you get zero in there and you +hear the hear the signal and then as + + align:start position:0% +hear the hear the signal and then as + + + align:start position:0% +hear the hear the signal and then as +soon as time goes past that it's past + + align:start position:0% +soon as time goes past that it's past + + + align:start position:0% +soon as time goes past that it's past +you so you get a big + + align:start position:0% +you so you get a big + + + align:start position:0% +you so you get a big +shock at and it comes to you with speed + + align:start position:0% +shock at and it comes to you with speed + + + align:start position:0% +shock at and it comes to you with speed +C if you look at that uh expression x + + align:start position:0% +C if you look at that uh expression x + + + align:start position:0% +C if you look at that uh expression x +minus CT it's telling you that the speed + + align:start position:0% +minus CT it's telling you that the speed + + + align:start position:0% +minus CT it's telling you that the speed +of the wave in in dxdt for the wave is C + + align:start position:0% +of the wave in in dxdt for the wave is C + + + align:start position:0% +of the wave in in dxdt for the wave is C +okay so that's a contrast for a very + + align:start position:0% +okay so that's a contrast for a very + + + align:start position:0% +okay so that's a contrast for a very +particular initial condition uh big wall + + align:start position:0% +particular initial condition uh big wall + + + align:start position:0% +particular initial condition uh big wall +of water a big noise a big bang okay uh + + align:start position:0% +of water a big noise a big bang okay uh + + + align:start position:0% +of water a big noise a big bang okay uh +I want to uh solve the wave equation + + align:start position:0% +I want to uh solve the wave equation + + + align:start position:0% +I want to uh solve the wave equation +study it further for other initial + + align:start position:0% +study it further for other initial + + + align:start position:0% +study it further for other initial +conditions and of course initial + + align:start position:0% +conditions and of course initial + + + align:start position:0% +conditions and of course initial +conditions plural because the wave + + align:start position:0% +conditions plural because the wave + + + align:start position:0% +conditions plural because the wave +equation is second order in time so I'm + + align:start position:0% + + + + align:start position:0% + +given U at tal 0 and all + + align:start position:0% +given U at tal 0 and all + + + align:start position:0% +given U at tal 0 and all +X and + + align:start position:0% + + + + align:start position:0% + +dudt I'm given initial distri dist ution + + align:start position:0% +dudt I'm given initial distri dist ution + + + align:start position:0% +dudt I'm given initial distri dist ution +of the wall of water shall we say and + + align:start position:0% +of the wall of water shall we say and + + + align:start position:0% +of the wall of water shall we say and +and its + + align:start position:0% +and its + + + align:start position:0% +and its +velocity the the normal + + align:start position:0% +velocity the the normal + + + align:start position:0% +velocity the the normal +thing when I have a second order + + align:start position:0% +thing when I have a second order + + + align:start position:0% +thing when I have a second order +equation I'm given initial condition and + + align:start position:0% +equation I'm given initial condition and + + + align:start position:0% +equation I'm given initial condition and +a initial velocity and of course because + + align:start position:0% +a initial velocity and of course because + + + align:start position:0% +a initial velocity and of course because +it's a partial differential equation I'm + + align:start position:0% +it's a partial differential equation I'm + + + align:start position:0% +it's a partial differential equation I'm +given those for every + + align:start position:0% +given those for every + + + align:start position:0% +given those for every +X so we have functions instead of just + + align:start position:0% +X so we have functions instead of just + + + align:start position:0% +X so we have functions instead of just +two numbers and that's where a fora + + align:start position:0% +two numbers and that's where a fora + + + align:start position:0% +two numbers and that's where a fora +series can come in so we can solve that + + align:start position:0% +series can come in so we can solve that + + + align:start position:0% +series can come in so we can solve that +by a 4A series if we're on a finite like + + align:start position:0% +by a 4A series if we're on a finite like + + + align:start position:0% +by a 4A series if we're on a finite like +a violin string youve plucked a violin + + align:start position:0% +a violin string youve plucked a violin + + + align:start position:0% +a violin string youve plucked a violin +string that starts waves going back and + + align:start position:0% +string that starts waves going back and + + + align:start position:0% +string that starts waves going back and +forth in the spr in the string they + + align:start position:0% +forth in the spr in the string they + + + align:start position:0% +forth in the spr in the string they +solve the wave equation you hear music + + align:start position:0% +solve the wave equation you hear music + + + align:start position:0% +solve the wave equation you hear music +great music if it's a good uh + + align:start position:0% +great music if it's a good uh + + + align:start position:0% +great music if it's a good uh +sound uh or we could solve it on an + + align:start position:0% +sound uh or we could solve it on an + + + align:start position:0% +sound uh or we could solve it on an +infinite line with no boundary as in a + + align:start position:0% +infinite line with no boundary as in a + + + align:start position:0% +infinite line with no boundary as in a +essentially infinite Ocean or or waves + + align:start position:0% +essentially infinite Ocean or or waves + + + align:start position:0% +essentially infinite Ocean or or waves +in space light waves in space are + + align:start position:0% +in space light waves in space are + + + align:start position:0% +in space light waves in space are +solving the wave equation with no + + align:start position:0% +solving the wave equation with no + + + align:start position:0% +solving the wave equation with no +boundary as far as we know okay so what + + align:start position:0% +boundary as far as we know okay so what + + + align:start position:0% +boundary as far as we know okay so what +shall I do so I I'll write the solution + + align:start position:0% +shall I do so I I'll write the solution + + + align:start position:0% +shall I do so I I'll write the solution +down in free + + align:start position:0% +down in free + + + align:start position:0% +down in free +space and then I'll write one down for a + + align:start position:0% +space and then I'll write one down for a + + + align:start position:0% +space and then I'll write one down for a +violin string so in space so so in uh + + align:start position:0% +violin string so in space so so in uh + + + align:start position:0% +violin string so in space so so in uh +well it's a one-dimensional space here + + align:start position:0% +well it's a one-dimensional space here + + + align:start position:0% +well it's a one-dimensional space here +so this would be minus infinity less + + align:start position:0% +so this would be minus infinity less + + + align:start position:0% +so this would be minus infinity less +than x less than infinity then what does + + align:start position:0% +than x less than infinity then what does + + + align:start position:0% +than x less than infinity then what does +the solution to the wave equation look + + align:start position:0% +the solution to the wave equation look + + + align:start position:0% +the solution to the wave equation look +like it looks like some + + align:start position:0% +like it looks like some + + + align:start position:0% +like it looks like some +function + + align:start position:0% +function + + + align:start position:0% +function +of + + align:start position:0% +of + + + align:start position:0% +of +plus some function of X+ CT well that's + + align:start position:0% +plus some function of X+ CT well that's + + + align:start position:0% +plus some function of X+ CT well that's +exactly the form that we have here when + + align:start position:0% +exactly the form that we have here when + + + align:start position:0% +exactly the form that we have here when +they were Delta + + align:start position:0% +they were Delta + + + align:start position:0% +they were Delta +functions here in general they don't + + align:start position:0% +functions here in general they don't + + + align:start position:0% +functions here in general they don't +have to be Delta functions I choose that + + align:start position:0% +have to be Delta functions I choose that + + + align:start position:0% +have to be Delta functions I choose that +function f and that function G so that + + align:start position:0% +function f and that function G so that + + + align:start position:0% +function f and that function G so that +at T equals z I'm good so at T equals 0 + + align:start position:0% +at T equals z I'm good so at T equals 0 + + + align:start position:0% +at T equals z I'm good so at T equals 0 +so I set t equal 0 at tal 0 U of 0 and x + + align:start position:0% +so I set t equal 0 at tal 0 U of 0 and x + + + align:start position:0% +so I set t equal 0 at tal 0 U of 0 and x +would be f of x + G of + + align:start position:0% +would be f of x + G of + + + align:start position:0% +would be f of x + G of +x good but that's only one condition and + + align:start position:0% +x good but that's only one condition and + + + align:start position:0% +x good but that's only one condition and +I have f and g to find so I would also + + align:start position:0% +I have f and g to find so I would also + + + align:start position:0% +I have f and g to find so I would also +use dud + + align:start position:0% +use dud + + + align:start position:0% +use dud +DT uh at the + + align:start position:0% +DT uh at the + + + align:start position:0% +DT uh at the +start what's the time derivative is + + align:start position:0% +start what's the time derivative is + + + align:start position:0% +start what's the time derivative is +minus c f Prime at + + align:start position:0% +minus c f Prime at + + + align:start position:0% +minus c f Prime at +X and the time derivative of this will + + align:start position:0% +X and the time derivative of this will + + + align:start position:0% +X and the time derivative of this will +be a plus c f Prime G + + align:start position:0% +be a plus c f Prime G + + + align:start position:0% +be a plus c f Prime G +Prime at X + + align:start position:0% +Prime at X + + + align:start position:0% +Prime at X +okay no big deal I'm given two functions + + align:start position:0% +okay no big deal I'm given two functions + + + align:start position:0% +okay no big deal I'm given two functions +I've got two functions to find in the + + align:start position:0% +I've got two functions to find in the + + + align:start position:0% +I've got two functions to find in the +answer and I've got two equations I + + align:start position:0% +answer and I've got two equations I + + + align:start position:0% +answer and I've got two equations I +could solve those for f and g and it + + align:start position:0% +could solve those for f and g and it + + + align:start position:0% +could solve those for f and g and it +gives a a formula called Dam Bear's + + align:start position:0% +gives a a formula called Dam Bear's + + + align:start position:0% +gives a a formula called Dam Bear's +formula named after the person who put + + align:start position:0% +formula named after the person who put + + + align:start position:0% +formula named after the person who put +this + + align:start position:0% +this + + + align:start position:0% +this +together I'd rather go on to the violin + + align:start position:0% +together I'd rather go on to the violin + + + align:start position:0% +together I'd rather go on to the violin +to a finite string okay so now I have a + + align:start position:0% +to a finite string okay so now I have a + + + align:start position:0% +to a finite string okay so now I have a +finite + + align:start position:0% +finite + + + align:start position:0% +finite +string and I'm holding U = 0 at the + + align:start position:0% +string and I'm holding U = 0 at the + + + align:start position:0% +string and I'm holding U = 0 at the +end okay and my solution will still be + + align:start position:0% +end okay and my solution will still be + + + align:start position:0% +end okay and my solution will still be +functions that depend on xus C waves my + + align:start position:0% +functions that depend on xus C waves my + + + align:start position:0% +functions that depend on xus C waves my +solution will still be waves it the + + align:start position:0% +solution will still be waves it the + + + align:start position:0% +solution will still be waves it the +solution that I'm going to write down + + align:start position:0% +solution that I'm going to write down + + + align:start position:0% +solution that I'm going to write down +comes from a very very important method + + align:start position:0% +comes from a very very important method + + + align:start position:0% +comes from a very very important method +called separation of variables I want to + + align:start position:0% +called separation of variables I want to + + + align:start position:0% +called separation of variables I want to +separate X from + + align:start position:0% +separate X from + + + align:start position:0% +separate X from +T I need to give you a full video about + + align:start position:0% +T I need to give you a full video about + + + align:start position:0% +T I need to give you a full video about +separation of variables that's the best + + align:start position:0% +separation of variables that's the best + + + align:start position:0% +separation of variables that's the best +tool we have to get uh solutions to lots + + align:start position:0% +tool we have to get uh solutions to lots + + + align:start position:0% +tool we have to get uh solutions to lots +of equations so let me just jump to the + + align:start position:0% +of equations so let me just jump to the + + + align:start position:0% +of equations so let me just jump to the +form of the solution here I'm imagining + + align:start position:0% +form of the solution here I'm imagining + + + align:start position:0% +form of the solution here I'm imagining +the violin string is at risk but then so + + align:start position:0% +the violin string is at risk but then so + + + align:start position:0% +the violin string is at risk but then so +it starts with I'm imagining let's say + + align:start position:0% +it starts with I'm imagining let's say + + + align:start position:0% +it starts with I'm imagining let's say +in our particular problem this is zero + + align:start position:0% +in our particular problem this is zero + + + align:start position:0% +in our particular problem this is zero +the initial velocity this is plucked you + + align:start position:0% +the initial velocity this is plucked you + + + align:start position:0% +the initial velocity this is plucked you +have the starting position is with your + + align:start position:0% +have the starting position is with your + + + align:start position:0% +have the starting position is with your +finger you've moved it off zero okay + + align:start position:0% +finger you've moved it off zero okay + + + align:start position:0% +finger you've moved it off zero okay +what is the what do the solutions look + + align:start position:0% +what is the what do the solutions look + + + align:start position:0% +what is the what do the solutions look +like U of T and + + align:start position:0% +like U of T and + + + align:start position:0% +like U of T and +X okay they will be a + + align:start position:0% +X okay they will be a + + + align:start position:0% +X okay they will be a +sum + + align:start position:0% + + + + align:start position:0% + +of neat special convenient separated + + align:start position:0% +of neat special convenient separated + + + align:start position:0% +of neat special convenient separated +Solutions with separated meaning T + + align:start position:0% +Solutions with separated meaning T + + + align:start position:0% +Solutions with separated meaning T +separated from X and I think we would + + align:start position:0% +separated from X and I think we would + + + align:start position:0% +separated from X and I think we would +have + + align:start position:0% +have + + + align:start position:0% +have +cosine of n c + + align:start position:0% +cosine of n c + + + align:start position:0% +cosine of n c +T I'm going to have a sum oh we'll have + + align:start position:0% +T I'm going to have a sum oh we'll have + + + align:start position:0% +T I'm going to have a sum oh we'll have +a coefficient of course a sub well or B + + align:start position:0% +a coefficient of course a sub well or B + + + align:start position:0% +a coefficient of course a sub well or B +or C or even D how about D for a new + + align:start position:0% +or C or even D how about D for a new + + + align:start position:0% +or C or even D how about D for a new +letter D subn and I think well let me + + align:start position:0% +letter D subn and I think well let me + + + align:start position:0% +letter D subn and I think well let me +finish here the I'm separating that from + + align:start position:0% +finish here the I'm separating that from + + + align:start position:0% +finish here the I'm separating that from +I think it would probably be the S of + + align:start position:0% +I think it would probably be the S of + + + align:start position:0% +I think it would probably be the S of +NX okay if we just look at that for a + + align:start position:0% +NX okay if we just look at that for a + + + align:start position:0% +NX okay if we just look at that for a +little bit that's the point of this + + align:start position:0% +little bit that's the point of this + + + align:start position:0% +little bit that's the point of this +video so this is this is X = 0 this is + + align:start position:0% +video so this is this is X = 0 this is + + + align:start position:0% +video so this is this is X = 0 this is +say x = Pi that's for convenience + + align:start position:0% +say x = Pi that's for convenience + + + align:start position:0% +say x = Pi that's for convenience +suppose we have a uh our violin strain + + align:start position:0% +suppose we have a uh our violin strain + + + align:start position:0% +suppose we have a uh our violin strain +has length Pi then uh I think that's + + align:start position:0% +has length Pi then uh I think that's + + + align:start position:0% +has length Pi then uh I think that's +what the solution looks like it starts + + align:start position:0% +what the solution looks like it starts + + + align:start position:0% +what the solution looks like it starts +from at at t equal + + align:start position:0% + + + + align:start position:0% + +0 at T equals 0 the cosine is 1 so at T + + align:start position:0% +0 at T equals 0 the cosine is 1 so at T + + + align:start position:0% +0 at T equals 0 the cosine is 1 so at T +equal 0 this is an initial condition + + align:start position:0% +equal 0 this is an initial condition + + + align:start position:0% +equal 0 this is an initial condition +that we have to match we this will tell + + align:start position:0% +that we have to match we this will tell + + + align:start position:0% +that we have to match we this will tell +us the D's will be the sum of d n sin n + + align:start position:0% + + + + align:start position:0% + +x that tells us the + + align:start position:0% + + + + align:start position:0% + +D's and then we have our answer so the + + align:start position:0% +D's and then we have our answer so the + + + align:start position:0% +D's and then we have our answer so the +initial condition remember it's starting + + align:start position:0% +initial condition remember it's starting + + + align:start position:0% +initial condition remember it's starting +at rest so the initial velocity is zero + + align:start position:0% +at rest so the initial velocity is zero + + + align:start position:0% +at rest so the initial velocity is zero +and that's why I don't have any sin T's + + align:start position:0% +and that's why I don't have any sin T's + + + align:start position:0% +and that's why I don't have any sin T's +because I'm starting with initial + + align:start position:0% +because I'm starting with initial + + + align:start position:0% +because I'm starting with initial +velocity zero I only have cosiness in + + align:start position:0% +velocity zero I only have cosiness in + + + align:start position:0% +velocity zero I only have cosiness in +the T Direction but I only have SS in + + align:start position:0% +the T Direction but I only have SS in + + + align:start position:0% +the T Direction but I only have SS in +the X Direction because the violin + + align:start position:0% +the X Direction because the violin + + + align:start position:0% +the X Direction because the violin +string is being held down at the two + + align:start position:0% +string is being held down at the two + + + align:start position:0% +string is being held down at the two +ends and it's the sign function that + + align:start position:0% +ends and it's the sign function that + + + align:start position:0% +ends and it's the sign function that +matches that perfectly so this is + + align:start position:0% +matches that perfectly so this is + + + align:start position:0% +matches that perfectly so this is +separation of variables T separated from + + align:start position:0% +separation of variables T separated from + + + align:start position:0% +separation of variables T separated from +X and I really have to do a proper + + align:start position:0% +X and I really have to do a proper + + + align:start position:0% +X and I really have to do a proper +explanation of that highly important + + align:start position:0% +explanation of that highly important + + + align:start position:0% +explanation of that highly important +method of getting Solutions like this + + align:start position:0% +method of getting Solutions like this + + + align:start position:0% +method of getting Solutions like this +thank + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/9lMOz_7bIGU.txt b/9lMOz_7bIGU.txt new file mode 100644 index 0000000000000000000000000000000000000000..33e7441e62deefe16ec9291939c1f5a98fa608c4 --- /dev/null +++ b/9lMOz_7bIGU.txt @@ -0,0 +1,243 @@ +align:start position:0% + +a harmonium is an online dating site + + align:start position:0% +a harmonium is an online dating site + + + align:start position:0% +a harmonium is an online dating site +focused on long-term relationships + + align:start position:0% +focused on long-term relationships + + + align:start position:0% +focused on long-term relationships +it takes a scientific approach to love + + align:start position:0% +it takes a scientific approach to love + + + align:start position:0% +it takes a scientific approach to love +and marriage about nearly 4 percent of + + align:start position:0% +and marriage about nearly 4 percent of + + + align:start position:0% +and marriage about nearly 4 percent of +u.s. marriages in 2012 are a result of + + align:start position:0% +u.s. marriages in 2012 are a result of + + + align:start position:0% +u.s. marriages in 2012 are a result of +the harmony the company has generated + + align:start position:0% +the harmony the company has generated + + + align:start position:0% +the harmony the company has generated +over 1 billion dollars in cumulative + + align:start position:0% +over 1 billion dollars in cumulative + + + align:start position:0% +over 1 billion dollars in cumulative +revenue from 2000 that they the year it + + align:start position:0% +revenue from 2000 that they the year it + + + align:start position:0% +revenue from 2000 that they the year it +was founded the overall approach first + + align:start position:0% +was founded the overall approach first + + + align:start position:0% +was founded the overall approach first +predicts a futures would be compatible + + align:start position:0% +predicts a futures would be compatible + + + align:start position:0% +predicts a futures would be compatible +using 29 different dimensions of + + align:start position:0% +using 29 different dimensions of + + + align:start position:0% +using 29 different dimensions of +personality and using linear regression + + align:start position:0% +personality and using linear regression + + + align:start position:0% +personality and using linear regression +then using optimization harm only finds + + align:start position:0% +then using optimization harm only finds + + + align:start position:0% +then using optimization harm only finds +matches for everyone a harmony has + + align:start position:0% +matches for everyone a harmony has + + + align:start position:0% +matches for everyone a harmony has +members in more than 150 countries since + + align:start position:0% +members in more than 150 countries since + + + align:start position:0% +members in more than 150 countries since +launching in 2000 it has more than 33 + + align:start position:0% +launching in 2000 it has more than 33 + + + align:start position:0% +launching in 2000 it has more than 33 +million members and it now operates a + + align:start position:0% +million members and it now operates a + + + align:start position:0% +million members and it now operates a +harmony labs a relationship research + + align:start position:0% +harmony labs a relationship research + + + align:start position:0% +harmony labs a relationship research +facility a harmony collects data through + + align:start position:0% +facility a harmony collects data through + + + align:start position:0% +facility a harmony collects data through +436 questions almost 15,000 people take + + align:start position:0% +436 questions almost 15,000 people take + + + align:start position:0% +436 questions almost 15,000 people take +the questionnaire each day what is the + + align:start position:0% +the questionnaire each day what is the + + + align:start position:0% +the questionnaire each day what is the +edge of eHarmony it relights much more + + align:start position:0% +edge of eHarmony it relights much more + + + align:start position:0% +edge of eHarmony it relights much more +on data than other dating sites it + + align:start position:0% +on data than other dating sites it + + + align:start position:0% +on data than other dating sites it +suggests a limited number of high + + align:start position:0% +suggests a limited number of high + + + align:start position:0% +suggests a limited number of high +quality matches users don't have to + + align:start position:0% +quality matches users don't have to + + + align:start position:0% +quality matches users don't have to +search and dig through profiles a + + align:start position:0% +search and dig through profiles a + + + align:start position:0% +search and dig through profiles a +harmonic has successfully leveraged the + + align:start position:0% +harmonic has successfully leveraged the + + + align:start position:0% +harmonic has successfully leveraged the +power of analytics to create a + + align:start position:0% +power of analytics to create a + + + align:start position:0% +power of analytics to create a +successful enthroning business it + + align:start position:0% +successful enthroning business it + + + align:start position:0% +successful enthroning business it +represents 14% of us online of the u.s. + + align:start position:0% +represents 14% of us online of the u.s. + + + align:start position:0% +represents 14% of us online of the u.s. +online dating market \ No newline at end of file diff --git a/A4IC92HVLLU.txt b/A4IC92HVLLU.txt new file mode 100644 index 0000000000000000000000000000000000000000..d08ab5acd065c5b30112bd4bf1c31812889e0e19 --- /dev/null +++ b/A4IC92HVLLU.txt @@ -0,0 +1,2011 @@ +align:start position:0% + +um so I'm Olivia + + align:start position:0% +um so I'm Olivia + + + align:start position:0% +um so I'm Olivia +I uh work at fathom information design + + align:start position:0% +I uh work at fathom information design + + + align:start position:0% +I uh work at fathom information design +we're over in Boston um and we do a lot + + align:start position:0% +we're over in Boston um and we do a lot + + + align:start position:0% +we're over in Boston um and we do a lot +of our work is in data visualization and + + align:start position:0% +of our work is in data visualization and + + + align:start position:0% +of our work is in data visualization and +information design and we use processing + + align:start position:0% +information design and we use processing + + + align:start position:0% +information design and we use processing +for that which is what we're going to be + + align:start position:0% +for that which is what we're going to be + + + align:start position:0% +for that which is what we're going to be +using today so processing is both a + + align:start position:0% +using today so processing is both a + + + align:start position:0% +using today so processing is both a +community a development environment and + + align:start position:0% +community a development environment and + + + align:start position:0% +community a development environment and +a language to kind of make it as simple + + align:start position:0% +a language to kind of make it as simple + + + align:start position:0% +a language to kind of make it as simple +as possible to get up and running with + + align:start position:0% +as possible to get up and running with + + + align:start position:0% +as possible to get up and running with +something visual on the screen um so you + + align:start position:0% +something visual on the screen um so you + + + align:start position:0% +something visual on the screen um so you +can use it for making 3D you can do what + + align:start position:0% +can use it for making 3D you can do what + + + align:start position:0% +can use it for making 3D you can do what +we're going to do image processing kind + + align:start position:0% +we're going to do image processing kind + + + align:start position:0% +we're going to do image processing kind +of looking at the pixel information of + + align:start position:0% +of looking at the pixel information of + + + align:start position:0% +of looking at the pixel information of +images or kind of pulling in data and + + align:start position:0% +images or kind of pulling in data and + + + align:start position:0% +images or kind of pulling in data and +creating Things based on + + align:start position:0% +creating Things based on + + + align:start position:0% +creating Things based on +that + + align:start position:0% +that + + + align:start position:0% +that +um so would do any of you guys have an + + align:start position:0% +um so would do any of you guys have an + + + align:start position:0% +um so would do any of you guys have an +idea of what you think of when you hear + + align:start position:0% +idea of what you think of when you hear + + + align:start position:0% +idea of what you think of when you hear +image processing or what that might be + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah so a lot of it is about + + align:start position:0% +yeah yeah yeah so a lot of it is about + + + align:start position:0% +yeah yeah yeah so a lot of it is about +kind of manipulating the information + + align:start position:0% +kind of manipulating the information + + + align:start position:0% +kind of manipulating the information +that you get when you kind of take a + + align:start position:0% +that you get when you kind of take a + + + align:start position:0% +that you get when you kind of take a +picture um usually it's to enhance it so + + align:start position:0% +picture um usually it's to enhance it so + + + align:start position:0% +picture um usually it's to enhance it so +whether that means you're making it more + + align:start position:0% +whether that means you're making it more + + + align:start position:0% +whether that means you're making it more +clear to be able to kind of analyze + + align:start position:0% +clear to be able to kind of analyze + + + align:start position:0% +clear to be able to kind of analyze +information in there or enhancing it in + + align:start position:0% +information in there or enhancing it in + + + align:start position:0% +information in there or enhancing it in +an aesthetic way kind of like with + + align:start position:0% +an aesthetic way kind of like with + + + align:start position:0% +an aesthetic way kind of like with +Instagram or + + align:start position:0% + + + + align:start position:0% + +SnapChat um so kind of doing that + + align:start position:0% +SnapChat um so kind of doing that + + + align:start position:0% +SnapChat um so kind of doing that +through code is what we're going to do + + align:start position:0% +through code is what we're going to do + + + align:start position:0% +through code is what we're going to do +today um and it uses mix of math and + + align:start position:0% +today um and it uses mix of math and + + + align:start position:0% +today um and it uses mix of math and +computer science so a lot of it is these + + align:start position:0% +computer science so a lot of it is these + + + align:start position:0% +computer science so a lot of it is these +mathematical functions that manipulate + + align:start position:0% +mathematical functions that manipulate + + + align:start position:0% +mathematical functions that manipulate +the different pieces of the image + + align:start position:0% +the different pieces of the image + + + align:start position:0% +the different pieces of the image +information and we're going to use + + align:start position:0% +information and we're going to use + + + align:start position:0% +information and we're going to use +computer science with processing to kind + + align:start position:0% +computer science with processing to kind + + + align:start position:0% +computer science with processing to kind +of mix it all together and create our + + align:start position:0% +of mix it all together and create our + + + align:start position:0% +of mix it all together and create our +filters so there are a lot of different + + align:start position:0% +filters so there are a lot of different + + + align:start position:0% +filters so there are a lot of different +things you can do it can be a simple as + + align:start position:0% +things you can do it can be a simple as + + + align:start position:0% +things you can do it can be a simple as +uh kind of enhancing the contrast so in + + align:start position:0% +uh kind of enhancing the contrast so in + + + align:start position:0% +uh kind of enhancing the contrast so in +this case this is a photo that's taken + + align:start position:0% +this case this is a photo that's taken + + + align:start position:0% +this case this is a photo that's taken +underwater on the left and you can't + + align:start position:0% +underwater on the left and you can't + + + align:start position:0% +underwater on the left and you can't +really see anything so later people have + + align:start position:0% +really see anything so later people have + + + align:start position:0% +really see anything so later people have +gone in and just enhanced the contrast + + align:start position:0% +gone in and just enhanced the contrast + + + align:start position:0% +gone in and just enhanced the contrast +which usually means playing with the + + align:start position:0% +which usually means playing with the + + + align:start position:0% +which usually means playing with the +values the light and the Dark of the + + align:start position:0% +values the light and the Dark of the + + + align:start position:0% +values the light and the Dark of the +image to start to make out the different + + align:start position:0% +image to start to make out the different + + + align:start position:0% +image to start to make out the different +shapes and then they can use it for + + align:start position:0% +shapes and then they can use it for + + + align:start position:0% +shapes and then they can use it for +analysis or to put in a + + align:start position:0% +analysis or to put in a + + + align:start position:0% +analysis or to put in a +book um sometimes we take images I you + + align:start position:0% +book um sometimes we take images I you + + + align:start position:0% +book um sometimes we take images I you +guys were building cameras earlier using + + align:start position:0% +guys were building cameras earlier using + + + align:start position:0% +guys were building cameras earlier using +visible light x-rays are another way of + + align:start position:0% +visible light x-rays are another way of + + + align:start position:0% +visible light x-rays are another way of +taking images but you're using x-rays + + align:start position:0% +taking images but you're using x-rays + + + align:start position:0% +taking images but you're using x-rays +instead of the visible light wavelengths + + align:start position:0% +instead of the visible light wavelengths + + + align:start position:0% +instead of the visible light wavelengths +and then again kind of enhancing those + + align:start position:0% +and then again kind of enhancing those + + + align:start position:0% +and then again kind of enhancing those +images so that we can find different + + align:start position:0% +images so that we can find different + + + align:start position:0% +images so that we can find different +medical + + align:start position:0% +medical + + + align:start position:0% +medical +anomalies you can also use x-rays to + + align:start position:0% +anomalies you can also use x-rays to + + + align:start position:0% +anomalies you can also use x-rays to +look at layers behind paint so a lot of + + align:start position:0% +look at layers behind paint so a lot of + + + align:start position:0% +look at layers behind paint so a lot of +times you might hear a story about oh + + align:start position:0% +times you might hear a story about oh + + + align:start position:0% +times you might hear a story about oh +they found that like a person was in + + align:start position:0% +they found that like a person was in + + + align:start position:0% +they found that like a person was in +this painting and then it got painted + + align:start position:0% +this painting and then it got painted + + + align:start position:0% +this painting and then it got painted +over the way they know that is through + + align:start position:0% +over the way they know that is through + + + align:start position:0% +over the way they know that is through +sort of taking these different images + + align:start position:0% +sort of taking these different images + + + align:start position:0% +sort of taking these different images +and enhancing the information in + + align:start position:0% +and enhancing the information in + + + align:start position:0% +and enhancing the information in +them and one that I think is really cool + + align:start position:0% +them and one that I think is really cool + + + align:start position:0% +them and one that I think is really cool +is uh so a lot of space images that you + + align:start position:0% +is uh so a lot of space images that you + + + align:start position:0% +is uh so a lot of space images that you +see are mixes of image data from + + align:start position:0% +see are mixes of image data from + + + align:start position:0% +see are mixes of image data from +different telescopes so this is actually + + align:start position:0% +different telescopes so this is actually + + + align:start position:0% +different telescopes so this is actually +a combination from three different + + align:start position:0% +a combination from three different + + + align:start position:0% +a combination from three different +telescopes I think the blue is x-ray + + align:start position:0% +telescopes I think the blue is x-ray + + + align:start position:0% +telescopes I think the blue is x-ray +information the gold is information from + + align:start position:0% +information the gold is information from + + + align:start position:0% +information the gold is information from +Hubble and then the red might be a + + align:start position:0% +Hubble and then the red might be a + + + align:start position:0% +Hubble and then the red might be a +different uh x-ray telescope so kind of + + align:start position:0% +different uh x-ray telescope so kind of + + + align:start position:0% +different uh x-ray telescope so kind of +merging all of those together and + + align:start position:0% +merging all of those together and + + + align:start position:0% +merging all of those together and +coloring them in a certain way so that + + align:start position:0% +coloring them in a certain way so that + + + align:start position:0% +coloring them in a certain way so that +people can start to get scientific + + align:start position:0% +people can start to get scientific + + + align:start position:0% +people can start to get scientific +knowledge from the photos + + align:start position:0% +knowledge from the photos + + + align:start position:0% +knowledge from the photos +and then there's also this kind of um + + align:start position:0% +and then there's also this kind of um + + + align:start position:0% +and then there's also this kind of um +cyclical process of so now we have + + align:start position:0% +cyclical process of so now we have + + + align:start position:0% +cyclical process of so now we have +cameras that are really good at + + align:start position:0% +cameras that are really good at + + + align:start position:0% +cameras that are really good at +recognizing faces so that our pictures + + align:start position:0% +recognizing faces so that our pictures + + + align:start position:0% +recognizing faces so that our pictures +of our family can be way better but the + + align:start position:0% +of our family can be way better but the + + + align:start position:0% +of our family can be way better but the +way we were able to do that is by + + align:start position:0% +way we were able to do that is by + + + align:start position:0% +way we were able to do that is by +looking at pictures of faces and kind of + + align:start position:0% +looking at pictures of faces and kind of + + + align:start position:0% +looking at pictures of faces and kind of +teaching the camera what to look for so + + align:start position:0% +teaching the camera what to look for so + + + align:start position:0% +teaching the camera what to look for so +kind of using images to enhance later + + align:start position:0% + + + + align:start position:0% + +images and what we're going to focus on + + align:start position:0% +images and what we're going to focus on + + + align:start position:0% +images and what we're going to focus on +today is kind of manipulating the uh + + align:start position:0% +today is kind of manipulating the uh + + + align:start position:0% +today is kind of manipulating the uh +color information of our photos for + + align:start position:0% +color information of our photos for + + + align:start position:0% +color information of our photos for +purely aesthetic purposes so Instagram + + align:start position:0% +purely aesthetic purposes so Instagram + + + align:start position:0% +purely aesthetic purposes so Instagram +uses a set of filters which really is + + align:start position:0% +uses a set of filters which really is + + + align:start position:0% +uses a set of filters which really is +just a set of mathematical functions + + align:start position:0% +just a set of mathematical functions + + + align:start position:0% +just a set of mathematical functions +that are applied to the image + + align:start position:0% +that are applied to the image + + + align:start position:0% +that are applied to the image +information and then spit back out your + + align:start position:0% +information and then spit back out your + + + align:start position:0% +information and then spit back out your +image with its new + + align:start position:0% + + + + align:start position:0% + +colors so in order for us to be able to + + align:start position:0% +colors so in order for us to be able to + + + align:start position:0% +colors so in order for us to be able to +do this I'm going to talk a little bit + + align:start position:0% +do this I'm going to talk a little bit + + + align:start position:0% +do this I'm going to talk a little bit +about the different ways you might + + align:start position:0% +about the different ways you might + + + align:start position:0% +about the different ways you might +access the color information of your + + align:start position:0% +access the color information of your + + + align:start position:0% +access the color information of your +photo and kind of how computers see + + align:start position:0% +photo and kind of how computers see + + + align:start position:0% +photo and kind of how computers see +color you might have talked about this a + + align:start position:0% +color you might have talked about this a + + + align:start position:0% +color you might have talked about this a +little bit with the cameras earlier so + + align:start position:0% +little bit with the cameras earlier so + + + align:start position:0% +little bit with the cameras earlier so +uh it's a good refresher but let's start + + align:start position:0% +uh it's a good refresher but let's start + + + align:start position:0% +uh it's a good refresher but let's start +with a grayscale image so on the left is + + align:start position:0% +with a grayscale image so on the left is + + + align:start position:0% +with a grayscale image so on the left is +our image of the + + align:start position:0% +our image of the + + + align:start position:0% +our image of the +baboon and when you have a grayscale + + align:start position:0% +baboon and when you have a grayscale + + + align:start position:0% +baboon and when you have a grayscale +image everything is either is on a range + + align:start position:0% +image everything is either is on a range + + + align:start position:0% +image everything is either is on a range +of black to white that can be stored as + + align:start position:0% +of black to white that can be stored as + + + align:start position:0% +of black to white that can be stored as +a number usually 0 to + + align:start position:0% +a number usually 0 to + + + align:start position:0% +a number usually 0 to +255 and then over here it's just kind of + + align:start position:0% +255 and then over here it's just kind of + + + align:start position:0% +255 and then over here it's just kind of +plotting what those values are so you + + align:start position:0% +plotting what those values are so you + + + align:start position:0% +plotting what those values are so you +start to get a sense of kind of how IM + + align:start position:0% +start to get a sense of kind of how IM + + + align:start position:0% +start to get a sense of kind of how IM +information can be seen as just sort of + + align:start position:0% +information can be seen as just sort of + + + align:start position:0% +information can be seen as just sort of +a set of numbers a set of + + align:start position:0% + + + + align:start position:0% + +values this is up close at like one + + align:start position:0% +values this is up close at like one + + + align:start position:0% +values this is up close at like one +square of your image so again every + + align:start position:0% +square of your image so again every + + + align:start position:0% +square of your image so again every +pixel in a grayscale image will have one + + align:start position:0% +pixel in a grayscale image will have one + + + align:start position:0% +pixel in a grayscale image will have one +value um and so it can be zero for black + + align:start position:0% +value um and so it can be zero for black + + + align:start position:0% +value um and so it can be zero for black +and 255 for + + align:start position:0% +and 255 for + + + align:start position:0% +and 255 for +white and then a color image is usually + + align:start position:0% +white and then a color image is usually + + + align:start position:0% +white and then a color image is usually +just like three layers of that + + align:start position:0% +just like three layers of that + + + align:start position:0% +just like three layers of that +information so if you're looking at an + + align:start position:0% +information so if you're looking at an + + + align:start position:0% +information so if you're looking at an +image in RGB mode which is pretty + + align:start position:0% +image in RGB mode which is pretty + + + align:start position:0% +image in RGB mode which is pretty +standard for sort of how digital cameras + + align:start position:0% +standard for sort of how digital cameras + + + align:start position:0% +standard for sort of how digital cameras +work usually how computers are thinking + + align:start position:0% +work usually how computers are thinking + + + align:start position:0% +work usually how computers are thinking +about color + + align:start position:0% +about color + + + align:start position:0% +about color +information uh it's three layers of + + align:start position:0% +information uh it's three layers of + + + align:start position:0% +information uh it's three layers of +those 0 to 255 values but in this case + + align:start position:0% +those 0 to 255 values but in this case + + + align:start position:0% +those 0 to 255 values but in this case +it's like from black to Pure red or + + align:start position:0% +it's like from black to Pure red or + + + align:start position:0% +it's like from black to Pure red or +black to pure green and black to pure + + align:start position:0% +black to pure green and black to pure + + + align:start position:0% +black to pure green and black to pure +blue and then when we kind of add those + + align:start position:0% +blue and then when we kind of add those + + + align:start position:0% +blue and then when we kind of add those +all together with the correct weights + + align:start position:0% +all together with the correct weights + + + align:start position:0% +all together with the correct weights +you'll get your full color image so this + + align:start position:0% +you'll get your full color image so this + + + align:start position:0% +you'll get your full color image so this +is one way to start pulling out the + + align:start position:0% +is one way to start pulling out the + + + align:start position:0% +is one way to start pulling out the +information and playing with it so in + + align:start position:0% +information and playing with it so in + + + align:start position:0% +information and playing with it so in +processing you'll see in the filters + + align:start position:0% +processing you'll see in the filters + + + align:start position:0% +processing you'll see in the filters +that sometimes people will go through + + align:start position:0% +that sometimes people will go through + + + align:start position:0% +that sometimes people will go through +and for every pixel take out what is the + + align:start position:0% +and for every pixel take out what is the + + + align:start position:0% +and for every pixel take out what is the +red what is the green and what is the + + align:start position:0% +red what is the green and what is the + + + align:start position:0% +red what is the green and what is the +blue of that pixel and then you can just + + align:start position:0% +blue of that pixel and then you can just + + + align:start position:0% +blue of that pixel and then you can just +say Okay add 10 to red and that will + + align:start position:0% +say Okay add 10 to red and that will + + + align:start position:0% +say Okay add 10 to red and that will +totally change your + + align:start position:0% + + + + align:start position:0% + +image so this is just an example of like + + align:start position:0% +image so this is just an example of like + + + align:start position:0% +image so this is just an example of like +what happens when you start playing with + + align:start position:0% +what happens when you start playing with + + + align:start position:0% +what happens when you start playing with +the different RGB values um and we'll + + align:start position:0% +the different RGB values um and we'll + + + align:start position:0% +the different RGB values um and we'll +see an example of a different kind of + + align:start position:0% +see an example of a different kind of + + + align:start position:0% +see an example of a different kind of +color scheme in a second + + align:start position:0% +color scheme in a second + + + align:start position:0% +color scheme in a second +but when so if this is my original image + + align:start position:0% +but when so if this is my original image + + + align:start position:0% +but when so if this is my original image +over here I've started like bumping up + + align:start position:0% +over here I've started like bumping up + + + align:start position:0% +over here I've started like bumping up +the blue or like taking down the red so + + align:start position:0% +the blue or like taking down the red so + + + align:start position:0% +the blue or like taking down the red so +the whole image has this color shift but + + align:start position:0% +the whole image has this color shift but + + + align:start position:0% +the whole image has this color shift but +it also starts to manipulate the lights + + align:start position:0% +it also starts to manipulate the lights + + + align:start position:0% +it also starts to manipulate the lights +and the darks because in RGB mode the + + align:start position:0% +and the darks because in RGB mode the + + + align:start position:0% +and the darks because in RGB mode the +lightness and the Darkness of an image + + align:start position:0% +lightness and the Darkness of an image + + + align:start position:0% +lightness and the Darkness of an image +is tied to the color of the image so + + align:start position:0% +is tied to the color of the image so + + + align:start position:0% +is tied to the color of the image so +sometimes you might want to edit those + + align:start position:0% +sometimes you might want to edit those + + + align:start position:0% +sometimes you might want to edit those +separately and that's where HSB mode is + + align:start position:0% +separately and that's where HSB mode is + + + align:start position:0% +separately and that's where HSB mode is +really helpful so Hue saturation and + + align:start position:0% +really helpful so Hue saturation and + + + align:start position:0% +really helpful so Hue saturation and +brightness so you can also uh through + + align:start position:0% +brightness so you can also uh through + + + align:start position:0% +brightness so you can also uh through +processing take the color information of + + align:start position:0% +processing take the color information of + + + align:start position:0% +processing take the color information of +your image but separate how bright it is + + align:start position:0% +your image but separate how bright it is + + + align:start position:0% +your image but separate how bright it is +what color it is and how intense that + + align:start position:0% +what color it is and how intense that + + + align:start position:0% +what color it is and how intense that +color is so in this case what we're + + align:start position:0% +color is so in this case what we're + + + align:start position:0% +color is so in this case what we're +looking at across here is where someone + + align:start position:0% +looking at across here is where someone + + + align:start position:0% +looking at across here is where someone +has if this is their original image + + align:start position:0% +has if this is their original image + + + align:start position:0% +has if this is their original image +they've shifted the Hue so Hue is like + + align:start position:0% +they've shifted the Hue so Hue is like + + + align:start position:0% +they've shifted the Hue so Hue is like +the color you see um but they haven't + + align:start position:0% +the color you see um but they haven't + + + align:start position:0% +the color you see um but they haven't +changed the lightness or the intensity + + align:start position:0% +changed the lightness or the intensity + + + align:start position:0% +changed the lightness or the intensity +of the color + + align:start position:0% +of the color + + + align:start position:0% +of the color +um if we think of an apple as red and + + align:start position:0% +um if we think of an apple as red and + + + align:start position:0% +um if we think of an apple as red and +this is also this is chalk which is also + + align:start position:0% +this is also this is chalk which is also + + + align:start position:0% +this is also this is chalk which is also +technically red but it looks more like + + align:start position:0% +technically red but it looks more like + + + align:start position:0% +technically red but it looks more like +pink because it has a lower saturation + + align:start position:0% +pink because it has a lower saturation + + + align:start position:0% +pink because it has a lower saturation +so this is like when you have like a + + align:start position:0% +so this is like when you have like a + + + align:start position:0% +so this is like when you have like a +pure red versus something that's lower + + align:start position:0% +pure red versus something that's lower + + + align:start position:0% +pure red versus something that's lower +saturation and then cherries are also + + align:start position:0% +saturation and then cherries are also + + + align:start position:0% +saturation and then cherries are also +red but they have a darker value so + + align:start position:0% +red but they have a darker value so + + + align:start position:0% +red but they have a darker value so +that's the brightness so again pure red + + align:start position:0% +that's the brightness so again pure red + + + align:start position:0% +that's the brightness so again pure red +versus something with a lot more black + + align:start position:0% +versus something with a lot more black + + + align:start position:0% +versus something with a lot more black +in it so you can also think of this as + + align:start position:0% +in it so you can also think of this as + + + align:start position:0% +in it so you can also think of this as +like if you were mixing colors with + + align:start position:0% +like if you were mixing colors with + + + align:start position:0% +like if you were mixing colors with +paint if it needs a lot of white to + + align:start position:0% +paint if it needs a lot of white to + + + align:start position:0% +paint if it needs a lot of white to +create that color then it probably has a + + align:start position:0% +create that color then it probably has a + + + align:start position:0% +create that color then it probably has a +lower saturation if you needed a lot of + + align:start position:0% +lower saturation if you needed a lot of + + + align:start position:0% +lower saturation if you needed a lot of +black to make that color then it + + align:start position:0% +black to make that color then it + + + align:start position:0% +black to make that color then it +probably has a lower value so here you + + align:start position:0% +probably has a lower value so here you + + + align:start position:0% +probably has a lower value so here you +can start to play with your image and + + align:start position:0% +can start to play with your image and + + + align:start position:0% +can start to play with your image and +say I want everything to be darker but I + + align:start position:0% +say I want everything to be darker but I + + + align:start position:0% +say I want everything to be darker but I +want it to stay the same color or like + + align:start position:0% +want it to stay the same color or like + + + align:start position:0% +want it to stay the same color or like +with the butterfly I want to like so + + align:start position:0% +with the butterfly I want to like so + + + align:start position:0% +with the butterfly I want to like so +like in this case I the one on the right + + align:start position:0% +like in this case I the one on the right + + + align:start position:0% +like in this case I the one on the right +I changed just the color but I didn't + + align:start position:0% +I changed just the color but I didn't + + + align:start position:0% +I changed just the color but I didn't +change any of the saturation or the + + align:start position:0% +change any of the saturation or the + + + align:start position:0% +change any of the saturation or the +value so you can see how kind of like + + align:start position:0% +value so you can see how kind of like + + + align:start position:0% +value so you can see how kind of like +these are equally bright and this one in + + align:start position:0% +these are equally bright and this one in + + + align:start position:0% +these are equally bright and this one in +the middle starts to get more gray cuz + + align:start position:0% +the middle starts to get more gray cuz + + + align:start position:0% +the middle starts to get more gray cuz +as I've manipulated the RGB values I've + + align:start position:0% +as I've manipulated the RGB values I've + + + align:start position:0% +as I've manipulated the RGB values I've +also manipulated like how light it + + align:start position:0% +also manipulated like how light it + + + align:start position:0% +also manipulated like how light it +is so now we can start to make filters + + align:start position:0% +is so now we can start to make filters + + + align:start position:0% +is so now we can start to make filters +of our + + align:start position:0% +of our + + + align:start position:0% +of our +own um and the filters that we have kind + + align:start position:0% +own um and the filters that we have kind + + + align:start position:0% +own um and the filters that we have kind +of set up for you guys to play through + + align:start position:0% +of set up for you guys to play through + + + align:start position:0% +of set up for you guys to play through +are these are some of them uh so there's + + align:start position:0% +are these are some of them uh so there's + + + align:start position:0% +are these are some of them uh so there's +this one which is kind of like + + align:start position:0% +this one which is kind of like + + + align:start position:0% +this one which is kind of like +posterization so so a lot of the time um + + align:start position:0% +posterization so so a lot of the time um + + + align:start position:0% +posterization so so a lot of the time um +like if you want to print something as a + + align:start position:0% +like if you want to print something as a + + + align:start position:0% +like if you want to print something as a +poster you kind of have to get it as + + align:start position:0% +poster you kind of have to get it as + + + align:start position:0% +poster you kind of have to get it as +close as possible to like black and + + align:start position:0% +close as possible to like black and + + + align:start position:0% +close as possible to like black and +white as opposed to like having all the + + align:start position:0% +white as opposed to like having all the + + + align:start position:0% +white as opposed to like having all the +range of uh gray values so kind of just + + align:start position:0% +range of uh gray values so kind of just + + + align:start position:0% +range of uh gray values so kind of just +messing around and seeing like what + + align:start position:0% +messing around and seeing like what + + + align:start position:0% +messing around and seeing like what +happens when you start to take out those + + align:start position:0% +happens when you start to take out those + + + align:start position:0% +happens when you start to take out those +middle values of gray um and then also + + align:start position:0% +middle values of gray um and then also + + + align:start position:0% +middle values of gray um and then also +manipulating the colors this one is not + + align:start position:0% +manipulating the colors this one is not + + + align:start position:0% +manipulating the colors this one is not +so much playing with the color + + align:start position:0% +so much playing with the color + + + align:start position:0% +so much playing with the color +information but if you have your image + + align:start position:0% +information but if you have your image + + + align:start position:0% +information but if you have your image +dimensions and you want to add something + + align:start position:0% +dimensions and you want to add something + + + align:start position:0% +dimensions and you want to add something +like a vignette to it being able to say + + align:start position:0% +like a vignette to it being able to say + + + align:start position:0% +like a vignette to it being able to say +here's where the center of my image is + + align:start position:0% +here's where the center of my image is + + + align:start position:0% +here's where the center of my image is +and then kind of how based on that you + + align:start position:0% +and then kind of how based on that you + + + align:start position:0% +and then kind of how based on that you +can add a color on top and so adding + + align:start position:0% +can add a color on top and so adding + + + align:start position:0% +can add a color on top and so adding +this ring on + + align:start position:0% +this ring on + + + align:start position:0% +this ring on +top um this one it allows as you click + + align:start position:0% +top um this one it allows as you click + + + align:start position:0% +top um this one it allows as you click +around the image it'll pick one color so + + align:start position:0% +around the image it'll pick one color so + + + align:start position:0% +around the image it'll pick one color so +this is using like Hue saturation and + + align:start position:0% +this is using like Hue saturation and + + + align:start position:0% +this is using like Hue saturation and +brightness so it'll pick the Hue and + + align:start position:0% +brightness so it'll pick the Hue and + + + align:start position:0% +brightness so it'll pick the Hue and +then light up all the other pixels with + + align:start position:0% +then light up all the other pixels with + + + align:start position:0% +then light up all the other pixels with +that Hue and get rid of the Hue and all + + align:start position:0% +that Hue and get rid of the Hue and all + + + align:start position:0% +that Hue and get rid of the Hue and all +the other ones so kind of seeing how + + align:start position:0% +the other ones so kind of seeing how + + + align:start position:0% +the other ones so kind of seeing how +many colors there are in an image or + + align:start position:0% +many colors there are in an image or + + + align:start position:0% +many colors there are in an image or +being able to highlight like just the + + align:start position:0% +being able to highlight like just the + + + align:start position:0% +being able to highlight like just the +red + + align:start position:0% +red + + + align:start position:0% +red +pieces and then the last one is so I + + align:start position:0% +pieces and then the last one is so I + + + align:start position:0% +pieces and then the last one is so I +don't know how many of you guys have + + align:start position:0% +don't know how many of you guys have + + + align:start position:0% +don't know how many of you guys have +ever played around with like Photoshop + + align:start position:0% +ever played around with like Photoshop + + + align:start position:0% +ever played around with like Photoshop +but they have this thing called blend + + align:start position:0% +but they have this thing called blend + + + align:start position:0% +but they have this thing called blend +modes which is like what a lot of people + + align:start position:0% +modes which is like what a lot of people + + + align:start position:0% +modes which is like what a lot of people +use to apply different colors on top and + + align:start position:0% +use to apply different colors on top and + + + align:start position:0% +use to apply different colors on top and +so that just says if you put a color on + + align:start position:0% +so that just says if you put a color on + + + align:start position:0% +so that just says if you put a color on +top how and what's the math that it's + + align:start position:0% +top how and what's the math that it's + + + align:start position:0% +top how and what's the math that it's +taking with that color on top and the + + align:start position:0% +taking with that color on top and the + + + align:start position:0% +taking with that color on top and the +image on the bottom and how it like adds + + align:start position:0% +image on the bottom and how it like adds + + + align:start position:0% +image on the bottom and how it like adds +them together so this is trying to like + + align:start position:0% +them together so this is trying to like + + + align:start position:0% +them together so this is trying to like +imitate the overlay mode which just kind + + align:start position:0% +imitate the overlay mode which just kind + + + align:start position:0% +imitate the overlay mode which just kind +of does this like taking part of one + + align:start position:0% +of does this like taking part of one + + + align:start position:0% +of does this like taking part of one +color and part of the other and then + + align:start position:0% +color and part of the other and then + + + align:start position:0% +color and part of the other and then +spitting back out a new + + align:start position:0% +spitting back out a new + + + align:start position:0% +spitting back out a new +color so those are the different filters + + align:start position:0% +color so those are the different filters + + + align:start position:0% +color so those are the different filters +we have today + + align:start position:0% +we have today + + + align:start position:0% +we have today +[Applause] \ No newline at end of file diff --git a/Ba8ZyAmffAM.txt b/Ba8ZyAmffAM.txt new file mode 100644 index 0000000000000000000000000000000000000000..9672bd014001f0503526406dad7765c4ffd5917c --- /dev/null +++ b/Ba8ZyAmffAM.txt @@ -0,0 +1,6079 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu uh first I want onor a + + align:start position:0% +ocw.mit.edu uh first I want onor a + + + align:start position:0% +ocw.mit.edu uh first I want onor a +personal note I went through the course + + align:start position:0% +personal note I went through the course + + + align:start position:0% +personal note I went through the course +this summer and I'm really happy to see + + align:start position:0% +this summer and I'm really happy to see + + + align:start position:0% +this summer and I'm really happy to see +so many Healthcare uh or so many + + align:start position:0% +so many Healthcare uh or so many + + + align:start position:0% +so many Healthcare uh or so many +attending from the healthcare sector + + align:start position:0% +attending from the healthcare sector + + + align:start position:0% +attending from the healthcare sector +because I think in the future it's going + + align:start position:0% +because I think in the future it's going + + + align:start position:0% +because I think in the future it's going +to be quite impossible to function in + + align:start position:0% +to be quite impossible to function in + + + align:start position:0% +to be quite impossible to function in +good structures without knowing + + align:start position:0% +good structures without knowing + + + align:start position:0% +good structures without knowing +something about this process Improvement + + align:start position:0% +something about this process Improvement + + + align:start position:0% +something about this process Improvement +lean and um and Six Sigma because + + align:start position:0% +lean and um and Six Sigma because + + + align:start position:0% +lean and um and Six Sigma because +otherwise I don't think that you're + + align:start position:0% +otherwise I don't think that you're + + + align:start position:0% +otherwise I don't think that you're +going to be able to contribute in a good + + align:start position:0% +going to be able to contribute in a good + + + align:start position:0% +going to be able to contribute in a good +and productive manner so really + + align:start position:0% +and productive manner so really + + + align:start position:0% +and productive manner so really +important and very nice to to see you + + align:start position:0% +important and very nice to to see you + + + align:start position:0% +important and very nice to to see you +all here all right at the end of this + + align:start position:0% +all here all right at the end of this + + + align:start position:0% +all here all right at the end of this +you'll be able to sketch a basic uh + + align:start position:0% +you'll be able to sketch a basic uh + + + align:start position:0% +you'll be able to sketch a basic uh +value stream map demonstrate um some + + align:start position:0% +value stream map demonstrate um some + + + align:start position:0% +value stream map demonstrate um some +basic analysis of those maps and then + + align:start position:0% +basic analysis of those maps and then + + + align:start position:0% +basic analysis of those maps and then +recognize some steps for process + + align:start position:0% +recognize some steps for process + + + align:start position:0% +recognize some steps for process +Improvement um using your value stream + + align:start position:0% +Improvement um using your value stream + + + align:start position:0% +Improvement um using your value stream +map you recognize + + align:start position:0% +map you recognize + + + align:start position:0% +map you recognize +this back to the uh the hot dog stand + + align:start position:0% +this back to the uh the hot dog stand + + + align:start position:0% +this back to the uh the hot dog stand +and um it may not look exactly like the + + align:start position:0% +and um it may not look exactly like the + + + align:start position:0% +and um it may not look exactly like the +ones um you made + + align:start position:0% +ones um you made + + + align:start position:0% +ones um you made +so starts with taking the order placing + + align:start position:0% +so starts with taking the order placing + + + align:start position:0% +so starts with taking the order placing +it in the + + align:start position:0% +it in the + + + align:start position:0% +it in the +inray get the order cook the dogs put + + align:start position:0% +inray get the order cook the dogs put + + + align:start position:0% +inray get the order cook the dogs put +them in the bun and wrap them at the + + align:start position:0% +them in the bun and wrap them at the + + + align:start position:0% +them in the bun and wrap them at the +fruit and then it's a question of do + + align:start position:0% +fruit and then it's a question of do + + + align:start position:0% +fruit and then it's a question of do +they need another hot dog or not if they + + align:start position:0% +they need another hot dog or not if they + + + align:start position:0% +they need another hot dog or not if they +don't they will go up to the order out + + align:start position:0% +don't they will go up to the order out + + + align:start position:0% +don't they will go up to the order out +if they do then you go + + align:start position:0% +if they do then you go + + + align:start position:0% +if they do then you go +over check if the order is okay add the + + align:start position:0% +over check if the order is okay add the + + + align:start position:0% +over check if the order is okay add the +beverage deliver it to the customer and + + align:start position:0% +beverage deliver it to the customer and + + + align:start position:0% +beverage deliver it to the customer and +the customer leaves with their hot dogs + + align:start position:0% +the customer leaves with their hot dogs + + + align:start position:0% +the customer leaves with their hot dogs +so value as as we think about it in in + + align:start position:0% +so value as as we think about it in in + + + align:start position:0% +so value as as we think about it in in +lean is really value for the + + align:start position:0% +lean is really value for the + + + align:start position:0% +lean is really value for the +customer right it's not value for us and + + align:start position:0% +customer right it's not value for us and + + + align:start position:0% +customer right it's not value for us and +in particular in healthcare I don't know + + align:start position:0% +in particular in healthcare I don't know + + + align:start position:0% +in particular in healthcare I don't know +so much about the engineering side but + + align:start position:0% +so much about the engineering side but + + + align:start position:0% +so much about the engineering side but +in healthcare we really have a difficult + + align:start position:0% +in healthcare we really have a difficult + + + align:start position:0% +in healthcare we really have a difficult +time coming to terms with this we + + align:start position:0% +time coming to terms with this we + + + align:start position:0% +time coming to terms with this we +struggle with it because it is often + + align:start position:0% +struggle with it because it is often + + + align:start position:0% +struggle with it because it is often +times about how do things work best for + + align:start position:0% +times about how do things work best for + + + align:start position:0% +times about how do things work best for +us and not so much how do things work + + align:start position:0% +us and not so much how do things work + + + align:start position:0% +us and not so much how do things work +best for for the patients right if it + + align:start position:0% +best for for the patients right if it + + + align:start position:0% +best for for the patients right if it +was the other way we probably wouldn't + + align:start position:0% +was the other way we probably wouldn't + + + align:start position:0% +was the other way we probably wouldn't +have waiting rooms we do have waiting + + align:start position:0% +have waiting rooms we do have waiting + + + align:start position:0% +have waiting rooms we do have waiting +rooms we have waiting rooms all + + align:start position:0% +rooms we have waiting rooms all + + + align:start position:0% +rooms we have waiting rooms all +over in fact I work in the emergency + + align:start position:0% +over in fact I work in the emergency + + + align:start position:0% +over in fact I work in the emergency +department over at bi and we have + + align:start position:0% +department over at bi and we have + + + align:start position:0% +department over at bi and we have +recently decided that we're going to + + align:start position:0% +recently decided that we're going to + + + align:start position:0% +recently decided that we're going to +make it a formal process to open our + + align:start position:0% +make it a formal process to open our + + + align:start position:0% +make it a formal process to open our +waiting room because we don't really + + align:start position:0% +waiting room because we don't really + + + align:start position:0% +waiting room because we don't really +want it and it's going to be paged out + + align:start position:0% +want it and it's going to be paged out + + + align:start position:0% +want it and it's going to be paged out +as a formal process as a formal step + + align:start position:0% +as a formal process as a formal step + + + align:start position:0% +as a formal process as a formal step +that now we decide we open it and we + + align:start position:0% +that now we decide we open it and we + + + align:start position:0% +that now we decide we open it and we +will not have it open if we have any + + align:start position:0% +will not have it open if we have any + + + align:start position:0% +will not have it open if we have any +open beds in the department CU it + + align:start position:0% +open beds in the department CU it + + + align:start position:0% +open beds in the department CU it +doesn't make any sense anyway that would + + align:start position:0% +doesn't make any sense anyway that would + + + align:start position:0% +doesn't make any sense anyway that would +be value for the um for the customer + + align:start position:0% +be value for the um for the customer + + + align:start position:0% +be value for the um for the customer +identify the value stream map out the + + align:start position:0% +identify the value stream map out the + + + align:start position:0% +identify the value stream map out the +endtoend linkages between the the uh the + + align:start position:0% +endtoend linkages between the the uh the + + + align:start position:0% +endtoend linkages between the the uh the +processes what goes on then we focus on + + align:start position:0% +processes what goes on then we focus on + + + align:start position:0% +processes what goes on then we focus on +making flow continuous from one end uh + + align:start position:0% +making flow continuous from one end uh + + + align:start position:0% +making flow continuous from one end uh +to to the other pole that we heard about + + align:start position:0% +to to the other pole that we heard about + + + align:start position:0% +to to the other pole that we heard about +earlier on let the customer pull the + + align:start position:0% +earlier on let the customer pull the + + + align:start position:0% +earlier on let the customer pull the +value rather than us producing a whole + + align:start position:0% +value rather than us producing a whole + + + align:start position:0% +value rather than us producing a whole +bunch of things that then get piled up + + align:start position:0% +bunch of things that then get piled up + + + align:start position:0% +bunch of things that then get piled up +and some of it gets wasted then um we do + + align:start position:0% +and some of it gets wasted then um we do + + + align:start position:0% +and some of it gets wasted then um we do +it over and over again because we're + + align:start position:0% +it over and over again because we're + + + align:start position:0% +it over and over again because we're +never really going to reach Perfection + + align:start position:0% +never really going to reach Perfection + + + align:start position:0% +never really going to reach Perfection +so but we're going to thrive for the P + + align:start position:0% +so but we're going to thrive for the P + + + align:start position:0% +so but we're going to thrive for the P +Perfection so value stream mapping it's + + align:start position:0% +Perfection so value stream mapping it's + + + align:start position:0% +Perfection so value stream mapping it's +a a tool to improve our processes our + + align:start position:0% +a a tool to improve our processes our + + + align:start position:0% +a a tool to improve our processes our +whole production by identifying steps + + align:start position:0% +whole production by identifying steps + + + align:start position:0% +whole production by identifying steps +that add value and also by identifying + + align:start position:0% +that add value and also by identifying + + + align:start position:0% +that add value and also by identifying +waste in our processes we follow the + + align:start position:0% +waste in our processes we follow the + + + align:start position:0% +waste in our processes we follow the +value creation process we talked about + + align:start position:0% +value creation process we talked about + + + align:start position:0% +value creation process we talked about +from one end to the other and you need + + align:start position:0% +from one end to the other and you need + + + align:start position:0% +from one end to the other and you need +to go to gima to get out there and see + + align:start position:0% +to go to gima to get out there and see + + + align:start position:0% +to go to gima to get out there and see +what happens right you can't sit in an + + align:start position:0% +what happens right you can't sit in an + + + align:start position:0% +what happens right you can't sit in an +office you can sit in an office and you + + align:start position:0% +office you can sit in an office and you + + + align:start position:0% +office you can sit in an office and you +can think that you know what is actually + + align:start position:0% +can think that you know what is actually + + + align:start position:0% +can think that you know what is actually +happening but you in reality you don't I + + align:start position:0% +happening but you in reality you don't I + + + align:start position:0% +happening but you in reality you don't I +have some examples I'll get to that a + + align:start position:0% +have some examples I'll get to that a + + + align:start position:0% +have some examples I'll get to that a +little later from our fine little + + align:start position:0% +little later from our fine little + + + align:start position:0% +little later from our fine little +hospital if we have half the time but + + align:start position:0% +hospital if we have half the time but + + + align:start position:0% +hospital if we have half the time but +when you go and look at what actually + + align:start position:0% +when you go and look at what actually + + + align:start position:0% +when you go and look at what actually +takes place you get surprised even in + + align:start position:0% +takes place you get surprised even in + + + align:start position:0% +takes place you get surprised even in +the environment that you work in + + align:start position:0% +the environment that you work in + + + align:start position:0% +the environment that you work in +yourself because we all think that we + + align:start position:0% +yourself because we all think that we + + + align:start position:0% +yourself because we all think that we +have the solutions to the problems that + + align:start position:0% +have the solutions to the problems that + + + align:start position:0% +have the solutions to the problems that +we encounter and um sometimes we do and + + align:start position:0% +we encounter and um sometimes we do and + + + align:start position:0% +we encounter and um sometimes we do and +sometimes we actually don't the uh value + + align:start position:0% +sometimes we actually don't the uh value + + + align:start position:0% +sometimes we actually don't the uh value +stream map is the process maps that + + align:start position:0% +stream map is the process maps that + + + align:start position:0% +stream map is the process maps that +we've done some of you have already + + align:start position:0% +we've done some of you have already + + + align:start position:0% +we've done some of you have already +added your data it can be time data it + + align:start position:0% +added your data it can be time data it + + + align:start position:0% +added your data it can be time data it +can be quality data inventory resources + + align:start position:0% +can be quality data inventory resources + + + align:start position:0% +can be quality data inventory resources +people things and whatever else but + + align:start position:0% +people things and whatever else but + + + align:start position:0% +people things and whatever else but +don't don't clot your maps with uh with + + align:start position:0% +don't don't clot your maps with uh with + + + align:start position:0% +don't don't clot your maps with uh with +things that are not really useful for + + align:start position:0% +things that are not really useful for + + + align:start position:0% +things that are not really useful for +you so there are some steps to uh + + align:start position:0% +you so there are some steps to uh + + + align:start position:0% +you so there are some steps to uh +creating these value stream maps and the + + align:start position:0% +creating these value stream maps and the + + + align:start position:0% +creating these value stream maps and the +first is to Define customer value and + + align:start position:0% +first is to Define customer value and + + + align:start position:0% +first is to Define customer value and +then the process and we can discuss what + + align:start position:0% +then the process and we can discuss what + + + align:start position:0% +then the process and we can discuss what +customer value is that is a debate you + + align:start position:0% +customer value is that is a debate you + + + align:start position:0% +customer value is that is a debate you +can see among yourselves here with the + + align:start position:0% +can see among yourselves here with the + + + align:start position:0% +can see among yourselves here with the +maps that you've created you did not all + + align:start position:0% +maps that you've created you did not all + + + align:start position:0% +maps that you've created you did not all +agree on what what adds value what + + align:start position:0% +agree on what what adds value what + + + align:start position:0% +agree on what what adds value what +customers potentially would be willing + + align:start position:0% +customers potentially would be willing + + + align:start position:0% +customers potentially would be willing +to pay for an example we've just done + + align:start position:0% +to pay for an example we've just done + + + align:start position:0% +to pay for an example we've just done +um a lean project with our registration + + align:start position:0% +um a lean project with our registration + + + align:start position:0% +um a lean project with our registration +people patients need to be registered + + align:start position:0% +people patients need to be registered + + + align:start position:0% +people patients need to be registered +right and um is that a value added + + align:start position:0% +right and um is that a value added + + + align:start position:0% +right and um is that a value added +process we weren't quite agreeing on + + align:start position:0% +process we weren't quite agreeing on + + + align:start position:0% +process we weren't quite agreeing on +that at least not initially because you + + align:start position:0% +that at least not initially because you + + + align:start position:0% +that at least not initially because you +can say well I mean patients they don't + + align:start position:0% +can say well I mean patients they don't + + + align:start position:0% +can say well I mean patients they don't +care but in fact in fact if you dig a + + align:start position:0% +care but in fact in fact if you dig a + + + align:start position:0% +care but in fact in fact if you dig a +Little Deeper they probably do because + + align:start position:0% +Little Deeper they probably do because + + + align:start position:0% +Little Deeper they probably do because +if you aren't registered your visit is + + align:start position:0% +if you aren't registered your visit is + + + align:start position:0% +if you aren't registered your visit is +not linked to your record and then it's + + align:start position:0% +not linked to your record and then it's + + + align:start position:0% +not linked to your record and then it's +not part of your history and then it's + + align:start position:0% +not part of your history and then it's + + + align:start position:0% +not part of your history and then it's +it's hard to tie everything together so + + align:start position:0% +it's hard to tie everything together so + + + align:start position:0% +it's hard to tie everything together so +identify the value added and the waste + + align:start position:0% +identify the value added and the waste + + + align:start position:0% +identify the value added and the waste +steps it's the next one and then in + + align:start position:0% +steps it's the next one and then in + + + align:start position:0% +steps it's the next one and then in +order to change things for the better in + + align:start position:0% +order to change things for the better in + + + align:start position:0% +order to change things for the better in +the future you need to understand what + + align:start position:0% +the future you need to understand what + + + align:start position:0% +the future you need to understand what +you're currently doing so you do a map + + align:start position:0% +you're currently doing so you do a map + + + align:start position:0% +you're currently doing so you do a map +of the current state where are we now + + align:start position:0% +of the current state where are we now + + + align:start position:0% +of the current state where are we now +right and then you Analyze That map and + + align:start position:0% +right and then you Analyze That map and + + + align:start position:0% +right and then you Analyze That map and +you find opportunities for improving + + align:start position:0% +you find opportunities for improving + + + align:start position:0% +you find opportunities for improving +things you can look at bottlenecks you + + align:start position:0% +things you can look at bottlenecks you + + + align:start position:0% +things you can look at bottlenecks you +can look at um at workload balancing and + + align:start position:0% +can look at um at workload balancing and + + + align:start position:0% +can look at um at workload balancing and +you can have that as an open discussion + + align:start position:0% +you can have that as an open discussion + + + align:start position:0% +you can have that as an open discussion +of what can you make better and now you + + align:start position:0% +of what can you make better and now you + + + align:start position:0% +of what can you make better and now you +just heard the uh the module on uh on + + align:start position:0% +just heard the uh the module on uh on + + + align:start position:0% +just heard the uh the module on uh on +people and that's actually interesting + + align:start position:0% +people and that's actually interesting + + + align:start position:0% +people and that's actually interesting +if you use if you involve everybody in + + align:start position:0% +if you use if you involve everybody in + + + align:start position:0% +if you use if you involve everybody in +this process you can get a lot of good + + align:start position:0% +this process you can get a lot of good + + + align:start position:0% +this process you can get a lot of good +Synergy in it and by involving some of + + align:start position:0% +Synergy in it and by involving some of + + + align:start position:0% +Synergy in it and by involving some of +the Skeptics you can actually win them + + align:start position:0% +the Skeptics you can actually win them + + + align:start position:0% +the Skeptics you can actually win them +over sometimes we've done that too + + align:start position:0% +over sometimes we've done that too + + + align:start position:0% +over sometimes we've done that too +surprisingly enough but uh it is + + align:start position:0% +surprisingly enough but uh it is + + + align:start position:0% +surprisingly enough but uh it is +possible then you use that to create + + align:start position:0% +possible then you use that to create + + + align:start position:0% +possible then you use that to create +your future state map and then you make + + align:start position:0% +your future state map and then you make + + + align:start position:0% +your future state map and then you make +an action plan for how you're going to + + align:start position:0% +an action plan for how you're going to + + + align:start position:0% +an action plan for how you're going to +get there and I think we'll get to that + + align:start position:0% +get there and I think we'll get to that + + + align:start position:0% +get there and I think we'll get to that +on day three in the uh in the A3 + + align:start position:0% +on day three in the uh in the A3 + + + align:start position:0% +on day three in the uh in the A3 +thinking all + + align:start position:0% +thinking all + + + align:start position:0% +thinking all +right we're back to this one it follows + + align:start position:0% +right we're back to this one it follows + + + align:start position:0% +right we're back to this one it follows +the uh value creation process and you + + align:start position:0% +the uh value creation process and you + + + align:start position:0% +the uh value creation process and you +have in your groups assess the values + + align:start position:0% +have in your groups assess the values + + + align:start position:0% +have in your groups assess the values +and the Wast for each of the + + align:start position:0% +and the Wast for each of the + + + align:start position:0% +and the Wast for each of the +processes and now it's time to add some + + align:start position:0% +processes and now it's time to add some + + + align:start position:0% +processes and now it's time to add some +data and I think that will + + align:start position:0% +data and I think that will + + + align:start position:0% +data and I think that will +just go with the map that you had handed + + align:start position:0% +just go with the map that you had handed + + + align:start position:0% +just go with the map that you had handed +out all the data should be on it times + + align:start position:0% +out all the data should be on it times + + + align:start position:0% +out all the data should be on it times +and seconds and there's some quality + + align:start position:0% +and seconds and there's some quality + + + align:start position:0% +and seconds and there's some quality +measurements as well because the + + align:start position:0% +measurements as well because the + + + align:start position:0% +measurements as well because the +processes they weren't perfect the whole + + align:start position:0% +processes they weren't perfect the whole + + + align:start position:0% +processes they weren't perfect the whole +way through right it wasn't 100% every + + align:start position:0% +way through right it wasn't 100% every + + + align:start position:0% +way through right it wasn't 100% every +time we know our demand our current + + align:start position:0% +time we know our demand our current + + + align:start position:0% +time we know our demand our current +demand at least + + align:start position:0% +demand at least + + + align:start position:0% +demand at least +for the 50 + + align:start position:0% +for the 50 + + + align:start position:0% +for the 50 +customers and we know how long we're + + align:start position:0% +customers and we know how long we're + + + align:start position:0% +customers and we know how long we're +open so we know how long time we have to + + align:start position:0% +open so we know how long time we have to + + + align:start position:0% +open so we know how long time we have to +uh to fulfill the orders as they are the + + align:start position:0% +uh to fulfill the orders as they are the + + + align:start position:0% +uh to fulfill the orders as they are the +TAC time is our available times it's 4 + + align:start position:0% +TAC time is our available times it's 4 + + + align:start position:0% +TAC time is our available times it's 4 +hours time 60 Minutes that should be 240 + + align:start position:0% +hours time 60 Minutes that should be 240 + + + align:start position:0% +hours time 60 Minutes that should be 240 +minutes and the demand is 50 customers + + align:start position:0% +minutes and the demand is 50 customers + + + align:start position:0% +minutes and the demand is 50 customers +so we have 4.8 or 288 seconds per + + align:start position:0% +so we have 4.8 or 288 seconds per + + + align:start position:0% +so we have 4.8 or 288 seconds per +customer we also know that the cycle + + align:start position:0% +customer we also know that the cycle + + + align:start position:0% +customer we also know that the cycle +time from what we added up is actually + + align:start position:0% +time from what we added up is actually + + + align:start position:0% +time from what we added up is actually + + align:start position:0% + + + align:start position:0% +seconds so we can all understand that + + align:start position:0% +seconds so we can all understand that + + + align:start position:0% +seconds so we can all understand that +they're pretty stressed right because + + align:start position:0% +they're pretty stressed right because + + + align:start position:0% +they're pretty stressed right because +they're spending more time than they + + align:start position:0% +they're spending more time than they + + + align:start position:0% +they're spending more time than they +really have and then there's the + + align:start position:0% +really have and then there's the + + + align:start position:0% +really have and then there's the +alternative calculation where you've uh + + align:start position:0% +alternative calculation where you've uh + + + align:start position:0% +alternative calculation where you've uh +taken the set out and the + + align:start position:0% +taken the set out and the + + + align:start position:0% +taken the set out and the +cleanout uh time out um some of you + + align:start position:0% +cleanout uh time out um some of you + + + align:start position:0% +cleanout uh time out um some of you +might have been thinking about that and + + align:start position:0% +might have been thinking about that and + + + align:start position:0% +might have been thinking about that and +done that when things are slow and that + + align:start position:0% +done that when things are slow and that + + + align:start position:0% +done that when things are slow and that +gives you a little uh shorter TCT time + + align:start position:0% +gives you a little uh shorter TCT time + + + align:start position:0% +gives you a little uh shorter TCT time +but there there's still an imbalance + + align:start position:0% +but there there's still an imbalance + + + align:start position:0% +but there there's still an imbalance +between the attack time and the cycle + + align:start position:0% +between the attack time and the cycle + + + align:start position:0% +between the attack time and the cycle +time so you're still um you're still in + + align:start position:0% +time so you're still um you're still in + + + align:start position:0% +time so you're still um you're still in +the negative but you have two workers so + + align:start position:0% +the negative but you have two workers so + + + align:start position:0% +the negative but you have two workers so +the question is can you meet their + + align:start position:0% +the question is can you meet their + + + align:start position:0% +the question is can you meet their +demands all right if you take the second + + align:start position:0% +demands all right if you take the second + + + align:start position:0% +demands all right if you take the second +handout that you got uh with the + + align:start position:0% +handout that you got uh with the + + + align:start position:0% +handout that you got uh with the +different processes + + align:start position:0% +different processes + + + align:start position:0% +different processes +on write down in your groups you have 10 + + align:start position:0% +on write down in your groups you have 10 + + + align:start position:0% +on write down in your groups you have 10 +minutes you'll get a warning after 7 + + align:start position:0% +minutes you'll get a warning after 7 + + + align:start position:0% +minutes you'll get a warning after 7 +write down who is doing what how much + + align:start position:0% +write down who is doing what how much + + + align:start position:0% +write down who is doing what how much +time they're + + align:start position:0% +time they're + + + align:start position:0% +time they're +spending and then as well whether it's + + align:start position:0% +spending and then as well whether it's + + + align:start position:0% +spending and then as well whether it's +value added or nonv value + + align:start position:0% +value added or nonv value + + + align:start position:0% +value added or nonv value +added ask all right all right we're + + align:start position:0% +added ask all right all right we're + + + align:start position:0% +added ask all right all right we're +going to start up here because I you + + align:start position:0% +going to start up here because I you + + + align:start position:0% +going to start up here because I you +look very ready you're starting to + + align:start position:0% +look very ready you're starting to + + + align:start position:0% +look very ready you're starting to +search for Solutions here Sasha how much + + align:start position:0% +search for Solutions here Sasha how much + + + align:start position:0% +search for Solutions here Sasha how much +is he working or + + align:start position:0% +is he working or + + + align:start position:0% +is he working or +she 159 okay + + align:start position:0% +she 159 okay + + + align:start position:0% +she 159 okay +Andy to + + align:start position:0% +Andy to + + + align:start position:0% +Andy to +24 okay now weight and neither should be + + align:start position:0% +24 okay now weight and neither should be + + + align:start position:0% +24 okay now weight and neither should be +the same so let's look at value add non + + align:start position:0% +the same so let's look at value add non + + + align:start position:0% +the same so let's look at value add non +value + + align:start position:0% +value + + + align:start position:0% +value +added + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +174 63 weight all right that seems + + align:start position:0% +174 63 weight all right that seems + + + align:start position:0% +174 63 weight all right that seems +reasonable let's see let's see if other + + align:start position:0% +reasonable let's see let's see if other + + + align:start position:0% +reasonable let's see let's see if other +folks agree and again we don't just like + + align:start position:0% +folks agree and again we don't just like + + + align:start position:0% +folks agree and again we don't just like +last time these things are kind of open + + align:start position:0% +last time these things are kind of open + + + align:start position:0% +last time these things are kind of open +to interpretation hopefully actually the + + align:start position:0% +to interpretation hopefully actually the + + + align:start position:0% +to interpretation hopefully actually the +this mix is pretty prescribed but this + + align:start position:0% +this mix is pretty prescribed but this + + + align:start position:0% +this mix is pretty prescribed but this +is up to your judgment right so we're + + align:start position:0% +is up to your judgment right so we're + + + align:start position:0% +is up to your judgment right so we're +expecting some different answers here + + align:start position:0% + + + + align:start position:0% + +so this time we've got basically because + + align:start position:0% +so this time we've got basically because + + + align:start position:0% +so this time we've got basically because +we con strained the problem down these + + align:start position:0% +we con strained the problem down these + + + align:start position:0% +we con strained the problem down these +answers tend to agree these are still + + align:start position:0% +answers tend to agree these are still + + + align:start position:0% +answers tend to agree these are still +you know you people have different + + align:start position:0% +you know you people have different + + + align:start position:0% +you know you people have different +opinions about different things and so + + align:start position:0% +opinions about different things and so + + + align:start position:0% +opinions about different things and so +we have a fair range there but it does + + align:start position:0% +we have a fair range there but it does + + + align:start position:0% +we have a fair range there but it does +look like as an overall that um this + + align:start position:0% +look like as an overall that um this + + + align:start position:0% +look like as an overall that um this +isn't a bad process it's more value ad + + align:start position:0% +isn't a bad process it's more value ad + + + align:start position:0% +isn't a bad process it's more value ad +than nonv value ad so that's that's + + align:start position:0% +than nonv value ad so that's that's + + + align:start position:0% +than nonv value ad so that's that's +pretty good actually so these people are + + align:start position:0% +pretty good actually so these people are + + + align:start position:0% +pretty good actually so these people are +not wasting their time but but there is + + align:start position:0% +not wasting their time but but there is + + + align:start position:0% +not wasting their time but but there is +a substantial fraction of nonv Val added + + align:start position:0% +a substantial fraction of nonv Val added + + + align:start position:0% +a substantial fraction of nonv Val added +and and weit time in the process and + + align:start position:0% +and and weit time in the process and + + + align:start position:0% +and and weit time in the process and +what can we say about Sash and Andy + + align:start position:0% +what can we say about Sash and Andy + + + align:start position:0% +what can we say about Sash and Andy +balance + + align:start position:0% +balance + + + align:start position:0% +balance +process uhuh no that that may + + align:start position:0% +process uhuh no that that may + + + align:start position:0% +process uhuh no that that may +be an opportunity to do better and gets + + align:start position:0% +be an opportunity to do better and gets + + + align:start position:0% +be an opportunity to do better and gets +right at this issue of well our cycle + + align:start position:0% +right at this issue of well our cycle + + + align:start position:0% +right at this issue of well our cycle +time our attack time the time that each + + align:start position:0% +time our attack time the time that each + + + align:start position:0% +time our attack time the time that each +individual person is + + align:start position:0% +individual person is + + + align:start position:0% +individual person is +working don't match up right now so back + + align:start position:0% +working don't match up right now so back + + + align:start position:0% +working don't match up right now so back +to Bow and we'll uh we'll see where we + + align:start position:0% +to Bow and we'll uh we'll see where we + + + align:start position:0% +to Bow and we'll uh we'll see where we +can go from here and you could also say + + align:start position:0% +can go from here and you could also say + + + align:start position:0% +can go from here and you could also say +with the uh with the differences on the + + align:start position:0% +with the uh with the differences on the + + + align:start position:0% +with the uh with the differences on the +value added and the non-value added time + + align:start position:0% +value added and the non-value added time + + + align:start position:0% +value added and the non-value added time +what would you do to understand that + + align:start position:0% +what would you do to understand that + + + align:start position:0% +what would you do to understand that +better now we're sitting and doing it on + + align:start position:0% +better now we're sitting and doing it on + + + align:start position:0% +better now we're sitting and doing it on +paper here + + align:start position:0% +paper here + + + align:start position:0% +paper here +right I can't answer that + + align:start position:0% +right I can't answer that + + + align:start position:0% +right I can't answer that +question I have another + + align:start position:0% +question I have another + + + align:start position:0% +question I have another +comments okay you'd watch the process + + align:start position:0% +comments okay you'd watch the process + + + align:start position:0% +comments okay you'd watch the process +yeah you could go and watch the process + + align:start position:0% +yeah you could go and watch the process + + + align:start position:0% +yeah you could go and watch the process +go and watch the process and how about + + align:start position:0% +go and watch the process and how about + + + align:start position:0% +go and watch the process and how about +talking to the people there right the + + align:start position:0% +talking to the people there right the + + + align:start position:0% +talking to the people there right the +customers okay your comment I guess that + + align:start position:0% +customers okay your comment I guess that + + + align:start position:0% +customers okay your comment I guess that +brings me to + + align:start position:0% +brings me to + + + align:start position:0% +brings me to +that um like in cqi you give it I can't + + align:start position:0% +that um like in cqi you give it I can't + + + align:start position:0% +that um like in cqi you give it I can't +actually remember now it's been a while + + align:start position:0% +actually remember now it's been a while + + + align:start position:0% +actually remember now it's been a while +since I've implemented these but you + + align:start position:0% +since I've implemented these but you + + + align:start position:0% +since I've implemented these but you +would give it a number so that not every + + align:start position:0% +would give it a number so that not every + + + align:start position:0% +would give it a number so that not every +time not every unit of Andy and Sasha + + align:start position:0% +time not every unit of Andy and Sasha + + + align:start position:0% +time not every unit of Andy and Sasha +would equal one um and I think maybe we + + align:start position:0% +would equal one um and I think maybe we + + + align:start position:0% +would equal one um and I think maybe we +would value maybe some of her chitchat + + align:start position:0% +would value maybe some of her chitchat + + + align:start position:0% +would value maybe some of her chitchat +as personal relations that actually + + align:start position:0% +as personal relations that actually + + + align:start position:0% +as personal relations that actually +maybe people may be coming back to get + + align:start position:0% +maybe people may be coming back to get + + + align:start position:0% +maybe people may be coming back to get +the hot dogs not because hot dogs are + + align:start position:0% +the hot dogs not because hot dogs are + + + align:start position:0% +the hot dogs not because hot dogs are +great to eat and they love these hot + + align:start position:0% +great to eat and they love these hot + + + align:start position:0% +great to eat and they love these hot +dogs but they she brings them back so + + align:start position:0% +dogs but they she brings them back so + + + align:start position:0% +dogs but they she brings them back so +her time spent chatting although taking + + align:start position:0% +her time spent chatting although taking + + + align:start position:0% +her time spent chatting although taking +up time may be given more like one or + + align:start position:0% +up time may be given more like one or + + + align:start position:0% +up time may be given more like one or +his less than one so they may be doing + + align:start position:0% +his less than one so they may be doing + + + align:start position:0% +his less than one so they may be doing +balance + + align:start position:0% +balance + + + align:start position:0% +balance +work if you look at it at a deeper level + + align:start position:0% +work if you look at it at a deeper level + + + align:start position:0% +work if you look at it at a deeper level +at least that's an assumption until + + align:start position:0% +at least that's an assumption until + + + align:start position:0% +at least that's an assumption until +you've clarified with the customers + + align:start position:0% +you've clarified with the customers + + + align:start position:0% +you've clarified with the customers +whether this is really something that + + align:start position:0% +whether this is really something that + + + align:start position:0% +whether this is really something that +they value the other I mean don't that's + + align:start position:0% +they value the other I mean don't that's + + + align:start position:0% +they value the other I mean don't that's +actually a a a comment with with that + + align:start position:0% +actually a a a comment with with that + + + align:start position:0% +actually a a a comment with with that +can be taken in a couple different + + align:start position:0% +can be taken in a couple different + + + align:start position:0% +can be taken in a couple different +directions right right now this is this + + align:start position:0% +directions right right now this is this + + + align:start position:0% +directions right right now this is this +is absolute time spent doing everything + + align:start position:0% +is absolute time spent doing everything + + + align:start position:0% +is absolute time spent doing everything +so should should based on this should + + align:start position:0% +so should should based on this should + + + align:start position:0% +so should should based on this should +Sasha chitchat more or less + + align:start position:0% +Sasha chitchat more or less + + + align:start position:0% +Sasha chitchat more or less +does it do any good if she does + + align:start position:0% +does it do any good if she does + + + align:start position:0% +does it do any good if she does +less no it actually solves nothing um + + align:start position:0% +less no it actually solves nothing um + + + align:start position:0% +less no it actually solves nothing um +and makes the customers annoyed so maybe + + align:start position:0% +and makes the customers annoyed so maybe + + + align:start position:0% +and makes the customers annoyed so maybe +maybe more is the answer there that's + + align:start position:0% +maybe more is the answer there that's + + + align:start position:0% +maybe more is the answer there that's +right um yeah now this is just the time + + align:start position:0% +right um yeah now this is just the time + + + align:start position:0% +right um yeah now this is just the time +right we're also you're also getting + + align:start position:0% +right we're also you're also getting + + + align:start position:0% +right we're also you're also getting +into sort of a value judgment of like + + align:start position:0% +into sort of a value judgment of like + + + align:start position:0% +into sort of a value judgment of like +who is doing more for the company and + + align:start position:0% +who is doing more for the company and + + + align:start position:0% +who is doing more for the company and +that's that's dangerous so we won't go + + align:start position:0% +that's that's dangerous so we won't go + + + align:start position:0% +that's that's dangerous so we won't go +there very far but but certainly it's + + align:start position:0% +there very far but but certainly it's + + + align:start position:0% +there very far but but certainly it's +not hurting anything for her to be doing + + align:start position:0% +not hurting anything for her to be doing + + + align:start position:0% +not hurting anything for her to be doing +that right right now because she's + + align:start position:0% +that right right now because she's + + + align:start position:0% +that right right now because she's +actually underutilized compar compared + + align:start position:0% +actually underutilized compar compared + + + align:start position:0% +actually underutilized compar compared +to an okay so that's we're actually + + align:start position:0% +to an okay so that's we're actually + + + align:start position:0% +to an okay so that's we're actually +going to do some numbers on that thought + + align:start position:0% +going to do some numbers on that thought + + + align:start position:0% +going to do some numbers on that thought +yeah um and we are going to do let's see + + align:start position:0% +yeah um and we are going to do let's see + + + align:start position:0% +yeah um and we are going to do let's see +here click there we go if we look sash's + + align:start position:0% +here click there we go if we look sash's + + + align:start position:0% +here click there we go if we look sash's +tasks we all got the + + align:start position:0% +tasks we all got the + + + align:start position:0% +tasks we all got the +159 50 orders so she is working 133 + + align:start position:0% +159 50 orders so she is working 133 + + + align:start position:0% +159 50 orders so she is working 133 +minutes out of the 240 minutes available + + align:start position:0% +minutes out of the 240 minutes available + + + align:start position:0% +minutes out of the 240 minutes available +all right that's at least and Andy was + + align:start position:0% +all right that's at least and Andy was + + + align:start position:0% +all right that's at least and Andy was + + align:start position:0% + + + align:start position:0% +4 uh seconds per + + align:start position:0% +4 uh seconds per + + + align:start position:0% +4 uh seconds per +order so working effectively 187 minutes + + align:start position:0% +order so working effectively 187 minutes + + + align:start position:0% +order so working effectively 187 minutes +out of the 240 minutes available and um + + align:start position:0% +out of the 240 minutes available and um + + + align:start position:0% +out of the 240 minutes available and um +so their their work time or their + + align:start position:0% +so their their work time or their + + + align:start position:0% +so their their work time or their +workload Sasha is working 55% of the + + align:start position:0% +workload Sasha is working 55% of the + + + align:start position:0% +workload Sasha is working 55% of the +available time and Andy is + + align:start position:0% +available time and Andy is + + + align:start position:0% +available time and Andy is +78 of the available + + align:start position:0% +78 of the available + + + align:start position:0% +78 of the available +time and um their capacity if you let me + + align:start position:0% +time and um their capacity if you let me + + + align:start position:0% +time and um their capacity if you let me +see here the touch time per order if you + + align:start position:0% +see here the touch time per order if you + + + align:start position:0% +see here the touch time per order if you +take the waiting time out should be 200 + + align:start position:0% +take the waiting time out should be 200 + + + align:start position:0% +take the waiting time out should be 200 +and 24 seconds which is defined by the + + align:start position:0% +and 24 seconds which is defined by the + + + align:start position:0% +and 24 seconds which is defined by the +one that's the slowest which is + + align:start position:0% +one that's the slowest which is + + + align:start position:0% +one that's the slowest which is +Andy + + align:start position:0% +Andy + + + align:start position:0% +Andy +okay so if you say that's 224 so they + + align:start position:0% +okay so if you say that's 224 so they + + + align:start position:0% +okay so if you say that's 224 so they +should be able to serve 64 + + align:start position:0% +should be able to serve 64 + + + align:start position:0% +should be able to serve 64 +customers that's if that's if Andy Max + + align:start position:0% +customers that's if that's if Andy Max + + + align:start position:0% +customers that's if that's if Andy Max +is out yeah yeah working 100% of the + + align:start position:0% +is out yeah yeah working 100% of the + + + align:start position:0% +is out yeah yeah working 100% of the +available time that's not always a good + + align:start position:0% +available time that's not always a good + + + align:start position:0% +available time that's not always a good +idea it's hard at least um so we're not + + align:start position:0% +idea it's hard at least um so we're not + + + align:start position:0% +idea it's hard at least um so we're not +going to talk about the variations right + + align:start position:0% +going to talk about the variations right + + + align:start position:0% +going to talk about the variations right +now we're going to do that later we got + + align:start position:0% +now we're going to do that later we got + + + align:start position:0% +now we're going to do that later we got +a question yeah so just looking at this + + align:start position:0% +a question yeah so just looking at this + + + align:start position:0% +a question yeah so just looking at this +data would our if we were analyzing this + + align:start position:0% +data would our if we were analyzing this + + + align:start position:0% +data would our if we were analyzing this +company saying okay what can we do to + + align:start position:0% +company saying okay what can we do to + + + align:start position:0% +company saying okay what can we do to +create a lead process would our initial + + align:start position:0% +create a lead process would our initial + + + align:start position:0% +create a lead process would our initial +thought be okay what are the tasks that + + align:start position:0% +thought be okay what are the tasks that + + + align:start position:0% +thought be okay what are the tasks that +aren't needed and how do we remove them + + align:start position:0% +aren't needed and how do we remove them + + + align:start position:0% +aren't needed and how do we remove them +from the process or would we say okay + + align:start position:0% +from the process or would we say okay + + + align:start position:0% +from the process or would we say okay +what are the tasks that Andy's currently + + align:start position:0% +what are the tasks that Andy's currently + + + align:start position:0% +what are the tasks that Andy's currently +doing that we could perhaps uh + + align:start position:0% +doing that we could perhaps uh + + + align:start position:0% +doing that we could perhaps uh +reallocate to Sasha such that we have a + + align:start position:0% +reallocate to Sasha such that we have a + + + align:start position:0% +reallocate to Sasha such that we have a +more continuous grow process that is + + align:start position:0% +more continuous grow process that is + + + align:start position:0% +more continuous grow process that is +what you're going to be discussing in + + align:start position:0% +what you're going to be discussing in + + + align:start position:0% +what you're going to be discussing in +the next exercise that is coming up here + + align:start position:0% +the next exercise that is coming up here + + + align:start position:0% +the next exercise that is coming up here +in a minute or two and then you can + + align:start position:0% +in a minute or two and then you can + + + align:start position:0% +in a minute or two and then you can +determine what you find more feasible + + align:start position:0% +determine what you find more feasible + + + align:start position:0% +determine what you find more feasible +right although although you have a good + + align:start position:0% +right although although you have a good + + + align:start position:0% +right although although you have a good +point there because the thing you said + + align:start position:0% +point there because the thing you said + + + align:start position:0% +point there because the thing you said +second is the one that's in the exercise + + align:start position:0% +second is the one that's in the exercise + + + align:start position:0% +second is the one that's in the exercise +the thing you said first gets at that + + align:start position:0% +the thing you said first gets at that + + + align:start position:0% +the thing you said first gets at that +issue of well let's make Sasha more + + align:start position:0% +issue of well let's make Sasha more + + + align:start position:0% +issue of well let's make Sasha more +efficient or not because as we get a + + align:start position:0% +efficient or not because as we get a + + + align:start position:0% +efficient or not because as we get a +little deeper into the analysis we find + + align:start position:0% +little deeper into the analysis we find + + + align:start position:0% +little deeper into the analysis we find +that that that's not actually going to + + align:start position:0% +that that that's not actually going to + + + align:start position:0% +that that that's not actually going to +help us first order so hold hold the + + align:start position:0% +help us first order so hold hold the + + + align:start position:0% +help us first order so hold hold the +rest of that + + align:start position:0% +rest of that + + + align:start position:0% +rest of that +thought but the best first step is to do + + align:start position:0% +thought but the best first step is to do + + + align:start position:0% +thought but the best first step is to do +what you've done now and analyze what's + + align:start position:0% +what you've done now and analyze what's + + + align:start position:0% +what you've done now and analyze what's +actually going + + align:start position:0% +actually going + + + align:start position:0% +actually going +on we saw that our current production + + align:start position:0% +on we saw that our current production + + + align:start position:0% +on we saw that our current production +the 50 customers is actually a little uh + + align:start position:0% +the 50 customers is actually a little uh + + + align:start position:0% +the 50 customers is actually a little uh +less that they can uh than they can + + align:start position:0% +less that they can uh than they can + + + align:start position:0% +less that they can uh than they can +produce the way they're doing uh um or + + align:start position:0% +produce the way they're doing uh um or + + + align:start position:0% +produce the way they're doing uh um or +the way they could be doing things if + + align:start position:0% +the way they could be doing things if + + + align:start position:0% +the way they could be doing things if +they were working 100% so um they need + + align:start position:0% +they were working 100% so um they need + + + align:start position:0% +they were working 100% so um they need +to improve their processes in order to + + align:start position:0% +to improve their processes in order to + + + align:start position:0% +to improve their processes in order to +meet their growing demand their popular + + align:start position:0% +meet their growing demand their popular + + + align:start position:0% +meet their growing demand their popular +stand whether it's the talking the + + align:start position:0% +stand whether it's the talking the + + + align:start position:0% +stand whether it's the talking the +chitchatting or the quality of the hot + + align:start position:0% +chitchatting or the quality of the hot + + + align:start position:0% +chitchatting or the quality of the hot +dogs we don't know at this point but um + + align:start position:0% +dogs we don't know at this point but um + + + align:start position:0% +dogs we don't know at this point but um +we can see that they're underutilized 55 + + align:start position:0% +we can see that they're underutilized 55 + + + align:start position:0% +we can see that they're underutilized 55 +to + + align:start position:0% +to + + + align:start position:0% +to +78% and their work is not balanced + + align:start position:0% +78% and their work is not balanced + + + align:start position:0% +78% and their work is not balanced +either and their cycle time per customer + + align:start position:0% +either and their cycle time per customer + + + align:start position:0% +either and their cycle time per customer +is too long regardless of how you + + align:start position:0% +is too long regardless of how you + + + align:start position:0% +is too long regardless of how you +calculate it um so we should be able to + + align:start position:0% +calculate it um so we should be able to + + + align:start position:0% +calculate it um so we should be able to +you should be able to shorten that by + + align:start position:0% +you should be able to shorten that by + + + align:start position:0% +you should be able to shorten that by +looking at it okay and that is your next + + align:start position:0% +looking at it okay and that is your next + + + align:start position:0% +looking at it okay and that is your next +job help them figure out what they can + + align:start position:0% +job help them figure out what they can + + + align:start position:0% +job help them figure out what they can +improve how can they improve their + + align:start position:0% +improve how can they improve their + + + align:start position:0% +improve how can they improve their +utilization how can they reduce their + + align:start position:0% +utilization how can they reduce their + + + align:start position:0% +utilization how can they reduce their +cycle times so now you can change the + + align:start position:0% +cycle times so now you can change the + + + align:start position:0% +cycle times so now you can change the +order that they do things in and um find + + align:start position:0% +order that they do things in and um find + + + align:start position:0% +order that they do things in and um find +out what they need to do in order to + + align:start position:0% +out what they need to do in order to + + + align:start position:0% +out what they need to do in order to +serve 75 customers + + align:start position:0% +serve 75 customers + + + align:start position:0% +serve 75 customers +and 100 + + align:start position:0% +and 100 + + + align:start position:0% +and 100 +customers so this is 10 minutes okay so + + align:start position:0% +customers so this is 10 minutes okay so + + + align:start position:0% +customers so this is 10 minutes okay so +this a brainstorm that that that's + + align:start position:0% +this a brainstorm that that that's + + + align:start position:0% +this a brainstorm that that that's +actually sort of a technical term right + + align:start position:0% +actually sort of a technical term right + + + align:start position:0% +actually sort of a technical term right +what's what have people gone through + + align:start position:0% +what's what have people gone through + + + align:start position:0% +what's what have people gone through +brainstorming exercises + + align:start position:0% +brainstorming exercises + + + align:start position:0% +brainstorming exercises +before yeah so it's interesting the + + align:start position:0% +before yeah so it's interesting the + + + align:start position:0% +before yeah so it's interesting the +medical people are saying yeah Engineers + + align:start position:0% +medical people are saying yeah Engineers + + + align:start position:0% +medical people are saying yeah Engineers +yeah okay so you're throwing ideas out + + align:start position:0% +yeah okay so you're throwing ideas out + + + align:start position:0% +yeah okay so you're throwing ideas out +there no idea is rejected at this point + + align:start position:0% +there no idea is rejected at this point + + + align:start position:0% +there no idea is rejected at this point +let's just collect + + align:start position:0% +let's just collect + + + align:start position:0% +let's just collect +thoughts let's start by back up and uh + + align:start position:0% +thoughts let's start by back up and uh + + + align:start position:0% +thoughts let's start by back up and uh +here if you have some uh some suggestion + + align:start position:0% +here if you have some uh some suggestion + + + align:start position:0% +here if you have some uh some suggestion +for changes + + align:start position:0% + + + + align:start position:0% + +Improvement go ahead uh so we started to + + align:start position:0% +Improvement go ahead uh so we started to + + + align:start position:0% +Improvement go ahead uh so we started to +look at the process uh of just taking + + align:start position:0% +look at the process uh of just taking + + + align:start position:0% +look at the process uh of just taking +the orders because it seemed like that + + align:start position:0% +the orders because it seemed like that + + + align:start position:0% +the orders because it seemed like that +was where a lot of kind of the + + align:start position:0% +was where a lot of kind of the + + + align:start position:0% +was where a lot of kind of the +inefficiencies were disseminating from + + align:start position:0% +inefficiencies were disseminating from + + + align:start position:0% +inefficiencies were disseminating from +or rather like a lot of the uh holdups + + align:start position:0% +or rather like a lot of the uh holdups + + + align:start position:0% +or rather like a lot of the uh holdups +from our chart were coming from so we + + align:start position:0% +from our chart were coming from so we + + + align:start position:0% +from our chart were coming from so we +thought that it it might actually be a + + align:start position:0% +thought that it it might actually be a + + + align:start position:0% +thought that it it might actually be a +better idea if there were um pre-created + + align:start position:0% +better idea if there were um pre-created + + + align:start position:0% +better idea if there were um pre-created +tickets where um a customer could write + + align:start position:0% +tickets where um a customer could write + + + align:start position:0% +tickets where um a customer could write +in their name write in what they want + + align:start position:0% +in their name write in what they want + + + align:start position:0% +in their name write in what they want +and then give it to Sasha and then + + align:start position:0% +and then give it to Sasha and then + + + align:start position:0% +and then give it to Sasha and then +well while Sasha was um filling their + + align:start position:0% +well while Sasha was um filling their + + + align:start position:0% +well while Sasha was um filling their +order they could pay her and that would + + align:start position:0% +order they could pay her and that would + + + align:start position:0% +order they could pay her and that would +uh get rid of kind of her adding the + + align:start position:0% +uh get rid of kind of her adding the + + + align:start position:0% +uh get rid of kind of her adding the +beverage later on for rechecking the + + align:start position:0% +beverage later on for rechecking the + + + align:start position:0% +beverage later on for rechecking the +order um and some of those + + align:start position:0% +order um and some of those + + + align:start position:0% +order um and some of those +insufficiencies okay and the other bird + + align:start position:0% +insufficiencies okay and the other bird + + + align:start position:0% +insufficiencies okay and the other bird +that it kills is that U while wait time + + align:start position:0% +that it kills is that U while wait time + + + align:start position:0% +that it kills is that U while wait time +actual weit time might not change + + align:start position:0% +actual weit time might not change + + + align:start position:0% +actual weit time might not change +initially the perceive way time would + + align:start position:0% +initially the perceive way time would + + + align:start position:0% +initially the perceive way time would +change for the customer because if you + + align:start position:0% +change for the customer because if you + + + align:start position:0% +change for the customer because if you +hand them the drink ahead of time then + + align:start position:0% +hand them the drink ahead of time then + + + align:start position:0% +hand them the drink ahead of time then +you know they have the perception that + + align:start position:0% +you know they have the perception that + + + align:start position:0% +you know they have the perception that +hey you + + align:start position:0% +hey you + + + align:start position:0% +hey you +know yeah they always bring your wine + + align:start position:0% +know yeah they always bring your wine + + + align:start position:0% +know yeah they always bring your wine +first get your drink first so they can + + align:start position:0% +first get your drink first so they can + + + align:start position:0% +first get your drink first so they can +sell you an extra glass you that's right + + align:start position:0% +sell you an extra glass you that's right + + + align:start position:0% +sell you an extra glass you that's right +it's already gone by the time dinner + + align:start position:0% +it's already gone by the time dinner + + + align:start position:0% +it's already gone by the time dinner +comes any other + + align:start position:0% +comes any other + + + align:start position:0% +comes any other +uh any other suggestions going to go + + align:start position:0% +uh any other suggestions going to go + + + align:start position:0% +uh any other suggestions going to go +with back table Yeah so we thought um + + align:start position:0% +with back table Yeah so we thought um + + + align:start position:0% +with back table Yeah so we thought um +for steps number 10 and 11 with some um + + align:start position:0% +for steps number 10 and 11 with some um + + + align:start position:0% +for steps number 10 and 11 with some um +different preparation work such as + + align:start position:0% +different preparation work such as + + + align:start position:0% +different preparation work such as +keeping double the amount of stocked + + align:start position:0% +keeping double the amount of stocked + + + align:start position:0% +keeping double the amount of stocked +items and double the amount of trash + + align:start position:0% +items and double the amount of trash + + + align:start position:0% +items and double the amount of trash +bins Etc condiments they could cut that + + align:start position:0% +bins Etc condiments they could cut that + + + align:start position:0% +bins Etc condiments they could cut that +time in half and only do that work every + + align:start position:0% +time in half and only do that work every + + + align:start position:0% +time in half and only do that work every +two hours right + + align:start position:0% +two hours right + + + align:start position:0% +two hours right +okay and also set up since Sasha is not + + align:start position:0% +okay and also set up since Sasha is not + + + align:start position:0% +okay and also set up since Sasha is not +the one direct taking the orders since + + align:start position:0% +the one direct taking the orders since + + + align:start position:0% +the one direct taking the orders since +the the people will just sping order + + align:start position:0% +the the people will just sping order + + + align:start position:0% +the the people will just sping order +tickets she will actually help Andy out + + align:start position:0% +tickets she will actually help Andy out + + + align:start position:0% +tickets she will actually help Andy out +in the kitchen by being the one to do + + align:start position:0% +in the kitchen by being the one to do + + + align:start position:0% +in the kitchen by being the one to do +part of steps four + + align:start position:0% +part of steps four + + + align:start position:0% +part of steps four +and + + align:start position:0% +and + + + align:start position:0% +and +uh five yeah if if Andy puts the dog in + + align:start position:0% +uh five yeah if if Andy puts the dog in + + + align:start position:0% +uh five yeah if if Andy puts the dog in +the bin and wraps it in foils she can + + align:start position:0% +the bin and wraps it in foils she can + + + align:start position:0% +the bin and wraps it in foils she can +just um add the fruit of choice and put + + align:start position:0% +just um add the fruit of choice and put + + + align:start position:0% +just um add the fruit of choice and put +in a seven container that way she + + align:start position:0% +in a seven container that way she + + + align:start position:0% +in a seven container that way she +doesn't have to recheck in Step seven + + align:start position:0% +doesn't have to recheck in Step seven + + + align:start position:0% +doesn't have to recheck in Step seven +because she's one doing it right so when + + align:start position:0% +because she's one doing it right so when + + + align:start position:0% +because she's one doing it right so when +we recalculate the numbers for that + + align:start position:0% +we recalculate the numbers for that + + + align:start position:0% +we recalculate the numbers for that +originally right now it's 50 a value at + + align:start position:0% +originally right now it's 50 a value at + + + align:start position:0% +originally right now it's 50 a value at +a time 36 of non from 4 to 8 is 36 of + + align:start position:0% +a time 36 of non from 4 to 8 is 36 of + + + align:start position:0% +a time 36 of non from 4 to 8 is 36 of +nonv value time and 33 of weit time when + + align:start position:0% +nonv value time and 33 of weit time when + + + align:start position:0% +nonv value time and 33 of weit time when +we change their what they're doing in + + align:start position:0% +we change their what they're doing in + + + align:start position:0% +we change their what they're doing in +each part of that so that he's just + + align:start position:0% +each part of that so that he's just + + + align:start position:0% +each part of that so that he's just +doing the dogs and she's doing + + align:start position:0% +doing the dogs and she's doing + + + align:start position:0% +doing the dogs and she's doing +everything else and we take out that + + align:start position:0% +everything else and we take out that + + + align:start position:0% +everything else and we take out that +sitting on the counter wait time it's + + align:start position:0% +sitting on the counter wait time it's + + + align:start position:0% +sitting on the counter wait time it's +all becomes 80 of value added time so we + + align:start position:0% +all becomes 80 of value added time so we + + + align:start position:0% +all becomes 80 of value added time so we +have no nonv value added time anymore + + align:start position:0% +have no nonv value added time anymore + + + align:start position:0% +have no nonv value added time anymore +and no weight time so we've eliminated + + align:start position:0% +and no weight time so we've eliminated + + + align:start position:0% +and no weight time so we've eliminated +all that and we have 80 of value versus + + align:start position:0% +all that and we have 80 of value versus + + + align:start position:0% +all that and we have 80 of value versus +the 50 that's originally there okay does + + align:start position:0% +the 50 that's originally there okay does + + + align:start position:0% +the 50 that's originally there okay does +it change any of the times in between + + align:start position:0% +it change any of the times in between + + + align:start position:0% +it change any of the times in between +the two of + + align:start position:0% + + + + align:start position:0% + +them yeah I I I um more Sasha is going + + align:start position:0% +them yeah I I I um more Sasha is going + + + align:start position:0% +them yeah I I I um more Sasha is going +to work more little bit s will be work + + align:start position:0% +to work more little bit s will be work + + + align:start position:0% +to work more little bit s will be work +20 seconds right she was originally I + + align:start position:0% +20 seconds right she was originally I + + + align:start position:0% +20 seconds right she was originally I +think for 4 to S like 21 and now she's + + align:start position:0% +think for 4 to S like 21 and now she's + + + align:start position:0% +think for 4 to S like 21 and now she's + + align:start position:0% + + + align:start position:0% +okay so and those are seconds that is + + align:start position:0% +okay so and those are seconds that is + + + align:start position:0% +okay so and those are seconds that is +going from Andy from Andy from + + align:start position:0% +going from Andy from Andy from + + + align:start position:0% +going from Andy from Andy from +Andy we kind of had a similar suggestion + + align:start position:0% +Andy we kind of had a similar suggestion + + + align:start position:0% +Andy we kind of had a similar suggestion +where Sasha would do some of the work of + + align:start position:0% +where Sasha would do some of the work of + + + align:start position:0% +where Sasha would do some of the work of +filling the container but we kind of + + align:start position:0% +filling the container but we kind of + + + align:start position:0% +filling the container but we kind of +envisioned it as like a flow or a can B + + align:start position:0% +envisioned it as like a flow or a can B + + + align:start position:0% +envisioned it as like a flow or a can B +and that she would fill containers and + + align:start position:0% +and that she would fill containers and + + + align:start position:0% +and that she would fill containers and +then and you could just look down see + + align:start position:0% +then and you could just look down see + + + align:start position:0% +then and you could just look down see +how many contain see how many containers + + align:start position:0% +how many contain see how many containers + + + align:start position:0% +how many contain see how many containers +just waiting for him and then he could + + align:start position:0% +just waiting for him and then he could + + + align:start position:0% +just waiting for him and then he could +just put the hot dogs in wrap them up + + align:start position:0% +just put the hot dogs in wrap them up + + + align:start position:0% +just put the hot dogs in wrap them up +and then give them back where they they + + align:start position:0% +and then give them back where they they + + + align:start position:0% +and then give them back where they they +would already have the fruit like she + + align:start position:0% +would already have the fruit like she + + + align:start position:0% +would already have the fruit like she +could put the the bun kind of in the + + align:start position:0% +could put the the bun kind of in the + + + align:start position:0% +could put the the bun kind of in the +foil + + align:start position:0% +foil + + + align:start position:0% +foil +ready good idea like that very + + align:start position:0% +ready good idea like that very + + + align:start position:0% +ready good idea like that very +nice + + align:start position:0% +nice + + + align:start position:0% +nice +others we had the customers getting + + align:start position:0% +others we had the customers getting + + + align:start position:0% +others we had the customers getting +their own beverage and putting their own + + align:start position:0% +their own beverage and putting their own + + + align:start position:0% +their own beverage and putting their own +toppings on + + align:start position:0% +toppings on + + + align:start position:0% +toppings on +um because that time and it also reduces + + align:start position:0% +um because that time and it also reduces + + + align:start position:0% +um because that time and it also reduces +the err you're only a hot you can't + + align:start position:0% +the err you're only a hot you can't + + + align:start position:0% +the err you're only a hot you can't +screw it up and then like the customer + + align:start position:0% +screw it up and then like the customer + + + align:start position:0% +screw it up and then like the customer +like knows what they want and it would + + align:start position:0% +like knows what they want and it would + + + align:start position:0% +like knows what they want and it would +also give them more control over like + + align:start position:0% +also give them more control over like + + + align:start position:0% +also give them more control over like +catch and + + align:start position:0% +catch and + + + align:start position:0% +catch and +wee if there some way to make sure they + + align:start position:0% + + + + align:start position:0% + +more + + align:start position:0% + + + + align:start position:0% + +suggestions all right so what what You' + + align:start position:0% +suggestions all right so what what You' + + + align:start position:0% +suggestions all right so what what You' +have done here is you have rearranged + + align:start position:0% +have done here is you have rearranged + + + align:start position:0% +have done here is you have rearranged +some of your processes right you have + + align:start position:0% +some of your processes right you have + + + align:start position:0% +some of your processes right you have +changed the the workload in + + align:start position:0% +changed the the workload in + + + align:start position:0% +changed the the workload in +between uh the + + align:start position:0% +between uh the + + + align:start position:0% +between uh the +two um in the business here as well so + + align:start position:0% +two um in the business here as well so + + + align:start position:0% +two um in the business here as well so +that they're working more even or have a + + align:start position:0% +that they're working more even or have a + + + align:start position:0% +that they're working more even or have a +more even + + align:start position:0% +more even + + + align:start position:0% +more even +workload and you're involving the + + align:start position:0% +workload and you're involving the + + + align:start position:0% +workload and you're involving the +customer saying customer can do some + + align:start position:0% +customer saying customer can do some + + + align:start position:0% +customer saying customer can do some +stuff themselves they can pick up their + + align:start position:0% +stuff themselves they can pick up their + + + align:start position:0% +stuff themselves they can pick up their +food they can pick up the drink uh don't + + align:start position:0% +food they can pick up the drink uh don't + + + align:start position:0% +food they can pick up the drink uh don't +need to have someone doing that for them + + align:start position:0% +need to have someone doing that for them + + + align:start position:0% +need to have someone doing that for them +right or and some of you focused on + + align:start position:0% +right or and some of you focused on + + + align:start position:0% +right or and some of you focused on +reducing the or involving the customers + + align:start position:0% +reducing the or involving the customers + + + align:start position:0% +reducing the or involving the customers +to make the weight time go down as well + + align:start position:0% +to make the weight time go down as well + + + align:start position:0% +to make the weight time go down as well +I like that what else do + + align:start position:0% +I like that what else do + + + align:start position:0% +I like that what else do +we so did anybody go to Fresco + + align:start position:0% +we so did anybody go to Fresco + + + align:start position:0% +we so did anybody go to Fresco +today at lunch Place Little Deli caddy + + align:start position:0% +today at lunch Place Little Deli caddy + + + align:start position:0% +today at lunch Place Little Deli caddy +corner I guess not now + + align:start position:0% +corner I guess not now + + + align:start position:0% +corner I guess not now +yeah they they have they have a great + + align:start position:0% +yeah they they have they have a great + + + align:start position:0% +yeah they they have they have a great +system there which is which is Apocrypha + + align:start position:0% +system there which is which is Apocrypha + + + align:start position:0% +system there which is which is Apocrypha +I'm not sure if the story is true but + + align:start position:0% +I'm not sure if the story is true but + + + align:start position:0% +I'm not sure if the story is true but +but I know one of the one of the + + align:start position:0% +but I know one of the one of the + + + align:start position:0% +but I know one of the one of the +Saturday live people actually lived in + + align:start position:0% +Saturday live people actually lived in + + + align:start position:0% +Saturday live people actually lived in +Cambridge for a long time um it's it's + + align:start position:0% +Cambridge for a long time um it's it's + + + align:start position:0% +Cambridge for a long time um it's it's +it's alleged to be the the cheeseburger + + align:start position:0% +it's alleged to be the the cheeseburger + + + align:start position:0% +it's alleged to be the the cheeseburger +cheeseburger + + align:start position:0% +cheeseburger + + + align:start position:0% +cheeseburger +inspiration you say what you want and + + align:start position:0% +inspiration you say what you want and + + + align:start position:0% +inspiration you say what you want and +they yell right there's no ticket + + align:start position:0% +they yell right there's no ticket + + + align:start position:0% +they yell right there's no ticket +there's no you + + align:start position:0% +there's no you + + + align:start position:0% +there's no you +know all right so and then they yell + + align:start position:0% +know all right so and then they yell + + + align:start position:0% +know all right so and then they yell +back to make sure they understood the + + align:start position:0% +back to make sure they understood the + + + align:start position:0% +back to make sure they understood the +order right so it's well that's good be + + align:start position:0% +order right so it's well that's good be + + + align:start position:0% +order right so it's well that's good be +small fries BLT small fries yeah takes + + align:start position:0% +small fries BLT small fries yeah takes + + + align:start position:0% +small fries BLT small fries yeah takes +one second to say low error rate high + + align:start position:0% +one second to say low error rate high + + + align:start position:0% +one second to say low error rate high +training that guy's got to keep it in + + align:start position:0% +training that guy's got to keep it in + + + align:start position:0% +training that guy's got to keep it in +his head + + align:start position:0% +his head + + + align:start position:0% +his head +right so uh but + + align:start position:0% +right so uh but + + + align:start position:0% +right so uh but +uh yeah + + align:start position:0% +uh yeah + + + align:start position:0% +uh yeah +so but most of the other possibilities + + align:start position:0% +so but most of the other possibilities + + + align:start position:0% +so but most of the other possibilities +are are definitely up here some good + + align:start position:0% +are are definitely up here some good + + + align:start position:0% +are are definitely up here some good +ideas and and this part by the way is is + + align:start position:0% +ideas and and this part by the way is is + + + align:start position:0% +ideas and and this part by the way is is +also pretty realistic in the sense that + + align:start position:0% +also pretty realistic in the sense that + + + align:start position:0% +also pretty realistic in the sense that +this is Art right you don't know the + + align:start position:0% +this is Art right you don't know the + + + align:start position:0% +this is Art right you don't know the +answers the none of these techniques + + align:start position:0% +answers the none of these techniques + + + align:start position:0% +answers the none of these techniques +tell you answer what they do is frame + + align:start position:0% +tell you answer what they do is frame + + + align:start position:0% +tell you answer what they do is frame +the problem and help you understand what + + align:start position:0% +the problem and help you understand what + + + align:start position:0% +the problem and help you understand what +you're trying to what you're what + + align:start position:0% +you're trying to what you're what + + + align:start position:0% +you're trying to what you're what +problems you're trying to solve you're + + align:start position:0% +problems you're trying to solve you're + + + align:start position:0% +problems you're trying to solve you're +not trying to make Sasha stop chatting + + align:start position:0% +not trying to make Sasha stop chatting + + + align:start position:0% +not trying to make Sasha stop chatting +you're trying to improve the overall + + align:start position:0% +you're trying to improve the overall + + + align:start position:0% +you're trying to improve the overall +performance of the uh of the + + align:start position:0% +performance of the uh of the + + + align:start position:0% +performance of the uh of the +system have been looking at this is that + + align:start position:0% +system have been looking at this is that + + + align:start position:0% +system have been looking at this is that +not all of the time is allocated and + + align:start position:0% +not all of the time is allocated and + + + align:start position:0% +not all of the time is allocated and +it's unclear exactly why the we times + + align:start position:0% +it's unclear exactly why the we times + + + align:start position:0% +it's unclear exactly why the we times +are the way that they + + align:start position:0% +are the way that they + + + align:start position:0% +are the way that they +are the question of like the flow of + + align:start position:0% +are the question of like the flow of + + + align:start position:0% +are the question of like the flow of +borders and so maybe from 11: to 1 they + + align:start position:0% +borders and so maybe from 11: to 1 they + + + align:start position:0% +borders and so maybe from 11: to 1 they +are at capacity and then there's just no + + align:start position:0% +are at capacity and then there's just no + + + align:start position:0% +are at capacity and then there's just no +demand from 10 to 11 once two so there + + align:start position:0% +demand from 10 to 11 once two so there + + + align:start position:0% +demand from 10 to 11 once two so there +might not even be the opportunity to to + + align:start position:0% +might not even be the opportunity to to + + + align:start position:0% +might not even be the opportunity to to +increase capacity without hre another + + align:start position:0% +increase capacity without hre another + + + align:start position:0% +increase capacity without hre another +person or doing something different that + + align:start position:0% +person or doing something different that + + + align:start position:0% +person or doing something different that +and that's the kind of thing you would + + align:start position:0% +and that's the kind of thing you would + + + align:start position:0% +and that's the kind of thing you would +find out by actually going and observing + + align:start position:0% +find out by actually going and observing + + + align:start position:0% +find out by actually going and observing +the process rather than us sitting in a + + align:start position:0% +the process rather than us sitting in a + + + align:start position:0% +the process rather than us sitting in a +classroom here and and saying this is + + align:start position:0% +classroom here and and saying this is + + + align:start position:0% +classroom here and and saying this is +the way it is I think that's right um on + + align:start position:0% +the way it is I think that's right um on + + + align:start position:0% +the way it is I think that's right um on +the other hand there are things there + + align:start position:0% +the other hand there are things there + + + align:start position:0% +the other hand there are things there +are things that always help even even if + + align:start position:0% +are things that always help even even if + + + align:start position:0% +are things that always help even even if +there is that issue of maybe some of the + + align:start position:0% +there is that issue of maybe some of the + + + align:start position:0% +there is that issue of maybe some of the +time they're slammed you know balancing + + align:start position:0% +time they're slammed you know balancing + + + align:start position:0% +time they're slammed you know balancing +always helps oh yeah right eliminating + + align:start position:0% +always helps oh yeah right eliminating + + + align:start position:0% +always helps oh yeah right eliminating +non-value added steps always helps so + + align:start position:0% +non-value added steps always helps so + + + align:start position:0% +non-value added steps always helps so +there are some things you can do + + align:start position:0% +there are some things you can do + + + align:start position:0% +there are some things you can do +confidently there are other things that + + align:start position:0% +confidently there are other things that + + + align:start position:0% +confidently there are other things that +you may have to actually go and see does + + align:start position:0% +you may have to actually go and see does + + + align:start position:0% +you may have to actually go and see does +this make sense will this work and + + align:start position:0% +this make sense will this work and + + + align:start position:0% +this make sense will this work and +possibly even experiment with try it see + + align:start position:0% +possibly even experiment with try it see + + + align:start position:0% +possibly even experiment with try it see +see how it goes the next couple days you + + align:start position:0% +see how it goes the next couple days you + + + align:start position:0% +see how it goes the next couple days you +know so all right + + align:start position:0% +know so all right + + + align:start position:0% +know so all right +so a few things that we thought about + + align:start position:0% +so a few things that we thought about + + + align:start position:0% +so a few things that we thought about +the in order where it's sitting what is + + align:start position:0% +the in order where it's sitting what is + + + align:start position:0% +the in order where it's sitting what is +it 30 seconds here in step two and the + + align:start position:0% +it 30 seconds here in step two and the + + + align:start position:0% +it 30 seconds here in step two and the +out + + align:start position:0% +out + + + align:start position:0% +out +order take those + + align:start position:0% + + + + align:start position:0% + +away the + + align:start position:0% +away the + + + align:start position:0% +away the +inspection we heard earlier you that + + align:start position:0% +inspection we heard earlier you that + + + align:start position:0% +inspection we heard earlier you that +inspection doesn't add much I really + + align:start position:0% +inspection doesn't add much I really + + + align:start position:0% +inspection doesn't add much I really +like this I don't think I've heard that + + align:start position:0% +like this I don't think I've heard that + + + align:start position:0% +like this I don't think I've heard that +one before the thought of of + + align:start position:0% +one before the thought of of + + + align:start position:0% +one before the thought of of +consolidating Sasha's work and the + + align:start position:0% +consolidating Sasha's work and the + + + align:start position:0% +consolidating Sasha's work and the +inspection into one step right so then + + align:start position:0% +inspection into one step right so then + + + align:start position:0% +inspection into one step right so then +you get the quality but there's no extra + + align:start position:0% +you get the quality but there's no extra + + + align:start position:0% +you get the quality but there's no extra +step so it's a good solution to to not + + align:start position:0% +step so it's a good solution to to not + + + align:start position:0% +step so it's a good solution to to not +our priority eliminate inspection which + + align:start position:0% +our priority eliminate inspection which + + + align:start position:0% +our priority eliminate inspection which +might lead to quality issues and balance + + align:start position:0% +might lead to quality issues and balance + + + align:start position:0% +might lead to quality issues and balance +the work you've already done as + + align:start position:0% +the work you've already done as + + + align:start position:0% +the work you've already done as +well now we're down here to create a + + align:start position:0% +well now we're down here to create a + + + align:start position:0% +well now we're down here to create a +future state map to visualize how we + + align:start position:0% +future state map to visualize how we + + + align:start position:0% +future state map to visualize how we +want this to look in the future and then + + align:start position:0% +want this to look in the future and then + + + align:start position:0% +want this to look in the future and then +create the action plan for how you're + + align:start position:0% +create the action plan for how you're + + + align:start position:0% +create the action plan for how you're +going to achieve your + + align:start position:0% +going to achieve your + + + align:start position:0% +going to achieve your +change because talk alone won't do it so + + align:start position:0% +change because talk alone won't do it so + + + align:start position:0% +change because talk alone won't do it so +make the map create a plan set some + + align:start position:0% +make the map create a plan set some + + + align:start position:0% +make the map create a plan set some +deadlines and uh and assign some + + align:start position:0% +deadlines and uh and assign some + + + align:start position:0% +deadlines and uh and assign some +responsibilities for who's going to do + + align:start position:0% +responsibilities for who's going to do + + + align:start position:0% +responsibilities for who's going to do +what to uh to change things so the uh + + align:start position:0% +what to uh to change things so the uh + + + align:start position:0% +what to uh to change things so the uh +value stream map is useful to visualize + + align:start position:0% +value stream map is useful to visualize + + + align:start position:0% +value stream map is useful to visualize +what is going on the interactions and + + align:start position:0% +what is going on the interactions and + + + align:start position:0% +what is going on the interactions and +the flows and uh gives you the linkages + + align:start position:0% +the flows and uh gives you the linkages + + + align:start position:0% +the flows and uh gives you the linkages +linkages between your um your + + align:start position:0% +linkages between your um your + + + align:start position:0% +linkages between your um your +information and your product + + align:start position:0% +information and your product + + + align:start position:0% +information and your product +flows gives you a language that you can + + align:start position:0% +flows gives you a language that you can + + + align:start position:0% +flows gives you a language that you can +talk about with the ones who are in the + + align:start position:0% +talk about with the ones who are in the + + + align:start position:0% +talk about with the ones who are in the +group and you can identify your + + align:start position:0% +group and you can identify your + + + align:start position:0% +group and you can identify your +constraints and capacities and + + align:start position:0% +constraints and capacities and + + + align:start position:0% +constraints and capacities and +wastes well you have a question oh I + + align:start position:0% +wastes well you have a question oh I + + + align:start position:0% +wastes well you have a question oh I +just have a question about the process + + align:start position:0% +just have a question about the process + + + align:start position:0% +just have a question about the process +maybe I'm having difficulty visualizing + + align:start position:0% +maybe I'm having difficulty visualizing + + + align:start position:0% +maybe I'm having difficulty visualizing +it but it seems like it's the hot like + + align:start position:0% +it but it seems like it's the hot like + + + align:start position:0% +it but it seems like it's the hot like +we're following the hot dog in a in a + + align:start position:0% +we're following the hot dog in a in a + + + align:start position:0% +we're following the hot dog in a in a +linear way whereas it seems like some of + + align:start position:0% +linear way whereas it seems like some of + + + align:start position:0% +linear way whereas it seems like some of +this stuff happen simultaneously so I'm + + align:start position:0% +this stuff happen simultaneously so I'm + + + align:start position:0% +this stuff happen simultaneously so I'm +not sure like some of the seconds + + align:start position:0% +not sure like some of the seconds + + + align:start position:0% +not sure like some of the seconds +overlap it's not like Sasha's seconds + + align:start position:0% +overlap it's not like Sasha's seconds + + + align:start position:0% +overlap it's not like Sasha's seconds +happen only after Andy's seconds happen + + align:start position:0% +happen only after Andy's seconds happen + + + align:start position:0% +happen only after Andy's seconds happen +so that's a little bit hard for me to + + align:start position:0% +so that's a little bit hard for me to + + + align:start position:0% +so that's a little bit hard for me to +understand in this flow model and that + + align:start position:0% +understand in this flow model and that + + + align:start position:0% +understand in this flow model and that +as I it that can sometimes be a problem + + align:start position:0% +as I it that can sometimes be a problem + + + align:start position:0% +as I it that can sometimes be a problem +to to look at it like that in a process + + align:start position:0% +to to look at it like that in a process + + + align:start position:0% +to to look at it like that in a process +map and there have a slide a little bit + + align:start position:0% +map and there have a slide a little bit + + + align:start position:0% +map and there have a slide a little bit +later where you can look at swim Lanes + + align:start position:0% +later where you can look at swim Lanes + + + align:start position:0% +later where you can look at swim Lanes +as well because it can depend on who is + + align:start position:0% +as well because it can depend on who is + + + align:start position:0% +as well because it can depend on who is +doing what and that can happen at the + + align:start position:0% +doing what and that can happen at the + + + align:start position:0% +doing what and that can happen at the +same time as well right so that you're + + align:start position:0% +same time as well right so that you're + + + align:start position:0% +same time as well right so that you're +absolutely right things they do happen + + align:start position:0% +absolutely right things they do happen + + + align:start position:0% +absolutely right things they do happen +simultaneously that the the classic + + align:start position:0% +simultaneously that the the classic + + + align:start position:0% +simultaneously that the the classic +issue which which you're which you're + + align:start position:0% +issue which which you're which you're + + + align:start position:0% +issue which which you're which you're +keying on I think is like in a real hot + + align:start position:0% +keying on I think is like in a real hot + + + align:start position:0% +keying on I think is like in a real hot +dog stand there'd be a bunch of hot dogs + + align:start position:0% +dog stand there'd be a bunch of hot dogs + + + align:start position:0% +dog stand there'd be a bunch of hot dogs +on the grill that would be cooking at + + align:start position:0% +on the grill that would be cooking at + + + align:start position:0% +on the grill that would be cooking at +the the same time that all this other + + align:start position:0% +the the same time that all this other + + + align:start position:0% +the the same time that all this other +stuff is going on right so there are + + align:start position:0% +stuff is going on right so there are + + + align:start position:0% +stuff is going on right so there are +some processes that are maybe out of + + align:start position:0% +some processes that are maybe out of + + + align:start position:0% +some processes that are maybe out of +phase and that that's true that's a real + + align:start position:0% +phase and that that's true that's a real + + + align:start position:0% +phase and that that's true that's a real +that's a real issue the map doesn't + + align:start position:0% +that's a real issue the map doesn't + + + align:start position:0% +that's a real issue the map doesn't +catch that very well right that issue of + + align:start position:0% +catch that very well right that issue of + + + align:start position:0% +catch that very well right that issue of +of some of some things happening kind of + + align:start position:0% +of some of some things happening kind of + + + align:start position:0% +of some of some things happening kind of +out of phase of other things um but it's + + align:start position:0% +out of phase of other things um but it's + + + align:start position:0% +out of phase of other things um but it's +a it's a tool it's not a perfect tool it + + align:start position:0% +a it's a tool it's not a perfect tool it + + + align:start position:0% +a it's a tool it's not a perfect tool it +doesn't solve all of your problems all + + align:start position:0% +doesn't solve all of your problems all + + + align:start position:0% +doesn't solve all of your problems all +right so tips for creating it involve + + align:start position:0% +right so tips for creating it involve + + + align:start position:0% +right so tips for creating it involve +the entire team everybody who's involved + + align:start position:0% +the entire team everybody who's involved + + + align:start position:0% +the entire team everybody who's involved +in these processes + + align:start position:0% +in these processes + + + align:start position:0% +in these processes +need to be involved it can't only be a + + align:start position:0% +need to be involved it can't only be a + + + align:start position:0% +need to be involved it can't only be a +few people that maybe have management + + align:start position:0% +few people that maybe have management + + + align:start position:0% +few people that maybe have management +positions you need to have the people + + align:start position:0% +positions you need to have the people + + + align:start position:0% +positions you need to have the people +doing the work come and be involved in + + align:start position:0% +doing the work come and be involved in + + + align:start position:0% +doing the work come and be involved in +this because they're the ones who + + align:start position:0% +this because they're the ones who + + + align:start position:0% +this because they're the ones who +understand work the best and can come up + + align:start position:0% +understand work the best and can come up + + + align:start position:0% +understand work the best and can come up +with the best suggestions for how to + + align:start position:0% +with the best suggestions for how to + + + align:start position:0% +with the best suggestions for how to +change it right and you need to actually + + align:start position:0% +change it right and you need to actually + + + align:start position:0% +change it right and you need to actually +go to gima go and see use the posted + + align:start position:0% +go to gima go and see use the posted + + + align:start position:0% +go to gima go and see use the posted +notes like you've done now on your map + + align:start position:0% +notes like you've done now on your map + + + align:start position:0% +notes like you've done now on your map +put that on and then you can use your + + align:start position:0% +put that on and then you can use your + + + align:start position:0% +put that on and then you can use your +symbols you can use + + align:start position:0% +symbols you can use + + + align:start position:0% +symbols you can use +whatever you pretty much like there are + + align:start position:0% +whatever you pretty much like there are + + + align:start position:0% +whatever you pretty much like there are +some that are more used than others but + + align:start position:0% +some that are more used than others but + + + align:start position:0% +some that are more used than others but +but that's however you want to however + + align:start position:0% +but that's however you want to however + + + align:start position:0% +but that's however you want to however +you want to do it as long as you make + + align:start position:0% +you want to do it as long as you make + + + align:start position:0% +you want to do it as long as you make +sure you have a Common Language here's a + + align:start position:0% +sure you have a Common Language here's a + + + align:start position:0% +sure you have a Common Language here's a +little bit about the swim lanes because + + align:start position:0% +little bit about the swim lanes because + + + align:start position:0% +little bit about the swim lanes because +you can have different providers or + + align:start position:0% +you can have different providers or + + + align:start position:0% +you can have different providers or +different processes at the same time in + + align:start position:0% +different processes at the same time in + + + align:start position:0% +different processes at the same time in +an organization and and you can try to + + align:start position:0% +an organization and and you can try to + + + align:start position:0% +an organization and and you can try to +map it out like this right so things + + align:start position:0% +map it out like this right so things + + + align:start position:0% +map it out like this right so things +that take place at the same time or you + + align:start position:0% +that take place at the same time or you + + + align:start position:0% +that take place at the same time or you +can have the castle wall with with uh + + align:start position:0% +can have the castle wall with with uh + + + align:start position:0% +can have the castle wall with with uh +production times and weit + + align:start position:0% +production times and weit + + + align:start position:0% +production times and weit +times right added up in the end have + + align:start position:0% +times right added up in the end have + + + align:start position:0% +times right added up in the end have +your weit times and your your production + + align:start position:0% +your weit times and your your production + + + align:start position:0% +your weit times and your your production +or your your productive times so there + + align:start position:0% +or your your productive times so there + + + align:start position:0% +or your your productive times so there +are many ways and uh there are some + + align:start position:0% +are many ways and uh there are some + + + align:start position:0% +are many ways and uh there are some +resources where you can learn a whole + + align:start position:0% +resources where you can learn a whole + + + align:start position:0% +resources where you can learn a whole +lot more about this + + align:start position:0% +lot more about this + + + align:start position:0% +lot more about this +okay say one more thing when you do a + + align:start position:0% +okay say one more thing when you do a + + + align:start position:0% +okay say one more thing when you do a +Val map make sure that you bring it to + + align:start position:0% +Val map make sure that you bring it to + + + align:start position:0% +Val map make sure that you bring it to +the people doing the work to get their + + align:start position:0% +the people doing the work to get their + + + align:start position:0% +the people doing the work to get their +validation say did I leave anything out + + align:start position:0% +validation say did I leave anything out + + + align:start position:0% +validation say did I leave anything out +that I forget anything because often + + align:start position:0% +that I forget anything because often + + + align:start position:0% +that I forget anything because often +times you miss something and they can + + align:start position:0% +times you miss something and they can + + + align:start position:0% +times you miss something and they can +say oh but you forgot that we do this + + align:start position:0% +say oh but you forgot that we do this + + + align:start position:0% +say oh but you forgot that we do this +and I think that's really important + + align:start position:0% +and I think that's really important + + + align:start position:0% +and I think that's really important +because then it gets them to buy into + + align:start position:0% +because then it gets them to buy into + + + align:start position:0% +because then it gets them to buy into +what you're doing as well and even more + + align:start position:0% +what you're doing as well and even more + + + align:start position:0% +what you're doing as well and even more +stronger you should have those people + + align:start position:0% +stronger you should have those people + + + align:start position:0% +stronger you should have those people +participating + + align:start position:0% +participating + + + align:start position:0% +participating +ination that's actually what what we do + + align:start position:0% +ination that's actually what what we do + + + align:start position:0% +ination that's actually what what we do +at bi the ones doing the processes and + + align:start position:0% +at bi the ones doing the processes and + + + align:start position:0% +at bi the ones doing the processes and +it's often from different provider + + align:start position:0% +it's often from different provider + + + align:start position:0% +it's often from different provider +groups we involve them we we invite them + + align:start position:0% +groups we involve them we we invite them + + + align:start position:0% +groups we involve them we we invite them +and we we help them come up with this + + align:start position:0% +and we we help them come up with this + + + align:start position:0% +and we we help them come up with this +and then post them on the floors or the + + align:start position:0% +and then post them on the floors or the + + + align:start position:0% +and then post them on the floors or the +W so they can see them and make comments + + align:start position:0% +W so they can see them and make comments + + + align:start position:0% +W so they can see them and make comments +good technique for all of these things + + align:start position:0% +good technique for all of these things + + + align:start position:0% +good technique for all of these things +that you do is take pictures of these + + align:start position:0% +that you do is take pictures of these + + + align:start position:0% +that you do is take pictures of these +things and you can post them or you can + + align:start position:0% +things and you can post them or you can + + + align:start position:0% +things and you can post them or you can +email them out to people and say this is + + align:start position:0% +email them out to people and say this is + + + align:start position:0% +email them out to people and say this is +this is what we found please give us if + + align:start position:0% +this is what we found please give us if + + + align:start position:0% +this is what we found please give us if +you have any comments or there's also + + align:start position:0% +you have any comments or there's also + + + align:start position:0% +you have any comments or there's also +this is also a really good link between + + align:start position:0% +this is also a really good link between + + + align:start position:0% +this is also a really good link between +Administration and Frontline workers + + align:start position:0% +Administration and Frontline workers + + + align:start position:0% +Administration and Frontline workers +because I know in most hospitals the + + align:start position:0% +because I know in most hospitals the + + + align:start position:0% +because I know in most hospitals the +administrators take turns walking around + + align:start position:0% +administrators take turns walking around + + + align:start position:0% +administrators take turns walking around +to visit the floors and a lot of them + + align:start position:0% +to visit the floors and a lot of them + + + align:start position:0% +to visit the floors and a lot of them +are not clinical it might be the CFO or + + align:start position:0% +are not clinical it might be the CFO or + + + align:start position:0% +are not clinical it might be the CFO or +something they come around they go how + + align:start position:0% +something they come around they go how + + + align:start position:0% +something they come around they go how +you doing today do you need anything how + + align:start position:0% +you doing today do you need anything how + + + align:start position:0% +you doing today do you need anything how +you doing today do you need anything but + + align:start position:0% +you doing today do you need anything but + + + align:start position:0% +you doing today do you need anything but +if you have a Bing Map posted they can + + align:start position:0% +if you have a Bing Map posted they can + + + align:start position:0% +if you have a Bing Map posted they can +go to that map and you can discuss what + + align:start position:0% +go to that map and you can discuss what + + + align:start position:0% +go to that map and you can discuss what +you're working on together and it just + + align:start position:0% +you're working on together and it just + + + align:start position:0% +you're working on together and it just +brings it to a different level we call + + align:start position:0% +brings it to a different level we call + + + align:start position:0% +brings it to a different level we call +it + + align:start position:0% +it + + + align:start position:0% +it +boardwalks give them something to look + + align:start position:0% +boardwalks give them something to look + + + align:start position:0% +boardwalks give them something to look +at and the same is true in an + + align:start position:0% +at and the same is true in an + + + align:start position:0% +at and the same is true in an +engineering environment it's not just a + + align:start position:0% +engineering environment it's not just a + + + align:start position:0% +engineering environment it's not just a +healthare absolutely + + align:start position:0% +healthare absolutely + + + align:start position:0% +healthare absolutely +yeah for + + align:start position:0% +yeah for + + + align:start position:0% +yeah for +healthcare if if you + + align:start position:0% +healthcare if if you + + + align:start position:0% +healthcare if if you +dare go and find a patient who's + + align:start position:0% +dare go and find a patient who's + + + align:start position:0% +dare go and find a patient who's +arriving to your emergency Department to + + align:start position:0% +arriving to your emergency Department to + + + align:start position:0% +arriving to your emergency Department to +your area of work wherever that may be + + align:start position:0% +your area of work wherever that may be + + + align:start position:0% +your area of work wherever that may be +follow that patient if you're a + + align:start position:0% +follow that patient if you're a + + + align:start position:0% +follow that patient if you're a +FLOTUS go find a patient registering for + + align:start position:0% +FLOTUS go find a patient registering for + + + align:start position:0% +FLOTUS go find a patient registering for +their blood draw follow them the whole + + align:start position:0% +their blood draw follow them the whole + + + align:start position:0% +their blood draw follow them the whole +way through + + align:start position:0% +way through + + + align:start position:0% +way through +okay take a chill pill before you do it + + align:start position:0% +okay take a chill pill before you do it + + + align:start position:0% +okay take a chill pill before you do it +because at least in my field in the + + align:start position:0% +because at least in my field in the + + + align:start position:0% +because at least in my field in the +emergency department I've tried and I + + align:start position:0% +emergency department I've tried and I + + + align:start position:0% +emergency department I've tried and I +think ihi calls it the Walk of Shame and + + align:start position:0% +think ihi calls it the Walk of Shame and + + + align:start position:0% +think ihi calls it the Walk of Shame and +and it really is but it is important + + align:start position:0% +and it really is but it is important + + + align:start position:0% +and it really is but it is important +because otherwise you will not + + align:start position:0% +because otherwise you will not + + + align:start position:0% +because otherwise you will not +understand most of us I mean we have + + align:start position:0% +understand most of us I mean we have + + + align:start position:0% +understand most of us I mean we have +different ways into the healthare system + + align:start position:0% +different ways into the healthare system + + + align:start position:0% +different ways into the healthare system +again I'm that is my perspective + + align:start position:0% +again I'm that is my perspective + + + align:start position:0% +again I'm that is my perspective +so let's be honest my wait time in my + + align:start position:0% +so let's be honest my wait time in my + + + align:start position:0% +so let's be honest my wait time in my +own emergency department is probably not + + align:start position:0% +own emergency department is probably not + + + align:start position:0% +own emergency department is probably not +going to be the same as somebody else's + + align:start position:0% +going to be the same as somebody else's + + + align:start position:0% +going to be the same as somebody else's +and another thing is I don't have the + + align:start position:0% +and another thing is I don't have the + + + align:start position:0% +and another thing is I don't have the +same need to frequent my an emergency + + align:start position:0% +same need to frequent my an emergency + + + align:start position:0% +same need to frequent my an emergency +department right the things I can just + + align:start position:0% +department right the things I can just + + + align:start position:0% +department right the things I can just +fix myself but go find a patient ask + + align:start position:0% +fix myself but go find a patient ask + + + align:start position:0% +fix myself but go find a patient ask +them politely if you can follow them for + + align:start position:0% +them politely if you can follow them for + + + align:start position:0% +them politely if you can follow them for +their journey and then stick with + + align:start position:0% +their journey and then stick with + + + align:start position:0% +their journey and then stick with +it take notes bring your stop watch all + + align:start position:0% +it take notes bring your stop watch all + + + align:start position:0% +it take notes bring your stop watch all +right here you + + align:start position:0% + + + + align:start position:0% + +go e \ No newline at end of file diff --git a/Bd7PVX7rohQ.txt b/Bd7PVX7rohQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..72589d181dce73aacbb06a26cb2b9a702dfdc7b7 --- /dev/null +++ b/Bd7PVX7rohQ.txt @@ -0,0 +1,2325 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Let's do a one minute +review, and then move + +onto the Clausius-Clapeyron +equation and see how far we + +can go on that. + +So, reminding you then, what +you learned last time about + +phase transitions is, you drew a +phase diagram in temperature + +pressure space here. + +And then you had a triple point +somewhere, which was a + +unique point. + +The triple point temperature, +triple point pressure. + +Then there was a gas, solid, +call it coexistence line. + +Which kept on going +ad infinitum. + +And the a gas liquid +coexistent line. + +With a critical point. + +So that allowed you +to go around. + +You wanted to go from liquid to +gas, you could actually go + +around this critical point, and +never actually see a phase + +transition. + +Then there was a solid liquid +coexistence line. + +Which usually has a negative +slope, except for the two most + +important substances on Earth, +which are water and silicon. + +So for water and silicon, +we have positive slope. + +H2O and silicon. + +This is why there's +life on Earth. + +Did you hear the story of why +there's life on Earth? + +This is the secret of life. + +Without this, this is +why we're here. + +Because of this property. + +So, the reason why these slopes +come from the, so I'll + +tell you the secret of life. + +But first let me remind you what +the coexistence curve is. + +dp/dT. + +Coexistence is delta S over +delta V, or delta H over T + +delta V. And that's the +Clapeyron equation. + +Now, the slope of the curves +points us by, look at this + +solid liquid line, delta +S, for solid liquid. + +I looked at it up here. + +It's going to be S liquid +minus S solid. + +And you know that's greater than +zero because the entropy + +in the liquid state is much +bigger than it is + +in the solid state. + +You have a crystal, entropy's +very small. + +Liquid state, much +more disorder. + +Got a positive sign here. + +Yes. + +Questions? + +STUDENT: [INAUDIBLE] + +PROFESSOR: So, this is +almost everything. + +It has this slope here. + +Which is a negative slope. + +And water has a positive slope. + +Right? + +Is that wrong? + +It's wrong. + +Let's go through the argument. + +All right. + +All right. + +Let's go through the argument. + +So, then you have delta V, and +delta V is V solid minus V + +liquid, this is per mole. + +Now, almost every +substance has V + +solid less than V liquid. + +So this is negative. + +So almost every substance, you +have delta S divided by delta + +V is negative. + +A negative slope. + +You're right. + +So I have it backwards. + +I do have it backwards. + +OK. + +See, I was really trying +to make it so that + +my drawing was right. + +Which is why I inverted the +solid and liquid here. + +So I really wanted to +be right, but I + +ended up being wrong. + +Liquid is less than solid. + +Well this is water. + +Why do I have it backwards +in my notes. + +I've got to correct that. + +So this is most substances, +is positive. + +OK so, and most substances, +OK? + +Except for water and silicon. + +Because for water and silicon +this is reversed. + +Because the molar volume of +solid for water is bigger than + +that for liquid. + +So this is bigger than here. + +Thank you. + +OK. + +Thanks for catching it. + +OK, so what happens if the molar +volume for the liquid is + +bigger than the molar +volume of the solid. + +The density of water which is +the inverse of the mole + +volume, so the density, the +molar density, is equal to one + +over the molar volume. + +So you've got the molar density +for liquid is then + +smaller than the molar density +for the solid. + +It's one over, right? + +So that's why ice floats. + +Because it's less dense +than liquid water. + +So what do you think would +happen in the winter if ice + +didn't float, in the +Charles River. + +It would go to the bottom. + +It would freeze, solid and +you would have no fish. + +You would have no life. + +It would freeze solid and that +would be the end of life. + +And you know, five hundred +million years ago there would + +be no fish. + +There would be no dinosaurs. + +There would be no anything, +there would be no humans. + +That's the secret of life. + +And the fact that this is also +the case is very useful for + +making silicon. + +For processing silicon. + +Another the secret of life. + +Where would we be +without silicon? + +Our civilization would be, we'd +still be using stones and + +things, right? + +OK, so it's super +super important. + +Alright, so this is +a Clapeyron story. + +Which we ended up +getting right. + +Even though I insisted +on getting it wrong. + +So what happens now is Mr. +Clausius came around and he + +realized that you can make some +approximations that are + +very useful. + +So the first approximation is, +you can realize that the molar + +volume of the gas is always much +bigger than the volume of + +the solid or the liquid. + +And so as a result whenever you +have these delta V's, for + +sublimation, or delta V for +vaporization, which is the + +volume the gas minus the +volume of the solid. + +Or the volume of the gas minus +the volume of the liquid, you + +might as well ignore +the volume of the + +liquid or of the solid. + +And this can just be equal to +roughly the volume of the gas. + +So this is the first +approximation he made. + +So now, if you go back to the +to the Clapeyron equation up + +here, with this approximation +then dp/dT, the coexistence + +line, is delta H divided +by T V gas. + +For sublimation. + +Or vaporization. + +You don't have the delta +V down there any more. + +Then the next thing that, next +assumption that he realized + +you can make was, well, all +these gases could, they're + +like ideal gases. + +So we can, instead of having the +volume of the gas here, we + +can use the ideal gas law. + +This is all, let's do +all this per mole. + +So V is equal to RT over p. + +You can plug this +back in here. + +And then you end up with the +Clausius-Clapeyron equation. + +So this is approximation now. + +We put in RT over p for here. + +We have p delta H, where this +is either sublimation or + +vaporization divided by RT +squared. dp/dT, sublimation or + +vaporization, and this is the +Clausius-Clapeyron equation. + +Two important approximations +that go in here. + +And it's not valid for +solids or liquid. + +You have to have a gas in there +because of the ideal gas + +for the approximation +that goes in here. + +And once you have that, you +can integrate both sides. + +You've got to put the +temperatures on one side. + +Put the pressures on +the other side. + +I'll go ahead and cover +this up here. + +So you have one over +p dp/dT is equal to + +delta H over RT squared. + +One over p dp/dT that's +just like d log p. + +And that's another form that +you're going to see often for + +the Clausius-Clapeyron +approximation is d log p / dT + +is equal to delta H +over RT squared. + +And I'm freely dropping the +sublimation and the + +vaporization because we know +that's what I mean here. + +It's only valid for +those two lines. + +So that's another form +that you'll see. + +And that's not dT here, that's +d log p, d log p dp. + +Yeah, that's right, +d log p / dT. + +And so now you can take +the dT to the + +other side and integrate. + +From point one to point two d +log p, is from point one to + +point two, delta H over +RT squared dT. + +And you make the usual +approximation, which we've + +made before. + +That delta H is roughly +independent of temperature, or + +very slowly changing +with temperature. + +And that's fine as long +as you're in a + +narrow temperature range. + +Which is usually the case +when you have these + +Clausius-Clapeyron equation +problems. + +So you can take the delta H out +of the integral, the R out + +of the integral. + +And you can integrate +both sides. + +To give you log p2 minus log +p1, is delta H times R, + +divided by R, delta H divided by +R. Delta H over R times T2 + +minus T1 over T1 T2. + +It looks a lot like and the +temperature dependence + +equilibrium constant. + +And in fact, but it's +not, right? + +And some people use that +equation here instead of + +equilibrium constant. + +Temperature dependence. + +That's, can give rise +to problems. + +Because obviously they're +not the same equation. + +But roughly has the same form. + +So, another way that you'll also +find this written is very + +often p1 and T1 will +be some reference. + +Pressures and temperature, +maybe one bar, let's say. + +T1, 298 degrees Kelvin. + +That's your reference point and +you want to find out the + +pressure temperature dependence +in an equation. + +So if you rearrange your +equations so p1, T1 are now + +some reference point. + +They become numbers. + +So you have log of a reference +point, T1 here is a number. + +So you often see this equation +rewritten then as log p is + +equal to delta H over RT. + +And I feel like I've got a minus +sign missing somewhere. + +Here. + +Oh yeah, when you integrate +this, the one over T squared, + +there's a minus sign. + +Oh, I took care of that by +doing T2 minus T1 here. + +I think there's still a minus +sign problem somewhere. + +I think there's a minus +sign problem. + +Let me check up the +notes here. + +Minus one over T1 minus +T2 over T1 T2. + +Where's my minus sign? + +T2 minus T1. + +OK, so I got minus T1, +minus T2 over T1 T2. + +T2 minus T1. + +This is fine, right. + +There's no minus sign problem. + +Plus a constant. + +OK, so you'll often see +it written like that. + +And that gives you a +relationship between the + +pressure and the temperature +then, for a substance where + +all the reference point +information is contained in + +this constant, C. Which +is where the T1's and + +the p's come from. + +OK, any questions? + +We'll do a little example here +of how this could be used. + +So let's switch to +an example now. + +Let's go to the example, let's +first do the example which is + +at the very end of the notes. + +So this is an example of RDX. + +RDX is a famous explosive, +as I'm sure you know. + +And it's plastic explosive. + +It's got a melting point +of 204 degrees Celsius. + +481 degrees Kelvin. + +And it's a problem for, so it's +a very powerful explosive + +and you can't see +it in X-rays. + +So it's a problem at airports. + +You've got be able to find if +somebody's carrying a little + +piece of RDX in their luggage. + +And so, the question becomes +what do you need to + +know to detect it? + +You want to find the +vapor pressure. + +You've gotta have, and the +machine which basically is + +sensitive enough to detect +molecules of RDX that are in + +vapor at room temperature. + +So the way that you do that +is, you do an experiment. + +Where you measure the pressure, +the vapor pressure, + +as a function of temperature. + +And room temperature, it turns +out if it's not volatile at + +all, if the vapor pressure +is very, really tiny. + +And so in order to get accurate +numbers, you actually + +do your measurements at +significantly higher + +temperatures than room +temperature. + +They do it close to the melting +point, so you're + +actually looking at the +sublimation of RDX. + +You do it, let's say, at 400 +degrees Kelvin, where the + +melting point is at 481 +degrees Kelvin. + +So slightly below the melting +point you're looking at + +sublimation. + +And you plot. + +Log p versus one over +T. And according to + +Clausius-Clapeyron, +that should give + +you a straight line. + +And in fact, that's exactly what +you see when you take RDX + +and do that experiment. + +You end up with a bunch +of data points. + +That's fall nicely on +this straight line. + +And then you can extrapolate +to room temperature. + +Somewhere here, let's say, +300 degrees Kelvin. + +And find out what log p is, +at 300 degrees Kelvin. + +And what you find is that, and +that's the graph that's on the + +last page of the lecture notes, +that the vapor pressure + +of RDX at room temperature is 10 +to the minus 11 bar, That's + +ten parts per trillion. + +So it tells you that if you +want to detect RDX with a + +sniffer machine at the airport, +that machine better + +be able to tell you, find one +molecule of RDX out of a tenth + +of a trillion other molecules, +basically. + +Which is a really hard +thing to do. + +So this gives you a +design rule for + +these pieces of equipment. + +And why they're so expensive. + +OK, before we do the next +example, let's see if any + +questions on Clausius-Clapeyron. + +Yeah. + +STUDENT: [INAUDIBLE] + +PROFESSOR: So, p as some +exponential here? + +You know, I don't recall +seeing it as + +an exponential form. + +But that doesn't mean it's not +used the exponential form. + +This is an easy way to do it, +because then you've got a + +linear relationship. + +And generally we like to +see straight lines. + +So this gives you a nice +straight line. + +OK, so now let's do a slightly +more complicated example. + +Which is, so most of the time +you don't have pure material. + +You have a mixture +of some sort. + +For instance, if I have a glass +of water on the table at + +room temperature. + +Above the glass of water, I have +air, there's my H2O here. + +And then I've got some air. + +Above the glass of water. + +And the air's inert +to the water. + +It's not reacting +with the water. + +So it's like an inert gas +sitting on top of the water. + +Then I want to ask the question, +what is the vapor + +pressure of the water? + +In the presence of this +inert gas, the air. + +It's not really the same as the +problem that we've been + +looking at up here. + +Right? + +Because this gas liquid +coexistence line, this + +diagram, and this Clapeyron +equation, is all done for a + +pure substance. + +And at room temperature, at +room temperature, we're + +sitting squarely in +the liquid phase. + +We're not on the coexistence +line. + +At room temperature and +one bar pressure. + +So instead of having this system +here, I looked at the + +system where I had the water, +H2O, with nothing on top. + +With no air on top. + +Except the cylinder. + +Now, I'd better make the surface +of my water a straight + +line, otherwise I'm going +to get in trouble. + +There's the water sitting +right here. + +And I put a cylinder with +one bar pressure on top. + +My cylinder's going to sit +squarely on the stump of the + +surface of the water. + +This is not going to be any +water vapor at one bar + +pressure on that cylinder. + +At one bar, we're way up +in the liquid phase. + +I would have to decrease the +pressure on that cylinder down + +to, I don't know, whatever the +water vapor pressure is at + +room temperature here on +this coexistence curve. + +0.1 bar or something. + +0.05 bar. + +Something pretty small. + +So that's what we've +been working on. + +This pure system. + +And now we're going to be +working on this system here, + +where we have air. + +With a cylinder on +top, one bar. + +And we want to know what is the +vapor pressure of H2O in + +this system here. + +Is it zero? + +Anybody want to guess, +if it's zero? + +We know there's vapor pressure +there, right? + +And a good guess is that that +vapor pressure here, it's + +pretty close to the pressure +that you would guess by using + +this diagram with +the pure water. + +But the key word is, +it's pretty close. + +It's not exactly the same. + +So, let me ask you this. + +Without looking at the notes, +now is p H2O in this problem + +here greater than, less than, +or the same as p H2O in the + +pure Clapeyron case? + +How many people think +that it's the same? + +How about smaller than? + +Smaller than? + +Few people think that +it's smaller than. + +How about greater than? + +A bunch of people don't +know what to answer. + +OK. + +I think that if you think about +it, what the difference + +is between here and there, you +could probably reason which + +way it should go. + +Which way the partial pressure +of the water should go under + +one bar pressure, room +temperature. + +Compared to what you might +expect it to be at room + +temperature with a diagram. + +So, I'm going to give you a +little bit of time just to + +think about it. + +Without looking at the notes, +what you think the + +right sign is here. + +Then we'll do the problem and +then we'll figure out if you + +were right or wrong. + +OK. + +How many people say +it's greater than? + +One, two. + +Two brave people here. + +Two. + +How many people say +it's smaller than? + +OK. + +Smaller than. + +So I'm going to say a +large number, OK? + +Many. + +How many people think +it's equal? + +One person thinks it's equal. + +Alright, let's do it out now +and see how it comes out. + +And then we can reason why it +came out the way it came out. + +Logically, without actually +doing math. + +Because there's a way to reason +it out that you should + +be able to do. + +OK, so this is what +we have here. + +Then the system is, we +have this container. + +Let me redo it instead +of writing air. + +So we have the liquid +state here. + +Some substance, and it doesn't +have to be water. + +That's a liquid, at +some pressure p. + +And I'm going to say P capital, +that's going to be + +the total pressure. + +And the total pressure is given +by the piston here. p + +total, p T. And on top here +I'm going to have two + +substances. + +I'm going to have A, +in the gas phase, + +that's the water vapor. + +Some partial pressure, p sub +A, temperature T. And I'm + +going to have the inert +gas, with some + +partial pressure p, inert. + +Such that the sum of the partial +pressure of the inert + +gas, plus the partial pressure +of A, is the total pressure. + +One bar, in our case. + +With the water with +the air on top. + +And the question, oh, let me +make a few more definitions. + +We're going to define p0 as +the vapor pressure of pure + +vapor pressure of pure A. So +that's what you would read off + +the diagram here. + +And what we want, the question +we ask is, what is the partial + +pressure of A as a function +of the total pressure? + +That's what we're asking. + +As I'm increasing the total +pressure, meaning I'm putting + +more and more inert +gas in there, + +which way is this going? + +Is it going up, down, +or staying the same? + +And we've got a bunch +of votes up here. + +Most people think that it's +going to go down. + +Because I put more +gas in there. + +OK, I know that if P, capital P, +is equal to pA, then pA is + +equal to p0. + +Right? + +There's no inert gas. + +So that's the one extreme +case here. + +There's no inert gas, then the +partial pressure's going to be + +what you read off +that graph here. + +So another way of saying what is +p as a function of capital + +P, is to ask the question +what is the slope? + +I've got one point here. + +If I can integrate the slope +then I have this equation. + +So the other way to ask the +question is, what is dpA/dp, + +at a constant temperature? + +Where I'm keeping the +temperature constant. + +And that turns out to be +easier to calculate. + +These slopes are always easier +to calculate than + +the absolute things. + +So we're doing an equilibrium +here. + +We have an equilibrium +between the liquid + +state and the gas phase. + +And we want to know something +about this equilibrium as we + +change a parameter. + +Equilibrium, what do we always +start with when we have an + +equilibrium. + +What's the first thing +we think about? + +We think about chemical +potential. + +Chemical potentials of A, in +the gas phase has to be the + +same as the chemical potential +of A in the liquid phase. + +Well, I can't think of anything +else to start with. + +So let me start with that. + +So let's start by writing the +chemical potentials being + +equal to each other. + +Because we know that's true. + +So mu A, in the gas phase, +temperature and with a partial + +pressure p sub A. Is equal to +mu A in the liquid phase, + +where the pressure on the +liquid is capital P. + +What else do we know? + +Well, we, what else are +we going to need? + +Before we do that, since what +we're after is the derivative, + +let's take the derivative +of both sides. + +We're looking at a derivative +with respect to pressure here. + +Let's take the derivative +outside with pressure and see + +what happens. + +So let's take the derivative +of this with + +respect to total pressure. + +Well, this isn't +total pressure. + +This is the partial pressure of +A. But it's a function of + +the total pressure. + +It's a function of the +total pressure. + +Partial pressure of A is total +pressure minus p inert. + +So, we have to use +the chain rule. + +So on this side here, we +have d mu A / dpA. + +So I'm taking d/dp +of both sides. + +Then by chain rule, dpA/dP. + +Constant temperature. + +And then on the right-hand +side, I have d mu A / dP, + +constant temperature. + +Well, d mu / dP, that may or may +not seem familiar to you. + +I never remember these things, +but I always remember that + +there's, that these +relationships are interesting. + +Especially when you're talking +about something like a + +chemical potential, which is +really nothing but the Gibbs + +free energy. + +With respect to pressure, when +we know that the variables + +that we use for Gibbs free +energy are pressure and + +temperature. + +Right? + +So this is the variable that +goes with Gibbs free energy. + +So this means that they were +taking the derivatives of the + +Gibbs free energy with respect +to one of its variables is + +something that we should know. + +So we go back to writing what +the Gibbs free energy is. + +So dG is equal to +V dp minus S dT. + +Which is the fundamental +equation + +for Gibbs free energy. + +And this is the Gibbs free +energy per mole. + +That's just the chemical +potential. + +The same thing. + +And this is the derivative +with respect to pressure. + +And this is the derivative with +respect to temperature. + +So this thing here +is d mu / dp. + +At constant temperature. + +It's just the volume. + +So now we have this equation, +where we started out with the + +chemical potentials. + +And we've got these d +mu A / dpA, we've + +got d mu A / dP here. + +That's just the molar +volume of the gas. + +Right, because this is mu +of the gas phase here. + +So this is the molar +volume of the gas. + +And I have dpa/dP. + +And, this is very nice. + +Because this is actually +what I'm trying to get. + +Trying to see how the partial +pressure of a changes with the + +total pressure. + +That's what I'm trying +to calculate here. + +I know what this is. + +This is just an experimental +number. + +And then on this side here +I have d mu A / dP. + +This is the liquid phase. + +Derivative with respect to total +pressure, that's the + +molar volume of the liquid. + +The liquid. + +Great, I'm done. dpA/dP total, +constant pressure, is the + +ratio of the molar volume of the +liquid of A divided by the + +molar volume of the gas. + +What's the sign? + +Volumes are positive, right? + +This has to be positive. + +There's no choice. + +It can't even be zero. + +It has to be positive, right? + +So that means the slope +is a positive slope. + +As I increase the total +pressure, p is going to go up. + +If I integrate now, this, +starting at, so the total + +pressure is equal to pA, I'm +going to get a curve that + +looks like this. + +OK, if I write on this axis p +inert, so when p inert is + +equal to zero, total +pressure is pA. + +I'm going to start at p0. + +And I'm going to go up from +there, positive slope. + +So. + +Who was right? + +A couple people are right. + +So let's think about it +in a different way. + +Let's think about it +in a different way. + +So we did the math, and we found +that actually it's, and + +that turns out to be a +very small amount. + +You do a very good job by just +taking this curve here. + +And using the pure substance. + +In fact, in the notes we have +an example of how much it + +changes for mercury. + +So for mercury, at 100 degrees +C, for pure mercury, the vapor + +pressure is 0.27 bar. + +If you add enough inert gas to +make it 1 bar for the total + +pressure, you go from +0.27 to 0.2701. + +Not much of a change. + +They do a really good job +of just picking this. + +And if you go to 100 bar, then +you increase it to 0.28. + +So it takes a lot of pressure +on top, a lot of extra inert + +gas to really make much +of a difference. + +But, let's think about +why it would make a + +difference, just logically. + +So in the absence of this inert +gas here, I just have + +the pure substance. + +I add some inert gas, what +happens to the entropy on top? + +It's increasing, right? + +Do systems like to have +more entropy? + +Yeah. + +So, I have a lot of +inert gas here. + +A small amount of A. What if I +had a little bit more A, in + +the presence of the inert gas? + +Which way would the +entropy go? + +It would go up a little +bit more, + +you'd have more disorder. + +If I have nothing, if I have +no A here, up here and just + +the inert gas, then there's +no entropy of mixing. + +I add a little bit of inert gas, +there's a little bit more + +entropy of mixing. + +Eventually, I add more and more, +entropy of mixing goes + +up and up and up, and eventually +it comes back down + +to where I have pure A on top. + +So the entropy of mixing up here +is driving the increase + +in the pressure of, in the +partial pressure of A. Entropy + +is this amazingly +important term. + +That's what we saw. + +Entropy of mixing was +responsible for equilibrium. + +Without entropy of mixing, +then everything would go + +directly to the products. + +You'd never have +an equilibrium. + +Another secret of life. + +So entropy of mixing here is +driving this positive slope. + +That's another way of +thinking about it. + +And that's why you can guess +ahead of time what the signs + +of these things ought to be. + +Without doing the math. + +Alright, any questions? + +OK. + +So there's another sample +problem with the notes, which + +is sort of like a standard +problem. + +Where you're given a +Clausius-Clapeyron equation + +for a substance in this form. + +So if you look at it, log p is +minus some energy divided by + +RT plus some number. + +In this case, it's negative, +the delta H is negative for + +the substance that +you have there. + +And you're given it for the +liquid phase, for the vapor + +pressure above the liquid +and the vapor + +pressure above the solid. + +You can, because the only way +it doesn't work is if you're + +looking at solid liquid. + +So, and then you're asked to +manipulate this equation to + +find different properties. + +For instance the triple point. + +It's a very common +thing to get, the + +triple point from this. + +The delta H, it's a way to get +delta H. Just like we saw for + +the RDX, right? + +The data points formed +a straight line. + +And the slope gave you +delta H, for RDX. + +Delta H of sublimation +for RDX. + +So this is the way that this +equation is used for problems. + +I'm not going to do +this problem. + +Instead I'm going to +go ahead and forge + +ahead to the next topic. + +And start it. + +This is the topic we're going +to do it after spring break. + +And and it really is a topic +that follows this pretty + +straightforwardly. + +Well, it's more complicated, +but it's similar to this + +problem here. + +So we saw that in real +life yes, question? + +STUDENT: [INAUDIBLE] + +PROFESSOR: The exam. + +Oh there's an exam is, +which is, oh I + +forgot about the exam. + +So let's see. + +There's a problem set +that's due today. + +The exam will be up to the +problem set that's due today. + +Which means that what I talked +about today is not going to be + +on the exam. + +Because it's not covered +in the problem set. + +So let's say it goes up to +Wednesday's lecture. + +Which means you might still +have a phase transition + +problem, right? + +In fact, you're very +likely to get a + +phase transition problem. + +It's very likely +to be the case. + +Because it's an easy problem +to put together. + +But you don't have to worry +about Clausius-Clapeyron. + +You do have to worry about +Clapeyron, but not + +Clausius-Clapeyron, OK? + +So, for the exam, we're going to +put on the Web last year's + +exam, and you guys are +going to do reviews. + +The usual thing. + +Yeah? + +STUDENT: [INAUDIBLE] + +PROFESSOR: So that you don't +see the answers. + +Yeah, absolutely this +can easily be done. + +We'll do that. + +Any other questions, +about the exam? + +Now, I don't remember. + +Is there a problem set that, so +I'm not assigning a problem + +set today, right, then? + +Right. + +OK. + +Good. + +Because I hadn't loaded +it up yet. + +And so now I won't load it up. + +OK. + +Anything else? + +OK, so let me tell you where +we're going to go + +then, after the break. + +So after the break, we're going +to be starting to talk + +about things that are called +colligative properties. + +Colligative properties are the +properties like the vapor + +pressure, lowering when you have +a mixture in a liquid, + +instead of having a pure +substance you have a mixture + +of substances here. + +And then the vapor +pressure of both + +substances above gets lowered. + +Anybody want to guess why +they got lowered? + +What's the magic word? + +Entropy of mixing, right. + +Right. + +There's more entropy of mixing +if you've got a mixture in the + +liquid than if you have +a pure gas up there. + +So usually, so let me back up. + +Usually it's when you have a +solute, like salt in water. + +Where water is volatile +and the salt is not. + +Right, a salt in water solution +will have a lower + +vapor pressure than a solution +of pure water. + +Because of the entropy +of mixing in a + +salt and water solution. + +The salt and water solution +we have a lowering, + +lower melting point. + +And that's significantly +lower. + +Which is why we use it +on roads, right? + +That's a colligative +properties. + +Osmotic pressure. + +Which you've already sort +of heard about. + +Why saltwater fish are unhappy +in fresh water. + +That's a colligative property. + +So we're going to go through +these colligative properties. + +And the mainstay of these +colligative properties is that + +we're going to be talking +about mixtures + +in the liquid phase. + +Here we talked about a mixture +in the gas phase, changing + +some property. + +From now on, we're going to be +talking about mixtures in the + +liquid phase, pretty much. + +And so our goal is going to +be able to, is going to be + +predict the way that properties +change as you have + +these mixtures. + +OK. so the standard mixture that +we're going to have, is + +to have a binary liquid +gas mixture. + +So that means we're going +to have two substances. + +A and B. And at first, we're +going to make it + +as general as possible. + +So we're going to have liquid +phase of A, the liquid phase + +of B. So, for instance, this +could be vodka, right? + +Water and ethanol. + +And water and ethanol +are both volatile. + +So we're going to have water and +ethanol in the gas phase. + +There, and it's a mixture, +they're perfectly miscible in + +the liquid phase, A and B. And +there's going to be some + +fraction, molar fraction, +of these things. + +We're going to have a molar +fraction in the liquid phase + +for A and B. And some molar +fraction in the gas phase, for + +A and B. We're going to call it +yA and yB, that's the molar + +fraction in the gas phase. + +And there's no reason why the +molar fractions in the gas + +phrase should be the same as +that in the liquid phase. + +And we know that. + +We know that ethanol is more +volatile than water. + +And so if you have a gas of +vodka, then you can smell the + +alcohol because it's +coming out. + +But the water is, vapor +pressure is, + +very slow, very small. + +It's the usual, it's +pretty close to + +the usual vapor pressure. + +And our question is, what we're +going to be asking is, + +how many, if I give you the +total pressure and the + +temperature here, what else do I +need to know to find out all + +these molar fractions? + +So let's first see what all the + +variables are that we have. + +Usually, we have +two variables. + +The temperature and pressure, +and that's enough to tell us + +everything. + +But here now we have +a mixture. + +So we're going to need +more than that. + +We're going to need +four variables. + +We're going to need +the temperature. + +The pressure, and we're going to +need the molar fraction of + +A in the liquid phase. + +And the molar fraction of +A in the gas phase. + +We're not going to need +any more than that. + +Actually we're going to +need less than that. + +But those are the four variables +that we can easily + +identify here. + +And we don't need yB and xB, +because the sum of the molar + +fraction has to be equal to one. +yB is one minus yA, xB is + +one minus xA. + +So we don't need y. + +So these are a priori the +independent variables that we + +have to work with. + +Now, we have some constraints +here. + +We have a constraint. + +Our constraint is that we are +the coexistence point. + +There's a coexistence between +the gas phase + +and the liquid phase. + +And what does it mean for A +liquid to be coexistent with A + +in the gas phase? + +Chemical potential. + +The chemical potential of a +molecule of A in the liquid + +phase here is the same as the +chemical potential of + +A in the gas phase. + +So we have two constraints. + +We have mu A for the liquid +phase is equal to mu A for the + +gas phase, and mu B for the +liquid phase equal to mu B for + +the gas phase. + +So we have four variables, +two constraints. + +That means that the total +number of independent + +variables we have is just two. + +It's the number of variables +four, minus the constraints. + +OK? + +Or you could say six variables +if you include yB and xB, and + +four constraints. + +Whatever we accounted, +you just have + +two degrees of freedom. + +So we have two degrees +of freedom. + +Which means that if you know the +temperature and pressure, + +then you still know +everything. + +At the coexistence point. + +You still know what the molar +fraction is of your two + +substances in both phases. + +So that's really powerful. + +Or if you know just the molar +fraction of A, and the + +temperature, then you know +the pressure above. + +And you know everything else. + +So in this very complicated +mixture here, you still only + +need to know a couple of things +to tell you everything + +about this mixture. + +And this example here is a +specific example of something + +called the Gibbs phase rule. + +Which you've seen before. + +In this diagram. + +In this diagram that +we wrote here. + +Where, let me write down what +the Gibbs phase rule is first. + +The Gibbs phase rule tells you +the number of independent + +variables given a number +of constraints. + +So, it tells you that the number +of degrees of freedom, + +the number of independent +variables in a mixture, in a + +complicated system like this, +is equal to C, which is the + +number of components. + +So in this case, it would +be two components. + +You have A and B. The components +is the number of + +independent species that +you have, minus + +the number of phases. + +So here we have two phases, the +gas phase and the water + +phase, plus two. + +So for this example here, then +we would have two components, + +C equals two. + +Two phases liquid and gas. + +A and B are the components. + +And then plus two. + +So two minus two plus two, +F equals to two. + +Two degrees of freedom, two +independent variables. + +If I'm looking at this diagram +here, in this diagram here I + +have C equals one. + +One component, right? + +If I'm sitting where there's +only one phase, say, the + +liquid phase or the gas phase, +then p equals one. + +Then F is one minus one plus +two, is equal to two. + +Two degrees of freedom. + +And so in the pure phase, +I am in a plane. + +The pressure and the temperature +are my two degrees + +of freedom. + +I can freely move around +the plane. + +At a coexistence line, +then the number of + +phases equals to two. + +Then I have one minus two is +minus one, plus two is one. + +The degrees of freedom is one. + +That's a line. + +I have one degree of freedom. + +I can move in the line, in +the line in a plane. + +Then if I change to the triple +point, where the number of + +phases is three, then the number +of degrees of freedom + +is one minus three is minus +two, two plus two is zero. + +I don't have any degrees +of freedom, I'm + +stuck at one point. + +So this is an example of the +Gibbs phase rule, specific + +where C happens to +be equal to one. + +And then, this is a more +generalized example. + +So next time, then, what we'll +do is we'll start by deriving + +the Gibbs phase rule. + +Which is not so hard. + +And then start on our way to +the colligative properties. + +And then you'll have an exam. \ No newline at end of file diff --git a/BkaJCbyyLEA.txt b/BkaJCbyyLEA.txt new file mode 100644 index 0000000000000000000000000000000000000000..5304f6076d2c14b89002f7309fa6fe82b3afa204 --- /dev/null +++ b/BkaJCbyyLEA.txt @@ -0,0 +1,23176 @@ +align:start position:0% + +okay okay so when we ended last class we + + align:start position:0% +okay okay so when we ended last class we + + + align:start position:0% +okay okay so when we ended last class we +were talking about lamp uh just to + + align:start position:0% +were talking about lamp uh just to + + + align:start position:0% +were talking about lamp uh just to +finish up um okay so where does + + align:start position:0% +finish up um okay so where does + + + align:start position:0% +finish up um okay so where does +copyright law make a distinction between + + align:start position:0% +copyright law make a distinction between + + + align:start position:0% +copyright law make a distinction between +anything digital and something + + align:start position:0% + + + + align:start position:0% + +analog somebody in the + + align:start position:0% +analog somebody in the + + + align:start position:0% +analog somebody in the +back Transmissions Transmissions oh + + align:start position:0% +back Transmissions Transmissions oh + + + align:start position:0% +back Transmissions Transmissions oh +anywhere else in the entire copyright + + align:start position:0% +anywhere else in the entire copyright + + + align:start position:0% +anywhere else in the entire copyright +law I + + align:start position:0% +law I + + + align:start position:0% +law I +think unless there's some weird + + align:start position:0% +think unless there's some weird + + + align:start position:0% +think unless there's some weird +exception somewhere I I haven't read all + + align:start position:0% +exception somewhere I I haven't read all + + + align:start position:0% +exception somewhere I I haven't read all +the yeah I mean the only major one is + + align:start position:0% +the yeah I mean the only major one is + + + align:start position:0% +the yeah I mean the only major one is +definitely transmission so if I'm giving + + align:start position:0% +definitely transmission so if I'm giving + + + align:start position:0% +definitely transmission so if I'm giving +you a CD versus giving you like a vinyl + + align:start position:0% +you a CD versus giving you like a vinyl + + + align:start position:0% +you a CD versus giving you like a vinyl +record does it Ma is that what is that + + align:start position:0% +record does it Ma is that what is that + + + align:start position:0% +record does it Ma is that what is that +by the way what activity distri + + align:start position:0% +by the way what activity distri + + + align:start position:0% +by the way what activity distri +distribution good and + + align:start position:0% +distribution good and + + + align:start position:0% +distribution good and +uh or or if I'm copying a CD versus + + align:start position:0% +uh or or if I'm copying a CD versus + + + align:start position:0% +uh or or if I'm copying a CD versus +copying of a vinyl record none of that + + align:start position:0% +copying of a vinyl record none of that + + + align:start position:0% +copying of a vinyl record none of that +matters the only time it matters if + + align:start position:0% +matters the only time it matters if + + + align:start position:0% +matters the only time it matters if +you're digital versus analog is for a + + align:start position:0% +you're digital versus analog is for a + + + align:start position:0% +you're digital versus analog is for a +digital audio + + align:start position:0% +digital audio + + + align:start position:0% +digital audio +transmission okay uh + + align:start position:0% +transmission okay uh + + + align:start position:0% +transmission okay uh +and uh let's say I want to release my + + align:start position:0% +and uh let's say I want to release my + + + align:start position:0% +and uh let's say I want to release my +own recording of uh American Pie people + + align:start position:0% +own recording of uh American Pie people + + + align:start position:0% +own recording of uh American Pie people +know that song who wrote + + align:start position:0% + + + + align:start position:0% + +it Don mlan yeah not not yeah Don mlan + + align:start position:0% +it Don mlan yeah not not yeah Don mlan + + + align:start position:0% +it Don mlan yeah not not yeah Don mlan +did he write any other songs of note not + + align:start position:0% +did he write any other songs of note not + + + align:start position:0% +did he write any other songs of note not +really yeah there's he has a greatest + + align:start position:0% +really yeah there's he has a greatest + + + align:start position:0% +really yeah there's he has a greatest +hit CD but it's just different versions + + align:start position:0% +hit CD but it's just different versions + + + align:start position:0% +hit CD but it's just different versions +of American Pie no that's not true that + + align:start position:0% +of American Pie no that's not true that + + + align:start position:0% +of American Pie no that's not true that +would be liable it's anyway sorry uh so + + align:start position:0% +would be liable it's anyway sorry uh so + + + align:start position:0% +would be liable it's anyway sorry uh so +so if I wanted to release my own version + + align:start position:0% +so if I wanted to release my own version + + + align:start position:0% +so if I wanted to release my own version +as Madonna did in 2000 what would I have + + align:start position:0% +as Madonna did in 2000 what would I have + + + align:start position:0% +as Madonna did in 2000 what would I have +to do would I have to go to Don mlan and + + align:start position:0% +to do would I have to go to Don mlan and + + + align:start position:0% +to do would I have to go to Don mlan and +get his + + align:start position:0% +get his + + + align:start position:0% +get his +permission sorry go to BMI no BMI only + + align:start position:0% +permission sorry go to BMI no BMI only + + + align:start position:0% +permission sorry go to BMI no BMI only +covers performances but if I'm just + + align:start position:0% +covers performances but if I'm just + + + align:start position:0% +covers performances but if I'm just +releasing my own + + align:start position:0% + + + + align:start position:0% + +copy ASCAP is also just performers just + + align:start position:0% +copy ASCAP is also just performers just + + + align:start position:0% +copy ASCAP is also just performers just +per they they license performances so a + + align:start position:0% +per they they license performances so a + + + align:start position:0% +per they they license performances so a +transmission like a radio station or + + align:start position:0% +transmission like a radio station or + + + align:start position:0% +transmission like a radio station or +like a night club you'd have to go to + + align:start position:0% +like a night club you'd have to go to + + + align:start position:0% +like a night club you'd have to go to +ASAP or BMI but for releasing recording + + align:start position:0% +ASAP or BMI but for releasing recording + + + align:start position:0% +ASAP or BMI but for releasing recording +what activities are we implicating + + align:start position:0% +what activities are we implicating + + + align:start position:0% +what activities are we implicating +what one section 106 + + align:start position:0% +what one section 106 + + + align:start position:0% +what one section 106 +activities derivative works very good + + align:start position:0% +activities derivative works very good + + + align:start position:0% +activities derivative works very good +what + + align:start position:0% +what + + + align:start position:0% +what +else making copies right reproduction + + align:start position:0% +else making copies right reproduction + + + align:start position:0% +else making copies right reproduction +making copies distri and + + align:start position:0% +making copies distri and + + + align:start position:0% +making copies distri and +distribution um but we and and those are + + align:start position:0% +distribution um but we and and those are + + + align:start position:0% +distribution um but we and and those are +three activities that ASCAP has no power + + align:start position:0% +three activities that ASCAP has no power + + + align:start position:0% +three activities that ASCAP has no power +to license the songwriters that are + + align:start position:0% +to license the songwriters that are + + + align:start position:0% +to license the songwriters that are +members of ASCAP do not give ASCAP the + + align:start position:0% +members of ASCAP do not give ASCAP the + + + align:start position:0% +members of ASCAP do not give ASCAP the +power to license those things so what do + + align:start position:0% +power to license those things so what do + + + align:start position:0% +power to license those things so what do +you have to do if you're uh if if you're + + align:start position:0% +you have to do if you're uh if if you're + + + align:start position:0% +you have to do if you're uh if if you're +you and you want to relas relas your own + + align:start position:0% +you and you want to relas relas your own + + + align:start position:0% +you and you want to relas relas your own +version of American + + align:start position:0% + + + + align:start position:0% + +Pi this is like part of the + + align:start position:0% +Pi this is like part of the + + + align:start position:0% +Pi this is like part of the +homework whatever what do you what did + + align:start position:0% +homework whatever what do you what did + + + align:start position:0% +homework whatever what do you what did +you say you can do it as long as you pay + + align:start position:0% +you say you can do it as long as you pay + + + align:start position:0% +you say you can do it as long as you pay +you can do it as long as you pay a fee + + align:start position:0% +you can do it as long as you pay a fee + + + align:start position:0% +you can do it as long as you pay a fee +very good so you don't have to get + + align:start position:0% +very good so you don't have to get + + + align:start position:0% +very good so you don't have to get +permission you just say Dear Mr + + align:start position:0% +permission you just say Dear Mr + + + align:start position:0% +permission you just say Dear Mr +mlan um or Mr + + align:start position:0% +mlan um or Mr + + + align:start position:0% +mlan um or Mr +Pi I'm gonna release my own version of + + align:start position:0% +Pi I'm gonna release my own version of + + + align:start position:0% +Pi I'm gonna release my own version of +the + + align:start position:0% +the + + + align:start position:0% +the +song that's life yeah but uh you have + + align:start position:0% +song that's life yeah but uh you have + + + align:start position:0% +song that's life yeah but uh you have +limited moral right so you could is moov + + align:start position:0% +limited moral right so you could is moov + + + align:start position:0% +limited moral right so you could is moov +the object if you were the songwriter + + align:start position:0% +the object if you were the songwriter + + + align:start position:0% +the object if you were the songwriter +and the song was used in some context + + align:start position:0% +and the song was used in some context + + + align:start position:0% +and the song was used in some context +you didn't + + align:start position:0% +you didn't + + + align:start position:0% +you didn't +like really you no sorry he says you + + align:start position:0% +like really you no sorry he says you + + + align:start position:0% +like really you no sorry he says you +have limited moral rights so you could + + align:start position:0% +have limited moral rights so you could + + + align:start position:0% +have limited moral rights so you could +object if the song were used in some + + align:start position:0% +object if the song were used in some + + + align:start position:0% +object if the song were used in some +context you didn't like that's just not + + align:start position:0% +context you didn't like that's just not + + + align:start position:0% +context you didn't like that's just not +right in + + align:start position:0% +right in + + + align:start position:0% +right in +America um did did you guys when I said + + align:start position:0% +America um did did you guys when I said + + + align:start position:0% +America um did did you guys when I said +limited moral rights we're talkinging + + align:start position:0% +limited moral rights we're talkinging + + + align:start position:0% +limited moral rights we're talkinging +about section 106a right what does 106a + + align:start position:0% +about section 106a right what does 106a + + + align:start position:0% +about section 106a right what does 106a +say visual art yeah it's just about + + align:start position:0% +say visual art yeah it's just about + + + align:start position:0% +say visual art yeah it's just about +visual art and I'm not really an expert + + align:start position:0% +visual art and I'm not really an expert + + + align:start position:0% +visual art and I'm not really an expert +in what 106a permits and doesn't permit + + align:start position:0% +in what 106a permits and doesn't permit + + + align:start position:0% +in what 106a permits and doesn't permit +but it's definitely not about music and + + align:start position:0% +but it's definitely not about music and + + + align:start position:0% +but it's definitely not about music and +why did we enact + + align:start position:0% +why did we enact + + + align:start position:0% +why did we enact +106a did Congress were they like let's + + align:start position:0% +106a did Congress were they like let's + + + align:start position:0% +106a did Congress were they like let's +have some moral + + align:start position:0% +have some moral + + + align:start position:0% +have some moral +rights or was there like a concerted + + align:start position:0% +rights or was there like a concerted + + + align:start position:0% +rights or was there like a concerted +lobbying campaign by like + + align:start position:0% + + + + align:start position:0% + +painters no it was because we were + + align:start position:0% +painters no it was because we were + + + align:start position:0% +painters no it was because we were +becoming part of various treaties like + + align:start position:0% +becoming part of various treaties like + + + align:start position:0% +becoming part of various treaties like +the burn convention which are + + align:start position:0% +the burn convention which are + + + align:start position:0% +the burn convention which are +international copyright treaties which + + align:start position:0% +international copyright treaties which + + + align:start position:0% +international copyright treaties which +are actually when you think of treaties + + align:start position:0% +are actually when you think of treaties + + + align:start position:0% +are actually when you think of treaties +you think of like important ones like + + align:start position:0% +you think of like important ones like + + + align:start position:0% +you think of like important ones like +the Treaty of Versailles or like + + align:start position:0% +the Treaty of Versailles or like + + + align:start position:0% +the Treaty of Versailles or like +international mail carriage or the NAFTA + + align:start position:0% +international mail carriage or the NAFTA + + + align:start position:0% +international mail carriage or the NAFTA +you know but the treaties that are the + + align:start position:0% +you know but the treaties that are the + + + align:start position:0% +you know but the treaties that are the +most complicated are about copyright I'm + + align:start position:0% +most complicated are about copyright I'm + + + align:start position:0% +most complicated are about copyright I'm +not kidding if you go and get this book + + align:start position:0% +not kidding if you go and get this book + + + align:start position:0% +not kidding if you go and get this book +called treaties in force which is + + align:start position:0% +called treaties in force which is + + + align:start position:0% +called treaties in force which is +published by the state department you go + + align:start position:0% +published by the state department you go + + + align:start position:0% +published by the state department you go +through they've got hundreds and + + align:start position:0% +through they've got hundreds and + + + align:start position:0% +through they've got hundreds and +hundreds of hundreds of treaties and + + align:start position:0% +hundreds of hundreds of treaties and + + + align:start position:0% +hundreds of hundreds of treaties and +every time some Ambassador sends + + align:start position:0% +every time some Ambassador sends + + + align:start position:0% +every time some Ambassador sends +somebody you know a letter that says we + + align:start position:0% +somebody you know a letter that says we + + + align:start position:0% +somebody you know a letter that says we +agree that our jute Imports will be + + align:start position:0% +agree that our jute Imports will be + + + align:start position:0% +agree that our jute Imports will be +encased in plastic instead of vinal you + + align:start position:0% +encased in plastic instead of vinal you + + + align:start position:0% +encased in plastic instead of vinal you +know that's all recorded and the state + + align:start position:0% +know that's all recorded and the state + + + align:start position:0% +know that's all recorded and the state +you know that's like what the state + + align:start position:0% +you know that's like what the state + + + align:start position:0% +you know that's like what the state +department does but they have to have a + + align:start position:0% +department does but they have to have a + + + align:start position:0% +department does but they have to have a +whole appendix it's like the only + + align:start position:0% +whole appendix it's like the only + + + align:start position:0% +whole appendix it's like the only +appendix is on copyright because it's so + + align:start position:0% +appendix is on copyright because it's so + + + align:start position:0% +appendix is on copyright because it's so +complicated in fact the burn convention + + align:start position:0% +complicated in fact the burn convention + + + align:start position:0% +complicated in fact the burn convention +has never been issued among our formal + + align:start position:0% +has never been issued among our formal + + + align:start position:0% +has never been issued among our formal +series of treaties that that the United + + align:start position:0% +series of treaties that that the United + + + align:start position:0% +series of treaties that that the United +States has acceded to I don't exactly + + align:start position:0% +States has acceded to I don't exactly + + + align:start position:0% +States has acceded to I don't exactly +know why but it's just like copyright + + align:start position:0% +know why but it's just like copyright + + + align:start position:0% +know why but it's just like copyright +treaties are like the most weird + + align:start position:0% +treaties are like the most weird + + + align:start position:0% +treaties are like the most weird +treaties anyway that's it doesn't have + + align:start position:0% +treaties anyway that's it doesn't have + + + align:start position:0% +treaties anyway that's it doesn't have +anything to do with anything oh so + + align:start position:0% +anything to do with anything oh so + + + align:start position:0% +anything to do with anything oh so +that's why we adopted that moral rights + + align:start position:0% +that's why we adopted that moral rights + + + align:start position:0% +that's why we adopted that moral rights +because we were trying to adopt the + + align:start position:0% +because we were trying to adopt the + + + align:start position:0% +because we were trying to adopt the +minimum possible and still plausibly be + + align:start position:0% +minimum possible and still plausibly be + + + align:start position:0% +minimum possible and still plausibly be +members of What's called the burn + + align:start position:0% +members of What's called the burn + + + align:start position:0% +members of What's called the burn +Union okay so so moral rights are not an + + align:start position:0% +Union okay so so moral rights are not an + + + align:start position:0% +Union okay so so moral rights are not an +obstacle to recording American p and I + + align:start position:0% +obstacle to recording American p and I + + + align:start position:0% +obstacle to recording American p and I +can't believe you'd say I would do + + align:start position:0% +can't believe you'd say I would do + + + align:start position:0% +can't believe you'd say I would do +Injustice to American Pie I + + align:start position:0% +Injustice to American Pie I + + + align:start position:0% +Injustice to American Pie I +would I really would respect the source + + align:start position:0% +would I really would respect the source + + + align:start position:0% +would I really would respect the source +material so all I have to do is pay Don + + align:start position:0% +material so all I have to do is pay Don + + + align:start position:0% +material so all I have to do is pay Don +mlan what eight cents eight like eight + + align:start position:0% +mlan what eight cents eight like eight + + + align:start position:0% +mlan what eight cents eight like eight +and a half cents per copy it might have + + align:start position:0% +and a half cents per copy it might have + + + align:start position:0% +and a half cents per copy it might have +gone up actually it goes up like every + + align:start position:0% +gone up actually it goes up like every + + + align:start position:0% +gone up actually it goes up like every +year um and who sets that price eight + + align:start position:0% +year um and who sets that price eight + + + align:start position:0% +year um and who sets that price eight +and a half cents is it like a free + + align:start position:0% +and a half cents is it like a free + + + align:start position:0% +and a half cents is it like a free +market + + align:start position:0% + + + + align:start position:0% + +thing is it by a contract like where + + align:start position:0% +thing is it by a contract like where + + + align:start position:0% +thing is it by a contract like where +does 8 and a half cents come from there + + align:start position:0% +does 8 and a half cents come from there + + + align:start position:0% +does 8 and a half cents come from there +a board somewhere + + align:start position:0% + + + + align:start position:0% + +yeah it comes from the government the + + align:start position:0% +yeah it comes from the government the + + + align:start position:0% +yeah it comes from the government the +copyright office which is part either of + + align:start position:0% +copyright office which is part either of + + + align:start position:0% +copyright office which is part either of +the legislative branch or the executive + + align:start position:0% +the legislative branch or the executive + + + align:start position:0% +the legislative branch or the executive +branch depending on which branch you ask + + align:start position:0% +branch depending on which branch you ask + + + align:start position:0% +branch depending on which branch you ask +but it's part of the federal government + + align:start position:0% +but it's part of the federal government + + + align:start position:0% +but it's part of the federal government +it just says they declaim the price will + + align:start position:0% +it just says they declaim the price will + + + align:start position:0% +it just says they declaim the price will +be8 and a half cents it's a government + + align:start position:0% +be8 and a half cents it's a government + + + align:start position:0% +be8 and a half cents it's a government +set price it's it's you + + align:start position:0% +set price it's it's you + + + align:start position:0% +set price it's it's you +know it's the most centralized kind of + + align:start position:0% +know it's the most centralized kind of + + + align:start position:0% +know it's the most centralized kind of +economy you can have just 8 and a half + + align:start position:0% +economy you can have just 8 and a half + + + align:start position:0% +economy you can have just 8 and a half +cents and so who is the I mean I mean + + align:start position:0% +cents and so who is the I mean I mean + + + align:start position:0% +cents and so who is the I mean I mean +who are the from an economic perspective + + align:start position:0% +who are the from an economic perspective + + + align:start position:0% +who are the from an economic perspective +who are the losers with this sort of + + align:start position:0% + + + + align:start position:0% + +deal the people who want to do the + + align:start position:0% +deal the people who want to do the + + + align:start position:0% +deal the people who want to do the +derived work why are they the losers + + align:start position:0% +derived work why are they the losers + + + align:start position:0% +derived work why are they the losers +well I mean it's a monop right they get + + align:start position:0% +well I mean it's a monop right they get + + + align:start position:0% +well I mean it's a monop right they get +to set price who gets to set the price + + align:start position:0% +to set price who gets to set the price + + + align:start position:0% +to set price who gets to set the price +government the government sets a price + + align:start position:0% +government the government sets a price + + + align:start position:0% +government the government sets a price +they say if you want to do this you can + + align:start position:0% +they say if you want to do this you can + + + align:start position:0% +they say if you want to do this you can +do it without having to ask permission + + align:start position:0% +do it without having to ask permission + + + align:start position:0% +do it without having to ask permission +all you have to do is pay 8 and a half + + align:start position:0% +all you have to do is pay 8 and a half + + + align:start position:0% +all you have to do is pay 8 and a half +cents I see well let's say the original + + align:start position:0% +cents I see well let's say the original + + + align:start position:0% +cents I see well let's say the original +songer because maybe they could have + + align:start position:0% +songer because maybe they could have + + + align:start position:0% +songer because maybe they could have +otherwise negotiated a contract for more + + align:start position:0% +otherwise negotiated a contract for more + + + align:start position:0% +otherwise negotiated a contract for more +but now they have to deal with this 8 + + align:start position:0% +but now they have to deal with this 8 + + + align:start position:0% +but now they have to deal with this 8 +and half cents okay so there's + + align:start position:0% + + + + align:start position:0% + +songwriters and sort of their output who + + align:start position:0% +songwriters and sort of their output who + + + align:start position:0% +songwriters and sort of their output who +who snarfs in the output from the + + align:start position:0% +who snarfs in the output from the + + + align:start position:0% +who snarfs in the output from the +songwriters who who uses songs as part + + align:start position:0% +songwriters who who uses songs as part + + + align:start position:0% +songwriters who who uses songs as part +of their + + align:start position:0% +of their + + + align:start position:0% +of their +business yeah record companies would be + + align:start position:0% +business yeah record companies would be + + + align:start position:0% +business yeah record companies would be +the Principal one and they're the people + + align:start position:0% +the Principal one and they're the people + + + align:start position:0% +the Principal one and they're the people +who actually record the + + align:start position:0% +who actually record the + + + align:start position:0% +who actually record the +songs and who are some other industry + + align:start position:0% +songs and who are some other industry + + + align:start position:0% +songs and who are some other industry +that use + + align:start position:0% + + + + align:start position:0% + +songs yeah like ads and movies + + align:start position:0% +songs yeah like ads and movies + + + align:start position:0% +songs yeah like ads and movies +right okay what's becoming big money + + align:start position:0% +right okay what's becoming big money + + + align:start position:0% +right okay what's becoming big money +these days in the sawing + + align:start position:0% + + + + align:start position:0% + +industry this is like a huge source of + + align:start position:0% +industry this is like a huge source of + + + align:start position:0% +industry this is like a huge source of +Revenue now for songwriters ringtones + + align:start position:0% +Revenue now for songwriters ringtones + + + align:start position:0% +Revenue now for songwriters ringtones +exactly this is like huge business uh + + align:start position:0% +exactly this is like huge business uh + + + align:start position:0% +exactly this is like huge business uh +mostly because the people who want to do + + align:start position:0% +mostly because the people who want to do + + + align:start position:0% +mostly because the people who want to do +ringtones don't have to get permission + + align:start position:0% +ringtones don't have to get permission + + + align:start position:0% +ringtones don't have to get permission +from the record + + align:start position:0% +from the record + + + align:start position:0% +from the record +companies do not no no because they're + + align:start position:0% +companies do not no no because they're + + + align:start position:0% +companies do not no no because they're +not taking like the Britney Spears + + align:start position:0% +not taking like the Britney Spears + + + align:start position:0% +not taking like the Britney Spears +version of oops I Did It Again they're + + align:start position:0% +version of oops I Did It Again they're + + + align:start position:0% +version of oops I Did It Again they're +just + + align:start position:0% +just + + + align:start position:0% +just +like and you don't have to pay Britney + + align:start position:0% +like and you don't have to pay Britney + + + align:start position:0% +like and you don't have to pay Britney +Spears for that okay so songwriters pay + + align:start position:0% +Spears for that okay so songwriters pay + + + align:start position:0% +Spears for that okay so songwriters pay +to these groups and also like + + align:start position:0% + + + + align:start position:0% + +jukeboxes song songwriters are sort of + + align:start position:0% +jukeboxes song songwriters are sort of + + + align:start position:0% +jukeboxes song songwriters are sort of +the I guess maybe um I mean before you + + align:start position:0% +the I guess maybe um I mean before you + + + align:start position:0% +the I guess maybe um I mean before you +we should do this a little more + + align:start position:0% +we should do this a little more + + + align:start position:0% +we should do this a little more +carefully because before you something + + align:start position:0% +carefully because before you something + + + align:start position:0% +carefully because before you something +can be in an ad or a movie it has to + + align:start position:0% +can be in an ad or a movie it has to + + + align:start position:0% +can be in an ad or a movie it has to +come from a record company + + align:start position:0% +come from a record company + + + align:start position:0% +come from a record company +right so it's really the record + + align:start position:0% +right so it's really the record + + + align:start position:0% +right so it's really the record +companies who go to the Juke boxes and + + align:start position:0% +companies who go to the Juke boxes and + + + align:start position:0% +companies who go to the Juke boxes and +the uh what was the other + + align:start position:0% +the uh what was the other + + + align:start position:0% +the uh what was the other +on ads and movies and who else benefits + + align:start position:0% +on ads and movies and who else benefits + + + align:start position:0% +on ads and movies and who else benefits +from the record companies who else takes + + align:start position:0% +from the record companies who else takes + + + align:start position:0% +from the record companies who else takes +recordings and makes money off of + + align:start position:0% + + + + align:start position:0% + +them well they're sort of they work part + + align:start position:0% +them well they're sort of they work part + + + align:start position:0% +them well they're sort of they work part +of the record yeah + + align:start position:0% + + + + align:start position:0% + +radio Okay and then who plays radio and + + align:start position:0% +radio Okay and then who plays radio and + + + align:start position:0% +radio Okay and then who plays radio and +gets money from it it's people + + align:start position:0% + + + + align:start position:0% + +like I don't know any store that you go + + align:start position:0% +like I don't know any store that you go + + + align:start position:0% +like I don't know any store that you go +in like Sears that might have the radio + + align:start position:0% +in like Sears that might have the radio + + + align:start position:0% +in like Sears that might have the radio +on so there's this whole you know chain + + align:start position:0% +on so there's this whole you know chain + + + align:start position:0% +on so there's this whole you know chain +here and uh Congress could have let this + + align:start position:0% +here and uh Congress could have let this + + + align:start position:0% +here and uh Congress could have let this +develop sort of in a free market way but + + align:start position:0% +develop sort of in a free market way but + + + align:start position:0% +develop sort of in a free market way but +they chose not to um mostly because uh + + align:start position:0% +they chose not to um mostly because uh + + + align:start position:0% +they chose not to um mostly because uh +in the early 1900s the dominant industry + + align:start position:0% +in the early 1900s the dominant industry + + + align:start position:0% +in the early 1900s the dominant industry +was not record companies or ringtones it + + align:start position:0% +was not record companies or ringtones it + + + align:start position:0% +was not record companies or ringtones it +was songwriters they were hugely + + align:start position:0% +was songwriters they were hugely + + + align:start position:0% +was songwriters they were hugely +dominant you know the ASCAP and BMI were + + align:start position:0% +dominant you know the ASCAP and BMI were + + + align:start position:0% +dominant you know the ASCAP and BMI were +even more power you know they're very + + align:start position:0% +even more power you know they're very + + + align:start position:0% +even more power you know they're very +powerful and people would go around + + align:start position:0% +powerful and people would go around + + + align:start position:0% +powerful and people would go around +playing things and and ask cap and the + + align:start position:0% +playing things and and ask cap and the + + + align:start position:0% +playing things and and ask cap and the +the songwriters were you know they were + + align:start position:0% +the songwriters were you know they were + + + align:start position:0% +the songwriters were you know they were +where it was at and there was a new + + align:start position:0% +where it was at and there was a new + + + align:start position:0% +where it was at and there was a new +industry that wanted to get in on things + + align:start position:0% +industry that wanted to get in on things + + + align:start position:0% +industry that wanted to get in on things +uh the player piano + + align:start position:0% + + + + align:start position:0% + +industry and uh in 1908 there was a + + align:start position:0% +industry and uh in 1908 there was a + + + align:start position:0% +industry and uh in 1908 there was a +Supreme Court decision called White + + align:start position:0% +Supreme Court decision called White + + + align:start position:0% +Supreme Court decision called White +Smith the question is whether player + + align:start position:0% +Smith the question is whether player + + + align:start position:0% +Smith the question is whether player +piano roles um if you distribute a + + align:start position:0% +piano roles um if you distribute a + + + align:start position:0% +piano roles um if you distribute a +player piano role of a song is that a + + align:start position:0% +player piano role of a song is that a + + + align:start position:0% +player piano role of a song is that a +recording of the song or is it a copy of + + align:start position:0% +recording of the song or is it a copy of + + + align:start position:0% +recording of the song or is it a copy of +the song you know what kind of thing is + + align:start position:0% +the song you know what kind of thing is + + + align:start position:0% +the song you know what kind of thing is +it and was a Supreme Court decision that + + align:start position:0% +it and was a Supreme Court decision that + + + align:start position:0% +it and was a Supreme Court decision that +went one way and then Congress didn't + + align:start position:0% +went one way and then Congress didn't + + + align:start position:0% +went one way and then Congress didn't +like the result and so in 1909 they + + align:start position:0% +like the result and so in 1909 they + + + align:start position:0% +like the result and so in 1909 they +passed the the Copyright Act of 1909 + + align:start position:0% +passed the the Copyright Act of 1909 + + + align:start position:0% +passed the the Copyright Act of 1909 +which was the major revision before 1976 + + align:start position:0% +which was the major revision before 1976 + + + align:start position:0% +which was the major revision before 1976 +and most of what we still have about + + align:start position:0% +and most of what we still have about + + + align:start position:0% +and most of what we still have about +music regulation or the way that music + + align:start position:0% +music regulation or the way that music + + + align:start position:0% +music regulation or the way that music +is legislated comes from 1909 and player + + align:start position:0% +is legislated comes from 1909 and player + + + align:start position:0% +is legislated comes from 1909 and player +piano roles people everybody knows what + + align:start position:0% +piano roles people everybody knows what + + + align:start position:0% +piano roles people everybody knows what +a player piano is + + align:start position:0% +a player piano is + + + align:start position:0% +a player piano is +right okay so anyway so Congress did not + + align:start position:0% +right okay so anyway so Congress did not + + + align:start position:0% +right okay so anyway so Congress did not +there's not really a a sort of + + align:start position:0% +there's not really a a sort of + + + align:start position:0% +there's not really a a sort of +unrestrained Market here the Congress + + align:start position:0% +unrestrained Market here the Congress + + + align:start position:0% +unrestrained Market here the Congress +has legis ated here that if a if a + + align:start position:0% +has legis ated here that if a if a + + + align:start position:0% +has legis ated here that if a if a +record company or somebody else wants to + + align:start position:0% +record company or somebody else wants to + + + align:start position:0% +record company or somebody else wants to +get something from a songwriter and if + + align:start position:0% +get something from a songwriter and if + + + align:start position:0% +get something from a songwriter and if +the song has already been recorded once + + align:start position:0% +the song has already been recorded once + + + align:start position:0% +the song has already been recorded once +they don't have to get permission they + + align:start position:0% +they don't have to get permission they + + + align:start position:0% +they don't have to get permission they +just pay this government set price of + + align:start position:0% +just pay this government set price of + + + align:start position:0% +just pay this government set price of +basically 8 and. half cents per so uh + + align:start position:0% +basically 8 and. half cents per so uh + + + align:start position:0% +basically 8 and. half cents per so uh +per copy it's more if the song is longer + + align:start position:0% +per copy it's more if the song is longer + + + align:start position:0% +per copy it's more if the song is longer +yeah you call that a + + align:start position:0% +yeah you call that a + + + align:start position:0% +yeah you call that a +royalty uh songwriters call it a + + align:start position:0% +royalty uh songwriters call it a + + + align:start position:0% +royalty uh songwriters call it a +mechanical maybe a mechanical royalty or + + align:start position:0% +mechanical maybe a mechanical royalty or + + + align:start position:0% +mechanical maybe a mechanical royalty or +a mechanical license fee um do you have + + align:start position:0% +a mechanical license fee um do you have + + + align:start position:0% +a mechanical license fee um do you have +is it the recording + + align:start position:0% +is it the recording + + + align:start position:0% +is it the recording +Association of America got that right + + align:start position:0% +Association of America got that right + + + align:start position:0% +Association of America got that right +that's enforcing this I know there's a + + align:start position:0% +that's enforcing this I know there's a + + + align:start position:0% +that's enforcing this I know there's a +big well the record industry assoc I + + align:start position:0% +big well the record industry assoc I + + + align:start position:0% +big well the record industry assoc I +mean that's an association of record + + align:start position:0% +mean that's an association of record + + + align:start position:0% +mean that's an association of record +companies right they that make sure you + + align:start position:0% +companies right they that make sure you + + + align:start position:0% +companies right they that make sure you +know if you're taking the song you're + + align:start position:0% +know if you're taking the song you're + + + align:start position:0% +know if you're taking the song you're +paying the money right for copyright + + align:start position:0% +paying the money right for copyright + + + align:start position:0% +paying the money right for copyright +well no they're the ones paying the + + align:start position:0% +well no they're the ones paying the + + + align:start position:0% +well no they're the ones paying the +money um to the songwriters the + + align:start position:0% +money um to the songwriters the + + + align:start position:0% +money um to the songwriters the +songwriters have their own associations + + align:start position:0% +songwriters have their own associations + + + align:start position:0% +songwriters have their own associations +called like The National Music + + align:start position:0% +called like The National Music + + + align:start position:0% +called like The National Music +Publishers Association and the Harry Fox + + align:start position:0% +Publishers Association and the Harry Fox + + + align:start position:0% +Publishers Association and the Harry Fox +agency those organizations represent + + align:start position:0% +agency those organizations represent + + + align:start position:0% +agency those organizations represent +songwriters and there's this whole + + align:start position:0% +songwriters and there's this whole + + + align:start position:0% +songwriters and there's this whole +battle because historically the song + + align:start position:0% +battle because historically the song + + + align:start position:0% +battle because historically the song +writers were incredibly dominant and now + + align:start position:0% +writers were incredibly dominant and now + + + align:start position:0% +writers were incredibly dominant and now +you know the the record industry is much + + align:start position:0% +you know the the record industry is much + + + align:start position:0% +you know the the record industry is much +more in the public Consciousness so they + + align:start position:0% +more in the public Consciousness so they + + + align:start position:0% +more in the public Consciousness so they +have started + + align:start position:0% +have started + + + align:start position:0% +have started +to um sort of be more dominant + + align:start position:0% +to um sort of be more dominant + + + align:start position:0% +to um sort of be more dominant +um but uh for instance for online for + + align:start position:0% +um but uh for instance for online for + + + align:start position:0% +um but uh for instance for online for +things like Napster the new Napster and + + align:start position:0% +things like Napster the new Napster and + + + align:start position:0% +things like Napster the new Napster and +um what's another one I don't know rapid + + align:start position:0% +um what's another one I don't know rapid + + + align:start position:0% +um what's another one I don't know rapid +those online services for those to + + align:start position:0% +those online services for those to + + + align:start position:0% +those online services for those to +happen the record companies had to sort + + align:start position:0% +happen the record companies had to sort + + + align:start position:0% +happen the record companies had to sort +of come begging to the songwriters and + + align:start position:0% +of come begging to the songwriters and + + + align:start position:0% +of come begging to the songwriters and +say please let us put our songs on + + align:start position:0% +say please let us put our songs on + + + align:start position:0% +say please let us put our songs on +Napster or whatever and in fact um in + + align:start position:0% +Napster or whatever and in fact um in + + + align:start position:0% +Napster or whatever and in fact um in +2001 Universal which is one of the four + + align:start position:0% +2001 Universal which is one of the four + + + align:start position:0% +2001 Universal which is one of the four +record labels then one of the five + + align:start position:0% +record labels then one of the five + + + align:start position:0% +record labels then one of the five +record labels Universal put it songs + + align:start position:0% +record labels Universal put it songs + + + align:start position:0% +record labels Universal put it songs +online for people to sort of you know to + + align:start position:0% +online for people to sort of you know to + + + align:start position:0% +online for people to sort of you know to +um to stream on demand and uh it was + + align:start position:0% +um to stream on demand and uh it was + + + align:start position:0% +um to stream on demand and uh it was +called farm club and I mean these were + + align:start position:0% +called farm club and I mean these were + + + align:start position:0% +called farm club and I mean these were +Universal's own songs was how they saw + + align:start position:0% +Universal's own songs was how they saw + + + align:start position:0% +Universal's own songs was how they saw +it but of course they weren't the + + align:start position:0% +it but of course they weren't the + + + align:start position:0% +it but of course they weren't the +songwriters and uh the songwriter says + + align:start position:0% +songwriters and uh the songwriter says + + + align:start position:0% +songwriters and uh the songwriter says +well what are you doing here and + + align:start position:0% +well what are you doing here and + + + align:start position:0% +well what are you doing here and +Universal says well we already paid you + + align:start position:0% +Universal says well we already paid you + + + align:start position:0% +Universal says well we already paid you +the 8 and a half cent so we can let + + align:start position:0% +the 8 and a half cent so we can let + + + align:start position:0% +the 8 and a half cent so we can let +people stream them whenever they want + + align:start position:0% +people stream them whenever they want + + + align:start position:0% +people stream them whenever they want +and the S was like that's not covered + + align:start position:0% +and the S was like that's not covered + + + align:start position:0% +and the S was like that's not covered +under your section 115 license and they + + align:start position:0% +under your section 115 license and they + + + align:start position:0% +under your section 115 license and they +went to court and the um the SAR letters + + align:start position:0% +went to court and the um the SAR letters + + + align:start position:0% +went to court and the um the SAR letters +won so um so then they had to negotiate + + align:start position:0% +won so um so then they had to negotiate + + + align:start position:0% +won so um so then they had to negotiate +this agreement and that it was between + + align:start position:0% +this agreement and that it was between + + + align:start position:0% +this agreement and that it was between +all of the record companies on the one + + align:start position:0% +all of the record companies on the one + + + align:start position:0% +all of the record companies on the one +hand and all of the major major music + + align:start position:0% +hand and all of the major major music + + + align:start position:0% +hand and all of the major major music +Publishers on the other hand about how + + align:start position:0% +Publishers on the other hand about how + + + align:start position:0% +Publishers on the other hand about how +the royalties were going to be split up + + align:start position:0% +the royalties were going to be split up + + + align:start position:0% +the royalties were going to be split up +for Napster and these new services and + + align:start position:0% +for Napster and these new services and + + + align:start position:0% +for Napster and these new services and +in fact it's still not actually decided + + align:start position:0% +in fact it's still not actually decided + + + align:start position:0% +in fact it's still not actually decided +how the royalties are going to be split + + align:start position:0% +how the royalties are going to be split + + + align:start position:0% +how the royalties are going to be split +up but the record companies are paying + + align:start position:0% +up but the record companies are paying + + + align:start position:0% +up but the record companies are paying +like a million dollars a year into some + + align:start position:0% +like a million dollars a year into some + + + align:start position:0% +like a million dollars a year into some +trust fund and then when they finally do + + align:start position:0% +trust fund and then when they finally do + + + align:start position:0% +trust fund and then when they finally do +agree how it's going to be split up + + align:start position:0% +agree how it's going to be split up + + + align:start position:0% +agree how it's going to be split up +they'll split it up but it's you know a + + align:start position:0% +they'll split it up but it's you know a + + + align:start position:0% +they'll split it up but it's you know a +lot of these details are not worked + + align:start position:0% +lot of these details are not worked + + + align:start position:0% +lot of these details are not worked +out okay so this one is sort of + + align:start position:0% +out okay so this one is sort of + + + align:start position:0% +out okay so this one is sort of +regulated by Congress and then um you + + align:start position:0% +regulated by Congress and then um you + + + align:start position:0% +regulated by Congress and then um you +know the Jukebox relationship is also + + align:start position:0% +know the Jukebox relationship is also + + + align:start position:0% +know the Jukebox relationship is also +regulated by Congress I don't know if + + align:start position:0% +regulated by Congress I don't know if + + + align:start position:0% +regulated by Congress I don't know if +you guys saw but there's a Congress set + + align:start position:0% +you guys saw but there's a Congress set + + + align:start position:0% +you guys saw but there's a Congress set +price for that Congress is so the record + + align:start position:0% +price for that Congress is so the record + + + align:start position:0% +price for that Congress is so the record +companies are sort of ripping off the + + align:start position:0% +companies are sort of ripping off the + + + align:start position:0% +companies are sort of ripping off the +songwriters right do people sort of + + align:start position:0% +songwriters right do people sort of + + + align:start position:0% +songwriters right do people sort of +agree with me here I mean it's a sort of + + align:start position:0% +agree with me here I mean it's a sort of + + + align:start position:0% +agree with me here I mean it's a sort of +a quick and dirty way to describe it but + + align:start position:0% +a quick and dirty way to describe it but + + + align:start position:0% +a quick and dirty way to describe it but +the record companies are not paying the + + align:start position:0% +the record companies are not paying the + + + align:start position:0% +the record companies are not paying the +market rate for these songs Congress has + + align:start position:0% +market rate for these songs Congress has + + + align:start position:0% +market rate for these songs Congress has +set a sort of maximum price + + align:start position:0% + + + + align:start position:0% + +um and the record companies you know + + align:start position:0% +um and the record companies you know + + + align:start position:0% +um and the record companies you know +they they strongly oppose this is called + + align:start position:0% +they they strongly oppose this is called + + + align:start position:0% +they they strongly oppose this is called +compulsory licensing the record + + align:start position:0% +compulsory licensing the record + + + align:start position:0% +compulsory licensing the record +companies strongly oppose compulsory + + align:start position:0% +companies strongly oppose compulsory + + + align:start position:0% +companies strongly oppose compulsory +licensing on their own products um you + + align:start position:0% +licensing on their own products um you + + + align:start position:0% +licensing on their own products um you +know people say well you should just let + + align:start position:0% +know people say well you should just let + + + align:start position:0% +know people say well you should just let +all file sharing be legal and we just + + align:start position:0% +all file sharing be legal and we just + + + align:start position:0% +all file sharing be legal and we just +have to pay you know $5 a month to the + + align:start position:0% +have to pay you know $5 a month to the + + + align:start position:0% +have to pay you know $5 a month to the +government and they would split it up + + align:start position:0% +government and they would split it up + + + align:start position:0% +government and they would split it up +among the record companies and that + + align:start position:0% +among the record companies and that + + + align:start position:0% +among the record companies and that +would be a better way of doing it than + + align:start position:0% +would be a better way of doing it than + + + align:start position:0% +would be a better way of doing it than +going after individual file sharers + + align:start position:0% +going after individual file sharers + + + align:start position:0% +going after individual file sharers +people say this and uh you know the + + align:start position:0% +people say this and uh you know the + + + align:start position:0% +people say this and uh you know the +record companies might actually get more + + align:start position:0% +record companies might actually get more + + + align:start position:0% +record companies might actually get more +money if that were the case nobody + + align:start position:0% +money if that were the case nobody + + + align:start position:0% +money if that were the case nobody +really knows but the record company say + + align:start position:0% +really knows but the record company say + + + align:start position:0% +really knows but the record company say +no that is not the American way you know + + align:start position:0% +no that is not the American way you know + + + align:start position:0% +no that is not the American way you know +we need the power to choose whether to + + align:start position:0% +we need the power to choose whether to + + + align:start position:0% +we need the power to choose whether to +license our works or not and um if you + + align:start position:0% +license our works or not and um if you + + + align:start position:0% +license our works or not and um if you +have compulsory licenses for music that + + align:start position:0% +have compulsory licenses for music that + + + align:start position:0% +have compulsory licenses for music that +will lead to compulsory licenses for + + align:start position:0% +will lead to compulsory licenses for + + + align:start position:0% +will lead to compulsory licenses for +books and compulsory licenses for movies + + align:start position:0% +books and compulsory licenses for movies + + + align:start position:0% +books and compulsory licenses for movies +and and you know the having government + + align:start position:0% +and and you know the having government + + + align:start position:0% +and and you know the having government +set prices centrally is just ridiculous + + align:start position:0% +set prices centrally is just ridiculous + + + align:start position:0% +set prices centrally is just ridiculous +uh of course the record companies are + + align:start position:0% +uh of course the record companies are + + + align:start position:0% +uh of course the record companies are +the principal beneficiary of this compul + + align:start position:0% +the principal beneficiary of this compul + + + align:start position:0% +the principal beneficiary of this compul +on the compulsory license of their input + + align:start position:0% +on the compulsory license of their input + + + align:start position:0% +on the compulsory license of their input +but they don't want a compulsory license + + align:start position:0% +but they don't want a compulsory license + + + align:start position:0% +but they don't want a compulsory license +on their + + align:start position:0% +on their + + + align:start position:0% +on their +output + + align:start position:0% +output + + + align:start position:0% +output +um uh In fairness the record companies + + align:start position:0% +um uh In fairness the record companies + + + align:start position:0% +um uh In fairness the record companies +have more recently said well we're + + align:start position:0% +have more recently said well we're + + + align:start position:0% +have more recently said well we're +willing to give this up but you know + + align:start position:0% +willing to give this up but you know + + + align:start position:0% +willing to give this up but you know +that's what they say okay so on the + + align:start position:0% +that's what they say okay so on the + + + align:start position:0% +that's what they say okay so on the +record company output of course then the + + align:start position:0% +record company output of course then the + + + align:start position:0% +record company output of course then the +these sort of derivative Industries get + + align:start position:0% +these sort of derivative Industries get + + + align:start position:0% +these sort of derivative Industries get +to rip off the record companies also + + align:start position:0% +to rip off the record companies also + + + align:start position:0% +to rip off the record companies also +under this Congressional scheme where + + align:start position:0% +under this Congressional scheme where + + + align:start position:0% +under this Congressional scheme where +jukeboxes can rip you know they don't + + align:start position:0% +jukeboxes can rip you know they don't + + + align:start position:0% +jukeboxes can rip you know they don't +have to really pay the full rate it's I + + align:start position:0% +have to really pay the full rate it's I + + + align:start position:0% +have to really pay the full rate it's I +don't think they have to pay anything to + + align:start position:0% +don't think they have to pay anything to + + + align:start position:0% +don't think they have to pay anything to +the record companies actually they just + + align:start position:0% +the record companies actually they just + + + align:start position:0% +the record companies actually they just +have to pay the songwriters and even + + align:start position:0% +have to pay the songwriters and even + + + align:start position:0% +have to pay the songwriters and even +that is a congressionally set rate and + + align:start position:0% +that is a congressionally set rate and + + + align:start position:0% +that is a congressionally set rate and +radio is the worst offender do they have + + align:start position:0% +radio is the worst offender do they have + + + align:start position:0% +radio is the worst offender do they have +to pay anything to the record + + align:start position:0% +to pay anything to the record + + + align:start position:0% +to pay anything to the record +companies nothing all they only have to + + align:start position:0% +companies nothing all they only have to + + + align:start position:0% +companies nothing all they only have to +pay the + + align:start position:0% +pay the + + + align:start position:0% +pay the +songwriters and is that a government set + + align:start position:0% + + + + align:start position:0% + +price generally not like when a + + align:start position:0% +price generally not like when a + + + align:start position:0% +price generally not like when a +commercial radio station pays uh it's + + align:start position:0% +commercial radio station pays uh it's + + + align:start position:0% +commercial radio station pays uh it's +pays ASCAP in BMI + + align:start position:0% +pays ASCAP in BMI + + + align:start position:0% +pays ASCAP in BMI +that's you know it's well that's + + align:start position:0% +that's you know it's well that's + + + align:start position:0% +that's you know it's well that's +actually kind of a government set rate I + + align:start position:0% +actually kind of a government set rate I + + + align:start position:0% +actually kind of a government set rate I +mean uh it's not set by the coperate ACT + + align:start position:0% +mean uh it's not set by the coperate ACT + + + align:start position:0% +mean uh it's not set by the coperate ACT +but it is set by uh an Anti-Trust + + align:start position:0% +but it is set by uh an Anti-Trust + + + align:start position:0% +but it is set by uh an Anti-Trust +lawsuit because ASCAP of course is this + + align:start position:0% +lawsuit because ASCAP of course is this + + + align:start position:0% +lawsuit because ASCAP of course is this +huge conglom at of songwriters that have + + align:start position:0% +huge conglom at of songwriters that have + + + align:start position:0% +huge conglom at of songwriters that have +sort of come together to demand + + align:start position:0% +sort of come together to demand + + + align:start position:0% +sort of come together to demand +licensing and that's not really + + align:start position:0% +licensing and that's not really + + + align:start position:0% +licensing and that's not really +permitted under the Monopoly the + + align:start position:0% +permitted under the Monopoly the + + + align:start position:0% +permitted under the Monopoly the +Anti-Trust laws and so there's all this + + align:start position:0% +Anti-Trust laws and so there's all this + + + align:start position:0% +Anti-Trust laws and so there's all this +court regulation so in practice it is + + align:start position:0% +court regulation so in practice it is + + + align:start position:0% +court regulation so in practice it is +sort of a government set + + align:start position:0% +sort of a government set + + + align:start position:0% +sort of a government set +rate and if if you go to ASAP and say + + align:start position:0% +rate and if if you go to ASAP and say + + + align:start position:0% +rate and if if you go to ASAP and say +and they say okay we want 10% of your + + align:start position:0% +and they say okay we want 10% of your + + + align:start position:0% +and they say okay we want 10% of your +profits and then you can play all the + + align:start position:0% +profits and then you can play all the + + + align:start position:0% +profits and then you can play all the +music you want and if you think that's + + align:start position:0% +music you want and if you think that's + + + align:start position:0% +music you want and if you think that's +too much you can go to this special + + align:start position:0% +too much you can go to this special + + + align:start position:0% +too much you can go to this special +Court in New York and say that's too + + align:start position:0% +Court in New York and say that's too + + + align:start position:0% +Court in New York and say that's too +much and the court has this hearing and + + align:start position:0% +much and the court has this hearing and + + + align:start position:0% +much and the court has this hearing and +anyway but generally this is not really + + align:start position:0% +anyway but generally this is not really + + + align:start position:0% +anyway but generally this is not really +a government set right although for some + + align:start position:0% +a government set right although for some + + + align:start position:0% +a government set right although for some +some radio stations like College radio + + align:start position:0% +some radio stations like College radio + + + align:start position:0% +some radio stations like College radio +stations Congress um the government does + + align:start position:0% +stations Congress um the government does + + + align:start position:0% +stations Congress um the government does +set the the maximum + + align:start position:0% +set the the maximum + + + align:start position:0% +set the the maximum +price okay anyway and then uh this radio + + align:start position:0% +price okay anyway and then uh this radio + + + align:start position:0% +price okay anyway and then uh this radio +Sears relationship again uh Sears would + + align:start position:0% +Sears relationship again uh Sears would + + + align:start position:0% +Sears relationship again uh Sears would +have to pay the songwriters for having + + align:start position:0% +have to pay the songwriters for having + + + align:start position:0% +have to pay the songwriters for having +the radio on again by going to ASAP but + + align:start position:0% +the radio on again by going to ASAP but + + + align:start position:0% +the radio on again by going to ASAP but +they don't have to pay the record + + align:start position:0% +they don't have to pay the record + + + align:start position:0% +they don't have to pay the record +companies a dime and they don't have to + + align:start position:0% +companies a dime and they don't have to + + + align:start position:0% +companies a dime and they don't have to +pay the radio stations to Dime um now is + + align:start position:0% +pay the radio stations to Dime um now is + + + align:start position:0% +pay the radio stations to Dime um now is +that really fair + + align:start position:0% + + + + align:start position:0% + +I mean I don't know but in in currently + + align:start position:0% +I mean I don't know but in in currently + + + align:start position:0% +I mean I don't know but in in currently +the law is that radio stations don't + + align:start position:0% +the law is that radio stations don't + + + align:start position:0% +the law is that radio stations don't +really have any proprietary interest in + + align:start position:0% +really have any proprietary interest in + + + align:start position:0% +really have any proprietary interest in +the works that they're broadcasting they + + align:start position:0% +the works that they're broadcasting they + + + align:start position:0% +the works that they're broadcasting they +don't own any sort of exclusive right to + + align:start position:0% +don't own any sort of exclusive right to + + + align:start position:0% +don't own any sort of exclusive right to +their broadcast it's just the owners of + + align:start position:0% +their broadcast it's just the owners of + + + align:start position:0% +their broadcast it's just the owners of +the works now there's you know some talk + + align:start position:0% +the works now there's you know some talk + + + align:start position:0% +the works now there's you know some talk +of changing that but that's the way it + + align:start position:0% +of changing that but that's the way it + + + align:start position:0% +of changing that but that's the way it +is now that okay so people have taken + + align:start position:0% +is now that okay so people have taken + + + align:start position:0% +is now that okay so people have taken +economics what's the problem when you + + align:start position:0% +economics what's the problem when you + + + align:start position:0% +economics what's the problem when you +set up the sort of Highly regulated + + align:start position:0% +set up the sort of Highly regulated + + + align:start position:0% +set up the sort of Highly regulated +government price controlled relationship + + align:start position:0% +government price controlled relationship + + + align:start position:0% +government price controlled relationship +among all these different entities in a + + align:start position:0% +among all these different entities in a + + + align:start position:0% +among all these different entities in a +in a + + align:start position:0% + + + + align:start position:0% + +market Michael the equilibrium at any + + align:start position:0% +market Michael the equilibrium at any + + + align:start position:0% +market Michael the equilibrium at any +point are staggering L yeah you're + + align:start position:0% +point are staggering L yeah you're + + + align:start position:0% +point are staggering L yeah you're +probably not in equilibrium and if some + + align:start position:0% +probably not in equilibrium and if some + + + align:start position:0% +probably not in equilibrium and if some +new entity comes in here that is able to + + align:start position:0% +new entity comes in here that is able to + + + align:start position:0% +new entity comes in here that is able to +disturb this you know this complicated + + align:start position:0% +disturb this you know this complicated + + + align:start position:0% +disturb this you know this complicated +equilibrium U then all hell can break + + align:start position:0% +equilibrium U then all hell can break + + + align:start position:0% +equilibrium U then all hell can break +loose or Napster is a bad example but + + align:start position:0% +loose or Napster is a bad example but + + + align:start position:0% +loose or Napster is a bad example but +let's say + + align:start position:0% + + + + align:start position:0% + +MP3 all hell can break loose because you + + align:start position:0% +MP3 all hell can break loose because you + + + align:start position:0% +MP3 all hell can break loose because you +know these guys didn't consider you know + + align:start position:0% +know these guys didn't consider you know + + + align:start position:0% +know these guys didn't consider you know +they they don't consider this sort of + + align:start position:0% +they they don't consider this sort of + + + align:start position:0% +they they don't consider this sort of +disruptive technology when they go to + + align:start position:0% +disruptive technology when they go to + + + align:start position:0% +disruptive technology when they go to +Congress and have this complicated + + align:start position:0% +Congress and have this complicated + + + align:start position:0% +Congress and have this complicated +system get put in place and the more + + align:start position:0% +system get put in place and the more + + + align:start position:0% +system get put in place and the more +sort of brittle it is with all these + + align:start position:0% +sort of brittle it is with all these + + + align:start position:0% +sort of brittle it is with all these +interconnected links and exceptions and + + align:start position:0% +interconnected links and exceptions and + + + align:start position:0% +interconnected links and exceptions and +exceptions to the exceptions and + + align:start position:0% +exceptions to the exceptions and + + + align:start position:0% +exceptions to the exceptions and +exceptions to the exceptions to the + + align:start position:0% +exceptions to the exceptions to the + + + align:start position:0% +exceptions to the exceptions to the +exceptions you know the more brittle it + + align:start position:0% +exceptions you know the more brittle it + + + align:start position:0% +exceptions you know the more brittle it +gets the more disruptive it can be for + + align:start position:0% +gets the more disruptive it can be for + + + align:start position:0% +gets the more disruptive it can be for +new uh Technologies and you know changes + + align:start position:0% +new uh Technologies and you know changes + + + align:start position:0% +new uh Technologies and you know changes +so what um what happened in like 1998 + + align:start position:0% +so what um what happened in like 1998 + + + align:start position:0% +so what um what happened in like 1998 +that set sort of the whole Music World + + align:start position:0% +that set sort of the whole Music World + + + align:start position:0% +that set sort of the whole Music World +on edge that we read about in a + + align:start position:0% + + + + align:start position:0% + +case Rio the Rio yeah does anybody have + + align:start position:0% +case Rio the Rio yeah does anybody have + + + align:start position:0% +case Rio the Rio yeah does anybody have +a Rio I remember them yeah it sucks I I + + align:start position:0% +a Rio I remember them yeah it sucks I I + + + align:start position:0% +a Rio I remember them yeah it sucks I I +think it was when like MP3 players I + + align:start position:0% +think it was when like MP3 players I + + + align:start position:0% +think it was when like MP3 players I +first started yeah the very first the + + align:start position:0% +first started yeah the very first the + + + align:start position:0% +first started yeah the very first the +first like portable MP3 player so we + + align:start position:0% +first like portable MP3 player so we + + + align:start position:0% +first like portable MP3 player so we +should remember now it's like what like + + align:start position:0% +should remember now it's like what like + + + align:start position:0% +should remember now it's like what like +seven years years later right I mean + + align:start position:0% +seven years years later right I mean + + + align:start position:0% +seven years years later right I mean +even though the Rio totally sucked by + + align:start position:0% +even though the Rio totally sucked by + + + align:start position:0% +even though the Rio totally sucked by +modern perspective to these guys it was + + align:start position:0% +modern perspective to these guys it was + + + align:start position:0% +modern perspective to these guys it was +like liquid + + align:start position:0% +like liquid + + + align:start position:0% +like liquid +death they were like oh my God and I + + align:start position:0% +death they were like oh my God and I + + + align:start position:0% +death they were like oh my God and I +mean if they had known about like the 60 + + align:start position:0% +mean if they had known about like the 60 + + + align:start position:0% +mean if they had known about like the 60 +gigabyte iPod that fits in your shirt + + align:start position:0% +gigabyte iPod that fits in your shirt + + + align:start position:0% +gigabyte iPod that fits in your shirt +pocket the Rio was pretty big right and + + align:start position:0% +pocket the Rio was pretty big right and + + + align:start position:0% +pocket the Rio was pretty big right and +it had a a I think a USB one + + align:start position:0% +it had a a I think a USB one + + + align:start position:0% +it had a a I think a USB one +connector than that it was parallel a + + align:start position:0% +connector than that it was parallel a + + + align:start position:0% +connector than that it was parallel a +parallel port really okay it had a + + align:start position:0% +parallel port really okay it had a + + + align:start position:0% +parallel port really okay it had a +parallel port and how much memory did it + + align:start position:0% +parallel port and how much memory did it + + + align:start position:0% +parallel port and how much memory did it +have like 32 megabytes you can get 256 + + align:start position:0% +have like 32 megabytes you can get 256 + + + align:start position:0% +have like 32 megabytes you can get 256 +smart media sticks you really hard but + + align:start position:0% +smart media sticks you really hard but + + + align:start position:0% +smart media sticks you really hard but +not at the beginning right okay so at + + align:start position:0% +not at the beginning right okay so at + + + align:start position:0% +not at the beginning right okay so at +the beginning it was 32 megabytes with a + + align:start position:0% +the beginning it was 32 megabytes with a + + + align:start position:0% +the beginning it was 32 megabytes with a +parallel port and you you could put + + align:start position:0% +parallel port and you you could put + + + align:start position:0% +parallel port and you you could put +maybe one CD in low quality on right and + + align:start position:0% +maybe one CD in low quality on right and + + + align:start position:0% +maybe one CD in low quality on right and +it would go down your P Port CH chu chu + + align:start position:0% +it would go down your P Port CH chu chu + + + align:start position:0% +it would go down your P Port CH chu chu +chu and probably people with Macintosh + + align:start position:0% +chu and probably people with Macintosh + + + align:start position:0% +chu and probably people with Macintosh +just couldn't use it right and uh and it + + align:start position:0% +just couldn't use it right and uh and it + + + align:start position:0% +just couldn't use it right and uh and it +was 32 megabytes and and it cost how + + align:start position:0% +was 32 megabytes and and it cost how + + + align:start position:0% +was 32 megabytes and and it cost how +much probably more than $100 right and + + align:start position:0% +much probably more than $100 right and + + + align:start position:0% +much probably more than $100 right and +yet it was like liquid death to the + + align:start position:0% +yet it was like liquid death to the + + + align:start position:0% +yet it was like liquid death to the +whole music industry they like oh my God + + align:start position:0% +whole music industry they like oh my God + + + align:start position:0% +whole music industry they like oh my God +and there were all these lawsuits uh I + + align:start position:0% +and there were all these lawsuits uh I + + + align:start position:0% +and there were all these lawsuits uh I +think I don't know if the songwriters + + align:start position:0% +think I don't know if the songwriters + + + align:start position:0% +think I don't know if the songwriters +were involved but certainly the + + align:start position:0% +were involved but certainly the + + + align:start position:0% +were involved but certainly the +companies but if they had known about + + align:start position:0% +companies but if they had known about + + + align:start position:0% +companies but if they had known about +the 60 GB super thin iPod video I mean + + align:start position:0% +the 60 GB super thin iPod video I mean + + + align:start position:0% +the 60 GB super thin iPod video I mean +they probably would have just gone out + + align:start position:0% +they probably would have just gone out + + + align:start position:0% +they probably would have just gone out +of business right there let's just give + + align:start position:0% +of business right there let's just give + + + align:start position:0% +of business right there let's just give +up so you should remember that when + + align:start position:0% +up so you should remember that when + + + align:start position:0% +up so you should remember that when +you're of course these guys did realize + + align:start position:0% +you're of course these guys did realize + + + align:start position:0% +you're of course these guys did realize +that they weren't just going to be + + align:start position:0% +that they weren't just going to be + + + align:start position:0% +that they weren't just going to be +dealing with the crappy Rio that you + + align:start position:0% +dealing with the crappy Rio that you + + + align:start position:0% +dealing with the crappy Rio that you +know the future if the Rio were allowed + + align:start position:0% +know the future if the Rio were allowed + + + align:start position:0% +know the future if the Rio were allowed +to live the future would hold maybe I + + align:start position:0% +to live the future would hold maybe I + + + align:start position:0% +to live the future would hold maybe I +don't know if they knew about 60 + + align:start position:0% +don't know if they knew about 60 + + + align:start position:0% +don't know if they knew about 60 +gigabyte + + align:start position:0% +gigabyte + + + align:start position:0% +gigabyte +firewire iPods but the future would be + + align:start position:0% +firewire iPods but the future would be + + + align:start position:0% +firewire iPods but the future would be +Bleak in their view so um so what did + + align:start position:0% +Bleak in their view so um so what did + + + align:start position:0% +Bleak in their view so um so what did +they do + + align:start position:0% +they do + + + align:start position:0% +they do +did they revamp their business model to + + align:start position:0% +did they revamp their business model to + + + align:start position:0% +did they revamp their business model to +accommodate portable + + align:start position:0% + + + + align:start position:0% + +MP3s they Su yeah and uh what was the + + align:start position:0% +MP3s they Su yeah and uh what was the + + + align:start position:0% +MP3s they Su yeah and uh what was the +basis of their + + align:start position:0% + + + + align:start position:0% + +lawsuit what was there how why what + + align:start position:0% +lawsuit what was there how why what + + + align:start position:0% +lawsuit what was there how why what +would the Rio be doing that they could + + align:start position:0% +would the Rio be doing that they could + + + align:start position:0% +would the Rio be doing that they could +claim to do with whether they were under + + align:start position:0% +claim to do with whether they were under + + + align:start position:0% +claim to do with whether they were under +that um that whether it was a digital + + align:start position:0% +that um that whether it was a digital + + + align:start position:0% +that um that whether it was a digital +audio + + align:start position:0% +audio + + + align:start position:0% +audio +whether it's a digital audio recording + + align:start position:0% +whether it's a digital audio recording + + + align:start position:0% +whether it's a digital audio recording +device mhm + + align:start position:0% +device mhm + + + align:start position:0% +device mhm +okay a + + align:start position:0% + + + + align:start position:0% + +dart + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +um where does that come from what is a + + align:start position:0% + + + + align:start position:0% + +dart what has any part of the copy act + + align:start position:0% +dart what has any part of the copy act + + + align:start position:0% +dart what has any part of the copy act +that we've read concerned darts I just + + align:start position:0% +that we've read concerned darts I just + + + align:start position:0% +that we've read concerned darts I just +told you that the only difference + + align:start position:0% +told you that the only difference + + + align:start position:0% +told you that the only difference +between digital and analog is in + + align:start position:0% +between digital and analog is in + + + align:start position:0% +between digital and analog is in +transmission + + align:start position:0% +transmission + + + align:start position:0% +transmission +right well that was not really + + align:start position:0% +right well that was not really + + + align:start position:0% +right well that was not really +true um why does it matter if something + + align:start position:0% +true um why does it matter if something + + + align:start position:0% +true um why does it matter if something +is a digital audio recording device then + + align:start position:0% +is a digital audio recording device then + + + align:start position:0% +is a digital audio recording device then +it has to use SM what's it called yeah + + align:start position:0% +it has to use SM what's it called yeah + + + align:start position:0% +it has to use SM what's it called yeah +because digital audio recording devices + + align:start position:0% +because digital audio recording devices + + + align:start position:0% +because digital audio recording devices +are are regulated by um the Copyright + + align:start position:0% +are are regulated by um the Copyright + + + align:start position:0% +are are regulated by um the Copyright +Act and did anybody read by the way the + + align:start position:0% +Act and did anybody read by the way the + + + align:start position:0% +Act and did anybody read by the way the +optional readings that I + + align:start position:0% +optional readings that I + + + align:start position:0% +optional readings that I +posted which one did you read the last + + align:start position:0% +posted which one did you read the last + + + align:start position:0% +posted which one did you read the last +one chart oh the the fairest of the fair + + align:start position:0% +one chart oh the the fairest of the fair + + + align:start position:0% +one chart oh the the fairest of the fair +use one that's good but my favorite one + + align:start position:0% +use one that's good but my favorite one + + + align:start position:0% +use one that's good but my favorite one +is nimmer's codifying copyright + + align:start position:0% +is nimmer's codifying copyright + + + align:start position:0% +is nimmer's codifying copyright +comprehensively which basically I mean + + align:start position:0% +comprehensively which basically I mean + + + align:start position:0% +comprehensively which basically I mean +it divides the Copyright Act into two + + align:start position:0% +it divides the Copyright Act into two + + + align:start position:0% +it divides the Copyright Act into two +parts the part that he calls the + + align:start position:0% +parts the part that he calls the + + + align:start position:0% +parts the part that he calls the +national copyright legislation the NCL + + align:start position:0% +national copyright legislation the NCL + + + align:start position:0% +national copyright legislation the NCL +which is sort of the parts that I signed + + align:start position:0% +which is sort of the parts that I signed + + + align:start position:0% +which is sort of the parts that I signed +and uh the the rest of it which I think + + align:start position:0% +and uh the the rest of it which I think + + + align:start position:0% +and uh the the rest of it which I think +he calls + + align:start position:0% +he calls + + + align:start position:0% +he calls +incomprehensible which um the more + + align:start position:0% +incomprehensible which um the more + + + align:start position:0% +incomprehensible which um the more +charitable term is parac copyright the + + align:start position:0% +charitable term is parac copyright the + + + align:start position:0% +charitable term is parac copyright the +parts of Copyright Act that are not + + align:start position:0% +parts of Copyright Act that are not + + + align:start position:0% +parts of Copyright Act that are not +really + + align:start position:0% +really + + + align:start position:0% +really +about Orthodox copyright and that's sort + + align:start position:0% +about Orthodox copyright and that's sort + + + align:start position:0% +about Orthodox copyright and that's sort +of what we're getting into today and one + + align:start position:0% +of what we're getting into today and one + + + align:start position:0% +of what we're getting into today and one +of those parts is this this part about + + align:start position:0% +of those parts is this this part about + + + align:start position:0% +of those parts is this this part about +digital audio recording devices which is + + align:start position:0% +digital audio recording devices which is + + + align:start position:0% +digital audio recording devices which is +called the audio home recording Act of + + align:start position:0% + + + + align:start position:0% + +1992 so what happened in 19 what was the + + align:start position:0% +1992 so what happened in 19 what was the + + + align:start position:0% +1992 so what happened in 19 what was the +the the technology like the Rio that + + align:start position:0% +the the technology like the Rio that + + + align:start position:0% +the the technology like the Rio that +came out in 1992 that was set to um ruin + + align:start position:0% +came out in 1992 that was set to um ruin + + + align:start position:0% +came out in 1992 that was set to um ruin +the record industry and Destroy them + + align:start position:0% +the record industry and Destroy them + + + align:start position:0% +the record industry and Destroy them +digital audio tapes yeah so 1992 saw the + + align:start position:0% +digital audio tapes yeah so 1992 saw the + + + align:start position:0% +digital audio tapes yeah so 1992 saw the +rise of digital audio tapes has anybody + + align:start position:0% +rise of digital audio tapes has anybody + + + align:start position:0% +rise of digital audio tapes has anybody +ever used a DAT deck do we now have like + + align:start position:0% +ever used a DAT deck do we now have like + + + align:start position:0% +ever used a DAT deck do we now have like +60 gab shirt pocket dat + + align:start position:0% +60 gab shirt pocket dat + + + align:start position:0% +60 gab shirt pocket dat +decks no but at the time dat decks were + + align:start position:0% +decks no but at the time dat decks were + + + align:start position:0% +decks no but at the time dat decks were +thought to be liquid death for the + + align:start position:0% +thought to be liquid death for the + + + align:start position:0% +thought to be liquid death for the +record industry I guess the Bost people + + align:start position:0% +record industry I guess the Bost people + + + align:start position:0% +record industry I guess the Bost people +know this quote about the Boston + + align:start position:0% +know this quote about the Boston + + + align:start position:0% +know this quote about the Boston +Strangler yeah so the + + align:start position:0% +Strangler yeah so the + + + align:start position:0% +Strangler yeah so the +um the DAT decks were like liquid death + + align:start position:0% +um the DAT decks were like liquid death + + + align:start position:0% +um the DAT decks were like liquid death +uh and and why were they so + + align:start position:0% +uh and and why were they so + + + align:start position:0% +uh and and why were they so +threatening you copy them you could copy + + align:start position:0% +threatening you copy them you could copy + + + align:start position:0% +threatening you copy them you could copy +the dats and but you could copy like + + align:start position:0% +the dats and but you could copy like + + + align:start position:0% +the dats and but you could copy like +tapes + + align:start position:0% +tapes + + + align:start position:0% +tapes +right you could make a perfect copy of a + + align:start position:0% +right you could make a perfect copy of a + + + align:start position:0% +right you could make a perfect copy of a +d and this the um the uh the the copy + + align:start position:0% +d and this the um the uh the the copy + + + align:start position:0% +d and this the um the uh the the copy +owners argue this was different this was + + align:start position:0% +owners argue this was different this was + + + align:start position:0% +owners argue this was different this was +Su generous what does that mean + + align:start position:0% +Su generous what does that mean + + + align:start position:0% +Su generous what does that mean +different of its own kind this was + + align:start position:0% +different of its own kind this was + + + align:start position:0% +different of its own kind this was +totally different than anything that had + + align:start position:0% +totally different than anything that had + + + align:start position:0% +totally different than anything that had +come before because with vinyl records + + align:start position:0% +come before because with vinyl records + + + align:start position:0% +come before because with vinyl records +or CDs things would degrade but with + + align:start position:0% +or CDs things would degrade but with + + + align:start position:0% +or CDs things would degrade but with +that tapes that things wouldn't degrade + + align:start position:0% +that tapes that things wouldn't degrade + + + align:start position:0% +that tapes that things wouldn't degrade +you could make a perfect copy + + align:start position:0% +you could make a perfect copy + + + align:start position:0% +you could make a perfect copy +um so the record industry says if we're + + align:start position:0% +um so the record industry says if we're + + + align:start position:0% +um so the record industry says if we're +going to start releasing our um material + + align:start position:0% +going to start releasing our um material + + + align:start position:0% +going to start releasing our um material +digitally you know the worry is that + + align:start position:0% +digitally you know the worry is that + + + align:start position:0% +digitally you know the worry is that +there could be a perfect + + align:start position:0% +there could be a perfect + + + align:start position:0% +there could be a perfect +copy now Professor susman who's an + + align:start position:0% +copy now Professor susman who's an + + + align:start position:0% +copy now Professor susman who's an +electrical engineering Professor is like + + align:start position:0% +electrical engineering Professor is like + + + align:start position:0% +electrical engineering Professor is like +Ah that's that's nothing I can make a + + align:start position:0% +Ah that's that's nothing I can make a + + + align:start position:0% +Ah that's that's nothing I can make a +almost perfect copy with my he has this + + align:start position:0% +almost perfect copy with my he has this + + + align:start position:0% +almost perfect copy with my he has this +fancy tape deck where you can adjust the + + align:start position:0% +fancy tape deck where you can adjust the + + + align:start position:0% +fancy tape deck where you can adjust the +angle of the heads for Optimum Fidelity + + align:start position:0% +angle of the heads for Optimum Fidelity + + + align:start position:0% +angle of the heads for Optimum Fidelity +and all these things but um but in + + align:start position:0% +and all these things but um but in + + + align:start position:0% +and all these things but um but in +practice it's it's sort of true right + + align:start position:0% +practice it's it's sort of true right + + + align:start position:0% +practice it's it's sort of true right +but I mean on the other hand you don't + + align:start position:0% +but I mean on the other hand you don't + + + align:start position:0% +but I mean on the other hand you don't +to be a record Pate you don't really + + align:start position:0% +to be a record Pate you don't really + + + align:start position:0% +to be a record Pate you don't really +have to make a copy of a copy right you + + align:start position:0% +have to make a copy of a copy right you + + + align:start position:0% +have to make a copy of a copy right you +could just get the original record and + + align:start position:0% +could just get the original record and + + + align:start position:0% +could just get the original record and +then make a bunch of tapes from the + + align:start position:0% +then make a bunch of tapes from the + + + align:start position:0% +then make a bunch of tapes from the +first + + align:start position:0% +first + + + align:start position:0% +first +record and those tapes would be you know + + align:start position:0% +record and those tapes would be you know + + + align:start position:0% +record and those tapes would be you know +a each a first generation copy even + + align:start position:0% +a each a first generation copy even + + + align:start position:0% +a each a first generation copy even +though you can put out thousands of them + + align:start position:0% +though you can put out thousands of them + + + align:start position:0% +though you can put out thousands of them +so I've never really understood the + + align:start position:0% +so I've never really understood the + + + align:start position:0% +so I've never really understood the +argument that it's this serial copying + + align:start position:0% +argument that it's this serial copying + + + align:start position:0% +argument that it's this serial copying +that's the problem the copy of a copy of + + align:start position:0% +that's the problem the copy of a copy of + + + align:start position:0% +that's the problem the copy of a copy of +a copy but uh the record industry sees a + + align:start position:0% +a copy but uh the record industry sees a + + + align:start position:0% +a copy but uh the record industry sees a +big difference and the ability to make + + align:start position:0% +big difference and the ability to make + + + align:start position:0% +big difference and the ability to make +perfect copies serially is very + + align:start position:0% +perfect copies serially is very + + + align:start position:0% +perfect copies serially is very +threatening them so they they went to + + align:start position:0% +threatening them so they they went to + + + align:start position:0% +threatening them so they they went to +Congress they said we need regulation to + + align:start position:0% +Congress they said we need regulation to + + + align:start position:0% +Congress they said we need regulation to +protect us because we have this you know + + align:start position:0% +protect us because we have this you know + + + align:start position:0% +protect us because we have this you know +fragile ecosystem and we need to + + align:start position:0% +fragile ecosystem and we need to + + + align:start position:0% +fragile ecosystem and we need to +preserve um preserve it they probably + + align:start position:0% +preserve um preserve it they probably + + + align:start position:0% +preserve um preserve it they probably +didn't phrase it that way they probably + + align:start position:0% +didn't phrase it that way they probably + + + align:start position:0% +didn't phrase it that way they probably +got a bunch of famous singers to go in + + align:start position:0% +got a bunch of famous singers to go in + + + align:start position:0% +got a bunch of famous singers to go in +front of Congress and say we need to + + align:start position:0% +front of Congress and say we need to + + + align:start position:0% +front of Congress and say we need to +help keep making a living which you know + + align:start position:0% +help keep making a living which you know + + + align:start position:0% +help keep making a living which you know +is a good lobbying tactic because then + + align:start position:0% +is a good lobbying tactic because then + + + align:start position:0% +is a good lobbying tactic because then +the Congress people get to have their + + align:start position:0% +the Congress people get to have their + + + align:start position:0% +the Congress people get to have their +arm around Madonna and they're like you + + align:start position:0% +arm around Madonna and they're like you + + + align:start position:0% +arm around Madonna and they're like you +know so um so they said we need + + align:start position:0% +know so um so they said we need + + + align:start position:0% +know so um so they said we need +regulation and they and they got it they + + align:start position:0% +regulation and they and they got it they + + + align:start position:0% +regulation and they and they got it they +got the audio home recording Act of + + align:start position:0% +got the audio home recording Act of + + + align:start position:0% +got the audio home recording Act of +1992 and uh do do you or I have to obey + + align:start position:0% +1992 and uh do do you or I have to obey + + + align:start position:0% +1992 and uh do do you or I have to obey +the audio home recording act 19 if we're + + align:start position:0% +the audio home recording act 19 if we're + + + align:start position:0% +the audio home recording act 19 if we're +building a device would we have to obey + + align:start position:0% +building a device would we have to obey + + + align:start position:0% +building a device would we have to obey +the audio home recording act does it + + align:start position:0% +the audio home recording act does it + + + align:start position:0% +the audio home recording act does it +apply to normal people who build devices + + align:start position:0% +apply to normal people who build devices + + + align:start position:0% +apply to normal people who build devices +Norm any every + + align:start position:0% + + + + align:start position:0% + +company well what was the argument + + align:start position:0% +company well what was the argument + + + align:start position:0% +company well what was the argument +they're going after this company + + align:start position:0% +they're going after this company + + + align:start position:0% +they're going after this company +diamonded right so so yes the audio home + + align:start position:0% +diamonded right so so yes the audio home + + + align:start position:0% +diamonded right so so yes the audio home +recording act has what's called a + + align:start position:0% +recording act has what's called a + + + align:start position:0% +recording act has what's called a +technology + + align:start position:0% + + + + align:start position:0% + +mandate it says if you build a digital + + align:start position:0% +mandate it says if you build a digital + + + align:start position:0% +mandate it says if you build a digital +audio recording device something that's + + align:start position:0% +audio recording device something that's + + + align:start position:0% +audio recording device something that's +defined + + align:start position:0% +defined + + + align:start position:0% +defined +um very with a lot of words in the home + + align:start position:0% +um very with a lot of words in the home + + + align:start position:0% +um very with a lot of words in the home +recording act says if you build one of + + align:start position:0% +recording act says if you build one of + + + align:start position:0% +recording act says if you build one of +these digital audio recording devices um + + align:start position:0% +these digital audio recording devices um + + + align:start position:0% +these digital audio recording devices um +you must Implement a certain technology + + align:start position:0% +you must Implement a certain technology + + + align:start position:0% +you must Implement a certain technology +so we're looking here in section + + align:start position:0% +so we're looking here in section + + + align:start position:0% +so we're looking here in section +1002 and it + + align:start position:0% +1002 and it + + + align:start position:0% +1002 and it +says prohibition so this applies to + + align:start position:0% +says prohibition so this applies to + + + align:start position:0% +says prohibition so this applies to +everybody no person none at all shall + + align:start position:0% +everybody no person none at all shall + + + align:start position:0% +everybody no person none at all shall +import manufacture distribute any + + align:start position:0% +import manufacture distribute any + + + align:start position:0% +import manufacture distribute any +digital audio recording device which + + align:start position:0% +digital audio recording device which + + + align:start position:0% +digital audio recording device which +means like that deck or CDR + + align:start position:0% +means like that deck or CDR + + + align:start position:0% +means like that deck or CDR +deck uh or digital audio interface + + align:start position:0% +deck uh or digital audio interface + + + align:start position:0% +deck uh or digital audio interface +device that does not conform to the + + align:start position:0% +device that does not conform to the + + + align:start position:0% +device that does not conform to the +serial copy management system so this is + + align:start position:0% +serial copy management system so this is + + + align:start position:0% +serial copy management system so this is +a straight government mandate they say + + align:start position:0% +a straight government mandate they say + + + align:start position:0% +a straight government mandate they say +if you build any digital audio recording + + align:start position:0% +if you build any digital audio recording + + + align:start position:0% +if you build any digital audio recording +device you must implement this + + align:start position:0% +device you must implement this + + + align:start position:0% +device you must implement this +particular + + align:start position:0% + + + + align:start position:0% + +technology + + align:start position:0% +technology + + + align:start position:0% +technology +um is there anything else like this in + + align:start position:0% +um is there anything else like this in + + + align:start position:0% +um is there anything else like this in +the in the entire federal law + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +I mean I I think there probably is + + align:start position:0% +I mean I I think there probably is + + + align:start position:0% +I mean I I think there probably is +uh although I I wish I had prepared for + + align:start position:0% +uh although I I wish I had prepared for + + + align:start position:0% +uh although I I wish I had prepared for +that + + align:start position:0% +that + + + align:start position:0% +that +question there definitely is elsewhere + + align:start position:0% +question there definitely is elsewhere + + + align:start position:0% +question there definitely is elsewhere +in the law these these technology + + align:start position:0% +in the law these these technology + + + align:start position:0% +in the law these these technology +mandates for instance oh if you're a um + + align:start position:0% +mandates for instance oh if you're a um + + + align:start position:0% +mandates for instance oh if you're a um +a hospital and you want to provide + + align:start position:0% +a hospital and you want to provide + + + align:start position:0% +a hospital and you want to provide +records to the government um or to other + + align:start position:0% +records to the government um or to other + + + align:start position:0% +records to the government um or to other +hospitals there's a very long and + + align:start position:0% +hospitals there's a very long and + + + align:start position:0% +hospitals there's a very long and +complicated act called Hippa of 1996 I + + align:start position:0% +complicated act called Hippa of 1996 I + + + align:start position:0% +complicated act called Hippa of 1996 I +think which is like the health + + align:start position:0% +think which is like the health + + + align:start position:0% +think which is like the health +information provider portability act + + align:start position:0% +information provider portability act + + + align:start position:0% +information provider portability act +something like that and that specifies + + align:start position:0% +something like that and that specifies + + + align:start position:0% +something like that and that specifies +these data formats um you know again + + align:start position:0% +these data formats um you know again + + + align:start position:0% +these data formats um you know again +this particular technology and uh I'm + + align:start position:0% +this particular technology and uh I'm + + + align:start position:0% +this particular technology and uh I'm +sure there's other examples but this one + + align:start position:0% +sure there's other examples but this one + + + align:start position:0% +sure there's other examples but this one +applies to everybody who's manufacturing + + align:start position:0% +applies to everybody who's manufacturing + + + align:start position:0% +applies to everybody who's manufacturing +technology this this kind of technology + + align:start position:0% +technology this this kind of technology + + + align:start position:0% +technology this this kind of technology +and says You must implement the serial + + align:start position:0% +and says You must implement the serial + + + align:start position:0% +and says You must implement the serial +copy management system now uh how do + + align:start position:0% +copy management system now uh how do + + + align:start position:0% +copy management system now uh how do +what how do we know what is the serial + + align:start position:0% +what how do we know what is the serial + + + align:start position:0% +what how do we know what is the serial +copy management + + align:start position:0% +copy management + + + align:start position:0% +copy management +system it it so there's a section of + + align:start position:0% +system it it so there's a section of + + + align:start position:0% +system it it so there's a section of +this act on uh definitions here it is + + align:start position:0% +this act on uh definitions here it is + + + align:start position:0% +this act on uh definitions here it is +let's see what the definitions are it + + align:start position:0% +let's see what the definitions are it + + + align:start position:0% +let's see what the definitions are it +tells us a digital audio copied + + align:start position:0% +tells us a digital audio copied + + + align:start position:0% +tells us a digital audio copied +recording and interface device and + + align:start position:0% +recording and interface device and + + + align:start position:0% +recording and interface device and +recording device recording medium you + + align:start position:0% +recording device recording medium you + + + align:start position:0% +recording device recording medium you +can see how these get kind of along + + align:start position:0% +can see how these get kind of along + + + align:start position:0% +can see how these get kind of along +let's see serial + + align:start position:0% +let's see serial + + + align:start position:0% +let's see serial +copy oh oh oh oh uh it doesn't + + align:start position:0% +copy oh oh oh oh uh it doesn't + + + align:start position:0% +copy oh oh oh oh uh it doesn't +say so this is like the central piece of + + align:start position:0% +say so this is like the central piece of + + + align:start position:0% +say so this is like the central piece of +this piece of legislation maybe they St + + align:start position:0% +this piece of legislation maybe they St + + + align:start position:0% +this piece of legislation maybe they St +in here no no they don't they actually + + align:start position:0% +in here no no they don't they actually + + + align:start position:0% +in here no no they don't they actually +uh never say it tells you what children + + align:start position:0% +uh never say it tells you what children + + + align:start position:0% +uh never say it tells you what children +are though it does tell you what + + align:start position:0% +are though it does tell you what + + + align:start position:0% +are though it does tell you what +children are yeah but it doesn't tell + + align:start position:0% +children are yeah but it doesn't tell + + + align:start position:0% +children are yeah but it doesn't tell +you oh that's that's probably because + + align:start position:0% +you oh that's that's probably because + + + align:start position:0% +you oh that's that's probably because +you all read the zitrin essay did you + + align:start position:0% +you all read the zitrin essay did you + + + align:start position:0% +you all read the zitrin essay did you +guys read that okay so it doesn't say + + align:start position:0% +guys read that okay so it doesn't say + + + align:start position:0% +guys read that okay so it doesn't say +what the Sheri copy management essay + + align:start position:0% +what the Sheri copy management essay + + + align:start position:0% +what the Sheri copy management essay +system is and why + + align:start position:0% +system is and why + + + align:start position:0% +system is and why +not a secret it's not a secret it's not + + align:start position:0% +not a secret it's not a secret it's not + + + align:start position:0% +not a secret it's not a secret it's not +it's not at all a secret it would be + + align:start position:0% +it's not at all a secret it would be + + + align:start position:0% +it's not at all a secret it would be +kind of a problem if it were a secret + + align:start position:0% +kind of a problem if it were a secret + + + align:start position:0% +kind of a problem if it were a secret +and yet it's part of the + + align:start position:0% +and yet it's part of the + + + align:start position:0% +and yet it's part of the +law uh no the reason they don't tell you + + align:start position:0% +law uh no the reason they don't tell you + + + align:start position:0% +law uh no the reason they don't tell you +in fact late versions of this bill when + + align:start position:0% +in fact late versions of this bill when + + + align:start position:0% +in fact late versions of this bill when +it was in Congress did contain the + + align:start position:0% +it was in Congress did contain the + + + align:start position:0% +it was in Congress did contain the +serial copy management system they told + + align:start position:0% +serial copy management system they told + + + align:start position:0% +serial copy management system they told +you all the technical details but + + align:start position:0% +you all the technical details but + + + align:start position:0% +you all the technical details but +Congress was very concerned that they + + align:start position:0% +Congress was very concerned that they + + + align:start position:0% +Congress was very concerned that they +did not want to mandate a particular + + align:start position:0% +did not want to mandate a particular + + + align:start position:0% +did not want to mandate a particular +technology they thought it would be set + + align:start position:0% +technology they thought it would be set + + + align:start position:0% +technology they thought it would be set +a bad precedent for the US you know + + align:start position:0% +a bad precedent for the US you know + + + align:start position:0% +a bad precedent for the US you know +because um they want to have free + + align:start position:0% +because um they want to have free + + + align:start position:0% +because um they want to have free +markets and um and these kinds of things + + align:start position:0% +markets and um and these kinds of things + + + align:start position:0% +markets and um and these kinds of things +and they they Congress generally does + + align:start position:0% +and they they Congress generally does + + + align:start position:0% +and they they Congress generally does +not like the perception that Congress is + + align:start position:0% +not like the perception that Congress is + + + align:start position:0% +not like the perception that Congress is +centrally deciding on technology for the + + align:start position:0% +centrally deciding on technology for the + + + align:start position:0% +centrally deciding on technology for the +whole country um so they did not want + + align:start position:0% +whole country um so they did not want + + + align:start position:0% +whole country um so they did not want +the the idea that Congress was setting + + align:start position:0% +the the idea that Congress was setting + + + align:start position:0% +the the idea that Congress was setting +out a technical standard by putting a + + align:start position:0% +out a technical standard by putting a + + + align:start position:0% +out a technical standard by putting a +technical standard in the law so they + + align:start position:0% +technical standard in the law so they + + + align:start position:0% +technical standard in the law so they +removed the definition of Serial copy + + align:start position:0% +removed the definition of Serial copy + + + align:start position:0% +removed the definition of Serial copy +management system from the + + align:start position:0% +management system from the + + + align:start position:0% +management system from the +law + + align:start position:0% +law + + + align:start position:0% +law +um and they put it sort of in some + + align:start position:0% +um and they put it sort of in some + + + align:start position:0% +um and they put it sort of in some +ancillary documents they're like well + + align:start position:0% +ancillary documents they're like well + + + align:start position:0% +ancillary documents they're like well +what we meant was this but it's not part + + align:start position:0% +what we meant was this but it's not part + + + align:start position:0% +what we meant was this but it's not part +of the law and + + align:start position:0% +of the law and + + + align:start position:0% +of the law and +uh in my view of course they're still + + align:start position:0% +uh in my view of course they're still + + + align:start position:0% +uh in my view of course they're still +mandating a particular technology and it + + align:start position:0% +mandating a particular technology and it + + + align:start position:0% +mandating a particular technology and it +only makes it worse to then not actually + + align:start position:0% +only makes it worse to then not actually + + + align:start position:0% +only makes it worse to then not actually +specify what it is does anybody disagree + + align:start position:0% +specify what it is does anybody disagree + + + align:start position:0% +specify what it is does anybody disagree +does anybody want to take congress's + + align:start position:0% +does anybody want to take congress's + + + align:start position:0% +does anybody want to take congress's +side + + align:start position:0% + + + + align:start position:0% + +well then they can update it more like + + align:start position:0% +well then they can update it more like + + + align:start position:0% +well then they can update it more like +if new format comes out seems + + align:start position:0% +if new format comes out seems + + + align:start position:0% +if new format comes out seems +like right any other system certified by + + align:start position:0% +like right any other system certified by + + + align:start position:0% +like right any other system certified by +the Secretary of Commerce well that's + + align:start position:0% +the Secretary of Commerce well that's + + + align:start position:0% +the Secretary of Commerce well that's +true but I don't see why they if they're + + align:start position:0% +true but I don't see why they if they're + + + align:start position:0% +true but I don't see why they if they're +going to mandate the serial copy + + align:start position:0% +going to mandate the serial copy + + + align:start position:0% +going to mandate the serial copy +management system I don't see what they + + align:start position:0% +management system I don't see what they + + + align:start position:0% +management system I don't see what they +couldn't yeah in fact I would prove it + + align:start position:0% +couldn't yeah in fact I would prove it + + + align:start position:0% +couldn't yeah in fact I would prove it +if if it has been precise where you can + + align:start position:0% +if if it has been precise where you can + + + align:start position:0% +if if it has been precise where you can +find the copy management system or uh + + align:start position:0% +find the copy management system or uh + + + align:start position:0% +find the copy management system or uh +what what organism should issue + + align:start position:0% + + + + align:start position:0% + +yeah I don't as far as I know it is not + + align:start position:0% +yeah I don't as far as I know it is not + + + align:start position:0% +yeah I don't as far as I know it is not +uh actually I don't think they ever tell + + align:start position:0% +uh actually I don't think they ever tell + + + align:start position:0% +uh actually I don't think they ever tell +you problem that they don't describe it + + align:start position:0% +you problem that they don't describe it + + + align:start position:0% +you problem that they don't describe it +because what do somebody say they you + + align:start position:0% +because what do somebody say they you + + + align:start position:0% +because what do somebody say they you +know did implement it but I mean they + + align:start position:0% +know did implement it but I mean they + + + align:start position:0% +know did implement it but I mean they +just say you know whatever that might be + + align:start position:0% +just say you know whatever that might be + + + align:start position:0% +just say you know whatever that might be +the Ser it could be problematic yes I + + align:start position:0% +the Ser it could be problematic yes I + + + align:start position:0% +the Ser it could be problematic yes I +agree it's problematic anyway um and + + align:start position:0% +agree it's problematic anyway um and + + + align:start position:0% +agree it's problematic anyway um and +then anybody who does make so what does + + align:start position:0% +then anybody who does make so what does + + + align:start position:0% +then anybody who does make so what does +the seroc copy management system + + align:start position:0% +the seroc copy management system + + + align:start position:0% +the seroc copy management system +actually do + + align:start position:0% +actually do + + + align:start position:0% +actually do +prent second generation copies right it + + align:start position:0% +prent second generation copies right it + + + align:start position:0% +prent second generation copies right it +stops you from making a copy of a copy + + align:start position:0% +stops you from making a copy of a copy + + + align:start position:0% +stops you from making a copy of a copy +so when you put in a DAT tape the DAT + + align:start position:0% +so when you put in a DAT tape the DAT + + + align:start position:0% +so when you put in a DAT tape the DAT +tape will say this is an original or + + align:start position:0% +tape will say this is an original or + + + align:start position:0% +tape will say this is an original or +this is a copy or this is a copy of a + + align:start position:0% +this is a copy or this is a copy of a + + + align:start position:0% +this is a copy or this is a copy of a +copy or maybe it's just original or copy + + align:start position:0% +copy or maybe it's just original or copy + + + align:start position:0% +copy or maybe it's just original or copy +but either way you it won't let you make + + align:start position:0% +but either way you it won't let you make + + + align:start position:0% +but either way you it won't let you make +a copy of a copy and when a DAT tape is + + align:start position:0% +a copy of a copy and when a DAT tape is + + + align:start position:0% +a copy of a copy and when a DAT tape is +connected digitally to any other dat + + align:start position:0% +connected digitally to any other dat + + + align:start position:0% +connected digitally to any other dat +deck um it'll it'll tell you whether + + align:start position:0% +deck um it'll it'll tell you whether + + + align:start position:0% +deck um it'll it'll tell you whether +it's a copy or a copy of a copy or an + + align:start position:0% +it's a copy or a copy of a copy or an + + + align:start position:0% +it's a copy or a copy of a copy or an +original or whatever and it'll increment + + align:start position:0% +original or whatever and it'll increment + + + align:start position:0% +original or whatever and it'll increment +that counter and it just will not let + + align:start position:0% +that counter and it just will not let + + + align:start position:0% +that counter and it just will not let +you make a copy of a copy what if you + + align:start position:0% +you make a copy of a copy what if you + + + align:start position:0% +you make a copy of a copy what if you +own the copyright on the + + align:start position:0% +own the copyright on the + + + align:start position:0% +own the copyright on the +recording well then will it let you like + + align:start position:0% +recording well then will it let you like + + + align:start position:0% +recording well then will it let you like +if it's your own + + align:start position:0% +if it's your own + + + align:start position:0% +if it's your own +band no I mean it wouldn't cuz otherwise + + align:start position:0% +band no I mean it wouldn't cuz otherwise + + + align:start position:0% +band no I mean it wouldn't cuz otherwise +you could just be like yeah I'm the + + align:start position:0% +you could just be like yeah I'm the + + + align:start position:0% +you could just be like yeah I'm the +copyright owner on oops I did it again + + align:start position:0% +copyright owner on oops I did it again + + + align:start position:0% +copyright owner on oops I did it again +and so even if it's your own recording + + align:start position:0% +and so even if it's your own recording + + + align:start position:0% +and so even if it's your own recording +it won't let you make a copy of a copy + + align:start position:0% +it won't let you make a copy of a copy + + + align:start position:0% +it won't let you make a copy of a copy +and this among other things basically + + align:start position:0% +and this among other things basically + + + align:start position:0% +and this among other things basically +kill that as a + + align:start position:0% +kill that as a + + + align:start position:0% +kill that as a +format um and it it this also applies to + + align:start position:0% +format um and it it this also applies to + + + align:start position:0% +format um and it it this also applies to +um CDR Decks that would go like in your + + align:start position:0% +um CDR Decks that would go like in your + + + align:start position:0% +um CDR Decks that would go like in your +stereo doesn't apply to computer CDR + + align:start position:0% +stereo doesn't apply to computer CDR + + + align:start position:0% +stereo doesn't apply to computer CDR +drives but it applies to CDR deck and it + + align:start position:0% +drives but it applies to CDR deck and it + + + align:start position:0% +drives but it applies to CDR deck and it +applies to the music cdrs the cdrs that + + align:start position:0% +applies to the music cdrs the cdrs that + + + align:start position:0% +applies to the music cdrs the cdrs that +are marketed for music that have like + + align:start position:0% +are marketed for music that have like + + + align:start position:0% +are marketed for music that have like +the word music on them but it doesn't + + align:start position:0% +the word music on them but it doesn't + + + align:start position:0% +the word music on them but it doesn't +apply to data + + align:start position:0% +apply to data + + + align:start position:0% +apply to data +cdrs uh and in fact the record industry + + align:start position:0% +cdrs uh and in fact the record industry + + + align:start position:0% +cdrs uh and in fact the record industry +probably wanted this act to regulate + + align:start position:0% +probably wanted this act to regulate + + + align:start position:0% +probably wanted this act to regulate +computers but you know they had to + + align:start position:0% +computers but you know they had to + + + align:start position:0% +computers but you know they had to +compromise and so they said okay we'll + + align:start position:0% +compromise and so they said okay we'll + + + align:start position:0% +compromise and so they said okay we'll +exempt computers because in 1992 + + align:start position:0% +exempt computers because in 1992 + + + align:start position:0% +exempt computers because in 1992 +everybody knows computers not really + + align:start position:0% +everybody knows computers not really + + + align:start position:0% +everybody knows computers not really +fast enough to handle the full audio + + align:start position:0% +fast enough to handle the full audio + + + align:start position:0% +fast enough to handle the full audio +stream from a DAT so we don't need to + + align:start position:0% +stream from a DAT so we don't need to + + + align:start position:0% +stream from a DAT so we don't need to +worry about them + + align:start position:0% +worry about them + + + align:start position:0% +worry about them +uh that proved to be a shortsighted + + align:start position:0% +uh that proved to be a shortsighted + + + align:start position:0% +uh that proved to be a shortsighted +decision anyway and then in so and then + + align:start position:0% +decision anyway and then in so and then + + + align:start position:0% +decision anyway and then in so and then +um furthermore people who manufacture + + align:start position:0% +um furthermore people who manufacture + + + align:start position:0% +um furthermore people who manufacture +these dat decks and the DAT media and um + + align:start position:0% +these dat decks and the DAT media and um + + + align:start position:0% +these dat decks and the DAT media and um +the the music cdrs they all have to pay + + align:start position:0% +the the music cdrs they all have to pay + + + align:start position:0% +the the music cdrs they all have to pay +a tax that goes to the government it's + + align:start position:0% +a tax that goes to the government it's + + + align:start position:0% +a tax that goes to the government it's +like a two or 3% tax and the idea is to + + align:start position:0% +like a two or 3% tax and the idea is to + + + align:start position:0% +like a two or 3% tax and the idea is to +compensate copyright owners for the + + align:start position:0% +compensate copyright owners for the + + + align:start position:0% +compensate copyright owners for the +losses that they're getting from these + + align:start position:0% +losses that they're getting from these + + + align:start position:0% +losses that they're getting from these +first generation perfect copies and the + + align:start position:0% +first generation perfect copies and the + + + align:start position:0% +first generation perfect copies and the +law specifies in exacting language that + + align:start position:0% +law specifies in exacting language that + + + align:start position:0% +law specifies in exacting language that +you know 55% of that money will go to + + align:start position:0% +you know 55% of that money will go to + + + align:start position:0% +you know 55% of that money will go to +the record industry and 45% will go to + + align:start position:0% +the record industry and 45% will go to + + + align:start position:0% +the record industry and 45% will go to +the songwriters and and a certain + + align:start position:0% +the songwriters and and a certain + + + align:start position:0% +the songwriters and and a certain +percentage will go to the backup singers + + align:start position:0% +percentage will go to the backup singers + + + align:start position:0% +percentage will go to the backup singers +and you know that are not listed on the + + align:start position:0% +and you know that are not listed on the + + + align:start position:0% +and you know that are not listed on the +CD booklet and you know it's it's it's + + align:start position:0% +CD booklet and you know it's it's it's + + + align:start position:0% +CD booklet and you know it's it's it's +very specific um but then in exchange + + align:start position:0% +very specific um but then in exchange + + + align:start position:0% +very specific um but then in exchange +the + + align:start position:0% +the + + + align:start position:0% +the +um the record industry agreed to give + + align:start position:0% +um the record industry agreed to give + + + align:start position:0% +um the record industry agreed to give +immunity to other kinds of devices they + + align:start position:0% +immunity to other kinds of devices they + + + align:start position:0% +immunity to other kinds of devices they +said okay in exchange for getting this + + align:start position:0% +said okay in exchange for getting this + + + align:start position:0% +said okay in exchange for getting this +licensing and and Technology regime for + + align:start position:0% +licensing and and Technology regime for + + + align:start position:0% +licensing and and Technology regime for +digital audio recording devices we are + + align:start position:0% +digital audio recording devices we are + + + align:start position:0% +digital audio recording devices we are +going to agree never to sue anybody and + + align:start position:0% +going to agree never to sue anybody and + + + align:start position:0% +going to agree never to sue anybody and +not to be able to sue anybody for their + + align:start position:0% +not to be able to sue anybody for their + + + align:start position:0% +not to be able to sue anybody for their +analog copies their their personal + + align:start position:0% +analog copies their their personal + + + align:start position:0% +analog copies their their personal +non-commercial analog cassette copies + + align:start position:0% +non-commercial analog cassette copies + + + align:start position:0% +non-commercial analog cassette copies +and their personal + + align:start position:0% +and their personal + + + align:start position:0% +and their personal +non-commercial um digital copies for + + align:start position:0% +non-commercial um digital copies for + + + align:start position:0% +non-commercial um digital copies for +that matter so if you make a a first + + align:start position:0% +that matter so if you make a a first + + + align:start position:0% +that matter so if you make a a first +generation copy with a with a DAT deck + + align:start position:0% +generation copy with a with a DAT deck + + + align:start position:0% +generation copy with a with a DAT deck +that uses the serial copy management + + align:start position:0% +that uses the serial copy management + + + align:start position:0% +that uses the serial copy management +system that could be an infringing copy + + align:start position:0% +system that could be an infringing copy + + + align:start position:0% +system that could be an infringing copy +right uh but the the copyri said okay + + align:start position:0% +right uh but the the copyri said okay + + + align:start position:0% +right uh but the the copyri said okay +fine put in the law that even if it is + + align:start position:0% +fine put in the law that even if it is + + + align:start position:0% +fine put in the law that even if it is +an infringing copy we're those people + + align:start position:0% +an infringing copy we're those people + + + align:start position:0% +an infringing copy we're those people +going to be immune from suit because of + + align:start position:0% +going to be immune from suit because of + + + align:start position:0% +going to be immune from suit because of +course we're getting this tax so sort of + + align:start position:0% +course we're getting this tax so sort of + + + align:start position:0% +course we're getting this tax so sort of +an exchange from the tax revenue we are + + align:start position:0% +an exchange from the tax revenue we are + + + align:start position:0% +an exchange from the tax revenue we are +going to make these people immune now + + align:start position:0% +going to make these people immune now + + + align:start position:0% +going to make these people immune now +does this let you copy things on the + + align:start position:0% + + + + align:start position:0% + +internet did the internet really exist + + align:start position:0% +internet did the internet really exist + + + align:start position:0% +internet did the internet really exist +in 1992 as far as Congress was + + align:start position:0% + + + + align:start position:0% + +concerned not not really + + align:start position:0% +concerned not not really + + + align:start position:0% +concerned not not really +no um + + align:start position:0% + + + + align:start position:0% + +yeah I mean the view of most modern + + align:start position:0% +yeah I mean the view of most modern + + + align:start position:0% +yeah I mean the view of most modern +commentators is that if you make a copy + + align:start position:0% +commentators is that if you make a copy + + + align:start position:0% +commentators is that if you make a copy +onto a music CDR that is + + align:start position:0% +onto a music CDR that is + + + align:start position:0% +onto a music CDR that is +immunized so if you pull something down + + align:start position:0% +immunized so if you pull something down + + + align:start position:0% +immunized so if you pull something down +off Napster and it sort of immediately + + align:start position:0% +off Napster and it sort of immediately + + + align:start position:0% +off Napster and it sort of immediately +burn it onto an audio + + align:start position:0% +burn it onto an audio + + + align:start position:0% +burn it onto an audio +CDR uh and by Napster I mean like groer + + align:start position:0% +CDR uh and by Napster I mean like groer + + + align:start position:0% +CDR uh and by Napster I mean like groer +kazah or I2 Hub if you pull something + + align:start position:0% +kazah or I2 Hub if you pull something + + + align:start position:0% +kazah or I2 Hub if you pull something +off the internet and immediately burn it + + align:start position:0% +off the internet and immediately burn it + + + align:start position:0% +off the internet and immediately burn it +onto an a music CDR that says music on + + align:start position:0% +onto an a music CDR that says music on + + + align:start position:0% +onto an a music CDR that says music on +it uh + + align:start position:0% +it uh + + + align:start position:0% +it uh +most people think that that's okay not + + align:start position:0% +most people think that that's okay not + + + align:start position:0% +most people think that that's okay not +that it's okay but that it's immunized + + align:start position:0% +that it's okay but that it's immunized + + + align:start position:0% +that it's okay but that it's immunized +uh that you can't be successfully sued + + align:start position:0% +uh that you can't be successfully sued + + + align:start position:0% +uh that you can't be successfully sued +for it but nobody really + + align:start position:0% +for it but nobody really + + + align:start position:0% +for it but nobody really +knows but anyway that's the audio home + + align:start position:0% +knows but anyway that's the audio home + + + align:start position:0% +knows but anyway that's the audio home +recording act and that is this sort of + + align:start position:0% +recording act and that is this sort of + + + align:start position:0% +recording act and that is this sort of +mandate style of Regulation where + + align:start position:0% +mandate style of Regulation where + + + align:start position:0% +mandate style of Regulation where +Congress says you will use this + + align:start position:0% +Congress says you will use this + + + align:start position:0% +Congress says you will use this +technology um oh another example would + + align:start position:0% +technology um oh another example would + + + align:start position:0% +technology um oh another example would +be like the FCC when they say you + + align:start position:0% +be like the FCC when they say you + + + align:start position:0% +be like the FCC when they say you +broadcast television they don't just say + + align:start position:0% +broadcast television they don't just say + + + align:start position:0% +broadcast television they don't just say +broadcast television however the hell + + align:start position:0% +broadcast television however the hell + + + align:start position:0% +broadcast television however the hell +you want they say use the television + + align:start position:0% +you want they say use the television + + + align:start position:0% +you want they say use the television +standard the ntsc + + align:start position:0% +standard the ntsc + + + align:start position:0% +standard the ntsc +standard um + + align:start position:0% +standard um + + + align:start position:0% +standard um +okay so um so that's the sort of + + align:start position:0% +okay so um so that's the sort of + + + align:start position:0% +okay so um so that's the sort of +underwork for this so that was the Rio + + align:start position:0% +underwork for this so that was the Rio + + + align:start position:0% +underwork for this so that was the Rio +case and and what was the question in + + align:start position:0% +case and and what was the question in + + + align:start position:0% +case and and what was the question in +the Rio case who can put in one sentence + + align:start position:0% +the Rio case who can put in one sentence + + + align:start position:0% +the Rio case who can put in one sentence +the the + + align:start position:0% + + + + align:start position:0% + +question the digal audio that's + + align:start position:0% +question the digal audio that's + + + align:start position:0% +question the digal audio that's +basically is the Rio a digital audio + + align:start position:0% +basically is the Rio a digital audio + + + align:start position:0% +basically is the Rio a digital audio +recording device because if it is they + + align:start position:0% +recording device because if it is they + + + align:start position:0% +recording device because if it is they +have to be paying these royalties and + + align:start position:0% +have to be paying these royalties and + + + align:start position:0% +have to be paying these royalties and +everything and they have to be + + align:start position:0% +everything and they have to be + + + align:start position:0% +everything and they have to be +preventing the serial copies and what + + align:start position:0% +preventing the serial copies and what + + + align:start position:0% +preventing the serial copies and what +was the Court's answer no no and was the + + align:start position:0% +was the Court's answer no no and was the + + + align:start position:0% +was the Court's answer no no and was the +Court's answer do you think that you + + align:start position:0% +Court's answer do you think that you + + + align:start position:0% +Court's answer do you think that you +could have gone on the same sort of + + align:start position:0% +could have gone on the same sort of + + + align:start position:0% +could have gone on the same sort of +reasoning + + align:start position:0% +reasoning + + + align:start position:0% +reasoning +process it was all about what is a + + align:start position:0% +process it was all about what is a + + + align:start position:0% +process it was all about what is a +digital musical recording is it the + + align:start position:0% +digital musical recording is it the + + + align:start position:0% +digital musical recording is it the +whole hard disk or the individ can a + + align:start position:0% +whole hard disk or the individ can a + + + align:start position:0% +whole hard disk or the individ can a +file be a digital musical recording and + + align:start position:0% +file be a digital musical recording and + + + align:start position:0% +file be a digital musical recording and +by the way is a digital musical + + align:start position:0% +by the way is a digital musical + + + align:start position:0% +by the way is a digital musical +recording we talked about photo records + + align:start position:0% +recording we talked about photo records + + + align:start position:0% +recording we talked about photo records +what's a photo + + align:start position:0% + + + + align:start position:0% + +record the actual recording phal yeah + + align:start position:0% +record the actual recording phal yeah + + + align:start position:0% +record the actual recording phal yeah +the actual disc is a phone record like a + + align:start position:0% +the actual disc is a phone record like a + + + align:start position:0% +the actual disc is a phone record like a +vinyl record or a CD that's the phone + + align:start position:0% +vinyl record or a CD that's the phone + + + align:start position:0% +vinyl record or a CD that's the phone +record what's a sound recording + + align:start position:0% + + + + align:start position:0% + +the information on right sound recording + + align:start position:0% +the information on right sound recording + + + align:start position:0% +the information on right sound recording +is like the work like like if we talked + + align:start position:0% +is like the work like like if we talked + + + align:start position:0% +is like the work like like if we talked +about like Moby Dick that's the work and + + align:start position:0% +about like Moby Dick that's the work and + + + align:start position:0% +about like Moby Dick that's the work and +the sound recording is the work but then + + align:start position:0% +the sound recording is the work but then + + + align:start position:0% +the sound recording is the work but then +you could have like a copy of Moby Dick + + align:start position:0% +you could have like a copy of Moby Dick + + + align:start position:0% +you could have like a copy of Moby Dick +or a photo record of Britney Spears so + + align:start position:0% +or a photo record of Britney Spears so + + + align:start position:0% +or a photo record of Britney Spears so +the photo record is a material object + + align:start position:0% +the photo record is a material object + + + align:start position:0% +the photo record is a material object +and then but in the audio home recording + + align:start position:0% +and then but in the audio home recording + + + align:start position:0% +and then but in the audio home recording +I Congress adopted this whole sort of + + align:start position:0% +I Congress adopted this whole sort of + + + align:start position:0% +I Congress adopted this whole sort of +parallel language like digital musical + + align:start position:0% +parallel language like digital musical + + + align:start position:0% +parallel language like digital musical +recordings because they said they didn't + + align:start position:0% +recordings because they said they didn't + + + align:start position:0% +recordings because they said they didn't +want to disturb the existing meaning of + + align:start position:0% +want to disturb the existing meaning of + + + align:start position:0% +want to disturb the existing meaning of +phono record so they had this whole sort + + align:start position:0% +phono record so they had this whole sort + + + align:start position:0% +phono record so they had this whole sort +of parallel I mean this these section + + align:start position:0% +of parallel I mean this these section + + + align:start position:0% +of parallel I mean this these section +1000 chapter 10 it doesn't really + + align:start position:0% +1000 chapter 10 it doesn't really + + + align:start position:0% +1000 chapter 10 it doesn't really +interact with the rest of the Copyright + + align:start position:0% +interact with the rest of the Copyright + + + align:start position:0% +interact with the rest of the Copyright +Act it's just sort of out there and they + + align:start position:0% +Act it's just sort of out there and they + + + align:start position:0% +Act it's just sort of out there and they +have their own definitions their own + + align:start position:0% +have their own definitions their own + + + align:start position:0% +have their own definitions their own +terms and and mostly it means that + + align:start position:0% +terms and and mostly it means that + + + align:start position:0% +terms and and mostly it means that +Congress either didn't really know what + + align:start position:0% +Congress either didn't really know what + + + align:start position:0% +Congress either didn't really know what +well the the the lobbyists who developed + + align:start position:0% +well the the the lobbyists who developed + + + align:start position:0% +well the the the lobbyists who developed +this law you know they they wanted to + + align:start position:0% +this law you know they they wanted to + + + align:start position:0% +this law you know they they wanted to +just have it exist by itself and not + + align:start position:0% +just have it exist by itself and not + + + align:start position:0% +just have it exist by itself and not +really either they didn't want they + + align:start position:0% +really either they didn't want they + + + align:start position:0% +really either they didn't want they +didn't want to have to worry about phono + + align:start position:0% +didn't want to have to worry about phono + + + align:start position:0% +didn't want to have to worry about phono +record and all this old copyright law + + align:start position:0% +record and all this old copyright law + + + align:start position:0% +record and all this old copyright law +stuff they just made this whole separate + + align:start position:0% +stuff they just made this whole separate + + + align:start position:0% +stuff they just made this whole separate +separate regime so it's this is why + + align:start position:0% +separate regime so it's this is why + + + align:start position:0% +separate regime so it's this is why +nimmer would call it outside the the + + align:start position:0% +nimmer would call it outside the the + + + align:start position:0% +nimmer would call it outside the the +sort of national copyright legislation + + align:start position:0% +sort of national copyright legislation + + + align:start position:0% +sort of national copyright legislation +but it is part of title + + align:start position:0% +but it is part of title + + + align:start position:0% +but it is part of title +17 okay so um so was the audio recording + + align:start position:0% +17 okay so um so was the audio recording + + + align:start position:0% +17 okay so um so was the audio recording +act like a success from anybody's + + align:start position:0% +act like a success from anybody's + + + align:start position:0% +act like a success from anybody's +perspective I mean it did sort of kill + + align:start position:0% +perspective I mean it did sort of kill + + + align:start position:0% +perspective I mean it did sort of kill +that but was anybody really happy with + + align:start position:0% +that but was anybody really happy with + + + align:start position:0% +that but was anybody really happy with +the + + align:start position:0% + + + + align:start position:0% + +result I mean the record industry wasn't + + align:start position:0% +result I mean the record industry wasn't + + + align:start position:0% +result I mean the record industry wasn't +really happy because you know it didn't + + align:start position:0% +really happy because you know it didn't + + + align:start position:0% +really happy because you know it didn't +stop things like the Rio you could sort + + align:start position:0% +stop things like the Rio you could sort + + + align:start position:0% +stop things like the Rio you could sort +of get around this technology mandate + + align:start position:0% +of get around this technology mandate + + + align:start position:0% +of get around this technology mandate +and uh I don't think Engineers like + + align:start position:0% +and uh I don't think Engineers like + + + align:start position:0% +and uh I don't think Engineers like +being told like you must use a certain + + align:start position:0% +being told like you must use a certain + + + align:start position:0% +being told like you must use a certain +technology + + align:start position:0% +technology + + + align:start position:0% +technology +so and it didn't apply to + + align:start position:0% +so and it didn't apply to + + + align:start position:0% +so and it didn't apply to +computers uh which was maybe the biggest + + align:start position:0% +computers uh which was maybe the biggest + + + align:start position:0% +computers uh which was maybe the biggest +failure because I mean how could you + + align:start position:0% +failure because I mean how could you + + + align:start position:0% +failure because I mean how could you +have a technology mandate apply to + + align:start position:0% +have a technology mandate apply to + + + align:start position:0% +have a technology mandate apply to +computers + + align:start position:0% +computers + + + align:start position:0% +computers +um it would I mean how would it + + align:start position:0% +um it would I mean how would it + + + align:start position:0% +um it would I mean how would it +work you define a computer well you + + align:start position:0% +work you define a computer well you + + + align:start position:0% +work you define a computer well you +define a computer but then who is + + align:start position:0% +define a computer but then who is + + + align:start position:0% +define a computer but then who is +responsible for making making sure that + + align:start position:0% +responsible for making making sure that + + + align:start position:0% +responsible for making making sure that +the computer obeys the Mandate I mean + + align:start position:0% +the computer obeys the Mandate I mean + + + align:start position:0% +the computer obeys the Mandate I mean +does it apply to software and are users + + align:start position:0% +does it apply to software and are users + + + align:start position:0% +does it apply to software and are users +can they would users have to be + + align:start position:0% +can they would users have to be + + + align:start position:0% +can they would users have to be +prevented from writing their own + + align:start position:0% +prevented from writing their own + + + align:start position:0% +prevented from writing their own +software I mean it's difficult to see + + align:start position:0% +software I mean it's difficult to see + + + align:start position:0% +software I mean it's difficult to see +how you would enforce this TR computer + + align:start position:0% +how you would enforce this TR computer + + + align:start position:0% +how you would enforce this TR computer +it's easy yeah it's I mean you might + + align:start position:0% +it's easy yeah it's I mean you might + + + align:start position:0% +it's easy yeah it's I mean you might +have to change when we think of a + + align:start position:0% +have to change when we think of a + + + align:start position:0% +have to change when we think of a +computer like now you can build one + + align:start position:0% +computer like now you can build one + + + align:start position:0% +computer like now you can build one +yourself you can buy the video card from + + align:start position:0% +yourself you can buy the video card from + + + align:start position:0% +yourself you can buy the video card from +one company the motherboard from a + + align:start position:0% +one company the motherboard from a + + + align:start position:0% +one company the motherboard from a +different company and you can write your + + align:start position:0% +different company and you can write your + + + align:start position:0% +different company and you can write your +own software I mean that might all have + + align:start position:0% +own software I mean that might all have + + + align:start position:0% +own software I mean that might all have +to change if you wanted to have some + + align:start position:0% +to change if you wanted to have some + + + align:start position:0% +to change if you wanted to have some +enforced technology mandate for + + align:start position:0% +enforced technology mandate for + + + align:start position:0% +enforced technology mandate for +computers and Congress is not willing to + + align:start position:0% +computers and Congress is not willing to + + + align:start position:0% +computers and Congress is not willing to +do that uh in + + align:start position:0% +do that uh in + + + align:start position:0% +do that uh in +1992 also because you know which + + align:start position:0% +1992 also because you know which + + + align:start position:0% +1992 also because you know which +industry + + align:start position:0% +industry + + + align:start position:0% +industry +is bigger like the consumer electronics + + align:start position:0% +is bigger like the consumer electronics + + + align:start position:0% +is bigger like the consumer electronics +and computer industry or the copyright + + align:start position:0% +and computer industry or the copyright + + + align:start position:0% +and computer industry or the copyright +owning + + align:start position:0% +owning + + + align:start position:0% +owning +Industries yeah I think the Consumer + + align:start position:0% +Industries yeah I think the Consumer + + + align:start position:0% +Industries yeah I think the Consumer +Electronics by far dwarfs the the + + align:start position:0% +Electronics by far dwarfs the the + + + align:start position:0% +Electronics by far dwarfs the the +copyright industries of course they may + + align:start position:0% +copyright industries of course they may + + + align:start position:0% +copyright industries of course they may +be all foreign I don't know anyway okay + + align:start position:0% +be all foreign I don't know anyway okay + + + align:start position:0% +be all foreign I don't know anyway okay +so it doesn't apply to computers it + + align:start position:0% +so it doesn't apply to computers it + + + align:start position:0% +so it doesn't apply to computers it +didn't really work very well so in um in + + align:start position:0% +didn't really work very well so in um in + + + align:start position:0% +didn't really work very well so in um in +the mid 90s the CATE owners got a new + + align:start position:0% +the mid 90s the CATE owners got a new + + + align:start position:0% +the mid 90s the CATE owners got a new +idea they say + + align:start position:0% +idea they say + + + align:start position:0% +idea they say +well you know we're really concerned + + align:start position:0% +well you know we're really concerned + + + align:start position:0% +well you know we're really concerned +that the cooperate Act is not going to + + align:start position:0% +that the cooperate Act is not going to + + + align:start position:0% +that the cooperate Act is not going to +support our new business models like we + + align:start position:0% +support our new business models like we + + + align:start position:0% +support our new business models like we +might want to have you know encrypted + + align:start position:0% +might want to have you know encrypted + + + align:start position:0% +might want to have you know encrypted +satellite television where we deliver to + + align:start position:0% +satellite television where we deliver to + + + align:start position:0% +satellite television where we deliver to +you the entire you know all 400 million + + align:start position:0% +you the entire you know all 400 million + + + align:start position:0% +you the entire you know all 400 million +CH 400 channels but they're all + + align:start position:0% +CH 400 channels but they're all + + + align:start position:0% +CH 400 channels but they're all +encrypted and um and you have to pay us + + align:start position:0% +encrypted and um and you have to pay us + + + align:start position:0% +encrypted and um and you have to pay us +you know to decode a particular Channel + + align:start position:0% +you know to decode a particular Channel + + + align:start position:0% +you know to decode a particular Channel +or maybe even a particular + + align:start position:0% +or maybe even a particular + + + align:start position:0% +or maybe even a particular +show and uh we don't want you know we're + + align:start position:0% +show and uh we don't want you know we're + + + align:start position:0% +show and uh we don't want you know we're +worried that there's going to be these + + align:start position:0% +worried that there's going to be these + + + align:start position:0% +worried that there's going to be these +black boxes that are going to be able to + + align:start position:0% +black boxes that are going to be able to + + + align:start position:0% +black boxes that are going to be able to +decode satellite television without + + align:start position:0% +decode satellite television without + + + align:start position:0% +decode satellite television without +people paying us and would that be + + align:start position:0% +people paying us and would that be + + + align:start position:0% +people paying us and would that be +copyright infringement + + align:start position:0% + + + + align:start position:0% + +well let's talk about like satellite + + align:start position:0% +well let's talk about like satellite + + + align:start position:0% +well let's talk about like satellite +television would that be copyright + + align:start position:0% +television would that be copyright + + + align:start position:0% +television would that be copyright +infringement to if somebody gave you a + + align:start position:0% +infringement to if somebody gave you a + + + align:start position:0% +infringement to if somebody gave you a +black Bo so sold on the market a black + + align:start position:0% +black Bo so sold on the market a black + + + align:start position:0% +black Bo so sold on the market a black +box that let you descramble satellite + + align:start position:0% +box that let you descramble satellite + + + align:start position:0% +box that let you descramble satellite +television without paying would that be + + align:start position:0% +television without paying would that be + + + align:start position:0% +television without paying would that be +copyright + + align:start position:0% + + + + align:start position:0% + +infringement which would it implicate + + align:start position:0% +infringement which would it implicate + + + align:start position:0% +infringement which would it implicate +any of the activities of copyright + + align:start position:0% +any of the activities of copyright + + + align:start position:0% +any of the activities of copyright +reproduction + + align:start position:0% +reproduction + + + align:start position:0% +reproduction +distribution no it's just sort of + + align:start position:0% +distribution no it's just sort of + + + align:start position:0% +distribution no it's just sort of +reception so um it wouldn't now it turns + + align:start position:0% +reception so um it wouldn't now it turns + + + align:start position:0% +reception so um it wouldn't now it turns +out there are other laws about theft of + + align:start position:0% +out there are other laws about theft of + + + align:start position:0% +out there are other laws about theft of +of services that it would implicate but + + align:start position:0% +of services that it would implicate but + + + align:start position:0% +of services that it would implicate but +but not the copyright not copyright + + align:start position:0% +but not the copyright not copyright + + + align:start position:0% +but not the copyright not copyright +infringement and they say and how about + + align:start position:0% +infringement and they say and how about + + + align:start position:0% +infringement and they say and how about +this we want to give you a a DVD that + + align:start position:0% +this we want to give you a a DVD that + + + align:start position:0% +this we want to give you a a DVD that +has a million a CD that has a million + + align:start position:0% +has a million a CD that has a million + + + align:start position:0% +has a million a CD that has a million +fonts on it you know gamand and times + + align:start position:0% +fonts on it you know gamand and times + + + align:start position:0% +fonts on it you know gamand and times +and CER and helvetica and we're going to + + align:start position:0% +and CER and helvetica and we're going to + + + align:start position:0% +and CER and helvetica and we're going to +give you all these fonts but they're all + + align:start position:0% +give you all these fonts but they're all + + + align:start position:0% +give you all these fonts but they're all +going to be encrypted and when you want + + align:start position:0% +going to be encrypted and when you want + + + align:start position:0% +going to be encrypted and when you want +to get one font you just um pay us the + + align:start position:0% +to get one font you just um pay us the + + + align:start position:0% +to get one font you just um pay us the +money and we'll give you the the + + align:start position:0% +money and we'll give you the the + + + align:start position:0% +money and we'll give you the the +decryption key for one font but we're + + align:start position:0% +decryption key for one font but we're + + + align:start position:0% +decryption key for one font but we're +concerned somebody might distrib a black + + align:start position:0% +concerned somebody might distrib a black + + + align:start position:0% +concerned somebody might distrib a black +box that will + + align:start position:0% +box that will + + + align:start position:0% +box that will +um that will uh let you decrypt all the + + align:start position:0% +um that will uh let you decrypt all the + + + align:start position:0% +um that will uh let you decrypt all the +fonts and that would ruin us or at least + + align:start position:0% +fonts and that would ruin us or at least + + + align:start position:0% +fonts and that would ruin us or at least +it would ruin this business model so and + + align:start position:0% +it would ruin this business model so and + + + align:start position:0% +it would ruin this business model so and +would that be copyright + + align:start position:0% + + + + align:start position:0% + +infringement would it be anything + + align:start position:0% + + + + align:start position:0% + +illegal you think it would be + + align:start position:0% +illegal you think it would be + + + align:start position:0% +illegal you think it would be +theft I mean literal theft you have to + + align:start position:0% +theft I mean literal theft you have to + + + align:start position:0% +theft I mean literal theft you have to +like steal something that belongs to + + align:start position:0% +like steal something that belongs to + + + align:start position:0% +like steal something that belongs to +somebody like steal actual + + align:start position:0% +somebody like steal actual + + + align:start position:0% +somebody like steal actual +property you're + + align:start position:0% + + + + align:start position:0% + +use what would they give to + + align:start position:0% + + + + align:start position:0% + +you is it the same thing is the same + + align:start position:0% +you is it the same thing is the same + + + align:start position:0% +you is it the same thing is the same +thing I mean you know there's laws about + + align:start position:0% +thing I mean you know there's laws about + + + align:start position:0% +thing I mean you know there's laws about +theft and they generally don't apply to + + align:start position:0% +theft and they generally don't apply to + + + align:start position:0% +theft and they generally don't apply to +things like copyright infringement so + + align:start position:0% +things like copyright infringement so + + + align:start position:0% +things like copyright infringement so +it's hard to see that they would apply + + align:start position:0% +it's hard to see that they would apply + + + align:start position:0% +it's hard to see that they would apply +to that but what other what else what + + align:start position:0% +to that but what other what else what + + + align:start position:0% +to that but what other what else what +other legal tools could the providers of + + align:start position:0% +other legal tools could the providers of + + + align:start position:0% +other legal tools could the providers of +these font cities use well there could + + align:start position:0% +these font cities use well there could + + + align:start position:0% +these font cities use well there could +be a trft license on the font City yeah + + align:start position:0% +be a trft license on the font City yeah + + + align:start position:0% +be a trft license on the font City yeah +there could be a contract between you + + align:start position:0% +there could be a contract between you + + + align:start position:0% +there could be a contract between you +and the font people that says I will not + + align:start position:0% +and the font people that says I will not + + + align:start position:0% +and the font people that says I will not +Des you know decrypt these fonts unless + + align:start position:0% +Des you know decrypt these fonts unless + + + align:start position:0% +Des you know decrypt these fonts unless +I've paid + + align:start position:0% +I've paid + + + align:start position:0% +I've paid +you and that would probably work but + + align:start position:0% +you and that would probably work but + + + align:start position:0% +you and that would probably work but +what are the problem with these + + align:start position:0% +what are the problem with these + + + align:start position:0% +what are the problem with these +contracts you cannot control all + + align:start position:0% +contracts you cannot control all + + + align:start position:0% +contracts you cannot control all +consumers you can't control everybody + + align:start position:0% +consumers you can't control everybody + + + align:start position:0% +consumers you can't control everybody +why + + align:start position:0% +why + + + align:start position:0% +why +not if if you have uh 1 million + + align:start position:0% +not if if you have uh 1 million + + + align:start position:0% +not if if you have uh 1 million +consumers and then you have someone who + + align:start position:0% +consumers and then you have someone who + + + align:start position:0% +consumers and then you have someone who +uh propose uh software able to this + + align:start position:0% +uh propose uh software able to this + + + align:start position:0% +uh propose uh software able to this +paramet you cannot control all 1 million + + align:start position:0% +paramet you cannot control all 1 million + + + align:start position:0% +paramet you cannot control all 1 million +of consumer uh checking if they don't + + align:start position:0% +of consumer uh checking if they don't + + + align:start position:0% +of consumer uh checking if they don't +use it okay so that's a problem the + + align:start position:0% +use it okay so that's a problem the + + + align:start position:0% +use it okay so that's a problem the +contract might apply to all the people + + align:start position:0% +contract might apply to all the people + + + align:start position:0% +contract might apply to all the people +who've actually bought the software but + + align:start position:0% +who've actually bought the software but + + + align:start position:0% +who've actually bought the software but +it doesn't apply to these Distributors + + align:start position:0% +it doesn't apply to these Distributors + + + align:start position:0% +it doesn't apply to these Distributors +just like the Copyright Act certainly + + align:start position:0% +just like the Copyright Act certainly + + + align:start position:0% +just like the Copyright Act certainly +applies to the people who go Library + + align:start position:0% +applies to the people who go Library + + + align:start position:0% +applies to the people who go Library +building by you know downloading all the + + align:start position:0% +building by you know downloading all the + + + align:start position:0% +building by you know downloading all the +or not downloading recording all the + + align:start position:0% +or not downloading recording all the + + + align:start position:0% +or not downloading recording all the +episodes of 24 when they're on TV and + + align:start position:0% +episodes of 24 when they're on TV and + + + align:start position:0% +episodes of 24 when they're on TV and +saving them um that's illegal and the + + align:start position:0% +saving them um that's illegal and the + + + align:start position:0% +saving them um that's illegal and the +cerate ACT reaches them but it does not + + align:start position:0% +cerate ACT reaches them but it does not + + + align:start position:0% +cerate ACT reaches them but it does not +reach Sony that distributes the the + + align:start position:0% +reach Sony that distributes the the + + + align:start position:0% +reach Sony that distributes the the +machine that makes this all possible so + + align:start position:0% +machine that makes this all possible so + + + align:start position:0% +machine that makes this all possible so +here uh Damian says that the kyber or + + align:start position:0% +here uh Damian says that the kyber or + + + align:start position:0% +here uh Damian says that the kyber or +you know the contract might reach those + + align:start position:0% +you know the contract might reach those + + + align:start position:0% +you know the contract might reach those +people who actually rip off the the + + align:start position:0% +people who actually rip off the the + + + align:start position:0% +people who actually rip off the the +fonts but it wouldn't reach the people + + align:start position:0% +fonts but it wouldn't reach the people + + + align:start position:0% +fonts but it wouldn't reach the people +who are making that possible who are + + align:start position:0% +who are making that possible who are + + + align:start position:0% +who are making that possible who are +Distributing the the technology so + + align:start position:0% +Distributing the the technology so + + + align:start position:0% +Distributing the the technology so +that's problem one what's another + + align:start position:0% +that's problem one what's another + + + align:start position:0% +that's problem one what's another +problem with contracts are they leging + + align:start position:0% +problem with contracts are they leging + + + align:start position:0% +problem with contracts are they leging +are they legally binding yeah like if I + + align:start position:0% +are they legally binding yeah like if I + + + align:start position:0% +are they legally binding yeah like if I +say like oh I bought this but I don't + + align:start position:0% +say like oh I bought this but I don't + + + align:start position:0% +say like oh I bought this but I don't +really feel like doing that contract so + + align:start position:0% +really feel like doing that contract so + + + align:start position:0% +really feel like doing that contract so +I wave my + + align:start position:0% +I wave my + + + align:start position:0% +I wave my +like like I mean am I supposed to obey + + align:start position:0% +like like I mean am I supposed to obey + + + align:start position:0% +like like I mean am I supposed to obey +whatever it say are you supposed to obey + + align:start position:0% +whatever it say are you supposed to obey + + + align:start position:0% +whatever it say are you supposed to obey +whatever it says on the package well + + align:start position:0% +whatever it says on the package well + + + align:start position:0% +whatever it says on the package well +that turns out to be an incredibly + + align:start position:0% +that turns out to be an incredibly + + + align:start position:0% +that turns out to be an incredibly +difficult issue uh and and and it it was + + align:start position:0% +difficult issue uh and and and it it was + + + align:start position:0% +difficult issue uh and and and it it was +an incredibly difficult issue before and + + align:start position:0% +an incredibly difficult issue before and + + + align:start position:0% +an incredibly difficult issue before and +now that it these questions are becoming + + align:start position:0% +now that it these questions are becoming + + + align:start position:0% +now that it these questions are becoming +more and more entangled with copyright + + align:start position:0% +more and more entangled with copyright + + + align:start position:0% +more and more entangled with copyright +it's um Beyond difficult because + + align:start position:0% +it's um Beyond difficult because + + + align:start position:0% +it's um Beyond difficult because +contracts are a state issue and + + align:start position:0% +contracts are a state issue and + + + align:start position:0% +contracts are a state issue and +different states can have different laws + + align:start position:0% +different states can have different laws + + + align:start position:0% +different states can have different laws +about what kinds of contracts + + align:start position:0% +about what kinds of contracts + + + align:start position:0% +about what kinds of contracts +permissible coperate is a federal issue + + align:start position:0% +permissible coperate is a federal issue + + + align:start position:0% +permissible coperate is a federal issue +um + + align:start position:0% +um + + + align:start position:0% +um +you know David nimmer is the world's + + align:start position:0% +you know David nimmer is the world's + + + align:start position:0% +you know David nimmer is the world's +expert on American copyright law and + + align:start position:0% +expert on American copyright law and + + + align:start position:0% +expert on American copyright law and +Raymond nimmer is a big expert on um + + align:start position:0% +Raymond nimmer is a big expert on um + + + align:start position:0% +Raymond nimmer is a big expert on um +shrink W licenses and when you get the + + align:start position:0% +shrink W licenses and when you get the + + + align:start position:0% +shrink W licenses and when you get the +two nimmers involved it's just a + + align:start position:0% +two nimmers involved it's just a + + + align:start position:0% +two nimmers involved it's just a +horrible mess um it's like having orange + + align:start position:0% +horrible mess um it's like having orange + + + align:start position:0% +horrible mess um it's like having orange +and lemon in the same dish it just it + + align:start position:0% +and lemon in the same dish it just it + + + align:start position:0% +and lemon in the same dish it just it +doesn't work so anyway it gets + + align:start position:0% +doesn't work so anyway it gets + + + align:start position:0% +doesn't work so anyway it gets +incredibly complicated so the and that + + align:start position:0% +incredibly complicated so the and that + + + align:start position:0% +incredibly complicated so the and that +that is people's fear about these + + align:start position:0% +that is people's fear about these + + + align:start position:0% +that is people's fear about these +contracts that even if they were largely + + align:start position:0% +contracts that even if they were largely + + + align:start position:0% +contracts that even if they were largely +enforcable uh you could have all sorts + + align:start position:0% +enforcable uh you could have all sorts + + + align:start position:0% +enforcable uh you could have all sorts +of problems like if an somebody who's 16 + + align:start position:0% +of problems like if an somebody who's 16 + + + align:start position:0% +of problems like if an somebody who's 16 +year old 16 years old agreed to the + + align:start position:0% +year old 16 years old agreed to the + + + align:start position:0% +year old 16 years old agreed to the +contract well there's all this stuff + + align:start position:0% +contract well there's all this stuff + + + align:start position:0% +contract well there's all this stuff +about young people uh may not be able to + + align:start position:0% +about young people uh may not be able to + + + align:start position:0% +about young people uh may not be able to +you know agree to a contract or what if + + align:start position:0% +you know agree to a contract or what if + + + align:start position:0% +you know agree to a contract or what if +somebody you know somebody might get the + + align:start position:0% +somebody you know somebody might get the + + + align:start position:0% +somebody you know somebody might get the +contract and then give the disc to + + align:start position:0% +contract and then give the disc to + + + align:start position:0% +contract and then give the disc to +somebody else and + + align:start position:0% +somebody else and + + + align:start position:0% +somebody else and +um that's legal under the first sale + + align:start position:0% +um that's legal under the first sale + + + align:start position:0% +um that's legal under the first sale +rule right but and that new person might + + align:start position:0% +rule right but and that new person might + + + align:start position:0% +rule right but and that new person might +not be bound by the + + align:start position:0% +not be bound by the + + + align:start position:0% +not be bound by the +contract so + + align:start position:0% +contract so + + + align:start position:0% +contract so +um anyway it + + align:start position:0% +um anyway it + + + align:start position:0% +um anyway it +becomes for for R reasons you know the + + align:start position:0% +becomes for for R reasons you know the + + + align:start position:0% +becomes for for R reasons you know the +the the providers are not confident that + + align:start position:0% +the the providers are not confident that + + + align:start position:0% +the the providers are not confident that +contracts will preserve their rights so + + align:start position:0% +contracts will preserve their rights so + + + align:start position:0% +contracts will preserve their rights so +they say + + align:start position:0% +they say + + + align:start position:0% +they say +um we need a new law to support these + + align:start position:0% +um we need a new law to support these + + + align:start position:0% +um we need a new law to support these +business models we need you know in our + + align:start position:0% +business models we need you know in our + + + align:start position:0% +business models we need you know in our +language we' say we need new exclusive + + align:start position:0% +language we' say we need new exclusive + + + align:start position:0% +language we' say we need new exclusive +rights because the the ones that we've + + align:start position:0% +rights because the the ones that we've + + + align:start position:0% +rights because the the ones that we've +got are not good enough now what was the + + align:start position:0% +got are not good enough now what was the + + + align:start position:0% +got are not good enough now what was the +um and and they had a further argument + + align:start position:0% +um and and they had a further argument + + + align:start position:0% +um and and they had a further argument +uh because in the mid 90s there was a + + align:start position:0% +uh because in the mid 90s there was a + + + align:start position:0% +uh because in the mid 90s there was a +new + + align:start position:0% +new + + + align:start position:0% +new +um new technology coming out what was + + align:start position:0% +um new technology coming out what was + + + align:start position:0% +um new technology coming out what was +that there was a big rallying cry in the + + align:start position:0% +that there was a big rallying cry in the + + + align:start position:0% +that there was a big rallying cry in the +election of + + align:start position:0% +election of + + + align:start position:0% +election of +1992 that the new presidential + + align:start position:0% +1992 that the new presidential + + + align:start position:0% +1992 that the new presidential +Administration was going to develop this + + align:start position:0% +Administration was going to develop this + + + align:start position:0% +Administration was going to develop this +new + + align:start position:0% + + + + align:start position:0% + +technology internet well they didn't + + align:start position:0% +technology internet well they didn't + + + align:start position:0% +technology internet well they didn't +call it that though what do they call + + align:start position:0% + + + + align:start position:0% + +it information super the information + + align:start position:0% +it information super the information + + + align:start position:0% +it information super the information +super highway is what it was called an + + align:start position:0% +super highway is what it was called an + + + align:start position:0% +super highway is what it was called an +Al Gore and everybody was talking about + + align:start position:0% +Al Gore and everybody was talking about + + + align:start position:0% +Al Gore and everybody was talking about +the information Super Highway and when + + align:start position:0% +the information Super Highway and when + + + align:start position:0% +the information Super Highway and when +once they got elected this happens to a + + align:start position:0% +once they got elected this happens to a + + + align:start position:0% +once they got elected this happens to a +lot of presid presidential + + align:start position:0% +lot of presid presidential + + + align:start position:0% +lot of presid presidential +administrations but things get a lot + + align:start position:0% +administrations but things get a lot + + + align:start position:0% +administrations but things get a lot +more sober when they get elected like + + align:start position:0% +more sober when they get elected like + + + align:start position:0% +more sober when they get elected like +President Bush says and we're going to + + align:start position:0% +President Bush says and we're going to + + + align:start position:0% +President Bush says and we're going to +have um regulation of carbon dioxide + + align:start position:0% +have um regulation of carbon dioxide + + + align:start position:0% +have um regulation of carbon dioxide +emissions and he got elected and he + + align:start position:0% +emissions and he got elected and he + + + align:start position:0% +emissions and he got elected and he +tampered that down and you know Hamas + + align:start position:0% +tampered that down and you know Hamas + + + align:start position:0% +tampered that down and you know Hamas +has said we're going to kill all + + align:start position:0% +has said we're going to kill all + + + align:start position:0% +has said we're going to kill all +everybody in Israel and they've got + + align:start position:0% +everybody in Israel and they've got + + + align:start position:0% +everybody in Israel and they've got +elected and actually nobody knows + + align:start position:0% +elected and actually nobody knows + + + align:start position:0% +elected and actually nobody knows +they're going to Tamper that down but + + align:start position:0% +they're going to Tamper that down but + + + align:start position:0% +they're going to Tamper that down but +anyway one hopes that when when regimes + + align:start position:0% +anyway one hopes that when when regimes + + + align:start position:0% +anyway one hopes that when when regimes +get elected and have to do actual + + align:start position:0% +get elected and have to do actual + + + align:start position:0% +get elected and have to do actual +governance that they tamper things down + + align:start position:0% +governance that they tamper things down + + + align:start position:0% +governance that they tamper things down +and so the Clinton Administration with + + align:start position:0% +and so the Clinton Administration with + + + align:start position:0% +and so the Clinton Administration with +all his exuberance they tampered it down + + align:start position:0% +all his exuberance they tampered it down + + + align:start position:0% +all his exuberance they tampered it down +and they stopped calling about the + + align:start position:0% +and they stopped calling about the + + + align:start position:0% +and they stopped calling about the +information Super Highway and they + + align:start position:0% +information Super Highway and they + + + align:start position:0% +information Super Highway and they +called it what it was the national + + align:start position:0% +called it what it was the national + + + align:start position:0% +called it what it was the national +information + + align:start position:0% +information + + + align:start position:0% +information +infrastructure the + + align:start position:0% +infrastructure the + + + align:start position:0% +infrastructure the +knee I like the old name anyway and they + + align:start position:0% +knee I like the old name anyway and they + + + align:start position:0% +knee I like the old name anyway and they +had all sorts of you know how the + + align:start position:0% +had all sorts of you know how the + + + align:start position:0% +had all sorts of you know how the +Clinton Administration was they had + + align:start position:0% +Clinton Administration was they had + + + align:start position:0% +Clinton Administration was they had +working groups and focus groups and + + align:start position:0% +working groups and focus groups and + + + align:start position:0% +working groups and focus groups and +sessions and meetings and that's just + + align:start position:0% +sessions and meetings and that's just + + + align:start position:0% +sessions and meetings and that's just +how they were and uh they had ones about + + align:start position:0% +how they were and uh they had ones about + + + align:start position:0% +how they were and uh they had ones about +this and the copyright owners were there + + align:start position:0% +this and the copyright owners were there + + + align:start position:0% +this and the copyright owners were there +and they says look in you know to to put + + align:start position:0% +and they says look in you know to to put + + + align:start position:0% +and they says look in you know to to put +our works on the internet you know + + align:start position:0% +our works on the internet you know + + + align:start position:0% +our works on the internet you know +unless we're gonna we're not going to + + align:start position:0% +unless we're gonna we're not going to + + + align:start position:0% +unless we're gonna we're not going to +have Time Magazine on the Internet or + + align:start position:0% +have Time Magazine on the Internet or + + + align:start position:0% +have Time Magazine on the Internet or +music on the internet or uh + + align:start position:0% +music on the internet or uh + + + align:start position:0% +music on the internet or uh +you know the New York we're not going to + + align:start position:0% +you know the New York we're not going to + + + align:start position:0% +you know the New York we're not going to +put um these works on the internet + + align:start position:0% +put um these works on the internet + + + align:start position:0% +put um these works on the internet +unless you give us added protections and + + align:start position:0% +unless you give us added protections and + + + align:start position:0% +unless you give us added protections and +you're just going to build all these + + align:start position:0% +you're just going to build all these + + + align:start position:0% +you're just going to build all these +pipes in the National information + + align:start position:0% +pipes in the National information + + + align:start position:0% +pipes in the National information +infrastructure you're going to build all + + align:start position:0% +infrastructure you're going to build all + + + align:start position:0% +infrastructure you're going to build all +these pipes but they're going to be + + align:start position:0% +these pipes but they're going to be + + + align:start position:0% +these pipes but they're going to be +empty because we will not put our works + + align:start position:0% +empty because we will not put our works + + + align:start position:0% +empty because we will not put our works +online unless you give us added + + align:start position:0% +online unless you give us added + + + align:start position:0% +online unless you give us added +protections now do people believe + + align:start position:0% + + + + align:start position:0% + +that I mean nobody really knows it's + + align:start position:0% +that I mean nobody really knows it's + + + align:start position:0% +that I mean nobody really knows it's +kind of a bargaining chip it's true that + + align:start position:0% +kind of a bargaining chip it's true that + + + align:start position:0% +kind of a bargaining chip it's true that +by the mid 90s and the late 90s + + align:start position:0% +by the mid 90s and the late 90s + + + align:start position:0% +by the mid 90s and the late 90s +certainly the major copyright owners + + align:start position:0% +certainly the major copyright owners + + + align:start position:0% +certainly the major copyright owners +were already putting their content + + align:start position:0% +were already putting their content + + + align:start position:0% +were already putting their content +online without prote you know without + + align:start position:0% +online without prote you know without + + + align:start position:0% +online without prote you know without +these added protections and they did + + align:start position:0% +these added protections and they did + + + align:start position:0% +these added protections and they did +already have copyright you could be like + + align:start position:0% +already have copyright you could be like + + + align:start position:0% +already have copyright you could be like +what more do you need but that was sort + + align:start position:0% +what more do you need but that was sort + + + align:start position:0% +what more do you need but that was sort +of the argument and there were all sorts + + align:start position:0% +of the argument and there were all sorts + + + align:start position:0% +of the argument and there were all sorts +of documents there was the green paper + + align:start position:0% +of documents there was the green paper + + + align:start position:0% +of documents there was the green paper +and the white paper and various laws and + + align:start position:0% +and the white paper and various laws and + + + align:start position:0% +and the white paper and various laws and +um and they were ultimately not really + + align:start position:0% +um and they were ultimately not really + + + align:start position:0% +um and they were ultimately not really +successful in + + align:start position:0% +successful in + + + align:start position:0% +successful in +Congress are + + align:start position:0% +Congress are + + + align:start position:0% +Congress are +they well we'll get to that but the the + + align:start position:0% +they well we'll get to that but the the + + + align:start position:0% +they well we'll get to that but the the +the sort of lawmaking process that came + + align:start position:0% +the sort of lawmaking process that came + + + align:start position:0% +the sort of lawmaking process that came +out of the national information + + align:start position:0% +out of the national information + + + align:start position:0% +out of the national information +infrastructure the the new rights that + + align:start position:0% +infrastructure the the new rights that + + + align:start position:0% +infrastructure the the new rights that +they wanted um were not they they + + align:start position:0% +they wanted um were not they they + + + align:start position:0% +they wanted um were not they they +Congress didn't pass + + align:start position:0% +Congress didn't pass + + + align:start position:0% +Congress didn't pass +them um and so they took a different + + align:start position:0% +them um and so they took a different + + + align:start position:0% +them um and so they took a different +strategy which is to say look um our + + align:start position:0% +strategy which is to say look um our + + + align:start position:0% +strategy which is to say look um our +works are being ripped off by people in + + align:start position:0% +works are being ripped off by people in + + + align:start position:0% +works are being ripped off by people in +other countries and you know we might + + align:start position:0% +other countries and you know we might + + + align:start position:0% +other countries and you know we might +distribute these encrypted whatevers and + + align:start position:0% +distribute these encrypted whatevers and + + + align:start position:0% +distribute these encrypted whatevers and +people in other countries are going to + + align:start position:0% +people in other countries are going to + + + align:start position:0% +people in other countries are going to +rip them off and we want the whole world + + align:start position:0% +rip them off and we want the whole world + + + align:start position:0% +rip them off and we want the whole world +to agree on a new copyright + + align:start position:0% +to agree on a new copyright + + + align:start position:0% +to agree on a new copyright +treaty uh to uh to out you know to + + align:start position:0% +treaty uh to uh to out you know to + + + align:start position:0% +treaty uh to uh to out you know to +prevent us from getting you know to give + + align:start position:0% +prevent us from getting you know to give + + + align:start position:0% +prevent us from getting you know to give +us new rights world uh yeah + + align:start position:0% +us new rights world uh yeah + + + align:start position:0% +us new rights world uh yeah +globally and so they had this whole + + align:start position:0% +globally and so they had this whole + + + align:start position:0% +globally and so they had this whole +treaty process uh with an organization + + align:start position:0% +treaty process uh with an organization + + + align:start position:0% +treaty process uh with an organization +that was + + align:start position:0% +that was + + + align:start position:0% +that was +called anybody know how this is + + align:start position:0% + + + + align:start position:0% + +pronounced it's actually + + align:start position:0% +pronounced it's actually + + + align:start position:0% +pronounced it's actually +weipo the world intellectual property + + align:start position:0% +weipo the world intellectual property + + + align:start position:0% +weipo the world intellectual property +organization that because they had an I + + align:start position:0% +organization that because they had an I + + + align:start position:0% +organization that because they had an I +I'm gon to screw this up they had an old + + align:start position:0% +I'm gon to screw this up they had an old + + + align:start position:0% +I'm gon to screw this up they had an old +name um I wish I remember their old name + + align:start position:0% +name um I wish I remember their old name + + + align:start position:0% +name um I wish I remember their old name +but in English like the acronym was like + + align:start position:0% +but in English like the acronym was like + + + align:start position:0% +but in English like the acronym was like +dumb or something like it was they + + align:start position:0% +dumb or something like it was they + + + align:start position:0% +dumb or something like it was they +didn't you know it's an international + + align:start position:0% +didn't you know it's an international + + + align:start position:0% +didn't you know it's an international +organization it's in Geneva Switzerland + + align:start position:0% +organization it's in Geneva Switzerland + + + align:start position:0% +organization it's in Geneva Switzerland +and there's all sorts of people coming + + align:start position:0% +and there's all sorts of people coming + + + align:start position:0% +and there's all sorts of people coming +together but they didn't like that in + + align:start position:0% +together but they didn't like that in + + + align:start position:0% +together but they didn't like that in +English people would call it this bad + + align:start position:0% +English people would call it this bad + + + align:start position:0% +English people would call it this bad +name and I don't remember the original + + align:start position:0% +name and I don't remember the original + + + align:start position:0% +name and I don't remember the original +name so they changed it to World + + align:start position:0% +name so they changed it to World + + + align:start position:0% +name so they changed it to World +intellectual property organization from + + align:start position:0% +intellectual property organization from + + + align:start position:0% +intellectual property organization from +whatever it had been and then they were + + align:start position:0% +whatever it had been and then they were + + + align:start position:0% +whatever it had been and then they were +you know immediately annoyed I guess + + align:start position:0% +you know immediately annoyed I guess + + + align:start position:0% +you know immediately annoyed I guess +they didn't realize but all the + + align:start position:0% +they didn't realize but all the + + + align:start position:0% +they didn't realize but all the +Americans started calling it The + + align:start position:0% +Americans started calling it The + + + align:start position:0% +Americans started calling it The +wio but they were like no it's weo so it + + align:start position:0% +wio but they were like no it's weo so it + + + align:start position:0% +wio but they were like no it's weo so it +is apparently weipo and that actually + + align:start position:0% +is apparently weipo and that actually + + + align:start position:0% +is apparently weipo and that actually +you know one of these Bo you know the + + align:start position:0% +you know one of these Bo you know the + + + align:start position:0% +you know one of these Bo you know the +the prices for the 8.5 cents there's a + + align:start position:0% +the prices for the 8.5 cents there's a + + + align:start position:0% +the prices for the 8.5 cents there's a +lot of those in the kyrid act and one of + + align:start position:0% +lot of those in the kyrid act and one of + + + align:start position:0% +lot of those in the kyrid act and one of +them is set by a group that was or used + + align:start position:0% +them is set by a group that was or used + + + align:start position:0% +them is set by a group that was or used +to be set by a group that was going to + + align:start position:0% +to be set by a group that was going to + + + align:start position:0% +to be set by a group that was going to +be called the copyright royalty + + align:start position:0% +be called the copyright royalty + + + align:start position:0% +be called the copyright royalty +arbitration + + align:start position:0% + + + + align:start position:0% + +tribunal uh but Congress was careful and + + align:start position:0% +tribunal uh but Congress was careful and + + + align:start position:0% +tribunal uh but Congress was careful and +so they decided to call it the copyright + + align:start position:0% +so they decided to call it the copyright + + + align:start position:0% +so they decided to call it the copyright +arbitration royalty sorry it's it's + + align:start position:0% +arbitration royalty sorry it's it's + + + align:start position:0% +arbitration royalty sorry it's it's +panel copyright arbitration royalty + + align:start position:0% +panel copyright arbitration royalty + + + align:start position:0% +panel copyright arbitration royalty +panel well I blew that one but it it I + + align:start position:0% +panel well I blew that one but it it I + + + align:start position:0% +panel well I blew that one but it it I +mean it really it's a copyright royalty + + align:start position:0% +mean it really it's a copyright royalty + + + align:start position:0% +mean it really it's a copyright royalty +arbitration panel but they they don't + + align:start position:0% +arbitration panel but they they don't + + + align:start position:0% +arbitration panel but they they don't +call it that so anyway so in the weipo + + align:start position:0% +call it that so anyway so in the weipo + + + align:start position:0% +call it that so anyway so in the weipo +they had these negotiations and they + + align:start position:0% +they had these negotiations and they + + + align:start position:0% +they had these negotiations and they +agreed on something called the weipo + + align:start position:0% +agreed on something called the weipo + + + align:start position:0% +agreed on something called the weipo +copyright treaty or the wct for short + + align:start position:0% +copyright treaty or the wct for short + + + align:start position:0% +copyright treaty or the wct for short +and + + align:start position:0% +and + + + align:start position:0% +and +uh and and this the weipo copyright + + align:start position:0% +uh and and this the weipo copyright + + + align:start position:0% +uh and and this the weipo copyright +treaty um you know treaties are written + + align:start position:0% +treaty um you know treaties are written + + + align:start position:0% +treaty um you know treaties are written +in sort of very broad language and it + + align:start position:0% +in sort of very broad language and it + + + align:start position:0% +in sort of very broad language and it +says member states will protect blah + + align:start position:0% +says member states will protect blah + + + align:start position:0% +says member states will protect blah +blah blah blah blah um but it says + + align:start position:0% +blah blah blah blah um but it says + + + align:start position:0% +blah blah blah blah um but it says +member states will protect um if their + + align:start position:0% +member states will protect um if their + + + align:start position:0% +member states will protect um if their +works are subject to access control + + align:start position:0% +works are subject to access control + + + align:start position:0% +works are subject to access control +control on the access uh that will be + + align:start position:0% +control on the access uh that will be + + + align:start position:0% +control on the access uh that will be +protected at + + align:start position:0% +protected at + + + align:start position:0% +protected at +law now that's sort of a new word right + + align:start position:0% +law now that's sort of a new word right + + + align:start position:0% +law now that's sort of a new word right +access is there any protection on access + + align:start position:0% +access is there any protection on access + + + align:start position:0% +access is there any protection on access +in the Copyright Act + + align:start position:0% +in the Copyright Act + + + align:start position:0% +in the Copyright Act +now I mean by now I mean + + align:start position:0% +now I mean by now I mean + + + align:start position:0% +now I mean by now I mean +1997 um no there's distribution + + align:start position:0% +1997 um no there's distribution + + + align:start position:0% +1997 um no there's distribution +reproduction derivative Works trans you + + align:start position:0% +reproduction derivative Works trans you + + + align:start position:0% +reproduction derivative Works trans you +know uh performance display but there's + + align:start position:0% +know uh performance display but there's + + + align:start position:0% +know uh performance display but there's +nothing on + + align:start position:0% +nothing on + + + align:start position:0% +nothing on +access um so there's nothing bad about + + align:start position:0% +access um so there's nothing bad about + + + align:start position:0% +access um so there's nothing bad about +accessing those encrypted fonts or on + + align:start position:0% +accessing those encrypted fonts or on + + + align:start position:0% +accessing those encrypted fonts or on +accessing the encrypted uh satellite TV + + align:start position:0% +accessing the encrypted uh satellite TV + + + align:start position:0% +accessing the encrypted uh satellite TV +at least not under the copyright act so + + align:start position:0% +at least not under the copyright act so + + + align:start position:0% +at least not under the copyright act so +they said we need new control on access + + align:start position:0% +they said we need new control on access + + + align:start position:0% +they said we need new control on access +and that's what the weipo copyright + + align:start position:0% +and that's what the weipo copyright + + + align:start position:0% +and that's what the weipo copyright +treaty the countries that ratify that + + align:start position:0% +treaty the countries that ratify that + + + align:start position:0% +treaty the countries that ratify that +pledged to um to to grant that and um + + align:start position:0% +pledged to um to to grant that and um + + + align:start position:0% +pledged to um to to grant that and um +and of course the protections of the weo + + align:start position:0% +and of course the protections of the weo + + + align:start position:0% +and of course the protections of the weo +copyright treaty are only available to + + align:start position:0% +copyright treaty are only available to + + + align:start position:0% +copyright treaty are only available to +Nations who have themselves adopted the + + align:start position:0% +Nations who have themselves adopted the + + + align:start position:0% +Nations who have themselves adopted the +weipo copyright treaty so for instance + + align:start position:0% +weipo copyright treaty so for instance + + + align:start position:0% +weipo copyright treaty so for instance +American Works would only gain the + + align:start position:0% +American Works would only gain the + + + align:start position:0% +American Works would only gain the +protections of the wct abroad in Europe + + align:start position:0% +protections of the wct abroad in Europe + + + align:start position:0% +protections of the wct abroad in Europe +if uh America had ratified the wct so + + align:start position:0% +if uh America had ratified the wct so + + + align:start position:0% +if uh America had ratified the wct so +there's definitely an incentive for us + + align:start position:0% +there's definitely an incentive for us + + + align:start position:0% +there's definitely an incentive for us +to do it especially because America is + + align:start position:0% +to do it especially because America is + + + align:start position:0% +to do it especially because America is +like the world's major exporter of + + align:start position:0% +like the world's major exporter of + + + align:start position:0% +like the world's major exporter of +copyrighted works it's probably us and + + align:start position:0% +copyrighted works it's probably us and + + + align:start position:0% +copyrighted works it's probably us and +then + + align:start position:0% +then + + + align:start position:0% +then +India who do you think is probably + + align:start position:0% +India who do you think is probably + + + align:start position:0% +India who do you think is probably +third I have no idea but + + align:start position:0% +third I have no idea but + + + align:start position:0% +third I have no idea but +uh I think we're in certainly in movies + + align:start position:0% +uh I think we're in certainly in movies + + + align:start position:0% +uh I think we're in certainly in movies +I think it's us and India and I don't + + align:start position:0% +I think it's us and India and I don't + + + align:start position:0% +I think it's us and India and I don't +think there's really I don't know maybe + + align:start position:0% +think there's really I don't know maybe + + + align:start position:0% +think there's really I don't know maybe +probably Japan I really have no idea but + + align:start position:0% +probably Japan I really have no idea but + + + align:start position:0% +probably Japan I really have no idea but +uh so that was another incentive so + + align:start position:0% +uh so that was another incentive so + + + align:start position:0% +uh so that was another incentive so +anyway the Clinton Administration + + align:start position:0% +anyway the Clinton Administration + + + align:start position:0% +anyway the Clinton Administration +decided to ratify the weo copyright + + align:start position:0% +decided to ratify the weo copyright + + + align:start position:0% +decided to ratify the weo copyright +treaty because then America would gain + + align:start position:0% +treaty because then America would gain + + + align:start position:0% +treaty because then America would gain +this these protections worldwide at + + align:start position:0% +this these protections worldwide at + + + align:start position:0% +this these protections worldwide at +least among all the other countries that + + align:start position:0% +least among all the other countries that + + + align:start position:0% +least among all the other countries that +had ratified the weipo copyright treaty + + align:start position:0% +had ratified the weipo copyright treaty + + + align:start position:0% +had ratified the weipo copyright treaty +and so we did ratify it in the fall of + + align:start position:0% +and so we did ratify it in the fall of + + + align:start position:0% +and so we did ratify it in the fall of +1998 six years actually the same day it + + align:start position:0% +1998 six years actually the same day it + + + align:start position:0% +1998 six years actually the same day it +was October 28th + + align:start position:0% +was October 28th + + + align:start position:0% +was October 28th +1998 uh 6 years after they had adopted + + align:start position:0% +1998 uh 6 years after they had adopted + + + align:start position:0% +1998 uh 6 years after they had adopted +the audio home recording act and even + + align:start position:0% +the audio home recording act and even + + + align:start position:0% +the audio home recording act and even +though basically very similar measures + + align:start position:0% +though basically very similar measures + + + align:start position:0% +though basically very similar measures +had failed in Congress in 1995 and 1996 + + align:start position:0% +had failed in Congress in 1995 and 1996 + + + align:start position:0% +had failed in Congress in 1995 and 1996 +once they were part of an international + + align:start position:0% +once they were part of an international + + + align:start position:0% +once they were part of an international +treaty and it was sort of a take it or + + align:start position:0% +treaty and it was sort of a take it or + + + align:start position:0% +treaty and it was sort of a take it or +leave situation in + + align:start position:0% +leave situation in + + + align:start position:0% +leave situation in +1998 um Congress adopted them by by + + align:start position:0% +1998 um Congress adopted them by by + + + align:start position:0% +1998 um Congress adopted them by by +passing a law called + + align:start position:0% +passing a law called + + + align:start position:0% +passing a law called +what the Digital Millennium that Clinton + + align:start position:0% +what the Digital Millennium that Clinton + + + align:start position:0% +what the Digital Millennium that Clinton +administration was really big on those + + align:start position:0% +administration was really big on those + + + align:start position:0% +administration was really big on those +millenniums people remember everything + + align:start position:0% +millenniums people remember everything + + + align:start position:0% +millenniums people remember everything +was about the New + + align:start position:0% +was about the New + + + align:start position:0% +was about the New +Millennium the Digital Millennium + + align:start position:0% +Millennium the Digital Millennium + + + align:start position:0% +Millennium the Digital Millennium +Copyright Act + + align:start position:0% +Copyright Act + + + align:start position:0% +Copyright Act +of + + align:start position:0% +of + + + align:start position:0% +of + + align:start position:0% + + + align:start position:0% +um and this for the first time uh it's + + align:start position:0% +um and this for the first time uh it's + + + align:start position:0% +um and this for the first time uh it's +it sort of added a new exclusive right + + align:start position:0% +it sort of added a new exclusive right + + + align:start position:0% +it sort of added a new exclusive right +and not the the first time but it added + + align:start position:0% +and not the the first time but it added + + + align:start position:0% +and not the the first time but it added +a new exclusive right to the Copyright + + align:start position:0% +a new exclusive right to the Copyright + + + align:start position:0% +a new exclusive right to the Copyright +Act of sorts and it was it it's sort of + + align:start position:0% +Act of sorts and it was it it's sort of + + + align:start position:0% +Act of sorts and it was it it's sort of +an exclusive right to control access to + + align:start position:0% +an exclusive right to control access to + + + align:start position:0% +an exclusive right to control access to +a copyrighted + + align:start position:0% +a copyrighted + + + align:start position:0% +a copyrighted +work so we can look at what it + + align:start position:0% + + + + align:start position:0% + +says oops + + align:start position:0% + + + + align:start position:0% + +okay so this is what they I've got chalk + + align:start position:0% +okay so this is what they I've got chalk + + + align:start position:0% +okay so this is what they I've got chalk +up my nose I'm sorry but uh this is what + + align:start position:0% +up my nose I'm sorry but uh this is what + + + align:start position:0% +up my nose I'm sorry but uh this is what +it says digital M Copyright Act so this + + align:start position:0% +it says digital M Copyright Act so this + + + align:start position:0% +it says digital M Copyright Act so this +is section 121 again sort of outside the + + align:start position:0% +is section 121 again sort of outside the + + + align:start position:0% +is section 121 again sort of outside the +copyri sort of ends at maybe 600 I would + + align:start position:0% +copyri sort of ends at maybe 600 I would + + + align:start position:0% +copyri sort of ends at maybe 600 I would +say but + + align:start position:0% +say but + + + align:start position:0% +say but +1201 I mean it doesn't literally end + + align:start position:0% +1201 I mean it doesn't literally end + + + align:start position:0% +1201 I mean it doesn't literally end +there but the national Cate legislation + + align:start position:0% +there but the national Cate legislation + + + align:start position:0% +there but the national Cate legislation +121 A1A no person so again this is a law + + align:start position:0% +121 A1A no person so again this is a law + + + align:start position:0% +121 A1A no person so again this is a law +that applies to the whole world no + + align:start position:0% +that applies to the whole world no + + + align:start position:0% +that applies to the whole world no +person shall + + align:start position:0% +person shall + + + align:start position:0% +person shall +circumvent a technological measure that + + align:start position:0% +circumvent a technological measure that + + + align:start position:0% +circumvent a technological measure that +effectively controls access to a work + + align:start position:0% +effectively controls access to a work + + + align:start position:0% +effectively controls access to a work +protected under this + + align:start position:0% + + + + align:start position:0% + +title so what does that mean we got we + + align:start position:0% +title so what does that mean we got we + + + align:start position:0% +title so what does that mean we got we +got a lot of terms here just in one + + align:start position:0% +got a lot of terms here just in one + + + align:start position:0% +got a lot of terms here just in one +sense this is basically the whole law of + + align:start position:0% +sense this is basically the whole law of + + + align:start position:0% +sense this is basically the whole law of +course it goes on for like 30 more pages + + align:start position:0% +course it goes on for like 30 more pages + + + align:start position:0% +course it goes on for like 30 more pages +but uh okay what is so we have to ask + + align:start position:0% +but uh okay what is so we have to ask + + + align:start position:0% +but uh okay what is so we have to ask +what is circumvent what is technological + + align:start position:0% +what is circumvent what is technological + + + align:start position:0% +what is circumvent what is technological +measure what's effectively control and + + align:start position:0% +measure what's effectively control and + + + align:start position:0% +measure what's effectively control and +then there's that word access and then + + align:start position:0% +then there's that word access and then + + + align:start position:0% +then there's that word access and then +work protected under this title the last + + align:start position:0% +work protected under this title the last + + + align:start position:0% +work protected under this title the last +one is easy what's a work protected + + align:start position:0% +one is easy what's a work protected + + + align:start position:0% +one is easy what's a work protected +under this + + align:start position:0% +under this + + + align:start position:0% +under this +title what's this + + align:start position:0% +title what's this + + + align:start position:0% +title what's this +title copyright it's title 17 okay and + + align:start position:0% +title copyright it's title 17 okay and + + + align:start position:0% +title copyright it's title 17 okay and +what is um okay so then we go down and + + align:start position:0% +what is um okay so then we go down and + + + align:start position:0% +what is um okay so then we go down and +it tells + + align:start position:0% +it tells + + + align:start position:0% +it tells +us tells + + align:start position:0% + + + + align:start position:0% + +us okay as used in this subsection to + + align:start position:0% +us okay as used in this subsection to + + + align:start position:0% +us okay as used in this subsection to +sech circumvent a technological measure + + align:start position:0% +sech circumvent a technological measure + + + align:start position:0% +sech circumvent a technological measure +means to descramble a scrambled work to + + align:start position:0% +means to descramble a scrambled work to + + + align:start position:0% +means to descramble a scrambled work to +decrypt an encrypted work or otherwise + + align:start position:0% +decrypt an encrypted work or otherwise + + + align:start position:0% +decrypt an encrypted work or otherwise +to avoid bypass remove deactivate or + + align:start position:0% +to avoid bypass remove deactivate or + + + align:start position:0% +to avoid bypass remove deactivate or +impair a technological + + align:start position:0% +impair a technological + + + align:start position:0% +impair a technological +measure without the authority of the + + align:start position:0% +measure without the authority of the + + + align:start position:0% +measure without the authority of the +copyright + + align:start position:0% +copyright + + + align:start position:0% +copyright +owner so it means so to circumvent it is + + align:start position:0% +owner so it means so to circumvent it is + + + align:start position:0% +owner so it means so to circumvent it is +to do any of those activities unless you + + align:start position:0% +to do any of those activities unless you + + + align:start position:0% +to do any of those activities unless you +are authorized by the copyright + + align:start position:0% + + + + align:start position:0% + +owner and and what does it mean if if a + + align:start position:0% +owner and and what does it mean if if a + + + align:start position:0% +owner and and what does it mean if if a +technological what is a technological + + align:start position:0% +technological what is a technological + + + align:start position:0% +technological what is a technological +measure by the way + + align:start position:0% +measure by the way + + + align:start position:0% +measure by the way +that would be like the encryption on the + + align:start position:0% +that would be like the encryption on the + + + align:start position:0% +that would be like the encryption on the +DVD or on the cable TV a technological + + align:start position:0% +DVD or on the cable TV a technological + + + align:start position:0% +DVD or on the cable TV a technological +measure effectively controls access to a + + align:start position:0% +measure effectively controls access to a + + + align:start position:0% +measure effectively controls access to a +work if the measure in the ordinary you + + align:start position:0% +work if the measure in the ordinary you + + + align:start position:0% +work if the measure in the ordinary you +can see how like there's all sorts of + + align:start position:0% +can see how like there's all sorts of + + + align:start position:0% +can see how like there's all sorts of +fodder for people to argue about here in + + align:start position:0% +fodder for people to argue about here in + + + align:start position:0% +fodder for people to argue about here in +the ordinary C this is like my entire + + align:start position:0% +the ordinary C this is like my entire + + + align:start position:0% +the ordinary C this is like my entire +freshman in sophomore year was arguing + + align:start position:0% +freshman in sophomore year was arguing + + + align:start position:0% +freshman in sophomore year was arguing +about this so in the ordinary course of + + align:start position:0% +about this so in the ordinary course of + + + align:start position:0% +about this so in the ordinary course of +his operation requires the application + + align:start position:0% +his operation requires the application + + + align:start position:0% +his operation requires the application +of information or a process or a + + align:start position:0% +of information or a process or a + + + align:start position:0% +of information or a process or a +treatment with the authority of the + + align:start position:0% +treatment with the authority of the + + + align:start position:0% +treatment with the authority of the +coperate owner to gain access to a work + + align:start position:0% + + + + align:start position:0% + +um so this is really hard um it's really + + align:start position:0% +um so this is really hard um it's really + + + align:start position:0% +um so this is really hard um it's really +hard to know what all this means and it + + align:start position:0% +hard to know what all this means and it + + + align:start position:0% +hard to know what all this means and it +doesn't help that they go on you know at + + align:start position:0% +doesn't help that they go on you know at + + + align:start position:0% +doesn't help that they go on you know at +Great + + align:start position:0% + + + + align:start position:0% + +length about this but um what do people + + align:start position:0% +length about this but um what do people + + + align:start position:0% +length about this but um what do people +think that Congress was was probably + + align:start position:0% +think that Congress was was probably + + + align:start position:0% +think that Congress was was probably +getting at here first of all how do we + + align:start position:0% +getting at here first of all how do we + + + align:start position:0% +getting at here first of all how do we +uh explain this kind of Regulation what + + align:start position:0% +uh explain this kind of Regulation what + + + align:start position:0% +uh explain this kind of Regulation what +kind of Regulation is this is it this + + align:start position:0% +kind of Regulation is this is it this + + + align:start position:0% +kind of Regulation is this is it this +kind of Regulation + + align:start position:0% +kind of Regulation + + + align:start position:0% +kind of Regulation +is there a technological + + align:start position:0% + + + + align:start position:0% + +mandate you can't do this versus you + + align:start position:0% +mandate you can't do this versus you + + + align:start position:0% +mandate you can't do this versus you +have to do yeah there's no technological + + align:start position:0% +have to do yeah there's no technological + + + align:start position:0% +have to do yeah there's no technological +mandate and the the um the sort of + + align:start position:0% +mandate and the the um the sort of + + + align:start position:0% +mandate and the the um the sort of +forces of anti like a group called The + + align:start position:0% +forces of anti like a group called The + + + align:start position:0% +forces of anti like a group called The +Home recording rights Coalition which is + + align:start position:0% +Home recording rights Coalition which is + + + align:start position:0% +Home recording rights Coalition which is +paid for by consumer electronics + + align:start position:0% +paid for by consumer electronics + + + align:start position:0% +paid for by consumer electronics +makers um it's all about home recording + + align:start position:0% +makers um it's all about home recording + + + align:start position:0% +makers um it's all about home recording +they were very concerned that there' be + + align:start position:0% +they were very concerned that there' be + + + align:start position:0% +they were very concerned that there' be +no mandate on the technology + + align:start position:0% +no mandate on the technology + + + align:start position:0% +no mandate on the technology +companies they were they said this law + + align:start position:0% +companies they were they said this law + + + align:start position:0% +companies they were they said this law +should not apply to us in the honest + + align:start position:0% +should not apply to us in the honest + + + align:start position:0% +should not apply to us in the honest +course of our business we should be able + + align:start position:0% +course of our business we should be able + + + align:start position:0% +course of our business we should be able +to design our DVD player however we like + + align:start position:0% +to design our DVD player however we like + + + align:start position:0% +to design our DVD player however we like +or our um you know our computer however + + align:start position:0% +or our um you know our computer however + + + align:start position:0% +or our um you know our computer however +we like and you you shouldn't tell us we + + align:start position:0% +we like and you you shouldn't tell us we + + + align:start position:0% +we like and you you shouldn't tell us we +have to implement some form of copy + + align:start position:0% +have to implement some form of copy + + + align:start position:0% +have to implement some form of copy +protection we have to look for in the + + align:start position:0% +protection we have to look for in the + + + align:start position:0% +protection we have to look for in the +audio home recording act you have to + + align:start position:0% +audio home recording act you have to + + + align:start position:0% +audio home recording act you have to +look for some flag that's getting sent + + align:start position:0% +look for some flag that's getting sent + + + align:start position:0% +look for some flag that's getting sent +to you that says that you can't let the + + align:start position:0% +to you that says that you can't let the + + + align:start position:0% +to you that says that you can't let the +user copy this anymore and if the flag + + align:start position:0% +user copy this anymore and if the flag + + + align:start position:0% +user copy this anymore and if the flag +says no more copies you cannot allow any + + align:start position:0% +says no more copies you cannot allow any + + + align:start position:0% +says no more copies you cannot allow any +more copies that's what the law says + + align:start position:0% +more copies that's what the law says + + + align:start position:0% +more copies that's what the law says +that's what the sereral copy management + + align:start position:0% +that's what the sereral copy management + + + align:start position:0% +that's what the sereral copy management +system does and you have to obey that + + align:start position:0% +system does and you have to obey that + + + align:start position:0% +system does and you have to obey that +you have to build that into your + + align:start position:0% +you have to build that into your + + + align:start position:0% +you have to build that into your +technology the Digital Millennium + + align:start position:0% +technology the Digital Millennium + + + align:start position:0% +technology the Digital Millennium +Copyright Act it's it's not like that it + + align:start position:0% +Copyright Act it's it's not like that it + + + align:start position:0% +Copyright Act it's it's not like that it +has no mandate if you're building a a + + align:start position:0% +has no mandate if you're building a a + + + align:start position:0% +has no mandate if you're building a a +um let's say You're Building Adobe + + align:start position:0% +um let's say You're Building Adobe + + + align:start position:0% +um let's say You're Building Adobe +Acrobat Reader and uh and the Adobe + + align:start position:0% +Acrobat Reader and uh and the Adobe + + + align:start position:0% +Acrobat Reader and uh and the Adobe +Acrobat file the PDF file has a little + + align:start position:0% +Acrobat file the PDF file has a little + + + align:start position:0% +Acrobat file the PDF file has a little +flag on the top that says the user + + align:start position:0% +flag on the top that says the user + + + align:start position:0% +flag on the top that says the user +cannot print this file and you're + + align:start position:0% +cannot print this file and you're + + + align:start position:0% +cannot print this file and you're +writing that software do you have to + + align:start position:0% +writing that software do you have to + + + align:start position:0% +writing that software do you have to +obey + + align:start position:0% + + + + align:start position:0% + +that if it says printing forbidden do + + align:start position:0% +that if it says printing forbidden do + + + align:start position:0% +that if it says printing forbidden do +you have to obey that if you're writing + + align:start position:0% +you have to obey that if you're writing + + + align:start position:0% +you have to obey that if you're writing +you know an acrobat + + align:start position:0% + + + + align:start position:0% + +reader yes + + align:start position:0% +reader yes + + + align:start position:0% +reader yes +why it says you can't copy it I mean you + + align:start position:0% +why it says you can't copy it I mean you + + + align:start position:0% +why it says you can't copy it I mean you +can't print it and that's technical + + align:start position:0% +can't print it and that's technical + + + align:start position:0% +can't print it and that's technical +measure which prevents you from + + align:start position:0% +measure which prevents you from + + + align:start position:0% +measure which prevents you from +accessing the printed word when + + align:start position:0% + + + + align:start position:0% + +it's yeah I mean so what's a + + align:start position:0% +it's yeah I mean so what's a + + + align:start position:0% +it's yeah I mean so what's a +technological + + align:start position:0% + + + + align:start position:0% + +measure um to circumvent Tech what's + + align:start position:0% +measure um to circumvent Tech what's + + + align:start position:0% +measure um to circumvent Tech what's +forbidden is + + align:start position:0% +forbidden is + + + align:start position:0% +forbidden is +circumventing and to circumvent means to + + align:start position:0% +circumventing and to circumvent means to + + + align:start position:0% +circumventing and to circumvent means to +descramble to decrypt to avoid bypass + + align:start position:0% +descramble to decrypt to avoid bypass + + + align:start position:0% +descramble to decrypt to avoid bypass +remove deactivate or impair a + + align:start position:0% +remove deactivate or impair a + + + align:start position:0% +remove deactivate or impair a +technological + + align:start position:0% + + + + align:start position:0% + +measure what what what is it mean if a + + align:start position:0% +measure what what what is it mean if a + + + align:start position:0% +measure what what what is it mean if a +technological measure effectively + + align:start position:0% +technological measure effectively + + + align:start position:0% +technological measure effectively +controls access it means that the + + align:start position:0% +controls access it means that the + + + align:start position:0% +controls access it means that the +measure in the ordinary course of its + + align:start position:0% +measure in the ordinary course of its + + + align:start position:0% +measure in the ordinary course of its +operation requires you you to put in + + align:start position:0% +operation requires you you to put in + + + align:start position:0% +operation requires you you to put in +information or a process or a treatment + + align:start position:0% +information or a process or a treatment + + + align:start position:0% +information or a process or a treatment +to get access is that little message + + align:start position:0% +to get access is that little message + + + align:start position:0% +to get access is that little message +that says no printing permitted is that + + align:start position:0% +that says no printing permitted is that + + + align:start position:0% +that says no printing permitted is that +really a technological + + align:start position:0% +really a technological + + + align:start position:0% +really a technological +measure well do you think do you say + + align:start position:0% +measure well do you think do you say + + + align:start position:0% +measure well do you think do you say +yes well if if the thing is just a + + align:start position:0% +yes well if if the thing is just a + + + align:start position:0% +yes well if if the thing is just a +message and you can still print it is + + align:start position:0% +message and you can still print it is + + + align:start position:0% +message and you can still print it is +going and hitting the print button well + + align:start position:0% +going and hitting the print button well + + + align:start position:0% +going and hitting the print button well +no but you're writing the sof you are + + align:start position:0% +no but you're writing the sof you are + + + align:start position:0% +no but you're writing the sof you are +writing the software and Adobe puts + + align:start position:0% +writing the software and Adobe puts + + + align:start position:0% +writing the software and Adobe puts +something in their specification that + + align:start position:0% +something in their specification that + + + align:start position:0% +something in their specification that +says if it says no printing the software + + align:start position:0% +says if it says no printing the software + + + align:start position:0% +says if it says no printing the software +writer must forbid printing that's in + + align:start position:0% +writer must forbid printing that's in + + + align:start position:0% +writer must forbid printing that's in +the + + align:start position:0% +the + + + align:start position:0% +the +specification that's probably not cover + + align:start position:0% +specification that's probably not cover + + + align:start position:0% +specification that's probably not cover +okay yeah Michael yeah but what if it + + align:start position:0% +okay yeah Michael yeah but what if it + + + align:start position:0% +okay yeah Michael yeah but what if it +says no printing without this encrypted + + align:start position:0% +says no printing without this encrypted + + + align:start position:0% +says no printing without this encrypted +password what do you mean like what if a + + align:start position:0% +password what do you mean like what if a + + + align:start position:0% +password what do you mean like what if a +PDF file requires the use of a password + + align:start position:0% +PDF file requires the use of a password + + + align:start position:0% +PDF file requires the use of a password +to print + + align:start position:0% +to print + + + align:start position:0% +to print +it + + align:start position:0% +it + + + align:start position:0% +it +uh like how would that work I don't know + + align:start position:0% +uh like how would that work I don't know + + + align:start position:0% +uh like how would that work I don't know +I've never looked at how the PDF files + + align:start position:0% +I've never looked at how the PDF files + + + align:start position:0% +I've never looked at how the PDF files +work but suppose that you wrote a format + + align:start position:0% +work but suppose that you wrote a format + + + align:start position:0% +work but suppose that you wrote a format +that did work that way would writing a + + align:start position:0% +that did work that way would writing a + + + align:start position:0% +that did work that way would writing a +reader that ignored that be a + + align:start position:0% +reader that ignored that be a + + + align:start position:0% +reader that ignored that be a +problem well it's a hard question we + + align:start position:0% +problem well it's a hard question we + + + align:start position:0% +problem well it's a hard question we +have to ask if it effectively controls + + align:start position:0% +have to ask if it effectively controls + + + align:start position:0% +have to ask if it effectively controls +access to the work if the if I mean what + + align:start position:0% +access to the work if the if I mean what + + + align:start position:0% +access to the work if the if I mean what +I would say is if the software can get + + align:start position:0% +I would say is if the software can get + + + align:start position:0% +I would say is if the software can get +enough of the PDF in order to render it + + align:start position:0% +enough of the PDF in order to render it + + + align:start position:0% +enough of the PDF in order to render it +on the screen without needing that + + align:start position:0% +on the screen without needing that + + + align:start position:0% +on the screen without needing that +password then it doesn't seem to me that + + align:start position:0% +password then it doesn't seem to me that + + + align:start position:0% +password then it doesn't seem to me that +the technological measure effectively + + align:start position:0% +the technological measure effectively + + + align:start position:0% +the technological measure effectively +controls access to the work and if the + + align:start position:0% +controls access to the work and if the + + + align:start position:0% +controls access to the work and if the +software is is happy to print the part + + align:start position:0% +software is is happy to print the part + + + align:start position:0% +software is is happy to print the part +of it that it can render the SC without + + align:start position:0% +of it that it can render the SC without + + + align:start position:0% +of it that it can render the SC without +the password seems to me that's not + + align:start position:0% +the password seems to me that's not + + + align:start position:0% +the password seems to me that's not +circumventing + + align:start position:0% + + + + align:start position:0% + +anything so so it's not like the audio + + align:start position:0% +anything so so it's not like the audio + + + align:start position:0% +anything so so it's not like the audio +home recording act it doesn't say if + + align:start position:0% +home recording act it doesn't say if + + + align:start position:0% +home recording act it doesn't say if +this flag is present you must look for + + align:start position:0% +this flag is present you must look for + + + align:start position:0% +this flag is present you must look for +it and you must design the circuit to + + align:start position:0% +it and you must design the circuit to + + + align:start position:0% +it and you must design the circuit to +look for it and Obey it it's not like + + align:start position:0% +look for it and Obey it it's not like + + + align:start position:0% +look for it and Obey it it's not like +that at all it says it it say it's not + + align:start position:0% +that at all it says it it say it's not + + + align:start position:0% +that at all it says it it say it's not +the job of the device manufacturer to + + align:start position:0% +the job of the device manufacturer to + + + align:start position:0% +the job of the device manufacturer to +control the copy which it is in the + + align:start position:0% +control the copy which it is in the + + + align:start position:0% +control the copy which it is in the +audio home recording act it's the job of + + align:start position:0% +audio home recording act it's the job of + + + align:start position:0% +audio home recording act it's the job of +the person who publishes the work to put + + align:start position:0% +the person who publishes the work to put + + + align:start position:0% +the person who publishes the work to put +this technological measure on it to + + align:start position:0% +this technological measure on it to + + + align:start position:0% +this technological measure on it to +control the copy so the responsibility + + align:start position:0% +control the copy so the responsibility + + + align:start position:0% +control the copy so the responsibility +is + + align:start position:0% +is + + + align:start position:0% +is +not it would have been smart to have + + align:start position:0% +not it would have been smart to have + + + align:start position:0% +not it would have been smart to have +some clever diagram but the + + align:start position:0% +some clever diagram but the + + + align:start position:0% +some clever diagram but the +responsibility is not on the consumer's + + align:start position:0% +responsibility is not on the consumer's + + + align:start position:0% +responsibility is not on the consumer's +side to obey some instruction the + + align:start position:0% +side to obey some instruction the + + + align:start position:0% +side to obey some instruction the +responsibility is on the publisher side + + align:start position:0% +responsibility is on the publisher side + + + align:start position:0% +responsibility is on the publisher side +to put this technological measure on it + + align:start position:0% +to put this technological measure on it + + + align:start position:0% +to put this technological measure on it +to stop you in the ordinary course of + + align:start position:0% +to stop you in the ordinary course of + + + align:start position:0% +to stop you in the ordinary course of +its operation from from doing whatever + + align:start position:0% +its operation from from doing whatever + + + align:start position:0% +its operation from from doing whatever +it is they don't want you to do gaining + + align:start position:0% +it is they don't want you to do gaining + + + align:start position:0% +it is they don't want you to do gaining +access without something extra some + + align:start position:0% +access without something extra some + + + align:start position:0% +access without something extra some +information some processor some + + align:start position:0% +information some processor some + + + align:start position:0% +information some processor some +treatment + + align:start position:0% +treatment + + + align:start position:0% +treatment +um and if they put that on then yes you + + align:start position:0% +um and if they put that on then yes you + + + align:start position:0% +um and if they put that on then yes you +can't be all clever and use your + + align:start position:0% +can't be all clever and use your + + + align:start position:0% +can't be all clever and use your +education to circumvent it but it it's + + align:start position:0% +education to circumvent it but it it's + + + align:start position:0% +education to circumvent it but it it's +their job at least initially to stop + + align:start position:0% +their job at least initially to stop + + + align:start position:0% +their job at least initially to stop +you so um is this you know do people + + align:start position:0% +you so um is this you know do people + + + align:start position:0% +you so um is this you know do people +have any thoughts on this this way of + + align:start position:0% +have any thoughts on this this way of + + + align:start position:0% +have any thoughts on this this way of +regulating + + align:start position:0% + + + + align:start position:0% + +I mean is this preferable to saying if + + align:start position:0% +I mean is this preferable to saying if + + + align:start position:0% +I mean is this preferable to saying if +you're making if you're making the PDF + + align:start position:0% +you're making if you're making the PDF + + + align:start position:0% +you're making if you're making the PDF +viewer you have to look for that + + align:start position:0% + + + + align:start position:0% + +flag it's more ambiguous more ambiguous + + align:start position:0% +flag it's more ambiguous more ambiguous + + + align:start position:0% +flag it's more ambiguous more ambiguous +yeah hard though I mean how do you + + align:start position:0% +yeah hard though I mean how do you + + + align:start position:0% +yeah hard though I mean how do you +expect to write your program to expect + + align:start position:0% +expect to write your program to expect + + + align:start position:0% +expect to write your program to expect +any type + + align:start position:0% +any type + + + align:start position:0% +any type +of like things to obey like what if it's + + align:start position:0% +of like things to obey like what if it's + + + align:start position:0% +of like things to obey like what if it's +not just printing what it's like other + + align:start position:0% +not just printing what it's like other + + + align:start position:0% +not just printing what it's like other +things as well and it seems so hard to + + align:start position:0% +things as well and it seems so hard to + + + align:start position:0% +things as well and it seems so hard to +read program to do that + + align:start position:0% +read program to do that + + + align:start position:0% +read program to do that +yeah well and and in here the dmca + + align:start position:0% +yeah well and and in here the dmca + + + align:start position:0% +yeah well and and in here the dmca +doesn't really put any obligations on + + align:start position:0% +doesn't really put any obligations on + + + align:start position:0% +doesn't really put any obligations on +the person who's writing the sort of + + align:start position:0% +the person who's writing the sort of + + + align:start position:0% +the person who's writing the sort of +viewer the + + align:start position:0% +viewer the + + + align:start position:0% +viewer the +receiver that person just has to do + + align:start position:0% +receiver that person just has to do + + + align:start position:0% +receiver that person just has to do +whatever they would normally do and it's + + align:start position:0% +whatever they would normally do and it's + + + align:start position:0% +whatever they would normally do and it's +the job of the publisher to put on a + + align:start position:0% +the job of the publisher to put on a + + + align:start position:0% +the job of the publisher to put on a +technological measure that will in + + align:start position:0% +technological measure that will in + + + align:start position:0% +technological measure that will in +ordinarily require something + + align:start position:0% +ordinarily require something + + + align:start position:0% +ordinarily require something +extra like that could be like an + + align:start position:0% +extra like that could be like an + + + align:start position:0% +extra like that could be like an +encryption key for a DVD or the people + + align:start position:0% +encryption key for a DVD or the people + + + align:start position:0% +encryption key for a DVD or the people +have like Direct + + align:start position:0% +have like Direct + + + align:start position:0% +have like Direct +TV Direct TV you have to you have to + + align:start position:0% +TV Direct TV you have to you have to + + + align:start position:0% +TV Direct TV you have to you have to +have like a little card right + + align:start position:0% +have like a little card right + + + align:start position:0% +have like a little card right +for it to + + align:start position:0% + + + + align:start position:0% + +work + + align:start position:0% +work + + + align:start position:0% +work +um okay so but you guys are many of you + + align:start position:0% +um okay so but you guys are many of you + + + align:start position:0% +um okay so but you guys are many of you +are majoring in course 6 right what are + + align:start position:0% +are majoring in course 6 right what are + + + align:start position:0% +are majoring in course 6 right what are +some of the problems with this + + align:start position:0% +some of the problems with this + + + align:start position:0% +some of the problems with this +approach first of all do these + + align:start position:0% +approach first of all do these + + + align:start position:0% +approach first of all do these +technological measures uh exist like + + align:start position:0% +technological measures uh exist like + + + align:start position:0% +technological measures uh exist like +what what is a technological + + align:start position:0% +what what is a technological + + + align:start position:0% +what what is a technological +measure do they like + + align:start position:0% + + + + align:start position:0% + +exist okay like what um like evds have + + align:start position:0% +exist okay like what um like evds have + + + align:start position:0% +exist okay like what um like evds have +some form of + + align:start position:0% +some form of + + + align:start position:0% +some form of +encryption yeah that's going to be my + + align:start position:0% +encryption yeah that's going to be my + + + align:start position:0% +encryption yeah that's going to be my +good example of something that's a very + + align:start position:0% +good example of something that's a very + + + align:start position:0% +good example of something that's a very +tricky case they work well but they + + align:start position:0% +tricky case they work well but they + + + align:start position:0% +tricky case they work well but they +exist yeah um + + align:start position:0% +exist yeah um + + + align:start position:0% +exist yeah um +okay I mean what is the Contemporary + + align:start position:0% +okay I mean what is the Contemporary + + + align:start position:0% +okay I mean what is the Contemporary +term for these technological measures + + align:start position:0% +term for these technological measures + + + align:start position:0% +term for these technological measures +what do + + align:start position:0% +what do + + + align:start position:0% +what do +people call + + align:start position:0% +people call + + + align:start position:0% +people call +it DRM yeah now that this is a pretty + + align:start position:0% +it DRM yeah now that this is a pretty + + + align:start position:0% +it DRM yeah now that this is a pretty +new term what does DRM stand + + align:start position:0% +new term what does DRM stand + + + align:start position:0% +new term what does DRM stand +for dig management what it does it okay + + align:start position:0% +for dig management what it does it okay + + + align:start position:0% +for dig management what it does it okay +and can somebody explain how DRM works + + align:start position:0% +and can somebody explain how DRM works + + + align:start position:0% +and can somebody explain how DRM works +like on a + + align:start position:0% + + + + align:start position:0% + +computer Comm people that can say uh you + + align:start position:0% +computer Comm people that can say uh you + + + align:start position:0% +computer Comm people that can say uh you +can't you can't uh move that file to + + align:start position:0% +can't you can't uh move that file to + + + align:start position:0% +can't you can't uh move that file to +computer yeah and how does that + + align:start position:0% +computer yeah and how does that + + + align:start position:0% +computer yeah and how does that +work secret it's a + + align:start position:0% +work secret it's a + + + align:start position:0% +work secret it's a +secret um how do computers work like + + align:start position:0% +secret um how do computers work like + + + align:start position:0% +secret um how do computers work like +when you get a program is the way it + + align:start position:0% +when you get a program is the way it + + + align:start position:0% +when you get a program is the way it +operates like a real secret you + + align:start position:0% +operates like a real secret you + + + align:start position:0% +operates like a real secret you +think I mean what is a computer program + + align:start position:0% +think I mean what is a computer program + + + align:start position:0% +think I mean what is a computer program +right instructions it's a like a list of + + align:start position:0% +right instructions it's a like a list of + + + align:start position:0% +right instructions it's a like a list of +instructions to the + + align:start position:0% +instructions to the + + + align:start position:0% +instructions to the +computer um so how how would you keep a + + align:start position:0% +computer um so how how would you keep a + + + align:start position:0% +computer um so how how would you keep a +secret about how iTunes + + align:start position:0% + + + + align:start position:0% + +works by making sure people don't tell + + align:start position:0% +works by making sure people don't tell + + + align:start position:0% +works by making sure people don't tell +other people okay but when Apple has to + + align:start position:0% +other people okay but when Apple has to + + + align:start position:0% +other people okay but when Apple has to +publish the software + + align:start position:0% +publish the software + + + align:start position:0% +publish the software +right so they they sort of do tell + + align:start position:0% +right so they they sort of do tell + + + align:start position:0% +right so they they sort of do tell +everybody encrytion they use + + align:start position:0% +everybody encrytion they use + + + align:start position:0% +everybody encrytion they use +encryption how does the encryption stop + + align:start position:0% +encryption how does the encryption stop + + + align:start position:0% +encryption how does the encryption stop +stop you from learning how it + + align:start position:0% +stop you from learning how it + + + align:start position:0% +stop you from learning how it +works it's if you can't decrypt it + + align:start position:0% +works it's if you can't decrypt it + + + align:start position:0% +works it's if you can't decrypt it +that's giberish that's true but we're + + align:start position:0% +that's giberish that's true but we're + + + align:start position:0% +that's giberish that's true but we're +talkinging about the program right you + + align:start position:0% +talkinging about the program right you + + + align:start position:0% +talkinging about the program right you +can't get the source code you can't get + + align:start position:0% +can't get the source code you can't get + + + align:start position:0% +can't get the source code you can't get +the source code that's true but you can + + align:start position:0% +the source code that's true but you can + + + align:start position:0% +the source code that's true but you can +get the computer code right the code + + align:start position:0% +get the computer code right the code + + + align:start position:0% +get the computer code right the code +that the chip uses and can the I mean + + align:start position:0% +that the chip uses and can the I mean + + + align:start position:0% +that the chip uses and can the I mean +the chip can decrypt it right somebody's + + align:start position:0% +the chip can decrypt it right somebody's + + + align:start position:0% +the chip can decrypt it right somebody's +got to be able to decrypt it in order to + + align:start position:0% +got to be able to decrypt it in order to + + + align:start position:0% +got to be able to decrypt it in order to +use it the US not supposed to see the + + align:start position:0% +use it the US not supposed to see the + + + align:start position:0% +use it the US not supposed to see the +decry version the user is not supposed + + align:start position:0% +decry version the user is not supposed + + + align:start position:0% +decry version the user is not supposed +to see the decrypted version that's true + + align:start position:0% +to see the decrypted version that's true + + + align:start position:0% +to see the decrypted version that's true +but still bre + + align:start position:0% +but still bre + + + align:start position:0% +but still bre +like I mean is there like a class at MIT + + align:start position:0% +like I mean is there like a class at MIT + + + align:start position:0% +like I mean is there like a class at MIT +where they teach you how to write + + align:start position:0% +where they teach you how to write + + + align:start position:0% +where they teach you how to write +computer program that can be run but not + + align:start position:0% +computer program that can be run but not + + + align:start position:0% +computer program that can be run but not +looked + + align:start position:0% +looked + + + align:start position:0% +looked +at 61 + + align:start position:0% +at 61 + + + align:start position:0% +at 61 +61 oh very + + align:start position:0% +61 oh very + + + align:start position:0% +61 oh very +clever uh I asked how the guest lecture + + align:start position:0% +clever uh I asked how the guest lecture + + + align:start position:0% +clever uh I asked how the guest lecture +today but he's + + align:start position:0% +today but he's + + + align:start position:0% +today but he's +like I don't know what he said he said + + align:start position:0% +like I don't know what he said he said + + + align:start position:0% +like I don't know what he said he said +no but what does it say in the 61 + + align:start position:0% +no but what does it say in the 61 + + + align:start position:0% +no but what does it say in the 61 +book about what is the purpose of of + + align:start position:0% +book about what is the purpose of of + + + align:start position:0% +book about what is the purpose of of +code people can read it people can read + + align:start position:0% +code people can read it people can read + + + align:start position:0% +code people can read it people can read +it but what else do they say well yeah + + align:start position:0% +it but what else do they say well yeah + + + align:start position:0% +it but what else do they say well yeah +so people can read it's also for a + + align:start position:0% +so people can read it's also for a + + + align:start position:0% +so people can read it's also for a +computer to read right but it's but + + align:start position:0% +computer to read right but it's but + + + align:start position:0% +computer to read right but it's but +people to read it and this is what we + + align:start position:0% +people to read it and this is what we + + + align:start position:0% +people to read it and this is what we +teach in the first day of computer + + align:start position:0% +teach in the first day of computer + + + align:start position:0% +teach in the first day of computer +science which they also say what's the + + align:start position:0% +science which they also say what's the + + + align:start position:0% +science which they also say what's the +also say in the first page of 61 book + + align:start position:0% +also say in the first page of 61 book + + + align:start position:0% +also say in the first page of 61 book +it's not about computers and it's not + + align:start position:0% +it's not about computers and it's not + + + align:start position:0% +it's not about computers and it's not +science that's what it says okay so um + + align:start position:0% +science that's what it says okay so um + + + align:start position:0% +science that's what it says okay so um +so is there a class in MIT how they'll + + align:start position:0% +so is there a class in MIT how they'll + + + align:start position:0% +so is there a class in MIT how they'll +teach you the reverse of that that you + + align:start position:0% +teach you the reverse of that that you + + + align:start position:0% +teach you the reverse of that that you +can write a computer program that + + align:start position:0% +can write a computer program that + + + align:start position:0% +can write a computer program that +computers can read but people cannot + + align:start position:0% +computers can read but people cannot + + + align:start position:0% +computers can read but people cannot +where where do we learn how to do + + align:start position:0% + + + + align:start position:0% + +that 64 64 how do you do + + align:start position:0% +that 64 64 how do you do + + + align:start position:0% +that 64 64 how do you do +it well you can write numbers just like + + align:start position:0% +it well you can write numbers just like + + + align:start position:0% +it well you can write numbers just like +the native go this and yeah I mean you + + align:start position:0% +the native go this and yeah I mean you + + + align:start position:0% +the native go this and yeah I mean you +can still read it it's just going to + + align:start position:0% +can still read it it's just going to + + + align:start position:0% +can still read it it's just going to +take you a very long time it would take + + align:start position:0% +take you a very long time it would take + + + align:start position:0% +take you a very long time it would take +you a long + + align:start position:0% +you a long + + + align:start position:0% +you a long +time + + align:start position:0% +time + + + align:start position:0% +time +yeah I mean this is a pretty nent field + + align:start position:0% +yeah I mean this is a pretty nent field + + + align:start position:0% +yeah I mean this is a pretty nent field +and uh it's not really what you would + + align:start position:0% +and uh it's not really what you would + + + align:start position:0% +and uh it's not really what you would +call like a legitimate field of + + align:start position:0% +call like a legitimate field of + + + align:start position:0% +call like a legitimate field of +engineering + + align:start position:0% +engineering + + + align:start position:0% +engineering +yet I mean there's no classes in it uh + + align:start position:0% +yet I mean there's no classes in it uh + + + align:start position:0% +yet I mean there's no classes in it uh +there's nobody who's really an expert on + + align:start position:0% +there's nobody who's really an expert on + + + align:start position:0% +there's nobody who's really an expert on +it + + align:start position:0% +it + + + align:start position:0% +it +um there's techniques that people use + + align:start position:0% +um there's techniques that people use + + + align:start position:0% +um there's techniques that people use +one of them that's very good is to have + + align:start position:0% +one of them that's very good is to have + + + align:start position:0% +one of them that's very good is to have +um some extra chip that's outside the + + align:start position:0% +um some extra chip that's outside the + + + align:start position:0% +um some extra chip that's outside the +processor and that's the chip that + + align:start position:0% +processor and that's the chip that + + + align:start position:0% +processor and that's the chip that +actually does the part that you're + + align:start position:0% +actually does the part that you're + + + align:start position:0% +actually does the part that you're +concerned about and then the chip can be + + align:start position:0% +concerned about and then the chip can be + + + align:start position:0% +concerned about and then the chip can be +sealed in uh the best kind or sealed in + + align:start position:0% +sealed in uh the best kind or sealed in + + + align:start position:0% +sealed in uh the best kind or sealed in +like sulfuric acid and if you try and + + align:start position:0% +like sulfuric acid and if you try and + + + align:start position:0% +like sulfuric acid and if you try and +break open the container it melts the + + align:start position:0% +break open the container it melts the + + + align:start position:0% +break open the container it melts the +chip those are awesome and in fact you + + align:start position:0% +chip those are awesome and in fact you + + + align:start position:0% +chip those are awesome and in fact you +know you can get the encyclopedia + + align:start position:0% +know you can get the encyclopedia + + + align:start position:0% +know you can get the encyclopedia +branica on cdrom but the cdrom will be + + align:start position:0% +branica on cdrom but the cdrom will be + + + align:start position:0% +branica on cdrom but the cdrom will be +encrypted and you have to plug in a + + align:start position:0% +encrypted and you have to plug in a + + + align:start position:0% +encrypted and you have to plug in a +little dongle to the keyboard port and + + align:start position:0% +little dongle to the keyboard port and + + + align:start position:0% +little dongle to the keyboard port and +the dongle has the encryption key and if + + align:start position:0% +the dongle has the encryption key and if + + + align:start position:0% +the dongle has the encryption key and if +you try and break it open sulfuric acid + + align:start position:0% +you try and break it open sulfuric acid + + + align:start position:0% +you try and break it open sulfuric acid +you know melts the encryption + + align:start position:0% +you know melts the encryption + + + align:start position:0% +you know melts the encryption +key so that's a good example of DRM that + + align:start position:0% +key so that's a good example of DRM that + + + align:start position:0% +key so that's a good example of DRM that +um I mean that's a good technique that + + align:start position:0% +um I mean that's a good technique that + + + align:start position:0% +um I mean that's a good technique that +you can't look at it because sulfuric + + align:start position:0% +you can't look at it because sulfuric + + + align:start position:0% +you can't look at it because sulfuric +acid will melt it um on the other hand + + align:start position:0% +acid will melt it um on the other hand + + + align:start position:0% +acid will melt it um on the other hand +for insect branica eventually the + + align:start position:0% +for insect branica eventually the + + + align:start position:0% +for insect branica eventually the +computer you know is gets to see the + + align:start position:0% +computer you know is gets to see the + + + align:start position:0% +computer you know is gets to see the +page of Encyclopedia britanica so you + + align:start position:0% +page of Encyclopedia britanica so you + + + align:start position:0% +page of Encyclopedia britanica so you +could write some sort of bad thing on + + align:start position:0% +could write some sort of bad thing on + + + align:start position:0% +could write some sort of bad thing on +the computer now maybe the encryption + + align:start position:0% +the computer now maybe the encryption + + + align:start position:0% +the computer now maybe the encryption +key makes you only be able to look at + + align:start position:0% +key makes you only be able to look at + + + align:start position:0% +key makes you only be able to look at +one page every three hours or something + + align:start position:0% +one page every three hours or something + + + align:start position:0% +one page every three hours or something +so you couldn't do it very quickly they + + align:start position:0% +so you couldn't do it very quickly they + + + align:start position:0% +so you couldn't do it very quickly they +can stop you there or maybe the + + align:start position:0% +can stop you there or maybe the + + + align:start position:0% +can stop you there or maybe the +encryption key you know the dongle has + + align:start position:0% +encryption key you know the dongle has + + + align:start position:0% +encryption key you know the dongle has +its own monitor built in and somehow + + align:start position:0% +its own monitor built in and somehow + + + align:start position:0% +its own monitor built in and somehow +they stop you from taking a picture of + + align:start position:0% +they stop you from taking a picture of + + + align:start position:0% +they stop you from taking a picture of +the monitor I it gets it gets very + + align:start position:0% +the monitor I it gets it gets very + + + align:start position:0% +the monitor I it gets it gets very +tricky yeah I think the princi is to + + align:start position:0% +tricky yeah I think the princi is to + + + align:start position:0% +tricky yeah I think the princi is to +prevent like copying with a reasonable + + align:start position:0% +prevent like copying with a reasonable + + + align:start position:0% +prevent like copying with a reasonable +amount of effort right like you could do + + align:start position:0% +amount of effort right like you could do + + + align:start position:0% +amount of effort right like you could do +copies few years doing it so a lot of + + align:start position:0% +copies few years doing it so a lot of + + + align:start position:0% +copies few years doing it so a lot of +people raised these concerns and the + + align:start position:0% +people raised these concerns and the + + + align:start position:0% +people raised these concerns and the +content Industries replied we're not out + + align:start position:0% +content Industries replied we're not out + + + align:start position:0% +content Industries replied we're not out +to + + align:start position:0% +to + + + align:start position:0% +to +stop the chin you know that we have a + + align:start position:0% +stop the chin you know that we have a + + + align:start position:0% +stop the chin you know that we have a +big there's a big problem for Chinese + + align:start position:0% +big there's a big problem for Chinese + + + align:start position:0% +big there's a big problem for Chinese +bootlegging um and you know you can go + + align:start position:0% +bootlegging um and you know you can go + + + align:start position:0% +bootlegging um and you know you can go +to my dad is a big fan of movies and he + + align:start position:0% +to my dad is a big fan of movies and he + + + align:start position:0% +to my dad is a big fan of movies and he +went to Beijing and he got all these + + align:start position:0% +went to Beijing and he got all these + + + align:start position:0% +went to Beijing and he got all these +DVDs and he brought them back from like + + align:start position:0% +DVDs and he brought them back from like + + + align:start position:0% +DVDs and he brought them back from like +Dad these are bootlegs but he's like + + align:start position:0% +Dad these are bootlegs but he's like + + + align:start position:0% +Dad these are bootlegs but he's like +it's so cheap you know but anyway um so + + align:start position:0% +it's so cheap you know but anyway um so + + + align:start position:0% +it's so cheap you know but anyway um so +the um the the the you know a lot of + + align:start position:0% +the um the the the you know a lot of + + + align:start position:0% +the um the the the you know a lot of +people raise these objections look DRM + + align:start position:0% +people raise these objections look DRM + + + align:start position:0% +people raise these objections look DRM +it just doesn't really at least in a + + align:start position:0% +it just doesn't really at least in a + + + align:start position:0% +it just doesn't really at least in a +computer doesn't really exist yes you + + align:start position:0% +computer doesn't really exist yes you + + + align:start position:0% +computer doesn't really exist yes you +can build a uh a direct TV receiver + + align:start position:0% +can build a uh a direct TV receiver + + + align:start position:0% +can build a uh a direct TV receiver +that's sealed in sulfuric acid um but + + align:start position:0% +that's sealed in sulfuric acid um but + + + align:start position:0% +that's sealed in sulfuric acid um but +that's not going to stop you from + + align:start position:0% +that's not going to stop you from + + + align:start position:0% +that's not going to stop you from +copying the movie once it gets out of + + align:start position:0% +copying the movie once it gets out of + + + align:start position:0% +copying the movie once it gets out of +the receiver uh and yes you can build a + + align:start position:0% +the receiver uh and yes you can build a + + + align:start position:0% +the receiver uh and yes you can build a +little dongle that's that's sealed in + + align:start position:0% +little dongle that's that's sealed in + + + align:start position:0% +little dongle that's that's sealed in +sulfuric acid or a DVD that's encrypted + + align:start position:0% +sulfuric acid or a DVD that's encrypted + + + align:start position:0% +sulfuric acid or a DVD that's encrypted +but that's not going to stop people if + + align:start position:0% +but that's not going to stop people if + + + align:start position:0% +but that's not going to stop people if +you make a computer able to decode DVDs + + align:start position:0% +you make a computer able to decode DVDs + + + align:start position:0% +you make a computer able to decode DVDs +that's not going to stop people from + + align:start position:0% +that's not going to stop people from + + + align:start position:0% +that's not going to stop people from +learning how that works because code is + + align:start position:0% +learning how that works because code is + + + align:start position:0% +learning how that works because code is +not just instructions to computer it's + + align:start position:0% +not just instructions to computer it's + + + align:start position:0% +not just instructions to computer it's +instructions to a people as well and + + align:start position:0% +instructions to a people as well and + + + align:start position:0% +instructions to a people as well and +they say well we know all that you know + + align:start position:0% +they say well we know all that you know + + + align:start position:0% +they say well we know all that you know +the rec the record the movie industry + + align:start position:0% +the rec the record the movie industry + + + align:start position:0% +the rec the record the movie industry +said we got a lot of money and we got a + + align:start position:0% +said we got a lot of money and we got a + + + align:start position:0% +said we got a lot of money and we got a +lot of smart people too but this is not + + align:start position:0% +lot of smart people too but this is not + + + align:start position:0% +lot of smart people too but this is not +going to stop the Chinese boo leers uh + + align:start position:0% +going to stop the Chinese boo leers uh + + + align:start position:0% +going to stop the Chinese boo leers uh +all we're out to do is to keep the + + align:start position:0% +all we're out to do is to keep the + + + align:start position:0% +all we're out to do is to keep the +honest people honest that was sort of + + align:start position:0% +honest people honest that was sort of + + + align:start position:0% +honest people honest that was sort of +the refrain they say if we can make it + + align:start position:0% +the refrain they say if we can make it + + + align:start position:0% +the refrain they say if we can make it +just difficult um that's good enough + + align:start position:0% +just difficult um that's good enough + + + align:start position:0% +just difficult um that's good enough +because that will keep the honest people + + align:start position:0% +because that will keep the honest people + + + align:start position:0% +because that will keep the honest people +honest uh what's one of the problems + + align:start position:0% +honest uh what's one of the problems + + + align:start position:0% +honest uh what's one of the problems +with this sort of line of + + align:start position:0% +with this sort of line of + + + align:start position:0% +with this sort of line of +thinking yeah if they're already honest + + align:start position:0% +thinking yeah if they're already honest + + + align:start position:0% +thinking yeah if they're already honest +then why do you need to keep them honest + + align:start position:0% +then why do you need to keep them honest + + + align:start position:0% +then why do you need to keep them honest +okay that's true if they're already + + align:start position:0% +okay that's true if they're already + + + align:start position:0% +okay that's true if they're already +honest then what but I mean uh who + + align:start position:0% +honest then what but I mean uh who + + + align:start position:0% +honest then what but I mean uh who +people here are basically honest right + + align:start position:0% +people here are basically honest right + + + align:start position:0% +people here are basically honest right +wouldn't you say and who here has never + + align:start position:0% +wouldn't you say and who here has never + + + align:start position:0% +wouldn't you say and who here has never +traded a song or gotten a song illegally + + align:start position:0% +traded a song or gotten a song illegally + + + align:start position:0% +traded a song or gotten a song illegally +on the + + align:start position:0% +on the + + + align:start position:0% +on the +internet one person do you want to be on + + align:start position:0% +internet one person do you want to be on + + + align:start position:0% +internet one person do you want to be on +the camera as like the Exemplar of MIT + + align:start position:0% +the camera as like the Exemplar of MIT + + + align:start position:0% +the camera as like the Exemplar of MIT +okay have you ever broken copyright at + + align:start position:0% +okay have you ever broken copyright at + + + align:start position:0% +okay have you ever broken copyright at +all in your life sure have okay but not + + align:start position:0% +all in your life sure have okay but not + + + align:start position:0% +all in your life sure have okay but not +with not online I I don't listen to okay + + align:start position:0% +with not online I I don't listen to okay + + + align:start position:0% +with not online I I don't listen to okay +so um but the entire rest of the class + + align:start position:0% +so um but the entire rest of the class + + + align:start position:0% +so um but the entire rest of the class +including me have all broken the law + + align:start position:0% +including me have all broken the law + + + align:start position:0% +including me have all broken the law +even though we're all honest so the C + + align:start position:0% +even though we're all honest so the C + + + align:start position:0% +even though we're all honest so the C +owner says look if we can just make it a + + align:start position:0% +owner says look if we can just make it a + + + align:start position:0% +owner says look if we can just make it a +little harder have a little speed bump + + align:start position:0% +little harder have a little speed bump + + + align:start position:0% +little harder have a little speed bump +then you know you'd be more likely to go + + align:start position:0% +then you know you'd be more likely to go + + + align:start position:0% +then you know you'd be more likely to go +buy it + + align:start position:0% +buy it + + + align:start position:0% +buy it +legitimately um you could go to the + + align:start position:0% +legitimately um you could go to the + + + align:start position:0% +legitimately um you could go to the +store you could get it on Amazon or now + + align:start position:0% +store you could get it on Amazon or now + + + align:start position:0% +store you could get it on Amazon or now +more recently you can get it on iTunes + + align:start position:0% +more recently you can get it on iTunes + + + align:start position:0% +more recently you can get it on iTunes +or or the new Napster or whatever but + + align:start position:0% +or or the new Napster or whatever but + + + align:start position:0% +or or the new Napster or whatever but +what what's a what's in what's a problem + + align:start position:0% +what what's a what's in what's a problem + + + align:start position:0% +what what's a what's in what's a problem +with they keep the honest people honest + + align:start position:0% +with they keep the honest people honest + + + align:start position:0% +with they keep the honest people honest +yeah what happens if you have someone + + align:start position:0% +yeah what happens if you have someone + + + align:start position:0% +yeah what happens if you have someone +who figures it out and just makes it + + align:start position:0% +who figures it out and just makes it + + + align:start position:0% +who figures it out and just makes it +easy yeah that's a real + + align:start position:0% +easy yeah that's a real + + + align:start position:0% +easy yeah that's a real +problem he says what happens if one + + align:start position:0% +problem he says what happens if one + + + align:start position:0% +problem he says what happens if one +person figures it out because the + + align:start position:0% +person figures it out because the + + + align:start position:0% +person figures it out because the +internet you know is sort of an A + + align:start position:0% +internet you know is sort of an A + + + align:start position:0% +internet you know is sort of an A +Lawrence lesing points us out was this + + align:start position:0% +Lawrence lesing points us out was this + + + align:start position:0% +Lawrence lesing points us out was this +in a zitan essay as + + align:start position:0% +in a zitan essay as + + + align:start position:0% +in a zitan essay as +well I hope it wasn't because then it + + align:start position:0% +well I hope it wasn't because then it + + + align:start position:0% +well I hope it wasn't because then it +can look like my idea but the internet + + align:start position:0% +can look like my idea but the internet + + + align:start position:0% +can look like my idea but the internet +is sort of an amplifier for you know + + align:start position:0% +is sort of an amplifier for you know + + + align:start position:0% +is sort of an amplifier for you know +Rogue people and if just one guy figures + + align:start position:0% +Rogue people and if just one guy figures + + + align:start position:0% +Rogue people and if just one guy figures +out um how your digital Rights + + align:start position:0% +out um how your digital Rights + + + align:start position:0% +out um how your digital Rights +Management works by the way does digital + + align:start position:0% +Management works by the way does digital + + + align:start position:0% +Management works by the way does digital +Rights Management does that protect + + align:start position:0% +Rights Management does that protect + + + align:start position:0% +Rights Management does that protect +rights under the copyright + + align:start position:0% + + + + align:start position:0% + +law I mean it's not about like + + align:start position:0% +law I mean it's not about like + + + align:start position:0% +law I mean it's not about like +distribution or um publication or or + + align:start position:0% +distribution or um publication or or + + + align:start position:0% +distribution or um publication or or +display or performance it's often not + + align:start position:0% +display or performance it's often not + + + align:start position:0% +display or performance it's often not +even really about + + align:start position:0% +even really about + + + align:start position:0% +even really about +access it's sort of about things you + + align:start position:0% +access it's sort of about things you + + + align:start position:0% +access it's sort of about things you +can't do even though the law would + + align:start position:0% +can't do even though the law would + + + align:start position:0% +can't do even though the law would +otherwise permit you and critics have + + align:start position:0% +otherwise permit you and critics have + + + align:start position:0% +otherwise permit you and critics have +adopted the term digital restrictions + + align:start position:0% +adopted the term digital restrictions + + + align:start position:0% +adopted the term digital restrictions +management + + align:start position:0% +management + + + align:start position:0% +management +um I just often call it like painful + + align:start position:0% +um I just often call it like painful + + + align:start position:0% +um I just often call it like painful +stuff because it always because anyway + + align:start position:0% +stuff because it always because anyway + + + align:start position:0% +stuff because it always because anyway +it makes things hard but + + align:start position:0% +it makes things hard but + + + align:start position:0% +it makes things hard but +um so yes the internet is like an + + align:start position:0% +um so yes the internet is like an + + + align:start position:0% +um so yes the internet is like an +amplifier for rogue people and uh you + + align:start position:0% +amplifier for rogue people and uh you + + + align:start position:0% +amplifier for rogue people and uh you +know for the new Britney Spear CD even + + align:start position:0% +know for the new Britney Spear CD even + + + align:start position:0% +know for the new Britney Spear CD even +if every copy of Britney Spears had been + + align:start position:0% +if every copy of Britney Spears had been + + + align:start position:0% +if every copy of Britney Spears had been +locked down and not easy to copy only + + align:start position:0% +locked down and not easy to copy only + + + align:start position:0% +locked down and not easy to copy only +one guy um would have have to do it and + + align:start position:0% +one guy um would have have to do it and + + + align:start position:0% +one guy um would have have to do it and +put it on the old Napster or Kaza or + + align:start position:0% +put it on the old Napster or Kaza or + + + align:start position:0% +put it on the old Napster or Kaza or +grer IU Hub or whatever you know it + + align:start position:0% +grer IU Hub or whatever you know it + + + align:start position:0% +grer IU Hub or whatever you know it +could be some guy from Vanuatu where + + align:start position:0% +could be some guy from Vanuatu where + + + align:start position:0% +could be some guy from Vanuatu where +they don't have laws um and suddenly + + align:start position:0% +they don't have laws um and suddenly + + + align:start position:0% +they don't have laws um and suddenly +once there's that one unlock copy it + + align:start position:0% +once there's that one unlock copy it + + + align:start position:0% +once there's that one unlock copy it +could go all around the + + align:start position:0% +could go all around the + + + align:start position:0% +could go all around the +world and suddenly there's no more speed + + align:start position:0% +world and suddenly there's no more speed + + + align:start position:0% +world and suddenly there's no more speed +bump for the honest + + align:start position:0% +bump for the honest + + + align:start position:0% +bump for the honest +people or yeah the mostly honest people + + align:start position:0% +people or yeah the mostly honest people + + + align:start position:0% +people or yeah the mostly honest people +largely honest people uh so that's + + align:start position:0% +largely honest people uh so that's + + + align:start position:0% +largely honest people uh so that's +that's a big problem + + align:start position:0% +that's a big problem + + + align:start position:0% +that's a big problem +um so what did they um what did they say + + align:start position:0% +um so what did they um what did they say + + + align:start position:0% +um so what did they um what did they say +okay well we're going to have a second + + align:start position:0% +okay well we're going to have a second + + + align:start position:0% +okay well we're going to have a second +level of protection we're not just going + + align:start position:0% +level of protection we're not just going + + + align:start position:0% +level of protection we're not just going +to stop people from getting around the + + align:start position:0% +to stop people from getting around the + + + align:start position:0% +to stop people from getting around the +DRM who else are we going to stop + + align:start position:0% + + + + align:start position:0% + +yeah people who uh like distributor + + align:start position:0% +yeah people who uh like distributor + + + align:start position:0% +yeah people who uh like distributor +links about how to in the Earth yeah so + + align:start position:0% +links about how to in the Earth yeah so + + + align:start position:0% +links about how to in the Earth yeah so +they we're going to attribute the second + + align:start position:0% +they we're going to attribute the second + + + align:start position:0% +they we're going to attribute the second +level people the Sony's of course at + + align:start position:0% +level people the Sony's of course at + + + align:start position:0% +level people the Sony's of course at +this point it was Sony the movie studio + + align:start position:0% +this point it was Sony the movie studio + + + align:start position:0% +this point it was Sony the movie studio +was like yeah + + align:start position:0% +was like yeah + + + align:start position:0% +was like yeah +um but we're going to get the second + + align:start position:0% +um but we're going to get the second + + + align:start position:0% +um but we're going to get the second +level people the people who + + align:start position:0% +level people the people who + + + align:start position:0% +level people the people who +distribute help in circumventing + + align:start position:0% +distribute help in circumventing + + + align:start position:0% +distribute help in circumventing +technological measures now can they get + + align:start position:0% +technological measures now can they get + + + align:start position:0% +technological measures now can they get +people who distribute like instructions + + align:start position:0% +people who distribute like instructions + + + align:start position:0% +people who distribute like instructions +like if Wired Magazine is like here is + + align:start position:0% +like if Wired Magazine is like here is + + + align:start position:0% +like if Wired Magazine is like here is +how to um descramble a you know a DVD or + + align:start position:0% +how to um descramble a you know a DVD or + + + align:start position:0% +how to um descramble a you know a DVD or +something can they get those people the + + align:start position:0% +something can they get those people the + + + align:start position:0% +something can they get those people the +Wired Magazine the New York + + align:start position:0% +Wired Magazine the New York + + + align:start position:0% +Wired Magazine the New York +Times first instruction yeah the first + + align:start position:0% +Times first instruction yeah the first + + + align:start position:0% +Times first instruction yeah the first +amendment is a problem so you can't just + + align:start position:0% +amendment is a problem so you can't just + + + align:start position:0% +amendment is a problem so you can't just +I mean can you put bomb making + + align:start position:0% +I mean can you put bomb making + + + align:start position:0% +I mean can you put bomb making +instructions in the New York Times like + + align:start position:0% +instructions in the New York Times like + + + align:start position:0% +instructions in the New York Times like +here's how to make a Molotov cocktail is + + align:start position:0% +here's how to make a Molotov cocktail is + + + align:start position:0% +here's how to make a Molotov cocktail is +that a bomb or just like no you can it's + + align:start position:0% +that a bomb or just like no you can it's + + + align:start position:0% +that a bomb or just like no you can it's +not predicted because the first + + align:start position:0% +not predicted because the first + + + align:start position:0% +not predicted because the first +amendment doesn't protect uh um to uh + + align:start position:0% +amendment doesn't protect uh um to uh + + + align:start position:0% +amendment doesn't protect uh um to uh +to instructions to do illegal stuff he + + align:start position:0% +to instructions to do illegal stuff he + + + align:start position:0% +to instructions to do illegal stuff he +says the first am doesn't protect + + align:start position:0% +says the first am doesn't protect + + + align:start position:0% +says the first am doesn't protect +instructions to do illegal + + align:start position:0% +instructions to do illegal + + + align:start position:0% +instructions to do illegal +stuff well that's what they said in the + + align:start position:0% +stuff well that's what they said in the + + + align:start position:0% +stuff well that's what they said in the +cor case in the which case in the cor + + align:start position:0% +cor case in the which case in the cor + + + align:start position:0% +cor case in the which case in the cor +against the what cor yeah yeah yeah um I + + align:start position:0% +against the what cor yeah yeah yeah um I + + + align:start position:0% +against the what cor yeah yeah yeah um I +mean in general the First Amendment does + + align:start position:0% +mean in general the First Amendment does + + + align:start position:0% +mean in general the First Amendment does +protect instructions to do illegal stuff + + align:start position:0% +protect instructions to do illegal stuff + + + align:start position:0% +protect instructions to do illegal stuff +you can even write like I think go I'm + + align:start position:0% +you can even write like I think go I'm + + + align:start position:0% +you can even write like I think go I'm +not going to say that + + align:start position:0% +not going to say that + + + align:start position:0% +not going to say that +uh um but okay let's talk about Hamas + + align:start position:0% +uh um but okay let's talk about Hamas + + + align:start position:0% +uh um but okay let's talk about Hamas +which was a poit I don't know what they + + align:start position:0% +which was a poit I don't know what they + + + align:start position:0% +which was a poit I don't know what they +are but they were recently elected to be + + align:start position:0% +are but they were recently elected to be + + + align:start position:0% +are but they were recently elected to be +in the majority government of the + + align:start position:0% +in the majority government of the + + + align:start position:0% +in the majority government of the +Palestinian Authority they regularly + + align:start position:0% +Palestinian Authority they regularly + + + align:start position:0% +Palestinian Authority they regularly +write things like we should kill + + align:start position:0% +write things like we should kill + + + align:start position:0% +write things like we should kill +everybody in Israel um and that would + + align:start position:0% +everybody in Israel um and that would + + + align:start position:0% +everybody in Israel um and that would +let's say they were in the United States + + align:start position:0% +let's say they were in the United States + + + align:start position:0% +let's say they were in the United States +that would be illegal right yes it would + + align:start position:0% +that would be illegal right yes it would + + + align:start position:0% +that would be illegal right yes it would +be illegal um but if they published in + + align:start position:0% +be illegal um but if they published in + + + align:start position:0% +be illegal um but if they published in +their newspaper you know we think as a + + align:start position:0% +their newspaper you know we think as a + + + align:start position:0% +their newspaper you know we think as a +political measure that it would be a + + align:start position:0% +political measure that it would be a + + + align:start position:0% +political measure that it would be a +good idea to kill all the people in + + align:start position:0% +good idea to kill all the people in + + + align:start position:0% +good idea to kill all the people in +Israel is is that illegal can the United + + align:start position:0% +Israel is is that illegal can the United + + + align:start position:0% +Israel is is that illegal can the United +States ban that kind of expression no + + align:start position:0% +States ban that kind of expression no + + + align:start position:0% +States ban that kind of expression no +and in fact uh you know there's domestic + + align:start position:0% +and in fact uh you know there's domestic + + + align:start position:0% +and in fact uh you know there's domestic +groups like the KKK which is not really + + align:start position:0% +groups like the KKK which is not really + + + align:start position:0% +groups like the KKK which is not really +longer any a major force in American + + align:start position:0% +longer any a major force in American + + + align:start position:0% +longer any a major force in American +politics but they you know write things + + align:start position:0% +politics but they you know write things + + + align:start position:0% +politics but they you know write things +like we we want + + align:start position:0% +like we we want + + + align:start position:0% +like we we want +to actually don't know what they write + + align:start position:0% +to actually don't know what they write + + + align:start position:0% +to actually don't know what they write +but I'm sure it's bad whatever it is and + + align:start position:0% +but I'm sure it's bad whatever it is and + + + align:start position:0% +but I'm sure it's bad whatever it is and +illegal and um and it's protected uh + + align:start position:0% +illegal and um and it's protected uh + + + align:start position:0% +illegal and um and it's protected uh +it's protected speech now there's some + + align:start position:0% +it's protected speech now there's some + + + align:start position:0% +it's protected speech now there's some +limits like um + + align:start position:0% +limits like um + + + align:start position:0% +limits like um +uh you know like if there's an imminent + + align:start position:0% +uh you know like if there's an imminent + + + align:start position:0% +uh you know like if there's an imminent +danger of incitement to Lawless action + + align:start position:0% +danger of incitement to Lawless action + + + align:start position:0% +danger of incitement to Lawless action +so if you're out there and there's like + + align:start position:0% +so if you're out there and there's like + + + align:start position:0% +so if you're out there and there's like +um the whole Klux Clan with the is the + + align:start position:0% +um the whole Klux Clan with the is the + + + align:start position:0% +um the whole Klux Clan with the is the +Klux Clan or anyway with their hats and + + align:start position:0% +Klux Clan or anyway with their hats and + + + align:start position:0% +Klux Clan or anyway with their hats and +the um the whole deal and you're like go + + align:start position:0% +the um the whole deal and you're like go + + + align:start position:0% +the um the whole deal and you're like go +okay go you know if you're like that + + align:start position:0% +okay go you know if you're like that + + + align:start position:0% +okay go you know if you're like that +then yes uh there could be some um it + + align:start position:0% +then yes uh there could be some um it + + + align:start position:0% +then yes uh there could be some um it +could be illegal but um if there's this + + align:start position:0% +could be illegal but um if there's this + + + align:start position:0% +could be illegal but um if there's this +imminent danger of Lawless action and + + align:start position:0% +imminent danger of Lawless action and + + + align:start position:0% +imminent danger of Lawless action and +there's some other exceptions like + + align:start position:0% +there's some other exceptions like + + + align:start position:0% +there's some other exceptions like +things that are um + + align:start position:0% +things that are um + + + align:start position:0% +things that are um +well there's a lot of exceptions there's + + align:start position:0% +well there's a lot of exceptions there's + + + align:start position:0% +well there's a lot of exceptions there's +um there's threats like if you're + + align:start position:0% +um there's threats like if you're + + + align:start position:0% +um there's threats like if you're +like there there's that too there's + + align:start position:0% +like there there's that too there's + + + align:start position:0% +like there there's that too there's +shouting fire in a crowded theater but + + align:start position:0% +shouting fire in a crowded theater but + + + align:start position:0% +shouting fire in a crowded theater but +there's also like I'm gonna kill you you + + align:start position:0% +there's also like I'm gonna kill you you + + + align:start position:0% +there's also like I'm gonna kill you you +know there's there's um or burning a + + align:start position:0% +know there's there's um or burning a + + + align:start position:0% +know there's there's um or burning a +cross on somebody's lawn um in many + + align:start position:0% +cross on somebody's lawn um in many + + + align:start position:0% +cross on somebody's lawn um in many +cases is not protected by the First + + align:start position:0% +cases is not protected by the First + + + align:start position:0% +cases is not protected by the First +Amendment um these sort of inherently + + align:start position:0% +Amendment um these sort of inherently + + + align:start position:0% +Amendment um these sort of inherently +threatening actions there's also liel uh + + align:start position:0% +threatening actions there's also liel uh + + + align:start position:0% +threatening actions there's also liel uh +is not protected by the First Amendment + + align:start position:0% +is not protected by the First Amendment + + + align:start position:0% +is not protected by the First Amendment +if I write + + align:start position:0% +if I write + + + align:start position:0% +if I write +um you know Kevin Chen kills little + + align:start position:0% +um you know Kevin Chen kills little + + + align:start position:0% +um you know Kevin Chen kills little +babies you know that's not protected by + + align:start position:0% +babies you know that's not protected by + + + align:start position:0% +babies you know that's not protected by +the First + + align:start position:0% +the First + + + align:start position:0% +the First +Amendment um what's some other + + align:start position:0% + + + + align:start position:0% + +exceptions what about burning the + + align:start position:0% +exceptions what about burning the + + + align:start position:0% +exceptions what about burning the +American flag in public how about that + + align:start position:0% +American flag in public how about that + + + align:start position:0% +American flag in public how about that +is that + + align:start position:0% +is that + + + align:start position:0% +is that +protected yeah yeah it actually is + + align:start position:0% +protected yeah yeah it actually is + + + align:start position:0% +protected yeah yeah it actually is +protected I mean for many years in + + align:start position:0% +protected I mean for many years in + + + align:start position:0% +protected I mean for many years in +America's history it was not but then in + + align:start position:0% +America's history it was not but then in + + + align:start position:0% +America's history it was not but then in +1989 this guy in Texas was like I don't + + align:start position:0% +1989 this guy in Texas was like I don't + + + align:start position:0% +1989 this guy in Texas was like I don't +know if he said anything but he burned + + align:start position:0% +know if he said anything but he burned + + + align:start position:0% +know if he said anything but he burned +the flag and it went to the Supreme + + align:start position:0% +the flag and it went to the Supreme + + + align:start position:0% +the flag and it went to the Supreme +Court of the there was a law in Texas + + align:start position:0% +Court of the there was a law in Texas + + + align:start position:0% +Court of the there was a law in Texas +against burning the American flag + + align:start position:0% +against burning the American flag + + + align:start position:0% +against burning the American flag +and which is a very emotional issue uh + + align:start position:0% +and which is a very emotional issue uh + + + align:start position:0% +and which is a very emotional issue uh +and it went to the Supreme Court and + + align:start position:0% +and it went to the Supreme Court and + + + align:start position:0% +and it went to the Supreme Court and +they ruled um I think 5 to four that uh + + align:start position:0% +they ruled um I think 5 to four that uh + + + align:start position:0% +they ruled um I think 5 to four that uh +the Constitution prevented a state from + + align:start position:0% +the Constitution prevented a state from + + + align:start position:0% +the Constitution prevented a state from +Banning um flag + + align:start position:0% +Banning um flag + + + align:start position:0% +Banning um flag +burning and then what did Congress do in + + align:start position:0% +burning and then what did Congress do in + + + align:start position:0% +burning and then what did Congress do in +response did they pass a constitutional + + align:start position:0% +response did they pass a constitutional + + + align:start position:0% +response did they pass a constitutional +amendment they tried I think they may + + align:start position:0% +amendment they tried I think they may + + + align:start position:0% +amendment they tried I think they may +have tried it didn't make it through + + align:start position:0% +have tried it didn't make it through + + + align:start position:0% +have tried it didn't make it through +Congress and so they just passed a + + align:start position:0% +Congress and so they just passed a + + + align:start position:0% +Congress and so they just passed a +federal law that said like the ex same + + align:start position:0% +federal law that said like the ex same + + + align:start position:0% +federal law that said like the ex same +thing that the Texas law had said and + + align:start position:0% +thing that the Texas law had said and + + + align:start position:0% +thing that the Texas law had said and +that went up to the Supreme Court the + + align:start position:0% +that went up to the Supreme Court the + + + align:start position:0% +that went up to the Supreme Court the +next year and again in a 5 to4 ruling + + align:start position:0% +next year and again in a 5 to4 ruling + + + align:start position:0% +next year and again in a 5 to4 ruling +the Supreme Court rulle unconstitutional + + align:start position:0% +the Supreme Court rulle unconstitutional + + + align:start position:0% +the Supreme Court rulle unconstitutional +and + + align:start position:0% +and + + + align:start position:0% +and +uh now of course Congress is anyway + + align:start position:0% +uh now of course Congress is anyway + + + align:start position:0% +uh now of course Congress is anyway +Congress is very close to passing a flag + + align:start position:0% +Congress is very close to passing a flag + + + align:start position:0% +Congress is very close to passing a flag +burning Amendment which is you know of + + align:start position:0% +burning Amendment which is you know of + + + align:start position:0% +burning Amendment which is you know of +course is only part of the + + align:start position:0% +course is only part of the + + + align:start position:0% +course is only part of the +Constitutional amendment process but the + + align:start position:0% +Constitutional amendment process but the + + + align:start position:0% +Constitutional amendment process but the +house is overwhelmingly in favor and the + + align:start position:0% +house is overwhelmingly in favor and the + + + align:start position:0% +house is overwhelmingly in favor and the +Senate is like two senators away from + + align:start position:0% +Senate is like two senators away from + + + align:start position:0% +Senate is like two senators away from +wanting to pass a flag burning Amendment + + align:start position:0% +wanting to pass a flag burning Amendment + + + align:start position:0% +wanting to pass a flag burning Amendment +so it could happen but U right now you + + align:start position:0% +so it could happen but U right now you + + + align:start position:0% +so it could happen but U right now you +can burn the American flag all you want + + align:start position:0% +can burn the American flag all you want + + + align:start position:0% +can burn the American flag all you want +if it's you know your American flag and + + align:start position:0% +if it's you know your American flag and + + + align:start position:0% +if it's you know your American flag and +unless the fire is going to set fire to + + align:start position:0% +unless the fire is going to set fire to + + + align:start position:0% +unless the fire is going to set fire to +something else uh what are some other + + align:start position:0% +something else uh what are some other + + + align:start position:0% +something else uh what are some other +exceptions to the First + + align:start position:0% +exceptions to the First + + + align:start position:0% +exceptions to the First +Amendment yeah obscenity and what's what + + align:start position:0% +Amendment yeah obscenity and what's what + + + align:start position:0% +Amendment yeah obscenity and what's what +did obscenity used to + + align:start position:0% + + + + align:start position:0% + +be I read a paper by the way it was the + + align:start position:0% +be I read a paper by the way it was the + + + align:start position:0% +be I read a paper by the way it was the +the Melville nimmer lecture Melville Nim + + align:start position:0% +the Melville nimmer lecture Melville Nim + + + align:start position:0% +the Melville nimmer lecture Melville Nim +nimmer was a David nimmer's father and + + align:start position:0% +nimmer was a David nimmer's father and + + + align:start position:0% +nimmer was a David nimmer's father and +he started this book nimron copyright + + align:start position:0% +he started this book nimron copyright + + + align:start position:0% +he started this book nimron copyright +and he was also a a a famous First + + align:start position:0% +and he was also a a a famous First + + + align:start position:0% +and he was also a a a famous First +Amendment attorney and he litigated case + + align:start position:0% +Amendment attorney and he litigated case + + + align:start position:0% +Amendment attorney and he litigated case +Cohen versus California in the Supreme + + align:start position:0% +Cohen versus California in the Supreme + + + align:start position:0% +Cohen versus California in the Supreme +Court do people know what that was + + align:start position:0% +Court do people know what that was + + + align:start position:0% +Court do people know what that was +about well this guy in California which + + align:start position:0% +about well this guy in California which + + + align:start position:0% +about well this guy in California which +is was at that time an oppressive regime + + align:start position:0% +is was at that time an oppressive regime + + + align:start position:0% +is was at that time an oppressive regime +in the west um he went into a count this + + align:start position:0% +in the west um he went into a count this + + + align:start position:0% +in the west um he went into a count this +is in the 60s probably the late 60s in + + align:start position:0% +is in the 60s probably the late 60s in + + + align:start position:0% +is in the 60s probably the late 60s in +in during the Vietnam war he went into a + + align:start position:0% +in during the Vietnam war he went into a + + + align:start position:0% +in during the Vietnam war he went into a +County Courthouse with a jacket and the + + align:start position:0% +County Courthouse with a jacket and the + + + align:start position:0% +County Courthouse with a jacket and the +jacket said the + + align:start position:0% +jacket said the + + + align:start position:0% +jacket said the +draft and uh he was arrested actually + + align:start position:0% +draft and uh he was arrested actually + + + align:start position:0% +draft and uh he was arrested actually +the the sheriff in the courthouse was + + align:start position:0% +the the sheriff in the courthouse was + + + align:start position:0% +the the sheriff in the courthouse was +like you better take that off and then + + align:start position:0% +like you better take that off and then + + + align:start position:0% +like you better take that off and then +the sheriff reported him to the judge to + + align:start position:0% +the sheriff reported him to the judge to + + + align:start position:0% +the sheriff reported him to the judge to +be cited for a contemp of court and the + + align:start position:0% +be cited for a contemp of court and the + + + align:start position:0% +be cited for a contemp of court and the +judge was like I have better things to + + align:start position:0% +judge was like I have better things to + + + align:start position:0% +judge was like I have better things to +do and then as the guy was leaving the + + align:start position:0% +do and then as the guy was leaving the + + + align:start position:0% +do and then as the guy was leaving the +same Sheriff arrested him himself anyway + + align:start position:0% +same Sheriff arrested him himself anyway + + + align:start position:0% +same Sheriff arrested him himself anyway +for + + align:start position:0% +for + + + align:start position:0% +for +um you know for public indecency or + + align:start position:0% +um you know for public indecency or + + + align:start position:0% +um you know for public indecency or +obscenity or something like that it went + + align:start position:0% +obscenity or something like that it went + + + align:start position:0% +obscenity or something like that it went +all the way to the Supreme Court and + + align:start position:0% +all the way to the Supreme Court and + + + align:start position:0% +all the way to the Supreme Court and +they ruled I think like 7 to2 that um it + + align:start position:0% +they ruled I think like 7 to2 that um it + + + align:start position:0% +they ruled I think like 7 to2 that um it +was okay to say the draft and that + + align:start position:0% +was okay to say the draft and that + + + align:start position:0% +was okay to say the draft and that +no state could prohibit you from wearing + + align:start position:0% +no state could prohibit you from wearing + + + align:start position:0% +no state could prohibit you from wearing +that on your jacket in a county + + align:start position:0% +that on your jacket in a county + + + align:start position:0% +that on your jacket in a county +courthouse and the Justice you know know + + align:start position:0% +courthouse and the Justice you know know + + + align:start position:0% +courthouse and the Justice you know know +the New York Times covered this case and + + align:start position:0% +the New York Times covered this case and + + + align:start position:0% +the New York Times covered this case and +you know they always love to talk with + + align:start position:0% +you know they always love to talk with + + + align:start position:0% +you know they always love to talk with +the Supreme Court and they never once + + align:start position:0% +the Supreme Court and they never once + + + align:start position:0% +the Supreme Court and they never once +used the word in fact that word has + + align:start position:0% +used the word in fact that word has + + + align:start position:0% +used the word in fact that word has +only appeared one time in the entire + + align:start position:0% +only appeared one time in the entire + + + align:start position:0% +only appeared one time in the entire +history of the New York Times when they + + align:start position:0% +history of the New York Times when they + + + align:start position:0% +history of the New York Times when they +printed the star report about President + + align:start position:0% +printed the star report about President + + + align:start position:0% +printed the star report about President +Clinton but anyway + + align:start position:0% +Clinton but anyway + + + align:start position:0% +Clinton but anyway +um oh yeah so and and there are ex + + align:start position:0% +um oh yeah so and and there are ex + + + align:start position:0% +um oh yeah so and and there are ex +um exceptions to the first amendment + + align:start position:0% +um exceptions to the first amendment + + + align:start position:0% +um exceptions to the first amendment +when it comes to obscenity um in + + align:start position:0% +when it comes to obscenity um in + + + align:start position:0% +when it comes to obscenity um in +including very hardcore pornography and + + align:start position:0% +including very hardcore pornography and + + + align:start position:0% +including very hardcore pornography and +um well that's basically it and another + + align:start position:0% +um well that's basically it and another + + + align:start position:0% +um well that's basically it and another +one would be child pornography which is + + align:start position:0% +one would be child pornography which is + + + align:start position:0% +one would be child pornography which is +not obscenity but is also not okay okay + + align:start position:0% +not obscenity but is also not okay okay + + + align:start position:0% +not obscenity but is also not okay okay +and but another one is this sort of uh + + align:start position:0% +and but another one is this sort of uh + + + align:start position:0% +and but another one is this sort of uh +it's speech that is tied up in + + align:start position:0% +it's speech that is tied up in + + + align:start position:0% +it's speech that is tied up in +conduct so uh you know the Constitution + + align:start position:0% +conduct so uh you know the Constitution + + + align:start position:0% +conduct so uh you know the Constitution +the Supreme Court says you can prohibit + + align:start position:0% +the Supreme Court says you can prohibit + + + align:start position:0% +the Supreme Court says you can prohibit +conduct like hitting people but and you + + align:start position:0% +conduct like hitting people but and you + + + align:start position:0% +conduct like hitting people but and you +can't prohibit speech but what if you do + + align:start position:0% +can't prohibit speech but what if you do + + + align:start position:0% +can't prohibit speech but what if you do +something that is sort of inherently + + align:start position:0% +something that is sort of inherently + + + align:start position:0% +something that is sort of inherently +both um for instance burning the + + align:start position:0% +both um for instance burning the + + + align:start position:0% +both um for instance burning the +American flag we say is speech and is + + align:start position:0% +American flag we say is speech and is + + + align:start position:0% +American flag we say is speech and is +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but what about burning your draft card + + align:start position:0% +but what about burning your draft card + + + align:start position:0% +but what about burning your draft card +because there's a law that there used to + + align:start position:0% +because there's a law that there used to + + + align:start position:0% +because there's a law that there used to +be the a law that says you have to have + + align:start position:0% +be the a law that says you have to have + + + align:start position:0% +be the a law that says you have to have +a a draft card you know to be in the + + align:start position:0% +a a draft card you know to be in the + + + align:start position:0% +a a draft card you know to be in the +Vietnam War and this dude Mr O I think + + align:start position:0% +Vietnam War and this dude Mr O I think + + + align:start position:0% +Vietnam War and this dude Mr O I think +Mr O'Brien uh he burned his draft card + + align:start position:0% +Mr O'Brien uh he burned his draft card + + + align:start position:0% +Mr O'Brien uh he burned his draft card +as part of a protest and uh is this + + align:start position:0% +as part of a protest and uh is this + + + align:start position:0% +as part of a protest and uh is this +protected no why + + align:start position:0% + + + + align:start position:0% + +not yeah + + align:start position:0% + + + + align:start position:0% + +yeah I mean I think I mean there there's + + align:start position:0% +yeah I mean I think I mean there there's + + + align:start position:0% +yeah I mean I think I mean there there's +this O'Brien case which is about when + + align:start position:0% +this O'Brien case which is about when + + + align:start position:0% +this O'Brien case which is about when +can you ban speech that is tied up with + + align:start position:0% +can you ban speech that is tied up with + + + align:start position:0% +can you ban speech that is tied up with +conduct and it's about is the regulation + + align:start position:0% +conduct and it's about is the regulation + + + align:start position:0% +conduct and it's about is the regulation +directed neutrally at the conduct and + + align:start position:0% +directed neutrally at the conduct and + + + align:start position:0% +directed neutrally at the conduct and +and not at the content of the speech and + + align:start position:0% +and not at the content of the speech and + + + align:start position:0% +and not at the content of the speech and +there's these various + + align:start position:0% +there's these various + + + align:start position:0% +there's these various +tests anyway so uh so here we're talking + + align:start position:0% +tests anyway so uh so here we're talking + + + align:start position:0% +tests anyway so uh so here we're talking +about keeping the honest people honest + + align:start position:0% +about keeping the honest people honest + + + align:start position:0% +about keeping the honest people honest +and we've said it's not enough just to + + align:start position:0% +and we've said it's not enough just to + + + align:start position:0% +and we've said it's not enough just to +stop people from + + align:start position:0% +stop people from + + + align:start position:0% +stop people from +circumventing uh we also have to stop + + align:start position:0% +circumventing uh we also have to stop + + + align:start position:0% +circumventing uh we also have to stop +people from helping people who + + align:start position:0% +people from helping people who + + + align:start position:0% +people from helping people who +circumvent and so there this there's + + align:start position:0% +circumvent and so there this there's + + + align:start position:0% +circumvent and so there this there's +this second part of the + + align:start position:0% +this second part of the + + + align:start position:0% +this second part of the +dmca the first part is no + + align:start position:0% +dmca the first part is no + + + align:start position:0% +dmca the first part is no +circumventing and the second part + + align:start position:0% +circumventing and the second part + + + align:start position:0% +circumventing and the second part +is no person shall manufacture import + + align:start position:0% +is no person shall manufacture import + + + align:start position:0% +is no person shall manufacture import +offer to the public provide or otherwise + + align:start position:0% +offer to the public provide or otherwise + + + align:start position:0% +offer to the public provide or otherwise +traffic in any technology product + + align:start position:0% +traffic in any technology product + + + align:start position:0% +traffic in any technology product +service device component or part thereof + + align:start position:0% +service device component or part thereof + + + align:start position:0% +service device component or part thereof +that okay now why do we have to be so + + align:start position:0% +that okay now why do we have to be so + + + align:start position:0% +that okay now why do we have to be so +careful with the definition here + + align:start position:0% + + + + align:start position:0% + +what what case is is um Congress + + align:start position:0% +what what case is is um Congress + + + align:start position:0% +what what case is is um Congress +concerned + + align:start position:0% +concerned + + + align:start position:0% +concerned +about that we read in this + + align:start position:0% +about that we read in this + + + align:start position:0% +about that we read in this +class about secondary + + align:start position:0% + + + + align:start position:0% + +liability Sony yes what happened to what + + align:start position:0% +liability Sony yes what happened to what + + + align:start position:0% +liability Sony yes what happened to what +was the rule in + + align:start position:0% + + + + align:start position:0% + +Sony yeah so the question is is Sony + + align:start position:0% +Sony yeah so the question is is Sony + + + align:start position:0% +Sony yeah so the question is is Sony +guilty of contributory infringement + + align:start position:0% +guilty of contributory infringement + + + align:start position:0% +guilty of contributory infringement +because they are helping people break + + align:start position:0% +because they are helping people break + + + align:start position:0% +because they are helping people break +the law right all these customers who + + align:start position:0% +the law right all these customers who + + + align:start position:0% +the law right all these customers who +are Library building are definitely + + align:start position:0% +are Library building are definitely + + + align:start position:0% +are Library building are definitely +breaking the law and it's the Sony + + align:start position:0% +breaking the law and it's the Sony + + + align:start position:0% +breaking the law and it's the Sony +device that's doing it and son is making + + align:start position:0% +device that's doing it and son is making + + + align:start position:0% +device that's doing it and son is making +a profit off all these people is Sony + + align:start position:0% +a profit off all these people is Sony + + + align:start position:0% +a profit off all these people is Sony +guilty of contributory infringement and + + align:start position:0% +guilty of contributory infringement and + + + align:start position:0% +guilty of contributory infringement and +what's the answer they didn't get in + + align:start position:0% +what's the answer they didn't get in + + + align:start position:0% +what's the answer they didn't get in +trouble they didn't get in trouble and + + align:start position:0% +trouble they didn't get in trouble and + + + align:start position:0% +trouble they didn't get in trouble and +why not they believe the majority of + + align:start position:0% +why not they believe the majority of + + + align:start position:0% +why not they believe the majority of +people weren't doing was it the majority + + align:start position:0% +people weren't doing was it the majority + + + align:start position:0% +people weren't doing was it the majority +what's the What's the + + align:start position:0% +what's the What's the + + + align:start position:0% +what's the What's the +phrase substantial legal use for the + + align:start position:0% +phrase substantial legal use for the + + + align:start position:0% +phrase substantial legal use for the +device substantial non-infringing use + + align:start position:0% +device substantial non-infringing use + + + align:start position:0% +device substantial non-infringing use +that's the test substantial maybe it's + + align:start position:0% +that's the test substantial maybe it's + + + align:start position:0% +that's the test substantial maybe it's +significant is it substantial + + align:start position:0% +significant is it substantial + + + align:start position:0% +significant is it substantial +substantial non-infringing use um + + align:start position:0% +substantial non-infringing use um + + + align:start position:0% +substantial non-infringing use um +so the of course the Consumer + + align:start position:0% +so the of course the Consumer + + + align:start position:0% +so the of course the Consumer +Electronics people in this case were + + align:start position:0% +Electronics people in this case were + + + align:start position:0% +Electronics people in this case were +like okay if you're going to ban + + align:start position:0% +like okay if you're going to ban + + + align:start position:0% +like okay if you're going to ban +circumvention you know don't ban the + + align:start position:0% +circumvention you know don't ban the + + + align:start position:0% +circumvention you know don't ban the +helping uh as long as there's a + + align:start position:0% +helping uh as long as there's a + + + align:start position:0% +helping uh as long as there's a +substantial not could they say + + align:start position:0% +substantial not could they say + + + align:start position:0% +substantial not could they say +non-infringing use is this about + + align:start position:0% +non-infringing use is this about + + + align:start position:0% +non-infringing use is this about +infringement by the way for instance is + + align:start position:0% +infringement by the way for instance is + + + align:start position:0% +infringement by the way for instance is +there a fair use let's say you want to + + align:start position:0% +there a fair use let's say you want to + + + align:start position:0% +there a fair use let's say you want to +circumvent the DRM but it's for the + + align:start position:0% +circumvent the DRM but it's for the + + + align:start position:0% +circumvent the DRM but it's for the +purpose of + + align:start position:0% +purpose of + + + align:start position:0% +purpose of +criticism or education or some sort of + + align:start position:0% +criticism or education or some sort of + + + align:start position:0% +criticism or education or some sort of +fair use can you circumvent then like oh + + align:start position:0% +fair use can you circumvent then like oh + + + align:start position:0% +fair use can you circumvent then like oh +it's fair use it's + + align:start position:0% +it's fair use it's + + + align:start position:0% +it's fair use it's +exempt Congress tells you you can yeah + + align:start position:0% +exempt Congress tells you you can yeah + + + align:start position:0% +exempt Congress tells you you can yeah +but let's talk about fair use are the + + align:start position:0% +but let's talk about fair use are the + + + align:start position:0% +but let's talk about fair use are the +exemptions to infringement applicable + + align:start position:0% +exemptions to infringement applicable + + + align:start position:0% +exemptions to infringement applicable +here I see + + align:start position:0% +here I see + + + align:start position:0% +here I see +so uh okay well let's let's look at what + + align:start position:0% +so uh okay well let's let's look at what + + + align:start position:0% +so uh okay well let's let's look at what +121 says about fair + + align:start position:0% + + + + align:start position:0% + +use okay well on fair use they say + + align:start position:0% +use okay well on fair use they say + + + align:start position:0% +use okay well on fair use they say +nothing in this section shall affect + + align:start position:0% +nothing in this section shall affect + + + align:start position:0% +nothing in this section shall affect +rights remedies limitations or defenses + + align:start position:0% +rights remedies limitations or defenses + + + align:start position:0% +rights remedies limitations or defenses +to copyright infringement including fair + + align:start position:0% +to copyright infringement including fair + + + align:start position:0% +to copyright infringement including fair +use under title 17 so you might look at + + align:start position:0% +use under title 17 so you might look at + + + align:start position:0% +use under title 17 so you might look at +that you say oh great fair use is still + + align:start position:0% +that you say oh great fair use is still + + + align:start position:0% +that you say oh great fair use is still +applicable as an exception would that be + + align:start position:0% +applicable as an exception would that be + + + align:start position:0% +applicable as an exception would that be +a I I defended this principle for like + + align:start position:0% +a I I defended this principle for like + + + align:start position:0% +a I I defended this principle for like +many weeks my freshman year but was that + + align:start position:0% +many weeks my freshman year but was that + + + align:start position:0% +many weeks my freshman year but was that +would that be + + align:start position:0% +would that be + + + align:start position:0% +would that be +correct I mean nothing in this section + + align:start position:0% +correct I mean nothing in this section + + + align:start position:0% +correct I mean nothing in this section +shall affect uh rights remedies + + align:start position:0% +shall affect uh rights remedies + + + align:start position:0% +shall affect uh rights remedies +limitations or defenses to cover + + align:start position:0% +limitations or defenses to cover + + + align:start position:0% +limitations or defenses to cover +infringement including fair use so fair + + align:start position:0% +infringement including fair use so fair + + + align:start position:0% +infringement including fair use so fair +use is still there what's the problem + + align:start position:0% +use is still there what's the problem + + + align:start position:0% +use is still there what's the problem +with this + + align:start position:0% +with this + + + align:start position:0% +with this +reasoning or that the you know the court + + align:start position:0% +reasoning or that the you know the court + + + align:start position:0% +reasoning or that the you know the court +said was a problem with the + + align:start position:0% + + + + align:start position:0% + +reasoning everything stantial fair use + + align:start position:0% +reasoning everything stantial fair use + + + align:start position:0% +reasoning everything stantial fair use +use all this illegal stuff for most + + align:start position:0% +use all this illegal stuff for most + + + align:start position:0% +use all this illegal stuff for most +people were useful for educational + + align:start position:0% +people were useful for educational + + + align:start position:0% +people were useful for educational +purposes that so why ises this 121 C1 + + align:start position:0% +purposes that so why ises this 121 C1 + + + align:start position:0% +purposes that so why ises this 121 C1 +why does this not immunize you as long + + align:start position:0% +why does this not immunize you as long + + + align:start position:0% +why does this not immunize you as long +as what you're doing is a fair use + + align:start position:0% +as what you're doing is a fair use + + + align:start position:0% +as what you're doing is a fair use +you're not + + align:start position:0% +you're not + + + align:start position:0% +you're not +infringing this is about copyright + + align:start position:0% +infringing this is about copyright + + + align:start position:0% +infringing this is about copyright +infringement but what is 121 + + align:start position:0% +infringement but what is 121 + + + align:start position:0% +infringement but what is 121 +about 121 is not about infringement what + + align:start position:0% +about 121 is not about infringement what + + + align:start position:0% +about 121 is not about infringement what +does infringement mean + + align:start position:0% + + + + align:start position:0% + +exactly it means trampling on the + + align:start position:0% +exactly it means trampling on the + + + align:start position:0% +exactly it means trampling on the +copyright the exclusive rights of the + + align:start position:0% +copyright the exclusive rights of the + + + align:start position:0% +copyright the exclusive rights of the +copyright owner which are reproduction + + align:start position:0% +copyright owner which are reproduction + + + align:start position:0% +copyright owner which are reproduction +and and and publication reproduction and + + align:start position:0% +and and and publication reproduction and + + + align:start position:0% +and and and publication reproduction and +display and performance and derivative + + align:start position:0% +display and performance and derivative + + + align:start position:0% +display and performance and derivative +works and the other + + align:start position:0% +works and the other + + + align:start position:0% +works and the other +one didn't I say that whatever yes + + align:start position:0% +one didn't I say that whatever yes + + + align:start position:0% +one didn't I say that whatever yes +distribution that that's infringement + + align:start position:0% +distribution that that's infringement + + + align:start position:0% +distribution that that's infringement +it's on the copyright but this + + align:start position:0% +it's on the copyright but this + + + align:start position:0% +it's on the copyright but this +section is not about copyright it's this + + align:start position:0% +section is not about copyright it's this + + + align:start position:0% +section is not about copyright it's this +sort of parac copyright and it's 121 + + align:start position:0% +sort of parac copyright and it's 121 + + + align:start position:0% +sort of parac copyright and it's 121 +it's you know at least 600 sections away + + align:start position:0% +it's you know at least 600 sections away + + + align:start position:0% +it's you know at least 600 sections away +from the last Wilderness of copyright um + + align:start position:0% +from the last Wilderness of copyright um + + + align:start position:0% +from the last Wilderness of copyright um +so this doesn't really help you because + + align:start position:0% +so this doesn't really help you because + + + align:start position:0% +so this doesn't really help you because +they would say well we're not talking + + align:start position:0% +they would say well we're not talking + + + align:start position:0% +they would say well we're not talking +about cooperate infringement we're not + + align:start position:0% +about cooperate infringement we're not + + + align:start position:0% +about cooperate infringement we're not +even accusing you of coate infringement + + align:start position:0% +even accusing you of coate infringement + + + align:start position:0% +even accusing you of coate infringement +we're accusing you of circumventing + + align:start position:0% +we're accusing you of circumventing + + + align:start position:0% +we're accusing you of circumventing +something that is illegal by itself Su + + align:start position:0% +something that is illegal by itself Su + + + align:start position:0% +something that is illegal by itself Su +generous + + align:start position:0% +generous + + + align:start position:0% +generous +um + + align:start position:0% +um + + + align:start position:0% +um +um when this open course is translated + + align:start position:0% +um when this open course is translated + + + align:start position:0% +um when this open course is translated +into Latin they're going to have a lot + + align:start position:0% +into Latin they're going to have a lot + + + align:start position:0% +into Latin they're going to have a lot +of problems translating my use of that + + align:start position:0% +of problems translating my use of that + + + align:start position:0% +of problems translating my use of that +um so so but they're conern so Sony is + + align:start position:0% +um so so but they're conern so Sony is + + + align:start position:0% +um so so but they're conern so Sony is +like well we want to keep you know this + + align:start position:0% +like well we want to keep you know this + + + align:start position:0% +like well we want to keep you know this +substantial non-infringing use Doctrine + + align:start position:0% +substantial non-infringing use Doctrine + + + align:start position:0% +substantial non-infringing use Doctrine +around you know we want to say you can + + align:start position:0% +around you know we want to say you can + + + align:start position:0% +around you know we want to say you can +still um help people you know distribute + + align:start position:0% +still um help people you know distribute + + + align:start position:0% +still um help people you know distribute +something that will help people + + align:start position:0% +something that will help people + + + align:start position:0% +something that will help people +circumvent as long as there's a + + align:start position:0% +circumvent as long as there's a + + + align:start position:0% +circumvent as long as there's a +substantial what would you say a + + align:start position:0% +substantial what would you say a + + + align:start position:0% +substantial what would you say a +substantial non circumventing use how + + align:start position:0% +substantial non circumventing use how + + + align:start position:0% +substantial non circumventing use how +would you say it I mean they're all + + align:start position:0% +would you say it I mean they're all + + + align:start position:0% +would you say it I mean they're all +going to be circumventing how would you + + align:start position:0% +going to be circumventing how would you + + + align:start position:0% +going to be circumventing how would you +even explain it what if you want to + + align:start position:0% +even explain it what if you want to + + + align:start position:0% +even explain it what if you want to +distribute a computer that obviously + + align:start position:0% +distribute a computer that obviously + + + align:start position:0% +distribute a computer that obviously +could be used for circumvention or it + + align:start position:0% +could be used for circumvention or it + + + align:start position:0% +could be used for circumvention or it +could be used not for circumvention that + + align:start position:0% +could be used not for circumvention that + + + align:start position:0% +could be used not for circumvention that +you would still want to be okay + + align:start position:0% +you would still want to be okay + + + align:start position:0% +you would still want to be okay +but how how would you phrase this + + align:start position:0% +but how how would you phrase this + + + align:start position:0% +but how how would you phrase this +um if you were the technology industry + + align:start position:0% +um if you were the technology industry + + + align:start position:0% +um if you were the technology industry +how what would be your wish list for an + + align:start position:0% +how what would be your wish list for an + + + align:start position:0% +how what would be your wish list for an +exemption here + + align:start position:0% +exemption here + + + align:start position:0% +exemption here +notri not primarily used for + + align:start position:0% +notri not primarily used for + + + align:start position:0% +notri not primarily used for +what you don't advertise Ed to something + + align:start position:0% +what you don't advertise Ed to something + + + align:start position:0% +what you don't advertise Ed to something +that's bad I mean okay let's talk about + + align:start position:0% +that's bad I mean okay let's talk about + + + align:start position:0% +that's bad I mean okay let's talk about +DVDs people know about DVDs right DVDs + + align:start position:0% +DVDs people know about DVDs right DVDs + + + align:start position:0% +DVDs people know about DVDs right DVDs +are + + align:start position:0% +are + + + align:start position:0% +are +encrypted and the encryption key uh and + + align:start position:0% +encrypted and the encryption key uh and + + + align:start position:0% +encrypted and the encryption key uh and +in fact the encryption method they're + + align:start position:0% +in fact the encryption method they're + + + align:start position:0% +in fact the encryption method they're +kept secret so you can get the DVD + + align:start position:0% +kept secret so you can get the DVD + + + align:start position:0% +kept secret so you can get the DVD +specification which is like that's also + + align:start position:0% +specification which is like that's also + + + align:start position:0% +specification which is like that's also +kept secret but um that's like $5,000 or + + align:start position:0% +kept secret but um that's like $5,000 or + + + align:start position:0% +kept secret but um that's like $5,000 or +something or maybe it's $5,000 per + + align:start position:0% +something or maybe it's $5,000 per + + + align:start position:0% +something or maybe it's $5,000 per +volume anyway it's expensive you can get + + align:start position:0% +volume anyway it's expensive you can get + + + align:start position:0% +volume anyway it's expensive you can get +that and you can make a DVD drive but + + align:start position:0% +that and you can make a DVD drive but + + + align:start position:0% +that and you can make a DVD drive but +that drive will be useless because you + + align:start position:0% +that drive will be useless because you + + + align:start position:0% +that drive will be useless because you +don't know uh the encryption or maybe + + align:start position:0% +don't know uh the encryption or maybe + + + align:start position:0% +don't know uh the encryption or maybe +you could make a DVD ROM drive this way + + align:start position:0% +you could make a DVD ROM drive this way + + + align:start position:0% +you could make a DVD ROM drive this way +but you couldn't play movies so if you + + align:start position:0% +but you couldn't play movies so if you + + + align:start position:0% +but you couldn't play movies so if you +want to play movies what do you have to + + align:start position:0% +want to play movies what do you have to + + + align:start position:0% +want to play movies what do you have to +do get the secret key you have to get a + + align:start position:0% +do get the secret key you have to get a + + + align:start position:0% +do get the secret key you have to get a +secret key and you have to get the + + align:start position:0% +secret key and you have to get the + + + align:start position:0% +secret key and you have to get the +encryption method so you go to the uh + + align:start position:0% +encryption method so you go to the uh + + + align:start position:0% +encryption method so you go to the uh +the organization that controls it which + + align:start position:0% +the organization that controls it which + + + align:start position:0% +the organization that controls it which +is basically the movie studios again and + + align:start position:0% +is basically the movie studios again and + + + align:start position:0% +is basically the movie studios again and +you say okay please give me the secret + + align:start position:0% +you say okay please give me the secret + + + align:start position:0% +you say okay please give me the secret +key and the secret method I'm going to + + align:start position:0% +key and the secret method I'm going to + + + align:start position:0% +key and the secret method I'm going to +make a DVD drive but in exchange what do + + align:start position:0% +make a DVD drive but in exchange what do + + + align:start position:0% +make a DVD drive but in exchange what do +you have to + + align:start position:0% +you have to + + + align:start position:0% +you have to +do yes you have to pay but what + + align:start position:0% +do yes you have to pay but what + + + align:start position:0% +do yes you have to pay but what +else nondisclosure yes it's a + + align:start position:0% +else nondisclosure yes it's a + + + align:start position:0% +else nondisclosure yes it's a +non-disclosure agreement and you have to + + align:start position:0% +non-disclosure agreement and you have to + + + align:start position:0% +non-disclosure agreement and you have to +agree to all these restrictions you + + align:start position:0% +agree to all these restrictions you + + + align:start position:0% +agree to all these restrictions you +can't let the people copy it you can't + + align:start position:0% +can't let the people copy it you can't + + + align:start position:0% +can't let the people copy it you can't +let the people fast forward when the + + align:start position:0% +let the people fast forward when the + + + align:start position:0% +let the people fast forward when the +little FBI warning is coming up people + + align:start position:0% +little FBI warning is coming up people + + + align:start position:0% +little FBI warning is coming up people +know this like when sometimes the + + align:start position:0% +know this like when sometimes the + + + align:start position:0% +know this like when sometimes the +previous you can't let them do that what + + align:start position:0% +previous you can't let them do that what + + + align:start position:0% +previous you can't let them do that what +else can't you let them + + align:start position:0% + + + + align:start position:0% + +do it used to be you could not give a + + align:start position:0% +do it used to be you could not give a + + + align:start position:0% +do it used to be you could not give a +progressive scan + + align:start position:0% + + + + align:start position:0% + +output um because it would be too high + + align:start position:0% +output um because it would be too high + + + align:start position:0% +output um because it would be too high +quality and too easy easy to copy and + + align:start position:0% +quality and too easy easy to copy and + + + align:start position:0% +quality and too easy easy to copy and +you can't um you can't ever send the + + align:start position:0% +you can't um you can't ever send the + + + align:start position:0% +you can't um you can't ever send the +bits out unencrypted so if you want to + + align:start position:0% +bits out unencrypted so if you want to + + + align:start position:0% +bits out unencrypted so if you want to +put them over HDTV or something you you + + align:start position:0% +put them over HDTV or something you you + + + align:start position:0% +put them over HDTV or something you you +can't hook it up directly to HDTV with + + align:start position:0% +can't hook it up directly to HDTV with + + + align:start position:0% +can't hook it up directly to HDTV with +the httv standard because httv is + + align:start position:0% +the httv standard because httv is + + + align:start position:0% +the httv standard because httv is +unencrypted so therefore you can't ever + + align:start position:0% +unencrypted so therefore you can't ever + + + align:start position:0% +unencrypted so therefore you can't ever +send the bits out that way so there's + + align:start position:0% +send the bits out that way so there's + + + align:start position:0% +send the bits out that way so there's +all these rules that you have to agree + + align:start position:0% +all these rules that you have to agree + + + align:start position:0% +all these rules that you have to agree +to and so um and of course the algorithm + + align:start position:0% +to and so um and of course the algorithm + + + align:start position:0% +to and so um and of course the algorithm +itself has to remain a + + align:start position:0% +itself has to remain a + + + align:start position:0% +itself has to remain a +secret so um there can never be like a + + align:start position:0% +secret so um there can never be like a + + + align:start position:0% +secret so um there can never be like a +free software + + align:start position:0% +free software + + + align:start position:0% +free software +algorithm so if you wanted to let's say + + align:start position:0% +algorithm so if you wanted to let's say + + + align:start position:0% +algorithm so if you wanted to let's say +you're on Linux and you want to + + align:start position:0% +you're on Linux and you want to + + + align:start position:0% +you're on Linux and you want to +distribute a free software an open- + + align:start position:0% +distribute a free software an open- + + + align:start position:0% +distribute a free software an open- +Source + + align:start position:0% +Source + + + align:start position:0% +Source +um uh DVD player uh can you do that I + + align:start position:0% +um uh DVD player uh can you do that I + + + align:start position:0% +um uh DVD player uh can you do that I +mean can you go to them and say I'm + + align:start position:0% +mean can you go to them and say I'm + + + align:start position:0% +mean can you go to them and say I'm +going to distribute the open source DVD + + align:start position:0% +going to distribute the open source DVD + + + align:start position:0% +going to distribute the open source DVD +player that's going to have all the code + + align:start position:0% +player that's going to have all the code + + + align:start position:0% +player that's going to have all the code +um can you is that will they be + + align:start position:0% +um can you is that will they be + + + align:start position:0% +um can you is that will they be +okay no why + + align:start position:0% + + + + align:start position:0% + +not yeah I mean they really want you to + + align:start position:0% +not yeah I mean they really want you to + + + align:start position:0% +not yeah I mean they really want you to +disguise how it works and they realize + + align:start position:0% +disguise how it works and they realize + + + align:start position:0% +disguise how it works and they realize +that you could still pick it apart but + + align:start position:0% +that you could still pick it apart but + + + align:start position:0% +that you could still pick it apart but +they say it has to be really disguised + + align:start position:0% +they say it has to be really disguised + + + align:start position:0% +they say it has to be really disguised +you can't put the source code and it + + align:start position:0% +you can't put the source code and it + + + align:start position:0% +you can't put the source code and it +can't be easy to modify so if the user + + align:start position:0% +can't be easy to modify so if the user + + + align:start position:0% +can't be easy to modify so if the user +can just go in and there's the part + + align:start position:0% +can just go in and there's the part + + + align:start position:0% +can just go in and there's the part +where like if it's during the FBI + + align:start position:0% +where like if it's during the FBI + + + align:start position:0% +where like if it's during the FBI +warning you can't fast forward and just + + align:start position:0% +warning you can't fast forward and just + + + align:start position:0% +warning you can't fast forward and just +comment that part out they're not going + + align:start position:0% +comment that part out they're not going + + + align:start position:0% +comment that part out they're not going +to let you do it and the user could also + + align:start position:0% +to let you do it and the user could also + + + align:start position:0% +to let you do it and the user could also +just take the bits instead of displaying + + align:start position:0% +just take the bits instead of displaying + + + align:start position:0% +just take the bits instead of displaying +them the screen could just save them all + + align:start position:0% +them the screen could just save them all + + + align:start position:0% +them the screen could just save them all +sorts of things that they wouldn't want + + align:start position:0% +sorts of things that they wouldn't want + + + align:start position:0% +sorts of things that they wouldn't want +you could play foreign movies so + + align:start position:0% +you could play foreign movies so + + + align:start position:0% +you could play foreign movies so +um so so they you know they would never + + align:start position:0% +um so so they you know they would never + + + align:start position:0% +um so so they you know they would never +want to approve a sort of a free + + align:start position:0% +want to approve a sort of a free + + + align:start position:0% +want to approve a sort of a free +software Linux + + align:start position:0% +software Linux + + + align:start position:0% +software Linux +player um now could you so but if you + + align:start position:0% +player um now could you so but if you + + + align:start position:0% +player um now could you so but if you +wanted to distribute this player on the + + align:start position:0% +wanted to distribute this player on the + + + align:start position:0% +wanted to distribute this player on the +ground that oh it's just letting people + + align:start position:0% +ground that oh it's just letting people + + + align:start position:0% +ground that oh it's just letting people +watch the movies and that's okay because + + align:start position:0% +watch the movies and that's okay because + + + align:start position:0% +watch the movies and that's okay because +they're just watching them they're not + + align:start position:0% +they're just watching them they're not + + + align:start position:0% +they're just watching them they're not +doing anything bad you know if there + + align:start position:0% +doing anything bad you know if there + + + align:start position:0% +doing anything bad you know if there +were a substantial non-infringing use + + align:start position:0% +were a substantial non-infringing use + + + align:start position:0% +were a substantial non-infringing use +standard would you be + + align:start position:0% + + + + align:start position:0% + +okay I mean yes because those people are + + align:start position:0% +okay I mean yes because those people are + + + align:start position:0% +okay I mean yes because those people are +not really infringing but uh it's not + + align:start position:0% +not really infringing but uh it's not + + + align:start position:0% +not really infringing but uh it's not +the standard is not substantial + + align:start position:0% +the standard is not substantial + + + align:start position:0% +the standard is not substantial +non-infringing use and if it were you + + align:start position:0% +non-infringing use and if it were you + + + align:start position:0% +non-infringing use and if it were you +know then the movie students areg well + + align:start position:0% +know then the movie students areg well + + + align:start position:0% +know then the movie students areg well +you could just distribute this you know + + align:start position:0% +you could just distribute this you know + + + align:start position:0% +you could just distribute this you know +all you wanted and then people could get + + align:start position:0% +all you wanted and then people could get + + + align:start position:0% +all you wanted and then people could get +it and then they could use it for their + + align:start position:0% +it and then they could use it for their + + + align:start position:0% +it and then they could use it for their +bad + + align:start position:0% +bad + + + align:start position:0% +bad +purposes so the law has written much + + align:start position:0% +purposes so the law has written much + + + align:start position:0% +purposes so the law has written much +closer than that substantial + + align:start position:0% +closer than that substantial + + + align:start position:0% +closer than that substantial +non-infringing use standard it says + + align:start position:0% +non-infringing use standard it says + + + align:start position:0% +non-infringing use standard it says +instead you can't manufacture import + + align:start position:0% +instead you can't manufacture import + + + align:start position:0% +instead you can't manufacture import +offer the public provide traffic in any + + align:start position:0% +offer the public provide traffic in any + + + align:start position:0% +offer the public provide traffic in any +technology product service device + + align:start position:0% +technology product service device + + + align:start position:0% +technology product service device +component or part that a is primarily + + align:start position:0% +component or part that a is primarily + + + align:start position:0% +component or part that a is primarily +designed or produced for the purpose of + + align:start position:0% +designed or produced for the purpose of + + + align:start position:0% +designed or produced for the purpose of +circumventing a technological measure B + + align:start position:0% +circumventing a technological measure B + + + align:start position:0% +circumventing a technological measure B +has only limited commercially + + align:start position:0% +has only limited commercially + + + align:start position:0% +has only limited commercially +significant purpose or use or C is + + align:start position:0% +significant purpose or use or C is + + + align:start position:0% +significant purpose or use or C is +marketed by the person or another acting + + align:start position:0% +marketed by the person or another acting + + + align:start position:0% +marketed by the person or another acting +in concert with that purpose person's + + align:start position:0% +in concert with that purpose person's + + + align:start position:0% +in concert with that purpose person's +knowledge for use in circumventing a + + align:start position:0% +knowledge for use in circumventing a + + + align:start position:0% +knowledge for use in circumventing a +technological measure that effectively + + align:start position:0% +technological measure that effectively + + + align:start position:0% +technological measure that effectively +controls access to work protected under + + align:start position:0% +controls access to work protected under + + + align:start position:0% +controls access to work protected under +this + + align:start position:0% +this + + + align:start position:0% +this +title so we're I'm going to go over + + align:start position:0% + + + + align:start position:0% + +here we're forbidding uh we're + + align:start position:0% +here we're forbidding uh we're + + + align:start position:0% +here we're forbidding uh we're +forbidding + + align:start position:0% + + + + align:start position:0% + +circumvention and we're also forbidding + + align:start position:0% +circumvention and we're also forbidding + + + align:start position:0% +circumvention and we're also forbidding +sort of help to circumvention and these + + align:start position:0% +sort of help to circumvention and these + + + align:start position:0% +sort of help to circumvention and these +are all in + + align:start position:0% +are all in + + + align:start position:0% +are all in +the + + align:start position:0% +the + + + align:start position:0% +the +access this is all the access control + + align:start position:0% +access this is all the access control + + + align:start position:0% +access this is all the access control +column let me let's try this + + align:start position:0% +column let me let's try this + + + align:start position:0% +column let me let's try this +again so we're + + align:start position:0% + + + + align:start position:0% + +fitting circumvention of access control + + align:start position:0% +fitting circumvention of access control + + + align:start position:0% +fitting circumvention of access control +that's the check means forbidden and + + align:start position:0% +that's the check means forbidden and + + + align:start position:0% +that's the check means forbidden and +we're forbidding help for people who + + align:start position:0% +we're forbidding help for people who + + + align:start position:0% +we're forbidding help for people who +would circumvent access + + align:start position:0% +would circumvent access + + + align:start position:0% +would circumvent access +control so we got them both so that DVD + + align:start position:0% +control so we got them both so that DVD + + + align:start position:0% +control so we got them both so that DVD +player uh + + align:start position:0% +player uh + + + align:start position:0% +player uh +um it's you know you you can't you just + + align:start position:0% +um it's you know you you can't you just + + + align:start position:0% +um it's you know you you can't you just +if even if you found out yourself how to + + align:start position:0% +if even if you found out yourself how to + + + align:start position:0% +if even if you found out yourself how to +make a DVD player you couldn't + + align:start position:0% +make a DVD player you couldn't + + + align:start position:0% +make a DVD player you couldn't +distribute a device that would + + align:start position:0% +distribute a device that would + + + align:start position:0% +distribute a device that would +circumvent the access control and that's + + align:start position:0% +circumvent the access control and that's + + + align:start position:0% +circumvent the access control and that's +what this whole corly case was about now + + align:start position:0% +what this whole corly case was about now + + + align:start position:0% +what this whole corly case was about now +part of it was about the first amendment + + align:start position:0% +part of it was about the first amendment + + + align:start position:0% +part of it was about the first amendment +was about can I publish source code + + align:start position:0% +was about can I publish source code + + + align:start position:0% +was about can I publish source code +under the you know as speech under the + + align:start position:0% +under the you know as speech under the + + + align:start position:0% +under the you know as speech under the +First + + align:start position:0% +First + + + align:start position:0% +First +Amendment um and what did the court + + align:start position:0% + + + + align:start position:0% + +say did did that argument carry the + + align:start position:0% +say did did that argument carry the + + + align:start position:0% +say did did that argument carry the +day no it no it didn't uh because the + + align:start position:0% +day no it no it didn't uh because the + + + align:start position:0% +day no it no it didn't uh because the +court said well this code it's true that + + align:start position:0% +court said well this code it's true that + + + align:start position:0% +court said well this code it's true that +it's speech but it's also functional and + + align:start position:0% +it's speech but it's also functional and + + + align:start position:0% +it's speech but it's also functional and +it performs a + + align:start position:0% +it performs a + + + align:start position:0% +it performs a +function um now did that stop DVD + + align:start position:0% +function um now did that stop DVD + + + align:start position:0% +function um now did that stop DVD +descramblers from being + + align:start position:0% +descramblers from being + + + align:start position:0% +descramblers from being +distributed I mean has has here anybody + + align:start position:0% +distributed I mean has has here anybody + + + align:start position:0% +distributed I mean has has here anybody +here ever watched a DVD with an illegal + + align:start position:0% +here ever watched a DVD with an illegal + + + align:start position:0% +here ever watched a DVD with an illegal +method like okay on Linux or on Windows + + align:start position:0% +method like okay on Linux or on Windows + + + align:start position:0% +method like okay on Linux or on Windows +or what Windows oh somebody on Windows + + align:start position:0% +or what Windows oh somebody on Windows + + + align:start position:0% +or what Windows oh somebody on Windows +okay I mean I wonder if I can just one + + align:start position:0% +okay I mean I wonder if I can just one + + + align:start position:0% +okay I mean I wonder if I can just one +right now let's see I think I can do app + + align:start position:0% +right now let's see I think I can do app + + + align:start position:0% +right now let's see I think I can do app +get install lib dvdc is that what I do + + align:start position:0% +get install lib dvdc is that what I do + + + align:start position:0% +get install lib dvdc is that what I do +let's see if this will just work oh no + + align:start position:0% +let's see if this will just work oh no + + + align:start position:0% +let's see if this will just work oh no +do + + align:start position:0% + + + + align:start position:0% + +I oh okay app get install lib DVD read + + align:start position:0% +I oh okay app get install lib DVD read + + + align:start position:0% +I oh okay app get install lib DVD read +3 uh okay there it is lib DVD CSS 2 I'm + + align:start position:0% +3 uh okay there it is lib DVD CSS 2 I'm + + + align:start position:0% +3 uh okay there it is lib DVD CSS 2 I'm +probably breaking the law right now + + align:start position:0% +probably breaking the law right now + + + align:start position:0% +probably breaking the law right now +anyway so um in I is this illegal what + + align:start position:0% +anyway so um in I is this illegal what + + + align:start position:0% +anyway so um in I is this illegal what +I'm doing right now + + align:start position:0% +I'm doing right now + + + align:start position:0% +I'm doing right now +instru instructional use what is that + + align:start position:0% +instru instructional use what is that + + + align:start position:0% +instru instructional use what is that +exe is there an exemption for + + align:start position:0% +exe is there an exemption for + + + align:start position:0% +exe is there an exemption for +instructional + + align:start position:0% +instructional + + + align:start position:0% +instructional +use face to- face classroom teaching is + + align:start position:0% +use face to- face classroom teaching is + + + align:start position:0% +use face to- face classroom teaching is +an exemption to + + align:start position:0% +an exemption to + + + align:start position:0% +an exemption to +what that's an exemption to infringement + + align:start position:0% +what that's an exemption to infringement + + + align:start position:0% +what that's an exemption to infringement +but I'm not but the I wouldn't the crime + + align:start position:0% +but I'm not but the I wouldn't the crime + + + align:start position:0% +but I'm not but the I wouldn't the crime +I'm committing here is not infringement + + align:start position:0% +I'm committing here is not infringement + + + align:start position:0% +I'm committing here is not infringement +it's just um well you're not really + + align:start position:0% +it's just um well you're not really + + + align:start position:0% +it's just um well you're not really +accessing you haven't used it to access + + align:start position:0% +accessing you haven't used it to access + + + align:start position:0% +accessing you haven't used it to access +anything yet though what if what if you + + align:start position:0% +anything yet though what if what if you + + + align:start position:0% +anything yet though what if what if you +make a seat DVD at home you to do that + + align:start position:0% +make a seat DVD at home you to do that + + + align:start position:0% +make a seat DVD at home you to do that +use this + + align:start position:0% +use this + + + align:start position:0% +use this +see I'm not I can't actually install lib + + align:start position:0% +see I'm not I can't actually install lib + + + align:start position:0% +see I'm not I can't actually install lib +DVD CSS to I think I have to get that + + align:start position:0% +DVD CSS to I think I have to get that + + + align:start position:0% +DVD CSS to I think I have to get that +from Europe or something the source of + + align:start position:0% +from Europe or something the source of + + + align:start position:0% +from Europe or something the source of +all illegal + + align:start position:0% +all illegal + + + align:start position:0% +all illegal +things okay well that's good to know + + align:start position:0% +things okay well that's good to know + + + align:start position:0% +things okay well that's good to know +sorry what was that well what if you + + align:start position:0% +sorry what was that well what if you + + + align:start position:0% +sorry what was that well what if you +make a home video DVDs my own DVDs yeah + + align:start position:0% +make a home video DVDs my own DVDs yeah + + + align:start position:0% +make a home video DVDs my own DVDs yeah +then should be able yeah if I have the + + align:start position:0% +then should be able yeah if I have the + + + align:start position:0% +then should be able yeah if I have the +well those wouldn't be encrypted but if + + align:start position:0% +well those wouldn't be encrypted but if + + + align:start position:0% +well those wouldn't be encrypted but if +they were I would have the authority of + + align:start position:0% +they were I would have the authority of + + + align:start position:0% +they were I would have the authority of +the copyright owner so you're right but + + align:start position:0% +the copyright owner so you're right but + + + align:start position:0% +the copyright owner so you're right but +I still couldn't distribute uh help that + + align:start position:0% +I still couldn't distribute uh help that + + + align:start position:0% +I still couldn't distribute uh help that +would help people circumvent the + + align:start position:0% +would help people circumvent the + + + align:start position:0% +would help people circumvent the +authority of some other copyright owner + + align:start position:0% +authority of some other copyright owner + + + align:start position:0% +authority of some other copyright owner +uh but it's you know and here's a guy at + + align:start position:0% +uh but it's you know and here's a guy at + + + align:start position:0% +uh but it's you know and here's a guy at +um Carnegie melon who um has distri you + + align:start position:0% +um Carnegie melon who um has distri you + + + align:start position:0% +um Carnegie melon who um has distri you +know he's tried to distribute all + + align:start position:0% +know he's tried to distribute all + + + align:start position:0% +know he's tried to distribute all +possible ways of expressing the code + + align:start position:0% +possible ways of expressing the code + + + align:start position:0% +possible ways of expressing the code +this is me um but there's other people + + align:start position:0% +this is me um but there's other people + + + align:start position:0% +this is me um but there's other people +here's another member of sippy um + + align:start position:0% +here's another member of sippy um + + + align:start position:0% +here's another member of sippy um +Charles Hanam and here it is in standard + + align:start position:0% +Charles Hanam and here it is in standard + + + align:start position:0% +Charles Hanam and here it is in standard +ML and in something other and JavaScript + + align:start position:0% +ML and in something other and JavaScript + + + align:start position:0% +ML and in something other and JavaScript +you got to be insane use that and oh + + align:start position:0% +you got to be insane use that and oh + + + align:start position:0% +you got to be insane use that and oh +here it is in scheme and and a gif + + align:start position:0% +here it is in scheme and and a gif + + + align:start position:0% +here it is in scheme and and a gif +and some other language and English and + + align:start position:0% +and some other language and English and + + + align:start position:0% +and some other language and English and +oh here's omry Schwarz another sippy + + align:start position:0% +oh here's omry Schwarz another sippy + + + align:start position:0% +oh here's omry Schwarz another sippy +member in + + align:start position:0% +member in + + + align:start position:0% +member in +English and oh and not only is his in + + align:start position:0% +English and oh and not only is his in + + + align:start position:0% +English and oh and not only is his in +English but he has an automated program + + align:start position:0% +English but he has an automated program + + + align:start position:0% +English but he has an automated program +for translating it back to + + align:start position:0% + + + + align:start position:0% + +C uh so there's some very tricky First + + align:start position:0% +C uh so there's some very tricky First + + + align:start position:0% +C uh so there's some very tricky First +Amendment questions here here it is in a + + align:start position:0% +Amendment questions here here it is in a + + + align:start position:0% +Amendment questions here here it is in a +Hau by Seth Shon and here's a crypt + + align:start position:0% +Hau by Seth Shon and here's a crypt + + + align:start position:0% +Hau by Seth Shon and here's a crypt +analysis here's a tie that has my code + + align:start position:0% +analysis here's a tie that has my code + + + align:start position:0% +analysis here's a tie that has my code +on it and uh here's a dramatic reading + + align:start position:0% +on it and uh here's a dramatic reading + + + align:start position:0% +on it and uh here's a dramatic reading +set to music here's a song you people + + align:start position:0% +set to music here's a song you people + + + align:start position:0% +set to music here's a song you people +heard this + + align:start position:0% +heard this + + + align:start position:0% +heard this +song uh maybe you haven't what is this + + align:start position:0% +song uh maybe you haven't what is this + + + align:start position:0% +song uh maybe you haven't what is this +again this is all the code to descramble + + align:start position:0% +again this is all the code to descramble + + + align:start position:0% +again this is all the code to descramble +a DVD this is sort of the code that was + + align:start position:0% +a DVD this is sort of the code that was + + + align:start position:0% +a DVD this is sort of the code that was +at issue in that corly + + align:start position:0% +at issue in that corly + + + align:start position:0% +at issue in that corly +case but expressed in different ways + + align:start position:0% +case but expressed in different ways + + + align:start position:0% +case but expressed in different ways +here's the logo of DVDs made out of the + + align:start position:0% +here's the logo of DVDs made out of the + + + align:start position:0% +here's the logo of DVDs made out of the +code did you scramble + + align:start position:0% +code did you scramble + + + align:start position:0% +code did you scramble +DVDs uh okay there's a lot of these and + + align:start position:0% +DVDs uh okay there's a lot of these and + + + align:start position:0% +DVDs uh okay there's a lot of these and +I mean has this guy gotten in + + align:start position:0% + + + + align:start position:0% + +trouble his what his website true yeah + + align:start position:0% +trouble his what his website true yeah + + + align:start position:0% +trouble his what his website true yeah +so I mean it's it's um it's sort of a + + align:start position:0% +so I mean it's it's um it's sort of a + + + align:start position:0% +so I mean it's it's um it's sort of a +mixed result here in this DVD case + + align:start position:0% +mixed result here in this DVD case + + + align:start position:0% +mixed result here in this DVD case +because in the law the uh movie studios + + align:start position:0% +because in the law the uh movie studios + + + align:start position:0% +because in the law the uh movie studios +were entirely successful they won on + + align:start position:0% +were entirely successful they won on + + + align:start position:0% +were entirely successful they won on +every + + align:start position:0% +every + + + align:start position:0% +every +um every claim before the court they + + align:start position:0% +um every claim before the court they + + + align:start position:0% +um every claim before the court they +said it's not first amendment they said + + align:start position:0% +said it's not first amendment they said + + + align:start position:0% +said it's not first amendment they said +first of all the um this DVD Des + + align:start position:0% +first of all the um this DVD Des + + + align:start position:0% +first of all the um this DVD Des +scramble does circumvent a technological + + align:start position:0% +scramble does circumvent a technological + + + align:start position:0% +scramble does circumvent a technological +measure which um I I'm not still not + + align:start position:0% +measure which um I I'm not still not + + + align:start position:0% +measure which um I I'm not still not +doesn't seem totally right + + align:start position:0% +doesn't seem totally right + + + align:start position:0% +doesn't seem totally right +I mean is it a technological measure + + align:start position:0% +I mean is it a technological measure + + + align:start position:0% +I mean is it a technological measure +more of a anyway it circumvent a + + align:start position:0% +more of a anyway it circumvent a + + + align:start position:0% +more of a anyway it circumvent a +technological measure so it does break + + align:start position:0% +technological measure so it does break + + + align:start position:0% +technological measure so it does break +the law and the law is + + align:start position:0% +the law and the law is + + + align:start position:0% +the law and the law is +constitutional and it's not covered by + + align:start position:0% +constitutional and it's not covered by + + + align:start position:0% +constitutional and it's not covered by +any of the exemptions and what else um + + align:start position:0% +any of the exemptions and what else um + + + align:start position:0% +any of the exemptions and what else um +oh and that they don't have the + + align:start position:0% +oh and that they don't have the + + + align:start position:0% +oh and that they don't have the +authority of the copyright + + align:start position:0% +authority of the copyright + + + align:start position:0% +authority of the copyright +owner now that has remained sort of + + align:start position:0% +owner now that has remained sort of + + + align:start position:0% +owner now that has remained sort of +mystifying to me because you think when + + align:start position:0% +mystifying to me because you think when + + + align:start position:0% +mystifying to me because you think when +you buy the DVD you have the authority + + align:start position:0% +you buy the DVD you have the authority + + + align:start position:0% +you buy the DVD you have the authority +to uh view it but uh what the court said + + align:start position:0% +to uh view it but uh what the court said + + + align:start position:0% +to uh view it but uh what the court said +what did the court + + align:start position:0% + + + + align:start position:0% + +say I think I have some slides on this + + align:start position:0% +say I think I have some slides on this + + + align:start position:0% +say I think I have some slides on this +here we go + + align:start position:0% + + + + align:start position:0% + +uh oh okay okay so + + align:start position:0% +uh oh okay okay so + + + align:start position:0% +uh oh okay okay so +um so in in the patent world if let's + + align:start position:0% +um so in in the patent world if let's + + + align:start position:0% +um so in in the patent world if let's +say you buy something that's patented + + align:start position:0% +say you buy something that's patented + + + align:start position:0% +say you buy something that's patented +you you you cannot make use or offer to + + align:start position:0% +you you you cannot make use or offer to + + + align:start position:0% +you you you cannot make use or offer to +sell the patented thing without + + align:start position:0% +sell the patented thing without + + + align:start position:0% +sell the patented thing without +Authority right so if you buy a patented + + align:start position:0% +Authority right so if you buy a patented + + + align:start position:0% +Authority right so if you buy a patented +what's something that's + + align:start position:0% +what's something that's + + + align:start position:0% +what's something that's +patented I I don't know a + + align:start position:0% +patented I I don't know a + + + align:start position:0% +patented I I don't know a +what okay a Blackberry yeah you can't + + align:start position:0% +what okay a Blackberry yeah you can't + + + align:start position:0% +what okay a Blackberry yeah you can't +make or use or offer to sell it without + + align:start position:0% +make or use or offer to sell it without + + + align:start position:0% +make or use or offer to sell it without +the permission of the patent owner but + + align:start position:0% +the permission of the patent owner but + + + align:start position:0% +the permission of the patent owner but +of course when you buy the thing they + + align:start position:0% +of course when you buy the thing they + + + align:start position:0% +of course when you buy the thing they +can't then say three years later oh we + + align:start position:0% +can't then say three years later oh we + + + align:start position:0% +can't then say three years later oh we +revoke your Authority because we don't + + align:start position:0% +revoke your Authority because we don't + + + align:start position:0% +revoke your Authority because we don't +like you when you buy you also sort of + + align:start position:0% +like you when you buy you also sort of + + + align:start position:0% +like you when you buy you also sort of +buy the authority and this case that I + + align:start position:0% +buy the authority and this case that I + + + align:start position:0% +buy the authority and this case that I +said here repo type stencil says + + align:start position:0% +said here repo type stencil says + + + align:start position:0% +said here repo type stencil says +generally when a seller sells a product + + align:start position:0% +generally when a seller sells a product + + + align:start position:0% +generally when a seller sells a product +without restriction it in effect + + align:start position:0% +without restriction it in effect + + + align:start position:0% +without restriction it in effect +promises the purchaser that in effect + + align:start position:0% +promises the purchaser that in effect + + + align:start position:0% +promises the purchaser that in effect +for the price in exchange for the price + + align:start position:0% +for the price in exchange for the price + + + align:start position:0% +for the price in exchange for the price +paid it will not interfere with the + + align:start position:0% +paid it will not interfere with the + + + align:start position:0% +paid it will not interfere with the +purchaser's full enjoyment of the + + align:start position:0% +purchaser's full enjoyment of the + + + align:start position:0% +purchaser's full enjoyment of the +product purchase this full enjoyment has + + align:start position:0% +product purchase this full enjoyment has + + + align:start position:0% +product purchase this full enjoyment has +a lot of meaning there the buyer has an + + align:start position:0% +a lot of meaning there the buyer has an + + + align:start position:0% +a lot of meaning there the buyer has an +no I mean I'm serious there the whole + + align:start position:0% +no I mean I'm serious there the whole + + + align:start position:0% +no I mean I'm serious there the whole +case about full enjoyment the buyer has + + align:start position:0% +case about full enjoyment the buyer has + + + align:start position:0% +case about full enjoyment the buyer has +an implied Li an implied license under + + align:start position:0% +an implied Li an implied license under + + + align:start position:0% +an implied Li an implied license under +any patents of the seller that dominate + + align:start position:0% +any patents of the seller that dominate + + + align:start position:0% +any patents of the seller that dominate +the product or any uses of the product + + align:start position:0% +the product or any uses of the product + + + align:start position:0% +the product or any uses of the product +to which the parties might reasonably + + align:start position:0% +to which the parties might reasonably + + + align:start position:0% +to which the parties might reasonably +contemplate the product will be + + align:start position:0% +contemplate the product will be + + + align:start position:0% +contemplate the product will be +put that seems like a pretty reasonable + + align:start position:0% +put that seems like a pretty reasonable + + + align:start position:0% +put that seems like a pretty reasonable +rule right like if you buy the + + align:start position:0% +rule right like if you buy the + + + align:start position:0% +rule right like if you buy the +Blackberry and later Blackberry comes + + align:start position:0% +Blackberry and later Blackberry comes + + + align:start position:0% +Blackberry and later Blackberry comes +out with some other state-of-the-art + + align:start position:0% +out with some other state-of-the-art + + + align:start position:0% +out with some other state-of-the-art +thing that is newly patented that they + + align:start position:0% +thing that is newly patented that they + + + align:start position:0% +thing that is newly patented that they +want more money for you can't like go in + + align:start position:0% +want more money for you can't like go in + + + align:start position:0% +want more money for you can't like go in +and modify your blackberry to do the new + + align:start position:0% +and modify your blackberry to do the new + + + align:start position:0% +and modify your blackberry to do the new +thing infringing their new patent that + + align:start position:0% +thing infringing their new patent that + + + align:start position:0% +thing infringing their new patent that +would be not okay but anything that you + + align:start position:0% +would be not okay but anything that you + + + align:start position:0% +would be not okay but anything that you +reasonably could contemplate the + + align:start position:0% +reasonably could contemplate the + + + align:start position:0% +reasonably could contemplate the +original blackb would be used for is + + align:start position:0% +original blackb would be used for is + + + align:start position:0% +original blackb would be used for is +fine um so you might use this argument + + align:start position:0% +fine um so you might use this argument + + + align:start position:0% +fine um so you might use this argument +you say look when you buy the DVD + + align:start position:0% +you say look when you buy the DVD + + + align:start position:0% +you say look when you buy the DVD +obviously you reasonably contemplate + + align:start position:0% +obviously you reasonably contemplate + + + align:start position:0% +obviously you reasonably contemplate +that I'm going to watch it so I do have + + align:start position:0% +that I'm going to watch it so I do have + + + align:start position:0% +that I'm going to watch it so I do have +the authority at least to watch it but + + align:start position:0% +the authority at least to watch it but + + + align:start position:0% +the authority at least to watch it but +the court in uh oh and so the language + + align:start position:0% +the court in uh oh and so the language + + + align:start position:0% +the court in uh oh and so the language +for patents is you know without + + align:start position:0% +for patents is you know without + + + align:start position:0% +for patents is you know without +Authority make use offer to sell or sell + + align:start position:0% +Authority make use offer to sell or sell + + + align:start position:0% +Authority make use offer to sell or sell +what's the language here is um the same + + align:start position:0% +what's the language here is um the same + + + align:start position:0% +what's the language here is um the same +thing + + align:start position:0% +thing + + + align:start position:0% +thing +to well to do it without the authority + + align:start position:0% +to well to do it without the authority + + + align:start position:0% +to well to do it without the authority +of the copyright honor so the first one + + align:start position:0% +of the copyright honor so the first one + + + align:start position:0% +of the copyright honor so the first one +is don't make use don't use it without + + align:start position:0% +is don't make use don't use it without + + + align:start position:0% +is don't make use don't use it without +Authority and here's don't do scramble + + align:start position:0% +Authority and here's don't do scramble + + + align:start position:0% +Authority and here's don't do scramble +without Authority and did the court + + align:start position:0% +without Authority and did the court + + + align:start position:0% +without Authority and did the court +agree with the sort of analogous + + align:start position:0% +agree with the sort of analogous + + + align:start position:0% +agree with the sort of analogous +argument that the same thing should + + align:start position:0% +argument that the same thing should + + + align:start position:0% +argument that the same thing should +apply in the dmca world oh here is okay + + align:start position:0% +apply in the dmca world oh here is okay + + + align:start position:0% +apply in the dmca world oh here is okay +so the scenario is you buy a DVD and you + + align:start position:0% +so the scenario is you buy a DVD and you + + + align:start position:0% +so the scenario is you buy a DVD and you +use there's this is the entire algorithm + + align:start position:0% +use there's this is the entire algorithm + + + align:start position:0% +use there's this is the entire algorithm +that was in question in that + + align:start position:0% +that was in question in that + + + align:start position:0% +that was in question in that +case uh in Pearl so and then in this + + align:start position:0% +case uh in Pearl so and then in this + + + align:start position:0% +case uh in Pearl so and then in this +case um so I'm making this argument oh I + + align:start position:0% +case um so I'm making this argument oh I + + + align:start position:0% +case um so I'm making this argument oh I +have the authority to view it and what + + align:start position:0% +have the authority to view it and what + + + align:start position:0% +have the authority to view it and what +does the court say in response it says + + align:start position:0% +does the court say in response it says + + + align:start position:0% +does the court say in response it says +I'm wrong it says the appellants argue + + align:start position:0% +I'm wrong it says the appellants argue + + + align:start position:0% +I'm wrong it says the appellants argue +that an individual who buys a DVD has + + align:start position:0% +that an individual who buys a DVD has + + + align:start position:0% +that an individual who buys a DVD has +the authority of the copyright owner to + + align:start position:0% +the authority of the copyright owner to + + + align:start position:0% +the authority of the copyright owner to +view the DVD yes that's what I said and + + align:start position:0% +view the DVD yes that's what I said and + + + align:start position:0% +view the DVD yes that's what I said and +therefore is Exempted from the dmca uh + + align:start position:0% +therefore is Exempted from the dmca uh + + + align:start position:0% +therefore is Exempted from the dmca uh +pursu to that section we're just reading + + align:start position:0% +pursu to that section we're just reading + + + align:start position:0% +pursu to that section we're just reading +when the buyer circumvents an encryption + + align:start position:0% +when the buyer circumvents an encryption + + + align:start position:0% +when the buyer circumvents an encryption +technology in order to view the DVD on a + + align:start position:0% +technology in order to view the DVD on a + + + align:start position:0% +technology in order to view the DVD on a +competing platform such as Linux so + + align:start position:0% +competing platform such as Linux so + + + align:start position:0% +competing platform such as Linux so +that's so far that that I think well + + align:start position:0% +that's so far that that I think well + + + align:start position:0% +that's so far that that I think well +summarizes our argument and the course + + align:start position:0% +summarizes our argument and the course + + + align:start position:0% +summarizes our argument and the course +says we're wrong the basic flaw in this + + align:start position:0% +says we're wrong the basic flaw in this + + + align:start position:0% +says we're wrong the basic flaw in this +argument is that it misreads what we + + align:start position:0% +argument is that it misreads what we + + + align:start position:0% +argument is that it misreads what we +were just reading that provision exempts + + align:start position:0% +were just reading that provision exempts + + + align:start position:0% +were just reading that provision exempts +from liability those who had decrypt an + + align:start position:0% +from liability those who had decrypt an + + + align:start position:0% +from liability those who had decrypt an +encrypted DVD with the authority of the + + align:start position:0% +encrypted DVD with the authority of the + + + align:start position:0% +encrypted DVD with the authority of the +cover owner not those who would view a + + align:start position:0% +cover owner not those who would view a + + + align:start position:0% +cover owner not those who would view a +DVD with the authority of a copyright + + align:start position:0% +DVD with the authority of a copyright + + + align:start position:0% +DVD with the authority of a copyright +owner + + align:start position:0% + + + + align:start position:0% + +um does anybody want to explain the + + align:start position:0% + + + + align:start position:0% + +difference like you can only view + + align:start position:0% +difference like you can only view + + + align:start position:0% +difference like you can only view +it legally but I mean if you have the + + align:start position:0% +it legally but I mean if you have the + + + align:start position:0% +it legally but I mean if you have the +authority to view it um surely I mean + + align:start position:0% +authority to view it um surely I mean + + + align:start position:0% +authority to view it um surely I mean +that includes the authority to decrypt + + align:start position:0% +that includes the authority to decrypt + + + align:start position:0% +that includes the authority to decrypt +it right why well you have to decrypt it + + align:start position:0% +it right why well you have to decrypt it + + + align:start position:0% +it right why well you have to decrypt it +to view it it you just get the image on + + align:start position:0% +to view it it you just get the image on + + + align:start position:0% +to view it it you just get the image on +a screen when you decrypt it you get a + + align:start position:0% +a screen when you decrypt it you get a + + + align:start position:0% +a screen when you decrypt it you get a +bunch of + + align:start position:0% +bunch of + + + align:start position:0% +bunch of +files + + align:start position:0% +files + + + align:start position:0% +files +okay but what about when you use um you + + align:start position:0% +okay but what about when you use um you + + + align:start position:0% +okay but what about when you use um you +know Zen or M player or one of these + + align:start position:0% +know Zen or M player or one of these + + + align:start position:0% +know Zen or M player or one of these +illegal programs ogal or totem to um to + + align:start position:0% +illegal programs ogal or totem to um to + + + align:start position:0% +illegal programs ogal or totem to um to +view it then you don't get files then + + align:start position:0% +view it then you don't get files then + + + align:start position:0% +view it then you don't get files then +you just watch it right is that okay + + align:start position:0% +you just watch it right is that okay + + + align:start position:0% +you just watch it right is that okay +excuse + + align:start position:0% +excuse + + + align:start position:0% +excuse +me I think so yeah you're right it's not + + align:start position:0% +me I think so yeah you're right it's not + + + align:start position:0% +me I think so yeah you're right it's not +but I don't I mean I don't really + + align:start position:0% +but I don't I mean I don't really + + + align:start position:0% +but I don't I mean I don't really +understand where the param are here + + align:start position:0% +understand where the param are here + + + align:start position:0% +understand where the param are here +because I just don't and I wrote to + + align:start position:0% +because I just don't and I wrote to + + + align:start position:0% +because I just don't and I wrote to +nimmer I was like what's up and he's + + align:start position:0% +nimmer I was like what's up and he's + + + align:start position:0% +nimmer I was like what's up and he's +like + + align:start position:0% + + + + align:start position:0% + +hey um I mean he doesn't know the answer + + align:start position:0% +hey um I mean he doesn't know the answer + + + align:start position:0% +hey um I mean he doesn't know the answer +either now um then we read this garage + + align:start position:0% +either now um then we read this garage + + + align:start position:0% +either now um then we read this garage +door opener case right oh so so anyway + + align:start position:0% +door opener case right oh so so anyway + + + align:start position:0% +door opener case right oh so so anyway +just to to sum up what the coop owners + + align:start position:0% +just to to sum up what the coop owners + + + align:start position:0% +just to to sum up what the coop owners +at least say is that um you don't get + + align:start position:0% +at least say is that um you don't get + + + align:start position:0% +at least say is that um you don't get +the unrestricted authority to to view + + align:start position:0% +the unrestricted authority to to view + + + align:start position:0% +the unrestricted authority to to view +and decrypt the DVD when you buy it what + + align:start position:0% +and decrypt the DVD when you buy it what + + + align:start position:0% +and decrypt the DVD when you buy it what +you get is the authority to view it on a + + align:start position:0% +you get is the authority to view it on a + + + align:start position:0% +you get is the authority to view it on a +licensed device they say we licens + + align:start position:0% +licensed device they say we licens + + + align:start position:0% +licensed device they say we licens +certain DVD players of our algorithm and + + align:start position:0% +certain DVD players of our algorithm and + + + align:start position:0% +certain DVD players of our algorithm and +those are the ones on which you have the + + align:start position:0% +those are the ones on which you have the + + + align:start position:0% +those are the ones on which you have the +authority to decrypt it not some other + + align:start position:0% +authority to decrypt it not some other + + + align:start position:0% +authority to decrypt it not some other +one like M player or Zen or or dcss + + align:start position:0% +one like M player or Zen or or dcss + + + align:start position:0% +one like M player or Zen or or dcss +that's what they + + align:start position:0% +that's what they + + + align:start position:0% +that's what they +say + + align:start position:0% +say + + + align:start position:0% +say +um so uh then Along come these uh garage + + align:start position:0% +um so uh then Along come these uh garage + + + align:start position:0% +um so uh then Along come these uh garage +door opener people the seirus Craftsman + + align:start position:0% +door opener people the seirus Craftsman + + + align:start position:0% +door opener people the seirus Craftsman +garage door opener and there were no + + align:start position:0% +garage door opener and there were no + + + align:start position:0% +garage door opener and there were no +stated restrictions on what you're + + align:start position:0% +stated restrictions on what you're + + + align:start position:0% +stated restrictions on what you're +allowed to do and uh the motor people + + align:start position:0% +allowed to do and uh the motor people + + + align:start position:0% +allowed to do and uh the motor people +taking + + align:start position:0% +taking + + + align:start position:0% +taking +6115 no okay well the motor is + + align:start position:0% +6115 no okay well the motor is + + + align:start position:0% +6115 no okay well the motor is +controlled by a pi micro processor + + align:start position:0% +controlled by a pi micro processor + + + align:start position:0% +controlled by a pi micro processor +and it's got some copyrighted software + + align:start position:0% +and it's got some copyrighted software + + + align:start position:0% +and it's got some copyrighted software +on there and when it receives the signal + + align:start position:0% +on there and when it receives the signal + + + align:start position:0% +on there and when it receives the signal +like open the garage door it starts the + + align:start position:0% +like open the garage door it starts the + + + align:start position:0% +like open the garage door it starts the +motor and then eventually it stops the + + align:start position:0% +motor and then eventually it stops the + + + align:start position:0% +motor and then eventually it stops the +motor and um the remote control um is + + align:start position:0% +motor and um the remote control um is + + + align:start position:0% +motor and um the remote control um is +made by the same company and they don't + + align:start position:0% +made by the same company and they don't + + + align:start position:0% +made by the same company and they don't +want if if you lose your remote control + + align:start position:0% +want if if you lose your remote control + + + align:start position:0% +want if if you lose your remote control +they want you to buy the replacement + + align:start position:0% +they want you to buy the replacement + + + align:start position:0% +they want you to buy the replacement +from the same company from Chamberlain + + align:start position:0% +from the same company from Chamberlain + + + align:start position:0% +from the same company from Chamberlain +but these other this Taiwanese company + + align:start position:0% +but these other this Taiwanese company + + + align:start position:0% +but these other this Taiwanese company +skyling + + align:start position:0% +skyling + + + align:start position:0% +skyling +Technologies um uh and it don't + + align:start position:0% +Technologies um uh and it don't + + + align:start position:0% +Technologies um uh and it don't +underestimate by the way there's always + + align:start position:0% +underestimate by the way there's always + + + align:start position:0% +underestimate by the way there's always +like a sort of there's often a trade or + + align:start position:0% +like a sort of there's often a trade or + + + align:start position:0% +like a sort of there's often a trade or +Internet AAL related component to these + + align:start position:0% +Internet AAL related component to these + + + align:start position:0% +Internet AAL related component to these +disputes but the Taiwanese company + + align:start position:0% +disputes but the Taiwanese company + + + align:start position:0% +disputes but the Taiwanese company +figured out how to make their own + + align:start position:0% +figured out how to make their own + + + align:start position:0% +figured out how to make their own +replacement remote controls presumably + + align:start position:0% +replacement remote controls presumably + + + align:start position:0% +replacement remote controls presumably +for cheaper and uh Chamberlin uh was + + align:start position:0% +for cheaper and uh Chamberlin uh was + + + align:start position:0% +for cheaper and uh Chamberlin uh was +like you got to ban these because um + + align:start position:0% +like you got to ban these because um + + + align:start position:0% +like you got to ban these because um +they're accessing our copyrighted work + + align:start position:0% +they're accessing our copyrighted work + + + align:start position:0% +they're accessing our copyrighted work +the software in the motor without our + + align:start position:0% +the software in the motor without our + + + align:start position:0% +the software in the motor without our +permission because when we sell you the + + align:start position:0% +permission because when we sell you the + + + align:start position:0% +permission because when we sell you the +uh the device we're giving you the + + align:start position:0% +uh the device we're giving you the + + + align:start position:0% +uh the device we're giving you the +authority to access that software only + + align:start position:0% +authority to access that software only + + + align:start position:0% +authority to access that software only +uh with our garage door opener not with + + align:start position:0% +uh with our garage door opener not with + + + align:start position:0% +uh with our garage door opener not with +some other knockoff garage door opener + + align:start position:0% +some other knockoff garage door opener + + + align:start position:0% +some other knockoff garage door opener +just like we give you the the motion + + align:start position:0% +just like we give you the the motion + + + align:start position:0% +just like we give you the the motion +picture companies say we give you the + + align:start position:0% +picture companies say we give you the + + + align:start position:0% +picture companies say we give you the +authority to watch the movie with our + + align:start position:0% +authority to watch the movie with our + + + align:start position:0% +authority to watch the movie with our +licensed DVD players but not with some + + align:start position:0% +licensed DVD players but not with some + + + align:start position:0% +licensed DVD players but not with some +knockoff DVD players and in fact there + + align:start position:0% +knockoff DVD players and in fact there + + + align:start position:0% +knockoff DVD players and in fact there +is an encrypted signal sort of weekly + + align:start position:0% +is an encrypted signal sort of weekly + + + align:start position:0% +is an encrypted signal sort of weekly +encrypted between the opener the remote + + align:start position:0% +encrypted between the opener the remote + + + align:start position:0% +encrypted between the opener the remote +control and the motor so why are they + + align:start position:0% +control and the motor so why are they + + + align:start position:0% +control and the motor so why are they +why are they wrong it's + + align:start position:0% +why are they wrong it's + + + align:start position:0% +why are they wrong it's +not she says because it's not the same + + align:start position:0% +not she says because it's not the same + + + align:start position:0% +not she says because it's not the same +thing okay um also maybe because uh + + align:start position:0% +thing okay um also maybe because uh + + + align:start position:0% +thing okay um also maybe because uh +Skylink hire David nimmer to represent + + align:start position:0% +Skylink hire David nimmer to represent + + + align:start position:0% +Skylink hire David nimmer to represent +them you can hire him yeah he's just + + align:start position:0% +them you can hire him yeah he's just + + + align:start position:0% +them you can hire him yeah he's just +expensive actually I don't know how much + + align:start position:0% +expensive actually I don't know how much + + + align:start position:0% +expensive actually I don't know how much +he is if you're watching this David not + + align:start position:0% +he is if you're watching this David not + + + align:start position:0% +he is if you're watching this David not +saying anything bad about you um uh + + align:start position:0% +saying anything bad about you um uh + + + align:start position:0% +saying anything bad about you um uh +anyway so so the courts this is not + + align:start position:0% +anyway so so the courts this is not + + + align:start position:0% +anyway so so the courts this is not +actually the court I'm citing here it's + + align:start position:0% +actually the court I'm citing here it's + + + align:start position:0% +actually the court I'm citing here it's +the International Trade Commission oh + + align:start position:0% +the International Trade Commission oh + + + align:start position:0% +the International Trade Commission oh +it's quoted by the court they said well + + align:start position:0% +it's quoted by the court they said well + + + align:start position:0% +it's quoted by the court they said well +the fact that the Chamberlain did not + + align:start position:0% +the fact that the Chamberlain did not + + + align:start position:0% +the fact that the Chamberlain did not +give customers any warning about not + + align:start position:0% +give customers any warning about not + + + align:start position:0% +give customers any warning about not +using any unauthorized transmitters uh + + align:start position:0% +using any unauthorized transmitters uh + + + align:start position:0% +using any unauthorized transmitters uh +because they say well we didn't do that + + align:start position:0% +because they say well we didn't do that + + + align:start position:0% +because they say well we didn't do that +cuz there weren't any unauthorized + + align:start position:0% +cuz there weren't any unauthorized + + + align:start position:0% +cuz there weren't any unauthorized +transmission and in fact if you buy a + + align:start position:0% +transmission and in fact if you buy a + + + align:start position:0% +transmission and in fact if you buy a +DVD has there always been a warning + + align:start position:0% +DVD has there always been a warning + + + align:start position:0% +DVD has there always been a warning +about don't use unauthorized DVD players + + align:start position:0% +about don't use unauthorized DVD players + + + align:start position:0% +about don't use unauthorized DVD players +no there's no + + align:start position:0% +no there's no + + + align:start position:0% +no there's no +warning um but they say because there + + align:start position:0% +warning um but they say because there + + + align:start position:0% +warning um but they say because there +were none at the time does not explain + + align:start position:0% +were none at the time does not explain + + + align:start position:0% +were none at the time does not explain +why Chamberlin has done nothing now that + + align:start position:0% +why Chamberlin has done nothing now that + + + align:start position:0% +why Chamberlin has done nothing now that +they know that there are transmitters + + align:start position:0% +they know that there are transmitters + + + align:start position:0% +they know that there are transmitters +that can be used with their garage door + + align:start position:0% +that can be used with their garage door + + + align:start position:0% +that can be used with their garage door +openers so they sort of blame them for + + align:start position:0% +openers so they sort of blame them for + + + align:start position:0% +openers so they sort of blame them for +not updating the manual which is sort of + + align:start position:0% +not updating the manual which is sort of + + + align:start position:0% +not updating the manual which is sort of +confusing because the customers who have + + align:start position:0% +confusing because the customers who have + + + align:start position:0% +confusing because the customers who have +already bought the thing should not be + + align:start position:0% +already bought the thing should not be + + + align:start position:0% +already bought the thing should not be +held responsible for what some later + + align:start position:0% +held responsible for what some later + + + align:start position:0% +held responsible for what some later +edition of the manual says so but uh + + align:start position:0% +edition of the manual says so but uh + + + align:start position:0% +edition of the manual says so but uh +chamber uh Chamberlain took that very + + align:start position:0% +chamber uh Chamberlain took that very + + + align:start position:0% +chamber uh Chamberlain took that very +literally and they here's their + + align:start position:0% +literally and they here's their + + + align:start position:0% +literally and they here's their +manual liftmas professional garage door + + align:start position:0% +manual liftmas professional garage door + + + align:start position:0% +manual liftmas professional garage door +opener they took their manual and on + + align:start position:0% +opener they took their manual and on + + + align:start position:0% +opener they took their manual and on +page do I say what page it is here's + + align:start position:0% +page do I say what page it is here's + + + align:start position:0% +page do I say what page it is here's +page two and then here's page + + align:start position:0% +page two and then here's page + + + align:start position:0% +page two and then here's page +31 uh and at the top of page but if + + align:start position:0% +31 uh and at the top of page but if + + + align:start position:0% +31 uh and at the top of page but if +anybody gets to page 31 of their garage + + align:start position:0% +anybody gets to page 31 of their garage + + + align:start position:0% +anybody gets to page 31 of their garage +door opener manual you get a special + + align:start position:0% +door opener manual you get a special + + + align:start position:0% +door opener manual you get a special +metal but at the top of this they say + + align:start position:0% +metal but at the top of this they say + + + align:start position:0% +metal but at the top of this they say +notice if this Security Plus Garage Door + + align:start position:0% +notice if this Security Plus Garage Door + + + align:start position:0% +notice if this Security Plus Garage Door +Openers operated with a non rolling code + + align:start position:0% +Openers operated with a non rolling code + + + align:start position:0% +Openers operated with a non rolling code +transmitter the technical measure in the + + align:start position:0% +transmitter the technical measure in the + + + align:start position:0% +transmitter the technical measure in the +receiver of the garage door opener which + + align:start position:0% +receiver of the garage door opener which + + + align:start position:0% +receiver of the garage door opener which +provides security against code theft + + align:start position:0% +provides security against code theft + + + align:start position:0% +provides security against code theft +devices will be circumvented the owner + + align:start position:0% +devices will be circumvented the owner + + + align:start position:0% +devices will be circumvented the owner +of the copyright in the garage door + + align:start position:0% +of the copyright in the garage door + + + align:start position:0% +of the copyright in the garage door +opener does not authorize the purchaser + + align:start position:0% +opener does not authorize the purchaser + + + align:start position:0% +opener does not authorize the purchaser +or supplier of the non-rolling code + + align:start position:0% +or supplier of the non-rolling code + + + align:start position:0% +or supplier of the non-rolling code +transmitter to circumvent that technical + + align:start position:0% +transmitter to circumvent that technical + + + align:start position:0% +transmitter to circumvent that technical +measure that's on page + + align:start position:0% +measure that's on page + + + align:start position:0% +measure that's on page +31 so + + align:start position:0% + + + + align:start position:0% + +um the + + align:start position:0% +um the + + + align:start position:0% +um the +yeah so now it looks like they're in the + + align:start position:0% +yeah so now it looks like they're in the + + + align:start position:0% +yeah so now it looks like they're in the +clear right you got clear warning that + + align:start position:0% +clear right you got clear warning that + + + align:start position:0% +clear right you got clear warning that +you're not authorized that's a lot more + + align:start position:0% +you're not authorized that's a lot more + + + align:start position:0% +you're not authorized that's a lot more +than the DVD people get + + align:start position:0% +than the DVD people get + + + align:start position:0% +than the DVD people get +you right the DVD people don't give you + + align:start position:0% +you right the DVD people don't give you + + + align:start position:0% +you right the DVD people don't give you +any notice you just have to sort of know + + align:start position:0% +any notice you just have to sort of know + + + align:start position:0% +any notice you just have to sort of know +but these people they give you notice on + + align:start position:0% +but these people they give you notice on + + + align:start position:0% +but these people they give you notice on +page 31 so uh do people think they would + + align:start position:0% +page 31 so uh do people think they would + + + align:start position:0% +page 31 so uh do people think they would +win that that they they now they won the + + align:start position:0% +win that that they they now they won the + + + align:start position:0% +win that that they they now they won the +case no why not oops sorry so here's + + align:start position:0% +case no why not oops sorry so here's + + + align:start position:0% +case no why not oops sorry so here's +their manual + + align:start position:0% +their manual + + + align:start position:0% +their manual +whoops uh + + align:start position:0% +whoops uh + + + align:start position:0% +whoops uh +oh so that's manual anyway um so they + + align:start position:0% +oh so that's manual anyway um so they + + + align:start position:0% +oh so that's manual anyway um so they +they didn't win right + + align:start position:0% +they didn't win right + + + align:start position:0% +they didn't win right +anyway and the decision was sort of + + align:start position:0% +anyway and the decision was sort of + + + align:start position:0% +anyway and the decision was sort of +about this Authority + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +yeah traditionally customers have been + + align:start position:0% +yeah traditionally customers have been + + + align:start position:0% +yeah traditionally customers have been +used to buying transmitters which would + + align:start position:0% +used to buying transmitters which would + + + align:start position:0% +used to buying transmitters which would +open open for All Brands and so that's + + align:start position:0% +open open for All Brands and so that's + + + align:start position:0% +open open for All Brands and so that's +true they had reasonable expectation + + align:start position:0% +true they had reasonable expectation + + + align:start position:0% +true they had reasonable expectation +that when so reasonable + + align:start position:0% +that when so reasonable + + + align:start position:0% +that when so reasonable +expectations um I mean do you think that + + align:start position:0% +expectations um I mean do you think that + + + align:start position:0% +expectations um I mean do you think that +these two rulings are sort of in + + align:start position:0% +these two rulings are sort of in + + + align:start position:0% +these two rulings are sort of in +Conflict the first ru came from the + + align:start position:0% +Conflict the first ru came from the + + + align:start position:0% +Conflict the first ru came from the +second Circuit Court of Appeals and + + align:start position:0% +second Circuit Court of Appeals and + + + align:start position:0% +second Circuit Court of Appeals and +where are + + align:start position:0% +where are + + + align:start position:0% +where are +they in New York the DVD one comes from + + align:start position:0% +they in New York the DVD one comes from + + + align:start position:0% +they in New York the DVD one comes from +New York I think they they control New + + align:start position:0% +New York I think they they control New + + + align:start position:0% +New York I think they they control New +York and um maybe Connecticut and and + + align:start position:0% +York and um maybe Connecticut and and + + + align:start position:0% +York and um maybe Connecticut and and +this one comes from the federal circuit + + align:start position:0% +this one comes from the federal circuit + + + align:start position:0% +this one comes from the federal circuit +which is + + align:start position:0% +which is + + + align:start position:0% +which is +um well they don't really have an + + align:start position:0% +um well they don't really have an + + + align:start position:0% +um well they don't really have an +authority over anywhere but uh anyway + + align:start position:0% +authority over anywhere but uh anyway + + + align:start position:0% +authority over anywhere but uh anyway +that's so but these rulings you know + + align:start position:0% +that's so but these rulings you know + + + align:start position:0% +that's so but these rulings you know +there's not like a constitutional crisis + + align:start position:0% +there's not like a constitutional crisis + + + align:start position:0% +there's not like a constitutional crisis +if these two appeals cours disagree but + + align:start position:0% +if these two appeals cours disagree but + + + align:start position:0% +if these two appeals cours disagree but +they they do in my opinion sort of + + align:start position:0% +they they do in my opinion sort of + + + align:start position:0% +they they do in my opinion sort of +disagree about the proper scope of + + align:start position:0% +disagree about the proper scope of + + + align:start position:0% +disagree about the proper scope of +authority and there's another case that + + align:start position:0% +authority and there's another case that + + + align:start position:0% +authority and there's another case that +we didn't read about toner + + align:start position:0% +we didn't read about toner + + + align:start position:0% +we didn't read about toner +cartridges um sort of a similar thing so + + align:start position:0% +cartridges um sort of a similar thing so + + + align:start position:0% +cartridges um sort of a similar thing so +I think there's still a lot of + + align:start position:0% +I think there's still a lot of + + + align:start position:0% +I think there's still a lot of +unresolved material here about the + + align:start position:0% +unresolved material here about the + + + align:start position:0% +unresolved material here about the +meaning of the the precise Contours of + + align:start position:0% +meaning of the the precise Contours of + + + align:start position:0% +meaning of the the precise Contours of +the Digital Millennium Copyright Act but + + align:start position:0% +the Digital Millennium Copyright Act but + + + align:start position:0% +the Digital Millennium Copyright Act but +um at least with the current status quo + + align:start position:0% +um at least with the current status quo + + + align:start position:0% +um at least with the current status quo +the um the sort of more traditional + + align:start position:0% +the um the sort of more traditional + + + align:start position:0% +the um the sort of more traditional +copyright owners the the songwriters and + + align:start position:0% +copyright owners the the songwriters and + + + align:start position:0% +copyright owners the the songwriters and +the motion picture companies have been + + align:start position:0% +the motion picture companies have been + + + align:start position:0% +the motion picture companies have been +successful in court in preventing + + align:start position:0% +successful in court in preventing + + + align:start position:0% +successful in court in preventing +anybody from sort of legal Distributing + + align:start position:0% +anybody from sort of legal Distributing + + + align:start position:0% +anybody from sort of legal Distributing +these knockoff DVD players but they've + + align:start position:0% +these knockoff DVD players but they've + + + align:start position:0% +these knockoff DVD players but they've +been totally unsuccessful like in real + + align:start position:0% +been totally unsuccessful like in real + + + align:start position:0% +been totally unsuccessful like in real +life doing that and in fact a lot of + + align:start position:0% +life doing that and in fact a lot of + + + align:start position:0% +life doing that and in fact a lot of +people just distribute them from like + + align:start position:0% +people just distribute them from like + + + align:start position:0% +people just distribute them from like +other countries where they don't have + + align:start position:0% +other countries where they don't have + + + align:start position:0% +other countries where they don't have +laws preventing it so this sort of a + + align:start position:0% +laws preventing it so this sort of a + + + align:start position:0% +laws preventing it so this sort of a +difference between the law and real life + + align:start position:0% +difference between the law and real life + + + align:start position:0% +difference between the law and real life +and I wanted to add one other thing if + + align:start position:0% +and I wanted to add one other thing if + + + align:start position:0% +and I wanted to add one other thing if +we look in the in the dmca there's a a + + align:start position:0% +we look in the in the dmca there's a a + + + align:start position:0% +we look in the in the dmca there's a a +third provision we ban we ban + + align:start position:0% +third provision we ban we ban + + + align:start position:0% +third provision we ban we ban +circumventing the access control and we + + align:start position:0% +circumventing the access control and we + + + align:start position:0% +circumventing the access control and we +ban helping with the AIS control and + + align:start position:0% +ban helping with the AIS control and + + + align:start position:0% +ban helping with the AIS control and +they also ban let me pull this up + + align:start position:0% + + + + align:start position:0% + +um uh here's additional violations no + + align:start position:0% +um uh here's additional violations no + + + align:start position:0% +um uh here's additional violations no +person shall manufactur import offer to + + align:start position:0% +person shall manufactur import offer to + + + align:start position:0% +person shall manufactur import offer to +the public provider although trafficing + + align:start position:0% +the public provider although trafficing + + + align:start position:0% +the public provider although trafficing +any technology product service device + + align:start position:0% +any technology product service device + + + align:start position:0% +any technology product service device +component apart that is primarily + + align:start position:0% +component apart that is primarily + + + align:start position:0% +component apart that is primarily +designed + + align:start position:0% +designed + + + align:start position:0% +designed +da uh technolog that effectively + + align:start position:0% +da uh technolog that effectively + + + align:start position:0% +da uh technolog that effectively +protects the right of a copyright + + align:start position:0% +protects the right of a copyright + + + align:start position:0% +protects the right of a copyright +owner so what is this one + + align:start position:0% + + + + align:start position:0% + +about it's not about access control it's + + align:start position:0% +about it's not about access control it's + + + align:start position:0% +about it's not about access control it's +about what kind of control + + align:start position:0% + + + + align:start position:0% + +yeah it's about + + align:start position:0% + + + + align:start position:0% + +copyright and does it stop you from + + align:start position:0% +copyright and does it stop you from + + + align:start position:0% +copyright and does it stop you from +doing it or from helping with + + align:start position:0% + + + + align:start position:0% + +it yeah from helping so it's these three + + align:start position:0% +it yeah from helping so it's these three + + + align:start position:0% +it yeah from helping so it's these three +things that are forbidden by + + align:start position:0% +things that are forbidden by + + + align:start position:0% +things that are forbidden by +121 why don't they why don't they forbid + + align:start position:0% +121 why don't they why don't they forbid + + + align:start position:0% +121 why don't they why don't they forbid +this + + align:start position:0% +this + + + align:start position:0% +this +one it's already covered it's already + + align:start position:0% +one it's already covered it's already + + + align:start position:0% +one it's already covered it's already +covered by what the rest of the exactly + + align:start position:0% +covered by what the rest of the exactly + + + align:start position:0% +covered by what the rest of the exactly +this box is copyright + + align:start position:0% + + + + align:start position:0% + +infringement um so the fair use defenses + + align:start position:0% +infringement um so the fair use defenses + + + align:start position:0% +infringement um so the fair use defenses +and everything apply to this box but + + align:start position:0% +and everything apply to this box but + + + align:start position:0% +and everything apply to this box but +they don't apply to any of + + align:start position:0% +they don't apply to any of + + + align:start position:0% +they don't apply to any of +these and just to as a quick question + + align:start position:0% +these and just to as a quick question + + + align:start position:0% +these and just to as a quick question +does the DVD uh copy protection or I I + + align:start position:0% +does the DVD uh copy protection or I I + + + align:start position:0% +does the DVD uh copy protection or I I +already prejudiced the answer there does + + align:start position:0% +already prejudiced the answer there does + + + align:start position:0% +already prejudiced the answer there does +the DVD content scramble system the + + align:start position:0% +the DVD content scramble system the + + + align:start position:0% +the DVD content scramble system the +thing that that case was about is that + + align:start position:0% +thing that that case was about is that + + + align:start position:0% +thing that that case was about is that +copyright protection that would be + + align:start position:0% +copyright protection that would be + + + align:start position:0% +copyright protection that would be +covered by subsection b or is it access + + align:start position:0% +covered by subsection b or is it access + + + align:start position:0% +covered by subsection b or is it access +control that would be covered by + + align:start position:0% +control that would be covered by + + + align:start position:0% +control that would be covered by +subsection + + align:start position:0% + + + + align:start position:0% + +a uh not reallying I mean they let you + + align:start position:0% +a uh not reallying I mean they let you + + + align:start position:0% +a uh not reallying I mean they let you +watch the move all you want right it + + align:start position:0% +watch the move all you want right it + + + align:start position:0% +watch the move all you want right it +doesn't stop you from accessing it it's + + align:start position:0% +doesn't stop you from accessing it it's + + + align:start position:0% +doesn't stop you from accessing it it's +not like pay $ per time you watch + + align:start position:0% +not like pay $ per time you watch + + + align:start position:0% +not like pay $ per time you watch +it sort of the trick + + align:start position:0% + + + + align:start position:0% + +question well that's true it could be + + align:start position:0% +question well that's true it could be + + + align:start position:0% +question well that's true it could be +both it could be both I mean the the + + align:start position:0% +both it could be both I mean the the + + + align:start position:0% +both it could be both I mean the the +problem is that this careful distinction + + align:start position:0% +problem is that this careful distinction + + + align:start position:0% +problem is that this careful distinction +that Congress um spent all this effort + + align:start position:0% +that Congress um spent all this effort + + + align:start position:0% +that Congress um spent all this effort +on and debated and all this stuff you + + align:start position:0% +on and debated and all this stuff you + + + align:start position:0% +on and debated and all this stuff you +know it's a distinction in law that + + align:start position:0% +know it's a distinction in law that + + + align:start position:0% +know it's a distinction in law that +doesn't really exist in real life it's + + align:start position:0% +doesn't really exist in real life it's + + + align:start position:0% +doesn't really exist in real life it's +very hard to say I mean how would you + + align:start position:0% +very hard to say I mean how would you + + + align:start position:0% +very hard to say I mean how would you +have could you even make a technological + + align:start position:0% +have could you even make a technological + + + align:start position:0% +have could you even make a technological +measure that didn't protect access but + + align:start position:0% +measure that didn't protect access but + + + align:start position:0% +measure that didn't protect access but +did stop you from copying I mean how + + align:start position:0% +did stop you from copying I mean how + + + align:start position:0% +did stop you from copying I mean how +would that even + + align:start position:0% + + + + align:start position:0% + +work so that you you can't read it but + + align:start position:0% +work so that you you can't read it but + + + align:start position:0% +work so that you you can't read it but +you can make a copy of it well that + + align:start position:0% +you can make a copy of it well that + + + align:start position:0% +you can make a copy of it well that +would + + align:start position:0% +would + + + align:start position:0% +would +protect accessing but not copying but + + align:start position:0% +protect accessing but not copying but + + + align:start position:0% +protect accessing but not copying but +I'm talking about the reverse how would + + align:start position:0% +I'm talking about the reverse how would + + + align:start position:0% +I'm talking about the reverse how would +you stop them if the guy can access it + + align:start position:0% +you stop them if the guy can access it + + + align:start position:0% +you stop them if the guy can access it +all he wants how can you stop him from + + align:start position:0% +all he wants how can you stop him from + + + align:start position:0% +all he wants how can you stop him from +copying + + align:start position:0% + + + + align:start position:0% + +it well so anyway so this just you know + + align:start position:0% +it well so anyway so this just you know + + + align:start position:0% +it well so anyway so this just you know +the the problem is that the law and real + + align:start position:0% +the the problem is that the law and real + + + align:start position:0% +the the problem is that the law and real +life often + + align:start position:0% +life often + + + align:start position:0% +life often +um you know it's not so easy to map them + + align:start position:0% +um you know it's not so easy to map them + + + align:start position:0% +um you know it's not so easy to map them +onto each other and the pro you know + + align:start position:0% +onto each other and the pro you know + + + align:start position:0% +onto each other and the pro you know +real life you know keeps changing so um + + align:start position:0% +real life you know keeps changing so um + + + align:start position:0% +real life you know keeps changing so um +you know the if you look at the debate + + align:start position:0% +you know the if you look at the debate + + + align:start position:0% +you know the if you look at the debate +in Congress it was not about + + align:start position:0% +in Congress it was not about + + + align:start position:0% +in Congress it was not about +DVDs um it was about these black boxes + + align:start position:0% +DVDs um it was about these black boxes + + + align:start position:0% +DVDs um it was about these black boxes +and in fact there's the whole question + + align:start position:0% +and in fact there's the whole question + + + align:start position:0% +and in fact there's the whole question +about is you know when they say + + align:start position:0% +about is you know when they say + + + align:start position:0% +about is you know when they say +Authority uh is that authority to block + + align:start position:0% +Authority uh is that authority to block + + + align:start position:0% +Authority uh is that authority to block +all access of a work or just initial + + align:start position:0% +all access of a work or just initial + + + align:start position:0% +all access of a work or just initial +access initial access would mean you + + align:start position:0% +access initial access would mean you + + + align:start position:0% +access initial access would mean you +decrypt the font and now you have the + + align:start position:0% +decrypt the font and now you have the + + + align:start position:0% +decrypt the font and now you have the +font or you pay for the cable channel + + align:start position:0% +font or you pay for the cable channel + + + align:start position:0% +font or you pay for the cable channel +now you have it but you could then send + + align:start position:0% +now you have it but you could then send + + + align:start position:0% +now you have it but you could then send +it to another TV in your home or is it + + align:start position:0% +it to another TV in your home or is it + + + align:start position:0% +it to another TV in your home or is it +every time you access it um and if you + + align:start position:0% +every time you access it um and if you + + + align:start position:0% +every time you access it um and if you +look at the floor statements of the + + align:start position:0% +look at the floor statements of the + + + align:start position:0% +look at the floor statements of the +Congress people they make conflicting + + align:start position:0% +Congress people they make conflicting + + + align:start position:0% +Congress people they make conflicting +statements one of them says I'm really + + align:start position:0% +statements one of them says I'm really + + + align:start position:0% +statements one of them says I'm really +happy that we modified this bill to be + + align:start position:0% +happy that we modified this bill to be + + + align:start position:0% +happy that we modified this bill to be +clear to protect the rights of the + + align:start position:0% +clear to protect the rights of the + + + align:start position:0% +clear to protect the rights of the +consumer that we will not have a payer + + align:start position:0% +consumer that we will not have a payer + + + align:start position:0% +consumer that we will not have a payer +use Society if you read the David nimmer + + align:start position:0% +use Society if you read the David nimmer + + + align:start position:0% +use Society if you read the David nimmer +paper the legislative history of the + + align:start position:0% +paper the legislative history of the + + + align:start position:0% +paper the legislative history of the +dmca he talks about this in uh all you + + align:start position:0% +dmca he talks about this in uh all you + + + align:start position:0% +dmca he talks about this in uh all you +know a lot but he says we not have a + + align:start position:0% +know a lot but he says we not have a + + + align:start position:0% +know a lot but he says we not have a +paper you society and we will it's only + + align:start position:0% +paper you society and we will it's only + + + align:start position:0% +paper you society and we will it's only +going to be about initial access but in + + align:start position:0% +going to be about initial access but in + + + align:start position:0% +going to be about initial access but in +fact the cover the law was not changed + + align:start position:0% +fact the cover the law was not changed + + + align:start position:0% +fact the cover the law was not changed +when he said that I mean they there's + + align:start position:0% +when he said that I mean they there's + + + align:start position:0% +when he said that I mean they there's +these conflicting statements about the + + align:start position:0% +these conflicting statements about the + + + align:start position:0% +these conflicting statements about the +meaning of the same law so + + align:start position:0% +meaning of the same law so + + + align:start position:0% +meaning of the same law so +um anyway but the so it's it's you know + + align:start position:0% +um anyway but the so it's it's you know + + + align:start position:0% +um anyway but the so it's it's you know +it's confusing and it's still not quite + + align:start position:0% +it's confusing and it's still not quite + + + align:start position:0% +it's confusing and it's still not quite +clear how to map real life on the copper + + align:start position:0% +clear how to map real life on the copper + + + align:start position:0% +clear how to map real life on the copper +deck but that's the um so that's the + + align:start position:0% +deck but that's the um so that's the + + + align:start position:0% +deck but that's the um so that's the +dmca does anybody have any questions + + align:start position:0% +dmca does anybody have any questions + + + align:start position:0% +dmca does anybody have any questions +about copyright or the dmca or anything + + align:start position:0% +about copyright or the dmca or anything + + + align:start position:0% +about copyright or the dmca or anything +else that we can answer at the + + align:start position:0% +else that we can answer at the + + + align:start position:0% +else that we can answer at the +end + + align:start position:0% + + + + align:start position:0% + +Michael oh + + align:start position:0% +Michael oh + + + align:start position:0% +Michael oh +no okay oh yeah I I have something to + + align:start position:0% +no okay oh yeah I I have something to + + + align:start position:0% +no okay oh yeah I I have something to +add because it's really funny it's about + + align:start position:0% +add because it's really funny it's about + + + align:start position:0% +add because it's really funny it's about +DVD protection INF because in France the + + align:start position:0% +DVD protection INF because in France the + + + align:start position:0% +DVD protection INF because in France the +law is slightly different you have every + + align:start position:0% +law is slightly different you have every + + + align:start position:0% +law is slightly different you have every +consumer has the right to make one + + align:start position:0% +consumer has the right to make one + + + align:start position:0% +consumer has the right to make one +personal copy for any kind + + align:start position:0% +personal copy for any kind + + + align:start position:0% +personal copy for any kind +of copyright of the device or book or + + align:start position:0% +of copyright of the device or book or + + + align:start position:0% +of copyright of the device or book or +DVD and the uh DVD production for video + + align:start position:0% +DVD and the uh DVD production for video + + + align:start position:0% +DVD and the uh DVD production for video +to do this so just this year well the uh + + align:start position:0% +to do this so just this year well the uh + + + align:start position:0% +to do this so just this year well the uh +court of appeal of of Paris has issued a + + align:start position:0% +court of appeal of of Paris has issued a + + + align:start position:0% +court of appeal of of Paris has issued a +ruling uh Banning uh the DVD protection + + align:start position:0% +ruling uh Banning uh the DVD protection + + + align:start position:0% +ruling uh Banning uh the DVD protection +uh from the DVD of M Drive is that a + + align:start position:0% +uh from the DVD of M Drive is that a + + + align:start position:0% +uh from the DVD of M Drive is that a +movie yeah okay M Drive okay no because + + align:start position:0% +movie yeah okay M Drive okay no because + + + align:start position:0% +movie yeah okay M Drive okay no because +it doesn't let you make a copy now isn't + + align:start position:0% +it doesn't let you make a copy now isn't + + + align:start position:0% +it doesn't let you make a copy now isn't +this true of every DVD yeah but why do + + align:start position:0% +this true of every DVD yeah but why do + + + align:start position:0% +this true of every DVD yeah but why do +they for m i mean not saying it's a bad + + align:start position:0% +they for m i mean not saying it's a bad + + + align:start position:0% +they for m i mean not saying it's a bad +movie why because one + + align:start position:0% +movie why because one + + + align:start position:0% +movie why because one +consumer the U movie company for about + + align:start position:0% +consumer the U movie company for about + + + align:start position:0% +consumer the U movie company for about +this one but it would apply for DVD + + align:start position:0% +this one but it would apply for DVD + + + align:start position:0% +this one but it would apply for DVD +inance well that's um um or even in + + align:start position:0% +inance well that's um um or even in + + + align:start position:0% +inance well that's um um or even in +Europe because this is is European + + align:start position:0% +Europe because this is is European + + + align:start position:0% +Europe because this is is European +recognize + + align:start position:0% +recognize + + + align:start position:0% +recognize +right well yeah it'll be interesting to + + align:start position:0% +right well yeah it'll be interesting to + + + align:start position:0% +right well yeah it'll be interesting to +see what France ends up + + align:start position:0% +see what France ends up + + + align:start position:0% +see what France ends up +doing I wanted to close basically they + + align:start position:0% +doing I wanted to close basically they + + + align:start position:0% +doing I wanted to close basically they +don't have any more right to to sell + + align:start position:0% +don't have any more right to to sell + + + align:start position:0% +don't have any more right to to sell +any with the prodection did they take it + + align:start position:0% +any with the prodection did they take it + + + align:start position:0% +any with the prodection did they take it +off or what did they do I hope that the + + align:start position:0% +off or what did they do I hope that the + + + align:start position:0% +off or what did they do I hope that the +French people are not deprived of + + align:start position:0% +French people are not deprived of + + + align:start position:0% +French people are not deprived of +Mulholland + + align:start position:0% +Mulholland + + + align:start position:0% +Mulholland +Drive um I wanted to close with this + + align:start position:0% +Drive um I wanted to close with this + + + align:start position:0% +Drive um I wanted to close with this +sentiment which is my sentiment which is + + align:start position:0% +sentiment which is my sentiment which is + + + align:start position:0% +sentiment which is my sentiment which is +that the job of all of you should be to + + align:start position:0% +that the job of all of you should be to + + + align:start position:0% +that the job of all of you should be to +be experts both in real life and by real + + align:start position:0% +be experts both in real life and by real + + + align:start position:0% +be experts both in real life and by real +life I mean what technology what we + + align:start position:0% +life I mean what technology what we + + + align:start position:0% +life I mean what technology what we +teach at MIT and also public policy and + + align:start position:0% +teach at MIT and also public policy and + + + align:start position:0% +teach at MIT and also public policy and +the law because we have this real + + align:start position:0% +the law because we have this real + + + align:start position:0% +the law because we have this real +disconnect between uh sort of people who + + align:start position:0% +disconnect between uh sort of people who + + + align:start position:0% +disconnect between uh sort of people who +are in public policy and copyright and + + align:start position:0% +are in public policy and copyright and + + + align:start position:0% +are in public policy and copyright and +um another kind of real life and uh + + align:start position:0% +um another kind of real life and uh + + + align:start position:0% +um another kind of real life and uh +people who are in technology and uh you + + align:start position:0% +people who are in technology and uh you + + + align:start position:0% +people who are in technology and uh you +know it's hard to find people around + + align:start position:0% +know it's hard to find people around + + + align:start position:0% +know it's hard to find people around +around here who think that copyright + + align:start position:0% +around here who think that copyright + + + align:start position:0% +around here who think that copyright +should be strengthened is anybody in + + align:start position:0% +should be strengthened is anybody in + + + align:start position:0% +should be strengthened is anybody in +this class of that mode of thought does + + align:start position:0% +this class of that mode of thought does + + + align:start position:0% +this class of that mode of thought does +anybody think copyright there should be + + align:start position:0% +anybody think copyright there should be + + + align:start position:0% +anybody think copyright there should be +more + + align:start position:0% +more + + + align:start position:0% +more +restrictions or it should last + + align:start position:0% +restrictions or it should last + + + align:start position:0% +restrictions or it should last +longer nobody here but but um in + + align:start position:0% +longer nobody here but but um in + + + align:start position:0% +longer nobody here but but um in +Congress the situation is reversed um + + align:start position:0% +Congress the situation is reversed um + + + align:start position:0% +Congress the situation is reversed um +and in in the you know obviously in + + align:start position:0% +and in in the you know obviously in + + + align:start position:0% +and in in the you know obviously in +Hollywood is widespread opinion that + + align:start position:0% +Hollywood is widespread opinion that + + + align:start position:0% +Hollywood is widespread opinion that +copyright is too weak and Technology + + align:start position:0% +copyright is too weak and Technology + + + align:start position:0% +copyright is too weak and Technology +people are are just you know we're we're + + align:start position:0% +people are are just you know we're we're + + + align:start position:0% +people are are just you know we're we're +going to bankrupt the copyright owners + + align:start position:0% +going to bankrupt the copyright owners + + + align:start position:0% +going to bankrupt the copyright owners +and uh it's a complete reversal and and + + align:start position:0% +and uh it's a complete reversal and and + + + align:start position:0% +and uh it's a complete reversal and and +similarly unanimous opinion + + align:start position:0% +similarly unanimous opinion + + + align:start position:0% +similarly unanimous opinion +and uh I think this really is bad + + align:start position:0% +and uh I think this really is bad + + + align:start position:0% +and uh I think this really is bad +because when you have you know these + + align:start position:0% +because when you have you know these + + + align:start position:0% +because when you have you know these +these big groups and nobody and they + + align:start position:0% +these big groups and nobody and they + + + align:start position:0% +these big groups and nobody and they +don't talk to each other and they don't + + align:start position:0% +don't talk to each other and they don't + + + align:start position:0% +don't talk to each other and they don't +understand each other you don't end up + + align:start position:0% +understand each other you don't end up + + + align:start position:0% +understand each other you don't end up +with um well you don't have + + align:start position:0% +with um well you don't have + + + align:start position:0% +with um well you don't have +communication it's not really to + + align:start position:0% +communication it's not really to + + + align:start position:0% +communication it's not really to +anybody's advantage and I interviewed + + align:start position:0% +anybody's advantage and I interviewed + + + align:start position:0% +anybody's advantage and I interviewed +Jack Valente when he was at MIT in in + + align:start position:0% +Jack Valente when he was at MIT in in + + + align:start position:0% +Jack Valente when he was at MIT in in +2004 and I say you know the broadcast + + align:start position:0% +2004 and I say you know the broadcast + + + align:start position:0% +2004 and I say you know the broadcast +flag I you know I object to it because + + align:start position:0% +flag I you know I object to it because + + + align:start position:0% +flag I you know I object to it because +it means you we haven't talked about the + + align:start position:0% +it means you we haven't talked about the + + + align:start position:0% +it means you we haven't talked about the +broadcast flag but it's a similar DRM + + align:start position:0% +broadcast flag but it's a similar DRM + + + align:start position:0% +broadcast flag but it's a similar DRM +mechanism um you know it would stop you + + align:start position:0% +mechanism um you know it would stop you + + + align:start position:0% +mechanism um you know it would stop you +from building your own TV set was + + align:start position:0% +from building your own TV set was + + + align:start position:0% +from building your own TV set was +argument and he says well how many + + align:start position:0% +argument and he says well how many + + + align:start position:0% +argument and he says well how many +people build their own sets I mean + + align:start position:0% +people build their own sets I mean + + + align:start position:0% +people build their own sets I mean +seriously um and he says the broadcast + + align:start position:0% +seriously um and he says the broadcast + + + align:start position:0% +seriously um and he says the broadcast +flag if you're in your own home you can + + align:start position:0% +flag if you're in your own home you can + + + align:start position:0% +flag if you're in your own home you can +copy anything that's on television to + + align:start position:0% +copy anything that's on television to + + + align:start position:0% +copy anything that's on television to +your heart's content the only time you + + align:start position:0% +your heart's content the only time you + + + align:start position:0% +your heart's content the only time you +will know there's a broadcast flag is if + + align:start position:0% +will know there's a broadcast flag is if + + + align:start position:0% +will know there's a broadcast flag is if +you try to take one of those copies and + + align:start position:0% +you try to take one of those copies and + + + align:start position:0% +you try to take one of those copies and +redistribute on the internet then the + + align:start position:0% +redistribute on the internet then the + + + align:start position:0% +redistribute on the internet then the +flag says no you can't redistribute it + + align:start position:0% +flag says no you can't redistribute it + + + align:start position:0% +flag says no you can't redistribute it +but you can do everything you're doing + + align:start position:0% +but you can do everything you're doing + + + align:start position:0% +but you can do everything you're doing +right now you'll never know there's a + + align:start position:0% +right now you'll never know there's a + + + align:start position:0% +right now you'll never know there's a +broadcast flag well why would people + + align:start position:0% +broadcast flag well why would people + + + align:start position:0% +broadcast flag well why would people +object to + + align:start position:0% +object to + + + align:start position:0% +object to +it um you know the problem is that Mr + + align:start position:0% +it um you know the problem is that Mr + + + align:start position:0% +it um you know the problem is that Mr +Valente is just is just + + align:start position:0% +Valente is just is just + + + align:start position:0% +Valente is just is just +wrong um that's you know no no DRM could + + align:start position:0% +wrong um that's you know no no DRM could + + + align:start position:0% +wrong um that's you know no no DRM could +could work that way at least not now + + align:start position:0% +could work that way at least not now + + + align:start position:0% +could work that way at least not now +because um you know if they let you + + align:start position:0% +because um you know if they let you + + + align:start position:0% +because um you know if they let you +distribute it within your own home like + + align:start position:0% +distribute it within your own home like + + + align:start position:0% +distribute it within your own home like +iTunes does um they will inexorably let + + align:start position:0% +iTunes does um they will inexorably let + + + align:start position:0% +iTunes does um they will inexorably let +you redistribute it on the internet as + + align:start position:0% +you redistribute it on the internet as + + + align:start position:0% +you redistribute it on the internet as +iTunes does um it just the technology + + align:start position:0% +iTunes does um it just the technology + + + align:start position:0% +iTunes does um it just the technology +just doesn't exist and I think if if you + + align:start position:0% +just doesn't exist and I think if if you + + + align:start position:0% +just doesn't exist and I think if if you +guys all graduate and go work for + + align:start position:0% +guys all graduate and go work for + + + align:start position:0% +guys all graduate and go work for +technology companies and you start + + align:start position:0% +technology companies and you start + + + align:start position:0% +technology companies and you start +saying we have this awesome technology + + align:start position:0% +saying we have this awesome technology + + + align:start position:0% +saying we have this awesome technology +that will let you control exactly what + + align:start position:0% +that will let you control exactly what + + + align:start position:0% +that will let you control exactly what +your Works can do and can't do will + + align:start position:0% +your Works can do and can't do will + + + align:start position:0% +your Works can do and can't do will +shame on you uh because you should not + + align:start position:0% +shame on you uh because you should not + + + align:start position:0% +shame on you uh because you should not +um misrepresent what Science and + + align:start position:0% +um misrepresent what Science and + + + align:start position:0% +um misrepresent what Science and +Technology do in the service of + + align:start position:0% +Technology do in the service of + + + align:start position:0% +Technology do in the service of +uh you know you just you shouldn't + + align:start position:0% +uh you know you just you shouldn't + + + align:start position:0% +uh you know you just you shouldn't +misrepresent it because it leads to + + align:start position:0% +misrepresent it because it leads to + + + align:start position:0% +misrepresent it because it leads to +these sort of public policy confusions + + align:start position:0% +these sort of public policy confusions + + + align:start position:0% +these sort of public policy confusions +and people thinking that they can uh + + align:start position:0% +and people thinking that they can uh + + + align:start position:0% +and people thinking that they can uh +demand things that don't + + align:start position:0% +demand things that don't + + + align:start position:0% +demand things that don't +exist so I charge you with the job of + + align:start position:0% +exist so I charge you with the job of + + + align:start position:0% +exist so I charge you with the job of +integrating the worlds of public policy + + align:start position:0% +integrating the worlds of public policy + + + align:start position:0% +integrating the worlds of public policy +and technology and uh ensuring that we + + align:start position:0% +and technology and uh ensuring that we + + + align:start position:0% +and technology and uh ensuring that we +don't have this disconnect anymore and + + align:start position:0% +don't have this disconnect anymore and + + + align:start position:0% +don't have this disconnect anymore and +uh so go forth thank you + + align:start position:0% + + + + align:start position:0% + +what \ No newline at end of file diff --git a/ByGXz_uHEdM.txt b/ByGXz_uHEdM.txt new file mode 100644 index 0000000000000000000000000000000000000000..c6cc1d1dddecf90f6921115426d65b4616e98c92 --- /dev/null +++ b/ByGXz_uHEdM.txt @@ -0,0 +1,7843 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open courseware under a Creative Commons + + align:start position:0% +open courseware under a Creative Commons + + + align:start position:0% +open courseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu + + align:start position:0% +ocw.mit.edu + + + align:start position:0% +ocw.mit.edu +okay so last time uh I talked about the + + align:start position:0% +okay so last time uh I talked about the + + + align:start position:0% +okay so last time uh I talked about the +heat + + align:start position:0% +heat + + + align:start position:0% +heat +equation started to talk about the heat + + align:start position:0% +equation started to talk about the heat + + + align:start position:0% +equation started to talk about the heat +equation also known as the diffusion + + align:start position:0% +equation also known as the diffusion + + + align:start position:0% +equation also known as the diffusion +equation + + align:start position:0% +equation + + + align:start position:0% +equation +and uh what we did then was to solve it + + align:start position:0% +and uh what we did then was to solve it + + + align:start position:0% +and uh what we did then was to solve it +give an analytical + + align:start position:0% +give an analytical + + + align:start position:0% +give an analytical +solution both for any initial value U of + + align:start position:0% +solution both for any initial value U of + + + align:start position:0% +solution both for any initial value U of +X and zero and then specifically for the + + align:start position:0% +X and zero and then specifically for the + + + align:start position:0% +X and zero and then specifically for the +point source so then we're talking about + + align:start position:0% +point source so then we're talking about + + + align:start position:0% +point source so then we're talking about +the impulse response or the fundamental + + align:start position:0% +the impulse response or the fundamental + + + align:start position:0% +the impulse response or the fundamental +solution when we start from a Delta + + align:start position:0% +solution when we start from a Delta + + + align:start position:0% +solution when we start from a Delta +function and it was that U gaussian + + align:start position:0% +function and it was that U gaussian + + + align:start position:0% +function and it was that U gaussian +bell-shaped curve fantastic fundamental + + align:start position:0% +bell-shaped curve fantastic fundamental + + + align:start position:0% +bell-shaped curve fantastic fundamental +solution so but that the formulas you + + align:start position:0% +solution so but that the formulas you + + + align:start position:0% +solution so but that the formulas you +get involving infinite integrals are not + + align:start position:0% +get involving infinite integrals are not + + + align:start position:0% +get involving infinite integrals are not +the greatest for actually getting + + align:start position:0% +the greatest for actually getting + + + align:start position:0% +the greatest for actually getting +numbers for the + + align:start position:0% +numbers for the + + + align:start position:0% +numbers for the +whole uh temperature + + align:start position:0% +whole uh temperature + + + align:start position:0% +whole uh temperature +history U of T and X so we got to we + + align:start position:0% +history U of T and X so we got to we + + + align:start position:0% +history U of T and X so we got to we +have to go to finite + + align:start position:0% +have to go to finite + + + align:start position:0% +have to go to finite +differences and of course we need finite + + align:start position:0% +differences and of course we need finite + + + align:start position:0% +differences and of course we need finite +differences also in the + + align:start position:0% +differences also in the + + + align:start position:0% +differences also in the +more General cases where uh the where + + align:start position:0% +more General cases where uh the where + + + align:start position:0% +more General cases where uh the where +the where nonlinear terms could appear + + align:start position:0% +the where nonlinear terms could appear + + + align:start position:0% +the where nonlinear terms could appear +or even just variation in x and t in the + + align:start position:0% +or even just variation in x and t in the + + + align:start position:0% +or even just variation in x and t in the +linear coefficient which I had just set + + align:start position:0% +linear coefficient which I had just set + + + align:start position:0% +linear coefficient which I had just set +to be + + align:start position:0% +to be + + + align:start position:0% +to be +one so so this is the first job + + align:start position:0% +one so so this is the first job + + + align:start position:0% +one so so this is the first job +difference equations for the heat + + align:start position:0% +difference equations for the heat + + + align:start position:0% +difference equations for the heat +difference methods for the heat equation + + align:start position:0% +difference methods for the heat equation + + + align:start position:0% +difference methods for the heat equation +and you'll see that uh we get pushed + + align:start position:0% +and you'll see that uh we get pushed + + + align:start position:0% +and you'll see that uh we get pushed +toward + + align:start position:0% +toward + + + align:start position:0% +toward +implicit + + align:start position:0% +implicit + + + align:start position:0% +implicit +methods because an explicit method will + + align:start position:0% +methods because an explicit method will + + + align:start position:0% +methods because an explicit method will +require delta T to be of that very small + + align:start position:0% +require delta T to be of that very small + + + align:start position:0% +require delta T to be of that very small +size Delta X squ and that's pretty + + align:start position:0% +size Delta X squ and that's pretty + + + align:start position:0% +size Delta X squ and that's pretty +slowo and of course what I'm + + align:start position:0% +slowo and of course what I'm + + + align:start position:0% +slowo and of course what I'm +saying applies equally to uh we might be + + align:start position:0% +saying applies equally to uh we might be + + + align:start position:0% +saying applies equally to uh we might be +in + + align:start position:0% +in + + + align:start position:0% +in +2D or in 3D diffusion of uh pollution + + align:start position:0% +2D or in 3D diffusion of uh pollution + + + align:start position:0% +2D or in 3D diffusion of uh pollution +for example environmental + + align:start position:0% +for example environmental + + + align:start position:0% +for example environmental +engineering uh the our fundamental + + align:start position:0% +engineering uh the our fundamental + + + align:start position:0% +engineering uh the our fundamental +solution from the Delta function would + + align:start position:0% +solution from the Delta function would + + + align:start position:0% +solution from the Delta function would +easily extend to two Dimensions or + + align:start position:0% +easily extend to two Dimensions or + + + align:start position:0% +easily extend to two Dimensions or +three and our difference methods will + + align:start position:0% +three and our difference methods will + + + align:start position:0% +three and our difference methods will +extend but we'll see what comes up and + + align:start position:0% +extend but we'll see what comes up and + + + align:start position:0% +extend but we'll see what comes up and +then let me point to + + align:start position:0% +then let me point to + + + align:start position:0% +then let me point to +this second problem which combines the + + align:start position:0% +this second problem which combines the + + + align:start position:0% +this second problem which combines the +two we already know about one-way + + align:start position:0% +two we already know about one-way + + + align:start position:0% +two we already know about one-way +waves coming from a con convection term + + align:start position:0% +waves coming from a con convection term + + + align:start position:0% +waves coming from a con convection term +now we're getting the basic ideas for + + align:start position:0% +now we're getting the basic ideas for + + + align:start position:0% +now we're getting the basic ideas for +the diffusion term and lot of real of + + align:start position:0% +the diffusion term and lot of real of + + + align:start position:0% +the diffusion term and lot of real of +very important real problems combine the + + align:start position:0% +very important real problems combine the + + + align:start position:0% +very important real problems combine the +two and then you have uh well you have a + + align:start position:0% +two and then you have uh well you have a + + + align:start position:0% +two and then you have uh well you have a +situation that I'm just sort of pointing + + align:start position:0% +situation that I'm just sort of pointing + + + align:start position:0% +situation that I'm just sort of pointing +to here that + + align:start position:0% +to here that + + + align:start position:0% +to here that +coefficient as before has the units of + + align:start position:0% +coefficient as before has the units of + + + align:start position:0% +coefficient as before has the units of +velocity this over time you see if I + + align:start position:0% +velocity this over time you see if I + + + align:start position:0% +velocity this over time you see if I +bring time up here I have time over + + align:start position:0% +bring time up here I have time over + + + align:start position:0% +bring time up here I have time over +distance there so I need distance over + + align:start position:0% +distance there so I need distance over + + + align:start position:0% +distance there so I need distance over +time from from C it's it's + + align:start position:0% +time from from C it's it's + + + align:start position:0% +time from from C it's it's +the what we've seen always and then the + + align:start position:0% +the what we've seen always and then the + + + align:start position:0% +the what we've seen always and then the +C delta T over Delta X the quantity + + align:start position:0% +C delta T over Delta X the quantity + + + align:start position:0% +C delta T over Delta X the quantity +R was dimensional so I'm taking three + + align:start position:0% +R was dimensional so I'm taking three + + + align:start position:0% +R was dimensional so I'm taking three +minutes to to speak about Dimensions + + align:start position:0% +minutes to to speak about Dimensions + + + align:start position:0% +minutes to to speak about Dimensions +it's a very dimensional analysis a very + + align:start position:0% +it's a very dimensional analysis a very + + + align:start position:0% +it's a very dimensional analysis a very +simple but useful thing to do at the + + align:start position:0% +simple but useful thing to do at the + + + align:start position:0% +simple but useful thing to do at the +beginning of a problem so here we had r + + align:start position:0% +beginning of a problem so here we had r + + + align:start position:0% +beginning of a problem so here we had r += c Delta t/ Delta + + align:start position:0% += c Delta t/ Delta + + + align:start position:0% += c Delta t/ Delta +X which is + + align:start position:0% +X which is + + + align:start position:0% +X which is +dimensionless and typically for explicit + + align:start position:0% +dimensionless and typically for explicit + + + align:start position:0% +dimensionless and typically for explicit +methods we uh it had to be bounded by + + align:start position:0% +methods we uh it had to be bounded by + + + align:start position:0% +methods we uh it had to be bounded by +one for + + align:start position:0% +one for + + + align:start position:0% +one for +example now for + + align:start position:0% +example now for + + + align:start position:0% +example now for +uh the diffusion + + align:start position:0% +uh the diffusion + + + align:start position:0% +uh the diffusion +term D what are the units of D well here + + align:start position:0% +term D what are the units of D well here + + + align:start position:0% +term D what are the units of D well here +now I have distance squared in the + + align:start position:0% +now I have distance squared in the + + + align:start position:0% +now I have distance squared in the +denominator so so D needs to have a + + align:start position:0% +denominator so so D needs to have a + + + align:start position:0% +denominator so so D needs to have a +distance to be a distance squared over a + + align:start position:0% +distance to be a distance squared over a + + + align:start position:0% +distance to be a distance squared over a +time so it's uh it has a different + + align:start position:0% +time so it's uh it has a different + + + align:start position:0% +time so it's uh it has a different +different + + align:start position:0% +different + + + align:start position:0% +different +dimensions + + align:start position:0% +dimensions + + + align:start position:0% +dimensions +and the quantity capital r that will + + align:start position:0% +and the quantity capital r that will + + + align:start position:0% +and the quantity capital r that will +meet parallel to this will be D delta T + + align:start position:0% +meet parallel to this will be D delta T + + + align:start position:0% +meet parallel to this will be D delta T +over Delta + + align:start position:0% + + + + align:start position:0% + +x^2 and again no it's + + align:start position:0% +x^2 and again no it's + + + align:start position:0% +x^2 and again no it's +dimensionless because if D has + + align:start position:0% +dimensionless because if D has + + + align:start position:0% +dimensionless because if D has +dimensions of distance squared over time + + align:start position:0% +dimensions of distance squared over time + + + align:start position:0% +dimensions of distance squared over time +that reverses it to give a dimensionless + + align:start position:0% +that reverses it to give a dimensionless + + + align:start position:0% +that reverses it to give a dimensionless +quantity and we'll see that explicit + + align:start position:0% +quantity and we'll see that explicit + + + align:start position:0% +quantity and we'll see that explicit +methods require a bound on capital r and + + align:start position:0% +methods require a bound on capital r and + + + align:start position:0% +methods require a bound on capital r and +that's what um so forces us into that + + align:start position:0% +that's what um so forces us into that + + + align:start position:0% +that's what um so forces us into that +small time step okay so you'll see + + align:start position:0% +small time step okay so you'll see + + + align:start position:0% +small time step okay so you'll see +capital r playing a similar role to + + align:start position:0% +capital r playing a similar role to + + + align:start position:0% +capital r playing a similar role to +little + + align:start position:0% +little + + + align:start position:0% +little +r and and actually while we're talking + + align:start position:0% +r and and actually while we're talking + + + align:start position:0% +r and and actually while we're talking +about dimensional + + align:start position:0% +about dimensional + + + align:start position:0% +about dimensional +analysis um back to the differential + + align:start position:0% +analysis um back to the differential + + + align:start position:0% +analysis um back to the differential +equation suppose we want as we certainly + + align:start position:0% +equation suppose we want as we certainly + + + align:start position:0% +equation suppose we want as we certainly +do to compare the + + align:start position:0% +do to compare the + + + align:start position:0% +do to compare the +importance of the convection term and + + align:start position:0% +importance of the convection term and + + + align:start position:0% +importance of the convection term and +the diffusion + + align:start position:0% +the diffusion + + + align:start position:0% +the diffusion +term + + align:start position:0% +term + + + align:start position:0% +term +well that comparison is somehow the + + align:start position:0% +well that comparison is somehow the + + + align:start position:0% +well that comparison is somehow the +ratio of C to + + align:start position:0% +ratio of C to + + + align:start position:0% +ratio of C to +D so we have + + align:start position:0% +D so we have + + + align:start position:0% +D so we have +a that somehow it's it's it's natural to + + align:start position:0% +a that somehow it's it's it's natural to + + + align:start position:0% +a that somehow it's it's it's natural to +think of the ratio of C to D + + align:start position:0% + + + + align:start position:0% + +as telling us a very important fact is + + align:start position:0% +as telling us a very important fact is + + + align:start position:0% +as telling us a very important fact is +our problem more like a wave problem do + + align:start position:0% +our problem more like a wave problem do + + + align:start position:0% +our problem more like a wave problem do +we have to uh um do we do we expect to + + align:start position:0% +we have to uh um do we do we expect to + + + align:start position:0% +we have to uh um do we do we expect to +be like on the unit circle or + + align:start position:0% +be like on the unit circle or + + + align:start position:0% +be like on the unit circle or +close with a term that in Fier space is + + align:start position:0% +close with a term that in Fier space is + + + align:start position:0% +close with a term that in Fier space is +pure imaginary from the ik or if D is + + align:start position:0% +pure imaginary from the ik or if D is + + + align:start position:0% +pure imaginary from the ik or if D is +big + + align:start position:0% + + + + align:start position:0% + +do we expect to be a we have then a + + align:start position:0% +do we expect to be a we have then a + + + align:start position:0% +do we expect to be a we have then a +small ratio and that tells us that the + + align:start position:0% +small ratio and that tells us that the + + + align:start position:0% +small ratio and that tells us that the +diffusion term is important that we've + + align:start position:0% +diffusion term is important that we've + + + align:start position:0% +diffusion term is important that we've +got lots of + + align:start position:0% +got lots of + + + align:start position:0% +got lots of +dissipation that uh the stability at + + align:start position:0% +dissipation that uh the stability at + + + align:start position:0% +dissipation that uh the stability at +least in the differential equation is + + align:start position:0% +least in the differential equation is + + + align:start position:0% +least in the differential equation is +like much greater because this is + + align:start position:0% +like much greater because this is + + + align:start position:0% +like much greater because this is +producing a a minus K squ in 4A space + + align:start position:0% +producing a a minus K squ in 4A space + + + align:start position:0% +producing a a minus K squ in 4A space +and uh a strongly negative term so it's + + align:start position:0% +and uh a strongly negative term so it's + + + align:start position:0% +and uh a strongly negative term so it's +that ratio C to D but of course my point + + align:start position:0% +that ratio C to D but of course my point + + + align:start position:0% +that ratio C to D but of course my point +here on the dimensional stuff is that c + + align:start position:0% +here on the dimensional stuff is that c + + + align:start position:0% +here on the dimensional stuff is that c +to + + align:start position:0% +to + + + align:start position:0% +to +D isn't quite okay as it is + + align:start position:0% +D isn't quite okay as it is + + + align:start position:0% +D isn't quite okay as it is +because they have different units and we + + align:start position:0% +because they have different units and we + + + align:start position:0% +because they have different units and we +need one more distance so we need the + + align:start position:0% +need one more distance so we need the + + + align:start position:0% +need one more distance so we need the +ratio of C where do I need an L I need + + align:start position:0% +ratio of C where do I need an L I need + + + align:start position:0% +ratio of C where do I need an L I need +another L up there I need another + + align:start position:0% +another L up there I need another + + + align:start position:0% +another L up there I need another +distance + + align:start position:0% + + + + align:start position:0% + +there to get something that that is + + align:start position:0% +there to get something that that is + + + align:start position:0% +there to get something that that is +altogether um + + align:start position:0% +altogether um + + + align:start position:0% +altogether um +dimensionless and so that's the critical + + align:start position:0% +dimensionless and so that's the critical + + + align:start position:0% +dimensionless and so that's the critical +number uh and it's known as the peklay + + align:start position:0% +number uh and it's known as the peklay + + + align:start position:0% +number uh and it's known as the peklay +number PE I'll call + + align:start position:0% +number PE I'll call + + + align:start position:0% +number PE I'll call +it that what is l l and we're talking + + align:start position:0% +it that what is l l and we're talking + + + align:start position:0% +it that what is l l and we're talking +here only about the differential + + align:start position:0% +here only about the differential + + + align:start position:0% +here only about the differential +equation L is a characteristic length if + + align:start position:0% +equation L is a characteristic length if + + + align:start position:0% +equation L is a characteristic length if +if our if our problem is set on a finite + + align:start position:0% +if our if our problem is set on a finite + + + align:start position:0% +if our if our problem is set on a finite +to interval then it's probably the + + align:start position:0% +to interval then it's probably the + + + align:start position:0% +to interval then it's probably the +length of the interval it's a + + align:start position:0% +length of the interval it's a + + + align:start position:0% +length of the interval it's a +characteristic length of the problem and + + align:start position:0% +characteristic length of the problem and + + + align:start position:0% +characteristic length of the problem and +then this quantity CL + + align:start position:0% +then this quantity CL + + + align:start position:0% +then this quantity CL +overd is + + align:start position:0% + + + + align:start position:0% + +U it gives us a a a good measure of the + + align:start position:0% +U it gives us a a a good measure of the + + + align:start position:0% +U it gives us a a a good measure of the +importance of these two and uh and we'll + + align:start position:0% +importance of these two and uh and we'll + + + align:start position:0% +importance of these two and uh and we'll +see in the finite difference case there + + align:start position:0% +see in the finite difference case there + + + align:start position:0% +see in the finite difference case there +will be a cell peklay number which is + + align:start position:0% +will be a cell peklay number which is + + + align:start position:0% +will be a cell peklay number which is +entirely different + + align:start position:0% +entirely different + + + align:start position:0% +entirely different +a sort of f pay number for the little + + align:start position:0% +a sort of f pay number for the little + + + align:start position:0% +a sort of f pay number for the little +finite different cell where this L is + + align:start position:0% +finite different cell where this L is + + + align:start position:0% +finite different cell where this L is +changed to a like a Delta + + align:start position:0% +changed to a like a Delta + + + align:start position:0% +changed to a like a Delta +X okay so uh I think we've we've uh got + + align:start position:0% +X okay so uh I think we've we've uh got + + + align:start position:0% +X okay so uh I think we've we've uh got +it + + align:start position:0% +it + + + align:start position:0% +it +there have I got the denominate the + + align:start position:0% +there have I got the denominate the + + + align:start position:0% +there have I got the denominate the +numerator and denominator correct there + + align:start position:0% +numerator and denominator correct there + + + align:start position:0% +numerator and denominator correct there +or should they be reversed is it time + + align:start position:0% +or should they be reversed is it time + + + align:start position:0% +or should they be reversed is it time +over + + align:start position:0% +over + + + align:start position:0% +over +distance I'm I'm a little I didn't + + align:start position:0% +distance I'm I'm a little I didn't + + + align:start position:0% +distance I'm I'm a little I didn't +expect it + + align:start position:0% + + + + align:start position:0% + +so it is isn't it time over distance + + align:start position:0% +so it is isn't it time over distance + + + align:start position:0% +so it is isn't it time over distance +that shows that I'm not a dimensional + + align:start position:0% +that shows that I'm not a dimensional + + + align:start position:0% +that shows that I'm not a dimensional +analyst let me fix it and then that will + + align:start position:0% +analyst let me fix it and then that will + + + align:start position:0% +analyst let me fix it and then that will +mean fixing this ah + + align:start position:0% + + + + align:start position:0% + +so let me just fix that it didn't sound + + align:start position:0% +so let me just fix that it didn't sound + + + align:start position:0% +so let me just fix that it didn't sound +right as I said it but I read it wrong + + align:start position:0% +right as I said it but I read it wrong + + + align:start position:0% +right as I said it but I read it wrong +okay so C is a time over a distance + + align:start position:0% +okay so C is a time over a distance + + + align:start position:0% +okay so C is a time over a distance +thanks + + align:start position:0% +thanks + + + align:start position:0% +thanks +is that + + align:start position:0% +is that + + + align:start position:0% +is that +right it was right the first time in + + align:start position:0% +right it was right the first time in + + + align:start position:0% +right it was right the first time in +that case we'll move + + align:start position:0% +that case we'll move + + + align:start position:0% +that case we'll move +on okay all right okay good + + align:start position:0% +on okay all right okay good + + + align:start position:0% +on okay all right okay good +thanks yeah yeah you're right thanks + + align:start position:0% +thanks yeah yeah you're right thanks + + + align:start position:0% +thanks yeah yeah you're right thanks +okay so we sorry that's on the tapes + + align:start position:0% +okay so we sorry that's on the tapes + + + align:start position:0% +okay so we sorry that's on the tapes +okay uh so now let's begin with uh a + + align:start position:0% +okay uh so now let's begin with uh a + + + align:start position:0% +okay uh so now let's begin with uh a +natural explicit method for the he + + align:start position:0% +natural explicit method for the he + + + align:start position:0% +natural explicit method for the he +equation what everybody would think of + + align:start position:0% +equation what everybody would think of + + + align:start position:0% +equation what everybody would think of +so this will be + + align:start position:0% +so this will be + + + align:start position:0% +so this will be +explicit for the heat + + align:start position:0% +explicit for the heat + + + align:start position:0% +explicit for the heat +equation and I'm in + + align:start position:0% +equation and I'm in + + + align:start position:0% +equation and I'm in +1D and what do you think of naturally + + align:start position:0% +1D and what do you think of naturally + + + align:start position:0% +1D and what do you think of naturally +forward difference in time so can I + + align:start position:0% +forward difference in time so can I + + + align:start position:0% +forward difference in time so can I +write it this way a time + + align:start position:0% +write it this way a time + + + align:start position:0% +write it this way a time +difference I'll use capital u as always + + align:start position:0% +difference I'll use capital u as always + + + align:start position:0% +difference I'll use capital u as always +for the finite difference solution + + align:start position:0% +for the finite difference solution + + + align:start position:0% +for the finite difference solution +divided by Delta + + align:start position:0% +divided by Delta + + + align:start position:0% +divided by Delta +X and and I'm doing the heat equation + + align:start position:0% +X and and I'm doing the heat equation + + + align:start position:0% +X and and I'm doing the heat equation +with c equal to 1 so I'm I'm just to + + align:start position:0% +with c equal to 1 so I'm I'm just to + + + align:start position:0% +with c equal to 1 so I'm I'm just to +keep things simple let's just do the + + align:start position:0% +keep things simple let's just do the + + + align:start position:0% +keep things simple let's just do the +heat + + align:start position:0% +heat + + + align:start position:0% +heat +equation uh + + align:start position:0% +equation uh + + + align:start position:0% +equation uh +normalized so here I'm going to take a + + align:start position:0% +normalized so here I'm going to take a + + + align:start position:0% +normalized so here I'm going to take a +second difference in the X direction of + + align:start position:0% +second difference in the X direction of + + + align:start position:0% +second difference in the X direction of +U / Delta + + align:start position:0% + + + + align:start position:0% + +X2 + + align:start position:0% + + + + align:start position:0% + +okay what's the + + align:start position:0% + + + + align:start position:0% + +accuracy well we know we know the + + align:start position:0% +accuracy well we know we know the + + + align:start position:0% +accuracy well we know we know the +accuracy of each term the center + + align:start position:0% +accuracy of each term the center + + + align:start position:0% +accuracy of each term the center +difference the error is so the the + + align:start position:0% +difference the error is so the the + + + align:start position:0% +difference the error is so the the +discretization + + align:start position:0% + + + + align:start position:0% + +error the local error the truncation + + align:start position:0% +error the local error the truncation + + + align:start position:0% +error the local error the truncation +error it's also called will be + + align:start position:0% +error it's also called will be + + + align:start position:0% +error it's also called will be +proportional to well oh I'm sorry that's + + align:start position:0% +proportional to well oh I'm sorry that's + + + align:start position:0% +proportional to well oh I'm sorry that's +delta T of course + + align:start position:0% + + + + align:start position:0% + +okay so the discretisation error in a + + align:start position:0% +okay so the discretisation error in a + + + align:start position:0% +okay so the discretisation error in a +forward + + align:start position:0% +forward + + + align:start position:0% +forward +difference when I divide by delta + + align:start position:0% +difference when I divide by delta + + + align:start position:0% +difference when I divide by delta +T if I if I so it's first order in T is + + align:start position:0% +T if I if I so it's first order in T is + + + align:start position:0% +T if I if I so it's first order in T is +first + + align:start position:0% +first + + + align:start position:0% +first +order in in T and Center difference + + align:start position:0% +order in in T and Center difference + + + align:start position:0% +order in in T and Center difference +because of the Symmetry is second order + + align:start position:0% +because of the Symmetry is second order + + + align:start position:0% +because of the Symmetry is second order +in + + align:start position:0% + + + + align:start position:0% + +X okay + + align:start position:0% + + + + align:start position:0% + +a and this would be another problem + + align:start position:0% +a and this would be another problem + + + align:start position:0% +a and this would be another problem +where uh I could have begun with a semi + + align:start position:0% +where uh I could have begun with a semi + + + align:start position:0% +where uh I could have begun with a semi +discretization I could have begun + + align:start position:0% +discretization I could have begun + + + align:start position:0% +discretization I could have begun +with keeping this as a derivative dudt + + align:start position:0% +with keeping this as a derivative dudt + + + align:start position:0% +with keeping this as a derivative dudt +equal this Center + + align:start position:0% +equal this Center + + + align:start position:0% +equal this Center +difference + + align:start position:0% +difference + + + align:start position:0% +difference +and the discussion would have been + + align:start position:0% +and the discussion would have been + + + align:start position:0% +and the discussion would have been +entirely parallel to what we'll have + + align:start position:0% +entirely parallel to what we'll have + + + align:start position:0% +entirely parallel to what we'll have +here so I've jumped right to the finite + + align:start position:0% +here so I've jumped right to the finite + + + align:start position:0% +here so I've jumped right to the finite +difference in x and t so in other words + + align:start position:0% +difference in x and t so in other words + + + align:start position:0% +difference in x and t so in other words +what What's Happening Here unu n + one U + + align:start position:0% +what What's Happening Here unu n + one U + + + align:start position:0% +what What's Happening Here unu n + one U +at the center point n + one of course + + align:start position:0% +at the center point n + one of course + + + align:start position:0% +at the center point n + one of course +we're our little molecule is Computing + + align:start position:0% +we're our little molecule is Computing + + + align:start position:0% +we're our little molecule is Computing +this backward difference and + + align:start position:0% +this backward difference and + + + align:start position:0% +this backward difference and +this or rather forward in time so this + + align:start position:0% +this or rather forward in time so this + + + align:start position:0% +this or rather forward in time so this +is the time Direction n + + + align:start position:0% +is the time Direction n + + + + align:start position:0% +is the time Direction n + +one and this Center difference in space + + align:start position:0% +one and this Center difference in space + + + align:start position:0% +one and this Center difference in space +so we have if I just write out what that + + align:start position:0% +so we have if I just write out what that + + + align:start position:0% +so we have if I just write out what that +does + + align:start position:0% +does + + + align:start position:0% +does +it's + + align:start position:0% +it's + + + align:start position:0% +it's +ujn right coming from the time + + align:start position:0% +ujn right coming from the time + + + align:start position:0% +ujn right coming from the time +difference then I'll multiply by delta T + + align:start position:0% +difference then I'll multiply by delta T + + + align:start position:0% +difference then I'll multiply by delta T +and I have a Delta x s so that ratio is + + align:start position:0% +and I have a Delta x s so that ratio is + + + align:start position:0% +and I have a Delta x s so that ratio is +what I'm calling capital + + align:start position:0% +what I'm calling capital + + + align:start position:0% +what I'm calling capital +r capital r to distinguish the + + align:start position:0% +r capital r to distinguish the + + + align:start position:0% +r capital r to distinguish the +diffusion ratio from + + align:start position:0% +diffusion ratio from + + + align:start position:0% +diffusion ratio from +the from the wave ratio times what so + + align:start position:0% +the from the wave ratio times what so + + + align:start position:0% +the from the wave ratio times what so +it's just going to be UJ + 1 at time n + + align:start position:0% +it's just going to be UJ + 1 at time n + + + align:start position:0% +it's just going to be UJ + 1 at time n +minus 2 u j at time n plus u J-1 at + + align:start position:0% +minus 2 u j at time n plus u J-1 at + + + align:start position:0% +minus 2 u j at time n plus u J-1 at +time we're good at writing that + + align:start position:0% +time we're good at writing that + + + align:start position:0% +time we're good at writing that +expression down we can take + + align:start position:0% +expression down we can take + + + align:start position:0% +expression down we can take +it we can follow e to the I KX of course + + align:start position:0% +it we can follow e to the I KX of course + + + align:start position:0% +it we can follow e to the I KX of course +that's that's always the idea start with + + align:start position:0% +that's that's always the idea start with + + + align:start position:0% +that's that's always the idea start with +uj0 as e to the i k + + align:start position:0% +uj0 as e to the i k + + + align:start position:0% +uj0 as e to the i k +J Delta X and follow it + + align:start position:0% +J Delta X and follow it + + + align:start position:0% +J Delta X and follow it +up we want to know we're looking for a + + align:start position:0% +up we want to know we're looking for a + + + align:start position:0% +up we want to know we're looking for a +growth factor + + align:start position:0% +growth factor + + + align:start position:0% +growth factor +g a growth factor G the the the + + align:start position:0% +g a growth factor G the the the + + + align:start position:0% +g a growth factor G the the the +the the growth factor in a single step + + align:start position:0% +the the growth factor in a single step + + + align:start position:0% +the the growth factor in a single step +and of course the point is it depends on + + align:start position:0% +and of course the point is it depends on + + + align:start position:0% +and of course the point is it depends on +the K okay so let's just I just want + + align:start position:0% +the K okay so let's just I just want + + + align:start position:0% +the K okay so let's just I just want +to at at every step we say we always + + align:start position:0% +to at at every step we say we always + + + align:start position:0% +to at at every step we say we always +have the the exponential is is always + + align:start position:0% +have the the exponential is is always + + + align:start position:0% +have the the exponential is is always +with us it's the it's the factor that + + align:start position:0% +with us it's the it's the factor that + + + align:start position:0% +with us it's the it's the factor that +multiplies that exponential that we want + + align:start position:0% +multiplies that exponential that we want + + + align:start position:0% +multiplies that exponential that we want +and you see what it is don't you can you + + align:start position:0% +and you see what it is don't you can you + + + align:start position:0% +and you see what it is don't you can you +see what G is + + align:start position:0% +see what G is + + + align:start position:0% +see what G is +here + + align:start position:0% +here + + + align:start position:0% +here +so if I put in that that and then + + align:start position:0% +so if I put in that that and then + + + align:start position:0% +so if I put in that that and then +ultimately factor out the exponential + + align:start position:0% +ultimately factor out the exponential + + + align:start position:0% +ultimately factor out the exponential +it'll be multiplied by a one from that + + align:start position:0% +it'll be multiplied by a one from that + + + align:start position:0% +it'll be multiplied by a one from that +part and an R from this and now in + + align:start position:0% +part and an R from this and now in + + + align:start position:0% +part and an R from this and now in +parentheses we have the now very + + align:start position:0% +parentheses we have the now very + + + align:start position:0% +parentheses we have the now very +familiar quantity that comes from e to + + align:start position:0% +familiar quantity that comes from e to + + + align:start position:0% +familiar quantity that comes from e to +the i k Delta x e to + + align:start position:0% +the i k Delta x e to + + + align:start position:0% +the i k Delta x e to +Theus i k Delta X those combine to give + + align:start position:0% +Theus i k Delta X those combine to give + + + align:start position:0% +Theus i k Delta X those combine to give +two cosine K Delta + + align:start position:0% +two cosine K Delta + + + align:start position:0% +two cosine K Delta +X and the center one is minus 2 + + align:start position:0% +X and the center one is minus 2 + + + align:start position:0% +X and the center one is minus 2 +okay that's our growth + + align:start position:0% +okay that's our growth + + + align:start position:0% +okay that's our growth +factor and the question is does it stay + + align:start position:0% +factor and the question is does it stay + + + align:start position:0% +factor and the question is does it stay +below one which is the stability re + + align:start position:0% +below one which is the stability re + + + align:start position:0% +below one which is the stability re +requirement for all K Delta + + align:start position:0% +requirement for all K Delta + + + align:start position:0% +requirement for all K Delta +X and so you can see the dangerous + + align:start position:0% +X and so you can see the dangerous + + + align:start position:0% +X and so you can see the dangerous +frequency as often the dangerous + + align:start position:0% +frequency as often the dangerous + + + align:start position:0% +frequency as often the dangerous +frequency is when K Delta X is + + align:start position:0% +frequency is when K Delta X is + + + align:start position:0% +frequency is when K Delta X is +pi and that coine becomes + + align:start position:0% +pi and that coine becomes + + + align:start position:0% +pi and that coine becomes +minus1 and then we have so stability so + + align:start position:0% +minus1 and then we have so stability so + + + align:start position:0% +minus1 and then we have so stability so +stability + + align:start position:0% +stability + + + align:start position:0% +stability +at at K Delta xal pi + + align:start position:0% + + + + align:start position:0% + +needs so this becomes one and this is -2 + + align:start position:0% +needs so this becomes one and this is -2 + + + align:start position:0% +needs so this becomes one and this is -2 +and that's -2 we have 1 - 4 + + align:start position:0% + + + + align:start position:0% + +R and that quantity has to be in + + align:start position:0% +R and that quantity has to be in + + + align:start position:0% +R and that quantity has to be in +absolute value not exceeding + + align:start position:0% +absolute value not exceeding + + + align:start position:0% +absolute value not exceeding +one well there's no danger that it's + + align:start position:0% +one well there's no danger that it's + + + align:start position:0% +one well there's no danger that it's +going to go above one the danger is will + + align:start position:0% +going to go above one the danger is will + + + align:start position:0% +going to go above one the danger is will +it go below minus one and it it's not + + align:start position:0% +it go below minus one and it it's not + + + align:start position:0% +it go below minus one and it it's not +allowed to so we need it to be greater + + align:start position:0% +allowed to so we need it to be greater + + + align:start position:0% +allowed to so we need it to be greater +than or equal to + + align:start position:0% +than or equal to + + + align:start position:0% +than or equal to +minus1 and now if I put the minus1 on + + align:start position:0% +minus1 and now if I put the minus1 on + + + align:start position:0% +minus1 and now if I put the minus1 on +this side and the 4 r on that side that + + align:start position:0% +this side and the 4 r on that side that + + + align:start position:0% +this side and the 4 r on that side that +means 2 is greater or equal to 4 R and I + + align:start position:0% +means 2 is greater or equal to 4 R and I + + + align:start position:0% +means 2 is greater or equal to 4 R and I +get the famous condition R less or equal + + align:start position:0% +get the famous condition R less or equal + + + align:start position:0% +get the famous condition R less or equal +a + + align:start position:0% +a + + + align:start position:0% +a +half that's the stability + + align:start position:0% + + + + align:start position:0% + +requirement and if there was a + + align:start position:0% +requirement and if there was a + + + align:start position:0% +requirement and if there was a +coefficient D in the heat equation the + + align:start position:0% +coefficient D in the heat equation the + + + align:start position:0% +coefficient D in the heat equation the +coefficient would be there in R okay so + + align:start position:0% +coefficient would be there in R okay so + + + align:start position:0% +coefficient would be there in R okay so +that's the stability condition and + + align:start position:0% +that's the stability condition and + + + align:start position:0% +that's the stability condition and +that's the the thing + + align:start position:0% +that's the the thing + + + align:start position:0% +that's the the thing +we would like to find a way around + + align:start position:0% +we would like to find a way around + + + align:start position:0% +we would like to find a way around +because it says that this delta T over + + align:start position:0% +because it says that this delta T over + + + align:start position:0% +because it says that this delta T over +Del now I'll just put that in less or + + align:start position:0% +Del now I'll just put that in less or + + + align:start position:0% +Del now I'll just put that in less or +equal a half and uh that means a very + + align:start position:0% +equal a half and uh that means a very + + + align:start position:0% +equal a half and uh that means a very +small delta T + + align:start position:0% +small delta T + + + align:start position:0% +small delta T +okay what's the way around it + + align:start position:0% +okay what's the way around it + + + align:start position:0% +okay what's the way around it +to go to an explicit method so let me go + + align:start position:0% +to go to an explicit method so let me go + + + align:start position:0% +to go to an explicit method so let me go +first to a completely explicit method + + align:start position:0% +first to a completely explicit method + + + align:start position:0% +first to a completely explicit method +fully + + align:start position:0% +fully + + + align:start position:0% +fully +explicit so now I'm going to make it I'm + + align:start position:0% +explicit so now I'm going to make it I'm + + + align:start position:0% +explicit so now I'm going to make it I'm +sorry to go to an implicit method now + + align:start position:0% +sorry to go to an implicit method now + + + align:start position:0% +sorry to go to an implicit method now +implicit + + align:start position:0% + + + + align:start position:0% + +method now I'm going to do I'm going to + + align:start position:0% +method now I'm going to do I'm going to + + + align:start position:0% +method now I'm going to do I'm going to +remove the switch to an implicit method + + align:start position:0% +remove the switch to an implicit method + + + align:start position:0% +remove the switch to an implicit method +by Computing this different at time n + + + align:start position:0% +by Computing this different at time n + + + + align:start position:0% +by Computing this different at time n + +1 so this is now n + + + align:start position:0% + + + + align:start position:0% + +1 and what's a change in + + align:start position:0% +1 and what's a change in + + + align:start position:0% +1 and what's a change in +g a big change okay so now I want to + + align:start position:0% +g a big change okay so now I want to + + + align:start position:0% +g a big change okay so now I want to +recompute + + align:start position:0% +recompute + + + align:start position:0% +recompute +G for the + + align:start position:0% +G for the + + + align:start position:0% +G for the +uh the the growth factor over a single + + align:start position:0% +uh the the growth factor over a single + + + align:start position:0% +uh the the growth factor over a single +step for the + + align:start position:0% +step for the + + + align:start position:0% +step for the +exponential when + + align:start position:0% +exponential when + + + align:start position:0% +exponential when +the right hand side the second + + align:start position:0% +the right hand side the second + + + align:start position:0% +the right hand side the second +difference is taken at the new time so + + align:start position:0% +difference is taken at the new time so + + + align:start position:0% +difference is taken at the new time so +it this has to move over to the other + + align:start position:0% +it this has to move over to the other + + + align:start position:0% +it this has to move over to the other +side of the + + align:start position:0% +side of the + + + align:start position:0% +side of the +equation that makes the stability better + + align:start position:0% +equation that makes the stability better + + + align:start position:0% +equation that makes the stability better +but of course it's going to make the + + align:start position:0% +but of course it's going to make the + + + align:start position:0% +but of course it's going to make the +computation more difficult let me just + + align:start position:0% +computation more difficult let me just + + + align:start position:0% +computation more difficult let me just +think about the stability for now so + + align:start position:0% +think about the stability for now so + + + align:start position:0% +think about the stability for now so +instead of this board this is the + + align:start position:0% +instead of this board this is the + + + align:start position:0% +instead of this board this is the +explicit + + align:start position:0% + + + + align:start position:0% + +case yeah + + align:start position:0% + + + + align:start position:0% + +oh uh in magnitude so so it has to be + + align:start position:0% +oh uh in magnitude so so it has to be + + + align:start position:0% +oh uh in magnitude so so it has to be +let's draw a little picture here so + + align:start position:0% +let's draw a little picture here so + + + align:start position:0% +let's draw a little picture here so +there's zero there's + + align:start position:0% +there's zero there's + + + align:start position:0% +there's zero there's +one and here's minus one and this + + align:start position:0% +one and here's minus one and this + + + align:start position:0% +one and here's minus one and this +quantity is starting at one and + + align:start position:0% +quantity is starting at one and + + + align:start position:0% +quantity is starting at one and +subtracting 4 R so the question is does + + align:start position:0% +subtracting 4 R so the question is does + + + align:start position:0% +subtracting 4 R so the question is does +it stop here if it stops there then it's + + align:start position:0% +it stop here if it stops there then it's + + + align:start position:0% +it stop here if it stops there then it's +this is these are both these in this + + align:start position:0% +this is these are both these in this + + + align:start position:0% +this is these are both these in this +picture these would both be negative + + align:start position:0% +picture these would both be negative + + + align:start position:0% +picture these would both be negative +this would be about minus a half but + + align:start position:0% +this would be about minus a half but + + + align:start position:0% +this would be about minus a half but +that is greater than minus1 so this + + align:start position:0% +that is greater than minus1 so this + + + align:start position:0% +that is greater than minus1 so this +would be the okay case when this is + + align:start position:0% +would be the okay case when this is + + + align:start position:0% +would be the okay case when this is +true and that's what required uh R less + + align:start position:0% +true and that's what required uh R less + + + align:start position:0% +true and that's what required uh R less +or equal to half so in this case uh um + + align:start position:0% +or equal to half so in this case uh um + + + align:start position:0% +or equal to half so in this case uh um +yeah in that case r is less than less + + align:start position:0% +yeah in that case r is less than less + + + align:start position:0% +yeah in that case r is less than less +but if r equal to half everybody sees + + align:start position:0% +but if r equal to half everybody sees + + + align:start position:0% +but if r equal to half everybody sees +this if r equal to half this would be 1 + + align:start position:0% +this if r equal to half this would be 1 + + + align:start position:0% +this if r equal to half this would be 1 +- 2 this would bring us all the way here + + align:start position:0% +- 2 this would bring us all the way here + + + align:start position:0% +- 2 this would bring us all the way here +and if R is bigger than a half then that + + align:start position:0% +and if R is bigger than a half then that + + + align:start position:0% +and if R is bigger than a half then that +would push us that would reverse that + + align:start position:0% +would push us that would reverse that + + + align:start position:0% +would push us that would reverse that +inequality and we would be unstable yeah + + align:start position:0% +inequality and we would be unstable yeah + + + align:start position:0% +inequality and we would be unstable yeah +I think it's + + align:start position:0% +I think it's + + + align:start position:0% +I think it's +okay + + align:start position:0% + + + + align:start position:0% + +thanks yeah it it's the difference + + align:start position:0% +thanks yeah it it's the difference + + + align:start position:0% +thanks yeah it it's the difference +between looking at the magnitude if I + + align:start position:0% +between looking at the magnitude if I + + + align:start position:0% +between looking at the magnitude if I +put magnitude then I would need less or + + align:start position:0% +put magnitude then I would need less or + + + align:start position:0% +put magnitude then I would need less or +equal or uh just realize that just + + align:start position:0% +equal or uh just realize that just + + + align:start position:0% +equal or uh just realize that just +taking it as a number 1 - 4r okay I + + align:start position:0% +taking it as a number 1 - 4r okay I + + + align:start position:0% +taking it as a number 1 - 4r okay I +think that's all right now the implicit + + align:start position:0% +think that's all right now the implicit + + + align:start position:0% +think that's all right now the implicit +case what happened to + + align:start position:0% +case what happened to + + + align:start position:0% +case what happened to +G what happened to + + align:start position:0% +G what happened to + + + align:start position:0% +G what happened to +G now let me put it here + + align:start position:0% + + + + align:start position:0% + +implicit okay so what's changed this + + align:start position:0% +implicit okay so what's changed this + + + align:start position:0% +implicit okay so what's changed this +term which came from the second + + align:start position:0% +term which came from the second + + + align:start position:0% +term which came from the second +difference is moved over to to the n + + + align:start position:0% +difference is moved over to to the n + + + + align:start position:0% +difference is moved over to to the n + +one side of the equation so we + + align:start position:0% + + + + align:start position:0% + +have in fora space we would have one + + align:start position:0% +have in fora space we would have one + + + align:start position:0% +have in fora space we would have one +from the ujn + one and then Min - 2 R + + align:start position:0% +from the ujn + one and then Min - 2 R + + + align:start position:0% +from the ujn + one and then Min - 2 R +and times our Expression 2 cosine K + + align:start position:0% +and times our Expression 2 cosine K + + + align:start position:0% +and times our Expression 2 cosine K +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +x minus + + align:start position:0% + + + + align:start position:0% + +2 that that's what multipli + + align:start position:0% +2 that that's what multipli + + + align:start position:0% +2 that that's what multipli +e to the + + align:start position:0% +e to the + + + align:start position:0% +e to the +I well yeah do do you see that that's + + align:start position:0% +I well yeah do do you see that that's + + + align:start position:0% +I well yeah do do you see that that's +showing up on the on the uh new side of + + align:start position:0% +showing up on the on the uh new side of + + + align:start position:0% +showing up on the on the uh new side of +the equation multiplying e to the i k + + align:start position:0% +the equation multiplying e to the i k + + + align:start position:0% +the equation multiplying e to the i k +Delta X and on the old side that the + + align:start position:0% +Delta X and on the old side that the + + + align:start position:0% +Delta X and on the old side that the +time the old time step we only have + + align:start position:0% +time the old time step we only have + + + align:start position:0% +time the old time step we only have +the the + + align:start position:0% + + + + align:start position:0% + +uh the one in other words the growth + + align:start position:0% +uh the one in other words the growth + + + align:start position:0% +uh the one in other words the growth +fact factor is this goes down into the + + align:start position:0% +fact factor is this goes down into the + + + align:start position:0% +fact factor is this goes down into the +denominator and and we can see what's + + align:start position:0% +denominator and and we can see what's + + + align:start position:0% +denominator and and we can see what's +going on so the growth factor is 1 over + + align:start position:0% +going on so the growth factor is 1 over + + + align:start position:0% +going on so the growth factor is 1 over +this expression 1 - + + align:start position:0% +this expression 1 - + + + align:start position:0% +this expression 1 - +2R * 2 cosine K Delta xus + + align:start position:0% +2R * 2 cosine K Delta xus + + + align:start position:0% +2R * 2 cosine K Delta xus +2 we keep running into that quantity + + align:start position:0% +2 we keep running into that quantity + + + align:start position:0% +2 we keep running into that quantity +from the second difference okay so + + align:start position:0% +from the second difference okay so + + + align:start position:0% +from the second difference okay so +what's if I look at that what's going on + + align:start position:0% +what's if I look at that what's going on + + + align:start position:0% +what's if I look at that what's going on +the the key point of this quantity is + + align:start position:0% +the the key point of this quantity is + + + align:start position:0% +the the key point of this quantity is +that it's always + + align:start position:0% +that it's always + + + align:start position:0% +that it's always +negative or zero but never + + align:start position:0% +negative or zero but never + + + align:start position:0% +negative or zero but never +positive because the cosine belows never + + align:start position:0% +positive because the cosine belows never + + + align:start position:0% +positive because the cosine belows never +this term is never as as large as this + + align:start position:0% +this term is never as as large as this + + + align:start position:0% +this term is never as as large as this +one so it's negative and now I have + + align:start position:0% +one so it's negative and now I have + + + align:start position:0% +one so it's negative and now I have +another minus sign here so I have 1 / 1 + + align:start position:0% +another minus sign here so I have 1 / 1 + + + align:start position:0% +another minus sign here so I have 1 / 1 +plus something and always for all K and + + align:start position:0% +plus something and always for all K and + + + align:start position:0% +plus something and always for all K and +all ratios are it's + + align:start position:0% +all ratios are it's + + + align:start position:0% +all ratios are it's +okay right one over one plus something + + align:start position:0% +okay right one over one plus something + + + align:start position:0% +okay right one over one plus something +positive and and you see that + + align:start position:0% +positive and and you see that + + + align:start position:0% +positive and and you see that +everything's real that's CU we're doing + + align:start position:0% +everything's real that's CU we're doing + + + align:start position:0% +everything's real that's CU we're doing +the diffusion equation where the wave + + align:start position:0% +the diffusion equation where the wave + + + align:start position:0% +the diffusion equation where the wave +equation took us we had some imaginary + + align:start position:0% +equation took us we had some imaginary + + + align:start position:0% +equation took us we had some imaginary +Parts okay so uh so absolutely stable + + align:start position:0% +Parts okay so uh so absolutely stable + + + align:start position:0% +Parts okay so uh so absolutely stable +stable for all delta + + align:start position:0% + + + + align:start position:0% + +T even I'll say even for large delta T + + align:start position:0% + + + + align:start position:0% + +okay that's good of course uh we're not + + align:start position:0% +okay that's good of course uh we're not + + + align:start position:0% +okay that's good of course uh we're not +going to take delta + + align:start position:0% +going to take delta + + + align:start position:0% +going to take delta +T equal to a + + align:start position:0% + + + + align:start position:0% + +thousand even if stability allows us the + + align:start position:0% +thousand even if stability allows us the + + + align:start position:0% +thousand even if stability allows us the +accuracy would be hopeless be terrible I + + align:start position:0% +accuracy would be hopeless be terrible I + + + align:start position:0% +accuracy would be hopeless be terrible I +can't take a giant time step and expect + + align:start position:0% +can't take a giant time step and expect + + + align:start position:0% +can't take a giant time step and expect +to follow the good the the true + + align:start position:0% +to follow the good the the true + + + align:start position:0% +to follow the good the the true +exponentials for for e the + + align:start position:0% +exponentials for for e the + + + align:start position:0% +exponentials for for e the +ikx + + align:start position:0% +ikx + + + align:start position:0% +ikx +but I can take a good a larger step than + + align:start position:0% +but I can take a good a larger step than + + + align:start position:0% +but I can take a good a larger step than +this very small Delta 1/2 Delta x s step + + align:start position:0% +this very small Delta 1/2 Delta x s step + + + align:start position:0% +this very small Delta 1/2 Delta x s step +so so this is good what's the price that + + align:start position:0% +so so this is good what's the price that + + + align:start position:0% +so so this is good what's the price that +we + + align:start position:0% + + + + align:start position:0% + +pay the price is that at + + align:start position:0% +pay the price is that at + + + align:start position:0% +pay the price is that at +every time step we have to solve this is + + align:start position:0% +every time step we have to solve this is + + + align:start position:0% +every time step we have to solve this is +now on the other side so this brings a + + align:start position:0% +now on the other side so this brings a + + + align:start position:0% +now on the other side so this brings a +whole Matrix + + align:start position:0% +whole Matrix + + + align:start position:0% +whole Matrix +over so this implicit + + align:start position:0% +over so this implicit + + + align:start position:0% +over so this implicit +case in our if when I bring that second + + align:start position:0% +case in our if when I bring that second + + + align:start position:0% +case in our if when I bring that second +difference Matrix over I've I've + + align:start position:0% + + + + align:start position:0% + +used capital + + align:start position:0% +used capital + + + align:start position:0% +used capital +K because the second difference Matrix + + align:start position:0% +K because the second difference Matrix + + + align:start position:0% +K because the second difference Matrix +there is the probably the most + + align:start position:0% +there is the probably the most + + + align:start position:0% +there is the probably the most +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +uh difference Matrix I'll say one of the + + align:start position:0% +uh difference Matrix I'll say one of the + + + align:start position:0% +uh difference Matrix I'll say one of the +most interesting matrices period uh it + + align:start position:0% +most interesting matrices period uh it + + + align:start position:0% +most interesting matrices period uh it +has minus tws on the diagonal and ones + + align:start position:0% +has minus tws on the diagonal and ones + + + align:start position:0% +has minus tws on the diagonal and ones +above the + + align:start position:0% +above the + + + align:start position:0% +above the +diagonal so + + align:start position:0% +diagonal so + + + align:start position:0% +diagonal so +actually with signs exchanged I called + + align:start position:0% +actually with signs exchanged I called + + + align:start position:0% +actually with signs exchanged I called +it K so can I just remember the the the + + align:start position:0% +it K so can I just remember the the the + + + align:start position:0% +it K so can I just remember the the the +uh meaning of this Matrix K I'm going to + + align:start position:0% +uh meaning of this Matrix K I'm going to + + + align:start position:0% +uh meaning of this Matrix K I'm going to +stay with that letter because it's it's + + align:start position:0% +stay with that letter because it's it's + + + align:start position:0% +stay with that letter because it's it's +a standard in finite elements for the + + align:start position:0% +a standard in finite elements for the + + + align:start position:0% +a standard in finite elements for the +stiffness Matrix so K by definition is + + align:start position:0% +stiffness Matrix so K by definition is + + + align:start position:0% +stiffness Matrix so K by definition is +the Matrix with twos on the diagonal + + align:start position:0% +the Matrix with twos on the diagonal + + + align:start position:0% +the Matrix with twos on the diagonal +minus On's above the diagonal and minus + + align:start position:0% +minus On's above the diagonal and minus + + + align:start position:0% +minus On's above the diagonal and minus +On's below the + + align:start position:0% +On's below the + + + align:start position:0% +On's below the +diagonal and what size is + + align:start position:0% +diagonal and what size is + + + align:start position:0% +diagonal and what size is +it well on the whole line where we're + + align:start position:0% +it well on the whole line where we're + + + align:start position:0% +it well on the whole line where we're +working for + + align:start position:0% +working for + + + align:start position:0% +working for +Simplicity I guess K is infinitely + + align:start position:0% +Simplicity I guess K is infinitely + + + align:start position:0% +Simplicity I guess K is infinitely +infinite in both directions twos and + + align:start position:0% +infinite in both directions twos and + + + align:start position:0% +infinite in both directions twos and +minus one on an interval where we + + align:start position:0% +minus one on an interval where we + + + align:start position:0% +minus one on an interval where we +would really compute + + align:start position:0% +would really compute + + + align:start position:0% +would really compute +K would be a finite Matrix okay but the + + align:start position:0% +K would be a finite Matrix okay but the + + + align:start position:0% +K would be a finite Matrix okay but the +main point is that this Matrix K is the + + align:start position:0% +main point is that this Matrix K is the + + + align:start position:0% +main point is that this Matrix K is the +second difference Matrix is minus the + + align:start position:0% +second difference Matrix is minus the + + + align:start position:0% +second difference Matrix is minus the +second difference Matrix so that when I + + align:start position:0% +second difference Matrix so that when I + + + align:start position:0% +second difference Matrix so that when I +bring it over to this side which which + + align:start position:0% +bring it over to this side which which + + + align:start position:0% +bring it over to this side which which +changes that plus to a minus I get this + + align:start position:0% +changes that plus to a minus I get this + + + align:start position:0% +changes that plus to a minus I get this +equation to solve the identity coming + + align:start position:0% +equation to solve the identity coming + + + align:start position:0% +equation to solve the identity coming +from the + + align:start position:0% +from the + + + align:start position:0% +from the +one plus r + + align:start position:0% +one plus r + + + align:start position:0% +one plus r +the ratio times this Matrix K multiplies + + align:start position:0% +the ratio times this Matrix K multiplies + + + align:start position:0% +the ratio times this Matrix K multiplies +this Vector of all the values at the new + + align:start position:0% +this Vector of all the values at the new + + + align:start position:0% +this Vector of all the values at the new +time step and equals in this + + align:start position:0% +time step and equals in this + + + align:start position:0% +time step and equals in this +case all the values at the old time step + + align:start position:0% +case all the values at the old time step + + + align:start position:0% +case all the values at the old time step +right because at the old time step I'm + + align:start position:0% +right because at the old time step I'm + + + align:start position:0% +right because at the old time step I'm +just I'm just have the identity are you + + align:start position:0% +just I'm just have the identity are you + + + align:start position:0% +just I'm just have the identity are you +okay with this this is the problem that + + align:start position:0% +okay with this this is the problem that + + + align:start position:0% +okay with this this is the problem that +we actually have to + + align:start position:0% +we actually have to + + + align:start position:0% +we actually have to +solve I mean I mean the main point about + + align:start position:0% +solve I mean I mean the main point about + + + align:start position:0% +solve I mean I mean the main point about +it is that we have a linear system the + + align:start position:0% +it is that we have a linear system the + + + align:start position:0% +it is that we have a linear system the +U's at the new time step are are coupled + + align:start position:0% +U's at the new time step are are coupled + + + align:start position:0% +U's at the new time step are are coupled +coupled by the second difference coupled + + align:start position:0% +coupled by the second difference coupled + + + align:start position:0% +coupled by the second difference coupled +by The Matrix K so we have to deal with + + align:start position:0% +by The Matrix K so we have to deal with + + + align:start position:0% +by The Matrix K so we have to deal with +that + + align:start position:0% +that + + + align:start position:0% +that +well actually in one dimension no + + align:start position:0% +well actually in one dimension no + + + align:start position:0% +well actually in one dimension no +problem because in one dimension K is + + align:start position:0% +problem because in one dimension K is + + + align:start position:0% +problem because in one dimension K is +just a tri diagonal matrix and we can + + align:start position:0% +just a tri diagonal matrix and we can + + + align:start position:0% +just a tri diagonal matrix and we can +solve Tri diagonal systems + + align:start position:0% +solve Tri diagonal systems + + + align:start position:0% +solve Tri diagonal systems +almost as fast as we could work with the + + align:start position:0% +almost as fast as we could work with the + + + align:start position:0% +almost as fast as we could work with the +identity + + align:start position:0% + + + + align:start position:0% + +Matrix and actually what + + align:start position:0% +Matrix and actually what + + + align:start position:0% +Matrix and actually what +we're seeing in this + + align:start position:0% +we're seeing in this + + + align:start position:0% +we're seeing in this +ratio are the exactly the igen values of + + align:start position:0% +ratio are the exactly the igen values of + + + align:start position:0% +ratio are the exactly the igen values of +the inverse Matrix so so if I use a + + align:start position:0% +the inverse Matrix so so if I use a + + + align:start position:0% +the inverse Matrix so so if I use a +formula I would say un n + 1 is the + + align:start position:0% +formula I would say un n + 1 is the + + + align:start position:0% +formula I would say un n + 1 is the +inverse Matrix times + + align:start position:0% +inverse Matrix times + + + align:start position:0% +inverse Matrix times +un and the growth + + align:start position:0% +un and the growth + + + align:start position:0% +un and the growth +factor is just the igen value + + align:start position:0% +factor is just the igen value + + + align:start position:0% +factor is just the igen value +the growth factor G is simply the igen + + align:start position:0% +the growth factor G is simply the igen + + + align:start position:0% +the growth factor G is simply the igen +values of this inverse + + align:start position:0% +values of this inverse + + + align:start position:0% +values of this inverse +Matrix and + + align:start position:0% +Matrix and + + + align:start position:0% +Matrix and +uh notice again that all the igen values + + align:start position:0% +uh notice again that all the igen values + + + align:start position:0% +uh notice again that all the igen values +of K + + align:start position:0% +of K + + + align:start position:0% +of K +are greater or equal zero it was a + + align:start position:0% +are greater or equal zero it was a + + + align:start position:0% +are greater or equal zero it was a +positive definite Matrix because I + + align:start position:0% +positive definite Matrix because I + + + align:start position:0% +positive definite Matrix because I +switched + + align:start position:0% +switched + + + align:start position:0% +switched +sign and the effect of the identity is + + align:start position:0% +sign and the effect of the identity is + + + align:start position:0% +sign and the effect of the identity is +to push it a little more positive here + + align:start position:0% +to push it a little more positive here + + + align:start position:0% +to push it a little more positive here +it's making this this this is this is a + + align:start position:0% +it's making this this this is this is a + + + align:start position:0% +it's making this this this is this is a +positive number there that's the igen + + align:start position:0% +positive number there that's the igen + + + align:start position:0% +positive number there that's the igen +values of RK and then I'm making a + + align:start position:0% +values of RK and then I'm making a + + + align:start position:0% +values of RK and then I'm making a +little more positive with this one so + + align:start position:0% +little more positive with this one so + + + align:start position:0% +little more positive with this one so +we're we we have a a problem that is + + align:start position:0% +we're we we have a a problem that is + + + align:start position:0% +we're we we have a a problem that is +safely + + align:start position:0% + + + + align:start position:0% + +invertible + + align:start position:0% +invertible + + + align:start position:0% +invertible +stable and in one dimension quite simple + + align:start position:0% +stable and in one dimension quite simple + + + align:start position:0% +stable and in one dimension quite simple +so in one dimension we're we're entirely + + align:start position:0% +so in one dimension we're we're entirely + + + align:start position:0% +so in one dimension we're we're entirely +ready to go + + align:start position:0% + + + + align:start position:0% + +implicit let me just while I'm thinking + + align:start position:0% +implicit let me just while I'm thinking + + + align:start position:0% +implicit let me just while I'm thinking +about it just uh recall that we had some + + align:start position:0% +about it just uh recall that we had some + + + align:start position:0% +about it just uh recall that we had some +other matric in the finite Matrix + + align:start position:0% +other matric in the finite Matrix + + + align:start position:0% +other matric in the finite Matrix +case we had some other + + align:start position:0% + + + + align:start position:0% + +matrices in the very in in the very + + align:start position:0% +matrices in the very in in the very + + + align:start position:0% +matrices in the very in in the very +first section of this of the original + + align:start position:0% +first section of this of the original + + + align:start position:0% +first section of this of the original +notes which had different boundary + + align:start position:0% +notes which had different boundary + + + align:start position:0% +notes which had different boundary +conditions in other + + align:start position:0% +conditions in other + + + align:start position:0% +conditions in other +words if we have + + align:start position:0% +words if we have + + + align:start position:0% +words if we have +if we're on a finite + + align:start position:0% +if we're on a finite + + + align:start position:0% +if we're on a finite +interval then this Matrix K corresponds + + align:start position:0% +interval then this Matrix K corresponds + + + align:start position:0% +interval then this Matrix K corresponds +to zero boundary conditions zero + + align:start position:0% +to zero boundary conditions zero + + + align:start position:0% +to zero boundary conditions zero +temperature at the end but we might + + align:start position:0% +temperature at the end but we might + + + align:start position:0% +temperature at the end but we might +have other boundary conditions like the + + align:start position:0% +have other boundary conditions like the + + + align:start position:0% +have other boundary conditions like the +derivative of the temperature is zero at + + align:start position:0% +derivative of the temperature is zero at + + + align:start position:0% +derivative of the temperature is zero at +one end or the other end and that would + + align:start position:0% +one end or the other end and that would + + + align:start position:0% +one end or the other end and that would +change this Matrix in the first row on + + align:start position:0% +change this Matrix in the first row on + + + align:start position:0% +change this Matrix in the first row on +the last row to another nice Matrix so + + align:start position:0% +the last row to another nice Matrix so + + + align:start position:0% +the last row to another nice Matrix so +we might have not K but one of the other + + align:start position:0% +we might have not K but one of the other + + + align:start position:0% +we might have not K but one of the other +triagonal + + align:start position:0% +triagonal + + + align:start position:0% +triagonal +matrices okay but here here's the real + + align:start position:0% +matrices okay but here here's the real + + + align:start position:0% +matrices okay but here here's the real +Point what happens in two Dimensions + + align:start position:0% +Point what happens in two Dimensions + + + align:start position:0% +Point what happens in two Dimensions +suppose I include now uh uy y term in + + align:start position:0% +suppose I include now uh uy y term in + + + align:start position:0% +suppose I include now uh uy y term in +the heat + + align:start position:0% +the heat + + + align:start position:0% +the heat +equation or three dimensions with a u ZZ + + align:start position:0% +equation or three dimensions with a u ZZ + + + align:start position:0% +equation or three dimensions with a u ZZ +term what's what's + + align:start position:0% +term what's what's + + + align:start position:0% +term what's what's +different well we can follow through the + + align:start position:0% +different well we can follow through the + + + align:start position:0% +different well we can follow through the +stability test for the explicit method + + align:start position:0% +stability test for the explicit method + + + align:start position:0% +stability test for the explicit method +and it will be it'll I'll have a a term + + align:start position:0% +and it will be it'll I'll have a a term + + + align:start position:0% +and it will be it'll I'll have a a term +from Delta x^2 and a term from Delta y^ + + align:start position:0% +from Delta x^2 and a term from Delta y^ + + + align:start position:0% +from Delta x^2 and a term from Delta y^ +2 and Delta z s will be even slightly + + align:start position:0% +2 and Delta z s will be even slightly + + + align:start position:0% +2 and Delta z s will be even slightly +tighter on delta T or I can follow + + align:start position:0% +tighter on delta T or I can follow + + + align:start position:0% +tighter on delta T or I can follow +through the implicit + + align:start position:0% +through the implicit + + + align:start position:0% +through the implicit +method where now this second difference + + align:start position:0% +method where now this second difference + + + align:start position:0% +method where now this second difference +in the X Direction appears also with a + + align:start position:0% +in the X Direction appears also with a + + + align:start position:0% +in the X Direction appears also with a +second difference in the y direction and + + align:start position:0% +second difference in the y direction and + + + align:start position:0% +second difference in the y direction and +a second difference in the Z Direction + + align:start position:0% +a second difference in the Z Direction + + + align:start position:0% +a second difference in the Z Direction +so + + align:start position:0% +so + + + align:start position:0% +so +this what's happening from The Matrix + + align:start position:0% +this what's happening from The Matrix + + + align:start position:0% +this what's happening from The Matrix +the point of view I still have nice + + align:start position:0% +the point of view I still have nice + + + align:start position:0% +the point of view I still have nice +matrices with twos and minus ones or + + align:start position:0% +matrices with twos and minus ones or + + + align:start position:0% +matrices with twos and minus ones or +maybe with a I guess what we would have + + align:start position:0% +maybe with a I guess what we would have + + + align:start position:0% +maybe with a I guess what we would have +can can we just remember what we would + + align:start position:0% +can can we just remember what we would + + + align:start position:0% +can can we just remember what we would +have in the two-dimensional case in the + + align:start position:0% +have in the two-dimensional case in the + + + align:start position:0% +have in the two-dimensional case in the +two-dimensional case instead of this + + align:start position:0% +two-dimensional case instead of this + + + align:start position:0% +two-dimensional case instead of this +second difference with a minus1 a two + + align:start position:0% +second difference with a minus1 a two + + + align:start position:0% +second difference with a minus1 a two +and a minus one in the X direction we + + align:start position:0% +and a minus one in the X direction we + + + align:start position:0% +and a minus one in the X direction we +also have a second difference coming + + align:start position:0% +also have a second difference coming + + + align:start position:0% +also have a second difference coming +from the uy y in the y direction so + + align:start position:0% +from the uy y in the y direction so + + + align:start position:0% +from the uy y in the y direction so +another minus one and that two moves up + + align:start position:0% +another minus one and that two moves up + + + align:start position:0% +another minus one and that two moves up +to a + + align:start position:0% +to a + + + align:start position:0% +to a +four so our + + align:start position:0% +four so our + + + align:start position:0% +four so our +Matrix in the 2D two space Dimension + + align:start position:0% +Matrix in the 2D two space Dimension + + + align:start position:0% +Matrix in the 2D two space Dimension +case will be have a fors on the diagonal + + align:start position:0% +case will be have a fors on the diagonal + + + align:start position:0% +case will be have a fors on the diagonal +so it grows from this one + + align:start position:0% +so it grows from this one + + + align:start position:0% +so it grows from this one +it's called the tensor product coming + + align:start position:0% +it's called the tensor product coming + + + align:start position:0% +it's called the tensor product coming +out of this anyway it it produces this + + align:start position:0% +out of this anyway it it produces this + + + align:start position:0% +out of this anyway it it produces this +famous 5 point molecule with fours on + + align:start position:0% +famous 5 point molecule with fours on + + + align:start position:0% +famous 5 point molecule with fours on +the diagonal and four minus ones going + + align:start position:0% +the diagonal and four minus ones going + + + align:start position:0% +the diagonal and four minus ones going +down other diagonals and the problem is + + align:start position:0% +down other diagonals and the problem is + + + align:start position:0% +down other diagonals and the problem is +that those + + align:start position:0% +that those + + + align:start position:0% +that those +diagonals are not you know two of the + + align:start position:0% +diagonals are not you know two of the + + + align:start position:0% +diagonals are not you know two of the +diagonals might be right next to the + + align:start position:0% +diagonals might be right next to the + + + align:start position:0% +diagonals might be right next to the +main diagonal but the other two will be + + align:start position:0% +main diagonal but the other two will be + + + align:start position:0% +main diagonal but the other two will be +farther + + align:start position:0% +farther + + + align:start position:0% +farther +away because we can't number the nodes + + align:start position:0% +away because we can't number the nodes + + + align:start position:0% +away because we can't number the nodes +to keep all these four numbered + + align:start position:0% +to keep all these four numbered + + + align:start position:0% +to keep all these four numbered +adjacently at at all the mesh points in + + align:start position:0% +adjacently at at all the mesh points in + + + align:start position:0% +adjacently at at all the mesh points in +other words we have a serious Matrix + + align:start position:0% +other words we have a serious Matrix + + + align:start position:0% +other words we have a serious Matrix +problem that's that's my comment we we + + align:start position:0% +problem that's that's my comment we we + + + align:start position:0% +problem that's that's my comment we we +we have a we have a + + align:start position:0% +we have a we have a + + + align:start position:0% +we have a we have a +matrix K in 2D so now what I'm speaking + + align:start position:0% +matrix K in 2D so now what I'm speaking + + + align:start position:0% +matrix K in 2D so now what I'm speaking +about is is this problem identity plus r + + align:start position:0% +about is is this problem identity plus r + + + align:start position:0% +about is is this problem identity plus r +k2d u at the new time equal U at the old + + align:start position:0% +k2d u at the new time equal U at the old + + + align:start position:0% +k2d u at the new time equal U at the old +time and k2d is by no means so easy to + + align:start position:0% +time and k2d is by no means so easy to + + + align:start position:0% +time and k2d is by no means so easy to +deal with as k1d + + align:start position:0% + + + + align:start position:0% + +it's not it doesn't have a nice narrow + + align:start position:0% +it's not it doesn't have a nice narrow + + + align:start position:0% +it's not it doesn't have a nice narrow +band like this the band stretches + + align:start position:0% +band like this the band stretches + + + align:start position:0% +band like this the band stretches +further and we'll see it oh we'll see it + + align:start position:0% +further and we'll see it oh we'll see it + + + align:start position:0% +further and we'll see it oh we'll see it +in Spades in the next part of the course + + align:start position:0% +in Spades in the next part of the course + + + align:start position:0% +in Spades in the next part of the course +which is about + + align:start position:0% + + + + align:start position:0% + +solving large linear systems so we have + + align:start position:0% +solving large linear systems so we have + + + align:start position:0% +solving large linear systems so we have +a large system because we've got lots of + + align:start position:0% +a large system because we've got lots of + + + align:start position:0% +a large system because we've got lots of +mesh + + align:start position:0% +mesh + + + align:start position:0% +mesh +points we have a matrix that is has a + + align:start position:0% +points we have a matrix that is has a + + + align:start position:0% +points we have a matrix that is has a +wider band and so you need new IDE + + align:start position:0% +wider band and so you need new IDE + + + align:start position:0% +wider band and so you need new IDE +in solving it so this this problem is + + align:start position:0% +in solving it so this this problem is + + + align:start position:0% +in solving it so this this problem is +what + + align:start position:0% +what + + + align:start position:0% +what +will will be a model is the connection + + align:start position:0% +will will be a model is the connection + + + align:start position:0% +will will be a model is the connection +really between this section of the + + align:start position:0% +really between this section of the + + + align:start position:0% +really between this section of the +course difference methods for initial + + align:start position:0% +course difference methods for initial + + + align:start position:0% +course difference methods for initial +value problems and the next section + + align:start position:0% +value problems and the next section + + + align:start position:0% +value problems and the next section +which is solving large linear systems + + align:start position:0% +which is solving large linear systems + + + align:start position:0% +which is solving large linear systems +because this will be a typical model + + align:start position:0% +because this will be a typical model + + + align:start position:0% +because this will be a typical model +large linear system okay so that's a + + align:start position:0% +large linear system okay so that's a + + + align:start position:0% +large linear system okay so that's a +comment of of the that that for implicit + + align:start position:0% +comment of of the that that for implicit + + + align:start position:0% +comment of of the that that for implicit +equations the price was low in 1D but + + align:start position:0% +equations the price was low in 1D but + + + align:start position:0% +equations the price was low in 1D but +the price is not so low in 2D okay now + + align:start position:0% +the price is not so low in 2D okay now + + + align:start position:0% +the price is not so low in 2D okay now +what have we got any other + + align:start position:0% +what have we got any other + + + align:start position:0% +what have we got any other +candidates + + align:start position:0% +candidates + + + align:start position:0% +candidates +between explicit and + + align:start position:0% +between explicit and + + + align:start position:0% +between explicit and +implicit + + align:start position:0% +implicit + + + align:start position:0% +implicit +well we did way back for ordinary + + align:start position:0% +well we did way back for ordinary + + + align:start position:0% +well we did way back for ordinary +differential equations we had a + + align:start position:0% +differential equations we had a + + + align:start position:0% +differential equations we had a +trapezoidal rule and what did that do + + align:start position:0% +trapezoidal rule and what did that do + + + align:start position:0% +trapezoidal rule and what did that do +that increased the accuracy by centering + + align:start position:0% +that increased the accuracy by centering + + + align:start position:0% +that increased the accuracy by centering +it at time n plus a half do you remember + + align:start position:0% +it at time n plus a half do you remember + + + align:start position:0% +it at time n plus a half do you remember +that it was half on the right hand side + + align:start position:0% +that it was half on the right hand side + + + align:start position:0% +that it was half on the right hand side +we used half the explicit difference and + + align:start position:0% +we used half the explicit difference and + + + align:start position:0% +we used half the explicit difference and +half of the implicit difference so uh + + align:start position:0% +half of the implicit difference so uh + + + align:start position:0% +half of the implicit difference so uh +natural to do it again it worked then + + align:start position:0% +natural to do it again it worked then + + + align:start position:0% +natural to do it again it worked then +and it'll work + + align:start position:0% +and it'll work + + + align:start position:0% +and it'll work +now so this will be the trapezoidal + + align:start position:0% +now so this will be the trapezoidal + + + align:start position:0% +now so this will be the trapezoidal +method but but most people in the + + align:start position:0% +method but but most people in the + + + align:start position:0% +method but but most people in the +diffusion application call it name it + + align:start position:0% +diffusion application call it name it + + + align:start position:0% +diffusion application call it name it +after these authors crank and + + align:start position:0% +after these authors crank and + + + align:start position:0% +after these authors crank and +Nicholson so it's the crank Nicholson + + align:start position:0% +Nicholson so it's the crank Nicholson + + + align:start position:0% +Nicholson so it's the crank Nicholson +method so it's so it's half the explicit + + align:start position:0% +method so it's so it's half the explicit + + + align:start position:0% +method so it's so it's half the explicit +part plus half the implicit part and and + + align:start position:0% +part plus half the implicit part and and + + + align:start position:0% +part plus half the implicit part and and +the Order of accuracy is increased by by + + align:start position:0% +the Order of accuracy is increased by by + + + align:start position:0% +the Order of accuracy is increased by by +centering it this way that that's the + + align:start position:0% +centering it this way that that's the + + + align:start position:0% +centering it this way that that's the +point of + + align:start position:0% +point of + + + align:start position:0% +point of +course so I guess the point will be we + + align:start position:0% +course so I guess the point will be we + + + align:start position:0% +course so I guess the point will be we +don't have any extra work + + align:start position:0% +don't have any extra work + + + align:start position:0% +don't have any extra work +compared to a fully implicit + + align:start position:0% +compared to a fully implicit + + + align:start position:0% +compared to a fully implicit +one and we get an extra of order of + + align:start position:0% +one and we get an extra of order of + + + align:start position:0% +one and we get an extra of order of +accuracy by looking at by centering it + + align:start position:0% +accuracy by looking at by centering it + + + align:start position:0% +accuracy by looking at by centering it +at a half so u n + 1 u j n + + + align:start position:0% +at a half so u n + 1 u j n + + + + align:start position:0% +at a half so u n + 1 u j n + +1 minus UJ n over delta + + align:start position:0% +1 minus UJ n over delta + + + align:start position:0% +1 minus UJ n over delta +T is r that ratio oh is sorry we've got + + align:start position:0% +T is r that ratio oh is sorry we've got + + + align:start position:0% +T is r that ratio oh is sorry we've got +delta T there so will be + + align:start position:0% +delta T there so will be + + + align:start position:0% +delta T there so will be +the second + + align:start position:0% +the second + + + align:start position:0% +the second +difference at the old + + align:start position:0% + + + + align:start position:0% + +time times a half just half of we just + + align:start position:0% +time times a half just half of we just + + + align:start position:0% +time times a half just half of we just +take half of that half of that explicit + + align:start position:0% +take half of that half of that explicit + + + align:start position:0% +take half of that half of that explicit +part plus half of of the implicit part + + align:start position:0% +part plus half of of the implicit part + + + align:start position:0% +part plus half of of the implicit part +this is a Time n + 1 over Delta + + align:start position:0% +this is a Time n + 1 over Delta + + + align:start position:0% +this is a Time n + 1 over Delta +x^2 you would think of that everybody + + align:start position:0% +x^2 you would think of that everybody + + + align:start position:0% +x^2 you would think of that everybody +would it's it's just a natural idea it + + align:start position:0% +would it's it's just a natural idea it + + + align:start position:0% +would it's it's just a natural idea it +increases the accuracy we still it's + + align:start position:0% +increases the accuracy we still it's + + + align:start position:0% +increases the accuracy we still it's +still implicit we still have to bring + + align:start position:0% +still implicit we still have to bring + + + align:start position:0% +still implicit we still have to bring +this term over onto this side when ujn + + align:start position:0% +this term over onto this side when ujn + + + align:start position:0% +this term over onto this side when ujn +moves over onto that + + align:start position:0% +moves over onto that + + + align:start position:0% +moves over onto that +side and we can look look at the growth + + align:start position:0% +side and we can look look at the growth + + + align:start position:0% +side and we can look look at the growth +factor so it's we have that's we have to + + align:start position:0% +factor so it's we have that's we have to + + + align:start position:0% +factor so it's we have that's we have to +do so bring that term over so I have and + + align:start position:0% +do so bring that term over so I have and + + + align:start position:0% +do so bring that term over so I have and +bring delta T up so is a delta T Delta + + align:start position:0% +bring delta T up so is a delta T Delta + + + align:start position:0% +bring delta T up so is a delta T Delta +divided Delta x^2 and R okay so when I + + align:start position:0% +divided Delta x^2 and R okay so when I + + + align:start position:0% +divided Delta x^2 and R okay so when I +I've got this term the one and when I + + align:start position:0% +I've got this term the one and when I + + + align:start position:0% +I've got this term the one and when I +bring that term over it's a half of what + + align:start position:0% +bring that term over it's a half of what + + + align:start position:0% +bring that term over it's a half of what +we brought over before which was the R 2 + + align:start position:0% +we brought over before which was the R 2 + + + align:start position:0% +we brought over before which was the R 2 +cosine K Delta x minus the + + align:start position:0% +cosine K Delta x minus the + + + align:start position:0% +cosine K Delta x minus the +2 that multiplies G + + align:start position:0% +2 that multiplies G + + + align:start position:0% +2 that multiplies G +and on the right side we have the one + + align:start position:0% +and on the right side we have the one + + + align:start position:0% +and on the right side we have the one +from the ujn plus a half * the r * 2 + + align:start position:0% +from the ujn plus a half * the r * 2 + + + align:start position:0% +from the ujn plus a half * the r * 2 +cine K Delta x - + + align:start position:0% + + + + align:start position:0% + +2 I'm certainly getting to the point + + align:start position:0% +2 I'm certainly getting to the point + + + align:start position:0% +2 I'm certainly getting to the point +where I write these Expressions down + + align:start position:0% +where I write these Expressions down + + + align:start position:0% +where I write these Expressions down +faster + + align:start position:0% +faster + + + align:start position:0% +faster +without explicitly writing e to the I K + + align:start position:0% +without explicitly writing e to the I K + + + align:start position:0% +without explicitly writing e to the I K +Delta X and then canceling it so G is a + + align:start position:0% +Delta X and then canceling it so G is a + + + align:start position:0% +Delta X and then canceling it so G is a +a ratio + + align:start position:0% +a ratio + + + align:start position:0% +a ratio +again in the explicit + + align:start position:0% +again in the explicit + + + align:start position:0% +again in the explicit +case in the explicit case G + + align:start position:0% +case in the explicit case G + + + align:start position:0% +case in the explicit case G +was all in the numerator there was no + + align:start position:0% +was all in the numerator there was no + + + align:start position:0% +was all in the numerator there was no +denominator in the implicit fully + + align:start position:0% +denominator in the implicit fully + + + align:start position:0% +denominator in the implicit fully +implicit + + align:start position:0% +implicit + + + align:start position:0% +implicit +case G was all + + align:start position:0% +case G was all + + + align:start position:0% +case G was all +denominator with just a one in the + + align:start position:0% +denominator with just a one in the + + + align:start position:0% +denominator with just a one in the +numerator + + align:start position:0% +numerator + + + align:start position:0% +numerator +now we have G as the ratio so I'm going + + align:start position:0% +now we have G as the ratio so I'm going + + + align:start position:0% +now we have G as the ratio so I'm going +to bring this down + + align:start position:0% + + + + align:start position:0% + +below and G is a ratio so it's a + + align:start position:0% +below and G is a ratio so it's a + + + align:start position:0% +below and G is a ratio so it's a +fraction because it's got an implicit + + align:start position:0% +fraction because it's got an implicit + + + align:start position:0% +fraction because it's got an implicit +explicit part in the denom in the + + align:start position:0% +explicit part in the denom in the + + + align:start position:0% +explicit part in the denom in the +numerator and an implicit part in the + + align:start position:0% +numerator and an implicit part in the + + + align:start position:0% +numerator and an implicit part in the +denominator and of course the main + + align:start position:0% +denominator and of course the main + + + align:start position:0% +denominator and of course the main +question is when is G less or equal to + + align:start position:0% +question is when is G less or equal to + + + align:start position:0% +question is when is G less or equal to +one + + align:start position:0% + + + + align:start position:0% + +well actually it's + + align:start position:0% +well actually it's + + + align:start position:0% +well actually it's +cool because G is simply look at the the + + align:start position:0% +cool because G is simply look at the the + + + align:start position:0% +cool because G is simply look at the the +numerator is one and all this stuff is + + align:start position:0% +numerator is one and all this stuff is + + + align:start position:0% +numerator is one and all this stuff is +negative so this is one minus + + align:start position:0% +negative so this is one minus + + + align:start position:0% +negative so this is one minus +something and what's going down + + align:start position:0% +something and what's going down + + + align:start position:0% +something and what's going down +here the sign's just reversed is one + + align:start position:0% +here the sign's just reversed is one + + + align:start position:0% +here the sign's just reversed is one +plus something so and this is this is a + + align:start position:0% +plus something so and this is this is a + + + align:start position:0% +plus something so and this is this is a +a positive quantity and this is the same + + align:start position:0% +a positive quantity and this is the same + + + align:start position:0% +a positive quantity and this is the same +positive quantity + + align:start position:0% +positive quantity + + + align:start position:0% +positive quantity +so this is one minus do you see that + + align:start position:0% +so this is one minus do you see that + + + align:start position:0% +so this is one minus do you see that +this because this is negative I'll write + + align:start position:0% +this because this is negative I'll write + + + align:start position:0% +this because this is negative I'll write +it as one minus something something + + align:start position:0% +it as one minus something something + + + align:start position:0% +it as one minus something something +positive and here this is minus and this + + align:start position:0% +positive and here this is minus and this + + + align:start position:0% +positive and here this is minus and this +is negative so that's this is one plus + + align:start position:0% +is negative so that's this is one plus + + + align:start position:0% +is negative so that's this is one plus +the same thing so what's the + + align:start position:0% + + + + align:start position:0% + +answer it's it's always works one minus + + align:start position:0% +answer it's it's always works one minus + + + align:start position:0% +answer it's it's always works one minus +a positive number over one plus that + + align:start position:0% +a positive number over one plus that + + + align:start position:0% +a positive number over one plus that +positive number can't go + + align:start position:0% +positive number can't go + + + align:start position:0% +positive number can't go +wrong we always have so for all + + align:start position:0% + + + + align:start position:0% + +R + + align:start position:0% +R + + + align:start position:0% +R +okay so in a way that has + + align:start position:0% +okay so in a way that has + + + align:start position:0% +okay so in a way that has +to be more attractive than uh fully + + align:start position:0% +to be more attractive than uh fully + + + align:start position:0% +to be more attractive than uh fully +implicit because it didn't take more + + align:start position:0% +implicit because it didn't take more + + + align:start position:0% +implicit because it didn't take more +work it wasn't any less stable and it + + align:start position:0% +work it wasn't any less stable and it + + + align:start position:0% +work it wasn't any less stable and it +was more accurate so crank Nicholson is + + align:start position:0% +was more accurate so crank Nicholson is + + + align:start position:0% +was more accurate so crank Nicholson is +uh sort of a a natural idea at this uh + + align:start position:0% +uh sort of a a natural idea at this uh + + + align:start position:0% +uh sort of a a natural idea at this uh +with at this level of of + + align:start position:0% +with at this level of of + + + align:start position:0% +with at this level of of +analysis yeah okay so those are the + + align:start position:0% +analysis yeah okay so those are the + + + align:start position:0% +analysis yeah okay so those are the +three methods to think about of + + align:start position:0% +three methods to think about of + + + align:start position:0% +three methods to think about of +course actual + + align:start position:0% +course actual + + + align:start position:0% +course actual +computations uh will bring in + + align:start position:0% +computations uh will bring in + + + align:start position:0% +computations uh will bring in +new questions boundary conditions + + align:start position:0% +new questions boundary conditions + + + align:start position:0% +new questions boundary conditions +nonlinearities and everything I'm just + + align:start position:0% +nonlinearities and everything I'm just + + + align:start position:0% +nonlinearities and everything I'm just +staying at this simple level where I'm + + align:start position:0% +staying at this simple level where I'm + + + align:start position:0% +staying at this simple level where I'm +comparing the + + align:start position:0% +comparing the + + + align:start position:0% +comparing the +the first ideas that would occur to us + + align:start position:0% +the first ideas that would occur to us + + + align:start position:0% +the first ideas that would occur to us +okay we we may want higher accuracy all + + align:start position:0% +okay we we may want higher accuracy all + + + align:start position:0% +okay we we may want higher accuracy all +sorts of things but but we're seeing the + + align:start position:0% +sorts of things but but we're seeing the + + + align:start position:0% +sorts of things but but we're seeing the +the contrast with the wave equation case + + align:start position:0% +the contrast with the wave equation case + + + align:start position:0% +the contrast with the wave equation case +that here we can get uh we have to we + + align:start position:0% +that here we can get uh we have to we + + + align:start position:0% +that here we can get uh we have to we +move toward more toward the implicit + + align:start position:0% +move toward more toward the implicit + + + align:start position:0% +move toward more toward the implicit +side and the reward is unconditional + + align:start position:0% +side and the reward is unconditional + + + align:start position:0% +side and the reward is unconditional +stability no condition on R but the + + align:start position:0% +stability no condition on R but the + + + align:start position:0% +stability no condition on R but the +price is is more computation + + align:start position:0% +price is is more computation + + + align:start position:0% +price is is more computation +okay well at that same + + align:start position:0% +okay well at that same + + + align:start position:0% +okay well at that same +level of thinking about the most natural + + align:start position:0% +level of thinking about the most natural + + + align:start position:0% +level of thinking about the most natural +methods that that uh occur to + + align:start position:0% +methods that that uh occur to + + + align:start position:0% +methods that that uh occur to +you I want to speak now about the big + + align:start position:0% +you I want to speak now about the big + + + align:start position:0% +you I want to speak now about the big +big issue of convection diffusion + + align:start position:0% +big issue of convection diffusion + + + align:start position:0% +big issue of convection diffusion +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +both types of problem are with us so so + + align:start position:0% +both types of problem are with us so so + + + align:start position:0% +both types of problem are with us so so +convection + + align:start position:0% +convection + + + align:start position:0% +convection +diffusion what would you do then + + align:start position:0% + + + + align:start position:0% + +so now I have both convection and + + align:start position:0% + + + + align:start position:0% + +diffusion in the + + align:start position:0% +diffusion in the + + + align:start position:0% +diffusion in the +equation UT = + + align:start position:0% +equation UT = + + + align:start position:0% +equation UT = +CX plus + + align:start position:0% + + + + align:start position:0% + +DX and I guess I want to say that this + + align:start position:0% +DX and I guess I want to say that this + + + align:start position:0% +DX and I guess I want to say that this +is + + align:start position:0% +is + + + align:start position:0% +is +uh something that the world has not come + + align:start position:0% +uh something that the world has not come + + + align:start position:0% +uh something that the world has not come +to a decision on the computational world + + align:start position:0% +to a decision on the computational world + + + align:start position:0% +to a decision on the computational world +is still + + align:start position:0% +is still + + + align:start position:0% +is still +debating what to do with convection + + align:start position:0% +debating what to do with convection + + + align:start position:0% +debating what to do with convection +diffusion so + + align:start position:0% +diffusion so + + + align:start position:0% +diffusion so +uh it's a very + + align:start position:0% +uh it's a very + + + align:start position:0% +uh it's a very +appropriate + + align:start position:0% +appropriate + + + align:start position:0% +appropriate +equation model + + align:start position:0% +equation model + + + align:start position:0% +equation model +to experiment + + align:start position:0% +to experiment + + + align:start position:0% +to experiment +with possible uh maybe I I'll ask you uh + + align:start position:0% +with possible uh maybe I I'll ask you uh + + + align:start position:0% +with possible uh maybe I I'll ask you uh +as the next kind of informal homework to + + align:start position:0% +as the next kind of informal homework to + + + align:start position:0% +as the next kind of informal homework to +uh begin to experiment with that and + + align:start position:0% +uh begin to experiment with that and + + + align:start position:0% +uh begin to experiment with that and +when I when I say experiment you you can + + align:start position:0% +when I when I say experiment you you can + + + align:start position:0% +when I when I say experiment you you can +think immediately of the of the uh + + align:start position:0% +think immediately of the of the uh + + + align:start position:0% +think immediately of the of the uh +methods you might think + + align:start position:0% +methods you might think + + + align:start position:0% +methods you might think +of the the first methods to try so the + + align:start position:0% +of the the first methods to try so the + + + align:start position:0% +of the the first methods to try so the +first method of course will be + + align:start position:0% + + + + align:start position:0% + +explicit fully + + align:start position:0% +explicit fully + + + align:start position:0% +explicit fully +explicit what do you expect to have + + align:start position:0% +explicit what do you expect to have + + + align:start position:0% +explicit what do you expect to have +happen there let's just see how the two + + align:start position:0% +happen there let's just see how the two + + + align:start position:0% +happen there let's just see how the two +different terms each + + align:start position:0% +different terms each + + + align:start position:0% +different terms each +uh give their + + align:start position:0% +uh give their + + + align:start position:0% +uh give their +little push toward the the stability + + align:start position:0% +little push toward the the stability + + + align:start position:0% +little push toward the the stability +requirement so explicit the is going to + + align:start position:0% +requirement so explicit the is going to + + + align:start position:0% +requirement so explicit the is going to +be Delta the time + + align:start position:0% +be Delta the time + + + align:start position:0% +be Delta the time +difference forward time + + align:start position:0% +difference forward time + + + align:start position:0% +difference forward time +difference equals c times what shall I + + align:start position:0% +difference equals c times what shall I + + + align:start position:0% +difference equals c times what shall I +choose first for uh the space + + align:start position:0% + + + + align:start position:0% + +difference upwind Maybe upwind in + + align:start position:0% +difference upwind Maybe upwind in + + + align:start position:0% +difference upwind Maybe upwind in +space so this is going to be explicit + + align:start position:0% +space so this is going to be explicit + + + align:start position:0% +space so this is going to be explicit +and + + align:start position:0% +and + + + align:start position:0% +and +upwind of course everybody knows that + + align:start position:0% +upwind of course everybody knows that + + + align:start position:0% +upwind of course everybody knows that +that refers to the windy term in the + + align:start position:0% +that refers to the windy term in the + + + align:start position:0% +that refers to the windy term in the +equation the the wave wave term okay so + + align:start position:0% +equation the the wave wave term okay so + + + align:start position:0% +equation the the wave wave term okay so +I of course I'll get a forward + + align:start position:0% +I of course I'll get a forward + + + align:start position:0% +I of course I'll get a forward +difference then in the X direction of U + + align:start position:0% +difference then in the X direction of U + + + align:start position:0% +difference then in the X direction of U +at time n / Delta X and then I'll have + + align:start position:0% +at time n / Delta X and then I'll have + + + align:start position:0% +at time n / Delta X and then I'll have +I'm going to do the natural one on a + + align:start position:0% +I'm going to do the natural one on a + + + align:start position:0% +I'm going to do the natural one on a +centered second difference at time n for + + align:start position:0% +centered second difference at time n for + + + align:start position:0% +centered second difference at time n for +the diffusion + + align:start position:0% +the diffusion + + + align:start position:0% +the diffusion +term + + align:start position:0% + + + + align:start position:0% + +okay we'll see what comes out of + + align:start position:0% +okay we'll see what comes out of + + + align:start position:0% +okay we'll see what comes out of +that it's going to involve not only the + + align:start position:0% +that it's going to involve not only the + + + align:start position:0% +that it's going to involve not only the +ratio it'll it'll involve both ratios + + align:start position:0% +ratio it'll it'll involve both ratios + + + align:start position:0% +ratio it'll it'll involve both ratios +naturally little r as soon as I multiply + + align:start position:0% +naturally little r as soon as I multiply + + + align:start position:0% +naturally little r as soon as I multiply +up by Delta X I have a little r there my + + align:start position:0% +up by Delta X I have a little r there my + + + align:start position:0% +up by Delta X I have a little r there my +my my wave equation ratio and I have a d + + align:start position:0% +my my wave equation ratio and I have a d + + + align:start position:0% +my my wave equation ratio and I have a d +Delta t/ Delta x^2 which I'm calling + + align:start position:0% +Delta t/ Delta x^2 which I'm calling + + + align:start position:0% +Delta t/ Delta x^2 which I'm calling +capital r that's the diffusion + + align:start position:0% +capital r that's the diffusion + + + align:start position:0% +capital r that's the diffusion +ratio and multiplied by all sorts of + + align:start position:0% +ratio and multiplied by all sorts of + + + align:start position:0% +ratio and multiplied by all sorts of +stuff yeah so actually why don't I write + + align:start position:0% +stuff yeah so actually why don't I write + + + align:start position:0% +stuff yeah so actually why don't I write +down what the equation really is + + align:start position:0% +down what the equation really is + + + align:start position:0% +down what the equation really is +explicitly it's + + align:start position:0% +explicitly it's + + + align:start position:0% +explicitly it's +UJ n + 1 is ujn so maybe I should + + align:start position:0% +UJ n + 1 is ujn so maybe I should + + + align:start position:0% +UJ n + 1 is ujn so maybe I should +collect all the terms here + + align:start position:0% +collect all the terms here + + + align:start position:0% +collect all the terms here +can I collect the terms that multiply u + + align:start position:0% +can I collect the terms that multiply u + + + align:start position:0% +can I collect the terms that multiply u +j + 1 + + align:start position:0% + + + + align:start position:0% + +n so what's going to multiply UJ + 1 n + + align:start position:0% +n so what's going to multiply UJ + 1 n + + + align:start position:0% +n so what's going to multiply UJ + 1 n +here it here I have a c delta T over + + align:start position:0% +here it here I have a c delta T over + + + align:start position:0% +here it here I have a c delta T over +Delta X I have an R right from this term + + align:start position:0% +Delta X I have an R right from this term + + + align:start position:0% +Delta X I have an R right from this term +and here I have a d + + align:start position:0% + + + + align:start position:0% + +right uh no D sorry I have a capital r + + align:start position:0% + + + + align:start position:0% + +is isn't that right when I multiply + + align:start position:0% +is isn't that right when I multiply + + + align:start position:0% +is isn't that right when I multiply +through by delta T I have D delta T over + + align:start position:0% +through by delta T I have D delta T over + + + align:start position:0% +through by delta T I have D delta T over +deltax S I have a capital R that's going + + align:start position:0% +deltax S I have a capital R that's going + + + align:start position:0% +deltax S I have a capital R that's going +to multiply the + + align:start position:0% +to multiply the + + + align:start position:0% +to multiply the +the that look + + align:start position:0% + + + + align:start position:0% + +right and then what's going to what + + align:start position:0% +right and then what's going to what + + + align:start position:0% +right and then what's going to what +multiplies the center guy the + + align:start position:0% + + + + align:start position:0% + +ujn well that's where the the time + + align:start position:0% +ujn well that's where the the time + + + align:start position:0% +ujn well that's where the the time +difference comes over there's the usual + + align:start position:0% +difference comes over there's the usual + + + align:start position:0% +difference comes over there's the usual +one then from + + align:start position:0% +one then from + + + align:start position:0% +one then from +this difference this upwind difference + + align:start position:0% +this difference this upwind difference + + + align:start position:0% +this difference this upwind difference +it's there's a minus at the center term + + align:start position:0% +it's there's a minus at the center term + + + align:start position:0% +it's there's a minus at the center term +because it's a forward difference so + + align:start position:0% +because it's a forward difference so + + + align:start position:0% +because it's a forward difference so +that will be a minus + + align:start position:0% +that will be a minus + + + align:start position:0% +that will be a minus +r and from this Center difference well + + align:start position:0% +r and from this Center difference well + + + align:start position:0% +r and from this Center difference well +remember that that's a second + + align:start position:0% +remember that that's a second + + + align:start position:0% +remember that that's a second +difference + + align:start position:0% +difference + + + align:start position:0% +difference +so it's there so there's a coefficient + + align:start position:0% +so it's there so there's a coefficient + + + align:start position:0% +so it's there so there's a coefficient +two of the middle term or minus 2 and + + align:start position:0% +two of the middle term or minus 2 and + + + align:start position:0% +two of the middle term or minus 2 and +when I bring the delta T up it's - 2 + + align:start position:0% +when I bring the delta T up it's - 2 + + + align:start position:0% +when I bring the delta T up it's - 2 +capital + + align:start position:0% + + + + align:start position:0% + +r and then the third + + align:start position:0% +r and then the third + + + align:start position:0% +r and then the third +one whatever this last coefficient is is + + align:start position:0% +one whatever this last coefficient is is + + + align:start position:0% +one whatever this last coefficient is is +multiplying u j n minus + + align:start position:0% +multiplying u j n minus + + + align:start position:0% +multiplying u j n minus +one and now where does that come it + + align:start position:0% +one and now where does that come it + + + align:start position:0% +one and now where does that come it +doesn't come from here it doesn't come + + align:start position:0% +doesn't come from here it doesn't come + + + align:start position:0% +doesn't come from here it doesn't come +from the upwind difference I guess it + + align:start position:0% +from the upwind difference I guess it + + + align:start position:0% +from the upwind difference I guess it +only comes from + + align:start position:0% +only comes from + + + align:start position:0% +only comes from +there and it's probably just r + + align:start position:0% + + + + align:start position:0% + +and I guess I would + + align:start position:0% +and I guess I would + + + align:start position:0% +and I guess I would +check any formula like that to be sure + + align:start position:0% +check any formula like that to be sure + + + align:start position:0% +check any formula like that to be sure +that the coefficients add to + + align:start position:0% + + + + align:start position:0% + +one and they + + align:start position:0% +one and they + + + align:start position:0% +one and they +do and why should they why should those + + align:start position:0% +do and why should they why should those + + + align:start position:0% +do and why should they why should those +coefficients add to + + align:start position:0% +coefficients add to + + + align:start position:0% +coefficients add to +one so that's my little test that that + + align:start position:0% +one so that's my little test that that + + + align:start position:0% +one so that's my little test that that +I've got the got it it right they should + + align:start position:0% +I've got the got it it right they should + + + align:start position:0% +I've got the got it it right they should +add to one + + align:start position:0% +add to one + + + align:start position:0% +add to one +because a + + align:start position:0% +because a + + + align:start position:0% +because a +constant initial a con if uj0 is a + + align:start position:0% +constant initial a con if uj0 is a + + + align:start position:0% +constant initial a con if uj0 is a +constant if I'm starting from a constant + + align:start position:0% +constant if I'm starting from a constant + + + align:start position:0% +constant if I'm starting from a constant +function all the it's its X derivatives + + align:start position:0% +function all the it's its X derivatives + + + align:start position:0% +function all the it's its X derivatives +would all be zero if I had U equal + + align:start position:0% +would all be zero if I had U equal + + + align:start position:0% +would all be zero if I had U equal +constant then the X derivatives would be + + align:start position:0% +constant then the X derivatives would be + + + align:start position:0% +constant then the X derivatives would be +zero so the time derivative would be + + align:start position:0% +zero so the time derivative would be + + + align:start position:0% +zero so the time derivative would be +zero so that constant would stay + + align:start position:0% +zero so that constant would stay + + + align:start position:0% +zero so that constant would stay +forever and so I would want to get the + + align:start position:0% +forever and so I would want to get the + + + align:start position:0% +forever and so I would want to get the +same constant out from constants going + + align:start position:0% +same constant out from constants going + + + align:start position:0% +same constant out from constants going +in and so the coefficient should add to + + align:start position:0% +in and so the coefficient should add to + + + align:start position:0% +in and so the coefficient should add to +one + + align:start position:0% +one + + + align:start position:0% +one +okay well + + align:start position:0% +okay well + + + align:start position:0% +okay well +um I can certainly see when I can see a + + align:start position:0% +um I can certainly see when I can see a + + + align:start position:0% +um I can certainly see when I can see a +situation when I know stability will be + + align:start position:0% + + + + align:start position:0% + +okay St stability can't fail if those + + align:start position:0% +okay St stability can't fail if those + + + align:start position:0% +okay St stability can't fail if those +con if those three coefficients are all + + align:start position:0% +con if those three coefficients are all + + + align:start position:0% +con if those three coefficients are all +positive if those three coefficients are + + align:start position:0% +positive if those three coefficients are + + + align:start position:0% +positive if those three coefficients are +all + + align:start position:0% +all + + + align:start position:0% +all +positive then my growth factor can't be + + align:start position:0% +positive then my growth factor can't be + + + align:start position:0% +positive then my growth factor can't be +larger than one those coefficients they + + align:start position:0% +larger than one those coefficients they + + + align:start position:0% +larger than one those coefficients they +add to one so the so the growth factor + + align:start position:0% +add to one so the so the growth factor + + + align:start position:0% +add to one so the so the growth factor +is this times a e should I write it down + + align:start position:0% +is this times a e should I write it down + + + align:start position:0% +is this times a e should I write it down +the growth factor will be this so this + + align:start position:0% +the growth factor will be this so this + + + align:start position:0% +the growth factor will be this so this +will be the growth factor G will be that + + align:start position:0% +will be the growth factor G will be that + + + align:start position:0% +will be the growth factor G will be that +number times e to the i k Delta X from + + align:start position:0% +number times e to the i k Delta X from + + + align:start position:0% +number times e to the i k Delta X from +shifting over one it'll be this number * + + align:start position:0% +shifting over one it'll be this number * + + + align:start position:0% +shifting over one it'll be this number * +1 and it'll be this number time e minus + + align:start position:0% +1 and it'll be this number time e minus + + + align:start position:0% +1 and it'll be this number time e minus +i k Delta X and my point is just that + + align:start position:0% +i k Delta X and my point is just that + + + align:start position:0% +i k Delta X and my point is just that +the the easiest estimate would say well + + align:start position:0% +the the easiest estimate would say well + + + align:start position:0% +the the easiest estimate would say well +this has magnitude one that has + + align:start position:0% +this has magnitude one that has + + + align:start position:0% +this has magnitude one that has +magnitude one that has magnitude one if + + align:start position:0% +magnitude one that has magnitude one if + + + align:start position:0% +magnitude one that has magnitude one if +I just add up magnitudes I'll get this + + align:start position:0% +I just add up magnitudes I'll get this + + + align:start position:0% +I just add up magnitudes I'll get this +qu this one and this one and this one + + align:start position:0% +qu this one and this one and this one + + + align:start position:0% +qu this one and this one and this one +and if they're all positive they add to + + align:start position:0% +and if they're all positive they add to + + + align:start position:0% +and if they're all positive they add to +one I'm safe so what's the stability + + align:start position:0% +one I'm safe so what's the stability + + + align:start position:0% +one I'm safe so what's the stability +condition that this + + align:start position:0% +condition that this + + + align:start position:0% +condition that this +simple argument requires well that's + + align:start position:0% +simple argument requires well that's + + + align:start position:0% +simple argument requires well that's +positive that's positive the danger is + + align:start position:0% +positive that's positive the danger is + + + align:start position:0% +positive that's positive the danger is +this + + align:start position:0% + + + + align:start position:0% + +one so I I guess I would like that to be + + align:start position:0% +one so I I guess I would like that to be + + + align:start position:0% +one so I I guess I would like that to be +positive so I would + + align:start position:0% +positive so I would + + + align:start position:0% +positive so I would +want I'm certainly stable if one if if + + align:start position:0% +want I'm certainly stable if one if if + + + align:start position:0% +want I'm certainly stable if one if if +this is positive which I might as well + + align:start position:0% +this is positive which I might as well + + + align:start position:0% +this is positive which I might as well +write as r + + align:start position:0% +write as r + + + align:start position:0% +write as r +plus 2 Big R being not larger than + + align:start position:0% + + + + align:start position:0% + +one because if that's true I'm taking a + + align:start position:0% +one because if that's true I'm taking a + + + align:start position:0% +one because if that's true I'm taking a +combination of with positive + + align:start position:0% +combination of with positive + + + align:start position:0% +combination of with positive +coefficients adding to one I can't go + + align:start position:0% +coefficients adding to one I can't go + + + align:start position:0% +coefficients adding to one I can't go +wrong okay and in fact that's that's + + align:start position:0% +wrong okay and in fact that's that's + + + align:start position:0% +wrong okay and in fact that's that's +uh pretty familiar cuz that's telling us + + align:start position:0% +uh pretty familiar cuz that's telling us + + + align:start position:0% +uh pretty familiar cuz that's telling us +that well it combines the the two + + align:start position:0% +that well it combines the the two + + + align:start position:0% +that well it combines the the two +conditions we know the condition that R + + align:start position:0% +conditions we know the condition that R + + + align:start position:0% +conditions we know the condition that R +should be less or equal one small R the + + align:start position:0% +should be less or equal one small R the + + + align:start position:0% +should be less or equal one small R the +wave coron Freed's Ley condition and the + + align:start position:0% +wave coron Freed's Ley condition and the + + + align:start position:0% +wave coron Freed's Ley condition and the +condition + + align:start position:0% +condition + + + align:start position:0% +condition +that capital r should be less or equal a + + align:start position:0% +that capital r should be less or equal a + + + align:start position:0% +that capital r should be less or equal a +half the defusion condition now they're + + align:start position:0% +half the defusion condition now they're + + + align:start position:0% +half the defusion condition now they're +both you know now I'm forcing them even + + align:start position:0% +both you know now I'm forcing them even + + + align:start position:0% +both you know now I'm forcing them even +more by saying that the sum has to be + + align:start position:0% +more by saying that the sum has to be + + + align:start position:0% +more by saying that the sum has to be +less or equal + + align:start position:0% +less or equal + + + align:start position:0% +less or equal +one okay + + align:start position:0% + + + + align:start position:0% + +so let + + align:start position:0% + + + + align:start position:0% + +me leave the explicit upwind at this + + align:start position:0% +me leave the explicit upwind at this + + + align:start position:0% +me leave the explicit upwind at this +point and ask you what else what other + + align:start position:0% +point and ask you what else what other + + + align:start position:0% +point and ask you what else what other +method might you want to + + align:start position:0% +method might you want to + + + align:start position:0% +method might you want to +try well it would be natural to think of + + align:start position:0% +try well it would be natural to think of + + + align:start position:0% +try well it would be natural to think of +explicit + + align:start position:0% +explicit + + + align:start position:0% +explicit +centered where you would Center + + align:start position:0% + + + + align:start position:0% + +this and uh we could follow that one + + align:start position:0% +this and uh we could follow that one + + + align:start position:0% +this and uh we could follow that one +through I'll do that I I guess I'll do + + align:start position:0% +through I'll do that I I guess I'll do + + + align:start position:0% +through I'll do that I I guess I'll do +that next time very quickly and the + + align:start position:0% +that next time very quickly and the + + + align:start position:0% +that next time very quickly and the +notes will'll do + + align:start position:0% +notes will'll do + + + align:start position:0% +notes will'll do +it and and I'm not sure which of those + + align:start position:0% +it and and I'm not sure which of those + + + align:start position:0% +it and and I'm not sure which of those +two ways is better + + align:start position:0% +two ways is better + + + align:start position:0% +two ways is better +or you're going to say go + + align:start position:0% +or you're going to say go + + + align:start position:0% +or you're going to say go +implicit and now I'm going to ask all + + align:start position:0% +implicit and now I'm going to ask all + + + align:start position:0% +implicit and now I'm going to ask all +right but what part of it do you want me + + align:start position:0% +right but what part of it do you want me + + + align:start position:0% +right but what part of it do you want me +to make + + align:start position:0% +to make + + + align:start position:0% +to make +implicit shall + + align:start position:0% +implicit shall + + + align:start position:0% +implicit shall +I maybe all I need to make implicit is + + align:start position:0% +I maybe all I need to make implicit is + + + align:start position:0% +I maybe all I need to make implicit is +the heat equation part + + align:start position:0% + + + + align:start position:0% + +and I can keep this explicit + + align:start position:0% + + + + align:start position:0% + +perhaps or and I could even think of + + align:start position:0% +perhaps or and I could even think of + + + align:start position:0% +perhaps or and I could even think of +splitting the + + align:start position:0% +splitting the + + + align:start position:0% +splitting the +step that's something we haven't done I + + align:start position:0% +step that's something we haven't done I + + + align:start position:0% +step that's something we haven't done I +could think of taking a wave step and + + align:start position:0% +could think of taking a wave step and + + + align:start position:0% +could think of taking a wave step and +then a diffusion + + align:start position:0% + + + + align:start position:0% + +step whatever putting them together into + + align:start position:0% +step whatever putting them together into + + + align:start position:0% +step whatever putting them together into +one step where the diffusion step is + + align:start position:0% +one step where the diffusion step is + + + align:start position:0% +one step where the diffusion step is +changed to implicit + + align:start position:0% + + + + align:start position:0% + +because of the great stability that that + + align:start position:0% +because of the great stability that that + + + align:start position:0% +because of the great stability that that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +provides okay I I think you're seeing + + align:start position:0% +provides okay I I think you're seeing + + + align:start position:0% +provides okay I I think you're seeing +the the the reality of of scientific + + align:start position:0% +the the the reality of of scientific + + + align:start position:0% +the the the reality of of scientific +computation even at this uh even at this + + align:start position:0% +computation even at this uh even at this + + + align:start position:0% +computation even at this uh even at this +um fundamental model level of a of a + + align:start position:0% +um fundamental model level of a of a + + + align:start position:0% +um fundamental model level of a of a +model with two uh quite different uh + + align:start position:0% +model with two uh quite different uh + + + align:start position:0% +model with two uh quite different uh +physical effects of motion with finite + + align:start position:0% +physical effects of motion with finite + + + align:start position:0% +physical effects of motion with finite +Speed Energy + + align:start position:0% +Speed Energy + + + align:start position:0% +Speed Energy +preserving magnitude of G tending to be + + align:start position:0% +preserving magnitude of G tending to be + + + align:start position:0% +preserving magnitude of G tending to be +right at one and + + align:start position:0% +right at one and + + + align:start position:0% +right at one and +diffusion at uh infinite + + align:start position:0% + + + + align:start position:0% + +speed giving us + + align:start position:0% +speed giving us + + + align:start position:0% +speed giving us +uh growth factor that tends to be real + + align:start position:0% +uh growth factor that tends to be real + + + align:start position:0% +uh growth factor that tends to be real +and Below one + + align:start position:0% +and Below one + + + align:start position:0% +and Below one +and + + align:start position:0% +and + + + align:start position:0% +and +uh but the price is it pushes us toward + + align:start position:0% +uh but the price is it pushes us toward + + + align:start position:0% +uh but the price is it pushes us toward +implicit + + align:start position:0% +implicit + + + align:start position:0% +implicit +methods okay I think that's really th + + align:start position:0% +methods okay I think that's really th + + + align:start position:0% +methods okay I think that's really th +that this one choice that I've worked + + align:start position:0% +that this one choice that I've worked + + + align:start position:0% +that this one choice that I've worked +through and the others that I've + + align:start position:0% +through and the others that I've + + + align:start position:0% +through and the others that I've +mentioned uh present a real problem I + + align:start position:0% +mentioned uh present a real problem I + + + align:start position:0% +mentioned uh present a real problem I +I'll I'll say another word about those + + align:start position:0% +I'll I'll say another word about those + + + align:start position:0% +I'll I'll say another word about those +about this topic next time and then + + align:start position:0% +about this topic next time and then + + + align:start position:0% +about this topic next time and then +we'll pretty soon move to to nonlinear + + align:start position:0% +we'll pretty soon move to to nonlinear + + + align:start position:0% +we'll pretty soon move to to nonlinear +equations and and + + align:start position:0% +equations and and + + + align:start position:0% +equations and and +and more + + align:start position:0% +and more + + + align:start position:0% +and more +realistic uh more difficult applications + + align:start position:0% +realistic uh more difficult applications + + + align:start position:0% +realistic uh more difficult applications +okay thanks \ No newline at end of file diff --git a/ChYAqW_MnW0.txt b/ChYAqW_MnW0.txt new file mode 100644 index 0000000000000000000000000000000000000000..0541a94dd5b4846468429e40fbb1533d3b55f73d --- /dev/null +++ b/ChYAqW_MnW0.txt @@ -0,0 +1,1619 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation, or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Ladies and gentlemen, +welcome to this + +lecture on nonlinear finite +element analysis of solids and + +structures. + +In this lecture I would like to +discuss with you the total + +Lagrangian formulation of the +two-noded truss element. + +In the previous lecture, we +considered the updated + +Lagrangian formulation +of the same element. + +We started from the general +continuum mechanics equation, + +and obtained the governing +finite element matrices. + +I would like to do the same now +for the total Lagrangian + +formulation. + +And we will see that to find +element matrices are indeed + +the same that we obtained in +the updated Lagrangian + +formulation. + +Here we have the governing +equation of the principle of + +virtual work that we derived +in an earlier lecture. + +This, of course, is a governing +equation that we + +apply to obtain the governing +equation, finite element + +equations, for two or three +dimensional analysis, and also + +for the truss element. + +It's a very general equation +that we discussed earlier in + +great detail. + +We use this equation now +for the truss element. + +And the first point that we have +to look at is what stress + +measure and corresponding +strain measure do we + +need to deal with? + +Now for the truss, it is +important to realize that the + +only non-zero stress is this +stress here, t0 S11. + +In other words, only the 11 +component is non-zero. + +Let us look at this +fact in detail. + +There's first of all, what we +might call a mathematical + +explanation. + +Let us assume, of course, that +the cross-section here is + +constant, the same way as we did +in the discussion of the + +updated Lagrangian +formulation. + +And here we have the element in +its original configuration, + +and the element has undergone +large displacements and large + +rotation to get into this +configuration at time t. + +Notice the length is +almost constant. + +We have an epsilon there. + +That, of course, stands for the +strain that the truss has + +undergone, but that epsilon +is assumed to + +be very, very small. + +We will later on also look at +a similar picture, but this + +red truss element at time t +will have to be moved into + +this configuration here, +starting, in other words, + +starting on the left-hand side +here, we simply move this + +truss element here straight back +so that this node lies on + +top of that node. + +In other words, if I just show +it to you like that, it will + +have rotated like that. + +Notice that as far as the +derivation of the stiffness + +matrix of the truss element in +this configuration, and as far + +as the element force vector +derivation are concerned, it + +does not matter whether we look +at this particular truss + +element in this configuration, +or whether we move it back to + +make this point coincide +with that point. + +Well if we drive using what we +have discussed earlier the + +deformation gradient for this +particular element, we + +recognize that this is the +general expression. + +Notice that X, of course, is +equal to R times U, R being + +the orthogonal matrix, and U +being the stretch matrix. + +Notice that in this X matrix +now, this here really is the R + +component, and the U matrix is +nothing else but the identity + +matrix with an epsilon added +to the 11 component. + +And the product of R times U +gives you then, of course, + +this right-hand side. + +Since the truss carries only +the Cauchy stress, tau11, + +corresponding to the tensile +force in the truss, we can + +directly write down the Cauchy +stress in the stationary + +coordinate frame +as given here. + +This, of course, is nothing +else but a Mohr's circle + +transformation. + +Notice that our truss element +moves through the stationary + +coordinate frame. + +I pointed out earlier very +strongly that we always deal + +with stationary coordinate +frames. + +So this is the expression of +tau, the stress in the truss, + +but written now in the +stationary coordinate frame. + +So we have sheer components +and normal components. + +Of course, if theta's is equal +to 0, then we have only here a + +1, and all of these are the +components drop to 0. + +If we now use our general +formula, that once again we + +discussed earlier, to evaluate +from Cauchy stresses, second + +Piola-Kirchhoff stresses, +we directly + +obtain this result here. + +Since epsilon is small, we +set this equal to 1. + +And we have, indeed, that's +the only non-zero stress + +component in this stress tensor +is the S11 component. + +Well there's also a physical +explanation. + +And that physical explanation +goes as follows. + +We have initially, say, this +situation here in the + +configuration at time zero +where 0S refer to the + +configuration at time 0 is equal +to tau0, and that is + +equal to nothing else than the +initial force in the truss + +divided by the area, 0 +components, of course, here. + +If we now think of first +extending that truss element + +by a very small amount as shown +here, notice that blue + +truss element here corresponds +to the extended truss element. + +It lies really on top of the +black, but in separating it + +slightly out so that you can see +the different coloration. + +Then this blue truss element can +be sort of corresponding + +to, and I'm showing it now up +here, equal to a time T star, + +which is really a +conceptual time. + +We are pulling out the truss +first, and this means of + +course, corresponding to that T +star conceptual time, we can + +write down this equation here. + +Surely there are 0 +components here. + +Now, we start rotating the truss +about the left node, and + +the result is shown +on this U graph. + +Now we have the RAD +configuration, theta is here, + +and the stress tensor +that we are talking + +about has not changed. + +Why has it not changed? + +Well because of this statement +down here, the components of + +the second Piola-Kirchhoff +stress tensor do not change + +doing a rigid body motion, +in particular doing + +a rigid body rotation. + +We discussed this statement +earlier in an earlier lecture. + +It's a very important property +of the second Piola-Kirchhoff + +stress tensor. + +And this means, of course, that +the 0s which we had here + +in blue remains 0's +here in red. + +Very important point. + +Well having identified then that +S11 is the only non-zero + +stress component that we really +need to deal with in + +the general principle of virtual +work, we can directly + +write down this relationship +here. + +It's nothing else than the +application of the general + +equation, which we looked at +earlier, reduced to the + +special form of the truss +element taking only the S11 + +component into account. + +See here, S11, of course, +corresponding strains-- + +eta11, and here we have only +the 11 components as well. + +The next step is to look at what +are the individual terms + +in that equation. + +Recognize that S11 is nothing +else than tP over A. C1111 is + +equal to E. The volume, +of course, is + +given as shown here. + +And of course, we also recognize +that the stress and + +strain states are constant +along the truss. + +Once again, because we're +dealing with two nodes only, + +and we can only have a lean +interpolation of displacement + +between these two nodes, meaning +that the strains must + +be constant, and the +corresponding stresses must be + +constant as well. + +We substitute these things into, +these relationships up + +here, into the equation that +I showed you earlier and we + +directly obtain this equation. + +Notice that in this equation +now, we want to, of course, + +express the strain terms +e11, eta11 in terms of + +displacements, nodal point +displacements. + +And that is achieved as +usual via a strain + +displacement matrix. + +This is the relationship here +corresponding to the linear + +strain increment, and that is +the relationship corresponding + +to the variation on the +nonlinear strain increment. + +Notice again, and I've pointed +it out a number of times + +already earlier, that we write +this right-hand side in such + +way that the right-hand +side is equal to + +the left-hand side. + +Therefore, these BNLs are +defined such that the + +right-hand side is equal +to the left-hand side. + +Also remember, u hat here, this +hat up there, the nodes, + +the [? discrete ?] + +nodal point displacements are +listed in this vector. + +And here they are. + +Notice upper superscript refers +to the nodal point. + +Lower subscript refers to the +directions, the coordinate + +directions that we +are looking at. + +Similarly, of course, for node +two, 2 up there, and + +1 and 2 down here. + +We go back to our general +continuum mechanics relations + +that we discussed earlier, and +identify that the total + +increment in the +Green-Lagrangian strain is + +given via this relationship +here. + +Notice that this relationship +is obtained from the general + +equation of this epsilon 0 IJ. + +Of course, I and J are now +equal to 11 for the truss + +because S11 is the only non-zero +stress that we just + +have been considering earlier. + +So we'll go into our earlier +view graphs, the information + +that we discussed earlier. + +To look up the equation on 0 +epsilon IJ, we set I and J + +equal to 1. + +There is a k also in that +equation if you look back. + +That k goes from 1 to 2 now +because we're looking at the + +two dimensional motion +of the truss. + +If you have a three dimensional +motion, then, of + +course, we would have to let +k go from 1 to 2 to 3. + +Here we have k only going from 1 +to 2, that's why you see the + +2 at the highest +subscript here. + +And automatically, you would +get this equation. + +Notice that the linear part in +here gives us the linear + +strain increment. + +And that the nonlinear part in +here gives us the nonlinear + +strain increment. + +And if we take the variation +on that part, we directly + +obtain this relationship here. + +We like to write this now in +matrix form, and that is + +achieved as shown down here. + +Notice this part, of course, is +nothing else than what we + +have up here written +in matrix form. + +There is, of course, in the +total Lagrangian formulation + +the initial displacement +effect. + +And that initial displacement +fact lies in + +these derivatives here. + +This one and that one. + +And we need to evaluate them. + +We can evaluate them from +kinematics, as shown in this + +picture here. + +Notice that we have moved +the truss now, as + +I pointed out earlier. + +We would do to the nodal point +to coincide such that, I + +should say such that the +nodal points or nodal + +point one has not moved. + +Once again, that is quite OK. + +If we want to derive the +stiffness matrix and force + +vector of the element, because +those quantities are not + +affected by this rigid +body translation. + +Here we have theta, and notice +these are displacements that + +we call delta tU2, delta tU1 +with a negative sign there + +because this displacement would +be measured positive in + +the opposite direction. + +And we can directly see that +this differentiation here is + +nothing else than this +value right here. + +From the kinematics. + +Similar, this differentiation +is nothing else than sin + +theta, once again, from +the kinematics. + +So we have the initial +displacement effect in these + +derivatives, and can evaluate +those as shown by these + +functions here. + +We also want to, of course, +evaluate these derivatives + +here, 0U11, and in fact, +0U2 comma 1. + +And we recognize that, as I +pointed out earlier, the + +strains are constant. + +Therefore, this is a constant +value, and in this + +differentiation it's really +nothing else than this + +relationship here. + +We take the difference in the +nodal point displacement, and + +divide by L. Quite the same +way as we did it for the + +updated Lagrangian +formulation. + +You can, therefore, write down +this differentiation, these + +two derivatives here, as shown +on the right-hand side. + +Now, we are ready to take +these expressions and + +substitute into the right-hand +side of the + +linear strain term. + +Notice that this gives +us one term here, and + +another term there. + +Let's look at these terms. + +This term here comes from +that part there. + +And this term here, down here, +comes from that part there. + +Let's look at this second +term a little closer. + +This here is, of course, the +initial displacement effect. + +All of that I should say +is really the initial + +displacement effect. + +But if these terms are 0 here, +then, of course, initial + +displacement effects drop out. + +So therefore, these two terms +here are the important ones, + +and we can see that they are +written in this vector here. + +We just derived them earlier. + +Notice that this matrix, this +vector here, is given by this + +matrix there multiplied +by the nodal point + +displacement vector. + +And of course, this total here +gives us the initial + +displacement effect, which +is captured in t0BL1. + +The sum of t0BL1 and t0BL0, of +course, gives us a linear + +strain displacement matrix. + +And that summation +is performed on + +this view graph here. + +Notice we have written these +terms once again. + +Of course, if you had to +multiply out in order to get + +t0BL1, the sum of these two +gives us this strain matrix, + +the linear strain displacement +matrix. + +And we now notice that in the +linear strain displacement + +matrix, cosines and +sines of thetas of + +the angle theta appear. + +That is something +to keep in mind. + +For the nonlinear strain +displacement matrix, we look + +at our nonlinear variation on +the nonlinear strain term. + +Here it is on the +left-hand side. + +And we substitute for the +differentations the way we + +have been doing it for the +updated Lagrangian formulation + +of the truss. + +And we recognize, of course, +that this part here is given + +by what is underlined as blue. + +And this part here is given +by, again what's + +underlined in blue. + +And then this part here is the +nonlinear strain displacement + +matrix, the BNL. + +That part right there. + +Well if we now use all this +information, we directly + +obtain the stiffness matrix and +stiffness matrices, and + +force vector off the +truss element. + +We substitute into here from +what we derived earlier, and + +directly obtained +this expression. + +And what's underlined here in +blue is, of course, the linear + +strain stiffness matrix +of the truss element. + +And notice that this linear +strain stiffness matrix is + +identically equal to the linear +strain stiffness matrix + +of the updated Lagrangian +formulation truss element. + +We use this term to obtain +the nonlinear + +strain stiffness matrix. + +And we notice that this +nonlinear strain stiffness + +matrix is identically equal to +what we derived earlier in the + +updated Lagrangian formulation +as well. + +The force vector, the F vector +for the truss element is given + +on this view graph and +is obtained from this + +relationship here. + +Notice it's, once again, +identically equal to the force + +vector of the updated Lagrangian +formulated truss + +element as well. + +And so we notice that to find +all the matrices that we + +obtain in this total Lagrangian +formulation are the + +same matrices that we already +had derived in the updated + +Lagrangian formulation. + +Important point to recognize +is that the coordinate + +transformation used in the U.L. +formulation is contained + +in the initial displacement +effect of the T.L. formation. + +Let's look at that a +little bit closer. + +What this means is that in +the updated Lagrangian + +formulation, we did the +evaluation corresponding to + +the configuration +at time t with a + +local coordinate system. + +And then after that derivation +was performed, we transformed + +the nodal point variables to the +global coordinate system. + +In the total Lagrangian +formulation, we obtain the + +matrices directly corresponding +to the global + +coordinate system through the +initial displacement effect. + +Now, the same can also be shown, +of course, for other + +elements, and we have looked +here, particularly at a + +two-noded beam element. + +And we have asked ourself the +question then which method or + +which formulation is always +more effective? + +If you use numerical +integration, as we might want + +to use for the beam element, +particular we have to use if + +we want to capture +elastoplasticity effects. + +Then clearly, the updated +Lagrangian formulation must be + +more effective because what +you are doing in the total + +Lagrangian formulation is to +carry these cosines and sines + +theta terms along for every +integration that you're + +considering. + +In the numerical integration, +the product of B transpose CB, + +with the B containing the +initial displacement effect + +now, is much more expensive +than the product for the + +updated Lagrangian formulation +where the B does not contain + +this initial displacement +effect. + +So in the updated Lagrangian +formulation, the B matrix is + +much simpler. + +We do the numerical integration +with a simpler B + +matrix along the beam element, +and the details are given in + +this paper. + +And once we have done the +numerical integration, we + +simply transform the nodal point +displacements from the + +local coordinate system. + +The [? coord ?] system, we call +it a [? coord ?] system + +when we discuss the updated +Lagrangian formulation of the + +truss element, and we transform +these nodal point + +displacements to the global +system only once by this t + +transpose kt product. + +So this means then that +certainly for a two-noded beam + +element, the total Lagrangian +formulation is not as + +effective as the updated +Lagrangian formulation, and it + +is very natural to use the +updated Lagrangian formulation + +because you get the same +result in the end. + +For the two-noded truss, of +course, the numerical + +operations involved are so +close, so close, that one can + +really say the updated and total +Lagrangian formulations + +are basically the same. + +Let's now look at an example. + +Here we have a truss, a simple +truss structure. + +And we perform the analysis of +this truss structure using the + +U.L. formulation, the T.L., +total Lagrangian formulation + +would give the same result, +as I just discussed. + +And we want to particularly +calculate the collapse load of + +this truss. + +We also want to test the MNO, +the Materially Nonlinear Only + +formulation. + +The reason for testing this +formulation is to identify + +what differences do occur, and +to understand more clearly the + +U.L. Formulation, as well +as the MNO formulation. + +Notice that for this truss, +the [? geo ?] matrix, the + +geometric data are given here. + +The material data are given +here in this table. + +Notice that, of course, these +nodes dawn here are fixed. + +Notice that we are putting a +load that pulls on the truss, + +P, as shown. + +And that we have two degrees of +freedom, U and V. So it's a + +fairly simple problem, yet there +is quite a bit of meat + +in it when one looks closely +at the solution. + +And that's what we +like to do now. + +We calculate first analytically, +the limit load, + +the elastic limit load. + +In other words, the load for +which the yield point is + +reached in one of the members. + +And in fact, for this particular +load, the side + +trusses just become plastic, +and this is the + +value of that load. + +The ultimate limit load, when +the side trusses are plastic + +and the center truss is plastic +as well, is reached at + +this level. + +If we use an automatic load +stepping incrementation, we + +will discuss that in one of the +next lectures, we obtain + +this response. + +Notice P plotted vertically +here, and V, the displacement + +corresponding to P, plotted +horizontally. + +Notice that we come up here in +the step-by-step solution and + +march along here. + +There are two solutions +given, actually. + +One with v1, very small, +and one with v1 larger. + +This is here the parameters +that we use to start a + +solution algorithm. + +We have to start the solution +algorithm by imposing a small + +value of displacement to a node, +and then the solution + +algorithm can perform +automatically the total + +step-by-step solution. + +We will discuss that in one +of the next lectures. + +And as you see, with the larger +value here, we get + +these discrete points. + +No difficulty solving +for this response. + +Notice also that there's no +difficulty going beyond this + +analytic elastic limit load, +shown here by the blue line. + +If we were to look very closely +at this slope here, we + +would see that it is +slightly positive. + +You can hardly see it +from this graph. + +This is the solution obtained +with the U.L. formulation, + +with the U.L. formulation. + +And once again, the T.L. +formulation would give + +identically the same result. + +We now consider an +MNO analysis. + +MNO means Materially +Nonlinear Only. + +No large displacement +effect included. + +No geometric stiffening +effect included. + +Geometric stiffening, meaning +the effect of the nonlinear + +strain stiffness matrix +being included. + +So we want to use this +formulation, and once again, + +apply the automatic load +stepping incrementation. + +If the stiffness matrix in +that automatic load step + +incrementation is not reformed, +in other words, we + +keep the original stiffness +matrix, then almost identical + +results are obtained to the +U.L. or T.L. formulation + +solution results. + +However, if the stiffness matrix +is reformed in the MNO + +formulation, and for a load +level larger than the elastic + +limit load-- + +remember, the elastic limit load +is quite a bit lower than + +the ultimate limit load-- + +then the structure is found to +be unstable, as 0 pivot is + +obtained in the stiffness +matrix. + +I like to ask the question why +is that so to you now? + +And ask you to just think +a little bit about it. + +A few minutes. + +And then when I come back, I +give you the explanation by + +looking at the problem +once again. + +I'd like to now address the +question that I asked you + +before the break. + +Namely, why, if we use the +MNO formulation do we get + +virtually identically the same +results as in the U.L. + +formulation if we only set up +a stiffness matrix that + +corresponds to a configuration +below the elastic limit load. + +If on the other hand, we setting +up a difference matrix + +above the elastic limit load in +the MNO formulation, then + +we cannot, so it's a problem. + +Well the answer is that as soon +as the two trusses on the + +side have become plastic, the +MNO formulation does not have + +any more stiffness corresponding +to this degree + +of freedom, meaning the matrix +is singular, and we cannot + +solve the system of equations. + +Whereas if we look at the U.L. +formulation, then we see that + +the geometric stiffening effect, +or the KNL effect, the + +nonlinear strain stiffness +effect, introduces the forces + +that are acting in these two +elements into the structure + +into the structure assemblage +as the stiffening part. + +And of course, is a KNL matrix +corresponding to + +this element as well. + +So in other words, these three +KNL matrices corresponding to + +these three elements, these +three truss elements, + +introduce a stiffness into the +total structure assemblage, + +meaning that we can still solve +the system of equations. + +We also notice that these KNL +effect that we are carrying + +along in the U.L. formulation, +when measured on the KL effect + +are rather small. + +And this means that the +response of the U.L. + +formulation calculated with +the U.L. formulation is + +basically the same as the +response calculated with the + +MNO formulation. + +As long, of course, we use +in the MNO formulation a + +stiffness matrix that +corresponds to a configuration + +below the elastic limit load. + +Well this completes +this example. + +Let us look at another +example. + +And in this example, I like to +consider with you a pre-stress + +cable, as shown up here, that +has initially a span of S. And + +we then prescribe on the +right-hand side a displacement + +to this node to bring this node +towards the left, meaning + +that the cable will +sag through. + +We want to calculate the +deformations of the cable, and + +in particular, we want to have +the final deformations when S + +is equal to 30 meters. + +Notice that the cable +carries an initial + +tension of 500 Newton. + +And here we see the other data +corresponding to the cable. + +This, of course, is a + +geometrically nonlinear problem. + +We want to use here the +U.L. formulation. + +And the interesting part is that +to solve this problem we + +have to use relatively small +time steps, or load steps, + +because they're considering +it to be, of + +course, a static solution. + +We need to only allow small +perturbations in the nodal + +point coordinates, because if +we do will allow too large + +perturbations in the nodal point +coordinates, we find + +that the out of balance loads at +the nodes become very large + +and we have difficulties +solving the equation. + +So we use many load steps with +equilibrium iterations so that + +the configuration of the cable +is never far from an + +equilibrium position. + +In this particular problem, we +used full Newton iterations + +without line searches. + +We will talk about this scheme +in detail in the next lecture. + +We use also convergence +criteria because we're + +iterating, we have to break up +that iteration or stop the + +iteration at some point. + +And we will use these two +convergence criteria. + +We consider these convergence +criteria in quite some detail + +in the next lecture. + +Notice that basically we are +saying is that the out of + +balance loads shall be small +enough, and here we have an + +energy criterion that +also has to be-- + +this measure has to be small +enough for convergence. + +Once again, we will talk about +these in detail when we + +consider the solution +of the equation. + +Here we have a table that +summarizes the results. + +In the first time step, puts the +gravity loading onto the + +cable with a mass density that +was given, of course, on the + +earlier view graph. + +And we notice that with this +iterative scheme, we need to + +14 iterations. + +We then from time or load step +2 to 1,001 prescribed the + +displacements in 1,000 equal +steps on the right-hand side + +of the cable. + +And we notice that we need +less than 5 or equal to 5 + +iterations per load step. + +This might appear to +be a fairly large + +number of load steps. + +Of course, one could +now experiment + +and bring this down. + +If you try to bring this +down, this number, of + +course, would go up. + +And one could experiment +around. + +But it shows what kind of +considerations are necessary + +when you solve this problem, +namely that you don't want to + +be too far away from the +equilibrium configuration + +force of the cable in any one of +the load steps, and if you + +are, then, of course, you will +need a large number of + +iterations here, and your +iterative scheme might not + +even converge. + +Pictorally, the results are +shown on this view graph here. + +Notice we have the undeformed +cable here. + +And then with S equal to 55 +meters, the cable takes on + +this configuration with +S equal to 30 meters. + +We see this configuration. + +And if you were to try to bring +this point in further, + +then to model the curvature +down here, of course, + +properly, you would have to have +a finite discretization. + +So this is probably the largest +amount that you want + +to bring this point over +with this particular + +discretization. + +If you were to use a finite +element discretization, this + +curve, of course, would +hardly change. + +And this one here will change +a bit down here. + +But these results are quite +acceptable up to S equal to 30 + +meters with this coarse +discretization. + +And we have learned a bit +from this problem. + +Thank you very much for +your attention. \ No newline at end of file diff --git a/CqJkz9SfGk4.txt b/CqJkz9SfGk4.txt new file mode 100644 index 0000000000000000000000000000000000000000..058116b9cc4021a470b4a0981ddef8e3805e560c --- /dev/null +++ b/CqJkz9SfGk4.txt @@ -0,0 +1,8168 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right this is + + align:start position:0% +ocw.mit.edu all right this is + + + align:start position:0% +ocw.mit.edu all right this is +920 I'm Schneider and this is the first + + align:start position:0% +920 I'm Schneider and this is the first + + + align:start position:0% +920 I'm Schneider and this is the first +class I will just talk briefly about the + + align:start position:0% +class I will just talk briefly about the + + + align:start position:0% +class I will just talk briefly about the +organization of the class the procedures + + align:start position:0% +organization of the class the procedures + + + align:start position:0% +organization of the class the procedures +and the + + align:start position:0% +and the + + + align:start position:0% +and the +assignments and then + + align:start position:0% +assignments and then + + + align:start position:0% +assignments and then +we'll there will be about the last part + + align:start position:0% +we'll there will be about the last part + + + align:start position:0% +we'll there will be about the last part +will just be a talk about various + + align:start position:0% +will just be a talk about various + + + align:start position:0% +will just be a talk about various +approaches study of animal behavior and + + align:start position:0% +approaches study of animal behavior and + + + align:start position:0% +approaches study of animal behavior and +the main ones we'll be using in this + + align:start position:0% + + + + align:start position:0% + +class so why did you sign up for + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +maybe because it's the + + align:start position:0% +maybe because it's the + + + align:start position:0% +maybe because it's the +house class + + align:start position:0% +house class + + + align:start position:0% +house class +uh but there are other half classes + + align:start position:0% +uh but there are other half classes + + + align:start position:0% +uh but there are other half classes +maybe it's your + + align:start position:0% +maybe it's your + + + align:start position:0% +maybe it's your +schedule I make it at 4:00 to decrease + + align:start position:0% +schedule I make it at 4:00 to decrease + + + align:start position:0% +schedule I make it at 4:00 to decrease +schedule conflicts but a few of you + + align:start position:0% +schedule conflicts but a few of you + + + align:start position:0% +schedule conflicts but a few of you +still have them especially with the lab + + align:start position:0% +still have them especially with the lab + + + align:start position:0% +still have them especially with the lab +on Friday how many of you have a lab at + + align:start position:0% +on Friday how many of you have a lab at + + + align:start position:0% +on Friday how many of you have a lab at +this time on + + align:start position:0% +this time on + + + align:start position:0% +this time on +Friday because of that I will I will be + + align:start position:0% +Friday because of that I will I will be + + + align:start position:0% +Friday because of that I will I will be +posting the slides + + align:start position:0% +posting the slides + + + align:start position:0% +posting the slides +um if not before class at least after + + align:start position:0% +um if not before class at least after + + + align:start position:0% +um if not before class at least after +the class and I am I will try to + + align:start position:0% +the class and I am I will try to + + + align:start position:0% +the class and I am I will try to +remember to record the class so I can + + align:start position:0% +remember to record the class so I can + + + align:start position:0% +remember to record the class so I can +post an MB MP3 file of the + + align:start position:0% +post an MB MP3 file of the + + + align:start position:0% +post an MB MP3 file of the +audio there won't be any + + align:start position:0% +audio there won't be any + + + align:start position:0% +audio there won't be any +video uh so you won't know what I'm + + align:start position:0% +video uh so you won't know what I'm + + + align:start position:0% +video uh so you won't know what I'm +pointing at in the uh in the slides but + + align:start position:0% +pointing at in the uh in the slides but + + + align:start position:0% +pointing at in the uh in the slides but +you should be able to make out what we + + align:start position:0% +you should be able to make out what we + + + align:start position:0% +you should be able to make out what we +said you probably won't hear student + + align:start position:0% +said you probably won't hear student + + + align:start position:0% +said you probably won't hear student +questions you will miss miss out on some + + align:start position:0% +questions you will miss miss out on some + + + align:start position:0% +questions you will miss miss out on some +of the discussion that way but you + + align:start position:0% +of the discussion that way but you + + + align:start position:0% +of the discussion that way but you +should still be able to keep up with the + + align:start position:0% + + + + align:start position:0% + +class so there are various practical + + align:start position:0% +class so there are various practical + + + align:start position:0% +class so there are various practical +reasons can anyone give me a + + align:start position:0% +reasons can anyone give me a + + + align:start position:0% +reasons can anyone give me a +non-practical reason for taking + + align:start position:0% +non-practical reason for taking + + + align:start position:0% +non-practical reason for taking +920 why should you be interested in + + align:start position:0% +920 why should you be interested in + + + align:start position:0% +920 why should you be interested in +animal + + align:start position:0% +animal + + + align:start position:0% +animal +behavior + + align:start position:0% + + + + align:start position:0% + +yes okay it might help you with human + + align:start position:0% +yes okay it might help you with human + + + align:start position:0% +yes okay it might help you with human +behavior well we're animals + + align:start position:0% +behavior well we're animals + + + align:start position:0% +behavior well we're animals +that doesn't mean I will stress animals + + align:start position:0% +that doesn't mean I will stress animals + + + align:start position:0% +that doesn't mean I will stress animals +but particularly when we talk actually + + align:start position:0% +but particularly when we talk actually + + + align:start position:0% +but particularly when we talk actually +in both parts of the class when we talk + + align:start position:0% +in both parts of the class when we talk + + + align:start position:0% +in both parts of the class when we talk +about + + align:start position:0% +about + + + align:start position:0% +about +ethology that is fixed action patterns + + align:start position:0% +ethology that is fixed action patterns + + + align:start position:0% +ethology that is fixed action patterns +instinctive behavior and when we talk + + align:start position:0% +instinctive behavior and when we talk + + + align:start position:0% +instinctive behavior and when we talk +about + + align:start position:0% +about + + + align:start position:0% +about +sociobiology adaptive Behavior + + align:start position:0% +sociobiology adaptive Behavior + + + align:start position:0% +sociobiology adaptive Behavior +especially social behavior humans will + + align:start position:0% +especially social behavior humans will + + + align:start position:0% +especially social behavior humans will +come out many + + align:start position:0% +come out many + + + align:start position:0% +come out many +times all right + + align:start position:0% + + + + align:start position:0% + +uh anyway why do I teach it well I think + + align:start position:0% +uh anyway why do I teach it well I think + + + align:start position:0% +uh anyway why do I teach it well I think +animal Behavior fun I have done research + + align:start position:0% +animal Behavior fun I have done research + + + align:start position:0% +animal Behavior fun I have done research +in animal behavior though that's not + + align:start position:0% +in animal behavior though that's not + + + align:start position:0% +in animal behavior though that's not +been the main thrust of my career I am a + + align:start position:0% +been the main thrust of my career I am a + + + align:start position:0% +been the main thrust of my career I am a +neuroscientist and I have done a lot of + + align:start position:0% +neuroscientist and I have done a lot of + + + align:start position:0% +neuroscientist and I have done a lot of +work on brain anatomy and anatomical + + align:start position:0% +work on brain anatomy and anatomical + + + align:start position:0% +work on brain anatomy and anatomical +changes after brain + + align:start position:0% +changes after brain + + + align:start position:0% +changes after brain +damage + + align:start position:0% + + + + align:start position:0% + +but I like animal behavior and I hope + + align:start position:0% +but I like animal behavior and I hope + + + align:start position:0% +but I like animal behavior and I hope +that will be evident as I talk I will + + align:start position:0% +that will be evident as I talk I will + + + align:start position:0% +that will be evident as I talk I will +use examples from my own work as well as + + align:start position:0% +use examples from my own work as well as + + + align:start position:0% +use examples from my own work as well as +from other people's + + align:start position:0% +from other people's + + + align:start position:0% +from other people's +work so it's sort of an undergraduate + + align:start position:0% +work so it's sort of an undergraduate + + + align:start position:0% +work so it's sort of an undergraduate +survey class at the beginning but in the + + align:start position:0% +survey class at the beginning but in the + + + align:start position:0% +survey class at the beginning but in the +second + + align:start position:0% +second + + + align:start position:0% +second +part it'll become more and more a + + align:start position:0% +part it'll become more and more a + + + align:start position:0% +part it'll become more and more a +special topic seminar and that's + + align:start position:0% +special topic seminar and that's + + + align:start position:0% +special topic seminar and that's +especially true the last part of the + + align:start position:0% +especially true the last part of the + + + align:start position:0% +especially true the last part of the +class when you guys will be giving your + + align:start position:0% +class when you guys will be giving your + + + align:start position:0% +class when you guys will be giving your +reports I'm I've already posted on the + + align:start position:0% +reports I'm I've already posted on the + + + align:start position:0% +reports I'm I've already posted on the +Stellar + + align:start position:0% +Stellar + + + align:start position:0% +Stellar +website an + + align:start position:0% +website an + + + align:start position:0% +website an +assignment it's not due until the + + align:start position:0% +assignment it's not due until the + + + align:start position:0% +assignment it's not due until the +Wednesday before the Thanksgiving break + + align:start position:0% +Wednesday before the Thanksgiving break + + + align:start position:0% +Wednesday before the Thanksgiving break +so you have a lot of + + align:start position:0% + + + + align:start position:0% + +time you will make a + + align:start position:0% +time you will make a + + + align:start position:0% +time you will make a +PowerPoint slide + + align:start position:0% +PowerPoint slide + + + align:start position:0% +PowerPoint slide +presentation and then you will prepare + + align:start position:0% +presentation and then you will prepare + + + align:start position:0% +presentation and then you will prepare +yourself to give that presentation + + align:start position:0% +yourself to give that presentation + + + align:start position:0% +yourself to give that presentation +orally your slides will + + align:start position:0% +orally your slides will + + + align:start position:0% +orally your slides will +include notes that will give me more + + align:start position:0% +include notes that will give me more + + + align:start position:0% +include notes that will give me more +detail about what you would like to talk + + align:start position:0% +detail about what you would like to talk + + + align:start position:0% +detail about what you would like to talk +about even if you don't get to talk + + align:start position:0% +about even if you don't get to talk + + + align:start position:0% +about even if you don't get to talk +about all of it in the notes section + + align:start position:0% +about all of it in the notes section + + + align:start position:0% +about all of it in the notes section +whenever you do PowerPoint there's a + + align:start position:0% +whenever you do PowerPoint there's a + + + align:start position:0% +whenever you do PowerPoint there's a +note section that is not shown during a + + align:start position:0% +note section that is not shown during a + + + align:start position:0% +note section that is not shown during a +presentation but you can make lots of + + align:start position:0% +presentation but you can make lots of + + + align:start position:0% +presentation but you can make lots of +notes and that gives me a better idea of + + align:start position:0% +notes and that gives me a better idea of + + + align:start position:0% +notes and that gives me a better idea of +the research you've + + align:start position:0% +the research you've + + + align:start position:0% +the research you've +done okay so read that assignment it's + + align:start position:0% +done okay so read that assignment it's + + + align:start position:0% +done okay so read that assignment it's +not we will let you know if we decide to + + align:start position:0% +not we will let you know if we decide to + + + align:start position:0% +not we will let you know if we decide to +make any alterations after talking with + + align:start position:0% +make any alterations after talking with + + + align:start position:0% +make any alterations after talking with +students and with each + + align:start position:0% + + + + align:start position:0% + +other make sure you check that Stell + + align:start position:0% +other make sure you check that Stell + + + align:start position:0% +other make sure you check that Stell +Stellar site + + align:start position:0% +Stellar site + + + align:start position:0% +Stellar site +regularly uh I will try after every + + align:start position:0% +regularly uh I will try after every + + + align:start position:0% +regularly uh I will try after every +class to make sure I post uh the slides + + align:start position:0% +class to make sure I post uh the slides + + + align:start position:0% +class to make sure I post uh the slides +but before the class I will usually post + + align:start position:0% +but before the class I will usually post + + + align:start position:0% +but before the class I will usually post +study questions the questions + + align:start position:0% +study questions the questions + + + align:start position:0% +study questions the questions +cover class sessions and they cover + + align:start position:0% +cover class sessions and they cover + + + align:start position:0% +cover class sessions and they cover +readings that will be + + align:start position:0% +readings that will be + + + align:start position:0% +readings that will be +assigned usually they don't cover + + align:start position:0% +assigned usually they don't cover + + + align:start position:0% +assigned usually they don't cover +readings that are listed as + + align:start position:0% +readings that are listed as + + + align:start position:0% +readings that are listed as +supplementary readings if you don't have + + align:start position:0% +supplementary readings if you don't have + + + align:start position:0% +supplementary readings if you don't have +time to do the supplementary readings + + align:start position:0% +time to do the supplementary readings + + + align:start position:0% +time to do the supplementary readings +it's all right if it's of particular + + align:start position:0% +it's all right if it's of particular + + + align:start position:0% +it's all right if it's of particular +interest to you you should do them and + + align:start position:0% +interest to you you should do them and + + + align:start position:0% +interest to you you should do them and +it will help you + + align:start position:0% +it will help you + + + align:start position:0% +it will help you +understand uh the + + align:start position:0% + + + + align:start position:0% + +material okay so there's just two small + + align:start position:0% +material okay so there's just two small + + + align:start position:0% +material okay so there's just two small +textbooks I + + align:start position:0% +textbooks I + + + align:start position:0% +textbooks I +choose a smaller book in animal behavior + + align:start position:0% +choose a smaller book in animal behavior + + + align:start position:0% +choose a smaller book in animal behavior +so that we have time to do other kinds + + align:start position:0% +so that we have time to do other kinds + + + align:start position:0% +so that we have time to do other kinds +of + + align:start position:0% +of + + + align:start position:0% +of +readings and uh like you'll be reading + + align:start position:0% +readings and uh like you'll be reading + + + align:start position:0% +readings and uh like you'll be reading +quite a bit of Conrad Lawrence and a + + align:start position:0% +quite a bit of Conrad Lawrence and a + + + align:start position:0% +quite a bit of Conrad Lawrence and a +little bit from nio tinbergen uh to the + + align:start position:0% +little bit from nio tinbergen uh to the + + + align:start position:0% +little bit from nio tinbergen uh to the +classical great + + align:start position:0% +classical great + + + align:start position:0% +classical great +ethologists + + align:start position:0% +ethologists + + + align:start position:0% +ethologists +uh and uh I think you'll + + align:start position:0% +uh and uh I think you'll + + + align:start position:0% +uh and uh I think you'll +appreciate uh their observations when + + align:start position:0% +appreciate uh their observations when + + + align:start position:0% +appreciate uh their observations when +you get them directly we also will see + + align:start position:0% +you get them directly we also will see + + + align:start position:0% +you get them directly we also will see +uh especially Lawrence in videos that we + + align:start position:0% +uh especially Lawrence in videos that we + + + align:start position:0% +uh especially Lawrence in videos that we +show in + + align:start position:0% +show in + + + align:start position:0% +show in +class + + align:start position:0% +class + + + align:start position:0% +class +there will be quizzes and homework and + + align:start position:0% +there will be quizzes and homework and + + + align:start position:0% +there will be quizzes and homework and +almost always these will be on + + align:start position:0% +almost always these will be on + + + align:start position:0% +almost always these will be on +Wednesdays that is if it's homework + + align:start position:0% +Wednesdays that is if it's homework + + + align:start position:0% +Wednesdays that is if it's homework +it'll normally be due on a Wednesday + + align:start position:0% +it'll normally be due on a Wednesday + + + align:start position:0% +it'll normally be due on a Wednesday +once in a while on different date but + + align:start position:0% +once in a while on different date but + + + align:start position:0% +once in a while on different date but +the quizzes I will try to + + align:start position:0% +the quizzes I will try to + + + align:start position:0% +the quizzes I will try to +keep limited to + + align:start position:0% +keep limited to + + + align:start position:0% +keep limited to +Wednesdays we don't always have a quiz + + align:start position:0% +Wednesdays we don't always have a quiz + + + align:start position:0% +Wednesdays we don't always have a quiz +that is in a week where we have homework + + align:start position:0% +that is in a week where we have homework + + + align:start position:0% +that is in a week where we have homework +I might decide not to give the quiz but + + align:start position:0% +I might decide not to give the quiz but + + + align:start position:0% +I might decide not to give the quiz but +we will always let you know in + + align:start position:0% + + + + align:start position:0% + +advance + + align:start position:0% +advance + + + align:start position:0% +advance +okay so first we'll be going through key + + align:start position:0% +okay so first we'll be going through key + + + align:start position:0% +okay so first we'll be going through key +Concepts emphasizing + + align:start position:0% +Concepts emphasizing + + + align:start position:0% +Concepts emphasizing +ethology and we'll talk about what that + + align:start position:0% +ethology and we'll talk about what that + + + align:start position:0% +ethology and we'll talk about what that +is + + align:start position:0% +is + + + align:start position:0% +is +today the readings will be in the Scott + + align:start position:0% +today the readings will be in the Scott + + + align:start position:0% +today the readings will be in the Scott +textbook but they'll also be uh as I + + align:start position:0% +textbook but they'll also be uh as I + + + align:start position:0% +textbook but they'll also be uh as I +mentioned from other + + align:start position:0% +mentioned from other + + + align:start position:0% +mentioned from other +readings and then we'll see some videos + + align:start position:0% +readings and then we'll see some videos + + + align:start position:0% +readings and then we'll see some videos +relevant to to + + align:start position:0% +relevant to to + + + align:start position:0% +relevant to to +ethology and then after the midterm + + align:start position:0% +ethology and then after the midterm + + + align:start position:0% +ethology and then after the midterm +we'll be talking about + + align:start position:0% +we'll be talking about + + + align:start position:0% +we'll be talking about +sociobiology that will be mentioned + + align:start position:0% +sociobiology that will be mentioned + + + align:start position:0% +sociobiology that will be mentioned +today uh as + + align:start position:0% +today uh as + + + align:start position:0% +today uh as +well and we'll have readings the + + align:start position:0% +well and we'll have readings the + + + align:start position:0% +well and we'll have readings the +readings will mainly be a a small book + + align:start position:0% +readings will mainly be a a small book + + + align:start position:0% +readings will mainly be a a small book +by John Alcock it's called the Triumph + + align:start position:0% +by John Alcock it's called the Triumph + + + align:start position:0% +by John Alcock it's called the Triumph +of sociobiology which was a very AP + + align:start position:0% +of sociobiology which was a very AP + + + align:start position:0% +of sociobiology which was a very AP +title it was written a few years ago but + + align:start position:0% +title it was written a few years ago but + + + align:start position:0% +title it was written a few years ago but +in + + align:start position:0% +in + + + align:start position:0% +in +fact it does Express well how + + align:start position:0% +fact it does Express well how + + + align:start position:0% +fact it does Express well how +sociobiology has become a + + align:start position:0% +sociobiology has become a + + + align:start position:0% +sociobiology has become a +major uh force in studies of animal + + align:start position:0% + + + + align:start position:0% + +behavior and I will go over some of the + + align:start position:0% +behavior and I will go over some of the + + + align:start position:0% +behavior and I will go over some of the +key ideas of EO Wilson some of them + + align:start position:0% +key ideas of EO Wilson some of them + + + align:start position:0% +key ideas of EO Wilson some of them +directly from his + + align:start position:0% + + + + align:start position:0% + +writings these are as examples of + + align:start position:0% +writings these are as examples of + + + align:start position:0% +writings these are as examples of +specific topics most of you have seen + + align:start position:0% +specific topics most of you have seen + + + align:start position:0% +specific topics most of you have seen +these kinds of things if you've had any + + align:start position:0% +these kinds of things if you've had any + + + align:start position:0% +these kinds of things if you've had any +encounter with animal + + align:start position:0% +encounter with animal + + + align:start position:0% +encounter with animal +behavior uh some of them might sound a + + align:start position:0% +behavior uh some of them might sound a + + + align:start position:0% +behavior uh some of them might sound a +little bit you know we use specialized + + align:start position:0% +little bit you know we use specialized + + + align:start position:0% +little bit you know we use specialized +language to talk about behavior and it's + + align:start position:0% +language to talk about behavior and it's + + + align:start position:0% +language to talk about behavior and it's +a little different from what you're used + + align:start position:0% +a little different from what you're used + + + align:start position:0% +a little different from what you're used +to from just + + align:start position:0% +to from just + + + align:start position:0% +to from just +talking about human behavior we talk + + align:start position:0% +talking about human behavior we talk + + + align:start position:0% +talking about human behavior we talk +about eating and animal behavior talk + + align:start position:0% +about eating and animal behavior talk + + + align:start position:0% +about eating and animal behavior talk +about feeding and foraging and stalking + + align:start position:0% +about feeding and foraging and stalking + + + align:start position:0% +about feeding and foraging and stalking +and prey capture and things like that we + + align:start position:0% +and prey capture and things like that we + + + align:start position:0% +and prey capture and things like that we +talk about anti-predator Behavior do + + align:start position:0% +talk about anti-predator Behavior do + + + align:start position:0% +talk about anti-predator Behavior do +humans show anti-predator Behavior you + + align:start position:0% +humans show anti-predator Behavior you + + + align:start position:0% +humans show anti-predator Behavior you +bet they do but we don't usually call it + + align:start position:0% +bet they do but we don't usually call it + + + align:start position:0% +bet they do but we don't usually call it +that + + align:start position:0% +that + + + align:start position:0% +that +okay since we don't have too many tigers + + align:start position:0% +okay since we don't have too many tigers + + + align:start position:0% +okay since we don't have too many tigers +and lines roaming the streets around + + align:start position:0% +and lines roaming the streets around + + + align:start position:0% +and lines roaming the streets around +here + + align:start position:0% +here + + + align:start position:0% +here +anymore uh terms for SE sexuality are + + align:start position:0% +anymore uh terms for SE sexuality are + + + align:start position:0% +anymore uh terms for SE sexuality are +used of course in human behavior and in + + align:start position:0% +used of course in human behavior and in + + + align:start position:0% +used of course in human behavior and in +animal + + align:start position:0% +animal + + + align:start position:0% +animal +behavior and that will be a little more + + align:start position:0% +behavior and that will be a little more + + + align:start position:0% +behavior and that will be a little more +familiar to you but more specialized + + align:start position:0% +familiar to you but more specialized + + + align:start position:0% +familiar to you but more specialized +terms will occur + + align:start position:0% +terms will occur + + + align:start position:0% +terms will occur +there uh these are examples you can read + + align:start position:0% +there uh these are examples you can read + + + align:start position:0% +there uh these are examples you can read +those other things I listed uh these are + + align:start position:0% +those other things I listed uh these are + + + align:start position:0% +those other things I listed uh these are +examples of questions and Concepts will + + align:start position:0% +examples of questions and Concepts will + + + align:start position:0% +examples of questions and Concepts will +that will come + + align:start position:0% +that will come + + + align:start position:0% +that will come +up we'll talk about what instinctive + + align:start position:0% +up we'll talk about what instinctive + + + align:start position:0% +up we'll talk about what instinctive +behavior is what a fixed action pattern + + align:start position:0% +behavior is what a fixed action pattern + + + align:start position:0% +behavior is what a fixed action pattern +is + + align:start position:0% +is + + + align:start position:0% +is +fix action patterns is it's an + + align:start position:0% +fix action patterns is it's an + + + align:start position:0% +fix action patterns is it's an +ethological term for instinctive + + align:start position:0% +ethological term for instinctive + + + align:start position:0% +ethological term for instinctive +Behavior but it's actually fairly + + align:start position:0% +Behavior but it's actually fairly + + + align:start position:0% +Behavior but it's actually fairly +complex but there's a regular pattern in + + align:start position:0% +complex but there's a regular pattern in + + + align:start position:0% +complex but there's a regular pattern in +in most of these + + align:start position:0% +in most of these + + + align:start position:0% +in most of these +behaviors uh they're not the same as + + align:start position:0% +behaviors uh they're not the same as + + + align:start position:0% +behaviors uh they're not the same as +reflexes and we will make that very + + align:start position:0% +reflexes and we will make that very + + + align:start position:0% +reflexes and we will make that very +clear in the + + align:start position:0% +clear in the + + + align:start position:0% +clear in the +class why do animals why do some animals + + align:start position:0% +class why do animals why do some animals + + + align:start position:0% +class why do animals why do some animals +migrate halfway around the earth just to + + align:start position:0% +migrate halfway around the earth just to + + + align:start position:0% +migrate halfway around the earth just to +made + + align:start position:0% +made + + + align:start position:0% +made +and rais + + align:start position:0% +and rais + + + align:start position:0% +and rais +young what is the evolutionary origin of + + align:start position:0% +young what is the evolutionary origin of + + + align:start position:0% +young what is the evolutionary origin of +kissing do animals kiss yes they do and + + align:start position:0% +kissing do animals kiss yes they do and + + + align:start position:0% +kissing do animals kiss yes they do and +it has its origins in animal behavior + + align:start position:0% +it has its origins in animal behavior + + + align:start position:0% +it has its origins in animal behavior +and it has been + + align:start position:0% +and it has been + + + align:start position:0% +and it has been +traced + + align:start position:0% +traced + + + align:start position:0% +traced +uh pretty + + align:start position:0% +uh pretty + + + align:start position:0% +uh pretty +convincingly why do animal behaviorists + + align:start position:0% +convincingly why do animal behaviorists + + + align:start position:0% +convincingly why do animal behaviorists +engage in genan + + align:start position:0% +engage in genan + + + align:start position:0% +engage in genan +County why would they have to do that + + align:start position:0% +County why would they have to do that + + + align:start position:0% +County why would they have to do that +it's related to a question down here why + + align:start position:0% +it's related to a question down here why + + + align:start position:0% +it's related to a question down here why +might a work the last one why might a + + align:start position:0% +might a work the last one why might a + + + align:start position:0% +might a work the last one why might a +worker ant behave differently depending + + align:start position:0% +worker ant behave differently depending + + + align:start position:0% +worker ant behave differently depending +on whether it mother + + align:start position:0% +on whether it mother + + + align:start position:0% +on whether it mother +Queen is promiscuous or + + align:start position:0% + + + + align:start position:0% + +monogamous it makes a difference they + + align:start position:0% +monogamous it makes a difference they + + + align:start position:0% +monogamous it makes a difference they +behave + + align:start position:0% +behave + + + align:start position:0% +behave +differently the question is + + align:start position:0% + + + + align:start position:0% + +why that why question has different + + align:start position:0% +why that why question has different + + + align:start position:0% +why that why question has different +levels it can be approximate question + + align:start position:0% +levels it can be approximate question + + + align:start position:0% +levels it can be approximate question +that is what stimuli is he responding to + + align:start position:0% +that is what stimuli is he responding to + + + align:start position:0% +that is what stimuli is he responding to +you know what what are the mechanisms of + + align:start position:0% +you know what what are the mechanisms of + + + align:start position:0% +you know what what are the mechanisms of +the behavior or it could be what we call + + align:start position:0% +the behavior or it could be what we call + + + align:start position:0% +the behavior or it could be what we call +an ultimate question which is not a + + align:start position:0% +an ultimate question which is not a + + + align:start position:0% +an ultimate question which is not a +theological term here ultimate question + + align:start position:0% +theological term here ultimate question + + + align:start position:0% +theological term here ultimate question +in this class simply means what is the + + align:start position:0% +in this class simply means what is the + + + align:start position:0% +in this class simply means what is the +evolutionary significance why what makes + + align:start position:0% +evolutionary significance why what makes + + + align:start position:0% +evolutionary significance why what makes +it + + align:start position:0% +it + + + align:start position:0% +it +adaptive for the an to behave in the way + + align:start position:0% +adaptive for the an to behave in the way + + + align:start position:0% +adaptive for the an to behave in the way +he does it's the major issue in + + align:start position:0% + + + + align:start position:0% + +sociobiology what's a darwinian puzzle + + align:start position:0% +sociobiology what's a darwinian puzzle + + + align:start position:0% +sociobiology what's a darwinian puzzle +behaviors appear that are difficult at + + align:start position:0% +behaviors appear that are difficult at + + + align:start position:0% +behaviors appear that are difficult at +least at the beginning to explain in + + align:start position:0% +least at the beginning to explain in + + + align:start position:0% +least at the beginning to explain in +terms of darwinian evolution we can't + + align:start position:0% +terms of darwinian evolution we can't + + + align:start position:0% +terms of darwinian evolution we can't +figure out how they're adapted so + + align:start position:0% +figure out how they're adapted so + + + align:start position:0% +figure out how they're adapted so +they're a puzzle we call them darwinian + + align:start position:0% + + + + align:start position:0% + +puzzles why is the killing of + + align:start position:0% +puzzles why is the killing of + + + align:start position:0% +puzzles why is the killing of +infants adaptive in some + + align:start position:0% +infants adaptive in some + + + align:start position:0% +infants adaptive in some +animals how could that ever be + + align:start position:0% +animals how could that ever be + + + align:start position:0% +animals how could that ever be +adaptive you should be able to explain + + align:start position:0% +adaptive you should be able to explain + + + align:start position:0% +adaptive you should be able to explain +that and we will do that in the + + align:start position:0% +that and we will do that in the + + + align:start position:0% +that and we will do that in the +class now some of your projects will be + + align:start position:0% +class now some of your projects will be + + + align:start position:0% +class now some of your projects will be +on topics we cover in the class but not + + align:start position:0% +on topics we cover in the class but not + + + align:start position:0% +on topics we cover in the class but not +all of + + align:start position:0% +all of + + + align:start position:0% +all of +them in fact most of them will not be + + align:start position:0% +them in fact most of them will not be + + + align:start position:0% +them in fact most of them will not be +directly on any details that I bring up + + align:start position:0% +directly on any details that I bring up + + + align:start position:0% +directly on any details that I bring up +in the + + align:start position:0% +in the + + + align:start position:0% +in the +class but I do expect you when you're + + align:start position:0% +class but I do expect you when you're + + + align:start position:0% +class but I do expect you when you're +dealing with the animal behaviors that + + align:start position:0% +dealing with the animal behaviors that + + + align:start position:0% +dealing with the animal behaviors that +you want to discuss in your reports I + + align:start position:0% +you want to discuss in your reports I + + + align:start position:0% +you want to discuss in your reports I +expect you to interpret them in terms of + + align:start position:0% +expect you to interpret them in terms of + + + align:start position:0% +expect you to interpret them in terms of +the principles and concepts of ethology + + align:start position:0% +the principles and concepts of ethology + + + align:start position:0% +the principles and concepts of ethology +and sociobiology that you learn in the + + align:start position:0% + + + + align:start position:0% + +class okay what do I + + align:start position:0% +class okay what do I + + + align:start position:0% +class okay what do I +expect outside of class + + align:start position:0% +expect outside of class + + + align:start position:0% +expect outside of class +readings study question + + align:start position:0% +readings study question + + + align:start position:0% +readings study question +questions I will post these study + + align:start position:0% +questions I will post these study + + + align:start position:0% +questions I will post these study +questions for every class I want you to + + align:start position:0% +questions for every class I want you to + + + align:start position:0% +questions for every class I want you to +try to answer them if possible at least + + align:start position:0% +try to answer them if possible at least + + + align:start position:0% +try to answer them if possible at least +some of them before the + + align:start position:0% +some of them before the + + + align:start position:0% +some of them before the +class I might just ask you sometimes + + align:start position:0% +class I might just ask you sometimes + + + align:start position:0% +class I might just ask you sometimes +some of these + + align:start position:0% +some of these + + + align:start position:0% +some of these +questions and I might not tell you who + + align:start position:0% +questions and I might not tell you who + + + align:start position:0% +questions and I might not tell you who +I'm going to + + align:start position:0% +I'm going to + + + align:start position:0% +I'm going to +ask + + align:start position:0% +ask + + + align:start position:0% +ask +otherwise you know you might say well I + + align:start position:0% +otherwise you know you might say well I + + + align:start position:0% +otherwise you know you might say well I +might as well be passive I can read it + + align:start position:0% +might as well be passive I can read it + + + align:start position:0% +might as well be passive I can read it +later but I find that when you say that + + align:start position:0% +later but I find that when you say that + + + align:start position:0% +later but I find that when you say that +it means usually you won't read it + + align:start position:0% +it means usually you won't read it + + + align:start position:0% +it means usually you won't read it +you'll try just to get + + align:start position:0% +you'll try just to get + + + align:start position:0% +you'll try just to get +it what I say in class and hope that + + align:start position:0% +it what I say in class and hope that + + + align:start position:0% +it what I say in class and hope that +gets you by no you will do much better + + align:start position:0% +gets you by no you will do much better + + + align:start position:0% +gets you by no you will do much better +if you + + align:start position:0% + + + + align:start position:0% + +read so read just for key Concepts there + + align:start position:0% +read so read just for key Concepts there + + + align:start position:0% +read so read just for key Concepts there +will be a lot of examples details of + + align:start position:0% +will be a lot of examples details of + + + align:start position:0% +will be a lot of examples details of +animal behavior but at least try to get + + align:start position:0% +animal behavior but at least try to get + + + align:start position:0% +animal behavior but at least try to get +the key ideas and that's what I'll be + + align:start position:0% +the key ideas and that's what I'll be + + + align:start position:0% +the key ideas and that's what I'll be +emphasizing I will try to if you think + + align:start position:0% +emphasizing I will try to if you think + + + align:start position:0% +emphasizing I will try to if you think +I'm talking about some detail that's not + + align:start position:0% +I'm talking about some detail that's not + + + align:start position:0% +I'm talking about some detail that's not +a key concept you let me know + + align:start position:0% +a key concept you let me know + + + align:start position:0% +a key concept you let me know +maybe some aspects of animal behavior + + align:start position:0% +maybe some aspects of animal behavior + + + align:start position:0% +maybe some aspects of animal behavior +are just I just find them + + align:start position:0% +are just I just find them + + + align:start position:0% +are just I just find them +fascinating okay I posted and some of + + align:start position:0% +fascinating okay I posted and some of + + + align:start position:0% +fascinating okay I posted and some of +you have seen this we've been looking at + + align:start position:0% +you have seen this we've been looking at + + + align:start position:0% +you have seen this we've been looking at +the Stellar site I posted quite a while + + align:start position:0% +the Stellar site I posted quite a while + + + align:start position:0% +the Stellar site I posted quite a while +ago a first reading from a book by Jim + + align:start position:0% +ago a first reading from a book by Jim + + + align:start position:0% +ago a first reading from a book by Jim +Corbett Corbett was not an ethologist + + align:start position:0% +Corbett Corbett was not an ethologist + + + align:start position:0% +Corbett Corbett was not an ethologist +and he was not a sociobiologist he was + + align:start position:0% +and he was not a sociobiologist he was + + + align:start position:0% +and he was not a sociobiologist he was +actually a + + align:start position:0% +actually a + + + align:start position:0% +actually a +hunter he was often hired to track down + + align:start position:0% +hunter he was often hired to track down + + + align:start position:0% +hunter he was often hired to track down +and kill manaing tigers and + + align:start position:0% +and kill manaing tigers and + + + align:start position:0% +and kill manaing tigers and +lions in Asia and in + + align:start position:0% +lions in Asia and in + + + align:start position:0% +lions in Asia and in +Africa he was probably the best of + + align:start position:0% +Africa he was probably the best of + + + align:start position:0% +Africa he was probably the best of +hunters that did that kind of thing and + + align:start position:0% +hunters that did that kind of thing and + + + align:start position:0% +hunters that did that kind of thing and +he was also an amateur + + align:start position:0% +he was also an amateur + + + align:start position:0% +he was also an amateur +naturalist and he's written some things + + align:start position:0% +naturalist and he's written some things + + + align:start position:0% +naturalist and he's written some things +about his uh hunting methods and I've + + align:start position:0% +about his uh hunting methods and I've + + + align:start position:0% +about his uh hunting methods and I've +posted some things about what he his + + align:start position:0% +posted some things about what he his + + + align:start position:0% +posted some things about what he his +his knowledge that display his knowledge + + align:start position:0% +his knowledge that display his knowledge + + + align:start position:0% +his knowledge that display his knowledge +about what he calls sensitivity to the + + align:start position:0% +about what he calls sensitivity to the + + + align:start position:0% +about what he calls sensitivity to the +Jungle the signs of the + + align:start position:0% +Jungle the signs of the + + + align:start position:0% +Jungle the signs of the +Jungle a good naturalist learns those + + align:start position:0% +Jungle a good naturalist learns those + + + align:start position:0% +Jungle a good naturalist learns those +kinds of + + align:start position:0% +kinds of + + + align:start position:0% +kinds of +things so please read that uh you'll be + + align:start position:0% +things so please read that uh you'll be + + + align:start position:0% +things so please read that uh you'll be +asked about it in the first + + align:start position:0% + + + + align:start position:0% + +homework I've written the first homework + + align:start position:0% +homework I've written the first homework + + + align:start position:0% +homework I've written the first homework +but I will wait for feedback from the + + align:start position:0% +but I will wait for feedback from the + + + align:start position:0% +but I will wait for feedback from the +teaching assistants before I finalize + + align:start position:0% +teaching assistants before I finalize + + + align:start position:0% +teaching assistants before I finalize +that + + align:start position:0% +that + + + align:start position:0% +that +it won't be due until a week from + + align:start position:0% + + + + align:start position:0% + +today so for the next + + align:start position:0% +today so for the next + + + align:start position:0% +today so for the next +session there's I posted the first + + align:start position:0% +session there's I posted the first + + + align:start position:0% +session there's I posted the first +chapter of Graham Scott in case you + + align:start position:0% +chapter of Graham Scott in case you + + + align:start position:0% +chapter of Graham Scott in case you +don't have it but I won't be posting + + align:start position:0% +don't have it but I won't be posting + + + align:start position:0% +don't have it but I won't be posting +later Scott readings since you're + + align:start position:0% +later Scott readings since you're + + + align:start position:0% +later Scott readings since you're +supposed to get that + + align:start position:0% +supposed to get that + + + align:start position:0% +supposed to get that +book but I do post I I did post chapter + + align:start position:0% +book but I do post I I did post chapter + + + align:start position:0% +book but I do post I I did post chapter +11 from Timber's + + align:start position:0% +11 from Timber's + + + align:start position:0% +11 from Timber's +book uh it's his semi- poopular book + + align:start position:0% +book uh it's his semi- poopular book + + + align:start position:0% +book uh it's his semi- poopular book +curious + + align:start position:0% +curious + + + align:start position:0% +curious +naturalists and uh I've posted study + + align:start position:0% +naturalists and uh I've posted study + + + align:start position:0% +naturalists and uh I've posted study +questions already on those readings as + + align:start position:0% +questions already on those readings as + + + align:start position:0% +questions already on those readings as +well as some for today's + + align:start position:0% + + + + align:start position:0% + +session okay these are things we've + + align:start position:0% +session okay these are things we've + + + align:start position:0% +session okay these are things we've +talked about so how have we learned + + align:start position:0% +talked about so how have we learned + + + align:start position:0% +talked about so how have we learned +about animals of course many of you have + + align:start position:0% +about animals of course many of you have + + + align:start position:0% +about animals of course many of you have +pets and have made some of your hobbies + + align:start position:0% +pets and have made some of your hobbies + + + align:start position:0% +pets and have made some of your hobbies +concern animals + + align:start position:0% +concern animals + + + align:start position:0% +concern animals +uh you've encountered animals in the + + align:start position:0% +uh you've encountered animals in the + + + align:start position:0% +uh you've encountered animals in the +natural world or at you've gone to + + align:start position:0% +natural world or at you've gone to + + + align:start position:0% +natural world or at you've gone to +Zoological + + align:start position:0% +Zoological + + + align:start position:0% +Zoological +Parks you've certainly encountered them + + align:start position:0% +Parks you've certainly encountered them + + + align:start position:0% +Parks you've certainly encountered them +in some + + align:start position:0% +in some + + + align:start position:0% +in some +films + + align:start position:0% +films + + + align:start position:0% +films +but we also picked them up from common + + align:start position:0% +but we also picked them up from common + + + align:start position:0% +but we also picked them up from common +beliefs we call folklore about animals + + align:start position:0% +beliefs we call folklore about animals + + + align:start position:0% +beliefs we call folklore about animals +there's a long history about + + align:start position:0% +there's a long history about + + + align:start position:0% +there's a long history about +that you can pick up in a + + align:start position:0% +that you can pick up in a + + + align:start position:0% +that you can pick up in a +library these books that appeared in the + + align:start position:0% +library these books that appeared in the + + + align:start position:0% +library these books that appeared in the +middle ages they're called the medieval + + align:start position:0% +middle ages they're called the medieval + + + align:start position:0% +middle ages they're called the medieval +be beastiaries or they they + + align:start position:0% +be beastiaries or they they + + + align:start position:0% +be beastiaries or they they +portray animals in a fantastic way and + + align:start position:0% +portray animals in a fantastic way and + + + align:start position:0% +portray animals in a fantastic way and +the reason + + align:start position:0% +the reason + + + align:start position:0% +the reason +was they heard stories that came from + + align:start position:0% +was they heard stories that came from + + + align:start position:0% +was they heard stories that came from +observations of African and Asian + + align:start position:0% +observations of African and Asian + + + align:start position:0% +observations of African and Asian +animals that they didn't have in + + align:start position:0% +animals that they didn't have in + + + align:start position:0% +animals that they didn't have in +Europe and these were stories in Europe + + align:start position:0% +Europe and these were stories in Europe + + + align:start position:0% +Europe and these were stories in Europe +and they because they were second third + + align:start position:0% +and they because they were second third + + + align:start position:0% +and they because they were second third +and fourth hand stories they were often + + align:start position:0% +and fourth hand stories they were often + + + align:start position:0% +and fourth hand stories they were often +greatly EX exaggerated and + + align:start position:0% +greatly EX exaggerated and + + + align:start position:0% +greatly EX exaggerated and +distorted but and it was commonly + + align:start position:0% +distorted but and it was commonly + + + align:start position:0% +distorted but and it was commonly +believed that in the Middle Ages people + + align:start position:0% +believed that in the Middle Ages people + + + align:start position:0% +believed that in the Middle Ages people +just didn't have any accur accurate + + align:start position:0% +just didn't have any accur accurate + + + align:start position:0% +just didn't have any accur accurate +ideas about animal behavior at all but + + align:start position:0% +ideas about animal behavior at all but + + + align:start position:0% +ideas about animal behavior at all but +recent scholarship in that field has + + align:start position:0% +recent scholarship in that field has + + + align:start position:0% +recent scholarship in that field has +shown that even though that may have + + align:start position:0% +shown that even though that may have + + + align:start position:0% +shown that even though that may have +been common folklore it was not + + align:start position:0% +been common folklore it was not + + + align:start position:0% +been common folklore it was not +generally representative of what was + + align:start position:0% +generally representative of what was + + + align:start position:0% +generally representative of what was +known uh the people who were really + + align:start position:0% +known uh the people who were really + + + align:start position:0% +known uh the people who were really +interested in details of animal behavior + + align:start position:0% +interested in details of animal behavior + + + align:start position:0% +interested in details of animal behavior +even in the Middle Ages and there was a + + align:start position:0% +even in the Middle Ages and there was a + + + align:start position:0% +even in the Middle Ages and there was a +lot more known + + align:start position:0% +lot more known + + + align:start position:0% +lot more known +you why would you expect people to know + + align:start position:0% +you why would you expect people to know + + + align:start position:0% +you why would you expect people to know +about animals in some realistic terms + + align:start position:0% +about animals in some realistic terms + + + align:start position:0% +about animals in some realistic terms +even even a long time ago even before + + align:start position:0% +even even a long time ago even before + + + align:start position:0% +even even a long time ago even before +the Middle + + align:start position:0% +the Middle + + + align:start position:0% +the Middle +Ages why would you expect + + align:start position:0% +Ages why would you expect + + + align:start position:0% +Ages why would you expect +it well think of + + align:start position:0% +it well think of + + + align:start position:0% +it well think of +farming if you're going to raise animals + + align:start position:0% +farming if you're going to raise animals + + + align:start position:0% +farming if you're going to raise animals +or use animals for work you have to + + align:start position:0% +or use animals for work you have to + + + align:start position:0% +or use animals for work you have to +understand something about their + + align:start position:0% + + + + align:start position:0% + +behavior dogs have been + + align:start position:0% +behavior dogs have been + + + align:start position:0% +behavior dogs have been +domesticated + + align:start position:0% +domesticated + + + align:start position:0% +domesticated +uh probably well before people could + + align:start position:0% +uh probably well before people could + + + align:start position:0% +uh probably well before people could +write okay + + align:start position:0% +write okay + + + align:start position:0% +write okay +so really goes back into prehistory and + + align:start position:0% +so really goes back into prehistory and + + + align:start position:0% +so really goes back into prehistory and +uh certainly uh people knew a lot + + align:start position:0% +uh certainly uh people knew a lot + + + align:start position:0% +uh certainly uh people knew a lot +about the domesticated wolves that we + + align:start position:0% +about the domesticated wolves that we + + + align:start position:0% +about the domesticated wolves that we +call + + align:start position:0% + + + + align:start position:0% + +dogs stories that in the folklore that + + align:start position:0% +dogs stories that in the folklore that + + + align:start position:0% +dogs stories that in the folklore that +still abound especially in cities + + align:start position:0% +still abound especially in cities + + + align:start position:0% +still abound especially in cities +concern rats + + align:start position:0% +concern rats + + + align:start position:0% +concern rats +and uh whole books have been written + + align:start position:0% +and uh whole books have been written + + + align:start position:0% +and uh whole books have been written +about that I have one of them here + + align:start position:0% +about that I have one of them here + + + align:start position:0% +about that I have one of them here +called more cunning than man it's + + align:start position:0% +called more cunning than man it's + + + align:start position:0% +called more cunning than man it's +basically three stories about + + align:start position:0% +basically three stories about + + + align:start position:0% +basically three stories about +rats uh it's not written by a scientist + + align:start position:0% +rats uh it's not written by a scientist + + + align:start position:0% +rats uh it's not written by a scientist +he's interested in reports newspaper + + align:start position:0% +he's interested in reports newspaper + + + align:start position:0% +he's interested in reports newspaper +reports uh what people say the stories + + align:start position:0% +reports uh what people say the stories + + + align:start position:0% +reports uh what people say the stories +they pass + + align:start position:0% +they pass + + + align:start position:0% +they pass +on and the stories about rats are most + + align:start position:0% +on and the stories about rats are most + + + align:start position:0% +on and the stories about rats are most +amazing you know there's stories about + + align:start position:0% +amazing you know there's stories about + + + align:start position:0% +amazing you know there's stories about +giant rats when you hear the story you'd + + align:start position:0% +giant rats when you hear the story you'd + + + align:start position:0% +giant rats when you hear the story you'd +swear the rat must be as big as a dog at + + align:start position:0% +swear the rat must be as big as a dog at + + + align:start position:0% +swear the rat must be as big as a dog at +least and + + align:start position:0% +least and + + + align:start position:0% +least and +uh stories about the incredible harm and + + align:start position:0% +uh stories about the incredible harm and + + + align:start position:0% +uh stories about the incredible harm and +the fact is they have caused incredible + + align:start position:0% +the fact is they have caused incredible + + + align:start position:0% +the fact is they have caused incredible +harm and that's one reason rats are + + align:start position:0% +harm and that's one reason rats are + + + align:start position:0% +harm and that's one reason rats are +often hated and feared now of course in + + align:start position:0% +often hated and feared now of course in + + + align:start position:0% +often hated and feared now of course in +a department like this they're used in + + align:start position:0% +a department like this they're used in + + + align:start position:0% +a department like this they're used in +the + + align:start position:0% +the + + + align:start position:0% +the +laboratory uh we don't look at rats that + + align:start position:0% +laboratory uh we don't look at rats that + + + align:start position:0% +laboratory uh we don't look at rats that +way at all but if if you're in New York + + align:start position:0% +way at all but if if you're in New York + + + align:start position:0% +way at all but if if you're in New York +and you're in a poor area and your + + align:start position:0% +and you're in a poor area and your + + + align:start position:0% +and you're in a poor area and your +building is infested with rats then it's + + align:start position:0% +building is infested with rats then it's + + + align:start position:0% +building is infested with rats then it's +a different + + align:start position:0% +a different + + + align:start position:0% +a different +story they uh they they have attack + + align:start position:0% +story they uh they they have attack + + + align:start position:0% +story they uh they they have attack +people damage them at + + align:start position:0% +people damage them at + + + align:start position:0% +people damage them at +night uh but probably the things that + + align:start position:0% +night uh but probably the things that + + + align:start position:0% +night uh but probably the things that +have made Rats the least popular is the + + align:start position:0% +have made Rats the least popular is the + + + align:start position:0% +have made Rats the least popular is the +diseases they have spread or in been + + align:start position:0% +diseases they have spread or in been + + + align:start position:0% +diseases they have spread or in been +some way responsible for the spread of + + align:start position:0% +some way responsible for the spread of + + + align:start position:0% +some way responsible for the spread of +diseases like shagas disease there's uh + + align:start position:0% +diseases like shagas disease there's uh + + + align:start position:0% +diseases like shagas disease there's uh +the book covers a lot of that and one of + + align:start position:0% +the book covers a lot of that and one of + + + align:start position:0% +the book covers a lot of that and one of +the + + align:start position:0% +the + + + align:start position:0% +the +uh there's there's quite a few diseases + + align:start position:0% +uh there's there's quite a few diseases + + + align:start position:0% +uh there's there's quite a few diseases +like that that rats have been involved + + align:start position:0% +like that that rats have been involved + + + align:start position:0% +like that that rats have been involved +in spreading but the one that is + + align:start position:0% +in spreading but the one that is + + + align:start position:0% +in spreading but the one that is +commonly attributed to rats is the the + + align:start position:0% +commonly attributed to rats is the the + + + align:start position:0% +commonly attributed to rats is the the +diseases that have caused the + + align:start position:0% +diseases that have caused the + + + align:start position:0% +diseases that have caused the +worst uh pandemics in human history what + + align:start position:0% +worst uh pandemics in human history what + + + align:start position:0% +worst uh pandemics in human history what +am I talking about what were the worst + + align:start position:0% +am I talking about what were the worst + + + align:start position:0% +am I talking about what were the worst +pandemics that killed a third of the + + align:start position:0% +pandemics that killed a third of the + + + align:start position:0% +pandemics that killed a third of the +population of + + align:start position:0% +population of + + + align:start position:0% +population of +Europe that + + align:start position:0% +Europe that + + + align:start position:0% +Europe that +killed probably more than 30 million + + align:start position:0% +killed probably more than 30 million + + + align:start position:0% +killed probably more than 30 million +people in + + align:start position:0% +people in + + + align:start position:0% +people in +Asia large numbers in + + align:start position:0% + + + + align:start position:0% + +Africa what do we call that + + align:start position:0% +Africa what do we call that + + + align:start position:0% +Africa what do we call that +disease the plague bubonic plague + + align:start position:0% + + + + align:start position:0% + +it was a horrible disease and there was + + align:start position:0% +it was a horrible disease and there was + + + align:start position:0% +it was a horrible disease and there was +no way to cure it so people tried + + align:start position:0% +no way to cure it so people tried + + + align:start position:0% +no way to cure it so people tried +various ways they had great fear of it + + align:start position:0% +various ways they had great fear of it + + + align:start position:0% +various ways they had great fear of it +many people thought the world was coming + + align:start position:0% +many people thought the world was coming + + + align:start position:0% +many people thought the world was coming +to an end during that period when they + + align:start position:0% +to an end during that period when they + + + align:start position:0% +to an end during that period when they +saw everybody in a + + align:start position:0% +saw everybody in a + + + align:start position:0% +saw everybody in a +building + + align:start position:0% + + + + align:start position:0% + +die children invented nursery rhymes in + + align:start position:0% +die children invented nursery rhymes in + + + align:start position:0% +die children invented nursery rhymes in +in their play singing about you know you + + align:start position:0% +in their play singing about you know you + + + align:start position:0% +in their play singing about you know you +know Ring Around the Rosie pocket full + + align:start position:0% +know Ring Around the Rosie pocket full + + + align:start position:0% +know Ring Around the Rosie pocket full +of + + align:start position:0% +of + + + align:start position:0% +of +posies why were they putting flowers in + + align:start position:0% +posies why were they putting flowers in + + + align:start position:0% +posies why were they putting flowers in +their pocket to counter the smell of + + align:start position:0% + + + + align:start position:0% + +death we make it a game now children you + + align:start position:0% +death we make it a game now children you + + + align:start position:0% +death we make it a game now children you +know I'm talk the game ends you know We + + align:start position:0% +know I'm talk the game ends you know We + + + align:start position:0% +know I'm talk the game ends you know We +All Fall Down that was + + align:start position:0% +All Fall Down that was + + + align:start position:0% +All Fall Down that was +dying the children turned it into a + + align:start position:0% +dying the children turned it into a + + + align:start position:0% +dying the children turned it into a +game + + align:start position:0% +game + + + align:start position:0% +game +uh but what how were rats + + align:start position:0% +uh but what how were rats + + + align:start position:0% +uh but what how were rats +involved what animals what + + align:start position:0% +involved what animals what + + + align:start position:0% +involved what animals what +really now we know it's a certain + + align:start position:0% +really now we know it's a certain + + + align:start position:0% +really now we know it's a certain +organism that causes it but what was the + + align:start position:0% +organism that causes it but what was the + + + align:start position:0% +organism that causes it but what was the +vector was it + + align:start position:0% + + + + align:start position:0% + +rats Excuse + + align:start position:0% +rats Excuse + + + align:start position:0% +rats Excuse +me yes it was the fleas on the rats and + + align:start position:0% +me yes it was the fleas on the rats and + + + align:start position:0% +me yes it was the fleas on the rats and +rats + + align:start position:0% +rats + + + align:start position:0% +rats +died and and when they + + align:start position:0% +died and and when they + + + align:start position:0% +died and and when they +died there they lost body heat children + + align:start position:0% +died there they lost body heat children + + + align:start position:0% +died there they lost body heat children +would sometimes play with the dead + + align:start position:0% + + + + align:start position:0% + +rats and the as the body heat dropped + + align:start position:0% +rats and the as the body heat dropped + + + align:start position:0% +rats and the as the body heat dropped +the the fleas would leave the dying body + + align:start position:0% +the the fleas would leave the dying body + + + align:start position:0% +the the fleas would leave the dying body +and jump on anything any warm live body + + align:start position:0% +and jump on anything any warm live body + + + align:start position:0% +and jump on anything any warm live body +which have often was + + align:start position:0% +which have often was + + + align:start position:0% +which have often was +children or other human beings and it + + align:start position:0% +children or other human beings and it + + + align:start position:0% +children or other human beings and it +was the fleas that were spreading the + + align:start position:0% +was the fleas that were spreading the + + + align:start position:0% +was the fleas that were spreading the +disease but people didn't know + + align:start position:0% +disease but people didn't know + + + align:start position:0% +disease but people didn't know +that and + + align:start position:0% +that and + + + align:start position:0% +that and +so they blamed various things some areas + + align:start position:0% +so they blamed various things some areas + + + align:start position:0% +so they blamed various things some areas +they killed every + + align:start position:0% +they killed every + + + align:start position:0% +they killed every +dog because they blamed dogs or + + align:start position:0% +dog because they blamed dogs or + + + align:start position:0% +dog because they blamed dogs or +cats or they + + align:start position:0% +cats or they + + + align:start position:0% +cats or they +blamed if you're in one country you + + align:start position:0% +blamed if you're in one country you + + + align:start position:0% +blamed if you're in one country you +blame the neighboring + + align:start position:0% +blame the neighboring + + + align:start position:0% +blame the neighboring +countries or in many cases it was + + align:start position:0% +countries or in many cases it was + + + align:start position:0% +countries or in many cases it was +blaming an ethnic group or blaming Jews + + align:start position:0% +blaming an ethnic group or blaming Jews + + + align:start position:0% +blaming an ethnic group or blaming Jews +it was horrible because they were + + align:start position:0% +it was horrible because they were + + + align:start position:0% +it was horrible because they were +desperate and + + align:start position:0% + + + + align:start position:0% + +ignorant and of course the way that + + align:start position:0% +ignorant and of course the way that + + + align:start position:0% +ignorant and of course the way that +disease has been controlled is through + + align:start position:0% +disease has been controlled is through + + + align:start position:0% +disease has been controlled is through +better hygiene and better + + align:start position:0% + + + + align:start position:0% + +knowledge anyway I just point out here + + align:start position:0% +knowledge anyway I just point out here + + + align:start position:0% +knowledge anyway I just point out here +not all Ro rodents are hated as much as + + align:start position:0% +not all Ro rodents are hated as much as + + + align:start position:0% +not all Ro rodents are hated as much as +rats we still have hamsters and Geral + + align:start position:0% +rats we still have hamsters and Geral + + + align:start position:0% +rats we still have hamsters and Geral +which are cute little rodents and used + + align:start position:0% +which are cute little rodents and used + + + align:start position:0% +which are cute little rodents and used +as pets as well as in some + + align:start position:0% +as pets as well as in some + + + align:start position:0% +as pets as well as in some +research and we know we use animals for + + align:start position:0% +research and we know we use animals for + + + align:start position:0% +research and we know we use animals for +various things so we know about them + + align:start position:0% +various things so we know about them + + + align:start position:0% +various things so we know about them +that way we use them for meat we use + + align:start position:0% +that way we use them for meat we use + + + align:start position:0% +that way we use them for meat we use +them to make + + align:start position:0% +them to make + + + align:start position:0% +them to make +leather + + align:start position:0% +leather + + + align:start position:0% +leather +uh uh we use them in + + align:start position:0% +uh uh we use them in + + + align:start position:0% +uh uh we use them in +sports for hunting and to helpess + + align:start position:0% +sports for hunting and to helpess + + + align:start position:0% +sports for hunting and to helpess +hunting we don't hunt dogs we use dogs + + align:start position:0% +hunting we don't hunt dogs we use dogs + + + align:start position:0% +hunting we don't hunt dogs we use dogs +to hunt other animals they're used in + + align:start position:0% +to hunt other animals they're used in + + + align:start position:0% +to hunt other animals they're used in +some religions as you + + align:start position:0% +some religions as you + + + align:start position:0% +some religions as you +know uh but we use them in science what + + align:start position:0% +know uh but we use them in science what + + + align:start position:0% +know uh but we use them in science what +what are they in + + align:start position:0% +what are they in + + + align:start position:0% +what are they in +science they are standin for humans + + align:start position:0% +science they are standin for humans + + + align:start position:0% +science they are standin for humans +usually we use them as models of course + + align:start position:0% +usually we use them as models of course + + + align:start position:0% +usually we use them as models of course +the most popular animal now for that is + + align:start position:0% +the most popular animal now for that is + + + align:start position:0% +the most popular animal now for that is +the mouse because of the genetic + + align:start position:0% +the mouse because of the genetic + + + align:start position:0% +the mouse because of the genetic +variance uh and the ease of uh + + align:start position:0% +variance uh and the ease of uh + + + align:start position:0% +variance uh and the ease of uh +creating specific models of pathologies + + align:start position:0% +creating specific models of pathologies + + + align:start position:0% +creating specific models of pathologies +by altering + + align:start position:0% + + + + align:start position:0% + +genes but when we're using animals we're + + align:start position:0% +genes but when we're using animals we're + + + align:start position:0% +genes but when we're using animals we're +often depending on behavioral + + align:start position:0% +often depending on behavioral + + + align:start position:0% +often depending on behavioral +tests and what are we + + align:start position:0% +tests and what are we + + + align:start position:0% +tests and what are we +studying we're studying a human + + align:start position:0% +studying we're studying a human + + + align:start position:0% +studying we're studying a human +disease but to understand what we're + + align:start position:0% +disease but to understand what we're + + + align:start position:0% +disease but to understand what we're +really doing we need to know something + + align:start position:0% +really doing we need to know something + + + align:start position:0% +really doing we need to know something +about animal + + align:start position:0% +about animal + + + align:start position:0% +about animal +behavior and unfortunately a lot of + + align:start position:0% +behavior and unfortunately a lot of + + + align:start position:0% +behavior and unfortunately a lot of +people using animals all the time don't + + align:start position:0% +people using animals all the time don't + + + align:start position:0% +people using animals all the time don't +know much about animal + + align:start position:0% +know much about animal + + + align:start position:0% +know much about animal +behavior we also know about them + + align:start position:0% +behavior we also know about them + + + align:start position:0% +behavior we also know about them +from groups like The Human Humane + + align:start position:0% +from groups like The Human Humane + + + align:start position:0% +from groups like The Human Humane +Society and the animal rights + + align:start position:0% +Society and the animal rights + + + align:start position:0% +Society and the animal rights +movement it's human oriented in a very + + align:start position:0% +movement it's human oriented in a very + + + align:start position:0% +movement it's human oriented in a very +different way sometimes with very + + align:start position:0% +different way sometimes with very + + + align:start position:0% +different way sometimes with very +anthropomorphic + + align:start position:0% +anthropomorphic + + + align:start position:0% +anthropomorphic +thinking sometimes it's more anthropo + + align:start position:0% +thinking sometimes it's more anthropo + + + align:start position:0% +thinking sometimes it's more anthropo +mentis think thinking their thinking + + align:start position:0% +mentis think thinking their thinking + + + align:start position:0% +mentis think thinking their thinking +must be like our thinking their feelings + + align:start position:0% +must be like our thinking their feelings + + + align:start position:0% +must be like our thinking their feelings +must be like our feelings I'm not + + align:start position:0% +must be like our feelings I'm not + + + align:start position:0% +must be like our feelings I'm not +arguing that they're + + align:start position:0% +arguing that they're + + + align:start position:0% +arguing that they're +not we know they have nervous systems if + + align:start position:0% +not we know they have nervous systems if + + + align:start position:0% +not we know they have nervous systems if +they're mammals that are very similar to + + align:start position:0% + + + + align:start position:0% + +ours + + align:start position:0% +ours + + + align:start position:0% +ours +but we think of them commonly as being + + align:start position:0% +but we think of them commonly as being + + + align:start position:0% +but we think of them commonly as being +conscious and I + + align:start position:0% +conscious and I + + + align:start position:0% +conscious and I +would argue that that's probably the + + align:start position:0% +would argue that that's probably the + + + align:start position:0% +would argue that that's probably the +case it's not the same as our + + align:start position:0% +case it's not the same as our + + + align:start position:0% +case it's not the same as our +Consciousness + + align:start position:0% +Consciousness + + + align:start position:0% +Consciousness +but we know it arises in nervous + + align:start position:0% +but we know it arises in nervous + + + align:start position:0% +but we know it arises in nervous +activity I'm not saying we can explain + + align:start position:0% +activity I'm not saying we can explain + + + align:start position:0% +activity I'm not saying we can explain +it by nervous activity but it's + + align:start position:0% +it by nervous activity but it's + + + align:start position:0% +it by nervous activity but it's +correlated with it and animals have that + + align:start position:0% + + + + align:start position:0% + +too different religions have very + + align:start position:0% +too different religions have very + + + align:start position:0% +too different religions have very +different attit itude so I'm sure some + + align:start position:0% +different attit itude so I'm sure some + + + align:start position:0% +different attit itude so I'm sure some +of you that are parts of different Rel + + align:start position:0% +of you that are parts of different Rel + + + align:start position:0% +of you that are parts of different Rel +or follow different religions uh if you + + align:start position:0% +or follow different religions uh if you + + + align:start position:0% +or follow different religions uh if you +do know some of these + + align:start position:0% +do know some of these + + + align:start position:0% +do know some of these +extremes on the one pole you have + + align:start position:0% +extremes on the one pole you have + + + align:start position:0% +extremes on the one pole you have +Judaism and Christianity that believe in + + align:start position:0% +Judaism and Christianity that believe in + + + align:start position:0% +Judaism and Christianity that believe in +control of nature dominance of Nature + + align:start position:0% +control of nature dominance of Nature + + + align:start position:0% +control of nature dominance of Nature +and so forth and then you have examples + + align:start position:0% +and so forth and then you have examples + + + align:start position:0% +and so forth and then you have examples +like + + align:start position:0% +like + + + align:start position:0% +like +jism where they they're totally Pacific + + align:start position:0% +jism where they they're totally Pacific + + + align:start position:0% +jism where they they're totally Pacific +and don't believe in harming any + + align:start position:0% +and don't believe in harming any + + + align:start position:0% +and don't believe in harming any +life and we've had examples of that in + + align:start position:0% +life and we've had examples of that in + + + align:start position:0% +life and we've had examples of that in +West too like Albert schwitzer was like + + align:start position:0% +West too like Albert schwitzer was like + + + align:start position:0% +West too like Albert schwitzer was like +that but in this class we take a basic + + align:start position:0% +that but in this class we take a basic + + + align:start position:0% +that but in this class we take a basic +science approach it will be descriptive + + align:start position:0% +science approach it will be descriptive + + + align:start position:0% +science approach it will be descriptive +and + + align:start position:0% +and + + + align:start position:0% +and +experimental and uh we will use the + + align:start position:0% +experimental and uh we will use the + + + align:start position:0% +experimental and uh we will use the +perspective of evolution throughout most + + align:start position:0% +perspective of evolution throughout most + + + align:start position:0% +perspective of evolution throughout most +of the + + align:start position:0% + + + + align:start position:0% + +class scientific work has focused + + align:start position:0% +class scientific work has focused + + + align:start position:0% +class scientific work has focused +on individual organisms we'll talk about + + align:start position:0% +on individual organisms we'll talk about + + + align:start position:0% +on individual organisms we'll talk about +that first it's focused on + + align:start position:0% +that first it's focused on + + + align:start position:0% +that first it's focused on +societies so we'll talk about that next + + align:start position:0% +societies so we'll talk about that next + + + align:start position:0% +societies so we'll talk about that next +but it's also had other focuses like on + + align:start position:0% +but it's also had other focuses like on + + + align:start position:0% +but it's also had other focuses like on +the habitat and the species in the + + align:start position:0% + + + + align:start position:0% + +habitat uh and the + + align:start position:0% +habitat uh and the + + + align:start position:0% +habitat uh and the +interactions of all living + + align:start position:0% +interactions of all living + + + align:start position:0% +interactions of all living +things that's with the non-living things + + align:start position:0% +things that's with the non-living things + + + align:start position:0% +things that's with the non-living things +in that particular habitat interactions + + align:start position:0% +in that particular habitat interactions + + + align:start position:0% +in that particular habitat interactions +with + + align:start position:0% +with + + + align:start position:0% +with +climate the topography and so forth and + + align:start position:0% +climate the topography and so forth and + + + align:start position:0% +climate the topography and so forth and +then there's sciences that Focus on a + + align:start position:0% +then there's sciences that Focus on a + + + align:start position:0% +then there's sciences that Focus on a +single species or group of species you + + align:start position:0% +single species or group of species you + + + align:start position:0% +single species or group of species you +have mology for example that deal + + align:start position:0% +have mology for example that deal + + + align:start position:0% +have mology for example that deal +generally with all aspects of mamals + + align:start position:0% +generally with all aspects of mamals + + + align:start position:0% +generally with all aspects of mamals +including + + align:start position:0% +including + + + align:start position:0% +including +Behavior Behavior Anatomy physiology and + + align:start position:0% +Behavior Behavior Anatomy physiology and + + + align:start position:0% +Behavior Behavior Anatomy physiology and +so forth or + + align:start position:0% +so forth or + + + align:start position:0% +so forth or +primatology dealing with primates as a + + align:start position:0% +primatology dealing with primates as a + + + align:start position:0% +primatology dealing with primates as a +group a major + + align:start position:0% +group a major + + + align:start position:0% +group a major +field but not we don't call it + + align:start position:0% +field but not we don't call it + + + align:start position:0% +field but not we don't call it +primatology within say experimental + + align:start position:0% +primatology within say experimental + + + align:start position:0% +primatology within say experimental +psychology generally but it's used that + + align:start position:0% +psychology generally but it's used that + + + align:start position:0% +psychology generally but it's used that +way and uh among anthropologists and + + align:start position:0% +way and uh among anthropologists and + + + align:start position:0% +way and uh among anthropologists and +others and then of course we have the + + align:start position:0% +others and then of course we have the + + + align:start position:0% +others and then of course we have the +amateur + + align:start position:0% +amateur + + + align:start position:0% +amateur +naturalists disciplined + + align:start position:0% +naturalists disciplined + + + align:start position:0% +naturalists disciplined +hobbyists and that's important in this + + align:start position:0% +hobbyists and that's important in this + + + align:start position:0% +hobbyists and that's important in this +field just like it has been in astronomy + + align:start position:0% +field just like it has been in astronomy + + + align:start position:0% +field just like it has been in astronomy +because they've made major + + align:start position:0% +because they've made major + + + align:start position:0% +because they've made major +contributions in fact it was amateur + + align:start position:0% +contributions in fact it was amateur + + + align:start position:0% +contributions in fact it was amateur +naturalists that led to the initial + + align:start position:0% +naturalists that led to the initial + + + align:start position:0% +naturalists that led to the initial +discoveries that led to the whole + + align:start position:0% +discoveries that led to the whole + + + align:start position:0% +discoveries that led to the whole +development of + + align:start position:0% +development of + + + align:start position:0% +development of +ethology so first of all focus on the + + align:start position:0% +ethology so first of all focus on the + + + align:start position:0% +ethology so first of all focus on the +individual + + align:start position:0% +individual + + + align:start position:0% +individual +organism in America it was called in the + + align:start position:0% +organism in America it was called in the + + + align:start position:0% +organism in America it was called in the +last century comparative psychology it's + + align:start position:0% +last century comparative psychology it's + + + align:start position:0% +last century comparative psychology it's +sometimes still called + + align:start position:0% +sometimes still called + + + align:start position:0% +sometimes still called +that uh the real Focus was on humans but + + align:start position:0% +that uh the real Focus was on humans but + + + align:start position:0% +that uh the real Focus was on humans but +they used animals uh their main the main + + align:start position:0% +they used animals uh their main the main + + + align:start position:0% +they used animals uh their main the main +type of study in the Heyday of that + + align:start position:0% +type of study in the Heyday of that + + + align:start position:0% +type of study in the Heyday of that +field in the middle of the last century + + align:start position:0% +field in the middle of the last century + + + align:start position:0% +field in the middle of the last century +was studies of learning and it still + + align:start position:0% +was studies of learning and it still + + + align:start position:0% +was studies of learning and it still +is uh in many Labs uh + + align:start position:0% +is uh in many Labs uh + + + align:start position:0% +is uh in many Labs uh +the animals used are mostly rats and + + align:start position:0% +the animals used are mostly rats and + + + align:start position:0% +the animals used are mostly rats and +mice as models for studying + + align:start position:0% + + + + align:start position:0% + +learning and that's it's interesting + + align:start position:0% +learning and that's it's interesting + + + align:start position:0% +learning and that's it's interesting +that that was not the approach to animal + + align:start position:0% +that that was not the approach to animal + + + align:start position:0% +that that was not the approach to animal +behavior in + + align:start position:0% +behavior in + + + align:start position:0% +behavior in +Europe at that same + + align:start position:0% + + + + align:start position:0% + +time why do you think that + + align:start position:0% +time why do you think that + + + align:start position:0% +time why do you think that +was well think of what was unique about + + align:start position:0% +was well think of what was unique about + + + align:start position:0% +was well think of what was unique about +what was going on in America what was + + align:start position:0% +what was going on in America what was + + + align:start position:0% +what was going on in America what was +our approach to + + align:start position:0% + + + + align:start position:0% + +education the idea + + align:start position:0% +education the idea + + + align:start position:0% +education the idea +was that we start life with pretty much + + align:start position:0% +was that we start life with pretty much + + + align:start position:0% +was that we start life with pretty much +a blank + + align:start position:0% +a blank + + + align:start position:0% +a blank +slate and by + + align:start position:0% +slate and by + + + align:start position:0% +slate and by +education we can create + + align:start position:0% +education we can create + + + align:start position:0% +education we can create +individuals we can influence individuals + + align:start position:0% +individuals we can influence individuals + + + align:start position:0% +individuals we can influence individuals +in very way various ways our children + + align:start position:0% +in very way various ways our children + + + align:start position:0% +in very way various ways our children +can become + + align:start position:0% +can become + + + align:start position:0% +can become +whatever they can become just through + + align:start position:0% +whatever they can become just through + + + align:start position:0% +whatever they can become just through +learning through making the + + align:start position:0% +learning through making the + + + align:start position:0% +learning through making the +effort you can do anything if you just + + align:start position:0% +effort you can do anything if you just + + + align:start position:0% +effort you can do anything if you just +put your mind to it how many of you have + + align:start position:0% +put your mind to it how many of you have + + + align:start position:0% +put your mind to it how many of you have +heard that from your parents most of us + + align:start position:0% +heard that from your parents most of us + + + align:start position:0% +heard that from your parents most of us +you + + align:start position:0% +you + + + align:start position:0% +you +know did you ever ever hear well you + + align:start position:0% +know did you ever ever hear well you + + + align:start position:0% +know did you ever ever hear well you +behave that way because you've inherited + + align:start position:0% +behave that way because you've inherited + + + align:start position:0% +behave that way because you've inherited +that behavior and that's your instinct + + align:start position:0% +that behavior and that's your instinct + + + align:start position:0% +that behavior and that's your instinct +no if you were in Europe it was very + + align:start position:0% +no if you were in Europe it was very + + + align:start position:0% +no if you were in Europe it was very +different okay but that was the belief + + align:start position:0% +different okay but that was the belief + + + align:start position:0% +different okay but that was the belief +in America it was + + align:start position:0% +in America it was + + + align:start position:0% +in America it was +wrong but it was also + + align:start position:0% +wrong but it was also + + + align:start position:0% +wrong but it was also +very beneficial because what did it lead + + align:start position:0% +very beneficial because what did it lead + + + align:start position:0% +very beneficial because what did it lead +to it led to Universal + + align:start position:0% + + + + align:start position:0% + +education arguably the best in the world + + align:start position:0% +education arguably the best in the world + + + align:start position:0% +education arguably the best in the world +the country that tried to educate + + align:start position:0% +the country that tried to educate + + + align:start position:0% +the country that tried to educate +everybody regardless of Origins + + align:start position:0% +everybody regardless of Origins + + + align:start position:0% +everybody regardless of Origins +regardless of + + align:start position:0% +regardless of + + + align:start position:0% +regardless of +wealth okay and that at the time that + + align:start position:0% +wealth okay and that at the time that + + + align:start position:0% +wealth okay and that at the time that +developed was + + align:start position:0% +developed was + + + align:start position:0% +developed was +unique and uh it's not we're not the + + align:start position:0% +unique and uh it's not we're not the + + + align:start position:0% +unique and uh it's not we're not the +only country that does that now but at + + align:start position:0% +only country that does that now but at + + + align:start position:0% +only country that does that now but at +that time it certainly was and it was + + align:start position:0% + + + + align:start position:0% + +encouraged in its popularity by ideas of + + align:start position:0% +encouraged in its popularity by ideas of + + + align:start position:0% +encouraged in its popularity by ideas of +Educators I used John Dewey as an + + align:start position:0% +Educators I used John Dewey as an + + + align:start position:0% +Educators I used John Dewey as an +example his dates are 1859 to 1952 he + + align:start position:0% +example his dates are 1859 to 1952 he + + + align:start position:0% +example his dates are 1859 to 1952 he +was very + + align:start position:0% + + + + align:start position:0% + +influential the emphasis was on + + align:start position:0% +influential the emphasis was on + + + align:start position:0% +influential the emphasis was on +practicality and the shaping of the + + align:start position:0% +practicality and the shaping of the + + + align:start position:0% +practicality and the shaping of the +individual through + + align:start position:0% +individual through + + + align:start position:0% +individual through +learning very important in the + + align:start position:0% +learning very important in the + + + align:start position:0% +learning very important in the +development of Educational Systems in + + align:start position:0% +development of Educational Systems in + + + align:start position:0% +development of Educational Systems in +America + + align:start position:0% + + + + align:start position:0% + +and either implicitly or explicitly they + + align:start position:0% +and either implicitly or explicitly they + + + align:start position:0% +and either implicitly or explicitly they +believe that we start life with a blank + + align:start position:0% +believe that we start life with a blank + + + align:start position:0% +believe that we start life with a blank +slate and that was the what came out of + + align:start position:0% +slate and that was the what came out of + + + align:start position:0% +slate and that was the what came out of +that in + + align:start position:0% +that in + + + align:start position:0% +that in +Psychology including this comparative + + align:start position:0% +Psychology including this comparative + + + align:start position:0% +Psychology including this comparative +psychology I'm talking + + align:start position:0% +psychology I'm talking + + + align:start position:0% +psychology I'm talking +about uh is that same idea they focus + + align:start position:0% +about uh is that same idea they focus + + + align:start position:0% +about uh is that same idea they focus +their whole effort on + + align:start position:0% +their whole effort on + + + align:start position:0% +their whole effort on +learning almost nothing on instinctive + + align:start position:0% +learning almost nothing on instinctive + + + align:start position:0% +learning almost nothing on instinctive +Behavior Behavior unless they wanted + + align:start position:0% +Behavior Behavior unless they wanted + + + align:start position:0% +Behavior Behavior unless they wanted +that that was the realm of the + + align:start position:0% +that that was the realm of the + + + align:start position:0% +that that was the realm of the +physiologist and who studied + + align:start position:0% + + + + align:start position:0% + +reflexes they didn't study more complex + + align:start position:0% +reflexes they didn't study more complex + + + align:start position:0% +reflexes they didn't study more complex +instinctive behavior that we'll be + + align:start position:0% +instinctive behavior that we'll be + + + align:start position:0% +instinctive behavior that we'll be +talking about in this + + align:start position:0% + + + + align:start position:0% + +class and so theorists arose who tried + + align:start position:0% +class and so theorists arose who tried + + + align:start position:0% +class and so theorists arose who tried +to come up with a system of learning to + + align:start position:0% +to come up with a system of learning to + + + align:start position:0% +to come up with a system of learning to +explain all human behavior you've all + + align:start position:0% +explain all human behavior you've all + + + align:start position:0% +explain all human behavior you've all +heard of BF Skinner you've probably + + align:start position:0% +heard of BF Skinner you've probably + + + align:start position:0% +heard of BF Skinner you've probably +heard of + + align:start position:0% +heard of + + + align:start position:0% +heard of +thorite inventor of various puzzle boxes + + align:start position:0% +thorite inventor of various puzzle boxes + + + align:start position:0% +thorite inventor of various puzzle boxes +and describer of instrumental + + align:start position:0% +and describer of instrumental + + + align:start position:0% +and describer of instrumental +learning so for a long time you pick up + + align:start position:0% +learning so for a long time you pick up + + + align:start position:0% +learning so for a long time you pick up +a book on learning and it was + + align:start position:0% +a book on learning and it was + + + align:start position:0% +a book on learning and it was +about instrumental learning and + + align:start position:0% +about instrumental learning and + + + align:start position:0% +about instrumental learning and +classical conditioning the two main + + align:start position:0% +classical conditioning the two main + + + align:start position:0% +classical conditioning the two main +kinds of learning are they hardly but in + + align:start position:0% +kinds of learning are they hardly but in + + + align:start position:0% +kinds of learning are they hardly but in +fact that's what was was + + align:start position:0% +fact that's what was was + + + align:start position:0% +fact that's what was was +taught and it was a major part of + + align:start position:0% +taught and it was a major part of + + + align:start position:0% +taught and it was a major part of +psychology in the middle of the last + + align:start position:0% +psychology in the middle of the last + + + align:start position:0% +psychology in the middle of the last +century in fact that persisted for some + + align:start position:0% +century in fact that persisted for some + + + align:start position:0% +century in fact that persisted for some +time in the second half the last century + + align:start position:0% +time in the second half the last century + + + align:start position:0% +time in the second half the last century +20th + + align:start position:0% + + + + align:start position:0% + +century but in Europe it was very + + align:start position:0% +century but in Europe it was very + + + align:start position:0% +century but in Europe it was very +different in Europe you had the + + align:start position:0% +different in Europe you had the + + + align:start position:0% +different in Europe you had the +development not within + + align:start position:0% +development not within + + + align:start position:0% +development not within +psychology but within the field of + + align:start position:0% +psychology but within the field of + + + align:start position:0% +psychology but within the field of +zoology part of biology okay zoy ol + + align:start position:0% +zoology part of biology okay zoy ol + + + align:start position:0% +zoology part of biology okay zoy ol +ologists zoology is the field wherein + + align:start position:0% +ologists zoology is the field wherein + + + align:start position:0% +ologists zoology is the field wherein +ethology the study of natural behavior + + align:start position:0% +ethology the study of natural behavior + + + align:start position:0% +ethology the study of natural behavior +patterns + + align:start position:0% + + + + align:start position:0% + +developed this is I will take Conrad + + align:start position:0% +developed this is I will take Conrad + + + align:start position:0% +developed this is I will take Conrad +Lawrence a leader in that field uh from + + align:start position:0% +Lawrence a leader in that field uh from + + + align:start position:0% +Lawrence a leader in that field uh from +his book the foundations of + + align:start position:0% +his book the foundations of + + + align:start position:0% +his book the foundations of +ethology uh he defined ethology this way + + align:start position:0% +ethology uh he defined ethology this way + + + align:start position:0% +ethology uh he defined ethology this way +it's the dis it's the discipline which + + align:start position:0% +it's the dis it's the discipline which + + + align:start position:0% +it's the dis it's the discipline which +applies to the behavior of animals and + + align:start position:0% +applies to the behavior of animals and + + + align:start position:0% +applies to the behavior of animals and +humans all those questions asked and + + align:start position:0% +humans all those questions asked and + + + align:start position:0% +humans all those questions asked and +methodologies used as a matter of course + + align:start position:0% +methodologies used as a matter of course + + + align:start position:0% +methodologies used as a matter of course +in all the other branches of biology + + align:start position:0% +in all the other branches of biology + + + align:start position:0% +in all the other branches of biology +since Charles Darwin's + + align:start position:0% +since Charles Darwin's + + + align:start position:0% +since Charles Darwin's +time ethology or the comparative study + + align:start position:0% +time ethology or the comparative study + + + align:start position:0% +time ethology or the comparative study +of behavior is based on the fact that + + align:start position:0% +of behavior is based on the fact that + + + align:start position:0% +of behavior is based on the fact that +there + + align:start position:0% +there + + + align:start position:0% +there +are mechanics mechanisms of behavior + + align:start position:0% +are mechanics mechanisms of behavior + + + align:start position:0% +are mechanics mechanisms of behavior +which evolve in philogyny that is among + + align:start position:0% +which evolve in philogyny that is among + + + align:start position:0% +which evolve in philogyny that is among +different animals of different types + + align:start position:0% +different animals of different types + + + align:start position:0% +different animals of different types +exactly as organ + + align:start position:0% + + + + align:start position:0% + +evolve so that the concept of homology + + align:start position:0% +evolve so that the concept of homology + + + align:start position:0% +evolve so that the concept of homology +can be applied to them as well as to + + align:start position:0% +can be applied to them as well as to + + + align:start position:0% +can be applied to them as well as to +morphological + + align:start position:0% +morphological + + + align:start position:0% +morphological +structures the origins of this approach + + align:start position:0% +structures the origins of this approach + + + align:start position:0% +structures the origins of this approach +was in Ornithology and in fact in + + align:start position:0% +was in Ornithology and in fact in + + + align:start position:0% +was in Ornithology and in fact in +amateur + + align:start position:0% +amateur + + + align:start position:0% +amateur +Ornithology and these are the two people + + align:start position:0% +Ornithology and these are the two people + + + align:start position:0% +Ornithology and these are the two people +that we attribute the initial + + align:start position:0% +that we attribute the initial + + + align:start position:0% +that we attribute the initial +discoveries + + align:start position:0% +discoveries + + + align:start position:0% +discoveries +to Charles Otis Whitman in America + + align:start position:0% +to Charles Otis Whitman in America + + + align:start position:0% +to Charles Otis Whitman in America +these were the dates of his + + align:start position:0% +these were the dates of his + + + align:start position:0% +these were the dates of his +Publications he kept a collection of + + align:start position:0% +Publications he kept a collection of + + + align:start position:0% +Publications he kept a collection of +doves and pigeons in aviaries and he + + align:start position:0% +doves and pigeons in aviaries and he + + + align:start position:0% +doves and pigeons in aviaries and he +studied them and then Oscar + + align:start position:0% +studied them and then Oscar + + + align:start position:0% +studied them and then Oscar +heinroth director of the Berlin + + align:start position:0% +heinroth director of the Berlin + + + align:start position:0% +heinroth director of the Berlin +Zoo his Publications 1910 1928 + + align:start position:0% + + + + align:start position:0% + +1930 he + + align:start position:0% +1930 he + + + align:start position:0% +1930 he +studied the a rich collection of + + align:start position:0% +studied the a rich collection of + + + align:start position:0% +studied the a rich collection of +waterfall kept at the Berlin Zoo + + align:start position:0% +waterfall kept at the Berlin Zoo + + + align:start position:0% +waterfall kept at the Berlin Zoo +so they were both studying captive + + align:start position:0% +so they were both studying captive + + + align:start position:0% +so they were both studying captive +animals captive + + align:start position:0% +animals captive + + + align:start position:0% +animals captive +Birds but very different kinds of birds + + align:start position:0% +Birds but very different kinds of birds + + + align:start position:0% +Birds but very different kinds of birds +and they independently discovered that + + align:start position:0% +and they independently discovered that + + + align:start position:0% +and they independently discovered that +motor patterns just like morphological + + align:start position:0% +motor patterns just like morphological + + + align:start position:0% +motor patterns just like morphological +characteristics can be inherited can be + + align:start position:0% +characteristics can be inherited can be + + + align:start position:0% +characteristics can be inherited can be +homologs across different + + align:start position:0% +homologs across different + + + align:start position:0% +homologs across different +species but Darwin knew a lot of this + + align:start position:0% +species but Darwin knew a lot of this + + + align:start position:0% +species but Darwin knew a lot of this +already and in his + + align:start position:0% +already and in his + + + align:start position:0% +already and in his +book he talks for example about dog + + align:start position:0% +book he talks for example about dog + + + align:start position:0% +book he talks for example about dog +behavior if you look at this picture + + align:start position:0% +behavior if you look at this picture + + + align:start position:0% +behavior if you look at this picture +compare this picture with this picture + + align:start position:0% +compare this picture with this picture + + + align:start position:0% +compare this picture with this picture +what's different about these two + + align:start position:0% +what's different about these two + + + align:start position:0% +what's different about these two +dogs you can tell right away this this + + align:start position:0% +dogs you can tell right away this this + + + align:start position:0% +dogs you can tell right away this this +is a friendly dog and this is not this + + align:start position:0% +is a friendly dog and this is not this + + + align:start position:0% +is a friendly dog and this is not this +is an aggressive + + align:start position:0% +is an aggressive + + + align:start position:0% +is an aggressive +dog how many of you can recognize that + + align:start position:0% +dog how many of you can recognize that + + + align:start position:0% +dog how many of you can recognize that +immediately oh come on surely you have + + align:start position:0% +immediately oh come on surely you have + + + align:start position:0% +immediately oh come on surely you have +pet dog and you know that difference + + align:start position:0% +pet dog and you know that difference + + + align:start position:0% +pet dog and you know that difference +this is what your dog looks like when + + align:start position:0% +this is what your dog looks like when + + + align:start position:0% +this is what your dog looks like when +he's greeting you and you've been gone + + align:start position:0% +he's greeting you and you've been gone + + + align:start position:0% +he's greeting you and you've been gone +for a long time and he's greeting you + + align:start position:0% +for a long time and he's greeting you + + + align:start position:0% +for a long time and he's greeting you +your especially his master coming home + + align:start position:0% +your especially his master coming home + + + align:start position:0% +your especially his master coming home +uh this is a dog usually when they act + + align:start position:0% +uh this is a dog usually when they act + + + align:start position:0% +uh this is a dog usually when they act +like this towards humans it can be + + align:start position:0% +like this towards humans it can be + + + align:start position:0% +like this towards humans it can be +dangerous okay but they certainly act + + align:start position:0% +dangerous okay but they certainly act + + + align:start position:0% +dangerous okay but they certainly act +like this in faced with other + + align:start position:0% +like this in faced with other + + + align:start position:0% +like this in faced with other +dogs and Darwin saw these patterns + + align:start position:0% +dogs and Darwin saw these patterns + + + align:start position:0% +dogs and Darwin saw these patterns +because he could recognize them in one + + align:start position:0% +because he could recognize them in one + + + align:start position:0% +because he could recognize them in one +dog after another these were + + align:start position:0% +dog after another these were + + + align:start position:0% +dog after another these were +inherited patterns of behavior they were + + align:start position:0% +inherited patterns of behavior they were + + + align:start position:0% +inherited patterns of behavior they were +instinctive behaviors + + align:start position:0% +instinctive behaviors + + + align:start position:0% +instinctive behaviors +and he applied that concept to human + + align:start position:0% +and he applied that concept to human + + + align:start position:0% +and he applied that concept to human +behavior as well for example in his book + + align:start position:0% +behavior as well for example in his book + + + align:start position:0% +behavior as well for example in his book +this is his from his book the expression + + align:start position:0% +this is his from his book the expression + + + align:start position:0% +this is his from his book the expression +of the emotions in man and animals uh as + + align:start position:0% +of the emotions in man and animals uh as + + + align:start position:0% +of the emotions in man and animals uh as +were these pictures here he's showing + + align:start position:0% +were these pictures here he's showing + + + align:start position:0% +were these pictures here he's showing +various pictures of human emotional + + align:start position:0% +various pictures of human emotional + + + align:start position:0% +various pictures of human emotional +Expressions our emotional expressions + + align:start position:0% +Expressions our emotional expressions + + + align:start position:0% +Expressions our emotional expressions +are instinctive patterns that are the + + align:start position:0% +are instinctive patterns that are the + + + align:start position:0% +are instinctive patterns that are the +same across all of us across + + align:start position:0% +same across all of us across + + + align:start position:0% +same across all of us across +various RAC + + align:start position:0% +various RAC + + + align:start position:0% +various RAC +all Homo sapiens show these kind same + + align:start position:0% +all Homo sapiens show these kind same + + + align:start position:0% +all Homo sapiens show these kind same +patterns yeah they they you say oh but + + align:start position:0% +patterns yeah they they you say oh but + + + align:start position:0% +patterns yeah they they you say oh but +the Japanese don't make the same + + align:start position:0% +the Japanese don't make the same + + + align:start position:0% +the Japanese don't make the same +Expressions when they're happier or this + + align:start position:0% +Expressions when they're happier or this + + + align:start position:0% +Expressions when they're happier or this +or oh yes they do but then in addition + + align:start position:0% +or oh yes they do but then in addition + + + align:start position:0% +or oh yes they do but then in addition +of course we develop certain ways of + + align:start position:0% +of course we develop certain ways of + + + align:start position:0% +of course we develop certain ways of +using + + align:start position:0% +using + + + align:start position:0% +using +Expressions uh for different + + align:start position:0% + + + + align:start position:0% + +meanings well ethology has been applied + + align:start position:0% +meanings well ethology has been applied + + + align:start position:0% +meanings well ethology has been applied +to + + align:start position:0% +to + + + align:start position:0% +to +human and and uh not just by Darwin but + + align:start position:0% +human and and uh not just by Darwin but + + + align:start position:0% +human and and uh not just by Darwin but +much as + + align:start position:0% +much as + + + align:start position:0% +much as +as Lauren pointed out the proof that + + align:start position:0% +as Lauren pointed out the proof that + + + align:start position:0% +as Lauren pointed out the proof that +humans really had instinctive inherited + + align:start position:0% +humans really had instinctive inherited + + + align:start position:0% +humans really had instinctive inherited +behavior + + align:start position:0% +behavior + + + align:start position:0% +behavior +patterns though it was suggested by + + align:start position:0% +patterns though it was suggested by + + + align:start position:0% +patterns though it was suggested by +Darwin and he was accurate in his + + align:start position:0% +Darwin and he was accurate in his + + + align:start position:0% +Darwin and he was accurate in his +descriptions but the real proof came + + align:start position:0% +descriptions but the real proof came + + + align:start position:0% +descriptions but the real proof came +from iel + + align:start position:0% +from iel + + + align:start position:0% +from iel +ield erus iel ield wrote + + align:start position:0% +ield erus iel ield wrote + + + align:start position:0% +ield erus iel ield wrote +a large book in called human ethology in + + align:start position:0% +a large book in called human ethology in + + + align:start position:0% +a large book in called human ethology in +1989 available in the library I have a + + align:start position:0% +1989 available in the library I have a + + + align:start position:0% +1989 available in the library I have a +copy in my office and if you're + + align:start position:0% +copy in my office and if you're + + + align:start position:0% +copy in my office and if you're +interested in how these ideas apply to + + align:start position:0% +interested in how these ideas apply to + + + align:start position:0% +interested in how these ideas apply to +human you will find them described there + + align:start position:0% +human you will find them described there + + + align:start position:0% +human you will find them described there +I'll say a little bit more about human + + align:start position:0% +I'll say a little bit more about human + + + align:start position:0% +I'll say a little bit more about human +ethology next + + align:start position:0% +ethology next + + + align:start position:0% +ethology next +time just so you'll know how H IUS felt + + align:start position:0% +time just so you'll know how H IUS felt + + + align:start position:0% +time just so you'll know how H IUS felt +went + + align:start position:0% +went + + + align:start position:0% +went +about uh + + align:start position:0% +about uh + + + align:start position:0% +about uh +proving to anybody who read studied his + + align:start position:0% +proving to anybody who read studied his + + + align:start position:0% +proving to anybody who read studied his +book that + + align:start position:0% +book that + + + align:start position:0% +book that +he was right about this more popularly + + align:start position:0% +he was right about this more popularly + + + align:start position:0% +he was right about this more popularly +we know about body + + align:start position:0% +we know about body + + + align:start position:0% +we know about body +language which became a really popular + + align:start position:0% +language which became a really popular + + + align:start position:0% +language which became a really popular +craze for a while some time ago uh now + + align:start position:0% +craze for a while some time ago uh now + + + align:start position:0% +craze for a while some time ago uh now +it's sort of entered the the common + + align:start position:0% +it's sort of entered the the common + + + align:start position:0% +it's sort of entered the the common +parlament but that is all based on these + + align:start position:0% +parlament but that is all based on these + + + align:start position:0% +parlament but that is all based on these +instinctive + + align:start position:0% + + + + align:start position:0% + +patterns we know about neuroethology + + align:start position:0% +patterns we know about neuroethology + + + align:start position:0% +patterns we know about neuroethology +we'll say a little bit about that in the + + align:start position:0% +we'll say a little bit about that in the + + + align:start position:0% +we'll say a little bit about that in the +class but it's not primarily a class on + + align:start position:0% +class but it's not primarily a class on + + + align:start position:0% +class but it's not primarily a class on +Neuroscience so I won't stress it but I + + align:start position:0% +Neuroscience so I won't stress it but I + + + align:start position:0% +Neuroscience so I won't stress it but I +can say that studies of the brain have + + align:start position:0% +can say that studies of the brain have + + + align:start position:0% +can say that studies of the brain have +led to uh studies of instinctive how + + align:start position:0% +led to uh studies of instinctive how + + + align:start position:0% +led to uh studies of instinctive how +instinctive behaviors are + + align:start position:0% +instinctive behaviors are + + + align:start position:0% +instinctive behaviors are +controlled and brain studies have been + + align:start position:0% +controlled and brain studies have been + + + align:start position:0% +controlled and brain studies have been +used to distinguish different kinds of + + align:start position:0% +used to distinguish different kinds of + + + align:start position:0% +used to distinguish different kinds of +aggression for example but they're all + + align:start position:0% +aggression for example but they're all + + + align:start position:0% +aggression for example but they're all +things already known to + + align:start position:0% +things already known to + + + align:start position:0% +things already known to +ethologists obviously if patterns are + + align:start position:0% +ethologists obviously if patterns are + + + align:start position:0% +ethologists obviously if patterns are +very different than they expressed + + align:start position:0% +very different than they expressed + + + align:start position:0% +very different than they expressed +differently in brain + + align:start position:0% + + + + align:start position:0% + +activity okay now if the focus is on + + align:start position:0% +activity okay now if the focus is on + + + align:start position:0% +activity okay now if the focus is on +societies and social behavior then we're + + align:start position:0% +societies and social behavior then we're + + + align:start position:0% +societies and social behavior then we're +usually not talking about ethology + + align:start position:0% +usually not talking about ethology + + + align:start position:0% +usually not talking about ethology +though I can should say there's a lot of + + align:start position:0% +though I can should say there's a lot of + + + align:start position:0% +though I can should say there's a lot of +overlap between ethological studies and + + align:start position:0% +overlap between ethological studies and + + + align:start position:0% +overlap between ethological studies and +sociobiological + + align:start position:0% +sociobiological + + + align:start position:0% +sociobiological +studies but the the main emphasis of the + + align:start position:0% +studies but the the main emphasis of the + + + align:start position:0% +studies but the the main emphasis of the +work in sociobiology has been + + align:start position:0% + + + + align:start position:0% + +different Edward O Wilson + + align:start position:0% +different Edward O Wilson + + + align:start position:0% +different Edward O Wilson +at Harvard was the one who invented the + + align:start position:0% +at Harvard was the one who invented the + + + align:start position:0% +at Harvard was the one who invented the +term sociobiology though it it had been + + align:start position:0% +term sociobiology though it it had been + + + align:start position:0% +term sociobiology though it it had been +used + + align:start position:0% +used + + + align:start position:0% +used +before for example by C Judson herck a + + align:start position:0% +before for example by C Judson herck a + + + align:start position:0% +before for example by C Judson herck a +comparative anatomist who wrote a book + + align:start position:0% +comparative anatomist who wrote a book + + + align:start position:0% +comparative anatomist who wrote a book +on human nature and + + align:start position:0% +on human nature and + + + align:start position:0% +on human nature and +Behavior Uh but it was very speculative + + align:start position:0% +Behavior Uh but it was very speculative + + + align:start position:0% +Behavior Uh but it was very speculative +and if you read what he actually says + + align:start position:0% +and if you read what he actually says + + + align:start position:0% +and if you read what he actually says +about sociobiology was very different + + align:start position:0% +about sociobiology was very different + + + align:start position:0% +about sociobiology was very different +from EO Wilson because he never even + + align:start position:0% +from EO Wilson because he never even + + + align:start position:0% +from EO Wilson because he never even +refers to + + align:start position:0% +refers to + + + align:start position:0% +refers to +Darwin so it was really Wilson that + + align:start position:0% +Darwin so it was really Wilson that + + + align:start position:0% +Darwin so it was really Wilson that +brought a lot of different he was + + align:start position:0% +brought a lot of different he was + + + align:start position:0% +brought a lot of different he was +basically a review of L many different + + align:start position:0% +basically a review of L many different + + + align:start position:0% +basically a review of L many different +aspects of social behavior in many + + align:start position:0% +aspects of social behavior in many + + + align:start position:0% +aspects of social behavior in many +different species and in his last + + align:start position:0% +different species and in his last + + + align:start position:0% +different species and in his last +chapter it was about + + align:start position:0% +chapter it was about + + + align:start position:0% +chapter it was about +humans and that is what caused him so + + align:start position:0% +humans and that is what caused him so + + + align:start position:0% +humans and that is what caused him so +much + + align:start position:0% +much + + + align:start position:0% +much +trouble it was actually a Revolt + + align:start position:0% +trouble it was actually a Revolt + + + align:start position:0% +trouble it was actually a Revolt +among humanists and even scientists here + + align:start position:0% +among humanists and even scientists here + + + align:start position:0% +among humanists and even scientists here +at MIT that tried to they wanted the + + align:start position:0% +at MIT that tried to they wanted the + + + align:start position:0% +at MIT that tried to they wanted the +whole field suppressed I know that's + + align:start position:0% +whole field suppressed I know that's + + + align:start position:0% +whole field suppressed I know that's +hard to believe that in recent years + + align:start position:0% +hard to believe that in recent years + + + align:start position:0% +hard to believe that in recent years +that actually + + align:start position:0% +that actually + + + align:start position:0% +that actually +happened but I was already at MIT when + + align:start position:0% +happened but I was already at MIT when + + + align:start position:0% +happened but I was already at MIT when +that was happening I met eel Wilson I + + align:start position:0% +that was happening I met eel Wilson I + + + align:start position:0% +that was happening I met eel Wilson I +liked Ed a lot and U I had also like he + + align:start position:0% +liked Ed a lot and U I had also like he + + + align:start position:0% +liked Ed a lot and U I had also like he +did trouble understanding why why people + + align:start position:0% +did trouble understanding why why people + + + align:start position:0% +did trouble understanding why why people +were getting so + + align:start position:0% +were getting so + + + align:start position:0% +were getting so +upset Conrad Lawrence has been attacked + + align:start position:0% +upset Conrad Lawrence has been attacked + + + align:start position:0% +upset Conrad Lawrence has been attacked +also because he applies ethology to + + align:start position:0% +also because he applies ethology to + + + align:start position:0% +also because he applies ethology to +human behavior too see a lot of people + + align:start position:0% +human behavior too see a lot of people + + + align:start position:0% +human behavior too see a lot of people +do not want any of the stuff that we + + align:start position:0% +do not want any of the stuff that we + + + align:start position:0% +do not want any of the stuff that we +apply to animals to apply to + + align:start position:0% +apply to animals to apply to + + + align:start position:0% +apply to animals to apply to +humans they it became it becomes a + + align:start position:0% +humans they it became it becomes a + + + align:start position:0% +humans they it became it becomes a +political thing and I will just urge you + + align:start position:0% +political thing and I will just urge you + + + align:start position:0% +political thing and I will just urge you +to keep politics separate from the + + align:start position:0% +to keep politics separate from the + + + align:start position:0% +to keep politics separate from the +science but that's what people were + + align:start position:0% +science but that's what people were + + + align:start position:0% +science but that's what people were +doing and at the time this came out it + + align:start position:0% +doing and at the time this came out it + + + align:start position:0% +doing and at the time this came out it +was ideologies were being argued a + + align:start position:0% +was ideologies were being argued a + + + align:start position:0% +was ideologies were being argued a +lot + + align:start position:0% +lot + + + align:start position:0% +lot +uh socialist ideologies communist + + align:start position:0% +uh socialist ideologies communist + + + align:start position:0% +uh socialist ideologies communist +ideologies believe strongly + + align:start position:0% +ideologies believe strongly + + + align:start position:0% +ideologies believe strongly +in not anything in + + align:start position:0% +in not anything in + + + align:start position:0% +in not anything in +herit okay in very for very different + + align:start position:0% +herit okay in very for very different + + + align:start position:0% +herit okay in very for very different +reasons than say what we talked about in + + align:start position:0% +reasons than say what we talked about in + + + align:start position:0% +reasons than say what we talked about in +the development of education in America + + align:start position:0% +the development of education in America + + + align:start position:0% +the development of education in America +very + + align:start position:0% +very + + + align:start position:0% +very +different approaches but that led to a + + align:start position:0% +different approaches but that led to a + + + align:start position:0% +different approaches but that led to a +more vent vent opposition to socio + + align:start position:0% +more vent vent opposition to socio + + + align:start position:0% +more vent vent opposition to socio +biology and we'll go through that + + align:start position:0% +biology and we'll go through that + + + align:start position:0% +biology and we'll go through that +history um in the middle of the class + + align:start position:0% +history um in the middle of the class + + + align:start position:0% +history um in the middle of the class +when we start talking about + + align:start position:0% + + + + align:start position:0% + +sociobiology it's very different from + + align:start position:0% +sociobiology it's very different from + + + align:start position:0% +sociobiology it's very different from +cultural anthropology it's very + + align:start position:0% +cultural anthropology it's very + + + align:start position:0% +cultural anthropology it's very +different from sociology in fact + + align:start position:0% +different from sociology in fact + + + align:start position:0% +different from sociology in fact +sociologists have been very resistant to + + align:start position:0% +sociologists have been very resistant to + + + align:start position:0% +sociologists have been very resistant to +applying to the application of darwinian + + align:start position:0% +applying to the application of darwinian + + + align:start position:0% +applying to the application of darwinian +ideas and evolution to social behavior + + align:start position:0% +ideas and evolution to social behavior + + + align:start position:0% +ideas and evolution to social behavior +of + + align:start position:0% +of + + + align:start position:0% +of +humans uh many cultural Anthropologist + + align:start position:0% +humans uh many cultural Anthropologist + + + align:start position:0% +humans uh many cultural Anthropologist +the same + + align:start position:0% +the same + + + align:start position:0% +the same +way it's culture that determines our + + align:start position:0% +way it's culture that determines our + + + align:start position:0% +way it's culture that determines our +Behavior not + + align:start position:0% +Behavior not + + + align:start position:0% +Behavior not +biology they that's almost a quote from + + align:start position:0% +biology they that's almost a quote from + + + align:start position:0% +biology they that's almost a quote from +some of these + + align:start position:0% +some of these + + + align:start position:0% +some of these +people I hope you don't end up believing + + align:start position:0% +people I hope you don't end up believing + + + align:start position:0% +people I hope you don't end up believing +that but anyway + + align:start position:0% +that but anyway + + + align:start position:0% +that but anyway +here's from EO Wilson's book I just + + align:start position:0% +here's from EO Wilson's book I just + + + align:start position:0% +here's from EO Wilson's book I just +wanted to show you how he conceptualized + + align:start position:0% +wanted to show you how he conceptualized + + + align:start position:0% +wanted to show you how he conceptualized +uh get this so you can see it + + align:start position:0% + + + + align:start position:0% + +here was the way he conceptualized these + + align:start position:0% +here was the way he conceptualized these + + + align:start position:0% +here was the way he conceptualized these +fields of studied behavior in 1950 he + + align:start position:0% +fields of studied behavior in 1950 he + + + align:start position:0% +fields of studied behavior in 1950 he +has ethology and comparative psychology + + align:start position:0% +has ethology and comparative psychology + + + align:start position:0% +has ethology and comparative psychology +in America ethology in Europe is quite + + align:start position:0% +in America ethology in Europe is quite + + + align:start position:0% +in America ethology in Europe is quite +separate which they were at that time + + align:start position:0% +separate which they were at that time + + + align:start position:0% +separate which they were at that time +here he has the beginnings of + + align:start position:0% +here he has the beginnings of + + + align:start position:0% +here he has the beginnings of +sociobiology but the word was not being + + align:start position:0% +sociobiology but the word was not being + + + align:start position:0% +sociobiology but the word was not being +used in 1950 it was part of Behavioral + + align:start position:0% +used in 1950 it was part of Behavioral + + + align:start position:0% +used in 1950 it was part of Behavioral +ecology okay just part of + + align:start position:0% +ecology okay just part of + + + align:start position:0% +ecology okay just part of +ecology and that was closely connected + + align:start position:0% +ecology and that was closely connected + + + align:start position:0% +ecology and that was closely connected +to population biology so that was that + + align:start position:0% +to population biology so that was that + + + align:start position:0% +to population biology so that was that +was the close link just like over here + + align:start position:0% +was the close link just like over here + + + align:start position:0% +was the close link just like over here +on the other side you have integrative + + align:start position:0% +on the other side you have integrative + + + align:start position:0% +on the other side you have integrative +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +neurophysiology closely linked to cell + + align:start position:0% + + + + align:start position:0% + +biology in the middle you have these + + align:start position:0% +biology in the middle you have these + + + align:start position:0% +biology in the middle you have these +behavioral fields ethology and + + align:start position:0% +behavioral fields ethology and + + + align:start position:0% +behavioral fields ethology and +comparative + + align:start position:0% +comparative + + + align:start position:0% +comparative +psychology okay so then + + align:start position:0% +psychology okay so then + + + align:start position:0% +psychology okay so then +1975 is when the term sociobiology + + align:start position:0% +1975 is when the term sociobiology + + + align:start position:0% +1975 is when the term sociobiology +originated the ties to population bi + + align:start position:0% +originated the ties to population bi + + + align:start position:0% +originated the ties to population bi +biology were made explicit by EO + + align:start position:0% +biology were made explicit by EO + + + align:start position:0% +biology were made explicit by EO +Wilson + + align:start position:0% +Wilson + + + align:start position:0% +Wilson +uh ethology and biopsychology or + + align:start position:0% +uh ethology and biopsychology or + + + align:start position:0% +uh ethology and biopsychology or +physiological psychology it went by + + align:start position:0% +physiological psychology it went by + + + align:start position:0% +physiological psychology it went by +various names now it's often just + + align:start position:0% +various names now it's often just + + + align:start position:0% +various names now it's often just +neuroscience and behavior or behavioral + + align:start position:0% +neuroscience and behavior or behavioral + + + align:start position:0% +neuroscience and behavior or behavioral +Neuroscience uh had become a little more + + align:start position:0% +Neuroscience uh had become a little more + + + align:start position:0% +Neuroscience uh had become a little more +closely linked but I think he's overly + + align:start position:0% +closely linked but I think he's overly + + + align:start position:0% +closely linked but I think he's overly +optimistic because in + + align:start position:0% +optimistic because in + + + align:start position:0% +optimistic because in +1975 those two Fields were still + + align:start position:0% +1975 those two Fields were still + + + align:start position:0% +1975 those two Fields were still +largely separate in the way they were + + align:start position:0% +largely separate in the way they were + + + align:start position:0% +largely separate in the way they were +carried out uh the work being done and + + align:start position:0% +carried out uh the work being done and + + + align:start position:0% +carried out uh the work being done and +here's the way he envisioned it back in + + align:start position:0% +here's the way he envisioned it back in + + + align:start position:0% +here's the way he envisioned it back in +1975 and 80 when he published his + + align:start position:0% +1975 and 80 when he published his + + + align:start position:0% +1975 and 80 when he published his +books he saw sociobiology increasing + + align:start position:0% +books he saw sociobiology increasing + + + align:start position:0% +books he saw sociobiology increasing +these fields + + align:start position:0% +these fields + + + align:start position:0% +these fields +decreasing it hasn't actually happened + + align:start position:0% +decreasing it hasn't actually happened + + + align:start position:0% +decreasing it hasn't actually happened +quite like that uh + + align:start position:0% +quite like that uh + + + align:start position:0% +quite like that uh +what has happened is + + align:start position:0% +what has happened is + + + align:start position:0% +what has happened is +that + + align:start position:0% +that + + + align:start position:0% +that +both + + align:start position:0% + + + + align:start position:0% + +ethology + + align:start position:0% +ethology + + + align:start position:0% +ethology +and experimental studies of animal + + align:start position:0% +and experimental studies of animal + + + align:start position:0% +and experimental studies of animal +behavior in America including of + + align:start position:0% +behavior in America including of + + + align:start position:0% +behavior in America including of +learning have become much more + + align:start position:0% +learning have become much more + + + align:start position:0% +learning have become much more +integrated with ideas of + + align:start position:0% +integrated with ideas of + + + align:start position:0% +integrated with ideas of +sociobiology uh in fact the most recent + + align:start position:0% +sociobiology uh in fact the most recent + + + align:start position:0% +sociobiology uh in fact the most recent +books in animal behavior I was reading + + align:start position:0% +books in animal behavior I was reading + + + align:start position:0% +books in animal behavior I was reading +them this Summer + + align:start position:0% +them this Summer + + + align:start position:0% +them this Summer +uh they go to Great Lengths to bring so + + align:start position:0% +uh they go to Great Lengths to bring so + + + align:start position:0% +uh they go to Great Lengths to bring so +to integrate almost discuss in a pretty + + align:start position:0% +to integrate almost discuss in a pretty + + + align:start position:0% +to integrate almost discuss in a pretty +seamless way sociobiology and ethology + + align:start position:0% +seamless way sociobiology and ethology + + + align:start position:0% +seamless way sociobiology and ethology +for + + align:start position:0% +for + + + align:start position:0% +for +example what I didn't like about them is + + align:start position:0% +example what I didn't like about them is + + + align:start position:0% +example what I didn't like about them is +that they start out with all this Gene + + align:start position:0% +that they start out with all this Gene + + + align:start position:0% +that they start out with all this Gene +counting and you feel like you're + + align:start position:0% +counting and you feel like you're + + + align:start position:0% +counting and you feel like you're +studying not animal behavior but the + + align:start position:0% +studying not animal behavior but the + + + align:start position:0% +studying not animal behavior but the +some uh mathematical field uh it's hard + + align:start position:0% +some uh mathematical field uh it's hard + + + align:start position:0% +some uh mathematical field uh it's hard +a little hard to describe but I didn't + + align:start position:0% +a little hard to describe but I didn't + + + align:start position:0% +a little hard to describe but I didn't +feel it was very successful if you don't + + align:start position:0% +feel it was very successful if you don't + + + align:start position:0% +feel it was very successful if you don't +know much about animal behavior in the + + align:start position:0% +know much about animal behavior in the + + + align:start position:0% +know much about animal behavior in the +first place you'll find it really dull + + align:start position:0% +first place you'll find it really dull + + + align:start position:0% +first place you'll find it really dull +so I didn't I don't take that TCH but + + align:start position:0% +so I didn't I don't take that TCH but + + + align:start position:0% +so I didn't I don't take that TCH but +you will learn the same + + align:start position:0% +you will learn the same + + + align:start position:0% +you will learn the same +things okay if you focus on the habitat + + align:start position:0% +things okay if you focus on the habitat + + + align:start position:0% +things okay if you focus on the habitat +and the species the habitat supports + + align:start position:0% +and the species the habitat supports + + + align:start position:0% +and the species the habitat supports +then you're talking about + + align:start position:0% +then you're talking about + + + align:start position:0% +then you're talking about +ecology and you can find the field of + + align:start position:0% +ecology and you can find the field of + + + align:start position:0% +ecology and you can find the field of +Behavioral ecology talking mainly about + + align:start position:0% +Behavioral ecology talking mainly about + + + align:start position:0% +Behavioral ecology talking mainly about +Behavior if you focus on a single + + align:start position:0% +Behavior if you focus on a single + + + align:start position:0% +Behavior if you focus on a single +species and we've already mentioned this + + align:start position:0% +species and we've already mentioned this + + + align:start position:0% +species and we've already mentioned this +you can talk about primatology orology + + align:start position:0% +you can talk about primatology orology + + + align:start position:0% +you can talk about primatology orology +if you're just studying + + align:start position:0% +if you're just studying + + + align:start position:0% +if you're just studying +sitations entomology if you're studying + + align:start position:0% +sitations entomology if you're studying + + + align:start position:0% +sitations entomology if you're studying +insects if you're looking in mology + + align:start position:0% +insects if you're looking in mology + + + align:start position:0% +insects if you're looking in mology +though you will find topics that you + + align:start position:0% +though you will find topics that you + + + align:start position:0% +though you will find topics that you +simply don't find in ethology or + + align:start position:0% +simply don't find in ethology or + + + align:start position:0% +simply don't find in ethology or +physiological + + align:start position:0% +physiological + + + align:start position:0% +physiological +psychology running speeds of land an + + align:start position:0% +psychology running speeds of land an + + + align:start position:0% +psychology running speeds of land an +mammals submersion times of aquatic + + align:start position:0% +mammals submersion times of aquatic + + + align:start position:0% +mammals submersion times of aquatic +mammals and amphibians tunnel structures + + align:start position:0% +mammals and amphibians tunnel structures + + + align:start position:0% +mammals and amphibians tunnel structures +of burrowing mammals the composition of + + align:start position:0% +of burrowing mammals the composition of + + + align:start position:0% +of burrowing mammals the composition of +milk in various + + align:start position:0% +milk in various + + + align:start position:0% +milk in various +mammals the biomass of animals the total + + align:start position:0% +mammals the biomass of animals the total + + + align:start position:0% +mammals the biomass of animals the total +mass of all animals in a habitat or in a + + align:start position:0% +mass of all animals in a habitat or in a + + + align:start position:0% +mass of all animals in a habitat or in a +region or the mass per unit area on the + + align:start position:0% +region or the mass per unit area on the + + + align:start position:0% +region or the mass per unit area on the +Earth's surface you don't find those in + + align:start position:0% +Earth's surface you don't find those in + + + align:start position:0% +Earth's surface you don't find those in +these other behavioral books but you do + + align:start position:0% +these other behavioral books but you do + + + align:start position:0% +these other behavioral books but you do +find them in mology + + align:start position:0% +find them in mology + + + align:start position:0% +find them in mology +books and then we discuss the amateur + + align:start position:0% +books and then we discuss the amateur + + + align:start position:0% +books and then we discuss the amateur +naturist and that's where I will end and + + align:start position:0% +naturist and that's where I will end and + + + align:start position:0% +naturist and that's where I will end and +we'll I will tell you a little bit more + + align:start position:0% +we'll I will tell you a little bit more + + + align:start position:0% +we'll I will tell you a little bit more +about these topics at the beginning of + + align:start position:0% +about these topics at the beginning of + + + align:start position:0% +about these topics at the beginning of +the next + + align:start position:0% + + + + align:start position:0% + +class \ No newline at end of file diff --git a/CzBtKHvaDr0.txt b/CzBtKHvaDr0.txt new file mode 100644 index 0000000000000000000000000000000000000000..88d44f781e45035cec7f14592576b010651f96bc --- /dev/null +++ b/CzBtKHvaDr0.txt @@ -0,0 +1,144 @@ +PROFESSOR: OK. + +We're going to get a little +bit more detail about how + +to sharpen images. + +Here's microfluidic +devices that we saw before + +in the flatbed scanner section. + +I cropped a larger +picture, and as we zoom in, + +we're actually seeing some +Newton rings, which we're not + +loving, but let's pretend +that they're not there. + +You know that we're going to get +Newton rings when you put glass + +on top of glass, +or-- this is PDMS, + +which is also going to +give us some Newton rings. + +So let's just take an area, +maybe around here, just + +to pay attention. + +I'm going to zoom +in a little more. + +Your eye should +focus around here + +and around the numbers, +and maybe over here. + +To see what happens when we +sharpen, we go to the Filter, + +we go down to Sharpen, +and use Unsharp Mask. + +There are all kinds of +things, but for our purposes, + +Unsharp Mask is the way to go. + +And it was already set +at 128 once before. + +Let's go down to almost +very little sharpening, + +almost kind of the +original image. + +And watch as I increase +the amount of sharpening. + +You're seeing more and +more getting sharp. + +But, unfortunately, what also +happens is you get a lot of, + +the dirt is sharpening as well. + +And we'll discuss that in +a moment, a little bit. + +But we're going to go at +length about cleaning images. + +For example, if I accepted this +with 228, which is considerably + +sharper than before-- let +me undo it with Command-Z. + +That was without sharpening. + +That's with sharpening. + +I hope you're seeing. + +Look over here now. + +Without sharpening. + +With sharpening. + +So we're getting some +real clarity here, + +which I think is +what we want to show. + +But, as I said, we are +also getting some junk, + +which, if I decided +to get rid of, + +let's say with +the Healing Brush. + +Little bit here. + +Get rid of this. + +Get rid of this. + +This is making +the image cleaner. + +And the question is, am +I permitted to do this? + +And we're going to have a very +important deeper discussion + +about how much we can, in fact, +enhance scientific images. + +For the time being, +let's leave it at this. + +And we're going +to save the image + +and clearly indicate +this has been sharpened. + +And that's it. + +There you go. \ No newline at end of file diff --git a/D-4cAzSmQUU.txt b/D-4cAzSmQUU.txt new file mode 100644 index 0000000000000000000000000000000000000000..f499d4f08236a3f7b8408e24c4109d4d749a60f8 --- /dev/null +++ b/D-4cAzSmQUU.txt @@ -0,0 +1,7067 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open courseware under a Creative Commons + + align:start position:0% +open courseware under a Creative Commons + + + align:start position:0% +open courseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay all right so let's uh + + align:start position:0% +ocw.mit.edu okay all right so let's uh + + + align:start position:0% +ocw.mit.edu okay all right so let's uh +let's continue then on this unit of + + align:start position:0% +let's continue then on this unit of + + + align:start position:0% +let's continue then on this unit of +kinetics and uh today we are going to + + align:start position:0% +kinetics and uh today we are going to + + + align:start position:0% +kinetics and uh today we are going to +talk about + + align:start position:0% +talk about + + + align:start position:0% +talk about +temperature and we're going to talk talk + + align:start position:0% +temperature and we're going to talk talk + + + align:start position:0% +temperature and we're going to talk talk +about collisions and we're going to talk + + align:start position:0% +about collisions and we're going to talk + + + align:start position:0% +about collisions and we're going to talk +about activation energies and activated + + align:start position:0% +about activation energies and activated + + + align:start position:0% +about activation energies and activated +complexes and uh we're still in Chapter + + align:start position:0% +complexes and uh we're still in Chapter + + + align:start position:0% +complexes and uh we're still in Chapter +13 in your + + align:start position:0% +13 in your + + + align:start position:0% +13 in your +book so when we started this unit on + + align:start position:0% +book so when we started this unit on + + + align:start position:0% +book so when we started this unit on +kinetics we listed a bunch of things + + align:start position:0% +kinetics we listed a bunch of things + + + align:start position:0% +kinetics we listed a bunch of things +that can affect the rate of a + + align:start position:0% +that can affect the rate of a + + + align:start position:0% +that can affect the rate of a +reaction and let's just review what + + align:start position:0% +reaction and let's just review what + + + align:start position:0% +reaction and let's just review what +we've talked about and what we have left + + align:start position:0% +we've talked about and what we have left + + + align:start position:0% +we've talked about and what we have left +to talk about so we talked about + + align:start position:0% +to talk about so we talked about + + + align:start position:0% +to talk about so we talked about +mechanisms of reactions one step two + + align:start position:0% +mechanisms of reactions one step two + + + align:start position:0% +mechanisms of reactions one step two +steps fast steps slow steps uh that can + + align:start position:0% +steps fast steps slow steps uh that can + + + align:start position:0% +steps fast steps slow steps uh that can +affect the rate of the reaction we + + align:start position:0% +affect the rate of the reaction we + + + align:start position:0% +affect the rate of the reaction we +talked about concentration of uh + + align:start position:0% +talked about concentration of uh + + + align:start position:0% +talked about concentration of uh +material we talked about nature of + + align:start position:0% +material we talked about nature of + + + align:start position:0% +material we talked about nature of +material talked about first order and + + align:start position:0% +material talked about first order and + + + align:start position:0% +material talked about first order and +second order integrated rate laws and uh + + align:start position:0% +second order integrated rate laws and uh + + + align:start position:0% +second order integrated rate laws and uh +so today we're going to talk about + + align:start position:0% +so today we're going to talk about + + + align:start position:0% +so today we're going to talk about +temperature and then Monday we're going + + align:start position:0% +temperature and then Monday we're going + + + align:start position:0% +temperature and then Monday we're going +to talk about the use of catalysts and + + align:start position:0% +to talk about the use of catalysts and + + + align:start position:0% +to talk about the use of catalysts and +then Wednesday again uh is a review so + + align:start position:0% +then Wednesday again uh is a review so + + + align:start position:0% +then Wednesday again uh is a review so +we're right at the uh the bottom of our + + align:start position:0% +we're right at the uh the bottom of our + + + align:start position:0% +we're right at the uh the bottom of our +list here of things affecting rates of + + align:start position:0% +list here of things affecting rates of + + + align:start position:0% +list here of things affecting rates of +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +so the effect of + + align:start position:0% +so the effect of + + + align:start position:0% +so the effect of +temperature so if you're in the uh gas + + align:start position:0% +temperature so if you're in the uh gas + + + align:start position:0% +temperature so if you're in the uh gas +phase there sort of the qualitative + + align:start position:0% +phase there sort of the qualitative + + + align:start position:0% +phase there sort of the qualitative +observation that if you increase the + + align:start position:0% +observation that if you increase the + + + align:start position:0% +observation that if you increase the +temperature the rate + + align:start position:0% +temperature the rate + + + align:start position:0% +temperature the rate +increases so um you've probably sort of + + align:start position:0% +increases so um you've probably sort of + + + align:start position:0% +increases so um you've probably sort of +thought about this that if you want to + + align:start position:0% +thought about this that if you want to + + + align:start position:0% +thought about this that if you want to +make something go faster you add some + + align:start position:0% +make something go faster you add some + + + align:start position:0% +make something go faster you add some +heat So today we're going to talk about + + align:start position:0% +heat So today we're going to talk about + + + align:start position:0% +heat So today we're going to talk about +quantitative effects and how you can + + align:start position:0% +quantitative effects and how you can + + + align:start position:0% +quantitative effects and how you can +actually calculate a change in rate + + align:start position:0% +actually calculate a change in rate + + + align:start position:0% +actually calculate a change in rate +constant if the temperature of the + + align:start position:0% +constant if the temperature of the + + + align:start position:0% +constant if the temperature of the +reaction is + + align:start position:0% + + + + align:start position:0% + +changed so here we go back to + + align:start position:0% +changed so here we go back to + + + align:start position:0% +changed so here we go back to +1889 and uh that's when uh uranius + + align:start position:0% +1889 and uh that's when uh uranius + + + align:start position:0% +1889 and uh that's when uh uranius +plotted rate constants versus uh + + align:start position:0% +plotted rate constants versus uh + + + align:start position:0% +plotted rate constants versus uh +temperature and he was looking to get a + + align:start position:0% +temperature and he was looking to get a + + + align:start position:0% +temperature and he was looking to get a +straight line so he found that if he + + align:start position:0% +straight line so he found that if he + + + align:start position:0% +straight line so he found that if he +used the natural log of the rate + + align:start position:0% +used the natural log of the rate + + + align:start position:0% +used the natural log of the rate +constants and he plotted that against + + align:start position:0% +constants and he plotted that against + + + align:start position:0% +constants and he plotted that against +inverse temperature he got a straight + + align:start position:0% + + + + align:start position:0% + +line and uh here is what one of those + + align:start position:0% +line and uh here is what one of those + + + align:start position:0% +line and uh here is what one of those +plots look like so the rates constants + + align:start position:0% +plots look like so the rates constants + + + align:start position:0% +plots look like so the rates constants +are varying exponentially with inverse + + align:start position:0% +are varying exponentially with inverse + + + align:start position:0% +are varying exponentially with inverse +temperature so on one axis we have the + + align:start position:0% +temperature so on one axis we have the + + + align:start position:0% +temperature so on one axis we have the +natural log of the rate constant K and + + align:start position:0% +natural log of the rate constant K and + + + align:start position:0% +natural log of the rate constant K and +on the other axis we have one over + + align:start position:0% +on the other axis we have one over + + + align:start position:0% +on the other axis we have one over +temperature and so this is the equation + + align:start position:0% +temperature and so this is the equation + + + align:start position:0% +temperature and so this is the equation +that is being plotted so again we have + + align:start position:0% +that is being plotted so again we have + + + align:start position:0% +that is being plotted so again we have +natural log of K on one axis that's rate + + align:start position:0% +natural log of K on one axis that's rate + + + align:start position:0% +natural log of K on one axis that's rate +constant and the other uh axis is one + + align:start position:0% +constant and the other uh axis is one + + + align:start position:0% +constant and the other uh axis is one +over temperature and so if this is one + + align:start position:0% +over temperature and so if this is one + + + align:start position:0% +over temperature and so if this is one +over temperature on this axis then the + + align:start position:0% +over temperature on this axis then the + + + align:start position:0% +over temperature on this axis then the +slope of the line is minus EA activation + + align:start position:0% +slope of the line is minus EA activation + + + align:start position:0% +slope of the line is minus EA activation +energy over R which is the gas constant + + align:start position:0% +energy over R which is the gas constant + + + align:start position:0% +energy over R which is the gas constant +so up here activation energy e sub A and + + align:start position:0% +so up here activation energy e sub A and + + + align:start position:0% +so up here activation energy e sub A and +R our friend the gas + + align:start position:0% +R our friend the gas + + + align:start position:0% +R our friend the gas +constant and The Intercept of the line + + align:start position:0% +constant and The Intercept of the line + + + align:start position:0% +constant and The Intercept of the line +then is the natural log of a capital A + + align:start position:0% +then is the natural log of a capital A + + + align:start position:0% +then is the natural log of a capital A +and capital A has several different + + align:start position:0% +and capital A has several different + + + align:start position:0% +and capital A has several different +names you'll see it listed in different + + align:start position:0% +names you'll see it listed in different + + + align:start position:0% +names you'll see it listed in different +books as different things uh I think our + + align:start position:0% +books as different things uh I think our + + + align:start position:0% +books as different things uh I think our +book usually refers to it as factor a or + + align:start position:0% +book usually refers to it as factor a or + + + align:start position:0% +book usually refers to it as factor a or +the pre-exponential factor and it would + + align:start position:0% +the pre-exponential factor and it would + + + align:start position:0% +the pre-exponential factor and it would +have the same units as + + align:start position:0% +have the same units as + + + align:start position:0% +have the same units as +K so if one plots rate constants natural + + align:start position:0% +K so if one plots rate constants natural + + + align:start position:0% +K so if one plots rate constants natural +log of rate constants over one of + + align:start position:0% +log of rate constants over one of + + + align:start position:0% +log of rate constants over one of +temperature one could determine the + + align:start position:0% +temperature one could determine the + + + align:start position:0% +temperature one could determine the +activation energy for a reaction or uh + + align:start position:0% +activation energy for a reaction or uh + + + align:start position:0% +activation energy for a reaction or uh +the factor a for a particular + + align:start position:0% + + + + align:start position:0% + +reaction so these quantities factor a + + align:start position:0% +reaction so these quantities factor a + + + align:start position:0% +reaction so these quantities factor a +and activation energy are dependent on + + align:start position:0% +and activation energy are dependent on + + + align:start position:0% +and activation energy are dependent on +the reaction being studied so there'll + + align:start position:0% +the reaction being studied so there'll + + + align:start position:0% +the reaction being studied so there'll +be a particular measured value for one + + align:start position:0% +be a particular measured value for one + + + align:start position:0% +be a particular measured value for one +particular reaction so let's think a + + align:start position:0% +particular reaction so let's think a + + + align:start position:0% +particular reaction so let's think a +little bit more about what what these + + align:start position:0% +little bit more about what what these + + + align:start position:0% +little bit more about what what these +quantities + + align:start position:0% +quantities + + + align:start position:0% +quantities +are so factor + + align:start position:0% +are so factor + + + align:start position:0% +are so factor +a is a temperature dependent + + align:start position:0% + + + + align:start position:0% + +no it's not temperature dependent so + + align:start position:0% +no it's not temperature dependent so + + + align:start position:0% +no it's not temperature dependent so +what is it well if we look over + + align:start position:0% +what is it well if we look over + + + align:start position:0% +what is it well if we look over +here Factor the natural log of a is + + align:start position:0% +here Factor the natural log of a is + + + align:start position:0% +here Factor the natural log of a is +going to equal the natural log of + + align:start position:0% +going to equal the natural log of + + + align:start position:0% +going to equal the natural log of +K at zero over here and that means when + + align:start position:0% +K at zero over here and that means when + + + align:start position:0% +K at zero over here and that means when +1/ + + align:start position:0% +1/ + + + align:start position:0% +1/ +T is approx o imately zero so at what + + align:start position:0% +T is approx o imately zero so at what + + + align:start position:0% +T is approx o imately zero so at what +kinds of temperatures would + + align:start position:0% +kinds of temperatures would + + + align:start position:0% +kinds of temperatures would +1/t be approximately + + align:start position:0% +1/t be approximately + + + align:start position:0% +1/t be approximately +zero really really + + align:start position:0% +zero really really + + + align:start position:0% +zero really really +big so factor a is the rate constant for + + align:start position:0% +big so factor a is the rate constant for + + + align:start position:0% +big so factor a is the rate constant for +that reaction at some infinitely huge + + align:start position:0% +that reaction at some infinitely huge + + + align:start position:0% +that reaction at some infinitely huge +temperature so that's the maximum value + + align:start position:0% +temperature so that's the maximum value + + + align:start position:0% +temperature so that's the maximum value +you could get for that rate constant at + + align:start position:0% +you could get for that rate constant at + + + align:start position:0% +you could get for that rate constant at +really really huge temperature that's + + align:start position:0% +really really huge temperature that's + + + align:start position:0% +really really huge temperature that's +what it is it's not temperature + + align:start position:0% +what it is it's not temperature + + + align:start position:0% +what it is it's not temperature +dependent it's a quantity that's the + + align:start position:0% +dependent it's a quantity that's the + + + align:start position:0% +dependent it's a quantity that's the +sort of Maximum rate + + align:start position:0% +sort of Maximum rate + + + align:start position:0% +sort of Maximum rate +constant at the biggest temperature you + + align:start position:0% +constant at the biggest temperature you + + + align:start position:0% +constant at the biggest temperature you +can think of so that's what factor a + + align:start position:0% +can think of so that's what factor a + + + align:start position:0% +can think of so that's what factor a +is what about activation energy is that + + align:start position:0% +is what about activation energy is that + + + align:start position:0% +is what about activation energy is that +going to be temperature + + align:start position:0% +going to be temperature + + + align:start position:0% +going to be temperature +dependent no it won't be temperature + + align:start position:0% +dependent no it won't be temperature + + + align:start position:0% +dependent no it won't be temperature +dependent either you can calculate it + + align:start position:0% +dependent either you can calculate it + + + align:start position:0% +dependent either you can calculate it +it's the slope of the line so you can + + align:start position:0% +it's the slope of the line so you can + + + align:start position:0% +it's the slope of the line so you can +get it out of plotting these values but + + align:start position:0% +get it out of plotting these values but + + + align:start position:0% +get it out of plotting these values but +it's going to depend on the reaction + + align:start position:0% +it's going to depend on the reaction + + + align:start position:0% +it's going to depend on the reaction +being studied not the particular + + align:start position:0% +being studied not the particular + + + align:start position:0% +being studied not the particular +temperature and this is going to be + + align:start position:0% +temperature and this is going to be + + + align:start position:0% +temperature and this is going to be +important in a few minutes because we're + + align:start position:0% +important in a few minutes because we're + + + align:start position:0% +important in a few minutes because we're +going to be talking about the effects of + + align:start position:0% +going to be talking about the effects of + + + align:start position:0% +going to be talking about the effects of +rate constants on different temperatures + + align:start position:0% +rate constants on different temperatures + + + align:start position:0% +rate constants on different temperatures +and looking at equations and doing some + + align:start position:0% + + + + align:start position:0% + +calculations + + align:start position:0% +calculations + + + align:start position:0% +calculations +okay so we can rewrite this equation in + + align:start position:0% +okay so we can rewrite this equation in + + + align:start position:0% +okay so we can rewrite this equation in +a couple of different ways so you will + + align:start position:0% +a couple of different ways so you will + + + align:start position:0% +a couple of different ways so you will +see that equation for the straight line + + align:start position:0% +see that equation for the straight line + + + align:start position:0% +see that equation for the straight line +that oranus came up with um it's often + + align:start position:0% +that oranus came up with um it's often + + + align:start position:0% +that oranus came up with um it's often +uh it's called the uranous equation + + align:start position:0% +uh it's called the uranous equation + + + align:start position:0% +uh it's called the uranous equation +and it can be written basically just + + align:start position:0% +and it can be written basically just + + + align:start position:0% +and it can be written basically just +reversing these two terms I guess + + align:start position:0% +reversing these two terms I guess + + + align:start position:0% +reversing these two terms I guess +because it looks better that way I'm not + + align:start position:0% +because it looks better that way I'm not + + + align:start position:0% +because it looks better that way I'm not +really sure why you can't just keep it + + align:start position:0% +really sure why you can't just keep it + + + align:start position:0% +really sure why you can't just keep it +like that uh but you'll see it this way + + align:start position:0% +like that uh but you'll see it this way + + + align:start position:0% +like that uh but you'll see it this way +and you'll also see it Rewritten uh this + + align:start position:0% +and you'll also see it Rewritten uh this + + + align:start position:0% +and you'll also see it Rewritten uh this +way so instead of natural log of K uh + + align:start position:0% +way so instead of natural log of K uh + + + align:start position:0% +way so instead of natural log of K uh +you you would see it as solved for K so + + align:start position:0% +you you would see it as solved for K so + + + align:start position:0% +you you would see it as solved for K so +here the rate constant is equal to a + + align:start position:0% +here the rate constant is equal to a + + + align:start position:0% +here the rate constant is equal to a +which is this factor a this rate + + align:start position:0% +which is this factor a this rate + + + align:start position:0% +which is this factor a this rate +constant an infinitely huge temp + + align:start position:0% +constant an infinitely huge temp + + + align:start position:0% +constant an infinitely huge temp +tempatures uh times uh e to the minus uh + + align:start position:0% +tempatures uh times uh e to the minus uh + + + align:start position:0% +tempatures uh times uh e to the minus uh +EA the activation energy over uh RT so + + align:start position:0% +EA the activation energy over uh RT so + + + align:start position:0% +EA the activation energy over uh RT so +you'll also see this equation this way + + align:start position:0% +you'll also see this equation this way + + + align:start position:0% +you'll also see this equation this way +so it's a way of figuring out if you + + align:start position:0% +so it's a way of figuring out if you + + + align:start position:0% +so it's a way of figuring out if you +know the activation energy and you know + + align:start position:0% +know the activation energy and you know + + + align:start position:0% +know the activation energy and you know +factor a you can calculate rate + + align:start position:0% +factor a you can calculate rate + + + align:start position:0% +factor a you can calculate rate +constants at a particular + + align:start position:0% + + + + align:start position:0% + +temperature so it's not only uh gases + + align:start position:0% +temperature so it's not only uh gases + + + align:start position:0% +temperature so it's not only uh gases +that behave in this way that exhibit + + align:start position:0% +that behave in this way that exhibit + + + align:start position:0% +that behave in this way that exhibit +this uranous uh behavor behavior and you + + align:start position:0% +this uranous uh behavor behavior and you + + + align:start position:0% +this uranous uh behavor behavior and you +can apply these equations to other + + align:start position:0% +can apply these equations to other + + + align:start position:0% +can apply these equations to other +systems and let's just look at one other + + align:start position:0% +systems and let's just look at one other + + + align:start position:0% +systems and let's just look at one other +example of something that behaves with + + align:start position:0% +example of something that behaves with + + + align:start position:0% +example of something that behaves with +orous + + align:start position:0% + + + + align:start position:0% + +behavior what is + + align:start position:0% +behavior what is + + + align:start position:0% +behavior what is +this + + align:start position:0% +this + + + align:start position:0% +this +crickets how many of you have heard + + align:start position:0% +crickets how many of you have heard + + + align:start position:0% +crickets how many of you have heard +crickets in the + + align:start position:0% +crickets in the + + + align:start position:0% +crickets in the +wild oh almost + + align:start position:0% +wild oh almost + + + align:start position:0% +wild oh almost +everybody yeah some people people uh I + + align:start position:0% +everybody yeah some people people uh I + + + align:start position:0% +everybody yeah some people people uh I +was uh I spent some years as a summer + + align:start position:0% +was uh I spent some years as a summer + + + align:start position:0% +was uh I spent some years as a summer +camp + + align:start position:0% +camp + + + align:start position:0% +camp +counselor and uh we always had kids + + align:start position:0% +counselor and uh we always had kids + + + align:start position:0% +counselor and uh we always had kids +coming to the country from the city and + + align:start position:0% +coming to the country from the city and + + + align:start position:0% +coming to the country from the city and +there would be crickets and Bullfrogs + + align:start position:0% +there would be crickets and Bullfrogs + + + align:start position:0% +there would be crickets and Bullfrogs +and these poor kids that grew up you + + align:start position:0% +and these poor kids that grew up you + + + align:start position:0% +and these poor kids that grew up you +know right outside a hospital where all + + align:start position:0% +know right outside a hospital where all + + + align:start position:0% +know right outside a hospital where all +night long there'd be ambulances going + + align:start position:0% +night long there'd be ambulances going + + + align:start position:0% +night long there'd be ambulances going +by and traffic and helicopters and all + + align:start position:0% +by and traffic and helicopters and all + + + align:start position:0% +by and traffic and helicopters and all +sorts of things and they would sleep + + align:start position:0% +sorts of things and they would sleep + + + align:start position:0% +sorts of things and they would sleep +fine at home but then they would come to + + align:start position:0% +fine at home but then they would come to + + + align:start position:0% +fine at home but then they would come to +the country and uh they couldn't sleep a + + align:start position:0% +the country and uh they couldn't sleep a + + + align:start position:0% +the country and uh they couldn't sleep a +wink because of all of this noise the + + align:start position:0% +wink because of all of this noise the + + + align:start position:0% +wink because of all of this noise the +country is not as Qui as people think it + + align:start position:0% +country is not as Qui as people think it + + + align:start position:0% +country is not as Qui as people think it +is uh so uh crickets crickets will + + align:start position:0% +is uh so uh crickets crickets will + + + align:start position:0% +is uh so uh crickets crickets will +behave they will respond to temperature + + align:start position:0% +behave they will respond to temperature + + + align:start position:0% +behave they will respond to temperature +and so they actually chirp faster when + + align:start position:0% +and so they actually chirp faster when + + + align:start position:0% +and so they actually chirp faster when +it's hotter so if you're out camping you + + align:start position:0% +it's hotter so if you're out camping you + + + align:start position:0% +it's hotter so if you're out camping you +can count how many chirps there are in + + align:start position:0% +can count how many chirps there are in + + + align:start position:0% +can count how many chirps there are in +14 seconds and add that to 40 and get + + align:start position:0% +14 seconds and add that to 40 and get + + + align:start position:0% +14 seconds and add that to 40 and get +the temperature in fahrenheit has anyone + + align:start position:0% +the temperature in fahrenheit has anyone + + + align:start position:0% +the temperature in fahrenheit has anyone +actually tried + + align:start position:0% +actually tried + + + align:start position:0% +actually tried +this did it + + align:start position:0% +this did it + + + align:start position:0% +this did it +work you think so did you have a control + + align:start position:0% +work you think so did you have a control + + + align:start position:0% +work you think so did you have a control +of a thermometer with you no yeah it + + align:start position:0% +of a thermometer with you no yeah it + + + align:start position:0% +of a thermometer with you no yeah it +probably works better if you don't + + align:start position:0% +probably works better if you don't + + + align:start position:0% +probably works better if you don't +actually have the control but it should + + align:start position:0% +actually have the control but it should + + + align:start position:0% +actually have the control but it should +theoretically work if you can do a good + + align:start position:0% +theoretically work if you can do a good + + + align:start position:0% +theoretically work if you can do a good +job counting so that's an example of a a + + align:start position:0% +job counting so that's an example of a a + + + align:start position:0% +job counting so that's an example of a a +non- gas exhibiting this this uh this + + align:start position:0% + + + + align:start position:0% + +Behavior All right so let's talk more + + align:start position:0% +Behavior All right so let's talk more + + + align:start position:0% +Behavior All right so let's talk more +about the activation energy we're going + + align:start position:0% +about the activation energy we're going + + + align:start position:0% +about the activation energy we're going +to talk a lot about activation energy + + align:start position:0% +to talk a lot about activation energy + + + align:start position:0% +to talk a lot about activation energy +today + + align:start position:0% +today + + + align:start position:0% +today +so activation energy + + align:start position:0% +so activation energy + + + align:start position:0% +so activation energy +EA so if you have two molecules coming + + align:start position:0% +EA so if you have two molecules coming + + + align:start position:0% +EA so if you have two molecules coming +together and + + align:start position:0% +together and + + + align:start position:0% +together and +colliding sometimes they'll form + + align:start position:0% +colliding sometimes they'll form + + + align:start position:0% +colliding sometimes they'll form +products and sometimes they'll just fall + + align:start position:0% +products and sometimes they'll just fall + + + align:start position:0% +products and sometimes they'll just fall +away back into + + align:start position:0% +away back into + + + align:start position:0% +away back into +reactants so not every Collision will + + align:start position:0% +reactants so not every Collision will + + + align:start position:0% +reactants so not every Collision will +result in product why is + + align:start position:0% + + + + align:start position:0% + +that only the collisions that have the + + align:start position:0% +that only the collisions that have the + + + align:start position:0% +that only the collisions that have the +right amount of energy + + align:start position:0% +right amount of energy + + + align:start position:0% +right amount of energy +can go on and form products so really + + align:start position:0% +can go on and form products so really + + + align:start position:0% +can go on and form products so really +what activation energy is is some + + align:start position:0% +what activation energy is is some + + + align:start position:0% +what activation energy is is some +critical amount of energy that's + + align:start position:0% +critical amount of energy that's + + + align:start position:0% +critical amount of energy that's +required to go on and result in a + + align:start position:0% +required to go on and result in a + + + align:start position:0% +required to go on and result in a +reaction so only the molecules with that + + align:start position:0% +reaction so only the molecules with that + + + align:start position:0% +reaction so only the molecules with that +critical energy when they come together + + align:start position:0% +critical energy when they come together + + + align:start position:0% +critical energy when they come together +they'll go on to product other molecules + + align:start position:0% +they'll go on to product other molecules + + + align:start position:0% +they'll go on to product other molecules +will come together and they'll just fall + + align:start position:0% +will come together and they'll just fall + + + align:start position:0% +will come together and they'll just fall +apart because they won't be able to + + align:start position:0% +apart because they won't be able to + + + align:start position:0% +apart because they won't be able to +overcome this activation energy barrier + + align:start position:0% + + + + align:start position:0% + +so let's look at the effect of + + align:start position:0% +so let's look at the effect of + + + align:start position:0% +so let's look at the effect of +temperature on the molecules that have + + align:start position:0% +temperature on the molecules that have + + + align:start position:0% +temperature on the molecules that have +critical amounts of + + align:start position:0% + + + + align:start position:0% + +energy so if we plot then fraction of + + align:start position:0% + + + + align:start position:0% + +molecules fraction of molecules + + align:start position:0% +molecules fraction of molecules + + + align:start position:0% +molecules fraction of molecules +versus + + align:start position:0% +versus + + + align:start position:0% +versus +kinetic energy + + align:start position:0% + + + + align:start position:0% + +and we can look at + + align:start position:0% +and we can look at + + + align:start position:0% +and we can look at +molecules that have a low temperature or + + align:start position:0% +molecules that have a low temperature or + + + align:start position:0% +molecules that have a low temperature or +molecules at low + + align:start position:0% +molecules at low + + + align:start position:0% +molecules at low +temperature so there are some molecules + + align:start position:0% +temperature so there are some molecules + + + align:start position:0% +temperature so there are some molecules +at low + + align:start position:0% + + + + align:start position:0% + +temperature and we can look at some + + align:start position:0% +temperature and we can look at some + + + align:start position:0% +temperature and we can look at some +fractions of molecules at higher + + align:start position:0% + + + + align:start position:0% + +temperature and then + + align:start position:0% +temperature and then + + + align:start position:0% +temperature and then +consider the critical energy needed to + + align:start position:0% + + + + align:start position:0% + +react so the activation energy so + + align:start position:0% +react so the activation energy so + + + align:start position:0% +react so the activation energy so +molecules with that amount of energy or + + align:start position:0% +molecules with that amount of energy or + + + align:start position:0% +molecules with that amount of energy or +more will be able to react and if you + + align:start position:0% +more will be able to react and if you + + + align:start position:0% +more will be able to react and if you +look at the fraction of molecules then + + align:start position:0% +look at the fraction of molecules then + + + align:start position:0% +look at the fraction of molecules then +that would have that + + align:start position:0% +that would have that + + + align:start position:0% +that would have that +energy at higher temperatures more + + align:start position:0% +energy at higher temperatures more + + + align:start position:0% +energy at higher temperatures more +molecules have that critical iCal amount + + align:start position:0% +molecules have that critical iCal amount + + + align:start position:0% +molecules have that critical iCal amount +of energy and at lower temperature fewer + + align:start position:0% +of energy and at lower temperature fewer + + + align:start position:0% +of energy and at lower temperature fewer +molecules have that critical amount of + + align:start position:0% +molecules have that critical amount of + + + align:start position:0% +molecules have that critical amount of +energy so temperature makes a difference + + align:start position:0% +energy so temperature makes a difference + + + align:start position:0% +energy so temperature makes a difference +at higher temperature more things will + + align:start position:0% +at higher temperature more things will + + + align:start position:0% +at higher temperature more things will +be able to react and that's what gets + + align:start position:0% +be able to react and that's what gets + + + align:start position:0% +be able to react and that's what gets +into this this uh observation that + + align:start position:0% +into this this uh observation that + + + align:start position:0% +into this this uh observation that +reactions occur faster at higher + + align:start position:0% +reactions occur faster at higher + + + align:start position:0% +reactions occur faster at higher +temperatures more molecules have the + + align:start position:0% +temperatures more molecules have the + + + align:start position:0% +temperatures more molecules have the +critical energy needed to react when + + align:start position:0% +critical energy needed to react when + + + align:start position:0% +critical energy needed to react when +they're at higher temperature at lower + + align:start position:0% +they're at higher temperature at lower + + + align:start position:0% +they're at higher temperature at lower +temperature it's more difficult fewer + + align:start position:0% +temperature it's more difficult fewer + + + align:start position:0% +temperature it's more difficult fewer +fractions of those molecules have that + + align:start position:0% +fractions of those molecules have that + + + align:start position:0% +fractions of those molecules have that +critical energy can overcome an + + align:start position:0% +critical energy can overcome an + + + align:start position:0% +critical energy can overcome an +activation energy + + align:start position:0% +activation energy + + + align:start position:0% +activation energy +barrier so let's look at an example now + + align:start position:0% +barrier so let's look at an example now + + + align:start position:0% +barrier so let's look at an example now +of if you know and what the activation + + align:start position:0% +of if you know and what the activation + + + align:start position:0% +of if you know and what the activation +energy barrier is figuring out uh + + align:start position:0% +energy barrier is figuring out uh + + + align:start position:0% +energy barrier is figuring out uh +different uh rate constants at different + + align:start position:0% +different uh rate constants at different + + + align:start position:0% +different uh rate constants at different +temperatures how temperature is + + align:start position:0% +temperatures how temperature is + + + align:start position:0% +temperatures how temperature is +affecting the rate of the + + align:start position:0% +affecting the rate of the + + + align:start position:0% +affecting the rate of the +reaction so the example that we'll we'll + + align:start position:0% +reaction so the example that we'll we'll + + + align:start position:0% +reaction so the example that we'll we'll +look at is the Hydra hydrolysis of + + align:start position:0% +look at is the Hydra hydrolysis of + + + align:start position:0% +look at is the Hydra hydrolysis of +sucrose and this is part of the + + align:start position:0% +sucrose and this is part of the + + + align:start position:0% +sucrose and this is part of the +digestive process and + + align:start position:0% +digestive process and + + + align:start position:0% +digestive process and +digestion is a good thing so let's look + + align:start position:0% +digestion is a good thing so let's look + + + align:start position:0% +digestion is a good thing so let's look +at this particular + + align:start position:0% + + + + align:start position:0% + +reaction we're given an activation + + align:start position:0% +reaction we're given an activation + + + align:start position:0% +reaction we're given an activation +energy so someone's measured the + + align:start position:0% +energy so someone's measured the + + + align:start position:0% +energy so someone's measured the +activation energy for the hydrolysis of + + align:start position:0% +activation energy for the hydrolysis of + + + align:start position:0% +activation energy for the hydrolysis of +sucrose 108 K per mole and someone's + + align:start position:0% +sucrose 108 K per mole and someone's + + + align:start position:0% +sucrose 108 K per mole and someone's +measured a rate an observe rate a k off + + align:start position:0% +measured a rate an observe rate a k off + + + align:start position:0% +measured a rate an observe rate a k off +s of 1.0 * + + align:start position:0% +s of 1.0 * + + + align:start position:0% +s of 1.0 * +10-3 per molar per second at body + + align:start position:0% +10-3 per molar per second at body + + + align:start position:0% +10-3 per molar per second at body +temperature now you're asked to figure + + align:start position:0% +temperature now you're asked to figure + + + align:start position:0% +temperature now you're asked to figure +out what would the observed rate + + align:start position:0% +out what would the observed rate + + + align:start position:0% +out what would the observed rate +constant be if you lowered that + + align:start position:0% +constant be if you lowered that + + + align:start position:0% +constant be if you lowered that +temperature if you lowered it by 2° to + + align:start position:0% + + + + align:start position:0% + +35 so you could write two different + + align:start position:0% +35 so you could write two different + + + align:start position:0% +35 so you could write two different +Expressions you can use aous equation + + align:start position:0% +Expressions you can use aous equation + + + align:start position:0% +Expressions you can use aous equation +and write two different expression + + align:start position:0% +and write two different expression + + + align:start position:0% +and write two different expression +questions so over here we have the + + align:start position:0% +questions so over here we have the + + + align:start position:0% +questions so over here we have the +natural log of K1 the rate constant at + + align:start position:0% +natural log of K1 the rate constant at + + + align:start position:0% +natural log of K1 the rate constant at +one at one time and T1 at that + + align:start position:0% +one at one time and T1 at that + + + align:start position:0% +one at one time and T1 at that +temperature so the rate constant at + + align:start position:0% +temperature so the rate constant at + + + align:start position:0% +temperature so the rate constant at +temperature one and so that would be + + align:start position:0% +temperature one and so that would be + + + align:start position:0% +temperature one and so that would be +equal to the natural log of factor a + + align:start position:0% +equal to the natural log of factor a + + + align:start position:0% +equal to the natural log of factor a +again that's uh not temperature + + align:start position:0% +again that's uh not temperature + + + align:start position:0% +again that's uh not temperature +dependent minus EA the activation energy + + align:start position:0% +dependent minus EA the activation energy + + + align:start position:0% +dependent minus EA the activation energy +and then it's over RT and we write the + + align:start position:0% +and then it's over RT and we write the + + + align:start position:0% +and then it's over RT and we write the +same expression for a second temperature + + align:start position:0% +same expression for a second temperature + + + align:start position:0% +same expression for a second temperature +and a second r + + align:start position:0% +and a second r + + + align:start position:0% +and a second r +constant now we can combine these two + + align:start position:0% +constant now we can combine these two + + + align:start position:0% +constant now we can combine these two +expressions and come up with one + + align:start position:0% +expressions and come up with one + + + align:start position:0% +expressions and come up with one +equation so if we + + align:start position:0% +equation so if we + + + align:start position:0% +equation so if we +subtract we have natural log of the rate + + align:start position:0% +subtract we have natural log of the rate + + + align:start position:0% +subtract we have natural log of the rate +constant 2 minus the natural log of rate + + align:start position:0% +constant 2 minus the natural log of rate + + + align:start position:0% +constant 2 minus the natural log of rate +constant 1 and that can also be + + align:start position:0% +constant 1 and that can also be + + + align:start position:0% +constant 1 and that can also be +expressed in terms of natural log of K2 + + align:start position:0% +expressed in terms of natural log of K2 + + + align:start position:0% +expressed in terms of natural log of K2 +over + + align:start position:0% +over + + + align:start position:0% +over +K1 and here we can pull out uh the + + align:start position:0% +K1 and here we can pull out uh the + + + align:start position:0% +K1 and here we can pull out uh the +temperature terms so both of these have + + align:start position:0% +temperature terms so both of these have + + + align:start position:0% +temperature terms so both of these have +the same expression minus EA over R the + + align:start position:0% +the same expression minus EA over R the + + + align:start position:0% +the same expression minus EA over R the +rate constant and now we have the two + + align:start position:0% +rate constant and now we have the two + + + align:start position:0% +rate constant and now we have the two +temperatures so this expression is + + align:start position:0% +temperatures so this expression is + + + align:start position:0% +temperatures so this expression is +telling us how the rate constants are + + align:start position:0% +telling us how the rate constants are + + + align:start position:0% +telling us how the rate constants are +going to change with temperature for a + + align:start position:0% +going to change with temperature for a + + + align:start position:0% +going to change with temperature for a +particular activation energy what does + + align:start position:0% +particular activation energy what does + + + align:start position:0% +particular activation energy what does +this equation look like it should look + + align:start position:0% +this equation look like it should look + + + align:start position:0% +this equation look like it should look +familiar to + + align:start position:0% +familiar to + + + align:start position:0% +familiar to +you something that we talked about + + align:start position:0% + + + + align:start position:0% + +before what was that equation called + + align:start position:0% + + + + align:start position:0% + +Vanhoff equation and instead of rate + + align:start position:0% +Vanhoff equation and instead of rate + + + align:start position:0% +Vanhoff equation and instead of rate +constants we had + + align:start position:0% + + + + align:start position:0% + +what instead of rate constants there + + align:start position:0% + + + + align:start position:0% + +were equilibrium + + align:start position:0% +were equilibrium + + + align:start position:0% +were equilibrium +constants and instead of EA we had what + + align:start position:0% + + + + align:start position:0% + +what tells us about how equilibrium + + align:start position:0% +what tells us about how equilibrium + + + align:start position:0% +what tells us about how equilibrium +constants changes with temperature if + + align:start position:0% +constants changes with temperature if + + + align:start position:0% +constants changes with temperature if +you have a reaction and you heat up the + + align:start position:0% +you have a reaction and you heat up the + + + align:start position:0% +you have a reaction and you heat up the +reaction how do you know which direction + + align:start position:0% +reaction how do you know which direction + + + align:start position:0% +reaction how do you know which direction +it shifts what's our predictive + + align:start position:0% +it shifts what's our predictive + + + align:start position:0% +it shifts what's our predictive +tool Delta H right so this equation is + + align:start position:0% +tool Delta H right so this equation is + + + align:start position:0% +tool Delta H right so this equation is +similar to one we saw before here we're + + align:start position:0% +similar to one we saw before here we're + + + align:start position:0% +similar to one we saw before here we're +comparing how rate constants change with + + align:start position:0% +comparing how rate constants change with + + + align:start position:0% +comparing how rate constants change with +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +and a predictive tool is the size the + + align:start position:0% +and a predictive tool is the size the + + + align:start position:0% +and a predictive tool is the size the +magnitude of the activation energy + + align:start position:0% +magnitude of the activation energy + + + align:start position:0% +magnitude of the activation energy +before we were talking about how rate + + align:start position:0% +before we were talking about how rate + + + align:start position:0% +before we were talking about how rate +constants change with temperature and + + align:start position:0% +constants change with temperature and + + + align:start position:0% +constants change with temperature and +the predictive tool there was Delta H so + + align:start position:0% +the predictive tool there was Delta H so + + + align:start position:0% +the predictive tool there was Delta H so +in case you need a review of this we + + align:start position:0% +in case you need a review of this we + + + align:start position:0% +in case you need a review of this we +will review this actually at the end of + + align:start position:0% +will review this actually at the end of + + + align:start position:0% +will review this actually at the end of +the class because this is very exciting + + align:start position:0% +the class because this is very exciting + + + align:start position:0% +the class because this is very exciting +at the end of the class we come back to + + align:start position:0% +at the end of the class we come back to + + + align:start position:0% +at the end of the class we come back to +lat Lea's principle and we can explain + + align:start position:0% +lat Lea's principle and we can explain + + + align:start position:0% +lat Lea's principle and we can explain +later's principle uh in terms of + + align:start position:0% +later's principle uh in terms of + + + align:start position:0% +later's principle uh in terms of +temperature in a different way than we + + align:start position:0% +temperature in a different way than we + + + align:start position:0% +temperature in a different way than we +did when we started the course because + + align:start position:0% +did when we started the course because + + + align:start position:0% +did when we started the course because +now we can think about it in terms of + + align:start position:0% +now we can think about it in terms of + + + align:start position:0% +now we can think about it in terms of +activation energies and Ray constants so + + align:start position:0% +activation energies and Ray constants so + + + align:start position:0% +activation energies and Ray constants so +um we'll we'll see we'll see that + + align:start position:0% +um we'll we'll see we'll see that + + + align:start position:0% +um we'll we'll see we'll see that +Vanhoff equation again all right so for + + align:start position:0% +Vanhoff equation again all right so for + + + align:start position:0% +Vanhoff equation again all right so for +the moment now we're just considering + + align:start position:0% +the moment now we're just considering + + + align:start position:0% +the moment now we're just considering +how rate constants are changing with + + align:start position:0% +how rate constants are changing with + + + align:start position:0% +how rate constants are changing with +temperature so we can plug in our + + align:start position:0% +temperature so we can plug in our + + + align:start position:0% +temperature so we can plug in our +values the uh initial observed rate uh + + align:start position:0% +values the uh initial observed rate uh + + + align:start position:0% +values the uh initial observed rate uh +for the reaction at + + align:start position:0% +for the reaction at + + + align:start position:0% +for the reaction at +37° and we have K2 that we're going to + + align:start position:0% +37° and we have K2 that we're going to + + + align:start position:0% +37° and we have K2 that we're going to +solve for we are given the activation + + align:start position:0% +solve for we are given the activation + + + align:start position:0% +solve for we are given the activation +energy and uh we know the gas constant + + align:start position:0% +energy and uh we know the gas constant + + + align:start position:0% +energy and uh we know the gas constant +and we're given the two temperatures so + + align:start position:0% +and we're given the two temperatures so + + + align:start position:0% +and we're given the two temperatures so +the only thing uh tricky thing here is + + align:start position:0% +the only thing uh tricky thing here is + + + align:start position:0% +the only thing uh tricky thing here is +to remember to get your units to cancel + + align:start position:0% +to remember to get your units to cancel + + + align:start position:0% +to remember to get your units to cancel +out often activation energies are given + + align:start position:0% +out often activation energies are given + + + align:start position:0% +out often activation energies are given +in kog whereas your gas constant is in + + align:start position:0% +in kog whereas your gas constant is in + + + align:start position:0% +in kog whereas your gas constant is in +Jewels uh the temperatures here uh were + + align:start position:0% +Jewels uh the temperatures here uh were + + + align:start position:0% +Jewels uh the temperatures here uh were +given in Celsius but if you're using the + + align:start position:0% +given in Celsius but if you're using the + + + align:start position:0% +given in Celsius but if you're using the +gas constant you're going to need to + + align:start position:0% +gas constant you're going to need to + + + align:start position:0% +gas constant you're going to need to +convert them to Kelvin for your units to + + align:start position:0% +convert them to Kelvin for your units to + + + align:start position:0% +convert them to Kelvin for your units to +cancel so the only thing tricky about + + align:start position:0% +cancel so the only thing tricky about + + + align:start position:0% +cancel so the only thing tricky about +this is to make sure that your units are + + align:start position:0% +this is to make sure that your units are + + + align:start position:0% +this is to make sure that your units are +going to + + align:start position:0% +going to + + + align:start position:0% +going to +cancel and so we can solve this for + + align:start position:0% +cancel and so we can solve this for + + + align:start position:0% +cancel and so we can solve this for +K2 and K2 comes out to be 7.6 * + + align:start position:0% +K2 and K2 comes out to be 7.6 * + + + align:start position:0% +K2 and K2 comes out to be 7.6 * +10-4 per molar per second so it would be + + align:start position:0% +10-4 per molar per second so it would be + + + align:start position:0% +10-4 per molar per second so it would be +the same units as + + align:start position:0% +the same units as + + + align:start position:0% +the same units as +K1 and that's quite a bit + + align:start position:0% +K1 and that's quite a bit + + + align:start position:0% +K1 and that's quite a bit +slower so we only changed our + + align:start position:0% +slower so we only changed our + + + align:start position:0% +slower so we only changed our +temperature by 2° and yet the rate is + + align:start position:0% +temperature by 2° and yet the rate is + + + align:start position:0% +temperature by 2° and yet the rate is +quite a bit + + align:start position:0% +quite a bit + + + align:start position:0% +quite a bit +slower so so the body + + align:start position:0% +slower so so the body + + + align:start position:0% +slower so so the body +temperature are the reactions the + + align:start position:0% +temperature are the reactions the + + + align:start position:0% +temperature are the reactions the +enzymes in our bodies and uh how much + + align:start position:0% +enzymes in our bodies and uh how much + + + align:start position:0% +enzymes in our bodies and uh how much +they need to uh work how well they need + + align:start position:0% +they need to uh work how well they need + + + align:start position:0% +they need to uh work how well they need +to work is really optimized for the + + align:start position:0% +to work is really optimized for the + + + align:start position:0% +to work is really optimized for the +temperature of our particular body so if + + align:start position:0% +temperature of our particular body so if + + + align:start position:0% +temperature of our particular body so if +your body temperature drops quite a bit + + align:start position:0% +your body temperature drops quite a bit + + + align:start position:0% +your body temperature drops quite a bit +or if your body temperature goes up + + align:start position:0% +or if your body temperature goes up + + + align:start position:0% +or if your body temperature goes up +quite a bit uh that's not good for the + + align:start position:0% +quite a bit uh that's not good for the + + + align:start position:0% +quite a bit uh that's not good for the +overall working of the human body so + + align:start position:0% +overall working of the human body so + + + align:start position:0% +overall working of the human body so +just some advice for today like a day + + align:start position:0% +just some advice for today like a day + + + align:start position:0% +just some advice for today like a day +like this + + align:start position:0% +like this + + + align:start position:0% +like this +um it's best to keep your body + + align:start position:0% +um it's best to keep your body + + + align:start position:0% +um it's best to keep your body +temperature at uh the normal body + + align:start position:0% +temperature at uh the normal body + + + align:start position:0% +temperature at uh the normal body +temperature if you're spending a lot out + + align:start position:0% +temperature if you're spending a lot out + + + align:start position:0% +temperature if you're spending a lot out +time outside wear a hat wear a scarf + + align:start position:0% +time outside wear a hat wear a scarf + + + align:start position:0% +time outside wear a hat wear a scarf +wear gloves wear real shoes not sort of + + align:start position:0% +wear gloves wear real shoes not sort of + + + align:start position:0% +wear gloves wear real shoes not sort of +flip-flop type things and uh you should + + align:start position:0% +flip-flop type things and uh you should + + + align:start position:0% +flip-flop type things and uh you should +be able to continue to hydrolize your + + align:start position:0% +be able to continue to hydrolize your + + + align:start position:0% +be able to continue to hydrolize your +sucrose and digest but you have to start + + align:start position:0% +sucrose and digest but you have to start + + + align:start position:0% +sucrose and digest but you have to start +worrying about uh what clothes you're + + align:start position:0% +worrying about uh what clothes you're + + + align:start position:0% +worrying about uh what clothes you're +wearing this time of year in Boston for + + align:start position:0% +wearing this time of year in Boston for + + + align:start position:0% +wearing this time of year in Boston for +those of you who are from warmer + + align:start position:0% +those of you who are from warmer + + + align:start position:0% +those of you who are from warmer +climates + + align:start position:0% +climates + + + align:start position:0% +climates +all right so if we look at this uh + + align:start position:0% +all right so if we look at this uh + + + align:start position:0% +all right so if we look at this uh +equation again we'll see that if this + + align:start position:0% +equation again we'll see that if this + + + align:start position:0% +equation again we'll see that if this +term is large if you have a large + + align:start position:0% +term is large if you have a large + + + align:start position:0% +term is large if you have a large +activation energy if you have a large + + align:start position:0% +activation energy if you have a large + + + align:start position:0% +activation energy if you have a large +critical energy needed for that reaction + + align:start position:0% +critical energy needed for that reaction + + + align:start position:0% +critical energy needed for that reaction +to go then the uh that reaction will be + + align:start position:0% +to go then the uh that reaction will be + + + align:start position:0% +to go then the uh that reaction will be +very sensitive to changes in temperature + + align:start position:0% +very sensitive to changes in temperature + + + align:start position:0% +very sensitive to changes in temperature +I if this is a big number then you're + + align:start position:0% +I if this is a big number then you're + + + align:start position:0% +I if this is a big number then you're +going to see a big difference between K1 + + align:start position:0% +going to see a big difference between K1 + + + align:start position:0% +going to see a big difference between K1 +and K2 so this will tell you a lot about + + align:start position:0% +and K2 so this will tell you a lot about + + + align:start position:0% +and K2 so this will tell you a lot about +the reaction and we'll come back come + + align:start position:0% +the reaction and we'll come back come + + + align:start position:0% +the reaction and we'll come back come +back to this idea in a little + + align:start position:0% +back to this idea in a little + + + align:start position:0% +back to this idea in a little +bit all right so let's consider the + + align:start position:0% +bit all right so let's consider the + + + align:start position:0% +bit all right so let's consider the +reaction coordinate and uh activated + + align:start position:0% +reaction coordinate and uh activated + + + align:start position:0% +reaction coordinate and uh activated +complexes so there's this critical + + align:start position:0% +complexes so there's this critical + + + align:start position:0% +complexes so there's this critical +Collision energy this activation energy + + align:start position:0% +Collision energy this activation energy + + + align:start position:0% +Collision energy this activation energy +that's needed uh for these re molecules + + align:start position:0% +that's needed uh for these re molecules + + + align:start position:0% +that's needed uh for these re molecules +to actually react so uh why does this + + align:start position:0% +to actually react so uh why does this + + + align:start position:0% +to actually react so uh why does this +happen well as two uh two molecules may + + align:start position:0% +happen well as two uh two molecules may + + + align:start position:0% +happen well as two uh two molecules may +come toward each + + align:start position:0% +come toward each + + + align:start position:0% +come toward each +other they may not be able to react if + + align:start position:0% +other they may not be able to react if + + + align:start position:0% +other they may not be able to react if +they don't have that energy well why do + + align:start position:0% +they don't have that energy well why do + + + align:start position:0% +they don't have that energy well why do +they need energy well they may need to + + align:start position:0% +they need energy well they may need to + + + align:start position:0% +they need energy well they may need to +sort of rearrange you know a bond may be + + align:start position:0% +sort of rearrange you know a bond may be + + + align:start position:0% +sort of rearrange you know a bond may be +broken an atom may fall to the ground um + + align:start position:0% +broken an atom may fall to the ground um + + + align:start position:0% +broken an atom may fall to the ground um +new reactions are occurring there is + + align:start position:0% +new reactions are occurring there is + + + align:start position:0% +new reactions are occurring there is +energy needed to get your desired + + align:start position:0% +energy needed to get your desired + + + align:start position:0% +energy needed to get your desired +product uh they have to distort the + + align:start position:0% +product uh they have to distort the + + + align:start position:0% +product uh they have to distort the +bonds need to distort and that requires + + align:start position:0% +bonds need to distort and that requires + + + align:start position:0% +bonds need to distort and that requires +energy so the result is that usually + + align:start position:0% +energy so the result is that usually + + + align:start position:0% +energy so the result is that usually +before you go on to your product + + align:start position:0% +before you go on to your product + + + align:start position:0% +before you go on to your product +say so say this is a one of uh your + + align:start position:0% +say so say this is a one of uh your + + + align:start position:0% +say so say this is a one of uh your +products that uh you need to usually + + align:start position:0% +products that uh you need to usually + + + align:start position:0% +products that uh you need to usually +form some kind of intermediate State + + align:start position:0% +form some kind of intermediate State + + + align:start position:0% +form some kind of intermediate State +some kind of activated complex or + + align:start position:0% +some kind of activated complex or + + + align:start position:0% +some kind of activated complex or +transition state and that transition + + align:start position:0% +transition state and that transition + + + align:start position:0% +transition state and that transition +state can either go on to products or + + align:start position:0% +state can either go on to products or + + + align:start position:0% +state can either go on to products or +fall back to uh two + + align:start position:0% +fall back to uh two + + + align:start position:0% +fall back to uh two +reactants and only those molecules with + + align:start position:0% +reactants and only those molecules with + + + align:start position:0% +reactants and only those molecules with +this energy can do this reaction can + + align:start position:0% +this energy can do this reaction can + + + align:start position:0% +this energy can do this reaction can +overcome this barrier and go on to form + + align:start position:0% +overcome this barrier and go on to form + + + align:start position:0% +overcome this barrier and go on to form +products + + align:start position:0% +products + + + align:start position:0% +products +and so I'll show you a little movie of + + align:start position:0% +and so I'll show you a little movie of + + + align:start position:0% +and so I'll show you a little movie of +two molecules coming + + align:start position:0% +two molecules coming + + + align:start position:0% +two molecules coming +together they're going to circle each + + align:start position:0% +together they're going to circle each + + + align:start position:0% +together they're going to circle each +other and figure out if they have the + + align:start position:0% +other and figure out if they have the + + + align:start position:0% +other and figure out if they have the +critical energy to react and when they + + align:start position:0% +critical energy to react and when they + + + align:start position:0% +critical energy to react and when they +when they have that critical energy + + align:start position:0% +when they have that critical energy + + + align:start position:0% +when they have that critical energy +you'll know it and go on to product so + + align:start position:0% +you'll know it and go on to product so + + + align:start position:0% +you'll know it and go on to product so +let's just take a look at this uh + + align:start position:0% +let's just take a look at this uh + + + align:start position:0% +let's just take a look at this uh +reaction so here comes molecule in red + + align:start position:0% +reaction so here comes molecule in red + + + align:start position:0% +reaction so here comes molecule in red +and in blue they're checking each other + + align:start position:0% +and in blue they're checking each other + + + align:start position:0% +and in blue they're checking each other +out oh they had enough energy and they + + align:start position:0% +out oh they had enough energy and they + + + align:start position:0% +out oh they had enough energy and they +went on and for formed + + align:start position:0% +went on and for formed + + + align:start position:0% +went on and for formed +product okay but only those molecules + + align:start position:0% +product okay but only those molecules + + + align:start position:0% +product okay but only those molecules +with that energy can go on and form the + + align:start position:0% +with that energy can go on and form the + + + align:start position:0% +with that energy can go on and form the +product all right so let's draw a + + align:start position:0% +product all right so let's draw a + + + align:start position:0% +product all right so let's draw a +reaction coordinate now and uh look at + + align:start position:0% +reaction coordinate now and uh look at + + + align:start position:0% +reaction coordinate now and uh look at +these activation energy barriers and + + align:start position:0% +these activation energy barriers and + + + align:start position:0% +these activation energy barriers and +these transition + + align:start position:0% + + + + align:start position:0% + +complexes all right so a reaction + + align:start position:0% +complexes all right so a reaction + + + align:start position:0% +complexes all right so a reaction +coordinate diagram has potential energy + + align:start position:0% +coordinate diagram has potential energy + + + align:start position:0% +coordinate diagram has potential energy +on one side + + align:start position:0% + + + + align:start position:0% + +and has the reaction + + align:start position:0% +and has the reaction + + + align:start position:0% +and has the reaction +coordinate on the other + + align:start position:0% +coordinate on the other + + + align:start position:0% +coordinate on the other +axis and that just means the direction + + align:start position:0% +axis and that just means the direction + + + align:start position:0% +axis and that just means the direction +of the reaction so a reaction will start + + align:start position:0% +of the reaction so a reaction will start + + + align:start position:0% +of the reaction so a reaction will start +with + + align:start position:0% +with + + + align:start position:0% +with +reactants with a particular + + align:start position:0% +reactants with a particular + + + align:start position:0% +reactants with a particular +energy so in this case we're going to + + align:start position:0% +energy so in this case we're going to + + + align:start position:0% +energy so in this case we're going to +look at NO2 plus Co so we have two + + align:start position:0% +look at NO2 plus Co so we have two + + + align:start position:0% +look at NO2 plus Co so we have two +reactants at a particular energy + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +then these will react they will need to + + align:start position:0% +then these will react they will need to + + + align:start position:0% +then these will react they will need to +form some kind of activated complex up + + align:start position:0% +form some kind of activated complex up + + + align:start position:0% +form some kind of activated complex up +here so say there's bonds distorting and + + align:start position:0% +here so say there's bonds distorting and + + + align:start position:0% +here so say there's bonds distorting and +new bonds + + align:start position:0% +new bonds + + + align:start position:0% +new bonds +forming so there's some kind of + + align:start position:0% +forming so there's some kind of + + + align:start position:0% +forming so there's some kind of +intermediate State some kind of + + align:start position:0% +intermediate State some kind of + + + align:start position:0% +intermediate State some kind of +activated complex + + align:start position:0% + + + + align:start position:0% + +or transition + + align:start position:0% + + + + align:start position:0% + +state so there will be energy associated + + align:start position:0% +state so there will be energy associated + + + align:start position:0% +state so there will be energy associated +with getting up here if they have the + + align:start position:0% +with getting up here if they have the + + + align:start position:0% +with getting up here if they have the +critical energy to react they will go on + + align:start position:0% +critical energy to react they will go on + + + align:start position:0% +critical energy to react they will go on +then to + + align:start position:0% + + + + align:start position:0% + +products and our products here are n + + align:start position:0% +products and our products here are n + + + align:start position:0% +products and our products here are n +plus + + align:start position:0% +plus + + + align:start position:0% +plus +CO2 and these are our products + + align:start position:0% +CO2 and these are our products + + + align:start position:0% +CO2 and these are our products +and so that's what the reaction + + align:start position:0% +and so that's what the reaction + + + align:start position:0% +and so that's what the reaction +coordinate will look like if they didn't + + align:start position:0% +coordinate will look like if they didn't + + + align:start position:0% +coordinate will look like if they didn't +have enough energy it would just come + + align:start position:0% +have enough energy it would just come + + + align:start position:0% +have enough energy it would just come +back down + + align:start position:0% +back down + + + align:start position:0% +back down +here so this barrier up here is the + + align:start position:0% +here so this barrier up here is the + + + align:start position:0% +here so this barrier up here is the +activation energy for the forward + + align:start position:0% +activation energy for the forward + + + align:start position:0% +activation energy for the forward +reaction and this over + + align:start position:0% +reaction and this over + + + align:start position:0% +reaction and this over +here is the activation energy for the + + align:start position:0% +here is the activation energy for the + + + align:start position:0% +here is the activation energy for the +reverse + + align:start position:0% +reverse + + + align:start position:0% +reverse +reaction and overall + + align:start position:0% +reaction and overall + + + align:start position:0% +reaction and overall +you + + align:start position:0% +you + + + align:start position:0% +you +have a Delta e for the system so the + + align:start position:0% +have a Delta e for the system so the + + + align:start position:0% +have a Delta e for the system so the +difference between the energy of the + + align:start position:0% +difference between the energy of the + + + align:start position:0% +difference between the energy of the +reactants and the + + align:start position:0% + + + + align:start position:0% + +products so Delta e is going to equal + + align:start position:0% +products so Delta e is going to equal + + + align:start position:0% +products so Delta e is going to equal +the activation energy for the uh forward + + align:start position:0% + + + + align:start position:0% + +reaction the forward reaction minus the + + align:start position:0% +reaction the forward reaction minus the + + + align:start position:0% +reaction the forward reaction minus the +activation energy for the reverse + + align:start position:0% +activation energy for the reverse + + + align:start position:0% +activation energy for the reverse +reaction and we can put some numbers on + + align:start position:0% +reaction and we can put some numbers on + + + align:start position:0% +reaction and we can put some numbers on +this for the forward reaction was 132 K + + align:start position:0% +this for the forward reaction was 132 K + + + align:start position:0% +this for the forward reaction was 132 K +per + + align:start position:0% + + + + align:start position:0% + +mole and uh for the reverse reaction we + + align:start position:0% +mole and uh for the reverse reaction we + + + align:start position:0% +mole and uh for the reverse reaction we +have + + align:start position:0% +have + + + align:start position:0% +have +358 K per + + align:start position:0% +358 K per + + + align:start position:0% +358 K per +mole and our + + align:start position:0% +mole and our + + + align:start position:0% +mole and our +overall Delta e value is going to be- 2 + + align:start position:0% +overall Delta e value is going to be- 2 + + + align:start position:0% +overall Delta e value is going to be- 2 +226 K per + + align:start position:0% +226 K per + + + align:start position:0% +226 K per +mole + + align:start position:0% +mole + + + align:start position:0% +mole +so - + + align:start position:0% +so - + + + align:start position:0% +so - +226 K per + + align:start position:0% +226 K per + + + align:start position:0% +226 K per +mole is going to be equal to the + + align:start position:0% +mole is going to be equal to the + + + align:start position:0% +mole is going to be equal to the +132 K per + + align:start position:0% +132 K per + + + align:start position:0% +132 K per +mole + + align:start position:0% +mole + + + align:start position:0% +mole +minus the + + align:start position:0% +minus the + + + align:start position:0% +minus the +358 K per + + align:start position:0% + + + + align:start position:0% + +mole so these are all going to add up + + align:start position:0% +mole so these are all going to add up + + + align:start position:0% +mole so these are all going to add up +and that's one of the equations on your + + align:start position:0% +and that's one of the equations on your + + + align:start position:0% +and that's one of the equations on your +equation sheet that you need to know for + + align:start position:0% +equation sheet that you need to know for + + + align:start position:0% +equation sheet that you need to know for +the final that won't be provided but it + + align:start position:0% +the final that won't be provided but it + + + align:start position:0% +the final that won't be provided but it +makes rational sense uh that these + + align:start position:0% +makes rational sense uh that these + + + align:start position:0% +makes rational sense uh that these +should all add up + + align:start position:0% +should all add up + + + align:start position:0% +should all add up +together all right so how does this + + align:start position:0% +together all right so how does this + + + align:start position:0% +together all right so how does this +relate Delta e what is this Delta e well + + align:start position:0% +relate Delta e what is this Delta e well + + + align:start position:0% +relate Delta e what is this Delta e well +this is a quantity that can be measured + + align:start position:0% +this is a quantity that can be measured + + + align:start position:0% +this is a quantity that can be measured +it's a thermodynamic quality quantity it + + align:start position:0% +it's a thermodynamic quality quantity it + + + align:start position:0% +it's a thermodynamic quality quantity it +can come from calorimetry experiments + + align:start position:0% +can come from calorimetry experiments + + + align:start position:0% +can come from calorimetry experiments +and it's related to a friend of ours + + align:start position:0% +and it's related to a friend of ours + + + align:start position:0% +and it's related to a friend of ours +it's related to Delta H so um if you + + align:start position:0% +it's related to Delta H so um if you + + + align:start position:0% +it's related to Delta H so um if you +recall Delta H equals Delta e plus the + + align:start position:0% +recall Delta H equals Delta e plus the + + + align:start position:0% +recall Delta H equals Delta e plus the +change in PV and I think this was a + + align:start position:0% +change in PV and I think this was a + + + align:start position:0% +change in PV and I think this was a +lecture 17 from Professor Sarah's notes + + align:start position:0% +lecture 17 from Professor Sarah's notes + + + align:start position:0% +lecture 17 from Professor Sarah's notes +when she started talking about + + align:start position:0% +when she started talking about + + + align:start position:0% +when she started talking about +thermodynamics and so most of the time + + align:start position:0% +thermodynamics and so most of the time + + + align:start position:0% +thermodynamics and so most of the time +these are pretty similar to each other + + align:start position:0% +these are pretty similar to each other + + + align:start position:0% +these are pretty similar to each other +um for um for gases um there's a little + + align:start position:0% +um for um for gases um there's a little + + + align:start position:0% +um for um for gases um there's a little +bit of a difference this term uh exists + + align:start position:0% +bit of a difference this term uh exists + + + align:start position:0% +bit of a difference this term uh exists +so you might have like a 1 to 2% + + align:start position:0% +so you might have like a 1 to 2% + + + align:start position:0% +so you might have like a 1 to 2% +difference but it's more less the same + + align:start position:0% +difference but it's more less the same + + + align:start position:0% +difference but it's more less the same +so if it helps you to think about this + + align:start position:0% +so if it helps you to think about this + + + align:start position:0% +so if it helps you to think about this +as more or less the same as the Delta H + + align:start position:0% +as more or less the same as the Delta H + + + align:start position:0% +as more or less the same as the Delta H +uh that that can be useful for you + + align:start position:0% +uh that that can be useful for you + + + align:start position:0% +uh that that can be useful for you +they're very similar quantities + + align:start position:0% +they're very similar quantities + + + align:start position:0% +they're very similar quantities +there okay so again there's a + + align:start position:0% +there okay so again there's a + + + align:start position:0% +there okay so again there's a +barrier and for this reaction there's a + + align:start position:0% +barrier and for this reaction there's a + + + align:start position:0% +barrier and for this reaction there's a +smaller barrier going in the forward + + align:start position:0% +smaller barrier going in the forward + + + align:start position:0% +smaller barrier going in the forward +Direction the smaller activation energy + + align:start position:0% +Direction the smaller activation energy + + + align:start position:0% +Direction the smaller activation energy +um and a much bigger barrier for the + + align:start position:0% +um and a much bigger barrier for the + + + align:start position:0% +um and a much bigger barrier for the +reverse direction of this reaction + + align:start position:0% +reverse direction of this reaction + + + align:start position:0% +reverse direction of this reaction +so if we think about activation energy + + align:start position:0% +so if we think about activation energy + + + align:start position:0% +so if we think about activation energy +barriers um every reaction is going to + + align:start position:0% +barriers um every reaction is going to + + + align:start position:0% +barriers um every reaction is going to +have some activation energy barrier just + + align:start position:0% +have some activation energy barrier just + + + align:start position:0% +have some activation energy barrier just +like most things we do in life have some + + align:start position:0% +like most things we do in life have some + + + align:start position:0% +like most things we do in life have some +activation energy barrier for me writing + + align:start position:0% +activation energy barrier for me writing + + + align:start position:0% +activation energy barrier for me writing +papers or writing grants there's a very + + align:start position:0% +papers or writing grants there's a very + + + align:start position:0% +papers or writing grants there's a very +large activation energy barrier to get + + align:start position:0% +large activation energy barrier to get + + + align:start position:0% +large activation energy barrier to get +started so the getting started part and + + align:start position:0% +started so the getting started part and + + + align:start position:0% +started so the getting started part and +it's usually kind of more like this + + align:start position:0% +it's usually kind of more like this + + + align:start position:0% +it's usually kind of more like this +direction this kind of size activation + + align:start position:0% +direction this kind of size activation + + + align:start position:0% +direction this kind of size activation +energy barrier once I manage to kind of + + align:start position:0% +energy barrier once I manage to kind of + + + align:start position:0% +energy barrier once I manage to kind of +get up over the hump really get started + + align:start position:0% +get up over the hump really get started + + + align:start position:0% +get up over the hump really get started +uh then then uh then it becomes much + + align:start position:0% +uh then then uh then it becomes much + + + align:start position:0% +uh then then uh then it becomes much +easier and I can really get going with + + align:start position:0% +easier and I can really get going with + + + align:start position:0% +easier and I can really get going with +this um I imagine that if I recall back + + align:start position:0% +this um I imagine that if I recall back + + + align:start position:0% +this um I imagine that if I recall back +to uh studying for final exams going + + align:start position:0% +to uh studying for final exams going + + + align:start position:0% +to uh studying for final exams going +back over the old material that you + + align:start position:0% +back over the old material that you + + + align:start position:0% +back over the old material that you +already covered and reviewing that there + + align:start position:0% +already covered and reviewing that there + + + align:start position:0% +already covered and reviewing that there +is a sizable activation energy barrier + + align:start position:0% +is a sizable activation energy barrier + + + align:start position:0% +is a sizable activation energy barrier +to pulling out those first set of notes + + align:start position:0% +to pulling out those first set of notes + + + align:start position:0% +to pulling out those first set of notes +and pulling out exam one and looking at + + align:start position:0% +and pulling out exam one and looking at + + + align:start position:0% +and pulling out exam one and looking at +the things that you got wrong and going + + align:start position:0% +the things that you got wrong and going + + + align:start position:0% +the things that you got wrong and going +back over it has an activation energy + + align:start position:0% +back over it has an activation energy + + + align:start position:0% +back over it has an activation energy +barrier and what we're going to talk + + align:start position:0% +barrier and what we're going to talk + + + align:start position:0% +barrier and what we're going to talk +about on Monday a little bit is some + + align:start position:0% +about on Monday a little bit is some + + + align:start position:0% +about on Monday a little bit is some +tricks to get over those activation + + align:start position:0% +tricks to get over those activation + + + align:start position:0% +tricks to get over those activation +energy barriers catalysts can lower the + + align:start position:0% +energy barriers catalysts can lower the + + + align:start position:0% +energy barriers catalysts can lower the +activation energy barrier um and uh for + + align:start position:0% +activation energy barrier um and uh for + + + align:start position:0% +activation energy barrier um and uh for +most of us an enormous level of stress + + align:start position:0% +most of us an enormous level of stress + + + align:start position:0% +most of us an enormous level of stress +can also help us get over that + + align:start position:0% +can also help us get over that + + + align:start position:0% +can also help us get over that +activation energy barrier uh your + + align:start position:0% +activation energy barrier uh your + + + align:start position:0% +activation energy barrier uh your +professor for example mentioning the + + align:start position:0% +professor for example mentioning the + + + align:start position:0% +professor for example mentioning the +final exam every day before a class + + align:start position:0% +final exam every day before a class + + + align:start position:0% +final exam every day before a class +starts can be a little help getting over + + align:start position:0% +starts can be a little help getting over + + + align:start position:0% +starts can be a little help getting over +that activation energy barrier to uh + + align:start position:0% +that activation energy barrier to uh + + + align:start position:0% +that activation energy barrier to uh +start reviewing material so this kind of + + align:start position:0% +start reviewing material so this kind of + + + align:start position:0% +start reviewing material so this kind of +plot should you should feel like you + + align:start position:0% +plot should you should feel like you + + + align:start position:0% +plot should you should feel like you +should bond with this idea of activation + + align:start position:0% +should bond with this idea of activation + + + align:start position:0% +should bond with this idea of activation +energy barriers you should understand + + align:start position:0% +energy barriers you should understand + + + align:start position:0% +energy barriers you should understand +the deepest level about these barriers + + align:start position:0% +the deepest level about these barriers + + + align:start position:0% +the deepest level about these barriers +that these molecules need to uh to + + align:start position:0% +that these molecules need to uh to + + + align:start position:0% +that these molecules need to uh to +overcome + + align:start position:0% + + + + align:start position:0% + +all right so let's look at the effect of + + align:start position:0% +all right so let's look at the effect of + + + align:start position:0% +all right so let's look at the effect of +temperature on whether molecules can + + align:start position:0% +temperature on whether molecules can + + + align:start position:0% +temperature on whether molecules can +make it over those activation energy + + align:start position:0% +make it over those activation energy + + + align:start position:0% +make it over those activation energy +barriers so again for an elementary + + align:start position:0% +barriers so again for an elementary + + + align:start position:0% +barriers so again for an elementary +reaction there's always a barrier it's + + align:start position:0% +reaction there's always a barrier it's + + + align:start position:0% +reaction there's always a barrier it's +always a barrier sometimes it's smaller + + align:start position:0% +always a barrier sometimes it's smaller + + + align:start position:0% +always a barrier sometimes it's smaller +sometimes it's larger but there's always + + align:start position:0% +sometimes it's larger but there's always + + + align:start position:0% +sometimes it's larger but there's always +a barrier to that so there's always a + + align:start position:0% +a barrier to that so there's always a + + + align:start position:0% +a barrier to that so there's always a +positive uh EA here + + align:start position:0% +positive uh EA here + + + align:start position:0% +positive uh EA here +okay so what happens if you increase + + align:start position:0% +okay so what happens if you increase + + + align:start position:0% +okay so what happens if you increase +temperature so if you increase + + align:start position:0% +temperature so if you increase + + + align:start position:0% +temperature so if you increase +temperature it should increase the rate + + align:start position:0% +temperature it should increase the rate + + + align:start position:0% +temperature it should increase the rate +because of this down here you increase + + align:start position:0% +because of this down here you increase + + + align:start position:0% +because of this down here you increase +temperature more molecules will have the + + align:start position:0% +temperature more molecules will have the + + + align:start position:0% +temperature more molecules will have the +energy required to make it over that + + align:start position:0% +energy required to make it over that + + + align:start position:0% +energy required to make it over that +barrier so for an elementary reaction + + align:start position:0% +barrier so for an elementary reaction + + + align:start position:0% +barrier so for an elementary reaction +increasing temperature will increase the + + align:start position:0% +increasing temperature will increase the + + + align:start position:0% +increasing temperature will increase the +rate they'll get over the barrier for an + + align:start position:0% +rate they'll get over the barrier for an + + + align:start position:0% +rate they'll get over the barrier for an +overall reactions for a more complicated + + align:start position:0% +overall reactions for a more complicated + + + align:start position:0% +overall reactions for a more complicated +reaction that has multiple steps um it's + + align:start position:0% +reaction that has multiple steps um it's + + + align:start position:0% +reaction that has multiple steps um it's +not necessarily clear the temperature is + + align:start position:0% +not necessarily clear the temperature is + + + align:start position:0% +not necessarily clear the temperature is +going to have this effect and let's + + align:start position:0% +going to have this effect and let's + + + align:start position:0% +going to have this effect and let's +consider uh why this is + + align:start position:0% +consider uh why this is + + + align:start position:0% +consider uh why this is +true so let's look at the same reaction + + align:start position:0% +true so let's look at the same reaction + + + align:start position:0% +true so let's look at the same reaction +we looked at with mechanisms last time + + align:start position:0% +we looked at with mechanisms last time + + + align:start position:0% +we looked at with mechanisms last time +and figure out what all the K observed + + align:start position:0% +and figure out what all the K observed + + + align:start position:0% +and figure out what all the K observed +terms are are there small rate constants + + align:start position:0% +terms are are there small rate constants + + + align:start position:0% +terms are are there small rate constants +are there equilibrium constants what + + align:start position:0% +are there equilibrium constants what + + + align:start position:0% +are there equilibrium constants what +does kobs really mean and then we can + + align:start position:0% +does kobs really mean and then we can + + + align:start position:0% +does kobs really mean and then we can +think about how temperature would affect + + align:start position:0% +think about how temperature would affect + + + align:start position:0% +think about how temperature would affect +those values so here we have a reaction + + align:start position:0% +those values so here we have a reaction + + + align:start position:0% +those values so here we have a reaction +with the fast reversible step followed + + align:start position:0% +with the fast reversible step followed + + + align:start position:0% +with the fast reversible step followed +by another step that's + + align:start position:0% +by another step that's + + + align:start position:0% +by another step that's +slow so we can say that the uh rate of + + align:start position:0% +slow so we can say that the uh rate of + + + align:start position:0% +slow so we can say that the uh rate of +product formation our product here is + + align:start position:0% +product formation our product here is + + + align:start position:0% +product formation our product here is +NO2 is going to be equal to two because + + align:start position:0% +NO2 is going to be equal to two because + + + align:start position:0% +NO2 is going to be equal to two because +two are formed K2 this rate constant + + align:start position:0% +two are formed K2 this rate constant + + + align:start position:0% +two are formed K2 this rate constant +times uh this intermediate here times + + align:start position:0% +times uh this intermediate here times + + + align:start position:0% +times uh this intermediate here times +the concentration of oxygen so that's + + align:start position:0% +the concentration of oxygen so that's + + + align:start position:0% +the concentration of oxygen so that's +just this last step this slow step rate + + align:start position:0% +just this last step this slow step rate + + + align:start position:0% +just this last step this slow step rate +of formation of product but this is an + + align:start position:0% +of formation of product but this is an + + + align:start position:0% +of formation of product but this is an +intermediate so we're not done we have + + align:start position:0% +intermediate so we're not done we have + + + align:start position:0% +intermediate so we're not done we have +to get rid of this + + align:start position:0% +to get rid of this + + + align:start position:0% +to get rid of this +intermediate and here we can do it + + align:start position:0% +intermediate and here we can do it + + + align:start position:0% +intermediate and here we can do it +fairly efficiently because we have a + + align:start position:0% +fairly efficiently because we have a + + + align:start position:0% +fairly efficiently because we have a +fast reversible step uh followed by a + + align:start position:0% +fast reversible step uh followed by a + + + align:start position:0% +fast reversible step uh followed by a +slow step so we can approximate that + + align:start position:0% +slow step so we can approximate that + + + align:start position:0% +slow step so we can approximate that +this step is an equilibrium and if we + + align:start position:0% +this step is an equilibrium and if we + + + align:start position:0% +this step is an equilibrium and if we +approximate that then we can solve for + + align:start position:0% +approximate that then we can solve for + + + align:start position:0% +approximate that then we can solve for +this intermediate in terms of an + + align:start position:0% +this intermediate in terms of an + + + align:start position:0% +this intermediate in terms of an +equilibrium expression + + align:start position:0% +equilibrium expression + + + align:start position:0% +equilibrium expression +so again the first step fast and + + align:start position:0% +so again the first step fast and + + + align:start position:0% +so again the first step fast and +reversible the Second Step slow so this + + align:start position:0% +reversible the Second Step slow so this + + + align:start position:0% +reversible the Second Step slow so this +is pretty much in equilibrium not much + + align:start position:0% +is pretty much in equilibrium not much + + + align:start position:0% +is pretty much in equilibrium not much +of this intermediate is being siphoned + + align:start position:0% +of this intermediate is being siphoned + + + align:start position:0% +of this intermediate is being siphoned +off to + + align:start position:0% +off to + + + align:start position:0% +off to +products so we can solve by setting up + + align:start position:0% +products so we can solve by setting up + + + align:start position:0% +products so we can solve by setting up +an equilibrium + + align:start position:0% +an equilibrium + + + align:start position:0% +an equilibrium +expression so here's the equilibrium + + align:start position:0% +expression so here's the equilibrium + + + align:start position:0% +expression so here's the equilibrium +expression equilibrium constant for step + + align:start position:0% +expression equilibrium constant for step + + + align:start position:0% +expression equilibrium constant for step +one equals rate constant for the forward + + align:start position:0% +one equals rate constant for the forward + + + align:start position:0% +one equals rate constant for the forward +reaction over rate constant for the + + align:start position:0% +reaction over rate constant for the + + + align:start position:0% +reaction over rate constant for the +reverse reaction equals products over + + align:start position:0% +reverse reaction equals products over + + + align:start position:0% +reverse reaction equals products over +reactants they're two reactants 2 n o so + + align:start position:0% +reactants they're two reactants 2 n o so + + + align:start position:0% +reactants they're two reactants 2 n o so +it's no^ sared and we could solve for + + align:start position:0% +it's no^ sared and we could solve for + + + align:start position:0% +it's no^ sared and we could solve for +the concentration of in the intermediate + + align:start position:0% +the concentration of in the intermediate + + + align:start position:0% +the concentration of in the intermediate +then uh which would be K1 time no^ + + align:start position:0% + + + + align:start position:0% + +2 so now we can substitute that in the + + align:start position:0% +2 so now we can substitute that in the + + + align:start position:0% +2 so now we can substitute that in the +overall expression and we have this + + align:start position:0% +overall expression and we have this + + + align:start position:0% +overall expression and we have this +expression here now our kovs is going to + + align:start position:0% +expression here now our kovs is going to + + + align:start position:0% +expression here now our kovs is going to +be equal to this 2 K2 2 and big + + align:start position:0% +be equal to this 2 K2 2 and big + + + align:start position:0% +be equal to this 2 K2 2 and big +K1 so this is uh what we need to + + align:start position:0% +K1 so this is uh what we need to + + + align:start position:0% +K1 so this is uh what we need to +consider how that's affected by + + align:start position:0% +consider how that's affected by + + + align:start position:0% +consider how that's affected by +temperature little + + align:start position:0% +temperature little + + + align:start position:0% +temperature little +K2 is an elementary rate constant so for + + align:start position:0% +K2 is an elementary rate constant so for + + + align:start position:0% +K2 is an elementary rate constant so for +an elementary reaction increasing + + align:start position:0% +an elementary reaction increasing + + + align:start position:0% +an elementary reaction increasing +temperature will always increase rate so + + align:start position:0% +temperature will always increase rate so + + + align:start position:0% +temperature will always increase rate so +we know how this is affected but now and + + align:start position:0% +we know how this is affected but now and + + + align:start position:0% +we know how this is affected but now and +here is our expression that we looked at + + align:start position:0% +here is our expression that we looked at + + + align:start position:0% +here is our expression that we looked at +before but now what about the + + align:start position:0% +before but now what about the + + + align:start position:0% +before but now what about the +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +constant an equilibrium constant how do + + align:start position:0% +constant an equilibrium constant how do + + + align:start position:0% +constant an equilibrium constant how do +you know what's going to happen with an + + align:start position:0% +you know what's going to happen with an + + + align:start position:0% +you know what's going to happen with an +equilibrium constant if it'll get bigger + + align:start position:0% +equilibrium constant if it'll get bigger + + + align:start position:0% +equilibrium constant if it'll get bigger +or smaller with temperature what's the + + align:start position:0% +or smaller with temperature what's the + + + align:start position:0% +or smaller with temperature what's the +equation that relates equilibrium + + align:start position:0% +equation that relates equilibrium + + + align:start position:0% +equation that relates equilibrium +constants and + + align:start position:0% + + + + align:start position:0% + +temperature Vanhoff right so uh so it + + align:start position:0% +temperature Vanhoff right so uh so it + + + align:start position:0% +temperature Vanhoff right so uh so it +depends on Delta H it depends on whether + + align:start position:0% +depends on Delta H it depends on whether + + + align:start position:0% +depends on Delta H it depends on whether +the reaction is endothermic or + + align:start position:0% +the reaction is endothermic or + + + align:start position:0% +the reaction is endothermic or +exothermic + + align:start position:0% +exothermic + + + align:start position:0% +exothermic +and here's that expression so the uh you + + align:start position:0% +and here's that expression so the uh you + + + align:start position:0% +and here's that expression so the uh you +can see these are really very similar + + align:start position:0% +can see these are really very similar + + + align:start position:0% +can see these are really very similar +Expressions so here we have the + + align:start position:0% +Expressions so here we have the + + + align:start position:0% +Expressions so here we have the +equilibrium constants Delta H is our + + align:start position:0% +equilibrium constants Delta H is our + + + align:start position:0% +equilibrium constants Delta H is our +predictive tool whether that's + + align:start position:0% +predictive tool whether that's + + + align:start position:0% +predictive tool whether that's +endothermic or exothermic will depend on + + align:start position:0% +endothermic or exothermic will depend on + + + align:start position:0% +endothermic or exothermic will depend on +what direction it goes it'll depend on + + align:start position:0% +what direction it goes it'll depend on + + + align:start position:0% +what direction it goes it'll depend on +whether K1 is bigger than K2 or K2 is + + align:start position:0% +whether K1 is bigger than K2 or K2 is + + + align:start position:0% +whether K1 is bigger than K2 or K2 is +bigger than K1 with a change in + + align:start position:0% +bigger than K1 with a change in + + + align:start position:0% +bigger than K1 with a change in +temperature and over here we have the + + align:start position:0% +temperature and over here we have the + + + align:start position:0% +temperature and over here we have the +expression that relates rate constants + + align:start position:0% +expression that relates rate constants + + + align:start position:0% +expression that relates rate constants +uh with temperature and in terms of sign + + align:start position:0% +uh with temperature and in terms of sign + + + align:start position:0% +uh with temperature and in terms of sign +that's not an issue here because + + align:start position:0% +that's not an issue here because + + + align:start position:0% +that's not an issue here because +activation energy is always positive + + align:start position:0% +activation energy is always positive + + + align:start position:0% +activation energy is always positive +there is always a barrier to overcome so + + align:start position:0% +there is always a barrier to overcome so + + + align:start position:0% +there is always a barrier to overcome so +that's always POS there never a negative + + align:start position:0% +that's always POS there never a negative + + + align:start position:0% +that's always POS there never a negative +barrier so there's no sign change here + + align:start position:0% +barrier so there's no sign change here + + + align:start position:0% +barrier so there's no sign change here +but there is an effect of magnitude of + + align:start position:0% +but there is an effect of magnitude of + + + align:start position:0% +but there is an effect of magnitude of +that value as there is with this so it's + + align:start position:0% +that value as there is with this so it's + + + align:start position:0% +that value as there is with this so it's +not so simple so if you have a + + align:start position:0% +not so simple so if you have a + + + align:start position:0% +not so simple so if you have a +multi-step reaction it's not always so + + align:start position:0% +multi-step reaction it's not always so + + + align:start position:0% +multi-step reaction it's not always so +simple to predict what temperature will + + align:start position:0% +simple to predict what temperature will + + + align:start position:0% +simple to predict what temperature will +the effect of temperature because it may + + align:start position:0% +the effect of temperature because it may + + + align:start position:0% +the effect of temperature because it may +be changing one thing in one way and + + align:start position:0% +be changing one thing in one way and + + + align:start position:0% +be changing one thing in one way and +something else in another + + align:start position:0% +something else in another + + + align:start position:0% +something else in another +way so let's uh let's consider uh this + + align:start position:0% +way so let's uh let's consider uh this + + + align:start position:0% +way so let's uh let's consider uh this +particular one here again um little K is + + align:start position:0% +particular one here again um little K is + + + align:start position:0% +particular one here again um little K is +always going to increase with + + align:start position:0% +always going to increase with + + + align:start position:0% +always going to increase with +temperature the equilibrium constant in + + align:start position:0% +temperature the equilibrium constant in + + + align:start position:0% +temperature the equilibrium constant in +this case will decrease because it's an + + align:start position:0% +this case will decrease because it's an + + + align:start position:0% +this case will decrease because it's an +exothermic reaction so this particular + + align:start position:0% +exothermic reaction so this particular + + + align:start position:0% +exothermic reaction so this particular +reaction is exothermic so if we think + + align:start position:0% +reaction is exothermic so if we think + + + align:start position:0% +reaction is exothermic so if we think +about lat leer or we think about the + + align:start position:0% +about lat leer or we think about the + + + align:start position:0% +about lat leer or we think about the +Vanhoff equation we say if it's an + + align:start position:0% +Vanhoff equation we say if it's an + + + align:start position:0% +Vanhoff equation we say if it's an +exothermic reaction action increasing + + align:start position:0% +exothermic reaction action increasing + + + align:start position:0% +exothermic reaction action increasing +the temperature will decrease the K + + align:start position:0% +the temperature will decrease the K + + + align:start position:0% +the temperature will decrease the K +because you're going to shift the + + align:start position:0% +because you're going to shift the + + + align:start position:0% +because you're going to shift the +reaction in the endothermic direction to + + align:start position:0% +reaction in the endothermic direction to + + + align:start position:0% +reaction in the endothermic direction to +use up the + + align:start position:0% + + + + align:start position:0% + +heat so the magnitude of the increase or + + align:start position:0% +heat so the magnitude of the increase or + + + align:start position:0% +heat so the magnitude of the increase or +decrease will depend on the magnitude of + + align:start position:0% +decrease will depend on the magnitude of + + + align:start position:0% +decrease will depend on the magnitude of +the energy barrier and the magnitude of + + align:start position:0% +the energy barrier and the magnitude of + + + align:start position:0% +the energy barrier and the magnitude of +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +H so if we look at this particular + + align:start position:0% +H so if we look at this particular + + + align:start position:0% +H so if we look at this particular +example + + align:start position:0% +example + + + align:start position:0% +example +and you're told for this particular + + align:start position:0% +and you're told for this particular + + + align:start position:0% +and you're told for this particular +example that the activation energy is a + + align:start position:0% +example that the activation energy is a + + + align:start position:0% +example that the activation energy is a +small number it's not a very big + + align:start position:0% +small number it's not a very big + + + align:start position:0% +small number it's not a very big +activation energy barrier and you're + + align:start position:0% +activation energy barrier and you're + + + align:start position:0% +activation energy barrier and you're +also told then that Delta H is a big + + align:start position:0% +also told then that Delta H is a big + + + align:start position:0% +also told then that Delta H is a big +number and it's a big negative number so + + align:start position:0% +number and it's a big negative number so + + + align:start position:0% +number and it's a big negative number so +what would that mean then well if you + + align:start position:0% +what would that mean then well if you + + + align:start position:0% +what would that mean then well if you +look at this if you have a small number + + align:start position:0% +look at this if you have a small number + + + align:start position:0% +look at this if you have a small number +for activation energy then there's not + + align:start position:0% +for activation energy then there's not + + + align:start position:0% +for activation energy then there's not +going to be a big difference between the + + align:start position:0% +going to be a big difference between the + + + align:start position:0% +going to be a big difference between the +K so the rate constants only going to + + align:start position:0% +K so the rate constants only going to + + + align:start position:0% +K so the rate constants only going to +increase a little bit because this is a + + align:start position:0% +increase a little bit because this is a + + + align:start position:0% +increase a little bit because this is a +small number on the other hand if Delta + + align:start position:0% +small number on the other hand if Delta + + + align:start position:0% +small number on the other hand if Delta +H is a big number and your told Delta H + + align:start position:0% +H is a big number and your told Delta H + + + align:start position:0% +H is a big number and your told Delta H +is a big number then you should have the + + align:start position:0% +is a big number then you should have the + + + align:start position:0% +is a big number then you should have the +equilibrium constant should be very + + align:start position:0% +equilibrium constant should be very + + + align:start position:0% +equilibrium constant should be very +sensitive to changes in temperature you + + align:start position:0% +sensitive to changes in temperature you + + + align:start position:0% +sensitive to changes in temperature you +should see a big difference in the + + align:start position:0% +should see a big difference in the + + + align:start position:0% +should see a big difference in the +equilibrium constants because this is a + + align:start position:0% +equilibrium constants because this is a + + + align:start position:0% +equilibrium constants because this is a +really big number so this particular + + align:start position:0% +really big number so this particular + + + align:start position:0% +really big number so this particular +reaction is an example where increasing + + align:start position:0% +reaction is an example where increasing + + + align:start position:0% +reaction is an example where increasing +the temperature can actually decrease + + align:start position:0% +the temperature can actually decrease + + + align:start position:0% +the temperature can actually decrease +the observed rate and the effect is + + align:start position:0% +the observed rate and the effect is + + + align:start position:0% +the observed rate and the effect is +because of the Delta + + align:start position:0% + + + + align:start position:0% + +H so again a large activation energy + + align:start position:0% +H so again a large activation energy + + + align:start position:0% +H so again a large activation energy +means that the rate constant is very + + align:start position:0% +means that the rate constant is very + + + align:start position:0% +means that the rate constant is very +sensitive to changes in temperature a + + align:start position:0% +sensitive to changes in temperature a + + + align:start position:0% +sensitive to changes in temperature a +large Delta h means that the equilibrium + + align:start position:0% +large Delta h means that the equilibrium + + + align:start position:0% +large Delta h means that the equilibrium +constant is very sensitive to changes in + + align:start position:0% +constant is very sensitive to changes in + + + align:start position:0% +constant is very sensitive to changes in +temperature so our predictors are uh + + align:start position:0% +temperature so our predictors are uh + + + align:start position:0% +temperature so our predictors are uh +activ ation energy and also Delta H and + + align:start position:0% +activ ation energy and also Delta H and + + + align:start position:0% +activ ation energy and also Delta H and +thinking about what might happen when + + align:start position:0% +thinking about what might happen when + + + align:start position:0% +thinking about what might happen when +the temperature of a reaction + + align:start position:0% + + + + align:start position:0% + +changes and I mentioned this is always + + align:start position:0% +changes and I mentioned this is always + + + align:start position:0% +changes and I mentioned this is always +that's always always going to increase + + align:start position:0% +that's always always going to increase + + + align:start position:0% +that's always always going to increase +rate constant will always increase with + + align:start position:0% +rate constant will always increase with + + + align:start position:0% +rate constant will always increase with +temperature and you can easily remember + + align:start position:0% +temperature and you can easily remember + + + align:start position:0% +temperature and you can easily remember +this that there's always a barrier you + + align:start position:0% +this that there's always a barrier you + + + align:start position:0% +this that there's always a barrier you +don't get a great deal there's always a + + align:start position:0% +don't get a great deal there's always a + + + align:start position:0% +don't get a great deal there's always a +barrier to + + align:start position:0% +barrier to + + + align:start position:0% +barrier to +overcome um and Delta H can be positive + + align:start position:0% +overcome um and Delta H can be positive + + + align:start position:0% +overcome um and Delta H can be positive +or negative so equal ibrium constants + + align:start position:0% +or negative so equal ibrium constants + + + align:start position:0% +or negative so equal ibrium constants +can increase or decrease uh with with + + align:start position:0% +can increase or decrease uh with with + + + align:start position:0% +can increase or decrease uh with with +temperature so for Delta H magnitude of + + align:start position:0% +temperature so for Delta H magnitude of + + + align:start position:0% +temperature so for Delta H magnitude of +Delta H indicates the magnitude of the + + align:start position:0% +Delta H indicates the magnitude of the + + + align:start position:0% +Delta H indicates the magnitude of the +change S of Delta H indicates the + + align:start position:0% +change S of Delta H indicates the + + + align:start position:0% +change S of Delta H indicates the +direction of the + + align:start position:0% +direction of the + + + align:start position:0% +direction of the +change and if you forget that you could + + align:start position:0% +change and if you forget that you could + + + align:start position:0% +change and if you forget that you could +just look at the equations and it'll + + align:start position:0% +just look at the equations and it'll + + + align:start position:0% +just look at the equations and it'll +tell they'll tell you the same + + align:start position:0% +tell they'll tell you the same + + + align:start position:0% +tell they'll tell you the same +thing so now we can come back to latti + + align:start position:0% +thing so now we can come back to latti + + + align:start position:0% +thing so now we can come back to latti +a so we can explain those observations + + align:start position:0% +a so we can explain those observations + + + align:start position:0% +a so we can explain those observations +about how equilibrium constants changed + + align:start position:0% +about how equilibrium constants changed + + + align:start position:0% +about how equilibrium constants changed +um and how the reaction was affected why + + align:start position:0% +um and how the reaction was affected why + + + align:start position:0% +um and how the reaction was affected why +you would shift in One Direction versus + + align:start position:0% +you would shift in One Direction versus + + + align:start position:0% +you would shift in One Direction versus +another when you changed the temperature + + align:start position:0% +another when you changed the temperature + + + align:start position:0% +another when you changed the temperature +so again + + align:start position:0% +so again + + + align:start position:0% +so again +lattier says that a system that's at + + align:start position:0% +lattier says that a system that's at + + + align:start position:0% +lattier says that a system that's at +equilibrium if you have the system at + + align:start position:0% +equilibrium if you have the system at + + + align:start position:0% +equilibrium if you have the system at +equilibrium and you apply a stress the + + align:start position:0% +equilibrium and you apply a stress the + + + align:start position:0% +equilibrium and you apply a stress the +system will respond in such a way to + + align:start position:0% +system will respond in such a way to + + + align:start position:0% +system will respond in such a way to +minimize that + + align:start position:0% +minimize that + + + align:start position:0% +minimize that +stress so if you increased the + + align:start position:0% +stress so if you increased the + + + align:start position:0% +stress so if you increased the +temperature the equilibrium should shift + + align:start position:0% +temperature the equilibrium should shift + + + align:start position:0% +temperature the equilibrium should shift +in the endothermic direction that would + + align:start position:0% +in the endothermic direction that would + + + align:start position:0% +in the endothermic direction that would +be what the prediction would be from + + align:start position:0% +be what the prediction would be from + + + align:start position:0% +be what the prediction would be from +lattier because if you put in more heat + + align:start position:0% +lattier because if you put in more heat + + + align:start position:0% +lattier because if you put in more heat +the reaction wants to respond in a way + + align:start position:0% +the reaction wants to respond in a way + + + align:start position:0% +the reaction wants to respond in a way +to decrease the Heat and so it goes in + + align:start position:0% +to decrease the Heat and so it goes in + + + align:start position:0% +to decrease the Heat and so it goes in +the direction that absorbs heat the + + align:start position:0% +the direction that absorbs heat the + + + align:start position:0% +the direction that absorbs heat the +endothermic Direction so this is what we + + align:start position:0% +endothermic Direction so this is what we + + + align:start position:0% +endothermic Direction so this is what we +talked about before but now we can think + + align:start position:0% +talked about before but now we can think + + + align:start position:0% +talked about before but now we can think +about this in a little bit of a + + align:start position:0% +about this in a little bit of a + + + align:start position:0% +about this in a little bit of a +different way in terms of these reaction + + align:start position:0% +different way in terms of these reaction + + + align:start position:0% +different way in terms of these reaction +coordinate + + align:start position:0% + + + + align:start position:0% + +diagrams so let's look at an endothermic + + align:start position:0% +diagrams so let's look at an endothermic + + + align:start position:0% +diagrams so let's look at an endothermic +versus exothermic reaction so here we + + align:start position:0% +versus exothermic reaction so here we + + + align:start position:0% +versus exothermic reaction so here we +have an endothermic reaction we have um + + align:start position:0% +have an endothermic reaction we have um + + + align:start position:0% +have an endothermic reaction we have um +reactants here we have a large + + align:start position:0% +reactants here we have a large + + + align:start position:0% +reactants here we have a large +activation energy in the forward + + align:start position:0% +activation energy in the forward + + + align:start position:0% +activation energy in the forward +Direction and we have products up here + + align:start position:0% +Direction and we have products up here + + + align:start position:0% +Direction and we have products up here +and a smaller activation energy in the + + align:start position:0% +and a smaller activation energy in the + + + align:start position:0% +and a smaller activation energy in the +reverse direction for this exothermic + + align:start position:0% +reverse direction for this exothermic + + + align:start position:0% +reverse direction for this exothermic +reaction we have a smaller activation + + align:start position:0% +reaction we have a smaller activation + + + align:start position:0% +reaction we have a smaller activation +energy in the forward Direction and a + + align:start position:0% +energy in the forward Direction and a + + + align:start position:0% +energy in the forward Direction and a +much larger one in the reverse + + align:start position:0% +much larger one in the reverse + + + align:start position:0% +much larger one in the reverse +Direction so uh our equation here would + + align:start position:0% +Direction so uh our equation here would + + + align:start position:0% +Direction so uh our equation here would +then indicate you have an endothermic + + align:start position:0% +then indicate you have an endothermic + + + align:start position:0% +then indicate you have an endothermic +reaction your Delta e is positive if you + + align:start position:0% +reaction your Delta e is positive if you + + + align:start position:0% +reaction your Delta e is positive if you +have a big number for the forward minus + + align:start position:0% +have a big number for the forward minus + + + align:start position:0% +have a big number for the forward minus +a small number for the reverse so that's + + align:start position:0% +a small number for the reverse so that's + + + align:start position:0% +a small number for the reverse so that's +going to give you a positive overall + + align:start position:0% +going to give you a positive overall + + + align:start position:0% +going to give you a positive overall +number whereas in uh in this case you'll + + align:start position:0% +number whereas in uh in this case you'll + + + align:start position:0% +number whereas in uh in this case you'll +have if you have a small number here + + align:start position:0% +have if you have a small number here + + + align:start position:0% +have if you have a small number here +minus a much bigger number you get a + + align:start position:0% +minus a much bigger number you get a + + + align:start position:0% +minus a much bigger number you get a +negative number for Delta e or an + + align:start position:0% +negative number for Delta e or an + + + align:start position:0% +negative number for Delta e or an +exothermic reaction so if you're given + + align:start position:0% +exothermic reaction so if you're given + + + align:start position:0% +exothermic reaction so if you're given +information about the activation energy + + align:start position:0% +information about the activation energy + + + align:start position:0% +information about the activation energy +in the forward Direction in the reverse + + align:start position:0% +in the forward Direction in the reverse + + + align:start position:0% +in the forward Direction in the reverse +Direction and ask if a reaction is + + align:start position:0% +Direction and ask if a reaction is + + + align:start position:0% +Direction and ask if a reaction is +endothermic or exothermic uh you can + + align:start position:0% +endothermic or exothermic uh you can + + + align:start position:0% +endothermic or exothermic uh you can +figure that out using this + + align:start position:0% +figure that out using this + + + align:start position:0% +figure that out using this +equation so now let's think about + + align:start position:0% +equation so now let's think about + + + align:start position:0% +equation so now let's think about +temperature so if there's a small + + align:start position:0% +temperature so if there's a small + + + align:start position:0% +temperature so if there's a small +barrier only a small barrier most of + + align:start position:0% +barrier only a small barrier most of + + + align:start position:0% +barrier only a small barrier most of +your molecules can probably get over + + align:start position:0% +your molecules can probably get over + + + align:start position:0% +your molecules can probably get over +that small barrier not that hard but if + + align:start position:0% +that small barrier not that hard but if + + + align:start position:0% +that small barrier not that hard but if +there's a very large barrier that's a + + align:start position:0% +there's a very large barrier that's a + + + align:start position:0% +there's a very large barrier that's a +problem so temperature helps with the + + align:start position:0% +problem so temperature helps with the + + + align:start position:0% +problem so temperature helps with the +big barriers the small barriers people + + align:start position:0% +big barriers the small barriers people + + + align:start position:0% +big barriers the small barriers people +are St the molecules are going over + + align:start position:0% +are St the molecules are going over + + + align:start position:0% +are St the molecules are going over +anyway the bigger barriers they need + + align:start position:0% +anyway the bigger barriers they need + + + align:start position:0% +anyway the bigger barriers they need +extra help they need the help of + + align:start position:0% +extra help they need the help of + + + align:start position:0% +extra help they need the help of +increased + + align:start position:0% +increased + + + align:start position:0% +increased +temperature so if we consider what + + align:start position:0% +temperature so if we consider what + + + align:start position:0% +temperature so if we consider what +happens increasing temperature here the + + align:start position:0% +happens increasing temperature here the + + + align:start position:0% +happens increasing temperature here the +big barrier is the forward Direction so + + align:start position:0% +big barrier is the forward Direction so + + + align:start position:0% +big barrier is the forward Direction so +increasing the temperature will make it + + align:start position:0% +increasing the temperature will make it + + + align:start position:0% +increasing the temperature will make it +easier to overcome this very large + + align:start position:0% +easier to overcome this very large + + + align:start position:0% +easier to overcome this very large +barrier makes very little difference + + align:start position:0% +barrier makes very little difference + + + align:start position:0% +barrier makes very little difference +here the molecules are already doing + + align:start position:0% +here the molecules are already doing + + + align:start position:0% +here the molecules are already doing +fine getting over the small barrier but + + align:start position:0% +fine getting over the small barrier but + + + align:start position:0% +fine getting over the small barrier but +here there's a big help so what this + + align:start position:0% +here there's a big help so what this + + + align:start position:0% +here there's a big help so what this +does then is it shifts the into shifts + + align:start position:0% +does then is it shifts the into shifts + + + align:start position:0% +does then is it shifts the into shifts +the equilibrium toward products so + + align:start position:0% +the equilibrium toward products so + + + align:start position:0% +the equilibrium toward products so +increasing temperature for an + + align:start position:0% +increasing temperature for an + + + align:start position:0% +increasing temperature for an +endothermic reaction shifts toward + + align:start position:0% +endothermic reaction shifts toward + + + align:start position:0% +endothermic reaction shifts toward +products that's what we learned before + + align:start position:0% +products that's what we learned before + + + align:start position:0% +products that's what we learned before +but we had a different rationale for it + + align:start position:0% +but we had a different rationale for it + + + align:start position:0% +but we had a different rationale for it +last time time now let's consider this + + align:start position:0% +last time time now let's consider this + + + align:start position:0% +last time time now let's consider this +case if you increase temperature it's + + align:start position:0% +case if you increase temperature it's + + + align:start position:0% +case if you increase temperature it's +going to affect the reverse barrier more + + align:start position:0% +going to affect the reverse barrier more + + + align:start position:0% +going to affect the reverse barrier more +that's the big barrier this is where + + align:start position:0% +that's the big barrier this is where + + + align:start position:0% +that's the big barrier this is where +molecules are having a difficult time + + align:start position:0% +molecules are having a difficult time + + + align:start position:0% +molecules are having a difficult time +this barrier they're getting over that + + align:start position:0% +this barrier they're getting over that + + + align:start position:0% +this barrier they're getting over that +barrier already so in this case when you + + align:start position:0% +barrier already so in this case when you + + + align:start position:0% +barrier already so in this case when you +have this exothermic reaction adding + + align:start position:0% +have this exothermic reaction adding + + + align:start position:0% +have this exothermic reaction adding +temperature is going to shift toward + + align:start position:0% +temperature is going to shift toward + + + align:start position:0% +temperature is going to shift toward +reactants so it'll shift it in the + + align:start position:0% +reactants so it'll shift it in the + + + align:start position:0% +reactants so it'll shift it in the +endothermic direction using up the heat + + align:start position:0% +endothermic direction using up the heat + + + align:start position:0% +endothermic direction using up the heat +again this is what we saw before but now + + align:start position:0% +again this is what we saw before but now + + + align:start position:0% +again this is what we saw before but now +we have a different e explanation for + + align:start position:0% +we have a different e explanation for + + + align:start position:0% +we have a different e explanation for +why so again a large activation energy + + align:start position:0% +why so again a large activation energy + + + align:start position:0% +why so again a large activation energy +barrier means that the rate constants + + align:start position:0% +barrier means that the rate constants + + + align:start position:0% +barrier means that the rate constants +are very sensitive to temperature it's + + align:start position:0% +are very sensitive to temperature it's + + + align:start position:0% +are very sensitive to temperature it's +highly affected if it's big it's large + + align:start position:0% +highly affected if it's big it's large + + + align:start position:0% +highly affected if it's big it's large +it needs temperature for the molecules + + align:start position:0% +it needs temperature for the molecules + + + align:start position:0% +it needs temperature for the molecules +to get over so increasing the + + align:start position:0% +to get over so increasing the + + + align:start position:0% +to get over so increasing the +temperature has a big effect now + + align:start position:0% +temperature has a big effect now + + + align:start position:0% +temperature has a big effect now +molecules can do it they can get over + + align:start position:0% +molecules can do it they can get over + + + align:start position:0% +molecules can do it they can get over +this is why a large um barrier means + + align:start position:0% +this is why a large um barrier means + + + align:start position:0% +this is why a large um barrier means +that a reaction is sensitive to + + align:start position:0% +that a reaction is sensitive to + + + align:start position:0% +that a reaction is sensitive to +temperature so big activation energy big + + align:start position:0% +temperature so big activation energy big + + + align:start position:0% +temperature so big activation energy big +difference small activation energy not + + align:start position:0% +difference small activation energy not + + + align:start position:0% +difference small activation energy not +such a big difference + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/DXf8JrCEaNk.txt b/DXf8JrCEaNk.txt new file mode 100644 index 0000000000000000000000000000000000000000..47ba3c97b7246ca7706cacc1095a088223e8bb0a --- /dev/null +++ b/DXf8JrCEaNk.txt @@ -0,0 +1,1715 @@ +align:start position:0% + +welcome back to 8701 + + align:start position:0% +welcome back to 8701 + + + align:start position:0% +welcome back to 8701 +so we continue our discussion our + + align:start position:0% +so we continue our discussion our + + + align:start position:0% +so we continue our discussion our +development of qed + + align:start position:0% +development of qed + + + align:start position:0% +development of qed +is a discussion of the photon we have + + align:start position:0% +is a discussion of the photon we have + + + align:start position:0% +is a discussion of the photon we have +already seen how we can describe + + align:start position:0% +already seen how we can describe + + + align:start position:0% +already seen how we can describe +electrons and positrons anti-electrons + + align:start position:0% +electrons and positrons anti-electrons + + + align:start position:0% +electrons and positrons anti-electrons +and now it's time to actually look at + + align:start position:0% +and now it's time to actually look at + + + align:start position:0% +and now it's time to actually look at +the quantum of electromagnetism of + + align:start position:0% +the quantum of electromagnetism of + + + align:start position:0% +the quantum of electromagnetism of +electromagnetic + + align:start position:0% +electromagnetic + + + align:start position:0% +electromagnetic +fields a few general remarks first + + align:start position:0% +fields a few general remarks first + + + align:start position:0% +fields a few general remarks first +quantum electrodynamic is a quantum + + align:start position:0% +quantum electrodynamic is a quantum + + + align:start position:0% +quantum electrodynamic is a quantum +field theory + + align:start position:0% +field theory + + + align:start position:0% +field theory +the quantum field theory of electro + + align:start position:0% +the quantum field theory of electro + + + align:start position:0% +the quantum field theory of electro +dynamic processes describing how light + + align:start position:0% +dynamic processes describing how light + + + align:start position:0% +dynamic processes describing how light +interactions matter + + align:start position:0% +interactions matter + + + align:start position:0% +interactions matter +specifically all processes where + + align:start position:0% +specifically all processes where + + + align:start position:0% +specifically all processes where +a photon is used + + align:start position:0% +a photon is used + + + align:start position:0% +a photon is used +as an exchange particle involving + + align:start position:0% +as an exchange particle involving + + + align:start position:0% +as an exchange particle involving +electrically charged particles + + align:start position:0% +electrically charged particles + + + align:start position:0% +electrically charged particles +can be described by qed the photon + + align:start position:0% +can be described by qed the photon + + + align:start position:0% +can be described by qed the photon +itself is the + + align:start position:0% +itself is the + + + align:start position:0% +itself is the +limit is an elementary particle and it's + + align:start position:0% +limit is an elementary particle and it's + + + align:start position:0% +limit is an elementary particle and it's +the quantum of the electromagnetic field + + align:start position:0% +the quantum of the electromagnetic field + + + align:start position:0% +the quantum of the electromagnetic field +good the real power in qed lies in the + + align:start position:0% +good the real power in qed lies in the + + + align:start position:0% +good the real power in qed lies in the +fact that we + + align:start position:0% +fact that we + + + align:start position:0% +fact that we +can describe it as a perturbation theory + + align:start position:0% +can describe it as a perturbation theory + + + align:start position:0% +can describe it as a perturbation theory +we'll see that we can + + align:start position:0% +we'll see that we can + + + align:start position:0% +we'll see that we can +write down finding diagrams calculate + + align:start position:0% +write down finding diagrams calculate + + + align:start position:0% +write down finding diagrams calculate +them and use those calculations for + + align:start position:0% +them and use those calculations for + + + align:start position:0% +them and use those calculations for +to describe processes we can observe in + + align:start position:0% +to describe processes we can observe in + + + align:start position:0% +to describe processes we can observe in +experiments + + align:start position:0% +experiments + + + align:start position:0% +experiments +and since we can do this with a very + + align:start position:0% +and since we can do this with a very + + + align:start position:0% +and since we can do this with a very +high precision uh we can use + + align:start position:0% +high precision uh we can use + + + align:start position:0% +high precision uh we can use +qud in order to make forecasts in order + + align:start position:0% +qud in order to make forecasts in order + + + align:start position:0% +qud in order to make forecasts in order +to understand in order to understand the + + align:start position:0% +to understand in order to understand the + + + align:start position:0% +to understand in order to understand the +inner dynamics of processes we can + + align:start position:0% +inner dynamics of processes we can + + + align:start position:0% +inner dynamics of processes we can +measure + + align:start position:0% +measure + + + align:start position:0% +measure +feinman called qd our pride and joy + + align:start position:0% +feinman called qd our pride and joy + + + align:start position:0% +feinman called qd our pride and joy +and it's in the in the really unmatched + + align:start position:0% +and it's in the in the really unmatched + + + align:start position:0% +and it's in the in the really unmatched +precision of the theory + + align:start position:0% +precision of the theory + + + align:start position:0% +precision of the theory +where the pride and joy lies + + align:start position:0% +where the pride and joy lies + + + align:start position:0% +where the pride and joy lies +but stepping back one step let's start + + align:start position:0% +but stepping back one step let's start + + + align:start position:0% +but stepping back one step let's start +with classical electron dynamics and + + align:start position:0% +with classical electron dynamics and + + + align:start position:0% +with classical electron dynamics and +let's start from + + align:start position:0% +let's start from + + + align:start position:0% +let's start from +maxwell equations and i'm going to use + + align:start position:0% +maxwell equations and i'm going to use + + + align:start position:0% +maxwell equations and i'm going to use +this and just + + align:start position:0% +this and just + + + align:start position:0% +this and just +to make a few points and remarks um + + align:start position:0% +to make a few points and remarks um + + + align:start position:0% +to make a few points and remarks um +this is really not in the direct path of + + align:start position:0% +this is really not in the direct path of + + + align:start position:0% +this is really not in the direct path of +our development but it + + align:start position:0% +our development but it + + + align:start position:0% +our development but it +connects the dots to something you have + + align:start position:0% +connects the dots to something you have + + + align:start position:0% +connects the dots to something you have +already studied + + align:start position:0% +already studied + + + align:start position:0% +already studied +meaning classical electrodynamics so you + + align:start position:0% +meaning classical electrodynamics so you + + + align:start position:0% +meaning classical electrodynamics so you +you know you all have seen maxwell + + align:start position:0% +you know you all have seen maxwell + + + align:start position:0% +you know you all have seen maxwell +equations they can be expressed in + + align:start position:0% +equations they can be expressed in + + + align:start position:0% +equations they can be expressed in +integral or differential form and you + + align:start position:0% +integral or differential form and you + + + align:start position:0% +integral or differential form and you +can + + align:start position:0% +can + + + align:start position:0% +can +write this even more compact then then + + align:start position:0% +write this even more compact then then + + + align:start position:0% +write this even more compact then then +it's given here + + align:start position:0% +it's given here + + + align:start position:0% +it's given here +so you see gauss's law where you see + + align:start position:0% +so you see gauss's law where you see + + + align:start position:0% +so you see gauss's law where you see +that + + align:start position:0% +that + + + align:start position:0% +that +electric charges generate electric + + align:start position:0% +electric charges generate electric + + + align:start position:0% +electric charges generate electric +fields + + align:start position:0% +fields + + + align:start position:0% +fields +you can see that you can produce + + align:start position:0% +you can see that you can produce + + + align:start position:0% +you can see that you can produce +currents + + align:start position:0% +currents + + + align:start position:0% +currents +by time changing electric fields or by + + align:start position:0% +by time changing electric fields or by + + + align:start position:0% +by time changing electric fields or by +changing especially changing magnetic + + align:start position:0% +changing especially changing magnetic + + + align:start position:0% +changing especially changing magnetic +fields + + align:start position:0% +fields + + + align:start position:0% +fields +gauss's law for magnetic fields + + align:start position:0% +gauss's law for magnetic fields + + + align:start position:0% +gauss's law for magnetic fields +saying that there is no magnetic charge + + align:start position:0% +saying that there is no magnetic charge + + + align:start position:0% +saying that there is no magnetic charge +no magnetic monopole + + align:start position:0% +no magnetic monopole + + + align:start position:0% +no magnetic monopole +at least as far as we know we haven't + + align:start position:0% +at least as far as we know we haven't + + + align:start position:0% +at least as far as we know we haven't +observed those + + align:start position:0% +observed those + + + align:start position:0% +observed those +and then there's faraday's law as well + + align:start position:0% +and then there's faraday's law as well + + + align:start position:0% +and then there's faraday's law as well +you can express the magnetic field and + + align:start position:0% +you can express the magnetic field and + + + align:start position:0% +you can express the magnetic field and +the electric field through + + align:start position:0% +the electric field through + + + align:start position:0% +the electric field through +potentials and vector potentials + + align:start position:0% +potentials and vector potentials + + + align:start position:0% +potentials and vector potentials +um and if you go one step further you + + align:start position:0% +um and if you go one step further you + + + align:start position:0% +um and if you go one step further you +see this very nice form + + align:start position:0% +see this very nice form + + + align:start position:0% +see this very nice form +using four vectors for the potential and + + align:start position:0% +using four vectors for the potential and + + + align:start position:0% +using four vectors for the potential and +the vector potential and + + align:start position:0% +the vector potential and + + + align:start position:0% +the vector potential and +the charge and the the current so what + + align:start position:0% +the charge and the the current so what + + + align:start position:0% +the charge and the the current so what +we're + + align:start position:0% +we're + + + align:start position:0% +we're +really doing here right now is we're + + align:start position:0% +really doing here right now is we're + + + align:start position:0% +really doing here right now is we're +just rewriting the very same equations + + align:start position:0% +just rewriting the very same equations + + + align:start position:0% +just rewriting the very same equations +and so when we use this um + + align:start position:0% +and so when we use this um + + + align:start position:0% +and so when we use this um +dalai bashin operator um + + align:start position:0% +dalai bashin operator um + + + align:start position:0% +dalai bashin operator um +the form of this equation looks like + + align:start position:0% +the form of this equation looks like + + + align:start position:0% +the form of this equation looks like +this + + align:start position:0% +this + + + align:start position:0% +this +you can already see this form is very + + align:start position:0% +you can already see this form is very + + + align:start position:0% +you can already see this form is very +similar to the + + align:start position:0% +similar to the + + + align:start position:0% +similar to the +to the um uh clan gordon equation we + + align:start position:0% +to the um uh clan gordon equation we + + + align:start position:0% +to the um uh clan gordon equation we +just looked at + + align:start position:0% +just looked at + + + align:start position:0% +just looked at +so let's you know go down this path a + + align:start position:0% +so let's you know go down this path a + + + align:start position:0% +so let's you know go down this path a +little bit more + + align:start position:0% +little bit more + + + align:start position:0% +little bit more +so this here is yet another form to + + align:start position:0% +so this here is yet another form to + + + align:start position:0% +so this here is yet another form to +write + + align:start position:0% +write + + + align:start position:0% +write +the maxwell equations um + + align:start position:0% +the maxwell equations um + + + align:start position:0% +the maxwell equations um +where f is our field strength tensor + + align:start position:0% +where f is our field strength tensor + + + align:start position:0% +where f is our field strength tensor +and the field strength has all the + + align:start position:0% +and the field strength has all the + + + align:start position:0% +and the field strength has all the +physics involved you see that you know + + align:start position:0% +physics involved you see that you know + + + align:start position:0% +physics involved you see that you know +you're describing the electromagnetic + + align:start position:0% +you're describing the electromagnetic + + + align:start position:0% +you're describing the electromagnetic +field in its components + + align:start position:0% +field in its components + + + align:start position:0% +field in its components +and then the simplification of the + + align:start position:0% +and then the simplification of the + + + align:start position:0% +and then the simplification of the +maxwell equations + + align:start position:0% +maxwell equations + + + align:start position:0% +maxwell equations +are sitting here so we have in a mixed + + align:start position:0% +are sitting here so we have in a mixed + + + align:start position:0% +are sitting here so we have in a mixed +equation in this form we have the + + align:start position:0% +equation in this form we have the + + + align:start position:0% +equation in this form we have the +maxwell equation in this form here + + align:start position:0% +maxwell equation in this form here + + + align:start position:0% +maxwell equation in this form here +so there's one interesting thing when we + + align:start position:0% +so there's one interesting thing when we + + + align:start position:0% +so there's one interesting thing when we +use + + align:start position:0% +use + + + align:start position:0% +use +potential in order to describe electric + + align:start position:0% +potential in order to describe electric + + + align:start position:0% +potential in order to describe electric +electromagnetic + + align:start position:0% +electromagnetic + + + align:start position:0% +electromagnetic +processes or + + align:start position:0% +processes or + + + align:start position:0% +processes or +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +properties is that we can actually + + align:start position:0% +properties is that we can actually + + + align:start position:0% +properties is that we can actually +choose + + align:start position:0% +choose + + + align:start position:0% +choose +the specifics of the gauge there's a + + align:start position:0% +the specifics of the gauge there's a + + + align:start position:0% +the specifics of the gauge there's a +degree of freedom + + align:start position:0% +degree of freedom + + + align:start position:0% +degree of freedom +which we can choose which doesn't have + + align:start position:0% +which we can choose which doesn't have + + + align:start position:0% +which we can choose which doesn't have +any impact on the physics and the + + align:start position:0% +any impact on the physics and the + + + align:start position:0% +any impact on the physics and the +reality of the physics + + align:start position:0% +reality of the physics + + + align:start position:0% +reality of the physics +right and you can see this here if you + + align:start position:0% +right and you can see this here if you + + + align:start position:0% +right and you can see this here if you +do this if you use a choice at this + + align:start position:0% +do this if you use a choice at this + + + align:start position:0% +do this if you use a choice at this +component here zero + + align:start position:0% +component here zero + + + align:start position:0% +component here zero +um this is called the column gauge + + align:start position:0% +um this is called the column gauge + + + align:start position:0% +um this is called the column gauge +we basically simplify again our maxwell + + align:start position:0% +we basically simplify again our maxwell + + + align:start position:0% +we basically simplify again our maxwell +equations to this point here + + align:start position:0% +equations to this point here + + + align:start position:0% +equations to this point here +great so um + + align:start position:0% +great so um + + + align:start position:0% +great so um +there's a number of things to be said so + + align:start position:0% +there's a number of things to be said so + + + align:start position:0% +there's a number of things to be said so +what we're basically doing here if we + + align:start position:0% +what we're basically doing here if we + + + align:start position:0% +what we're basically doing here if we +fix + + align:start position:0% +fix + + + align:start position:0% +fix +a gauge so if we fix our potential we + + align:start position:0% +a gauge so if we fix our potential we + + + align:start position:0% +a gauge so if we fix our potential we +tie um the choice of the potential + + align:start position:0% +tie um the choice of the potential + + + align:start position:0% +tie um the choice of the potential +to the frame to the inertial frame we're + + align:start position:0% +to the frame to the inertial frame we're + + + align:start position:0% +to the frame to the inertial frame we're +using here and you could say + + align:start position:0% +using here and you could say + + + align:start position:0% +using here and you could say +ah that's not nice that doesn't seem + + align:start position:0% +ah that's not nice that doesn't seem + + + align:start position:0% +ah that's not nice that doesn't seem +lauren's in variant + + align:start position:0% +lauren's in variant + + + align:start position:0% +lauren's in variant +it is actually okay to do this the issue + + align:start position:0% +it is actually okay to do this the issue + + + align:start position:0% +it is actually okay to do this the issue +with that is that you + + align:start position:0% +with that is that you + + + align:start position:0% +with that is that you +you tie you know if you go from one + + align:start position:0% +you tie you know if you go from one + + + align:start position:0% +you tie you know if you go from one +frame and the other + + align:start position:0% +frame and the other + + + align:start position:0% +frame and the other +you have to actually change the the + + align:start position:0% +you have to actually change the the + + + align:start position:0% +you have to actually change the the +gauge + + align:start position:0% +gauge + + + align:start position:0% +gauge +as you go along with changing the + + align:start position:0% +as you go along with changing the + + + align:start position:0% +as you go along with changing the +reference frame + + align:start position:0% +reference frame + + + align:start position:0% +reference frame +but there's nothing bad it's just a + + align:start position:0% +but there's nothing bad it's just a + + + align:start position:0% +but there's nothing bad it's just a +little bit awkward + + align:start position:0% +little bit awkward + + + align:start position:0% +little bit awkward +all right then moving back so we have + + align:start position:0% +all right then moving back so we have + + + align:start position:0% +all right then moving back so we have +this equation now + + align:start position:0% + + + + align:start position:0% + +and this equation obviously simplifies + + align:start position:0% +and this equation obviously simplifies + + + align:start position:0% +and this equation obviously simplifies +if there is no current or no charged + + align:start position:0% +if there is no current or no charged + + + align:start position:0% +if there is no current or no charged +around for three photons + + align:start position:0% +around for three photons + + + align:start position:0% +around for three photons +um to this one and for this you can find + + align:start position:0% +um to this one and for this you can find + + + align:start position:0% +um to this one and for this you can find +the solution it's again the free wave so + + align:start position:0% +the solution it's again the free wave so + + + align:start position:0% +the solution it's again the free wave so +this was the goal of this lecture + + align:start position:0% +this was the goal of this lecture + + + align:start position:0% +this was the goal of this lecture +finding the free weight + + align:start position:0% +finding the free weight + + + align:start position:0% +finding the free weight +so you could have probably written this + + align:start position:0% +so you could have probably written this + + + align:start position:0% +so you could have probably written this +down before any of the discussion but i + + align:start position:0% +down before any of the discussion but i + + + align:start position:0% +down before any of the discussion but i +just want to make the connection + + align:start position:0% +just want to make the connection + + + align:start position:0% +just want to make the connection +so now this in qed this a new + + align:start position:0% +so now this in qed this a new + + + align:start position:0% +so now this in qed this a new +becomes our back function for the photon + + align:start position:0% +becomes our back function for the photon + + + align:start position:0% +becomes our back function for the photon +again we have to you know this is + + align:start position:0% +again we have to you know this is + + + align:start position:0% +again we have to you know this is +as a result of the of the gauge we we + + align:start position:0% +as a result of the of the gauge we we + + + align:start position:0% +as a result of the of the gauge we we +made so we made a specific choice in our + + align:start position:0% +made so we made a specific choice in our + + + align:start position:0% +made so we made a specific choice in our +reference frame + + align:start position:0% +reference frame + + + align:start position:0% +reference frame +and then we can we can describe the full + + align:start position:0% +and then we can we can describe the full + + + align:start position:0% +and then we can we can describe the full +term with our wave function here + + align:start position:0% +term with our wave function here + + + align:start position:0% +term with our wave function here +there's this epsilon here epsilon is our + + align:start position:0% +there's this epsilon here epsilon is our + + + align:start position:0% +there's this epsilon here epsilon is our +polarization vector + + align:start position:0% +polarization vector + + + align:start position:0% +polarization vector +and a is a normalization factor we + + align:start position:0% +and a is a normalization factor we + + + align:start position:0% +and a is a normalization factor we +always always have to + + align:start position:0% +always always have to + + + align:start position:0% +always always have to +normalize our wave functions to you know + + align:start position:0% +normalize our wave functions to you know + + + align:start position:0% +normalize our wave functions to you know +specific + + align:start position:0% +specific + + + align:start position:0% +specific +um sets of units all right that's good + + align:start position:0% +um sets of units all right that's good + + + align:start position:0% +um sets of units all right that's good +um we can now analyze this we find that + + align:start position:0% +um we can now analyze this we find that + + + align:start position:0% +um we can now analyze this we find that +those conditions + + align:start position:0% +those conditions + + + align:start position:0% +those conditions +are fulfilled here uh + + align:start position:0% +are fulfilled here uh + + + align:start position:0% +are fulfilled here uh +basically saying that you know photon + + align:start position:0% +basically saying that you know photon + + + align:start position:0% +basically saying that you know photon +behaves like a photon the energy of the + + align:start position:0% +behaves like a photon the energy of the + + + align:start position:0% +behaves like a photon the energy of the +photon is equal to + + align:start position:0% +photon is equal to + + + align:start position:0% +photon is equal to +the momentum times c um that's great + + align:start position:0% +the momentum times c um that's great + + + align:start position:0% +the momentum times c um that's great +but it's also not a surprise because the + + align:start position:0% +but it's also not a surprise because the + + + align:start position:0% +but it's also not a surprise because the +form of this equation here + + align:start position:0% +form of this equation here + + + align:start position:0% +form of this equation here +is exactly that of the clangordin + + align:start position:0% +is exactly that of the clangordin + + + align:start position:0% +is exactly that of the clangordin +equation with small for masses particles + + align:start position:0% +equation with small for masses particles + + + align:start position:0% +equation with small for masses particles +and the clang gordon equation we got + + align:start position:0% +and the clang gordon equation we got + + + align:start position:0% +and the clang gordon equation we got +from this very same relation so it's not + + align:start position:0% +from this very same relation so it's not + + + align:start position:0% +from this very same relation so it's not +surprised that this works out + + align:start position:0% +surprised that this works out + + + align:start position:0% +surprised that this works out +all right one more word on the + + align:start position:0% +all right one more word on the + + + align:start position:0% +all right one more word on the +polarization vector + + align:start position:0% +polarization vector + + + align:start position:0% +polarization vector +um so the choice we just made + + align:start position:0% +um so the choice we just made + + + align:start position:0% +um so the choice we just made +i'm rewriting the choice here this is + + align:start position:0% +i'm rewriting the choice here this is + + + align:start position:0% +i'm rewriting the choice here this is +our coulomb gauge um + + align:start position:0% +our coulomb gauge um + + + align:start position:0% +our coulomb gauge um +requires that the zeroth component of + + align:start position:0% +requires that the zeroth component of + + + align:start position:0% +requires that the zeroth component of +our polarization vector is + + align:start position:0% +our polarization vector is + + + align:start position:0% +our polarization vector is +zero and that the polarization vector is + + align:start position:0% +zero and that the polarization vector is + + + align:start position:0% +zero and that the polarization vector is +orthogonal + + align:start position:0% +orthogonal + + + align:start position:0% +orthogonal +to the momentum vector so in principle + + align:start position:0% +to the momentum vector so in principle + + + align:start position:0% +to the momentum vector so in principle +you have the three vector the three + + align:start position:0% +you have the three vector the three + + + align:start position:0% +you have the three vector the three +vector is + + align:start position:0% +vector is + + + align:start position:0% +vector is +perpendicular to the direction of motion + + align:start position:0% +perpendicular to the direction of motion + + + align:start position:0% +perpendicular to the direction of motion +and that allows us + + align:start position:0% +and that allows us + + + align:start position:0% +and that allows us +to find two polarization states which + + align:start position:0% +to find two polarization states which + + + align:start position:0% +to find two polarization states which +are independent of each other + + align:start position:0% +are independent of each other + + + align:start position:0% +are independent of each other +so different to our electrons before now + + align:start position:0% +so different to our electrons before now + + + align:start position:0% +so different to our electrons before now +we don't have + + align:start position:0% +we don't have + + + align:start position:0% +we don't have +four states you only have two states as + + align:start position:0% +four states you only have two states as + + + align:start position:0% +four states you only have two states as +independent solutions + + align:start position:0% +independent solutions + + + align:start position:0% +independent solutions +for a given for a given momentum + + align:start position:0% +for a given for a given momentum + + + align:start position:0% +for a given for a given momentum +all right so with this now we have + + align:start position:0% +all right so with this now we have + + + align:start position:0% +all right so with this now we have +electrons we can describe those we can + + align:start position:0% +electrons we can describe those we can + + + align:start position:0% +electrons we can describe those we can +describe photons + + align:start position:0% +describe photons + + + align:start position:0% +describe photons +the next step now is to look at the + + align:start position:0% +the next step now is to look at the + + + align:start position:0% +the next step now is to look at the +feynman rules which allows us to + + align:start position:0% +feynman rules which allows us to + + + align:start position:0% +feynman rules which allows us to +describe the interaction between those + + align:start position:0% +describe the interaction between those + + + align:start position:0% +describe the interaction between those +two \ No newline at end of file diff --git a/DwBK4duYhTU.txt b/DwBK4duYhTU.txt new file mode 100644 index 0000000000000000000000000000000000000000..b8e7dac033abfd7460d7bf9a7c82228083632dae --- /dev/null +++ b/DwBK4duYhTU.txt @@ -0,0 +1,871 @@ +Welcome back. + +So now we're going to finish +the rest of this problem. + +For part e, we've calculated +what the map and LMS + +estimators are. + +And now we're going to calculate +what the conditional + +mean squared error is. + +So it's a way to measure how +good these estimators are. + +So let's start out +generically. + +For any estimator theta hat, +the conditional MSE is-- + +conditional mean +squared error-- + + + +is equal to this. + + + +It's the estimator minus the +actual value squared + +conditioned on X being equal +to some little x. + +So the mean squared error. + +So you take the error, which is +the difference between your + +estimator and the true +value, square it, and + +then take the mean. + +And it's conditioned on the +actual value of what x is. + +Or, conditioned on the +data that you get is. + +So to calculate this, we use +our standard definition of + +what conditional expectation +would be. + +So it's theta hat minus +theta squared. + +And we weight that by the +appropriate conditional PDF, + +which in this case would +be the posterior. + +And we integrate this from x-- + +from theta equals x +to theta equals 1. + +Now, we can go through some +algebra and this will tell us + +that this is theta hat squared +minus 2 theta hat theta minus + +plus theta squared. + +And this posterior we know from +before is 1 over theta + +times absolute value +of log x d theta. + +And when we do out this +integral, it's going to be-- + +we can split up in to three +different terms. + +So there's theta hat squared +times this and + +you integrate it. + +But in fact, this is just +a conditional density. + +When you integrate it from x to +1, this will just integrate + +up to 1 because it is +a valid density. + +So the first term is just +theta hat squared. + +Now, the second term is you can +pull out of 2 theta hat + +and integrate theta times 1 +over theta times absolute + +value of log of x d +theta from x to 1. + +And then the last one is +integral of theta squared 1 + +over theta absolute value of +log x d theta from x to 1. + +OK, so we can do some more-- + +with some more calculus, we get +a final answer is this. + +So this will integrate to +1 minus x over absolute + +value of log x. + +And this will integrate to 1 +minus x squared over 2 times + +absolute value of log x. + +So this tells us for any generic +estimate theta hat, + +this would be what the +conditional mean + +squared error would be. + +Now, let's calculate what it +actually is for the specific + +estimates that we actually +came up with. + +So for the MAP rule, the +estimate of theta hat is just + +equal to x. + +So when we plug that into +this, we get that the + +conditional MSE is just equal to +x squared minus 2x 1 minus + +x absolute value of log x plus 1 +minus x squared over 2 times + +absolute value of log of x. + +And for the LMS estimate, +remember this was equal to-- + +theta hat was 1 minus x over +absolute value of log x. + +And so when you plug this +particular theta hat into this + +formula, what you get is that +the conditional mean squared + +error is equal to 1 minus x +squared over 2 times absolute + +value of log of x minus +1 minus x over log + +of x quantity squared. + +So these two expressions tells +us what the mean squared error + +is for the MAP rule +and the LMS rule. + +And it's kind of hard to +actually interpret exactly + +which one is better based on +just these expressions. + +So it's helpful to plot out +what the conditional mean + +squared error is. + +So we're plotting for x. + +For each possible actual +data that we observe-- + +data point that we observe, +what is the + +mean squared error? + +So let's do the MAP +rule first. + +The MAP rule would look +something like this. + + + +And it turns out that the LMS +rule is better, and it will + +look like this dotted line +here on the bottom. + +And so it turns out that if your +metric for how good your + +estimate is is the conditional +mean squared error, then LMS + +is better than MAP. + +And this is true because LMS +is actually designed to + +actually minimize what this +mean squared error is. + +And so in this case, the LMS +estimator should have a better + +mean squared error than +the map estimator. + +OK, now the last part of the +problem, we calculate one more + +type of estimator, which is +the linear LMS estimator. + +So notice that the LMS estimator +was this one. + +It was 1 minus x over absolute +value of log of x. + +And this is not linear in x, +which means sometimes it's + +difficult to calculate. + +And so what we do is we tried to +come up with a linear form + +of this, something that is like +ax plus b, where a and b + +are some constant numbers. + +But that also does well in terms +of having a small mean + +squared error. + +And so we know from the class +that in order to calculate the + +linear LMS, the linear LMS we +know we just need to calculate + +a few different parts. + +So it's equal to the expectation +of the parameter + +plus the covariance of theta and +x over the variance of x + +times x minus expectation +of x. + + + +Now, in order to do this, +we just need to + +calculate four things. + +We need the expectation of +theta, the covariance, the + +variance, and the expectation +of x. + +OK, so let's calculate what +these things are. + +Expectation of theta. + +We know that theta is uniformly +distributed + +between 0 and 1. + +And so the expectation +of theta is the + +easiest one to calculate. + +It's just 1/2. + +What about the expectation +of x? + +Well, expectation of x is a +little bit more complicated. + +But remember, like in previous +problems, it's helpful when + +you have a hierarchy of +randomness to try to use the + +law of iterated expectations. + +So the delay, which +is x, is random. + +But it's randomness depends +on the actual + +distribution, which is theta. + +Which itself is random. + +And so let's try to condition +on theta and see + +if that helps us. + +OK, so if we knew what theta +was, then what is the + +expectation of x? + +Well, we know that given +theta, x is uniformly + +distributed between +0 and theta. + +And so the mean would be +just theta over 2. + +And so this would just be +expectation of theta over 2. + +And we know this is just 1/2 +times the expectation of + +theta, which is 1/2. + +So this is just 1/4. + + + +Now, let's calculate +the variance of x. + +The variance of x takes some +more work because we need to + +use the law of total variance, +which is this. + +That the variance of theta is +equal to the expectation of + +the conditional variance plus +the variance of the + +conditional expectation. + + + +Let's see if we can figure +out what these + +different parts are. + +What is the conditional variance +of x given theta? + +Well, given theta, x we know +is uniformly distributed + +between 0 and theta. + +And remember for uniform +distribution of width c, the + +variance of that uniform +distribution is just c + +squared over 12. + +And so in this case, what is +the width of this uniform + +distribution? + +Well, it's uniformly distributed +between 0 and + +theta, so the width is theta. + +So this variance should be +theta squared over 12. + + + +OK, what about the expectation +of x given theta? + +Well, we already argued earlier +that the expectation + +of x given theta is +just theta over 2. + +So now let's fill in the rest. + +What's the expectation of +theta squared over 12? + +Well, that takes a little bit +more work because this is + +just-- you can think +of it as 1/12. + +You could pull the 1/12 +out times the + +expectation of theta squared. + +Well, the expectation of theta +squared we can calculate from + +the variance of theta plus +the expectation of + +theta quantity squared. + +Because that is just the +definition of variance. + +Variance is equal to expectation +of theta squared + +minus expectation of theta +quantity squared. + +So we've just reversed +the formula. + +Now, the second half is the +variance of theta over 2. + +Well, remember when you pull +out a constant from a + +variance, you have +to square it. + +So this is just equal to 1/4 +times the variance of theta. + + + +Well, what is the variance +of theta? + +The variance of theta is +the variance of uniform + +between 0 and 1. + +So the width is 1. + +So you get 1 squared over 12. + +And the variance is 1/12. + +What is the mean of theta? + +It's 1/2 when you square +that, you get 1/4. + + + +Finally for here, the +variance of theta + +like we said, is 1/12. + +So you get 1/12. + +And now, when you combine all +these, you get that the + +variance ends up being 7/144. + +Now we have almost everything. + +The last thing we need +to calculate is + +this covariance term. + +What is the covariance +of theta and x? + +Well, the covariance we know is +just the expectation of the + +product of theta and x minus +the product of the + +expectations. + +So the expectation of x times +the expectation of theta. + +All right, so we already know +what expectation of theta is. + +That's 1/2. + +And expectation of x was 1/4. + +So the only thing that we don't +know is expectation of + +the product of the two. + +So once again, let's try to +use iterated expectations. + +So let's calculate this as +the expectation of this + +conditional expectation. + +So we, again, condition +on theta. + +And minus the expectation +of theta is 1/2. + +Times 1/4, which is the +expectation of x. + +Now, what is this conditional +expectation? + + + +Well, the expectation +of theta-- + +if you know what theta is, then +the expectation of theta + +is just theta. + +You already know what it is, so +you know for sure that the + +expectation is just +equal to theta. + +And what is the expectation +of x given theta? + +Well, the expectation of x given +theta we already said + +was theta over 2. + +So what you get is this entire +expression is just going to be + +equal to theta times theta +over 2, or expectation of + +theta squared over +2 minus 1/8. + +Now, what is the expectation +of theta squared over 2? + +Well, we know that-- + +we already calculated out +what expectation of + +theta squared is. + +So we know that expectation +of theta squared + +is 1/12 plus 1/4. + +So what we get is we need a 1/2 +times 1/12 plus 1/4, which + +is 1/3 minus 1/8. + +So the answer is 1/6 minus +1/8, which is 1/24. + + + +Now, let's actually plug +this in and figure out + +what this value is. + +So when you get everything-- + + + +when you combine everything, +you get that the + +LMS estimator is-- + +the linear LMS estimator +is going to be-- + + + +expectation of theta is 1/2. + + + +The covariance is 1/24. + +The variance is 7/144. + +And when you divide that, it's +equal to 6/7 times x minus 1/4 + +because expectation +of x is 1/4. + +And you can simplify this a +little bit and get that this + +is equal to 6/7 times +x plus 2/7. + + + +So now we have three different +types of estimators. + +The map estimator, +which is this. + +Notice that it's kind +of complicated. + +You have x squared terms. + +You have more x squared terms. + +And you have absolute +value of log of x. + +And then you have the LMS, which +is, again, nonlinear. + +And now you have something +that looks very simple-- + +much simpler. + +It's just 6/7 x plus 2/7. + +And that is the linear +LMS estimator. + +And it turns out that you can, +again, plot these to see what + +this one looks like. + +So here is our original plot +of x and theta hat. + +So the map estimator-- + + + +sorry, the map estimator was +just theta hat equals x. + +This was the mean squared error +of the map estimator. + +So the map estimator is just +this diagonal straight line. + +The LMS estimator looked +like this. + +And it turns out that the linear +LMS estimator will look + +something like this. + +So it is fairly close to +the LMS estimator, but + +not quite the same. + +And note, especially that +depending on what x is, if x + +is fairly close to the 1, you +might actually get an estimate + +of theta that's greater +than 1. + +So for example, if you observe +that Julian is actually an + +hour late, then x is 1 and your +estimate of theta from + +the linear LMS estimator +would be 8/7, which is + +greater than 1. + +That doesn't quite make sense +because we know that theta is + +bounded to be only +between 0 and 1. + +So you shouldn't get an estimate +of theta that's + +greater than 1. + +And that's one of the side +effects of having the linear + +LMS estimator. + +So that sometimes you will have +an estimator that doesn't + +quite make sense. + +But what you get instead when +sacrificing that is you get a + +simple form of the estimator +that's linear. + +And now, let's actually +consider what + +the performance is. + +And it turns out that the +performance in terms of the + +conditional mean squared error +is actually fairly close to + +the LMS estimator. + +So it looks like this. + +Pretty close, pretty close, +until you get close to 1. + +In which case, it does worse. + +And it does worse precisely +because it will come up with + +estimates of theta which +are greater than 1, + +which are too large. + +But otherwise, it does pretty +well with a estimator that is + +much simpler in form than +the LMS estimator. + +So in this problem, which had +several parts, we actually + +went through, basically, all +the different concepts and + +tools within Chapter Eight +for Bayesian inference. + +We talked about the prior, the +posterior, calculating the + +posterior using the +Bayes' rule. + +We calculated the +MAP estimator. + +We calculated the +LMS estimator. + +From those, we calculated what +the mean squared error for + +each one of those and +compared the two. + +And then, we looked at the +linear LMS estimator as + +another example and calculated +what that estimator is, along + +with the mean squared error +for that and compared all + +three of these. + +So I hope that was a good review +problem for Chapter + +Eight, and we'll see +you next time. \ No newline at end of file diff --git a/DyuQsaqXhwU.txt b/DyuQsaqXhwU.txt new file mode 100644 index 0000000000000000000000000000000000000000..c2e64bc08394f773c1099064a55ba9203192de0f --- /dev/null +++ b/DyuQsaqXhwU.txt @@ -0,0 +1,10811 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right I guess we can get + + align:start position:0% +ocw.mit.edu all right I guess we can get + + + align:start position:0% +ocw.mit.edu all right I guess we can get +started here so welcome today we're + + align:start position:0% +started here so welcome today we're + + + align:start position:0% +started here so welcome today we're +going to do basian updating which is to + + align:start position:0% +going to do basian updating which is to + + + align:start position:0% +going to do basian updating which is to +say we're going to be using base theorem + + align:start position:0% +say we're going to be using base theorem + + + align:start position:0% +say we're going to be using base theorem +to learn from data we're going to update + + align:start position:0% +to learn from data we're going to update + + + align:start position:0% +to learn from data we're going to update +our beliefs about various hypotheses + + align:start position:0% +our beliefs about various hypotheses + + + align:start position:0% +our beliefs about various hypotheses +based on the data for this week we're + + align:start position:0% +based on the data for this week we're + + + align:start position:0% +based on the data for this week we're +going to have known priors we're going + + align:start position:0% +going to have known priors we're going + + + align:start position:0% +going to have known priors we're going +to know our belief about the data ahead + + align:start position:0% +to know our belief about the data ahead + + + align:start position:0% +to know our belief about the data ahead +of time for certain we'll draw coins out + + align:start position:0% +of time for certain we'll draw coins out + + + align:start position:0% +of time for certain we'll draw coins out +of um we'll draw coins out of drawers or + + align:start position:0% +of um we'll draw coins out of drawers or + + + align:start position:0% +of um we'll draw coins out of drawers or +pull things out of hats things like that + + align:start position:0% +pull things out of hats things like that + + + align:start position:0% +pull things out of hats things like that +starting next week and we discussed this + + align:start position:0% +starting next week and we discussed this + + + align:start position:0% +starting next week and we discussed this +a little last time we'll have unknown + + align:start position:0% +a little last time we'll have unknown + + + align:start position:0% +a little last time we'll have unknown +priors which is you'll have to be making + + align:start position:0% +priors which is you'll have to be making + + + align:start position:0% +priors which is you'll have to be making +up those priors and we'll learn will + + align:start position:0% +up those priors and we'll learn will + + + align:start position:0% +up those priors and we'll learn will +teach you techniques for making it up + + align:start position:0% +teach you techniques for making it up + + + align:start position:0% +teach you techniques for making it up +so the first slide is just xkcd's view + + align:start position:0% +so the first slide is just xkcd's view + + + align:start position:0% +so the first slide is just xkcd's view +of Base + + align:start position:0% +of Base + + + align:start position:0% +of Base +theorem let's go on we want to start + + align:start position:0% +theorem let's go on we want to start + + + align:start position:0% +theorem let's go on we want to start +with a uh clicker question + + align:start position:0% + + + + align:start position:0% + +here so the question is uh which + + align:start position:0% +here so the question is uh which + + + align:start position:0% +here so the question is uh which +treatment would you choose if you needed + + align:start position:0% +treatment would you choose if you needed + + + align:start position:0% +treatment would you choose if you needed +a treatment treatment one cured 100% of + + align:start position:0% +a treatment treatment one cured 100% of + + + align:start position:0% +a treatment treatment one cured 100% of +the patients treatment 2 cured + + align:start position:0% +the patients treatment 2 cured + + + align:start position:0% +the patients treatment 2 cured +95% in a trial and treatment three cured + + align:start position:0% +95% in a trial and treatment three cured + + + align:start position:0% +95% in a trial and treatment three cured +90% so with this information which would + + align:start position:0% +90% so with this information which would + + + align:start position:0% +90% so with this information which would +you + + align:start position:0% + + + + align:start position:0% + +choose um with only this information + + align:start position:0% +choose um with only this information + + + align:start position:0% +choose um with only this information +with only this if this is all I told + + align:start position:0% +with only this if this is all I told + + + align:start position:0% +with only this if this is all I told +you which would you choose I I recognize + + align:start position:0% +you which would you choose I I recognize + + + align:start position:0% +you which would you choose I I recognize +that you might not be too happy with + + align:start position:0% +that you might not be too happy with + + + align:start position:0% +that you might not be too happy with +just this information but if this is + + align:start position:0% +just this information but if this is + + + align:start position:0% +just this information but if this is +their best information what would you + + align:start position:0% +their best information what would you + + + align:start position:0% +their best information what would you +choose all right there there's some + + align:start position:0% +choose all right there there's some + + + align:start position:0% +choose all right there there's some +holdouts for the 95% cure I'm not sure + + align:start position:0% +holdouts for the 95% cure I'm not sure + + + align:start position:0% +holdouts for the 95% cure I'm not sure +why um + + align:start position:0% +why um + + + align:start position:0% +why um +really that 95% was just you know they + + align:start position:0% +really that 95% was just you know they + + + align:start position:0% +really that 95% was just you know they +cured one person 19 out of 20 um they + + align:start position:0% +cured one person 19 out of 20 um they + + + align:start position:0% +cured one person 19 out of 20 um they +got them 19 out of 20 well however say + + align:start position:0% +got them 19 out of 20 well however say + + + align:start position:0% +got them 19 out of 20 well however say +that yeah all right so uh there's even a + + align:start position:0% +that yeah all right so uh there's even a + + + align:start position:0% +that yeah all right so uh there's even a +few more + + align:start position:0% +few more + + + align:start position:0% +few more +holdouts all right what if I gave you + + align:start position:0% +holdouts all right what if I gave you + + + align:start position:0% +holdouts all right what if I gave you +this + + align:start position:0% +this + + + align:start position:0% +this +information treatment one cured one out + + align:start position:0% +information treatment one cured one out + + + align:start position:0% +information treatment one cured one out +of three or one three out of three + + align:start position:0% +of three or one three out of three + + + align:start position:0% +of three or one three out of three +patients that's 100% treatment two cured + + align:start position:0% +patients that's 100% treatment two cured + + + align:start position:0% +patients that's 100% treatment two cured +19 out of 20 patients that's + + align:start position:0% +19 out of 20 patients that's + + + align:start position:0% +19 out of 20 patients that's +95% or you have a standard treatment + + align:start position:0% +95% or you have a standard treatment + + + align:start position:0% +95% or you have a standard treatment +which has cured 990,000 out of 100,000 + + align:start position:0% +which has cured 990,000 out of 100,000 + + + align:start position:0% +which has cured 990,000 out of 100,000 +patients 90% in clinical practice now + + align:start position:0% +patients 90% in clinical practice now + + + align:start position:0% +patients 90% in clinical practice now +which one would you choose + + align:start position:0% + + + + align:start position:0% + +went oh it's very + + align:start position:0% +went oh it's very + + + align:start position:0% +went oh it's very +interesting yeah it totally changed + + align:start position:0% +interesting yeah it totally changed + + + align:start position:0% +interesting yeah it totally changed +what's that it totally shifted it it + + align:start position:0% +what's that it totally shifted it it + + + align:start position:0% +what's that it totally shifted it it +totally Shi really we have a bunch of + + align:start position:0% +totally Shi really we have a bunch of + + + align:start position:0% +totally Shi really we have a bunch of +very conservative people + + align:start position:0% +very conservative people + + + align:start position:0% +very conservative people +right um so the majority would + + align:start position:0% +right um so the majority would + + + align:start position:0% +right um so the majority would +choose the third choice 90 out of + + align:start position:0% +choose the third choice 90 out of + + + align:start position:0% +choose the third choice 90 out of +100,000 I think well someone tell me + + align:start position:0% +100,000 I think well someone tell me + + + align:start position:0% +100,000 I think well someone tell me +what's the intuition there because it's + + align:start position:0% +what's the intuition there because it's + + + align:start position:0% +what's the intuition there because it's +been more tested it's been more tested + + align:start position:0% +been more tested it's been more tested + + + align:start position:0% +been more tested it's been more tested +three out of three is 100% but do you + + align:start position:0% +three out of three is 100% but do you + + + align:start position:0% +three out of three is 100% but do you +really believe 100% not yet maybe it'll + + align:start position:0% +really believe 100% not yet maybe it'll + + + align:start position:0% +really believe 100% not yet maybe it'll +prove out in time 19 out of 20 is a + + align:start position:0% +prove out in time 19 out of 20 is a + + + align:start position:0% +prove out in time 19 out of 20 is a +little more but for most people for 79% + + align:start position:0% +little more but for most people for 79% + + + align:start position:0% +little more but for most people for 79% +of you that's not + + align:start position:0% +of you that's not + + + align:start position:0% +of you that's not +enough the 90 out of 100,000 seems like + + align:start position:0% +enough the 90 out of 100,000 seems like + + + align:start position:0% +enough the 90 out of 100,000 seems like +good + + align:start position:0% +good + + + align:start position:0% +good +odds and it's well tested 19 out of 20 + + align:start position:0% +odds and it's well tested 19 out of 20 + + + align:start position:0% +odds and it's well tested 19 out of 20 +if the next + + align:start position:0% +if the next + + + align:start position:0% +if the next +person tested doesn't get better now + + align:start position:0% +person tested doesn't get better now + + + align:start position:0% +person tested doesn't get better now +you're back to + + align:start position:0% +you're back to + + + align:start position:0% +you're back to +90% so that doesn't seem like quite + + align:start position:0% +90% so that doesn't seem like quite + + + align:start position:0% +90% so that doesn't seem like quite +enough what if it were 95 out of 100 + + align:start position:0% +enough what if it were 95 out of 100 + + + align:start position:0% +enough what if it were 95 out of 100 +patients we let you click in there + + align:start position:0% +patients we let you click in there + + + align:start position:0% +patients we let you click in there +change number two to 95 out of 100 and + + align:start position:0% +change number two to 95 out of 100 and + + + align:start position:0% +change number two to 95 out of 100 and +let's see what people would do + + align:start position:0% +let's see what people would do + + + align:start position:0% +let's see what people would do +oh you're very obliging 95 out of 100 + + align:start position:0% +oh you're very obliging 95 out of 100 + + + align:start position:0% +oh you're very obliging 95 out of 100 +now it's about 50/50 about + + align:start position:0% +now it's about 50/50 about + + + align:start position:0% +now it's about 50/50 about +50/50 between two and + + align:start position:0% +50/50 between two and + + + align:start position:0% +50/50 between two and +three realistically of course what would + + align:start position:0% +three realistically of course what would + + + align:start position:0% +three realistically of course what would +you want to do you'd want to do a little + + align:start position:0% +you want to do you'd want to do a little + + + align:start position:0% +you want to do you'd want to do a little +more of a research and find out what + + align:start position:0% +more of a research and find out what + + + align:start position:0% +more of a research and find out what +these trials were how good experiments + + align:start position:0% +these trials were how good experiments + + + align:start position:0% +these trials were how good experiments +you thought they they were what people + + align:start position:0% +you thought they they were what people + + + align:start position:0% +you thought they they were what people +are thinking about it but with just this + + align:start position:0% +are thinking about it but with just this + + + align:start position:0% +are thinking about it but with just this +data that's what people would choose and + + align:start position:0% +data that's what people would choose and + + + align:start position:0% +data that's what people would choose and +people would choose differently + + align:start position:0% +people would choose differently + + + align:start position:0% +people would choose differently +okay let's see + + align:start position:0% +okay let's see + + + align:start position:0% +okay let's see +so now I'm going to give you a toy + + align:start position:0% +so now I'm going to give you a toy + + + align:start position:0% +so now I'm going to give you a toy +problem that actually mirrors the same + + align:start position:0% +problem that actually mirrors the same + + + align:start position:0% +problem that actually mirrors the same +kind of effect we saw on the last slide + + align:start position:0% +kind of effect we saw on the last slide + + + align:start position:0% +kind of effect we saw on the last slide +so suppose in this MIT + + align:start position:0% +so suppose in this MIT + + + align:start position:0% +so suppose in this MIT +mug I have dice of two types four-sided + + align:start position:0% +mug I have dice of two types four-sided + + + align:start position:0% +mug I have dice of two types four-sided +and 20-sided all right so I'm going to + + align:start position:0% +and 20-sided all right so I'm going to + + + align:start position:0% +and 20-sided all right so I'm going to +reach into the + + align:start position:0% +reach into the + + + align:start position:0% +reach into the +mug not going to + + align:start position:0% +mug not going to + + + align:start position:0% +mug not going to +look + + align:start position:0% +look + + + align:start position:0% +look +much I'm going to randomly pull out a + + align:start position:0% +much I'm going to randomly pull out a + + + align:start position:0% +much I'm going to randomly pull out a +die I'm going to roll + + align:start position:0% +die I'm going to roll + + + align:start position:0% +die I'm going to roll +it all right I got a + + align:start position:0% +it all right I got a + + + align:start position:0% +it all right I got a +one okay I got a one + + align:start position:0% +one okay I got a one + + + align:start position:0% +one okay I got a one +now just based on this + + align:start position:0% +now just based on this + + + align:start position:0% +now just based on this +information which type of die do you + + align:start position:0% +information which type of die do you + + + align:start position:0% +information which type of die do you +think I randomly + + align:start position:0% + + + + align:start position:0% + +chose the foursided someone want to give + + align:start position:0% +chose the foursided someone want to give + + + align:start position:0% +chose the foursided someone want to give +an explanation of why they think the + + align:start position:0% +an explanation of why they think the + + + align:start position:0% +an explanation of why they think the +four-sided is more + + align:start position:0% +four-sided is more + + + align:start position:0% +four-sided is more +likely it's greater probability what's + + align:start position:0% +likely it's greater probability what's + + + align:start position:0% +likely it's greater probability what's +the probability of getting a one on the + + align:start position:0% +the probability of getting a one on the + + + align:start position:0% +the probability of getting a one on the +four-sided die and what about on the + + align:start position:0% +four-sided die and what about on the + + + align:start position:0% +four-sided die and what about on the +20-sided + + align:start position:0% +20-sided + + + align:start position:0% +20-sided +okay so we see that it would be more + + align:start position:0% +okay so we see that it would be more + + + align:start position:0% +okay so we see that it would be more +likely to roll a one with a four-sided + + align:start position:0% +likely to roll a one with a four-sided + + + align:start position:0% +likely to roll a one with a four-sided +die than with a 20-sided die + + align:start position:0% +die than with a 20-sided die + + + align:start position:0% +die than with a 20-sided die +so you know suppose I tell you that I + + align:start position:0% +so you know suppose I tell you that I + + + align:start position:0% +so you know suppose I tell you that I +really in this cup only have one D of + + align:start position:0% +really in this cup only have one D of + + + align:start position:0% +really in this cup only have one D of +each type all right so does that change + + align:start position:0% +each type all right so does that change + + + align:start position:0% +each type all right so does that change +your analysis of which D is most likely + + align:start position:0% +your analysis of which D is most likely + + + align:start position:0% +your analysis of which D is most likely +don't hit forward yet I wouldn't think + + align:start position:0% +don't hit forward yet I wouldn't think + + + align:start position:0% +don't hit forward yet I wouldn't think +of it my hands are + + align:start position:0% +of it my hands are + + + align:start position:0% +of it my hands are +still or do you want to stick with the + + align:start position:0% +still or do you want to stick with the + + + align:start position:0% +still or do you want to stick with the +same the same reasoning same reason all + + align:start position:0% +same the same reasoning same reason all + + + align:start position:0% +same the same reasoning same reason all +right let me show you what's actually in + + align:start position:0% +right let me show you what's actually in + + + align:start position:0% +right let me show you what's actually in +this + + align:start position:0% + + + + align:start position:0% + +cup ouch well you can't see it + + align:start position:0% +cup ouch well you can't see it + + + align:start position:0% +cup ouch well you can't see it +yet let's go + + align:start position:0% +yet let's go + + + align:start position:0% +yet let's go +with document + + align:start position:0% + + + + align:start position:0% + +camera okay that was actually what I had + + align:start position:0% +camera okay that was actually what I had + + + align:start position:0% +camera okay that was actually what I had +in this cup uh now now now what so does + + align:start position:0% +in this cup uh now now now what so does + + + align:start position:0% +in this cup uh now now now what so does +this change at all your analysis of + + align:start position:0% +this change at all your analysis of + + + align:start position:0% +this change at all your analysis of +which die you think I rolled and got a + + align:start position:0% +which die you think I rolled and got a + + + align:start position:0% +which die you think I rolled and got a +one with what type die rather yeah yeah + + align:start position:0% +one with what type die rather yeah yeah + + + align:start position:0% +one with what type die rather yeah yeah +now what do you think is more likely + + align:start position:0% +now what do you think is more likely + + + align:start position:0% +now what do you think is more likely +four-sided or 20-sided how many I think + + align:start position:0% +four-sided or 20-sided how many I think + + + align:start position:0% +four-sided or 20-sided how many I think +I got 20 20-sided die + + align:start position:0% + + + + align:start position:0% + +there all right so raise your hand if + + align:start position:0% +there all right so raise your hand if + + + align:start position:0% +there all right so raise your hand if +you like the four-sided + + align:start position:0% +you like the four-sided + + + align:start position:0% +you like the four-sided +die raise your hand if you like the + + align:start position:0% +die raise your hand if you like the + + + align:start position:0% +die raise your hand if you like the +20-sided + + align:start position:0% +20-sided + + + align:start position:0% +20-sided +die great so that reasoning that you're + + align:start position:0% +die great so that reasoning that you're + + + align:start position:0% +die great so that reasoning that you're +doing intuitively is something that we + + align:start position:0% +doing intuitively is something that we + + + align:start position:0% +doing intuitively is something that we +want to formalize this week and next + + align:start position:0% +want to formalize this week and next + + + align:start position:0% +want to formalize this week and next +week using base theorem to do these + + align:start position:0% +week using base theorem to do these + + + align:start position:0% +week using base theorem to do these +calculations in a systematic way to + + align:start position:0% +calculations in a systematic way to + + + align:start position:0% +calculations in a systematic way to +evaluate hypotheses Based on data and + + align:start position:0% +evaluate hypotheses Based on data and + + + align:start position:0% +evaluate hypotheses Based on data and +these numbers of for example how many + + align:start position:0% +these numbers of for example how many + + + align:start position:0% +these numbers of for example how many +die I had of one type versus another we + + align:start position:0% +die I had of one type versus another we + + + align:start position:0% +die I had of one type versus another we +can encode that information in what's + + align:start position:0% +can encode that information in what's + + + align:start position:0% +can encode that information in what's +called a prior and we'll come to that + + align:start position:0% +called a prior and we'll come to that + + + align:start position:0% +called a prior and we'll come to that +today and you should have seen in your + + align:start position:0% +today and you should have seen in your + + + align:start position:0% +today and you should have seen in your +reading this + + align:start position:0% + + + + align:start position:0% + +idea okay so I'm going to work through + + align:start position:0% +idea okay so I'm going to work through + + + align:start position:0% +idea okay so I'm going to work through +an example to start with we have three + + align:start position:0% +an example to start with we have three + + + align:start position:0% +an example to start with we have three +types of coins type A B and C + + align:start position:0% +types of coins type A B and C + + + align:start position:0% +types of coins type A B and C +uh however it happens the probability of + + align:start position:0% +uh however it happens the probability of + + + align:start position:0% +uh however it happens the probability of +getting heads with type A is 0.5 that's + + align:start position:0% +getting heads with type A is 0.5 that's + + + align:start position:0% +getting heads with type A is 0.5 that's +a Fair coin probability of getting heads + + align:start position:0% +a Fair coin probability of getting heads + + + align:start position:0% +a Fair coin probability of getting heads +with type B is 6 and of type c is + + align:start position:0% +with type B is 6 and of type c is + + + align:start position:0% +with type B is 6 and of type c is +.9 and here's a box that contains um two + + align:start position:0% +.9 and here's a box that contains um two + + + align:start position:0% +.9 and here's a box that contains um two +of the fair coins and one of each of the + + align:start position:0% +of the fair coins and one of each of the + + + align:start position:0% +of the fair coins and one of each of the +others so two of type a one of type B + + align:start position:0% +others so two of type a one of type B + + + align:start position:0% +others so two of type a one of type B +and one of type + + align:start position:0% +and one of type + + + align:start position:0% +and one of type +c suppose I pick one at random and I get + + align:start position:0% +c suppose I pick one at random and I get + + + align:start position:0% +c suppose I pick one at random and I get +heads so this was like John picking a + + align:start position:0% +heads so this was like John picking a + + + align:start position:0% +heads so this was like John picking a +die at random and getting a one I get + + align:start position:0% +die at random and getting a one I get + + + align:start position:0% +die at random and getting a one I get +heads here's the question before I + + align:start position:0% +heads here's the question before I + + + align:start position:0% +heads here's the question before I +flipped it I have a prior belief in what + + align:start position:0% +flipped it I have a prior belief in what + + + align:start position:0% +flipped it I have a prior belief in what +the coin the probability that the coin + + align:start position:0% +the coin the probability that the coin + + + align:start position:0% +the coin the probability that the coin +was of each type based on the number in + + align:start position:0% +was of each type based on the number in + + + align:start position:0% +was of each type based on the number in +my + + align:start position:0% +my + + + align:start position:0% +my +drawer after flipping + + align:start position:0% +drawer after flipping + + + align:start position:0% +drawer after flipping +it my belief changes the probability + + align:start position:0% +it my belief changes the probability + + + align:start position:0% +it my belief changes the probability +will change based on the data I get and + + align:start position:0% +will change based on the data I get and + + + align:start position:0% +will change based on the data I get and +so a question you could ask what was + + align:start position:0% +so a question you could ask what was + + + align:start position:0% +so a question you could ask what was +learned by flipping the + + align:start position:0% +learned by flipping the + + + align:start position:0% +learned by flipping the +coin well we want to teach you to do to + + align:start position:0% +coin well we want to teach you to do to + + + align:start position:0% +coin well we want to teach you to do to +answer these questions we have a nice + + align:start position:0% +answer these questions we have a nice + + + align:start position:0% +answer these questions we have a nice +way of summarizing all of that at once + + align:start position:0% +way of summarizing all of that at once + + + align:start position:0% +way of summarizing all of that at once +in a table so here the notation we have + + align:start position:0% +in a table so here the notation we have + + + align:start position:0% +in a table so here the notation we have +this nice scripty a or H that's no + + align:start position:0% + + + + align:start position:0% + +good H is our + + align:start position:0% + + + + align:start position:0% + +hypothesis that is you're of + + align:start position:0% +hypothesis that is you're of + + + align:start position:0% +hypothesis that is you're of +type A or B or C we're going to make a + + align:start position:0% +type A or B or C we're going to make a + + + align:start position:0% +type A or B or C we're going to make a +conjecture on what we + + align:start position:0% +conjecture on what we + + + align:start position:0% +conjecture on what we +think the coin + + align:start position:0% +think the coin + + + align:start position:0% +think the coin +was before we do anything we + + align:start position:0% +was before we do anything we + + + align:start position:0% +was before we do anything we +have a prior so what's the probability + + align:start position:0% +have a prior so what's the probability + + + align:start position:0% +have a prior so what's the probability +of how did I label this that the coin + + align:start position:0% +of how did I label this that the coin + + + align:start position:0% +of how did I label this that the coin +was of type + + align:start position:0% + + + + align:start position:0% + +A where all you know is I pulled it out + + align:start position:0% +A where all you know is I pulled it out + + + align:start position:0% +A where all you know is I pulled it out +of the drawer so what's the probability + + align:start position:0% +of the drawer so what's the probability + + + align:start position:0% +of the drawer so what's the probability +it's of type A here let me go back and + + align:start position:0% +it's of type A here let me go back and + + + align:start position:0% +it's of type A here let me go back and +remind you what the drawer looks like + + align:start position:0% + + + + align:start position:0% + +what is + + align:start position:0% +what is + + + align:start position:0% +what is +it0 five 0 five or I'll write it like + + align:start position:0% +it0 five 0 five or I'll write it like + + + align:start position:0% +it0 five 0 five or I'll write it like +this two out of four which is 0.5 and + + align:start position:0% +this two out of four which is 0.5 and + + + align:start position:0% +this two out of four which is 0.5 and +what's the probability I'll shorten this + + align:start position:0% +what's the probability I'll shorten this + + + align:start position:0% +what's the probability I'll shorten this +we're just + + align:start position:0% +we're just + + + align:start position:0% +we're just +type + + align:start position:0% + + + + align:start position:0% + +B yeah 1/4 or + + align:start position:0% + + + + align:start position:0% + +0.25 and probability that we're of + + align:start position:0% +0.25 and probability that we're of + + + align:start position:0% +0.25 and probability that we're of +type c is 1/4 or 0.25 this was a + + align:start position:0% +type c is 1/4 or 0.25 this was a + + + align:start position:0% +type c is 1/4 or 0.25 this was a +one of our simpler counting + + align:start position:0% +one of our simpler counting + + + align:start position:0% +one of our simpler counting +problems in the table you can see that's + + align:start position:0% +problems in the table you can see that's + + + align:start position:0% +problems in the table you can see that's +encoded in the line in the column marked + + align:start position:0% +encoded in the line in the column marked + + + align:start position:0% +encoded in the line in the column marked +prior before we take any data this is + + align:start position:0% +prior before we take any data this is + + + align:start position:0% +prior before we take any data this is +what we'd say this is the sort of odds + + align:start position:0% +what we'd say this is the sort of odds + + + align:start position:0% +what we'd say this is the sort of odds +we'd give if we were going to bet on + + align:start position:0% +we'd give if we were going to bet on + + + align:start position:0% +we'd give if we were going to bet on +this but now we have some + + align:start position:0% + + + + align:start position:0% + +data so once we have data we can + + align:start position:0% + + + + align:start position:0% + +get the likelihood + + align:start position:0% + + + + align:start position:0% + +the likelihood is the probability of + + align:start position:0% +the likelihood is the probability of + + + align:start position:0% +the likelihood is the probability of +seeing the data given a + + align:start position:0% +seeing the data given a + + + align:start position:0% +seeing the data given a +hypothesis I won't write this out I'll + + align:start position:0% +hypothesis I won't write this out I'll + + + align:start position:0% +hypothesis I won't write this out I'll +just point at the uh the slide John has + + align:start position:0% +just point at the uh the slide John has + + + align:start position:0% +just point at the uh the slide John has +a you were going to make your mouse + + align:start position:0% +a you were going to make your mouse + + + align:start position:0% +a you were going to make your mouse +bigger I was oh + + align:start position:0% + + + + align:start position:0% + +okay so the likelihood column we use + + align:start position:0% +okay so the likelihood column we use + + + align:start position:0% +okay so the likelihood column we use +this term when we talking about maximum + + align:start position:0% +this term when we talking about maximum + + + align:start position:0% +this term when we talking about maximum +likelihood is the probability of the + + align:start position:0% +likelihood is the probability of the + + + align:start position:0% +likelihood is the probability of the +data hypothesis and this is typically + + align:start position:0% +data hypothesis and this is typically + + + align:start position:0% +data hypothesis and this is typically +easy or often easy to figure out what's + + align:start position:0% +easy or often easy to figure out what's + + + align:start position:0% +easy or often easy to figure out what's +the probability of seeing heads our data + + align:start position:0% +the probability of seeing heads our data + + + align:start position:0% +the probability of seeing heads our data +was I flipped a heads if my coin is a + + align:start position:0% +was I flipped a heads if my coin is a + + + align:start position:0% +was I flipped a heads if my coin is a +0.5 probability + + align:start position:0% + + + + align:start position:0% + +coin so the probability of seeing + + align:start position:0% +coin so the probability of seeing + + + align:start position:0% +coin so the probability of seeing +heads given a type a + + align:start position:0% +heads given a type a + + + align:start position:0% +heads given a type a +coin is what + + align:start position:0% +coin is what + + + align:start position:0% +coin is what +somebody it's 05 + + align:start position:0% +somebody it's 05 + + + align:start position:0% +somebody it's 05 +this is particularly easy because that's + + align:start position:0% +this is particularly easy because that's + + + align:start position:0% +this is particularly easy because that's +what we told you the probability of + + align:start position:0% +what we told you the probability of + + + align:start position:0% +what we told you the probability of +heads with a type a coin + + align:start position:0% +heads with a type a coin + + + align:start position:0% +heads with a type a coin +is5 what about for B and + + align:start position:0% + + + + align:start position:0% + +C 6 and + + align:start position:0% + + + + align:start position:0% + +0.9 so there um right here is the + + align:start position:0% +0.9 so there um right here is the + + + align:start position:0% +0.9 so there um right here is the +likelihood column in the table now how + + align:start position:0% +likelihood column in the table now how + + + align:start position:0% +likelihood column in the table now how +do we get the + + align:start position:0% +do we get the + + + align:start position:0% +do we get the +posterior base + + align:start position:0% +posterior base + + + align:start position:0% +posterior base +theorem says the probability of H given + + align:start position:0% +theorem says the probability of H given + + + align:start position:0% +theorem says the probability of H given +D which is what I want I want to know + + align:start position:0% +D which is what I want I want to know + + + align:start position:0% +D which is what I want I want to know +given this data what do I believe the + + align:start position:0% +given this data what do I believe the + + + align:start position:0% +given this data what do I believe the +coin to be what's its + + align:start position:0% +coin to be what's its + + + align:start position:0% +coin to be what's its +probability is the probability of D + + align:start position:0% +probability is the probability of D + + + align:start position:0% +probability is the probability of D +given H times the probability of H all + + align:start position:0% +given H times the probability of H all + + + align:start position:0% +given H times the probability of H all +over the probability of D well notice + + align:start position:0% +over the probability of D well notice + + + align:start position:0% +over the probability of D well notice +this numerator right here that's just + + align:start position:0% +this numerator right here that's just + + + align:start position:0% +this numerator right here that's just +our + + align:start position:0% +our + + + align:start position:0% +our +likelihood times our hypothesis our + + align:start position:0% +likelihood times our hypothesis our + + + align:start position:0% +likelihood times our hypothesis our +prior belief in our + + align:start position:0% +prior belief in our + + + align:start position:0% +prior belief in our +hypothesis and so what do we get when I + + align:start position:0% +hypothesis and so what do we get when I + + + align:start position:0% +hypothesis and so what do we get when I +multiply the prior column by the + + align:start position:0% +multiply the prior column by the + + + align:start position:0% +multiply the prior column by the +likelihood column I get this column in + + align:start position:0% +likelihood column I get this column in + + + align:start position:0% +likelihood column I get this column in +red and I'll call that the unnormalized + + align:start position:0% +red and I'll call that the unnormalized + + + align:start position:0% +red and I'll call that the unnormalized +posterior why unnormalized because it + + align:start position:0% +posterior why unnormalized because it + + + align:start position:0% +posterior why unnormalized because it +doesn't sum + + align:start position:0% +doesn't sum + + + align:start position:0% +doesn't sum +to one how do I get it to sum to one + + align:start position:0% +to one how do I get it to sum to one + + + align:start position:0% +to one how do I get it to sum to one +there I have to + + align:start position:0% +there I have to + + + align:start position:0% +there I have to +divide by the probability of the data + + align:start position:0% +divide by the probability of the data + + + align:start position:0% +divide by the probability of the data +and how do I get the probability of the + + align:start position:0% + + + + align:start position:0% + +data that's called the + + align:start position:0% + + + + align:start position:0% + +I see someone mouthing it the law of + + align:start position:0% +I see someone mouthing it the law of + + + align:start position:0% +I see someone mouthing it the law of +total + + align:start position:0% + + + + align:start position:0% + +probability and the LA total probability + + align:start position:0% +probability and the LA total probability + + + align:start position:0% +probability and the LA total probability +says you multiply for each + + align:start position:0% +says you multiply for each + + + align:start position:0% +says you multiply for each +hypothesis this value times this value + + align:start position:0% +hypothesis this value times this value + + + align:start position:0% +hypothesis this value times this value +and add them + + align:start position:0% +and add them + + + align:start position:0% +and add them +up which is in fact just the + + align:start position:0% +up which is in fact just the + + + align:start position:0% +up which is in fact just the +sum of the red column so there I've + + align:start position:0% +sum of the red column so there I've + + + align:start position:0% +sum of the red column so there I've +written it 625 and now how do I + + align:start position:0% +written it 625 and now how do I + + + align:start position:0% +written it 625 and now how do I +normalize I just divide by all my values + + align:start position:0% +normalize I just divide by all my values + + + align:start position:0% +normalize I just divide by all my values +in my unnormalized column by that + + align:start position:0% +in my unnormalized column by that + + + align:start position:0% +in my unnormalized column by that +normalizing factor + + align:start position:0% +normalizing factor + + + align:start position:0% +normalizing factor +625 and I get + + align:start position:0% +625 and I get + + + align:start position:0% +625 and I get +these what I call the + + align:start position:0% + + + + align:start position:0% + +posterior uh let's say well now let's + + align:start position:0% +posterior uh let's say well now let's + + + align:start position:0% +posterior uh let's say well now let's +analyze it so now what's your belief + + align:start position:0% +analyze it so now what's your belief + + + align:start position:0% +analyze it so now what's your belief +which coin is the most likely + + align:start position:0% +which coin is the most likely + + + align:start position:0% +which coin is the most likely +coin after seeing this + + align:start position:0% +coin after seeing this + + + align:start position:0% +coin after seeing this +data still a still a but what's happened + + align:start position:0% +data still a still a but what's happened + + + align:start position:0% +data still a still a but what's happened +to the probability from our prior + + align:start position:0% +to the probability from our prior + + + align:start position:0% +to the probability from our prior +probability it's dropped which one has + + align:start position:0% +probability it's dropped which one has + + + align:start position:0% +probability it's dropped which one has +gained probability c c does that makes + + align:start position:0% +gained probability c c does that makes + + + align:start position:0% +gained probability c c does that makes +sense if I if I flip a heads which coin + + align:start position:0% +sense if I if I flip a heads which coin + + + align:start position:0% +sense if I if I flip a heads which coin +is the most likely to flip + + align:start position:0% +is the most likely to flip + + + align:start position:0% +is the most likely to flip +heads C so I've shifted it suppose I + + align:start position:0% +heads C so I've shifted it suppose I + + + align:start position:0% +heads C so I've shifted it suppose I +flipped heads three more times what + + align:start position:0% +flipped heads three more times what + + + align:start position:0% +flipped heads three more times what +would you see in the probability is I + + align:start position:0% +would you see in the probability is I + + + align:start position:0% +would you see in the probability is I +kept updating + + align:start position:0% + + + + align:start position:0% + +say it again probability the probability + + align:start position:0% +say it again probability the probability + + + align:start position:0% +say it again probability the probability +of C would get bigger at the expense of + + align:start position:0% +of C would get bigger at the expense of + + + align:start position:0% +of C would get bigger at the expense of +the probabilities of the others if I + + align:start position:0% +the probabilities of the others if I + + + align:start position:0% +the probabilities of the others if I +flipped heads nine times in a row I'd be + + align:start position:0% +flipped heads nine times in a row I'd be + + + align:start position:0% +flipped heads nine times in a row I'd be +very + + align:start position:0% +very + + + align:start position:0% +very +convinced that I had a type uh C coin + + align:start position:0% +convinced that I had a type uh C coin + + + align:start position:0% +convinced that I had a type uh C coin +one last thing to note about this + + align:start position:0% +one last thing to note about this + + + align:start position:0% +one last thing to note about this +table I put totals down here what does + + align:start position:0% +table I put totals down here what does + + + align:start position:0% +table I put totals down here what does +this total of one represent in the First + + align:start position:0% + + + + align:start position:0% + +Column Emily toal + + align:start position:0% +Column Emily toal + + + align:start position:0% +Column Emily toal +anything so theal + + align:start position:0% +anything so theal + + + align:start position:0% +anything so theal +yeah when I sum up the total + + align:start position:0% +yeah when I sum up the total + + + align:start position:0% +yeah when I sum up the total +probabilities they sum up to + + align:start position:0% +probabilities they sum up to + + + align:start position:0% +probabilities they sum up to +one same with this last that's a + + align:start position:0% +one same with this last that's a + + + align:start position:0% +one same with this last that's a +probability this I could sum because + + align:start position:0% +probability this I could sum because + + + align:start position:0% +probability this I could sum because +they were probabilities why didn't I sum + + align:start position:0% +they were probabilities why didn't I sum + + + align:start position:0% +they were probabilities why didn't I sum +this + + align:start position:0% + + + + align:start position:0% + +column those are the likelihoods and + + align:start position:0% +column those are the likelihoods and + + + align:start position:0% +column those are the likelihoods and +what's changing as I move down this + + align:start position:0% +what's changing as I move down this + + + align:start position:0% +what's changing as I move down this +column what's changing is H that's not a + + align:start position:0% +column what's changing is H that's not a + + + align:start position:0% +column what's changing is H that's not a +prob ility function it doesn't sum to + + align:start position:0% +prob ility function it doesn't sum to + + + align:start position:0% +prob ility function it doesn't sum to +one there's no reason + + align:start position:0% +one there's no reason + + + align:start position:0% +one there's no reason +that the likelihoods have to sum to one + + align:start position:0% +that the likelihoods have to sum to one + + + align:start position:0% +that the likelihoods have to sum to one +and here you can see they they clearly + + align:start position:0% +and here you can see they they clearly + + + align:start position:0% +and here you can see they they clearly +don't sum to + + align:start position:0% +don't sum to + + + align:start position:0% +don't sum to +one so I don't sum that that's a a + + align:start position:0% +one so I don't sum that that's a a + + + align:start position:0% +one so I don't sum that that's a a +important maybe slightly subtle point + + align:start position:0% +important maybe slightly subtle point + + + align:start position:0% +important maybe slightly subtle point +that the the likelihood function is not + + align:start position:0% +that the the likelihood function is not + + + align:start position:0% +that the the likelihood function is not +a probability + + align:start position:0% +a probability + + + align:start position:0% +a probability +function okay any questions + + align:start position:0% + + + + align:start position:0% + +here all + + align:start position:0% +here all + + + align:start position:0% +here all +right so let's go back to this document + + align:start position:0% + + + + align:start position:0% + +camera got my trusty platonic + + align:start position:0% + + + + align:start position:0% + +solids + + align:start position:0% +solids + + + align:start position:0% +solids +so we're going to go through a series of + + align:start position:0% +so we're going to go through a series of + + + align:start position:0% +so we're going to go through a series of +board questions now three board + + align:start position:0% +board questions now three board + + + align:start position:0% +board questions now three board +questions which are going to allow you + + align:start position:0% +questions which are going to allow you + + + align:start position:0% +questions which are going to allow you +to practice making these tables and + + align:start position:0% +to practice making these tables and + + + align:start position:0% +to practice making these tables and +getting a sense for how to do basian + + align:start position:0% +getting a sense for how to do basian + + + align:start position:0% +getting a sense for how to do basian +updating how to iterate it just how it + + align:start position:0% +updating how to iterate it just how it + + + align:start position:0% +updating how to iterate it just how it +works + + align:start position:0% +works + + + align:start position:0% +works +and our toy problem is going to be + + align:start position:0% +and our toy problem is going to be + + + align:start position:0% +and our toy problem is going to be +involving these five platonic dice you + + align:start position:0% +involving these five platonic dice you + + + align:start position:0% +involving these five platonic dice you +all have them but let's not break them + + align:start position:0% +all have them but let's not break them + + + align:start position:0% +all have them but let's not break them +out today because it' be very noisy with + + align:start position:0% +out today because it' be very noisy with + + + align:start position:0% +out today because it' be very noisy with +the cameras I think we'll + + align:start position:0% +the cameras I think we'll + + + align:start position:0% +the cameras I think we'll +use our + + align:start position:0% +use our + + + align:start position:0% +use our +four-sided here I got big + + align:start position:0% +four-sided here I got big + + + align:start position:0% +four-sided here I got big +ones we got our four-sided eight-sided + + align:start position:0% +ones we got our four-sided eight-sided + + + align:start position:0% +ones we got our four-sided eight-sided +six-sided no six-sided no I don't have a + + align:start position:0% +six-sided no six-sided no I don't have a + + + align:start position:0% +six-sided no six-sided no I don't have a +six-sided + + align:start position:0% +six-sided + + + align:start position:0% +six-sided +I have the wrong dice hold on we got 20 + + align:start position:0% +I have the wrong dice hold on we got 20 + + + align:start position:0% +I have the wrong dice hold on we got 20 +we got four we got 12 12 we got eight ah + + align:start position:0% +we got four we got 12 12 we got eight ah + + + align:start position:0% +we got four we got 12 12 we got eight ah +10 what are you doing there that's not + + align:start position:0% + + + + align:start position:0% + +platonic + + align:start position:0% +platonic + + + align:start position:0% +platonic +okay and + + align:start position:0% + + + + align:start position:0% + +six so now I'm actually going to take + + align:start position:0% +six so now I'm actually going to take + + + align:start position:0% +six so now I'm actually going to take +these you can watch this all right this + + align:start position:0% +these you can watch this all right this + + + align:start position:0% +these you can watch this all right this +is empty + + align:start position:0% + + + + align:start position:0% + +cup okay they're in there right + + align:start position:0% +cup okay they're in there right + + + align:start position:0% +cup okay they're in there right +okay how do we do this how do we + + align:start position:0% +okay how do we do this how do we + + + align:start position:0% +okay how do we do this how do we +convince them R yeah + + align:start position:0% + + + + align:start position:0% + +um all right choose it don't let anyone + + align:start position:0% +um all right choose it don't let anyone + + + align:start position:0% +um all right choose it don't let anyone +see hand it to me okay so I have this + + align:start position:0% +see hand it to me okay so I have this + + + align:start position:0% +see hand it to me okay so I have this +die don't look at the + + align:start position:0% +die don't look at the + + + align:start position:0% +die don't look at the +others I'm going to start rolling it all + + align:start position:0% +others I'm going to start rolling it all + + + align:start position:0% +others I'm going to start rolling it all +right in the secret bin Jerry you can + + align:start position:0% +right in the secret bin Jerry you can + + + align:start position:0% +right in the secret bin Jerry you can +ver we can have a student come verify + + align:start position:0% +ver we can have a student come verify + + + align:start position:0% +ver we can have a student come verify +that I'm not making this + + align:start position:0% +that I'm not making this + + + align:start position:0% +that I'm not making this +up you ready okay here we go + + align:start position:0% +up you ready okay here we go + + + align:start position:0% +up you ready okay here we go +okay what' I get eight eight all right + + align:start position:0% +okay what' I get eight eight all right + + + align:start position:0% +okay what' I get eight eight all right +so which die is it so far what do you + + align:start position:0% +so which die is it so far what do you + + + align:start position:0% +so which die is it so far what do you +think could it be four the four-sided + + align:start position:0% +think could it be four the four-sided + + + align:start position:0% +think could it be four the four-sided +die six-sided + + align:start position:0% +die six-sided + + + align:start position:0% +die six-sided +eight 12 20 what's most + + align:start position:0% +eight 12 20 what's most + + + align:start position:0% +eight 12 20 what's most +likely all + + align:start position:0% +likely all + + + align:start position:0% +likely all +right come take a look at another + + align:start position:0% +right come take a look at another + + + align:start position:0% +right come take a look at another +one + + align:start position:0% + + + + align:start position:0% + +ready ah one got a one is this the same + + align:start position:0% +ready ah one got a one is this the same + + + align:start position:0% +ready ah one got a one is this the same +the same D it's the same die all right + + align:start position:0% +the same D it's the same die all right + + + align:start position:0% +the same D it's the same die all right +so now what well how does this change + + align:start position:0% +so now what well how does this change + + + align:start position:0% +so now what well how does this change +anyone want to tell me how do how would + + align:start position:0% +anyone want to tell me how do how would + + + align:start position:0% +anyone want to tell me how do how would +this now change from before what you + + align:start position:0% +this now change from before what you + + + align:start position:0% +this now change from before what you +believe to be does it change what you + + align:start position:0% +believe to be does it change what you + + + align:start position:0% +believe to be does it change what you +believe at all in any way you still + + align:start position:0% +believe at all in any way you still + + + align:start position:0% +believe at all in any way you still +think it's the eight-sided does it make + + align:start position:0% +think it's the eight-sided does it make + + + align:start position:0% +think it's the eight-sided does it make +the eight-sided less likely more likely + + align:start position:0% +the eight-sided less likely more likely + + + align:start position:0% +the eight-sided less likely more likely +relative to the others more likely + + align:start position:0% +relative to the others more likely + + + align:start position:0% +relative to the others more likely +wonderful see you guys all sense this in + + align:start position:0% +wonderful see you guys all sense this in + + + align:start position:0% +wonderful see you guys all sense this in +your bones it's great this G to be so + + align:start position:0% +your bones it's great this G to be so + + + align:start position:0% +your bones it's great this G to be so +easy for all of you all right we got to + + align:start position:0% +easy for all of you all right we got to + + + align:start position:0% +easy for all of you all right we got to +keep going until we figure out what this + + align:start position:0% +keep going until we figure out what this + + + align:start position:0% +keep going until we figure out what this +die is + + align:start position:0% +die is + + + align:start position:0% +die is +you you love to participate come + + align:start position:0% + + + + align:start position:0% + +on + + align:start position:0% +on + + + align:start position:0% +on +ready three three oh man all + + align:start position:0% + + + + align:start position:0% + +right ready + + align:start position:0% +right ready + + + align:start position:0% +right ready +MH 12 + + align:start position:0% + + + + align:start position:0% + +oo now what + + align:start position:0% +oo now what + + + align:start position:0% +oo now what +happen it's a 12-sided die but it could + + align:start position:0% +happen it's a 12-sided die but it could + + + align:start position:0% +happen it's a 12-sided die but it could +be the 20-sided die right all right let + + align:start position:0% +be the 20-sided die right all right let + + + align:start position:0% +be the 20-sided die right all right let +me just do a few more I'll tell you what + + align:start position:0% +me just do a few more I'll tell you what + + + align:start position:0% +me just do a few more I'll tell you what +I get I get one I get 10 I get 10 I get + + align:start position:0% +I get I get one I get 10 I get 10 I get + + + align:start position:0% +I get I get one I get 10 I get 10 I get +12 I get three I get 10 all right who + + align:start position:0% +12 I get three I get 10 all right who + + + align:start position:0% +12 I get three I get 10 all right who +wants to + + align:start position:0% +wants to + + + align:start position:0% +wants to +bet what would you be willing to bet + + align:start position:0% +bet what would you be willing to bet + + + align:start position:0% +bet what would you be willing to bet +suppose I was willing to give you like + + align:start position:0% +suppose I was willing to give you like + + + align:start position:0% +suppose I was willing to give you like +uh I don't know 10 to one odds that it's + + align:start position:0% +uh I don't know 10 to one odds that it's + + + align:start position:0% +uh I don't know 10 to one odds that it's +the 20-sided + + align:start position:0% + + + + align:start position:0% + +die I mean of course I maybe I I know + + align:start position:0% +die I mean of course I maybe I I know + + + align:start position:0% +die I mean of course I maybe I I know +something so I I can see the die + + align:start position:0% +something so I I can see the die + + + align:start position:0% +something so I I can see the die +right so what we want to be able to do + + align:start position:0% +right so what we want to be able to do + + + align:start position:0% +right so what we want to be able to do +is is precisely answer that question all + + align:start position:0% +is is precisely answer that question all + + + align:start position:0% +is is precisely answer that question all +right and it's just through this basian + + align:start position:0% +right and it's just through this basian + + + align:start position:0% +right and it's just through this basian +updating it's not so hard but organizing + + align:start position:0% +updating it's not so hard but organizing + + + align:start position:0% +updating it's not so hard but organizing +your work is really important so all + + align:start position:0% +your work is really important so all + + + align:start position:0% +your work is really important so all +right it was the 12-sided uh after all + + align:start position:0% +right it was the 12-sided uh after all + + + align:start position:0% +right it was the 12-sided uh after all +so y all did good all right so this is + + align:start position:0% +so y all did good all right so this is + + + align:start position:0% +so y all did good all right so this is +the first board + + align:start position:0% +the first board + + + align:start position:0% +the first board +question all right I want you to + + align:start position:0% +question all right I want you to + + + align:start position:0% +question all right I want you to +practice making the table Jerry showed + + align:start position:0% +practice making the table Jerry showed + + + align:start position:0% +practice making the table Jerry showed +you make one for if it were 13 make one + + align:start position:0% +you make one for if it were 13 make one + + + align:start position:0% +you make one for if it were 13 make one +if it were if I had rolled a five + + align:start position:0% +if it were if I had rolled a five + + + align:start position:0% +if it were if I had rolled a five +instead or do the same question if I had + + align:start position:0% +instead or do the same question if I had + + + align:start position:0% +instead or do the same question if I had +rolled a nine and each case compute the + + align:start position:0% +rolled a nine and each case compute the + + + align:start position:0% +rolled a nine and each case compute the +posterior probabilities of each of the + + align:start position:0% +posterior probabilities of each of the + + + align:start position:0% +posterior probabilities of each of the +five types of + + align:start position:0% + + + + align:start position:0% + +dice you knew it was a 20 set of Die + + align:start position:0% +dice you knew it was a 20 set of Die + + + align:start position:0% +dice you knew it was a 20 set of Die +yeah all right what about if it's a five + + align:start position:0% +yeah all right what about if it's a five + + + align:start position:0% +yeah all right what about if it's a five +yeah but that's it but you see how that + + align:start position:0% +yeah but that's it but you see how that + + + align:start position:0% +yeah but that's it but you see how that +captures very nicely in a + + align:start position:0% +captures very nicely in a + + + align:start position:0% +captures very nicely in a +table all of your intuition you knew it + + align:start position:0% +table all of your intuition you knew it + + + align:start position:0% +table all of your intuition you knew it +was + + align:start position:0% + + + + align:start position:0% + +a and for + + align:start position:0% +a and for + + + align:start position:0% +a and for +the for the general case we would just + + align:start position:0% +the for the general case we would just + + + align:start position:0% +the for the general case we would just +multiply these things but there's no + + align:start position:0% +multiply these things but there's no + + + align:start position:0% +multiply these things but there's no +point in doing that so right now you're + + align:start position:0% +point in doing that so right now you're + + + align:start position:0% +point in doing that so right now you're +doing the D equals 13 case yeah + + align:start position:0% + + + + align:start position:0% + +see oh I'm sorry you're not combining + + align:start position:0% +see oh I'm sorry you're not combining + + + align:start position:0% +see oh I'm sorry you're not combining +tables this is your likelihood column + + align:start position:0% +tables this is your likelihood column + + + align:start position:0% +tables this is your likelihood column +here and then this is your unnormalized + + align:start position:0% +here and then this is your unnormalized + + + align:start position:0% +here and then this is your unnormalized +posterior column is it right or no this + + align:start position:0% +posterior column is it right or no this + + + align:start position:0% +posterior column is it right or no this +is actually normalized this is for this + + align:start position:0% +is actually normalized this is for this + + + align:start position:0% +is actually normalized this is for this +is for like if it were like any number + + align:start position:0% +is for like if it were like any number + + + align:start position:0% +is for like if it were like any number +like if we wouldn't know what number it + + align:start position:0% +like if we wouldn't know what number it + + + align:start position:0% +like if we wouldn't know what number it +was there's CH the likelihood yes + + align:start position:0% +was there's CH the likelihood yes + + + align:start position:0% +was there's CH the likelihood yes +absolutely so the likelihood doesn't + + align:start position:0% +absolutely so the likelihood doesn't + + + align:start position:0% +absolutely so the likelihood doesn't +depend on uh wait what are we doing + + align:start position:0% +depend on uh wait what are we doing + + + align:start position:0% +depend on uh wait what are we doing +rolling a five or a 13 Rolling a 13 + + align:start position:0% +rolling a five or a 13 Rolling a 13 + + + align:start position:0% +rolling a five or a 13 Rolling a 13 +right right so rolling a 13 for the + + align:start position:0% +right right so rolling a 13 for the + + + align:start position:0% +right right so rolling a 13 for the +likelihood you're Computing the + + align:start position:0% +likelihood you're Computing the + + + align:start position:0% +likelihood you're Computing the +probability of data that you saw the 13 + + align:start position:0% +probability of data that you saw the 13 + + + align:start position:0% +probability of data that you saw the 13 +yeah given the hypothesis say that it's + + align:start position:0% +yeah given the hypothesis say that it's + + + align:start position:0% +yeah given the hypothesis say that it's +the four-sided die so if it's the + + align:start position:0% +the four-sided die so if it's the + + + align:start position:0% +the four-sided die so if it's the +foursided die what's the probability you + + align:start position:0% +foursided die what's the probability you + + + align:start position:0% +foursided die what's the probability you +would roll a 13 zero great same with + + align:start position:0% +would roll a 13 zero great same with + + + align:start position:0% +would roll a 13 zero great same with +this this and this but what about here + + align:start position:0% +this this and this but what about here + + + align:start position:0% +this this and this but what about here +if it's the 20 side of die that's your + + align:start position:0% +if it's the 20 side of die that's your + + + align:start position:0% +if it's the 20 side of die that's your +hypothesis what's the probability You' + + align:start position:0% +hypothesis what's the probability You' + + + align:start position:0% +hypothesis what's the probability You' +roll with 13 oh no 12 exactly so that's + + align:start position:0% +roll with 13 oh no 12 exactly so that's + + + align:start position:0% +roll with 13 oh no 12 exactly so that's +that's the likelihood column so this + + align:start position:0% +that's the likelihood column so this + + + align:start position:0% +that's the likelihood column so this +we're going to + + align:start position:0% +we're going to + + + align:start position:0% +we're going to +erase okay so then we mulp + + align:start position:0% + + + + align:start position:0% + +by exactly + + align:start position:0% +by exactly + + + align:start position:0% +by exactly +exactly does that make sense wait we + + align:start position:0% +exactly does that make sense wait we + + + align:start position:0% +exactly does that make sense wait we +multiply these multip those two together + + align:start position:0% +multiply these multip those two together + + + align:start position:0% +multiply these multip those two together +get + + align:start position:0% + + + + align:start position:0% + +this and and then we divide by 1 100 so + + align:start position:0% +this and and then we divide by 1 100 so + + + align:start position:0% +this and and then we divide by 1 100 so +it's going to be zero + + align:start position:0% + + + + align:start position:0% + +this is + + align:start position:0% +this is + + + align:start position:0% +this is +isal so yeah so you get to just same + + align:start position:0% +isal so yeah so you get to just same + + + align:start position:0% +isal so yeah so you get to just same +it's just oh I meant HD no no uh yeah no + + align:start position:0% +it's just oh I meant HD no no uh yeah no + + + align:start position:0% +it's just oh I meant HD no no uh yeah no +you're right HD HD + + align:start position:0% +you're right HD HD + + + align:start position:0% +you're right HD HD +HD um one thing I want to point out + + align:start position:0% +HD um one thing I want to point out + + + align:start position:0% +HD um one thing I want to point out +is instead of using a comma all right + + align:start position:0% +is instead of using a comma all right + + + align:start position:0% +is instead of using a comma all right +this is conditional probability so it's + + align:start position:0% +this is conditional probability so it's + + + align:start position:0% +this is conditional probability so it's +probability of D given H oh yeah like + + align:start position:0% +probability of D given H oh yeah like + + + align:start position:0% +probability of D given H oh yeah like +this okay there you + + align:start position:0% +this okay there you + + + align:start position:0% +this okay there you +go so that's absolutely right right at + + align:start position:0% +go so that's absolutely right right at + + + align:start position:0% +go so that's absolutely right right at +the end Know How likely each gu was + + align:start position:0% +the end Know How likely each gu was + + + align:start position:0% +the end Know How likely each gu was +given the + + align:start position:0% + + + + align:start position:0% + +data that's + + align:start position:0% + + + + align:start position:0% + +right which is one over 100 + + align:start position:0% +right which is one over 100 + + + align:start position:0% +right which is one over 100 +[Music] + + align:start position:0% + + + + align:start position:0% + +m great so now do it again yeah exactly + + align:start position:0% +m great so now do it again yeah exactly + + + align:start position:0% +m great so now do it again yeah exactly +you don't need to even make a new table + + align:start position:0% + + + + align:start position:0% + +awesome so this column probably right + + align:start position:0% +awesome so this column probably right + + + align:start position:0% +awesome so this column probably right +sum over all the different hypothesis a + + align:start position:0% +sum over all the different hypothesis a + + + align:start position:0% +sum over all the different hypothesis a +yeah you for each hypothesis you take + + align:start position:0% +yeah you for each hypothesis you take + + + align:start position:0% +yeah you for each hypothesis you take +each hypothesis times probability of the + + align:start position:0% +each hypothesis times probability of the + + + align:start position:0% +each hypothesis times probability of the +data hypothesis which is the same as the + + align:start position:0% +data hypothesis which is the same as the + + + align:start position:0% +data hypothesis which is the same as the +probability of D and H right so you're + + align:start position:0% +probability of D and H right so you're + + + align:start position:0% +probability of D and H right so you're +partitioning it up sort of based on + + align:start position:0% +partitioning it up sort of based on + + + align:start position:0% +partitioning it up sort of based on +hypothesis this equals that time prob + + align:start position:0% +hypothesis this equals that time prob + + + align:start position:0% +hypothesis this equals that time prob +that's right that's right confus what is + + align:start position:0% +that's right that's right confus what is + + + align:start position:0% +that's right that's right confus what is +probability of the data + + align:start position:0% +probability of the data + + + align:start position:0% +probability of the data +so right so a priority you don't know + + align:start position:0% +so right so a priority you don't know + + + align:start position:0% +so right so a priority you don't know +which diet is right but there's still a + + align:start position:0% +which diet is right but there's still a + + + align:start position:0% +which diet is right but there's still a +probability that getting of getting a 13 + + align:start position:0% +probability that getting of getting a 13 + + + align:start position:0% +probability that getting of getting a 13 +right and what is that probability well + + align:start position:0% +right and what is that probability well + + + align:start position:0% +right and what is that probability well +first we would have to in this case we + + align:start position:0% +first we would have to in this case we + + + align:start position:0% +first we would have to in this case we +could only pick the 20-sided die that is + + align:start position:0% +could only pick the 20-sided die that is + + + align:start position:0% +could only pick the 20-sided die that is +a 1 chance of happening and then given + + align:start position:0% +a 1 chance of happening and then given + + + align:start position:0% +a 1 chance of happening and then given +that we pick the 20-sided die we have to + + align:start position:0% +that we pick the 20-sided die we have to + + + align:start position:0% +that we pick the 20-sided die we have to +roll a a 13 which is a 12th chance which + + align:start position:0% +roll a a 13 which is a 12th chance which + + + align:start position:0% +roll a a 13 which is a 12th chance which +is exactly why this sums to one and 100 + + align:start position:0% +is exactly why this sums to one and 100 + + + align:start position:0% +is exactly why this sums to one and 100 +yeah right and then generally you have + + align:start position:0% +yeah right and then generally you have + + + align:start position:0% +yeah right and then generally you have +the law of total probability + + align:start position:0% +the law of total probability + + + align:start position:0% +the law of total probability +yeah + + align:start position:0% + + + + align:start position:0% + +great so + + align:start position:0% + + + + align:start position:0% + +here I think you should keep in mind + + align:start position:0% +here I think you should keep in mind + + + align:start position:0% +here I think you should keep in mind +which is the D and which is the H maybe + + align:start position:0% +which is the D and which is the H maybe + + + align:start position:0% +which is the D and which is the H maybe +write it above otherwise like it's a + + align:start position:0% +write it above otherwise like it's a + + + align:start position:0% +write it above otherwise like it's a +little confusing to know + + align:start position:0% +little confusing to know + + + align:start position:0% +little confusing to know +what great okay and so this is these are + + align:start position:0% +what great okay and so this is these are + + + align:start position:0% +what great okay and so this is these are +the final probabilities you got if you + + align:start position:0% +the final probabilities you got if you + + + align:start position:0% +the final probabilities you got if you +rolled a nine + + align:start position:0% +rolled a nine + + + align:start position:0% +rolled a nine +right so there's something there's + + align:start position:0% +right so there's something there's + + + align:start position:0% +right so there's something there's +something off here right + + align:start position:0% +something off here right + + + align:start position:0% +something off here right +because these are our prior right sorry + + align:start position:0% +because these are our prior right sorry + + + align:start position:0% +because these are our prior right sorry +these are priors I I'm not labeling this + + align:start position:0% +these are priors I I'm not labeling this + + + align:start position:0% +these are priors I I'm not labeling this +these are PRI this is going to + + align:start position:0% +these are PRI this is going to + + + align:start position:0% +these are PRI this is going to +beest two + + align:start position:0% + + + + align:start position:0% + +test so actually here I think you have + + align:start position:0% +test so actually here I think you have + + + align:start position:0% +test so actually here I think you have +likelihood this is likelihood here + + align:start position:0% +likelihood this is likelihood here + + + align:start position:0% +likelihood this is likelihood here +exactly that's + + align:start position:0% +exactly that's + + + align:start position:0% +exactly that's +likelihood your prior should be um what2 + + align:start position:0% +likelihood your prior should be um what2 + + + align:start position:0% +likelihood your prior should be um what2 +for every what should it be2 for each oh + + align:start position:0% +for every what should it be2 for each oh + + + align:start position:0% +for every what should it be2 for each oh +I didn't see the points yeah so that's + + align:start position:0% +I didn't see the points yeah so that's + + + align:start position:0% +I didn't see the points yeah so that's +your prior 1 for each this is your + + align:start position:0% +your prior 1 for each this is your + + + align:start position:0% +your prior 1 for each this is your +likelihood then you multiply them and + + align:start position:0% +likelihood then you multiply them and + + + align:start position:0% +likelihood then you multiply them and +that's the unnormalized posterior + + align:start position:0% +that's the unnormalized posterior + + + align:start position:0% +that's the unnormalized posterior +right let's have a brief discussion + + align:start position:0% +right let's have a brief discussion + + + align:start position:0% +right let's have a brief discussion +about it and then we're going to give + + align:start position:0% +about it and then we're going to give + + + align:start position:0% +about it and then we're going to give +you something a little more + + align:start position:0% + + + + align:start position:0% + +challenging so for rolling a 13 right + + align:start position:0% +challenging so for rolling a 13 right + + + align:start position:0% +challenging so for rolling a 13 right +the first thing you do is ask what is + + align:start position:0% +the first thing you do is ask what is + + + align:start position:0% +the first thing you do is ask what is +the prior and you saw I had five dice I + + align:start position:0% +the prior and you saw I had five dice I + + + align:start position:0% +the prior and you saw I had five dice I +shook it around a student reached in + + align:start position:0% +shook it around a student reached in + + + align:start position:0% +shook it around a student reached in +randomly not even me so we can trust + + align:start position:0% +randomly not even me so we can trust + + + align:start position:0% +randomly not even me so we can trust +that it was 1/5 for each die equally + + align:start position:0% +that it was 1/5 for each die equally + + + align:start position:0% +that it was 1/5 for each die equally +likely that's a uniform prior right + + align:start position:0% +likely that's a uniform prior right + + + align:start position:0% +likely that's a uniform prior right +discret probability Mass + + align:start position:0% +discret probability Mass + + + align:start position:0% +discret probability Mass +function great likelihood well that's + + align:start position:0% +function great likelihood well that's + + + align:start position:0% +function great likelihood well that's +going to depend on the data because it's + + align:start position:0% +going to depend on the data because it's + + + align:start position:0% +going to depend on the data because it's +the probability of the data given the + + align:start position:0% +the probability of the data given the + + + align:start position:0% +the probability of the data given the +hypothesis the hypothesis in this case + + align:start position:0% +hypothesis the hypothesis in this case + + + align:start position:0% +hypothesis the hypothesis in this case +is how many sides on the die so if the + + align:start position:0% +is how many sides on the die so if the + + + align:start position:0% +is how many sides on the die so if the +data is 13 what's the probability that I + + align:start position:0% +data is 13 what's the probability that I + + + align:start position:0% +data is 13 what's the probability that I +would roll that data a 13 given that it + + align:start position:0% +would roll that data a 13 given that it + + + align:start position:0% +would roll that data a 13 given that it +was the foursided die + + align:start position:0% +was the foursided die + + + align:start position:0% +was the foursided die +zero right it's impossible similarly for + + align:start position:0% +zero right it's impossible similarly for + + + align:start position:0% +zero right it's impossible similarly for +six 8 and 12 + + align:start position:0% +six 8 and 12 + + + align:start position:0% +six 8 and 12 +sides but given that I had the 20-sided + + align:start position:0% +sides but given that I had the 20-sided + + + align:start position:0% +sides but given that I had the 20-sided +die there would be a 120th probability + + align:start position:0% +die there would be a 120th probability + + + align:start position:0% +die there would be a 120th probability +of rolling a 13 that's the likelihood + + align:start position:0% +of rolling a 13 that's the likelihood + + + align:start position:0% +of rolling a 13 that's the likelihood +column all right the next column what we + + align:start position:0% +column all right the next column what we + + + align:start position:0% +column all right the next column what we +call the unnormalized posterior we + + align:start position:0% +call the unnormalized posterior we + + + align:start position:0% +call the unnormalized posterior we +multiply everything is zero and then we + + align:start position:0% +multiply everything is zero and then we + + + align:start position:0% +multiply everything is zero and then we +get one out of 100 as the product + + align:start position:0% +get one out of 100 as the product + + + align:start position:0% +get one out of 100 as the product +for the 20-sided die if we sum this + + align:start position:0% +for the 20-sided die if we sum this + + + align:start position:0% +for the 20-sided die if we sum this +up by the law total probability we get + + align:start position:0% +up by the law total probability we get + + + align:start position:0% +up by the law total probability we get +the probability of the data now a + + align:start position:0% +the probability of the data now a + + + align:start position:0% +the probability of the data now a +student ask what does that what does + + align:start position:0% +student ask what does that what does + + + align:start position:0% +student ask what does that what does +that mean we don't know which die it was + + align:start position:0% +that mean we don't know which die it was + + + align:start position:0% +that mean we don't know which die it was +well in this case what it means is that + + align:start position:0% +well in this case what it means is that + + + align:start position:0% +well in this case what it means is that +you know it's reasonable to ask the + + align:start position:0% +you know it's reasonable to ask the + + + align:start position:0% +you know it's reasonable to ask the +question well if someone reaches in + + align:start position:0% +question well if someone reaches in + + + align:start position:0% +question well if someone reaches in +grabs one of these five dice randomly + + align:start position:0% +grabs one of these five dice randomly + + + align:start position:0% +grabs one of these five dice randomly +and rolls it and gets I mean what's the + + align:start position:0% +and rolls it and gets I mean what's the + + + align:start position:0% +and rolls it and gets I mean what's the +probability that the result would be a + + align:start position:0% +probability that the result would be a + + + align:start position:0% +probability that the result would be a +13 right that's a reasonable + + align:start position:0% +13 right that's a reasonable + + + align:start position:0% +13 right that's a reasonable +question and in this case it's not so + + align:start position:0% +question and in this case it's not so + + + align:start position:0% +question and in this case it's not so +hard to analyze that directly because + + align:start position:0% +hard to analyze that directly because + + + align:start position:0% +hard to analyze that directly because +the only way that could happen is if + + align:start position:0% +the only way that could happen is if + + + align:start position:0% +the only way that could happen is if +they picked the 20-sided die and then + + align:start position:0% +they picked the 20-sided die and then + + + align:start position:0% +they picked the 20-sided die and then +rolled a + + align:start position:0% +rolled a + + + align:start position:0% +rolled a +13 well given that they picked the + + align:start position:0% +13 well given that they picked the + + + align:start position:0% +13 well given that they picked the +20-sided die well there's a one fifth + + align:start position:0% +20-sided die well there's a one fifth + + + align:start position:0% +20-sided die well there's a one fifth +chance they pick the 20-sided die and + + align:start position:0% +chance they pick the 20-sided die and + + + align:start position:0% +chance they pick the 20-sided die and +then a 12th chance they roll a 13 given + + align:start position:0% +then a 12th chance they roll a 13 given + + + align:start position:0% +then a 12th chance they roll a 13 given +that they pick the 20-sided die so the + + align:start position:0% +that they pick the 20-sided die so the + + + align:start position:0% +that they pick the 20-sided die so the +only so the probability of rolling a 13 + + align:start position:0% +only so the probability of rolling a 13 + + + align:start position:0% +only so the probability of rolling a 13 +overall is one in 100 the probability of + + align:start position:0% +overall is one in 100 the probability of + + + align:start position:0% +overall is one in 100 the probability of +the data okay John let me just say one + + align:start position:0% +the data okay John let me just say one + + + align:start position:0% +the data okay John let me just say one +thing the way we would have done this + + align:start position:0% +thing the way we would have done this + + + align:start position:0% +thing the way we would have done this +before is you would have made a tree + + align:start position:0% +before is you would have made a tree + + + align:start position:0% +before is you would have made a tree +the top branch of the tree would have + + align:start position:0% +the top branch of the tree would have + + + align:start position:0% +the top branch of the tree would have +gone to the five types of dye and then + + align:start position:0% +gone to the five types of dye and then + + + align:start position:0% +gone to the five types of dye and then +each of those dye would have gone to all + + align:start position:0% +each of those dye would have gone to all + + + align:start position:0% +each of those dye would have gone to all +the possibilities and the only branch + + align:start position:0% +the possibilities and the only branch + + + align:start position:0% +the possibilities and the only branch +that leads to a + + align:start position:0% +that leads to a + + + align:start position:0% +that leads to a +13 is down to the 20-sided die and then + + align:start position:0% +13 is down to the 20-sided die and then + + + align:start position:0% +13 is down to the 20-sided die and then +down to the 13 notice also that this + + align:start position:0% +down to the 13 notice also that this + + + align:start position:0% +down to the 13 notice also that this +would be a very big tree right you have + + align:start position:0% +would be a very big tree right you have + + + align:start position:0% +would be a very big tree right you have +sort of five branches and then this + + align:start position:0% +sort of five branches and then this + + + align:start position:0% +sort of five branches and then this +would have four and six and eight and 12 + + align:start position:0% +would have four and six and eight and 12 + + + align:start position:0% +would have four and six and eight and 12 +and 20 coming off of it finally we + + align:start position:0% +and 20 coming off of it finally we + + + align:start position:0% +and 20 coming off of it finally we +normalize using bay rule this gives us a + + align:start position:0% +normalize using bay rule this gives us a + + + align:start position:0% +normalize using bay rule this gives us a +posterior probability Mass function it's + + align:start position:0% +posterior probability Mass function it's + + + align:start position:0% +posterior probability Mass function it's +zero for everything but the 20-sided + + align:start position:0% +zero for everything but the 20-sided + + + align:start position:0% +zero for everything but the 20-sided +hypothesis therefore we get 100% belief + + align:start position:0% +hypothesis therefore we get 100% belief + + + align:start position:0% +hypothesis therefore we get 100% belief +100% probability given that we rolled a + + align:start position:0% +100% probability given that we rolled a + + + align:start position:0% +100% probability given that we rolled a +13 that it was the 20-sided die now of + + align:start position:0% +13 that it was the 20-sided die now of + + + align:start position:0% +13 that it was the 20-sided die now of +course you all knew that immediately if + + align:start position:0% +course you all knew that immediately if + + + align:start position:0% +course you all knew that immediately if +you roll a 13 it has to be the 20s side + + align:start position:0% +you roll a 13 it has to be the 20s side + + + align:start position:0% +you roll a 13 it has to be the 20s side +to die so let's look at a more + + align:start position:0% +to die so let's look at a more + + + align:start position:0% +to die so let's look at a more +interesting one that you did the five so + + align:start position:0% +interesting one that you did the five so + + + align:start position:0% +interesting one that you did the five so +what changes that's the big + + align:start position:0% +what changes that's the big + + + align:start position:0% +what changes that's the big +question the only thing that + + align:start position:0% +question the only thing that + + + align:start position:0% +question the only thing that +changes is the likelihood I mean granted + + align:start position:0% +changes is the likelihood I mean granted + + + align:start position:0% +changes is the likelihood I mean granted +the rest changes but everything these + + align:start position:0% +the rest changes but everything these + + + align:start position:0% +the rest changes but everything these +two columns are computed from the first + + align:start position:0% +two columns are computed from the first + + + align:start position:0% +two columns are computed from the first +two the prior stays the same okay but + + align:start position:0% +two the prior stays the same okay but + + + align:start position:0% +two the prior stays the same okay but +the likelihood function changes because + + align:start position:0% +the likelihood function changes because + + + align:start position:0% +the likelihood function changes because +we have different data in this case if + + align:start position:0% +we have different data in this case if + + + align:start position:0% +we have different data in this case if +we roll a five we can't get that on the + + align:start position:0% +we roll a five we can't get that on the + + + align:start position:0% +we roll a five we can't get that on the +four seted die we have a one sixth + + align:start position:0% +four seted die we have a one sixth + + + align:start position:0% +four seted die we have a one sixth +chance on the six-sided 1/8 on the + + align:start position:0% +chance on the six-sided 1/8 on the + + + align:start position:0% +chance on the six-sided 1/8 on the +eight-sided 112th on the 12-sided and + + align:start position:0% +eight-sided 112th on the 12-sided and + + + align:start position:0% +eight-sided 112th on the 12-sided and +120 on the 20-sided multiply those + + align:start position:0% +120 on the 20-sided multiply those + + + align:start position:0% +120 on the 20-sided multiply those +columns get the unnormalized probability + + align:start position:0% +columns get the unnormalized probability + + + align:start position:0% +columns get the unnormalized probability +or the unnormalized + + align:start position:0% +or the unnormalized + + + align:start position:0% +or the unnormalized +posterior that sums to the probability + + align:start position:0% +posterior that sums to the probability + + + align:start position:0% +posterior that sums to the probability +of getting a five when you divide by it + + align:start position:0% +of getting a five when you divide by it + + + align:start position:0% +of getting a five when you divide by it +it normalizes the posterior and what do + + align:start position:0% +it normalizes the posterior and what do + + + align:start position:0% +it normalizes the posterior and what do +we see + + align:start position:0% +we see + + + align:start position:0% +we see +well of course you couldn't have used + + align:start position:0% +well of course you couldn't have used + + + align:start position:0% +well of course you couldn't have used +the foursided die and of the remaining + + align:start position:0% +the foursided die and of the remaining + + + align:start position:0% +the foursided die and of the remaining +the most likely the most probable given + + align:start position:0% +the most likely the most probable given + + + align:start position:0% +the most likely the most probable given +the data is the six-sided die it has a + + align:start position:0% +the data is the six-sided die it has a + + + align:start position:0% +the data is the six-sided die it has a +probability that hypothesis has a + + align:start position:0% +probability that hypothesis has a + + + align:start position:0% +probability that hypothesis has a +probability of about + + align:start position:0% +probability of about + + + align:start position:0% +probability of about +40% compared to the 20-sided die which + + align:start position:0% +40% compared to the 20-sided die which + + + align:start position:0% +40% compared to the 20-sided die which +is only about 12% okay last + + align:start position:0% +is only about 12% okay last + + + align:start position:0% +is only about 12% okay last +one so this is the same deal again the + + align:start position:0% +one so this is the same deal again the + + + align:start position:0% +one so this is the same deal again the +likelihood function is the changes the + + align:start position:0% +likelihood function is the changes the + + + align:start position:0% +likelihood function is the changes the +prior is the same we go through the + + align:start position:0% +prior is the same we go through the + + + align:start position:0% +prior is the same we go through the +table the only two possibilities are the + + align:start position:0% +table the only two possibilities are the + + + align:start position:0% +table the only two possibilities are the +12 and 20-sided and the 12-sided given + + align:start position:0% +12 and 20-sided and the 12-sided given + + + align:start position:0% +12 and 20-sided and the 12-sided given +that you're r a nine is about twice as + + align:start position:0% +that you're r a nine is about twice as + + + align:start position:0% +that you're r a nine is about twice as +likely as the 20-sided which should fit + + align:start position:0% +likely as the 20-sided which should fit + + + align:start position:0% +likely as the 20-sided which should fit +with your intuition + + align:start position:0% +with your intuition + + + align:start position:0% +with your intuition +right okay so next we want you to not + + align:start position:0% +right okay so next we want you to not + + + align:start position:0% +right okay so next we want you to not +erase but go back to the board you've + + align:start position:0% +erase but go back to the board you've + + + align:start position:0% +erase but go back to the board you've +already made and we're going to explore + + align:start position:0% +already made and we're going to explore + + + align:start position:0% +already made and we're going to explore +a little bit the idea of repeated trials + + align:start position:0% +a little bit the idea of repeated trials + + + align:start position:0% +a little bit the idea of repeated trials +right often if you're collecting data + + align:start position:0% +right often if you're collecting data + + + align:start position:0% +right often if you're collecting data +you don't just collect one data point + + align:start position:0% +you don't just collect one data point + + + align:start position:0% +you don't just collect one data point +you collect a series of data points + + align:start position:0% +you collect a series of data points + + + align:start position:0% +you collect a series of data points +maybe a series of patients in a clinical + + align:start position:0% +maybe a series of patients in a clinical + + + align:start position:0% +maybe a series of patients in a clinical +trial you have data coming in right and + + align:start position:0% +trial you have data coming in right and + + + align:start position:0% +trial you have data coming in right and +you can update you can update each time + + align:start position:0% +you can update you can update each time + + + align:start position:0% +you can update you can update each time +you get more data and when you do this + + align:start position:0% +you get more data and when you do this + + + align:start position:0% +you get more data and when you do this +your prior becomes a posterior on the + + align:start position:0% +your prior becomes a posterior on the + + + align:start position:0% +your prior becomes a posterior on the +first update and then you use that + + align:start position:0% +first update and then you use that + + + align:start position:0% +first update and then you use that +posterior as the prior for the next + + align:start position:0% +posterior as the prior for the next + + + align:start position:0% +posterior as the prior for the next +update your beliefs are being updated as + + align:start position:0% +update your beliefs are being updated as + + + align:start position:0% +update your beliefs are being updated as +more data comes + + align:start position:0% +more data comes + + + align:start position:0% +more data comes +in if you think about it like when you + + align:start position:0% +in if you think about it like when you + + + align:start position:0% +in if you think about it like when you +walk outside this course if you're like + + align:start position:0% +walk outside this course if you're like + + + align:start position:0% +walk outside this course if you're like +me like you'll you'll sort of suddenly + + align:start position:0% +me like you'll you'll sort of suddenly + + + align:start position:0% +me like you'll you'll sort of suddenly +realize you're doing this process all + + align:start position:0% +realize you're doing this process all + + + align:start position:0% +realize you're doing this process all +the time in your life and you'll start + + align:start position:0% +the time in your life and you'll start + + + align:start position:0% +the time in your life and you'll start +approaching problems this way and if + + align:start position:0% +approaching problems this way and if + + + align:start position:0% +approaching problems this way and if +you're really like me you'll change your + + align:start position:0% +you're really like me you'll change your + + + align:start position:0% +you're really like me you'll change your +religion on Facebook to basian um but + + align:start position:0% +religion on Facebook to basian um but + + + align:start position:0% +religion on Facebook to basian um but +you don't have to be that + + align:start position:0% +you don't have to be that + + + align:start position:0% +you don't have to be that +extreme so great so here what we want + + align:start position:0% +extreme so great so here what we want + + + align:start position:0% +extreme so great so here what we want +you to do is pretend that I wrote the + + align:start position:0% +you to do is pretend that I wrote the + + + align:start position:0% +you to do is pretend that I wrote the +die and I got a five and then I rolled + + align:start position:0% +die and I got a five and then I rolled + + + align:start position:0% +die and I got a five and then I rolled +the same die I didn't get a different + + align:start position:0% +the same die I didn't get a different + + + align:start position:0% +the same die I didn't get a different +one I just rolled the same die just like + + align:start position:0% +one I just rolled the same die just like + + + align:start position:0% +one I just rolled the same die just like +I did in that demonstration and then I + + align:start position:0% +I did in that demonstration and then I + + + align:start position:0% +I did in that demonstration and then I +got a nine okay so now we have a + + align:start position:0% +got a nine okay so now we have a + + + align:start position:0% +got a nine okay so now we have a +sequence of two pieces of data five and + + align:start position:0% +sequence of two pieces of data five and + + + align:start position:0% +sequence of two pieces of data five and +nine so I want you to find the posterior + + align:start position:0% + + + + align:start position:0% + +that update in two steps then up I'm + + align:start position:0% +that update in two steps then up I'm + + + align:start position:0% +that update in two steps then up I'm +doing this one I'm doing this one okay + + align:start position:0% +doing this one I'm doing this one okay + + + align:start position:0% +doing this one I'm doing this one okay +so let me show you how to do this and + + align:start position:0% +so let me show you how to do this and + + + align:start position:0% +so let me show you how to do this and +then you'll do it okay so first we're + + align:start position:0% +then you'll do it okay so first we're + + + align:start position:0% +then you'll do it okay so first we're +going to update for the five then we're + + align:start position:0% +going to update for the five then we're + + + align:start position:0% +going to update for the five then we're +going to update again for the + + align:start position:0% +going to update again for the + + + align:start position:0% +going to update again for the +nine + + align:start position:0% +nine + + + align:start position:0% +nine +magic the prior 1 for each right that's + + align:start position:0% +magic the prior 1 for each right that's + + + align:start position:0% +magic the prior 1 for each right that's +where we're starting from we roll a five + + align:start position:0% +where we're starting from we roll a five + + + align:start position:0% +where we're starting from we roll a five +that's our lik Ood again you get a zero + + align:start position:0% +that's our lik Ood again you get a zero + + + align:start position:0% +that's our lik Ood again you get a zero +for the foursided and you get one n for + + align:start position:0% +for the foursided and you get one n for + + + align:start position:0% +for the foursided and you get one n for +each of the other n-sided possibilities + + align:start position:0% +each of the other n-sided possibilities + + + align:start position:0% +each of the other n-sided possibilities +we multiply that gives us our + + align:start position:0% +we multiply that gives us our + + + align:start position:0% +we multiply that gives us our +unnormalized posterior for the first + + align:start position:0% +unnormalized posterior for the first + + + align:start position:0% +unnormalized posterior for the first +piece of data great now that is going to + + align:start position:0% +piece of data great now that is going to + + + align:start position:0% +piece of data great now that is going to +be our new prior now you may complain + + align:start position:0% +be our new prior now you may complain + + + align:start position:0% +be our new prior now you may complain +wait a minute this doesn't add to one + + align:start position:0% +wait a minute this doesn't add to one + + + align:start position:0% +wait a minute this doesn't add to one +but it's okay because we're going to do + + align:start position:0% +but it's okay because we're going to do + + + align:start position:0% +but it's okay because we're going to do +it again at the very end we'll normalize + + align:start position:0% +it again at the very end we'll normalize + + + align:start position:0% +it again at the very end we'll normalize +and we'll get the same answer as if we + + align:start position:0% +and we'll get the same answer as if we + + + align:start position:0% +and we'll get the same answer as if we +had normalized here and then normalized + + align:start position:0% +had normalized here and then normalized + + + align:start position:0% +had normalized here and then normalized +again because we're just multiplying the + + align:start position:0% +again because we're just multiplying the + + + align:start position:0% +again because we're just multiplying the +whole column by the same scaler by the + + align:start position:0% +whole column by the same scaler by the + + + align:start position:0% +whole column by the same scaler by the +same real number okay so it saves you + + align:start position:0% +same real number okay so it saves you + + + align:start position:0% +same real number okay so it saves you +work to not bother to normalize the + + align:start position:0% +work to not bother to normalize the + + + align:start position:0% +work to not bother to normalize the +first + + align:start position:0% +first + + + align:start position:0% +first +time great so that's our new prior we + + align:start position:0% +time great so that's our new prior we + + + align:start position:0% +time great so that's our new prior we +get our next piece of data the nine we + + align:start position:0% +get our next piece of data the nine we + + + align:start position:0% +get our next piece of data the nine we +have 0 00 0 112th and 12th as the + + align:start position:0% +have 0 00 0 112th and 12th as the + + + align:start position:0% +have 0 00 0 112th and 12th as the +likelihoods we multiply the this new + + align:start position:0% +likelihoods we multiply the this new + + + align:start position:0% +likelihoods we multiply the this new +prior by this likelihood get the new + + align:start position:0% +prior by this likelihood get the new + + + align:start position:0% +prior by this likelihood get the new +unnormalized posterior it only has two + + align:start position:0% +unnormalized posterior it only has two + + + align:start position:0% +unnormalized posterior it only has two +possible uh nonzero probabilities in it + + align:start position:0% +possible uh nonzero probabilities in it + + + align:start position:0% +possible uh nonzero probabilities in it +the sum the total probability of rolling + + align:start position:0% +the sum the total probability of rolling + + + align:start position:0% +the sum the total probability of rolling +a five in then a nine is + + align:start position:0% +a five in then a nine is + + + align:start position:0% +a five in then a nine is +only + + align:start position:0% + + + + align:start position:0% + +0.0019 + + align:start position:0% +0.0019 + + + align:start position:0% +0.0019 +okay that's that's using + + align:start position:0% +okay that's that's using + + + align:start position:0% +okay that's that's using +unnormalized ah Jerry caught me I was + + align:start position:0% +unnormalized ah Jerry caught me I was + + + align:start position:0% +unnormalized ah Jerry caught me I was +hoping a student would catch me okay + + align:start position:0% +hoping a student would catch me okay + + + align:start position:0% +hoping a student would catch me okay +maybe not maybe I was fooling myself we + + align:start position:0% +maybe not maybe I was fooling myself we + + + align:start position:0% +maybe not maybe I was fooling myself we +haven't normalized so it's not quite + + align:start position:0% +haven't normalized so it's not quite + + + align:start position:0% +haven't normalized so it's not quite +right + + align:start position:0% +right + + + align:start position:0% +right +if we had normalized here then by the + + align:start position:0% +if we had normalized here then by the + + + align:start position:0% +if we had normalized here then by the +time we got to here we could interpret + + align:start position:0% +time we got to here we could interpret + + + align:start position:0% +time we got to here we could interpret +this as that total probability but in + + align:start position:0% +this as that total probability but in + + + align:start position:0% +this as that total probability but in +any case the point is we can normalize + + align:start position:0% +any case the point is we can normalize + + + align:start position:0% +any case the point is we can normalize +to get to the final stage this final + + align:start position:0% +to get to the final stage this final + + + align:start position:0% +to get to the final stage this final +posterior by dividing by the sum here + + align:start position:0% +posterior by dividing by the sum here + + + align:start position:0% +posterior by dividing by the sum here +now it adds to one and at the end of the + + align:start position:0% +now it adds to one and at the end of the + + + align:start position:0% +now it adds to one and at the end of the +day what do we conclude we conclude that + + align:start position:0% +day what do we conclude we conclude that + + + align:start position:0% +day what do we conclude we conclude that +it's almost three times more + + align:start position:0% +it's almost three times more + + + align:start position:0% +it's almost three times more +likely that it was the 12-sided die than + + align:start position:0% +likely that it was the 12-sided die than + + + align:start position:0% +likely that it was the 12-sided die than +that it was the 20-sided die right so + + align:start position:0% +that it was the 20-sided die right so + + + align:start position:0% +that it was the 20-sided die right so +this is very similar to what what + + align:start position:0% +this is very similar to what what + + + align:start position:0% +this is very similar to what what +happened when I you know when I randomly + + align:start position:0% +happened when I you know when I randomly + + + align:start position:0% +happened when I you know when I randomly +had the 12-sided and rolled it after two + + align:start position:0% +had the 12-sided and rolled it after two + + + align:start position:0% +had the 12-sided and rolled it after two +times I had data that looked a lot like + + align:start position:0% +times I had data that looked a lot like + + + align:start position:0% +times I had data that looked a lot like +this and if we had rigorously computed + + align:start position:0% +this and if we had rigorously computed + + + align:start position:0% +this and if we had rigorously computed +those probabilities this is what we + + align:start position:0% +those probabilities this is what we + + + align:start position:0% +those probabilities this is what we +would have gotten + + align:start position:0% +would have gotten + + + align:start position:0% +would have gotten +okay so now now it's your + + align:start position:0% +okay so now now it's your + + + align:start position:0% +okay so now now it's your +turn so we want you to try the same + + align:start position:0% +turn so we want you to try the same + + + align:start position:0% +turn so we want you to try the same +thing but in the other order suppose I + + align:start position:0% +thing but in the other order suppose I + + + align:start position:0% +thing but in the other order suppose I +first rolled a nine and then I rolled a + + align:start position:0% +first rolled a nine and then I rolled a + + + align:start position:0% +first rolled a nine and then I rolled a +five so that's the first question the + + align:start position:0% +five so that's the first question the + + + align:start position:0% +five so that's the first question the +second question is can you do it in one + + align:start position:0% +second question is can you do it in one + + + align:start position:0% +second question is can you do it in one +go instead of doing it updating for the + + align:start position:0% +go instead of doing it updating for the + + + align:start position:0% +go instead of doing it updating for the +and then for the five can you + + align:start position:0% +and then for the five can you + + + align:start position:0% +and then for the five can you +incorporate both the n and the five into + + align:start position:0% +incorporate both the n and the five into + + + align:start position:0% +incorporate both the n and the five into +a single likelihood + + align:start position:0% +a single likelihood + + + align:start position:0% +a single likelihood +function and do the updating in one step + + align:start position:0% +function and do the updating in one step + + + align:start position:0% +function and do the updating in one step +all right so try these and think about + + align:start position:0% +all right so try these and think about + + + align:start position:0% +all right so try these and think about +what's similar what's different than + + align:start position:0% +what's similar what's different than + + + align:start position:0% +what's similar what's different than +what I just did you don't have to you + + align:start position:0% +what I just did you don't have to you + + + align:start position:0% +what I just did you don't have to you +don't have to you can you could + + align:start position:0% +don't have to you can you could + + + align:start position:0% +don't have to you can you could +normalize it yeah then you would + + align:start position:0% +normalize it yeah then you would + + + align:start position:0% +normalize it yeah then you would +multiply by the likelihood youd get + + align:start position:0% +multiply by the likelihood youd get + + + align:start position:0% +multiply by the likelihood youd get +something again unnormalized and then + + align:start position:0% +something again unnormalized and then + + + align:start position:0% +something again unnormalized and then +you have to normalize again and then you + + align:start position:0% +you have to normalize again and then you + + + align:start position:0% +you have to normalize again and then you +get to your final answer or don't bother + + align:start position:0% +get to your final answer or don't bother + + + align:start position:0% +get to your final answer or don't bother +normalizing at this stage just multiply + + align:start position:0% +normalizing at this stage just multiply + + + align:start position:0% +normalizing at this stage just multiply +this by the likelihood and then just + + align:start position:0% +this by the likelihood and then just + + + align:start position:0% +this by the likelihood and then just +only normalize once at the very end and + + align:start position:0% +only normalize once at the very end and + + + align:start position:0% +only normalize once at the very end and +you'll get the same answer because you + + align:start position:0% +you'll get the same answer because you + + + align:start position:0% +you'll get the same answer because you +know normalizing once and the + + align:start position:0% +know normalizing once and the + + + align:start position:0% +know normalizing once and the +normalizing again the same as just + + align:start position:0% +normalizing again the same as just + + + align:start position:0% +normalizing again the same as just +normalizing at the very end you're just + + align:start position:0% +normalizing at the very end you're just + + + align:start position:0% +normalizing at the very end you're just +multiplying a vector this column by by a + + align:start position:0% +multiplying a vector this column by by a + + + align:start position:0% +multiplying a vector this column by by a +scaler by rescaling it to make it unit + + align:start position:0% +scaler by rescaling it to make it unit + + + align:start position:0% +scaler by rescaling it to make it unit +length and it's or unit you know so the + + align:start position:0% +length and it's or unit you know so the + + + align:start position:0% +length and it's or unit you know so the +sum is one something exactly exactly + + align:start position:0% +sum is one something exactly exactly + + + align:start position:0% +sum is one something exactly exactly +isn't number one going to be the same + + align:start position:0% +isn't number one going to be the same + + + align:start position:0% +isn't number one going to be the same +answer as the examp we just did cuz + + align:start position:0% +answer as the examp we just did cuz + + + align:start position:0% +answer as the examp we just did cuz +we're going to be updating I mean this + + align:start position:0% +we're going to be updating I mean this + + + align:start position:0% +we're going to be updating I mean this +going to be different okay well we just + + align:start position:0% +going to be different okay well we just + + + align:start position:0% +going to be different okay well we just +have to do it + + align:start position:0% +have to do it + + + align:start position:0% +have to do it +so so yes absolutely all of these should + + align:start position:0% +so so yes absolutely all of these should + + + align:start position:0% +so so yes absolutely all of these should +give you the same answer because it's + + align:start position:0% +give you the same answer because it's + + + align:start position:0% +give you the same answer because it's +the same exact data right starting from + + align:start position:0% +the same exact data right starting from + + + align:start position:0% +the same exact data right starting from +the same prior but what we want you to + + align:start position:0% +the same prior but what we want you to + + + align:start position:0% +the same prior but what we want you to +really see is how the math proves that I + + align:start position:0% +really see is how the math proves that I + + + align:start position:0% +really see is how the math proves that I +mean we're just multiplying different + + align:start position:0% +mean we're just multiplying different + + + align:start position:0% +mean we're just multiplying different +order that's right so it all comes down + + align:start position:0% +order that's right so it all comes down + + + align:start position:0% +order that's right so it all comes down +to what um what property of + + align:start position:0% +to what um what property of + + + align:start position:0% +to what um what property of +multiplication Associated it's commun + + align:start position:0% +multiplication Associated it's commun + + + align:start position:0% +multiplication Associated it's commun +commun commutative I guess you're also + + align:start position:0% +commun commutative I guess you're also + + + align:start position:0% +commun commutative I guess you're also +using ativity it's just that + + align:start position:0% +using ativity it's just that + + + align:start position:0% +using ativity it's just that +multiplication is commutative right so + + align:start position:0% +multiplication is commutative right so + + + align:start position:0% +multiplication is commutative right so +doesn't matter what order you multiply + + align:start position:0% +doesn't matter what order you multiply + + + align:start position:0% +doesn't matter what order you multiply +these columns in the final result is + + align:start position:0% +these columns in the final result is + + + align:start position:0% +these columns in the final result is +going to be the same right so just think + + align:start position:0% +going to be the same right so just think + + + align:start position:0% +going to be the same right so just think +about how the order changes depending on + + align:start position:0% +about how the order changes depending on + + + align:start position:0% +about how the order changes depending on +the order of the five versus the nine + + align:start position:0% +the order of the five versus the nine + + + align:start position:0% +the order of the five versus the nine +and also what happens if you think of + + align:start position:0% +and also what happens if you think of + + + align:start position:0% +and also what happens if you think of +both at once how would you then make a + + align:start position:0% +both at once how would you then make a + + + align:start position:0% +both at once how would you then make a +table directly for that right so + + align:start position:0% + + + + align:start position:0% + +we so + + align:start position:0% + + + + align:start position:0% + +five I see and so you multiplied here is + + align:start position:0% +five I see and so you multiplied here is + + + align:start position:0% +five I see and so you multiplied here is +this your + + align:start position:0% +this your + + + align:start position:0% +this your +likelihood that's you multiplied that + + align:start position:0% +likelihood that's you multiplied that + + + align:start position:0% +likelihood that's you multiplied that +where's your P times this by this oh you + + align:start position:0% +where's your P times this by this oh you + + + align:start position:0% +where's your P times this by this oh you +even normalize yeah you might I see + + align:start position:0% +even normalize yeah you might I see + + + align:start position:0% +even normalize yeah you might I see +right so did you understand John's + + align:start position:0% +right so did you understand John's + + + align:start position:0% +right so did you understand John's +statement that you didn't actually have + + align:start position:0% +statement that you didn't actually have + + + align:start position:0% +statement that you didn't actually have +to normalize right already done it no I + + align:start position:0% +to normalize right already done it no I + + + align:start position:0% +to normalize right already done it no I +understand it's a nicer number than one + + align:start position:0% +understand it's a nicer number than one + + + align:start position:0% +understand it's a nicer number than one +over 60 but if you didn't have it you + + align:start position:0% +over 60 but if you didn't have it you + + + align:start position:0% +over 60 but if you didn't have it you +could have just used this column and + + align:start position:0% +could have just used this column and + + + align:start position:0% +could have just used this column and +normalize at the end that makes sense + + align:start position:0% + + + + align:start position:0% + +excellent and I'm trying to this is just + + align:start position:0% +excellent and I'm trying to this is just + + + align:start position:0% +excellent and I'm trying to this is just +if you do it in one step you just did + + align:start position:0% +if you do it in one step you just did + + + align:start position:0% +if you do it in one step you just did +you get different answers no no it's the + + align:start position:0% +you get different answers no no it's the + + + align:start position:0% +you get different answers no no it's the +same it's the same makes sense you have + + align:start position:0% +same it's the same makes sense you have + + + align:start position:0% +same it's the same makes sense you have +the data that's the evidence you have + + align:start position:0% +the data that's the evidence you have + + + align:start position:0% +the data that's the evidence you have +yes right um so was this all clear was + + align:start position:0% +yes right um so was this all clear was + + + align:start position:0% +yes right um so was this all clear was +John's statement about not only needing + + align:start position:0% +John's statement about not only needing + + + align:start position:0% +John's statement about not only needing +the unnormalized posterior in the middle + + align:start position:0% +the unnormalized posterior in the middle + + + align:start position:0% +the unnormalized posterior in the middle +reasonably clear so what what we were + + align:start position:0% +reasonably clear so what what we were + + + align:start position:0% +reasonably clear so what what we were +talking about is that if you were to use + + align:start position:0% +talking about is that if you were to use + + + align:start position:0% +talking about is that if you were to use +the + + align:start position:0% +the + + + align:start position:0% +the +one um with then your unnormalized plus + + align:start position:0% +one um with then your unnormalized plus + + + align:start position:0% +one um with then your unnormalized plus +the actual probabilities so add them + + align:start position:0% +the actual probabilities so add them + + + align:start position:0% +the actual probabilities so add them +with because in order to use a law of + + align:start position:0% +with because in order to use a law of + + + align:start position:0% +with because in order to use a law of +total probability you have to multiply + + align:start position:0% +total probability you have to multiply + + + align:start position:0% +total probability you have to multiply +your likelihood by genuine probabilities + + align:start position:0% +your likelihood by genuine probabilities + + + align:start position:0% +your likelihood by genuine probabilities +and the unnormalized posterior is not a + + align:start position:0% +and the unnormalized posterior is not a + + + align:start position:0% +and the unnormalized posterior is not a +genuine probability if you use the + + align:start position:0% +genuine probability if you use the + + + align:start position:0% +genuine probability if you use the +normalized one if you use the normalized + + align:start position:0% +normalized one if you use the normalized + + + align:start position:0% +normalized one if you use the normalized +one then it would be this would be the + + align:start position:0% +one then it would be this would be the + + + align:start position:0% +one then it would be this would be the +the that would be the total probability + + align:start position:0% +the that would be the total probability + + + align:start position:0% +the that would be the total probability +of of that that's exactly right but in + + align:start position:0% +of of that that's exactly right but in + + + align:start position:0% +of of that that's exactly right but in +this case it's this that's the total + + align:start position:0% +this case it's this that's the total + + + align:start position:0% +this case it's this that's the total +probability + + align:start position:0% +probability + + + align:start position:0% +probability +yeah this is now your posterior + + align:start position:0% +yeah this is now your posterior + + + align:start position:0% +yeah this is now your posterior +probability this is these are now the + + align:start position:0% +probability this is these are now the + + + align:start position:0% +probability this is these are now the +probab so make a distinction the total + + align:start position:0% +probab so make a distinction the total + + + align:start position:0% +probab so make a distinction the total +probability is about the data and these + + align:start position:0% +probability is about the data and these + + + align:start position:0% +probability is about the data and these +probabilities here are about the + + align:start position:0% +probabilities here are about the + + + align:start position:0% +probabilities here are about the +hypothesis right sort of like the fit of + + align:start position:0% +hypothesis right sort of like the fit of + + + align:start position:0% +hypothesis right sort of like the fit of +the + + align:start position:0% +the + + + align:start position:0% +the +hypoth um you could think of that + + align:start position:0% +hypoth um you could think of that + + + align:start position:0% +hypoth um you could think of that +they're genuine probabilities this is + + align:start position:0% +they're genuine probabilities this is + + + align:start position:0% +they're genuine probabilities this is +the probability that you chose the + + align:start position:0% +the probability that you chose the + + + align:start position:0% +the probability that you chose the +12-sided die given the data that is if + + align:start position:0% +12-sided die given the data that is if + + + align:start position:0% +12-sided die given the data that is if +we I get did this a million times and + + align:start position:0% +we I get did this a million times and + + + align:start position:0% +we I get did this a million times and +every time I rolled I I only looked at + + align:start position:0% +every time I rolled I I only looked at + + + align:start position:0% +every time I rolled I I only looked at +the times I rolled a nine and then a + + align:start position:0% +the times I rolled a nine and then a + + + align:start position:0% +the times I rolled a nine and then a +five you would find this fraction of + + align:start position:0% +five you would find this fraction of + + + align:start position:0% +five you would find this fraction of +those times would be it would be a + + align:start position:0% +those times would be it would be a + + + align:start position:0% +those times would be it would be a +12-sided and this fraction would be a + + align:start position:0% +12-sided and this fraction would be a + + + align:start position:0% +12-sided and this fraction would be a +20-sided so I forget what the numbers + + align:start position:0% +20-sided so I forget what the numbers + + + align:start position:0% +20-sided so I forget what the numbers +were like 3 to one okay yeah Mak sense + + align:start position:0% +were like 3 to one okay yeah Mak sense + + + align:start position:0% +were like 3 to one okay yeah Mak sense +excellent so we multiply them together + + align:start position:0% +excellent so we multiply them together + + + align:start position:0% +excellent so we multiply them together +but + + align:start position:0% +but + + + align:start position:0% +but +then you get the same exact answer right + + align:start position:0% +then you get the same exact answer right + + + align:start position:0% +then you get the same exact answer right +so we get we give these this + + align:start position:0% +so we get we give these this + + + align:start position:0% +so we get we give these this +answer and then you normalize it you get + + align:start position:0% +answer and then you normalize it you get + + + align:start position:0% +answer and then you normalize it you get +this okay right okay there's no way to + + align:start position:0% +this okay right okay there's no way to + + + align:start position:0% +this okay right okay there's no way to +normalize it + + align:start position:0% +normalize it + + + align:start position:0% +normalize it +without all right let's come back + + align:start position:0% +without all right let's come back + + + align:start position:0% +without all right let's come back +together and take a look at what + + align:start position:0% +together and take a look at what + + + align:start position:0% +together and take a look at what +happened + + align:start position:0% + + + + align:start position:0% + +here I saw I saw some aha moments that + + align:start position:0% +here I saw I saw some aha moments that + + + align:start position:0% +here I saw I saw some aha moments that +was + + align:start position:0% + + + + align:start position:0% + +great some people cited the commutative + + align:start position:0% +great some people cited the commutative + + + align:start position:0% +great some people cited the commutative +property of multiplication that made me + + align:start position:0% +property of multiplication that made me + + + align:start position:0% +property of multiplication that made me +very + + align:start position:0% +very + + + align:start position:0% +very +happy so what do we + + align:start position:0% +happy so what do we + + + align:start position:0% +happy so what do we +do so when we do the nine and then the + + align:start position:0% +do so when we do the nine and then the + + + align:start position:0% +do so when we do the nine and then the +five it looks just like what I did with + + align:start position:0% +five it looks just like what I did with + + + align:start position:0% +five it looks just like what I did with +the five and the nine except the + + align:start position:0% +the five and the nine except the + + + align:start position:0% +the five and the nine except the +likelihood columns are flipped so we + + align:start position:0% +likelihood columns are flipped so we + + + align:start position:0% +likelihood columns are flipped so we +have our prior the + + align:start position:0% +have our prior the + + + align:start position:0% +have our prior the +likelihood for the nine gives us this + + align:start position:0% +likelihood for the nine gives us this + + + align:start position:0% +likelihood for the nine gives us this +colum the product gives us an first + + align:start position:0% +colum the product gives us an first + + + align:start position:0% +colum the product gives us an first +unnormalized posterior then we do the + + align:start position:0% +unnormalized posterior then we do the + + + align:start position:0% +unnormalized posterior then we do the +likelihood for rolling a + + align:start position:0% +likelihood for rolling a + + + align:start position:0% +likelihood for rolling a +five the product of the unnormalized + + align:start position:0% +five the product of the unnormalized + + + align:start position:0% +five the product of the unnormalized +posterior and the second likelihood + + align:start position:0% +posterior and the second likelihood + + + align:start position:0% +posterior and the second likelihood +gives us our final unnormalized + + align:start position:0% +gives us our final unnormalized + + + align:start position:0% +gives us our final unnormalized +posterior and notice the sum is still + + align:start position:0% +posterior and notice the sum is still + + + align:start position:0% +posterior and notice the sum is still +exactly what it was before 0019 + + align:start position:0% +exactly what it was before 0019 + + + align:start position:0% +exactly what it was before 0019 +when we normalize we get exactly the + + align:start position:0% +when we normalize we get exactly the + + + align:start position:0% +when we normalize we get exactly the +same answer that we had before now if + + align:start position:0% +same answer that we had before now if + + + align:start position:0% +same answer that we had before now if +you contrast this with the table we + + align:start position:0% +you contrast this with the table we + + + align:start position:0% +you contrast this with the table we +looked at when we did the five and then + + align:start position:0% +looked at when we did the five and then + + + align:start position:0% +looked at when we did the five and then +the nine what changed is these two + + align:start position:0% +the nine what changed is these two + + + align:start position:0% +the nine what changed is these two +columns were flipped + + align:start position:0% +columns were flipped + + + align:start position:0% +columns were flipped +around and so I suppose this column was + + align:start position:0% +around and so I suppose this column was + + + align:start position:0% +around and so I suppose this column was +different and this column was different + + align:start position:0% +different and this column was different + + + align:start position:0% +different and this column was different +as a result and then the final result + + align:start position:0% +as a result and then the final result + + + align:start position:0% +as a result and then the final result +however was exactly the same okay now + + align:start position:0% +however was exactly the same okay now + + + align:start position:0% +however was exactly the same okay now +what if we do them both at once what + + align:start position:0% +what if we do them both at once what + + + align:start position:0% +what if we do them both at once what +should that + + align:start position:0% +should that + + + align:start position:0% +should that +mean if we do them both at once then + + align:start position:0% +mean if we do them both at once then + + + align:start position:0% +mean if we do them both at once then +well we start from the same uniform + + align:start position:0% +well we start from the same uniform + + + align:start position:0% +well we start from the same uniform +prior and our likelihood now we should + + align:start position:0% +prior and our likelihood now we should + + + align:start position:0% +prior and our likelihood now we should +think of the data as both roles the five + + align:start position:0% +think of the data as both roles the five + + + align:start position:0% +think of the data as both roles the five +and the nine Okay now what's important + + align:start position:0% +and the nine Okay now what's important + + + align:start position:0% +and the nine Okay now what's important +here is + + align:start position:0% +here is + + + align:start position:0% +here is +that if we condition on a given + + align:start position:0% +that if we condition on a given + + + align:start position:0% +that if we condition on a given +hypothesis for example if we condition + + align:start position:0% +hypothesis for example if we condition + + + align:start position:0% +hypothesis for example if we condition +on the hypothesis that it's a 12-sided + + align:start position:0% +on the hypothesis that it's a 12-sided + + + align:start position:0% +on the hypothesis that it's a 12-sided +die then the first role and the second + + align:start position:0% +die then the first role and the second + + + align:start position:0% +die then the first role and the second +role are independent events right it + + align:start position:0% +role are independent events right it + + + align:start position:0% +role are independent events right it +means that we can figure out the + + align:start position:0% +means that we can figure out the + + + align:start position:0% +means that we can figure out the +probability of a five and then a n on + + align:start position:0% +probability of a five and then a n on + + + align:start position:0% +probability of a five and then a n on +the 12-sided die it's just the product + + align:start position:0% +the 12-sided die it's just the product + + + align:start position:0% +the 12-sided die it's just the product +of the probability of a five on a + + align:start position:0% +of the probability of a five on a + + + align:start position:0% +of the probability of a five on a +12-sided die and the probability of a n + + align:start position:0% +12-sided die and the probability of a n + + + align:start position:0% +12-sided die and the probability of a n +on a 12-sided die that's why we're + + align:start position:0% +on a 12-sided die that's why we're + + + align:start position:0% +on a 12-sided die that's why we're +justified in taking the product if we + + align:start position:0% +justified in taking the product if we + + + align:start position:0% +justified in taking the product if we +condition on the die that it is on the + + align:start position:0% +condition on the die that it is on the + + + align:start position:0% +condition on the die that it is on the +hypothesis 12-sided then the roles are + + align:start position:0% +hypothesis 12-sided then the roles are + + + align:start position:0% +hypothesis 12-sided then the roles are +all independent of each other in + + align:start position:0% +all independent of each other in + + + align:start position:0% +all independent of each other in +particular we get 112th * + + align:start position:0% +particular we get 112th * + + + align:start position:0% +particular we get 112th * +112th for rolling a five and then + + align:start position:0% +112th for rolling a five and then + + + align:start position:0% +112th for rolling a five and then +rolling a 9 and for the 20 side of die + + align:start position:0% +rolling a 9 and for the 20 side of die + + + align:start position:0% +rolling a 9 and for the 20 side of die +we get get 12th * + + align:start position:0% +we get get 12th * + + + align:start position:0% +we get get 12th * +12th so now in one step we + + align:start position:0% +12th so now in one step we + + + align:start position:0% +12th so now in one step we +update same exact sum we + + align:start position:0% +update same exact sum we + + + align:start position:0% +update same exact sum we +normalize same exact answer and I + + align:start position:0% +normalize same exact answer and I + + + align:start position:0% +normalize same exact answer and I +mentioned that some groups maybe when + + align:start position:0% +mentioned that some groups maybe when + + + align:start position:0% +mentioned that some groups maybe when +slightly prompted by me said oh + + align:start position:0% +slightly prompted by me said oh + + + align:start position:0% +slightly prompted by me said oh +multiplication is commutative all right + + align:start position:0% +multiplication is commutative all right + + + align:start position:0% +multiplication is commutative all right +that's all that's going on here in the + + align:start position:0% +that's all that's going on here in the + + + align:start position:0% +that's all that's going on here in the +end all we're doing is taking a prior + + align:start position:0% +end all we're doing is taking a prior + + + align:start position:0% +end all we're doing is taking a prior +the first likelihood column the second + + align:start position:0% +the first likelihood column the second + + + align:start position:0% +the first likelihood column the second +likelihood column multiplying them + + align:start position:0% +likelihood column multiplying them + + + align:start position:0% +likelihood column multiplying them +together and then normalizing it right + + align:start position:0% +together and then normalizing it right + + + align:start position:0% +together and then normalizing it right +it doesn't matter what order those + + align:start position:0% +it doesn't matter what order those + + + align:start position:0% +it doesn't matter what order those +likelihood columns are in it doesn't + + align:start position:0% +likelihood columns are in it doesn't + + + align:start position:0% +likelihood columns are in it doesn't +matter if we think of the five and then + + align:start position:0% +matter if we think of the five and then + + + align:start position:0% +matter if we think of the five and then +the nine the nine and the five or the + + align:start position:0% +the nine the nine and the five or the + + + align:start position:0% +the nine the nine and the five or the +five and nine multiplied together to + + align:start position:0% +five and nine multiplied together to + + + align:start position:0% +five and nine multiplied together to +make their own likelihood column you get + + align:start position:0% +make their own likelihood column you get + + + align:start position:0% +make their own likelihood column you get +the same exact unnormalized result no + + align:start position:0% +the same exact unnormalized result no + + + align:start position:0% +the same exact unnormalized result no +matter + + align:start position:0% +matter + + + align:start position:0% +matter +what okay so this is all there is to why + + align:start position:0% +what okay so this is all there is to why + + + align:start position:0% +what okay so this is all there is to why +it doesn't matter what order you update + + align:start position:0% +it doesn't matter what order you update + + + align:start position:0% +it doesn't matter what order you update +the data in + + align:start position:0% +the data in + + + align:start position:0% +the data in +sequentially just matters what the data + + align:start position:0% +sequentially just matters what the data + + + align:start position:0% +sequentially just matters what the data +is now I also had a question + + align:start position:0% +is now I also had a question + + + align:start position:0% +is now I also had a question +why if you could do it all at once would + + align:start position:0% +why if you could do it all at once would + + + align:start position:0% +why if you could do it all at once would +you even + + align:start position:0% +you even + + + align:start position:0% +you even +bother with doing it once and then doing + + align:start position:0% +bother with doing it once and then doing + + + align:start position:0% +bother with doing it once and then doing +it again okay it's a very good question + + align:start position:0% +it again okay it's a very good question + + + align:start position:0% +it again okay it's a very good question +does anyone want to suggest a reason + + align:start position:0% +does anyone want to suggest a reason + + + align:start position:0% +does anyone want to suggest a reason +maybe other than the group that I talked + + align:start position:0% +maybe other than the group that I talked + + + align:start position:0% +maybe other than the group that I talked +to specifically about + + align:start position:0% +to specifically about + + + align:start position:0% +to specifically about +it yeah well I'm just thinking uh as + + align:start position:0% +it yeah well I'm just thinking uh as + + + align:start position:0% +it yeah well I'm just thinking uh as +you're saying if you have ongoing + + align:start position:0% +you're saying if you have ongoing + + + align:start position:0% +you're saying if you have ongoing +patience and you have to like + + align:start position:0% +patience and you have to like + + + align:start position:0% +patience and you have to like +continuously update then um like the + + align:start position:0% +continuously update then um like the + + + align:start position:0% +continuously update then um like the +first data set may be all that you have + + align:start position:0% +first data set may be all that you have + + + align:start position:0% +first data set may be all that you have +at that moment but then you have to like + + align:start position:0% +at that moment but then you have to like + + + align:start position:0% +at that moment but then you have to like +keep that's exactly right that's exactly + + align:start position:0% +keep that's exactly right that's exactly + + + align:start position:0% +keep that's exactly right that's exactly +right so in life and in clinical trials + + align:start position:0% +right so in life and in clinical trials + + + align:start position:0% +right so in life and in clinical trials +right you don't get all the data + + align:start position:0% +right you don't get all the data + + + align:start position:0% +right you don't get all the data +necessarily at once it sort of comes in + + align:start position:0% +necessarily at once it sort of comes in + + + align:start position:0% +necessarily at once it sort of comes in +continuously you know when I wake up in + + align:start position:0% +continuously you know when I wake up in + + + align:start position:0% +continuously you know when I wake up in +the morning I don't know what + + align:start position:0% +the morning I don't know what + + + align:start position:0% +the morning I don't know what +temperature it is + + align:start position:0% +temperature it is + + + align:start position:0% +temperature it is +outside um I have a prior based on what + + align:start position:0% +outside um I have a prior based on what + + + align:start position:0% +outside um I have a prior based on what +temperature it was yesterday at about + + align:start position:0% +temperature it was yesterday at about + + + align:start position:0% +temperature it was yesterday at about +the same time like I have a memory of + + align:start position:0% +the same time like I have a memory of + + + align:start position:0% +the same time like I have a memory of +that so that gives me some prior + + align:start position:0% +that so that gives me some prior + + + align:start position:0% +that so that gives me some prior +Distribution on the temperature okay + + align:start position:0% +Distribution on the temperature okay + + + align:start position:0% +Distribution on the temperature okay +that might be a continuous one like + + align:start position:0% +that might be a continuous one like + + + align:start position:0% +that might be a continuous one like +maybe a Bel curve we're going to get to + + align:start position:0% +maybe a Bel curve we're going to get to + + + align:start position:0% +maybe a Bel curve we're going to get to +that next week these continuous updating + + align:start position:0% +that next week these continuous updating + + + align:start position:0% +that next week these continuous updating +problems okay and then when I get out of + + align:start position:0% +problems okay and then when I get out of + + + align:start position:0% +problems okay and then when I get out of +bed I see that the window is covered in + + align:start position:0% +bed I see that the window is covered in + + + align:start position:0% +bed I see that the window is covered in +condensation that's some data I can + + align:start position:0% +condensation that's some data I can + + + align:start position:0% +condensation that's some data I can +update my beliefs probably means it's + + align:start position:0% +update my beliefs probably means it's + + + align:start position:0% +update my beliefs probably means it's +kind of cold uh great then I can you + + align:start position:0% +kind of cold uh great then I can you + + + align:start position:0% +kind of cold uh great then I can you +know open the window to let the cat out + + align:start position:0% +know open the window to let the cat out + + + align:start position:0% +know open the window to let the cat out +and a burst of freezing cold air comes + + align:start position:0% +and a burst of freezing cold air comes + + + align:start position:0% +and a burst of freezing cold air comes +in like it did this morning well + + align:start position:0% +in like it did this morning well + + + align:start position:0% +in like it did this morning well +actually not this morning this morning + + align:start position:0% +actually not this morning this morning + + + align:start position:0% +actually not this morning this morning +was + + align:start position:0% +was + + + align:start position:0% +was +great yesterday it was cold all right + + align:start position:0% +great yesterday it was cold all right + + + align:start position:0% +great yesterday it was cold all right +and and and again I now I have more data + + align:start position:0% +and and and again I now I have more data + + + align:start position:0% +and and and again I now I have more data +and I update my beliefs all right you + + align:start position:0% +and I update my beliefs all right you + + + align:start position:0% +and I update my beliefs all right you +can go through life this way it'll give + + align:start position:0% +can go through life this way it'll give + + + align:start position:0% +can go through life this way it'll give +you a headache but you can do it now + + align:start position:0% +you a headache but you can do it now + + + align:start position:0% +you a headache but you can do it now +with clinical trials the same thing can + + align:start position:0% +with clinical trials the same thing can + + + align:start position:0% +with clinical trials the same thing can +happen maybe you do a pilot study maybe + + align:start position:0% +happen maybe you do a pilot study maybe + + + align:start position:0% +happen maybe you do a pilot study maybe +you have some belief that you know + + align:start position:0% +you have some belief that you know + + + align:start position:0% +you have some belief that you know +eating almonds + + align:start position:0% + + + + align:start position:0% + +causes something stomach stomach cramps + + align:start position:0% +causes something stomach stomach cramps + + + align:start position:0% +causes something stomach stomach cramps +great and maybe it's just for you but + + align:start position:0% +great and maybe it's just for you but + + + align:start position:0% +great and maybe it's just for you but +you want to do a study about that so you + + align:start position:0% +you want to do a study about that so you + + + align:start position:0% +you want to do a study about that so you +maybe you know for yourself that eating + + align:start position:0% +maybe you know for yourself that eating + + + align:start position:0% +maybe you know for yourself that eating +almonds give you stomach cramps you're + + align:start position:0% +almonds give you stomach cramps you're + + + align:start position:0% +almonds give you stomach cramps you're +you're you're you're at the Harvard + + align:start position:0% +you're you're you're at the Harvard + + + align:start position:0% +you're you're you're at the Harvard +School of Public Health and you really + + align:start position:0% +School of Public Health and you really + + + align:start position:0% +School of Public Health and you really +want to investigate this further so you + + align:start position:0% +want to investigate this further so you + + + align:start position:0% +want to investigate this further so you +you gather a few willing subjects you + + align:start position:0% +you gather a few willing subjects you + + + align:start position:0% +you gather a few willing subjects you +feed them some almonds you see if they + + align:start position:0% +feed them some almonds you see if they + + + align:start position:0% +feed them some almonds you see if they +get stomach cramps how many of them and + + align:start position:0% +get stomach cramps how many of them and + + + align:start position:0% +get stomach cramps how many of them and +you know maybe your prior ahead was you + + align:start position:0% +you know maybe your prior ahead was you + + + align:start position:0% +you know maybe your prior ahead was you +just kind of felt like you have this + + align:start position:0% +just kind of felt like you have this + + + align:start position:0% +just kind of felt like you have this +really strong belief that almonds CA + + align:start position:0% +really strong belief that almonds CA + + + align:start position:0% +really strong belief that almonds CA +stomach cramps because it does for you + + align:start position:0% +stomach cramps because it does for you + + + align:start position:0% +stomach cramps because it does for you +and you really Haven an ass a lot of + + align:start position:0% +and you really Haven an ass a lot of + + + align:start position:0% +and you really Haven an ass a lot of +other people so you might have a lot of + + align:start position:0% +other people so you might have a lot of + + + align:start position:0% +other people so you might have a lot of +Prior probability on that hypothesis + + align:start position:0% +Prior probability on that hypothesis + + + align:start position:0% +Prior probability on that hypothesis +being true once you collect a few more + + align:start position:0% +being true once you collect a few more + + + align:start position:0% +being true once you collect a few more +people maybe you ask your friends maybe + + align:start position:0% +people maybe you ask your friends maybe + + + align:start position:0% +people maybe you ask your friends maybe +you find that most of them don't have + + align:start position:0% +you find that most of them don't have + + + align:start position:0% +you find that most of them don't have +the same problem suddenly your posterior + + align:start position:0% +the same problem suddenly your posterior + + + align:start position:0% +the same problem suddenly your posterior +belief changes and now you're not quite + + align:start position:0% +belief changes and now you're not quite + + + align:start position:0% +belief changes and now you're not quite +so convinced that it's true and then if + + align:start position:0% +so convinced that it's true and then if + + + align:start position:0% +so convinced that it's true and then if +you're really ambitious and you have a + + align:start position:0% +you're really ambitious and you have a + + + align:start position:0% +you're really ambitious and you have a +lot of grant money from the NIH you + + align:start position:0% +lot of grant money from the NIH you + + + align:start position:0% +lot of grant money from the NIH you +recruit a thousand people and you do a + + align:start position:0% +recruit a thousand people and you do a + + + align:start position:0% +recruit a thousand people and you do a +randomized controlled trial with Placebo + + align:start position:0% +randomized controlled trial with Placebo + + + align:start position:0% +randomized controlled trial with Placebo +and you find out that exactly 10% of the + + align:start position:0% +and you find out that exactly 10% of the + + + align:start position:0% +and you find out that exactly 10% of the +folks you know complain about the + + align:start position:0% +folks you know complain about the + + + align:start position:0% +folks you know complain about the +stomach cramps with almonds maybe 10% on + + align:start position:0% +stomach cramps with almonds maybe 10% on + + + align:start position:0% +stomach cramps with almonds maybe 10% on +the placebo also so you're not quite + + align:start position:0% +the placebo also so you're not quite + + + align:start position:0% +the placebo also so you're not quite +sure what's going on but the point is + + align:start position:0% +sure what's going on but the point is + + + align:start position:0% +sure what's going on but the point is +you're getting data a little a little + + align:start position:0% +you're getting data a little a little + + + align:start position:0% +you're getting data a little a little +more a little more and you can keep + + align:start position:0% +more a little more and you can keep + + + align:start position:0% +more a little more and you can keep +incorporating it updating your beliefs + + align:start position:0% +incorporating it updating your beliefs + + + align:start position:0% +incorporating it updating your beliefs +all right so that's that's the principle + + align:start position:0% +all right so that's that's the principle + + + align:start position:0% +all right so that's that's the principle +one last thing I'll point out is what if + + align:start position:0% +one last thing I'll point out is what if + + + align:start position:0% +one last thing I'll point out is what if +you have a prior belief that is so + + align:start position:0% +you have a prior belief that is so + + + align:start position:0% +you have a prior belief that is so +strong so you're so sure for example + + align:start position:0% +strong so you're so sure for example + + + align:start position:0% +strong so you're so sure for example +that almonds don't cause stomach pain + + align:start position:0% +that almonds don't cause stomach pain + + + align:start position:0% +that almonds don't cause stomach pain +because it doesn't for you and you're + + align:start position:0% +because it doesn't for you and you're + + + align:start position:0% +because it doesn't for you and you're +just sure that that would be ridiculous + + align:start position:0% +just sure that that would be ridiculous + + + align:start position:0% +just sure that that would be ridiculous +right so you put your prior probability + + align:start position:0% +right so you put your prior probability + + + align:start position:0% +right so you put your prior probability +at + + align:start position:0% +at + + + align:start position:0% +at +zero right how much evidence will it + + align:start position:0% +zero right how much evidence will it + + + align:start position:0% +zero right how much evidence will it +take how much data will it take for you + + align:start position:0% +take how much data will it take for you + + + align:start position:0% +take how much data will it take for you +to be + + align:start position:0% + + + + align:start position:0% + +convinced infinite no amount amount of + + align:start position:0% +convinced infinite no amount amount of + + + align:start position:0% +convinced infinite no amount amount of +data is going to convince you otherwise + + align:start position:0% +data is going to convince you otherwise + + + align:start position:0% +data is going to convince you otherwise +this is why whenever you do this kind of + + align:start position:0% +this is why whenever you do this kind of + + + align:start position:0% +this is why whenever you do this kind of +basan updating it's generally best to + + align:start position:0% +basan updating it's generally best to + + + align:start position:0% +basan updating it's generally best to +leave a little bit of possibility for + + align:start position:0% +leave a little bit of possibility for + + + align:start position:0% +leave a little bit of possibility for +Santa Claus okay like a little bit just + + align:start position:0% +Santa Claus okay like a little bit just + + + align:start position:0% +Santa Claus okay like a little bit just +so that + + align:start position:0% +so that + + + align:start position:0% +so that +should a fat white man come down your + + align:start position:0% +should a fat white man come down your + + + align:start position:0% +should a fat white man come down your +chimney and deliver the presentence one + + align:start position:0% +chimney and deliver the presentence one + + + align:start position:0% +chimney and deliver the presentence one +year you have the possibility to adjust + + align:start position:0% +year you have the possibility to adjust + + + align:start position:0% +year you have the possibility to adjust +okay so that that those are some some + + align:start position:0% +okay so that that those are some some + + + align:start position:0% +okay so that that those are some some +things to keep in mind I think we got + + align:start position:0% +things to keep in mind I think we got + + + align:start position:0% +things to keep in mind I think we got +one more board question that Jerry's + + align:start position:0% +one more board question that Jerry's + + + align:start position:0% +one more board question that Jerry's +gonna gonna lead right + + align:start position:0% +gonna gonna lead right + + + align:start position:0% +gonna gonna lead right +so it's nice to get probabilities for + + align:start position:0% +so it's nice to get probabilities for + + + align:start position:0% +so it's nice to get probabilities for +hypotheses but one thing you also want + + align:start position:0% +hypotheses but one thing you also want + + + align:start position:0% +hypotheses but one thing you also want +to do is predict what's going to come + + align:start position:0% +to do is predict what's going to come + + + align:start position:0% +to do is predict what's going to come +next and so that's what we call + + align:start position:0% +next and so that's what we call + + + align:start position:0% +next and so that's what we call +probabilistic + + align:start position:0% +probabilistic + + + align:start position:0% +probabilistic +prediction if I pick one of John's five + + align:start position:0% +prediction if I pick one of John's five + + + align:start position:0% +prediction if I pick one of John's five +die and I'm about to roll it you could + + align:start position:0% +die and I'm about to roll it you could + + + align:start position:0% +die and I'm about to roll it you could +tell me using the law of total + + align:start position:0% +tell me using the law of total + + + align:start position:0% +tell me using the law of total +probability the probability that I get a + + align:start position:0% +probability the probability that I get a + + + align:start position:0% +probability the probability that I get a +five + + align:start position:0% +five + + + align:start position:0% +five +and we've done that we did that in the + + align:start position:0% +and we've done that we did that in the + + + align:start position:0% +and we've done that we did that in the +the first unit on probability in this + + align:start position:0% +the first unit on probability in this + + + align:start position:0% +the first unit on probability in this +class but suppose he rolls a five + + align:start position:0% +class but suppose he rolls a five + + + align:start position:0% +class but suppose he rolls a five +first now I can update my probabilities + + align:start position:0% +first now I can update my probabilities + + + align:start position:0% +first now I can update my probabilities +for which diet is which is going to + + align:start position:0% +for which diet is which is going to + + + align:start position:0% +for which diet is which is going to +update my estimation of the probability + + align:start position:0% +update my estimation of the probability + + + align:start position:0% +update my estimation of the probability +of rolling say a four on the next roll + + align:start position:0% +of rolling say a four on the next roll + + + align:start position:0% +of rolling say a four on the next roll +so this is what we'll call probabilistic + + align:start position:0% +so this is what we'll call probabilistic + + + align:start position:0% +so this is what we'll call probabilistic +prediction we can predict what's going + + align:start position:0% +prediction we can predict what's going + + + align:start position:0% +prediction we can predict what's going +to happen next at least with + + align:start position:0% +to happen next at least with + + + align:start position:0% +to happen next at least with +probabilities based Bas + + align:start position:0% +probabilities based Bas + + + align:start position:0% +probabilities based Bas +on the data that we've seen we update + + align:start position:0% +on the data that we've seen we update + + + align:start position:0% +on the data that we've seen we update +our predictions based on that so here's + + align:start position:0% +our predictions based on that so here's + + + align:start position:0% +our predictions based on that so here's +a a setup D1 is the first Ro D2 is the + + align:start position:0% + + + + align:start position:0% + +second I'll do this example oh no this + + align:start position:0% +second I'll do this example oh no this + + + align:start position:0% +second I'll do this example oh no this +is a board question you're going to do + + align:start position:0% +is a board question you're going to do + + + align:start position:0% +is a board question you're going to do +this on your own um you're on your own + + align:start position:0% +this on your own um you're on your own + + + align:start position:0% +this on your own um you're on your own +here so first you don't know anything + + align:start position:0% +here so first you don't know anything + + + align:start position:0% +here so first you don't know anything +about the die except that one of the + + align:start position:0% +about the die except that one of the + + + align:start position:0% +about the die except that one of the +five was chosen at random what's the + + align:start position:0% +five was chosen at random what's the + + + align:start position:0% +five was chosen at random what's the +probability that the first row will be a + + align:start position:0% +probability that the first row will be a + + + align:start position:0% +probability that the first row will be a +five now you've rolled that + + align:start position:0% +five now you've rolled that + + + align:start position:0% +five now you've rolled that +once and you're going to roll again and + + align:start position:0% +once and you're going to roll again and + + + align:start position:0% +once and you're going to roll again and +you can ask well now I've I've seen some + + align:start position:0% +you can ask well now I've I've seen some + + + align:start position:0% +you can ask well now I've I've seen some +data I have some information about which + + align:start position:0% +data I have some information about which + + + align:start position:0% +data I have some information about which +die was + + align:start position:0% +die was + + + align:start position:0% +die was +chosen what's the probability that I'll + + align:start position:0% +chosen what's the probability that I'll + + + align:start position:0% +chosen what's the probability that I'll +see a four on the next die so that + + align:start position:0% +see a four on the next die so that + + + align:start position:0% +see a four on the next die so that +that's your job to to find that for this + + align:start position:0% +that's your job to to find that for this + + + align:start position:0% +that's your job to to find that for this +problem + + align:start position:0% + + + + align:start position:0% + +four cool all right so this is your + + align:start position:0% +four cool all right so this is your + + + align:start position:0% +four cool all right so this is your +first answer right and then now multiply + + align:start position:0% +first answer right and then now multiply + + + align:start position:0% +first answer right and then now multiply +and + + align:start position:0% +and + + + align:start position:0% +and +cross get + + align:start position:0% +cross get + + + align:start position:0% +cross get +zero + + align:start position:0% +zero + + + align:start position:0% +zero +um + + align:start position:0% + + + + align:start position:0% + +180 and + + align:start position:0% +180 and + + + align:start position:0% +180 and +then add those + + align:start position:0% +then add those + + + align:start position:0% +then add those +up yeah get out your + + align:start position:0% +up yeah get out your + + + align:start position:0% +up yeah get out your +calculator what are you dividing by the + + align:start position:0% +calculator what are you dividing by the + + + align:start position:0% +calculator what are you dividing by the +normalize this I don't know that's right + + align:start position:0% +normalize this I don't know that's right + + + align:start position:0% +normalize this I don't know that's right +that's so this this is this is when you + + align:start position:0% +that's so this this is this is when you + + + align:start position:0% +that's so this this is this is when you +add these up exactly the probability of + + align:start position:0% +add these up exactly the probability of + + + align:start position:0% +add these up exactly the probability of +the five right so now if you want to + + align:start position:0% +the five right so now if you want to + + + align:start position:0% +the five right so now if you want to +repeat this process you need to use your + + align:start position:0% +repeat this process you need to use your + + + align:start position:0% +repeat this process you need to use your +normalized posterior instead of the + + align:start position:0% +normalized posterior instead of the + + + align:start position:0% +normalized posterior instead of the +original prior yeah + + align:start position:0% +original prior yeah + + + align:start position:0% +original prior yeah +great now you just need to do + + align:start position:0% +great now you just need to do + + + align:start position:0% +great now you just need to do +division that I can't help you + + align:start position:0% +division that I can't help you + + + align:start position:0% +division that I can't help you +with + + align:start position:0% +with + + + align:start position:0% +with +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +calculator division skills either + + align:start position:0% +calculator division skills either + + + align:start position:0% +calculator division skills either +way 3000 + + align:start position:0% + + + + align:start position:0% + +dividing all those by + + align:start position:0% + + + + align:start position:0% + +that 3 + + align:start position:0% + + + + align:start position:0% + +18 now is this the probability of four + + align:start position:0% +18 now is this the probability of four + + + align:start position:0% +18 now is this the probability of four +or the probability of four given five + + align:start position:0% +or the probability of four given five + + + align:start position:0% +or the probability of four given five +that's + + align:start position:0% +that's + + + align:start position:0% +that's +right so let's see so tell me what you + + align:start position:0% +right so let's see so tell me what you + + + align:start position:0% +right so let's see so tell me what you +did to get + + align:start position:0% +did to get + + + align:start position:0% +did to get +these so um this + + align:start position:0% +these so um this + + + align:start position:0% +these so um this +hypothesis which we and Su it up to get + + align:start position:0% +hypothesis which we and Su it up to get + + + align:start position:0% +hypothesis which we and Su it up to get +theal probility of getting a five and + + align:start position:0% +theal probility of getting a five and + + + align:start position:0% +theal probility of getting a five and +then and took + + align:start position:0% +then and took + + + align:start position:0% +then and took +the same likelihood + + align:start position:0% + + + + align:start position:0% + +great perfect now you said just just for + + align:start position:0% +great perfect now you said just just for + + + align:start position:0% +great perfect now you said just just for +the heck of it you normalized it but + + align:start position:0% +the heck of it you normalized it but + + + align:start position:0% +the heck of it you normalized it but +it's actually really important that you + + align:start position:0% +it's actually really important that you + + + align:start position:0% +it's actually really important that you +normalize it because if you're going to + + align:start position:0% +normalize it because if you're going to + + + align:start position:0% +normalize it because if you're going to +use the law of total probability again + + align:start position:0% +use the law of total probability again + + + align:start position:0% +use the law of total probability again +right you got to be working with a + + align:start position:0% +right you got to be working with a + + + align:start position:0% +right you got to be working with a +probability Mass function something that + + align:start position:0% +probability Mass function something that + + + align:start position:0% +probability Mass function something that +adds to one here if you didn't normalize + + align:start position:0% +adds to one here if you didn't normalize + + + align:start position:0% +adds to one here if you didn't normalize +then your final answer get multiplied by + + align:start position:0% +then your final answer get multiplied by + + + align:start position:0% +then your final answer get multiplied by +something right whatever that + + align:start position:0% +something right whatever that + + + align:start position:0% +something right whatever that +normalization constant what or it's + + align:start position:0% +normalization constant what or it's + + + align:start position:0% +normalization constant what or it's +reciprocal perfect + + align:start position:0% + + + + align:start position:0% + +okay check these guys + + align:start position:0% + + + + align:start position:0% + +out and this right here is not a pro + + align:start position:0% +out and this right here is not a pro + + + align:start position:0% +out and this right here is not a pro +this right here is not a probability + + align:start position:0% +this right here is not a probability + + + align:start position:0% +this right here is not a probability +because it's unnormalized so what should + + align:start position:0% +because it's unnormalized so what should + + + align:start position:0% +because it's unnormalized so what should +you normalize this by + + align:start position:0% +you normalize this by + + + align:start position:0% +you normalize this by +yeah yeah in other words if you made a + + align:start position:0% +yeah yeah in other words if you made a + + + align:start position:0% +yeah yeah in other words if you made a +normalized probability here it would be + + align:start position:0% +normalized probability here it would be + + + align:start position:0% +normalized probability here it would be +this divided by that this divided by + + align:start position:0% +this divided by that this divided by + + + align:start position:0% +this divided by that this divided by +that so all we have to do is divide this + + align:start position:0% +that so all we have to do is divide this + + + align:start position:0% +that so all we have to do is divide this +exactly right exactly + + align:start position:0% + + + + align:start position:0% + +right how's it going it's going fine + + align:start position:0% +right how's it going it's going fine + + + align:start position:0% +right how's it going it's going fine +so we're saying + + align:start position:0% +so we're saying + + + align:start position:0% +so we're saying +like the that's + + align:start position:0% + + + + align:start position:0% + +okay I know on the board it + + align:start position:0% + + + + align:start position:0% + +say8 that's really + + align:start position:0% +say8 that's really + + + align:start position:0% +say8 that's really +small I don't know what it + + align:start position:0% +small I don't know what it + + + align:start position:0% +small I don't know what it +is we didn't do it so what what did you + + align:start position:0% +is we didn't do it so what what did you + + + align:start position:0% +is we didn't do it so what what did you +get for this how did you find it so you + + align:start position:0% +get for this how did you find it so you + + + align:start position:0% +get for this how did you find it so you +summed up this this right yeah great and + + align:start position:0% +summed up this this right yeah great and + + + align:start position:0% +summed up this this right yeah great and +then what did you what did you do next + + align:start position:0% +then what did you what did you do next + + + align:start position:0% +then what did you what did you do next +same four so star from scratch started + + align:start position:0% +same four so star from scratch started + + + align:start position:0% +same four so star from scratch started +from scratch if you roll a four okay so + + align:start position:0% +from scratch if you roll a four okay so + + + align:start position:0% +from scratch if you roll a four okay so +how does that + + align:start position:0% +how does that + + + align:start position:0% +how does that +incorporate the fact that you first + + align:start position:0% +incorporate the fact that you first + + + align:start position:0% +incorporate the fact that you first +rolled a five so we're trying to go back + + align:start position:0% +rolled a five so we're trying to go back + + + align:start position:0% +rolled a five so we're trying to go back +to the original base but that didn't + + align:start position:0% +to the original base but that didn't + + + align:start position:0% +to the original base but that didn't +work out so well because we don't know + + align:start position:0% +work out so well because we don't know + + + align:start position:0% +work out so well because we don't know +how to calculate this exactly all right + + align:start position:0% +how to calculate this exactly all right + + + align:start position:0% +how to calculate this exactly all right +so this is no easier than that okay so + + align:start position:0% +so this is no easier than that okay so + + + align:start position:0% +so this is no easier than that okay so +here's so here's the idea here's the + + align:start position:0% +here's so here's the idea here's the + + + align:start position:0% +here's so here's the idea here's the +idea before so you start with this + + align:start position:0% +idea before so you start with this + + + align:start position:0% +idea before so you start with this +belief right and and you have your + + align:start position:0% +belief right and and you have your + + + align:start position:0% +belief right and and you have your +likelihood you multiply them total + + align:start position:0% +likelihood you multiply them total + + + align:start position:0% +likelihood you multiply them total +probability you get the probability of + + align:start position:0% +probability you get the probability of + + + align:start position:0% +probability you get the probability of +rolling a five right now at that point + + align:start position:0% +rolling a five right now at that point + + + align:start position:0% +rolling a five right now at that point +that after you've rolled this five your + + align:start position:0% +that after you've rolled this five your + + + align:start position:0% +that after you've rolled this five your +beliefs have changed based on that about + + align:start position:0% +beliefs have changed based on that about + + + align:start position:0% +beliefs have changed based on that about +the probability that you have each of + + align:start position:0% +the probability that you have each of + + + align:start position:0% +the probability that you have each of +the five dice so if you take that and + + align:start position:0% +the five dice so if you take that and + + + align:start position:0% +the five dice so if you take that and +you use that as your prior here then the + + align:start position:0% +you use that as your prior here then the + + + align:start position:0% +you use that as your prior here then the +likelihood multiply and sum there we go + + align:start position:0% +likelihood multiply and sum there we go + + + align:start position:0% +likelihood multiply and sum there we go +that should give + + align:start position:0% +that should give + + + align:start position:0% +that should give +you I like that okay okay oh but now we + + align:start position:0% +you I like that okay okay oh but now we + + + align:start position:0% +you I like that okay okay oh but now we +have oh decimals okay that's okay now + + align:start position:0% +have oh decimals okay that's okay now + + + align:start position:0% +have oh decimals okay that's okay now +you have decimals I can't you know make + + align:start position:0% +you have decimals I can't you know make + + + align:start position:0% +you have decimals I can't you know make +your life too easy + + align:start position:0% +your life too easy + + + align:start position:0% +your life too easy +[Music] + + align:start position:0% + + + + align:start position:0% + +no we use these + + align:start position:0% +no we use these + + + align:start position:0% +no we use these +numers right so you multiply this this + + align:start position:0% +numers right so you multiply this this + + + align:start position:0% +numers right so you multiply this this +number by this this number by this so in + + align:start position:0% +number by this this number by this so in + + + align:start position:0% +number by this this number by this so in +the end you'll get all of these numbers + + align:start position:0% +the end you'll get all of these numbers + + + align:start position:0% +the end you'll get all of these numbers +except they're all multiplied divided by + + align:start position:0% +except they're all multiplied divided by + + + align:start position:0% +except they're all multiplied divided by +so you should divide this by to get a + + align:start position:0% +so you should divide this by to get a + + + align:start position:0% +so you should divide this by to get a +probability okay that make sense yeah um + + align:start position:0% +probability okay that make sense yeah um + + + align:start position:0% +probability okay that make sense yeah um +so you have to be careful + + align:start position:0% +so you have to be careful + + + align:start position:0% +so you have to be careful +for figuring out probabilities of + + align:start position:0% +for figuring out probabilities of + + + align:start position:0% +for figuring out probabilities of +hypotheses we could not we could avoid + + align:start position:0% +hypotheses we could not we could avoid + + + align:start position:0% +hypotheses we could not we could avoid +using the unnormalized we could use the + + align:start position:0% +using the unnormalized we could use the + + + align:start position:0% +using the unnormalized we could use the +we didn't have to keep normalizing but + + align:start position:0% +we didn't have to keep normalizing but + + + align:start position:0% +we didn't have to keep normalizing but +when you want to do posterior prediction + + align:start position:0% +when you want to do posterior prediction + + + align:start position:0% +when you want to do posterior prediction +you want real probabilities of data okay + + align:start position:0% +you want real probabilities of data okay + + + align:start position:0% +you want real probabilities of data okay +so you have to you're going to have to + + align:start position:0% +so you have to you're going to have to + + + align:start position:0% +so you have to you're going to have to +normalize these numbers at some point + + align:start position:0% +normalize these numbers at some point + + + align:start position:0% +normalize these numbers at some point +either first or or at the end okay it's + + align:start position:0% +either first or or at the end okay it's + + + align:start position:0% +either first or or at the end okay it's +probably if you're going to do it a lot + + align:start position:0% +probably if you're going to do it a lot + + + align:start position:0% +probably if you're going to do it a lot +easier just to keep doing it + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay r + + align:start position:0% +okay r + + + align:start position:0% +okay r +so this one is + + align:start position:0% + + + + align:start position:0% + +not how we doing um I'm you tell + + align:start position:0% + + + + align:start position:0% + +me it's a beautiful use of + + align:start position:0% + + + + align:start position:0% + +colority we set thatal + + align:start position:0% +colority we set thatal + + + align:start position:0% +colority we set thatal +to and + + align:start position:0% +to and + + + align:start position:0% +to and +then uh so is this is this normalized or + + align:start position:0% +then uh so is this is this normalized or + + + align:start position:0% +then uh so is this is this normalized or +not normalized normalized good because + + align:start position:0% +not normalized normalized good because + + + align:start position:0% +not normalized normalized good because +you want real probabilities there yes + + align:start position:0% +you want real probabilities there yes + + + align:start position:0% +you want real probabilities there yes +thank you + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah and now you're gonna sum them + + align:start position:0% +yeah and now you're gonna sum them + + + align:start position:0% +yeah and now you're gonna sum them +up that's + + align:start position:0% +up that's + + + align:start position:0% +up that's +perfect because the law of total + + align:start position:0% +perfect because the law of total + + + align:start position:0% +perfect because the law of total +probability says multiply this by this + + align:start position:0% +probability says multiply this by this + + + align:start position:0% +probability says multiply this by this +that's just what you did with the trees + + align:start position:0% +that's just what you did with the trees + + + align:start position:0% +that's just what you did with the trees +do you see it in the trees when I wave + + align:start position:0% +do you see it in the trees when I wave + + + align:start position:0% +do you see it in the trees when I wave +my hands + + align:start position:0% + + + + align:start position:0% + +new + + align:start position:0% + + + + align:start position:0% + +prior that's good you're adding them + + align:start position:0% +prior that's good you're adding them + + + align:start position:0% +prior that's good you're adding them +up still a okay so that looks + + align:start position:0% + + + + align:start position:0% + +right so let's think how does this + + align:start position:0% +right so let's think how does this + + + align:start position:0% +right so let's think how does this +number compare to what you would have if + + align:start position:0% +number compare to what you would have if + + + align:start position:0% +number compare to what you would have if +you didn't know this other information + + align:start position:0% +you didn't know this other information + + + align:start position:0% +you didn't know this other information +so suppose you knew nothing going + + align:start position:0% +so suppose you knew nothing going + + + align:start position:0% +so suppose you knew nothing going +in do you think + + align:start position:0% +in do you think + + + align:start position:0% +in do you think +that the fact that you rolled a five the + + align:start position:0% +that the fact that you rolled a five the + + + align:start position:0% +that the fact that you rolled a five the +first time makes it more or less likely + + align:start position:0% +first time makes it more or less likely + + + align:start position:0% +first time makes it more or less likely +that you roll a four actually less + + align:start position:0% +that you roll a four actually less + + + align:start position:0% +that you roll a four actually less +likely is it less likely because you get + + align:start position:0% +likely is it less likely because you get + + + align:start position:0% +likely is it less likely because you get +rid of the four the die that has only + + align:start position:0% +rid of the four the die that has only + + + align:start position:0% +rid of the four the die that has only +four sides so it might make it go down + + align:start position:0% +four sides so it might make it go down + + + align:start position:0% +four sides so it might make it go down +right on the other hand you're going to + + align:start position:0% +right on the other hand you're going to + + + align:start position:0% +right on the other hand you're going to +give more probability to the six-sided + + align:start position:0% +give more probability to the six-sided + + + align:start position:0% +give more probability to the six-sided +let's say than it had originally so they + + align:start position:0% +let's say than it had originally so they + + + align:start position:0% +let's say than it had originally so they +sort of competing forces so I'm not I'm + + align:start position:0% +sort of competing forces so I'm not I'm + + + align:start position:0% +sort of competing forces so I'm not I'm +actually not sure I'm not actually sure + + align:start position:0% +actually not sure I'm not actually sure + + + align:start position:0% +actually not sure I'm not actually sure +which is the right answer but anyway + + align:start position:0% +which is the right answer but anyway + + + align:start position:0% +which is the right answer but anyway +something you can easily + + align:start position:0% + + + + align:start position:0% + +check yeah yeah this is a standard day + + align:start position:0% +check yeah yeah this is a standard day + + + align:start position:0% +check yeah yeah this is a standard day +we always finish ahead of time + + align:start position:0% +we always finish ahead of time + + + align:start position:0% +we always finish ahead of time +um all right oh I don't need that right + + align:start position:0% +um all right oh I don't need that right + + + align:start position:0% +um all right oh I don't need that right +here + + align:start position:0% + + + + align:start position:0% + +um okay like like with all the other + + align:start position:0% +um okay like like with all the other + + + align:start position:0% +um okay like like with all the other +answers today it's it we'll use the the + + align:start position:0% +answers today it's it we'll use the the + + + align:start position:0% +answers today it's it we'll use the the +screens + + align:start position:0% +screens + + + align:start position:0% +screens +to show the + + align:start position:0% + + + + align:start position:0% + +table so when we go through it we do the + + align:start position:0% +table so when we go through it we do the + + + align:start position:0% +table so when we go through it we do the +usual thing we did before we started + + align:start position:0% +usual thing we did before we started + + + align:start position:0% +usual thing we did before we started +with a five so we'll + + align:start position:0% +with a five so we'll + + + align:start position:0% +with a five so we'll +update our probabilities of the + + align:start position:0% +update our probabilities of the + + + align:start position:0% +update our probabilities of the +hypothesis based on that five so that's + + align:start position:0% +hypothesis based on that five so that's + + + align:start position:0% +hypothesis based on that five so that's +the the First Column is the prior then + + align:start position:0% +the the First Column is the prior then + + + align:start position:0% +the the First Column is the prior then +the likelihood of getting a + + align:start position:0% +the likelihood of getting a + + + align:start position:0% +the likelihood of getting a +five uh which is zero if you have the + + align:start position:0% +five uh which is zero if you have the + + + align:start position:0% +five uh which is zero if you have the +foursided die 1 16 1/8 112th and 12th we + + align:start position:0% +foursided die 1 16 1/8 112th and 12th we + + + align:start position:0% +foursided die 1 16 1/8 112th and 12th we +get our unnormalized posterior and then + + align:start position:0% +get our unnormalized posterior and then + + + align:start position:0% +get our unnormalized posterior and then +in this table I actually got the + + align:start position:0% +in this table I actually got the + + + align:start position:0% +in this table I actually got the +normalized posterior because when you're + + align:start position:0% +normalized posterior because when you're + + + align:start position:0% +normalized posterior because when you're +Computing predictive probabilities you + + align:start position:0% +Computing predictive probabilities you + + + align:start position:0% +Computing predictive probabilities you +need use normalized probabilities they + + align:start position:0% +need use normalized probabilities they + + + align:start position:0% +need use normalized probabilities they +should be true probabilities uh so we us + + align:start position:0% +should be true probabilities uh so we us + + + align:start position:0% +should be true probabilities uh so we us +this column here of the posterior + + align:start position:0% +this column here of the posterior + + + align:start position:0% +this column here of the posterior +probability there's different orders you + + align:start position:0% +probability there's different orders you + + + align:start position:0% +probability there's different orders you +could do this calculation I think this + + align:start position:0% +could do this calculation I think this + + + align:start position:0% +could do this calculation I think this +is one of the straightforward + + align:start position:0% +is one of the straightforward + + + align:start position:0% +is one of the straightforward +ones then we look at the + + align:start position:0% + + + + align:start position:0% + +likelihood of the of D2 in the next + + align:start position:0% +likelihood of the of D2 in the next + + + align:start position:0% +likelihood of the of D2 in the next +column now I put a star for H4 because + + align:start position:0% +column now I put a star for H4 because + + + align:start position:0% +column now I put a star for H4 because +there's no way you could + + align:start position:0% +there's no way you could + + + align:start position:0% +there's no way you could +get a probability there + + align:start position:0% +get a probability there + + + align:start position:0% +get a probability there +if you have D1 and D2 if I had left off + + align:start position:0% +if you have D1 and D2 if I had left off + + + align:start position:0% +if you have D1 and D2 if I had left off +the D1 which most people did and which + + align:start position:0% +the D1 which most people did and which + + + align:start position:0% +the D1 which most people did and which +is okay because of the independence John + + align:start position:0% +is okay because of the independence John + + + align:start position:0% +is okay because of the independence John +talked about given the hypothesis the + + align:start position:0% +talked about given the hypothesis the + + + align:start position:0% +talked about given the hypothesis the +roles are independent I would have had a + + align:start position:0% +roles are independent I would have had a + + + align:start position:0% +roles are independent I would have had a +1/4 where I have the star but I'm going + + align:start position:0% +1/4 where I have the star but I'm going + + + align:start position:0% +1/4 where I have the star but I'm going +to multiply it by zero + + align:start position:0% +to multiply it by zero + + + align:start position:0% +to multiply it by zero +anyway so who cares so I have my new + + align:start position:0% +anyway so who cares so I have my new + + + align:start position:0% +anyway so who cares so I have my new +priors I mean excuse me my new + + align:start position:0% +priors I mean excuse me my new + + + align:start position:0% +priors I mean excuse me my new +likelihoods for the second bit of data + + align:start position:0% +likelihoods for the second bit of data + + + align:start position:0% +likelihoods for the second bit of data +which are the same as the old ones 1 16 + + align:start position:0% +which are the same as the old ones 1 16 + + + align:start position:0% +which are the same as the old ones 1 16 +1/ 18 112th 20th now my total + + align:start position:0% +1/ 18 112th 20th now my total + + + align:start position:0% +1/ 18 112th 20th now my total +probability is done the same way you + + align:start position:0% +probability is done the same way you + + + align:start position:0% +probability is done the same way you +multiply in this new language posterior + + align:start position:0% +multiply in this new language posterior + + + align:start position:0% +multiply in this new language posterior +one which is your prior for likelihood 2 + + align:start position:0% +one which is your prior for likelihood 2 + + + align:start position:0% +one which is your prior for likelihood 2 +times likelihood 2 and sum them up and I + + align:start position:0% +times likelihood 2 and sum them up and I + + + align:start position:0% +times likelihood 2 and sum them up and I +get this last + + align:start position:0% + + + + align:start position:0% + +column so again once I have my new my + + align:start position:0% +column so again once I have my new my + + + align:start position:0% +column so again once I have my new my +posterior for the first bit of data I + + align:start position:0% +posterior for the first bit of data I + + + align:start position:0% +posterior for the first bit of data I +can use that in the law of total + + align:start position:0% +can use that in the law of total + + + align:start position:0% +can use that in the law of total +probability to make a prediction so + + align:start position:0% +probability to make a prediction so + + + align:start position:0% +probability to make a prediction so +what's happened right here what's become + + align:start position:0% +what's happened right here what's become + + + align:start position:0% +what's happened right here what's become +more likely well what + + align:start position:0% + + + + align:start position:0% + +what's this + + align:start position:0% +what's this + + + align:start position:0% +what's this +.124 seems a little bit uh larger than I + + align:start position:0% +.124 seems a little bit uh larger than I + + + align:start position:0% +.124 seems a little bit uh larger than I +would have guessed ahead of + + align:start position:0% + + + + align:start position:0% + +time what's happened with rolling a five + + align:start position:0% +time what's happened with rolling a five + + + align:start position:0% +time what's happened with rolling a five +and then a four to make that a little + + align:start position:0% +and then a four to make that a little + + + align:start position:0% +and then a four to make that a little +bit + + align:start position:0% + + + + align:start position:0% + +bigger any idea + + align:start position:0% + + + + align:start position:0% + +when you roll a five first it increases + + align:start position:0% +when you roll a five first it increases + + + align:start position:0% +when you roll a five first it increases +the probability that it's one of the + + align:start position:0% +the probability that it's one of the + + + align:start position:0% +the probability that it's one of the +lower dies excellent um so then it makes + + align:start position:0% +lower dies excellent um so then it makes + + + align:start position:0% +lower dies excellent um so then it makes +it more likely that you'll get a four + + align:start position:0% +it more likely that you'll get a four + + + align:start position:0% +it more likely that you'll get a four +excellent that that's what I would think + + align:start position:0% +excellent that that's what I would think + + + align:start position:0% +excellent that that's what I would think +too that seeing a five and a four what' + + align:start position:0% +too that seeing a five and a four what' + + + align:start position:0% +too that seeing a five and a four what' +We Roll first a five makes the smaller + + align:start position:0% +We Roll first a five makes the smaller + + + align:start position:0% +We Roll first a five makes the smaller +die more likely if the smaller D is more + + align:start position:0% +die more likely if the smaller D is more + + + align:start position:0% +die more likely if the smaller D is more +likely then you're more likely to roll a + + align:start position:0% +likely then you're more likely to roll a + + + align:start position:0% +likely then you're more likely to roll a +four and a five for instance if I had + + align:start position:0% +four and a five for instance if I had + + + align:start position:0% +four and a five for instance if I had +the six-sided + + align:start position:0% +the six-sided + + + align:start position:0% +the six-sided +die what's the probability I'd roll a + + align:start position:0% +die what's the probability I'd roll a + + + align:start position:0% +die what's the probability I'd roll a +four and a five with the six-sided + + align:start position:0% + + + + align:start position:0% + +die 1 and 36 which is about 3% so this + + align:start position:0% +die 1 and 36 which is about 3% so this + + + align:start position:0% +die 1 and 36 which is about 3% so this +doesn't get up to 3% but it's a little + + align:start position:0% +doesn't get up to 3% but it's a little + + + align:start position:0% +doesn't get up to 3% but it's a little +bigger than if I had the 20-sided die + + align:start position:0% +bigger than if I had the 20-sided die + + + align:start position:0% +bigger than if I had the 20-sided die +where it would be what's + + align:start position:0% +where it would be what's + + + align:start position:0% +where it would be what's +1/400th very small small John says it's + + align:start position:0% +1/400th very small small John says it's + + + align:start position:0% +1/400th very small small John says it's +small so this is one argument you can + + align:start position:0% +small so this is one argument you can + + + align:start position:0% +small so this is one argument you can +make right that roll the the five makes + + align:start position:0% +make right that roll the the five makes + + + align:start position:0% +make right that roll the the five makes +it likely that it's a smaller die uh and + + align:start position:0% +it likely that it's a smaller die uh and + + + align:start position:0% +it likely that it's a smaller die uh and +therefore more likely to roll a four + + align:start position:0% +therefore more likely to roll a four + + + align:start position:0% +therefore more likely to roll a four +next but is there another argument you + + align:start position:0% +next but is there another argument you + + + align:start position:0% +next but is there another argument you +could make for why maybe rolling the + + align:start position:0% +could make for why maybe rolling the + + + align:start position:0% +could make for why maybe rolling the +five would have the opposite effect it + + align:start position:0% +five would have the opposite effect it + + + align:start position:0% +five would have the opposite effect it +might make it less likely to roll a four + + align:start position:0% +might make it less likely to roll a four + + + align:start position:0% +might make it less likely to roll a four +next my initial thought was you roll a + + align:start position:0% +next my initial thought was you roll a + + + align:start position:0% +next my initial thought was you roll a +five you know it's not the foursided die + + align:start position:0% +five you know it's not the foursided die + + + align:start position:0% +five you know it's not the foursided die +and that's your die that you're least or + + align:start position:0% +and that's your die that you're least or + + + align:start position:0% +and that's your die that you're least or +that you're most likely to roll forward + + align:start position:0% +that you're most likely to roll forward + + + align:start position:0% +that you're most likely to roll forward +that's right so I'm not as sure as you + + align:start position:0% +that's right so I'm not as sure as you + + + align:start position:0% +that's right so I'm not as sure as you +as to whether this goes up or down I + + align:start position:0% +as to whether this goes up or down I + + + align:start position:0% +as to whether this goes up or down I +think there are two competing arguments + + align:start position:0% +think there are two competing arguments + + + align:start position:0% +think there are two competing arguments +that on the one hand it makes it more + + align:start position:0% +that on the one hand it makes it more + + + align:start position:0% +that on the one hand it makes it more +likely it's a six or eight sided but it + + align:start position:0% +likely it's a six or eight sided but it + + + align:start position:0% +likely it's a six or eight sided but it +also makes it completely impossible that + + align:start position:0% +also makes it completely impossible that + + + align:start position:0% +also makes it completely impossible that +it's a forid give you three to one odds + + align:start position:0% +it's a forid give you three to one odds + + + align:start position:0% +it's a forid give you three to one odds +that it goes up oh + + align:start position:0% +that it goes up oh + + + align:start position:0% +that it goes up oh +crap so what he doesn't know is whether + + align:start position:0% +crap so what he doesn't know is whether + + + align:start position:0% +crap so what he doesn't know is whether +I've computed it already or not he + + align:start position:0% +I've computed it already or not he + + + align:start position:0% +I've computed it already or not he +probably + + align:start position:0% +probably + + + align:start position:0% +probably +has but he probably did it at like 3:00 + + align:start position:0% +has but he probably did it at like 3:00 + + + align:start position:0% +has but he probably did it at like 3:00 +a.m. so I don't trust it I simulated it + + align:start position:0% +a.m. so I don't trust it I simulated it + + + align:start position:0% +a.m. so I don't trust it I simulated it +in R I + + align:start position:0% +in R I + + + align:start position:0% +in R I +see right are there any questions that's + + align:start position:0% +see right are there any questions that's + + + align:start position:0% +see right are there any questions that's +uh that's what we have for today so are + + align:start position:0% +uh that's what we have for today so are + + + align:start position:0% +uh that's what we have for today so are +there any question questions about Basi + + align:start position:0% +there any question questions about Basi + + + align:start position:0% +there any question questions about Basi +and updating or doing these + + align:start position:0% + + + + align:start position:0% + +computations all right great \ No newline at end of file diff --git a/EDGRxqnILUM.txt b/EDGRxqnILUM.txt new file mode 100644 index 0000000000000000000000000000000000000000..43e0dd5def1b20de2a41f969a815e9cb0f828ec8 --- /dev/null +++ b/EDGRxqnILUM.txt @@ -0,0 +1,9419 @@ +align:start position:0% + +um today we're g to continue our sort of + + align:start position:0% +um today we're g to continue our sort of + + + align:start position:0% +um today we're g to continue our sort of +application we learned so far and today + + align:start position:0% +application we learned so far and today + + + align:start position:0% +application we learned so far and today +we are going to really dive in and sort + + align:start position:0% +we are going to really dive in and sort + + + align:start position:0% +we are going to really dive in and sort +of in some sense what we could sort of + + align:start position:0% +of in some sense what we could sort of + + + align:start position:0% +of in some sense what we could sort of +consider consider the mother of all + + align:start position:0% +consider consider the mother of all + + + align:start position:0% +consider consider the mother of all +market failures which is externalities + + align:start position:0% +market failures which is externalities + + + align:start position:0% +market failures which is externalities +the classic the single most classic + + align:start position:0% +the classic the single most classic + + + align:start position:0% +the classic the single most classic +example that economists use when they + + align:start position:0% +example that economists use when they + + + align:start position:0% +example that economists use when they +talk about market failure is + + align:start position:0% + + + + align:start position:0% + +externalities and today we're going to + + align:start position:0% +externalities and today we're going to + + + align:start position:0% +externalities and today we're going to +talk about + + align:start position:0% +talk about + + + align:start position:0% +talk about +externalities uh what they are why they + + align:start position:0% +externalities uh what they are why they + + + align:start position:0% +externalities uh what they are why they +represent market failures and what + + align:start position:0% +represent market failures and what + + + align:start position:0% +represent market failures and what +governments can do about + + align:start position:0% +governments can do about + + + align:start position:0% +governments can do about +them so an externality + + align:start position:0% +them so an externality + + + align:start position:0% +them so an externality +exists whenever the actions of one party + + align:start position:0% +exists whenever the actions of one party + + + align:start position:0% +exists whenever the actions of one party +make another party better or worse + + align:start position:0% +make another party better or worse + + + align:start position:0% +make another party better or worse +off but the first party doesn't get the + + align:start position:0% +off but the first party doesn't get the + + + align:start position:0% +off but the first party doesn't get the +benefits or consequence of doing so + + align:start position:0% +benefits or consequence of doing so + + + align:start position:0% +benefits or consequence of doing so +soever my actions make you better or + + align:start position:0% +soever my actions make you better or + + + align:start position:0% +soever my actions make you better or +worse but none of the benefits of making + + align:start position:0% +worse but none of the benefits of making + + + align:start position:0% +worse but none of the benefits of making +you better or the cost of making you + + align:start position:0% +you better or the cost of making you + + + align:start position:0% +you better or the cost of making you +worse accre to me + + align:start position:0% +worse accre to me + + + align:start position:0% +worse accre to me +individually in that context that's an + + align:start position:0% +individually in that context that's an + + + align:start position:0% +individually in that context that's an +externality okay and we will talk about + + align:start position:0% +externality okay and we will talk about + + + align:start position:0% +externality okay and we will talk about +why this C is a fundamental source of + + align:start position:0% +why this C is a fundamental source of + + + align:start position:0% +why this C is a fundamental source of +market failure and we're going to talk + + align:start position:0% +market failure and we're going to talk + + + align:start position:0% +market failure and we're going to talk +about four different types of + + align:start position:0% +about four different types of + + + align:start position:0% +about four different types of +externalities so we're going to start + + align:start position:0% +externalities so we're going to start + + + align:start position:0% +externalities so we're going to start +with the most classic case which is a + + align:start position:0% +with the most classic case which is a + + + align:start position:0% +with the most classic case which is a +negative + + align:start position:0% +negative + + + align:start position:0% +negative +production + + align:start position:0% +production + + + align:start position:0% +production +externality this is the most classic + + align:start position:0% +externality this is the most classic + + + align:start position:0% +externality this is the most classic +example of + + align:start position:0% +example of + + + align:start position:0% +example of +externalities okay so suppose that + + align:start position:0% +externalities okay so suppose that + + + align:start position:0% +externalities okay so suppose that +there's a a steel plant located on a + + align:start position:0% +there's a a steel plant located on a + + + align:start position:0% +there's a a steel plant located on a +river how many guys read The + + align:start position:0% +river how many guys read The + + + align:start position:0% +river how many guys read The +Lorax guys go excellent good job Dr + + align:start position:0% +Lorax guys go excellent good job Dr + + + align:start position:0% +Lorax guys go excellent good job Dr +Seuss greatest second greatest author of + + align:start position:0% +Seuss greatest second greatest author of + + + align:start position:0% +Seuss greatest second greatest author of +history behind Shakespeare is Dr Seuss + + align:start position:0% +history behind Shakespeare is Dr Seuss + + + align:start position:0% +history behind Shakespeare is Dr Seuss +okay so the lorax tells the story of + + align:start position:0% +okay so the lorax tells the story of + + + align:start position:0% +okay so the lorax tells the story of +this plant sort of dumping crap into the + + align:start position:0% +this plant sort of dumping crap into the + + + align:start position:0% +this plant sort of dumping crap into the +river well think about The Lorax think + + align:start position:0% +river well think about The Lorax think + + + align:start position:0% +river well think about The Lorax think +about a plant on a river a steel plant + + align:start position:0% +about a plant on a river a steel plant + + + align:start position:0% +about a plant on a river a steel plant +in a river dumping sludge into the river + + align:start position:0% +in a river dumping sludge into the river + + + align:start position:0% +in a river dumping sludge into the river +it's a natural byproduct of the steel + + align:start position:0% +it's a natural byproduct of the steel + + + align:start position:0% +it's a natural byproduct of the steel +they's not making sedes he's making + + align:start position:0% +they's not making sedes he's making + + + align:start position:0% +they's not making sedes he's making +steel natural bipart byproduct of the + + align:start position:0% +steel natural bipart byproduct of the + + + align:start position:0% +steel natural bipart byproduct of the +steel plant is uh this sludge and every + + align:start position:0% +steel plant is uh this sludge and every + + + align:start position:0% +steel plant is uh this sludge and every +unit of Steel that's made produces one + + align:start position:0% +unit of Steel that's made produces one + + + align:start position:0% +unit of Steel that's made produces one +unit of sludge that gets dumped by a + + align:start position:0% +unit of sludge that gets dumped by a + + + align:start position:0% +unit of sludge that gets dumped by a +pipe out the back into the river just + + align:start position:0% +pipe out the back into the river just + + + align:start position:0% +pipe out the back into the river just +like in The + + align:start position:0% +like in The + + + align:start position:0% +like in The +Lorax okay however the steel plant is + + align:start position:0% +Lorax okay however the steel plant is + + + align:start position:0% +Lorax okay however the steel plant is +not the only user of this River farther + + align:start position:0% +not the only user of this River farther + + + align:start position:0% +not the only user of this River farther +Downstream from the steel plant is a set + + align:start position:0% +Downstream from the steel plant is a set + + + align:start position:0% +Downstream from the steel plant is a set +of fishermen and they fish in this River + + align:start position:0% +of fishermen and they fish in this River + + + align:start position:0% +of fishermen and they fish in this River +and they make their living uh fishing in + + align:start position:0% +and they make their living uh fishing in + + + align:start position:0% +and they make their living uh fishing in +this River and it turns out that the + + align:start position:0% +this River and it turns out that the + + + align:start position:0% +this River and it turns out that the +sludge that the steel plant's dumping in + + align:start position:0% +sludge that the steel plant's dumping in + + + align:start position:0% +sludge that the steel plant's dumping in +is killing the fish and hurting the + + align:start position:0% +is killing the fish and hurting the + + + align:start position:0% +is killing the fish and hurting the +livelihood of the fisherman down the + + align:start position:0% +livelihood of the fisherman down the + + + align:start position:0% +livelihood of the fisherman down the +river now this is a classic negative + + align:start position:0% +river now this is a classic negative + + + align:start position:0% +river now this is a classic negative +production externality it's negative + + align:start position:0% +production externality it's negative + + + align:start position:0% +production externality it's negative +because my action as a steel plant + + align:start position:0% +because my action as a steel plant + + + align:start position:0% +because my action as a steel plant +affects another party which is the + + align:start position:0% +affects another party which is the + + + align:start position:0% +affects another party which is the +fisherman it's production because it's a + + align:start position:0% +fisherman it's production because it's a + + + align:start position:0% +fisherman it's production because it's a +byproduct of the production process + + align:start position:0% +byproduct of the production process + + + align:start position:0% +byproduct of the production process +we'll talk later about consumption + + align:start position:0% +we'll talk later about consumption + + + align:start position:0% +we'll talk later about consumption +externals you'll see the difference + + align:start position:0% +externals you'll see the difference + + + align:start position:0% +externals you'll see the difference +um and so this is a classic negative + + align:start position:0% +um and so this is a classic negative + + + align:start position:0% +um and so this is a classic negative +production externality and the way we + + align:start position:0% +production externality and the way we + + + align:start position:0% +production externality and the way we +Analyze That is shown in figure + + align:start position:0% +Analyze That is shown in figure + + + align:start position:0% +Analyze That is shown in figure +241 once again from my textbook okay we + + align:start position:0% +241 once again from my textbook okay we + + + align:start position:0% +241 once again from my textbook okay we +think about the market for steel the + + align:start position:0% +think about the market for steel the + + + align:start position:0% +think about the market for steel the +market Standard Market diagram you got + + align:start position:0% +market Standard Market diagram you got + + + align:start position:0% +market Standard Market diagram you got +the quantity of Steel on the xaxis + + align:start position:0% +the quantity of Steel on the xaxis + + + align:start position:0% +the quantity of Steel on the xaxis +you've got the price of steel on the Y + + align:start position:0% +you've got the price of steel on the Y + + + align:start position:0% +you've got the price of steel on the Y +AIS you've got um uh a demand for steel + + align:start position:0% +AIS you've got um uh a demand for steel + + + align:start position:0% +AIS you've got um uh a demand for steel +which is the blue downward sloping line + + align:start position:0% +which is the blue downward sloping line + + + align:start position:0% +which is the blue downward sloping line +and supply of + + align:start position:0% +and supply of + + + align:start position:0% +and supply of +Steel now the key distinction we're + + align:start position:0% +Steel now the key distinction we're + + + align:start position:0% +Steel now the key distinction we're +going to make here that we haven't drawn + + align:start position:0% +going to make here that we haven't drawn + + + align:start position:0% +going to make here that we haven't drawn +before is when we've talked about what + + align:start position:0% +before is when we've talked about what + + + align:start position:0% +before is when we've talked about what +demand and Supply represent we've talked + + align:start position:0% +demand and Supply represent we've talked + + + align:start position:0% +demand and Supply represent we've talked +about them as private Concepts the + + align:start position:0% +about them as private Concepts the + + + align:start position:0% +about them as private Concepts the +domain curve is individual's willingness + + align:start position:0% +domain curve is individual's willingness + + + align:start position:0% +domain curve is individual's willingness +to + + align:start position:0% +to + + + align:start position:0% +to +pay the supply curve is an individual's + + align:start position:0% +pay the supply curve is an individual's + + + align:start position:0% +pay the supply curve is an individual's +firm's willingness to + + align:start position:0% +firm's willingness to + + + align:start position:0% +firm's willingness to +supply but implicit in that and implicit + + align:start position:0% +supply but implicit in that and implicit + + + align:start position:0% +supply but implicit in that and implicit +in the welfare analysis would be way + + align:start position:0% +in the welfare analysis would be way + + + align:start position:0% +in the welfare analysis would be way +back in lecture 12 is the notion they + + align:start position:0% +back in lecture 12 is the notion they + + + align:start position:0% +back in lecture 12 is the notion they +also represent social curves implicit in + + align:start position:0% +also represent social curves implicit in + + + align:start position:0% +also represent social curves implicit in +all the analysis we've done is the + + align:start position:0% +all the analysis we've done is the + + + align:start position:0% +all the analysis we've done is the +assumption that the aggregation of + + align:start position:0% +assumption that the aggregation of + + + align:start position:0% +assumption that the aggregation of +individuals represents society and + + align:start position:0% +individuals represents society and + + + align:start position:0% +individuals represents society and +therefore what's best for individuals is + + align:start position:0% +therefore what's best for individuals is + + + align:start position:0% +therefore what's best for individuals is +best for society so implicit what we've + + align:start position:0% +best for society so implicit what we've + + + align:start position:0% +best for society so implicit what we've +done is that private benefits equal + + align:start position:0% +done is that private benefits equal + + + align:start position:0% +done is that private benefits equal +social benefits so the domain curve for + + align:start position:0% +social benefits so the domain curve for + + + align:start position:0% +social benefits so the domain curve for +example the slope of the domain curve is + + align:start position:0% +example the slope of the domain curve is + + + align:start position:0% +example the slope of the domain curve is +the private marginal benefit of another + + align:start position:0% +the private marginal benefit of another + + + align:start position:0% +the private marginal benefit of another +unit of Steel it's also the social + + align:start position:0% +unit of Steel it's also the social + + + align:start position:0% +unit of Steel it's also the social +marginal benefit now we haven't raised + + align:start position:0% +marginal benefit now we haven't raised + + + align:start position:0% +marginal benefit now we haven't raised +this before because it didn't matter + + align:start position:0% +this before because it didn't matter + + + align:start position:0% +this before because it didn't matter +before but today it will likewise the + + align:start position:0% +before but today it will likewise the + + + align:start position:0% +before but today it will likewise the +supply curve is the private marginal + + align:start position:0% +supply curve is the private marginal + + + align:start position:0% +supply curve is the private marginal +cost a producing number unit of Steel we + + align:start position:0% +cost a producing number unit of Steel we + + + align:start position:0% +cost a producing number unit of Steel we +just called it marginal cost we didn't + + align:start position:0% +just called it marginal cost we didn't + + + align:start position:0% +just called it marginal cost we didn't +call it private but that's what it is + + align:start position:0% +call it private but that's what it is + + + align:start position:0% +call it private but that's what it is +and we also represent that as a social + + align:start position:0% +and we also represent that as a social + + + align:start position:0% +and we also represent that as a social +marginal cost of producing steel it's + + align:start position:0% +marginal cost of producing steel it's + + + align:start position:0% +marginal cost of producing steel it's +what it cost Society to produce steel is + + align:start position:0% +what it cost Society to produce steel is + + + align:start position:0% +what it cost Society to produce steel is +what it cost the + + align:start position:0% +what it cost the + + + align:start position:0% +what it cost the +producer the difference with an + + align:start position:0% +producer the difference with an + + + align:start position:0% +producer the difference with an +externality is social costs now deviate + + align:start position:0% +externality is social costs now deviate + + + align:start position:0% +externality is social costs now deviate +from private costs so if you think about + + align:start position:0% +from private costs so if you think about + + + align:start position:0% +from private costs so if you think about +what is the cost of producing unit of + + align:start position:0% +what is the cost of producing unit of + + + align:start position:0% +what is the cost of producing unit of +Steel well there's the marginal cost of + + align:start position:0% +Steel well there's the marginal cost of + + + align:start position:0% +Steel well there's the marginal cost of +that steel all the stuff that goes into + + align:start position:0% +that steel all the stuff that goes into + + + align:start position:0% +that steel all the stuff that goes into +it plus there's the fact that every unit + + align:start position:0% +it plus there's the fact that every unit + + + align:start position:0% +it plus there's the fact that every unit +of Steel creates unit of sludge and that + + align:start position:0% +of Steel creates unit of sludge and that + + + align:start position:0% +of Steel creates unit of sludge and that +kills + + align:start position:0% +kills + + + align:start position:0% +kills +fish now that is not a private cost the + + align:start position:0% +fish now that is not a private cost the + + + align:start position:0% +fish now that is not a private cost the +steel planter couldn't give a it's + + align:start position:0% +steel planter couldn't give a it's + + + align:start position:0% +steel planter couldn't give a it's +a social cost because but Society is + + align:start position:0% +a social cost because but Society is + + + align:start position:0% +a social cost because but Society is +worse off because the fish are dying + + align:start position:0% +worse off because the fish are dying + + + align:start position:0% +worse off because the fish are dying +societ is comprised of everyone in + + align:start position:0% +societ is comprised of everyone in + + + align:start position:0% +societ is comprised of everyone in +society so the cost of producing steel + + align:start position:0% +society so the cost of producing steel + + + align:start position:0% +society so the cost of producing steel +the social cost is now the + + align:start position:0% +the social cost is now the + + + align:start position:0% +the social cost is now the +manufacturer's private marginal cost + + align:start position:0% +manufacturer's private marginal cost + + + align:start position:0% +manufacturer's private marginal cost +plus the marginal damage so the social + + align:start position:0% +plus the marginal damage so the social + + + align:start position:0% +plus the marginal damage so the social +marginal cost is the manufacturer + + align:start position:0% +marginal cost is the manufacturer + + + align:start position:0% +marginal cost is the manufacturer +private marginal cost plus the marginal + + align:start position:0% +private marginal cost plus the marginal + + + align:start position:0% +private marginal cost plus the marginal +damage that that production does to + + align:start position:0% +damage that that production does to + + + align:start position:0% +damage that that production does to +society in this case society's + + align:start position:0% +society in this case society's + + + align:start position:0% +society in this case society's +represented just by the + + align:start position:0% +represented just by the + + + align:start position:0% +represented just by the +fisherman the other rest of society we + + align:start position:0% +fisherman the other rest of society we + + + align:start position:0% +fisherman the other rest of society we +are going to assume to make life easy + + align:start position:0% +are going to assume to make life easy + + + align:start position:0% +are going to assume to make life easy +that marginal damage is constant you + + align:start position:0% +that marginal damage is constant you + + + align:start position:0% +that marginal damage is constant you +could imagine upward or downward sloping + + align:start position:0% +could imagine upward or downward sloping + + + align:start position:0% +could imagine upward or downward sloping +marginal demand curves let's leave that + + align:start position:0% +marginal demand curves let's leave that + + + align:start position:0% +marginal demand curves let's leave that +alone that which makes it harder all the + + align:start position:0% +alone that which makes it harder all the + + + align:start position:0% +alone that which makes it harder all the +math and all the intuition goes through + + align:start position:0% +math and all the intuition goes through + + + align:start position:0% +math and all the intuition goes through +assume a constant assume that every + + align:start position:0% +assume a constant assume that every + + + align:start position:0% +assume a constant assume that every +single unit of sludge dump causes a + + align:start position:0% +single unit of sludge dump causes a + + + align:start position:0% +single unit of sludge dump causes a +constant marginal demand marginal damage + + align:start position:0% +constant marginal demand marginal damage + + + align:start position:0% +constant marginal demand marginal damage +MD in terms of killing + + align:start position:0% +MD in terms of killing + + + align:start position:0% +MD in terms of killing +fish okay what does that + + align:start position:0% +fish okay what does that + + + align:start position:0% +fish okay what does that +imply for both private and social + + align:start position:0% +imply for both private and social + + + align:start position:0% +imply for both private and social +welfare so for private welfare for what + + align:start position:0% +welfare so for private welfare for what + + + align:start position:0% +welfare so for private welfare for what +the market delivers what the this is + + align:start position:0% +the market delivers what the this is + + + align:start position:0% +the market delivers what the this is +otherwise a perfectly competitive market + + align:start position:0% +otherwise a perfectly competitive market + + + align:start position:0% +otherwise a perfectly competitive market +it delivers the outcome at Point a the + + align:start position:0% +it delivers the outcome at Point a the + + + align:start position:0% +it delivers the outcome at Point a the +perfectly competitive market delivers + + align:start position:0% +perfectly competitive market delivers + + + align:start position:0% +perfectly competitive market delivers +outcome at Point a with no externalities + + align:start position:0% +outcome at Point a with no externalities + + + align:start position:0% +outcome at Point a with no externalities +that is also the socially optimal + + align:start position:0% +that is also the socially optimal + + + align:start position:0% +that is also the socially optimal +outcome we covered that that's the first + + align:start position:0% +outcome we covered that that's the first + + + align:start position:0% +outcome we covered that that's the first +fundamental + + align:start position:0% +fundamental + + + align:start position:0% +fundamental +theorem but now we say no the social + + align:start position:0% +theorem but now we say no the social + + + align:start position:0% +theorem but now we say no the social +cost is not the blue line it's the red + + align:start position:0% +cost is not the blue line it's the red + + + align:start position:0% +cost is not the blue line it's the red +line it's the private marginal cost plus + + align:start position:0% +line it's the private marginal cost plus + + + align:start position:0% +line it's the private marginal cost plus +the marginal damage which is a shift + + align:start position:0% +the marginal damage which is a shift + + + align:start position:0% +the marginal damage which is a shift +upwards it's a constant shift upwards + + align:start position:0% +upwards it's a constant shift upwards + + + align:start position:0% +upwards it's a constant shift upwards +because we're assuming marginal damage + + align:start position:0% +because we're assuming marginal damage + + + align:start position:0% +because we're assuming marginal damage +is constant so the social Optimum is not + + align:start position:0% +is constant so the social Optimum is not + + + align:start position:0% +is constant so the social Optimum is not +at a it's at + + align:start position:0% +at a it's at + + + align:start position:0% +at a it's at +C in other words from society's + + align:start position:0% +C in other words from society's + + + align:start position:0% +C in other words from society's +perspective the steel company + + align:start position:0% +perspective the steel company + + + align:start position:0% +perspective the steel company +overproduces + + align:start position:0% +overproduces + + + align:start position:0% +overproduces +steel why does it overproduce steel + + align:start position:0% +steel why does it overproduce steel + + + align:start position:0% +steel why does it overproduce steel +because a steel compan is saying I'm + + align:start position:0% +because a steel compan is saying I'm + + + align:start position:0% +because a steel compan is saying I'm +going to produce steel until the cost to + + align:start position:0% +going to produce steel until the cost to + + + align:start position:0% +going to produce steel until the cost to +me equals the benefits to + + align:start position:0% +me equals the benefits to + + + align:start position:0% +me equals the benefits to +Consumers but from society's perspective + + align:start position:0% +Consumers but from society's perspective + + + align:start position:0% +Consumers but from society's perspective +you should produce D the cost to society + + align:start position:0% +you should produce D the cost to society + + + align:start position:0% +you should produce D the cost to society +equals the benefits to society the + + align:start position:0% +equals the benefits to society the + + + align:start position:0% +equals the benefits to society the +benefit to society is the demand + + align:start position:0% +benefit to society is the demand + + + align:start position:0% +benefit to society is the demand +curve but the cost Society supply curve + + align:start position:0% +curve but the cost Society supply curve + + + align:start position:0% +curve but the cost Society supply curve +plus the marginal damage as a result the + + align:start position:0% +plus the marginal damage as a result the + + + align:start position:0% +plus the marginal damage as a result the +steel plant is overproducing steel + + align:start position:0% +steel plant is overproducing steel + + + align:start position:0% +steel plant is overproducing steel +because it's not accounting for the + + align:start position:0% +because it's not accounting for the + + + align:start position:0% +because it's not accounting for the +externality it's not accounting for the + + align:start position:0% +externality it's not accounting for the + + + align:start position:0% +externality it's not accounting for the +Damage Done to the other party and as a + + align:start position:0% +Damage Done to the other party and as a + + + align:start position:0% +Damage Done to the other party and as a +result we get overproduction of Steel + + align:start position:0% +result we get overproduction of Steel + + + align:start position:0% +result we get overproduction of Steel +and a dead weight + + align:start position:0% +and a dead weight + + + align:start position:0% +and a dead weight +loss the dead weight loss is a New + + align:start position:0% +loss the dead weight loss is a New + + + align:start position:0% +loss the dead weight loss is a New +Concept because we haven't had private + + align:start position:0% +Concept because we haven't had private + + + align:start position:0% +Concept because we haven't had private +and social cost deviating before we've + + align:start position:0% +and social cost deviating before we've + + + align:start position:0% +and social cost deviating before we've +seen deadweight losses before but this + + align:start position:0% +seen deadweight losses before but this + + + align:start position:0% +seen deadweight losses before but this +is a new kind of dead weight loss that + + align:start position:0% +is a new kind of dead weight loss that + + + align:start position:0% +is a new kind of dead weight loss that +arises because the fact that the steel + + align:start position:0% +arises because the fact that the steel + + + align:start position:0% +arises because the fact that the steel +kills + + align:start position:0% +kills + + + align:start position:0% +kills +fish creates an externality + + align:start position:0% +fish creates an externality + + + align:start position:0% +fish creates an externality +which causes the steel producer to + + align:start position:0% +which causes the steel producer to + + + align:start position:0% +which causes the steel producer to +overproduce steel and as a result of + + align:start position:0% +overproduce steel and as a result of + + + align:start position:0% +overproduce steel and as a result of +that excess production of Steel we get a + + align:start position:0% +that excess production of Steel we get a + + + align:start position:0% +that excess production of Steel we get a +dead weight loss dead weight losses + + align:start position:0% +dead weight loss dead weight losses + + + align:start position:0% +dead weight loss dead weight losses +here's the trick are done relevant to + + align:start position:0% +here's the trick are done relevant to + + + align:start position:0% +here's the trick are done relevant to +social marginal costs the ultimate goals + + align:start position:0% +social marginal costs the ultimate goals + + + align:start position:0% +social marginal costs the ultimate goals +to have is to have social welfare + + align:start position:0% +to have is to have social welfare + + + align:start position:0% +to have is to have social welfare +maximization that's at C not at a so + + align:start position:0% +maximization that's at C not at a so + + + align:start position:0% +maximization that's at C not at a so +you've created a dead weight + + align:start position:0% +you've created a dead weight + + + align:start position:0% +you've created a dead weight +loss okay questions a little + + align:start position:0% +loss okay questions a little + + + align:start position:0% +loss okay questions a little +mind-blowing different concept question + + align:start position:0% +mind-blowing different concept question + + + align:start position:0% +mind-blowing different concept question +about how this works yeah + + align:start position:0% + + + + align:start position:0% + +no so see the thing is societ well it + + align:start position:0% +no so see the thing is societ well it + + + align:start position:0% +no so see the thing is societ well it +depends defined Society the market can + + align:start position:0% +depends defined Society the market can + + + align:start position:0% +depends defined Society the market can +only operate as the market the Market's + + align:start position:0% +only operate as the market the Market's + + + align:start position:0% +only operate as the market the Market's +the market for steel that's what I've + + align:start position:0% +the market for steel that's what I've + + + align:start position:0% +the market for steel that's what I've +drawn here Society being the government + + align:start position:0% +drawn here Society being the government + + + align:start position:0% +drawn here Society being the government +could decide to address this and we'll + + align:start position:0% +could decide to address this and we'll + + + align:start position:0% +could decide to address this and we'll +talk about later but the market itself + + align:start position:0% +talk about later but the market itself + + + align:start position:0% +talk about later but the market itself +leads to point a so the Market's leading + + align:start position:0% +leads to point a so the Market's leading + + + align:start position:0% +leads to point a so the Market's leading +us to overproduced + + align:start position:0% +us to overproduced + + + align:start position:0% +us to overproduced +Steel okay so this is not a this is not + + align:start position:0% +Steel okay so this is not a this is not + + + align:start position:0% +Steel okay so this is not a this is not +a positive analysis the positive + + align:start position:0% +a positive analysis the positive + + + align:start position:0% +a positive analysis the positive +analysis we already know how to do posi + + align:start position:0% +analysis we already know how to do posi + + + align:start position:0% +analysis we already know how to do posi +you get to point a this a normative + + align:start position:0% +you get to point a this a normative + + + align:start position:0% +you get to point a this a normative +analysis which is point a is over + + align:start position:0% +analysis which is point a is over + + + align:start position:0% +analysis which is point a is over +production producing too much course are + + align:start position:0% +production producing too much course are + + + align:start position:0% +production producing too much course are +not accounting for the Damage Done to + + align:start position:0% +not accounting for the Damage Done to + + + align:start position:0% +not accounting for the Damage Done to +the + + align:start position:0% +the + + + align:start position:0% +the +fisherman okay let's drill this + + align:start position:0% +fisherman okay let's drill this + + + align:start position:0% +fisherman okay let's drill this +intuition home by talking about another + + align:start position:0% +intuition home by talking about another + + + align:start position:0% +intuition home by talking about another +case let's talk about a negative + + align:start position:0% +case let's talk about a negative + + + align:start position:0% +case let's talk about a negative +consumption + + align:start position:0% +consumption + + + align:start position:0% +consumption +externality let's talk about a negative + + align:start position:0% +externality let's talk about a negative + + + align:start position:0% +externality let's talk about a negative +consumption externality the classic + + align:start position:0% +consumption externality the classic + + + align:start position:0% +consumption externality the classic +example of which is + + align:start position:0% +example of which is + + + align:start position:0% +example of which is +smoking when I + + align:start position:0% +smoking when I + + + align:start position:0% +smoking when I +smoke I exert a negative effect on + + align:start position:0% +smoke I exert a negative effect on + + + align:start position:0% +smoke I exert a negative effect on +society partly because um I raised the + + align:start position:0% +society partly because um I raised the + + + align:start position:0% +society partly because um I raised the +cost of medical care for dealing with + + align:start position:0% +cost of medical care for dealing with + + + align:start position:0% +cost of medical care for dealing with +with me when I'm old partly because I + + align:start position:0% +with me when I'm old partly because I + + + align:start position:0% +with me when I'm old partly because I +create secondhand smoke but for lots of + + align:start position:0% +create secondhand smoke but for lots of + + + align:start position:0% +create secondhand smoke but for lots of +reasons my smoking creates extra cost + + align:start position:0% +reasons my smoking creates extra cost + + + align:start position:0% +reasons my smoking creates extra cost +for society so my smoking decision is + + align:start position:0% +for society so my smoking decision is + + + align:start position:0% +for society so my smoking decision is +represented in figure + + align:start position:0% +represented in figure + + + align:start position:0% +represented in figure +242 the cost of producing cigarettes + + align:start position:0% +242 the cost of producing cigarettes + + + align:start position:0% +242 the cost of producing cigarettes +we're assuming no production externality + + align:start position:0% +we're assuming no production externality + + + align:start position:0% +we're assuming no production externality +here so the supply curve is both the + + align:start position:0% +here so the supply curve is both the + + + align:start position:0% +here so the supply curve is both the +private marginal cost and the social + + align:start position:0% +private marginal cost and the social + + + align:start position:0% +private marginal cost and the social +marginal cost there's no production + + align:start position:0% +marginal cost there's no production + + + align:start position:0% +marginal cost there's no production +externality but I choose to smoke it + + align:start position:0% +externality but I choose to smoke it + + + align:start position:0% +externality but I choose to smoke it +point a or the market chooses smoking at + + align:start position:0% +point a or the market chooses smoking at + + + align:start position:0% +point a or the market chooses smoking at +Point a which is where the so the + + align:start position:0% +Point a which is where the so the + + + align:start position:0% +Point a which is where the so the +private marginal cost equals the private + + align:start position:0% +private marginal cost equals the private + + + align:start position:0% +private marginal cost equals the private +marginal + + align:start position:0% +marginal + + + align:start position:0% +marginal +benefit however the social marginal + + align:start position:0% +benefit however the social marginal + + + align:start position:0% +benefit however the social marginal +benefit is lower than the private + + align:start position:0% +benefit is lower than the private + + + align:start position:0% +benefit is lower than the private +marginal benefit the social marginal + + align:start position:0% +marginal benefit the social marginal + + + align:start position:0% +marginal benefit the social marginal +benefit is equal to the private marginal + + align:start position:0% +benefit is equal to the private marginal + + + align:start position:0% +benefit is equal to the private marginal +benefit minus the marginal damage which + + align:start position:0% +benefit minus the marginal damage which + + + align:start position:0% +benefit minus the marginal damage which +once again I assume is + + align:start position:0% +once again I assume is + + + align:start position:0% +once again I assume is +constant done by my + + align:start position:0% +constant done by my + + + align:start position:0% +constant done by my +smoking in other words I over + + align:start position:0% +smoking in other words I over + + + align:start position:0% +smoking in other words I over +smoke because when I decide to smoke I + + align:start position:0% +smoke because when I decide to smoke I + + + align:start position:0% +smoke because when I decide to smoke I +just compare my benefits to the cost of + + align:start position:0% +just compare my benefits to the cost of + + + align:start position:0% +just compare my benefits to the cost of +cigarettes I don't consider the fact + + align:start position:0% +cigarettes I don't consider the fact + + + align:start position:0% +cigarettes I don't consider the fact +that I'm making you sick and making your + + align:start position:0% +that I'm making you sick and making your + + + align:start position:0% +that I'm making you sick and making your +tax dollars go up by my + + align:start position:0% +tax dollars go up by my + + + align:start position:0% +tax dollars go up by my +smoking as a result I smoke too much + + align:start position:0% +smoking as a result I smoke too much + + + align:start position:0% +smoking as a result I smoke too much +from society's perspective think of + + align:start position:0% +from society's perspective think of + + + align:start position:0% +from society's perspective think of +society as the bubble that includes + + align:start position:0% +society as the bubble that includes + + + align:start position:0% +society as the bubble that includes +everyone whereas my decision is a bubble + + align:start position:0% +everyone whereas my decision is a bubble + + + align:start position:0% +everyone whereas my decision is a bubble +that just includes me so I'm only + + align:start position:0% +that just includes me so I'm only + + + align:start position:0% +that just includes me so I'm only +deciding based on me I'm ignoring the + + align:start position:0% +deciding based on me I'm ignoring the + + + align:start position:0% +deciding based on me I'm ignoring the +rest of that bubble if my smoking + + align:start position:0% +rest of that bubble if my smoking + + + align:start position:0% +rest of that bubble if my smoking +decisions affect the rest of that + + align:start position:0% +decisions affect the rest of that + + + align:start position:0% +decisions affect the rest of that +bubble then I'm over + + align:start position:0% +bubble then I'm over + + + align:start position:0% +bubble then I'm over +consuming okay and therefore we get too + + align:start position:0% +consuming okay and therefore we get too + + + align:start position:0% +consuming okay and therefore we get too +many cigarettes consumed and a parallel + + align:start position:0% +many cigarettes consumed and a parallel + + + align:start position:0% +many cigarettes consumed and a parallel +dead weight + + align:start position:0% +dead weight + + + align:start position:0% +dead weight +loss okay this time it comes from a + + align:start position:0% +loss okay this time it comes from a + + + align:start position:0% +loss okay this time it comes from a +shift in the demand + + align:start position:0% +shift in the demand + + + align:start position:0% +shift in the demand +curve okay so that is another example uh + + align:start position:0% +curve okay so that is another example uh + + + align:start position:0% +curve okay so that is another example uh +you note here we used a number we Ed 40 + + align:start position:0% +you note here we used a number we Ed 40 + + + align:start position:0% +you note here we used a number we Ed 40 +cents that's the best estimate 40 40 or + + align:start position:0% +cents that's the best estimate 40 40 or + + + align:start position:0% +cents that's the best estimate 40 40 or +50 cents is the best estimate of what + + align:start position:0% +50 cents is the best estimate of what + + + align:start position:0% +50 cents is the best estimate of what +the negative externality is from smoking + + align:start position:0% +the negative externality is from smoking + + + align:start position:0% +the negative externality is from smoking +about 40 to 50 cents a pack if you add + + align:start position:0% +about 40 to 50 cents a pack if you add + + + align:start position:0% +about 40 to 50 cents a pack if you add +up all the costs smokers impose on + + align:start position:0% +up all the costs smokers impose on + + + align:start position:0% +up all the costs smokers impose on +society it's 40 to 50 cents a pack and + + align:start position:0% +society it's 40 to 50 cents a pack and + + + align:start position:0% +society it's 40 to 50 cents a pack and +that's why we use that as a constant + + align:start position:0% +that's why we use that as a constant + + + align:start position:0% +that's why we use that as a constant +marginal damage here so given this + + align:start position:0% +marginal damage here so given this + + + align:start position:0% +marginal damage here so given this +there's over + + align:start position:0% +there's over + + + align:start position:0% +there's over +consumption um of uh of + + align:start position:0% +consumption um of uh of + + + align:start position:0% +consumption um of uh of +cigarettes externals can also be + + align:start position:0% +cigarettes externals can also be + + + align:start position:0% +cigarettes externals can also be +positive we could have a + + align:start position:0% +positive we could have a + + + align:start position:0% +positive we could have a +positive production + + align:start position:0% + + + + align:start position:0% + +externality the classic example of that + + align:start position:0% +externality the classic example of that + + + align:start position:0% +externality the classic example of that +so let's think about what we what we're + + align:start position:0% +so let's think about what we what we're + + + align:start position:0% +so let's think about what we what we're +now you sort of are in the concept think + + align:start position:0% +now you sort of are in the concept think + + + align:start position:0% +now you sort of are in the concept think +about what I'm going to talk about here + + align:start position:0% +about what I'm going to talk about here + + + align:start position:0% +about what I'm going to talk about here +I'm going talk about something something + + align:start position:0% +I'm going talk about something something + + + align:start position:0% +I'm going talk about something something +that firms + + align:start position:0% +that firms + + + align:start position:0% +that firms +do that has benefits on others that the + + align:start position:0% +do that has benefits on others that the + + + align:start position:0% +do that has benefits on others that the +firms don't + + align:start position:0% +firms don't + + + align:start position:0% +firms don't +realize what's the classical example of + + align:start position:0% +realize what's the classical example of + + + align:start position:0% +realize what's the classical example of +that research and + + align:start position:0% +that research and + + + align:start position:0% +that research and +development when a firm does + + align:start position:0% +development when a firm does + + + align:start position:0% +development when a firm does +R&D it creates new science which + + align:start position:0% +R&D it creates new science which + + + align:start position:0% +R&D it creates new science which +benefits consumers but consumers pay for + + align:start position:0% +benefits consumers but consumers pay for + + + align:start position:0% +benefits consumers but consumers pay for +that but other firms learn and go + + align:start position:0% +that but other firms learn and go + + + align:start position:0% +that but other firms learn and go +further up the development curve based + + align:start position:0% +further up the development curve based + + + align:start position:0% +further up the development curve based +on what the first firm did so if you + + align:start position:0% +on what the first firm did so if you + + + align:start position:0% +on what the first firm did so if you +think about if you go go to figure + + align:start position:0% +think about if you go go to figure + + + align:start position:0% +think about if you go go to figure +234 think about the market for R&D when + + align:start position:0% +234 think about the market for R&D when + + + align:start position:0% +234 think about the market for R&D when +a firm's deciding how much R&D to do it + + align:start position:0% +a firm's deciding how much R&D to do it + + + align:start position:0% +a firm's deciding how much R&D to do it +considers what's the cost of R&D R&D is + + align:start position:0% +considers what's the cost of R&D R&D is + + + align:start position:0% +considers what's the cost of R&D R&D is +a cost you got to hire scientists and + + align:start position:0% +a cost you got to hire scientists and + + + align:start position:0% +a cost you got to hire scientists and +build labs and so that's the uh + + align:start position:0% +build labs and so that's the uh + + + align:start position:0% +build labs and so that's the uh +private marginal cost and there's a + + align:start position:0% +private marginal cost and there's a + + + align:start position:0% +private marginal cost and there's a +benefit for R&D which is how many + + align:start position:0% +benefit for R&D which is how many + + + align:start position:0% +benefit for R&D which is how many +patents does it deliver for the firm + + align:start position:0% +patents does it deliver for the firm + + + align:start position:0% +patents does it deliver for the firm +that's going to drive the demand okay + + align:start position:0% +that's going to drive the demand okay + + + align:start position:0% +that's going to drive the demand okay +what the firm is ignoring is that by + + align:start position:0% +what the firm is ignoring is that by + + + align:start position:0% +what the firm is ignoring is that by +doing + + align:start position:0% +doing + + + align:start position:0% +doing +R&D they are actually producing knowled + + align:start position:0% +R&D they are actually producing knowled + + + align:start position:0% +R&D they are actually producing knowled +that cannot be held totally privately + + align:start position:0% +that cannot be held totally privately + + + align:start position:0% +that cannot be held totally privately +eventually when the patent runs out it's + + align:start position:0% +eventually when the patent runs out it's + + + align:start position:0% +eventually when the patent runs out it's +public even before that firms May learn + + align:start position:0% +public even before that firms May learn + + + align:start position:0% +public even before that firms May learn +and that's going to benefit other firms + + align:start position:0% +and that's going to benefit other firms + + + align:start position:0% +and that's going to benefit other firms +that's going to lower the cost of + + align:start position:0% +that's going to lower the cost of + + + align:start position:0% +that's going to lower the cost of +development for other firms so there's a + + align:start position:0% +development for other firms so there's a + + + align:start position:0% +development for other firms so there's a +social marginal + + align:start position:0% +social marginal + + + align:start position:0% +social marginal +benefit which effectively lowers the + + align:start position:0% +benefit which effectively lowers the + + + align:start position:0% +benefit which effectively lowers the +marginal cost of + + align:start position:0% +marginal cost of + + + align:start position:0% +marginal cost of +R&D from society's + + align:start position:0% +R&D from society's + + + align:start position:0% +R&D from society's +perspective when firms do R&D it's more + + align:start position:0% +perspective when firms do R&D it's more + + + align:start position:0% +perspective when firms do R&D it's more +valuable than the firm at self + + align:start position:0% +valuable than the firm at self + + + align:start position:0% +valuable than the firm at self +sees indeed the best estimates are that + + align:start position:0% +sees indeed the best estimates are that + + + align:start position:0% +sees indeed the best estimates are that +the private rate of return to + + align:start position:0% +the private rate of return to + + + align:start position:0% +the private rate of return to +firms is on the order of about 15 to 20% + + align:start position:0% +firms is on the order of about 15 to 20% + + + align:start position:0% +firms is on the order of about 15 to 20% +pretty high rate of return because a + + align:start position:0% +pretty high rate of return because a + + + align:start position:0% +pretty high rate of return because a +risky investment the social rate of + + align:start position:0% +risky investment the social rate of + + + align:start position:0% +risky investment the social rate of +return which is accounting for the + + align:start position:0% +return which is accounting for the + + + align:start position:0% +return which is accounting for the +benefits other firms get from that R&D + + align:start position:0% +benefits other firms get from that R&D + + + align:start position:0% +benefits other firms get from that R&D +are something like two to three times as + + align:start position:0% +are something like two to three times as + + + align:start position:0% +are something like two to three times as +large because of all the benefits of + + align:start position:0% +large because of all the benefits of + + + align:start position:0% +large because of all the benefits of +society and one firm does it spills over + + align:start position:0% +society and one firm does it spills over + + + align:start position:0% +society and one firm does it spills over +and other firms benefit as + + align:start position:0% +and other firms benefit as + + + align:start position:0% +and other firms benefit as +well okay so that is a positive + + align:start position:0% +well okay so that is a positive + + + align:start position:0% +well okay so that is a positive +production externality as a result firms + + align:start position:0% +production externality as a result firms + + + align:start position:0% +production externality as a result firms +do too little + + align:start position:0% +do too little + + + align:start position:0% +do too little +R&D just like a negative production + + align:start position:0% +R&D just like a negative production + + + align:start position:0% +R&D just like a negative production +externality causes the steel plants to + + align:start position:0% +externality causes the steel plants to + + + align:start position:0% +externality causes the steel plants to +produce too much steel a positive + + align:start position:0% +produce too much steel a positive + + + align:start position:0% +produce too much steel a positive +production externality causes firms to + + align:start position:0% +production externality causes firms to + + + align:start position:0% +production externality causes firms to +do too little + + align:start position:0% +do too little + + + align:start position:0% +do too little +R&D okay that's one reason why in the US + + align:start position:0% +R&D okay that's one reason why in the US + + + align:start position:0% +R&D okay that's one reason why in the US +we have a tax credit to promote + + align:start position:0% +we have a tax credit to promote + + + align:start position:0% +we have a tax credit to promote +R&D finally we have the last example + + align:start position:0% +R&D finally we have the last example + + + align:start position:0% +R&D finally we have the last example +which is a positive consumption + + align:start position:0% +which is a positive consumption + + + align:start position:0% +which is a positive consumption +externality and here let me move away + + align:start position:0% +externality and here let me move away + + + align:start position:0% +externality and here let me move away +from the graphs and talk about an + + align:start position:0% +from the graphs and talk about an + + + align:start position:0% +from the graphs and talk about an +example okay um I have a neighbor who + + align:start position:0% +example okay um I have a neighbor who + + + align:start position:0% +example okay um I have a neighbor who +I'm not fond of I may have mentioned + + align:start position:0% +I'm not fond of I may have mentioned + + + align:start position:0% +I'm not fond of I may have mentioned +this before uh I do not like my neighbor + + align:start position:0% +this before uh I do not like my neighbor + + + align:start position:0% +this before uh I do not like my neighbor +uh part of the reason I do not like my + + align:start position:0% +uh part of the reason I do not like my + + + align:start position:0% +uh part of the reason I do not like my +neighbor is my neighbor has a tendency + + align:start position:0% +neighbor is my neighbor has a tendency + + + align:start position:0% +neighbor is my neighbor has a tendency +to do big projects about halfway and + + align:start position:0% +to do big projects about halfway and + + + align:start position:0% +to do big projects about halfway and +then stop because he gets bored one such + + align:start position:0% +then stop because he gets bored one such + + + align:start position:0% +then stop because he gets bored one such +project he started about 20 years ago he + + align:start position:0% +project he started about 20 years ago he + + + align:start position:0% +project he started about 20 years ago he +decided do a massive landscaping job on + + align:start position:0% +decided do a massive landscaping job on + + + align:start position:0% +decided do a massive landscaping job on +his + + align:start position:0% +his + + + align:start position:0% +his +yard and as part of that I produced a + + align:start position:0% +yard and as part of that I produced a + + + align:start position:0% +yard and as part of that I produced a +giant mound of dirt that was directly + + align:start position:0% +giant mound of dirt that was directly + + + align:start position:0% +giant mound of dirt that was directly +out the window of our kitchen and then + + align:start position:0% +out the window of our kitchen and then + + + align:start position:0% +out the window of our kitchen and then +he stopped and that Dirt has sat there + + align:start position:0% +he stopped and that Dirt has sat there + + + align:start position:0% +he stopped and that Dirt has sat there +for 20 years at one point my wife snuck + + align:start position:0% +for 20 years at one point my wife snuck + + + align:start position:0% +for 20 years at one point my wife snuck +out and planted wild flowers on it so it + + align:start position:0% +out and planted wild flowers on it so it + + + align:start position:0% +out and planted wild flowers on it so it +wouldn't look so bad but the bottom line + + align:start position:0% +wouldn't look so bad but the bottom line + + + align:start position:0% +wouldn't look so bad but the bottom line +is we got this pile of dirt this guy + + align:start position:0% +is we got this pile of dirt this guy + + + align:start position:0% +is we got this pile of dirt this guy +created so let's think about his + + align:start position:0% +created so let's think about his + + + align:start position:0% +created so let's think about his +decision about whether to get rid of + + align:start position:0% +decision about whether to get rid of + + + align:start position:0% +decision about whether to get rid of +that pile of dirt imagine that it would + + align:start position:0% +that pile of dirt imagine that it would + + + align:start position:0% +that pile of dirt imagine that it would +cost him + + align:start position:0% +cost him + + + align:start position:0% +cost him +$1,000 to get rid of that pile of dirt + + align:start position:0% +$1,000 to get rid of that pile of dirt + + + align:start position:0% +$1,000 to get rid of that pile of dirt +and imagine because he doesn't mind + + align:start position:0% +and imagine because he doesn't mind + + + align:start position:0% +and imagine because he doesn't mind +looking at dirt it's only worth 800 + + align:start position:0% +looking at dirt it's only worth 800 + + + align:start position:0% +looking at dirt it's only worth 800 +bucks to him so the marginal cost is a + + align:start position:0% +bucks to him so the marginal cost is a + + + align:start position:0% +bucks to him so the marginal cost is a +th000 the marginal benefit privately is + + align:start position:0% +th000 the marginal benefit privately is + + + align:start position:0% +th000 the marginal benefit privately is +800 you won't get rid of it but what if + + align:start position:0% +800 you won't get rid of it but what if + + + align:start position:0% +800 you won't get rid of it but what if +it's also worth another 500 bucks to + + align:start position:0% +it's also worth another 500 bucks to + + + align:start position:0% +it's also worth another 500 bucks to +me well in that case the social marginal + + align:start position:0% +me well in that case the social marginal + + + align:start position:0% +me well in that case the social marginal +benefit is + + align:start position:0% +benefit is + + + align:start position:0% +benefit is +$1,300 which is above the cost so he + + align:start position:0% +$1,300 which is above the cost so he + + + align:start position:0% +$1,300 which is above the cost so he +should remove the dirt but he won't + + align:start position:0% +should remove the dirt but he won't + + + align:start position:0% +should remove the dirt but he won't +because he's a jerk Okay and like he + + align:start position:0% +because he's a jerk Okay and like he + + + align:start position:0% +because he's a jerk Okay and like he +doesn't care what I think he's just his + + align:start position:0% +doesn't care what I think he's just his + + + align:start position:0% +doesn't care what I think he's just his +own and he's look he's not it he won't + + align:start position:0% +own and he's look he's not it he won't + + + align:start position:0% +own and he's look he's not it he won't +not do it not just because he's jerk but + + align:start position:0% +not do it not just because he's jerk but + + + align:start position:0% +not do it not just because he's jerk but +because he's considering his own private + + align:start position:0% +because he's considering his own private + + + align:start position:0% +because he's considering his own private +marginal cost of medits it's not worth + + align:start position:0% +marginal cost of medits it's not worth + + + align:start position:0% +marginal cost of medits it's not worth +it because it's an ex because removing + + align:start position:0% +it because it's an ex because removing + + + align:start position:0% +it because it's an ex because removing +it would have a positive effect on me + + align:start position:0% +it would have a positive effect on me + + + align:start position:0% +it would have a positive effect on me +and he's not accounting for that so he's + + align:start position:0% +and he's not accounting for that so he's + + + align:start position:0% +and he's not accounting for that so he's +under he is underusing + + align:start position:0% +under he is underusing + + + align:start position:0% +under he is underusing +Landscaping + + align:start position:0% +Landscaping + + + align:start position:0% +Landscaping +okay questions about any of + + align:start position:0% +okay questions about any of + + + align:start position:0% +okay questions about any of +this + + align:start position:0% + + + + align:start position:0% + +yeah uh they're just twoo totally + + align:start position:0% +yeah uh they're just twoo totally + + + align:start position:0% +yeah uh they're just twoo totally +different market + + align:start position:0% +different market + + + align:start position:0% +different market +failures uh I think you know we could + + align:start position:0% +failures uh I think you know we could + + + align:start position:0% +failures uh I think you know we could +discuss that more another time but + + align:start position:0% +discuss that more another time but + + + align:start position:0% +discuss that more another time but +they're just they're really not related + + align:start position:0% +they're just they're really not related + + + align:start position:0% +they're just they're really not related +in in fundamental ways I mean in + + align:start position:0% +in in fundamental ways I mean in + + + align:start position:0% +in in fundamental ways I mean in +subsense you could think of information + + align:start position:0% +subsense you could think of information + + + align:start position:0% +subsense you could think of information +Imes creating things that look like + + align:start position:0% +Imes creating things that look like + + + align:start position:0% +Imes creating things that look like +externalities but they're just two + + align:start position:0% +externalities but they're just two + + + align:start position:0% +externalities but they're just two +different ways the market can + + align:start position:0% +different ways the market can + + + align:start position:0% +different ways the market can +fail um okay so now but my neighbor + + align:start position:0% +fail um okay so now but my neighbor + + + align:start position:0% +fail um okay so now but my neighbor +example raises a really interesting + + align:start position:0% +example raises a really interesting + + + align:start position:0% +example raises a really interesting +question okay I now hopefully have + + align:start position:0% +question okay I now hopefully have + + + align:start position:0% +question okay I now hopefully have +convinced you extra NS exist they're + + align:start position:0% +convinced you extra NS exist they're + + + align:start position:0% +convinced you extra NS exist they're +real they cause inefficiencies but do we + + align:start position:0% +real they cause inefficiencies but do we + + + align:start position:0% +real they cause inefficiencies but do we +need the government to fix them I mean + + align:start position:0% +need the government to fix them I mean + + + align:start position:0% +need the government to fix them I mean +after all I could go to my neighbor and + + align:start position:0% +after all I could go to my neighbor and + + + align:start position:0% +after all I could go to my neighbor and +offer him 500 bucks to the Landscaping + + align:start position:0% +offer him 500 bucks to the Landscaping + + + align:start position:0% +offer him 500 bucks to the Landscaping +right we don't need + + align:start position:0% +right we don't need + + + align:start position:0% +right we don't need +government indeed there's a very famous + + align:start position:0% +government indeed there's a very famous + + + align:start position:0% +government indeed there's a very famous +economist lawyer and Economist named + + align:start position:0% +economist lawyer and Economist named + + + align:start position:0% +economist lawyer and Economist named +Ronald + + align:start position:0% +Ronald + + + align:start position:0% +Ronald +Co who POS what we call the Coan + + align:start position:0% +Co who POS what we call the Coan + + + align:start position:0% +Co who POS what we call the Coan +solution externalities which is just + + align:start position:0% +solution externalities which is just + + + align:start position:0% +solution externalities which is just +negotiate okay + + align:start position:0% +negotiate okay + + + align:start position:0% +negotiate okay +basically this + + align:start position:0% +basically this + + + align:start position:0% +basically this +fisherman could say hey you're doing + + align:start position:0% +fisherman could say hey you're doing + + + align:start position:0% +fisherman could say hey you're doing +this damage to our fishing let's + + align:start position:0% +this damage to our fishing let's + + + align:start position:0% +this damage to our fishing let's +negotiate and have you produce less + + align:start position:0% +negotiate and have you produce less + + + align:start position:0% +negotiate and have you produce less +steel okay so + + align:start position:0% +steel okay so + + + align:start position:0% +steel okay so +basically theide idea is we don't really + + align:start position:0% +basically theide idea is we don't really + + + align:start position:0% +basically theide idea is we don't really +necessarily need a government was K's + + align:start position:0% +necessarily need a government was K's + + + align:start position:0% +necessarily need a government was K's +argument because we could solve some + + align:start position:0% +argument because we could solve some + + + align:start position:0% +argument because we could solve some +negotiation in practice he's wrong and + + align:start position:0% +negotiation in practice he's wrong and + + + align:start position:0% +negotiation in practice he's wrong and +he's wrong for a number of reasons the + + align:start position:0% +he's wrong for a number of reasons the + + + align:start position:0% +he's wrong for a number of reasons the +first reason he's wrong is that the most + + align:start position:0% +first reason he's wrong is that the most + + + align:start position:0% +first reason he's wrong is that the most +important externalities are not things + + align:start position:0% +important externalities are not things + + + align:start position:0% +important externalities are not things +like me and my neighbor things like + + align:start position:0% +like me and my neighbor things like + + + align:start position:0% +like me and my neighbor things like +global + + align:start position:0% +global + + + align:start position:0% +global +warming global war is the ultimate + + align:start position:0% +warming global war is the ultimate + + + align:start position:0% +warming global war is the ultimate +externality okay when you drove your car + + align:start position:0% +externality okay when you drove your car + + + align:start position:0% +externality okay when you drove your car +last you were ever so incrementally + + align:start position:0% +last you were ever so incrementally + + + align:start position:0% +last you were ever so incrementally +putting Bangladesh + + align:start position:0% +putting Bangladesh + + + align:start position:0% +putting Bangladesh +underwater even if it's an EV Le as an + + align:start position:0% +underwater even if it's an EV Le as an + + + align:start position:0% +underwater even if it's an EV Le as an +EV but even still okay did you think + + align:start position:0% +EV but even still okay did you think + + + align:start position:0% +EV but even still okay did you think +about that did you think well I'm going + + align:start position:0% +about that did you think well I'm going + + + align:start position:0% +about that did you think well I'm going +to drive you thought about my drive is + + align:start position:0% +to drive you thought about my drive is + + + align:start position:0% +to drive you thought about my drive is +it worth it did you think oh but also + + align:start position:0% +it worth it did you think oh but also + + + align:start position:0% +it worth it did you think oh but also +I'm putting Bangladesh underwater no you + + align:start position:0% +I'm putting Bangladesh underwater no you + + + align:start position:0% +I'm putting Bangladesh underwater no you +didn't okay because that's an + + align:start position:0% +didn't okay because that's an + + + align:start position:0% +didn't okay because that's an +externality you're not accounting for + + align:start position:0% +externality you're not accounting for + + + align:start position:0% +externality you're not accounting for +that the problem is externality that's + + align:start position:0% +that the problem is externality that's + + + align:start position:0% +that the problem is externality that's +created every day by billions of people + + align:start position:0% +created every day by billions of people + + + align:start position:0% +created every day by billions of people +and affects billions of people how would + + align:start position:0% +and affects billions of people how would + + + align:start position:0% +and affects billions of people how would +they negotiate how would the billions of + + align:start position:0% +they negotiate how would the billions of + + + align:start position:0% +they negotiate how would the billions of +people who create carbon get to the + + align:start position:0% +people who create carbon get to the + + + align:start position:0% +people who create carbon get to the +billions of people who are affected by + + align:start position:0% +billions of people who are affected by + + + align:start position:0% +billions of people who are affected by +carbon negotiate they can't it's + + align:start position:0% +carbon negotiate they can't it's + + + align:start position:0% +carbon negotiate they can't it's +implausible so one problem with Coast is + + align:start position:0% +implausible so one problem with Coast is + + + align:start position:0% +implausible so one problem with Coast is +it's simply plausible for the most + + align:start position:0% +it's simply plausible for the most + + + align:start position:0% +it's simply plausible for the most +important externalities which involve + + align:start position:0% +important externalities which involve + + + align:start position:0% +important externalities which involve +many parties on both + + align:start position:0% +many parties on both + + + align:start position:0% +many parties on both +sides that's the first problem with + + align:start position:0% +sides that's the first problem with + + + align:start position:0% +sides that's the first problem with +saying we can have a private solution to + + align:start position:0% +saying we can have a private solution to + + + align:start position:0% +saying we can have a private solution to +this okay the second problem is that + + align:start position:0% +this okay the second problem is that + + + align:start position:0% +this okay the second problem is that +it's kind of socially awkward I mean you + + align:start position:0% +it's kind of socially awkward I mean you + + + align:start position:0% +it's kind of socially awkward I mean you +notice I haven't in 20 years gone to my + + align:start position:0% +notice I haven't in 20 years gone to my + + + align:start position:0% +notice I haven't in 20 years gone to my +neighbor and offered him $500 to get rid + + align:start position:0% +neighbor and offered him $500 to get rid + + + align:start position:0% +neighbor and offered him $500 to get rid +of the Dirt Pile it's kind of socially + + align:start position:0% +of the Dirt Pile it's kind of socially + + + align:start position:0% +of the Dirt Pile it's kind of socially +awkward it'd be kind of a super bizarre + + align:start position:0% +awkward it'd be kind of a super bizarre + + + align:start position:0% +awkward it'd be kind of a super bizarre +thing to do right uh there's a famous + + align:start position:0% +thing to do right uh there's a famous + + + align:start position:0% +thing to do right uh there's a famous +story of an economist who was on a plane + + align:start position:0% +story of an economist who was on a plane + + + align:start position:0% +story of an economist who was on a plane +back before he had phones we used to + + align:start position:0% +back before he had phones we used to + + + align:start position:0% +back before he had phones we used to +talk people on planes and is on a plane + + align:start position:0% +talk people on planes and is on a plane + + + align:start position:0% +talk people on planes and is on a plane +trying to get some reading done and the + + align:start position:0% +trying to get some reading done and the + + + align:start position:0% +trying to get some reading done and the +guy next to him wouldn't stop talking so + + align:start position:0% +guy next to him wouldn't stop talking so + + + align:start position:0% +guy next to him wouldn't stop talking so +we offered him 10 bucks to shut up now + + align:start position:0% +we offered him 10 bucks to shut up now + + + align:start position:0% +we offered him 10 bucks to shut up now +we laugh CU like in reality like that + + align:start position:0% +we laugh CU like in reality like that + + + align:start position:0% +we laugh CU like in reality like that +can't be right no one would do that it's + + align:start position:0% +can't be right no one would do that it's + + + align:start position:0% +can't be right no one would do that it's +just because it's not how we really + + align:start position:0% +just because it's not how we really + + + align:start position:0% +just because it's not how we really +interact in society so there's both sort + + align:start position:0% +interact in society so there's both sort + + + align:start position:0% +interact in society so there's both sort +of negotiating barriers and Norms that + + align:start position:0% +of negotiating barriers and Norms that + + + align:start position:0% +of negotiating barriers and Norms that +get in the way think about a classic + + align:start position:0% +get in the way think about a classic + + + align:start position:0% +get in the way think about a classic +classic negative production external + + align:start position:0% +classic negative production external + + + align:start position:0% +classic negative production external +negative consumption + + align:start position:0% +negative consumption + + + align:start position:0% +negative consumption +externality is when your neighbor in the + + align:start position:0% +externality is when your neighbor in the + + + align:start position:0% +externality is when your neighbor in the +door room next to you plays their music + + align:start position:0% +door room next to you plays their music + + + align:start position:0% +door room next to you plays their music +too + + align:start position:0% +too + + + align:start position:0% +too +loud okay that they consumtion they are + + align:start position:0% +loud okay that they consumtion they are + + + align:start position:0% +loud okay that they consumtion they are +choosing the the volume which optimizes + + align:start position:0% +choosing the the volume which optimizes + + + align:start position:0% +choosing the the volume which optimizes +the Music Experience for them the + + align:start position:0% +the Music Experience for them the + + + align:start position:0% +the Music Experience for them the +benefits and costs they're weighing off + + align:start position:0% +benefits and costs they're weighing off + + + align:start position:0% +benefits and costs they're weighing off +they're not accounting for the fact it's + + align:start position:0% +they're not accounting for the fact it's + + + align:start position:0% +they're not accounting for the fact it's +making it harder for you to study now do + + align:start position:0% +making it harder for you to study now do + + + align:start position:0% +making it harder for you to study now do +you ever go to your neighbor and say + + align:start position:0% +you ever go to your neighbor and say + + + align:start position:0% +you ever go to your neighbor and say +look I've calculated that this ladder + + align:start position:0% +look I've calculated that this ladder + + + align:start position:0% +look I've calculated that this ladder +music will cause me to do five points + + align:start position:0% +music will cause me to do five points + + + align:start position:0% +music will cause me to do five points +worse on my tests which will affect my + + align:start position:0% +worse on my tests which will affect my + + + align:start position:0% +worse on my tests which will affect my +lifetime earnings by this amount pay me + + align:start position:0% +lifetime earnings by this amount pay me + + + align:start position:0% +lifetime earnings by this amount pay me +this or turn down the music no you + + align:start position:0% +this or turn down the music no you + + + align:start position:0% +this or turn down the music no you +either ignore it or tell them to stop it + + align:start position:0% +either ignore it or tell them to stop it + + + align:start position:0% +either ignore it or tell them to stop it +you don't tell them to shut it off okay + + align:start position:0% +you don't tell them to shut it off okay + + + align:start position:0% +you don't tell them to shut it off okay +we don't do coing negotiations in + + align:start position:0% +we don't do coing negotiations in + + + align:start position:0% +we don't do coing negotiations in +reality okay and as a result this is why + + align:start position:0% +reality okay and as a result this is why + + + align:start position:0% +reality okay and as a result this is why +we need to bring in Government + + align:start position:0% + + + + align:start position:0% + +Solutions the government needs to step + + align:start position:0% +Solutions the government needs to step + + + align:start position:0% +Solutions the government needs to step +in and solve the problem of + + align:start position:0% +in and solve the problem of + + + align:start position:0% +in and solve the problem of +externalities now how can the government + + align:start position:0% +externalities now how can the government + + + align:start position:0% +externalities now how can the government +solve this problem well one easy example + + align:start position:0% +solve this problem well one easy example + + + align:start position:0% +solve this problem well one easy example +is they can just + + align:start position:0% +is they can just + + + align:start position:0% +is they can just +regulate they can just regulate they + + align:start position:0% +regulate they can just regulate they + + + align:start position:0% +regulate they can just regulate they +could say if the government knows what + + align:start position:0% +could say if the government knows what + + + align:start position:0% +could say if the government knows what +the social opal production is it can + + align:start position:0% +the social opal production is it can + + + align:start position:0% +the social opal production is it can +just impose it so for example let's go + + align:start position:0% +just impose it so for example let's go + + + align:start position:0% +just impose it so for example let's go +back to our steel plants example okay + + align:start position:0% +back to our steel plants example okay + + + align:start position:0% +back to our steel plants example okay +let's go back to figure + + align:start position:0% +let's go back to figure + + + align:start position:0% +let's go back to figure +241 what if the government just came in + + align:start position:0% +241 what if the government just came in + + + align:start position:0% +241 what if the government just came in +and said you know what steel plants + + align:start position:0% +and said you know what steel plants + + + align:start position:0% +and said you know what steel plants +you're producing Q2 that's a socially + + align:start position:0% +you're producing Q2 that's a socially + + + align:start position:0% +you're producing Q2 that's a socially +optimal amount then boom problem solved + + align:start position:0% +optimal amount then boom problem solved + + + align:start position:0% +optimal amount then boom problem solved +we've produced a socially optimal amount + + align:start position:0% +we've produced a socially optimal amount + + + align:start position:0% +we've produced a socially optimal amount +the government through regulation has + + align:start position:0% +the government through regulation has + + + align:start position:0% +the government through regulation has +enforced the social + + align:start position:0% +enforced the social + + + align:start position:0% +enforced the social +Optimum so that would be the the + + align:start position:0% +Optimum so that would be the the + + + align:start position:0% +Optimum so that would be the the +theoretically sort of easiest + + align:start position:0% +theoretically sort of easiest + + + align:start position:0% +theoretically sort of easiest +case the problem in practice is to + + align:start position:0% +case the problem in practice is to + + + align:start position:0% +case the problem in practice is to +determine what Q2 is you need to know a + + align:start position:0% +determine what Q2 is you need to know a + + + align:start position:0% +determine what Q2 is you need to know a +lot you need to know what the demand + + align:start position:0% +lot you need to know what the demand + + + align:start position:0% +lot you need to know what the demand +curve looks like you need to know what + + align:start position:0% +curve looks like you need to know what + + + align:start position:0% +curve looks like you need to know what +the supply curve looks like and you need + + align:start position:0% +the supply curve looks like and you need + + + align:start position:0% +the supply curve looks like and you need +to know the size of the marginal + + align:start position:0% +to know the size of the marginal + + + align:start position:0% +to know the size of the marginal +damage those are three hard things to + + align:start position:0% +damage those are three hard things to + + + align:start position:0% +damage those are three hard things to +learn and in particular we've talked + + align:start position:0% +learn and in particular we've talked + + + align:start position:0% +learn and in particular we've talked +before in the concept of Regulation + + align:start position:0% +before in the concept of Regulation + + + align:start position:0% +before in the concept of Regulation +about why it's very hard to measure + + align:start position:0% +about why it's very hard to measure + + + align:start position:0% +about why it's very hard to measure +these Curves in practice the firms will + + align:start position:0% +these Curves in practice the firms will + + + align:start position:0% +these Curves in practice the firms will +lie to you about what the marginal cost + + align:start position:0% +lie to you about what the marginal cost + + + align:start position:0% +lie to you about what the marginal cost +is it's hard to measure it it's hard to + + align:start position:0% +is it's hard to measure it it's hard to + + + align:start position:0% +is it's hard to measure it it's hard to +consumers to actually reveal what + + align:start position:0% +consumers to actually reveal what + + + align:start position:0% +consumers to actually reveal what +stuff's Worth to them for all the + + align:start position:0% +stuff's Worth to them for all the + + + align:start position:0% +stuff's Worth to them for all the +reasons we talked about it's very hard + + align:start position:0% +reasons we talked about it's very hard + + + align:start position:0% +reasons we talked about it's very hard +to actually in practice measure these + + align:start position:0% +to actually in practice measure these + + + align:start position:0% +to actually in practice measure these +curves so there's a lot of information + + align:start position:0% +curves so there's a lot of information + + + align:start position:0% +curves so there's a lot of information +need to gather to get that + + align:start position:0% +need to gather to get that + + + align:start position:0% +need to gather to get that +right but what if there was a simpler + + align:start position:0% +right but what if there was a simpler + + + align:start position:0% +right but what if there was a simpler +solution what if the government said + + align:start position:0% +solution what if the government said + + + align:start position:0% +solution what if the government said +look I do know the marginal damage but I + + align:start position:0% +look I do know the marginal damage but I + + + align:start position:0% +look I do know the marginal damage but I +don't know what demand and Supply curves + + align:start position:0% +don't know what demand and Supply curves + + + align:start position:0% +don't know what demand and Supply curves +look like in fact you don't need to know + + align:start position:0% +look like in fact you don't need to know + + + align:start position:0% +look like in fact you don't need to know +that because what the government can do + + align:start position:0% +that because what the government can do + + + align:start position:0% +that because what the government can do +like I said it can + + align:start position:0% +like I said it can + + + align:start position:0% +like I said it can +regulate which is sort of easy in theory + + align:start position:0% +regulate which is sort of easy in theory + + + align:start position:0% +regulate which is sort of easy in theory +hard in practice the other thing it can + + align:start position:0% +hard in practice the other thing it can + + + align:start position:0% +hard in practice the other thing it can +do corrective + + align:start position:0% + + + + align:start position:0% + +taxation which is imagine if the + + align:start position:0% +taxation which is imagine if the + + + align:start position:0% +taxation which is imagine if the +government went to the steel plant and + + align:start position:0% +government went to the steel plant and + + + align:start position:0% +government went to the steel plant and +said I am going to Levy a tax of the + + align:start position:0% +said I am going to Levy a tax of the + + + align:start position:0% +said I am going to Levy a tax of the +amount MD on every unit you produce all + + align:start position:0% +amount MD on every unit you produce all + + + align:start position:0% +amount MD on every unit you produce all +I know is MD I don't know anything + + align:start position:0% +I know is MD I don't know anything + + + align:start position:0% +I know is MD I don't know anything +else and it's only works MD is constant + + align:start position:0% +else and it's only works MD is constant + + + align:start position:0% +else and it's only works MD is constant +but let's assume I know MD it's constant + + align:start position:0% +but let's assume I know MD it's constant + + + align:start position:0% +but let's assume I know MD it's constant +then I can go to the steel plant and say + + align:start position:0% +then I can go to the steel plant and say + + + align:start position:0% +then I can go to the steel plant and say +I'm going to Levy a taxing of MD what + + align:start position:0% +I'm going to Levy a taxing of MD what + + + align:start position:0% +I'm going to Levy a taxing of MD what +would that do to the steel producer + + align:start position:0% +would that do to the steel producer + + + align:start position:0% +would that do to the steel producer +decision well let's go to figure 24 + + align:start position:0% +decision well let's go to figure 24 + + + align:start position:0% +decision well let's go to figure 24 +44 the steel producer the former e was + + align:start position:0% +44 the steel producer the former e was + + + align:start position:0% +44 the steel producer the former e was +at + + align:start position:0% +at + + + align:start position:0% +at +a now the government is coming along and + + align:start position:0% +a now the government is coming along and + + + align:start position:0% +a now the government is coming along and +saying I'm going to Levy a tax on every + + align:start position:0% +saying I'm going to Levy a tax on every + + + align:start position:0% +saying I'm going to Levy a tax on every +unit you produce a marginal tax of MD + + align:start position:0% +unit you produce a marginal tax of MD + + + align:start position:0% +unit you produce a marginal tax of MD +will that raises their marginal cost by + + align:start position:0% +will that raises their marginal cost by + + + align:start position:0% +will that raises their marginal cost by +the amount MD therefore shifting their + + align:start position:0% +the amount MD therefore shifting their + + + align:start position:0% +the amount MD therefore shifting their +private marginal cost curve up to the + + align:start position:0% +private marginal cost curve up to the + + + align:start position:0% +private marginal cost curve up to the +point where it equals the social + + align:start position:0% +point where it equals the social + + + align:start position:0% +point where it equals the social +marginal cost curve what the government + + align:start position:0% +marginal cost curve what the government + + + align:start position:0% +marginal cost curve what the government +does through corrective taxation is + + align:start position:0% +does through corrective taxation is + + + align:start position:0% +does through corrective taxation is +caused the firm to internalize the + + align:start position:0% +caused the firm to internalize the + + + align:start position:0% +caused the firm to internalize the +externality by basically pricing the + + align:start position:0% +externality by basically pricing the + + + align:start position:0% +externality by basically pricing the +externality it causes the firm to + + align:start position:0% +externality it causes the firm to + + + align:start position:0% +externality it causes the firm to +incorporate that into their + + align:start position:0% +incorporate that into their + + + align:start position:0% +incorporate that into their +decisions + + align:start position:0% +decisions + + + align:start position:0% +decisions +thereby thereby doing so getting to the + + align:start position:0% +thereby thereby doing so getting to the + + + align:start position:0% +thereby thereby doing so getting to the +socially optimal + + align:start position:0% +socially optimal + + + align:start position:0% +socially optimal +outcome so the government can + + align:start position:0% + + + + align:start position:0% + +essentially solve this problem with + + align:start position:0% +essentially solve this problem with + + + align:start position:0% +essentially solve this problem with +fairly limited information knows what MD + + align:start position:0% +fairly limited information knows what MD + + + align:start position:0% +fairly limited information knows what MD +is it can solve this so for example one + + align:start position:0% +is it can solve this so for example one + + + align:start position:0% +is it can solve this so for example one +of my former colleagues Michael + + align:start position:0% +of my former colleagues Michael + + + align:start position:0% +of my former colleagues Michael +greenstone served in the Obama + + align:start position:0% +greenstone served in the Obama + + + align:start position:0% +greenstone served in the Obama +Administration and his main goal there + + align:start position:0% +Administration and his main goal there + + + align:start position:0% +Administration and his main goal there +was to measure what he called the social + + align:start position:0% +was to measure what he called the social + + + align:start position:0% +was to measure what he called the social +cost of carbon which was what is the + + align:start position:0% +cost of carbon which was what is the + + + align:start position:0% +cost of carbon which was what is the +marginal cost of what each unit of + + align:start position:0% +marginal cost of what each unit of + + + align:start position:0% +marginal cost of what each unit of +carbon does in terms of damage through + + align:start position:0% +carbon does in terms of damage through + + + align:start position:0% +carbon does in terms of damage through +global warming obviously incredibly hard + + align:start position:0% +global warming obviously incredibly hard + + + align:start position:0% +global warming obviously incredibly hard +calculation but we have lots of + + align:start position:0% +calculation but we have lots of + + + align:start position:0% +calculation but we have lots of +engineering models about how carbon + + align:start position:0% +engineering models about how carbon + + + align:start position:0% +engineering models about how carbon +affects the environment he computed the + + align:start position:0% +affects the environment he computed the + + + align:start position:0% +affects the environment he computed the +social cost of carbon this is incredibly + + align:start position:0% +social cost of carbon this is incredibly + + + align:start position:0% +social cost of carbon this is incredibly +important because this became a basis + + align:start position:0% +important because this became a basis + + + align:start position:0% +important because this became a basis +for thinking about how we can tax the + + align:start position:0% +for thinking about how we can tax the + + + align:start position:0% +for thinking about how we can tax the +use of carbon if greenstone's + + align:start position:0% +use of carbon if greenstone's + + + align:start position:0% +use of carbon if greenstone's +calculations were right he came up at + + align:start position:0% +calculations were right he came up at + + + align:start position:0% +calculations were right he came up at +the point time was about $50 per ton of + + align:start position:0% +the point time was about $50 per ton of + + + align:start position:0% +the point time was about $50 per ton of +carbon $50 per ton of carbon is + + align:start position:0% +carbon $50 per ton of carbon is + + + align:start position:0% +carbon $50 per ton of carbon is +something like I forget it's something + + align:start position:0% +something like I forget it's something + + + align:start position:0% +something like I forget it's something +like 25 cents a gallon of gas maybe it's + + align:start position:0% +like 25 cents a gallon of gas maybe it's + + + align:start position:0% +like 25 cents a gallon of gas maybe it's +closer to 50 cents I don't remember + + align:start position:0% +closer to 50 cents I don't remember + + + align:start position:0% +closer to 50 cents I don't remember +exactly we could just say look that's + + align:start position:0% +exactly we could just say look that's + + + align:start position:0% +exactly we could just say look that's +the tax every time you use carbon you're + + align:start position:0% +the tax every time you use carbon you're + + + align:start position:0% +the tax every time you use carbon you're +going to pay this tax at a social cost + + align:start position:0% +going to pay this tax at a social cost + + + align:start position:0% +going to pay this tax at a social cost +and we would cause people to internalize + + align:start position:0% +and we would cause people to internalize + + + align:start position:0% +and we would cause people to internalize +the externality we could address global + + align:start position:0% +the externality we could address global + + + align:start position:0% +the externality we could address global +warming with one + + align:start position:0% +warming with one + + + align:start position:0% +warming with one +calculation that one calculation is + + align:start position:0% +calculation that one calculation is + + + align:start position:0% +calculation that one calculation is +simply what is the damage the margin of + + align:start position:0% +simply what is the damage the margin of + + + align:start position:0% +simply what is the damage the margin of +carbon doses does to the world to the US + + align:start position:0% +carbon doses does to the world to the US + + + align:start position:0% +carbon doses does to the world to the US +or the world we have to decide what + + align:start position:0% +or the world we have to decide what + + + align:start position:0% +or the world we have to decide what +we're optimizing and then we're done + + align:start position:0% +we're optimizing and then we're done + + + align:start position:0% +we're optimizing and then we're done +incredibly powerful if you think about + + align:start position:0% +incredibly powerful if you think about + + + align:start position:0% +incredibly powerful if you think about +it okay and this is the beauty of + + align:start position:0% +it okay and this is the beauty of + + + align:start position:0% +it okay and this is the beauty of +corrective + + align:start position:0% +corrective + + + align:start position:0% +corrective +taxation okay note that um what you have + + align:start position:0% +taxation okay note that um what you have + + + align:start position:0% +taxation okay note that um what you have +here is a + + align:start position:0% +here is a + + + align:start position:0% +here is a +let's go back to last + + align:start position:0% +let's go back to last + + + align:start position:0% +let's go back to last +lecture last lecture we talked about the + + align:start position:0% +lecture last lecture we talked about the + + + align:start position:0% +lecture last lecture we talked about the +dead weight loss of + + align:start position:0% +dead weight loss of + + + align:start position:0% +dead weight loss of +Taxation we talked about how taxes + + align:start position:0% +Taxation we talked about how taxes + + + align:start position:0% +Taxation we talked about how taxes +create dead weight loss because they + + align:start position:0% +create dead weight loss because they + + + align:start position:0% +create dead weight loss because they +reduce the quantity produced trades that + + align:start position:0% +reduce the quantity produced trades that + + + align:start position:0% +reduce the quantity produced trades that +are productive are not + + align:start position:0% +are productive are not + + + align:start position:0% +are productive are not +made here we're saying a tax gets rid of + + align:start position:0% +made here we're saying a tax gets rid of + + + align:start position:0% +made here we're saying a tax gets rid of +a dead weight loss it's exactly the + + align:start position:0% +a dead weight loss it's exactly the + + + align:start position:0% +a dead weight loss it's exactly the +opposite why because the trades it's + + align:start position:0% +opposite why because the trades it's + + + align:start position:0% +opposite why because the trades it's +getting rid of are not socially valuable + + align:start position:0% +getting rid of are not socially valuable + + + align:start position:0% +getting rid of are not socially valuable +when you have a negative externality + + align:start position:0% +when you have a negative externality + + + align:start position:0% +when you have a negative externality +there are socially invaluable trades + + align:start position:0% +there are socially invaluable trades + + + align:start position:0% +there are socially invaluable trades +being made all the units consumed + + align:start position:0% +being made all the units consumed + + + align:start position:0% +being made all the units consumed +between q1 and + + align:start position:0% +between q1 and + + + align:start position:0% +between q1 and +Q2 are losers for society so if you go + + align:start position:0% +Q2 are losers for society so if you go + + + align:start position:0% +Q2 are losers for society so if you go +back to figure 241 everything to the + + align:start position:0% +back to figure 241 everything to the + + + align:start position:0% +back to figure 241 everything to the +right of + + align:start position:0% +right of + + + align:start position:0% +right of +Q2 has a social marginal cost above its + + align:start position:0% +Q2 has a social marginal cost above its + + + align:start position:0% +Q2 has a social marginal cost above its +private marginal benefit its social + + align:start position:0% +private marginal benefit its social + + + align:start position:0% +private marginal benefit its social +marginal + + align:start position:0% +marginal + + + align:start position:0% +marginal +benefit those units which are hurting + + align:start position:0% +benefit those units which are hurting + + + align:start position:0% +benefit those units which are hurting +Society so by taxing the firm we are + + align:start position:0% +Society so by taxing the firm we are + + + align:start position:0% +Society so by taxing the firm we are +bringing them to the social margin to + + align:start position:0% +bringing them to the social margin to + + + align:start position:0% +bringing them to the social margin to +the socially optimal outcome so taxes + + align:start position:0% +the socially optimal outcome so taxes + + + align:start position:0% +the socially optimal outcome so taxes +can create dead weight loss taxes can + + align:start position:0% +can create dead weight loss taxes can + + + align:start position:0% +can create dead weight loss taxes can +also get rid of dead weight loss it + + align:start position:0% +also get rid of dead weight loss it + + + align:start position:0% +also get rid of dead weight loss it +depends on your starting point if your + + align:start position:0% +depends on your starting point if your + + + align:start position:0% +depends on your starting point if your +starting point is already the socially + + align:start position:0% +starting point is already the socially + + + align:start position:0% +starting point is already the socially +optimal outcome then taxes create dead + + align:start position:0% +optimal outcome then taxes create dead + + + align:start position:0% +optimal outcome then taxes create dead +weight loss but if you're starting from + + align:start position:0% +weight loss but if you're starting from + + + align:start position:0% +weight loss but if you're starting from +a point of maybe too much production + + align:start position:0% +a point of maybe too much production + + + align:start position:0% +a point of maybe too much production +taxes can reduce dead weight + + align:start position:0% +taxes can reduce dead weight + + + align:start position:0% +taxes can reduce dead weight +loss okay and that's kind of how we uh + + align:start position:0% +loss okay and that's kind of how we uh + + + align:start position:0% +loss okay and that's kind of how we uh +how we think about it okay questions + + align:start position:0% +how we think about it okay questions + + + align:start position:0% +how we think about it okay questions +about that + + align:start position:0% + + + + align:start position:0% + +okay now let's talk about government + + align:start position:0% +okay now let's talk about government + + + align:start position:0% +okay now let's talk about government +policy in practice let's talk about what + + align:start position:0% +policy in practice let's talk about what + + + align:start position:0% +policy in practice let's talk about what +the government does in + + align:start position:0% + + + + align:start position:0% + +practice because this is one of the most + + align:start position:0% +practice because this is one of the most + + + align:start position:0% +practice because this is one of the most +important things the government does is + + align:start position:0% +important things the government does is + + + align:start position:0% +important things the government does is +regulate and address + + align:start position:0% +regulate and address + + + align:start position:0% +regulate and address +externalities and let's talk about the + + align:start position:0% +externalities and let's talk about the + + + align:start position:0% +externalities and let's talk about the +two biggest sources of negative + + align:start position:0% +two biggest sources of negative + + + align:start position:0% +two biggest sources of negative +externalities that we have the first is + + align:start position:0% +externalities that we have the first is + + + align:start position:0% +externalities that we have the first is +environmental + + align:start position:0% + + + + align:start position:0% + +externalities and of course as I said + + align:start position:0% +externalities and of course as I said + + + align:start position:0% +externalities and of course as I said +the mother of all externalities which is + + align:start position:0% +the mother of all externalities which is + + + align:start position:0% +the mother of all externalities which is +global warming this is it this is the + + align:start position:0% +global warming this is it this is the + + + align:start position:0% +global warming this is it this is the +most important external that exists it's + + align:start position:0% +most important external that exists it's + + + align:start position:0% +most important external that exists it's +it's an existential threat to life on + + align:start position:0% +it's an existential threat to life on + + + align:start position:0% +it's an existential threat to life on +Earth okay and it is a classic + + align:start position:0% +Earth okay and it is a classic + + + align:start position:0% +Earth okay and it is a classic +externality because our use of carbon + + align:start position:0% +externality because our use of carbon + + + align:start position:0% +externality because our use of carbon +our little use of carbon is creating + + align:start position:0% +our little use of carbon is creating + + + align:start position:0% +our little use of carbon is creating +damage to the entire future of the world + + align:start position:0% +damage to the entire future of the world + + + align:start position:0% +damage to the entire future of the world +okay so it's a classicality when I drive + + align:start position:0% +okay so it's a classicality when I drive + + + align:start position:0% +okay so it's a classicality when I drive +my car I don't acknowledge the damage + + align:start position:0% +my car I don't acknowledge the damage + + + align:start position:0% +my car I don't acknowledge the damage +that's being + + align:start position:0% +that's being + + + align:start position:0% +that's being +done okay so basically uh and we all + + align:start position:0% +done okay so basically uh and we all + + + align:start position:0% +done okay so basically uh and we all +know how terrible global warming is I + + align:start position:0% +know how terrible global warming is I + + + align:start position:0% +know how terrible global warming is I +don't have to give you the scary facts + + align:start position:0% +don't have to give you the scary facts + + + align:start position:0% +don't have to give you the scary facts +uh carbon dioxide in the atmosphere is + + align:start position:0% +uh carbon dioxide in the atmosphere is + + + align:start position:0% +uh carbon dioxide in the atmosphere is +now its highest level in 400,000 years + + align:start position:0% +now its highest level in 400,000 years + + + align:start position:0% +now its highest level in 400,000 years +um temperatures have risen by more than + + align:start position:0% +um temperatures have risen by more than + + + align:start position:0% +um temperatures have risen by more than +one degree Fahrenheit in the last 70 + + align:start position:0% +one degree Fahrenheit in the last 70 + + + align:start position:0% +one degree Fahrenheit in the last 70 +years which is the most rapid increase + + align:start position:0% +years which is the most rapid increase + + + align:start position:0% +years which is the most rapid increase +in the last 10,000 years um what you + + align:start position:0% +in the last 10,000 years um what you + + + align:start position:0% +in the last 10,000 years um what you +might not know is how bad it's going to + + align:start position:0% +might not know is how bad it's going to + + + align:start position:0% +might not know is how bad it's going to +be uh basically scientists predict that + + align:start position:0% +be uh basically scientists predict that + + + align:start position:0% +be uh basically scientists predict that +by the end of the century uh 20 to 40% + + align:start position:0% +by the end of the century uh 20 to 40% + + + align:start position:0% +by the end of the century uh 20 to 40% +of Bangladesh will be underwater Cape + + align:start position:0% +of Bangladesh will be underwater Cape + + + align:start position:0% +of Bangladesh will be underwater Cape +cot will be gone much of Florida will be + + align:start position:0% +cot will be gone much of Florida will be + + + align:start position:0% +cot will be gone much of Florida will be +gone + + align:start position:0% +gone + + + align:start position:0% +gone +um and the economic D the economic + + align:start position:0% +um and the economic D the economic + + + align:start position:0% +um and the economic D the economic +damage to Society on the order of10 + + align:start position:0% +damage to Society on the order of10 + + + align:start position:0% +damage to Society on the order of10 +trillion uh uh in terms of uh in terms + + align:start position:0% +trillion uh uh in terms of uh in terms + + + align:start position:0% +trillion uh uh in terms of uh in terms +of economic damage indeed the the world + + align:start position:0% +of economic damage indeed the the world + + + align:start position:0% +of economic damage indeed the the world +as a whole will be about 10% poor by + + align:start position:0% +as a whole will be about 10% poor by + + + align:start position:0% +as a whole will be about 10% poor by +2100 uh if uh through the physical + + align:start position:0% +2100 uh if uh through the physical + + + align:start position:0% +2100 uh if uh through the physical +damage done by global warming okay so + + align:start position:0% +damage done by global warming okay so + + + align:start position:0% +damage done by global warming okay so +what could the government do well I just + + align:start position:0% +what could the government do well I just + + + align:start position:0% +what could the government do well I just +described an easy answer corrective + + align:start position:0% +described an easy answer corrective + + + align:start position:0% +described an easy answer corrective +taxation we use engineering models to + + align:start position:0% +taxation we use engineering models to + + + align:start position:0% +taxation we use engineering models to +compute the social cost of carbon like + + align:start position:0% +compute the social cost of carbon like + + + align:start position:0% +compute the social cost of carbon like +greenstone had us do and + + align:start position:0% +greenstone had us do and + + + align:start position:0% +greenstone had us do and +we say okay we're going to put that into + + align:start position:0% +we say okay we're going to put that into + + + align:start position:0% +we say okay we're going to put that into +a tax we'll basically compute for every + + align:start position:0% +a tax we'll basically compute for every + + + align:start position:0% +a tax we'll basically compute for every +carbon producing activity how much + + align:start position:0% +carbon producing activity how much + + + align:start position:0% +carbon producing activity how much +carbon it produces and we'll tax it + + align:start position:0% +carbon it produces and we'll tax it + + + align:start position:0% +carbon it produces and we'll tax it +accordingly + + align:start position:0% +accordingly + + + align:start position:0% +accordingly +indeed Europe does this a lot if you've + + align:start position:0% +indeed Europe does this a lot if you've + + + align:start position:0% +indeed Europe does this a lot if you've +ever driven in Europe gas even at + + align:start position:0% +ever driven in Europe gas even at + + + align:start position:0% +ever driven in Europe gas even at +today's high prices is about twice as + + align:start position:0% +today's high prices is about twice as + + + align:start position:0% +today's high prices is about twice as +expensive in Europe about twice as much + + align:start position:0% +expensive in Europe about twice as much + + + align:start position:0% +expensive in Europe about twice as much +per gallon of gas in Europe it's hard to + + align:start position:0% +per gallon of gas in Europe it's hard to + + + align:start position:0% +per gallon of gas in Europe it's hard to +mislead if you see the signs because + + align:start position:0% +mislead if you see the signs because + + + align:start position:0% +mislead if you see the signs because +it's done by leader it's all you got to + + align:start position:0% +it's done by leader it's all you got to + + + align:start position:0% +it's done by leader it's all you got to +convert but it's basically about twice + + align:start position:0% +convert but it's basically about twice + + + align:start position:0% +convert but it's basically about twice +as expensive why because of + + align:start position:0% +as expensive why because of + + + align:start position:0% +as expensive why because of +taxes because European nations + + align:start position:0% +taxes because European nations + + + align:start position:0% +taxes because European nations +significantly tax gasoline we tax + + align:start position:0% +significantly tax gasoline we tax + + + align:start position:0% +significantly tax gasoline we tax +gasoline but at a much much lower + + align:start position:0% +gasoline but at a much much lower + + + align:start position:0% +gasoline but at a much much lower +level okay they have much higher taxes + + align:start position:0% +level okay they have much higher taxes + + + align:start position:0% +level okay they have much higher taxes +now so the easy answer is let's just tax + + align:start position:0% +now so the easy answer is let's just tax + + + align:start position:0% +now so the easy answer is let's just tax +gas here the problem is + + align:start position:0% +gas here the problem is + + + align:start position:0% +gas here the problem is +political Bill Clinton who was president + + align:start position:0% +political Bill Clinton who was president + + + align:start position:0% +political Bill Clinton who was president +had a lot of controversies during his + + align:start position:0% +had a lot of controversies during his + + + align:start position:0% +had a lot of controversies during his +presidency one that them talked about a + + align:start position:0% +presidency one that them talked about a + + + align:start position:0% +presidency one that them talked about a +lot is he osed a 3 Cent per gallon tax + + align:start position:0% +lot is he osed a 3 Cent per gallon tax + + + align:start position:0% +lot is he osed a 3 Cent per gallon tax +on gasoline and that was one of the most + + align:start position:0% +on gasoline and that was one of the most + + + align:start position:0% +on gasoline and that was one of the most +consequentially negative things he ever + + align:start position:0% +consequentially negative things he ever + + + align:start position:0% +consequentially negative things he ever +did for his electoral prospects a lot of + + align:start position:0% +did for his electoral prospects a lot of + + + align:start position:0% +did for his electoral prospects a lot of +the reason that Republicans took + + align:start position:0% +the reason that Republicans took + + + align:start position:0% +the reason that Republicans took +Congress in 1994 was because Bill + + align:start position:0% +Congress in 1994 was because Bill + + + align:start position:0% +Congress in 1994 was because Bill +Clinton's 3 Cent a gallon tax proposal + + align:start position:0% +Clinton's 3 Cent a gallon tax proposal + + + align:start position:0% +Clinton's 3 Cent a gallon tax proposal +gas tax + + align:start position:0% +gas tax + + + align:start position:0% +gas tax +proposal so basically we know the right + + align:start position:0% +proposal so basically we know the right + + + align:start position:0% +proposal so basically we know the right +answer the answer economists have pushed + + align:start position:0% +answer the answer economists have pushed + + + align:start position:0% +answer the answer economists have pushed +for for 50 plus years which is a carbon + + align:start position:0% +for for 50 plus years which is a carbon + + + align:start position:0% +for for 50 plus years which is a carbon +tax but politically it's been + + align:start position:0% +tax but politically it's been + + + align:start position:0% +tax but politically it's been +challenging there therefore the + + align:start position:0% +challenging there therefore the + + + align:start position:0% +challenging there therefore the +framework that's been adopted since + + align:start position:0% +framework that's been adopted since + + + align:start position:0% +framework that's been adopted since +1992 is instead Quan + + align:start position:0% +1992 is instead Quan + + + align:start position:0% +1992 is instead Quan +regulation and in particular a cap and + + align:start position:0% +regulation and in particular a cap and + + + align:start position:0% +regulation and in particular a cap and +trade + + align:start position:0% +trade + + + align:start position:0% +trade +system for regulating carbon what that + + align:start position:0% +system for regulating carbon what that + + + align:start position:0% +system for regulating carbon what that +means is we're going to we're going to + + align:start position:0% +means is we're going to we're going to + + + align:start position:0% +means is we're going to we're going to +limit each company is going to limit how + + align:start position:0% +limit each company is going to limit how + + + align:start position:0% +limit each company is going to limit how +much carbon it + + align:start position:0% +much carbon it + + + align:start position:0% +much carbon it +produces okay that's the cap part it's a + + align:start position:0% +produces okay that's the cap part it's a + + + align:start position:0% +produces okay that's the cap part it's a +regulatory + + align:start position:0% +regulatory + + + align:start position:0% +regulatory +Target okay but we're going to allow + + align:start position:0% +Target okay but we're going to allow + + + align:start position:0% +Target okay but we're going to allow +countries to trade to take advantage of + + align:start position:0% +countries to trade to take advantage of + + + align:start position:0% +countries to trade to take advantage of +efficient opportunities let me explain + + align:start position:0% +efficient opportunities let me explain + + + align:start position:0% +efficient opportunities let me explain +what this means so basically um in the + + align:start position:0% +what this means so basically um in the + + + align:start position:0% +what this means so basically um in the +US we do not it is very expensive to + + align:start position:0% +US we do not it is very expensive to + + + align:start position:0% +US we do not it is very expensive to +convert to clean energy and the reason + + align:start position:0% +convert to clean energy and the reason + + + align:start position:0% +convert to clean energy and the reason +is because we built an entire economy + + align:start position:0% +is because we built an entire economy + + + align:start position:0% +is because we built an entire economy +around dirty energy think of a simple + + align:start position:0% +around dirty energy think of a simple + + + align:start position:0% +around dirty energy think of a simple +example if I want a natural gas plant I + + align:start position:0% +example if I want a natural gas plant I + + + align:start position:0% +example if I want a natural gas plant I +got to First tear down the coal plant or + + align:start position:0% +got to First tear down the coal plant or + + + align:start position:0% +got to First tear down the coal plant or +retrofit the coal plant to get the + + align:start position:0% +retrofit the coal plant to get the + + + align:start position:0% +retrofit the coal plant to get the +natural gas plant if you take + + align:start position:0% +natural gas plant if you take + + + align:start position:0% +natural gas plant if you take +China they're building new plants + + align:start position:0% +China they're building new plants + + + align:start position:0% +China they're building new plants +rapidly well it's not that much more + + align:start position:0% +rapidly well it's not that much more + + + align:start position:0% +rapidly well it's not that much more +expensive to build a natural gas plant + + align:start position:0% +expensive to build a natural gas plant + + + align:start position:0% +expensive to build a natural gas plant +than a coal plant so for them it's cheap + + align:start position:0% +than a coal plant so for them it's cheap + + + align:start position:0% +than a coal plant so for them it's cheap +to convert from gold to natural gas + + align:start position:0% +to convert from gold to natural gas + + + align:start position:0% +to convert from gold to natural gas +because they're going to build a plant + + align:start position:0% +because they're going to build a plant + + + align:start position:0% +because they're going to build a plant +anyway they don't have to tear something + + align:start position:0% +anyway they don't have to tear something + + + align:start position:0% +anyway they don't have to tear something +down it's a very crude description of + + align:start position:0% +down it's a very crude description of + + + align:start position:0% +down it's a very crude description of +why it's cheaper but roughly speaking + + align:start position:0% +why it's cheaper but roughly speaking + + + align:start position:0% +why it's cheaper but roughly speaking +it's cheaper for developing + + align:start position:0% +it's cheaper for developing + + + align:start position:0% +it's cheaper for developing +countries to grow to grow in a more + + align:start position:0% +countries to grow to grow in a more + + + align:start position:0% +countries to grow to grow in a more +environmentally sensitive way than us + + align:start position:0% +environmentally sensitive way than us + + + align:start position:0% +environmentally sensitive way than us +for us for us to retrofit our economy + + align:start position:0% +for us for us to retrofit our economy + + + align:start position:0% +for us for us to retrofit our economy +now that's great but if you go to these + + align:start position:0% +now that's great but if you go to these + + + align:start position:0% +now that's great but if you go to these +countries say that they're like you you + + align:start position:0% +countries say that they're like you you + + + align:start position:0% +countries say that they're like you you +guys got to party you put all this + + align:start position:0% +guys got to party you put all this + + + align:start position:0% +guys got to party you put all this +carbon in the air now you want us to fix + + align:start position:0% +carbon in the air now you want us to fix + + + align:start position:0% +carbon in the air now you want us to fix +it no way we get to have air + + align:start position:0% +it no way we get to have air + + + align:start position:0% +it no way we get to have air +conditioning we get to have + + align:start position:0% +conditioning we get to have + + + align:start position:0% +conditioning we get to have +refrigerators all the stuff you guys + + align:start position:0% +refrigerators all the stuff you guys + + + align:start position:0% +refrigerators all the stuff you guys +benefited from for all these years now + + align:start position:0% +benefited from for all these years now + + + align:start position:0% +benefited from for all these years now +we're going to get it so the challenge + + align:start position:0% +we're going to get it so the challenge + + + align:start position:0% +we're going to get it so the challenge +is the quantity idea makes + + align:start position:0% +is the quantity idea makes + + + align:start position:0% +is the quantity idea makes +sense but the problem is how do you get + + align:start position:0% +sense but the problem is how do you get + + + align:start position:0% +sense but the problem is how do you get +the world to buy in and the way you get + + align:start position:0% +the world to buy in and the way you get + + + align:start position:0% +the world to buy in and the way you get +the world to buy in is but through + + align:start position:0% +the world to buy in is but through + + + align:start position:0% +the world to buy in is but through +trading the idea here is let's have + + align:start position:0% +trading the idea here is let's have + + + align:start position:0% +trading the idea here is let's have +permits of how much carbon can be + + align:start position:0% +permits of how much carbon can be + + + align:start position:0% +permits of how much carbon can be +polluted and let's make those permits + + align:start position:0% +polluted and let's make those permits + + + align:start position:0% +polluted and let's make those permits +tradable so the US can say to China look + + align:start position:0% +tradable so the US can say to China look + + + align:start position:0% +tradable so the US can say to China look +it's very expensive for us to reduce + + align:start position:0% +it's very expensive for us to reduce + + + align:start position:0% +it's very expensive for us to reduce +carbon it's less expensive for you so + + align:start position:0% +carbon it's less expensive for you so + + + align:start position:0% +carbon it's less expensive for you so +what I'm going to do is I'm going to buy + + align:start position:0% +what I'm going to do is I'm going to buy + + + align:start position:0% +what I'm going to do is I'm going to buy +from + + align:start position:0% +from + + + align:start position:0% +from +you your clean production I'm going to + + align:start position:0% +you your clean production I'm going to + + + align:start position:0% +you your clean production I'm going to +essentially pay you off to the reduction + + align:start position:0% +essentially pay you off to the reduction + + + align:start position:0% +essentially pay you off to the reduction +that I would otherwise have to do so in + + align:start position:0% +that I would otherwise have to do so in + + + align:start position:0% +that I would otherwise have to do so in +other words instead of inefficiently the + + align:start position:0% +other words instead of inefficiently the + + + align:start position:0% +other words instead of inefficiently the +US reducing pollution a lot and China + + align:start position:0% +US reducing pollution a lot and China + + + align:start position:0% +US reducing pollution a lot and China +not much we're going to more efficiently + + align:start position:0% +not much we're going to more efficiently + + + align:start position:0% +not much we're going to more efficiently +have the US send China a bunch of money + + align:start position:0% +have the US send China a bunch of money + + + align:start position:0% +have the US send China a bunch of money +and have China do the pollution + + align:start position:0% +and have China do the pollution + + + align:start position:0% +and have China do the pollution +reduction and you know it's the same + + align:start position:0% +reduction and you know it's the same + + + align:start position:0% +reduction and you know it's the same +outcome because it's global warming a + + align:start position:0% +outcome because it's global warming a + + + align:start position:0% +outcome because it's global warming a +unit of carbon in the air doesn't matter + + align:start position:0% +unit of carbon in the air doesn't matter + + + align:start position:0% +unit of carbon in the air doesn't matter +where it came from we are totally IND + + align:start position:0% +where it came from we are totally IND + + + align:start position:0% +where it came from we are totally IND +different worldwide where carbon comes + + align:start position:0% +different worldwide where carbon comes + + + align:start position:0% +different worldwide where carbon comes +from so if we have someone who can + + align:start position:0% +from so if we have someone who can + + + align:start position:0% +from so if we have someone who can +produce it more efficiently and some + + align:start position:0% +produce it more efficiently and some + + + align:start position:0% +produce it more efficiently and some +produce it less efficiently it makes + + align:start position:0% +produce it less efficiently it makes + + + align:start position:0% +produce it less efficiently it makes +sense for the less efficient guy to + + align:start position:0% +sense for the less efficient guy to + + + align:start position:0% +sense for the less efficient guy to +bribe the more efficient guy and that's + + align:start position:0% +bribe the more efficient guy and that's + + + align:start position:0% +bribe the more efficient guy and that's +how we get this system to + + align:start position:0% +how we get this system to + + + align:start position:0% +how we get this system to +work okay okay now this is a brilliant + + align:start position:0% +work okay okay now this is a brilliant + + + align:start position:0% +work okay okay now this is a brilliant +Insight that economists once again dude + + align:start position:0% +Insight that economists once again dude + + + align:start position:0% +Insight that economists once again dude +Economist pioneered for many years + + align:start position:0% +Economist pioneered for many years + + + align:start position:0% +Economist pioneered for many years +environmentalists were were against this + + align:start position:0% +environmentalists were were against this + + + align:start position:0% +environmentalists were were against this +they've adopted it um and this is how we + + align:start position:0% +they've adopted it um and this is how we + + + align:start position:0% +they've adopted it um and this is how we +try to regulate carbon now the problem + + align:start position:0% +try to regulate carbon now the problem + + + align:start position:0% +try to regulate carbon now the problem +is it's still politically enormously + + align:start position:0% +is it's still politically enormously + + + align:start position:0% +is it's still politically enormously +challenging because ultimately the costs + + align:start position:0% +challenging because ultimately the costs + + + align:start position:0% +challenging because ultimately the costs +of using carbon have to one way or + + align:start position:0% +of using carbon have to one way or + + + align:start position:0% +of using carbon have to one way or +another go up we will never really solve + + align:start position:0% +another go up we will never really solve + + + align:start position:0% +another go up we will never really solve +the problem of global warming until we + + align:start position:0% +the problem of global warming until we + + + align:start position:0% +the problem of global warming until we +make the cost of + + align:start position:0% +make the cost of + + + align:start position:0% +make the cost of +carbon feature the damage they're doing + + align:start position:0% +carbon feature the damage they're doing + + + align:start position:0% +carbon feature the damage they're doing +okay now the Biden Administration took a + + align:start position:0% +okay now the Biden Administration took a + + + align:start position:0% +okay now the Biden Administration took a +somewhat different T to this they said + + align:start position:0% +somewhat different T to this they said + + + align:start position:0% +somewhat different T to this they said +look economists for years have been + + align:start position:0% +look economists for years have been + + + align:start position:0% +look economists for years have been +saying tax carbon regulate carbon + + align:start position:0% +saying tax carbon regulate carbon + + + align:start position:0% +saying tax carbon regulate carbon +politically we're getting nowhere here's + + align:start position:0% +politically we're getting nowhere here's + + + align:start position:0% +politically we're getting nowhere here's +a different idea let's subsidize green + + align:start position:0% +a different idea let's subsidize green + + + align:start position:0% +a different idea let's subsidize green +energy remember the opposite of a tax is + + align:start position:0% +energy remember the opposite of a tax is + + + align:start position:0% +energy remember the opposite of a tax is +a subsidy so instead of trying to tax + + align:start position:0% +a subsidy so instead of trying to tax + + + align:start position:0% +a subsidy so instead of trying to tax +the bad stuff let's subsidize the good + + align:start position:0% +the bad stuff let's subsidize the good + + + align:start position:0% +the bad stuff let's subsidize the good +stuff and the inflation reduction act + + align:start position:0% +stuff and the inflation reduction act + + + align:start position:0% +stuff and the inflation reduction act +which was passed last year has hundreds + + align:start position:0% +which was passed last year has hundreds + + + align:start position:0% +which was passed last year has hundreds +of billions of dollars for subsidies + + align:start position:0% +of billions of dollars for subsidies + + + align:start position:0% +of billions of dollars for subsidies +things like a $7,500 tax credit if you + + align:start position:0% +things like a $7,500 tax credit if you + + + align:start position:0% +things like a $7,500 tax credit if you +buy a us-made electric vehicle subsidies + + align:start position:0% +buy a us-made electric vehicle subsidies + + + align:start position:0% +buy a us-made electric vehicle subsidies +for discovering new uh new sources of + + align:start position:0% +for discovering new uh new sources of + + + align:start position:0% +for discovering new uh new sources of +green energy for carbon capture for + + align:start position:0% +green energy for carbon capture for + + + align:start position:0% +green energy for carbon capture for +hydrogen development Etc basically + + align:start position:0% +hydrogen development Etc basically + + + align:start position:0% +hydrogen development Etc basically +saying look politically it's a lot + + align:start position:0% +saying look politically it's a lot + + + align:start position:0% +saying look politically it's a lot +easier to spend money than tax money so + + align:start position:0% +easier to spend money than tax money so + + + align:start position:0% +easier to spend money than tax money so +let's spend money to try to jump start a + + align:start position:0% +let's spend money to try to jump start a + + + align:start position:0% +let's spend money to try to jump start a +green economy that can move forward + + align:start position:0% +green economy that can move forward + + + align:start position:0% +green economy that can move forward +politically it was + + align:start position:0% +politically it was + + + align:start position:0% +politically it was +brilliant okay practically it's still + + align:start position:0% +brilliant okay practically it's still + + + align:start position:0% +brilliant okay practically it's still +not enough ultim Ely if we're going to + + align:start position:0% +not enough ultim Ely if we're going to + + + align:start position:0% +not enough ultim Ely if we're going to +truly as a world address global war + + align:start position:0% +truly as a world address global war + + + align:start position:0% +truly as a world address global war +we're going to have to make people face + + align:start position:0% +we're going to have to make people face + + + align:start position:0% +we're going to have to make people face +the true price for what they're doing + + align:start position:0% +the true price for what they're doing + + + align:start position:0% +the true price for what they're doing +which is to make carbon more expensive + + align:start position:0% +which is to make carbon more expensive + + + align:start position:0% +which is to make carbon more expensive +okay questions about + + align:start position:0% +okay questions about + + + align:start position:0% +okay questions about +that all right let's talk about the + + align:start position:0% +that all right let's talk about the + + + align:start position:0% +that all right let's talk about the +other big topic the other big source of + + align:start position:0% +other big topic the other big source of + + + align:start position:0% +other big topic the other big source of +negative externalities which is Health + + align:start position:0% +negative externalities which is Health + + + align:start position:0% +negative externalities which is Health +ex negative Health + + align:start position:0% +ex negative Health + + + align:start position:0% +ex negative Health +externalities negative Health + + align:start position:0% +externalities negative Health + + + align:start position:0% +externalities negative Health +externalities so much of there's a + + align:start position:0% +externalities so much of there's a + + + align:start position:0% +externalities so much of there's a +there's a class of goods that are + + align:start position:0% +there's a class of goods that are + + + align:start position:0% +there's a class of goods that are +sometimes called sin Goods smoking + + align:start position:0% +sometimes called sin Goods smoking + + + align:start position:0% +sometimes called sin Goods smoking +drinking driving because it causes uh + + align:start position:0% +drinking driving because it causes uh + + + align:start position:0% +drinking driving because it causes uh +because it causes global warming other + + align:start position:0% +because it causes global warming other + + + align:start position:0% +because it causes global warming other +drugs and much of the consumption that + + align:start position:0% +drugs and much of the consumption that + + + align:start position:0% +drugs and much of the consumption that +we do of these sin Goods imposes + + align:start position:0% +we do of these sin Goods imposes + + + align:start position:0% +we do of these sin Goods imposes +negative externalities on others so for + + align:start position:0% +negative externalities on others so for + + + align:start position:0% +negative externalities on others so for +smoking I already mentioned there's + + align:start position:0% +smoking I already mentioned there's + + + align:start position:0% +smoking I already mentioned there's +higher medical costs we spend about 80 + + align:start position:0% +higher medical costs we spend about 80 + + + align:start position:0% +higher medical costs we spend about 80 +billion dollar a year in medical costs + + align:start position:0% +billion dollar a year in medical costs + + + align:start position:0% +billion dollar a year in medical costs +due to smoking related + + align:start position:0% +due to smoking related + + + align:start position:0% +due to smoking related +illness um there's secondhand smoke + + align:start position:0% +illness um there's secondhand smoke + + + align:start position:0% +illness um there's secondhand smoke +there's fires thousands of people die + + align:start position:0% +there's fires thousands of people die + + + align:start position:0% +there's fires thousands of people die +every year in fire started by smoke ERS + + align:start position:0% +every year in fire started by smoke ERS + + + align:start position:0% +every year in fire started by smoke ERS +etc for drinking this drunk driving we + + align:start position:0% +etc for drinking this drunk driving we + + + align:start position:0% +etc for drinking this drunk driving we +have 13,000 deaths a year and 400,000 + + align:start position:0% +have 13,000 deaths a year and 400,000 + + + align:start position:0% +have 13,000 deaths a year and 400,000 +injuries a year due to drunk driving + + align:start position:0% +injuries a year due to drunk driving + + + align:start position:0% +injuries a year due to drunk driving +classic externality if I drive when I + + align:start position:0% +classic externality if I drive when I + + + align:start position:0% +classic externality if I drive when I +decide to get behind the wheel okay I'm + + align:start position:0% +decide to get behind the wheel okay I'm + + + align:start position:0% +decide to get behind the wheel okay I'm +weighing the benefits and cost of + + align:start position:0% +weighing the benefits and cost of + + + align:start position:0% +weighing the benefits and cost of +driving drunk I'm not accounting for the + + align:start position:0% +driving drunk I'm not accounting for the + + + align:start position:0% +driving drunk I'm not accounting for the +fact that I might ruin your life or ruin + + align:start position:0% +fact that I might ruin your life or ruin + + + align:start position:0% +fact that I might ruin your life or ruin +your family's + + align:start position:0% +your family's + + + align:start position:0% +your family's +life okay we have gasoline we talked + + align:start position:0% +life okay we have gasoline we talked + + + align:start position:0% +life okay we have gasoline we talked +about that and Other Drugs indeed drug + + align:start position:0% +about that and Other Drugs indeed drug + + + align:start position:0% +about that and Other Drugs indeed drug +overdose deaths are now the largest + + align:start position:0% +overdose deaths are now the largest + + + align:start position:0% +overdose deaths are now the largest +cause of accidental death in the US + + align:start position:0% +cause of accidental death in the US + + + align:start position:0% +cause of accidental death in the US +about 100,000 people + + align:start position:0% +about 100,000 people + + + align:start position:0% +about 100,000 people +year here's the tricky + + align:start position:0% +year here's the tricky + + + align:start position:0% +year here's the tricky +thing when are things externalities is + + align:start position:0% +thing when are things externalities is + + + align:start position:0% +thing when are things externalities is +not obvious because + + align:start position:0% +not obvious because + + + align:start position:0% +not obvious because +remember the definition it's when my + + align:start position:0% +remember the definition it's when my + + + align:start position:0% +remember the definition it's when my +actions affect you but I don't bear the + + align:start position:0% +actions affect you but I don't bear the + + + align:start position:0% +actions affect you but I don't bear the +consequence think about drunk driving I + + align:start position:0% +consequence think about drunk driving I + + + align:start position:0% +consequence think about drunk driving I +do bear the consequences of getting + + align:start position:0% +do bear the consequences of getting + + + align:start position:0% +do bear the consequences of getting +caught so is that really an externality + + align:start position:0% +caught so is that really an externality + + + align:start position:0% +caught so is that really an externality +because I bear the consequences or let's + + align:start position:0% +because I bear the consequences or let's + + + align:start position:0% +because I bear the consequences or let's +take the case the interesting case of + + align:start position:0% +take the case the interesting case of + + + align:start position:0% +take the case the interesting case of +smoking imagine that someone Sat by + + align:start position:0% +smoking imagine that someone Sat by + + + align:start position:0% +smoking imagine that someone Sat by +themselves on a rock in a nonflammable + + align:start position:0% +themselves on a rock in a nonflammable + + + align:start position:0% +themselves on a rock in a nonflammable +part of the world and smoked themselves + + align:start position:0% +part of the world and smoked themselves + + + align:start position:0% +part of the world and smoked themselves +to + + align:start position:0% +to + + + align:start position:0% +to +death would there be externalities from + + align:start position:0% +death would there be externalities from + + + align:start position:0% +death would there be externalities from +that + + align:start position:0% +that + + + align:start position:0% +that +no okay or imagine that I um smoke and + + align:start position:0% +no okay or imagine that I um smoke and + + + align:start position:0% +no okay or imagine that I um smoke and +uh and it does ultimately raise my + + align:start position:0% +uh and it does ultimately raise my + + + align:start position:0% +uh and it does ultimately raise my +medical costs but my insurers charge me + + align:start position:0% +medical costs but my insurers charge me + + + align:start position:0% +medical costs but my insurers charge me +more indeed for the first time in + + align:start position:0% +more indeed for the first time in + + + align:start position:0% +more indeed for the first time in +history the Affordable Care Act which I + + align:start position:0% +history the Affordable Care Act which I + + + align:start position:0% +history the Affordable Care Act which I +talked about in the last lecture allow + + align:start position:0% +talked about in the last lecture allow + + + align:start position:0% +talked about in the last lecture allow +insurers to charge smokers more for + + align:start position:0% +insurers to charge smokers more for + + + align:start position:0% +insurers to charge smokers more for +their health + + align:start position:0% +their health + + + align:start position:0% +their health +insurance well if the amount I pay in + + align:start position:0% +insurance well if the amount I pay in + + + align:start position:0% +insurance well if the amount I pay in +extra premiums is equal to the damage + + align:start position:0% +extra premiums is equal to the damage + + + align:start position:0% +extra premiums is equal to the damage +I'm doing by smoking then there's no + + align:start position:0% +I'm doing by smoking then there's no + + + align:start position:0% +I'm doing by smoking then there's no +more externality I've internalized it so + + align:start position:0% +more externality I've internalized it so + + + align:start position:0% +more externality I've internalized it so +externalities only arise when they're + + align:start position:0% +externalities only arise when they're + + + align:start position:0% +externalities only arise when they're +not + + align:start position:0% +not + + + align:start position:0% +not +internalized that's a very important + + align:start position:0% +internalized that's a very important + + + align:start position:0% +internalized that's a very important +thing feature to think about okay so the + + align:start position:0% +thing feature to think about okay so the + + + align:start position:0% +thing feature to think about okay so the +key is that people don't bear the + + align:start position:0% +key is that people don't bear the + + + align:start position:0% +key is that people don't bear the +cost okay let's talk about secondhand + + align:start position:0% +cost okay let's talk about secondhand + + + align:start position:0% +cost okay let's talk about secondhand +smoke let's imagine the way secondhand + + align:start position:0% +smoke let's imagine the way secondhand + + + align:start position:0% +smoke let's imagine the way secondhand +smoke works smoke you all cough let's + + align:start position:0% +smoke works smoke you all cough let's + + + align:start position:0% +smoke works smoke you all cough let's +imagine way secondhand smoke worked was + + align:start position:0% +imagine way secondhand smoke worked was + + + align:start position:0% +imagine way secondhand smoke worked was +I took my cigarette and stabbed you in + + align:start position:0% +I took my cigarette and stabbed you in + + + align:start position:0% +I took my cigarette and stabbed you in +the arm with + + align:start position:0% + + + + align:start position:0% + +it let's imagine second smoke work by + + align:start position:0% +it let's imagine second smoke work by + + + align:start position:0% +it let's imagine second smoke work by +taking my cigarettes that that's the + + align:start position:0% +taking my cigarettes that that's the + + + align:start position:0% +taking my cigarettes that that's the +only way second Head smoke could affect + + align:start position:0% +only way second Head smoke could affect + + + align:start position:0% +only way second Head smoke could affect +you would that be an + + align:start position:0% +you would that be an + + + align:start position:0% +you would that be an +externality maybe not because you could + + align:start position:0% +externality maybe not because you could + + + align:start position:0% +externality maybe not because you could +punch me you could sue me you could make + + align:start position:0% +punch me you could sue me you could make + + + align:start position:0% +punch me you could sue me you could make +me bear the cost of that secondhand + + align:start position:0% +me bear the cost of that secondhand + + + align:start position:0% +me bear the cost of that secondhand +smoke why is secondhand smoke an next + + align:start position:0% +smoke why is secondhand smoke an next + + + align:start position:0% +smoke why is secondhand smoke an next +because no one owns the air so you can't + + align:start position:0% +because no one owns the air so you can't + + + align:start position:0% +because no one owns the air so you can't +sue me for smoking in the in in the air + + align:start position:0% +sue me for smoking in the in in the air + + + align:start position:0% +sue me for smoking in the in in the air +unless there's a law that says I can't + + align:start position:0% +unless there's a law that says I can't + + + align:start position:0% +unless there's a law that says I can't +so external + + align:start position:0% +so external + + + align:start position:0% +so external +arise when there's not an individual + + align:start position:0% +arise when there's not an individual + + + align:start position:0% +arise when there's not an individual +remediation that can make the person + + align:start position:0% +remediation that can make the person + + + align:start position:0% +remediation that can make the person +bear the cost okay an important + + align:start position:0% +bear the cost okay an important + + + align:start position:0% +bear the cost okay an important +distinction now when we think about Sin + + align:start position:0% +distinction now when we think about Sin + + + align:start position:0% +distinction now when we think about Sin +consumption of sin Goods the government + + align:start position:0% +consumption of sin Goods the government + + + align:start position:0% +consumption of sin Goods the government +has a wide variety of tools it can try + + align:start position:0% +has a wide variety of tools it can try + + + align:start position:0% +has a wide variety of tools it can try +to use to address the + + align:start position:0% +to use to address the + + + align:start position:0% +to use to address the +externalities okay the first is so what + + align:start position:0% +externalities okay the first is so what + + + align:start position:0% +externalities okay the first is so what +are the government tools one tool is + + align:start position:0% +are the government tools one tool is + + + align:start position:0% +are the government tools one tool is +information + + align:start position:0% +information + + + align:start position:0% +information +the government can tell people + + align:start position:0% +the government can tell people + + + align:start position:0% +the government can tell people +hey what you're doing uh is um is really + + align:start position:0% +hey what you're doing uh is um is really + + + align:start position:0% +hey what you're doing uh is um is really +bad okay uh indeed um for smoking + + align:start position:0% +bad okay uh indeed um for smoking + + + align:start position:0% +bad okay uh indeed um for smoking +information's played a huge role in the + + align:start position:0% +information's played a huge role in the + + + align:start position:0% +information's played a huge role in the +US in the 1950s half of all Americans + + align:start position:0% +US in the 1950s half of all Americans + + + align:start position:0% +US in the 1950s half of all Americans +smoked half of all Americans smoked and + + align:start position:0% +smoked half of all Americans smoked and + + + align:start position:0% +smoked half of all Americans smoked and +of all education groups smoking rate was + + align:start position:0% +of all education groups smoking rate was + + + align:start position:0% +of all education groups smoking rate was +pretty equal across the entire + + align:start position:0% +pretty equal across the entire + + + align:start position:0% +pretty equal across the entire +distribution of + + align:start position:0% +distribution of + + + align:start position:0% +distribution of +income then we started realizing smoking + + align:start position:0% +income then we started realizing smoking + + + align:start position:0% +income then we started realizing smoking +was bad for you and about 1980 smoking + + align:start position:0% +was bad for you and about 1980 smoking + + + align:start position:0% +was bad for you and about 1980 smoking +started to fall but here's what's + + align:start position:0% +started to fall but here's what's + + + align:start position:0% +started to fall but here's what's +fascinating it fell differently by + + align:start position:0% +fascinating it fell differently by + + + align:start position:0% +fascinating it fell differently by +education group smoking when the Highly + + align:start position:0% +education group smoking when the Highly + + + align:start position:0% +education group smoking when the Highly +Educated has virtually + + align:start position:0% +Educated has virtually + + + align:start position:0% +Educated has virtually +disappeared smoking on the less educated + + align:start position:0% +disappeared smoking on the less educated + + + align:start position:0% +disappeared smoking on the less educated +continues to be lower but still + + align:start position:0% +continues to be lower but still + + + align:start position:0% +continues to be lower but still +consequential still about 18% of + + align:start position:0% +consequential still about 18% of + + + align:start position:0% +consequential still about 18% of +American + + align:start position:0% +American + + + align:start position:0% +American +smoke the limitation information is only + + align:start position:0% +smoke the limitation information is only + + + align:start position:0% +smoke the limitation information is only +works if people process it and use it + + align:start position:0% +works if people process it and use it + + + align:start position:0% +works if people process it and use it +and account for it in their + + align:start position:0% +and account for it in their + + + align:start position:0% +and account for it in their +decisions okay so the limit information + + align:start position:0% +decisions okay so the limit information + + + align:start position:0% +decisions okay so the limit information +it's really created the in the + + align:start position:0% +it's really created the in the + + + align:start position:0% +it's really created the in the +information solution has created just + + align:start position:0% +information solution has created just + + + align:start position:0% +information solution has created just +sort of more inqu quity in who smokes in + + align:start position:0% +sort of more inqu quity in who smokes in + + + align:start position:0% +sort of more inqu quity in who smokes in +America so that's one + + align:start position:0% +America so that's one + + + align:start position:0% +America so that's one +solution the other solution is taxes we + + align:start position:0% +solution the other solution is taxes we + + + align:start position:0% +solution the other solution is taxes we +can basically try to get smokers to + + align:start position:0% +can basically try to get smokers to + + + align:start position:0% +can basically try to get smokers to +internalize the + + align:start position:0% +internalize the + + + align:start position:0% +internalize the +externality by taxing + + align:start position:0% +externality by taxing + + + align:start position:0% +externality by taxing +them okay and now that only works of + + align:start position:0% +them okay and now that only works of + + + align:start position:0% +them okay and now that only works of +course if people respond to taxes by + + align:start position:0% +course if people respond to taxes by + + + align:start position:0% +course if people respond to taxes by +smoking less and it turns out they do it + + align:start position:0% +smoking less and it turns out they do it + + + align:start position:0% +smoking less and it turns out they do it +turns out people are somewhat price + + align:start position:0% +turns out people are somewhat price + + + align:start position:0% +turns out people are somewhat price +sensitive just think price estimated + + align:start position:0% +sensitive just think price estimated + + + align:start position:0% +sensitive just think price estimated +elasticity aboutus point4 that for every + + align:start position:0% +elasticity aboutus point4 that for every + + + align:start position:0% +elasticity aboutus point4 that for every +10% you raise cigarette prices people + + align:start position:0% +10% you raise cigarette prices people + + + align:start position:0% +10% you raise cigarette prices people +smoke about 4% less so one way to + + align:start position:0% +smoke about 4% less so one way to + + + align:start position:0% +smoke about 4% less so one way to +address those your tax indeed smoking's + + align:start position:0% +address those your tax indeed smoking's + + + align:start position:0% +address those your tax indeed smoking's +declined enormously it declined slowly + + align:start position:0% +declined enormously it declined slowly + + + align:start position:0% +declined enormously it declined slowly +starting 19 due information it picked up + + align:start position:0% +starting 19 due information it picked up + + + align:start position:0% +starting 19 due information it picked up +rapidly after 2000 due to massive + + align:start position:0% +rapidly after 2000 due to massive + + + align:start position:0% +rapidly after 2000 due to massive +increase in taxes on cigarettes is a lot + + align:start position:0% +increase in taxes on cigarettes is a lot + + + align:start position:0% +increase in taxes on cigarettes is a lot +of what drove the decline in smoking in + + align:start position:0% +of what drove the decline in smoking in + + + align:start position:0% +of what drove the decline in smoking in +the US from 50% to + + align:start position:0% +the US from 50% to + + + align:start position:0% +the US from 50% to +18% okay and that's great but while + + align:start position:0% +18% okay and that's great but while + + + align:start position:0% +18% okay and that's great but while +that's an easy answer for cigarettes + + align:start position:0% +that's an easy answer for cigarettes + + + align:start position:0% +that's an easy answer for cigarettes +it's much harder for other externalities + + align:start position:0% +it's much harder for other externalities + + + align:start position:0% +it's much harder for other externalities +take drinking + + align:start position:0% +take drinking + + + align:start position:0% +take drinking +the first couple drinks might actually + + align:start position:0% +the first couple drinks might actually + + + align:start position:0% +the first couple drinks might actually +be good for you we don't know but + + align:start position:0% +be good for you we don't know but + + + align:start position:0% +be good for you we don't know but +certainly you know many many people + + align:start position:0% +certainly you know many many people + + + align:start position:0% +certainly you know many many people +thing is every cigarette you smoke is + + align:start position:0% +thing is every cigarette you smoke is + + + align:start position:0% +thing is every cigarette you smoke is +bad for you there's no such thing a + + align:start position:0% +bad for you there's no such thing a + + + align:start position:0% +bad for you there's no such thing a +cigarette's good for a harmless + + align:start position:0% +cigarette's good for a harmless + + + align:start position:0% +cigarette's good for a harmless +cigarette every cigarette's bad whereas + + align:start position:0% +cigarette every cigarette's bad whereas + + + align:start position:0% +cigarette every cigarette's bad whereas +drinks much of drinking is not harmful + + align:start position:0% +drinks much of drinking is not harmful + + + align:start position:0% +drinks much of drinking is not harmful +to you indeed if you look at the big + + align:start position:0% +to you indeed if you look at the big + + + align:start position:0% +to you indeed if you look at the big +source of externalities of drinking the + + align:start position:0% +source of externalities of drinking the + + + align:start position:0% +source of externalities of drinking the +biggest source of externality is drunk + + align:start position:0% +biggest source of externality is drunk + + + align:start position:0% +biggest source of externality is drunk +driving well most of us will drink + + align:start position:0% +driving well most of us will drink + + + align:start position:0% +driving well most of us will drink +successfully in our lives without + + align:start position:0% +successfully in our lives without + + + align:start position:0% +successfully in our lives without +driving drunk so if I deal with alcohol + + align:start position:0% +driving drunk so if I deal with alcohol + + + align:start position:0% +driving drunk so if I deal with alcohol +by tax it it's a little bit harder + + align:start position:0% +by tax it it's a little bit harder + + + align:start position:0% +by tax it it's a little bit harder +because what I'm doing is I'm collecting + + align:start position:0% +because what I'm doing is I'm collecting + + + align:start position:0% +because what I'm doing is I'm collecting +a lot of the revenues people who won't + + align:start position:0% +a lot of the revenues people who won't + + + align:start position:0% +a lot of the revenues people who won't +cause the + + align:start position:0% +cause the + + + align:start position:0% +cause the +damage so that's a harder issue to deal + + align:start position:0% +damage so that's a harder issue to deal + + + align:start position:0% +damage so that's a harder issue to deal +with politically that's a little more + + align:start position:0% +with politically that's a little more + + + align:start position:0% +with politically that's a little more +challenging think about the number one + + align:start position:0% +challenging think about the number one + + + align:start position:0% +challenging think about the number one +Health externality facing our society in + + align:start position:0% +Health externality facing our society in + + + align:start position:0% +Health externality facing our society in +The Next Century + + align:start position:0% +The Next Century + + + align:start position:0% +The Next Century +obesity okay one in every three babies + + align:start position:0% +obesity okay one in every three babies + + + align:start position:0% +obesity okay one in every three babies +born in America today will love diabetes + + align:start position:0% +born in America today will love diabetes + + + align:start position:0% +born in America today will love diabetes +before they die one and three because of + + align:start position:0% +before they die one and three because of + + + align:start position:0% +before they die one and three because of +the Obesity crisis more than 30 35 % of + + align:start position:0% +the Obesity crisis more than 30 35 % of + + + align:start position:0% +the Obesity crisis more than 30 35 % of +Americans are + + align:start position:0% +Americans are + + + align:start position:0% +Americans are +obese once again huge inequality I don't + + align:start position:0% +obese once again huge inequality I don't + + + align:start position:0% +obese once again huge inequality I don't +think I've taught an obese student at + + align:start position:0% +think I've taught an obese student at + + + align:start position:0% +think I've taught an obese student at +MIT in 10 + + align:start position:0% +MIT in 10 + + + align:start position:0% +MIT in 10 +years okay but 35% of people your age or + + align:start position:0% +years okay but 35% of people your age or + + + align:start position:0% +years okay but 35% of people your age or +30% of people your age are obese so + + align:start position:0% +30% of people your age are obese so + + + align:start position:0% +30% of people your age are obese so +there's a huge amount of + + align:start position:0% +there's a huge amount of + + + align:start position:0% +there's a huge amount of +inequality okay in that the trick is + + align:start position:0% +inequality okay in that the trick is + + + align:start position:0% +inequality okay in that the trick is +address not through taxation is hard + + align:start position:0% +address not through taxation is hard + + + align:start position:0% +address not through taxation is hard +because we all know eating is actually + + align:start position:0% +because we all know eating is actually + + + align:start position:0% +because we all know eating is actually +pretty good for you you got to eat so + + align:start position:0% +pretty good for you you got to eat so + + + align:start position:0% +pretty good for you you got to eat so +addressing obesity through taxation is + + align:start position:0% +addressing obesity through taxation is + + + align:start position:0% +addressing obesity through taxation is +really + + align:start position:0% +really + + + align:start position:0% +really +hard okay we can't just tax food that's + + align:start position:0% +hard okay we can't just tax food that's + + + align:start position:0% +hard okay we can't just tax food that's +going to really hurt poor people so that + + align:start position:0% +going to really hurt poor people so that + + + align:start position:0% +going to really hurt poor people so that +becomes a place where it's even harder + + align:start position:0% +becomes a place where it's even harder + + + align:start position:0% +becomes a place where it's even harder +to addess through + + align:start position:0% +to addess through + + + align:start position:0% +to addess through +taxation okay a third solution we can do + + align:start position:0% +taxation okay a third solution we can do + + + align:start position:0% +taxation okay a third solution we can do +is + + align:start position:0% + + + + align:start position:0% + +penalties for example losing your + + align:start position:0% +penalties for example losing your + + + align:start position:0% +penalties for example losing your +license if you drive drunk that's great + + align:start position:0% +license if you drive drunk that's great + + + align:start position:0% +license if you drive drunk that's great +because that targets people who are + + align:start position:0% +because that targets people who are + + + align:start position:0% +because that targets people who are +causing the + + align:start position:0% +causing the + + + align:start position:0% +causing the +externality if you guys drink a little + + align:start position:0% +externality if you guys drink a little + + + align:start position:0% +externality if you guys drink a little +and you're fine you're not causing + + align:start position:0% +and you're fine you're not causing + + + align:start position:0% +and you're fine you're not causing +externality so this T targets the person + + align:start position:0% +externality so this T targets the person + + + align:start position:0% +externality so this T targets the person +causing the externality + + align:start position:0% +causing the externality + + + align:start position:0% +causing the externality +the problem is it doesn't really help + + align:start position:0% +the problem is it doesn't really help + + + align:start position:0% +the problem is it doesn't really help +penalties change in Behavior remind + + align:start position:0% +penalties change in Behavior remind + + + align:start position:0% +penalties change in Behavior remind +relies on me making a rational decision + + align:start position:0% +relies on me making a rational decision + + + align:start position:0% +relies on me making a rational decision +to say wow I better not drunk drive + + align:start position:0% +to say wow I better not drunk drive + + + align:start position:0% +to say wow I better not drunk drive +because I'll get caught when you're + + align:start position:0% +because I'll get caught when you're + + + align:start position:0% +because I'll get caught when you're +drunk you're not exactly making rational + + align:start position:0% +drunk you're not exactly making rational + + + align:start position:0% +drunk you're not exactly making rational +decisions problem with penalties is they + + align:start position:0% +decisions problem with penalties is they + + + align:start position:0% +decisions problem with penalties is they +sort of don't work if the sin good + + align:start position:0% +sort of don't work if the sin good + + + align:start position:0% +sort of don't work if the sin good +itself is causing + + align:start position:0% +itself is causing + + + align:start position:0% +itself is causing +irrationality ATT Tax Works because you + + align:start position:0% +irrationality ATT Tax Works because you + + + align:start position:0% +irrationality ATT Tax Works because you +just don't buy it in the first place say + + align:start position:0% +just don't buy it in the first place say + + + align:start position:0% +just don't buy it in the first place say +wow I can't afford that a penalty + + align:start position:0% +wow I can't afford that a penalty + + + align:start position:0% +wow I can't afford that a penalty +doesn't work because it involves Forward + + align:start position:0% +doesn't work because it involves Forward + + + align:start position:0% +doesn't work because it involves Forward +Thinking of the Tye that might not be + + align:start position:0% +Thinking of the Tye that might not be + + + align:start position:0% +Thinking of the Tye that might not be +done why consuming these + + align:start position:0% +done why consuming these + + + align:start position:0% +done why consuming these +Goods okay well then finally we have + + align:start position:0% + + + + align:start position:0% + +illegality illegality we could just say + + align:start position:0% +illegality illegality we could just say + + + align:start position:0% +illegality illegality we could just say +look it's illegal and that's in fact + + align:start position:0% +look it's illegal and that's in fact + + + align:start position:0% +look it's illegal and that's in fact +what we do with hard drugs in this + + align:start position:0% +what we do with hard drugs in this + + + align:start position:0% +what we do with hard drugs in this +country and in Most states still with + + align:start position:0% +country and in Most states still with + + + align:start position:0% +country and in Most states still with +marijuana we make it illegal we say look + + align:start position:0% +marijuana we make it illegal we say look + + + align:start position:0% +marijuana we make it illegal we say look +there's these externalities so not + + align:start position:0% +there's these externalities so not + + + align:start position:0% +there's these externalities so not +people consume it the problem with that + + align:start position:0% +people consume it the problem with that + + + align:start position:0% +people consume it the problem with that +is that is is almost certainly not + + align:start position:0% +is that is is almost certainly not + + + align:start position:0% +is that is is almost certainly not +optimal because + + align:start position:0% +optimal because + + + align:start position:0% +optimal because +remember even if there's externalities + + align:start position:0% +remember even if there's externalities + + + align:start position:0% +remember even if there's externalities +unless those externalities are enormous + + align:start position:0% +unless those externalities are enormous + + + align:start position:0% +unless those externalities are enormous +or + + align:start position:0% +or + + + align:start position:0% +or +infinite some people still derive + + align:start position:0% +infinite some people still derive + + + align:start position:0% +infinite some people still derive +benefits above the social + + align:start position:0% +benefits above the social + + + align:start position:0% +benefits above the social +cost okay some people still right now + + align:start position:0% +cost okay some people still right now + + + align:start position:0% +cost okay some people still right now +say cigarette taxs are close to Optimal + + align:start position:0% +say cigarette taxs are close to Optimal + + + align:start position:0% +say cigarette taxs are close to Optimal +but people still choose to smoke does + + align:start position:0% +but people still choose to smoke does + + + align:start position:0% +but people still choose to smoke does +that mean we should ban smoking not + + align:start position:0% +that mean we should ban smoking not + + + align:start position:0% +that mean we should ban smoking not +necessarily it might mean that they just + + align:start position:0% +necessarily it might mean that they just + + + align:start position:0% +necessarily it might mean that they just +enjoy smoking so much they're willing to + + align:start position:0% +enjoy smoking so much they're willing to + + + align:start position:0% +enjoy smoking so much they're willing to +pay eight bucks a pack for cigarettes + + align:start position:0% +pay eight bucks a pack for cigarettes + + + align:start position:0% +pay eight bucks a pack for cigarettes +so basically the question is whether you + + align:start position:0% +so basically the question is whether you + + + align:start position:0% +so basically the question is whether you +should ban an activity is depend very + + align:start position:0% +should ban an activity is depend very + + + align:start position:0% +should ban an activity is depend very +much on whether you think the + + align:start position:0% +much on whether you think the + + + align:start position:0% +much on whether you think the +externality is so large that overcomes + + align:start position:0% +externality is so large that overcomes + + + align:start position:0% +externality is so large that overcomes +any possible benefit of consuming the + + align:start position:0% +any possible benefit of consuming the + + + align:start position:0% +any possible benefit of consuming the +good that's exactly the way we're having + + align:start position:0% +good that's exactly the way we're having + + + align:start position:0% +good that's exactly the way we're having +now oh and there's one other thing + + align:start position:0% +now oh and there's one other thing + + + align:start position:0% +now oh and there's one other thing +there's another wrinkle which is if you + + align:start position:0% +there's another wrinkle which is if you + + + align:start position:0% +there's another wrinkle which is if you +think about it what is the largest + + align:start position:0% +think about it what is the largest + + + align:start position:0% +think about it what is the largest +source of externalities for illegal + + align:start position:0% +source of externalities for illegal + + + align:start position:0% +source of externalities for illegal +drugs the crime associated with + + align:start position:0% +drugs the crime associated with + + + align:start position:0% +drugs the crime associated with +obtaining and distributing those drugs + + align:start position:0% +obtaining and distributing those drugs + + + align:start position:0% +obtaining and distributing those drugs +which would not happen if they were + + align:start position:0% +which would not happen if they were + + + align:start position:0% +which would not happen if they were +legal so not + + align:start position:0% + + + + align:start position:0% + +only might the extern not be infinite + + align:start position:0% +only might the extern not be infinite + + + align:start position:0% +only might the extern not be infinite +actually making the goods illegal + + align:start position:0% +actually making the goods illegal + + + align:start position:0% +actually making the goods illegal +creates externalities in a way that + + align:start position:0% +creates externalities in a way that + + + align:start position:0% +creates externalities in a way that +taxing them would + + align:start position:0% +taxing them would + + + align:start position:0% +taxing them would +not and this is the argument for why + + align:start position:0% +not and this is the argument for why + + + align:start position:0% +not and this is the argument for why +many people supported legalization of + + align:start position:0% +many people supported legalization of + + + align:start position:0% +many people supported legalization of +marijuana because basically argument was + + align:start position:0% +marijuana because basically argument was + + + align:start position:0% +marijuana because basically argument was +look there's externalities of marijuana + + align:start position:0% +look there's externalities of marijuana + + + align:start position:0% +look there's externalities of marijuana +people driving High still kill people + + align:start position:0% +people driving High still kill people + + + align:start position:0% +people driving High still kill people +it's less bad than drunk driving there's + + align:start position:0% +it's less bad than drunk driving there's + + + align:start position:0% +it's less bad than drunk driving there's +still some + + align:start position:0% +still some + + + align:start position:0% +still some +externalities but they are not large + + align:start position:0% +externalities but they are not large + + + align:start position:0% +externalities but they are not large +enough to rule out the benefits some + + align:start position:0% +enough to rule out the benefits some + + + align:start position:0% +enough to rule out the benefits some +people get from consuming + + align:start position:0% +people get from consuming + + + align:start position:0% +people get from consuming +marijuana and we're creating new extra + + align:start position:0% +marijuana and we're creating new extra + + + align:start position:0% +marijuana and we're creating new extra +Nows by making it illegal all the money + + align:start position:0% +Nows by making it illegal all the money + + + align:start position:0% +Nows by making it illegal all the money +we're spending on police all the money + + align:start position:0% +we're spending on police all the money + + + align:start position:0% +we're spending on police all the money +we spent on jails all the damage that's + + align:start position:0% +we spent on jails all the damage that's + + + align:start position:0% +we spent on jails all the damage that's +done by enforcing those laws and that + + align:start position:0% +done by enforcing those laws and that + + + align:start position:0% +done by enforcing those laws and that +was the argument for making marijuana + + align:start position:0% +was the argument for making marijuana + + + align:start position:0% +was the argument for making marijuana +legal and that's an argument that's one + + align:start position:0% +legal and that's an argument that's one + + + align:start position:0% +legal and that's an argument that's one +in some states and not one in others you + + align:start position:0% +in some states and not one in others you + + + align:start position:0% +in some states and not one in others you +have to ask yourself why does AR going + + align:start position:0% +have to ask yourself why does AR going + + + align:start position:0% +have to ask yourself why does AR going +to apply to marijuana and not cocaine or + + align:start position:0% +to apply to marijuana and not cocaine or + + + align:start position:0% +to apply to marijuana and not cocaine or +heroin okay well if you really want to + + align:start position:0% +heroin okay well if you really want to + + + align:start position:0% +heroin okay well if you really want to +have a co coherent argument you've got + + align:start position:0% +have a co coherent argument you've got + + + align:start position:0% +have a co coherent argument you've got +to argue that the + + align:start position:0% +to argue that the + + + align:start position:0% +to argue that the +externalities from cocaine or heroin are + + align:start position:0% +externalities from cocaine or heroin are + + + align:start position:0% +externalities from cocaine or heroin are +so much larger than + + align:start position:0% +so much larger than + + + align:start position:0% +so much larger than +marijuana that we should allow marijuana + + align:start position:0% +marijuana that we should allow marijuana + + + align:start position:0% +marijuana that we should allow marijuana +to be legal and cocaine and heroin to + + align:start position:0% +to be legal and cocaine and heroin to + + + align:start position:0% +to be legal and cocaine and heroin to +not be legal and in fact you'd be wrong + + align:start position:0% +not be legal and in fact you'd be wrong + + + align:start position:0% +not be legal and in fact you'd be wrong +in fact the externalities from these + + align:start position:0% +in fact the externalities from these + + + align:start position:0% +in fact the externalities from these +Goods largely arrive from the illegality + + align:start position:0% +Goods largely arrive from the illegality + + + align:start position:0% +Goods largely arrive from the illegality +and that is why most economists think + + align:start position:0% +and that is why most economists think + + + align:start position:0% +and that is why most economists think +all drugs should be legal not most + + align:start position:0% +all drugs should be legal not most + + + align:start position:0% +all drugs should be legal not most +economists many economists think all + + align:start position:0% +economists many economists think all + + + align:start position:0% +economists many economists think all +drugs should be legal + + align:start position:0% +drugs should be legal + + + align:start position:0% +drugs should be legal +taxed that we should follow the model + + align:start position:0% +taxed that we should follow the model + + + align:start position:0% +taxed that we should follow the model +that we showed in figure + + align:start position:0% +that we showed in figure + + + align:start position:0% +that we showed in figure +244 we should have corrective taxation + + align:start position:0% +244 we should have corrective taxation + + + align:start position:0% +244 we should have corrective taxation +account for the externality not B the + + align:start position:0% +account for the externality not B the + + + align:start position:0% +account for the externality not B the +good now I hope that discussion made you + + align:start position:0% +good now I hope that discussion made you + + + align:start position:0% +good now I hope that discussion made you +a little + + align:start position:0% +a little + + + align:start position:0% +a little +uncomfortable as it does me and the + + align:start position:0% +uncomfortable as it does me and the + + + align:start position:0% +uncomfortable as it does me and the +reason it made you + + align:start position:0% +reason it made you + + + align:start position:0% +reason it made you +uncomfortable is because the framework + + align:start position:0% +uncomfortable is because the framework + + + align:start position:0% +uncomfortable is because the framework +we're using Embraces key assumptions + + align:start position:0% +we're using Embraces key assumptions + + + align:start position:0% +we're using Embraces key assumptions +that have been unstayed this whole + + align:start position:0% +that have been unstayed this whole + + + align:start position:0% +that have been unstayed this whole +semester assumptions like rationality + + align:start position:0% +semester assumptions like rationality + + + align:start position:0% +semester assumptions like rationality +okay what we're going to do next time is + + align:start position:0% +okay what we're going to do next time is + + + align:start position:0% +okay what we're going to do next time is +ask how everything changes when we + + align:start position:0% +ask how everything changes when we + + + align:start position:0% +ask how everything changes when we +question those assumptions and we're + + align:start position:0% +question those assumptions and we're + + + align:start position:0% +question those assumptions and we're +talking about behavioral + + align:start position:0% +talking about behavioral + + + align:start position:0% +talking about behavioral +economics but I wanted you to leave you + + align:start position:0% +economics but I wanted you to leave you + + + align:start position:0% +economics but I wanted you to leave you +with this to remember absent behavioral + + align:start position:0% +with this to remember absent behavioral + + + align:start position:0% +with this to remember absent behavioral +economics which talk about next time + + align:start position:0% +economics which talk about next time + + + align:start position:0% +economics which talk about next time +it's really hard to justify making + + align:start position:0% +it's really hard to justify making + + + align:start position:0% +it's really hard to justify making +something illegal okay on something like + + align:start position:0% +something illegal okay on something like + + + align:start position:0% +something illegal okay on something like +externality grounds alone all right + + align:start position:0% +externality grounds alone all right + + + align:start position:0% +externality grounds alone all right +let's stop there we'll come back next + + align:start position:0% +let's stop there we'll come back next + + + align:start position:0% +let's stop there we'll come back next +time talk about behavioral economics \ No newline at end of file diff --git a/EWjWv1YBB7A.txt b/EWjWv1YBB7A.txt new file mode 100644 index 0000000000000000000000000000000000000000..aa34f19711c8f45143d00be1934f29fab11444c7 --- /dev/null +++ b/EWjWv1YBB7A.txt @@ -0,0 +1,10532 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +BRADY ENSTAD: Hi, +everybody, we're Team Paul. + +I'm Brady Enstad, +and I've primarily + +been the interviewer +for the project. + +LEXI DIEN: I'm Lexi Dien, and +I've primarily the videographer + +and video editor. + +YI ZHONG: And I'm Yi Zhong. + +I've been the lead +scribe for this project. + +[INAUDIBLE] + +So the first thing +we started with + +is contextual inquiry using +the HAAT model so just + +a quick review of what +the HAAT model is. + +We are looking at the +human activity assistive + +technology and then the +context, and then trying + +to get all the +aspect of the problem + +that we're trying to solve. + +So the first thing we're +going to talk about + +is Paul, our client. + +He has been an amputee +for the past 30 years. + +He worked in IT before, but +for the past two or three years + +he had a really +severe hip problem. + +He couldn't really get around, +and he had to stay home a lot. + +And he had a surgery +in June, so he's + +able to walk again but +with reduced arm strength. + +So that means he wouldn't be +able to walk a long distance. + +He wouldn't be able to +carry really heavy things. + +And this is the AT he uses. + +It's custom-made +forearm crutches. + +It's really expensive, and +it's customized to Paul. + +And so some of the +activities that he + +wanted us to do a project on +are self-standing crutches, + +a mechanism to pull +a suitcase, something + +to carry a slice +of pizza, something + +to carry a cup of coffee, +a self-standing umbrella, + +so he doesn't get +wet in the rain. + +So all of these activities +just kind of show + +that Paul really just wants +to do things that people do + +and that he really wants to get +out there again after this hip + +problem isn't bothering him. + +And we narrowed it +down to this problem; + +this is a quote by +Paul, "it would be nice + +if I can bring my way +of a cup of coffee. + +Wouldn't that be nice?" + +And we think, yeah, so +this is the problem we + +that ended up pursuing. + +And then we dove into the +context of this problem more. + +So looking at it from +a few perspectives, + +so culturally he doesn't +want to use a wheelchair. + +Like I said, he had +a hip problem before, + +so he had to be on +an electric scooter, + +and he actually +didn't like that all. + +He wants to use crutches. + +He wants to be able to stand. + +But because of the +nature of his injury, + +he couldn't use prosthetics, +so he had to use crutches. + +And socially his wife helps +him with many activities, + +including bringing him coffee. + +But his wife does have +work, so he needs to do this + +by himself when he's at home. + +And physically he just wants +to do this in his apartment. + +When he brews a cup of +coffee in the morning. + +He wants to be able to +carry it to the living room, + +something like simple like that. + +And looking at it one +statement, so this + +is our problem +statement-- a design, + +a mechanism, that help him carry +a cup of coffee around his home + +without spilling, +and such that he + +doesn't have to grab onto it. + +And this is the way he +carries it right now. + +It's kind of a grip +and then while trying + +to use crutches at the same +time, so you can imagine, + +it's really tough. + +And we kind of break it down +to two main problems, which + +is how do we do it hands-free, +so he doesn't have to hold it, + +and how do we do no-spill, +so he doesn't spill coffee + +on his hands. + +And I'll let Lexi talk +about the success metrics. + +LEXI DIEN: So right +now, basically, Paul + +can carry a cup of coffee +around with that claw grip, + +and he can only fill +it about a third + +full if he doesn't want to +spill it all over his hands + +or on the floor. + +We'd like to make that a +larger amount of coffee, + +and we'd like to make sure +that it isn't spilled. + +So for a livable goal we +decided that maybe the coffee + +would be 2/3 full and +he could not spill it. + +And then as an +ambitious goal, we + +would say 3/4 full +and also no spill. + +Some other additional +things we talked about + +were making it easy to +remove from his crutch + +or from whatever it is; +the technology is just + +easy to use and take away. + +And so we said 20 seconds for +a livable and then 10 seconds + +preferably. + +We want it to be +as quick possible. + +We also decided that +we wanted to take + +Paul's perspective into this. + +I think that's very important. + +We wanted, especially, +him to rate + +it, and we're hoping ambitiously +to get an 8 out of 10. + +More livably, we +think a 6 out of 10 + +will be something +that we'd accept, + +but we really want to get as +high as possible on his rating. + +And the last thing we +wanted to make sure + +is that we actually are +able to use it with a mug. + +He uses his own mugs, and wants +to be able to use his own mugs. + +So we want to make sure that +it works for at least that mug, + +and preferably it works +for a lot of his mugs + +or all of his mugs. + +So we're going to show you +the video that we put together + +that gives you a little bit +more background into Paul. + +[VIDEO PLAYBACK] + +-You know, it would be +just nice if I could + +bring my wife cup of coffee. + +I mean, wouldn't that be nice? + +My name's Paul [? Nershimski. ?] +I'm 62 years old. + +I've been disabled +since I was 24. + +-Paul uses forearm crutches +because his imputation + +doesn't allow for a prosthetic. + +Despite the fact that his +forearm crutches don't really + +let him carry things while +he's walking, for Paul, + +the most important +thing is to be + +able to move around +and go places. + +-And one the big +dreams of my life + +has been to be able to +carry around a coffee + +cup around the house +like a normal human + +being with burning my +fingers and ruining the rug. + +-What really drew me to Paul +was just the very simple nature + +of what he wanted, something +that you and I take + +for granted, just the ability +to transport food and even just + +a cup of coffee from his +crutches to his living room + +without spilling it +all over his floor. + +-Cup full of water, +not far from the brim, + +I would have to carry it like +that, with my hand wrapped + +around the crutch handle. + +And maybe you can realized +that would be a horror show. + +-He wants to carry +a cup of coffee + +around without burning himself, +and that's very, very different + +from other people, other +clients, had in mind. + +But this project's +very mechanical. + +It' very simple, yet a +really challenging problem. + +-That may seem like not +much to most people, + +but it's huge to me. + +-There are many, many +ideas floating around, + +but one of them is a +gyroscope, something + +that would with the +gyroscopic motion + +that can keep the coffee level +while he's with his crutches. + +And this is one of +the designs that we + +saw online that kind of +resembles what we want to have. + +It's basically a cup +holder that allows + +motion, that allows it to stay +level when there is motion. + +-There's a kind of silicon cover +that goes over the coffee mug, + +and if it gets a good seal, then +it works really, really well. + +-Silicone cover does +wonders-- nothing. + +[LAUGHTER] + +-So you have water in there? + +-Yeah, it's pretty full. + +-Wow, that's great. + +-That really works. + +I mean, that's full. + +I try no to over think things, +get like a real simple thing + +that I couldn't do. + +And you're making it so I'm +going to be able to do it. + +[END PLAYBACK] + +LEXI DIEN: So, as +you saw in the video, + +we've been trying out a +lot of different prototypes + +with Paul, mainly things +that we found online, + +some things like this on-stage +cup holder, which is basically + +a cup holder that can +statically be just clicked + +on to his crutch, and it +doesn't help tipping at all, + +so if it was an open cup, +it would just pour out. + +But it's something that +helps the hands-free aspect. + +And something like the +water bottle holder + +would also do this maybe, +except for it might not + +fit a mug very well. + +So right now we're looking +into some snap-on clamps, + +like this one. + +It would just be easy to +snap on and off of his crutch + +so that he could take +it off and on the crutch + +very easily and very quickly. + +So I'm going to +pass these around + +for people to look at it. + +Some ideas for the +no-spill solution-- as you + +saw, we were thinking +gyroscope maybe. + +It turns out that that's a +little bit more complicated + +than we thought it would be. + +It's a little touchy. + +So we're trying to look a +little bit in a different way. + +The second thing we +did was the CoverFlex, + +which we showed in the video. + +It takes a little bit of time +to put on and off though, + +so we were looking into some +other ways, which one of them + +is this suction cover. + +So this is a mug, very easy. + +I'm going to pour +some water into it + +and then put one of these +section covers on top of it, + +and no water will spill out. + +So we're hoping that this will +be able to work for his mugs + +as well, and work on +that a little bit. + +Another thing that we're looking +into, which is coming in today, + +is this Spill-Not, which is +a device that's specifically + +made to counteract movement. + +When you place a mug +on it, basically, that + +would make it so that it +wouldn't spill hopefully. + +So we're looking into +that a little bit more. + +BRADY ENSTAD: So at +our client meaning + +for the first +prototype, like I said, + +we showed Paul the +on-stage microphone clip, + +and we showed him the +CoverFlex silicon cover, + +and we left those with +him this past week, + +and we're going to go back +on Wednesday after class + +and get is feedback on those. + +He was actually more +excited because we told him + +that the Spill-Not was coming. + +He was more excited about +that than anything else. + +But the CoverFlex, as +you saw in the video, + +actually worked +really, really well. + +The only difficulty with +it is that once you have it + +on and take it off, +like if there's + +been any spillage at all, +it's a little difficult + +to get it back on again, +which is why we decided to go + +with these suction covers. + +The only problem with those is +they might not fit his mugs. + +So there's a +possibility that we'll + +have to do a little bit +more shopping around + +to find larger covers that +will probably fit his mugs. + +That's honestly the biggest +problem is his mugs are huge. + +So coffee addict, or +something, but yeah, + +like I said he's super, duper +excited about the Spill-Not. + +And honestly one of +our biggest visions + +for what will end +up happening is + +that we'll be able to +incorporate the Spill-Not + +with a quick on-and-off +clamp, like the one that's + +going around. + +Like I said, the clamp, it +works really well on-stage, + +but it doesn't really +prevent spilling, + +and it's pretty slow because +it's a screw-on/screw-off type + +mechanism, as opposed +to just a quick clamp. + +He liked the CoverFlex, +but if there's + +something that's easier, +like those suction covers, + +then he would prefer that. + +So for future work, +as I said, we're + +going to be testing more +off-the-shell prototypes, + +different suction +mug covers maybe. + +The bike cup holder, +we haven't entirely + +abandoned that idea yet either. + +And then obviously, +the Spill-Not + +is what we're most +excited about. + +We're going to go get +feedback from Paul. + +And if he has some +feedback for us + +that we can't meet with any +off-the-shelf prototypes, + +then we're just going +to do some customization + +for his final prototype. + +PROFESSOR: So first +of all, you guys + +have scoped this really well, in +the sense that this is a really + +well-defined problem that +you've worked out with Paul. + +And it seems like you're +finding a lot of pieces + +to the solution that are already +out there, that maybe you + +can combine to make something +that's really good for him. + +So I would encourage you, or +have you thought about-- let + +me phrase this as a question. + +Have you thought about +the sustainability + +of your solution? + +So these cover flex things, +for example, how do they fail? + +And how will things break? + +And what is going +to have to replace? + +And sort of what is +the lifetime of what + +you're building for him? + +BRADY ENSTAD: So the great +thing about the CoverFlex + +is that it's actually +oven and dishwasher safe. + +So presumably, it's got a +relatively long life cycle, + +and we're thinking, honestly, +on the order of, hopefully, + +years because it is oven +and dishwasher safe, + +unless he somehow super-duper +heats it beyond what it's rated + +for, which I don't +really know how you'd + +do that because it's oven safe. + +And as far as the clamp, the +hands-free solution goes, + +frankly it's a purely +mechanical systems. + +So unless he finds +some way to snap off + +the clamp, which it could +happen, don't get me wrong, + +but the great thing about +these components that we found + +is that they're actually +relatively inexpensive. + +And so the idea we have +is that after the class + +is over we would leave him +with these part numbers. + +Because he has a computer +at home-- he's tech savvy. + +He used to work in IT-- so +if something were to break, + +he could just purchased +himself another one, + +assuming that there's not a +great deal of customization + +that goes into it. + +And we don't actually know the +scope of customization that's + +going to have to go into it +just yet because, as I said, + +what we're most excited +about is the Spill-Not, + +and we're not really +sure how that's + +going to be incorporated +with the clamp just yet. + +PROFESSOR 2: So I would +just kind of encourage + +as you're thinking about +the failure modes, not just + +the individual failure +modes, but kind + +of the cross-coupled +failure modes-- + +as I was looking at the +seal, one of the ways + +that you release the seal is +by kind of flipping that edge, + +so you want to be careful +that that edge isn't actually + +going to be affected by +whatever your mechanism is + +for holding it. + +So think about the +kind of the coupling + +that you get between +your solutions, + +and not just the independent +issues that you have with them. + +One of the questions that +I had for you was regarding + +your performance metrics, +how you selected those on/off + +times, and how that +related to his function + +versus the mechanical +structure itself? + +And kind of from looking +at some of your video, + +I'm wondering-- +I couldn't really + +tell if he had any additional +tremors or other issues + +as well that might +affect his function that + +might affect that timing. + +So if you could just talk on +that generation of timing? + +BRADY ENSTAD: Yeah, sure, so +honestly, we just asked Paul. + +We said, Paul, how quickly do +you want this thing be put on + +and be taken off? + +And he said, well, +relatively quickly, + +and he wouldn't give +us a solid number. + +So we were just +like, OK, you know, + +20 seconds is a little long. + +10 seconds seems like +a reasonable time. + +The great thing about Paul +is the only disability + +that he has is the fact +that his leg is amputated. + +So doesn't have any +tremors or anything + +else, any other +sort of disability. + +So I mean, as we talked +about actually in lecture + +earlier today, it's +possible as he gets older, + +those hands might start +shaking and that sort of thing. + +But that's actually why +we're excited about the clamp + +is because there's less +precision involved. + +It's just a pretty +simple snapping motion. + +So as far as like +generating those numbers, + +it was just basically a +kind of a general feeling + +we got from Paul, and +we went with, well, + +what do you think +about these numbers? + +And the great thing +about Paul is also + +one of the worst things +he's incredibly laid back, + +so he wasn't particularly +zealous about giving + +us had numbers. + +So he was pretty +willing to along + +with anything that we suggested. + +PROFESSOR 2: What are ways that +you think that you guys might + +be able to validate those +numbers a little bit more + +as you keep going +and looking at some + +of these different designs? + +BRADY ENSTAD: Sure, so if +you take a look at the clamp, + +between positioning +it and snapping it, + +I think you're probably looking +at realistically probably + +less than five seconds. + +It's not real picky about +where you put it on the crutch. + +So obviously, we're +just going to keep + +adjusting those +numbers as what's + +realistic becomes more apparent. + +Like I said, we don't +really know the degree + +of customization we're going to +have to go to yet, especially + +if we're going to +incorporate the Spill-Not. + +So once we get that and we do +a little bit more prototyping, + +I'd be able to give you +more solid answer for that. + +But as of right now, +we don't really know. + +PROFESSOR 3: I am a +coffee aficionado, + +and I just am OCD about +the cup that I have. + +I have two or three +mugs that I just love. + +I can press the Keurig twice, +and it fills it up just right. + +So I get that. + +But I'm wondering, +have you talked + +with this gentleman about +his ability or willingness + +to negotiate? + +To me, one of the +obvious solutions + +would be to have-- because +he has good hand function, + +presumably-- is to +fill up a thermos mug + +and have a simple clip that +you can put on his foreleg + +crutches, walk to a +table, and pour the coffee + +into his delightful cup. + +BRADY ENSTAD: So that's actually +one of the very first thoughts + +that we had, and we +asked Paul about that. + +And his reply honestly +surprised us a little bit. + +He's not honestly +concerned about carrying + +the cup of coffee +so much for himself, + +as it is that he wants +to help his wife out. + +Because while he was stuck in +the wheelchair, he was really, + +really reliant on +her, and so he wants + +to be able to carry a cup +of coffee for his wife. + +And his whole +thing about that is + +that I want to be able +to carry it in the mug + +and just give it +to her, and I don't + +want have to pour it out at the +table or anything like that. + +PROFESSOR 4: One or two quick +questions from the audience. + +AUDIENCE: So his Paul willing to +have something on his crutches, + +or is that [INAUDIBLE], +like the [INAUDIBLE]? + +BRADY ENSTAD: So that's why we +were talking about quick on/off + +times, and the answer to +that is, no, not really. + +He's OK with using it for +the short period of time + +that it takes to transport +the cup of coffee. + +But once he gets +to the couch, he + +wants to be able to take +it off because the way + +that he stores his crutches +when he's sitting down, + +is he puts them on the floor. + +And so if there's +anything attached to them + +that might possibly get in +the way was his concerned. + +So the quicker on/off +time, the better. + +PROFESSOR 4: [INAUDIBLE] +last question, + +then we can have Team Margaret +also begin to set up as well. + +PROFESSOR 3: The other +quick thing I wanted to ask + +is, have you consulted +an occupational therapist + +at all, someone who deals +with these kinds of approaches + +on a daily basis? + +There might be some other simple +solution that-- or maybe not so + +simple solution, +but an established + +solution that someone +has already dealt with. + +Because obviously, amputation +and this kind of injury + +is fairly common and ubiquitous. + +BRADY ENSTAD: And the answer +to that is, no, we haven't. + +But that sounds like +a really great idea, + +so we'll look into that. + +PROFESSOR 4: Thank you. + +BRADY ENSTAD: Thanks. + +TANYA TALKAR: So, hi, everyone. + +We're Team Margaret. + +I'm Tanya. + +LAURA D'AQUILA: I'm Laura. + +TANYA TALKAR: And +Beth his third member, + +but she's unable to get make +it to the presentation today. + +So this is the team. + +I think we might have shown +you this picture last week, + +but this is +Margaret, our client. + +Interesting story +about this picture-- + +she was actually the +one who suggested + +that we take a selfie. + +So she's a great person. + +So a little bit about +her as a person. + +She is an artist, so she loves +to paint, loves to make arts + +and crafts. + +Her room is filled +with a bunch of crafts. + +She's also an advocate, so +she's on the Safety Council + +for The Boston Home, +which means that she's + +talking a lot with residents +to make sure that they are + +comfortable with their +position at The Boston Home + +and everything that's going on. + +And Laura will talk a little +bit about The Boston Home. + +She's also a friend. + +She FaceTimes a lot on her +iPad with friends and family, + +And she's an immensely +helpful mentor, + +not only to us, but also +all of the other residents + +of the Boston Home. + +So about her +disability-- she was + +diagnosed with +multiple sclerosis, + +and she decided on her own +to live at The Boston Home. + +So she has been +at The Boston Home + +for about eight years, gotten +during admission process. + +She gets around on a +motorized wheelchair. + +All of the resonance +have wheelchairs, + +and she's relatively +independent. + +She has some fatigue in terms +of trying to sign documents, + +or after using her iPad for a +while, she will get fatigued, + +and her fingers will drag. + +But she is still +relatively independent. + +And she was a social +worker before she + +came to The Boston +Home, which means + +that all of her thoughts and +actions are really altruistic. + +She's always thinking +about other people. + +LAURA D'AQUILA: +So this over here + +is a picture of The Boston Home. + +It's located in +Dorchester, Massachusetts. + +And Beth, Tanya, and I +go visit it every Friday + +to meet with Margaret, +other residents, and staff + +members of the home. + +To tell you a little +bit more about the home, + +it was founded in 1881 +as a long-term care + +center for adults with +multiple sclerosis + +and other progressive +neurodegenerative diseases. + +The average resident in The +Boston Home is 58 years old, + +and The Boston Home +places great emphasis + +on independence of residents. + +So we'll see later +on that there's + +a lot of assistive +technology that does + +exist within The Boston Home. + +There's 96 residents in the +home and approximately 200 staff + +members. + +And it's a really +nice place to live. + +They have activities, +meetings, other social events, + +and it's known nationally for +providing exceptional care + +to residents. + +And this over here is a picture +of Don, one of our panelists. + +He's done a lot of +great work in the home + +for making sure that +residents do have access + +to assistive technology. + +For example, he mounts iPads +on the motorized wheelchairs + +of residents. + +He also has a 3D +printer that he's + +used to design pieces +of assistive technology. + +TANYA TALKAR: So +specifically, the activity + +that we've been working +with for the past month has + +been the nurse call system +or the call light system. + +And so what this is, +is that residents, + +if they're in their room, can +press a button-- we'll show it + +in a bit-- to call a +nurse and call and aide + +to come and help +them in their room. + +So there's a wired-in +call light system. + +It's a button that it has +been wired to the wall, + +and nurses are currently +trained to place this button + +in the middle of bed. + +Many times though, +it's forgotten about. + +So it's either not placed +in the middle of the better, + +or it's placed in +an unreachable spot. + +So Margaret sometimes +has to come up to a table + +and has to either +pull on the wire + +or pull on sheets to +try and get the button. + +And there's also just no +way of using the system + +if the resident is +outside the home. + +So. + +For example, there was a +resident who had gone outside, + +got stuck in a ditch, and +his wheelchair tipped over, + +and he was unable to call +The Boston Home to let them + +know that this has happened. + +So they had to have someone +who was passing by tell them + +that that happened. + +So this is the +call light system. + +The button is pretty +easy to press. + +It's just like a simple press. + +But, again, it's placed in +this kind of inconvenient spot, + +where Margaret can't reach. + +She doesn't have +much of a reach, + +so she can't reach up to +press the button if need be. + +And so in addition to that, +there's some other issues. + +Only one nurse is allowed to +answer the calls at any time. + +Her name's Angela. + +And so she sit at +the front desk, + +and this takes a +long time if there + +are multiple +residents calling in + +or if she has gone from +the desk and has to address + +another resident's issues. + +So an aide also has to come in +to turn off the call system, + +otherwise it keeps +on beeping, and that + +is quite annoying for both +the resident and the nurse. + +Many times, if there are +two rooms within a suite, + +as it is with Margaret, +so enter a door + +and there are two rooms there, +sometimes the wrong room + +is answered, so you'll have the +nurse call into the other room. + +And since this is +a speaker system, + +if the resident is unable +to speak really loudly, + +or, in Margaret's case, she once +pulling out a chest of drawers + +and it fell on her. + +So she was unable to both +reach the call light system. + +And if she had, +she wouldn't have + +been able to speak loud enough +for the nurse to hear her. + +And actually, to add +to that, so that's + +the reason why we're +planning on using + +an iPad for this solution. + +So we're planning on +creating application, + +because Margaret always +has her iPod with her, + +such that she can just +press a couple of buttons + +and be able to talk with +the nurses directly. + +LAURA D'AQUILA: So to talk more +about assistive technology, + +both what Margaret +herself uses and what + +other residents at +The Boston Home use, + +Margaret, along with +many other residents, + +uses a motorized +wheelchair to get around. + +And Margaret is very tech savvy. + +She owns both an +iPad and an iPhone, + +which she always has with her. + +And she owns a special +stylus so that she's actually + +able to use her iPad and +reach all ends of the screen. + +And they've come in handy +in emergency situations. + +Tanya mentioned the time when +the drawer fell on Margaret + +and she was unable to reach +the existing call light system + +button. + +But fortunately, because +she had her iPhone, + +she was able to call +for help that way. + +And the Tanya had mentioned +that Margaret is an artist, + +and she's able to +use a mouthpiece + +to hold her paintbrush, +and that's something + +that Don had designed for her. + +And along with other +residents in the home, + +Margaret has the call light +system button in her bedroom + +and also in the bathroom. + +So thanks to much of Don's work, +The Boston Home is very open + +to assistive +technology, and it's + +very prevalent +within the home now. + +For example, there exists a +cyber cafe, where resonance + +are able to use computers, and +both the keyboards and mice + +within the cyber cafe are +accessible to the needs + +of the residents with +their limited arm mobility. + +And there are also speech +therapists and occupational + +therapists on site, and these +individuals use technology, + +such as iPads, in +order to assess + +the progress of the residents. + +And Don has added many +features to wheelchairs + +throughout his time +their too, accommodating + +the different needs +of the residents. + +TANYA TALKAR: So to assess +how this application is going + +to work for Margaret and for the +residents, because her vision + +is that at the +end of this, we'll + +be able to have all 35 +residents who are using iPads + +also use the system. + +We have a couple +of success metrics. + +They're mostly qualitative. + +So, one, we just +want to make sure + +that the correct iPad is +being called and answered + +and that the correct +resident is getting aid. + +We will also want to +time the amount of time + +that it takes for a +task to be completed. + +So suppose Margaret +needs a refill of water, + +so the nurse will come in +with the call light system, + +get the request, and then +go back to get the water. + +versus if we have this on the +iPad application, how much time + +that'll take. + +And then just success overall-- +does this application actually + +integrate into the current +system with the nurses? + +Will the nurses actually +end up using the system? + +Will the residents actually end +up using the system as well? + +LAURA D'AQUILA: So +a few weeks ago we + +started discussing with +Margaret potential solutions + +to this problem. + +Tanya had mentioned that we're +going to be using an iPad. + +We work with Margaret to get +her input and her feedback + +to actually develop some +early sketches of what + +her end of this app looked like. + +And then within +the next week, we + +developed this into a +low fidelity iOS app, + +which I'll walk through now. + +So this is the home +screen of the app + +that Margaret is going +to have access to. + +It has two large +by things that are + +color-coded red and black, for +urgent and non-urgent requests. + +And should Margaret +press Non-Urgent Request, + +she's taken to the +next screen, which + +has six potentially customizable +buttons for a common requests + +that Margaret may +have for the nurse. + +For example, if she +needs a cup of water + +or if she wants a nurse +to come to a room, + +if she wants to be able to +video conference with a nurse, + +these are all buttons +that are easily + +accessible for her to press. + +And similarly, if Margaret +presses the Urgent button, + +she's taken directly into +a video call with a nurse. + +And at the bottom, there is +a Cancel Call button for her + +to cancel in the event +that she inadvertently + +pressed the button. + +TANYA TALKAR: So +amazingly enough, + +right after we transferred +this application to her iPad, + +she immediately +went off to go talk + +to some of the other residents +about the application, which + +is great. + +And so some of the feedback +that she came up with + +was that she wanted to make +sure that the buttons were + +large enough, in case residents +end up having some fatigue + +and their fingers start +dragging on the iPad. + +So she uses a stylus, but +not all of the residents do. + +So we just make sure that we +have larger buttons for this. + +She also wanted to make +sure that there was + +an option to type in messages. + +So suppose any of the +requests that a resident + +has isn't on the screen +with six buttons, + +that they will be able to +type in their own customized + +request. + +She also wants to make +sure that she's always + +talking with the nurse +through a video call + +because sometimes her +message or what she wants + +isn't conveyed through text. + +And something that all of the +residents said they wanted + +was that the application +be voice-activated + +because not all of +them are able to press + +the buttons at every +time, and that they'll + +be able to go forward +with this if they + +can't speak super well either. + +LAURA D'AQUILA: So in +addition to Margaret, + +because of the nature of the +system that we're building, + +we actually have an +additional client, + +and that's the nurse on +the other end of the system + +that Margaret's trying to reach. + +So we had mentioned all +of these nice features + +that we want the app to have, +for example, video chat. + +And none of this stuff is +feasible with the existing + +call light system that exists +already within the home. + +So because of that, we're +hoping to bypass the existing + +system altogether and have +the nurse on the other end + +have an iPad or +a computer screen + +as well with an instance +of this app running + +so that she can receive +the requests from Margaret + +on this app. + +So because of this, we've +had to speak with and work + +with Angela, who, +as Tanya mentioned, + +is the nurse on the first floor, +which is Margaret's floor, so + +that we can make sure that +we can accommodate her needs. + +In addition to Margaret's +needs in terms of what + +this application should have. + +And we've also worked +with Don to make sure + +that this app is feasible to +be adopted within the nurse's + +station. + +And within the next +few weeks, we're + +also going to work on speaking +with other management level + +people within The +Boston Home to make sure + +that we're able to get +their go-to as well. + +And one potential thing +that we're still discussing + +is how to acquire a potential +iPad that the nurse would + +need at her station. + +So we're looking into whether +this is something The Boston + +Home would purchase, or +whether it's something + +that we may need to get +with our own team budget. + +So in terms of the timeline, we +spent the first month speaking + +with Margaret, getting +to know her, her needs, + +and what she's looking for +in a potential solution. + +And then in October, +we were able to assess + +in greater detail +the feasibility + +of an iPad-based +solution on both ends. + +We worked with +Margaret and Angela. + +We developed a low fidelity +prototypes for Margaret + +and tested this out +and received feedback. + +And then in November, +our plans include + +developing a low fidelity +prototypes for Angela, + +for the nurses' side of +the nurse call system. + +We hope to receive +feedback from that + +and iterate through +those prototypes as well. + +We also want to work on the +back end of actually sending + +requests from Margaret's +iPad to the nurses' iPads. + +And we want to get video +conferencing set up + +the week after that. + +And then finally, hopefully +by the end of November + +or beginning of +December, we'll have + +an app that's able to +be used within the home + +by not only Margaret, but +potentially other residents + +in the home as well, and we can +continue to test it out and get + +feedback from them. + +TANYA TALKAR: So a +little bit about how + +the logistics for this +project go-- our meetings are + +pretty conversational. + +They're less like an +interview, and more + +just us talking with +Margaret, Angela, Don. + +So Laura is mostly in charge +of the videos and pictures, + +and then Beth and I are the +ones who are taking notes, + +asking the questions. + +And we meet before the meetings +to go over speaking notes + +and go over an agenda +of what exactly + +we want to be accomplished +during the meeting. + +As for division of work for the +application itself, all of us + +are new to iOS development. + +So we're learning +all of this together. + +We're planning on mostly +working on the application + +as a team, all three +of us together. + +And then for other things, +Beth and Laura mainly + +worked on the video, and I was +mostly in charge of the report + +and the presentation for +the mid-semester panels. + +LAURA D'AQUILA: So +to conclude, we're + +very excited to be working +on this project with Margaret + +this semester. + +It's been a lot of fun so +far, and it's exciting to us + +that this is something +that could potentially not + +only benefit Margaret, +but could also + +benefit many other residents +of The Boston Home, + +should this be more +universally adopted. + +PROFESSOR 2: So +one of the things + +that you guys mentioned +at the beginning, + +as you were talking +about the call system, + +was some of the regulations +that are in place at the home. + +Can you talk about how +your system actually + +can map to some of +those regulations, + +and if they have to change in +any way to use your system? + +TANYA TALKAR: So that was +actually one of the things + +that we are considering when we +were thinking about whether we + +wanted to interface with the +current call light system, + +or whether we would create +this separate iPad application. + +And that's also one +of things we need + +to talk with for administration. + +We believe that due to this +being a separate application, + +we shouldn't need to +have the nurses go in + +and turn off anything +on the iPad, which + +is what they need to currently +do with the call light system. + +And that's something that +the company themselves + +had come up with as +a regulation, that it + +would have to be turned +off by a nurse aide. + +But for this, because it's the +resident who's in charge of it, + +and they'll be video +calling with the nurse, + +we believe that it +shouldn't be a problem. + +PROFESSOR 2: So I guess +my question is, how does + +that regulation actually map? + +So not the fact that +the system requires it, + +but what is the kind of +the purpose of having + +that regulation +requirement, and is + +it something that you guys +should be matching or not + +matching? + +It's an open question. + +Is there a benefit to having +the nurse specifically + +go there and turn +off, and did they + +design that into the +system not because it + +was needed for the +system, but because it + +was important for the task? + +TANYA TALKAR: So we've +asked everyone about that. + +They haven't really +been able to come up + +with an answer for that. + +Margaret herself kind +of finds it intrusive + +that you have to come in and +turn off the light manually, + +instead of her just being +able to turn it off. + +So, yeah, we're not +really completely sure + +why that is there. + +We just know that it's a +regulation on the company's + +part. + +PROFESSOR 3: Well, it's clearly +a Department of Public Health + +regulation, and it evolved out +of abuse and neglect issues, + +where you could +respond to a resident + +or just repeatedly shut +their call request off, + +without really +addressing a need. + +But skirting DPH-- +sometimes you sort of + +have to play the +game a little bit. + +So if it's an experimental +or a redundant system, + +it may not have to +match their regulations + +as long as the primary one meets +those specific requirements + +of having someone go +to attend to them. + +But I am curious how you honed +in on that specific approach + +that you've taken of using the +iPad and using that simple GUI, + +versus some of the ideas +I had pitched initially. + +TANYA TALKAR: So I think +I was mostly through just + +talking to Margaret. + +And her approach to this was +that if she was in a situation + +where she wasn't able to +reach the call light system, + +her immediate thought +would be to use her iPhone + +and call The Boston +Home and try and reach + +the nurses through that. + +And so we felt that that would +be a little easier to interface + +in that way, in terms of +she always has her iPad + +or her iPhone with her. + +And so suppose there were +connectivity issues in terms + +of like we weren't unable +to reach the-- suppose + +there was like a Bluetooth that +was attached to the call light + +system, if that connectivity +wasn't established and wasn't + +stable, then that +would be an issue, + +as opposed to having +Wi-Fi, which I think + +would be more reliable +within the home and slightly + +outside of the home as well. + +PROFESSOR 3: Good. + +PROFESSOR 1: What I would ask is +how much function does Margaret + +herself actually have? + +It's clear that you're +trying to broaden + +this other members of The +Boston Home, which is great, + +but what can Margaret +herself do with an iPad app, + +and have you measured +that, or have you observed + +her use of the prototype? + +LAURA D'AQUILA: So Margaret +has limited use of her arms, + +and it varies depending +on how tired she is. + +So when she's +particularly fatigued, + +it's even harder for her +to reach the full screen + +coverage of the iPad. + +But because of the fact that +she has a stylus that definitely + +helps, but that's also +part of the reason + +why we had looked into +adding the large buttons + +so that it's more feasible for +Margaret and other residents + +to be able to use all of these +functionalities of the app. + +But, yeah, she can move her +arms a little bit, but not very + +much. + +Tanya had mentioned that on +the first day we met with her, + +we needed her to sign a +contract for our team contract, + +and it was clearly +a struggle for her + +to be able to move her +arms to sign the document. + +When she paints, she +uses a mouthpiece + +so that she can do it that way. + +So I'd say that her arm +movement is pretty limited, + +but because of the stylus, +she's able to at least get + +by with the iPad. + +PROFESSOR 2: We can probably +take another one or two + +questions if anyone +has comments. + +AUDIENCE: I have a question. + +You talked about there was that +situation when someone fell + +over and was stuck in a ditch. + +How could they access this +application in the iPad? + +Are you considering [INAUDIBLE]? + +LAURA D'AQUILA: Right, +so maybe depending + +on the exact situation, +they personally may not + +be able to use this app. + +But in the event +that maybe there's + +another resident +who's also outside, + +it may be a little bit easier +for that second resident + +to call for help while they're +still outside, as opposed + +to having to go +into the building + +to alert the nurses +of what had happened. + +But, yeah, in the +event that it's + +just one person outside and +depending on the situation, + +if they're not able to use +the iPad, like if it fell + +or something, then I guess +it wouldn't help them. + +But it's more so +in the situation + +where there's multiple people. + +AUDIENCE: I thought +it was interesting + +that you had identified the +nurses as your second client. + +It's very smart +of you to do that. + +How many signals are they being +bombarded by on an average day, + +and how is that going to +affect how you would get + +their attention [INAUDIBLE]? + +TANYA TALKAR: So +Angela currently just + +has the nurse call system plus +a computer set up at the desk. + +And then, of course, +if there any nurses + +who are coming up +to her to talk, + +that will be a +distraction as well. + +So that was one of +the primary things + +that we wanted to address with +her when we talked to her. + +So that's why we're wondering, +should it be on the computer, + +or should it be on +a separate iPad? + +And she did tell us that +with all the signals + +that she's getting, if +it was on the computer, + +she would not be looking at it +because you'll be most probably + +browsing other applications, +if it's email or whatever. + +And then with the +call light system, + +that is also something that +beeps whenever someone calls + +in, so she will address that. + +But if there is an +iPad just mounted + +like right in the +middle there, she'll + +be able to see that as a +notification coming in. + +And she said that +because of where + +she is sitting at the desk, +then she'll be able to see that. + +AUDIENCE: I just had a question. + +I noticed I didn't hear +anything about what + +was the client [INAUDIBLE] +nurse [INAUDIBLE] + +in terms of the [? hybrid ?] +liability of this application. + +Have you guys considered +putting that into your metric + +as well for success? + +Like what does +she expect to work + +90% of the time, +80% of the time? + +And also, what [INAUDIBLE]? + +You know, complicated +systems are complicated + +for a reason Maybe that's +something-- like have you + +guys had a conversation +with the client about this? + +LAURA D'AQUILA: We +haven't had a conversation + +about a specific number, +but one of the benefits + +to the fact that we have +this iPad system on top + +of the existing system is that +in the event that Wi-Fi goes + +out or something like +that in the home, + +and the iPad app +that isn't working, + +then Margaret does +have the ability + +to simply use the system +that's in place, which I think + +is known to at least go through +to the nurse pretty reliably, + +if not receive a +response all the time. + +PROFESSOR 2: All right, let's +have Team [? Aaron ?] come up. + +PHILIP: So hello, everyone. + +We're Team Kate. + +My name is Philip [INAUDIBLE]. + +And my teammates here are-- + +JENNY: Jenny. + +RAQUEL: Hi, I'm Raquel. + +[? PHILIP: So ?] today we're +just going to talk about + +the progress that we've made +over the course of the last few + +weeks in our project with Kate. + +Let me quickly introduce +who our client is. + +Over the last few weeks, +we've been talking about Kate. + +She's our client, and she works +at the Cambridge Disabilities + +Commission. + +She has profound hearing loss, +and wears a cochlear implant. + +We also have this really short +video, about two minutes long, + +in which talks about herself +and a little bit more + +about the hearing +impairment that she has. + +[VIDEO PLAYBACK] + +-Without my cochlear implants, +I have no residual hearing + +at all, so that would +be considered profound. + +With my cochlear implants, I +have a mild to moderate hearing + +loss. + +But obviously, I do really +well with my implants. + +You through in any +background noise, + +and it's just you +can forget about it. + +In this kind of +setting I do really + +well with my cochlear implants. + +So I was born with a +very mild hearing loss. + +I just had like preferential +seating in school. + +And it became profound +or rapidly progressive + +when I was 13. + +It went from mild to moderate +to severe and then to profound. + +I got my first cochlear +implant my left side in 1999. + +I had my right side done in +2008, so nine years later. + +It is not a quick fix. + +So when it was first +turned on, everything, + +like my brother's would +like stomp their feet, + +and it would sound like someone +was ringing little bells. + +It was weird. + +And I couldn't +understand any speech, + +but I had to force myself +to turn my hearing aid off + +on the right side. + +And I was home from college +for six or seven weeks. + +and I did all these listening +exercises with my family. + +We made it a game. + +Like my mom would +take children's books. + +And at first, she +would read them aloud, + +and I would follow along, +trying to place what + +I was hearing with the words. + +And then I would +graduate from that, + +and I wasn't allowed to +follow along-- to read along. + +and I was trying to +follow the story, + +just basically +training my brain. + +So my brain was receiving the +signal in a slightly new way. + +And so I basically had +to retrain my brain + +how to take that signal and +interpret it into usable sound. + +I mean, I can't +tell you how much + +it has changed my life though. + +Like I used to +walk around college + +with a little whiteboard, and +people would write notes to me. + +It has completely changed +my life-- completely. + +So for me. + +It was so worth it. + +[END PLAYBACK] + +PHILIP: So we've already +seen from the video + +that Katie uses +cochlear implants, + +and on this I would +just like to mention + +that a lot of people who +have hearing impediments + +still have functional nerve +ending, the auditory nerves. + +The main problem is +just that the part + +of the ear that is +responsible for transmitting + +sound to an electric +signals that are translated + +by the brain aren't functional. + +So it is that part of the +ear that the cochlear implant + +tries to fix. + +So the cochlear +implant basically + +provides a new channel +through which sound + +signals can be transmitted +to electrical signals + +for the brain to interpret. + +RAQUEL: So now we can get +into a little bit of what + +our goals is a Team Kate. + +So our major goal here is +to create cochlear implant + +attachments, so whether it's +covers or clip-on add-ons + +to her cochlear implant +to kind of hit on three + +particular sub-goals in this. + +So the first is to provide +some water resistance + +to her implant. + +So currently, it +isn't water resistant, + +and she doesn't have a cover +that she uses for that. + +So to give some +context for that desire + +is that she, just +like any of us, + +often finds ourselves +in the rain. + +It seems like it's a +great day to begin with, + +and by the end of +day, it's pouring. + +So for Kate that means +walking around with her hands + +like this, covering +her implants, + +or taking off her +implants entirely, + +and that's not ideal because +she can no longer hear. + +A second goal for +our implant covers + +are to provide some +sort of sound blocking. + +So Kate has issues in +noisy environments. + +And what I mean by this is +like in a lobby or a restaurant + +where there's just lots of +background noise going on, + +she has problems +distinguishing sounds + +that are coming from behind +her from sounds that are + +coming from in front of her. + +So she's having a +conversation with somebody. + +It's hard to actually +comprehend what + +they're saying when there's +lots of noise from behind. + +And currently, her implant +just has a single microphone + +so there's no kind of +sound directionality + +capability to it. + +And so an idea for +this is just provide + +some sort of physical barrier +to basically block sound + +from behind her. + +The third thing here +is attachedness. + +So she has a problem with +her cochlear implants + +just falling off all the +time for different reasons. + +But one goal for us is +to try to just provide + +something that gives it a +little bit more stability + +so it just stays +on her head more. + +So the context of +that one in particular + +is really just any +place, any time. + +The context for all +of these are kind + +of just very portable +things that she + +can use in her everyday life. + +So we've come up with +a few success metrics. + +We haven't formally +tested these yet. + +But for the water +resistance goal + +here, we'll be doing something +like a water bead test + +for the material to make sure +that it's water resistant. + +I guess I should say +that Kate has gotten + +a demo of her cochlear +implant from the company that + +makes her implants, so we can +do these water resistance tests + +not on her actual implant. + +But something like putting a +material, like a paper towel + +or something that would show +wetness, around the implant, + +putting on her cover, +spraying it, and looking + +for signs of wetness and where +that wetness is coming in. + +Sound blocking, +what we plan to do + +is kind of a human subject +experiment with her. + +So what we'll do is play noise, +a noisy environment behind her + +from different audio clips. + +and then have audio +clips in front of her + +of speech or just +a conversation, + +and try to kind of get +her subjective feedback, + +and identify her threshold for +the volume of that conversation + +in front of her, and +when she recognize that + +with and without our different +sound-blocking devices. + +And then attachedness-- +so currently, we've + +talked to Kate, and her +cochlear implants can fall out + +up to 10 or 12 times a day, +and this isn't even necessarily + +when she's being +particularly active. + +So our goal is something +less than three time a day, + +just something more reasonable +for her to deal with. + +JENNY: So during our design +process, we talked to Kate, + +and he's really, really +excited about this project + +because it has been a problem +for her for a very long time, + +and she showed us a bunch of +her existing solutions she has. + +She had a head band that you +could hook the implants into, + +and that would +keep them in place. + +But it's very sporty. + +It's a bright colored headband, +and it wasn't something + +that she was pleased with. + +And then she also had some +other kind of neoprene sleeves + +that she could put +over her implants, + +but these technologies were +all like pretty primitive, + +and they only served to +solve one problem at once. + +So through talking to her, we +identified a bunch of feature + +that we wanted to +address, the three + +features-- the water +resistance, sound blocking, + +and attachedness-- and +we began prototyping. + +So we each individually +sketched designs + +so we could come up with many +ideas when we came together. + +And as a team we chose +the few to prototype out. + +And I'll show that +on the next slide. + +But we used [INAUDIBLE], which +were two materials that we + +discovered during lecture. + +And then last week we presented +the prototypes to Kate + +and did some informal testing. + +And she was pretty +impressed them, + +and that leads me to the next +slide of what we made so far. + +So at the beginning, +we wanted to create + +some sort of +all-on-one attachment + +that would address all +three of the problems. + +So on the left, you can see +it's like a unibody cover that + +covers the entire +implant that also + +provides a hood over the +microphone at the very top. + +And then there's +also a little ear bud + +that would help with +the attachments. + +We decide not to go with that +because Kate wanted something + +a little more modular, +something that she could just + +have separate accessories +for each problem. + +So when we prototyped +keeping this in mind, + +we created separate covers. + +So the left of the +top right photo + +are covers for the +coil and the implant + +itself, the device +with processor. + +And then we also created +some sort of hood + +that you can put right +over the microphone, which + +it's a little hard to tell, +but the microphone right here. + +So this hood, it +provides a small barrier + +from the sound traveling from +behind to hit the microphone. + +So we tried this out +and then also compared + +it to these previously +existing devices. + +They're called Ear Glasses, +and these help also + +amplify sound that's +coming toward you. + +And she was pretty +pleased with them. + +And this was like +very informal, so we + +plan to continue to prototype +and iterate our design + +and then bring something +to show her on Thursday. + +For the rest of +the semester, we're + +looking to continue measuring +and testing out our success + +metrics with the prototypes +that we're planning to build. + +And then in November, +we hope to finalize + +the design and the +materials that we're + +going to use and then create +our final deliverable. + +We're looking, like +materials wise, + +we're keeping 3D +printing in mind + +to actually create +the attachments. + +But we haven't finalized it +yet, so that's just something + +that we're looking at ahead. + +And that concludes +our presentation. + +Thank you, and we'll +take any questions. + +PROFESSOR 1: First, that was +a really nice video explaining + +her story with getting +the cochlear implants + +and what kind of change +they've made in her life. + +I'm curious about a couple of +other aspects of your client + +that you alluded +to a little bit, + +but I was wondering +how important they are. + +First, how active or athletic is +she, and is it important to her + +that these things be +really, really secure? + +And second, how sensitive +is she to her appearance? + +RAQUEL: So she's not +particularly active. + +What she did tell +us is that she'll + +starting pool therapy +soon for another condition + +that she has that we +didn't talk about here, + +but that she'll be using +the headband because it's + +really important that they +don't fall off at all. + +And she'll be in shallow +end and there will basically + +be no water touching them. + +But so for these it's really +just kind of daily life. + +She works in an office. + +She attends a lot of meetings. + +So nothing too active. + +She does ride her bike +every once in awhile, + +and she has issues when +she puts on her helmet. + +But again, she +uses that headband + +that just really keeps it secure +on her head for those purposes. + +And about her caring about what +she looks like, we actually + +did ask her straight +up, how do you feel + +about looking a little silly? + +Is that OK? + +And she said that's fine. + +I think there's a fine line. + +We don't want something +that's crazy sticking out. + +But I think she's willing to +have a little bit of something + +extra on her head. + +She's even told us +that she prefers it + +when people can see that she +has a cochlear implant, instead + +of covering it up so that they +automatically know that she has + +hearing loss so that they can +communicate better with her + +from the beginning +of talking with them. + +PROFESSOR 2: So I'm wondering +if you could talk more + +about that design shape. + +So you had the +kind of Ear Glasses + +as something that was clearly +doing something similar that + +provides that directionality. + +And in your design, you showed +kind of two different methods + +of a different shape that +was on that hood for how + +you're doing that. + +I'm wondering-- I know you +said you guys are still + +kind of the middle of testing +and testing out of it. + +How is that shape playing into +your kind of design decisions? + +Are you are you specifically +designing shapes and testing + +them, or is that more aesthetic? + +JENNY: To be honest, +we haven't tested + +that many shapes out yet. + +I think that when we +do create a lot shapes, + +we're going to look +at effectiveness + +before aesthetics. + +And we tried out +different sizes so far, + +or we tried out +three different sizes + +so far of the sound +blocking piece, + +and definitely the +largest one actually + +works the most effectively. + +So we're going to find a +balance between portability + +and effectiveness. + +PROFESSOR 3: Any questions +from the audience here? + +If we can have the +last team as well. + +Jeffrey, [INAUDIBLE] +and get set up as well. + +Any other questions or comments? + +AUDIENCE: How are the ear +glasses supposed to stay on? + +JENNY: As advertised, +they were supposed + +to have some sort +of adhesive strip + +that you can just pull +off and then stick on. + +But they don't actually do that. + +It didn't actually +come with that, + +so they just sit on your ear. + +But when we had her +try them on, we just + +wanted her to try it on for +the shape of the ear glasses. + +And she was really impressed +by how big of a difference + +it made with her microphone. + +RAQUEL: But these, +in particular, + +won't stay on very well +for us, and they definitely + +don't stay on with +her cochlear implant. + +PROFESSOR 3: I assume +that magnets would + +be a problem with the implants. + +I don't know if you +address that specifically. + +I'm just thinking of how +well devices click in place. + +I'm just thinking quick +one in the extruder head + +on the 3D printer, how would +you just get sort of lined up, + +and it jumps into place. + +And I like that +functionality, but I'm + +wondering-- I'm +assuming-- that that would + +be problem with the implants. + +PHILIP: It's actually one of +the things that we considered. + +But just like you +said, we weren't + +sure about how adding +a magnet to the system + +would affect the +way the outer part + +of the implanted part of it. + +So we haven't really +tried that yet here. + +But I think we're going +to explore that option + +a little bit more and see how +it affects the communication. + +If it doesn't have +that much of an impact, + +then we would use it. + +PROFESSOR 3: Any final +questions or anything like that? + +AUDIENCE: One quick thing +is you may [INAUDIBLE] + +think about the shape, +the engineering of it. + +There's some principles to +apply to kind of engineer + +a shape that is most +effective for sound filtering + +or sound blocking. + +That kind of thing. + +OK, Thank you. + +Hi, so we're Team Jeffery. + +JODIE CHEN: I'm Jodie. + +DAVID KE: I'm David. + +JODIE CHEN: And our +client is Jeffrey. + +Here's a picture of +him, and he's blind. + +So first, we're going to +talk about contextual inquiry + +and how we worked +with the HAAT model. + +So we came up with +a few questions + +that we planned on +asking him to kind of get + +an idea of what +activities he enjoys doing + +and which activities +we can help streamline + +or make more efficient and allow +him to, I guess, enjoy it more. + +So we kind of +asked him questions + +like, what activities +do you want + +to be able to do independently? + +And we asked him to +show as an activity + +that he enjoyed in his +free time and also like + +how he uses computers, +because it turns out + +that he uses computers a lot. + +So I think one +thing that we found + +about Jeffrey is that he's +actually extremely independent, + +even though he's blind. + +He told us that like +75% of blind people + +are like unemployed, +but he's been employed + +in multiple places before, +and he also continues + +to do a lot of financial work. + +So we have a video to +kind of show, I guess, + +how he's l challenged +our misconceptions. + +[VIDEO PLAYBACK] + +-Hi, so I'm David, and +I'm part of Team Jeffrey + +with Jodie Chen and Yi Tong. + +And the client that we're +working with for PPAT, his name + +is Jeffrey, and he's blind. + +I guess initially going +into this project, + +I didn't really know what I was +expecting in terms of working + +with a person with blindness. + +I guess, part of it's +like I didn't expect them + +to be super self-sufficient. + +And I thought they +would have to be + +relying on a lot of technologies +to go through their day. + +[? And so I was like ?] struggle +with like a decent portion + +of the daily activities. + +-I guess something that really +surprised me about Jeffrey + +was how autonomous he is in +like his travel and other stuff. + +So what you might not +know about Jeffrey + +is that during our Monday and +Wednesday classes sessions as + +well as class labs, +he actually comes over + +and he listens and he also +participates in our team + +discussions, gives all +of like helpful advice + +as to like how do we +really work on the project + +and how to build it. + +-So I have plan +A, plan B, plan C, + +and plan D. That's how you +have to live OK, so here we're + +on my email. + +-Jeffrey is-- you can +barely tell Jeffrey's blind + +when he's at his +place because he knows + +exactly where everything is. + +He's really passionate +about technology. + +-He is really passionate. + +He told me that he as +the coolest gadgets. + +-[INAUDIBLE]? + +-What toys? + +-You looked at this other wall +while you were sitting there. + +I said, Jeff, what is it? + +-I don't know. + +-Remember, I said +when I got here + +and he had this-- it's +a talking thermometer. + +-Oh, it's a talking thermometer, +indoor/outdoor temperature. + +Neil plays with it more than +I do because, frankly, I + +don't give a damn. + +It's too much information. + +-The indoor temperature is +68.3 degrees Fahrenheit. + +-I don't even know +how accurate it is. + +It's a toy. + +-And then he [? bought ?] +this when he started cooking. + +It's a talking kitchen +thermometer-- a kitchen scale. + +-Oh, yeah, I tell you, he +knows more the toys-- I forgot. + +-Because I found them. + +-(SINGING) Ah-- + +-Ah. + +[END PLAYBACK] + +JODIE CHEN: So here's some +information about Jeffrey. + +So Jeffrey, he's +visually impaired, + +and he has been kind +of for his whole life. + +He used to be able to +see like different things + +if you blew them up really +large on like a projector. + +But now, all he can see is like +just like light and darkness. + +So he's used computers +for practically his whole, + +so he's actually very, very +good at using his JAWS screen + +reading software. + +And he actually +teaches people how + +to use it in the Carroll +Center for the Blind. + +And he also knows +braille, and he told us + +that actually a +lot of blind people + +don't know how to read +braille, so he's actually + +one of the few +people that actually + +does know how to read braille. + +And he also does a lot +of financial paperwork + +for his homeowner's +association for his condo, + +and he does a lot of +taxes for his friends. + +So he's constantly +on his computer, + +checking his email, using +Excel to work on that. + +So we kind of wanted to +narrow down like an activity + +that Jeffrey has to do that he +wants, I guess, like more help + +in. + +So he's a pretty +opinionated person, + +so he already had an idea +of what problems he exactly + +wanted us to solve +and also solutions + +as to how to solve them. + +So on the activities that +he kind of narrowed down + +for us is finding a way to +sign a paper with a wet ink + +signature. + +So he gets a lot of financial +sheets and documents from banks + +and stuff that need him +to sign the document + +and not have a +digital signature. + +So in order to +sign a document, he + +has to have his visual +aide Neil come over + +and like help him find the +exact line where he has to sign. + +And if he doesn't +have a visual aide, + +then there's no way for +him to get that done. + +And she also uses +Excel a lot, and he + +doesn't like the +new format of Excel, + +so he wants us to +kind of like change + +it to be more compatible +with like the versions + +that he's used to. + +So we narrowed it down +to being able to help + +him sign a document when he's +like independent and alone, + +without a visual +aide to help him. + +So to kind of get a better idea +of what we have to work with, + +we kind of asked him like, +what assistive technologies + +that he currently +use so to find out + +which assistive technologies +that he was comfortable with. + +So he told us that he's +really comfortable with JAWS, + +and that like when he +does OCR on a document, + +he can determine where a +signature line is because JAWS + +will just say like, underscore, +underscore, underscore. + +So all we had to do +is kind of find a way + +to guide like his +mouse pointer to like + +the position of the +underline and then + +to find a way to convert +that into like something + +that could be translated +onto a piece of paper. + +So for our success +metrics we kind of wanted + +to be able to evaluate +like how well he + +can sign a document by seeing if +he can actually find the place + +where to sign +independently on his own, + +which he isn't able +to do right now. + +And we also wanted to measure +like how long it takes + +for him to measure a document. + +And I guess that's +pretty easy to improve on + +because currently it takes +infinite time for him to sign + +a document. + +And we also wanted +to measure kind + +of how accurate he is +with finding the position + +and also signing +because we don't + +want him to sign +somewhere that's + +really far away from the line. + +So that's kind of +like the scope. + +YI TONG: So I'm +just going to talk + +about the project organization, +the progress so far. + +So the first is the ideation. + +So we're very lucky, so +Jeffrey's always in the lab, + +as you all can see. + +So he's been meeting +with us every lab + +and also contributes +a lot of good ideas. + +So we go to the lab with +ideas and then consult Jeffrey + +and ask him for the feedback. + +And then we narrow +down the solutions + +after every discussion. + +And then finally, we decided +on the mechi and software + +combined solution. + +So for the software +part, so we all + +know that JAWS can +detect a signature line + +and read out underscore +and also like signatures + +and different kinds of words. + +So we just need to find a way to +get coordinates from the mouse + +location, and then take in the +mouse location two inches so + +that that can be the +input for the mechi part. + +So for mechanical +part, we need a frame + +the holds standard sized +paper so it won't slide away. + +And then we need sliding +braille rulers, or rails, + +to move horizontally and +vertically so that Jeffrey can + +adjust to the exacty x-, +y-coordinates by sliding + +the two rails. + +So here's the early sketches +and also the prototype + +that we have. + +So on the right is just +some white board drawings + +about different ideas +that we had before. + +So the first one you can say +something more or less like + +the magnifier that we see +on [? Ability ?] [? Expo ?]. + +So basically the +advantage of that is he + +doesn't have any restriction +while he's signing things. + +But that is really hard to +implement because the camera's + +on top of the paper. + +And also we also get inspired +by the idea of a project built + +by an MIT Media Lab. + +So it's a finger reader, so +like whenever he scans a line, + +he hears "signature." + +Then he will start signing. + +But then that would +require Jeffrey + +to scan through the whole page. + +And then so we finalized +on this sketch. + +So there are two siting rulers. + +Ideally, each ruler will +have like brailles on it + +so that he can know how +far he's gone on the page. + +So both rulers kind of slide +left and right and also + +the other's up and down. + +Yeah and then just the +idea-- you don't you read it. + +But it's just how much +Jeffrey's input is given to us, + +and also he's really +passionate about this project. + +DAVID KE: So this is the general +timeline for what we're doing. + +So in the next few +weeks, it's going + +to be focused on mostly +making more prototypes + +for these projects, +and we're really + +ramping up our +interactions with Jeffrey + +to get feedback and +iterate on our designs. + +So like as you've seen +in the previous slides, + +we already have a +really lo-fi prototype. + +So what we're going to +do in the next two weeks + +is prepare multiple versions +with minor detail differences + +to Jeffrey to see +which ones he likes. + +Because a lot of it, the +general idea is pretty solid, + +but a lot of it's +like in the details + +of how unexpected +things might come up + +as he uses it day to day. + +And in a few weeks, once we +kind of have that hammered out, + +we'll try to work on +like a more high fidelity + +prototype that this +more closer to what + +we'll be presenting at the end +in the beginning of November. + +And on the software side, +this is more like on our side + +because we need to +kind of get familiar + +with hows JAWS is working, +as well as like what kind + +of inputs to outputs we can give +to JAWS as well as from JAWS. + +And then we're aiming to sort +of complete that little bit + +after hardware, +so we can kind of + +combine it together and have a +few weeks to see how that would + +work as a complete package. + +And this is just what we've +done so far-- yay, teamwork. + +OK, and that's the last slide. + +YI TONG: Well, he obviously +had a lot of ideas, + +and I'm wondering how +you chose, or what + +process you used to choose +this signature project? + +Was it sort of an embodiment +of your skills and interests, + +or was it like clear +front runner for him? + +DAVID KE: So I think +two main categories + +we were considering +in that was, one, + +is it something that +aligned with our skills, + +because we're all +studying computer science. + +He also had a bunch +of projects that + +were pretty cool that +wasn't that involved, + +like mostly mechanical +engineering. + +So that was like a little out +of the reach of our abilities. + +At the same time, something +else we have to consider + +was we needed a project that was +the right scope for the class. + +So like, for example, the +Excel thing he mentioned, + +it's mostly computers, +but it was very simple. + +So we wanted something that +had more substance to it that + +could be applied to +more people afterwards. + +PROFESSOR 1: I have a question +about your baseline success + +metrics because you did say that +signing documents is something + +does do with Neil's help. + +Have you watched him to +do that with Niel's help? + +Have you sort of collected +examples of his signature + +that he's done with Neils help? + +Seems like that you're not +just operating with something + +that he's completely +unable to do, + +but something he just +can't do independently yet. + +JODIE CHEN: Well, he wants to +be able to do it independently + +because Neil isn't always there. + +And we haven't really had a +chance to watch Neil show him + +where the signature line is and +how to sign it because, so far, + +we've only gone to his +house once because he comes + +to Monday, Wednesday +class sections, + +but also lab sections, +so we've been + +meeting with him for +around four hours + +every week during class time. + +DAVID KE: Yeah, but I +think that's a good idea, + +and it's something we +should definitely do + +the next time we meet with him. + +I suspect we'll have +to consider that + +as like two different +categories of like metrics, + +but it's something +that should be included + +PROFESSOR 2: So I'm curious +more about the mechanical aspect + +then. + +So you guys are really +comfortable with the software + +side, and you presented +the first prototype + +of the mechanical +side, and you've + +showed kind of your sketch of +how the camera might be there + +and where the rulers might be. + +But you talked about +some of the limitations + +potentially for just +being able to kind of look + +at where you put your head, +where you put your hand. + +I want you to talk +a little bit more + +about some of those +limitations and things + +you're thinking about +from the mechanical side, + +and what you think you +might do to balance that. + +YI TONG: I think I might have +misrepresented because I feel + +like the camera thing is just +like the earlier prototypes + +that we explored, but we're not +going to do the camera side. + +We're just going to +keep the software part, + +the mechi part separate. + +So the mechi part +is independent. + +It only takes in +the coordinates. + +And then Jeffrey +will get feedback + +when he's sliding the rulers, +so he knows how far he's gone, + +but he doesn't have to +have a camera take down + +where his hand is currently on. + +DAVID KE: Yeah, and one +good thing about this + +is I think Jeffrey +and us are pretty + +aligned in that we +want to keep the amount + +of complicated components in +the final project like minimized + +to reduce possibility +of failure. + +So a lot of the +things we've actually + +talked about in +the past few weeks + +are ways to simplify the +parts so that it still + +has the relevant information, +but it's like as simple + +as possible. + +PROFESSOR 4: Any +questions or comments? + +AUDIENCE: You mentioned +using a mouse [INAUDIBLE]. + +But wouldn't that require him +to click all over the screen + +to find out where the +signature line is, or are you + +just going to have he +reads through it with JAWS + +and then stops when +he finds lines. + +JODIE CHEN: So it's more +likely to be like the latter + +because he's done that. + +For JAWS, when JAWS is reading +something on the screen, + +it has a [INAUDIBLE] somewhat +similar [? to mouse clicks, ?] + +but they're not actually +mouse [INAUDIBLE]. + +And then there's like +a function in JAWS + +where it moves the mouse +pointer to the location of where + +it's currently reading. + +So that's how we're +planning on doing it. + +PROFESSOR 4: Any +questions, comments? + +So quick clarification, so +is there like a scanning-- + +maybe I missed it. + +Is there some scanning +of the document first? + +Are you buying a scanner? + +JODIE CHEN: Oh, he always +scans in his documents. + +AUDIENCE: I was hoping to +[INAUDIBLE] Jeffrey briefly. + +Is it going to be an issue when +the line is like a drawn line, + +as opposed to [INAUDIBLE] line? + +Or will that resolve +with the scanner? + +DAVID KE: That just depends on +like the of quality of the line + +as well as like the character +recognition software. + +So we'll probably +do tests with that + +to see like how much +tolerance the software has. + +PROFESSOR 4: Michelle, +last question. + +AUDIENCE: Is there +a general location + +where you know the +lines are going to be. + +Just out of curiosity, +like if I sign a paper, + +it's usually at the +bottom right-hand corner. + +Do you guys have +an understanding + +of what kind of documents +he's currently signing, + +like what they look like? + +YI TONG: According to Jeffrey, +I think it varies a lot. + +And also sometimes like +there's a huge line, + +but then the signature +word is under the line, + +but sometimes it's +just next to it. + +And then sometimes, +the signature's + +right here on the left +of page, but then you + +have to sign it to +the right of the page. + +So it really depends on +different kinds of paperwork. + +So we tried to collect all +different kinds of paperwork + +that he normally +gets, and then we + +tried to characterize like what +different kinds of signature + +box that he normally gets +and then work on that. + +JODIE CHEN: And also +what Jeffrey does + +is he scans a document, +and then he runs OCR on it, + +and then he translates +it into a Word document, + +and then he prints out +the Word document to sign. + +So what's going to happen is +that he alters the document + +that he gets in mail +pretty significantly when + +he runs OCR and changes +it to a Word document. + +DAVID KE: But overall he gets +a lot of different signatures + +on that. + +PROFESSOR 2: It would be really +interesting to actually try out + +that and get those documents for +all these different signature + +lines. + +And I think that's +a really good point + +about whether it's an +underscore line or a drawn line, + +and some signatures are actually +boxes as opposed to lines + +and how that might affect it. + +PROFESSOR 4: OK, thank you. + +VYNNIE KONG: Everyone, +we are Team Beverly Ann. + +This is our mid-semester review. + +My name's Vynnie. + +SHRUTHI NARAYANAN: I'm Shruthi. + +ROBERT LUO : I'm Robert. + +VYNNIE KONG: And +we're just going + +to provide you a brief +introduction to our client. + +So some of the non technical +things-- Beverly-Ann + +is a social worker +for DCF, so that's + +the Division of +Children with Families, + +so she basically works +at a sort of law firm. + +And she's actually +learning how to code using + +and Scratch Arduino, which +we thought were pretty cool. + +She loves playing Wi tennis. + +She has a backyard +garden, so she + +grows tomatoes and marigolds. + +And most importantly, she wants +to maintain an active mind + +in order to keep +busy and kind of like + +find something useful +for the rest of her life. + +And before we explain +more about stuff + +related to the HAAT +model, we think + +the video would be a +very good descriptor + +of a lot of these things. + +[VIDEO PLAYBACK] + +-Hello, my name is +Beverly Ann Rock, + +and I have been +diagnosed with CMT, which + +stands for Charcot-Marie-Tooth. + +I was diagnosed +about 11 years ago. + +If there's any blessings +to this disease + +or anything good +about this disease, is + +it only affects the +hands and the legs, + +which means I'll always +have my ability to talk. + +Three of my 10 fingers have +taken on the deformity, which + +means they're kind of locked. + +And eventually, they will +end up in gnarled positions. + +But fortunately, 7 +is better than none. + +So I use my seven +fingers very effectively. + +My right hand, it has +become numb in many places. + +Thus it doesn't give +me the opportunity + +to use very simple devices. + +So if I were to be trying +to drink something hot, + +I would make sure to try +to grip it as best I can + +and support it. + +But over time, it's +not going to hold. + +It's going to slip, I'm +going to lose the grip. + +That's one of my concerns +is dropping stuff + +and why I'm so +guarded about dropping + +is if you drop a glass, a +shard, I had a couple times, + +a little thing has just +stuck into my foot, + +and I didn't realize it +till I looked down and said, + +why am I bleeding? + +I Constantly fall, and I +always have devices or walkers + +or scooters or things +that will enable + +me to maintain balance +and continue to be mobile. + +I choose, at this point +in my life, to work, + +even though I'm +at retirement age, + +and that's because it +keeps my mind busy. + +And hopefully every day +they're working on a cure, + +or I stumble on a +program like you + +that is going to assist me to +make things a little easier. + +So if I had a device +that was telling me, + +if I got too into +the conversation, + +that it's loosening, then I +when know to go back and not + +use the assistance to go back +and try to tighten the grip. + +-We have to distract +you some how. + +-You are distracting me +because why you're talking, + +I'm saying, OK, hold on. + +[END PLAYBACK] + +SHRUTHI NARAYANAN: So, as she +said in the video, she has CMT. + +It's a neurodegenerative +disease that + +affects the extremities, +so the hands and the feet. + +It results in a loss of touch +sensation and muscle control. + +So she has involuntary +muscle spasms. + +For her, in particular, we're +interested in her hands. + +So it means that she has sensory +failures in part of your hands + +and muscle failure in others. + +And this is like +a general diagram + +of her left and right hand. + +On her left hand, you can see +the green fingers are curled in + +like this. + +And that's because that's +their natural position. + +So when she tries to open +them, they automatically + +curl back in. + +So this is like the +involuntary muscle movement. + +But her other two +fingers are very mobile. + +So even though she +can't grip anything just + +with the left hand, +she uses her left hand + +to support what +she's gripping a lot. + +On her right hand, +the red regions, + +which are most of +her fingers, are + +the places where +her hands are numb, + +so she can't feel anything. + +And so she has a +hard time gripping + +with those parts of her fingers. + +But the tips of her fingertips, +which are marked in blue, + +are actually fully sensitive. + +So she tends to claw whenever +she's picking things up. + +But over time, she still loses +grip with her right hand. + +VYNNIE KONG: Because +of the combination + +of loss of pressure and also +involuntary muscle movements, + +there are certain activities +that Beverly Ann has trouble + +with on a day-to-day basis. + +And then I made a table +with modifications + +that she's learned +to do to adapt. + +So a lot of the things +she has trouble with + +is having to consciously +think about doing + +everything she does. + +So any time she has to pick up +something to drink of water, + +any time she has +to type something, + +she needs to think about +every single letter she types, + +rather than just typing +out of muscle memory. + +And that's difficult, +especially when + +you're holding a +conversation with someone + +or if you're just thinking +about something else. + +You can't always think about +what you're doing all the time. + +This also helps with +walking down stairwells, + +because she has to +grip onto the stairwell + +and make sure she squeezes +every couple of seconds, + +so if she's managed to stumble, +she'll still have the grip + +and be able to +stabilize herself. + +And the last thing is actually +cooking, which he brought up + +in a meeting, where she realized +when she was cooking potatoes + +and she was picking up +potatoes to put them in the pot + +that she wasn't actually +grabbing on to them. + +So she had to use this +sort of like clawing motion + +to get them from the +cutting board into the pot. + +ROBERT LUO : So the basic +problem we're dealing with here + +is that she has to constantly +think about the things + +she's grabbing whenever she's +grabbing some kind of object. + +And also, she is not +really confident in using + +just her right hand +for grabbing objects. + +Instead she normally uses her +left hand to do the support. + +And we want to come up with +the device which would help her + +by notifying her when she +first-- helping her to have + +the confidence to grab objects +with just her right hand, + +and then notifying her whenever +her gripping starts to become + +loose. + +So then we came up with +the success metrics + +for our project. + +There are few things +we can think about. + +So the first thing is we want +to see how much of a percentage + +our device could +give her the warning. + +So right now, of +course, it's zero. + +But we think a +reasonable goal will 50%. + +Meaning that our device +will be able to alert + +her 50% of the time whenever +her grip starts to become loose, + +and then with an +ambitious goal of 90%. + +And then the second +success metric + +is the dropping rate +with just her right hand. + +And so this part we still need +to measure how many times, + +how many things she drops +on average in a day, + +and then we want +to decrease that + +by 50% as our reasonable +goal, and 20% off the original + +as our ambitious goal. + +And then we want to boost her +confidence in gripping objects + +with just her right hand. + +And we can measure +how many times + +she grabs things in a weekly +basis or a daily basis. + +And then we want to increase +the percentage of her just + +using her the right hand to grab +to 60%, then eventually 90%. + +And so this is our design +process for this device. + +So first, we define the goals. + +So we noticed that she +has two different problems + +for her left hand +and her right hand. + +And after talking +with our mentor Jeff, + +we decided to focus +on solving her problem + +with the right hand, so +meaning the gripping part. + +Then we brainstormed +of different ideas. + +We mainly focused on whether +we should use a sensor, + +and if yes, where +should we put the sensor + +as well as how we can attach +the sensor to her hand? + +Then we come with various +types of prototypes, + +many based on the +location of the sensor + +as well as the style of +attachment of the sensor. + +So the fundamental +idea of our design + +is to have a way to quantify +the pressures she exercises when + +she grabs things +as well as trying + +to have a way to notify her +when her grip becomes loose. + +SHRUTHI NARAYANAN: So +the first concept we had + +was to place the sensors near +the palm of her right hand, + +so that would be in this area. + +We figured that we +wanted as little material + +on her hand as possible, so it +wouldn't weigh her down and so + +that it wouldn't look like +a very obvious device. + +And then on the +back of the hand, + +you can see there's a square. + +That would be where the +sensors read out to. + +There would be +some sort of output + +there that she could look +or that would notify her + +when her grip is slipping. + +So this was good because it +was very small and condensed, + +and she'd still have +use of her fingers. + +But it was bad because she tends +to grip with her fingertips. + +So we wouldn't actually be +able to sense a lot of the grip + +that she was using. + +And so we would basically get +no reading most of the time + +So then we came up with +an exciting concept, + +which was to place the sensors +on the tips of the fingers. + +If you can see, everything +except for the index finger + +has a sensor. + +That's because she actually +doesn't use your index finger + +very much when gripping. + +So the other four +fingers have sensors. + +They wrap around +the back of the hand + +to go to the same output box. + +This is much better because she +grips with their fingertips, + +so we can actually sense +what's she's gripping. + +But it does take up +more of her hand. + +In the end, we went +with a second concept, + +and this is because we asked her +about how she felt about having + +a device on her hand. + +And she was like, I don't +care what it looks like. + +It could be pretty big, and I +would be OK with that as long + +as it helps me to grip. + +So we made some very basic +prototypes of just the shape + +of what they would look like. + +So the sensors are the +sort of strips of paper, + +and we just wanted +to see how they + +would look so that we can +sort of experiment with how + +they fit on her hand. + +So if you want to-- + +VYNNIE KONG: So a bit +of a future timeline, + +we are planning by next week, +so October 29th, to start + +and basically +finished figuring out + +the circuitry for connecting +these sensors to some sort + +of output voltage, and we +want to tune the circuit so + +that whatever output +voltage the sensors produce + +will be in a format that's +interpretable to our needs. + +SHRUTHI NARAYANAN: Then +we want to write code + +to respond to the +sensor so that we + +can give her a sort of output +on when she's losing grip. + +So we want to study what +the sensor voltage looks + +like as her grip loosens +and try to figure out + +where we can start +notifying her, + +when like this certain thing +happens that, oh, your grip is + +loosening. + +So we plan to try multiple +different algorithms for this, + +and this will hopefully +be our second prototype, + +and we'll have it done by +the first week of November. + +ROBERT LUO : And then the third +step is the actual glove we + +will use to attach +the sensor with. + +So some things we want to +think about in this stage + +is how we want to keep +the sensors safe, which + +means we don't want +the sensors to be + +exposed to the outside +environment as well + +as her hand. + +So maybe something +we're thinking about + +is knitting two +layers of the gloves + +together and having the +sensors to be in the middle. + +So that could protect the sensor +from the outside environment + +as well as her hand. + +And then we also want to +think about questions like, + +what happens to the sensors +when she curls her hand? + +So the way we think +about it is that as long + +as we put the sensor +on the back of her hand + +or on the wristband, +it depends on which one + +we choose eventually. + +Both designs would able +to help stable, even + +when she curls her hand. + +And, of course, after we're +having the prototypes, + +we want to keep improving on +the device based on our test + +results with Beverly Ann. + +VYNNIE KONG: A little bit +about our division of work-- + +so during our client +meetings, Shruthi + +he has been primarily +doing the video. + +I've been primarily doing +the interviews, and then + +Robert, the notes. + +And looking onwards, +Shruthi and I + +will be planning +on working mostly + +on the circuits, and then +Robert on most of the gloves + +and figuring out what +materials to use. + +And thank you, +guys, for listening. + +If you have any +questions, let us know. + +PROFESSOR 4: Questions +comments from [INAUDIBLE]? + +PROFESSOR 1: I'm +wondering if you thought + +about what you +might do passively + +with the material of +the glove to make it + +less likely that it would slip? + +You know what I mean? + +You have a very active +solution right now + +that depends on sensors and +electronics and batteries. + +Are there anymore +passive things that you + +might do, either with +material or with the design + +of the glove, or +have you thought + +about that part of the space? + +SHRUTHI NARAYANAN: So +one of the big things + +we thought about was when we +get the material for designing + +the glove, to have +like sort of grip. + +So certain gloves do +come with like rubber + +on the outside of them +to have more grip, + +and we thought that +something like this + +would also be able +to help her generally + +keep her grip on +slippery objects, + +especially with the glove on. + +So that's one example +of a passive solution. + +We did think of entirely passive +solutions at the beginning, + +like having some sort +of exoskeleton that + +would like hold her group +in place that she could + +lock into place or something. + +But we figured that then +she'd be having to manipulate + +the device too much herself. + +And so we went with the more +active solution in general. + +But yes, smaller passive +things, like the rubber grips + +and having some fingers open +so that she has better grip, + +will hopefully help her +with her grip anyways. + +VYNNIE KONG: And we +actually found out + +that a lot of her problems don't +come from muscular strength. + +So it's not that she can't +physically lift the plate. + +It's just that she can't feel +how hard she's gripping it. + +So balancing it becomes a +bit of an issue, for example. + +PROFESSOR 5: Well, following +on what you just said, + +did you think of any +sort of way of giving + +maybe auditory +feedback or some way + +to in terms of the gripping, +like is there a user interface + +aspect to this? + +ROBERT LUO : Right, so some +things we think about is + +so after having a sensors, we +want to be able to quantify her + +grip. + +And so some things +we are thinking about + +is we can test how much of a +grip she exercises on an object + +initially, and then set +that as a threshold. + +And whenever the grip comes down +to 50% of the original grip, + +then that's the threshold +we think of warning her. + +And then and then the +ways of warning her + +include having a beeping +sound, or it vibrates + +so she will be notified. + +PROFESSOR 5: Did you +think about cost? + +Did you say cost, +like what it would + +cost to make one of these +in quantity or something? + +ROBERT LUO : Oh, right, so we +already have the sensors ready. + +So we already got the sensors, +so they were not too expensive. + +They were $60, $70. + +And then we know are on +the stage of figuring out + +how the circuits would work, +and we would approach it + +by making it on a +breadboard first, + +then thinking of whether +it's possible to make + +this circuits into a +smaller circuit board + +and attaching it to the glove. + +And then the glove +itself shouldn't really + +be that expensive. + +PROFESSOR 5: Any quick +questions from the audience? + +AUDIENCE: [INAUDIBLE]? + +VYNNIE KONG: We have not. + +What is that? + +AUDIENCE: Oh, it's like +thread that's in buckets, + +so it's like a wire, +but it's thread. + +[INTERPOSING VOICES] + +SHRUTHI NARAYANAN: Yeah, +I guess like once we + +have the sensors +attached inside the glove + +to get it to the output, +we could use that. + +Thank you for the idea. + +STUDENT 1: Hi, +we're team Barbara. + +So this is Barbara. + +She has been a +teacher for 29 years, + +but she had to retire +early because she has PLS. + +So PLS is kind of like ALS. + +It's a disease where +your muscles get weaker. + +And right now she is living in +the Leonard Florence Center, + +and she really +values independence. + +And as of right now, she has +fine motor skills in her hands, + +but is slowly losing +her strength, especially + +in her left hand +because she does + +a lot of crocheting during +her free time, which keeps + +her right hand more flexible. + +And she's also constrained +to a wheelchair, + +and her speech is +sometimes unclear + +because the muscles in her +face are also weakening. + +So some of the activities +that she has trouble with + +is opening and closing +the door in her room. + +This is her door. + +And it's difficult for because +the door is very heavy, + +and also it does not swing open. + +When she's trying to open +it, it stays where you + +leave it and locks in place. + +Also, because her +wheelchair gets in the way + +because the door +opens towards her, + +so she has to open +it a little bit. + +scoot her chair back, +and then open it some + +more, which makes +it very difficult. + +Another problem that +she has is turning off + +the lights before she goes +to sleep because once she's + +in bed, it's very +difficult for her to get up + +and turn off the lights. + +Currently, she has an +iPhone, and on her iPhone, + +these are some of +the apps that she + +uses for assistive technology. + +The ones on the +bottom here, some + +are for speaking because +her speech is unclear. + +So, for example, there's one +for her to say yes or no, + +and some of them where +she can type in phrases, + +and it'll speak it for her. + +Or there's also apps for her +to indicate the amount of pain + +she has right now. + +She also recently +got an iPad, but she + +hasn't been using it that +much because it's heavy. + +But she has no +assistive technology + +that she uses currently +for opening the door + +or turning out the lights. + +So some of the context is +that her room is right next + +to the dining area, +so sometimes there's + +a lot of noise that bothers her. + +Also, she has +concern for privacy + +because since the door +is so hard to open, + +she leaves it open +most of the time. + +And right now, the staff at +the Leonard Florence Center + +has to open and close +the door for every day + +and turn on and off the lights. + +And although she didn't ask +for a solution for her voice + +problem, she did +tell us that this + +is a major concern for her. + +So based on my +contextual inquiry, + +we decided on our +project, which is + +to automate the door +because she really + +wants to have the independence +to be able to open and close + +the door by herself, and also +have privacy in her room, + +and she doesn't currently +have any assistive technology + +for that. + +And that is like the most +difficult problem for her right + +now. + +So for success metrics we think +the best possible solution + +would be for her to +have an app on her phone + +that she would just be able +to click or some sensors, + +so she doesn't have to +actually opened the door. + +And a less successful +solution would be for her + +to press a button and +something that would just + +be able to reduce the +amount of effort she needs + +is to have her pull something +that would then open the door, + +instead of actually +opening the door itself. + +STUDENT 2: So next +we're going to explain + +a little bit about our +ideation process for this door. + +So we're going to +start by showing you + +a video of our design process +and to give you a bit of sense. + +[VIDEO PLAYBACK] + +-This place, the Leonard +Florence Center, is wonderful. + +They encourage you to be +independent the best you can. + +I like the attitude. + +Hello, my name is +Barbara [INAUDIBLE]. + +I was a teacher for 29 +years before I got sick. + +I had to retire early. + +I miss the kids. + +I miss the nonsense. + +-What are your typical +daily activities? + +-Some days Bingo. + +I never played Bingo +before I came here. + +It's to socialize more. + +I struggle with the door +since my room is so small. + +I'm in my own way +with the chair, + +so to make it so it's easier +without crashing into the door. + +The doors are very +heavy for my left arm. + +Automatic doors in the +room, would be very helpful. + +-What would be your +perfect world interaction + +with the door? + +-I can open and close +it without touching it. + +Some of the rooms already +have the technology. + +Mine doesn't. + +-So it's easy to open it. + +But then once it's not moving, +it's hard to do either. + +Also, like the door +will not swing open, + +so you can't just +push it because it + +doesn't let it happen. + +It locks itself. + +-Then we began our +design process, + +which consisted of +numerous measurements + +on everything related +to Barbara's door. + +We then considered whether +we wanted an app, button, + +or mechanical solution and +started our ideation process. + +These ranged from an +automatic collapsible door + +that opens with a pulley, +to a mechanical lever + +that closes the door +when you push on it, + +as well as a pulley system that +opens and closes the door when + +you pull on the string. + +And lastly, we considered an +automatic soundproof curtain + +system which would open with a +touch of a button from pulleys. + +We decided to pursue +the curtain idea, + +and are now beginning to +prototype over and over + +and over again until we create +the perfect automatic door. + +STUDENT 2: So that's just an +overview of our design process. + +So I'm going to take you +through the specifics of it now. + +So these are the three idea that +we were pursuing for the door. + +And the first thing +that we did was + +weigh the pros and cons +of each possibility. + +So with the automatic +collapsible door, + +we thought that this would +serve as a good alternative + +because it's rigid, +so it does still + +have the appearance of a door. + +But some issues we +had with is that it + +was hard to find the parts +to create a rigid collapsible + +door that was cheap and +easy to put together. + +Next, we considered automatic +curtains, which we thought + +would be very easy to +implement and test, + +and we get soundproof +curtains that could + +implement that part of it. + +But one issue is that it +might not be door-like enough + +and fit in with like the norms +of what doors simply look like, + +and the pulley system +could get stuck as well. + +Lastly, we considered a +mechanical lever and pulley + +system, so this would +alter the door itself, + +so we wouldn't have +any extra parts, + +and it should make the whole +thing flow a little bit more + +smoothly. + +But it's kind of +hard to implement, + +as we are not mechanical +engineering students. + +So we decided to go with +the middle approach, + +as it is very easy to +test and prototype. + +But when we went to the +Leonard Florence Center + +with our idea to see if +there were any issues, + +we found that there were a lot. + +One of the first ones is +that they consider curtains + +a major fire hazard because +she could get stuck, + +or the curtains could get in the +way of her leaving or entering + +her room. + +They also told is that this +idea must be fail proof. + +So if there were a fire, the +door must be able to close, + +and nothing should +inhibit its way. + +So we tried to brainstorm +another solution, + +and decided to go with +our mechanical approach. + +But there we found +that if we connected it + +with the fire alarm system, +we could get our pulley + +to dislodge from the door if +the fire alarm system goes off. + +And then this +would hopefully not + +in impede with the +door's mechanism + +when there is a fire alarm. + +But still they raised the +problems of a fire hazard, that + +must be fail proof, and +they also did not really + +understand how we would +connect our new door system + +to the main system itself. + +And if we were to go through the +peak system that is currently + +at the Leonard Florence +Center, it's super expensive. + +And so we found it this idea +is not very feasible for us. + +So this led us to work into +her secondary problem, which + +is light automation. + +So the reason why this was her +secondary preferences it's she, + +with third condition +of PLS, she actually + +can't get up from her bed to +shut off the light before she + +goes to bed. + +So she has to call +a nurse to do so. + +So this impedes on +her independence. + +This happens every day. + +So this would be a problem +that if we could solve, + +it would help +frequently, so she'd + +be able to have +very good use of it. + +It's not like a +one-case scenario. + +And this will also help her +because in the future, when + +she is in a +wheelchair, she may not + +be able to have the +strength to reach up + +to the light to switch. + +Whereas with an application, +she could, since PLS + +is progressive. + +So as a condition worsens +this would be one of the this + +will be a possible solution +that can like at least + +allow her to shut off the +light when she wants to, + +and she's not in her bed +for a longer period of time. + +So different processes +we thought of doing this, + +we thought of using X10. + +So while we were +searching, we found X10, + +so it's possible through Wi-Fi +to send a signal to the X10 + +transceiver. + +That sends a message +to the outlet + +through electricity, some +sort of like Morse code + +for electricity kind of, to +give an idea of what it's doing. + +And then that can be used +to turn on or off the light. + +So the process would be a +little straight forward, + +since the products +are available. + +It would just be +us connecting them, + +and then the actual +application already exists. + +And the price tag +was about $100. + +Another idea we thought +of was a more hands + +on approach of getting in +Arduino to send a radio + +frequency signal to the light. + +We could buy the light that have +as a receiver for this radio + +frequency signal. + +So then we would basically +send a Bluetooth signal + +from her phone to the +Arduino [? BLE ?] shield, + +and then that would +send the signal + +to the corresponding light. + +So this was an option +that we could also + +have that basically +we just have to have + +multiple receivers, radio +frequency receivers that + +are on the bottom +right hand corner. + +So then she could +send different signals + +from her phone to control each +and every light independently. + +So it was an approach +we thought of. + +The price tag on +it was about $70 + +because we would have to have +the [? BLE ?] shield as well + +as the Arduino. + +And then the outlet, +the receiver, + +was also a little bit of cash. + +So then after that +we like started + +trying to come up with how +we were going to do this. + +And our next idea was WeMo. + +We saw this online. + +Basically, they have +their own solution for it. + +Basically, you can connect +to it through an application + +that they already have provided. + +The application is free, and +the product actually costs $41. + +So we thought of having this +implemented in her system + +and then possibly expanding +the SDK for the application + +so that she could have +an easier time using it, + +and then have it +basically tailored to her + +so that she only had to +look at the application + +and touch larger buttons +since the buttons are + +a little smaller +than we would hope. + +Possible next steps +is what I just + +said, where we expand +an application based + +off the SDK for WeMo and make +that app available for her. + +Or if this ends up being a +solution right of the shell, + +then we could possibly +taken an avenue where + +after fixing this light +problem with WeMo, + +go into the voice +applications so try and see + +if we can tailor voice +application for her. + +So our timeline is by +the end of October, + +we hope to have WeMo installed. + +The first half of +November we hope + +to prototype the like UI +for either the voice app, + +also, possibly, if +necessary, the light app. + +Second half, we would like +to have this app done in iOS. + +The reason for prototyping +[INAUDIBLE] it's faster, + +and we can get a lot of +the UI feel really quickly. + +And then after +that we would just + +keep testing and iterating +until we have a product that + +fits Barbara's needs. + +Any questions? + +PROFESSOR 1: Could you +say a bit about how + +you're going to divide the +work among the three of you? + +STUDENT 3: OK, so in terms +of the work for the door, + +we've been all +going to the center + +to speak with as many +people as possible. + +So for the time +being, it's been a lot + +of contextual inquiry and a lot +like designing all together. + +But in terms of the next +steps for installing the WeMo, + +we were going to go +to the center together + +and while two of +the members were + +going to be working on +installing this in the room, + +we were also going to continue +to ask about the door, + +we are pushing towards +like at least speaking + +to a lot of members in +the center about the door, + +since that is an issue +that we would hope + +would be solved in the future. + +After that is installed, the +dividing the actual application + +process, so since we, +as a team, don't all + +have like skills in +App Inventor and iOS, + +we were going to divide +up so that we would end up + +having some of the base +code that would definitely + +be necessary for iOS built +right from the beginning + +while the UI is being +prototyping in App Inventor. + +So in terms of +like team specific, + +it would be two members +working on the iOS application, + +while one member just +continually prototypes + +the ideas that the team comes +up with in App Inventory + +to like give a feel for it. + +We would always go as a team +to show this to Barbara. + +And then once the App +Inventor UI decision is made, + +we would all be +working on the iOS apps + +since that's going to be +the majority of the part. + +Any other questions? + +PROFESSOR 5: So +basically, the door + +is sort of too +hard is basically-- + +it's just not workable? + +STUDENT 2: There a lot of +regulations with the door. + +We'd have to get it +approved by the fire + +department, the public health +department, and the people + +at the center, a lot +of them don't even + +know how it functions +and how it connects up + +to like the central system +that closes all the doors when + +a fire alarm goes off. + +So it would require +a lot more research, + +and we're not sure if +it's feasible to finish + +this project in the next two +or three months that we have. + +JESSICA HERRING: +So we are Team Art. + +I'm Jessica. + +RACHEL ELLISON: Rachel. + +STEPHANIE CHEN : I'm Stephanie. + +JESSICA HERRING: And what +we have decided to build + +is a power lift. + +So first, we're going +to introduce our client. + +His name is Art. + +He is an adaptive rock +climber, a hacker, a tinkerer. + +He likes to build +stuff-- adapt stuff + +to his specifications +and his desires, + +and he's a very active +member of his community. + +He has a girlfriend, and she +works in his hacker space + +at the Artisans +Asylum in Somerville, + +which is pretty much +a hacker space, where + +people build stuff. + +However, he has T5 Asia +B Paraplegia, which + +is an incomplete paraplegic. + +So he has some sensory +function below his waist, + +but no motor function. + +In addition to this, he has +a grade 2 shoulder separation + +that is not quite bad +enough to need surgery, + +but we do want to consider +this when making our design. + +We don't want to make our +mechanisms too manual. + +So Art wants to be able +to work on the floor. + +He wants to be able to get under +some of his bigger projects, + +like he'll lift up a wheelchair +on his lift that he's designed, + +and he'll want to get under it. + +But it's really +hard to do that when + +you're getting out +of a wheelchair + +and you can't move your legs. + +So, in addition to that, if you +were to fall out of his chair, + +he would like to be able to +use something to get back up + +alone independently. + +[VIDEO PLAYBACK] + +-Well, I'm a [INAUDIBLE] minded +person, a lot of independence. + +Before I got hurt +in March of 2010, + +I was the person who took +care of all of our household + +maintenance. + +I did a lot of +motorcycle repair. + +[INAUDIBLE] + +Pretty much [INAUDIBLE], +I worked on it. + +Now, I still try to do +as much of that as I can. + +We're filming this at +Artisan's Asylum, which + +is one of the world's +largest hacker spaces, + +maker spaces and +collaborative workshops + +that anyone [INAUDIBLE]. + +We have shops that cover an +incredibly wide range of skills + +and technology. + +What they call a T-5 Asia B, +which basically means that + +from about here down I +have no motor function. + +Because I can't get in and +out of my chair easily, + +I'm more or less +limited to doing things + +that I can sit in front of. + +[END PLAYBACK] + +JESSICA HERRING: He +is quite a character, + +and he's very specific +about he wants. + +But we figure that we can +help him out with that. + +So our goal is to design +something that's portable, + +something that's +lightweight, something + +that is about the +height of his chair + +that he can get in and out +of and get up and down with. + +So the height of the +wheelchair seat-- Art cat + +only move about three or four +inches vertically by himself. + +And so we need our device +to be about the height + +of his wheelchair seat, +which is 22 inches tall, + +but we'd also like it to be used +anywhere he wants to use it. + +So we originally wanted him to +be able to take it with him, + +and that's still +one of our goals. + +We also need it to +weigh under 20 pounds. + +This is because he +wants his girlfriend + +to be able to take it to him +if he falls out of his chair + +and needs it or for +some other reason. + +His girlfriend can +only lift 20 pounds + +because she has a medical +condition that restricts that. + +So our major success +metric is time. + +A lot of these +design constraints + +will make or break the project, +but the time is a variable. + +So we would like it to be +approximately one minute. + +Art wanted something a +little more like 30 seconds + +to 45 seconds, but we think +a minute would also be OK. + +STEPHANIE CHEN : So after +taking these design limitations + +into account, we decided to +look into products that were + +commercially available. + +So at first, we began looking +into commercially available + +medical technology. + +For example, that up +there is something called + +an [? elk ?] emergency lift. + +It's probably the most +ideal out of these products + +for our client because it +weighs approximately five pounds + +and it can support 1,000 pounds. + +The only problem with it is +that it costs $3,000 at least, + +and there's no guaranteed +stability if he's actually + +lifting in the chair. + +There's nothing preventing +them from falling to the side. + +And just for fun, +we decided to look + +into other types +of lifting cushions + +available in other industries. + +We actually found something +called the Map Jack, which + +is something similar. + +It costs about $800, and it +can lift probably six tons-- + +fun fact. + +We then decided to look into the +idea of a scissor lift, which + +is a relatively prevalent +lifting mechanism. + +You can find it in construction +sites and warehouses and so on. + +The problem with that +idea is that there + +is a lot of friction losses +associated with scissor lifts, + +and considering the +fact that none of us + +are mechanical +engineers, we decided + +it would be best if we +started off with something + +a little simpler. + +And actually, if we consider +the weight of a scissor lift + +into account, it would certainly +weigh more than 20 pounds. + +We then decided to look into a +pool lift, which Art actually + +owns. + +The main issue with this idea +is that unfortunately it's + +stationary, and we require a +very powerful linear actuator, + +so we decided to +scrap those ideas. + +One idea that we +actually came across + +is something similar to +one of those stair lifts. + +It's essentially a sliding lift. + +It'll bring someone who's not +capable of going to upstairs + +from the bottom to the +top of their staircase. + +And Art was actually in +preference of this idea. + +As you can see, based +on the lower sketch, + +it appears to be +relatively light design. + +And it's incredibly portable +because it essentially + +looked like a tripod. + +And unfortunately, the +major disadvantages of this + +is we, again, have to deal +with a lot of friction losses, + +and we also have +to include a bunch + +of fail safes such +as hand brakes, + +just to ensure that he doesn't +accidentally slide down when + +he's near the top of the ramp. + +And for this design +we actually need + +a very specialized motor, +something that's low speed + +and high in torque. + +One idea that-- so +this is actually our + +currently most worked done idea. + +It's a screw lift essentially. + +And that is a smaller +scale prototype. + +Based on this drawing, you +can see that we essentially + +take multiple 80-20 +rods and arrange them + +in that sort of fashion, so +you have one rod on this side + +and one rod on the other, where +there's a seat in the middle. + +And in between those two +rods, and what's holding up + +the chair, is a threaded rod. + +So essentially we'd +be using either + +a drill motor or +any sort of motor + +to twist that threaded +rod to lift or to cause + +the chair to ascend or descend. + +The major advantage +to this is it + +can be designed to +be rather foldable, + +and we don't have to +build in any fail safes + +because we're dealing +with a threaded rod. + +And actually, the motors +required for this design + +are also relatively cheaper. + +But the major +disadvantages to this idea, + +in particular, is that we have +to work with multiple parts, + +and this could be a +potentially heavy idea. + +So here is actually a +video of the prototype. + +RACHEL ELLISON: So this +showing it does move. + +This me turning it by hand. + +And so if you're turning +it at maybe 100, 150, + +it would be moving a lot faster. + +The [INAUDIBLE] we're looking +at are eight turns per inch. + +So at 22 inches, we are +looking at about 200 turns. + +So the next steps in +our process really + +are to expand on these +two ideas and decide + +which design to pursue. + +Stephanie is handing +around now 80-20 + +rod, which is the basis +of our sliding mechanism. + +And really what +we're trying to do + +is understand what +parts we'll be + +able to get within +our budget constraints + +and which one will +provide a lighter weight + +design that fits more of +our design specifications. + +We'd like it to be full +scale, our next prototype, + +and we're going to prioritize +durability and sturdiness. + +After that, we'd like to make +a more polished prototype + +of our final idea. + +We'd like this one to fold +up to be transportable + +and to be within our +weight specifications. + +For our first +prototype, we're not + +going to worry so +much about that. + +We'd like to try to +optimize the lifting + +time and the speed at +which the motor turns + +to lift Art up and down. + +And finally, we'd like to +think about the feasibility + +of mass production +of this device + +and what is going into it +and whether those things will + +be available for other users. + +And so our projected costs +with the slider design + +which is a little bit +more expensive we're + +going to need a linear bearing +to slide up and down the broad + +with hand brake built +in so that it will be + +stable at the top of the ramp. + +And that's about $65. + +For a high torque, +low speed motor, + +those are pretty pricey +and come at $60 to $80 new. + +We've been looking into +scavenging this part + +to try to cut down costs. + +We'll also need other parts, +such as hinges and legs, + +so that'll fold up. + +For the screw lift +design, we're looking + +at using a threaded rod, +and this Acme thread design + +is a special kind of threading +designed to bear weight + +and not snag so that we can turn +it hopefully at higher speeds. + +We'll also need a low +torque, higher speed motor. + +Those will be +significantly cheaper, + +and actually we have several +of those on hand right now. + +And the rest of +the lift is going + +to be aluminum or +wooden parts which can + +come from the hardware store. + +So with that, I'd like to +thank teammates Jessica, who's + +been in charge of +videotaping our meetings + +and edited both the lovely +videos you saw earlier, + +Stephanie, who's been +heading up our prototyping + +and is going to be +doing a lot of stuff + +with building in +the next few weeks, + +and then I'm not +going to thank myself, + +but I've been doing a lot of +the interviewing and client + +communication. + +We'd also like to give a +special thanks to Don Fredette + +at The Boston House, +who's provided us + +with a lot of guidance, +parts, moral support, Joseph + +Parse, in the Department +of Material Science + +and Engineering, who helped +us figure out the screw lift + +design and what parts +we'd need to make it work, + +and finally our client +himself has helped us + +a lot with the design +feasibility and sourcing parts, + +and since he works +at this hacker space, + +he's also volunteered to +help us put it together, + +and, of course, the PPAT staff +makes this class possible. + +Any questions? + +PROFESSOR 4: We have about +three minutes for questions. + +PROFESSOR 4: Have you looked +at Kiva Systems, a robot + +for warehouse automation? + +They were bought +for $600 million + +by Amazon a couple years ago. + +But they have a lift, a +clever lift mechanism. + +Their founder talked to +[? Mickey ?] last week. + +Maybe I can give you +a pointer or two. + +They have a clever design. + +Maybe it's the same. + +But I do worry about the overall +electromechanical robustness. + +Have you thought about +how the whole-- the power, + +the connectors, the control +everything puts together? + +RACHEL ELLISON: We should +have said something about this + +during the presentation, +but Art has + +hacked into 24 volt +battery system in his chair + +and has an Anderson +volt connector that we + +can use to power our devices. + +PROFESSOR 4: So you'll connect +in to the wheelchair battery. + +PROFESSOR 6: So that partly +answered one of my question. + +I had two. + +One, what equipment does Art +use at makers space, and two, + +has he adapted or hacked +any of his existing? + +So yes, he has hacked +his wheelchair. + +JESSICA HERRING: He does that +quite frequently actually. + +He replaces his joystick. + +He [INAUDIBLE] adjust the +sensitivity for [INAUDIBLE]. + +RACHEL ELLISON: I think +he uses the [INAUDIBLE], + +and he's built this foot peddle +to help him use variable speed + +devices. + +He can't use his feet. + +I'm not sure +realistically how much + +he's going to be able to help +us with putting it together. + +But we thought it was +really kind that he offered, + +and maybe there will be things +that he's able to assist with. + +PROFESSOR 6: +[INAUDIBLE] it could + +be interesting to think about +then going forward, even + +beyond the class, how +do you design this + +so that he can +continue tinkering + +with it after the +semester is done, + +if he's already in +a position and is + +interested in doing that. + +That's great. + +PROFESSOR 1: So this is +interesting in the sense + +that he's intentionally +on the ground, right? + +You're not trying to +recover from fall, + +which I think is where many +of the other assistive devices + +are thinking about. + +I want to actually probe +on this one minute time + +because if he's intentionally +getting on the ground, + +he's maybe planning +to get back up, + +and he might do it, in fact, +frequently-- getting under, + +getting back in the chair to +go somewhere else for a tool, + +then going back and +getting under again. + +Does the one minute that you're +talking about, is that just + +measuring the time that +it takes like the motor + +to propel him up to +wheelchair height, + +or are we talking about the time +to set it all up, get on it, + +as well as move up? + +STEPHANIE CHEN : That's the +time he wants to spend actually + +maneuvering himself on +the floor to his chair. + +So we haven't actually taken +into consideration setup time, + +though I guess that's +another thing we can add in. + +But, again, that's going +to depend on the design + +we choose, but some +may be, I guess, + +modular in the sense that +it may take some [INAUDIBLE] + +apart and actually have to +assemble the entire apparatus. + +But for now, we're just +focusing on the time length + +between him getting +from the floor + +to the chair or vice versa. + +RACHEL ELLISON: So +another reason to favor + +this screw lift +over the slider lift + +is that that's a lot more +flexibility in how fast + +the thing goes up and down. + +With a slider lift, +because so much torque + +is required to just +move a pulley that way, + +we'd be looking at-- we have a +minimum possible time of about + +45 seconds. + +Whereas with the screw +lift, pretty much the faster + +you turn the motor, the +faster the thing moves. + +And then the only +top consideration + +really is how fast we +can move it safely. + +We certainly don't +want to put him + +in risk of being +propelled off the chair + +or dumped onto the floor. + +PROFESSOR 1: I'd +encourage you to include + +setup time as one of +your metrics for at least + +[INAUDIBLE]. + +PROFESSOR 4: OK, any final +questions or comments? + +All right, thank you, Team Art. + +And we'll jump right in. + +Thank you. + +Hi, everyone. + +We're team Chris. + +So I'll introduce ourselves. + +This is Arthie. + +She's a senior, and +she is our point + +of contact for the semester +with our client, who + +we'll introduce later. + +Next is Carolyn +right over there. + +She is also a senior, +and she is the person + +in charge of keeping us on +task during our meetings, + +make sure focused, and make sure +that we're following our goals + +and aiming for +goals every meeting. + +PHOEBE: Next, we have +Dirk, who's a junior, + +and he is our main +scribe for the semester. + +And then there's me, Phoebe. + +I'm the main photographer and +videographer for this semester. + +And, of course, our most +important member of the team + +is Chris. + +He is a first year MBA +student at Boston College. + +He loves to read, blog, +and he loves baseball. + +So he has this rare +condition called + +Miyoshi Myopathy, which is a +progressive muscular dystrophy + +condition. + +So he can only walk +short distances + +and can only carry a +small load at a time. + +STUDENT 4: The +activity that Chris + +would like us to +help him with is just + +as daily movements +throughout the world. + +Since he uses forearm +crutches and a scooter, + +he needs place that don't have +stairs and elevators to get + +around. + +Currently, when he +wants to go anywhere, + +he has to research +that place online. + +He uses Google Maps, +and he uses Yelp. + +Yelp has a little +bit of information. + +But really what he uses is the +Google Maps Street View feature + +because he can actually +see where he can get up + +onto a sidewalk +or the front door, + +if there's stairs up to the +door and things like that. + +If he can't get +enough information + +from online resources, +sometimes he + +can call the building, +the restaurant, whatever + +he wants to do, and +they can give him + +some more information that way. + +On campus, he primarily uses +the disabilities office, + +and oftentimes he +has to go in and talk + +to them because there's +not very much information + +on their website. + +And can you go back? + +One thing that's really hard +about some of these things, + +except for the phone +call, of course, + +is that he doesn't know what's +going on inside the building. + +He can't see that on +a virtual application. + +So we've decided he needs this +in everywhere that he goes, + +but we've decided for +the scope of the class + +to focus on his school +and Boston College. + +Particularly, we're +starting with the building + +that he uses every day, +which is Fulton Hall. + +One thing about Boston College +is that it's very hilly. + +So for Chris, that's really +difficult. Some of the paths + +are sort of ramps up the +hills, but they're very steep, + +which can be difficult for +his chair and also scary. + +If he's going down, he +might not be able to stop. + +And there's a lot of stairs +on some of these paths. + +So actually he needs to go +through buildings sometimes + +and use elevators +within the buildings + +to get from a lower +level of campus + +to a higher level or vice versa. + +And then he's a +very busy students. + +So if he needs a route +like that that's not easy + +for him to see online, +he might take a long time + +to get to his meetings +or his classes, + +and that's a problem for him. + +And the other thing is +students on campus don't really + +know these routes, and +they're also very busy, + +so it's hard for them to +help him out sometimes. + +So our goal is to +take the things + +that he uses right now-- Google, +Yelp, knowing about stairs, + +and just going out +trial and error, + +and finding these warnings +by himself-- we're + +trying to take that uncertainty +and bring all of these elements + +together into a +central application + +that he can just go to +this one place, see a map, + +and also go inside +buildings and find out + +what things might be difficult. +If an elevator isn't working. + +If an automatic +door isn't working, + +if there happens to be something +in the middle of the hallway + +that could be in his way, or +a classroom that has stairs up + +to the seats, so he knows +about these things in advance + +and doesn't have to deal +with that uncertainty + +that he deals with every day. + +DIRK: So Chris came +into this project having + +a pretty good idea of what +he wanted us to create, + +and that is an +application that presents + +him all of this information +in an easily accessible form. + +So our first goal was we needed +to narrow down the scope, which + +we decided was Boston College. + +And even more than +that, we decided + +to look at three different +tiers of information. + +So the first one being +at the building level. + +So this would entail +essentially being + +able to see the +entrances and exits that + +are accessible to +buildings, being + +able to see information that is +things like potholes or places + +like hills that are hard to +access outside of the building. + +The second tier is that +of the floor level, + +actually being able to +look into the buildings + +and seeing where the +locations of elevators + +are, if there's +stairs to get places, + +where the accessible +bathrooms are located. + +And then the third tier is +that of rooms, in particular, + +if there are difficult +doors to get in, + +if it's like a lecture +hall where the accessible + +seating is, which +entrances he can use, + +and being able to present all +of that in a tiered format. + +So for our goals, we +want to definitely + +be able to do the first +and the second level. + +We think those +are both feasible. + +We're hoping to get to +the third tier as well. + +Beyond that, there are +two different aspects + +the application, that being +the front end and the back end. + +The front end is the +visual display, what + +Chris will actually be using. + +And the back end is where +this data that is being + +displayed actually comes from. + +Now, the interesting +aspect of this project + +is that because it +is navigation-based, + +it's based on buildings and +wherever Chris wants to go, + +ultimately his vision is to have +this available for everywhere + +he wants to go. + +Obviously, that's not all +feasible for the scope + +of this project. + +But we really want to have +some sort of method built + +in that allows us to +expand to future locations + +and be able to bring +in different locations + +to this application. + +So we want to, alongside +the front end on display, + +have some sort of +method for bringing + +in new places and new +data into the application. + +As far as our actual +prototypes go, + +we initially started by all +four of us creating drawings + +explaining how sort of we +saw this application coming + +together, and we presented +all of these to Chris + +and discussed with him what +he liked about each of them, + +and took the best +aspects of each, + +and condensed them down into +a singular paper prototype. + +So initially, he +liked the map view + +that showed each +of the buildings + +with alerts for where +the entrances are + +and then being able +to have things pop up, + +such as potholes, +things outside actually + +getting to the building the +he might need to be aware of. + +Then, when he actually +clicked on the building, + +it would show up a +actual floor plan, + +being able to look at different +floors within the building. + +He liked the floor plan because +it was very easy to navigate. + +And on top of that, having +different notifications, + +different alerts, +potentially color-coded + +that show different +pieces of information, + +being where there are doors, +stairs, elevators, bathrooms, + +all this information +that he wanted to be + +able to see very easily marked. + +One of the other big things +that he wanted to make sure of + +is that we were presenting +just facts about the building. + +He wants the information to be +presented in a fairly raw form + +so he can then determine for +himself this is somewhere + +I can go, or this is +somewhere I can't go. + +As far as actually +creating this, + +we decided on a web application +because it was easier for us, + +as far as our skills +coming in, and it + +was a lot more universal. + +He can access it from his +phone, from this computer. + +And then we want to use +JavaScript Node Express as far + +as our languages to be +able to code that and Mongo + +for our database structure. + +The success metrics +that we want to use + +to measure this apply +to the user experience + +side of this project, to make +sure that Chris is getting + +the most benefit out +of the application + +that we're creating. + +And so one of the +metrics that we are using + +is the number of +clicks it's going + +to take Chris to get a +specific item of information + +that he needs. + +So, for instance, starting +from the full campus map, + +we want him to only have +to click three times + +to get a specific floor +plan of a building + +that he wants to +go into for class. + +And upon that, click +only one more time + +to look at a specific +room in that building + +or the specific elevator +and to get the information + +that you need to know for +that specific facility. + +The second metric that +we are going to use + +is how much time it takes for +him to gather this information. + +So, as we mentioned +earlier, his current methods + +are to call the +restaurant he's going to, + +call the disabilities office, +look at their website, + +and just look +through Google Maps. + +And so we want to +be able to time + +how long it takes him to +get to find information + +about a specific classroom +through those ways, + +and then make sure that +it's about 60% less + +time for him to use our website +to get that same information. + +The third metric we're using is +to allow for uncertainty-- not + +allow for uncertainty, but to +reduce as much uncertainty as + +possible. + +And so that way +within our website, + +he's not confused when +using it, and so we + +want to count how +many questions he has, + +and have a little help menu that +he can use to clarify things. + +But also just to +reduce uncertainty + +within all of his +travel procedures + +and to allow him to answer +his questions before actually + +going out. + +Now for our future +plans of what we're + +doing for the rest of the +semester, as Dirk mentioned, + +we're going to split this into +the back end and the front end. + +So Dirk and Caroline +are going to work on + +in the data aggregation +and database set up, + +so getting all the information +that we want to display + +and then creating a database +structure that we can scope + +later on to add more details-- +different types of buildings, + +different floors, +different facilities. + +And Phoebe and I are going to +be working on the front end + +to increase the user +usability of the whole design. + +And since Chris +wants actual facts + +that he can interpret +for himself, + +we want to have a good +balance of images and text + +and just make sure +that he's able to use + +this in a clear way. + +The timeline for this semester +is until the end of October, + +we want to start +our coding process + +and come up with a +software prototype, + +and in the first +week of November, + +work through our +software prototype, + +and by the end of that, have +something to present to Chris + +and have him actually +test it and use it + +so that way we can +revise and reiterate + +and keep going with it. + +And by the end of +November, we want + +to have our final version +that we can continue + +to reiterate throughout. + +And that's it. + +Any questions? + +PROFESSOR 5: All right, we have +four minutes for questions. + +Have you tried to work +with Boston College + +to get the actual floor +plans, like PDFs and things? + +Do you have all that? + +STUDENT 6: Yes, +so we're actually + +in contact with Boston College +Disabilities Office right now, + +and they are working +with the head architect + +to get the information. + +Right now we're just working +through the legal procedures + +of which information +he's actually + +allowed to give us and so +what we're allowed to display. + +PROFESSOR 5: MIT has +a whole database. + +If you ever want MIT, +I'll show you where it is. + +AUDIENCE: How does he update +it, like if a pothole is fixed. + +DIRK: Yeah, so that's +an area that we're still + +trying to figure out. + +We've had a couple +a different ideas, + +one being trying to +crowdsource that out somehow, + +having the ability +in the app for users, + +if they notice something, +to put that in as an alert. + +We've thought about +contacting Boston College, + +like the maintenance or +the facilities office, + +and if their staff +notices things, + +having a way to put that in. + +So those are a couple +ideas, and we're still + +trying to figure out +exactly how the best + +way to go about that is. + +AUDIENCE: Excuse me, +we have a colleague + +in New York City that's +done, in the past, + +maybe two or three years +ago, like a Yelp for people + +with disabilities for +accessibility to buildings. + +I'm fairly sure the +site no longer as fresh + +as it was during his +NYU [? ITP ?] days, + +but we could put you +in touch with them + +and see how they've updated or +how they basically populated + +that information. + +DIRK: Yeah, that would be great. + +CIMMY: Hi, we're Team Felicity. + +I'm Cimmy. + +This Ari. + +This is Becca, and +we're Team Felicity. + +This is our mid-semester review. + +Today we're going to +show you our video, talk + +about the HAAT +model for Felicity, + +our project vision, and +our accomplishments so far. + +So we'll start off by +showing you our video. + +[VIDEO PLAYBACK] + +-Let's like together +develop a prototype + +of assistive technology +that you will find useful. + +-I have a disease called +neurofibromatosis, + +which causes tumors to build +up in the brain and spine. + +I had surgery last +February in 2014 + +to remove the tumor on this +side, which also took out + +my hearing nerve completely, +so now absolutely profoundly + +deaf on each side. + +I also have a tumor on my +optic nerve behind this eye. + +My vision, I have days where +my vision is perfectly fine, + +and I can see +everything clearly. + +Then I have other days where +things are just like really + +cloudy and I lose +depth perception + +or have trouble seeing +like walk signals, + +like seeing whether it's +white or red or flashing. + +And I had a really close call +a few weeks ago over in Fenway, + +where, because I +know I'm impaired, + +so I'm looking for the light, +and I still kind of like + +look because I just +don't trust anyone. + +But I look for the light, +and then a big truck + +comes right towards me. + +It was terrifying. + +I pretty much rely on like +reading people's lips, + +and then I'll take +out pen and paper + +if it's like something that's +really, really important + +or if I'm just +particularly tired + +and don't have the energy. + +I'm moving to a new +apartment on October 1st, + +and they're installing flashing +smoke detectors, CO detector, + +and a doorbell. + +I've never used a +flashing doorbell before, + +so that will be exciting. + +I can feel the vibes. + +And I have like a +computer that I watch + +captioned DVDs on sometimes. + +I don't have a TV or radio. + +I set my phone to vibrate all +the time for when I get emails + +and so forth. + +If I call you, then they'll +be a relay operator. + +-I'm doing fine. + +Thanks for asking. + +Go ahead. + +-Hi, I'm Ari. + +Hi, I'm Cimmy. + +Hey, I'm Becca, and +we're Team Felicity. + +We've gotten to know Felicity a +lot better through our meetings + +and have come up with +a lot of neat ideas. + +We're excited to get going. + +[END PLAYBACK] + +CIMMY: So, as you +can see, Felicity + +has neurofibromatosis, which +is a genetic disorder that + +can causes tumors to +grow on nerve tissue. + +She had a few surgeries +to take away some tumors, + +and due to those surgeries, +she lost a lot of her vision. + +She can use her +peripherals, and she's + +profoundly deaf on both sides. + +The activities that +Felicity likes to do + +are she really enjoys +walking around Boston. + +She also actually has routine +doctor's appointments, + +so she's usually between +our home and the hospital. + +And in terms of +context, Felicity + +lives alone at her apartment. + +She is unemployed +and frequents doctors + +offices and the hospital. + +And she leaves the house +minimally during evening. + +She doesn't like +to be out at night. + +And she happens to be +very open to letting + +people know that she +is deaf and using + +assistive technology +between that. + +In terms of assistive +technology that Felicity already + +uses, so to +communicate with her, + +we have been using a notepad +or a laptop with size 36 font + +so she can read it. + +And she also uses her iPhone, +as you saw on the video. + +She receives emails +from her doctor + +when she's out the doctor's +office to notify her + +when they're ready for her. + +And she uses a Sprint relay +app for phone calls and so on. + +And, as you saw on the video, +a flashing smoke detector, + +and a CO alarm are +installed in her home, + +and she also has a flashing +doorbell, which the noise is + +loud enough that she actually +feel the vibrations when + +they're occurring. + +So now I'll switch +over to Becca. + +BECCA: So I guess along +the way of getting + +to know Felicity +and her daily life, + +we like discussed +a lot of activities + +that we could potentially help +her design an AT solution for. + +We had to kind of whittle +it down to one motivation + +that we could center +a project around. + +And so the problem that +we're going to focus on + +is that Felicity can't always +detect when events occur + +because she's mostly deaf. + +And so these include like +if people call her name, + +either at a cafe or at +the doctor's office, + +or if a laundry +machine's done, or when + +she's going on her walks, +she can't hear cars + +honking from incoming traffic. + +And so these are +all situations where + +somehow RET could help her. + +And so our goal +for the project is + +to develop an AT that +will notify Felicity + +when particular events happen. + +So this is variation came +particularly from an email + +that Felicity sent to us with +this hearing dogs video in it. + +I guess we don't have +time to show the video, + +but the idea was just that she +saw this hearing dog video, + +and at the end of +her email she said, + +it would be really +cool if I could have + +my own handheld hearing dog. + +And so that was a cool +step towards, for us, + +to find a solution for her. + +And so throughout so +far, we've currently + +been going through an +iterative design process + +to kind of whittle +go down a solution + +and find something +that works for her. + +We've been using low +fidelity prototypes + +to get feedback from +Felicity, even to narrow down + +for our project solution. + +And as we'll talk +about a little later, + +our initial design +process showed us + +that our project problem changed +after discussions with her. + +So this is just some example +of some of the sketches + +we've done. + +In this example, we had +two parts of a solution. + +One was a button that someone +could pass for her attention, + +and the other would be some +sort of wearable device + +that would vibrate, telling +her once like this button has + +been pushed. + +Now Ari is going to +share a little bit more + +about our initial problem +statement and problem overview. + +ARI: Right, so the first +project we wanted to tackle + +was trying to let Felicity +know when someone called out + +her name. + +And because she can't hear +and she has limited vision, + +it's pretty difficult if +she was in like a waiting + +room or the doctor's +office or in a classroom + +to like figure out if someone's +trying to contact her. + +So the idea we came up with +was rather than having someone + +try to call out their name, we +would have them have a button + +that they could press. + +And when they press +the button, it + +would contact Felicity +that they were + +trying to get her attention. + +So this is the kind of +overview of that design. + +We have a button that +someone could press. + +It would send a +message to her iPhone, + +and then the iPhone +would display + +some sort of notification. + +And then we'd also +have a wearable device + +that she could use, and they +both display notifications. + +So kind of a two-step +notification. + +Luckily, we really worked +on doing iterative design + +and also user-centered +design because we + +try talking with her +about how well does + +she think this will work, and +she really liked this idea. + +But she was concerned about +other people using it. + +And so one thing we +tried talking with her + +is what would you like more? + +And particularly, she +would want something + +that she could use possibly more +often and also independently + +because this original project +involves two clients-- Felicity + +and whoever we +give the button to. + +And so the new +focus of our project + +changed to try and +make some sort of way + +to make sound emitting +appliances within her home + +accessible for Felicity. + +So basically within +Felicity's apartment + +she has a few different +household appliances + +that she doesn't know +when they're done working. + +In particular, the laundry +machine, when it's done, + +it just triggers a beep, +and it doesn't have a timer. + +So she would like a way to +know when it's finished. + +And basically the +idea we have is + +we could have some +sort of device + +that she could place next +to the household appliance. + +And then when the +appliance is finished + +doing whatever its task is, +it will emit some noise, + +and this device +would pick up on it + +and send a signal +to Felicity to let + +her know that whatever +the household appliance + +task has completed. + +So again, we kind of kept +last half of the project + +that we started scoping +out and just talking about. + +And instead, now we +have a microphone + +that would be placed next +to the household appliance, + +and then the microphone would +be sending sound to the iPhone. + +And within the iPhone we +could have an application + +that would notify when the +sound of the appliance finishing + +has happened. + +So for the +implementation we decide + +to use Bluetooth because +this is in her apartment. + +It's less than 30 +feet, and also Felicity + +leaves her phone plugged in +while she's at her house. + +So we're not too +worried about that part. + +And then right now we're all +working on developing an iPhone + +application for detecting +the sound and also + +the Bluetooth integration. + +So these are kind of +the hardware pieces + +we've been also testing out. + +The first one was a Bluetooth +camera shutter button, + +and we also have a +headset that we're just + +using as a microphone +because we already have it, + +and we're just trying to +do low-cost prototyping. + +BECCA: So to talk a little +bit about the success metrics + +that we set up for our project, +for the technical side, + +we broke down our +project in two parts. + +There's going to be a noise +detection to the iPhone part, + +and then the iPhone to +the notification part. + +And so from there, we +have like two activities-- + +the amount of noise +that this microphone + +could withstand before, and also +correctly detect the appliance. + +And those are kind of +our levels of how good + +it would be, where level +two would be ideal, + +and level zero is not actually +doing its job, and then + +the number of noises +it would detect. + +And then for the iPhone +to notification part, + +the success metric would +be like the percent + +times the notification actually +succeeds and is correctly + +pinging Felicity. + +And then we have for +overall performance, + +I guess the best way to +measure our success is + +just how many appliances we +can actually adapt this to. + +And so the laundry machine, +dryer, toaster oven, + +and tea pot are just +five things that we + +are kind of aiming towards +being able to make this for. + +And also we're considering +maintenance as well. + +Once we finish +with this project, + +we want to make sure that +all the parts of our project + +are replaceable so that +Felicity can continue + +to use it once we're not there. + +From the UI perspective side, +the best way quantitatively + +to measure this is +just the average time + +it would take to set up a +notification for a machine task + +that she has, and then +also her own perspective + +about whether or not +she things the UI + +is intuitive and easy to use. + +CIMMY: And in terms of our +project development so far, + +we have purchased at Bluetooth +camera shutter remote button, + +which was actually +for our previous idea, + +in order for Felicity to be +able to give a button to someone + +so that they could press +it to a signal her phone + +that she's getting a signal. + +And we started developing +an iPhone application + +for the project that +we've moved towards, + +and now we're investigating +wearable devices that Felicity + +could wear for notification. + +And we're leaning +more towards the side + +of some sort of wrist +wearable or something + +that she could hold. + +And in terms of our project's +plans and timelines, + +this is just a general +timeline that we have. + +We hope to get her iPhone +app working at a low scale + +so that we can just have +her iPhone connected + +with some microphone and see +how well that works, if we're + +getting a vibration +notification, + +gather appliances and a sound +library by November 7th, + +and then test the +app functionality. + +We want to focus a lot on +having Felicity test out the app + +and see how well it works. + +And then probably by +the 28th of November, + +we want to clean up the final +project and work on the UI + +and fix bugs on the last week. + +Thank you. + +PROFESSOR 4: Questions +and comments? + +AUDIENCE: So for the appliances +you were talking about, + +like tea pot, laundry, +and [INAUDIBLE], + +would it make more sense +to use a timer for that? + +Because each of those +appliances are pretty set + +timings for the [INAUDIBLE]. + +Would that be easier than +detecting a sound [INAUDIBLE]? + +BECCA: So that's something +that we asked Felicity about, + +and I think she-- oh sorry. + +That is something we +asked, we brought up + +when we were talking about +this is with Felicity. + +But, I think, one thing +is like you don't always + +remember to set up the +timer, or sometimes + +you just like run into +something else that you do. + +And so you told yourself, +oh, I was going to do that. + +But she just forgets. + +And also when she's home, she +doesn't keep her iPhone on her. + +So she usually +has it plugged in, + +so if she can't hear the alarm, +or even if it was vibrating, + +she just doesn't know +if she's in another room + +or she's taking a nap to +actually go and check on it. + +So I think when we did +introduce this idea to her, + +and we told her, well, there +are like other alternatives that + +seem more feasible, +she really liked + +the idea of having +something that's preferably + +a wearable that just vibrates. + +Then she doesn't have +to be thinking about it. + +But she'll know exactly +when it's ringing that she + +should go back and see it. + +AUDIENCE: Why do +you need the phone? + +BECCA: So I think first in +terms of like implementation, + +it's a bit easier +to have an iPhone + +app be the one that's sending +the Bluetooth signal back + +to the wearable. + +And also in terms of +modularity, I think, + +it would be a more +complicated hardware solution + +if it was intelligently +picking up just + +to send to the specific +hardware device. + +I'm sorry, from like sound +detector to the wearable, + +it's two more complicated +hardware solutions. + +And so then it's the +question of maintenance, + +like how is she going +to replace these more + +complicated solutions? + +But instead, we're +using two kind + +of just all they have to do is +either send a Bluetooth signal + +and then receive a +Bluetooth signal, + +and that's like two much cheaper +hardware pieces for us to get. + +And she could always +replace those. + +And then the iPhone +app is something + +that she'd already have. + +AUDIENCE: How much is +a Bluetooth switch? + +BECCA: Yeah, so what +we looked at so far, + +like out-of-the0box solutions +to be like $30 to $40. + +AUDIENCE: If you +skip the phone, I + +guess, you would be able +to use an RF link for $5? + +BECCA: OK, but would +that be able to know-- + +like would the +notification collector, + +I mean the sound detector, +know to send it exactly + +to this Bluetooth wearable? + +Or is that a Bluetooth +[INAUDIBLE] RF? + +ARI: I guess one thing +we'd also like to include + +is one of the reasons we +kind of stuck with iPhone + +is we were interested in finding +commercial products that we + +don't have to customize +any of the hardware, + +especially with +the button design. + +If it broke, she could +easily purchase a new one. + +Like those buttons that we +first shows, they're under $10 + +to get similar designs. + +So what we're +really hoping to get + +is something that +will work after we're + +done with the class. + +So you can purchase +these designs + +and keep making designs that +work with the iPhone, then + +why don't we capitalize on that? + +PROFESSOR 4: So, Leonard, +do you have a question? + +PROFESSOR 5: Did you +make an actual prototype + +for-- what was your prototype? + +BECCA: It was mostly so +far just like sketches. + +It was mostly +sketches to show her + +like, OK, these are +three pieces, two pieces, + +or like, these are kinds of +pieces we're talking about, + +and then like whether or +not you even like the idea. + +PROFESSOR 5: Sort of +like a storyboard? + +BECCA: Yeah, and +user [? flows. ?] + +ARI: And we also brought +the physical hardware + +of that button to kind of +see how she liked it, would + +she feel like it's OK to use. + +PROFESSOR 5: So you're +going to run with that one? + +The you bought, is that +what you're going to use, + +or are you going to +use something else? + +ARI: No, we're +planning on switching + +to try to make something +that only works + +with her independently because +we're concerned about having + +the extra client that +couldn't really control, + +make sure they were on board. + +BECCA: So it's like +microphone, iPhone, and then + +wearable or something +to like [INAUDIBLE]. + +PROFESSOR 5: OK, I +think we're at time. + +Thank you very much. + +EANN: Hi, we're Team +Don, and my name is Eann. + +This is Christina, +and over here is Jan. + +First, we'd like to tell +you a little bit more + +about our client. + +Our client's name is Don, and +he is a male senior citizen + +who currently lives alone. + +He's a strong advocate +for support groups, + +and he constantly tells us +about how he goes to conferences + +and speaks to health +professionals. + +And he suffered from polio +during his childhood, + +and that is affected +his left leg. + +But in 2002, he also +suffer from a stroke + +that affected the right +hemisphere of his brain. + +So currently he has limited use +of his left side and especially + +his left arm, and +this has also resulted + +in cognitive +difficulties, especially + +in the late afternoon +or early afternoon, + +whenever sometimes it's a +little bit harder for him + +to process and to focus +and to just kind of stay + +on track with +whatever conversation + +he's currently engaged in. + +From our very first meeting, +we knew that Don loved food, + +and he loved to cook. + +So one of our very +first questions + +was, what's your favorite +flavor of ice cream? + +And this kind of transcended +into this conversation of food, + +and we discovered +that Don was actually + +a food catering manager +prior to his disability. + +And when you first +started at his job at KFC, + +he learned about his passion for +cooking and expressing himself + +through food. + +And so as a result, +he still cooks, + +and he constantly talks +about different recipes. + +And we got the opportunity +to make omelettes + +with him one day. + +And so with his left hand, +it typically is stable, + +and he uses his +right hand to cook. + +And with his left hand +held typically either + +brace apart or hold +onto a cheese package, + +and rip open the top. + +But typically, it's +only just his right arm + +that he uses, and +it's essentially + +his only method of cooking-- +or only manner of cooking. + +And so this you can see is +in his actual apartment. + +We got the opportunity to go +visit Don in his apartment + +and kind of see where he lives +and see where he actually + +takes the time to cook. + +And so we noticed +that is apartment + +is actually-- his kitchen +is actually fairly small. + +It is about the size of a small +kitchen in Burton Conner, which + +is a dorm on campus. + +And you can see +in the next slide + +that the stove is fairly +close to the sink, + +and so it's a pretty +small quarter for cooking. + +And he's looking +for a way to improve + +the mobility in his kitchen. + +The assistive +technology that Don uses + +includes Velcro, which +is on the left hand side. + +He constantly tells us +that Velcro is his friend, + +and he uses Velcro +for his shoes. + +And on the far +right side, he also + +uses a leg brace +that prevents him + +from hyperextending his knee. + +But the most important assistive +technology that he uses + +is in the center, his iPhone. + +So you can see, he's clearly +really excited about it, + +and he's constantly using it to +schedule tasks, to send emails, + +and he depends on this iPhone to +remind him of his daily tasks. + +So in addition to +those three items, + +he also uses a cane +to help him walk. + +And so this is a quick +video of him using his cane, + +and it's just simply +to help him walk + +and to assist him +in being mobile. + +JAN: So some challenges +we've already + +seemed to have +faced in this design + +project is our team scheduling. + +So it's really hard for +us three to get together + +with Don at the same time, same +place, and get something going. + +And with Don's +cognitive overload, + +he also has issues +focusing and telling us + +what he really wants for +us to do on our project. + +So we initially started +out with two projects + +that we were going to work for +helping him with his cooking. + +As you can see here, we +started off thinking of ways + +that we can help him +out in the kitchen. + +So something that +he did mention to us + +was the fact that he needs +some help carrying big pots. + +So since he has one +arm, it's really hard + +to actually stabilize the +pot and move it from point A + +to point B without +having the contents spill + +and move around too much. + +And another thing that was +mentioned to us by-- oh, he's + +not here today-- another one +of the actual participants + +of this class, +Jeffrey, was something + +used for stirring or +stabilizing the pot + +whenever he's either +stirring or doing something + +with the contents of the pot. + +And we initially started off +with two different projects + +that we were going +to test out with Don + +and figure out what he really +wanted out of us in this class. + +So the first one was the +stability of the mixing pot + +or doing something +with the pot or a bow. + +And we decided that we wanted +to focus on these three + +little things, so minimizing +how much the bowl moves, + +how much it tips over, and +making sure that whatever + +we use is fast and easy to use. + +And as for moving +pots, we wanted + +to focus more on how he can +take these pots from point A + +to point B, so large pots with +a lot of things inside of them, + +and minimize how +much effort he has + +to put into moving these +things and stabilizing them, + +while making it very +easy to use as well + +and minimizing how +much liquid falls off + +or how many things could +go wrong with this. + +So we initially started off +with some design prototypes + +for the stirring or for slipping +is something that we called it. + +So we started for +slipping, and we showed him + +some of these designs, and we +got some very good feedback + +from him. + +He was very, very opposed +to having something + +big and clunky in his +desk or his workspace + +whenever he was cooking. + +And we used that to +further our designs + +and make sure that we go with +something smaller, something + +that doesn't get in the way and +is very easy for him to use. + +And after that, +we showed him some + +of the things that he may +want to use for moving a pot. + +So over here, we +can see something + +that can adjust to a pot +and use some sort of strap + +around his forearm or +shoulder to move the pot. + +Because he mentioned that +he has some what we thought + +were really big +pots to move around + +for a pretty long distance. + +This was before we actually +went over to his house + +and found out what +we were working with. + +And another thing that +we thought was maybe-- he + +says he slides the pots a +lot because it's a lot harder + +for him to carry them. + +Something that we +thought of was maybe + +having a little mobile +station for him to use, + +where he can slide the pot onto +it, slide it across the floor, + +and then move it onto +the actual stove itself. + +And finally, this is just some +brainstorming/prototyping. + +We thought of like those +things that drummers use, + +where they attach +it to their chest, + +and you can pot in there. + +But this is just +for brainstorming. + +We just threw ideas out there. + +And we showed +these ideas to Don, + +and we decided +that we were going + +to go much further into the +actual movement of the pot, + +rather than the +stirring, since he + +says that that's one of the +big challenges that he has. + +And that's where we +are currently at. + +We have identified the +problem and know what we're + +going to do from here on out. + +CHRISTINA: So this +past Friday we + +actually got to go +to Don's apartment + +to actually see what +his kitchen is like + +and what his cooking +environment is like. + +And so before we were +initially imagining + +that he was using pots +that were like this big + +and that you would need to +use like two hands to carry. + +But we actually found +out that they're actually + +normal sized pots which you +can carry with one hand, + +and also the thing about his +kitchen space being very small + +made some of our initial +designs not feasible. + +So here you can see a +video of Don in action. + +So, as you can see, +Don has trouble + +moving filled pots from +his sink to his stove top + +without having some of +the contents spill out. + +And so we kind of made a +sketch of his kitchen layout. + +And so the task requirement +that we decided on + +was that we wanted to +help him be able to lift + +and move the filled pot and also +not spill any of the contents. + +And so these are +success metrics. + +Them metrics include lifting +and moving the pot vertically + +as well as horizontally, and +then the amount of spill there + +is , and also how much time it +takes for him to move the pot + +from the sink to his stove top. + +And so we kind of evaluated +the current state of how + +he accomplishes the task, and +we used a scale from 1 to 10, + +one being we would +really like to help + +him improve in this aspect, +and 10 being this is OK, + +and this is great. + +So we have our current goals, or +we have the current situation, + +and we have the target. + +And we also have +our reached goals. + +So our contributions +up to date-- + +since we haven't really gotten +into the prototyping part yet, + +we have all been designing +and brainstorming together. + +And so Jan has been +facilitating the meetings. + +Eann has been documenting +and taking notes, + +and I have been taking +videos and also photos. + +And for our future +contributions, + +we are going to continue doing +what we're doing right now. + +Also, once we get a better idea +of what are design will be, + +maybe split up +the tasks for what + +different components +of our product + +that we are going +to be working on. + +So I guess like our +most crucial step + +is our next step, which is +like in the immediate future. + +So we really need to +be able to come up + +with a design for our first +prototype and get it to Don + +and get his feedback on it. + +So one of the main things +that we will be focusing on + +for this first prototype will +be mechanisms and concepts + +for how he can move a +pot from a certain height + +to a higher place. + +And also, we might be +considering the material + +that we will be using +the product because that + +relates to, I guess, like +how much mass he can move. + +And we will also be doing a +more quantitative evaluation + +of Don's skills, so maybe like +how much mass he can life, + +or how long can he +hold up a pot for. + +And so I these are +our project plans. + +So, as I mentioned before, +our main thing right now + +is to get our first prototype +out and get his feedback on it. + +And then from then on, +we can add more details + +into our planning for how we are +going to finish this product. + +PROFESSOR 5: Any questions? + +Great, thank you. + +PROFESSOR 6: Did he +articulate any other scenarios + +of where her would move the +pot, aside from stove to sink? + +JAN: No, that's the +only one we actually + +saw him doing physically. + +But I imagine that he would have +to potentially move something + +that has like maybe spaghetti +to cool it down somewhere else + +and maybe actually serving +my the pot, so from his + +to the kitchen table. + +But that's the only one +we actually saw him doing, + +and that's why we are going to +get some further tests to see + +distance, weight, and other +things that could potentially + +play into our design. + +PROFESSOR 6: So I +was wondering that + +about how that may +impact your metrics + +or quantitative metrics of being +able to move it three feet. + +AUDIENCE: Maybe you +want to try to try + +to get him to fill +the pot and move it + +while there's hot liquid because +that may make a big difference. + +And he was very aloof +about splashing cold water, + +but he might not want to +do that with boiling water. + +JAN: No, we didn't want +anybody to get hurt there. + +AUDIENCE: Did you guys +try the pot-moving thing + +yourselves to see +how much-- you filled + +the pot all the way to the top. + +How feasible is it for +like one of you to do that? + +JAN: No, we did not. + +It's something that +we should have done. + +You're right. + +PROFESSOR 5: So imagine +everything goes amazingly well. + +What will you actually make? + +What will you actually do? + +Will it be a redesigned pot? + +Is it sort of like thinking +about the procedure + +of how to do these tasks? + +You can imagine building +a robot that could do it. + +It would be like really hard. + +What are you +actually going to do? + +JAN: So what really +thought was an attachment + +that you can adjust to +almost any type of pot. + +So one that I showed +over there was something + +that you can put around +the top side of the pot, + +so a belt or some +type of thing, where + +it hooks on to the +top of the pot, + +and you have belt on top +of it, where he can-- + +he says he would really like +to be able to really use + +his forearm because his fingers +also get really tired, to be + +able to put the belt over his +arm and then carry it over, + +using that, rather +than the handle, + +where he doesn't have +as much stability. + +PROFESSOR 1: I do want to +echo what was said over here + +about heat. + +I think that the fact +that you didn't mentioned + +that at all in your success +metrics or in your constraints + +is actually a pretty +serious problem, right? + +He's moving a pot to his +sink-- I'm sorry to the stove + +in order to heat it up. + +And then if he's going to +continue to be independent, + +he's going to have +to do something + +with that hot, still heavy pot. + +So you need a +consideration here which is + +that he doesn't burn himself. + +And I think that +spillage may be something + +that you should give a little +less concern to because that + +can be solved by not filling it +up as much because that would + +boil over anyway, if you filled +it up as much as he actually + +did in that video or +by putting lids on it. + +But I really would encourage +you to worry much more + +and pay much more attention +to the problem of heat. + +JAN: That's something +that we'll definitely + +take into account then. + +AUDIENCE: Especially +if you're going + +in the direction of +putting something + +that's close to his body. + +And you can do tests +with him not burning him, + +like put food coloring. + +Have him wear something he +doesn't care about, and see + +if he an immediate reflex if +he's spilling food coloring + +on his clothes. + +It'll give you a better +sense of is he really + +that confident with this +forearm, for instance. + +PROFESSOR 5: So it's +a really hard problem. + +In some ways, I'll +just be honest, + +like when I first saw +this compelling client, + +and it's like, this +is a great person. + +It would be great +to help him, and I + +know that he loves to cook. + +But dealing with pots full +of water, possibly hot water, + +that just seems like +a really hard problem. + +And I wonder if +there's something else + +you can do for him that's not +so physically, like something + +that doesn't have +a safety dimension. + +You don't want to +give him something + +he's going to burn himself +with badly on his own. + +You know what I mean? + +JAN: Yeah, we could also take +the alternative approach, + +the actual stirring or moving +the things within the pot. + +PROFESSOR 5: Or +maybe he just lets + +it cool for a really long time. + +But how do you get the food out? + +I don't know. + +Maybe there's a way to +rethink the entire-- I mean, + +the goal is to have cooked food. + +Is there a way to rethink +how you get cooked food + +at the end of the day +that avoids lifting + +a heavy pot from the sink. + +AUDIENCE: Have a longer hose. + +AUDIENCE: That's another +way to do the filling right? + +PROFESSOR 5: You can +imagine filling it + +with like small-- +you know, a ferry + +system of smaller +things that get + +added a little bit at a time. + +AUDIENCE: Or an interesting +pump [INAUDIBLE]. + +PROFESSOR 5: If you can sort of +train him how to do the task. + +I wonder if there +are experts out there + +in the world that figure +out how to do this. + +Disabled cooking, is +there such a thing? + +But I admire you +for taking it on. + +It just seems really +hard and dangerous. + +PROFESSOR 4: Great, +thank you, Team Don. + +Thanks again. + +We managed to get +through them all. + +We have maybe two or +three minutes left. + +Maybe I'll ask if the +panelists or the support staff + +have general comments on +all the presentation today, + +for the panelists here today. + +And Professor Miller, if you +have general comments or advice + +on the presentations or the +project progress in general, + +give you the +opportunity to do that. + +But while you think about +that, just one reminder + +is to remember to upload your +slides from the presentation + +today, so that we can integrate +these things into the video, + +and so that we can look +at your slides as well. + +And then the reports +are due Friday, + +and then next week, we'll +have read all the reports, + +and we'll give you some more +written feedback, a letter + +grade at this point in time. + +But I'll of the +panelists, Jose or Anna, + +Professor Leonard, +Professor Miller, + +if you have any general +comments or advice for teams + +at this point in time. + +PROFESSOR 1: Great to see the +progress that you're making. + +Keep meeting with your +clients, and focus + +on trying to finish that +prototype that you're + +going to deliver at the +end of the semester. + +PROFESSOR 5: I would +just say, like I've + +taught design classes +and mechanical and ocean + +engineering, and it's +really challenging + +when the schedule crunch +at the end of the semester, + +and so sometimes +you're going to have + +to down scope towards the end. + +But if you try to really think +about a measurable result, + +that you really +accomplish something, + +and what that would be, and make +sure you at least get that far. + +Like it would be a disaster +if you didn't at least do x. + +What is x? + +Have a prototype that +does something, that gives + +some value to your client. + +And so the time's going +to go really quickly, + +and you're going +to run out of time. + +PROFESSOR 6: I would say +it's great to that you all + +are meeting what seems +like a regular basis + +with your collaborators +for these projects. + +And so take advantage +of every time + +you're meeting with +them to bring something + +you can hold in your hand +that is going to impact + +the final design, whether +a potential material + +you could use, a prototype +of a looks-like design, + +or this is a feature design. + +But that'll really +help you to continue + +to iterate on those features. + +AUDIENCE: I would echo +Professor Leonard's comments + +of take something. + +If you're going towards +the end of the semester, + +pick that one item +that you know is going + +to make a critical difference. + +If you spend too much +time picking pots, + +we know what pots look +like, and how they behave. + +But if you don't know how +another mechanism that you're + +designing behaves, +then focus on that one. + +And just in case you +do run out of time, + +you know that that's an +addressable thing to leave out. + +Don't leave out the +[? core ?] [INAUDIBLE]. + +PROFESSOR 4: Michelle, +[INAUDIBLE], Grace, + +you have general comments? + +OK, cool. + +I think one thing I'll +say is I think you all + +have gotten to know your +clients really well, + +from the presentations. + +On Monday and Wednesday and on +Friday night or on the weekend, + +Grace and I watched all the +videos that where submitted. + +We're all very impressed. + +You really have +spent a lot of time + +and really gotten +to know the people. + +One thing I would +suggest is you really, + +maybe in the next couple +weeks, really, really get + +to know the client's task. + +I mean really break +it down and come up + +with these measurable +metrics, try things out, + +food color the water, things +like that, so you can really + +get a sense of +whether your device + +or whether the system you're +building is going to work. + +PROFESSOR 5: Like really +put yourself in their shoes. + +PROFESSOR 4: OK, I think +that's pretty much it. + +Next week we're going to do +a bunch of electronic device + +labs, so bring your +laptop computer + +is what we're hoping +for people to bring. + +Grace, you have a +final announcement? + +GRACE: Yeah, we sent +out a poll today. + +We're going to set up twice +weekly hobby shop office hours. + +So if you think you're going +to be using a hobby shop + +or building anything mechanical, +please fill out the-- we'll + +decide by Friday what +those office hours are. + +Thanks. + +PROFESSOR 4: And +Monday's class lecture + +and lab will both +be in this room + +because we're doing these +electronic device access + +labs, so 32044 at both +1:00 PM and 3:00 PM. + +OK, thanks. \ No newline at end of file diff --git a/EtPw85aeLtg.txt b/EtPw85aeLtg.txt new file mode 100644 index 0000000000000000000000000000000000000000..64d8cbdbbe717d7ac1226c106947e3ae1e90f931 --- /dev/null +++ b/EtPw85aeLtg.txt @@ -0,0 +1,78 @@ +Hi. This is Elizabeth from the Publication +Team at MIT OpenCourseWare. + +I'd like to show you some videos we've published +to help you learn about Calculus: how it works + +and why it is important. You can find them +in the Supplemental Resources section under + +Mathematics. + +The series is called "Highlights of Calculus" +and was developed by MIT Professor Gil Strang. + +What you'll find here is a collection of videos +that introduce the basic ideas of calculus. + +It's for high school students, college students, +or anyone who might need help understanding + +or remembering the subject. + +Let's take a look at The Big Picture of Calculus. + +You can watch the video here, or you can download +it for free from iTunes U or the Internet + +Archive locations. + +There's a brief description, as well as a +more detailed index of the topics and where + +to find them in the video. + +Each video begins with an outline of the content +to be covered. As Professor Strang presents + +the calculus lesson, text appears on the lower +part of the screen to reinforce key points. + +"...will help. For me, calculus is about the +relation between two functions. And one example + +for those two functions is function one: the +distance, distance traveled. What you see + +on a tripmeter in a car. And function two, +the one that goes with distance, is speed." + +Summary slides and practice problems, including +an audio track, are available to help guide + +you through the material. There is also a +link to his free Calculus Textbook. + +This program is also available through MIT +OpenCourseWare's Highlights for High School. + +It includes the same videos and other materials +found on the main OCW site. + +I'm pleased to report that thousands of people +have viewed this program since it was first + +published in May, and the feedback has been +wonderful. I hope you enjoy learning about + +the highlights of calculus too. + +If you'd like to receive updates on newly-published +courses and staff picks like this one, please + +sign up for our newsletter. + +OpenCoureWare is free to use, but we rely +on donations from users like you to support + +our publication. \ No newline at end of file diff --git a/F0VsQWWVWU4.txt b/F0VsQWWVWU4.txt new file mode 100644 index 0000000000000000000000000000000000000000..4041c9a5aa510a386df7cb56b93ff21ebb8217ef --- /dev/null +++ b/F0VsQWWVWU4.txt @@ -0,0 +1,10720 @@ +align:start position:0% + +okay good + + align:start position:0% +okay good + + + align:start position:0% +okay good +morning so today we're going to continue + + align:start position:0% +morning so today we're going to continue + + + align:start position:0% +morning so today we're going to continue +our exploration of um multi-threaded + + align:start position:0% +our exploration of um multi-threaded + + + align:start position:0% +our exploration of um multi-threaded +algorithms last time we talked about uh + + align:start position:0% +algorithms last time we talked about uh + + + align:start position:0% +algorithms last time we talked about uh +some aspects of scheduling and a little + + align:start position:0% +some aspects of scheduling and a little + + + align:start position:0% +some aspects of scheduling and a little +bit about um + + align:start position:0% +bit about um + + + align:start position:0% +bit about um +Linguistics uh to describe a + + align:start position:0% +Linguistics uh to describe a + + + align:start position:0% +Linguistics uh to describe a +multi-threaded uh computation and today + + align:start position:0% +multi-threaded uh computation and today + + + align:start position:0% +multi-threaded uh computation and today +we're going to actually deal with some + + align:start position:0% +we're going to actually deal with some + + + align:start position:0% +we're going to actually deal with some +[Applause] + + align:start position:0% + + + + align:start position:0% + +algorithms so we're going to start out + + align:start position:0% +algorithms so we're going to start out + + + align:start position:0% +algorithms so we're going to start out +with a really simple thing actually + + align:start position:0% +with a really simple thing actually + + + align:start position:0% +with a really simple thing actually +what's what's fun about this actually is + + align:start position:0% +what's what's fun about this actually is + + + align:start position:0% +what's what's fun about this actually is +that everything I'm going to teach you + + align:start position:0% +that everything I'm going to teach you + + + align:start position:0% +that everything I'm going to teach you +today I could have taught you in week + + align:start position:0% +today I could have taught you in week + + + align:start position:0% +today I could have taught you in week +two okay because basically it's just you + + align:start position:0% +two okay because basically it's just you + + + align:start position:0% +two okay because basically it's just you +know taking the divide and conquer or + + align:start position:0% +know taking the divide and conquer or + + + align:start position:0% +know taking the divide and conquer or +hammer and just smashing you know + + align:start position:0% +hammer and just smashing you know + + + align:start position:0% +hammer and just smashing you know +problem after problem with it okay uh + + align:start position:0% +problem after problem with it okay uh + + + align:start position:0% +problem after problem with it okay uh +and and so and actually uh next week's + + align:start position:0% +and and so and actually uh next week's + + + align:start position:0% +and and so and actually uh next week's +lectures on caching also very similar + + align:start position:0% +lectures on caching also very similar + + + align:start position:0% +lectures on caching also very similar +okay so everybody should bone up on + + align:start position:0% +okay so everybody should bone up on + + + align:start position:0% +okay so everybody should bone up on +their Master theorem and uh and uh + + align:start position:0% +their Master theorem and uh and uh + + + align:start position:0% +their Master theorem and uh and uh +substitution methods for recurrences and + + align:start position:0% +substitution methods for recurrences and + + + align:start position:0% +substitution methods for recurrences and +so forth because that's what we're going + + align:start position:0% +so forth because that's what we're going + + + align:start position:0% +so forth because that's what we're going +to be doing and of course all this stuff + + align:start position:0% +to be doing and of course all this stuff + + + align:start position:0% +to be doing and of course all this stuff +will be on the + + align:start position:0% +will be on the + + + align:start position:0% +will be on the +final so we'll start with matrix + + align:start position:0% +final so we'll start with matrix + + + align:start position:0% +final so we'll start with matrix +multiplication + + align:start position:0% + + + + align:start position:0% + +uh we'll do n by + + align:start position:0% +uh we'll do n by + + + align:start position:0% +uh we'll do n by +n so our problem is to do c uh equal a * + + align:start position:0% +n so our problem is to do c uh equal a * + + + align:start position:0% +n so our problem is to do c uh equal a * +B and the way we'll do that is using + + align:start position:0% +B and the way we'll do that is using + + + align:start position:0% +B and the way we'll do that is using +divide and + + align:start position:0% + + + + align:start position:0% + +conquer as we saw before although we're + + align:start position:0% +conquer as we saw before although we're + + + align:start position:0% +conquer as we saw before although we're +not going to + + align:start position:0% +not going to + + + align:start position:0% +not going to +use um sten's method + + align:start position:0% +use um sten's method + + + align:start position:0% +use um sten's method +okay we'll just use uh the ordinary + + align:start position:0% +okay we'll just use uh the ordinary + + + align:start position:0% +okay we'll just use uh the ordinary +thing and I'll leave strin as an + + align:start position:0% +thing and I'll leave strin as an + + + align:start position:0% +thing and I'll leave strin as an +exercise so the idea is we're going to + + align:start position:0% +exercise so the idea is we're going to + + + align:start position:0% +exercise so the idea is we're going to +look at um matrix multiplication in + + align:start position:0% +look at um matrix multiplication in + + + align:start position:0% +look at um matrix multiplication in +terms of of an N byn Matrix in terms of + + align:start position:0% +terms of of an N byn Matrix in terms of + + + align:start position:0% +terms of of an N byn Matrix in terms of +n/2 by n /2 matrices so I partition C + + align:start position:0% +n/2 by n /2 matrices so I partition C + + + align:start position:0% +n/2 by n /2 matrices so I partition C +into four + + align:start position:0% + + + + align:start position:0% + +blocks and likewise with a and b + + align:start position:0% + + + + align:start position:0% + +okay and we multiply those out and that + + align:start position:0% +okay and we multiply those out and that + + + align:start position:0% +okay and we multiply those out and that +gives + + align:start position:0% +gives + + + align:start position:0% +gives +us the following + + align:start position:0% + + + + align:start position:0% + +make sure you get all my indices right + + align:start position:0% + + + + align:start position:0% + +okay so it gives us the sum of these two + + align:start position:0% +okay so it gives us the sum of these two + + + align:start position:0% +okay so it gives us the sum of these two +n byn + + align:start position:0% +n byn + + + align:start position:0% +n byn +matrices okay so for example if I + + align:start position:0% +matrices okay so for example if I + + + align:start position:0% +matrices okay so for example if I +multiply the first row by the First + + align:start position:0% +multiply the first row by the First + + + align:start position:0% +multiply the first row by the First +Column I'm putting the first term a11 * + + align:start position:0% +Column I'm putting the first term a11 * + + + align:start position:0% +Column I'm putting the first term a11 * +b11 in this Matrix and the second one + + align:start position:0% +b11 in this Matrix and the second one + + + align:start position:0% +b11 in this Matrix and the second one +a12 * + + align:start position:0% +a12 * + + + align:start position:0% +a12 * +B21 gets placed here so when I sum and + + align:start position:0% +B21 gets placed here so when I sum and + + + align:start position:0% +B21 gets placed here so when I sum and +so forth for the other entries and when + + align:start position:0% +so forth for the other entries and when + + + align:start position:0% +so forth for the other entries and when +I sum them I'm going to get uh my result + + align:start position:0% +I sum them I'm going to get uh my result + + + align:start position:0% +I sum them I'm going to get uh my result +so we can write that + + align:start position:0% +so we can write that + + + align:start position:0% +so we can write that +out as a + + align:start position:0% +out as a + + + align:start position:0% +out as a +um + + align:start position:0% +um + + + align:start position:0% +um +uh let's see not sure this going to all + + align:start position:0% +uh let's see not sure this going to all + + + align:start position:0% +uh let's see not sure this going to all +fit on + + align:start position:0% +fit on + + + align:start position:0% +fit on +one board but we'll see what we can do + + align:start position:0% +one board but we'll see what we can do + + + align:start position:0% +one board but we'll see what we can do +okay so we can write that out as a + + align:start position:0% +okay so we can write that out as a + + + align:start position:0% +okay so we can write that out as a +multi-threaded program + + align:start position:0% + + + + align:start position:0% + +so this we're going to assume that n is + + align:start position:0% +so this we're going to assume that n is + + + align:start position:0% +so this we're going to assume that n is +an + + align:start position:0% +an + + + align:start position:0% +an +exact power of + + align:start position:0% + + + + align:start position:0% + +two for + + align:start position:0% + + + + align:start position:0% + +Simplicity and since we're going to have + + align:start position:0% +Simplicity and since we're going to have + + + align:start position:0% +Simplicity and since we're going to have +two matrices that we have to uh add uh + + align:start position:0% +two matrices that we have to uh add uh + + + align:start position:0% +two matrices that we have to uh add uh +we're going to basically put one of them + + align:start position:0% +we're going to basically put one of them + + + align:start position:0% +we're going to basically put one of them +in uh in our output C that'll be the + + align:start position:0% +in uh in our output C that'll be the + + + align:start position:0% +in uh in our output C that'll be the +first one and we're going to use a + + align:start position:0% +first one and we're going to use a + + + align:start position:0% +first one and we're going to use a +temporary Matrix + + align:start position:0% + + + + align:start position:0% + +uh T which is also n by + + align:start position:0% + + + + align:start position:0% + +n okay and the code looks something like + + align:start position:0% +n okay and the code looks something like + + + align:start position:0% +n okay and the code looks something like +this okay if n equals + + align:start position:0% + + + + align:start position:0% + +one and C of + + align:start position:0% +one and C of + + + align:start position:0% +one and C of +one + + align:start position:0% +one + + + align:start position:0% +one +one gets a of 1 one + + align:start position:0% + + + + align:start position:0% + +time B of one + + align:start position:0% +time B of one + + + align:start position:0% +time B of one +one and + + align:start position:0% + + + + align:start position:0% + +otherwise what we do then is we + + align:start position:0% + + + + align:start position:0% + +partition the + + align:start position:0% + + + + align:start position:0% + +matrices okay so we partition them into + + align:start position:0% +matrices okay so we partition them into + + + align:start position:0% +matrices okay so we partition them into +the block so how long does it take me to + + align:start position:0% +the block so how long does it take me to + + + align:start position:0% +the block so how long does it take me to +partition a matrix into + + align:start position:0% +partition a matrix into + + + align:start position:0% +partition a matrix into +blocks if I'm clever in my programming + + align:start position:0% + + + + align:start position:0% + +yeah uh no time or it actually does take + + align:start position:0% +yeah uh no time or it actually does take + + + align:start position:0% +yeah uh no time or it actually does take +a little bit of time one yeah order one + + align:start position:0% +a little bit of time one yeah order one + + + align:start position:0% +a little bit of time one yeah order one +basically okay because all it is is just + + align:start position:0% +basically okay because all it is is just + + + align:start position:0% +basically okay because all it is is just +index calculations you have to change + + align:start position:0% +index calculations you have to change + + + align:start position:0% +index calculations you have to change +what the index is you'd have to pass in + + align:start position:0% +what the index is you'd have to pass in + + + align:start position:0% +what the index is you'd have to pass in +when you're passing these in addition to + + align:start position:0% +when you're passing these in addition to + + + align:start position:0% +when you're passing these in addition to +a b and c for example pass in a Range + + align:start position:0% +a b and c for example pass in a Range + + + align:start position:0% +a b and c for example pass in a Range +which would have essentially a constant + + align:start position:0% +which would have essentially a constant + + + align:start position:0% +which would have essentially a constant +overhead but it's basically order one + + align:start position:0% +overhead but it's basically order one + + + align:start position:0% +overhead but it's basically order one +time + + align:start position:0% + + + + align:start position:0% + +basically order one + + align:start position:0% +basically order one + + + align:start position:0% +basically order one +time okay to partition the matrices + + align:start position:0% +time okay to partition the matrices + + + align:start position:0% +time okay to partition the matrices +because all we're doing is index + + align:start position:0% +because all we're doing is index + + + align:start position:0% +because all we're doing is index +calculations okay and all we have to do + + align:start position:0% +calculations okay and all we have to do + + + align:start position:0% +calculations okay and all we have to do +is just as we go through is just make + + align:start position:0% +is just as we go through is just make + + + align:start position:0% +is just as we go through is just make +sure we keep track of the + + align:start position:0% +sure we keep track of the + + + align:start position:0% +sure we keep track of the +indices okay any questions about that + + align:start position:0% +indices okay any questions about that + + + align:start position:0% +indices okay any questions about that +people follow yeah okay okay just you + + align:start position:0% +people follow yeah okay okay just you + + + align:start position:0% +people follow yeah okay okay just you +that's sort of standard programming so + + align:start position:0% +that's sort of standard programming so + + + align:start position:0% +that's sort of standard programming so +then what I do is I spawn + + align:start position:0% + + + + align:start position:0% + +multiplication of + + align:start position:0% + + + + align:start position:0% + +whoops of the + + align:start position:0% + + + + align:start position:0% + +submatrices and spawn + + align:start position:0% + + + + align:start position:0% + +continues c21 gets a + + align:start position:0% +continues c21 gets a + + + align:start position:0% +continues c21 gets a + + align:start position:0% + + + align:start position:0% +b11 + + align:start position:0% +b11 + + + align:start position:0% +b11 +two + + align:start position:0% +two + + + align:start position:0% +two +then + + align:start position:0% +then + + + align:start position:0% +then +c22 gets + + align:start position:0% + + + + align:start position:0% + +a21 okay and continuing on to the next + + align:start position:0% +a21 okay and continuing on to the next + + + align:start position:0% +a21 okay and continuing on to the next +page + + align:start position:0% +page + + + align:start position:0% +page +uh let me just make sure I somehow get + + align:start position:0% +uh let me just make sure I somehow get + + + align:start position:0% +uh let me just make sure I somehow get +the indentation right so this is my + + align:start position:0% +the indentation right so this is my + + + align:start position:0% +the indentation right so this is my +level of indentation and I'm continuing + + align:start position:0% +level of indentation and I'm continuing + + + align:start position:0% +level of indentation and I'm continuing +right + + align:start position:0% + + + + align:start position:0% + +along and now what I do is put the + + align:start position:0% +along and now what I do is put the + + + align:start position:0% +along and now what I do is put the +results in + + align:start position:0% + + + + align:start position:0% + +T and then + + align:start position:0% + + + + align:start position:0% + +okay so I've spawn off all these + + align:start position:0% +okay so I've spawn off all these + + + align:start position:0% +okay so I've spawn off all these +multiplication so that means when I + + align:start position:0% +multiplication so that means when I + + + align:start position:0% +multiplication so that means when I +spawn I get to to after I spawn + + align:start position:0% +spawn I get to to after I spawn + + + align:start position:0% +spawn I get to to after I spawn +something I can go on to the next + + align:start position:0% +something I can go on to the next + + + align:start position:0% +something I can go on to the next +statement okay and execute that even as + + align:start position:0% +statement okay and execute that even as + + + align:start position:0% +statement okay and execute that even as +this is executing okay so that's our + + align:start position:0% +this is executing okay so that's our + + + align:start position:0% +this is executing okay so that's our +notion of multi-threaded programming I + + align:start position:0% +notion of multi-threaded programming I + + + align:start position:0% +notion of multi-threaded programming I +spawn off these eight things what do I + + align:start position:0% +spawn off these eight things what do I + + + align:start position:0% +spawn off these eight things what do I +do + + align:start position:0% + + + + align:start position:0% + +next what's the next step in this + + align:start position:0% +next what's the next step in this + + + align:start position:0% +next what's the next step in this +code sync yeah okay I got to wait for + + align:start position:0% +code sync yeah okay I got to wait for + + + align:start position:0% +code sync yeah okay I got to wait for +them to be done before I can use their + + align:start position:0% +them to be done before I can use their + + + align:start position:0% +them to be done before I can use their +results okay so I put a sync + + align:start position:0% + + + + align:start position:0% + +in saying wait for all those things I + + align:start position:0% +in saying wait for all those things I + + + align:start position:0% +in saying wait for all those things I +spawned off to be done and then + + align:start position:0% + + + + align:start position:0% + +what TNC yeah then you have to add + + align:start position:0% +what TNC yeah then you have to add + + + align:start position:0% +what TNC yeah then you have to add +TNC so let's do that with a sub routine + + align:start position:0% + + + + align:start position:0% + +call okay and then we're done we do a + + align:start position:0% +call okay and then we're done we do a + + + align:start position:0% +call okay and then we're done we do a +return at the end + + align:start position:0% +return at the end + + + align:start position:0% +return at the end +okay so let's write the uh code for for + + align:start position:0% +okay so let's write the uh code for for + + + align:start position:0% +okay so let's write the uh code for for +ad because add we also would like to do + + align:start position:0% +ad because add we also would like to do + + + align:start position:0% +ad because add we also would like to do +in parallel if we + + align:start position:0% + + + + align:start position:0% + +can and what we're doing here is doing C + + align:start position:0% +can and what we're doing here is doing C + + + align:start position:0% +can and what we're doing here is doing C +gets + + align:start position:0% +gets + + + align:start position:0% +gets +C+ + + align:start position:0% +C+ + + + align:start position:0% +C+ +t Okay so we're going to add T + + align:start position:0% +t Okay so we're going to add T + + + align:start position:0% +t Okay so we're going to add T +into uh into + + align:start position:0% +into uh into + + + align:start position:0% +into uh into +C so have some code here to do our base + + align:start position:0% +C so have some code here to do our base + + + align:start position:0% +C so have some code here to do our base +case and uh + + align:start position:0% + + + + align:start position:0% + +partitioning because we're going to do + + align:start position:0% +partitioning because we're going to do + + + align:start position:0% +partitioning because we're going to do +it with divide and conquer as before and + + align:start position:0% +it with divide and conquer as before and + + + align:start position:0% +it with divide and conquer as before and +this one's actually a lot easier we just + + align:start position:0% + + + + align:start position:0% + +spawn add of C11 + + align:start position:0% +spawn add of C11 + + + align:start position:0% +spawn add of C11 +t11 n / + + align:start position:0% +t11 n / + + + align:start position:0% +t11 n / +two C12 T12 n/ + + align:start position:0% +two C12 T12 n/ + + + align:start position:0% +two C12 T12 n/ +two c c21 + + align:start position:0% +two c c21 + + + align:start position:0% +two c c21 +t21 number two + + align:start position:0% +t21 number two + + + align:start position:0% +t21 number two +c22 + + align:start position:0% +c22 + + + align:start position:0% +c22 +t22 and over two and then + + align:start position:0% + + + + align:start position:0% + +sync and return the + + align:start position:0% + + + + align:start position:0% + +result okay so so all we're doing here + + align:start position:0% +result okay so so all we're doing here + + + align:start position:0% +result okay so so all we're doing here +is just dividing it into four pieces + + align:start position:0% +is just dividing it into four pieces + + + align:start position:0% +is just dividing it into four pieces +spawning them off that's it okay wait + + align:start position:0% +spawning them off that's it okay wait + + + align:start position:0% +spawning them off that's it okay wait +till they're all done then we return + + align:start position:0% +till they're all done then we return + + + align:start position:0% +till they're all done then we return +with + + align:start position:0% + + + + align:start position:0% + +result okay so anybody any questions + + align:start position:0% +result okay so anybody any questions + + + align:start position:0% +result okay so anybody any questions +about how this code works so remember + + align:start position:0% +about how this code works so remember + + + align:start position:0% +about how this code works so remember +that here we're going to have a + + align:start position:0% +that here we're going to have a + + + align:start position:0% +that here we're going to have a +scheduler underneath which is scheduling + + align:start position:0% +scheduler underneath which is scheduling + + + align:start position:0% +scheduler underneath which is scheduling +this onto our processors and we're going + + align:start position:0% +this onto our processors and we're going + + + align:start position:0% +this onto our processors and we're going +to have to worry about how well that + + align:start position:0% +to have to worry about how well that + + + align:start position:0% +to have to worry about how well that +scheduler is doing it and from last time + + align:start position:0% +scheduler is doing it and from last time + + + align:start position:0% +scheduler is doing it and from last time +we learned there were two important + + align:start position:0% +we learned there were two important + + + align:start position:0% +we learned there were two important +measures okay uh that uh that can be + + align:start position:0% +measures okay uh that uh that can be + + + align:start position:0% +measures okay uh that uh that can be +used essentially to predict the + + align:start position:0% +used essentially to predict the + + + align:start position:0% +used essentially to predict the +performance on any number of processors + + align:start position:0% +performance on any number of processors + + + align:start position:0% +performance on any number of processors +and what are those two + + align:start position:0% + + + + align:start position:0% + +measures yeah T1 and T Infinity so that + + align:start position:0% +measures yeah T1 and T Infinity so that + + + align:start position:0% +measures yeah T1 and T Infinity so that +we had some names T1 is + + align:start position:0% +we had some names T1 is + + + align:start position:0% +we had some names T1 is +the the work good and T Infinity + + align:start position:0% +the the work good and T Infinity + + + align:start position:0% +the the work good and T Infinity +is critical path length good okay so + + align:start position:0% +is critical path length good okay so + + + align:start position:0% +is critical path length good okay so +have the work in the critical path + + align:start position:0% +have the work in the critical path + + + align:start position:0% +have the work in the critical path +length if we know the work in the + + align:start position:0% +length if we know the work in the + + + align:start position:0% +length if we know the work in the +critical path length we can do things + + align:start position:0% +critical path length we can do things + + + align:start position:0% +critical path length we can do things +like uh say what the parallelism is of + + align:start position:0% +like uh say what the parallelism is of + + + align:start position:0% +like uh say what the parallelism is of +our + + align:start position:0% +our + + + align:start position:0% +our +uh of our uh program and from that + + align:start position:0% +uh of our uh program and from that + + + align:start position:0% +uh of our uh program and from that +understand how many processors it makes + + align:start position:0% +understand how many processors it makes + + + align:start position:0% +understand how many processors it makes +sense to run this program + + align:start position:0% +sense to run this program + + + align:start position:0% +sense to run this program +on + + align:start position:0% +on + + + align:start position:0% +on +okay so uh let's do that + + align:start position:0% + + + + align:start position:0% + +analysis okay so let's + + align:start position:0% +analysis okay so let's + + + align:start position:0% +analysis okay so let's +let um M subp of + + align:start position:0% +let um M subp of + + + align:start position:0% +let um M subp of +n be the P + + align:start position:0% +n be the P + + + align:start position:0% +n be the P +processor uh execution time + + align:start position:0% +processor uh execution time + + + align:start position:0% +processor uh execution time +for our + + align:start position:0% +for our + + + align:start position:0% +for our +maltt code and uh a subp of n be the + + align:start position:0% +maltt code and uh a subp of n be the + + + align:start position:0% +maltt code and uh a subp of n be the +same thing for + + align:start position:0% +same thing for + + + align:start position:0% +same thing for +our Matrix addition + + align:start position:0% +our Matrix addition + + + align:start position:0% +our Matrix addition +code so the first thing we're going to + + align:start position:0% +code so the first thing we're going to + + + align:start position:0% +code so the first thing we're going to +analyze is work and what do we hope our + + align:start position:0% +analyze is work and what do we hope our + + + align:start position:0% +analyze is work and what do we hope our +answer to our work + + align:start position:0% + + + + align:start position:0% + +is when we analyze work what do we hope + + align:start position:0% +is when we analyze work what do we hope + + + align:start position:0% +is when we analyze work what do we hope +it's going to be + + align:start position:0% + + + + align:start position:0% + +we hope it's going to be small grant you + + align:start position:0% +we hope it's going to be small grant you + + + align:start position:0% +we hope it's going to be small grant you +that okay what what could we Benchmark + + align:start position:0% +that okay what what could we Benchmark + + + align:start position:0% +that okay what what could we Benchmark +it + + align:start position:0% + + + + align:start position:0% + +against yeah if we wrote just something + + align:start position:0% +against yeah if we wrote just something + + + align:start position:0% +against yeah if we wrote just something +that didn't use have any + + align:start position:0% +that didn't use have any + + + align:start position:0% +that didn't use have any +parallelism okay we'd like our parallel + + align:start position:0% +parallelism okay we'd like our parallel + + + align:start position:0% +parallelism okay we'd like our parallel +code when run on One processor to be + + align:start position:0% +code when run on One processor to be + + + align:start position:0% +code when run on One processor to be +just as fast as our serial code the + + align:start position:0% +just as fast as our serial code the + + + align:start position:0% +just as fast as our serial code the +normal code that we would write to do + + align:start position:0% +normal code that we would write to do + + + align:start position:0% +normal code that we would write to do +this problem that's generally the way + + align:start position:0% +this problem that's generally the way + + + align:start position:0% +this problem that's generally the way +that we would like uh like these things + + align:start position:0% +that we would like uh like these things + + + align:start position:0% +that we would like uh like these things +to operate okay so uh let's see so what + + align:start position:0% +to operate okay so uh let's see so what + + + align:start position:0% +to operate okay so uh let's see so what +is that for matrix + + align:start position:0% +is that for matrix + + + align:start position:0% +is that for matrix +multiplication in the naive way yeah + + align:start position:0% +multiplication in the naive way yeah + + + align:start position:0% +multiplication in the naive way yeah +it's n cubed of course if we use stren's + + align:start position:0% +it's n cubed of course if we use stren's + + + align:start position:0% +it's n cubed of course if we use stren's +algorithm or one of the other U faster + + align:start position:0% +algorithm or one of the other U faster + + + align:start position:0% +algorithm or one of the other U faster +uh algorithms uh we can beat n cubed but + + align:start position:0% +uh algorithms uh we can beat n cubed but + + + align:start position:0% +uh algorithms uh we can beat n cubed but +for this problem we're just going to + + align:start position:0% +for this problem we're just going to + + + align:start position:0% +for this problem we're just going to +we're just going to focus on N cubed and + + align:start position:0% +we're just going to focus on N cubed and + + + align:start position:0% +we're just going to focus on N cubed and +let you do the stren uh as an exercise + + align:start position:0% +let you do the stren uh as an exercise + + + align:start position:0% +let you do the stren uh as an exercise +so let's analyze the + + align:start position:0% +so let's analyze the + + + align:start position:0% +so let's analyze the +work okay since we have a sub routine + + align:start position:0% +work okay since we have a sub routine + + + align:start position:0% +work okay since we have a sub routine +for ad that we're using in the multiply + + align:start position:0% +for ad that we're using in the multiply + + + align:start position:0% +for ad that we're using in the multiply +code okay we'll start by analyzing uh + + align:start position:0% +code okay we'll start by analyzing uh + + + align:start position:0% +code okay we'll start by analyzing uh +the + + align:start position:0% +the + + + align:start position:0% +the +ad so we have A1 of + + align:start position:0% +ad so we have A1 of + + + align:start position:0% +ad so we have A1 of +n okay is well can somebody give me a + + align:start position:0% +n okay is well can somebody give me a + + + align:start position:0% +n okay is well can somebody give me a +recurrence + + align:start position:0% +recurrence + + + align:start position:0% +recurrence +here how can I what's the recurrence for + + align:start position:0% +here how can I what's the recurrence for + + + align:start position:0% +here how can I what's the recurrence for +understanding the running time of this + + align:start position:0% + + + + align:start position:0% + +code okay this is basically this is + + align:start position:0% +code okay this is basically this is + + + align:start position:0% +code okay this is basically this is +week two is this this is lecture one + + align:start position:0% +week two is this this is lecture one + + + align:start position:0% +week two is this this is lecture one +actually this is like lecture two + + align:start position:0% +actually this is like lecture two + + + align:start position:0% +actually this is like lecture two +or at worst lecture + + align:start position:0% + + + + align:start position:0% + +three well a of one + + align:start position:0% + + + + align:start position:0% + +plus order one + + align:start position:0% +plus order one + + + align:start position:0% +plus order one +right okay that's + + align:start position:0% +right okay that's + + + align:start position:0% +right okay that's +right okay so so we have four problems + + align:start position:0% +right okay so so we have four problems + + + align:start position:0% +right okay so so we have four problems +of size n /2 that we're + + align:start position:0% +of size n /2 that we're + + + align:start position:0% +of size n /2 that we're +solving okay so to to see this you don't + + align:start position:0% +solving okay so to to see this you don't + + + align:start position:0% +solving okay so to to see this you don't +even have to know that we're doing this + + align:start position:0% +even have to know that we're doing this + + + align:start position:0% +even have to know that we're doing this +in parallel because the work is + + align:start position:0% +in parallel because the work is + + + align:start position:0% +in parallel because the work is +basically what would happen if it + + align:start position:0% +basically what would happen if it + + + align:start position:0% +basically what would happen if it +executed on a Serial machine so we have + + align:start position:0% +executed on a Serial machine so we have + + + align:start position:0% +executed on a Serial machine so we have +four problems of size n / two plus order + + align:start position:0% +four problems of size n / two plus order + + + align:start position:0% +four problems of size n / two plus order +one is the total work any questions + + align:start position:0% +one is the total work any questions + + + align:start position:0% +one is the total work any questions +about how I got that + + align:start position:0% +about how I got that + + + align:start position:0% +about how I got that +recurrence is that is that pretty + + align:start position:0% +recurrence is that is that pretty + + + align:start position:0% +recurrence is that is that pretty +straightforward okay if not let me know + + align:start position:0% +straightforward okay if not let me know + + + align:start position:0% +straightforward okay if not let me know +okay and so what's the solution to this + + align:start position:0% + + + + align:start position:0% + +recurrence yeah order N squared how do + + align:start position:0% +recurrence yeah order N squared how do + + + align:start position:0% +recurrence yeah order N squared how do +we know + + align:start position:0% +we know + + + align:start position:0% +we know +that Master method yeah Master method so + + align:start position:0% +that Master method yeah Master method so + + + align:start position:0% +that Master method yeah Master method so +n to the log base 2 of + + align:start position:0% +n to the log base 2 of + + + align:start position:0% +n to the log base 2 of +4 right is + + align:start position:0% +4 right is + + + align:start position:0% +4 right is +n^2 compare that with + + align:start position:0% +n^2 compare that with + + + align:start position:0% +n^2 compare that with +order one this dramatically dominates so + + align:start position:0% +order one this dramatically dominates so + + + align:start position:0% +order one this dramatically dominates so +this is the answer the N to log base 2 + + align:start position:0% +this is the answer the N to log base 2 + + + align:start position:0% +this is the answer the N to log base 2 +of four n squar okay everybody remember + + align:start position:0% +of four n squar okay everybody remember + + + align:start position:0% +of four n squar okay everybody remember +that so I want people to Bone up because + + align:start position:0% +that so I want people to Bone up because + + + align:start position:0% +that so I want people to Bone up because +this is going to be you know recurrences + + align:start position:0% +this is going to be you know recurrences + + + align:start position:0% +this is going to be you know recurrences +and dividing conent stuff is going to be + + align:start position:0% +and dividing conent stuff is going to be + + + align:start position:0% +and dividing conent stuff is going to be +on the final okay even though we haven't + + align:start position:0% +on the final okay even though we haven't + + + align:start position:0% +on the final okay even though we haven't +seen it in many moons okay so that's + + align:start position:0% +seen it in many moons okay so that's + + + align:start position:0% +seen it in many moons okay so that's +good that's the same as a serial if I + + align:start position:0% +good that's the same as a serial if I + + + align:start position:0% +good that's the same as a serial if I +have to add two n byn matrices how long + + align:start position:0% +have to add two n byn matrices how long + + + align:start position:0% +have to add two n byn matrices how long +does it take me to do it n squar time + + align:start position:0% +does it take me to do it n squar time + + + align:start position:0% +does it take me to do it n squar time +okay input is size n squ so you're not + + align:start position:0% +okay input is size n squ so you're not + + + align:start position:0% +okay input is size n squ so you're not +going to beat the size of the input if + + align:start position:0% +going to beat the size of the input if + + + align:start position:0% +going to beat the size of the input if +you have to you know look at every piece + + align:start position:0% +you have to you know look at every piece + + + align:start position:0% +you have to you know look at every piece +of the input okay let's now + + align:start position:0% +of the input okay let's now + + + align:start position:0% +of the input okay let's now +do the um work of the uh matrix + + align:start position:0% +do the um work of the uh matrix + + + align:start position:0% +do the um work of the uh matrix +multiplication so once again we want to + + align:start position:0% +multiplication so once again we want to + + + align:start position:0% +multiplication so once again we want to +get a recurrence + + align:start position:0% + + + + align:start position:0% + +here so what's + + align:start position:0% +here so what's + + + align:start position:0% +here so what's +our recurrence + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +yeah uh not + + align:start position:0% + + + + align:start position:0% + +quite eight right good okay 8 M1 n + + align:start position:0% +quite eight right good okay 8 M1 n + + + align:start position:0% +quite eight right good okay 8 M1 n +/2 + + align:start position:0% + + + + align:start position:0% + +plus yeah there's Theta n squ for the + + align:start position:0% +plus yeah there's Theta n squ for the + + + align:start position:0% +plus yeah there's Theta n squ for the +for the + + align:start position:0% +for the + + + align:start position:0% +for the +addition and then there's extra Theta 1 + + align:start position:0% +addition and then there's extra Theta 1 + + + align:start position:0% +addition and then there's extra Theta 1 +that we can absorb into the Theta n^ s + + align:start position:0% +that we can absorb into the Theta n^ s + + + align:start position:0% +that we can absorb into the Theta n^ s +isn't a isn't astics + + align:start position:0% +isn't a isn't astics + + + align:start position:0% +isn't a isn't astics +great okay it's just great + + align:start position:0% +great okay it's just great + + + align:start position:0% +great okay it's just great +okay so uh and so what's the solution to + + align:start position:0% +okay so uh and so what's the solution to + + + align:start position:0% +okay so uh and so what's the solution to +that + + align:start position:0% + + + + align:start position:0% + +one Theta NQ how do we have that how why + + align:start position:0% +one Theta NQ how do we have that how why + + + align:start position:0% +one Theta NQ how do we have that how why +is + + align:start position:0% +is + + + align:start position:0% +is +that man we're exercising old muscles + + align:start position:0% +that man we're exercising old muscles + + + align:start position:0% +that man we're exercising old muscles +aren't we and they're just creaking I + + align:start position:0% +aren't we and they're just creaking I + + + align:start position:0% +aren't we and they're just creaking I +can hear + + align:start position:0% +can hear + + + align:start position:0% +can hear +them okay why is that Master method yeah + + align:start position:0% +them okay why is that Master method yeah + + + align:start position:0% +them okay why is that Master method yeah +Master method because we're looking at + + align:start position:0% +Master method because we're looking at + + + align:start position:0% +Master method because we're looking at +what are we + + align:start position:0% +what are we + + + align:start position:0% +what are we +comparing yeah n to the log base 2 of 8 + + align:start position:0% +comparing yeah n to the log base 2 of 8 + + + align:start position:0% +comparing yeah n to the log base 2 of 8 +or n cubed versus n s this one dominates + + align:start position:0% +or n cubed versus n s this one dominates + + + align:start position:0% +or n cubed versus n s this one dominates +order n cubed okay so this is same as + + align:start position:0% +order n cubed okay so this is same as + + + align:start position:0% +order n cubed okay so this is same as +serial this was the same as serial this + + align:start position:0% +serial this was the same as serial this + + + align:start position:0% +serial this was the same as serial this +was the same as cial that's good okay we + + align:start position:0% +was the same as cial that's good okay we + + + align:start position:0% +was the same as cial that's good okay we +know we have a program that on One + + align:start position:0% +know we have a program that on One + + + align:start position:0% +know we have a program that on One +processor will execute the same as um as + + align:start position:0% +processor will execute the same as um as + + + align:start position:0% +processor will execute the same as um as +a uh + + align:start position:0% +a uh + + + align:start position:0% +a uh +serial uh as our serial code on which + + align:start position:0% +serial uh as our serial code on which + + + align:start position:0% +serial uh as our serial code on which +it's based namely we could have done + + align:start position:0% +it's based namely we could have done + + + align:start position:0% +it's based namely we could have done +this if I had just gotten rid of all the + + align:start position:0% +this if I had just gotten rid of all the + + + align:start position:0% +this if I had just gotten rid of all the +spawns and + + align:start position:0% +spawns and + + + align:start position:0% +spawns and +SNS that would have just been a + + align:start position:0% +SNS that would have just been a + + + align:start position:0% +SNS that would have just been a +perfectly good piece of pseudo code + + align:start position:0% +perfectly good piece of pseudo code + + + align:start position:0% +perfectly good piece of pseudo code +describing uh the runtime of the + + align:start position:0% +describing uh the runtime of the + + + align:start position:0% +describing uh the runtime of the +algorithm describing the serial + + align:start position:0% +algorithm describing the serial + + + align:start position:0% +algorithm describing the serial +algorithm and its runtime would be the + + align:start position:0% +algorithm and its runtime would be the + + + align:start position:0% +algorithm and its runtime would be the +the you know ends up being being exactly + + align:start position:0% +the you know ends up being being exactly + + + align:start position:0% +the you know ends up being being exactly +the same not too surprising okay okay so + + align:start position:0% +the same not too surprising okay okay so + + + align:start position:0% +the same not too surprising okay okay so +now we do the new stuff critical path + + align:start position:0% + + + + align:start position:0% + +length Okay so here we have a Infinity + + align:start position:0% +length Okay so here we have a Infinity + + + align:start position:0% +length Okay so here we have a Infinity +of + + align:start position:0% + + + + align:start position:0% + +n + + align:start position:0% +n + + + align:start position:0% +n +o okay so we're going to add up the + + align:start position:0% +o okay so we're going to add up the + + + align:start position:0% +o okay so we're going to add up the +critical path of this code here + + align:start position:0% + + + + align:start position:0% + +H how do I figure out the critical path + + align:start position:0% +H how do I figure out the critical path + + + align:start position:0% +H how do I figure out the critical path +of a piece of code like + + align:start position:0% + + + + align:start position:0% + +that so it's going to expand into one of + + align:start position:0% +that so it's going to expand into one of + + + align:start position:0% +that so it's going to expand into one of +those + + align:start position:0% +those + + + align:start position:0% +those +dags what's the dag in to look like how + + align:start position:0% +dags what's the dag in to look like how + + + align:start position:0% +dags what's the dag in to look like how +do I reason so it's actually easier not + + align:start position:0% +do I reason so it's actually easier not + + + align:start position:0% +do I reason so it's actually easier not +to think about the dag but just simply + + align:start position:0% +to think about the dag but just simply + + + align:start position:0% +to think about the dag but just simply +think about what's going on in the code + + align:start position:0% + + + + align:start position:0% + +yeah yeah so it's basically since all + + align:start position:0% +yeah yeah so it's basically since all + + + align:start position:0% +yeah yeah so it's basically since all +four + + align:start position:0% +four + + + align:start position:0% +four +spawns are spawning off the same thing + + align:start position:0% +spawns are spawning off the same thing + + + align:start position:0% +spawns are spawning off the same thing +and they're operating in + + align:start position:0% +and they're operating in + + + align:start position:0% +and they're operating in +parallel I can just look at one or in + + align:start position:0% +parallel I can just look at one or in + + + align:start position:0% +parallel I can just look at one or in +general if I spawn off several things I + + align:start position:0% +general if I spawn off several things I + + + align:start position:0% +general if I spawn off several things I +look at whichever one is going to have + + align:start position:0% +look at whichever one is going to have + + + align:start position:0% +look at whichever one is going to have +the maximum critical + + align:start position:0% +the maximum critical + + + align:start position:0% +the maximum critical +path for the things that I've spawned + + align:start position:0% +path for the things that I've spawned + + + align:start position:0% +path for the things that I've spawned +off so when we do work we're usually + + align:start position:0% +off so when we do work we're usually + + + align:start position:0% +off so when we do work we're usually +doing plus when I have multiple sub + + align:start position:0% +doing plus when I have multiple sub + + + align:start position:0% +doing plus when I have multiple sub +routines when we do critical path I'm + + align:start position:0% +routines when we do critical path I'm + + + align:start position:0% +routines when we do critical path I'm +doing Max it's going to be the max over + + align:start position:0% +doing Max it's going to be the max over + + + align:start position:0% +doing Max it's going to be the max over +the S the critical Paths of the subes + + align:start position:0% +the S the critical Paths of the subes + + + align:start position:0% +the S the critical Paths of the subes +that I call okay and here they're all + + align:start position:0% +that I call okay and here they're all + + + align:start position:0% +that I call okay and here they're all +equal so what's the recurrence that I + + align:start position:0% +equal so what's the recurrence that I + + + align:start position:0% +equal so what's the recurrence that I +get + + align:start position:0% + + + + align:start position:0% + +what's the recurrence I'm going to get + + align:start position:0% +what's the recurrence I'm going to get + + + align:start position:0% +what's the recurrence I'm going to get +out of this + + align:start position:0% + + + + align:start position:0% + +one yeah a Infinity n / + + align:start position:0% + + + + align:start position:0% + +two plus + + align:start position:0% + + + + align:start position:0% + +constant okay cuz this is what the worst + + align:start position:0% +constant okay cuz this is what the worst + + + align:start position:0% +constant okay cuz this is what the worst +is of any of those four + + align:start position:0% +is of any of those four + + + align:start position:0% +is of any of those four +because they're all the same they're all + + align:start position:0% +because they're all the same they're all + + + align:start position:0% +because they're all the same they're all +a problem looking at the critical path + + align:start position:0% +a problem looking at the critical path + + + align:start position:0% +a problem looking at the critical path +of + + align:start position:0% +of + + + align:start position:0% +of +something that's + + align:start position:0% +something that's + + + align:start position:0% +something that's +uh uh that's half the that's half the + + align:start position:0% +uh uh that's half the that's half the + + + align:start position:0% +uh uh that's half the that's half the +size a problem that's half the size + + align:start position:0% +size a problem that's half the size + + + align:start position:0% +size a problem that's half the size +okay people with me okay so what's the + + align:start position:0% +okay people with me okay so what's the + + + align:start position:0% +okay people with me okay so what's the +solution to + + align:start position:0% + + + + align:start position:0% + +this yeah that's Theta log n that's + + align:start position:0% +this yeah that's Theta log n that's + + + align:start position:0% +this yeah that's Theta log n that's +just once again Master theorem case + + align:start position:0% +just once again Master theorem case + + + align:start position:0% +just once again Master theorem case +two because the solution of this is n to + + align:start position:0% +two because the solution of this is n to + + + align:start position:0% +two because the solution of this is n to +the log base 2 of + + align:start position:0% +the log base 2 of + + + align:start position:0% +the log base 2 of +one which is n to + + align:start position:0% +one which is n to + + + align:start position:0% +one which is n to +the Zer so we have on this side we have + + align:start position:0% +the Zer so we have on this side we have + + + align:start position:0% +the Zer so we have on this side we have +one and here we're comparing it with one + + align:start position:0% +one and here we're comparing it with one + + + align:start position:0% +one and here we're comparing it with one +they're the same so therefore we tack on + + align:start position:0% +they're the same so therefore we tack on + + + align:start position:0% +they're the same so therefore we tack on +that extra log + + align:start position:0% +that extra log + + + align:start position:0% +that extra log +n okay so tack on One log in okay so + + align:start position:0% +n okay so tack on One log in okay so + + + align:start position:0% +n okay so tack on One log in okay so +case two of the master + + align:start position:0% +case two of the master + + + align:start position:0% +case two of the master +method pretty good okay so that's pretty + + align:start position:0% +method pretty good okay so that's pretty + + + align:start position:0% +method pretty good okay so that's pretty +good cuz the critical path is pretty + + align:start position:0% +good cuz the critical path is pretty + + + align:start position:0% +good cuz the critical path is pretty +short log n compared to the Work N + + align:start position:0% +short log n compared to the Work N + + + align:start position:0% +short log n compared to the Work N +squared okay so let's do uh then this + + align:start position:0% +squared okay so let's do uh then this + + + align:start position:0% +squared okay so let's do uh then this +one which is a little bit more + + align:start position:0% +one which is a little bit more + + + align:start position:0% +one which is a little bit more +interesting but not much harder how + + align:start position:0% +interesting but not much harder how + + + align:start position:0% +interesting but not much harder how +about uh how about this + + align:start position:0% +about uh how about this + + + align:start position:0% +about uh how about this +one what's the recurrence going to + + align:start position:0% + + + + align:start position:0% + +be critical path of the + + align:start position:0% + + + + align:start position:0% + +multiplication so once again it's going + + align:start position:0% +multiplication so once again it's going + + + align:start position:0% +multiplication so once again it's going +to be the maximum of everything we + + align:start position:0% +to be the maximum of everything we + + + align:start position:0% +to be the maximum of everything we +spawned off in parallel which is by + + align:start position:0% +spawned off in parallel which is by + + + align:start position:0% +spawned off in parallel which is by +symmetry the same as one of them so what + + align:start position:0% +symmetry the same as one of them so what + + + align:start position:0% +symmetry the same as one of them so what +do I get + + align:start position:0% +do I get + + + align:start position:0% +do I get +here M + + align:start position:0% +here M + + + align:start position:0% +here M +Infinity of n / + + align:start position:0% +Infinity of n / + + + align:start position:0% +Infinity of n / +two plus plus Theta log n where did the + + align:start position:0% +two plus plus Theta log n where did the + + + align:start position:0% +two plus plus Theta log n where did the +Theta log n come from + + align:start position:0% +Theta log n come from + + + align:start position:0% +Theta log n come from +the addition yeah from the addition + + align:start position:0% +the addition yeah from the addition + + + align:start position:0% +the addition yeah from the addition +that's the critical path of the addition + + align:start position:0% +that's the critical path of the addition + + + align:start position:0% +that's the critical path of the addition +now why isn't + + align:start position:0% +now why isn't + + + align:start position:0% +now why isn't +that the maximum of that with all the + + align:start position:0% + + + + align:start position:0% + +spawns we said that when you spawn + + align:start position:0% +spawns we said that when you spawn + + + align:start position:0% +spawns we said that when you spawn +things off you're going to do + + align:start position:0% + + + + align:start position:0% + +them yeah you sync first and sync says + + align:start position:0% +them yeah you sync first and sync says + + + align:start position:0% +them yeah you sync first and sync says +you wait for all those to be done so + + align:start position:0% +you wait for all those to be done so + + + align:start position:0% +you wait for all those to be done so +you're only taking a maximum and across + + align:start position:0% +you're only taking a maximum and across + + + align:start position:0% +you're only taking a maximum and across +syns you're adding + + align:start position:0% +syns you're adding + + + align:start position:0% +syns you're adding +so you add across syns and across things + + align:start position:0% +so you add across syns and across things + + + align:start position:0% +so you add across syns and across things +that you spawned off in parallel that's + + align:start position:0% +that you spawned off in parallel that's + + + align:start position:0% +that you spawned off in parallel that's +where you're doing the + + align:start position:0% +where you're doing the + + + align:start position:0% +where you're doing the +max okay but if you have a sync it says + + align:start position:0% +max okay but if you have a sync it says + + + align:start position:0% +max okay but if you have a sync it says +whoop that's the end you got to wait for + + align:start position:0% +whoop that's the end you got to wait for + + + align:start position:0% +whoop that's the end you got to wait for +everything there to end this isn't going + + align:start position:0% +everything there to end this isn't going + + + align:start position:0% +everything there to end this isn't going +on in parallel with it this is going on + + align:start position:0% +on in parallel with it this is going on + + + align:start position:0% +on in parallel with it this is going on +after it so whatever the critical path + + align:start position:0% +after it so whatever the critical path + + + align:start position:0% +after it so whatever the critical path +is + + align:start position:0% +is + + + align:start position:0% +is +here okay if I had an infinite number of + + align:start position:0% +here okay if I had an infinite number of + + + align:start position:0% +here okay if I had an infinite number of +processors I'd still have to wait up at + + align:start position:0% +processors I'd still have to wait up at + + + align:start position:0% +processors I'd still have to wait up at +this point and that would therefore make + + align:start position:0% +this point and that would therefore make + + + align:start position:0% +this point and that would therefore make +it so that the um that the uh remaining + + align:start position:0% +it so that the um that the uh remaining + + + align:start position:0% +it so that the um that the uh remaining +execution here was whatever the critical + + align:start position:0% +execution here was whatever the critical + + + align:start position:0% +execution here was whatever the critical +I would have to add whatever the + + align:start position:0% +I would have to add whatever the + + + align:start position:0% +I would have to add whatever the +critical path was to this one is that + + align:start position:0% +critical path was to this one is that + + + align:start position:0% +critical path was to this one is that +clear to + + align:start position:0% +clear to + + + align:start position:0% +clear to +everybody okay so we get this + + align:start position:0% +everybody okay so we get this + + + align:start position:0% +everybody okay so we get this +recurrence and that has solution + + align:start position:0% + + + + align:start position:0% + +what yeah Theta log s + + align:start position:0% + + + + align:start position:0% + +n okay once again + + align:start position:0% +n okay once again + + + align:start position:0% +n okay once again +by Master method case two where this + + align:start position:0% +by Master method case two where this + + + align:start position:0% +by Master method case two where this +ends up being a constant versus log n + + align:start position:0% +ends up being a constant versus log n + + + align:start position:0% +ends up being a constant versus log n +those don't differ by a polinomial + + align:start position:0% +those don't differ by a polinomial + + + align:start position:0% +those don't differ by a polinomial +amount but in fact or equal to a log + + align:start position:0% +amount but in fact or equal to a log + + + align:start position:0% +amount but in fact or equal to a log +factor and what we do in that + + align:start position:0% +factor and what we do in that + + + align:start position:0% +factor and what we do in that +circumstance is tack on an extra log + + align:start position:0% +circumstance is tack on an extra log + + + align:start position:0% +circumstance is tack on an extra log +Factor okay so as I say good idea to + + align:start position:0% +Factor okay so as I say good idea to + + + align:start position:0% +Factor okay so as I say good idea to +review the master + + align:start position:0% +review the master + + + align:start position:0% +review the master +method okay that's great um so + + align:start position:0% +method okay that's great um so + + + align:start position:0% +method okay that's great um so +now let's take a look at + + align:start position:0% +now let's take a look at + + + align:start position:0% +now let's take a look at +um uh let's take a look at uh the + + align:start position:0% +um uh let's take a look at uh the + + + align:start position:0% +um uh let's take a look at uh the +parallelism that we + + align:start position:0% + + + + align:start position:0% + +get uh let just do it over + + align:start position:0% + + + + align:start position:0% + +here for the + + align:start position:0% +here for the + + + align:start position:0% +here for the +multiplication okay so parallelism is + + align:start position:0% +multiplication okay so parallelism is + + + align:start position:0% +multiplication okay so parallelism is +what for the multiplication what's the + + align:start position:0% +what for the multiplication what's the + + + align:start position:0% +what for the multiplication what's the +formula for + + align:start position:0% + + + + align:start position:0% + +parallelism so we + + align:start position:0% +parallelism so we + + + align:start position:0% +parallelism so we +have P bar is the notation we use + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +problem what's the parallelism going to + + align:start position:0% +problem what's the parallelism going to + + + align:start position:0% +problem what's the parallelism going to +be what's the ratio I + + align:start position:0% + + + + align:start position:0% + +take yes it's M1 so it's M1 of n ided by + + align:start position:0% +take yes it's M1 so it's M1 of n ided by + + + align:start position:0% +take yes it's M1 so it's M1 of n ided by +m Infinity of n okay and that's equal to + + align:start position:0% +m Infinity of n okay and that's equal to + + + align:start position:0% +m Infinity of n okay and that's equal to +that's n cubed that's n SAR + + align:start position:0% + + + + align:start position:0% + +or log n squ sorry log squ + + align:start position:0% +or log n squ sorry log squ + + + align:start position:0% +or log n squ sorry log squ +n okay so that says this is the + + align:start position:0% +n okay so that says this is the + + + align:start position:0% +n okay so that says this is the +parallelism that says you could run up + + align:start position:0% +parallelism that says you could run up + + + align:start position:0% +parallelism that says you could run up +to this many processors and expect to be + + align:start position:0% +to this many processors and expect to be + + + align:start position:0% +to this many processors and expect to be +getting linear speed up if I ran with + + align:start position:0% +getting linear speed up if I ran with + + + align:start position:0% +getting linear speed up if I ran with +more processors than the parallelism I + + align:start position:0% +more processors than the parallelism I + + + align:start position:0% +more processors than the parallelism I +don't expect to be getting linear speed + + align:start position:0% +don't expect to be getting linear speed + + + align:start position:0% +don't expect to be getting linear speed +up anymore okay because I'll hit the + + align:start position:0% +up anymore okay because I'll hit the + + + align:start position:0% +up anymore okay because I'll hit the +bound but what I expect to run in is + + align:start position:0% +bound but what I expect to run in is + + + align:start position:0% +bound but what I expect to run in is +just time proportional to the critical + + align:start position:0% +just time proportional to the critical + + + align:start position:0% +just time proportional to the critical +path length and throwing more processors + + align:start position:0% +path length and throwing more processors + + + align:start position:0% +path length and throwing more processors +at the problem is not going to help me + + align:start position:0% +at the problem is not going to help me + + + align:start position:0% +at the problem is not going to help me +very much okay so let's just look at + + align:start position:0% +very much okay so let's just look at + + + align:start position:0% +very much okay so let's just look at +this just to get a sense of what's going + + align:start position:0% +this just to get a sense of what's going + + + align:start position:0% +this just to get a sense of what's going +on here let's imagine that the constants + + align:start position:0% +on here let's imagine that the constants + + + align:start position:0% +on here let's imagine that the constants +are irrelevant and we have say th by, + + align:start position:0% + + + + align:start position:0% + +matrices okay so in that + + align:start position:0% +matrices okay so in that + + + align:start position:0% +matrices okay so in that +case + + align:start position:0% +case + + + align:start position:0% +case +uh our our parallelism is 1,00 cubed + + align:start position:0% + + + + align:start position:0% + +divided by log of a 10000 squar what's + + align:start position:0% +divided by log of a 10000 squar what's + + + align:start position:0% +divided by log of a 10000 squar what's +log of a + + align:start position:0% + + + + align:start position:0% + +th 10 approximately right log base 2 of + + align:start position:0% +th 10 approximately right log base 2 of + + + align:start position:0% +th 10 approximately right log base 2 of +a th000 is about 10 so that's uh 10 + + align:start position:0% +a th000 is about 10 so that's uh 10 + + + align:start position:0% +a th000 is about 10 so that's uh 10 +squared so we about 10 the 7th + + align:start position:0% +squared so we about 10 the 7th + + + align:start position:0% +squared so we about 10 the 7th +parallelism how big is 10 to the + + align:start position:0% +parallelism how big is 10 to the + + + align:start position:0% +parallelism how big is 10 to the +7th 10 million + + align:start position:0% +7th 10 million + + + align:start position:0% +7th 10 million +processors okay + + align:start position:0% +processors okay + + + align:start position:0% +processors okay +so who knows of a machine with 10 + + align:start position:0% +so who knows of a machine with 10 + + + align:start position:0% +so who knows of a machine with 10 +million + + align:start position:0% +million + + + align:start position:0% +million +processors what's the most number of + + align:start position:0% +processors what's the most number of + + + align:start position:0% +processors what's the most number of +processors anybody knows + + align:start position:0% + + + + align:start position:0% + +about yeah not quite Blue Jean has the + + align:start position:0% +about yeah not quite Blue Jean has the + + + align:start position:0% +about yeah not quite Blue Jean has the +IBM Blue Jean has humongous number of + + align:start position:0% +IBM Blue Jean has humongous number of + + + align:start position:0% +IBM Blue Jean has humongous number of +processors up in the 10 exceeding + + align:start position:0% +processors up in the 10 exceeding + + + align:start position:0% +processors up in the 10 exceeding +10,000 + + align:start position:0% +10,000 + + + align:start position:0% +10,000 +okay yeah those were one bit processors + + align:start position:0% + + + + align:start position:0% + +okay so so this is this is actually uh a + + align:start position:0% +okay so so this is this is actually uh a + + + align:start position:0% +okay so so this is this is actually uh a +pretty big number and so + + align:start position:0% +pretty big number and so + + + align:start position:0% +pretty big number and so +um and so you know our parallelism is + + align:start position:0% +um and so you know our parallelism is + + + align:start position:0% +um and so you know our parallelism is +much + + align:start position:0% + + + + align:start position:0% + +bigger than a + + align:start position:0% +bigger than a + + + align:start position:0% +bigger than a +typical uh actual number + + align:start position:0% +typical uh actual number + + + align:start position:0% +typical uh actual number +processors so we would expect to be able + + align:start position:0% +processors so we would expect to be able + + + align:start position:0% +processors so we would expect to be able +to run this and get very good + + align:start position:0% +to run this and get very good + + + align:start position:0% +to run this and get very good +performance okay because we're never + + align:start position:0% +performance okay because we're never + + + align:start position:0% +performance okay because we're never +going to be limited in this algorithm by + + align:start position:0% +going to be limited in this algorithm by + + + align:start position:0% +going to be limited in this algorithm by +performance however there's some there + + align:start position:0% +performance however there's some there + + + align:start position:0% +performance however there's some there +are some tricks we can do one of the + + align:start position:0% +are some tricks we can do one of the + + + align:start position:0% +are some tricks we can do one of the +things in this code is that we have a we + + align:start position:0% +things in this code is that we have a we + + + align:start position:0% +things in this code is that we have a we +actually have some overhead that's not + + align:start position:0% +actually have some overhead that's not + + + align:start position:0% +actually have some overhead that's not +apparent because we haven't I haven't + + align:start position:0% +apparent because we haven't I haven't + + + align:start position:0% +apparent because we haven't I haven't +run this code with you although I could + + align:start position:0% +run this code with you although I could + + + align:start position:0% +run this code with you although I could +um which is that we have this temporary + + align:start position:0% +um which is that we have this temporary + + + align:start position:0% +um which is that we have this temporary +Matrix + + align:start position:0% + + + + align:start position:0% + +T and we can you know if you look at the + + align:start position:0% +T and we can you know if you look at the + + + align:start position:0% +T and we can you know if you look at the +execution stack we're always allocating + + align:start position:0% +execution stack we're always allocating + + + align:start position:0% +execution stack we're always allocating +t and getting rid of it Etc and one of + + align:start position:0% +t and getting rid of it Etc and one of + + + align:start position:0% +t and getting rid of it Etc and one of +the things when you actually look at the + + align:start position:0% +the things when you actually look at the + + + align:start position:0% +the things when you actually look at the +performance of real code which is now + + align:start position:0% +performance of real code which is now + + + align:start position:0% +performance of real code which is now +that you have your algorithmic + + align:start position:0% +that you have your algorithmic + + + align:start position:0% +that you have your algorithmic +background you're ready to go and do + + align:start position:0% +background you're ready to go and do + + + align:start position:0% +background you're ready to go and do +that with some some insight of course + + align:start position:0% +that with some some insight of course + + + align:start position:0% +that with some some insight of course +you're interested in getting more than + + align:start position:0% +you're interested in getting more than + + + align:start position:0% +you're interested in getting more than +just um asymptotic Behavior you're + + align:start position:0% +just um asymptotic Behavior you're + + + align:start position:0% +just um asymptotic Behavior you're +interested in getting real performance + + align:start position:0% +interested in getting real performance + + + align:start position:0% +interested in getting real performance +behavior on real things so you do care + + align:start position:0% +behavior on real things so you do care + + + align:start position:0% +behavior on real things so you do care +about constants in that nature okay and + + align:start position:0% +about constants in that nature okay and + + + align:start position:0% +about constants in that nature okay and +one of the things is having a large + + align:start position:0% +one of the things is having a large + + + align:start position:0% +one of the things is having a large +temporary variable that's that turns out + + align:start position:0% +temporary variable that's that turns out + + + align:start position:0% +temporary variable that's that turns out +to be lot of overhead and in fact uh + + align:start position:0% +to be lot of overhead and in fact uh + + + align:start position:0% +to be lot of overhead and in fact uh +it's often the case when you're looking + + align:start position:0% +it's often the case when you're looking + + + align:start position:0% +it's often the case when you're looking +at real code that if you can optimize + + align:start position:0% +at real code that if you can optimize + + + align:start position:0% +at real code that if you can optimize +for space you also optimize for time if + + align:start position:0% +for space you also optimize for time if + + + align:start position:0% +for space you also optimize for time if +you can run your code with smaller space + + align:start position:0% +you can run your code with smaller space + + + align:start position:0% +you can run your code with smaller space +you can actually run it with uh with + + align:start position:0% +you can actually run it with uh with + + + align:start position:0% +you can actually run it with uh with +smaller time tends to be a constant + + align:start position:0% +smaller time tends to be a constant + + + align:start position:0% +smaller time tends to be a constant +Factor Advantage but those constants can + + align:start position:0% +Factor Advantage but those constants can + + + align:start position:0% +Factor Advantage but those constants can +can add up and can make a uh a + + align:start position:0% +can add up and can make a uh a + + + align:start position:0% +can add up and can make a uh a +difference in whether somebody else's + + align:start position:0% +difference in whether somebody else's + + + align:start position:0% +difference in whether somebody else's +code is faster your code is faster okay + + align:start position:0% +code is faster your code is faster okay + + + align:start position:0% +code is faster your code is faster okay +once you have your basic algorithm so + + align:start position:0% +once you have your basic algorithm so + + + align:start position:0% +once you have your basic algorithm so +the idea is to and this case we're going + + align:start position:0% +the idea is to and this case we're going + + + align:start position:0% +the idea is to and this case we're going +to get rid of it by trading + + align:start position:0% +to get rid of it by trading + + + align:start position:0% +to get rid of it by trading +parallelism because we got Oodles of + + align:start position:0% +parallelism because we got Oodles of + + + align:start position:0% +parallelism because we got Oodles of +parallelism + + align:start position:0% +parallelism + + + align:start position:0% +parallelism +here for space + + align:start position:0% + + + + align:start position:0% + +efficiency okay and the idea is we're + + align:start position:0% +efficiency okay and the idea is we're + + + align:start position:0% +efficiency okay and the idea is we're +going to get rid of + + align:start position:0% + + + + align:start position:0% + +t Okay so let's + + align:start position:0% +t Okay so let's + + + align:start position:0% +t Okay so let's +uh throw this up + + align:start position:0% + + + + align:start position:0% + +so who can suggest how I might get rid + + align:start position:0% +so who can suggest how I might get rid + + + align:start position:0% +so who can suggest how I might get rid +of T + + align:start position:0% + + + + align:start position:0% + +here get rid of this temporary + + align:start position:0% + + + + align:start position:0% + +Matrix yeah + + align:start position:0% +Matrix yeah + + + align:start position:0% +Matrix yeah +you do by for the base Cas you change it + + align:start position:0% +you do by for the base Cas you change it + + + align:start position:0% +you do by for the base Cas you change it +to adding it to whatever's already in + + align:start position:0% +to adding it to whatever's already in + + + align:start position:0% +to adding it to whatever's already in +C then for the the last four calls to M + + align:start position:0% +C then for the the last four calls to M + + + align:start position:0% +C then for the the last four calls to M +you change it from T to C and then you + + align:start position:0% +you change it from T to C and then you + + + align:start position:0% +you change it from T to C and then you +get rid of the + + align:start position:0% +get rid of the + + + align:start position:0% +get rid of the +ad uh so if you just did adding it into + + align:start position:0% +ad uh so if you just did adding it into + + + align:start position:0% +ad uh so if you just did adding it into +C so the issue that you get there if + + align:start position:0% +C so the issue that you get there if + + + align:start position:0% +C so the issue that you get there if +they're both adding into C is you can + + align:start position:0% +they're both adding into C is you can + + + align:start position:0% +they're both adding into C is you can +get interference between the two subc + + align:start position:0% +get interference between the two subc + + + align:start position:0% +get interference between the two subc +computations now there are ways of doing + + align:start position:0% +computations now there are ways of doing + + + align:start position:0% +computations now there are ways of doing +that that work out but you now have to + + align:start position:0% +that that work out but you now have to + + + align:start position:0% +that that work out but you now have to +worry about things we're not going to + + align:start position:0% +worry about things we're not going to + + + align:start position:0% +worry about things we're not going to +talk about such as Mutual exclusion + + align:start position:0% +talk about such as Mutual exclusion + + + align:start position:0% +talk about such as Mutual exclusion +to make sure that as you're updating it + + align:start position:0% +to make sure that as you're updating it + + + align:start position:0% +to make sure that as you're updating it +somebody else isn't updating it you + + align:start position:0% +somebody else isn't updating it you + + + align:start position:0% +somebody else isn't updating it you +don't have race conditions but you can + + align:start position:0% +don't have race conditions but you can + + + align:start position:0% +don't have race conditions but you can +actually do it in this context with no + + align:start position:0% +actually do it in this context with no + + + align:start position:0% +actually do it in this context with no +race conditions you could add another + + align:start position:0% +race conditions you could add another + + + align:start position:0% +race conditions you could add another +syn before the second set of for SPS in + + align:start position:0% +syn before the second set of for SPS in + + + align:start position:0% +syn before the second set of for SPS in +yeah exactly okay exactly so the idea + + align:start position:0% +yeah exactly okay exactly so the idea + + + align:start position:0% +yeah exactly okay exactly so the idea +is spawn off four of + + align:start position:0% +is spawn off four of + + + align:start position:0% +is spawn off four of +them okay they all update their copy of + + align:start position:0% +them okay they all update their copy of + + + align:start position:0% +them okay they all update their copy of +c and then spawn off the other four that + + align:start position:0% +c and then spawn off the other four that + + + align:start position:0% +c and then spawn off the other four that +add their values in + + align:start position:0% +add their values in + + + align:start position:0% +add their values in +so that's uh is a piece of code we'll + + align:start position:0% +so that's uh is a piece of code we'll + + + align:start position:0% +so that's uh is a piece of code we'll +call MTT + + align:start position:0% + + + + align:start position:0% + +add and it's actually going to do c gets + + align:start position:0% +add and it's actually going to do c gets + + + align:start position:0% +add and it's actually going to do c gets +C + a * + + align:start position:0% +C + a * + + + align:start position:0% +C + a * +B okay so it's actually going to add it + + align:start position:0% +B okay so it's actually going to add it + + + align:start position:0% +B okay so it's actually going to add it +in so initially you'd have to zero out C + + align:start position:0% +in so initially you'd have to zero out C + + + align:start position:0% +in so initially you'd have to zero out C +but we can do that with code very + + align:start position:0% +but we can do that with code very + + + align:start position:0% +but we can do that with code very +similar to the addition code in uh uh + + align:start position:0% +similar to the addition code in uh uh + + + align:start position:0% +similar to the addition code in uh uh +with order n squ work and Order log n + + align:start position:0% +with order n squ work and Order log n + + + align:start position:0% +with order n squ work and Order log n +critical path so that's not going to be + + align:start position:0% +critical path so that's not going to be + + + align:start position:0% +critical path so that's not going to be +a big part of what we uh have to deal + + align:start position:0% +a big part of what we uh have to deal + + + align:start position:0% +a big part of what we uh have to deal +with okay so here's the here's the code + + align:start position:0% +with okay so here's the here's the code + + + align:start position:0% +with okay so here's the here's the code +we basically once again do the base and + + align:start position:0% + + + + align:start position:0% + +partition which I'm not going to write + + align:start position:0% +partition which I'm not going to write + + + align:start position:0% +partition which I'm not going to write +out the code + + align:start position:0% +out the code + + + align:start position:0% +out the code +for and then we + + align:start position:0% +for and then we + + + align:start position:0% +for and then we +spawn a Mt add + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% +of + + + align:start position:0% +of +C11 + + align:start position:0% +C11 + + + align:start position:0% +C11 +a11 + + align:start position:0% +a11 + + + align:start position:0% +a11 +b11 and/ + + align:start position:0% +b11 and/ + + + align:start position:0% +b11 and/ +two and we do a few more of those down + + align:start position:0% +two and we do a few more of those down + + + align:start position:0% +two and we do a few more of those down +to the fourth + + align:start position:0% + + + + align:start position:0% + +one and then we put in a sync + + align:start position:0% + + + + align:start position:0% + +and then we do the other + + align:start position:0% + + + + align:start position:0% + +four + + align:start position:0% +four + + + align:start position:0% +four +and down to + + align:start position:0% + + + + align:start position:0% + +and then sync when we're done with + + align:start position:0% + + + + align:start position:0% + +that okay so everybody understand that + + align:start position:0% +that okay so everybody understand that + + + align:start position:0% +that okay so everybody understand that +code see that it basically does the same + + align:start position:0% +code see that it basically does the same + + + align:start position:0% +code see that it basically does the same +calculation we don't actually need to + + align:start position:0% +calculation we don't actually need to + + + align:start position:0% +calculation we don't actually need to +call add anymore because we're doing + + align:start position:0% +call add anymore because we're doing + + + align:start position:0% +call add anymore because we're doing +that as part of the multiply because + + align:start position:0% +that as part of the multiply because + + + align:start position:0% +that as part of the multiply because +we're because we're adding in but we do + + align:start position:0% +we're because we're adding in but we do + + + align:start position:0% +we're because we're adding in but we do +have to + + align:start position:0% +have to + + + align:start position:0% +have to +initialize okay we do have to initialize + + align:start position:0% +initialize okay we do have to initialize + + + align:start position:0% +initialize okay we do have to initialize +the Matrix in this case Okay so there is + + align:start position:0% +the Matrix in this case Okay so there is + + + align:start position:0% +the Matrix in this case Okay so there is +another uh phase so people understand + + align:start position:0% +another uh phase so people understand + + + align:start position:0% +another uh phase so people understand +the semantics of this of this code so + + align:start position:0% +the semantics of this of this code so + + + align:start position:0% +the semantics of this of this code so +let's analyze + + align:start position:0% + + + + align:start position:0% + +it okay so um what's the work of + + align:start position:0% +it okay so um what's the work of + + + align:start position:0% +it okay so um what's the work of +multiply add of n + + align:start position:0% + + + + align:start position:0% + +it's + + align:start position:0% +it's + + + align:start position:0% +it's +like it's basically the same + + align:start position:0% +like it's basically the same + + + align:start position:0% +like it's basically the same +thing right it's order n + + align:start position:0% +thing right it's order n + + + align:start position:0% +thing right it's order n +cubed because the serial code is almost + + align:start position:0% +cubed because the serial code is almost + + + align:start position:0% +cubed because the serial code is almost +the same as the serial code up there + + align:start position:0% +the same as the serial code up there + + + align:start position:0% +the same as the serial code up there +okay not quite okay but you get + + align:start position:0% +okay not quite okay but you get + + + align:start position:0% +okay not quite okay but you get +essentially the same recurrence except + + align:start position:0% +essentially the same recurrence except + + + align:start position:0% +essentially the same recurrence except +you don't even have the ad you just get + + align:start position:0% +you don't even have the ad you just get + + + align:start position:0% +you don't even have the ad you just get +you get the same recurrence but with uh + + align:start position:0% +you get the same recurrence but with uh + + + align:start position:0% +you get the same recurrence but with uh +order one here whoops order one order + + align:start position:0% +order one here whoops order one order + + + align:start position:0% +order one here whoops order one order +one up here + + align:start position:0% +one up here + + + align:start position:0% +one up here +so it still got the order n cubed + + align:start position:0% +so it still got the order n cubed + + + align:start position:0% +so it still got the order n cubed +solution okay so that I think + + align:start position:0% +solution okay so that I think + + + align:start position:0% +solution okay so that I think +is is not too hard okay so the critical + + align:start position:0% +is is not too hard okay so the critical + + + align:start position:0% +is is not too hard okay so the critical +path + + align:start position:0% +path + + + align:start position:0% +path +length so there let's write out our um + + align:start position:0% +length so there let's write out our um + + + align:start position:0% +length so there let's write out our um +so multiply add of + + align:start position:0% +so multiply add of + + + align:start position:0% +so multiply add of +n okay what's my recurrence for this + + align:start position:0% +n okay what's my recurrence for this + + + align:start position:0% +n okay what's my recurrence for this +code + + align:start position:0% + + + + align:start position:0% + +have + + align:start position:0% + + + + align:start position:0% + +two 2 ma 2 m + + align:start position:0% +two 2 ma 2 m + + + align:start position:0% +two 2 ma 2 m +Infinity n over + + align:start position:0% + + + + align:start position:0% + +two plus we lost that so order one plus + + align:start position:0% +two plus we lost that so order one plus + + + align:start position:0% +two plus we lost that so order one plus +order one + + align:start position:0% +order one + + + align:start position:0% +order one +yeah okay so the point is that we're + + align:start position:0% +yeah okay so the point is that we're + + + align:start position:0% +yeah okay so the point is that we're +going to have for the critical path + + align:start position:0% +going to have for the critical path + + + align:start position:0% +going to have for the critical path +we're going to spawn these four off and + + align:start position:0% +we're going to spawn these four off and + + + align:start position:0% +we're going to spawn these four off and +so I take the maximum of whatever those + + align:start position:0% +so I take the maximum of whatever those + + + align:start position:0% +so I take the maximum of whatever those +is which since they're symmetric is any + + align:start position:0% +is which since they're symmetric is any + + + align:start position:0% +is which since they're symmetric is any +one of + + align:start position:0% +one of + + + align:start position:0% +one of +them okay and then I have to wait and + + align:start position:0% +them okay and then I have to wait and + + + align:start position:0% +them okay and then I have to wait and +then I do it again so that sync once + + align:start position:0% +then I do it again so that sync once + + + align:start position:0% +then I do it again so that sync once +again translates into in the analysis it + + align:start position:0% +again translates into in the analysis it + + + align:start position:0% +again translates into in the analysis it +translates into a plus of the critical + + align:start position:0% +translates into a plus of the critical + + + align:start position:0% +translates into a plus of the critical +path whereas the things I spawn off in + + align:start position:0% +path whereas the things I spawn off in + + + align:start position:0% +path whereas the things I spawn off in +parallel I do the + + align:start position:0% +parallel I do the + + + align:start position:0% +parallel I do the +max okay so people see that so I get + + align:start position:0% +max okay so people see that so I get + + + align:start position:0% +max okay so people see that so I get +this recurrence to m a of n /2 plus + + align:start position:0% +this recurrence to m a of n /2 plus + + + align:start position:0% +this recurrence to m a of n /2 plus +order n and so for order one and what's + + align:start position:0% +order n and so for order one and what's + + + align:start position:0% +order n and so for order one and what's +the solution of that + + align:start position:0% + + + + align:start position:0% + +yeah that's order + + align:start position:0% + + + + align:start position:0% + +n okay so because n to the log base 2 of + + align:start position:0% +n okay so because n to the log base 2 of + + + align:start position:0% +n okay so because n to the log base 2 of +two is n that's bigger than one so we + + align:start position:0% +two is n that's bigger than one so we + + + align:start position:0% +two is n that's bigger than one so we +get order + + align:start position:0% + + + + align:start position:0% + +n + + align:start position:0% +n + + + align:start position:0% +n +okay so the + + align:start position:0% + + + + align:start position:0% + +parallelism we have p is equal to m one + + align:start position:0% +parallelism we have p is equal to m one + + + align:start position:0% +parallelism we have p is equal to m one +of n over M A Infinity of n is equal to + + align:start position:0% +of n over M A Infinity of n is equal to + + + align:start position:0% +of n over M A Infinity of n is equal to +in this case n cubed Over N or order n + + align:start position:0% +in this case n cubed Over N or order n + + + align:start position:0% +in this case n cubed Over N or order n +squar okay so for for thousand by, + + align:start position:0% +squar okay so for for thousand by, + + + align:start position:0% +squar okay so for for thousand by, +matrices for + + align:start position:0% +matrices for + + + align:start position:0% +matrices for +example by the way th by th000 is a + + align:start position:0% +example by the way th by th000 is a + + + align:start position:0% +example by the way th by th000 is a +considered a small Matrix these days + + align:start position:0% + + + + align:start position:0% + +because that's only a million entries + + align:start position:0% +because that's only a million entries + + + align:start position:0% +because that's only a million entries +put that on your laptop no + + align:start position:0% +put that on your laptop no + + + align:start position:0% +put that on your laptop no +sweat okay so uh but for thousand by, + + align:start position:0% +sweat okay so uh but for thousand by, + + + align:start position:0% +sweat okay so uh but for thousand by, +matrices our parallelism is + + align:start position:0% +matrices our parallelism is + + + align:start position:0% +matrices our parallelism is +about 10 the + + align:start position:0% + + + + align:start position:0% + +6th okay so once + + align:start position:0% +6th okay so once + + + align:start position:0% +6th okay so once +again ample parallelism for anything we + + align:start position:0% +again ample parallelism for anything we + + + align:start position:0% +again ample parallelism for anything we +would run it on today and it as it turns + + align:start position:0% +would run it on today and it as it turns + + + align:start position:0% +would run it on today and it as it turns +out it's fast + + align:start position:0% + + + + align:start position:0% + +practice because we have less + + align:start position:0% + + + + align:start position:0% + +space okay so here's a game where so + + align:start position:0% +space okay so here's a game where so + + + align:start position:0% +space okay so here's a game where so +often the game you'll see in theory + + align:start position:0% +often the game you'll see in theory + + + align:start position:0% +often the game you'll see in theory +um uh papers if you look at research + + align:start position:0% +um uh papers if you look at research + + + align:start position:0% +um uh papers if you look at research +papers people are often striving to get + + align:start position:0% +papers people are often striving to get + + + align:start position:0% +papers people are often striving to get +the most + + align:start position:0% +the most + + + align:start position:0% +the most +parallelism and that's a that's a good + + align:start position:0% +parallelism and that's a that's a good + + + align:start position:0% +parallelism and that's a that's a good +game to play okay but it's not + + align:start position:0% +game to play okay but it's not + + + align:start position:0% +game to play okay but it's not +necessarily the only game particular if + + align:start position:0% +necessarily the only game particular if + + + align:start position:0% +necessarily the only game particular if +you have a lot of parallelism one of the + + align:start position:0% +you have a lot of parallelism one of the + + + align:start position:0% +you have a lot of parallelism one of the +things that's very easy to do is to + + align:start position:0% +things that's very easy to do is to + + + align:start position:0% +things that's very easy to do is to +retreat on the parallelism and gain + + align:start position:0% +retreat on the parallelism and gain + + + align:start position:0% +retreat on the parallelism and gain +other aspects that you may want in your + + align:start position:0% +other aspects that you may want in your + + + align:start position:0% +other aspects that you may want in your +code okay and so this is a good example + + align:start position:0% +code okay and so this is a good example + + + align:start position:0% +code okay and so this is a good example +of that in + + align:start position:0% +of that in + + + align:start position:0% +of that in +fact um and this is an exercise you can + + align:start position:0% +fact um and this is an exercise you can + + + align:start position:0% +fact um and this is an exercise you can +actually achieve Work N + + align:start position:0% +actually achieve Work N + + + align:start position:0% +actually achieve Work N +cubed order n cubed work and a critical + + align:start position:0% +cubed order n cubed work and a critical + + + align:start position:0% +cubed order n cubed work and a critical +path of log + + align:start position:0% +path of log + + + align:start position:0% +path of log +n so even better than either of these + + align:start position:0% +n so even better than either of these + + + align:start position:0% +n so even better than either of these +two algorithms in term terms of + + align:start position:0% +two algorithms in term terms of + + + align:start position:0% +two algorithms in term terms of +parallelism okay so that gives you n + + align:start position:0% +parallelism okay so that gives you n + + + align:start position:0% +parallelism okay so that gives you n +cubed over log n parallelism so that's + + align:start position:0% +cubed over log n parallelism so that's + + + align:start position:0% +cubed over log n parallelism so that's +an exercise and then the other exercise + + align:start position:0% +an exercise and then the other exercise + + + align:start position:0% +an exercise and then the other exercise +that I mentioned that's good to do is + + align:start position:0% +that I mentioned that's good to do is + + + align:start position:0% +that I mentioned that's good to do is +parallel + + align:start position:0% +parallel + + + align:start position:0% +parallel +strasen okay doing the same thing with + + align:start position:0% +strasen okay doing the same thing with + + + align:start position:0% +strasen okay doing the same thing with +strasen and analyze what's the work in + + align:start position:0% +strasen and analyze what's the work in + + + align:start position:0% +strasen and analyze what's the work in +critical path and parallelism of of uh + + align:start position:0% +critical path and parallelism of of uh + + + align:start position:0% +critical path and parallelism of of uh +the stren + + align:start position:0% +the stren + + + align:start position:0% +the stren +code okay any any questions about M + + align:start position:0% + + + + align:start position:0% + +multiplication yeah + + align:start position:0% + + + + align:start position:0% + +yeah so that would take that would add a + + align:start position:0% +yeah so that would take that would add a + + + align:start position:0% +yeah so that would take that would add a +log in to the critical path which is + + align:start position:0% +log in to the critical path which is + + + align:start position:0% +log in to the critical path which is +nothing compared to the N what you do + + align:start position:0% +nothing compared to the N what you do + + + align:start position:0% +nothing compared to the N what you do +exactly excuse me is initial well you + + align:start position:0% +exactly excuse me is initial well you + + + align:start position:0% +exactly excuse me is initial well you +got to make sure C is zero to begin + + align:start position:0% +got to make sure C is zero to begin + + + align:start position:0% +got to make sure C is zero to begin +with okay so just you have to set all + + align:start position:0% +with okay so just you have to set all + + + align:start position:0% +with okay so just you have to set all +the entries to zero and so that will + + align:start position:0% +the entries to zero and so that will + + + align:start position:0% +the entries to zero and so that will +take you uh N squared work which is + + align:start position:0% +take you uh N squared work which is + + + align:start position:0% +take you uh N squared work which is +nothing compared to the N cubed work + + align:start position:0% +nothing compared to the N cubed work + + + align:start position:0% +nothing compared to the N cubed work +you're doing here and it'll cost cost + + align:start position:0% +you're doing here and it'll cost cost + + + align:start position:0% +you're doing here and it'll cost cost +you log in uh additional to the critical + + align:start position:0% +you log in uh additional to the critical + + + align:start position:0% +you log in uh additional to the critical +path which is nothing compared to the + + align:start position:0% +path which is nothing compared to the + + + align:start position:0% +path which is nothing compared to the +order n that you're + + align:start position:0% +order n that you're + + + align:start position:0% +order n that you're +spending okay good any other questions + + align:start position:0% +spending okay good any other questions + + + align:start position:0% +spending okay good any other questions +about matrix + + align:start position:0% +about matrix + + + align:start position:0% +about matrix +multiplication okay as I say this is all + + align:start position:0% +multiplication okay as I say this is all + + + align:start position:0% +multiplication okay as I say this is all +like goes back to uh goes back to to + + align:start position:0% +like goes back to uh goes back to to + + + align:start position:0% +like goes back to uh goes back to to +week two or something in the class do + + align:start position:0% +week two or something in the class do + + + align:start position:0% +week two or something in the class do +you have a comment is there + + align:start position:0% + + + + align:start position:0% + +easy uh can yes you can okay yes you can + + align:start position:0% +easy uh can yes you can okay yes you can + + + align:start position:0% +easy uh can yes you can okay yes you can +it's actually kind of interesting to to + + align:start position:0% +it's actually kind of interesting to to + + + align:start position:0% +it's actually kind of interesting to to +look at that actually we can talk later + + align:start position:0% +look at that actually we can talk later + + + align:start position:0% +look at that actually we can talk later +okay we'll write a research paper after + + align:start position:0% +okay we'll write a research paper after + + + align:start position:0% +okay we'll write a research paper after +the class is over okay because there's + + align:start position:0% +the class is over okay because there's + + + align:start position:0% +the class is over okay because there's +actually some interesting open questions + + align:start position:0% + + + + align:start position:0% + +there + + align:start position:0% +there + + + align:start position:0% +there +okay let's move + + align:start position:0% + + + + align:start position:0% + +on + + align:start position:0% +on + + + align:start position:0% +on +to something that you thought you had + + align:start position:0% +to something that you thought you had + + + align:start position:0% +to something that you thought you had +gotten rid of weeks + + align:start position:0% +gotten rid of weeks + + + align:start position:0% +gotten rid of weeks +ago and that would be the + + align:start position:0% +ago and that would be the + + + align:start position:0% +ago and that would be the +topic of + + align:start position:0% + + + + align:start position:0% + +sorting back to + + align:start position:0% +sorting back to + + + align:start position:0% +sorting back to +sorting okay so we want a parallel sort + + align:start position:0% +sorting okay so we want a parallel sort + + + align:start position:0% +sorting okay so we want a parallel sort +now okay hugely important + + align:start position:0% +now okay hugely important + + + align:start position:0% +now okay hugely important +problem um so let's take a look at so if + + align:start position:0% +problem um so let's take a look at so if + + + align:start position:0% +problem um so let's take a look at so if +I think about algorithms for sorting + + align:start position:0% +I think about algorithms for sorting + + + align:start position:0% +I think about algorithms for sorting +that sound easy to parallelize which + + align:start position:0% +that sound easy to parallelize which + + + align:start position:0% +that sound easy to parallelize which +ones kind of sound easy to parallelize + + align:start position:0% + + + + align:start position:0% + +quick sort yep that's a good one yeah + + align:start position:0% +quick sort yep that's a good one yeah + + + align:start position:0% +quick sort yep that's a good one yeah +quick sort is is pretty uh good one to + + align:start position:0% +quick sort is is pretty uh good one to + + + align:start position:0% +quick sort is is pretty uh good one to +parallelize and analyze but remember + + align:start position:0% +parallelize and analyze but remember + + + align:start position:0% +parallelize and analyze but remember +quick swort has a little bit more + + align:start position:0% +quick swort has a little bit more + + + align:start position:0% +quick swort has a little bit more +complicated analysis than some other + + align:start position:0% +complicated analysis than some other + + + align:start position:0% +complicated analysis than some other +sorts what's another one that looks like + + align:start position:0% +sorts what's another one that looks like + + + align:start position:0% +sorts what's another one that looks like +it should be pretty easy to + + align:start position:0% +it should be pretty easy to + + + align:start position:0% +it should be pretty easy to +parallelize merge sort okay like when + + align:start position:0% +parallelize merge sort okay like when + + + align:start position:0% +parallelize merge sort okay like when +did we teach merge + + align:start position:0% +did we teach merge + + + align:start position:0% +did we teach merge +sort day + + align:start position:0% +sort day + + + align:start position:0% +sort day +one okay so do merge sort okay because + + align:start position:0% +one okay so do merge sort okay because + + + align:start position:0% +one okay so do merge sort okay because +just a little bit easier to analyze okay + + align:start position:0% +just a little bit easier to analyze okay + + + align:start position:0% +just a little bit easier to analyze okay +we could do the same thing for quick + + align:start position:0% +we could do the same thing for quick + + + align:start position:0% +we could do the same thing for quick +sort + + align:start position:0% +sort + + + align:start position:0% +sort +so here's merge + + align:start position:0% + + + + align:start position:0% + +sort okay and it's going to + + align:start position:0% +sort okay and it's going to + + + align:start position:0% +sort okay and it's going to +sort a of P to + + align:start position:0% +sort a of P to + + + align:start position:0% +sort a of P to +R so if p is less than + + align:start position:0% + + + + align:start position:0% + +R + + align:start position:0% +R + + + align:start position:0% +R +then we get the middle + + align:start position:0% + + + + align:start position:0% + +element and then we'll SP on + + align:start position:0% +element and then we'll SP on + + + align:start position:0% +element and then we'll SP on +off since we have to as you recall when + + align:start position:0% +off since we have to as you recall when + + + align:start position:0% +off since we have to as you recall when +you merge sort you first recursively + + align:start position:0% +you merge sort you first recursively + + + align:start position:0% +you merge sort you first recursively +sort the two subres there's no reason + + align:start position:0% +sort the two subres there's no reason + + + align:start position:0% +sort the two subres there's no reason +not to do those in parallel let's just + + align:start position:0% +not to do those in parallel let's just + + + align:start position:0% +not to do those in parallel let's just +do them in parallel let's spawn + + align:start position:0% +do them in parallel let's spawn + + + align:start position:0% +do them in parallel let's spawn +off merge + + align:start position:0% +off merge + + + align:start position:0% +off merge +sort of a p + + align:start position:0% +sort of a p + + + align:start position:0% +sort of a p +q and spawn off + + align:start position:0% + + + + align:start position:0% + +then word + + align:start position:0% +then word + + + align:start position:0% +then word +sort of a + + align:start position:0% +sort of a + + + align:start position:0% +sort of a +Q + 1 + + align:start position:0% +Q + 1 + + + align:start position:0% +Q + 1 +R and then + + align:start position:0% +R and then + + + align:start position:0% +R and then +we wait for them to be done sink don't + + align:start position:0% +we wait for them to be done sink don't + + + align:start position:0% +we wait for them to be done sink don't +forget your + + align:start position:0% +forget your + + + align:start position:0% +forget your +sinks okay you sink or + + align:start position:0% +sinks okay you sink or + + + align:start position:0% +sinks okay you sink or +swim okay and then what do we do when + + align:start position:0% +swim okay and then what do we do when + + + align:start position:0% +swim okay and then what do we do when +we're done with + + align:start position:0% + + + + align:start position:0% + +this okay we merge okay so we + + align:start position:0% + + + + align:start position:0% + +merge of a p + + align:start position:0% +merge of a p + + + align:start position:0% +merge of a p +QR which + + align:start position:0% + + + + align:start position:0% + +is merge a of P up to Q + + align:start position:0% + + + + align:start position:0% + +with uh a of Q + 1 up to + + align:start position:0% +with uh a of Q + 1 up to + + + align:start position:0% +with uh a of Q + 1 up to +R okay and once we've merged we're done + + align:start position:0% +R okay and once we've merged we're done + + + align:start position:0% +R okay and once we've merged we're done +okay so this is the same code AS we saw + + align:start position:0% +okay so this is the same code AS we saw + + + align:start position:0% +okay so this is the same code AS we saw +before in day + + align:start position:0% +before in day + + + align:start position:0% +before in day +one okay except we've got a couple + + align:start position:0% +one okay except we've got a couple + + + align:start position:0% +one okay except we've got a couple +spawns in the + + align:start position:0% + + + + align:start position:0% + +sink so let's analyze + + align:start position:0% + + + + align:start position:0% + +this so the + + align:start position:0% + + + + align:start position:0% + +work let's call it T1 of + + align:start position:0% +work let's call it T1 of + + + align:start position:0% +work let's call it T1 of +n is what's the recurrence for the + + align:start position:0% + + + + align:start position:0% + +this this really is going back to day + + align:start position:0% +this this really is going back to day + + + align:start position:0% +this this really is going back to day +one right we actually did this on day + + align:start position:0% +one right we actually did this on day + + + align:start position:0% +one right we actually did this on day +one of this + + align:start position:0% +one of this + + + align:start position:0% +one of this +class okay so what's the + + align:start position:0% + + + + align:start position:0% + +recurrence 2 T1 of n + + align:start position:0% +recurrence 2 T1 of n + + + align:start position:0% +recurrence 2 T1 of n +/2 + + align:start position:0% +/2 + + + align:start position:0% +/2 +plus order n merg is an order end time + + align:start position:0% +plus order n merg is an order end time + + + align:start position:0% +plus order n merg is an order end time +operation okay and so that gives us a + + align:start position:0% +operation okay and so that gives us a + + + align:start position:0% +operation okay and so that gives us a +solution + + align:start position:0% +solution + + + align:start position:0% +solution +of n log n okay even if you didn't know + + align:start position:0% +of n log n okay even if you didn't know + + + align:start position:0% +of n log n okay even if you didn't know +the solution you should know the + + align:start position:0% +the solution you should know the + + + align:start position:0% +the solution you should know the +answer okay which is the same as the + + align:start position:0% +answer okay which is the same as the + + + align:start position:0% +answer okay which is the same as the +serial code not surprisingly that's what + + align:start position:0% +serial code not surprisingly that's what + + + align:start position:0% +serial code not surprisingly that's what +we want okay critical path + + align:start position:0% +we want okay critical path + + + align:start position:0% +we want okay critical path +length Okay T Infinity of + + align:start position:0% +length Okay T Infinity of + + + align:start position:0% +length Okay T Infinity of +n is equal to okay + + align:start position:0% + + + + align:start position:0% + +T Infinity of n + + align:start position:0% + + + + align:start position:0% + +/2 plus order n again and that's equal + + align:start position:0% +/2 plus order n again and that's equal + + + align:start position:0% +/2 plus order n again and that's equal +to order + + align:start position:0% + + + + align:start position:0% + +n okay so the + + align:start position:0% + + + + align:start position:0% + +parallelism is then P bar equals T1 of n + + align:start position:0% +parallelism is then P bar equals T1 of n + + + align:start position:0% +parallelism is then P bar equals T1 of n +over T Infinity of + + align:start position:0% +over T Infinity of + + + align:start position:0% +over T Infinity of +n is equal + + align:start position:0% + + + + align:start position:0% + +to Theta of log + + align:start position:0% + + + + align:start position:0% + +n okay is that a lot of + + align:start position:0% +n okay is that a lot of + + + align:start position:0% +n okay is that a lot of +parallelism no that's what we have a + + align:start position:0% +parallelism no that's what we have a + + + align:start position:0% +parallelism no that's what we have a +technical name for that we call it + + align:start position:0% + + + + align:start position:0% + +puny okay that's puny parallelism log n + + align:start position:0% +puny okay that's puny parallelism log n + + + align:start position:0% +puny okay that's puny parallelism log n +now so this is actually probably a + + align:start position:0% +now so this is actually probably a + + + align:start position:0% +now so this is actually probably a +decent um + + align:start position:0% +decent um + + + align:start position:0% +decent um +algorithm for uh uh for some of the + + align:start position:0% +algorithm for uh uh for some of the + + + align:start position:0% +algorithm for uh uh for some of the +small scale processors especially the + + align:start position:0% +small scale processors especially the + + + align:start position:0% +small scale processors especially the +multicore processors that are coming on + + align:start position:0% +multicore processors that are coming on + + + align:start position:0% +multicore processors that are coming on +the market and some of the smaller uh s + + align:start position:0% +the market and some of the smaller uh s + + + align:start position:0% +the market and some of the smaller uh s +SMP symmetric multiprocessors that are + + align:start position:0% +SMP symmetric multiprocessors that are + + + align:start position:0% +SMP symmetric multiprocessors that are +available you know they have four eight + + align:start position:0% +available you know they have four eight + + + align:start position:0% +available you know they have four eight +processors something might be okay + + align:start position:0% +processors something might be okay + + + align:start position:0% +processors something might be okay +there's not a lot of parallelism okay + + align:start position:0% +there's not a lot of parallelism okay + + + align:start position:0% +there's not a lot of parallelism okay +it's it's uh you know for a million + + align:start position:0% +it's it's uh you know for a million + + + align:start position:0% +it's it's uh you know for a million +elements uh log in is about + + align:start position:0% +elements uh log in is about + + + align:start position:0% +elements uh log in is about +20 okay so and then there constant + + align:start position:0% +20 okay so and then there constant + + + align:start position:0% +20 okay so and then there constant +overheads Etc this is not very much + + align:start position:0% +overheads Etc this is not very much + + + align:start position:0% +overheads Etc this is not very much +parallelism at all + + align:start position:0% + + + + align:start position:0% + +question yeah so how can we do + + align:start position:0% + + + + align:start position:0% + +better I mean there's there's it's like + + align:start position:0% +better I mean there's there's it's like + + + align:start position:0% +better I mean there's there's it's like +man that + + align:start position:0% +man that + + + align:start position:0% +man that +merge right takes order + + align:start position:0% +merge right takes order + + + align:start position:0% +merge right takes order +in if I want to do better what should I + + align:start position:0% +in if I want to do better what should I + + + align:start position:0% +in if I want to do better what should I +do yeah sort in place you don't + + align:start position:0% +do yeah sort in place you don't + + + align:start position:0% +do yeah sort in place you don't +have sort in place but for example if + + align:start position:0% +have sort in place but for example if + + + align:start position:0% +have sort in place but for example if +you do quick sort and partition you + + align:start position:0% +you do quick sort and partition you + + + align:start position:0% +you do quick sort and partition you +still have a linear time + + align:start position:0% +still have a linear time + + + align:start position:0% +still have a linear time +partition so you're going to be very + + align:start position:0% +partition so you're going to be very + + + align:start position:0% +partition so you're going to be very +much in the same + + align:start position:0% +much in the same + + + align:start position:0% +much in the same +situation so what but what can I do + + align:start position:0% + + + + align:start position:0% + +here parallel + + align:start position:0% +here parallel + + + align:start position:0% +here parallel +merge okay let's make merge go in + + align:start position:0% +merge okay let's make merge go in + + + align:start position:0% +merge okay let's make merge go in +parallel that's where all the the + + align:start position:0% +parallel that's where all the the + + + align:start position:0% +parallel that's where all the the +critical path is let's figure out a way + + align:start position:0% +critical path is let's figure out a way + + + align:start position:0% +critical path is let's figure out a way +of building a + + align:start position:0% +of building a + + + align:start position:0% +of building a +merge uh program that that has a very + + align:start position:0% +merge uh program that that has a very + + + align:start position:0% +merge uh program that that has a very +short critical path okay you have to + + align:start position:0% +short critical path okay you have to + + + align:start position:0% +short critical path okay you have to +paralyze the + + align:start position:0% + + + + align:start position:0% + +merge this is great you guys + + align:start position:0% + + + + align:start position:0% + +are it's so nice to see at the end of a + + align:start position:0% +are it's so nice to see at the end of a + + + align:start position:0% +are it's so nice to see at the end of a +course like this that you know people + + align:start position:0% +course like this that you know people + + + align:start position:0% +course like this that you know people +have the intuition for you know oh you + + align:start position:0% +have the intuition for you know oh you + + + align:start position:0% +have the intuition for you know oh you +can look at it and sort of see where's + + align:start position:0% +can look at it and sort of see where's + + + align:start position:0% +can look at it and sort of see where's +where should you put in your work okay + + align:start position:0% +where should you put in your work okay + + + align:start position:0% +where should you put in your work okay +the one thing about algorithms is it + + align:start position:0% +the one thing about algorithms is it + + + align:start position:0% +the one thing about algorithms is it +doesn't it doesn't stop you from having + + align:start position:0% +doesn't it doesn't stop you from having + + + align:start position:0% +doesn't it doesn't stop you from having +to + + align:start position:0% +to + + + align:start position:0% +to +engineer a program when you code it + + align:start position:0% +engineer a program when you code it + + + align:start position:0% +engineer a program when you code it +there's a lot more to coding a program + + align:start position:0% +there's a lot more to coding a program + + + align:start position:0% +there's a lot more to coding a program +well than just having the algorithm as + + align:start position:0% +well than just having the algorithm as + + + align:start position:0% +well than just having the algorithm as +we talked about also in day one there's + + align:start position:0% +we talked about also in day one there's + + + align:start position:0% +we talked about also in day one there's +things like making it modular and making + + align:start position:0% +things like making it modular and making + + + align:start position:0% +things like making it modular and making +it maintainable and and a whole bunch of + + align:start position:0% +it maintainable and and a whole bunch of + + + align:start position:0% +it maintainable and and a whole bunch of +things like that but one of the things + + align:start position:0% +things like that but one of the things + + + align:start position:0% +things like that but one of the things +that algorithms does it tells you where + + align:start position:0% +that algorithms does it tells you where + + + align:start position:0% +that algorithms does it tells you where +should you focus your + + align:start position:0% +should you focus your + + + align:start position:0% +should you focus your +work okay there's no point in for + + align:start position:0% +work okay there's no point in for + + + align:start position:0% +work okay there's no point in for +example sort of saying okay let me let + + align:start position:0% +example sort of saying okay let me let + + + align:start position:0% +example sort of saying okay let me let +me Spawn off four of these things of + + align:start position:0% +me Spawn off four of these things of + + + align:start position:0% +me Spawn off four of these things of +size n over4 in hopes of getting you + + align:start position:0% +size n over4 in hopes of getting you + + + align:start position:0% +size n over4 in hopes of getting you +know it's like that's not where you put + + align:start position:0% +know it's like that's not where you put + + + align:start position:0% +know it's like that's not where you put +the work you put the work in the merge + + align:start position:0% +the work you put the work in the merge + + + align:start position:0% +the work you put the work in the merge +because that's the one that's the + + align:start position:0% +because that's the one that's the + + + align:start position:0% +because that's the one that's the +bottleneck okay and and that's the nice + + align:start position:0% +bottleneck okay and and that's the nice + + + align:start position:0% +bottleneck okay and and that's the nice +thing about algorithms is it very + + align:start position:0% +thing about algorithms is it very + + + align:start position:0% +thing about algorithms is it very +quickly lets you hone in on where you + + align:start position:0% +quickly lets you hone in on where you + + + align:start position:0% +quickly lets you hone in on where you +should put your effort okay when you're + + align:start position:0% +should put your effort okay when you're + + + align:start position:0% +should put your effort okay when you're +doing uh algorithmic design in uh in + + align:start position:0% +doing uh algorithmic design in uh in + + + align:start position:0% +doing uh algorithmic design in uh in +engineering practice so must parallelize + + align:start position:0% +engineering practice so must parallelize + + + align:start position:0% +engineering practice so must parallelize +the + + align:start position:0% + + + + align:start position:0% + +merge the merge + + align:start position:0% +merge the merge + + + align:start position:0% +merge the merge +routine so here's the basic idea we're + + align:start position:0% +routine so here's the basic idea we're + + + align:start position:0% +routine so here's the basic idea we're +going to + + align:start position:0% +going to + + + align:start position:0% +going to +use so in general when we merge when I + + align:start position:0% +use so in general when we merge when I + + + align:start position:0% +use so in general when we merge when I +do our recursive merge we're going to + + align:start position:0% +do our recursive merge we're going to + + + align:start position:0% +do our recursive merge we're going to +have two + + align:start position:0% +have two + + + align:start position:0% +have two +arrays let's call them A and B I call + + align:start position:0% +arrays let's call them A and B I call + + + align:start position:0% +arrays let's call them A and B I call +them a there I should probably shouldn't + + align:start position:0% +them a there I should probably shouldn't + + + align:start position:0% +them a there I should probably shouldn't +have used a i probably should have + + align:start position:0% +have used a i probably should have + + + align:start position:0% +have used a i probably should have +called them something else but that's + + align:start position:0% +called them something else but that's + + + align:start position:0% +called them something else but that's +what my notes have so we're going to + + align:start position:0% +what my notes have so we're going to + + + align:start position:0% +what my notes have so we're going to +stick to + + align:start position:0% +stick to + + + align:start position:0% +stick to +it uh let me give a little bit more + + align:start position:0% +it uh let me give a little bit more + + + align:start position:0% +it uh let me give a little bit more +space + + align:start position:0% +space + + + align:start position:0% +space +there see what's going + + align:start position:0% + + + + align:start position:0% + +on we have two arrays I'll call them A + + align:start position:0% +on we have two arrays I'll call them A + + + align:start position:0% +on we have two arrays I'll call them A +and + + align:start position:0% + + + + align:start position:0% + +B + + align:start position:0% +B + + + align:start position:0% +B +okay and what we're going to do these + + align:start position:0% +okay and what we're going to do these + + + align:start position:0% +okay and what we're going to do these +are going to be already + + align:start position:0% +are going to be already + + + align:start position:0% +are going to be already +sorted and our job is going to be to + + align:start position:0% +sorted and our job is going to be to + + + align:start position:0% +sorted and our job is going to be to +merge them + + align:start position:0% +merge them + + + align:start position:0% +merge them +together so what I'll do is I'll take + + align:start position:0% +together so what I'll do is I'll take + + + align:start position:0% +together so what I'll do is I'll take +the middle element of a so this let's + + align:start position:0% +the middle element of a so this let's + + + align:start position:0% +the middle element of a so this let's +say goes from one to + + align:start position:0% +say goes from one to + + + align:start position:0% +say goes from one to +L and this goes from one to + + align:start position:0% + + + + align:start position:0% + +M okay I'll take the middle element the + + align:start position:0% +M okay I'll take the middle element the + + + align:start position:0% +M okay I'll take the middle element the +element at L over2 + + align:start position:0% + + + + align:start position:0% + +say and what I'll do is use binary + + align:start position:0% +say and what I'll do is use binary + + + align:start position:0% +say and what I'll do is use binary +search to figure out where does it go in + + align:start position:0% +search to figure out where does it go in + + + align:start position:0% +search to figure out where does it go in +the array B + + align:start position:0% +the array B + + + align:start position:0% +the array B +where does this element go and it goes + + align:start position:0% +where does this element go and it goes + + + align:start position:0% +where does this element go and it goes +to some point + + align:start position:0% +to some point + + + align:start position:0% +to some point +here where we have J here and J + one + + align:start position:0% + + + + align:start position:0% + +here so we know since this is sorted + + align:start position:0% +here so we know since this is sorted + + + align:start position:0% +here so we know since this is sorted +that all these things are less than or + + align:start position:0% +that all these things are less than or + + + align:start position:0% +that all these things are less than or +equal to a of L + + align:start position:0% +equal to a of L + + + align:start position:0% +equal to a of L +over2 and all these things are greater + + align:start position:0% +over2 and all these things are greater + + + align:start position:0% +over2 and all these things are greater +than or equal to a of L + + align:start position:0% + + + + align:start position:0% + +over2 and similarly since that element + + align:start position:0% +over2 and similarly since that element + + + align:start position:0% +over2 and similarly since that element +Falls here all these are less than or + + align:start position:0% +Falls here all these are less than or + + + align:start position:0% +Falls here all these are less than or +equal to a of + + align:start position:0% +equal to a of + + + align:start position:0% +equal to a of +L2 and all these are going to be less + + align:start position:0% +L2 and all these are going to be less + + + align:start position:0% +L2 and all these are going to be less +than or greater than or equal + + align:start position:0% + + + + align:start position:0% + +to okay and so now what I can do is once + + align:start position:0% +to okay and so now what I can do is once + + + align:start position:0% +to okay and so now what I can do is once +I figured out where this goes I can + + align:start position:0% +I figured out where this goes I can + + + align:start position:0% +I figured out where this goes I can +recursively + + align:start position:0% +recursively + + + align:start position:0% +recursively +merge this array with this + + align:start position:0% +merge this array with this + + + align:start position:0% +merge this array with this +one and this one with this + + align:start position:0% +one and this one with this + + + align:start position:0% +one and this one with this +one and and then if I just concatenate + + align:start position:0% +one and and then if I just concatenate + + + align:start position:0% +one and and then if I just concatenate +them all together I've got my my merged + + align:start position:0% +them all together I've got my my merged + + + align:start position:0% +them all together I've got my my merged +array okay so let's write that + + align:start position:0% +array okay so let's write that + + + align:start position:0% +array okay so let's write that +code everybody get the gist of what's + + align:start position:0% +code everybody get the gist of what's + + + align:start position:0% +code everybody get the gist of what's +going on there how we're going to + + align:start position:0% +going on there how we're going to + + + align:start position:0% +going on there how we're going to +parallelize this merge course you can + + align:start position:0% +parallelize this merge course you can + + + align:start position:0% +parallelize this merge course you can +see it's going to get a little + + align:start position:0% +see it's going to get a little + + + align:start position:0% +see it's going to get a little +messy because you know J could be + + align:start position:0% + + + + align:start position:0% + +anywhere so here's my code parallel + + align:start position:0% +anywhere so here's my code parallel + + + align:start position:0% +anywhere so here's my code parallel +merge + + align:start position:0% + + + + align:start position:0% + +of and we're going to put it in C of one + + align:start position:0% +of and we're going to put it in C of one + + + align:start position:0% +of and we're going to put it in C of one +to n so I'm going to have n + + align:start position:0% +to n so I'm going to have n + + + align:start position:0% +to n so I'm going to have n +elements so this is doing + + align:start position:0% + + + + align:start position:0% + +merge A and + + align:start position:0% +merge A and + + + align:start position:0% +merge A and +B into + + align:start position:0% +B into + + + align:start position:0% +B into +C and and N is equal to l + + + align:start position:0% + + + + align:start position:0% + +m okay so we're going to take two arrays + + align:start position:0% +m okay so we're going to take two arrays + + + align:start position:0% +m okay so we're going to take two arrays +and merge it + + align:start position:0% +and merge it + + + align:start position:0% +and merge it +into the third array + + align:start position:0% +into the third array + + + align:start position:0% +into the third array +okay + + align:start position:0% + + + + align:start position:0% + +so let's see without loss of generality + + align:start position:0% +so let's see without loss of generality + + + align:start position:0% +so let's see without loss of generality +I'm going to say l is bigger than + + align:start position:0% +I'm going to say l is bigger than + + + align:start position:0% +I'm going to say l is bigger than +M as I showed here because if it's not + + align:start position:0% +M as I showed here because if it's not + + + align:start position:0% +M as I showed here because if it's not +what do I + + align:start position:0% +what do I + + + align:start position:0% +what do I +do just do it the other way around right + + align:start position:0% +do just do it the other way around right + + + align:start position:0% +do just do it the other way around right +so I figure out which one is bigger so + + align:start position:0% +so I figure out which one is bigger so + + + align:start position:0% +so I figure out which one is bigger so +that's only cost me order one to test + + align:start position:0% +that's only cost me order one to test + + + align:start position:0% +that's only cost me order one to test +that or whatever and then I basically do + + align:start position:0% +that or whatever and then I basically do + + + align:start position:0% +that or whatever and then I basically do +a base + + align:start position:0% +a base + + + align:start position:0% +a base +case you know if the two arrays are you + + align:start position:0% +case you know if the two arrays are you + + + align:start position:0% +case you know if the two arrays are you +know empty or whatever what you do in + + align:start position:0% +know empty or whatever what you do in + + + align:start position:0% +know empty or whatever what you do in +practice of course is you know if + + align:start position:0% +practice of course is you know if + + + align:start position:0% +practice of course is you know if +they're small enough you just do a + + align:start position:0% +they're small enough you just do a + + + align:start position:0% +they're small enough you just do a +Serial + + align:start position:0% +Serial + + + align:start position:0% +Serial +merge okay if they're small enough and I + + align:start position:0% +merge okay if they're small enough and I + + + align:start position:0% +merge okay if they're small enough and I +don't really expect to get much + + align:start position:0% +don't really expect to get much + + + align:start position:0% +don't really expect to get much +parallelism there isn't much work there + + align:start position:0% +parallelism there isn't much work there + + + align:start position:0% +parallelism there isn't much work there +might as well just do a Serial merge be + + align:start position:0% +might as well just do a Serial merge be + + + align:start position:0% +might as well just do a Serial merge be +a little bit more efficient okay so do + + align:start position:0% +a little bit more efficient okay so do + + + align:start position:0% +a little bit more efficient okay so do +the base case + + align:start position:0% +the base case + + + align:start position:0% +the base case +so then what I do is I + + align:start position:0% + + + + align:start position:0% + +find the J such that b of + + align:start position:0% +find the J such that b of + + + align:start position:0% +find the J such that b of +J is less than or equal to a of L + + align:start position:0% +J is less than or equal to a of L + + + align:start position:0% +J is less than or equal to a of L +over2 less than equal to B of J + + + align:start position:0% +over2 less than equal to B of J + + + + align:start position:0% +over2 less than equal to B of J + +one + + align:start position:0% +one + + + align:start position:0% +one +using binary + + align:start position:0% + + + + align:start position:0% + +search when did we cover binary search + + align:start position:0% +search when did we cover binary search + + + align:start position:0% +search when did we cover binary search +oh yeah + + align:start position:0% +oh yeah + + + align:start position:0% +oh yeah +that was a weak one right is that in + + align:start position:0% +that was a weak one right is that in + + + align:start position:0% +that was a weak one right is that in +first recitation or something yeah it's + + align:start position:0% +first recitation or something yeah it's + + + align:start position:0% +first recitation or something yeah it's +amazing okay and now what we do is we + + align:start position:0% +amazing okay and now what we do is we + + + align:start position:0% +amazing okay and now what we do is we +spawn + + align:start position:0% + + + + align:start position:0% + +off uh P + + align:start position:0% + + + + align:start position:0% + +merge of a of 1 L + + align:start position:0% + + + + align:start position:0% + +over2 B of one to J and St it into C of + + align:start position:0% +over2 B of one to J and St it into C of + + + align:start position:0% +over2 B of one to J and St it into C of +1 2 l/ 2 + + + align:start position:0% + + + + align:start position:0% + +J + + align:start position:0% +J + + + align:start position:0% +J +okay and similarly now we can spawn + + align:start position:0% + + + + align:start position:0% + +off a + + align:start position:0% + + + + align:start position:0% + +merge + + align:start position:0% +merge + + + align:start position:0% +merge +of a + + align:start position:0% +of a + + + align:start position:0% +of a +of L l/ 2 + 1 up to + + align:start position:0% +of L l/ 2 + 1 up to + + + align:start position:0% +of L l/ 2 + 1 up to +L A B of + + align:start position:0% +L A B of + + + align:start position:0% +L A B of +J + + + align:start position:0% +J + + + + align:start position:0% +J + +one up to + + align:start position:0% +one up to + + + align:start position:0% +one up to +M and A C of l/2 + J + 1 up to + + align:start position:0% +M and A C of l/2 + J + 1 up to + + + align:start position:0% +M and A C of l/2 + J + 1 up to +n and then I sync + + align:start position:0% + + + + align:start position:0% + +so code is pretty straightforward doing + + align:start position:0% +so code is pretty straightforward doing + + + align:start position:0% +so code is pretty straightforward doing +exactly what I said we were going to do + + align:start position:0% +exactly what I said we were going to do + + + align:start position:0% +exactly what I said we were going to do +over + + align:start position:0% +over + + + align:start position:0% +over +here + + align:start position:0% +here + + + align:start position:0% +here +analysis little + + align:start position:0% +analysis little + + + align:start position:0% +analysis little +Messier a little + + align:start position:0% + + + + align:start position:0% + +Messier so + + align:start position:0% +Messier so + + + align:start position:0% +Messier so +why let's just try to understand this + + align:start position:0% +why let's just try to understand this + + + align:start position:0% +why let's just try to understand this +before we do the + + align:start position:0% +before we do the + + + align:start position:0% +before we do the +analysis why is it that I want to pick + + align:start position:0% +analysis why is it that I want to pick + + + align:start position:0% +analysis why is it that I want to pick +the middle of the big array rather than + + align:start position:0% +the middle of the big array rather than + + + align:start position:0% +the middle of the big array rather than +the small + + align:start position:0% + + + + align:start position:0% + +array what's sort of my rationale + + align:start position:0% + + + + align:start position:0% + +there that's actually a key part going + + align:start position:0% +there that's actually a key part going + + + align:start position:0% +there that's actually a key part going +to be a key part of the + + align:start position:0% + + + + align:start position:0% + +analysis + + align:start position:0% + + + + align:start position:0% + +yeah a okay if you if is better than + + align:start position:0% +yeah a okay if you if is better than + + + align:start position:0% +yeah a okay if you if is better than +guar because a is biger yeah imagine + + align:start position:0% +guar because a is biger yeah imagine + + + align:start position:0% +guar because a is biger yeah imagine +that b for example had only one element + + align:start position:0% +that b for example had only one element + + + align:start position:0% +that b for example had only one element +in + + align:start position:0% + + + + align:start position:0% + +it okay or just a few elements then + + align:start position:0% +it okay or just a few elements then + + + align:start position:0% +it okay or just a few elements then +finding it in a might mean finding + + align:start position:0% +finding it in a might mean finding + + + align:start position:0% +finding it in a might mean finding +it right near the beginning of a and now + + align:start position:0% +it right near the beginning of a and now + + + align:start position:0% +it right near the beginning of a and now +I'd be + + align:start position:0% +I'd be + + + align:start position:0% +I'd be +left you know with sub problems that + + align:start position:0% +left you know with sub problems that + + + align:start position:0% +left you know with sub problems that +were that were very big + + align:start position:0% +were that were very big + + + align:start position:0% +were that were very big +whereas here as you're pointing out if I + + align:start position:0% +whereas here as you're pointing out if I + + + align:start position:0% +whereas here as you're pointing out if I +start here if my total number of + + align:start position:0% +start here if my total number of + + + align:start position:0% +start here if my total number of +elements is + + align:start position:0% +elements is + + + align:start position:0% +elements is +n what's the smallest that one of these + + align:start position:0% +n what's the smallest that one of these + + + align:start position:0% +n what's the smallest that one of these +recursions could + + align:start position:0% + + + + align:start position:0% + +be n over4 is the smallest it could + + align:start position:0% +be n over4 is the smallest it could + + + align:start position:0% +be n over4 is the smallest it could +be + + align:start position:0% +be + + + align:start position:0% +be +okay okay because I would have at least + + align:start position:0% +okay okay because I would have at least + + + align:start position:0% +okay okay because I would have at least +a quarter of the total number of + + align:start position:0% +a quarter of the total number of + + + align:start position:0% +a quarter of the total number of +elements to the left here or to the + + align:start position:0% +elements to the left here or to the + + + align:start position:0% +elements to the left here or to the +right here but if I do it the other way + + align:start position:0% +right here but if I do it the other way + + + align:start position:0% +right here but if I do it the other way +around my recursion I might get a + + align:start position:0% +around my recursion I might get a + + + align:start position:0% +around my recursion I might get a +recursion that was nearly as big as n + + align:start position:0% +recursion that was nearly as big as n + + + align:start position:0% +recursion that was nearly as big as n +and that's sort of once again sort of + + align:start position:0% +and that's sort of once again sort of + + + align:start position:0% +and that's sort of once again sort of +like the difference when we were + + align:start position:0% +like the difference when we were + + + align:start position:0% +like the difference when we were +analyzing uh quick sort with whether we + + align:start position:0% +analyzing uh quick sort with whether we + + + align:start position:0% +analyzing uh quick sort with whether we +got a good a good uh partitioning + + align:start position:0% +got a good a good uh partitioning + + + align:start position:0% +got a good a good uh partitioning +element or not if the partitioning + + align:start position:0% +element or not if the partitioning + + + align:start position:0% +element or not if the partitioning +element is somewhere in the middle we're + + align:start position:0% +element is somewhere in the middle we're + + + align:start position:0% +element is somewhere in the middle we're +really good but if it's always at one + + align:start position:0% +really good but if it's always at one + + + align:start position:0% +really good but if it's always at one +end it's no better than insertion sort + + align:start position:0% +end it's no better than insertion sort + + + align:start position:0% +end it's no better than insertion sort +you want to cut off at least a constant + + align:start position:0% +you want to cut off at least a constant + + + align:start position:0% +you want to cut off at least a constant +fraction in your divide and conquer in + + align:start position:0% +fraction in your divide and conquer in + + + align:start position:0% +fraction in your divide and conquer in +order to get the logarithmic + + align:start position:0% +order to get the logarithmic + + + align:start position:0% +order to get the logarithmic +Behavior okay so we'll see that in the + + align:start position:0% +Behavior okay so we'll see that in the + + + align:start position:0% +Behavior okay so we'll see that in the +analysis but the key thing here is that + + align:start position:0% +analysis but the key thing here is that + + + align:start position:0% +analysis but the key thing here is that +when we're going to uh uh do the + + align:start position:0% +when we're going to uh uh do the + + + align:start position:0% +when we're going to uh uh do the +recursion we're going to have at least n + + align:start position:0% +recursion we're going to have at least n + + + align:start position:0% +recursion we're going to have at least n +over4 elements in whatever the smaller + + align:start position:0% +over4 elements in whatever the smaller + + + align:start position:0% +over4 elements in whatever the smaller +thing + + align:start position:0% +thing + + + align:start position:0% +thing +is okay so but let's start it turns out + + align:start position:0% +is okay so but let's start it turns out + + + align:start position:0% +is okay so but let's start it turns out +the work is the hard part of this we'll + + align:start position:0% +the work is the hard part of this we'll + + + align:start position:0% +the work is the hard part of this we'll +start with critical path + + align:start position:0% +start with critical path + + + align:start position:0% +start with critical path +length okay look at that critical path + + align:start position:0% +length okay look at that critical path + + + align:start position:0% +length okay look at that critical path +length + + align:start position:0% + + + + align:start position:0% + +okay so parallel + + align:start position:0% +okay so parallel + + + align:start position:0% +okay so parallel +merge sub Infinity of + + align:start position:0% +merge sub Infinity of + + + align:start position:0% +merge sub Infinity of +n is going to be at + + align:start position:0% + + + + align:start position:0% + +most so the smaller piece has at least a + + align:start position:0% +most so the smaller piece has at least a + + + align:start position:0% +most so the smaller piece has at least a +quarter what's the larger piece going to + + align:start position:0% +quarter what's the larger piece going to + + + align:start position:0% +quarter what's the larger piece going to +be of these + + align:start position:0% +be of these + + + align:start position:0% +be of these +two of these two things here + + align:start position:0% + + + + align:start position:0% + +so we have two problems responding off + + align:start position:0% +so we have two problems responding off + + + align:start position:0% +so we have two problems responding off +now it's a little bit now we really have + + align:start position:0% +now it's a little bit now we really have + + + align:start position:0% +now it's a little bit now we really have +to do Max because they're not symmetric + + align:start position:0% +to do Max because they're not symmetric + + + align:start position:0% +to do Max because they're not symmetric +which one's going to be + + align:start position:0% + + + + align:start position:0% + +worse one could have at most + + align:start position:0% +worse one could have at most + + + align:start position:0% +worse one could have at most +3/4 okay of n 3 n + + align:start position:0% + + + + align:start position:0% + +whoops of 3 n over4 + + align:start position:0% + + + + align:start position:0% + +plus okay so the worst of these those + + align:start position:0% +plus okay so the worst of these those + + + align:start position:0% +plus okay so the worst of these those +two is going to be 3/4 of the elements + + align:start position:0% +two is going to be 3/4 of the elements + + + align:start position:0% +two is going to be 3/4 of the elements +plus + + align:start position:0% + + + + align:start position:0% + +what plus log + + align:start position:0% +what plus log + + + align:start position:0% +what plus log +n what's the log + + align:start position:0% +n what's the log + + + align:start position:0% +n what's the log +n the binary + + align:start position:0% +n the binary + + + align:start position:0% +n the binary +search okay and that gives me a solution + + align:start position:0% +search okay and that gives me a solution + + + align:start position:0% +search okay and that gives me a solution +of + + align:start position:0% + + + + align:start position:0% + +of this ends up being into + + align:start position:0% +of this ends up being into + + + align:start position:0% +of this ends up being into +the + + align:start position:0% + + + + align:start position:0% + +what that n to the zero right okay it's + + align:start position:0% +what that n to the zero right okay it's + + + align:start position:0% +what that n to the zero right okay it's +it's n to the log base 4/3 of + + align:start position:0% +it's n to the log base 4/3 of + + + align:start position:0% +it's n to the log base 4/3 of +one okay n to anything of one is zero so + + align:start position:0% +one okay n to anything of one is zero so + + + align:start position:0% +one okay n to anything of one is zero so +it's n to the zero so that's just one + + align:start position:0% +it's n to the zero so that's just one + + + align:start position:0% +it's n to the zero so that's just one +compared with log + + align:start position:0% +compared with log + + + align:start position:0% +compared with log +n tack on it's log squ + + align:start position:0% + + + + align:start position:0% + +n so we have a critical path of log squ + + align:start position:0% +n so we have a critical path of log squ + + + align:start position:0% +n so we have a critical path of log squ +n that's good news now let's hope that + + align:start position:0% +n that's good news now let's hope that + + + align:start position:0% +n that's good news now let's hope that +we didn't blow up the work by a + + align:start position:0% +we didn't blow up the work by a + + + align:start position:0% +we didn't blow up the work by a +substantial + + align:start position:0% + + + + align:start position:0% + +amount okay so the + + align:start position:0% +amount okay so the + + + align:start position:0% +amount okay so the +work is p m sub one of + + align:start position:0% +work is p m sub one of + + + align:start position:0% +work is p m sub one of +n is equal + + align:start position:0% +n is equal + + + align:start position:0% +n is equal +to okay so we don't know what the split + + align:start position:0% +to okay so we don't know what the split + + + align:start position:0% +to okay so we don't know what the split +is so let's call it + + align:start position:0% +is so let's call it + + + align:start position:0% +is so let's call it +Alpha okay so alpha n in one + + align:start position:0% + + + + align:start position:0% + +side and then the work on the other side + + align:start position:0% +side and then the work on the other side + + + align:start position:0% +side and then the work on the other side +will be P sub M of one of 1us alpha + + align:start position:0% +will be P sub M of one of 1us alpha + + + align:start position:0% +will be P sub M of one of 1us alpha +n plus and then still order log n for + + align:start position:0% +n plus and then still order log n for + + + align:start position:0% +n plus and then still order log n for +the binary + + align:start position:0% +the binary + + + align:start position:0% +the binary +search okay where + + align:start position:0% + + + + align:start position:0% + +as we've + + align:start position:0% +as we've + + + align:start position:0% +as we've +said Alpha is going to fall between 1 qu + + align:start position:0% +said Alpha is going to fall between 1 qu + + + align:start position:0% +said Alpha is going to fall between 1 qu +and + + align:start position:0% + + + + align:start position:0% + +3/4 okay how do we solve a recurrence + + align:start position:0% +3/4 okay how do we solve a recurrence + + + align:start position:0% +3/4 okay how do we solve a recurrence +like + + align:start position:0% + + + + align:start position:0% + +this what's the technical name for this + + align:start position:0% +this what's the technical name for this + + + align:start position:0% +this what's the technical name for this +kind of recurrence + + align:start position:0% + + + + align:start position:0% + +hariry it's a hairy recurrence how do we + + align:start position:0% +hariry it's a hairy recurrence how do we + + + align:start position:0% +hariry it's a hairy recurrence how do we +solve hary + + align:start position:0% +solve hary + + + align:start position:0% +solve hary +recurrences + + align:start position:0% +recurrences + + + align:start position:0% +recurrences +substitution okay good + + align:start position:0% + + + + align:start position:0% + +substitution okay so we're going to say + + align:start position:0% +substitution okay so we're going to say + + + align:start position:0% +substitution okay so we're going to say +pm1 of + + align:start position:0% +pm1 of + + + align:start position:0% +pm1 of +K is less than or equal to + + align:start position:0% + + + + align:start position:0% + +okay I'm going to make a good guess here + + align:start position:0% +okay I'm going to make a good guess here + + + align:start position:0% +okay I'm going to make a good guess here +okay because I fooled around with it I + + align:start position:0% +okay because I fooled around with it I + + + align:start position:0% +okay because I fooled around with it I +want it to be linear so it's going to + + align:start position:0% +want it to be linear so it's going to + + + align:start position:0% +want it to be linear so it's going to +have a linear term a * K minus and then + + align:start position:0% +have a linear term a * K minus and then + + + align:start position:0% +have a linear term a * K minus and then +I'm going to do B log K so this is this + + align:start position:0% +I'm going to do B log K so this is this + + + align:start position:0% +I'm going to do B log K so this is this +trick of subtracting a low order term + + align:start position:0% +trick of subtracting a low order term + + + align:start position:0% +trick of subtracting a low order term +remember that in substitution in order + + align:start position:0% +remember that in substitution in order + + + align:start position:0% +remember that in substitution in order +to make it stronger if I just did AK + + align:start position:0% +to make it stronger if I just did AK + + + align:start position:0% +to make it stronger if I just did AK +it's not going to work because here I + + align:start position:0% +it's not going to work because here I + + + align:start position:0% +it's not going to work because here I +would get n and then when I do the + + align:start position:0% +would get n and then when I do the + + + align:start position:0% +would get n and then when I do the +substitution I'm going to get Alpha uh I + + align:start position:0% +substitution I'm going to get Alpha uh I + + + align:start position:0% +substitution I'm going to get Alpha uh I +get a alpha n and then a a 1- alpha n + + align:start position:0% +get a alpha n and then a a 1- alpha n + + + align:start position:0% +get a alpha n and then a a 1- alpha n +and those two together are already going + + align:start position:0% +and those two together are already going + + + align:start position:0% +and those two together are already going +to add up to everything here so there's + + align:start position:0% +to add up to everything here so there's + + + align:start position:0% +to add up to everything here so there's +no way I'm going to get it bounded when + + align:start position:0% +no way I'm going to get it bounded when + + + align:start position:0% +no way I'm going to get it bounded when +I add this term in so I need to subtract + + align:start position:0% +I add this term in so I need to subtract + + + align:start position:0% +I add this term in so I need to subtract +something from both of these so as to + + align:start position:0% +something from both of these so as to + + + align:start position:0% +something from both of these so as to +absorb this + + align:start position:0% +absorb this + + + align:start position:0% +absorb this +term okay so I'm skipping over those + + align:start position:0% +term okay so I'm skipping over those + + + align:start position:0% +term okay so I'm skipping over those +steps okay because we did those steps in + + align:start position:0% +steps okay because we did those steps in + + + align:start position:0% +steps okay because we did those steps in +week in lecture two or something right + + align:start position:0% +week in lecture two or something right + + + align:start position:0% +week in lecture two or something right +okay so that's the thing I'm going to + + align:start position:0% +okay so that's the thing I'm going to + + + align:start position:0% +okay so that's the thing I'm going to +guess where + + align:start position:0% + + + + align:start position:0% + +uh A and B are greater than + + align:start position:0% +uh A and B are greater than + + + align:start position:0% +uh A and B are greater than +zero okay so let's do the + + align:start position:0% + + + + align:start position:0% + +substitution okay so if P M1 of n is + + align:start position:0% +substitution okay so if P M1 of n is + + + align:start position:0% +substitution okay so if P M1 of n is +less than equal + + align:start position:0% +less than equal + + + align:start position:0% +less than equal +to okay + + align:start position:0% +to okay + + + align:start position:0% +to okay +substitute this inductive hypo + + align:start position:0% +substitute this inductive hypo + + + align:start position:0% +substitute this inductive hypo +hypothesis in for these two guys so we + + align:start position:0% +hypothesis in for these two guys so we + + + align:start position:0% +hypothesis in for these two guys so we +get a alpha n minus + + align:start position:0% +get a alpha n minus + + + align:start position:0% +get a alpha n minus +B log of alpha + + align:start position:0% +B log of alpha + + + align:start position:0% +B log of alpha +n + + align:start position:0% +n + + + align:start position:0% +n +plus a of 1 - alpha + + align:start position:0% +plus a of 1 - alpha + + + align:start position:0% +plus a of 1 - alpha +n + + align:start position:0% +n + + + align:start position:0% +n +minus + + align:start position:0% +minus + + + align:start position:0% +minus +B log of 1 - + + align:start position:0% +B log of 1 - + + + align:start position:0% +B log of 1 - +Alpha need another parenthesis there 1us + + align:start position:0% +Alpha need another parenthesis there 1us + + + align:start position:0% +Alpha need another parenthesis there 1us +alpha + + align:start position:0% +alpha + + + align:start position:0% +alpha +n didn't even leave myself enough space + + align:start position:0% +n didn't even leave myself enough space + + + align:start position:0% +n didn't even leave myself enough space +here plus let me just move this over so + + align:start position:0% +here plus let me just move this over so + + + align:start position:0% +here plus let me just move this over so +I don't end up using too much space so + + align:start position:0% +I don't end up using too much space so + + + align:start position:0% +I don't end up using too much space so +B log of 1 - alpha n plus Theta of log + + align:start position:0% + + + + align:start position:0% + +n how's + + align:start position:0% + + + + align:start position:0% + +that we okay on + + align:start position:0% + + + + align:start position:0% + +that okay so that's just substitution + + align:start position:0% +that okay so that's just substitution + + + align:start position:0% +that okay so that's just substitution +let's do a little + + align:start position:0% +let's do a little + + + align:start position:0% +let's do a little +algebra that's equal to a * alpha n a * + + align:start position:0% +algebra that's equal to a * alpha n a * + + + align:start position:0% +algebra that's equal to a * alpha n a * +1 minus alpha n that's just a + + align:start position:0% +1 minus alpha n that's just a + + + align:start position:0% +1 minus alpha n that's just a +n okay minus well the B isn't quite so + + align:start position:0% +n okay minus well the B isn't quite so + + + align:start position:0% +n okay minus well the B isn't quite so +simple okay so I have a b term now I got + + align:start position:0% +simple okay so I have a b term now I got + + + align:start position:0% +simple okay so I have a b term now I got +a whole bunch of stuff there I get log + + align:start position:0% +a whole bunch of stuff there I get log + + + align:start position:0% +a whole bunch of stuff there I get log +of alpha + + align:start position:0% +of alpha + + + align:start position:0% +of alpha +n I have then this + + align:start position:0% +n I have then this + + + align:start position:0% +n I have then this +log of 1us alpha n + + align:start position:0% + + + + align:start position:0% + +okay Al + + align:start position:0% +okay Al + + + align:start position:0% +okay Al +n and + + align:start position:0% +n and + + + align:start position:0% +n and +then plus Theta log + + align:start position:0% + + + + align:start position:0% + +n they do that + + align:start position:0% +n they do that + + + align:start position:0% +n they do that +right does that look + + align:start position:0% + + + + align:start position:0% + +okay okay + + align:start position:0% + + + + align:start position:0% + +so look at that + + align:start position:0% +so look at that + + + align:start position:0% +so look at that +okay so now let's just multiply some of + + align:start position:0% +okay so now let's just multiply some of + + + align:start position:0% +okay so now let's just multiply some of +this stuff out so I have a n minus B + + align:start position:0% +this stuff out so I have a n minus B + + + align:start position:0% +this stuff out so I have a n minus B +Time Well Log of alpha n is just log + + align:start position:0% +Time Well Log of alpha n is just log + + + align:start position:0% +Time Well Log of alpha n is just log +Alpha plus log + + align:start position:0% +Alpha plus log + + + align:start position:0% +Alpha plus log +n and then I have plus log of 1us alpha + + align:start position:0% +n and then I have plus log of 1us alpha + + + align:start position:0% +n and then I have plus log of 1us alpha +plus log + + align:start position:0% + + + + align:start position:0% + +n okay plus Theta log + + align:start position:0% +n okay plus Theta log + + + align:start position:0% +n okay plus Theta log +n that's just more + + align:start position:0% +n that's just more + + + align:start position:0% +n that's just more +algebra okay using our rules for logs + + align:start position:0% +algebra okay using our rules for logs + + + align:start position:0% +algebra okay using our rules for logs +now let me Express this as a my solution + + align:start position:0% +now let me Express this as a my solution + + + align:start position:0% +now let me Express this as a my solution +minus my desired solution minus a + + align:start position:0% +minus my desired solution minus a + + + align:start position:0% +minus my desired solution minus a +residual a n minus B log + + align:start position:0% +residual a n minus B log + + + align:start position:0% +residual a n minus B log +n okay + + align:start position:0% +n okay + + + align:start position:0% +n okay +minus okay and now so that was one of + + align:start position:0% +minus okay and now so that was one of + + + align:start position:0% +minus okay and now so that was one of +these B log NS right is here the other + + align:start position:0% +these B log NS right is here the other + + + align:start position:0% +these B log NS right is here the other +one's going to end up in here have + + align:start position:0% +one's going to end up in here have + + + align:start position:0% +one's going to end up in here have +B uh + + align:start position:0% + + + + align:start position:0% + +time log + + align:start position:0% +time log + + + align:start position:0% +time log +n+ log of alpha Time 1 minus + + align:start position:0% + + + + align:start position:0% + +Alpha minus whoops I got too many do I + + align:start position:0% +Alpha minus whoops I got too many do I + + + align:start position:0% +Alpha minus whoops I got too many do I +have the write number of closes log of + + align:start position:0% +have the write number of closes log of + + + align:start position:0% +have the write number of closes log of +alpha 1us alpha close that close that + + align:start position:0% +alpha 1us alpha close that close that + + + align:start position:0% +alpha 1us alpha close that close that +that's good + + align:start position:0% +that's good + + + align:start position:0% +that's good +minus uh Theta log in + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +two one's there boy my writing is + + align:start position:0% + + + + align:start position:0% + +degrading okay did I do that right do I + + align:start position:0% +degrading okay did I do that right do I + + + align:start position:0% +degrading okay did I do that right do I +have the parenthesis + + align:start position:0% +have the parenthesis + + + align:start position:0% +have the parenthesis +right that matches that matches that + + align:start position:0% +right that matches that matches that + + + align:start position:0% +right that matches that matches that +matches good and then B goes to that + + align:start position:0% +matches good and then B goes to that + + + align:start position:0% +matches good and then B goes to that +okay + + align:start position:0% +okay + + + align:start position:0% +okay +good okay and I claim that is less than + + align:start position:0% +good okay and I claim that is less than + + + align:start position:0% +good okay and I claim that is less than +or equal to a n minus B log + + align:start position:0% +or equal to a n minus B log + + + align:start position:0% +or equal to a n minus B log +n + + align:start position:0% +n + + + align:start position:0% +n +if we choose + + align:start position:0% +if we choose + + + align:start position:0% +if we choose +B large + + align:start position:0% + + + + align:start position:0% + +enough okay + + align:start position:0% +enough okay + + + align:start position:0% +enough okay +that uh this mess dominates + + align:start position:0% +that uh this mess dominates + + + align:start position:0% +that uh this mess dominates +this because this is basically a log n + + align:start position:0% +this because this is basically a log n + + + align:start position:0% +this because this is basically a log n +here and this is essentially a + + align:start position:0% +here and this is essentially a + + + align:start position:0% +here and this is essentially a +constant okay and so if I increase + + align:start position:0% +constant okay and so if I increase + + + align:start position:0% +constant okay and so if I increase +B okay Times log N I can overcome that + + align:start position:0% +B okay Times log N I can overcome that + + + align:start position:0% +B okay Times log N I can overcome that +uh log n whatever the constant is hidden + + align:start position:0% +uh log n whatever the constant is hidden + + + align:start position:0% +uh log n whatever the constant is hidden +by the uh uh by the uh ASM totic + + align:start position:0% +by the uh uh by the uh ASM totic + + + align:start position:0% +by the uh uh by the uh ASM totic +notation okay so if I such that + + align:start position:0% +notation okay so if I such that + + + align:start position:0% +notation okay so if I such that +b Times log + + align:start position:0% +b Times log + + + align:start position:0% +b Times log +n b log and plus log of alpha * 1 - + + align:start position:0% +n b log and plus log of alpha * 1 - + + + align:start position:0% +n b log and plus log of alpha * 1 - +Alpha dominant + + align:start position:0% + + + + align:start position:0% + +the Theta log + + align:start position:0% + + + + align:start position:0% + +n okay and I can also choose my base + + align:start position:0% +n okay and I can also choose my base + + + align:start position:0% +n okay and I can also choose my base +condition to be big enough to handle the + + align:start position:0% +condition to be big enough to handle the + + + align:start position:0% +condition to be big enough to handle the +initial conditions whatever they might + + align:start position:0% +initial conditions whatever they might + + + align:start position:0% +initial conditions whatever they might +be okay so + + align:start position:0% + + + + align:start position:0% + +so we'll choose a big + + align:start position:0% + + + + align:start position:0% + +enough to satisfy the base of the + + align:start position:0% + + + + align:start position:0% + +induction okay + + align:start position:0% + + + + align:start position:0% + +so the + + align:start position:0% +so the + + + align:start position:0% +so the +pm1 of n is equal to Theta + + align:start position:0% +pm1 of n is equal to Theta + + + align:start position:0% +pm1 of n is equal to Theta +n + + align:start position:0% +n + + + align:start position:0% +n +okay um so I actually showed + + align:start position:0% +okay um so I actually showed + + + align:start position:0% +okay um so I actually showed +o and it turns out the lower bound that + + align:start position:0% +o and it turns out the lower bound that + + + align:start position:0% +o and it turns out the lower bound that +it is Omega n is more straightforward + + align:start position:0% +it is Omega n is more straightforward + + + align:start position:0% +it is Omega n is more straightforward +because the recurrence is easier because + + align:start position:0% +because the recurrence is easier because + + + align:start position:0% +because the recurrence is easier because +I can do the same substitution I just + + align:start position:0% +I can do the same substitution I just + + + align:start position:0% +I can do the same substitution I just +don't have + + align:start position:0% +don't have + + + align:start position:0% +don't have +to um subtract off low order terms okay + + align:start position:0% +to um subtract off low order terms okay + + + align:start position:0% +to um subtract off low order terms okay +so it's actually Theta not just + + align:start position:0% +so it's actually Theta not just + + + align:start position:0% +so it's actually Theta not just +o + + align:start position:0% +o + + + align:start position:0% +o +okay okay so that gives us a log what + + align:start position:0% +okay okay so that gives us a log what + + + align:start position:0% +okay okay so that gives us a log what +did we say the critical path was + + align:start position:0% +did we say the critical path was + + + align:start position:0% +did we say the critical path was +critical path is log squared n for the + + align:start position:0% +critical path is log squared n for the + + + align:start position:0% +critical path is log squared n for the +parallel merge so let's do um the + + align:start position:0% +parallel merge so let's do um the + + + align:start position:0% +parallel merge so let's do um the +analysis of merge sort using + + align:start position:0% + + + + align:start position:0% + +this so the + + align:start position:0% +this so the + + + align:start position:0% +this so the +work is we know already is T1 of + + align:start position:0% +work is we know already is T1 of + + + align:start position:0% +work is we know already is T1 of +n is Theta of n log n + + align:start position:0% +n is Theta of n log n + + + align:start position:0% +n is Theta of n log n +because our work that we just analyzed + + align:start position:0% +because our work that we just analyzed + + + align:start position:0% +because our work that we just analyzed +was order n same as for the serial + + align:start position:0% +was order n same as for the serial + + + align:start position:0% +was order n same as for the serial +algorithm okay the critical path length + + align:start position:0% +algorithm okay the critical path length + + + align:start position:0% +algorithm okay the critical path length +now is T Infinity of + + align:start position:0% +now is T Infinity of + + + align:start position:0% +now is T Infinity of +n is equal + + align:start position:0% +n is equal + + + align:start position:0% +n is equal +to okay so in normal merge sort we have + + align:start position:0% +to okay so in normal merge sort we have + + + align:start position:0% +to okay so in normal merge sort we have +a problem of half the size T of n + + align:start position:0% +a problem of half the size T of n + + + align:start position:0% +a problem of half the size T of n +/2 plus now my critical path + + align:start position:0% +/2 plus now my critical path + + + align:start position:0% +/2 plus now my critical path +of for merging is not order n as it was + + align:start position:0% +of for merging is not order n as it was + + + align:start position:0% +of for merging is not order n as it was +before instead + + align:start position:0% + + + + align:start position:0% + +it's just over + + align:start position:0% + + + + align:start position:0% + +there log squ n there we + + align:start position:0% +there log squ n there we + + + align:start position:0% +there log squ n there we +go log s + + align:start position:0% +go log s + + + align:start position:0% +go log s +n okay and so that gives + + align:start position:0% + + + + align:start position:0% + +us Theta + + align:start position:0% +us Theta + + + align:start position:0% +us Theta +of log cubed n + + align:start position:0% + + + + align:start position:0% + +okay so our + + align:start position:0% +okay so our + + + align:start position:0% +okay so our +parallelism is then Theta of n + + align:start position:0% +parallelism is then Theta of n + + + align:start position:0% +parallelism is then Theta of n +over log cubed + + align:start position:0% + + + + align:start position:0% + +n and in fact the best that's been + + align:start position:0% + + + + align:start position:0% + +done is oh n over sorry log squ n you're + + align:start position:0% +done is oh n over sorry log squ n you're + + + align:start position:0% +done is oh n over sorry log squ n you're +right + + align:start position:0% +right + + + align:start position:0% +right +how come I have log squ n because it's n + + align:start position:0% +how come I have log squ n because it's n + + + align:start position:0% +how come I have log squ n because it's n +log n + + align:start position:0% +log n + + + align:start position:0% +log n +over log cubed n it's n over log squ n + + align:start position:0% +over log cubed n it's n over log squ n + + + align:start position:0% +over log cubed n it's n over log squ n +okay and the best so now I wonder if I + + align:start position:0% +okay and the best so now I wonder if I + + + align:start position:0% +okay and the best so now I wonder if I +have I have a typo here I have that the + + align:start position:0% +have I have a typo here I have that the + + + align:start position:0% +have I have a typo here I have that the +best + + align:start position:0% +best + + + align:start position:0% +best +is p bar is Theta of n over log n is + + align:start position:0% +is p bar is Theta of n over log n is + + + align:start position:0% +is p bar is Theta of n over log n is +that right I think so + + align:start position:0% + + + + align:start position:0% + +yeah that's the best to + + align:start position:0% + + + + align:start position:0% + +date that's the best to + + align:start position:0% + + + + align:start position:0% + +date by AAL I believe is who did + + align:start position:0% +date by AAL I believe is who did + + + align:start position:0% +date by AAL I believe is who did +this for this + + align:start position:0% + + + + align:start position:0% + +uh okay so so you can actually get a + + align:start position:0% +uh okay so so you can actually get a + + + align:start position:0% +uh okay so so you can actually get a +fairly good but it turns out sorting is + + align:start position:0% +fairly good but it turns out sorting is + + + align:start position:0% +fairly good but it turns out sorting is +a really tough problem to parallelize to + + align:start position:0% +a really tough problem to parallelize to + + + align:start position:0% +a really tough problem to parallelize to +get really good constants where you want + + align:start position:0% +get really good constants where you want + + + align:start position:0% +get really good constants where you want +to make it so that it's running exactly + + align:start position:0% +to make it so that it's running exactly + + + align:start position:0% +to make it so that it's running exactly +the same major small application you can + + align:start position:0% +the same major small application you can + + + align:start position:0% +the same major small application you can +make it run in parallel and get straight + + align:start position:0% +make it run in parallel and get straight + + + align:start position:0% +make it run in parallel and get straight +hard rail linear speed up with a number + + align:start position:0% +hard rail linear speed up with a number + + + align:start position:0% +hard rail linear speed up with a number +of processors there's plenty of + + align:start position:0% +of processors there's plenty of + + + align:start position:0% +of processors there's plenty of +parallelism and running on more + + align:start position:0% +parallelism and running on more + + + align:start position:0% +parallelism and running on more +processors every processor carries a + + align:start position:0% +processors every processor carries a + + + align:start position:0% +processors every processor carries a +full rate with sorting typically you + + align:start position:0% +full rate with sorting typically you + + + align:start position:0% +full rate with sorting typically you +lose you know I don't know 20% in my + + align:start position:0% +lose you know I don't know 20% in my + + + align:start position:0% +lose you know I don't know 20% in my +experience okay of in terms of other + + align:start position:0% +experience okay of in terms of other + + + align:start position:0% +experience okay of in terms of other +stuff going on because you know you have + + align:start position:0% +stuff going on because you know you have + + + align:start position:0% +stuff going on because you know you have +to work really hard to get the uh + + align:start position:0% +to work really hard to get the uh + + + align:start position:0% +to work really hard to get the uh +constants of this merge algorithm down + + align:start position:0% +constants of this merge algorithm down + + + align:start position:0% +constants of this merge algorithm down +to the constants of that normal merge + + align:start position:0% +to the constants of that normal merge + + + align:start position:0% +to the constants of that normal merge +right I mean that's a pretty good + + align:start position:0% +right I mean that's a pretty good + + + align:start position:0% +right I mean that's a pretty good +algorithm right the one that just goes + + align:start position:0% +algorithm right the one that just goes + + + align:start position:0% +algorithm right the one that just goes +and just takes two lists and and uh and + + align:start position:0% +and just takes two lists and and uh and + + + align:start position:0% +and just takes two lists and and uh and +merges them like that so um so so it's + + align:start position:0% +merges them like that so um so so it's + + + align:start position:0% +merges them like that so um so so it's +an interesting uh issue to to you know + + align:start position:0% +an interesting uh issue to to you know + + + align:start position:0% +an interesting uh issue to to you know +and a lot of people work very hard on + + align:start position:0% +and a lot of people work very hard on + + + align:start position:0% +and a lot of people work very hard on +sorting because it's a hugely important + + align:start position:0% +sorting because it's a hugely important + + + align:start position:0% +sorting because it's a hugely important +problem and how it is that you can + + align:start position:0% +problem and how it is that you can + + + align:start position:0% +problem and how it is that you can +actually get the constants down while + + align:start position:0% +actually get the constants down while + + + align:start position:0% +actually get the constants down while +still guaranteeing that it's uh will + + align:start position:0% +still guaranteeing that it's uh will + + + align:start position:0% +still guaranteeing that it's uh will +will scale up with number of + + align:start position:0% +will scale up with number of + + + align:start position:0% +will scale up with number of +processors okay okay that's our our + + align:start position:0% +processors okay okay that's our our + + + align:start position:0% +processors okay okay that's our our +little uh sojourn into uh parallel land + + align:start position:0% +little uh sojourn into uh parallel land + + + align:start position:0% +little uh sojourn into uh parallel land +and uh next week we're going to uh talk + + align:start position:0% +and uh next week we're going to uh talk + + + align:start position:0% +and uh next week we're going to uh talk +about caching which is another very + + align:start position:0% +about caching which is another very + + + align:start position:0% +about caching which is another very +important area + + align:start position:0% +important area + + + align:start position:0% +important area +uh of um of algorithms and of + + align:start position:0% +uh of um of algorithms and of + + + align:start position:0% +uh of um of algorithms and of +programming and general \ No newline at end of file diff --git a/FK1n3TVQIhc.txt b/FK1n3TVQIhc.txt new file mode 100644 index 0000000000000000000000000000000000000000..f01e462ef9152d86df684e534d6fbb99da59bdd0 --- /dev/null +++ b/FK1n3TVQIhc.txt @@ -0,0 +1,2115 @@ +align:start position:0% + +hi welcome back to recitation we've been + + align:start position:0% +hi welcome back to recitation we've been + + + align:start position:0% +hi welcome back to recitation we've been +talking about tailor series for a number + + align:start position:0% +talking about tailor series for a number + + + align:start position:0% +talking about tailor series for a number +of functions and rules by which you can + + align:start position:0% +of functions and rules by which you can + + + align:start position:0% +of functions and rules by which you can +compute tailor series I have here an + + align:start position:0% +compute tailor series I have here an + + + align:start position:0% +compute tailor series I have here an +example that I don't think we did in + + align:start position:0% +example that I don't think we did in + + + align:start position:0% +example that I don't think we did in +lecture so this is the uh function f ofx + + align:start position:0% +lecture so this is the uh function f ofx + + + align:start position:0% +lecture so this is the uh function f ofx +equals secant of X now unlike some of + + align:start position:0% +equals secant of X now unlike some of + + + align:start position:0% +equals secant of X now unlike some of +the other ones you've seen there's not a + + align:start position:0% +the other ones you've seen there's not a + + + align:start position:0% +the other ones you've seen there's not a +really simple formula for the for the + + align:start position:0% +really simple formula for the for the + + + align:start position:0% +really simple formula for the for the +whole tailor series of cant X so what + + align:start position:0% +whole tailor series of cant X so what + + + align:start position:0% +whole tailor series of cant X so what +I'd like you to do is not to find the + + align:start position:0% +I'd like you to do is not to find the + + + align:start position:0% +I'd like you to do is not to find the +the you know a formula for the general + + align:start position:0% +the you know a formula for the general + + + align:start position:0% +the you know a formula for the general +term but rather just to to to use some + + align:start position:0% +term but rather just to to to use some + + + align:start position:0% +term but rather just to to to use some +of the the tools that we've learned to + + align:start position:0% +of the the tools that we've learned to + + + align:start position:0% +of the the tools that we've learned to +compute the first few terms of the + + align:start position:0% +compute the first few terms of the + + + align:start position:0% +compute the first few terms of the +Taylor series for f ofx equals cant XA + + align:start position:0% +Taylor series for f ofx equals cant XA + + + align:start position:0% +Taylor series for f ofx equals cant XA +up through the X to the fourth term if + + align:start position:0% +up through the X to the fourth term if + + + align:start position:0% +up through the X to the fourth term if +you wanted or even a little further if + + align:start position:0% +you wanted or even a little further if + + + align:start position:0% +you wanted or even a little further if +you were feeling ambitious so why don't + + align:start position:0% +you were feeling ambitious so why don't + + + align:start position:0% +you were feeling ambitious so why don't +you pause the video have a go at that + + align:start position:0% +you pause the video have a go at that + + + align:start position:0% +you pause the video have a go at that +come back and we can do it + + align:start position:0% + + + + align:start position:0% + +together so welcome back I asked you to + + align:start position:0% +together so welcome back I asked you to + + + align:start position:0% +together so welcome back I asked you to +compute the first few terms of a tailor + + align:start position:0% +compute the first few terms of a tailor + + + align:start position:0% +compute the first few terms of a tailor +series um one thing you can always do in + + align:start position:0% +series um one thing you can always do in + + + align:start position:0% +series um one thing you can always do in +this case is you can go and you can + + align:start position:0% +this case is you can go and you can + + + align:start position:0% +this case is you can go and you can +apply the general formula that we have + + align:start position:0% +apply the general formula that we have + + + align:start position:0% +apply the general formula that we have +for tailor series and and use it to to + + align:start position:0% +for tailor series and and use it to to + + + align:start position:0% +for tailor series and and use it to to +compute the series that way so in order + + align:start position:0% +compute the series that way so in order + + + align:start position:0% +compute the series that way so in order +to do that you just need to compute a + + align:start position:0% +to do that you just need to compute a + + + align:start position:0% +to do that you just need to compute a +few derivatives of your function um so + + align:start position:0% +few derivatives of your function um so + + + align:start position:0% +few derivatives of your function um so +remember that the general formula for a + + align:start position:0% +remember that the general formula for a + + + align:start position:0% +remember that the general formula for a +tailor series is the tailor series for f + + align:start position:0% +tailor series is the tailor series for f + + + align:start position:0% +tailor series is the tailor series for f +ofx is equal to the + + align:start position:0% +ofx is equal to the + + + align:start position:0% +ofx is equal to the +sum from n equal 0 to Infinity inity of + + align:start position:0% +sum from n equal 0 to Infinity inity of + + + align:start position:0% +sum from n equal 0 to Infinity inity of +the nth derivative of f taken at zero / + + align:start position:0% +the nth derivative of f taken at zero / + + + align:start position:0% +the nth derivative of f taken at zero / +n factorial * x to the n and since we're + + align:start position:0% +n factorial * x to the n and since we're + + + align:start position:0% +n factorial * x to the n and since we're +only interested in the first few terms + + align:start position:0% +only interested in the first few terms + + + align:start position:0% +only interested in the first few terms +this is f of + + align:start position:0% +this is f of + + + align:start position:0% +this is f of +0 plus FR Prime of 0 X Plus fpre of 0/ + + align:start position:0% +0 plus FR Prime of 0 X Plus fpre of 0/ + + + align:start position:0% +0 plus FR Prime of 0 X Plus fpre of 0/ +2x^2 plus dot dot dot all right I'm not + + align:start position:0% +2x^2 plus dot dot dot all right I'm not + + + align:start position:0% +2x^2 plus dot dot dot all right I'm not +going to write out the next few terms + + align:start position:0% +going to write out the next few terms + + + align:start position:0% +going to write out the next few terms +and if you wanted to apply this form to + + align:start position:0% +and if you wanted to apply this form to + + + align:start position:0% +and if you wanted to apply this form to +secant of X what you would have to do is + + align:start position:0% +secant of X what you would have to do is + + + align:start position:0% +secant of X what you would have to do is +you would have to compute these + + align:start position:0% +you would have to compute these + + + align:start position:0% +you would have to compute these +derivatives and so we can we could try + + align:start position:0% +derivatives and so we can we could try + + + align:start position:0% +derivatives and so we can we could try +doing that so so in our case f ofx is + + align:start position:0% +doing that so so in our case f ofx is + + + align:start position:0% +doing that so so in our case f ofx is +equal to secant of X so F of 0 is secant + + align:start position:0% +equal to secant of X so F of 0 is secant + + + align:start position:0% +equal to secant of X so F of 0 is secant +of 0 which is just one so then we need + + align:start position:0% +of 0 which is just one so then we need + + + align:start position:0% +of 0 which is just one so then we need +to know F Prime of X so that's the + + align:start position:0% +to know F Prime of X so that's the + + + align:start position:0% +to know F Prime of X so that's the +derivative of secant of X so this is one + + align:start position:0% +derivative of secant of X so this is one + + + align:start position:0% +derivative of secant of X so this is one +you should remember this is equal to + + align:start position:0% +you should remember this is equal to + + + align:start position:0% +you should remember this is equal to +secant x + + align:start position:0% +secant x + + + align:start position:0% +secant x +time Tan x and when you plug in x equal + + align:start position:0% +time Tan x and when you plug in x equal + + + align:start position:0% +time Tan x and when you plug in x equal +to Zer well the Tan x is 0 so frime of + + align:start position:0% +to Zer well the Tan x is 0 so frime of + + + align:start position:0% +to Zer well the Tan x is 0 so frime of +0 is equal to 0 and then you could keep + + align:start position:0% +0 is equal to 0 and then you could keep + + + align:start position:0% +0 is equal to 0 and then you could keep +going so you could compute F Prime of X + + align:start position:0% +going so you could compute F Prime of X + + + align:start position:0% +going so you could compute F Prime of X +so we would have to compute the + + align:start position:0% +so we would have to compute the + + + align:start position:0% +so we would have to compute the +derivative of secant x Tan x and you + + align:start position:0% +derivative of secant x Tan x and you + + + align:start position:0% +derivative of secant x Tan x and you +would do that by the product rule you + + align:start position:0% +would do that by the product rule you + + + align:start position:0% +would do that by the product rule you +know you take the derivative of secant + + align:start position:0% +know you take the derivative of secant + + + align:start position:0% +know you take the derivative of secant +of X and that gives you secant x Tan + + align:start position:0% +of X and that gives you secant x Tan + + + align:start position:0% +of X and that gives you secant x Tan +x * tan X Plus and then you okay so you + + align:start position:0% +x * tan X Plus and then you okay so you + + + align:start position:0% +x * tan X Plus and then you okay so you +leave secant of + + align:start position:0% +leave secant of + + + align:start position:0% +leave secant of +X and you multiply it by the derivative + + align:start position:0% +X and you multiply it by the derivative + + + align:start position:0% +X and you multiply it by the derivative +of tangent which is secant squ x and now + + align:start position:0% +of tangent which is secant squ x and now + + + align:start position:0% +of tangent which is secant squ x and now +when you put in zero here you get F + + align:start position:0% +when you put in zero here you get F + + + align:start position:0% +when you put in zero here you get F +Prime of zero well okay so this has a + + align:start position:0% +Prime of zero well okay so this has a + + + align:start position:0% +Prime of zero well okay so this has a +tan X in it so that part's going to give + + align:start position:0% +tan X in it so that part's going to give + + + align:start position:0% +tan X in it so that part's going to give +you zero and here we end up with secant + + align:start position:0% +you zero and here we end up with secant + + + align:start position:0% +you zero and here we end up with secant +of 0 time secant squar of 0 so that's 1 + + align:start position:0% +of 0 time secant squar of 0 so that's 1 + + + align:start position:0% +of 0 time secant squar of 0 so that's 1 +* 1 * 1 so that's just one so fpre of 0 + + align:start position:0% +* 1 * 1 so that's just one so fpre of 0 + + + align:start position:0% +* 1 * 1 so that's just one so fpre of 0 +is one and you could keep doing this now + + align:start position:0% +is one and you could keep doing this now + + + align:start position:0% +is one and you could keep doing this now +one thing you'll notice is that this is + + align:start position:0% +one thing you'll notice is that this is + + + align:start position:0% +one thing you'll notice is that this is +getting more and more complicated I mean + + align:start position:0% +getting more and more complicated I mean + + + align:start position:0% +getting more and more complicated I mean +we could we can simplify this expression + + align:start position:0% +we could we can simplify this expression + + + align:start position:0% +we could we can simplify this expression +a little bit we could write it as secant + + align:start position:0% +a little bit we could write it as secant + + + align:start position:0% +a little bit we could write it as secant +x tan squ X Plus secant cubed x and + + align:start position:0% +x tan squ X Plus secant cubed x and + + + align:start position:0% +x tan squ X Plus secant cubed x and +there are you know all sorts of trig + + align:start position:0% +there are you know all sorts of trig + + + align:start position:0% +there are you know all sorts of trig +manipulations you could do if you wanted + + align:start position:0% +manipulations you could do if you wanted + + + align:start position:0% +manipulations you could do if you wanted +to try and rewrite that in some simpler + + align:start position:0% +to try and rewrite that in some simpler + + + align:start position:0% +to try and rewrite that in some simpler +form um but uh but fundamentally it's + + align:start position:0% +form um but uh but fundamentally it's + + + align:start position:0% +form um but uh but fundamentally it's +it's more complicated than the than the + + align:start position:0% +it's more complicated than the than the + + + align:start position:0% +it's more complicated than the than the +first derivative was and it's and that's + + align:start position:0% +first derivative was and it's and that's + + + align:start position:0% +first derivative was and it's and that's +more complicated than the function and + + align:start position:0% +more complicated than the function and + + + align:start position:0% +more complicated than the function and +it'll keep getting more complicated as + + align:start position:0% +it'll keep getting more complicated as + + + align:start position:0% +it'll keep getting more complicated as +you compute more derivatives um so we + + align:start position:0% +you compute more derivatives um so we + + + align:start position:0% +you compute more derivatives um so we +can do this um so so far this shows us + + align:start position:0% +can do this um so so far this shows us + + + align:start position:0% +can do this um so so far this shows us +by the way that this is equal to 1 + 0x + + align:start position:0% +by the way that this is equal to 1 + 0x + + + align:start position:0% +by the way that this is equal to 1 + 0x ++ x^2 / 2 dot dot dot and if you wanted + + align:start position:0% ++ x^2 / 2 dot dot dot and if you wanted + + + align:start position:0% ++ x^2 / 2 dot dot dot and if you wanted +to compute you know up through the + + align:start position:0% +to compute you know up through the + + + align:start position:0% +to compute you know up through the +fourth degree term or something like + + align:start position:0% +fourth degree term or something like + + + align:start position:0% +fourth degree term or something like +this that's that's something that's + + align:start position:0% +this that's that's something that's + + + align:start position:0% +this that's that's something that's +manageable um but I want to suggest that + + align:start position:0% +manageable um but I want to suggest that + + + align:start position:0% +manageable um but I want to suggest that +there are maybe some nicer ways to do it + + align:start position:0% +there are maybe some nicer ways to do it + + + align:start position:0% +there are maybe some nicer ways to do it +um so one thing to + + align:start position:0% +um so one thing to + + + align:start position:0% +um so one thing to +notice is that secant of X is closely + + align:start position:0% +notice is that secant of X is closely + + + align:start position:0% +notice is that secant of X is closely +related to the function cosine of x and + + align:start position:0% +related to the function cosine of x and + + + align:start position:0% +related to the function cosine of x and +you know the tailor series for cosine of + + align:start position:0% +you know the tailor series for cosine of + + + align:start position:0% +you know the tailor series for cosine of +x so one thing you could think to do is + + align:start position:0% +x so one thing you could think to do is + + + align:start position:0% +x so one thing you could think to do is +to leverage the information that you + + align:start position:0% +to leverage the information that you + + + align:start position:0% +to leverage the information that you +have about cosine of x in order to use + + align:start position:0% +have about cosine of x in order to use + + + align:start position:0% +have about cosine of x in order to use +it to get some information about secant + + align:start position:0% +it to get some information about secant + + + align:start position:0% +it to get some information about secant +of X so one one simple way to do that is + + align:start position:0% +of X so one one simple way to do that is + + + align:start position:0% +of X so one one simple way to do that is +that you + + align:start position:0% + + + + align:start position:0% + +know + + align:start position:0% +know + + + align:start position:0% +know +that cosine of + + align:start position:0% +that cosine of + + + align:start position:0% +that cosine of +x is even it's an even function cosine + + align:start position:0% +x is even it's an even function cosine + + + align:start position:0% +x is even it's an even function cosine +of minus X is equal to cosine of x so + + align:start position:0% +of minus X is equal to cosine of x so + + + align:start position:0% +of minus X is equal to cosine of x so +that means secant of X is also + + align:start position:0% + + + + align:start position:0% + +even secant of X is an even function and + + align:start position:0% +even secant of X is an even function and + + + align:start position:0% +even secant of X is an even function and +you've seen that even functions they're + + align:start position:0% +you've seen that even functions they're + + + align:start position:0% +you've seen that even functions they're +series all the odd Powers have have + + align:start position:0% +series all the odd Powers have have + + + align:start position:0% +series all the odd Powers have have +coefficient zero so what that means is + + align:start position:0% +coefficient zero so what that means is + + + align:start position:0% +coefficient zero so what that means is +without ever Computing the third + + align:start position:0% +without ever Computing the third + + + align:start position:0% +without ever Computing the third +derivative we can know already that the + + align:start position:0% +derivative we can know already that the + + + align:start position:0% +derivative we can know already that the +next term in this tailor series is going + + align:start position:0% +next term in this tailor series is going + + + align:start position:0% +next term in this tailor series is going +to be 0x cubed over + + align:start position:0% +to be 0x cubed over + + + align:start position:0% +to be 0x cubed over +6 okay so so that's nice + + align:start position:0% +6 okay so so that's nice + + + align:start position:0% +6 okay so so that's nice +um + + align:start position:0% +um + + + align:start position:0% +um +so so the + + align:start position:0% +so so the + + + align:start position:0% +so so the +odd + + align:start position:0% + + + + align:start position:0% + +terms of the Taylor series + + align:start position:0% +terms of the Taylor series + + + align:start position:0% +terms of the Taylor series +for secant of + + align:start position:0% +for secant of + + + align:start position:0% +for secant of +X are zero okay so that's one thing you + + align:start position:0% +X are zero okay so that's one thing you + + + align:start position:0% +X are zero okay so that's one thing you +can get right away so that gives you if + + align:start position:0% +can get right away so that gives you if + + + align:start position:0% +can get right away so that gives you if +you like that gives you half of the + + align:start position:0% +you like that gives you half of the + + + align:start position:0% +you like that gives you half of the +terms of the Taylor series it's a little + + align:start position:0% +terms of the Taylor series it's a little + + + align:start position:0% +terms of the Taylor series it's a little +bit of a joke but um okay so so then you + + align:start position:0% +bit of a joke but um okay so so then you + + + align:start position:0% +bit of a joke but um okay so so then you +only need to figure out the even terms + + align:start position:0% +only need to figure out the even terms + + + align:start position:0% +only need to figure out the even terms +that's that's one way we can leverage + + align:start position:0% +that's that's one way we can leverage + + + align:start position:0% +that's that's one way we can leverage +the relationship between secant and + + align:start position:0% +the relationship between secant and + + + align:start position:0% +the relationship between secant and +cosine the other way is that we can + + align:start position:0% +cosine the other way is that we can + + + align:start position:0% +cosine the other way is that we can +remember that tailor series multiply + + align:start position:0% +remember that tailor series multiply + + + align:start position:0% +remember that tailor series multiply +just like pols do so if if um secant is + + align:start position:0% +just like pols do so if if um secant is + + + align:start position:0% +just like pols do so if if um secant is +1/ cosine that means secant time cosine + + align:start position:0% +1/ cosine that means secant time cosine + + + align:start position:0% +1/ cosine that means secant time cosine +is equal to 1 + + align:start position:0% +is equal to 1 + + + align:start position:0% +is equal to 1 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +idea secant of X + + align:start position:0% +idea secant of X + + + align:start position:0% +idea secant of X +time cosine of x is equal to one now + + align:start position:0% +time cosine of x is equal to one now + + + align:start position:0% +time cosine of x is equal to one now +that means that the tailor series for + + align:start position:0% +that means that the tailor series for + + + align:start position:0% +that means that the tailor series for +secant of x times the tailor series for + + align:start position:0% +secant of x times the tailor series for + + + align:start position:0% +secant of x times the tailor series for +cosine of x has to simplify just to one + + align:start position:0% +cosine of x has to simplify just to one + + + align:start position:0% +cosine of x has to simplify just to one +so we can write down that product as a + + align:start position:0% +so we can write down that product as a + + + align:start position:0% +so we can write down that product as a +product of two infinite polinomial and + + align:start position:0% +product of two infinite polinomial and + + + align:start position:0% +product of two infinite polinomial and +we can start multiplying term by term + + align:start position:0% +we can start multiplying term by term + + + align:start position:0% +we can start multiplying term by term +and that'll allow us to solve for a + + align:start position:0% +and that'll allow us to solve for a + + + align:start position:0% +and that'll allow us to solve for a +bunch of terms uh just by solving some + + align:start position:0% +bunch of terms uh just by solving some + + + align:start position:0% +bunch of terms uh just by solving some +simple linear equation so let me show + + align:start position:0% +simple linear equation so let me show + + + align:start position:0% +simple linear equation so let me show +you what I mean so we know that let me + + align:start position:0% +you what I mean so we know that let me + + + align:start position:0% +you what I mean so we know that let me +write it as cosine time secant so we + + align:start position:0% +write it as cosine time secant so we + + + align:start position:0% +write it as cosine time secant so we +know that cosine of x is 1 - x^2 / 2 + x + + align:start position:0% +know that cosine of x is 1 - x^2 / 2 + x + + + align:start position:0% +know that cosine of x is 1 - x^2 / 2 + x +4 over 24 that's 4 factorial - x 6 over + + align:start position:0% +4 over 24 that's 4 factorial - x 6 over + + + align:start position:0% +4 over 24 that's 4 factorial - x 6 over +720 which is 6 factorial plus dot dot + + align:start position:0% +720 which is 6 factorial plus dot dot + + + align:start position:0% +720 which is 6 factorial plus dot dot +dot and so we know that if we multiply + + align:start position:0% +dot and so we know that if we multiply + + + align:start position:0% +dot and so we know that if we multiply +this by the the series for cant of X + + align:start position:0% +this by the the series for cant of X + + + align:start position:0% +this by the the series for cant of X +well what is the series for secant of X + + align:start position:0% +well what is the series for secant of X + + + align:start position:0% +well what is the series for secant of X +well we've already computed a few terms + + align:start position:0% +well we've already computed a few terms + + + align:start position:0% +well we've already computed a few terms +we know that it's + + align:start position:0% +we know that it's + + + align:start position:0% +we know that it's +1 plus x^2 over 2 we computed that + + align:start position:0% +1 plus x^2 over 2 we computed that + + + align:start position:0% +1 plus x^2 over 2 we computed that +already and we know that the third + + align:start position:0% +already and we know that the third + + + align:start position:0% +already and we know that the third +degree term is zero so there's some + + align:start position:0% +degree term is zero so there's some + + + align:start position:0% +degree term is zero so there's some +fourth degree coefficient A4 x 4 4 + + align:start position:0% +fourth degree coefficient A4 x 4 4 + + + align:start position:0% +fourth degree coefficient A4 x 4 4 +factorial and there's some well we know + + align:start position:0% +factorial and there's some well we know + + + align:start position:0% +factorial and there's some well we know +we said it's even so we know the fifth + + align:start position:0% +we said it's even so we know the fifth + + + align:start position:0% +we said it's even so we know the fifth +degree coefficient is zero so then the + + align:start position:0% +degree coefficient is zero so then the + + + align:start position:0% +degree coefficient is zero so then the +sixth degree coefficient we don't know + + align:start position:0% +sixth degree coefficient we don't know + + + align:start position:0% +sixth degree coefficient we don't know +yet so this is plus a sub 6 * x 6/ 6 + + align:start position:0% +yet so this is plus a sub 6 * x 6/ 6 + + + align:start position:0% +yet so this is plus a sub 6 * x 6/ 6 +factorial plus dot dot dot so we know + + align:start position:0% +factorial plus dot dot dot so we know + + + align:start position:0% +factorial plus dot dot dot so we know +that when we multiply these two things + + align:start position:0% +that when we multiply these two things + + + align:start position:0% +that when we multiply these two things +together it has to give us just one all + + align:start position:0% +together it has to give us just one all + + + align:start position:0% +together it has to give us just one all +the higher order terms have to cancel + + align:start position:0% +the higher order terms have to cancel + + + align:start position:0% +the higher order terms have to cancel +because over here we have a one so what + + align:start position:0% +because over here we have a one so what + + + align:start position:0% +because over here we have a one so what +you can do is you can actually try + + align:start position:0% +you can do is you can actually try + + + align:start position:0% +you can do is you can actually try +multiplying these things out so it's + + align:start position:0% +multiplying these things out so it's + + + align:start position:0% +multiplying these things out so it's +easy to see for example that the + + align:start position:0% +easy to see for example that the + + + align:start position:0% +easy to see for example that the +constant term of this product is just + + align:start position:0% +constant term of this product is just + + + align:start position:0% +constant term of this product is just +one 1 which is one which is good so + + align:start position:0% +one 1 which is one which is good so + + + align:start position:0% +one 1 which is one which is good so +that's a check on what we've done so far + + align:start position:0% +that's a check on what we've done so far + + + align:start position:0% +that's a check on what we've done so far +and the there is no X term because there + + align:start position:0% +and the there is no X term because there + + + align:start position:0% +and the there is no X term because there +are no X's the X squ term here is 1 * + + align:start position:0% +are no X's the X squ term here is 1 * + + + align:start position:0% +are no X's the X squ term here is 1 * +x^2 / 2 - x^2 over 2 * 1 well that gives + + align:start position:0% +x^2 / 2 - x^2 over 2 * 1 well that gives + + + align:start position:0% +x^2 / 2 - x^2 over 2 * 1 well that gives +us zero so that's good so this is this + + align:start position:0% +us zero so that's good so this is this + + + align:start position:0% +us zero so that's good so this is this +product is equal to well it's 1 plus we + + align:start position:0% +product is equal to well it's 1 plus we + + + align:start position:0% +product is equal to well it's 1 plus we +saw 0x plus 0 x^2 how about the X Cub + + align:start position:0% +saw 0x plus 0 x^2 how about the X Cub + + + align:start position:0% +saw 0x plus 0 x^2 how about the X Cub +term well there are no odd terms in this + + align:start position:0% +term well there are no odd terms in this + + + align:start position:0% +term well there are no odd terms in this +product so there's no X Cub how about + + align:start position:0% +product so there's no X Cub how about + + + align:start position:0% +product so there's no X Cub how about +the X to the 4th term well okay so how + + align:start position:0% +the X to the 4th term well okay so how + + + align:start position:0% +the X to the 4th term well okay so how +do we get an x to the 4th we could have + + align:start position:0% +do we get an x to the 4th we could have + + + align:start position:0% +do we get an x to the 4th we could have +an X 4 here times a constant so that's x + + align:start position:0% +an X 4 here times a constant so that's x + + + align:start position:0% +an X 4 here times a constant so that's x +4/ + + align:start position:0% +4/ + + + align:start position:0% +4/ +24 or we could have an x^2 * an x^2 so + + align:start position:0% +24 or we could have an x^2 * an x^2 so + + + align:start position:0% +24 or we could have an x^2 * an x^2 so +in this case that gives us - x^2 over 2 + + align:start position:0% +in this case that gives us - x^2 over 2 + + + align:start position:0% +in this case that gives us - x^2 over 2 +* x^2 over 2 which is - x 4 over 4 or we + + align:start position:0% +* x^2 over 2 which is - x 4 over 4 or we + + + align:start position:0% +* x^2 over 2 which is - x 4 over 4 or we +could have a constant times an X to 4th + + align:start position:0% +could have a constant times an X to 4th + + + align:start position:0% +could have a constant times an X to 4th +so this is plus + + align:start position:0% +so this is plus + + + align:start position:0% +so this is plus +A4 X 4th over + + align:start position:0% +A4 X 4th over + + + align:start position:0% +A4 X 4th over +24 and then we'll have a sixth degree + + align:start position:0% +24 and then we'll have a sixth degree + + + align:start position:0% +24 and then we'll have a sixth degree +term and so on notice that there's never + + align:start position:0% +term and so on notice that there's never + + + align:start position:0% +term and so on notice that there's never +any involv M from the higher order terms + + align:start position:0% +any involv M from the higher order terms + + + align:start position:0% +any involv M from the higher order terms +in the fourth power here right if you + + align:start position:0% +in the fourth power here right if you + + + align:start position:0% +in the fourth power here right if you +ever took an x to the 6th here well then + + align:start position:0% +ever took an x to the 6th here well then + + + align:start position:0% +ever took an x to the 6th here well then +everything you multiply it by has at + + align:start position:0% +everything you multiply it by has at + + + align:start position:0% +everything you multiply it by has at +least an x to the 6th power so we don't + + align:start position:0% +least an x to the 6th power so we don't + + + align:start position:0% +least an x to the 6th power so we don't +have to worry about that showing up in + + align:start position:0% +have to worry about that showing up in + + + align:start position:0% +have to worry about that showing up in +the X to the fourth term well okay we + + align:start position:0% +the X to the fourth term well okay we + + + align:start position:0% +the X to the fourth term well okay we +know this is actually equal to one so we + + align:start position:0% +know this is actually equal to one so we + + + align:start position:0% +know this is actually equal to one so we +know that this thing has to be zero this + + align:start position:0% +know that this thing has to be zero this + + + align:start position:0% +know that this thing has to be zero this +is the X to the fourth term it has to be + + align:start position:0% +is the X to the fourth term it has to be + + + align:start position:0% +is the X to the fourth term it has to be +zero so that means that 1 over + + align:start position:0% +zero so that means that 1 over + + + align:start position:0% +zero so that means that 1 over +24 - 1 over 4 + A4 over 24 equals z so + + align:start position:0% +24 - 1 over 4 + A4 over 24 equals z so + + + align:start position:0% +24 - 1 over 4 + A4 over 24 equals z so +okay so now you can multiply everything + + align:start position:0% +okay so now you can multiply everything + + + align:start position:0% +okay so now you can multiply everything +through by 24 and rearrange to figure + + align:start position:0% +through by 24 and rearrange to figure + + + align:start position:0% +through by 24 and rearrange to figure +out that A4 is equal to 5 if I've done + + align:start position:0% +out that A4 is equal to 5 if I've done + + + align:start position:0% +out that A4 is equal to 5 if I've done +that correctly and if then if you wanted + + align:start position:0% +that correctly and if then if you wanted + + + align:start position:0% +that correctly and if then if you wanted +it would be fairly easy to go back up + + align:start position:0% +it would be fairly easy to go back up + + + align:start position:0% +it would be fairly easy to go back up +and then you look at the X to the sixth + + align:start position:0% +and then you look at the X to the sixth + + + align:start position:0% +and then you look at the X to the sixth +term and from there you could figure out + + align:start position:0% +term and from there you could figure out + + + align:start position:0% +term and from there you could figure out +that A6 was equal to say 61 or something + + align:start position:0% +that A6 was equal to say 61 or something + + + align:start position:0% +that A6 was equal to say 61 or something +like that I think 61 um and you could + + align:start position:0% +like that I think 61 um and you could + + + align:start position:0% +like that I think 61 um and you could +keep doing this so this is one way to to + + align:start position:0% +keep doing this so this is one way to to + + + align:start position:0% +keep doing this so this is one way to to +compute more terms of the series for + + align:start position:0% +compute more terms of the series for + + + align:start position:0% +compute more terms of the series for +secant of X um another thing you could + + align:start position:0% +secant of X um another thing you could + + + align:start position:0% +secant of X um another thing you could +do which I'll just mention very briefly + + align:start position:0% +do which I'll just mention very briefly + + + align:start position:0% +do which I'll just mention very briefly +I'm not going to show you how to do it + + align:start position:0% +I'm not going to show you how to do it + + + align:start position:0% +I'm not going to show you how to do it +is that you can do a long division on + + align:start position:0% +is that you can do a long division on + + + align:start position:0% +is that you can do a long division on +power Series so it actually works out + + align:start position:0% +power Series so it actually works out + + + align:start position:0% +power Series so it actually works out +very it works out just like this it it's + + align:start position:0% +very it works out just like this it it's + + + align:start position:0% +very it works out just like this it it's +mathematically equivalent the the way + + align:start position:0% +mathematically equivalent the the way + + + align:start position:0% +mathematically equivalent the the way +you actually do it looks different it + + align:start position:0% +you actually do it looks different it + + + align:start position:0% +you actually do it looks different it +looks like long division um with when + + align:start position:0% +looks like long division um with when + + + align:start position:0% +looks like long division um with when +you do long division with pooms you + + align:start position:0% +you do long division with pooms you + + + align:start position:0% +you do long division with pooms you +start with the highest order term of + + align:start position:0% +start with the highest order term of + + + align:start position:0% +start with the highest order term of +course power series don't have highest + + align:start position:0% +course power series don't have highest + + + align:start position:0% +course power series don't have highest +order terms what you actually do with a + + align:start position:0% +order terms what you actually do with a + + + align:start position:0% +order terms what you actually do with a +power series is you start with the + + align:start position:0% +power series is you start with the + + + align:start position:0% +power series is you start with the +lowest order term so to divide this into + + align:start position:0% +lowest order term so to divide this into + + + align:start position:0% +lowest order term so to divide this into +one you say oh you need a factor of one + + align:start position:0% +one you say oh you need a factor of one + + + align:start position:0% +one you say oh you need a factor of one +and then you'll have a you know you + + align:start position:0% +and then you'll have a you know you + + + align:start position:0% +and then you'll have a you know you +subtract off one times this and that + + align:start position:0% +subtract off one times this and that + + + align:start position:0% +subtract off one times this and that +gives you an X squ plus two and so okay + + align:start position:0% +gives you an X squ plus two and so okay + + + align:start position:0% +gives you an X squ plus two and so okay +so you say I need a you know a A plus + + align:start position:0% +so you say I need a you know a A plus + + + align:start position:0% +so you say I need a you know a A plus +and x s plus 2 and and so on so um that + + align:start position:0% +and x s plus 2 and and so on so um that + + + align:start position:0% +and x s plus 2 and and so on so um that +was too brief for you to understand it + + align:start position:0% +was too brief for you to understand it + + + align:start position:0% +was too brief for you to understand it +properly but um but you can go and look + + align:start position:0% +properly but um but you can go and look + + + align:start position:0% +properly but um but you can go and look +up somewhere uh the the method of long + + align:start position:0% +up somewhere uh the the method of long + + + align:start position:0% +up somewhere uh the the method of long +division on power Series so just to to + + align:start position:0% +division on power Series so just to to + + + align:start position:0% +division on power Series so just to to +recap um we talked about three methods + + align:start position:0% +recap um we talked about three methods + + + align:start position:0% +recap um we talked about three methods +for computing the coefficients of a + + align:start position:0% +for computing the coefficients of a + + + align:start position:0% +for computing the coefficients of a +power series there's the the formula + + align:start position:0% +power series there's the the formula + + + align:start position:0% +power series there's the the formula +that you were that you were given um + + align:start position:0% +that you were that you were given um + + + align:start position:0% +that you were that you were given um +which works and which you could use in + + align:start position:0% +which works and which you could use in + + + align:start position:0% +which works and which you could use in +this case it's a little complicated um + + align:start position:0% +this case it's a little complicated um + + + align:start position:0% +this case it's a little complicated um +then there's the method of using a + + align:start position:0% +then there's the method of using a + + + align:start position:0% +then there's the method of using a +relationship between your power series + + align:start position:0% +relationship between your power series + + + align:start position:0% +relationship between your power series +and other known power Series in this + + align:start position:0% +and other known power Series in this + + + align:start position:0% +and other known power Series in this +case we can use the relationship that we + + align:start position:0% +case we can use the relationship that we + + + align:start position:0% +case we can use the relationship that we +know our power series satisfies a + + align:start position:0% +know our power series satisfies a + + + align:start position:0% +know our power series satisfies a +certain product we know that our power + + align:start position:0% +certain product we know that our power + + + align:start position:0% +certain product we know that our power +seriestimes cosine of x equals to 1 and + + align:start position:0% +seriestimes cosine of x equals to 1 and + + + align:start position:0% +seriestimes cosine of x equals to 1 and +we can use that to solve for some of the + + align:start position:0% +we can use that to solve for some of the + + + align:start position:0% +we can use that to solve for some of the +coefficients or you can also similarly + + align:start position:0% +coefficients or you can also similarly + + + align:start position:0% +coefficients or you can also similarly +when you have that situation you can + + align:start position:0% +when you have that situation you can + + + align:start position:0% +when you have that situation you can +also use long division to compute the + + align:start position:0% +also use long division to compute the + + + align:start position:0% +also use long division to compute the +coefficients I'll end there \ No newline at end of file diff --git a/G46Vpp0jPDg.txt b/G46Vpp0jPDg.txt new file mode 100644 index 0000000000000000000000000000000000000000..422cabe57b6ef5db70bf9094ca23987ff209ebb4 --- /dev/null +++ b/G46Vpp0jPDg.txt @@ -0,0 +1,3387 @@ +align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +I'm Sarah Hansen in the last episode of + + align:start position:0% +I'm Sarah Hansen in the last episode of + + + align:start position:0% +I'm Sarah Hansen in the last episode of +chalk radio we spoke with Dr Ari Epstein + + align:start position:0% +chalk radio we spoke with Dr Ari Epstein + + + align:start position:0% +chalk radio we spoke with Dr Ari Epstein +associate director and Senior lecturer + + align:start position:0% +associate director and Senior lecturer + + + align:start position:0% +associate director and Senior lecturer +in the terrascope program at MIT + + align:start position:0% +in the terrascope program at MIT + + + align:start position:0% +in the terrascope program at MIT +terrascope is a first year Learning + + align:start position:0% +terrascope is a first year Learning + + + align:start position:0% +terrascope is a first year Learning +Community for students interested in + + align:start position:0% +Community for students interested in + + + align:start position:0% +Community for students interested in +collaboratively solving our planet's + + align:start position:0% +collaboratively solving our planet's + + + align:start position:0% +collaboratively solving our planet's +most complex + + align:start position:0% +most complex + + + align:start position:0% +most complex +challenges as part of their work some + + align:start position:0% +challenges as part of their work some + + + align:start position:0% +challenges as part of their work some +students contribute to terrascope radio + + align:start position:0% +students contribute to terrascope radio + + + align:start position:0% +students contribute to terrascope radio +which as Ari says allows them to use the + + align:start position:0% +which as Ari says allows them to use the + + + align:start position:0% +which as Ari says allows them to use the +power of sound as a tool for + + align:start position:0% +power of sound as a tool for + + + align:start position:0% +power of sound as a tool for +communicating ideas to a variety of + + align:start position:0% +communicating ideas to a variety of + + + align:start position:0% +communicating ideas to a variety of +audiences teris scope radio episodes are + + align:start position:0% +audiences teris scope radio episodes are + + + align:start position:0% +audiences teris scope radio episodes are +shared on 88.1 wmbr mit's radio station + + align:start position:0% +shared on 88.1 wmbr mit's radio station + + + align:start position:0% +shared on 88.1 wmbr mit's radio station +and they're just so good we couldn't not + + align:start position:0% +and they're just so good we couldn't not + + + align:start position:0% +and they're just so good we couldn't not +share one of them with you here the + + align:start position:0% +share one of them with you here the + + + align:start position:0% +share one of them with you here the +terrascope radio episode you're about to + + align:start position:0% +terrascope radio episode you're about to + + + align:start position:0% +terrascope radio episode you're about to +hear is called everything here is sacred + + align:start position:0% +hear is called everything here is sacred + + + align:start position:0% +hear is called everything here is sacred +which as the students explain explored + + align:start position:0% +which as the students explain explored + + + align:start position:0% +which as the students explain explored +ways in which seemingly everyday places + + align:start position:0% +ways in which seemingly everyday places + + + align:start position:0% +ways in which seemingly everyday places +and activities such as a cornfield or + + align:start position:0% +and activities such as a cornfield or + + + align:start position:0% +and activities such as a cornfield or +the meeting place of two rivers are + + align:start position:0% +the meeting place of two rivers are + + + align:start position:0% +the meeting place of two rivers are +imbued with sacredness in Navajo culture + + align:start position:0% +imbued with sacredness in Navajo culture + + + align:start position:0% +imbued with sacredness in Navajo culture +we hope you enjoy it as much as we + + align:start position:0% + + + + align:start position:0% + +did thank you for + + align:start position:0% +did thank you for + + + align:start position:0% +did thank you for +coming thank you for being here that was + + align:start position:0% +coming thank you for being here that was + + + align:start position:0% +coming thank you for being here that was +Tony goldtooth welcoming Us in the + + align:start position:0% +Tony goldtooth welcoming Us in the + + + align:start position:0% +Tony goldtooth welcoming Us in the +Navajo language when we joined his his + + align:start position:0% +Navajo language when we joined his his + + + align:start position:0% +Navajo language when we joined his his +family for an outdoor Navajo style lunch + + align:start position:0% +family for an outdoor Navajo style lunch + + + align:start position:0% +family for an outdoor Navajo style lunch +why were we joining Tony we were a group + + align:start position:0% +why were we joining Tony we were a group + + + align:start position:0% +why were we joining Tony we were a group +of first year students from MIT and we + + align:start position:0% +of first year students from MIT and we + + + align:start position:0% +of first year students from MIT and we +traveled to the Navajo Nation to + + align:start position:0% +traveled to the Navajo Nation to + + + align:start position:0% +traveled to the Navajo Nation to +initially learn about agriculture but + + align:start position:0% +initially learn about agriculture but + + + align:start position:0% +initially learn about agriculture but +what we learned was so much more than + + align:start position:0% +what we learned was so much more than + + + align:start position:0% +what we learned was so much more than +that we met truly amazing and inspiring + + align:start position:0% +that we met truly amazing and inspiring + + + align:start position:0% +that we met truly amazing and inspiring +Navajo people or Denette who showed us + + align:start position:0% +Navajo people or Denette who showed us + + + align:start position:0% +Navajo people or Denette who showed us +that agriculture was much more than just + + align:start position:0% +that agriculture was much more than just + + + align:start position:0% +that agriculture was much more than just +a job it's essential tenant of their + + align:start position:0% +a job it's essential tenant of their + + + align:start position:0% +a job it's essential tenant of their +culture and identity as a people one + + align:start position:0% +culture and identity as a people one + + + align:start position:0% +culture and identity as a people one +person we met was Brandon Francis a + + align:start position:0% +person we met was Brandon Francis a + + + align:start position:0% +person we met was Brandon Francis a +research technician at New Mexico State + + align:start position:0% +research technician at New Mexico State + + + align:start position:0% +research technician at New Mexico State +University NMSU he showed us around the + + align:start position:0% +University NMSU he showed us around the + + + align:start position:0% +University NMSU he showed us around the +NMSU agricultural experiment station and + + align:start position:0% +NMSU agricultural experiment station and + + + align:start position:0% +NMSU agricultural experiment station and +where we got to see things like Gardens + + align:start position:0% +where we got to see things like Gardens + + + align:start position:0% +where we got to see things like Gardens +of native plants experimental Vineyards + + align:start position:0% +of native plants experimental Vineyards + + + align:start position:0% +of native plants experimental Vineyards +and the equipment he uses to conduct his + + align:start position:0% + + + + align:start position:0% + +research at one point Brandon stopped us + + align:start position:0% +research at one point Brandon stopped us + + + align:start position:0% +research at one point Brandon stopped us +to take in the landscape looking down + + align:start position:0% +to take in the landscape looking down + + + align:start position:0% +to take in the landscape looking down +the path of tan soft soil under our feet + + align:start position:0% +the path of tan soft soil under our feet + + + align:start position:0% +the path of tan soft soil under our feet +an artificial Grove of poplar trees now + + align:start position:0% +an artificial Grove of poplar trees now + + + align:start position:0% +an artificial Grove of poplar trees now +brown and bare walled off the landscape + + align:start position:0% +brown and bare walled off the landscape + + + align:start position:0% +brown and bare walled off the landscape +to our left while paler Brown equally + + align:start position:0% +to our left while paler Brown equally + + + align:start position:0% +to our left while paler Brown equally +bare Fields waiting for growing season + + align:start position:0% +bare Fields waiting for growing season + + + align:start position:0% +bare Fields waiting for growing season +stretched off to our right perfectly + + align:start position:0% +stretched off to our right perfectly + + + align:start position:0% +stretched off to our right perfectly +framed between the two seeming to Mark + + align:start position:0% +framed between the two seeming to Mark + + + align:start position:0% +framed between the two seeming to Mark +the end of our dirt path at the Horizon + + align:start position:0% +the end of our dirt path at the Horizon + + + align:start position:0% +the end of our dirt path at the Horizon +was the bluish silhouette of a far off + + align:start position:0% +was the bluish silhouette of a far off + + + align:start position:0% +was the bluish silhouette of a far off +monolith named Ship Rock This geologic + + align:start position:0% +monolith named Ship Rock This geologic + + + align:start position:0% +monolith named Ship Rock This geologic +structure a remnant of an ancient + + align:start position:0% +structure a remnant of an ancient + + + align:start position:0% +structure a remnant of an ancient +volcano is deeply intertwined with the + + align:start position:0% +volcano is deeply intertwined with the + + + align:start position:0% +volcano is deeply intertwined with the +traditional stories of the daet and it + + align:start position:0% +traditional stories of the daet and it + + + align:start position:0% +traditional stories of the daet and it +is considered a sacred place obscuring + + align:start position:0% +is considered a sacred place obscuring + + + align:start position:0% +is considered a sacred place obscuring +the bottom half of ship Rock's profile + + align:start position:0% +the bottom half of ship Rock's profile + + + align:start position:0% +the bottom half of ship Rock's profile +was the chimney of a power plant puffing + + align:start position:0% +was the chimney of a power plant puffing + + + align:start position:0% +was the chimney of a power plant puffing +short-lived white clouds + + align:start position:0% +short-lived white clouds + + + align:start position:0% +short-lived white clouds +this is what I call the perfect image of + + align:start position:0% +this is what I call the perfect image of + + + align:start position:0% +this is what I call the perfect image of +the reservation you have a coold fired + + align:start position:0% +the reservation you have a coold fired + + + align:start position:0% +the reservation you have a coold fired +power plant you have picture of + + align:start position:0% +power plant you have picture of + + + align:start position:0% +power plant you have picture of +Agriculture then you have the then you + + align:start position:0% +Agriculture then you have the then you + + + align:start position:0% +Agriculture then you have the then you +have um chip rock in the background + + align:start position:0% +have um chip rock in the background + + + align:start position:0% +have um chip rock in the background +that's the what I like to say the r and + + align:start position:0% +that's the what I like to say the r and + + + align:start position:0% +that's the what I like to say the r and +a Pinon shell agriculture cold fire + + align:start position:0% +a Pinon shell agriculture cold fire + + + align:start position:0% +a Pinon shell agriculture cold fire +power plant chip rock at that's in one + + align:start position:0% +power plant chip rock at that's in one + + + align:start position:0% +power plant chip rock at that's in one +picture right + + align:start position:0% +picture right + + + align:start position:0% +picture right +there Brandon also took us to the + + align:start position:0% +there Brandon also took us to the + + + align:start position:0% +there Brandon also took us to the +Confluence of the Animus and sand Juan + + align:start position:0% +Confluence of the Animus and sand Juan + + + align:start position:0% +Confluence of the Animus and sand Juan +rivers near Farmington Mexico when we + + align:start position:0% +rivers near Farmington Mexico when we + + + align:start position:0% +rivers near Farmington Mexico when we +arrived the winds chilled us to the Bone + + align:start position:0% +arrived the winds chilled us to the Bone + + + align:start position:0% +arrived the winds chilled us to the Bone +the spring sunshine in late March not + + align:start position:0% +the spring sunshine in late March not + + + align:start position:0% +the spring sunshine in late March not +yet warm enough to offer any relief the + + align:start position:0% +yet warm enough to offer any relief the + + + align:start position:0% +yet warm enough to offer any relief the +San Juan River's surface was a + + align:start position:0% +San Juan River's surface was a + + + align:start position:0% +San Juan River's surface was a +shimmering reflection of the sky while + + align:start position:0% +shimmering reflection of the sky while + + + align:start position:0% +shimmering reflection of the sky while +the animous river was a murky Brown + + align:start position:0% +the animous river was a murky Brown + + + align:start position:0% +the animous river was a murky Brown +mirroring the bare overhanging + + align:start position:0% +mirroring the bare overhanging + + + align:start position:0% +mirroring the bare overhanging +Cottonwood branches when the rivers + + align:start position:0% +Cottonwood branches when the rivers + + + align:start position:0% +Cottonwood branches when the rivers +merged at the Confluence the water of + + align:start position:0% +merged at the Confluence the water of + + + align:start position:0% +merged at the Confluence the water of +the two rivers would flow in parallel + + align:start position:0% +the two rivers would flow in parallel + + + align:start position:0% +the two rivers would flow in parallel +Lanes of color only beginning to mix at + + align:start position:0% +Lanes of color only beginning to mix at + + + align:start position:0% +Lanes of color only beginning to mix at +their border where the water encountered + + align:start position:0% +their border where the water encountered + + + align:start position:0% +their border where the water encountered +many islands of beige sand and + + align:start position:0% +many islands of beige sand and + + + align:start position:0% +many islands of beige sand and +rocks this is our Temple you know we we + + align:start position:0% +rocks this is our Temple you know we we + + + align:start position:0% +rocks this is our Temple you know we we +we view this part as this land that's + + align:start position:0% +we view this part as this land that's + + + align:start position:0% +we view this part as this land that's +water as sacred you know providing life + + align:start position:0% +water as sacred you know providing life + + + align:start position:0% +water as sacred you know providing life +and we pray right here and we pray for + + align:start position:0% +and we pray right here and we pray for + + + align:start position:0% +and we pray right here and we pray for +for things because we always believe + + align:start position:0% +for things because we always believe + + + align:start position:0% +for things because we always believe +that water takes our prayers to the big + + align:start position:0% +that water takes our prayers to the big + + + align:start position:0% +that water takes our prayers to the big +water down on to the Colorado then goes + + align:start position:0% +water down on to the Colorado then goes + + + align:start position:0% +water down on to the Colorado then goes +into the ocean then eventually comes + + align:start position:0% +into the ocean then eventually comes + + + align:start position:0% +into the ocean then eventually comes +back to us so it carries our prayers for + + align:start position:0% +back to us so it carries our prayers for + + + align:start position:0% +back to us so it carries our prayers for +us and so every time we we we pray we + + align:start position:0% +us and so every time we we we pray we + + + align:start position:0% +us and so every time we we we pray we +pray we pray to the water not only do we + + align:start position:0% +pray we pray to the water not only do we + + + align:start position:0% +pray we pray to the water not only do we +view the river as um a part of our our + + align:start position:0% +view the river as um a part of our our + + + align:start position:0% +view the river as um a part of our our +family but a part of our our way of life + + align:start position:0% +family but a part of our our way of life + + + align:start position:0% +family but a part of our our way of life +and when we grow things and we grow + + align:start position:0% +and when we grow things and we grow + + + align:start position:0% +and when we grow things and we grow +plants we view them as our children as + + align:start position:0% +plants we view them as our children as + + + align:start position:0% +plants we view them as our children as +our relatives and when we're watering + + align:start position:0% +our relatives and when we're watering + + + align:start position:0% +our relatives and when we're watering +them or when we're attending to them we + + align:start position:0% +them or when we're attending to them we + + + align:start position:0% +them or when we're attending to them we +always talk to them and no you know grow + + align:start position:0% +always talk to them and no you know grow + + + align:start position:0% +always talk to them and no you know grow +my little one you know and we we treat + + align:start position:0% +my little one you know and we we treat + + + align:start position:0% +my little one you know and we we treat +them as as um as family but what if the + + align:start position:0% +them as as um as family but what if the + + + align:start position:0% +them as as um as family but what if the +water is contaminated we learned about + + align:start position:0% +water is contaminated we learned about + + + align:start position:0% +water is contaminated we learned about +the gold King M spill that happened in + + align:start position:0% +the gold King M spill that happened in + + + align:start position:0% +the gold King M spill that happened in +2015 when a mine in Colorado spilled + + align:start position:0% +2015 when a mine in Colorado spilled + + + align:start position:0% +2015 when a mine in Colorado spilled +toxic Wastewater into to the Animus + + align:start position:0% +toxic Wastewater into to the Animus + + + align:start position:0% +toxic Wastewater into to the Animus +River where it spread to the Confluence + + align:start position:0% +River where it spread to the Confluence + + + align:start position:0% +River where it spread to the Confluence +and much of the sanan river Downstream + + align:start position:0% +and much of the sanan river Downstream + + + align:start position:0% +and much of the sanan river Downstream +turning the waters caution tape yellow + + align:start position:0% +turning the waters caution tape yellow + + + align:start position:0% +turning the waters caution tape yellow +Farmers relying on the San Juan River + + align:start position:0% +Farmers relying on the San Juan River + + + align:start position:0% +Farmers relying on the San Juan River +for water were forced to shut down their + + align:start position:0% +for water were forced to shut down their + + + align:start position:0% +for water were forced to shut down their +irrigation lines so when the gold King + + align:start position:0% +irrigation lines so when the gold King + + + align:start position:0% +irrigation lines so when the gold King +mind spill happened and they they they + + align:start position:0% +mind spill happened and they they they + + + align:start position:0% +mind spill happened and they they they +shut off the water for a lot of Navajo + + align:start position:0% +shut off the water for a lot of Navajo + + + align:start position:0% +shut off the water for a lot of Navajo +people or a lot of the net people was + + align:start position:0% +people or a lot of the net people was + + + align:start position:0% +people or a lot of the net people was +like watching their relatives die out in + + align:start position:0% +like watching their relatives die out in + + + align:start position:0% +like watching their relatives die out in +the field and die of thirst you know + + align:start position:0% +the field and die of thirst you know + + + align:start position:0% +the field and die of thirst you know +wither and die + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +after our stroll with Brandon along the + + align:start position:0% +after our stroll with Brandon along the + + + align:start position:0% +after our stroll with Brandon along the +river we headed to the Lane Family Farm + + align:start position:0% +river we headed to the Lane Family Farm + + + align:start position:0% +river we headed to the Lane Family Farm +owned by Gloria and Harry Lane through + + align:start position:0% +owned by Gloria and Harry Lane through + + + align:start position:0% +owned by Gloria and Harry Lane through +the farm Gloria and Harry aimed to teach + + align:start position:0% +the farm Gloria and Harry aimed to teach + + + align:start position:0% +the farm Gloria and Harry aimed to teach +da culture and traditional farming the + + align:start position:0% +da culture and traditional farming the + + + align:start position:0% +da culture and traditional farming the +farm consists of a one-story house + + align:start position:0% +farm consists of a one-story house + + + align:start position:0% +farm consists of a one-story house +painted a light tan that almost + + align:start position:0% +painted a light tan that almost + + + align:start position:0% +painted a light tan that almost +camouflage with the surrounding soft + + align:start position:0% +camouflage with the surrounding soft + + + align:start position:0% +camouflage with the surrounding soft +khaki colored soil the house overlooks + + align:start position:0% +khaki colored soil the house overlooks + + + align:start position:0% +khaki colored soil the house overlooks +the San Juan River and a pot of Farmland + + align:start position:0% +the San Juan River and a pot of Farmland + + + align:start position:0% +the San Juan River and a pot of Farmland +which was clear of weeds when we visited + + align:start position:0% +which was clear of weeds when we visited + + + align:start position:0% +which was clear of weeds when we visited +as the family prepared for the upcoming + + align:start position:0% +as the family prepared for the upcoming + + + align:start position:0% +as the family prepared for the upcoming +planting season there standing next to + + align:start position:0% +planting season there standing next to + + + align:start position:0% +planting season there standing next to +the field we met Kevin Balin director of + + align:start position:0% +the field we met Kevin Balin director of + + + align:start position:0% +the field we met Kevin Balin director of +The Da bizard Institute at the Navajo + + align:start position:0% +The Da bizard Institute at the Navajo + + + align:start position:0% +The Da bizard Institute at the Navajo +prepatory school who exended the ideas + + align:start position:0% +prepatory school who exended the ideas + + + align:start position:0% +prepatory school who exended the ideas +of sacredness Brandon mentioned earlier + + align:start position:0% +of sacredness Brandon mentioned earlier + + + align:start position:0% +of sacredness Brandon mentioned earlier +and you hear that from native people oh + + align:start position:0% +and you hear that from native people oh + + + align:start position:0% +and you hear that from native people oh +everything is sacred look at the ground + + align:start position:0% +everything is sacred look at the ground + + + align:start position:0% +everything is sacred look at the ground +you touch is sacred that River there is + + align:start position:0% +you touch is sacred that River there is + + + align:start position:0% +you touch is sacred that River there is +sacred those trees the birds look fill + + align:start position:0% +sacred those trees the birds look fill + + + align:start position:0% +sacred those trees the birds look fill +the is it sacred it is it truly truly is + + align:start position:0% +the is it sacred it is it truly truly is + + + align:start position:0% +the is it sacred it is it truly truly is +for Kevin one particularly sacred plant + + align:start position:0% +for Kevin one particularly sacred plant + + + align:start position:0% +for Kevin one particularly sacred plant +is corn we were told that our bodies are + + align:start position:0% +is corn we were told that our bodies are + + + align:start position:0% +is corn we were told that our bodies are +made of corn when we were created we + + align:start position:0% +made of corn when we were created we + + + align:start position:0% +made of corn when we were created we +were told this is what our bodies Were + + align:start position:0% +were told this is what our bodies Were + + + align:start position:0% +were told this is what our bodies Were +Made of This Is How We are going to + + align:start position:0% +Made of This Is How We are going to + + + align:start position:0% +Made of This Is How We are going to +interact with the world around us when + + align:start position:0% +interact with the world around us when + + + align:start position:0% +interact with the world around us when +you're creating a corn field you're + + align:start position:0% +you're creating a corn field you're + + + align:start position:0% +you're creating a corn field you're +creating + + align:start position:0% +creating + + + align:start position:0% +creating +life when you plant that seed worm right + + align:start position:0% +life when you plant that seed worm right + + + align:start position:0% +life when you plant that seed worm right +egg when you're creating that field you + + align:start position:0% +egg when you're creating that field you + + + align:start position:0% +egg when you're creating that field you +create your + + align:start position:0% +create your + + + align:start position:0% +create your +home de Brandon and Kevin agriculture is + + align:start position:0% +home de Brandon and Kevin agriculture is + + + align:start position:0% +home de Brandon and Kevin agriculture is +not just a means to an end a way to + + align:start position:0% +not just a means to an end a way to + + + align:start position:0% +not just a means to an end a way to +deliver food to the grocery store for + + align:start position:0% +deliver food to the grocery store for + + + align:start position:0% +deliver food to the grocery store for +the convenience of modern society even + + align:start position:0% +the convenience of modern society even + + + align:start position:0% +the convenience of modern society even +though there are challenges waking up + + align:start position:0% +though there are challenges waking up + + + align:start position:0% +though there are challenges waking up +before the blazing sun rises and + + align:start position:0% +before the blazing sun rises and + + + align:start position:0% +before the blazing sun rises and +removing weeds in the blistering heat + + align:start position:0% +removing weeds in the blistering heat + + + align:start position:0% +removing weeds in the blistering heat +practicing agriculture is a fundamental + + align:start position:0% +practicing agriculture is a fundamental + + + align:start position:0% +practicing agriculture is a fundamental +part of who they are as the net people + + align:start position:0% +part of who they are as the net people + + + align:start position:0% +part of who they are as the net people +for us as the net people you have to + + align:start position:0% +for us as the net people you have to + + + align:start position:0% +for us as the net people you have to +have a passion for growing corn you have + + align:start position:0% +have a passion for growing corn you have + + + align:start position:0% +have a passion for growing corn you have +to have the will you have to have the + + align:start position:0% +to have the will you have to have the + + + align:start position:0% +to have the will you have to have the +motivation to come over here look at + + align:start position:0% +motivation to come over here look at + + + align:start position:0% +motivation to come over here look at +this piece of dirt and think it's going + + align:start position:0% +this piece of dirt and think it's going + + + align:start position:0% +this piece of dirt and think it's going +to be productive you have to have that + + align:start position:0% +to be productive you have to have that + + + align:start position:0% +to be productive you have to have that +mindset that this land here I'm going to + + align:start position:0% +mindset that this land here I'm going to + + + align:start position:0% +mindset that this land here I'm going to +have to work it to ensure we have food + + align:start position:0% +have to work it to ensure we have food + + + align:start position:0% +have to work it to ensure we have food +and while some of us were listening to + + align:start position:0% +and while some of us were listening to + + + align:start position:0% +and while some of us were listening to +Kevin others of us were talking to + + align:start position:0% +Kevin others of us were talking to + + + align:start position:0% +Kevin others of us were talking to +Gabrielle Henderson also known as Gabby + + align:start position:0% +Gabrielle Henderson also known as Gabby + + + align:start position:0% +Gabrielle Henderson also known as Gabby +and newx meico State University + + align:start position:0% +and newx meico State University + + + align:start position:0% +and newx meico State University +undergraduate student who also + + align:start position:0% +undergraduate student who also + + + align:start position:0% +undergraduate student who also +volunteers her time at the lane family + + align:start position:0% +volunteers her time at the lane family + + + align:start position:0% +volunteers her time at the lane family +farm so why does she put in the time and + + align:start position:0% +farm so why does she put in the time and + + + align:start position:0% +farm so why does she put in the time and +effort to help with harming it all + + align:start position:0% +effort to help with harming it all + + + align:start position:0% +effort to help with harming it all +started with Gloria and Harry's daughter + + align:start position:0% +started with Gloria and Harry's daughter + + + align:start position:0% +started with Gloria and Harry's daughter +Nana balain who unfortunately passed + + align:start position:0% +Nana balain who unfortunately passed + + + align:start position:0% +Nana balain who unfortunately passed +away 6 months prior to us meeting the + + align:start position:0% +away 6 months prior to us meeting the + + + align:start position:0% +away 6 months prior to us meeting the +lane family but in her lifetime nanaba + + align:start position:0% +lane family but in her lifetime nanaba + + + align:start position:0% +lane family but in her lifetime nanaba +was an educator an environmental + + align:start position:0% +was an educator an environmental + + + align:start position:0% +was an educator an environmental +sustainability specialist who also + + align:start position:0% +sustainability specialist who also + + + align:start position:0% +sustainability specialist who also +became a role model for Gabby so I + + align:start position:0% +became a role model for Gabby so I + + + align:start position:0% +became a role model for Gabby so I +personally got involved with this was + + align:start position:0% +personally got involved with this was + + + align:start position:0% +personally got involved with this was +through through n + + align:start position:0% +through through n + + + align:start position:0% +through through n +um she's kind of been there for me since + + align:start position:0% +um she's kind of been there for me since + + + align:start position:0% +um she's kind of been there for me since +childhood making cookies and uh she + + align:start position:0% +childhood making cookies and uh she + + + align:start position:0% +childhood making cookies and uh she +would she's just a really really + + align:start position:0% +would she's just a really really + + + align:start position:0% +would she's just a really really +outgoing person like she would travel + + align:start position:0% +outgoing person like she would travel + + + align:start position:0% +outgoing person like she would travel +everywhere she tell me everything about + + align:start position:0% +everywhere she tell me everything about + + + align:start position:0% +everywhere she tell me everything about +it and that was when I was a little kid + + align:start position:0% +it and that was when I was a little kid + + + align:start position:0% +it and that was when I was a little kid +and then when I got into High + + align:start position:0% +and then when I got into High + + + align:start position:0% +and then when I got into High +School uh I came more mature I guess not + + align:start position:0% +School uh I came more mature I guess not + + + align:start position:0% +School uh I came more mature I guess not +really but a little bit and I got to + + align:start position:0% +really but a little bit and I got to + + + align:start position:0% +really but a little bit and I got to +know the way of + + align:start position:0% +know the way of + + + align:start position:0% +know the way of +like kind of like the farm but then um + + align:start position:0% +like kind of like the farm but then um + + + align:start position:0% +like kind of like the farm but then um +when n would tell me about like these + + align:start position:0% +when n would tell me about like these + + + align:start position:0% +when n would tell me about like these +opportunities and these stuff about the + + align:start position:0% +opportunities and these stuff about the + + + align:start position:0% +opportunities and these stuff about the +farm I wouldn't be intrigued by it I + + align:start position:0% +farm I wouldn't be intrigued by it I + + + align:start position:0% +farm I wouldn't be intrigued by it I +think about it but then I like I don't + + align:start position:0% +think about it but then I like I don't + + + align:start position:0% +think about it but then I like I don't +have time for it when really I did and + + align:start position:0% +have time for it when really I did and + + + align:start position:0% +have time for it when really I did and +but now now that when she passed it's + + align:start position:0% +but now now that when she passed it's + + + align:start position:0% +but now now that when she passed it's +just like it really affected me like I + + align:start position:0% +just like it really affected me like I + + + align:start position:0% +just like it really affected me like I +needed to be more involved and I wanted + + align:start position:0% +needed to be more involved and I wanted + + + align:start position:0% +needed to be more involved and I wanted +to do something more more of my life I + + align:start position:0% +to do something more more of my life I + + + align:start position:0% +to do something more more of my life I +guess so Gabby got her start in the + + align:start position:0% +guess so Gabby got her start in the + + + align:start position:0% +guess so Gabby got her start in the +place where we met her the lane Family + + align:start position:0% +place where we met her the lane Family + + + align:start position:0% +place where we met her the lane Family +Farm currently managed by nuna's parents + + align:start position:0% +Farm currently managed by nuna's parents + + + align:start position:0% +Farm currently managed by nuna's parents +Gloria and Harry Lane and her brother + + align:start position:0% +Gloria and Harry Lane and her brother + + + align:start position:0% +Gloria and Harry Lane and her brother +Bruce Lane and although we never got to + + align:start position:0% +Bruce Lane and although we never got to + + + align:start position:0% +Bruce Lane and although we never got to +meet nanaba ourselves she's continued to + + align:start position:0% +meet nanaba ourselves she's continued to + + + align:start position:0% +meet nanaba ourselves she's continued to +have an impact on those around her I was + + align:start position:0% +have an impact on those around her I was + + + align:start position:0% +have an impact on those around her I was +just like yeah I can do this for her and + + align:start position:0% +just like yeah I can do this for her and + + + align:start position:0% +just like yeah I can do this for her and +I I also noticed that the farm need help + + align:start position:0% +I I also noticed that the farm need help + + + align:start position:0% +I I also noticed that the farm need help +because goria is kind of like getting + + align:start position:0% +because goria is kind of like getting + + + align:start position:0% +because goria is kind of like getting +old and Har is getting old and I was + + align:start position:0% +old and Har is getting old and I was + + + align:start position:0% +old and Har is getting old and I was +just like I just need to help them so I + + align:start position:0% +just like I just need to help them so I + + + align:start position:0% +just like I just need to help them so I +first started here I would just come + + align:start position:0% +first started here I would just come + + + align:start position:0% +first started here I would just come +here for maybe 3 days a week for maybe a + + align:start position:0% +here for maybe 3 days a week for maybe a + + + align:start position:0% +here for maybe 3 days a week for maybe a +couple hours but then um goria got me + + align:start position:0% +couple hours but then um goria got me + + + align:start position:0% +couple hours but then um goria got me +connected with Dr Lumbard from + + align:start position:0% +connected with Dr Lumbard from + + + align:start position:0% +connected with Dr Lumbard from +NMSU he works at the AV culture center + + align:start position:0% +NMSU he works at the AV culture center + + + align:start position:0% +NMSU he works at the AV culture center +and I got an internship over there too + + align:start position:0% +and I got an internship over there too + + + align:start position:0% +and I got an internship over there too +so I just started that I think December + + align:start position:0% +so I just started that I think December + + + align:start position:0% +so I just started that I think December +and I'm learning new stuff and while the + + align:start position:0% +and I'm learning new stuff and while the + + + align:start position:0% +and I'm learning new stuff and while the +lane Farm continues Opera ating both as + + align:start position:0% +lane Farm continues Opera ating both as + + + align:start position:0% +lane Farm continues Opera ating both as +a farm and the center of the Navajo ethn + + align:start position:0% +a farm and the center of the Navajo ethn + + + align:start position:0% +a farm and the center of the Navajo ethn +agriculture program co-founded by naaba + + align:start position:0% +agriculture program co-founded by naaba + + + align:start position:0% +agriculture program co-founded by naaba +Gabby is slowly but steadily making + + align:start position:0% +Gabby is slowly but steadily making + + + align:start position:0% +Gabby is slowly but steadily making +progress with her own projects in + + align:start position:0% +progress with her own projects in + + + align:start position:0% +progress with her own projects in +agriculture I'm learn I'm learning + + align:start position:0% +agriculture I'm learn I'm learning + + + align:start position:0% +agriculture I'm learn I'm learning +pruning and I'm learning sea planting + + align:start position:0% +pruning and I'm learning sea planting + + + align:start position:0% +pruning and I'm learning sea planting +with different + + align:start position:0% +with different + + + align:start position:0% +with different +um like experimental seeds I + + align:start position:0% +um like experimental seeds I + + + align:start position:0% +um like experimental seeds I +[Music] + + align:start position:0% + + + + align:start position:0% + +guess while Gabby is working on growing + + align:start position:0% +guess while Gabby is working on growing + + + align:start position:0% +guess while Gabby is working on growing +food others are working on how to get + + align:start position:0% +food others are working on how to get + + + align:start position:0% +food others are working on how to get +the food from the farm to the table + + align:start position:0% +the food from the farm to the table + + + align:start position:0% +the food from the farm to the table +we're very happy that you all came out + + align:start position:0% +we're very happy that you all came out + + + align:start position:0% +we're very happy that you all came out +to visit us today here at our uh our new + + align:start position:0% +to visit us today here at our uh our new + + + align:start position:0% +to visit us today here at our uh our new +little farm area where we're going to be + + align:start position:0% +little farm area where we're going to be + + + align:start position:0% +little farm area where we're going to be +putting together some some new new and + + align:start position:0% +putting together some some new new and + + + align:start position:0% +putting together some some new new and +exciting things hopefully Daniel + + align:start position:0% +exciting things hopefully Daniel + + + align:start position:0% +exciting things hopefully Daniel +goldtooth and her partner Alan Moore + + align:start position:0% +goldtooth and her partner Alan Moore + + + align:start position:0% +goldtooth and her partner Alan Moore +became involved in food sovereignty and + + align:start position:0% +became involved in food sovereignty and + + + align:start position:0% +became involved in food sovereignty and +traditional Navajo Cuisine because of + + align:start position:0% +traditional Navajo Cuisine because of + + + align:start position:0% +traditional Navajo Cuisine because of +one particular food hamburgers he likes + + align:start position:0% +one particular food hamburgers he likes + + + align:start position:0% +one particular food hamburgers he likes +telling the story but I'll tell it this + + align:start position:0% +telling the story but I'll tell it this + + + align:start position:0% +telling the story but I'll tell it this +time we were uh we were cruising through + + align:start position:0% +time we were uh we were cruising through + + + align:start position:0% +time we were uh we were cruising through +uh Phoenix and we were stopping off at a + + align:start position:0% +uh Phoenix and we were stopping off at a + + + align:start position:0% +uh Phoenix and we were stopping off at a +burger joint to you know get a get a + + align:start position:0% +burger joint to you know get a get a + + + align:start position:0% +burger joint to you know get a get a +hamburger and it's a local place maybe + + align:start position:0% +hamburger and it's a local place maybe + + + align:start position:0% +hamburger and it's a local place maybe +about a year ago or so and we go in and + + align:start position:0% +about a year ago or so and we go in and + + + align:start position:0% +about a year ago or so and we go in and +they're like well we don't have any beef + + align:start position:0% +they're like well we don't have any beef + + + align:start position:0% +they're like well we don't have any beef +and we're like we have supply chain + + align:start position:0% +and we're like we have supply chain + + + align:start position:0% +and we're like we have supply chain +issues and we're coming from working as + + align:start position:0% +issues and we're coming from working as + + + align:start position:0% +issues and we're coming from working as +a Slaughter woman and a at a you know + + align:start position:0% +a Slaughter woman and a at a you know + + + align:start position:0% +a Slaughter woman and a at a you know +and a and a butcher so we were very + + align:start position:0% +and a and a butcher so we were very + + + align:start position:0% +and a and a butcher so we were very +befuddled we're like we just came out + + align:start position:0% +befuddled we're like we just came out + + + align:start position:0% +befuddled we're like we just came out +from where these people can't even sell + + align:start position:0% +from where these people can't even sell + + + align:start position:0% +from where these people can't even sell +all of their cows right now what's going + + align:start position:0% +all of their cows right now what's going + + + align:start position:0% +all of their cows right now what's going +on here how am I not having beef you + + align:start position:0% +on here how am I not having beef you + + + align:start position:0% +on here how am I not having beef you +know 50 miles away from where I'm also + + align:start position:0% +know 50 miles away from where I'm also + + + align:start position:0% +know 50 miles away from where I'm also +processing this something here is is not + + align:start position:0% +processing this something here is is not + + + align:start position:0% +processing this something here is is not +right why is this not um uh closer to + + align:start position:0% +right why is this not um uh closer to + + + align:start position:0% +right why is this not um uh closer to +home why are we not having beef where we + + align:start position:0% +home why are we not having beef where we + + + align:start position:0% +home why are we not having beef where we +should be having it but it wasn't just a + + align:start position:0% +should be having it but it wasn't just a + + + align:start position:0% +should be having it but it wasn't just a +supply chain issue Danielle and Allan + + align:start position:0% +supply chain issue Danielle and Allan + + + align:start position:0% +supply chain issue Danielle and Allan +also noticed that the farmers in their + + align:start position:0% +also noticed that the farmers in their + + + align:start position:0% +also noticed that the farmers in their +area were getting older a lot of our + + align:start position:0% +area were getting older a lot of our + + + align:start position:0% +area were getting older a lot of our +elderly are still um farming but our + + align:start position:0% +elderly are still um farming but our + + + align:start position:0% +elderly are still um farming but our +middle-age people and our younger people + + align:start position:0% +middle-age people and our younger people + + + align:start position:0% +middle-age people and our younger people +are not and so it is our Hope by coming + + align:start position:0% +are not and so it is our Hope by coming + + + align:start position:0% +are not and so it is our Hope by coming +back to this this uh space that we're + + align:start position:0% +back to this this uh space that we're + + + align:start position:0% +back to this this uh space that we're +able to uh help Revitalize but also help + + align:start position:0% +able to uh help Revitalize but also help + + + align:start position:0% +able to uh help Revitalize but also help +demonstrate that the daa way of life and + + align:start position:0% +demonstrate that the daa way of life and + + + align:start position:0% +demonstrate that the daa way of life and +uh the way that we have had our + + align:start position:0% +uh the way that we have had our + + + align:start position:0% +uh the way that we have had our +communities put together with a basis of + + align:start position:0% +communities put together with a basis of + + + align:start position:0% +communities put together with a basis of +Agriculture is a way that we can + + align:start position:0% +Agriculture is a way that we can + + + align:start position:0% +Agriculture is a way that we can +continue to move forward in this newer + + align:start position:0% +continue to move forward in this newer + + + align:start position:0% +continue to move forward in this newer +World using technologies that are going + + align:start position:0% +World using technologies that are going + + + align:start position:0% +World using technologies that are going +to be helpful not just for ourselves but + + align:start position:0% +to be helpful not just for ourselves but + + + align:start position:0% +to be helpful not just for ourselves but +for uh the Earth so that's kind of U our + + align:start position:0% +for uh the Earth so that's kind of U our + + + align:start position:0% +for uh the Earth so that's kind of U our +and in essence our our mission um Alan + + align:start position:0% +and in essence our our mission um Alan + + + align:start position:0% +and in essence our our mission um Alan +and I have our own food company called D + + align:start position:0% +and I have our own food company called D + + + align:start position:0% +and I have our own food company called D +enough food start to finish their + + align:start position:0% +enough food start to finish their + + + align:start position:0% +enough food start to finish their +business produces traditional Navajo + + align:start position:0% +business produces traditional Navajo + + + align:start position:0% +business produces traditional Navajo +food starting at their own farm and + + align:start position:0% +food starting at their own farm and + + + align:start position:0% +food starting at their own farm and +finishing at the table they hosted us + + align:start position:0% +finishing at the table they hosted us + + + align:start position:0% +finishing at the table they hosted us +for lunch near where their Farm is + + align:start position:0% +for lunch near where their Farm is + + + align:start position:0% +for lunch near where their Farm is +located and we arrived just in time to + + align:start position:0% +located and we arrived just in time to + + + align:start position:0% +located and we arrived just in time to +watch the final preparations for the + + align:start position:0% +watch the final preparations for the + + + align:start position:0% +watch the final preparations for the +food rocks of mutton pissed and spat on + + align:start position:0% +food rocks of mutton pissed and spat on + + + align:start position:0% +food rocks of mutton pissed and spat on +a grill over a fire outsides charring to + + align:start position:0% +a grill over a fire outsides charring to + + + align:start position:0% +a grill over a fire outsides charring to +form a dark brown black crust bags of + + align:start position:0% +form a dark brown black crust bags of + + + align:start position:0% +form a dark brown black crust bags of +vegetables tumbled into walks sizzling + + align:start position:0% +vegetables tumbled into walks sizzling + + + align:start position:0% +vegetables tumbled into walks sizzling +UNC contact with the hot metal ears of + + align:start position:0% +UNC contact with the hot metal ears of + + + align:start position:0% +UNC contact with the hot metal ears of +corn and foil wrapped potatoes were + + align:start position:0% +corn and foil wrapped potatoes were + + + align:start position:0% +corn and foil wrapped potatoes were +buried all around smoldering Embers + + align:start position:0% +buried all around smoldering Embers + + + align:start position:0% +buried all around smoldering Embers +dusted with + + align:start position:0% + + + + align:start position:0% + +ashes interestingly all this cooking was + + align:start position:0% +ashes interestingly all this cooking was + + + align:start position:0% +ashes interestingly all this cooking was +executed on the ground pits had been dug + + align:start position:0% +executed on the ground pits had been dug + + + align:start position:0% +executed on the ground pits had been dug +out and structured into a cooking area + + align:start position:0% +out and structured into a cooking area + + + align:start position:0% +out and structured into a cooking area +using stone blocks which pots pans and + + align:start position:0% +using stone blocks which pots pans and + + + align:start position:0% +using stone blocks which pots pans and +metal grill grates were set over and as + + align:start position:0% +metal grill grates were set over and as + + + align:start position:0% +metal grill grates were set over and as +we waited we learned that these + + align:start position:0% +we waited we learned that these + + + align:start position:0% +we waited we learned that these +particular Stones actually held special + + align:start position:0% +particular Stones actually held special + + + align:start position:0% +particular Stones actually held special +value for Danielle and her family what + + align:start position:0% +value for Danielle and her family what + + + align:start position:0% +value for Danielle and her family what +we were doing this week uh in + + align:start position:0% +we were doing this week uh in + + + align:start position:0% +we were doing this week uh in +preparation for you all to be here + + align:start position:0% +preparation for you all to be here + + + align:start position:0% +preparation for you all to be here +um the first thing that we actually did + + align:start position:0% +um the first thing that we actually did + + + align:start position:0% +um the first thing that we actually did +was um we took down an old uh an old uh + + align:start position:0% +was um we took down an old uh an old uh + + + align:start position:0% +was um we took down an old uh an old uh +little uh oven a little oven and all of + + align:start position:0% +little uh oven a little oven and all of + + + align:start position:0% +little uh oven a little oven and all of +these little rocks that are here or the + + align:start position:0% +these little rocks that are here or the + + + align:start position:0% +these little rocks that are here or the +big rocks were here were actually + + align:start position:0% +big rocks were here were actually + + + align:start position:0% +big rocks were here were actually +quarried by our um our our forefathers + + align:start position:0% +quarried by our um our our forefathers + + + align:start position:0% +quarried by our um our our forefathers +this uh this specific one was probably + + align:start position:0% +this uh this specific one was probably + + + align:start position:0% +this uh this specific one was probably +from our great great great great + + align:start position:0% +from our great great great great + + + align:start position:0% +from our great great great great +grandfathers Hogan and they hand + + align:start position:0% +grandfathers Hogan and they hand + + + align:start position:0% +grandfathers Hogan and they hand +quarried these Stones themselves and + + align:start position:0% +quarried these Stones themselves and + + + align:start position:0% +quarried these Stones themselves and +this used to be a part of a a Hogan um a + + align:start position:0% +this used to be a part of a a Hogan um a + + + align:start position:0% +this used to be a part of a a Hogan um a +traditional Navajo home out near the + + align:start position:0% +traditional Navajo home out near the + + + align:start position:0% +traditional Navajo home out near the +ship rock rock area um as the years have + + align:start position:0% +ship rock rock area um as the years have + + + align:start position:0% +ship rock rock area um as the years have +gone by we've reused these Stones um + + align:start position:0% +gone by we've reused these Stones um + + + align:start position:0% +gone by we've reused these Stones um +over and over for uh fire pits or for + + align:start position:0% +over and over for uh fire pits or for + + + align:start position:0% +over and over for uh fire pits or for +our uh for our um our cooking Adobes and + + align:start position:0% +our uh for our um our cooking Adobes and + + + align:start position:0% +our uh for our um our cooking Adobes and +such as the intense winds blew wood + + align:start position:0% +such as the intense winds blew wood + + + align:start position:0% +such as the intense winds blew wood +smoke and the mouthwatering Aromas of + + align:start position:0% +smoke and the mouthwatering Aromas of + + + align:start position:0% +smoke and the mouthwatering Aromas of +grilling meat STD fried vegetables and + + align:start position:0% +grilling meat STD fried vegetables and + + + align:start position:0% +grilling meat STD fried vegetables and +roasted corn Tor us Danielle introduced + + align:start position:0% +roasted corn Tor us Danielle introduced + + + align:start position:0% +roasted corn Tor us Danielle introduced +the menu for the day consisting of + + align:start position:0% +the menu for the day consisting of + + + align:start position:0% +the menu for the day consisting of +traditional Navajo recipes made using + + align:start position:0% +traditional Navajo recipes made using + + + align:start position:0% +traditional Navajo recipes made using +Farm Fresh inred ingredients this is uh + + align:start position:0% +Farm Fresh inred ingredients this is uh + + + align:start position:0% +Farm Fresh inred ingredients this is uh +what we would love to offer you we have + + align:start position:0% +what we would love to offer you we have + + + align:start position:0% +what we would love to offer you we have +a three sister soup um for our + + align:start position:0% +a three sister soup um for our + + + align:start position:0% +a three sister soup um for our +vegetarian folks uh we have a I believe + + align:start position:0% +vegetarian folks uh we have a I believe + + + align:start position:0% +vegetarian folks uh we have a I believe +it's going to be uh anastasi beans with + + align:start position:0% +it's going to be uh anastasi beans with + + + align:start position:0% +it's going to be uh anastasi beans with +a split pea um yellow pea uh Pino beans + + align:start position:0% +a split pea um yellow pea uh Pino beans + + + align:start position:0% +a split pea um yellow pea uh Pino beans +and a few other uh beans that you would + + align:start position:0% +and a few other uh beans that you would + + + align:start position:0% +and a few other uh beans that you would +have found in this area that were um + + align:start position:0% +have found in this area that were um + + + align:start position:0% +have found in this area that were um +traditionally brought here by uh and + + align:start position:0% +traditionally brought here by uh and + + + align:start position:0% +traditionally brought here by uh and +cultivated by the Anasazi + + align:start position:0% +cultivated by the Anasazi + + + align:start position:0% +cultivated by the Anasazi +themselves for those of you who are our + + align:start position:0% +themselves for those of you who are our + + + align:start position:0% +themselves for those of you who are our +meat eaters uh the other thing that's + + align:start position:0% +meat eaters uh the other thing that's + + + align:start position:0% +meat eaters uh the other thing that's +special about these ribs is uh my + + align:start position:0% +special about these ribs is uh my + + + align:start position:0% +special about these ribs is uh my +grandmother went and she picked out a + + align:start position:0% +grandmother went and she picked out a + + + align:start position:0% +grandmother went and she picked out a +chi chin which is a red berry um + + align:start position:0% +chi chin which is a red berry um + + + align:start position:0% +chi chin which is a red berry um +sumac and the food was + + align:start position:0% +sumac and the food was + + + align:start position:0% +sumac and the food was +delicious before we left we asked + + align:start position:0% +delicious before we left we asked + + + align:start position:0% +delicious before we left we asked +Danielle about the significance of her + + align:start position:0% +Danielle about the significance of her + + + align:start position:0% +Danielle about the significance of her +work I imagine that our impact is going + + align:start position:0% +work I imagine that our impact is going + + + align:start position:0% +work I imagine that our impact is going +to be very small but that's okay as long + + align:start position:0% +to be very small but that's okay as long + + + align:start position:0% +to be very small but that's okay as long +as we're we're doing this for our + + align:start position:0% +as we're we're doing this for our + + + align:start position:0% +as we're we're doing this for our +community and we have our hearts in it + + align:start position:0% +community and we have our hearts in it + + + align:start position:0% +community and we have our hearts in it +that's uh what matters to us + + align:start position:0% +that's uh what matters to us + + + align:start position:0% +that's uh what matters to us +[Music] + + align:start position:0% + + + + align:start position:0% + +it seems that it's not just the + + align:start position:0% +it seems that it's not just the + + + align:start position:0% +it seems that it's not just the +surrounding land that is sacred for the + + align:start position:0% +surrounding land that is sacred for the + + + align:start position:0% +surrounding land that is sacred for the +Denette people we met they also Place + + align:start position:0% +Denette people we met they also Place + + + align:start position:0% +Denette people we met they also Place +purpose in their actions and how they + + align:start position:0% +purpose in their actions and how they + + + align:start position:0% +purpose in their actions and how they +pursue their goals so what seems + + align:start position:0% +pursue their goals so what seems + + + align:start position:0% +pursue their goals so what seems +immediately ordinary and everyday such + + align:start position:0% +immediately ordinary and everyday such + + + align:start position:0% +immediately ordinary and everyday such +as farming could hold deeper and richer + + align:start position:0% +as farming could hold deeper and richer + + + align:start position:0% +as farming could hold deeper and richer +meanings reflecting back on the trip + + align:start position:0% +meanings reflecting back on the trip + + + align:start position:0% +meanings reflecting back on the trip +this idea was definitely something that + + align:start position:0% +this idea was definitely something that + + + align:start position:0% +this idea was definitely something that +resonated with each of us we couldn't + + align:start position:0% +resonated with each of us we couldn't + + + align:start position:0% +resonated with each of us we couldn't +help thinking about about our own lives + + align:start position:0% +help thinking about about our own lives + + + align:start position:0% +help thinking about about our own lives +why do we do the things that we do and + + align:start position:0% +why do we do the things that we do and + + + align:start position:0% +why do we do the things that we do and +what if any is the greater meaning in + + align:start position:0% +what if any is the greater meaning in + + + align:start position:0% +what if any is the greater meaning in +our everyday + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +actions this show was produced by the + + align:start position:0% +actions this show was produced by the + + + align:start position:0% +actions this show was produced by the +spring 2023 MIT terc radio class sheener + + align:start position:0% +spring 2023 MIT terc radio class sheener + + + align:start position:0% +spring 2023 MIT terc radio class sheener +low Jaclyn praa Nea stovich and Alisa + + align:start position:0% +low Jaclyn praa Nea stovich and Alisa + + + align:start position:0% +low Jaclyn praa Nea stovich and Alisa +sha the Periscope radio class is a part + + align:start position:0% +sha the Periscope radio class is a part + + + align:start position:0% +sha the Periscope radio class is a part +of MIT Periscope a learning community + + align:start position:0% +of MIT Periscope a learning community + + + align:start position:0% +of MIT Periscope a learning community +for first year undergraduate students + + align:start position:0% +for first year undergraduate students + + + align:start position:0% +for first year undergraduate students +focused on solving complex environmental + + align:start position:0% +focused on solving complex environmental + + + align:start position:0% +focused on solving complex environmental +problems the class was developed in + + align:start position:0% +problems the class was developed in + + + align:start position:0% +problems the class was developed in +collaboration with mit's comparative + + align:start position:0% +collaboration with mit's comparative + + + align:start position:0% +collaboration with mit's comparative +media studies + + align:start position:0% +media studies + + + align:start position:0% +media studies +program we would like to thank the + + align:start position:0% +program we would like to thank the + + + align:start position:0% +program we would like to thank the +members of the MIT Periscope Community + + align:start position:0% +members of the MIT Periscope Community + + + align:start position:0% +members of the MIT Periscope Community +director David M Community coordinator + + align:start position:0% +director David M Community coordinator + + + align:start position:0% +director David M Community coordinator +Michelle Kos and associate director and + + align:start position:0% +Michelle Kos and associate director and + + + align:start position:0% +Michelle Kos and associate director and +lecturer Ari Epstein Ari Epstein is also + + align:start position:0% +lecturer Ari Epstein Ari Epstein is also + + + align:start position:0% +lecturer Ari Epstein Ari Epstein is also +our instructor for teris scope radio + + align:start position:0% +our instructor for teris scope radio + + + align:start position:0% +our instructor for teris scope radio +along with the undergraduate teaching + + align:start position:0% +along with the undergraduate teaching + + + align:start position:0% +along with the undergraduate teaching +fellows Richard Chen and Athena Wong who + + align:start position:0% +fellows Richard Chen and Athena Wong who + + + align:start position:0% +fellows Richard Chen and Athena Wong who +gave much support and feedback + + align:start position:0% +gave much support and feedback + + + align:start position:0% +gave much support and feedback +throughout the + + align:start position:0% +throughout the + + + align:start position:0% +throughout the +class we would also like to thank + + align:start position:0% +class we would also like to thank + + + align:start position:0% +class we would also like to thank +everyone who made the Periscope spring + + align:start position:0% +everyone who made the Periscope spring + + + align:start position:0% +everyone who made the Periscope spring +break trip possible Joel Grimm Libby Shu + + align:start position:0% +break trip possible Joel Grimm Libby Shu + + + align:start position:0% +break trip possible Joel Grimm Libby Shu +Ben tiger and vippy Y as well as the + + align:start position:0% +Ben tiger and vippy Y as well as the + + + align:start position:0% +Ben tiger and vippy Y as well as the +people who talked to us throughout our + + align:start position:0% +people who talked to us throughout our + + + align:start position:0% +people who talked to us throughout our +trip Steve sekin Danielle goldtooth and + + align:start position:0% +trip Steve sekin Danielle goldtooth and + + + align:start position:0% +trip Steve sekin Danielle goldtooth and +Alan Moore Tony and cor goldtooth Lula + + align:start position:0% +Alan Moore Tony and cor goldtooth Lula + + + align:start position:0% +Alan Moore Tony and cor goldtooth Lula +sandal Brandon Francis and Karen Denny + + align:start position:0% +sandal Brandon Francis and Karen Denny + + + align:start position:0% +sandal Brandon Francis and Karen Denny +Kevin Lombard Adrian oi Gabrielle + + align:start position:0% +Kevin Lombard Adrian oi Gabrielle + + + align:start position:0% +Kevin Lombard Adrian oi Gabrielle +Henderson Gloria Harry and Bruce Lane + + align:start position:0% +Henderson Gloria Harry and Bruce Lane + + + align:start position:0% +Henderson Gloria Harry and Bruce Lane +Bri Laman Dean Dempsey Cindy how and + + align:start position:0% +Bri Laman Dean Dempsey Cindy how and + + + align:start position:0% +Bri Laman Dean Dempsey Cindy how and +Daryl Jones without these amazing and + + align:start position:0% +Daryl Jones without these amazing and + + + align:start position:0% +Daryl Jones without these amazing and +wonderful people this program would have + + align:start position:0% +wonderful people this program would have + + + align:start position:0% +wonderful people this program would have +truly been + + align:start position:0% +truly been + + + align:start position:0% +truly been +Impossible music from Blue Dot sessions + + align:start position:0% +Impossible music from Blue Dot sessions + + + align:start position:0% +Impossible music from Blue Dot sessions +thank you for listening + + align:start position:0% + + + + align:start position:0% + +you can find this episode and all the + + align:start position:0% +you can find this episode and all the + + + align:start position:0% +you can find this episode and all the +other terrascope radio episodes on the + + align:start position:0% +other terrascope radio episodes on the + + + align:start position:0% +other terrascope radio episodes on the +Periscope website which we'll share in + + align:start position:0% +Periscope website which we'll share in + + + align:start position:0% +Periscope website which we'll share in +the show notes signing off from + + align:start position:0% +the show notes signing off from + + + align:start position:0% +the show notes signing off from +Cambridge Massachusetts I'm Sarah Hansen + + align:start position:0% +Cambridge Massachusetts I'm Sarah Hansen + + + align:start position:0% +Cambridge Massachusetts I'm Sarah Hansen +from MIT open courseware \ No newline at end of file diff --git a/Gb5o6VNboV0.txt b/Gb5o6VNboV0.txt new file mode 100644 index 0000000000000000000000000000000000000000..db61a12f44645cb70c56cadba6837b2cc714d339 --- /dev/null +++ b/Gb5o6VNboV0.txt @@ -0,0 +1,1003 @@ +align:start position:0% + +the damped vibrations applet illustrates + + align:start position:0% +the damped vibrations applet illustrates + + + align:start position:0% +the damped vibrations applet illustrates +several different concepts related to + + align:start position:0% +several different concepts related to + + + align:start position:0% +several different concepts related to +differential equations initial + + align:start position:0% +differential equations initial + + + align:start position:0% +differential equations initial +conditions for second order equations + + align:start position:0% +conditions for second order equations + + + align:start position:0% +conditions for second order equations +the phase plane for autonomous equations + + align:start position:0% +the phase plane for autonomous equations + + + align:start position:0% +the phase plane for autonomous equations +and damping conditions for second order + + align:start position:0% +and damping conditions for second order + + + align:start position:0% +and damping conditions for second order +homogeneous linear + + align:start position:0% +homogeneous linear + + + align:start position:0% +homogeneous linear +equations the differential we're + + align:start position:0% +equations the differential we're + + + align:start position:0% +equations the differential we're +studying appears at upper + + align:start position:0% +studying appears at upper + + + align:start position:0% +studying appears at upper +right the parameter names reflect the + + align:start position:0% +right the parameter names reflect the + + + align:start position:0% +right the parameter names reflect the +fact that this equation describes a mass + + align:start position:0% +fact that this equation describes a mass + + + align:start position:0% +fact that this equation describes a mass +spring dashpot system with mass m Das + + align:start position:0% +spring dashpot system with mass m Das + + + align:start position:0% +spring dashpot system with mass m Das +pot constant B and spring constant K the + + align:start position:0% +pot constant B and spring constant K the + + + align:start position:0% +pot constant B and spring constant K the +right hand side of the equation is zero + + align:start position:0% +right hand side of the equation is zero + + + align:start position:0% +right hand side of the equation is zero +there's no forcing term the equation is + + align:start position:0% +there's no forcing term the equation is + + + align:start position:0% +there's no forcing term the equation is +homogeneous the sliders at bottom + + align:start position:0% +homogeneous the sliders at bottom + + + align:start position:0% +homogeneous the sliders at bottom +control the values of the system + + align:start position:0% +control the values of the system + + + align:start position:0% +control the values of the system +parameters with the selected values for + + align:start position:0% +parameters with the selected values for + + + align:start position:0% +parameters with the selected values for +M B and K the solutions are damped + + align:start position:0% +M B and K the solutions are damped + + + align:start position:0% +M B and K the solutions are damped +vibrations I can let the solution evolve + + align:start position:0% +vibrations I can let the solution evolve + + + align:start position:0% +vibrations I can let the solution evolve +by grabbing the time + + align:start position:0% +by grabbing the time + + + align:start position:0% +by grabbing the time +slider or by using using the animation + + align:start position:0% +slider or by using using the animation + + + align:start position:0% +slider or by using using the animation +key which also serves to stop the + + align:start position:0% +key which also serves to stop the + + + align:start position:0% +key which also serves to stop the +animation if the value of the solution + + align:start position:0% +animation if the value of the solution + + + align:start position:0% +animation if the value of the solution +gets too small I can blow the picture up + + align:start position:0% +gets too small I can blow the picture up + + + align:start position:0% +gets too small I can blow the picture up +using the zoom slider at the upper left + + align:start position:0% +using the zoom slider at the upper left + + + align:start position:0% +using the zoom slider at the upper left +moving it to the right squeezes the + + align:start position:0% +moving it to the right squeezes the + + + align:start position:0% +moving it to the right squeezes the +solutions moving it to the left makes + + align:start position:0% +solutions moving it to the left makes + + + align:start position:0% +solutions moving it to the left makes +them + + align:start position:0% + + + + align:start position:0% + +larger the window on the left lets you + + align:start position:0% +larger the window on the left lets you + + + align:start position:0% +larger the window on the left lets you +set the initial condition of this system + + align:start position:0% +set the initial condition of this system + + + align:start position:0% +set the initial condition of this system +there there are two components to the + + align:start position:0% +there there are two components to the + + + align:start position:0% +there there are two components to the +initial condition of a second order + + align:start position:0% +initial condition of a second order + + + align:start position:0% +initial condition of a second order +equation position and velocity that is x + + align:start position:0% +equation position and velocity that is x + + + align:start position:0% +equation position and velocity that is x +and x + + align:start position:0% +and x + + + align:start position:0% +and x +dot together they form the coordinates + + align:start position:0% +dot together they form the coordinates + + + align:start position:0% +dot together they form the coordinates +of a point on this plane I can grab the + + align:start position:0% +of a point on this plane I can grab the + + + align:start position:0% +of a point on this plane I can grab the +point and change both x and x Prime + + align:start position:0% + + + + align:start position:0% + +simultaneously the x coordinate is + + align:start position:0% +simultaneously the x coordinate is + + + align:start position:0% +simultaneously the x coordinate is +written vertically because that's how + + align:start position:0% +written vertically because that's how + + + align:start position:0% +written vertically because that's how +it's written on the right hand graphing + + align:start position:0% +it's written on the right hand graphing + + + align:start position:0% +it's written on the right hand graphing +window and you can see that they keep + + align:start position:0% +window and you can see that they keep + + + align:start position:0% +window and you can see that they keep +Pace with each other the horizontal + + align:start position:0% +Pace with each other the horizontal + + + align:start position:0% +Pace with each other the horizontal +component is x dot the initial velocity + + align:start position:0% +component is x dot the initial velocity + + + align:start position:0% +component is x dot the initial velocity +that's positive when we're to the right + + align:start position:0% +that's positive when we're to the right + + + align:start position:0% +that's positive when we're to the right +and becomes negative when we're to the + + align:start position:0% + + + + align:start position:0% + +left the left window represents phase + + align:start position:0% +left the left window represents phase + + + align:start position:0% +left the left window represents phase +space for any time T the values of x and + + align:start position:0% +space for any time T the values of x and + + + align:start position:0% +space for any time T the values of x and +x dot are the coordinates of a point in + + align:start position:0% +x dot are the coordinates of a point in + + + align:start position:0% +x dot are the coordinates of a point in +in Phase space and and as the solution + + align:start position:0% +in Phase space and and as the solution + + + align:start position:0% +in Phase space and and as the solution +evolves through time that point follows + + align:start position:0% +evolves through time that point follows + + + align:start position:0% +evolves through time that point follows +a path sweeps out a path in Phase + + align:start position:0% +a path sweeps out a path in Phase + + + align:start position:0% +a path sweeps out a path in Phase +space in with these selected choices of + + align:start position:0% +space in with these selected choices of + + + align:start position:0% +space in with these selected choices of +MB and K the path is a spiral this + + align:start position:0% +MB and K the path is a spiral this + + + align:start position:0% +MB and K the path is a spiral this +reflects the fact that both x and x dot + + align:start position:0% +reflects the fact that both x and x dot + + + align:start position:0% +reflects the fact that both x and x dot +undergo a damped + + align:start position:0% +undergo a damped + + + align:start position:0% +undergo a damped +vibration the system parameters can be + + align:start position:0% +vibration the system parameters can be + + + align:start position:0% +vibration the system parameters can be +set using these sliders at lower left + + align:start position:0% +set using these sliders at lower left + + + align:start position:0% +set using these sliders at lower left +let's adjust the mass to to be 1 12 and + + align:start position:0% +let's adjust the mass to to be 1 12 and + + + align:start position:0% +let's adjust the mass to to be 1 12 and +leave K to be one and watch what happens + + align:start position:0% +leave K to be one and watch what happens + + + align:start position:0% +leave K to be one and watch what happens +to the solutions as we vary the damping + + align:start position:0% +to the solutions as we vary the damping + + + align:start position:0% +to the solutions as we vary the damping +constant + + align:start position:0% +constant + + + align:start position:0% +constant +B when B is + + align:start position:0% +B when B is + + + align:start position:0% +B when B is +small the solution doesn't damp out as + + align:start position:0% +small the solution doesn't damp out as + + + align:start position:0% +small the solution doesn't damp out as +quickly and when B is large it damps out + + align:start position:0% +quickly and when B is large it damps out + + + align:start position:0% +quickly and when B is large it damps out +more + + align:start position:0% + + + + align:start position:0% + +quickly these things become much clearer + + align:start position:0% +quickly these things become much clearer + + + align:start position:0% +quickly these things become much clearer +when you think about them in terms of + + align:start position:0% +when you think about them in terms of + + + align:start position:0% +when you think about them in terms of +the roots of the characteristic + + align:start position:0% +the roots of the characteristic + + + align:start position:0% +the roots of the characteristic +polinomial of this equation and we can + + align:start position:0% +polinomial of this equation and we can + + + align:start position:0% +polinomial of this equation and we can +display those roots by clicking The + + align:start position:0% +display those roots by clicking The + + + align:start position:0% +display those roots by clicking The +Roots button + + align:start position:0% +Roots button + + + align:start position:0% +Roots button +here what's shown here is the comp + + align:start position:0% +here what's shown here is the comp + + + align:start position:0% +here what's shown here is the comp +complex plane with the roots of the + + align:start position:0% +complex plane with the roots of the + + + align:start position:0% +complex plane with the roots of the +characteristic polinomial drawn on it + + align:start position:0% +characteristic polinomial drawn on it + + + align:start position:0% +characteristic polinomial drawn on it +also we have a read out of the two roots + + align:start position:0% +also we have a read out of the two roots + + + align:start position:0% +also we have a read out of the two roots +in green over here so let's watch what + + align:start position:0% +in green over here so let's watch what + + + align:start position:0% +in green over here so let's watch what +happens when we CH when we adjust B I'm + + align:start position:0% +happens when we CH when we adjust B I'm + + + align:start position:0% +happens when we CH when we adjust B I'm +going to start with b equal to + + align:start position:0% +going to start with b equal to + + + align:start position:0% +going to start with b equal to +zero in this case there's no damping the + + align:start position:0% +zero in this case there's no damping the + + + align:start position:0% +zero in this case there's no damping the +solutions are + + align:start position:0% +solutions are + + + align:start position:0% +solutions are +sinusoidal the roots of the + + align:start position:0% +sinusoidal the roots of the + + + align:start position:0% +sinusoidal the roots of the +characteristic polinomial are purely + + align:start position:0% +characteristic polinomial are purely + + + align:start position:0% +characteristic polinomial are purely +imaginary and the trajectory in Phase + + align:start position:0% +imaginary and the trajectory in Phase + + + align:start position:0% +imaginary and the trajectory in Phase +space is an ellipse both the solution + + align:start position:0% +space is an ellipse both the solution + + + align:start position:0% +space is an ellipse both the solution +and its derivative vary + + align:start position:0% +and its derivative vary + + + align:start position:0% +and its derivative vary +sinusoidally as I increase B away from + + align:start position:0% +sinusoidally as I increase B away from + + + align:start position:0% +sinusoidally as I increase B away from +zero I get + + align:start position:0% +zero I get + + + align:start position:0% +zero I get +Spirals and at the same time the roots + + align:start position:0% +Spirals and at the same time the roots + + + align:start position:0% +Spirals and at the same time the roots +move off the imaginary axis they acquire + + align:start position:0% +move off the imaginary axis they acquire + + + align:start position:0% +move off the imaginary axis they acquire +a negative real part which is minus B + + align:start position:0% +a negative real part which is minus B + + + align:start position:0% +a negative real part which is minus B +over 2m + + align:start position:0% +over 2m + + + align:start position:0% +over 2m +incidentally and as I increase B + + align:start position:0% +incidentally and as I increase B + + + align:start position:0% +incidentally and as I increase B +further the spiral opens up the damping + + align:start position:0% +further the spiral opens up the damping + + + align:start position:0% +further the spiral opens up the damping +occurs more quickly The Roots move away + + align:start position:0% +occurs more quickly The Roots move away + + + align:start position:0% +occurs more quickly The Roots move away +from the imaginary axis they increase + + align:start position:0% +from the imaginary axis they increase + + + align:start position:0% +from the imaginary axis they increase +their the size of their real + + align:start position:0% +their the size of their real + + + align:start position:0% +their the size of their real +part the damping occurs more quickly and + + align:start position:0% +part the damping occurs more quickly and + + + align:start position:0% +part the damping occurs more quickly and +you'll notice that they get closer and + + align:start position:0% +you'll notice that they get closer and + + + align:start position:0% +you'll notice that they get closer and +closer to the IM the real axis as well + + align:start position:0% +closer to the IM the real axis as well + + + align:start position:0% +closer to the IM the real axis as well +their imaginary part is is decreasing + + align:start position:0% +their imaginary part is is decreasing + + + align:start position:0% +their imaginary part is is decreasing +that means that the circular frequency + + align:start position:0% +that means that the circular frequency + + + align:start position:0% +that means that the circular frequency +the angular frequency of the solution is + + align:start position:0% +the angular frequency of the solution is + + + align:start position:0% +the angular frequency of the solution is +decreasing the period or pseudo period + + align:start position:0% +decreasing the period or pseudo period + + + align:start position:0% +decreasing the period or pseudo period +of the solution is decreasing you can + + align:start position:0% +of the solution is decreasing you can + + + align:start position:0% +of the solution is decreasing you can +see that in the graph but it's much + + align:start position:0% +see that in the graph but it's much + + + align:start position:0% +see that in the graph but it's much +clearer to see what's happening to these + + align:start position:0% +clearer to see what's happening to these + + + align:start position:0% +clearer to see what's happening to these +roots of the characteristic polinomial + + align:start position:0% +roots of the characteristic polinomial + + + align:start position:0% +roots of the characteristic polinomial +they're converging on the real axis and + + align:start position:0% +they're converging on the real axis and + + + align:start position:0% +they're converging on the real axis and +eventually they merge into a double root + + align:start position:0% +eventually they merge into a double root + + + align:start position:0% +eventually they merge into a double root +on the real axis this is critical + + align:start position:0% +on the real axis this is critical + + + align:start position:0% +on the real axis this is critical +damping + + align:start position:0% + + + + align:start position:0% + +from the readout we see that it seems to + + align:start position:0% +from the readout we see that it seems to + + + align:start position:0% +from the readout we see that it seems to +occur at about uh we seem we see that + + align:start position:0% +occur at about uh we seem we see that + + + align:start position:0% +occur at about uh we seem we see that +the uh value of B seems to be about + + align:start position:0% +the uh value of B seems to be about + + + align:start position:0% +the uh value of B seems to be about +1.41 why don't you take a moment and + + align:start position:0% +1.41 why don't you take a moment and + + + align:start position:0% +1.41 why don't you take a moment and +calculate what B is for these values of + + align:start position:0% +calculate what B is for these values of + + + align:start position:0% +calculate what B is for these values of +M and K when critical damping + + align:start position:0% + + + + align:start position:0% + +occurs if we continue to increase B + + align:start position:0% +occurs if we continue to increase B + + + align:start position:0% +occurs if we continue to increase B +Beyond critical damping + + align:start position:0% +Beyond critical damping + + + align:start position:0% +Beyond critical damping +Now The Roots move out on the real axis + + align:start position:0% +Now The Roots move out on the real axis + + + align:start position:0% +Now The Roots move out on the real axis +the there are two exponential Solutions + + align:start position:0% +the there are two exponential Solutions + + + align:start position:0% +the there are two exponential Solutions +and the general solution is a linear + + align:start position:0% +and the general solution is a linear + + + align:start position:0% +and the general solution is a linear +combination of + + align:start position:0% +combination of + + + align:start position:0% +combination of +them and there's no oscillation in any + + align:start position:0% +them and there's no oscillation in any + + + align:start position:0% +them and there's no oscillation in any +solution \ No newline at end of file diff --git a/HIMxdWDLEK8.txt b/HIMxdWDLEK8.txt new file mode 100644 index 0000000000000000000000000000000000000000..70c28fc7d706da1f14a5c0bc09f799b455d1ea6f --- /dev/null +++ b/HIMxdWDLEK8.txt @@ -0,0 +1,2465 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +JOHN TSITSIKLIS: So what we're +going to do is to review what + +we have discussed last time. + +Then we're going to talk about +the classic application of + +Markov chains to analyze +how do you + +dimension a phone system. + +And finally, there will be +two new things today. + +We will see how we can calculate +certain interesting + +quantities that have to +do with Markov chains. + +So let us start. + +We've got our Markov chain and +let's make the assumption that + +our chain is kind of nice. + +And by nice we mean that +we've got maybe + +some transient states. + +And then we've got a single +recurrent class + +of recurrent states. + +So this is a single recurrent +class in the sense that from + +any state in that class you can +get to any other state. + +So once you're in here you're +going to circulate and keep + +visiting all of those states. + +Those states appear transient. + +The trajectory may move around +here, but eventually one of + +these transitions will happen +and you're going to + +end up in this lump. + +Let's make the assumption that +the single recurrent class is + +not periodic. + +These are the nicest kind +of Markov chains. + +And they're nicest because +they have the following + +property, the probability that +you find yourself at some + +particular state j at +the time n when that + +time is very large. + +That probability settles to a +steady state value that we + +denote by pi sub j. + +And there are two parts +in the statement. + +One part is that this +limit exists. + +So the probability of state j +settles to something, and + +furthermore that probability +is not affected by i. + +It doesn't matter where you +started, no matter where you + +started, the probability of +state j is going to be the + +same in the long run. + +Maybe a clearer notation +could be of this form. + +The probability of being at +state j given the initial + +state being i is equal to +pi(j) in the limit. + +Now, if I don't tell you where +you started and you look at + +the unconditional probability +of being at state i, you can + +average over the initial +states, use the total + +expectation theorem and you're +going to get the same answer + +pi(j) in the limit. + +So this tells you that to the +conditional probability given + +the initial state in the limit +is the same as the + +unconditional probability. + +And that's a situation that we +recognize as being one where + +we have independence. + +So what this result tells +us is that Xn and Xi are + +approximately independent. + +They become independent in the +limit as n goes to infinity. + +So that's what the steady +state theorem tells us. + +The initial conditions don't +matter, so your state at some + +large time n has nothing to do, +is not affected by what + +your initial state was. + +Knowing the initial state +doesn't tell you anything + +about your state at time +n, therefore the + +states at the times-- + +sorry that should be a 1, +or it should be a 0 -- + +so the state is not affected by +where the process started. + +So if the Markov chain is to +operate for a long time and + +we're interested in the question +where is the state, + +then your answer would be, I +don't know, it's random. + +But it's going to be a +particular j with this + +particular probability. + +So the steady state +probabilities are interesting + +to us and that raises +the question of how + +do we compute them. + +The way we compute them is by +solving a linear system of + +equations, which are called +the balance equations, + +together with an extra equation, +the normalization + +equation that has to be +satisfied by probability, + +because probabilities must +always add up to 1. + +We talked about the +interpretation of this + +equation last time. + +It's basically a conservation +of probability + +flow in some sense. + +What comes in must get out. + +The probability of finding +yourself at state j at a + +particular time is the total +probability of the last + +transition taking +me into state j. + +The last transition takes me +into state j in various ways. + +It could be that the previous +time I was at the particular + +state, j and i made a transition +from k into j. + +So this number here, we +interpret as the frequency + +with which transitions +of these particular + +type k to j, occur. + +And then by adding over all k's +we consider transitions of + +all types that lead +us inside state j. + +So the probability of being at +the j is the sum total of the + +probabilities of +getting into j. + +What if we had multiple +recurrent classes? + +So if we take this picture +and change it to this. + +So here we got a secondary +recurrent class. + +If you're here, you +cannot get there. + +If you are here, you +cannot get there. + +What happens in the long run? + +Well, in the long run, if you +start from here you're going + +to make a transition eventually, +either of this + +type and you would end up +here, or you will make a + +transitional of that type and +you will end up there. + +If you end up here, the long +term statistics of your chain, + +that is, the probabilities of +the different states, will be + +the steady state probabilities +of this + +chain regarded in isolation. + +So you go ahead and you solve +this system of equations just + +for this chain, and these will +be your steady state + +probabilities. + +If you happened to +get in here. + +If, on the other hand, it +happens that you went there, + +given that event, then what +happens in the long run has to + +do with just this chain +running by itself. + +So you find the steady +state probabilities + +inside that sub chain. + +So you solve the linear system, +the steady state + +equations, for this chain +separately and for that chain + +separately. + +If you happen to start inside +here then the steady state + +probabilities for this sub +chain are going to apply. + +Now of course this raises the +question, if I start here, how + +do I know whether I'm going +to get here or there? + +Well, you don't know, +it's random. + +It may turn out that you get to +here, it may turn out that + +you get there. + +So we will be interested in +calculating the probabilities + +that eventually you end up here +versus the probability + +that eventually you +end up there. + +This is something that we're +going to do towards the end of + +today's lecture. + +So, as a warm up, just to see +how we interpret those steady + +state probabilities, let us look +at our familiar example. + +This is a 2-state +Markov chain. + +Last time we did write down the +balance equations for this + +chain and we found the steady +state probabilities to be 2/7 + +and 5/7 respectively. + +So let us try to calculate +some quantities. + +Suppose that you start at +state 1, and you want to + +calculate to this particular +probability. + +So since we're assuming that +we're starting at state 1, + +essentially here we are +conditioning on the initial + +state being equal to 1. + +Now the conditional probability +of two things + +happening is the probability +that the first thing happens. + +But we're living in the world +where we said that the initial + +state was 1. + +And then given that this thing +happened, the probability that + +the second thing happens. + +But again, we're talking about +conditional probabilities + +given that the initial +state was 1. + +So what is this quantity? + +This one is the transition +probability from state 1 to + +state 1, so it's P11. + +How about the second +probability? + +So given that you started at 1 +and the next time you were at + +1, what's the probability that +at the time 100 you are at 1? + +Now because of the Markov +property, if I tell you that + +at this time you are +at 1, it doesn't + +matter how you get there. + +So this part of the conditioning +doesn't matter. + +And what we have is the 99 step +transition probability + +from state 1 to state 1. + +So the probability that you +get to 1 and then 99 steps + +later you find yourself again at +one is the probability that + +the first transition takes you +to 1 times the probability + +that over the next 99 +transitions starting from 1, + +after 99 steps you end +up again at state 1. + +Now, 99 is possibly a big +number, and so we approximate + +this quantity. + +We're using the steady state +probability of state 1. + +And that gives us an +approximation for this + +particular expression. + +We can do the same thing +to calculate + +something of the same kind. + +So you start at state 1. + +What's the probability that 100 +steps later you are again + +at state 1? + +So that's going to be P11-- + +not P -- + +R11. + +The 100 step transition +probability that starting from + +1 you get to 1, and then after +you get to 1 at time 100 + +what's the probability that +the next time you find + +yourself at state 2? + +This is going to be the +probability P12. + +And approximately, since 100 +is a large number, this is + +approximately pi(1) times P12. + +OK. + +So that's how we can use steady +state probabilities to + +make approximations. + +Or you could, for example, if +you continue doing examples of + +this kind, you could ask for +what's the probability that X + +at time 100 is 1, and also X +at time 200 is equal to 1. + +Then this is going to be the +transition probability from 1 + +to 1 in 100 steps, and then over +the next 100 steps from 1 + +you get again to 1. + +And this is going to be + +approximately pi(1) times pi(1). + +So we approximate multi-step +transition probabilities by + +the steady state probabilities +when the number n that's + +involved in here is big. + +Now I said that's 99 +or 100 is big. + +How do we know that it's big +enough so that the limit has + +taken effect, and that our +approximation is good? + +This has something to do with +the time scale of our Markov + +chain, and by time scale, I mean +how long does it take for + +the initial states +to be forgotten. + +How long does it take for there +to be enough randomness + +so that things sort of +mix and it doesn't + +matter where you started? + +So if you look at this chain, it +takes on the average, let's + +say 5 tries to make a transition +of this kind. + +It takes on the average 2 tries +for a transition of that + +kind to take place. + +So every 10 time steps or so +there's a little bit of + +randomness. + +Over 100 times steps there's +a lot of randomness, so you + +expect that the initial state +will have been forgotten. + +It doesn't matter. + +There's enough mixing and +randomness that happens over + +100 time steps. + +And so this approximation +is good. + +On the other hand, if the +numbers were different, the + +story would have +been different. + +Suppose that this number is +0.999 and that number is + +something like 0.998, so that +this number becomes 0.002, and + +that number becomes 0.001. + +Suppose that the numbers +were of this kind. + +How long does it take to forget +the initial state? + +If I start here, there's a +probability of 1 in 1,000 that + +next time I'm going +to be there. + +So on the average it's going +to take me about a thousand + +tries just to leave +that state. + +So, over roughly a thousand time +steps my initial state + +really does matter. + +If I tell you that you started +here, you're pretty certain + +that, let's say over the next +100 time steps, you + +will still be here. + +So the initial state +has a big effect. + +In this case we say that this +Markov chain has a much slower + +time scale. + +It takes a much longer time to +mix, it takes a much longer + +time for the initial state to +be forgotten, and this means + +that we cannot do this kind of +approximation if the number of + +steps is just 99. + +Here we might need n to be as +large as, let's say, 10,000 or + +so before we can start using +the approximation. + +So when one uses that +approximation, one needs to + +have some sense of how quickly +does the state move around and + +take that into account. + +So there's a whole sub-field +that deals with estimating or + +figuring out how quickly +different Markov chains mix, + +and that's the question of +when can you apply those + +steady state approximations. + +So now let's get a little closer +to the real world. + +We're going to talk about a +famous problem that was posed, + +started, and solved by +a Danish engineer + +by the name of Erlang. + +This is the same person whose +name is given to the Erlang + +distribution that we +saw in the context + +of the Poisson processes. + +So this was more than 100 years +ago, when phones had + +just started existing. + +And he was trying to figure out +what it would take to set + +up a phone system that how many +lines should you set up + +for a community to be +able to communicate + +to the outside world. + +So here's the story. + +You've got a village, and that +village has a certain + +population, and you want +to set up phone lines. + +So you want to set up a number +of phone lines, let's say that + +number is B, to the +outside world. + +And how do you want +to do that? + +Well, you want B to +be kind of small. + +You don't want to set +up too many wires + +because that's expensive. + +On the other hand, you want to +have enough wires so that if a + +reasonable number of people +place phone calls + +simultaneously, they will all +get a line and they will be + +able to talk. + +So if B is 10 and 12 people want +to talk at the same time, + +then 2 of these people would get +a busy signal, and that's + +not something that we like. + +We would like B to be large +enough so that there's a + +substantial probability, that +there's almost certainty that, + +under reasonable conditions, +no one is going + +to get a busy signal. + +So how do we go about modeling +a situation like this? + +Well, to set up a model you +need two pieces, one is to + +describe how do phone calls +get initiated, and once a + +phone call gets started, how +long does it take until the + +phone call is terminated? + +So we're going to make the +simplest assumptions possible. + +Let's assume that phone +calls originate + +as a Poisson process. + +That is, out of that population +people do not + +really coordinate. + +At completely random times, +different people with decide + +to pick up the phone. + +There's no dependencies between +different people, + +there's nothing special about +different times, different + +times are independent. + +So a Poisson model is a +reasonable way of modeling + +this situation. + +And it's going to be a Poisson +process with some rate lambda. + +Now, the rate lambda would be +easy to estimate in practice. + +You observe what happens in +that village just over a + +couple of days, and you figure +out what's the rate at which + +people attempt to place +phone calls. + +Now, about phone calls +themselves, we're going to + +make the assumption that the +duration of a phone call is a + +random variable that has an +exponential distribution with + +a certain parameter mu. + +So 1/mu is the mean duration +of a phone call. + +So the mean duration, , again, +is easy to estimate. + +You just observe what's +happening, see on the average + +how long these phone +calls are. + +Is the exponential assumption +a good assumption? + +Well, it's means that most phone +calls will be kind of + +short, but there's going to be a +fraction of phone calls that + +are going to be larger, and +then a very small fraction + +that are going to +be even larger. + +So it sounds plausible. + +It's not exactly realistic, that +is, phone calls that last + +short of 15 seconds are +not that common. + +So either nothing happens +or you have to say a few + +sentences and so on. + +Also, back into the days when +people used to connect to the + +internet using dial up modems, +that assumption was completely + +destroyed, because people would +dial up and then keep + +their phone line busy for a few +hours, if the phone call + +was a free one. + +So at those times the +exponential assumption for the + +phone call duration was +completely destroyed. + +But leaving that detail aside, +it's sort of a reasonable + +assumption to just get started +with this problem. + +All right, so now that we have +those assumptions, let's try + +to come up with the model. + +And we're going to set up +a Markov process model. + +Now the Poisson process runs in +continuous time, and call + +durations being exponential +random variables also are + +continuous random variables, so +it seems that we are in a + +continuous time universe. + +But we have only started +Markov chains for the + +discrete time case. + +What are we going to do? + +We can either develop the theory +of continuous time + +Markov chains, which +is possible. + +But we are not going to +do that in this class. + +Or we can discretize time +and work with a + +discrete time model. + +So we're going to discretize +time in the familiar way, the + +way we did it when we started +the Poisson process. + +We're going to take the time +axis and split it into little + +discrete mini slots, where +every mini slot + +has a duration delta. + +So this delta is supposed to +be a very small number. + +So what is the state +of the system? + +So, you look at the situation +in the system at some + +particular time and I ask you +what is going on right now, + +what's the information +you would tell me? + +Well, you would tell me that +right now out of these capital + +B lines, 10 of them are busy, +or 12 of them are busy. + +That describes the state of +the system, that tells me + +what's happening +at this point. + +So we set up our states base by +being the numbers from 0 to + +B. 0 corresponds to a state in +which all the phone lines are + +free, no one is talking. + +Capital B corresponds to +a case where all the + +phone lines are busy. + +And then you've got +states in between. + +And now let's look at the +transition probabilities. + +Suppose that right so now we +have i-1 lines that are busy. + +Or maybe, let me look here. + +Suppose that there's i +lines that are busy. + +What can happen the next time? + +What can happen is that the new +phone call gets placed, in + +which case my state moves up +by 1, or an existing call + +terminates, in which case my +state goes down by 1, or none + +of the two happens, in which +case I stay at the same state. + +Well, it's also possible that +the phone call gets terminated + +and a new phone call gets placed +sort of simultaneously. + +But when you take your time +slots to be very, very small, + +this is going to have a +negligible probability order + +of delta squared, so +we ignore this. + +So what's the probability of +an upwards transition? + +That's the probability that the +Poisson process records an + +arrival during a mini slot +of duration delta. + +By the definition of the +Poisson process, the + +probability of this happening +is just lambda delta. + +So each one of these upwards +transitions has the same + +probability of lambda delta. + +So you've got lambda deltas +everywhere in this diagram. + +How about, now, phone +call terminations? + +If you had the single call that +was active, so if you + +were here, what's the +probability that the phone + +call terminates? + +So the phone call has an +exponential duration with + +parameter mu. + +And we discussed before that an +exponential random variable + +can be thought of as the +first arrival time + +in a Poisson process. + +So the probability that you get +this event to happen over + +a delta time interval is +just mu times delta. + +So if you have a single phone +call that's happening right + +now, with probability +mu times delta, that + +call is going to terminate. + +But suppose that we have +i phone calls that + +are currently active. + +Each one of them has a +probability of mu delta, of + +terminating, but collectively +the probability that one of + +them terminates becomes +i times mu delta. + +So that's because you get the +mu delta contribution -- + +the probability of termination +from each one of the different + +phone calls. + +OK, now this is an approximate +calculation, because it + +ignores the possibility that two +phone calls terminate at + +the same time. + +Again, the way to think of why +this is the correct rate, when + +you have i phone calls that are +simultaneously running and + +waiting for one of them to +terminate, this is like having + +i separate Poisson processes +that are running in parallel, + +and you ask for the probability +that one of those + +processes records an event. + +Now when you put all those +process together, it's like + +having a Poisson process with +total rate i times mu, and so + +i times mu delta is the overall +probability that + +something happens in terms of +phone call terminations at + +those times. + +So in any case, this is the +transition probability for + +downwards transitions. + +Now that we've got this, we +can analyze this chain. + +This chain has the birth death +form that we discussed towards + +the end of last lecture. + +And for birth death chains, it's +easy to write it out to + +find the steady state +probabilities. + +Instead of writing down the +balance equations in the + +general form, we think in terms +of a conservation of + +probabilities or of transitions +by looking at what + +happens across a particular +cut in this diagram. + +Number of transitions in the +chain that cross from here to + +here has to be approximately +equal to the number of + +transitions from here to there +because whatever comes up must + +come down and then come +up and so on. + +So the frequency with which +transitions of this kind are + +observed has to be the same as +the frequency of transitions + +of this kind. + +What's the frequency of how +often the transitions of this + +kind happen? + +And by frequency I mean quite +percentage of the mini slots + +involve a transition +of this kind? + +Well, for a transition of that +kind to happen we need to be + +at states i-1, which happens +this much of the time. + +And then the probability +lambda delta that the + +transition is of this kind. + +So the frequency of transitions +of with which this + +kind of transition is observed +is lambda delta times pi(i-1). + +This is the fraction of time +steps at which a transition + +from specifically this +state to specifically + +that state are observed. + +This has to be the same as +the frequency with which + +transitions of that kind are +observed, and that frequency + +is going to be i mu delta +times pi(i), and then we + +cancel the deltas, and we are +left with this equation here. + +So this equation expresses pi(i) +in terms of pi(i-1). + +So if we knew pi(0) we +can use that equation + +to determine pi(1). + +Once we know pi(1), we can use +that equation to determine + +pi(2), and so on, +you keep going. + +And the general formula that +comes out of this, I will not + +do the algebra, it's a +straightforward substitution, + +you find that pi(i), the steady +state probability of + +state i is given by this +expression, which involves the + +pi(0) from which we started. + +Now what is pi(0)? + +Well, we don't know yet, but +we can find it by using the + +normalization equation. + +The sum of pi(i) has +to be equal to 1. + +So the sum of all of those +numbers has to be equal to 1. + +And the only way that this can +happen is by setting pi(0) to + +be equal to that particular +number. + +So if I tell you the value of +capital B, you can set up this + +Markov chain, you can calculate +pi(0), and then you + +can calculate pi(i), and so you +know what fraction, you + +know the steady state +probabilities of this chain, + +so you can answer +the question. + +If I drop in at a random time, +how likely is it that I'm + +going to find the states +to be here, or the + +states to be there? + +So the steady state +probabilities are + +probabilities, but we also +interpret them as frequencies. + +So once I find pi(i), it also +tells me what fraction of the + +time is the state equal to i. + +And you can answer that question +for every possible i. + +Now, why did we do +this exercise? + +We're interested in +the probability of + +the system is busy. + +So if a person, a new phone +call gets placed, it just + +drops out of the sky. + +According to that Poisson +process, that new phone call + +is going to find the system +at a random state. + +That random state is described +in steady state by the + +probabilities pi(i)'s. + +And the probability that you +find the system to be busy is + +the probability that when you +drop in the state happens to + +be that particular number B. So +i sub b is the probability + +of being busy. + +And this is the probability +that you would like to be + +small in a well engineered +system. + +So you ask the question, how +should, given my lambda and + +mu, my design question is to +determine capital B the number + +of phone lines so that +this number is small. + +Could we have done, could we +figure out a good value for B + +by doing a back of the +envelope calculation? + +Let's suppose that lambda is +30 and that mu is 1/3. + +So I guess that's, let +us these rates to + +be calls per minute. + +And this mu, again, is +a rate per minute. + +Again, the units of mu are going +to be calls per minute. + +So since our time unit is +minutes, the mean duration of + +calls is 1/mu minutes. + +So a typical call, or +on the average a + +call lasts for 3 minutes. + +So you get 30 calls +per minute. + +Each call lasts for 3 minutes +on the average. + +So on the average, if +B was infinite, + +every call goes through. + +How many calls would be +active on the average? + +So you get 30 per minute. + +If a call lasted exactly 1 +minute, then at any time you + +would have 30 calls +being active. + +Now a call lasts on the +average for 3 minutes. + +So during each minute +you generate 90 + +minutes of talking time. + +So by thinking in terms of +averages you would expect that + +at any time there would +be about 90 + +calls that are active. + +And if 90 calls are active on +the average, you could say OK, + +I'm going to set up my +capital B to be 90. + +But that's not very good, +because if the average number + +of phone calls that want to +happen is if the average + +number is 90, sometimes you're +going to have 85, sometimes + +you will have 95. + +And to be sure that the phone +calls will go through you + +probably want to choose your +capital B to be a number a + +little larger than 90. + +How much larger than 90? + +Well, this is a question that +you can answer numerically. + +So you go through the +following procedure. + +I tried different values of +capital B. For any given value + +of capital B, I do this +numerical calculation, I find + +the probability that the system +is busy, and then I ask + +what's the value of B that makes +my probability of being + +busy to be, let's say, +roughly 1 %. + +And if you do that calculation +with the parameters that they + +gave you, you find that B would +be something like 106. + +So with the parameters they gave +where you have, on the + +average, 90 phone calls being +active, you actually need some + +margin to protect against the +[?] fluctuation, if suddenly + +by chance more people want to +talk, and if you want to have + +a good guarantee that an +incoming person will have a + +very small probability of +finding a busy system, then + +you will need about +106 phone lines. + +So that's the calculation and +the argument that the Erlang + +went through a long time ago. + +It's actually interesting that +Erlang did this calculation + +before Markov chains +were invented. + +So Markov's work, and the +beginning of work on Markov + +chains, happens about 10-15 +years after Erlang. + +So obviously he didn't call +that a Markov chain. + +But it was something that he +could study from first + +principles. + +So this is a pretty +useful thing. + +These probabilities that come +out of that model, at least in + +the old days, they would all +be very well tabulated in + +handbooks that every decent +phone company engineer would + +sort of have with them. + +So this is about as practical +as it gets. + +It's one of the sort of +standard real world + +applications of Markov chains. + +So now to close our subjects, +we're going to consider a + +couple of new skills and see how +we can calculate the few + +additional interesting +quantities that have to do + +with the Markov chain. + +So the problem we're going to +deal with here is the one I + +hinted that when I was talking +about this picture. + +You start at a transient +state, you're going to + +eventually end up +here or there. + +We want to find the +probabilities of one option of + +the two happening or the +other happening. + +So in this picture we +have a class of + +states that's are transient. + +These are transient because +you're going to move around + +those states, but there's a +transition that you can make, + +and you go to a state from +which you cannot escape + +afterwards. + +Are you going to end +up here or are you + +going to end up there? + +You don't know. + +It's random. + +Let's try to calculate the +probability that you + +end up at state 4. + +Now, the probability that you +end up at state 4 will depend + +on where you start. + +Because if you start here, you +probably have more chances of + +getting to 4 because you get +that chance immediately, + +whereas if you start here +there's more chances that + +you're going to escape that way +because it kind of takes + +you time to get there. + +It's more likely that +you exit right away. + +So the probability of exiting +and ending up at state 4 will + +depend on the initial state. + +That's why when we talk about +these absorption probability + +we include an index i that +tells us what the + +initial state is. + +And we want to find this +absorption probability, the + +probability that we end +up here for the + +different initial states. + +Now for some initial states this +is very easy to answer. + +If you start at state 4, what's +the probability that + +eventually you end up in +this part of the chain? + +It's 1. + +You're certain to be there, +that's where you started. + +If you start at state 5, what's +the probability that + +you end up eventually +at state 4? + +It's probability 0, there's +no way to get there. + +Now, how about if you start +at a state like state 2? + +If you start at state 2 then +there's a few different things + +that can happen. + +Either you end up at state 4 +right away and this happens + +with probability 0.2, or you +end up at state 1, and this + +happens with probability 0.6. + +So if you end up at state +4, you are done. + +We are there. + +If you end up at state +1, then what? + +Starting from state 1 there's +two possibilities. + +Either eventually you're going +to end up at state 4, or + +eventually you're going +to end up at state 5. + +What's the probability +of this happening? + +We don't know what it is, but +it's what we defined to be a1. + +This is the probability -- + +a1 is the probability -- + +that eventually you settle in +state 4 given that the initial + +state was 1. + +So this probability is a1. + +So our event of interest +can happen in two ways. + +Either I go there directly, +or I go here + +with probability 0.6. + +And given that I go there, +eventually I end up at state + +4, which happens with +probability a1. + +So the total probability of +ending up at state 4 is going + +to be the sum of the +probabilities of the different + +ways that this event +can happen. + +So our equation, in this case, +is going to be, that's a2, is + +going to be 0.2 (that's the +probability of going there + +directly) plus with probability +0.8 I end up at + +state 1, and then from state 1 +I will end up at state 4 with + +probability a1. + +So this is one particular +equation that we've got for + +what happens if we start +from this state. + +We can do a similar argument +starting from any other state. + +Starting from state i the +probability that eventually I + +end up at state 4 is, we +consider the different + +possible scenarios of where do +I go next, which is my state + +j, with probability Pij. + +Next time I go to j, and given +that I started at j, this is + +the probability that I +end up at state 4. + +So this equation that we have +here is just an abstract + +version in symbols of what we +wrote down for the particular + +case where the initial +state was 2. + +So you write down an equation +of this type for every state + +inside here. + +You'll have a separate equation +for a1, a2, and a3. + +And that's going to be a system +of 3 equations with 3 + +unknowns, the a's inside +the transient states. + +So you can solve that 3 by +3 system of equations. + +Fortunately, it turns out to +have a unique solution, and so + +once you solve it you have found +the probabilities of + +absorption and the probability +that eventually you get + +absorbed at state 4. + +Now, in the picture that we had +here, this was a single + +state, and that one was +a single state. + +How do things change if our +recurrent, or trapping sets + +consist of multiple states? + +Well, it doesn't really matter +that we have multiple states. + +All that matters is that this +is one lump and once we get + +there we are stuck in there. + +So if the picture was, let's +say, like this, 0.1 and 0.2, + +that basically means that +whenever you are in that state + +there's a total probability of +0.3 of ending in that lump and + +getting stuck inside +that lump. + +So you would take that picture +and change it and make it + +instead a total probability of +0.3, of ending somewhere + +inside that lump. + +And similarly, you take this +lump and you view it as just + +one entity, and from any state +you record the total + +probability that given +that I'm here I + +end up in that entity. + +So basically, if the only +thing you care is the + +probability that you're going +to end up in this lump, you + +can replace that lump with a +single state, view it as a + +single state, and calculate + +probabilities using this formula. + +All right, so now we know +where the chain is + +going to get to. + +At least we know +probabilistically. + +We know with what probability +it is going to go here, and + +that also tells us the +probability that eventually + +it's going to get there. + +Other question, how long is it +going to take until we get to + +either this state +or that state? + +We can call that event +absorption, meaning that the + +state got somewhere into a +recurrent class from which it + +could not get out. + +Okay. + +Let's deal with that question +for the case where we have + +only 1 absorbing state. + +So here our Markov chain is a +little simpler than the one in + +the previous slide. + +We've got our transient +states, we've got our + +recurrent state, and once you +get into the recurrent state + +you just stay there. + +So here we're certain that no +matter where we start we're + +going to end up here. + +How long is it going to take? + +Well, we don't know. + +It's a random variable. + +The expected value of that +random variable, + +let's call it mu. + +But how long it takes to get +there certainly depends on + +where we start. + +So let's put in our notation +again this index i that + +indicates where we +started from. + +And now the argument is going to +be of the same type as the + +one we used before. + +We can think in terms of a tree +once more, that considers + +all the possible options. + +So suppose that you +start at state 1. + +Starting from state 1, the +expected time until you end up + +dropping states is mu1. + +Now, starting from state 1, what +are the possibilities? + +You make your first transition, +and that first + +transition is going to take +you either to state + +2 or to state 3. + +It takes you to state 2 with +probability 0.6, it takes you + +to state 3 with probability +0.4. + +Starting from state 2, +eventually you're going to get + +to state 4. + +How long does it take? + +We don't know, it's +a random variable. + +But the expected time until +this happens is mu2. + +Starting from state 2, how long +does it take you to get + +to state 4. + +And similarly starting from +state 3, it's going to take + +you on the average mu3 +time steps until you + +get to state 4. + +So what's the expected value +of the time until I + +end at state 4? + +So with probability 0.6, I'm +going to end up at state 2 and + +from there on it's going to be +expected time mu2, and with + +probability 0.4 I'm going to +end up at state 3, and from + +there it's going to take +me so much time. + +So this is the expected time +it's going to take me after + +the first transition. + +But we also spent 1 time step +for the first transition. + +The total time to get there +is the time of the first + +transition, which is 1, plus +the expected time starting + +from the next state. + +This expression here is the +expected time starting from + +the next state, but we also need +to account for the first + +transition, so we add 1. + +And this is going +to be our mu1. + +So once more we have a linear +equation that ties together + +the different mu's. + +And the equation starting from +state 4 in this case, of + +course is going to be simple, +starting from that state the + +expected number of steps it +takes you to get there for the + +first time is of course, 0 +because you're already there. + +So for that state this is fine, +and for all the other + +states you get an equation +of this form. + +Now we're going to have an +equation for every state. + +It's a system of linear +equations, once more we can + +solve them, and this gives us +the expected times until our + +chain gets absorbed in +this absorbing state. + +And it's nice to know that +this system of equations + +always has a unique solution. + +OK so this was the expected +time to absorption. + +For this case where we had this +scene absorbing state. + +Suppose that we have our +transient states and that we + +have multiple recurrent +classes, or + +multiple absorbing states. + +Suppose you've got the +picture like this. + +And we want to calculate the +expected time until we get + +here or there. + +Expected time until we get +to an absorbing state. + +What's the trick? + +Well, we can lump both of these +states together and + +think of them as just one bad +state, one place for which + +we're interested in how long +it takes us to get there. + +So lump them as one state, and +accordingly kind of merge all + +of those probabilities. + +So starting from here, my +probability that the next I + +end up in this lump and they +get absorbed is going to be + +this probability plus +that probability. + +So we would change +that picture. + +Think of this as being +just one big state. + +And sort of add those two +probabilities together to come + +up with a single probability, +which is the probability that + +starting from here next +time I find myself at + +some absorbing state. + +So once you know how to deal +with a situation like this, + +you can also find expected times +to absorption for the + +case where you've got multiple +absorbing states. + +You just lump all of those +multiple absorbing states into + +a single one. + +Finally, there's a +kind of related + +quantity that's of interest. + +The question is almost the same +as in the previous slide, + +except that here we do not have +any absorbing states. + +Rather, we have a single +recurrent class of states. + +You start at some state i. + +You have a special state, +that is state s. + +And you ask the question, how +long is it going to take me + +until I get to s for +the first time? + +It's a single recurrent +class of states. + +So you know that the state keeps +circulating here and it + +keeps visiting all of +the possible states. + +So eventually this state +will be visited. + +How long does it take +for this to happen? + +Ok. + +So we're interested in how +long it takes for this to + +happen, how long it takes until +we get to s for the + +first time. + +And we don't care about what +happens afterwards. + +So we might as well change this +picture and remove the + +transitions out of s and to make +them self transitions. + +Is the answer going to change? + +No. + +The only thing that we changed +was what happens + +after you get to s. + +But what happens after you +get to s doesn't matter. + +The question we're dealing with +is how long does it take + +us to get to s. + +So essentially, it's after we +do this transformation -- + +it's the same question as +before, what's the time it + +takes until eventually +we hit this state. + +And it's now in this new +picture, this state is an + +absorbing state. + +Or you can just think from +first principles. + +Starting from the state itself, +s, it takes you 0 time + +steps until you get to s. + +Starting from anywhere else, +you need one transition and + +then after the first transition +you find yourself + +at state j with probability Pij +and from then on you are + +going to take expected time +Tj until you get to that + +terminal state s. + +So once more these equations +have a unique solution, you + +can solve them and +find the answer. + +And finally, there's a related +question, which is the mean + +recurrence time of s. + +In that question you start +at s, the chain will move + +randomly, and you ask how long +is it going to take until I + +come back to s for +the next time. + +So notice the difference. + +Here we're talking the first +time after time 0, whereas + +here it's just the first +time anywhere. + +So here if you start from +s, Ts* is not 0. + +You want to do at least one +transition and that's how long + +it's going to take me until +it gets back to s. + +Well, how long does it take +me until I get back to s? + +I do my first transition, and +then after my first transition + +I calculate the expected time +from the next state how long + +it's going to take me until +I come back to s. + +So all of these equations that I +wrote down, they all kind of + +look the same. + +But they are different. + +So you can either memorize all +of these equations, or instead + +what's better is to just +to get the basic idea. + +That is, to calculate +probabilities or expected + +values you use the total +probability or total + +expectation theorem and +conditional the first + +transition and take +it from there. + +So you're going to get a little +bit of practice with + +these skills in recitation +tomorrow, and of course it's + +in your problem set as well. \ No newline at end of file diff --git a/HWnEifmgAdU.txt b/HWnEifmgAdU.txt new file mode 100644 index 0000000000000000000000000000000000000000..fd25e469c1b7d92c3d9ae5b494e086efedaec275 --- /dev/null +++ b/HWnEifmgAdU.txt @@ -0,0 +1,8795 @@ +align:start position:0% + +okay why don't we get + + align:start position:0% +okay why don't we get + + + align:start position:0% +okay why don't we get +started so what I wanted to do in the + + align:start position:0% +started so what I wanted to do in the + + + align:start position:0% +started so what I wanted to do in the +next few lectures is talk about + + align:start position:0% +next few lectures is talk about + + + align:start position:0% +next few lectures is talk about +filtering and and this is you know + + align:start position:0% +filtering and and this is you know + + + align:start position:0% +filtering and and this is you know +Ripple filtering or Emi electromagnetic + + align:start position:0% +Ripple filtering or Emi electromagnetic + + + align:start position:0% +Ripple filtering or Emi electromagnetic +interference + + align:start position:0% +interference + + + align:start position:0% +interference +filtering and why am I going to spend so + + align:start position:0% +filtering and why am I going to spend so + + + align:start position:0% +filtering and why am I going to spend so +much time talking about filters and the + + align:start position:0% +much time talking about filters and the + + + align:start position:0% +much time talking about filters and the +reason is because in most power supplies + + align:start position:0% +reason is because in most power supplies + + + align:start position:0% +reason is because in most power supplies +and fact a lot of power electron + + align:start position:0% +and fact a lot of power electron + + + align:start position:0% +and fact a lot of power electron +circuits generally the filters take up a + + align:start position:0% +circuits generally the filters take up a + + + align:start position:0% +circuits generally the filters take up a +large fraction of the overall volume and + + align:start position:0% +large fraction of the overall volume and + + + align:start position:0% +large fraction of the overall volume and +cost so if you look at a typical offline + + align:start position:0% +cost so if you look at a typical offline + + + align:start position:0% +cost so if you look at a typical offline +power supply 25% of the volume might be + + align:start position:0% +power supply 25% of the volume might be + + + align:start position:0% +power supply 25% of the volume might be +donate devoted to just filters all right + + align:start position:0% +donate devoted to just filters all right + + + align:start position:0% +donate devoted to just filters all right +because you know we're switching we're + + align:start position:0% +because you know we're switching we're + + + align:start position:0% +because you know we're switching we're +transferring energy and the Ripple we + + align:start position:0% +transferring energy and the Ripple we + + + align:start position:0% +transferring energy and the Ripple we +generate we really need to suppress okay + + align:start position:0% +generate we really need to suppress okay + + + align:start position:0% +generate we really need to suppress okay +and you know we want to suppress it + + align:start position:0% +and you know we want to suppress it + + + align:start position:0% +and you know we want to suppress it +maybe to meet some application desire + + align:start position:0% +maybe to meet some application desire + + + align:start position:0% +maybe to meet some application desire +but we might want to suppress it also + + align:start position:0% +but we might want to suppress it also + + + align:start position:0% +but we might want to suppress it also +because you know we're not allowed to + + align:start position:0% +because you know we're not allowed to + + + align:start position:0% +because you know we're not allowed to +sell something that you plug into the + + align:start position:0% +sell something that you plug into the + + + align:start position:0% +sell something that you plug into the +wall that has too much Ripple okay so + + align:start position:0% +wall that has too much Ripple okay so + + + align:start position:0% +wall that has too much Ripple okay so +um if we think about it there's kind of + + align:start position:0% +um if we think about it there's kind of + + + align:start position:0% +um if we think about it there's kind of +two kinds or two flavors of + + align:start position:0% +two kinds or two flavors of + + + align:start position:0% +two kinds or two flavors of +specifications we of to have often have + + align:start position:0% +specifications we of to have often have + + + align:start position:0% +specifications we of to have often have +to meet one of them is in the time + + align:start position:0% + + + + align:start position:0% + +domain right if I'm developing a power + + align:start position:0% +domain right if I'm developing a power + + + align:start position:0% +domain right if I'm developing a power +supply somebody might tell me oh look + + align:start position:0% +supply somebody might tell me oh look + + + align:start position:0% +supply somebody might tell me oh look +I'm only going to allow you to have 20 + + align:start position:0% +I'm only going to allow you to have 20 + + + align:start position:0% +I'm only going to allow you to have 20 +molts either Peak or RMS of output RI + + align:start position:0% +molts either Peak or RMS of output RI + + + align:start position:0% +molts either Peak or RMS of output RI +triple because that we want such and + + align:start position:0% +triple because that we want such and + + + align:start position:0% +triple because that we want such and +such a level of noise in our output + + align:start position:0% +such a level of noise in our output + + + align:start position:0% +such a level of noise in our output +right and that's one kind of + + align:start position:0% +right and that's one kind of + + + align:start position:0% +right and that's one kind of +specification you might need to + + align:start position:0% +specification you might need to + + + align:start position:0% +specification you might need to +meet more typically however and almost + + align:start position:0% +meet more typically however and almost + + + align:start position:0% +meet more typically however and almost +universally if it's something like + + align:start position:0% +universally if it's something like + + + align:start position:0% +universally if it's something like +you're you're talking about an input + + align:start position:0% +you're you're talking about an input + + + align:start position:0% +you're you're talking about an input +filter uh you're going to plug it into + + align:start position:0% +filter uh you're going to plug it into + + + align:start position:0% +filter uh you're going to plug it into +the wall uh is in the frequency + + align:start position:0% + + + + align:start position:0% + +domain okay uh that is you know how much + + align:start position:0% +domain okay uh that is you know how much + + + align:start position:0% +domain okay uh that is you know how much +energy can you inject in a given uh + + align:start position:0% +energy can you inject in a given uh + + + align:start position:0% +energy can you inject in a given uh +frequency bandwidth so a typical thing + + align:start position:0% +frequency bandwidth so a typical thing + + + align:start position:0% +frequency bandwidth so a typical thing +was you might detect this with like a 9 + + align:start position:0% +was you might detect this with like a 9 + + + align:start position:0% +was you might detect this with like a 9 +KZ resolution bandwidth for where you're + + align:start position:0% +KZ resolution bandwidth for where you're + + + align:start position:0% +KZ resolution bandwidth for where you're +picking up energy and look in the span + + align:start position:0% +picking up energy and look in the span + + + align:start position:0% +picking up energy and look in the span +say between for conduced emissions look + + align:start position:0% +say between for conduced emissions look + + + align:start position:0% +say between for conduced emissions look +in the span between like 150 khz and 30 + + align:start position:0% +in the span between like 150 khz and 30 + + + align:start position:0% +in the span between like 150 khz and 30 +megahertz is most kind of commercial + + align:start position:0% +megahertz is most kind of commercial + + + align:start position:0% +megahertz is most kind of commercial +standards for conducted Emi above 30 + + align:start position:0% +standards for conducted Emi above 30 + + + align:start position:0% +standards for conducted Emi above 30 +mahz you typically use antennas and + + align:start position:0% +mahz you typically use antennas and + + + align:start position:0% +mahz you typically use antennas and +stuff to pick it up and we're not going + + align:start position:0% +stuff to pick it up and we're not going + + + align:start position:0% +stuff to pick it up and we're not going +to talk about radiated electromagnetic + + align:start position:0% +to talk about radiated electromagnetic + + + align:start position:0% +to talk about radiated electromagnetic +interference but in fact if you don't + + align:start position:0% +interference but in fact if you don't + + + align:start position:0% +interference but in fact if you don't +conduct pass conducted interference you + + align:start position:0% +conduct pass conducted interference you + + + align:start position:0% +conduct pass conducted interference you +won't pass radiated either because you + + align:start position:0% +won't pass radiated either because you + + + align:start position:0% +won't pass radiated either because you +know basically when you conduct energy + + align:start position:0% +know basically when you conduct energy + + + align:start position:0% +know basically when you conduct energy +into your input leads your output leads + + align:start position:0% +into your input leads your output leads + + + align:start position:0% +into your input leads your output leads +that's an antenna and it broadcasts off + + align:start position:0% +that's an antenna and it broadcasts off + + + align:start position:0% +that's an antenna and it broadcasts off +noise okay so um it's important to meet + + align:start position:0% +noise okay so um it's important to meet + + + align:start position:0% +noise okay so um it's important to meet +these things if you're going to sell + + align:start position:0% +these things if you're going to sell + + + align:start position:0% +these things if you're going to sell +commercial products that plug into a + + align:start position:0% +commercial products that plug into a + + + align:start position:0% +commercial products that plug into a +wall or into a vehicle into the wall you + + align:start position:0% +wall or into a vehicle into the wall you + + + align:start position:0% +wall or into a vehicle into the wall you +got to deal with the FCC if you're going + + align:start position:0% +got to deal with the FCC if you're going + + + align:start position:0% +got to deal with the FCC if you're going +to plug it into the vehicle you got to + + align:start position:0% +to plug it into the vehicle you got to + + + align:start position:0% +to plug it into the vehicle you got to +deal with the Vehicle + + align:start position:0% +deal with the Vehicle + + + align:start position:0% +deal with the Vehicle +Manufacturer and you're going to have to + + align:start position:0% +Manufacturer and you're going to have to + + + align:start position:0% +Manufacturer and you're going to have to +pass these specifications in order to + + align:start position:0% +pass these specifications in order to + + + align:start position:0% +pass these specifications in order to +sell + + align:start position:0% +sell + + + align:start position:0% +sell +something and it's quite important let + + align:start position:0% +something and it's quite important let + + + align:start position:0% +something and it's quite important let +me just give you an + + align:start position:0% +me just give you an + + + align:start position:0% +me just give you an +example um once upon a time I I + + align:start position:0% +example um once upon a time I I + + + align:start position:0% +example um once upon a time I I +consulted for I'd call it a garage + + align:start position:0% +consulted for I'd call it a garage + + + align:start position:0% +consulted for I'd call it a garage +startup but they were really they were + + align:start position:0% +startup but they were really they were + + + align:start position:0% +startup but they were really they were +in the guy's basement so it was a + + align:start position:0% +in the guy's basement so it was a + + + align:start position:0% +in the guy's basement so it was a +basement startup um and what they were + + align:start position:0% +basement startup um and what they were + + + align:start position:0% +basement startup um and what they were +developing this is early days they were + + align:start position:0% +developing this is early days they were + + + align:start position:0% +developing this is early days they were +developing a solar inverter to sell + + align:start position:0% +developing a solar inverter to sell + + + align:start position:0% +developing a solar inverter to sell +right and so they were they were + + align:start position:0% +right and so they were they were + + + align:start position:0% +right and so they were they were +developing the power stage to convert + + align:start position:0% +developing the power stage to convert + + + align:start position:0% +developing the power stage to convert +energy into the grid and you know + + align:start position:0% +energy into the grid and you know + + + align:start position:0% +energy into the grid and you know +getting the up and doing all these + + align:start position:0% +getting the up and doing all these + + + align:start position:0% +getting the up and doing all these +things but they hadn't gotten around + + align:start position:0% +things but they hadn't gotten around + + + align:start position:0% +things but they hadn't gotten around +designing the Emi filter yet okay and so + + align:start position:0% +designing the Emi filter yet okay and so + + + align:start position:0% +designing the Emi filter yet okay and so +the guy's neighbor came up to him and + + align:start position:0% +the guy's neighbor came up to him and + + + align:start position:0% +the guy's neighbor came up to him and +said you know are you having trouble + + align:start position:0% +said you know are you having trouble + + + align:start position:0% +said you know are you having trouble +around every day around 3:00 I can't + + align:start position:0% +around every day around 3:00 I can't + + + align:start position:0% +around every day around 3:00 I can't +watch television because I don't know + + align:start position:0% +watch television because I don't know + + + align:start position:0% +watch television because I don't know +like everything just fuzzes out on me + + align:start position:0% +like everything just fuzzes out on me + + + align:start position:0% +like everything just fuzzes out on me +and what the guy in the startup didn't + + align:start position:0% +and what the guy in the startup didn't + + + align:start position:0% +and what the guy in the startup didn't +tell him was 3 o'cl was when he started + + align:start position:0% +tell him was 3 o'cl was when he started + + + align:start position:0% +tell him was 3 o'cl was when he started +testing every day right he was dumping + + align:start position:0% +testing every day right he was dumping + + + align:start position:0% +testing every day right he was dumping +too much Ripple into the grid and the + + align:start position:0% +too much Ripple into the grid and the + + + align:start position:0% +too much Ripple into the grid and the +next house over suddenly couldn't watch + + align:start position:0% +next house over suddenly couldn't watch + + + align:start position:0% +next house over suddenly couldn't watch +television right so you know these are + + align:start position:0% +television right so you know these are + + + align:start position:0% +television right so you know these are +real problems right that it's not just + + align:start position:0% +real problems right that it's not just + + + align:start position:0% +real problems right that it's not just +you got to pass a spec it's you you will + + align:start position:0% +you got to pass a spec it's you you will + + + align:start position:0% +you got to pass a spec it's you you will +interfere with things if you think about + + align:start position:0% +interfere with things if you think about + + + align:start position:0% +interfere with things if you think about +it in a car if you're plugging something + + align:start position:0% +it in a car if you're plugging something + + + align:start position:0% +it in a car if you're plugging something +into the USB outlet or into the + + align:start position:0% +into the USB outlet or into the + + + align:start position:0% +into the USB outlet or into the +cigarette lighter or something + + align:start position:0% +cigarette lighter or something + + + align:start position:0% +cigarette lighter or something +right any Ripple you conduct is running + + align:start position:0% +right any Ripple you conduct is running + + + align:start position:0% +right any Ripple you conduct is running +around on the wires in the car and it's + + align:start position:0% +around on the wires in the car and it's + + + align:start position:0% +around on the wires in the car and it's +right what is it right next to a radio + + align:start position:0% +right what is it right next to a radio + + + align:start position:0% +right what is it right next to a radio +right so your radio is a very sensitive + + align:start position:0% +right so your radio is a very sensitive + + + align:start position:0% +right so your radio is a very sensitive +detector of very very small quantities + + align:start position:0% +detector of very very small quantities + + + align:start position:0% +detector of very very small quantities +of noise and you will mess with that if + + align:start position:0% +of noise and you will mess with that if + + + align:start position:0% +of noise and you will mess with that if +you do not have very very good filtering + + align:start position:0% +you do not have very very good filtering + + + align:start position:0% +you do not have very very good filtering +okay so what we're going to find is that + + align:start position:0% +okay so what we're going to find is that + + + align:start position:0% +okay so what we're going to find is that +you got to do filtering but it's not + + align:start position:0% +you got to do filtering but it's not + + + align:start position:0% +you got to do filtering but it's not +just oh I need to make my ripple a + + align:start position:0% +just oh I need to make my ripple a + + + align:start position:0% +just oh I need to make my ripple a +little bit small you got to make it + + align:start position:0% +little bit small you got to make it + + + align:start position:0% +little bit small you got to make it +really small in radio frequency bands in + + align:start position:0% +really small in radio frequency bands in + + + align:start position:0% +really small in radio frequency bands in +order to not interfere with things okay + + align:start position:0% +order to not interfere with things okay + + + align:start position:0% +order to not interfere with things okay +so we're going to talk about conducted + + align:start position:0% +so we're going to talk about conducted + + + align:start position:0% +so we're going to talk about conducted +emissions and what I'm going to mostly + + align:start position:0% +emissions and what I'm going to mostly + + + align:start position:0% +emissions and what I'm going to mostly +Focus most of what I'm going to say + + align:start position:0% +Focus most of what I'm going to say + + + align:start position:0% +Focus most of what I'm going to say +about input filters you know that's like + + align:start position:0% +about input filters you know that's like + + + align:start position:0% +about input filters you know that's like +you know if I'm plugging my power + + align:start position:0% +you know if I'm plugging my power + + + align:start position:0% +you know if I'm plugging my power +converter in the wall it's between you + + align:start position:0% +converter in the wall it's between you + + + align:start position:0% +converter in the wall it's between you +know power stage of my powder converter + + align:start position:0% +know power stage of my powder converter + + + align:start position:0% +know power stage of my powder converter +and the wall so that's the input side + + align:start position:0% +and the wall so that's the input side + + + align:start position:0% +and the wall so that's the input side +filter most of it applies to Output side + + align:start position:0% +filter most of it applies to Output side + + + align:start position:0% +filter most of it applies to Output side +filters too okay so but we'll focus on + + align:start position:0% +filters too okay so but we'll focus on + + + align:start position:0% +filters too okay so but we'll focus on +input + + align:start position:0% +input + + + align:start position:0% +input +filters so let's just think to get a + + align:start position:0% +filters so let's just think to get a + + + align:start position:0% +filters so let's just think to get a +sense of + + align:start position:0% +sense of + + + align:start position:0% +sense of +the challenges or issues I I want to + + align:start position:0% +the challenges or issues I I want to + + + align:start position:0% +the challenges or issues I I want to +start by talking about you know how do + + align:start position:0% +start by talking about you know how do + + + align:start position:0% +start by talking about you know how do +you measure these things and and what + + align:start position:0% +you measure these things and and what + + + align:start position:0% +you measure these things and and what +drives that so let's just think about a + + align:start position:0% +drives that so let's just think about a + + + align:start position:0% +drives that so let's just think about a +very simple Buck converter so suppose I + + align:start position:0% +very simple Buck converter so suppose I + + + align:start position:0% +very simple Buck converter so suppose I +go off and build a buck + + align:start position:0% +go off and build a buck + + + align:start position:0% +go off and build a buck +converter okay so here's my buck + + align:start position:0% +converter okay so here's my buck + + + align:start position:0% +converter okay so here's my buck +converter and I'm not going to worry + + align:start position:0% +converter and I'm not going to worry + + + align:start position:0% +converter and I'm not going to worry +about the output filter let's just + + align:start position:0% +about the output filter let's just + + + align:start position:0% +about the output filter let's just +assume he's connected to a resistor but + + align:start position:0% +assume he's connected to a resistor but + + + align:start position:0% +assume he's connected to a resistor but +here I have the input filter and maybe I + + align:start position:0% +here I have the input filter and maybe I + + + align:start position:0% +here I have the input filter and maybe I +can consider the capacitor for the buck + + align:start position:0% +can consider the capacitor for the buck + + + align:start position:0% +can consider the capacitor for the buck +converter the first part of the input + + align:start position:0% +converter the first part of the input + + + align:start position:0% +converter the first part of the input +filter and here I have I'm going to draw + + align:start position:0% +filter and here I have I'm going to draw + + + align:start position:0% +filter and here I have I'm going to draw +some current iix okay I'm going to put + + align:start position:0% +some current iix okay I'm going to put + + + align:start position:0% +some current iix okay I'm going to put +some input filter + + align:start position:0% +some input filter + + + align:start position:0% +some input filter +here but for the moment let's just + + align:start position:0% +here but for the moment let's just + + + align:start position:0% +here but for the moment let's just +assume my capacitor is the input filter + + align:start position:0% +assume my capacitor is the input filter + + + align:start position:0% +assume my capacitor is the input filter +I've got okay so this thing right here + + align:start position:0% +I've got okay so this thing right here + + + align:start position:0% +I've got okay so this thing right here +is right now my filter and now I'm going + + align:start position:0% +is right now my filter and now I'm going + + + align:start position:0% +is right now my filter and now I'm going +to connect this up to some Sour SCE + + align:start position:0% +to connect this up to some Sour SCE + + + align:start position:0% +to connect this up to some Sour SCE +okay and maybe this source is the + + align:start position:0% +okay and maybe this source is the + + + align:start position:0% +okay and maybe this source is the +battery in my car right but it's vs and + + align:start position:0% +battery in my car right but it's vs and + + + align:start position:0% +battery in my car right but it's vs and +then there's some Source impedance Zs + + align:start position:0% +then there's some Source impedance Zs + + + align:start position:0% +then there's some Source impedance Zs +and that may be at DC that might be very + + align:start position:0% +and that may be at DC that might be very + + + align:start position:0% +and that may be at DC that might be very +small but at AC maybe it's not okay so + + align:start position:0% +small but at AC maybe it's not okay so + + + align:start position:0% +small but at AC maybe it's not okay so +there's some Source impedance that I'm + + align:start position:0% +there's some Source impedance that I'm + + + align:start position:0% +there's some Source impedance that I'm +driving in + + align:start position:0% +driving in + + + align:start position:0% +driving in +okay and here's the + + align:start position:0% +okay and here's the + + + align:start position:0% +okay and here's the +challenge um what would what would be a + + align:start position:0% +challenge um what would what would be a + + + align:start position:0% +challenge um what would what would be a +model for this as far as conducting + + align:start position:0% +model for this as far as conducting + + + align:start position:0% +model for this as far as conducting +noise into the input and maybe I would + + align:start position:0% +noise into the input and maybe I would + + + align:start position:0% +noise into the input and maybe I would +consider my noise to be you know + + align:start position:0% +consider my noise to be you know + + + align:start position:0% +consider my noise to be you know +whatever Ripple here is I'll call this + + align:start position:0% +whatever Ripple here is I'll call this + + + align:start position:0% +whatever Ripple here is I'll call this +iy right so if I'm driving Ripple + + align:start position:0% +iy right so if I'm driving Ripple + + + align:start position:0% +iy right so if I'm driving Ripple +current back into this input um then I'm + + align:start position:0% +current back into this input um then I'm + + + align:start position:0% +current back into this input um then I'm +generating noise in the input maybe + + align:start position:0% +generating noise in the input maybe + + + align:start position:0% +generating noise in the input maybe +that's what's interfering with my radio + + align:start position:0% +that's what's interfering with my radio + + + align:start position:0% +that's what's interfering with my radio +okay so how would I model this maybe the + + align:start position:0% +okay so how would I model this maybe the + + + align:start position:0% +okay so how would I model this maybe the +easiest thing for me to do is say let me + + align:start position:0% +easiest thing for me to do is say let me + + + align:start position:0% +easiest thing for me to do is say let me +Pretend This is a + + align:start position:0% +Pretend This is a + + + align:start position:0% +Pretend This is a +uh constant current inductor right I'm + + align:start position:0% +uh constant current inductor right I'm + + + align:start position:0% +uh constant current inductor right I'm +not going to worry about the inductor + + align:start position:0% +not going to worry about the inductor + + + align:start position:0% +not going to worry about the inductor +Ripple and a simplified model for this + + align:start position:0% +Ripple and a simplified model for this + + + align:start position:0% +Ripple and a simplified model for this +would be something like this I'd have + + align:start position:0% +would be something like this I'd have + + + align:start position:0% +would be something like this I'd have +some current + + align:start position:0% + + + + align:start position:0% + +iix which is you know some Square wave + + align:start position:0% +iix which is you know some Square wave + + + align:start position:0% +iix which is you know some Square wave +right and then maybe I would I would + + align:start position:0% +right and then maybe I would I would + + + align:start position:0% +right and then maybe I would I would +only care about IX Tilda the AC + + align:start position:0% +only care about IX Tilda the AC + + + align:start position:0% +only care about IX Tilda the AC +component of that right so maybe I'll + + align:start position:0% +component of that right so maybe I'll + + + align:start position:0% +component of that right so maybe I'll +just worry about the AC component of + + align:start position:0% +just worry about the AC component of + + + align:start position:0% +just worry about the AC component of +this current Right is coming into the + + align:start position:0% +this current Right is coming into the + + + align:start position:0% +this current Right is coming into the +filter capacitor into the source + + align:start position:0% + + + + align:start position:0% + +impedance okay and maybe I will worry + + align:start position:0% +impedance okay and maybe I will worry + + + align:start position:0% +impedance okay and maybe I will worry +about + + align:start position:0% +about + + + align:start position:0% +about +iy or maybe I will worry about the + + align:start position:0% +iy or maybe I will worry about the + + + align:start position:0% +iy or maybe I will worry about the +voltage here + + align:start position:0% + + + + align:start position:0% + +VX right where I could specify either + + align:start position:0% +VX right where I could specify either + + + align:start position:0% +VX right where I could specify either +thing to worry about the filter right + + align:start position:0% +thing to worry about the filter right + + + align:start position:0% +thing to worry about the filter right +well let's just think about the effect + + align:start position:0% +well let's just think about the effect + + + align:start position:0% +well let's just think about the effect +of the source impedance on my + + align:start position:0% +of the source impedance on my + + + align:start position:0% +of the source impedance on my +measurements right if + + align:start position:0% +measurements right if + + + align:start position:0% +measurements right if +Zs goes to + + align:start position:0% +Zs goes to + + + align:start position:0% +Zs goes to +zero right if I had a really good + + align:start position:0% +zero right if I had a really good + + + align:start position:0% +zero right if I had a really good +source then what would happen if Zs goes + + align:start position:0% +source then what would happen if Zs goes + + + align:start position:0% +source then what would happen if Zs goes +to zero I uh i y goes to iix right if + + align:start position:0% +to zero I uh i y goes to iix right if + + + align:start position:0% +to zero I uh i y goes to iix right if +there's no Source impedance this + + align:start position:0% +there's no Source impedance this + + + align:start position:0% +there's no Source impedance this +capacitor does nothing and all the + + align:start position:0% +capacitor does nothing and all the + + + align:start position:0% +capacitor does nothing and all the +Ripple goes back into my input + + align:start position:0% +Ripple goes back into my input + + + align:start position:0% +Ripple goes back into my input +right um of course if Zs goes to zero + + align:start position:0% +right um of course if Zs goes to zero + + + align:start position:0% +right um of course if Zs goes to zero +then V subx tlda goes to zero + + align:start position:0% +then V subx tlda goes to zero + + + align:start position:0% +then V subx tlda goes to zero +all right so if I had no Source + + align:start position:0% +all right so if I had no Source + + + align:start position:0% +all right so if I had no Source +impedance I'd get all of my input would + + align:start position:0% +impedance I'd get all of my input would + + + align:start position:0% +impedance I'd get all of my input would +see the Ripple current from the + + align:start position:0% +see the Ripple current from the + + + align:start position:0% +see the Ripple current from the +converter but I wouldn't have any + + align:start position:0% +converter but I wouldn't have any + + + align:start position:0% +converter but I wouldn't have any +voltage ripple at the input in my + + align:start position:0% +voltage ripple at the input in my + + + align:start position:0% +voltage ripple at the input in my +converter on the other hand if zass at + + align:start position:0% +converter on the other hand if zass at + + + align:start position:0% +converter on the other hand if zass at +Ripple frequencies went to + + align:start position:0% +Ripple frequencies went to + + + align:start position:0% +Ripple frequencies went to +Infinity what would happen in that case + + align:start position:0% +Infinity what would happen in that case + + + align:start position:0% +Infinity what would happen in that case +well then I'd have a really high + + align:start position:0% +well then I'd have a really high + + + align:start position:0% +well then I'd have a really high +impedance here the Ripple current that + + align:start position:0% +impedance here the Ripple current that + + + align:start position:0% +impedance here the Ripple current that +I'd measure would go to zero right + + align:start position:0% +I'd measure would go to zero right + + + align:start position:0% +I'd measure would go to zero right +because this is just a very high source + + align:start position:0% +because this is just a very high source + + + align:start position:0% +because this is just a very high source +impedance and I wouldn't all the current + + align:start position:0% +impedance and I wouldn't all the current + + + align:start position:0% +impedance and I wouldn't all the current +would go through the + + align:start position:0% +would go through the + + + align:start position:0% +would go through the +capacitor and V subx would go to you + + align:start position:0% +capacitor and V subx would go to you + + + align:start position:0% +capacitor and V subx would go to you +know sort of the it would go to I subx / + + align:start position:0% +know sort of the it would go to I subx / + + + align:start position:0% +know sort of the it would go to I subx / +by J Omega C + + align:start position:0% +by J Omega C + + + align:start position:0% +by J Omega C +right so my point is this depending upon + + align:start position:0% +right so my point is this depending upon + + + align:start position:0% +right so my point is this depending upon +what I care about whether I'm measuring + + align:start position:0% +what I care about whether I'm measuring + + + align:start position:0% +what I care about whether I'm measuring +voltage here or current + + align:start position:0% +voltage here or current + + + align:start position:0% +voltage here or current +here the source impedance affects both + + align:start position:0% +here the source impedance affects both + + + align:start position:0% +here the source impedance affects both +of those + + align:start position:0% +of those + + + align:start position:0% +of those +measurements all right and that's a + + align:start position:0% +measurements all right and that's a + + + align:start position:0% +measurements all right and that's a +problem because here's the way Emi works + + align:start position:0% +problem because here's the way Emi works + + + align:start position:0% +problem because here's the way Emi works +so so if I want to + + align:start position:0% +so so if I want to + + + align:start position:0% +so so if I want to +go if I want to go sell a power supply a + + align:start position:0% +go if I want to go sell a power supply a + + + align:start position:0% +go if I want to go sell a power supply a +commercial power supply that I'm going + + align:start position:0% +commercial power supply that I'm going + + + align:start position:0% +commercial power supply that I'm going +to plug into the wall I have to go test + + align:start position:0% +to plug into the wall I have to go test + + + align:start position:0% +to plug into the wall I have to go test +it and make it meet + + align:start position:0% +it and make it meet + + + align:start position:0% +it and make it meet +standards okay and then I don't do + + align:start position:0% +standards okay and then I don't do + + + align:start position:0% +standards okay and then I don't do +anything I just take that result and I + + align:start position:0% +anything I just take that result and I + + + align:start position:0% +anything I just take that result and I +put in a d drawer and as long as nobody + + align:start position:0% +put in a d drawer and as long as nobody + + + align:start position:0% +put in a d drawer and as long as nobody +complains great but if somebody comes + + align:start position:0% +complains great but if somebody comes + + + align:start position:0% +complains great but if somebody comes +back and says oh you've got to you know + + align:start position:0% +back and says oh you've got to you know + + + align:start position:0% +back and says oh you've got to you know +you're emitting too much Emi then I've + + align:start position:0% +you're emitting too much Emi then I've + + + align:start position:0% +you're emitting too much Emi then I've +got to produce this test result and we + + align:start position:0% +got to produce this test result and we + + + align:start position:0% +got to produce this test result and we +got to come to some agreement or they've + + align:start position:0% +got to come to some agreement or they've + + + align:start position:0% +got to come to some agreement or they've +got to be they've got to be able to + + align:start position:0% +got to be they've got to be able to + + + align:start position:0% +got to be they've got to be able to +ascertain did my power supply pass the + + align:start position:0% +ascertain did my power supply pass the + + + align:start position:0% +ascertain did my power supply pass the +test or not and what I'm telling you + + align:start position:0% +test or not and what I'm telling you + + + align:start position:0% +test or not and what I'm telling you +here is that if you try to just plug a + + align:start position:0% +here is that if you try to just plug a + + + align:start position:0% +here is that if you try to just plug a +power supply into a source the result + + align:start position:0% +power supply into a source the result + + + align:start position:0% +power supply into a source the result +you get depends very very heavily on the + + align:start position:0% +you get depends very very heavily on the + + + align:start position:0% +you get depends very very heavily on the +source + + align:start position:0% +source + + + align:start position:0% +source +impedance so if I'm designing a power + + align:start position:0% +impedance so if I'm designing a power + + + align:start position:0% +impedance so if I'm designing a power +converter for a + + align:start position:0% +converter for a + + + align:start position:0% +converter for a +car that Source impedance depends upon + + align:start position:0% +car that Source impedance depends upon + + + align:start position:0% +car that Source impedance depends upon +what model car what weak it is you know + + align:start position:0% +what model car what weak it is you know + + + align:start position:0% +what model car what weak it is you know +what else they have plugged into the bus + + align:start position:0% +what else they have plugged into the bus + + + align:start position:0% +what else they have plugged into the bus +it depends on all kinds of stuff that I + + align:start position:0% +it depends on all kinds of stuff that I + + + align:start position:0% +it depends on all kinds of stuff that I +don't control right so if I'm going to + + align:start position:0% +don't control right so if I'm going to + + + align:start position:0% +don't control right so if I'm going to +sell a power supply to plug into the BMW + + align:start position:0% +sell a power supply to plug into the BMW + + + align:start position:0% +sell a power supply to plug into the BMW +or into some other brand car they have + + align:start position:0% +or into some other brand car they have + + + align:start position:0% +or into some other brand car they have +no way of you know coming to an + + align:start position:0% +no way of you know coming to an + + + align:start position:0% +no way of you know coming to an +agreement with me as to whether my power + + align:start position:0% +agreement with me as to whether my power + + + align:start position:0% +agreement with me as to whether my power +supply passes because on a different + + align:start position:0% +supply passes because on a different + + + align:start position:0% +supply passes because on a different +model or with different stuff plugged in + + align:start position:0% +model or with different stuff plugged in + + + align:start position:0% +model or with different stuff plugged in +you might get a completely different + + align:start position:0% +you might get a completely different + + + align:start position:0% +you might get a completely different +result does that make sense + + align:start position:0% + + + + align:start position:0% + +everybody so what do you do about this + + align:start position:0% +everybody so what do you do about this + + + align:start position:0% +everybody so what do you do about this +okay and this is what underpins Emi test + + align:start position:0% +okay and this is what underpins Emi test + + + align:start position:0% +okay and this is what underpins Emi test +procedures and I will say that um for + + align:start position:0% +procedures and I will say that um for + + + align:start position:0% +procedures and I will say that um for +any procedure you want to test like + + align:start position:0% +any procedure you want to test like + + + align:start position:0% +any procedure you want to test like +there's sa has a set of specifications + + align:start position:0% +there's sa has a set of specifications + + + align:start position:0% +there's sa has a set of specifications +that they recommend Ted test procedures + + align:start position:0% +that they recommend Ted test procedures + + + align:start position:0% +that they recommend Ted test procedures +if you want to PL qualify for something + + align:start position:0% +if you want to PL qualify for something + + + align:start position:0% +if you want to PL qualify for something +into the wall FCC title 17 has a whole + + align:start position:0% +into the wall FCC title 17 has a whole + + + align:start position:0% +into the wall FCC title 17 has a whole +set of procedures that you follow and + + align:start position:0% +set of procedures that you follow and + + + align:start position:0% +set of procedures that you follow and +these procedures are designed to deal + + align:start position:0% +these procedures are designed to deal + + + align:start position:0% +these procedures are designed to deal +with this issue that you've got to frame + + align:start position:0% +with this issue that you've got to frame + + + align:start position:0% +with this issue that you've got to frame +a test that if I tested this we week and + + align:start position:0% +a test that if I tested this we week and + + + align:start position:0% +a test that if I tested this we week and +I test it next week and I test it the + + align:start position:0% +I test it next week and I test it the + + + align:start position:0% +I test it next week and I test it the +week after that in some other place I'm + + align:start position:0% +week after that in some other place I'm + + + align:start position:0% +week after that in some other place I'm +going to get more or less the same + + align:start position:0% +going to get more or less the same + + + align:start position:0% +going to get more or less the same +result right so it's not that it + + align:start position:0% +result right so it's not that it + + + align:start position:0% +result right so it's not that it +necessarily reflects the real + + align:start position:0% +necessarily reflects the real + + + align:start position:0% +necessarily reflects the real +environment but it reflects a + + align:start position:0% +environment but it reflects a + + + align:start position:0% +environment but it reflects a +standardized environment that I can I I + + align:start position:0% +standardized environment that I can I I + + + align:start position:0% +standardized environment that I can I I +can rely on okay so here's how they do + + align:start position:0% +can rely on okay so here's how they do + + + align:start position:0% +can rely on okay so here's how they do +it um what we would really do is the + + align:start position:0% +it um what we would really do is the + + + align:start position:0% +it um what we would really do is the +following or this is actually I'm going + + align:start position:0% +following or this is actually I'm going + + + align:start position:0% +following or this is actually I'm going +to give you a slightly simplified + + align:start position:0% +to give you a slightly simplified + + + align:start position:0% +to give you a slightly simplified +version of what you would really do um + + align:start position:0% + + + + align:start position:0% + +suppose here's my load and I'm talking + + align:start position:0% +suppose here's my load and I'm talking + + + align:start position:0% +suppose here's my load and I'm talking +about an input filter because I'm going + + align:start position:0% +about an input filter because I'm going + + + align:start position:0% +about an input filter because I'm going +to plug this thing into the wall so + + align:start position:0% +to plug this thing into the wall so + + + align:start position:0% +to plug this thing into the wall so +here's my + + align:start position:0% +here's my + + + align:start position:0% +here's my +converter right and it's generating some + + align:start position:0% +converter right and it's generating some + + + align:start position:0% +converter right and it's generating some +Ripple current + + align:start position:0% +Ripple current + + + align:start position:0% +Ripple current +iix and here's + + align:start position:0% +iix and here's + + + align:start position:0% +iix and here's +my you know whatever my filter is and + + align:start position:0% +my you know whatever my filter is and + + + align:start position:0% +my you know whatever my filter is and +here I'm just going to draw my filter as + + align:start position:0% +here I'm just going to draw my filter as + + + align:start position:0% +here I'm just going to draw my filter as +a capacitor okay what I'm going to do is + + align:start position:0% +a capacitor okay what I'm going to do is + + + align:start position:0% +a capacitor okay what I'm going to do is +I'm not going to plug this into my power + + align:start position:0% +I'm not going to plug this into my power + + + align:start position:0% +I'm not going to plug this into my power +source which could be my vehicle battery + + align:start position:0% +source which could be my vehicle battery + + + align:start position:0% +source which could be my vehicle battery +but instead I'm going to go get another + + align:start position:0% +but instead I'm going to go get another + + + align:start position:0% +but instead I'm going to go get another +box and connect this up to a box that + + align:start position:0% +box and connect this up to a box that + + + align:start position:0% +box and connect this up to a box that +looks like this uh it has a series + + align:start position:0% +looks like this uh it has a series + + + align:start position:0% +looks like this uh it has a series +inductance l + + align:start position:0% +inductance l + + + align:start position:0% +inductance l +lizen and a shun capacitance C + + align:start position:0% +lizen and a shun capacitance C + + + align:start position:0% +lizen and a shun capacitance C +lizen sometimes it has another capacitor + + align:start position:0% +lizen sometimes it has another capacitor + + + align:start position:0% +lizen sometimes it has another capacitor +here to ground and then this is going to + + align:start position:0% +here to ground and then this is going to + + + align:start position:0% +here to ground and then this is going to +have some + + align:start position:0% +have some + + + align:start position:0% +have some +output + + align:start position:0% +output + + + align:start position:0% +output +okay and then I'm going to connect this + + align:start position:0% +okay and then I'm going to connect this + + + align:start position:0% +okay and then I'm going to connect this +into the power source so here we go + + align:start position:0% +into the power source so here we go + + + align:start position:0% +into the power source so here we go +here's + + align:start position:0% +here's + + + align:start position:0% +here's +Zs and here is uh vs right so this is + + align:start position:0% +Zs and here is uh vs right so this is + + + align:start position:0% +Zs and here is uh vs right so this is +whatever my usual source is if this is + + align:start position:0% +whatever my usual source is if this is + + + align:start position:0% +whatever my usual source is if this is +my vehicle battery that's what I'm going + + align:start position:0% +my vehicle battery that's what I'm going + + + align:start position:0% +my vehicle battery that's what I'm going +to plug it into okay and this element + + align:start position:0% +to plug it into okay and this element + + + align:start position:0% +to plug it into okay and this element +here comes in a box it's a standardized + + align:start position:0% +here comes in a box it's a standardized + + + align:start position:0% +here comes in a box it's a standardized +element and then I'm going to go plug + + align:start position:0% +element and then I'm going to go plug + + + align:start position:0% +element and then I'm going to go plug +this output of this thing + + align:start position:0% +this output of this thing + + + align:start position:0% +this output of this thing +into a spectrum analizer + + align:start position:0% + + + + align:start position:0% + +and this is going to be the input of the + + align:start position:0% +and this is going to be the input of the + + + align:start position:0% +and this is going to be the input of the +spectrum analyzer is you know has a 50 + + align:start position:0% +spectrum analyzer is you know has a 50 + + + align:start position:0% +spectrum analyzer is you know has a 50 +ohm input right so basically my spectr + + align:start position:0% +ohm input right so basically my spectr + + + align:start position:0% +ohm input right so basically my spectr +analyzer looks like a 50 ohm input okay + + align:start position:0% +analyzer looks like a 50 ohm input okay + + + align:start position:0% +analyzer looks like a 50 ohm input okay +and the idea of this this box is called + + align:start position:0% +and the idea of this this box is called + + + align:start position:0% +and the idea of this this box is called +a line impedance stabilization Network + + align:start position:0% + + + + align:start position:0% + +or lizen line imped and stabilization + + align:start position:0% +or lizen line imped and stabilization + + + align:start position:0% +or lizen line imped and stabilization +Network and its job is to prevent a + + align:start position:0% +Network and its job is to prevent a + + + align:start position:0% +Network and its job is to prevent a +present a + + align:start position:0% +present a + + + align:start position:0% +present a +consistent measurement point for + + align:start position:0% +consistent measurement point for + + + align:start position:0% +consistent measurement point for +Emi so what does this thing do it's it's + + align:start position:0% +Emi so what does this thing do it's it's + + + align:start position:0% +Emi so what does this thing do it's it's +its own kind of filter but the idea is + + align:start position:0% +its own kind of filter but the idea is + + + align:start position:0% +its own kind of filter but the idea is +at DC all the DC current I want to + + align:start position:0% +at DC all the DC current I want to + + + align:start position:0% +at DC all the DC current I want to +provide to my converter from my source + + align:start position:0% +provide to my converter from my source + + + align:start position:0% +provide to my converter from my source +will just pass through this + + align:start position:0% +will just pass through this + + + align:start position:0% +will just pass through this +inductor okay this will have some cut + + align:start position:0% +inductor okay this will have some cut + + + align:start position:0% +inductor okay this will have some cut +off frequency and L lizen and C lizen in + + align:start position:0% +off frequency and L lizen and C lizen in + + + align:start position:0% +off frequency and L lizen and C lizen in +this capacitor depending upon the lizen + + align:start position:0% +this capacitor depending upon the lizen + + + align:start position:0% +this capacitor depending upon the lizen +will be + + align:start position:0% +will be + + + align:start position:0% +will be +specified okay and a below some + + align:start position:0% +specified okay and a below some + + + align:start position:0% +specified okay and a below some +frequency all the currents just going to + + align:start position:0% +frequency all the currents just going to + + + align:start position:0% +frequency all the currents just going to +come from the input and it'll you know + + align:start position:0% +come from the input and it'll you know + + + align:start position:0% +come from the input and it'll you know +draw power just as normal when I get to + + align:start position:0% +draw power just as normal when I get to + + + align:start position:0% +draw power just as normal when I get to +really really high frequencies you know + + align:start position:0% +really really high frequencies you know + + + align:start position:0% +really really high frequencies you know +tens of megahertz or whatever the idea + + align:start position:0% +tens of megahertz or whatever the idea + + + align:start position:0% +tens of megahertz or whatever the idea +is that this path will look like an open + + align:start position:0% +is that this path will look like an open + + + align:start position:0% +is that this path will look like an open +circuit cism will look like a short + + align:start position:0% +circuit cism will look like a short + + + align:start position:0% +circuit cism will look like a short +circuit and I will be when I look back + + align:start position:0% +circuit and I will be when I look back + + + align:start position:0% +circuit and I will be when I look back +into here if I look back this way at + + align:start position:0% +into here if I look back this way at + + + align:start position:0% +into here if I look back this way at +radio frequencies what I'm going to see + + align:start position:0% +radio frequencies what I'm going to see + + + align:start position:0% +radio frequencies what I'm going to see +is 50 + + align:start position:0% +is 50 + + + align:start position:0% +is 50 +ohms okay and so whatever noise I + + align:start position:0% +ohms okay and so whatever noise I + + + align:start position:0% +ohms okay and so whatever noise I +conduct from my switching is going to be + + align:start position:0% +conduct from my switching is going to be + + + align:start position:0% +conduct from my switching is going to be +looking back into 50 ohms and if we plug + + align:start position:0% +looking back into 50 ohms and if we plug + + + align:start position:0% +looking back into 50 ohms and if we plug +this test setup into here where the Zs + + align:start position:0% +this test setup into here where the Zs + + + align:start position:0% +this test setup into here where the Zs +is one thing and and somebody else plugs + + align:start position:0% +is one thing and and somebody else plugs + + + align:start position:0% +is one thing and and somebody else plugs +it into the Zs is another thing you're + + align:start position:0% +it into the Zs is another thing you're + + + align:start position:0% +it into the Zs is another thing you're +still going to get pretty close to the + + align:start position:0% +still going to get pretty close to the + + + align:start position:0% +still going to get pretty close to the +same results okay so this box this lizen + + align:start position:0% +same results okay so this box this lizen + + + align:start position:0% +same results okay so this box this lizen +is only for testing it's not something + + align:start position:0% +is only for testing it's not something + + + align:start position:0% +is only for testing it's not something +that goes with your converter it's just + + align:start position:0% +that goes with your converter it's just + + + align:start position:0% +that goes with your converter it's just +part of the test stand okay to make + + align:start position:0% +part of the test stand okay to make + + + align:start position:0% +part of the test stand okay to make +measurements okay and I give you + + align:start position:0% +measurements okay and I give you + + + align:start position:0% +measurements okay and I give you +examples of values what are the values + + align:start position:0% +examples of values what are the values + + + align:start position:0% +examples of values what are the values +of those things it depends are you + + align:start position:0% +of those things it depends are you + + + align:start position:0% +of those things it depends are you +building something for a car or they + + align:start position:0% +building something for a car or they + + + align:start position:0% +building something for a car or they +have one set of Standards you're + + align:start position:0% +have one set of Standards you're + + + align:start position:0% +have one set of Standards you're +building it for for uh for FCC plug into + + align:start position:0% +building it for for uh for FCC plug into + + + align:start position:0% +building it for for uh for FCC plug into +a wall they have another set of + + align:start position:0% +a wall they have another set of + + + align:start position:0% +a wall they have another set of +Standards but all that is documented and + + align:start position:0% +Standards but all that is documented and + + + align:start position:0% +Standards but all that is documented and +you test according to that standard + + align:start position:0% +you test according to that standard + + + align:start position:0% +you test according to that standard +okay any questions about this so + + align:start position:0% +okay any questions about this so + + + align:start position:0% +okay any questions about this so +far yeah so thator over there um on the + + align:start position:0% +far yeah so thator over there um on the + + + align:start position:0% +far yeah so thator over there um on the +left side + + align:start position:0% + + + + align:start position:0% + +yeah it depends on the lizen so it + + align:start position:0% +yeah it depends on the lizen so it + + + align:start position:0% +yeah it depends on the lizen so it +depends on the standard yeah some some + + align:start position:0% +depends on the standard yeah some some + + + align:start position:0% +depends on the standard yeah some some +will just have an inductor and a + + align:start position:0% +will just have an inductor and a + + + align:start position:0% +will just have an inductor and a +capacitor others will have another + + align:start position:0% +capacitor others will have another + + + align:start position:0% +capacitor others will have another +capacitor on the other side that that's + + align:start position:0% +capacitor on the other side that that's + + + align:start position:0% +capacitor on the other side that that's +a function of what the lizen looks like + + align:start position:0% +a function of what the lizen looks like + + + align:start position:0% +a function of what the lizen looks like +exactly inside depends on the + + align:start position:0% +exactly inside depends on the + + + align:start position:0% +exactly inside depends on the +standard other + + align:start position:0% + + + + align:start position:0% + +questions okay so presenting a known + + align:start position:0% +questions okay so presenting a known + + + align:start position:0% +questions okay so presenting a known +lizen impedance lets me make repeatable + + align:start position:0% +lizen impedance lets me make repeatable + + + align:start position:0% +lizen impedance lets me make repeatable +measurements on on my converter and you + + align:start position:0% +measurements on on my converter and you + + + align:start position:0% +measurements on on my converter and you +know if I measure it this week I get the + + align:start position:0% +know if I measure it this week I get the + + + align:start position:0% +know if I measure it this week I get the +same result as next week usually the way + + align:start position:0% +same result as next week usually the way + + + align:start position:0% +same result as next week usually the way +you would do this I should say by the + + align:start position:0% +you would do this I should say by the + + + align:start position:0% +you would do this I should say by the +way there's a lot of if you if you look + + align:start position:0% +way there's a lot of if you if you look + + + align:start position:0% +way there's a lot of if you if you look +up to get very very repeatable + + align:start position:0% +up to get very very repeatable + + + align:start position:0% +up to get very very repeatable +measurements they have all kinds of + + align:start position:0% +measurements they have all kinds of + + + align:start position:0% +measurements they have all kinds of +standards you know your your converter + + align:start position:0% +standards you know your your converter + + + align:start position:0% +standards you know your your converter +has to be you know one meter or some + + align:start position:0% +has to be you know one meter or some + + + align:start position:0% +has to be you know one meter or some +some specified height over a ground + + align:start position:0% +some specified height over a ground + + + align:start position:0% +some specified height over a ground +plane it's like they they make all the + + align:start position:0% +plane it's like they they make all the + + + align:start position:0% +plane it's like they they make all the +conditions exactly identical which + + align:start position:0% +conditions exactly identical which + + + align:start position:0% +conditions exactly identical which +aren't real world conditions but they're + + align:start position:0% +aren't real world conditions but they're + + + align:start position:0% +aren't real world conditions but they're +just designed to make the test + + align:start position:0% +just designed to make the test + + + align:start position:0% +just designed to make the test +repeatable + + align:start position:0% +repeatable + + + align:start position:0% +repeatable +and you follow that okay so very often + + align:start position:0% +and you follow that okay so very often + + + align:start position:0% +and you follow that okay so very often +if you're trying to qualify a power + + align:start position:0% +if you're trying to qualify a power + + + align:start position:0% +if you're trying to qualify a power +supply you'll ultimately go to a test + + align:start position:0% +supply you'll ultimately go to a test + + + align:start position:0% +supply you'll ultimately go to a test +house but that's what they do okay what + + align:start position:0% +house but that's what they do okay what + + + align:start position:0% +house but that's what they do okay what +you do in the lab is you can set up an + + align:start position:0% +you do in the lab is you can set up an + + + align:start position:0% +you do in the lab is you can set up an +approximation to that usually I mean you + + align:start position:0% +approximation to that usually I mean you + + + align:start position:0% +approximation to that usually I mean you +can set up a real test stand if you're a + + align:start position:0% +can set up a real test stand if you're a + + + align:start position:0% +can set up a real test stand if you're a +company that's making lots of Parts but + + align:start position:0% +company that's making lots of Parts but + + + align:start position:0% +company that's making lots of Parts but +at home you can go buy a lizen and you + + align:start position:0% +at home you can go buy a lizen and you + + + align:start position:0% +at home you can go buy a lizen and you +know do an approximation to that it'll + + align:start position:0% +know do an approximation to that it'll + + + align:start position:0% +know do an approximation to that it'll +be pretty good it's good enough for + + align:start position:0% +be pretty good it's good enough for + + + align:start position:0% +be pretty good it's good enough for +designing a power supply if you put a + + align:start position:0% +designing a power supply if you put a + + + align:start position:0% +designing a power supply if you put a +bunch of margin in your answers and the + + align:start position:0% +bunch of margin in your answers and the + + + align:start position:0% +bunch of margin in your answers and the +way this thing the way the + + align:start position:0% +way this thing the way the + + + align:start position:0% +way this thing the way the +specifications are R is for conducted + + align:start position:0% +specifications are R is for conducted + + + align:start position:0% +specifications are R is for conducted +Emi you'll look at this + + align:start position:0% +Emi you'll look at this + + + align:start position:0% +Emi you'll look at this +response Spectrum analyzer configured a + + align:start position:0% +response Spectrum analyzer configured a + + + align:start position:0% +response Spectrum analyzer configured a +certain way with certain kinds of you + + align:start position:0% +certain way with certain kinds of you + + + align:start position:0% +certain way with certain kinds of you +know quasi Peak or Peak detectors + + align:start position:0% +know quasi Peak or Peak detectors + + + align:start position:0% +know quasi Peak or Peak detectors +there's a whole bunch of rules around it + + align:start position:0% +there's a whole bunch of rules around it + + + align:start position:0% +there's a whole bunch of rules around it +and you're generally measuring the + + align:start position:0% +and you're generally measuring the + + + align:start position:0% +and you're generally measuring the +energy in different frequency bands and + + align:start position:0% +energy in different frequency bands and + + + align:start position:0% +energy in different frequency bands and +seeing do they go above an allowed limit + + align:start position:0% +seeing do they go above an allowed limit + + + align:start position:0% +seeing do they go above an allowed limit +okay and those allowed limits are really + + align:start position:0% +okay and those allowed limits are really + + + align:start position:0% +okay and those allowed limits are really +small so if I thought I had you know uh + + align:start position:0% +small so if I thought I had you know uh + + + align:start position:0% +small so if I thought I had you know uh +you know this was you know switching + + align:start position:0% +you know this was you know switching + + + align:start position:0% +you know this was you know switching +tens of amps here I might be required to + + align:start position:0% +tens of amps here I might be required to + + + align:start position:0% +tens of amps here I might be required to +get tens of + + align:start position:0% +get tens of + + + align:start position:0% +get tens of +microamps right so it's really small + + align:start position:0% +microamps right so it's really small + + + align:start position:0% +microamps right so it's really small +currents that you've got to attenuate + + align:start position:0% +currents that you've got to attenuate + + + align:start position:0% +currents that you've got to attenuate +down to okay so um you know when I when + + align:start position:0% +down to okay so um you know when I when + + + align:start position:0% +down to okay so um you know when I when +I show you oh we've got a capacitor here + + align:start position:0% +I show you oh we've got a capacitor here + + + align:start position:0% +I show you oh we've got a capacitor here +right uh the model for this would then + + align:start position:0% +right uh the model for this would then + + + align:start position:0% +right uh the model for this would then +be you know basically a capacitor and + + align:start position:0% +be you know basically a capacitor and + + + align:start position:0% +be you know basically a capacitor and +parallel with 50 ohms and I'm trying to + + align:start position:0% +parallel with 50 ohms and I'm trying to + + + align:start position:0% +parallel with 50 ohms and I'm trying to +measure that voltage Ripple on the 50 + + align:start position:0% +measure that voltage Ripple on the 50 + + + align:start position:0% +measure that voltage Ripple on the 50 +ohms you're going to need more than a + + align:start position:0% +ohms you're going to need more than a + + + align:start position:0% +ohms you're going to need more than a +capacitor to make this work + + align:start position:0% +capacitor to make this work + + + align:start position:0% +capacitor to make this work +okay so you're very often you're going + + align:start position:0% +okay so you're very often you're going + + + align:start position:0% +okay so you're very often you're going +to need a multi-stage filter I will say + + align:start position:0% +to need a multi-stage filter I will say + + + align:start position:0% +to need a multi-stage filter I will say +one other thing by the + + align:start position:0% +one other thing by the + + + align:start position:0% +one other thing by the +way I've drawn this as if you have a + + align:start position:0% +way I've drawn this as if you have a + + + align:start position:0% +way I've drawn this as if you have a +lizen that you stick in between your + + align:start position:0% +lizen that you stick in between your + + + align:start position:0% +lizen that you stick in between your +power source and your converter and you + + align:start position:0% +power source and your converter and you + + + align:start position:0% +power source and your converter and you +do but typically most specifications + + align:start position:0% +do but typically most specifications + + + align:start position:0% +do but typically most specifications +require that you put a lizen on this + + align:start position:0% +require that you put a lizen on this + + + align:start position:0% +require that you put a lizen on this +lead and a separate lizen on this lead + + align:start position:0% +lead and a separate lizen on this lead + + + align:start position:0% +lead and a separate lizen on this lead +right so so there's actually two liens + + align:start position:0% +right so so there's actually two liens + + + align:start position:0% +right so so there's actually two liens +involved in a in a DC System test will + + align:start position:0% +involved in a in a DC System test will + + + align:start position:0% +involved in a in a DC System test will +come back to why you would do that uh + + align:start position:0% +come back to why you would do that uh + + + align:start position:0% +come back to why you would do that uh +later but the basic concept is not + + align:start position:0% +later but the basic concept is not + + + align:start position:0% +later but the basic concept is not +changed it's the same idea + + align:start position:0% +changed it's the same idea + + + align:start position:0% +changed it's the same idea +okay now um let's just think of what we + + align:start position:0% +okay now um let's just think of what we + + + align:start position:0% +okay now um let's just think of what we +would need I said okay um a capacitor is + + align:start position:0% +would need I said okay um a capacitor is + + + align:start position:0% +would need I said okay um a capacitor is +not really going to cut it for this + + align:start position:0% +not really going to cut it for this + + + align:start position:0% +not really going to cut it for this +measurement okay so let me think about + + align:start position:0% +measurement okay so let me think about + + + align:start position:0% +measurement okay so let me think about +um my converter is some current + + align:start position:0% + + + + align:start position:0% + +or iix Tia this is the Ripple for my + + align:start position:0% +or iix Tia this is the Ripple for my + + + align:start position:0% +or iix Tia this is the Ripple for my +converter right + + align:start position:0% +converter right + + + align:start position:0% +converter right +um if a converter if + + align:start position:0% + + + + align:start position:0% + +a if a capacitor is not going to be + + align:start position:0% +a if a capacitor is not going to be + + + align:start position:0% +a if a capacitor is not going to be +enough what would be my basic building + + align:start position:0% +enough what would be my basic building + + + align:start position:0% +enough what would be my basic building +block okay my basic building block might + + align:start position:0% +block okay my basic building block might + + + align:start position:0% +block okay my basic building block might +look something like this it might be + + align:start position:0% +look something like this it might be + + + align:start position:0% +look something like this it might be +some filter capacitor CF right and this + + align:start position:0% +some filter capacitor CF right and this + + + align:start position:0% +some filter capacitor CF right and this +could the first stage could be just my + + align:start position:0% +could the first stage could be just my + + + align:start position:0% +could the first stage could be just my +input capacitor my converter which I + + align:start position:0% +input capacitor my converter which I + + + align:start position:0% +input capacitor my converter which I +would always have um and some inductor + + align:start position:0% +would always have um and some inductor + + + align:start position:0% +would always have um and some inductor +LF now this is not the lizen inductor + + align:start position:0% +LF now this is not the lizen inductor + + + align:start position:0% +LF now this is not the lizen inductor +this is my filter inductor okay so this + + align:start position:0% +this is my filter inductor okay so this + + + align:start position:0% +this is my filter inductor okay so this +is my filter and then eventually I look + + align:start position:0% +is my filter and then eventually I look + + + align:start position:0% +is my filter and then eventually I look +back into the lizen impedance and this + + align:start position:0% +back into the lizen impedance and this + + + align:start position:0% +back into the lizen impedance and this +would be Z lizen looking + + align:start position:0% +would be Z lizen looking + + + align:start position:0% +would be Z lizen looking +here and at Ripple frequencies maybe + + align:start position:0% +here and at Ripple frequencies maybe + + + align:start position:0% +here and at Ripple frequencies maybe +that looks like 50 + + align:start position:0% +that looks like 50 + + + align:start position:0% +that looks like 50 +ohms + + align:start position:0% +ohms + + + align:start position:0% +ohms +okay so a basic building block is an LC + + align:start position:0% +okay so a basic building block is an LC + + + align:start position:0% +okay so a basic building block is an LC +filter okay um what is the what is the + + align:start position:0% +filter okay um what is the what is the + + + align:start position:0% +filter okay um what is the what is the +transfer function if I said this was iix + + align:start position:0% +transfer function if I said this was iix + + + align:start position:0% +transfer function if I said this was iix +Tilda and this was i i y Tilda what is + + align:start position:0% +Tilda and this was i i y Tilda what is + + + align:start position:0% +Tilda and this was i i y Tilda what is +the transfer function of this thing look + + align:start position:0% +the transfer function of this thing look + + + align:start position:0% +the transfer function of this thing look +like + + align:start position:0% +like + + + align:start position:0% +like +right the magnitude of i y Tilda over + + align:start position:0% +right the magnitude of i y Tilda over + + + align:start position:0% +right the magnitude of i y Tilda over +iix tlda versus Omega and this is going + + align:start position:0% +iix tlda versus Omega and this is going + + + align:start position:0% +iix tlda versus Omega and this is going +to be a log scale and this is going to + + align:start position:0% +to be a log scale and this is going to + + + align:start position:0% +to be a log scale and this is going to +be a log + + align:start position:0% +be a log + + + align:start position:0% +be a log +scale okay at DC all the current goes + + align:start position:0% +scale okay at DC all the current goes + + + align:start position:0% +scale okay at DC all the current goes +back right so a DC + + align:start position:0% +back right so a DC + + + align:start position:0% +back right so a DC +you know I'm going to get this at really + + align:start position:0% +you know I'm going to get this at really + + + align:start position:0% +you know I'm going to get this at really +low frequencies then I'm going to have + + align:start position:0% +low frequencies then I'm going to have + + + align:start position:0% +low frequencies then I'm going to have +some + + align:start position:0% +some + + + align:start position:0% +some +region that's one over the square root + + align:start position:0% +region that's one over the square root + + + align:start position:0% +region that's one over the square root +of LF + + align:start position:0% +of LF + + + align:start position:0% +of LF +CF which is going to be the cut off of + + align:start position:0% +CF which is going to be the cut off of + + + align:start position:0% +CF which is going to be the cut off of +this filter okay and at really high + + align:start position:0% +this filter okay and at really high + + + align:start position:0% +this filter okay and at really high +frequencies right this is going to fall + + align:start position:0% +frequencies right this is going to fall + + + align:start position:0% +frequencies right this is going to fall +off as 1 over Omega + + align:start position:0% +off as 1 over Omega + + + align:start position:0% +off as 1 over Omega +squar okay or + + align:start position:0% +squar okay or + + + align:start position:0% +squar okay or +minus uh 40 DB per decade all right so + + align:start position:0% +minus uh 40 DB per decade all right so + + + align:start position:0% +minus uh 40 DB per decade all right so +you know the idea here is I can go get a + + align:start position:0% +you know the idea here is I can go get a + + + align:start position:0% +you know the idea here is I can go get a +bunch of attenuation I'm going to put + + align:start position:0% +bunch of attenuation I'm going to put + + + align:start position:0% +bunch of attenuation I'm going to put +this cut off of this filter well below + + align:start position:0% +this cut off of this filter well below + + + align:start position:0% +this cut off of this filter well below +my 150 khz that I care about attenuating + + align:start position:0% +my 150 khz that I care about attenuating + + + align:start position:0% +my 150 khz that I care about attenuating +uh and kind of live off of this + + align:start position:0% +uh and kind of live off of this + + + align:start position:0% +uh and kind of live off of this +attenuation out here now why is that + + align:start position:0% +attenuation out here now why is that + + + align:start position:0% +attenuation out here now why is that +going as one over Omega squar just as a + + align:start position:0% +going as one over Omega squar just as a + + + align:start position:0% +going as one over Omega squar just as a +reminder the impedance of the + + align:start position:0% +reminder the impedance of the + + + align:start position:0% +reminder the impedance of the +capacitor the magnitude of + + align:start position:0% +capacitor the magnitude of + + + align:start position:0% +capacitor the magnitude of +zc is is goes as uh one over Omega C so + + align:start position:0% +zc is is goes as uh one over Omega C so + + + align:start position:0% +zc is is goes as uh one over Omega C so +this is getting to be a smaller + + align:start position:0% +this is getting to be a smaller + + + align:start position:0% +this is getting to be a smaller +impedance as frequency goes up and Z + + align:start position:0% +impedance as frequency goes up and Z + + + align:start position:0% +impedance as frequency goes up and Z +subel is going as Omega l so basically + + align:start position:0% +subel is going as Omega l so basically + + + align:start position:0% +subel is going as Omega l so basically +you get an Omega squar Factor because + + align:start position:0% +you get an Omega squar Factor because + + + align:start position:0% +you get an Omega squar Factor because +he's getting it's a current divider and + + align:start position:0% +he's getting it's a current divider and + + + align:start position:0% +he's getting it's a current divider and +he's getting smaller proportional + + align:start position:0% +he's getting smaller proportional + + + align:start position:0% +he's getting smaller proportional +inversely proportional to Omega and he's + + align:start position:0% +inversely proportional to Omega and he's + + + align:start position:0% +inversely proportional to Omega and he's +getting bigger proportional to Omega so + + align:start position:0% +getting bigger proportional to Omega so + + + align:start position:0% +getting bigger proportional to Omega so +you get a kind of an Omega squar + + align:start position:0% +you get a kind of an Omega squar + + + align:start position:0% +you get a kind of an Omega squar +attenuation right so the the way you + + align:start position:0% +attenuation right so the the way you + + + align:start position:0% +attenuation right so the the way you +might want to think about this is your + + align:start position:0% +might want to think about this is your + + + align:start position:0% +might want to think about this is your +filters working because of the mismatch + + align:start position:0% +filters working because of the mismatch + + + align:start position:0% +filters working because of the mismatch +between the shun path and the series + + align:start position:0% +between the shun path and the series + + + align:start position:0% +between the shun path and the series +path okay and if I don't like this I can + + align:start position:0% +path okay and if I don't like this I can + + + align:start position:0% +path okay and if I don't like this I can +can build higher order filters and so + + align:start position:0% +can build higher order filters and so + + + align:start position:0% +can build higher order filters and so +forth and we'll talk about that all + + align:start position:0% +forth and we'll talk about that all + + + align:start position:0% +forth and we'll talk about that all +right I haven't said what happens in the + + align:start position:0% +right I haven't said what happens in the + + + align:start position:0% +right I haven't said what happens in the +vicinity of cut off that's an important + + align:start position:0% +vicinity of cut off that's an important + + + align:start position:0% +vicinity of cut off that's an important +thing and we're going to have to think + + align:start position:0% +thing and we're going to have to think + + + align:start position:0% +thing and we're going to have to think +about that but you know let's for the + + align:start position:0% +about that but you know let's for the + + + align:start position:0% +about that but you know let's for the +moment uh not worry + + align:start position:0% +moment uh not worry + + + align:start position:0% +moment uh not worry +about uh not worry about what's going on + + align:start position:0% +about uh not worry about what's going on + + + align:start position:0% +about uh not worry about what's going on +here we'll come back to that point okay + + align:start position:0% +here we'll come back to that point okay + + + align:start position:0% +here we'll come back to that point okay +so any questions up to now + + align:start position:0% + + + + align:start position:0% + +okay so I want to build this + + align:start position:0% +okay so I want to build this + + + align:start position:0% +okay so I want to build this +filter okay and as I said I need a lot + + align:start position:0% +filter okay and as I said I need a lot + + + align:start position:0% +filter okay and as I said I need a lot +of + + align:start position:0% +of + + + align:start position:0% +of +attenuation okay I need you know if I'm + + align:start position:0% +attenuation okay I need you know if I'm + + + align:start position:0% +attenuation okay I need you know if I'm +going from 100 amps to 100 microamps + + align:start position:0% +going from 100 amps to 100 microamps + + + align:start position:0% +going from 100 amps to 100 microamps +right that's that's uh six orders of + + align:start position:0% +right that's that's uh six orders of + + + align:start position:0% +right that's that's uh six orders of +attenuation right so I'm going to + + align:start position:0% +attenuation right so I'm going to + + + align:start position:0% +attenuation right so I'm going to +probably need a low pretty low cut off + + align:start position:0% +probably need a low pretty low cut off + + + align:start position:0% +probably need a low pretty low cut off +filter here okay I'm going to need a + + align:start position:0% +filter here okay I'm going to need a + + + align:start position:0% +filter here okay I'm going to need a +bunch of + + align:start position:0% +bunch of + + + align:start position:0% +bunch of +attenuation and + + align:start position:0% +attenuation and + + + align:start position:0% +attenuation and +one of the things that people find about + + align:start position:0% +one of the things that people find about + + + align:start position:0% +one of the things that people find about +designing Emi filters your average Power + + align:start position:0% +designing Emi filters your average Power + + + align:start position:0% +designing Emi filters your average Power +Electronics guy hates it okay why do + + align:start position:0% +Electronics guy hates it okay why do + + + align:start position:0% +Electronics guy hates it okay why do +they hate it they hate it because you + + align:start position:0% +they hate it they hate it because you + + + align:start position:0% +they hate it they hate it because you +can very get you can very often get very + + align:start position:0% +can very get you can very often get very + + + align:start position:0% +can very get you can very often get very +kind of seemingly anomalous results like + + align:start position:0% +kind of seemingly anomalous results like + + + align:start position:0% +kind of seemingly anomalous results like +you're doing stuff and and you're just + + align:start position:0% +you're doing stuff and and you're just + + + align:start position:0% +you're doing stuff and and you're just +getting noise and you don't want this + + align:start position:0% +getting noise and you don't want this + + + align:start position:0% +getting noise and you don't want this +noise and and + + align:start position:0% +noise and and + + + align:start position:0% +noise and and +uh it becomes a pro like it's hard to + + align:start position:0% +uh it becomes a pro like it's hard to + + + align:start position:0% +uh it becomes a pro like it's hard to +get the good result that a simple + + align:start position:0% +get the good result that a simple + + + align:start position:0% +get the good result that a simple +picture like this would suggest that you + + align:start position:0% +picture like this would suggest that you + + + align:start position:0% +picture like this would suggest that you +can get okay so let me tell you just + + align:start position:0% +can get okay so let me tell you just + + + align:start position:0% +can get okay so let me tell you just +give you a heads up about some of the + + align:start position:0% +give you a heads up about some of the + + + align:start position:0% +give you a heads up about some of the +things you got to pay attention to when + + align:start position:0% +things you got to pay attention to when + + + align:start position:0% +things you got to pay attention to when +you're doing this okay and the first of + + align:start position:0% +you're doing this okay and the first of + + + align:start position:0% +you're doing this okay and the first of +these things is component parasitics + + align:start position:0% +these things is component parasitics + + + align:start position:0% +these things is component parasitics +okay so if I were to look at this filter + + align:start position:0% +okay so if I were to look at this filter + + + align:start position:0% +okay so if I were to look at this filter +and I'd say geez + + align:start position:0% +and I'd say geez + + + align:start position:0% +and I'd say geez +uh you know what is what does this look + + align:start position:0% +uh you know what is what does this look + + + align:start position:0% +uh you know what is what does this look +like well I said my + + align:start position:0% +like well I said my + + + align:start position:0% +like well I said my +capacitor right + + align:start position:0% +capacitor right + + + align:start position:0% +capacitor right +if I looked at my capacitor right and I + + align:start position:0% +if I looked at my capacitor right and I + + + align:start position:0% +if I looked at my capacitor right and I +said what is the magnitude of Z + + align:start position:0% +said what is the magnitude of Z + + + align:start position:0% +said what is the magnitude of Z +subc right I said that the magnitude of + + align:start position:0% +subc right I said that the magnitude of + + + align:start position:0% +subc right I said that the magnitude of +Z subc should fall off as one over Omega + + align:start position:0% +Z subc should fall off as one over Omega + + + align:start position:0% +Z subc should fall off as one over Omega +C right so this is the magnitude of Z + + align:start position:0% +C right so this is the magnitude of Z + + + align:start position:0% +C right so this is the magnitude of Z +subc right and if I had an ideal + + align:start position:0% +subc right and if I had an ideal + + + align:start position:0% +subc right and if I had an ideal +capacitor you know it would do that + + align:start position:0% +capacitor you know it would do that + + + align:start position:0% +capacitor you know it would do that +forever okay but what about a real + + align:start position:0% +forever okay but what about a real + + + align:start position:0% +forever okay but what about a real +capacitor well a real capacitor you know + + align:start position:0% +capacitor well a real capacitor you know + + + align:start position:0% +capacitor well a real capacitor you know +even though + + align:start position:0% +even though + + + align:start position:0% +even though +um even + + align:start position:0% +um even + + + align:start position:0% +um even +though you know I think of it as an + + align:start position:0% +though you know I think of it as an + + + align:start position:0% +though you know I think of it as an +energy storage element the plates do + + align:start position:0% +energy storage element the plates do + + + align:start position:0% +energy storage element the plates do +have some resistance right like there's + + align:start position:0% +have some resistance right like there's + + + align:start position:0% +have some resistance right like there's +actually some resistance of the wiring + + align:start position:0% +actually some resistance of the wiring + + + align:start position:0% +actually some resistance of the wiring +going into that thing right so as a + + align:start position:0% +going into that thing right so as a + + + align:start position:0% +going into that thing right so as a +practical matter a real + + align:start position:0% +practical matter a real + + + align:start position:0% +practical matter a real +capacitor is going to have some + + align:start position:0% +capacitor is going to have some + + + align:start position:0% +capacitor is going to have some +ESR series resistance right so what's + + align:start position:0% +ESR series resistance right so what's + + + align:start position:0% +ESR series resistance right so what's +that going to do well that's there's + + align:start position:0% +that going to do well that's there's + + + align:start position:0% +that going to do well that's there's +going to be some + + align:start position:0% +going to be some + + + align:start position:0% +going to be some +frequency above + + align:start position:0% +frequency above + + + align:start position:0% +frequency above +which this ESR has a bigger impedance in + + align:start position:0% +which this ESR has a bigger impedance in + + + align:start position:0% +which this ESR has a bigger impedance in +the + + align:start position:0% +the + + + align:start position:0% +the +capacitor the ideal portion of the + + align:start position:0% +capacitor the ideal portion of the + + + align:start position:0% +capacitor the ideal portion of the +capacitor right so what I would expect + + align:start position:0% +capacitor right so what I would expect + + + align:start position:0% +capacitor right so what I would expect +is beyond some + + align:start position:0% +is beyond some + + + align:start position:0% +is beyond some +frequency there's going to be some + + align:start position:0% +frequency there's going to be some + + + align:start position:0% +frequency there's going to be some +place um where + + align:start position:0% +place um where + + + align:start position:0% +place um where +RR is dominant so instead of falling off + + align:start position:0% +RR is dominant so instead of falling off + + + align:start position:0% +RR is dominant so instead of falling off +forever as one over Omega it flattens + + align:start position:0% +forever as one over Omega it flattens + + + align:start position:0% +forever as one over Omega it flattens +out eventually right and then if I keep + + align:start position:0% +out eventually right and then if I keep + + + align:start position:0% +out eventually right and then if I keep +going up in + + align:start position:0% +going up in + + + align:start position:0% +going up in +frequency right I'm going to get to some + + align:start position:0% +frequency right I'm going to get to some + + + align:start position:0% +frequency right I'm going to get to some +point where + + align:start position:0% +point where + + + align:start position:0% +point where +um I have some equivalent series + + align:start position:0% +um I have some equivalent series + + + align:start position:0% +um I have some equivalent series +inductance + + align:start position:0% +inductance + + + align:start position:0% +inductance +LL why does that exist because there is + + align:start position:0% +LL why does that exist because there is + + + align:start position:0% +LL why does that exist because there is +space between the capacitors and if I + + align:start position:0% +space between the capacitors and if I + + + align:start position:0% +space between the capacitors and if I +have current through it there's some + + align:start position:0% +have current through it there's some + + + align:start position:0% +have current through it there's some +magnetic field in there and there's just + + align:start position:0% +magnetic field in there and there's just + + + align:start position:0% +magnetic field in there and there's just +a little bit of inductance right doesn't + + align:start position:0% +a little bit of inductance right doesn't + + + align:start position:0% +a little bit of inductance right doesn't +have to be very much but we're talking + + align:start position:0% +have to be very much but we're talking + + + align:start position:0% +have to be very much but we're talking +about going to very high frequencies + + align:start position:0% +about going to very high frequencies + + + align:start position:0% +about going to very high frequencies +right so at some point + + align:start position:0% +right so at some point + + + align:start position:0% +right so at some point +this ESL will even get to be have a high + + align:start position:0% +this ESL will even get to be have a high + + + align:start position:0% +this ESL will even get to be have a high +because this is growing with Omega it's + + align:start position:0% +because this is growing with Omega it's + + + align:start position:0% +because this is growing with Omega it's +going to go + + align:start position:0% + + + + align:start position:0% + +up right so my overall Contour of my + + align:start position:0% +up right so my overall Contour of my + + + align:start position:0% +up right so my overall Contour of my +impedance doesn't fall forever but + + align:start position:0% +impedance doesn't fall forever but + + + align:start position:0% +impedance doesn't fall forever but +rather it sort of does this kind of + + align:start position:0% +rather it sort of does this kind of + + + align:start position:0% +rather it sort of does this kind of +falls flattens out and goes up and maybe + + align:start position:0% +falls flattens out and goes up and maybe + + + align:start position:0% +falls flattens out and goes up and maybe +this you know I've shown you a high ESR + + align:start position:0% +this you know I've shown you a high ESR + + + align:start position:0% +this you know I've shown you a high ESR +capacitor depending upon whether the ESR + + align:start position:0% +capacitor depending upon whether the ESR + + + align:start position:0% +capacitor depending upon whether the ESR +is greater than less than the of L over + + align:start position:0% +is greater than less than the of L over + + + align:start position:0% +is greater than less than the of L over +c l l over C you know this will be very + + align:start position:0% +c l l over C you know this will be very + + + align:start position:0% +c l l over C you know this will be very +sharply tuned or very broad but either + + align:start position:0% +sharply tuned or very broad but either + + + align:start position:0% +sharply tuned or very broad but either +way you're going to get this kind of + + align:start position:0% +way you're going to get this kind of + + + align:start position:0% +way you're going to get this kind of +behavior all right why am I harping on + + align:start position:0% +behavior all right why am I harping on + + + align:start position:0% +behavior all right why am I harping on +this because if I thought of this as my + + align:start position:0% +this because if I thought of this as my + + + align:start position:0% +this because if I thought of this as my +real + + align:start position:0% +real + + + align:start position:0% +real +element now I plug this thing in place + + align:start position:0% +element now I plug this thing in place + + + align:start position:0% +element now I plug this thing in place +of my + + align:start position:0% +of my + + + align:start position:0% +of my +capacitor what would I expect my + + align:start position:0% +capacitor what would I expect my + + + align:start position:0% +capacitor what would I expect my +attenuation to look like in that case + + align:start position:0% +attenuation to look like in that case + + + align:start position:0% +attenuation to look like in that case +well right I said it was based on the + + align:start position:0% +well right I said it was based on the + + + align:start position:0% +well right I said it was based on the +mismatch between this impedance going + + align:start position:0% +mismatch between this impedance going + + + align:start position:0% +mismatch between this impedance going +down and this impedance going up right + + align:start position:0% +down and this impedance going up right + + + align:start position:0% +down and this impedance going up right +So eventually instead of turning into uh + + align:start position:0% +So eventually instead of turning into uh + + + align:start position:0% +So eventually instead of turning into uh +an LC filter it turns into an LR filter + + align:start position:0% +an LC filter it turns into an LR filter + + + align:start position:0% +an LC filter it turns into an LR filter +right so instead of falling off as 1 + + align:start position:0% +right so instead of falling off as 1 + + + align:start position:0% +right so instead of falling off as 1 +over Omega squar it's going to fall off + + align:start position:0% +over Omega squar it's going to fall off + + + align:start position:0% +over Omega squar it's going to fall off +as one over + + align:start position:0% +as one over + + + align:start position:0% +as one over +Omega okay and when I get to really high + + align:start position:0% +Omega okay and when I get to really high + + + align:start position:0% +Omega okay and when I get to really high +frequencies ESL is going to dominate and + + align:start position:0% +frequencies ESL is going to dominate and + + + align:start position:0% +frequencies ESL is going to dominate and +then I'm just going to have a I'm just + + align:start position:0% +then I'm just going to have a I'm just + + + align:start position:0% +then I'm just going to have a I'm just +going to have a current divider between + + align:start position:0% +going to have a current divider between + + + align:start position:0% +going to have a current divider between +LL and L filter right in fact what + + align:start position:0% +LL and L filter right in fact what + + + align:start position:0% +LL and L filter right in fact what +that's going to mean is my attenuation + + align:start position:0% +that's going to mean is my attenuation + + + align:start position:0% +that's going to mean is my attenuation +is just going to flatten out right so if + + align:start position:0% +is just going to flatten out right so if + + + align:start position:0% +is just going to flatten out right so if +I design my filter thinking oh jeez + + align:start position:0% +I design my filter thinking oh jeez + + + align:start position:0% +I design my filter thinking oh jeez +that's how I get my Sixers of + + align:start position:0% +that's how I get my Sixers of + + + align:start position:0% +that's how I get my Sixers of +magnitude and I come back and I'm really + + align:start position:0% +magnitude and I come back and I'm really + + + align:start position:0% +magnitude and I come back and I'm really +dealing with something where at that + + align:start position:0% +dealing with something where at that + + + align:start position:0% +dealing with something where at that +frequency this capacitor doesn't look + + align:start position:0% +frequency this capacitor doesn't look + + + align:start position:0% +frequency this capacitor doesn't look +like a capacitor it looks like a little + + align:start position:0% +like a capacitor it looks like a little + + + align:start position:0% +like a capacitor it looks like a little +inductor my Emi might be way higher than + + align:start position:0% +inductor my Emi might be way higher than + + + align:start position:0% +inductor my Emi might be way higher than +I thought it was going to + + align:start position:0% +I thought it was going to + + + align:start position:0% +I thought it was going to +be okay my filtering is just going to + + align:start position:0% +be okay my filtering is just going to + + + align:start position:0% +be okay my filtering is just going to +get clobbered by the + + align:start position:0% +get clobbered by the + + + align:start position:0% +get clobbered by the +parasitic inductance of my capacitor + + align:start position:0% +parasitic inductance of my capacitor + + + align:start position:0% +parasitic inductance of my capacitor +okay now I will say that by the way you + + align:start position:0% +okay now I will say that by the way you + + + align:start position:0% +okay now I will say that by the way you +know this and by the way where does this + + align:start position:0% +know this and by the way where does this + + + align:start position:0% +know this and by the way where does this +kind of phenomena happen well you know + + align:start position:0% +kind of phenomena happen well you know + + + align:start position:0% +kind of phenomena happen well you know +it depends on the size of your capacitor + + align:start position:0% +it depends on the size of your capacitor + + + align:start position:0% +it depends on the size of your capacitor +the physical size of your capacitor and + + align:start position:0% +the physical size of your capacitor and + + + align:start position:0% +the physical size of your capacitor and +depends on one whether it's a good + + align:start position:0% +depends on one whether it's a good + + + align:start position:0% +depends on one whether it's a good +capacitor or not Etc but very often like + + align:start position:0% +capacitor or not Etc but very often like + + + align:start position:0% +capacitor or not Etc but very often like +10 megahertz kind of frequencies is + + align:start position:0% +10 megahertz kind of frequencies is + + + align:start position:0% +10 megahertz kind of frequencies is +where this these things are happening as + + align:start position:0% +where this these things are happening as + + + align:start position:0% +where this these things are happening as +an example or even one megahertz depends + + align:start position:0% +an example or even one megahertz depends + + + align:start position:0% +an example or even one megahertz depends +on the size of the component and that's + + align:start position:0% +on the size of the component and that's + + + align:start position:0% +on the size of the component and that's +right in the band that you're caring + + align:start position:0% +right in the band that you're caring + + + align:start position:0% +right in the band that you're caring +about and trying to attenuate okay so + + align:start position:0% +about and trying to attenuate okay so + + + align:start position:0% +about and trying to attenuate okay so +these bad + + align:start position:0% +these bad + + + align:start position:0% +these bad +parasitics of the components and usually + + align:start position:0% +parasitics of the components and usually + + + align:start position:0% +parasitics of the components and usually +the capacitor is the first thing to give + + align:start position:0% +the capacitor is the first thing to give + + + align:start position:0% +the capacitor is the first thing to give +out on you if you design the inductors + + align:start position:0% +out on you if you design the inductors + + + align:start position:0% +out on you if you design the inductors +right will cause you to get a lot less + + align:start position:0% +right will cause you to get a lot less + + + align:start position:0% +right will cause you to get a lot less +attenuation out of this LC filter than + + align:start position:0% +attenuation out of this LC filter than + + + align:start position:0% +attenuation out of this LC filter than +you + + align:start position:0% +you + + + align:start position:0% +you +thought any questions about + + align:start position:0% + + + + align:start position:0% + +that so you know that's kind of a + + align:start position:0% +that so you know that's kind of a + + + align:start position:0% +that so you know that's kind of a +problem okay + + align:start position:0% +problem okay + + + align:start position:0% +problem okay +um what would I do about it + + align:start position:0% +um what would I do about it + + + align:start position:0% +um what would I do about it +um what I might do about it is not just + + align:start position:0% +um what I might do about it is not just + + + align:start position:0% +um what I might do about it is not just +have one capacitor but have a bunch of + + align:start position:0% +have one capacitor but have a bunch of + + + align:start position:0% +have one capacitor but have a bunch of +capacitors some of which might be good + + align:start position:0% +capacitors some of which might be good + + + align:start position:0% +capacitors some of which might be good +at the they're not a very high C value + + align:start position:0% +at the they're not a very high C value + + + align:start position:0% +at the they're not a very high C value +but they're they don't have as much + + align:start position:0% +but they're they don't have as much + + + align:start position:0% +but they're they don't have as much +inductance and so they look better at + + align:start position:0% +inductance and so they look better at + + + align:start position:0% +inductance and so they look better at +high frequencies and then bigger + + align:start position:0% +high frequencies and then bigger + + + align:start position:0% +high frequencies and then bigger +capacitors that have better performance + + align:start position:0% +capacitors that have better performance + + + align:start position:0% +capacitors that have better performance +at low frequencies but not as good as + + align:start position:0% +at low frequencies but not as good as + + + align:start position:0% +at low frequencies but not as good as +high frequencies so I can certainly do + + align:start position:0% +high frequencies so I can certainly do + + + align:start position:0% +high frequencies so I can certainly do +it by sort of being careful about how I + + align:start position:0% +it by sort of being careful about how I + + + align:start position:0% +it by sort of being careful about how I +pick this component or picking multiple + + align:start position:0% +pick this component or picking multiple + + + align:start position:0% +pick this component or picking multiple +components to cover different frequency + + align:start position:0% +components to cover different frequency + + + align:start position:0% +components to cover different frequency +ranges and if I have multiple components + + align:start position:0% +ranges and if I have multiple components + + + align:start position:0% +ranges and if I have multiple components +by the way I can get resonances between + + align:start position:0% +by the way I can get resonances between + + + align:start position:0% +by the way I can get resonances between +them but that's another story okay what + + align:start position:0% +them but that's another story okay what + + + align:start position:0% +them but that's another story okay what +else can I + + align:start position:0% +else can I + + + align:start position:0% +else can I +do I might say well okay if I'm limited + + align:start position:0% +do I might say well okay if I'm limited + + + align:start position:0% +do I might say well okay if I'm limited +by ESL I will use a bigger LF but you're + + align:start position:0% +by ESL I will use a bigger LF but you're + + + align:start position:0% +by ESL I will use a bigger LF but you're +still only getting a sort of a divider + + align:start position:0% +still only getting a sort of a divider + + + align:start position:0% +still only getting a sort of a divider +that's a proportion between these two + + align:start position:0% +that's a proportion between these two + + + align:start position:0% +that's a proportion between these two +the ratio of those two if I want really + + align:start position:0% +the ratio of those two if I want really + + + align:start position:0% +the ratio of those two if I want really +more + + align:start position:0% +more + + + align:start position:0% +more +attenuation uh what I can do + + align:start position:0% +attenuation uh what I can do + + + align:start position:0% +attenuation uh what I can do +is do a higher stage filter so + + align:start position:0% +is do a higher stage filter so + + + align:start position:0% +is do a higher stage filter so +here's you know iix + + align:start position:0% +here's you know iix + + + align:start position:0% +here's you know iix +Tilda okay maybe I build a first + + align:start position:0% +Tilda okay maybe I build a first + + + align:start position:0% +Tilda okay maybe I build a first +stage I'll call This + + align:start position:0% +stage I'll call This + + + align:start position:0% +stage I'll call This +cf1 And + + align:start position:0% + + + + align:start position:0% + +lf1 and I'm leaving out damping and + + align:start position:0% +lf1 and I'm leaving out damping and + + + align:start position:0% +lf1 and I'm leaving out damping and +other things I'm going to talk about in + + align:start position:0% +other things I'm going to talk about in + + + align:start position:0% +other things I'm going to talk about in +the future and then maybe I have + + align:start position:0% + + + + align:start position:0% + +cf2 and lf2 + + align:start position:0% + + + + align:start position:0% + +all right and so forth and then maybe I + + align:start position:0% +all right and so forth and then maybe I + + + align:start position:0% +all right and so forth and then maybe I +have my I'm looking back into + + align:start position:0% +have my I'm looking back into + + + align:start position:0% +have my I'm looking back into +arism back here okay so you know maybe I + + align:start position:0% +arism back here okay so you know maybe I + + + align:start position:0% +arism back here okay so you know maybe I +can get 40 DB per decade out of this and + + align:start position:0% +can get 40 DB per decade out of this and + + + align:start position:0% +can get 40 DB per decade out of this and +40 DB decade out of this and maybe I do + + align:start position:0% +40 DB decade out of this and maybe I do + + + align:start position:0% +40 DB decade out of this and maybe I do +better and it may be better to do that + + align:start position:0% +better and it may be better to do that + + + align:start position:0% +better and it may be better to do that +even in a lot of cases because even + + align:start position:0% +even in a lot of cases because even + + + align:start position:0% +even in a lot of cases because even +putting aside the + + align:start position:0% +putting aside the + + + align:start position:0% +putting aside the +parasitics I can move the cut off + + align:start position:0% +parasitics I can move the cut off + + + align:start position:0% +parasitics I can move the cut off +frequency down one over theare of LC + + align:start position:0% +frequency down one over theare of LC + + + align:start position:0% +frequency down one over theare of LC +right by using bigger and bigger + + align:start position:0% +right by using bigger and bigger + + + align:start position:0% +right by using bigger and bigger +components I can move that cut off + + align:start position:0% +components I can move that cut off + + + align:start position:0% +components I can move that cut off +filter down here + + align:start position:0% +filter down here + + + align:start position:0% +filter down here +maybe I use smaller components but + + align:start position:0% +maybe I use smaller components but + + + align:start position:0% +maybe I use smaller components but +instead of + + align:start position:0% +instead of + + + align:start position:0% +instead of +getting + + align:start position:0% +getting + + + align:start position:0% +getting +a a 40 DB per decade roll off I could + + align:start position:0% +a a 40 DB per decade roll off I could + + + align:start position:0% +a a 40 DB per decade roll off I could +theoretically get 80 out of this so even + + align:start position:0% +theoretically get 80 out of this so even + + + align:start position:0% +theoretically get 80 out of this so even +if the net cut off's higher that fast + + align:start position:0% +if the net cut off's higher that fast + + + align:start position:0% +if the net cut off's higher that fast +attenuation will help me so it's often + + align:start position:0% +attenuation will help me so it's often + + + align:start position:0% +attenuation will help me so it's often +better to go for smaller multi-stage + + align:start position:0% +better to go for smaller multi-stage + + + align:start position:0% +better to go for smaller multi-stage +filters than um one big fat single + + align:start position:0% +filters than um one big fat single + + + align:start position:0% +filters than um one big fat single +filter stage trying to get the + + align:start position:0% +filter stage trying to get the + + + align:start position:0% +filter stage trying to get the +attenuation I want okay and by the way + + align:start position:0% +attenuation I want okay and by the way + + + align:start position:0% +attenuation I want okay and by the way +when you do this for reasons I'm I'm not + + align:start position:0% +when you do this for reasons I'm I'm not + + + align:start position:0% +when you do this for reasons I'm I'm not +really going to go into the details of + + align:start position:0% +really going to go into the details of + + + align:start position:0% +really going to go into the details of +this because we don't have time when you + + align:start position:0% +this because we don't have time when you + + + align:start position:0% +this because we don't have time when you +design these kind of things it might be + + align:start position:0% +design these kind of things it might be + + + align:start position:0% +design these kind of things it might be +your inclination to say oh let me use + + align:start position:0% +your inclination to say oh let me use + + + align:start position:0% +your inclination to say oh let me use +the same LF CF cut off here and here and + + align:start position:0% +the same LF CF cut off here and here and + + + align:start position:0% +the same LF CF cut off here and here and +put two filters with the same cut off it + + align:start position:0% +put two filters with the same cut off it + + + align:start position:0% +put two filters with the same cut off it +turns out to be better to stagger these + + align:start position:0% +turns out to be better to stagger these + + + align:start position:0% +turns out to be better to stagger these +things so usually you'd make this one a + + align:start position:0% +things so usually you'd make this one a + + + align:start position:0% +things so usually you'd make this one a +low cut off and then this one a higher + + align:start position:0% +low cut off and then this one a higher + + + align:start position:0% +low cut off and then this one a higher +cut off to deal with the higher + + align:start position:0% +cut off to deal with the higher + + + align:start position:0% +cut off to deal with the higher +frequency and so forth turns out to be a + + align:start position:0% +frequency and so forth turns out to be a + + + align:start position:0% +frequency and so forth turns out to be a +better kind of design strategy for these + + align:start position:0% +better kind of design strategy for these + + + align:start position:0% +better kind of design strategy for these +kind of filters Okay so you can kind of + + align:start position:0% +kind of filters Okay so you can kind of + + + align:start position:0% +kind of filters Okay so you can kind of +cascade filter sections until you get + + align:start position:0% +cascade filter sections until you get + + + align:start position:0% +cascade filter sections until you get +the attenuation you need and if you look + + align:start position:0% +the attenuation you need and if you look + + + align:start position:0% +the attenuation you need and if you look +in a typical offline power supply that + + align:start position:0% +in a typical offline power supply that + + + align:start position:0% +in a typical offline power supply that +you plug into the wall they usually have + + align:start position:0% +you plug into the wall they usually have + + + align:start position:0% +you plug into the wall they usually have +a couple filter stages like this okay + + align:start position:0% +a couple filter stages like this okay + + + align:start position:0% +a couple filter stages like this okay +any questions about + + align:start position:0% + + + + align:start position:0% + +that I should warn you too I said oh + + align:start position:0% +that I should warn you too I said oh + + + align:start position:0% +that I should warn you too I said oh +people hate + + align:start position:0% +people hate + + + align:start position:0% +people hate +these um you they they hate dealing with + + align:start position:0% +these um you they they hate dealing with + + + align:start position:0% +these um you they they hate dealing with +the Emi because you go to measure stuff + + align:start position:0% +the Emi because you go to measure stuff + + + align:start position:0% +the Emi because you go to measure stuff +and then what you measure doesn't seem + + align:start position:0% +and then what you measure doesn't seem + + + align:start position:0% +and then what you measure doesn't seem +to make sense and it all does make sense + + align:start position:0% +to make sense and it all does make sense + + + align:start position:0% +to make sense and it all does make sense +but very small phenoma can mess you up + + align:start position:0% +but very small phenoma can mess you up + + + align:start position:0% +but very small phenoma can mess you up +so think about this this this filter in + + align:start position:0% +so think about this this this filter in + + + align:start position:0% +so think about this this this filter in +its cut off regene putting aside these + + align:start position:0% +its cut off regene putting aside these + + + align:start position:0% +its cut off regene putting aside these +parasitics I was talking about + + align:start position:0% +parasitics I was talking about + + + align:start position:0% +parasitics I was talking about +um could give you 80 DB per decade right + + align:start position:0% +um could give you 80 DB per decade right + + + align:start position:0% +um could give you 80 DB per decade right +you can get really like Wham lots of + + align:start position:0% +you can get really like Wham lots of + + + align:start position:0% +you can get really like Wham lots of +attenuation and that's good because you + + align:start position:0% +attenuation and that's good because you + + + align:start position:0% +attenuation and that's good because you +need a lot of attenuation but what's the + + align:start position:0% +need a lot of attenuation but what's the + + + align:start position:0% +need a lot of attenuation but what's the +downside well one thing is the component + + align:start position:0% +downside well one thing is the component + + + align:start position:0% +downside well one thing is the component +parasitics themselves and I focused on + + align:start position:0% +parasitics themselves and I focused on + + + align:start position:0% +parasitics themselves and I focused on +the capacitor the inductors do have you + + align:start position:0% +the capacitor the inductors do have you + + + align:start position:0% +the capacitor the inductors do have you +know if you put a capacitance you know + + align:start position:0% +know if you put a capacitance you know + + + align:start position:0% +know if you put a capacitance you know +inductors do have a parasitic parallel + + align:start position:0% +inductors do have a parasitic parallel + + + align:start position:0% +inductors do have a parasitic parallel +capacitance you also have to worry about + + align:start position:0% +capacitance you also have to worry about + + + align:start position:0% +capacitance you also have to worry about +that one okay but putting aside that + + align:start position:0% +that one okay but putting aside that + + + align:start position:0% +that one okay but putting aside that +parasitic you also have layout + + align:start position:0% +parasitic you also have layout + + + align:start position:0% +parasitic you also have layout +parasitics + + align:start position:0% +parasitics + + + align:start position:0% +parasitics +meaning if I do a crummy job and I don't + + align:start position:0% +meaning if I do a crummy job and I don't + + + align:start position:0% +meaning if I do a crummy job and I don't +stick the components into the board all + + align:start position:0% +stick the components into the board all + + + align:start position:0% +stick the components into the board all +the way or I put two components next to + + align:start position:0% +the way or I put two components next to + + + align:start position:0% +the way or I put two components next to +each other they can have capacitance + + align:start position:0% +each other they can have capacitance + + + align:start position:0% +each other they can have capacitance +between them okay or I so I can + + align:start position:0% +between them okay or I so I can + + + align:start position:0% +between them okay or I so I can +accidentally insert inductance or I can + + align:start position:0% +accidentally insert inductance or I can + + + align:start position:0% +accidentally insert inductance or I can +accidentally insert in capacitance and + + align:start position:0% +accidentally insert in capacitance and + + + align:start position:0% +accidentally insert in capacitance and +what one of the things that can happen + + align:start position:0% +what one of the things that can happen + + + align:start position:0% +what one of the things that can happen +is + + align:start position:0% +is + + + align:start position:0% +is +imagine you know this is my power supply + + align:start position:0% +imagine you know this is my power supply + + + align:start position:0% +imagine you know this is my power supply +input leads and you know over here is + + align:start position:0% +input leads and you know over here is + + + align:start position:0% +input leads and you know over here is +where it's going to go off to you know + + align:start position:0% +where it's going to go off to you know + + + align:start position:0% +where it's going to go off to you know +I'm showing the lizen here but this is + + align:start position:0% +I'm showing the lizen here but this is + + + align:start position:0% +I'm showing the lizen here but this is +where it goes off to the power supply + + align:start position:0% +where it goes off to the power supply + + + align:start position:0% +where it goes off to the power supply +input right what if I put those leads + + align:start position:0% +input right what if I put those leads + + + align:start position:0% +input right what if I put those leads +near each + + align:start position:0% +near each + + + align:start position:0% +near each +other well then maybe what I would end + + align:start position:0% +other well then maybe what I would end + + + align:start position:0% +other well then maybe what I would end +up with is some small parasitic + + align:start position:0% +up with is some small parasitic + + + align:start position:0% +up with is some small parasitic +capacitance from this node + + align:start position:0% + + + + align:start position:0% + +you know pass my filter to this + + align:start position:0% +you know pass my filter to this + + + align:start position:0% +you know pass my filter to this +node and so what happens this filter is + + align:start position:0% +node and so what happens this filter is + + + align:start position:0% +node and so what happens this filter is +doing some great job massively killing + + align:start position:0% +doing some great job massively killing + + + align:start position:0% +doing some great job massively killing +the noise but this because this node has + + align:start position:0% +the noise but this because this node has + + + align:start position:0% +the noise but this because this node has +some switching ripple at it it's being + + align:start position:0% +some switching ripple at it it's being + + + align:start position:0% +some switching ripple at it it's being +injected through this you know maybe + + align:start position:0% +injected through this you know maybe + + + align:start position:0% +injected through this you know maybe +it's a paa farad of capacitance it + + align:start position:0% +it's a paa farad of capacitance it + + + align:start position:0% +it's a paa farad of capacitance it +doesn't even have to be very much if you + + align:start position:0% +doesn't even have to be very much if you + + + align:start position:0% +doesn't even have to be very much if you +have a high attenuation filter getting + + align:start position:0% +have a high attenuation filter getting + + + align:start position:0% +have a high attenuation filter getting +over to here and completely bypassing + + align:start position:0% +over to here and completely bypassing + + + align:start position:0% +over to here and completely bypassing +your filter right so you're getting bad + + align:start position:0% +your filter right so you're getting bad + + + align:start position:0% +your filter right so you're getting bad +results you're measuring stuff over here + + align:start position:0% +results you're measuring stuff over here + + + align:start position:0% +results you're measuring stuff over here +and you make this filter better and + + align:start position:0% +and you make this filter better and + + + align:start position:0% +and you make this filter better and +nothing happens you make this filter + + align:start position:0% +nothing happens you make this filter + + + align:start position:0% +nothing happens you make this filter +better and nothing happens why because + + align:start position:0% +better and nothing happens why because + + + align:start position:0% +better and nothing happens why because +it's not going through your filter it's + + align:start position:0% +it's not going through your filter it's + + + align:start position:0% +it's not going through your filter it's +going around your filter all right and + + align:start position:0% +going around your filter all right and + + + align:start position:0% +going around your filter all right and +that's that's the kind of thing that + + align:start position:0% +that's that's the kind of thing that + + + align:start position:0% +that's that's the kind of thing that +drives people nuts um so you have to + + align:start position:0% +drives people nuts um so you have to + + + align:start position:0% +drives people nuts um so you have to +think very carefully about your layout + + align:start position:0% +think very carefully about your layout + + + align:start position:0% +think very carefully about your layout +people really try to have sort of a + + align:start position:0% +people really try to have sort of a + + + align:start position:0% +people really try to have sort of a +quiet side and a noisy side so that they + + align:start position:0% +quiet side and a noisy side so that they + + + align:start position:0% +quiet side and a noisy side so that they +they stay physically far apart so you + + align:start position:0% +they stay physically far apart so you + + + align:start position:0% +they stay physically far apart so you +don't get capacitive + + align:start position:0% +don't get capacitive + + + align:start position:0% +don't get capacitive +bridging you can also have magnetic + + align:start position:0% +bridging you can also have magnetic + + + align:start position:0% +bridging you can also have magnetic +bridging I if I have this if this loop + + align:start position:0% +bridging I if I have this if this loop + + + align:start position:0% +bridging I if I have this if this loop +with a lot of switching Ripple has + + align:start position:0% +with a lot of switching Ripple has + + + align:start position:0% +with a lot of switching Ripple has +Mutual inductance to this Loop even if + + align:start position:0% +Mutual inductance to this Loop even if + + + align:start position:0% +Mutual inductance to this Loop even if +there's no capacitance I can get + + align:start position:0% +there's no capacitance I can get + + + align:start position:0% +there's no capacitance I can get +magnetically coupled right across + + align:start position:0% +magnetically coupled right across + + + align:start position:0% +magnetically coupled right across +through my + + align:start position:0% +through my + + + align:start position:0% +through my +layout okay and completely ruined my + + align:start position:0% +layout okay and completely ruined my + + + align:start position:0% +layout okay and completely ruined my +filter + + align:start position:0% +filter + + + align:start position:0% +filter +performance we had + + align:start position:0% +performance we had + + + align:start position:0% +performance we had +some I there's a power supply I worked + + align:start position:0% +some I there's a power supply I worked + + + align:start position:0% +some I there's a power supply I worked +on with a friend for commercial + + align:start position:0% +on with a friend for commercial + + + align:start position:0% +on with a friend for commercial +application and uh you know we designed + + align:start position:0% +application and uh you know we designed + + + align:start position:0% +application and uh you know we designed +it and it didn't quite make + + align:start position:0% +it and it didn't quite make + + + align:start position:0% +it and it didn't quite make +the couldn't pass the spec we weren't + + align:start position:0% +the couldn't pass the spec we weren't + + + align:start position:0% +the couldn't pass the spec we weren't +passing the spec we went and we moved on + + align:start position:0% +passing the spec we went and we moved on + + + align:start position:0% +passing the spec we went and we moved on +the board a + + align:start position:0% +the board a + + + align:start position:0% +the board a +trace about 3 4 + + align:start position:0% +trace about 3 4 + + + align:start position:0% +trace about 3 4 +millimeters suddenly we were passing it + + align:start position:0% +millimeters suddenly we were passing it + + + align:start position:0% +millimeters suddenly we were passing it +fine it was it was exactly that + + align:start position:0% +fine it was it was exactly that + + + align:start position:0% +fine it was it was exactly that +phenomena it was there was a noisy Port + + align:start position:0% +phenomena it was there was a noisy Port + + + align:start position:0% +phenomena it was there was a noisy Port +that was too close to the input and + + align:start position:0% +that was too close to the input and + + + align:start position:0% +that was too close to the input and +we're capably couple the energy into the + + align:start position:0% +we're capably couple the energy into the + + + align:start position:0% +we're capably couple the energy into the +input and all we had to do is move the + + align:start position:0% +input and all we had to do is move the + + + align:start position:0% +input and all we had to do is move the +trace and you know that that Trace that + + align:start position:0% +trace and you know that that Trace that + + + align:start position:0% +trace and you know that that Trace that +parasitic isn't showing up in your + + align:start position:0% +parasitic isn't showing up in your + + + align:start position:0% +parasitic isn't showing up in your +schematic it's not showing up anywhere + + align:start position:0% +schematic it's not showing up anywhere + + + align:start position:0% +schematic it's not showing up anywhere +but it's there in the real world and you + + align:start position:0% +but it's there in the real world and you + + + align:start position:0% +but it's there in the real world and you +have to go find it we move that one + + align:start position:0% +have to go find it we move that one + + + align:start position:0% +have to go find it we move that one +plane we're fine okay so you've got to + + align:start position:0% +plane we're fine okay so you've got to + + + align:start position:0% +plane we're fine okay so you've got to +you got to spend a lot of time thinking + + align:start position:0% +you got to spend a lot of time thinking + + + align:start position:0% +you got to spend a lot of time thinking +about this what they do in commercial + + align:start position:0% +about this what they do in commercial + + + align:start position:0% +about this what they do in commercial +Emi filters is they often will have a + + align:start position:0% +Emi filters is they often will have a + + + align:start position:0% +Emi filters is they often will have a +filter stage like this and put this + + align:start position:0% +filter stage like this and put this + + + align:start position:0% +filter stage like this and put this +inside a shielded box and then have some + + align:start position:0% +inside a shielded box and then have some + + + align:start position:0% +inside a shielded box and then have some +feed throughs going to the next filter + + align:start position:0% +feed throughs going to the next filter + + + align:start position:0% +feed throughs going to the next filter +stage and so forth and they can build + + align:start position:0% +stage and so forth and they can build + + + align:start position:0% +stage and so forth and they can build +commercial Emi filters that way and + + align:start position:0% +commercial Emi filters that way and + + + align:start position:0% +commercial Emi filters that way and +that's great the sad news about being a + + align:start position:0% +that's great the sad news about being a + + + align:start position:0% +that's great the sad news about being a +Power Electronics designer is usually + + align:start position:0% +Power Electronics designer is usually + + + align:start position:0% +Power Electronics designer is usually +they won't let you do that right + + align:start position:0% +they won't let you do that right + + + align:start position:0% +they won't let you do that right +nobody's going to let you have shielded + + align:start position:0% +nobody's going to let you have shielded + + + align:start position:0% +nobody's going to let you have shielded +boxes and so forth in your converter so + + align:start position:0% +boxes and so forth in your converter so + + + align:start position:0% +boxes and so forth in your converter so +you've just got to be very clever about + + align:start position:0% +you've just got to be very clever about + + + align:start position:0% +you've just got to be very clever about +how you lay things out and keep things + + align:start position:0% +how you lay things out and keep things + + + align:start position:0% +how you lay things out and keep things +from coupling magnetically and keep + + align:start position:0% +from coupling magnetically and keep + + + align:start position:0% +from coupling magnetically and keep +things from coupling capacitively and + + align:start position:0% +things from coupling capacitively and + + + align:start position:0% +things from coupling capacitively and +that's often an iterative process to get + + align:start position:0% +that's often an iterative process to get + + + align:start position:0% +that's often an iterative process to get +it to the point where you've realized + + align:start position:0% +it to the point where you've realized + + + align:start position:0% +it to the point where you've realized +what's going to happen with all the + + align:start position:0% +what's going to happen with all the + + + align:start position:0% +what's going to happen with all the +parasitics so that's sort of a a way to + + align:start position:0% +parasitics so that's sort of a a way to + + + align:start position:0% +parasitics so that's sort of a a way to +first of all warn you what's to come if + + align:start position:0% +first of all warn you what's to come if + + + align:start position:0% +first of all warn you what's to come if +you go do this and to not get frustrated + + align:start position:0% +you go do this and to not get frustrated + + + align:start position:0% +you go do this and to not get frustrated +just kind of look for where non + + align:start position:0% +just kind of look for where non + + + align:start position:0% +just kind of look for where non +idealities either lay out parasitics or + + align:start position:0% +idealities either lay out parasitics or + + + align:start position:0% +idealities either lay out parasitics or +component parasitics are going to come + + align:start position:0% +component parasitics are going to come + + + align:start position:0% +component parasitics are going to come +bite you and then + + align:start position:0% +bite you and then + + + align:start position:0% +bite you and then +um and then you know fix those you also + + align:start position:0% +um and then you know fix those you also + + + align:start position:0% +um and then you know fix those you also +got to worry about the measurements + + align:start position:0% +got to worry about the measurements + + + align:start position:0% +got to worry about the measurements +being right too um on one project I did + + align:start position:0% +being right too um on one project I did + + + align:start position:0% +being right too um on one project I did +with a colleague we took our prototype + + align:start position:0% +with a colleague we took our prototype + + + align:start position:0% +with a colleague we took our prototype +to a to a test house you know one of + + align:start position:0% +to a to a test house you know one of + + + align:start position:0% +to a to a test house you know one of +these commercial facilities tested it + + align:start position:0% +these commercial facilities tested it + + + align:start position:0% +these commercial facilities tested it +qualified the power supply yes it you + + align:start position:0% +qualified the power supply yes it you + + + align:start position:0% +qualified the power supply yes it you +can plug this thing into the wall when + + align:start position:0% +can plug this thing into the wall when + + + align:start position:0% +can plug this thing into the wall when +in our marry way company calls us up and + + align:start position:0% +in our marry way company calls us up and + + + align:start position:0% +in our marry way company calls us up and +then this was a power supply that went + + align:start position:0% +then this was a power supply that went + + + align:start position:0% +then this was a power supply that went +into a water Purity meter that then went + + align:start position:0% +into a water Purity meter that then went + + + align:start position:0% +into a water Purity meter that then went +on other semiconductor equipment and you + + align:start position:0% +on other semiconductor equipment and you + + + align:start position:0% +on other semiconductor equipment and you +know get a call from the the people we + + align:start position:0% +know get a call from the the people we + + + align:start position:0% +know get a call from the the people we +designed the power supply + + align:start position:0% +designed the power supply + + + align:start position:0% +designed the power supply +for yeah our customers came back to us + + align:start position:0% +for yeah our customers came back to us + + + align:start position:0% +for yeah our customers came back to us +and said um that you know their + + align:start position:0% +and said um that you know their + + + align:start position:0% +and said um that you know their +equipment was failing Emi tests and they + + align:start position:0% +equipment was failing Emi tests and they + + + align:start position:0% +equipment was failing Emi tests and they +tracked their failure of Emi test back + + align:start position:0% +tracked their failure of Emi test back + + + align:start position:0% +tracked their failure of Emi test back +to this one box that we make + + align:start position:0% +to this one box that we make + + + align:start position:0% +to this one box that we make +and of course you know we had designed + + align:start position:0% +and of course you know we had designed + + + align:start position:0% +and of course you know we had designed +the Mi filter for it what's going on we + + align:start position:0% +the Mi filter for it what's going on we + + + align:start position:0% +the Mi filter for it what's going on we +got to fix this problem because you know + + align:start position:0% +got to fix this problem because you know + + + align:start position:0% +got to fix this problem because you know +their customers is unhappy because + + align:start position:0% +their customers is unhappy because + + + align:start position:0% +their customers is unhappy because +they're not passing FCC but of course + + align:start position:0% +they're not passing FCC but of course + + + align:start position:0% +they're not passing FCC but of course +we're puzzled because we think we've + + align:start position:0% +we're puzzled because we think we've + + + align:start position:0% +we're puzzled because we think we've +passed the + + align:start position:0% +passed the + + + align:start position:0% +passed the +test come to track back what happened is + + align:start position:0% +test come to track back what happened is + + + align:start position:0% +test come to track back what happened is +we took it to a commercial test facility + + align:start position:0% +we took it to a commercial test facility + + + align:start position:0% +we took it to a commercial test facility +and they had been doing work on their + + align:start position:0% +and they had been doing work on their + + + align:start position:0% +and they had been doing work on their +test setup and their test setup had + + align:start position:0% +test setup and their test setup had + + + align:start position:0% +test setup and their test setup had +gotten messed up and wasn't grounded + + align:start position:0% +gotten messed up and wasn't grounded + + + align:start position:0% +gotten messed up and wasn't grounded +properly so basically the results they + + align:start position:0% +properly so basically the results they + + + align:start position:0% +properly so basically the results they +were showing from their result from + + align:start position:0% +were showing from their result from + + + align:start position:0% +were showing from their result from +their test setup said it was passing and + + align:start position:0% +their test setup said it was passing and + + + align:start position:0% +their test setup said it was passing and +it wasn't we took it to a different + + align:start position:0% +it wasn't we took it to a different + + + align:start position:0% +it wasn't we took it to a different +facility it was failing and that's when + + align:start position:0% +facility it was failing and that's when + + + align:start position:0% +facility it was failing and that's when +we went back and changed the design + + align:start position:0% +we went back and changed the design + + + align:start position:0% +we went back and changed the design +improved it and suddenly it passed + + align:start position:0% +improved it and suddenly it passed + + + align:start position:0% +improved it and suddenly it passed +everything okay so there's a lot of + + align:start position:0% +everything okay so there's a lot of + + + align:start position:0% +everything okay so there's a lot of +layout challenges and there's a lot of + + align:start position:0% +layout challenges and there's a lot of + + + align:start position:0% +layout challenges and there's a lot of +measurement challenges and you just got + + align:start position:0% +measurement challenges and you just got + + + align:start position:0% +measurement challenges and you just got +to be willing to dig through them and + + align:start position:0% +to be willing to dig through them and + + + align:start position:0% +to be willing to dig through them and +eventually you'll get something but when + + align:start position:0% +eventually you'll get something but when + + + align:start position:0% +eventually you'll get something but when +you're dealing with power supplies you + + align:start position:0% +you're dealing with power supplies you + + + align:start position:0% +you're dealing with power supplies you +don't try to design something that's + + align:start position:0% +don't try to design something that's + + + align:start position:0% +don't try to design something that's +going to pass by a few DB the + + align:start position:0% +going to pass by a few DB the + + + align:start position:0% +going to pass by a few DB the +specifications like by a small margin + + align:start position:0% +specifications like by a small margin + + + align:start position:0% +specifications like by a small margin +you want to give yourself a you want to + + align:start position:0% +you want to give yourself a you want to + + + align:start position:0% +you want to give yourself a you want to +you want to really pass it because the + + align:start position:0% +you want to really pass it because the + + + align:start position:0% +you want to really pass it because the +reason is is even with all that + + align:start position:0% +reason is is even with all that + + + align:start position:0% +reason is is even with all that +craziness to try to keep everything + + align:start position:0% +craziness to try to keep everything + + + align:start position:0% +craziness to try to keep everything +identical you're going to have + + align:start position:0% +identical you're going to have + + + align:start position:0% +identical you're going to have +variations in your design in one test + + align:start position:0% +variations in your design in one test + + + align:start position:0% +variations in your design in one test +setup or another or component variations + + align:start position:0% +setup or another or component variations + + + align:start position:0% +setup or another or component variations +in the manufacturing that you know + + align:start position:0% +in the manufacturing that you know + + + align:start position:0% +in the manufacturing that you know +aren't quite the same so if you give you + + align:start position:0% +aren't quite the same so if you give you + + + align:start position:0% +aren't quite the same so if you give you +need to give yourself a bunch of margin + + align:start position:0% +need to give yourself a bunch of margin + + + align:start position:0% +need to give yourself a bunch of margin +around the specifications and if we had + + align:start position:0% +around the specifications and if we had + + + align:start position:0% +around the specifications and if we had +had more margin in the first design they + + align:start position:0% +had more margin in the first design they + + + align:start position:0% +had more margin in the first design they +probably wouldn't have even come back + + align:start position:0% +probably wouldn't have even come back + + + align:start position:0% +probably wouldn't have even come back +even though the test results were you + + align:start position:0% +even though the test results were you + + + align:start position:0% +even though the test results were you +know it wasn't our fault that the test + + align:start position:0% +know it wasn't our fault that the test + + + align:start position:0% +know it wasn't our fault that the test +system was wrong actually we got nicely + + align:start position:0% +system was wrong actually we got nicely + + + align:start position:0% +system was wrong actually we got nicely +paid to debug the my facilities problems + + align:start position:0% +paid to debug the my facilities problems + + + align:start position:0% +paid to debug the my facilities problems +for them but that was another story all + + align:start position:0% +for them but that was another story all + + + align:start position:0% +for them but that was another story all +right so + + align:start position:0% +right so + + + align:start position:0% +right so +um just to + + align:start position:0% +um just to + + + align:start position:0% +um just to +illustrate + + align:start position:0% +illustrate + + + align:start position:0% +illustrate +um these phenomena and so what are we + + align:start position:0% +um these phenomena and so what are we + + + align:start position:0% +um these phenomena and so what are we +going to talk about we're going to talk + + align:start position:0% +going to talk about we're going to talk + + + align:start position:0% +going to talk about we're going to talk +about a bit more about filter design and + + align:start position:0% +about a bit more about filter design and + + + align:start position:0% +about a bit more about filter design and +and a bunch of other phenomena that come + + align:start position:0% +and a bunch of other phenomena that come + + + align:start position:0% +and a bunch of other phenomena that come +up but I just wanted to illustrate this + + align:start position:0% +up but I just wanted to illustrate this + + + align:start position:0% +up but I just wanted to illustrate this +whole question about first of all + + align:start position:0% +whole question about first of all + + + align:start position:0% +whole question about first of all +component parasitics which are very real + + align:start position:0% +component parasitics which are very real + + + align:start position:0% +component parasitics which are very real +even if you do your best layout but also + + align:start position:0% +even if you do your best layout but also + + + align:start position:0% +even if you do your best layout but also +if you do a bad job if you uh + + align:start position:0% +if you do a bad job if you uh + + + align:start position:0% +if you do a bad job if you uh +accidentally put a capacitance here or + + align:start position:0% +accidentally put a capacitance here or + + + align:start position:0% +accidentally put a capacitance here or +you accidentally because you don't place + + align:start position:0% +you accidentally because you don't place + + + align:start position:0% +you accidentally because you don't place +this capacitor very well you know have + + align:start position:0% +this capacitor very well you know have + + + align:start position:0% +this capacitor very well you know have +extra lead length going to it and you + + align:start position:0% +extra lead length going to it and you + + + align:start position:0% +extra lead length going to it and you +insert some inductance you'll make + + align:start position:0% +insert some inductance you'll make + + + align:start position:0% +insert some inductance you'll make +everything worse so you want to be + + align:start position:0% +everything worse so you want to be + + + align:start position:0% +everything worse so you want to be +really careful about your circuit layout + + align:start position:0% +really careful about your circuit layout + + + align:start position:0% +really careful about your circuit layout +we have a demo of this and what this is + + align:start position:0% +we have a demo of this and what this is + + + align:start position:0% +we have a demo of this and what this is +essentially is a set of four filters + + align:start position:0% +essentially is a set of four filters + + + align:start position:0% +essentially is a set of four filters +here these are just LC filters and I'm + + align:start position:0% +here these are just LC filters and I'm + + + align:start position:0% +here these are just LC filters and I'm +going to let Rafa demonstrate and what + + align:start position:0% +going to let Rafa demonstrate and what + + + align:start position:0% +going to let Rafa demonstrate and what +we have is a + + align:start position:0% +we have is a + + + align:start position:0% +we have is a +a a network analyzer what a network + + align:start position:0% +a a network analyzer what a network + + + align:start position:0% +a a network analyzer what a network +analyzer does is it sort of drives at + + align:start position:0% +analyzer does is it sort of drives at + + + align:start position:0% +analyzer does is it sort of drives at +one port which be like our signal I and + + align:start position:0% +one port which be like our signal I and + + + align:start position:0% +one port which be like our signal I and +then it measures into another Port which + + align:start position:0% +then it measures into another Port which + + + align:start position:0% +then it measures into another Port which +would be like our signal at the lizen + + align:start position:0% +would be like our signal at the lizen + + + align:start position:0% +would be like our signal at the lizen +okay and let's see the behavior of the + + align:start position:0% +okay and let's see the behavior of the + + + align:start position:0% +okay and let's see the behavior of the +same filter it has the same physical + + align:start position:0% +same filter it has the same physical + + + align:start position:0% +same filter it has the same physical +components just plac slightly + + align:start position:0% +components just plac slightly + + + align:start position:0% +components just plac slightly +differently on the performance of the + + align:start position:0% +differently on the performance of the + + + align:start position:0% +differently on the performance of the +filter and with that I'll I'll hand it + + align:start position:0% +filter and with that I'll I'll hand it + + + align:start position:0% +filter and with that I'll I'll hand it +over to Rafa and let her + + align:start position:0% +over to Rafa and let her + + + align:start position:0% +over to Rafa and let her +explain do I have to the microphone I + + align:start position:0% +explain do I have to the microphone I + + + align:start position:0% +explain do I have to the microphone I +think so okay all right so like Dave + + align:start position:0% +think so okay all right so like Dave + + + align:start position:0% +think so okay all right so like Dave +mentioned we have four different filters + + align:start position:0% +mentioned we have four different filters + + + align:start position:0% +mentioned we have four different filters +with four different layout strategies in + + align:start position:0% +with four different layout strategies in + + + align:start position:0% +with four different layout strategies in +some of them we care we are being + + align:start position:0% +some of them we care we are being + + + align:start position:0% +some of them we care we are being +careful about both the parasitic + + align:start position:0% +careful about both the parasitic + + + align:start position:0% +careful about both the parasitic +inductance and capacitance in some of + + align:start position:0% +inductance and capacitance in some of + + + align:start position:0% +inductance and capacitance in some of +them only one okay so yeah I'll I'll let + + align:start position:0% +them only one okay so yeah I'll I'll let + + + align:start position:0% +them only one okay so yeah I'll I'll let +Rafa I'll let Rafa do the uh testing + + align:start position:0% +Rafa I'll let Rafa do the uh testing + + + align:start position:0% +Rafa I'll let Rafa do the uh testing +while I do the explaining okay so we + + align:start position:0% +while I do the explaining okay so we + + + align:start position:0% +while I do the explaining okay so we +have four + + align:start position:0% +have four + + + align:start position:0% +have four +filters the one she's going to start + + align:start position:0% +filters the one she's going to start + + + align:start position:0% +filters the one she's going to start +with we it's an LC filter just like this + + align:start position:0% +with we it's an LC filter just like this + + + align:start position:0% +with we it's an LC filter just like this +and all that happened is we were sloppy + + align:start position:0% +and all that happened is we were sloppy + + + align:start position:0% +and all that happened is we were sloppy +about both how we inserted the capacitor + + align:start position:0% +about both how we inserted the capacitor + + + align:start position:0% +about both how we inserted the capacitor +so there's a little extra um inductance + + align:start position:0% +so there's a little extra um inductance + + + align:start position:0% +so there's a little extra um inductance +in here and the the inductor we place + + align:start position:0% +in here and the the inductor we place + + + align:start position:0% +in here and the the inductor we place +traces nearby so there's a bit of extra + + align:start position:0% +traces nearby so there's a bit of extra + + + align:start position:0% +traces nearby so there's a bit of extra +capacitance across it okay so that's the + + align:start position:0% +capacitance across it okay so that's the + + + align:start position:0% +capacitance across it okay so that's the +first Trace we're going to see and let's + + align:start position:0% +first Trace we're going to see and let's + + + align:start position:0% +first Trace we're going to see and let's +see what this + + align:start position:0% + + + + align:start position:0% + +does so this is a filter where we don't + + align:start position:0% +does so this is a filter where we don't + + + align:start position:0% +does so this is a filter where we don't +have where we are not careful about the + + align:start position:0% +have where we are not careful about the + + + align:start position:0% +have where we are not careful about the +capacitance and the inductance right so + + align:start position:0% +capacitance and the inductance right so + + + align:start position:0% +capacitance and the inductance right so +this is bad this is parasitic + + align:start position:0% +this is bad this is parasitic + + + align:start position:0% +this is bad this is parasitic +capacitance and parastic inductance and + + align:start position:0% +capacitance and parastic inductance and + + + align:start position:0% +capacitance and parastic inductance and +so this is the attenuation of the filter + + align:start position:0% +so this is the attenuation of the filter + + + align:start position:0% +so this is the attenuation of the filter +and we can see that the filter + + align:start position:0% +and we can see that the filter + + + align:start position:0% +and we can see that the filter +attenuates down Rum by the way we're + + align:start position:0% +attenuates down Rum by the way we're + + + align:start position:0% +attenuates down Rum by the way we're +going from 1 khz to 20 megahertz here + + align:start position:0% +going from 1 khz to 20 megahertz here + + + align:start position:0% +going from 1 khz to 20 megahertz here +you can see even before we get very far + + align:start position:0% +you can see even before we get very far + + + align:start position:0% +you can see even before we get very far +out the filter ceases to attenuating and + + align:start position:0% +out the filter ceases to attenuating and + + + align:start position:0% +out the filter ceases to attenuating and +then it gets bad right and these were + + align:start position:0% +then it gets bad right and these were + + + align:start position:0% +then it gets bad right and these were +good filter components but we're just + + align:start position:0% +good filter components but we're just + + + align:start position:0% +good filter components but we're just +getting bad results okay the next one + + align:start position:0% +getting bad results okay the next one + + + align:start position:0% +getting bad results okay the next one +we're going to try + + align:start position:0% +we're going to try + + + align:start position:0% +we're going to try +uh what we did was we said okay uh we're + + align:start position:0% +uh what we did was we said okay uh we're + + + align:start position:0% +uh what we did was we said okay uh we're +going to have um okay layout of the + + align:start position:0% +going to have um okay layout of the + + + align:start position:0% +going to have um okay layout of the +capacitor so no in parasitic inductance + + align:start position:0% +capacitor so no in parasitic inductance + + + align:start position:0% +capacitor so no in parasitic inductance +or as little as we can get from the + + align:start position:0% +or as little as we can get from the + + + align:start position:0% +or as little as we can get from the +component itself but we didn't fix the + + align:start position:0% +component itself but we didn't fix the + + + align:start position:0% +component itself but we didn't fix the +bad layout across the inductor and so + + align:start position:0% +bad layout across the inductor and so + + + align:start position:0% +bad layout across the inductor and so +here we go and what you can see is yeah + + align:start position:0% +here we go and what you can see is yeah + + + align:start position:0% +here we go and what you can see is yeah +you know this is a little bit better + + align:start position:0% +you know this is a little bit better + + + align:start position:0% +you know this is a little bit better +because of what we we got but it's still + + align:start position:0% +because of what we we got but it's still + + + align:start position:0% +because of what we we got but it's still +terrible + + align:start position:0% +terrible + + + align:start position:0% +terrible +okay the next one uh we have a bad + + align:start position:0% +okay the next one uh we have a bad + + + align:start position:0% +okay the next one uh we have a bad +layout with parasitic inductance in + + align:start position:0% +layout with parasitic inductance in + + + align:start position:0% +layout with parasitic inductance in +series with the capacitor but we fix the + + align:start position:0% +series with the capacitor but we fix the + + + align:start position:0% +series with the capacitor but we fix the +problem with the inductor right so we're + + align:start position:0% +problem with the inductor right so we're + + + align:start position:0% +problem with the inductor right so we're +fixing one at a + + align:start position:0% + + + + align:start position:0% + +time and I should say by the way that + + align:start position:0% +time and I should say by the way that + + + align:start position:0% +time and I should say by the way that +this test notice we don't have a ground + + align:start position:0% +this test notice we don't have a ground + + + align:start position:0% +this test notice we don't have a ground +plan set up we don't have all this other + + align:start position:0% +plan set up we don't have all this other + + + align:start position:0% +plan set up we don't have all this other +stuff so this this test St wouldn't + + align:start position:0% +stuff so this this test St wouldn't + + + align:start position:0% +stuff so this this test St wouldn't +wouldn't qualify for getting repeatable + + align:start position:0% +wouldn't qualify for getting repeatable + + + align:start position:0% +wouldn't qualify for getting repeatable +results in all kinds of systems but here + + align:start position:0% +results in all kinds of systems but here + + + align:start position:0% +results in all kinds of systems but here +we go we have again you know I didn't + + align:start position:0% +we go we have again you know I didn't + + + align:start position:0% +we go we have again you know I didn't +fix both problems and hence I still have + + align:start position:0% +fix both problems and hence I still have + + + align:start position:0% +fix both problems and hence I still have +bad performance right so this is the + + align:start position:0% +bad performance right so this is the + + + align:start position:0% +bad performance right so this is the +frustrating thing about these things + + align:start position:0% +frustrating thing about these things + + + align:start position:0% +frustrating thing about these things +that yeah you fix one thing but not the + + align:start position:0% +that yeah you fix one thing but not the + + + align:start position:0% +that yeah you fix one thing but not the +other and you get the same kind of bad + + align:start position:0% +other and you get the same kind of bad + + + align:start position:0% +other and you get the same kind of bad +result you know now let's do the final + + align:start position:0% +result you know now let's do the final + + + align:start position:0% +result you know now let's do the final +case and this final case is we've taken + + align:start position:0% +case and this final case is we've taken + + + align:start position:0% +case and this final case is we've taken +the same components but we've tried to + + align:start position:0% +the same components but we've tried to + + + align:start position:0% +the same components but we've tried to +do a good job of laying out the filter + + align:start position:0% +do a good job of laying out the filter + + + align:start position:0% +do a good job of laying out the filter +okay so this is our attempt to you know + + align:start position:0% +okay so this is our attempt to you know + + + align:start position:0% +okay so this is our attempt to you know +we're still going to have + + align:start position:0% +we're still going to have + + + align:start position:0% +we're still going to have +component parasitics you know the the + + align:start position:0% +component parasitics you know the the + + + align:start position:0% +component parasitics you know the the +internal resistance and inductance of + + align:start position:0% +internal resistance and inductance of + + + align:start position:0% +internal resistance and inductance of +the the components but we're going to + + align:start position:0% +the the components but we're going to + + + align:start position:0% +the the components but we're going to +try to do a slightly better job about + + align:start position:0% +try to do a slightly better job about + + + align:start position:0% +try to do a slightly better job about +how we configure them on the board okay + + align:start position:0% +how we configure them on the board okay + + + align:start position:0% +how we configure them on the board okay +so here we go what do we get + + align:start position:0% + + + + align:start position:0% + +now well okay there we go boom now you + + align:start position:0% +now well okay there we go boom now you + + + align:start position:0% +now well okay there we go boom now you +say well is that very good or do we + + align:start position:0% +say well is that very good or do we + + + align:start position:0% +say well is that very good or do we +change it very much but notice that this + + align:start position:0% +change it very much but notice that this + + + align:start position:0% +change it very much but notice that this +is is um this log magnitude scale is 20 + + align:start position:0% +is is um this log magnitude scale is 20 + + + align:start position:0% +is is um this log magnitude scale is 20 +DB per + + align:start position:0% +DB per + + + align:start position:0% +DB per +division all right that means the noise + + align:start position:0% +division all right that means the noise + + + align:start position:0% +division all right that means the noise +of the blue Trace is about a factor of a + + align:start position:0% +of the blue Trace is about a factor of a + + + align:start position:0% +of the blue Trace is about a factor of a +100 below the noise at the white Trace + + align:start position:0% +100 below the noise at the white Trace + + + align:start position:0% +100 below the noise at the white Trace +right so that's a really big difference + + align:start position:0% +right so that's a really big difference + + + align:start position:0% +right so that's a really big difference +and and for the others it's maybe a + + align:start position:0% +and and for the others it's maybe a + + + align:start position:0% +and and for the others it's maybe a +factor of 50 or something like that so + + align:start position:0% +factor of 50 or something like that so + + + align:start position:0% +factor of 50 or something like that so +it's a + + align:start position:0% +it's a + + + align:start position:0% +it's a +substantial amount below and this is + + align:start position:0% +substantial amount below and this is + + + align:start position:0% +substantial amount below and this is +just one example of just one filter + + align:start position:0% +just one example of just one filter + + + align:start position:0% +just one example of just one filter +stage whether you've done a good job or + + align:start position:0% +stage whether you've done a good job or + + + align:start position:0% +stage whether you've done a good job or +bad job with the parasitic elements okay + + align:start position:0% +bad job with the parasitic elements okay + + + align:start position:0% +bad job with the parasitic elements okay +so when you go out to do this stuff this + + align:start position:0% +so when you go out to do this stuff this + + + align:start position:0% +so when you go out to do this stuff this +the whole thing I want you to take away + + align:start position:0% +the whole thing I want you to take away + + + align:start position:0% +the whole thing I want you to take away +from this is really think about all the + + align:start position:0% +from this is really think about all the + + + align:start position:0% +from this is really think about all the +second order effects the parasitics of + + align:start position:0% +second order effects the parasitics of + + + align:start position:0% +second order effects the parasitics of +the components and how you use them and + + align:start position:0% +the components and how you use them and + + + align:start position:0% +the components and how you use them and +you know we try really hard to do things + + align:start position:0% +you know we try really hard to do things + + + align:start position:0% +you know we try really hard to do things +like keep the noisy input or sorry the + + align:start position:0% +like keep the noisy input or sorry the + + + align:start position:0% +like keep the noisy input or sorry the +noisy converter away from the quiet + + align:start position:0% +noisy converter away from the quiet + + + align:start position:0% +noisy converter away from the quiet +input we're going to plug into the wall + + align:start position:0% +input we're going to plug into the wall + + + align:start position:0% +input we're going to plug into the wall +some days you just don't get away from + + align:start position:0% +some days you just don't get away from + + + align:start position:0% +some days you just don't get away from +it because the the they tell oh no can't + + align:start position:0% +it because the the they tell oh no can't + + + align:start position:0% +it because the the they tell oh no can't +change where our connector is and just + + align:start position:0% +change where our connector is and just + + + align:start position:0% +change where our connector is and just +because the connector is right next to + + align:start position:0% +because the connector is right next to + + + align:start position:0% +because the connector is right next to +the noisy power supply you're go figure + + align:start position:0% +the noisy power supply you're go figure + + + align:start position:0% +the noisy power supply you're go figure +it out and you have to live with it but + + align:start position:0% +it out and you have to live with it but + + + align:start position:0% +it out and you have to live with it but +if you can try to keep your noisy stuff + + align:start position:0% +if you can try to keep your noisy stuff + + + align:start position:0% +if you can try to keep your noisy stuff +far away from your quiet stuff try to + + align:start position:0% +far away from your quiet stuff try to + + + align:start position:0% +far away from your quiet stuff try to +reduce the parasitics by like being very + + align:start position:0% +reduce the parasitics by like being very + + + align:start position:0% +reduce the parasitics by like being very +careful about how you lay out your + + align:start position:0% +careful about how you lay out your + + + align:start position:0% +careful about how you lay out your +components low inductance insertion low + + align:start position:0% +components low inductance insertion low + + + align:start position:0% +components low inductance insertion low +capacitance across the components and + + align:start position:0% +capacitance across the components and + + + align:start position:0% +capacitance across the components and +that will go a long way towards getting + + align:start position:0% +that will go a long way towards getting + + + align:start position:0% +that will go a long way towards getting +around weird anomalous behavior and + + align:start position:0% +around weird anomalous behavior and + + + align:start position:0% +around weird anomalous behavior and +getting to be as good as you can and + + align:start position:0% +getting to be as good as you can and + + + align:start position:0% +getting to be as good as you can and +then even when you do that and you're + + align:start position:0% +then even when you do that and you're + + + align:start position:0% +then even when you do that and you're +getting some worse performance you know + + align:start position:0% +getting some worse performance you know + + + align:start position:0% +getting some worse performance you know +getting worse around 20 MHz fine now + + align:start position:0% +getting worse around 20 MHz fine now + + + align:start position:0% +getting worse around 20 MHz fine now +we'll Cascade another filter stage to + + align:start position:0% +we'll Cascade another filter stage to + + + align:start position:0% +we'll Cascade another filter stage to +handle the higher + + align:start position:0% +handle the higher + + + align:start position:0% +handle the higher +frequencies okay so that's that's about + + align:start position:0% +frequencies okay so that's that's about + + + align:start position:0% +frequencies okay so that's that's about +it for today are there any questions + + align:start position:0% +it for today are there any questions + + + align:start position:0% +it for today are there any questions +before we wrap up this just first + + align:start position:0% +before we wrap up this just first + + + align:start position:0% +before we wrap up this just first +introduction to Emi + + align:start position:0% + + + + align:start position:0% + +measurements okay we will see you next + + align:start position:0% +measurements okay we will see you next + + + align:start position:0% +measurements okay we will see you next +week \ No newline at end of file diff --git a/I1IeF7D7kkY.txt b/I1IeF7D7kkY.txt new file mode 100644 index 0000000000000000000000000000000000000000..ef20cdb02c4983500283405beea8f0f678168a24 --- /dev/null +++ b/I1IeF7D7kkY.txt @@ -0,0 +1,475 @@ +align:start position:0% + +the technique of debate is a really + + align:start position:0% +the technique of debate is a really + + + align:start position:0% +the technique of debate is a really +interesting and useful technique I make + + align:start position:0% +interesting and useful technique I make + + + align:start position:0% +interesting and useful technique I make +sure to arbitrarily assign students the + + align:start position:0% +sure to arbitrarily assign students the + + + align:start position:0% +sure to arbitrarily assign students the +side that they'll be taking in the + + align:start position:0% +side that they'll be taking in the + + + align:start position:0% +side that they'll be taking in the +debate because it's pretty easy to + + align:start position:0% +debate because it's pretty easy to + + + align:start position:0% +debate because it's pretty easy to +debate something that you feel + + align:start position:0% +debate something that you feel + + + align:start position:0% +debate something that you feel +passionate about it's not so easy to + + align:start position:0% +passionate about it's not so easy to + + + align:start position:0% +passionate about it's not so easy to +debate something that you don't feel + + align:start position:0% +debate something that you don't feel + + + align:start position:0% +debate something that you don't feel +passionate about or where you feel the + + align:start position:0% +passionate about or where you feel the + + + align:start position:0% +passionate about or where you feel the +other side is correct um in terms of + + align:start position:0% +other side is correct um in terms of + + + align:start position:0% +other side is correct um in terms of +learning it really is a I think it's a + + align:start position:0% +learning it really is a I think it's a + + + align:start position:0% +learning it really is a I think it's a +great exercise because it forces people + + align:start position:0% +great exercise because it forces people + + + align:start position:0% +great exercise because it forces people +to at least superficially understand the + + align:start position:0% +to at least superficially understand the + + + align:start position:0% +to at least superficially understand the +stated Arguments for the side they're + + align:start position:0% +stated Arguments for the side they're + + + align:start position:0% +stated Arguments for the side they're +taking and then find a way to at least + + align:start position:0% +taking and then find a way to at least + + + align:start position:0% +taking and then find a way to at least +be semi- convincing about those + + align:start position:0% +be semi- convincing about those + + + align:start position:0% +be semi- convincing about those +arguments and then I give them a period + + align:start position:0% +arguments and then I give them a period + + + align:start position:0% +arguments and then I give them a period +of time to prepare to sort of prepare + + align:start position:0% +of time to prepare to sort of prepare + + + align:start position:0% +of time to prepare to sort of prepare +their arguments about how they're going + + align:start position:0% +their arguments about how they're going + + + align:start position:0% +their arguments about how they're going +to defend their positions and uh and + + align:start position:0% +to defend their positions and uh and + + + align:start position:0% +to defend their positions and uh and +then I have them voice voice their + + align:start position:0% +then I have them voice voice their + + + align:start position:0% +then I have them voice voice their +arguments for the particular side that + + align:start position:0% +arguments for the particular side that + + + align:start position:0% +arguments for the particular side that +that they've been assigned so in + + align:start position:0% +that they've been assigned so in + + + align:start position:0% +that they've been assigned so in +crafting the arguments Pro if you're con + + align:start position:0% +crafting the arguments Pro if you're con + + + align:start position:0% +crafting the arguments Pro if you're con +um you really have to start to + + align:start position:0% +um you really have to start to + + + align:start position:0% +um you really have to start to +understand what goes behind those + + align:start position:0% +understand what goes behind those + + + align:start position:0% +understand what goes behind those +arguments a little bit better and so + + align:start position:0% +arguments a little bit better and so + + + align:start position:0% +arguments a little bit better and so +that's where the learning takes place I + + align:start position:0% +that's where the learning takes place I + + + align:start position:0% +that's where the learning takes place I +think the other thing is that the + + align:start position:0% +think the other thing is that the + + + align:start position:0% +think the other thing is that the +students get a little bit competitive so + + align:start position:0% +students get a little bit competitive so + + + align:start position:0% +students get a little bit competitive so +they want to construct a good argument + + align:start position:0% +they want to construct a good argument + + + align:start position:0% +they want to construct a good argument +they want to sound convincing and so + + align:start position:0% +they want to sound convincing and so + + + align:start position:0% +they want to sound convincing and so +that extra little bit means that they + + align:start position:0% +that extra little bit means that they + + + align:start position:0% +that extra little bit means that they +really do put in the effort to construct + + align:start position:0% +really do put in the effort to construct + + + align:start position:0% +really do put in the effort to construct +a good argument and to make it + + align:start position:0% +a good argument and to make it + + + align:start position:0% +a good argument and to make it +believable if I were making + + align:start position:0% +believable if I were making + + + align:start position:0% +believable if I were making +recommendations to someone who had never + + align:start position:0% +recommendations to someone who had never + + + align:start position:0% +recommendations to someone who had never +used a debate before I would say that + + align:start position:0% +used a debate before I would say that + + + align:start position:0% +used a debate before I would say that +you you should first of all don't pick + + align:start position:0% +you you should first of all don't pick + + + align:start position:0% +you you should first of all don't pick +anything that's really emotional uh to + + align:start position:0% +anything that's really emotional uh to + + + align:start position:0% +anything that's really emotional uh to +start out with so people can feel have a + + align:start position:0% +start out with so people can feel have a + + + align:start position:0% +start out with so people can feel have a +pretty strong opinion about it but it's + + align:start position:0% +pretty strong opinion about it but it's + + + align:start position:0% +pretty strong opinion about it but it's +not something that's really deep um so I + + align:start position:0% +not something that's really deep um so I + + + align:start position:0% +not something that's really deep um so I +would stay away from something too too + + align:start position:0% +would stay away from something too too + + + align:start position:0% +would stay away from something too too +touchy um the other thing is there + + align:start position:0% +touchy um the other thing is there + + + align:start position:0% +touchy um the other thing is there +should be it should be something where + + align:start position:0% +should be it should be something where + + + align:start position:0% +should be it should be something where +it's really not a slam dunk one way or + + align:start position:0% +it's really not a slam dunk one way or + + + align:start position:0% +it's really not a slam dunk one way or +the other so you want to make sure that + + align:start position:0% +the other so you want to make sure that + + + align:start position:0% +the other so you want to make sure that +the that the the topic that you choose + + align:start position:0% +the that the the topic that you choose + + + align:start position:0% +the that the the topic that you choose +really does have two reasonable + + align:start position:0% +really does have two reasonable + + + align:start position:0% +really does have two reasonable +positions you don't want to give one + + align:start position:0% +positions you don't want to give one + + + align:start position:0% +positions you don't want to give one +team just a terrible thing to happen to + + align:start position:0% +team just a terrible thing to happen to + + + align:start position:0% +team just a terrible thing to happen to +argue the other thing you want to make + + align:start position:0% +argue the other thing you want to make + + + align:start position:0% +argue the other thing you want to make +sure is that you give students enough + + align:start position:0% +sure is that you give students enough + + + align:start position:0% +sure is that you give students enough +time to craft their arguments and to to + + align:start position:0% +time to craft their arguments and to to + + + align:start position:0% +time to craft their arguments and to to +debate to debate the points so that if + + align:start position:0% +debate to debate the points so that if + + + align:start position:0% +debate to debate the points so that if +you cut the debate short after three + + align:start position:0% +you cut the debate short after three + + + align:start position:0% +you cut the debate short after three +minutes it's just not going to help so + + align:start position:0% +minutes it's just not going to help so + + + align:start position:0% +minutes it's just not going to help so +you have to set aside a pretty good + + align:start position:0% +you have to set aside a pretty good + + + align:start position:0% +you have to set aside a pretty good +chunk of time \ No newline at end of file diff --git a/I_LcUur7quE.txt b/I_LcUur7quE.txt new file mode 100644 index 0000000000000000000000000000000000000000..b2498ec2d9432c4867e2a9d3eaaa179b22ac4f27 --- /dev/null +++ b/I_LcUur7quE.txt @@ -0,0 +1,3136 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: We'll begin this time +by looking at some probability + +distribution that you +should be familiar + +with from this +perspective, starting + +with a Gaussian distribution +for one variable. + +We're focused on a +variable that takes + +real values in the interval +minus infinity to infinity + +and the Gaussian has the +form exponential that + +is centered around some +value, let's call it lambda, + +and has fluctuations around this +value parameterized by sigma. + +And the integral of +this p over the interval + +should be normalized +to unity, giving you + +this hopefully very +family of form. + +Now, if you want to characterize +the characteristic function, + +all we need to do is to +Fourier transform this. + +So I have the integral +dx e the minus ikx. + +So this-- let's remind +you alternatively + +was the expectation value +of e to the minus ikx. + +minus x minus lambda squared +over 2 sigma squared, + +which is the probably +distribution. + +And you should know what +the answer to that is, + +but I will remind. + +You can change variables to +x minus lambda [INAUDIBLE] y. + +So from here we will +get the factor of 2 + +to the minus ik lambda. + +You have then the +integral over y minus y + +squared over 2 sigma squared. + +And then what we need to do is +to complete this square over + +here. + +And you can do +that, essentially, + +by adding and +subtracting a minus + +k squared sigma squared over 2. + +So that if I change variable +to y plus ik sigma squared, + +let's call that z, then I +have outside the integral e + +to the minus ik lambda minus k +squared sigma squared over 2. + +And the remainder I can +write as a full square. + +And this is just a +normalized Gaussian integral + +that comes to 1. + +So as you well know, a Fourier +transform of a Gaussian + +is itself a Gaussian, and +that's what we've established. + +E to the minus ik lambda minus +k squared sigma squared over 2m. + +And if I haven't made a mistake +when I said k equals to 0, + +the answer should be 1 because +k equals to 0 expectation + +value of 1 just amounts +to normalization. + +Now what we said was that +a more interesting function + +is obtained by taking +the log of this. + +So from here we go to the +log of [INAUDIBLE] of k. + +Log of [INAUDIBLE] of k is +very simple for the Gaussian. + +And what we had said +was that by definition + +this log of the +characteristic function + +generates cumulants +through the series + +minus ik to the power of n over +n factorial, the end cumulant. + +So looking at this, +we can immediately + +see that the Guassian +is characterized + +by a first cumulant, which is +the coefficient of minus ik. + +It's lambda. + +It is characterized by +a second cumulant, which + +is the coefficient +of minus ik squared. + +This, you know, is the variance. + +And we can explicitly +see that the coefficient + +of minus ik squared +over 2 factorial + +is simply sigma squared. + +So this is reputation. + +But one thing that +is interesting + +is that our series +has now terminates, + +which means that +if I were to look + +at the third cumulant, if I were +to look at the fourth cumulant, + +and so forth, for the +Guassian, they're all 0. + +So the Gaussian is +the distribution + +that is completely +characterized just + +by its first and second +cumulants, all the rest + +being 0. + +So, now our last +time we developed + +some kind of a graphical method. + +We said that I can graphically +describe the first cumulant + +as a bag with one point in it. + +Second cumulant with something +that has two points in it. + +A third cumulant +with three three, + +fourth cumulant with four +and four points and so forth. + +This is just rewriting. + +Now, the interesting +thing was that we + +said that the various moments +we could express graphically. + +So that, for example, +the second moment + +is either this or this, +which then graphically + +is the same thing as lambda +squared plus sigma squared + +because this is indicated +by sigma squared. + +Now, x cubed you +would say is either + +three things by themselves +or put two of them + +together and then one separate. + +And this I could do in +three different ways. + +And in general, for a +general distribution, + +I would have had another +term, which is a triangle. + +But the triangle is 0. + +So for the Gaussian, +this terminates here. + +I have lambda cubed plus +3 lambda sigma squared. + +If I want to calculate +x to the fourth, + +maybe the old way +of doing it would + +have been too multiply the +Gaussian distribution against x + +to the fourth and try +to do the integration. + +And you would ultimately be able +to do that rearranging things + +and looking at the various +powers of the Gaussian + +integrated from minus +infinity to infinity. + +But you can do it graphically. + +You can say, OK. + +It's either this or +I can have-- well, + +I cannot put one aside +and three together, + +because that doesn't exist. + +I could have two together +and two not together. + +And this I can do in +six different ways. + +You can convince +yourself of that. + +What I could do two pairs, which +I can do three different ways + +because I can either do one, +two; one, three; one, four + +and then the other is satisfied. + +So this is lambda to the +fourth plus 6 lambda squared + +sigma squared plus 3 +sigma to the fourth. + +And you can keep going and +doing different things. + +OK. + +Question? + +Yeah? + +AUDIENCE: Is the +second-- [INAUDIBLE]. + +PROFESSOR: There? + +AUDIENCE: Because-- so you said +that the second cumulative-- + +PROFESSOR: Oh. + +AUDIENCE: --x sqaured. + +Yes. + +PROFESSOR: Yes. + +So that's the wrong-- + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: The coefficient of k +squared is the second cumulant. + +The additional 2 was a mistake. + +OK. + +Anything else? + +All right. + +Let's take a look at couple +of other distributions, + +this time discrete. + +So the binomial distribution +is repeat a binary random + +variable. + +And what does this mean? + +It means two outcomes +that's binary, + +let's call them +A and B. And if I + +have a coin that's head +or tails, it's binary. + +Two possibilities. + +And I can assign probabilities +to the two outcomes + +to PA and PB, which +has to be 1 minus PA. + +And the question +is if you repeat + +this binary random +variables n times, + +what is the probability +of NA outcomes of A? + +And I forget to say +something important, + +so I write it in red. + +This should be independent. + +That is the outcome of +a coin toss at, say, + +the fifth time +should not influence + +the sixth time and future times. + +OK. + +So this is easy. + +The probability to have NA +occurrences of A in N trials. + +So it has to be index yn. + +Is that within the n times that +I tossed, A came up NA times. + +So it has to be proportional +to the probability + +of A independently multiplied +by itself NA times. + +But if I have exactly +NA occurrences of A, + +all the other times +I had B occurring. + +So I have the probability +of B for the remainder, + +which is N minus NA. + +Now this is the probability +for a specific occurrence, + +like the first NA times that +I threw the coin I will get A. + +The remaining times +I would get B. + +But the order is not +important and the number + +of ways that I can +shuffle the order + +and have a total of NA out of +N times is the binomial factor. + +Fine. + +Again, well known. + +Let's look at its +characteristic function. + +So p tilde, which is +now a function of k, + +is expectation value +of e to the minus ik + +NA, which means that I +have to weigh e minus ik + +NA against the probability +of occurrences of NA times, + +which is this binomial factor +PA to the power of NA, PB + +to the power of N minus NA. + +And of course, I have to sum +over all possible values of NA + +that go all the way from 0 to N. + +So what we have +here is something + +which is this combination, +PA e to the minus ik + +raised to the power of NA. + +PB raised to the complement +N minus NA multiplied + +by the binomial factor summed +over all possible values. + +So this is just the definition +of the binomial expansion of PA + +e to the minus ik plus PB +raised to the power of N. + +And again, let's check. + +If I set k equals to +0, I have PA plus PB, + +which is 1 raised to the +power of N. So things are OK. + +So this is the +characteristic function. + +At this stage, the only thing +that I will note about this + +is that if I look at the +characteristic function + +I will get N times. + +So this is-- actually, +let's make sure + +that we maintain the +index N. So this is + +the characteristic function +appropriate to N trials. + +And what I get is that +up to factor of N, + +I will get the +characteristic function + +that would be +appropriate to one trial. + +So what that means +if I were to look + +at powers of k, the expectation +value of some cumulant, + +if I go to repeat things +N times-- so this carries + +an index N. It is going to be +simply N times what I would + +have had in a single trial. + +So for a single +trial, you really + +have two outcomes-- 0 or 1 +occurrences of this object. + +So for a binary variable, +you can really easily compute + +these quantities +and then you can + +calculate the corresponding +ones for N trials simply + +multiplying by N. +And we will see + +that this is +characteristic, essentially, + +of anything that is repeated N +times, not just the binomial. + +So this form that you have +N independent objects, + +you would get N +times what you would + +have for one object +is generally valid + +and actually something +that we will build + +a lot of statistical +mechanics on because we + +are interested in +the [INAUDIBLE]. + +So we will see that shortly. + +But rather than +following this, let's + +look at a third distribution +that is closely related, + +which is the Poisson. + +And the question +that we are asking + +is-- we have an interval. + +And the question is, +what is the probability + +of m events in an +interval from 0 to T? + +And I kind of +expressed it this way + +because prototypical Poisson +distribution is, let's say, + +the radioactivity. + +And you can be waiting for +some time interval from 0 + +to 1 minute and asking within +that time interval, what's + +the probability that you will +see m radioactive decay events? + +So what is the probability +if two things happen? + +One is that the probability of 1 +and only 1 event in interval dt + +is alpha dt as dt goes to 0. + +OK? + +So basically if you look +at this over 1 minute, + +the chances are that you +will see so many events, + +so many radioactivities. + +If you shorten the +interval, the chances + +that you would see events +would become less and less. + +If you make your +event infinitesimal, + +most of the time +nothing would happen + +with very small +probability that vanishes. + +As the size of the interval +goes to 0, you will see 1 event. + +So this is one condition. + +And the second condition is +events in different intervals + +are independent. + +And since I wrote +independent in red up there, + +let me write it in red here +because it sort of harks back + +to the same condition. + +And so this is the question. + +What is this probability? + +And the to get the +answer, what we do + +is to subdivide our +big interval into N, + +which is big T divided by +the small dt subintervals. + +So basically, originally +let's say on the time axis, + +we were covering a distance +that went from 0 to big T + +and we were asking +what happens here. + +So what we are +doing now is we are + +sort of dividing this interval +to lots of subintervals, + +the size of each one +of them being dt. + +And therefore, the total +number is big T over dt. + +And ultimately, +clearly, I want to sit + +dt going to 0 so that this +condition is satisfied. + +So also because of the second +condition, each one of these + +will independently tell me +whether or not I have an event. + +And so if I want to count +the total number of events, + +I have to add things +that are occurring + +in different intervals. + +And we can see that +this problem now + +became identical to that +problem because each one + +of these intervals has two +possible outcomes-- nothing + +happens with probability +1 minus alpha dt, + +something happens with +probability alpha dt. + +So no event is probability +1 minus alpha dt. + +One event means +probability alpha dt. + +So this is a binomial process. + +So we can calculate, +for example, + +the characteristic function. + +And I will indicate +that we are looking + +at some interval of +size T and parameterized + +by this straight +alpha, we'll see + +that only the +product will occur. + +So this is this before +Fourier variable. + +We said that it's +a binary, so it + +is one of the probabilities +plus e to the minus ik + +plus the other probability +raised to the power of N. + +Now we just substitute +the probabilities that we + +have over here. + +So the probability of not having +an event is 1 minus alpha dt. + +The probability of having +an event is alpha dt. + +So alpha dt is going +to appear here as e + +to the minus ik minus 1. + +So alpha st, e to the +minus ik, is from here. + +From PB I will get +1 minus alpha dt. + +And I bunched +together the two terms + +that are proportional +to alpha dt. + +And then I have to raise +to the power of N, which + +is T divided by dt. + +And this whole prescription +is valid in the limit + +where dt is going to 0. + +So what you have is 1 +plus an infinitesimal + +raised to a huge power. + +And this limiting procedure +is equivalent to taking + +the exponential. + +So basically this +is the same thing + +as exponential of what is here +multiplied by what is here. + +The dt's cancel each +other out and the answer + +is alpha T e to the +minus ik minus 1. + +So the characteristic +function for this process + +that we described is +simply given by this form. + +You say, wait. + +I didn't ask for the +characteristic function. + +I wanted the probability. + +Well, I say, OK. + +Characteristic function is +simply the Fourier transform. + +So let me Fourier +transform back, + +and I would say that the +probability along not + +the Fourier axis +but the actual axis + +is open by the inverse +Fourier process. + +So I have to do an +integral dk over 2 pi + +e to the ikx times the +characteristic function. + +And the characteristic function +is e to minus-- what was it? + +e to the alpha T. E to +the minus ik k minus 1. + +Well, there is an +equal to minus alpha + +T that I can simply take +outside the integration. + +I have the integration +over k e to that ikx. + +And then what I will do +is I have this factor of e + +to the something in the-- e to +the alpha T to the minus ik. + +I will use the expansion +of the exponential. + +So the expansion +of the exponential + +is a sum over m running +from 0 to infinity. + +The exponent raised +to the m-th power. + +So I have alpha T raised +to the m-th power, + +e to the minus ik raised +to the m-th power divided + +m factor here. + +So now I reorder the +sum and the integration. + +The sum is over m, the +integration is over k. + +I can reorder them. + +So on the things +that go outside I + +have a sum over m running from +0 to infinity e to the minus + +alpha T, alpha T to the power +of m divided by m factorial. + +Then I have the integral +over k over 2 pi e to the ik. + +Well, I had the x here and I +have e to the minus ikm here. + +So I have x minus m. + +And then I say, OK, this is +an integral that I recognize. + +The integral of e to +the ik times something + +is simply a delta function. + +So this whole thing +is a delta function + +that's says, oh, x +has to be an integer. + +Because I kind of did something +that maybe, in retrospect, + +you would have said +why are you doing this. + +Because along how many +times things have occurred, + +they have either occurred +0 times, 1 times, 2 decays, + +3 decays. + +I don't have 2.5 decays. + +So I treated x as a +continuous variable, + +but the mathematics was really +clever enough to say that, no. + +The only places that you can +have are really integer values. + +And the probability that you +have some particular value + +integer m is simply what we have +over here, e to the minus alpha + +T alpha T to the power of m +divided by m factorial, which + +is the Poisson distribution. + +OK. + +But fine. + +So this is the +Poisson distribution, + +but really we go +through the root + +of the characteristic +function in order + +to use this machinery +that we developed earlier + +for cumulants et cetera. + +So let's look at the +cumulant generating function. + +So I have to take the +log of the function + +that I had calculated there. + +It is nicely in the +exponential, so I + +get alpha T e to the +minus ik minus 1. + +So now I can make an expansion +of this in powers of k + +so I can expand the exponential. + +The first term vanishes +because this starts with one. + +So really I have alpha +T sum running from 1 + +to infinity or N running +from 1 to infinity minus ik + +to the power of n +over n factorial. + +So my task for +identifying the cumulants + +is to look at the +expansion of this log + +and read off powers of minus +ikn to the power of n factorial. + +So what do we see? + +We see that the first cumulant +of the Poisson is alpha T, + +but all the coefficients +are the same thing. + +The expectation value-- sorry. + +The second cumulant is +alpha T. The third cumulant, + +the fourth cumulant, +all the other cumulants + +are also alpha T. + +So the average number of decays +that you see in the interval + +is simply alpha T. But +there are fluctuations, + +and if somebody +should, for example, + +ask you what's the average +number cubed of events, + +you would say, OK. + +I'm going to use the +relationship between moments + +and cumulants. + +I can either have +three first objects + +or I can put one of +them separate in three + +different factions. + +But this is a case where +the triangle is allowed, + +so diagrammatically +all three are possible. + +And so the answer for the +first term is alpha T cubed. + +For the second term, +it is a factor of 3. + +Both this variance and the mean +give me a factor of alpha T, + +so I will get alpha T squared. + +And the third term, which +is the third cumulant, + +is also alpha T. So the +answer is simply of this form. + +Again, m is an integer. + +Alpha T is dimensionless. + +So there is no dimension problem +by it having different powers. + +OK. + +Any questions? + +All right. + +So that's what I wanted +to say about one variable. + +Now let's go and look at +corresponding definitions + +when you have +multiple variables. + +So for many random variables, +the set of possible outcomes, + +let's say, has variables x1, x2. + +Let's be precise. + +Let's end it a xn. + +And if these are +distributed, each one of them + +continuously over the +interval, to each point + +we can characterize some kind +of a probability density. + +So this entity is called the +joint probability density + +function. + +And its definition would be to +look at probability of outcome + +in some interval that +is between, say, x1, x1 + +plus dx1 in one, x2, x2 plus +dx2 in the second variable. + +xn plus dxn in +the last variable. + +So you sort of look at +the particular point + +in this multi-dimensional +space that you are interested. + +You build a little +cube around it. + +You ask, what's the +probability to being that cube? + +And then you divide by +the volume of that cube. + +So dx1, dx2, dxn, +which is the same thing + +that you would be doing in +constructing any density + +and by ultimately taking the +limit that all of the x's + +go to 0. + +All right. + +So this is the joint +probability distribution. + +You can construct, now, the +joint characteristic function. + +Now how do you do that? + +Well, again, just like you +would do for your transform + +with multiple variables. + +So you would go +for each variable + +to a conjugate variable. + +So x1 would go to k1. + +x2 would go to k2. + +xn would go to kn. + +And this would +mathematically amount + +to calculating the +expectation value of e + +to the minus i k1x1 x1, +k2x2 and so forth, which + +you would obtain by integrating +over all of these variables, e + +to the minus ik alpha x alpha, +against the probability of x1 + +through xn. + +Question? + +AUDIENCE: It's a +bit hard to read. + +It's getting really small. + +PROFESSOR: OK. + +[LAUGHTER] + +PROFESSOR: But it's just +multi-dimensional integral. + +OK? + +All right. + +So this is, as +the case of one, I + +think the problem is not the +size but the angle I see. + +I can't do much for that. + +You have to move to the center. + +OK. + +So what we can look at +now is joint moment. + +So you can-- when +we had one variable, + +we could look at something +like the expectation + +value of x to the m. + +That would be the m-th moment. + +But if you have two +variable, we can raise x1 + +to some other, x2 +to another power, + +and actually xn +to another power. + +So this is a joint moment. + +Now the thing is, that +the same way that moments + +for one variable +could be generated + +by expanding the +characteristic function, + +if I were to expand this +function in powers of k, + +you can see that in meeting +the expectation value, + +I will get various powers +of x1 to some power, + +x2 to some power, et cetera. + +So by appropriate +expansion of that function, + +I can generate all of-- read +off all of these moments. + +Now, a more common way of +generating the Taylor series + +expansion is +through derivatives. + +So what I can do is I can +take a derivative with respect + +to, say, ik1. + +If I take a derivative +with respect + +to ik1 here, what happens +is I will bring down + +a factor of minus x alpha. + +So actually let me +put the minus so it + +becomes a factor of x alpha. + +And if I integrate x +alpha against this, + +I will be generating +the expectation value + +of x alpha provided that +ultimately I set all of the k's + +to 0. + +So I will calculate +the derivative + +of this function with respect +to all of these arguments. + +At the end of the day, I +will set k equals to 0. + +That will give me the +expectation value of x1. + +But I don't want x1, I want +x1 raised to the power of m1. + +So I do this. + +Each time I take a derivative +with respect to minus ik, + +I will bring down the factor +of the corresponding x. + +And I can do this with +multiple different things. + +So d by the ik2 raised +to the power of m2 + +minus d by the ikn, +the whole thing + +raised to the power of mn. + +So I can either +take this function + +of multiple variables-- +k1 through kn-- + +and expand it and read off the +appropriate powers of k1k2. + +Or I can say that the +terms in this expansion + +are generated through taking +appropriate derivative. + +Yes? + +AUDIENCE: Is there +any reason why + +you're choosing to take +a derivative with respect + +to ikj instead of simply +putting the i in the numerator? + +Or are there-- are there +things that I'm not-- + +PROFESSOR: No. + +No. + +There is no reason. + +So you're saying why didn't I +write this as this like this? + +i divided? + +AUDIENCE: Yeah. + +PROFESSOR: I think +I just visually saw + +that it was kind +of more that way. + +But it's exactly the same thing. + +Yes. + +OK. + +All right. + +Now the interesting +object, of course, to us + +is more the joint cumulants. + +So how do we generate +joint cumulants? + +Well previously, essentially +we had a bunch of objects + +for one variable +that was some moment. + +And in order to +make them cumulants, + +we just put a sub C here. + +So we do that and we are done. + +But what did +operationally happen + +was that we did the +expansion rather + +than for the +characteristic function + +for the log of the +characteristic function. + +So all I need to do +is to do precisely + +this set of derivatives +applied rather + +than to the joint +characteristic function + +to the log of the joint +characteristic function. + +And at the end, set +all of the case to 0. + +OK? + +So by looking at these two +definitions and the expansion + +of the log, for example, you +can calculate various things. + +Like, for example, x1x2 with +a C is the expectation value + +of x1x2. + +This joint moment minus x1x2, +just as you would have thought, + +would be the appropriate +generalization of the variance. + +And this is the covariance. + +And you can construct +appropriate extensions. + +OK. + +Now we made a lot of use of the +relationship between moments + +and cumulants. + +We just-- so the +idea, really, was + +that the essence of a +probability distribution + +is characterized +in the cumulants. + +Moments kind of depend on +how you look at things. + +The essence is in the cumulants, +but sometimes the moments + +are more usefully +computed, and there + +was a relationship between +moments and cumulants, + +we can generalize that +graphical relation + +to the case joint moments +and joint cumulants. + +So graphical relation +applies as long + +as points are labeled +by appropriate + +or by corresponding variable. + +So suppose I wanted to calculate +some kind of a moment that + +is x1 squared. + +Let's say x2, x3. + +This may generate +for me many diagrams, + +so let's stop from here. + +So what I can do is +I can have points + +that I label 1, 1, and 2. + +And have them separate +from each other. + +Or I can start +pairing them together. + +So one possibility is that I +put the 1's together and the 2 + +starts separately. + +Another possibility is that +I can group the 1 and the 2 + +together. + +And then the other +1 starts separately. + +But I had a choice of +two ways to do this, + +so this comes-- this diagram +with an overall factor of 2. + +And then there's the +possibility to put all of them + +in the same bag. + +And so mathematically, +that means + +that the third-- this +particular joint moment + +is obtained by taking average +of x1 squared x2 average, which + +is the first term. + +The second term is +the variance of x1. + +And then multiplied by x2. + +The third term is twice the +covariance of x1 and x2 times + +the mean of x1. + +And the final term is +just the third cumulant. + +So again, you would need to +compute these, presumably, + +from the law of the +characteristic function + +and then you would be done. + +Couple of other definitions. + +One of them is an +unconditional probability. + +So very soon we will be talking +about, say, probabilities + +appropriate to the +gas in this room. + +And the particles in +the gas in this room + +will be characterized +where they are, + +some position vector q, and +how fast they are moving, + +some momentum vector p. + +And there would be some kind +of a probability density + +associated with finding a +particle with some momentum + +at some location in space. + +But sometimes I +say, well, I really + +don't care about where +the particles are, + +I just want to know how +fast they are moving. + +So what I really care +is the probability + +that I have a particle +moving with some momentum p, + +irrespective of where it is. + +Then all I need to +do is to integrate + +over the position the joint +probability distribution. + +And the check that +this is correct + +is that if I first do not +integrate this over p, + +this would be integrated +over the entire space + +and the joint +probabilities appropriately + +normalized so that the joint +integration will give me one. + +So this is a correct +normalized probability. + +And more generally, if I'm +interested in, say, a bunch of + +coordinates x1 through xs, out +of a larger list of coordinates + +that spans x1 through xs all +the way to something else, + +all I need to do to get +unconditional probability is + +to integrate over the variables +that I'm not interested. + +Again, check is that it's +a good properly normalized. + +Now, this is to +be contrasted with + +the conditional probability. + +The conditional +probability, let's + +say we would be interested in +calculating the pressure that + +is exerted on the board. + +The pressure is exerted +by the particles that + +impinge on the board +and then go away, + +so I'm interested in the +momentum of particles + +right at the board, not +anywhere else in space. + +So if I'm interested in +the momentum of particles + +at the particular location, +which could in principle depend + +on location-- so now q is a +parameter p is the variable, + +but the probability +distribution could depend on q. + +How do we obtain this? + +This, again. + +is going to be proportional +to the probability + +that I will find +a particle both at + +this location with momentum p. + +So I need to have that. + +But it's not +exactly that there's + +a normalization involved. + +And the way to get +normalization is + +to note that if I integrate this +probability over its variable p + +but not over the parameter +q, the answer should be 1. + +So this is going to +be, if I apply it + +to the right-hand side, +the integral over p + +of p of p and q, +which we recognize + +as an example of an +unconditional probability + +to find something at position 1. + +So the normalization is going to +be this so that the ratio is 1. + +So most generally, we +find that the probability + +to have some subset +of variables, given + +that the location of the +other variables in the list + +are somewhat fixed, is given +by the joint probability of all + +of the variables x1 +through xn divided + +by the unconditional +probability that that applies + +to the parameters of our fixed. + +And this is called +Bayes' theorem. + +By the way, if variables +are independent, + +which actually does apply +to the case of the particles + +in this room as far as their +momentum and position is + +concerned, then the +joint probability + +is going to be the +product of one that + +is appropriate to +the position and one + +that is appropriate +to the momentum. + +And if you have +this independence, + +then what you'll +find is that there + +is no difference between +conditional and unconditional + +probabilities. + +And when you go +through this procedure, + +you will find that all the +joint cumulants-- but not + +the joint moments, naturally-- +all the joint cumulants + +will be 0. + +OK. + +Any questions? + +Yes? + +AUDIENCE: Could you explain +how the condition of p-- + +PROFESSOR: How +this was obtained? + +Or the one above? + +AUDIENCE: Yeah. + +The condition you applied +that the integral is 1. + +PROFESSOR: OK. + +So first of all, what +I want to look at + +is the probability that +is appropriate to one + +random variable at +the fixed value of all + +the other random variables. + +Like you say, in general I +should specify the probability + +as a function of momentum and +position throughout space. + +But I'm really interested +only at this point. + +I don't really care +about other points. + +However, the answer may depend +whether I'm looking at here + +or I'm looking at here. + +So the answer for the +probability of momentum + +is parametrized by q. + +On the other hand, +I say that I know + +the probability over +the entire space + +to be a disposition +with the momentum p + +as given by this +joint probability. + +But if I just set +that equal to this, + +the answer is not +correct because the way + +that this quantity is normalized +is if I first integrate over + +all possible values +of its variable, p. + +The answer should be 1, +irrespective of what q is. + +So I can define a conditional +probability for momentum + +here, a conditional +probability for momentum there. + +In both cases the momentum +would be the variable it. + +And integrating over all +possible values of momentum + +should give me one for a +properly normalized probability + +distribution. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Given +that q is something. + +So q could be some-- +now here q can + +be regarded as some parameter. + +So the condition is that this +integration should give me 1. + +I said that on +physical grounds, I + +expect this +conditional probability + +to be the joint probability +up to some normalization + +that I don't know. + +OK. + +So what is that normalization? + +The whole answer should be 1. + +What I have to do +is an integration + +over momentum of the +joint probability. + +I have said that an integration +over some set of variables + +of a joint probability +will give me + +the unconditional probability +for all the others. + +So integrating over all momentum +of this joint probability + +will give me the unconditional +probability for position. + +So the normalization of 1 is +the unconditional probability + +for position divided by n. + +So n-- this has to be this. + +And in general, it would +have to be this in order + +to ensure that if +I integrate over + +this first set of variables +of the joint probability + +distribution which would +give me the unconditional, + +cancels the unconditional in +the denominator to give me 1. + +Other questions? + +OK. + +So I'm going to +erase this last board + +to be underneath that +top board in looking + +at the joint Gaussian +distribution. + +So that was the +Gaussian, and we want + +to look at the joint Gaussian. + +So we want to +generalize the formula + +that we have over there for one +variable to multiple variables. + +So what I have there +initially is a factor, which + +is exponential of minus +1/2, x minus lambda squared. + +I can write this x +minus lambda squared + +as x minus lambda +x minus lambda. + +And then put the variance. + +Let's call it is 1 over sigma +rather than a small sigma + +squared or something like this. + +Actually, let me +just write it as 1 + +over sigma squared +for the time being. + +And then the normalization was +1 over root 2 pi sigma squared. + +But you say, well, I +have multiple variables, + +so maybe this is what I +would give for my B variable. + +And then I would sum over +all N, running from 1 to N. + +So this is essentially +the form that I + +would have for an independent +Gaussian variables. + +And then I would +have to multiply here + +factors of 2 pi sigma squared, +so I would have 2 pi to the N + +over 2. + +And I would have +product of-- actually, + +let's write it as 2 pi +to the N square root. + +I would have the product +of sigma i squared. + +But that's just too +limiting a form. + +The most general form that these +quadratic will allow me to have + +also cross terms where it is +not only the diagonal terms + +x1 and x1 that's are multiplying +each other, but x2 and x3, + +et cetera. + +So I would have a sum over both +m and n running from 1 to n. + +And then to coefficient +here, rather + +than just being a number, +would be the variables + +that would be like a matrix. + +Because for each pair m and +n, I would have some number. + +And I will call them the +inverse of some matrix C. + +And if you, again, think +of the problem as a matrix, + +if I have the diagonal +matrix, then the product + +of elements along the +diagonal is the same thing + +as the determinant. + +If I were to rotate the matrix +to have off diagonal elements, + +the determinant will +always be there. + +So this is really +the determinant of C + +that will appear here. + +Yes? + +AUDIENCE: So are you inverting +the individual elements of C + +or are you inverting the matrix +C and taking its elements? + +PROFESSOR: Actually +a very good point. + +I really wanted to write it +as the inverse of the matrix + +and then peak the +mn [INAUDIBLE]. + +So we imagine that +we have the matrix. + +And these are the +elements of some-- + +so I could have called +this whatever I want. + +So I could have called the +coefficients of x and n. + +I have chosen to regard +them as the inverse + +of some other matrix C. +And the reason for that + +becomes shortly clear, +because the covariances will + +be related to the +inverse of this matrix. + +And hence, that's the +appropriate way to look at it. + +AUDIENCE: Can [INAUDIBLE] +what C means up there? + +PROFESSOR: OK. + +So let's forget +about this lambdas. + +So I would have in +general for two variables + +some coefficient for x1 +squared, some coefficient + +for x2 squared, and some +coefficient for x1, x2. + +So I could call this a11. + +I could call this a22. + +I could call this 2a12. + +Or actually I +could, if I wanted, + +just write it as +a12 plus a21 x2x1 + +or do a1 to an a21 +would be the same. + +So what I could then +regard this is as x1 2. + +The matrix a11, a12, +a21, a22, x1, x2. + +So this is exactly +the same as that. + +All right? + +So these objects +here are the elements + +of this matrix C inverse. + +So I could call this x1, +x2 some matrix A x1 x2. + +That A is 2 by 2 matrix. + +The name I have given to that +2 by 2 matrix in C inverse. + +Yes? + +AUDIENCE: The matrix +is required to be + +symmetric though, isn't it? + +PROFESSOR: The +matrix is required + +to be symmetric for +any quadrant form. + +Yes. + +So when I wrote it +initially, I wrote as 2 a12. + +And then I said, well, +I can also write it + +this fashion provided the +two of them are the same. + +Yes? + +AUDIENCE: How did you know +the determinant of C belonged + +there? + +PROFESSOR: Pardon? + +AUDIENCE: How did you +know that the determinant + +of C [INAUDIBLE]? + +PROFESSOR: OK. + +How do I know the +determinant of C? + +Let's say I give you this form. + +And then I don't know +what the normalization is. + +What I can do is I can do a +change of variables from x1 x2 + +to something like y1 y2 such +that when I look at y1 and y2, + +the matrix becomes diagonal. + +So I can rotate the matrix. + +So any matrix I can imagine +that I will find some U such + +that A U U dagger is this +diagonal matrix lambda. + +Now under these procedures, +one thing that does not change + +is the determinant. + +It's always the product +of the eigenvalues. + +The way that I set +up the problem, + +I said that if I hadn't made +the problem to have cross terms, + +I knew the answers to be the +product of that eigenvalues. + +So if you like, I can start from +there and then do a rotation + +and have the more general form. + +The answer would stay +as the determinant. + +Yes? + +AUDIENCE: The matrix should +be positive as well or no? + +PROFESSOR: The matrix should +be positive definite in order + +for the probability to be +well-defined and exist, yes. + +OK. + +So if you like, by stating +that this is a probability, + +I have imposed a +number of conditions + +such as symmetry, as +well as positivity. + +Yes. + +OK. + +But this is just linear algebra. + +I will assume that you +know linear algebra. + +OK. + +So this property normalized +Gaussian joint probability. + +We are interested in the +characteristic function. + +So what we are interested is the +joint Gaussian characteristic. + +And so again we +saw the procedure + +was that I have to do +the Fourier transform. + +So I have to take this +probability that I + +have over there and do +an integration product, + +say, alpha running +from 1 to N dx + +alpha of e to the +minus ik alpha x alpha. + +This product exists +for all values. + +Then I have to multiply +with this probability + +that I have up there, +which would appear here. + +OK. + +Now, again maybe an +easy way to imagine + +is what I was saying +to previously. + +Let's imagine that +I have rotated + +into a basis where +everything is diagonal. + +Then in the rotated +basis, all you need to do + +is to essentially do product +of characteristic functions + +such as what we have over here. + +So the corresponding +product to this first term + +would be exponential of +minus i sum over N running + +from 1 to N k +alpha lambda alpha. + +kn lambda n. + +I guess I'm using n +as the variable here. + +And as long as things +would be diagonal, + +the next ordered +term would be a sum + +over alpha kn squared the +corresponding eigenvalue + +inverted. + +So remember that in the diagonal +form, each one of these sigmas + +would appear as the diagonal. + +If I do my rotation, +essentially this term + +would not be affected. + +The next term would give me +minus 1/2 sum over m and n + +rather than just having k1 +squared k2 squared, et cetera. + +Just like here, I +would have km kn. + +What happened previously +was that each eigenvalue + +would get inverted. + +If you think about rotating a +matrix, all of its eigenvalues + +are inverted, you are really +rotating the inverse matrix. + +So this here would be the +inverse of whatever matrix + +I have here. + +So this would be C mn. + +So I did will leave you to +do the corresponding linear + +algebra here, but the +answer is correct. + +So the answer is that the +generator of cumulants + +for a joint Gaussian +distribution + +has a form which has a bunch of +the linear terms-- kn lambda n. + +And a bunch of +second order terms, + +so we will have minus +1/2 sum over m and n km + +kn times some coefficient. + +And the series terminates here. + +So for the joint Gaussian, +you have first cumulant. + +So the expectation +value of nm cumulant + +is the same thing as lambda m. + +You have covariances or second +cumulants xm, xn, C is Cmn. + +And in particular, +the diagonal elements + +would correspond +to the variances. + +And all the higher orders +are 0 because there's + +no further term +in the expansion. + +So for example, if I were to +calculate this thing that I + +have on the board here for +the case of a Gaussian, + +for the case of the Gaussian, I +would not have this third term. + +So the answer that +I would write down + +for the case of the +third term would + +be something that +didn't have this. + +And in the way that we +have written things, + +the answer would +have been x1 squared + +x2-- would be just a +lambda 1 squared lambda + +2 plus sigma 1 squared, +or let's call it + +C11, times lambda 2 +plus 2 lambda 1 C12. + +And that's it. + +So there is something +that follows from this + +that it is used a +lot in field theory. + +And it's called Wick's theorem. + +So that's just a +particular case of this, + +but let's state it anyway. + +So for Gaussian distributed +variables of 0 mean, + +following condition applies. + +I can take the first +variable raised + +to power n1, the +second variable to n2, + +the last variable +to some other nN + +and look at a joint +expectation value such as this. + +And this is 0 if sum +over alpha and alpha + +is odd and is called sum +over all pairwise contraction + +if a sum over alpha +and alpha is even. + +So actually, I have right +here an example of this. + +If I have a Gaussian +variable-- jointly + +distributed Gaussian variables +where the means are all 0-- so + +if I say that lambda +1 and lambda 2 are 0, + +then this is an odd +power, x1 squared x2. + +Because of the symmetry +it has to be 0, + +but you explicitly see +that every term that I have + +will be multiplying some +power of [INAUDIBLE]. + +Whereas if for +other than this, I + +was looking at something +like x1 squared x2 x3 + +where the net power +is even, then I + +could sort of +imagine putting them + +into these kinds of diagrams. + +Or alternatively, I can +imagine pairing these things + +in all possible ways. + +So one pairing would +be this with this, + +this with this, which would have +given me x1 squared C x2 x3 C. + +Another pairing would +have been x1 with x2. + +And then, naturally, x1 with x3. + +So I would have gotten +x1 with x2 covariance x1 + +with extreme x3 covariance. + +But I could have connected +the x1 to x2 or the second x1 + +to x2. + +So this comes in 2 variance. + +And so the answer here would +be C11 C23 plus 2 C1 2 C13. + +Yes? + +AUDIENCE: In your writing +of x1 to the n1 [INAUDIBLE]. + +It should be the +cumulant, right? + +Or is it the moment? + +PROFESSOR: This is the moment. + +AUDIENCE: OK. + +PROFESSOR: The contractions +are the covariances. + +AUDIENCE: OK. + +PROFESSOR: So the point is +that the Gaussian distribution + +is completely characterized +in terms of its covariances. + +Once you know the +covariances, essentially you + +know everything. + +And in particular, you may be +interested in some particular + +combination of x's. + +And then you use to +express that in terms + +of all possible +pairwise contractions, + +which are the covariances. + +And essentially, in +all of field theory, + +you expand around some kind +of a Gaussian background + +or Gaussian 0 toward the result. + +And then in your +perturbation theory + +you need various +powers of your field + +or some combination of +powers, and you express them + +through these kinds +of relationships. + +Any questions? + +OK. + +This is fine. + +Let's get rid of this. + +OK. + +Now there is one result that +all of statistical mechanics + +hangs on. + +So I expect that +as I get old and I + +get infirm or whatever +and my memory vanishes, + +the last thing that I +will remember before I die + +would be the central +limit theorem. + +And why is this important +is because you end up + +in statistical physics +adding lots of things. + +So really, the question that +you have or you should be asking + +is thermodynamics is +a very precise thing. + +It says that heat +goes from the higher + +temperature to +lower temperature. + +It doesn't say it does that 50% +of the time or 95% of the time. + +It's a definite statement. + +If I am telling you +that ultimately I'm + +going to express everything +in terms of probabilities, + +how does that jive? + +The reason that it jives +is because of this theorem. + +It's because in order to go from +the probabilistic description, + +you will be dealing with +so many different-- so many + +large number of variables-- +that probabilistic statements + +actually become precise +deterministic statements. + +And that's captured +by this theorem, which + +says that let's look at the +sum of N random variables. + +And I will indicate the sum +by x and my random variables + +as small x's. + +And let's say that this is, for +the individual set of things + +that I'm adding up +together, some kind + +of a joint probability +distribution + +out of which I take +these random variables. + +So each instance of this sum is +selected from this joint PDF, + +so x itself is a random variable +because of possible choices + +of different xi from this +probability distribution. + +So what I'm interested is what +is the probability for the sum? + +So what is the p that +determines this sum? + +I will go by the root of these +characteristic functions. + +I will say, OK, what's the +expectation value of-- well, + +let's-- what's the Fourier +transform of this probability + +distribution? + +If we transform, by definition +it is the expectation of e + +to the minus ik this big X, +which is the sum over all off + +the small x's. + +Do I have that +definition somewhere? + +I erased it. + +Basically, what is this? + +If this k was, in fact, +different k's-- if I had a k1 + +multiplying x1, +k2 multiplying x2, + +that would be the definition +of the joint characteristics + +function for this joint +probability distribution. + +So what this is is you take the +joint characteristic function, + +which depends on k1 +k2, all the way to kn. + +And you set all of +them to be the same. + +So take the joint +characteristic function + +depends on N Fourier variables. + +Put all of them the same k +and you have that for the sum. + +So I can certainly do +that by adding a log here. + +Nothing has changed. + +I know that the log is the +generator of the cumulants. + +So this is a sum +over, let's say, n + +running from 1 to +infinity minus ik + +to the power of n +over n factorial, + +the joint cumulant of the sum. + +So what is the +expansion that I would + +have for log of the joint +characteristic function? + +Well, typically I would say have +at the lowest order k1 times + +the mean of the first +variable, k2 times + +the mean of the second variable. + +But all of them are the same. + +So the first order, +I would get minus i + +the same k sum over n +of the first cumulant + +of the N-th variable. + +Typically, this +second order term, + +I would have all +kinds of products. + +I would have k1 k3 k2 k4, +as well as k1 squared. + +But now all of them +become the same, + +and so what I will have +is a minus ik squared. + +But then I have all possible +pairings mn of xm xn cumulants. + +AUDIENCE: Question. + +PROFESSOR: Yes? + +AUDIENCE: [INAUDIBLE] +expression you probably + +should use different +indices when you're + +summing over elements +of Taylor serious + +and when you're summing +over your [INAUDIBLE] + +random variables. + +Just-- it gets confusing +when both indexes are n. + +PROFESSOR: This here, you +want me to right here, say, i? + +AUDIENCE: Yeah. + +PROFESSOR: OK. + +And here I can write i and j. + +So I think there's +still a 2 factorial. + +And then there's higher orders. + +Essentially then, matching +the coefficients of minus ik + +from the left minus +ik from the right + +will enable me to calculate +relationships between cumulants + +of the sum and cumulants of +the individual variables. + +This first one of them is +not particularly surprising. + +You would say that +the mean of the sum + +is sum of the means of +the individual variables. + +The second statement is +that the variance of the sum + +really involves a pair, i +and j, running from 1 to N. + +So if these variable +were independent, + +you would be just +adding the variances. + +Since they are +potentially dependent, + +you have to also keep +track of covariances. + +And this kind of summation +extends to higher and higher + +cumulants, essentially +including more and more powers + +of cumulants that you +would put on that side. + +And what we do +with that, I guess + +we'll start next time around. \ No newline at end of file diff --git a/J0bAFdMzBbs.txt b/J0bAFdMzBbs.txt new file mode 100644 index 0000000000000000000000000000000000000000..569508f1d42f6226bdd1c5761a70232d1d8445a2 --- /dev/null +++ b/J0bAFdMzBbs.txt @@ -0,0 +1 @@ +[MUSIC PLAYING] \ No newline at end of file diff --git a/J1uHGy1tRmM.txt b/J1uHGy1tRmM.txt new file mode 100644 index 0000000000000000000000000000000000000000..c1159fbd5c0dda554a97a1027d2a95a1c53d3173 --- /dev/null +++ b/J1uHGy1tRmM.txt @@ -0,0 +1,8523 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license + + align:start position:0% +a Creative Commons license + + + align:start position:0% +a Creative Commons license +your support will help MIT + + align:start position:0% +your support will help MIT + + + align:start position:0% +your support will help MIT +OpenCourseWare continue to offer high + + align:start position:0% +OpenCourseWare continue to offer high + + + align:start position:0% +OpenCourseWare continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +welcome back everybody to AO 3 today we + + align:start position:0% +welcome back everybody to AO 3 today we + + + align:start position:0% +welcome back everybody to AO 3 today we +are going to continue the discussion of + + align:start position:0% +are going to continue the discussion of + + + align:start position:0% +are going to continue the discussion of +symmetry metrics which we start the last + + align:start position:0% +symmetry metrics which we start the last + + + align:start position:0% +symmetry metrics which we start the last +time and this is actually what we have + + align:start position:0% +time and this is actually what we have + + + align:start position:0% +time and this is actually what we have +been doing ok so solo so the thing which + + align:start position:0% +been doing ok so solo so the thing which + + + align:start position:0% +been doing ok so solo so the thing which +we have been doing is to solve the + + align:start position:0% +we have been doing is to solve the + + + align:start position:0% +we have been doing is to solve the +normal mode frequencies of kappahd + + align:start position:0% +normal mode frequencies of kappahd + + + align:start position:0% +normal mode frequencies of kappahd +system by looking at equation of motion + + align:start position:0% +system by looking at equation of motion + + + align:start position:0% +system by looking at equation of motion +and X double dot equal to minus KX and + + align:start position:0% +and X double dot equal to minus KX and + + + align:start position:0% +and X double dot equal to minus KX and +in the end of the day what we are doing + + align:start position:0% +in the end of the day what we are doing + + + align:start position:0% +in the end of the day what we are doing +is really to solve I can value pop 1 n + + align:start position:0% +is really to solve I can value pop 1 n + + + align:start position:0% +is really to solve I can value pop 1 n +minus 1 K matrix eigen value problem and + + align:start position:0% +minus 1 K matrix eigen value problem and + + + align:start position:0% +minus 1 K matrix eigen value problem and +we have been exercising this several + + align:start position:0% +we have been exercising this several + + + align:start position:0% +we have been exercising this several +times last last few lectures to the and + + align:start position:0% +times last last few lectures to the and + + + align:start position:0% +times last last few lectures to the and +the N minus 1 K matrices with describing + + align:start position:0% +the N minus 1 K matrices with describing + + + align:start position:0% +the N minus 1 K matrices with describing +how each component in the system intact + + align:start position:0% +how each component in the system intact + + + align:start position:0% +how each component in the system intact +which each other ok so that's actually + + align:start position:0% +which each other ok so that's actually + + + align:start position:0% +which each other ok so that's actually +what we are trying to do in order to + + align:start position:0% +what we are trying to do in order to + + + align:start position:0% +what we are trying to do in order to +solve the normal modes so we have been + + align:start position:0% +solve the normal modes so we have been + + + align:start position:0% +solve the normal modes so we have been +making progress and we are increasing + + align:start position:0% +making progress and we are increasing + + + align:start position:0% +making progress and we are increasing +the number of coupled oscillators as a + + align:start position:0% +the number of coupled oscillators as a + + + align:start position:0% +the number of coupled oscillators as a +function of time and now we finally + + align:start position:0% +function of time and now we finally + + + align:start position:0% +function of time and now we finally +arrived our limit which is infinite + + align:start position:0% +arrived our limit which is infinite + + + align:start position:0% +arrived our limit which is infinite +system I so basically what we have been + + align:start position:0% +system I so basically what we have been + + + align:start position:0% +system I so basically what we have been +discussing is a special kind of infinite + + align:start position:0% +discussing is a special kind of infinite + + + align:start position:0% +discussing is a special kind of infinite +system which actually satisfies + + align:start position:0% +system which actually satisfies + + + align:start position:0% +system which actually satisfies +translational symmetry right so in + + align:start position:0% +translational symmetry right so in + + + align:start position:0% +translational symmetry right so in +general we don't know how to solve + + align:start position:0% +general we don't know how to solve + + + align:start position:0% +general we don't know how to solve +infant assistant if if this system is + + align:start position:0% +infant assistant if if this system is + + + align:start position:0% +infant assistant if if this system is +really complicated no symmetry then who + + align:start position:0% +really complicated no symmetry then who + + + align:start position:0% +really complicated no symmetry then who +knows how to solve this right but well + + align:start position:0% +knows how to solve this right but well + + + align:start position:0% +knows how to solve this right but well +actually in l3 which you can started to + + align:start position:0% +actually in l3 which you can started to + + + align:start position:0% +actually in l3 which you can started to +do get highly symmetric infinite system + + align:start position:0% +do get highly symmetric infinite system + + + align:start position:0% +do get highly symmetric infinite system +and in this case this translation + + align:start position:0% +and in this case this translation + + + align:start position:0% +and in this case this translation +symmetry and that is really pretty nice + + align:start position:0% +symmetry and that is really pretty nice + + + align:start position:0% +symmetry and that is really pretty nice +and that we can actually use this + + align:start position:0% +and that we can actually use this + + + align:start position:0% +and that we can actually use this +example to + + align:start position:0% +example to + + + align:start position:0% +example to +learn interesting in fact which we can + + align:start position:0% +learn interesting in fact which we can + + + align:start position:0% +learn interesting in fact which we can +see from the physical system we discuss + + align:start position:0% +see from the physical system we discuss + + + align:start position:0% +see from the physical system we discuss +here so one thing which we have been + + align:start position:0% +here so one thing which we have been + + + align:start position:0% +here so one thing which we have been +discussing is the space translation + + align:start position:0% +discussing is the space translation + + + align:start position:0% +discussing is the space translation +symmetry matrix as a reminder as matrix + + align:start position:0% +symmetry matrix as a reminder as matrix + + + align:start position:0% +symmetry matrix as a reminder as matrix +actually is defined here basically if + + align:start position:0% +actually is defined here basically if + + + align:start position:0% +actually is defined here basically if +you have a vector a which describe the + + align:start position:0% +you have a vector a which describe the + + + align:start position:0% +you have a vector a which describe the +amplitude of individual component in a + + align:start position:0% +amplitude of individual component in a + + + align:start position:0% +amplitude of individual component in a +system basically this factor have AJ AJ + + align:start position:0% +system basically this factor have AJ AJ + + + align:start position:0% +system basically this factor have AJ AJ +plus one at a pass through blah blah + + align:start position:0% +plus one at a pass through blah blah + + + align:start position:0% +plus one at a pass through blah blah +blah all those amplitudes are including + + align:start position:0% +blah all those amplitudes are including + + + align:start position:0% +blah all those amplitudes are including +in included in this vector and what does + + align:start position:0% +in included in this vector and what does + + + align:start position:0% +in included in this vector and what does +this S matrix does to essentially the + + align:start position:0% +this S matrix does to essentially the + + + align:start position:0% +this S matrix does to essentially the +following so so if a prime is equal to s + + align:start position:0% +following so so if a prime is equal to s + + + align:start position:0% +following so so if a prime is equal to s +times a then the component sales + + align:start position:0% +times a then the component sales + + + align:start position:0% +times a then the component sales +component of apron will be equal to AJ + + align:start position:0% +component of apron will be equal to AJ + + + align:start position:0% +component of apron will be equal to AJ +plus 1 ok so that's actually what this s + + align:start position:0% +plus 1 ok so that's actually what this s + + + align:start position:0% +plus 1 ok so that's actually what this s +matrix does to a vector ok so you can + + align:start position:0% +matrix does to a vector ok so you can + + + align:start position:0% +matrix does to a vector ok so you can +think about s matrix as a operator it's + + align:start position:0% +think about s matrix as a operator it's + + + align:start position:0% +think about s matrix as a operator it's +actually picking up the AJ price my one + + align:start position:0% +actually picking up the AJ price my one + + + align:start position:0% +actually picking up the AJ price my one +component and move it to AJ in the new + + align:start position:0% +component and move it to AJ in the new + + + align:start position:0% +component and move it to AJ in the new +vector ok so that's actually what this s + + align:start position:0% +vector ok so that's actually what this s + + + align:start position:0% +vector ok so that's actually what this s +matrix does and we were talking about + + align:start position:0% +matrix does and we were talking about + + + align:start position:0% +matrix does and we were talking about +the eigenvector of s matrix for example + + align:start position:0% +the eigenvector of s matrix for example + + + align:start position:0% +the eigenvector of s matrix for example +if a is an eigenvector of s matrix then + + align:start position:0% +if a is an eigenvector of s matrix then + + + align:start position:0% +if a is an eigenvector of s matrix then +we have this relation as a equal to beta + + align:start position:0% +we have this relation as a equal to beta + + + align:start position:0% +we have this relation as a equal to beta +the beta is actually the eigenvalue of a + + align:start position:0% +the beta is actually the eigenvalue of a + + + align:start position:0% +the beta is actually the eigenvalue of a +match a of s matrix ok and we also + + align:start position:0% +match a of s matrix ok and we also + + + align:start position:0% +match a of s matrix ok and we also +discussed that time that means based on + + align:start position:0% +discussed that time that means based on + + + align:start position:0% +discussed that time that means based on +this logical extension AJ prime will be + + align:start position:0% +this logical extension AJ prime will be + + + align:start position:0% +this logical extension AJ prime will be +equal to AJ plus 1 + + align:start position:0% +equal to AJ plus 1 + + + align:start position:0% +equal to AJ plus 1 +based on the definition s matrix and + + align:start position:0% +based on the definition s matrix and + + + align:start position:0% +based on the definition s matrix and +that is going to be equal to beta times + + align:start position:0% +that is going to be equal to beta times + + + align:start position:0% +that is going to be equal to beta times +a day right because we assume that AJ + + align:start position:0% +a day right because we assume that AJ + + + align:start position:0% +a day right because we assume that AJ +also we assume that a vector is a is an + + align:start position:0% +also we assume that a vector is a is an + + + align:start position:0% +also we assume that a vector is a is an +eigen vector of s matrix ok that means + + align:start position:0% +eigen vector of s matrix ok that means + + + align:start position:0% +eigen vector of s matrix ok that means +AJ will be equal to beta to let say a 0 + + align:start position:0% +AJ will be equal to beta to let say a 0 + + + align:start position:0% +AJ will be equal to beta to let say a 0 +right + + align:start position:0% +right + + + align:start position:0% +right +according to this relation this relation + + align:start position:0% +according to this relation this relation + + + align:start position:0% +according to this relation this relation +therefore we can conclude that a J will + + align:start position:0% +therefore we can conclude that a J will + + + align:start position:0% +therefore we can conclude that a J will +be proportional to beta to the day okay + + align:start position:0% +be proportional to beta to the day okay + + + align:start position:0% +be proportional to beta to the day okay +beta is still some coefficient which we + + align:start position:0% +beta is still some coefficient which we + + + align:start position:0% +beta is still some coefficient which we +have not determined and it can be + + align:start position:0% +have not determined and it can be + + + align:start position:0% +have not determined and it can be +anything okay so in order to consider a + + align:start position:0% +anything okay so in order to consider a + + + align:start position:0% +anything okay so in order to consider a +system of of little mass which are + + align:start position:0% +system of of little mass which are + + + align:start position:0% +system of of little mass which are +oscillating up and down instead of you + + align:start position:0% +oscillating up and down instead of you + + + align:start position:0% +oscillating up and down instead of you +know going going in one direction + + align:start position:0% +know going going in one direction + + + align:start position:0% +know going going in one direction +forever or or the amplitude closed you + + align:start position:0% +forever or or the amplitude closed you + + + align:start position:0% +forever or or the amplitude closed you +know exponentially and we also don't + + align:start position:0% +know exponentially and we also don't + + + align:start position:0% +know exponentially and we also don't +want the system to have amplitude goes + + align:start position:0% +want the system to have amplitude goes + + + align:start position:0% +want the system to have amplitude goes +to infinity when we go to very large a + + align:start position:0% +to infinity when we go to very large a + + + align:start position:0% +to infinity when we go to very large a +value or very small T value therefore we + + align:start position:0% +value or very small T value therefore we + + + align:start position:0% +value or very small T value therefore we +limit our discussion in the case of beta + + align:start position:0% +limit our discussion in the case of beta + + + align:start position:0% +limit our discussion in the case of beta +equal to exponential I K a okay in this + + align:start position:0% +equal to exponential I K a okay in this + + + align:start position:0% +equal to exponential I K a okay in this +case the beta is a absolute value of + + align:start position:0% +case the beta is a absolute value of + + + align:start position:0% +case the beta is a absolute value of +beta is 1 right okay and that means okay + + align:start position:0% +beta is 1 right okay and that means okay + + + align:start position:0% +beta is 1 right okay and that means okay +AJ essentially equal proportion of beta + + align:start position:0% +AJ essentially equal proportion of beta + + + align:start position:0% +AJ essentially equal proportion of beta +to a right so if you take a ratio of + + align:start position:0% +to a right so if you take a ratio of + + + align:start position:0% +to a right so if you take a ratio of +it's a plus one and the AJ the ratio is + + align:start position:0% +it's a plus one and the AJ the ratio is + + + align:start position:0% +it's a plus one and the AJ the ratio is +beta if beta is not equal to one or it's + + align:start position:0% +beta if beta is not equal to one or it's + + + align:start position:0% +beta if beta is not equal to one or it's +a possible value is now equal to 1 then + + align:start position:0% +a possible value is now equal to 1 then + + + align:start position:0% +a possible value is now equal to 1 then +this AJ value is going to be increasing + + align:start position:0% +this AJ value is going to be increasing + + + align:start position:0% +this AJ value is going to be increasing +according to a power law right so so the + + align:start position:0% +according to a power law right so so the + + + align:start position:0% +according to a power law right so so the +amplitude is going to be going to very + + align:start position:0% +amplitude is going to be going to very + + + align:start position:0% +amplitude is going to be going to very +very large value right and that + + align:start position:0% +very large value right and that + + + align:start position:0% +very large value right and that +corresponds to some kind of physical + + align:start position:0% +corresponds to some kind of physical + + + align:start position:0% +corresponds to some kind of physical +system but not corresponding to + + align:start position:0% +system but not corresponding to + + + align:start position:0% +system but not corresponding to +oscillation okay and if we do this and + + align:start position:0% +oscillation okay and if we do this and + + + align:start position:0% +oscillation okay and if we do this and +assume that beta is equal to exponential + + align:start position:0% +assume that beta is equal to exponential + + + align:start position:0% +assume that beta is equal to exponential +I K a okay if we do this what is going + + align:start position:0% +I K a okay if we do this what is going + + + align:start position:0% +I K a okay if we do this what is going +to happen is the power so so again the + + align:start position:0% +to happen is the power so so again the + + + align:start position:0% +to happen is the power so so again the +ratio of AJ plus 1 and AJ is a fixed + + align:start position:0% +ratio of AJ plus 1 and AJ is a fixed + + + align:start position:0% +ratio of AJ plus 1 and AJ is a fixed +value beta equal to exponential say ika + + align:start position:0% +value beta equal to exponential say ika + + + align:start position:0% +value beta equal to exponential say ika +but what it does is not instead of + + align:start position:0% +but what it does is not instead of + + + align:start position:0% +but what it does is not instead of +changing the + + align:start position:0% +changing the + + + align:start position:0% +changing the +AmpliTube essentially doing a rotation + + align:start position:0% +AmpliTube essentially doing a rotation + + + align:start position:0% +AmpliTube essentially doing a rotation +in the complex friend okay so if if if + + align:start position:0% +in the complex friend okay so if if if + + + align:start position:0% +in the complex friend okay so if if if +this is a say J plus 1 J plus 2 as a + + align:start position:0% +this is a say J plus 1 J plus 2 as a + + + align:start position:0% +this is a say J plus 1 J plus 2 as a +child as a function of a J the label + + align:start position:0% +child as a function of a J the label + + + align:start position:0% +child as a function of a J the label +then what it does is that this operation + + align:start position:0% +then what it does is that this operation + + + align:start position:0% +then what it does is that this operation +multiplied by beta is really a rotation + + align:start position:0% +multiplied by beta is really a rotation + + + align:start position:0% +multiplied by beta is really a rotation +in the complex pram and while we as you + + align:start position:0% +in the complex pram and while we as you + + + align:start position:0% +in the complex pram and while we as you +see in the physical system is actually a + + align:start position:0% +see in the physical system is actually a + + + align:start position:0% +see in the physical system is actually a +projection of this complex imaginary + + align:start position:0% +projection of this complex imaginary + + + align:start position:0% +projection of this complex imaginary +plan to the real axis and that will give + + align:start position:0% +plan to the real axis and that will give + + + align:start position:0% +plan to the real axis and that will give +you a sine function and cosine function + + align:start position:0% +you a sine function and cosine function + + + align:start position:0% +you a sine function and cosine function +so so very interestingly if we choose + + align:start position:0% +so so very interestingly if we choose + + + align:start position:0% +so so very interestingly if we choose +wisely the beta to have absolute value + + align:start position:0% +wisely the beta to have absolute value + + + align:start position:0% +wisely the beta to have absolute value +of 1 then now we'll give you a assistant + + align:start position:0% +of 1 then now we'll give you a assistant + + + align:start position:0% +of 1 then now we'll give you a assistant +Wichita is actually oscillating up and + + align:start position:0% +Wichita is actually oscillating up and + + + align:start position:0% +Wichita is actually oscillating up and +down and the amplitudes as you can't + + align:start position:0% +down and the amplitudes as you can't + + + align:start position:0% +down and the amplitudes as you can't +find who is doing some somebody okay so + + align:start position:0% +find who is doing some somebody okay so + + + align:start position:0% +find who is doing some somebody okay so +that essentially finding the other thing + + align:start position:0% +that essentially finding the other thing + + + align:start position:0% +that essentially finding the other thing +which I would like to talk about is okay + + align:start position:0% +which I would like to talk about is okay + + + align:start position:0% +which I would like to talk about is okay +I choose to have exponential I K a as my + + align:start position:0% +I choose to have exponential I K a as my + + + align:start position:0% +I choose to have exponential I K a as my +beta okay + + align:start position:0% +beta okay + + + align:start position:0% +beta okay +YK a right this looks really strange + + align:start position:0% +YK a right this looks really strange + + + align:start position:0% +YK a right this looks really strange +certainly K and a trying to pray right + + align:start position:0% +certainly K and a trying to pray right + + + align:start position:0% +certainly K and a trying to pray right +so what is actually the small a the + + align:start position:0% +so what is actually the small a the + + + align:start position:0% +so what is actually the small a the +small a is actually the the distance + + align:start position:0% +small a is actually the the distance + + + align:start position:0% +small a is actually the the distance +between little mass because a reminder + + align:start position:0% +between little mass because a reminder + + + align:start position:0% +between little mass because a reminder +so this is actually the land scale + + align:start position:0% +so this is actually the land scale + + + align:start position:0% +so this is actually the land scale +between all those little mass right + + align:start position:0% +between all those little mass right + + + align:start position:0% +between all those little mass right +there for what I'm doing is to fatter + + align:start position:0% +there for what I'm doing is to fatter + + + align:start position:0% +there for what I'm doing is to fatter +eyes ow + + align:start position:0% +eyes ow + + + align:start position:0% +eyes ow +the land scale and then we've we + + align:start position:0% +the land scale and then we've we + + + align:start position:0% +the land scale and then we've we +suddenly found that okay after I do this + + align:start position:0% +suddenly found that okay after I do this + + + align:start position:0% +suddenly found that okay after I do this +I define beta equal to exponential I K a + + align:start position:0% +I define beta equal to exponential I K a + + + align:start position:0% +I define beta equal to exponential I K a +instead of explanation I Sita right so + + align:start position:0% +instead of explanation I Sita right so + + + align:start position:0% +instead of explanation I Sita right so +you can also to exponential I theta + + align:start position:0% +you can also to exponential I theta + + + align:start position:0% +you can also to exponential I theta +right but instead I give Sita a fancy + + align:start position:0% +right but instead I give Sita a fancy + + + align:start position:0% +right but instead I give Sita a fancy +name which is K times a a is actually + + align:start position:0% +name which is K times a a is actually + + + align:start position:0% +name which is K times a a is actually +the distance between mass the instance + + align:start position:0% +the distance between mass the instance + + + align:start position:0% +the distance between mass the instance +interesting happen because K suddenly + + align:start position:0% +interesting happen because K suddenly + + + align:start position:0% +interesting happen because K suddenly +also we have a meaning is actually the + + align:start position:0% +also we have a meaning is actually the + + + align:start position:0% +also we have a meaning is actually the +wave number of the resulting + + align:start position:0% +wave number of the resulting + + + align:start position:0% +wave number of the resulting +essentially the know the wave number of + + align:start position:0% +essentially the know the wave number of + + + align:start position:0% +essentially the know the wave number of +the resulting sine wave okay so that's + + align:start position:0% +the resulting sine wave okay so that's + + + align:start position:0% +the resulting sine wave okay so that's +actually why we actually factor out this + + align:start position:0% +actually why we actually factor out this + + + align:start position:0% +actually why we actually factor out this +a factor since then after that we + + align:start position:0% +a factor since then after that we + + + align:start position:0% +a factor since then after that we +actually found out the amplitude will be + + align:start position:0% +actually found out the amplitude will be + + + align:start position:0% +actually found out the amplitude will be +proportional to explanation I take a a + + align:start position:0% +proportional to explanation I take a a + + + align:start position:0% +proportional to explanation I take a a +and say is actually just a label of this + + align:start position:0% +and say is actually just a label of this + + + align:start position:0% +and say is actually just a label of this +component in the system okay so we have + + align:start position:0% +component in the system okay so we have + + + align:start position:0% +component in the system okay so we have +once we have solved this the the + + align:start position:0% +once we have solved this the the + + + align:start position:0% +once we have solved this the the +eigenvalue problem for the symmetry + + align:start position:0% +eigenvalue problem for the symmetry + + + align:start position:0% +eigenvalue problem for the symmetry +matrix s as we discussed before if we + + align:start position:0% +matrix s as we discussed before if we + + + align:start position:0% +matrix s as we discussed before if we +look at the slide okay if s and the M + + align:start position:0% +look at the slide okay if s and the M + + + align:start position:0% +look at the slide okay if s and the M +minus 1 K matrix they commute okay + + align:start position:0% +minus 1 K matrix they commute okay + + + align:start position:0% +minus 1 K matrix they commute okay +commute means that they can issue you + + align:start position:0% +commute means that they can issue you + + + align:start position:0% +commute means that they can issue you +can as you change s and as n minus 1 + + align:start position:0% +can as you change s and as n minus 1 + + + align:start position:0% +can as you change s and as n minus 1 +matrix you can swap then okay when you + + align:start position:0% +matrix you can swap then okay when you + + + align:start position:0% +matrix you can swap then okay when you +multiply them together okay if you can + + align:start position:0% +multiply them together okay if you can + + + align:start position:0% +multiply them together okay if you can +swap as n minus 1 K matrix that means + + align:start position:0% +swap as n minus 1 K matrix that means + + + align:start position:0% +swap as n minus 1 K matrix that means +they commute and our conclusion from + + align:start position:0% +they commute and our conclusion from + + + align:start position:0% +they commute and our conclusion from +last time is that they will share the + + align:start position:0% +last time is that they will share the + + + align:start position:0% +last time is that they will share the +same eigen vectors okay of course not + + align:start position:0% +same eigen vectors okay of course not + + + align:start position:0% +same eigen vectors okay of course not +necessarily the same eigen value but + + align:start position:0% +necessarily the same eigen value but + + + align:start position:0% +necessarily the same eigen value but +they share the same eigen vector so + + align:start position:0% +they share the same eigen vector so + + + align:start position:0% +they share the same eigen vector so +that's a great news because instead of + + align:start position:0% +that's a great news because instead of + + + align:start position:0% +that's a great news because instead of +solving M minus 1 K matrix which can be + + align:start position:0% +solving M minus 1 K matrix which can be + + + align:start position:0% +solving M minus 1 K matrix which can be +really complicated depends on what kind + + align:start position:0% +really complicated depends on what kind + + + align:start position:0% +really complicated depends on what kind +of physical system you are talking about + + align:start position:0% +of physical system you are talking about + + + align:start position:0% +of physical system you are talking about +I can solve as matrix eigenvalue problem + + align:start position:0% +I can solve as matrix eigenvalue problem + + + align:start position:0% +I can solve as matrix eigenvalue problem +okay and then this eigenvector which i + + align:start position:0% +okay and then this eigenvector which i + + + align:start position:0% +okay and then this eigenvector which i +just found here it's going to be the + + align:start position:0% +just found here it's going to be the + + + align:start position:0% +just found here it's going to be the +eigenvector of M minus 1 K matrix and + + align:start position:0% +eigenvector of M minus 1 K matrix and + + + align:start position:0% +eigenvector of M minus 1 K matrix and +that's actually really making things + + align:start position:0% +that's actually really making things + + + align:start position:0% +that's actually really making things +much easier because now instead of + + align:start position:0% +much easier because now instead of + + + align:start position:0% +much easier because now instead of +solving I can build your problem of n + + align:start position:0% +solving I can build your problem of n + + + align:start position:0% +solving I can build your problem of n +minus 1 K matrix what I am doing is just + + align:start position:0% +minus 1 K matrix what I am doing is just + + + align:start position:0% +minus 1 K matrix what I am doing is just +multiply n minus 1 K times a then you + + align:start position:0% +multiply n minus 1 K times a then you + + + align:start position:0% +multiply n minus 1 K times a then you +can actually obtain the normal frequency + + align:start position:0% +can actually obtain the normal frequency + + + align:start position:0% +can actually obtain the normal frequency +Omega okay so that is actually the great + + align:start position:0% +Omega okay so that is actually the great + + + align:start position:0% +Omega okay so that is actually the great +excitement what does that mean that + + align:start position:0% +excitement what does that mean that + + + align:start position:0% +excitement what does that mean that +means if you have all kindnesses + + align:start position:0% +means if you have all kindnesses + + + align:start position:0% +means if you have all kindnesses +which are translation symmetric you can + + align:start position:0% +which are translation symmetric you can + + + align:start position:0% +which are translation symmetric you can +have a line we have however many people + + align:start position:0% +have a line we have however many people + + + align:start position:0% +have a line we have however many people +together whatever I mean whatever a + + align:start position:0% +together whatever I mean whatever a + + + align:start position:0% +together whatever I mean whatever a +system which is so much yeah + + align:start position:0% +system which is so much yeah + + + align:start position:0% +system which is so much yeah +they are all going to have the same + + align:start position:0% +they are all going to have the same + + + align:start position:0% +they are all going to have the same +eigen vector + + align:start position:0% +eigen vector + + + align:start position:0% +eigen vector +you see you already know how they are + + align:start position:0% +you see you already know how they are + + + align:start position:0% +you see you already know how they are +going to interact with each other and + + align:start position:0% +going to interact with each other and + + + align:start position:0% +going to interact with each other and +what is actually the amplitude as a + + align:start position:0% +what is actually the amplitude as a + + + align:start position:0% +what is actually the amplitude as a +function of T which is the location + + align:start position:0% +function of T which is the location + + + align:start position:0% +function of T which is the location +label okay so that's actually really + + align:start position:0% +label okay so that's actually really + + + align:start position:0% +label okay so that's actually really +wonderful so in order to help you with + + align:start position:0% +wonderful so in order to help you with + + + align:start position:0% +wonderful so in order to help you with +understanding of this system some more + + align:start position:0% +understanding of this system some more + + + align:start position:0% +understanding of this system some more +we are going to discuss another system + + align:start position:0% +we are going to discuss another system + + + align:start position:0% +we are going to discuss another system +which is actually also very interesting + + align:start position:0% +which is actually also very interesting + + + align:start position:0% +which is actually also very interesting +essentially a spring okay last time we + + align:start position:0% +essentially a spring okay last time we + + + align:start position:0% +essentially a spring okay last time we +discussed a spring and mass system right + + align:start position:0% +discussed a spring and mass system right + + + align:start position:0% +discussed a spring and mass system right +and we solve it together and this time + + align:start position:0% +and we solve it together and this time + + + align:start position:0% +and we solve it together and this time +we are going to solve a system which is + + align:start position:0% +we are going to solve a system which is + + + align:start position:0% +we are going to solve a system which is +are made of mass and the streets okay so + + align:start position:0% +are made of mass and the streets okay so + + + align:start position:0% +are made of mass and the streets okay so +that means should be happy okay so let + + align:start position:0% +that means should be happy okay so let + + + align:start position:0% +that means should be happy okay so let +me actually introduce you this new + + align:start position:0% +me actually introduce you this new + + + align:start position:0% +me actually introduce you this new +system we are going to talk about today + + align:start position:0% +system we are going to talk about today + + + align:start position:0% +system we are going to talk about today +he has many little mass here from the + + align:start position:0% +he has many little mass here from the + + + align:start position:0% +he has many little mass here from the +lapis I open universe and right-hand + + align:start position:0% +lapis I open universe and right-hand + + + align:start position:0% +lapis I open universe and right-hand +side of believers take forever to as you + + align:start position:0% +side of believers take forever to as you + + + align:start position:0% +side of believers take forever to as you +can try this system okay then my student + + align:start position:0% +can try this system okay then my student + + + align:start position:0% +can try this system okay then my student +is you care for the link length by + + align:start position:0% +is you care for the link length by + + + align:start position:0% +is you care for the link length by +strings and that we make sure that the + + align:start position:0% +strings and that we make sure that the + + + align:start position:0% +strings and that we make sure that the +string tension okay you say should be a + + align:start position:0% +string tension okay you say should be a + + + align:start position:0% +string tension okay you say should be a +fixed value which is T okay Jesus with a + + align:start position:0% +fixed value which is T okay Jesus with a + + + align:start position:0% +fixed value which is T okay Jesus with a +string tension and of course as as what + + align:start position:0% +string tension and of course as as what + + + align:start position:0% +string tension and of course as as what +we discussed before the space or the + + align:start position:0% +we discussed before the space or the + + + align:start position:0% +we discussed before the space or the +distance between little mass is as your + + align:start position:0% +distance between little mass is as your + + + align:start position:0% +distance between little mass is as your +a ok ok so that's again the same length + + align:start position:0% +a ok ok so that's again the same length + + + align:start position:0% +a ok ok so that's again the same length +scale which we were using and finally + + align:start position:0% +scale which we were using and finally + + + align:start position:0% +scale which we were using and finally +you want to describe all those little + + align:start position:0% +you want to describe all those little + + + align:start position:0% +you want to describe all those little +mass masses under in this system I label + + align:start position:0% +mass masses under in this system I label + + + align:start position:0% +mass masses under in this system I label +them as I say J plus 1 J plus 2 etcetera + + align:start position:0% +them as I say J plus 1 J plus 2 etcetera + + + align:start position:0% +them as I say J plus 1 J plus 2 etcetera +etcetera + + align:start position:0% +etcetera + + + align:start position:0% +etcetera +ok so what the question we are asking is + + align:start position:0% +ok so what the question we are asking is + + + align:start position:0% +ok so what the question we are asking is +what would be the resulting motion of + + align:start position:0% +what would be the resulting motion of + + + align:start position:0% +what would be the resulting motion of +this system right so what we can do + + align:start position:0% +this system right so what we can do + + + align:start position:0% +this system right so what we can do +is us what we have done last time right + + align:start position:0% +is us what we have done last time right + + + align:start position:0% +is us what we have done last time right +we take chase object in the system and + + align:start position:0% +we take chase object in the system and + + + align:start position:0% +we take chase object in the system and +we do get the force diagram and the + + align:start position:0% +we do get the force diagram and the + + + align:start position:0% +we do get the force diagram and the +street construct and my one look to + + align:start position:0% +street construct and my one look to + + + align:start position:0% +street construct and my one look to +write down the equation of motion and + + align:start position:0% +write down the equation of motion and + + + align:start position:0% +write down the equation of motion and +also the M is 1 K matrix so what is + + align:start position:0% +also the M is 1 K matrix so what is + + + align:start position:0% +also the M is 1 K matrix so what is +issue the post diagram of phase + + align:start position:0% +issue the post diagram of phase + + + align:start position:0% +issue the post diagram of phase +component okay if I if I take this so so + + align:start position:0% +component okay if I if I take this so so + + + align:start position:0% +component okay if I if I take this so so +first I can I take my chase mass and + + align:start position:0% +first I can I take my chase mass and + + + align:start position:0% +first I can I take my chase mass and +that it's connected to two strings right + + align:start position:0% +that it's connected to two strings right + + + align:start position:0% +that it's connected to two strings right +so there are two strings connected to + + align:start position:0% +so there are two strings connected to + + + align:start position:0% +so there are two strings connected to +this mass okay and I of course love + + align:start position:0% +this mass okay and I of course love + + + align:start position:0% +this mass okay and I of course love +inside you have another mass right hand + + align:start position:0% +inside you have another mass right hand + + + align:start position:0% +inside you have another mass right hand +side you have another object okay and I + + align:start position:0% +side you have another object okay and I + + + align:start position:0% +side you have another object okay and I +know the tension of this of the string + + align:start position:0% +know the tension of this of the string + + + align:start position:0% +know the tension of this of the string +it's actually a fixed value and the + + align:start position:0% +it's actually a fixed value and the + + + align:start position:0% +it's actually a fixed value and the +string tension is fixed at at the T okay + + align:start position:0% +string tension is fixed at at the T okay + + + align:start position:0% +string tension is fixed at at the T okay +so in order to describe this system I + + align:start position:0% +so in order to describe this system I + + + align:start position:0% +so in order to describe this system I +need to confine my coordinate system + + align:start position:0% +need to confine my coordinate system + + + align:start position:0% +need to confine my coordinate system +right as usual so what is actually a + + align:start position:0% +right as usual so what is actually a + + + align:start position:0% +right as usual so what is actually a +coordinate system I'm going to use so I + + align:start position:0% +coordinate system I'm going to use so I + + + align:start position:0% +coordinate system I'm going to use so I +need to find oriental direction to be X + + align:start position:0% +need to find oriental direction to be X + + + align:start position:0% +need to find oriental direction to be X +and the vertical direction to be Y + + align:start position:0% +and the vertical direction to be Y + + + align:start position:0% +and the vertical direction to be Y +therefore I can now express this little + + align:start position:0% +therefore I can now express this little + + + align:start position:0% +therefore I can now express this little +mass to be the position of this chase + + align:start position:0% +mass to be the position of this chase + + + align:start position:0% +mass to be the position of this chase +little mass as XT and YT okay we can do + + align:start position:0% +little mass as XT and YT okay we can do + + + align:start position:0% +little mass as XT and YT okay we can do +the same thing for the extreme for the + + align:start position:0% +the same thing for the extreme for the + + + align:start position:0% +the same thing for the extreme for the +lapin side mass is XA minus 1 YJ minus 1 + + align:start position:0% +lapin side mass is XA minus 1 YJ minus 1 + + + align:start position:0% +lapin side mass is XA minus 1 YJ minus 1 +and si plus 1 YJ plus 1 so to simplify + + align:start position:0% +and si plus 1 YJ plus 1 so to simplify + + + align:start position:0% +and si plus 1 YJ plus 1 so to simplify +the discussion what I am going to assume + + align:start position:0% +the discussion what I am going to assume + + + align:start position:0% +the discussion what I am going to assume +is that all those little mass can only + + align:start position:0% +is that all those little mass can only + + + align:start position:0% +is that all those little mass can only +move up and down okay instead of back + + align:start position:0% +move up and down okay instead of back + + + align:start position:0% +move up and down okay instead of back +and forth okay so only one direction is + + align:start position:0% +and forth okay so only one direction is + + + align:start position:0% +and forth okay so only one direction is +allowed and also I + + align:start position:0% +allowed and also I + + + align:start position:0% +allowed and also I +soon that the up and down motion of all + + align:start position:0% +soon that the up and down motion of all + + + align:start position:0% +soon that the up and down motion of all +those little mass is really really very + + align:start position:0% +those little mass is really really very + + + align:start position:0% +those little mass is really really very +small so I can use small angle + + align:start position:0% +small so I can use small angle + + + align:start position:0% +small so I can use small angle +approximation okay so so therefore I can + + align:start position:0% +approximation okay so so therefore I can + + + align:start position:0% +approximation okay so so therefore I can +please essentially the the zero of y + + align:start position:0% +please essentially the the zero of y + + + align:start position:0% +please essentially the the zero of y +axis when I actually before I actually + + align:start position:0% +axis when I actually before I actually + + + align:start position:0% +axis when I actually before I actually +move the one of the mass away from the + + align:start position:0% +move the one of the mass away from the + + + align:start position:0% +move the one of the mass away from the +equilibrium position so when the three + + align:start position:0% +equilibrium position so when the three + + + align:start position:0% +equilibrium position so when the three +mass system is at rest okay not really + + align:start position:0% +mass system is at rest okay not really + + + align:start position:0% +mass system is at rest okay not really +moving then all the mass are at y equal + + align:start position:0% +moving then all the mass are at y equal + + + align:start position:0% +moving then all the mass are at y equal +to zero okay so now I actually move this + + align:start position:0% +to zero okay so now I actually move this + + + align:start position:0% +to zero okay so now I actually move this +mass to why why + + align:start position:0% +mass to why why + + + align:start position:0% +mass to why why +say okay then I apparently there are two + + align:start position:0% +say okay then I apparently there are two + + + align:start position:0% +say okay then I apparently there are two +force acting on this mass the lap inside + + align:start position:0% +force acting on this mass the lap inside + + + align:start position:0% +force acting on this mass the lap inside +a stream force and the right-hand side + + align:start position:0% +a stream force and the right-hand side + + + align:start position:0% +a stream force and the right-hand side +stream force and the magnitude of the + + align:start position:0% +stream force and the magnitude of the + + + align:start position:0% +stream force and the magnitude of the +force is a sheet okay so in order to + + align:start position:0% +force is a sheet okay so in order to + + + align:start position:0% +force is a sheet okay so in order to +help us with solving this problem I + + align:start position:0% +help us with solving this problem I + + + align:start position:0% +help us with solving this problem I +would define two angle the left hand + + align:start position:0% +would define two angle the left hand + + + align:start position:0% +would define two angle the left hand +side angle to be a sitter one and the + + align:start position:0% +side angle to be a sitter one and the + + + align:start position:0% +side angle to be a sitter one and the +right hand side angle to be Sita to then + + align:start position:0% +right hand side angle to be Sita to then + + + align:start position:0% +right hand side angle to be Sita to then +I can now write down the equation of + + align:start position:0% +I can now write down the equation of + + + align:start position:0% +I can now write down the equation of +motion in the horizontal direction and + + align:start position:0% +motion in the horizontal direction and + + + align:start position:0% +motion in the horizontal direction and +in the vertical direction okay all right + + align:start position:0% +in the vertical direction okay all right + + + align:start position:0% +in the vertical direction okay all right +since I have assumed that this told all + + align:start position:0% +since I have assumed that this told all + + + align:start position:0% +since I have assumed that this told all +those mass can only move up and down + + align:start position:0% +those mass can only move up and down + + + align:start position:0% +those mass can only move up and down +lambing and also the the displacement + + align:start position:0% +lambing and also the the displacement + + + align:start position:0% +lambing and also the the displacement +with respect to the equilibrium position + + align:start position:0% +with respect to the equilibrium position + + + align:start position:0% +with respect to the equilibrium position +which is y equal to zero is really small + + align:start position:0% +which is y equal to zero is really small + + + align:start position:0% +which is y equal to zero is really small +compared to for example design scale a + + align:start position:0% +compared to for example design scale a + + + align:start position:0% +compared to for example design scale a +okay so therefore I can write that + + align:start position:0% +okay so therefore I can write that + + + align:start position:0% +okay so therefore I can write that +condition explicitly so I have a + + align:start position:0% +condition explicitly so I have a + + + align:start position:0% +condition explicitly so I have a +condition + + align:start position:0% +condition + + + align:start position:0% +condition +I assume that YJ is actually much much + + align:start position:0% +I assume that YJ is actually much much + + + align:start position:0% +I assume that YJ is actually much much +smaller than a which is the distance + + align:start position:0% +smaller than a which is the distance + + + align:start position:0% +smaller than a which is the distance +between los meses and that means theta + + align:start position:0% +between los meses and that means theta + + + align:start position:0% +between los meses and that means theta +one and the sitter two are going to be + + align:start position:0% +one and the sitter two are going to be + + + align:start position:0% +one and the sitter two are going to be +much much smaller than one + + align:start position:0% + + + + align:start position:0% + +so that actually give us a chance to use + + align:start position:0% +so that actually give us a chance to use + + + align:start position:0% +so that actually give us a chance to use +small angle approximation so based on + + align:start position:0% +small angle approximation so based on + + + align:start position:0% +small angle approximation so based on +this force diagram I can now write down + + align:start position:0% +this force diagram I can now write down + + + align:start position:0% +this force diagram I can now write down +the two equation of motion when in the + + align:start position:0% +the two equation of motion when in the + + + align:start position:0% +the two equation of motion when in the +horizontal direction the other one in + + align:start position:0% +horizontal direction the other one in + + + align:start position:0% +horizontal direction the other one in +the vertical direction so what I'm going + + align:start position:0% +the vertical direction so what I'm going + + + align:start position:0% +the vertical direction so what I'm going +to get in the horizontal Direction is an + + align:start position:0% +to get in the horizontal Direction is an + + + align:start position:0% +to get in the horizontal Direction is an +X a double dot this will be equal to + + align:start position:0% +X a double dot this will be equal to + + + align:start position:0% +X a double dot this will be equal to +okay there are two fourths right in the + + align:start position:0% +okay there are two fourths right in the + + + align:start position:0% +okay there are two fourths right in the +hole rental direction I would need to + + align:start position:0% +hole rental direction I would need to + + + align:start position:0% +hole rental direction I would need to +calculate the projection to the X + + align:start position:0% +calculate the projection to the X + + + align:start position:0% +calculate the projection to the X +direction therefore the left-hand side + + align:start position:0% +direction therefore the left-hand side + + + align:start position:0% +direction therefore the left-hand side +force will give you minus t cosine theta + + align:start position:0% +force will give you minus t cosine theta + + + align:start position:0% +force will give you minus t cosine theta +one and the right-hand side of the + + align:start position:0% +one and the right-hand side of the + + + align:start position:0% +one and the right-hand side of the +stream force is going to keep you prosti + + align:start position:0% +stream force is going to keep you prosti + + + align:start position:0% +stream force is going to keep you prosti +cosine theta two okay and in the + + align:start position:0% +cosine theta two okay and in the + + + align:start position:0% +cosine theta two okay and in the +vertical direction in the vertical + + align:start position:0% +vertical direction in the vertical + + + align:start position:0% +vertical direction in the vertical +direction what I'm going to get is and + + align:start position:0% +direction what I'm going to get is and + + + align:start position:0% +direction what I'm going to get is and +why they tower dot this is equal to + + align:start position:0% +why they tower dot this is equal to + + + align:start position:0% +why they tower dot this is equal to +minus T sine theta one now I'm now doing + + align:start position:0% +minus T sine theta one now I'm now doing + + + align:start position:0% +minus T sine theta one now I'm now doing +the projection in the y axis in the + + align:start position:0% +the projection in the y axis in the + + + align:start position:0% +the projection in the y axis in the +vertical direction and minus G sine + + align:start position:0% +vertical direction and minus G sine + + + align:start position:0% +vertical direction and minus G sine +theta two okay and the since I have this + + align:start position:0% +theta two okay and the since I have this + + + align:start position:0% +theta two okay and the since I have this +condition all the maths can only move up + + align:start position:0% +condition all the maths can only move up + + + align:start position:0% +condition all the maths can only move up +and down and also the the moment the + + align:start position:0% +and down and also the the moment the + + + align:start position:0% +and down and also the the moment the +displacement is much much smaller than a + + align:start position:0% +displacement is much much smaller than a + + + align:start position:0% +displacement is much much smaller than a +therefore I have the small angle + + align:start position:0% +therefore I have the small angle + + + align:start position:0% +therefore I have the small angle +approximation cosine theta is roughly + + align:start position:0% +approximation cosine theta is roughly + + + align:start position:0% +approximation cosine theta is roughly +equal to 1 and the sine theta is roughly + + align:start position:0% +equal to 1 and the sine theta is roughly + + + align:start position:0% +equal to 1 and the sine theta is roughly +equal to theta okay and I will call this + + align:start position:0% +equal to theta okay and I will call this + + + align:start position:0% +equal to theta okay and I will call this +equation number one and the second + + align:start position:0% +equation number one and the second + + + align:start position:0% +equation number one and the second +equation in the vertical direction to be + + align:start position:0% +equation in the vertical direction to be + + + align:start position:0% +equation in the vertical direction to be +equation number two okay so once so up + + align:start position:0% +equation number two okay so once so up + + + align:start position:0% +equation number two okay so once so up +to here everything is actually exact and + + align:start position:0% +to here everything is actually exact and + + + align:start position:0% +to here everything is actually exact and +now I would like to make a small angle + + align:start position:0% +now I would like to make a small angle + + + align:start position:0% +now I would like to make a small angle +approximation and see what happened and + + align:start position:0% +approximation and see what happened and + + + align:start position:0% +approximation and see what happened and +now equation + + align:start position:0% +now equation + + + align:start position:0% +now equation +one will be K and X de da ba da equal to + + align:start position:0% +one will be K and X de da ba da equal to + + + align:start position:0% +one will be K and X de da ba da equal to +minus T plus T and this is equal to zero + + align:start position:0% +minus T plus T and this is equal to zero + + + align:start position:0% +minus T plus T and this is equal to zero +okay so that means we will not have her + + align:start position:0% +okay so that means we will not have her + + + align:start position:0% +okay so that means we will not have her +enter Direction acceleration therefore + + align:start position:0% +enter Direction acceleration therefore + + + align:start position:0% +enter Direction acceleration therefore +in the horizontal direction there will + + align:start position:0% +in the horizontal direction there will + + + align:start position:0% +in the horizontal direction there will +be no acceleration therefore no no + + align:start position:0% +be no acceleration therefore no no + + + align:start position:0% +be no acceleration therefore no no +movement in the X direction or + + align:start position:0% +movement in the X direction or + + + align:start position:0% +movement in the X direction or +horizontal direction okay and now I can + + align:start position:0% +horizontal direction okay and now I can + + + align:start position:0% +horizontal direction okay and now I can +take a look at the vertical direction + + align:start position:0% +take a look at the vertical direction + + + align:start position:0% +take a look at the vertical direction +okay so basically what I am going to get + + align:start position:0% +okay so basically what I am going to get + + + align:start position:0% +okay so basically what I am going to get +is and why say double dot and this will + + align:start position:0% +is and why say double dot and this will + + + align:start position:0% +is and why say double dot and this will +be equal to minus P now sine theta 1 + + align:start position:0% +be equal to minus P now sine theta 1 + + + align:start position:0% +be equal to minus P now sine theta 1 +will be proposed it will be roughly + + align:start position:0% +will be proposed it will be roughly + + + align:start position:0% +will be proposed it will be roughly +equal to theta 1 so what this issue is + + align:start position:0% +equal to theta 1 so what this issue is + + + align:start position:0% +equal to theta 1 so what this issue is +theta 1 theta 1 is going to be okay so + + align:start position:0% +theta 1 theta 1 is going to be okay so + + + align:start position:0% +theta 1 theta 1 is going to be okay so +this is actually YJ minus YJ minus 1 + + align:start position:0% +this is actually YJ minus YJ minus 1 + + + align:start position:0% +this is actually YJ minus YJ minus 1 +right so that is actually the difference + + align:start position:0% +right so that is actually the difference + + + align:start position:0% +right so that is actually the difference +between the amplitude of the it is the + + align:start position:0% +between the amplitude of the it is the + + + align:start position:0% +between the amplitude of the it is the +displacement of the mass say and the + + align:start position:0% +displacement of the mass say and the + + + align:start position:0% +displacement of the mass say and the +displacement of mass semis one right / a + + align:start position:0% +displacement of mass semis one right / a + + + align:start position:0% +displacement of mass semis one right / a +I gets it out see that one right there + + align:start position:0% +I gets it out see that one right there + + + align:start position:0% +I gets it out see that one right there +for the first time Sita one would become + + align:start position:0% +for the first time Sita one would become + + + align:start position:0% +for the first time Sita one would become +YJ minus y3 minus one divided by a okay + + align:start position:0% +YJ minus y3 minus one divided by a okay + + + align:start position:0% +YJ minus y3 minus one divided by a okay +and of course you can do the same thing + + align:start position:0% +and of course you can do the same thing + + + align:start position:0% +and of course you can do the same thing +for the sine theta2 right which is + + align:start position:0% +for the sine theta2 right which is + + + align:start position:0% +for the sine theta2 right which is +proposed this ratio is roughly theta 2 + + align:start position:0% +proposed this ratio is roughly theta 2 + + + align:start position:0% +proposed this ratio is roughly theta 2 +then basically what I am going to get + + align:start position:0% +then basically what I am going to get + + + align:start position:0% +then basically what I am going to get +this - t-white say minus YJ plus 1/8 + + align:start position:0% +this - t-white say minus YJ plus 1/8 + + + align:start position:0% +this - t-white say minus YJ plus 1/8 +okay any questions okay I hope everybody + + align:start position:0% +okay any questions okay I hope everybody + + + align:start position:0% +okay any questions okay I hope everybody +is following it okay so now I can + + align:start position:0% +is following it okay so now I can + + + align:start position:0% +is following it okay so now I can +actually simplify equation number two + + align:start position:0% +actually simplify equation number two + + + align:start position:0% +actually simplify equation number two +and basically why I'm going to get this + + align:start position:0% +and basically why I'm going to get this + + + align:start position:0% +and basically why I'm going to get this +and YJ double dot will be equal to minus + + align:start position:0% +and YJ double dot will be equal to minus + + + align:start position:0% +and YJ double dot will be equal to minus +T over a basically I + + align:start position:0% +T over a basically I + + + align:start position:0% +T over a basically I +toal double again and I also collect all + + align:start position:0% +toal double again and I also collect all + + + align:start position:0% +toal double again and I also collect all +the times related to YT minus 1 minus 2 + + align:start position:0% +the times related to YT minus 1 minus 2 + + + align:start position:0% +the times related to YT minus 1 minus 2 +YT plus white + + align:start position:0% +YT plus white + + + align:start position:0% +YT plus white +okay just I should read write a question + + align:start position:0% +okay just I should read write a question + + + align:start position:0% +okay just I should read write a question +number 2 in a form which we like more + + align:start position:0% +number 2 in a form which we like more + + + align:start position:0% +number 2 in a form which we like more +okay so that is actually the equation of + + align:start position:0% +okay so that is actually the equation of + + + align:start position:0% +okay so that is actually the equation of +motion so sum from now on I'm going to + + align:start position:0% +motion so sum from now on I'm going to + + + align:start position:0% +motion so sum from now on I'm going to +ignore all the motion in the in the + + align:start position:0% +ignore all the motion in the in the + + + align:start position:0% +ignore all the motion in the in the +horizontal direction because in this + + align:start position:0% +horizontal direction because in this + + + align:start position:0% +horizontal direction because in this +small angle approximation we have shown + + align:start position:0% +small angle approximation we have shown + + + align:start position:0% +small angle approximation we have shown +you that there will be no acceleration + + align:start position:0% +you that there will be no acceleration + + + align:start position:0% +you that there will be no acceleration +in the X direction right so now it's + + align:start position:0% +in the X direction right so now it's + + + align:start position:0% +in the X direction right so now it's +actually getting a straight forward + + align:start position:0% +actually getting a straight forward + + + align:start position:0% +actually getting a straight forward +again basically we have the equation of + + align:start position:0% +again basically we have the equation of + + + align:start position:0% +again basically we have the equation of +motion and what is actually the next + + align:start position:0% +motion and what is actually the next + + + align:start position:0% +motion and what is actually the next +step the next step is to write down what + + align:start position:0% +step the next step is to write down what + + + align:start position:0% +step the next step is to write down what +metrics anybody can help me n minus 1 + + align:start position:0% +metrics anybody can help me n minus 1 + + + align:start position:0% +metrics anybody can help me n minus 1 +key metrics right + + align:start position:0% +key metrics right + + + align:start position:0% +key metrics right +so as usual we actually follow the the + + align:start position:0% +so as usual we actually follow the the + + + align:start position:0% +so as usual we actually follow the the +first seizure now I would like to write + + align:start position:0% +first seizure now I would like to write + + + align:start position:0% +first seizure now I would like to write +down and my swim K metrics okay so the + + align:start position:0% +down and my swim K metrics okay so the + + + align:start position:0% +down and my swim K metrics okay so the +first before I do that I would define I + + align:start position:0% +first before I do that I would define I + + + align:start position:0% +first before I do that I would define I +will actually assume my normal mall have + + align:start position:0% +will actually assume my normal mall have + + + align:start position:0% +will actually assume my normal mall have +this functional form YJ is equal to the + + align:start position:0% +this functional form YJ is equal to the + + + align:start position:0% +this functional form YJ is equal to the +real part of AJ exponential I Omega T + + align:start position:0% +real part of AJ exponential I Omega T + + + align:start position:0% +real part of AJ exponential I Omega T +plus Phi so basically that tells you + + align:start position:0% +plus Phi so basically that tells you + + + align:start position:0% +plus Phi so basically that tells you +that all the components are oscillating + + align:start position:0% +that all the components are oscillating + + + align:start position:0% +that all the components are oscillating +at the same frequency Omega L SFA's fine + + align:start position:0% +at the same frequency Omega L SFA's fine + + + align:start position:0% +at the same frequency Omega L SFA's fine +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +ah this one yeah ah okay maybe I made a + + align:start position:0% +ah this one yeah ah okay maybe I made a + + + align:start position:0% +ah this one yeah ah okay maybe I made a +mistake somewhere yeah I think it should + + align:start position:0% +mistake somewhere yeah I think it should + + + align:start position:0% +mistake somewhere yeah I think it should +be Pross okay all right + + align:start position:0% +be Pross okay all right + + + align:start position:0% +be Pross okay all right +thank you very much so so now we have + + align:start position:0% +thank you very much so so now we have + + + align:start position:0% +thank you very much so so now we have +all the ingredients and we assume that + + align:start position:0% +all the ingredients and we assume that + + + align:start position:0% +all the ingredients and we assume that +it has a normal mode okay j YJ in this + + align:start position:0% +it has a normal mode okay j YJ in this + + + align:start position:0% +it has a normal mode okay j YJ in this +functional form and now I can the next + + align:start position:0% +functional form and now I can the next + + + align:start position:0% +functional form and now I can the next +step is to get M minus one key metrics + + align:start position:0% +step is to get M minus one key metrics + + + align:start position:0% +step is to get M minus one key metrics +alright so what is a should n matrix and + + align:start position:0% +alright so what is a should n matrix and + + + align:start position:0% +alright so what is a should n matrix and +matrix is reduced rate for this mm and + + align:start position:0% +matrix is reduced rate for this mm and + + + align:start position:0% +matrix is reduced rate for this mm and +in in diagonal turns and all the rest of + + align:start position:0% +in in diagonal turns and all the rest of + + + align:start position:0% +in in diagonal turns and all the rest of +the turns are 0 right and those course + + align:start position:0% +the turns are 0 right and those course + + + align:start position:0% +the turns are 0 right and those course +you can also write down k matrix right + + align:start position:0% +you can also write down k matrix right + + + align:start position:0% +you can also write down k matrix right +so the K matrix will be equal to the + + align:start position:0% +so the K matrix will be equal to the + + + align:start position:0% +so the K matrix will be equal to the +mini turns and in the middle you have + + align:start position:0% +mini turns and in the middle you have + + + align:start position:0% +mini turns and in the middle you have +minus T over a 2t over 8 minus T over a + + align:start position:0% +minus T over a 2t over 8 minus T over a + + + align:start position:0% +minus T over a 2t over 8 minus T over a +and all the rest of the turns are 0 and + + align:start position:0% +and all the rest of the turns are 0 and + + + align:start position:0% +and all the rest of the turns are 0 and +of course these patterns go on and on + + align:start position:0% +of course these patterns go on and on + + + align:start position:0% +of course these patterns go on and on +minus T over a 2t over a minus T over a + + align:start position:0% +minus T over a 2t over a minus T over a + + + align:start position:0% +minus T over a 2t over a minus T over a +and zeros etcetera etcetera and this + + align:start position:0% +and zeros etcetera etcetera and this + + + align:start position:0% +and zeros etcetera etcetera and this +pattern is going to go on forever and + + align:start position:0% +pattern is going to go on forever and + + + align:start position:0% +pattern is going to go on forever and +the pitch because this is actually + + align:start position:0% +the pitch because this is actually + + + align:start position:0% +the pitch because this is actually +infinitely long matrix infinity times + + align:start position:0% +infinitely long matrix infinity times + + + align:start position:0% +infinitely long matrix infinity times +infinity long matrix + + align:start position:0% + + + + align:start position:0% + +okay so once we have this we can now + + align:start position:0% +okay so once we have this we can now + + + align:start position:0% +okay so once we have this we can now +write down the immense one key metrics + + align:start position:0% +write down the immense one key metrics + + + align:start position:0% +write down the immense one key metrics +what is actually the ms-20 metrics it + + align:start position:0% +what is actually the ms-20 metrics it + + + align:start position:0% +what is actually the ms-20 metrics it +has a similar structure as k metrics + + align:start position:0% +has a similar structure as k metrics + + + align:start position:0% +has a similar structure as k metrics +right + + align:start position:0% +right + + + align:start position:0% +right +all those are zeros okay + + align:start position:0% +all those are zeros okay + + + align:start position:0% +all those are zeros okay +all those are other values but it has a + + align:start position:0% +all those are other values but it has a + + + align:start position:0% +all those are other values but it has a +fixed structure minus T over MA - T over + + align:start position:0% +fixed structure minus T over MA - T over + + + align:start position:0% +fixed structure minus T over MA - T over +MA minus T over MA and the zeros and + + align:start position:0% +MA minus T over MA and the zeros and + + + align:start position:0% +MA minus T over MA and the zeros and +this will go on forever you know tired + + align:start position:0% +this will go on forever you know tired + + + align:start position:0% +this will go on forever you know tired +look in the diagonal turn and also the + + align:start position:0% +look in the diagonal turn and also the + + + align:start position:0% +look in the diagonal turn and also the +next two techno trance and all the rest + + align:start position:0% +next two techno trance and all the rest + + + align:start position:0% +next two techno trance and all the rest +of the turns are zero okay any questions + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +okay so that's really nice now we have + + align:start position:0% +okay so that's really nice now we have + + + align:start position:0% +okay so that's really nice now we have +MS one key metrics and the good news is + + align:start position:0% +MS one key metrics and the good news is + + + align:start position:0% +MS one key metrics and the good news is +that you don't have to solve n minus 1 K + + align:start position:0% +that you don't have to solve n minus 1 K + + + align:start position:0% +that you don't have to solve n minus 1 K +matrix eigenvalue again right because we + + align:start position:0% +matrix eigenvalue again right because we + + + align:start position:0% +matrix eigenvalue again right because we +have solved the eigenvalue problem of s + + align:start position:0% +have solved the eigenvalue problem of s + + + align:start position:0% +have solved the eigenvalue problem of s +matrix therefore what is out lab over is + + align:start position:0% +matrix therefore what is out lab over is + + + align:start position:0% +matrix therefore what is out lab over is +to multiply M minus 1 K by a by a they + + align:start position:0% +to multiply M minus 1 K by a by a they + + + align:start position:0% +to multiply M minus 1 K by a by a they +should be the eigenvector 1 of the eigen + + align:start position:0% +should be the eigenvector 1 of the eigen + + + align:start position:0% +should be the eigenvector 1 of the eigen +batter of asthmatics okay so I'm going + + align:start position:0% +batter of asthmatics okay so I'm going + + + align:start position:0% +batter of asthmatics okay so I'm going +to multiply that for you and now we + + align:start position:0% +to multiply that for you and now we + + + align:start position:0% +to multiply that for you and now we +calculate M minus 1 k equal to Omega + + align:start position:0% +calculate M minus 1 k equal to Omega + + + align:start position:0% +calculate M minus 1 k equal to Omega +square a then I can get omega square out + + align:start position:0% +square a then I can get omega square out + + + align:start position:0% +square a then I can get omega square out +of this calculation okay if I again for + + align:start position:0% +of this calculation okay if I again for + + + align:start position:0% +of this calculation okay if I again for +some focus on Jays turn okay so + + align:start position:0% +some focus on Jays turn okay so + + + align:start position:0% +some focus on Jays turn okay so +basically what I'm going to get this + + align:start position:0% +basically what I'm going to get this + + + align:start position:0% +basically what I'm going to get this +right hand side I have Omega square AJ + + align:start position:0% +right hand side I have Omega square AJ + + + align:start position:0% +right hand side I have Omega square AJ +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that is a 3 from the right hand side + + align:start position:0% +that is a 3 from the right hand side + + + align:start position:0% +that is a 3 from the right hand side +okay and a lap inside M minus 1 K times + + align:start position:0% +okay and a lap inside M minus 1 K times + + + align:start position:0% +okay and a lap inside M minus 1 K times +8 what I am going to get is P over m + + align:start position:0% + + + + align:start position:0% + +- AJ minus 1 plus 2 AJ - AJ plus 1 right + + align:start position:0% +- AJ minus 1 plus 2 AJ - AJ plus 1 right + + + align:start position:0% +- AJ minus 1 plus 2 AJ - AJ plus 1 right +because if you take this this turn is + + align:start position:0% +because if you take this this turn is + + + align:start position:0% +because if you take this this turn is +actually in the exact diagonal in the + + align:start position:0% +actually in the exact diagonal in the + + + align:start position:0% +actually in the exact diagonal in the +diagonal of this n minus 1 K matrix + + align:start position:0% +diagonal of this n minus 1 K matrix + + + align:start position:0% +diagonal of this n minus 1 K matrix +therefore this match mistake and this + + align:start position:0% +therefore this match mistake and this + + + align:start position:0% +therefore this match mistake and this +will match with same as one match when + + align:start position:0% +will match with same as one match when + + + align:start position:0% +will match with same as one match when +they press 1 okay therefore if you + + align:start position:0% +they press 1 okay therefore if you + + + align:start position:0% +they press 1 okay therefore if you +multiply n minus 1 K and the a you get + + align:start position:0% +multiply n minus 1 K and the a you get + + + align:start position:0% +multiply n minus 1 K and the a you get +this result + + align:start position:0% +this result + + + align:start position:0% +this result +okay and we also know that a day is + + align:start position:0% +okay and we also know that a day is + + + align:start position:0% +okay and we also know that a day is +proportional to exponential ijk a right + + align:start position:0% +proportional to exponential ijk a right + + + align:start position:0% +proportional to exponential ijk a right +therefore I can take AJ out of this and + + align:start position:0% +therefore I can take AJ out of this and + + + align:start position:0% +therefore I can take AJ out of this and +the basically I get T over na AJ minus + + align:start position:0% +the basically I get T over na AJ minus + + + align:start position:0% +the basically I get T over na AJ minus +exponential minus I K a plus 2 because I + + align:start position:0% +exponential minus I K a plus 2 because I + + + align:start position:0% +exponential minus I K a plus 2 because I +take AJ out of the of the of this + + align:start position:0% +take AJ out of the of the of this + + + align:start position:0% +take AJ out of the of the of this +bracket ok and minus exponential I K + + align:start position:0% + + + + align:start position:0% + +okay nitrogen actually can cancel AJ + + align:start position:0% +okay nitrogen actually can cancel AJ + + + align:start position:0% +okay nitrogen actually can cancel AJ +basically what I get is Omega Square + + align:start position:0% +basically what I get is Omega Square + + + align:start position:0% +basically what I get is Omega Square +will be equal to P over ma 2 minus + + align:start position:0% +will be equal to P over ma 2 minus + + + align:start position:0% +will be equal to P over ma 2 minus +exponential I K a press exponential + + align:start position:0% +exponential I K a press exponential + + + align:start position:0% +exponential I K a press exponential +minus I K and that will be equal to 2t + + align:start position:0% +minus I K and that will be equal to 2t + + + align:start position:0% +minus I K and that will be equal to 2t +over MA + + align:start position:0% +over MA + + + align:start position:0% +over MA +okay 1 - so okay so so called + + align:start position:0% +okay 1 - so okay so so called + + + align:start position:0% +okay 1 - so okay so so called +exponential I K a plus exponential minus + + align:start position:0% +exponential I K a plus exponential minus + + + align:start position:0% +exponential I K a plus exponential minus +I K a you are going to get 2 cosine okay + + align:start position:0% +I K a you are going to get 2 cosine okay + + + align:start position:0% +I K a you are going to get 2 cosine okay +all right all right + + align:start position:0% +all right all right + + + align:start position:0% +all right all right +therefore you get 1 minus cosine + + align:start position:0% +therefore you get 1 minus cosine + + + align:start position:0% +therefore you get 1 minus cosine +okay okay I can define I define Omega + + align:start position:0% +okay okay I can define I define Omega + + + align:start position:0% +okay okay I can define I define Omega +zero to be square root of T over ma just + + align:start position:0% +zero to be square root of T over ma just + + + align:start position:0% +zero to be square root of T over ma just +to make my life easier + + align:start position:0% +to make my life easier + + + align:start position:0% +to make my life easier +okay then what is going to happen is + + align:start position:0% +okay then what is going to happen is + + + align:start position:0% +okay then what is going to happen is +that I will have Omega squared equal to + + align:start position:0% +that I will have Omega squared equal to + + + align:start position:0% +that I will have Omega squared equal to +2 Omega 0 Square 1 minus cosine okay any + + align:start position:0% +2 Omega 0 Square 1 minus cosine okay any + + + align:start position:0% +2 Omega 0 Square 1 minus cosine okay any +questions okay + + align:start position:0% +questions okay + + + align:start position:0% +questions okay +of course if you if you like you can + + align:start position:0% +of course if you if you like you can + + + align:start position:0% +of course if you if you like you can +also rewrite this as 4 Omega 0 square + + align:start position:0% +also rewrite this as 4 Omega 0 square + + + align:start position:0% +also rewrite this as 4 Omega 0 square +sine sine K okay so if you if you like + + align:start position:0% +sine sine K okay so if you if you like + + + align:start position:0% +sine sine K okay so if you if you like +okay so look at what we have done we + + align:start position:0% +okay so look at what we have done we + + + align:start position:0% +okay so look at what we have done we +study a highly symmetric system which is + + align:start position:0% +study a highly symmetric system which is + + + align:start position:0% +study a highly symmetric system which is +actually shown in a slide okay basically + + align:start position:0% +actually shown in a slide okay basically + + + align:start position:0% +actually shown in a slide okay basically +you satisfy the space translation + + align:start position:0% +you satisfy the space translation + + + align:start position:0% +you satisfy the space translation +symmetry okay then what we have been + + align:start position:0% +symmetry okay then what we have been + + + align:start position:0% +symmetry okay then what we have been +doing is to derive the equation of + + align:start position:0% +doing is to derive the equation of + + + align:start position:0% +doing is to derive the equation of +motion make use of the small angle + + align:start position:0% +motion make use of the small angle + + + align:start position:0% +motion make use of the small angle +approximation then you will be able to + + align:start position:0% +approximation then you will be able to + + + align:start position:0% +approximation then you will be able to +find that okay only the Y direction as u + + align:start position:0% +find that okay only the Y direction as u + + + align:start position:0% +find that okay only the Y direction as u +is actually moving as a function of time + + align:start position:0% +is actually moving as a function of time + + + align:start position:0% +is actually moving as a function of time +therefore based on this deviation of ms1 + + align:start position:0% +therefore based on this deviation of ms1 + + + align:start position:0% +therefore based on this deviation of ms1 +key metrics I arrived and also based on + + align:start position:0% +key metrics I arrived and also based on + + + align:start position:0% +key metrics I arrived and also based on +the equation of motion which I derived + + align:start position:0% +the equation of motion which I derived + + + align:start position:0% +the equation of motion which I derived +from the force diagram I get this n + + align:start position:0% +from the force diagram I get this n + + + align:start position:0% +from the force diagram I get this n +minus 1 key metrics and since we know + + align:start position:0% +minus 1 key metrics and since we know + + + align:start position:0% +minus 1 key metrics and since we know +that n minus 1 K metrics and the S + + align:start position:0% +that n minus 1 K metrics and the S + + + align:start position:0% +that n minus 1 K metrics and the S +matrix we share the same eigen vector I + + align:start position:0% +matrix we share the same eigen vector I + + + align:start position:0% +matrix we share the same eigen vector I +can multiply n minus 1 K metrics and + + align:start position:0% +can multiply n minus 1 K metrics and + + + align:start position:0% +can multiply n minus 1 K metrics and +like a vector a then I will be able to + + align:start position:0% +like a vector a then I will be able to + + + align:start position:0% +like a vector a then I will be able to +solve the functional form of Omega + + align:start position:0% +solve the functional form of Omega + + + align:start position:0% +solve the functional form of Omega +square + + align:start position:0% +square + + + align:start position:0% +square +and that is actually given here Omega + + align:start position:0% +and that is actually given here Omega + + + align:start position:0% +and that is actually given here Omega +square is equal to 2 Omega 0 Square 1 + + align:start position:0% +square is equal to 2 Omega 0 Square 1 + + + align:start position:0% +square is equal to 2 Omega 0 Square 1 +minus cosine K ok and this is actually + + align:start position:0% +minus cosine K ok and this is actually + + + align:start position:0% +minus cosine K ok and this is actually +telling you that Omega is a function of + + align:start position:0% +telling you that Omega is a function of + + + align:start position:0% +telling you that Omega is a function of +ok ok what is K T is actually the wave + + align:start position:0% +ok ok what is K T is actually the wave + + + align:start position:0% +ok ok what is K T is actually the wave +number and Omega is actually the angular + + align:start position:0% +number and Omega is actually the angular + + + align:start position:0% +number and Omega is actually the angular +frequency of the normal mode right so + + align:start position:0% +frequency of the normal mode right so + + + align:start position:0% +frequency of the normal mode right so +that means what we are we're talking + + align:start position:0% +that means what we are we're talking + + + align:start position:0% +that means what we are we're talking +about la means if we fix the wave flash + + align:start position:0% +about la means if we fix the wave flash + + + align:start position:0% +about la means if we fix the wave flash +ok or the wave number K then there will + + align:start position:0% +ok or the wave number K then there will + + + align:start position:0% +ok or the wave number K then there will +be a corresponding Omega okay if you fix + + align:start position:0% +be a corresponding Omega okay if you fix + + + align:start position:0% +be a corresponding Omega okay if you fix +a wavelength we are talking about then + + align:start position:0% +a wavelength we are talking about then + + + align:start position:0% +a wavelength we are talking about then +then the Omega is also fixed by this + + align:start position:0% +then the Omega is also fixed by this + + + align:start position:0% +then the Omega is also fixed by this +Omega of K function ok now we actually + + align:start position:0% +Omega of K function ok now we actually + + + align:start position:0% +Omega of K function ok now we actually +call it dispersion relation this term + + align:start position:0% +call it dispersion relation this term + + + align:start position:0% +call it dispersion relation this term +may not mean much to you now but later + + align:start position:0% +may not mean much to you now but later + + + align:start position:0% +may not mean much to you now but later +in the discussion you will find out how + + align:start position:0% +in the discussion you will find out how + + + align:start position:0% +in the discussion you will find out how +it really makes sense and we will talk + + align:start position:0% +it really makes sense and we will talk + + + align:start position:0% +it really makes sense and we will talk +about dispersion in the later lectures + + align:start position:0% +about dispersion in the later lectures + + + align:start position:0% +about dispersion in the later lectures +okay so so so the conclusion from here + + align:start position:0% +okay so so so the conclusion from here + + + align:start position:0% +okay so so so the conclusion from here +is that basically if I have this system + + align:start position:0% +is that basically if I have this system + + + align:start position:0% +is that basically if I have this system +satisfy this as translation symmetry + + align:start position:0% +satisfy this as translation symmetry + + + align:start position:0% +satisfy this as translation symmetry +then what it tells us is that the normal + + align:start position:0% +then what it tells us is that the normal + + + align:start position:0% +then what it tells us is that the normal +modes would looks like some kind of sign + + align:start position:0% +modes would looks like some kind of sign + + + align:start position:0% +modes would looks like some kind of sign +so little function right as we discussed + + align:start position:0% +so little function right as we discussed + + + align:start position:0% +so little function right as we discussed +last time and also this + + align:start position:0% +last time and also this + + + align:start position:0% +last time and also this +okay so this is actually the amplitude + + align:start position:0% +okay so this is actually the amplitude + + + align:start position:0% +okay so this is actually the amplitude +what I'm drawing here those this curve + + align:start position:0% +what I'm drawing here those this curve + + + align:start position:0% +what I'm drawing here those this curve +and all those maths are only moving up + + align:start position:0% +and all those maths are only moving up + + + align:start position:0% +and all those maths are only moving up +and down okay as a function of time and + + align:start position:0% +and down okay as a function of time and + + + align:start position:0% +and down okay as a function of time and +this is AJ and the oscillation frequency + + align:start position:0% +this is AJ and the oscillation frequency + + + align:start position:0% +this is AJ and the oscillation frequency +which is actually the frequency of + + align:start position:0% +which is actually the frequency of + + + align:start position:0% +which is actually the frequency of +moving up and down this kind of motion + + align:start position:0% +moving up and down this kind of motion + + + align:start position:0% +moving up and down this kind of motion +is actually Omega and also we learn that + + align:start position:0% +is actually Omega and also we learn that + + + align:start position:0% +is actually Omega and also we learn that +Omega is equal to Omega okay and not + + align:start position:0% +Omega is equal to Omega okay and not + + + align:start position:0% +Omega is equal to Omega okay and not +essentially decided by the lens and all + + align:start position:0% +essentially decided by the lens and all + + + align:start position:0% +essentially decided by the lens and all +how distorted is this normal mode that + + align:start position:0% +how distorted is this normal mode that + + + align:start position:0% +how distorted is this normal mode that +the shape of the normal mode and this is + + align:start position:0% +the shape of the normal mode and this is + + + align:start position:0% +the shape of the normal mode and this is +actually determined by the K which is + + align:start position:0% +actually determined by the K which is + + + align:start position:0% +actually determined by the K which is +actually the wetlands and which is + + align:start position:0% +actually the wetlands and which is + + + align:start position:0% +actually the wetlands and which is +actually a web number and of course you + + align:start position:0% +actually a web number and of course you + + + align:start position:0% +actually a web number and of course you +can also get the wavelength from 2pi + + align:start position:0% +can also get the wavelength from 2pi + + + align:start position:0% +can also get the wavelength from 2pi +over k okay in short if you give it a + + align:start position:0% +over k okay in short if you give it a + + + align:start position:0% +over k okay in short if you give it a +specific width lambda or with + + align:start position:0% +specific width lambda or with + + + align:start position:0% +specific width lambda or with +wavelengths then the oscillation + + align:start position:0% +wavelengths then the oscillation + + + align:start position:0% +wavelengths then the oscillation +frequency is already fixed because of + + align:start position:0% +frequency is already fixed because of + + + align:start position:0% +frequency is already fixed because of +the equation of motion which we derive + + align:start position:0% +the equation of motion which we derive + + + align:start position:0% +the equation of motion which we derive +from the force diagram any questions + + align:start position:0% + + + + align:start position:0% + +okay the last point which I would like + + align:start position:0% +okay the last point which I would like + + + align:start position:0% +okay the last point which I would like +to remind you is that at this point + + align:start position:0% +to remind you is that at this point + + + align:start position:0% +to remind you is that at this point +since we are talking about infinite long + + align:start position:0% +since we are talking about infinite long + + + align:start position:0% +since we are talking about infinite long +system therefore all possible K are + + align:start position:0% +system therefore all possible K are + + + align:start position:0% +system therefore all possible K are +allowed right because we pitch it you + + align:start position:0% +allowed right because we pitch it you + + + align:start position:0% +allowed right because we pitch it you +have infinite number of coupled + + align:start position:0% +have infinite number of coupled + + + align:start position:0% +have infinite number of coupled +oscillators and therefore you have + + align:start position:0% +oscillators and therefore you have + + + align:start position:0% +oscillators and therefore you have +infinite number of normal modes so all + + align:start position:0% +infinite number of normal modes so all + + + align:start position:0% +infinite number of normal modes so all +possible case are allowed and and that + + align:start position:0% +possible case are allowed and and that + + + align:start position:0% +possible case are allowed and and that +that is actually because we have an + + align:start position:0% +that is actually because we have an + + + align:start position:0% +that is actually because we have an +infinite long system after the break + + align:start position:0% +infinite long system after the break + + + align:start position:0% +infinite long system after the break +which we will take a five-minute break + + align:start position:0% +which we will take a five-minute break + + + align:start position:0% +which we will take a five-minute break +we'll discuss how to use infinity long + + align:start position:0% +we'll discuss how to use infinity long + + + align:start position:0% +we'll discuss how to use infinity long +system to actually understand a finite + + align:start position:0% +system to actually understand a finite + + + align:start position:0% +system to actually understand a finite +as + + align:start position:0% +as + + + align:start position:0% +as +so you will see that actually I can use + + align:start position:0% +so you will see that actually I can use + + + align:start position:0% +so you will see that actually I can use +now this space translation symmetry and + + align:start position:0% +now this space translation symmetry and + + + align:start position:0% +now this space translation symmetry and +to solve in general infinite long system + + align:start position:0% +to solve in general infinite long system + + + align:start position:0% +to solve in general infinite long system +and I can actually even go back to + + align:start position:0% +and I can actually even go back to + + + align:start position:0% +and I can actually even go back to +finite system and see what we can get on + + align:start position:0% +finite system and see what we can get on + + + align:start position:0% +finite system and see what we can get on +there okay so we would be back at 12:20 + + align:start position:0% +there okay so we would be back at 12:20 + + + align:start position:0% +there okay so we would be back at 12:20 +if you have any questions I will be here + + align:start position:0% + + + + align:start position:0% + +okay welcome back + + align:start position:0% +okay welcome back + + + align:start position:0% +okay welcome back +everybody so we will continue the + + align:start position:0% +everybody so we will continue the + + + align:start position:0% +everybody so we will continue the +discussion so so there are a few + + align:start position:0% +discussion so so there are a few + + + align:start position:0% +discussion so so there are a few +questions asked during the break so the + + align:start position:0% +questions asked during the break so the + + + align:start position:0% +questions asked during the break so the +first question is related to how we + + align:start position:0% +first question is related to how we + + + align:start position:0% +first question is related to how we +actually arrived this equation and that + + align:start position:0% +actually arrived this equation and that + + + align:start position:0% +actually arrived this equation and that +is actually because ok 2t over na is + + align:start position:0% +is actually because ok 2t over na is + + + align:start position:0% +is actually because ok 2t over na is +actually really happening in a diagonal + + align:start position:0% +actually really happening in a diagonal + + + align:start position:0% +actually really happening in a diagonal +turn therefore if you multiply n minus 1 + + align:start position:0% +turn therefore if you multiply n minus 1 + + + align:start position:0% +turn therefore if you multiply n minus 1 +K matrix and a matrix which is actually + + align:start position:0% +K matrix and a matrix which is actually + + + align:start position:0% +K matrix and a matrix which is actually +shown there then you will get this term + + align:start position:0% +shown there then you will get this term + + + align:start position:0% +shown there then you will get this term +minus T of n a multiplied by ei J minus + + align:start position:0% +minus T of n a multiplied by ei J minus + + + align:start position:0% +minus T of n a multiplied by ei J minus +1 plus 2t over na times AJ prime minus T + + align:start position:0% +1 plus 2t over na times AJ prime minus T + + + align:start position:0% +1 plus 2t over na times AJ prime minus T +over na times AJ plus 1 and that is + + align:start position:0% +over na times AJ plus 1 and that is + + + align:start position:0% +over na times AJ plus 1 and that is +actually why we can actually arrive this + + align:start position:0% +actually why we can actually arrive this + + + align:start position:0% +actually why we can actually arrive this +expression ok then what happens + + align:start position:0% +expression ok then what happens + + + align:start position:0% +expression ok then what happens +afterwards is that we found that AJ can + + align:start position:0% +afterwards is that we found that AJ can + + + align:start position:0% +afterwards is that we found that AJ can +be factorized out and they cancel and + + align:start position:0% +be factorized out and they cancel and + + + align:start position:0% +be factorized out and they cancel and +now my solution is independent of the + + align:start position:0% +now my solution is independent of the + + + align:start position:0% +now my solution is independent of the +amplitude and still Omega is actually + + align:start position:0% +amplitude and still Omega is actually + + + align:start position:0% +amplitude and still Omega is actually +dependent on the K value which way we + + align:start position:0% +dependent on the K value which way we + + + align:start position:0% +dependent on the K value which way we +actually choose ok the second question + + align:start position:0% +actually choose ok the second question + + + align:start position:0% +actually choose ok the second question +is ok why do I say K is the wave number + + align:start position:0% +is ok why do I say K is the wave number + + + align:start position:0% +is ok why do I say K is the wave number +okay where is that coming from so that + + align:start position:0% +okay where is that coming from so that + + + align:start position:0% +okay where is that coming from so that +is because ok so AJ is proportional to + + align:start position:0% +is because ok so AJ is proportional to + + + align:start position:0% +is because ok so AJ is proportional to +exponential ijk a ok it has a fancy net + + align:start position:0% +exponential ijk a ok it has a fancy net + + + align:start position:0% +exponential ijk a ok it has a fancy net +if I take the real part ok as we did + + align:start position:0% +if I take the real part ok as we did + + + align:start position:0% +if I take the real part ok as we did +when we go to the the description of + + align:start position:0% +when we go to the the description of + + + align:start position:0% +when we go to the the description of +physical system then you get cosine say + + align:start position:0% +physical system then you get cosine say + + + align:start position:0% +physical system then you get cosine say +ka ok + + align:start position:0% +ka ok + + + align:start position:0% +ka ok +and take times a essentially say it says + + align:start position:0% +and take times a essentially say it says + + + align:start position:0% +and take times a essentially say it says +you a label like labeling which mass are + + align:start position:0% +you a label like labeling which mass are + + + align:start position:0% +you a label like labeling which mass are +in talking about a shoe the distance + + align:start position:0% +in talking about a shoe the distance + + + align:start position:0% +in talking about a shoe the distance +between all those mass say times a will + + align:start position:0% +between all those mass say times a will + + + align:start position:0% +between all those mass say times a will +give you the X the location of the mass + + align:start position:0% +give you the X the location of the mass + + + align:start position:0% +give you the X the location of the mass +so 2 times a is actually the X X + + align:start position:0% +so 2 times a is actually the X X + + + align:start position:0% +so 2 times a is actually the X X +position of the mass ok therefore if you + + align:start position:0% +position of the mass ok therefore if you + + + align:start position:0% +position of the mass ok therefore if you +accept that this become cosine KX and + + align:start position:0% +accept that this become cosine KX and + + + align:start position:0% +accept that this become cosine KX and +from there you will see immediately that + + align:start position:0% +from there you will see immediately that + + + align:start position:0% +from there you will see immediately that +K have a meaning which is actually the + + align:start position:0% +K have a meaning which is actually the + + + align:start position:0% +K have a meaning which is actually the +web number okay + + align:start position:0% +web number okay + + + align:start position:0% +web number okay +all right is that okay so that was the + + align:start position:0% +all right is that okay so that was the + + + align:start position:0% +all right is that okay so that was the +questions raised which I can quickly + + align:start position:0% +questions raised which I can quickly + + + align:start position:0% +questions raised which I can quickly +explain so what I'm going to do now is + + align:start position:0% +explain so what I'm going to do now is + + + align:start position:0% +explain so what I'm going to do now is +that okay we have solved in general an + + align:start position:0% +that okay we have solved in general an + + + align:start position:0% +that okay we have solved in general an +infinitely long system what is actually + + align:start position:0% +infinitely long system what is actually + + + align:start position:0% +infinitely long system what is actually +that the resulting normal mode of + + align:start position:0% +that the resulting normal mode of + + + align:start position:0% +that the resulting normal mode of +infinite long system it has infinitely + + align:start position:0% +infinite long system it has infinitely + + + align:start position:0% +infinite long system it has infinitely +number of normal modes and we were + + align:start position:0% +number of normal modes and we were + + + align:start position:0% +number of normal modes and we were +wondering if I can actually power this + + align:start position:0% +wondering if I can actually power this + + + align:start position:0% +wondering if I can actually power this +infinite long system and solve finite + + align:start position:0% +infinite long system and solve finite + + + align:start position:0% +infinite long system and solve finite +system to to see if we I can arrive the + + align:start position:0% +system to to see if we I can arrive the + + + align:start position:0% +system to to see if we I can arrive the +solution really quickly okay so so the + + align:start position:0% +solution really quickly okay so so the + + + align:start position:0% +solution really quickly okay so so the +answer is actually yes so if I consider + + align:start position:0% +answer is actually yes so if I consider + + + align:start position:0% +answer is actually yes so if I consider +a finite system like look like this so I + + align:start position:0% +a finite system like look like this so I + + + align:start position:0% +a finite system like look like this so I +have many many little mass on this + + align:start position:0% +have many many little mass on this + + + align:start position:0% +have many many little mass on this +system and they are connected to each + + align:start position:0% +system and they are connected to each + + + align:start position:0% +system and they are connected to each +other by the same strings which I + + align:start position:0% +other by the same strings which I + + + align:start position:0% +other by the same strings which I +prepared before okay and I call this the + + align:start position:0% +prepared before okay and I call this the + + + align:start position:0% +prepared before okay and I call this the +position in the Y direction of the of + + align:start position:0% +position in the Y direction of the of + + + align:start position:0% +position in the Y direction of the of +this object y1 and the next object Y 2 + + align:start position:0% +this object y1 and the next object Y 2 + + + align:start position:0% +this object y1 and the next object Y 2 +by 3 etc and I have an object in this + + align:start position:0% +by 3 etc and I have an object in this + + + align:start position:0% +by 3 etc and I have an object in this +system and the post end of the string is + + align:start position:0% +system and the post end of the string is + + + align:start position:0% +system and the post end of the string is +fixed on the wall okay so I can actually + + align:start position:0% +fixed on the wall okay so I can actually + + + align:start position:0% +fixed on the wall okay so I can actually +now argue that that infinitely long + + align:start position:0% +now argue that that infinitely long + + + align:start position:0% +now argue that that infinitely long +system can help us with the + + align:start position:0% +system can help us with the + + + align:start position:0% +system can help us with the +understanding of this finite system why + + align:start position:0% +understanding of this finite system why + + + align:start position:0% +understanding of this finite system why +is that + + align:start position:0% +is that + + + align:start position:0% +is that +that is because now I can assume that + + align:start position:0% +that is because now I can assume that + + + align:start position:0% +that is because now I can assume that +this is actually just part of an + + align:start position:0% +this is actually just part of an + + + align:start position:0% +this is actually just part of an +infinitely long system right ok so I + + align:start position:0% +infinitely long system right ok so I + + + align:start position:0% +infinitely long system right ok so I +can't run my infinitely long system and + + align:start position:0% +can't run my infinitely long system and + + + align:start position:0% +can't run my infinitely long system and +now I know the wise mass I know why I'm + + align:start position:0% +now I know the wise mass I know why I'm + + + align:start position:0% +now I know the wise mass I know why I'm +past one mass and I fixed that so that + + align:start position:0% +past one mass and I fixed that so that + + + align:start position:0% +past one mass and I fixed that so that +it cannot move okay so it's still + + align:start position:0% +it cannot move okay so it's still + + + align:start position:0% +it cannot move okay so it's still +infinite long system + + align:start position:0% +infinite long system + + + align:start position:0% +infinite long system +but there are two interesting boundary + + align:start position:0% +but there are two interesting boundary + + + align:start position:0% +but there are two interesting boundary +conditions at white a equal to zero and + + align:start position:0% +conditions at white a equal to zero and + + + align:start position:0% +conditions at white a equal to zero and +a day equal to n plus one okay what are + + align:start position:0% +a day equal to n plus one okay what are + + + align:start position:0% +a day equal to n plus one okay what are +the two boundary conditions + + align:start position:0% + + + + align:start position:0% + +the first one is y 0 equal to 0 okay and + + align:start position:0% +the first one is y 0 equal to 0 okay and + + + align:start position:0% +the first one is y 0 equal to 0 okay and +the second condition is y n plus 1 equal + + align:start position:0% +the second condition is y n plus 1 equal + + + align:start position:0% +the second condition is y n plus 1 equal +to 0 okay so there are two boundary + + align:start position:0% +to 0 okay so there are two boundary + + + align:start position:0% +to 0 okay so there are two boundary +conditions also basically what I'm + + align:start position:0% +conditions also basically what I'm + + + align:start position:0% +conditions also basically what I'm +looking at it's still an infinitely long + + align:start position:0% +looking at it's still an infinitely long + + + align:start position:0% +looking at it's still an infinitely long +system but I'd require y 0 and y n plus + + align:start position:0% +system but I'd require y 0 and y n plus + + + align:start position:0% +system but I'd require y 0 and y n plus +1 to satisfy these two conditions ok and + + align:start position:0% +1 to satisfy these two conditions ok and + + + align:start position:0% +1 to satisfy these two conditions ok and +we will find that huh with this + + align:start position:0% +we will find that huh with this + + + align:start position:0% +we will find that huh with this +procedure we can also solve this finite + + align:start position:0% +procedure we can also solve this finite + + + align:start position:0% +procedure we can also solve this finite +number of couple oscillator problem this + + align:start position:0% +number of couple oscillator problem this + + + align:start position:0% +number of couple oscillator problem this +in this case we have a coupled + + align:start position:0% +in this case we have a coupled + + + align:start position:0% +in this case we have a coupled +oscillator ok so the first thing which I + + align:start position:0% +oscillator ok so the first thing which I + + + align:start position:0% +oscillator ok so the first thing which I +would like to say is based on the + + align:start position:0% +would like to say is based on the + + + align:start position:0% +would like to say is based on the +function of for the functional form of + + align:start position:0% +function of for the functional form of + + + align:start position:0% +function of for the functional form of +Omega square that is equal to 4 Omega 0 + + align:start position:0% +Omega square that is equal to 4 Omega 0 + + + align:start position:0% +Omega square that is equal to 4 Omega 0 +square sine square ka / - okay what we + + align:start position:0% +square sine square ka / - okay what we + + + align:start position:0% +square sine square ka / - okay what we +actually have is that Omega K is equal + + align:start position:0% +actually have is that Omega K is equal + + + align:start position:0% +actually have is that Omega K is equal +to Omega minus K okay so both of them + + align:start position:0% +to Omega minus K okay so both of them + + + align:start position:0% +to Omega minus K okay so both of them +will give you the same and grow + + align:start position:0% +will give you the same and grow + + + align:start position:0% +will give you the same and grow +frequency okay + + align:start position:0% +frequency okay + + + align:start position:0% +frequency okay +therefore what what does that mean this + + align:start position:0% +therefore what what does that mean this + + + align:start position:0% +therefore what what does that mean this +means that linear combination of + + align:start position:0% +means that linear combination of + + + align:start position:0% +means that linear combination of +exponential I say ka and the explanation + + align:start position:0% +exponential I say ka and the explanation + + + align:start position:0% +exponential I say ka and the explanation +- I take a a ok linear combination of + + align:start position:0% +- I take a a ok linear combination of + + + align:start position:0% +- I take a a ok linear combination of +these two vectors okay it's also an + + align:start position:0% +these two vectors okay it's also an + + + align:start position:0% +these two vectors okay it's also an +eigen vector of n minus 1 K matrix okay + + align:start position:0% +eigen vector of n minus 1 K matrix okay + + + align:start position:0% +eigen vector of n minus 1 K matrix okay +so you can do linear combination of this + + align:start position:0% +so you can do linear combination of this + + + align:start position:0% +so you can do linear combination of this +two vectors okay so we if we do that now + + align:start position:0% +two vectors okay so we if we do that now + + + align:start position:0% +two vectors okay so we if we do that now +I can guess my solution will be like YJ + + align:start position:0% +I can guess my solution will be like YJ + + + align:start position:0% +I can guess my solution will be like YJ +equal to real part of exponential I + + align:start position:0% +equal to real part of exponential I + + + align:start position:0% +equal to real part of exponential I +Omega T plus Phi I can now have a linear + + align:start position:0% +Omega T plus Phi I can now have a linear + + + align:start position:0% +Omega T plus Phi I can now have a linear +combination of exponential I Chi ka and + + align:start position:0% +combination of exponential I Chi ka and + + + align:start position:0% +combination of exponential I Chi ka and +the explanation - I take a a basically I + + align:start position:0% +the explanation - I take a a basically I + + + align:start position:0% +the explanation - I take a a basically I +have alpha exponential I K a plus beta + + align:start position:0% +have alpha exponential I K a plus beta + + + align:start position:0% +have alpha exponential I K a plus beta +exponential minus I theta + + align:start position:0% + + + + align:start position:0% + +okay and I would like to determine what + + align:start position:0% +okay and I would like to determine what + + + align:start position:0% +okay and I would like to determine what +is actually Appa and the beta which + + align:start position:0% +is actually Appa and the beta which + + + align:start position:0% +is actually Appa and the beta which +actually satisfies this boundary + + align:start position:0% +actually satisfies this boundary + + + align:start position:0% +actually satisfies this boundary +condition one and two okay so now I can + + align:start position:0% +condition one and two okay so now I can + + + align:start position:0% +condition one and two okay so now I can +use the first boundary condition y 0 + + align:start position:0% +use the first boundary condition y 0 + + + align:start position:0% +use the first boundary condition y 0 +equal to 0 right so sotae equal to 0 + + align:start position:0% +equal to 0 right so sotae equal to 0 + + + align:start position:0% +equal to 0 right so sotae equal to 0 +therefore PCD what i get is when j is + + align:start position:0% +therefore PCD what i get is when j is + + + align:start position:0% +therefore PCD what i get is when j is +equal to 0 then this is actually 1 and + + align:start position:0% +equal to 0 then this is actually 1 and + + + align:start position:0% +equal to 0 then this is actually 1 and +this is actually 1 right so and this is + + align:start position:0% +this is actually 1 right so and this is + + + align:start position:0% +this is actually 1 right so and this is +it + + align:start position:0% +it + + + align:start position:0% +it +this is should give you y at y 0 equal + + align:start position:0% +this is should give you y at y 0 equal + + + align:start position:0% +this is should give you y at y 0 equal +to 0 if y 0 is equal to 0 at all time no + + align:start position:0% +to 0 if y 0 is equal to 0 at all time no + + + align:start position:0% +to 0 if y 0 is equal to 0 at all time no +matter what t as you keep it to this + + align:start position:0% +matter what t as you keep it to this + + + align:start position:0% +matter what t as you keep it to this +system the basically you have alpha plus + + align:start position:0% +system the basically you have alpha plus + + + align:start position:0% +system the basically you have alpha plus +beta equal to 0 right because k is equal + + align:start position:0% +beta equal to 0 right because k is equal + + + align:start position:0% +beta equal to 0 right because k is equal +to 0 so you have a purpose beta and that + + align:start position:0% +to 0 so you have a purpose beta and that + + + align:start position:0% +to 0 so you have a purpose beta and that +has to be equal to 0 therefore you can + + align:start position:0% +has to be equal to 0 therefore you can + + + align:start position:0% +has to be equal to 0 therefore you can +conclude that alpha is equal to minus + + align:start position:0% +conclude that alpha is equal to minus + + + align:start position:0% +conclude that alpha is equal to minus +beta and if we use the second boundary + + align:start position:0% +beta and if we use the second boundary + + + align:start position:0% +beta and if we use the second boundary +condition Y and plus 1 equal to 0 + + align:start position:0% +condition Y and plus 1 equal to 0 + + + align:start position:0% +condition Y and plus 1 equal to 0 +because I know this mass and fix that so + + align:start position:0% +because I know this mass and fix that so + + + align:start position:0% +because I know this mass and fix that so +that you cannot move then basically what + + align:start position:0% +that you cannot move then basically what + + + align:start position:0% +that you cannot move then basically what +you get is by a path 1 + + align:start position:0% +you get is by a path 1 + + + align:start position:0% +you get is by a path 1 +equal to zero then basically you have + + align:start position:0% +equal to zero then basically you have + + + align:start position:0% +equal to zero then basically you have +alpha exponential I and press 1 ka + so + + align:start position:0% +alpha exponential I and press 1 ka + so + + + align:start position:0% +alpha exponential I and press 1 ka + so +okay so so beta is u equal to minus + + align:start position:0% +okay so so beta is u equal to minus + + + align:start position:0% +okay so so beta is u equal to minus +alpha right so basically you can get + + align:start position:0% + + + + align:start position:0% + +yeah so so so basically you can get + + align:start position:0% +yeah so so so basically you can get + + + align:start position:0% +yeah so so so basically you can get +minus exponential minus I plus 1 ka + + align:start position:0% +minus exponential minus I plus 1 ka + + + align:start position:0% +minus exponential minus I plus 1 ka +right multiplied by alpha and that is + + align:start position:0% +right multiplied by alpha and that is + + + align:start position:0% +right multiplied by alpha and that is +actually equal to zero now we have the + + align:start position:0% +actually equal to zero now we have the + + + align:start position:0% +actually equal to zero now we have the +choice we can actually set alpha to be + + align:start position:0% +choice we can actually set alpha to be + + + align:start position:0% +choice we can actually set alpha to be +equal to zero but if I set up a to be + + align:start position:0% +equal to zero but if I set up a to be + + + align:start position:0% +equal to zero but if I set up a to be +equal to zero then beta is also 0 then I + + align:start position:0% +equal to zero then beta is also 0 then I + + + align:start position:0% +equal to zero then beta is also 0 then I +have zero everywhere right then there's + + align:start position:0% +have zero everywhere right then there's + + + align:start position:0% +have zero everywhere right then there's +no oscillation and that's not fun right + + align:start position:0% +no oscillation and that's not fun right + + + align:start position:0% +no oscillation and that's not fun right +okay therefore what I am going to set is + + align:start position:0% +okay therefore what I am going to set is + + + align:start position:0% +okay therefore what I am going to set is +actually the second turn equal to zero + + align:start position:0% +actually the second turn equal to zero + + + align:start position:0% +actually the second turn equal to zero +ok the second turn I can actually + + align:start position:0% +ok the second turn I can actually + + + align:start position:0% +ok the second turn I can actually +simplify that to be a 2 I sign first 1 + + align:start position:0% +simplify that to be a 2 I sign first 1 + + + align:start position:0% +simplify that to be a 2 I sign first 1 +ka and not AC actually equal to 0 okay + + align:start position:0% +ka and not AC actually equal to 0 okay + + + align:start position:0% +ka and not AC actually equal to 0 okay +what is actually the condition of this + + align:start position:0% +what is actually the condition of this + + + align:start position:0% +what is actually the condition of this +thing equal to 0 basically impossible + + align:start position:0% +thing equal to 0 basically impossible + + + align:start position:0% +thing equal to 0 basically impossible +initially a given number a stage with + + align:start position:0% +initially a given number a stage with + + + align:start position:0% +initially a given number a stage with +the distance between those masses + + align:start position:0% +the distance between those masses + + + align:start position:0% +the distance between those masses +therefore what I can actually change is + + align:start position:0% +therefore what I can actually change is + + + align:start position:0% +therefore what I can actually change is +the K value right so I can now solve + + align:start position:0% +the K value right so I can now solve + + + align:start position:0% +the K value right so I can now solve +this condition and I will conclude RK + + align:start position:0% +this condition and I will conclude RK + + + align:start position:0% +this condition and I will conclude RK +will have to be equal to n times pi + + align:start position:0% +will have to be equal to n times pi + + + align:start position:0% +will have to be equal to n times pi +divided by plus 1 I hope you can see it + + align:start position:0% +divided by plus 1 I hope you can see it + + + align:start position:0% +divided by plus 1 I hope you can see it +where small n is equal to 1 2 3 + + align:start position:0% +where small n is equal to 1 2 3 + + + align:start position:0% +where small n is equal to 1 2 3 +until capital + + align:start position:0% + + + + align:start position:0% + +so what does that mean + + align:start position:0% +so what does that mean + + + align:start position:0% +so what does that mean +this means that okay originally before I + + align:start position:0% +this means that okay originally before I + + + align:start position:0% +this means that okay originally before I +introduced the boundary condition this + + align:start position:0% +introduced the boundary condition this + + + align:start position:0% +introduced the boundary condition this +system is infinitely long okay and it + + align:start position:0% +system is infinitely long okay and it + + + align:start position:0% +system is infinitely long okay and it +has infinite number of normal modes + + align:start position:0% +has infinite number of normal modes + + + align:start position:0% +has infinite number of normal modes +right but once I introduced these + + align:start position:0% +right but once I introduced these + + + align:start position:0% +right but once I introduced these +boundary conditions which I actually did + + align:start position:0% +boundary conditions which I actually did + + + align:start position:0% +boundary conditions which I actually did +require y 0 equal to 0 because I fixed + + align:start position:0% +require y 0 equal to 0 because I fixed + + + align:start position:0% +require y 0 equal to 0 because I fixed +this point on the wall yn plus 1 equal + + align:start position:0% +this point on the wall yn plus 1 equal + + + align:start position:0% +this point on the wall yn plus 1 equal +to 0 because I picked also that point on + + align:start position:0% +to 0 because I picked also that point on + + + align:start position:0% +to 0 because I picked also that point on +the wall something really happened that + + align:start position:0% +the wall something really happened that + + + align:start position:0% +the wall something really happened that +actually give us first the the shape of + + align:start position:0% +actually give us first the the shape of + + + align:start position:0% +actually give us first the the shape of +the system when it is actually in normal + + align:start position:0% +the system when it is actually in normal + + + align:start position:0% +the system when it is actually in normal +mode basically the shape what I mean + + align:start position:0% +mode basically the shape what I mean + + + align:start position:0% +mode basically the shape what I mean +here is the amplitude as a function of T + + align:start position:0% +here is the amplitude as a function of T + + + align:start position:0% +here is the amplitude as a function of T +ok that's actually what I mean by shape + + align:start position:0% +ok that's actually what I mean by shape + + + align:start position:0% +ok that's actually what I mean by shape +okay the shape is now like a sine + + align:start position:0% +okay the shape is now like a sine + + + align:start position:0% +okay the shape is now like a sine +function that's the first thing which we + + align:start position:0% +function that's the first thing which we + + + align:start position:0% +function that's the first thing which we +get from here the second thing which + + align:start position:0% +get from here the second thing which + + + align:start position:0% +get from here the second thing which +I've kept which we get here is that now + + align:start position:0% +I've kept which we get here is that now + + + align:start position:0% +I've kept which we get here is that now +the K values are not arbitrary anymore + + align:start position:0% +the K values are not arbitrary anymore + + + align:start position:0% +the K values are not arbitrary anymore +the K values is equal to n pi over n + + align:start position:0% +the K values is equal to n pi over n + + + align:start position:0% +the K values is equal to n pi over n +plus 1 and the unvalued small n is + + align:start position:0% +plus 1 and the unvalued small n is + + + align:start position:0% +plus 1 and the unvalued small n is +actually equal to 4 1 2 or 3 and tol so + + align:start position:0% +actually equal to 4 1 2 or 3 and tol so + + + align:start position:0% +actually equal to 4 1 2 or 3 and tol so +now once you as we fix this pool point + + align:start position:0% +now once you as we fix this pool point + + + align:start position:0% +now once you as we fix this pool point +you actually have only how many normal + + align:start position:0% +you actually have only how many normal + + + align:start position:0% +you actually have only how many normal +modes and normal modes right so so what + + align:start position:0% +modes and normal modes right so so what + + + align:start position:0% +modes and normal modes right so so what +I want to tell you is that ok in general + + align:start position:0% +I want to tell you is that ok in general + + + align:start position:0% +I want to tell you is that ok in general +this sinusoidal shape is actually fixed + + align:start position:0% +this sinusoidal shape is actually fixed + + + align:start position:0% +this sinusoidal shape is actually fixed +already by this translation symmetry + + align:start position:0% +already by this translation symmetry + + + align:start position:0% +already by this translation symmetry +argument ok and and once we now pose a + + align:start position:0% +argument ok and and once we now pose a + + + align:start position:0% +argument ok and and once we now pose a +side as we also restrict ourselves to + + align:start position:0% +side as we also restrict ourselves to + + + align:start position:0% +side as we also restrict ourselves to +the discussion of only a few case + + align:start position:0% +the discussion of only a few case + + + align:start position:0% +the discussion of only a few case +which actually satisfy the boundary + + align:start position:0% +which actually satisfy the boundary + + + align:start position:0% +which actually satisfy the boundary +conditions and if I prat all those + + align:start position:0% +conditions and if I prat all those + + + align:start position:0% +conditions and if I prat all those +normal modes as a functional I basically + + align:start position:0% +normal modes as a functional I basically + + + align:start position:0% +normal modes as a functional I basically +what we you can see from here you can + + align:start position:0% +what we you can see from here you can + + + align:start position:0% +what we you can see from here you can +see if I have an equal to 1 and capital + + align:start position:0% +see if I have an equal to 1 and capital + + + align:start position:0% +see if I have an equal to 1 and capital +urn equal to 4 in this case + + align:start position:0% +urn equal to 4 in this case + + + align:start position:0% +urn equal to 4 in this case +okay so I have 4 basically I have I'm + + align:start position:0% +okay so I have 4 basically I have I'm + + + align:start position:0% +okay so I have 4 basically I have I'm +going to have 4 normal modes the first + + align:start position:0% +going to have 4 normal modes the first + + + align:start position:0% +going to have 4 normal modes the first +one will be like a really long + + align:start position:0% +one will be like a really long + + + align:start position:0% +one will be like a really long +wavelength one when n is equal to 1 and + + align:start position:0% +wavelength one when n is equal to 1 and + + + align:start position:0% +wavelength one when n is equal to 1 and +if I increase the small n value so that + + align:start position:0% +if I increase the small n value so that + + + align:start position:0% +if I increase the small n value so that +the K becomes bigger then you can see + + align:start position:0% +the K becomes bigger then you can see + + + align:start position:0% +the K becomes bigger then you can see +that there are more distortion when this + + align:start position:0% +that there are more distortion when this + + + align:start position:0% +that there are more distortion when this +system is in one of the noble mo and the + + align:start position:0% +system is in one of the noble mo and the + + + align:start position:0% +system is in one of the noble mo and the +decide should be going to the district + + align:start position:0% +decide should be going to the district + + + align:start position:0% +decide should be going to the district +is actually going to be oscillating up + + align:start position:0% +is actually going to be oscillating up + + + align:start position:0% +is actually going to be oscillating up +and down instead of okay so all those + + align:start position:0% +and down instead of okay so all those + + + align:start position:0% +and down instead of okay so all those +points are only moving up and down right + + align:start position:0% +points are only moving up and down right + + + align:start position:0% +points are only moving up and down right +just a reminder ok and and why why we + + align:start position:0% +just a reminder ok and and why why we + + + align:start position:0% +just a reminder ok and and why why we +have all those cases because of the + + align:start position:0% +have all those cases because of the + + + align:start position:0% +have all those cases because of the +boundary conditions ok any questions ok + + align:start position:0% +boundary conditions ok any questions ok + + + align:start position:0% +boundary conditions ok any questions ok +so I have several other cases which is + + align:start position:0% +so I have several other cases which is + + + align:start position:0% +so I have several other cases which is +open n and the closed end and also + + align:start position:0% +open n and the closed end and also + + + align:start position:0% +open n and the closed end and also +treatment coupled oscillator examples + + align:start position:0% +treatment coupled oscillator examples + + + align:start position:0% +treatment coupled oscillator examples +also in the lecture notes but + + align:start position:0% +also in the lecture notes but + + + align:start position:0% +also in the lecture notes but +unfortunately we will not be able to go + + align:start position:0% +unfortunately we will not be able to go + + + align:start position:0% +unfortunately we will not be able to go +over them but I think they are very + + align:start position:0% +over them but I think they are very + + + align:start position:0% +over them but I think they are very +detailed notes in the lecture notes ok + + align:start position:0% +detailed notes in the lecture notes ok + + + align:start position:0% +detailed notes in the lecture notes ok +so let me before I move on to a + + align:start position:0% +so let me before I move on to a + + + align:start position:0% +so let me before I move on to a +discussion of continuous system ok I + + align:start position:0% +discussion of continuous system ok I + + + align:start position:0% +discussion of continuous system ok I +would like to discuss with you what we + + align:start position:0% +would like to discuss with you what we + + + align:start position:0% +would like to discuss with you what we +have learned so far so what we have + + align:start position:0% +have learned so far so what we have + + + align:start position:0% +have learned so far so what we have +learned is that if I have a symmetry + + align:start position:0% +learned is that if I have a symmetry + + + align:start position:0% +learned is that if I have a symmetry +which is a translational symmetry and + + align:start position:0% +which is a translational symmetry and + + + align:start position:0% +which is a translational symmetry and +press we only limit ourselves in the + + align:start position:0% +press we only limit ourselves in the + + + align:start position:0% +press we only limit ourselves in the +discussion of oscillation ok + + align:start position:0% +discussion of oscillation ok + + + align:start position:0% +discussion of oscillation ok +in other words we do meet the amplitude + + align:start position:0% +in other words we do meet the amplitude + + + align:start position:0% +in other words we do meet the amplitude +so that it doesn't explode at the edge + + align:start position:0% +so that it doesn't explode at the edge + + + align:start position:0% +so that it doesn't explode at the edge +of the universe + + align:start position:0% +of the universe + + + align:start position:0% +of the universe +ok and that will give you a beta value + + align:start position:0% +ok and that will give you a beta value + + + align:start position:0% +ok and that will give you a beta value +which is in the functional form of + + align:start position:0% +which is in the functional form of + + + align:start position:0% +which is in the functional form of +Bonilla like a a X and equation motion + + align:start position:0% +Bonilla like a a X and equation motion + + + align:start position:0% +Bonilla like a a X and equation motion +can be derived from force diagram once + + align:start position:0% +can be derived from force diagram once + + + align:start position:0% +can be derived from force diagram once +way we entry derive the equation of + + align:start position:0% +way we entry derive the equation of + + + align:start position:0% +way we entry derive the equation of +motion we can get em s1 care matrix then + + align:start position:0% +motion we can get em s1 care matrix then + + + align:start position:0% +motion we can get em s1 care matrix then +we can derive Omega Square from this + + align:start position:0% +we can derive Omega Square from this + + + align:start position:0% +we can derive Omega Square from this +expression and finally we actually can + + align:start position:0% +expression and finally we actually can + + + align:start position:0% +expression and finally we actually can +simplify everything and get the + + align:start position:0% +simplify everything and get the + + + align:start position:0% +simplify everything and get the +dispersion relation Omega equal to Omega + + align:start position:0% +dispersion relation Omega equal to Omega + + + align:start position:0% +dispersion relation Omega equal to Omega +K which is a function of K the wave + + align:start position:0% +K which is a function of K the wave + + + align:start position:0% +K which is a function of K the wave +number before we actually introduce + + align:start position:0% +number before we actually introduce + + + align:start position:0% +number before we actually introduce +boundary condition to go from infinite + + align:start position:0% +boundary condition to go from infinite + + + align:start position:0% +boundary condition to go from infinite +long system to a finite system all the K + + align:start position:0% +long system to a finite system all the K + + + align:start position:0% +long system to a finite system all the K +values are allowed once you introduce + + align:start position:0% +values are allowed once you introduce + + + align:start position:0% +values are allowed once you introduce +boundary condition you will find that + + align:start position:0% +boundary condition you will find that + + + align:start position:0% +boundary condition you will find that +you only have limited number of normal + + align:start position:0% +you only have limited number of normal + + + align:start position:0% +you only have limited number of normal +modes second the K value now not + + align:start position:0% +modes second the K value now not + + + align:start position:0% +modes second the K value now not +continuous any value any more it becomes + + align:start position:0% +continuous any value any more it becomes + + + align:start position:0% +continuous any value any more it becomes +discrete and only M values are allowed + + align:start position:0% +discrete and only M values are allowed + + + align:start position:0% +discrete and only M values are allowed +from this exercise and finally what is + + align:start position:0% +from this exercise and finally what is + + + align:start position:0% +from this exercise and finally what is +actually the most general solution is as + + align:start position:0% +actually the most general solution is as + + + align:start position:0% +actually the most general solution is as +a linear combination of all those normal + + align:start position:0% +a linear combination of all those normal + + + align:start position:0% +a linear combination of all those normal +modes which we show here and and what is + + align:start position:0% +modes which we show here and and what is + + + align:start position:0% +modes which we show here and and what is +actually ratio meeting all those normal + + align:start position:0% +actually ratio meeting all those normal + + + align:start position:0% +actually ratio meeting all those normal +modes all those free coefficients are + + align:start position:0% +modes all those free coefficients are + + + align:start position:0% +modes all those free coefficients are +determined by initial conditions if you + + align:start position:0% +determined by initial conditions if you + + + align:start position:0% +determined by initial conditions if you +are given okay so that's issue what we + + align:start position:0% +are given okay so that's issue what we + + + align:start position:0% +are given okay so that's issue what we +have learned so far + + align:start position:0% + + + + align:start position:0% + +and now I would like to make a leap of + + align:start position:0% +and now I would like to make a leap of + + + align:start position:0% +and now I would like to make a leap of +faith to see how happen okay what we are + + align:start position:0% +faith to see how happen okay what we are + + + align:start position:0% +faith to see how happen okay what we are +we going to do is to introduce you a + + align:start position:0% +we going to do is to introduce you a + + + align:start position:0% +we going to do is to introduce you a +continuous infinite number of coupled + + align:start position:0% +continuous infinite number of coupled + + + align:start position:0% +continuous infinite number of coupled +oscillator okay so what does I mean what + + align:start position:0% +oscillator okay so what does I mean what + + + align:start position:0% +oscillator okay so what does I mean what +I'm going to do is to go from this so I + + align:start position:0% +I'm going to do is to go from this so I + + + align:start position:0% +I'm going to do is to go from this so I +have P and the 80 a lot of a string and + + align:start position:0% +have P and the 80 a lot of a string and + + + align:start position:0% +have P and the 80 a lot of a string and +mass system as a try etcetera I would + + align:start position:0% +mass system as a try etcetera I would + + + align:start position:0% +mass system as a try etcetera I would +like to go from there to just infinitely + + align:start position:0% +like to go from there to just infinitely + + + align:start position:0% +like to go from there to just infinitely +long spring including long string with + + align:start position:0% +long spring including long string with + + + align:start position:0% +long spring including long string with +string tension T and in the some some + + align:start position:0% +string tension T and in the some some + + + align:start position:0% +string tension T and in the some some +time though mass density of mass okay we + + align:start position:0% +time though mass density of mass okay we + + + align:start position:0% +time though mass density of mass okay we +like to make it continuous you see what + + align:start position:0% +like to make it continuous you see what + + + align:start position:0% +like to make it continuous you see what +would happen + + align:start position:0% +would happen + + + align:start position:0% +would happen +okay so just a reminder of the taste + + align:start position:0% +okay so just a reminder of the taste + + + align:start position:0% +okay so just a reminder of the taste +turn of the mm minus 1 matrix operation + + align:start position:0% +turn of the mm minus 1 matrix operation + + + align:start position:0% +turn of the mm minus 1 matrix operation +basically we have MS 1 K times a ok at a + + align:start position:0% +basically we have MS 1 K times a ok at a + + + align:start position:0% +basically we have MS 1 K times a ok at a +stern of MS 1 K 8 that is as you given + + align:start position:0% +stern of MS 1 K 8 that is as you given + + + align:start position:0% +stern of MS 1 K 8 that is as you given +by Omega square a day this is equal to P + + align:start position:0% +by Omega square a day this is equal to P + + + align:start position:0% +by Omega square a day this is equal to P +over m a - AJ minus 1 plus 2 AJ - is it + + align:start position:0% +over m a - AJ minus 1 plus 2 AJ - is it + + + align:start position:0% +over m a - AJ minus 1 plus 2 AJ - is it +possible ok so this is H is just a copy + + align:start position:0% +possible ok so this is H is just a copy + + + align:start position:0% +possible ok so this is H is just a copy +of that formula here ok so if I make it + + align:start position:0% +of that formula here ok so if I make it + + + align:start position:0% +of that formula here ok so if I make it +continuous + + align:start position:0% +continuous + + + align:start position:0% +continuous +ok ok so that means what angle do get is + + align:start position:0% +ok ok so that means what angle do get is + + + align:start position:0% +ok ok so that means what angle do get is +omega square a but evaluated at position + + align:start position:0% +omega square a but evaluated at position + + + align:start position:0% +omega square a but evaluated at position +X where X is actually equal to say times + + align:start position:0% +X where X is actually equal to say times + + + align:start position:0% +X where X is actually equal to say times +F ok + + align:start position:0% +F ok + + + align:start position:0% +F ok +and this will be equal to P over MA - a + + align:start position:0% +and this will be equal to P over MA - a + + + align:start position:0% +and this will be equal to P over MA - a +evaluated at X minus a plus 2a X minus a + + align:start position:0% +evaluated at X minus a plus 2a X minus a + + + align:start position:0% +evaluated at X minus a plus 2a X minus a +X plus a now I'm going to make this a + + align:start position:0% +X plus a now I'm going to make this a + + + align:start position:0% +X plus a now I'm going to make this a +very very small right so that when I + + align:start position:0% +very very small right so that when I + + + align:start position:0% +very very small right so that when I +make a very very small then it become a + + align:start position:0% +make a very very small then it become a + + + align:start position:0% +make a very very small then it become a +very continuous system okay so what I'm + + align:start position:0% +very continuous system okay so what I'm + + + align:start position:0% +very continuous system okay so what I'm +going to do is I can now make a goes to + + align:start position:0% +going to do is I can now make a goes to + + + align:start position:0% +going to do is I can now make a goes to +zero I can now use Tyler's series F X + + align:start position:0% +zero I can now use Tyler's series F X + + + align:start position:0% +zero I can now use Tyler's series F X +plus a FX plus Delta X and just a + + align:start position:0% +plus a FX plus Delta X and just a + + + align:start position:0% +plus a FX plus Delta X and just a +reminder if you do a Taylor expansion of + + align:start position:0% +reminder if you do a Taylor expansion of + + + align:start position:0% +reminder if you do a Taylor expansion of +this you are going to get f of X plus + + align:start position:0% +this you are going to get f of X plus + + + align:start position:0% +this you are going to get f of X plus +Delta X from X plus 1 over 2 factorial + + align:start position:0% +Delta X from X plus 1 over 2 factorial + + + align:start position:0% +Delta X from X plus 1 over 2 factorial +Delta x squared F double prime X okay so + + align:start position:0% +Delta x squared F double prime X okay so + + + align:start position:0% +Delta x squared F double prime X okay so +that means now I can add you to a Taylor + + align:start position:0% +that means now I can add you to a Taylor + + + align:start position:0% +that means now I can add you to a Taylor +expansion of a X minus a and a express a + + align:start position:0% +expansion of a X minus a and a express a + + + align:start position:0% +expansion of a X minus a and a express a +so what I'm going to get it's like this + + align:start position:0% +so what I'm going to get it's like this + + + align:start position:0% +so what I'm going to get it's like this +so a X minus a copic on a of X minus a a + + align:start position:0% +so a X minus a copic on a of X minus a a + + + align:start position:0% +so a X minus a copic on a of X minus a a +prime X plus 1 over 2 a squared a couple + + align:start position:0% +prime X plus 1 over 2 a squared a couple + + + align:start position:0% +prime X plus 1 over 2 a squared a couple +projects + + align:start position:0% + + + + align:start position:0% + +I can also to the same thing to do it + + align:start position:0% +I can also to the same thing to do it + + + align:start position:0% +I can also to the same thing to do it +either expansion for a express a a + + align:start position:0% +either expansion for a express a a + + + align:start position:0% +either expansion for a express a a +express a will be equal to a of X plus a + + align:start position:0% +express a will be equal to a of X plus a + + + align:start position:0% +express a will be equal to a of X plus a +a prong X plus 1 over 2 a square a + + align:start position:0% +a prong X plus 1 over 2 a square a + + + align:start position:0% +a prong X plus 1 over 2 a square a +double prime X ok once I have done this + + align:start position:0% +double prime X ok once I have done this + + + align:start position:0% +double prime X ok once I have done this +basically I can calculate minus a X + + align:start position:0% +basically I can calculate minus a X + + + align:start position:0% +basically I can calculate minus a X +minus a plus 2 a of X minus a express a + + align:start position:0% +minus a plus 2 a of X minus a express a + + + align:start position:0% +minus a plus 2 a of X minus a express a +ok I'm just taking the meter turn and + + align:start position:0% +ok I'm just taking the meter turn and + + + align:start position:0% +ok I'm just taking the meter turn and +copy it yeah okay if I if I use now this + + align:start position:0% +copy it yeah okay if I if I use now this + + + align:start position:0% +copy it yeah okay if I if I use now this +expression okay then basically I will + + align:start position:0% +expression okay then basically I will + + + align:start position:0% +expression okay then basically I will +see that okay + + align:start position:0% +see that okay + + + align:start position:0% +see that okay +a of X turns as you cancel right because + + align:start position:0% +a of X turns as you cancel right because + + + align:start position:0% +a of X turns as you cancel right because +I have 2 a of X from this to turn and + + align:start position:0% +I have 2 a of X from this to turn and + + + align:start position:0% +I have 2 a of X from this to turn and +they cancel with these two a X okay and + + align:start position:0% +they cancel with these two a X okay and + + + align:start position:0% +they cancel with these two a X okay and +also a prong turned also cancel right + + align:start position:0% +also a prong turned also cancel right + + + align:start position:0% +also a prong turned also cancel right +because you have M X minus 1 and a + + align:start position:0% +because you have M X minus 1 and a + + + align:start position:0% +because you have M X minus 1 and a +express one a X minus a and a express a + + align:start position:0% +express one a X minus a and a express a + + + align:start position:0% +express one a X minus a and a express a +therefore the X front and cancel here + + align:start position:0% +therefore the X front and cancel here + + + align:start position:0% +therefore the X front and cancel here +this is minus sign this is processing + + align:start position:0% +this is minus sign this is processing + + + align:start position:0% +this is minus sign this is processing +you see + + align:start position:0% +you see + + + align:start position:0% +you see +so therefore what essentially lap over + + align:start position:0% +so therefore what essentially lap over + + + align:start position:0% +so therefore what essentially lap over +is all those turns this is going to give + + align:start position:0% +is all those turns this is going to give + + + align:start position:0% +is all those turns this is going to give +you a double prime x squared plus many + + align:start position:0% +you a double prime x squared plus many + + + align:start position:0% +you a double prime x squared plus many +other higher order turns right because + + align:start position:0% +other higher order turns right because + + + align:start position:0% +other higher order turns right because +those are actually not country we have + + align:start position:0% +those are actually not country we have + + + align:start position:0% +those are actually not country we have +many many higher order terms okay in the + + align:start position:0% +many many higher order terms okay in the + + + align:start position:0% +many many higher order terms okay in the +limit of X go to there + + align:start position:0% +limit of X go to there + + + align:start position:0% +limit of X go to there +yes yeah oh yeah all right thank you + + align:start position:0% +yes yeah oh yeah all right thank you + + + align:start position:0% +yes yeah oh yeah all right thank you +very much okay thank you for that so + + align:start position:0% +very much okay thank you for that so + + + align:start position:0% +very much okay thank you for that so +there should be a minus sign in front of + + align:start position:0% +there should be a minus sign in front of + + + align:start position:0% +there should be a minus sign in front of +it okay so basically what we have is a + + align:start position:0% +it okay so basically what we have is a + + + align:start position:0% +it okay so basically what we have is a +double prime x times a square plus some + + align:start position:0% +double prime x times a square plus some + + + align:start position:0% +double prime x times a square plus some +higher order turn up a cube is a choice + + align:start position:0% +higher order turn up a cube is a choice + + + align:start position:0% +higher order turn up a cube is a choice +it's okay since we are talking about the + + align:start position:0% +it's okay since we are talking about the + + + align:start position:0% +it's okay since we are talking about the +limit of a goes to zero we can safely + + align:start position:0% +limit of a goes to zero we can safely + + + align:start position:0% +limit of a goes to zero we can safely +ignore all the higher order terms okay + + align:start position:0% +ignore all the higher order terms okay + + + align:start position:0% +ignore all the higher order terms okay +so now if we go back to this equation + + align:start position:0% + + + + align:start position:0% + +Omega square a will become basically T + + align:start position:0% +Omega square a will become basically T + + + align:start position:0% +Omega square a will become basically T +over N minus T over N a a double power x + + align:start position:0% +over N minus T over N a a double power x + + + align:start position:0% +over N minus T over N a a double power x +times a screw okay + + align:start position:0% +times a screw okay + + + align:start position:0% +times a screw okay +and the price some higher order terms + + align:start position:0% +and the price some higher order terms + + + align:start position:0% +and the price some higher order terms +okay now I can define Rho L to be equal + + align:start position:0% +okay now I can define Rho L to be equal + + + align:start position:0% +okay now I can define Rho L to be equal +to n divided by a okay and I will never + + align:start position:0% +to n divided by a okay and I will never + + + align:start position:0% +to n divided by a okay and I will never +have to be very careful when I go to the + + align:start position:0% +have to be very careful when I go to the + + + align:start position:0% +have to be very careful when I go to the +continuous limit okay + + align:start position:0% +continuous limit okay + + + align:start position:0% +continuous limit okay +I also do not want to make this system + + align:start position:0% +I also do not want to make this system + + + align:start position:0% +I also do not want to make this system +infinitely massive right therefore I + + align:start position:0% +infinitely massive right therefore I + + + align:start position:0% +infinitely massive right therefore I +would like to fix the Rowell when I go + + align:start position:0% +would like to fix the Rowell when I go + + + align:start position:0% +would like to fix the Rowell when I go +to the continuous limit so so basically + + align:start position:0% +to the continuous limit so so basically + + + align:start position:0% +to the continuous limit so so basically +what I am doing is that I cut this + + align:start position:0% +what I am doing is that I cut this + + + align:start position:0% +what I am doing is that I cut this +system in half so that a pecan smolder + + align:start position:0% +system in half so that a pecan smolder + + + align:start position:0% +system in half so that a pecan smolder +and the mass also becomes smoother so + + align:start position:0% +and the mass also becomes smoother so + + + align:start position:0% +and the mass also becomes smoother so +that Rho L stay as a constant okay when + + align:start position:0% +that Rho L stay as a constant okay when + + + align:start position:0% +that Rho L stay as a constant okay when +I go to continuously okay so what I am + + align:start position:0% +I go to continuously okay so what I am + + + align:start position:0% +I go to continuously okay so what I am +going to get is omega squared a will be + + align:start position:0% +going to get is omega squared a will be + + + align:start position:0% +going to get is omega squared a will be +equal to minus T over Rho L + + align:start position:0% +equal to minus T over Rho L + + + align:start position:0% +equal to minus T over Rho L +a double prime X and to write it + + align:start position:0% +a double prime X and to write it + + + align:start position:0% +a double prime X and to write it +explicitly this is actually equal to + + align:start position:0% +explicitly this is actually equal to + + + align:start position:0% +explicitly this is actually equal to +minus T over Rho L I just square a + + align:start position:0% +minus T over Rho L I just square a + + + align:start position:0% +minus T over Rho L I just square a +partial x squared okay because each + + align:start position:0% +partial x squared okay because each + + + align:start position:0% +partial x squared okay because each +prong is actually a differentiation + + align:start position:0% +prong is actually a differentiation + + + align:start position:0% +prong is actually a differentiation +which is fed to X right okay + + align:start position:0% +which is fed to X right okay + + + align:start position:0% +which is fed to X right okay +don't forget what is issue at this this + + align:start position:0% +don't forget what is issue at this this + + + align:start position:0% +don't forget what is issue at this this +is actually M minus 1 okay a write equal + + align:start position:0% +is actually M minus 1 okay a write equal + + + align:start position:0% +is actually M minus 1 okay a write equal +to Omega squared and that essentially + + align:start position:0% +to Omega squared and that essentially + + + align:start position:0% +to Omega squared and that essentially +just partial squared X partial squared a + + align:start position:0% +just partial squared X partial squared a + + + align:start position:0% +just partial squared X partial squared a +partial T squared right because this is + + align:start position:0% +partial T squared right because this is + + + align:start position:0% +partial T squared right because this is +actually M minus 1 K matrix is actually + + align:start position:0% +actually M minus 1 K matrix is actually + + + align:start position:0% +actually M minus 1 K matrix is actually +originally going back to the original + + align:start position:0% +originally going back to the original + + + align:start position:0% +originally going back to the original +equation we are actually solving an X + + align:start position:0% +equation we are actually solving an X + + + align:start position:0% +equation we are actually solving an X +double dot minus equal to minus KX + + align:start position:0% +double dot minus equal to minus KX + + + align:start position:0% +double dot minus equal to minus KX +poppin right so there should be a minus + + align:start position:0% +poppin right so there should be a minus + + + align:start position:0% +poppin right so there should be a minus +sign there as well right so M and X + + align:start position:0% +sign there as well right so M and X + + + align:start position:0% +sign there as well right so M and X +double dot equal to minus K X therefore + + align:start position:0% +double dot equal to minus K X therefore + + + align:start position:0% +double dot equal to minus K X therefore +X double dot will be equal to minus M + + align:start position:0% +X double dot will be equal to minus M + + + align:start position:0% +X double dot will be equal to minus M +minus 1 K X right so minus M minus 1 K + + align:start position:0% +minus 1 K X right so minus M minus 1 K + + + align:start position:0% +minus 1 K X right so minus M minus 1 K +matrix will be equal to X double dot + + align:start position:0% +matrix will be equal to X double dot + + + align:start position:0% +matrix will be equal to X double dot +right therefore what this is X double + + align:start position:0% +right therefore what this is X double + + + align:start position:0% +right therefore what this is X double +dot is basically in the in the in the + + align:start position:0% +dot is basically in the in the in the + + + align:start position:0% +dot is basically in the in the in the +current presentation it's actually just + + align:start position:0% +current presentation it's actually just + + + align:start position:0% +current presentation it's actually just +passive square a partial T Square okay + + align:start position:0% +passive square a partial T Square okay + + + align:start position:0% +passive square a partial T Square okay +can everybody except this okay so so now + + align:start position:0% +can everybody except this okay so so now + + + align:start position:0% +can everybody except this okay so so now +we have successfully going from a + + align:start position:0% +we have successfully going from a + + + align:start position:0% +we have successfully going from a +discrete system which you have a length + + align:start position:0% +discrete system which you have a length + + + align:start position:0% +discrete system which you have a length +scale of a to continuous system because + + align:start position:0% +scale of a to continuous system because + + + align:start position:0% +scale of a to continuous system because +a goes to 0 but at same time I fix the + + align:start position:0% +a goes to 0 but at same time I fix the + + + align:start position:0% +a goes to 0 but at same time I fix the +ratio of M and a so that the system + + align:start position:0% +ratio of M and a so that the system + + + align:start position:0% +ratio of M and a so that the system +doesn't go to infinity the massive okay + + align:start position:0% +doesn't go to infinity the massive okay + + + align:start position:0% +doesn't go to infinity the massive okay +so if I do this then in short you get + + align:start position:0% +so if I do this then in short you get + + + align:start position:0% +so if I do this then in short you get +this equation partial square a title T + + align:start position:0% +this equation partial square a title T + + + align:start position:0% +this equation partial square a title T +squared + + align:start position:0% +squared + + + align:start position:0% +squared +and that is equal to t over Rho L by 2 + + align:start position:0% +and that is equal to t over Rho L by 2 + + + align:start position:0% +and that is equal to t over Rho L by 2 +square a partial x squared okay I can + + align:start position:0% +square a partial x squared okay I can + + + align:start position:0% +square a partial x squared okay I can +now define V P equal to square root of G + + align:start position:0% +now define V P equal to square root of G + + + align:start position:0% +now define V P equal to square root of G +over L Rho L okay and this will become + + align:start position:0% +over L Rho L okay and this will become + + + align:start position:0% +over L Rho L okay and this will become +VP square partial square a partial x + + align:start position:0% +VP square partial square a partial x + + + align:start position:0% +VP square partial square a partial x +squared what is this this is a what + + align:start position:0% +squared what is this this is a what + + + align:start position:0% +squared what is this this is a what +equation wave equation okay you see that + + align:start position:0% +equation wave equation okay you see that + + + align:start position:0% +equation wave equation okay you see that +now after all the hard work okay + + align:start position:0% +now after all the hard work okay + + + align:start position:0% +now after all the hard work okay +going from infinitely long system I mean + + align:start position:0% +going from infinitely long system I mean + + + align:start position:0% +going from infinitely long system I mean +this quiz is an anchor to a continuous + + align:start position:0% +this quiz is an anchor to a continuous + + + align:start position:0% +this quiz is an anchor to a continuous +limit with this covered wave equation + + align:start position:0% +limit with this covered wave equation + + + align:start position:0% +limit with this covered wave equation +this is probably the most important + + align:start position:0% +this is probably the most important + + + align:start position:0% +this is probably the most important +question equation you actually learn + + align:start position:0% +question equation you actually learn + + + align:start position:0% +question equation you actually learn +until now more important than equal to + + align:start position:0% +until now more important than equal to + + + align:start position:0% +until now more important than equal to +na right because you cannot listen to my + + align:start position:0% +na right because you cannot listen to my + + + align:start position:0% +na right because you cannot listen to my +lecture even if this equation doesn't + + align:start position:0% +lecture even if this equation doesn't + + + align:start position:0% +lecture even if this equation doesn't +exist right thing I cannot propagate a + + align:start position:0% +exist right thing I cannot propagate a + + + align:start position:0% +exist right thing I cannot propagate a +sound wave to you here right and you + + align:start position:0% +sound wave to you here right and you + + + align:start position:0% +sound wave to you here right and you +cannot even see the blackboard because + + align:start position:0% +cannot even see the blackboard because + + + align:start position:0% +cannot even see the blackboard because +the electromagnetic wave which I will + + align:start position:0% +the electromagnetic wave which I will + + + align:start position:0% +the electromagnetic wave which I will +show it in a later lecture also kind of + + align:start position:0% +show it in a later lecture also kind of + + + align:start position:0% +show it in a later lecture also kind of +satisfy the same functional form so I + + align:start position:0% +satisfy the same functional form so I + + + align:start position:0% +satisfy the same functional form so I +think this is an achievement a highlight + + align:start position:0% +think this is an achievement a highlight + + + align:start position:0% +think this is an achievement a highlight +of today's class we actually realize + + align:start position:0% +of today's class we actually realize + + + align:start position:0% +of today's class we actually realize +that what we have been doing is really + + align:start position:0% +that what we have been doing is really + + + align:start position:0% +that what we have been doing is really +solving something related to wave + + align:start position:0% +solving something related to wave + + + align:start position:0% +solving something related to wave +equation and next time which I would + + align:start position:0% +equation and next time which I would + + + align:start position:0% +equation and next time which I would +like to actually discuss with you is the + + align:start position:0% +like to actually discuss with you is the + + + align:start position:0% +like to actually discuss with you is the +solution of all this wave equation so + + align:start position:0% +solution of all this wave equation so + + + align:start position:0% +solution of all this wave equation so +here I have again last time you have + + align:start position:0% +here I have again last time you have + + + align:start position:0% +here I have again last time you have +seen this this is a coupled oscillator + + align:start position:0% +seen this this is a coupled oscillator + + + align:start position:0% +seen this this is a coupled oscillator +system + + align:start position:0% +system + + + align:start position:0% +system +it has 72 components other physicists + + align:start position:0% +it has 72 components other physicists + + + align:start position:0% +it has 72 components other physicists +that's actually equal to infinite number + + align:start position:0% +that's actually equal to infinite number + + + align:start position:0% +that's actually equal to infinite number +of coupled oscillators okay that's good + + align:start position:0% +of coupled oscillators okay that's good + + + align:start position:0% +of coupled oscillators okay that's good +enough and you can see that if I do this + + align:start position:0% + + + + align:start position:0% + +it does something really strange hey you + + align:start position:0% +it does something really strange hey you + + + align:start position:0% +it does something really strange hey you +see a progressing wave going back and + + align:start position:0% +see a progressing wave going back and + + + align:start position:0% +see a progressing wave going back and +forth and it disappeared because of + + align:start position:0% +forth and it disappeared because of + + + align:start position:0% +forth and it disappeared because of +friction okay if I can construct + + align:start position:0% +friction okay if I can construct + + + align:start position:0% +friction okay if I can construct +something closer to a velvet couple + + align:start position:0% +something closer to a velvet couple + + + align:start position:0% +something closer to a velvet couple +system without friction what is going to + + align:start position:0% +system without friction what is going to + + + align:start position:0% +system without friction what is going to +happen is that this wave is going to be + + align:start position:0% +happen is that this wave is going to be + + + align:start position:0% +happen is that this wave is going to be +there bouncing back and forth forever + + align:start position:0% +there bouncing back and forth forever + + + align:start position:0% +there bouncing back and forth forever +and that essentially can be understood + + align:start position:0% +and that essentially can be understood + + + align:start position:0% +and that essentially can be understood +by wave equation and also if I assert a + + align:start position:0% +by wave equation and also if I assert a + + + align:start position:0% +by wave equation and also if I assert a +this system at fixed frequency you will + + align:start position:0% +this system at fixed frequency you will + + + align:start position:0% +this system at fixed frequency you will +see that this began standing waves and + + align:start position:0% +see that this began standing waves and + + + align:start position:0% +see that this began standing waves and +of course I can I can do crazy things + + align:start position:0% +of course I can I can do crazy things + + + align:start position:0% +of course I can I can do crazy things +I can also they and stop it and it + + align:start position:0% +I can also they and stop it and it + + + align:start position:0% +I can also they and stop it and it +becomes really really complicated motion + + align:start position:0% +becomes really really complicated motion + + + align:start position:0% +becomes really really complicated motion +and of course you are welcome to come + + align:start position:0% +and of course you are welcome to come + + + align:start position:0% +and of course you are welcome to come +here and pray up to the class and next + + align:start position:0% +here and pray up to the class and next + + + align:start position:0% +here and pray up to the class and next +time Thursday we are going to talk about + + align:start position:0% +time Thursday we are going to talk about + + + align:start position:0% +time Thursday we are going to talk about +the solution to this equation and how to + + align:start position:0% +the solution to this equation and how to + + + align:start position:0% +the solution to this equation and how to +understand all kinds of fancy motion + + align:start position:0% +understand all kinds of fancy motion + + + align:start position:0% +understand all kinds of fancy motion +this system can do and can do given by + + align:start position:0% +this system can do and can do given by + + + align:start position:0% +this system can do and can do given by +the natural thank you very much \ No newline at end of file diff --git a/JAxRgACOQtA.txt b/JAxRgACOQtA.txt new file mode 100644 index 0000000000000000000000000000000000000000..a70dbe06e81d1f2deea948b901d92c5231a46c76 --- /dev/null +++ b/JAxRgACOQtA.txt @@ -0,0 +1,4803 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +hi in the last unit we introduced the + + align:start position:0% +hi in the last unit we introduced the + + + align:start position:0% +hi in the last unit we introduced the +notion of the structure of vectors in + + align:start position:0% +notion of the structure of vectors in + + + align:start position:0% +notion of the structure of vectors in +terms of arrows in the plane and today + + align:start position:0% +terms of arrows in the plane and today + + + align:start position:0% +terms of arrows in the plane and today +we want to talk about the added + + align:start position:0% +we want to talk about the added + + + align:start position:0% +we want to talk about the added +geometric property of what I could call + + align:start position:0% +geometric property of what I could call + + + align:start position:0% +geometric property of what I could call +three-dimensional vectors or + + align:start position:0% +three-dimensional vectors or + + + align:start position:0% +three-dimensional vectors or +threedimensional arrows now before I say + + align:start position:0% +threedimensional arrows now before I say + + + align:start position:0% +threedimensional arrows now before I say +that I guess I've already said it but + + align:start position:0% +that I guess I've already said it but + + + align:start position:0% +that I guess I've already said it but +before I say any more about it let me + + align:start position:0% +before I say any more about it let me + + + align:start position:0% +before I say any more about it let me +point out of course that this is a + + align:start position:0% +point out of course that this is a + + + align:start position:0% +point out of course that this is a +matter of semantics obviously an narrow + + align:start position:0% +matter of semantics obviously an narrow + + + align:start position:0% +matter of semantics obviously an narrow +being a line has only one dimension be + + align:start position:0% +being a line has only one dimension be + + + align:start position:0% +being a line has only one dimension be +it in the direction of the x- axis be it + + align:start position:0% +it in the direction of the x- axis be it + + + align:start position:0% +it in the direction of the x- axis be it +in the XY plane or be it in + + align:start position:0% +in the XY plane or be it in + + + align:start position:0% +in the XY plane or be it in +three-dimensional space when we say + + align:start position:0% +three-dimensional space when we say + + + align:start position:0% +three-dimensional space when we say +three-dimensional vectors we do not + + align:start position:0% +three-dimensional vectors we do not + + + align:start position:0% +three-dimensional vectors we do not +negate the fact that we're talking about + + align:start position:0% +negate the fact that we're talking about + + + align:start position:0% +negate the fact that we're talking about +arrows but rather that we are dealing + + align:start position:0% +arrows but rather that we are dealing + + + align:start position:0% +arrows but rather that we are dealing +with a coordinate system which takes + + align:start position:0% +with a coordinate system which takes + + + align:start position:0% +with a coordinate system which takes +into consideration the fact that the + + align:start position:0% +into consideration the fact that the + + + align:start position:0% +into consideration the fact that the +line is drawn through three-dimensional + + align:start position:0% +line is drawn through three-dimensional + + + align:start position:0% +line is drawn through three-dimensional +space SP in other words whereas I call + + align:start position:0% +space SP in other words whereas I call + + + align:start position:0% +space SP in other words whereas I call +the lecture three-dimensional vectors or + + align:start position:0% +the lecture three-dimensional vectors or + + + align:start position:0% +the lecture three-dimensional vectors or +arrows and by the way both in the notes + + align:start position:0% +arrows and by the way both in the notes + + + align:start position:0% +arrows and by the way both in the notes +and as I'm lecturing I will very often + + align:start position:0% +and as I'm lecturing I will very often + + + align:start position:0% +and as I'm lecturing I will very often +whenever I write the word Vector put + + align:start position:0% +whenever I write the word Vector put + + + align:start position:0% +whenever I write the word Vector put +arrow in parentheses whenever I write + + align:start position:0% +arrow in parentheses whenever I write + + + align:start position:0% +arrow in parentheses whenever I write +the word Arrow put Vector in parenthesis + + align:start position:0% +the word Arrow put Vector in parenthesis + + + align:start position:0% +the word Arrow put Vector in parenthesis +so you can see the jux position between + + align:start position:0% +so you can see the jux position between + + + align:start position:0% +so you can see the jux position between +these two the geometry versus the + + align:start position:0% +these two the geometry versus the + + + align:start position:0% +these two the geometry versus the +physical our mathematical concept but + + align:start position:0% +physical our mathematical concept but + + + align:start position:0% +physical our mathematical concept but +the idea is something like this in + + align:start position:0% +the idea is something like this in + + + align:start position:0% +the idea is something like this in +three-dimensional space we have a + + align:start position:0% +three-dimensional space we have a + + + align:start position:0% +three-dimensional space we have a +natural extension of cartisian + + align:start position:0% +natural extension of cartisian + + + align:start position:0% +natural extension of cartisian +coordinates rather than talk about the + + align:start position:0% +coordinates rather than talk about the + + + align:start position:0% +coordinates rather than talk about the +XY plane we pick a third axis a third + + align:start position:0% +XY plane we pick a third axis a third + + + align:start position:0% +XY plane we pick a third axis a third +number line which goes through the + + align:start position:0% +number line which goes through the + + + align:start position:0% +number line which goes through the +origin perpendicular to the XY plane and + + align:start position:0% +origin perpendicular to the XY plane and + + + align:start position:0% +origin perpendicular to the XY plane and +which has the sense that if the xaxis is + + align:start position:0% +which has the sense that if the xaxis is + + + align:start position:0% +which has the sense that if the xaxis is +rotated into the Y AIS through the + + align:start position:0% +rotated into the Y AIS through the + + + align:start position:0% +rotated into the Y AIS through the +positive 90° angle here that the z-axis + + align:start position:0% +positive 90° angle here that the z-axis + + + align:start position:0% +positive 90° angle here that the z-axis +is in the direction in which a + + align:start position:0% +is in the direction in which a + + + align:start position:0% +is in the direction in which a +right-handed screw would turn uh I won't + + align:start position:0% +right-handed screw would turn uh I won't + + + align:start position:0% +right-handed screw would turn uh I won't +be labor this it's done very very nicely + + align:start position:0% +be labor this it's done very very nicely + + + align:start position:0% +be labor this it's done very very nicely +in the textbook and I'm sure that you + + align:start position:0% +in the textbook and I'm sure that you + + + align:start position:0% +in the textbook and I'm sure that you +have seen this type of coordinate system + + align:start position:0% +have seen this type of coordinate system + + + align:start position:0% +have seen this type of coordinate system +before if you haven't it's something + + align:start position:0% +before if you haven't it's something + + + align:start position:0% +before if you haven't it's something +that takes a matter of some 20 or 30 + + align:start position:0% +that takes a matter of some 20 or 30 + + + align:start position:0% +that takes a matter of some 20 or 30 +seconds to pick up but at any rate what + + align:start position:0% +seconds to pick up but at any rate what + + + align:start position:0% +seconds to pick up but at any rate what +we're saying is let's imagine this + + align:start position:0% +we're saying is let's imagine this + + + align:start position:0% +we're saying is let's imagine this +threedimensional coordinate system + + align:start position:0% +threedimensional coordinate system + + + align:start position:0% +threedimensional coordinate system +three-dimensional cartisian coordinates + + align:start position:0% +three-dimensional cartisian coordinates + + + align:start position:0% +three-dimensional cartisian coordinates +the convention is that just as in the + + align:start position:0% +the convention is that just as in the + + + align:start position:0% +the convention is that just as in the +plane we labeled the point by its X and + + align:start position:0% +plane we labeled the point by its X and + + + align:start position:0% +plane we labeled the point by its X and +Y components in three space a point is + + align:start position:0% +Y components in three space a point is + + + align:start position:0% +Y components in three space a point is +labeled by its x y Y and Z components so + + align:start position:0% +labeled by its x y Y and Z components so + + + align:start position:0% +labeled by its x y Y and Z components so +for example if I take a vector in three + + align:start position:0% +for example if I take a vector in three + + + align:start position:0% +for example if I take a vector in three +space meaning what it's a line that goes + + align:start position:0% +space meaning what it's a line that goes + + + align:start position:0% +space meaning what it's a line that goes +through three-dimensional space I again + + align:start position:0% +through three-dimensional space I again + + + align:start position:0% +through three-dimensional space I again +shift it parallel to itself so it begins + + align:start position:0% +shift it parallel to itself so it begins + + + align:start position:0% +shift it parallel to itself so it begins +at my origin and at the risk of causing + + align:start position:0% +at my origin and at the risk of causing + + + align:start position:0% +at my origin and at the risk of causing +some confusion here I still think it's + + align:start position:0% +some confusion here I still think it's + + + align:start position:0% +some confusion here I still think it's +worth doing let me call the vector a and + + align:start position:0% +worth doing let me call the vector a and + + + align:start position:0% +worth doing let me call the vector a and +let me call the point at which the + + align:start position:0% +let me call the point at which the + + + align:start position:0% +let me call the point at which the +vector terminates the point a and let's + + align:start position:0% +vector terminates the point a and let's + + + align:start position:0% +vector terminates the point a and let's +suppose that the point a has coordinates + + align:start position:0% +suppose that the point a has coordinates + + + align:start position:0% +suppose that the point a has coordinates +A1 A2 A3 the reason that this doesn't + + align:start position:0% +A1 A2 A3 the reason that this doesn't + + + align:start position:0% +A1 A2 A3 the reason that this doesn't +make much difference if you get confused + + align:start position:0% +make much difference if you get confused + + + align:start position:0% +make much difference if you get confused +is that if the vector which originates + + align:start position:0% +is that if the vector which originates + + + align:start position:0% +is that if the vector which originates +at the origin terminates at the point + + align:start position:0% +at the origin terminates at the point + + + align:start position:0% +at the origin terminates at the point +whose coordinates are A1 A2 and A3 then + + align:start position:0% +whose coordinates are A1 A2 and A3 then + + + align:start position:0% +whose coordinates are A1 A2 and A3 then +the components of that Vector will have + + align:start position:0% +the components of that Vector will have + + + align:start position:0% +the components of that Vector will have +what the I component will be A1 the J + + align:start position:0% +what the I component will be A1 the J + + + align:start position:0% +what the I component will be A1 the J +component will be A2 and by the way we + + align:start position:0% +component will be A2 and by the way we + + + align:start position:0% +component will be A2 and by the way we +let K be the unit Vector in the positive + + align:start position:0% +let K be the unit Vector in the positive + + + align:start position:0% +let K be the unit Vector in the positive +Z Direction and the K component will be + + align:start position:0% +Z Direction and the K component will be + + + align:start position:0% +Z Direction and the K component will be +A3 to see this thing pictorially notice + + align:start position:0% +A3 to see this thing pictorially notice + + + align:start position:0% +A3 to see this thing pictorially notice +that the three-dimensional effect of the + + align:start position:0% +that the three-dimensional effect of the + + + align:start position:0% +that the three-dimensional effect of the +vector a it means that if we drop a + + align:start position:0% +vector a it means that if we drop a + + + align:start position:0% +vector a it means that if we drop a +perpendicular from the head of a to the + + align:start position:0% +perpendicular from the head of a to the + + + align:start position:0% +perpendicular from the head of a to the +XY plane then you see this distance is + + align:start position:0% +XY plane then you see this distance is + + + align:start position:0% +XY plane then you see this distance is +A1 this distance is A2 and this height + + align:start position:0% +A1 this distance is A2 and this height + + + align:start position:0% +A1 this distance is A2 and this height +is A3 and notice again in terms of + + align:start position:0% +is A3 and notice again in terms of + + + align:start position:0% +is A3 and notice again in terms of +adding vectors head to tail Etc notice + + align:start position:0% +adding vectors head to tail Etc notice + + + align:start position:0% +adding vectors head to tail Etc notice +that as a vector this would be the + + align:start position:0% +that as a vector this would be the + + + align:start position:0% +that as a vector this would be the +vector A1 I this would be be the vector + + align:start position:0% +vector A1 I this would be be the vector + + + align:start position:0% +vector A1 I this would be be the vector +A2 J and this would be the vector A3 K + + align:start position:0% +A2 J and this would be the vector A3 K + + + align:start position:0% +A2 J and this would be the vector A3 K +and other words the vector a is the sum + + align:start position:0% +and other words the vector a is the sum + + + align:start position:0% +and other words the vector a is the sum +of the three vectors A1 I A2 J and A3 K + + align:start position:0% +of the three vectors A1 I A2 J and A3 K + + + align:start position:0% +of the three vectors A1 I A2 J and A3 K +and other words to summarize this the + + align:start position:0% +and other words to summarize this the + + + align:start position:0% +and other words to summarize this the +vector a is simply what A1 I plus A2 J + + align:start position:0% +vector a is simply what A1 I plus A2 J + + + align:start position:0% +vector a is simply what A1 I plus A2 J +plus A3 K and again notice the jued + + align:start position:0% +plus A3 K and again notice the jued + + + align:start position:0% +plus A3 K and again notice the jued +positioning if you wish between the + + align:start position:0% +positioning if you wish between the + + + align:start position:0% +positioning if you wish between the +components of the vector and the co + + align:start position:0% +components of the vector and the co + + + align:start position:0% +components of the vector and the co +coordinates of the + + align:start position:0% +coordinates of the + + + align:start position:0% +coordinates of the +point also we can get a hold of the + + align:start position:0% +point also we can get a hold of the + + + align:start position:0% +point also we can get a hold of the +magnitude of this Vector remember the + + align:start position:0% +magnitude of this Vector remember the + + + align:start position:0% +magnitude of this Vector remember the +magnitude is the length and how can we + + align:start position:0% +magnitude is the length and how can we + + + align:start position:0% +magnitude is the length and how can we +figure out the length of this Vector + + align:start position:0% +figure out the length of this Vector + + + align:start position:0% +figure out the length of this Vector +notice by the way the geometry gets much + + align:start position:0% +notice by the way the geometry gets much + + + align:start position:0% +notice by the way the geometry gets much +tougher in three-dimensional space but I + + align:start position:0% +tougher in three-dimensional space but I + + + align:start position:0% +tougher in three-dimensional space but I +want to show you something interesting + + align:start position:0% +want to show you something interesting + + + align:start position:0% +want to show you something interesting +in a minute let's suffer through the + + align:start position:0% +in a minute let's suffer through the + + + align:start position:0% +in a minute let's suffer through the +geometry for a minute let's see how we + + align:start position:0% +geometry for a minute let's see how we + + + align:start position:0% +geometry for a minute let's see how we +can find the length of the vector a well + + align:start position:0% +can find the length of the vector a well + + + align:start position:0% +can find the length of the vector a well +notice by the way that a happens to be + + align:start position:0% +notice by the way that a happens to be + + + align:start position:0% +notice by the way that a happens to be +or the magnitude of a happens to be the + + align:start position:0% +or the magnitude of a happens to be the + + + align:start position:0% +or the magnitude of a happens to be the +hypotenuse of a right triangle what + + align:start position:0% +hypotenuse of a right triangle what + + + align:start position:0% +hypotenuse of a right triangle what +right triangle is it it's the right + + align:start position:0% +right triangle is it it's the right + + + align:start position:0% +right triangle is it it's the right +triangle that joins the origin let me + + align:start position:0% +triangle that joins the origin let me + + + align:start position:0% +triangle that joins the origin let me +call this point here + + align:start position:0% +call this point here + + + align:start position:0% +call this point here +b and a in other words triangle OB a is + + align:start position:0% +b and a in other words triangle OB a is + + + align:start position:0% +b and a in other words triangle OB a is +a right triangle because OB is in the XY + + align:start position:0% +a right triangle because OB is in the XY + + + align:start position:0% +a right triangle because OB is in the XY +plane and ab is perpendicular to the XY + + align:start position:0% +plane and ab is perpendicular to the XY + + + align:start position:0% +plane and ab is perpendicular to the XY +plane therefore by the Pythagorean + + align:start position:0% +plane therefore by the Pythagorean + + + align:start position:0% +plane therefore by the Pythagorean +theorem the magnitude of a will be the + + align:start position:0% +theorem the magnitude of a will be the + + + align:start position:0% +theorem the magnitude of a will be the +square root of the square of the + + align:start position:0% +square root of the square of the + + + align:start position:0% +square root of the square of the +magnitude of OB plus the square of the + + align:start position:0% +magnitude of OB plus the square of the + + + align:start position:0% +magnitude of OB plus the square of the +magnitude of ab on the other hand notice + + align:start position:0% +magnitude of ab on the other hand notice + + + align:start position:0% +magnitude of ab on the other hand notice +that o c b is also a right triangle so + + align:start position:0% +that o c b is also a right triangle so + + + align:start position:0% +that o c b is also a right triangle so +by the Pythagorean theorem the length of + + align:start position:0% +by the Pythagorean theorem the length of + + + align:start position:0% +by the Pythagorean theorem the length of +OB is the square root of A1 2 + A2 2 and + + align:start position:0% +OB is the square root of A1 2 + A2 2 and + + + align:start position:0% +OB is the square root of A1 2 + A2 2 and +therefore you see by the Pythagorean + + align:start position:0% +therefore you see by the Pythagorean + + + align:start position:0% +therefore you see by the Pythagorean +theorem the square of the magnitude of a + + align:start position:0% +theorem the square of the magnitude of a + + + align:start position:0% +theorem the square of the magnitude of a +is this squar plus this squared in other + + align:start position:0% +is this squar plus this squared in other + + + align:start position:0% +is this squar plus this squared in other +words the magnitude of a is the square + + align:start position:0% +words the magnitude of a is the square + + + align:start position:0% +words the magnitude of a is the square +root of A1 2 + A2 2 + A3 2 in other + + align:start position:0% +root of A1 2 + A2 2 + A3 2 in other + + + align:start position:0% +root of A1 2 + A2 2 + A3 2 in other +words in cartisian coordinates to find + + align:start position:0% +words in cartisian coordinates to find + + + align:start position:0% +words in cartisian coordinates to find +the magnitude of a vector you need only + + align:start position:0% +the magnitude of a vector you need only + + + align:start position:0% +the magnitude of a vector you need only +take the positive square root of the sum + + align:start position:0% +take the positive square root of the sum + + + align:start position:0% +take the positive square root of the sum +of the squares of the components it's + + align:start position:0% +of the squares of the components it's + + + align:start position:0% +of the squares of the components it's +the regular distance formula the + + align:start position:0% +the regular distance formula the + + + align:start position:0% +the regular distance formula the +Pythagorean theorem by the way just a + + align:start position:0% +Pythagorean theorem by the way just a + + + align:start position:0% +Pythagorean theorem by the way just a +very very quick review from part one of + + align:start position:0% +very very quick review from part one of + + + align:start position:0% +very very quick review from part one of +our course remember that technically + + align:start position:0% +our course remember that technically + + + align:start position:0% +our course remember that technically +speaking the square root is a double + + align:start position:0% +speaking the square root is a double + + + align:start position:0% +speaking the square root is a double +valued function namely any positive + + align:start position:0% +valued function namely any positive + + + align:start position:0% +valued function namely any positive +number has two square roots right in + + align:start position:0% +number has two square roots right in + + + align:start position:0% +number has two square roots right in +other words the square root of 16 is 4 + + align:start position:0% +other words the square root of 16 is 4 + + + align:start position:0% +other words the square root of 16 is 4 +it's also -4 but by convention when we + + align:start position:0% +it's also -4 but by convention when we + + + align:start position:0% +it's also -4 but by convention when we +don't indicate a sign we're always + + align:start position:0% +don't indicate a sign we're always + + + align:start position:0% +don't indicate a sign we're always +referring to the positive square root + + align:start position:0% +referring to the positive square root + + + align:start position:0% +referring to the positive square root +and that's fine because after all the + + align:start position:0% +and that's fine because after all the + + + align:start position:0% +and that's fine because after all the +magnitude the length of an arrow is + + align:start position:0% +magnitude the length of an arrow is + + + align:start position:0% +magnitude the length of an arrow is +always looked upon as being what some + + align:start position:0% +always looked upon as being what some + + + align:start position:0% +always looked upon as being what some +non- negative number notice that the + + align:start position:0% +non- negative number notice that the + + + align:start position:0% +non- negative number notice that the +negativeness is taken care of by the + + align:start position:0% +negativeness is taken care of by the + + + align:start position:0% +negativeness is taken care of by the +sense okay and this is what's rather + + align:start position:0% +sense okay and this is what's rather + + + align:start position:0% +sense okay and this is what's rather +interesting I think it's worth noting if + + align:start position:0% +interesting I think it's worth noting if + + + align:start position:0% +interesting I think it's worth noting if +we use cartisan coordinates in one + + align:start position:0% +we use cartisan coordinates in one + + + align:start position:0% +we use cartisan coordinates in one +dimension all you have is the xais in + + align:start position:0% +dimension all you have is the xais in + + + align:start position:0% +dimension all you have is the xais in +which case any Vector is some scal + + align:start position:0% +which case any Vector is some scal + + + align:start position:0% +which case any Vector is some scal +multiple of the unit Vector I in other + + align:start position:0% +multiple of the unit Vector I in other + + + align:start position:0% +multiple of the unit Vector I in other +words a is equal to A1 I in this case + + align:start position:0% +words a is equal to A1 I in this case + + + align:start position:0% +words a is equal to A1 I in this case +the magnitude of a is just what it's the + + align:start position:0% +the magnitude of a is just what it's the + + + align:start position:0% +the magnitude of a is just what it's the +square root of A1 squ and notice that + + align:start position:0% +square root of A1 squ and notice that + + + align:start position:0% +square root of A1 squ and notice that +means the positive square root notice by + + align:start position:0% +means the positive square root notice by + + + align:start position:0% +means the positive square root notice by +the way that that's the usual meaning of + + align:start position:0% +the way that that's the usual meaning of + + + align:start position:0% +the way that that's the usual meaning of +absolute value after all if A1 were + + align:start position:0% +absolute value after all if A1 were + + + align:start position:0% +absolute value after all if A1 were +already positive taking the positive + + align:start position:0% +already positive taking the positive + + + align:start position:0% +already positive taking the positive +square root of it square root of its + + align:start position:0% +square root of it square root of its + + + align:start position:0% +square root of it square root of its +Square these tongue Tes the positive + + align:start position:0% +Square these tongue Tes the positive + + + align:start position:0% +Square these tongue Tes the positive +square root of the square would give you + + align:start position:0% +square root of the square would give you + + + align:start position:0% +square root of the square would give you +the number back again on the other hand + + align:start position:0% +the number back again on the other hand + + + align:start position:0% +the number back again on the other hand +if A1 were negative and then you square + + align:start position:0% +if A1 were negative and then you square + + + align:start position:0% +if A1 were negative and then you square +it and then take the positive square + + align:start position:0% +it and then take the positive square + + + align:start position:0% +it and then take the positive square +root all you do is change the sign of A1 + + align:start position:0% +root all you do is change the sign of A1 + + + align:start position:0% +root all you do is change the sign of A1 +and since it was negative changing its + + align:start position:0% +and since it was negative changing its + + + align:start position:0% +and since it was negative changing its +sign makes it positive so this is the + + align:start position:0% +sign makes it positive so this is the + + + align:start position:0% +sign makes it positive so this is the +usual absolute value all right now in + + align:start position:0% +usual absolute value all right now in + + + align:start position:0% +usual absolute value all right now in +terms of the previous unit we saw that + + align:start position:0% +terms of the previous unit we saw that + + + align:start position:0% +terms of the previous unit we saw that +in two-dimensional space using I and J + + align:start position:0% +in two-dimensional space using I and J + + + align:start position:0% +in two-dimensional space using I and J +as our basic vectors that if a was the + + align:start position:0% +as our basic vectors that if a was the + + + align:start position:0% +as our basic vectors that if a was the +vector A1 I I plus A2 J then the + + align:start position:0% +vector A1 I I plus A2 J then the + + + align:start position:0% +vector A1 I I plus A2 J then the +magnitude of a Again by the Pythagorean + + align:start position:0% +magnitude of a Again by the Pythagorean + + + align:start position:0% +magnitude of a Again by the Pythagorean +theorem was just the square root of A1 S + + align:start position:0% +theorem was just the square root of A1 S + + + align:start position:0% +theorem was just the square root of A1 S +Plus A2 2 and now we've seen that + + align:start position:0% +Plus A2 2 and now we've seen that + + + align:start position:0% +Plus A2 2 and now we've seen that +structurally even though geometrically + + align:start position:0% +structurally even though geometrically + + + align:start position:0% +structurally even though geometrically +it was harder to show that the that if a + + align:start position:0% +it was harder to show that the that if a + + + align:start position:0% +it was harder to show that the that if a +in three-dimensional space is A1 I plus + + align:start position:0% +in three-dimensional space is A1 I plus + + + align:start position:0% +in three-dimensional space is A1 I plus +A2 J plus A3 k then a is what the + + align:start position:0% +A2 J plus A3 k then a is what the + + + align:start position:0% +A2 J plus A3 k then a is what the +positive sare root of A1 2 + A2 2 + A3 2 + + align:start position:0% +positive sare root of A1 2 + A2 2 + A3 2 + + + align:start position:0% +positive sare root of A1 2 + A2 2 + A3 2 +and notice you see this structure + + align:start position:0% +and notice you see this structure + + + align:start position:0% +and notice you see this structure +resemblance this is a beautiful + + align:start position:0% +resemblance this is a beautiful + + + align:start position:0% +resemblance this is a beautiful +structural resemblance why is it a + + align:start position:0% +structural resemblance why is it a + + + align:start position:0% +structural resemblance why is it a +beautiful structural resemblance because + + align:start position:0% +beautiful structural resemblance because + + + align:start position:0% +beautiful structural resemblance because +now maybe we're getting the feeling that + + align:start position:0% +now maybe we're getting the feeling that + + + align:start position:0% +now maybe we're getting the feeling that +once our rules and recipes are made up + + align:start position:0% +once our rules and recipes are made up + + + align:start position:0% +once our rules and recipes are made up +we don't have to worry about how + + align:start position:0% +we don't have to worry about how + + + align:start position:0% +we don't have to worry about how +difficult the geometry is in other words + + align:start position:0% +difficult the geometry is in other words + + + align:start position:0% +difficult the geometry is in other words +except for the fact that you have an + + align:start position:0% +except for the fact that you have an + + + align:start position:0% +except for the fact that you have an +extra component to worry about here + + align:start position:0% +extra component to worry about here + + + align:start position:0% +extra component to worry about here +there is no basic difference + + align:start position:0% +there is no basic difference + + + align:start position:0% +there is no basic difference +structurally between finding the length + + align:start position:0% +structurally between finding the length + + + align:start position:0% +structurally between finding the length +of a vector in onedimensional space or + + align:start position:0% +of a vector in onedimensional space or + + + align:start position:0% +of a vector in onedimensional space or +in three-dimensional space and in fact + + align:start position:0% +in three-dimensional space and in fact + + + align:start position:0% +in three-dimensional space and in fact +another reason that I'm harping on this + + align:start position:0% +another reason that I'm harping on this + + + align:start position:0% +another reason that I'm harping on this +is the fact that in a little + + align:start position:0% +is the fact that in a little + + + align:start position:0% +is the fact that in a little +meaning within the next few lessons we + + align:start position:0% +meaning within the next few lessons we + + + align:start position:0% +meaning within the next few lessons we +are going to be talking about some + + align:start position:0% +are going to be talking about some + + + align:start position:0% +are going to be talking about some +horrible thing called n-dimensional + + align:start position:0% +horrible thing called n-dimensional + + + align:start position:0% +horrible thing called n-dimensional +space which geometrically cannot be + + align:start position:0% +space which geometrically cannot be + + + align:start position:0% +space which geometrically cannot be +drawn but which analytically preserves + + align:start position:0% +drawn but which analytically preserves + + + align:start position:0% +drawn but which analytically preserves +the same structure that we're talking + + align:start position:0% +the same structure that we're talking + + + align:start position:0% +the same structure that we're talking +about here you see the whole bag is + + align:start position:0% +about here you see the whole bag is + + + align:start position:0% +about here you see the whole bag is +still this idea of structure we're + + align:start position:0% +still this idea of structure we're + + + align:start position:0% +still this idea of structure we're +trying to emphasize that the recipes + + align:start position:0% +trying to emphasize that the recipes + + + align:start position:0% +trying to emphasize that the recipes +remain the same independently of the + + align:start position:0% +remain the same independently of the + + + align:start position:0% +remain the same independently of the +dimension and just to carry this idea a + + align:start position:0% +dimension and just to carry this idea a + + + align:start position:0% +dimension and just to carry this idea a +few steps + + align:start position:0% +few steps + + + align:start position:0% +few steps +further what we're saying is remember in + + align:start position:0% +further what we're saying is remember in + + + align:start position:0% +further what we're saying is remember in +the last unit we talked about the fact + + align:start position:0% +the last unit we talked about the fact + + + align:start position:0% +the last unit we talked about the fact +that the nice thing about I andj + + align:start position:0% +that the nice thing about I andj + + + align:start position:0% +that the nice thing about I andj +components was that the definition for + + align:start position:0% +components was that the definition for + + + align:start position:0% +components was that the definition for +adding two vectors was that if they were + + align:start position:0% +adding two vectors was that if they were + + + align:start position:0% +adding two vectors was that if they were +in terms of I andj components you just + + align:start position:0% +in terms of I andj components you just + + + align:start position:0% +in terms of I andj components you just +added component by component well again + + align:start position:0% +added component by component well again + + + align:start position:0% +added component by component well again +without belaboring the point and leaving + + align:start position:0% +without belaboring the point and leaving + + + align:start position:0% +without belaboring the point and leaving +the details to the text and to the + + align:start position:0% +the details to the text and to the + + + align:start position:0% +the details to the text and to the +exercises let's keep in mind that it's + + align:start position:0% +exercises let's keep in mind that it's + + + align:start position:0% +exercises let's keep in mind that it's +relatively easy to show that the same + + align:start position:0% +relatively easy to show that the same + + + align:start position:0% +relatively easy to show that the same +formal definition of addition namely + + align:start position:0% +formal definition of addition namely + + + align:start position:0% +formal definition of addition namely +placing the arrows head to tail Etc + + align:start position:0% +placing the arrows head to tail Etc + + + align:start position:0% +placing the arrows head to tail Etc +forgetting about cartisian coordinates + + align:start position:0% +forgetting about cartisian coordinates + + + align:start position:0% +forgetting about cartisian coordinates +but notice the definition of addition + + align:start position:0% +but notice the definition of addition + + + align:start position:0% +but notice the definition of addition +doesn't mention the coordinate system it + + align:start position:0% +doesn't mention the coordinate system it + + + align:start position:0% +doesn't mention the coordinate system it +just says put the vectors head to tail + + align:start position:0% +just says put the vectors head to tail + + + align:start position:0% +just says put the vectors head to tail +Etc and what I'm saying is it's easy to + + align:start position:0% +Etc and what I'm saying is it's easy to + + + align:start position:0% +Etc and what I'm saying is it's easy to +show under those conditions that if a is + + align:start position:0% +show under those conditions that if a is + + + align:start position:0% +show under those conditions that if a is +the vector A1 I plus A2 J plus A3 K and + + align:start position:0% +the vector A1 I plus A2 J plus A3 K and + + + align:start position:0% +the vector A1 I plus A2 J plus A3 K and +B is the vector B1 I plus b2j plus B3 k + + align:start position:0% +B is the vector B1 I plus b2j plus B3 k + + + align:start position:0% +B is the vector B1 I plus b2j plus B3 k +then you still add vectors the same way + + align:start position:0% +then you still add vectors the same way + + + align:start position:0% +then you still add vectors the same way +in three space as you did in two space + + align:start position:0% +in three space as you did in two space + + + align:start position:0% +in three space as you did in two space +again the gometric arguments are a + + align:start position:0% +again the gometric arguments are a + + + align:start position:0% +again the gometric arguments are a +little bit more sophisticated if only + + align:start position:0% +little bit more sophisticated if only + + + align:start position:0% +little bit more sophisticated if only +because it's harder to draw three + + align:start position:0% +because it's harder to draw three + + + align:start position:0% +because it's harder to draw three +dimensions to scale then it is two + + align:start position:0% +dimensions to scale then it is two + + + align:start position:0% +dimensions to scale then it is two +Dimensions but the idea is what a plus b + + align:start position:0% +Dimensions but the idea is what a plus b + + + align:start position:0% +Dimensions but the idea is what a plus b +is just obtained by adding what the two + + align:start position:0% +is just obtained by adding what the two + + + align:start position:0% +is just obtained by adding what the two +I components the two J components the + + align:start position:0% +I components the two J components the + + + align:start position:0% +I components the two J components the +two k components and similarly for Scala + + align:start position:0% +two k components and similarly for Scala + + + align:start position:0% +two k components and similarly for Scala +multiplication in the same way in terms + + align:start position:0% +multiplication in the same way in terms + + + align:start position:0% +multiplication in the same way in terms +of I and J components you simply + + align:start position:0% +of I and J components you simply + + + align:start position:0% +of I and J components you simply +multiplied each component by the scal of + + align:start position:0% +multiplied each component by the scal of + + + align:start position:0% +multiplied each component by the scal of +C if C is any number and a is still the + + align:start position:0% +C if C is any number and a is still the + + + align:start position:0% +C if C is any number and a is still the +vector A1 I plus A2 J plus A3 K the + + align:start position:0% +vector A1 I plus A2 J plus A3 K the + + + align:start position:0% +vector A1 I plus A2 J plus A3 K the +Scala multiple C * a turns out to be C + + align:start position:0% +Scala multiple C * a turns out to be C + + + align:start position:0% +Scala multiple C * a turns out to be C +A1 I plus ca2 J plus ca3 K that you just + + align:start position:0% +A1 I plus ca2 J plus ca3 K that you just + + + align:start position:0% +A1 I plus ca2 J plus ca3 K that you just +multiply component by component and by + + align:start position:0% +multiply component by component and by + + + align:start position:0% +multiply component by component and by +the way don't lose track of this + + align:start position:0% +the way don't lose track of this + + + align:start position:0% +the way don't lose track of this +important point that the Scala multiple + + align:start position:0% +important point that the Scala multiple + + + align:start position:0% +important point that the Scala multiple +CA means the same thing in two + + align:start position:0% +CA means the same thing in two + + + align:start position:0% +CA means the same thing in two +Dimensions as it did in three because + + align:start position:0% +Dimensions as it did in three because + + + align:start position:0% +Dimensions as it did in three because +after all when you draw that Vector once + + align:start position:0% +after all when you draw that Vector once + + + align:start position:0% +after all when you draw that Vector once +that arrow is drawn it's a + + align:start position:0% +that arrow is drawn it's a + + + align:start position:0% +that arrow is drawn it's a +one-dimensional thing if you pick Azure + + align:start position:0% +one-dimensional thing if you pick Azure + + + align:start position:0% +one-dimensional thing if you pick Azure +axis the line of action of the + + align:start position:0% +axis the line of action of the + + + align:start position:0% +axis the line of action of the +particular arrow in other words Scala + + align:start position:0% +particular arrow in other words Scala + + + align:start position:0% +particular arrow in other words Scala +multiplication means the same thing + + align:start position:0% +multiplication means the same thing + + + align:start position:0% +multiplication means the same thing +what's happening is is that you're + + align:start position:0% +what's happening is is that you're + + + align:start position:0% +what's happening is is that you're +looking at it in terms of different + + align:start position:0% +looking at it in terms of different + + + align:start position:0% +looking at it in terms of different +components you're looking at in terms of + + align:start position:0% +components you're looking at in terms of + + + align:start position:0% +components you're looking at in terms of +i j and k rather than just I and J or in + + align:start position:0% +i j and k rather than just I and J or in + + + align:start position:0% +i j and k rather than just I and J or in +terms of any other coordinate system but + + align:start position:0% +terms of any other coordinate system but + + + align:start position:0% +terms of any other coordinate system but +carrying this out in particular notice + + align:start position:0% +carrying this out in particular notice + + + align:start position:0% +carrying this out in particular notice +then the connection between the vector + + align:start position:0% +then the connection between the vector + + + align:start position:0% +then the connection between the vector +minus B negative B and the vector -1 * B + + align:start position:0% +minus B negative B and the vector -1 * B + + + align:start position:0% +minus B negative B and the vector -1 * B +namely the vector negative B which has + + align:start position:0% +namely the vector negative B which has + + + align:start position:0% +namely the vector negative B which has +the same magnitude and direction is B + + align:start position:0% +the same magnitude and direction is B + + + align:start position:0% +the same magnitude and direction is B +but the opposite sense is the same way + + align:start position:0% +but the opposite sense is the same way + + + align:start position:0% +but the opposite sense is the same way +as saying what multiply B by minus one + + align:start position:0% +as saying what multiply B by minus one + + + align:start position:0% +as saying what multiply B by minus one +because that gives you a vector which + + align:start position:0% +because that gives you a vector which + + + align:start position:0% +because that gives you a vector which +has the same magnitude namely one times + + align:start position:0% +has the same magnitude namely one times + + + align:start position:0% +has the same magnitude namely one times +as much as B the same direction and the + + align:start position:0% +as much as B the same direction and the + + + align:start position:0% +as much as B the same direction and the +opposite sense in other words the vector + + align:start position:0% +opposite sense in other words the vector + + + align:start position:0% +opposite sense in other words the vector +negative B in three-dimensional space is + + align:start position:0% +negative B in three-dimensional space is + + + align:start position:0% +negative B in three-dimensional space is +minus B1 I minus B2 J minus B3 K and + + align:start position:0% +minus B1 I minus B2 J minus B3 K and + + + align:start position:0% +minus B1 I minus B2 J minus B3 K and +therefore since a minus B still means a + + align:start position:0% +therefore since a minus B still means a + + + align:start position:0% +therefore since a minus B still means a ++ netive b the vector a minus B is + + align:start position:0% ++ netive b the vector a minus B is + + + align:start position:0% ++ netive b the vector a minus B is +simply obtained how you subtract the + + align:start position:0% +simply obtained how you subtract the + + + align:start position:0% +simply obtained how you subtract the +same way as we did in order orary + + align:start position:0% +same way as we did in order orary + + + align:start position:0% +same way as we did in order orary +one-dimensional analytic geometry in + + align:start position:0% +one-dimensional analytic geometry in + + + align:start position:0% +one-dimensional analytic geometry in +terms of a number line in other words + + align:start position:0% +terms of a number line in other words + + + align:start position:0% +terms of a number line in other words +you subtract component by component + + align:start position:0% +you subtract component by component + + + align:start position:0% +you subtract component by component +subtracting what from the first number + + align:start position:0% +subtracting what from the first number + + + align:start position:0% +subtracting what from the first number +minus the corresponding the first Vector + + align:start position:0% +minus the corresponding the first Vector + + + align:start position:0% +minus the corresponding the first Vector +minus the corresponding component of the + + align:start position:0% +minus the corresponding component of the + + + align:start position:0% +minus the corresponding component of the +second Vector in other words in + + align:start position:0% +second Vector in other words in + + + align:start position:0% +second Vector in other words in +cartisian coordinates the vector a minus + + align:start position:0% +cartisian coordinates the vector a minus + + + align:start position:0% +cartisian coordinates the vector a minus +B once we know A1 A2 and A3 as the + + align:start position:0% +B once we know A1 A2 and A3 as the + + + align:start position:0% +B once we know A1 A2 and A3 as the +components of a B1 B2 and B3 three as + + align:start position:0% +components of a B1 B2 and B3 three as + + + align:start position:0% +components of a B1 B2 and B3 three as +the components of B we just subtract + + align:start position:0% +the components of B we just subtract + + + align:start position:0% +the components of B we just subtract +component by component to get this + + align:start position:0% +component by component to get this + + + align:start position:0% +component by component to get this +particular result and this is I think + + align:start position:0% +particular result and this is I think + + + align:start position:0% +particular result and this is I think +very important to understand by the same + + align:start position:0% +very important to understand by the same + + + align:start position:0% +very important to understand by the same +token as simple as this is it's going to + + align:start position:0% +token as simple as this is it's going to + + + align:start position:0% +token as simple as this is it's going to +cause if we're not careful great + + align:start position:0% +cause if we're not careful great + + + align:start position:0% +cause if we're not careful great +misinterpretation + + align:start position:0% +misinterpretation + + + align:start position:0% +misinterpretation +namely the vector arithmetic that we're + + align:start position:0% +namely the vector arithmetic that we're + + + align:start position:0% +namely the vector arithmetic that we're +talking about does not depend on + + align:start position:0% +talking about does not depend on + + + align:start position:0% +talking about does not depend on +cartisian + + align:start position:0% +cartisian + + + align:start position:0% +cartisian +coordinates vectors are arrows as we're + + align:start position:0% +coordinates vectors are arrows as we're + + + align:start position:0% +coordinates vectors are arrows as we're +looking at them and the arrows exist no + + align:start position:0% +looking at them and the arrows exist no + + + align:start position:0% +looking at them and the arrows exist no +matter what coordinate system we using + + align:start position:0% +matter what coordinate system we using + + + align:start position:0% +matter what coordinate system we using +what is particularly important however + + align:start position:0% +what is particularly important however + + + align:start position:0% +what is particularly important however +is that many of the luxuries of using + + align:start position:0% +is that many of the luxuries of using + + + align:start position:0% +is that many of the luxuries of using +Vector arithmetic hinge on using + + align:start position:0% +Vector arithmetic hinge on using + + + align:start position:0% +Vector arithmetic hinge on using +cartisian coordinates now what do I mean + + align:start position:0% +cartisian coordinates now what do I mean + + + align:start position:0% +cartisian coordinates now what do I mean +by that well let me just emphasize note + + align:start position:0% +by that well let me just emphasize note + + + align:start position:0% +by that well let me just emphasize note +the need for cartisian + + align:start position:0% +the need for cartisian + + + align:start position:0% +the need for cartisian +coordinates let me talk instead you see + + align:start position:0% +coordinates let me talk instead you see + + + align:start position:0% +coordinates let me talk instead you see +about something called polar coordinates + + align:start position:0% +about something called polar coordinates + + + align:start position:0% +about something called polar coordinates +now later on we're going to talk about + + align:start position:0% +now later on we're going to talk about + + + align:start position:0% +now later on we're going to talk about +polar coordinates in more detail in fact + + align:start position:0% +polar coordinates in more detail in fact + + + align:start position:0% +polar coordinates in more detail in fact +in very very much more detail but for + + align:start position:0% +in very very much more detail but for + + + align:start position:0% +in very very much more detail but for +the time time being let's view polar + + align:start position:0% +the time time being let's view polar + + + align:start position:0% +the time time being let's view polar +coordinates simply as a radar type thing + + align:start position:0% +coordinates simply as a radar type thing + + + align:start position:0% +coordinates simply as a radar type thing +as a range and bearing type navigation + + align:start position:0% +as a range and bearing type navigation + + + align:start position:0% +as a range and bearing type navigation +namely in polar coordinates the way you + + align:start position:0% +namely in polar coordinates the way you + + + align:start position:0% +namely in polar coordinates the way you +specify a vector in the plain say is you + + align:start position:0% +specify a vector in the plain say is you + + + align:start position:0% +specify a vector in the plain say is you +specify its length which we'll call R + + align:start position:0% +specify its length which we'll call R + + + align:start position:0% +specify its length which we'll call R +and the angle that it makes with the + + align:start position:0% +and the angle that it makes with the + + + align:start position:0% +and the angle that it makes with the +Positive x-axis that we'll call Theta in + + align:start position:0% +Positive x-axis that we'll call Theta in + + + align:start position:0% +Positive x-axis that we'll call Theta in +other words in polar coordinates the + + align:start position:0% +other words in polar coordinates the + + + align:start position:0% +other words in polar coordinates the +vector a which I've labeled R2 comma + + align:start position:0% +vector a which I've labeled R2 comma + + + align:start position:0% +vector a which I've labeled R2 comma +Theta 2 that would indicate that the + + align:start position:0% +Theta 2 that would indicate that the + + + align:start position:0% +Theta 2 that would indicate that the +magnitude of a is + + align:start position:0% +magnitude of a is + + + align:start position:0% +magnitude of a is +R2 and at the angle that a makes with + + align:start position:0% +R2 and at the angle that a makes with + + + align:start position:0% +R2 and at the angle that a makes with +the Positive xais + + align:start position:0% +the Positive xais + + + align:start position:0% +the Positive xais +is Theta 2 and when I label the vector b + + align:start position:0% +is Theta 2 and when I label the vector b + + + align:start position:0% +is Theta 2 and when I label the vector b +as R1 comma Theta 1 it's simply my way + + align:start position:0% +as R1 comma Theta 1 it's simply my way + + + align:start position:0% +as R1 comma Theta 1 it's simply my way +of saying that the magnitude of the + + align:start position:0% +of saying that the magnitude of the + + + align:start position:0% +of saying that the magnitude of the +vector B is some length which we'll call + + align:start position:0% +vector B is some length which we'll call + + + align:start position:0% +vector B is some length which we'll call +R1 and the angle that b makes with the + + align:start position:0% +R1 and the angle that b makes with the + + + align:start position:0% +R1 and the angle that b makes with the +Positive x axis is some angle which + + align:start position:0% +Positive x axis is some angle which + + + align:start position:0% +Positive x axis is some angle which +we'll call Theta 1 + + align:start position:0% +we'll call Theta 1 + + + align:start position:0% +we'll call Theta 1 +okay perfectly well- defined system + + align:start position:0% +okay perfectly well- defined system + + + align:start position:0% +okay perfectly well- defined system +isn't it in other words if I tell you + + align:start position:0% +isn't it in other words if I tell you + + + align:start position:0% +isn't it in other words if I tell you +the range in bearing I've certainly + + align:start position:0% +the range in bearing I've certainly + + + align:start position:0% +the range in bearing I've certainly +given you as much information as if I + + align:start position:0% +given you as much information as if I + + + align:start position:0% +given you as much information as if I +told you the I and J components now + + align:start position:0% +told you the I and J components now + + + align:start position:0% +told you the I and J components now +here's the important point the real + + align:start position:0% +here's the important point the real + + + align:start position:0% +here's the important point the real +kicker to this thing and that is that + + align:start position:0% +kicker to this thing and that is that + + + align:start position:0% +kicker to this thing and that is that +the vector a minus B and A minus B is + + align:start position:0% +the vector a minus B and A minus B is + + + align:start position:0% +the vector a minus B and A minus B is +what it's this Vector + + align:start position:0% + + + + align:start position:0% + +here and by the way notice how Vector + + align:start position:0% +here and by the way notice how Vector + + + align:start position:0% +here and by the way notice how Vector +arithmetic goes how could you tell quick + + align:start position:0% +arithmetic goes how could you tell quick + + + align:start position:0% +arithmetic goes how could you tell quick +whether this is a minus b or B minus a + + align:start position:0% +whether this is a minus b or B minus a + + + align:start position:0% +whether this is a minus b or B minus a +we talked about this in the previous + + align:start position:0% +we talked about this in the previous + + + align:start position:0% +we talked about this in the previous +unit and had exercises and discussion on + + align:start position:0% +unit and had exercises and discussion on + + + align:start position:0% +unit and had exercises and discussion on +it but notice again the structure of + + align:start position:0% +it but notice again the structure of + + + align:start position:0% +it but notice again the structure of +vector arithmetic if you look at + + align:start position:0% +vector arithmetic if you look at + + + align:start position:0% +vector arithmetic if you look at +addition what is a what is this Vector + + align:start position:0% +addition what is a what is this Vector + + + align:start position:0% +addition what is a what is this Vector +here this is the vector which must be + + align:start position:0% +here this is the vector which must be + + + align:start position:0% +here this is the vector which must be +added on to B to give the vector a and + + align:start position:0% +added on to B to give the vector a and + + + align:start position:0% +added on to B to give the vector a and +that by definition is called what a + + align:start position:0% +that by definition is called what a + + + align:start position:0% +that by definition is called what a +minus B A minus B is what Vector the + + align:start position:0% +minus B A minus B is what Vector the + + + align:start position:0% +minus B A minus B is what Vector the +vector you must add on to B to you yield + + align:start position:0% +vector you must add on to B to you yield + + + align:start position:0% +vector you must add on to B to you yield +a a subtraction is still the inverse of + + align:start position:0% +a a subtraction is still the inverse of + + + align:start position:0% +a a subtraction is still the inverse of +addition and hopefully by now you should + + align:start position:0% +addition and hopefully by now you should + + + align:start position:0% +addition and hopefully by now you should +be becoming much less fearful of this + + align:start position:0% +be becoming much less fearful of this + + + align:start position:0% +be becoming much less fearful of this +Vector notation that structurally it's + + align:start position:0% +Vector notation that structurally it's + + + align:start position:0% +Vector notation that structurally it's +the same as our first unit of + + align:start position:0% +the same as our first unit of + + + align:start position:0% +the same as our first unit of +arithmetic uh Ari what numerical + + align:start position:0% +arithmetic uh Ari what numerical + + + align:start position:0% +arithmetic uh Ari what numerical +arithmetic okay the more regular type + + align:start position:0% +arithmetic okay the more regular type + + + align:start position:0% +arithmetic okay the more regular type +ordinary type of arithmetic but here's + + align:start position:0% +ordinary type of arithmetic but here's + + + align:start position:0% +ordinary type of arithmetic but here's +the important point this Vector is still + + align:start position:0% +the important point this Vector is still + + + align:start position:0% +the important point this Vector is still +a minus B but I claim that it's trivial + + align:start position:0% +a minus B but I claim that it's trivial + + + align:start position:0% +a minus B but I claim that it's trivial +to + + align:start position:0% +to + + + align:start position:0% +to +see that this Vector is not the vector + + align:start position:0% +see that this Vector is not the vector + + + align:start position:0% +see that this Vector is not the vector +whose magnitude is R2 - R1 and whose + + align:start position:0% +whose magnitude is R2 - R1 and whose + + + align:start position:0% +whose magnitude is R2 - R1 and whose +angle of bearing is data 2 minus data + + align:start position:0% +angle of bearing is data 2 minus data + + + align:start position:0% +angle of bearing is data 2 minus data +one now the word trivial is a very + + align:start position:0% +one now the word trivial is a very + + + align:start position:0% +one now the word trivial is a very +misleading word in mathematics one of + + align:start position:0% +misleading word in mathematics one of + + + align:start position:0% +misleading word in mathematics one of +our famous mathematical anecdotes is the + + align:start position:0% +our famous mathematical anecdotes is the + + + align:start position:0% +our famous mathematical anecdotes is the +professor who said that a proof was + + align:start position:0% +professor who said that a proof was + + + align:start position:0% +professor who said that a proof was +trivial the student says it doesn't seem + + align:start position:0% +trivial the student says it doesn't seem + + + align:start position:0% +trivial the student says it doesn't seem +trivial to me the professor says well it + + align:start position:0% +trivial to me the professor says well it + + + align:start position:0% +trivial to me the professor says well it +is Trivial he didn't quite see it in + + align:start position:0% +is Trivial he didn't quite see it in + + + align:start position:0% +is Trivial he didn't quite see it in +thear he says wait here he ran down to + + align:start position:0% +thear he says wait here he ran down to + + + align:start position:0% +thear he says wait here he ran down to +his office came up 3 hours later with a + + align:start position:0% +his office came up 3 hours later with a + + + align:start position:0% +his office came up 3 hours later with a +ream of papers that he had written on + + align:start position:0% +ream of papers that he had written on + + + align:start position:0% +ream of papers that he had written on +bathed in perspiration and a big smile + + align:start position:0% +bathed in perspiration and a big smile + + + align:start position:0% +bathed in perspiration and a big smile +and he said I was right it was trivial + + align:start position:0% +and he said I was right it was trivial + + + align:start position:0% +and he said I was right it was trivial +so just because what I think is Trivial + + align:start position:0% +so just because what I think is Trivial + + + align:start position:0% +so just because what I think is Trivial +may not be what you think is Trivial let + + align:start position:0% +may not be what you think is Trivial let + + + align:start position:0% +may not be what you think is Trivial let +me go through this statement in more + + align:start position:0% +me go through this statement in more + + + align:start position:0% +me go through this statement in more +computational detail what I'm saying is + + align:start position:0% +computational detail what I'm saying is + + + align:start position:0% +computational detail what I'm saying is +let V denote the vector that we called a + + align:start position:0% +let V denote the vector that we called a + + + align:start position:0% +let V denote the vector that we called a +minus B before notice that in terms of + + align:start position:0% +minus B before notice that in terms of + + + align:start position:0% +minus B before notice that in terms of +what the vectors A and B are this length + + align:start position:0% +what the vectors A and B are this length + + + align:start position:0% +what the vectors A and B are this length +is R1 this length is R2 and notice that + + align:start position:0% +is R1 this length is R2 and notice that + + + align:start position:0% +is R1 this length is R2 and notice that +since this whole angle was Thea 2 and + + align:start position:0% +since this whole angle was Thea 2 and + + + align:start position:0% +since this whole angle was Thea 2 and +the angle from here to here was Theta 1 + + align:start position:0% +the angle from here to here was Theta 1 + + + align:start position:0% +the angle from here to here was Theta 1 +this angle in here must be the + + align:start position:0% +this angle in here must be the + + + align:start position:0% +this angle in here must be the +difference between those two angles + + align:start position:0% +difference between those two angles + + + align:start position:0% +difference between those two angles +which is Theta 2 minus Theta 1 now + + align:start position:0% +which is Theta 2 minus Theta 1 now + + + align:start position:0% +which is Theta 2 minus Theta 1 now +notice that this is still a triangle the + + align:start position:0% +notice that this is still a triangle the + + + align:start position:0% +notice that this is still a triangle the +length of this triangle is still + + align:start position:0% +length of this triangle is still + + + align:start position:0% +length of this triangle is still +expressible in terms of these sides and + + align:start position:0% +expressible in terms of these sides and + + + align:start position:0% +expressible in terms of these sides and +the included angle but you may recall + + align:start position:0% +the included angle but you may recall + + + align:start position:0% +the included angle but you may recall +from plain trigonometry and our + + align:start position:0% +from plain trigonometry and our + + + align:start position:0% +from plain trigonometry and our +refresher of that in the first part of + + align:start position:0% +refresher of that in the first part of + + + align:start position:0% +refresher of that in the first part of +our course part one that to find the + + align:start position:0% +our course part one that to find the + + + align:start position:0% +our course part one that to find the +third side of a triangle given two sides + + align:start position:0% +third side of a triangle given two sides + + + align:start position:0% +third side of a triangle given two sides +and the included angle one must use the + + align:start position:0% +and the included angle one must use the + + + align:start position:0% +and the included angle one must use the +law of cosin in other words the + + align:start position:0% +law of cosin in other words the + + + align:start position:0% +law of cosin in other words the +magnitude of V has what property that + + align:start position:0% +magnitude of V has what property that + + + align:start position:0% +magnitude of V has what property that +its square is equal to the sum of the + + align:start position:0% +its square is equal to the sum of the + + + align:start position:0% +its square is equal to the sum of the +squares of these two sides minus twice + + align:start position:0% +squares of these two sides minus twice + + + align:start position:0% +squares of these two sides minus twice +the product of these two lengths times + + align:start position:0% +the product of these two lengths times + + + align:start position:0% +the product of these two lengths times +the cosine of the included angle in + + align:start position:0% +the cosine of the included angle in + + + align:start position:0% +the cosine of the included angle in +other words this is just I hope this + + align:start position:0% +other words this is just I hope this + + + align:start position:0% +other words this is just I hope this +shows up all right this is the law of + + align:start position:0% +shows up all right this is the law of + + + align:start position:0% +shows up all right this is the law of +cosiness and if it's difficult to read + + align:start position:0% +cosiness and if it's difficult to read + + + align:start position:0% +cosiness and if it's difficult to read +don't bother reading it it's still the + + align:start position:0% +don't bother reading it it's still the + + + align:start position:0% +don't bother reading it it's still the +law of cosines and hopefully you + + align:start position:0% +law of cosines and hopefully you + + + align:start position:0% +law of cosines and hopefully you +recognize it as such in other words to + + align:start position:0% +recognize it as such in other words to + + + align:start position:0% +recognize it as such in other words to +the magnitude of V it's not just R1 or + + align:start position:0% +the magnitude of V it's not just R1 or + + + align:start position:0% +the magnitude of V it's not just R1 or +R2 minus R1 it's the square root of R1 2 + + align:start position:0% +R2 minus R1 it's the square root of R1 2 + + + align:start position:0% +R2 minus R1 it's the square root of R1 2 ++ R2 2- 2 R1 R2 cosine Theta 2us Theta 1 + + align:start position:0% ++ R2 2- 2 R1 R2 cosine Theta 2us Theta 1 + + + align:start position:0% ++ R2 2- 2 R1 R2 cosine Theta 2us Theta 1 +can you use polar coordinates if you + + align:start position:0% +can you use polar coordinates if you + + + align:start position:0% +can you use polar coordinates if you +want the answer is you bet you can but + + align:start position:0% +want the answer is you bet you can but + + + align:start position:0% +want the answer is you bet you can but +when you do use it make sure that + + align:start position:0% +when you do use it make sure that + + + align:start position:0% +when you do use it make sure that +whenever you're going to find the + + align:start position:0% +whenever you're going to find the + + + align:start position:0% +whenever you're going to find the +magnitude that you don't just subtract + + align:start position:0% +magnitude that you don't just subtract + + + align:start position:0% +magnitude that you don't just subtract +the two magnitudes you have to use this + + align:start position:0% +the two magnitudes you have to use this + + + align:start position:0% +the two magnitudes you have to use this +and by the way notice I haven't even + + align:start position:0% +and by the way notice I haven't even + + + align:start position:0% +and by the way notice I haven't even +gone into this part because it's + + align:start position:0% +gone into this part because it's + + + align:start position:0% +gone into this part because it's +irrelevant from the point of view I'm + + align:start position:0% +irrelevant from the point of view I'm + + + align:start position:0% +irrelevant from the point of view I'm +trying to emphasize now this mess just + + align:start position:0% +trying to emphasize now this mess just + + + align:start position:0% +trying to emphasize now this mess just +gives you the magnitude of the vector it + + align:start position:0% +gives you the magnitude of the vector it + + + align:start position:0% +gives you the magnitude of the vector it +doesn't even tell you what direction + + align:start position:0% +doesn't even tell you what direction + + + align:start position:0% +doesn't even tell you what direction +it's in I have to still do a heck of a + + align:start position:0% +it's in I have to still do a heck of a + + + align:start position:0% +it's in I have to still do a heck of a +lot of geometry if I want to find + + align:start position:0% +lot of geometry if I want to find + + + align:start position:0% +lot of geometry if I want to find +out what this angle here + + align:start position:0% +out what this angle here + + + align:start position:0% +out what this angle here +is I'm a lot of work involved I can use + + align:start position:0% +is I'm a lot of work involved I can use + + + align:start position:0% +is I'm a lot of work involved I can use +polar coordinates but I lose some of the + + align:start position:0% +polar coordinates but I lose some of the + + + align:start position:0% +polar coordinates but I lose some of the +luxury of cartisian coordinates in fact + + align:start position:0% +luxury of cartisian coordinates in fact + + + align:start position:0% +luxury of cartisian coordinates in fact +notice that the vector R2 minus whose + + align:start position:0% +notice that the vector R2 minus whose + + + align:start position:0% +notice that the vector R2 minus whose +magnitude is R2 minus R1 and whose angle + + align:start position:0% +magnitude is R2 minus R1 and whose angle + + + align:start position:0% +magnitude is R2 minus R1 and whose angle +of bearing is Theta 2 minus Theta 1 can + + align:start position:0% +of bearing is Theta 2 minus Theta 1 can + + + align:start position:0% +of bearing is Theta 2 minus Theta 1 can +also be computed namely how do we find + + align:start position:0% +also be computed namely how do we find + + + align:start position:0% +also be computed namely how do we find +Theta 2 minus Theta 1 well up here we + + align:start position:0% +Theta 2 minus Theta 1 well up here we + + + align:start position:0% +Theta 2 minus Theta 1 well up here we +have the angle Theta 2 we have the angle + + align:start position:0% +have the angle Theta 2 we have the angle + + + align:start position:0% +have the angle Theta 2 we have the angle +Theta 1 we computed Theta 2 minus Theta + + align:start position:0% +Theta 1 we computed Theta 2 minus Theta + + + align:start position:0% +Theta 1 we computed Theta 2 minus Theta +1 I can now Mark off that angle here + + align:start position:0% +1 I can now Mark off that angle here + + + align:start position:0% +1 I can now Mark off that angle here +Theta 2 minus Theta 1 I can now take a + + align:start position:0% +Theta 2 minus Theta 1 I can now take a + + + align:start position:0% +Theta 2 minus Theta 1 I can now take a +circle of radius R1 or Mark well why + + align:start position:0% +circle of radius R1 or Mark well why + + + align:start position:0% +circle of radius R1 or Mark well why +even say a circle mark off a length R1 + + align:start position:0% +even say a circle mark off a length R1 + + + align:start position:0% +even say a circle mark off a length R1 +onto R2 assuming R2 is the greater of + + align:start position:0% +onto R2 assuming R2 is the greater of + + + align:start position:0% +onto R2 assuming R2 is the greater of +the two lengths that difference will be + + align:start position:0% +the two lengths that difference will be + + + align:start position:0% +the two lengths that difference will be +R2 minus R1 in other words if I swing an + + align:start position:0% +R2 minus R1 in other words if I swing an + + + align:start position:0% +R2 minus R1 in other words if I swing an +arc over here this would be R1 also this + + align:start position:0% +arc over here this would be R1 also this + + + align:start position:0% +arc over here this would be R1 also this +distance here would be R2 minus R1 I + + align:start position:0% +distance here would be R2 minus R1 I + + + align:start position:0% +distance here would be R2 minus R1 I +take that distance and Mark it off down + + align:start position:0% +take that distance and Mark it off down + + + align:start position:0% +take that distance and Mark it off down +here and what Vector is this this is the + + align:start position:0% +here and what Vector is this this is the + + + align:start position:0% +here and what Vector is this this is the +vector which in polar coordinates would + + align:start position:0% +vector which in polar coordinates would + + + align:start position:0% +vector which in polar coordinates would +have its magnitude equal to R2 minus R1 + + align:start position:0% +have its magnitude equal to R2 minus R1 + + + align:start position:0% +have its magnitude equal to R2 minus R1 +and have its angle equal to Theta 2 + + align:start position:0% +and have its angle equal to Theta 2 + + + align:start position:0% +and have its angle equal to Theta 2 +minus Theta 1 and all I want you to see + + align:start position:0% +minus Theta 1 and all I want you to see + + + align:start position:0% +minus Theta 1 and all I want you to see +is no matter how you slice it just from + + align:start position:0% +is no matter how you slice it just from + + + align:start position:0% +is no matter how you slice it just from +this picture alone this + + align:start position:0% +this picture alone this + + + align:start position:0% +this picture alone this +Vector is not the same as this vector + + align:start position:0% +Vector is not the same as this vector + + + align:start position:0% +Vector is not the same as this vector +and by the way don't make the mistake of + + align:start position:0% +and by the way don't make the mistake of + + + align:start position:0% +and by the way don't make the mistake of +saying GE the way you've drawn them they + + align:start position:0% +saying GE the way you've drawn them they + + + align:start position:0% +saying GE the way you've drawn them they +look like they could be the same length + + align:start position:0% +look like they could be the same length + + + align:start position:0% +look like they could be the same length +remember that even if by coincidence + + align:start position:0% +remember that even if by coincidence + + + align:start position:0% +remember that even if by coincidence +these two vectors had the same length + + align:start position:0% +these two vectors had the same length + + + align:start position:0% +these two vectors had the same length +you must remember that Vector equality + + align:start position:0% +you must remember that Vector equality + + + align:start position:0% +you must remember that Vector equality +requires not just the same magnitude but + + align:start position:0% +requires not just the same magnitude but + + + align:start position:0% +requires not just the same magnitude but +the same direction and even with the + + align:start position:0% +the same direction and even with the + + + align:start position:0% +the same direction and even with the +same direction the same sense what + + align:start position:0% +same direction the same sense what + + + align:start position:0% +same direction the same sense what +should be obvious is at least based on + + align:start position:0% +should be obvious is at least based on + + + align:start position:0% +should be obvious is at least based on +this one picture that the direction of + + align:start position:0% +this one picture that the direction of + + + align:start position:0% +this one picture that the direction of +this Vector certainly is not the same as + + align:start position:0% +this Vector certainly is not the same as + + + align:start position:0% +this Vector certainly is not the same as +the direction of this Vector in other + + align:start position:0% +the direction of this Vector in other + + + align:start position:0% +the direction of this Vector in other +words I guess I've said this many times + + align:start position:0% +words I guess I've said this many times + + + align:start position:0% +words I guess I've said this many times +in part one and even though it comes out + + align:start position:0% +in part one and even though it comes out + + + align:start position:0% +in part one and even though it comes out +like phony fous I mean it quite + + align:start position:0% +like phony fous I mean it quite + + + align:start position:0% +like phony fous I mean it quite +sincerely given two vectors in polar + + align:start position:0% +sincerely given two vectors in polar + + + align:start position:0% +sincerely given two vectors in polar +coordinates one certainly has the + + align:start position:0% +coordinates one certainly has the + + + align:start position:0% +coordinates one certainly has the +right to invent the vector R2 - R1 comma + + align:start position:0% +right to invent the vector R2 - R1 comma + + + align:start position:0% +right to invent the vector R2 - R1 comma +Theta 2us comma Theta 1 you certainly + + align:start position:0% +Theta 2us comma Theta 1 you certainly + + + align:start position:0% +Theta 2us comma Theta 1 you certainly +have the right to do that but you don't + + align:start position:0% +have the right to do that but you don't + + + align:start position:0% +have the right to do that but you don't +have the right to call that a minus B I + + align:start position:0% +have the right to call that a minus B I + + + align:start position:0% +have the right to call that a minus B I +meant by being phous is you have the + + align:start position:0% +meant by being phous is you have the + + + align:start position:0% +meant by being phous is you have the +right to call it that but you're going + + align:start position:0% +right to call it that but you're going + + + align:start position:0% +right to call it that but you're going +to be wrong because a minus B has + + align:start position:0% +to be wrong because a minus B has + + + align:start position:0% +to be wrong because a minus B has +already been defined and all we have now + + align:start position:0% +already been defined and all we have now + + + align:start position:0% +already been defined and all we have now +is a choice of what the answer looks + + align:start position:0% +is a choice of what the answer looks + + + align:start position:0% +is a choice of what the answer looks +like in a + + align:start position:0% +like in a + + + align:start position:0% +like in a +particular coordinate system and by the + + align:start position:0% +particular coordinate system and by the + + + align:start position:0% +particular coordinate system and by the +way just as a quick review assuming that + + align:start position:0% +way just as a quick review assuming that + + + align:start position:0% +way just as a quick review assuming that +you've studied different number bases at + + align:start position:0% +you've studied different number bases at + + + align:start position:0% +you've studied different number bases at +one time in your careers this has come + + align:start position:0% +one time in your careers this has come + + + align:start position:0% +one time in your careers this has come +up many times in the Mathematics + + align:start position:0% +up many times in the Mathematics + + + align:start position:0% +up many times in the Mathematics +Curriculum Under The Heading of number + + align:start position:0% +Curriculum Under The Heading of number + + + align:start position:0% +Curriculum Under The Heading of number +versus numer umal or more generally I + + align:start position:0% +versus numer umal or more generally I + + + align:start position:0% +versus numer umal or more generally I +call it the heading of name versus + + align:start position:0% +call it the heading of name versus + + + align:start position:0% +call it the heading of name versus +concept for example consider the number + + align:start position:0% +concept for example consider the number + + + align:start position:0% +concept for example consider the number +six six is this many and no matter how + + align:start position:0% +six six is this many and no matter how + + + align:start position:0% +six six is this many and no matter how +it slice it again this many is an even + + align:start position:0% +it slice it again this many is an even + + + align:start position:0% +it slice it again this many is an even +number it breaks up into an even bundles + + align:start position:0% +number it breaks up into an even bundles + + + align:start position:0% +number it breaks up into an even bundles +of into bundles of two with none left + + align:start position:0% +of into bundles of two with none left + + + align:start position:0% +of into bundles of two with none left +over okay if you were to write six as a + + align:start position:0% +over okay if you were to write six as a + + + align:start position:0% +over okay if you were to write six as a +base five numeral it's what one bundle + + align:start position:0% +base five numeral it's what one bundle + + + align:start position:0% +base five numeral it's what one bundle +of five with one left over in other + + align:start position:0% +of five with one left over in other + + + align:start position:0% +of five with one left over in other +words notice that the number six ends in + + align:start position:0% +words notice that the number six ends in + + + align:start position:0% +words notice that the number six ends in +an odd digit in base five in other words + + align:start position:0% +an odd digit in base five in other words + + + align:start position:0% +an odd digit in base five in other words +the test for evenness by looking at the + + align:start position:0% +the test for evenness by looking at the + + + align:start position:0% +the test for evenness by looking at the +last digit depends on the number base in + + align:start position:0% +last digit depends on the number base in + + + align:start position:0% +last digit depends on the number base in +other words in an even base a number is + + align:start position:0% +other words in an even base a number is + + + align:start position:0% +other words in an even base a number is +even if its units digit is even in an + + align:start position:0% +even if its units digit is even in an + + + align:start position:0% +even if its units digit is even in an +odd base a number may may or may not be + + align:start position:0% +odd base a number may may or may not be + + + align:start position:0% +odd base a number may may or may not be +even depending on whether its units + + align:start position:0% +even depending on whether its units + + + align:start position:0% +even depending on whether its units +digit is even in other words the actual + + align:start position:0% +digit is even in other words the actual + + + align:start position:0% +digit is even in other words the actual +test that you're using the actual + + align:start position:0% +test that you're using the actual + + + align:start position:0% +test that you're using the actual +convenient computational property + + align:start position:0% +convenient computational property + + + align:start position:0% +convenient computational property +depends on the base but the important + + align:start position:0% +depends on the base but the important + + + align:start position:0% +depends on the base but the important +point is that six is always is even + + align:start position:0% +point is that six is always is even + + + align:start position:0% +point is that six is always is even +independently of a number basee in fact + + align:start position:0% +independently of a number basee in fact + + + align:start position:0% +independently of a number basee in fact +the number six as six tally marks was + + align:start position:0% +the number six as six tally marks was + + + align:start position:0% +the number six as six tally marks was +invented long before place value + + align:start position:0% +invented long before place value + + + align:start position:0% +invented long before place value +enumeration you see what I'm driving at + + align:start position:0% +enumeration you see what I'm driving at + + + align:start position:0% +enumeration you see what I'm driving at +in other words the number concept stays + + align:start position:0% +in other words the number concept stays + + + align:start position:0% +in other words the number concept stays +the same the concept stays the same what + + align:start position:0% +the same the concept stays the same what + + + align:start position:0% +the same the concept stays the same what +the thing looks like in terms of a + + align:start position:0% +the thing looks like in terms of a + + + align:start position:0% +the thing looks like in terms of a +particular set of names that's what + + align:start position:0% +particular set of names that's what + + + align:start position:0% +particular set of names that's what +depends on the names that you choose all + + align:start position:0% +depends on the names that you choose all + + + align:start position:0% +depends on the names that you choose all +right I think that's very very important + + align:start position:0% +right I think that's very very important + + + align:start position:0% +right I think that's very very important +to see the vector properties do not + + align:start position:0% +to see the vector properties do not + + + align:start position:0% +to see the vector properties do not +change the convenient computational + + align:start position:0% +change the convenient computational + + + align:start position:0% +change the convenient computational +recipes do depend on what coordinate + + align:start position:0% +recipes do depend on what coordinate + + + align:start position:0% +recipes do depend on what coordinate +system you're choosing and that's one of + + align:start position:0% +system you're choosing and that's one of + + + align:start position:0% +system you're choosing and that's one of +the reasons the same as in part one of + + align:start position:0% +the reasons the same as in part one of + + + align:start position:0% +the reasons the same as in part one of +this course why we find it very + + align:start position:0% +this course why we find it very + + + align:start position:0% +this course why we find it very +convenient whenever possible to use + + align:start position:0% +convenient whenever possible to use + + + align:start position:0% +convenient whenever possible to use +cartisian coordinates okay and let me + + align:start position:0% +cartisian coordinates okay and let me + + + align:start position:0% +cartisian coordinates okay and let me +just summarize this some + + align:start position:0% + + + + align:start position:0% + +more structurally this is very important + + align:start position:0% +more structurally this is very important + + + align:start position:0% +more structurally this is very important +here structurally Arrow arithmetic is + + align:start position:0% +here structurally Arrow arithmetic is + + + align:start position:0% +here structurally Arrow arithmetic is +the same for both two and three + + align:start position:0% +the same for both two and three + + + align:start position:0% +the same for both two and three +dimensions for example without be + + align:start position:0% +dimensions for example without be + + + align:start position:0% +dimensions for example without be +laboring the point whether we're dealing + + align:start position:0% +laboring the point whether we're dealing + + + align:start position:0% +laboring the point whether we're dealing +with two-dimensional arrows or + + align:start position:0% +with two-dimensional arrows or + + + align:start position:0% +with two-dimensional arrows or +three-dimensional arrows a plus b is B+ + + align:start position:0% +three-dimensional arrows a plus b is B+ + + + align:start position:0% +three-dimensional arrows a plus b is B+ +a a + B+ C is equal to a plus b plus C + + align:start position:0% +a a + B+ C is equal to a plus b plus C + + + align:start position:0% +a a + B+ C is equal to a plus b plus C +and let me just say Etc and not belabor + + align:start position:0% +and let me just say Etc and not belabor + + + align:start position:0% +and let me just say Etc and not belabor +this particular point that structurally + + align:start position:0% +this particular point that structurally + + + align:start position:0% +this particular point that structurally +we cannot tell the difference between + + align:start position:0% +we cannot tell the difference between + + + align:start position:0% +we cannot tell the difference between +two-dimensional vectors and + + align:start position:0% +two-dimensional vectors and + + + align:start position:0% +two-dimensional vectors and +three-dimensional vectors what we can + + align:start position:0% +three-dimensional vectors what we can + + + align:start position:0% +three-dimensional vectors what we can +tell the difference between I guess is + + align:start position:0% +tell the difference between I guess is + + + align:start position:0% +tell the difference between I guess is +the geometry the geom omry may be more + + align:start position:0% +the geometry the geom omry may be more + + + align:start position:0% +the geometry the geom omry may be more +difficult to visualize in three space + + align:start position:0% +difficult to visualize in three space + + + align:start position:0% +difficult to visualize in three space +than in two space but structurally we + + align:start position:0% +than in two space but structurally we + + + align:start position:0% +than in two space but structurally we +cannot tell the difference and I guess + + align:start position:0% +cannot tell the difference and I guess + + + align:start position:0% +cannot tell the difference and I guess +this is what this thing is all about + + align:start position:0% +this is what this thing is all about + + + align:start position:0% +this is what this thing is all about +that as you read the textbook and do + + align:start position:0% +that as you read the textbook and do + + + align:start position:0% +that as you read the textbook and do +your assignment there is going to be a + + align:start position:0% +your assignment there is going to be a + + + align:start position:0% +your assignment there is going to be a +tendency on your part to try to rely on + + align:start position:0% +tendency on your part to try to rely on + + + align:start position:0% +tendency on your part to try to rely on +diagrams and boy you have to be an + + align:start position:0% +diagrams and boy you have to be an + + + align:start position:0% +diagrams and boy you have to be an +expert in descriptive geometry to be + + align:start position:0% +expert in descriptive geometry to be + + + align:start position:0% +expert in descriptive geometry to be +able to take a view of something in + + align:start position:0% +able to take a view of something in + + + align:start position:0% +able to take a view of something in +three dimensions and try to get its true + + align:start position:0% +three dimensions and try to get its true + + + align:start position:0% +three dimensions and try to get its true +lengths as you look along various axes + + align:start position:0% +lengths as you look along various axes + + + align:start position:0% +lengths as you look along various axes +and lines of sight the beauty is going + + align:start position:0% +and lines of sight the beauty is going + + + align:start position:0% +and lines of sight the beauty is going +to be that as we continue on with this + + align:start position:0% +to be that as we continue on with this + + + align:start position:0% +to be that as we continue on with this +course we will use geometry for + + align:start position:0% +course we will use geometry for + + + align:start position:0% +course we will use geometry for +motivation but once we have motivated + + align:start position:0% +motivation but once we have motivated + + + align:start position:0% +motivation but once we have motivated +things by geometry we will extract those + + align:start position:0% +things by geometry we will extract those + + + align:start position:0% +things by geometry we will extract those +rules that we can use even in cases + + align:start position:0% +rules that we can use even in cases + + + align:start position:0% +rules that we can use even in cases +where we can't see the picture in much + + align:start position:0% +where we can't see the picture in much + + + align:start position:0% +where we can't see the picture in much +the same way going back to our first + + align:start position:0% +the same way going back to our first + + + align:start position:0% +the same way going back to our first +lecture when we talked about why B to + + align:start position:0% +lecture when we talked about why B to + + + align:start position:0% +lecture when we talked about why B to +the 0 equals 1 we made up our rules to + + align:start position:0% +the 0 equals 1 we made up our rules to + + + align:start position:0% +the 0 equals 1 we made up our rules to +make sure that they would conform with + + align:start position:0% +make sure that they would conform with + + + align:start position:0% +make sure that they would conform with +the nice or conform to the nice + + align:start position:0% +the nice or conform to the nice + + + align:start position:0% +the nice or conform to the nice +computational recipes that were + + align:start position:0% +computational recipes that were + + + align:start position:0% +computational recipes that were +prevalent in the more simple cases and + + align:start position:0% +prevalent in the more simple cases and + + + align:start position:0% +prevalent in the more simple cases and +we are going to play this thing to the + + align:start position:0% +we are going to play this thing to the + + + align:start position:0% +we are going to play this thing to the +hilt we're going to really exploit this + + align:start position:0% +hilt we're going to really exploit this + + + align:start position:0% +hilt we're going to really exploit this +and explore it in future lectures and in + + align:start position:0% +and explore it in future lectures and in + + + align:start position:0% +and explore it in future lectures and in +fact throughout the rest of this course + + align:start position:0% +fact throughout the rest of this course + + + align:start position:0% +fact throughout the rest of this course +but more about that next time and until + + align:start position:0% +but more about that next time and until + + + align:start position:0% +but more about that next time and until +next time + + align:start position:0% +next time + + + align:start position:0% +next time +goodbye funding for the publication of + + align:start position:0% +goodbye funding for the publication of + + + align:start position:0% +goodbye funding for the publication of +this video was provided by the Gabriella + + align:start position:0% +this video was provided by the Gabriella + + + align:start position:0% +this video was provided by the Gabriella +and Paul rosenbom Foundation + + align:start position:0% +and Paul rosenbom Foundation + + + align:start position:0% +and Paul rosenbom Foundation +help ocw continue to provide free and + + align:start position:0% +help ocw continue to provide free and + + + align:start position:0% +help ocw continue to provide free and +open access to MIT courses by making a + + align:start position:0% +open access to MIT courses by making a + + + align:start position:0% +open access to MIT courses by making a +donation at ocw.mit.edu/donate \ No newline at end of file diff --git a/JF-5nlUNx_g.txt b/JF-5nlUNx_g.txt new file mode 100644 index 0000000000000000000000000000000000000000..e58ea53139a7575b5d3a799b3b594391da7e6e9a --- /dev/null +++ b/JF-5nlUNx_g.txt @@ -0,0 +1,459 @@ +align:start position:0% + +hey everyone this is our first video + + align:start position:0% +hey everyone this is our first video + + + align:start position:0% +hey everyone this is our first video +update we are now starting week one of + + align:start position:0% +update we are now starting week one of + + + align:start position:0% +update we are now starting week one of +the course I think that what we'll + + align:start position:0% +the course I think that what we'll + + + align:start position:0% +the course I think that what we'll +probably say now more than anything else + + align:start position:0% +probably say now more than anything else + + + align:start position:0% +probably say now more than anything else +is a quick conversation about the + + align:start position:0% +is a quick conversation about the + + + align:start position:0% +is a quick conversation about the +equipment many of you are concerned that + + align:start position:0% +equipment many of you are concerned that + + + align:start position:0% +equipment many of you are concerned that +I'm being a little too picky in what I'm + + align:start position:0% +I'm being a little too picky in what I'm + + + align:start position:0% +I'm being a little too picky in what I'm +requiring of you now first of all I am + + align:start position:0% +requiring of you now first of all I am + + + align:start position:0% +requiring of you now first of all I am +not requiring anything of you what I'm + + align:start position:0% +not requiring anything of you what I'm + + + align:start position:0% +not requiring anything of you what I'm +doing is showing you what I do and my + + align:start position:0% +doing is showing you what I do and my + + + align:start position:0% +doing is showing you what I do and my +technique My Hope Is that you'll like + + align:start position:0% +technique My Hope Is that you'll like + + + align:start position:0% +technique My Hope Is that you'll like +what I make the images that I make and + + align:start position:0% +what I make the images that I make and + + + align:start position:0% +what I make the images that I make and +follow my lead and for the most part the + + align:start position:0% +follow my lead and for the most part the + + + align:start position:0% +follow my lead and for the most part the +exercises that we've developed really + + align:start position:0% +exercises that we've developed really + + + align:start position:0% +exercises that we've developed really +are intended to be used with a 105 macro + + align:start position:0% +are intended to be used with a 105 macro + + + align:start position:0% +are intended to be used with a 105 macro +lens on a camera that can take lenses it + + align:start position:0% +lens on a camera that can take lenses it + + + align:start position:0% +lens on a camera that can take lenses it +is not going to work for you if you're + + align:start position:0% +is not going to work for you if you're + + + align:start position:0% +is not going to work for you if you're +going to just use a a a snap and shoot + + align:start position:0% +going to just use a a a snap and shoot + + + align:start position:0% +going to just use a a a snap and shoot +or whatever you call it these days it + + align:start position:0% +or whatever you call it these days it + + + align:start position:0% +or whatever you call it these days it +you you really want to uh meet the + + align:start position:0% +you you really want to uh meet the + + + align:start position:0% +you you really want to uh meet the +standards if I could say that that we + + align:start position:0% +standards if I could say that that we + + + align:start position:0% +standards if I could say that that we +are suggesting you pay attention to uh + + align:start position:0% +are suggesting you pay attention to uh + + + align:start position:0% +are suggesting you pay attention to uh +it is true that you can on occasion use + + align:start position:0% +it is true that you can on occasion use + + + align:start position:0% +it is true that you can on occasion use +extension tubes instead of for example + + align:start position:0% +extension tubes instead of for example + + + align:start position:0% +extension tubes instead of for example +let's say you don't have as much of a + + align:start position:0% +let's say you don't have as much of a + + + align:start position:0% +let's say you don't have as much of a +macro lens as you'd like and so you can + + align:start position:0% +macro lens as you'd like and so you can + + + align:start position:0% +macro lens as you'd like and so you can +use tube extensions as long as long as + + align:start position:0% +use tube extensions as long as long as + + + align:start position:0% +use tube extensions as long as long as +they don't have any glass but you're + + align:start position:0% +they don't have any glass but you're + + + align:start position:0% +they don't have any glass but you're +going to be using F sorry you'll be + + align:start position:0% +going to be using F sorry you'll be + + + align:start position:0% +going to be using F sorry you'll be +losing f-stops in the process and you'll + + align:start position:0% +losing f-stops in the process and you'll + + + align:start position:0% +losing f-stops in the process and you'll +find out more about aperture and f-stops + + align:start position:0% +find out more about aperture and f-stops + + + align:start position:0% +find out more about aperture and f-stops +in in the oncoming weeks so those of you + + align:start position:0% +in in the oncoming weeks so those of you + + + align:start position:0% +in in the oncoming weeks so those of you +who are technically Savvy I I hope that + + align:start position:0% +who are technically Savvy I I hope that + + + align:start position:0% +who are technically Savvy I I hope that +you'll find what our exercises have + + align:start position:0% +you'll find what our exercises have + + + align:start position:0% +you'll find what our exercises have +become developed into and the and the + + align:start position:0% +become developed into and the and the + + + align:start position:0% +become developed into and the and the +ideas in the course will be uh + + align:start position:0% +ideas in the course will be uh + + + align:start position:0% +ideas in the course will be uh +appropriate for your needs as well but + + align:start position:0% +appropriate for your needs as well but + + + align:start position:0% +appropriate for your needs as well but +just getting back to the equipment I I + + align:start position:0% +just getting back to the equipment I I + + + align:start position:0% +just getting back to the equipment I I +for for example when we get up to using + + align:start position:0% +for for example when we get up to using + + + align:start position:0% +for for example when we get up to using +a camera and a lens uh which is in week + + align:start position:0% +a camera and a lens uh which is in week + + + align:start position:0% +a camera and a lens uh which is in week +two you're going to see that I'm going + + align:start position:0% +two you're going to see that I'm going + + + align:start position:0% +two you're going to see that I'm going +to suggest using software and you'll + + align:start position:0% +to suggest using software and you'll + + + align:start position:0% +to suggest using software and you'll +probably say why is she doing that well + + align:start position:0% +probably say why is she doing that well + + + align:start position:0% +probably say why is she doing that well +I'd like to hope that I'm going to be + + align:start position:0% +I'd like to hope that I'm going to be + + + align:start position:0% +I'd like to hope that I'm going to be +making a case for that so in the end + + align:start position:0% +making a case for that so in the end + + + align:start position:0% +making a case for that so in the end +please consider following what we're + + align:start position:0% +please consider following what we're + + + align:start position:0% +please consider following what we're +suggesting uh it works for me and my + + align:start position:0% +suggesting uh it works for me and my + + + align:start position:0% +suggesting uh it works for me and my +hope is that what works for me is going + + align:start position:0% +hope is that what works for me is going + + + align:start position:0% +hope is that what works for me is going +to work for you but this coming week + + align:start position:0% +to work for you but this coming week + + + align:start position:0% +to work for you but this coming week +we're going to have more fun in the + + align:start position:0% +we're going to have more fun in the + + + align:start position:0% +we're going to have more fun in the +sense it's you're not going to work that + + align:start position:0% +sense it's you're not going to work that + + + align:start position:0% +sense it's you're not going to work that +hard because you're going to be using a + + align:start position:0% +hard because you're going to be using a + + + align:start position:0% +hard because you're going to be using a +flatbed scanner and you're going to be a + + align:start position:0% +flatbed scanner and you're going to be a + + + align:start position:0% +flatbed scanner and you're going to be a +bit shocked at some of the wonderful + + align:start position:0% +bit shocked at some of the wonderful + + + align:start position:0% +bit shocked at some of the wonderful +images you can get from that so in any + + align:start position:0% +images you can get from that so in any + + + align:start position:0% +images you can get from that so in any +event we hope we're going to create + + align:start position:0% +event we hope we're going to create + + + align:start position:0% +event we hope we're going to create +something wonderful for you have fun + + align:start position:0% +something wonderful for you have fun + + + align:start position:0% +something wonderful for you have fun +this week \ No newline at end of file diff --git a/JSm74ghAvJc.txt b/JSm74ghAvJc.txt new file mode 100644 index 0000000000000000000000000000000000000000..36e99df4a2c98e40b5322051ee704508de9edbcf --- /dev/null +++ b/JSm74ghAvJc.txt @@ -0,0 +1,1187 @@ +align:start position:0% + +the beta is an example of a reduced + + align:start position:0% +the beta is an example of a reduced + + + align:start position:0% +the beta is an example of a reduced +instruction set computer architecture + + align:start position:0% +instruction set computer architecture + + + align:start position:0% +instruction set computer architecture +reduced refers to the fact that in the + + align:start position:0% +reduced refers to the fact that in the + + + align:start position:0% +reduced refers to the fact that in the +beta is a most instructions only access + + align:start position:0% +beta is a most instructions only access + + + align:start position:0% +beta is a most instructions only access +the internal registers for their + + align:start position:0% +the internal registers for their + + + align:start position:0% +the internal registers for their +operands and destination memory values + + align:start position:0% +operands and destination memory values + + + align:start position:0% +operands and destination memory values +are loaded in store using separate + + align:start position:0% +are loaded in store using separate + + + align:start position:0% +are loaded in store using separate +memory access instructions which + + align:start position:0% +memory access instructions which + + + align:start position:0% +memory access instructions which +implement only a simple address + + align:start position:0% +implement only a simple address + + + align:start position:0% +implement only a simple address +calculation these reductions lead to + + align:start position:0% +calculation these reductions lead to + + + align:start position:0% +calculation these reductions lead to +smaller higher performance hardware + + align:start position:0% +smaller higher performance hardware + + + align:start position:0% +smaller higher performance hardware +implementations and simpler compilers on + + align:start position:0% +implementations and simpler compilers on + + + align:start position:0% +implementations and simpler compilers on +the software side the arm and MIPS ISAs + + align:start position:0% +the software side the arm and MIPS ISAs + + + align:start position:0% +the software side the arm and MIPS ISAs +are other examples of RISC architectures + + align:start position:0% +are other examples of RISC architectures + + + align:start position:0% +are other examples of RISC architectures +Intel's x86 ISA is more complex there is + + align:start position:0% +Intel's x86 ISA is more complex there is + + + align:start position:0% +Intel's x86 ISA is more complex there is +a limited amount of storage inside of + + align:start position:0% +a limited amount of storage inside of + + + align:start position:0% +a limited amount of storage inside of +the CPU using the language of sequential + + align:start position:0% +the CPU using the language of sequential + + + align:start position:0% +the CPU using the language of sequential +logic we refer to this as the CPU State + + align:start position:0% +logic we refer to this as the CPU State + + + align:start position:0% +logic we refer to this as the CPU State +there is a 32-bit program counter PC for + + align:start position:0% +there is a 32-bit program counter PC for + + + align:start position:0% +there is a 32-bit program counter PC for +short that holds the address of the + + align:start position:0% +short that holds the address of the + + + align:start position:0% +short that holds the address of the +current instruction in main memory and + + align:start position:0% +current instruction in main memory and + + + align:start position:0% +current instruction in main memory and +there are 32 registers numbered 0 + + align:start position:0% +there are 32 registers numbered 0 + + + align:start position:0% +there are 32 registers numbered 0 +through 31 + + align:start position:0% +through 31 + + + align:start position:0% +through 31 +each registers holds a 32-bit value will + + align:start position:0% +each registers holds a 32-bit value will + + + align:start position:0% +each registers holds a 32-bit value will +use 5 bit fields in the instruction to + + align:start position:0% +use 5 bit fields in the instruction to + + + align:start position:0% +use 5 bit fields in the instruction to +specify the number of the register to be + + align:start position:0% +specify the number of the register to be + + + align:start position:0% +specify the number of the register to be +used as an operand or destination a + + align:start position:0% +used as an operand or destination a + + + align:start position:0% +used as an operand or destination a +shorthand will refer to a register using + + align:start position:0% +shorthand will refer to a register using + + + align:start position:0% +shorthand will refer to a register using +the prefix are followed by his number + + align:start position:0% +the prefix are followed by his number + + + align:start position:0% +the prefix are followed by his number +for example r0 refers to the register + + align:start position:0% +for example r0 refers to the register + + + align:start position:0% +for example r0 refers to the register +selected by the 5-bit field 0 0 0 0 0 + + align:start position:0% +selected by the 5-bit field 0 0 0 0 0 + + + align:start position:0% +selected by the 5-bit field 0 0 0 0 0 +register 31 are 31 is special its value + + align:start position:0% +register 31 are 31 is special its value + + + align:start position:0% +register 31 are 31 is special its value +always reads a 0 and writes to R 31 have + + align:start position:0% +always reads a 0 and writes to R 31 have + + + align:start position:0% +always reads a 0 and writes to R 31 have +no effect on this value the number of + + align:start position:0% +no effect on this value the number of + + + align:start position:0% +no effect on this value the number of +bits in each register and has the number + + align:start position:0% +bits in each register and has the number + + + align:start position:0% +bits in each register and has the number +of bits supported by ALU operations is a + + align:start position:0% +of bits supported by ALU operations is a + + + align:start position:0% +of bits supported by ALU operations is a +fundamental parameter of the ISA the + + align:start position:0% +fundamental parameter of the ISA the + + + align:start position:0% +fundamental parameter of the ISA the +beta is a 32-bit architecture many + + align:start position:0% +beta is a 32-bit architecture many + + + align:start position:0% +beta is a 32-bit architecture many +modern computers are 64-bit + + align:start position:0% +modern computers are 64-bit + + + align:start position:0% +modern computers are 64-bit +architectures meaning they have 64-bit + + align:start position:0% +architectures meaning they have 64-bit + + + align:start position:0% +architectures meaning they have 64-bit +registers and a 64-bit data path main + + align:start position:0% +registers and a 64-bit data path main + + + align:start position:0% +registers and a 64-bit data path main +memory is an array of 32-bit words each + + align:start position:0% +memory is an array of 32-bit words each + + + align:start position:0% +memory is an array of 32-bit words each +word contains four 8-bit bytes the bytes + + align:start position:0% +word contains four 8-bit bytes the bytes + + + align:start position:0% +word contains four 8-bit bytes the bytes +are numbered 0 through 3 with byte 0 + + align:start position:0% +are numbered 0 through 3 with byte 0 + + + align:start position:0% +are numbered 0 through 3 with byte 0 +corresponding to the low-order 7 bits of + + align:start position:0% +corresponding to the low-order 7 bits of + + + align:start position:0% +corresponding to the low-order 7 bits of +the 32-bit value and so on the beta is a + + align:start position:0% +the 32-bit value and so on the beta is a + + + align:start position:0% +the 32-bit value and so on the beta is a +only supports word accesses either + + align:start position:0% +only supports word accesses either + + + align:start position:0% +only supports word accesses either +loading or storing full + + align:start position:0% +loading or storing full + + + align:start position:0% +loading or storing full +two-bit words most real computers also + + align:start position:0% +two-bit words most real computers also + + + align:start position:0% +two-bit words most real computers also +support accesses to bytes and half words + + align:start position:0% +support accesses to bytes and half words + + + align:start position:0% +support accesses to bytes and half words +even though the beta only accesses four + + align:start position:0% +even though the beta only accesses four + + + align:start position:0% +even though the beta only accesses four +words following a convention used by + + align:start position:0% +words following a convention used by + + + align:start position:0% +words following a convention used by +many is a it uses byte addresses since + + align:start position:0% +many is a it uses byte addresses since + + + align:start position:0% +many is a it uses byte addresses since +there are four bytes in each word + + align:start position:0% +there are four bytes in each word + + + align:start position:0% +there are four bytes in each word +consecutive words in memory have + + align:start position:0% +consecutive words in memory have + + + align:start position:0% +consecutive words in memory have +addresses that differ by four so the + + align:start position:0% +addresses that differ by four so the + + + align:start position:0% +addresses that differ by four so the +first word in memory has address zero + + align:start position:0% +first word in memory has address zero + + + align:start position:0% +first word in memory has address zero +the second word address four and so on + + align:start position:0% +the second word address four and so on + + + align:start position:0% +the second word address four and so on +you can see the addresses to the left of + + align:start position:0% +you can see the addresses to the left of + + + align:start position:0% +you can see the addresses to the left of +each memory location in the diagram + + align:start position:0% +each memory location in the diagram + + + align:start position:0% +each memory location in the diagram +shown here note that will usually use + + align:start position:0% +shown here note that will usually use + + + align:start position:0% +shown here note that will usually use +hexadecimal notation when specifying + + align:start position:0% +hexadecimal notation when specifying + + + align:start position:0% +hexadecimal notation when specifying +addresses and other binary values the 0x + + align:start position:0% +addresses and other binary values the 0x + + + align:start position:0% +addresses and other binary values the 0x +prefix indicates when a number is in hex + + align:start position:0% +prefix indicates when a number is in hex + + + align:start position:0% +prefix indicates when a number is in hex +when drawing a memory diagram will + + align:start position:0% +when drawing a memory diagram will + + + align:start position:0% +when drawing a memory diagram will +follow the convention that addresses + + align:start position:0% +follow the convention that addresses + + + align:start position:0% +follow the convention that addresses +increase as you read from top to bottom + + align:start position:0% +increase as you read from top to bottom + + + align:start position:0% +increase as you read from top to bottom +the beta supports 32-bit byte addressing + + align:start position:0% +the beta supports 32-bit byte addressing + + + align:start position:0% +the beta supports 32-bit byte addressing +so an address fits exactly into one + + align:start position:0% +so an address fits exactly into one + + + align:start position:0% +so an address fits exactly into one +32-bit register or memory location the + + align:start position:0% +32-bit register or memory location the + + + align:start position:0% +32-bit register or memory location the +maximum memory size is 2 to the 32nd + + align:start position:0% +maximum memory size is 2 to the 32nd + + + align:start position:0% +maximum memory size is 2 to the 32nd +bytes or 2 to the 30th words that's 4 + + align:start position:0% +bytes or 2 to the 30th words that's 4 + + + align:start position:0% +bytes or 2 to the 30th words that's 4 +gigabytes or 1 billion words of main + + align:start position:0% +gigabytes or 1 billion words of main + + + align:start position:0% +gigabytes or 1 billion words of main +memory some beta implementations might + + align:start position:0% +memory some beta implementations might + + + align:start position:0% +memory some beta implementations might +actually have a smaller main memory in + + align:start position:0% +actually have a smaller main memory in + + + align:start position:0% +actually have a smaller main memory in +other words one with fewer than 1 + + align:start position:0% +other words one with fewer than 1 + + + align:start position:0% +other words one with fewer than 1 +billion locations why have separate + + align:start position:0% +billion locations why have separate + + + align:start position:0% +billion locations why have separate +registers in main memory well modern + + align:start position:0% +registers in main memory well modern + + + align:start position:0% +registers in main memory well modern +programs and data sets are very large so + + align:start position:0% +programs and data sets are very large so + + + align:start position:0% +programs and data sets are very large so +we'll want to have a large memory to + + align:start position:0% +we'll want to have a large memory to + + + align:start position:0% +we'll want to have a large memory to +hold everything but large memories are + + align:start position:0% +hold everything but large memories are + + + align:start position:0% +hold everything but large memories are +slow and usually only support access to + + align:start position:0% +slow and usually only support access to + + + align:start position:0% +slow and usually only support access to +one location at a time so they don't + + align:start position:0% +one location at a time so they don't + + + align:start position:0% +one location at a time so they don't +make good storage for use in each + + align:start position:0% +make good storage for use in each + + + align:start position:0% +make good storage for use in each +instruction which needs to access + + align:start position:0% +instruction which needs to access + + + align:start position:0% +instruction which needs to access +several operands and store a result if + + align:start position:0% +several operands and store a result if + + + align:start position:0% +several operands and store a result if +we used only one large storage array + + align:start position:0% +we used only one large storage array + + + align:start position:0% +we used only one large storage array +then an instruction would need to have + + align:start position:0% +then an instruction would need to have + + + align:start position:0% +then an instruction would need to have +three 32-bit addresses to specify the + + align:start position:0% +three 32-bit addresses to specify the + + + align:start position:0% +three 32-bit addresses to specify the +two source operands and destination each + + align:start position:0% +two source operands and destination each + + + align:start position:0% +two source operands and destination each +instruction encoding would be huge and + + align:start position:0% +instruction encoding would be huge and + + + align:start position:0% +instruction encoding would be huge and +that required memory accesses would have + + align:start position:0% +that required memory accesses would have + + + align:start position:0% +that required memory accesses would have +to be one after the other really slowing + + align:start position:0% +to be one after the other really slowing + + + align:start position:0% +to be one after the other really slowing +down instruction execution on the other + + align:start position:0% +down instruction execution on the other + + + align:start position:0% +down instruction execution on the other +hand if we use registers to hold the + + align:start position:0% +hand if we use registers to hold the + + + align:start position:0% +hand if we use registers to hold the +operands and service the destination we + + align:start position:0% +operands and service the destination we + + + align:start position:0% +operands and service the destination we +can design the register hardware for + + align:start position:0% +can design the register hardware for + + + align:start position:0% +can design the register hardware for +parallel access and make it very fast to + + align:start position:0% +parallel access and make it very fast to + + + align:start position:0% +parallel access and make it very fast to +keep the speed up we won't be able to + + align:start position:0% +keep the speed up we won't be able to + + + align:start position:0% +keep the speed up we won't be able to +have very many registers + + align:start position:0% +have very many registers + + + align:start position:0% +have very many registers +a classic size versus speed performance + + align:start position:0% +a classic size versus speed performance + + + align:start position:0% +a classic size versus speed performance +trade-off we see in digital systems all + + align:start position:0% +trade-off we see in digital systems all + + + align:start position:0% +trade-off we see in digital systems all +the time in the end the trade-off + + align:start position:0% +the time in the end the trade-off + + + align:start position:0% +the time in the end the trade-off +leading to the best performance is to + + align:start position:0% +leading to the best performance is to + + + align:start position:0% +leading to the best performance is to +have a small number of very fast + + align:start position:0% +have a small number of very fast + + + align:start position:0% +have a small number of very fast +registers used by most instructions and + + align:start position:0% +registers used by most instructions and + + + align:start position:0% +registers used by most instructions and +a large but slow main memory so that's + + align:start position:0% +a large but slow main memory so that's + + + align:start position:0% +a large but slow main memory so that's +what the beta is a does in general all + + align:start position:0% +what the beta is a does in general all + + + align:start position:0% +what the beta is a does in general all +program data will reside in main memory + + align:start position:0% +program data will reside in main memory + + + align:start position:0% +program data will reside in main memory +each variable used by the program lives + + align:start position:0% +each variable used by the program lives + + + align:start position:0% +each variable used by the program lives +in a specific main memory location and + + align:start position:0% +in a specific main memory location and + + + align:start position:0% +in a specific main memory location and +so has a specific memory address for + + align:start position:0% +so has a specific memory address for + + + align:start position:0% +so has a specific memory address for +example in the diagram below the value + + align:start position:0% +example in the diagram below the value + + + align:start position:0% +example in the diagram below the value +of the variable X is stored in memory + + align:start position:0% +of the variable X is stored in memory + + + align:start position:0% +of the variable X is stored in memory +location hex 108 and the value of y is + + align:start position:0% +location hex 108 and the value of y is + + + align:start position:0% +location hex 108 and the value of y is +stored in memory location hex 1000 and C + + align:start position:0% +stored in memory location hex 1000 and C + + + align:start position:0% +stored in memory location hex 1000 and C +and so on to perform a computation for + + align:start position:0% +and so on to perform a computation for + + + align:start position:0% +and so on to perform a computation for +example to compute x times 37 and stir + + align:start position:0% +example to compute x times 37 and stir + + + align:start position:0% +example to compute x times 37 and stir +the result in Y we would have to first + + align:start position:0% +the result in Y we would have to first + + + align:start position:0% +the result in Y we would have to first +load the value of X into a register say + + align:start position:0% +load the value of X into a register say + + + align:start position:0% +load the value of X into a register say +r0 then we would have the datapath + + align:start position:0% +r0 then we would have the datapath + + + align:start position:0% +r0 then we would have the datapath +multiply the value in r0 by 37 stirring + + align:start position:0% +multiply the value in r0 by 37 stirring + + + align:start position:0% +multiply the value in r0 by 37 stirring +the result back in r0 here we've assumed + + align:start position:0% +the result back in r0 here we've assumed + + + align:start position:0% +the result back in r0 here we've assumed +that the constant 37 is somehow + + align:start position:0% +that the constant 37 is somehow + + + align:start position:0% +that the constant 37 is somehow +available to the data path and doesn't + + align:start position:0% +available to the data path and doesn't + + + align:start position:0% +available to the data path and doesn't +itself need to be loaded from memory + + align:start position:0% +itself need to be loaded from memory + + + align:start position:0% +itself need to be loaded from memory +finally we would write the updated value + + align:start position:0% +finally we would write the updated value + + + align:start position:0% +finally we would write the updated value +in r0 back into memory at the location + + align:start position:0% +in r0 back into memory at the location + + + align:start position:0% +in r0 back into memory at the location +for Y a lot of steps of course we could + + align:start position:0% +for Y a lot of steps of course we could + + + align:start position:0% +for Y a lot of steps of course we could +avoid all the loading and storing if we + + align:start position:0% +avoid all the loading and storing if we + + + align:start position:0% +avoid all the loading and storing if we +chose to keep the values for x and y in + + align:start position:0% +chose to keep the values for x and y in + + + align:start position:0% +chose to keep the values for x and y in +registers since there are only 32 + + align:start position:0% +registers since there are only 32 + + + align:start position:0% +registers since there are only 32 +registers we can't do this for all of + + align:start position:0% +registers we can't do this for all of + + + align:start position:0% +registers we can't do this for all of +our variables but maybe we could arrange + + align:start position:0% +our variables but maybe we could arrange + + + align:start position:0% +our variables but maybe we could arrange +to load x and y into registers do all + + align:start position:0% +to load x and y into registers do all + + + align:start position:0% +to load x and y into registers do all +the required computations involving x + + align:start position:0% +the required computations involving x + + + align:start position:0% +the required computations involving x +and y by referring to those registers + + align:start position:0% +and y by referring to those registers + + + align:start position:0% +and y by referring to those registers +and then when we're done store changes + + align:start position:0% +and then when we're done store changes + + + align:start position:0% +and then when we're done store changes +to x and y back into memory for later + + align:start position:0% +to x and y back into memory for later + + + align:start position:0% +to x and y back into memory for later +use optimizing performance by keeping + + align:start position:0% +use optimizing performance by keeping + + + align:start position:0% +use optimizing performance by keeping +often to use values in registers is a + + align:start position:0% +often to use values in registers is a + + + align:start position:0% +often to use values in registers is a +favorite trick of programmers and + + align:start position:0% +favorite trick of programmers and + + + align:start position:0% +favorite trick of programmers and +compiler writers so the basic program + + align:start position:0% +compiler writers so the basic program + + + align:start position:0% +compiler writers so the basic program +template is some loads to bring in + + align:start position:0% +template is some loads to bring in + + + align:start position:0% +template is some loads to bring in +values into the registers followed by + + align:start position:0% +values into the registers followed by + + + align:start position:0% +values into the registers followed by +computation followed by any necessary + + align:start position:0% +computation followed by any necessary + + + align:start position:0% +computation followed by any necessary +stores ISAs that use this template are + + align:start position:0% +stores ISAs that use this template are + + + align:start position:0% +stores ISAs that use this template are +usually referred to as load store + + align:start position:0% +usually referred to as load store + + + align:start position:0% +usually referred to as load store +architecture \ No newline at end of file diff --git a/JgMXrmpq1vg.txt b/JgMXrmpq1vg.txt new file mode 100644 index 0000000000000000000000000000000000000000..ce1441ff937ca77705ca47730cde40c3592bd030 --- /dev/null +++ b/JgMXrmpq1vg.txt @@ -0,0 +1,223 @@ +PHIL: The prize for the biggest +crystal is a lunch + +with John and the TAs at Legal +Seafood, which I'm personally + +very excited about. + +[MUSIC PLAYING] + +NARRATOR: Today the students are +going to learn a totally + +different technique, +recrystallization. + +PHIL: Pesticides, +pharmaceuticals, food + +colorings, and products where +they have to produce tons per + +year, recrystallization +is the key method. + +Yesterday you were working +with about 100 + +megs of each compound. + +Today, you're going to be +working with 2 grams. + +NARRATOR: But there's more on +the line than just getting + +those 2 grams back. + +This is practice for next week's +crystal competition. + +If the students do well, they'll +have a better shot at + +winning a free lunch with +the teaching staff. + +The first step in a +recrystallization is to choose + +the right solvent. + +The students need a liquid that +will not dissolve the + +target molecule when it's cold, +but will dissolve it + +when it's hot. + +The students then dissolve the +sample in hot solvent and + +filter out any solid +impurities. + +Then they cool it down +in an ice bath. + +The target molecule should +crystallized out of solution + +forming a pure solid. + +The impurities should +stay in the liquid. + +ANTHONY: Fresh. + +IKE: Yep. + +That's how we want it. + +Crystal clear. + +NARRATOR: Ike, Ethan, and +Anthony are having + +no problems at all. + +ETHAN: Ain't nothing too hard +for an MIT chemist. + +NARRATOR: Hansol, Jason, and +Fred on the other hand-- + +HANSOL: I made like two, +actually three mistakes today. + +JASON: I've made so many +stupid mistakes today. + +HANSOL: Yeah, I didn't realize +it would heat that fast. + +FRED: Um, it exploded all over +the side of my flask. + +HANSOL: And then it exploded, +so then I had to start over. + +PAUL: It started sputtering +out and actually + +it was kind of scary. + +Some of it almost like +hit me in the face. + +JASON: I've broken +a test tube. + +HANSOL: And then I put it +through a small funnel which + +was a total mistake. + +JASON: I put too much solvent +losing some product. + +HANSOL: The funnel, +I just dropped it. + +So-- + +JASON: The yield on this +is almost nothing. + +NARRATOR: After filtering, +washing and drying, everyone + +eventually makes it to the +final step, weighing the + +purified crystals. + +Getting 90% yield is the goal. + +That would be 1.8 grams of +the original crystal. + +LEALIA: So far my yield +says 1.9 grams. + +So I don't know if that's right +because there is only + +supposed to be two grams. + +JULIE: That's probably not going +to be that good because + +that all I have. + +There were some problems with +filtering and then also + +noticed trying to put the stuff +in the beginning, I + +spilled it everywhere. + +YI-SHIUAN: Is it really pure? + +JULIE: 7%. + +LEALIA: 101% yield. + +JULIE: Good job. + +JASON: 3%. + +So besides 3% yield, my melting + +point's almost perfect. + +NARRATOR: For some today, +a good start. + +For others-- + +JASON: 3% yield. + +You needed 90%. + +I only got 3%. + +NARRATOR: Not looking so +hot for next week. + +Tune in, and see how +it all unfolds. + +PHIL: Just make observations, +write down what could have + +went wrong, what you could +do differently next time. + +JASON: Not spill. + +Sleep more beforehand so +I don't make mistakes. + +Not spill. + +PHIL: Take your vitamins. + +JASON: Not be an idiot. + +I don't know. + +[MUSIC PLAYING] \ No newline at end of file diff --git a/JuwErrBz3b4.txt b/JuwErrBz3b4.txt new file mode 100644 index 0000000000000000000000000000000000000000..3a338841b61b706f481d8f79e9f8ff42e53b06dd --- /dev/null +++ b/JuwErrBz3b4.txt @@ -0,0 +1,6875 @@ +align:start position:0% + +and today I'm going to talk about + + align:start position:0% +and today I'm going to talk about + + + align:start position:0% +and today I'm going to talk about +sequencing and I want to start by just + + align:start position:0% +sequencing and I want to start by just + + + align:start position:0% +sequencing and I want to start by just +sort of illustrating an example of how + + align:start position:0% +sort of illustrating an example of how + + + align:start position:0% +sort of illustrating an example of how +knowing the DNA sequence can be helpful + + align:start position:0% +knowing the DNA sequence can be helpful + + + align:start position:0% +knowing the DNA sequence can be helpful +so you remember in last lecture we + + align:start position:0% +so you remember in last lecture we + + + align:start position:0% +so you remember in last lecture we +talked about how one might identify a + + align:start position:0% +talked about how one might identify a + + + align:start position:0% +talked about how one might identify a +gene through functional complementation + + align:start position:0% +gene through functional complementation + + + align:start position:0% +gene through functional complementation +and this process involved making a DNA + + align:start position:0% +and this process involved making a DNA + + + align:start position:0% +and this process involved making a DNA +library that different fragments of DNA + + align:start position:0% +library that different fragments of DNA + + + align:start position:0% +library that different fragments of DNA +cloned into different plasmids and and + + align:start position:0% +cloned into different plasmids and and + + + align:start position:0% +cloned into different plasmids and and +then involved finding the needle in the + + align:start position:0% +then involved finding the needle in the + + + align:start position:0% +then involved finding the needle in the +haystack where you're you find the gene + + align:start position:0% +haystack where you're you find the gene + + + align:start position:0% +haystack where you're you find the gene +that can rescue a defect in a mutant + + align:start position:0% +that can rescue a defect in a mutant + + + align:start position:0% +that can rescue a defect in a mutant +that you have so if this line that I'm + + align:start position:0% +that you have so if this line that I'm + + + align:start position:0% +that you have so if this line that I'm +drawing here is genomic DNA and it could + + align:start position:0% +drawing here is genomic DNA and it could + + + align:start position:0% +drawing here is genomic DNA and it could +be genomic DNA from let's say a proto + + align:start position:0% +be genomic DNA from let's say a proto + + + align:start position:0% +be genomic DNA from let's say a proto +truth for Lou to the leucine to gene so + + align:start position:0% +truth for Lou to the leucine to gene so + + + align:start position:0% +truth for Lou to the leucine to gene so +this is from a proto troph then you + + align:start position:0% +this is from a proto troph then you + + + align:start position:0% +this is from a proto troph then you +could cut up the the DNA with eco r1 and + + align:start position:0% +could cut up the the DNA with eco r1 and + + + align:start position:0% +could cut up the the DNA with eco r1 and +if there's not a restriction site in + + align:start position:0% +if there's not a restriction site in + + + align:start position:0% +if there's not a restriction site in +this loo to gene you get a fragment that + + align:start position:0% +this loo to gene you get a fragment that + + + align:start position:0% +this loo to gene you get a fragment that +contains the Lu to gene and then you + + align:start position:0% +contains the Lu to gene and then you + + + align:start position:0% +contains the Lu to gene and then you +could clone this into some type of + + align:start position:0% +could clone this into some type of + + + align:start position:0% +could clone this into some type of +plasmid that replicates in the organism + + align:start position:0% +plasmid that replicates in the organism + + + align:start position:0% +plasmid that replicates in the organism +that you're introducing and propagating + + align:start position:0% +that you're introducing and propagating + + + align:start position:0% +that you're introducing and propagating +it in and so that would allow you to + + align:start position:0% +it in and so that would allow you to + + + align:start position:0% +it in and so that would allow you to +then test whether or not this piece of + + align:start position:0% +then test whether or not this piece of + + + align:start position:0% +then test whether or not this piece of +DNA that you have complements allude to + + align:start position:0% +DNA that you have complements allude to + + + align:start position:0% +DNA that you have complements allude to +auxotrophs + + align:start position:0% +auxotrophs + + + align:start position:0% +auxotrophs +okay now one thing I want to point out + + align:start position:0% +okay now one thing I want to point out + + + align:start position:0% +okay now one thing I want to point out +is that because these eco r1 sites these + + align:start position:0% +is that because these eco r1 sites these + + + align:start position:0% +is that because these eco r1 sites these +sticky ends they recognized they + + align:start position:0% +sticky ends they recognized they + + + align:start position:0% +sticky ends they recognized they +recognized they would recognize this eco + + align:start position:0% +recognized they would recognize this eco + + + align:start position:0% +recognized they would recognize this eco +r1 and or this eco R at one end you can + + align:start position:0% +r1 and or this eco R at one end you can + + + align:start position:0% +r1 and or this eco R at one end you can +imagine that this gene if the gene reads + + align:start position:0% +imagine that this gene if the gene reads + + + align:start position:0% +imagine that this gene if the gene reads +this + + align:start position:0% +this + + + align:start position:0% +this +this way it could insert this way into + + align:start position:0% +this way it could insert this way into + + + align:start position:0% +this way it could insert this way into +the plasmid or it could insert in the + + align:start position:0% +the plasmid or it could insert in the + + + align:start position:0% +the plasmid or it could insert in the +opposite direction so it could be + + align:start position:0% +opposite direction so it could be + + + align:start position:0% +opposite direction so it could be +inverted okay so this would have some + + align:start position:0% +inverted okay so this would have some + + + align:start position:0% +inverted okay so this would have some +sort of origin of replication and some + + align:start position:0% +sort of origin of replication and some + + + align:start position:0% +sort of origin of replication and some +type of selectable marker but if you + + align:start position:0% +type of selectable marker but if you + + + align:start position:0% +type of selectable marker but if you +have the same restriction site right it + + align:start position:0% +have the same restriction site right it + + + align:start position:0% +have the same restriction site right it +can insert one way or the opposite way + + align:start position:0% +can insert one way or the opposite way + + + align:start position:0% +can insert one way or the opposite way +that's just one thing I wanted to point + + align:start position:0% +that's just one thing I wanted to point + + + align:start position:0% +that's just one thing I wanted to point +out okay now let's say let's say rather + + align:start position:0% +out okay now let's say let's say rather + + + align:start position:0% +out okay now let's say let's say rather +than leucine you are interested in + + align:start position:0% +than leucine you are interested in + + + align:start position:0% +than leucine you are interested in +cyclin dependent kinase and you had a + + align:start position:0% +cyclin dependent kinase and you had a + + + align:start position:0% +cyclin dependent kinase and you had a +mutant in cdk and you had this sequence + + align:start position:0% +mutant in cdk and you had this sequence + + + align:start position:0% +mutant in cdk and you had this sequence +of your yeast cdk gene well rather than + + align:start position:0% +of your yeast cdk gene well rather than + + + align:start position:0% +of your yeast cdk gene well rather than +having to dig through a whole library of + + align:start position:0% +having to dig through a whole library of + + + align:start position:0% +having to dig through a whole library of +pieces of DNA for the cdk dean gene and + + align:start position:0% +pieces of DNA for the cdk dean gene and + + + align:start position:0% +pieces of DNA for the cdk dean gene and +basically you're sort of fishing for + + align:start position:0% +basically you're sort of fishing for + + + align:start position:0% +basically you're sort of fishing for +that needle in the haystack if you knew + + align:start position:0% +that needle in the haystack if you knew + + + align:start position:0% +that needle in the haystack if you knew +the sequence of the human genome you'd + + align:start position:0% +the sequence of the human genome you'd + + + align:start position:0% +the sequence of the human genome you'd +be able to identify similar genes by + + align:start position:0% +be able to identify similar genes by + + + align:start position:0% +be able to identify similar genes by +sequence homology and you could then + + align:start position:0% +sequence homology and you could then + + + align:start position:0% +sequence homology and you could then +take a more direct approach where you + + align:start position:0% +take a more direct approach where you + + + align:start position:0% +take a more direct approach where you +take let's say you have a piece of human + + align:start position:0% +take let's say you have a piece of human + + + align:start position:0% +take let's say you have a piece of human +DNA now double-stranded DNA and it has + + align:start position:0% +DNA now double-stranded DNA and it has + + + align:start position:0% +DNA now double-stranded DNA and it has +the cdk gene you could take human DNA + + align:start position:0% +the cdk gene you could take human DNA + + + align:start position:0% +the cdk gene you could take human DNA +with the cdk gene and you have unique + + align:start position:0% +with the cdk gene and you have unique + + + align:start position:0% +with the cdk gene and you have unique +sequence around the cdk gene which would + + align:start position:0% +sequence around the cdk gene which would + + + align:start position:0% +sequence around the cdk gene which would +allow you to denature this DNA and if + + align:start position:0% +allow you to denature this DNA and if + + + align:start position:0% +allow you to denature this DNA and if +you denature the DNA you'd get two + + align:start position:0% +you denature the DNA you'd get two + + + align:start position:0% +you denature the DNA you'd get two +single strands of DNA and you could then + + align:start position:0% +single strands of DNA and you could then + + + align:start position:0% +single strands of DNA and you could then +design primers that recognize unique + + align:start position:0% +design primers that recognize unique + + + align:start position:0% +design primers that recognize unique +sequences flanking the cdk gene so you + + align:start position:0% +sequences flanking the cdk gene so you + + + align:start position:0% +sequences flanking the cdk gene so you +can imagine you'd have a primer here and + + align:start position:0% +can imagine you'd have a primer here and + + + align:start position:0% +can imagine you'd have a primer here and +a primer here and then you could use PCR + + align:start position:0% +a primer here and then you could use PCR + + + align:start position:0% +a primer here and then you could use PCR +to amplify specifically the cdk gene + + align:start position:0% +to amplify specifically the cdk gene + + + align:start position:0% +to amplify specifically the cdk gene +from it could be the genome or from some + + align:start position:0% +from it could be the genome or from some + + + align:start position:0% +from it could be the genome or from some +library and then you get this fragment + + align:start position:0% +library and then you get this fragment + + + align:start position:0% +library and then you get this fragment +here which includes CDK + + align:start position:0% +here which includes CDK + + + align:start position:0% +here which includes CDK +okay so knowing the sequence of the + + align:start position:0% +okay so knowing the sequence of the + + + align:start position:0% +okay so knowing the sequence of the +genome would allow you to more rapidly + + align:start position:0% +genome would allow you to more rapidly + + + align:start position:0% +genome would allow you to more rapidly +go from maybe a gene that you've + + align:start position:0% +go from maybe a gene that you've + + + align:start position:0% +go from maybe a gene that you've +identified as being important in one + + align:start position:0% +identified as being important in one + + + align:start position:0% +identified as being important in one +organism and find the human equivalent + + align:start position:0% +organism and find the human equivalent + + + align:start position:0% +organism and find the human equivalent +that might have be doing something + + align:start position:0% +that might have be doing something + + + align:start position:0% +that might have be doing something +similar in humans okay + + align:start position:0% +similar in humans okay + + + align:start position:0% +similar in humans okay +so this step here is basically PCR okay + + align:start position:0% +so this step here is basically PCR okay + + + align:start position:0% +so this step here is basically PCR okay +and let's say the cdk gene had + + align:start position:0% +and let's say the cdk gene had + + + align:start position:0% +and let's say the cdk gene had +restriction sites let's see we'll use + + align:start position:0% +restriction sites let's see we'll use + + + align:start position:0% +restriction sites let's see we'll use +will say restriction site k and a here + + align:start position:0% +will say restriction site k and a here + + + align:start position:0% +will say restriction site k and a here +then if you have these restriction sites + + align:start position:0% +then if you have these restriction sites + + + align:start position:0% +then if you have these restriction sites +in your fragment of DNA you can then + + align:start position:0% +in your fragment of DNA you can then + + + align:start position:0% +in your fragment of DNA you can then +digest or cut that piece of DNA with + + align:start position:0% +digest or cut that piece of DNA with + + + align:start position:0% +digest or cut that piece of DNA with +these restriction endonucleases and then + + align:start position:0% +these restriction endonucleases and then + + + align:start position:0% +these restriction endonucleases and then +you'd get a fragment of cdk + + align:start position:0% +you'd get a fragment of cdk + + + align:start position:0% +you'd get a fragment of cdk +that has K and a sticky ends we'll + + align:start position:0% +that has K and a sticky ends we'll + + + align:start position:0% +that has K and a sticky ends we'll +pretend that both of these have sticky + + align:start position:0% +pretend that both of these have sticky + + + align:start position:0% +pretend that both of these have sticky +ends and now you have unique sticky ends + + align:start position:0% +ends and now you have unique sticky ends + + + align:start position:0% +ends and now you have unique sticky ends +between K and a and you might have a + + align:start position:0% +between K and a and you might have a + + + align:start position:0% +between K and a and you might have a +vector that also has these two sites and + + align:start position:0% +vector that also has these two sites and + + + align:start position:0% +vector that also has these two sites and +you could digest this vector with these + + align:start position:0% +you could digest this vector with these + + + align:start position:0% +you could digest this vector with these +two enzymes and that would allow you to + + align:start position:0% +two enzymes and that would allow you to + + + align:start position:0% +two enzymes and that would allow you to +insert the specific gene in this plasmid + + align:start position:0% +insert the specific gene in this plasmid + + + align:start position:0% +insert the specific gene in this plasmid +and if you have two unique sites because + + align:start position:0% +and if you have two unique sites because + + + align:start position:0% +and if you have two unique sites because +K only recognizes K here and a only + + align:start position:0% +K only recognizes K here and a only + + + align:start position:0% +K only recognizes K here and a only +recognizes a then it will like a t' in + + align:start position:0% +recognizes a then it will like a t' in + + + align:start position:0% +recognizes a then it will like a t' in +but you can do it with a specific + + align:start position:0% +but you can do it with a specific + + + align:start position:0% +but you can do it with a specific +orientation because you have two + + align:start position:0% +orientation because you have two + + + align:start position:0% +orientation because you have two +different restriction sites okay so I + + align:start position:0% +different restriction sites okay so I + + + align:start position:0% +different restriction sites okay so I +hope you all see sort of how how it's + + align:start position:0% +hope you all see sort of how how it's + + + align:start position:0% +hope you all see sort of how how it's +different with one restriction site + + align:start position:0% +different with one restriction site + + + align:start position:0% +different with one restriction site +versus two okay + + align:start position:0% + + + + align:start position:0% + +all right now let's say you want to do + + align:start position:0% +all right now let's say you want to do + + + align:start position:0% +all right now let's say you want to do +something more complicated than this + + align:start position:0% +something more complicated than this + + + align:start position:0% +something more complicated than this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +let's say rather than just identifying + + align:start position:0% +let's say rather than just identifying + + + align:start position:0% +let's say rather than just identifying +the gene that's involved in cell + + align:start position:0% +the gene that's involved in cell + + + align:start position:0% +the gene that's involved in cell +division let's say you want to engineer + + align:start position:0% +division let's say you want to engineer + + + align:start position:0% +division let's say you want to engineer +a new gene in order to determine let's + + align:start position:0% +a new gene in order to determine let's + + + align:start position:0% +a new gene in order to determine let's +say where this particular protein CDK + + align:start position:0% +say where this particular protein CDK + + + align:start position:0% +say where this particular protein CDK +localizes in the cell + + align:start position:0% +localizes in the cell + + + align:start position:0% +localizes in the cell +okay so we have cdk which could be from + + align:start position:0% +okay so we have cdk which could be from + + + align:start position:0% +okay so we have cdk which could be from +yeast or human it doesn't matter and you + + align:start position:0% +yeast or human it doesn't matter and you + + + align:start position:0% +yeast or human it doesn't matter and you +want to engineer a new protein if you + + align:start position:0% +want to engineer a new protein if you + + + align:start position:0% +want to engineer a new protein if you +would basically that you can see that + + align:start position:0% +would basically that you can see that + + + align:start position:0% +would basically that you can see that +you can see okay so remember professor + + align:start position:0% +you can see okay so remember professor + + + align:start position:0% +you can see okay so remember professor +Imperiali + + align:start position:0% +Imperiali + + + align:start position:0% +Imperiali +introduced green fluorescent protein + + align:start position:0% +introduced green fluorescent protein + + + align:start position:0% +introduced green fluorescent protein +earlier in the year and this green + + align:start position:0% +earlier in the year and this green + + + align:start position:0% +earlier in the year and this green +fluorescent protein is from a gene from + + align:start position:0% +fluorescent protein is from a gene from + + + align:start position:0% +fluorescent protein is from a gene from +jellyfish so now we could using what + + align:start position:0% +jellyfish so now we could using what + + + align:start position:0% +jellyfish so now we could using what +I've told you reconstruct or engineer a + + align:start position:0% +I've told you reconstruct or engineer a + + + align:start position:0% +I've told you reconstruct or engineer a +gene that has DNA from three different + + align:start position:0% +gene that has DNA from three different + + + align:start position:0% +gene that has DNA from three different +organisms in order to make a cdk a + + align:start position:0% +organisms in order to make a cdk a + + + align:start position:0% +organisms in order to make a cdk a +variant that we are able to see in the + + align:start position:0% +variant that we are able to see in the + + + align:start position:0% +variant that we are able to see in the +cell so remember green fluorescent + + align:start position:0% +cell so remember green fluorescent + + + align:start position:0% +cell so remember green fluorescent +protein is like Amalek it's like a + + align:start position:0% +protein is like Amalek it's like a + + + align:start position:0% +protein is like Amalek it's like a +beacon if it's attached to a protein if + + align:start position:0% +beacon if it's attached to a protein if + + + align:start position:0% +beacon if it's attached to a protein if +you shine blue light on it it emits + + align:start position:0% +you shine blue light on it it emits + + + align:start position:0% +you shine blue light on it it emits +green light and so you can use a + + align:start position:0% +green light and so you can use a + + + align:start position:0% +green light and so you can use a +fluorescent microscope in order to see + + align:start position:0% +fluorescent microscope in order to see + + + align:start position:0% +fluorescent microscope in order to see +it okay in this case let's say there's + + align:start position:0% +it okay in this case let's say there's + + + align:start position:0% +it okay in this case let's say there's +also another restriction site here R and + + align:start position:0% +also another restriction site here R and + + + align:start position:0% +also another restriction site here R and +let's say you have a fragment of GFP + + align:start position:0% +let's say you have a fragment of GFP + + + align:start position:0% +let's say you have a fragment of GFP +that has two restriction sites a and are + + align:start position:0% +that has two restriction sites a and are + + + align:start position:0% +that has two restriction sites a and are +you could then cut this fragment and + + align:start position:0% +you could then cut this fragment and + + + align:start position:0% +you could then cut this fragment and +this fragment with these restriction + + align:start position:0% +this fragment with these restriction + + + align:start position:0% +this fragment with these restriction +enzymes a and R and you could insert GFP + + align:start position:0% +enzymes a and R and you could insert GFP + + + align:start position:0% +enzymes a and R and you could insert GFP +at the c-terminus of the cdk gene okay + + align:start position:0% +at the c-terminus of the cdk gene okay + + + align:start position:0% +at the c-terminus of the cdk gene okay +so you could go and have a gene that has + + align:start position:0% +so you could go and have a gene that has + + + align:start position:0% +so you could go and have a gene that has +cdk GFP inserted inside a bacterial + + align:start position:0% +cdk GFP inserted inside a bacterial + + + align:start position:0% +cdk GFP inserted inside a bacterial +vector okay now which one of these sort + + align:start position:0% +vector okay now which one of these sort + + + align:start position:0% +vector okay now which one of these sort +of Junction sites do you think would be + + align:start position:0% +of Junction sites do you think would be + + + align:start position:0% +of Junction sites do you think would be +most sensitive in doing this type of + + align:start position:0% +most sensitive in doing this type of + + + align:start position:0% +most sensitive in doing this type of +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +so there are three Junction sites right + + align:start position:0% +so there are three Junction sites right + + + align:start position:0% +so there are three Junction sites right +there's this one this one in this one + + align:start position:0% +there's this one this one in this one + + + align:start position:0% +there's this one this one in this one +which is the one you're probably gonna + + align:start position:0% +which is the one you're probably gonna + + + align:start position:0% +which is the one you're probably gonna +put the most thought into when you're + + align:start position:0% +put the most thought into when you're + + + align:start position:0% +put the most thought into when you're +doing this experiment yes miles the + + align:start position:0% +doing this experiment yes miles the + + + align:start position:0% +doing this experiment yes miles the +exact miles is exactly right this one's + + align:start position:0% +exact miles is exactly right this one's + + + align:start position:0% +exact miles is exactly right this one's +going to be important right and why did + + align:start position:0% +going to be important right and why did + + + align:start position:0% +going to be important right and why did +you choose that site and if you're + + align:start position:0% +you choose that site and if you're + + + align:start position:0% +you choose that site and if you're +trying to make a fusion protein what's + + align:start position:0% +trying to make a fusion protein what's + + + align:start position:0% +trying to make a fusion protein what's +going to be an important sort of quality + + align:start position:0% +going to be an important sort of quality + + + align:start position:0% +going to be an important sort of quality +of this you have a point + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +excellent job so Malik just pointed out + + align:start position:0% +excellent job so Malik just pointed out + + + align:start position:0% +excellent job so Malik just pointed out +two really important things right to + + align:start position:0% +two really important things right to + + + align:start position:0% +two really important things right to +make this a fusion protein right you + + align:start position:0% +make this a fusion protein right you + + + align:start position:0% +make this a fusion protein right you +have two different open reading frames + + align:start position:0% +have two different open reading frames + + + align:start position:0% +have two different open reading frames +these two open reading frames have to be + + align:start position:0% +these two open reading frames have to be + + + align:start position:0% +these two open reading frames have to be +in frame with each other okay so this + + align:start position:0% +in frame with each other okay so this + + + align:start position:0% +in frame with each other okay so this +Junction here has to be in frame where + + align:start position:0% +Junction here has to be in frame where + + + align:start position:0% +Junction here has to be in frame where +GFP is in frame with cdk meaning that + + align:start position:0% +GFP is in frame with cdk meaning that + + + align:start position:0% +GFP is in frame with cdk meaning that +you're reading sort of the same sort of + + align:start position:0% +you're reading sort of the same sort of + + + align:start position:0% +you're reading sort of the same sort of +triplet codons for GFP they're in the + + align:start position:0% +triplet codons for GFP they're in the + + + align:start position:0% +triplet codons for GFP they're in the +same frame as cdk also you want to make + + align:start position:0% +same frame as cdk also you want to make + + + align:start position:0% +same frame as cdk also you want to make +sure there's no stop codon here is if + + align:start position:0% +sure there's no stop codon here is if + + + align:start position:0% +sure there's no stop codon here is if +you had a stop codon here you're just + + align:start position:0% +you had a stop codon here you're just + + + align:start position:0% +you had a stop codon here you're just +gonna make a cdk protein and then it's + + align:start position:0% +gonna make a cdk protein and then it's + + + align:start position:0% +gonna make a cdk protein and then it's +gonna stop and then you won't have it + + align:start position:0% +gonna stop and then you won't have it + + + align:start position:0% +gonna stop and then you won't have it +fused to gfp okay and you guys will work + + align:start position:0% +fused to gfp okay and you guys will work + + + align:start position:0% +fused to gfp okay and you guys will work +through more of these and the homework + + align:start position:0% +through more of these and the homework + + + align:start position:0% +through more of these and the homework +so you'll be able to get a sense of it + + align:start position:0% +so you'll be able to get a sense of it + + + align:start position:0% +so you'll be able to get a sense of it +okay so now for the remainder of this + + align:start position:0% +okay so now for the remainder of this + + + align:start position:0% +okay so now for the remainder of this +lecture and also for Monday's lecture I + + align:start position:0% +lecture and also for Monday's lecture I + + + align:start position:0% +lecture and also for Monday's lecture I +want to go through a problem with you + + align:start position:0% +want to go through a problem with you + + + align:start position:0% +want to go through a problem with you +which is basically if you have a given + + align:start position:0% +which is basically if you have a given + + + align:start position:0% +which is basically if you have a given +disease that's heritable how might you + + align:start position:0% +disease that's heritable how might you + + + align:start position:0% +disease that's heritable how might you +go from sort of knowing that that + + align:start position:0% +go from sort of knowing that that + + + align:start position:0% +go from sort of knowing that that +disease is heritable to finding out what + + align:start position:0% +disease is heritable to finding out what + + + align:start position:0% +disease is heritable to finding out what +gene is responsible for that given + + align:start position:0% +gene is responsible for that given + + + align:start position:0% +gene is responsible for that given +disease okay and this is going to + + align:start position:0% +disease okay and this is going to + + + align:start position:0% +disease okay and this is going to +involve thinking about different levels + + align:start position:0% +involve thinking about different levels + + + align:start position:0% +involve thinking about different levels +of resolution in terms of maps so the + + align:start position:0% +of resolution in terms of maps so the + + + align:start position:0% +of resolution in terms of maps so the +highest resolution map you can have for + + align:start position:0% +highest resolution map you can have for + + + align:start position:0% +highest resolution map you can have for +a genome is the sequence you can have + + align:start position:0% +a genome is the sequence you can have + + + align:start position:0% +a genome is the sequence you can have +the full nucleotide sequence of a genome + + align:start position:0% +the full nucleotide sequence of a genome + + + align:start position:0% +the full nucleotide sequence of a genome +okay and that's the highest possible + + align:start position:0% +okay and that's the highest possible + + + align:start position:0% +okay and that's the highest possible +resolution because you have single + + align:start position:0% +resolution because you have single + + + align:start position:0% +resolution because you have single +nucleotide resolution as to what every + + align:start position:0% +nucleotide resolution as to what every + + + align:start position:0% +nucleotide resolution as to what every +single base pair is okay but that's like + + align:start position:0% +single base pair is okay but that's like + + + align:start position:0% +single base pair is okay but that's like +you know that's like knowing like your + + align:start position:0% +you know that's like knowing like your + + + align:start position:0% +you know that's like knowing like your +apartment number and your street number + + align:start position:0% +apartment number and your street number + + + align:start position:0% +apartment number and your street number +and basically knowing everything right + + align:start position:0% +and basically knowing everything right + + + align:start position:0% +and basically knowing everything right +but starting out you might want to know + + align:start position:0% +but starting out you might want to know + + + align:start position:0% +but starting out you might want to know +like what continent it's on or what what + + align:start position:0% +like what continent it's on or what what + + + align:start position:0% +like what continent it's on or what what +country is it in okay and so you first + + align:start position:0% +country is it in okay and so you first + + + align:start position:0% +country is it in okay and so you first +have to sort of + + align:start position:0% +have to sort of + + + align:start position:0% +have to sort of +the possible locations for a given + + align:start position:0% +the possible locations for a given + + + align:start position:0% +the possible locations for a given +disease gene and that will first involve + + align:start position:0% +disease gene and that will first involve + + + align:start position:0% +disease gene and that will first involve +establishing what chromosome and what + + align:start position:0% +establishing what chromosome and what + + + align:start position:0% +establishing what chromosome and what +region of a chromosome a given disease + + align:start position:0% +region of a chromosome a given disease + + + align:start position:0% +region of a chromosome a given disease +allele is linked to okay and that's + + align:start position:0% +allele is linked to okay and that's + + + align:start position:0% +allele is linked to okay and that's +known as its that involves making + + align:start position:0% +known as its that involves making + + + align:start position:0% +known as its that involves making +essentially a linkage map where you + + align:start position:0% +essentially a linkage map where you + + + align:start position:0% +essentially a linkage map where you +establish where a disease gene is + + align:start position:0% +establish where a disease gene is + + + align:start position:0% +establish where a disease gene is +located based on its linkage to known + + align:start position:0% +located based on its linkage to known + + + align:start position:0% +located based on its linkage to known +markers that are present in the genome + + align:start position:0% +markers that are present in the genome + + + align:start position:0% +markers that are present in the genome +okay now this is going to require that + + align:start position:0% +okay now this is going to require that + + + align:start position:0% +okay now this is going to require that +you remember back we week or two weeks + + align:start position:0% +you remember back we week or two weeks + + + align:start position:0% +you remember back we week or two weeks +ago to when we talked about linkage and + + align:start position:0% +ago to when we talked about linkage and + + + align:start position:0% +ago to when we talked about linkage and +recombination and you'll recall that we + + align:start position:0% +recombination and you'll recall that we + + + align:start position:0% +recombination and you'll recall that we +were looking at the linkage between + + align:start position:0% +were looking at the linkage between + + + align:start position:0% +were looking at the linkage between +genes and flies and genes and yeast + + align:start position:0% +genes and flies and genes and yeast + + + align:start position:0% +genes and flies and genes and yeast +right one difference between that type + + align:start position:0% +right one difference between that type + + + align:start position:0% +right one difference between that type +of linkage mapping and human linkage + + align:start position:0% +of linkage mapping and human linkage + + + align:start position:0% +of linkage mapping and human linkage +mapping is we don't have really clear + + align:start position:0% +mapping is we don't have really clear + + + align:start position:0% +mapping is we don't have really clear +traits that are defined by single genes + + align:start position:0% +traits that are defined by single genes + + + align:start position:0% +traits that are defined by single genes +right you can't just take hair color and + + align:start position:0% +right you can't just take hair color and + + + align:start position:0% +right you can't just take hair color and +map like the hair color gene to link it + + align:start position:0% +map like the hair color gene to link it + + + align:start position:0% +map like the hair color gene to link it +to a disease gene okay because hair + + align:start position:0% +to a disease gene okay because hair + + + align:start position:0% +to a disease gene okay because hair +color is determined by many many + + align:start position:0% +color is determined by many many + + + align:start position:0% +color is determined by many many +different genes okay so in fruit flies + + align:start position:0% +different genes okay so in fruit flies + + + align:start position:0% +different genes okay so in fruit flies +you can take white eyes and see if it's + + align:start position:0% +you can take white eyes and see if it's + + + align:start position:0% +you can take white eyes and see if it's +connected with yellow body color because + + align:start position:0% +connected with yellow body color because + + + align:start position:0% +connected with yellow body color because +both of those are determined by single + + align:start position:0% +both of those are determined by single + + + align:start position:0% +both of those are determined by single +genes so we need something other than + + align:start position:0% +genes so we need something other than + + + align:start position:0% +genes so we need something other than +just having sort of phenotypic traits + + align:start position:0% +just having sort of phenotypic traits + + + align:start position:0% +just having sort of phenotypic traits +that we can track we need what are known + + align:start position:0% +that we can track we need what are known + + + align:start position:0% +that we can track we need what are known +as molecular markers to be able to + + align:start position:0% +as molecular markers to be able to + + + align:start position:0% +as molecular markers to be able to +perform linkage mapping okay and so what + + align:start position:0% +perform linkage mapping okay and so what + + + align:start position:0% +perform linkage mapping okay and so what +would we need in these molecular markers + + align:start position:0% +would we need in these molecular markers + + + align:start position:0% +would we need in these molecular markers +well if we just think about if we wanted + + align:start position:0% +well if we just think about if we wanted + + + align:start position:0% +well if we just think about if we wanted +to determine the linkage between the a + + align:start position:0% +to determine the linkage between the a + + + align:start position:0% +to determine the linkage between the a +and B genes right and if you did this + + align:start position:0% +and B genes right and if you did this + + + align:start position:0% +and B genes right and if you did this +cross would you be able to determine + + align:start position:0% +cross would you be able to determine + + + align:start position:0% +cross would you be able to determine +linkage + + align:start position:0% + + + + align:start position:0% + +giorgia you made a motion that was + + align:start position:0% +giorgia you made a motion that was + + + align:start position:0% +giorgia you made a motion that was +correct tell me why why did you shake + + align:start position:0% +correct tell me why why did you shake + + + align:start position:0% +correct tell me why why did you shake +your head no yeah they'd all be + + align:start position:0% +your head no yeah they'd all be + + + align:start position:0% +your head no yeah they'd all be +heterozygous right you can't because + + align:start position:0% +heterozygous right you can't because + + + align:start position:0% +heterozygous right you can't because +this individual has the same allele on + + align:start position:0% +this individual has the same allele on + + + align:start position:0% +this individual has the same allele on +both chromosomes you're not going to be + + align:start position:0% +both chromosomes you're not going to be + + + align:start position:0% +both chromosomes you're not going to be +able to differentiate one chromosome + + align:start position:0% +able to differentiate one chromosome + + + align:start position:0% +able to differentiate one chromosome +from the other okay and so the point I + + align:start position:0% +from the other okay and so the point I + + + align:start position:0% +from the other okay and so the point I +want to make is that in order to see + + align:start position:0% +want to make is that in order to see + + + align:start position:0% +want to make is that in order to see +linkage what you need is variation okay + + align:start position:0% + + + + align:start position:0% + +so we need to have variation and another + + align:start position:0% +so we need to have variation and another + + + align:start position:0% +so we need to have variation and another +term for genetic variation is + + align:start position:0% +term for genetic variation is + + + align:start position:0% +term for genetic variation is +polymorphism okay so we need + + align:start position:0% +polymorphism okay so we need + + + align:start position:0% +polymorphism okay so we need +polymorphism or genetic variation + + align:start position:0% +polymorphism or genetic variation + + + align:start position:0% +polymorphism or genetic variation +between these molecular markers we also + + align:start position:0% +between these molecular markers we also + + + align:start position:0% +between these molecular markers we also +need genetic variation in the disease + + align:start position:0% +need genetic variation in the disease + + + align:start position:0% +need genetic variation in the disease +but we have that right we don't we have + + align:start position:0% +but we have that right we don't we have + + + align:start position:0% +but we have that right we don't we have +individuals that are affected by a + + align:start position:0% +individuals that are affected by a + + + align:start position:0% +individuals that are affected by a +disease and individuals that are not + + align:start position:0% +disease and individuals that are not + + + align:start position:0% +disease and individuals that are not +affected by a disease so we have + + align:start position:0% +affected by a disease so we have + + + align:start position:0% +affected by a disease so we have +variation and alleles there but we in + + align:start position:0% +variation and alleles there but we in + + + align:start position:0% +variation and alleles there but we in +order to map it with two Amalek with a + + align:start position:0% +order to map it with two Amalek with a + + + align:start position:0% +order to map it with two Amalek with a +molecular marker to map linkage to a + + align:start position:0% +molecular marker to map linkage to a + + + align:start position:0% +molecular marker to map linkage to a +molecular marker you also need variation + + align:start position:0% +molecular marker you also need variation + + + align:start position:0% +molecular marker you also need variation +here right so the problem with this + + align:start position:0% +here right so the problem with this + + + align:start position:0% +here right so the problem with this +cross is here you need to have a + + align:start position:0% +cross is here you need to have a + + + align:start position:0% +cross is here you need to have a +heterozygote right there needs to be + + align:start position:0% +heterozygote right there needs to be + + + align:start position:0% +heterozygote right there needs to be +individual there needs to be variation + + align:start position:0% +individual there needs to be variation + + + align:start position:0% +individual there needs to be variation +in this individual where both of these + + align:start position:0% +in this individual where both of these + + + align:start position:0% +in this individual where both of these +alleles are heterozygous okay so now I + + align:start position:0% +alleles are heterozygous okay so now I + + + align:start position:0% +alleles are heterozygous okay so now I +want to talk about some of these + + align:start position:0% +want to talk about some of these + + + align:start position:0% +want to talk about some of these +molecular markers that we can use and + + align:start position:0% +molecular markers that we can use and + + + align:start position:0% +molecular markers that we can use and +how they vary between individuals and + + align:start position:0% +how they vary between individuals and + + + align:start position:0% +how they vary between individuals and +between chromosomes okay + + align:start position:0% +between chromosomes okay + + + align:start position:0% +between chromosomes okay +now this is going to be maybe the lowest + + align:start position:0% +now this is going to be maybe the lowest + + + align:start position:0% +now this is going to be maybe the lowest +resolution map but I'm talking about + + align:start position:0% +resolution map but I'm talking about + + + align:start position:0% +resolution map but I'm talking about +sort of this linkage map here and you + + align:start position:0% +sort of this linkage map here and you + + + align:start position:0% +sort of this linkage map here and you +can see highlighted at the bottom here + + align:start position:0% +can see highlighted at the bottom here + + + align:start position:0% +can see highlighted at the bottom here +are various types of polymorphisms that + + align:start position:0% +are various types of polymorphisms that + + + align:start position:0% +are various types of polymorphisms that +we can use to link given + + align:start position:0% +we can use to link given + + + align:start position:0% +we can use to link given +zees allele to a specific chromosome and + + align:start position:0% +zees allele to a specific chromosome and + + + align:start position:0% +zees allele to a specific chromosome and +a specific place on a chromosome okay so + + align:start position:0% +a specific place on a chromosome okay so + + + align:start position:0% +a specific place on a chromosome okay so +I'll start with the first one which is a + + align:start position:0% + + + + align:start position:0% + +say a simple sequence repeat it goes by + + align:start position:0% +say a simple sequence repeat it goes by + + + align:start position:0% +say a simple sequence repeat it goes by +many names but I will stick with what's + + align:start position:0% +many names but I will stick with what's + + + align:start position:0% +many names but I will stick with what's +on the slide so a simple sequence repeat + + align:start position:0% +on the slide so a simple sequence repeat + + + align:start position:0% +on the slide so a simple sequence repeat +is also known as a microsatellite so you + + align:start position:0% +is also known as a microsatellite so you + + + align:start position:0% +is also known as a microsatellite so you +might see that term floating around if + + align:start position:0% +might see that term floating around if + + + align:start position:0% +might see that term floating around if +you're reading about this and what a + + align:start position:0% +you're reading about this and what a + + + align:start position:0% +you're reading about this and what a +what a simple sequence repeat is is as + + align:start position:0% +what a simple sequence repeat is is as + + + align:start position:0% +what a simple sequence repeat is is as +the name implies it's a simple sequence + + align:start position:0% +the name implies it's a simple sequence + + + align:start position:0% +the name implies it's a simple sequence +like it could be a dinucleotide like CA + + align:start position:0% +like it could be a dinucleotide like CA + + + align:start position:0% +like it could be a dinucleotide like CA +and it's just a dinucleotide that's + + align:start position:0% +and it's just a dinucleotide that's + + + align:start position:0% +and it's just a dinucleotide that's +repeated over and over again okay so you + + align:start position:0% +repeated over and over again okay so you + + + align:start position:0% +repeated over and over again okay so you +might have on a chromosome you might + + align:start position:0% +might have on a chromosome you might + + + align:start position:0% +might have on a chromosome you might +have a unique sequence which I'll just + + align:start position:0% +have a unique sequence which I'll just + + + align:start position:0% +have a unique sequence which I'll just +draw as a line and then you could have a + + align:start position:0% +draw as a line and then you could have a + + + align:start position:0% +draw as a line and then you could have a +see a dinucleotide that's repeated some + + align:start position:0% +see a dinucleotide that's repeated some + + + align:start position:0% +see a dinucleotide that's repeated some +number of times N and then that's + + align:start position:0% +number of times N and then that's + + + align:start position:0% +number of times N and then that's +followed by another unique sequence okay + + align:start position:0% +followed by another unique sequence okay + + + align:start position:0% +followed by another unique sequence okay +and that's what's present image so that + + align:start position:0% +and that's what's present image so that + + + align:start position:0% +and that's what's present image so that +would be one strand and then in the + + align:start position:0% +would be one strand and then in the + + + align:start position:0% +would be one strand and then in the +opposite strand you'd have unique + + align:start position:0% +opposite strand you'd have unique + + + align:start position:0% +opposite strand you'd have unique +sequence the complement of C a which is + + align:start position:0% +sequence the complement of C a which is + + + align:start position:0% +sequence the complement of C a which is +G T and then again unique sequence okay + + align:start position:0% +G T and then again unique sequence okay + + + align:start position:0% +G T and then again unique sequence okay +and so there's variation in the number + + align:start position:0% +and so there's variation in the number + + + align:start position:0% +and so there's variation in the number +of repeats of the CA and so there's + + align:start position:0% +of repeats of the CA and so there's + + + align:start position:0% +of repeats of the CA and so there's +polymorphism so we can use this to + + align:start position:0% +polymorphism so we can use this to + + + align:start position:0% +polymorphism so we can use this to +establish linkage between this marker + + align:start position:0% +establish linkage between this marker + + + align:start position:0% +establish linkage between this marker +and a phenotype like a disease phenotype + + align:start position:0% +and a phenotype like a disease phenotype + + + align:start position:0% +and a phenotype like a disease phenotype +okay so how might you detect the number + + align:start position:0% +okay so how might you detect the number + + + align:start position:0% +okay so how might you detect the number +of repeats that are present here anyone + + align:start position:0% +of repeats that are present here anyone + + + align:start position:0% +of repeats that are present here anyone +have an idea of a tool that we've + + align:start position:0% +have an idea of a tool that we've + + + align:start position:0% +have an idea of a tool that we've +discussed that could be used here so one + + align:start position:0% +discussed that could be used here so one + + + align:start position:0% +discussed that could be used here so one +hint that I gave you is that the + + align:start position:0% +hint that I gave you is that the + + + align:start position:0% +hint that I gave you is that the +sequence here is unique and the sequence + + align:start position:0% +sequence here is unique and the sequence + + + align:start position:0% +sequence here is unique and the sequence +here is unique so is there a way we can + + align:start position:0% +here is unique so is there a way we can + + + align:start position:0% +here is unique so is there a way we can +leverage that unique sequence to + + align:start position:0% +leverage that unique sequence to + + + align:start position:0% +leverage that unique sequence to +determine whether there's a difference + + align:start position:0% +determine whether there's a difference + + + align:start position:0% +determine whether there's a difference +in the number of repeats + + align:start position:0% + + + + align:start position:0% + +what technique we discussed that + + align:start position:0% +what technique we discussed that + + + align:start position:0% +what technique we discussed that +involves some component of the technique + + align:start position:0% +involves some component of the technique + + + align:start position:0% +involves some component of the technique +recognizing a unique sequence yeah + + align:start position:0% +recognizing a unique sequence yeah + + + align:start position:0% +recognizing a unique sequence yeah +Natalie + + align:start position:0% +Natalie + + + align:start position:0% +Natalie +well CRISPR casts nine is a possibility + + align:start position:0% +well CRISPR casts nine is a possibility + + + align:start position:0% +well CRISPR casts nine is a possibility +Jeremy did you have an idea PCR so I + + align:start position:0% +Jeremy did you have an idea PCR so I + + + align:start position:0% +Jeremy did you have an idea PCR so I +mean it's true you could you could get + + align:start position:0% +mean it's true you could you could get + + + align:start position:0% +mean it's true you could you could get +it to recognize that but then you have + + align:start position:0% +it to recognize that but then you have + + + align:start position:0% +it to recognize that but then you have +to detect it somehow so what's more + + align:start position:0% +to detect it somehow so what's more + + + align:start position:0% +to detect it somehow so what's more +commonly used is PCR those are both good + + align:start position:0% +commonly used is PCR those are both good + + + align:start position:0% +commonly used is PCR those are both good +ideas but using PCR you could design a + + align:start position:0% +ideas but using PCR you could design a + + + align:start position:0% +ideas but using PCR you could design a +primer here and a primer here and you + + align:start position:0% +primer here and a primer here and you + + + align:start position:0% +primer here and a primer here and you +could amplify this repeat sequence and + + align:start position:0% +could amplify this repeat sequence and + + + align:start position:0% +could amplify this repeat sequence and +the number of repeats would determine + + align:start position:0% +the number of repeats would determine + + + align:start position:0% +the number of repeats would determine +the size of your PCR fragment okay so if + + align:start position:0% +the size of your PCR fragment okay so if + + + align:start position:0% +the size of your PCR fragment okay so if +you did PCR then you get a PCR fragment + + align:start position:0% +you did PCR then you get a PCR fragment + + + align:start position:0% +you did PCR then you get a PCR fragment +that has the primers on each end but + + align:start position:0% +that has the primers on each end but + + + align:start position:0% +that has the primers on each end but +then has this certain size based on the + + align:start position:0% +then has this certain size based on the + + + align:start position:0% +then has this certain size based on the +number of repeats okay so in that case + + align:start position:0% +number of repeats okay so in that case + + + align:start position:0% +number of repeats okay so in that case +we need some sort of tool that enables + + align:start position:0% +we need some sort of tool that enables + + + align:start position:0% +we need some sort of tool that enables +us to determine the size of a particular + + align:start position:0% +us to determine the size of a particular + + + align:start position:0% +us to determine the size of a particular +DNA fragment and so I'm gonna just + + align:start position:0% +DNA fragment and so I'm gonna just + + + align:start position:0% +DNA fragment and so I'm gonna just +introduce to you one such tool which is + + align:start position:0% +introduce to you one such tool which is + + + align:start position:0% +introduce to you one such tool which is +gel electrophoresis and gel + + align:start position:0% +gel electrophoresis and gel + + + align:start position:0% +gel electrophoresis and gel +electrophoresis involves taking DNA that + + align:start position:0% +electrophoresis involves taking DNA that + + + align:start position:0% +electrophoresis involves taking DNA that +you've generated by either PCR or by + + align:start position:0% +you've generated by either PCR or by + + + align:start position:0% +you've generated by either PCR or by +cutting up DNA with the restriction + + align:start position:0% +cutting up DNA with the restriction + + + align:start position:0% +cutting up DNA with the restriction +enzyme and loading it in the well on in + + align:start position:0% +enzyme and loading it in the well on in + + + align:start position:0% +enzyme and loading it in the well on in +a gel that has agarose maybe it's + + align:start position:0% +a gel that has agarose maybe it's + + + align:start position:0% +a gel that has agarose maybe it's +composed of agarose it could be composed + + align:start position:0% +composed of agarose it could be composed + + + align:start position:0% +composed of agarose it could be composed +of poly acrylamide and then because DNA + + align:start position:0% +of poly acrylamide and then because DNA + + + align:start position:0% +of poly acrylamide and then because DNA +is negatively charged the backbone if + + align:start position:0% +is negatively charged the backbone if + + + align:start position:0% +is negatively charged the backbone if +you run a current through it such that + + align:start position:0% +you run a current through it such that + + + align:start position:0% +you run a current through it such that +the positive electrode is at the bottom + + align:start position:0% +the positive electrode is at the bottom + + + align:start position:0% +the positive electrode is at the bottom +then the DNA is going to snake through + + align:start position:0% +then the DNA is going to snake through + + + align:start position:0% +then the DNA is going to snake through +this gel okay now we'll do a quick + + align:start position:0% +this gel okay now we'll do a quick + + + align:start position:0% +this gel okay now we'll do a quick +demonstration if you two could come up I + + align:start position:0% +demonstration if you two could come up I + + + align:start position:0% +demonstration if you two could come up I +need one volunteer Ori find ten of your + + align:start position:0% +need one volunteer Ori find ten of your + + + align:start position:0% +need one volunteer Ori find ten of your +friends and bring them down + + align:start position:0% + + + + align:start position:0% + +all right that's that's that's that's + + align:start position:0% +all right that's that's that's that's + + + align:start position:0% +all right that's that's that's that's +probably good yeah + + align:start position:0% +probably good yeah + + + align:start position:0% +probably good yeah +all right Hanna won't you you guys have + + align:start position:0% +all right Hanna won't you you guys have + + + align:start position:0% +all right Hanna won't you you guys have +to link up okay + + align:start position:0% + + + + align:start position:0% + +stay over here we'll start at this end + + align:start position:0% +stay over here we'll start at this end + + + align:start position:0% +stay over here we'll start at this end +this is the negative electrode over here + + align:start position:0% +this is the negative electrode over here + + + align:start position:0% +this is the negative electrode over here +okay the positive electrode is going to + + align:start position:0% +okay the positive electrode is going to + + + align:start position:0% +okay the positive electrode is going to +be down there and Jackie is gonna be our + + align:start position:0% +be down there and Jackie is gonna be our + + + align:start position:0% +be down there and Jackie is gonna be our +single nucleotide + + align:start position:0% +single nucleotide + + + align:start position:0% +single nucleotide +okay you guys link link like yeah you + + align:start position:0% +okay you guys link link like yeah you + + + align:start position:0% +okay you guys link link like yeah you +know you don't have to dosey doe or + + align:start position:0% +know you don't have to dosey doe or + + + align:start position:0% +know you don't have to dosey doe or +anything like that but uh all right now + + align:start position:0% +anything like that but uh all right now + + + align:start position:0% +anything like that but uh all right now +what I want you guys to do is I want you + + align:start position:0% +what I want you guys to do is I want you + + + align:start position:0% +what I want you guys to do is I want you +to slalom through these cones like it's + + align:start position:0% +to slalom through these cones like it's + + + align:start position:0% +to slalom through these cones like it's +a gross gel so that you're going towards + + align:start position:0% +a gross gel so that you're going towards + + + align:start position:0% +a gross gel so that you're going towards +the other side okay and I'm going to + + align:start position:0% +the other side okay and I'm going to + + + align:start position:0% +the other side okay and I'm going to +turn on the current now so go + + align:start position:0% + + + + align:start position:0% + +all right stop all right see how the + + align:start position:0% +all right stop all right see how the + + + align:start position:0% +all right stop all right see how the +shorter DNA fragment is able to more + + align:start position:0% +shorter DNA fragment is able to more + + + align:start position:0% +shorter DNA fragment is able to more +easily navigate through the cones and + + align:start position:0% +easily navigate through the cones and + + + align:start position:0% +easily navigate through the cones and +get farther okay okay so then you know + + align:start position:0% +get farther okay okay so then you know + + + align:start position:0% +get farther okay okay so then you know +this is it was somewhat rigged I know + + align:start position:0% +this is it was somewhat rigged I know + + + align:start position:0% +this is it was somewhat rigged I know +but I just needed some way to make sure + + align:start position:0% +but I just needed some way to make sure + + + align:start position:0% +but I just needed some way to make sure +you always remember that the shorter + + align:start position:0% +you always remember that the shorter + + + align:start position:0% +you always remember that the shorter +nucleotide or the shorter fragment is + + align:start position:0% +nucleotide or the shorter fragment is + + + align:start position:0% +nucleotide or the shorter fragment is +going to migrate faster okay you guys + + align:start position:0% +going to migrate faster okay you guys + + + align:start position:0% +going to migrate faster okay you guys +can go back up thank you for your + + align:start position:0% +can go back up thank you for your + + + align:start position:0% +can go back up thank you for your +participation let's give them a round of + + align:start position:0% +participation let's give them a round of + + + align:start position:0% +participation let's give them a round of +applause all right so what you just saw + + align:start position:0% +applause all right so what you just saw + + + align:start position:0% +applause all right so what you just saw +is that the longer DNA fragments right + + align:start position:0% +is that the longer DNA fragments right + + + align:start position:0% +is that the longer DNA fragments right +they're going to be more inhibited by + + align:start position:0% +they're going to be more inhibited by + + + align:start position:0% +they're going to be more inhibited by +moving through the gel and so they're + + align:start position:0% +moving through the gel and so they're + + + align:start position:0% +moving through the gel and so they're +gonna move slower and thus not move as + + align:start position:0% +gonna move slower and thus not move as + + + align:start position:0% +gonna move slower and thus not move as +far in the gel whereas the small + + align:start position:0% +far in the gel whereas the small + + + align:start position:0% +far in the gel whereas the small +fragments are going to move much faster + + align:start position:0% +fragments are going to move much faster + + + align:start position:0% +fragments are going to move much faster +because they're able to sort of maneuver + + align:start position:0% +because they're able to sort of maneuver + + + align:start position:0% +because they're able to sort of maneuver +their way through this gel much more + + align:start position:0% +their way through this gel much more + + + align:start position:0% +their way through this gel much more +quickly so there's gonna be an inverse + + align:start position:0% +quickly so there's gonna be an inverse + + + align:start position:0% +quickly so there's gonna be an inverse +proportionality between the size of the + + align:start position:0% +proportionality between the size of the + + + align:start position:0% +proportionality between the size of the +DNA chain and its rate of movement okay + + align:start position:0% +DNA chain and its rate of movement okay + + + align:start position:0% +DNA chain and its rate of movement okay +where you're always gonna see the + + align:start position:0% +where you're always gonna see the + + + align:start position:0% +where you're always gonna see the +shorter DNA fragment moving faster okay + + align:start position:0% +shorter DNA fragment moving faster okay + + + align:start position:0% +shorter DNA fragment moving faster okay +so what one of these gels actually looks + + align:start position:0% +so what one of these gels actually looks + + + align:start position:0% +so what one of these gels actually looks +like is shown here + + align:start position:0% +like is shown here + + + align:start position:0% +like is shown here +so this is a DNA gel this agarose and + + align:start position:0% +so this is a DNA gel this agarose and + + + align:start position:0% +so this is a DNA gel this agarose and +DNA has been run in these different + + align:start position:0% +DNA has been run in these different + + + align:start position:0% +DNA has been run in these different +samples and what you're seeing is this + + align:start position:0% +samples and what you're seeing is this + + + align:start position:0% +samples and what you're seeing is this +gel is subsequently stained with a dye + + align:start position:0% +gel is subsequently stained with a dye + + + align:start position:0% +gel is subsequently stained with a dye +like a thin iam bromide which allows you + + align:start position:0% +like a thin iam bromide which allows you + + + align:start position:0% +like a thin iam bromide which allows you +to visualize the individual DNA + + align:start position:0% +to visualize the individual DNA + + + align:start position:0% +to visualize the individual DNA +fragments and so a band on this gel + + align:start position:0% +fragments and so a band on this gel + + + align:start position:0% +fragments and so a band on this gel +indicates a whole bunch of DNA fragments + + align:start position:0% +indicates a whole bunch of DNA fragments + + + align:start position:0% +indicates a whole bunch of DNA fragments +that are all roughly the same length + + align:start position:0% +that are all roughly the same length + + + align:start position:0% +that are all roughly the same length +okay so you essentially you can measure + + align:start position:0% +okay so you essentially you can measure + + + align:start position:0% +okay so you essentially you can measure +DNA length using this technique what's + + align:start position:0% +DNA length using this technique what's + + + align:start position:0% +DNA length using this technique what's +over here at the end of the gel this is + + align:start position:0% +over here at the end of the gel this is + + + align:start position:0% +over here at the end of the gel this is +probably some sort of DNA ladder where + + align:start position:0% +probably some sort of DNA ladder where + + + align:start position:0% +probably some sort of DNA ladder where +you have DNA fragments of known length + + align:start position:0% +you have DNA fragments of known length + + + align:start position:0% +you have DNA fragments of known length +that you can use to calibrate the length + + align:start position:0% +that you can use to calibrate the length + + + align:start position:0% +that you can use to calibrate the length +of these bands over here okay so this is + + align:start position:0% +of these bands over here okay so this is + + + align:start position:0% +of these bands over here okay so this is +how you measure DNA length and we're + + align:start position:0% +how you measure DNA length and we're + + + align:start position:0% +how you measure DNA length and we're +going to use it over and over again as + + align:start position:0% +going to use it over and over again as + + + align:start position:0% +going to use it over and over again as +we talk about DNA and sequencing so now + + align:start position:0% +we talk about DNA and sequencing so now + + + align:start position:0% +we talk about DNA and sequencing so now +let's think about how this is going to + + align:start position:0% +let's think about how this is going to + + + align:start position:0% +let's think about how this is going to +help us + + align:start position:0% +help us + + + align:start position:0% +help us +establish linkage between a particular + + align:start position:0% +establish linkage between a particular + + + align:start position:0% +establish linkage between a particular +marker in the genome and a genetic + + align:start position:0% +marker in the genome and a genetic + + + align:start position:0% +marker in the genome and a genetic +disease okay so if we think about these + + align:start position:0% +disease okay so if we think about these + + + align:start position:0% +disease okay so if we think about these +microsatellite repeats right I told you + + align:start position:0% +microsatellite repeats right I told you + + + align:start position:0% +microsatellite repeats right I told you +they're polymorphic they exhibit a lot + + align:start position:0% +they're polymorphic they exhibit a lot + + + align:start position:0% +they're polymorphic they exhibit a lot +of variation in size and so here's an + + align:start position:0% +of variation in size and so here's an + + + align:start position:0% +of variation in size and so here's an +example showing you a female who has two + + align:start position:0% +example showing you a female who has two + + + align:start position:0% +example showing you a female who has two +intermediate sized microsatellites and + + align:start position:0% +intermediate sized microsatellites and + + + align:start position:0% +intermediate sized microsatellites and +if you look at this the if you did PCR + + align:start position:0% +if you look at this the if you did PCR + + + align:start position:0% +if you look at this the if you did PCR +and measured the size of these you get + + align:start position:0% +and measured the size of these you get + + + align:start position:0% +and measured the size of these you get +two different bands because there are + + align:start position:0% +two different bands because there are + + + align:start position:0% +two different bands because there are +two different alleles of different + + align:start position:0% +two different alleles of different + + + align:start position:0% +two different alleles of different +lengths here okay so you can see this + + align:start position:0% +lengths here okay so you can see this + + + align:start position:0% +lengths here okay so you can see this +individual has two intermediate length + + align:start position:0% +individual has two intermediate length + + + align:start position:0% +individual has two intermediate length +repeats and this person has had children + + align:start position:0% +repeats and this person has had children + + + align:start position:0% +repeats and this person has had children +with an individual that has a short and + + align:start position:0% +with an individual that has a short and + + + align:start position:0% +with an individual that has a short and +a long microsatellite and you can see + + align:start position:0% +a long microsatellite and you can see + + + align:start position:0% +a long microsatellite and you can see +that on the gel here okay now this + + align:start position:0% +that on the gel here okay now this + + + align:start position:0% +that on the gel here okay now this +female is affected by some disease and + + align:start position:0% +female is affected by some disease and + + + align:start position:0% +female is affected by some disease and +these two individuals have children and + + align:start position:0% +these two individuals have children and + + + align:start position:0% +these two individuals have children and +you can see that a number of those + + align:start position:0% +you can see that a number of those + + + align:start position:0% +you can see that a number of those +children are affected by the disease + + align:start position:0% +children are affected by the disease + + + align:start position:0% +children are affected by the disease +so what mode of inheritance does this + + align:start position:0% +so what mode of inheritance does this + + + align:start position:0% +so what mode of inheritance does this +look like if you had your choice between + + align:start position:0% +look like if you had your choice between + + + align:start position:0% +look like if you had your choice between +autosomal recessive autosomal dominant + + align:start position:0% +autosomal recessive autosomal dominant + + + align:start position:0% +autosomal recessive autosomal dominant +sex link dominance x-linked recessive + + align:start position:0% +sex link dominance x-linked recessive + + + align:start position:0% +sex link dominance x-linked recessive +which what mode of inheritance is this + + align:start position:0% +which what mode of inheritance is this + + + align:start position:0% +which what mode of inheritance is this +looking like oh Carmen + + align:start position:0% +looking like oh Carmen + + + align:start position:0% +looking like oh Carmen +autosomal recessive why why do you go + + align:start position:0% +autosomal recessive why why do you go + + + align:start position:0% +autosomal recessive why why do you go +with recessive so yeah go ahead + + align:start position:0% + + + + align:start position:0% + +seems like + + align:start position:0% + + + + align:start position:0% + +fathers + + align:start position:0% + + + + align:start position:0% + +that's possible that's that's definitely + + align:start position:0% +that's possible that's that's definitely + + + align:start position:0% +that's possible that's that's definitely +that's exactly the logic I want to see + + align:start position:0% +that's exactly the logic I want to see + + + align:start position:0% +that's exactly the logic I want to see +is there another possibility yeah Jeremy + + align:start position:0% +is there another possibility yeah Jeremy + + + align:start position:0% +is there another possibility yeah Jeremy +it could also be autosomal dominant okay + + align:start position:0% +it could also be autosomal dominant okay + + + align:start position:0% +it could also be autosomal dominant okay +so you're right you're right if this was + + align:start position:0% +so you're right you're right if this was + + + align:start position:0% +so you're right you're right if this was +not a rare disease than that that male + + align:start position:0% +not a rare disease than that that male + + + align:start position:0% +not a rare disease than that that male +could be a carrier and could be passing + + align:start position:0% +could be a carrier and could be passing + + + align:start position:0% +could be a carrier and could be passing +it on to half the children so that's + + align:start position:0% +it on to half the children so that's + + + align:start position:0% +it on to half the children so that's +good you'd you'd essentially need more + + align:start position:0% +good you'd you'd essentially need more + + + align:start position:0% +good you'd you'd essentially need more +information to differentiate between + + align:start position:0% +information to differentiate between + + + align:start position:0% +information to differentiate between +autosomal recessive and autosomal + + align:start position:0% +autosomal recessive and autosomal + + + align:start position:0% +autosomal recessive and autosomal +dominant for the purposes of this we're + + align:start position:0% +dominant for the purposes of this we're + + + align:start position:0% +dominant for the purposes of this we're +gonna go with dominant autosomal + + align:start position:0% +gonna go with dominant autosomal + + + align:start position:0% +gonna go with dominant autosomal +dominant and what you see is that you + + align:start position:0% +dominant and what you see is that you + + + align:start position:0% +dominant and what you see is that you +want to look at the affected individuals + + align:start position:0% +want to look at the affected individuals + + + align:start position:0% +want to look at the affected individuals +and see if the disease phenotype is + + align:start position:0% +and see if the disease phenotype is + + + align:start position:0% +and see if the disease phenotype is +linked or connected with one of these + + align:start position:0% +linked or connected with one of these + + + align:start position:0% +linked or connected with one of these +microsatellite alleles okay so if we + + align:start position:0% +microsatellite alleles okay so if we + + + align:start position:0% +microsatellite alleles okay so if we +look at you know we basically PCR DNA + + align:start position:0% +look at you know we basically PCR DNA + + + align:start position:0% +look at you know we basically PCR DNA +from all these individuals and if you + + align:start position:0% +from all these individuals and if you + + + align:start position:0% +from all these individuals and if you +look at who's affected each one of the + + align:start position:0% +look at who's affected each one of the + + + align:start position:0% +look at who's affected each one of the +individuals has this M double prime band + + align:start position:0% +individuals has this M double prime band + + + align:start position:0% +individuals has this M double prime band +and none of the unaffected individuals + + align:start position:0% +and none of the unaffected individuals + + + align:start position:0% +and none of the unaffected individuals +has it okay so you know this obviously + + align:start position:0% +has it okay so you know this obviously + + + align:start position:0% +has it okay so you know this obviously +it would be better to have more + + align:start position:0% +it would be better to have more + + + align:start position:0% +it would be better to have more +pedigrees and more data to really + + align:start position:0% +pedigrees and more data to really + + + align:start position:0% +pedigrees and more data to really +establish significance between this + + align:start position:0% +establish significance between this + + + align:start position:0% +establish significance between this +linkage but this is just a simple + + align:start position:0% +linkage but this is just a simple + + + align:start position:0% +linkage but this is just a simple +example showing what you could possibly + + align:start position:0% +example showing what you could possibly + + + align:start position:0% +example showing what you could possibly +see if you have one of these molecular + + align:start position:0% +see if you have one of these molecular + + + align:start position:0% +see if you have one of these molecular +markers linked to a particular disease + + align:start position:0% +markers linked to a particular disease + + + align:start position:0% +markers linked to a particular disease +allele okay so that kind of establishes + + align:start position:0% +allele okay so that kind of establishes + + + align:start position:0% +allele okay so that kind of establishes +the principle now let's think about what + + align:start position:0% +the principle now let's think about what + + + align:start position:0% +the principle now let's think about what +are some other molecular markers that + + align:start position:0% +are some other molecular markers that + + + align:start position:0% +are some other molecular markers that +are possible so another type of marker + + align:start position:0% +are possible so another type of marker + + + align:start position:0% +are possible so another type of marker +and this is one that's the most common + + align:start position:0% +and this is one that's the most common + + + align:start position:0% +and this is one that's the most common +one if I go here so here you see here's + + align:start position:0% +one if I go here so here you see here's + + + align:start position:0% +one if I go here so here you see here's +a linkage map here and you see most of + + align:start position:0% +a linkage map here and you see most of + + + align:start position:0% +a linkage map here and you see most of +these bands are green and the green + + align:start position:0% +these bands are green and the green + + + align:start position:0% +these bands are green and the green +markers here are what are known as + + align:start position:0% +markers here are what are known as + + + align:start position:0% +markers here are what are known as +single nucleotide polymorphism Kali + + align:start position:0% +single nucleotide polymorphism Kali + + + align:start position:0% +single nucleotide polymorphism Kali +morphisms or snips okay + + align:start position:0% +morphisms or snips okay + + + align:start position:0% +morphisms or snips okay +so single nucleotide polymorphisms and + + align:start position:0% +so single nucleotide polymorphisms and + + + align:start position:0% +so single nucleotide polymorphisms and +this is abbreviated snip okay and what a + + align:start position:0% +this is abbreviated snip okay and what a + + + align:start position:0% +this is abbreviated snip okay and what a +single nucleotide polymorphism is is + + align:start position:0% +single nucleotide polymorphism is is + + + align:start position:0% +single nucleotide polymorphism is is +it's a variation of a nucleotide at a + + align:start position:0% +it's a variation of a nucleotide at a + + + align:start position:0% +it's a variation of a nucleotide at a +single position in the genome okay so + + align:start position:0% +single position in the genome okay so + + + align:start position:0% +single position in the genome okay so +it's just a one base pair difference in + + align:start position:0% +it's just a one base pair difference in + + + align:start position:0% +it's just a one base pair difference in +the in at a position so this variation + + align:start position:0% +the in at a position so this variation + + + align:start position:0% +the in at a position so this variation +of single nucleotide at a given position + + align:start position:0% +of single nucleotide at a given position + + + align:start position:0% +of single nucleotide at a given position +at a position in the genome okay and + + align:start position:0% +at a position in the genome okay and + + + align:start position:0% +at a position in the genome okay and +because that's a pretty general + + align:start position:0% +because that's a pretty general + + + align:start position:0% +because that's a pretty general +definition there are tons of these in + + align:start position:0% +definition there are tons of these in + + + align:start position:0% +definition there are tons of these in +the genome okay now one thing to think + + align:start position:0% +the genome okay now one thing to think + + + align:start position:0% +the genome okay now one thing to think +about is you could have a mutation in an + + align:start position:0% +about is you could have a mutation in an + + + align:start position:0% +about is you could have a mutation in an +individual that creates a snip okay so + + align:start position:0% +individual that creates a snip okay so + + + align:start position:0% +individual that creates a snip okay so +you could have a de novo formation of a + + align:start position:0% +you could have a de novo formation of a + + + align:start position:0% +you could have a de novo formation of a +snip but if you have a snip and it gets + + align:start position:0% +snip but if you have a snip and it gets + + + align:start position:0% +snip but if you have a snip and it gets +incorporated to the gametes of an + + align:start position:0% +incorporated to the gametes of an + + + align:start position:0% +incorporated to the gametes of an +individual then that variant is going to + + align:start position:0% +individual then that variant is going to + + + align:start position:0% +individual then that variant is going to +be passed on to the next generation okay + + align:start position:0% +be passed on to the next generation okay + + + align:start position:0% +be passed on to the next generation okay +so this is something that could occur de + + align:start position:0% +so this is something that could occur de + + + align:start position:0% +so this is something that could occur de +novo but it is also heritable and if + + align:start position:0% +novo but it is also heritable and if + + + align:start position:0% +novo but it is also heritable and if +it's heritable then you can use it you + + align:start position:0% +it's heritable then you can use it you + + + align:start position:0% +it's heritable then you can use it you +can follow it and use it to determine if + + align:start position:0% +can follow it and use it to determine if + + + align:start position:0% +can follow it and use it to determine if +a given variant is linked to a given + + align:start position:0% +a given variant is linked to a given + + + align:start position:0% +a given variant is linked to a given +phenotype like a disease so to identify + + align:start position:0% +phenotype like a disease so to identify + + + align:start position:0% +phenotype like a disease so to identify +a single nucleotide polymorphism it's + + align:start position:0% +a single nucleotide polymorphism it's + + + align:start position:0% +a single nucleotide polymorphism it's +helpful to be able to sequence the DNA + + align:start position:0% +helpful to be able to sequence the DNA + + + align:start position:0% +helpful to be able to sequence the DNA +and I'll talk about how we could do that + + align:start position:0% +and I'll talk about how we could do that + + + align:start position:0% +and I'll talk about how we could do that +in just a minute but before I go on I + + align:start position:0% +in just a minute but before I go on I + + + align:start position:0% +in just a minute but before I go on I +just want to point out a subclass of + + align:start position:0% +just want to point out a subclass of + + + align:start position:0% +just want to point out a subclass of +snips that can be visualized without + + align:start position:0% +snips that can be visualized without + + + align:start position:0% +snips that can be visualized without +sequencing and these are called + + align:start position:0% +sequencing and these are called + + + align:start position:0% +sequencing and these are called +restriction fragment length + + align:start position:0% +restriction fragment length + + + align:start position:0% +restriction fragment length +polymorphisms so restriction fragment so + + align:start position:0% +polymorphisms so restriction fragment so + + + align:start position:0% +polymorphisms so restriction fragment so +it's going to involve some type of + + align:start position:0% +it's going to involve some type of + + + align:start position:0% +it's going to involve some type of +restriction enzyme digest + + align:start position:0% +restriction enzyme digest + + + align:start position:0% +restriction enzyme digest +length polymorphism it's a long word but + + align:start position:0% +length polymorphism it's a long word but + + + align:start position:0% +length polymorphism it's a long word but +it's abbreviated rift lip okay and what + + align:start position:0% +it's abbreviated rift lip okay and what + + + align:start position:0% +it's abbreviated rift lip okay and what +this is is it's a variation of a single + + align:start position:0% +this is is it's a variation of a single + + + align:start position:0% +this is is it's a variation of a single +nucleotide but this is a subclass of + + align:start position:0% +nucleotide but this is a subclass of + + + align:start position:0% +nucleotide but this is a subclass of +snip because this is when the variation + + align:start position:0% +snip because this is when the variation + + + align:start position:0% +snip because this is when the variation +occurs any restriction site for a + + align:start position:0% +occurs any restriction site for a + + + align:start position:0% +occurs any restriction site for a +restriction enzyme okay so if you + + align:start position:0% +restriction enzyme okay so if you + + + align:start position:0% +restriction enzyme okay so if you +remember your good friend eco r1 eco r1 + + align:start position:0% +remember your good friend eco r1 eco r1 + + + align:start position:0% +remember your good friend eco r1 eco r1 +recognizes the nucleotide sequence + + align:start position:0% +recognizes the nucleotide sequence + + + align:start position:0% +recognizes the nucleotide sequence +g-a-a-t-t-c and eco r1 only cleaves DNA + + align:start position:0% +g-a-a-t-t-c and eco r1 only cleaves DNA + + + align:start position:0% +g-a-a-t-t-c and eco r1 only cleaves DNA +sequence that has g-a-a-t-t-c okay so if + + align:start position:0% +sequence that has g-a-a-t-t-c okay so if + + + align:start position:0% +sequence that has g-a-a-t-t-c okay so if +there was a single variation there's a + + align:start position:0% +there was a single variation there's a + + + align:start position:0% +there was a single variation there's a +single nucleotide variation in the + + align:start position:0% +single nucleotide variation in the + + + align:start position:0% +single nucleotide variation in the +sequence such that it's now GA t t t c + + align:start position:0% +sequence such that it's now GA t t t c + + + align:start position:0% +sequence such that it's now GA t t t c +or something like that that destroys the + + align:start position:0% +or something like that that destroys the + + + align:start position:0% +or something like that that destroys the +eco r1 site and so eco r1 will no longer + + align:start position:0% +eco r1 site and so eco r1 will no longer + + + align:start position:0% +eco r1 site and so eco r1 will no longer +be able to recognize this site in the + + align:start position:0% +be able to recognize this site in the + + + align:start position:0% +be able to recognize this site in the +genome and cut it okay so you could + + align:start position:0% +genome and cut it okay so you could + + + align:start position:0% +genome and cut it okay so you could +imagine that if you had one individual + + align:start position:0% +imagine that if you had one individual + + + align:start position:0% +imagine that if you had one individual +in the genome having three equal r1 + + align:start position:0% +in the genome having three equal r1 + + + align:start position:0% +in the genome having three equal r1 +sites if you digest this region you'd + + align:start position:0% +sites if you digest this region you'd + + + align:start position:0% +sites if you digest this region you'd +get two fragments but if you destroyed + + align:start position:0% +get two fragments but if you destroyed + + + align:start position:0% +get two fragments but if you destroyed +the one in the middle then if you + + align:start position:0% +the one in the middle then if you + + + align:start position:0% +the one in the middle then if you +digested this piece of DNA then you'd + + align:start position:0% +digested this piece of DNA then you'd + + + align:start position:0% +digested this piece of DNA then you'd +only get one fragment okay and that's + + align:start position:0% +only get one fragment okay and that's + + + align:start position:0% +only get one fragment okay and that's +something because it results in + + align:start position:0% +something because it results in + + + align:start position:0% +something because it results in +different sizes of fragments that's + + align:start position:0% +different sizes of fragments that's + + + align:start position:0% +different sizes of fragments that's +something you can see just by doing DNA + + align:start position:0% +something you can see just by doing DNA + + + align:start position:0% +something you can see just by doing DNA +electrophoresis and maybe you would use + + align:start position:0% +electrophoresis and maybe you would use + + + align:start position:0% +electrophoresis and maybe you would use +some method to detect this specific + + align:start position:0% +some method to detect this specific + + + align:start position:0% +some method to detect this specific +region so that you're not looking at all + + align:start position:0% +region so that you're not looking at all + + + align:start position:0% +region so that you're not looking at all +the DNA in the genome but you're + + align:start position:0% +the DNA in the genome but you're + + + align:start position:0% +the DNA in the genome but you're +establishing linkage to this specific + + align:start position:0% +establishing linkage to this specific + + + align:start position:0% +establishing linkage to this specific +area okay you could use PCR right you + + align:start position:0% +area okay you could use PCR right you + + + align:start position:0% +area okay you could use PCR right you +can have PCR primers here and here and + + align:start position:0% +can have PCR primers here and here and + + + align:start position:0% +can have PCR primers here and here and +you could then cut with eco r1 in one + + align:start position:0% +you could then cut with eco r1 in one + + + align:start position:0% +you could then cut with eco r1 in one +case you'd get two fragments in this + + align:start position:0% +case you'd get two fragments in this + + + align:start position:0% +case you'd get two fragments in this +case you get two fragments in this case + + align:start position:0% +case you get two fragments in this case + + + align:start position:0% +case you get two fragments in this case +if you amplified this region of the + + align:start position:0% +if you amplified this region of the + + + align:start position:0% +if you amplified this region of the +genome and cut with eco r1 you'd only + + align:start position:0% +genome and cut with eco r1 you'd only + + + align:start position:0% +genome and cut with eco r1 you'd only +get one fragment + + align:start position:0% +get one fragment + + + align:start position:0% +get one fragment +okay so you'd be able to differentiate + + align:start position:0% +okay so you'd be able to differentiate + + + align:start position:0% +okay so you'd be able to differentiate +between those possibilities yes + + align:start position:0% +between those possibilities yes + + + align:start position:0% +between those possibilities yes +Malik what's up oh you're saying what + + align:start position:0% +Malik what's up oh you're saying what + + + align:start position:0% +Malik what's up oh you're saying what +causes it to stop + + align:start position:0% +causes it to stop + + + align:start position:0% +causes it to stop +that's a great question Malik yeah so + + align:start position:0% +that's a great question Malik yeah so + + + align:start position:0% +that's a great question Malik yeah so +initially it's not gonna stop that's + + align:start position:0% +initially it's not gonna stop that's + + + align:start position:0% +initially it's not gonna stop that's +absolutely right but because every step + + align:start position:0% +absolutely right but because every step + + + align:start position:0% +absolutely right but because every step +each time you replicate it's then primed + + align:start position:0% +each time you replicate it's then primed + + + align:start position:0% +each time you replicate it's then primed +with another primer right so you'd + + align:start position:0% +with another primer right so you'd + + + align:start position:0% +with another primer right so you'd +replicate something like this right + + align:start position:0% +replicate something like this right + + + align:start position:0% +replicate something like this right +that's too long but then the reverse + + align:start position:0% +that's too long but then the reverse + + + align:start position:0% +that's too long but then the reverse +primer would replicate like this and it + + align:start position:0% +primer would replicate like this and it + + + align:start position:0% +primer would replicate like this and it +would stop okay + + align:start position:0% +would stop okay + + + align:start position:0% +would stop okay +so if you go back to my slide from last + + align:start position:0% +so if you go back to my slide from last + + + align:start position:0% +so if you go back to my slide from last +lecture you look through that and see if + + align:start position:0% +lecture you look through that and see if + + + align:start position:0% +lecture you look through that and see if +it makes sense how it's ending because + + align:start position:0% +it makes sense how it's ending because + + + align:start position:0% +it makes sense how it's ending because +if you do this 30 times you really will + + align:start position:0% +if you do this 30 times you really will + + + align:start position:0% +if you do this 30 times you really will +enrich for a fragment that sort of stops + + align:start position:0% +enrich for a fragment that sort of stops + + + align:start position:0% +enrich for a fragment that sort of stops +and ends at the two primers or begins + + align:start position:0% +and ends at the two primers or begins + + + align:start position:0% +and ends at the two primers or begins +and ends at the two primers I should say + + align:start position:0% +and ends at the two primers I should say + + + align:start position:0% +and ends at the two primers I should say +okay + + align:start position:0% +okay + + + align:start position:0% +okay +good question thank you all right now + + align:start position:0% +good question thank you all right now + + + align:start position:0% +good question thank you all right now +let's talk about DNA sequencing because + + align:start position:0% +let's talk about DNA sequencing because + + + align:start position:0% +let's talk about DNA sequencing because +as I showed you obviously these snips + + align:start position:0% +as I showed you obviously these snips + + + align:start position:0% +as I showed you obviously these snips +because they're so many of them are + + align:start position:0% +because they're so many of them are + + + align:start position:0% +because they're so many of them are +probably the most useful of these + + align:start position:0% +probably the most useful of these + + + align:start position:0% +probably the most useful of these +markers to narrow in on where your + + align:start position:0% +markers to narrow in on where your + + + align:start position:0% +markers to narrow in on where your +disease gene is and to detect a snip we + + align:start position:0% +disease gene is and to detect a snip we + + + align:start position:0% +disease gene is and to detect a snip we +need to have we need to be able to + + align:start position:0% +need to have we need to be able to + + + align:start position:0% +need to have we need to be able to +sequence DNA so I'm gonna start with an + + align:start position:0% +sequence DNA so I'm gonna start with an + + + align:start position:0% +sequence DNA so I'm gonna start with an +older method for DNA sequencing which + + align:start position:0% +older method for DNA sequencing which + + + align:start position:0% +older method for DNA sequencing which +conceptually is very similar to how we + + align:start position:0% +conceptually is very similar to how we + + + align:start position:0% +conceptually is very similar to how we +do DNA sequencing today and so it will + + align:start position:0% +do DNA sequencing today and so it will + + + align:start position:0% +do DNA sequencing today and so it will +illustrate my point and then at the end + + align:start position:0% +illustrate my point and then at the end + + + align:start position:0% +illustrate my point and then at the end +I'll sort I'll talk about how more + + align:start position:0% +I'll sort I'll talk about how more + + + align:start position:0% +I'll sort I'll talk about how more +modern techniques distinct sequencing so + + align:start position:0% +modern techniques distinct sequencing so + + + align:start position:0% +modern techniques distinct sequencing so +the technique I'm going to introduce to + + align:start position:0% +the technique I'm going to introduce to + + + align:start position:0% +the technique I'm going to introduce to +you is called Sanger sequencing and + + align:start position:0% +you is called Sanger sequencing and + + + align:start position:0% +you is called Sanger sequencing and +that's because it was a an individual it + + align:start position:0% +that's because it was a an individual it + + + align:start position:0% +that's because it was a an individual it +was identified by an individual named + + align:start position:0% +was identified by an individual named + + + align:start position:0% +was identified by an individual named +Fred Sanger and I'm going to just take a + + align:start position:0% +Fred Sanger and I'm going to just take a + + + align:start position:0% +Fred Sanger and I'm going to just take a +very simple DNA sequence in order to + + align:start position:0% +very simple DNA sequence in order to + + + align:start position:0% +very simple DNA sequence in order to +illustrate how Sanger sequencing works + + align:start position:0% + + + + align:start position:0% + +so let's take a sequence that's really + + align:start position:0% +so let's take a sequence that's really + + + align:start position:0% +so let's take a sequence that's really +simple this is very very simple right so + + align:start position:0% +simple this is very very simple right so + + + align:start position:0% +simple this is very very simple right so +and then more sequence here so let's say + + align:start position:0% +and then more sequence here so let's say + + + align:start position:0% +and then more sequence here so let's say +we want to determine the nucleotide + + align:start position:0% +we want to determine the nucleotide + + + align:start position:0% +we want to determine the nucleotide +that's at every position of this DNA + + align:start position:0% +that's at every position of this DNA + + + align:start position:0% +that's at every position of this DNA +fragment okay so one way we could maybe + + align:start position:0% +fragment okay so one way we could maybe + + + align:start position:0% +fragment okay so one way we could maybe +conceptually think about doing this is + + align:start position:0% +conceptually think about doing this is + + + align:start position:0% +conceptually think about doing this is +to try to let DNA polymerase tell us + + align:start position:0% +to try to let DNA polymerase tell us + + + align:start position:0% +to try to let DNA polymerase tell us +we're given nucleotides are and if we're + + align:start position:0% +we're given nucleotides are and if we're + + + align:start position:0% +we're given nucleotides are and if we're +gonna use DNA polymerase what are we + + align:start position:0% +gonna use DNA polymerase what are we + + + align:start position:0% +gonna use DNA polymerase what are we +going to need to in order to facilitate + + align:start position:0% +going to need to in order to facilitate + + + align:start position:0% +going to need to in order to facilitate +this process yes Rachel you're going to + + align:start position:0% +this process yes Rachel you're going to + + + align:start position:0% +this process yes Rachel you're going to +need nucleotides definitely so we're + + align:start position:0% +need nucleotides definitely so we're + + + align:start position:0% +need nucleotides definitely so we're +gonna need nucleotides what else to + + align:start position:0% +gonna need nucleotides what else to + + + align:start position:0% +gonna need nucleotides what else to +start what are you going to need miles + + align:start position:0% +start what are you going to need miles + + + align:start position:0% +start what are you going to need miles +you're gonna need a primer exactly good + + align:start position:0% +you're gonna need a primer exactly good + + + align:start position:0% +you're gonna need a primer exactly good +job so we're gonna need a primer okay so + + align:start position:0% +job so we're gonna need a primer okay so + + + align:start position:0% +job so we're gonna need a primer okay so +here's a primer and now we're gonna try + + align:start position:0% +here's a primer and now we're gonna try + + + align:start position:0% +here's a primer and now we're gonna try +to get DNA polymerase to tell us + + align:start position:0% +to get DNA polymerase to tell us + + + align:start position:0% +to get DNA polymerase to tell us +whenever there is a given nucleotide in + + align:start position:0% +whenever there is a given nucleotide in + + + align:start position:0% +whenever there is a given nucleotide in +this DNA sequence okay and so think me + + align:start position:0% +this DNA sequence okay and so think me + + + align:start position:0% +this DNA sequence okay and so think me +think with me let's say we were able to + + align:start position:0% +think with me let's say we were able to + + + align:start position:0% +think with me let's say we were able to +get DNA polymerase to stop whenever + + align:start position:0% +get DNA polymerase to stop whenever + + + align:start position:0% +get DNA polymerase to stop whenever +there was a certain nucleotide okay so + + align:start position:0% +there was a certain nucleotide okay so + + + align:start position:0% +there was a certain nucleotide okay so +if we go through just a couple + + align:start position:0% +if we go through just a couple + + + align:start position:0% +if we go through just a couple +nucleotides let's say at first we want + + align:start position:0% +nucleotides let's say at first we want + + + align:start position:0% +nucleotides let's say at first we want +DNA polymerized DNA polymerase to stop + + align:start position:0% +DNA polymerized DNA polymerase to stop + + + align:start position:0% +DNA polymerized DNA polymerase to stop +whenever there's an a okay so let's say + + align:start position:0% +whenever there's an a okay so let's say + + + align:start position:0% +whenever there's an a okay so let's say +there was a possibility it would stop at + + align:start position:0% +there was a possibility it would stop at + + + align:start position:0% +there was a possibility it would stop at +this a if it stopped at this a you + + align:start position:0% +this a if it stopped at this a you + + + align:start position:0% +this a if it stopped at this a you +generate a fragment of this length but + + align:start position:0% +generate a fragment of this length but + + + align:start position:0% +generate a fragment of this length but +if it read on through that a there's + + align:start position:0% +if it read on through that a there's + + + align:start position:0% +if it read on through that a there's +another possibility that it would stop + + align:start position:0% +another possibility that it would stop + + + align:start position:0% +another possibility that it would stop +at this a so we're kind of looking at + + align:start position:0% +at this a so we're kind of looking at + + + align:start position:0% +at this a so we're kind of looking at +when these are stopping + + align:start position:0% +when these are stopping + + + align:start position:0% +when these are stopping +and the final possibility is it goes on + + align:start position:0% +and the final possibility is it goes on + + + align:start position:0% +and the final possibility is it goes on +and stops at this a okay so if this DNA + + align:start position:0% +and stops at this a okay so if this DNA + + + align:start position:0% +and stops at this a okay so if this DNA +polymerase stopped only at A's you get + + align:start position:0% +polymerase stopped only at A's you get + + + align:start position:0% +polymerase stopped only at A's you get +fragments that are these three discrete + + align:start position:0% +fragments that are these three discrete + + + align:start position:0% +fragments that are these three discrete +lengths okay + + align:start position:0% +lengths okay + + + align:start position:0% +lengths okay +now let's consider another possibility + + align:start position:0% +now let's consider another possibility + + + align:start position:0% +now let's consider another possibility +so pink here is stopped at a and in blue + + align:start position:0% +so pink here is stopped at a and in blue + + + align:start position:0% +so pink here is stopped at a and in blue +I'm gonna draw what would happen if it + + align:start position:0% +I'm gonna draw what would happen if it + + + align:start position:0% +I'm gonna draw what would happen if it +stopped at T okay so they all start from + + align:start position:0% +stopped at T okay so they all start from + + + align:start position:0% +stopped at T okay so they all start from +the same place if it stopped at T it + + align:start position:0% +the same place if it stopped at T it + + + align:start position:0% +the same place if it stopped at T it +would just stop one nucleotide beyond + + align:start position:0% +would just stop one nucleotide beyond + + + align:start position:0% +would just stop one nucleotide beyond +this a in this simple sequence okay so + + align:start position:0% +this a in this simple sequence okay so + + + align:start position:0% +this a in this simple sequence okay so +in blue here this is stopped at T okay + + align:start position:0% +in blue here this is stopped at T okay + + + align:start position:0% +in blue here this is stopped at T okay +but if it's if it's just a possibility + + align:start position:0% +but if it's if it's just a possibility + + + align:start position:0% +but if it's if it's just a possibility +it stops and some of the polymerase is + + align:start position:0% +it stops and some of the polymerase is + + + align:start position:0% +it stops and some of the polymerase is +could go beyond this T and go to the + + align:start position:0% +could go beyond this T and go to the + + + align:start position:0% +could go beyond this T and go to the +next T and stop here and again this + + align:start position:0% +next T and stop here and again this + + + align:start position:0% +next T and stop here and again this +would be one nucleotide length longer + + align:start position:0% +would be one nucleotide length longer + + + align:start position:0% +would be one nucleotide length longer +than this pink one here and the final + + align:start position:0% +than this pink one here and the final + + + align:start position:0% +than this pink one here and the final +one would I'll just draw it down here + + align:start position:0% +one would I'll just draw it down here + + + align:start position:0% +one would I'll just draw it down here +would get out to this last T here okay + + align:start position:0% +would get out to this last T here okay + + + align:start position:0% +would get out to this last T here okay +so what you see is if we could get DNA + + align:start position:0% +so what you see is if we could get DNA + + + align:start position:0% +so what you see is if we could get DNA +polymerase to stop at these discrete + + align:start position:0% +polymerase to stop at these discrete + + + align:start position:0% +polymerase to stop at these discrete +positions we'd get a different sized + + align:start position:0% +positions we'd get a different sized + + + align:start position:0% +positions we'd get a different sized +fragments whether it was stopping it one + + align:start position:0% +fragments whether it was stopping it one + + + align:start position:0% +fragments whether it was stopping it one +nucleotide versus the other nucleotide + + align:start position:0% +nucleotide versus the other nucleotide + + + align:start position:0% +nucleotide versus the other nucleotide +okay you all see how this is resulting + + align:start position:0% +okay you all see how this is resulting + + + align:start position:0% +okay you all see how this is resulting +in different fragment lengths yes Andrew + + align:start position:0% + + + + align:start position:0% + +there's there are companies now you can + + align:start position:0% +there's there are companies now you can + + + align:start position:0% +there's there are companies now you can +basically take nucleotides and + + align:start position:0% +basically take nucleotides and + + + align:start position:0% +basically take nucleotides and +synthesize these primers chemically okay + + align:start position:0% +synthesize these primers chemically okay + + + align:start position:0% +synthesize these primers chemically okay +I'm not using DNA polymerase in this + + align:start position:0% +I'm not using DNA polymerase in this + + + align:start position:0% +I'm not using DNA polymerase in this +case you'd have to start with some + + align:start position:0% +case you'd have to start with some + + + align:start position:0% +case you'd have to start with some +sequence that you know right so in most + + align:start position:0% +sequence that you know right so in most + + + align:start position:0% +sequence that you know right so in most +sequencing technologies you take you + + align:start position:0% +sequencing technologies you take you + + + align:start position:0% +sequencing technologies you take you +kind of make a DNA library where you + + align:start position:0% +kind of make a DNA library where you + + + align:start position:0% +kind of make a DNA library where you +know the sequence of the vector and then + + align:start position:0% +know the sequence of the vector and then + + + align:start position:0% +know the sequence of the vector and then +you'd use the vector sequence as a + + align:start position:0% +you'd use the vector sequence as a + + + align:start position:0% +you'd use the vector sequence as a +primer to sequence into the unknown + + align:start position:0% +primer to sequence into the unknown + + + align:start position:0% +primer to sequence into the unknown +sequence okay great question + + align:start position:0% +sequence okay great question + + + align:start position:0% +sequence okay great question +good job all right so so what we need + + align:start position:0% +good job all right so so what we need + + + align:start position:0% +good job all right so so what we need +now then is some sort of tool or ability + + align:start position:0% +now then is some sort of tool or ability + + + align:start position:0% +now then is some sort of tool or ability +to stop DNA polymerase at when there's a + + align:start position:0% +to stop DNA polymerase at when there's a + + + align:start position:0% +to stop DNA polymerase at when there's a +certain nucleotide base okay and to do + + align:start position:0% +certain nucleotide base okay and to do + + + align:start position:0% +certain nucleotide base okay and to do +that we can use this type of molecule + + align:start position:0% +that we can use this type of molecule + + + align:start position:0% +that we can use this type of molecule +here which is known as the dye deoxy + + align:start position:0% +here which is known as the dye deoxy + + + align:start position:0% +here which is known as the dye deoxy +nucleotide remember for DNA polymer for + + align:start position:0% +nucleotide remember for DNA polymer for + + + align:start position:0% +nucleotide remember for DNA polymer for +DNA polymerase to elongate a chain it + + align:start position:0% +DNA polymerase to elongate a chain it + + + align:start position:0% +DNA polymerase to elongate a chain it +requires that the last base have a three + + align:start position:0% +requires that the last base have a three + + + align:start position:0% +requires that the last base have a three +prime hydroxyl okay and so what this dye + + align:start position:0% +prime hydroxyl okay and so what this dye + + + align:start position:0% +prime hydroxyl okay and so what this dye +dye oxy nucleoside triphosphate is is + + align:start position:0% +dye oxy nucleoside triphosphate is is + + + align:start position:0% +dye oxy nucleoside triphosphate is is +it's a nucleoside triphosphate that + + align:start position:0% +it's a nucleoside triphosphate that + + + align:start position:0% +it's a nucleoside triphosphate that +lacks a three prime hydroxyl okay here + + align:start position:0% +lacks a three prime hydroxyl okay here + + + align:start position:0% +lacks a three prime hydroxyl okay here +I'll highlight that so you see this guy + + align:start position:0% +I'll highlight that so you see this guy + + + align:start position:0% +I'll highlight that so you see this guy +you see both the high light H there's a + + align:start position:0% +you see both the high light H there's a + + + align:start position:0% +you see both the high light H there's a +hydrogen there on the three prime carbon + + align:start position:0% +hydrogen there on the three prime carbon + + + align:start position:0% +hydrogen there on the three prime carbon +rather than the normal hydroxyl group + + align:start position:0% +rather than the normal hydroxyl group + + + align:start position:0% +rather than the normal hydroxyl group +okay so if this if this base gets + + align:start position:0% +okay so if this if this base gets + + + align:start position:0% +okay so if this if this base gets +incorporated into a elongating chain + + align:start position:0% +incorporated into a elongating chain + + + align:start position:0% +incorporated into a elongating chain +right Diamond DNA polymerase is not + + align:start position:0% +right Diamond DNA polymerase is not + + + align:start position:0% +right Diamond DNA polymerase is not +going to be able to move on okay so this + + align:start position:0% +going to be able to move on okay so this + + + align:start position:0% +going to be able to move on okay so this +method where you can add a certain dye + + align:start position:0% +method where you can add a certain dye + + + align:start position:0% +method where you can add a certain dye +deoxy nucleoside triphosphate to stop + + align:start position:0% +deoxy nucleoside triphosphate to stop + + + align:start position:0% +deoxy nucleoside triphosphate to stop +chain elongation is known as a chain + + align:start position:0% +chain elongation is known as a chain + + + align:start position:0% +chain elongation is known as a chain +termination method so you're getting + + align:start position:0% +termination method so you're getting + + + align:start position:0% +termination method so you're getting +turn chain termination and you're + + align:start position:0% +turn chain termination and you're + + + align:start position:0% +turn chain termination and you're +getting this chain termination with a + + align:start position:0% +getting this chain termination with a + + + align:start position:0% +getting this chain termination with a +specific dye deoxy nucleus + + align:start position:0% +specific dye deoxy nucleus + + + align:start position:0% +specific dye deoxy nucleus +side triphosphate so these dyed + + align:start position:0% +side triphosphate so these dyed + + + align:start position:0% +side triphosphate so these dyed +deoxynucleotide triphosphates well if + + align:start position:0% +deoxynucleotide triphosphates well if + + + align:start position:0% +deoxynucleotide triphosphates well if +they get incorporated into the DNA are + + align:start position:0% +they get incorporated into the DNA are + + + align:start position:0% +they get incorporated into the DNA are +going to halt the synthesis of that DNA + + align:start position:0% +going to halt the synthesis of that DNA + + + align:start position:0% +going to halt the synthesis of that DNA +strand so if we take our example here + + align:start position:0% +strand so if we take our example here + + + align:start position:0% +strand so if we take our example here +right this might be a reaction that has + + align:start position:0% +right this might be a reaction that has + + + align:start position:0% +right this might be a reaction that has +dye deoxy thymidine triphosphate so if + + align:start position:0% +dye deoxy thymidine triphosphate so if + + + align:start position:0% +dye deoxy thymidine triphosphate so if +we had tidy oxy thymidine triphosphate + + align:start position:0% +we had tidy oxy thymidine triphosphate + + + align:start position:0% +we had tidy oxy thymidine triphosphate +in this sample and it's elongating then + + align:start position:0% +in this sample and it's elongating then + + + align:start position:0% +in this sample and it's elongating then +when the polymerase reaches this point + + align:start position:0% +when the polymerase reaches this point + + + align:start position:0% +when the polymerase reaches this point +there's a possibility that it will + + align:start position:0% +there's a possibility that it will + + + align:start position:0% +there's a possibility that it will +incorporate the dye deoxy nucleotide + + align:start position:0% +incorporate the dye deoxy nucleotide + + + align:start position:0% +incorporate the dye deoxy nucleotide +triphosphate and if this is a dye deoxy + + align:start position:0% +triphosphate and if this is a dye deoxy + + + align:start position:0% +triphosphate and if this is a dye deoxy +nucleoside triphosphate then there will + + align:start position:0% +nucleoside triphosphate then there will + + + align:start position:0% +nucleoside triphosphate then there will +note alone there won't be a three prime + + align:start position:0% +note alone there won't be a three prime + + + align:start position:0% +note alone there won't be a three prime +hydroxyl and DNA polymerase will just be + + align:start position:0% +hydroxyl and DNA polymerase will just be + + + align:start position:0% +hydroxyl and DNA polymerase will just be +like oh I can't go on okay because it's + + align:start position:0% +like oh I can't go on okay because it's + + + align:start position:0% +like oh I can't go on okay because it's +not going to have a three prime hydroxyl + + align:start position:0% +not going to have a three prime hydroxyl + + + align:start position:0% +not going to have a three prime hydroxyl +so it's not going to be able to continue + + align:start position:0% +so it's not going to be able to continue + + + align:start position:0% +so it's not going to be able to continue +with the next nucleotide okay so this is + + align:start position:0% +with the next nucleotide okay so this is + + + align:start position:0% +with the next nucleotide okay so this is +known as chain termination okay so let + + align:start position:0% +known as chain termination okay so let + + + align:start position:0% +known as chain termination okay so let +me take you through an example here + + align:start position:0% +me take you through an example here + + + align:start position:0% +me take you through an example here +alright so here's an example that you + + align:start position:0% +alright so here's an example that you + + + align:start position:0% +alright so here's an example that you +have a slide of and there again there's + + align:start position:0% +have a slide of and there again there's + + + align:start position:0% +have a slide of and there again there's +a there's a template strand which is the + + align:start position:0% +a there's a template strand which is the + + + align:start position:0% +a there's a template strand which is the +top strand and this method requires that + + align:start position:0% +top strand and this method requires that + + + align:start position:0% +top strand and this method requires that +you have a primer and what's often done + + align:start position:0% +you have a primer and what's often done + + + align:start position:0% +you have a primer and what's often done +is you label the primer okay so the + + align:start position:0% +is you label the primer okay so the + + + align:start position:0% +is you label the primer okay so the +first step is you have to denature your + + align:start position:0% +first step is you have to denature your + + + align:start position:0% +first step is you have to denature your +DNA so you have to go from + + align:start position:0% +DNA so you have to go from + + + align:start position:0% +DNA so you have to go from +double-stranded DNA to single-stranded + + align:start position:0% +double-stranded DNA to single-stranded + + + align:start position:0% +double-stranded DNA to single-stranded +DNA and then you mix the double-stranded + + align:start position:0% +DNA and then you mix the double-stranded + + + align:start position:0% +DNA and then you mix the double-stranded +DNA with first this labeled primer such + + align:start position:0% +DNA with first this labeled primer such + + + align:start position:0% +DNA with first this labeled primer such +that the primer can anneal to the + + align:start position:0% +that the primer can anneal to the + + + align:start position:0% +that the primer can anneal to the +single-stranded DNA you need DNA + + align:start position:0% +single-stranded DNA you need DNA + + + align:start position:0% +single-stranded DNA you need DNA +polymerase as I've mentioned + + align:start position:0% + + + + align:start position:0% + +and as I believe Rachel mentioned before + + align:start position:0% +and as I believe Rachel mentioned before + + + align:start position:0% +and as I believe Rachel mentioned before +you need the building blocks of DNA so + + align:start position:0% +you need the building blocks of DNA so + + + align:start position:0% +you need the building blocks of DNA so +you need the four deoxy nucleoside + + align:start position:0% +you need the four deoxy nucleoside + + + align:start position:0% +you need the four deoxy nucleoside +triphosphates so you always have the + + align:start position:0% +triphosphates so you always have the + + + align:start position:0% +triphosphates so you always have the +four die oxy nucleotide triphosphates + + align:start position:0% +four die oxy nucleotide triphosphates + + + align:start position:0% +four die oxy nucleotide triphosphates +well what's special here is you're going + + align:start position:0% +well what's special here is you're going + + + align:start position:0% +well what's special here is you're going +to spike several reactions with a + + align:start position:0% +to spike several reactions with a + + + align:start position:0% +to spike several reactions with a +certain with one of the die deoxy + + align:start position:0% +certain with one of the die deoxy + + + align:start position:0% +certain with one of the die deoxy +nucleoside triphosphates so you spike + + align:start position:0% +nucleoside triphosphates so you spike + + + align:start position:0% +nucleoside triphosphates so you spike +the reaction with a tiny amount of one + + align:start position:0% +the reaction with a tiny amount of one + + + align:start position:0% +the reaction with a tiny amount of one +of your die deoxy nucleoside + + align:start position:0% +of your die deoxy nucleoside + + + align:start position:0% +of your die deoxy nucleoside +triphosphates okay so let's say you have + + align:start position:0% +triphosphates okay so let's say you have + + + align:start position:0% +triphosphates okay so let's say you have +a reaction here and this this one here + + align:start position:0% +a reaction here and this this one here + + + align:start position:0% +a reaction here and this this one here +has died deoxy adenosine triphosphate + + align:start position:0% +has died deoxy adenosine triphosphate + + + align:start position:0% +has died deoxy adenosine triphosphate +then polymerase will elongate this + + align:start position:0% +then polymerase will elongate this + + + align:start position:0% +then polymerase will elongate this +straight strand until there's a + + align:start position:0% +straight strand until there's a + + + align:start position:0% +straight strand until there's a +thymidine on the template and then + + align:start position:0% +thymidine on the template and then + + + align:start position:0% +thymidine on the template and then +there's a possibility that it will + + align:start position:0% +there's a possibility that it will + + + align:start position:0% +there's a possibility that it will +incorporate this dye deoxy ntp and if it + + align:start position:0% +incorporate this dye deoxy ntp and if it + + + align:start position:0% +incorporate this dye deoxy ntp and if it +does then you get chain termination and + + align:start position:0% +does then you get chain termination and + + + align:start position:0% +does then you get chain termination and +you get a fragment of this length but + + align:start position:0% +you get a fragment of this length but + + + align:start position:0% +you get a fragment of this length but +the other possibility because there is + + align:start position:0% +the other possibility because there is + + + align:start position:0% +the other possibility because there is +still the deoxy form of the ntp present + + align:start position:0% +still the deoxy form of the ntp present + + + align:start position:0% +still the deoxy form of the ntp present +is possible that it incorporates a + + align:start position:0% +is possible that it incorporates a + + + align:start position:0% +is possible that it incorporates a +deoxyadenosine triphosphate there and + + align:start position:0% +deoxyadenosine triphosphate there and + + + align:start position:0% +deoxyadenosine triphosphate there and +keeps going and then incorporates a dye + + align:start position:0% +keeps going and then incorporates a dye + + + align:start position:0% +keeps going and then incorporates a dye +deoxy ATP later on where you have + + align:start position:0% +deoxy ATP later on where you have + + + align:start position:0% +deoxy ATP later on where you have +another tea okay and so the polymerase + + align:start position:0% +another tea okay and so the polymerase + + + align:start position:0% +another tea okay and so the polymerase +will essentially randomly stop at these + + align:start position:0% +will essentially randomly stop at these + + + align:start position:0% +will essentially randomly stop at these +different thymidine residues where + + align:start position:0% +different thymidine residues where + + + align:start position:0% +different thymidine residues where +depending on whether or not a dye deoxy + + align:start position:0% +depending on whether or not a dye deoxy + + + align:start position:0% +depending on whether or not a dye deoxy +nucleoside triphosphate is incorporated + + align:start position:0% +nucleoside triphosphate is incorporated + + + align:start position:0% +nucleoside triphosphate is incorporated +and that means for a given reaction one + + align:start position:0% +and that means for a given reaction one + + + align:start position:0% +and that means for a given reaction one +in which you have dye deoxy ATP you get + + align:start position:0% +in which you have dye deoxy ATP you get + + + align:start position:0% +in which you have dye deoxy ATP you get +a certain pattern of bands that we + + align:start position:0% +a certain pattern of bands that we + + + align:start position:0% +a certain pattern of bands that we +represent the length of fragments where + + align:start position:0% +represent the length of fragments where + + + align:start position:0% +represent the length of fragments where +you have in this case a thymine base + + align:start position:0% +you have in this case a thymine base + + + align:start position:0% +you have in this case a thymine base +okay and then you do this for all four + + align:start position:0% +okay and then you do this for all four + + + align:start position:0% +okay and then you do this for all four +bases where you have four reactions each + + align:start position:0% +bases where you have four reactions each + + + align:start position:0% +bases where you have four reactions each +with a different base that's dye deoxy + + align:start position:0% +with a different base that's dye deoxy + + + align:start position:0% +with a different base that's dye deoxy +okay so when you're adding these you're + + align:start position:0% +okay so when you're adding these you're + + + align:start position:0% +okay so when you're adding these you're +gonna do four reactions one with dye + + align:start position:0% +gonna do four reactions one with dye + + + align:start position:0% +gonna do four reactions one with dye +deoxy ATP + + align:start position:0% +deoxy ATP + + + align:start position:0% +deoxy ATP +spiked in one with dye deoxy TTP one + + align:start position:0% +spiked in one with dye deoxy TTP one + + + align:start position:0% +spiked in one with dye deoxy TTP one +with dye deoxy CTP and the last with dye + + align:start position:0% +with dye deoxy CTP and the last with dye + + + align:start position:0% +with dye deoxy CTP and the last with dye +deoxy gtp and because the these + + align:start position:0% +deoxy gtp and because the these + + + align:start position:0% +deoxy gtp and because the these +nucleotides are present in different + + align:start position:0% +nucleotides are present in different + + + align:start position:0% +nucleotides are present in different +positions along the sequence you're + + align:start position:0% +positions along the sequence you're + + + align:start position:0% +positions along the sequence you're +gonna get this distinct banding pattern + + align:start position:0% +gonna get this distinct banding pattern + + + align:start position:0% +gonna get this distinct banding pattern +for each of these reactions but using + + align:start position:0% +for each of these reactions but using + + + align:start position:0% +for each of these reactions but using +that banding pattern you can then read + + align:start position:0% +that banding pattern you can then read + + + align:start position:0% +that banding pattern you can then read +off the sequence of DNA that's present + + align:start position:0% +off the sequence of DNA that's present + + + align:start position:0% +off the sequence of DNA that's present +on the template strand okay so this is + + align:start position:0% +on the template strand okay so this is + + + align:start position:0% +on the template strand okay so this is +how sequencing was done for many many + + align:start position:0% +how sequencing was done for many many + + + align:start position:0% +how sequencing was done for many many +years these days it's been made cheaper + + align:start position:0% +years these days it's been made cheaper + + + align:start position:0% +years these days it's been made cheaper +and faster and now what's often used is + + align:start position:0% +and faster and now what's often used is + + + align:start position:0% +and faster and now what's often used is +next-generation sequencing and you know + + align:start position:0% +next-generation sequencing and you know + + + align:start position:0% +next-generation sequencing and you know +one sort of the pain in the ass about + + align:start position:0% +one sort of the pain in the ass about + + + align:start position:0% +one sort of the pain in the ass about +sequencing before is you'd use a lot of + + align:start position:0% +sequencing before is you'd use a lot of + + + align:start position:0% +sequencing before is you'd use a lot of +radioactivity your primer would be + + align:start position:0% +radioactivity your primer would be + + + align:start position:0% +radioactivity your primer would be +radioactive a do active so that you + + align:start position:0% +radioactive a do active so that you + + + align:start position:0% +radioactive a do active so that you +could detect to these bands right now + + align:start position:0% +could detect to these bands right now + + + align:start position:0% +could detect to these bands right now +everything's done using fluorescence + + align:start position:0% +everything's done using fluorescence + + + align:start position:0% +everything's done using fluorescence +which makes it much nicer I think and so + + align:start position:0% +which makes it much nicer I think and so + + + align:start position:0% +which makes it much nicer I think and so +in next-generation sequencing your + + align:start position:0% +in next-generation sequencing your + + + align:start position:0% +in next-generation sequencing your +template DNA is attached to a solid + + align:start position:0% +template DNA is attached to a solid + + + align:start position:0% +template DNA is attached to a solid +substrate such as its immobilized on + + align:start position:0% +substrate such as its immobilized on + + + align:start position:0% +substrate such as its immobilized on +some type of substrate and then you add + + align:start position:0% +some type of substrate and then you add + + + align:start position:0% +some type of substrate and then you add +each of the four nucleoside + + align:start position:0% +each of the four nucleoside + + + align:start position:0% +each of the four nucleoside +triphosphates in this case they're + + align:start position:0% +triphosphates in this case they're + + + align:start position:0% +triphosphates in this case they're +labeled with a dye such that each one is + + align:start position:0% +labeled with a dye such that each one is + + + align:start position:0% +labeled with a dye such that each one is +a different color but the dye also + + align:start position:0% +a different color but the dye also + + + align:start position:0% +a different color but the dye also +functions to prevent elongation such + + align:start position:0% +functions to prevent elongation such + + + align:start position:0% +functions to prevent elongation such +that again it's this chain termination + + align:start position:0% +that again it's this chain termination + + + align:start position:0% +that again it's this chain termination +when you incorporate one of these the + + align:start position:0% +when you incorporate one of these the + + + align:start position:0% +when you incorporate one of these the +polymerase just can't run along the DNA + + align:start position:0% +polymerase just can't run along the DNA + + + align:start position:0% +polymerase just can't run along the DNA +it incorporates one and then stops so if + + align:start position:0% +it incorporates one and then stops so if + + + align:start position:0% +it incorporates one and then stops so if +you get your first nucleotide + + align:start position:0% +you get your first nucleotide + + + align:start position:0% +you get your first nucleotide +incorporated it will incorporate one of + + align:start position:0% +incorporated it will incorporate one of + + + align:start position:0% +incorporated it will incorporate one of +these four and it will be fluorescent at + + align:start position:0% +these four and it will be fluorescent at + + + align:start position:0% +these four and it will be fluorescent at +a certain wavelength which you can see + + align:start position:0% +a certain wavelength which you can see + + + align:start position:0% +a certain wavelength which you can see +using them using a device or microscope + + align:start position:0% +using them using a device or microscope + + + align:start position:0% +using them using a device or microscope +and then what you then do is chemically + + align:start position:0% +and then what you then do is chemically + + + align:start position:0% +and then what you then do is chemically +modify this base such that you remove + + align:start position:0% +modify this base such that you remove + + + align:start position:0% +modify this base such that you remove +the dye and allow it to extend one more + + align:start position:0% +the dye and allow it to extend one more + + + align:start position:0% +the dye and allow it to extend one more +base pair and so you go sort of or one + + align:start position:0% +base pair and so you go sort of or one + + + align:start position:0% +base pair and so you go sort of or one +nucleotide at a time and you read out + + align:start position:0% +nucleotide at a time and you read out + + + align:start position:0% +nucleotide at a time and you read out +the pattern of fluorescence that appears + + align:start position:0% +the pattern of fluorescence that appears + + + align:start position:0% +the pattern of fluorescence that appears +and that gives you the sequence of DNA + + align:start position:0% +and that gives you the sequence of DNA + + + align:start position:0% +and that gives you the sequence of DNA +on this molecule that stuck to your + + align:start position:0% +on this molecule that stuck to your + + + align:start position:0% +on this molecule that stuck to your +substrate right you can do this in + + align:start position:0% +substrate right you can do this in + + + align:start position:0% +substrate right you can do this in +parallel you can have tons many + + align:start position:0% +parallel you can have tons many + + + align:start position:0% +parallel you can have tons many +different strands of DNA and you can be + + align:start position:0% +different strands of DNA and you can be + + + align:start position:0% +different strands of DNA and you can be +reading out the sequence of each one of + + align:start position:0% +reading out the sequence of each one of + + + align:start position:0% +reading out the sequence of each one of +these strands in parallel okay great any + + align:start position:0% +these strands in parallel okay great any + + + align:start position:0% +these strands in parallel okay great any +questions about DNA sequencing okay very + + align:start position:0% +questions about DNA sequencing okay very + + + align:start position:0% +questions about DNA sequencing okay very +good I will see you on Monday + + align:start position:0% +good I will see you on Monday + + + align:start position:0% +good I will see you on Monday +have a great weekend + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/KPkOkiwAlbY.txt b/KPkOkiwAlbY.txt new file mode 100644 index 0000000000000000000000000000000000000000..82923ed73cbd292dd9818fca3c1f5403c06dd646 --- /dev/null +++ b/KPkOkiwAlbY.txt @@ -0,0 +1,16091 @@ +align:start position:0% + +so today uh we're going to continue in + + align:start position:0% +so today uh we're going to continue in + + + align:start position:0% +so today uh we're going to continue in +our discussion of uh dynamic programming + + align:start position:0% +our discussion of uh dynamic programming + + + align:start position:0% +our discussion of uh dynamic programming +I actually found this set of problem + + align:start position:0% +I actually found this set of problem + + + align:start position:0% +I actually found this set of problem +session problems to be easier than the + + align:start position:0% +session problems to be easier than the + + + align:start position:0% +session problems to be easier than the +previous one I think the fun there's a + + align:start position:0% +previous one I think the fun there's a + + + align:start position:0% +previous one I think the fun there's a +funny thing which is uh we learned in + + align:start position:0% +funny thing which is uh we learned in + + + align:start position:0% +funny thing which is uh we learned in +class about sort of pseudo polinomial + + align:start position:0% +class about sort of pseudo polinomial + + + align:start position:0% +class about sort of pseudo polinomial +time style Dynamic programs somehow that + + align:start position:0% +time style Dynamic programs somehow that + + + align:start position:0% +time style Dynamic programs somehow that +language is a little bit liberating in + + align:start position:0% +language is a little bit liberating in + + + align:start position:0% +language is a little bit liberating in +the sense that you're sort of using + + align:start position:0% +the sense that you're sort of using + + + align:start position:0% +the sense that you're sort of using +parameters that you really shouldn't uh + + align:start position:0% +parameters that you really shouldn't uh + + + align:start position:0% +parameters that you really shouldn't uh +when it comes to the runtime of your + + align:start position:0% +when it comes to the runtime of your + + + align:start position:0% +when it comes to the runtime of your +algorithm well I I suppose you should in + + align:start position:0% +algorithm well I I suppose you should in + + + align:start position:0% +algorithm well I I suppose you should in +the sense that it's it's allowed if you + + align:start position:0% +the sense that it's it's allowed if you + + + align:start position:0% +the sense that it's it's allowed if you +call your algorithm pseudo polinomial + + align:start position:0% +call your algorithm pseudo polinomial + + + align:start position:0% +call your algorithm pseudo polinomial +time but somehow makes it a little + + align:start position:0% +time but somehow makes it a little + + + align:start position:0% +time but somehow makes it a little +easier to formulate your dynamic + + align:start position:0% +easier to formulate your dynamic + + + align:start position:0% +easier to formulate your dynamic +programming algorithm because sort of + + align:start position:0% +programming algorithm because sort of + + + align:start position:0% +programming algorithm because sort of +all the numbers are staring you right in + + align:start position:0% +all the numbers are staring you right in + + + align:start position:0% +all the numbers are staring you right in +the face like you don't have to be so + + align:start position:0% +the face like you don't have to be so + + + align:start position:0% +the face like you don't have to be so +careful about what's a fair game and + + align:start position:0% +careful about what's a fair game and + + + align:start position:0% +careful about what's a fair game and +what's not uh when you when you post + + align:start position:0% +what's not uh when you when you post + + + align:start position:0% +what's not uh when you when you post +your algorithm so long as it's + + align:start position:0% +your algorithm so long as it's + + + align:start position:0% +your algorithm so long as it's +sufficient in the values that you care + + align:start position:0% +sufficient in the values that you care + + + align:start position:0% +sufficient in the values that you care +about uh and so uh today's problem + + align:start position:0% +about uh and so uh today's problem + + + align:start position:0% +about uh and so uh today's problem +session has five problems squeezed in + + align:start position:0% +session has five problems squeezed in + + + align:start position:0% +session has five problems squeezed in +instead of the usual four uh we'll see + + align:start position:0% +instead of the usual four uh we'll see + + + align:start position:0% +instead of the usual four uh we'll see +how far we get see that I usually talk + + align:start position:0% +how far we get see that I usually talk + + + align:start position:0% +how far we get see that I usually talk +too much anyway uh but I'll try to stay + + align:start position:0% +too much anyway uh but I'll try to stay + + + align:start position:0% +too much anyway uh but I'll try to stay +on schedule here and we'll see how well + + align:start position:0% +on schedule here and we'll see how well + + + align:start position:0% +on schedule here and we'll see how well +we do um any questions from our students + + align:start position:0% +we do um any questions from our students + + + align:start position:0% +we do um any questions from our students +about dynamic programming before we get + + align:start position:0% +about dynamic programming before we get + + + align:start position:0% +about dynamic programming before we get +started here cut one if you want we can + + align:start position:0% +started here cut one if you want we can + + + align:start position:0% +started here cut one if you want we can +cut one oh I I will gladly cut one if I + + align:start position:0% +cut one oh I I will gladly cut one if I + + + align:start position:0% +cut one oh I I will gladly cut one if I +run out of time yeah + + align:start position:0% +run out of time yeah + + + align:start position:0% +run out of time yeah +okay so without further Ado uh let's get + + align:start position:0% +okay so without further Ado uh let's get + + + align:start position:0% +okay so without further Ado uh let's get +started with uh coin crafting which is + + align:start position:0% +started with uh coin crafting which is + + + align:start position:0% +started with uh coin crafting which is +problem -1 here so I suppose it should + + align:start position:0% +problem -1 here so I suppose it should + + + align:start position:0% +problem -1 here so I suppose it should +be Keel nafy if I were to work uh + + align:start position:0% +be Keel nafy if I were to work uh + + + align:start position:0% +be Keel nafy if I were to work uh +through my spoonerism properly here um + + align:start position:0% +through my spoonerism properly here um + + + align:start position:0% +through my spoonerism properly here um +in any event we have a thief who's in + + align:start position:0% +in any event we have a thief who's in + + + align:start position:0% +in any event we have a thief who's in +desperate need of money uh as with many + + align:start position:0% +desperate need of money uh as with many + + + align:start position:0% +desperate need of money uh as with many +thieves or else of course they wouldn't + + align:start position:0% +thieves or else of course they wouldn't + + + align:start position:0% +thieves or else of course they wouldn't +resort to the world of crime uh and uh + + align:start position:0% +resort to the world of crime uh and uh + + + align:start position:0% +resort to the world of crime uh and uh +ke nafy here um has uh n identical + + align:start position:0% + + + + align:start position:0% + +coins I've been very self-conscious + + align:start position:0% +coins I've been very self-conscious + + + align:start position:0% +coins I've been very self-conscious +about the way that I write the letter I + + align:start position:0% +about the way that I write the letter I + + + align:start position:0% +about the way that I write the letter I +ever since Eric pointed it out and it's + + align:start position:0% +ever since Eric pointed it out and it's + + + align:start position:0% +ever since Eric pointed it out and it's +only gotten worse now it's inconsistent + + align:start position:0% +only gotten worse now it's inconsistent + + + align:start position:0% +only gotten worse now it's inconsistent +and and hard to read uh but in any event + + align:start position:0% +and and hard to read uh but in any event + + + align:start position:0% +and and hard to read uh but in any event +uh so we have uh n uh identical coins + + align:start position:0% +uh so we have uh n uh identical coins + + + align:start position:0% +uh so we have uh n uh identical coins +and of course you know these coins have + + align:start position:0% +and of course you know these coins have + + + align:start position:0% +and of course you know these coins have +very distinctive markings and so we + + align:start position:0% +very distinctive markings and so we + + + align:start position:0% +very distinctive markings and so we +can't possibly run away with them as is + + align:start position:0% +can't possibly run away with them as is + + + align:start position:0% +can't possibly run away with them as is +because if you take them to your + + align:start position:0% +because if you take them to your + + + align:start position:0% +because if you take them to your +standard Jeweler they'll immediately + + align:start position:0% +standard Jeweler they'll immediately + + + align:start position:0% +standard Jeweler they'll immediately +recognize that these markings are bad + + align:start position:0% +recognize that these markings are bad + + + align:start position:0% +recognize that these markings are bad +and stolen and and that's not so good so + + align:start position:0% +and stolen and and that's not so good so + + + align:start position:0% +and stolen and and that's not so good so +instead we can melt uh these coins into + + align:start position:0% +instead we can melt uh these coins into + + + align:start position:0% +instead we can melt uh these coins into +other + + align:start position:0% +other + + + align:start position:0% +other +objects so uh you know our sneaky uh + + align:start position:0% +objects so uh you know our sneaky uh + + + align:start position:0% +objects so uh you know our sneaky uh +Thief here has identified a potential + + align:start position:0% +Thief here has identified a potential + + + align:start position:0% +Thief here has identified a potential +buyer and uh the buyer has a few + + align:start position:0% +buyer and uh the buyer has a few + + + align:start position:0% +buyer and uh the buyer has a few +criteria here right so we have a + + align:start position:0% + + + + align:start position:0% + +buyer um and the buyer has the buyer has + + align:start position:0% +buyer um and the buyer has the buyer has + + + align:start position:0% +buyer um and the buyer has the buyer has +a very strange value system thing that + + align:start position:0% +a very strange value system thing that + + + align:start position:0% +a very strange value system thing that +apparently it's easy to take coins and + + align:start position:0% +apparently it's easy to take coins and + + + align:start position:0% +apparently it's easy to take coins and +make them into other things uh but but + + align:start position:0% +make them into other things uh but but + + + align:start position:0% +make them into other things uh but but +in any event the the the buyer what they + + align:start position:0% +in any event the the the buyer what they + + + align:start position:0% +in any event the the the buyer what they +care about is not the fact that the + + align:start position:0% +care about is not the fact that the + + + align:start position:0% +care about is not the fact that the +coins are made of gold but rather that + + align:start position:0% +coins are made of gold but rather that + + + align:start position:0% +coins are made of gold but rather that +they like particular objects better than + + align:start position:0% +they like particular objects better than + + + align:start position:0% +they like particular objects better than +others made out of said gold um so in + + align:start position:0% +others made out of said gold um so in + + + align:start position:0% +others made out of said gold um so in +particular they have a different rate uh + + align:start position:0% +particular they have a different rate uh + + + align:start position:0% +particular they have a different rate uh +for each object like a different price + + align:start position:0% +for each object like a different price + + + align:start position:0% +for each object like a different price +they're willing to pay um and so they + + align:start position:0% +they're willing to pay um and so they + + + align:start position:0% +they're willing to pay um and so they +have a list of + + align:start position:0% + + + + align:start position:0% + +um uh uh + + align:start position:0% +um uh uh + + + align:start position:0% +um uh uh +n objects that they're interested in uh + + align:start position:0% +n objects that they're interested in uh + + + align:start position:0% +n objects that they're interested in uh +and each one uh is associated with two + + align:start position:0% +and each one uh is associated with two + + + align:start position:0% +and each one uh is associated with two +things and objects uh they have a price + + align:start position:0% +things and objects uh they have a price + + + align:start position:0% +things and objects uh they have a price +so the amount that the buyer is willing + + align:start position:0% +so the amount that the buyer is willing + + + align:start position:0% +so the amount that the buyer is willing +to pay for that object which again is + + align:start position:0% +to pay for that object which again is + + + align:start position:0% +to pay for that object which again is +not just the weight and gold for some + + align:start position:0% +not just the weight and gold for some + + + align:start position:0% +not just the weight and gold for some +reason you know there's a value added + + align:start position:0% +reason you know there's a value added + + + align:start position:0% +reason you know there's a value added +tax uh in in in in this universe uh and + + align:start position:0% +tax uh in in in in this universe uh and + + + align:start position:0% +tax uh in in in in this universe uh and +uh it takes a different number of coins + + align:start position:0% +uh it takes a different number of coins + + + align:start position:0% +uh it takes a different number of coins +to + + align:start position:0% +to + + + align:start position:0% +to +manufacture right like so maybe maybe + + align:start position:0% +manufacture right like so maybe maybe + + + align:start position:0% +manufacture right like so maybe maybe +you know I can make like a golden + + align:start position:0% +you know I can make like a golden + + + align:start position:0% +you know I can make like a golden +chocolate fountain and that takes like + + align:start position:0% +chocolate fountain and that takes like + + + align:start position:0% +chocolate fountain and that takes like +10 coins but I don't want two of those + + align:start position:0% +10 coins but I don't want two of those + + + align:start position:0% +10 coins but I don't want two of those +so if I make that then the next thing I + + align:start position:0% +so if I make that then the next thing I + + + align:start position:0% +so if I make that then the next thing I +have to do is like a figurine of of Eric + + align:start position:0% +have to do is like a figurine of of Eric + + + align:start position:0% +have to do is like a figurine of of Eric +and Jason to to put alongside it um and + + align:start position:0% +and Jason to to put alongside it um and + + + align:start position:0% +and Jason to to put alongside it um and +having more than one of those would also + + align:start position:0% +having more than one of those would also + + + align:start position:0% +having more than one of those would also +be like creepy and weird right so so I + + align:start position:0% +be like creepy and weird right so so I + + + align:start position:0% +be like creepy and weird right so so I +can only make one of each object uh and + + align:start position:0% +can only make one of each object uh and + + + align:start position:0% +can only make one of each object uh and +of course uh my goal here is I have end + + align:start position:0% +of course uh my goal here is I have end + + + align:start position:0% +of course uh my goal here is I have end +coins by the way the fact that there's + + align:start position:0% +coins by the way the fact that there's + + + align:start position:0% +coins by the way the fact that there's +end coins and end objects for the buyer + + align:start position:0% +end coins and end objects for the buyer + + + align:start position:0% +end coins and end objects for the buyer +doesn't really matter I mean it will for + + align:start position:0% +doesn't really matter I mean it will for + + + align:start position:0% +doesn't really matter I mean it will for +the runtime but like you could imagine + + align:start position:0% +the runtime but like you could imagine + + + align:start position:0% +the runtime but like you could imagine +this being n and M so I wouldn't be too + + align:start position:0% +this being n and M so I wouldn't be too + + + align:start position:0% +this being n and M so I wouldn't be too +hung up on that um and what you're + + align:start position:0% +hung up on that um and what you're + + + align:start position:0% +hung up on that um and what you're +trying to do is is of course maximize + + align:start position:0% +trying to do is is of course maximize + + + align:start position:0% +trying to do is is of course maximize +your Revenue uh subject to the + + align:start position:0% +your Revenue uh subject to the + + + align:start position:0% +your Revenue uh subject to the +constraints that uh you have end coins + + align:start position:0% +constraints that uh you have end coins + + + align:start position:0% +constraints that uh you have end coins +uh and you can't make two objects that + + align:start position:0% +uh and you can't make two objects that + + + align:start position:0% +uh and you can't make two objects that +are the same hopefully I've captured the + + align:start position:0% +are the same hopefully I've captured the + + + align:start position:0% +are the same hopefully I've captured the +essence of our problem okay okay + + align:start position:0% +essence of our problem okay okay + + + align:start position:0% +essence of our problem okay okay +fabulous so uh as with uh all of our our + + align:start position:0% +fabulous so uh as with uh all of our our + + + align:start position:0% +fabulous so uh as with uh all of our our +our dynamic programming problems in + + align:start position:0% +our dynamic programming problems in + + + align:start position:0% +our dynamic programming problems in +6006 uh we have a paradigm for how how + + align:start position:0% +6006 uh we have a paradigm for how how + + + align:start position:0% +6006 uh we have a paradigm for how how +to approach them um which has a cute + + align:start position:0% +to approach them um which has a cute + + + align:start position:0% +to approach them um which has a cute +acronym which is sort bot uh and I think + + align:start position:0% +acronym which is sort bot uh and I think + + + align:start position:0% +acronym which is sort bot uh and I think +sbot is a totally relevant and + + align:start position:0% +sbot is a totally relevant and + + + align:start position:0% +sbot is a totally relevant and +straightforward approach to uh this + + align:start position:0% +straightforward approach to uh this + + + align:start position:0% +straightforward approach to uh this +problem here yeah so uh in particular + + align:start position:0% +problem here yeah so uh in particular + + + align:start position:0% +problem here yeah so uh in particular +let's let's give ourselves a bit of of + + align:start position:0% +let's let's give ourselves a bit of of + + + align:start position:0% +let's let's give ourselves a bit of of +notation right so we're going to number + + align:start position:0% +notation right so we're going to number + + + align:start position:0% +notation right so we're going to number +our objects between one and N uh just + + align:start position:0% +our objects between one and N uh just + + + align:start position:0% +our objects between one and N uh just +for convenience so we'll say that uh p i + + align:start position:0% +for convenience so we'll say that uh p i + + + align:start position:0% +for convenience so we'll say that uh p i +is the + + align:start position:0% +is the + + + align:start position:0% +is the +price of uh object + + align:start position:0% +price of uh object + + + align:start position:0% +price of uh object +I + + align:start position:0% +I + + + align:start position:0% +I +okay and uh we'll say that Ki is the + + align:start position:0% +okay and uh we'll say that Ki is the + + + align:start position:0% +okay and uh we'll say that Ki is the +what the problem calls the + + align:start position:0% +what the problem calls the + + + align:start position:0% +what the problem calls the +melting uh number in other words if I + + align:start position:0% +melting uh number in other words if I + + + align:start position:0% +melting uh number in other words if I +want to make object I this is the amount + + align:start position:0% +want to make object I this is the amount + + + align:start position:0% +want to make object I this is the amount +of coins that I'd have to me uh melt to + + align:start position:0% +of coins that I'd have to me uh melt to + + + align:start position:0% +of coins that I'd have to me uh melt to +to make that object okay so just a tiny + + align:start position:0% +to make that object okay so just a tiny + + + align:start position:0% +to make that object okay so just a tiny +bit of + + align:start position:0% +bit of + + + align:start position:0% +bit of +notation and in general so okay what do + + align:start position:0% +notation and in general so okay what do + + + align:start position:0% +notation and in general so okay what do +we do when we formulate our dynamic + + align:start position:0% +we do when we formulate our dynamic + + + align:start position:0% +we do when we formulate our dynamic +programming problems we want to identify + + align:start position:0% +programming problems we want to identify + + + align:start position:0% +programming problems we want to identify +interesting sub problems we could solve + + align:start position:0% +interesting sub problems we could solve + + + align:start position:0% +interesting sub problems we could solve +that are smaller uh and when we compose + + align:start position:0% +that are smaller uh and when we compose + + + align:start position:0% +that are smaller uh and when we compose +them all together uh we get the the + + align:start position:0% +them all together uh we get the the + + + align:start position:0% +them all together uh we get the the +final solution to our problem and this + + align:start position:0% +final solution to our problem and this + + + align:start position:0% +final solution to our problem and this +uh particular problem uh involving + + align:start position:0% +uh particular problem uh involving + + + align:start position:0% +uh particular problem uh involving +manufacturing objects out of coins I + + align:start position:0% +manufacturing objects out of coins I + + + align:start position:0% +manufacturing objects out of coins I +think is like a really classic one when + + align:start position:0% +think is like a really classic one when + + + align:start position:0% +think is like a really classic one when +it comes to dynamic programming this is + + align:start position:0% +it comes to dynamic programming this is + + + align:start position:0% +it comes to dynamic programming this is +the sort of thing where you know someday + + align:start position:0% +the sort of thing where you know someday + + + align:start position:0% +the sort of thing where you know someday +when you're trying to to to pay for your + + align:start position:0% +when you're trying to to to pay for your + + + align:start position:0% +when you're trying to to to pay for your +tuition by doing these like hacker + + align:start position:0% +tuition by doing these like hacker + + + align:start position:0% +tuition by doing these like hacker +contests online you know like this is + + align:start position:0% +contests online you know like this is + + + align:start position:0% +contests online you know like this is +the sort of thing that comes up all the + + align:start position:0% +the sort of thing that comes up all the + + + align:start position:0% +the sort of thing that comes up all the +time in in that Universe right um so in + + align:start position:0% +time in in that Universe right um so in + + + align:start position:0% +time in in that Universe right um so in +particular uh the two sort of variables + + align:start position:0% +particular uh the two sort of variables + + + align:start position:0% +particular uh the two sort of variables +here uh you know when I make new object + + align:start position:0% +here uh you know when I make new object + + + align:start position:0% +here uh you know when I make new object +is what object did I make and how many + + align:start position:0% +is what object did I make and how many + + + align:start position:0% +is what object did I make and how many +coins did I spend when I did that so + + align:start position:0% +coins did I spend when I did that so + + + align:start position:0% +coins did I spend when I did that so +sort of the two natural parameters to + + align:start position:0% +sort of the two natural parameters to + + + align:start position:0% +sort of the two natural parameters to +use uh when I solve my Dynamic uh + + align:start position:0% +use uh when I solve my Dynamic uh + + + align:start position:0% +use uh when I solve my Dynamic uh +programming problem yeah and and of + + align:start position:0% +programming problem yeah and and of + + + align:start position:0% +programming problem yeah and and of +course it's going to be sort of + + align:start position:0% +course it's going to be sort of + + + align:start position:0% +course it's going to be sort of +recursive in the sense that um I can + + align:start position:0% +recursive in the sense that um I can + + + align:start position:0% +recursive in the sense that um I can +either choose to make object I or not + + align:start position:0% +either choose to make object I or not + + + align:start position:0% +either choose to make object I or not +and it doesn't matter what order I make + + align:start position:0% +and it doesn't matter what order I make + + + align:start position:0% +and it doesn't matter what order I make +my objects in or similarly what order I + + align:start position:0% +my objects in or similarly what order I + + + align:start position:0% +my objects in or similarly what order I +spend my coins in which is usually a + + align:start position:0% +spend my coins in which is usually a + + + align:start position:0% +spend my coins in which is usually a +nice property to have in a dynamic + + align:start position:0% +nice property to have in a dynamic + + + align:start position:0% +nice property to have in a dynamic +programming universe so in particular oh + + align:start position:0% +programming universe so in particular oh + + + align:start position:0% +programming universe so in particular oh +this thing is my + + align:start position:0% + + + + align:start position:0% + +Nemesis um this is + + align:start position:0% +Nemesis um this is + + + align:start position:0% +Nemesis um this is +front I think this classroom is + + align:start position:0% +front I think this classroom is + + + align:start position:0% +front I think this classroom is +particularly tough for short people + + align:start position:0% +particularly tough for short people + + + align:start position:0% +particularly tough for short people +because I like I'm moving it up and down + + align:start position:0% +because I like I'm moving it up and down + + + align:start position:0% +because I like I'm moving it up and down +all the time okay uh so given our our + + align:start position:0% +all the time okay uh so given our our + + + align:start position:0% +all the time okay uh so given our our +observation here uh if we're doing sort + + align:start position:0% +observation here uh if we're doing sort + + + align:start position:0% +observation here uh if we're doing sort +bot uh right so uh what's our our s + + align:start position:0% +bot uh right so uh what's our our s + + + align:start position:0% +bot uh right so uh what's our our s +again let me ask myself that sub + + align:start position:0% +again let me ask myself that sub + + + align:start position:0% +again let me ask myself that sub +problems thank you uh Professor domain + + align:start position:0% +problems thank you uh Professor domain + + + align:start position:0% +problems thank you uh Professor domain +uh then uh essentially what we want to + + align:start position:0% +uh then uh essentially what we want to + + + align:start position:0% +uh then uh essentially what we want to +do based on what I sort of argued + + align:start position:0% +do based on what I sort of argued + + + align:start position:0% +do based on what I sort of argued +verbally is maybe Define our variable XI + + align:start position:0% +verbally is maybe Define our variable XI + + + align:start position:0% +verbally is maybe Define our variable XI +J the thing we're going to compute to be + + align:start position:0% +J the thing we're going to compute to be + + + align:start position:0% +J the thing we're going to compute to be +the + + align:start position:0% + + + + align:start position:0% + +revenue uh from + + align:start position:0% +revenue uh from + + + align:start position:0% +revenue uh from +using I + + align:start position:0% +using I + + + align:start position:0% +using I +coins uh and uh objects uh one to + + align:start position:0% + + + + align:start position:0% + +J okay so in other words you know I have + + align:start position:0% +J okay so in other words you know I have + + + align:start position:0% +J okay so in other words you know I have +I coins left in the bank and I'm only + + align:start position:0% +I coins left in the bank and I'm only + + + align:start position:0% +I coins left in the bank and I'm only +allowed to use the first J objects and + + align:start position:0% +allowed to use the first J objects and + + + align:start position:0% +allowed to use the first J objects and +we can already see that this kind of a + + align:start position:0% +we can already see that this kind of a + + + align:start position:0% +we can already see that this kind of a +sensible way to approach this uh dynamic + + align:start position:0% +sensible way to approach this uh dynamic + + + align:start position:0% +sensible way to approach this uh dynamic +programming problem in the sense that + + align:start position:0% +programming problem in the sense that + + + align:start position:0% +programming problem in the sense that +you know there's an obvious recursion + + align:start position:0% +you know there's an obvious recursion + + + align:start position:0% +you know there's an obvious recursion +here I choose to make an object I have + + align:start position:0% +here I choose to make an object I have + + + align:start position:0% +here I choose to make an object I have +fewer coins uh and I can sort of imagine + + align:start position:0% +fewer coins uh and I can sort of imagine + + + align:start position:0% +fewer coins uh and I can sort of imagine +there being a topological order in the + + align:start position:0% +there being a topological order in the + + + align:start position:0% +there being a topological order in the +sense that I could first decide about + + align:start position:0% +sense that I could first decide about + + + align:start position:0% +sense that I could first decide about +object one and then object two and + + align:start position:0% +object one and then object two and + + + align:start position:0% +object one and then object two and +object three and so on or vice versa + + align:start position:0% +object three and so on or vice versa + + + align:start position:0% +object three and so on or vice versa +depending on whether you're a prefix or + + align:start position:0% +depending on whether you're a prefix or + + + align:start position:0% +depending on whether you're a prefix or +suffix kind of guy um which I still get + + align:start position:0% +suffix kind of guy um which I still get + + + align:start position:0% +suffix kind of guy um which I still get +backward but the the the good news is + + align:start position:0% +backward but the the the good news is + + + align:start position:0% +backward but the the the good news is +that uh doesn't really matter what + + align:start position:0% +that uh doesn't really matter what + + + align:start position:0% +that uh doesn't really matter what +matters is is formulating the equation + + align:start position:0% +matters is is formulating the equation + + + align:start position:0% +matters is is formulating the equation +okay any questions about our our our + + align:start position:0% +okay any questions about our our our + + + align:start position:0% +okay any questions about our our our +definition of the thing that we're going + + align:start position:0% +definition of the thing that we're going + + + align:start position:0% +definition of the thing that we're going +to chase after + + align:start position:0% +to chase after + + + align:start position:0% +to chase after +here + + align:start position:0% + + + + align:start position:0% + +fabulous okay right so uh let's do uh + + align:start position:0% +fabulous okay right so uh let's do uh + + + align:start position:0% +fabulous okay right so uh let's do uh +let's continue sort bot so our next uh + + align:start position:0% +let's continue sort bot so our next uh + + + align:start position:0% +let's continue sort bot so our next uh +uh uh piece of our puzzle here is the r + + align:start position:0% +uh uh piece of our puzzle here is the r + + + align:start position:0% +uh uh piece of our puzzle here is the r +I believe R stands for recursion this is + + align:start position:0% +I believe R stands for recursion this is + + + align:start position:0% +I believe R stands for recursion this is +a new acronym for me too oh nope no + + align:start position:0% +a new acronym for me too oh nope no + + + align:start position:0% +a new acronym for me too oh nope no +relate but it might as well be recursion + + align:start position:0% +relate but it might as well be recursion + + + align:start position:0% +relate but it might as well be recursion +for for most of these problems uh right + + align:start position:0% +for for most of these problems uh right + + + align:start position:0% +for for most of these problems uh right +so the basic relationship here is that + + align:start position:0% +so the basic relationship here is that + + + align:start position:0% +so the basic relationship here is that +of course I can either use object J or I + + align:start position:0% +of course I can either use object J or I + + + align:start position:0% +of course I can either use object J or I +can not use object J uh and and in both + + align:start position:0% +can not use object J uh and and in both + + + align:start position:0% +can not use object J uh and and in both +of those cases right if J is the very + + align:start position:0% +of those cases right if J is the very + + + align:start position:0% +of those cases right if J is the very +last guy that I'm going to consider uh + + align:start position:0% +last guy that I'm going to consider uh + + + align:start position:0% +last guy that I'm going to consider uh +that'll be a totally reasonable + + align:start position:0% +that'll be a totally reasonable + + + align:start position:0% +that'll be a totally reasonable +recursive rule right so in + + align:start position:0% +recursive rule right so in + + + align:start position:0% +recursive rule right so in +particular um I have that uh XI + + align:start position:0% +particular um I have that uh XI + + + align:start position:0% +particular um I have that uh XI +J um essentially can take one of two + + align:start position:0% +J um essentially can take one of two + + + align:start position:0% +J um essentially can take one of two +values a parenthesis in case you're + + align:start position:0% +values a parenthesis in case you're + + + align:start position:0% +values a parenthesis in case you're +wondering um and and of course you're + + align:start position:0% +wondering um and and of course you're + + + align:start position:0% +wondering um and and of course you're +trying to maximize your + + align:start position:0% +trying to maximize your + + + align:start position:0% +trying to maximize your +Revenue uh so so let's do that okay so + + align:start position:0% + + + + align:start position:0% + +um so we have sort of two OB uh + + align:start position:0% +um so we have sort of two OB uh + + + align:start position:0% +um so we have sort of two OB uh +potentially potential options but we + + align:start position:0% +potentially potential options but we + + + align:start position:0% +potentially potential options but we +have to be a bit careful is there a case + + align:start position:0% +have to be a bit careful is there a case + + + align:start position:0% +have to be a bit careful is there a case +where I can't make object + + align:start position:0% + + + + align:start position:0% + +J yes class there is uh which is uh the + + align:start position:0% +J yes class there is uh which is uh the + + + align:start position:0% +J yes class there is uh which is uh the +case where I don't have enough coins + + align:start position:0% +case where I don't have enough coins + + + align:start position:0% +case where I don't have enough coins +left in the bank right so I want to make + + align:start position:0% +left in the bank right so I want to make + + + align:start position:0% +left in the bank right so I want to make +that really expensive Fountain but I + + align:start position:0% +that really expensive Fountain but I + + + align:start position:0% +that really expensive Fountain but I +only have one coin then I'm I'm sort of + + align:start position:0% +only have one coin then I'm I'm sort of + + + align:start position:0% +only have one coin then I'm I'm sort of +out of luck yep so uh let's do these two + + align:start position:0% +out of luck yep so uh let's do these two + + + align:start position:0% +out of luck yep so uh let's do these two +cases so + + align:start position:0% +cases so + + + align:start position:0% +cases so +first um you know if + + align:start position:0% + + + + align:start position:0% + +uh oops I got my cases + + align:start position:0% +uh oops I got my cases + + + align:start position:0% +uh oops I got my cases +backward that's okay um right so let's + + align:start position:0% +backward that's okay um right so let's + + + align:start position:0% +backward that's okay um right so let's +say that I choose not to uh make uh + + align:start position:0% +say that I choose not to uh make uh + + + align:start position:0% +say that I choose not to uh make uh +object J okay so what does that mean so + + align:start position:0% +object J okay so what does that mean so + + + align:start position:0% +object J okay so what does that mean so +so did I spend any coins + + align:start position:0% +so did I spend any coins + + + align:start position:0% +so did I spend any coins +no and moreover what is my maximum + + align:start position:0% +no and moreover what is my maximum + + + align:start position:0% +no and moreover what is my maximum +profit well it's going to be the same as + + align:start position:0% +profit well it's going to be the same as + + + align:start position:0% +profit well it's going to be the same as +the maximum profit using objects 1 + + align:start position:0% +the maximum profit using objects 1 + + + align:start position:0% +the maximum profit using objects 1 +through J minus one because I didn't use + + align:start position:0% +through J minus one because I didn't use + + + align:start position:0% +through J minus one because I didn't use +object J yeah so in particular that + + align:start position:0% +object J yeah so in particular that + + + align:start position:0% +object J yeah so in particular that +would be + + align:start position:0% +would be + + + align:start position:0% +would be +X um let's see I got it backward in my + + align:start position:0% +X um let's see I got it backward in my + + + align:start position:0% +X um let's see I got it backward in my +notes so we're going to do it live uh + + align:start position:0% +notes so we're going to do it live uh + + + align:start position:0% +notes so we're going to do it live uh +like that okay and otherwise let's say + + align:start position:0% +like that okay and otherwise let's say + + + align:start position:0% +like that okay and otherwise let's say +that I did choose to make object J well + + align:start position:0% +that I did choose to make object J well + + + align:start position:0% +that I did choose to make object J well +what happens so I did get some Revenue + + align:start position:0% +what happens so I did get some Revenue + + + align:start position:0% +what happens so I did get some Revenue +now right so I got man what on Earth did + + align:start position:0% +now right so I got man what on Earth did + + + align:start position:0% +now right so I got man what on Earth did +I write on these uh not um so I get the + + align:start position:0% +I write on these uh not um so I get the + + + align:start position:0% +I write on these uh not um so I get the +uh price of object J here as my Revenue + + align:start position:0% +uh price of object J here as my Revenue + + + align:start position:0% +uh price of object J here as my Revenue +but I spent uh some coins in the + + align:start position:0% +but I spent uh some coins in the + + + align:start position:0% +but I spent uh some coins in the +process so I have I minus uh K sub I + + align:start position:0% +process so I have I minus uh K sub I + + + align:start position:0% +process so I have I minus uh K sub I +which is the number of + + align:start position:0% +which is the number of + + + align:start position:0% +which is the number of +coins what was that oh thank you sorry K + + align:start position:0% +coins what was that oh thank you sorry K + + + align:start position:0% +coins what was that oh thank you sorry K +subj that's why we should be consistent + + align:start position:0% +subj that's why we should be consistent + + + align:start position:0% +subj that's why we should be consistent +with our indices when we write these + + align:start position:0% +with our indices when we write these + + + align:start position:0% +with our indices when we write these +things down um right so I spent K sub J + + align:start position:0% +things down um right so I spent K sub J + + + align:start position:0% +things down um right so I spent K sub J +coins uh making this thing uh object J + + align:start position:0% +coins uh making this thing uh object J + + + align:start position:0% +coins uh making this thing uh object J +uh and uh moreover I can still choose to + + align:start position:0% +uh and uh moreover I can still choose to + + + align:start position:0% +uh and uh moreover I can still choose to +make any of the previous object so it's + + align:start position:0% +make any of the previous object so it's + + + align:start position:0% +make any of the previous object so it's +still just J minus + + align:start position:0% +still just J minus + + + align:start position:0% +still just J minus +one but I have to be careful because I + + align:start position:0% +one but I have to be careful because I + + + align:start position:0% +one but I have to be careful because I +can't always do this in + + align:start position:0% +can't always do this in + + + align:start position:0% +can't always do this in +particular this it better be a positive + + align:start position:0% +particular this it better be a positive + + + align:start position:0% +particular this it better be a positive +number if I end or at least a non- + + align:start position:0% +number if I end or at least a non- + + + align:start position:0% +number if I end or at least a non- +negative number because if I end up with + + align:start position:0% +negative number because if I end up with + + + align:start position:0% +negative number because if I end up with +a negative number of coins well that + + align:start position:0% +a negative number of coins well that + + + align:start position:0% +a negative number of coins well that +that's not a physical universe that I + + align:start position:0% +that's not a physical universe that I + + + align:start position:0% +that's not a physical universe that I +choose to be in uh so in + + align:start position:0% +choose to be in uh so in + + + align:start position:0% +choose to be in uh so in +particular uh what we need in some sense + + align:start position:0% +particular uh what we need in some sense + + + align:start position:0% +particular uh what we need in some sense +is I minus K minus J KJ to be greater or + + align:start position:0% +is I minus K minus J KJ to be greater or + + + align:start position:0% +is I minus K minus J KJ to be greater or +equal to zero or equivalently I is + + align:start position:0% +equal to zero or equivalently I is + + + align:start position:0% +equal to zero or equivalently I is +greater than or equal to K so J I think + + align:start position:0% +greater than or equal to K so J I think + + + align:start position:0% +greater than or equal to K so J I think +you guys could all do that one at home + + align:start position:0% +you guys could all do that one at home + + + align:start position:0% +you guys could all do that one at home +okay and this is our recursion uh + + align:start position:0% +okay and this is our recursion uh + + + align:start position:0% +okay and this is our recursion uh +hopefully I've gotten it right because + + align:start position:0% +hopefully I've gotten it right because + + + align:start position:0% +hopefully I've gotten it right because +it disagrees with the crazy thing I + + align:start position:0% +it disagrees with the crazy thing I + + + align:start position:0% +it disagrees with the crazy thing I +wrote in my notes at 1 a.m. yesterday uh + + align:start position:0% +wrote in my notes at 1 a.m. yesterday uh + + + align:start position:0% +wrote in my notes at 1 a.m. yesterday uh +but uh I think it's pretty + + align:start position:0% +but uh I think it's pretty + + + align:start position:0% +but uh I think it's pretty +straightforward essentially either I can + + align:start position:0% +straightforward essentially either I can + + + align:start position:0% +straightforward essentially either I can +choose to use the last object or I + + align:start position:0% +choose to use the last object or I + + + align:start position:0% +choose to use the last object or I +choose not to uh and either one of those + + align:start position:0% +choose not to uh and either one of those + + + align:start position:0% +choose not to uh and either one of those +uh of course decrements uh J cuz that's + + align:start position:0% +uh of course decrements uh J cuz that's + + + align:start position:0% +uh of course decrements uh J cuz that's +the index of the object I'm considering + + align:start position:0% +the index of the object I'm considering + + + align:start position:0% +the index of the object I'm considering +uh and I either account for the price + + align:start position:0% +uh and I either account for the price + + + align:start position:0% +uh and I either account for the price +but have to pay in gold or I don't + + align:start position:0% +but have to pay in gold or I don't + + + align:start position:0% +but have to pay in gold or I don't +account for the price so implicitly + + align:start position:0% +account for the price so implicitly + + + align:start position:0% +account for the price so implicitly +there's a zero and I don't have to pay + + align:start position:0% +there's a zero and I don't have to pay + + + align:start position:0% +there's a zero and I don't have to pay +in Gold okay good all right so let's + + align:start position:0% +in Gold okay good all right so let's + + + align:start position:0% +in Gold okay good all right so let's +continue with uh sort bot we might later + + align:start position:0% +continue with uh sort bot we might later + + + align:start position:0% +continue with uh sort bot we might later +in the problem session relax going + + align:start position:0% +in the problem session relax going + + + align:start position:0% +in the problem session relax going +through every one of these steps because + + align:start position:0% +through every one of these steps because + + + align:start position:0% +through every one of these steps because +a lot of the arguments are kind of + + align:start position:0% +a lot of the arguments are kind of + + + align:start position:0% +a lot of the arguments are kind of +similar but for now we'll do one or two + + align:start position:0% +similar but for now we'll do one or two + + + align:start position:0% +similar but for now we'll do one or two +carefully so t uh I believe stands for + + align:start position:0% +carefully so t uh I believe stands for + + + align:start position:0% +carefully so t uh I believe stands for +topological order uh and here it's uh + + align:start position:0% +topological order uh and here it's uh + + + align:start position:0% +topological order uh and here it's uh +staring Us in the face because notice + + align:start position:0% +staring Us in the face because notice + + + align:start position:0% +staring Us in the face because notice +that + + align:start position:0% +that + + + align:start position:0% +that +um x i j + + align:start position:0% +um x i j + + + align:start position:0% +um x i j +only + + align:start position:0% +only + + + align:start position:0% +only +depends on um x i x question mark comma + + align:start position:0% +depends on um x i x question mark comma + + + align:start position:0% +depends on um x i x question mark comma +J minus + + align:start position:0% +J minus + + + align:start position:0% +J minus +one right so of course on your problem + + align:start position:0% +one right so of course on your problem + + + align:start position:0% +one right so of course on your problem +set you should write things more + + align:start position:0% +set you should write things more + + + align:start position:0% +set you should write things more +carefully uh but the basic Point here is + + align:start position:0% +carefully uh but the basic Point here is + + + align:start position:0% +carefully uh but the basic Point here is +that there's a clear topological order + + align:start position:0% +that there's a clear topological order + + + align:start position:0% +that there's a clear topological order +just by looking at that second index + + align:start position:0% +just by looking at that second index + + + align:start position:0% +just by looking at that second index +because you kind of if you think of all + + align:start position:0% +because you kind of if you think of all + + + align:start position:0% +because you kind of if you think of all +of your X's as variables in a graph + + align:start position:0% +of your X's as variables in a graph + + + align:start position:0% +of your X's as variables in a graph +which we've actually drawn in lecture so + + align:start position:0% +which we've actually drawn in lecture so + + + align:start position:0% +which we've actually drawn in lecture so +like maybe these are all the I's and + + align:start position:0% +like maybe these are all the I's and + + + align:start position:0% +like maybe these are all the I's and +then you know the J you know so like I + + align:start position:0% +then you know the J you know so like I + + + align:start position:0% +then you know the J you know so like I +goes down and J goes to the right then + + align:start position:0% +goes down and J goes to the right then + + + align:start position:0% +goes down and J goes to the right then +essentially this argument is saying that + + align:start position:0% +essentially this argument is saying that + + + align:start position:0% +essentially this argument is saying that +all the arrows kind of Point left in + + align:start position:0% +all the arrows kind of Point left in + + + align:start position:0% +all the arrows kind of Point left in +this + + align:start position:0% +this + + + align:start position:0% +this +graph + + align:start position:0% +graph + + + align:start position:0% +graph +um suppose the way I've drawn my arrows + + align:start position:0% +um suppose the way I've drawn my arrows + + + align:start position:0% +um suppose the way I've drawn my arrows +this isn't quite accurate but it + + align:start position:0% +this isn't quite accurate but it + + + align:start position:0% +this isn't quite accurate but it +actually doesn't matter the only thing + + align:start position:0% +actually doesn't matter the only thing + + + align:start position:0% +actually doesn't matter the only thing +that matters is that it goes from right + + align:start position:0% +that matters is that it goes from right + + + align:start position:0% +that matters is that it goes from right +to left um but I'm going to erase this + + align:start position:0% +to left um but I'm going to erase this + + + align:start position:0% +to left um but I'm going to erase this +so you don't remember it + + align:start position:0% +so you don't remember it + + + align:start position:0% +so you don't remember it +okay so in general just when you when + + align:start position:0% +okay so in general just when you when + + + align:start position:0% +okay so in general just when you when +you want to make your topological order + + align:start position:0% +you want to make your topological order + + + align:start position:0% +you want to make your topological order +argument I think a totally sensible one + + align:start position:0% +argument I think a totally sensible one + + + align:start position:0% +argument I think a totally sensible one +is like looking at the indices of your + + align:start position:0% +is like looking at the indices of your + + + align:start position:0% +is like looking at the indices of your +recursion and then just trying to find + + align:start position:0% +recursion and then just trying to find + + + align:start position:0% +recursion and then just trying to find +some number that + + align:start position:0% +some number that + + + align:start position:0% +some number that +decreases incidentally if you take a + + align:start position:0% +decreases incidentally if you take a + + + align:start position:0% +decreases incidentally if you take a +differential equation course uh that's + + align:start position:0% +differential equation course uh that's + + + align:start position:0% +differential equation course uh that's +roughly how you prove that a lot of + + align:start position:0% +roughly how you prove that a lot of + + + align:start position:0% +roughly how you prove that a lot of +those things converge too um so there's + + align:start position:0% +those things converge too um so there's + + + align:start position:0% +those things converge too um so there's +a a sort of a generic math trick that we + + align:start position:0% +a a sort of a generic math trick that we + + + align:start position:0% +a a sort of a generic math trick that we +use a lot you call that in in in od + + align:start position:0% +use a lot you call that in in in od + + + align:start position:0% +use a lot you call that in in in od +where you have some number that + + align:start position:0% +where you have some number that + + + align:start position:0% +where you have some number that +decreases I would call potential + + align:start position:0% +decreases I would call potential + + + align:start position:0% +decreases I would call potential +function potential function that's a + + align:start position:0% +function potential function that's a + + + align:start position:0% +function potential function that's a +perfectly sensible one there's the it's + + align:start position:0% +perfectly sensible one there's the it's + + + align:start position:0% +perfectly sensible one there's the it's +not lip shits it's some other + + align:start position:0% +not lip shits it's some other + + + align:start position:0% +not lip shits it's some other +mathematician anyway uh okay so let's + + align:start position:0% +mathematician anyway uh okay so let's + + + align:start position:0% +mathematician anyway uh okay so let's +continue uh sord bot so next we need B + + align:start position:0% +continue uh sord bot so next we need B + + + align:start position:0% +continue uh sord bot so next we need B +which is our base + + align:start position:0% +which is our base + + + align:start position:0% +which is our base +case uh so in this case uh is pretty + + align:start position:0% +case uh so in this case uh is pretty + + + align:start position:0% +case uh so in this case uh is pretty +straightforward if I if I don't have any + + align:start position:0% +straightforward if I if I don't have any + + + align:start position:0% +straightforward if I if I don't have any +coins I can't make any + + align:start position:0% +coins I can't make any + + + align:start position:0% +coins I can't make any +money I have a t-shirt that that says + + align:start position:0% +money I have a t-shirt that that says + + + align:start position:0% +money I have a t-shirt that that says +that at home uh and moreover uh if I + + align:start position:0% +that at home uh and moreover uh if I + + + align:start position:0% +that at home uh and moreover uh if I +can't sell anything I can't make any + + align:start position:0% +can't sell anything I can't make any + + + align:start position:0% +can't sell anything I can't make any +money uh so those are are pretty + + align:start position:0% +money uh so those are are pretty + + + align:start position:0% +money uh so those are are pretty +straight forward cases so we have that + + align:start position:0% +straight forward cases so we have that + + + align:start position:0% +straight forward cases so we have that +zero + + align:start position:0% +zero + + + align:start position:0% +zero +equals x of 0 comma J remember the first + + align:start position:0% +equals x of 0 comma J remember the first + + + align:start position:0% +equals x of 0 comma J remember the first +index is the number of coins you have so + + align:start position:0% +index is the number of coins you have so + + + align:start position:0% +index is the number of coins you have so +this is saying I don't I can't make + + align:start position:0% +this is saying I don't I can't make + + + align:start position:0% +this is saying I don't I can't make +anything if I don't have any coins and + + align:start position:0% +anything if I don't have any coins and + + + align:start position:0% +anything if I don't have any coins and +similarly equals x i comma 0 for all i j + + align:start position:0% +similarly equals x i comma 0 for all i j + + + align:start position:0% +similarly equals x i comma 0 for all i j +right so this is the coins and the uh + + align:start position:0% +right so this is the coins and the uh + + + align:start position:0% +right so this is the coins and the uh +objects okay so let's see I keep writing + + align:start position:0% +objects okay so let's see I keep writing + + + align:start position:0% +objects okay so let's see I keep writing +these problem sessions too big and then + + align:start position:0% +these problem sessions too big and then + + + align:start position:0% +these problem sessions too big and then +spending half of it erasing so let's + + align:start position:0% +spending half of it erasing so let's + + + align:start position:0% +spending half of it erasing so let's +let's try and fit this on one board here + + align:start position:0% +let's try and fit this on one board here + + + align:start position:0% +let's try and fit this on one board here +so we're going to do sort but then the + + align:start position:0% +so we're going to do sort but then the + + + align:start position:0% +so we're going to do sort but then the +second no the first o because there's no + + align:start position:0% +second no the first o because there's no + + + align:start position:0% +second no the first o because there's no +o in sort um is the uh the uh what the + + align:start position:0% +o in sort um is the uh the uh what the + + + align:start position:0% +o in sort um is the uh the uh what the +original problem that you want to solve + + align:start position:0% +original problem that you want to solve + + + align:start position:0% +original problem that you want to solve +so of course you start out with n + + align:start position:0% +so of course you start out with n + + + align:start position:0% +so of course you start out with n +objects and N + + align:start position:0% +objects and N + + + align:start position:0% +objects and N +coins uh + + align:start position:0% +coins uh + + + align:start position:0% +coins uh +so the original problem we want to solve + + align:start position:0% +so the original problem we want to solve + + + align:start position:0% +so the original problem we want to solve +uh is equivalent to Computing xn comma n + + align:start position:0% +uh is equivalent to Computing xn comma n + + + align:start position:0% +uh is equivalent to Computing xn comma n +and then finally we got to do our + + align:start position:0% +and then finally we got to do our + + + align:start position:0% +and then finally we got to do our +runtime T stands for runtime or time I + + align:start position:0% +runtime T stands for runtime or time I + + + align:start position:0% +runtime T stands for runtime or time I +suppose um so first of all how many many + + align:start position:0% +suppose um so first of all how many many + + + align:start position:0% +suppose um so first of all how many many +sub problems are there well there's x i + + align:start position:0% +sub problems are there well there's x i + + + align:start position:0% +sub problems are there well there's x i +j both I can go from 0er to n this is a + + align:start position:0% +j both I can go from 0er to n this is a + + + align:start position:0% +j both I can go from 0er to n this is a +great way to be off by one um so there's + + align:start position:0% +great way to be off by one um so there's + + + align:start position:0% +great way to be off by one um so there's +n + 1 squared + + align:start position:0% +n + 1 squared + + + align:start position:0% +n + 1 squared +sub + + align:start position:0% +sub + + + align:start position:0% +sub +problems uh and how much work does each + + align:start position:0% +problems uh and how much work does each + + + align:start position:0% +problems uh and how much work does each +sub problem do well it does boring work + + align:start position:0% +sub problem do well it does boring work + + + align:start position:0% +sub problem do well it does boring work +it's just a formula right so there's + + align:start position:0% +it's just a formula right so there's + + + align:start position:0% +it's just a formula right so there's +order one + + align:start position:0% +order one + + + align:start position:0% +order one +work per sub problem so the overall + + align:start position:0% +work per sub problem so the overall + + + align:start position:0% +work per sub problem so the overall +algorithm takes n^2 + + align:start position:0% +algorithm takes n^2 + + + align:start position:0% +algorithm takes n^2 +time so I promised to do something last + + align:start position:0% +time so I promised to do something last + + + align:start position:0% +time so I promised to do something last +in our last problem session then I + + align:start position:0% +in our last problem session then I + + + align:start position:0% +in our last problem session then I +didn't actually do it uh so I did think + + align:start position:0% +didn't actually do it uh so I did think + + + align:start position:0% +didn't actually do it uh so I did think +I would spend just a minute uh here sort + + align:start position:0% +I would spend just a minute uh here sort + + + align:start position:0% +I would spend just a minute uh here sort +of translating what this sbot thing + + align:start position:0% +of translating what this sbot thing + + + align:start position:0% +of translating what this sbot thing +would mean in terms of of code because I + + align:start position:0% +would mean in terms of of code because I + + + align:start position:0% +would mean in terms of of code because I +think that it's a little bit implicit + + align:start position:0% +think that it's a little bit implicit + + + align:start position:0% +think that it's a little bit implicit +here in particular I think this step + + align:start position:0% +here in particular I think this step + + + align:start position:0% +here in particular I think this step +here I mean you will'll see that it + + align:start position:0% +here I mean you will'll see that it + + + align:start position:0% +here I mean you will'll see that it +really clearly is going to give you an + + align:start position:0% +really clearly is going to give you an + + + align:start position:0% +really clearly is going to give you an +algorithm but I think it's kind of easy + + align:start position:0% +algorithm but I think it's kind of easy + + + align:start position:0% +algorithm but I think it's kind of easy +to like again just to to forget what + + align:start position:0% +to like again just to to forget what + + + align:start position:0% +to like again just to to forget what +what your code actually looks like and + + align:start position:0% +what your code actually looks like and + + + align:start position:0% +what your code actually looks like and +actually the coding problems on these + + align:start position:0% +actually the coding problems on these + + + align:start position:0% +actually the coding problems on these +problem sessions are almost too + + align:start position:0% +problem sessions are almost too + + + align:start position:0% +problem sessions are almost too +interesting and and and can obscure it a + + align:start position:0% +interesting and and and can obscure it a + + + align:start position:0% +interesting and and and can obscure it a +little bit so I thought we'd do a boring + + align:start position:0% +little bit so I thought we'd do a boring + + + align:start position:0% +little bit so I thought we'd do a boring +problem and show you uh that it's really + + align:start position:0% +problem and show you uh that it's really + + + align:start position:0% +problem and show you uh that it's really +not so hard to to do this and in fact uh + + align:start position:0% +not so hard to to do this and in fact uh + + + align:start position:0% +not so hard to to do this and in fact uh +we covered two different strategies in + + align:start position:0% +we covered two different strategies in + + + align:start position:0% +we covered two different strategies in +class for how to take sort bot and + + align:start position:0% +class for how to take sort bot and + + + align:start position:0% +class for how to take sort bot and +convert it into a piece of code although + + align:start position:0% +convert it into a piece of code although + + + align:start position:0% +convert it into a piece of code although +they might have uh kind of zipped past + + align:start position:0% +they might have uh kind of zipped past + + + align:start position:0% +they might have uh kind of zipped past +you in in this you know 2x speed uh + + align:start position:0% +you in in this you know 2x speed uh + + + align:start position:0% +you in in this you know 2x speed uh +thing that you can do now um so right so + + align:start position:0% +thing that you can do now um so right so + + + align:start position:0% +thing that you can do now um so right so +here are two options um one of them is + + align:start position:0% +here are two options um one of them is + + + align:start position:0% +here are two options um one of them is +called memorization uh and the other I + + align:start position:0% +called memorization uh and the other I + + + align:start position:0% +called memorization uh and the other I +don't know bottom up I guess is a + + align:start position:0% +don't know bottom up I guess is a + + + align:start position:0% +don't know bottom up I guess is a +reasonable phrase uh to describe and so + + align:start position:0% +reasonable phrase uh to describe and so + + + align:start position:0% +reasonable phrase uh to describe and so +I thought we'd do them both because + + align:start position:0% +I thought we'd do them both because + + + align:start position:0% +I thought we'd do them both because +they're both easy for this particular + + align:start position:0% +they're both easy for this particular + + + align:start position:0% +they're both easy for this particular +problem + + align:start position:0% +problem + + + align:start position:0% +problem +um + + align:start position:0% +um + + + align:start position:0% +um +okay right so um let's do that so let's + + align:start position:0% +okay right so um let's do that so let's + + + align:start position:0% +okay right so um let's do that so let's +uh so is this necessary on your homework + + align:start position:0% +uh so is this necessary on your homework + + + align:start position:0% +uh so is this necessary on your homework +strictly speaking no like if you've + + align:start position:0% +strictly speaking no like if you've + + + align:start position:0% +strictly speaking no like if you've +you've gone through sort bot then + + align:start position:0% +you've gone through sort bot then + + + align:start position:0% +you've gone through sort bot then +essentially everything that happens + + align:start position:0% +essentially everything that happens + + + align:start position:0% +essentially everything that happens +after that is sort of boilerplate in + + align:start position:0% +after that is sort of boilerplate in + + + align:start position:0% +after that is sort of boilerplate in +terms of converting these steps into a + + align:start position:0% +terms of converting these steps into a + + + align:start position:0% +terms of converting these steps into a +piece of code or an out algorithm but I + + align:start position:0% +piece of code or an out algorithm but I + + + align:start position:0% +piece of code or an out algorithm but I +do think just for understanding why sort + + align:start position:0% +do think just for understanding why sort + + + align:start position:0% +do think just for understanding why sort +bot makes sense uh it's worth thinking + + align:start position:0% +bot makes sense uh it's worth thinking + + + align:start position:0% +bot makes sense uh it's worth thinking +about for a minute um so option A here + + align:start position:0% +about for a minute um so option A here + + + align:start position:0% +about for a minute um so option A here +is + + align:start position:0% + + + + align:start position:0% + +memoization ironically I've taught and + + align:start position:0% +memoization ironically I've taught and + + + align:start position:0% +memoization ironically I've taught and +ta algorithms a few times and I never + + align:start position:0% +ta algorithms a few times and I never + + + align:start position:0% +ta algorithms a few times and I never +actually knew what memorization uh meant + + align:start position:0% +actually knew what memorization uh meant + + + align:start position:0% +actually knew what memorization uh meant +so I I learned something from from + + align:start position:0% +so I I learned something from from + + + align:start position:0% +so I I learned something from from +Eric's lecture the other day um which + + align:start position:0% +Eric's lecture the other day um which + + + align:start position:0% +Eric's lecture the other day um which +remember memorization the key thing and + + align:start position:0% +remember memorization the key thing and + + + align:start position:0% +remember memorization the key thing and +then what apparently is kind of a madeup + + align:start position:0% +then what apparently is kind of a madeup + + + align:start position:0% +then what apparently is kind of a madeup +word is memo like you know if you're + + align:start position:0% +word is memo like you know if you're + + + align:start position:0% +word is memo like you know if you're +back in the day you had a what a stopad + + align:start position:0% +back in the day you had a what a stopad + + + align:start position:0% +back in the day you had a what a stopad +and you were writing down stuff because + + align:start position:0% +and you were writing down stuff because + + + align:start position:0% +and you were writing down stuff because +that's where you solve problems with + + align:start position:0% +that's where you solve problems with + + + align:start position:0% +that's where you solve problems with +your slide rule um then uh essentially + + align:start position:0% +your slide rule um then uh essentially + + + align:start position:0% +your slide rule um then uh essentially +the idea is that if I compute xig for + + align:start position:0% +the idea is that if I compute xig for + + + align:start position:0% +the idea is that if I compute xig for +some pair I shouldn't compute it again I + + align:start position:0% +some pair I shouldn't compute it again I + + + align:start position:0% +some pair I shouldn't compute it again I +should just write it down on my memo pad + + align:start position:0% +should just write it down on my memo pad + + + align:start position:0% +should just write it down on my memo pad +um steno isation sounds better to me but + + align:start position:0% +um steno isation sounds better to me but + + + align:start position:0% +um steno isation sounds better to me but +I suppose we'd have to go back to the 19 + + align:start position:0% +I suppose we'd have to go back to the 19 + + + align:start position:0% +I suppose we'd have to go back to the 19 +what 40s and fix it um okay so let's uh + + align:start position:0% +what 40s and fix it um okay so let's uh + + + align:start position:0% +what 40s and fix it um okay so let's uh +actually write down I'm going to write + + align:start position:0% +actually write down I'm going to write + + + align:start position:0% +actually write down I'm going to write +down pseudo code that'll probably look + + align:start position:0% +down pseudo code that'll probably look + + + align:start position:0% +down pseudo code that'll probably look +more like mat lab cuz I'm that kind of + + align:start position:0% +more like mat lab cuz I'm that kind of + + + align:start position:0% +more like mat lab cuz I'm that kind of +guy uh so uh let's say that I wanted to + + align:start position:0% +guy uh so uh let's say that I wanted to + + + align:start position:0% +guy uh so uh let's say that I wanted to +make a + + align:start position:0% +make a + + + align:start position:0% +make a +function um which I guess is + + align:start position:0% +function um which I guess is + + + align:start position:0% +function um which I guess is +revenue of i j uh like + + align:start position:0% +revenue of i j uh like + + + align:start position:0% +revenue of i j uh like +that um and and and and this is the + + align:start position:0% +that um and and and and this is the + + + align:start position:0% +that um and and and and this is the +thing I wanted to + + align:start position:0% +thing I wanted to + + + align:start position:0% +thing I wanted to +compute oh that's actually going to be a + + align:start position:0% +compute oh that's actually going to be a + + + align:start position:0% +compute oh that's actually going to be a +problem because we're not be able to + + align:start position:0% +problem because we're not be able to + + + align:start position:0% +problem because we're not be able to +see okay right so in addition to + + align:start position:0% +see okay right so in addition to + + + align:start position:0% +see okay right so in addition to +this I I'm going to kind of pass in an + + align:start position:0% +this I I'm going to kind of pass in an + + + align:start position:0% +this I I'm going to kind of pass in an +array X um which is going to be like the + + align:start position:0% +array X um which is going to be like the + + + align:start position:0% +array X um which is going to be like the +my my memo pad this is going to be + + align:start position:0% +my my memo pad this is going to be + + + align:start position:0% +my my memo pad this is going to be +terrible coding practice but easy board + + align:start position:0% +terrible coding practice but easy board + + + align:start position:0% +terrible coding practice but easy board +coding uh practice so like if I were in + + align:start position:0% +coding uh practice so like if I were in + + + align:start position:0% +coding uh practice so like if I were in +C++ maybe I pass it by reference so that + + align:start position:0% +C++ maybe I pass it by reference so that + + + align:start position:0% +C++ maybe I pass it by reference so that +like when I edit it's a treble cleff but + + align:start position:0% +like when I edit it's a treble cleff but + + + align:start position:0% +like when I edit it's a treble cleff but +whatever + + align:start position:0% +whatever + + + align:start position:0% +whatever +uh you know when I edit X it actually + + align:start position:0% +uh you know when I edit X it actually + + + align:start position:0% +uh you know when I edit X it actually +persists when I when I recurse this is + + align:start position:0% +persists when I when I recurse this is + + + align:start position:0% +persists when I when I recurse this is +terrible coding practice and you + + align:start position:0% +terrible coding practice and you + + + align:start position:0% +terrible coding practice and you +shouldn't do it okay um but it's just + + align:start position:0% +shouldn't do it okay um but it's just + + + align:start position:0% +shouldn't do it okay um but it's just +going to be because I don't want to + + align:start position:0% +going to be because I don't want to + + + align:start position:0% +going to be because I don't want to +write too many lines on the board here + + align:start position:0% +write too many lines on the board here + + + align:start position:0% +write too many lines on the board here +um and maybe we initialize like we have + + align:start position:0% +um and maybe we initialize like we have + + + align:start position:0% +um and maybe we initialize like we have +some helper + + align:start position:0% + + + + align:start position:0% + +function uh to Let's see we want our + + align:start position:0% +function uh to Let's see we want our + + + align:start position:0% +function uh to Let's see we want our +Revenue to be big well actually no we'll + + align:start position:0% +Revenue to be big well actually no we'll + + + align:start position:0% +Revenue to be big well actually no we'll +just initialize it to like not a number + + align:start position:0% +just initialize it to like not a number + + + align:start position:0% +just initialize it to like not a number +so that like we know that we haven't + + align:start position:0% +so that like we know that we haven't + + + align:start position:0% +so that like we know that we haven't +computed it yet how about + + align:start position:0% +computed it yet how about + + + align:start position:0% +computed it yet how about +that okay so + + align:start position:0% +that okay so + + + align:start position:0% +that okay so +uh what should we do well if we're going + + align:start position:0% +uh what should we do well if we're going + + + align:start position:0% +uh what should we do well if we're going +to memoize the first thing we should do + + align:start position:0% +to memoize the first thing we should do + + + align:start position:0% +to memoize the first thing we should do +anytime that I call my Revenue function + + align:start position:0% +anytime that I call my Revenue function + + + align:start position:0% +anytime that I call my Revenue function +on on an AJ pair is check have already + + align:start position:0% +on on an AJ pair is check have already + + + align:start position:0% +on on an AJ pair is check have already +computed it yeah um so in my kind of + + align:start position:0% +computed it yeah um so in my kind of + + + align:start position:0% +computed it yeah um so in my kind of +goofy bad board coding style here what + + align:start position:0% +goofy bad board coding style here what + + + align:start position:0% +goofy bad board coding style here what +could I do I'd say well if I've already + + align:start position:0% +could I do I'd say well if I've already + + + align:start position:0% +could I do I'd say well if I've already +computed it then this thing won't equal + + align:start position:0% +computed it then this thing won't equal + + + align:start position:0% +computed it then this thing won't equal +Nan anymore it won't be not a number so + + align:start position:0% +Nan anymore it won't be not a number so + + + align:start position:0% +Nan anymore it won't be not a number so +I can say okay if x i j is not equal not + + align:start position:0% +I can say okay if x i j is not equal not + + + align:start position:0% +I can say okay if x i j is not equal not +a number so in other words it is a + + align:start position:0% +a number so in other words it is a + + + align:start position:0% +a number so in other words it is a +number um + + align:start position:0% + + + + align:start position:0% + +return and this like I think that this + + align:start position:0% +return and this like I think that this + + + align:start position:0% +return and this like I think that this +little line of code here it gets like a + + align:start position:0% +little line of code here it gets like a + + + align:start position:0% +little line of code here it gets like a +little loss but this is like we should + + align:start position:0% +little loss but this is like we should + + + align:start position:0% +little loss but this is like we should +put like sparkles around it right this + + align:start position:0% +put like sparkles around it right this + + + align:start position:0% +put like sparkles around it right this +is the magic of dynamic programming + + align:start position:0% +is the magic of dynamic programming + + + align:start position:0% +is the magic of dynamic programming +because I just killed recursive CS right + + align:start position:0% +because I just killed recursive CS right + + + align:start position:0% +because I just killed recursive CS right +like I even if I and J are like 17 and + + align:start position:0% +like I even if I and J are like 17 and + + + align:start position:0% +like I even if I and J are like 17 and +23 if I already computed it I'm done + + align:start position:0% +23 if I already computed it I'm done + + + align:start position:0% +23 if I already computed it I'm done +right I I don't have to call my + + align:start position:0% +right I I don't have to call my + + + align:start position:0% +right I I don't have to call my +recursion again okay and otherwise what + + align:start position:0% +recursion again okay and otherwise what + + + align:start position:0% +recursion again okay and otherwise what +am I going to do + + align:start position:0% +am I going to do + + + align:start position:0% +am I going to do +um well otherwise I'll you know maybe + + align:start position:0% +um well otherwise I'll you know maybe + + + align:start position:0% +um well otherwise I'll you know maybe +call do I want to write it all down I + + align:start position:0% +call do I want to write it all down I + + + align:start position:0% +call do I want to write it all down I +don't want to write that all down + + align:start position:0% +don't want to write that all down + + + align:start position:0% +don't want to write that all down +um so otherwise + + align:start position:0% +um so otherwise + + + align:start position:0% +um so otherwise +I'm going to + + align:start position:0% + + + + align:start position:0% + +evaluate R where R is this formula over + + align:start position:0% +evaluate R where R is this formula over + + + align:start position:0% +evaluate R where R is this formula over +here notice that this will + + align:start position:0% +here notice that this will + + + align:start position:0% +here notice that this will +require um recursive calls right uh and + + align:start position:0% +require um recursive calls right uh and + + + align:start position:0% +require um recursive calls right uh and +I'm going to store it in + + align:start position:0% + + + + align:start position:0% + +x i + + align:start position:0% +x i + + + align:start position:0% +x i +j and then return x i + + align:start position:0% + + + + align:start position:0% + +j okay so B basically the only + + align:start position:0% +j okay so B basically the only + + + align:start position:0% +j okay so B basically the only +difference between like what we've seen + + align:start position:0% +difference between like what we've seen + + + align:start position:0% +difference between like what we've seen +in the first two3 of 66 and now is this + + align:start position:0% +in the first two3 of 66 and now is this + + + align:start position:0% +in the first two3 of 66 and now is this +beautiful line of code saying if I + + align:start position:0% +beautiful line of code saying if I + + + align:start position:0% +beautiful line of code saying if I +already computed this thing return it + + align:start position:0% +already computed this thing return it + + + align:start position:0% +already computed this thing return it +and this is the memorized version of our + + align:start position:0% +and this is the memorized version of our + + + align:start position:0% +and this is the memorized version of our +algorithm um I think this is sort of the + + align:start position:0% +algorithm um I think this is sort of the + + + align:start position:0% +algorithm um I think this is sort of the +easiest one to maybe think about but + + align:start position:0% +easiest one to maybe think about but + + + align:start position:0% +easiest one to maybe think about but +actually from a runtime analysis it's a + + align:start position:0% +actually from a runtime analysis it's a + + + align:start position:0% +actually from a runtime analysis it's a +little bit annoying um it's not in the + + align:start position:0% +little bit annoying um it's not in the + + + align:start position:0% +little bit annoying um it's not in the +sense that we convince ourselves that SB + + align:start position:0% +sense that we convince ourselves that SB + + + align:start position:0% +sense that we convince ourselves that SB +is okay but of course like if you're + + align:start position:0% +is okay but of course like if you're + + + align:start position:0% +is okay but of course like if you're +thinking about your recursion tree like + + align:start position:0% +thinking about your recursion tree like + + + align:start position:0% +thinking about your recursion tree like +what's happening is that you're sort of + + align:start position:0% +what's happening is that you're sort of + + + align:start position:0% +what's happening is that you're sort of +maybe convincing yourself that like this + + align:start position:0% +maybe convincing yourself that like this + + + align:start position:0% +maybe convincing yourself that like this +piece can be lopped off in your function + + align:start position:0% +piece can be lopped off in your function + + + align:start position:0% +piece can be lopped off in your function +calls um so you sort of have to do your + + align:start position:0% +calls um so you sort of have to do your + + + align:start position:0% +calls um so you sort of have to do your +counting uh + + align:start position:0% +counting uh + + + align:start position:0% +counting uh +carefully uh there's a different way to + + align:start position:0% +carefully uh there's a different way to + + + align:start position:0% +carefully uh there's a different way to +uh implement the same thing so this + + align:start position:0% +uh implement the same thing so this + + + align:start position:0% +uh implement the same thing so this +would be option b this is maybe more + + align:start position:0% +would be option b this is maybe more + + + align:start position:0% +would be option b this is maybe more +efficient maybe less efficient depending + + align:start position:0% +efficient maybe less efficient depending + + + align:start position:0% +efficient maybe less efficient depending +on your problem um but these are all + + align:start position:0% +on your problem um but these are all + + + align:start position:0% +on your problem um but these are all +within constant factors of each other + + align:start position:0% +within constant factors of each other + + + align:start position:0% +within constant factors of each other +for the most part not always but for the + + align:start position:0% +for the most part not always but for the + + + align:start position:0% +for the most part not always but for the +most part this would be bottom + + align:start position:0% +most part this would be bottom + + + align:start position:0% +most part this would be bottom +up and this is the idea of rather than + + align:start position:0% +up and this is the idea of rather than + + + align:start position:0% +up and this is the idea of rather than +just taking our recursive algorithm that + + align:start position:0% +just taking our recursive algorithm that + + + align:start position:0% +just taking our recursive algorithm that +we already know know and then just like + + align:start position:0% +we already know know and then just like + + + align:start position:0% +we already know know and then just like +checking a table to see like okay did I + + align:start position:0% +checking a table to see like okay did I + + + align:start position:0% +checking a table to see like okay did I +already do this in this in that case + + align:start position:0% +already do this in this in that case + + + align:start position:0% +already do this in this in that case +return it uh in the bottom up version + + align:start position:0% +return it uh in the bottom up version + + + align:start position:0% +return it uh in the bottom up version +I'm going to build up my array XI J um + + align:start position:0% +I'm going to build up my array XI J um + + + align:start position:0% +I'm going to build up my array XI J um +so there's no recursion at all um so + + align:start position:0% +so there's no recursion at all um so + + + align:start position:0% +so there's no recursion at all um so +right so what would that look like so in + + align:start position:0% +right so what would that look like so in + + + align:start position:0% +right so what would that look like so in +the bottom up case notice that in some + + align:start position:0% +the bottom up case notice that in some + + + align:start position:0% +the bottom up case notice that in some +sense memorization is a top down + + align:start position:0% +sense memorization is a top down + + + align:start position:0% +sense memorization is a top down +strategy right I would call it on N + + align:start position:0% +strategy right I would call it on N + + + align:start position:0% +strategy right I would call it on N +comma n here we're going to start from + + align:start position:0% +comma n here we're going to start from + + + align:start position:0% +comma n here we're going to start from +zero and work our way toward n right so + + align:start position:0% +zero and work our way toward n right so + + + align:start position:0% +zero and work our way toward n right so +we'll start with x 0 J equals uh x + + align:start position:0% +we'll start with x 0 J equals uh x + + + align:start position:0% +we'll start with x 0 J equals uh x +i0 equal 0 for all i j obviously I can + + align:start position:0% +i0 equal 0 for all i j obviously I can + + + align:start position:0% +i0 equal 0 for all i j obviously I can +do this with a + + align:start position:0% +do this with a + + + align:start position:0% +do this with a +forloop uh and + + align:start position:0% +forloop uh and + + + align:start position:0% +forloop uh and +now well remember if we think about our + + align:start position:0% +now well remember if we think about our + + + align:start position:0% +now well remember if we think about our +topological order x i j only depends on + + align:start position:0% +topological order x i j only depends on + + + align:start position:0% +topological order x i j only depends on +previous JS right so it makes sense to + + align:start position:0% +previous JS right so it makes sense to + + + align:start position:0% +previous JS right so it makes sense to +have an outer loop which is over + + align:start position:0% + + + + align:start position:0% + +J and now inside of inside of this out + + align:start position:0% +J and now inside of inside of this out + + + align:start position:0% +J and now inside of inside of this out +loop I can uh compute anything that I + + align:start position:0% +loop I can uh compute anything that I + + + align:start position:0% +loop I can uh compute anything that I +want in that J column of X and I'm in + + align:start position:0% +want in that J column of X and I'm in + + + align:start position:0% +want in that J column of X and I'm in +good shape because I'm building it up + + align:start position:0% +good shape because I'm building it up + + + align:start position:0% +good shape because I'm building it up +one column at a time right so in + + align:start position:0% +one column at a time right so in + + + align:start position:0% +one column at a time right so in +particular now we can + + align:start position:0% + + + + align:start position:0% + +do you know our Loop over I and then + + align:start position:0% +do you know our Loop over I and then + + + align:start position:0% +do you know our Loop over I and then +just have you know x j um and now you + + align:start position:0% +just have you know x j um and now you + + + align:start position:0% +just have you know x j um and now you +know evaluate our R step in our sort bot + + align:start position:0% +know evaluate our R step in our sort bot + + + align:start position:0% +know evaluate our R step in our sort bot +uh Paradigm and and notice that that's + + align:start position:0% +uh Paradigm and and notice that that's + + + align:start position:0% +uh Paradigm and and notice that that's +perfectly fine because by the time I get + + align:start position:0% +perfectly fine because by the time I get + + + align:start position:0% +perfectly fine because by the time I get +to Computing XI J I've already filled in + + align:start position:0% +to Computing XI J I've already filled in + + + align:start position:0% +to Computing XI J I've already filled in +x j for you know minus one which is all + + align:start position:0% +x j for you know minus one which is all + + + align:start position:0% +x j for you know minus one which is all +I needed to evaluate that formula so + + align:start position:0% +I needed to evaluate that formula so + + + align:start position:0% +I needed to evaluate that formula so +what are the advantages and the + + align:start position:0% +what are the advantages and the + + + align:start position:0% +what are the advantages and the +disadvantages here so notice that here + + align:start position:0% +disadvantages here so notice that here + + + align:start position:0% +disadvantages here so notice that here +our our our runtime is staring you in + + align:start position:0% +our our our runtime is staring you in + + + align:start position:0% +our our our runtime is staring you in +the face right we have N squ Sub + + align:start position:0% +the face right we have N squ Sub + + + align:start position:0% +the face right we have N squ Sub +problems order one work and you're done + + align:start position:0% +problems order one work and you're done + + + align:start position:0% +problems order one work and you're done +on the other hand there's some + + align:start position:0% +on the other hand there's some + + + align:start position:0% +on the other hand there's some +possibility like if you were an old + + align:start position:0% +possibility like if you were an old + + + align:start position:0% +possibility like if you were an old +school AI person that you might be able + + align:start position:0% +school AI person that you might be able + + + align:start position:0% +school AI person that you might be able +to do some pruning on on the the your + + align:start position:0% +to do some pruning on on the the your + + + align:start position:0% +to do some pruning on on the the your +left hand side uh that I can't do over + + align:start position:0% +left hand side uh that I can't do over + + + align:start position:0% +left hand side uh that I can't do over +here right so here I'm literally + + align:start position:0% +here right so here I'm literally + + + align:start position:0% +here right so here I'm literally +evaluating every entry of xij it could + + align:start position:0% +evaluating every entry of xij it could + + + align:start position:0% +evaluating every entry of xij it could +be the case it's not the case for this + + align:start position:0% +be the case it's not the case for this + + + align:start position:0% +be the case it's not the case for this +particular problem but maybe X only + + align:start position:0% +particular problem but maybe X only + + + align:start position:0% +particular problem but maybe X only +depends on x i j minus 5 right this + + align:start position:0% +depends on x i j minus 5 right this + + + align:start position:0% +depends on x i j minus 5 right this +strategy is going to still build up that + + align:start position:0% +strategy is going to still build up that + + + align:start position:0% +strategy is going to still build up that +whole table this one maybe can skip over + + align:start position:0% +whole table this one maybe can skip over + + + align:start position:0% +whole table this one maybe can skip over +some entry so in practice it could help + + align:start position:0% +some entry so in practice it could help + + + align:start position:0% +some entry so in practice it could help +on the other hand here I've got a bunch + + align:start position:0% +on the other hand here I've got a bunch + + + align:start position:0% +on the other hand here I've got a bunch +of recursive calls I put on the stack of + + align:start position:0% +of recursive calls I put on the stack of + + + align:start position:0% +of recursive calls I put on the stack of +my computer that here I don't have so I + + align:start position:0% +my computer that here I don't have so I + + + align:start position:0% +my computer that here I don't have so I +think actually because of the overhead + + align:start position:0% +think actually because of the overhead + + + align:start position:0% +think actually because of the overhead +of recursion typically the strategy on + + align:start position:0% +of recursion typically the strategy on + + + align:start position:0% +of recursion typically the strategy on +the right is is is preferred also for + + align:start position:0% +the right is is is preferred also for + + + align:start position:0% +the right is is is preferred also for +clarity but that's a blanket statement + + align:start position:0% +clarity but that's a blanket statement + + + align:start position:0% +clarity but that's a blanket statement +that I shouldn't make okay so anyway I + + align:start position:0% +that I shouldn't make okay so anyway I + + + align:start position:0% +that I shouldn't make okay so anyway I +think i' I've done this uh this problem + + align:start position:0% +think i' I've done this uh this problem + + + align:start position:0% +think i' I've done this uh this problem +to death uh are there there any uh + + align:start position:0% +to death uh are there there any uh + + + align:start position:0% +to death uh are there there any uh +questions here I just thought I'd fill + + align:start position:0% +questions here I just thought I'd fill + + + align:start position:0% +questions here I just thought I'd fill +in for something I promised last time + + align:start position:0% +in for something I promised last time + + + align:start position:0% +in for something I promised last time +and and didn't actually + + align:start position:0% +and and didn't actually + + + align:start position:0% +and and didn't actually +do okay fabulous so we'll go on to + + align:start position:0% +do okay fabulous so we'll go on to + + + align:start position:0% +do okay fabulous so we'll go on to +problem + + align:start position:0% +problem + + + align:start position:0% +problem +92 um so this is continuing from last + + align:start position:0% +92 um so this is continuing from last + + + align:start position:0% +92 um so this is continuing from last +time in The Saga of Tim the beaver here + + align:start position:0% +time in The Saga of Tim the beaver here + + + align:start position:0% +time in The Saga of Tim the beaver here +so I forget what Tim the beaver was + + align:start position:0% +so I forget what Tim the beaver was + + + align:start position:0% +so I forget what Tim the beaver was +doing in our last problem session but + + align:start position:0% +doing in our last problem session but + + + align:start position:0% +doing in our last problem session but +today Tim the beaver is going to the + + align:start position:0% +today Tim the beaver is going to the + + + align:start position:0% +today Tim the beaver is going to the +career fair and as we all know the only + + align:start position:0% +career fair and as we all know the only + + + align:start position:0% +career fair and as we all know the only +real purpose of going to a career + + align:start position:0% +real purpose of going to a career + + + align:start position:0% +real purpose of going to a career +fair is to pick up free + + align:start position:0% +fair is to pick up free + + + align:start position:0% +fair is to pick up free +stuff um you know we joke actually you + + align:start position:0% +stuff um you know we joke actually you + + + align:start position:0% +stuff um you know we joke actually you +guys should all go to the career fair I + + align:start position:0% +guys should all go to the career fair I + + + align:start position:0% +guys should all go to the career fair I +I got my first job out of college by + + align:start position:0% +I got my first job out of college by + + + align:start position:0% +I got my first job out of college by +going to a career fair um and hanging + + align:start position:0% +going to a career fair um and hanging + + + align:start position:0% +going to a career fair um and hanging +somebody that picks our booth until they + + align:start position:0% +somebody that picks our booth until they + + + align:start position:0% +somebody that picks our booth until they +let me in uh but in any event um so Tim + + align:start position:0% +let me in uh but in any event um so Tim + + + align:start position:0% +let me in uh but in any event um so Tim +the + + align:start position:0% +the + + + align:start position:0% +the +beaver uh is not interested in getting a + + align:start position:0% +beaver uh is not interested in getting a + + + align:start position:0% +beaver uh is not interested in getting a +job but rather just wants uh swag just + + align:start position:0% +job but rather just wants uh swag just + + + align:start position:0% +job but rather just wants uh swag just +wants free stuff out of booths at the + + align:start position:0% +wants free stuff out of booths at the + + + align:start position:0% +wants free stuff out of booths at the +career fair okay uh so in in this + + align:start position:0% +career fair okay uh so in in this + + + align:start position:0% +career fair okay uh so in in this +particular problem there's n + + align:start position:0% +particular problem there's n + + + align:start position:0% +particular problem there's n +booths is it Boos certainly not boots um + + align:start position:0% +booths is it Boos certainly not boots um + + + align:start position:0% +booths is it Boos certainly not boots um +I don't know there there end booths Each + + align:start position:0% +I don't know there there end booths Each + + + align:start position:0% +I don't know there there end booths Each +of which has a swag uh and in particular + + align:start position:0% +of which has a swag uh and in particular + + + align:start position:0% +of which has a swag uh and in particular +each swag has a value Associated to it + + align:start position:0% +each swag has a value Associated to it + + + align:start position:0% +each swag has a value Associated to it +which is CI which is the + + align:start position:0% +which is CI which is the + + + align:start position:0% +which is CI which is the +coolness of object + + align:start position:0% +coolness of object + + + align:start position:0% +coolness of object +I uh it additionally has wi I this is + + align:start position:0% +I uh it additionally has wi I this is + + + align:start position:0% +I uh it additionally has wi I this is +the + + align:start position:0% +the + + + align:start position:0% +the +weight of object I + + align:start position:0% +weight of object I + + + align:start position:0% +weight of object I +and just to make this problem verbally + + align:start position:0% +and just to make this problem verbally + + + align:start position:0% +and just to make this problem verbally +difficult to communicate there's a w AI + + align:start position:0% +difficult to communicate there's a w AI + + + align:start position:0% +difficult to communicate there's a w AI +T associated with each object which is + + align:start position:0% +T associated with each object which is + + + align:start position:0% +T associated with each object which is +the time it takes to wait in line and + + align:start position:0% +the time it takes to wait in line and + + + align:start position:0% +the time it takes to wait in line and +pick up object I okay and and Tim the + + align:start position:0% +pick up object I okay and and Tim the + + + align:start position:0% +pick up object I okay and and Tim the +beaver like if there's some ridiculously + + align:start position:0% +beaver like if there's some ridiculously + + + align:start position:0% +beaver like if there's some ridiculously +cool object with like a low weight time + + align:start position:0% +cool object with like a low weight time + + + align:start position:0% +cool object with like a low weight time +he might just keep getting in line and + + align:start position:0% +he might just keep getting in line and + + + align:start position:0% +he might just keep getting in line and +and and and getting more of that object + + align:start position:0% +and and and getting more of that object + + + align:start position:0% +and and and getting more of that object +so unlike um ke nafy on our first + + align:start position:0% +so unlike um ke nafy on our first + + + align:start position:0% +so unlike um ke nafy on our first +problem uh Tim the beaver is perfectly + + align:start position:0% +problem uh Tim the beaver is perfectly + + + align:start position:0% +problem uh Tim the beaver is perfectly +happy to to have more than one of the + + align:start position:0% +happy to to have more than one of the + + + align:start position:0% +happy to to have more than one of the +same thing okay + + align:start position:0% +same thing okay + + + align:start position:0% +same thing okay +um in addition to this uh just to make + + align:start position:0% +um in addition to this uh just to make + + + align:start position:0% +um in addition to this uh just to make +this problem in my opinion slightly more + + align:start position:0% +this problem in my opinion slightly more + + + align:start position:0% +this problem in my opinion slightly more +annoying and and point losing um Tim the + + align:start position:0% +annoying and and point losing um Tim the + + + align:start position:0% +annoying and and point losing um Tim the +beaver also takes one minute to get in + + align:start position:0% +beaver also takes one minute to get in + + + align:start position:0% +beaver also takes one minute to get in +line at any booth um so we're just going + + align:start position:0% +line at any booth um so we're just going + + + align:start position:0% +line at any booth um so we're just going +to have to remember that when we account + + align:start position:0% +to have to remember that when we account + + + align:start position:0% +to have to remember that when we account +for our our time + + align:start position:0% +for our our time + + + align:start position:0% +for our our time +TI + + align:start position:0% +TI + + + align:start position:0% +TI +okay so uh let's continue adding some + + align:start position:0% +okay so uh let's continue adding some + + + align:start position:0% +okay so uh let's continue adding some +more constants to our our problem so + + align:start position:0% +more constants to our our problem so + + + align:start position:0% +more constants to our our problem so +each uh booth has an object which has + + align:start position:0% +each uh booth has an object which has + + + align:start position:0% +each uh booth has an object which has +coolness CI weight wi time TI um Tim uh + + align:start position:0% +coolness CI weight wi time TI um Tim uh + + + align:start position:0% +coolness CI weight wi time TI um Tim uh +is carrying a bag the + + align:start position:0% +is carrying a bag the + + + align:start position:0% +is carrying a bag the +bag uh has uh can can hold uh a + + align:start position:0% +bag uh has uh can can hold uh a + + + align:start position:0% +bag uh has uh can can hold uh a +particular weight B um so this is the + + align:start position:0% +particular weight B um so this is the + + + align:start position:0% +particular weight B um so this is the +max weight + + align:start position:0% +max weight + + + align:start position:0% +max weight +weight that Tim uh can hold in his bag + + align:start position:0% +weight that Tim uh can hold in his bag + + + align:start position:0% +weight that Tim uh can hold in his bag +at any given + + align:start position:0% +at any given + + + align:start position:0% +at any given +time uh and + + align:start position:0% +time uh and + + + align:start position:0% +time uh and +finally you know Tim is a a greedy + + align:start position:0% +finally you know Tim is a a greedy + + + align:start position:0% +finally you know Tim is a a greedy +Beaver but he also uh can go home uh you + + align:start position:0% +Beaver but he also uh can go home uh you + + + align:start position:0% +Beaver but he also uh can go home uh you +know or go back to his Dam I suppose uh + + align:start position:0% +know or go back to his Dam I suppose uh + + + align:start position:0% +know or go back to his Dam I suppose uh +and empty his bag right and so H is the + + align:start position:0% +and empty his bag right and so H is the + + + align:start position:0% +and empty his bag right and so H is the +amount of + + align:start position:0% +amount of + + + align:start position:0% +amount of +time uh to go + + align:start position:0% +time uh to go + + + align:start position:0% +time uh to go +home uh and + + align:start position:0% +home uh and + + + align:start position:0% +home uh and +back uh and and empty his bag in the + + align:start position:0% +back uh and and empty his bag in the + + + align:start position:0% +back uh and and empty his bag in the +meantime and again just to be annoying + + align:start position:0% +meantime and again just to be annoying + + + align:start position:0% +meantime and again just to be annoying +don't forget he encouraged plus one to + + align:start position:0% +don't forget he encouraged plus one to + + + align:start position:0% +don't forget he encouraged plus one to +get in the next line this is what made + + align:start position:0% +get in the next line this is what made + + + align:start position:0% +get in the next line this is what made +my answer wrong and I'm bitter so I'm + + align:start position:0% +my answer wrong and I'm bitter so I'm + + + align:start position:0% +my answer wrong and I'm bitter so I'm +going to keep complaining about it okay + + align:start position:0% +going to keep complaining about it okay + + + align:start position:0% +going to keep complaining about it okay +so of course uh what he wants is the max + + align:start position:0% +so of course uh what he wants is the max + + + align:start position:0% +so of course uh what he wants is the max +you know it's sort of a what would + + align:start position:0% +you know it's sort of a what would + + + align:start position:0% +you know it's sort of a what would +economists uh call this I I don't know + + align:start position:0% +economists uh call this I I don't know + + + align:start position:0% +economists uh call this I I don't know +but but for for Tim the beaver he wants + + align:start position:0% +but but for for Tim the beaver he wants + + + align:start position:0% +but but for for Tim the beaver he wants +the Max total + + align:start position:0% +the Max total + + + align:start position:0% +the Max total +coolness um or MTC uh which is of course + + align:start position:0% +coolness um or MTC uh which is of course + + + align:start position:0% +coolness um or MTC uh which is of course +a number that we're all trying to + + align:start position:0% +a number that we're all trying to + + + align:start position:0% +a number that we're all trying to +optimize um in K + + align:start position:0% +optimize um in K + + + align:start position:0% +optimize um in K +minutes like you might remember those + + align:start position:0% +minutes like you might remember those + + + align:start position:0% +minutes like you might remember those +old uh TV shows where you get like some + + align:start position:0% +old uh TV shows where you get like some + + + align:start position:0% +old uh TV shows where you get like some +like one minute in a grocery store to + + align:start position:0% +like one minute in a grocery store to + + + align:start position:0% +like one minute in a grocery store to +empty the shelves into your cart uh kind + + align:start position:0% +empty the shelves into your cart uh kind + + + align:start position:0% +empty the shelves into your cart uh kind +of thing um so he wants to do this uh + + align:start position:0% +of thing um so he wants to do this uh + + + align:start position:0% +of thing um so he wants to do this uh +and and uh the computation time that + + align:start position:0% +and and uh the computation time that + + + align:start position:0% +and and uh the computation time that +he's reserved for this is order + + align:start position:0% +he's reserved for this is order + + + align:start position:0% +he's reserved for this is order +nbk I know that was a big setup I tried + + align:start position:0% +nbk I know that was a big setup I tried + + + align:start position:0% +nbk I know that was a big setup I tried +to document all the different Conant um + + align:start position:0% +to document all the different Conant um + + + align:start position:0% +to document all the different Conant um +that are in this problem I don't think I + + align:start position:0% +that are in this problem I don't think I + + + align:start position:0% +that are in this problem I don't think I +missed any here okay fabulous so + + align:start position:0% +missed any here okay fabulous so + + + align:start position:0% +missed any here okay fabulous so +incidentally you know continuing + + align:start position:0% +incidentally you know continuing + + + align:start position:0% +incidentally you know continuing +on K uh K is the total amount of time uh + + align:start position:0% +on K uh K is the total amount of time uh + + + align:start position:0% +on K uh K is the total amount of time uh +that Tim the beaver has allotted uh to + + align:start position:0% +that Tim the beaver has allotted uh to + + + align:start position:0% +that Tim the beaver has allotted uh to +do his job fair uh uh + + align:start position:0% +do his job fair uh uh + + + align:start position:0% +do his job fair uh uh +Scavenging fabulous uh right any any + + align:start position:0% +Scavenging fabulous uh right any any + + + align:start position:0% +Scavenging fabulous uh right any any +other + + align:start position:0% +other + + + align:start position:0% +other +uh cool okay um notice that this is + + align:start position:0% +uh cool okay um notice that this is + + + align:start position:0% +uh cool okay um notice that this is +going to be an example of of a problem + + align:start position:0% +going to be an example of of a problem + + + align:start position:0% +going to be an example of of a problem +that was sort of not Kosher in last + + align:start position:0% +that was sort of not Kosher in last + + + align:start position:0% +that was sort of not Kosher in last +week's problem session in the sense that + + align:start position:0% +week's problem session in the sense that + + + align:start position:0% +week's problem session in the sense that +K is included in our runtime right but + + align:start position:0% +K is included in our runtime right but + + + align:start position:0% +K is included in our runtime right but +like what is K it's just a number K + + align:start position:0% +like what is K it's just a number K + + + align:start position:0% +like what is K it's just a number K +doesn't scale in the size of your + + align:start position:0% +doesn't scale in the size of your + + + align:start position:0% +doesn't scale in the size of your +problem in a linear way um so it's it's + + align:start position:0% +problem in a linear way um so it's it's + + + align:start position:0% +problem in a linear way um so it's it's +not going to matter for how we solve our + + align:start position:0% +not going to matter for how we solve our + + + align:start position:0% +not going to matter for how we solve our +problem but it is just a feature that's + + align:start position:0% +problem but it is just a feature that's + + + align:start position:0% +problem but it is just a feature that's +worth uh pointing + + align:start position:0% +worth uh pointing + + + align:start position:0% +worth uh pointing +out okay so how do we solve uh dynamic + + align:start position:0% +out okay so how do we solve uh dynamic + + + align:start position:0% +out okay so how do we solve uh dynamic +programming problems we use a sword poot + + align:start position:0% +programming problems we use a sword poot + + + align:start position:0% +programming problems we use a sword poot +um or a Senor uh BST uh if you are + + align:start position:0% +um or a Senor uh BST uh if you are + + + align:start position:0% +um or a Senor uh BST uh if you are +watching previous iterations of this + + align:start position:0% +watching previous iterations of this + + + align:start position:0% +watching previous iterations of this +course okay so uh right so let's let's + + align:start position:0% +course okay so uh right so let's let's + + + align:start position:0% +course okay so uh right so let's let's +do + + align:start position:0% +do + + + align:start position:0% +do +that see I'm trying to conserve board + + align:start position:0% +that see I'm trying to conserve board + + + align:start position:0% +that see I'm trying to conserve board +space this is not going to end up uh + + align:start position:0% +space this is not going to end up uh + + + align:start position:0% +space this is not going to end up uh +succeeding so again like what are all + + align:start position:0% +succeeding so again like what are all + + + align:start position:0% +succeeding so again like what are all +the different sub problems here well + + align:start position:0% +the different sub problems here well + + + align:start position:0% +the different sub problems here well +somehow what are what are the different + + align:start position:0% +somehow what are what are the different + + + align:start position:0% +somehow what are what are the different +things that are are limiting Tim the + + align:start position:0% +things that are are limiting Tim the + + + align:start position:0% +things that are are limiting Tim the +beaver you know what are what are his uh + + align:start position:0% +beaver you know what are what are his uh + + + align:start position:0% +beaver you know what are what are his uh +constraints well he only has so much + + align:start position:0% +constraints well he only has so much + + + align:start position:0% +constraints well he only has so much +time and somehow this is going to sound + + align:start position:0% +time and somehow this is going to sound + + + align:start position:0% +time and somehow this is going to sound +more philosophical than I intend but you + + align:start position:0% +more philosophical than I intend but you + + + align:start position:0% +more philosophical than I intend but you +know time always moves forward for Tim + + align:start position:0% +know time always moves forward for Tim + + + align:start position:0% +know time always moves forward for Tim +the beaver so it's a pretty good + + align:start position:0% +the beaver so it's a pretty good + + + align:start position:0% +the beaver so it's a pretty good +candidate uh in terms of of dynamic + + align:start position:0% +candidate uh in terms of of dynamic + + + align:start position:0% +candidate uh in terms of of dynamic +programming because there's not going to + + align:start position:0% +programming because there's not going to + + + align:start position:0% +programming because there's not going to +be some cyclical dependency remember + + align:start position:0% +be some cyclical dependency remember + + + align:start position:0% +be some cyclical dependency remember +that in dynamic programming we're all + + align:start position:0% +that in dynamic programming we're all + + + align:start position:0% +that in dynamic programming we're all +about trying to identify topological + + align:start position:0% +about trying to identify topological + + + align:start position:0% +about trying to identify topological +orderings in our sub problems and when + + align:start position:0% +orderings in our sub problems and when + + + align:start position:0% +orderings in our sub problems and when +you see something like time not only + + align:start position:0% +you see something like time not only + + + align:start position:0% +you see something like time not only +does it also begin with t uh but it's + + align:start position:0% +does it also begin with t uh but it's + + + align:start position:0% +does it also begin with t uh but it's +it's useful in the sense that time moves + + align:start position:0% +it's useful in the sense that time moves + + + align:start position:0% +it's useful in the sense that time moves +forward uh there's never a case where + + align:start position:0% +forward uh there's never a case where + + + align:start position:0% +forward uh there's never a case where +Tim the beaver you know purchases like a + + align:start position:0% +Tim the beaver you know purchases like a + + + align:start position:0% +Tim the beaver you know purchases like a +weird warp speed airplane and somehow + + align:start position:0% +weird warp speed airplane and somehow + + + align:start position:0% +weird warp speed airplane and somehow +goes back into in time um that that + + align:start position:0% +goes back into in time um that that + + + align:start position:0% +goes back into in time um that that +doesn't happen in this particular + + align:start position:0% +doesn't happen in this particular + + + align:start position:0% +doesn't happen in this particular +homework problem and and for Tim the + + align:start position:0% +homework problem and and for Tim the + + + align:start position:0% +homework problem and and for Tim the +beaver's sake I hope in in no homework + + align:start position:0% +beaver's sake I hope in in no homework + + + align:start position:0% +beaver's sake I hope in in no homework +problems um so instead of the so so this + + align:start position:0% +problems um so instead of the so so this + + + align:start position:0% +problems um so instead of the so so this +is a Long window way of saying that time + + align:start position:0% +is a Long window way of saying that time + + + align:start position:0% +is a Long window way of saying that time +is a pretty reasonable uh uh constraint + + align:start position:0% +is a pretty reasonable uh uh constraint + + + align:start position:0% +is a pretty reasonable uh uh constraint +to put in our problem or not constraint + + align:start position:0% +to put in our problem or not constraint + + + align:start position:0% +to put in our problem or not constraint +as much as index I + + align:start position:0% +as much as index I + + + align:start position:0% +as much as index I +guess moreover there's another thing + + align:start position:0% +guess moreover there's another thing + + + align:start position:0% +guess moreover there's another thing +which is uh limiting Tim the beaver + + align:start position:0% +which is uh limiting Tim the beaver + + + align:start position:0% +which is uh limiting Tim the beaver +which is the capacity of his bag + + align:start position:0% +which is the capacity of his bag + + + align:start position:0% +which is the capacity of his bag +remember he can only hold weight uh + + align:start position:0% +remember he can only hold weight uh + + + align:start position:0% +remember he can only hold weight uh +B but this one should give you the + + align:start position:0% +B but this one should give you the + + + align:start position:0% +B but this one should give you the +heebie jibbies a little bit because this + + align:start position:0% +heebie jibbies a little bit because this + + + align:start position:0% +heebie jibbies a little bit because this +problem as a + + align:start position:0% +problem as a + + + align:start position:0% +problem as a +Twist has allowed the bag to empty + + align:start position:0% +Twist has allowed the bag to empty + + + align:start position:0% +Twist has allowed the bag to empty +itself out right so it's not true that + + align:start position:0% +itself out right so it's not true that + + + align:start position:0% +itself out right so it's not true that +somehow you can come up with Sub sub + + align:start position:0% +somehow you can come up with Sub sub + + + align:start position:0% +somehow you can come up with Sub sub +problems where um Tim the beaver is just + + align:start position:0% +problems where um Tim the beaver is just + + + align:start position:0% +problems where um Tim the beaver is just +monotonically decreasing the weight of + + align:start position:0% +monotonically decreasing the weight of + + + align:start position:0% +monotonically decreasing the weight of +his + + align:start position:0% +his + + + align:start position:0% +his +bag however if he does choose to + + align:start position:0% +bag however if he does choose to + + + align:start position:0% +bag however if he does choose to +decrease the weight of his bag he has to + + align:start position:0% +decrease the weight of his bag he has to + + + align:start position:0% +decrease the weight of his bag he has to +spend time doing it so time continues to + + align:start position:0% +spend time doing it so time continues to + + + align:start position:0% +spend time doing it so time continues to +move forward for Tim the beaver and + + align:start position:0% +move forward for Tim the beaver and + + + align:start position:0% +move forward for Tim the beaver and +that's what's going to give us our our + + align:start position:0% +that's what's going to give us our our + + + align:start position:0% +that's what's going to give us our our +topological order yeah this is a little + + align:start position:0% +topological order yeah this is a little + + + align:start position:0% +topological order yeah this is a little +too philosophical I guess but in some + + align:start position:0% +too philosophical I guess but in some + + + align:start position:0% +too philosophical I guess but in some +sense this is a long-winded way of + + align:start position:0% +sense this is a long-winded way of + + + align:start position:0% +sense this is a long-winded way of +saying for our sbot Paradigm here um a + + align:start position:0% +saying for our sbot Paradigm here um a + + + align:start position:0% +saying for our sbot Paradigm here um a +totally reasonable thing to do would be + + align:start position:0% +totally reasonable thing to do would be + + + align:start position:0% +totally reasonable thing to do would be +to have x i + + align:start position:0% +to have x i + + + align:start position:0% +to have x i +j uh I don't think in this class we do + + align:start position:0% +j uh I don't think in this class we do + + + align:start position:0% +j uh I don't think in this class we do +this definition notation so just x i j + + align:start position:0% +this definition notation so just x i j + + + align:start position:0% +this definition notation so just x i j +equals um the max + + align:start position:0% + + + + align:start position:0% + +coolness um where he has I + + align:start position:0% +coolness um where he has I + + + align:start position:0% +coolness um where he has I +minutes uh and he has J + + align:start position:0% + + + + align:start position:0% + +weight let me glance at my answer to see + + align:start position:0% +weight let me glance at my answer to see + + + align:start position:0% +weight let me glance at my answer to see +if it's left in his bag or weight that + + align:start position:0% +if it's left in his bag or weight that + + + align:start position:0% +if it's left in his bag or weight that +he's carrying left in his bag either one + + align:start position:0% +he's carrying left in his bag either one + + + align:start position:0% +he's carrying left in his bag either one +would make a reasonable uh problem I'm + + align:start position:0% +would make a reasonable uh problem I'm + + + align:start position:0% +would make a reasonable uh problem I'm +just bad at looking at my notes and + + align:start position:0% +just bad at looking at my notes and + + + align:start position:0% +just bad at looking at my notes and +seeing them disagree with the board so + + align:start position:0% +seeing them disagree with the board so + + + align:start position:0% +seeing them disagree with the board so +I'm going to try and and and stay + + align:start position:0% +I'm going to try and and and stay + + + align:start position:0% +I'm going to try and and and stay +consistent okay so XI is the MTC but in + + align:start position:0% +consistent okay so XI is the MTC but in + + + align:start position:0% +consistent okay so XI is the MTC but in +I minutes with J weight left rather than + + align:start position:0% +I minutes with J weight left rather than + + + align:start position:0% +I minutes with J weight left rather than +in K minutes with B we which is going to + + align:start position:0% +in K minutes with B we which is going to + + + align:start position:0% +in K minutes with B we which is going to +be our base uh problem okay oh no I did + + align:start position:0% +be our base uh problem okay oh no I did + + + align:start position:0% +be our base uh problem okay oh no I did +it out of order like disregard that + + align:start position:0% +it out of order like disregard that + + + align:start position:0% +it out of order like disregard that +we'll get to the b in a minute + + align:start position:0% + + + + align:start position:0% + +okay okay so now uh so so that's our our + + align:start position:0% +okay okay so now uh so so that's our our + + + align:start position:0% +okay okay so now uh so so that's our our +our our uh sub + + align:start position:0% + + + + align:start position:0% + +problems so now uh let's do the r and + + align:start position:0% +problems so now uh let's do the r and + + + align:start position:0% +problems so now uh let's do the r and +sort + + align:start position:0% + + + + align:start position:0% + +hate this classroom so + + align:start position:0% + + + + align:start position:0% + +much I'm sorry so right so so let's say + + align:start position:0% +much I'm sorry so right so so let's say + + + align:start position:0% +much I'm sorry so right so so let's say +that that that Tim the beaver uh has has + + align:start position:0% +that that that Tim the beaver uh has has + + + align:start position:0% +that that that Tim the beaver uh has has +IM minutes left in the clock uh and he + + align:start position:0% +IM minutes left in the clock uh and he + + + align:start position:0% +IM minutes left in the clock uh and he +has J weight in his bag he's got a + + align:start position:0% +has J weight in his bag he's got a + + + align:start position:0% +has J weight in his bag he's got a +number of actions that he can take yeah + + align:start position:0% +number of actions that he can take yeah + + + align:start position:0% +number of actions that he can take yeah +uh and and let's think about what all + + align:start position:0% +uh and and let's think about what all + + + align:start position:0% +uh and and let's think about what all +those actions are by the way there's one + + align:start position:0% +those actions are by the way there's one + + + align:start position:0% +those actions are by the way there's one +thing that plausibly Tim the beaver + + align:start position:0% +thing that plausibly Tim the beaver + + + align:start position:0% +thing that plausibly Tim the beaver +could do but he doesn't really need to + + align:start position:0% +could do but he doesn't really need to + + + align:start position:0% +could do but he doesn't really need to +is is like do nothing now but then in 10 + + align:start position:0% +is is like do nothing now but then in 10 + + + align:start position:0% +is is like do nothing now but then in 10 +seconds do + + align:start position:0% +seconds do + + + align:start position:0% +seconds do +something like it just you could do + + align:start position:0% +something like it just you could do + + + align:start position:0% +something like it just you could do +account for that in this problem but + + align:start position:0% +account for that in this problem but + + + align:start position:0% +account for that in this problem but +like there's there's sort of not a + + align:start position:0% +like there's there's sort of not a + + + align:start position:0% +like there's there's sort of not a +reason right like he might as well stack + + align:start position:0% +reason right like he might as well stack + + + align:start position:0% +reason right like he might as well stack +up all of his actions and then leave all + + align:start position:0% +up all of his actions and then leave all + + + align:start position:0% +up all of his actions and then leave all +of his leftover time at the end um you + + align:start position:0% +of his leftover time at the end um you + + + align:start position:0% +of his leftover time at the end um you +convince yourself that that's sort of + + align:start position:0% +convince yourself that that's sort of + + + align:start position:0% +convince yourself that that's sort of +okay you know Tim prefers a compressed + + align:start position:0% +okay you know Tim prefers a compressed + + + align:start position:0% +okay you know Tim prefers a compressed +uh schedule um right so he's he's got a + + align:start position:0% +uh schedule um right so he's he's got a + + + align:start position:0% +uh schedule um right so he's he's got a +lot of energy this this Beaver it's what + + align:start position:0% +lot of energy this this Beaver it's what + + + align:start position:0% +lot of energy this this Beaver it's what +they say their nature is uh construction + + align:start position:0% +they say their nature is uh construction + + + align:start position:0% +they say their nature is uh construction +workers something + + align:start position:0% +workers something + + + align:start position:0% +workers something +okay right so let's think about all of + + align:start position:0% +okay right so let's think about all of + + + align:start position:0% +okay right so let's think about all of +our options so for one Tim the beaver + + align:start position:0% +our options so for one Tim the beaver + + + align:start position:0% +our options so for one Tim the beaver +could not do a damn thing he could just + + align:start position:0% +could not do a damn thing he could just + + + align:start position:0% +could not do a damn thing he could just +sit around for the rest of time and and + + align:start position:0% +sit around for the rest of time and and + + + align:start position:0% +sit around for the rest of time and and +that would be perfectly fine so another + + align:start position:0% +that would be perfectly fine so another + + + align:start position:0% +that would be perfectly fine so another +different way of putting that um is that + + align:start position:0% +different way of putting that um is that + + + align:start position:0% +different way of putting that um is that +he could give up how much coolness would + + align:start position:0% +he could give up how much coolness would + + + align:start position:0% +he could give up how much coolness would +Tim get from giving up zero that's right + + align:start position:0% +Tim get from giving up zero that's right + + + align:start position:0% +Tim get from giving up zero that's right +kids giving up makes you zero cool um so + + align:start position:0% +kids giving up makes you zero cool um so + + + align:start position:0% +kids giving up makes you zero cool um so +okay uh right so um Tim the beaver is + + align:start position:0% +okay uh right so um Tim the beaver is + + + align:start position:0% +okay uh right so um Tim the beaver is +trying to maximize uh he has a lot of + + align:start position:0% +trying to maximize uh he has a lot of + + + align:start position:0% +trying to maximize uh he has a lot of +different options one of them is zero + + align:start position:0% + + + + align:start position:0% + +meaning he gave + + align:start position:0% +meaning he gave + + + align:start position:0% +meaning he gave +up right notice he could recurse like X + + align:start position:0% +up right notice he could recurse like X + + + align:start position:0% +up right notice he could recurse like X +I guess what would be you know he could + + align:start position:0% +I guess what would be you know he could + + + align:start position:0% +I guess what would be you know he could +give up for one minute right and have + + align:start position:0% +give up for one minute right and have + + + align:start position:0% +give up for one minute right and have +that be X IUS one J or something um + + align:start position:0% +that be X IUS one J or something um + + + align:start position:0% +that be X IUS one J or something um +forget if I'm going to do i+ one or IUS + + align:start position:0% +forget if I'm going to do i+ one or IUS + + + align:start position:0% +forget if I'm going to do i+ one or IUS +one I minus one + + align:start position:0% +one I minus one + + + align:start position:0% +one I minus one +J but there's no reason like he can just + + align:start position:0% +J but there's no reason like he can just + + + align:start position:0% +J but there's no reason like he can just +give up and and stop like that would + + align:start position:0% +give up and and stop like that would + + + align:start position:0% +give up and and stop like that would +just be extra recursive calls for For No + + align:start position:0% +just be extra recursive calls for For No + + + align:start position:0% +just be extra recursive calls for For No +Good + + align:start position:0% +Good + + + align:start position:0% +Good +Reason okay the next thing that he could + + align:start position:0% +Reason okay the next thing that he could + + + align:start position:0% +Reason okay the next thing that he could +do is he could get in for a booth right + + align:start position:0% +do is he could get in for a booth right + + + align:start position:0% +do is he could get in for a booth right +um so first let's work out what happens + + align:start position:0% +um so first let's work out what happens + + + align:start position:0% +um so first let's work out what happens +uh then so for one um he gets coolness + + align:start position:0% +uh then so for one um he gets coolness + + + align:start position:0% +uh then so for one um he gets coolness +let's say that he gets into Booth K so + + align:start position:0% +let's say that he gets into Booth K so + + + align:start position:0% +let's say that he gets into Booth K so +he gets coolness CK when he does + + align:start position:0% +he gets coolness CK when he does + + + align:start position:0% +he gets coolness CK when he does +that and now he can recurse so first we + + align:start position:0% +that and now he can recurse so first we + + + align:start position:0% +that and now he can recurse so first we +have to account for the time so it takes + + align:start position:0% +have to account for the time so it takes + + + align:start position:0% +have to account for the time so it takes +I so it takes TK that's a + + align:start position:0% +I so it takes TK that's a + + + align:start position:0% +I so it takes TK that's a +t time or does it no because it takes an + + align:start position:0% +t time or does it no because it takes an + + + align:start position:0% +t time or does it no because it takes an +extra minute for him to get in the next + + align:start position:0% +extra minute for him to get in the next + + + align:start position:0% +extra minute for him to get in the next +line or to get in this line line I guess + + align:start position:0% +line or to get in this line line I guess + + + align:start position:0% +line or to get in this line line I guess +this is better um and + + align:start position:0% +this is better um and + + + align:start position:0% +this is better um and +moreover uh he needs to account for J + + align:start position:0% +moreover uh he needs to account for J + + + align:start position:0% +moreover uh he needs to account for J +minus WK like that can he always do this + + align:start position:0% +minus WK like that can he always do this + + + align:start position:0% +minus WK like that can he always do this +no he needs to have this much time + + align:start position:0% +no he needs to have this much time + + + align:start position:0% +no he needs to have this much time +remaining and he needs this much time in + + align:start position:0% +remaining and he needs this much time in + + + align:start position:0% +remaining and he needs this much time in +his bag + + align:start position:0% +his bag + + + align:start position:0% +his bag +or this much weight remaining in his bag + + align:start position:0% +or this much weight remaining in his bag + + + align:start position:0% +or this much weight remaining in his bag +um you guys can work out the inequality + + align:start position:0% +um you guys can work out the inequality + + + align:start position:0% +um you guys can work out the inequality +but since I only have a foot here I'll + + align:start position:0% +but since I only have a foot here I'll + + + align:start position:0% +but since I only have a foot here I'll +just say if + + align:start position:0% +just say if + + + align:start position:0% +just say if +applicable + + align:start position:0% +applicable + + + align:start position:0% +applicable +this is a great way to lose points on + + align:start position:0% +this is a great way to lose points on + + + align:start position:0% +this is a great way to lose points on +your homework uh but for Board Writing + + align:start position:0% +your homework uh but for Board Writing + + + align:start position:0% +your homework uh but for Board Writing +it's okay so so when I say applicable I + + align:start position:0% +it's okay so so when I say applicable I + + + align:start position:0% +it's okay so so when I say applicable I +mean these two numbers have better be + + align:start position:0% +mean these two numbers have better be + + + align:start position:0% +mean these two numbers have better be +greater than or equal to zero okay uh + + align:start position:0% +greater than or equal to zero okay uh + + + align:start position:0% +greater than or equal to zero okay uh +and you can do this for all K right so + + align:start position:0% +and you can do this for all K right so + + + align:start position:0% +and you can do this for all K right so +in other words he can choose to get into + + align:start position:0% +in other words he can choose to get into + + + align:start position:0% +in other words he can choose to get into +Booth + + align:start position:0% +Booth + + + align:start position:0% +Booth +K and Tim has the third option which is + + align:start position:0% +K and Tim has the third option which is + + + align:start position:0% +K and Tim has the third option which is +he can go home okay so what happens if + + align:start position:0% +he can go home okay so what happens if + + + align:start position:0% +he can go home okay so what happens if +he goes home does he is he cool when he + + align:start position:0% +he goes home does he is he cool when he + + + align:start position:0% +he goes home does he is he cool when he +does Tim the beaver get cooler when he + + align:start position:0% +does Tim the beaver get cooler when he + + + align:start position:0% +does Tim the beaver get cooler when he +goes home + + align:start position:0% +goes home + + + align:start position:0% +goes home +no I'm afraid to to to say so + + align:start position:0% +no I'm afraid to to to say so + + + align:start position:0% +no I'm afraid to to to say so +um in par but he does spend time yeah so + + align:start position:0% +um in par but he does spend time yeah so + + + align:start position:0% +um in par but he does spend time yeah so +how much time does he + + align:start position:0% +how much time does he + + + align:start position:0% +how much time does he +spend + + align:start position:0% + + + + align:start position:0% + +age what was + + align:start position:0% +age what was + + + align:start position:0% +age what was +that he should have lost coolness by + + align:start position:0% +that he should have lost coolness by + + + align:start position:0% +that he should have lost coolness by +going home no home is cool guys + + align:start position:0% +going home no home is cool guys + + + align:start position:0% +going home no home is cool guys +especially this semester stay home stay + + align:start position:0% +especially this semester stay home stay + + + align:start position:0% +especially this semester stay home stay +indoors um so he he uh right so he he + + align:start position:0% +indoors um so he he uh right so he he + + + align:start position:0% +indoors um so he he uh right so he he +loses home time H and one to get in the + + align:start position:0% +loses home time H and one to get in the + + + align:start position:0% +loses home time H and one to get in the +next line okay um but you know he's got + + align:start position:0% +next line okay um but you know he's got + + + align:start position:0% +next line okay um but you know he's got +a devil's bargain of sorts uh he he he + + align:start position:0% +a devil's bargain of sorts uh he he he + + + align:start position:0% +a devil's bargain of sorts uh he he he +loses time but he gains bag bagginess + + align:start position:0% +loses time but he gains bag bagginess + + + align:start position:0% +loses time but he gains bag bagginess +weight is the word that I'm looking for + + align:start position:0% +weight is the word that I'm looking for + + + align:start position:0% +weight is the word that I'm looking for +um B like that okay um again in this + + align:start position:0% +um B like that okay um again in this + + + align:start position:0% +um B like that okay um again in this +case remember that he still needs if I + + align:start position:0% +case remember that he still needs if I + + + align:start position:0% +case remember that he still needs if I +is greater than H right otherwise he's + + align:start position:0% +is greater than H right otherwise he's + + + align:start position:0% +is greater than H right otherwise he's +in + + align:start position:0% +in + + + align:start position:0% +in +trouble by the way I wrote this in kind + + align:start position:0% +trouble by the way I wrote this in kind + + + align:start position:0% +trouble by the way I wrote this in kind +of an annoying way this is a different + + align:start position:0% +of an annoying way this is a different + + + align:start position:0% +of an annoying way this is a different +way of saying that is IUS H minus one is + + align:start position:0% +way of saying that is IUS H minus one is + + + align:start position:0% +way of saying that is IUS H minus one is +greater than equal to zero which is + + align:start position:0% +greater than equal to zero which is + + + align:start position:0% +greater than equal to zero which is +really what's applicable in our + + align:start position:0% +really what's applicable in our + + + align:start position:0% +really what's applicable in our +recursive call but this is strict + + align:start position:0% +recursive call but this is strict + + + align:start position:0% +recursive call but this is strict +greater than sign that was another + + align:start position:0% +greater than sign that was another + + + align:start position:0% +greater than sign that was another +little thing that caught me up when I + + align:start position:0% +little thing that caught me up when I + + + align:start position:0% +little thing that caught me up when I +was reading the answer here okay and + + align:start position:0% +was reading the answer here okay and + + + align:start position:0% +was reading the answer here okay and +those are all the options for Tim the + + align:start position:0% +those are all the options for Tim the + + + align:start position:0% +those are all the options for Tim the +beaver yeah um notice that every one of + + align:start position:0% +beaver yeah um notice that every one of + + + align:start position:0% +beaver yeah um notice that every one of +our options either gives up + + align:start position:0% +our options either gives up + + + align:start position:0% +our options either gives up +completely or decreases time so we have + + align:start position:0% +completely or decreases time so we have + + + align:start position:0% +completely or decreases time so we have +our topological order which is again + + align:start position:0% +our topological order which is again + + + align:start position:0% +our topological order which is again +that the arrow of time always continues + + align:start position:0% +that the arrow of time always continues + + + align:start position:0% +that the arrow of time always continues +to move forward I'm going to prove that + + align:start position:0% +to move forward I'm going to prove that + + + align:start position:0% +to move forward I'm going to prove that +rigorously by putting a check mark next + + align:start position:0% +rigorously by putting a check mark next + + + align:start position:0% +rigorously by putting a check mark next +to the letter T again on your homework + + align:start position:0% +to the letter T again on your homework + + + align:start position:0% +to the letter T again on your homework +you should write out your answers uh + + align:start position:0% +you should write out your answers uh + + + align:start position:0% +you should write out your answers uh +what is our base case for + + align:start position:0% +what is our base case for + + + align:start position:0% +what is our base case for +Tim + + align:start position:0% +Tim + + + align:start position:0% +Tim +well how much coolness do you get if you + + align:start position:0% +well how much coolness do you get if you + + + align:start position:0% +well how much coolness do you get if you +have no time zero coolness that's how + + align:start position:0% +have no time zero coolness that's how + + + align:start position:0% +have no time zero coolness that's how +much um + + align:start position:0% + + + + align:start position:0% + +so we have this expression x0j equals z + + align:start position:0% +so we have this expression x0j equals z + + + align:start position:0% +so we have this expression x0j equals z +for all J incidentally um although it's + + align:start position:0% +for all J incidentally um although it's + + + align:start position:0% +for all J incidentally um although it's +perfectly fine to have this be your your + + align:start position:0% +perfectly fine to have this be your your + + + align:start position:0% +perfectly fine to have this be your your +base case you actually in some sense + + align:start position:0% +base case you actually in some sense + + + align:start position:0% +base case you actually in some sense +didn't need it because Tim the beaver + + align:start position:0% +didn't need it because Tim the beaver + + + align:start position:0% +didn't need it because Tim the beaver +always had the option of giving up um so + + align:start position:0% +always had the option of giving up um so + + + align:start position:0% +always had the option of giving up um so +you could I guess in this problem have + + align:start position:0% +you could I guess in this problem have + + + align:start position:0% +you could I guess in this problem have +no base case if you really wanted um + + align:start position:0% +no base case if you really wanted um + + + align:start position:0% +no base case if you really wanted um +would be okay but kind of + + align:start position:0% +would be okay but kind of + + + align:start position:0% +would be okay but kind of +weird um + + align:start position:0% +weird um + + + align:start position:0% +weird um +okay what's our original problem well he + + align:start position:0% +okay what's our original problem well he + + + align:start position:0% +okay what's our original problem well he +starts out with time K and weight uh + + align:start position:0% +starts out with time K and weight uh + + + align:start position:0% +starts out with time K and weight uh +capacity B in his bag so it's x k b and + + align:start position:0% +capacity B in his bag so it's x k b and + + + align:start position:0% +capacity B in his bag so it's x k b and +then finally uh we need to do our + + align:start position:0% +then finally uh we need to do our + + + align:start position:0% +then finally uh we need to do our +runtime + + align:start position:0% +runtime + + + align:start position:0% +runtime +analysis so how many sub problems are + + align:start position:0% +analysis so how many sub problems are + + + align:start position:0% +analysis so how many sub problems are +there well again I sub problem is + + align:start position:0% +there well again I sub problem is + + + align:start position:0% +there well again I sub problem is +basically just the number of indexes for + + align:start position:0% +basically just the number of indexes for + + + align:start position:0% +basically just the number of indexes for +for most of our our dynamic programming + + align:start position:0% +for most of our our dynamic programming + + + align:start position:0% +for most of our our dynamic programming +problems right so there's + + align:start position:0% +problems right so there's + + + align:start position:0% +problems right so there's +um so the first index is time the second + + align:start position:0% +um so the first index is time the second + + + align:start position:0% +um so the first index is time the second +one is bag size this is always between + + align:start position:0% +one is bag size this is always between + + + align:start position:0% +one is bag size this is always between +zero and B this is always between zero + + align:start position:0% +zero and B this is always between zero + + + align:start position:0% +zero and B this is always between zero +and K so there's order k b sub + + align:start position:0% +and K so there's order k b sub + + + align:start position:0% +and K so there's order k b sub +problems um how much time does each sub + + align:start position:0% +problems um how much time does each sub + + + align:start position:0% +problems um how much time does each sub +problem take well notice that I have to + + align:start position:0% +problem take well notice that I have to + + + align:start position:0% +problem take well notice that I have to +lose + + align:start position:0% +lose + + + align:start position:0% +lose +over all of my different options K here + + align:start position:0% +over all of my different options K here + + + align:start position:0% +over all of my different options K here +so I + + align:start position:0% + + + + align:start position:0% + +incur oh I'm + + align:start position:0% +incur oh I'm + + + align:start position:0% +incur oh I'm +noticing K is abused in our answer to + + align:start position:0% +noticing K is abused in our answer to + + + align:start position:0% +noticing K is abused in our answer to +this problem we should use K only + + align:start position:0% +this problem we should use K only + + + align:start position:0% +this problem we should use K only +once okay so here's here's here's where + + align:start position:0% +once okay so here's here's here's where + + + align:start position:0% +once okay so here's here's here's where +uh I made a mistake and I believe it's + + align:start position:0% +uh I made a mistake and I believe it's + + + align:start position:0% +uh I made a mistake and I believe it's +in the written solution but I'm not + + align:start position:0% +in the written solution but I'm not + + + align:start position:0% +in the written solution but I'm not +going to check now um there's K which is + + align:start position:0% +going to check now um there's K which is + + + align:start position:0% +going to check now um there's K which is +the total time that Tim the beaver has + + align:start position:0% +the total time that Tim the beaver has + + + align:start position:0% +the total time that Tim the beaver has +and there's the K that I use as an index + + align:start position:0% +and there's the K that I use as an index + + + align:start position:0% +and there's the K that I use as an index +here and those are are not the same I + + align:start position:0% +here and those are are not the same I + + + align:start position:0% +here and those are are not the same I +guess I can make this K Bar really + + align:start position:0% +guess I can make this K Bar really + + + align:start position:0% +guess I can make this K Bar really +fast there you go problem + + align:start position:0% +fast there you go problem + + + align:start position:0% +fast there you go problem +solve and I just noticed that because I + + align:start position:0% +solve and I just noticed that because I + + + align:start position:0% +solve and I just noticed that because I +was doing my runtime and it's not order + + align:start position:0% +was doing my runtime and it's not order + + + align:start position:0% +was doing my runtime and it's not order +k um it's the loop over all the K + + align:start position:0% +k um it's the loop over all the K + + + align:start position:0% +k um it's the loop over all the K +bars how many K bars are there well + + align:start position:0% +bars how many K bars are there well + + + align:start position:0% +bars how many K bars are there well +these are all the different booths and + + align:start position:0% +these are all the different booths and + + + align:start position:0% +these are all the different booths and +there's order n of those so this is + + align:start position:0% +there's order n of those so this is + + + align:start position:0% +there's order n of those so this is +order n time per sub problem which gives + + align:start position:0% +order n time per sub problem which gives + + + align:start position:0% +order n time per sub problem which gives +me a total runtime of order K + + align:start position:0% +me a total runtime of order K + + + align:start position:0% +me a total runtime of order K +BN um which I believe uh oh our desired + + align:start position:0% +BN um which I believe uh oh our desired + + + align:start position:0% +BN um which I believe uh oh our desired +run time was order nbk but I think we + + align:start position:0% +run time was order nbk but I think we + + + align:start position:0% +run time was order nbk but I think we +can convince ourselves that indeed those + + align:start position:0% +can convince ourselves that indeed those + + + align:start position:0% +can convince ourselves that indeed those +are are the same thing okay so my + + align:start position:0% +are are the same thing okay so my + + + align:start position:0% +are are the same thing okay so my +apologies for a slight uh uh overloaded + + align:start position:0% +apologies for a slight uh uh overloaded + + + align:start position:0% +apologies for a slight uh uh overloaded +uh character here but honestly it's kind + + align:start position:0% +uh character here but honestly it's kind + + + align:start position:0% +uh character here but honestly it's kind +of one of those things if you read the + + align:start position:0% +of one of those things if you read the + + + align:start position:0% +of one of those things if you read the +answer you probably wouldn't even notice + + align:start position:0% +answer you probably wouldn't even notice + + + align:start position:0% +answer you probably wouldn't even notice +but now that I'm saying it out loud I I + + align:start position:0% +but now that I'm saying it out loud I I + + + align:start position:0% +but now that I'm saying it out loud I I +am okay and that uh solves uh Tim the + + align:start position:0% +am okay and that uh solves uh Tim the + + + align:start position:0% +am okay and that uh solves uh Tim the +beaver's uh maximization problem he's a + + align:start position:0% +beaver's uh maximization problem he's a + + + align:start position:0% +beaver's uh maximization problem he's a +very cool Beaver any uh any questions + + align:start position:0% +very cool Beaver any uh any questions + + + align:start position:0% +very cool Beaver any uh any questions +about this one notice that both of these + + align:start position:0% +about this one notice that both of these + + + align:start position:0% +about this one notice that both of these +problems are are very similar in nature + + align:start position:0% +problems are are very similar in nature + + + align:start position:0% +problems are are very similar in nature +I basically just wrote sub Problems + + align:start position:0% +I basically just wrote sub Problems + + + align:start position:0% +I basically just wrote sub Problems +indexed by every possible thing uh and + + align:start position:0% +indexed by every possible thing uh and + + + align:start position:0% +indexed by every possible thing uh and +then enumerated every possible solution + + align:start position:0% +then enumerated every possible solution + + + align:start position:0% +then enumerated every possible solution +U I think this is totally sensible like + + align:start position:0% +U I think this is totally sensible like + + + align:start position:0% +U I think this is totally sensible like +I again I remember I had a math + + align:start position:0% +I again I remember I had a math + + + align:start position:0% +I again I remember I had a math +professor in college that always would + + align:start position:0% +professor in college that always would + + + align:start position:0% +professor in college that always would +use this phrase like it's important not + + align:start position:0% +use this phrase like it's important not + + + align:start position:0% +use this phrase like it's important not +to think here um and and I think this is + + align:start position:0% +to think here um and and I think this is + + + align:start position:0% +to think here um and and I think this is +is absolutely true uh for these dynamic + + align:start position:0% +is absolutely true uh for these dynamic + + + align:start position:0% +is absolutely true uh for these dynamic +programming problems somehow they look a + + align:start position:0% +programming problems somehow they look a + + + align:start position:0% +programming problems somehow they look a +lot more complicated than they + + align:start position:0% +lot more complicated than they + + + align:start position:0% +lot more complicated than they +are fabulous so problem three protein + + align:start position:0% +are fabulous so problem three protein + + + align:start position:0% +are fabulous so problem three protein +parsing ah yeah so this one + + align:start position:0% +parsing ah yeah so this one + + + align:start position:0% +parsing ah yeah so this one +this one also got me tripped up for a + + align:start position:0% +this one also got me tripped up for a + + + align:start position:0% +this one also got me tripped up for a +minute because the runtime they want is + + align:start position:0% +minute because the runtime they want is + + + align:start position:0% +minute because the runtime they want is +not the runtime of the obvious solution + + align:start position:0% +not the runtime of the obvious solution + + + align:start position:0% +not the runtime of the obvious solution +but it kind of sort of is after a little + + align:start position:0% +but it kind of sort of is after a little + + + align:start position:0% +but it kind of sort of is after a little +bit of uh uh fixing okay so uh Professor + + align:start position:0% +bit of uh uh fixing okay so uh Professor + + + align:start position:0% +bit of uh uh fixing okay so uh Professor +uh laric Ander uh has a + + align:start position:0% +uh laric Ander uh has a + + + align:start position:0% +uh laric Ander uh has a +laboratory and that laboratory processes + + align:start position:0% +laboratory and that laboratory processes + + + align:start position:0% +laboratory and that laboratory processes +DNA Tada um okay so let me go to my + + align:start position:0% +DNA Tada um okay so let me go to my + + + align:start position:0% +DNA Tada um okay so let me go to my +notes here because I think they're + + align:start position:0% +notes here because I think they're + + + align:start position:0% +notes here because I think they're +easier to + + align:start position:0% +easier to + + + align:start position:0% +easier to +read right so a of DNA as we all know + + align:start position:0% +read right so a of DNA as we all know + + + align:start position:0% +read right so a of DNA as we all know +because we're MIT + + align:start position:0% +because we're MIT + + + align:start position:0% +because we're MIT +students uh is is equal to basically + + align:start position:0% +students uh is is equal to basically + + + align:start position:0% +students uh is is equal to basically +strand of characters that are like a and + + align:start position:0% +strand of characters that are like a and + + + align:start position:0% +strand of characters that are like a and +g if you ask me to name what those stood + + align:start position:0% +g if you ask me to name what those stood + + + align:start position:0% +g if you ask me to name what those stood +for I I could make a stab at like one or + + align:start position:0% +for I I could make a stab at like one or + + + align:start position:0% +for I I could make a stab at like one or +two of them but I'm a failure of a like + + align:start position:0% +two of them but I'm a failure of a like + + + align:start position:0% +two of them but I'm a failure of a like +I did not have the G because I went to + + align:start position:0% +I did not have the G because I went to + + + align:start position:0% +I did not have the G because I went to +Stanford and this is why I'm apparently + + align:start position:0% +Stanford and this is why I'm apparently + + + align:start position:0% +Stanford and this is why I'm apparently +a poorly educated person according to a + + align:start position:0% +a poorly educated person according to a + + + align:start position:0% +a poorly educated person according to a +person in a faculty meeting um but in + + align:start position:0% +person in a faculty meeting um but in + + + align:start position:0% +person in a faculty meeting um but in +any event um + + align:start position:0% +any event um + + + align:start position:0% +any event um +right so we have a strand of DNA is + + align:start position:0% +right so we have a strand of DNA is + + + align:start position:0% +right so we have a strand of DNA is +basically a long string of characters + + align:start position:0% +basically a long string of characters + + + align:start position:0% +basically a long string of characters +that are one of four options I'm told + + align:start position:0% +that are one of four options I'm told + + + align:start position:0% +that are one of four options I'm told +that there's sometimes like a fifth and + + align:start position:0% +that there's sometimes like a fifth and + + + align:start position:0% +that there's sometimes like a fifth and +a sixth option but not too often this + + align:start position:0% +a sixth option but not too often this + + + align:start position:0% +a sixth option but not too often this +problem there's not um and uh moreover + + align:start position:0% +problem there's not um and uh moreover + + + align:start position:0% +problem there's not um and uh moreover +um so a strand can be cut up so I have + + align:start position:0% +um so a strand can be cut up so I have + + + align:start position:0% +um so a strand can be cut up so I have +this big long Strand and I'm looking for + + align:start position:0% +this big long Strand and I'm looking for + + + align:start position:0% +this big long Strand and I'm looking for +certain like markers in particular I + + align:start position:0% +certain like markers in particular I + + + align:start position:0% +certain like markers in particular I +have a + + align:start position:0% +have a + + + align:start position:0% +have a +list P of uh + + align:start position:0% +list P of uh + + + align:start position:0% +list P of uh +markers um which are really a sequence + + align:start position:0% +markers um which are really a sequence + + + align:start position:0% +markers um which are really a sequence +of less than or equal to K uh + + align:start position:0% + + + + align:start position:0% + +nucleotides by the way this really is uh + + align:start position:0% +nucleotides by the way this really is uh + + + align:start position:0% +nucleotides by the way this really is uh +something that the people do like like + + align:start position:0% +something that the people do like like + + + align:start position:0% +something that the people do like like +string searching really is applicable to + + align:start position:0% +string searching really is applicable to + + + align:start position:0% +string searching really is applicable to +processing the these DNA strands + + align:start position:0% +processing the these DNA strands + + + align:start position:0% +processing the these DNA strands +obviously I think in in practice these + + align:start position:0% +obviously I think in in practice these + + + align:start position:0% +obviously I think in in practice these +techniques have to be a lot more + + align:start position:0% +techniques have to be a lot more + + + align:start position:0% +techniques have to be a lot more +resilient to error um but really A lot + + align:start position:0% +resilient to error um but really A lot + + + align:start position:0% +resilient to error um but really A lot +of these algorithm recovering are not + + align:start position:0% +of these algorithm recovering are not + + + align:start position:0% +of these algorithm recovering are not +all that far off from from how people + + align:start position:0% +all that far off from from how people + + + align:start position:0% +all that far off from from how people +process these giant data sets which is + + align:start position:0% +process these giant data sets which is + + + align:start position:0% +process these giant data sets which is +pretty cool I think um okay so what are + + align:start position:0% +pretty cool I think um okay so what are + + + align:start position:0% +pretty cool I think um okay so what are +we going to do we have uh a string uh + + align:start position:0% +we going to do we have uh a string uh + + + align:start position:0% +we going to do we have uh a string uh +and then we're going to make a division + + align:start position:0% + + + + align:start position:0% + +um so we'll call our string s and our + + align:start position:0% +um so we'll call our string s and our + + + align:start position:0% +um so we'll call our string s and our +division D um which kind of looks like + + align:start position:0% +division D um which kind of looks like + + + align:start position:0% +division D um which kind of looks like +D1 to + + align:start position:0% +D1 to + + + align:start position:0% +D1 to +DM which are uh + + align:start position:0% +DM which are uh + + + align:start position:0% +DM which are uh +substrings uh that concatenate to make + + align:start position:0% +substrings uh that concatenate to make + + + align:start position:0% +substrings uh that concatenate to make +uh uh the full the full + + align:start position:0% +uh uh the full the full + + + align:start position:0% +uh uh the full the full +guy + + align:start position:0% + + + + align:start position:0% + +so if s is our our our input string then + + align:start position:0% +so if s is our our our input string then + + + align:start position:0% +so if s is our our our input string then +a division D is just like chopping up S + + align:start position:0% +a division D is just like chopping up S + + + align:start position:0% +a division D is just like chopping up S +into little substrings uh Each of which + + align:start position:0% +into little substrings uh Each of which + + + align:start position:0% +into little substrings uh Each of which +we can give a name Little D here so big + + align:start position:0% +we can give a name Little D here so big + + + align:start position:0% +we can give a name Little D here so big +D is the full uh division Little D is is + + align:start position:0% +D is the full uh division Little D is is + + + align:start position:0% +D is the full uh division Little D is is +all the little pieces you know there's + + align:start position:0% +all the little pieces you know there's + + + align:start position:0% +all the little pieces you know there's +that that old song about going through + + align:start position:0% +that that old song about going through + + + align:start position:0% +that that old song about going through +the Big D and do me Dallas I think it's + + align:start position:0% +the Big D and do me Dallas I think it's + + + align:start position:0% +the Big D and do me Dallas I think it's +for divorce I don't know um right so uh + + align:start position:0% +for divorce I don't know um right so uh + + + align:start position:0% +for divorce I don't know um right so uh +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the + + align:start position:0% +so the + + + align:start position:0% +so the +value of a + + align:start position:0% + + + + align:start position:0% + +division is the number of uh + + align:start position:0% +division is the number of uh + + + align:start position:0% +division is the number of uh +strands so strands are these little D's + + align:start position:0% +strands so strands are these little D's + + + align:start position:0% +strands so strands are these little D's +here + + align:start position:0% +here + + + align:start position:0% +here +um that are in our list uh P okay uh and + + align:start position:0% +um that are in our list uh P okay uh and + + + align:start position:0% +um that are in our list uh P okay uh and +so uh right so given S and P what we + + align:start position:0% +so uh right so given S and P what we + + + align:start position:0% +so uh right so given S and P what we +want is the max + + align:start position:0% + + + + align:start position:0% + +value + + align:start position:0% +value + + + align:start position:0% +value +and the runtime that we're budgeted is + + align:start position:0% +and the runtime that we're budgeted is + + + align:start position:0% +and the runtime that we're budgeted is +kind of a weird runtime and this should + + align:start position:0% +kind of a weird runtime and this should + + + align:start position:0% +kind of a weird runtime and this should +make us a little suspicious um so the + + align:start position:0% +make us a little suspicious um so the + + + align:start position:0% +make us a little suspicious um so the +the max value is Big + + align:start position:0% +the max value is Big + + + align:start position:0% +the max value is Big +O of I think I wrote it slightly + + align:start position:0% +O of I think I wrote it slightly + + + align:start position:0% +O of I think I wrote it slightly +differently in the problem but whatever + + align:start position:0% +differently in the problem but whatever + + + align:start position:0% +differently in the problem but whatever +I distributed a + + align:start position:0% +I distributed a + + + align:start position:0% +I distributed a +k like that so it's K mod P uh plus k^ s + + align:start position:0% +k like that so it's K mod P uh plus k^ s + + + align:start position:0% +k like that so it's K mod P uh plus k^ s +mod s right so so we have two terms here + + align:start position:0% +mod s right so so we have two terms here + + + align:start position:0% +mod s right so so we have two terms here +which somehow smells funny in dynamic + + align:start position:0% +which somehow smells funny in dynamic + + + align:start position:0% +which somehow smells funny in dynamic +programming okay + + align:start position:0% +programming okay + + + align:start position:0% +programming okay +so what are we to do well what I did is + + align:start position:0% +so what are we to do well what I did is + + + align:start position:0% +so what are we to do well what I did is +I ignored our desired runtime came up + + align:start position:0% +I ignored our desired runtime came up + + + align:start position:0% +I ignored our desired runtime came up +with a dynamic program noticed that it + + align:start position:0% +with a dynamic program noticed that it + + + align:start position:0% +with a dynamic program noticed that it +was a little wrong and then fixed it by + + align:start position:0% +was a little wrong and then fixed it by + + + align:start position:0% +was a little wrong and then fixed it by +wrong I mean it was it was correct it + + align:start position:0% +wrong I mean it was it was correct it + + + align:start position:0% +wrong I mean it was it was correct it +just wasn't fast enough okay so let's do + + align:start position:0% +just wasn't fast enough okay so let's do + + + align:start position:0% +just wasn't fast enough okay so let's do +version one + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% +here + + + align:start position:0% +here +1.0 that makes it more + + align:start position:0% +1.0 that makes it more + + + align:start position:0% +1.0 that makes it more +accurate um they're more precise right I + + align:start position:0% +accurate um they're more precise right I + + + align:start position:0% +accurate um they're more precise right I +always confuse those two uh so so here's + + align:start position:0% +always confuse those two uh so so here's + + + align:start position:0% +always confuse those two uh so so here's +a sort of thing that it's going to be a + + align:start position:0% +a sort of thing that it's going to be a + + + align:start position:0% +a sort of thing that it's going to be a +little bit funny because it's going to + + align:start position:0% +little bit funny because it's going to + + + align:start position:0% +little bit funny because it's going to +look like we're going to have an easy + + align:start position:0% +look like we're going to have an easy + + + align:start position:0% +look like we're going to have an easy +computational problem but then it's + + align:start position:0% +computational problem but then it's + + + align:start position:0% +computational problem but then it's +going to turn out that it's actually too + + align:start position:0% +going to turn out that it's actually too + + + align:start position:0% +going to turn out that it's actually too +slow so in particular uh in our s in + + align:start position:0% +slow so in particular uh in our s in + + + align:start position:0% +slow so in particular uh in our s in +sbot um what we could do is + + align:start position:0% +sbot um what we could do is + + + align:start position:0% +sbot um what we could do is +say XI is going to be the + + align:start position:0% +say XI is going to be the + + + align:start position:0% +say XI is going to be the +max + + align:start position:0% +max + + + align:start position:0% +max +value of a + + align:start position:0% +value of a + + + align:start position:0% +value of a +suffix if you're wondering I don't know + + align:start position:0% +suffix if you're wondering I don't know + + + align:start position:0% +suffix if you're wondering I don't know +the difference between prefix and suffix + + align:start position:0% +the difference between prefix and suffix + + + align:start position:0% +the difference between prefix and suffix +but I wrote the word suffix in my notes + + align:start position:0% +but I wrote the word suffix in my notes + + + align:start position:0% +but I wrote the word suffix in my notes +and checked it at home + + align:start position:0% +and checked it at home + + + align:start position:0% +and checked it at home +um s i comma colon see it's suffix + + align:start position:0% +um s i comma colon see it's suffix + + + align:start position:0% +um s i comma colon see it's suffix +because it starts at I and it goes to + + align:start position:0% +because it starts at I and it goes to + + + align:start position:0% +because it starts at I and it goes to +the end huh no + + align:start position:0% +the end huh no + + + align:start position:0% +the end huh no +comma in mat lab it would be a comma and + + align:start position:0% +comma in mat lab it would be a comma and + + + align:start position:0% +comma in mat lab it would be a comma and +that's a colon and that's an i okay + + align:start position:0% +that's a colon and that's an i okay + + + align:start position:0% +that's a colon and that's an i okay +thanks um I'm inventing my own + + align:start position:0% +thanks um I'm inventing my own + + + align:start position:0% +thanks um I'm inventing my own +programming language on the board as we + + align:start position:0% +programming language on the board as we + + + align:start position:0% +programming language on the board as we +go + + align:start position:0% +go + + + align:start position:0% +go +today all right so um and notice this is + + align:start position:0% +today all right so um and notice this is + + + align:start position:0% +today all right so um and notice this is +kind of a reasonable set of sub problems + + align:start position:0% +kind of a reasonable set of sub problems + + + align:start position:0% +kind of a reasonable set of sub problems +right because kind of obviously if I if + + align:start position:0% +right because kind of obviously if I if + + + align:start position:0% +right because kind of obviously if I if +I Lop off off you you know some some + + align:start position:0% +I Lop off off you you know some some + + + align:start position:0% +I Lop off off you you know some some +piece of my string then the max value I + + align:start position:0% +piece of my string then the max value I + + + align:start position:0% +piece of my string then the max value I +can get is just the the value of + + align:start position:0% +can get is just the the value of + + + align:start position:0% +can get is just the the value of +whatever remains yeah so spiritually + + align:start position:0% +whatever remains yeah so spiritually + + + align:start position:0% +whatever remains yeah so spiritually +this somehow feels like the right uh uh + + align:start position:0% +this somehow feels like the right uh uh + + + align:start position:0% +this somehow feels like the right uh uh +dynamic programming and indeed we'll see + + align:start position:0% +dynamic programming and indeed we'll see + + + align:start position:0% +dynamic programming and indeed we'll see +that it is but it it just requires a + + align:start position:0% +that it is but it it just requires a + + + align:start position:0% +that it is but it it just requires a +little bit of liptick at the end to to + + align:start position:0% +little bit of liptick at the end to to + + + align:start position:0% +little bit of liptick at the end to to +run in the right time okay so let's do + + align:start position:0% +run in the right time okay so let's do + + + align:start position:0% +run in the right time okay so let's do +our recursive call and this is actually + + align:start position:0% +our recursive call and this is actually + + + align:start position:0% +our recursive call and this is actually +straightforward + + align:start position:0% +straightforward + + + align:start position:0% +straightforward +um at least the sort of recursive call + + align:start position:0% +um at least the sort of recursive call + + + align:start position:0% +um at least the sort of recursive call +that you want to make uh is + + align:start position:0% +that you want to make uh is + + + align:start position:0% +that you want to make uh is +straightforward and then we'll see that + + align:start position:0% +straightforward and then we'll see that + + + align:start position:0% +straightforward and then we'll see that +there's an equivalent formula which is + + align:start position:0% +there's an equivalent formula which is + + + align:start position:0% +there's an equivalent formula which is +the one you'll see in the solution which + + align:start position:0% +the one you'll see in the solution which + + + align:start position:0% +the one you'll see in the solution which +looks more complicated but is is the + + align:start position:0% +looks more complicated but is is the + + + align:start position:0% +looks more complicated but is is the +same thing so I'm going to write it as + + align:start position:0% +same thing so I'm going to write it as + + + align:start position:0% +same thing so I'm going to write it as +pseudo code for a recursive call rather + + align:start position:0% +pseudo code for a recursive call rather + + + align:start position:0% +pseudo code for a recursive call rather +than as one giant formula because I + + align:start position:0% +than as one giant formula because I + + + align:start position:0% +than as one giant formula because I +think it's easier to follow not pseudo + + align:start position:0% +think it's easier to follow not pseudo + + + align:start position:0% +think it's easier to follow not pseudo +code I know that's that's frowned upon + + align:start position:0% +code I know that's that's frowned upon + + + align:start position:0% +code I know that's that's frowned upon +in this class a a a description of a set + + align:start position:0% +in this class a a a description of a set + + + align:start position:0% +in this class a a a description of a set +of steps for obtaining our recursive + + align:start position:0% +of steps for obtaining our recursive + + + align:start position:0% +of steps for obtaining our recursive +call rather than um a formula so in + + align:start position:0% +call rather than um a formula so in + + + align:start position:0% +call rather than um a formula so in +particular uh we're going to initialize + + align:start position:0% +particular uh we're going to initialize + + + align:start position:0% +particular uh we're going to initialize +XI to be zero + + align:start position:0% + + + + align:start position:0% + +uh we want to do a maximization problem + + align:start position:0% +uh we want to do a maximization problem + + + align:start position:0% +uh we want to do a maximization problem +so initializing a variable to zero is a + + align:start position:0% +so initializing a variable to zero is a + + + align:start position:0% +so initializing a variable to zero is a +sensible thing to do and remember what + + align:start position:0% +sensible thing to do and remember what + + + align:start position:0% +sensible thing to do and remember what +what can we do here so we're looking at + + align:start position:0% +what can we do here so we're looking at + + + align:start position:0% +what can we do here so we're looking at +a suffix I could go down my list P of + + align:start position:0% +a suffix I could go down my list P of + + + align:start position:0% +a suffix I could go down my list P of +all the different markers see if any of + + align:start position:0% +all the different markers see if any of + + + align:start position:0% +all the different markers see if any of +them matches the first couple characters + + align:start position:0% +them matches the first couple characters + + + align:start position:0% +them matches the first couple characters +of my string if it does I get some value + + align:start position:0% +of my string if it does I get some value + + + align:start position:0% +of my string if it does I get some value +and then I hop on to the next thing does + + align:start position:0% +and then I hop on to the next thing does + + + align:start position:0% +and then I hop on to the next thing does +that make sense + + align:start position:0% + + + + align:start position:0% + +um oops I'm realizing I have a slight + + align:start position:0% +um oops I'm realizing I have a slight + + + align:start position:0% +um oops I'm realizing I have a slight +mistake here um rather than initializing + + align:start position:0% +mistake here um rather than initializing + + + align:start position:0% +mistake here um rather than initializing +to + + align:start position:0% + + + + align:start position:0% + +zero I actually have one additional + + align:start position:0% +zero I actually have one additional + + + align:start position:0% +zero I actually have one additional +option that I forgot to account for + + align:start position:0% +option that I forgot to account for + + + align:start position:0% +option that I forgot to account for +which is I could just not use this + + align:start position:0% +which is I could just not use this + + + align:start position:0% +which is I could just not use this +character I could I could I could put it + + align:start position:0% +character I could I could I could put it + + + align:start position:0% +character I could I could I could put it +in its own little snippet and and get no + + align:start position:0% +in its own little snippet and and get no + + + align:start position:0% +in its own little snippet and and get no +value from it right so maybe initially I + + align:start position:0% +value from it right so maybe initially I + + + align:start position:0% +value from it right so maybe initially I +make a recessive call like that it would + + align:start position:0% +make a recessive call like that it would + + + align:start position:0% +make a recessive call like that it would +be okay to initialize it to zero and + + align:start position:0% +be okay to initialize it to zero and + + + align:start position:0% +be okay to initialize it to zero and +then do this but + + align:start position:0% +then do this but + + + align:start position:0% +then do this but +whatever notice we're already seeing the + + align:start position:0% +whatever notice we're already seeing the + + + align:start position:0% +whatever notice we're already seeing the +T in our sort bot start to kind of stick + + align:start position:0% +T in our sort bot start to kind of stick + + + align:start position:0% +T in our sort bot start to kind of stick +out at us we're going to only depend on + + align:start position:0% +out at us we're going to only depend on + + + align:start position:0% +out at us we're going to only depend on +bigger indices I okay but in addition to + + align:start position:0% +bigger indices I okay but in addition to + + + align:start position:0% +bigger indices I okay but in addition to +this this isn't enough right this would + + align:start position:0% +this this isn't enough right this would + + + align:start position:0% +this this isn't enough right this would +obviously just recurse the end of our + + align:start position:0% +obviously just recurse the end of our + + + align:start position:0% +obviously just recurse the end of our +list and and do nothing uh we get value + + align:start position:0% +list and and do nothing uh we get value + + + align:start position:0% +list and and do nothing uh we get value +if we can find a substring that's in our + + align:start position:0% +if we can find a substring that's in our + + + align:start position:0% +if we can find a substring that's in our +our our list so what we could do is um + + align:start position:0% +our our list so what we could do is um + + + align:start position:0% +our our list so what we could do is um +for each + + align:start position:0% + + + + align:start position:0% + +marker uh in P remember p is the list of + + align:start position:0% +marker uh in P remember p is the list of + + + align:start position:0% +marker uh in P remember p is the list of +things that we're looking + + align:start position:0% + + + + align:start position:0% + +for okay um um what could I do uh if the + + align:start position:0% +for okay um um what could I do uh if the + + + align:start position:0% +for okay um um what could I do uh if the +marker + + align:start position:0% +marker + + + align:start position:0% +marker +matches um s starting at + + align:start position:0% +matches um s starting at + + + align:start position:0% +matches um s starting at +I I'm going to just not even attempt to + + align:start position:0% +I I'm going to just not even attempt to + + + align:start position:0% +I I'm going to just not even attempt to +do python uh starting at I and ending at + + align:start position:0% +do python uh starting at I and ending at + + + align:start position:0% +do python uh starting at I and ending at +the length of the + + align:start position:0% + + + + align:start position:0% + +marker well what could I do I could get + + align:start position:0% +marker well what could I do I could get + + + align:start position:0% +marker well what could I do I could get +one dollar by by Mark you know by + + align:start position:0% +one dollar by by Mark you know by + + + align:start position:0% +one dollar by by Mark you know by +matching that + + align:start position:0% +matching that + + + align:start position:0% +matching that +object and then I have to hop forward + + align:start position:0% +object and then I have to hop forward + + + align:start position:0% +object and then I have to hop forward +the length of the string uh in my + + align:start position:0% +the length of the string uh in my + + + align:start position:0% +the length of the string uh in my +recursive call right so + + align:start position:0% + + + + align:start position:0% + +um well I could do that or I could not + + align:start position:0% +um well I could do that or I could not + + + align:start position:0% +um well I could do that or I could not +do that and I want to maximize right + + align:start position:0% +do that and I want to maximize right + + + align:start position:0% +do that and I want to maximize right +so I could keep my old value or um I + + align:start position:0% +so I could keep my old value or um I + + + align:start position:0% +so I could keep my old value or um I +could get one point by using this as my + + align:start position:0% +could get one point by using this as my + + + align:start position:0% +could get one point by using this as my +match plus x i plus um the length of the + + align:start position:0% +match plus x i plus um the length of the + + + align:start position:0% +match plus x i plus um the length of the +marker okay and this is actually in my + + align:start position:0% +marker okay and this is actually in my + + + align:start position:0% +marker okay and this is actually in my +mind the simplest possible Dynamic + + align:start position:0% +mind the simplest possible Dynamic + + + align:start position:0% +mind the simplest possible Dynamic +program you could come up with this is + + align:start position:0% +program you could come up with this is + + + align:start position:0% +program you could come up with this is +actually a totally fine Dynamic program + + align:start position:0% +actually a totally fine Dynamic program + + + align:start position:0% +actually a totally fine Dynamic program +we'll just see that the runtime isn't + + align:start position:0% +we'll just see that the runtime isn't + + + align:start position:0% +we'll just see that the runtime isn't +good + + align:start position:0% + + + + align:start position:0% + +enough okay um so does everybody agree + + align:start position:0% +enough okay um so does everybody agree + + + align:start position:0% +enough okay um so does everybody agree +this is a way I could solve this this + + align:start position:0% +this is a way I could solve this this + + + align:start position:0% +this is a way I could solve this this +problem and it would give me a correct + + align:start position:0% +problem and it would give me a correct + + + align:start position:0% +problem and it would give me a correct +uh answer um I'll do the + + align:start position:0% +uh answer um I'll do the + + + align:start position:0% +uh answer um I'll do the +tabbot yeah that's what we're going to + + align:start position:0% +tabbot yeah that's what we're going to + + + align:start position:0% +tabbot yeah that's what we're going to +do but we're we're going to maybe skip + + align:start position:0% +do but we're we're going to maybe skip + + + align:start position:0% +do but we're we're going to maybe skip +some parts of sort bot um so in in + + align:start position:0% +some parts of sort bot um so in in + + + align:start position:0% +some parts of sort bot um so in in +particular um what's the topological + + align:start position:0% +particular um what's the topological + + + align:start position:0% +particular um what's the topological +order notice that I always look to the + + align:start position:0% +order notice that I always look to the + + + align:start position:0% +order notice that I always look to the +right uh when I make a recursive call um + + align:start position:0% +right uh when I make a recursive call um + + + align:start position:0% +right uh when I make a recursive call um +what's my base case well in this case + + align:start position:0% +what's my base case well in this case + + + align:start position:0% +what's my base case well in this case +it's just uh X of of zero I guess + + align:start position:0% +it's just uh X of of zero I guess + + + align:start position:0% +it's just uh X of of zero I guess +because I'm looking forward oh I'm sorry + + align:start position:0% +because I'm looking forward oh I'm sorry + + + align:start position:0% +because I'm looking forward oh I'm sorry +my base case is X of of the whole length + + align:start position:0% +my base case is X of of the whole length + + + align:start position:0% +my base case is X of of the whole length +of the string which is going to return + + align:start position:0% +of the string which is going to return + + + align:start position:0% +of the string which is going to return +zero right because if I have no string I + + align:start position:0% +zero right because if I have no string I + + + align:start position:0% +zero right because if I have no string I +can't get any value out of it the uh + + align:start position:0% +can't get any value out of it the uh + + + align:start position:0% +can't get any value out of it the uh +original is X of zero meaning that I + + align:start position:0% +original is X of zero meaning that I + + + align:start position:0% +original is X of zero meaning that I +want the whole string and let's actually + + align:start position:0% +want the whole string and let's actually + + + align:start position:0% +want the whole string and let's actually +do the runtime analysis as as uh Jason + + align:start position:0% +do the runtime analysis as as uh Jason + + + align:start position:0% +do the runtime analysis as as uh Jason +suggests because that's of course the + + align:start position:0% +suggests because that's of course the + + + align:start position:0% +suggests because that's of course the +relevant computation here um so this is + + align:start position:0% +relevant computation here um so this is + + + align:start position:0% +relevant computation here um so this is +T2 because it's the second T in sort F + + align:start position:0% +T2 because it's the second T in sort F + + + align:start position:0% +T2 because it's the second T in sort F +okay so how many sub problems are + + align:start position:0% +okay so how many sub problems are + + + align:start position:0% +okay so how many sub problems are +there well there's I mean it almost + + align:start position:0% +there well there's I mean it almost + + + align:start position:0% +there well there's I mean it almost +looks like we should have a fast + + align:start position:0% +looks like we should have a fast + + + align:start position:0% +looks like we should have a fast +algorithm because our our sub problems + + align:start position:0% +algorithm because our our sub problems + + + align:start position:0% +algorithm because our our sub problems +are only indexed by I right um so + + align:start position:0% +are only indexed by I right um so + + + align:start position:0% +are only indexed by I right um so +there's one sub problem um for basically + + align:start position:0% +there's one sub problem um for basically + + + align:start position:0% +there's one sub problem um for basically +each character in the string so there's + + align:start position:0% +each character in the string so there's + + + align:start position:0% +each character in the string so there's +mod S Sub problems + + align:start position:0% + + + + align:start position:0% + +total but how much time does it take for + + align:start position:0% +total but how much time does it take for + + + align:start position:0% +total but how much time does it take for +each sub problem well let's be + + align:start position:0% +each sub problem well let's be + + + align:start position:0% +each sub problem well let's be +careful so there's a for Loop over all + + align:start position:0% +careful so there's a for Loop over all + + + align:start position:0% +careful so there's a for Loop over all +the markers in P so I know that I + + align:start position:0% +the markers in P so I know that I + + + align:start position:0% +the markers in P so I know that I +incur at least mod P work uh in my sub + + align:start position:0% +incur at least mod P work uh in my sub + + + align:start position:0% +incur at least mod P work uh in my sub +problem is that all the work that I + + align:start position:0% +problem is that all the work that I + + + align:start position:0% +problem is that all the work that I +incur kind of looks like it because + + align:start position:0% +incur kind of looks like it because + + + align:start position:0% +incur kind of looks like it because +there's only one for Loop and there's an + + align:start position:0% +there's only one for Loop and there's an + + + align:start position:0% +there's only one for Loop and there's an +if but how do I check if strings are + + align:start position:0% +if but how do I check if strings are + + + align:start position:0% +if but how do I check if strings are +equal I have to iterate over the length + + align:start position:0% +equal I have to iterate over the length + + + align:start position:0% +equal I have to iterate over the length +of the string so I incur a second cost + + align:start position:0% +of the string so I incur a second cost + + + align:start position:0% +of the string so I incur a second cost +which is checking if two strings are + + align:start position:0% +which is checking if two strings are + + + align:start position:0% +which is checking if two strings are +equal we know that our strings are at + + align:start position:0% +equal we know that our strings are at + + + align:start position:0% +equal we know that our strings are at +most well I didn't actually write it + + align:start position:0% +most well I didn't actually write it + + + align:start position:0% +most well I didn't actually write it +down but the problem tells us that our + + align:start position:0% +down but the problem tells us that our + + + align:start position:0% +down but the problem tells us that our +strings are at at most length + + align:start position:0% +strings are at at most length + + + align:start position:0% +strings are at at most length +K so I incur another factor of K in + + align:start position:0% +K so I incur another factor of K in + + + align:start position:0% +K so I incur another factor of K in +every one of my sub problems and that + + align:start position:0% +every one of my sub problems and that + + + align:start position:0% +every one of my sub problems and that +implies that our whole algorithm that + + align:start position:0% +implies that our whole algorithm that + + + align:start position:0% +implies that our whole algorithm that +I've I've outline for y'all above takes + + align:start position:0% +I've I've outline for y'all above takes + + + align:start position:0% +I've I've outline for y'all above takes +mod S k^ + + align:start position:0% +mod S k^ + + + align:start position:0% +mod S k^ +2 oh I'm sorry that was a lie if I + + align:start position:0% +2 oh I'm sorry that was a lie if I + + + align:start position:0% +2 oh I'm sorry that was a lie if I +actually multiply these things together + + align:start position:0% +actually multiply these things together + + + align:start position:0% +actually multiply these things together +what I get sorry this is I need more + + align:start position:0% +what I get sorry this is I need more + + + align:start position:0% +what I get sorry this is I need more +sleep s PK and that is against the rules + + align:start position:0% +sleep s PK and that is against the rules + + + align:start position:0% +sleep s PK and that is against the rules +that's frowny face yeah uh because in + + align:start position:0% +that's frowny face yeah uh because in + + + align:start position:0% +that's frowny face yeah uh because in +particular I took two big numbers in + + align:start position:0% +particular I took two big numbers in + + + align:start position:0% +particular I took two big numbers in +some sense and multiplied them together + + align:start position:0% +some sense and multiplied them together + + + align:start position:0% +some sense and multiplied them together +uh and and and and that's no good so + + align:start position:0% +uh and and and and that's no good so + + + align:start position:0% +uh and and and and that's no good so +what what is a person to do you know I I + + align:start position:0% +what what is a person to do you know I I + + + align:start position:0% +what what is a person to do you know I I +tried to solve my problem I came up with + + align:start position:0% +tried to solve my problem I came up with + + + align:start position:0% +tried to solve my problem I came up with +by the way for from a partial credit + + align:start position:0% +by the way for from a partial credit + + + align:start position:0% +by the way for from a partial credit +perspective I think you'd be be doing + + align:start position:0% +perspective I think you'd be be doing + + + align:start position:0% +perspective I think you'd be be doing +okay if you got to to this point okay + + align:start position:0% +okay if you got to to this point okay + + + align:start position:0% +okay if you got to to this point okay +not great but okay um but of course the + + align:start position:0% +not great but okay um but of course the + + + align:start position:0% +not great but okay um but of course the +problem is is is asking you uh to solve + + align:start position:0% +problem is is is asking you uh to solve + + + align:start position:0% +problem is is is asking you uh to solve +this in this funny uh runtime which is + + align:start position:0% +this in this funny uh runtime which is + + + align:start position:0% +this in this funny uh runtime which is +KP plus k^2 uh uh s yep when I see a sum + + align:start position:0% +KP plus k^2 uh uh s yep when I see a sum + + + align:start position:0% +KP plus k^2 uh uh s yep when I see a sum +like this in a you know remember that + + align:start position:0% +like this in a you know remember that + + + align:start position:0% +like this in a you know remember that +there are two problems to solve there + + align:start position:0% +there are two problems to solve there + + + align:start position:0% +there are two problems to solve there +are two strategies for solving problems + + align:start position:0% +are two strategies for solving problems + + + align:start position:0% +are two strategies for solving problems +in algorith class there's one which is + + align:start position:0% +in algorith class there's one which is + + + align:start position:0% +in algorith class there's one which is +useful in your everyday lives which is + + align:start position:0% +useful in your everyday lives which is + + + align:start position:0% +useful in your everyday lives which is +to devise algorithms there's a second + + align:start position:0% +to devise algorithms there's a second + + + align:start position:0% +to devise algorithms there's a second +which is to psychologically diagnose + + align:start position:0% +which is to psychologically diagnose + + + align:start position:0% +which is to psychologically diagnose +your instructors um and I think that + + align:start position:0% +your instructors um and I think that + + + align:start position:0% +your instructors um and I think that +second strategy is actually pretty + + align:start position:0% +second strategy is actually pretty + + + align:start position:0% +second strategy is actually pretty +effective here I see two terms most of + + align:start position:0% +effective here I see two terms most of + + + align:start position:0% +effective here I see two terms most of +our dynamic programming things involve + + align:start position:0% +our dynamic programming things involve + + + align:start position:0% +our dynamic programming things involve +filling in a table where you would + + align:start position:0% +filling in a table where you would + + + align:start position:0% +filling in a table where you would +expect there to be a product so in + + align:start position:0% +expect there to be a product so in + + + align:start position:0% +expect there to be a product so in +general I would kind of squint at this + + align:start position:0% +general I would kind of squint at this + + + align:start position:0% +general I would kind of squint at this +and Think Like H maybe I have to do some + + align:start position:0% +and Think Like H maybe I have to do some + + + align:start position:0% +and Think Like H maybe I have to do some +pre-computation yep in particular um we + + align:start position:0% +pre-computation yep in particular um we + + + align:start position:0% +pre-computation yep in particular um we +got to do a lot of string matching in + + align:start position:0% +got to do a lot of string matching in + + + align:start position:0% +got to do a lot of string matching in +our problem and maybe we can make that + + align:start position:0% +our problem and maybe we can make that + + + align:start position:0% +our problem and maybe we can make that +more efficient yeah that that's sort of + + align:start position:0% +more efficient yeah that that's sort of + + + align:start position:0% +more efficient yeah that that's sort of +the the the main question here + + align:start position:0% +the the the main question here + + + align:start position:0% +the the the main question here +um right so so this thing is too slow + + align:start position:0% +um right so so this thing is too slow + + + align:start position:0% +um right so so this thing is too slow +and we're trying to fix it the way I'm + + align:start position:0% +and we're trying to fix it the way I'm + + + align:start position:0% +and we're trying to fix it the way I'm +going to try and fix it is to say like + + align:start position:0% +going to try and fix it is to say like + + + align:start position:0% +going to try and fix it is to say like +okay well I have mod S Sub problems if I + + align:start position:0% +okay well I have mod S Sub problems if I + + + align:start position:0% +okay well I have mod S Sub problems if I +look at these two terms how much work + + align:start position:0% +look at these two terms how much work + + + align:start position:0% +look at these two terms how much work +can I actually do in my sub problem + + align:start position:0% +can I actually do in my sub problem + + + align:start position:0% +can I actually do in my sub problem +something that looks like K squ maybe + + align:start position:0% +something that looks like K squ maybe + + + align:start position:0% +something that looks like K squ maybe +plus this amount of pre-computation see + + align:start position:0% +plus this amount of pre-computation see + + + align:start position:0% +plus this amount of pre-computation see +what I did there okay so let's uh let's + + align:start position:0% +what I did there okay so let's uh let's + + + align:start position:0% +what I did there okay so let's uh let's +do + + align:start position:0% +do + + + align:start position:0% +do +that so in particular here are the types + + align:start position:0% +that so in particular here are the types + + + align:start position:0% +that so in particular here are the types +of queries that I'm going to have to + + align:start position:0% +of queries that I'm going to have to + + + align:start position:0% +of queries that I'm going to have to +make + + align:start position:0% +make + + + align:start position:0% +make +there's a bunch of times in my code when + + align:start position:0% +there's a bunch of times in my code when + + + align:start position:0% +there's a bunch of times in my code when +uh here's a number that he falling apart + + align:start position:0% +uh here's a number that he falling apart + + + align:start position:0% +uh here's a number that he falling apart +that's what I get for sprinting across + + align:start position:0% +that's what I get for sprinting across + + + align:start position:0% +that's what I get for sprinting across +campus to get here uh I'm going to + + align:start position:0% +campus to get here uh I'm going to + + + align:start position:0% +campus to get here uh I'm going to +define a me a number m + + align:start position:0% +define a me a number m + + + align:start position:0% +define a me a number m +j and it's going to be + + align:start position:0% +j and it's going to be + + + align:start position:0% +j and it's going to be +one if the substring + + align:start position:0% +one if the substring + + + align:start position:0% +one if the substring +s i oh man + + align:start position:0% +s i oh man + + + align:start position:0% +s i oh man +2J uh is in my list of markers p + + align:start position:0% +2J uh is in my list of markers p + + + align:start position:0% +2J uh is in my list of markers p +and zero + + align:start position:0% + + + + align:start position:0% + +otherwise by the way why is this enough + + align:start position:0% +otherwise by the way why is this enough + + + align:start position:0% +otherwise by the way why is this enough +like notice that I'm not answering which + + align:start position:0% +like notice that I'm not answering which + + + align:start position:0% +like notice that I'm not answering which +marker but the problem doesn't really + + align:start position:0% +marker but the problem doesn't really + + + align:start position:0% +marker but the problem doesn't really +care right like this problem just checks + + align:start position:0% +care right like this problem just checks + + + align:start position:0% +care right like this problem just checks +if there is a marker and if so then I I + + align:start position:0% +if there is a marker and if so then I I + + + align:start position:0% +if there is a marker and if so then I I +use it yeah so if I have this thing + + align:start position:0% +use it yeah so if I have this thing + + + align:start position:0% +use it yeah so if I have this thing +that's going to somehow make this for + + align:start position:0% +that's going to somehow make this for + + + align:start position:0% +that's going to somehow make this for +Loop a heck a lot easier because now I + + align:start position:0% +Loop a heck a lot easier because now I + + + align:start position:0% +Loop a heck a lot easier because now I +don't have to do string matching we'll + + align:start position:0% +don't have to do string matching we'll + + + align:start position:0% +don't have to do string matching we'll +return to that in a + + align:start position:0% +return to that in a + + + align:start position:0% +return to that in a +minute okay so my question is how can I + + align:start position:0% +minute okay so my question is how can I + + + align:start position:0% +minute okay so my question is how can I +compute this thing and by the way notice + + align:start position:0% + + + + align:start position:0% + +that I know how to compute this when the + + align:start position:0% +that I know how to compute this when the + + + align:start position:0% +that I know how to compute this when the +difference between I and J is bigger + + align:start position:0% +difference between I and J is bigger + + + align:start position:0% +difference between I and J is bigger +than K right because I know that all of + + align:start position:0% +than K right because I know that all of + + + align:start position:0% +than K right because I know that all of +my markers have length K or less that's + + align:start position:0% +my markers have length K or less that's + + + align:start position:0% +my markers have length K or less that's +going to be important because even + + align:start position:0% +going to be important because even + + + align:start position:0% +going to be important because even +though m is doubly indexed uh I don't + + align:start position:0% +though m is doubly indexed uh I don't + + + align:start position:0% +though m is doubly indexed uh I don't +actually need to do that in fact I could + + align:start position:0% +actually need to do that in fact I could + + + align:start position:0% +actually need to do that in fact I could +even store it uh using less memory than + + align:start position:0% +even store it uh using less memory than + + + align:start position:0% +even store it uh using less memory than +that if I wanted to by kind of just + + align:start position:0% +that if I wanted to by kind of just + + + align:start position:0% +that if I wanted to by kind of just +storing that that diagonal block okay uh + + align:start position:0% +storing that that diagonal block okay uh + + + align:start position:0% +storing that that diagonal block okay uh +right so the other thing which I think + + align:start position:0% +right so the other thing which I think + + + align:start position:0% +right so the other thing which I think +we saw in a previous uh problem session + + align:start position:0% +we saw in a previous uh problem session + + + align:start position:0% +we saw in a previous uh problem session +as well is that when we do a lot of + + align:start position:0% +as well is that when we do a lot of + + + align:start position:0% +as well is that when we do a lot of +string matching it often pays to put our + + align:start position:0% +string matching it often pays to put our + + + align:start position:0% +string matching it often pays to put our +strings into a hash table uh so that + + align:start position:0% +strings into a hash table uh so that + + + align:start position:0% +strings into a hash table uh so that +they're easier to look up later like + + align:start position:0% +they're easier to look up later like + + + align:start position:0% +they're easier to look up later like +does this string exist in in this thing + + align:start position:0% +does this string exist in in this thing + + + align:start position:0% +does this string exist in in this thing +or not right rather than matching every + + align:start position:0% +or not right rather than matching every + + + align:start position:0% +or not right rather than matching every +character every single time um so maybe + + align:start position:0% +character every single time um so maybe + + + align:start position:0% +character every single time um so maybe +we do that just for for for for fun uh + + align:start position:0% +we do that just for for for for fun uh + + + align:start position:0% +we do that just for for for for fun uh +and in general when you see a string + + align:start position:0% +and in general when you see a string + + + align:start position:0% +and in general when you see a string +matching problem I might and you have a + + align:start position:0% +matching problem I might and you have a + + + align:start position:0% +matching problem I might and you have a +list of strings I'd suggest thinking + + align:start position:0% +list of strings I'd suggest thinking + + + align:start position:0% +list of strings I'd suggest thinking +about hash tables just for for Fun and + + align:start position:0% +about hash tables just for for Fun and + + + align:start position:0% +about hash tables just for for Fun and +Profit yeah so in in step one here maybe + + align:start position:0% +Profit yeah so in in step one here maybe + + + align:start position:0% +Profit yeah so in in step one here maybe +I put + + align:start position:0% +I put + + + align:start position:0% +I put +all the strings in P into a + + align:start position:0% + + + + align:start position:0% + +hash okay um how much time does that + + align:start position:0% +hash okay um how much time does that + + + align:start position:0% +hash okay um how much time does that +take well I have to process every string + + align:start position:0% +take well I have to process every string + + + align:start position:0% +take well I have to process every string +right find its its code um which is + + align:start position:0% +right find its its code um which is + + + align:start position:0% +right find its its code um which is +going to take order K time there's mod P + + align:start position:0% +going to take order K time there's mod P + + + align:start position:0% +going to take order K time there's mod P +of them so this is K mod P + + align:start position:0% +of them so this is K mod P + + + align:start position:0% +of them so this is K mod P +time notice that that conveniently + + align:start position:0% +time notice that that conveniently + + + align:start position:0% +time notice that that conveniently +agrees with our first term here so we + + align:start position:0% +agrees with our first term here so we + + + align:start position:0% +agrees with our first term here so we +feel like aha we're in we're in good + + align:start position:0% +feel like aha we're in we're in good + + + align:start position:0% +feel like aha we're in we're in good +shape we're making progress here um and + + align:start position:0% +shape we're making progress here um and + + + align:start position:0% +shape we're making progress here um and +now uh maybe I want to fill in this M J + + align:start position:0% +now uh maybe I want to fill in this M J + + + align:start position:0% +now uh maybe I want to fill in this M J +uh object uh here how could I do + + align:start position:0% +uh object uh here how could I do + + + align:start position:0% +uh object uh here how could I do +that well for one I'm certainly going + + align:start position:0% +that well for one I'm certainly going + + + align:start position:0% +that well for one I'm certainly going +have to iterate over all possible eyes + + align:start position:0% +have to iterate over all possible eyes + + + align:start position:0% +have to iterate over all possible eyes +yeah so let's let's uh let's do that so + + align:start position:0% +yeah so let's let's uh let's do that so + + + align:start position:0% +yeah so let's let's uh let's do that so +we're going to do two by the way I mean + + align:start position:0% +we're going to do two by the way I mean + + + align:start position:0% +we're going to do two by the way I mean +like using ones and twos and as's and + + align:start position:0% +like using ones and twos and as's and + + + align:start position:0% +like using ones and twos and as's and +B's and whatever these are just ways to + + align:start position:0% +B's and whatever these are just ways to + + + align:start position:0% +B's and whatever these are just ways to +denote steps of + + align:start position:0% +denote steps of + + + align:start position:0% +denote steps of +things uh okay + + align:start position:0% + + + + align:start position:0% + +so let's say that I just want to fill in + + align:start position:0% +so let's say that I just want to fill in + + + align:start position:0% +so let's say that I just want to fill in +M um using a brain dead algorithm so I + + align:start position:0% +M um using a brain dead algorithm so I + + + align:start position:0% +M um using a brain dead algorithm so I +could go from one to the size of my + + align:start position:0% +could go from one to the size of my + + + align:start position:0% +could go from one to the size of my +strings for + + align:start position:0% +strings for + + + align:start position:0% +strings for +I careful now I can't incur an S squ but + + align:start position:0% +I careful now I can't incur an S squ but + + + align:start position:0% +I careful now I can't incur an S squ but +I know that my strings are always at + + align:start position:0% +I know that my strings are always at + + + align:start position:0% +I know that my strings are always at +most length K so I could do + + align:start position:0% +most length K so I could do + + + align:start position:0% +most length K so I could do +for J + + align:start position:0% +for J + + + align:start position:0% +for J +equals uh I + 1 + + align:start position:0% +equals uh I + 1 + + + align:start position:0% +equals uh I + 1 +2 I + K so this for Loop actually incurs + + align:start position:0% +2 I + K so this for Loop actually incurs + + + align:start position:0% +2 I + K so this for Loop actually incurs +K time not mod s time and now uh I can + + align:start position:0% +K time not mod s time and now uh I can + + + align:start position:0% +K time not mod s time and now uh I can +do two things right I can find the uh + + align:start position:0% +do two things right I can find the uh + + + align:start position:0% +do two things right I can find the uh +hash of the string from I to J right + + align:start position:0% +hash of the string from I to J right + + + align:start position:0% +hash of the string from I to J right +this is going to take order K + + align:start position:0% +this is going to take order K + + + align:start position:0% +this is going to take order K +time + + align:start position:0% +time + + + align:start position:0% +time +and I + + align:start position:0% +and I + + + align:start position:0% +and I +can uh search for it + + align:start position:0% + + + + align:start position:0% + +ah + + align:start position:0% +ah + + + align:start position:0% +ah +[Music] + + align:start position:0% + + + + align:start position:0% + +no uh um to see if it's actually in our + + align:start position:0% +no uh um to see if it's actually in our + + + align:start position:0% +no uh um to see if it's actually in our +uh hash table of p and if it is uh then + + align:start position:0% +uh hash table of p and if it is uh then + + + align:start position:0% +uh hash table of p and if it is uh then +I set m equal to one otherwise I set m + + align:start position:0% +I set m equal to one otherwise I set m + + + align:start position:0% +I set m equal to one otherwise I set m +equal to + + align:start position:0% + + + + align:start position:0% + +zero uh right and these are our sort of + + align:start position:0% +zero uh right and these are our sort of + + + align:start position:0% +zero uh right and these are our sort of +constant time operations at least in + + align:start position:0% +constant time operations at least in + + + align:start position:0% +constant time operations at least in +expectation so how much uh cost to it + + align:start position:0% +expectation so how much uh cost to it + + + align:start position:0% +expectation so how much uh cost to it +and and so this you can convince + + align:start position:0% +and and so this you can convince + + + align:start position:0% +and and so this you can convince +yourself uh fills in that array M how + + align:start position:0% +yourself uh fills in that array M how + + + align:start position:0% +yourself uh fills in that array M how +much times does it take well I have a + + align:start position:0% +much times does it take well I have a + + + align:start position:0% +much times does it take well I have a +loop to the size of s I have a loop of + + align:start position:0% +loop to the size of s I have a loop of + + + align:start position:0% +loop to the size of s I have a loop of +size K I have a second second Loop of + + align:start position:0% +size K I have a second second Loop of + + + align:start position:0% +size K I have a second second Loop of +size K here to compute the hash so this + + align:start position:0% +size K here to compute the hash so this + + + align:start position:0% +size K here to compute the hash so this +whole thing is going to take order k^ 2 + + align:start position:0% +whole thing is going to take order k^ 2 + + + align:start position:0% +whole thing is going to take order k^ 2 +mod s time like that notice + + align:start position:0% +mod s time like that notice + + + align:start position:0% +mod s time like that notice +conveniently there's chalk on the floor + + align:start position:0% +conveniently there's chalk on the floor + + + align:start position:0% +conveniently there's chalk on the floor +and this is uh the second term in our + + align:start position:0% +and this is uh the second term in our + + + align:start position:0% +and this is uh the second term in our +runtime so this is kosher we can fill in + + align:start position:0% +runtime so this is kosher we can fill in + + + align:start position:0% +runtime so this is kosher we can fill in +m and and and and and that's a + + align:start position:0% +m and and and and and that's a + + + align:start position:0% +m and and and and and that's a +convenient object to have around so the + + align:start position:0% +convenient object to have around so the + + + align:start position:0% +convenient object to have around so the +only thing that remains is to revise our + + align:start position:0% +only thing that remains is to revise our + + + align:start position:0% +only thing that remains is to revise our +R from above um to make use of the M + + align:start position:0% +R from above um to make use of the M + + + align:start position:0% +R from above um to make use of the M +that we have uh and that's pretty + + align:start position:0% +that we have uh and that's pretty + + + align:start position:0% +that we have uh and that's pretty +straightforward + + align:start position:0% + + + + align:start position:0% + +um so the trick is to not lean against + + align:start position:0% +um so the trick is to not lean against + + + align:start position:0% +um so the trick is to not lean against +this thing and to actually hit the stop + + align:start position:0% +this thing and to actually hit the stop + + + align:start position:0% +this thing and to actually hit the stop +button I'm I'm learning so now I suppose + + align:start position:0% +button I'm I'm learning so now I suppose + + + align:start position:0% +button I'm I'm learning so now I suppose +we had T2 for the second + + align:start position:0% +we had T2 for the second + + + align:start position:0% +we had T2 for the second +T So for our revised R we should have R + + align:start position:0% +T So for our revised R we should have R + + + align:start position:0% +T So for our revised R we should have R +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +um what was that the Der that's that's + + align:start position:0% +um what was that the Der that's that's + + + align:start position:0% +um what was that the Der that's that's +right the derivative yeah we could do + + align:start position:0% +right the derivative yeah we could do + + + align:start position:0% +right the derivative yeah we could do +you know like christopal symbols like I + + align:start position:0% +you know like christopal symbols like I + + + align:start position:0% +you know like christopal symbols like I +J Prime semicolon K + + align:start position:0% +J Prime semicolon K + + + align:start position:0% +J Prime semicolon K +uh take 6838 if you want to learn what + + align:start position:0% +uh take 6838 if you want to learn what + + + align:start position:0% +uh take 6838 if you want to learn what +christopal symbols are um right so uh + + align:start position:0% +christopal symbols are um right so uh + + + align:start position:0% +christopal symbols are um right so uh +Now what is my recursive call for + + align:start position:0% +Now what is my recursive call for + + + align:start position:0% +Now what is my recursive call for +XI well I want to + + align:start position:0% + + + + align:start position:0% + +maximize uh well what can I do I can + + align:start position:0% +maximize uh well what can I do I can + + + align:start position:0% +maximize uh well what can I do I can +check every possible length of a string + + align:start position:0% +check every possible length of a string + + + align:start position:0% +check every possible length of a string +um that could be in P che check if it is + + align:start position:0% +um that could be in P che check if it is + + + align:start position:0% +um that could be in P che check if it is +using my array m + + align:start position:0% +using my array m + + + align:start position:0% +using my array m +um and and get that amount of profit so + + align:start position:0% +um and and get that amount of profit so + + + align:start position:0% +um and and get that amount of profit so +in particular I get + + align:start position:0% +in particular I get + + + align:start position:0% +in particular I get +M by the way I keep using the word + + align:start position:0% +M by the way I keep using the word + + + align:start position:0% +M by the way I keep using the word +profit here I'm essentially using that + + align:start position:0% +profit here I'm essentially using that + + + align:start position:0% +profit here I'm essentially using that +to mean increment in every single one of + + align:start position:0% +to mean increment in every single one of + + + align:start position:0% +to mean increment in every single one of +our our problems here I like to think of + + align:start position:0% +our our problems here I like to think of + + + align:start position:0% +our our problems here I like to think of +our problems as maximizing profit + + align:start position:0% +our problems as maximizing profit + + + align:start position:0% +our problems as maximizing profit +because I'm a greedy Professor so this + + align:start position:0% +because I'm a greedy Professor so this + + + align:start position:0% +because I'm a greedy Professor so this +is m i j which would be like one if I + + align:start position:0% +is m i j which would be like one if I + + + align:start position:0% +is m i j which would be like one if I +found a string there and zero if I'm not + + align:start position:0% +found a string there and zero if I'm not + + + align:start position:0% +found a string there and zero if I'm not +plus + + align:start position:0% +plus + + + align:start position:0% +plus +x i + J to account for the length uh uh + + align:start position:0% +x i + J to account for the length uh uh + + + align:start position:0% +x i + J to account for the length uh uh +here where J + + align:start position:0% +here where J + + + align:start position:0% +here where J +is in one to uh well + + align:start position:0% +is in one to uh well + + + align:start position:0% +is in one to uh well +either the length of the string or I get + + align:start position:0% +either the length of the string or I get + + + align:start position:0% +either the length of the string or I get +to the end of either the maximum length + + align:start position:0% +to the end of either the maximum length + + + align:start position:0% +to the end of either the maximum length +of a string in P or I get to the end of + + align:start position:0% +of a string in P or I get to the end of + + + align:start position:0% +of a string in P or I get to the end of +my + + align:start position:0% +my + + + align:start position:0% +my +array like that okay and this is our new + + align:start position:0% +array like that okay and this is our new + + + align:start position:0% +array like that okay and this is our new +recursive call the one thing we should + + align:start position:0% +recursive call the one thing we should + + + align:start position:0% +recursive call the one thing we should +double check is what is the runtime for + + align:start position:0% +double check is what is the runtime for + + + align:start position:0% +double check is what is the runtime for +actually filling in X now well there's + + align:start position:0% +actually filling in X now well there's + + + align:start position:0% +actually filling in X now well there's +still mod S Sub + + align:start position:0% +still mod S Sub + + + align:start position:0% +still mod S Sub +problems and now how long does it take + + align:start position:0% +problems and now how long does it take + + + align:start position:0% +problems and now how long does it take +well now I just have one Loop over K + + align:start position:0% +well now I just have one Loop over K + + + align:start position:0% +well now I just have one Loop over K +things this is mod s * K it's actually + + align:start position:0% +things this is mod s * K it's actually + + + align:start position:0% +things this is mod s * K it's actually +less than any of the terms that's in our + + align:start position:0% +less than any of the terms that's in our + + + align:start position:0% +less than any of the terms that's in our +uh + + align:start position:0% +uh + + + align:start position:0% +uh +runtime and so this is fine this + + align:start position:0% +runtime and so this is fine this + + + align:start position:0% +runtime and so this is fine this +actually is kind of a funny example + + align:start position:0% +actually is kind of a funny example + + + align:start position:0% +actually is kind of a funny example +where the dynamic programming part of + + align:start position:0% +where the dynamic programming part of + + + align:start position:0% +where the dynamic programming part of +our our algorithm once we've done all + + align:start position:0% +our our algorithm once we've done all + + + align:start position:0% +our our algorithm once we've done all +this cute pre-computation is actually + + align:start position:0% +this cute pre-computation is actually + + + align:start position:0% +this cute pre-computation is actually +insignificant um compared to all the + + align:start position:0% +insignificant um compared to all the + + + align:start position:0% +insignificant um compared to all the +pre-computation that we had to do uh in + + align:start position:0% +pre-computation that we had to do uh in + + + align:start position:0% +pre-computation that we had to do uh in +our final runtime + + align:start position:0% +our final runtime + + + align:start position:0% +our final runtime +sneaky all right any questions about uh + + align:start position:0% +sneaky all right any questions about uh + + + align:start position:0% +sneaky all right any questions about uh +protein folding or whatever it is that + + align:start position:0% +protein folding or whatever it is that + + + align:start position:0% +protein folding or whatever it is that +we just just + + align:start position:0% +we just just + + + align:start position:0% +we just just +did okay so as usual I'm talking too + + align:start position:0% +did okay so as usual I'm talking too + + + align:start position:0% +did okay so as usual I'm talking too +much cut one of yeah which one would you + + align:start position:0% +much cut one of yeah which one would you + + + align:start position:0% +much cut one of yeah which one would you +prefer to cut I have very few + + align:start position:0% + + + + align:start position:0% + +preferences okay so one of the problems + + align:start position:0% +preferences okay so one of the problems + + + align:start position:0% +preferences okay so one of the problems +um I would take a vote but with our + + align:start position:0% +um I would take a vote but with our + + + align:start position:0% +um I would take a vote but with our +audience there's a high probability of a + + align:start position:0% +audience there's a high probability of a + + + align:start position:0% +audience there's a high probability of a +split jury here um right so there's two + + align:start position:0% +split jury here um right so there's two + + + align:start position:0% +split jury here um right so there's two +remaining problems in the problem + + align:start position:0% +remaining problems in the problem + + + align:start position:0% +remaining problems in the problem +session as usual uh your + + align:start position:0% +session as usual uh your + + + align:start position:0% +session as usual uh your +instructor you can leave it there this + + align:start position:0% +instructor you can leave it there this + + + align:start position:0% +instructor you can leave it there this +is another problem learn about + + align:start position:0% +is another problem learn about + + + align:start position:0% +is another problem learn about +um uh right as usual I've talked too + + align:start position:0% +um uh right as usual I've talked too + + + align:start position:0% +um uh right as usual I've talked too +much and and and haven't gotten to the + + align:start position:0% +much and and and haven't gotten to the + + + align:start position:0% +much and and and haven't gotten to the +end I get the impression that in 66 this + + align:start position:0% +end I get the impression that in 66 this + + + align:start position:0% +end I get the impression that in 66 this +egg drop thing is a bit of a tradition + + align:start position:0% +egg drop thing is a bit of a tradition + + + align:start position:0% +egg drop thing is a bit of a tradition +anyway um so maybe we'll we'll cover + + align:start position:0% +anyway um so maybe we'll we'll cover + + + align:start position:0% +anyway um so maybe we'll we'll cover +that problem really fast do they do that + + align:start position:0% +that problem really fast do they do that + + + align:start position:0% +that problem really fast do they do that +in section some variation not this time + + align:start position:0% +in section some variation not this time + + + align:start position:0% +in section some variation not this time +even + + align:start position:0% +even + + + align:start position:0% +even +better okay so yeah so maybe we'll do uh + + align:start position:0% +better okay so yeah so maybe we'll do uh + + + align:start position:0% +better okay so yeah so maybe we'll do uh +this this egg drop thing mostly because + + align:start position:0% +this this egg drop thing mostly because + + + align:start position:0% +this this egg drop thing mostly because +the other one I think takes a lot of + + align:start position:0% +the other one I think takes a lot of + + + align:start position:0% +the other one I think takes a lot of +verbal setup the other one is + + align:start position:0% +verbal setup the other one is + + + align:start position:0% +verbal setup the other one is +is I would say from a dynamic + + align:start position:0% +is I would say from a dynamic + + + align:start position:0% +is I would say from a dynamic +programming perspective Maybe not super + + align:start position:0% +programming perspective Maybe not super + + + align:start position:0% +programming perspective Maybe not super +exciting but from like a interesting + + align:start position:0% +exciting but from like a interesting + + + align:start position:0% +exciting but from like a interesting +problem perspective is is is is kind of + + align:start position:0% +problem perspective is is is is kind of + + + align:start position:0% +problem perspective is is is is kind of +cool uh to think about um so I'd + + align:start position:0% +cool uh to think about um so I'd + + + align:start position:0% +cool uh to think about um so I'd +encourage you to leave it in there and + + align:start position:0% +encourage you to leave it in there and + + + align:start position:0% +encourage you to leave it in there and +you guys can can read it at home um from + + align:start position:0% +you guys can can read it at home um from + + + align:start position:0% +you guys can can read it at home um from +a coding perspective it's also kind of + + align:start position:0% +a coding perspective it's also kind of + + + align:start position:0% +a coding perspective it's also kind of +fun I noticed the solution didn't do + + align:start position:0% +fun I noticed the solution didn't do + + + align:start position:0% +fun I noticed the solution didn't do +what I would do which would be to use + + align:start position:0% +what I would do which would be to use + + + align:start position:0% +what I would do which would be to use +the the bits in the you know like assume + + align:start position:0% +the the bits in the you know like assume + + + align:start position:0% +the the bits in the you know like assume +that something wasn't too tall and use + + align:start position:0% +that something wasn't too tall and use + + + align:start position:0% +that something wasn't too tall and use +the bits in like an integer to store + + align:start position:0% +the bits in like an integer to store + + + align:start position:0% +the bits in like an integer to store +your binary + + align:start position:0% +your binary + + + align:start position:0% +your binary +variables but that's an old hack right + + align:start position:0% +variables but that's an old hack right + + + align:start position:0% +variables but that's an old hack right +that's sort of like you know this this + + align:start position:0% +that's sort of like you know this this + + + align:start position:0% +that's sort of like you know this this +old hack for computing the square root + + align:start position:0% +old hack for computing the square root + + + align:start position:0% +old hack for computing the square root +of a number that's apparently in the + + align:start position:0% +of a number that's apparently in the + + + align:start position:0% +of a number that's apparently in the +Doom the code for the Doom video game + + align:start position:0% +Doom the code for the Doom video game + + + align:start position:0% +Doom the code for the Doom video game +which involves like bit shifting and it + + align:start position:0% +which involves like bit shifting and it + + + align:start position:0% +which involves like bit shifting and it +happens to agree with square root for + + align:start position:0% +happens to agree with square root for + + + align:start position:0% +happens to agree with square root for +some magic reason that numerical + + align:start position:0% +some magic reason that numerical + + + align:start position:0% +some magic reason that numerical +analysts really hate um okay so right so + + align:start position:0% +analysts really hate um okay so right so + + + align:start position:0% +analysts really hate um okay so right so +uh let's do a lazy egg drop instead so + + align:start position:0% +uh let's do a lazy egg drop instead so + + + align:start position:0% +uh let's do a lazy egg drop instead so +that's problem + + align:start position:0% +that's problem + + + align:start position:0% +that's problem +four + + align:start position:0% +four + + + align:start position:0% +four +okay so we're in a + + align:start position:0% +okay so we're in a + + + align:start position:0% +okay so we're in a +building our building has n + + align:start position:0% +building our building has n + + + align:start position:0% +building our building has n +floors um and K + + align:start position:0% +floors um and K + + + align:start position:0% +floors um and K +eggs I guess it's debatable whether the + + align:start position:0% +eggs I guess it's debatable whether the + + + align:start position:0% +eggs I guess it's debatable whether the +building has eggs or the residence but + + align:start position:0% +building has eggs or the residence but + + + align:start position:0% +building has eggs or the residence but +uh in any event I have some set of eggs + + align:start position:0% +uh in any event I have some set of eggs + + + align:start position:0% +uh in any event I have some set of eggs +uh and maybe I'm in the state of Center + + align:start position:0% +uh and maybe I'm in the state of Center + + + align:start position:0% +uh and maybe I'm in the state of Center +or some other weird building so I don't + + align:start position:0% +or some other weird building so I don't + + + align:start position:0% +or some other weird building so I don't +have Heights of floors that are + + align:start position:0% +have Heights of floors that are + + + align:start position:0% +have Heights of floors that are +isotropic but rather each floor has a + + align:start position:0% +isotropic but rather each floor has a + + + align:start position:0% +isotropic but rather each floor has a +different height which could vary + + align:start position:0% +different height which could vary + + + align:start position:0% +different height which could vary +um so it's height of + + align:start position:0% + + + + align:start position:0% + +floor or I really want to write flower + + align:start position:0% +floor or I really want to write flower + + + align:start position:0% +floor or I really want to write flower +um but I digress + + align:start position:0% +um but I digress + + + align:start position:0% +um but I digress +uh and we're going to assume that that + + align:start position:0% +uh and we're going to assume that that + + + align:start position:0% +uh and we're going to assume that that +our our list is already + + align:start position:0% +our our list is already + + + align:start position:0% +our our list is already +sorted so in other words like the fifth + + align:start position:0% +sorted so in other words like the fifth + + + align:start position:0% +sorted so in other words like the fifth +floor is taller than the fourth floor uh + + align:start position:0% +floor is taller than the fourth floor uh + + + align:start position:0% +floor is taller than the fourth floor uh +and we don't have to like spend nlog end + + align:start position:0% +and we don't have to like spend nlog end + + + align:start position:0% +and we don't have to like spend nlog end +time uh doing that okay uh right + + align:start position:0% +time uh doing that okay uh right + + + align:start position:0% +time uh doing that okay uh right +so apparently in our our problem we have + + align:start position:0% +so apparently in our our problem we have + + + align:start position:0% +so apparently in our our problem we have +an egg with a mysterious mechanical + + align:start position:0% +an egg with a mysterious mechanical + + + align:start position:0% +an egg with a mysterious mechanical +property that we are trying to + + align:start position:0% +property that we are trying to + + + align:start position:0% +property that we are trying to +recover and all eggs as we know are + + align:start position:0% +recover and all eggs as we know are + + + align:start position:0% +recover and all eggs as we know are +identical so you know the only + + align:start position:0% +identical so you know the only + + + align:start position:0% +identical so you know the only +difference between eggs is like chicken + + align:start position:0% +difference between eggs is like chicken + + + align:start position:0% +difference between eggs is like chicken +versus Goose versus like struggling to + + align:start position:0% +versus Goose versus like struggling to + + + align:start position:0% +versus Goose versus like struggling to +think of a third category of poultry + + align:start position:0% +think of a third category of poultry + + + align:start position:0% +think of a third category of poultry +turkey thank you um right but assuming + + align:start position:0% +turkey thank you um right but assuming + + + align:start position:0% +turkey thank you um right but assuming +that I got all of my eggs at the same + + align:start position:0% +that I got all of my eggs at the same + + + align:start position:0% +that I got all of my eggs at the same +Stop and Shop and they all come from the + + align:start position:0% +Stop and Shop and they all come from the + + + align:start position:0% +Stop and Shop and they all come from the +same species then they have roughly the + + align:start position:0% +same species then they have roughly the + + + align:start position:0% +same species then they have roughly the +same mechanical properties actually the + + align:start position:0% +same mechanical properties actually the + + + align:start position:0% +same mechanical properties actually the +probably the better setup is that floors + + align:start position:0% +probably the better setup is that floors + + + align:start position:0% +probably the better setup is that floors +are very far apart relative to the size + + align:start position:0% +are very far apart relative to the size + + + align:start position:0% +are very far apart relative to the size +of an egg um and if I get high enough my + + align:start position:0% +of an egg um and if I get high enough my + + + align:start position:0% +of an egg um and if I get high enough my +egg when I drop them on the + + align:start position:0% +egg when I drop them on the + + + align:start position:0% +egg when I drop them on the +ground like that uh + + align:start position:0% +ground like that uh + + + align:start position:0% +ground like that uh +breaks didn't break but it could have + + align:start position:0% +breaks didn't break but it could have + + + align:start position:0% +breaks didn't break but it could have +broken uh and of course if I drop it + + align:start position:0% +broken uh and of course if I drop it + + + align:start position:0% +broken uh and of course if I drop it +from an even higher height my egg still + + align:start position:0% +from an even higher height my egg still + + + align:start position:0% +from an even higher height my egg still +get going to break however if I have a + + align:start position:0% +get going to break however if I have a + + + align:start position:0% +get going to break however if I have a +very low floor apparently a very low + + align:start position:0% +very low floor apparently a very low + + + align:start position:0% +very low floor apparently a very low +floor maybe this is a house for mice um + + align:start position:0% +floor maybe this is a house for mice um + + + align:start position:0% +floor maybe this is a house for mice um +you know when I drop my egg it actually + + align:start position:0% +you know when I drop my egg it actually + + + align:start position:0% +you know when I drop my egg it actually +stays intact uh and and the question um + + align:start position:0% +stays intact uh and and the question um + + + align:start position:0% +stays intact uh and and the question um +as all good scientists want to know is + + align:start position:0% +as all good scientists want to know is + + + align:start position:0% +as all good scientists want to know is +what is the highest floor in my building + + align:start position:0% +what is the highest floor in my building + + + align:start position:0% +what is the highest floor in my building +from which I can drop an egg and uh have + + align:start position:0% +from which I can drop an egg and uh have + + + align:start position:0% +from which I can drop an egg and uh have +it remain + + align:start position:0% +it remain + + + align:start position:0% +it remain +intact + + align:start position:0% +intact + + + align:start position:0% +intact +and the question + + align:start position:0% +and the question + + + align:start position:0% +and the question +isn't is kind of a funny one it's sort + + align:start position:0% +isn't is kind of a funny one it's sort + + + align:start position:0% +isn't is kind of a funny one it's sort +of like experimental design in some + + align:start position:0% +of like experimental design in some + + + align:start position:0% +of like experimental design in some +sense it's it's not asking like what is + + align:start position:0% +sense it's it's not asking like what is + + + align:start position:0% +sense it's it's not asking like what is +the you know like given this and like a + + align:start position:0% +the you know like given this and like a + + + align:start position:0% +the you know like given this and like a +list of experiments you know try and + + align:start position:0% +list of experiments you know try and + + + align:start position:0% +list of experiments you know try and +figure infer something about the eggs + + align:start position:0% +figure infer something about the eggs + + + align:start position:0% +figure infer something about the eggs +but rather it's saying sort of if I + + align:start position:0% +but rather it's saying sort of if I + + + align:start position:0% +but rather it's saying sort of if I +carefully design a sequence of floors to + + align:start position:0% +carefully design a sequence of floors to + + + align:start position:0% +carefully design a sequence of floors to +drop my eggs from from which upon I drop + + align:start position:0% +drop my eggs from from which upon I drop + + + align:start position:0% +drop my eggs from from which upon I drop +my eggs then um you know in sort of what + + align:start position:0% +my eggs then um you know in sort of what + + + align:start position:0% +my eggs then um you know in sort of what +is the maximum number of experiments I + + align:start position:0% +is the maximum number of experiments I + + + align:start position:0% +is the maximum number of experiments I +need to do to triangulate in on that + + align:start position:0% +need to do to triangulate in on that + + + align:start position:0% +need to do to triangulate in on that +that floor that critical floor above + + align:start position:0% +that floor that critical floor above + + + align:start position:0% +that floor that critical floor above +which my eggs break yep um so what I'm + + align:start position:0% +which my eggs break yep um so what I'm + + + align:start position:0% +which my eggs break yep um so what I'm +given are the heights of the floors and + + align:start position:0% +given are the heights of the floors and + + + align:start position:0% +given are the heights of the floors and +a budget of eggs in some sense the + + align:start position:0% +a budget of eggs in some sense the + + + align:start position:0% +a budget of eggs in some sense the +budget of + + align:start position:0% +budget of + + + align:start position:0% +budget of +eggs sort of doesn't matter more than + + align:start position:0% +eggs sort of doesn't matter more than + + + align:start position:0% +eggs sort of doesn't matter more than +just like putting a cap on the size of + + align:start position:0% +just like putting a cap on the size of + + + align:start position:0% +just like putting a cap on the size of +our our problem in some sense what + + align:start position:0% +our our problem in some sense what + + + align:start position:0% +our our problem in some sense what +really matters is I'd like to use fewer + + align:start position:0% +really matters is I'd like to use fewer + + + align:start position:0% +really matters is I'd like to use fewer +than K eggs to determine that because of + + align:start position:0% +than K eggs to determine that because of + + + align:start position:0% +than K eggs to determine that because of +course the remaining ones I'm going to + + align:start position:0% +course the remaining ones I'm going to + + + align:start position:0% +course the remaining ones I'm going to +use to make an + + align:start position:0% +use to make an + + + align:start position:0% +use to make an +omelet but notice the I can be a little + + align:start position:0% +omelet but notice the I can be a little + + + align:start position:0% +omelet but notice the I can be a little +sneaky in my experimental + + align:start position:0% +sneaky in my experimental + + + align:start position:0% +sneaky in my experimental +design that + + align:start position:0% +design that + + + align:start position:0% +design that +like what happens if I drop my egg from + + align:start position:0% +like what happens if I drop my egg from + + + align:start position:0% +like what happens if I drop my egg from +a really low floor in my + + align:start position:0% +a really low floor in my + + + align:start position:0% +a really low floor in my +building well it remains intact so I can + + align:start position:0% +building well it remains intact so I can + + + align:start position:0% +building well it remains intact so I can +slep down the stairs I can pick up my + + align:start position:0% +slep down the stairs I can pick up my + + + align:start position:0% +slep down the stairs I can pick up my +egg and I can use it for my next + + align:start position:0% +egg and I can use it for my next + + + align:start position:0% +egg and I can use it for my next +experiment and I have not paid an + + align:start position:0% +experiment and I have not paid an + + + align:start position:0% +experiment and I have not paid an +egg yeah um so the first question you + + align:start position:0% +egg yeah um so the first question you + + + align:start position:0% +egg yeah um so the first question you +might ask is like well why the heck + + align:start position:0% +might ask is like well why the heck + + + align:start position:0% +might ask is like well why the heck +wouldn't I just start on the first floor + + align:start position:0% +wouldn't I just start on the first floor + + + align:start position:0% +wouldn't I just start on the first floor +drop the egg if it's not + + align:start position:0% +drop the egg if it's not + + + align:start position:0% +drop the egg if it's not +broken you know go on to the next one + + align:start position:0% +broken you know go on to the next one + + + align:start position:0% +broken you know go on to the next one +and then drop the egg and so on that + + align:start position:0% +and then drop the egg and so on that + + + align:start position:0% +and then drop the egg and so on that +would be the most egg efficient plan and + + align:start position:0% +would be the most egg efficient plan and + + + align:start position:0% +would be the most egg efficient plan and +indeed that is the case because you'll + + align:start position:0% +indeed that is the case because you'll + + + align:start position:0% +indeed that is the case because you'll +only break at most one egg but you're + + align:start position:0% +only break at most one egg but you're + + + align:start position:0% +only break at most one egg but you're +spping up and down the stairs a bunch of + + align:start position:0% +spping up and down the stairs a bunch of + + + align:start position:0% +spping up and down the stairs a bunch of +times when you solve that right like + + align:start position:0% +times when you solve that right like + + + align:start position:0% +times when you solve that right like +every single time you got to go retrieve + + align:start position:0% +every single time you got to go retrieve + + + align:start position:0% +every single time you got to go retrieve +the The Unbroken egg you got to run down + + align:start position:0% +the The Unbroken egg you got to run down + + + align:start position:0% +the The Unbroken egg you got to run down +the stairs pick the thing up and then + + align:start position:0% +the stairs pick the thing up and then + + + align:start position:0% +the stairs pick the thing up and then +run up to the next floor and maybe uh in + + align:start position:0% +run up to the next floor and maybe uh in + + + align:start position:0% +run up to the next floor and maybe uh in +your optimization problem rather than + + align:start position:0% +your optimization problem rather than + + + align:start position:0% +your optimization problem rather than +trying to like minimize the number of + + align:start position:0% +trying to like minimize the number of + + + align:start position:0% +trying to like minimize the number of +eggs that you break you're trying to + + align:start position:0% +eggs that you break you're trying to + + + align:start position:0% +eggs that you break you're trying to +minimize you know the expense on your + + align:start position:0% +minimize you know the expense on your + + + align:start position:0% +minimize you know the expense on your +your your quads and and and so instead + + align:start position:0% +your your quads and and and so instead + + + align:start position:0% +your your quads and and and so instead +you're trying you know you you skipped + + align:start position:0% +you're trying you know you you skipped + + + align:start position:0% +you're trying you know you you skipped +your leg day or whatever and the thing + + align:start position:0% +your leg day or whatever and the thing + + + align:start position:0% +your leg day or whatever and the thing +that you're trying to + + align:start position:0% +that you're trying to + + + align:start position:0% +that you're trying to +minimize is the sum over the + + align:start position:0% + + + + align:start position:0% + +heights of the drops in your experiments + + align:start position:0% +heights of the drops in your experiments + + + align:start position:0% +heights of the drops in your experiments +right so you're trying to determine the + + align:start position:0% +right so you're trying to determine the + + + align:start position:0% +right so you're trying to determine the +um mechanical property of your egg uh by + + align:start position:0% +um mechanical property of your egg uh by + + + align:start position:0% +um mechanical property of your egg uh by +designing an experiment like like sort + + align:start position:0% +designing an experiment like like sort + + + align:start position:0% +designing an experiment like like sort +of a procedure that minimizes number of + + align:start position:0% +of a procedure that minimizes number of + + + align:start position:0% +of a procedure that minimizes number of +times that you need to to drop uh eggs + + align:start position:0% +times that you need to to drop uh eggs + + + align:start position:0% +times that you need to to drop uh eggs +because every time you do you got to run + + align:start position:0% +because every time you do you got to run + + + align:start position:0% +because every time you do you got to run +all the way back down the stairs and go + + align:start position:0% +all the way back down the stairs and go + + + align:start position:0% +all the way back down the stairs and go +look at the pavement and see if the egg + + align:start position:0% +look at the pavement and see if the egg + + + align:start position:0% +look at the pavement and see if the egg +broke or not that's a lot of work okay + + align:start position:0% +broke or not that's a lot of work okay + + + align:start position:0% +broke or not that's a lot of work okay +uh this is different from the sort of + + align:start position:0% +uh this is different from the sort of + + + align:start position:0% +uh this is different from the sort of +classic egg drop 66 problem which I + + align:start position:0% +classic egg drop 66 problem which I + + + align:start position:0% +classic egg drop 66 problem which I +encourage you guys to go uh seek out in + + align:start position:0% +encourage you guys to go uh seek out in + + + align:start position:0% +encourage you guys to go uh seek out in +previous uh iterations of this + + align:start position:0% +previous uh iterations of this + + + align:start position:0% +previous uh iterations of this +course uh let me see so so right and and + + align:start position:0% +course uh let me see so so right and and + + + align:start position:0% +course uh let me see so so right and and +so the the question is what is the + + align:start position:0% +so the the question is what is the + + + align:start position:0% +so the the question is what is the +minimum the minimum number of egg drops + + align:start position:0% +minimum the minimum number of egg drops + + + align:start position:0% +minimum the minimum number of egg drops +you need to do to ascertain that for any + + align:start position:0% +you need to do to ascertain that for any + + + align:start position:0% +you need to do to ascertain that for any +type of egg + + align:start position:0% +type of egg + + + align:start position:0% +type of egg +yeah so I give you a mystery back basket + + align:start position:0% +yeah so I give you a mystery back basket + + + align:start position:0% +yeah so I give you a mystery back basket +of eggs and you have to design an + + align:start position:0% +of eggs and you have to design an + + + align:start position:0% +of eggs and you have to design an +experimental procedure uh and bound the + + align:start position:0% +experimental procedure uh and bound the + + + align:start position:0% +experimental procedure uh and bound the +number of of of this this particular + + align:start position:0% +number of of of this this particular + + + align:start position:0% +number of of of this this particular +value here given a budget of of + + align:start position:0% +value here given a budget of of + + + align:start position:0% +value here given a budget of of +kxs okay uh and um the amount of time + + align:start position:0% +kxs okay uh and um the amount of time + + + align:start position:0% +kxs okay uh and um the amount of time +that we have to do that is order n cubed + + align:start position:0% +that we have to do that is order n cubed + + + align:start position:0% +that we have to do that is order n cubed +K apparently our building we have lots + + align:start position:0% +K apparently our building we have lots + + + align:start position:0% +K apparently our building we have lots +of eggs and not very many + + align:start position:0% +of eggs and not very many + + + align:start position:0% +of eggs and not very many +floors okay because our our setup uh + + align:start position:0% +floors okay because our our setup uh + + + align:start position:0% +floors okay because our our setup uh +make some sense here we're just trying + + align:start position:0% +make some sense here we're just trying + + + align:start position:0% +make some sense here we're just trying +to avoid running up and down the stairs + + align:start position:0% +to avoid running up and down the stairs + + + align:start position:0% +to avoid running up and down the stairs +that's the M the main takeaway + + align:start position:0% +that's the M the main takeaway + + + align:start position:0% +that's the M the main takeaway +okay so uh what are we going to do sort + + align:start position:0% +okay so uh what are we going to do sort + + + align:start position:0% +okay so uh what are we going to do sort +bot because that's all we know how to do + + align:start position:0% +bot because that's all we know how to do + + + align:start position:0% +bot because that's all we know how to do +yeah um and and in particular we're + + align:start position:0% +yeah um and and in particular we're + + + align:start position:0% +yeah um and and in particular we're +going to make one observation which is + + align:start position:0% +going to make one observation which is + + + align:start position:0% +going to make one observation which is +kind of Handy if I drop a floor o if I + + align:start position:0% +kind of Handy if I drop a floor o if I + + + align:start position:0% +kind of Handy if I drop a floor o if I +drop an egg from a + + align:start position:0% +drop an egg from a + + + align:start position:0% +drop an egg from a +floor you know in this deterministic + + align:start position:0% +floor you know in this deterministic + + + align:start position:0% +floor you know in this deterministic +universe where egg mechanics are very + + align:start position:0% +universe where egg mechanics are very + + + align:start position:0% +universe where egg mechanics are very +predictable um there's only one of two + + align:start position:0% +predictable um there's only one of two + + + align:start position:0% +predictable um there's only one of two +things that can happen either egg broke + + align:start position:0% +things that can happen either egg broke + + + align:start position:0% +things that can happen either egg broke +broke or + + align:start position:0% +broke or + + + align:start position:0% +broke or +didn't or I run into the board again um + + align:start position:0% +didn't or I run into the board again um + + + align:start position:0% +didn't or I run into the board again um +so let's think about our experiment + + align:start position:0% +so let's think about our experiment + + + align:start position:0% +so let's think about our experiment +remember at the end of the day we're + + align:start position:0% +remember at the end of the day we're + + + align:start position:0% +remember at the end of the day we're +trying to figure out the tallest floor + + align:start position:0% +trying to figure out the tallest floor + + + align:start position:0% +trying to figure out the tallest floor +in my building that I can safely from + + align:start position:0% +in my building that I can safely from + + + align:start position:0% +in my building that I can safely from +which I can safely drop an + + align:start position:0% +which I can safely drop an + + + align:start position:0% +which I can safely drop an +egg so if I think about kind of + + align:start position:0% +egg so if I think about kind of + + + align:start position:0% +egg so if I think about kind of +bracketing that height of that floor + + align:start position:0% +bracketing that height of that floor + + + align:start position:0% +bracketing that height of that floor +notice that I can + + align:start position:0% +notice that I can + + + align:start position:0% +notice that I can +always for one thing do I ever need a + + align:start position:0% +always for one thing do I ever need a + + + align:start position:0% +always for one thing do I ever need a +bracket that's like not a continuous or + + align:start position:0% +bracket that's like not a continuous or + + + align:start position:0% +bracket that's like not a continuous or +like a connected set of numbers the is + + align:start position:0% +like a connected set of numbers the is + + + align:start position:0% +like a connected set of numbers the is +no right it's never it should never be + + align:start position:0% +no right it's never it should never be + + + align:start position:0% +no right it's never it should never be +the casee that like I think that my eggs + + align:start position:0% +the casee that like I think that my eggs + + + align:start position:0% +the casee that like I think that my eggs +could be on Floors one you know like + + align:start position:0% +could be on Floors one you know like + + + align:start position:0% +could be on Floors one you know like +only the prime numbered floors in my + + align:start position:0% +only the prime numbered floors in my + + + align:start position:0% +only the prime numbered floors in my +building or something that really makes + + align:start position:0% +building or something that really makes + + + align:start position:0% +building or something that really makes +no sense right because if I convince + + align:start position:0% +no sense right because if I convince + + + align:start position:0% +no sense right because if I convince +myself my egg breaks at floor five then + + align:start position:0% +myself my egg breaks at floor five then + + + align:start position:0% +myself my egg breaks at floor five then +obviously floor 6 through n my egg also + + align:start position:0% +obviously floor 6 through n my egg also + + + align:start position:0% +obviously floor 6 through n my egg also +breaks in so I always can kind of just + + align:start position:0% +breaks in so I always can kind of just + + + align:start position:0% +breaks in so I always can kind of just +keep narrowing down some + + align:start position:0% +keep narrowing down some + + + align:start position:0% +keep narrowing down some +interval right uh so in particular + + align:start position:0% +interval right uh so in particular + + + align:start position:0% +interval right uh so in particular +here's kind of a clever s in my sort bot + + align:start position:0% +here's kind of a clever s in my sort bot + + + align:start position:0% +here's kind of a clever s in my sort bot +which is to + + align:start position:0% +which is to + + + align:start position:0% +which is to +say that I'm going to say that x i j + + align:start position:0% +say that I'm going to say that x i j + + + align:start position:0% +say that I'm going to say that x i j +e is equal + + align:start position:0% +e is equal + + + align:start position:0% +e is equal +to the + + align:start position:0% +to the + + + align:start position:0% +to the +minimum by the way this is I'm writing + + align:start position:0% +minimum by the way this is I'm writing + + + align:start position:0% +minimum by the way this is I'm writing +this as minimum total height so this is + + align:start position:0% +this as minimum total height so this is + + + align:start position:0% +this as minimum total height so this is +like the minimum total times I got to + + align:start position:0% +like the minimum total times I got to + + + align:start position:0% +like the minimum total times I got to +run down the stairs and check my EGS um + + align:start position:0% +run down the stairs and check my EGS um + + + align:start position:0% +run down the stairs and check my EGS um +or total height that I run down the + + align:start position:0% +or total height that I run down the + + + align:start position:0% +or total height that I run down the +stairs the number of stairs I run down + + align:start position:0% +stairs the number of stairs I run down + + + align:start position:0% +stairs the number of stairs I run down +uh assuming my stairs are one foot tall + + align:start position:0% +uh assuming my stairs are one foot tall + + + align:start position:0% +uh assuming my stairs are one foot tall +um where I have e eggs + + align:start position:0% + + + + align:start position:0% + +left notice the way that we've written + + align:start position:0% +left notice the way that we've written + + + align:start position:0% +left notice the way that we've written +the problem this time I might as well + + align:start position:0% +the problem this time I might as well + + + align:start position:0% +the problem this time I might as well +use all of my K eggs like that doesn't + + align:start position:0% +use all of my K eggs like that doesn't + + + align:start position:0% +use all of my K eggs like that doesn't +cost me anything what cost me is running + + align:start position:0% +cost me anything what cost me is running + + + align:start position:0% +cost me anything what cost me is running +up and down the stairs um + + align:start position:0% +up and down the stairs um + + + align:start position:0% +up and down the stairs um +and uh that I have floors I through J + + align:start position:0% +and uh that I have floors I through J + + + align:start position:0% +and uh that I have floors I through J +inclusive uh to + + align:start position:0% +inclusive uh to + + + align:start position:0% +inclusive uh to +check so in other words if I'm on a + + align:start position:0% +check so in other words if I'm on a + + + align:start position:0% +check so in other words if I'm on a +floor below floor I I've convinced + + align:start position:0% +floor below floor I I've convinced + + + align:start position:0% +floor below floor I I've convinced +myself my egg won't break then if I'm + + align:start position:0% +myself my egg won't break then if I'm + + + align:start position:0% +myself my egg won't break then if I'm +going to floor above floor J I'm + + align:start position:0% +going to floor above floor J I'm + + + align:start position:0% +going to floor above floor J I'm +convinced my egg will break + + align:start position:0% +convinced my egg will break + + + align:start position:0% +convinced my egg will break +okay so what do I do well remember that + + align:start position:0% +okay so what do I do well remember that + + + align:start position:0% +okay so what do I do well remember that +this is sort of an experimental design + + align:start position:0% +this is sort of an experimental design + + + align:start position:0% +this is sort of an experimental design +problem I can drop my egg from any + + align:start position:0% + + + + align:start position:0% + +floor um f which is in the range I to J + + align:start position:0% +floor um f which is in the range I to J + + + align:start position:0% +floor um f which is in the range I to J +right and of course there's never a + + align:start position:0% +right and of course there's never a + + + align:start position:0% +right and of course there's never a +reason for me to drop an egg from a + + align:start position:0% +reason for me to drop an egg from a + + + align:start position:0% +reason for me to drop an egg from a +floor below I or above J because we + + align:start position:0% +floor below I or above J because we + + + align:start position:0% +floor below I or above J because we +already know what happens in that case + + align:start position:0% +already know what happens in that case + + + align:start position:0% +already know what happens in that case +okay + + align:start position:0% + + + + align:start position:0% + +so what happens uh when we do that well + + align:start position:0% +so what happens uh when we do that well + + + align:start position:0% +so what happens uh when we do that well +if I drop it from floor F I have to pay + + align:start position:0% +if I drop it from floor F I have to pay + + + align:start position:0% +if I drop it from floor F I have to pay +uh in terms of my cost function right + + align:start position:0% +uh in terms of my cost function right + + + align:start position:0% +uh in terms of my cost function right +because I have to pay the height of F I + + align:start position:0% +because I have to pay the height of F I + + + align:start position:0% +because I have to pay the height of F I +got to run down the the the + + align:start position:0% +got to run down the the the + + + align:start position:0% +got to run down the the the +stairs okay um but in exchange for that + + align:start position:0% +stairs okay um but in exchange for that + + + align:start position:0% +stairs okay um but in exchange for that +I learned a little bit about my egg + + align:start position:0% +I learned a little bit about my egg + + + align:start position:0% +I learned a little bit about my egg +problem right I either get an upper or a + + align:start position:0% +problem right I either get an upper or a + + + align:start position:0% +problem right I either get an upper or a +lower bound of f depending whether the + + align:start position:0% +lower bound of f depending whether the + + + align:start position:0% +lower bound of f depending whether the +egg broke okay so let's uh let's let's + + align:start position:0% +egg broke okay so let's uh let's let's + + + align:start position:0% +egg broke okay so let's uh let's let's +let's let's form that mathematically so + + align:start position:0% +let's let's form that mathematically so + + + align:start position:0% +let's let's form that mathematically so +in particular we have x i j + + align:start position:0% + + + + align:start position:0% + +e well what do I get to control in my + + align:start position:0% +e well what do I get to control in my + + + align:start position:0% +e well what do I get to control in my +life and what do I have have to deal + + align:start position:0% +life and what do I have have to deal + + + align:start position:0% +life and what do I have have to deal +with what I have to deal with is the + + align:start position:0% +with what I have to deal with is the + + + align:start position:0% +with what I have to deal with is the +fact I don't know what's going to happen + + align:start position:0% +fact I don't know what's going to happen + + + align:start position:0% +fact I don't know what's going to happen +to the egg it might break it might not + + align:start position:0% +to the egg it might break it might not + + + align:start position:0% +to the egg it might break it might not +right and the Egg might be an + + align:start position:0% +right and the Egg might be an + + + align:start position:0% +right and the Egg might be an +adversarial egg like it wants you to run + + align:start position:0% +adversarial egg like it wants you to run + + + align:start position:0% +adversarial egg like it wants you to run +up and down the stairs and I have to + + align:start position:0% +up and down the stairs and I have to + + + align:start position:0% +up and down the stairs and I have to +account for that but uh I am the eggs + + align:start position:0% +account for that but uh I am the eggs + + + align:start position:0% +account for that but uh I am the eggs +adversary and get to choose what floor I + + align:start position:0% +adversary and get to choose what floor I + + + align:start position:0% +adversary and get to choose what floor I +drop it from so remember like uh we saw + + align:start position:0% +drop it from so remember like uh we saw + + + align:start position:0% +drop it from so remember like uh we saw +an example I forget what from class + + align:start position:0% +an example I forget what from class + + + align:start position:0% +an example I forget what from class +where there was sort of a game right one + + align:start position:0% +where there was sort of a game right one + + + align:start position:0% +where there was sort of a game right one +guy was trying to minimize the other was + + align:start position:0% +guy was trying to minimize the other was + + + align:start position:0% +guy was trying to minimize the other was +trying to + + align:start position:0% +trying to + + + align:start position:0% +trying to +maximize in some sense the egg is trying + + align:start position:0% +maximize in some sense the egg is trying + + + align:start position:0% +maximize in some sense the egg is trying +to maximize the amount of work you have + + align:start position:0% +to maximize the amount of work you have + + + align:start position:0% +to maximize the amount of work you have +to do running up and down the stairs uh + + align:start position:0% +to do running up and down the stairs uh + + + align:start position:0% +to do running up and down the stairs uh +uh to do your experiment a better way to + + align:start position:0% +uh to do your experiment a better way to + + + align:start position:0% +uh to do your experiment a better way to +put it is that we're trying to Upper + + align:start position:0% +put it is that we're trying to Upper + + + align:start position:0% +put it is that we're trying to Upper +bound uh the amount of work in your + + align:start position:0% +bound uh the amount of work in your + + + align:start position:0% +bound uh the amount of work in your +experimental + + align:start position:0% +experimental + + + align:start position:0% +experimental +procedure and I'm trying to design a + + align:start position:0% +procedure and I'm trying to design a + + + align:start position:0% +procedure and I'm trying to design a +procedure that minimizes my work right + + align:start position:0% +procedure that minimizes my work right + + + align:start position:0% +procedure that minimizes my work right +so let's say that I'm the player so I + + align:start position:0% +so let's say that I'm the player so I + + + align:start position:0% +so let's say that I'm the player so I +want to minimize + + align:start position:0% +want to minimize + + + align:start position:0% +want to minimize +um + + align:start position:0% +um + + + align:start position:0% +um +and the decision that I get to make the + + align:start position:0% +and the decision that I get to make the + + + align:start position:0% +and the decision that I get to make the +control that I have is what well it's + + align:start position:0% +control that I have is what well it's + + + align:start position:0% +control that I have is what well it's +what floor I choose right so let's say I + + align:start position:0% +what floor I choose right so let's say I + + + align:start position:0% +what floor I choose right so let's say I +choose floor F Well I have to go down + + align:start position:0% +choose floor F Well I have to go down + + + align:start position:0% +choose floor F Well I have to go down +the stairs so that takes me + + align:start position:0% +the stairs so that takes me + + + align:start position:0% +the stairs so that takes me +HF I suppose going up the stairs is + + align:start position:0% +HF I suppose going up the stairs is + + + align:start position:0% +HF I suppose going up the stairs is +probably what incurs the HF and going + + align:start position:0% +probably what incurs the HF and going + + + align:start position:0% +probably what incurs the HF and going +down is nothing um but I digress but now + + align:start position:0% +down is nothing um but I digress but now + + + align:start position:0% +down is nothing um but I digress but now +my I still am not done I've narrowed + + align:start position:0% +my I still am not done I've narrowed + + + align:start position:0% +my I still am not done I've narrowed +down into one of two cases right either + + align:start position:0% +down into one of two cases right either + + + align:start position:0% +down into one of two cases right either +f is my new lower bound my new upper + + align:start position:0% +f is my new lower bound my new upper + + + align:start position:0% +f is my new lower bound my new upper +bound and I have to account for both of + + align:start position:0% +bound and I have to account for both of + + + align:start position:0% +bound and I have to account for both of +those in my recursion and I have to take + + align:start position:0% +those in my recursion and I have to take + + + align:start position:0% +those in my recursion and I have to take +the max of those two in the sense that I + + align:start position:0% +the max of those two in the sense that I + + + align:start position:0% +the max of those two in the sense that I +need an every possible case that my AEG + + align:start position:0% +need an every possible case that my AEG + + + align:start position:0% +need an every possible case that my AEG +drop experiment Narrows down my floor uh + + align:start position:0% +drop experiment Narrows down my floor uh + + + align:start position:0% +drop experiment Narrows down my floor uh +to to to a width of of zero y so in + + align:start position:0% +to to to a width of of zero y so in + + + align:start position:0% +to to to a width of of zero y so in +particular this's actually a this is a + + align:start position:0% +particular this's actually a this is a + + + align:start position:0% +particular this's actually a this is a +Minimax problem there's a Max inside of + + align:start position:0% +Minimax problem there's a Max inside of + + + align:start position:0% +Minimax problem there's a Max inside of +a Min here um so what's either the egg + + align:start position:0% +a Min here um so what's either the egg + + + align:start position:0% +a Min here um so what's either the egg +broke in my experiment or it didn't + + align:start position:0% +broke in my experiment or it didn't + + + align:start position:0% +broke in my experiment or it didn't +right so if it did broke + + align:start position:0% +right so if it did broke + + + align:start position:0% +right so if it did broke +then well what happened well let's see + + align:start position:0% +then well what happened well let's see + + + align:start position:0% +then well what happened well let's see +here um if the egg broke then I got an + + align:start position:0% +here um if the egg broke then I got an + + + align:start position:0% +here um if the egg broke then I got an +upper Bound for my floor so my lower + + align:start position:0% +upper Bound for my floor so my lower + + + align:start position:0% +upper Bound for my floor so my lower +bound Remains the Same it's I my upper + + align:start position:0% +bound Remains the Same it's I my upper + + + align:start position:0% +bound Remains the Same it's I my upper +bound it's F minus one because it broke + + align:start position:0% +bound it's F minus one because it broke + + + align:start position:0% +bound it's F minus one because it broke +on floor F well what happens to egg eggs + + align:start position:0% +on floor F well what happens to egg eggs + + + align:start position:0% +on floor F well what happens to egg eggs +when they break I can't drop them from + + align:start position:0% +when they break I can't drop them from + + + align:start position:0% +when they break I can't drop them from +floors again so I lost an + + align:start position:0% +floors again so I lost an + + + align:start position:0% +floors again so I lost an +egg + + align:start position:0% +egg + + + align:start position:0% +egg +okay so this is uh my egg brow + + align:start position:0% +okay so this is uh my egg brow + + + align:start position:0% +okay so this is uh my egg brow +okay or my egg didn't break so in that + + align:start position:0% +okay or my egg didn't break so in that + + + align:start position:0% +okay or my egg didn't break so in that +case well my egg didn't break now I have + + align:start position:0% +case well my egg didn't break now I have + + + align:start position:0% +case well my egg didn't break now I have +a lower + + align:start position:0% +a lower + + + align:start position:0% +a lower +bound so I'm only unclear about floor is + + align:start position:0% +bound so I'm only unclear about floor is + + + align:start position:0% +bound so I'm only unclear about floor is +f+ one uh but uh the upper bound didn't + + align:start position:0% +f+ one uh but uh the upper bound didn't + + + align:start position:0% +f+ one uh but uh the upper bound didn't +change it's still + + align:start position:0% +change it's still + + + align:start position:0% +change it's still +J and how many eggs do I have well my + + align:start position:0% +J and how many eggs do I have well my + + + align:start position:0% +J and how many eggs do I have well my +egg didn't break so I can run down the + + align:start position:0% +egg didn't break so I can run down the + + + align:start position:0% +egg didn't break so I can run down the +stairs which is going to be tiring right + + align:start position:0% +stairs which is going to be tiring right + + + align:start position:0% +stairs which is going to be tiring right +I've accounted for that here but at + + align:start position:0% +I've accounted for that here but at + + + align:start position:0% +I've accounted for that here but at +least I can reuse my egg so I didn't + + align:start position:0% +least I can reuse my egg so I didn't + + + align:start position:0% +least I can reuse my egg so I didn't +lose + + align:start position:0% +lose + + + align:start position:0% +lose +anything okay + + align:start position:0% +anything okay + + + align:start position:0% +anything okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and I get to choose so notice + + align:start position:0% +and I get to choose so notice + + + align:start position:0% +and I get to choose so notice +oops so do you guys see why there's a + + align:start position:0% +oops so do you guys see why there's a + + + align:start position:0% +oops so do you guys see why there's a +Max here essentially I have to account + + align:start position:0% +Max here essentially I have to account + + + align:start position:0% +Max here essentially I have to account +for every possible scenario when I'm + + align:start position:0% +for every possible scenario when I'm + + + align:start position:0% +for every possible scenario when I'm +when I'm designing my experimental + + align:start position:0% +when I'm designing my experimental + + + align:start position:0% +when I'm designing my experimental +procedure but I get to minimize in the + + align:start position:0% +procedure but I get to minimize in the + + + align:start position:0% +procedure but I get to minimize in the +sense that I can choose what floor at + + align:start position:0% +sense that I can choose what floor at + + + align:start position:0% +sense that I can choose what floor at +every step so um right so in particular + + align:start position:0% +every step so um right so in particular + + + align:start position:0% +every step so um right so in particular +uh my f here is in the range I to + + align:start position:0% +uh my f here is in the range I to + + + align:start position:0% +uh my f here is in the range I to +J like that + + align:start position:0% +J like that + + + align:start position:0% +J like that +okay and now we have our recursive + + align:start position:0% +okay and now we have our recursive + + + align:start position:0% +okay and now we have our recursive +formula for our our our egg drop that + + align:start position:0% +formula for our our our egg drop that + + + align:start position:0% +formula for our our our egg drop that +minimizes total height um so now let's + + align:start position:0% +minimizes total height um so now let's + + + align:start position:0% +minimizes total height um so now let's +uh finish off sort bot in four minutes + + align:start position:0% +uh finish off sort bot in four minutes + + + align:start position:0% +uh finish off sort bot in four minutes +it's actually not too hard so I think + + align:start position:0% +it's actually not too hard so I think + + + align:start position:0% +it's actually not too hard so I think +we'll actually make it for once by + + align:start position:0% +we'll actually make it for once by + + + align:start position:0% +we'll actually make it for once by +removing 20% of the problems I'm + + align:start position:0% +removing 20% of the problems I'm + + + align:start position:0% +removing 20% of the problems I'm +supposed to cover um all + + align:start position:0% + + + + align:start position:0% + +right so first of all what's our + + align:start position:0% +right so first of all what's our + + + align:start position:0% +right so first of all what's our +topological + + align:start position:0% +topological + + + align:start position:0% +topological +order so + + align:start position:0% + + + + align:start position:0% + +this one seems kind of annoying + + align:start position:0% +this one seems kind of annoying + + + align:start position:0% +this one seems kind of annoying +because I think usually we think of + + align:start position:0% +because I think usually we think of + + + align:start position:0% +because I think usually we think of +spending stuff in a lot of these uh + + align:start position:0% +spending stuff in a lot of these uh + + + align:start position:0% +spending stuff in a lot of these uh +dynamic programming problems but do we + + align:start position:0% +dynamic programming problems but do we + + + align:start position:0% +dynamic programming problems but do we +actually spend an egg not necessarily + + align:start position:0% +actually spend an egg not necessarily + + + align:start position:0% +actually spend an egg not necessarily +right because in this recursive + + align:start position:0% +right because in this recursive + + + align:start position:0% +right because in this recursive +call you know the number of eggs I had + + align:start position:0% +call you know the number of eggs I had + + + align:start position:0% +call you know the number of eggs I had +remained the same so maybe that's not + + align:start position:0% +remained the same so maybe that's not + + + align:start position:0% +remained the same so maybe that's not +actually a great way to establish a + + align:start position:0% +actually a great way to establish a + + + align:start position:0% +actually a great way to establish a +topological order but instead what do we + + align:start position:0% +topological order but instead what do we + + + align:start position:0% +topological order but instead what do we +know like what is in science the purpose + + align:start position:0% +know like what is in science the purpose + + + align:start position:0% +know like what is in science the purpose +of an experiment you know uh it's to + + align:start position:0% +of an experiment you know uh it's to + + + align:start position:0% +of an experiment you know uh it's to +improve our understanding of the world + + align:start position:0% +improve our understanding of the world + + + align:start position:0% +improve our understanding of the world +in this case our world consists only of + + align:start position:0% +in this case our world consists only of + + + align:start position:0% +in this case our world consists only of +eggs and floors of buildings um and in + + align:start position:0% +eggs and floors of buildings um and in + + + align:start position:0% +eggs and floors of buildings um and in +particular once I dropped that egg I + + align:start position:0% +particular once I dropped that egg I + + + align:start position:0% +particular once I dropped that egg I +learned something about my building and + + align:start position:0% +learned something about my building and + + + align:start position:0% +learned something about my building and +I narrowed down the range of floors that + + align:start position:0% +I narrowed down the range of floors that + + + align:start position:0% +I narrowed down the range of floors that +are uncertain for me so in + + align:start position:0% +are uncertain for me so in + + + align:start position:0% +are uncertain for me so in +particular I know that x i j e + + align:start position:0% +particular I know that x i j e + + + align:start position:0% +particular I know that x i j e +only uh + + align:start position:0% +only uh + + + align:start position:0% +only uh +depends on X I guess I prime J Prime e + + align:start position:0% +depends on X I guess I prime J Prime e + + + align:start position:0% +depends on X I guess I prime J Prime e +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +um with what well my sub problems I + + align:start position:0% +um with what well my sub problems I + + + align:start position:0% +um with what well my sub problems I +always have a smaller range of floors + + align:start position:0% +always have a smaller range of floors + + + align:start position:0% +always have a smaller range of floors +than I did before so in particular J + + align:start position:0% +than I did before so in particular J + + + align:start position:0% +than I did before so in particular J +Prime minus I prime is going to be + + align:start position:0% +Prime minus I prime is going to be + + + align:start position:0% +Prime minus I prime is going to be +smaller strictly than J minus I and + + align:start position:0% +smaller strictly than J minus I and + + + align:start position:0% +smaller strictly than J minus I and +that'll give me my topological + + align:start position:0% + + + + align:start position:0% + +order cool uh and so that's actually to + + align:start position:0% +order cool uh and so that's actually to + + + align:start position:0% +order cool uh and so that's actually to +I think the sort of annoying part other + + align:start position:0% +I think the sort of annoying part other + + + align:start position:0% +I think the sort of annoying part other +than working out this Minimax expression + + align:start position:0% +than working out this Minimax expression + + + align:start position:0% +than working out this Minimax expression +here uh the remaining uh things are not + + align:start position:0% +here uh the remaining uh things are not + + + align:start position:0% +here uh the remaining uh things are not +so hard so uh what are our base cases + + align:start position:0% +so hard so uh what are our base cases + + + align:start position:0% +so hard so uh what are our base cases +well let's say I have zero eggs left but + + align:start position:0% +well let's say I have zero eggs left but + + + align:start position:0% +well let's say I have zero eggs left but +I still have a set of Uncertain floors + + align:start position:0% +I still have a set of Uncertain floors + + + align:start position:0% +I still have a set of Uncertain floors +that's bad news yeah so yeah so that + + align:start position:0% +that's bad news yeah so yeah so that + + + align:start position:0% +that's bad news yeah so yeah so that +should be + + align:start position:0% +should be + + + align:start position:0% +should be +infinity and the reason um is of course + + align:start position:0% +infinity and the reason um is of course + + + align:start position:0% +infinity and the reason um is of course +um I'm going to take the Min here right + + align:start position:0% +um I'm going to take the Min here right + + + align:start position:0% +um I'm going to take the Min here right +and so I obviously I should never choose + + align:start position:0% +and so I obviously I should never choose + + + align:start position:0% +and so I obviously I should never choose +Infinity as a as a Min um so in other + + align:start position:0% +Infinity as a as a Min um so in other + + + align:start position:0% +Infinity as a as a Min um so in other +words I I should never choose an option + + align:start position:0% +words I I should never choose an option + + + align:start position:0% +words I I should never choose an option +for a floor that could possibly lead me + + align:start position:0% +for a floor that could possibly lead me + + + align:start position:0% +for a floor that could possibly lead me +to an uncertain scenario um when I run + + align:start position:0% +to an uncertain scenario um when I run + + + align:start position:0% +to an uncertain scenario um when I run +out of achs yeah um in addition to that + + align:start position:0% +out of achs yeah um in addition to that + + + align:start position:0% +out of achs yeah um in addition to that +there's another base case here right so + + align:start position:0% +there's another base case here right so + + + align:start position:0% +there's another base case here right so +this is like I've got no eggs left but + + align:start position:0% +this is like I've got no eggs left but + + + align:start position:0% +this is like I've got no eggs left but +some FL us to check uh there's a second + + align:start position:0% +some FL us to check uh there's a second + + + align:start position:0% +some FL us to check uh there's a second +one + + align:start position:0% +one + + + align:start position:0% +one +I IUS one e so in this case I've got e + + align:start position:0% +I IUS one e so in this case I've got e + + + align:start position:0% +I IUS one e so in this case I've got e +eggs left and I'm done right i' I've + + align:start position:0% +eggs left and I'm done right i' I've + + + align:start position:0% +eggs left and I'm done right i' I've +narrowed it down to uh uh the bounce + + align:start position:0% +narrowed it down to uh uh the bounce + + + align:start position:0% +narrowed it down to uh uh the bounce +incidentally the way I wrote it in terms + + align:start position:0% +incidentally the way I wrote it in terms + + + align:start position:0% +incidentally the way I wrote it in terms +of inclusive versus exclusive might be a + + align:start position:0% +of inclusive versus exclusive might be a + + + align:start position:0% +of inclusive versus exclusive might be a +little + + align:start position:0% +little + + + align:start position:0% +little +fishy over here you guys shouldn't be + + align:start position:0% +fishy over here you guys shouldn't be + + + align:start position:0% +fishy over here you guys shouldn't be +off by one like your inspector often is + + align:start position:0% +off by one like your inspector often is + + + align:start position:0% +off by one like your inspector often is +um but in any event you're you're zero + + align:start position:0% +um but in any event you're you're zero + + + align:start position:0% +um but in any event you're you're zero +right there's no more floors left to + + align:start position:0% +right there's no more floors left to + + + align:start position:0% +right there's no more floors left to +check you you've narrowed it down to a + + align:start position:0% +check you you've narrowed it down to a + + + align:start position:0% +check you you've narrowed it down to a +range of one again something that I'm + + align:start position:0% +range of one again something that I'm + + + align:start position:0% +range of one again something that I'm +out of time so I'm not going to check + + align:start position:0% +out of time so I'm not going to check + + + align:start position:0% +out of time so I'm not going to check +carefully is if my bounds are inclusive + + align:start position:0% +carefully is if my bounds are inclusive + + + align:start position:0% +carefully is if my bounds are inclusive +should that be i j minus one I IUS one + + align:start position:0% +should that be i j minus one I IUS one + + + align:start position:0% +should that be i j minus one I IUS one +or just I I but I think you guys are all + + align:start position:0% +or just I I but I think you guys are all + + + align:start position:0% +or just I I but I think you guys are all +smart enough to work that out at home + + align:start position:0% +smart enough to work that out at home + + + align:start position:0% +smart enough to work that out at home +what should my original case be well now + + align:start position:0% +what should my original case be well now + + + align:start position:0% +what should my original case be well now +I have all the floors to check and all + + align:start position:0% +I have all the floors to check and all + + + align:start position:0% +I have all the floors to check and all +my eggs in my uh metaphorical basket + + align:start position:0% +my eggs in my uh metaphorical basket + + + align:start position:0% +my eggs in my uh metaphorical basket +here so I have um floors is one 2 N here + + align:start position:0% +here so I have um floors is one 2 N here + + + align:start position:0% +here so I have um floors is one 2 N here +uh and the problem tells me I have K + + align:start position:0% +uh and the problem tells me I have K + + + align:start position:0% +uh and the problem tells me I have K +eggs when I start and then finally I + + align:start position:0% +eggs when I start and then finally I + + + align:start position:0% +eggs when I start and then finally I +need to do my uh sub problems + + align:start position:0% + + + + align:start position:0% + +here I think you can actually simplify + + align:start position:0% +here I think you can actually simplify + + + align:start position:0% +here I think you can actually simplify +the the argument that that's written + + align:start position:0% +the the argument that that's written + + + align:start position:0% +the the argument that that's written +down a tiny bit um and just again look + + align:start position:0% +down a tiny bit um and just again look + + + align:start position:0% +down a tiny bit um and just again look +at your your sub problems so they're + + align:start position:0% +at your your sub problems so they're + + + align:start position:0% +at your your sub problems so they're +indexed by three + + align:start position:0% +indexed by three + + + align:start position:0% +indexed by three +numbers I'm going to do a really + + align:start position:0% +numbers I'm going to do a really + + + align:start position:0% +numbers I'm going to do a really +conservative estimate I think the + + align:start position:0% +conservative estimate I think the + + + align:start position:0% +conservative estimate I think the +problem actually works out a better + + align:start position:0% +problem actually works out a better + + + align:start position:0% +problem actually works out a better +estimate but then ASM totically it's the + + align:start position:0% +estimate but then ASM totically it's the + + + align:start position:0% +estimate but then ASM totically it's the +same um what's our bound on the first + + align:start position:0% +same um what's our bound on the first + + + align:start position:0% +same um what's our bound on the first +and second index well they're both just + + align:start position:0% +and second index well they're both just + + + align:start position:0% +and second index well they're both just +the index of floors um which which go + + align:start position:0% +the index of floors um which which go + + + align:start position:0% +the index of floors um which which go +between zero and and N yeah obviously + + align:start position:0% +between zero and and N yeah obviously + + + align:start position:0% +between zero and and N yeah obviously +you could do better than that because + + align:start position:0% +you could do better than that because + + + align:start position:0% +you could do better than that because +the lower floor is always less than the + + align:start position:0% +the lower floor is always less than the + + + align:start position:0% +the lower floor is always less than the +Upper Floor which is what the problem + + align:start position:0% +Upper Floor which is what the problem + + + align:start position:0% +Upper Floor which is what the problem +accounts for um but if I'm being lazy + + align:start position:0% +accounts for um but if I'm being lazy + + + align:start position:0% +accounts for um but if I'm being lazy +then you know well there's n + + align:start position:0% +then you know well there's n + + + align:start position:0% +then you know well there's n +squared uh sub problems to account for + + align:start position:0% +squared uh sub problems to account for + + + align:start position:0% +squared uh sub problems to account for +the two floors uh and the third index uh + + align:start position:0% +the two floors uh and the third index uh + + + align:start position:0% +the two floors uh and the third index uh +is is your eggs which you have MOS K + + align:start position:0% +is is your eggs which you have MOS K + + + align:start position:0% +is is your eggs which you have MOS K +of okay uh how much work um do we have + + align:start position:0% +of okay uh how much work um do we have + + + align:start position:0% +of okay uh how much work um do we have +per sub problem well uh let's see here + + align:start position:0% +per sub problem well uh let's see here + + + align:start position:0% +per sub problem well uh let's see here +there's a for Loop over f f is over + + align:start position:0% +there's a for Loop over f f is over + + + align:start position:0% +there's a for Loop over f f is over +floor again if I'm going to be really + + align:start position:0% +floor again if I'm going to be really + + + align:start position:0% +floor again if I'm going to be really +conservative right well there's a most + + align:start position:0% +conservative right well there's a most + + + align:start position:0% +conservative right well there's a most +uh n uh Flor is total my build and so + + align:start position:0% +uh n uh Flor is total my build and so + + + align:start position:0% +uh n uh Flor is total my build and so +that leads us to a runtime of n Cub K + + align:start position:0% +that leads us to a runtime of n Cub K + + + align:start position:0% +that leads us to a runtime of n Cub K +which is what we wanted at the end of + + align:start position:0% +which is what we wanted at the end of + + + align:start position:0% +which is what we wanted at the end of +the day okay + + align:start position:0% +the day okay + + + align:start position:0% +the day okay +um there should be a big O here because + + align:start position:0% +um there should be a big O here because + + + align:start position:0% +um there should be a big O here because +I think technically this is n plus one + + align:start position:0% +I think technically this is n plus one + + + align:start position:0% +I think technically this is n plus one +to account for floor + + align:start position:0% +to account for floor + + + align:start position:0% +to account for floor +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay and that uh that solves our our ACH + + align:start position:0% +okay and that uh that solves our our ACH + + + align:start position:0% +okay and that uh that solves our our ACH +drop uh experiment again I think this is + + align:start position:0% +drop uh experiment again I think this is + + + align:start position:0% +drop uh experiment again I think this is +a nice one and I think in my mind + + align:start position:0% +a nice one and I think in my mind + + + align:start position:0% +a nice one and I think in my mind +actually in terms of dynamic programming + + align:start position:0% +actually in terms of dynamic programming + + + align:start position:0% +actually in terms of dynamic programming +this is one of the harder things to get + + align:start position:0% +this is one of the harder things to get + + + align:start position:0% +this is one of the harder things to get +right which are these sort of + + align:start position:0% +right which are these sort of + + + align:start position:0% +right which are these sort of +Minimax games you could probably I'd + + align:start position:0% +Minimax games you could probably I'd + + + align:start position:0% +Minimax games you could probably I'd +have to think about it which in my + + align:start position:0% +have to think about it which in my + + + align:start position:0% +have to think about it which in my +negative -2 minutes I'm not going to + + align:start position:0% +negative -2 minutes I'm not going to + + + align:start position:0% +negative -2 minutes I'm not going to +have time to do I think in in lecture + + align:start position:0% +have time to do I think in in lecture + + + align:start position:0% +have time to do I think in in lecture +the way that we solved Minimax problem + + align:start position:0% +the way that we solved Minimax problem + + + align:start position:0% +the way that we solved Minimax problem +was we separated out the Min and the Max + + align:start position:0% +was we separated out the Min and the Max + + + align:start position:0% +was we separated out the Min and the Max +and we thought of there being two + + align:start position:0% +and we thought of there being two + + + align:start position:0% +and we thought of there being two +dynamic programming problems that were + + align:start position:0% +dynamic programming problems that were + + + align:start position:0% +dynamic programming problems that were +sort of interacting with each other you + + align:start position:0% +sort of interacting with each other you + + + align:start position:0% +sort of interacting with each other you +could probably write this one in that + + align:start position:0% +could probably write this one in that + + + align:start position:0% +could probably write this one in that +form as well I guess just by kind of + + align:start position:0% +form as well I guess just by kind of + + + align:start position:0% +form as well I guess just by kind of +pulling this term out and thinking of it + + align:start position:0% +pulling this term out and thinking of it + + + align:start position:0% +pulling this term out and thinking of it +as a different array um but this form is + + align:start position:0% +as a different array um but this form is + + + align:start position:0% +as a different array um but this form is +perfectly fine too either one's all + + align:start position:0% +perfectly fine too either one's all + + + align:start position:0% +perfectly fine too either one's all +right but in my mind these are are sort + + align:start position:0% +right but in my mind these are are sort + + + align:start position:0% +right but in my mind these are are sort +of the hardest things to get right in + + align:start position:0% +of the hardest things to get right in + + + align:start position:0% +of the hardest things to get right in +dynamic programming so I would choose + + align:start position:0% +dynamic programming so I would choose + + + align:start position:0% +dynamic programming so I would choose +whichever one jibes in your uh brain so + + align:start position:0% +whichever one jibes in your uh brain so + + + align:start position:0% +whichever one jibes in your uh brain so +uh in your thing should we choose to + + align:start position:0% +uh in your thing should we choose to + + + align:start position:0% +uh in your thing should we choose to +leave it alone there is a fifth problem + + align:start position:0% +leave it alone there is a fifth problem + + + align:start position:0% +leave it alone there is a fifth problem +here which as usual I haven't managed to + + align:start position:0% +here which as usual I haven't managed to + + + align:start position:0% +here which as usual I haven't managed to +uh get to where you're kind of building + + align:start position:0% +uh get to where you're kind of building + + + align:start position:0% +uh get to where you're kind of building +Walls by placing tiles this is an + + align:start position:0% +Walls by placing tiles this is an + + + align:start position:0% +Walls by placing tiles this is an +interesting one because your runtime is + + align:start position:0% +interesting one because your runtime is + + + align:start position:0% +interesting one because your runtime is +exponential um but the problem tells you + + align:start position:0% +exponential um but the problem tells you + + + align:start position:0% +exponential um but the problem tells you +that that's + + align:start position:0% +that that's + + + align:start position:0% +that that's +allowed but there's like some + + align:start position:0% +allowed but there's like some + + + align:start position:0% +allowed but there's like some +exponential things which are okay and + + align:start position:0% +exponential things which are okay and + + + align:start position:0% +exponential things which are okay and +some that are not right like essentially + + align:start position:0% +some that are not right like essentially + + + align:start position:0% +some that are not right like essentially +what you don't want is like product of + + align:start position:0% +what you don't want is like product of + + + align:start position:0% +what you don't want is like product of +two giant exponentials you'd like to + + align:start position:0% +two giant exponentials you'd like to + + + align:start position:0% +two giant exponentials you'd like to +just get it down to one um basically + + align:start position:0% +just get it down to one um basically + + + align:start position:0% +just get it down to one um basically +saying it's going to be polom if you a + + align:start position:0% +saying it's going to be polom if you a + + + align:start position:0% +saying it's going to be polom if you a +small height that's right or it's it's + + align:start position:0% +small height that's right or it's it's + + + align:start position:0% +small height that's right or it's it's +polinomial in everything except for the + + align:start position:0% +polinomial in everything except for the + + + align:start position:0% +polinomial in everything except for the +things that's exponential in and and and + + align:start position:0% +things that's exponential in and and and + + + align:start position:0% +things that's exponential in and and and +moreover the things it's exponential in + + align:start position:0% +moreover the things it's exponential in + + + align:start position:0% +moreover the things it's exponential in +are are small and and the problem say + + align:start position:0% +are are small and and the problem say + + + align:start position:0% +are are small and and the problem say +that so I I encourage you guys to take a + + align:start position:0% +that so I I encourage you guys to take a + + + align:start position:0% +that so I I encourage you guys to take a +look because it really does take some + + align:start position:0% +look because it really does take some + + + align:start position:0% +look because it really does take some +time to logic through it but the setup + + align:start position:0% +time to logic through it but the setup + + + align:start position:0% +time to logic through it but the setup +for that problem is I think longer than + + align:start position:0% +for that problem is I think longer than + + + align:start position:0% +for that problem is I think longer than +my glacially slow board uh writing can + + align:start position:0% +my glacially slow board uh writing can + + + align:start position:0% +my glacially slow board uh writing can +can handle um but with that uh we'll + + align:start position:0% +can handle um but with that uh we'll + + + align:start position:0% +can handle um but with that uh we'll +call for the + + align:start position:0% + + + + align:start position:0% + +day \ No newline at end of file diff --git a/KYQ2dPW5nEU.txt b/KYQ2dPW5nEU.txt new file mode 100644 index 0000000000000000000000000000000000000000..14de083aec0feaafa0fa1aaa342333b1c3d15e08 --- /dev/null +++ b/KYQ2dPW5nEU.txt @@ -0,0 +1,3989 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So everybody +ready to rock and roll today? + +Or at least roll? + +OK, if not rock. + +Welcome back to lecture 20. + +On Thursday, we have a special +guest appearance just for you + +from Professor Ron Weiss. + +He's going to be talking +about synthetic biology. + +You know, on Richard +Feynman's blackboard, + +when he died, was a little +statement I've always + +really enjoyed that was actually +encased in a little chalk line. + +And it said, "What I cannot +create, I do not understand." + +And so synthetic +biology is one way + +to approach questions in +the biological sciences + +by seeing what we +can make-- you know, + +whole organisms, new +genomes, rewiring circuitry. + +So I think you'll find it to be +a very interesting discussion + +on Thursday. + +But first, before we talk +about synthetic biology, + +we have the very +exciting discussion today + +on human genetics, which of +course concerns all of us. + +And so we're going to +have an exploration today. + +And you know, as I +prepared today's lecture, + +I wanted to give you the latest +and greatest research findings. + +So we're going to talk today +from fundamental techniques + +to things that are very +controversial that have caused + +fistfights in bars, so +I'm hopeful that you'll + +be as engaged as the +people drinking beer are. + +So we'll be turning to that +at the end of the lecture, + +but first I wanted to tell you +about the broad narrative arc + +once again that we're going +to be talking about today. + +And we're going to +be looking at how + +to discover human variation. + +We're all different, about +1 based in every 1,000. + +And there are two different +broad approaches historically + +people have used. + +Microarrays for +discovering variants, + +and we'll talk about +how those were designed. + +And we'll talk about +how to actually test + +for the significance +of human variation + +with respect to a particular +disease in a case and control + +study. + +And then we'll talk about how +to use whole genome read data + +to detect variation +between humans + +and some of the +challenges in that, + +because it does not +make as many assumptions + +as the microarray studies, +and therefore is much, much + +more complicated to process. + +And so we're going to +take a view into the best + +practices of processing +human read data + +so you can understand what +the state of the art is. + +And then we're going to +turn to a study showing + +how we can bring together +different threads we've + +talked about in this subject. + +In particular, we've +talked about the idea + +that we can use other genomic +signals such as histone marks + +to identify things like +regulatory elements. + +So we're going to talk about +how we can take that lens + +and focus it on the +genome to discover + +particular genomic variants that +have been revealed to be very + +important in a +particular disease. + +And finally, we'll +talk about the idea + +that what-- the beginning +we're going to talk about today + +is all about correlation. + +And as all of you go forward +in your scientific career, + +I'm hopeful that you'll always +be careful to not confuse + +association or correlation +with causation. + +You're always respected +when you clearly + +articulate the difference when +you're giving a talk saying + +that this is correlated, +but we don't necessarily + +know it's causative until we do +the right set of experiments. + +OK, on that note, we'll turn +to the computational approaches + +we're going to talk about. + +We'll talk about contingency +tables and various ways + +of thinking about +them when we discuss + +how to identify whether or not +a particular SNP is associated + +with a disease using +various kinds of tests. + +And then we talk +about read data, + +and we'll talk about +likelihood based tests. + +How to do things like +take a population + +of individuals and +their read data + +and estimate the +genotypic frequencies + +at a particular +locus using that data + +in toto using EM +based techniques. + +OK? + +So let us begin then. + +Some of the things we're +not going to talk about + +include non-random +genotyping failure, + +methods to correct for +population stratification, + +and structural variants +and copy number variations. + +Point three we'll +just briefly touch on, + +but fundamentally they're +just embellishments + +on the fundamental techniques +we're talking about, + +and so I didn't really want +to confuse today's discussion. + +Now a Mendelian +disorder is a disorder + +defined by a single gene, +and therefore, they're + +relatively easy to map. + +And they also tend to +be in low frequency + +in the population because +they're selected against, + +especially the more severe +Mendelian disorders. + +And therefore, they correspond +to very rare mutations + +in the population. + +By point of contrast, if you +thought about the genetics + +we discussed last +time, if you think + +about a trait that +actually perhaps + +is influenced by 200 genes and +maybe that one of those genes + +is not necessary or sufficient +for a particular disease. + +As a consequence, it could +be a fairly common variant + +and it's only if you're unlucky +enough to get all the other 199 + +variants will you actually +come down with that syndrome. + +And therefore, you can see +that the effect of variation + +in the human genome +is inversely related + +to its frequency-- that +fairly rare variants can have + +very serious effects, whereas +fairly common variants tend + +to have fewer effects. + +And in the first phase of +mapping human variation, + +people thought that +common variants + +were things that had +an allelic frequency + +in the population +of 5% or greater. + +And then to burrow down deeper, +the 1000 Genomes Project + +surveyed a collection of +different populations. + +And therefore, if you +thought that a variant was + +prevalent in the +population at frequency + +of 0.5%, how many people +would have in the 1000 Genomes + +Project roughly? + +Just make sure among you +we're phase-locked here. + +0.5%, 1,000 people-- + +AUDIENCE: 5. + +PROFESSOR: 5, great. + +OK. + +Good. + +Now of course, these are three +different populations or more, + +and so it might be that, +in fact, that variant's + +only present in one +of the population. + +So it just might be +one or two people + +that actually have a +particular variant. + +So the idea is that the way that +you design SNP chips to detect + +single nucleotide polymorphisms, +otherwise known as "SNPs," + +is that you do these +population-based sequencing + +studies and you +design the array based + +upon all of the common +variants that you find, OK? + +And therefore, the array +gives you a direct readout + +in terms of the +variation, in terms + +of all of these common variants. + +That's where we'll start today. + +And where we'll end today is +sequencing based approaches, + +which make no assumptions +whatsoever and just all hell + +breaks loose. + +So you'll see what happens, OK? + +But I wanted just to +reinforce the idea + +that there are different +allelic frequencies of variants + +and that as we get down to +rarer and rarer alleles, right, + +we have larger effects. + +But these higher +frequency alleles + +could also have effects even +though they're much smaller. + +OK, so let's talk about +how these variants arise + +and what they mean in terms +of a small little cartoon. + +So long, long ago, +in a world far, + +far away, a mutation +occurred where + +a base G got mutated +to a base A, OK? + +And this was in the context of +a population of individuals-- + +all happy, smiling individuals +because they all actually + +do not have a disease. + +And our story goes, +what happens is + +that we had yet another +generation of people who + +are all happy, smiling because +they do not have the disease. + +Right? + +Yes, I do tell +stories at night, too. + +And then another +mutation occurred. + +And that mutation caused +some subset of those people + +to get the mutation and for +them to get the disease. + +So the original mutation was +not sufficient for people + +to get this genetic disease. + +It required a second +mutation for them + +to get the genetic disease, OK? + +So we got at least two +genes involved in it. + +OK, the other thing +that we know is + +that, in this particular +case, some of the people + +have the disease that +don't have this mutation. + +And therefore, this +mutation is not necessary. + +It's neither necessary +nor sufficient. + +Still, it is a marker of a +gene that increases risk. + +And that's a +fundamental idea, right, + +that you can increase +risk without being + +necessary or sufficient to cause +a particular genetic disorder. + +OK? + +And so you get this association +then between genotype + +and phenotype, and +that's what we're + +going to go looking +for right now. + +We're on the hunt. + +We're going to go looking +for this relationship. + +So in certain older +individuals-- hopefully, + +not myself in the +future-- what happens + +is that your maculus, which +is the center of your eye, + +degenerates as shown here. + +And you get this +unfortunate property + +where you can't actually +see in the center + +of your field of vision. + +It's called age-related +macular degeneration. + +So to look for the +causes of this, which + +is known to be +genetically related, + +the authors of the study +collected a collection-- + +a cohort, as it's called-- +of these European-descent + +individuals, all who are at +least 60 years old, to study + +the genetic foundations +for this disorder. + +And so they found +934 controls that + +were unaffected by age-related +macular degeneration and 1,238 + +cases, and they genotyped +them all using arrays. + +Now the question is, are +any of the identified + +SNPs on the array related +to this particular disorder? + +So I'll give you +the answer first + +and then we'll +talk about a couple + +of different ways of +thinking about this data, OK? + +So here's the answer. + +Here's a particular +SNP, rs1061170. + +There are the individuals +with AMD and the controls. + +And what you're +looking at up here, + +these numbers are the +allelic counts, all right? + +So each person has +how many alleles? + +Two, right? + +That's double the +number of individuals. + +And the question is, +are the C and T alleles + +associated with the cases +or controls significantly? + +And so you can compute +a Chi-square metric + +on this so-called +contingency table. + +And one of the things +about contingency tables + +that I think is +important to point out + +is that you hear about +marginal probabilities, right? + +And people probably +know that originally + +derived from the +idea of these margins + +along the side of a +contingency table, right? + +If you think about the marginal +probability of somebody + +having a C allele, regardless +of whether a case or control, + +it would be 2,192 +over 4,344, right? + +So the formula for computing +the Chi-square statistic + +is shown here. + +It's this sort of +scary-looking polynomial. + +And the number of +degrees of freedom is 1. + +It's the number of rows +minus 1 times the number + +of columns minus 1. + +And the P-value we get is +indeed quite small-- 10 + +to the minus 62. + +Therefore, the +chance this happened + +at random-- even with +multiple hypothesis + +correction, given that we're +testing a million SNPs-- + +is indeed very, very low. + +This looks like a winner. + +Looks like we've got a +SNP that is associated + +with this particular disease. + +Now just to remind you about +Chi-square statistics-- + +I'm sure people have seen this +before-- the usual formulation + +is that you compute this +Chi-square polynomial + +on the right-hand side, +which is the observed + +number of something minus the +expected number of something + +squared over the expected +number or something, right? + +And you sum it up over +all the different cases. + +And you can see that the +expected number of As + +is given by the little +formula on the left. + +Suffice to say, if you expand +that formula and manipulate it, + +you get the equation we +had on the previous slide. + +So it's still that fuzzy, +friendly Chi-square formula + +you always knew, just +in a different form, OK? + +Now is there +another way to think + +about computing the likelihood +of seeing data in a contingency + +table at random, right? + +Because we're always asking, +could this just be random? + +I mean, could this have +occurred by chance, + +that we see the data arranged +in this particular form? + +Well, we've another +convenient way + +of thinking about +this, which is we could + +do Fisher's Exact Test, +which is very related + +to the idea of the +hypergeometric test + +that we've talked +about before, right? + +What are the chances we would +see exactly this arrangement? + +Well, we would need to have, +out of a plus b C alleles, + +we'd have 8 of them be cases, +which is the first term there + +in that equation. + +And of the T alleles, we need to +have c of them out of c plus d + +be there. + +And then we need to have a +plus b plus c plus d choose + +a plus c-- that's the +total number of chances + +of seeing things. + +So this is the probability +of the arrangement + +in the table in this +particular form. + +Now people-- I'll let +you digest that for one + +second before I go on. + +So this is the number of ways +on the numerator of arranging + +things to get the table +the way that we see it + +over the total number or +ways of arranging the table, + +keeping the marginal +totals the same. + +Is that clear? + +So this is the probability, +the exact probability, + +of seeing the table +in this configuration. + +And then what you do is you +take that probability and all + +of the probabilities for all the +more extreme values, say, of a. + +And you sum them all +up and that gives you + +the probability of +a null hypothesis. + +So this is another +way to approach + +looking at the chance a +particular contingency table + +set of values would +occur at random. + +So if people talk about +Fisher's Exact Test-- you know, + +tonight at that cocktail party. + +"Oh yeah, I know about that. + +Yeah, it's like +the hypergeometric. + +It's no big deal." + +You know? + +Right. + +All right. + +So now let us suppose that +we do an association test + +and you do the following design. + +You say, well, I've +got all my cases. + +They're all at Mass General and +I want to genotype them all. + +And Mass General +is the best place + +for this particular disease, +so I'm going to go up there. + +I need some controls but I'm +running out of budgetary money, + +so I'm going to do all my +controls in China, right? + +Because I know it's going +to be less expensive there + +to genotype them. + +And furthermore-- +as a little aside, + +I was once meeting +with this guy who + +is like one of the ministers +of research in China. + +He came to my office. + +I said, so what do +you do in China? + +And he said, well, I guess +the best way to describe + +it is that I'm in charge of the +equivalent of the NSF, DARPA, + +and the NIH. + +I said, oh. + +I said, would like to +meet the president? + +Because I'd be happy to +call MIT's president. + +I'm sure they'd be +happy to meet with you. + +He said, no. + +He said, I like going direct. + +So, at any rate, +I told him I was + +working in stem cell research. + +He said, you know, one thing I +can say about China-- in China, + +stem cells, ethics, no problem. + +[LAUGHTER] + +At any rate, so you go to +China to do your controls, OK? + +And why is that a bad +experimental design? + +Can anybody tell me? + +You do all your cases here, +you do your controls in China. + +Yes? + +AUDIENCE: Because +the SNPs in China + +are not necessarily the same. + +PROFESSOR: Yes. + +The Chinese population's +going to have + +a different set of SNPs, +right, because it's + +been a contained population. + +So you're going to +pick up all these SNPs + +that you think are going to +be related to the disease that + +are simply a consequence of +population stratification, + +right? + +So what you need to do +is to control for that. + +And the way you do that is you +pick a bunch of control SNPs + +that you think are +unrelated to a disease + +and you do a Chi-square +test on those + +to make sure that they're +not significant, right? + +And methodologies for +controlling for population + +stratification by picking +apart your individuals + +and re-clustering +them is something + +that is a topic of +current research. + +And finally, the good news +about age-related macular + +degeneration is that +there are three genes + +with five common variants +that explain 50% of the risk. + +And so it has been viewed as +sort of a very successful study + +of a polygenic-- that +is, multiple gene-- + +genetic disorder that +has been dissected + +using this methodology. + +And with these genes, now +people can go after them + +and see if they can come up +appropriate therapeutics. + +Now using the same idea-- cases, +controls-- you look at each SNP + +individually and you +query it for significance + +based upon a null model. + +You can take a wide +range of common diseases + +and ask whether or +not you can detect + +any genetic elements that +might influence risk. + +And so here are a set +of different diseases, + +starting with bipolar +disorder at the top, + +going down to type 2 +diabetes at the bottom. + +This is a so-called +Manhattan plot, + +because you see the buildings +along the plot, right? + +And when there are +skyscrapers, you + +go, whoa, that could be +a problem, all right? + +And so this is the +style-- you see, + +this came out in +2007-- of research + +that attempts to do genome +wide scans for loci that + +are related to +particular diseases. + +OK, now, I'd like to go on +and talk about other ways + +that these studies can +be influenced, which + +is the idea of linkage +disequilibrium. + +So for example, let us say that +I have a particular individual + +who's going to produce a +gamete and the gamete's going + +to be haploid, right? + +And it's going have one +allele from one of these two + +chromosomes and one allele from +one of these two chromosomes. + +We've talked about +this before last time. + +And there are four +possibilities-- + +AB, aB, Ab, and ab, OK? + +And if this was a +coin flip, then each + +of these genotypes +for this gamete + +would be identical, right? + +But let us suppose +that I tell you + +that there are only two +that result-- this one, AB, + +and the small one, ab, OK? + +If you look at this, you +say, aha, these two things + +are linked and they're +very closely linked. + +And so, if they're always +inherited together, + +we might think that the distance +between them on the genome + +is small. + +So in the human genome, +what's the average distance + +between crossover events +during a meiotic event? + +Does anybody know, roughly +speaking, how many bases? + +Hm? + +AUDIENCE: A megabase? + +PROFESSOR: A megabase. + +Little low. + +How many centimorgans +long is the human genome? + +All right? + +Anybody know? + +3,000? + +4,000? + +Something like that? + +So maybe 50 to 100 megabases +between crossover events, OK? + +So if these markers +are very closely + +organized along the genome, +the likelihood of a crossover + +is very small. + +And therefore, they're going +to be in very high LD, right? + +And a way to measure that is +with the following formula, + +which is that if you link the +two locuses-- we have L1 and L2 + +here. + +And now we're talking about +the population instead + +of a particular individual. + +If the likelihood of the +capital allele A is piece of A + +and the probability +of the big B allele + +is piece of B, then if they +were completely unlinked, + +then the likelihood of +inheriting both of them + +together with would be +piece of A times piece of B, + +showing independence. + +However if they +aren't independent, + +we can come up +with a single value + +D which allows us to quantify +the amount of disequilibrium + +between those two alleles. + +And the formula for D +is given on the slide. + +And furthermore, if it's +more convenient for you + +to think about in terms +of r-squared correlation, + +we can define the +r-squared correlation + +as D squared over +PA, QA, PB, QB, + +as shown in the lower left +hand part of this slide, OK? + +This is simply a +way of describing + +how skewed the +probabilities are from being + +independent for +inheriting these two + +different loci in a population. + +Are there any questions +at all about that, + +the details of that? + +OK. + +So just to give you an example, +if you look at chromosome 22, + +the physical distance on +the bottom is in kilobases, + +so that's from 0 to 1 +megabase on the bottom. + +And you look at the +r-squared values, + +you can see things that +are quite physically close, + +as we suggested earlier, +have a high r-squared value. + +But there are still +some things that + +are pretty far away +that have surprisingly + +high r-squared values. + +There are recombination +hot spots in the genome. + +And it's, once again, a topic +of current research trying + +to figure out how the genome +recombines and recombination is + +targeted. + +But suffice it to say, as you +can see, it's not uniform. + +Now what happens as +a consequence of this + +is that you get regions +of the genome where + +things stick together, right? + +They're all drinking +buddies, right? + +They all hang out together, OK? + +But here's what I'm going to ask +you-- how much of your genome + +came from your dad? + +Half. + +How much came from +your dad's dad? + +AUDIENCE: A quarter. + +PROFESSOR: And from +your dad's dad's dad? + +AUDIENCE: An eighth. + +PROFESSOR: An eighth, OK? + +So the amount of your genome +going back up the family tree + +is falling off exponentially +up a particular path, right? + +So if you think about groups +of things that came together + +from your great, +great grandfather + +or his great, great +grandfather, right, + +the further back you go, the +less and less contribution + +they're going to +have to your genome. + +And so the blocks are +going to be smaller-- + +that is, the amount +of information + +you're getting from +way back up the tree. + +So if you think about +this, the question + +of what blocks of things +are inherited together + +is not something that you +can write an equation for. + +It's something that you +study in a population. + +You go out and you +ask, what things do we + +observe coming together? + +And generally, larger +blocks of things + +are inherited together, occur +in more recent generations, + +because there's less +dilution, right? + +Whereas if you go way +back in time-- not quite + +to where the dinosaurs +roamed the land, + +but you get the idea-- the +blocks are, fact, quite small. + +And so, the HapMap project +went about looking at blocks + +and how they were +inherited in the genome. + +And what suffices to know is +that they found blocks-- here + +you can see three +different blocks. + +And these are called +haplotype blocks + +and the things that +are colored red + +are high r-squared +values between + +different genetic markers. + +And we talked earlier +about how to compute + +that r-squared value. + +So those blocks typically +are inherited together. + +Yes? + +AUDIENCE: Are these blocks +like fuzzy boundaries? + +PROFESSOR: No. + +Well, remember in this +particular example, + +we're only querying at +specified markers which + +are not necessarily at regular +intervals along the genome. + +So in this case, the blocks +don't have fuzzy boundaries. + +As we get into +sequencing-based approaches, + +they could have +fuzzier boundaries. + +But haplotype +blocks are typically + +thought to be discrete blocks +that are inherited, OK? + +Good question. + +Any other questions? + +OK. + +So I want to impress +upon the idea + +that this is empirical, right? + +There's no magic here in +terms of fundamental theory + +about what things should +be haplotype blocks. + +It's simply that you +look at a population + +and you're look at what +markers are drinking buddies + +and those make haplotype blocks +and you empirically categorize + +and catalog them-- which can +be very helpful, as you'll see. + +And thus, when we think +about genetic studies, + +when we think about the +length of shared segments, + +if you're thinking +about studying a family, + +like a trio-- a trio is a mom, +a dad, and a child, right? + +They're going to share a +lot of genetic information, + +and so the haplotype blocks that +are shared amongst those three + +individuals are going +to be very large indeed. + +Whereas if you go +back generations, + +the blocks-- like the +second cousins or things + +like that-- the +blocks get smaller. + +So the x-axis on this +plot is the median length + +of a shared segment. + +And as an association +study, which + +is taking random people +out of the population, + +has very small shared +blocks indeed, OK? + +And so the techniques +that we're talking about + +today are applicable +almost in any range, + +but they're particularly +useful where + +you can't depend upon +the fact that you're + +sharing a lot of information +along the genome proximal + +to where the marker +is that's associated + +with a particular disease. + +Now the other thing +that is true is + +that we should note that +the fact that markers have + +this LD associated +with them means + +that it may be that a particular +marker is bang on-- what's + +called a causative SNP. + +Or something that, +for example, sits + +in the middle of a gene +causing a missense mutation. + +Or it sits right in the middle +of a protein binding site, + +causing the factor +not to bind anymore. + +But also it could be something +that is actually a little bit + +away, but is highly correlated +to the causative SNP. + +So just keep in mind that +when you have an association + +and you're looking at a SNP, it +may not be the causative SNP. + +It might be just linked +to the causative SNP. + +And sometimes these things +are called proxy SNPs. + +OK, so we've talked +about the idea of SNPs + +and discovering them. + +Let me ask you one more question +about where these SNPs reside + +and see if you +could help me out. + +OK, this is a really +important gene, OK? + +Call it RIG for short, OK? + +Now let us suppose that +you know that there + +are some mutations here. + +And my question for you is, +does it matter whether or not + +the two mutations look +like this or the mutations + +look like this, in your opinion? + +That is, both mutations +occur in one copy + +or on one chromosome +of the gene, + +whereas in the other case, we +see two different SNPs that + +are different than +reference, but they're + +referring in both +mom and dad alleles. + +Is there a difference +between those two cases? + +Yeah? + +AUDIENCE: In terms of +the phenotype displayed? + +PROFESSOR: In terms of +the phenotype, sorry. + +AUDIENCE: It depends. + +PROFESSOR: It depends? + +AUDIENCE: Yes. + +PROFESSOR: OK. + +AUDIENCE: So if it causes a +recessive mutation, then no, + +because other genes will +be able to rescue it. + +But if it's dominant, +then it'll still-- + +PROFESSOR: It's actually +the other way around. + +If it's recessive, +this does matter. + +AUDIENCE: Oh, I see. + +PROFESSOR: Because in this +case, with the purple ones, + +you still have one good +copy of the gene, right? + +However, with the +green ones, it's + +possible that you have +ablated both good copies + +of the gene, this +really important gene, + +and therefore, you're +going to get a higher + +risk of having a +genetic disorder. + +So when you're scanning down +the genome then-- you know, + +we've been asking where +are there differences + +from reference or from +between cases and controls + +down the genome, but we +haven't asked whether or not + +they're on mom or dad, right? + +We're just asking, +are they there? + +But it turns out that +for questions like this, + +we have to know whether or +not the mutation occurred + +in only in mom's chromosome +or in both chromosomes + +in this particular +neighborhood, all right? + +This is called phasing +of the variants. + +Phasing means +placing the variants + +on a particular chromosome. + +And then, by phasing +the variants, + +you can figure out some +of the possible phenotypic + +consequences of them. + +Because if they're not +they phased, in this case, + +it's going to be much less +clear what's going on. + +So then the question +becomes, how + +do we phase variants, right? + +So phasing assigns alleles +to the parental chromosomes. + +And so, the set of alleles along +a chromosomes is a haplotype. + +We've talked about the +idea of haplotypes. + +So imagine one way to phase +is that if I tell you, + +by magic, in this population +you're looking at, + +here are all the +haplotypes and these + +are the only ones that exist. + +You look in your +haplotypes and you go, aha, + +this haplotype exists but +this one does not, right? + +That this is a haplotype-- +this two purples together + +is a haplotype, and +this green without one + +is another haplotype. + +So you see which +haplotypes exist-- that is, + +what patterns of inheritance +of alleles along a chromosome + +you can detect. + +And using the established +empirical haplotypes, + +you can phase the variants, OK? + +Now the other way to +phase the variants + +is much, much simpler +and much better, right? + +The other way to +phase variants is + +you just have a single read that +covers the entire thing, right? + +And then the read, it +will be manifest, right? + +The read will cover +the entire region + +and then you see +the two mutations + +in that single +region of the genome. + +The problem we're up against +is that most of our reads + +are quite short and we're +reassembling our genotypes + +from a shattered genome. + +If the genome wasn't +shattered, then we + +wouldn't have this problem. + +So everybody's +working to fix this. + +Illumina has sort of a +cute trick for fixing this. + +And PacBio, which is +another sequence instrument + +manufacturer, can produce reads +that are tens of thousands + +of bases long, which allows +you to directly phase + +the variants from the reads. + +But if somebody, +once again, comes up + +to you at the cocktail party +tonight and says, you know, + +I've never understood why +you have to phase variants. + +You know, this is a popular +question I get all the time. + +[LAUGHTER] + +You can tell them, +hey, you know, + +you have to know whether or +not mom and dad both have + +got big problems or just all +the problems are with mom, OK? + +Or dad. + +So you can put +their mind at ease + +as you're finishing +off the hors d'oeuvres. + +OK, so I wanted just to tell +you about phasing variants + +because we're about to go on to +the next part of our discussion + +today. + +We are leaving the very +clean and pristine world + +of very defined SNPs, +defined by microarrays, + +into the wild and woolly world +of sequencing data, right? + +Which is all bets are off. + +It's all raw +sequencing data and you + +have to make sense +of it-- hundreds + +of millions of sequencing reads. + +So today's lecture is drawn from +a couple of different sources. + +I've posted some of +them on the internet. + +There's a very nice article +by Heng Li on the underlying + +mathematics of SNP calling and +variation which I've posted. + +In addition, some of +the material today + +is taken from the Genome +Analysis Toolkit, which + +is a set of tools +over at the Broad, + +and we'll be talking about +that during today's lecture. + +The best possible case when +you're looking at sequence data + +today is that you get +something like this, all right? + +Which is that you have +a collection of reads + +for one individual and you +align them to the genome + +and then you see that +some of the reads + +have a C at a particular base +position and other of the reads + +have a T at that base position. + +And so it's a very +clean call, right? + +You have a CT heterozygote +at that position-- that + +is, whatever person that +is is a heterozygote there. + +You can see the reference genome +at the very bottom, right? + +So it's very difficult for +you to read in the back, + +but C is the reference allele. + +And the way that +the IGV viewer works + +is that it shows non-reference +alleles in color, + +so all those are the T alleles +you see there in red, OK? + +And it's very, very +beautiful, right? + +I mean you can tell +exactly what's going on. + +Now we don't know whether +or not the C or the T allele + +are a mom and dad +respectively, right? + +We don't know which of the +chromosomes they're on, + +but suffice to say, +it's very clean. + +And the way that all of +this starts, of course, + +is with a BAM file. + +You guys have seen +BAM files before. + +I'm not going to belabor this. + +There's a definition +here and you + +can add extra +annotations on BAM files. + +But the other thing +I wanted to point out + +is that you know that BAM +files include quality scores. + +So we'll be using those quality +scores in our discussion. + +The output of all +this typically is + +something called a variant +call file or a VCF file. + +And just so you are +not completely scared + +by these files, I want to +describe just a little bit + +about their structure. + +So there's a header +at the top telling you + +what you actually did. + +And then chromosome 20 at this +base location has this SNP. + +The reference allele is +G, the alternative allele + +is A. This is some +of the statistics + +as described by this +header information, + +like DP is the read depth. + +And this tells you the status +of a trio that you processed. + +So this is the +allele number for one + +of the chromosomes, +which is 0, which + +is a G. The other one's +a G, and so forth. + +And then this data right +here is GT, GQ, GP, + +which are defined up here. + +So you have one person, +second person, third person, + +along with which one +of the alleles, 0 or 1, + +they have on each of +their chromosomes, OK? + +So this is the output. + +You put in raw reads +and what you get out + +is a VCF file that for +bases along the genome + +calls variance, OK? + +So that's all there +is to it, right? + +You take in your read data. + +You take your genome, throw +it through the sequencer. + +You take the BAM file, +you call the variants, + +and then you make your +medical diagnosis, right? + +So what we're going to +talk about is what goes on + +in the middle there, +that little step-- how + +do you actually +call the variants? + +And you might say, gee, +that does not seem too hard. + +I mean, I looked at +the slide you showed me + +with the CT heterozygote. + +That looked beautiful, right? + +I mean, that was just gorgeous. + +I mean, these sequencers are +so great and do so many reads, + +what can be hard +about this, after all? + +You know, it's a quarter +to 2:00, time to go home. + +Not quite, OK? + +Not quite. + +The reason is actual +data looks like this. + +So these are all reads +aligned to the genome + +and, as I told you +before, all the colors are + +non-reference bases. + +And so you can see that +the reads that come out + +of an individual are +very messy indeed. + +And so we need to deal with +those in a principled way. + +We need to make good, +probabilistic assessments of + +whether or not there's a +variant at a particular base. + +And I'm not going to belabor +all the steps of the Genome + +Analysis Toolkit, +suffice to say, + +here is a flow chart of all +the steps that go through it. + +First, you map your reads. + +You recalibrate the scores. + +You compress the +read set and then + +you have read sets for +n different individuals. + +And then you jointly call +the variants and then you + +improve upon the variants +and then you evaluate, OK? + +So I'll touch upon some of +the aspects of this pipeline, + +the ones that I think +are most relevant, + +so that you can appreciate +some of the complexity + +in dealing with this. + +Let me begin with the +following question. + +Let us suppose that you have +a reference genome here, + +indicated by this line, +and you align a read to it. + +And then there's some base +errors that are non-reference, + +so it's variants calls down +at this end of the read, OK? + +So this is the five +prime, three prime. + +And then you align a read +from the opposite strand + +and you have some variant +calls on the opposite end + +of the read like this. + +And you'll say to yourself, +what could be going on here, + +you know? + +Why is it that they're +not concordant, right, + +when they're mapped, but +they're in the same region + +of the genome? + +And then you think +to yourself, well, + +what happens if I map this +successfully here correctly + +to the reference genome +and this correctly + +to the reference genome here, +but this individual actually + +had a chromosome that had +a deletion right here, OK? + +Then what would happen would +be that all these reads down + +here are going to be +misaligned, all of these bases + +are going to be misaligned +with the reference. + +And so you're going +to get variant calls. + +And these bases will be also +misaligned with the reference, + +you'll get variant calls. + +So deletions in +an individual can + +cause things to +be mapped but you + +get variant calls at the end. + +And so that is shown +here, where you + +have reads that are being mapped +and you have variant calls + +at the end of the reads. + +And it's also a +little suspicious + +because in the middle here is +a seven-base pair homopolymer + +which is all T's. + +And as we know, +sequencers are notoriously + +bad at correctly +reading homopolymers. + +So if you then +correct things, you + +discover that some +fraction of the reads + +actually have one of the T's +missing and all the variants + +that were present +before go away. + +So this is a process +of INDEL adjustment + +when you are mapping the +region looking for variants. + +Now this does not occur we're +talking about SNP microarrays. + +So this is a problem +that's unique to the fact + +that we're making many +fewer assumptions when + +we map reads to +the genome de novo. + +The second and another +very important step + +that they're very proud +of is essentially-- + +I guess how to put this +politely-- finding out + +that manufacturers of +sequencing instruments, + +as you know, for every +base that they give you, + +they give you an estimate +of the probability + +that the base is correct-- +or it's wrong, actually. + +A so-called Phred score-- +we've talked about that before. + +And as you would imagine, +manufacturers' instruments + +are sometimes optimistic, +to say the least, about + +the quality of their scores. + +And so they did a survey of +a whole bunch of instruments + +and they plotted the reported +score against the actual score, + +OK? + +And then they have a whole +step in their pipeline + +to adjust the scores, whether +you be a Solexa GA instrument, + +a 454 instrument, a SOLiD +instrument, a HiSeq instrument, + +or what have you. + +And there is a way to adjust the +score based upon the raw score + +and also how far down +the read you are, + +as the second line shows. + +The second line is a +function of score correction + +versus how far down the read or +number of cycles you have gone. + +And the bottom is adjustments +for dinucleotides, + +because some +instruments are worse + +a certain dinucleotides +than others. + +As you can see, they're very +proud of the upper left hand + +part. + +This is one of the major +methodological advances + +of 1000 Genome +Project, figuring out + +how to recalibrate quality +scores for instruments. + +Why is this so important? + +The reason it's important +is that the estimate + +of the veracity of +bases figures centrally + +in determining whether or +not a variant is real or not. + +So you need to have as best +an estimate as you possibly + +can of whether or not a base +coming out of the sequencer + +is correct, OK? + +Now if you're doing +lots of sequencing + +of either individuals +or exomes-- + +I should talk about exome +sequencing for a moment. + +Up until recently, +it has not really + +been practical to +do whole genome + +sequencing of individuals. + +That's why these SNP arrays +were originally invented. + +Instead, people sequenced the +expressed part of the genome, + +right? + +All of the genes. + +And they can do this +by capture, right? + +They go fishing. + +They create fishing poles out of +the genes that they care about + +and they pull out the +sequences of those genes + +and they sequence them. + +So you're looking at a +subset of the genome, + +but it's an important part. + +Nonetheless, whether or +not you do exome sequencing + +or you do sequencing +of the entire genome, + +you have a lot of reads. + +And so the reads that you +care about are the reads that + +are different from reference. + +And so you can reduce the +representation of their BAM + +file simply by throwing all +the reads on the floor that + +don't matter, right? + +And so here's an example of +the original BAM file and all + +the reads, and what +you do is you just + +trim it to only the +variable regions, right? + +And so you are +stripping information + +around the variant regions +out of the BAM file + +and things greatly compress +and the downstream processing + +becomes much more efficient. + +OK. + +Now let's turn to the +methodological approaches + +once we have gotten the +data in as good a form + +as we possibly can get it, we +have the best quality scores + +that we can possibly +come up with, + +and for every base position, +we have an indication + +of how many reads say +that the base is this + +and how many reads say +the base is that, OK? + +So we have these raw read counts +of the different allelic forms. + +And returning to this, +we now can go back + +and we can attempt +to take these reads + +and determine what the +underlying genotypes are + +for an individual. + +Now I want to be clear +about the difference + +between a genotype +for an individual + +and an allelic spectrum +for a population. + +A genotype for an +individual thinks + +about both of the alleles +that that individual has, + +and they can be phased +or unphased, right? + +If they're phased, +it means you know + +which allele belongs to mom and +which allele belongs to dad, + +so to speak, right? + +If they're unphased, you +simply know the number + +of reference alleles that +you have in that individual. + +Typically, people think about +there being a reference allele + +and an alternative allele, +which means that a genotype can + +be expressed as +0, 1, or 2, which + +is the number of +reference alleles + +present at a particular base +if it's unphased, right? + +0, 1, or 2-- 0 mean there are +no reference alleles there, + +1 meaning that it's +a heterozygote, + +2 mean there are two reference +alleles in that individual. + +OK? + +So there are different ways +of representing genotype, + +but once again, it represents +the different allelic forms + +of the two chromosomes. + +And whatever form you +choose, the probability + +over those genotypes +has to sum to 1. + +You can think about +the genotype ranging + +over all the possible bases from +mom and from dad or over 0, 1, + +and 2. + +Doesn't really matter, +depending upon which way you + +want to simplify the problem. + +And what we would like to do +is, for a given population-- + +let's say cases +or controls-- we'd + +like to compute the +probability over the genotypes + +with high veracity, OK? + +So in order to do +that, we'll start + +by taking all the +reads for each one + +of the individuals +in a population, OK? + +And we're going to compute +the genotype likelihoods + +for each individual. + +So let's talk about +how to do that. + +Now everything I've written on +the board is on the next slide. + +The problem is, if I +put it on the slide, + +it will flash in front +of you and you'll go, + +yes, I understand that, I think. + +This way, I'll put +it on the board first + +and you'll look at +it and you'll say, + +hm, maybe I don't +understand that, I think. + +And then you'll +ask any questions + +and we can look at the +slide in a moment, OK? + +But here's the fundamental +idea, all right? + +At a given base in the +genome, the probability + +of the reads that we see based +upon the genotype that we think + +is there can be expressed +in the following form, which + +is that we take the product over +all the reads that we see, OK? + +And the genotype is going to +be a composition of the base we + +get from mom and the base +that we get from dad, + +or it could simply +be 0, 1, and 2. + +We'll put that +aside for a moment. + +So what's the chance that +we inherited something + +from a particular base from mom? + +It's this base over +a particular read. + +What's the chance +a particular read + +came from mom's chromosome? + +That's one half +times the probability + +of the data given +the base that we see. + +And once again, since +it could be a coin + +flip whether the read came +from mom or dad's chromosome, + +divide it by 2-- the +probability of the data + +that we see with dad's version +of that particular base. + +So once again, for +all the reads we're + +going to compute the +probability of the read set + +that we see given a particular +hypothesized genotype + +by looking at what's the +likelihood or the probability + +of all those reads. + +And for each read, +we don't know if it + +came from mom or from dad. + +But in any event, we're going +to compute the probability + +on the next blackboard, +this bit right here. + +OK? + +Yes? + +AUDIENCE: So if you assume +that mom and dad have + +a different phase at +a particular base, + +couldn't that possibly +skew the probability + +of getting a read from mom's +chromosome or dad's chromosome? + +PROFESSOR: A different phase? + +AUDIENCE: So the composition +of bases affect what you get. + +I think certain +base compositions + +are more likely to be +sequenced, for example. + +PROFESSOR: Yes. + +AUDIENCE: Could that bias-- + +PROFESSOR: Yes. + +In fact, that's why on, +I think, the third slide, + +I said non-random genotyping +error was being excluded. + +AUDIENCE: Oh. + +PROFESSOR: Right? + +From our discussion today? + +But you're right that it might +be that certain sequences are + +more difficult to +see, but we're going + +to exclude that +for the time being. + +OK? + +So this is the +probability of the reads + +that we see given a +hypothesized genotype. + +And I'll just show you, +that's very simple. + +That we have a read, let's +call the read D sub j, + +and we have the base that +we think we should see. + +And if the base is correct, +then the probability + +that that's correct is 1 +minus the error, right, + +that the machine reported. + +And if it isn't +correct, the probability + +is just the error at that base +that the machine reported. + +So we're using the error +statistics from the machine + +and if it matches what we +expect, it's 1 minus the error. + +And if it doesn't match, +it's just simply going + +to be the error +that's reported, OK? + +So this is the probability of +seeing a particular read given + +a hypothesized base +that should be there. + +Here's how we use that, looking +at all the possible bases that + +could be there given a +hypothesized genotype. + +Remember, this genotype is +only going to be one pair. + +It's only going to be AA or +TT or what have you, right? + +So it's going to be one pair. + +So we're going to be testing +for either one or two bases + +being present. + +And finally, we want to +compute the posterior + +of the genotype given the +data we have observed, OK? + +So we want to compute what's +the probability of the genotype + +given the reads that +we have in our hand. + +This is really important. + +That is what that genotype +likelihood is up there. + +It's the probability of the read +set given the genotype times + +the probability of +the genotype-- this + +is a prior-- over the +probability of the data. + +This is simply Bayes' Rule. + +So with this, for +an individual now, + +we can compute the +posterior of the genotype + +given the read set. + +Very simple concept. + +So in another form, you can +see the same thing here, + +which is the Bayesian model. + +And we've talked about this +haploid likelihood function, + +which was on the +blackboard I showed you. + +And we're assuming all +the reads are independent + +and that they're +going to come equally + +from mom and dad, more +or less, et cetera, OK? + +And the haploid likelihood +function, once again, + +just is using the error +statistics for the machine. + +So I'm asking if the +machine says this is an A + +and I think it's an A, then the +probability that that's correct + +is 1 minus the error +of the machine. + +If the two are not +in agreement, it's + +simply the error in the +machine that I'm using. + +So this allows me now to +give a posterior probability + +of a genotype given a +whole bunch of reads. + +And the one part that +we haven't discussed + +is this prior, +which is how do we + +establish what we think is +going on in the population + +and how do we set that? + +So if you look back +at the slide again, + +you can see that we +have these individuals + +and there's this magic step +on the right-hand side, which + +is that somehow we're +going to compute + +a joint estimate +across all the samples + +to come up with an estimate +of what the genotypes are + +in a particular SNP position. + +And the way that we can do +that is with an iterative EM + +procedure-- looks +like this-- so we + +can estimate the probability +of the population genotype + +iteratively using this +equation until convergence. + +And there are various tricks. + +As you'll see if you +want to delve further + +into this in the +paper I posted, there + +are ways to deal with some +of the numerical issues + +and do allele count +frequencies and so forth. + +But fundamentally, +in a population + +we're going to +estimate a probability + +over the genotypes for +a particular position. + +And just to keep +it simple, you can + +think about the +genotypes being 0, 1, + +or 2-- 0, no reference +alleles present; + +1, one reference allele present +to that site; 2, two reference + +alleles present +to that site, OK? + +So we get a +probability of each one + +of those states for +that population. + +Any questions at all about that? + +The details or anything at all? + +People get the general idea +that what we're just doing + +is we're taking a bunch of +reads at a particular position + +for an individual and +computing the posterior + +probability of a genotype +seeing all of those reads + +and then, when we think about +the entire population-- say + +either the cases +or the controls-- + +we're computing the +probability over the genotypes + +within that population +using this kind + +of iterative procedure. + +OK, so going on then, if +we go back to our 0, 1, + +2 kind of genotype +representation, + +we can marginalize psi, +which is the probability + +of the reference allele +being in the population, + +and 1 minus psi +being the probability + +of the non-reference allele, +where the capital alleles are + +reference and the little +ones are non-reference. + +And then we could also +for epsilon 0, epsilon 1, + +And Epsilon 2, those +are the probabilities + +of the various allelic +forms, the various genotypes. + +And actually, I think +epsilon 0 should be little A, + +little A. Must have +got the two of them + +flipped, but it's not +really that important. + +OK, so what do we know +about a population? + +Who's heard about +Hardy-Weinberg before? + +Hardy-Weinberg equilibrium? + +OK. + +So Hardy-Weinberg equilibrium +says that, for example, + +in a population, if the allelic +frequency of the reference + +allele is psi, right, what's +the chance that an individual + +should be AA, big A, big +A, reference, reference? + +In a population? + +Pardon? + +I think I heard it. + +Psi squared, right? + +We're going to assume +diploid organisms, + +we're going to +assume random mating, + +we're going to +assume no selection, + +we're going to assume no +bottlenecks, and so forth, + +right? + +That over time, the population +will come to its equilibrium + +in the exchange of alleles. + +However, if there's +strong selection + +or if part of the +population gets up and moves + +to a different continent +or something of that sort, + +you can get out of equilibrium. + +And so one question, +whenever you're + +doing a genetic +study like this-- + +is your population in +equilibrium or not? + +And we have a direct way for +testing for that because we're + +actually estimating +the genotypes, right? + +So what we can do is this test. + +We can do a log likelihood +test directly, right? + +And we can compare the +probability of the observed + +genotypes-- these are E1 and +E2, where the number indicates + +the number of reference +copies-- over the probability + +of the genotypes being +composed directly + +from the frequency of +the reference allele. + +And this will tell +us whether or not + +these are concordant or not. + +And if the Chi-square +value is large enough, + +we're going to say that this +divergence couldn't have + +occurred at random and +therefore the population is not + +in equilibrium. + +And you might say, +well, gee, why + +do I really care if it's +in equilibrium or not? + +I mean, you know, +what relevance does + +that have to me when +I'm doing my test? + +Well, here's the issue. + +The issue is this-- you're going +to be testing whether or not + +genotypes are different +between a case and a control + +population, let's say, OK? + +And you have a couple +different tests you can do. + +The first test is +the test on the top + +and the second test is +the test on the bottom. + +Let's look at the test on +the bottom for a moment, OK? + +The test in the bottom +is saying you consider + +the likelihood of +the data in group one + +and group two +multiplied together + +over the probability of the +data with the groups combined + +and you ask whether or not the +increased likelihood-- you're + +willing to pay for that given +the two degrees of freedom + +that model implies, right? + +Because you have to have two +additional degrees of freedom + +to pay for that in the bottom. + +On the other hand, +in the top, you only + +have one degree of +additional freedom + +to pay for the difference in +simply the reference allele + +frequency. + +And so these are two +different metrics + +you can use to test +for associations + +for a particular SNP in two +different case and control + +populations. + +The problem comes is that if the +population is in equilibrium, + +then the bottom has too many +degrees of freedom, right? + +Because the bottom, +in some sense, + +can be computed +directly from the top. + +You can compute the epsilons +directly from the size + +if it's in equilibrium. + +So you need to +know whether or not + +you're in equilibrium or not +to figure out what kind of test + +to use to see whether or not a +particular SNP is significant. + +OK, so just a brief review where +we've come to at this point. + +I've handed you a +basket of reads. + +We're focusing on a particular +location in the genome. + +For an individual, we can +look at that basket of reads + +and compute a posterior +probability of the genotype + +at that location. + +We then asked if we take +all of the individuals + +in a given interesting +population, like the cases, + +we could compute the +posterior or the probability + +of the genotype over +all those cases. + +We then can take the +cases and the controls + +and test for associations using +this likelihood ratio, OK? + +So that is the way to go +at the question of SNPs. + +And I'll pause here +and see if there + +any other questions about this. + +OK, now there are +lots of other ways + +of approaching +structural variation. + +I said I would touch upon it. + +There is another +method which is-- + +we've not been here assigning +what haplotypes to things + +or paying attention to +which chromosome or mom + +or dad a particularly +allele came from. + +But suffice to +say-- I'll let you + +read this slide +at your leisure-- + +the key thing is that, imagine +you have a bunch of reads. + +What you can do in +a particular area + +there's going to +be a variant is you + +can do local assembly +of the reads. + +We want to do local assembly +because local assembly handles + +general cases of +structural variation. + +And if you then take +the most likely cases + +of the local assembly +supported by reads, + +you have the different possible +haplotypes or collections + +of bases along the +genome from the assembly. + +And we've already talked +about, earlier in class, + +how to take a given +sequence of bases + +and estimate the probability +of the divergence + +from another string. + +So you can estimate +the divergence + +of each one of those +assemblies from the reference + +and compute likelihoods, like +we did before for single bases, + +although it's +somewhat more complex. + +And so another way +to approach this + +is, instead of asking +about individual bases + +and looking at the likelihood +of individual bases, + +you can look at doing +localized assembly of the reads + +that handle +structural variation. + +And if you do that, +what happens is + +that you can recover +INDEL issues that + +appear to call SNP variants that +actually are actually induced + +by insertions and deletions +in one of the chromosomes. + +So as you can see, as things +get more sophisticated + +in the analysis of +human genome data, + +one needs a variety +of techniques, + +including local assembly, +to be able to recover + +what's going on. + +Because of course, +the reference genome + +is only an approximate +idea of what's + +there and is being +used as a scaffold. + +So we've already talked +about the idea of phasing, + +and we talked about why phasing +is important, especially + +when we're trying to +recover whether or not + +you have a loss of +function event, right? + +And so the phasing +part of genomics + +right now is highly +heuristic, relies partly + +upon empirical data from +things like the HapMap Project + +and is outside the +scope of what we're + +going to talk about, +because we could talk + +about phasing for +an entire lecture. + +But suffice it to +say, it's important. + +And if you look at +what actually goes on, + +here's a trio, mom, +dad, and the daughter. + +You can see down at the +bottom, you see mom's reads. + +And you see dad actually +has two haplotypes. + +He got one haplotype +from one of his parents + +and the other haplotype +from both of his parents. + +And then the daughter actually +has the haplotype number one + +from dad and no haplotype +number one from mom. + +So you can see how these +blocks of mutations + +are inherited through the +generation in this form. + +And finally, if you +look at a VCF file, + +if you see a +vertical bar, that's + +telling you that the +chromosomal origin is fixed. + +So it tells you, for +example, in this case, + +the one where the +arrow's pointed to + +is that variant +number one, which + +is the alternative +variant T came from mom + +and a T came from dad. + +So VCF, when it has +slashes between the two + +different alleles of a +genotype is unphased, + +but you can actually have +a phased VCF version. + +And so there's a whole +phase in the GATK tool kit + +that does phasing. + +And finally, we get +through all this, + +the question is how important +are the variants you discover? + +And so there's a +variant analysis phase + +and it will go through and +annotate all the variants. + +For example, this is a +splice site acceptor variant + +which is in a +protein coating gene + +and it's thought +to be important. + +And so at the end +of this pipeline, + +what's going to +happen is you're going + +to be spitting out not +only the variants but, + +for some of them, what +their annotated function is. + +OK, so that ends the +part of our lecture + +where we're talking about +how to process raw read data. + +And I encourage you to look +at the GATK and other websites + +to actually look at +the state of the art. + +But as you can see, it's +an evolving discipline + +that has a kernel of principal +probabilistic analysis in part + +of its core surrounded by +a whole lot of baling wire, + +right, to hold it all together. + +And you get the +reads marshalled, + +organized, compressed, +aligned properly, phased, + +and so forth, OK? + +Let's talk now about how +to prioritize variants. + +And I just wanted to show you +a very beautiful result that + +is represented by this paper, +which came out very recently. + +And here is a portion +of the genome. + +And we're looking +here at-- you see + +here-- a pancreatic disorder. + +And there is an enhancer +on the right-hand side + +of the screen where that +little red square is. + +And recall that we said that +certain histone marks were + +present typically +over active enhancers. + +And so you can see the +H3K4 mono-methyl mark being + +present over that little +red box as well as + +the binding of two pancreatic +regulators, FoxA2 and Pdx1. + +And within that +enhancer you can see + +there are a whole lot of +variants being called. + +Well, not a whole lot. + +There are actually +five different variants + +being called. + +And in addition to those +five specific SNP variants, + +there's also another +variation that was observed + +in the population of a 7.6-kb +deletion right around that + +enhancer. + +And if you look at the +inheritance of those mutations + +with disease +prevalence, you can see + +that there's a very +marked correlation. + +That when you inherit +these variants, + +you get this Mendelian disorder. + +So it's a single +gene disorder really. + +And in order to confirm this, +what the authors of this study + +did was they took +that enhancer and they + +looked at all the different +SNPs and they mutated it. + +And in the upper +left-hand corner, + +you can see that the five little +asterisks note the decrease + +in activity of that +enhancer when they mutated + +the bases indicated +at SNP positions. + +The three C's on the +panel on the right + +with the y-axis being +relative interaction + +shows that that +enhancer is interacting + +with the promoter of that gene. + +And they further +elucidated the motifs + +that were being interacted with +and the little arrows point + +to where the mutations +in those motifs occur. + +So they've gone +from an association + +with that particular disease +to the actual functional + +characterization +of what's going on. + +I'll leave you with a final +thought to think about. + +This is the thing +that caused the brawls + +in the bars I told you about +at the beginning of today's + +lecture. + +Let's suppose you look +at identical twins, + +monozygotic twins, and you +ask the following question. + +You say, OK, in +monozygotic twins, + +the prevalence of a particular +disease is a 30% correlative. + +That is, if one individual +in a twin has the disease, + +there's a 30% chance that the +other twin's going to get it. + +Now there are two +possibilities here, + +which is that for +all pairs of twins, + +there's a very low risk +that you're going to get it, + +or that there are some +subset of genotypes where + +if one twin has it, the other +one's always going to get it. + +So the author of the +study actually looked + +at a block of identical twin +data and asked two questions. + +The first was if you look at +the percentage of cases that + +would test positive, making +no assumptions about genotype, + +using twin data, you +can see the percentage + +of people that actually +have a disease that + +will test positive +is actually fairly + +low for a wide +variety of diseases. + +All these diseases were +studied in the context + +of identical twins. + +And this suggested to +them that, in fact, + +personal genomic +sequencing might not + +be as predictive +as one might like. + +That is, if you have a disease, +for over half of these, + +the test will not be positive. + +And furthermore, if you test +negative for the disease, + +your relative risk-- +that is, the chance + +you're going to get this +disease to the chance you get it + +at random in the population-- +is not really reduced that much. + +And so, since this study +relied solely on twin data + +and didn't make any +other assumptions, + +it raised the question in +the field of to what extent + +is personal genome sequencing +going to be really helpful? + +So on that note, we've +talked a lot today + +about the analysis of +human genetic variation. + +I hope you've enjoyed it. + +Once again, on Thursday +we have Ron Weiss coming. + +Thank you very much. + +This concludes lecture 20 of the +formal material in the course + +and we'll see you in lecture. + +Thank you very much. \ No newline at end of file diff --git a/LodNVAJ1zE0.txt b/LodNVAJ1zE0.txt new file mode 100644 index 0000000000000000000000000000000000000000..fbccfcb1f622cc19c14a615302452de91113fd57 --- /dev/null +++ b/LodNVAJ1zE0.txt @@ -0,0 +1,3123 @@ +align:start position:0% + +there are several um mediums of working + + align:start position:0% +there are several um mediums of working + + + align:start position:0% +there are several um mediums of working +with students in the process of + + align:start position:0% +with students in the process of + + + align:start position:0% +with students in the process of +Designing there are uh desar crits there + + align:start position:0% +Designing there are uh desar crits there + + + align:start position:0% +Designing there are uh desar crits there +are reviews there are lectures and there + + align:start position:0% +are reviews there are lectures and there + + + align:start position:0% +are reviews there are lectures and there +are + + align:start position:0% +are + + + align:start position:0% +are +Pinups um in this studio every week a + + align:start position:0% +Pinups um in this studio every week a + + + align:start position:0% +Pinups um in this studio every week a +piece of the project is + + align:start position:0% +piece of the project is + + + align:start position:0% +piece of the project is +due whether it be a model or + + align:start position:0% +due whether it be a model or + + + align:start position:0% +due whether it be a model or +drawing and we have what we call pinup + + align:start position:0% +drawing and we have what we call pinup + + + align:start position:0% +drawing and we have what we call pinup +when all the students pin up their + + align:start position:0% +when all the students pin up their + + + align:start position:0% +when all the students pin up their +work and quickly explain what they are + + align:start position:0% +work and quickly explain what they are + + + align:start position:0% +work and quickly explain what they are +doing and then I and other members of + + align:start position:0% +doing and then I and other members of + + + align:start position:0% +doing and then I and other members of +the class try to give comments on what + + align:start position:0% +the class try to give comments on what + + + align:start position:0% +the class try to give comments on what +they've seen to try to help to The Next + + align:start position:0% +they've seen to try to help to The Next + + + align:start position:0% +they've seen to try to help to The Next +Step because architecture is not just + + align:start position:0% +Step because architecture is not just + + + align:start position:0% +Step because architecture is not just +one step it's a Contin process it + + align:start position:0% +one step it's a Contin process it + + + align:start position:0% +one step it's a Contin process it +changes perhaps people have the idea + + align:start position:0% +changes perhaps people have the idea + + + align:start position:0% +changes perhaps people have the idea +that it comes all once it doesn't it + + align:start position:0% +that it comes all once it doesn't it + + + align:start position:0% +that it comes all once it doesn't it +comes over a period of time so the pinup + + align:start position:0% +comes over a period of time so the pinup + + + align:start position:0% +comes over a period of time so the pinup +is a very valuable part of that uh + + align:start position:0% +is a very valuable part of that uh + + + align:start position:0% +is a very valuable part of that uh +because it's giving students a feedback + + align:start position:0% +because it's giving students a feedback + + + align:start position:0% +because it's giving students a feedback +as to how they're moving and slowly uh + + align:start position:0% +as to how they're moving and slowly uh + + + align:start position:0% +as to how they're moving and slowly uh +adjustments are made for the next step + + align:start position:0% +adjustments are made for the next step + + + align:start position:0% +adjustments are made for the next step +so what your are about to see is a + + align:start position:0% +so what your are about to see is a + + + align:start position:0% +so what your are about to see is a +typical pan up of which happens uh + + align:start position:0% +typical pan up of which happens uh + + + align:start position:0% +typical pan up of which happens uh +almost every week during the + + align:start position:0% + + + + align:start position:0% + +semester when I first visited the site I + + align:start position:0% +semester when I first visited the site I + + + align:start position:0% +semester when I first visited the site I +was pretty Amazed by The View obviously + + align:start position:0% +was pretty Amazed by The View obviously + + + align:start position:0% +was pretty Amazed by The View obviously +cuz we're up on the roof we get to look + + align:start position:0% +cuz we're up on the roof we get to look + + + align:start position:0% +cuz we're up on the roof we get to look +over all of the north end + + align:start position:0% +over all of the north end + + + align:start position:0% +over all of the north end +and I unfortunately am blocked from + + align:start position:0% +and I unfortunately am blocked from + + + align:start position:0% +and I unfortunately am blocked from +Boston um I have a wall there's + + align:start position:0% +Boston um I have a wall there's + + + align:start position:0% +Boston um I have a wall there's +a better be well there's a wall on + + align:start position:0% +a better be well there's a wall on + + + align:start position:0% +a better be well there's a wall on +the what side is that is the East that + + align:start position:0% +the what side is that is the East that + + + align:start position:0% +the what side is that is the East that +would be more than yeah the east east + + align:start position:0% +would be more than yeah the east east + + + align:start position:0% +would be more than yeah the east east +side well on the east side there's a + + align:start position:0% +side well on the east side there's a + + + align:start position:0% +side well on the east side there's a +wall so I can't I can't see Boston but I + + align:start position:0% +wall so I can't I can't see Boston but I + + + align:start position:0% +wall so I can't I can't see Boston but I +see all of the harbor and the North End + + align:start position:0% +see all of the harbor and the North End + + + align:start position:0% +see all of the harbor and the North End +um + + align:start position:0% +um + + + align:start position:0% +um +anyway that wall is going to act as my + + align:start position:0% +anyway that wall is going to act as my + + + align:start position:0% +anyway that wall is going to act as my +entrance um it's perfect for that um but + + align:start position:0% +entrance um it's perfect for that um but + + + align:start position:0% +entrance um it's perfect for that um but +I still want to be able to see over that + + align:start position:0% +I still want to be able to see over that + + + align:start position:0% +I still want to be able to see over that +um I'd love to have my + + align:start position:0% +um I'd love to have my + + + align:start position:0% +um I'd love to have my +bedroom like looking over Boston that + + align:start position:0% +bedroom like looking over Boston that + + + align:start position:0% +bedroom like looking over Boston that +would be pretty cool um so my idea was + + align:start position:0% +would be pretty cool um so my idea was + + + align:start position:0% +would be pretty cool um so my idea was +to have my main floor + + align:start position:0% +to have my main floor + + + align:start position:0% +to have my main floor +on uh below the wall and then have uh + + align:start position:0% +on uh below the wall and then have uh + + + align:start position:0% +on uh below the wall and then have uh +some kind of spiral staircase that leads + + align:start position:0% +some kind of spiral staircase that leads + + + align:start position:0% +some kind of spiral staircase that leads +up to a room + + align:start position:0% +up to a room + + + align:start position:0% +up to a room +on + + align:start position:0% +on + + + align:start position:0% +on +posts um out looking over Boston and + + align:start position:0% +posts um out looking over Boston and + + + align:start position:0% +posts um out looking over Boston and +another one that's looking out + + align:start position:0% +another one that's looking out + + + align:start position:0% +another one that's looking out +over um the harbor uh in 10 years I see + + align:start position:0% +over um the harbor uh in 10 years I see + + + align:start position:0% +over um the harbor uh in 10 years I see +myself happily married with a firm of my + + align:start position:0% +myself happily married with a firm of my + + + align:start position:0% +myself happily married with a firm of my +own successful + + align:start position:0% +own successful + + + align:start position:0% +own successful +firm arit firm architectural firm + + align:start position:0% +firm arit firm architectural firm + + + align:start position:0% +firm arit firm architectural firm +um + + align:start position:0% +um + + + align:start position:0% +um +and yeah so no kids no kids no no kids + + align:start position:0% +and yeah so no kids no kids no no kids + + + align:start position:0% +and yeah so no kids no kids no no kids +no time how about catch drugs I actually + + align:start position:0% +no time how about catch drugs I actually + + + align:start position:0% +no time how about catch drugs I actually +I didn't think about + + align:start position:0% +I didn't think about + + + align:start position:0% +I didn't think about +that not + + align:start position:0% +that not + + + align:start position:0% +that not +not I'll think more on that + + align:start position:0% +not I'll think more on that + + + align:start position:0% +not I'll think more on that +um anyway uh my needs would be a bedroom + + align:start position:0% +um anyway uh my needs would be a bedroom + + + align:start position:0% +um anyway uh my needs would be a bedroom +a guest bedroom two bathrooms uh kitchen + + align:start position:0% +a guest bedroom two bathrooms uh kitchen + + + align:start position:0% +a guest bedroom two bathrooms uh kitchen +dining room and a + + align:start position:0% +dining room and a + + + align:start position:0% +dining room and a +study and I'd like the study to be the + + align:start position:0% +study and I'd like the study to be the + + + align:start position:0% +study and I'd like the study to be the +other room that's + + align:start position:0% +other room that's + + + align:start position:0% +other room that's +elevated um that would be the one + + align:start position:0% +elevated um that would be the one + + + align:start position:0% +elevated um that would be the one +looking over the harbor and then the my + + align:start position:0% +looking over the harbor and then the my + + + align:start position:0% +looking over the harbor and then the my +bedroom would be looking over at + + align:start position:0% +bedroom would be looking over at + + + align:start position:0% +bedroom would be looking over at +Boston + + align:start position:0% + + + + align:start position:0% + +uh oh my site clue funny story so I was + + align:start position:0% +uh oh my site clue funny story so I was + + + align:start position:0% +uh oh my site clue funny story so I was +going up on a fire escape to get photos + + align:start position:0% +going up on a fire escape to get photos + + + align:start position:0% +going up on a fire escape to get photos +of my site this photo actually you can + + align:start position:0% +of my site this photo actually you can + + + align:start position:0% +of my site this photo actually you can +see the fire escape + + align:start position:0% +see the fire escape + + + align:start position:0% +see the fire escape +um got up there and the thing is + + align:start position:0% +um got up there and the thing is + + + align:start position:0% +um got up there and the thing is +horrible it is Rusty and it's about to + + align:start position:0% +horrible it is Rusty and it's about to + + + align:start position:0% +horrible it is Rusty and it's about to +fall down the entire thing and about + + align:start position:0% +fall down the entire thing and about + + + align:start position:0% +fall down the entire thing and about +every + + align:start position:0% +every + + + align:start position:0% +every +step uh every something was shaking and + + align:start position:0% +step uh every something was shaking and + + + align:start position:0% +step uh every something was shaking and +finally like I stepped on one step and + + align:start position:0% +finally like I stepped on one step and + + + align:start position:0% +finally like I stepped on one step and +it just completely gave away and then it + + align:start position:0% +it just completely gave away and then it + + + align:start position:0% +it just completely gave away and then it +clink clink clink all the way down and + + align:start position:0% +clink clink clink all the way down and + + + align:start position:0% +clink clink clink all the way down and +landed on the ground so I didn't think + + align:start position:0% +landed on the ground so I didn't think + + + align:start position:0% +landed on the ground so I didn't think +of bringing it back as a sight clue + + align:start position:0% +of bringing it back as a sight clue + + + align:start position:0% +of bringing it back as a sight clue +until later um and I just I went up and + + align:start position:0% +until later um and I just I went up and + + + align:start position:0% +until later um and I just I went up and +saw the Paul R thing and then someone uh + + align:start position:0% +saw the Paul R thing and then someone uh + + + align:start position:0% +saw the Paul R thing and then someone uh +helped me think of it that that would be + + align:start position:0% +helped me think of it that that would be + + + align:start position:0% +helped me think of it that that would be +an amazing Cy so I went back and it was + + align:start position:0% +an amazing Cy so I went back and it was + + + align:start position:0% +an amazing Cy so I went back and it was +laying on the ground so I grabbed it + + align:start position:0% +laying on the ground so I grabbed it + + + align:start position:0% +laying on the ground so I grabbed it +yeah so it's pretty straight straight + + align:start position:0% +yeah so it's pretty straight straight + + + align:start position:0% +yeah so it's pretty straight straight +forward should be fun I think it okay I + + align:start position:0% +forward should be fun I think it okay I + + + align:start position:0% +forward should be fun I think it okay I +was inspired I think these + + align:start position:0% +was inspired I think these + + + align:start position:0% +was inspired I think these +are like greeneries or I don't I don't + + align:start position:0% +are like greeneries or I don't I don't + + + align:start position:0% +are like greeneries or I don't I don't +know exactly but they're just + + align:start position:0% +know exactly but they're just + + + align:start position:0% +know exactly but they're just +cylindrical and metal and there's a barn + + align:start position:0% +cylindrical and metal and there's a barn + + + align:start position:0% +cylindrical and metal and there's a barn +underneath and I kind of want to I want + + align:start position:0% +underneath and I kind of want to I want + + + align:start position:0% +underneath and I kind of want to I want +a rectangular main floor with a kind of + + align:start position:0% +a rectangular main floor with a kind of + + + align:start position:0% +a rectangular main floor with a kind of +metallic um + + align:start position:0% +metallic um + + + align:start position:0% +metallic um +spiral uh staircase and then these rooms + + align:start position:0% +spiral uh staircase and then these rooms + + + align:start position:0% +spiral uh staircase and then these rooms +off shooting as curve like partial + + align:start position:0% +off shooting as curve like partial + + + align:start position:0% +off shooting as curve like partial +circles um I want to kind of capture the + + align:start position:0% +circles um I want to kind of capture the + + + align:start position:0% +circles um I want to kind of capture the +panoramic + + align:start position:0% +panoramic + + + align:start position:0% +panoramic +view and like as it's done on this + + align:start position:0% +view and like as it's done on this + + + align:start position:0% +view and like as it's done on this +corner is curve + + align:start position:0% +corner is curve + + + align:start position:0% +corner is curve +like uh just so you can see the + + align:start position:0% + + + + align:start position:0% + +whole I like that a lot so that was the + + align:start position:0% +whole I like that a lot so that was the + + + align:start position:0% +whole I like that a lot so that was the +way I wanted to incorporate + + align:start position:0% +way I wanted to incorporate + + + align:start position:0% +way I wanted to incorporate +it um + + align:start position:0% +it um + + + align:start position:0% +it um +yeah and I'm just going to pump for some + + align:start position:0% +yeah and I'm just going to pump for some + + + align:start position:0% +yeah and I'm just going to pump for some +more information sure what about the + + align:start position:0% +more information sure what about the + + + align:start position:0% +more information sure what about the +area or the North End what you how' you + + align:start position:0% +area or the North End what you how' you + + + align:start position:0% +area or the North End what you how' you +react to it oh I really like the rooftop + + align:start position:0% +react to it oh I really like the rooftop + + + align:start position:0% +react to it oh I really like the rooftop +view like uh what do you mean North End + + align:start position:0% +view like uh what do you mean North End + + + align:start position:0% +view like uh what do you mean North End +like well is North End is + + align:start position:0% +like well is North End is + + + align:start position:0% +like well is North End is +a very special kind of physical + + align:start position:0% +a very special kind of physical + + + align:start position:0% +a very special kind of physical +neighborhood as where it's + + align:start position:0% +neighborhood as where it's + + + align:start position:0% +neighborhood as where it's +social in the United States there's very + + align:start position:0% +social in the United States there's very + + + align:start position:0% +social in the United States there's very +touristy I noticed um and I like the + + align:start position:0% +touristy I noticed um and I like the + + + align:start position:0% +touristy I noticed um and I like the +roof because you get away from most the + + align:start position:0% +roof because you get away from most the + + + align:start position:0% +roof because you get away from most the +you know all the tourists and uh I gree + + align:start position:0% +you know all the tourists and uh I gree + + + align:start position:0% +you know all the tourists and uh I gree +there's a with you there's like a + + align:start position:0% +there's a with you there's like a + + + align:start position:0% +there's a with you there's like a +completely separate World up there um I + + align:start position:0% +completely separate World up there um I + + + align:start position:0% +completely separate World up there um I +know personally like my roof like of my + + align:start position:0% +know personally like my roof like of my + + + align:start position:0% +know personally like my roof like of my +house right now like if you go up there + + align:start position:0% +house right now like if you go up there + + + align:start position:0% +house right now like if you go up there +there's people having parties like + + align:start position:0% +there's people having parties like + + + align:start position:0% +there's people having parties like +randomly on rooftops and it's kind of + + align:start position:0% +randomly on rooftops and it's kind of + + + align:start position:0% +randomly on rooftops and it's kind of +cool just to check it out and like I + + align:start position:0% +cool just to check it out and like I + + + align:start position:0% +cool just to check it out and like I +went by to one like the other day like + + align:start position:0% +went by to one like the other day like + + + align:start position:0% +went by to one like the other day like +the next door neighbors were having like + + align:start position:0% +the next door neighbors were having like + + + align:start position:0% +the next door neighbors were having like +a barbecue and everything on their roof + + align:start position:0% +a barbecue and everything on their roof + + + align:start position:0% +a barbecue and everything on their roof +so that was kind of cool but I think + + align:start position:0% +so that was kind of cool but I think + + + align:start position:0% +so that was kind of cool but I think +that that's going to happen a lot here + + align:start position:0% +that that's going to happen a lot here + + + align:start position:0% +that that's going to happen a lot here +so I want to have roof access as well + + align:start position:0% +so I want to have roof access as well + + + align:start position:0% +so I want to have roof access as well +well for me seeing the site for the + + align:start position:0% +well for me seeing the site for the + + + align:start position:0% +well for me seeing the site for the +first time is one of the most ex + + align:start position:0% +first time is one of the most ex + + + align:start position:0% +first time is one of the most ex +exciting parts of architecture I can't + + align:start position:0% +exciting parts of architecture I can't + + + align:start position:0% +exciting parts of architecture I can't +sleep the night before when I see a site + + align:start position:0% +sleep the night before when I see a site + + + align:start position:0% +sleep the night before when I see a site +um and I was curious how you people were + + align:start position:0% +um and I was curious how you people were + + + align:start position:0% +um and I was curious how you people were +going to react to the North + + align:start position:0% +going to react to the North + + + align:start position:0% +going to react to the North +End the night + + align:start position:0% +End the night + + + align:start position:0% +End the night +before I find I'm like a kid I'm up all + + align:start position:0% +before I find I'm like a kid I'm up all + + + align:start position:0% +before I find I'm like a kid I'm up all +night I'm going to see a new site next + + align:start position:0% +night I'm going to see a new site next + + + align:start position:0% +night I'm going to see a new site next +week and I just I can't wait to see + + align:start position:0% +week and I just I can't wait to see + + + align:start position:0% +week and I just I can't wait to see +consing + + align:start position:0% + + + + align:start position:0% + +myy well that's a little different + + align:start position:0% +myy well that's a little different + + + align:start position:0% +myy well that's a little different +problem and I got another site from + + align:start position:0% +problem and I got another site from + + + align:start position:0% +problem and I got another site from +Turkey today which I have to go + + align:start position:0% +Turkey today which I have to go + + + align:start position:0% +Turkey today which I have to go +for um I will be going on a Friday and + + align:start position:0% +for um I will be going on a Friday and + + + align:start position:0% +for um I will be going on a Friday and +coming back on a Monday morning in a + + align:start position:0% +coming back on a Monday morning in a + + + align:start position:0% +coming back on a Monday morning in a +couple weeks or so so but I saw the site + + align:start position:0% +couple weeks or so so but I saw the site + + + align:start position:0% +couple weeks or so so but I saw the site +um in photographs and it's very exciting + + align:start position:0% +um in photographs and it's very exciting + + + align:start position:0% +um in photographs and it's very exciting +to see a new site so I was curious to + + align:start position:0% +to see a new site so I was curious to + + + align:start position:0% +to see a new site so I was curious to +see how you folks would react to that um + + align:start position:0% +see how you folks would react to that um + + + align:start position:0% +see how you folks would react to that um +a couple of things good start start guys + + align:start position:0% +a couple of things good start start guys + + + align:start position:0% +a couple of things good start start guys +as always guys + + align:start position:0% +as always guys + + + align:start position:0% +as always guys +always have good + + align:start position:0% +always have good + + + align:start position:0% +always have good +starts in Philip's case a couple things + + align:start position:0% +starts in Philip's case a couple things + + + align:start position:0% +starts in Philip's case a couple things +that I thought was + + align:start position:0% +that I thought was + + + align:start position:0% +that I thought was +interesting he did not tell us that his + + align:start position:0% +interesting he did not tell us that his + + + align:start position:0% +interesting he did not tell us that his +site is probably one of the most + + align:start position:0% +site is probably one of the most + + + align:start position:0% +site is probably one of the most +important ones because where did he go + + align:start position:0% +important ones because where did he go + + + align:start position:0% +important ones because where did he go +there he is he is the Busy Body or the + + align:start position:0% +there he is he is the Busy Body or the + + + align:start position:0% +there he is he is the Busy Body or the +caretaker of our public site down below + + align:start position:0% +caretaker of our public site down below + + + align:start position:0% +caretaker of our public site down below +um the the other thing is immediately + + align:start position:0% +um the the other thing is immediately + + + align:start position:0% +um the the other thing is immediately +jumping to from the prog + + align:start position:0% +jumping to from the prog + + + align:start position:0% +jumping to from the prog +no kids or one kid I can't remember no + + align:start position:0% +no kids or one kid I can't remember no + + + align:start position:0% +no kids or one kid I can't remember no +kids okay that's good because you may + + align:start position:0% +kids okay that's good because you may + + + align:start position:0% +kids okay that's good because you may +lose them all up here in + + align:start position:0% + + + + align:start position:0% + +the right that's what this could be uh + + align:start position:0% +the right that's what this could be uh + + + align:start position:0% +the right that's what this could be uh +what's quickly very interesting about + + align:start position:0% +what's quickly very interesting about + + + align:start position:0% +what's quickly very interesting about +this sketch from where he is is that we + + align:start position:0% +this sketch from where he is is that we + + + align:start position:0% +this sketch from where he is is that we +have a delicate kind of dance between + + align:start position:0% +have a delicate kind of dance between + + + align:start position:0% +have a delicate kind of dance between +contextual and + + align:start position:0% +contextual and + + + align:start position:0% +contextual and +non-contextual uh architecture + + align:start position:0% +non-contextual uh architecture + + + align:start position:0% +non-contextual uh architecture +that which fits and that which doesn't + + align:start position:0% +that which fits and that which doesn't + + + align:start position:0% +that which fits and that which doesn't +which is the was the case with the last + + align:start position:0% +which is the was the case with the last + + + align:start position:0% +which is the was the case with the last +project it's no different it's always + + align:start position:0% +project it's no different it's always + + + align:start position:0% +project it's no different it's always +the case whether it's a built quy as + + align:start position:0% +the case whether it's a built quy as + + + align:start position:0% +the case whether it's a built quy as +we're using this or so-called natural + + align:start position:0% +we're using this or so-called natural + + + align:start position:0% +we're using this or so-called natural +quy is the last one what I find + + align:start position:0% +quy is the last one what I find + + + align:start position:0% +quy is the last one what I find +interesting is that this kind of + + align:start position:0% +interesting is that this kind of + + + align:start position:0% +interesting is that this kind of +vocabulary which we can start to imagine + + align:start position:0% +vocabulary which we can start to imagine + + + align:start position:0% +vocabulary which we can start to imagine +fits in very much to the roofscapes that + + align:start position:0% +fits in very much to the roofscapes that + + + align:start position:0% +fits in very much to the roofscapes that +we know for instance those who are from + + align:start position:0% +we know for instance those who are from + + + align:start position:0% +we know for instance those who are from +New York you will find every roof has a + + align:start position:0% +New York you will find every roof has a + + + align:start position:0% +New York you will find every roof has a +water tower on it uh and here we don't + + align:start position:0% +water tower on it uh and here we don't + + + align:start position:0% +water tower on it uh and here we don't +for some reason I know not sure why but + + align:start position:0% +for some reason I know not sure why but + + + align:start position:0% +for some reason I know not sure why but +the kind of form that this is starting s + + align:start position:0% +the kind of form that this is starting s + + + align:start position:0% +the kind of form that this is starting s +to suggest suggested as part of the roof + + align:start position:0% +to suggest suggested as part of the roof + + + align:start position:0% +to suggest suggested as part of the roof +part of the sky I I don't know how it + + align:start position:0% +part of the sky I I don't know how it + + + align:start position:0% +part of the sky I I don't know how it +works yet but I think your decision of + + align:start position:0% +works yet but I think your decision of + + + align:start position:0% +works yet but I think your decision of +using the back wall to move into it and + + align:start position:0% +using the back wall to move into it and + + + align:start position:0% +using the back wall to move into it and +using this as a + + align:start position:0% +using this as a + + + align:start position:0% +using this as a +generator a very strong generator of of + + align:start position:0% +generator a very strong generator of of + + + align:start position:0% +generator a very strong generator of of +the view and then I'm not sure what this + + align:start position:0% +the view and then I'm not sure what this + + + align:start position:0% +the view and then I'm not sure what this +is moving in off of this is very + + align:start position:0% +is moving in off of this is very + + + align:start position:0% +is moving in off of this is very +powerful so it's a good start for what + + align:start position:0% +powerful so it's a good start for what + + + align:start position:0% +powerful so it's a good start for what +we got to do now is to make this work in + + align:start position:0% +we got to do now is to make this work in + + + align:start position:0% +we got to do now is to make this work in +in plan I mean there's no plan there yet + + align:start position:0% +in plan I mean there's no plan there yet + + + align:start position:0% +in plan I mean there's no plan there yet +there's ideas but the idea that the + + align:start position:0% +there's ideas but the idea that the + + + align:start position:0% +there's ideas but the idea that the +conceptual form making is is very strong + + align:start position:0% +conceptual form making is is very strong + + + align:start position:0% +conceptual form making is is very strong +um I would invite you to use this as a + + align:start position:0% +um I would invite you to use this as a + + + align:start position:0% +um I would invite you to use this as a +clue as to what kind of architecture you + + align:start position:0% +clue as to what kind of architecture you + + + align:start position:0% +clue as to what kind of architecture you +might find up here that is a light steel + + align:start position:0% +might find up here that is a light steel + + + align:start position:0% +might find up here that is a light steel +construction uh might work + + align:start position:0% + + + + align:start position:0% + +huh yeah as opposed to heavy this is + + align:start position:0% +huh yeah as opposed to heavy this is + + + align:start position:0% +huh yeah as opposed to heavy this is +heavy but the notion of the kind of form + + align:start position:0% +heavy but the notion of the kind of form + + + align:start position:0% +heavy but the notion of the kind of form +might be another interesting way of + + align:start position:0% +might be another interesting way of + + + align:start position:0% +might be another interesting way of +being up + + align:start position:0% + + + + align:start position:0% + +there so my first ideas when I got to + + align:start position:0% +there so my first ideas when I got to + + + align:start position:0% +there so my first ideas when I got to +the North End the first things that I + + align:start position:0% +the North End the first things that I + + + align:start position:0% +the North End the first things that I +noticed um were just the fact that um + + align:start position:0% +noticed um were just the fact that um + + + align:start position:0% +noticed um were just the fact that um +there is a lot of layering and and I + + align:start position:0% +there is a lot of layering and and I + + + align:start position:0% +there is a lot of layering and and I +like the fact that material sort of + + align:start position:0% +like the fact that material sort of + + + align:start position:0% +like the fact that material sort of +merged into other materials um here I + + align:start position:0% +merged into other materials um here I + + + align:start position:0% +merged into other materials um here I +tried to to mimic the cobblestones in + + align:start position:0% +tried to to mimic the cobblestones in + + + align:start position:0% +tried to to mimic the cobblestones in +the street and then it + + align:start position:0% +the street and then it + + + align:start position:0% +the street and then it +um the pavement how it just merged into + + align:start position:0% +um the pavement how it just merged into + + + align:start position:0% +um the pavement how it just merged into +the pavement + + align:start position:0% +the pavement + + + align:start position:0% +the pavement +um just that idea I liked a lot how + + align:start position:0% +um just that idea I liked a lot how + + + align:start position:0% +um just that idea I liked a lot how +materials merged into other materials + + align:start position:0% +materials merged into other materials + + + align:start position:0% +materials merged into other materials +and this is the facade of my building + + align:start position:0% +and this is the facade of my building + + + align:start position:0% +and this is the facade of my building +um here is where we met and my building + + align:start position:0% +um here is where we met and my building + + + align:start position:0% +um here is where we met and my building +is or it's really two buildings and I my + + align:start position:0% +is or it's really two buildings and I my + + + align:start position:0% +is or it's really two buildings and I my +site is either on top of both or on top + + align:start position:0% +site is either on top of both or on top + + + align:start position:0% +site is either on top of both or on top +of one of them and I'm sort of thinking + + align:start position:0% +of one of them and I'm sort of thinking + + + align:start position:0% +of one of them and I'm sort of thinking +of taking over both sides for now um but + + align:start position:0% +of taking over both sides for now um but + + + align:start position:0% +of taking over both sides for now um but +what I liked a lot about the facade just + + align:start position:0% +what I liked a lot about the facade just + + + align:start position:0% +what I liked a lot about the facade just +looking at it it is the fact that you + + align:start position:0% +looking at it it is the fact that you + + + align:start position:0% +looking at it it is the fact that you +can tell you can tell the history of the + + align:start position:0% +can tell you can tell the history of the + + + align:start position:0% +can tell you can tell the history of the +building you can see how it it has + + align:start position:0% +building you can see how it it has + + + align:start position:0% +building you can see how it it has +evolved over time um this is somewhat + + align:start position:0% +evolved over time um this is somewhat + + + align:start position:0% +evolved over time um this is somewhat +different to the next level which is + + align:start position:0% +different to the next level which is + + + align:start position:0% +different to the next level which is +somewhat different to the next level but + + align:start position:0% +somewhat different to the next level but + + + align:start position:0% +somewhat different to the next level but +they merg I like the way the materials + + align:start position:0% +they merg I like the way the materials + + + align:start position:0% +they merg I like the way the materials +merged and uh I want my my building my + + align:start position:0% +merged and uh I want my my building my + + + align:start position:0% +merged and uh I want my my building my +apartment to to merge with that to be + + align:start position:0% +apartment to to merge with that to be + + + align:start position:0% +apartment to to merge with that to be +another layer of the building + + align:start position:0% +another layer of the building + + + align:start position:0% +another layer of the building +um so that that's my main idea + + align:start position:0% +um so that that's my main idea + + + align:start position:0% +um so that that's my main idea +I envisioned myself being married I + + align:start position:0% +I envisioned myself being married I + + + align:start position:0% +I envisioned myself being married I +think at first I thought well I I'm I'm + + align:start position:0% +think at first I thought well I I'm I'm + + + align:start position:0% +think at first I thought well I I'm I'm +not sure there's so much to do before + + align:start position:0% +not sure there's so much to do before + + + align:start position:0% +not sure there's so much to do before +getting married so many places to visit + + align:start position:0% +getting married so many places to visit + + + align:start position:0% +getting married so many places to visit +um in the world that I wanted to visit + + align:start position:0% +um in the world that I wanted to visit + + + align:start position:0% +um in the world that I wanted to visit +but uh right across from this is the + + align:start position:0% +but uh right across from this is the + + + align:start position:0% +but uh right across from this is the +playground and I sat in the little + + align:start position:0% +playground and I sat in the little + + + align:start position:0% +playground and I sat in the little +playground and I thought this would be + + align:start position:0% +playground and I thought this would be + + + align:start position:0% +playground and I thought this would be +really nice to have kids so if I I + + align:start position:0% +really nice to have kids so if I I + + + align:start position:0% +really nice to have kids so if I I +hopefully we'll be married and if I am + + align:start position:0% +hopefully we'll be married and if I am + + + align:start position:0% +hopefully we'll be married and if I am +I'd have two kids but if I wasn't I + + align:start position:0% +I'd have two kids but if I wasn't I + + + align:start position:0% +I'd have two kids but if I wasn't I +think at that point I'd adopt uh a child + + align:start position:0% +think at that point I'd adopt uh a child + + + align:start position:0% +think at that point I'd adopt uh a child +and uh and if I live here I have to have + + align:start position:0% +and uh and if I live here I have to have + + + align:start position:0% +and uh and if I live here I have to have +a kid there's a beautiful playground + + align:start position:0% +a kid there's a beautiful playground + + + align:start position:0% +a kid there's a beautiful playground +right across um so and that just the + + align:start position:0% +right across um so and that just the + + + align:start position:0% +right across um so and that just the +community seemed very friendly um just + + align:start position:0% +community seemed very friendly um just + + + align:start position:0% +community seemed very friendly um just +when I was there I talked to a woman and + + align:start position:0% +when I was there I talked to a woman and + + + align:start position:0% +when I was there I talked to a woman and +she had her child with her and just a + + align:start position:0% +she had her child with her and just a + + + align:start position:0% +she had her child with her and just a +very open sort of um it seemed like a + + align:start position:0% +very open sort of um it seemed like a + + + align:start position:0% +very open sort of um it seemed like a +lot of parents were there + + align:start position:0% +lot of parents were there + + + align:start position:0% +lot of parents were there +so um so with this idea of merging and + + align:start position:0% +so um so with this idea of merging and + + + align:start position:0% +so um so with this idea of merging and +this idea of uh creating + + align:start position:0% +this idea of uh creating + + + align:start position:0% +this idea of uh creating +layers um I I decided that I I would + + align:start position:0% +layers um I I decided that I I would + + + align:start position:0% +layers um I I decided that I I would +sort of use the facade to to guide um + + align:start position:0% +sort of use the facade to to guide um + + + align:start position:0% +sort of use the facade to to guide um +the way that I was going to + + align:start position:0% +the way that I was going to + + + align:start position:0% +the way that I was going to +design because I couldn't get myself + + align:start position:0% +design because I couldn't get myself + + + align:start position:0% +design because I couldn't get myself +away from this sort of idea that I want + + align:start position:0% +away from this sort of idea that I want + + + align:start position:0% +away from this sort of idea that I want +the materials to merge I just couldn't + + align:start position:0% +the materials to merge I just couldn't + + + align:start position:0% +the materials to merge I just couldn't +start thinking about what the form of + + align:start position:0% +start thinking about what the form of + + + align:start position:0% +start thinking about what the form of +the building would be so what I did was + + align:start position:0% +the building would be so what I did was + + + align:start position:0% +the building would be so what I did was +I I just decided that I'd make a grid + + align:start position:0% +I I just decided that I'd make a grid + + + align:start position:0% +I I just decided that I'd make a grid +sort of I I feel like I have a lot of + + align:start position:0% +sort of I I feel like I have a lot of + + + align:start position:0% +sort of I I feel like I have a lot of +leeway here I have a site that doesn't + + align:start position:0% +leeway here I have a site that doesn't + + + align:start position:0% +leeway here I have a site that doesn't +have a problem such as Sarah's Sarah has + + align:start position:0% +have a problem such as Sarah's Sarah has + + + align:start position:0% +have a problem such as Sarah's Sarah has +a church she has to deal with I feel + + align:start position:0% +a church she has to deal with I feel + + + align:start position:0% +a church she has to deal with I feel +like I'm I don't have such a problem + + align:start position:0% +like I'm I don't have such a problem + + + align:start position:0% +like I'm I don't have such a problem +that is prominent and so I need some + + align:start position:0% +that is prominent and so I need some + + + align:start position:0% +that is prominent and so I need some +sort of parameters to help me try to + + align:start position:0% +sort of parameters to help me try to + + + align:start position:0% +sort of parameters to help me try to +design um so part of my program would be + + align:start position:0% +design um so part of my program would be + + + align:start position:0% +design um so part of my program would be +um I wanted to have a fencing room + + align:start position:0% +um I wanted to have a fencing room + + + align:start position:0% +um I wanted to have a fencing room +because I saw myself as either an + + align:start position:0% +because I saw myself as either an + + + align:start position:0% +because I saw myself as either an +assistant coach or a competitive fencer + + align:start position:0% +assistant coach or a competitive fencer + + + align:start position:0% +assistant coach or a competitive fencer +but um I was told that that would be a + + align:start position:0% +but um I was told that that would be a + + + align:start position:0% +but um I was told that that would be a +better idea for the community center so + + align:start position:0% +better idea for the community center so + + + align:start position:0% +better idea for the community center so +I can coach there if I need to um well + + align:start position:0% +I can coach there if I need to um well + + + align:start position:0% +I can coach there if I need to um well +you might fall off the roof this + + align:start position:0% +you might fall off the roof this + + + align:start position:0% +you might fall off the roof this +point um but I I do want a garden uh I I + + align:start position:0% +point um but I I do want a garden uh I I + + + align:start position:0% +point um but I I do want a garden uh I I +think I I love Gardens I love trees and + + align:start position:0% +think I I love Gardens I love trees and + + + align:start position:0% +think I I love Gardens I love trees and +um I'd like some way to have a garden + + align:start position:0% +um I'd like some way to have a garden + + + align:start position:0% +um I'd like some way to have a garden +surrounding the house to + + align:start position:0% + + + + align:start position:0% + +make right this very little corner they + + align:start position:0% +make right this very little corner they + + + align:start position:0% +make right this very little corner they +they merge and they they continue and so + + align:start position:0% +they merge and they they continue and so + + + align:start position:0% +they merge and they they continue and so +I like that idea and I'm thinking even + + align:start position:0% +I like that idea and I'm thinking even + + + align:start position:0% +I like that idea and I'm thinking even +there having my chimy just extend from + + align:start position:0% +there having my chimy just extend from + + + align:start position:0% +there having my chimy just extend from +there + + align:start position:0% +there + + + align:start position:0% +there +um this is another view from the back + + align:start position:0% +um this is another view from the back + + + align:start position:0% +um this is another view from the back +from the alley uh just to see where + + align:start position:0% +from the alley uh just to see where + + + align:start position:0% +from the alley uh just to see where +things are and that that's Sarah's um + + align:start position:0% +things are and that that's Sarah's um + + + align:start position:0% +things are and that that's Sarah's um +sight and mind right on top so maybe we + + align:start position:0% +sight and mind right on top so maybe we + + + align:start position:0% +sight and mind right on top so maybe we +can I don't know get together but I I + + align:start position:0% +can I don't know get together but I I + + + align:start position:0% +can I don't know get together but I I +don't have any sort of idea what my + + align:start position:0% +don't have any sort of idea what my + + + align:start position:0% +don't have any sort of idea what my +forms of my building is going to be I + + align:start position:0% +forms of my building is going to be I + + + align:start position:0% +forms of my building is going to be I +just I think the last couple days it's + + align:start position:0% +just I think the last couple days it's + + + align:start position:0% +just I think the last couple days it's +just given me the opportunity to think + + align:start position:0% +just given me the opportunity to think + + + align:start position:0% +just given me the opportunity to think +about what kind of parameters I want I + + align:start position:0% +about what kind of parameters I want I + + + align:start position:0% +about what kind of parameters I want I +think it's interesting for me to see how + + align:start position:0% +think it's interesting for me to see how + + + align:start position:0% +think it's interesting for me to see how +people um relate to the + + align:start position:0% +people um relate to the + + + align:start position:0% +people um relate to the +northin and one of the reasons why I + + align:start position:0% +northin and one of the reasons why I + + + align:start position:0% +northin and one of the reasons why I +chose the North in is it's a very rich + + align:start position:0% +chose the North in is it's a very rich + + + align:start position:0% +chose the North in is it's a very rich +place our architecturally + + align:start position:0% +place our architecturally + + + align:start position:0% +place our architecturally +socially + + align:start position:0% +socially + + + align:start position:0% +socially +um and she has found this notion that + + align:start position:0% +um and she has found this notion that + + + align:start position:0% +um and she has found this notion that +she calls + + align:start position:0% +she calls + + + align:start position:0% +she calls +merging of materials time which is what + + align:start position:0% +merging of materials time which is what + + + align:start position:0% +merging of materials time which is what +the Northend is all about is mer merging + + align:start position:0% +the Northend is all about is mer merging + + + align:start position:0% +the Northend is all about is mer merging +of time and we get Paul R around the + + align:start position:0% +of time and we get Paul R around the + + + align:start position:0% +of time and we get Paul R around the +corner but we can find u u you know + + align:start position:0% +corner but we can find u u you know + + + align:start position:0% +corner but we can find u u you know +young professionals living here so + + align:start position:0% +young professionals living here so + + + align:start position:0% +young professionals living here so +there's a merging over time and also of + + align:start position:0% +there's a merging over time and also of + + + align:start position:0% +there's a merging over time and also of +that results I think in what happens + + align:start position:0% +that results I think in what happens + + + align:start position:0% +that results I think in what happens +here of the style + + align:start position:0% +here of the style + + + align:start position:0% +here of the style +I'd like to as I mentioned to her the + + align:start position:0% +I'd like to as I mentioned to her the + + + align:start position:0% +I'd like to as I mentioned to her the +other day consider another word which I + + align:start position:0% +other day consider another word which I + + + align:start position:0% +other day consider another word which I +will talk about on Thursday which is + + align:start position:0% +will talk about on Thursday which is + + + align:start position:0% +will talk about on Thursday which is +layering there are layers of + + align:start position:0% +layering there are layers of + + + align:start position:0% +layering there are layers of +different TH or different materials in + + align:start position:0% +different TH or different materials in + + + align:start position:0% +different TH or different materials in +the Northend which is quite different + + align:start position:0% +the Northend which is quite different + + + align:start position:0% +the Northend which is quite different +than any place else that we would be you + + align:start position:0% +than any place else that we would be you + + + align:start position:0% +than any place else that we would be you +have the layers of of uh different + + align:start position:0% +have the layers of of uh different + + + align:start position:0% +have the layers of of uh different +materials the uh fire escapes for me is + + align:start position:0% +materials the uh fire escapes for me is + + + align:start position:0% +materials the uh fire escapes for me is +a layer of something against the + + align:start position:0% +a layer of something against the + + + align:start position:0% +a layer of something against the +hardness very + + align:start position:0% +hardness very + + + align:start position:0% +hardness very +skeleton so this not as indicated by the + + align:start position:0% +skeleton so this not as indicated by the + + + align:start position:0% +skeleton so this not as indicated by the +sketch by the way how many kids we got 1 + + align:start position:0% +sketch by the way how many kids we got 1 + + + align:start position:0% +sketch by the way how many kids we got 1 +three and two so we got six already it's + + align:start position:0% +three and two so we got six already it's + + + align:start position:0% +three and two so we got six already it's +beats last year's class where we only + + align:start position:0% +beats last year's class where we only + + + align:start position:0% +beats last year's class where we only +had three I think um and incidentally + + align:start position:0% +had three I think um and incidentally + + + align:start position:0% +had three I think um and incidentally +the observation is very uh + + align:start position:0% +the observation is very uh + + + align:start position:0% +the observation is very uh +revealing of the North End as a + + align:start position:0% +revealing of the North End as a + + + align:start position:0% +revealing of the North End as a +playground if you think about um the + + align:start position:0% +playground if you think about um the + + + align:start position:0% +playground if you think about um the +exposure of children or us to other + + align:start position:0% +exposure of children or us to other + + + align:start position:0% +exposure of children or us to other +people which is quite different than if + + align:start position:0% +people which is quite different than if + + + align:start position:0% +people which is quite different than if +we had have picked the site in the + + align:start position:0% +we had have picked the site in the + + + align:start position:0% +we had have picked the site in the +suburbs which we wouldn't + + align:start position:0% +suburbs which we wouldn't + + + align:start position:0% +suburbs which we wouldn't +have um because this has a lot of + + align:start position:0% +have um because this has a lot of + + + align:start position:0% +have um because this has a lot of +opportunities for exposures all kinds of + + align:start position:0% +opportunities for exposures all kinds of + + + align:start position:0% +opportunities for exposures all kinds of +exposure you meet somebody from Iowa + + align:start position:0% +exposure you meet somebody from Iowa + + + align:start position:0% +exposure you meet somebody from Iowa +walking up and I find I I've asked you + + align:start position:0% +walking up and I find I I've asked you + + + align:start position:0% +walking up and I find I I've asked you +but I continually find that the north + + align:start position:0% +but I continually find that the north + + + align:start position:0% +but I continually find that the north +Enders are friendly people they they'll + + align:start position:0% +Enders are friendly people they they'll + + + align:start position:0% +Enders are friendly people they they'll +stop and talk with you I never have been + + align:start position:0% +stop and talk with you I never have been + + + align:start position:0% +stop and talk with you I never have been +challenged um unlike the suburbs you go + + align:start position:0% +challenged um unlike the suburbs you go + + + align:start position:0% +challenged um unlike the suburbs you go +in the suburbs and you try to talk to + + align:start position:0% +in the suburbs and you try to talk to + + + align:start position:0% +in the suburbs and you try to talk to +someone you'll be arrested probably on + + align:start position:0% +someone you'll be arrested probably on + + + align:start position:0% +someone you'll be arrested probably on +the spot because you're up to no good + + align:start position:0% +the spot because you're up to no good + + + align:start position:0% +the spot because you're up to no good +but that's not the case here it's a very + + align:start position:0% +but that's not the case here it's a very + + + align:start position:0% +but that's not the case here it's a very +public thing so I thought that was an + + align:start position:0% +public thing so I thought that was an + + + align:start position:0% +public thing so I thought that was an +interesting observation but I just want + + align:start position:0% +interesting observation but I just want + + + align:start position:0% +interesting observation but I just want +to pick up on this which she + + align:start position:0% +to pick up on this which she + + + align:start position:0% +to pick up on this which she +has suggested in a geometric way and I + + align:start position:0% +has suggested in a geometric way and I + + + align:start position:0% +has suggested in a geometric way and I +think she's actually suggested in an + + align:start position:0% +think she's actually suggested in an + + + align:start position:0% +think she's actually suggested in an +architectural way what I would like to + + align:start position:0% +architectural way what I would like to + + + align:start position:0% +architectural way what I would like to +talk about but in + + align:start position:0% +talk about but in + + + align:start position:0% +talk about but in +plan if this is the + + align:start position:0% +plan if this is the + + + align:start position:0% +plan if this is the +roof that these + + align:start position:0% +roof that these + + + align:start position:0% +roof that these +layers might + + align:start position:0% +layers might + + + align:start position:0% +layers might +not necessarily these are + + align:start position:0% +not necessarily these are + + + align:start position:0% +not necessarily these are +planes of part of the floor and the + + align:start position:0% +planes of part of the floor and the + + + align:start position:0% +planes of part of the floor and the +walls I should say may not at all line + + align:start position:0% +walls I should say may not at all line + + + align:start position:0% +walls I should say may not at all line +up with the old layer they may miss it + + align:start position:0% +up with the old layer they may miss it + + + align:start position:0% +up with the old layer they may miss it +in two ways this is if you're following + + align:start position:0% +in two ways this is if you're following + + + align:start position:0% +in two ways this is if you're following +me this is a setback of a plan this is + + align:start position:0% +me this is a setback of a plan this is + + + align:start position:0% +me this is a setback of a plan this is +her garden and her + + align:start position:0% +her garden and her + + + align:start position:0% +her garden and her +Design This is light comes through but + + align:start position:0% +Design This is light comes through but + + + align:start position:0% +Design This is light comes through but +that's one way and then the other way if + + align:start position:0% +that's one way and then the other way if + + + align:start position:0% +that's one way and then the other way if +that's the boundary the layers could + + align:start position:0% +that's the boundary the layers could + + + align:start position:0% +that's the boundary the layers could +come out which we may see in others so + + align:start position:0% +come out which we may see in others so + + + align:start position:0% +come out which we may see in others so +instead of a direct interpretation of it + + align:start position:0% +instead of a direct interpretation of it + + + align:start position:0% +instead of a direct interpretation of it +you could think of this as coming up to + + align:start position:0% +you could think of this as coming up to + + + align:start position:0% +you could think of this as coming up to +here and the geometry pick up but the + + align:start position:0% +here and the geometry pick up but the + + + align:start position:0% +here and the geometry pick up but the +layers are maybe set + + align:start position:0% +layers are maybe set + + + align:start position:0% +layers are maybe set +back which means that on top of this + + align:start position:0% +back which means that on top of this + + + align:start position:0% +back which means that on top of this +then we have this kind of transitions or + + align:start position:0% +then we have this kind of transitions or + + + align:start position:0% +then we have this kind of transitions or +layers of different materials and they + + align:start position:0% +layers of different materials and they + + + align:start position:0% +layers of different materials and they +could be entirely different you didn't + + align:start position:0% +could be entirely different you didn't + + + align:start position:0% +could be entirely different you didn't +talk about the roof form sky form uh you + + align:start position:0% +talk about the roof form sky form uh you + + + align:start position:0% +talk about the roof form sky form uh you +may need you know a cloud floating by or + + align:start position:0% +may need you know a cloud floating by or + + + align:start position:0% +may need you know a cloud floating by or +something to think about that but um + + align:start position:0% +something to think about that but um + + + align:start position:0% +something to think about that but um +that quality of this sketch is very + + align:start position:0% +that quality of this sketch is very + + + align:start position:0% +that quality of this sketch is very +powerful on that place so I think that's + + align:start position:0% +powerful on that place so I think that's + + + align:start position:0% +powerful on that place so I think that's +a great start \ No newline at end of file diff --git a/MGqoLm2aAgc.txt b/MGqoLm2aAgc.txt new file mode 100644 index 0000000000000000000000000000000000000000..8d9c935350937f5029b3fb6b53d7cea18c8b344e --- /dev/null +++ b/MGqoLm2aAgc.txt @@ -0,0 +1,17883 @@ +align:start position:0% + +hi everybody + + align:start position:0% +hi everybody + + + align:start position:0% +hi everybody +can you hear me + + align:start position:0% + + + + align:start position:0% + +yes good + + align:start position:0% +yes good + + + align:start position:0% +yes good +um + + align:start position:0% +um + + + align:start position:0% +um +welcome back uh + + align:start position:0% +welcome back uh + + + align:start position:0% +welcome back uh +to um + + align:start position:0% +to um + + + align:start position:0% +to um +to the course and um + + align:start position:0% +to the course and um + + + align:start position:0% +to the course and um +so we are now at lecture 10 and um uh + + align:start position:0% +so we are now at lecture 10 and um uh + + + align:start position:0% +so we are now at lecture 10 and um uh +i + + align:start position:0% +i + + + align:start position:0% +i +let's see what have we been doing we've + + align:start position:0% +let's see what have we been doing we've + + + align:start position:0% +let's see what have we been doing we've +been talking about um + + align:start position:0% +been talking about um + + + align:start position:0% +been talking about um +undecidability + + align:start position:0% +undecidability + + + align:start position:0% +undecidability +um so we + + align:start position:0% +um so we + + + align:start position:0% +um so we +introduced last time + + align:start position:0% +introduced last time + + + align:start position:0% +introduced last time +uh reducibilities and mapping + + align:start position:0% +uh reducibilities and mapping + + + align:start position:0% +uh reducibilities and mapping +reducibilities for proving + + align:start position:0% + + + + align:start position:0% + +various problems are undecidable + + align:start position:0% +various problems are undecidable + + + align:start position:0% +various problems are undecidable +and + + align:start position:0% +and + + + align:start position:0% +and +this time we're going to and today we're + + align:start position:0% +this time we're going to and today we're + + + align:start position:0% +this time we're going to and today we're +going to introduce a a + + align:start position:0% +going to introduce a a + + + align:start position:0% +going to introduce a a +more sophisticated method for proving + + align:start position:0% +more sophisticated method for proving + + + align:start position:0% +more sophisticated method for proving +undecidability uh using reduceabilities + + align:start position:0% +undecidability uh using reduceabilities + + + align:start position:0% +undecidability uh using reduceabilities +and that's called the computation + + align:start position:0% +and that's called the computation + + + align:start position:0% +and that's called the computation +history method and and that's pretty + + align:start position:0% +history method and and that's pretty + + + align:start position:0% +history method and and that's pretty +much + + align:start position:0% +much + + + align:start position:0% +much +what's + + align:start position:0% +what's + + + align:start position:0% +what's +used in all of the + + align:start position:0% +used in all of the + + + align:start position:0% +used in all of the +you know more + + align:start position:0% +you know more + + + align:start position:0% +you know more +serious cases where people have proved + + align:start position:0% +serious cases where people have proved + + + align:start position:0% +serious cases where people have proved +problems undecidable it's it's pretty + + align:start position:0% +problems undecidable it's it's pretty + + + align:start position:0% +problems undecidable it's it's pretty +much a widespread uh + + align:start position:0% +much a widespread uh + + + align:start position:0% +much a widespread uh +uh method for uh especially you know + + align:start position:0% +uh method for uh especially you know + + + align:start position:0% +uh method for uh especially you know +it's not an active area of research + + align:start position:0% +it's not an active area of research + + + align:start position:0% +it's not an active area of research +these days but at times when people were + + align:start position:0% +these days but at times when people were + + + align:start position:0% +these days but at times when people were +proving problems undecidable + + align:start position:0% +proving problems undecidable + + + align:start position:0% +proving problems undecidable +this was frequently a method that was + + align:start position:0% +this was frequently a method that was + + + align:start position:0% +this was frequently a method that was +used + + align:start position:0% +used + + + align:start position:0% +used +um so we'll go over that today and we'll + + align:start position:0% +um so we'll go over that today and we'll + + + align:start position:0% +um so we'll go over that today and we'll +prove um + + align:start position:0% +prove um + + + align:start position:0% +prove um +a few examples of problems undecidable + + align:start position:0% +a few examples of problems undecidable + + + align:start position:0% +a few examples of problems undecidable +using that method + + align:start position:0% +using that method + + + align:start position:0% +using that method +all right so why don't we get started um + + align:start position:0% +all right so why don't we get started um + + + align:start position:0% +all right so why don't we get started um +uh so first of all + + align:start position:0% +uh so first of all + + + align:start position:0% +uh so first of all +most importantly + + align:start position:0% +most importantly + + + align:start position:0% +most importantly +you should remember how we you how we + + align:start position:0% +you should remember how we you how we + + + align:start position:0% +you should remember how we you how we +prove um problems are undecidable in the + + align:start position:0% +prove um problems are undecidable in the + + + align:start position:0% +prove um problems are undecidable in the +first place + + align:start position:0% +first place + + + align:start position:0% +first place +and that is by showing + + align:start position:0% +and that is by showing + + + align:start position:0% +and that is by showing +um some other undecidable problem that + + align:start position:0% +um some other undecidable problem that + + + align:start position:0% +um some other undecidable problem that +we already know is undecidable is + + align:start position:0% +we already know is undecidable is + + + align:start position:0% +we already know is undecidable is +reducible to the problem of interest + + align:start position:0% +reducible to the problem of interest + + + align:start position:0% +reducible to the problem of interest +so typically you might be reducing atm + + align:start position:0% +so typically you might be reducing atm + + + align:start position:0% +so typically you might be reducing atm +um which is a problem that we started + + align:start position:0% +um which is a problem that we started + + + align:start position:0% +um which is a problem that we started +with and showed to be undecidable by the + + align:start position:0% +with and showed to be undecidable by the + + + align:start position:0% +with and showed to be undecidable by the +diagonalization method + + align:start position:0% +diagonalization method + + + align:start position:0% +diagonalization method +um or might be some other problem that + + align:start position:0% +um or might be some other problem that + + + align:start position:0% +um or might be some other problem that +we've subsequently shown to be + + align:start position:0% +we've subsequently shown to be + + + align:start position:0% +we've subsequently shown to be +undecidable and you take that problem + + align:start position:0% +undecidable and you take that problem + + + align:start position:0% +undecidable and you take that problem +and you reduce it to + + align:start position:0% +and you reduce it to + + + align:start position:0% +and you reduce it to +the problem you're trying to show + + align:start position:0% +the problem you're trying to show + + + align:start position:0% +the problem you're trying to show +undecidable + + align:start position:0% +undecidable + + + align:start position:0% +undecidable +okay oops + + align:start position:0% +okay oops + + + align:start position:0% +okay oops +let me fix that + + align:start position:0% +let me fix that + + + align:start position:0% +let me fix that +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +um + + align:start position:0% +um + + + align:start position:0% +um +so um + + align:start position:0% +so um + + + align:start position:0% +so um +so this is the thing to keep in mind to + + align:start position:0% +so this is the thing to keep in mind to + + + align:start position:0% +so this is the thing to keep in mind to +prove a language is undecidable show + + align:start position:0% +prove a language is undecidable show + + + align:start position:0% +prove a language is undecidable show +that atm or some other known undecidable + + align:start position:0% +that atm or some other known undecidable + + + align:start position:0% +that atm or some other known undecidable +language is reducible to the problem b + + align:start position:0% +language is reducible to the problem b + + + align:start position:0% +language is reducible to the problem b +that you have at hand that you're trying + + align:start position:0% +that you have at hand that you're trying + + + align:start position:0% +that you have at hand that you're trying +to show undecidable + + align:start position:0% +to show undecidable + + + align:start position:0% +to show undecidable +all right so we are now going to + + align:start position:0% +all right so we are now going to + + + align:start position:0% +all right so we are now going to +um + + align:start position:0% +um + + + align:start position:0% +um +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +first i'm going to start off by + + align:start position:0% +first i'm going to start off by + + + align:start position:0% +first i'm going to start off by +remembering um hilbert's 10th problem + + align:start position:0% +remembering um hilbert's 10th problem + + + align:start position:0% +remembering um hilbert's 10th problem +which we discussed briefly a few + + align:start position:0% +which we discussed briefly a few + + + align:start position:0% +which we discussed briefly a few +lectures back um + + align:start position:0% +lectures back um + + + align:start position:0% +lectures back um +and as you may remember + + align:start position:0% +and as you may remember + + + align:start position:0% +and as you may remember +so that's a problem where uh you're + + align:start position:0% +so that's a problem where uh you're + + + align:start position:0% +so that's a problem where uh you're +given + + align:start position:0% +given + + + align:start position:0% +given +say some polynomial + + align:start position:0% +say some polynomial + + + align:start position:0% +say some polynomial +you know over several variables + + align:start position:0% +you know over several variables + + + align:start position:0% +you know over several variables +you know like three x squared y minus + + align:start position:0% +you know like three x squared y minus + + + align:start position:0% +you know like three x squared y minus +15z + + align:start position:0% +15z + + + align:start position:0% +15z +plus + + align:start position:0% +plus + + + align:start position:0% +plus +2xz + + align:start position:0% +2xz + + + align:start position:0% +2xz +equals 5. + + align:start position:0% + + + + align:start position:0% + +and you want to solve that problem + + align:start position:0% +and you want to solve that problem + + + align:start position:0% +and you want to solve that problem +you want to find a solution + + align:start position:0% +you want to find a solution + + + align:start position:0% +you want to find a solution +that solves that equation + + align:start position:0% +that solves that equation + + + align:start position:0% +that solves that equation +but you require that the solution + + align:start position:0% +but you require that the solution + + + align:start position:0% +but you require that the solution +involves only integers + + align:start position:0% + + + + align:start position:0% + +so those are so called diaphantine + + align:start position:0% +so those are so called diaphantine + + + align:start position:0% +so those are so called diaphantine +problems because the requirement is that + + align:start position:0% +problems because the requirement is that + + + align:start position:0% +problems because the requirement is that +the solution being integers + + align:start position:0% +the solution being integers + + + align:start position:0% +the solution being integers +and + + align:start position:0% + + + + align:start position:0% + +hilbert's problem was to + + align:start position:0% +hilbert's problem was to + + + align:start position:0% +hilbert's problem was to +ask for a + + align:start position:0% +ask for a + + + align:start position:0% +ask for a +an algorithm + + align:start position:0% +an algorithm + + + align:start position:0% +an algorithm +not the language that he used but + + align:start position:0% +not the language that he used but + + + align:start position:0% +not the language that he used but +doesn't matter he essentially he asked + + align:start position:0% +doesn't matter he essentially he asked + + + align:start position:0% +doesn't matter he essentially he asked +for an algorithm to test whether a + + align:start position:0% +for an algorithm to test whether a + + + align:start position:0% +for an algorithm to test whether a +polynomial has a solution in integers or + + align:start position:0% +polynomial has a solution in integers or + + + align:start position:0% +polynomial has a solution in integers or +the polynomial equation has a solution + + align:start position:0% +the polynomial equation has a solution + + + align:start position:0% +the polynomial equation has a solution +in integers + + align:start position:0% +in integers + + + align:start position:0% +in integers +and um + + align:start position:0% +and um + + + align:start position:0% +and um +as + + align:start position:0% +as + + + align:start position:0% +as +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um as we now know that problem was posed + + align:start position:0% +um as we now know that problem was posed + + + align:start position:0% +um as we now know that problem was posed +back in 1900 + + align:start position:0% +back in 1900 + + + align:start position:0% +back in 1900 +it took 71 years to find the solution + + align:start position:0% +it took 71 years to find the solution + + + align:start position:0% +it took 71 years to find the solution +but the answer is no + + align:start position:0% +but the answer is no + + + align:start position:0% +but the answer is no +there is no there is no such algorithm + + align:start position:0% +there is no there is no such algorithm + + + align:start position:0% +there is no there is no such algorithm +we talked about this when we were + + align:start position:0% +we talked about this when we were + + + align:start position:0% +we talked about this when we were +discussing the church turing thesis + + align:start position:0% +discussing the church turing thesis + + + align:start position:0% +discussing the church turing thesis +um + + align:start position:0% +um + + + align:start position:0% +um +and um + + align:start position:0% +and um + + + align:start position:0% +and um +the method + + align:start position:0% +the method + + + align:start position:0% +the method +showing + + align:start position:0% +showing + + + align:start position:0% +showing +that there is no algorithm is by a + + align:start position:0% +that there is no algorithm is by a + + + align:start position:0% +that there is no algorithm is by a +reduction from atm to that problem + + align:start position:0% +reduction from atm to that problem + + + align:start position:0% +reduction from atm to that problem +so one can use exactly the method that + + align:start position:0% +so one can use exactly the method that + + + align:start position:0% +so one can use exactly the method that +we're using today to prove that problem + + align:start position:0% +we're using today to prove that problem + + + align:start position:0% +we're using today to prove that problem +is undecidable + + align:start position:0% +is undecidable + + + align:start position:0% +is undecidable +about polynomials the only thing is is + + align:start position:0% +about polynomials the only thing is is + + + align:start position:0% +about polynomials the only thing is is +that the reduction that single reduction + + align:start position:0% +that the reduction that single reduction + + + align:start position:0% +that the reduction that single reduction +would take the entire semester + + align:start position:0% +would take the entire semester + + + align:start position:0% +would take the entire semester +um + + align:start position:0% +um + + + align:start position:0% +um +and i know that's + + align:start position:0% +and i know that's + + + align:start position:0% +and i know that's +in fact correct because when i was a + + align:start position:0% +in fact correct because when i was a + + + align:start position:0% +in fact correct because when i was a +graduate student um there was a woman in + + align:start position:0% +graduate student um there was a woman in + + + align:start position:0% +graduate student um there was a woman in +the math department at berkeley where i + + align:start position:0% +the math department at berkeley where i + + + align:start position:0% +the math department at berkeley where i +where i studied and she uh the whole the + + align:start position:0% +where i studied and she uh the whole the + + + align:start position:0% +where i studied and she uh the whole the +whole course + + align:start position:0% +whole course + + + align:start position:0% +whole course +was to go through the proof of hilbert's + + align:start position:0% +was to go through the proof of hilbert's + + + align:start position:0% +was to go through the proof of hilbert's +tenth problem + + align:start position:0% +tenth problem + + + align:start position:0% +tenth problem +um of the solution to hillary problem + + align:start position:0% +um of the solution to hillary problem + + + align:start position:0% +um of the solution to hillary problem +the the proof of the undecidability of + + align:start position:0% +the the proof of the undecidability of + + + align:start position:0% +the the proof of the undecidability of +the uh of the solution + + align:start position:0% +the uh of the solution + + + align:start position:0% +the uh of the solution +uh of the undecidability of testing + + align:start position:0% +uh of the undecidability of testing + + + align:start position:0% +uh of the undecidability of testing +whether a polynomial has an integral + + align:start position:0% +whether a polynomial has an integral + + + align:start position:0% +whether a polynomial has an integral +solution um + + align:start position:0% +solution um + + + align:start position:0% +solution um +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +the thing is that involves some + + align:start position:0% +the thing is that involves some + + + align:start position:0% +the thing is that involves some +fairly hairy number theory in order to + + align:start position:0% +fairly hairy number theory in order to + + + align:start position:0% +fairly hairy number theory in order to +um + + align:start position:0% +um + + + align:start position:0% +um +to come up with the right polynomials to + + align:start position:0% +to come up with the right polynomials to + + + align:start position:0% +to come up with the right polynomials to +basically simulate the turing machine + + align:start position:0% +basically simulate the turing machine + + + align:start position:0% +basically simulate the turing machine +which so that's kind of getting ahead of + + align:start position:0% +which so that's kind of getting ahead of + + + align:start position:0% +which so that's kind of getting ahead of +ourselves that's what we're going to be + + align:start position:0% +ourselves that's what we're going to be + + + align:start position:0% +ourselves that's what we're going to be +doing today um but we're going to + + align:start position:0% +doing today um but we're going to + + + align:start position:0% +doing today um but we're going to +instead of looking at that problem + + align:start position:0% +instead of looking at that problem + + + align:start position:0% +instead of looking at that problem +because we don't have a whole semester + + align:start position:0% +because we don't have a whole semester + + + align:start position:0% +because we don't have a whole semester +to spend on it um we're going to look at + + align:start position:0% +to spend on it um we're going to look at + + + align:start position:0% +to spend on it um we're going to look at +a toy problem instead + + align:start position:0% +a toy problem instead + + + align:start position:0% +a toy problem instead +where there's no number theory but it + + align:start position:0% +where there's no number theory but it + + + align:start position:0% +where there's no number theory but it +still has the same basic underlying idea + + align:start position:0% +still has the same basic underlying idea + + + align:start position:0% +still has the same basic underlying idea +um to that that was employed in um the + + align:start position:0% +um to that that was employed in um the + + + align:start position:0% +um to that that was employed in um the +solution to hilbert's tenth problem + + align:start position:0% +solution to hilbert's tenth problem + + + align:start position:0% +solution to hilbert's tenth problem +um so that toy problem is called the + + align:start position:0% +um so that toy problem is called the + + + align:start position:0% +um so that toy problem is called the +post correspondence problem + + align:start position:0% +post correspondence problem + + + align:start position:0% +post correspondence problem +and it's going to have some other + + align:start position:0% +and it's going to have some other + + + align:start position:0% +and it's going to have some other +utility for us + + align:start position:0% +utility for us + + + align:start position:0% +utility for us +well + + align:start position:0% +well + + + align:start position:0% +well +the main reason we're studying it is + + align:start position:0% +the main reason we're studying it is + + + align:start position:0% +the main reason we're studying it is +just to illustrate the method um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so + + align:start position:0% +so + + + align:start position:0% +so +and the method is going to be as i've + + align:start position:0% +and the method is going to be as i've + + + align:start position:0% +and the method is going to be as i've +been saying is this computation history + + align:start position:0% +been saying is this computation history + + + align:start position:0% +been saying is this computation history +method + + align:start position:0% +method + + + align:start position:0% +method +okay so one we will first talk about uh + + align:start position:0% +okay so one we will first talk about uh + + + align:start position:0% +okay so one we will first talk about uh +this post-correspondence problem because + + align:start position:0% +this post-correspondence problem because + + + align:start position:0% +this post-correspondence problem because +that's very easy to understand + + align:start position:0% +that's very easy to understand + + + align:start position:0% +that's very easy to understand +and then we'll spend a little time + + align:start position:0% +and then we'll spend a little time + + + align:start position:0% +and then we'll spend a little time +introducing that method + + align:start position:0% +introducing that method + + + align:start position:0% +introducing that method +um + + align:start position:0% +um + + + align:start position:0% +um +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so um + + align:start position:0% +so um + + + align:start position:0% +so um +the + + align:start position:0% +the + + + align:start position:0% +the +uh the post the post correspondence + + align:start position:0% +uh the post the post correspondence + + + align:start position:0% +uh the post the post correspondence +problem is + + align:start position:0% +problem is + + + align:start position:0% +problem is +as follows you're given + + align:start position:0% +as follows you're given + + + align:start position:0% +as follows you're given +uh + + align:start position:0% +uh + + + align:start position:0% +uh +a bunch of pairs of strings + + align:start position:0% +a bunch of pairs of strings + + + align:start position:0% +a bunch of pairs of strings +um so here is + + align:start position:0% +um so here is + + + align:start position:0% +um so here is +one pair t1 and b1 + + align:start position:0% +one pair t1 and b1 + + + align:start position:0% +one pair t1 and b1 +and i'm writing them as + + align:start position:0% +and i'm writing them as + + + align:start position:0% +and i'm writing them as +dominoes i'm calling them dominoes + + align:start position:0% +dominoes i'm calling them dominoes + + + align:start position:0% +dominoes i'm calling them dominoes +because i'm writing one pair one one of + + align:start position:0% +because i'm writing one pair one one of + + + align:start position:0% +because i'm writing one pair one one of +the strings on top of the other string + + align:start position:0% +the strings on top of the other string + + + align:start position:0% +the strings on top of the other string +in fact i'm + + align:start position:0% +in fact i'm + + + align:start position:0% +in fact i'm +using t and b for top and bottom here so + + align:start position:0% +using t and b for top and bottom here so + + + align:start position:0% +using t and b for top and bottom here so +this is t1 is the top string b1 is the + + align:start position:0% +this is t1 is the top string b1 is the + + + align:start position:0% +this is t1 is the top string b1 is the +bottom string in the first domino + + align:start position:0% +bottom string in the first domino + + + align:start position:0% +bottom string in the first domino +and then in the second domino we have + + align:start position:0% +and then in the second domino we have + + + align:start position:0% +and then in the second domino we have +two other strings to a top and a bottom + + align:start position:0% +two other strings to a top and a bottom + + + align:start position:0% +two other strings to a top and a bottom +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +um + + align:start position:0% +um + + + align:start position:0% +um +so we have these here + + align:start position:0% +so we have these here + + + align:start position:0% +so we have these here +uh this collection of dominoes + + align:start position:0% +uh this collection of dominoes + + + align:start position:0% +uh this collection of dominoes +um + + align:start position:0% +um + + + align:start position:0% +um +as + + align:start position:0% +as + + + align:start position:0% +as +sort of the legal dominoes um and what + + align:start position:0% +sort of the legal dominoes um and what + + + align:start position:0% +sort of the legal dominoes um and what +the goal is to find a sequence of those + + align:start position:0% +the goal is to find a sequence of those + + + align:start position:0% +the goal is to find a sequence of those +dominoes um + + align:start position:0% +dominoes um + + + align:start position:0% +dominoes um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so you want to pick from these dominoes + + align:start position:0% +so you want to pick from these dominoes + + + align:start position:0% +so you want to pick from these dominoes +here you're allowed to repeat dominoes + + align:start position:0% +here you're allowed to repeat dominoes + + + align:start position:0% +here you're allowed to repeat dominoes +so you want to pick a sequence of those + + align:start position:0% +so you want to pick a sequence of those + + + align:start position:0% +so you want to pick a sequence of those +dominoes + + align:start position:0% +dominoes + + + align:start position:0% +dominoes +line them up next to each other + + align:start position:0% +line them up next to each other + + + align:start position:0% +line them up next to each other +and so that the string that you get by + + align:start position:0% +and so that the string that you get by + + + align:start position:0% +and so that the string that you get by +reading along the top all of the t's + + align:start position:0% +reading along the top all of the t's + + + align:start position:0% +reading along the top all of the t's +together + + align:start position:0% +together + + + align:start position:0% +together +is going to be exactly the same as the + + align:start position:0% +is going to be exactly the same as the + + + align:start position:0% +is going to be exactly the same as the +string you get by reading along all the + + align:start position:0% +string you get by reading along all the + + + align:start position:0% +string you get by reading along all the +bottoms + + align:start position:0% +bottoms + + + align:start position:0% +bottoms +i'll give you an example + + align:start position:0% +i'll give you an example + + + align:start position:0% +i'll give you an example +um so here to write it down a little bit + + align:start position:0% +um so here to write it down a little bit + + + align:start position:0% +um so here to write it down a little bit +more formally + + align:start position:0% +more formally + + + align:start position:0% +more formally +so uh what i'm calling a match + + align:start position:0% +so uh what i'm calling a match + + + align:start position:0% +so uh what i'm calling a match +is a sequence of these dominoes so it's + + align:start position:0% +is a sequence of these dominoes so it's + + + align:start position:0% +is a sequence of these dominoes so it's +t i1 ti2 + + align:start position:0% +t i1 ti2 + + + align:start position:0% +t i1 ti2 +as well it's it's i1 is the first domino + + align:start position:0% +as well it's it's i1 is the first domino + + + align:start position:0% +as well it's it's i1 is the first domino +i2 is the second domino and so on + + align:start position:0% +i2 is the second domino and so on + + + align:start position:0% +i2 is the second domino and so on +and then you what you're going to have + + align:start position:0% +and then you what you're going to have + + + align:start position:0% +and then you what you're going to have +is + + align:start position:0% +is + + + align:start position:0% +is +all the top strings concatenated + + align:start position:0% +all the top strings concatenated + + + align:start position:0% +all the top strings concatenated +concatenated together is exactly the + + align:start position:0% +concatenated together is exactly the + + + align:start position:0% +concatenated together is exactly the +same as what you get by concatenating + + align:start position:0% +same as what you get by concatenating + + + align:start position:0% +same as what you get by concatenating +together all the bottom strings + + align:start position:0% +together all the bottom strings + + + align:start position:0% +together all the bottom strings +um so here's an example and i think + + align:start position:0% +um so here's an example and i think + + + align:start position:0% +um so here's an example and i think +it'll become clear if you didn't + + align:start position:0% +it'll become clear if you didn't + + + align:start position:0% +it'll become clear if you didn't +understand it so far but it'll be + + align:start position:0% +understand it so far but it'll be + + + align:start position:0% +understand it so far but it'll be +completely clear from the example i hope + + align:start position:0% + + + + align:start position:0% + +so here is a bunch of dominoes + + align:start position:0% +so here is a bunch of dominoes + + + align:start position:0% +so here is a bunch of dominoes +um four + + align:start position:0% +um four + + + align:start position:0% +um four +um + + align:start position:0% +um + + + align:start position:0% +um +and um + + align:start position:0% +and um + + + align:start position:0% +and um +what i wanna know is is there some + + align:start position:0% +what i wanna know is is there some + + + align:start position:0% +what i wanna know is is there some +selection of these dominoes again you + + align:start position:0% +selection of these dominoes again you + + + align:start position:0% +selection of these dominoes again you +can repeat dominoes otherwise it would + + align:start position:0% +can repeat dominoes otherwise it would + + + align:start position:0% +can repeat dominoes otherwise it would +be not an interesting problem so you can + + align:start position:0% +be not an interesting problem so you can + + + align:start position:0% +be not an interesting problem so you can +repeat these as many times as you like + + align:start position:0% +repeat these as many times as you like + + + align:start position:0% +repeat these as many times as you like +and i want to pick up pick these + + align:start position:0% +and i want to pick up pick these + + + align:start position:0% +and i want to pick up pick these +dominoes and line them up so that what + + align:start position:0% +dominoes and line them up so that what + + + align:start position:0% +dominoes and line them up so that what +you get by reading along the top is the + + align:start position:0% +you get by reading along the top is the + + + align:start position:0% +you get by reading along the top is the +same as what you get by reading along + + align:start position:0% +same as what you get by reading along + + + align:start position:0% +same as what you get by reading along +the bottom + + align:start position:0% +the bottom + + + align:start position:0% +the bottom +so first of all if you just stare at + + align:start position:0% +so first of all if you just stare at + + + align:start position:0% +so first of all if you just stare at +this + + align:start position:0% +this + + + align:start position:0% +this +and you're trying to make a match + + align:start position:0% +and you're trying to make a match + + + align:start position:0% +and you're trying to make a match +you'll see that there's only one + + align:start position:0% +you'll see that there's only one + + + align:start position:0% +you'll see that there's only one +possibility possible way to start this + + align:start position:0% +possibility possible way to start this + + + align:start position:0% +possibility possible way to start this +um you know + + align:start position:0% +um you know + + + align:start position:0% +um you know +for example if you started with the + + align:start position:0% +for example if you started with the + + + align:start position:0% +for example if you started with the +third domino here b a over a a + + align:start position:0% +third domino here b a over a a + + + align:start position:0% +third domino here b a over a a +it would fail immediately because + + align:start position:0% +it would fail immediately because + + + align:start position:0% +it would fail immediately because +um you know the b and the a are + + align:start position:0% +um you know the b and the a are + + + align:start position:0% +um you know the b and the a are +different + + align:start position:0% +different + + + align:start position:0% +different +um and and if you you use the second + + align:start position:0% +um and and if you you use the second + + + align:start position:0% +um and and if you you use the second +domino as your starting point that would + + align:start position:0% +domino as your starting point that would + + + align:start position:0% +domino as your starting point that would +fail the match as well + + align:start position:0% +fail the match as well + + + align:start position:0% +fail the match as well +because a a has to would have to e um be + + align:start position:0% +because a a has to would have to e um be + + + align:start position:0% +because a a has to would have to e um be +the the the top string would start with + + align:start position:0% +the the the top string would start with + + + align:start position:0% +the the the top string would start with +a a the bottom string would start with a + + align:start position:0% +a a the bottom string would start with a + + + align:start position:0% +a a the bottom string would start with a +b and they could never be equal + + align:start position:0% +b and they could never be equal + + + align:start position:0% +b and they could never be equal +um so by looking at this you can see + + align:start position:0% +um so by looking at this you can see + + + align:start position:0% +um so by looking at this you can see +that the only possible choice that you + + align:start position:0% +that the only possible choice that you + + + align:start position:0% +that the only possible choice that you +have is to start with the first domino + + align:start position:0% +have is to start with the first domino + + + align:start position:0% +have is to start with the first domino +okay so i'm going to start to build the + + align:start position:0% +okay so i'm going to start to build the + + + align:start position:0% +okay so i'm going to start to build the +domino for you just so you can see it so + + align:start position:0% +domino for you just so you can see it so + + + align:start position:0% +domino for you just so you can see it so +here's the very the the match as um so + + align:start position:0% +here's the very the the match as um so + + + align:start position:0% +here's the very the the match as um so +you can see um the process so the match + + align:start position:0% +you can see um the process so the match + + + align:start position:0% +you can see um the process so the match +starts with the very first domino and + + align:start position:0% +starts with the very first domino and + + + align:start position:0% +starts with the very first domino and +the way i'm going to write it is i'm + + align:start position:0% +the way i'm going to write it is i'm + + + align:start position:0% +the way i'm going to write it is i'm +going to take the dominoes and kind of + + align:start position:0% +going to take the dominoes and kind of + + + align:start position:0% +going to take the dominoes and kind of +skew them + + align:start position:0% +skew them + + + align:start position:0% +skew them +so that you can see how the top and + + align:start position:0% +so that you can see how the top and + + + align:start position:0% +so that you can see how the top and +bottom strings are lining up + + align:start position:0% +bottom strings are lining up + + + align:start position:0% +bottom strings are lining up +um + + align:start position:0% +um + + + align:start position:0% +um +but they're just mouth the same dominoes + + align:start position:0% +but they're just mouth the same dominoes + + + align:start position:0% +but they're just mouth the same dominoes +they've just been + + align:start position:0% +they've just been + + + align:start position:0% +they've just been +i changed the shape + + align:start position:0% +i changed the shape + + + align:start position:0% +i changed the shape +so this is the first domino a b over aba + + align:start position:0% +so this is the first domino a b over aba + + + align:start position:0% +so this is the first domino a b over aba +now uh the second domino in my and my + + align:start position:0% +now uh the second domino in my and my + + + align:start position:0% +now uh the second domino in my and my +match it's gotta start with an a + + align:start position:0% +match it's gotta start with an a + + + align:start position:0% +match it's gotta start with an a +as the leftmost symbol on the top string + + align:start position:0% +as the leftmost symbol on the top string + + + align:start position:0% +as the leftmost symbol on the top string +so that would rule out this one for + + align:start position:0% +so that would rule out this one for + + + align:start position:0% +so that would rule out this one for +example um but there might be several + + align:start position:0% +example um but there might be several + + + align:start position:0% +example um but there might be several +choices and so it's not exactly obvious + + align:start position:0% +choices and so it's not exactly obvious + + + align:start position:0% +choices and so it's not exactly obvious +which one you should take + + align:start position:0% +which one you should take + + + align:start position:0% +which one you should take +what i'm going to suggest is we take + + align:start position:0% +what i'm going to suggest is we take + + + align:start position:0% +what i'm going to suggest is we take +this one here + + align:start position:0% +this one here + + + align:start position:0% +this one here +so we take a a over a b a you see it a a + + align:start position:0% +so we take a a over a b a you see it a a + + + align:start position:0% +so we take a a over a b a you see it a a +over a b a it's just + + align:start position:0% +over a b a it's just + + + align:start position:0% +over a b a it's just +you know written i'm just skewing uh + + align:start position:0% +you know written i'm just skewing uh + + + align:start position:0% +you know written i'm just skewing uh +skewing it so that um i can line up the + + align:start position:0% +skewing it so that um i can line up the + + + align:start position:0% +skewing it so that um i can line up the +a over a the b over b the a over a and + + align:start position:0% +a over a the b over b the a over a and + + + align:start position:0% +a over a the b over b the a over a and +so on so i'm starting to build + + align:start position:0% +so on so i'm starting to build + + + align:start position:0% +so on so i'm starting to build +this concatenation of the top being + + align:start position:0% +this concatenation of the top being + + + align:start position:0% +this concatenation of the top being +equal to the concatenation of the bottom + + align:start position:0% + + + + align:start position:0% + +following me so far i hope + + align:start position:0% +following me so far i hope + + + align:start position:0% +following me so far i hope +so now um what's what's next so i need + + align:start position:0% +so now um what's what's next so i need + + + align:start position:0% +so now um what's what's next so i need +to have something where + + align:start position:0% +to have something where + + + align:start position:0% +to have something where +the top string is going to start with a + + align:start position:0% +the top string is going to start with a + + + align:start position:0% +the top string is going to start with a +ba + + align:start position:0% +ba + + + align:start position:0% +ba +in fact there's only one choice for that + + align:start position:0% +in fact there's only one choice for that + + + align:start position:0% +in fact there's only one choice for that +so it's clearly going to have to be this + + align:start position:0% +so it's clearly going to have to be this + + + align:start position:0% +so it's clearly going to have to be this +domino is going to be next so it's going + + align:start position:0% +domino is going to be next so it's going + + + align:start position:0% +domino is going to be next so it's going +to put a ba up here but then it's going + + align:start position:0% +to put a ba up here but then it's going + + + align:start position:0% +to put a ba up here but then it's going +to a force an a a down below because + + align:start position:0% +to a force an a a down below because + + + align:start position:0% +to a force an a a down below because +that's what this domino does um + + align:start position:0% +that's what this domino does um + + + align:start position:0% +that's what this domino does um +so this ba matches with that now we have + + align:start position:0% +so this ba matches with that now we have + + + align:start position:0% +so this ba matches with that now we have +the aaa + + align:start position:0% +the aaa + + + align:start position:0% +the aaa +to deal with um + + align:start position:0% +to deal with um + + + align:start position:0% +to deal with um +so + + align:start position:0% +so + + + align:start position:0% +so +we're going to reuse this domino because + + align:start position:0% +we're going to reuse this domino because + + + align:start position:0% +we're going to reuse this domino because +that's the only one that starts with an + + align:start position:0% +that's the only one that starts with an + + + align:start position:0% +that's the only one that starts with an +aa so we're going to reuse that one + + align:start position:0% +aa so we're going to reuse that one + + + align:start position:0% +aa so we're going to reuse that one +now we have a a and aba now we need + + align:start position:0% +now we have a a and aba now we need + + + align:start position:0% +now we have a a and aba now we need +something that starts with aba + + align:start position:0% +something that starts with aba + + + align:start position:0% +something that starts with aba +i see two choices + + align:start position:0% +i see two choices + + + align:start position:0% +i see two choices +it could be this one because this is + + align:start position:0% +it could be this one because this is + + + align:start position:0% +it could be this one because this is +consistent with a it's at least it + + align:start position:0% +consistent with a it's at least it + + + align:start position:0% +consistent with a it's at least it +captures the a b we could we could try + + align:start position:0% +captures the a b we could we could try + + + align:start position:0% +captures the a b we could we could try +putting this one over here but a better + + align:start position:0% +putting this one over here but a better + + + align:start position:0% +putting this one over here but a better +choice would it be would be to use this + + align:start position:0% +choice would it be would be to use this + + + align:start position:0% +choice would it be would be to use this +one because if we use this one we finish + + align:start position:0% +one because if we use this one we finish + + + align:start position:0% +one because if we use this one we finish +the match + + align:start position:0% + + + + align:start position:0% + +and therefore we have found what we're + + align:start position:0% +and therefore we have found what we're + + + align:start position:0% +and therefore we have found what we're +looking for + + align:start position:0% +looking for + + + align:start position:0% +looking for +um and this + + align:start position:0% +um and this + + + align:start position:0% +um and this +this + + align:start position:0% +this + + + align:start position:0% +this +this collection of + + align:start position:0% +this collection of + + + align:start position:0% +this collection of +dominoes here has a mat has a match + + align:start position:0% +dominoes here has a mat has a match + + + align:start position:0% +dominoes here has a mat has a match +now it's not always obvious + + align:start position:0% +now it's not always obvious + + + align:start position:0% +now it's not always obvious +some some collections of dominoes may + + align:start position:0% +some some collections of dominoes may + + + align:start position:0% +some some collections of dominoes may +not have a match + + align:start position:0% +not have a match + + + align:start position:0% +not have a match +and so the computational problem is + + align:start position:0% +and so the computational problem is + + + align:start position:0% +and so the computational problem is +is there a match + + align:start position:0% +is there a match + + + align:start position:0% +is there a match +um + + align:start position:0% +um + + + align:start position:0% +um +and + + align:start position:0% +and + + + align:start position:0% +and +the theorem that we're going to prove + + align:start position:0% +the theorem that we're going to prove + + + align:start position:0% +the theorem that we're going to prove +today is that this problem is + + align:start position:0% +today is that this problem is + + + align:start position:0% +today is that this problem is +undecidable + + align:start position:0% +undecidable + + + align:start position:0% +undecidable +simple as it is simple little + + align:start position:0% +simple as it is simple little + + + align:start position:0% +simple as it is simple little +combinatorial problem of you know uh + + align:start position:0% +combinatorial problem of you know uh + + + align:start position:0% +combinatorial problem of you know uh +trying to put together different um + + align:start position:0% +trying to put together different um + + + align:start position:0% +trying to put together different um +uh different tiles like that to form + + align:start position:0% +uh different tiles like that to form + + + align:start position:0% +uh different tiles like that to form +form a match + + align:start position:0% +form a match + + + align:start position:0% +form a match +uh there was no algorithm for solving + + align:start position:0% +uh there was no algorithm for solving + + + align:start position:0% +uh there was no algorithm for solving +that problem + + align:start position:0% +that problem + + + align:start position:0% +that problem +um and and i think this is kind of + + align:start position:0% +um and and i think this is kind of + + + align:start position:0% +um and and i think this is kind of +interesting because it's the first + + align:start position:0% +interesting because it's the first + + + align:start position:0% +interesting because it's the first +example of a problem that we have where + + align:start position:0% +example of a problem that we have where + + + align:start position:0% +example of a problem that we have where +the underlying + + align:start position:0% +the underlying + + + align:start position:0% +the underlying +question + + align:start position:0% +question + + + align:start position:0% +question +does not really seem to have anything to + + align:start position:0% +does not really seem to have anything to + + + align:start position:0% +does not really seem to have anything to +do with computation + + align:start position:0% +do with computation + + + align:start position:0% +do with computation +you know you might argue that atm being + + align:start position:0% +you know you might argue that atm being + + + align:start position:0% +you know you might argue that atm being +undecidable + + align:start position:0% +undecidable + + + align:start position:0% +undecidable +is perhaps + + align:start position:0% +is perhaps + + + align:start position:0% +is perhaps +a little unsurprising after the fact + + align:start position:0% +a little unsurprising after the fact + + + align:start position:0% +a little unsurprising after the fact +because you know it's a problem about + + align:start position:0% +because you know it's a problem about + + + align:start position:0% +because you know it's a problem about +touring machines so you can imagine + + align:start position:0% +touring machines so you can imagine + + + align:start position:0% +touring machines so you can imagine +turing machines are going to have a + + align:start position:0% +turing machines are going to have a + + + align:start position:0% +turing machines are going to have a +tough time answering it um but here's a + + align:start position:0% +tough time answering it um but here's a + + + align:start position:0% +tough time answering it um but here's a +problem just about strings + + align:start position:0% +problem just about strings + + + align:start position:0% +problem just about strings +um and we're going to show it's + + align:start position:0% +um and we're going to show it's + + + align:start position:0% +um and we're going to show it's +undecidable + + align:start position:0% +undecidable + + + align:start position:0% +undecidable +so + + align:start position:0% +so + + + align:start position:0% +so +just to formulate this as a language i'm + + align:start position:0% +just to formulate this as a language i'm + + + align:start position:0% +just to formulate this as a language i'm +going to call the pcp language + + align:start position:0% +going to call the pcp language + + + align:start position:0% +going to call the pcp language +is the collection of these um + + align:start position:0% +is the collection of these um + + + align:start position:0% +is the collection of these um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +pcp + + align:start position:0% +pcp + + + align:start position:0% +pcp +uh problems pcp instances which are just + + align:start position:0% +uh problems pcp instances which are just + + + align:start position:0% +uh problems pcp instances which are just +collect themselves each one is a + + align:start position:0% +collect themselves each one is a + + + align:start position:0% +collect themselves each one is a +collection of dominoes so it's the + + align:start position:0% +collection of dominoes so it's the + + + align:start position:0% +collection of dominoes so it's the +language of all + + align:start position:0% +language of all + + + align:start position:0% +language of all +uh collections of these dominoes where + + align:start position:0% +uh collections of these dominoes where + + + align:start position:0% +uh collections of these dominoes where +there is a match + + align:start position:0% +there is a match + + + align:start position:0% +there is a match +so it's all of the pcp problems where + + align:start position:0% +so it's all of the pcp problems where + + + align:start position:0% +so it's all of the pcp problems where +you can solve them with a match + + align:start position:0% +you can solve them with a match + + + align:start position:0% +you can solve them with a match +and + + align:start position:0% +and + + + align:start position:0% +and +uh we're going to prove that it's + + align:start position:0% +uh we're going to prove that it's + + + align:start position:0% +uh we're going to prove that it's +undecidable by showing that atm is + + align:start position:0% +undecidable by showing that atm is + + + align:start position:0% +undecidable by showing that atm is +reducible to that pcp language + + align:start position:0% +reducible to that pcp language + + + align:start position:0% +reducible to that pcp language +um now uh before we do that i'm going to + + align:start position:0% +um now uh before we do that i'm going to + + + align:start position:0% +um now uh before we do that i'm going to +have to i'm going to explain to you what + + align:start position:0% +have to i'm going to explain to you what + + + align:start position:0% +have to i'm going to explain to you what +the computation history method is in the + + align:start position:0% +the computation history method is in the + + + align:start position:0% +the computation history method is in the +first place that we're going to be using + + align:start position:0% +first place that we're going to be using + + + align:start position:0% +first place that we're going to be using +uh so before we do that here's our first + + align:start position:0% +uh so before we do that here's our first + + + align:start position:0% +uh so before we do that here's our first +check-in for the day + + align:start position:0% + + + + align:start position:0% + +just to make sure you're following me + + align:start position:0% +just to make sure you're following me + + + align:start position:0% +just to make sure you're following me +about + + align:start position:0% +about + + + align:start position:0% +about +uh what the um + + align:start position:0% + + + + align:start position:0% + +what this pcp problem is + + align:start position:0% +what this pcp problem is + + + align:start position:0% +what this pcp problem is +i am + + align:start position:0% +i am + + + align:start position:0% +i am +going to give you + + align:start position:0% +going to give you + + + align:start position:0% +going to give you +a question to + + align:start position:0% +a question to + + + align:start position:0% +a question to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +test + + align:start position:0% +test + + + align:start position:0% +test +is there a match + + align:start position:0% +is there a match + + + align:start position:0% +is there a match +with these three dominoes + + align:start position:0% +with these three dominoes + + + align:start position:0% +with these three dominoes +so what you think about that + + align:start position:0% + + + + align:start position:0% + +i mean the main thing i'm i want to make + + align:start position:0% +i mean the main thing i'm i want to make + + + align:start position:0% +i mean the main thing i'm i want to make +sure you understand is what a match is + + align:start position:0% +sure you understand is what a match is + + + align:start position:0% +sure you understand is what a match is +in the first place this is not a super + + align:start position:0% +in the first place this is not a super + + + align:start position:0% +in the first place this is not a super +hard problem + + align:start position:0% +hard problem + + + align:start position:0% +hard problem +uh to tell whether or not there's a + + align:start position:0% +uh to tell whether or not there's a + + + align:start position:0% +uh to tell whether or not there's a +match + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +five seconds + + align:start position:0% + + + + align:start position:0% + +already + + align:start position:0% +already + + + align:start position:0% +already +okay + + align:start position:0% +okay + + + align:start position:0% +okay +closing it out um + + align:start position:0% +closing it out um + + + align:start position:0% +closing it out um +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so + + align:start position:0% +so + + + align:start position:0% +so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +for those of you who said there is a + + align:start position:0% +for those of you who said there is a + + + align:start position:0% +for those of you who said there is a +match + + align:start position:0% +match + + + align:start position:0% +match +i want you to + + align:start position:0% +i want you to + + + align:start position:0% +i want you to +exhibit exhibit the match because in + + align:start position:0% +exhibit exhibit the match because in + + + align:start position:0% +exhibit exhibit the match because in +fact there is no such map there is no + + align:start position:0% +fact there is no such map there is no + + + align:start position:0% +fact there is no such map there is no +match + + align:start position:0% +match + + + align:start position:0% +match +um + + align:start position:0% +um + + + align:start position:0% +um +and uh i mean you could get by fiddling + + align:start position:0% +and uh i mean you could get by fiddling + + + align:start position:0% +and uh i mean you could get by fiddling +around with it i think if you try to + + align:start position:0% +around with it i think if you try to + + + align:start position:0% +around with it i think if you try to +find a match you'll pretty quickly uh + + align:start position:0% +find a match you'll pretty quickly uh + + + align:start position:0% +find a match you'll pretty quickly uh +see that it's you're gonna get um i + + align:start position:0% +see that it's you're gonna get um i + + + align:start position:0% +see that it's you're gonna get um i +think what happens is you kind of get + + align:start position:0% +think what happens is you kind of get + + + align:start position:0% +think what happens is you kind of get +into if you try to build build a match + + align:start position:0% +into if you try to build build a match + + + align:start position:0% +into if you try to build build a match +with this particular setup + + align:start position:0% +with this particular setup + + + align:start position:0% +with this particular setup +you're just going to get stuck + + align:start position:0% +you're just going to get stuck + + + align:start position:0% +you're just going to get stuck +sort of repeating yourself and + + align:start position:0% +sort of repeating yourself and + + + align:start position:0% +sort of repeating yourself and +um + + align:start position:0% +um + + + align:start position:0% +um +one point here that you may have missed + + align:start position:0% +one point here that you may have missed + + + align:start position:0% +one point here that you may have missed +is that a match has to be a finite + + align:start position:0% +is that a match has to be a finite + + + align:start position:0% +is that a match has to be a finite +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +so if you were thinking about there + + align:start position:0% +so if you were thinking about there + + + align:start position:0% +so if you were thinking about there +there is there is a kind of an infinite + + align:start position:0% +there is there is a kind of an infinite + + + align:start position:0% +there is there is a kind of an infinite +match uh that you can build with this uh + + align:start position:0% +match uh that you can build with this uh + + + align:start position:0% +match uh that you can build with this uh +this this set of dominoes but that's not + + align:start position:0% +this this set of dominoes but that's not + + + align:start position:0% +this this set of dominoes but that's not +allowed we're only allowing finite + + align:start position:0% +allowed we're only allowing finite + + + align:start position:0% +allowed we're only allowing finite +matches + + align:start position:0% +matches + + + align:start position:0% +matches +and so that may they might change your + + align:start position:0% +and so that may they might change your + + + align:start position:0% +and so that may they might change your +answer as a result but too late um + + align:start position:0% +answer as a result but too late um + + + align:start position:0% +answer as a result but too late um +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +and one way to see that you can't have a + + align:start position:0% +and one way to see that you can't have a + + + align:start position:0% +and one way to see that you can't have a +uh a match in this problem is that you + + align:start position:0% +uh a match in this problem is that you + + + align:start position:0% +uh a match in this problem is that you +know you're going to have to start + + align:start position:0% +know you're going to have to start + + + align:start position:0% +know you're going to have to start +you you + + align:start position:0% +you you + + + align:start position:0% +you you +you know neither of these two are + + align:start position:0% +you know neither of these two are + + + align:start position:0% +you know neither of these two are +possible starting points so this one is + + align:start position:0% +possible starting points so this one is + + + align:start position:0% +possible starting points so this one is +going to be clearly the only chance that + + align:start position:0% +going to be clearly the only chance that + + + align:start position:0% +going to be clearly the only chance that +you're going to have as a match uh the + + align:start position:0% +you're going to have as a match uh the + + + align:start position:0% +you're going to have as a match uh the +first domino here but then once you put + + align:start position:0% +first domino here but then once you put + + + align:start position:0% +first domino here but then once you put +this one down + + align:start position:0% +this one down + + + align:start position:0% +this one down +um the bottom one the bottom string the + + align:start position:0% +um the bottom one the bottom string the + + + align:start position:0% +um the bottom one the bottom string the +the bottom b's that you're going to get + + align:start position:0% +the bottom b's that you're going to get + + + align:start position:0% +the bottom b's that you're going to get +the bottom string is going to be longer + + align:start position:0% +the bottom string is going to be longer + + + align:start position:0% +the bottom string is going to be longer +than the top string + + align:start position:0% +than the top string + + + align:start position:0% +than the top string +and then the other two are going to be + + align:start position:0% +and then the other two are going to be + + + align:start position:0% +and then the other two are going to be +have the same length um so you're never + + align:start position:0% +have the same length um so you're never + + + align:start position:0% +have the same length um so you're never +going to have the bottom uh the top be + + align:start position:0% +going to have the bottom uh the top be + + + align:start position:0% +going to have the bottom uh the top be +the same length as the bottom the bottom + + align:start position:0% +the same length as the bottom the bottom + + + align:start position:0% +the same length as the bottom the bottom +is always going to be longer no matter + + align:start position:0% +is always going to be longer no matter + + + align:start position:0% +is always going to be longer no matter +how many uh + + align:start position:0% +how many uh + + + align:start position:0% +how many uh +more dominoes you lay out so this + + align:start position:0% +more dominoes you lay out so this + + + align:start position:0% +more dominoes you lay out so this +there's no chance of there being a match + + align:start position:0% +there's no chance of there being a match + + + align:start position:0% +there's no chance of there being a match +here um + + align:start position:0% +here um + + + align:start position:0% +here um +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now we're gonna + + align:start position:0% +so now we're gonna + + + align:start position:0% +so now we're gonna +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +work our way up to introducing this + + align:start position:0% +work our way up to introducing this + + + align:start position:0% +work our way up to introducing this +computation history method + + align:start position:0% +computation history method + + + align:start position:0% +computation history method +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um um + + align:start position:0% +um um + + + align:start position:0% +um um +first + + align:start position:0% +first + + + align:start position:0% +first +let me + + align:start position:0% +let me + + + align:start position:0% +let me +define something for a turing machine + + align:start position:0% +define something for a turing machine + + + align:start position:0% +define something for a turing machine +that i'm going to call a configuration + + align:start position:0% +that i'm going to call a configuration + + + align:start position:0% +that i'm going to call a configuration +um + + align:start position:0% +um + + + align:start position:0% +um +configuration is just a snapshot of the + + align:start position:0% +configuration is just a snapshot of the + + + align:start position:0% +configuration is just a snapshot of the +turing machine in the middle of its + + align:start position:0% +turing machine in the middle of its + + + align:start position:0% +turing machine in the middle of its +computation + + align:start position:0% +computation + + + align:start position:0% +computation +so + + align:start position:0% +so + + + align:start position:0% +so +if you're running the turing machine and + + align:start position:0% +if you're running the turing machine and + + + align:start position:0% +if you're running the turing machine and +you just + + align:start position:0% +you just + + + align:start position:0% +you just +stop it at some moment + + align:start position:0% +stop it at some moment + + + align:start position:0% +stop it at some moment +it's going to be in a certain state + + align:start position:0% +it's going to be in a certain state + + + align:start position:0% +it's going to be in a certain state +the head is going to be on a certain + + align:start position:0% +the head is going to be on a certain + + + align:start position:0% +the head is going to be on a certain +position + + align:start position:0% +position + + + align:start position:0% +position +and the tape is going to have a certain + + align:start position:0% +and the tape is going to have a certain + + + align:start position:0% +and the tape is going to have a certain +contents + + align:start position:0% +contents + + + align:start position:0% +contents +and with that information + + align:start position:0% +and with that information + + + align:start position:0% +and with that information +you can then um continue the copy the + + align:start position:0% +you can then um continue the copy the + + + align:start position:0% +you can then um continue the copy the +computation of the turing machine that's + + align:start position:0% +computation of the turing machine that's + + + align:start position:0% +computation of the turing machine that's +a full set of the information that you + + align:start position:0% +a full set of the information that you + + + align:start position:0% +a full set of the information that you +need about the turing machine that tells + + align:start position:0% +need about the turing machine that tells + + + align:start position:0% +need about the turing machine that tells +you everything about its cut its + + align:start position:0% +you everything about its cut its + + + align:start position:0% +you everything about its cut its +computation at that moment in time + + align:start position:0% +computation at that moment in time + + + align:start position:0% +computation at that moment in time +the state head position and tape + + align:start position:0% +the state head position and tape + + + align:start position:0% +the state head position and tape +contents and so that we're calling that + + align:start position:0% +contents and so that we're calling that + + + align:start position:0% +contents and so that we're calling that +that information together + + align:start position:0% +that information together + + + align:start position:0% +that information together +uh state head position tape contents + + align:start position:0% +uh state head position tape contents + + + align:start position:0% +uh state head position tape contents +we're calling that a configuration it's + + align:start position:0% +we're calling that a configuration it's + + + align:start position:0% +we're calling that a configuration it's +a + + align:start position:0% +a + + + align:start position:0% +a +fairly + + align:start position:0% +fairly + + + align:start position:0% +fairly +um + + align:start position:0% +um + + + align:start position:0% +um +basic notion i mean if you if you + + align:start position:0% +basic notion i mean if you if you + + + align:start position:0% +basic notion i mean if you if you +program if you have something if you + + align:start position:0% +program if you have something if you + + + align:start position:0% +program if you have something if you +have like the states of all the + + align:start position:0% +have like the states of all the + + + align:start position:0% +have like the states of all the +variables and where the current + + align:start position:0% +variables and where the current + + + align:start position:0% +variables and where the current +execution of the program is at + + align:start position:0% +execution of the program is at + + + align:start position:0% +execution of the program is at +a moment in time same idea + + align:start position:0% +a moment in time same idea + + + align:start position:0% +a moment in time same idea +um + + align:start position:0% + + + + align:start position:0% + +okay so in terms of a picture here here + + align:start position:0% +okay so in terms of a picture here here + + + align:start position:0% +okay so in terms of a picture here here +is the turing machine + + align:start position:0% +is the turing machine + + + align:start position:0% +is the turing machine +imagine it's in state q3 + + align:start position:0% +imagine it's in state q3 + + + align:start position:0% +imagine it's in state q3 +um the head position is in the sixth + + align:start position:0% +um the head position is in the sixth + + + align:start position:0% +um the head position is in the sixth +position on the tape so + + align:start position:0% +position on the tape so + + + align:start position:0% +position on the tape so +p would be six + + align:start position:0% +p would be six + + + align:start position:0% +p would be six +um because it's in the sixth position + + align:start position:0% +um because it's in the sixth position + + + align:start position:0% +um because it's in the sixth position +and the tape contents is going to be + + align:start position:0% +and the tape contents is going to be + + + align:start position:0% +and the tape contents is going to be +this bunch of a's followed by this bunch + + align:start position:0% +this bunch of a's followed by this bunch + + + align:start position:0% +this bunch of a's followed by this bunch +of b's so i would write it down like + + align:start position:0% +of b's so i would write it down like + + + align:start position:0% +of b's so i would write it down like +this + + align:start position:0% +this + + + align:start position:0% +this +states in q3 + + align:start position:0% +states in q3 + + + align:start position:0% +states in q3 +head position number six + + align:start position:0% +head position number six + + + align:start position:0% +head position number six +this is the contents of the tape + + align:start position:0% +this is the contents of the tape + + + align:start position:0% +this is the contents of the tape +um now what we're going to often do + + align:start position:0% +um now what we're going to often do + + + align:start position:0% +um now what we're going to often do +for convenience in using this notion in + + align:start position:0% +for convenience in using this notion in + + + align:start position:0% +for convenience in using this notion in +proofs + + align:start position:0% +proofs + + + align:start position:0% +proofs +is that we're going to want to represent + + align:start position:0% +is that we're going to want to represent + + + align:start position:0% +is that we're going to want to represent +a con + + align:start position:0% +a con + + + align:start position:0% +a con +a configuration as a string + + align:start position:0% +a configuration as a string + + + align:start position:0% +a configuration as a string +um + + align:start position:0% +um + + + align:start position:0% +um +in a particular way that's going to be + + align:start position:0% +in a particular way that's going to be + + + align:start position:0% +in a particular way that's going to be +that's going to + + align:start position:0% +that's going to + + + align:start position:0% +that's going to +this is this concept is going to come up + + align:start position:0% +this is this concept is going to come up + + + align:start position:0% +this is this concept is going to come up +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +again and again during the during during + + align:start position:0% +again and again during the during during + + + align:start position:0% +again and again during the during during +uh the course and so it's going to be + + align:start position:0% +uh the course and so it's going to be + + + align:start position:0% +uh the course and so it's going to be +handy to have a particular way of + + align:start position:0% +handy to have a particular way of + + + align:start position:0% +handy to have a particular way of +writing down configurations + + align:start position:0% +writing down configurations + + + align:start position:0% +writing down configurations +um + + align:start position:0% +um + + + align:start position:0% +um +you know for doing um + + align:start position:0% +you know for doing um + + + align:start position:0% +you know for doing um +proofs about them and so the way we're + + align:start position:0% +proofs about them and so the way we're + + + align:start position:0% +proofs about them and so the way we're +going to write them down is + + align:start position:0% +going to write them down is + + + align:start position:0% +going to write them down is +i think it's just maybe i can just put + + align:start position:0% +i think it's just maybe i can just put + + + align:start position:0% +i think it's just maybe i can just put +it right up here like this + + align:start position:0% +it right up here like this + + + align:start position:0% +it right up here like this +um + + align:start position:0% +um + + + align:start position:0% +um +we're going to write down + + align:start position:0% +we're going to write down + + + align:start position:0% +we're going to write down +the + + align:start position:0% +the + + + align:start position:0% +the +the symbols of the tape + + align:start position:0% +the symbols of the tape + + + align:start position:0% +the symbols of the tape +but what we're going to do is stick in + + align:start position:0% +but what we're going to do is stick in + + + align:start position:0% +but what we're going to do is stick in +the middle of those symbols the the + + align:start position:0% +the middle of those symbols the the + + + align:start position:0% +the middle of those symbols the the +state + + align:start position:0% +state + + + align:start position:0% +state +of the machine + + align:start position:0% +of the machine + + + align:start position:0% +of the machine +immediately to the left + + align:start position:0% +immediately to the left + + + align:start position:0% +immediately to the left +of the + + align:start position:0% +of the + + + align:start position:0% +of the +position that the machine is currently + + align:start position:0% +position that the machine is currently + + + align:start position:0% +position that the machine is currently +reading + + align:start position:0% +reading + + + align:start position:0% +reading +so you can imagine + + align:start position:0% +so you can imagine + + + align:start position:0% +so you can imagine +you know the the head here which is + + align:start position:0% +you know the the head here which is + + + align:start position:0% +you know the the head here which is +coming you know imagine the state is + + align:start position:0% +coming you know imagine the state is + + + align:start position:0% +coming you know imagine the state is +kind of where the head is it's pointing + + align:start position:0% +kind of where the head is it's pointing + + + align:start position:0% +kind of where the head is it's pointing +at the symbol immediately to its right + + align:start position:0% + + + + align:start position:0% + +so this is just another way of writing + + align:start position:0% +so this is just another way of writing + + + align:start position:0% +so this is just another way of writing +down a configuration here's the tape + + align:start position:0% +down a configuration here's the tape + + + align:start position:0% +down a configuration here's the tape +contents which i'm i'm sort of writing + + align:start position:0% +contents which i'm i'm sort of writing + + + align:start position:0% +contents which i'm i'm sort of writing +formally here i'm breaking the the the + + align:start position:0% +formally here i'm breaking the the the + + + align:start position:0% +formally here i'm breaking the the the +the tape contents into two parts which + + align:start position:0% +the tape contents into two parts which + + + align:start position:0% +the tape contents into two parts which +i'm calling t1 and t2 + + align:start position:0% +i'm calling t1 and t2 + + + align:start position:0% +i'm calling t1 and t2 +um this is the t1 part the t2 part + + align:start position:0% +um this is the t1 part the t2 part + + + align:start position:0% +um this is the t1 part the t2 part +and i'm + + align:start position:0% +and i'm + + + align:start position:0% +and i'm +putting the uh + + align:start position:0% +putting the uh + + + align:start position:0% +putting the uh +the + + align:start position:0% +the + + + align:start position:0% +the +the state + + align:start position:0% +the state + + + align:start position:0% +the state +in between t1 and t2 + + align:start position:0% +in between t1 and t2 + + + align:start position:0% +in between t1 and t2 +where i have in mind that the machine's + + align:start position:0% +where i have in mind that the machine's + + + align:start position:0% +where i have in mind that the machine's +head position is right at the beginning + + align:start position:0% +head position is right at the beginning + + + align:start position:0% +head position is right at the beginning +of t2 + + align:start position:0% +of t2 + + + align:start position:0% +of t2 +but maybe this picture just says it all + + align:start position:0% +but maybe this picture just says it all + + + align:start position:0% +but maybe this picture just says it all +and it's clear enough + + align:start position:0% +and it's clear enough + + + align:start position:0% +and it's clear enough +um + + align:start position:0% +um + + + align:start position:0% +um +so just keep in mind that when when + + align:start position:0% +so just keep in mind that when when + + + align:start position:0% +so just keep in mind that when when +we're going to be writing down + + align:start position:0% +we're going to be writing down + + + align:start position:0% +we're going to be writing down +configurations of machines we're + + align:start position:0% +configurations of machines we're + + + align:start position:0% +configurations of machines we're +typically going to write it down this + + align:start position:0% +typically going to write it down this + + + align:start position:0% +typically going to write it down this +way + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay so i think this is a good moment to + + align:start position:0% +okay so i think this is a good moment to + + + align:start position:0% +okay so i think this is a good moment to +take uh to take a moment uh for + + align:start position:0% +take uh to take a moment uh for + + + align:start position:0% +take uh to take a moment uh for +questions + + align:start position:0% +questions + + + align:start position:0% +questions +oh i see there's a lot of questions + + align:start position:0% +oh i see there's a lot of questions + + + align:start position:0% +oh i see there's a lot of questions +already um + + align:start position:0% + + + + align:start position:0% + +um so one's question is how does the + + align:start position:0% +um so one's question is how does the + + + align:start position:0% +um so one's question is how does the +encoding differentiate between the + + align:start position:0% +encoding differentiate between the + + + align:start position:0% +encoding differentiate between the +string and the state + + align:start position:0% +string and the state + + + align:start position:0% +string and the state +um + + align:start position:0% +um + + + align:start position:0% +um +i if i'm understanding you correctly i'm + + align:start position:0% +i if i'm understanding you correctly i'm + + + align:start position:0% +i if i'm understanding you correctly i'm +going to be assuming + + align:start position:0% +going to be assuming + + + align:start position:0% +going to be assuming +that um + + align:start position:0% +that um + + + align:start position:0% +that um +the state the symbols that represent + + align:start position:0% +the state the symbols that represent + + + align:start position:0% +the state the symbols that represent +states and the symbols that appear on + + align:start position:0% +states and the symbols that appear on + + + align:start position:0% +states and the symbols that appear on +the tape + + align:start position:0% +the tape + + + align:start position:0% +the tape +are distinct from one another so you can + + align:start position:0% +are distinct from one another so you can + + + align:start position:0% +are distinct from one another so you can +always tell just like usually the way we + + align:start position:0% +always tell just like usually the way we + + + align:start position:0% +always tell just like usually the way we +write things down when you have a state + + align:start position:0% +write things down when you have a state + + + align:start position:0% +write things down when you have a state +symbol or whether you have a tape symbol + + align:start position:0% +symbol or whether you have a tape symbol + + + align:start position:0% +symbol or whether you have a tape symbol +and so in a configuration you're going + + align:start position:0% +and so in a configuration you're going + + + align:start position:0% +and so in a configuration you're going +to have a bunch + + align:start position:0% +to have a bunch + + + align:start position:0% +to have a bunch +of uh tape symbols and a single state + + align:start position:0% +of uh tape symbols and a single state + + + align:start position:0% +of uh tape symbols and a single state +symbol represent you know in the + + align:start position:0% +symbol represent you know in the + + + align:start position:0% +symbol represent you know in the +position where the head is + + align:start position:0% +position where the head is + + + align:start position:0% +position where the head is +um + + align:start position:0% +um + + + align:start position:0% +um +somebody says + + align:start position:0% +somebody says + + + align:start position:0% +somebody says +6 here is just you know this is one two + + align:start position:0% +6 here is just you know this is one two + + + align:start position:0% +6 here is just you know this is one two +three four five six we're in head the + + align:start position:0% +three four five six we're in head the + + + align:start position:0% +three four five six we're in head the +head is in position six that's all i had + + align:start position:0% +head is in position six that's all i had + + + align:start position:0% +head is in position six that's all i had +in mind for six and that's why that six + + align:start position:0% +in mind for six and that's why that six + + + align:start position:0% +in mind for six and that's why that six +is appearing over there because that's + + align:start position:0% +is appearing over there because that's + + + align:start position:0% +is appearing over there because that's +the position of the head + + align:start position:0% +the position of the head + + + align:start position:0% +the position of the head +um + + align:start position:0% +um + + + align:start position:0% +um +good + + align:start position:0% +good + + + align:start position:0% +good +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so why don't we continue um + + align:start position:0% + + + + align:start position:0% + +now we're all ready to start defining + + align:start position:0% +now we're all ready to start defining + + + align:start position:0% +now we're all ready to start defining +computation histories + + align:start position:0% +computation histories + + + align:start position:0% +computation histories +um which themselves is not very + + align:start position:0% +um which themselves is not very + + + align:start position:0% +um which themselves is not very +difficult concept + + align:start position:0% +difficult concept + + + align:start position:0% +difficult concept +computation history for a turing machine + + align:start position:0% +computation history for a turing machine + + + align:start position:0% +computation history for a turing machine +m on an input w + + align:start position:0% +m on an input w + + + align:start position:0% +m on an input w +is just the sequence of configurations + + align:start position:0% +is just the sequence of configurations + + + align:start position:0% +is just the sequence of configurations +you go through + + align:start position:0% +you go through + + + align:start position:0% +you go through +when you start the machine + + align:start position:0% +when you start the machine + + + align:start position:0% +when you start the machine +at the beginning + + align:start position:0% +at the beginning + + + align:start position:0% +at the beginning +um with uh m on the um + + align:start position:0% +um with uh m on the um + + + align:start position:0% +um with uh m on the um +on the tape + + align:start position:0% +on the tape + + + align:start position:0% +on the tape +with w on the tape i'm sorry um and then + + align:start position:0% +with w on the tape i'm sorry um and then + + + align:start position:0% +with w on the tape i'm sorry um and then +and the + + align:start position:0% +and the + + + align:start position:0% +and the +the st the head at the beginning is in + + align:start position:0% +the st the head at the beginning is in + + + align:start position:0% +the st the head at the beginning is in +position one + + align:start position:0% +position one + + + align:start position:0% +position one +and the uh state in q zero or whatever + + align:start position:0% +and the uh state in q zero or whatever + + + align:start position:0% +and the uh state in q zero or whatever +the start state is of the machine + + align:start position:0% +the start state is of the machine + + + align:start position:0% +the start state is of the machine +so + + align:start position:0% +so + + + align:start position:0% +so +that's going to be the very the starting + + align:start position:0% +that's going to be the very the starting + + + align:start position:0% +that's going to be the very the starting +configuration here and these are the + + align:start position:0% +configuration here and these are the + + + align:start position:0% +configuration here and these are the +sequence of configuration that mean + + align:start position:0% +sequence of configuration that mean + + + align:start position:0% +sequence of configuration that mean +machines go through that the machine + + align:start position:0% +machines go through that the machine + + + align:start position:0% +machines go through that the machine +goes through step by step + + align:start position:0% +goes through step by step + + + align:start position:0% +goes through step by step +every step of the machine is getting + + align:start position:0% +every step of the machine is getting + + + align:start position:0% +every step of the machine is getting +represented here until it ends up at an + + align:start position:0% +represented here until it ends up at an + + + align:start position:0% +represented here until it ends up at an +accept + + align:start position:0% +accept + + + align:start position:0% +accept +that's what we mean by a computation + + align:start position:0% +that's what we mean by a computation + + + align:start position:0% +that's what we mean by a computation +history or sometimes we're going to + + align:start position:0% +history or sometimes we're going to + + + align:start position:0% +history or sometimes we're going to +emphasize that by calling and accepting + + align:start position:0% +emphasize that by calling and accepting + + + align:start position:0% +emphasize that by calling and accepting +computation history + + align:start position:0% +computation history + + + align:start position:0% +computation history +represent meaning that the machine has + + align:start position:0% +represent meaning that the machine has + + + align:start position:0% +represent meaning that the machine has +accepted its input and these are the + + align:start position:0% +accepted its input and these are the + + + align:start position:0% +accepted its input and these are the +sequence of configurations that the + + align:start position:0% +sequence of configurations that the + + + align:start position:0% +sequence of configurations that the +machine goes through + + align:start position:0% +machine goes through + + + align:start position:0% +machine goes through +that's what i mean by a computation + + align:start position:0% +that's what i mean by a computation + + + align:start position:0% +that's what i mean by a computation +history you know i'm sure in i mean i + + align:start position:0% +history you know i'm sure in i mean i + + + align:start position:0% +history you know i'm sure in i mean i +think the terminology changes over the + + align:start position:0% +think the terminology changes over the + + + align:start position:0% +think the terminology changes over the +years but the there's a notion similar + + align:start position:0% +years but the there's a notion similar + + + align:start position:0% +years but the there's a notion similar +to that + + align:start position:0% +to that + + + align:start position:0% +to that +for any kind of um you know if you're + + align:start position:0% +for any kind of um you know if you're + + + align:start position:0% +for any kind of um you know if you're +you know running a program + + align:start position:0% +you know running a program + + + align:start position:0% +you know running a program +and you just want to keep track of how + + align:start position:0% +and you just want to keep track of how + + + align:start position:0% +and you just want to keep track of how +the variables are changing um as you're + + align:start position:0% +the variables are changing um as you're + + + align:start position:0% +the variables are changing um as you're +you know in this particular run of the + + align:start position:0% +you know in this particular run of the + + + align:start position:0% +you know in this particular run of the +machine and you're writing them all down + + align:start position:0% +machine and you're writing them all down + + + align:start position:0% +machine and you're writing them all down +um it's like a log of the uh + + align:start position:0% +um it's like a log of the uh + + + align:start position:0% +um it's like a log of the uh +history of the settings of the internal + + align:start position:0% +history of the settings of the internal + + + align:start position:0% +history of the settings of the internal +states of the machine and variables and + + align:start position:0% +states of the machine and variables and + + + align:start position:0% +states of the machine and variables and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +um + + align:start position:0% +um + + + align:start position:0% +um +so this is just all of the + + align:start position:0% +so this is just all of the + + + align:start position:0% +so this is just all of the +configurations the machine goes through + + align:start position:0% +configurations the machine goes through + + + align:start position:0% +configurations the machine goes through +are on the way to accepting its input + + align:start position:0% +are on the way to accepting its input + + + align:start position:0% +are on the way to accepting its input +if the machine does not accept its input + + align:start position:0% +if the machine does not accept its input + + + align:start position:0% +if the machine does not accept its input +there is no computation history + + align:start position:0% + + + + align:start position:0% + +okay so there is no accepting + + align:start position:0% +okay so there is no accepting + + + align:start position:0% +okay so there is no accepting +computation history at least to + + align:start position:0% +computation history at least to + + + align:start position:0% +computation history at least to +emphasize that point um + + align:start position:0% +emphasize that point um + + + align:start position:0% +emphasize that point um +because that can only occur obviously if + + align:start position:0% +because that can only occur obviously if + + + align:start position:0% +because that can only occur obviously if +the machine has accepted its input + + align:start position:0% + + + + align:start position:0% + +okay so just as we had with + + align:start position:0% +okay so just as we had with + + + align:start position:0% +okay so just as we had with +configurations + + align:start position:0% +configurations + + + align:start position:0% +configurations +we're going to might want to be able to + + align:start position:0% +we're going to might want to be able to + + + align:start position:0% +we're going to might want to be able to +write down computation histories as + + align:start position:0% +write down computation histories as + + + align:start position:0% +write down computation histories as +strings + + align:start position:0% +strings + + + align:start position:0% +strings +and it'll be convenient to have a + + align:start position:0% +and it'll be convenient to have a + + + align:start position:0% +and it'll be convenient to have a +particular format for doing that as well + + align:start position:0% +particular format for doing that as well + + + align:start position:0% +particular format for doing that as well +and it's kind of the obvious thing + + align:start position:0% +and it's kind of the obvious thing + + + align:start position:0% +and it's kind of the obvious thing +we're just going to take + + align:start position:0% +we're just going to take + + + align:start position:0% +we're just going to take +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the sequence of configurations in the + + align:start position:0% +the sequence of configurations in the + + + align:start position:0% +the sequence of configurations in the +computation history and write them down + + align:start position:0% +computation history and write them down + + + align:start position:0% +computation history and write them down +as a string where each + + align:start position:0% +as a string where each + + + align:start position:0% +as a string where each +configuration is going to be the string + + align:start position:0% +configuration is going to be the string + + + align:start position:0% +configuration is going to be the string +for that configuration + + align:start position:0% +for that configuration + + + align:start position:0% +for that configuration +i'll show you kind of a little example + + align:start position:0% +i'll show you kind of a little example + + + align:start position:0% +i'll show you kind of a little example +in a second but just to + + align:start position:0% +in a second but just to + + + align:start position:0% +in a second but just to +you know focus on the concept here we're + + align:start position:0% +you know focus on the concept here we're + + + align:start position:0% +you know focus on the concept here we're +just going to write down the string for + + align:start position:0% +just going to write down the string for + + + align:start position:0% +just going to write down the string for +this configuration the starting + + align:start position:0% +this configuration the starting + + + align:start position:0% +this configuration the starting +configuration and then the next + + align:start position:0% +configuration and then the next + + + align:start position:0% +configuration and then the next +configuration and so on until you get to + + align:start position:0% +configuration and so on until you get to + + + align:start position:0% +configuration and so on until you get to +the accepting configuration and separate + + align:start position:0% +the accepting configuration and separate + + + align:start position:0% +the accepting configuration and separate +each of those strings by some pound sign + + align:start position:0% +each of those strings by some pound sign + + + align:start position:0% +each of those strings by some pound sign +okay so here is a computation history + + align:start position:0% +okay so here is a computation history + + + align:start position:0% +okay so here is a computation history +for m on w um + + align:start position:0% +for m on w um + + + align:start position:0% +for m on w um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +uh + + align:start position:0% +uh + + + align:start position:0% +uh +where w is the string w on w2 dot wn + + align:start position:0% +where w is the string w on w2 dot wn + + + align:start position:0% +where w is the string w on w2 dot wn +so here is the uh + + align:start position:0% + + + + align:start position:0% + +here is the first + + align:start position:0% +here is the first + + + align:start position:0% +here is the first +uh configuration + + align:start position:0% +uh configuration + + + align:start position:0% +uh configuration +so that this part here is that is the + + align:start position:0% +so that this part here is that is the + + + align:start position:0% +so that this part here is that is the +computation history encoded as a string + + align:start position:0% +computation history encoded as a string + + + align:start position:0% +computation history encoded as a string +i'm just i'm giving you this extra + + align:start position:0% +i'm just i'm giving you this extra + + + align:start position:0% +i'm just i'm giving you this extra +um + + align:start position:0% +um + + + align:start position:0% +um +side information just to make it clearer + + align:start position:0% +side information just to make it clearer + + + align:start position:0% +side information just to make it clearer +what's what's going on there so this is + + align:start position:0% +what's what's going on there so this is + + + align:start position:0% +what's what's going on there so this is +the first configuration this is the + + align:start position:0% +the first configuration this is the + + + align:start position:0% +the first configuration this is the +second configuration and so on and i'm + + align:start position:0% +second configuration and so on and i'm + + + align:start position:0% +second configuration and so on and i'm +i'm trying to even give you a little bit + + align:start position:0% +i'm trying to even give you a little bit + + + align:start position:0% +i'm trying to even give you a little bit +more you know um detail of how it might + + align:start position:0% +more you know um detail of how it might + + + align:start position:0% +more you know um detail of how it might +look uh by kind of + + align:start position:0% +look uh by kind of + + + align:start position:0% +look uh by kind of +you know making the example a little bit + + align:start position:0% +you know making the example a little bit + + + align:start position:0% +you know making the example a little bit +more concrete so let's say that the + + align:start position:0% +more concrete so let's say that the + + + align:start position:0% +more concrete so let's say that the +turing machine + + align:start position:0% +turing machine + + + align:start position:0% +turing machine +when it's in the starting state q0 + + align:start position:0% +when it's in the starting state q0 + + + align:start position:0% +when it's in the starting state q0 +looking at the very first symbol of of + + align:start position:0% +looking at the very first symbol of of + + + align:start position:0% +looking at the very first symbol of of +the end of the the input tape in this + + align:start position:0% +the end of the the input tape in this + + + align:start position:0% +the end of the the input tape in this +particular input say w1 + + align:start position:0% +particular input say w1 + + + align:start position:0% +particular input say w1 +um it goes from q0 to q7 and writes an a + + align:start position:0% +um it goes from q0 to q7 and writes an a + + + align:start position:0% +um it goes from q0 to q7 and writes an a +on the tape and moves its head to the + + align:start position:0% +on the tape and moves its head to the + + + align:start position:0% +on the tape and moves its head to the +right + + align:start position:0% +right + + + align:start position:0% +right +so that's why the second configuration + + align:start position:0% +so that's why the second configuration + + + align:start position:0% +so that's why the second configuration +reflects that + + align:start position:0% +reflects that + + + align:start position:0% +reflects that +see here it went from q0 to q7 + + align:start position:0% +see here it went from q0 to q7 + + + align:start position:0% +see here it went from q0 to q7 +now the head is in the second position + + align:start position:0% +now the head is in the second position + + + align:start position:0% +now the head is in the second position +so that's why that state symbol has + + align:start position:0% +so that's why that state symbol has + + + align:start position:0% +so that's why that state symbol has +moved over one + + align:start position:0% +moved over one + + + align:start position:0% +moved over one +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +the very first position now has become + + align:start position:0% +the very first position now has become + + + align:start position:0% +the very first position now has become +an a + + align:start position:0% +an a + + + align:start position:0% +an a +because the machine has changed whatever + + align:start position:0% +because the machine has changed whatever + + + align:start position:0% +because the machine has changed whatever +was on that + + align:start position:0% +was on that + + + align:start position:0% +was on that +input tape there on the first position + + align:start position:0% +input tape there on the first position + + + align:start position:0% +input tape there on the first position +to an a + + align:start position:0% +to an a + + + align:start position:0% +to an a +and then the next step it goes from q7 + + align:start position:0% +and then the next step it goes from q7 + + + align:start position:0% +and then the next step it goes from q7 +reading w2 which is where the head is uh + + align:start position:0% +reading w2 which is where the head is uh + + + align:start position:0% +reading w2 which is where the head is uh +now it's looking at the w2 + + align:start position:0% +now it's looking at the w2 + + + align:start position:0% +now it's looking at the w2 +and goes to q8 writing a c and again + + align:start position:0% +and goes to q8 writing a c and again + + + align:start position:0% +and goes to q8 writing a c and again +moves right + + align:start position:0% +moves right + + + align:start position:0% +moves right +okay so that's why i drew these in the + + align:start position:0% +okay so that's why i drew these in the + + + align:start position:0% +okay so that's why i drew these in the +way i did and so you go through a + + align:start position:0% +way i did and so you go through a + + + align:start position:0% +way i did and so you go through a +sequence of those you get to cue accept + + align:start position:0% +sequence of those you get to cue accept + + + align:start position:0% +sequence of those you get to cue accept +and that's + + align:start position:0% +and that's + + + align:start position:0% +and that's +the encoded form of the computation + + align:start position:0% +the encoded form of the computation + + + align:start position:0% +the encoded form of the computation +history + + align:start position:0% +history + + + align:start position:0% +history +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um + + align:start position:0% +um + + + align:start position:0% +um +i think that's is that all i wanted to + + align:start position:0% +i think that's is that all i wanted to + + + align:start position:0% +i think that's is that all i wanted to +say yeah um + + align:start position:0% +say yeah um + + + align:start position:0% +say yeah um +so you can uh feel free + + align:start position:0% +so you can uh feel free + + + align:start position:0% +so you can uh feel free +to ask another question if you want um + + align:start position:0% +to ask another question if you want um + + + align:start position:0% +to ask another question if you want um +i'm just gonna relaunch this + + align:start position:0% + + + + align:start position:0% + +yeah good + + align:start position:0% + + + + align:start position:0% + +so if you for all to for all together on + + align:start position:0% +so if you for all to for all together on + + + align:start position:0% +so if you for all to for all together on +configurations + + align:start position:0% +configurations + + + align:start position:0% +configurations +computation histories + + align:start position:0% +computation histories + + + align:start position:0% +computation histories +and how we're going to be writing them + + align:start position:0% +and how we're going to be writing them + + + align:start position:0% +and how we're going to be writing them +down as strings + + align:start position:0% +down as strings + + + align:start position:0% +down as strings +that's what we've done so far + + align:start position:0% + + + + align:start position:0% + +no questions so i'm going to move on + + align:start position:0% +no questions so i'm going to move on + + + align:start position:0% +no questions so i'm going to move on +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so let me define a new + + align:start position:0% +so let me define a new + + + align:start position:0% +so let me define a new +um automaton + + align:start position:0% +um automaton + + + align:start position:0% +um automaton +that we're going to + + align:start position:0% +that we're going to + + + align:start position:0% +that we're going to +mainly use + + align:start position:0% +mainly use + + + align:start position:0% +mainly use +as uh just + + align:start position:0% +as uh just + + + align:start position:0% +as uh just +to + + align:start position:0% +to + + + align:start position:0% +to +provide an example + + align:start position:0% +provide an example + + + align:start position:0% +provide an example +for us + + align:start position:0% +for us + + + align:start position:0% +for us +today + + align:start position:0% + + + + align:start position:0% + +i'm going to call this a linearly + + align:start position:0% +i'm going to call this a linearly + + + align:start position:0% +i'm going to call this a linearly +bounded automaton + + align:start position:0% +bounded automaton + + + align:start position:0% +bounded automaton +and all it is is a turing machine + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +where the turing machine is going to be + + align:start position:0% +where the turing machine is going to be + + + align:start position:0% +where the turing machine is going to be +restricted + + align:start position:0% +restricted + + + align:start position:0% +restricted +in where it can uh + + align:start position:0% +in where it can uh + + + align:start position:0% +in where it can uh +the tape is not going to be infinite + + align:start position:0% +the tape is not going to be infinite + + + align:start position:0% +the tape is not going to be infinite +anymore the tape is just going to be big + + align:start position:0% +anymore the tape is just going to be big + + + align:start position:0% +anymore the tape is just going to be big +enough to hold the input + + align:start position:0% + + + + align:start position:0% + +so the machine no longer has the ability + + align:start position:0% +so the machine no longer has the ability + + + align:start position:0% +so the machine no longer has the ability +to move into the portion of the tape to + + align:start position:0% +to move into the portion of the tape to + + + align:start position:0% +to move into the portion of the tape to +the right of the input because there is + + align:start position:0% +the right of the input because there is + + + align:start position:0% +the right of the input because there is +no tape out there it just has the tape + + align:start position:0% +no tape out there it just has the tape + + + align:start position:0% +no tape out there it just has the tape +sitting here um that contains the input + + align:start position:0% +sitting here um that contains the input + + + align:start position:0% +sitting here um that contains the input +which can the tape itself can vary in + + align:start position:0% +which can the tape itself can vary in + + + align:start position:0% +which can the tape itself can vary in +size however big the input is that's how + + align:start position:0% +size however big the input is that's how + + + align:start position:0% +size however big the input is that's how +big the tape is + + align:start position:0% +big the tape is + + + align:start position:0% +big the tape is +so the tape adjusts to the length of the + + align:start position:0% +so the tape adjusts to the length of the + + + align:start position:0% +so the tape adjusts to the length of the +input + + align:start position:0% +input + + + align:start position:0% +input +but once you've started the machine with + + align:start position:0% +but once you've started the machine with + + + align:start position:0% +but once you've started the machine with +some particular input that's as big as + + align:start position:0% +some particular input that's as big as + + + align:start position:0% +some particular input that's as big as +the tape is there's no more + + align:start position:0% +the tape is there's no more + + + align:start position:0% +the tape is there's no more +um the reason why it's called linearly + + align:start position:0% +um the reason why it's called linearly + + + align:start position:0% +um the reason why it's called linearly +bounded is because the amount of memory + + align:start position:0% +bounded is because the amount of memory + + + align:start position:0% +bounded is because the amount of memory +is a linear function of the of the size + + align:start position:0% +is a linear function of the of the size + + + align:start position:0% +is a linear function of the of the size +of the input because you can effectively + + align:start position:0% +of the input because you can effectively + + + align:start position:0% +of the input because you can effectively +get + + align:start position:0% +get + + + align:start position:0% +get +somewhat more memory by enlarging the + + align:start position:0% +somewhat more memory by enlarging the + + + align:start position:0% +somewhat more memory by enlarging the +tape alphabet + + align:start position:0% +tape alphabet + + + align:start position:0% +tape alphabet +but that's going to be fixed for any + + align:start position:0% +but that's going to be fixed for any + + + align:start position:0% +but that's going to be fixed for any +given machine so that's + + align:start position:0% +given machine so that's + + + align:start position:0% +given machine so that's +where the linear comes from if that's + + align:start position:0% +where the linear comes from if that's + + + align:start position:0% +where the linear comes from if that's +helpful but if you don't get that + + align:start position:0% +helpful but if you don't get that + + + align:start position:0% +helpful but if you don't get that +that's + + align:start position:0% +that's + + + align:start position:0% +that's +sort of a side remark + + align:start position:0% +sort of a side remark + + + align:start position:0% +sort of a side remark +uh + + align:start position:0% + + + + align:start position:0% + +but um + + align:start position:0% +but um + + + align:start position:0% +but um +what's important to me is that your + + align:start position:0% +what's important to me is that your + + + align:start position:0% +what's important to me is that your +understand what i mean by an uh a + + align:start position:0% +understand what i mean by an uh a + + + align:start position:0% +understand what i mean by an uh a +linearly bounded automaton or an lba + + align:start position:0% +linearly bounded automaton or an lba + + + align:start position:0% +linearly bounded automaton or an lba +it's just like a turing machine but this + + align:start position:0% +it's just like a turing machine but this + + + align:start position:0% +it's just like a turing machine but this +that portion of the tape that originally + + align:start position:0% +that portion of the tape that originally + + + align:start position:0% +that portion of the tape that originally +had blanks is just not there + + align:start position:0% +had blanks is just not there + + + align:start position:0% +had blanks is just not there +the machine tries to move its head off + + align:start position:0% +the machine tries to move its head off + + + align:start position:0% +the machine tries to move its head off +the off the right end of the input it + + align:start position:0% +the off the right end of the input it + + + align:start position:0% +the off the right end of the input it +just sticks there just as if it tried to + + align:start position:0% +just sticks there just as if it tried to + + + align:start position:0% +just sticks there just as if it tried to +move its head off the left end of the + + align:start position:0% +move its head off the left end of the + + + align:start position:0% +move its head off the left end of the +input + + align:start position:0% +input + + + align:start position:0% +input +doesn't go anywhere + + align:start position:0% +doesn't go anywhere + + + align:start position:0% +doesn't go anywhere +okay so now i'm gonna we're gonna ask + + align:start position:0% +okay so now i'm gonna we're gonna ask + + + align:start position:0% +okay so now i'm gonna we're gonna ask +the same kinds of questions about lbas + + align:start position:0% +the same kinds of questions about lbas + + + align:start position:0% +the same kinds of questions about lbas +that we asked for other automata + + align:start position:0% +that we asked for other automata + + + align:start position:0% +that we asked for other automata +so the acceptance problem + + align:start position:0% +so the acceptance problem + + + align:start position:0% +so the acceptance problem +if i give you a + + align:start position:0% +if i give you a + + + align:start position:0% +if i give you a +an input + + align:start position:0% +an input + + + align:start position:0% +an input +and some particular + + align:start position:0% +and some particular + + + align:start position:0% +and some particular +lba + + align:start position:0% +lba + + + align:start position:0% +lba +and i want to know + + align:start position:0% +and i want to know + + + align:start position:0% +and i want to know +does the lba accept that input + + align:start position:0% +does the lba accept that input + + + align:start position:0% +does the lba accept that input +well you know and now the question is is + + align:start position:0% +well you know and now the question is is + + + align:start position:0% +well you know and now the question is is +that decidable um or not + + align:start position:0% +that decidable um or not + + + align:start position:0% +that decidable um or not +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +it's + + align:start position:0% + + + + align:start position:0% + +um at first glance you might think well + + align:start position:0% +um at first glance you might think well + + + align:start position:0% +um at first glance you might think well +um an lba is like a turing machine + + align:start position:0% +um an lba is like a turing machine + + + align:start position:0% +um an lba is like a turing machine +and the atm problem is undecidable + + align:start position:0% +and the atm problem is undecidable + + + align:start position:0% +and the atm problem is undecidable +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +you know that that might be a good first + + align:start position:0% +you know that that might be a good first + + + align:start position:0% +you know that that might be a good first +guess + + align:start position:0% +guess + + + align:start position:0% +guess +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and also if you try to uh + + align:start position:0% + + + + align:start position:0% + +to simulate them if you try to figure + + align:start position:0% +to simulate them if you try to figure + + + align:start position:0% +to simulate them if you try to figure +out how you would go about simulating + + align:start position:0% +out how you would go about simulating + + + align:start position:0% +out how you would go about simulating +the machine um + + align:start position:0% +the machine um + + + align:start position:0% +the machine um +you know if you if a given b and w if + + align:start position:0% +you know if you if a given b and w if + + + align:start position:0% +you know if you if a given b and w if +you actually try to simulate the machine + + align:start position:0% +you actually try to simulate the machine + + + align:start position:0% +you actually try to simulate the machine +to get the answer so you run b on w well + + align:start position:0% +to get the answer so you run b on w well + + + align:start position:0% +to get the answer so you run b on w well +of course if you run it for a while and + + align:start position:0% +of course if you run it for a while and + + + align:start position:0% +of course if you run it for a while and +it eventually halts either accepting or + + align:start position:0% +it eventually halts either accepting or + + + align:start position:0% +it eventually halts either accepting or +rejecting then you know the answer and + + align:start position:0% +rejecting then you know the answer and + + + align:start position:0% +rejecting then you know the answer and +you're finished but you know this + + align:start position:0% +you're finished but you know this + + + align:start position:0% +you're finished but you know this +machine might get into a loop + + align:start position:0% +machine might get into a loop + + + align:start position:0% +machine might get into a loop +um + + align:start position:0% +um + + + align:start position:0% +um +you know nothing to prevent the machine + + align:start position:0% +you know nothing to prevent the machine + + + align:start position:0% +you know nothing to prevent the machine +from looping on that finite amount of on + + align:start position:0% +from looping on that finite amount of on + + + align:start position:0% +from looping on that finite amount of on +that limited amount of tape that it has + + align:start position:0% +that limited amount of tape that it has + + + align:start position:0% +that limited amount of tape that it has +um and then + + align:start position:0% +um and then + + + align:start position:0% +um and then +you know + + align:start position:0% +you know + + + align:start position:0% +you know +you might be in trouble + + align:start position:0% +you might be in trouble + + + align:start position:0% +you might be in trouble +but in fact that's not the case + + align:start position:0% +but in fact that's not the case + + + align:start position:0% +but in fact that's not the case +because + + align:start position:0% +because + + + align:start position:0% +because +when you start out with a limited amount + + align:start position:0% +when you start out with a limited amount + + + align:start position:0% +when you start out with a limited amount +of tape + + align:start position:0% +of tape + + + align:start position:0% +of tape +if you run the machine for a long time + + align:start position:0% +if you run the machine for a long time + + + align:start position:0% +if you run the machine for a long time +and it's not holding it's going and + + align:start position:0% +and it's not holding it's going and + + + align:start position:0% +and it's not holding it's going and +going and going + + align:start position:0% +going and going + + + align:start position:0% +going and going +inevitably it's going to have to repeat + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +get into exactly the same configuration + + align:start position:0% +get into exactly the same configuration + + + align:start position:0% +get into exactly the same configuration +that it did before because there's only + + align:start position:0% +that it did before because there's only + + + align:start position:0% +that it did before because there's only +a limited number of configurations that + + align:start position:0% +a limited number of configurations that + + + align:start position:0% +a limited number of configurations that +the machine has + + align:start position:0% +the machine has + + + align:start position:0% +the machine has +and once it repeats a configuration it's + + align:start position:0% +and once it repeats a configuration it's + + + align:start position:0% +and once it repeats a configuration it's +going to be repeating that configuration + + align:start position:0% +going to be repeating that configuration + + + align:start position:0% +going to be repeating that configuration +forever and it's going to be in a loop + + align:start position:0% +forever and it's going to be in a loop + + + align:start position:0% +forever and it's going to be in a loop +so + + align:start position:0% + + + + align:start position:0% + +this problem in fact is decidable um + + align:start position:0% +this problem in fact is decidable um + + + align:start position:0% +this problem in fact is decidable um +because the idea is if bmw runs for for + + align:start position:0% +because the idea is if bmw runs for for + + + align:start position:0% +because the idea is if bmw runs for for +a very long time and + + align:start position:0% +a very long time and + + + align:start position:0% +a very long time and +an amount that you can calculate then + + align:start position:0% +an amount that you can calculate then + + + align:start position:0% +an amount that you can calculate then +you know it's got to be you know cycling + + align:start position:0% +you know it's got to be you know cycling + + + align:start position:0% +you know it's got to be you know cycling +you know more than just looping it's got + + align:start position:0% +you know more than just looping it's got + + + align:start position:0% +you know more than just looping it's got +to be repeating itself + + align:start position:0% +to be repeating itself + + + align:start position:0% +to be repeating itself +um + + align:start position:0% +um + + + align:start position:0% +um +and so therefore once it starts + + align:start position:0% +and so therefore once it starts + + + align:start position:0% +and so therefore once it starts +repeating itself it's going to be going + + align:start position:0% +repeating itself it's going to be going + + + align:start position:0% +repeating itself it's going to be going +forever + + align:start position:0% + + + + align:start position:0% + +so um and here's the actual calculation + + align:start position:0% +so um and here's the actual calculation + + + align:start position:0% +so um and here's the actual calculation +which is something i'm sure you could do + + align:start position:0% +which is something i'm sure you could do + + + align:start position:0% +which is something i'm sure you could do +on your own but just to spell it out + + align:start position:0% +on your own but just to spell it out + + + align:start position:0% +on your own but just to spell it out +so if you have an input of length n + + align:start position:0% +so if you have an input of length n + + + align:start position:0% +so if you have an input of length n +um that you're providing to uh b so if w + + align:start position:0% +um that you're providing to uh b so if w + + + align:start position:0% +um that you're providing to uh b so if w +is of length n + + align:start position:0% +is of length n + + + align:start position:0% +is of length n +um the the lba can only go + + align:start position:0% +um the the lba can only go + + + align:start position:0% +um the the lba can only go +uh for + + align:start position:0% +uh for + + + align:start position:0% +uh for +uh this number of different it can only + + align:start position:0% +uh this number of different it can only + + + align:start position:0% +uh this number of different it can only +have this number of different + + align:start position:0% +have this number of different + + + align:start position:0% +have this number of different +configurations the number of states + + align:start position:0% +configurations the number of states + + + align:start position:0% +configurations the number of states +times the number of head positions which + + align:start position:0% +times the number of head positions which + + + align:start position:0% +times the number of head positions which +is n the number of head positions on the + + align:start position:0% +is n the number of head positions on the + + + align:start position:0% +is n the number of head positions on the +tape + + align:start position:0% +tape + + + align:start position:0% +tape +times the number of different tape + + align:start position:0% +times the number of different tape + + + align:start position:0% +times the number of different tape +contents + + align:start position:0% +contents + + + align:start position:0% +contents +you know if if the tape was only one + + align:start position:0% +you know if if the tape was only one + + + align:start position:0% +you know if if the tape was only one +long you know this is the this is the + + align:start position:0% +long you know this is the this is the + + + align:start position:0% +long you know this is the this is the +size of the tape alphabet so if the tape + + align:start position:0% +size of the tape alphabet so if the tape + + + align:start position:0% +size of the tape alphabet so if the tape +were too long it would you know + + align:start position:0% +were too long it would you know + + + align:start position:0% +were too long it would you know +had the tape had two + + align:start position:0% +had the tape had two + + + align:start position:0% +had the tape had two +uh + + align:start position:0% +uh + + + align:start position:0% +uh +two cells on it the number of possible + + align:start position:0% +two cells on it the number of possible + + + align:start position:0% +two cells on it the number of possible +tape contents is would be um the square + + align:start position:0% +tape contents is would be um the square + + + align:start position:0% +tape contents is would be um the square +of the of the alphabet and then and if + + align:start position:0% +of the of the alphabet and then and if + + + align:start position:0% +of the of the alphabet and then and if +if the tape is going to be n + + align:start position:0% +if the tape is going to be n + + + align:start position:0% +if the tape is going to be n +uh symbols long it's going to be + + align:start position:0% +uh symbols long it's going to be + + + align:start position:0% +uh symbols long it's going to be +the tape alphabet size to the nth power + + align:start position:0% +the tape alphabet size to the nth power + + + align:start position:0% +the tape alphabet size to the nth power +uh so therefore if a turning machine + + align:start position:0% +uh so therefore if a turning machine + + + align:start position:0% +uh so therefore if a turning machine +runs for longer it's got to repeat + + align:start position:0% +runs for longer it's got to repeat + + + align:start position:0% +runs for longer it's got to repeat +some configuration and it'll never hold + + align:start position:0% +some configuration and it'll never hold + + + align:start position:0% +some configuration and it'll never hold +so the decider is going to be + + align:start position:0% +so the decider is going to be + + + align:start position:0% +so the decider is going to be +hopefully uh clear at this point + + align:start position:0% +hopefully uh clear at this point + + + align:start position:0% +hopefully uh clear at this point +you're given b and w + + align:start position:0% +you're given b and w + + + align:start position:0% +you're given b and w +says that this is the decider for alba + + align:start position:0% +says that this is the decider for alba + + + align:start position:0% +says that this is the decider for alba +it's going to run bmw for this number of + + align:start position:0% +it's going to run bmw for this number of + + + align:start position:0% +it's going to run bmw for this number of +steps + + align:start position:0% +steps + + + align:start position:0% +steps +if it's accepted by then then you accept + + align:start position:0% +if it's accepted by then then you accept + + + align:start position:0% +if it's accepted by then then you accept +and if it hasn't if it's rejected or + + align:start position:0% +and if it hasn't if it's rejected or + + + align:start position:0% +and if it hasn't if it's rejected or +it's still running + + align:start position:0% +it's still running + + + align:start position:0% +it's still running +then you can reject and you know if it's + + align:start position:0% +then you can reject and you know if it's + + + align:start position:0% +then you can reject and you know if it's +still running at this point it's never + + align:start position:0% +still running at this point it's never + + + align:start position:0% +still running at this point it's never +going to accept + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +any questions on this + + align:start position:0% + + + + align:start position:0% + +okay let's move on + + align:start position:0% +okay let's move on + + + align:start position:0% +okay let's move on +um + + align:start position:0% +um + + + align:start position:0% +um +all right so now um + + align:start position:0% + + + + align:start position:0% + +but what's different now or what's it + + align:start position:0% +but what's different now or what's it + + + align:start position:0% +but what's different now or what's it +perhaps interesting now is that even + + align:start position:0% +perhaps interesting now is that even + + + align:start position:0% +perhaps interesting now is that even +though the + + align:start position:0% +though the + + + align:start position:0% +though the +acceptance problem for lbas is the is is + + align:start position:0% +acceptance problem for lbas is the is is + + + align:start position:0% +acceptance problem for lbas is the is is +decidable + + align:start position:0% +decidable + + + align:start position:0% +decidable +the emptiness problem is undecidable + + align:start position:0% + + + + align:start position:0% + +and that's where the computation history + + align:start position:0% +and that's where the computation history + + + align:start position:0% +and that's where the computation history +method is going to come in so this is + + align:start position:0% +method is going to come in so this is + + + align:start position:0% +method is going to come in so this is +where we're going to be starting to do + + align:start position:0% +where we're going to be starting to do + + + align:start position:0% +where we're going to be starting to do +something new in terms of a proof + + align:start position:0% +something new in terms of a proof + + + align:start position:0% +something new in terms of a proof +technique + + align:start position:0% +technique + + + align:start position:0% +technique +um because + + align:start position:0% + + + + align:start position:0% + +so we're going to reduce atm to elba the + + align:start position:0% +so we're going to reduce atm to elba the + + + align:start position:0% +so we're going to reduce atm to elba the +emptiness problem for lbas + + align:start position:0% +emptiness problem for lbas + + + align:start position:0% +emptiness problem for lbas +um + + align:start position:0% +um + + + align:start position:0% +um +so given an lba does it accept anything + + align:start position:0% +so given an lba does it accept anything + + + align:start position:0% +so given an lba does it accept anything +or not + + align:start position:0% +or not + + + align:start position:0% +or not +and this is going to use the computation + + align:start position:0% +and this is going to use the computation + + + align:start position:0% +and this is going to use the computation +history method so + + align:start position:0% +history method so + + + align:start position:0% +history method so +this will be a chance to illustrate that + + align:start position:0% +this will be a chance to illustrate that + + + align:start position:0% +this will be a chance to illustrate that +method for the first time + + align:start position:0% +method for the first time + + + align:start position:0% +method for the first time +so this the setup initially is just like + + align:start position:0% +so this the setup initially is just like + + + align:start position:0% +so this the setup initially is just like +before we're going to assume we have a + + align:start position:0% +before we're going to assume we have a + + + align:start position:0% +before we're going to assume we have a +turing machine that decides the cb elba + + align:start position:0% +turing machine that decides the cb elba + + + align:start position:0% +turing machine that decides the cb elba +problem that of interest + + align:start position:0% +problem that of interest + + + align:start position:0% +problem that of interest +and we're going to use that to construct + + align:start position:0% +and we're going to use that to construct + + + align:start position:0% +and we're going to use that to construct +turing machine deciding atm for our + + align:start position:0% +turing machine deciding atm for our + + + align:start position:0% +turing machine deciding atm for our +contradiction + + align:start position:0% +contradiction + + + align:start position:0% +contradiction +okay so here's s + + align:start position:0% +okay so here's s + + + align:start position:0% +okay so here's s +supposedly deciding atm + + align:start position:0% +supposedly deciding atm + + + align:start position:0% +supposedly deciding atm +what it's going to do and this is going + + align:start position:0% +what it's going to do and this is going + + + align:start position:0% +what it's going to do and this is going +to be the tricky part + + align:start position:0% +to be the tricky part + + + align:start position:0% +to be the tricky part +s + + align:start position:0% +s + + + align:start position:0% +s +is going to use m and w to design an + + align:start position:0% +is going to use m and w to design an + + + align:start position:0% +is going to use m and w to design an +llba + + align:start position:0% + + + + align:start position:0% + +that lba + + align:start position:0% +that lba + + + align:start position:0% +that lba +is going to be built + + align:start position:0% +is going to be built + + + align:start position:0% +is going to be built +with the knowledge of m w in fact it's + + align:start position:0% +with the knowledge of m w in fact it's + + + align:start position:0% +with the knowledge of m w in fact it's +going to have m and w built into it + + align:start position:0% +going to have m and w built into it + + + align:start position:0% +going to have m and w built into it +so + + align:start position:0% +so + + + align:start position:0% +so +that's why i'm calling that lba + + align:start position:0% +that's why i'm calling that lba + + + align:start position:0% +that's why i'm calling that lba +b sub mw + + align:start position:0% +b sub mw + + + align:start position:0% +b sub mw +because it depends on mw + + align:start position:0% +because it depends on mw + + + align:start position:0% +because it depends on mw +um + + align:start position:0% +um + + + align:start position:0% +um +as i'll describe and what that lba does + + align:start position:0% + + + + align:start position:0% + +it takes its input + + align:start position:0% +it takes its input + + + align:start position:0% +it takes its input +let's call it the x the input to the the + + align:start position:0% +let's call it the x the input to the the + + + align:start position:0% +let's call it the x the input to the the +lba + + align:start position:0% +lba + + + align:start position:0% +lba +and + + align:start position:0% +and + + + align:start position:0% +and +examines that input to see + + align:start position:0% +examines that input to see + + + align:start position:0% +examines that input to see +if that input is an accepting + + align:start position:0% +if that input is an accepting + + + align:start position:0% +if that input is an accepting +computation history for m on w + + align:start position:0% + + + + align:start position:0% + +then that lba is just looking for + + align:start position:0% +then that lba is just looking for + + + align:start position:0% +then that lba is just looking for +computation histories for mw + + align:start position:0% + + + + align:start position:0% + +and that's the only thing it's going to + + align:start position:0% +and that's the only thing it's going to + + + align:start position:0% +and that's the only thing it's going to +ever accept + + align:start position:0% + + + + align:start position:0% + +if you feed it something which is not + + align:start position:0% +if you feed it something which is not + + + align:start position:0% +if you feed it something which is not +a computation history you know that + + align:start position:0% +a computation history you know that + + + align:start position:0% +a computation history you know that +sequence of configurations + + align:start position:0% +sequence of configurations + + + align:start position:0% +sequence of configurations +uh for mmw leading to an accept if you + + align:start position:0% +uh for mmw leading to an accept if you + + + align:start position:0% +uh for mmw leading to an accept if you +feed it something else + + align:start position:0% +feed it something else + + + align:start position:0% +feed it something else +the lba is just going to reject it + + align:start position:0% +the lba is just going to reject it + + + align:start position:0% +the lba is just going to reject it +it only accepts + + align:start position:0% +it only accepts + + + align:start position:0% +it only accepts +the accepting computation history for m + + align:start position:0% +the accepting computation history for m + + + align:start position:0% +the accepting computation history for m +w + + align:start position:0% +w + + + align:start position:0% +w +and now + + align:start position:0% +and now + + + align:start position:0% +and now +if you can build such a thing + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +you can + + align:start position:0% +you can + + + align:start position:0% +you can +use that machine + + align:start position:0% +use that machine + + + align:start position:0% +use that machine +in your emptiness tester to see if it + + align:start position:0% +in your emptiness tester to see if it + + + align:start position:0% +in your emptiness tester to see if it +accepts any strings at all + + align:start position:0% +accepts any strings at all + + + align:start position:0% +accepts any strings at all +because the only thing that could + + align:start position:0% +because the only thing that could + + + align:start position:0% +because the only thing that could +possibly be accepting is an accepting + + align:start position:0% +possibly be accepting is an accepting + + + align:start position:0% +possibly be accepting is an accepting +computation history you don't even know + + align:start position:0% +computation history you don't even know + + + align:start position:0% +computation history you don't even know +if there exists one because you don't + + align:start position:0% +if there exists one because you don't + + + align:start position:0% +if there exists one because you don't +know if m accepts w + + align:start position:0% +know if m accepts w + + + align:start position:0% +know if m accepts w +so you're going to build this lba + + align:start position:0% +so you're going to build this lba + + + align:start position:0% +so you're going to build this lba +um + + align:start position:0% +um + + + align:start position:0% +um +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +which is looking for accepting + + align:start position:0% +which is looking for accepting + + + align:start position:0% +which is looking for accepting +computation histories + + align:start position:0% +computation histories + + + align:start position:0% +computation histories +and then see if its language is empty or + + align:start position:0% +and then see if its language is empty or + + + align:start position:0% +and then see if its language is empty or +not + + align:start position:0% +not + + + align:start position:0% +not +if its language is not empty + + align:start position:0% +if its language is not empty + + + align:start position:0% +if its language is not empty +the only thing it could be accepting is + + align:start position:0% +the only thing it could be accepting is + + + align:start position:0% +the only thing it could be accepting is +this computation history so you know m + + align:start position:0% +this computation history so you know m + + + align:start position:0% +this computation history so you know m +except w + + align:start position:0% +except w + + + align:start position:0% +except w +whereas if the language is empty you + + align:start position:0% +whereas if the language is empty you + + + align:start position:0% +whereas if the language is empty you +know that there is no computation + + align:start position:0% +know that there is no computation + + + align:start position:0% +know that there is no computation +history for m w and so m does not accept + + align:start position:0% +history for m w and so m does not accept + + + align:start position:0% +history for m w and so m does not accept +the leaf + + align:start position:0% +the leaf + + + align:start position:0% +the leaf +so that's the whole idea the trick is + + align:start position:0% +so that's the whole idea the trick is + + + align:start position:0% +so that's the whole idea the trick is +how do you build + + align:start position:0% +how do you build + + + align:start position:0% +how do you build +this uh this lba um + + align:start position:0% +this uh this lba um + + + align:start position:0% +this uh this lba um +so first you're going to make this lba + + align:start position:0% +so first you're going to make this lba + + + align:start position:0% +so first you're going to make this lba +which tests its input to see if it's an + + align:start position:0% +which tests its input to see if it's an + + + align:start position:0% +which tests its input to see if it's an +accepting computation history for m on w + + align:start position:0% + + + + align:start position:0% + +and you have to build this + + align:start position:0% +and you have to build this + + + align:start position:0% +and you have to build this +um + + align:start position:0% +um + + + align:start position:0% +um +uh lba without even knowing whether + + align:start position:0% +uh lba without even knowing whether + + + align:start position:0% +uh lba without even knowing whether +there is a computation history + + align:start position:0% +there is a computation history + + + align:start position:0% +there is a computation history +um it's not like you can take that + + align:start position:0% +um it's not like you can take that + + + align:start position:0% +um it's not like you can take that +string and just build the string into + + align:start position:0% +string and just build the string into + + + align:start position:0% +string and just build the string into +the lba because they don't even know if + + align:start position:0% +the lba because they don't even know if + + + align:start position:0% +the lba because they don't even know if +that string exists + + align:start position:0% +that string exists + + + align:start position:0% +that string exists +but what you can do + + align:start position:0% +but what you can do + + + align:start position:0% +but what you can do +is you can make the lba + + align:start position:0% +is you can make the lba + + + align:start position:0% +is you can make the lba +um + + align:start position:0% +um + + + align:start position:0% +um +follow the rules of m it knows w + + align:start position:0% +follow the rules of m it knows w + + + align:start position:0% +follow the rules of m it knows w +and knows m so it can test take the its + + align:start position:0% +and knows m so it can test take the its + + + align:start position:0% +and knows m so it can test take the its +input and using w and the rules of m see + + align:start position:0% +input and using w and the rules of m see + + + align:start position:0% +input and using w and the rules of m see +if that input is a computation history + + align:start position:0% +if that input is a computation history + + + align:start position:0% +if that input is a computation history +for m and w + + align:start position:0% +for m and w + + + align:start position:0% +for m and w +um and that's what it's going to do + + align:start position:0% +um and that's what it's going to do + + + align:start position:0% +um and that's what it's going to do +so here is + + align:start position:0% +so here is + + + align:start position:0% +so here is +um + + align:start position:0% +um + + + align:start position:0% +um +this machine i'm going to construct i'll + + align:start position:0% +this machine i'm going to construct i'll + + + align:start position:0% +this machine i'm going to construct i'll +i'll give it to you written down and + + align:start position:0% +i'll give it to you written down and + + + align:start position:0% +i'll give it to you written down and +with a little bit more um details of its + + align:start position:0% +with a little bit more um details of its + + + align:start position:0% +with a little bit more um details of its +procedure but just to kind of illustrate + + align:start position:0% +procedure but just to kind of illustrate + + + align:start position:0% +procedure but just to kind of illustrate +it so here is a proposed input to b sub + + align:start position:0% +it so here is a proposed input to b sub + + + align:start position:0% +it so here is a proposed input to b sub +mw this would be the x here this would + + align:start position:0% +mw this would be the x here this would + + + align:start position:0% +mw this would be the x here this would +be an x that would be accepted + + align:start position:0% +be an x that would be accepted + + + align:start position:0% +be an x that would be accepted +but anything else that would be provided + + align:start position:0% +but anything else that would be provided + + + align:start position:0% +but anything else that would be provided +would not be accepted + + align:start position:0% +would not be accepted + + + align:start position:0% +would not be accepted +so this is the sequence of + + align:start position:0% +so this is the sequence of + + + align:start position:0% +so this is the sequence of +configurations written down as a string + + align:start position:0% +configurations written down as a string + + + align:start position:0% +configurations written down as a string +that would be the x that i'm providing + + align:start position:0% +that would be the x that i'm providing + + + align:start position:0% +that would be the x that i'm providing +to the b c b b sub mw and it's supposed + + align:start position:0% +to the b c b b sub mw and it's supposed + + + align:start position:0% +to the b c b b sub mw and it's supposed +to be checking this to make sure it's + + align:start position:0% +to be checking this to make sure it's + + + align:start position:0% +to be checking this to make sure it's +legit + + align:start position:0% +legit + + + align:start position:0% +legit +um so + + align:start position:0% +um so + + + align:start position:0% +um so +so on on input x the way it's gonna the + + align:start position:0% +so on on input x the way it's gonna the + + + align:start position:0% +so on on input x the way it's gonna the +way it's going to proceed + + align:start position:0% +way it's going to proceed + + + align:start position:0% +way it's going to proceed +it's going to first check to see whether + + align:start position:0% +it's going to first check to see whether + + + align:start position:0% +it's going to first check to see whether +x begins in the right way + + align:start position:0% +x begins in the right way + + + align:start position:0% +x begins in the right way +because you know + + align:start position:0% + + + + align:start position:0% + +this lba it knows m and it knows w + + align:start position:0% +this lba it knows m and it knows w + + + align:start position:0% +this lba it knows m and it knows w +so the very first thing is it takes a + + align:start position:0% +so the very first thing is it takes a + + + align:start position:0% +so the very first thing is it takes a +look at the first part of the string up + + align:start position:0% +look at the first part of the string up + + + align:start position:0% +look at the first part of the string up +to the pound sign you know there's no + + align:start position:0% +to the pound sign you know there's no + + + align:start position:0% +to the pound sign you know there's no +pound sign if you're going to just feed + + align:start position:0% +pound sign if you're going to just feed + + + align:start position:0% +pound sign if you're going to just feed +junk in it's going to be easily + + align:start position:0% +junk in it's going to be easily + + + align:start position:0% +junk in it's going to be easily +identifiable as junk + + align:start position:0% +identifiable as junk + + + align:start position:0% +identifiable as junk +um + + align:start position:0% +um + + + align:start position:0% +um +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +you know if you're going to feed + + align:start position:0% +you know if you're going to feed + + + align:start position:0% +you know if you're going to feed +something so it's going to the lba is + + align:start position:0% +something so it's going to the lba is + + + align:start position:0% +something so it's going to the lba is +going to take everything up to the first + + align:start position:0% +going to take everything up to the first + + + align:start position:0% +going to take everything up to the first +pound sign and just confirm that that + + align:start position:0% +pound sign and just confirm that that + + + align:start position:0% +pound sign and just confirm that that +thing is + + align:start position:0% +thing is + + + align:start position:0% +thing is +the first configuration the starting + + align:start position:0% +the first configuration the starting + + + align:start position:0% +the first configuration the starting +configuration of um + + align:start position:0% +configuration of um + + + align:start position:0% +configuration of um +of m on w which means it has to start + + align:start position:0% +of m on w which means it has to start + + + align:start position:0% +of m on w which means it has to start +with the start state and here is w + + align:start position:0% +with the start state and here is w + + + align:start position:0% +with the start state and here is w +so just going to check that + + align:start position:0% +so just going to check that + + + align:start position:0% +so just going to check that +um + + align:start position:0% +um + + + align:start position:0% +um +then it's going to check that each + + align:start position:0% +then it's going to check that each + + + align:start position:0% +then it's going to check that each +each one of these guys follows legally + + align:start position:0% +each one of these guys follows legally + + + align:start position:0% +each one of these guys follows legally +from the previous one according to the + + align:start position:0% +from the previous one according to the + + + align:start position:0% +from the previous one according to the +rules of f it's going to first checks + + align:start position:0% +rules of f it's going to first checks + + + align:start position:0% +rules of f it's going to first checks +that this one is correct and then this + + align:start position:0% +that this one is correct and then this + + + align:start position:0% +that this one is correct and then this +one leads to that one + + align:start position:0% +one leads to that one + + + align:start position:0% +one leads to that one +according to the rules of m then this + + align:start position:0% +according to the rules of m then this + + + align:start position:0% +according to the rules of m then this +one leads to that one according to the + + align:start position:0% +one leads to that one according to the + + + align:start position:0% +one leads to that one according to the +rules of m + + align:start position:0% +rules of m + + + align:start position:0% +rules of m +all of that you know the knowledge of m + + align:start position:0% +all of that you know the knowledge of m + + + align:start position:0% +all of that you know the knowledge of m +and w is built in so it can do that + + align:start position:0% +and w is built in so it can do that + + + align:start position:0% +and w is built in so it can do that +um + + align:start position:0% +um + + + align:start position:0% +um +and then it just + + align:start position:0% +and then it just + + + align:start position:0% +and then it just +follows along checking this computation + + align:start position:0% +follows along checking this computation + + + align:start position:0% +follows along checking this computation +you know it's easy to check that a + + align:start position:0% +you know it's easy to check that a + + + align:start position:0% +you know it's easy to check that a +computation is correct that's all that's + + align:start position:0% +computation is correct that's all that's + + + align:start position:0% +computation is correct that's all that's +really going on here + + align:start position:0% +really going on here + + + align:start position:0% +really going on here +um + + align:start position:0% +um + + + align:start position:0% +um +it's going to check that the computation + + align:start position:0% +it's going to check that the computation + + + align:start position:0% +it's going to check that the computation +is correct until it gets to the end and + + align:start position:0% +is correct until it gets to the end and + + + align:start position:0% +is correct until it gets to the end and +then make sure that the last uh + + align:start position:0% +then make sure that the last uh + + + align:start position:0% +then make sure that the last uh +configuration that it's been given as + + align:start position:0% +configuration that it's been given as + + + align:start position:0% +configuration that it's been given as +input is an accepting configuration + + align:start position:0% +input is an accepting configuration + + + align:start position:0% +input is an accepting configuration +that there's an accept state in it + + align:start position:0% +that there's an accept state in it + + + align:start position:0% +that there's an accept state in it +um and if everything that passes it it + + align:start position:0% +um and if everything that passes it it + + + align:start position:0% +um and if everything that passes it it +accepts otherwise it uh rejects + + align:start position:0% +accepts otherwise it uh rejects + + + align:start position:0% +accepts otherwise it uh rejects +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +and the point is that this is an lba you + + align:start position:0% +and the point is that this is an lba you + + + align:start position:0% +and the point is that this is an lba you +don't oh i just kind of jumped ahead of + + align:start position:0% +don't oh i just kind of jumped ahead of + + + align:start position:0% +don't oh i just kind of jumped ahead of +myself you don't need any additional + + align:start position:0% +myself you don't need any additional + + + align:start position:0% +myself you don't need any additional +information so how does it actually do + + align:start position:0% +information so how does it actually do + + + align:start position:0% +information so how does it actually do +this + + align:start position:0% +this + + + align:start position:0% +this +so you know how do you actually do this + + align:start position:0% +so you know how do you actually do this + + + align:start position:0% +so you know how do you actually do this +on the tape so i claim that the lba + + align:start position:0% +on the tape so i claim that the lba + + + align:start position:0% +on the tape so i claim that the lba +doesn't need any extra space to do this + + align:start position:0% +doesn't need any extra space to do this + + + align:start position:0% +doesn't need any extra space to do this +um to do this check you know it's just + + align:start position:0% +um to do this check you know it's just + + + align:start position:0% +um to do this check you know it's just +going to be zigzagging back and forth + + align:start position:0% +going to be zigzagging back and forth + + + align:start position:0% +going to be zigzagging back and forth +here on the on on the + + align:start position:0% +here on the on on the + + + align:start position:0% +here on the on on the +on the input + + align:start position:0% + + + + align:start position:0% + +you know checking that the corresponding + + align:start position:0% +you know checking that the corresponding + + + align:start position:0% +you know checking that the corresponding +symbols match up except around the the + + align:start position:0% +symbols match up except around the the + + + align:start position:0% +symbols match up except around the the +head position where it gets updated or + + align:start position:0% +head position where it gets updated or + + + align:start position:0% +head position where it gets updated or +correctly + + align:start position:0% +correctly + + + align:start position:0% +correctly +and it seems it may need to mark it will + + align:start position:0% +and it seems it may need to mark it will + + + align:start position:0% +and it seems it may need to mark it will +need to mark on the tape it's allowed to + + align:start position:0% +need to mark on the tape it's allowed to + + + align:start position:0% +need to mark on the tape it's allowed to +write on the tape just to make sure it + + align:start position:0% +write on the tape just to make sure it + + + align:start position:0% +write on the tape just to make sure it +keeps track of where it is + + align:start position:0% +keeps track of where it is + + + align:start position:0% +keeps track of where it is +but this is a very simple + + align:start position:0% +but this is a very simple + + + align:start position:0% +but this is a very simple +i mean i'm not trying to uh if you're + + align:start position:0% +i mean i'm not trying to uh if you're + + + align:start position:0% +i mean i'm not trying to uh if you're +not following i'm not trying to uh alarm + + align:start position:0% +not following i'm not trying to uh alarm + + + align:start position:0% +not following i'm not trying to uh alarm +you but i'm just trying to help you + + align:start position:0% +you but i'm just trying to help you + + + align:start position:0% +you but i'm just trying to help you +understand that + + align:start position:0% +understand that + + + align:start position:0% +understand that +this is not a complicated procedure here + + align:start position:0% +this is not a complicated procedure here + + + align:start position:0% +this is not a complicated procedure here +to do this check that the that the + + align:start position:0% +to do this check that the that the + + + align:start position:0% +to do this check that the that the +actual computation of the that's written + + align:start position:0% +actual computation of the that's written + + + align:start position:0% +actual computation of the that's written +down of the turing machine is valid + + align:start position:0% +down of the turing machine is valid + + + align:start position:0% +down of the turing machine is valid +um but you know we can deal with a + + align:start position:0% +um but you know we can deal with a + + + align:start position:0% +um but you know we can deal with a +question here + + align:start position:0% +question here + + + align:start position:0% +question here +uh + + align:start position:0% +uh + + + align:start position:0% +uh +oh good + + align:start position:0% +oh good + + + align:start position:0% +oh good +now we got some questions + + align:start position:0% +now we got some questions + + + align:start position:0% +now we got some questions +oops + + align:start position:0% +oops + + + align:start position:0% +oops +you can be thinking about while i'm + + align:start position:0% +you can be thinking about while i'm + + + align:start position:0% +you can be thinking about while i'm +thinking about this you can think about + + align:start position:0% +thinking about this you can think about + + + align:start position:0% +thinking about this you can think about +that uh check-in over there + + align:start position:0% + + + + align:start position:0% + +so here's a good question + + align:start position:0% +so here's a good question + + + align:start position:0% +so here's a good question +going from each configuration to the + + align:start position:0% +going from each configuration to the + + + align:start position:0% +going from each configuration to the +next configuration is it a unique + + align:start position:0% +next configuration is it a unique + + + align:start position:0% +next configuration is it a unique +uh next + + align:start position:0% +uh next + + + align:start position:0% +uh next +step + + align:start position:0% +step + + + align:start position:0% +step +um well i'm assuming that the turing + + align:start position:0% +um well i'm assuming that the turing + + + align:start position:0% +um well i'm assuming that the turing +machine we're starting with is + + align:start position:0% +machine we're starting with is + + + align:start position:0% +machine we're starting with is +deterministic so this should be only one + + align:start position:0% +deterministic so this should be only one + + + align:start position:0% +deterministic so this should be only one +way to go so the answer to that + + align:start position:0% +way to go so the answer to that + + + align:start position:0% +way to go so the answer to that +question is yes + + align:start position:0% +question is yes + + + align:start position:0% +question is yes +this is going to be a unique + + align:start position:0% +this is going to be a unique + + + align:start position:0% +this is going to be a unique +um string here there's really going to + + align:start position:0% +um string here there's really going to + + + align:start position:0% +um string here there's really going to +be only one + + align:start position:0% +be only one + + + align:start position:0% +be only one +um + + align:start position:0% +um + + + align:start position:0% +um +computation history not that it really + + align:start position:0% +computation history not that it really + + + align:start position:0% +computation history not that it really +matters in a sense um the answer to that + + align:start position:0% +matters in a sense um the answer to that + + + align:start position:0% +matters in a sense um the answer to that +question um + + align:start position:0% +question um + + + align:start position:0% +question um +as long as that accepting computation + + align:start position:0% +as long as that accepting computation + + + align:start position:0% +as long as that accepting computation +history corresponds to the machine + + align:start position:0% +history corresponds to the machine + + + align:start position:0% +history corresponds to the machine +actually accepting + + align:start position:0% + + + + align:start position:0% + +uh oh boy we're all + + align:start position:0% +uh oh boy we're all + + + align:start position:0% +uh oh boy we're all +all over the place here uh okay + + align:start position:0% +all over the place here uh okay + + + align:start position:0% +all over the place here uh okay +are you ready to end this um + + align:start position:0% + + + + align:start position:0% + +in this um + + align:start position:0% +in this um + + + align:start position:0% +in this um +in this bowl + + align:start position:0% +in this bowl + + + align:start position:0% +in this bowl +uh + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +well this is where we are + + align:start position:0% +well this is where we are + + + align:start position:0% +well this is where we are +uh + + align:start position:0% +uh + + + align:start position:0% +uh +everybody who said they'd rather be in + + align:start position:0% +everybody who said they'd rather be in + + + align:start position:0% +everybody who said they'd rather be in +six or four fig six or four six i know + + align:start position:0% +six or four fig six or four six i know + + + align:start position:0% +six or four fig six or four six i know +who you are + + align:start position:0% +who you are + + + align:start position:0% +who you are +you're all + + align:start position:0% +you're all + + + align:start position:0% +you're all +going to be expelled + + align:start position:0% +going to be expelled + + + align:start position:0% +going to be expelled +no i'm joking uh + + align:start position:0% +no i'm joking uh + + + align:start position:0% +no i'm joking uh +i don't know who you are so um + + align:start position:0% +i don't know who you are so um + + + align:start position:0% +i don't know who you are so um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +yeah good + + align:start position:0% +yeah good + + + align:start position:0% +yeah good +so um + + align:start position:0% +so um + + + align:start position:0% +so um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +wha what so we are here at the at the + + align:start position:0% +wha what so we are here at the at the + + + align:start position:0% +wha what so we are here at the at the +break + + align:start position:0% +break + + + align:start position:0% +break +um i and i made this poll on purpose uh + + align:start position:0% +um i and i made this poll on purpose uh + + + align:start position:0% +um i and i made this poll on purpose uh +at this moment so we can spend a little + + align:start position:0% +at this moment so we can spend a little + + + align:start position:0% +at this moment so we can spend a little +time let me just start our clock going + + align:start position:0% +time let me just start our clock going + + + align:start position:0% +time let me just start our clock going +and i can try to help you those of you + + align:start position:0% +and i can try to help you those of you + + + align:start position:0% +and i can try to help you those of you +who are who answered see that you're + + align:start position:0% +who are who answered see that you're + + + align:start position:0% +who are who answered see that you're +baffled um + + align:start position:0% +baffled um + + + align:start position:0% +baffled um +i'll i can try to uh help you understand + + align:start position:0% +i'll i can try to uh help you understand + + + align:start position:0% +i'll i can try to uh help you understand +what's going on + + align:start position:0% +what's going on + + + align:start position:0% +what's going on +all right so this is a this is a good + + align:start position:0% +all right so this is a this is a good + + + align:start position:0% +all right so this is a this is a good +question here um + + align:start position:0% +question here um + + + align:start position:0% +question here um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +okay well okay there's several good + + align:start position:0% +okay well okay there's several good + + + align:start position:0% +okay well okay there's several good +questions here so um + + align:start position:0% +questions here so um + + + align:start position:0% +questions here so um +somebody asks why don't we just test all + + align:start position:0% +somebody asks why don't we just test all + + + align:start position:0% +somebody asks why don't we just test all +possible strings uh for b remember if + + align:start position:0% +possible strings uh for b remember if + + + align:start position:0% +possible strings uh for b remember if +we're trying to test emptiness + + align:start position:0% +we're trying to test emptiness + + + align:start position:0% +we're trying to test emptiness +for b's language + + align:start position:0% +for b's language + + + align:start position:0% +for b's language +um + + align:start position:0% +um + + + align:start position:0% +um +that's the e-lba problem + + align:start position:0% +that's the e-lba problem + + + align:start position:0% +that's the e-lba problem +nor do we just try all possible strings + + align:start position:0% +nor do we just try all possible strings + + + align:start position:0% +nor do we just try all possible strings +um + + align:start position:0% +um + + + align:start position:0% +um +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +that would work if we had enough time + + align:start position:0% +that would work if we had enough time + + + align:start position:0% +that would work if we had enough time +but there's infinitely many strings and + + align:start position:0% +but there's infinitely many strings and + + + align:start position:0% +but there's infinitely many strings and +so that's not going to be good if we're + + align:start position:0% +so that's not going to be good if we're + + + align:start position:0% +so that's not going to be good if we're +trying to be a decider + + align:start position:0% +trying to be a decider + + + align:start position:0% +trying to be a decider +so + + align:start position:0% + + + + align:start position:0% + +so that is + + align:start position:0% +so that is + + + align:start position:0% +so that is +that's why we don't just try all strings + + align:start position:0% +that's why we don't just try all strings + + + align:start position:0% +that's why we don't just try all strings +so but here's this other question here + + align:start position:0% +so but here's this other question here + + + align:start position:0% +so but here's this other question here +this is a + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +the question is how do we find the input + + align:start position:0% +the question is how do we find the input + + + align:start position:0% +the question is how do we find the input +x + + align:start position:0% +x + + + align:start position:0% +x +so this is an important question um + + align:start position:0% +so this is an important question um + + + align:start position:0% +so this is an important question um +because + + align:start position:0% +because + + + align:start position:0% +because +uh + + align:start position:0% +uh + + + align:start position:0% +uh +we don't find the input x + + align:start position:0% +we don't find the input x + + + align:start position:0% +we don't find the input x +there's no + + align:start position:0% +there's no + + + align:start position:0% +there's no +you know we + + align:start position:0% +you know we + + + align:start position:0% +you know we +the input x um at least the accepted + + align:start position:0% +the input x um at least the accepted + + + align:start position:0% +the input x um at least the accepted +input x would be the accepting + + align:start position:0% +input x would be the accepting + + + align:start position:0% +input x would be the accepting +computation history + + align:start position:0% +computation history + + + align:start position:0% +computation history +um + + align:start position:0% +um + + + align:start position:0% +um +for m on w + + align:start position:0% +for m on w + + + align:start position:0% +for m on w +we're never going to find it + + align:start position:0% +we're never going to find it + + + align:start position:0% +we're never going to find it +you know we're never going to find an x + + align:start position:0% +you know we're never going to find an x + + + align:start position:0% +you know we're never going to find an x +we're not we're building this um this + + align:start position:0% +we're not we're building this um this + + + align:start position:0% +we're not we're building this um this +lba + + align:start position:0% +lba + + + align:start position:0% +lba +not we're never going to run that lba + + align:start position:0% +not we're never going to run that lba + + + align:start position:0% +not we're never going to run that lba +we're designing that lba not for the + + align:start position:0% +we're designing that lba not for the + + + align:start position:0% +we're designing that lba not for the +purposes of running it + + align:start position:0% +purposes of running it + + + align:start position:0% +purposes of running it +we're building that lba only for the + + align:start position:0% +we're building that lba only for the + + + align:start position:0% +we're building that lba only for the +purpose + + align:start position:0% +purpose + + + align:start position:0% +purpose +of + + align:start position:0% +of + + + align:start position:0% +of +uh using the lba language emptiness + + align:start position:0% +uh using the lba language emptiness + + + align:start position:0% +uh using the lba language emptiness +tester we're going to build that end lba + + align:start position:0% +tester we're going to build that end lba + + + align:start position:0% +tester we're going to build that end lba +and feed it into the machine turing + + align:start position:0% +and feed it into the machine turing + + + align:start position:0% +and feed it into the machine turing +machine r + + align:start position:0% +machine r + + + align:start position:0% +machine r +which is going to tell us whether that + + align:start position:0% +which is going to tell us whether that + + + align:start position:0% +which is going to tell us whether that +lba's language is empty we ourselves is + + align:start position:0% +lba's language is empty we ourselves is + + + align:start position:0% +lba's language is empty we ourselves is +not never going to run that machine + + align:start position:0% +not never going to run that machine + + + align:start position:0% +not never going to run that machine +we're never going to come up with an x + + align:start position:0% +we're never going to come up with an x + + + align:start position:0% +we're never going to come up with an x +we're just having we're we're we are + + align:start position:0% +we're just having we're we're we are + + + align:start position:0% +we're just having we're we're we are +designing a computation + + align:start position:0% +designing a computation + + + align:start position:0% +designing a computation +checker + + align:start position:0% +checker + + + align:start position:0% +checker +and then + + align:start position:0% +and then + + + align:start position:0% +and then +um + + align:start position:0% +um + + + align:start position:0% +um +the emptiness tester for that + + align:start position:0% +the emptiness tester for that + + + align:start position:0% +the emptiness tester for that +that we assumed to exist for for + + align:start position:0% +that we assumed to exist for for + + + align:start position:0% +that we assumed to exist for for +elba is going to say yes there is some + + align:start position:0% +elba is going to say yes there is some + + + align:start position:0% +elba is going to say yes there is some +computation + + align:start position:0% +computation + + + align:start position:0% +computation +which this machine accepts or no there + + align:start position:0% +which this machine accepts or no there + + + align:start position:0% +which this machine accepts or no there +is no computation which this machine + + align:start position:0% +is no computation which this machine + + + align:start position:0% +is no computation which this machine +accepts and that's going to be a + + align:start position:0% +accepts and that's going to be a + + + align:start position:0% +accepts and that's going to be a +computation for m on w + + align:start position:0% +computation for m on w + + + align:start position:0% +computation for m on w +and so that's going to tell us whether + + align:start position:0% +and so that's going to tell us whether + + + align:start position:0% +and so that's going to tell us whether +or not m accepts w + + align:start position:0% +or not m accepts w + + + align:start position:0% +or not m accepts w +so we're never going to actually be + + align:start position:0% +so we're never going to actually be + + + align:start position:0% +so we're never going to actually be +finding an x we're never going to be + + align:start position:0% +finding an x we're never going to be + + + align:start position:0% +finding an x we're never going to be +running that lba + + align:start position:0% +running that lba + + + align:start position:0% +running that lba +we're just feeding using that lba + + align:start position:0% +we're just feeding using that lba + + + align:start position:0% +we're just feeding using that lba +as + + align:start position:0% +as + + + align:start position:0% +as +as an input + + align:start position:0% +as an input + + + align:start position:0% +as an input +to r + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +does the computation history method + + align:start position:0% +does the computation history method + + + align:start position:0% +does the computation history method +always use lbas no + + align:start position:0% +always use lbas no + + + align:start position:0% +always use lbas no +as you'll see uh right after the break + + align:start position:0% +as you'll see uh right after the break + + + align:start position:0% +as you'll see uh right after the break +because that's the lbas is just + + align:start position:0% +because that's the lbas is just + + + align:start position:0% +because that's the lbas is just +kind of an easy place to get started but + + align:start position:0% +kind of an easy place to get started but + + + align:start position:0% +kind of an easy place to get started but +we're going to use the computation + + align:start position:0% +we're going to use the computation + + + align:start position:0% +we're going to use the computation +history method and computation histories + + align:start position:0% +history method and computation histories + + + align:start position:0% +history method and computation histories +next on the on the post correspondence + + align:start position:0% +next on the on the post correspondence + + + align:start position:0% +next on the on the post correspondence +problem + + align:start position:0% + + + + align:start position:0% + +yes the the computation histories and + + align:start position:0% +yes the the computation histories and + + + align:start position:0% +yes the the computation histories and +the input x are always going to be + + align:start position:0% +the input x are always going to be + + + align:start position:0% +the input x are always going to be +finite + + align:start position:0% +finite + + + align:start position:0% +finite +so that that was an answer to a question + + align:start position:0% +so that that was an answer to a question + + + align:start position:0% +so that that was an answer to a question +about whether these histories or the + + align:start position:0% +about whether these histories or the + + + align:start position:0% +about whether these histories or the +inputs are going to be finite or not so + + align:start position:0% +inputs are going to be finite or not so + + + align:start position:0% +inputs are going to be finite or not so +the the they're all those strings are + + align:start position:0% +the the they're all those strings are + + + align:start position:0% +the the they're all those strings are +always going to be finite and the + + align:start position:0% +always going to be finite and the + + + align:start position:0% +always going to be finite and the +computation history is going to be + + align:start position:0% +computation history is going to be + + + align:start position:0% +computation history is going to be +finite + + align:start position:0% +finite + + + align:start position:0% +finite +um + + align:start position:0% +um + + + align:start position:0% +um +so we are at the end of our five minutes + + align:start position:0% +so we are at the end of our five minutes + + + align:start position:0% +so we are at the end of our five minutes +um let me just see if there was another + + align:start position:0% +um let me just see if there was another + + + align:start position:0% +um let me just see if there was another +question i wanted to answer + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +let me let's move on + + align:start position:0% +let me let's move on + + + align:start position:0% +let me let's move on +okay now + + align:start position:0% +okay now + + + align:start position:0% +okay now +getting coming back to the + + align:start position:0% +getting coming back to the + + + align:start position:0% +getting coming back to the +undecidability of this + + align:start position:0% +undecidability of this + + + align:start position:0% +undecidability of this +post-correspondence problem so remember + + align:start position:0% +post-correspondence problem so remember + + + align:start position:0% +post-correspondence problem so remember +the post course upon you know this this + + align:start position:0% +the post course upon you know this this + + + align:start position:0% +the post course upon you know this this +problem you're given those dominoes you + + align:start position:0% +problem you're given those dominoes you + + + align:start position:0% +problem you're given those dominoes you +want to know if there's a match here is + + align:start position:0% +want to know if there's a match here is + + + align:start position:0% +want to know if there's a match here is +a little mini version of the the diagram + + align:start position:0% +a little mini version of the the diagram + + + align:start position:0% +a little mini version of the the diagram +if that helps you remember it um + + align:start position:0% +if that helps you remember it um + + + align:start position:0% +if that helps you remember it um +and we're going to prove + + align:start position:0% +and we're going to prove + + + align:start position:0% +and we're going to prove +that this language is undecidable and so + + align:start position:0% +that this language is undecidable and so + + + align:start position:0% +that this language is undecidable and so +it's undecidable to test whether + + align:start position:0% +it's undecidable to test whether + + + align:start position:0% +it's undecidable to test whether +you have + + align:start position:0% + + + + align:start position:0% + +a match given a set of dominoes + + align:start position:0% +a match given a set of dominoes + + + align:start position:0% +a match given a set of dominoes +whether a match is possible + + align:start position:0% +whether a match is possible + + + align:start position:0% +whether a match is possible +and we're going to use we're going to + + align:start position:0% +and we're going to use we're going to + + + align:start position:0% +and we're going to use we're going to +reduce atm to to this language using the + + align:start position:0% +reduce atm to to this language using the + + + align:start position:0% +reduce atm to to this language using the +computation history method so how in the + + align:start position:0% +computation history method so how in the + + + align:start position:0% +computation history method so how in the +world are we going to do that + + align:start position:0% +world are we going to do that + + + align:start position:0% +world are we going to do that +um + + align:start position:0% +um + + + align:start position:0% +um +first of all there's a little detail + + align:start position:0% +first of all there's a little detail + + + align:start position:0% +first of all there's a little detail +here i want to mention + + align:start position:0% +here i want to mention + + + align:start position:0% +here i want to mention +uh just + + align:start position:0% + + + + align:start position:0% + +uh um + + align:start position:0% +uh um + + + align:start position:0% +uh um +don't focus on this but + + align:start position:0% +don't focus on this but + + + align:start position:0% +don't focus on this but +i'm going to assume the matches always + + align:start position:0% +i'm going to assume the matches always + + + align:start position:0% +i'm going to assume the matches always +start + + align:start position:0% +start + + + align:start position:0% +start +with the very first domino on the list + + align:start position:0% +with the very first domino on the list + + + align:start position:0% +with the very first domino on the list +um the very first domino in the + + align:start position:0% +um the very first domino in the + + + align:start position:0% +um the very first domino in the +collection + + align:start position:0% +collection + + + align:start position:0% +collection +so this is going to be like a starting + + align:start position:0% +so this is going to be like a starting + + + align:start position:0% +so this is going to be like a starting +domino this is going to make my proof a + + align:start position:0% +domino this is going to make my proof a + + + align:start position:0% +domino this is going to make my proof a +little simpler to do it that way and + + align:start position:0% +little simpler to do it that way and + + + align:start position:0% +little simpler to do it that way and +then you can fix that assumption uh + + align:start position:0% +then you can fix that assumption uh + + + align:start position:0% +then you can fix that assumption uh +later and if we have time at the end + + align:start position:0% +later and if we have time at the end + + + align:start position:0% +later and if we have time at the end +i'll do that or maybe after the lecture + + align:start position:0% +i'll do that or maybe after the lecture + + + align:start position:0% +i'll do that or maybe after the lecture +is over if there are questions i can + + align:start position:0% +is over if there are questions i can + + + align:start position:0% +is over if there are questions i can +show you how to fix that assumption but + + align:start position:0% +show you how to fix that assumption but + + + align:start position:0% +show you how to fix that assumption but +for now + + align:start position:0% +for now + + + align:start position:0% +for now +um to simplify the proof we're going to + + align:start position:0% +um to simplify the proof we're going to + + + align:start position:0% +um to simplify the proof we're going to +assume that there is a starting + + align:start position:0% +assume that there is a starting + + + align:start position:0% +assume that there is a starting +domino that the matches always have to + + align:start position:0% +domino that the matches always have to + + + align:start position:0% +domino that the matches always have to +start with that particular domino + + align:start position:0% +start with that particular domino + + + align:start position:0% +start with that particular domino +um + + align:start position:0% +um + + + align:start position:0% +um +if you didn't follow that point don't + + align:start position:0% +if you didn't follow that point don't + + + align:start position:0% +if you didn't follow that point don't +worry you can just ignore it you'll see + + align:start position:0% +worry you can just ignore it you'll see + + + align:start position:0% +worry you can just ignore it you'll see +where it comes up later + + align:start position:0% +where it comes up later + + + align:start position:0% +where it comes up later +so um now we're going to reduce atm to + + align:start position:0% +so um now we're going to reduce atm to + + + align:start position:0% +so um now we're going to reduce atm to +the pcp + + align:start position:0% +the pcp + + + align:start position:0% +the pcp +so assuming we have a machine that + + align:start position:0% +so assuming we have a machine that + + + align:start position:0% +so assuming we have a machine that +decides the pcp we're going to use that + + align:start position:0% +decides the pcp we're going to use that + + + align:start position:0% +decides the pcp we're going to use that +to make a machine that decides the atm + + align:start position:0% +to make a machine that decides the atm + + + align:start position:0% +to make a machine that decides the atm +as before so here's the turing machine s + + align:start position:0% +as before so here's the turing machine s + + + align:start position:0% +as before so here's the turing machine s +which is going to decide atm + + align:start position:0% +which is going to decide atm + + + align:start position:0% +which is going to decide atm +um + + align:start position:0% +um + + + align:start position:0% +um +and the way we're going to do it is like + + align:start position:0% +and the way we're going to do it is like + + + align:start position:0% +and the way we're going to do it is like +this + + align:start position:0% + + + + align:start position:0% + +we're given m and w we want to know + + align:start position:0% +we're given m and w we want to know + + + align:start position:0% +we're given m and w we want to know +as always + + align:start position:0% +as always + + + align:start position:0% +as always +does m accept w + + align:start position:0% +does m accept w + + + align:start position:0% +does m accept w +what we're going to do is we're going to + + align:start position:0% +what we're going to do is we're going to + + + align:start position:0% +what we're going to do is we're going to +build an instance + + align:start position:0% +build an instance + + + align:start position:0% +build an instance +of the pcp problem so we're going to + + align:start position:0% +of the pcp problem so we're going to + + + align:start position:0% +of the pcp problem so we're going to +build a bun a collection of dominoes + + align:start position:0% +build a bun a collection of dominoes + + + align:start position:0% +build a bun a collection of dominoes +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +uh which are going to dip + + align:start position:0% +uh which are going to dip + + + align:start position:0% +uh which are going to dip +and that collection is going to be built + + align:start position:0% +and that collection is going to be built + + + align:start position:0% +and that collection is going to be built +knowing m w so that's going to affect + + align:start position:0% +knowing m w so that's going to affect + + + align:start position:0% +knowing m w so that's going to affect +the dominoes we're going to create so + + align:start position:0% +the dominoes we're going to create so + + + align:start position:0% +the dominoes we're going to create so +this collection of dominoes is going to + + align:start position:0% +this collection of dominoes is going to + + + align:start position:0% +this collection of dominoes is going to +be called p sub mw + + align:start position:0% +be called p sub mw + + + align:start position:0% +be called p sub mw +depends on an m w + + align:start position:0% +depends on an m w + + + align:start position:0% +depends on an m w +and + + align:start position:0% +and + + + align:start position:0% +and +finding a match for this set of w + + align:start position:0% +finding a match for this set of w + + + align:start position:0% +finding a match for this set of w +is is going to force you to simulate + + align:start position:0% +is is going to force you to simulate + + + align:start position:0% +is is going to force you to simulate +m on w because the match is going to + + align:start position:0% +m on w because the match is going to + + + align:start position:0% +m on w because the match is going to +correspond to a computation history for + + align:start position:0% +correspond to a computation history for + + + align:start position:0% +correspond to a computation history for +m on w + + align:start position:0% +m on w + + + align:start position:0% +m on w +so uh we're going to use + + align:start position:0% +so uh we're going to use + + + align:start position:0% +so uh we're going to use +once we do that + + align:start position:0% +once we do that + + + align:start position:0% +once we do that +um once we build + + align:start position:0% +um once we build + + + align:start position:0% +um once we build +uh the set of dominoes who's where a + + align:start position:0% +uh the set of dominoes who's where a + + + align:start position:0% +uh the set of dominoes who's where a +match corresponds to a computation + + align:start position:0% +match corresponds to a computation + + + align:start position:0% +match corresponds to a computation +history + + align:start position:0% +history + + + align:start position:0% +history +we're going to use r to determine + + align:start position:0% +we're going to use r to determine + + + align:start position:0% +we're going to use r to determine +whether or not there is a match + + align:start position:0% +whether or not there is a match + + + align:start position:0% +whether or not there is a match +or in other words whether or not there + + align:start position:0% +or in other words whether or not there + + + align:start position:0% +or in other words whether or not there +is a computation history which is + + align:start position:0% +is a computation history which is + + + align:start position:0% +is a computation history which is +whether or not m accepts w + + align:start position:0% +whether or not m accepts w + + + align:start position:0% +whether or not m accepts w +um so if there is a match we're going to + + align:start position:0% +um so if there is a match we're going to + + + align:start position:0% +um so if there is a match we're going to +accept because we know m accepts w + + align:start position:0% +accept because we know m accepts w + + + align:start position:0% +accept because we know m accepts w +and if and if there is no uh match we're + + align:start position:0% +and if and if there is no uh match we're + + + align:start position:0% +and if and if there is no uh match we're +going to reject + + align:start position:0% +going to reject + + + align:start position:0% +going to reject +because we know m does not accept w + + align:start position:0% +because we know m does not accept w + + + align:start position:0% +because we know m does not accept w +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +this is the plan i haven't told you how + + align:start position:0% +this is the plan i haven't told you how + + + align:start position:0% +this is the plan i haven't told you how +to do this yet + + align:start position:0% + + + + align:start position:0% + +i mean i'm worried about the + + align:start position:0% +i mean i'm worried about the + + + align:start position:0% +i mean i'm worried about the +significant number of you who are + + align:start position:0% +significant number of you who are + + + align:start position:0% +significant number of you who are +feeling um + + align:start position:0% +feeling um + + + align:start position:0% +feeling um +confused by the method i mean you should + + align:start position:0% +confused by the method i mean you should + + + align:start position:0% +confused by the method i mean you should +you guys should be uh texting me in the + + align:start position:0% +you guys should be uh texting me in the + + + align:start position:0% +you guys should be uh texting me in the +tas + + align:start position:0% +tas + + + align:start position:0% +tas +um to try to at least get a sense of how + + align:start position:0% +um to try to at least get a sense of how + + + align:start position:0% +um to try to at least get a sense of how +this is working i mean that we're going + + align:start position:0% +this is working i mean that we're going + + + align:start position:0% +this is working i mean that we're going +to be going + + align:start position:0% +to be going + + + align:start position:0% +to be going +we're going to be doing the method again + + align:start position:0% +we're going to be doing the method again + + + align:start position:0% +we're going to be doing the method again +um it's just going to be a little more + + align:start position:0% +um it's just going to be a little more + + + align:start position:0% +um it's just going to be a little more +complicated because we have to also deal + + align:start position:0% +complicated because we have to also deal + + + align:start position:0% +complicated because we have to also deal +with these dominoes and all this all + + align:start position:0% +with these dominoes and all this all + + + align:start position:0% +with these dominoes and all this all +that stuff and that's why i presented it + + align:start position:0% +that stuff and that's why i presented it + + + align:start position:0% +that stuff and that's why i presented it +to the fir to you the first time + + align:start position:0% +to the fir to you the first time + + + align:start position:0% +to the fir to you the first time +in the setting of the lbas which where + + align:start position:0% +in the setting of the lbas which where + + + align:start position:0% +in the setting of the lbas which where +in a sense the method comes out + + align:start position:0% +in a sense the method comes out + + + align:start position:0% +in a sense the method comes out +perhaps more simply + + align:start position:0% + + + + align:start position:0% + +so a match is going to correspond to an + + align:start position:0% +so a match is going to correspond to an + + + align:start position:0% +so a match is going to correspond to an +accepting computation history + + align:start position:0% +accepting computation history + + + align:start position:0% +accepting computation history +um sometimes i + + align:start position:0% +um sometimes i + + + align:start position:0% +um sometimes i +if i don't use the word accepting + + align:start position:0% +if i don't use the word accepting + + + align:start position:0% +if i don't use the word accepting +um + + align:start position:0% +um + + + align:start position:0% +um +you know i'm just + + align:start position:0% +you know i'm just + + + align:start position:0% +you know i'm just +being a little sloppy + + align:start position:0% +being a little sloppy + + + align:start position:0% +being a little sloppy +computation history and accepting + + align:start position:0% +computation history and accepting + + + align:start position:0% +computation history and accepting +computation history for us right now + + align:start position:0% +computation history for us right now + + + align:start position:0% +computation history for us right now +they're the same + + align:start position:0% +they're the same + + + align:start position:0% +they're the same +i mean later on we may actually talk + + align:start position:0% +i mean later on we may actually talk + + + align:start position:0% +i mean later on we may actually talk +about rejecting computation histories + + align:start position:0% +about rejecting computation histories + + + align:start position:0% +about rejecting computation histories +but + + align:start position:0% +but + + + align:start position:0% +but +let's not + + align:start position:0% +let's not + + + align:start position:0% +let's not +get ourselves confused + + align:start position:0% +get ourselves confused + + + align:start position:0% +get ourselves confused +all the except computation histories + + align:start position:0% +all the except computation histories + + + align:start position:0% +all the except computation histories +always have to end with the machine + + align:start position:0% +always have to end with the machine + + + align:start position:0% +always have to end with the machine +accepting + + align:start position:0% + + + + align:start position:0% + +okay uh somebody's asking what does it + + align:start position:0% +okay uh somebody's asking what does it + + + align:start position:0% +okay uh somebody's asking what does it +mean for a match to correspond to a + + align:start position:0% +mean for a match to correspond to a + + + align:start position:0% +mean for a match to correspond to a +computation history you'll see that's + + align:start position:0% +computation history you'll see that's + + + align:start position:0% +computation history you'll see that's +going to be on my next slide + + align:start position:0% + + + + align:start position:0% + +oh so this is a good question um + + align:start position:0% +oh so this is a good question um + + + align:start position:0% +oh so this is a good question um +is my step two trying to use r to + + align:start position:0% +is my step two trying to use r to + + + align:start position:0% +is my step two trying to use r to +determine whether m accepts w + + align:start position:0% +determine whether m accepts w + + + align:start position:0% +determine whether m accepts w +well yes but i'm doing that by testing + + align:start position:0% +well yes but i'm doing that by testing + + + align:start position:0% +well yes but i'm doing that by testing +whether whether this these dominoes have + + align:start position:0% +whether whether this these dominoes have + + + align:start position:0% +whether whether this these dominoes have +a match + + align:start position:0% +a match + + + align:start position:0% +a match +because r + + align:start position:0% +because r + + + align:start position:0% +because r +is besides pcp i can only use r to test + + align:start position:0% +is besides pcp i can only use r to test + + + align:start position:0% +is besides pcp i can only use r to test +whether things have a match + + align:start position:0% +whether things have a match + + + align:start position:0% +whether things have a match +because someone asked + + align:start position:0% +because someone asked + + + align:start position:0% +because someone asked +should step two be to use r to determine + + align:start position:0% +should step two be to use r to determine + + + align:start position:0% +should step two be to use r to determine +whether m accepts w + + align:start position:0% +whether m accepts w + + + align:start position:0% +whether m accepts w +well in effect that's what it's doing + + align:start position:0% +well in effect that's what it's doing + + + align:start position:0% +well in effect that's what it's doing +but it's doing indirectly through + + align:start position:0% +but it's doing indirectly through + + + align:start position:0% +but it's doing indirectly through +um testing whether this + + align:start position:0% +um testing whether this + + + align:start position:0% +um testing whether this +um pcp whether these dominoes have a + + align:start position:0% +um pcp whether these dominoes have a + + + align:start position:0% +um pcp whether these dominoes have a +match because those dominoes are going + + align:start position:0% +match because those dominoes are going + + + align:start position:0% +match because those dominoes are going +to force you to simulate mlw + + align:start position:0% +to force you to simulate mlw + + + align:start position:0% +to force you to simulate mlw +okay i think i'm repeating myself here + + align:start position:0% +okay i think i'm repeating myself here + + + align:start position:0% +okay i think i'm repeating myself here +so let's uh avoid getting into a loop on + + align:start position:0% +so let's uh avoid getting into a loop on + + + align:start position:0% +so let's uh avoid getting into a loop on +the lecture and um + + align:start position:0% +the lecture and um + + + align:start position:0% +the lecture and um +uh see how we actually build piece of mw + + align:start position:0% +uh see how we actually build piece of mw + + + align:start position:0% +uh see how we actually build piece of mw +so now you understand what you have to + + align:start position:0% +so now you understand what you have to + + + align:start position:0% +so now you understand what you have to +under have the plan in your mind + + align:start position:0% +under have the plan in your mind + + + align:start position:0% +under have the plan in your mind +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +we are given m w + + align:start position:0% +we are given m w + + + align:start position:0% +we are given m w +we're trying to make a set of dominoes + + align:start position:0% +we're trying to make a set of dominoes + + + align:start position:0% +we're trying to make a set of dominoes +where a match is going to be + + align:start position:0% +where a match is going to be + + + align:start position:0% +where a match is going to be +a computation history for m w so the + + align:start position:0% +a computation history for m w so the + + + align:start position:0% +a computation history for m w so the +string you're going to get in that match + + align:start position:0% +string you're going to get in that match + + + align:start position:0% +string you're going to get in that match +the top string and the bottom string + + align:start position:0% +the top string and the bottom string + + + align:start position:0% +the top string and the bottom string +which are going to be you have to have + + align:start position:0% +which are going to be you have to have + + + align:start position:0% +which are going to be you have to have +to have to match + + align:start position:0% +to have to match + + + align:start position:0% +to have to match +um there they're going to be computation + + align:start position:0% +um there they're going to be computation + + + align:start position:0% +um there they're going to be computation +histories + + align:start position:0% +histories + + + align:start position:0% +histories +but they're going to be a computation + + align:start position:0% +but they're going to be a computation + + + align:start position:0% +but they're going to be a computation +history of m w so i want to figure out + + align:start position:0% +history of m w so i want to figure out + + + align:start position:0% +history of m w so i want to figure out +how to make my dominoes force that + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so my starting domino as i told you + + align:start position:0% +so my starting domino as i told you + + + align:start position:0% +so my starting domino as i told you +there's going to be a special starting + + align:start position:0% +there's going to be a special starting + + + align:start position:0% +there's going to be a special starting +domino in my collection so which is + + align:start position:0% +domino in my collection so which is + + + align:start position:0% +domino in my collection so which is +going to require the match to start with + + align:start position:0% +going to require the match to start with + + + align:start position:0% +going to require the match to start with +that domino it's going to be this one + + align:start position:0% +that domino it's going to be this one + + + align:start position:0% +that domino it's going to be this one +here + + align:start position:0% +here + + + align:start position:0% +here +it's going to have these two strings in + + align:start position:0% +it's going to have these two strings in + + + align:start position:0% +it's going to have these two strings in +it + + align:start position:0% +it + + + align:start position:0% +it +and you can see already it's starting to + + align:start position:0% +and you can see already it's starting to + + + align:start position:0% +and you can see already it's starting to +look like a + + align:start position:0% +look like a + + + align:start position:0% +look like a +a computation history + + align:start position:0% +a computation history + + + align:start position:0% +a computation history +the dominoes going to have that + + align:start position:0% +the dominoes going to have that + + + align:start position:0% +the dominoes going to have that +feature + + align:start position:0% +feature + + + align:start position:0% +feature +so + + align:start position:0% +so + + + align:start position:0% +so +uh it's the pair of strings and i've + + align:start position:0% +uh it's the pair of strings and i've + + + align:start position:0% +uh it's the pair of strings and i've +written it kind of to help you see + + align:start position:0% +written it kind of to help you see + + + align:start position:0% +written it kind of to help you see +what's kind of going on it's a pound + + align:start position:0% +what's kind of going on it's a pound + + + align:start position:0% +what's kind of going on it's a pound +sign on the top + + align:start position:0% +sign on the top + + + align:start position:0% +sign on the top +and the + + align:start position:0% +and the + + + align:start position:0% +and the +the starting configuration for mmw on + + align:start position:0% +the starting configuration for mmw on + + + align:start position:0% +the starting configuration for mmw on +the bottom + + align:start position:0% + + + + align:start position:0% + +and what i'm going to do for you here + + align:start position:0% +and what i'm going to do for you here + + + align:start position:0% +and what i'm going to do for you here +is at the bottom of the slide + + align:start position:0% +is at the bottom of the slide + + + align:start position:0% +is at the bottom of the slide +i'm going to take the dominoes i've + + align:start position:0% +i'm going to take the dominoes i've + + + align:start position:0% +i'm going to take the dominoes i've +written down so far and try to be + + align:start position:0% +written down so far and try to be + + + align:start position:0% +written down so far and try to be +building a match and you'll see how that + + align:start position:0% +building a match and you'll see how that + + + align:start position:0% +building a match and you'll see how that +match is forcing a simulation of the + + align:start position:0% +match is forcing a simulation of the + + + align:start position:0% +match is forcing a simulation of the +machine + + align:start position:0% +machine + + + align:start position:0% +machine +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let's take this as an illustration + + align:start position:0% +so let's take this as an illustration + + + align:start position:0% +so let's take this as an illustration +let's assume the input to m + + align:start position:0% +let's assume the input to m + + + align:start position:0% +let's assume the input to m +so i'm running m on w now i'm trying to + + align:start position:0% +so i'm running m on w now i'm trying to + + + align:start position:0% +so i'm running m on w now i'm trying to +see does m accept w + + align:start position:0% +see does m accept w + + + align:start position:0% +see does m accept w +um w is a string two two three + + align:start position:0% +um w is a string two two three + + + align:start position:0% +um w is a string two two three +so the + + align:start position:0% +so the + + + align:start position:0% +so the +start configuration for m on w + + align:start position:0% +start configuration for m on w + + + align:start position:0% +start configuration for m on w +is + + align:start position:0% +is + + + align:start position:0% +is +q zero that's the starting state for m + + align:start position:0% +q zero that's the starting state for m + + + align:start position:0% +q zero that's the starting state for m +and then w following is 2 2 3 that's + + align:start position:0% +and then w following is 2 2 3 that's + + + align:start position:0% +and then w following is 2 2 3 that's +what it's going to appear on the on the + + align:start position:0% +what it's going to appear on the on the + + + align:start position:0% +what it's going to appear on the on the +tape of the turing machine to start off + + align:start position:0% +tape of the turing machine to start off + + + align:start position:0% +tape of the turing machine to start off +so this is the start configuration + + align:start position:0% +so this is the start configuration + + + align:start position:0% +so this is the start configuration +for on w + + align:start position:0% +for on w + + + align:start position:0% +for on w +and + + align:start position:0% +and + + + align:start position:0% +and +assuming that i had this particular + + align:start position:0% +assuming that i had this particular + + + align:start position:0% +assuming that i had this particular +string is input string to w + + align:start position:0% +string is input string to w + + + align:start position:0% +string is input string to w +and so uh given the match + + align:start position:0% +and so uh given the match + + + align:start position:0% +and so uh given the match +the dominoes that i've given you so far + + align:start position:0% +the dominoes that i've given you so far + + + align:start position:0% +the dominoes that i've given you so far +just one + + align:start position:0% +just one + + + align:start position:0% +just one +um this is how the match is going to + + align:start position:0% +um this is how the match is going to + + + align:start position:0% +um this is how the match is going to +start + + align:start position:0% + + + + align:start position:0% + +uh now there's going to be more dominoes + + align:start position:0% +uh now there's going to be more dominoes + + + align:start position:0% +uh now there's going to be more dominoes +coming + + align:start position:0% +coming + + + align:start position:0% +coming +so for every possible tape symbol and + + align:start position:0% +so for every possible tape symbol and + + + align:start position:0% +so for every possible tape symbol and +state + + align:start position:0% +state + + + align:start position:0% +state +don't get confused by the language here + + align:start position:0% +don't get confused by the language here + + + align:start position:0% +don't get confused by the language here +this is the important thing if if in the + + align:start position:0% +this is the important thing if if in the + + + align:start position:0% +this is the important thing if if in the +turing machine + + align:start position:0% +turing machine + + + align:start position:0% +turing machine +um and i'll just read this in english to + + align:start position:0% +um and i'll just read this in english to + + + align:start position:0% +um and i'll just read this in english to +you if the turing machine when it's in + + align:start position:0% +you if the turing machine when it's in + + + align:start position:0% +you if the turing machine when it's in +state q + + align:start position:0% +state q + + + align:start position:0% +state q +and the head is reading an a + + align:start position:0% +and the head is reading an a + + + align:start position:0% +and the head is reading an a +it moves to state r + + align:start position:0% +it moves to state r + + + align:start position:0% +it moves to state r +writes a b at that point + + align:start position:0% +writes a b at that point + + + align:start position:0% +writes a b at that point +and its head moves to the right + + align:start position:0% +and its head moves to the right + + + align:start position:0% +and its head moves to the right +i'm focusing on right rightward moving + + align:start position:0% +i'm focusing on right rightward moving + + + align:start position:0% +i'm focusing on right rightward moving +uh + + align:start position:0% +uh + + + align:start position:0% +uh +turing machine steps right now + + align:start position:0% +turing machine steps right now + + + align:start position:0% +turing machine steps right now +but for every possible + + align:start position:0% +but for every possible + + + align:start position:0% +but for every possible +uh + + align:start position:0% +uh + + + align:start position:0% +uh +state and and tape symbol + + align:start position:0% +state and and tape symbol + + + align:start position:0% +state and and tape symbol +and looking at where what happens + + align:start position:0% +and looking at where what happens + + + align:start position:0% +and looking at where what happens +i'm going to have a + + align:start position:0% +i'm going to have a + + + align:start position:0% +i'm going to have a +domino that's going to capture this + + align:start position:0% +domino that's going to capture this + + + align:start position:0% +domino that's going to capture this +information + + align:start position:0% +information + + + align:start position:0% +information +and it's going to be this domino here + + align:start position:0% +and it's going to be this domino here + + + align:start position:0% +and it's going to be this domino here +q a + + align:start position:0% +q a + + + align:start position:0% +q a +on top + + align:start position:0% +on top + + + align:start position:0% +on top +br on the bottom so just the string qa + + align:start position:0% +br on the bottom so just the string qa + + + align:start position:0% +br on the bottom so just the string qa +on the top + + align:start position:0% +on the top + + + align:start position:0% +on the top +br on the bottom + + align:start position:0% +br on the bottom + + + align:start position:0% +br on the bottom +so let's see why with that sort of + + align:start position:0% +so let's see why with that sort of + + + align:start position:0% +so let's see why with that sort of +arcane looking + + align:start position:0% +arcane looking + + + align:start position:0% +arcane looking +why is that a good thing to why is that + + align:start position:0% +why is that a good thing to why is that + + + align:start position:0% +why is that a good thing to why is that +a useful domino to put in here + + align:start position:0% +a useful domino to put in here + + + align:start position:0% +a useful domino to put in here +well if you take a look + + align:start position:0% +well if you take a look + + + align:start position:0% +well if you take a look +um + + align:start position:0% + + + + align:start position:0% + +let's assume from my turing machine + + align:start position:0% +let's assume from my turing machine + + + align:start position:0% +let's assume from my turing machine +when it's in state q0 which is the + + align:start position:0% +when it's in state q0 which is the + + + align:start position:0% +when it's in state q0 which is the +starting state and the head is reading a + + align:start position:0% +starting state and the head is reading a + + + align:start position:0% +starting state and the head is reading a +two which it will happen to be reading + + align:start position:0% +two which it will happen to be reading + + + align:start position:0% +two which it will happen to be reading +because the + + align:start position:0% +because the + + + align:start position:0% +because the +uh this the string w starts with a two + + align:start position:0% +uh this the string w starts with a two + + + align:start position:0% +uh this the string w starts with a two +if it goes into state q4 no q7 and + + align:start position:0% +if it goes into state q4 no q7 and + + + align:start position:0% +if it goes into state q4 no q7 and +writes a four and then moves right + + align:start position:0% +writes a four and then moves right + + + align:start position:0% +writes a four and then moves right +i'm going to have in this in this domino + + align:start position:0% +i'm going to have in this in this domino + + + align:start position:0% +i'm going to have in this in this domino +i'm going to have + + align:start position:0% +i'm going to have + + + align:start position:0% +i'm going to have +q02 on top + + align:start position:0% +q02 on top + + + align:start position:0% +q02 on top +and 4 + + align:start position:0% +and 4 + + + align:start position:0% +and 4 +q7 on the bottom + + align:start position:0% +q7 on the bottom + + + align:start position:0% +q7 on the bottom +because 4 is what i wrote right here + + align:start position:0% +because 4 is what i wrote right here + + + align:start position:0% +because 4 is what i wrote right here +that's you know that's the b + + align:start position:0% +that's you know that's the b + + + align:start position:0% +that's you know that's the b +and this and the new state that i'm + + align:start position:0% +and this and the new state that i'm + + + align:start position:0% +and this and the new state that i'm +going into is q7 + + align:start position:0% +going into is q7 + + + align:start position:0% +going into is q7 +so that's going to be this + + align:start position:0% +so that's going to be this + + + align:start position:0% +so that's going to be this +the domino that i'm going to get + + align:start position:0% +the domino that i'm going to get + + + align:start position:0% +the domino that i'm going to get +and here it is here's that domino + + align:start position:0% +and here it is here's that domino + + + align:start position:0% +and here it is here's that domino +appearing in the match + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +it's going to take + + align:start position:0% +it's going to take + + + align:start position:0% +it's going to take +match up with q q 0 2 + + align:start position:0% +match up with q q 0 2 + + + align:start position:0% +match up with q q 0 2 +um + + align:start position:0% +um + + + align:start position:0% +um +which you know + + align:start position:0% +which you know + + + align:start position:0% +which you know +you know don't forget the the the top + + align:start position:0% +you know don't forget the the the top + + + align:start position:0% +you know don't forget the the the top +string has to equal the bottom string so + + align:start position:0% +string has to equal the bottom string so + + + align:start position:0% +string has to equal the bottom string so +and this is going to be the only choice + + align:start position:0% +and this is going to be the only choice + + + align:start position:0% +and this is going to be the only choice +that i have for extending the match so + + align:start position:0% +that i have for extending the match so + + + align:start position:0% +that i have for extending the match so +q02 um is going to be on the top when i + + align:start position:0% +q02 um is going to be on the top when i + + + align:start position:0% +q02 um is going to be on the top when i +put that there but that's going to force + + align:start position:0% +put that there but that's going to force + + + align:start position:0% +put that there but that's going to force +um 427 to appear at the bottom because + + align:start position:0% +um 427 to appear at the bottom because + + + align:start position:0% +um 427 to appear at the bottom because +that's what's going to be the bottom + + align:start position:0% +that's what's going to be the bottom + + + align:start position:0% +that's what's going to be the bottom +string corresponding to the q02 on the + + align:start position:0% +string corresponding to the q02 on the + + + align:start position:0% +string corresponding to the q02 on the +top + + align:start position:0% +top + + + align:start position:0% +top +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +if you're looking down here this is the + + align:start position:0% +if you're looking down here this is the + + + align:start position:0% +if you're looking down here this is the +the beginning of the second + + align:start position:0% +the beginning of the second + + + align:start position:0% +the beginning of the second +configuration of the machine that's what + + align:start position:0% +configuration of the machine that's what + + + align:start position:0% +configuration of the machine that's what +i want to be happening + + align:start position:0% +i want to be happening + + + align:start position:0% +i want to be happening +i want to be + + align:start position:0% +i want to be + + + align:start position:0% +i want to be +for + + align:start position:0% +for + + + align:start position:0% +for +that match should look like a + + align:start position:0% +that match should look like a + + + align:start position:0% +that match should look like a +computation history + + align:start position:0% + + + + align:start position:0% + +so now um so this is going to be all + + align:start position:0% +so now um so this is going to be all + + + align:start position:0% +so now um so this is going to be all +possible right moves are going to be + + align:start position:0% +possible right moves are going to be + + + align:start position:0% +possible right moves are going to be +handled in this way it's going to be a + + align:start position:0% +handled in this way it's going to be a + + + align:start position:0% +handled in this way it's going to be a +similar process for the left moves but + + align:start position:0% +similar process for the left moves but + + + align:start position:0% +similar process for the left moves but +let me not you know i'll leave that to + + align:start position:0% +let me not you know i'll leave that to + + + align:start position:0% +let me not you know i'll leave that to +your imagination + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% + + + + align:start position:0% + +how do i continue on from there what + + align:start position:0% +how do i continue on from there what + + + align:start position:0% +how do i continue on from there what +does the rest of this configuration look + + align:start position:0% +does the rest of this configuration look + + + align:start position:0% +does the rest of this configuration look +like + + align:start position:0% +like + + + align:start position:0% +like +well that should just be a copying over + + align:start position:0% +well that should just be a copying over + + + align:start position:0% +well that should just be a copying over +of the remaining symbols that were on + + align:start position:0% +of the remaining symbols that were on + + + align:start position:0% +of the remaining symbols that were on +the tape because they don't change + + align:start position:0% +the tape because they don't change + + + align:start position:0% +the tape because they don't change +things only change around the head + + align:start position:0% +things only change around the head + + + align:start position:0% +things only change around the head +the rest of those symbols which is the + + align:start position:0% +the rest of those symbols which is the + + + align:start position:0% +the rest of those symbols which is the +two and the three those should just get + + align:start position:0% +two and the three those should just get + + + align:start position:0% +two and the three those should just get +copied over here so i'm gonna have two + + align:start position:0% +copied over here so i'm gonna have two + + + align:start position:0% +copied over here so i'm gonna have two +additional + + align:start position:0% +additional + + + align:start position:0% +additional +i'm gonna have additional uh symbols in + + align:start position:0% +i'm gonna have additional uh symbols in + + + align:start position:0% +i'm gonna have additional uh symbols in +my dominoes in my uh + + align:start position:0% +my dominoes in my uh + + + align:start position:0% +my dominoes in my uh +in my collection so for every + + align:start position:0% +in my collection so for every + + + align:start position:0% +in my collection so for every +um + + align:start position:0% +um + + + align:start position:0% +um +tape symbol i'm gonna have a a + + align:start position:0% +tape symbol i'm gonna have a a + + + align:start position:0% +tape symbol i'm gonna have a a +be a + + align:start position:0% + + + + align:start position:0% + +domino so and for every type symbol a + + align:start position:0% +domino so and for every type symbol a + + + align:start position:0% +domino so and for every type symbol a +i'm going to have a a be a domino in my + + align:start position:0% +i'm going to have a a be a domino in my + + + align:start position:0% +i'm going to have a a be a domino in my +collection + + align:start position:0% +collection + + + align:start position:0% +collection +and so that says + + align:start position:0% +and so that says + + + align:start position:0% +and so that says +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i can have + + align:start position:0% +i can have + + + align:start position:0% +i can have +uh so that there's going to be a 2 2 + + align:start position:0% +uh so that there's going to be a 2 2 + + + align:start position:0% +uh so that there's going to be a 2 2 +domino so i can match up this 2 over + + align:start position:0% +domino so i can match up this 2 over + + + align:start position:0% +domino so i can match up this 2 over +here but that forces me to put a 2 down + + align:start position:0% +here but that forces me to put a 2 down + + + align:start position:0% +here but that forces me to put a 2 down +over there + + align:start position:0% +over there + + + align:start position:0% +over there +there's also going to be a 3 3 domino + + align:start position:0% +there's also going to be a 3 3 domino + + + align:start position:0% +there's also going to be a 3 3 domino +which is going to match up with that 3 + + align:start position:0% +which is going to match up with that 3 + + + align:start position:0% +which is going to match up with that 3 +but it's going to force me to push it + + align:start position:0% +but it's going to force me to push it + + + align:start position:0% +but it's going to force me to push it +put a 3 down over there that's the only + + align:start position:0% +put a 3 down over there that's the only + + + align:start position:0% +put a 3 down over there that's the only +way i can extend this + + align:start position:0% +way i can extend this + + + align:start position:0% +way i can extend this +um + + align:start position:0% +um + + + align:start position:0% +um +match that i've built so far + + align:start position:0% +match that i've built so far + + + align:start position:0% +match that i've built so far +i have no choice + + align:start position:0% +i have no choice + + + align:start position:0% +i have no choice +those are the only + + align:start position:0% +those are the only + + + align:start position:0% +those are the only +dominoes that i'm going to be given + + align:start position:0% +dominoes that i'm going to be given + + + align:start position:0% +dominoes that i'm going to be given +and by and so doing i'm forcing you to + + align:start position:0% +and by and so doing i'm forcing you to + + + align:start position:0% +and by and so doing i'm forcing you to +basically simulate the machine + + align:start position:0% +basically simulate the machine + + + align:start position:0% +basically simulate the machine +now what i want to have happen next is a + + align:start position:0% +now what i want to have happen next is a + + + align:start position:0% +now what i want to have happen next is a +pound sign to appear here and that will + + align:start position:0% +pound sign to appear here and that will + + + align:start position:0% +pound sign to appear here and that will +conclude my second configuration + + align:start position:0% +conclude my second configuration + + + align:start position:0% +conclude my second configuration +so there's going to be a pound sign + + align:start position:0% +so there's going to be a pound sign + + + align:start position:0% +so there's going to be a pound sign +pound sign domino as well because + + align:start position:0% +pound sign domino as well because + + + align:start position:0% +pound sign domino as well because +there's a pound sign here + + align:start position:0% +there's a pound sign here + + + align:start position:0% +there's a pound sign here +it's going to get matched with a pound + + align:start position:0% +it's going to get matched with a pound + + + align:start position:0% +it's going to get matched with a pound +sign up top forces a pound sign to come + + align:start position:0% +sign up top forces a pound sign to come + + + align:start position:0% +sign up top forces a pound sign to come +down um on the bottom + + align:start position:0% +down um on the bottom + + + align:start position:0% +down um on the bottom +and if you look at where we are right + + align:start position:0% +and if you look at where we are right + + + align:start position:0% +and if you look at where we are right +now we're exactly like where we were at + + align:start position:0% +now we're exactly like where we were at + + + align:start position:0% +now we're exactly like where we were at +the beginning when we had just this + + align:start position:0% +the beginning when we had just this + + + align:start position:0% +the beginning when we had just this +first domino appearing but now we're one + + align:start position:0% +first domino appearing but now we're one + + + align:start position:0% +first domino appearing but now we're one +configuration later + + align:start position:0% + + + + align:start position:0% + +so if you understood that + + align:start position:0% +so if you understood that + + + align:start position:0% +so if you understood that +and i admit it it's it's + + align:start position:0% +and i admit it it's it's + + + align:start position:0% +and i admit it it's it's +you know this is a there's just one idea + + align:start position:0% +you know this is a there's just one idea + + + align:start position:0% +you know this is a there's just one idea +here um + + align:start position:0% +here um + + + align:start position:0% +here um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and + + align:start position:0% +and + + + align:start position:0% +and +once you get the idea + + align:start position:0% +once you get the idea + + + align:start position:0% +once you get the idea +it's all trivial it's all very simple + + align:start position:0% +it's all trivial it's all very simple + + + align:start position:0% +it's all trivial it's all very simple +but there's just you have to get that + + align:start position:0% +but there's just you have to get that + + + align:start position:0% +but there's just you have to get that +idea i'm trying to figure out how to get + + align:start position:0% +idea i'm trying to figure out how to get + + + align:start position:0% +idea i'm trying to figure out how to get +that idea into your head once you get + + align:start position:0% +that idea into your head once you get + + + align:start position:0% +that idea into your head once you get +the idea you can write all this stuff + + align:start position:0% +the idea you can write all this stuff + + + align:start position:0% +the idea you can write all this stuff +yourself + + align:start position:0% +yourself + + + align:start position:0% +yourself +um + + align:start position:0% +um + + + align:start position:0% +um +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +so following the this uh the this + + align:start position:0% +so following the this uh the this + + + align:start position:0% +so following the this uh the this +description of how uh the you know the + + align:start position:0% +description of how uh the you know the + + + align:start position:0% +description of how uh the you know the +the transition function of the machine + + align:start position:0% +the transition function of the machine + + + align:start position:0% +the transition function of the machine +works and copying over uh the symbols + + align:start position:0% +works and copying over uh the symbols + + + align:start position:0% +works and copying over uh the symbols +from the tape to the next configuration + + align:start position:0% +from the tape to the next configuration + + + align:start position:0% +from the tape to the next configuration +i'm going to be able to get + + align:start position:0% +i'm going to be able to get + + + align:start position:0% +i'm going to be able to get +configuration after configuration going + + align:start position:0% +configuration after configuration going + + + align:start position:0% +configuration after configuration going +until i get to a point when there's an + + align:start position:0% +until i get to a point when there's an + + + align:start position:0% +until i get to a point when there's an +accept + + align:start position:0% + + + + align:start position:0% + +and now from the machine's perspective + + align:start position:0% +and now from the machine's perspective + + + align:start position:0% +and now from the machine's perspective +we're done + + align:start position:0% +we're done + + + align:start position:0% +we're done +the machine has accepted its input this + + align:start position:0% +the machine has accepted its input this + + + align:start position:0% +the machine has accepted its input this +is our computation history but is it a + + align:start position:0% +is our computation history but is it a + + + align:start position:0% +is our computation history but is it a +match + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +you know up until this this bottom thing + + align:start position:0% +you know up until this this bottom thing + + + align:start position:0% +you know up until this this bottom thing +um is the computation history but it's + + align:start position:0% +um is the computation history but it's + + + align:start position:0% +um is the computation history but it's +not a match because the top doesn't + + align:start position:0% +not a match because the top doesn't + + + align:start position:0% +not a match because the top doesn't +equal the bottom there's still extra + + align:start position:0% +equal the bottom there's still extra + + + align:start position:0% +equal the bottom there's still extra +stuff at the bottom which the top is not + + align:start position:0% +stuff at the bottom which the top is not + + + align:start position:0% +stuff at the bottom which the top is not +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know + + align:start position:0% +you know + + + align:start position:0% +you know +it doesn't have + + align:start position:0% +it doesn't have + + + align:start position:0% +it doesn't have +so what i'm going to need to do now is + + align:start position:0% +so what i'm going to need to do now is + + + align:start position:0% +so what i'm going to need to do now is +is add some additional kind of + + align:start position:0% +is add some additional kind of + + + align:start position:0% +is add some additional kind of +pseudo steps of the machine + + align:start position:0% +pseudo steps of the machine + + + align:start position:0% +pseudo steps of the machine +where i'm going to allow + + align:start position:0% +where i'm going to allow + + + align:start position:0% +where i'm going to allow +the top to catch up to the bottom + + align:start position:0% +the top to catch up to the bottom + + + align:start position:0% +the top to catch up to the bottom +and the way i'm going to be thinking + + align:start position:0% +and the way i'm going to be thinking + + + align:start position:0% +and the way i'm going to be thinking +about that and this is not real for a + + align:start position:0% +about that and this is not real for a + + + align:start position:0% +about that and this is not real for a +turning machine as much as the turn + + align:start position:0% +turning machine as much as the turn + + + align:start position:0% +turning machine as much as the turn +machine's real anyway but you're going + + align:start position:0% +machine's real anyway but you're going + + + align:start position:0% +machine's real anyway but you're going +to imagine i'm going to add + + align:start position:0% +to imagine i'm going to add + + + align:start position:0% +to imagine i'm going to add +a new kind of uh move to the machine + + align:start position:0% +a new kind of uh move to the machine + + + align:start position:0% +a new kind of uh move to the machine +which is going to allow the head to eat + + align:start position:0% +which is going to allow the head to eat + + + align:start position:0% +which is going to allow the head to eat +the symbols off the tape + + align:start position:0% +the symbols off the tape + + + align:start position:0% +the symbols off the tape +like pac-man + + align:start position:0% +like pac-man + + + align:start position:0% +like pac-man +okay and the way i'm gonna get that + + align:start position:0% +okay and the way i'm gonna get that + + + align:start position:0% +okay and the way i'm gonna get that +effect um + + align:start position:0% + + + + align:start position:0% + +on the top if i have any tape symbol + + align:start position:0% +on the top if i have any tape symbol + + + align:start position:0% +on the top if i have any tape symbol +next to a cue except on either side + + align:start position:0% +next to a cue except on either side + + + align:start position:0% +next to a cue except on either side +on the top + + align:start position:0% +on the top + + + align:start position:0% +on the top +what i'm going to get you to write on + + align:start position:0% +what i'm going to get you to write on + + + align:start position:0% +what i'm going to get you to write on +the bottom is just to accept with that + + align:start position:0% +the bottom is just to accept with that + + + align:start position:0% +the bottom is just to accept with that +taste with that tape symbol gone + + align:start position:0% +taste with that tape symbol gone + + + align:start position:0% +taste with that tape symbol gone +and by repeating that + + align:start position:0% +and by repeating that + + + align:start position:0% +and by repeating that +you know move after move the the the + + align:start position:0% +you know move after move the the the + + + align:start position:0% +you know move after move the the the +actual tape is going to be shrinking the + + align:start position:0% +actual tape is going to be shrinking the + + + align:start position:0% +actual tape is going to be shrinking the +symbols on the tape are going to be + + align:start position:0% +symbols on the tape are going to be + + + align:start position:0% +symbols on the tape are going to be +going down one by one move by move until + + align:start position:0% +going down one by one move by move until + + + align:start position:0% +going down one by one move by move until +there's nothing left except just the um + + align:start position:0% +there's nothing left except just the um + + + align:start position:0% +there's nothing left except just the um +you accept all by itself + + align:start position:0% +you accept all by itself + + + align:start position:0% +you accept all by itself +okay so i have this sort of pac-man idea + + align:start position:0% +okay so i have this sort of pac-man idea + + + align:start position:0% +okay so i have this sort of pac-man idea +of eating the symbols on the tape um + + align:start position:0% +of eating the symbols on the tape um + + + align:start position:0% +of eating the symbols on the tape um +and then + + align:start position:0% +and then + + + align:start position:0% +and then +finally i get to a point when there's + + align:start position:0% +finally i get to a point when there's + + + align:start position:0% +finally i get to a point when there's +just the cue except + + align:start position:0% +just the cue except + + + align:start position:0% +just the cue except +alone on the tape there's no symbols + + align:start position:0% +alone on the tape there's no symbols + + + align:start position:0% +alone on the tape there's no symbols +left to consume + + align:start position:0% +left to consume + + + align:start position:0% +left to consume +and then i'm going to add one last + + align:start position:0% +and then i'm going to add one last + + + align:start position:0% +and then i'm going to add one last +domino here which is q accept pound + + align:start position:0% +domino here which is q accept pound + + + align:start position:0% +domino here which is q accept pound +pound matching with just pound which + + align:start position:0% +pound matching with just pound which + + + align:start position:0% +pound matching with just pound which +just conveniently + + align:start position:0% + + + + align:start position:0% + +finishes off the um + + align:start position:0% +finishes off the um + + + align:start position:0% +finishes off the um +uh the + + align:start position:0% +uh the + + + align:start position:0% +uh the +uh the match + + align:start position:0% +uh the match + + + align:start position:0% +uh the match +and so the match is completed + + align:start position:0% +and so the match is completed + + + align:start position:0% +and so the match is completed +there's actually a little detail here i + + align:start position:0% +there's actually a little detail here i + + + align:start position:0% +there's actually a little detail here i +i hesitate even to bring it up because i + + align:start position:0% +i hesitate even to bring it up because i + + + align:start position:0% +i hesitate even to bring it up because i +i think it's a kind of thing where if + + align:start position:0% +i think it's a kind of thing where if + + + align:start position:0% +i think it's a kind of thing where if +you understand everything up to this + + align:start position:0% +you understand everything up to this + + + align:start position:0% +you understand everything up to this +point you could fill it in yourself but + + align:start position:0% +point you could fill it in yourself but + + + align:start position:0% +point you could fill it in yourself but +just for completeness sake + + align:start position:0% +just for completeness sake + + + align:start position:0% +just for completeness sake +uh you have to deal with the situation + + align:start position:0% +uh you have to deal with the situation + + + align:start position:0% +uh you have to deal with the situation +when the the + + align:start position:0% +when the the + + + align:start position:0% +when the the +uh the head + + align:start position:0% +uh the head + + + align:start position:0% +uh the head +um of the turing machine + + align:start position:0% +um of the turing machine + + + align:start position:0% +um of the turing machine +might move into the blank portion of the + + align:start position:0% +might move into the blank portion of the + + + align:start position:0% +might move into the blank portion of the +tape + + align:start position:0% +tape + + + align:start position:0% +tape +which is not taken into account here and + + align:start position:0% +which is not taken into account here and + + + align:start position:0% +which is not taken into account here and +the way we get that effect is by having + + align:start position:0% +the way we get that effect is by having + + + align:start position:0% +the way we get that effect is by having +another domino here which allows me to + + align:start position:0% +another domino here which allows me to + + + align:start position:0% +another domino here which allows me to +add blank symbols at the bottom as + + align:start position:0% +add blank symbols at the bottom as + + + align:start position:0% +add blank symbols at the bottom as +needed + + align:start position:0% +needed + + + align:start position:0% +needed +that's just a detail + + align:start position:0% +that's just a detail + + + align:start position:0% +that's just a detail +you know i'm more worried that you + + align:start position:0% +you know i'm more worried that you + + + align:start position:0% +you know i'm more worried that you +understand the underlying concept um + + align:start position:0% +understand the underlying concept um + + + align:start position:0% +understand the underlying concept um +so here's going to be um + + align:start position:0% +so here's going to be um + + + align:start position:0% +so here's going to be um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +a check-in um + + align:start position:0% +a check-in um + + + align:start position:0% +a check-in um +trying to remember + + align:start position:0% +trying to remember + + + align:start position:0% +trying to remember +um + + align:start position:0% + + + + align:start position:0% + +okay but you know + + align:start position:0% +okay but you know + + + align:start position:0% +okay but you know +so okay so + + align:start position:0% +so okay so + + + align:start position:0% +so okay so +what else can we conclude from this + + align:start position:0% +what else can we conclude from this + + + align:start position:0% +what else can we conclude from this +information + + align:start position:0% +information + + + align:start position:0% +information +we know so at this point we know that + + align:start position:0% +we know so at this point we know that + + + align:start position:0% +we know so at this point we know that +pcp is undecidable that's what we just + + align:start position:0% +pcp is undecidable that's what we just + + + align:start position:0% +pcp is undecidable that's what we just +finished proving + + align:start position:0% +finished proving + + + align:start position:0% +finished proving +what else do we know + + align:start position:0% +what else do we know + + + align:start position:0% +what else do we know +if anything + + align:start position:0% +if anything + + + align:start position:0% +if anything +or do we even know that + + align:start position:0% +or do we even know that + + + align:start position:0% +or do we even know that +uh see my picture is a little bit + + align:start position:0% +uh see my picture is a little bit + + + align:start position:0% +uh see my picture is a little bit +covering the check in but it's still + + align:start position:0% +covering the check in but it's still + + + align:start position:0% +covering the check in but it's still +readable + + align:start position:0% + + + + align:start position:0% + +so i mean this is not an easy concept to + + align:start position:0% +so i mean this is not an easy concept to + + + align:start position:0% +so i mean this is not an easy concept to +get the to get the idea but once you get + + align:start position:0% +get the to get the idea but once you get + + + align:start position:0% +get the to get the idea but once you get +it + + align:start position:0% +it + + + align:start position:0% +it +you know it's um + + align:start position:0% +you know it's um + + + align:start position:0% +you know it's um +you know it's you'll see it's not that + + align:start position:0% +you know it's you'll see it's not that + + + align:start position:0% +you know it's you'll see it's not that +bad + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +another 15 seconds + + align:start position:0% + + + + align:start position:0% + +so this portion doesn't this question is + + align:start position:0% +so this portion doesn't this question is + + + align:start position:0% +so this portion doesn't this question is +not really relying so much on the + + align:start position:0% +not really relying so much on the + + + align:start position:0% +not really relying so much on the +computation history method it's just + + align:start position:0% +computation history method it's just + + + align:start position:0% +computation history method it's just +relying on the fact about + + align:start position:0% +relying on the fact about + + + align:start position:0% +relying on the fact about +pcp being undecidable + + align:start position:0% +pcp being undecidable + + + align:start position:0% +pcp being undecidable +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +okay everybody + + align:start position:0% +okay everybody + + + align:start position:0% +okay everybody +almost done + + align:start position:0% +almost done + + + align:start position:0% +almost done +five seconds + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um + + align:start position:0% + + + + align:start position:0% + +so i can see that there is uh + + align:start position:0% +so i can see that there is uh + + + align:start position:0% +so i can see that there is uh +some level of confusion um + + align:start position:0% + + + + align:start position:0% + +uh so the reason why b is correct + + align:start position:0% + + + + align:start position:0% + +is that + + align:start position:0% +is that + + + align:start position:0% +is that +we know pcp is undecidable + + align:start position:0% +we know pcp is undecidable + + + align:start position:0% +we know pcp is undecidable +but + + align:start position:0% +but + + + align:start position:0% +but +we also know that it's recognizable + + align:start position:0% +we also know that it's recognizable + + + align:start position:0% +we also know that it's recognizable +because you could try all possible + + align:start position:0% +because you could try all possible + + + align:start position:0% +because you could try all possible +uh ways of combining dominoes + + align:start position:0% +uh ways of combining dominoes + + + align:start position:0% +uh ways of combining dominoes +and + + align:start position:0% +and + + + align:start position:0% +and +one after the + + align:start position:0% +one after the + + + align:start position:0% +one after the +next um and you accept if you ever find + + align:start position:0% +next um and you accept if you ever find + + + align:start position:0% +next um and you accept if you ever find +a match + + align:start position:0% +a match + + + align:start position:0% +a match +so they might go forever but if there is + + align:start position:0% +so they might go forever but if there is + + + align:start position:0% +so they might go forever but if there is +a match + + align:start position:0% +a match + + + align:start position:0% +a match +uh possible you'll find it eventually so + + align:start position:0% +uh possible you'll find it eventually so + + + align:start position:0% +uh possible you'll find it eventually so +pcp is a recognizable language + + align:start position:0% +pcp is a recognizable language + + + align:start position:0% +pcp is a recognizable language +undecidable and so therefore we know + + align:start position:0% +undecidable and so therefore we know + + + align:start position:0% +undecidable and so therefore we know +it's complement it has to be + + align:start position:0% +it's complement it has to be + + + align:start position:0% +it's complement it has to be +unrecognizable because you know that's + + align:start position:0% +unrecognizable because you know that's + + + align:start position:0% +unrecognizable because you know that's +something we've shown before if a + + align:start position:0% +something we've shown before if a + + + align:start position:0% +something we've shown before if a +language and its complement are both + + align:start position:0% +language and its complement are both + + + align:start position:0% +language and its complement are both +recognizable then it's decidable but we + + align:start position:0% +recognizable then it's decidable but we + + + align:start position:0% +recognizable then it's decidable but we +know pcp is not decidable so they both + + align:start position:0% +know pcp is not decidable so they both + + + align:start position:0% +know pcp is not decidable so they both +both sides can't be recognizable + + align:start position:0% +both sides can't be recognizable + + + align:start position:0% +both sides can't be recognizable +um okay so let's + + align:start position:0% + + + + align:start position:0% + +let me prove to you one last theorem + + align:start position:0% +let me prove to you one last theorem + + + align:start position:0% +let me prove to you one last theorem +that's going to be useful for your + + align:start position:0% +that's going to be useful for your + + + align:start position:0% +that's going to be useful for your +homework + + align:start position:0% +homework + + + align:start position:0% +homework +uh involving the computation history + + align:start position:0% +uh involving the computation history + + + align:start position:0% +uh involving the computation history +method so you'll have one last chance + + align:start position:0% +method so you'll have one last chance + + + align:start position:0% +method so you'll have one last chance +to get the + + align:start position:0% +to get the + + + align:start position:0% +to get the +way we're going to use this though this + + align:start position:0% +way we're going to use this though this + + + align:start position:0% +way we're going to use this though this +one is going to be a little bit more + + align:start position:0% +one is going to be a little bit more + + + align:start position:0% +one is going to be a little bit more +similar in spirit + + align:start position:0% +similar in spirit + + + align:start position:0% +similar in spirit +to the lba version + + align:start position:0% +to the lba version + + + align:start position:0% +to the lba version +uh than to the pcp version which has + + align:start position:0% +uh than to the pcp version which has + + + align:start position:0% +uh than to the pcp version which has +this extra kind of complication about + + align:start position:0% +this extra kind of complication about + + + align:start position:0% +this extra kind of complication about +coding the computations of the machine + + align:start position:0% +coding the computations of the machine + + + align:start position:0% +coding the computations of the machine +into dominoes here um you know we're + + align:start position:0% +into dominoes here um you know we're + + + align:start position:0% +into dominoes here um you know we're +going to operate with another automaton + + align:start position:0% +going to operate with another automaton + + + align:start position:0% +going to operate with another automaton +which where it's going to be more + + align:start position:0% +which where it's going to be more + + + align:start position:0% +which where it's going to be more +straightforward but anyway okay getting + + align:start position:0% +straightforward but anyway okay getting + + + align:start position:0% +straightforward but anyway okay getting +ahead of myself + + align:start position:0% +ahead of myself + + + align:start position:0% +ahead of myself +so if you remember for the for + + align:start position:0% +so if you remember for the for + + + align:start position:0% +so if you remember for the for +context-free grammars we had the + + align:start position:0% +context-free grammars we had the + + + align:start position:0% +context-free grammars we had the +problem the emptiness problem + + align:start position:0% +problem the emptiness problem + + + align:start position:0% +problem the emptiness problem +we showed that was decidable + + align:start position:0% +we showed that was decidable + + + align:start position:0% +we showed that was decidable +so testing whether a context-free + + align:start position:0% +so testing whether a context-free + + + align:start position:0% +so testing whether a context-free +grammar's language is empty + + align:start position:0% +grammar's language is empty + + + align:start position:0% +grammar's language is empty +is decidable + + align:start position:0% +is decidable + + + align:start position:0% +is decidable +however testing whether a context-free + + align:start position:0% +however testing whether a context-free + + + align:start position:0% +however testing whether a context-free +grammar's language is everything whether + + align:start position:0% +grammar's language is everything whether + + + align:start position:0% +grammar's language is everything whether +it's equal to sigma star + + align:start position:0% +it's equal to sigma star + + + align:start position:0% +it's equal to sigma star +that turns out to be um + + align:start position:0% +that turns out to be um + + + align:start position:0% +that turns out to be um +uh that turns out to be undecidable + + align:start position:0% +uh that turns out to be undecidable + + + align:start position:0% +uh that turns out to be undecidable +okay so emptiness testing for + + align:start position:0% +okay so emptiness testing for + + + align:start position:0% +okay so emptiness testing for +context-free grammars decidable + + align:start position:0% +context-free grammars decidable + + + align:start position:0% +context-free grammars decidable +sigma-star testing + + align:start position:0% +sigma-star testing + + + align:start position:0% +sigma-star testing +undecidable + + align:start position:0% +undecidable + + + align:start position:0% +undecidable +um + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +we'll show that atm is reducible to all + + align:start position:0% +we'll show that atm is reducible to all + + + align:start position:0% +we'll show that atm is reducible to all +pda via the computation history method + + align:start position:0% +pda via the computation history method + + + align:start position:0% +pda via the computation history method +um + + align:start position:0% +um + + + align:start position:0% +um +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +so uh assume we have same patterns + + align:start position:0% +so uh assume we have same patterns + + + align:start position:0% +so uh assume we have same patterns +assuming we have a decider for all pda + + align:start position:0% +assuming we have a decider for all pda + + + align:start position:0% +assuming we have a decider for all pda +and make a decider for ulti + + align:start position:0% +and make a decider for ulti + + + align:start position:0% +and make a decider for ulti +decider for atm + + align:start position:0% +decider for atm + + + align:start position:0% +decider for atm +here's the atm decider + + align:start position:0% +here's the atm decider + + + align:start position:0% +here's the atm decider +and now + + align:start position:0% +and now + + + align:start position:0% +and now +similar to what we did for the + + align:start position:0% +similar to what we did for the + + + align:start position:0% +similar to what we did for the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +lba case but with a with a twist + + align:start position:0% +lba case but with a with a twist + + + align:start position:0% +lba case but with a with a twist +we're going to make a push down + + align:start position:0% +we're going to make a push down + + + align:start position:0% +we're going to make a push down +automaton + + align:start position:0% +automaton + + + align:start position:0% +automaton +that's going to check its input to see + + align:start position:0% +that's going to check its input to see + + + align:start position:0% +that's going to check its input to see +whether it's an accepting computation + + align:start position:0% +whether it's an accepting computation + + + align:start position:0% +whether it's an accepting computation +history of m w just like the lba did if + + align:start position:0% +history of m w just like the lba did if + + + align:start position:0% +history of m w just like the lba did if +you think back to how that worked + + align:start position:0% +you think back to how that worked + + + align:start position:0% +you think back to how that worked +remember remember you know we um the lba + + align:start position:0% +remember remember you know we um the lba + + + align:start position:0% +remember remember you know we um the lba +tested its input to see whether it's uh + + align:start position:0% +tested its input to see whether it's uh + + + align:start position:0% +tested its input to see whether it's uh +an accepting computation history accept + + align:start position:0% +an accepting computation history accept + + + align:start position:0% +an accepting computation history accept +it if it did and then we test the lba's + + align:start position:0% +it if it did and then we test the lba's + + + align:start position:0% +it if it did and then we test the lba's +language for emptiness to see if there + + align:start position:0% +language for emptiness to see if there + + + align:start position:0% +language for emptiness to see if there +are any computation histories so we're + + align:start position:0% +are any computation histories so we're + + + align:start position:0% +are any computation histories so we're +doing the same kind of thing + + align:start position:0% +doing the same kind of thing + + + align:start position:0% +doing the same kind of thing +except now + + align:start position:0% +except now + + + align:start position:0% +except now +uh the pda is going to test its input to + + align:start position:0% +uh the pda is going to test its input to + + + align:start position:0% +uh the pda is going to test its input to +see whether it's a an accepting + + align:start position:0% +see whether it's a an accepting + + + align:start position:0% +see whether it's a an accepting +computation history and if it is it's + + align:start position:0% +computation history and if it is it's + + + align:start position:0% +computation history and if it is it's +going to reject + + align:start position:0% +going to reject + + + align:start position:0% +going to reject +it's going to do + + align:start position:0% +it's going to do + + + align:start position:0% +it's going to do +the reverse of what the lba + + align:start position:0% +the reverse of what the lba + + + align:start position:0% +the reverse of what the lba +did + + align:start position:0% +did + + + align:start position:0% +did +and that's going to turn out to be + + align:start position:0% +and that's going to turn out to be + + + align:start position:0% +and that's going to turn out to be +necessary but for the for the moment + + align:start position:0% +necessary but for the for the moment + + + align:start position:0% +necessary but for the for the moment +let's just go with it and maybe we'll + + align:start position:0% +let's just go with it and maybe we'll + + + align:start position:0% +let's just go with it and maybe we'll +see in the proof why the proof needs it + + align:start position:0% +see in the proof why the proof needs it + + + align:start position:0% +see in the proof why the proof needs it +to be this way + + align:start position:0% +to be this way + + + align:start position:0% +to be this way +so um this p pushdown automaton is going + + align:start position:0% +so um this p pushdown automaton is going + + + align:start position:0% +so um this p pushdown automaton is going +to accept its input if it's not + + align:start position:0% +to accept its input if it's not + + + align:start position:0% +to accept its input if it's not +an accepting computation history for m + + align:start position:0% +an accepting computation history for m + + + align:start position:0% +an accepting computation history for m +on w otherwise it will accept so you can + + align:start position:0% +on w otherwise it will accept so you can + + + align:start position:0% +on w otherwise it will accept so you can +think of this pda + + align:start position:0% +think of this pda + + + align:start position:0% +think of this pda +as + + align:start position:0% +as + + + align:start position:0% +as +accepting all the junk + + align:start position:0% +accepting all the junk + + + align:start position:0% +accepting all the junk +it just + + align:start position:0% +it just + + + align:start position:0% +it just +doesn't accept + + align:start position:0% +doesn't accept + + + align:start position:0% +doesn't accept +um the good stuff the accepting + + align:start position:0% +um the good stuff the accepting + + + align:start position:0% +um the good stuff the accepting +computation history + + align:start position:0% +computation history + + + align:start position:0% +computation history +okay it's it's just it it's uh accepting + + align:start position:0% +okay it's it's just it it's uh accepting + + + align:start position:0% +okay it's it's just it it's uh accepting +all the things which fail + + align:start position:0% +all the things which fail + + + align:start position:0% +all the things which fail +to be an accepting computation history + + align:start position:0% +to be an accepting computation history + + + align:start position:0% +to be an accepting computation history +okay and then once we have that we we + + align:start position:0% +okay and then once we have that we we + + + align:start position:0% +okay and then once we have that we we +test whether + + align:start position:0% +test whether + + + align:start position:0% +test whether +ours language is everything but whether + + align:start position:0% +ours language is everything but whether + + + align:start position:0% +ours language is everything but whether +bmw's languages everything using r + + align:start position:0% +bmw's languages everything using r + + + align:start position:0% +bmw's languages everything using r +because it if if that pda's language is + + align:start position:0% +because it if if that pda's language is + + + align:start position:0% +because it if if that pda's language is +everything + + align:start position:0% +everything + + + align:start position:0% +everything +then we know um + + align:start position:0% +then we know um + + + align:start position:0% +then we know um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +there could not be an accepting + + align:start position:0% +there could not be an accepting + + + align:start position:0% +there could not be an accepting +computation history because that's the + + align:start position:0% +computation history because that's the + + + align:start position:0% +computation history because that's the +one thing that gets um + + align:start position:0% + + + + align:start position:0% + +not accepted that's the one thing that + + align:start position:0% +not accepted that's the one thing that + + + align:start position:0% +not accepted that's the one thing that +gets rejected + + align:start position:0% +gets rejected + + + align:start position:0% +gets rejected +so if it's accepting everything there is + + align:start position:0% +so if it's accepting everything there is + + + align:start position:0% +so if it's accepting everything there is +not going to be an accepting computation + + align:start position:0% +not going to be an accepting computation + + + align:start position:0% +not going to be an accepting computation +history + + align:start position:0% + + + + align:start position:0% + +so if there is no + + align:start position:0% +so if there is no + + + align:start position:0% +so if there is no +uh if this is equal to sigma star + + align:start position:0% +uh if this is equal to sigma star + + + align:start position:0% +uh if this is equal to sigma star +then there couldn't be an accepting + + align:start position:0% +then there couldn't be an accepting + + + align:start position:0% +then there couldn't be an accepting +computation history and so we're going + + align:start position:0% +computation history and so we're going + + + align:start position:0% +computation history and so we're going +to accept + + align:start position:0% +to accept + + + align:start position:0% +to accept +okay so how is this going to work so + + align:start position:0% +okay so how is this going to work so + + + align:start position:0% +okay so how is this going to work so +what's different now + + align:start position:0% +what's different now + + + align:start position:0% +what's different now +about uh this case + + align:start position:0% +about uh this case + + + align:start position:0% +about uh this case +uh from the lba case is remember the lba + + align:start position:0% +uh from the lba case is remember the lba + + + align:start position:0% +uh from the lba case is remember the lba +uh got you know in + + align:start position:0% +uh got you know in + + + align:start position:0% +uh got you know in +the the computation history on its input + + align:start position:0% +the the computation history on its input + + + align:start position:0% +the the computation history on its input +and it used its ability to write on the + + align:start position:0% +and it used its ability to write on the + + + align:start position:0% +and it used its ability to write on the +tape to check that each + + align:start position:0% +tape to check that each + + + align:start position:0% +tape to check that each +configuration follows the next one + + align:start position:0% +configuration follows the next one + + + align:start position:0% +configuration follows the next one +we don't have the ability to write on + + align:start position:0% +we don't have the ability to write on + + + align:start position:0% +we don't have the ability to write on +the tape and push on automaton and by + + align:start position:0% +the tape and push on automaton and by + + + align:start position:0% +the tape and push on automaton and by +the way i hope you're all comfortable + + align:start position:0% +the way i hope you're all comfortable + + + align:start position:0% +the way i hope you're all comfortable +with my using pdas instead of grammars + + align:start position:0% +with my using pdas instead of grammars + + + align:start position:0% +with my using pdas instead of grammars +because we can interchange one to the + + align:start position:0% +because we can interchange one to the + + + align:start position:0% +because we can interchange one to the +other um i should have mentioned that + + align:start position:0% +other um i should have mentioned that + + + align:start position:0% +other um i should have mentioned that +when when i did it but + + align:start position:0% +when when i did it but + + + align:start position:0% +when when i did it but +um + + align:start position:0% +um + + + align:start position:0% +um +so the the pda is going to be using its + + align:start position:0% +so the the pda is going to be using its + + + align:start position:0% +so the the pda is going to be using its +stack to compare each configuration with + + align:start position:0% +stack to compare each configuration with + + + align:start position:0% +stack to compare each configuration with +the next one + + align:start position:0% +the next one + + + align:start position:0% +the next one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the way that's going to happen is + + align:start position:0% +so the way that's going to happen is + + + align:start position:0% +so the way that's going to happen is +it's going to non-deterministically + + align:start position:0% +it's going to non-deterministically + + + align:start position:0% +it's going to non-deterministically +take one of these so the very first + + align:start position:0% +take one of these so the very first + + + align:start position:0% +take one of these so the very first +thing it does + + align:start position:0% +thing it does + + + align:start position:0% +thing it does +is as before it checks to make sure that + + align:start position:0% +is as before it checks to make sure that + + + align:start position:0% +is as before it checks to make sure that +the beginning + + align:start position:0% +the beginning + + + align:start position:0% +the beginning +of the input is the start configuration + + align:start position:0% +of the input is the start configuration + + + align:start position:0% +of the input is the start configuration +but then once that's that's the easy + + align:start position:0% +but then once that's that's the easy + + + align:start position:0% +but then once that's that's the easy +part but once we get going with that we + + align:start position:0% +part but once we get going with that we + + + align:start position:0% +part but once we get going with that we +can we push each configuration well we + + align:start position:0% +can we push each configuration well we + + + align:start position:0% +can we push each configuration well we +first of all we now deterministically + + align:start position:0% +first of all we now deterministically + + + align:start position:0% +first of all we now deterministically +choose which configuration might be the + + align:start position:0% +choose which configuration might be the + + + align:start position:0% +choose which configuration might be the +bet the one that fails + + align:start position:0% +bet the one that fails + + + align:start position:0% +bet the one that fails +um + + align:start position:0% +um + + + align:start position:0% +um +where + + align:start position:0% +where + + + align:start position:0% +where +where one fails to go to the next one + + align:start position:0% +where one fails to go to the next one + + + align:start position:0% +where one fails to go to the next one +because those are the ones we're trying + + align:start position:0% +because those are the ones we're trying + + + align:start position:0% +because those are the ones we're trying +to accept when there's a failure + + align:start position:0% + + + + align:start position:0% + +so we now deterministically look for the + + align:start position:0% +so we now deterministically look for the + + + align:start position:0% +so we now deterministically look for the +place that there's a failure we push + + align:start position:0% +place that there's a failure we push + + + align:start position:0% +place that there's a failure we push +that onto the stack + + align:start position:0% +that onto the stack + + + align:start position:0% +that onto the stack +um and then we pop it off the stack and + + align:start position:0% +um and then we pop it off the stack and + + + align:start position:0% +um and then we pop it off the stack and +compare it with the next configuration + + align:start position:0% +compare it with the next configuration + + + align:start position:0% +compare it with the next configuration +so that's how we're using the stack + + align:start position:0% +so that's how we're using the stack + + + align:start position:0% +so that's how we're using the stack +instead of being able to mark on the + + align:start position:0% +instead of being able to mark on the + + + align:start position:0% +instead of being able to mark on the +input + + align:start position:0% +input + + + align:start position:0% +input +now there's a so i'm kind of going to + + align:start position:0% +now there's a so i'm kind of going to + + + align:start position:0% +now there's a so i'm kind of going to +illustrate that here + + align:start position:0% +illustrate that here + + + align:start position:0% +illustrate that here +so + + align:start position:0% +so + + + align:start position:0% +so +you know we're going as we're going to + + align:start position:0% +you know we're going as we're going to + + + align:start position:0% +you know we're going as we're going to +read this thing here and we're going to + + align:start position:0% +read this thing here and we're going to + + + align:start position:0% +read this thing here and we're going to +put it onto the stack so this thing + + align:start position:0% +put it onto the stack so this thing + + + align:start position:0% +put it onto the stack so this thing +moves over to here + + align:start position:0% +moves over to here + + + align:start position:0% +moves over to here +and + + align:start position:0% +and + + + align:start position:0% +and +this input here got put onto the stack + + align:start position:0% +this input here got put onto the stack + + + align:start position:0% +this input here got put onto the stack +you know q 0 w 1 w 2 it's q 0 w 1 w 2 + + align:start position:0% +you know q 0 w 1 w 2 it's q 0 w 1 w 2 + + + align:start position:0% +you know q 0 w 1 w 2 it's q 0 w 1 w 2 +you see that that first configuration is + + align:start position:0% +you see that that first configuration is + + + align:start position:0% +you see that that first configuration is +now sitting on the stack now as we're + + align:start position:0% +now sitting on the stack now as we're + + + align:start position:0% +now sitting on the stack now as we're +going to pop it off we're going to match + + align:start position:0% +going to pop it off we're going to match + + + align:start position:0% +going to pop it off we're going to match +it with the second configuration + + align:start position:0% +it with the second configuration + + + align:start position:0% +it with the second configuration +now if you're following me + + align:start position:0% +now if you're following me + + + align:start position:0% +now if you're following me +you'll realize that there's a there's a + + align:start position:0% +you'll realize that there's a there's a + + + align:start position:0% +you'll realize that there's a there's a +difficulty here because it's coming out + + align:start position:0% +difficulty here because it's coming out + + + align:start position:0% +difficulty here because it's coming out +in reverse + + align:start position:0% +in reverse + + + align:start position:0% +in reverse +you know it comes out in the reverse + + align:start position:0% +you know it comes out in the reverse + + + align:start position:0% +you know it comes out in the reverse +order that we put it in and that's not + + align:start position:0% +order that we put it in and that's not + + + align:start position:0% +order that we put it in and that's not +what we need to do so what we're going + + align:start position:0% +what we need to do so what we're going + + + align:start position:0% +what we need to do so what we're going +to do here and here's a little sort of a + + align:start position:0% +to do here and here's a little sort of a + + + align:start position:0% +to do here and here's a little sort of a +twist we're going to change the way + + align:start position:0% +twist we're going to change the way + + + align:start position:0% +twist we're going to change the way +we're writing down computation histories + + align:start position:0% +we're writing down computation histories + + + align:start position:0% +we're writing down computation histories +by making them by writing them uh + + align:start position:0% +by making them by writing them uh + + + align:start position:0% +by making them by writing them uh +reversing the even numbered ones so this + + align:start position:0% +reversing the even numbered ones so this + + + align:start position:0% +reversing the even numbered ones so this +one here is going to be written down in + + align:start position:0% +one here is going to be written down in + + + align:start position:0% +one here is going to be written down in +reverse + + align:start position:0% + + + + align:start position:0% + +and that's perfectly okay we can write + + align:start position:0% +and that's perfectly okay we can write + + + align:start position:0% +and that's perfectly okay we can write +down configuration computation histories + + align:start position:0% +down configuration computation histories + + + align:start position:0% +down configuration computation histories +in any way we want + + align:start position:0% +in any way we want + + + align:start position:0% +in any way we want +to um to meet our needs so we're going + + align:start position:0% +to um to meet our needs so we're going + + + align:start position:0% +to um to meet our needs so we're going +to reverse we're going to reverse the + + align:start position:0% +to reverse we're going to reverse the + + + align:start position:0% +to reverse we're going to reverse the +alternate ones + + align:start position:0% +alternate ones + + + align:start position:0% +alternate ones +and now when we push one it's going to + + align:start position:0% +and now when we push one it's going to + + + align:start position:0% +and now when we push one it's going to +come off in the right order to compare + + align:start position:0% +come off in the right order to compare + + + align:start position:0% +come off in the right order to compare +with the next one + + align:start position:0% +with the next one + + + align:start position:0% +with the next one +and so that's how the the procedure + + align:start position:0% +and so that's how the the procedure + + + align:start position:0% +and so that's how the the procedure +works + + align:start position:0% +works + + + align:start position:0% +works +okay + + align:start position:0% +okay + + + align:start position:0% +okay +we're running a little short on time um + + align:start position:0% +we're running a little short on time um + + + align:start position:0% +we're running a little short on time um +you need to be let's see so let let me + + align:start position:0% +you need to be let's see so let let me + + + align:start position:0% +you need to be let's see so let let me +just go to um + + align:start position:0% +just go to um + + + align:start position:0% +just go to um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +quick recap the computation history + + align:start position:0% +quick recap the computation history + + + align:start position:0% +quick recap the computation history +method is useful for showing the + + align:start position:0% +method is useful for showing the + + + align:start position:0% +method is useful for showing the +undecidability of problems when you're + + align:start position:0% +undecidability of problems when you're + + + align:start position:0% +undecidability of problems when you're +testing for the existence of an object + + align:start position:0% +testing for the existence of an object + + + align:start position:0% +testing for the existence of an object +each of those four cases that we showed + + align:start position:0% +each of those four cases that we showed + + + align:start position:0% +each of those four cases that we showed +today involving testing whether + + align:start position:0% +today involving testing whether + + + align:start position:0% +today involving testing whether +something exists + + align:start position:0% +something exists + + + align:start position:0% +something exists +so is there an integer solution to the + + align:start position:0% +so is there an integer solution to the + + + align:start position:0% +so is there an integer solution to the +polynomial + + align:start position:0% +polynomial + + + align:start position:0% +polynomial +is there some string in the language is + + align:start position:0% +is there some string in the language is + + + align:start position:0% +is there some string in the language is +there a string that's not in the + + align:start position:0% +there a string that's not in the + + + align:start position:0% +there a string that's not in the +language + + align:start position:0% +language + + + align:start position:0% +language +um or is there a match + + align:start position:0% +um or is there a match + + + align:start position:0% +um or is there a match +so that's a typical case + + align:start position:0% +so that's a typical case + + + align:start position:0% +so that's a typical case +when um + + align:start position:0% +when um + + + align:start position:0% +when um +this computation history method comes up + + align:start position:0% +this computation history method comes up + + + align:start position:0% +this computation history method comes up +and so as a quick review + + align:start position:0% +and so as a quick review + + + align:start position:0% +and so as a quick review +uh these are the things we showed today + + align:start position:0% + + + + align:start position:0% + +okay so why don't we uh uh we're we're + + align:start position:0% +okay so why don't we uh uh we're we're + + + align:start position:0% +okay so why don't we uh uh we're we're +just out of time um and so i'm i'm gonna + + align:start position:0% +just out of time um and so i'm i'm gonna + + + align:start position:0% +just out of time um and so i'm i'm gonna +let you go um + + align:start position:0% +let you go um + + + align:start position:0% +let you go um +but i will stick around uh for another + + align:start position:0% +but i will stick around uh for another + + + align:start position:0% +but i will stick around uh for another +five minutes or ten minutes uh happy to + + align:start position:0% +five minutes or ten minutes uh happy to + + + align:start position:0% +five minutes or ten minutes uh happy to +answer any questions if you if you have + + align:start position:0% +answer any questions if you if you have + + + align:start position:0% +answer any questions if you if you have +them um but that's that's officially the + + align:start position:0% +them um but that's that's officially the + + + align:start position:0% +them um but that's that's officially the +end of the lecture + + align:start position:0% +end of the lecture + + + align:start position:0% +end of the lecture +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +so let's let me try to get to there's a + + align:start position:0% +so let's let me try to get to there's a + + + align:start position:0% +so let's let me try to get to there's a +lot of questions in the chat don't + + align:start position:0% +lot of questions in the chat don't + + + align:start position:0% +lot of questions in the chat don't +forget you know write to the tas too + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +if m does not accept w + + align:start position:0% +if m does not accept w + + + align:start position:0% +if m does not accept w +what will happen to the computation + + align:start position:0% +what will happen to the computation + + + align:start position:0% +what will happen to the computation +history so if m does not accept w + + align:start position:0% +history so if m does not accept w + + + align:start position:0% +history so if m does not accept w +um + + align:start position:0% +um + + + align:start position:0% +um +uh then there is no computation there is + + align:start position:0% +uh then there is no computation there is + + + align:start position:0% +uh then there is no computation there is +no accepting computation history that's + + align:start position:0% +no accepting computation history that's + + + align:start position:0% +no accepting computation history that's +the only kind of computation histories + + align:start position:0% +the only kind of computation histories + + + align:start position:0% +the only kind of computation histories +we're considering + + align:start position:0% +we're considering + + + align:start position:0% +we're considering +so if m does not accept w there is no + + align:start position:0% +so if m does not accept w there is no + + + align:start position:0% +so if m does not accept w there is no +accepting computation history there's no + + align:start position:0% +accepting computation history there's no + + + align:start position:0% +accepting computation history there's no +computation history + + align:start position:0% +computation history + + + align:start position:0% +computation history +um so i don't know what it means what + + align:start position:0% +um so i don't know what it means what + + + align:start position:0% +um so i don't know what it means what +will happen to it it just doesn't + + align:start position:0% +will happen to it it just doesn't + + + align:start position:0% +will happen to it it just doesn't +doesn't exist + + align:start position:0% +doesn't exist + + + align:start position:0% +doesn't exist +um + + align:start position:0% +um + + + align:start position:0% +um +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +i hope that's + + align:start position:0% +i hope that's + + + align:start position:0% +i hope that's +helpful um + + align:start position:0% + + + + align:start position:0% + +don't we need to be able to add states + + align:start position:0% +don't we need to be able to add states + + + align:start position:0% +don't we need to be able to add states +to the end of the tape + + align:start position:0% +to the end of the tape + + + align:start position:0% +to the end of the tape +i don't know what that means + + align:start position:0% +i don't know what that means + + + align:start position:0% +i don't know what that means +it's taped to the end of the tape + + align:start position:0% +it's taped to the end of the tape + + + align:start position:0% +it's taped to the end of the tape +i i don't know you'll have to repeat + + align:start position:0% +i i don't know you'll have to repeat + + + align:start position:0% +i i don't know you'll have to repeat +that one sorry or explain that better + + align:start position:0% +that one sorry or explain that better + + + align:start position:0% +that one sorry or explain that better +um + + align:start position:0% + + + + align:start position:0% + +ah + + align:start position:0% +ah + + + align:start position:0% +ah +so this is a good this is a very good + + align:start position:0% +so this is a good this is a very good + + + align:start position:0% +so this is a good this is a very good +question here where does the previous + + align:start position:0% +question here where does the previous + + + align:start position:0% +question here where does the previous +proof fail + + align:start position:0% +proof fail + + + align:start position:0% +proof fail +when trying to reduce atm to + + align:start position:0% +when trying to reduce atm to + + + align:start position:0% +when trying to reduce atm to +ecfg + + align:start position:0% +ecfg + + + align:start position:0% +ecfg +it's got to fail + + align:start position:0% +it's got to fail + + + align:start position:0% +it's got to fail +because ecfg is + + align:start position:0% +because ecfg is + + + align:start position:0% +because ecfg is +decidable um + + align:start position:0% +decidable um + + + align:start position:0% +decidable um +so that that's a very good question + + align:start position:0% +so that that's a very good question + + + align:start position:0% +so that that's a very good question +maybe we can just go back to that + + align:start position:0% +maybe we can just go back to that + + + align:start position:0% +maybe we can just go back to that +last slide here + + align:start position:0% + + + + align:start position:0% + +because i was running a little short on + + align:start position:0% +because i was running a little short on + + + align:start position:0% +because i was running a little short on +time i didn't really focus on why we + + align:start position:0% +time i didn't really focus on why we + + + align:start position:0% +time i didn't really focus on why we +have to accept + + align:start position:0% +have to accept + + + align:start position:0% +have to accept +um + + align:start position:0% +um + + + align:start position:0% +um +the non-computation history strings we + + align:start position:0% +the non-computation history strings we + + + align:start position:0% +the non-computation history strings we +why are we accepting all the junk + + align:start position:0% +why are we accepting all the junk + + + align:start position:0% +why are we accepting all the junk +strings + + align:start position:0% +strings + + + align:start position:0% +strings +and + + align:start position:0% +and + + + align:start position:0% +and +only rejecting + + align:start position:0% +only rejecting + + + align:start position:0% +only rejecting +um + + align:start position:0% +um + + + align:start position:0% +um +the strings which are the uh the + + align:start position:0% +the strings which are the uh the + + + align:start position:0% +the strings which are the uh the +computation histories so you know we're + + align:start position:0% +computation histories so you know we're + + + align:start position:0% +computation histories so you know we're +looking for strings that fail + + align:start position:0% +looking for strings that fail + + + align:start position:0% +looking for strings that fail +you know if the string could fail + + align:start position:0% +you know if the string could fail + + + align:start position:0% +you know if the string could fail +because it starts wrong + + align:start position:0% +because it starts wrong + + + align:start position:0% +because it starts wrong +string it doesn't have the start + + align:start position:0% +string it doesn't have the start + + + align:start position:0% +string it doesn't have the start +configurat configuration or it doesn't + + align:start position:0% +configurat configuration or it doesn't + + + align:start position:0% +configurat configuration or it doesn't +maybe doesn't end with the accepting + + align:start position:0% +maybe doesn't end with the accepting + + + align:start position:0% +maybe doesn't end with the accepting +configuration or maybe one configuration + + align:start position:0% +configuration or maybe one configuration + + + align:start position:0% +configuration or maybe one configuration +doesn't lead properly to the next one + + align:start position:0% +doesn't lead properly to the next one + + + align:start position:0% +doesn't lead properly to the next one +any of those cases are a failure + + align:start position:0% +any of those cases are a failure + + + align:start position:0% +any of those cases are a failure +and there are going to be reason to + + align:start position:0% +and there are going to be reason to + + + align:start position:0% +and there are going to be reason to +accept + + align:start position:0% + + + + align:start position:0% + +the reason why we can do do it do that + + align:start position:0% +the reason why we can do do it do that + + + align:start position:0% +the reason why we can do do it do that +um is because the we're taking advantage + + align:start position:0% +um is because the we're taking advantage + + + align:start position:0% +um is because the we're taking advantage +of the push downs non-determinism + + align:start position:0% +of the push downs non-determinism + + + align:start position:0% +of the push downs non-determinism +we don't know where the + + align:start position:0% +we don't know where the + + + align:start position:0% +we don't know where the +um the failure + + align:start position:0% +um the failure + + + align:start position:0% +um the failure +might occur + + align:start position:0% +might occur + + + align:start position:0% +might occur +so we're going to non-deterministically + + align:start position:0% +so we're going to non-deterministically + + + align:start position:0% +so we're going to non-deterministically +guess where that failure occurs + + align:start position:0% +guess where that failure occurs + + + align:start position:0% +guess where that failure occurs +if we were going to flip this around and + + align:start position:0% +if we were going to flip this around and + + + align:start position:0% +if we were going to flip this around and +say + + align:start position:0% +say + + + align:start position:0% +say +let's accept only the good ones and + + align:start position:0% +let's accept only the good ones and + + + align:start position:0% +let's accept only the good ones and +reject everything else we would have to + + align:start position:0% +reject everything else we would have to + + + align:start position:0% +reject everything else we would have to +test that each configuration led to the + + align:start position:0% +test that each configuration led to the + + + align:start position:0% +test that each configuration led to the +next one + + align:start position:0% +next one + + + align:start position:0% +next one +so we have to check them all + + align:start position:0% +so we have to check them all + + + align:start position:0% +so we have to check them all +so + + align:start position:0% +so + + + align:start position:0% +so +if something fails it only has to fail + + align:start position:0% +if something fails it only has to fail + + + align:start position:0% +if something fails it only has to fail +in one place + + align:start position:0% +in one place + + + align:start position:0% +in one place +and then you know we can accept if it um + + align:start position:0% +and then you know we can accept if it um + + + align:start position:0% +and then you know we can accept if it um +if it's a good computation history + + align:start position:0% +if it's a good computation history + + + align:start position:0% +if it's a good computation history +we have to + + align:start position:0% +we have to + + + align:start position:0% +we have to +it has to be good everywhere + + align:start position:0% +it has to be good everywhere + + + align:start position:0% +it has to be good everywhere +and so the push down automaton really if + + align:start position:0% +and so the push down automaton really if + + + align:start position:0% +and so the push down automaton really if +you're going to get down to the + + align:start position:0% +you're going to get down to the + + + align:start position:0% +you're going to get down to the +nitty-gritty the push on automaton can + + align:start position:0% +nitty-gritty the push on automaton can + + + align:start position:0% +nitty-gritty the push on automaton can +check that this configuration leads to + + align:start position:0% +check that this configuration leads to + + + align:start position:0% +check that this configuration leads to +that configuration + + align:start position:0% +that configuration + + + align:start position:0% +that configuration +using pushing on the stack and then + + align:start position:0% +using pushing on the stack and then + + + align:start position:0% +using pushing on the stack and then +popping it + + align:start position:0% +popping it + + + align:start position:0% +popping it +but now by the time you get to here you + + align:start position:0% +but now by the time you get to here you + + + align:start position:0% +but now by the time you get to here you +want to check that this second + + align:start position:0% +want to check that this second + + + align:start position:0% +want to check that this second +configuration leads to the third one + + align:start position:0% +configuration leads to the third one + + + align:start position:0% +configuration leads to the third one +you would need to push the second + + align:start position:0% +you would need to push the second + + + align:start position:0% +you would need to push the second +configuration onto the stack but at this + + align:start position:0% +configuration onto the stack but at this + + + align:start position:0% +configuration onto the stack but at this +point you're already + + align:start position:0% +point you're already + + + align:start position:0% +point you're already +at after the second configuration so we + + align:start position:0% +at after the second configuration so we + + + align:start position:0% +at after the second configuration so we +cannot back up and push the second one + + align:start position:0% +cannot back up and push the second one + + + align:start position:0% +cannot back up and push the second one +on the stack + + align:start position:0% +on the stack + + + align:start position:0% +on the stack +so the the push on tom dot is not able + + align:start position:0% +so the the push on tom dot is not able + + + align:start position:0% +so the the push on tom dot is not able +to check um in the positive sense that + + align:start position:0% +to check um in the positive sense that + + + align:start position:0% +to check um in the positive sense that +you have a computation history it's only + + align:start position:0% +you have a computation history it's only + + + align:start position:0% +you have a computation history it's only +able to and accept them it's only to + + align:start position:0% +able to and accept them it's only to + + + align:start position:0% +able to and accept them it's only to +check in the negative sense that you + + align:start position:0% +check in the negative sense that you + + + align:start position:0% +check in the negative sense that you +don't have a con + + align:start position:0% +don't have a con + + + align:start position:0% +don't have a con +a computation history + + align:start position:0% +a computation history + + + align:start position:0% +a computation history +and uh accept all the ones that fail + + align:start position:0% +and uh accept all the ones that fail + + + align:start position:0% +and uh accept all the ones that fail +and that's just because it only has to + + align:start position:0% +and that's just because it only has to + + + align:start position:0% +and that's just because it only has to +fail in one place + + align:start position:0% + + + + align:start position:0% + +i hope that helps um + + align:start position:0% +i hope that helps um + + + align:start position:0% +i hope that helps um +so that's why we couldn't flip this + + align:start position:0% +so that's why we couldn't flip this + + + align:start position:0% +so that's why we couldn't flip this +around and make this proof work for the + + align:start position:0% +around and make this proof work for the + + + align:start position:0% +around and make this proof work for the +emptiness problem and only have to work + + align:start position:0% +emptiness problem and only have to work + + + align:start position:0% +emptiness problem and only have to work +for the the everything problem + + align:start position:0% +for the the everything problem + + + align:start position:0% +for the the everything problem +the old problem + + align:start position:0% + + + + align:start position:0% + +all right um + + align:start position:0% + + + + align:start position:0% + +okay so bye bye everybody and i will see + + align:start position:0% +okay so bye bye everybody and i will see + + + align:start position:0% +okay so bye bye everybody and i will see +you on tuesday \ No newline at end of file diff --git a/McyxfIYo4lM.txt b/McyxfIYo4lM.txt new file mode 100644 index 0000000000000000000000000000000000000000..942fed43db4f24f5ae7159d2309015eeb2f70fbf --- /dev/null +++ b/McyxfIYo4lM.txt @@ -0,0 +1,1323 @@ +align:start position:0% + +an important part of your image making + + align:start position:0% +an important part of your image making + + + align:start position:0% +an important part of your image making +mostly small devices is what you use for + + align:start position:0% +mostly small devices is what you use for + + + align:start position:0% +mostly small devices is what you use for +backgrounds or how to view backgrounds + + align:start position:0% +backgrounds or how to view backgrounds + + + align:start position:0% +backgrounds or how to view backgrounds +you could make some very interesting + + align:start position:0% +you could make some very interesting + + + align:start position:0% +you could make some very interesting +images even more interesting if you + + align:start position:0% +images even more interesting if you + + + align:start position:0% +images even more interesting if you +subtly suggest a certain kind of + + align:start position:0% +subtly suggest a certain kind of + + + align:start position:0% +subtly suggest a certain kind of +background that works that's relevant + + align:start position:0% +background that works that's relevant + + + align:start position:0% +background that works that's relevant +your selection can really change your + + align:start position:0% +your selection can really change your + + + align:start position:0% +your selection can really change your +image sometimes you have to be kind of + + align:start position:0% +image sometimes you have to be kind of + + + align:start position:0% +image sometimes you have to be kind of +careful because the background can + + align:start position:0% +careful because the background can + + + align:start position:0% +careful because the background can +overtake what what it is that you want + + align:start position:0% +overtake what what it is that you want + + + align:start position:0% +overtake what what it is that you want +to say and we'll see that in a moment so + + align:start position:0% +to say and we'll see that in a moment so + + + align:start position:0% +to say and we'll see that in a moment so +take for example this image that I made + + align:start position:0% +take for example this image that I made + + + align:start position:0% +take for example this image that I made +of a assemblage of pieces and I took it + + align:start position:0% +of a assemblage of pieces and I took it + + + align:start position:0% +of a assemblage of pieces and I took it +on a Surface against a white wall which + + align:start position:0% +on a Surface against a white wall which + + + align:start position:0% +on a Surface against a white wall which +is what a lot of you do and the issue + + align:start position:0% +is what a lot of you do and the issue + + + align:start position:0% +is what a lot of you do and the issue +for me is that even though you don't + + align:start position:0% +for me is that even though you don't + + + align:start position:0% +for me is that even though you don't +think the viewer sees it the viewer does + + align:start position:0% +think the viewer sees it the viewer does + + + align:start position:0% +think the viewer sees it the viewer does +see the Horizon where the two pieces of + + align:start position:0% +see the Horizon where the two pieces of + + + align:start position:0% +see the Horizon where the two pieces of +material meet you might say what's + + align:start position:0% +material meet you might say what's + + + align:start position:0% +material meet you might say what's +what's the big deal well you should + + align:start position:0% +what's the big deal well you should + + + align:start position:0% +what's the big deal well you should +start really getting into the habit of + + align:start position:0% +start really getting into the habit of + + + align:start position:0% +start really getting into the habit of +trying to edit out anything that is + + align:start position:0% +trying to edit out anything that is + + + align:start position:0% +trying to edit out anything that is +ambiguous or that is not giving the + + align:start position:0% +ambiguous or that is not giving the + + + align:start position:0% +ambiguous or that is not giving the +viewer a very clear view of what it is + + align:start position:0% +viewer a very clear view of what it is + + + align:start position:0% +viewer a very clear view of what it is +you want them to see so it's much better + + align:start position:0% +you want them to see so it's much better + + + align:start position:0% +you want them to see so it's much better +to just keep a piece of paper handy and + + align:start position:0% +to just keep a piece of paper handy and + + + align:start position:0% +to just keep a piece of paper handy and +just simply fold it up towards the back + + align:start position:0% +just simply fold it up towards the back + + + align:start position:0% +just simply fold it up towards the back +and you'll get yourself a very nice + + align:start position:0% +and you'll get yourself a very nice + + + align:start position:0% +and you'll get yourself a very nice +background without seeing that + + align:start position:0% +background without seeing that + + + align:start position:0% +background without seeing that +distracting horizontal line I really do + + align:start position:0% +distracting horizontal line I really do + + + align:start position:0% +distracting horizontal line I really do +suggest you you start doing these kinds + + align:start position:0% +suggest you you start doing these kinds + + + align:start position:0% +suggest you you start doing these kinds +of things it's easy with such small + + align:start position:0% +of things it's easy with such small + + + align:start position:0% +of things it's easy with such small +devices here's a device that was taken + + align:start position:0% +devices here's a device that was taken + + + align:start position:0% +devices here's a device that was taken +just in the lab a quick image and once + + align:start position:0% +just in the lab a quick image and once + + + align:start position:0% +just in the lab a quick image and once +again the researcher knows what it is to + + align:start position:0% +again the researcher knows what it is to + + + align:start position:0% +again the researcher knows what it is to +look for but you cannot expect the + + align:start position:0% +look for but you cannot expect the + + + align:start position:0% +look for but you cannot expect the +firsttime viewer to see what you want + + align:start position:0% +firsttime viewer to see what you want + + + align:start position:0% +firsttime viewer to see what you want +them to see and so they do see all the + + align:start position:0% +them to see and so they do see all the + + + align:start position:0% +them to see and so they do see all the +mess behind it so just take that piece + + align:start position:0% +mess behind it so just take that piece + + + align:start position:0% +mess behind it so just take that piece +of paper that we used before and just + + align:start position:0% +of paper that we used before and just + + + align:start position:0% +of paper that we used before and just +put the device on it lean it against the + + align:start position:0% +put the device on it lean it against the + + + align:start position:0% +put the device on it lean it against the +same background that you had before but + + align:start position:0% +same background that you had before but + + + align:start position:0% +same background that you had before but +this time with the paper going up hiding + + align:start position:0% +this time with the paper going up hiding + + + align:start position:0% +this time with the paper going up hiding +that material in the back you could see + + align:start position:0% +that material in the back you could see + + + align:start position:0% +that material in the back you could see +a much clearer device sometimes echoing + + align:start position:0% +a much clearer device sometimes echoing + + + align:start position:0% +a much clearer device sometimes echoing +what it is that you're looking at it + + align:start position:0% +what it is that you're looking at it + + + align:start position:0% +what it is that you're looking at it +could be very helpful uh I was asked to + + align:start position:0% +could be very helpful uh I was asked to + + + align:start position:0% +could be very helpful uh I was asked to +take some images of some copper sulfate + + align:start position:0% +take some images of some copper sulfate + + + align:start position:0% +take some images of some copper sulfate +crystals and so I found a piece of + + align:start position:0% +crystals and so I found a piece of + + + align:start position:0% +crystals and so I found a piece of +copper two pieces of copper actually and + + align:start position:0% +copper two pieces of copper actually and + + + align:start position:0% +copper two pieces of copper actually and +just uh suggested the presence of copper + + align:start position:0% +just uh suggested the presence of copper + + + align:start position:0% +just uh suggested the presence of copper +in this material and here with these + + align:start position:0% +in this material and here with these + + + align:start position:0% +in this material and here with these +plastic shapes that were fabricated in + + align:start position:0% +plastic shapes that were fabricated in + + + align:start position:0% +plastic shapes that were fabricated in +the lab I just thought it would be fun + + align:start position:0% +the lab I just thought it would be fun + + + align:start position:0% +the lab I just thought it would be fun +to put it against a grid not a very + + align:start position:0% +to put it against a grid not a very + + + align:start position:0% +to put it against a grid not a very +clean grid by the way this was taken + + align:start position:0% +clean grid by the way this was taken + + + align:start position:0% +clean grid by the way this was taken +quite a long time ago but what it did + + align:start position:0% +quite a long time ago but what it did + + + align:start position:0% +quite a long time ago but what it did +show was sort of helping to Define these + + align:start position:0% +show was sort of helping to Define these + + + align:start position:0% +show was sort of helping to Define these +shapes and how those lines were changed + + align:start position:0% +shapes and how those lines were changed + + + align:start position:0% +shapes and how those lines were changed +when these plastic pieces were put over + + align:start position:0% +when these plastic pieces were put over + + + align:start position:0% +when these plastic pieces were put over +it here's an image I took for a book + + align:start position:0% +it here's an image I took for a book + + + align:start position:0% +it here's an image I took for a book +trying to talk about a drop of water + + align:start position:0% +trying to talk about a drop of water + + + align:start position:0% +trying to talk about a drop of water +which is very complicated and what I did + + align:start position:0% +which is very complicated and what I did + + + align:start position:0% +which is very complicated and what I did +was remember we're using a 105 lens + + align:start position:0% +was remember we're using a 105 lens + + + align:start position:0% +was remember we're using a 105 lens +focusing on the drop so as you probably + + align:start position:0% +focusing on the drop so as you probably + + + align:start position:0% +focusing on the drop so as you probably +know by now you get a very narrow depth + + align:start position:0% +know by now you get a very narrow depth + + + align:start position:0% +know by now you get a very narrow depth +of field with these 105 lenses which is + + align:start position:0% +of field with these 105 lenses which is + + + align:start position:0% +of field with these 105 lenses which is +what we wanted in this case because the + + align:start position:0% +what we wanted in this case because the + + + align:start position:0% +what we wanted in this case because the +background is blurred the next image + + align:start position:0% +background is blurred the next image + + + align:start position:0% +background is blurred the next image +shows you the background I mean it it's + + align:start position:0% +shows you the background I mean it it's + + + align:start position:0% +shows you the background I mean it it's +something I bought quite a while ago + + align:start position:0% +something I bought quite a while ago + + + align:start position:0% +something I bought quite a while ago +knowing someday I would use it for a + + align:start position:0% +knowing someday I would use it for a + + + align:start position:0% +knowing someday I would use it for a +background because I like the look of it + + align:start position:0% +background because I like the look of it + + + align:start position:0% +background because I like the look of it +and I also knew that with a 105 lens it + + align:start position:0% +and I also knew that with a 105 lens it + + + align:start position:0% +and I also knew that with a 105 lens it +would become a whole different thing as + + align:start position:0% +would become a whole different thing as + + + align:start position:0% +would become a whole different thing as +you see take a real hard look at that + + align:start position:0% +you see take a real hard look at that + + + align:start position:0% +you see take a real hard look at that +drop and you'll see that the drop itself + + align:start position:0% +drop and you'll see that the drop itself + + + align:start position:0% +drop and you'll see that the drop itself +became lens that has focused the + + align:start position:0% +became lens that has focused the + + + align:start position:0% +became lens that has focused the +background so it's a little playful + + align:start position:0% +background so it's a little playful + + + align:start position:0% +background so it's a little playful +thing that I forgot would happen but it + + align:start position:0% +thing that I forgot would happen but it + + + align:start position:0% +thing that I forgot would happen but it +did but here's a background totally out + + align:start position:0% +did but here's a background totally out + + + align:start position:0% +did but here's a background totally out +of focus that you want to be out of + + align:start position:0% +of focus that you want to be out of + + + align:start position:0% +of focus that you want to be out of +focus otherwise it would just be too + + align:start position:0% +focus otherwise it would just be too + + + align:start position:0% +focus otherwise it would just be too +much of an image on this one image of a + + align:start position:0% +much of an image on this one image of a + + + align:start position:0% +much of an image on this one image of a +basilis on in a Petri dish I just + + align:start position:0% +basilis on in a Petri dish I just + + + align:start position:0% +basilis on in a Petri dish I just +decided to layer the petri dish on a + + align:start position:0% +decided to layer the petri dish on a + + + align:start position:0% +decided to layer the petri dish on a +particular plastic blue and then I put + + align:start position:0% +particular plastic blue and then I put + + + align:start position:0% +particular plastic blue and then I put +the blue over orange and I just was + + align:start position:0% +the blue over orange and I just was + + + align:start position:0% +the blue over orange and I just was +having kind of fun on this one we're + + align:start position:0% +having kind of fun on this one we're + + + align:start position:0% +having kind of fun on this one we're +showing sketches of the cad that was + + align:start position:0% +showing sketches of the cad that was + + + align:start position:0% +showing sketches of the cad that was +used to make these devices and it's just + + align:start position:0% +used to make these devices and it's just + + + align:start position:0% +used to make these devices and it's just +a sketchy like idea which I like very + + align:start position:0% +a sketchy like idea which I like very + + + align:start position:0% +a sketchy like idea which I like very +much I still like the idea of showing + + align:start position:0% +much I still like the idea of showing + + + align:start position:0% +much I still like the idea of showing +some sort of human hand to the + + align:start position:0% +some sort of human hand to the + + + align:start position:0% +some sort of human hand to the +fabrication of very high technology I + + align:start position:0% +fabrication of very high technology I + + + align:start position:0% +fabrication of very high technology I +think that we should use more of these + + align:start position:0% +think that we should use more of these + + + align:start position:0% +think that we should use more of these +kinds of ideas that's my point of view + + align:start position:0% +kinds of ideas that's my point of view + + + align:start position:0% +kinds of ideas that's my point of view +and here's another it's a wafer made + + align:start position:0% +and here's another it's a wafer made + + + align:start position:0% +and here's another it's a wafer made +into electronic device with one + + align:start position:0% +into electronic device with one + + + align:start position:0% +into electronic device with one +background and I took the same wafer put + + align:start position:0% +background and I took the same wafer put + + + align:start position:0% +background and I took the same wafer put +it on another + + align:start position:0% +it on another + + + align:start position:0% +it on another +background and then again on another + + align:start position:0% +background and then again on another + + + align:start position:0% +background and then again on another +background and changing the angle a + + align:start position:0% +background and changing the angle a + + + align:start position:0% +background and changing the angle a +little bit so you actually see a very + + align:start position:0% +little bit so you actually see a very + + + align:start position:0% +little bit so you actually see a very +different color palette and that's what + + align:start position:0% +different color palette and that's what + + + align:start position:0% +different color palette and that's what +I'm talking about it's all related you + + align:start position:0% +I'm talking about it's all related you + + + align:start position:0% +I'm talking about it's all related you +make one change in one spot and then + + align:start position:0% +make one change in one spot and then + + + align:start position:0% +make one change in one spot and then +it's going to change your composition or + + align:start position:0% +it's going to change your composition or + + + align:start position:0% +it's going to change your composition or +your point of view it's just ongoing the + + align:start position:0% +your point of view it's just ongoing the + + + align:start position:0% +your point of view it's just ongoing the +permutations for this image we wanted to + + align:start position:0% +permutations for this image we wanted to + + + align:start position:0% +permutations for this image we wanted to +show the ability to make these crystals + + align:start position:0% +show the ability to make these crystals + + + align:start position:0% +show the ability to make these crystals +and I decided to use some weighing paper + + align:start position:0% +and I decided to use some weighing paper + + + align:start position:0% +and I decided to use some weighing paper +against a desk and it just Happ that the + + align:start position:0% +against a desk and it just Happ that the + + + align:start position:0% +against a desk and it just Happ that the +light is coming in from the window I + + align:start position:0% +light is coming in from the window I + + + align:start position:0% +light is coming in from the window I +actually used it compositionally and as + + align:start position:0% +actually used it compositionally and as + + + align:start position:0% +actually used it compositionally and as +part of the background and here we're + + align:start position:0% +part of the background and here we're + + + align:start position:0% +part of the background and here we're +seeing material that results into a + + align:start position:0% +seeing material that results into a + + + align:start position:0% +seeing material that results into a +powder and again I'm using weighing + + align:start position:0% +powder and again I'm using weighing + + + align:start position:0% +powder and again I'm using weighing +paper and make a sort of an interesting + + align:start position:0% +paper and make a sort of an interesting + + + align:start position:0% +paper and make a sort of an interesting +overlay of shapes because it's a pretty + + align:start position:0% +overlay of shapes because it's a pretty + + + align:start position:0% +overlay of shapes because it's a pretty +boring picture otherwise I think it's a + + align:start position:0% +boring picture otherwise I think it's a + + + align:start position:0% +boring picture otherwise I think it's a +little more successful these are things + + align:start position:0% +little more successful these are things + + + align:start position:0% +little more successful these are things +are not easy to photograph as I'm sure + + align:start position:0% +are not easy to photograph as I'm sure + + + align:start position:0% +are not easy to photograph as I'm sure +you know and on this I use the + + align:start position:0% +you know and on this I use the + + + align:start position:0% +you know and on this I use the +reflective quality of glass might not be + + align:start position:0% +reflective quality of glass might not be + + + align:start position:0% +reflective quality of glass might not be +as successful as I thought because maybe + + align:start position:0% +as successful as I thought because maybe + + + align:start position:0% +as successful as I thought because maybe +you can't quite tell where the glass + + align:start position:0% +you can't quite tell where the glass + + + align:start position:0% +you can't quite tell where the glass +begins and the real slide with these + + align:start position:0% +begins and the real slide with these + + + align:start position:0% +begins and the real slide with these +These are highly hydrophobic slides + + align:start position:0% +These are highly hydrophobic slides + + + align:start position:0% +These are highly hydrophobic slides +that's why you're seeing the water + + align:start position:0% +that's why you're seeing the water + + + align:start position:0% +that's why you're seeing the water +bubble as it does I don't know it's + + align:start position:0% +bubble as it does I don't know it's + + + align:start position:0% +bubble as it does I don't know it's +something to think about and here I used + + align:start position:0% +something to think about and here I used + + + align:start position:0% +something to think about and here I used +I kind of was echoing the shape of this + + align:start position:0% +I kind of was echoing the shape of this + + + align:start position:0% +I kind of was echoing the shape of this +material how it coils into these nice + + align:start position:0% +material how it coils into these nice + + + align:start position:0% +material how it coils into these nice +Scoops and I decided to use a small + + align:start position:0% +Scoops and I decided to use a small + + + align:start position:0% +Scoops and I decided to use a small +table + + align:start position:0% +table + + + align:start position:0% +table +to Echo the shape of the naturally + + align:start position:0% +to Echo the shape of the naturally + + + align:start position:0% +to Echo the shape of the naturally +occurring + + align:start position:0% +occurring + + + align:start position:0% +occurring +curves here's an example where I put the + + align:start position:0% +curves here's an example where I put the + + + align:start position:0% +curves here's an example where I put the +device on stickums just a blue Post-it + + align:start position:0% +device on stickums just a blue Post-it + + + align:start position:0% +device on stickums just a blue Post-it +onto which I on that I put Post-it on a + + align:start position:0% +onto which I on that I put Post-it on a + + + align:start position:0% +onto which I on that I put Post-it on a +black surface I think this works I think + + align:start position:0% +black surface I think this works I think + + + align:start position:0% +black surface I think this works I think +the next one where I used a crazy + + align:start position:0% +the next one where I used a crazy + + + align:start position:0% +the next one where I used a crazy +background that I got a card that was + + align:start position:0% +background that I got a card that was + + + align:start position:0% +background that I got a card that was +kind of fun it's fun to look at the card + + align:start position:0% +kind of fun it's fun to look at the card + + + align:start position:0% +kind of fun it's fun to look at the card +but not with the device on it it's just + + align:start position:0% +but not with the device on it it's just + + + align:start position:0% +but not with the device on it it's just +way way over the top and too much where + + align:start position:0% +way way over the top and too much where + + + align:start position:0% +way way over the top and too much where +the background just really gets in the + + align:start position:0% +the background just really gets in the + + + align:start position:0% +the background just really gets in the +way I needed to take a photograph of + + align:start position:0% +way I needed to take a photograph of + + + align:start position:0% +way I needed to take a photograph of +this very small robot flying robot which + + align:start position:0% +this very small robot flying robot which + + + align:start position:0% +this very small robot flying robot which +measures about 1 cm long and used the + + align:start position:0% +measures about 1 cm long and used the + + + align:start position:0% +measures about 1 cm long and used the +Box the plastic box that it arrived in + + align:start position:0% +Box the plastic box that it arrived in + + + align:start position:0% +Box the plastic box that it arrived in +as part of the composition which I think + + align:start position:0% +as part of the composition which I think + + + align:start position:0% +as part of the composition which I think +fills the background in an interesting + + align:start position:0% +fills the background in an interesting + + + align:start position:0% +fills the background in an interesting +way in this image this was a very quick + + align:start position:0% +way in this image this was a very quick + + + align:start position:0% +way in this image this was a very quick +image that I just made just to see how + + align:start position:0% +image that I just made just to see how + + + align:start position:0% +image that I just made just to see how +what kind of depth of field I was going + + align:start position:0% +what kind of depth of field I was going + + + align:start position:0% +what kind of depth of field I was going +to get with these small devices and it + + align:start position:0% +to get with these small devices and it + + + align:start position:0% +to get with these small devices and it +turns out that I sort of like the + + align:start position:0% +turns out that I sort of like the + + + align:start position:0% +turns out that I sort of like the +haphazardness of this image the + + align:start position:0% +haphazardness of this image the + + + align:start position:0% +haphazardness of this image the +background just was + + align:start position:0% +background just was + + + align:start position:0% +background just was +accidental for me it works maybe not for + + align:start position:0% +accidental for me it works maybe not for + + + align:start position:0% +accidental for me it works maybe not for +you but for me it does backgrounds + + align:start position:0% +you but for me it does backgrounds + + + align:start position:0% +you but for me it does backgrounds +should be part of your vocabulary there + + align:start position:0% +should be part of your vocabulary there + + + align:start position:0% +should be part of your vocabulary there +is no question in my mind about that \ No newline at end of file diff --git a/MrQwihmwKoc.txt b/MrQwihmwKoc.txt new file mode 100644 index 0000000000000000000000000000000000000000..efa13c815c8f52c07d401ce41471ba24ed18bb12 --- /dev/null +++ b/MrQwihmwKoc.txt @@ -0,0 +1,683 @@ +align:start position:0% + +education education education some + + align:start position:0% +education education education some + + + align:start position:0% +education education education some +people say that's the key to success in + + align:start position:0% +people say that's the key to success in + + + align:start position:0% +people say that's the key to success in +this knowledge-based economy that we're + + align:start position:0% +this knowledge-based economy that we're + + + align:start position:0% +this knowledge-based economy that we're +in and they're right but the reality is + + align:start position:0% +in and they're right but the reality is + + + align:start position:0% +in and they're right but the reality is +the education model that we have + + align:start position:0% +the education model that we have + + + align:start position:0% +the education model that we have +inherited today was built for the + + align:start position:0% +inherited today was built for the + + + align:start position:0% +inherited today was built for the +farming economy and maybe the industrial + + align:start position:0% +farming economy and maybe the industrial + + + align:start position:0% +farming economy and maybe the industrial +economy of the last century and so we're + + align:start position:0% +economy of the last century and so we're + + + align:start position:0% +economy of the last century and so we're +going to have to adapt it to meet the + + align:start position:0% +going to have to adapt it to meet the + + + align:start position:0% +going to have to adapt it to meet the +needs of the Next Generation Workforce + + align:start position:0% +needs of the Next Generation Workforce + + + align:start position:0% +needs of the Next Generation Workforce +and you as members of the Next + + align:start position:0% +and you as members of the Next + + + align:start position:0% +and you as members of the Next +Generation Workforce are going to have + + align:start position:0% +Generation Workforce are going to have + + + align:start position:0% +Generation Workforce are going to have +to have your own strategy for addressing + + align:start position:0% +to have your own strategy for addressing + + + align:start position:0% +to have your own strategy for addressing +how when where and how much over the + + align:start position:0% +how when where and how much over the + + + align:start position:0% +how when where and how much over the +course of your life of Education you are + + align:start position:0% +course of your life of Education you are + + + align:start position:0% +course of your life of Education you are +going to invest in let's start with + + align:start position:0% +going to invest in let's start with + + + align:start position:0% +going to invest in let's start with +early childhood education and I'll start + + align:start position:0% +early childhood education and I'll start + + + align:start position:0% +early childhood education and I'll start +with a story several months ago I was + + align:start position:0% +with a story several months ago I was + + + align:start position:0% +with a story several months ago I was +sitting at a lunch uh with International + + align:start position:0% +sitting at a lunch uh with International + + + align:start position:0% +sitting at a lunch uh with International +students here at MIT and they were + + align:start position:0% +students here at MIT and they were + + + align:start position:0% +students here at MIT and they were +midcareer students and so I was sitting + + align:start position:0% +midcareer students and so I was sitting + + + align:start position:0% +midcareer students and so I was sitting +between two mothers one from Portugal + + align:start position:0% +between two mothers one from Portugal + + + align:start position:0% +between two mothers one from Portugal +and one from China and I asked them when + + align:start position:0% +and one from China and I asked them when + + + align:start position:0% +and one from China and I asked them when +did your children start uh School in + + align:start position:0% +did your children start uh School in + + + align:start position:0% +did your children start uh School in +your countries and one said right after + + align:start position:0% +your countries and one said right after + + + align:start position:0% +your countries and one said right after +I finished maternity leave and the other + + align:start position:0% +I finished maternity leave and the other + + + align:start position:0% +I finished maternity leave and the other +said at age three they were amazed to + + align:start position:0% +said at age three they were amazed to + + + align:start position:0% +said at age three they were amazed to +hear from me that basically our children + + align:start position:0% +hear from me that basically our children + + + align:start position:0% +hear from me that basically our children +in this country start in kindergarten at + + align:start position:0% +in this country start in kindergarten at + + + align:start position:0% +in this country start in kindergarten at +age five unless there's some private + + align:start position:0% +age five unless there's some private + + + align:start position:0% +age five unless there's some private +alternative well about 70% of the + + align:start position:0% +alternative well about 70% of the + + + align:start position:0% +alternative well about 70% of the +industrialized world starts education + + align:start position:0% +industrialized world starts education + + + align:start position:0% +industrialized world starts education +earlier + + align:start position:0% +earlier + + + align:start position:0% +earlier +so why is this so important well let's + + align:start position:0% +so why is this so important well let's + + + align:start position:0% +so why is this so important well let's +take a look this is Professor James + + align:start position:0% +take a look this is Professor James + + + align:start position:0% +take a look this is Professor James +Heckman from the University of Chicago a + + align:start position:0% +Heckman from the University of Chicago a + + + align:start position:0% +Heckman from the University of Chicago a +Nobel prizewinning Economist and he is + + align:start position:0% +Nobel prizewinning Economist and he is + + + align:start position:0% +Nobel prizewinning Economist and he is +the world's expert on the economics of + + align:start position:0% +the world's expert on the economics of + + + align:start position:0% +the world's expert on the economics of +early childhood education he has studied + + align:start position:0% +early childhood education he has studied + + + align:start position:0% +early childhood education he has studied +this in experiments he studied it in + + align:start position:0% +this in experiments he studied it in + + + align:start position:0% +this in experiments he studied it in +Chicago he studied it around the world + + align:start position:0% +Chicago he studied it around the world + + + align:start position:0% +Chicago he studied it around the world +and what he finds is that there's a 7 to + + align:start position:0% +and what he finds is that there's a 7 to + + + align:start position:0% +and what he finds is that there's a 7 to +10% rate of return for Society for every + + align:start position:0% +10% rate of return for Society for every + + + align:start position:0% +10% rate of return for Society for every +year of early childhood + + align:start position:0% +year of early childhood + + + align:start position:0% +year of early childhood +education that return is measured not + + align:start position:0% +education that return is measured not + + + align:start position:0% +education that return is measured not +only in lifetime earnings it's measured + + align:start position:0% +only in lifetime earnings it's measured + + + align:start position:0% +only in lifetime earnings it's measured +in lower Dropout rates less violence and + + align:start position:0% +in lower Dropout rates less violence and + + + align:start position:0% +in lower Dropout rates less violence and +less criminal records the ability to + + align:start position:0% +less criminal records the ability to + + + align:start position:0% +less criminal records the ability to +achieve one's objectives within one's + + align:start position:0% +achieve one's objectives within one's + + + align:start position:0% +achieve one's objectives within one's +career a whole set of data tell us that + + align:start position:0% +career a whole set of data tell us that + + + align:start position:0% +career a whole set of data tell us that +getting children into school early is + + align:start position:0% +getting children into school early is + + + align:start position:0% +getting children into school early is +very very important to their + + align:start position:0% +very very important to their + + + align:start position:0% +very very important to their +success well it's even more important + + align:start position:0% +success well it's even more important + + + align:start position:0% +success well it's even more important +for children who are at risk inner city + + align:start position:0% +for children who are at risk inner city + + + align:start position:0% +for children who are at risk inner city +students from disadvantaged + + align:start position:0% +students from disadvantaged + + + align:start position:0% +students from disadvantaged +neighborhoods have even higher rates of + + align:start position:0% +neighborhoods have even higher rates of + + + align:start position:0% +neighborhoods have even higher rates of +return for early childhood education so + + align:start position:0% +return for early childhood education so + + + align:start position:0% +return for early childhood education so +it's very clear that if we want to have + + align:start position:0% +it's very clear that if we want to have + + + align:start position:0% +it's very clear that if we want to have +the next generation's children well + + align:start position:0% +the next generation's children well + + + align:start position:0% +the next generation's children well +educated so they can move on to achieve + + align:start position:0% +educated so they can move on to achieve + + + align:start position:0% +educated so they can move on to achieve +their dreams in the workforce then we + + align:start position:0% +their dreams in the workforce then we + + + align:start position:0% +their dreams in the workforce then we +have to get on with this the challenge + + align:start position:0% +have to get on with this the challenge + + + align:start position:0% +have to get on with this the challenge +is that uh it's very expensive the good + + align:start position:0% +is that uh it's very expensive the good + + + align:start position:0% +is that uh it's very expensive the good +news is that Mayors and governers around + + align:start position:0% +news is that Mayors and governers around + + + align:start position:0% +news is that Mayors and governers around +the country are beginning to recognize + + align:start position:0% +the country are beginning to recognize + + + align:start position:0% +the country are beginning to recognize +the importance so from Seattle to New + + align:start position:0% +the importance so from Seattle to New + + + align:start position:0% +the importance so from Seattle to New +York to Boston and many other cities + + align:start position:0% +York to Boston and many other cities + + + align:start position:0% +York to Boston and many other cities +we're seeing Mayors take the lead and + + align:start position:0% +we're seeing Mayors take the lead and + + + align:start position:0% +we're seeing Mayors take the lead and +saying let's figure out how we invest in + + align:start position:0% +saying let's figure out how we invest in + + + align:start position:0% +saying let's figure out how we invest in +early childhood education and let's get + + align:start position:0% +early childhood education and let's get + + + align:start position:0% +early childhood education and let's get +on with that task for individual parents + + align:start position:0% +on with that task for individual parents + + + align:start position:0% +on with that task for individual parents +it is very expensive and so we have to + + align:start position:0% +it is very expensive and so we have to + + + align:start position:0% +it is very expensive and so we have to +work together as a community to figure + + align:start position:0% +work together as a community to figure + + + align:start position:0% +work together as a community to figure +out how we can fund early childhood + + align:start position:0% +out how we can fund early childhood + + + align:start position:0% +out how we can fund early childhood +education for all and for every parent + + align:start position:0% +education for all and for every parent + + + align:start position:0% +education for all and for every parent +it's critical that you think as you can + + align:start position:0% +it's critical that you think as you can + + + align:start position:0% +it's critical that you think as you can +about what do you need what do your + + align:start position:0% +about what do you need what do your + + + align:start position:0% +about what do you need what do your +children need what's appropriate for + + align:start position:0% +children need what's appropriate for + + + align:start position:0% +children need what's appropriate for +different age groups from early uh + + align:start position:0% +different age groups from early uh + + + align:start position:0% +different age groups from early uh +childhood right through uh Elementary + + align:start position:0% +childhood right through uh Elementary + + + align:start position:0% +childhood right through uh Elementary +School what can you afford and how can + + align:start position:0% +School what can you afford and how can + + + align:start position:0% +School what can you afford and how can +you make it fit into your work and other + + align:start position:0% +you make it fit into your work and other + + + align:start position:0% +you make it fit into your work and other +family + + align:start position:0% +family + + + align:start position:0% +family +responsibilities but if we don't start + + align:start position:0% +responsibilities but if we don't start + + + align:start position:0% +responsibilities but if we don't start +early then we will pay the price + + align:start position:0% + + + + align:start position:0% + +later for \ No newline at end of file diff --git a/N28g_YBXY8Y.txt b/N28g_YBXY8Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..2d21e193eecf3687fb2186b40cb6b2ef89496d06 --- /dev/null +++ b/N28g_YBXY8Y.txt @@ -0,0 +1,16651 @@ +align:start position:0% + +alrighty when we get started + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +welcome back nice to see you all + + align:start position:0% +welcome back nice to see you all + + + align:start position:0% +welcome back nice to see you all +um + + align:start position:0% +um + + + align:start position:0% +um +and + + align:start position:0% +and + + + align:start position:0% +and +what have we been doing + + align:start position:0% +what have we been doing + + + align:start position:0% +what have we been doing +in theory of computation + + align:start position:0% +in theory of computation + + + align:start position:0% +in theory of computation +we have been talking about touring + + align:start position:0% +we have been talking about touring + + + align:start position:0% +we have been talking about touring +machines + + align:start position:0% +machines + + + align:start position:0% +machines +and about uh + + align:start position:0% +and about uh + + + align:start position:0% +and about uh +the power of touring machines we started + + align:start position:0% +the power of touring machines we started + + + align:start position:0% +the power of touring machines we started +uh at the beginning by + + align:start position:0% +uh at the beginning by + + + align:start position:0% +uh at the beginning by +showing um a bunch of decidability + + align:start position:0% +showing um a bunch of decidability + + + align:start position:0% +showing um a bunch of decidability +theorems that exhibit the power of + + align:start position:0% +theorems that exhibit the power of + + + align:start position:0% +theorems that exhibit the power of +turing machines + + align:start position:0% +turing machines + + + align:start position:0% +turing machines +to + + align:start position:0% + + + + align:start position:0% + +calculate properties of + + align:start position:0% +calculate properties of + + + align:start position:0% +calculate properties of +finite automata context-free grammars + + align:start position:0% +finite automata context-free grammars + + + align:start position:0% +finite automata context-free grammars +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +in some cases and last lecture we talked + + align:start position:0% +in some cases and last lecture we talked + + + align:start position:0% +in some cases and last lecture we talked +about the limitations of + + align:start position:0% +about the limitations of + + + align:start position:0% +about the limitations of +the power of turing machines by + + align:start position:0% +the power of turing machines by + + + align:start position:0% +the power of turing machines by +um + + align:start position:0% +um + + + align:start position:0% +um +proving undecidability theorems so we + + align:start position:0% +proving undecidability theorems so we + + + align:start position:0% +proving undecidability theorems so we +showed that + + align:start position:0% +showed that + + + align:start position:0% +showed that +this language atm + + align:start position:0% +this language atm + + + align:start position:0% +this language atm +the acceptance problem for turing + + align:start position:0% +the acceptance problem for turing + + + align:start position:0% +the acceptance problem for turing +machines itself is an undecidable + + align:start position:0% +machines itself is an undecidable + + + align:start position:0% +machines itself is an undecidable +problem + + align:start position:0% +problem + + + align:start position:0% +problem +that was the first of many undecidable + + align:start position:0% +that was the first of many undecidable + + + align:start position:0% +that was the first of many undecidable +problems that we're going to encounter + + align:start position:0% +problems that we're going to encounter + + + align:start position:0% +problems that we're going to encounter +and though we proved the undecidability + + align:start position:0% +and though we proved the undecidability + + + align:start position:0% +and though we proved the undecidability +of atm using the diagonalization method + + align:start position:0% +of atm using the diagonalization method + + + align:start position:0% +of atm using the diagonalization method +as you hopefully remember + + align:start position:0% +as you hopefully remember + + + align:start position:0% +as you hopefully remember +we're going to introduce a new method + + align:start position:0% +we're going to introduce a new method + + + align:start position:0% +we're going to introduce a new method +which we kind of basically previewed + + align:start position:0% +which we kind of basically previewed + + + align:start position:0% +which we kind of basically previewed +last time called the reducibility method + + align:start position:0% +last time called the reducibility method + + + align:start position:0% +last time called the reducibility method +which is the way other problems are + + align:start position:0% +which is the way other problems are + + + align:start position:0% +which is the way other problems are +typically shown to be undecidable + + align:start position:0% +typically shown to be undecidable + + + align:start position:0% +typically shown to be undecidable +um + + align:start position:0% +um + + + align:start position:0% +um +and so we're going to stick with that uh + + align:start position:0% +and so we're going to stick with that uh + + + align:start position:0% +and so we're going to stick with that uh +for uh this lecture and also next + + align:start position:0% +for uh this lecture and also next + + + align:start position:0% +for uh this lecture and also next +lecture um we're going to be talking + + align:start position:0% +lecture um we're going to be talking + + + align:start position:0% +lecture um we're going to be talking +about um + + align:start position:0% +about um + + + align:start position:0% +about um +undecidability and i think there's going + + align:start position:0% +undecidability and i think there's going + + + align:start position:0% +undecidability and i think there's going +to be a few additional uh discussions + + align:start position:0% +to be a few additional uh discussions + + + align:start position:0% +to be a few additional uh discussions +after that but this is one of the + + align:start position:0% +after that but this is one of the + + + align:start position:0% +after that but this is one of the +important uh themes of the course is to + + align:start position:0% +important uh themes of the course is to + + + align:start position:0% +important uh themes of the course is to +understand kind of that threshold + + align:start position:0% +understand kind of that threshold + + + align:start position:0% +understand kind of that threshold +between decidability and undecidability + + align:start position:0% +between decidability and undecidability + + + align:start position:0% +between decidability and undecidability +or the limitations of computation + + align:start position:0% +or the limitations of computation + + + align:start position:0% +or the limitations of computation +um + + align:start position:0% +um + + + align:start position:0% +um +so today um as i mentioned we're going + + align:start position:0% +so today um as i mentioned we're going + + + align:start position:0% +so today um as i mentioned we're going +to talk about the reducibility method + + align:start position:0% +to talk about the reducibility method + + + align:start position:0% +to talk about the reducibility method +for proving problems undecidable and + + align:start position:0% +for proving problems undecidable and + + + align:start position:0% +for proving problems undecidable and +also for proving problems + + align:start position:0% +also for proving problems + + + align:start position:0% +also for proving problems +non-touring recognizable uh turning + + align:start position:0% +non-touring recognizable uh turning + + + align:start position:0% +non-touring recognizable uh turning +unrecognizable + + align:start position:0% +unrecognizable + + + align:start position:0% +unrecognizable +we're going to introduce + + align:start position:0% +we're going to introduce + + + align:start position:0% +we're going to introduce +this notion of a reducibility um in + + align:start position:0% +this notion of a reducibility um in + + + align:start position:0% +this notion of a reducibility um in +general and we'll also talk about a very + + align:start position:0% +general and we'll also talk about a very + + + align:start position:0% +general and we'll also talk about a very +specific kind of reducibility called the + + align:start position:0% +specific kind of reducibility called the + + + align:start position:0% +specific kind of reducibility called the +mapping reducibility so today as + + align:start position:0% +mapping reducibility so today as + + + align:start position:0% +mapping reducibility so today as +promised we're going to talk about using + + align:start position:0% +promised we're going to talk about using + + + align:start position:0% +promised we're going to talk about using +reduce abilities + + align:start position:0% +reduce abilities + + + align:start position:0% +reduce abilities +to prove problems are undecidable or + + align:start position:0% +to prove problems are undecidable or + + + align:start position:0% +to prove problems are undecidable or +unrecognizable + + align:start position:0% +unrecognizable + + + align:start position:0% +unrecognizable +so that's going to be our general method + + align:start position:0% +so that's going to be our general method + + + align:start position:0% +so that's going to be our general method +oops make myself smaller thank you + + align:start position:0% +oops make myself smaller thank you + + + align:start position:0% +oops make myself smaller thank you +i always forget + + align:start position:0% +i always forget + + + align:start position:0% +i always forget +uh + + align:start position:0% +uh + + + align:start position:0% +uh +thank you um + + align:start position:0% +thank you um + + + align:start position:0% +thank you um +for the reminder + + align:start position:0% +for the reminder + + + align:start position:0% +for the reminder +so + + align:start position:0% +so + + + align:start position:0% +so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so using um reducibilities to prove + + align:start position:0% +so using um reducibilities to prove + + + align:start position:0% +so using um reducibilities to prove +problems are undecidable or + + align:start position:0% +problems are undecidable or + + + align:start position:0% +problems are undecidable or +unrecognizable + + align:start position:0% +unrecognizable + + + align:start position:0% +unrecognizable +and the basic way that works is we're + + align:start position:0% +and the basic way that works is we're + + + align:start position:0% +and the basic way that works is we're +going to leverage another some problem + + align:start position:0% +going to leverage another some problem + + + align:start position:0% +going to leverage another some problem +we already know + + align:start position:0% +we already know + + + align:start position:0% +we already know +is undecidable say or unrecognizable to + + align:start position:0% +is undecidable say or unrecognizable to + + + align:start position:0% +is undecidable say or unrecognizable to +prove other problems are unrecognizable + + align:start position:0% +prove other problems are unrecognizable + + + align:start position:0% +prove other problems are unrecognizable +so we did a quick example of that last + + align:start position:0% +so we did a quick example of that last + + + align:start position:0% +so we did a quick example of that last +time we're going to go over that example + + align:start position:0% +time we're going to go over that example + + + align:start position:0% +time we're going to go over that example +again um just to set this set the stage + + align:start position:0% +again um just to set this set the stage + + + align:start position:0% +again um just to set this set the stage +and then we're going to talk about that + + align:start position:0% +and then we're going to talk about that + + + align:start position:0% +and then we're going to talk about that +in greater detail + + align:start position:0% +in greater detail + + + align:start position:0% +in greater detail +um + + align:start position:0% +um + + + align:start position:0% +um +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +as you recall from last time we had this + + align:start position:0% +as you recall from last time we had this + + + align:start position:0% +as you recall from last time we had this +problem halt tm + + align:start position:0% +problem halt tm + + + align:start position:0% +problem halt tm +which is the problem of testing for a + + align:start position:0% +which is the problem of testing for a + + + align:start position:0% +which is the problem of testing for a +given turing machine and an input to + + align:start position:0% +given turing machine and an input to + + + align:start position:0% +given turing machine and an input to +that turing machine whether the turing + + align:start position:0% +that turing machine whether the turing + + + align:start position:0% +that turing machine whether the turing +machine halts either accepting or + + align:start position:0% +machine halts either accepting or + + + align:start position:0% +machine halts either accepting or +rejecting but just whether it holds um + + align:start position:0% +rejecting but just whether it holds um + + + align:start position:0% +rejecting but just whether it holds um +which is a somewhat different problem + + align:start position:0% +which is a somewhat different problem + + + align:start position:0% +which is a somewhat different problem +closely related obviously but somewhat + + align:start position:0% +closely related obviously but somewhat + + + align:start position:0% +closely related obviously but somewhat +different than the atm problem which is + + align:start position:0% +different than the atm problem which is + + + align:start position:0% +different than the atm problem which is +just testing whether the turing machine + + align:start position:0% +just testing whether the turing machine + + + align:start position:0% +just testing whether the turing machine +accepts + + align:start position:0% +accepts + + + align:start position:0% +accepts +um you know it's we already showed that + + align:start position:0% +um you know it's we already showed that + + + align:start position:0% +um you know it's we already showed that +atm is undecidable + + align:start position:0% +atm is undecidable + + + align:start position:0% +atm is undecidable +um now + + align:start position:0% +um now + + + align:start position:0% +um now +conceivably whole tm might be decidable + + align:start position:0% +conceivably whole tm might be decidable + + + align:start position:0% +conceivably whole tm might be decidable +um you know it's not exactly the same + + align:start position:0% +um you know it's not exactly the same + + + align:start position:0% +um you know it's not exactly the same +problem + + align:start position:0% +problem + + + align:start position:0% +problem +but we're going to show that whole tm is + + align:start position:0% +but we're going to show that whole tm is + + + align:start position:0% +but we're going to show that whole tm is +likewise undecidable uh we did this last + + align:start position:0% +likewise undecidable uh we did this last + + + align:start position:0% +likewise undecidable uh we did this last +time but i'm just going over it again uh + + align:start position:0% +time but i'm just going over it again uh + + + align:start position:0% +time but i'm just going over it again uh +i'm going to likewise show that whole tm + + align:start position:0% +i'm going to likewise show that whole tm + + + align:start position:0% +i'm going to likewise show that whole tm +is undecidable we could go back to the + + align:start position:0% +is undecidable we could go back to the + + + align:start position:0% +is undecidable we could go back to the +um the diagonalization method and do it + + align:start position:0% +um the diagonalization method and do it + + + align:start position:0% +um the diagonalization method and do it +from scratch + + align:start position:0% +from scratch + + + align:start position:0% +from scratch +but uh generally that's not what's done + + align:start position:0% +but uh generally that's not what's done + + + align:start position:0% +but uh generally that's not what's done +generally what people do is they use a + + align:start position:0% +generally what people do is they use a + + + align:start position:0% +generally what people do is they use a +reduceability from a known undecidable + + align:start position:0% +reduceability from a known undecidable + + + align:start position:0% +reduceability from a known undecidable +problem um so what we're going to show + + align:start position:0% +problem um so what we're going to show + + + align:start position:0% +problem um so what we're going to show +is a proof by contradiction which says + + align:start position:0% +is a proof by contradiction which says + + + align:start position:0% +is a proof by contradiction which says +that + + align:start position:0% +that + + + align:start position:0% +that +if + + align:start position:0% +if + + + align:start position:0% +if +um + + align:start position:0% +um + + + align:start position:0% +um +halt tm were decidable then atm would + + align:start position:0% +halt tm were decidable then atm would + + + align:start position:0% +halt tm were decidable then atm would +also be decidable and we know it isn't + + align:start position:0% +also be decidable and we know it isn't + + + align:start position:0% +also be decidable and we know it isn't +um that and that's by virtue of what we + + align:start position:0% +um that and that's by virtue of what we + + + align:start position:0% +um that and that's by virtue of what we +call a reduceability from atm to whole + + align:start position:0% +call a reduceability from atm to whole + + + align:start position:0% +call a reduceability from atm to whole +tm and i'll explain with the terminology + + align:start position:0% +tm and i'll explain with the terminology + + + align:start position:0% +tm and i'll explain with the terminology +and and we'll have a chance to play with + + align:start position:0% +and and we'll have a chance to play with + + + align:start position:0% +and and we'll have a chance to play with +the concept all all lecture long um so + + align:start position:0% +the concept all all lecture long um so + + + align:start position:0% +the concept all all lecture long um so +we're going to see it in all sorts of + + align:start position:0% +we're going to see it in all sorts of + + + align:start position:0% +we're going to see it in all sorts of +different vari variations um + + align:start position:0% +different vari variations um + + + align:start position:0% +different vari variations um +so + + align:start position:0% +so + + + align:start position:0% +so +as i said we'll assume whole tm is + + align:start position:0% +as i said we'll assume whole tm is + + + align:start position:0% +as i said we'll assume whole tm is +decidable and use that to show that atm + + align:start position:0% +decidable and use that to show that atm + + + align:start position:0% +decidable and use that to show that atm +is decidable which we know is not true + + align:start position:0% +is decidable which we know is not true + + + align:start position:0% +is decidable which we know is not true +um + + align:start position:0% +um + + + align:start position:0% +um +so quickly going through it because we + + align:start position:0% +so quickly going through it because we + + + align:start position:0% +so quickly going through it because we +we did it already once before um + + align:start position:0% +we did it already once before um + + + align:start position:0% +we did it already once before um +we're gonna assume + + align:start position:0% +we're gonna assume + + + align:start position:0% +we're gonna assume +you know that whole tm is decidable + + align:start position:0% +you know that whole tm is decidable + + + align:start position:0% +you know that whole tm is decidable +let's say turing machine r + + align:start position:0% +let's say turing machine r + + + align:start position:0% +let's say turing machine r +is the decider + + align:start position:0% +is the decider + + + align:start position:0% +is the decider +and now we're going to show that atm is + + align:start position:0% +and now we're going to show that atm is + + + align:start position:0% +and now we're going to show that atm is +decidable by constructing a turing + + align:start position:0% +decidable by constructing a turing + + + align:start position:0% +decidable by constructing a turing +machine s + + align:start position:0% +machine s + + + align:start position:0% +machine s +which uses r + + align:start position:0% +which uses r + + + align:start position:0% +which uses r +to decide atm + + align:start position:0% +to decide atm + + + align:start position:0% +to decide atm +that's going to be our contradiction + + align:start position:0% +that's going to be our contradiction + + + align:start position:0% +that's going to be our contradiction +so here is the machine s + + align:start position:0% +so here is the machine s + + + align:start position:0% +so here is the machine s +the machine is you know you have to keep + + align:start position:0% +the machine is you know you have to keep + + + align:start position:0% +the machine is you know you have to keep +in mind what the goal of s is go s is + + align:start position:0% +in mind what the goal of s is go s is + + + align:start position:0% +in mind what the goal of s is go s is +this we're going to design s to solve + + align:start position:0% +this we're going to design s to solve + + + align:start position:0% +this we're going to design s to solve +atm + + align:start position:0% +atm + + + align:start position:0% +atm +which we know is not decidable so that + + align:start position:0% +which we know is not decidable so that + + + align:start position:0% +which we know is not decidable so that +don't get confused by that we're aiming + + align:start position:0% +don't get confused by that we're aiming + + + align:start position:0% +don't get confused by that we're aiming +for a contradiction + + align:start position:0% +for a contradiction + + + align:start position:0% +for a contradiction +so we're going to use + + align:start position:0% +so we're going to use + + + align:start position:0% +so we're going to use +s is typically + + align:start position:0% +s is typically + + + align:start position:0% +s is typically +well there might be other variations but + + align:start position:0% +well there might be other variations but + + + align:start position:0% +well there might be other variations but +for now s is going to be used to decide + + align:start position:0% +for now s is going to be used to decide + + + align:start position:0% +for now s is going to be used to decide +atm + + align:start position:0% + + + + align:start position:0% + +so we can try to figure out how can we + + align:start position:0% +so we can try to figure out how can we + + + align:start position:0% +so we can try to figure out how can we +decide atm + + align:start position:0% +decide atm + + + align:start position:0% +decide atm +and the way we're going to do it is + + align:start position:0% +and the way we're going to do it is + + + align:start position:0% +and the way we're going to do it is +use our halt tm + + align:start position:0% +use our halt tm + + + align:start position:0% +use our halt tm +tester that we assumed um to have + + align:start position:0% +tester that we assumed um to have + + + align:start position:0% +tester that we assumed um to have +and we'll first take our + + align:start position:0% +and we'll first take our + + + align:start position:0% +and we'll first take our +m and w where we're trying to determine + + align:start position:0% +m and w where we're trying to determine + + + align:start position:0% +m and w where we're trying to determine +it does m accept w + + align:start position:0% +it does m accept w + + + align:start position:0% +it does m accept w +and we'll first test whether m holds on + + align:start position:0% +and we'll first test whether m holds on + + + align:start position:0% +and we'll first test whether m holds on +w + + align:start position:0% +w + + + align:start position:0% +w +if it doesn't or done + + align:start position:0% +if it doesn't or done + + + align:start position:0% +if it doesn't or done +because it couldn't be accepting w + + align:start position:0% +because it couldn't be accepting w + + + align:start position:0% +because it couldn't be accepting w +m couldn't be accepting w if it's not + + align:start position:0% +m couldn't be accepting w if it's not + + + align:start position:0% +m couldn't be accepting w if it's not +even this whole thing on w + + align:start position:0% +even this whole thing on w + + + align:start position:0% +even this whole thing on w +um + + align:start position:0% +um + + + align:start position:0% +um +so if it + + align:start position:0% +so if it + + + align:start position:0% +so if it +uh + + align:start position:0% +uh + + + align:start position:0% +uh +r reports doesn't halt we can reject + + align:start position:0% +r reports doesn't halt we can reject + + + align:start position:0% +r reports doesn't halt we can reject +right off + + align:start position:0% +right off + + + align:start position:0% +right off +but + + align:start position:0% +but + + + align:start position:0% +but +um even if r says it does hold + + align:start position:0% +um even if r says it does hold + + + align:start position:0% +um even if r says it does hold +we're still in good shape because now we + + align:start position:0% +we're still in good shape because now we + + + align:start position:0% +we're still in good shape because now we +can run m on w until completion because + + align:start position:0% +can run m on w until completion because + + + align:start position:0% +can run m on w until completion because +r has promised us that it's going to + + align:start position:0% +r has promised us that it's going to + + + align:start position:0% +r has promised us that it's going to +halt + + align:start position:0% +halt + + + align:start position:0% +halt +r r stated and r is assumed to be + + align:start position:0% +r r stated and r is assumed to be + + + align:start position:0% +r r stated and r is assumed to be +correct + + align:start position:0% +correct + + + align:start position:0% +correct +r is stated that m holds on w so now we + + align:start position:0% +r is stated that m holds on w so now we + + + align:start position:0% +r is stated that m holds on w so now we +don't have to worry about getting into a + + align:start position:0% +don't have to worry about getting into a + + + align:start position:0% +don't have to worry about getting into a +loop which we're not allowed to do since + + align:start position:0% +loop which we're not allowed to do since + + + align:start position:0% +loop which we're not allowed to do since +we're making a decider + + align:start position:0% +we're making a decider + + + align:start position:0% +we're making a decider +um we're trying to decide atm here so we + + align:start position:0% +um we're trying to decide atm here so we + + + align:start position:0% +um we're trying to decide atm here so we +but now we can run them on w to + + align:start position:0% +but now we can run them on w to + + + align:start position:0% +but now we can run them on w to +completion we can find out what what um + + align:start position:0% +completion we can find out what what um + + + align:start position:0% +completion we can find out what what um +m does on w and then we can act + + align:start position:0% +m does on w and then we can act + + + align:start position:0% +m does on w and then we can act +accordingly + + align:start position:0% + + + + align:start position:0% + +so we're using the whole tm decider to + + align:start position:0% +so we're using the whole tm decider to + + + align:start position:0% +so we're using the whole tm decider to +decide atm that's the name of the game + + align:start position:0% +decide atm that's the name of the game + + + align:start position:0% +decide atm that's the name of the game +here okay um + + align:start position:0% +here okay um + + + align:start position:0% +here okay um +and that's a contradiction and so + + align:start position:0% +and that's a contradiction and so + + + align:start position:0% +and that's a contradiction and so +therefore our assumption that whole tm + + align:start position:0% +therefore our assumption that whole tm + + + align:start position:0% +therefore our assumption that whole tm +was decidable had to be false so it's + + align:start position:0% +was decidable had to be false so it's + + + align:start position:0% +was decidable had to be false so it's +undecidable + + align:start position:0% +undecidable + + + align:start position:0% +undecidable +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +important to understand this + + align:start position:0% +important to understand this + + + align:start position:0% +important to understand this +uh because this is + + align:start position:0% +uh because this is + + + align:start position:0% +uh because this is +um sort of the prototype + + align:start position:0% +um sort of the prototype + + + align:start position:0% +um sort of the prototype +for all of the other uh + + align:start position:0% +for all of the other uh + + + align:start position:0% +for all of the other uh +uh undecidable undecidability uh proofs + + align:start position:0% +uh undecidable undecidability uh proofs + + + align:start position:0% +uh undecidable undecidability uh proofs +that we're gonna do going forward + + align:start position:0% +that we're gonna do going forward + + + align:start position:0% +that we're gonna do going forward +okay so we can just take a few seconds + + align:start position:0% +okay so we can just take a few seconds + + + align:start position:0% +okay so we can just take a few seconds +here if there's something that you're + + align:start position:0% +here if there's something that you're + + + align:start position:0% +here if there's something that you're +not getting about this + + align:start position:0% +not getting about this + + + align:start position:0% +not getting about this +it's a good time to ask + + align:start position:0% + + + + align:start position:0% + +not seeing many messages here or any so + + align:start position:0% +not seeing many messages here or any so + + + align:start position:0% +not seeing many messages here or any so +why don't we go on + + align:start position:0% +why don't we go on + + + align:start position:0% +why don't we go on +um but if you know if you ask i can get + + align:start position:0% +um but if you know if you ask i can get + + + align:start position:0% +um but if you know if you ask i can get +to it uh next slide too + + align:start position:0% +to it uh next slide too + + + align:start position:0% +to it uh next slide too +all right here we go so here's the + + align:start position:0% +all right here we go so here's the + + + align:start position:0% +all right here we go so here's the +concept of reducibility + + align:start position:0% + + + + align:start position:0% + +and i know i've taught this course many + + align:start position:0% +and i know i've taught this course many + + + align:start position:0% +and i know i've taught this course many +times i know where the bumpy uh places + + align:start position:0% +times i know where the bumpy uh places + + + align:start position:0% +times i know where the bumpy uh places +are in terms of people struggling with + + align:start position:0% +are in terms of people struggling with + + + align:start position:0% +are in terms of people struggling with +material + + align:start position:0% +material + + + align:start position:0% +material +the concept of reducibility is um + + align:start position:0% + + + + align:start position:0% + +is a bit tricky + + align:start position:0% +is a bit tricky + + + align:start position:0% +is a bit tricky +so don't feel bad if you don't get it + + align:start position:0% +so don't feel bad if you don't get it + + + align:start position:0% +so don't feel bad if you don't get it +right away + + align:start position:0% +right away + + + align:start position:0% +right away +you know so that's why i'm going to try + + align:start position:0% +you know so that's why i'm going to try + + + align:start position:0% +you know so that's why i'm going to try +to go slowly in this lecture to make + + align:start position:0% +to go slowly in this lecture to make + + + align:start position:0% +to go slowly in this lecture to make +sure we're all together + + align:start position:0% +sure we're all together + + + align:start position:0% +sure we're all together +on understanding how redu reducibility + + align:start position:0% +on understanding how redu reducibility + + + align:start position:0% +on understanding how redu reducibility +works + + align:start position:0% +works + + + align:start position:0% +works +okay so the concept of reducibility is + + align:start position:0% +okay so the concept of reducibility is + + + align:start position:0% +okay so the concept of reducibility is +that we say one problem is reducible to + + align:start position:0% +that we say one problem is reducible to + + + align:start position:0% +that we say one problem is reducible to +another say a reducible to b + + align:start position:0% +another say a reducible to b + + + align:start position:0% +another say a reducible to b +it means + + align:start position:0% +it means + + + align:start position:0% +it means +that you can use b + + align:start position:0% +that you can use b + + + align:start position:0% +that you can use b +to solve a + + align:start position:0% + + + + align:start position:0% + +that's what it means for a to be + + align:start position:0% +that's what it means for a to be + + + align:start position:0% +that's what it means for a to be +reducible to b + + align:start position:0% + + + + align:start position:0% + +okay so uh i'm going to give a bunch of + + align:start position:0% +okay so uh i'm going to give a bunch of + + + align:start position:0% +okay so uh i'm going to give a bunch of +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +informal examples of that or or easy + + align:start position:0% +informal examples of that or or easy + + + align:start position:0% +informal examples of that or or easy +examples of that and and then we'll + + align:start position:0% +examples of that and and then we'll + + + align:start position:0% +examples of that and and then we'll +start to use it for real + + align:start position:0% +start to use it for real + + + align:start position:0% +start to use it for real +so example one this is sort of you know + + align:start position:0% +so example one this is sort of you know + + + align:start position:0% +so example one this is sort of you know +really outside material from the course + + align:start position:0% +really outside material from the course + + + align:start position:0% +really outside material from the course +but i think it's something uh you can + + align:start position:0% +but i think it's something uh you can + + + align:start position:0% +but i think it's something uh you can +appreciate + + align:start position:0% +appreciate + + + align:start position:0% +appreciate +you know everybody knows you can measure + + align:start position:0% +you know everybody knows you can measure + + + align:start position:0% +you know everybody knows you can measure +uh the area of a rectangle + + align:start position:0% +uh the area of a rectangle + + + align:start position:0% +uh the area of a rectangle +by measuring the lengths of the of the + + align:start position:0% +by measuring the lengths of the of the + + + align:start position:0% +by measuring the lengths of the of the +of the two sides + + align:start position:0% +of the two sides + + + align:start position:0% +of the two sides +measuring the lengths of its uh it's + + align:start position:0% +measuring the lengths of its uh it's + + + align:start position:0% +measuring the lengths of its uh it's +measuring the length and width + + align:start position:0% +measuring the length and width + + + align:start position:0% +measuring the length and width +uh of the rectangle + + align:start position:0% +uh of the rectangle + + + align:start position:0% +uh of the rectangle +so in other words if + + align:start position:0% +so in other words if + + + align:start position:0% +so in other words if +you had the problem of determining the + + align:start position:0% +you had the problem of determining the + + + align:start position:0% +you had the problem of determining the +area + + align:start position:0% +area + + + align:start position:0% +area +you could reduce that problem to the + + align:start position:0% +you could reduce that problem to the + + + align:start position:0% +you could reduce that problem to the +problem of measuring uh the length and + + align:start position:0% +problem of measuring uh the length and + + + align:start position:0% +problem of measuring uh the length and +width + + align:start position:0% +width + + + align:start position:0% +width +of the retaining rectangle + + align:start position:0% +of the retaining rectangle + + + align:start position:0% +of the retaining rectangle +uh so here um we you know we're taking + + align:start position:0% +uh so here um we you know we're taking + + + align:start position:0% +uh so here um we you know we're taking +one problem and reducing it to another + + align:start position:0% +one problem and reducing it to another + + + align:start position:0% +one problem and reducing it to another +problem you know it's conceivable that + + align:start position:0% +problem you know it's conceivable that + + + align:start position:0% +problem you know it's conceivable that +measuring the + + align:start position:0% +measuring the + + + align:start position:0% +measuring the +um length and width + + align:start position:0% +um length and width + + + align:start position:0% +um length and width +is easier + + align:start position:0% +is easier + + + align:start position:0% +is easier +um than it would be to measure the area + + align:start position:0% +um than it would be to measure the area + + + align:start position:0% +um than it would be to measure the area +directly by somehow covering the space + + align:start position:0% +directly by somehow covering the space + + + align:start position:0% +directly by somehow covering the space +with + + align:start position:0% +with + + + align:start position:0% +with +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know uh tiles as one way of + + align:start position:0% +you know uh tiles as one way of + + + align:start position:0% +you know uh tiles as one way of +measuring it um + + align:start position:0% +measuring it um + + + align:start position:0% +measuring it um +but um it tells you you don't have to do + + align:start position:0% +but um it tells you you don't have to do + + + align:start position:0% +but um it tells you you don't have to do +that + + align:start position:0% +that + + + align:start position:0% +that +the problem of measuring the area is + + align:start position:0% +the problem of measuring the area is + + + align:start position:0% +the problem of measuring the area is +easier than measure covering with tiles + + align:start position:0% +easier than measure covering with tiles + + + align:start position:0% +easier than measure covering with tiles +you can just measure the length and + + align:start position:0% +you can just measure the length and + + + align:start position:0% +you can just measure the length and +width and you're done + + align:start position:0% +width and you're done + + + align:start position:0% +width and you're done +so reducibility is a way of making + + align:start position:0% +so reducibility is a way of making + + + align:start position:0% +so reducibility is a way of making +problems easier + + align:start position:0% +problems easier + + + align:start position:0% +problems easier +by by + + align:start position:0% +by by + + + align:start position:0% +by by +translating them into some easier + + align:start position:0% +translating them into some easier + + + align:start position:0% +translating them into some easier +problem + + align:start position:0% +problem + + + align:start position:0% +problem +so here's another example that we've + + align:start position:0% +so here's another example that we've + + + align:start position:0% +so here's another example that we've +already seen we didn't talk we didn't + + align:start position:0% +already seen we didn't talk we didn't + + + align:start position:0% +already seen we didn't talk we didn't +call it a reduceability but + + align:start position:0% +call it a reduceability but + + + align:start position:0% +call it a reduceability but +um if you remember back uh a a couple of + + align:start position:0% +um if you remember back uh a a couple of + + + align:start position:0% +um if you remember back uh a a couple of +weeks ago we were talking about the + + align:start position:0% +weeks ago we were talking about the + + + align:start position:0% +weeks ago we were talking about the +languages anfa and adfa the acceptance + + align:start position:0% +languages anfa and adfa the acceptance + + + align:start position:0% +languages anfa and adfa the acceptance +problems for you know nfas and dfas + + align:start position:0% +problems for you know nfas and dfas + + + align:start position:0% +problems for you know nfas and dfas +and we gave a way of solving the a d of + + align:start position:0% +and we gave a way of solving the a d of + + + align:start position:0% +and we gave a way of solving the a d of +a problem as do you remember you know + + align:start position:0% +a problem as do you remember you know + + + align:start position:0% +a problem as do you remember you know +the turing machine simulated uh the fine + + align:start position:0% +the turing machine simulated uh the fine + + + align:start position:0% +the turing machine simulated uh the fine +art automaton + + align:start position:0% +art automaton + + + align:start position:0% +art automaton +and we solved the a nfa problem + + align:start position:0% +and we solved the a nfa problem + + + align:start position:0% +and we solved the a nfa problem +not by doing it directly + + align:start position:0% +not by doing it directly + + + align:start position:0% +not by doing it directly +but by converting the nfa to a dfa + + align:start position:0% +but by converting the nfa to a dfa + + + align:start position:0% +but by converting the nfa to a dfa +and then using the solution for adfa + + align:start position:0% +and then using the solution for adfa + + + align:start position:0% +and then using the solution for adfa +in fact in effect what we were doing was + + align:start position:0% +in fact in effect what we were doing was + + + align:start position:0% +in fact in effect what we were doing was +we were reducing the a nfa problem to + + align:start position:0% +we were reducing the a nfa problem to + + + align:start position:0% +we were reducing the a nfa problem to +the adfa problem + + align:start position:0% +the adfa problem + + + align:start position:0% +the adfa problem +um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +um so + + align:start position:0% +um so + + + align:start position:0% +um so +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +let's do another example + + align:start position:0% +let's do another example + + + align:start position:0% +let's do another example +here's a problem you know here's an + + align:start position:0% +here's a problem you know here's an + + + align:start position:0% +here's a problem you know here's an +example that + + align:start position:0% +example that + + + align:start position:0% +example that +you you again probably didn't think + + align:start position:0% +you you again probably didn't think + + + align:start position:0% +you you again probably didn't think +about it this way but from your homework + + align:start position:0% +about it this way but from your homework + + + align:start position:0% +about it this way but from your homework +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh we had this pusher problem the + + align:start position:0% +uh we had this pusher problem the + + + align:start position:0% +uh we had this pusher problem the +problem of determining whether a + + align:start position:0% +problem of determining whether a + + + align:start position:0% +problem of determining whether a +push-down automaton ever + + align:start position:0% +push-down automaton ever + + + align:start position:0% +push-down automaton ever +pushes on its stack for any input + + align:start position:0% +pushes on its stack for any input + + + align:start position:0% +pushes on its stack for any input +i know a bunch of you are struggling + + align:start position:0% +i know a bunch of you are struggling + + + align:start position:0% +i know a bunch of you are struggling +with that problem um working on it + + align:start position:0% +with that problem um working on it + + + align:start position:0% +with that problem um working on it +hopefully + + align:start position:0% +hopefully + + + align:start position:0% +hopefully +hopefully solving it in one way or + + align:start position:0% +hopefully solving it in one way or + + + align:start position:0% +hopefully solving it in one way or +another so there's one way to solve it + + align:start position:0% +another so there's one way to solve it + + + align:start position:0% +another so there's one way to solve it +is an effect by reducing the pusher + + align:start position:0% +is an effect by reducing the pusher + + + align:start position:0% +is an effect by reducing the pusher +problem to the ecfg the emptiness for + + align:start position:0% +problem to the ecfg the emptiness for + + + align:start position:0% +problem to the ecfg the emptiness for +cfgs + + align:start position:0% +cfgs + + + align:start position:0% +cfgs +which is equivalent to the emptiness for + + align:start position:0% +which is equivalent to the emptiness for + + + align:start position:0% +which is equivalent to the emptiness for +pdas + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% +because + + + align:start position:0% +because +um + + align:start position:0% +um + + + align:start position:0% +um +you can take your i mean this is the the + + align:start position:0% +you can take your i mean this is the the + + + align:start position:0% +you can take your i mean this is the the +solution i had in mind which is a + + align:start position:0% +solution i had in mind which is a + + + align:start position:0% +solution i had in mind which is a +particularly simple and short solution + + align:start position:0% +particularly simple and short solution + + + align:start position:0% +particularly simple and short solution +of course not the only solution + + align:start position:0% +of course not the only solution + + + align:start position:0% +of course not the only solution +um you can take your push down automaton + + align:start position:0% +um you can take your push down automaton + + + align:start position:0% +um you can take your push down automaton +where you're trying to determine if it + + align:start position:0% +where you're trying to determine if it + + + align:start position:0% +where you're trying to determine if it +ever pushes + + align:start position:0% +ever pushes + + + align:start position:0% +ever pushes +and you can take the states + + align:start position:0% +and you can take the states + + + align:start position:0% +and you can take the states +um that are about to make a push + + align:start position:0% +um that are about to make a push + + + align:start position:0% +um that are about to make a push +and instead of making them + + align:start position:0% +and instead of making them + + + align:start position:0% +and instead of making them +make a push you make them accept states + + align:start position:0% +make a push you make them accept states + + + align:start position:0% +make a push you make them accept states +and you get rid of the original states + + align:start position:0% + + + + align:start position:0% + +so now you've converted + + align:start position:0% +so now you've converted + + + align:start position:0% +so now you've converted +this + + align:start position:0% +this + + + align:start position:0% +this +automaton + + align:start position:0% +automaton + + + align:start position:0% +automaton +to one + + align:start position:0% +to one + + + align:start position:0% +to one +that + + align:start position:0% +that + + + align:start position:0% +that +accepts every time the original push + + align:start position:0% +accepts every time the original push + + + align:start position:0% +accepts every time the original push +down automaton pushes + + align:start position:0% +down automaton pushes + + + align:start position:0% +down automaton pushes +and it accepts you know and then it has + + align:start position:0% +and it accepts you know and then it has + + + align:start position:0% +and it accepts you know and then it has +to move to the end of the input of + + align:start position:0% +to move to the end of the input of + + + align:start position:0% +to move to the end of the input of +course so um so it goes into an accept + + align:start position:0% +course so um so it goes into an accept + + + align:start position:0% +course so um so it goes into an accept +state and moves to the end of the input + + align:start position:0% +state and moves to the end of the input + + + align:start position:0% +state and moves to the end of the input +so every time the original machine was + + align:start position:0% +so every time the original machine was + + + align:start position:0% +so every time the original machine was +about to push the new machine that + + align:start position:0% +about to push the new machine that + + + align:start position:0% +about to push the new machine that +you're you're just creating here + + align:start position:0% +you're you're just creating here + + + align:start position:0% +you're you're just creating here +is going to go into an except state at + + align:start position:0% +is going to go into an except state at + + + align:start position:0% +is going to go into an except state at +the end of the input + + align:start position:0% +the end of the input + + + align:start position:0% +the end of the input +now to test whether the original machine + + align:start position:0% +now to test whether the original machine + + + align:start position:0% +now to test whether the original machine +ever uses stack it's enough to test + + align:start position:0% +ever uses stack it's enough to test + + + align:start position:0% +ever uses stack it's enough to test +whether the new machine ever accepts a + + align:start position:0% +whether the new machine ever accepts a + + + align:start position:0% +whether the new machine ever accepts a +string + + align:start position:0% + + + + align:start position:0% + +okay so that's a way i don't want to + + align:start position:0% +okay so that's a way i don't want to + + + align:start position:0% +okay so that's a way i don't want to +over complicate this right here and get + + align:start position:0% +over complicate this right here and get + + + align:start position:0% +over complicate this right here and get +you thinking about the homework again + + align:start position:0% +you thinking about the homework again + + + align:start position:0% +you thinking about the homework again +but this is a way of + + align:start position:0% +but this is a way of + + + align:start position:0% +but this is a way of +reducing one problem to another problem + + align:start position:0% +reducing one problem to another problem + + + align:start position:0% +reducing one problem to another problem +and you know if you're + + align:start position:0% +and you know if you're + + + align:start position:0% +and you know if you're +you don't quite get this one just focus + + align:start position:0% +you don't quite get this one just focus + + + align:start position:0% +you don't quite get this one just focus +on the other two examples i don't want + + align:start position:0% +on the other two examples i don't want + + + align:start position:0% +on the other two examples i don't want +to spend time on the on the homework set + + align:start position:0% +to spend time on the on the homework set + + + align:start position:0% +to spend time on the on the homework set +too right now so we can address that + + align:start position:0% +too right now so we can address that + + + align:start position:0% +too right now so we can address that +offline or separately if you if you want + + align:start position:0% +offline or separately if you if you want + + + align:start position:0% +offline or separately if you if you want +it's also the solution that's written up + + align:start position:0% +it's also the solution that's written up + + + align:start position:0% +it's also the solution that's written up +in the um + + align:start position:0% +in the um + + + align:start position:0% +in the um +the solution set that's posted on uh + + align:start position:0% +the solution set that's posted on uh + + + align:start position:0% +the solution set that's posted on uh +on the home page by the way + + align:start position:0% +on the home page by the way + + + align:start position:0% +on the home page by the way +um + + align:start position:0% +um + + + align:start position:0% +um +okay uh + + align:start position:0% +okay uh + + + align:start position:0% +okay uh +so getting back to let's see thinking + + align:start position:0% +so getting back to let's see thinking + + + align:start position:0% +so getting back to let's see thinking +about uh reducibility + + align:start position:0% + + + + align:start position:0% + +what i have in mind again this is sort + + align:start position:0% +what i have in mind again this is sort + + + align:start position:0% +what i have in mind again this is sort +of rephrasing it but i'm trying to + + align:start position:0% +of rephrasing it but i'm trying to + + + align:start position:0% +of rephrasing it but i'm trying to +hammer it in + + align:start position:0% +hammer it in + + + align:start position:0% +hammer it in +that if a is reducible to b + + align:start position:0% +that if a is reducible to b + + + align:start position:0% +that if a is reducible to b +then solving b gives a solution to a + + align:start position:0% + + + + align:start position:0% + +okay that's what happens in each of + + align:start position:0% +okay that's what happens in each of + + + align:start position:0% +okay that's what happens in each of +these examples + + align:start position:0% +these examples + + + align:start position:0% +these examples +now that now how we're going to use that + + align:start position:0% +now that now how we're going to use that + + + align:start position:0% +now that now how we're going to use that +we're going to use that + + align:start position:0% +we're going to use that + + + align:start position:0% +we're going to use that +in the following two ways + + align:start position:0% +in the following two ways + + + align:start position:0% +in the following two ways +one is to observe that if a is reducible + + align:start position:0% +one is to observe that if a is reducible + + + align:start position:0% +one is to observe that if a is reducible +to b + + align:start position:0% +to b + + + align:start position:0% +to b +and b is an easy problem + + align:start position:0% + + + + align:start position:0% + +then a is an also then a must also be + + align:start position:0% +then a is an also then a must also be + + + align:start position:0% +then a is an also then a must also be +easy because we have a way of converting + + align:start position:0% +easy because we have a way of converting + + + align:start position:0% +easy because we have a way of converting +a problems into b problem you know an a + + align:start position:0% +a problems into b problem you know an a + + + align:start position:0% +a problems into b problem you know an a +we have a way of solving a using b + + align:start position:0% + + + + align:start position:0% + +so b is easy + + align:start position:0% +so b is easy + + + align:start position:0% +so b is easy +then now you can solve a two easily + + align:start position:0% +then now you can solve a two easily + + + align:start position:0% +then now you can solve a two easily +because you can solve a using b which is + + align:start position:0% +because you can solve a using b which is + + + align:start position:0% +because you can solve a using b which is +easy + + align:start position:0% +easy + + + align:start position:0% +easy +maybe that's the clearest up here in + + align:start position:0% +maybe that's the clearest up here in + + + align:start position:0% +maybe that's the clearest up here in +example one + + align:start position:0% +example one + + + align:start position:0% +example one +where measuring the area might seem at + + align:start position:0% +where measuring the area might seem at + + + align:start position:0% +where measuring the area might seem at +first glance hard you could have to walk + + align:start position:0% +first glance hard you could have to walk + + + align:start position:0% +first glance hard you could have to walk +out over the all the the whole area but + + align:start position:0% +out over the all the the whole area but + + + align:start position:0% +out over the all the the whole area but +it's not hard because you only have to + + align:start position:0% +it's not hard because you only have to + + + align:start position:0% +it's not hard because you only have to +measure the length and the width + + align:start position:0% +measure the length and the width + + + align:start position:0% +measure the length and the width +um + + align:start position:0% +um + + + align:start position:0% +um +so the fact that b is easy tells you + + align:start position:0% +so the fact that b is easy tells you + + + align:start position:0% +so the fact that b is easy tells you +that a z but actually this is not the + + align:start position:0% +that a z but actually this is not the + + + align:start position:0% +that a z but actually this is not the +way we're going to be using it most + + align:start position:0% +way we're going to be using it most + + + align:start position:0% +way we're going to be using it most +typically we're going to be most using + + align:start position:0% +typically we're going to be most using + + + align:start position:0% +typically we're going to be most using +it most typically using it in the second + + align:start position:0% +it most typically using it in the second + + + align:start position:0% +it most typically using it in the second +version which is a little bit uh come + + align:start position:0% +version which is a little bit uh come + + + align:start position:0% +version which is a little bit uh come +more a little bit more convoluted + + align:start position:0% +more a little bit more convoluted + + + align:start position:0% +more a little bit more convoluted +but this is the way you're gonna have to + + align:start position:0% +but this is the way you're gonna have to + + + align:start position:0% +but this is the way you're gonna have to +get used to this + + align:start position:0% +get used to this + + + align:start position:0% +get used to this +so if a is reducible to b + + align:start position:0% +so if a is reducible to b + + + align:start position:0% +so if a is reducible to b +and you know a is hard + + align:start position:0% +and you know a is hard + + + align:start position:0% +and you know a is hard +undecidable unrecognizable whatever the + + align:start position:0% +undecidable unrecognizable whatever the + + + align:start position:0% +undecidable unrecognizable whatever the +form of hard you care about + + align:start position:0% +form of hard you care about + + + align:start position:0% +form of hard you care about +if you know a is hard + + align:start position:0% +if you know a is hard + + + align:start position:0% +if you know a is hard +and a is reducible to b + + align:start position:0% +and a is reducible to b + + + align:start position:0% +and a is reducible to b +then that tells you b also has to be + + align:start position:0% +then that tells you b also has to be + + + align:start position:0% +then that tells you b also has to be +hard + + align:start position:0% + + + + align:start position:0% + +why because if b were easy then a would + + align:start position:0% +why because if b were easy then a would + + + align:start position:0% +why because if b were easy then a would +be easy + + align:start position:0% +be easy + + + align:start position:0% +be easy +but we know + + align:start position:0% +but we know + + + align:start position:0% +but we know +by us we're assuming that a is hard so b + + align:start position:0% +by us we're assuming that a is hard so b + + + align:start position:0% +by us we're assuming that a is hard so b +also has to be hard + + align:start position:0% + + + + align:start position:0% + +okay so there's a + + align:start position:0% +okay so there's a + + + align:start position:0% +okay so there's a +you know uh um + + align:start position:0% +you know uh um + + + align:start position:0% +you know uh um +i'm inverting the logic here but this is + + align:start position:0% +i'm inverting the logic here but this is + + + align:start position:0% +i'm inverting the logic here but this is +logically equivalent + + align:start position:0% +logically equivalent + + + align:start position:0% +logically equivalent +um so you have to mull that over a bit + + align:start position:0% +um so you have to mull that over a bit + + + align:start position:0% +um so you have to mull that over a bit +um + + align:start position:0% + + + + align:start position:0% + +and um we will um + + align:start position:0% +and um we will um + + + align:start position:0% +and um we will um +uh so why don't you think about that + + align:start position:0% +uh so why don't you think about that + + + align:start position:0% +uh so why don't you think about that +and uh let me just take a few questions + + align:start position:0% +and uh let me just take a few questions + + + align:start position:0% +and uh let me just take a few questions +on the chat and don't forget the tas are + + align:start position:0% +on the chat and don't forget the tas are + + + align:start position:0% +on the chat and don't forget the tas are +there too so you can they're happy to + + align:start position:0% +there too so you can they're happy to + + + align:start position:0% +there too so you can they're happy to +answer your questions don't + + align:start position:0% +answer your questions don't + + + align:start position:0% +answer your questions don't +don't make them sit there lonely um + + align:start position:0% +don't make them sit there lonely um + + + align:start position:0% +don't make them sit there lonely um +all right + + align:start position:0% + + + + align:start position:0% + +so somebody's asking is it possible + + align:start position:0% +so somebody's asking is it possible + + + align:start position:0% +so somebody's asking is it possible +that a is reducible to b and that b is + + align:start position:0% +that a is reducible to b and that b is + + + align:start position:0% +that a is reducible to b and that b is +also reducible to a + + align:start position:0% +also reducible to a + + + align:start position:0% +also reducible to a +so that's a good question uh that can + + align:start position:0% +so that's a good question uh that can + + + align:start position:0% +so that's a good question uh that can +certainly happen um in that case in a + + align:start position:0% +certainly happen um in that case in a + + + align:start position:0% +certainly happen um in that case in a +certain sense a and b are going to be + + align:start position:0% +certain sense a and b are going to be + + + align:start position:0% +certain sense a and b are going to be +equivalent + + align:start position:0% +equivalent + + + align:start position:0% +equivalent +so solving one is going to be just as + + align:start position:0% +so solving one is going to be just as + + + align:start position:0% +so solving one is going to be just as +easy or hard as solving the other one + + align:start position:0% +easy or hard as solving the other one + + + align:start position:0% +easy or hard as solving the other one +okay so they're going to be equivalent + + align:start position:0% +okay so they're going to be equivalent + + + align:start position:0% +okay so they're going to be equivalent +from the perspective of the difficulty + + align:start position:0% +from the perspective of the difficulty + + + align:start position:0% +from the perspective of the difficulty +of solving them + + align:start position:0% +of solving them + + + align:start position:0% +of solving them +so somebody's asking and this is a this + + align:start position:0% +so somebody's asking and this is a this + + + align:start position:0% +so somebody's asking and this is a this +is a perennial confusion + + align:start position:0% +is a perennial confusion + + + align:start position:0% +is a perennial confusion +somebody's asking so you know in in the + + align:start position:0% +somebody's asking so you know in in the + + + align:start position:0% +somebody's asking so you know in in the +case for in the previous uh slide here + + align:start position:0% +case for in the previous uh slide here + + + align:start position:0% +case for in the previous uh slide here +maybe i'll just flip back to it here + + align:start position:0% +maybe i'll just flip back to it here + + + align:start position:0% +maybe i'll just flip back to it here +so what which direction are we doing are + + align:start position:0% +so what which direction are we doing are + + + align:start position:0% +so what which direction are we doing are +we reducing atm to whole tm or whole tmt + + align:start position:0% +we reducing atm to whole tm or whole tmt + + + align:start position:0% +we reducing atm to whole tm or whole tmt +atm + + align:start position:0% +atm + + + align:start position:0% +atm +the way it's written on the slide is + + align:start position:0% +the way it's written on the slide is + + + align:start position:0% +the way it's written on the slide is +what i have in mind here we're reducing + + align:start position:0% +what i have in mind here we're reducing + + + align:start position:0% +what i have in mind here we're reducing +atm to haltia + + align:start position:0% +atm to haltia + + + align:start position:0% +atm to haltia +because we're using whole tm to solve + + align:start position:0% +because we're using whole tm to solve + + + align:start position:0% +because we're using whole tm to solve +atm + + align:start position:0% +atm + + + align:start position:0% +atm +and that's reducing atm to holtia + + align:start position:0% +and that's reducing atm to holtia + + + align:start position:0% +and that's reducing atm to holtia +just like + + align:start position:0% +just like + + + align:start position:0% +just like +um you know uh + + align:start position:0% +um you know uh + + + align:start position:0% +um you know uh +here + + align:start position:0% +here + + + align:start position:0% +here +measuring the area + + align:start position:0% +measuring the area + + + align:start position:0% +measuring the area +is reducible to measuring the lengths of + + align:start position:0% +is reducible to measuring the lengths of + + + align:start position:0% +is reducible to measuring the lengths of +the sides we're using measuring the + + align:start position:0% +the sides we're using measuring the + + + align:start position:0% +the sides we're using measuring the +length of the sides to solve the area + + align:start position:0% + + + + align:start position:0% + +so we're reducing the area to the to the + + align:start position:0% +so we're reducing the area to the to the + + + align:start position:0% +so we're reducing the area to the to the +lengths + + align:start position:0% +lengths + + + align:start position:0% +lengths +the area to the length of the sides + + align:start position:0% +the area to the length of the sides + + + align:start position:0% +the area to the length of the sides +but you know + + align:start position:0% +but you know + + + align:start position:0% +but you know +i know it's + + align:start position:0% +i know it's + + + align:start position:0% +i know it's +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you have to you're going to have to play + + align:start position:0% +you have to you're going to have to play + + + align:start position:0% +you have to you're going to have to play +with it + + align:start position:0% +with it + + + align:start position:0% +with it +digest it get used to it + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +okay so let's continue + + align:start position:0% +okay so let's continue + + + align:start position:0% +okay so let's continue +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +as i said + + align:start position:0% +as i said + + + align:start position:0% +as i said +this latter one because we're the focus + + align:start position:0% +this latter one because we're the focus + + + align:start position:0% +this latter one because we're the focus +on this course is mainly on the + + align:start position:0% +on this course is mainly on the + + + align:start position:0% +on this course is mainly on the +limitations of computation + + align:start position:0% +limitations of computation + + + align:start position:0% +limitations of computation +so we're going to be looking at + + align:start position:0% +so we're going to be looking at + + + align:start position:0% +so we're going to be looking at +uh ways of showing problems are + + align:start position:0% +uh ways of showing problems are + + + align:start position:0% +uh ways of showing problems are +difficult + + align:start position:0% +difficult + + + align:start position:0% +difficult +it could be difficult in principle like + + align:start position:0% +it could be difficult in principle like + + + align:start position:0% +it could be difficult in principle like +undecidable or it could be difficult in + + align:start position:0% +undecidable or it could be difficult in + + + align:start position:0% +undecidable or it could be difficult in +terms of complexity which is what we're + + align:start position:0% +terms of complexity which is what we're + + + align:start position:0% +terms of complexity which is what we're +going to focus on in the second half but + + align:start position:0% +going to focus on in the second half but + + + align:start position:0% +going to focus on in the second half but +in both cases we're going to be using + + align:start position:0% +in both cases we're going to be using + + + align:start position:0% +in both cases we're going to be using +the concept of reducibility so + + align:start position:0% +the concept of reducibility so + + + align:start position:0% +the concept of reducibility so +reducibility is going to be a theme + + align:start position:0% +reducibility is going to be a theme + + + align:start position:0% +reducibility is going to be a theme +you've got to get comfortable with + + align:start position:0% +you've got to get comfortable with + + + align:start position:0% +you've got to get comfortable with +reducibility + + align:start position:0% +reducibility + + + align:start position:0% +reducibility +okay so we're going to be focusing more + + align:start position:0% +okay so we're going to be focusing more + + + align:start position:0% +okay so we're going to be focusing more +on the notion that + + align:start position:0% +on the notion that + + + align:start position:0% +on the notion that +if you reduce a to b and you know a is + + align:start position:0% +if you reduce a to b and you know a is + + + align:start position:0% +if you reduce a to b and you know a is +hard that tells you b is also hard + + align:start position:0% +hard that tells you b is also hard + + + align:start position:0% +hard that tells you b is also hard +okay so i'm going to try to + + align:start position:0% +okay so i'm going to try to + + + align:start position:0% +okay so i'm going to try to +i'm going to say that a few times during + + align:start position:0% +i'm going to say that a few times during + + + align:start position:0% +i'm going to say that a few times during +the course of today's lecture to try to + + align:start position:0% +the course of today's lecture to try to + + + align:start position:0% +the course of today's lecture to try to +help you uh get it + + align:start position:0% +help you uh get it + + + align:start position:0% +help you uh get it +all right here's a check-in + + align:start position:0% +all right here's a check-in + + + align:start position:0% +all right here's a check-in +a little bit sort of uh + + align:start position:0% +a little bit sort of uh + + + align:start position:0% +a little bit sort of uh +sort of off to the side but i thought it + + align:start position:0% +sort of off to the side but i thought it + + + align:start position:0% +sort of off to the side but i thought it +was fun a fun check-in more + + align:start position:0% + + + + align:start position:0% + +the question is some people say biology + + align:start position:0% +the question is some people say biology + + + align:start position:0% +the question is some people say biology +is reducible to physics well maybe + + align:start position:0% +is reducible to physics well maybe + + + align:start position:0% +is reducible to physics well maybe +everything is reducible to physics since + + align:start position:0% +everything is reducible to physics since + + + align:start position:0% +everything is reducible to physics since +physics is + + align:start position:0% +physics is + + + align:start position:0% +physics is +tells you about the laws of the universe + + align:start position:0% +tells you about the laws of the universe + + + align:start position:0% +tells you about the laws of the universe +and biology is in you know part of the + + align:start position:0% +and biology is in you know part of the + + + align:start position:0% +and biology is in you know part of the +universe + + align:start position:0% +universe + + + align:start position:0% +universe +so my question to you is do you think + + align:start position:0% +so my question to you is do you think + + + align:start position:0% +so my question to you is do you think +and there's no right answer here + + align:start position:0% +and there's no right answer here + + + align:start position:0% +and there's no right answer here +do you think in your opinion + + align:start position:0% +do you think in your opinion + + + align:start position:0% +do you think in your opinion +is biology reducible to physics + + align:start position:0% +is biology reducible to physics + + + align:start position:0% +is biology reducible to physics +maybe yes + + align:start position:0% +maybe yes + + + align:start position:0% +maybe yes +or maybe there are some things like + + align:start position:0% +or maybe there are some things like + + + align:start position:0% +or maybe there are some things like +let's consciousness + + align:start position:0% +let's consciousness + + + align:start position:0% +let's consciousness +which cannot be reduced to physics + + align:start position:0% +which cannot be reduced to physics + + + align:start position:0% +which cannot be reduced to physics +um + + align:start position:0% +um + + + align:start position:0% +um +or maybe we don't know + + align:start position:0% +or maybe we don't know + + + align:start position:0% +or maybe we don't know +so + + align:start position:0% + + + + align:start position:0% + +curious to know your thoughts + + align:start position:0% + + + + align:start position:0% + +but it does kind of use in a sense + + align:start position:0% +but it does kind of use in a sense + + + align:start position:0% +but it does kind of use in a sense +the notion of reducible in the spirit of + + align:start position:0% +the notion of reducible in the spirit of + + + align:start position:0% +the notion of reducible in the spirit of +what i have in mind here + + align:start position:0% +what i have in mind here + + + align:start position:0% +what i have in mind here +in the sense that if you could fully + + align:start position:0% +in the sense that if you could fully + + + align:start position:0% +in the sense that if you could fully +understand physics + + align:start position:0% +understand physics + + + align:start position:0% +understand physics +would that allow you to fully understand + + align:start position:0% +would that allow you to fully understand + + + align:start position:0% +would that allow you to fully understand +biology + + align:start position:0% + + + + align:start position:0% + +okay here we are we're + + align:start position:0% +okay here we are we're + + + align:start position:0% +okay here we are we're +almost + + align:start position:0% +almost + + + align:start position:0% +almost +kind of interesting + + align:start position:0% +kind of interesting + + + align:start position:0% +kind of interesting +uh + + align:start position:0% +uh + + + align:start position:0% +uh +though not too unexpected i suppose + + align:start position:0% +though not too unexpected i suppose + + + align:start position:0% +though not too unexpected i suppose +uh + + align:start position:0% + + + + align:start position:0% + +um so we are i think just about done + + align:start position:0% +um so we are i think just about done + + + align:start position:0% +um so we are i think just about done +five seconds pick anything if you + + align:start position:0% +five seconds pick anything if you + + + align:start position:0% +five seconds pick anything if you +want to get credit for this and you + + align:start position:0% +want to get credit for this and you + + + align:start position:0% +want to get credit for this and you +don't + + align:start position:0% +don't + + + align:start position:0% +don't +haven't uh selected yet + + align:start position:0% +haven't uh selected yet + + + align:start position:0% +haven't uh selected yet +ready to go ending polling + + align:start position:0% + + + + align:start position:0% + +here are the results + + align:start position:0% + + + + align:start position:0% + +and as i say there's no right answer + + align:start position:0% +and as i say there's no right answer + + + align:start position:0% +and as i say there's no right answer +here + + align:start position:0% +here + + + align:start position:0% +here +but but + + align:start position:0% +but but + + + align:start position:0% +but but +if if i had been + + align:start position:0% +if if i had been + + + align:start position:0% +if if i had been +in the class i would have picked b + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +but i'm not surprised + + align:start position:0% +but i'm not surprised + + + align:start position:0% +but i'm not surprised +uh that especially in an mit crowd that + + align:start position:0% +uh that especially in an mit crowd that + + + align:start position:0% +uh that especially in an mit crowd that +a is a winner + + align:start position:0% +a is a winner + + + align:start position:0% +a is a winner +all right uh + + align:start position:0% +all right uh + + + align:start position:0% +all right uh +let's continue + + align:start position:0% +let's continue + + + align:start position:0% +let's continue +um + + align:start position:0% + + + + align:start position:0% + +okay so now we're going to use + + align:start position:0% +okay so now we're going to use + + + align:start position:0% +okay so now we're going to use +reduceability again um this is going to + + align:start position:0% +reduceability again um this is going to + + + align:start position:0% +reduceability again um this is going to +be yet another example like the whole tm + + align:start position:0% +be yet another example like the whole tm + + + align:start position:0% +be yet another example like the whole tm +example but a little bit more a little + + align:start position:0% +example but a little bit more a little + + + align:start position:0% +example but a little bit more a little +bit uh harder um + + align:start position:0% +bit uh harder um + + + align:start position:0% +bit uh harder um +and we're going to be doing this you + + align:start position:0% +and we're going to be doing this you + + + align:start position:0% +and we're going to be doing this you +know the next lecture we're going to be + + align:start position:0% +know the next lecture we're going to be + + + align:start position:0% +know the next lecture we're going to be +doing more reducibilities but much + + align:start position:0% +doing more reducibilities but much + + + align:start position:0% +doing more reducibilities but much +harder + + align:start position:0% +harder + + + align:start position:0% +harder +so we really got to get + + align:start position:0% +so we really got to get + + + align:start position:0% +so we really got to get +you know really comfortable + + align:start position:0% +you know really comfortable + + + align:start position:0% +you know really comfortable +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +all right we're going to show etm see + + align:start position:0% +all right we're going to show etm see + + + align:start position:0% +all right we're going to show etm see +etm is the emptiness problem for touring + + align:start position:0% +etm is the emptiness problem for touring + + + align:start position:0% +etm is the emptiness problem for touring +machines is this language empty + + align:start position:0% +machines is this language empty + + + align:start position:0% +machines is this language empty +i'm just going to give you a machine i + + align:start position:0% +i'm just going to give you a machine i + + + align:start position:0% +i'm just going to give you a machine i +want to know is this language empty or + + align:start position:0% +want to know is this language empty or + + + align:start position:0% +want to know is this language empty or +not does it accept something or is its + + align:start position:0% +not does it accept something or is its + + + align:start position:0% +not does it accept something or is its +language empty + + align:start position:0% +language empty + + + align:start position:0% +language empty +um that's going to be undecidable no + + align:start position:0% +um that's going to be undecidable no + + + align:start position:0% +um that's going to be undecidable no +surprise + + align:start position:0% +surprise + + + align:start position:0% +surprise +proof by contradiction and we're going + + align:start position:0% +proof by contradiction and we're going + + + align:start position:0% +proof by contradiction and we're going +to show that atm is reducible to etm + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +um these things + + align:start position:0% +um these things + + + align:start position:0% +um these things +often take a very similar form and i'm + + align:start position:0% +often take a very similar form and i'm + + + align:start position:0% +often take a very similar form and i'm +going to try to use the same form so if + + align:start position:0% +going to try to use the same form so if + + + align:start position:0% +going to try to use the same form so if +you're feeling shaking on it at least + + align:start position:0% +you're feeling shaking on it at least + + + align:start position:0% +you're feeling shaking on it at least +you'll get the + + align:start position:0% +you'll get the + + + align:start position:0% +you'll get the +the form of the way the solution goes + + align:start position:0% +the form of the way the solution goes + + + align:start position:0% +the form of the way the solution goes +and that will help you maybe plug in um + + align:start position:0% +and that will help you maybe plug in um + + + align:start position:0% +and that will help you maybe plug in um +to solve problems + + align:start position:0% +to solve problems + + + align:start position:0% +to solve problems +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +proof by contradiction um assume that + + align:start position:0% +proof by contradiction um assume that + + + align:start position:0% +proof by contradiction um assume that +etm is decidable opposite of what we're + + align:start position:0% +etm is decidable opposite of what we're + + + align:start position:0% +etm is decidable opposite of what we're +trying to show + + align:start position:0% +trying to show + + + align:start position:0% +trying to show +and then show that atm is decidable + + align:start position:0% +and then show that atm is decidable + + + align:start position:0% +and then show that atm is decidable +which we know is false + + align:start position:0% +which we know is false + + + align:start position:0% +which we know is false +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +let's say we have a decider for + + align:start position:0% +let's say we have a decider for + + + align:start position:0% +let's say we have a decider for +etm r + + align:start position:0% +etm r + + + align:start position:0% +etm r +using the same letters + + align:start position:0% +using the same letters + + + align:start position:0% +using the same letters +on purpose here just to try to get the + + align:start position:0% +on purpose here just to try to get the + + + align:start position:0% +on purpose here just to try to get the +pattern for you + + align:start position:0% +pattern for you + + + align:start position:0% +pattern for you +so our designing etm + + align:start position:0% +so our designing etm + + + align:start position:0% +so our designing etm +construct s deciding atm + + align:start position:0% + + + + align:start position:0% + +okay so now um + + align:start position:0% + + + + align:start position:0% + +let's think about it together for a + + align:start position:0% +let's think about it together for a + + + align:start position:0% +let's think about it together for a +minute before i just put it up there + + align:start position:0% + + + + align:start position:0% + +um so s i'm trying to make a decider + + align:start position:0% +um so s i'm trying to make a decider + + + align:start position:0% +um so s i'm trying to make a decider +for atm + + align:start position:0% +for atm + + + align:start position:0% +for atm +using my decider + + align:start position:0% +using my decider + + + align:start position:0% +using my decider +for the emptiness problem + + align:start position:0% + + + + align:start position:0% + +okay so we have r which can tell us + + align:start position:0% +okay so we have r which can tell us + + + align:start position:0% +okay so we have r which can tell us +whether the whether m's language is + + align:start position:0% +whether the whether m's language is + + + align:start position:0% +whether the whether m's language is +empty + + align:start position:0% +empty + + + align:start position:0% +empty +so why don't we just + + align:start position:0% +so why don't we just + + + align:start position:0% +so why don't we just +i don't know stick m + + align:start position:0% +i don't know stick m + + + align:start position:0% +i don't know stick m +into that emptiness tester + + align:start position:0% +into that emptiness tester + + + align:start position:0% +into that emptiness tester +see what it says + + align:start position:0% +see what it says + + + align:start position:0% +see what it says +i'm just i'm not saying this is the + + align:start position:0% +i'm just i'm not saying this is the + + + align:start position:0% +i'm just i'm not saying this is the +solution but this is how one might think + + align:start position:0% +solution but this is how one might think + + + align:start position:0% +solution but this is how one might think +about coming up with the solution + + align:start position:0% + + + + align:start position:0% + +so are you with me we're going to take m + + align:start position:0% +so are you with me we're going to take m + + + align:start position:0% +so are you with me we're going to take m +we have an emptiness tester + + align:start position:0% +we have an emptiness tester + + + align:start position:0% +we have an emptiness tester +let's take m + + align:start position:0% +let's take m + + + align:start position:0% +let's take m +and plug it into r see what r says + + align:start position:0% +and plug it into r see what r says + + + align:start position:0% +and plug it into r see what r says +r is going to come back and tell us + + align:start position:0% +r is going to come back and tell us + + + align:start position:0% +r is going to come back and tell us +whether m's language is empty or not + + align:start position:0% + + + + align:start position:0% + +now one of those answers + + align:start position:0% +now one of those answers + + + align:start position:0% +now one of those answers +will make us happy + + align:start position:0% + + + + align:start position:0% + +why + + align:start position:0% +why + + + align:start position:0% +why +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +r + + align:start position:0% +r + + + align:start position:0% +r +tells us that m's language is empty + + align:start position:0% +tells us that m's language is empty + + + align:start position:0% +tells us that m's language is empty +why is that good + + align:start position:0% +why is that good + + + align:start position:0% +why is that good +well now we're done + + align:start position:0% +well now we're done + + + align:start position:0% +well now we're done +because what s is trying to figure out + + align:start position:0% +because what s is trying to figure out + + + align:start position:0% +because what s is trying to figure out +we're trying to figure out + + align:start position:0% +we're trying to figure out + + + align:start position:0% +we're trying to figure out +exactly somebody + + align:start position:0% +exactly somebody + + + align:start position:0% +exactly somebody +told me the answer which is correct + + align:start position:0% +told me the answer which is correct + + + align:start position:0% +told me the answer which is correct +because now we can reject + + align:start position:0% +because now we can reject + + + align:start position:0% +because now we can reject +if m's language is empty it's clearly + + align:start position:0% +if m's language is empty it's clearly + + + align:start position:0% +if m's language is empty it's clearly +not accepting w because it's not + + align:start position:0% +not accepting w because it's not + + + align:start position:0% +not accepting w because it's not +accepting anything + + align:start position:0% + + + + align:start position:0% + +so if r says m language is empty then + + align:start position:0% +so if r says m language is empty then + + + align:start position:0% +so if r says m language is empty then +we're good + + align:start position:0% +we're good + + + align:start position:0% +we're good +the only problem is r may also say m's + + align:start position:0% +the only problem is r may also say m's + + + align:start position:0% +the only problem is r may also say m's +language is not empty and then what do + + align:start position:0% +language is not empty and then what do + + + align:start position:0% +language is not empty and then what do +we know + + align:start position:0% +we know + + + align:start position:0% +we know +well not much + + align:start position:0% +well not much + + + align:start position:0% +well not much +not much that's useful + + align:start position:0% +not much that's useful + + + align:start position:0% +not much that's useful +for testing whether m accepts w we just + + align:start position:0% +for testing whether m accepts w we just + + + align:start position:0% +for testing whether m accepts w we just +know m accepts something + + align:start position:0% +know m accepts something + + + align:start position:0% +know m accepts something +but that something may or may not be w + + align:start position:0% + + + + align:start position:0% + +okay so what do we do + + align:start position:0% +okay so what do we do + + + align:start position:0% +okay so what do we do +well the problem is that m + + align:start position:0% +well the problem is that m + + + align:start position:0% +well the problem is that m +is + + align:start position:0% +is + + + align:start position:0% +is +possibly accepting all sorts of strings + + align:start position:0% +possibly accepting all sorts of strings + + + align:start position:0% +possibly accepting all sorts of strings +besides w + + align:start position:0% +besides w + + + align:start position:0% +besides w +which are kind of mucking up the works + + align:start position:0% +which are kind of mucking up the works + + + align:start position:0% +which are kind of mucking up the works +they're making + + align:start position:0% +they're making + + + align:start position:0% +they're making +th they're interfering + + align:start position:0% +th they're interfering + + + align:start position:0% +th they're interfering +with the solution that we'd like + + align:start position:0% +with the solution that we'd like + + + align:start position:0% +with the solution that we'd like +uh we'd like to be able to use r + + align:start position:0% +uh we'd like to be able to use r + + + align:start position:0% +uh we'd like to be able to use r +on m + + align:start position:0% +on m + + + align:start position:0% +on m +to tell us whether m is accepting w but + + align:start position:0% +to tell us whether m is accepting w but + + + align:start position:0% +to tell us whether m is accepting w but +m is accepting other things and that's + + align:start position:0% +m is accepting other things and that's + + + align:start position:0% +m is accepting other things and that's +making + + align:start position:0% +making + + + align:start position:0% +making +the picture complicated so what i + + align:start position:0% +the picture complicated so what i + + + align:start position:0% +the picture complicated so what i +propose we do + + align:start position:0% +propose we do + + + align:start position:0% +propose we do +why don't we modify m + + align:start position:0% +why don't we modify m + + + align:start position:0% +why don't we modify m +so that it never accepts anything + + align:start position:0% +so that it never accepts anything + + + align:start position:0% +so that it never accepts anything +besides w + + align:start position:0% +besides w + + + align:start position:0% +besides w +the very first thing m does in the + + align:start position:0% +the very first thing m does in the + + + align:start position:0% +the very first thing m does in the +modified form + + align:start position:0% +modified form + + + align:start position:0% +modified form +is it looks at its input and sees + + align:start position:0% +is it looks at its input and sees + + + align:start position:0% +is it looks at its input and sees +whether it's different from w + + align:start position:0% +whether it's different from w + + + align:start position:0% +whether it's different from w +if it's different from w it immediately + + align:start position:0% +if it's different from w it immediately + + + align:start position:0% +if it's different from w it immediately +rejects + + align:start position:0% + + + + align:start position:0% + +now we take that modified machine + + align:start position:0% +now we take that modified machine + + + align:start position:0% +now we take that modified machine +and we feed it into the emptiness tester + + align:start position:0% + + + + align:start position:0% + +now the emptiness tester is going to + + align:start position:0% +now the emptiness tester is going to + + + align:start position:0% +now the emptiness tester is going to +give us the information we're looking + + align:start position:0% +give us the information we're looking + + + align:start position:0% +give us the information we're looking +for + + align:start position:0% +for + + + align:start position:0% +for +because if + + align:start position:0% +because if + + + align:start position:0% +because if +the emptiness tester says the modified + + align:start position:0% +the emptiness tester says the modified + + + align:start position:0% +the emptiness tester says the modified +machine's language is empty well we know + + align:start position:0% +machine's language is empty well we know + + + align:start position:0% +machine's language is empty well we know +that + + align:start position:0% +that + + + align:start position:0% +that +m is not accepting w because we haven't + + align:start position:0% +m is not accepting w because we haven't + + + align:start position:0% +m is not accepting w because we haven't +changed how m behaves when it's when + + align:start position:0% +changed how m behaves when it's when + + + align:start position:0% +changed how m behaves when it's when +it's given w + + align:start position:0% +it's given w + + + align:start position:0% +it's given w +but if + + align:start position:0% +but if + + + align:start position:0% +but if +r says m's language is not empty + + align:start position:0% + + + + align:start position:0% + +well then it must be that m is accepting + + align:start position:0% +well then it must be that m is accepting + + + align:start position:0% +well then it must be that m is accepting +w + + align:start position:0% +w + + + align:start position:0% +w +because we've already filtered out all + + align:start position:0% +because we've already filtered out all + + + align:start position:0% +because we've already filtered out all +of the other possibilities in the + + align:start position:0% +of the other possibilities in the + + + align:start position:0% +of the other possibilities in the +modified when we've modified the machine + + align:start position:0% +modified when we've modified the machine + + + align:start position:0% +modified when we've modified the machine +so let me repeat that on the slide and + + align:start position:0% +so let me repeat that on the slide and + + + align:start position:0% +so let me repeat that on the slide and +write it down a little bit more formally + + align:start position:0% +write it down a little bit more formally + + + align:start position:0% +write it down a little bit more formally +so what i'm going to do is i'm going to + + align:start position:0% +so what i'm going to do is i'm going to + + + align:start position:0% +so what i'm going to do is i'm going to +transform m to a new turing machine i'm + + align:start position:0% +transform m to a new turing machine i'm + + + align:start position:0% +transform m to a new turing machine i'm +going to call it m sub w + + align:start position:0% +going to call it m sub w + + + align:start position:0% +going to call it m sub w +to emphasize the fact that this new + + align:start position:0% +to emphasize the fact that this new + + + align:start position:0% +to emphasize the fact that this new +machine depends on w it's going to + + align:start position:0% +machine depends on w it's going to + + + align:start position:0% +machine depends on w it's going to +actually have w built into as part of + + align:start position:0% +actually have w built into as part of + + + align:start position:0% +actually have w built into as part of +the rules of the machine + + align:start position:0% +the rules of the machine + + + align:start position:0% +the rules of the machine +so for a different w we're going to end + + align:start position:0% +so for a different w we're going to end + + + align:start position:0% +so for a different w we're going to end +up with a different machine here so this + + align:start position:0% +up with a different machine here so this + + + align:start position:0% +up with a different machine here so this +is a machine + + align:start position:0% +is a machine + + + align:start position:0% +is a machine +whose structure is going to depend on + + align:start position:0% +whose structure is going to depend on + + + align:start position:0% +whose structure is going to depend on +knowing w + + align:start position:0% + + + + align:start position:0% + +and that machine is going to be very + + align:start position:0% +and that machine is going to be very + + + align:start position:0% +and that machine is going to be very +much like the original machine m + + align:start position:0% +much like the original machine m + + + align:start position:0% +much like the original machine m +except that when it gets an input let's + + align:start position:0% +except that when it gets an input let's + + + align:start position:0% +except that when it gets an input let's +say it's called x now + + align:start position:0% +say it's called x now + + + align:start position:0% +say it's called x now +it that machine is going to compare x + + align:start position:0% +it that machine is going to compare x + + + align:start position:0% +it that machine is going to compare x +with w + + align:start position:0% + + + + align:start position:0% + +and reject if it's not equal + + align:start position:0% + + + + align:start position:0% + +if otherwise + + align:start position:0% +if otherwise + + + align:start position:0% +if otherwise +if x is equal to w it's going to run m + + align:start position:0% +if x is equal to w it's going to run m + + + align:start position:0% +if x is equal to w it's going to run m +on w as before so it's not going to + + align:start position:0% +on w as before so it's not going to + + + align:start position:0% +on w as before so it's not going to +change the behavior + + align:start position:0% +change the behavior + + + align:start position:0% +change the behavior +when the input is w it's only going to + + align:start position:0% +when the input is w it's only going to + + + align:start position:0% +when the input is w it's only going to +change the + + align:start position:0% +change the + + + align:start position:0% +change the +behavior when the input is something + + align:start position:0% +behavior when the input is something + + + align:start position:0% +behavior when the input is something +different than w and then it's going to + + align:start position:0% +different than w and then it's going to + + + align:start position:0% +different than w and then it's going to +reject + + align:start position:0% + + + + align:start position:0% + +all + + align:start position:0% +all + + + align:start position:0% +all +right so + + align:start position:0% +right so + + + align:start position:0% +right so +let's just um i'm going to look at two + + align:start position:0% +let's just um i'm going to look at two + + + align:start position:0% +let's just um i'm going to look at two +aspects of this first to make let's + + align:start position:0% +aspects of this first to make let's + + + align:start position:0% +aspects of this first to make let's +understand + + align:start position:0% +understand + + + align:start position:0% +understand +the language of this new machine and + + align:start position:0% +the language of this new machine and + + + align:start position:0% +the language of this new machine and +then we'll also talk about how we go + + align:start position:0% +then we'll also talk about how we go + + + align:start position:0% +then we'll also talk about how we go +about doing this transformation um + + align:start position:0% +about doing this transformation um + + + align:start position:0% +about doing this transformation um +so first of all + + align:start position:0% +so first of all + + + align:start position:0% +so first of all +let just to for + + align:start position:0% +let just to for + + + align:start position:0% +let just to for +emphasis uh + + align:start position:0% +emphasis uh + + + align:start position:0% +emphasis uh +so mw works just like m it has all the + + align:start position:0% +so mw works just like m it has all the + + + align:start position:0% +so mw works just like m it has all the +rules of m in it + + align:start position:0% +rules of m in it + + + align:start position:0% +rules of m in it +except some extra rules + + align:start position:0% +except some extra rules + + + align:start position:0% +except some extra rules +um it always at the very first step + + align:start position:0% +um it always at the very first step + + + align:start position:0% +um it always at the very first step +it tests whether um x + + align:start position:0% +it tests whether um x + + + align:start position:0% +it tests whether um x +is + + align:start position:0% +is + + + align:start position:0% +is +equal to w or not + + align:start position:0% +equal to w or not + + + align:start position:0% +equal to w or not +and if it's not equal to + + align:start position:0% +and if it's not equal to + + + align:start position:0% +and if it's not equal to +it rejects + + align:start position:0% +it rejects + + + align:start position:0% +it rejects +not equal to w reject so the language of + + align:start position:0% +not equal to w reject so the language of + + + align:start position:0% +not equal to w reject so the language of +that new machine + + align:start position:0% +that new machine + + + align:start position:0% +that new machine +is either going to be just the string w + + align:start position:0% +is either going to be just the string w + + + align:start position:0% +is either going to be just the string w +when m accepts w because everything else + + align:start position:0% +when m accepts w because everything else + + + align:start position:0% +when m accepts w because everything else +is filtered out + + align:start position:0% +is filtered out + + + align:start position:0% +is filtered out +or the empty set if n rejects w + + align:start position:0% + + + + align:start position:0% + +got it so it's important that you + + align:start position:0% +got it so it's important that you + + + align:start position:0% +got it so it's important that you +understand + + align:start position:0% +understand + + + align:start position:0% +understand +how the behavior at least of this new + + align:start position:0% +how the behavior at least of this new + + + align:start position:0% +how the behavior at least of this new +machine + + align:start position:0% + + + + align:start position:0% + +it's just like m except filtering out + + align:start position:0% +it's just like m except filtering out + + + align:start position:0% +it's just like m except filtering out +all of the + + align:start position:0% +all of the + + + align:start position:0% +all of the +um inputs + + align:start position:0% +um inputs + + + align:start position:0% +um inputs +which are not w those are going to be + + align:start position:0% +which are not w those are going to be + + + align:start position:0% +which are not w those are going to be +all + + align:start position:0% +all + + + align:start position:0% +all +automatically rejected + + align:start position:0% +automatically rejected + + + align:start position:0% +automatically rejected +now you + + align:start position:0% +now you + + + align:start position:0% +now you +so it's also important that s + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +be able to make this transformation + + align:start position:0% +be able to make this transformation + + + align:start position:0% +be able to make this transformation +but i claim that you know you'll have to + + align:start position:0% +but i claim that you know you'll have to + + + align:start position:0% +but i claim that you know you'll have to +accept this if you don't uh totally see + + align:start position:0% +accept this if you don't uh totally see + + + align:start position:0% +accept this if you don't uh totally see +it but + + align:start position:0% +it but + + + align:start position:0% +it but +the + + align:start position:0% +the + + + align:start position:0% +the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the transformation is simply taking m + + align:start position:0% +the transformation is simply taking m + + + align:start position:0% +the transformation is simply taking m +and adding some new rules some new uh + + align:start position:0% +and adding some new rules some new uh + + + align:start position:0% +and adding some new rules some new uh +transitions and states + + align:start position:0% +transitions and states + + + align:start position:0% +transitions and states +so that the very first thing + + align:start position:0% +so that the very first thing + + + align:start position:0% +so that the very first thing +that + + align:start position:0% +that + + + align:start position:0% +that +m sub w does + + align:start position:0% +m sub w does + + + align:start position:0% +m sub w does +is it + + align:start position:0% +is it + + + align:start position:0% +is it +you know just has a sequence of moves + + align:start position:0% +you know just has a sequence of moves + + + align:start position:0% +you know just has a sequence of moves +where it's uh checking that the input + + align:start position:0% +where it's uh checking that the input + + + align:start position:0% +where it's uh checking that the input +string + + align:start position:0% +string + + + align:start position:0% +string +is equal to w or not + + align:start position:0% +is equal to w or not + + + align:start position:0% +is equal to w or not +and if it's not equal to w it just + + align:start position:0% +and if it's not equal to w it just + + + align:start position:0% +and if it's not equal to w it just +just rejects + + align:start position:0% +just rejects + + + align:start position:0% +just rejects +so it's easy to modify m you could + + align:start position:0% +so it's easy to modify m you could + + + align:start position:0% +so it's easy to modify m you could +easily write a program which would + + align:start position:0% +easily write a program which would + + + align:start position:0% +easily write a program which would +modify the you know the states and + + align:start position:0% +modify the you know the states and + + + align:start position:0% +modify the you know the states and +transitions of m to make it do that test + + align:start position:0% +transitions of m to make it do that test + + + align:start position:0% +transitions of m to make it do that test +at the beginning + + align:start position:0% +at the beginning + + + align:start position:0% +at the beginning +so i'm not going to elaborate on those + + align:start position:0% +so i'm not going to elaborate on those + + + align:start position:0% +so i'm not going to elaborate on those +kinds of things in the future but just + + align:start position:0% +kinds of things in the future but just + + + align:start position:0% +kinds of things in the future but just +for the very first time i just want to + + align:start position:0% +for the very first time i just want to + + + align:start position:0% +for the very first time i just want to +make sure you understand that we're not + + align:start position:0% +make sure you understand that we're not + + + align:start position:0% +make sure you understand that we're not +doing anything fishy here this is + + align:start position:0% +doing anything fishy here this is + + + align:start position:0% +doing anything fishy here this is +completely legitimate + + align:start position:0% +completely legitimate + + + align:start position:0% +completely legitimate +um thing for s to be able to do + + align:start position:0% + + + + align:start position:0% + +so s can modify m + + align:start position:0% +so s can modify m + + + align:start position:0% +so s can modify m +to this new machine mw + + align:start position:0% +to this new machine mw + + + align:start position:0% +to this new machine mw +which filters that new machine + + align:start position:0% +which filters that new machine + + + align:start position:0% +which filters that new machine +filters out all strings except for w and + + align:start position:0% +filters out all strings except for w and + + + align:start position:0% +filters out all strings except for w and +rejects them + + align:start position:0% +rejects them + + + align:start position:0% +rejects them +now we so s takes that new machine and + + align:start position:0% +now we so s takes that new machine and + + + align:start position:0% +now we so s takes that new machine and +what is it going to do with it is it + + align:start position:0% +what is it going to do with it is it + + + align:start position:0% +what is it going to do with it is it +ever going to run that machine no + + align:start position:0% +ever going to run that machine no + + + align:start position:0% +ever going to run that machine no +this machine is built not for running + + align:start position:0% +this machine is built not for running + + + align:start position:0% +this machine is built not for running +this machine is built for feeding into r + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% +because + + + align:start position:0% +because +as you remember feeding m into r had the + + align:start position:0% +as you remember feeding m into r had the + + + align:start position:0% +as you remember feeding m into r had the +problem that m might accept things + + align:start position:0% +problem that m might accept things + + + align:start position:0% +problem that m might accept things +besides w and that confuses the result + + align:start position:0% +besides w and that confuses the result + + + align:start position:0% +besides w and that confuses the result +that we get from r in the sense that + + align:start position:0% +that we get from r in the sense that + + + align:start position:0% +that we get from r in the sense that +it's not useful + + align:start position:0% +it's not useful + + + align:start position:0% +it's not useful +but if we feed m w into r + + align:start position:0% +but if we feed m w into r + + + align:start position:0% +but if we feed m w into r +now now we're good because if r s you + + align:start position:0% +now now we're good because if r s you + + + align:start position:0% +now now we're good because if r s you +know the answer the information about + + align:start position:0% +know the answer the information about + + + align:start position:0% +know the answer the information about +whether mw's language is empty + + align:start position:0% +whether mw's language is empty + + + align:start position:0% +whether mw's language is empty +from over here tells us whether or not m + + align:start position:0% +from over here tells us whether or not m + + + align:start position:0% +from over here tells us whether or not m +accepts lb + + align:start position:0% + + + + align:start position:0% + +if m's if mw's language is not empty + + align:start position:0% +if m's if mw's language is not empty + + + align:start position:0% +if m's if mw's language is not empty +then m accepts w if m's language is + + align:start position:0% +then m accepts w if m's language is + + + align:start position:0% +then m accepts w if m's language is +empty and rejects w + + align:start position:0% +empty and rejects w + + + align:start position:0% +empty and rejects w +um + + align:start position:0% + + + + align:start position:0% + +okay uh so let me um starting to get + + align:start position:0% +okay uh so let me um starting to get + + + align:start position:0% +okay uh so let me um starting to get +some good questions here uh let me just + + align:start position:0% +some good questions here uh let me just + + + align:start position:0% +some good questions here uh let me just +finish the description of s + + align:start position:0% +finish the description of s + + + align:start position:0% +finish the description of s +um uh so somebody's asking here so again + + align:start position:0% +um uh so somebody's asking here so again + + + align:start position:0% +um uh so somebody's asking here so again +this is a good this is an excellent + + align:start position:0% +this is a good this is an excellent + + + align:start position:0% +this is a good this is an excellent +question um + + align:start position:0% +question um + + + align:start position:0% +question um +uh + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +how do we know that m + + align:start position:0% +how do we know that m + + + align:start position:0% +how do we know that m +w + + align:start position:0% +w + + + align:start position:0% +w +halts or + + align:start position:0% +halts or + + + align:start position:0% +halts or +you know under on w or whatever we don't + + align:start position:0% +you know under on w or whatever we don't + + + align:start position:0% +you know under on w or whatever we don't +mw may not hold on w we don't care + + align:start position:0% +mw may not hold on w we don't care + + + align:start position:0% +mw may not hold on w we don't care +we're never going to run mw on anything + + align:start position:0% + + + + align:start position:0% + +we're going to take mw as a machine and + + align:start position:0% +we're going to take mw as a machine and + + + align:start position:0% +we're going to take mw as a machine and +we're going to feed it into r + + align:start position:0% +we're going to feed it into r + + + align:start position:0% +we're going to feed it into r +as a description we're going to take the + + align:start position:0% +as a description we're going to take the + + + align:start position:0% +as a description we're going to take the +description of mw and feed it into r + + align:start position:0% +description of mw and feed it into r + + + align:start position:0% +description of mw and feed it into r +then it's ours problem + + align:start position:0% +then it's ours problem + + + align:start position:0% +then it's ours problem +but r has been + + align:start position:0% +but r has been + + + align:start position:0% +but r has been +assumed + + align:start position:0% +assumed + + + align:start position:0% +assumed +to answer + + align:start position:0% +to answer + + + align:start position:0% +to answer +emptiness testing + + align:start position:0% +emptiness testing + + + align:start position:0% +emptiness testing +so we're going to just take the we just + + align:start position:0% +so we're going to just take the we just + + + align:start position:0% +so we're going to just take the we just +we just took the original machine + + align:start position:0% +we just took the original machine + + + align:start position:0% +we just took the original machine +modified it so that the only possible + + align:start position:0% +modified it so that the only possible + + + align:start position:0% +modified it so that the only possible +thing it could accept is w + + align:start position:0% +thing it could accept is w + + + align:start position:0% +thing it could accept is w +and now feed it into the emptiness + + align:start position:0% +and now feed it into the emptiness + + + align:start position:0% +and now feed it into the emptiness +tester to see whether it's language is + + align:start position:0% +tester to see whether it's language is + + + align:start position:0% +tester to see whether it's language is +empty or not + + align:start position:0% +empty or not + + + align:start position:0% +empty or not +now if its language is not empty it has + + align:start position:0% +now if its language is not empty it has + + + align:start position:0% +now if its language is not empty it has +to be accepting w because it's built not + + align:start position:0% +to be accepting w because it's built not + + + align:start position:0% +to be accepting w because it's built not +to accept anything else + + align:start position:0% +to accept anything else + + + align:start position:0% +to accept anything else +so we know we don't care whether mw + + align:start position:0% +so we know we don't care whether mw + + + align:start position:0% +so we know we don't care whether mw +might end up looping + + align:start position:0% +might end up looping + + + align:start position:0% +might end up looping +we're never going to run mw + + align:start position:0% + + + + align:start position:0% + +i i acknowledge + + align:start position:0% +i i acknowledge + + + align:start position:0% +i i acknowledge +it's a leap for for many of you so + + align:start position:0% +it's a leap for for many of you so + + + align:start position:0% +it's a leap for for many of you so +you're going to have to mull it mull it + + align:start position:0% +you're going to have to mull it mull it + + + align:start position:0% +you're going to have to mull it mull it +over + + align:start position:0% +over + + + align:start position:0% +over +so we're going to use r to test whether + + align:start position:0% +so we're going to use r to test whether + + + align:start position:0% +so we're going to use r to test whether +mw um language is empty + + align:start position:0% +mw um language is empty + + + align:start position:0% +mw um language is empty +if yes + + align:start position:0% +if yes + + + align:start position:0% +if yes +that means that m rejects w so then + + align:start position:0% +that means that m rejects w so then + + + align:start position:0% +that means that m rejects w so then +we're going to reject if we know that + + align:start position:0% +we're going to reject if we know that + + + align:start position:0% +we're going to reject if we know that +mw's language is empty + + align:start position:0% +mw's language is empty + + + align:start position:0% +mw's language is empty +that must have been that m rejected w so + + align:start position:0% +that must have been that m rejected w so + + + align:start position:0% +that must have been that m rejected w so +now as an atm decider which is what s is + + align:start position:0% +now as an atm decider which is what s is + + + align:start position:0% +now as an atm decider which is what s is +m is + + align:start position:0% +m is + + + align:start position:0% +m is +s is supposed to reject which is what we + + align:start position:0% +s is supposed to reject which is what we + + + align:start position:0% +s is supposed to reject which is what we +we have here in the description and if + + align:start position:0% +we have here in the description and if + + + align:start position:0% +we have here in the description and if +no + + align:start position:0% +no + + + align:start position:0% +no +that means m the language is not empty + + align:start position:0% +that means m the language is not empty + + + align:start position:0% +that means m the language is not empty +so m accepts w and so therefore we're + + align:start position:0% +so m accepts w and so therefore we're + + + align:start position:0% +so m accepts w and so therefore we're +accepting so there's a little bit of a + + align:start position:0% +accepting so there's a little bit of a + + + align:start position:0% +accepting so there's a little bit of a +twist here also + + align:start position:0% +twist here also + + + align:start position:0% +twist here also +okay so let's let's take some more um + + align:start position:0% + + + + align:start position:0% + +i'm expecting some questions here + + align:start position:0% +i'm expecting some questions here + + + align:start position:0% +i'm expecting some questions here +so somebody's asking um how do you + + align:start position:0% +so somebody's asking um how do you + + + align:start position:0% +so somebody's asking um how do you +determine if a language is decidable + + align:start position:0% + + + + align:start position:0% + +that's what we're doing + + align:start position:0% +that's what we're doing + + + align:start position:0% +that's what we're doing +you know + + align:start position:0% +you know + + + align:start position:0% +you know +you can show a language is decidable + + align:start position:0% +you can show a language is decidable + + + align:start position:0% +you can show a language is decidable +by exhibiting a turing machine which + + align:start position:0% +by exhibiting a turing machine which + + + align:start position:0% +by exhibiting a turing machine which +decides it and you can show a language + + align:start position:0% +decides it and you can show a language + + + align:start position:0% +decides it and you can show a language +is not decidable which is what we're + + align:start position:0% +is not decidable which is what we're + + + align:start position:0% +is not decidable which is what we're +doing here by proving that no it's not + + align:start position:0% +doing here by proving that no it's not + + + align:start position:0% +doing here by proving that no it's not +possible for a turing machine to decide + + align:start position:0% +possible for a turing machine to decide + + + align:start position:0% +possible for a turing machine to decide +it + + align:start position:0% +it + + + align:start position:0% +it +you know we did that first with atm + + align:start position:0% +you know we did that first with atm + + + align:start position:0% +you know we did that first with atm +we got that contradiction + + align:start position:0% +we got that contradiction + + + align:start position:0% +we got that contradiction +by + + align:start position:0% +by + + + align:start position:0% +by +diagonalization and here we're doing a + + align:start position:0% +diagonalization and here we're doing a + + + align:start position:0% +diagonalization and here we're doing a +reduceability um to show as as a method + + align:start position:0% +reduceability um to show as as a method + + + align:start position:0% +reduceability um to show as as a method +of proof + + align:start position:0% +of proof + + + align:start position:0% +of proof +um + + align:start position:0% + + + + align:start position:0% + +all right let's let's uh let's continue + + align:start position:0% +all right let's let's uh let's continue + + + align:start position:0% +all right let's let's uh let's continue +so now we're gonna talk about a special + + align:start position:0% +so now we're gonna talk about a special + + + align:start position:0% +so now we're gonna talk about a special +kind so so far we we talked about + + align:start position:0% +kind so so far we we talked about + + + align:start position:0% +kind so so far we we talked about +reducibility + + align:start position:0% +reducibility + + + align:start position:0% +reducibility +we didn't define it in a precise way um + + align:start position:0% +we didn't define it in a precise way um + + + align:start position:0% +we didn't define it in a precise way um +because there are several different ways + + align:start position:0% +because there are several different ways + + + align:start position:0% +because there are several different ways +to get at the notion of reducibility + + align:start position:0% +to get at the notion of reducibility + + + align:start position:0% +to get at the notion of reducibility +precisely um + + align:start position:0% +precisely um + + + align:start position:0% +precisely um +and i'm going to introduce a one version + + align:start position:0% +and i'm going to introduce a one version + + + align:start position:0% +and i'm going to introduce a one version +which is a little bit more restrictive i + + align:start position:0% +which is a little bit more restrictive i + + + align:start position:0% +which is a little bit more restrictive i +mean you know somewhat more restrictive + + align:start position:0% +mean you know somewhat more restrictive + + + align:start position:0% +mean you know somewhat more restrictive +and a little bit different way of + + align:start position:0% +and a little bit different way of + + + align:start position:0% +and a little bit different way of +looking at it than we have been doing so + + align:start position:0% +looking at it than we have been doing so + + + align:start position:0% +looking at it than we have been doing so +far + + align:start position:0% +far + + + align:start position:0% +far +but there are going to be some benefits + + align:start position:0% +but there are going to be some benefits + + + align:start position:0% +but there are going to be some benefits +to looking at this particular kind of + + align:start position:0% +to looking at this particular kind of + + + align:start position:0% +to looking at this particular kind of +reducibility which we're calling mapping + + align:start position:0% +reducibility which we're calling mapping + + + align:start position:0% +reducibility which we're calling mapping +reducibility + + align:start position:0% +reducibility + + + align:start position:0% +reducibility +um it's going to have several benefits + + align:start position:0% +um it's going to have several benefits + + + align:start position:0% +um it's going to have several benefits +for us uh immediately and down the road + + align:start position:0% +for us uh immediately and down the road + + + align:start position:0% +for us uh immediately and down the road +but it's a little + + align:start position:0% +but it's a little + + + align:start position:0% +but it's a little +this is also + + align:start position:0% +this is also + + + align:start position:0% +this is also +you know a little technical so you're + + align:start position:0% +you know a little technical so you're + + + align:start position:0% +you know a little technical so you're +going to have to + + align:start position:0% +going to have to + + + align:start position:0% +going to have to +go don't uh + + align:start position:0% +go don't uh + + + align:start position:0% +go don't uh +you know + + align:start position:0% +you know + + + align:start position:0% +you know +don't don't + + align:start position:0% +don't don't + + + align:start position:0% +don't don't +don't don't get scared off + + align:start position:0% +don't don't get scared off + + + align:start position:0% +don't don't get scared off +you know we'll will + + align:start position:0% +you know we'll will + + + align:start position:0% +you know we'll will +it it might look complicated at first + + align:start position:0% +it it might look complicated at first + + + align:start position:0% +it it might look complicated at first +we'll um try to unpack it for you + + align:start position:0% +we'll um try to unpack it for you + + + align:start position:0% +we'll um try to unpack it for you +um + + align:start position:0% +um + + + align:start position:0% +um +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so first of all uh + + align:start position:0% +so first of all uh + + + align:start position:0% +so first of all uh +if we have here a um + + align:start position:0% +if we have here a um + + + align:start position:0% +if we have here a um +we have to first of all talk about the + + align:start position:0% +we have to first of all talk about the + + + align:start position:0% +we have to first of all talk about the +notion of a computable function + + align:start position:0% +notion of a computable function + + + align:start position:0% +notion of a computable function +so so you know generally when we've had + + align:start position:0% +so so you know generally when we've had + + + align:start position:0% +so so you know generally when we've had +turing machines + + align:start position:0% +turing machines + + + align:start position:0% +turing machines +you know they're they're doing yes no + + align:start position:0% +you know they're they're doing yes no + + + align:start position:0% +you know they're they're doing yes no +they're doing except reject uh kinds of + + align:start position:0% +they're doing except reject uh kinds of + + + align:start position:0% +they're doing except reject uh kinds of +things um so it's like a function + + align:start position:0% +things um so it's like a function + + + align:start position:0% +things um so it's like a function +just sort of a computing sort of a + + align:start position:0% +just sort of a computing sort of a + + + align:start position:0% +just sort of a computing sort of a +binary function + + align:start position:0% +binary function + + + align:start position:0% +binary function +um + + align:start position:0% +um + + + align:start position:0% +um +you know + + align:start position:0% +you know + + + align:start position:0% +you know +for here we're going to want to talk + + align:start position:0% +for here we're going to want to talk + + + align:start position:0% +for here we're going to want to talk +about turing machines that are computing + + align:start position:0% +about turing machines that are computing + + + align:start position:0% +about turing machines that are computing +some more gener it's a function which + + align:start position:0% +some more gener it's a function which + + + align:start position:0% +some more gener it's a function which +converts one string to another string + + align:start position:0% +converts one string to another string + + + align:start position:0% +converts one string to another string +um so it's a it's a mapping from strings + + align:start position:0% +um so it's a it's a mapping from strings + + + align:start position:0% +um so it's a it's a mapping from strings +to strings + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +you know + + align:start position:0% +you know + + + align:start position:0% +you know +could be like the function which + + align:start position:0% +could be like the function which + + + align:start position:0% +could be like the function which +reverses the string for example + + align:start position:0% +reverses the string for example + + + align:start position:0% +reverses the string for example +um that's one uh possible function you + + align:start position:0% +um that's one uh possible function you + + + align:start position:0% +um that's one uh possible function you +you could be + + align:start position:0% +you could be + + + align:start position:0% +you could be +having here but there of course met + + align:start position:0% +having here but there of course met + + + align:start position:0% +having here but there of course met +zillions of possible functions here and + + align:start position:0% +zillions of possible functions here and + + + align:start position:0% +zillions of possible functions here and +we're going to talk about functions that + + align:start position:0% +we're going to talk about functions that + + + align:start position:0% +we're going to talk about functions that +you can compute with the turing machine + + align:start position:0% +you can compute with the turing machine + + + align:start position:0% +you can compute with the turing machine +and that basically means you provide the + + align:start position:0% +and that basically means you provide the + + + align:start position:0% +and that basically means you provide the +input to the function as input to the + + align:start position:0% +input to the function as input to the + + + align:start position:0% +input to the function as input to the +turing machine + + align:start position:0% +turing machine + + + align:start position:0% +turing machine +and the output of the function the the + + align:start position:0% +and the output of the function the the + + + align:start position:0% +and the output of the function the the +value of the function comes out as the + + align:start position:0% +value of the function comes out as the + + + align:start position:0% +value of the function comes out as the +output of the turing machine + + align:start position:0% +output of the turing machine + + + align:start position:0% +output of the turing machine +which let's just say it leaves that + + align:start position:0% +which let's just say it leaves that + + + align:start position:0% +which let's just say it leaves that +value on its tape when it holds it holds + + align:start position:0% +value on its tape when it holds it holds + + + align:start position:0% +value on its tape when it holds it holds +with the value of the function on the + + align:start position:0% +with the value of the function on the + + + align:start position:0% +with the value of the function on the +tape + + align:start position:0% +tape + + + align:start position:0% +tape +um + + align:start position:0% +um + + + align:start position:0% +um +but just you know we're thinking about + + align:start position:0% +but just you know we're thinking about + + + align:start position:0% +but just you know we're thinking about +algorithms here + + align:start position:0% +algorithms here + + + align:start position:0% +algorithms here +come up with your favorite method of + + align:start position:0% +come up with your favorite method of + + + align:start position:0% +come up with your favorite method of +thinking about algorithms it has an + + align:start position:0% +thinking about algorithms it has an + + + align:start position:0% +thinking about algorithms it has an +input and an output and the algorithm + + align:start position:0% +input and an output and the algorithm + + + align:start position:0% +input and an output and the algorithm +just computes the function by taking as + + align:start position:0% +just computes the function by taking as + + + align:start position:0% +just computes the function by taking as +input w and the output is f of w it + + align:start position:0% +input w and the output is f of w it + + + align:start position:0% +input w and the output is f of w it +doesn't have to be turing machines just + + align:start position:0% +doesn't have to be turing machines just + + + align:start position:0% +doesn't have to be turing machines just +any any algorithm that can compute + + align:start position:0% +any any algorithm that can compute + + + align:start position:0% +any any algorithm that can compute +something is good enough + + align:start position:0% +something is good enough + + + align:start position:0% +something is good enough +they're all equivalent + + align:start position:0% +they're all equivalent + + + align:start position:0% +they're all equivalent +um + + align:start position:0% +um + + + align:start position:0% +um +and now we're going to use this notion + + align:start position:0% +and now we're going to use this notion + + + align:start position:0% +and now we're going to use this notion +of a function that you can compute + + align:start position:0% +of a function that you can compute + + + align:start position:0% +of a function that you can compute +to define a a kind of reducibility + + align:start position:0% +to define a a kind of reducibility + + + align:start position:0% +to define a a kind of reducibility +called mapping reducibility i'm going to + + align:start position:0% +called mapping reducibility i'm going to + + + align:start position:0% +called mapping reducibility i'm going to +say that a is mapping reducible to b + + align:start position:0% +say that a is mapping reducible to b + + + align:start position:0% +say that a is mapping reducible to b +written with this + + align:start position:0% +written with this + + + align:start position:0% +written with this +less than or equal to sub m symbol + + align:start position:0% +less than or equal to sub m symbol + + + align:start position:0% +less than or equal to sub m symbol +you're going to see that a lot it's on + + align:start position:0% +you're going to see that a lot it's on + + + align:start position:0% +you're going to see that a lot it's on +the homework also by the way + + align:start position:0% + + + + align:start position:0% + +if there is some computable function as + + align:start position:0% +if there is some computable function as + + + align:start position:0% +if there is some computable function as +i just described + + align:start position:0% +i just described + + + align:start position:0% +i just described +where whenever w is in a + + align:start position:0% +where whenever w is in a + + + align:start position:0% +where whenever w is in a +f of w is in b + + align:start position:0% + + + + align:start position:0% + +and the way to think about it is with + + align:start position:0% +and the way to think about it is with + + + align:start position:0% +and the way to think about it is with +this picture + + align:start position:0% +this picture + + + align:start position:0% +this picture +so a and b are languages + + align:start position:0% +so a and b are languages + + + align:start position:0% +so a and b are languages +written like here's a and here's b + + align:start position:0% + + + + align:start position:0% + +and now there are + + align:start position:0% +and now there are + + + align:start position:0% +and now there are +strings + + align:start position:0% + + + + align:start position:0% + +so w might be + + align:start position:0% +so w might be + + + align:start position:0% +so w might be +in a it might be out of a + + align:start position:0% +in a it might be out of a + + + align:start position:0% +in a it might be out of a +and you think if you're trying to solve + + align:start position:0% +and you think if you're trying to solve + + + align:start position:0% +and you think if you're trying to solve +a + + align:start position:0% +a + + + align:start position:0% +a +you're trying to have a + + align:start position:0% +you're trying to have a + + + align:start position:0% +you're trying to have a +you're trying to decide + + align:start position:0% +you're trying to decide + + + align:start position:0% +you're trying to decide +membership in a + + align:start position:0% +membership in a + + + align:start position:0% +membership in a +so you want to test whether w is in a or + + align:start position:0% +so you want to test whether w is in a or + + + align:start position:0% +so you want to test whether w is in a or +not + + align:start position:0% + + + + align:start position:0% + +a mapping reducible is a function + + align:start position:0% +a mapping reducible is a function + + + align:start position:0% +a mapping reducible is a function +which + + align:start position:0% + + + + align:start position:0% + +maps things from this space over to that + + align:start position:0% +maps things from this space over to that + + + align:start position:0% +maps things from this space over to that +space + + align:start position:0% +space + + + align:start position:0% +space +in a way that strings that are in a get + + align:start position:0% +in a way that strings that are in a get + + + align:start position:0% +in a way that strings that are in a get +mapped to strings that are in b + + align:start position:0% +mapped to strings that are in b + + + align:start position:0% +mapped to strings that are in b +so if you start out with w and a f of w + + align:start position:0% +so if you start out with w and a f of w + + + align:start position:0% +so if you start out with w and a f of w +is in b + + align:start position:0% +is in b + + + align:start position:0% +is in b +and if w is not in a + + align:start position:0% +and if w is not in a + + + align:start position:0% +and if w is not in a +then f of w is not in b + + align:start position:0% + + + + align:start position:0% + +it's a you know pictorially it's a + + align:start position:0% +it's a you know pictorially it's a + + + align:start position:0% +it's a you know pictorially it's a +simple idea + + align:start position:0% +simple idea + + + align:start position:0% +simple idea +we'll have to make sure we understand + + align:start position:0% +we'll have to make sure we understand + + + align:start position:0% +we'll have to make sure we understand +why this + + align:start position:0% +why this + + + align:start position:0% +why this +fits with our + + align:start position:0% +fits with our + + + align:start position:0% +fits with our +um concept of a re reducibility but + + align:start position:0% +um concept of a re reducibility but + + + align:start position:0% +um concept of a re reducibility but +we'll do that but anyway let's first + + align:start position:0% +we'll do that but anyway let's first + + + align:start position:0% +we'll do that but anyway let's first +understand just what we're doing here + + align:start position:0% +understand just what we're doing here + + + align:start position:0% +understand just what we're doing here +we're just coming up with a function + + align:start position:0% +we're just coming up with a function + + + align:start position:0% +we're just coming up with a function +that can do this kind of a mapping + + align:start position:0% +that can do this kind of a mapping + + + align:start position:0% +that can do this kind of a mapping +it sort of translates + + align:start position:0% +it sort of translates + + + align:start position:0% +it sort of translates +problems which you know inputs which may + + align:start position:0% +problems which you know inputs which may + + + align:start position:0% +problems which you know inputs which may +or may not be an a + + align:start position:0% +or may not be an a + + + align:start position:0% +or may not be an a +into um + + align:start position:0% +into um + + + align:start position:0% +into um +other strings which may or may not be in + + align:start position:0% +other strings which may or may not be in + + + align:start position:0% +other strings which may or may not be in +b but sort of maintaining that um uh the + + align:start position:0% +b but sort of maintaining that um uh the + + + align:start position:0% +b but sort of maintaining that um uh the +same input + + align:start position:0% +same input + + + align:start position:0% +same input +property + + align:start position:0% +property + + + align:start position:0% +property +uh that's + + align:start position:0% +uh that's + + + align:start position:0% +uh that's +the same membership property so if you + + align:start position:0% +the same membership property so if you + + + align:start position:0% +the same membership property so if you +start out with something in a + + align:start position:0% +start out with something in a + + + align:start position:0% +start out with something in a +when you play f you're going to end up + + align:start position:0% +when you play f you're going to end up + + + align:start position:0% +when you play f you're going to end up +with something in b + + align:start position:0% +with something in b + + + align:start position:0% +with something in b +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +and conversely if you're not in a then + + align:start position:0% +and conversely if you're not in a then + + + align:start position:0% +and conversely if you're not in a then +you won't be in b + + align:start position:0% + + + + align:start position:0% + +okay um uh some somebody's asking + + align:start position:0% +okay um uh some somebody's asking + + + align:start position:0% +okay um uh some somebody's asking +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so just a couple of questions here + + align:start position:0% +so just a couple of questions here + + + align:start position:0% +so just a couple of questions here +not necessarily one to one no so the + + align:start position:0% +not necessarily one to one no so the + + + align:start position:0% +not necessarily one to one no so the +function doesn't have to be one to one + + align:start position:0% +function doesn't have to be one to one + + + align:start position:0% +function doesn't have to be one to one +there could be multiple things that map + + align:start position:0% +there could be multiple things that map + + + align:start position:0% +there could be multiple things that map +to the same point + + align:start position:0% +to the same point + + + align:start position:0% +to the same point +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +and is it is there any restriction on + + align:start position:0% +and is it is there any restriction on + + + align:start position:0% +and is it is there any restriction on +the alphabet no + + align:start position:0% +the alphabet no + + + align:start position:0% +the alphabet no +um + + align:start position:0% + + + + align:start position:0% + +so uh + + align:start position:0% + + + + align:start position:0% + +before we actually get into the example + + align:start position:0% +before we actually get into the example + + + align:start position:0% +before we actually get into the example +let me try to give you a sense about why + + align:start position:0% +let me try to give you a sense about why + + + align:start position:0% +let me try to give you a sense about why +um we call this a reducibility + + align:start position:0% +um we call this a reducibility + + + align:start position:0% +um we call this a reducibility +and the reason is + + align:start position:0% +and the reason is + + + align:start position:0% +and the reason is +suppose we have + + align:start position:0% +suppose we have + + + align:start position:0% +suppose we have +such an f + + align:start position:0% +such an f + + + align:start position:0% +such an f +which can do the mapping as i described + + align:start position:0% +which can do the mapping as i described + + + align:start position:0% +which can do the mapping as i described +and we also have a way + + align:start position:0% +and we also have a way + + + align:start position:0% +and we also have a way +of deciding membership in b + + align:start position:0% +of deciding membership in b + + + align:start position:0% +of deciding membership in b +so we have so b is decidable + + align:start position:0% +so we have so b is decidable + + + align:start position:0% +so we have so b is decidable +so that's going to tell us right away + + align:start position:0% +so that's going to tell us right away + + + align:start position:0% +so that's going to tell us right away +that a is decidable + + align:start position:0% +that a is decidable + + + align:start position:0% +that a is decidable +because if you have some + + align:start position:0% +because if you have some + + + align:start position:0% +because if you have some +input and you want to know is it an a or + + align:start position:0% +input and you want to know is it an a or + + + align:start position:0% +input and you want to know is it an a or +not + + align:start position:0% +not + + + align:start position:0% +not +you can now apply + + align:start position:0% +you can now apply + + + align:start position:0% +you can now apply +f + + align:start position:0% +f + + + align:start position:0% +f +and test whether f w is in b + + align:start position:0% + + + + align:start position:0% + +so the test of w is an a + + align:start position:0% +so the test of w is an a + + + align:start position:0% +so the test of w is an a +you uh you're going to instead test + + align:start position:0% +you uh you're going to instead test + + + align:start position:0% +you uh you're going to instead test +whether f of w is in b and we'll we're + + align:start position:0% +whether f of w is in b and we'll we're + + + align:start position:0% +whether f of w is in b and we'll we're +assuming we have a that that shows that + + align:start position:0% +assuming we have a that that shows that + + + align:start position:0% +assuming we have a that that shows that +a is reducible to b so if you could + + align:start position:0% +a is reducible to b so if you could + + + align:start position:0% +a is reducible to b so if you could +solve + + align:start position:0% +solve + + + align:start position:0% +solve +the b problem that allows gives you a + + align:start position:0% +the b problem that allows gives you a + + + align:start position:0% +the b problem that allows gives you a +way to solve the a problem + + align:start position:0% +way to solve the a problem + + + align:start position:0% +way to solve the a problem +again we're going to say this several + + align:start position:0% +again we're going to say this several + + + align:start position:0% +again we're going to say this several +times in several different ways so if + + align:start position:0% +times in several different ways so if + + + align:start position:0% +times in several different ways so if +you didn't quite get it yet + + align:start position:0% +you didn't quite get it yet + + + align:start position:0% +you didn't quite get it yet +you know don't don't panic + + align:start position:0% +you know don't don't panic + + + align:start position:0% +you know don't don't panic +um + + align:start position:0% +um + + + align:start position:0% +um +so here's going to be an + + align:start position:0% +so here's going to be an + + + align:start position:0% +so here's going to be an +example sort of building on what we just + + align:start position:0% +example sort of building on what we just + + + align:start position:0% +example sort of building on what we just +showed last time + + align:start position:0% +showed last time + + + align:start position:0% +showed last time +in the previous slide atm we're going to + + align:start position:0% +in the previous slide atm we're going to + + + align:start position:0% +in the previous slide atm we're going to +show how atm is actually mapping + + align:start position:0% +show how atm is actually mapping + + + align:start position:0% +show how atm is actually mapping +reducible to the complement of etm + + align:start position:0% +reducible to the complement of etm + + + align:start position:0% +reducible to the complement of etm +and the complement is necessary here + + align:start position:0% + + + + align:start position:0% + +the computable function that we're going + + align:start position:0% +the computable function that we're going + + + align:start position:0% +the computable function that we're going +to give + + align:start position:0% +to give + + + align:start position:0% +to give +which is basically if you're going to + + align:start position:0% +which is basically if you're going to + + + align:start position:0% +which is basically if you're going to +the computable function is going to + + align:start position:0% +the computable function is going to + + + align:start position:0% +the computable function is going to +translate + + align:start position:0% +translate + + + align:start position:0% +translate +problems about atm to problems about + + align:start position:0% +problems about atm to problems about + + + align:start position:0% +problems about atm to problems about +uh etm because we're mapping reducing + + align:start position:0% +uh etm because we're mapping reducing + + + align:start position:0% +uh etm because we're mapping reducing +atm to the complement of etf + + align:start position:0% +atm to the complement of etf + + + align:start position:0% +atm to the complement of etf +so we're going to what we're doing here + + align:start position:0% +so we're going to what we're doing here + + + align:start position:0% +so we're going to what we're doing here +is with mapping m and w + + align:start position:0% +is with mapping m and w + + + align:start position:0% +is with mapping m and w +to the uh machine mw + + align:start position:0% + + + + align:start position:0% + +kind of in a way we're boiling out the + + align:start position:0% +kind of in a way we're boiling out the + + + align:start position:0% +kind of in a way we're boiling out the +essence boiling down to the essence of + + align:start position:0% +essence boiling down to the essence of + + + align:start position:0% +essence boiling down to the essence of +the proof that we gave in the previous + + align:start position:0% +the proof that we gave in the previous + + + align:start position:0% +the proof that we gave in the previous +slide + + align:start position:0% +slide + + + align:start position:0% +slide +this is really the the the core of the + + align:start position:0% +this is really the the the core of the + + + align:start position:0% +this is really the the the core of the +proof this translation of mw where you + + align:start position:0% +proof this translation of mw where you + + + align:start position:0% +proof this translation of mw where you +want to know is m accepting w + + align:start position:0% +want to know is m accepting w + + + align:start position:0% +want to know is m accepting w +to a new machine mw where you're testing + + align:start position:0% +to a new machine mw where you're testing + + + align:start position:0% +to a new machine mw where you're testing +whether + + align:start position:0% +whether + + + align:start position:0% +whether +mw's language is empty + + align:start position:0% +mw's language is empty + + + align:start position:0% +mw's language is empty +and so this is the you know so remember + + align:start position:0% +and so this is the you know so remember + + + align:start position:0% +and so this is the you know so remember +mw from before it's the machine that + + align:start position:0% +mw from before it's the machine that + + + align:start position:0% +mw from before it's the machine that +filters out all the non-ws and rejects + + align:start position:0% +filters out all the non-ws and rejects + + + align:start position:0% +filters out all the non-ws and rejects +them + + align:start position:0% +them + + + align:start position:0% +them +um and the reason why this reduction + + align:start position:0% +um and the reason why this reduction + + + align:start position:0% +um and the reason why this reduction +function works + + align:start position:0% +function works + + + align:start position:0% +function works +um is that + + align:start position:0% +um is that + + + align:start position:0% +um is that +mw is in atm + + align:start position:0% +mw is in atm + + + align:start position:0% +mw is in atm +if and only if m sub w is in the + + align:start position:0% +if and only if m sub w is in the + + + align:start position:0% +if and only if m sub w is in the +complement of etf + + align:start position:0% +complement of etf + + + align:start position:0% +complement of etf +so m accepts w exactly when mw's + + align:start position:0% +so m accepts w exactly when mw's + + + align:start position:0% +so m accepts w exactly when mw's +language is not empty + + align:start position:0% + + + + align:start position:0% + +okay so m accepts w if and only if + + align:start position:0% +okay so m accepts w if and only if + + + align:start position:0% +okay so m accepts w if and only if +the language of mw is not empty + + align:start position:0% +the language of mw is not empty + + + align:start position:0% +the language of mw is not empty +so you have to mull this over a bit + + align:start position:0% +so you have to mull this over a bit + + + align:start position:0% +so you have to mull this over a bit +realize it's + + align:start position:0% +realize it's + + + align:start position:0% +realize it's +you know i i know this is + + align:start position:0% +you know i i know this is + + + align:start position:0% +you know i i know this is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +can be a little tricky + + align:start position:0% +can be a little tricky + + + align:start position:0% +can be a little tricky +but i think what we're going to do here + + align:start position:0% +but i think what we're going to do here + + + align:start position:0% +but i think what we're going to do here +i think we're at the uh break the time + + align:start position:0% +i think we're at the uh break the time + + + align:start position:0% +i think we're at the uh break the time +for the break so + + align:start position:0% +for the break so + + + align:start position:0% +for the break so +uh oh no there's one more slide i + + align:start position:0% +uh oh no there's one more slide i + + + align:start position:0% +uh oh no there's one more slide i +apologize so let's let's talk about this + + align:start position:0% +apologize so let's let's talk about this + + + align:start position:0% +apologize so let's let's talk about this +and then we're going to have our coffee + + align:start position:0% +and then we're going to have our coffee + + + align:start position:0% +and then we're going to have our coffee +break + + align:start position:0% +break + + + align:start position:0% +break +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so there are um + + align:start position:0% +so there are um + + + align:start position:0% +so there are um +the reason why so this + + align:start position:0% +the reason why so this + + + align:start position:0% +the reason why so this +these properties are really gonna be + + align:start position:0% +these properties are really gonna be + + + align:start position:0% +these properties are really gonna be +getting at + + align:start position:0% +getting at + + + align:start position:0% +getting at +what makes mapping reducible + + align:start position:0% +what makes mapping reducible + + + align:start position:0% +what makes mapping reducible +mapping reducibility + + align:start position:0% +mapping reducibility + + + align:start position:0% +mapping reducibility +fit with our + + align:start position:0% +fit with our + + + align:start position:0% +fit with our +understanding of what a reducibility + + align:start position:0% +understanding of what a reducibility + + + align:start position:0% +understanding of what a reducibility +should be + + align:start position:0% +should be + + + align:start position:0% +should be +so if a is mapping reducible to b and b + + align:start position:0% +so if a is mapping reducible to b and b + + + align:start position:0% +so if a is mapping reducible to b and b +is decidable then so is a + + align:start position:0% +is decidable then so is a + + + align:start position:0% +is decidable then so is a +um so that + + align:start position:0% +um so that + + + align:start position:0% +um so that +fits with what we want because if a is + + align:start position:0% +fits with what we want because if a is + + + align:start position:0% +fits with what we want because if a is +reducible to b and b is easy then a is + + align:start position:0% +reducible to b and b is easy then a is + + + align:start position:0% +reducible to b and b is easy then a is +easy so here easy means decidable + + align:start position:0% +easy so here easy means decidable + + + align:start position:0% +easy so here easy means decidable +and here's the proof let's take a turing + + align:start position:0% +and here's the proof let's take a turing + + + align:start position:0% +and here's the proof let's take a turing +machine that decides b and construct a + + align:start position:0% +machine that decides b and construct a + + + align:start position:0% +machine that decides b and construct a +turing machine that decides a + + align:start position:0% +turing machine that decides a + + + align:start position:0% +turing machine that decides a +as claimed + + align:start position:0% +as claimed + + + align:start position:0% +as claimed +s operates like this + + align:start position:0% +s operates like this + + + align:start position:0% +s operates like this +it takes its input + + align:start position:0% +it takes its input + + + align:start position:0% +it takes its input +computes + + align:start position:0% +computes + + + align:start position:0% +computes +f of that input + + align:start position:0% +f of that input + + + align:start position:0% +f of that input +tests + + align:start position:0% +tests + + + align:start position:0% +tests +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +whether that + + align:start position:0% +whether that + + + align:start position:0% +whether that +f + + align:start position:0% +f + + + align:start position:0% +f +whether f w is in b using the uh r + + align:start position:0% +whether f w is in b using the uh r + + + align:start position:0% +whether f w is in b using the uh r +machine that we were assuming you know + + align:start position:0% +machine that we were assuming you know + + + align:start position:0% +machine that we were assuming you know +we have r deciding b + + align:start position:0% +we have r deciding b + + + align:start position:0% +we have r deciding b +and if r + + align:start position:0% +and if r + + + align:start position:0% +and if r +holds then output the same result + + align:start position:0% +holds then output the same result + + + align:start position:0% +holds then output the same result +so if r accepts we're going to accept if + + align:start position:0% +so if r accepts we're going to accept if + + + align:start position:0% +so if r accepts we're going to accept if +our holds and rejects we'll reject and + + align:start position:0% +our holds and rejects we'll reject and + + + align:start position:0% +our holds and rejects we'll reject and +of course we're going to be simula + + align:start position:0% +of course we're going to be simula + + + align:start position:0% +of course we're going to be simula +running r so if r is not going to be + + align:start position:0% +running r so if r is not going to be + + + align:start position:0% +running r so if r is not going to be +halting we're not going to end up + + align:start position:0% +halting we're not going to end up + + + align:start position:0% +halting we're not going to end up +halting either + + align:start position:0% +halting either + + + align:start position:0% +halting either +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the corollary is and this is the way + + align:start position:0% +so the corollary is and this is the way + + + align:start position:0% +so the corollary is and this is the way +we're going to be using it + + align:start position:0% + + + + align:start position:0% + +if a is reducible to b and b and a is + + align:start position:0% +if a is reducible to b and b and a is + + + align:start position:0% +if a is reducible to b and b and a is +undecidable then so is b + + align:start position:0% + + + + align:start position:0% + +so this is as i mentioned we're going to + + align:start position:0% +so this is as i mentioned we're going to + + + align:start position:0% +so this is as i mentioned we're going to +be the focus on for us is going to be on + + align:start position:0% +be the focus on for us is going to be on + + + align:start position:0% +be the focus on for us is going to be on +undecidability and you may want to think + + align:start position:0% +undecidability and you may want to think + + + align:start position:0% +undecidability and you may want to think +about a is like the atm problem + + align:start position:0% +about a is like the atm problem + + + align:start position:0% +about a is like the atm problem +which we know is undecidable we're going + + align:start position:0% +which we know is undecidable we're going + + + align:start position:0% +which we know is undecidable we're going +to show the atm is mapping reducible to + + align:start position:0% +to show the atm is mapping reducible to + + + align:start position:0% +to show the atm is mapping reducible to +some other problem to show that that + + align:start position:0% +some other problem to show that that + + + align:start position:0% +some other problem to show that that +other problem is undecidable + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and the important thing about mapping + + align:start position:0% +and the important thing about mapping + + + align:start position:0% +and the important thing about mapping +reducibility is that also applies to + + align:start position:0% +reducibility is that also applies to + + + align:start position:0% +reducibility is that also applies to +recognizing to recognizers so if a is + + align:start position:0% +recognizing to recognizers so if a is + + + align:start position:0% +recognizing to recognizers so if a is +mapping reducible to b and b is turning + + align:start position:0% +mapping reducible to b and b is turning + + + align:start position:0% +mapping reducible to b and b is turning +recognizable then so is a + + align:start position:0% +recognizable then so is a + + + align:start position:0% +recognizable then so is a +so if you map you're reducing a to a + + align:start position:0% +so if you map you're reducing a to a + + + align:start position:0% +so if you map you're reducing a to a +recognizable problem then a is also + + align:start position:0% +recognizable problem then a is also + + + align:start position:0% +recognizable problem then a is also +recognizable + + align:start position:0% +recognizable + + + align:start position:0% +recognizable +same proof because you can just + + align:start position:0% +same proof because you can just + + + align:start position:0% +same proof because you can just +map your w to f of w and feed it into + + align:start position:0% +map your w to f of w and feed it into + + + align:start position:0% +map your w to f of w and feed it into +the recognizer that's going to give you + + align:start position:0% +the recognizer that's going to give you + + + align:start position:0% +the recognizer that's going to give you +a recognizer for the original language + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +the corollary is that if a + + align:start position:0% +the corollary is that if a + + + align:start position:0% +the corollary is that if a +is + + align:start position:0% +is + + + align:start position:0% +is +mapping reducible to b and a is + + align:start position:0% +mapping reducible to b and a is + + + align:start position:0% +mapping reducible to b and a is +unrecognizable then so is b so this is + + align:start position:0% +unrecognizable then so is b so this is + + + align:start position:0% +unrecognizable then so is b so this is +again that sort of um + + align:start position:0% +again that sort of um + + + align:start position:0% +again that sort of um +inverted logic + + align:start position:0% +inverted logic + + + align:start position:0% +inverted logic +okay so now i think where + + align:start position:0% +okay so now i think where + + + align:start position:0% +okay so now i think where +uh oops i meant to put this picture up + + align:start position:0% +uh oops i meant to put this picture up + + + align:start position:0% +uh oops i meant to put this picture up +earlier + + align:start position:0% +earlier + + + align:start position:0% +earlier +uh + + align:start position:0% +uh + + + align:start position:0% +uh +okay so here's a check in + + align:start position:0% +okay so here's a check in + + + align:start position:0% +okay so here's a check in +um + + align:start position:0% +um + + + align:start position:0% +um +be more of a check-in for me to see how + + align:start position:0% +be more of a check-in for me to see how + + + align:start position:0% +be more of a check-in for me to see how +well you're following me + + align:start position:0% + + + + align:start position:0% + +so these are some properties of + + align:start position:0% +so these are some properties of + + + align:start position:0% +so these are some properties of +um i'll give you a minute here to think + + align:start position:0% +um i'll give you a minute here to think + + + align:start position:0% +um i'll give you a minute here to think +about this some properties of mapping + + align:start position:0% +about this some properties of mapping + + + align:start position:0% +about this some properties of mapping +reducibility + + align:start position:0% +reducibility + + + align:start position:0% +reducibility +um + + align:start position:0% +um + + + align:start position:0% +um +suppose a is mapping reducible to b what + + align:start position:0% +suppose a is mapping reducible to b what + + + align:start position:0% +suppose a is mapping reducible to b what +can we conclude + + align:start position:0% +can we conclude + + + align:start position:0% +can we conclude +does that mean that + + align:start position:0% +does that mean that + + + align:start position:0% +does that mean that +we can flip it around + + align:start position:0% +we can flip it around + + + align:start position:0% +we can flip it around +if a is mapping reducible to b does that + + align:start position:0% +if a is mapping reducible to b does that + + + align:start position:0% +if a is mapping reducible to b does that +mean a b is mapping reducible to a + + align:start position:0% +mean a b is mapping reducible to a + + + align:start position:0% +mean a b is mapping reducible to a +what about this one um if a is mapping + + align:start position:0% +what about this one um if a is mapping + + + align:start position:0% +what about this one um if a is mapping +inducible to b + + align:start position:0% +inducible to b + + + align:start position:0% +inducible to b +to the is the complement of a mapping + + align:start position:0% +to the is the complement of a mapping + + + align:start position:0% +to the is the complement of a mapping +reducible to the complement of b or + + align:start position:0% +reducible to the complement of b or + + + align:start position:0% +reducible to the complement of b or +maybe neither so you can and you can um + + align:start position:0% +maybe neither so you can and you can um + + + align:start position:0% +maybe neither so you can and you can um +uh check all that apply um + + align:start position:0% + + + + align:start position:0% + +multiple choice + + align:start position:0% + + + + align:start position:0% + +five seconds + + align:start position:0% + + + + align:start position:0% + +sorry to pressure you but + + align:start position:0% +sorry to pressure you but + + + align:start position:0% +sorry to pressure you but +we have to move on here + + align:start position:0% +we have to move on here + + + align:start position:0% +we have to move on here +pick anything + + align:start position:0% +pick anything + + + align:start position:0% +pick anything +uh if you don't know okay + + align:start position:0% +uh if you don't know okay + + + align:start position:0% +uh if you don't know okay +one two three + + align:start position:0% +one two three + + + align:start position:0% +one two three +the end + + align:start position:0% +the end + + + align:start position:0% +the end +um + + align:start position:0% +um + + + align:start position:0% +um +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +well the majority is correct + + align:start position:0% +well the majority is correct + + + align:start position:0% +well the majority is correct +um + + align:start position:0% +um + + + align:start position:0% +um +in fact it's only that uh + + align:start position:0% +in fact it's only that uh + + + align:start position:0% +in fact it's only that uh +only b + + align:start position:0% +only b + + + align:start position:0% +only b +um now + + align:start position:0% +um now + + + align:start position:0% +um now +um + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% +a + + + align:start position:0% +a +really is not in the spirit of + + align:start position:0% +really is not in the spirit of + + + align:start position:0% +really is not in the spirit of +reducibility because um + + align:start position:0% +reducibility because um + + + align:start position:0% +reducibility because um +as suggested even by the inequality sign + + align:start position:0% +as suggested even by the inequality sign + + + align:start position:0% +as suggested even by the inequality sign +there um + + align:start position:0% +there um + + + align:start position:0% +there um +a being reducible to b is really a + + align:start position:0% +a being reducible to b is really a + + + align:start position:0% +a being reducible to b is really a +rather different thing than b being + + align:start position:0% +rather different thing than b being + + + align:start position:0% +rather different thing than b being +reducible to a + + align:start position:0% +reducible to a + + + align:start position:0% +reducible to a +um + + align:start position:0% +um + + + align:start position:0% +um +so that that's something to we're not + + align:start position:0% +so that that's something to we're not + + + align:start position:0% +so that that's something to we're not +going to prove that right here but um + + align:start position:0% +going to prove that right here but um + + + align:start position:0% +going to prove that right here but um +that's something that you um could uh + + align:start position:0% +that's something that you um could uh + + + align:start position:0% +that's something that you um could uh +think about + + align:start position:0% +think about + + + align:start position:0% +think about +and uh but part b + + align:start position:0% +and uh but part b + + + align:start position:0% +and uh but part b +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +i think you you know if you just look + + align:start position:0% +i think you you know if you just look + + + align:start position:0% +i think you you know if you just look +here + + align:start position:0% +here + + + align:start position:0% +here +at the definition of mapping + + align:start position:0% +at the definition of mapping + + + align:start position:0% +at the definition of mapping +reducibility + + align:start position:0% +reducibility + + + align:start position:0% +reducibility +it maps strings in + + align:start position:0% +it maps strings in + + + align:start position:0% +it maps strings in +to in and out to out + + align:start position:0% +to in and out to out + + + align:start position:0% +to in and out to out +well that's just going to be if you + + align:start position:0% +well that's just going to be if you + + + align:start position:0% +well that's just going to be if you +exchange in and out as you do when + + align:start position:0% +exchange in and out as you do when + + + align:start position:0% +exchange in and out as you do when +you're flipping complements on both + + align:start position:0% +you're flipping complements on both + + + align:start position:0% +you're flipping complements on both +sides it's still by the same f gonna + + align:start position:0% +sides it's still by the same f gonna + + + align:start position:0% +sides it's still by the same f gonna +still work as a mapping reduction + + align:start position:0% +still work as a mapping reduction + + + align:start position:0% +still work as a mapping reduction +okay so uh now we're um at our + + align:start position:0% +okay so uh now we're um at our + + + align:start position:0% +okay so uh now we're um at our +co break so we're going to take five + + align:start position:0% +co break so we're going to take five + + + align:start position:0% +co break so we're going to take five +minutes here + + align:start position:0% +minutes here + + + align:start position:0% +minutes here +and + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +and i'll be happy to + + align:start position:0% +and i'll be happy to + + + align:start position:0% +and i'll be happy to +[Music] + + align:start position:0% + + + + align:start position:0% + +take a questions here but don't forget + + align:start position:0% +take a questions here but don't forget + + + align:start position:0% +take a questions here but don't forget +the tas they're here too + + align:start position:0% +the tas they're here too + + + align:start position:0% +the tas they're here too +um + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +okay so this is a fair question here you + + align:start position:0% +okay so this is a fair question here you + + + align:start position:0% +okay so this is a fair question here you +know + + align:start position:0% +know + + + align:start position:0% +know +so we had this notion of a general + + align:start position:0% +so we had this notion of a general + + + align:start position:0% +so we had this notion of a general +reduction and a mapping reduction + + align:start position:0% +reduction and a mapping reduction + + + align:start position:0% +reduction and a mapping reduction +um they're not the same + + align:start position:0% +um they're not the same + + + align:start position:0% +um they're not the same +so + + align:start position:0% +so + + + align:start position:0% +so +anytime you have a mapping reduction + + align:start position:0% +anytime you have a mapping reduction + + + align:start position:0% +anytime you have a mapping reduction +it's going to be an example of a general + + align:start position:0% +it's going to be an example of a general + + + align:start position:0% +it's going to be an example of a general +reduction but not not the other way + + align:start position:0% +reduction but not not the other way + + + align:start position:0% +reduction but not not the other way +around + + align:start position:0% +around + + + align:start position:0% +around +um so you know if you go back and look + + align:start position:0% +um so you know if you go back and look + + + align:start position:0% +um so you know if you go back and look +at the reduction that we we offered + + align:start position:0% +at the reduction that we we offered + + + align:start position:0% +at the reduction that we we offered +for halt tm that where we + + align:start position:0% +for halt tm that where we + + + align:start position:0% +for halt tm that where we +showed atm is reducible to whole tm + + align:start position:0% +showed atm is reducible to whole tm + + + align:start position:0% +showed atm is reducible to whole tm +where we started it's actually not a + + align:start position:0% +where we started it's actually not a + + + align:start position:0% +where we started it's actually not a +mapping reduction um + + align:start position:0% +mapping reduction um + + + align:start position:0% +mapping reduction um +uh because if we're doing something more + + align:start position:0% +uh because if we're doing something more + + + align:start position:0% +uh because if we're doing something more +complicated than that's translating an + + align:start position:0% +complicated than that's translating an + + + align:start position:0% +complicated than that's translating an +atm problem to a whole tm problem we're + + align:start position:0% +atm problem to a whole tm problem we're + + + align:start position:0% +atm problem to a whole tm problem we're +kind of using it using the whole tm + + align:start position:0% +kind of using it using the whole tm + + + align:start position:0% +kind of using it using the whole tm +decider in a more complicated way and + + align:start position:0% +decider in a more complicated way and + + + align:start position:0% +decider in a more complicated way and +there are cases where that that's + + align:start position:0% +there are cases where that that's + + + align:start position:0% +there are cases where that that's +actually necessary um + + align:start position:0% +actually necessary um + + + align:start position:0% +actually necessary um +so we won't uh um + + align:start position:0% +so we won't uh um + + + align:start position:0% +so we won't uh um +not not going to discuss that here but + + align:start position:0% +not not going to discuss that here but + + + align:start position:0% +not not going to discuss that here but +uh it's actually kind of maybe an + + align:start position:0% +uh it's actually kind of maybe an + + + align:start position:0% +uh it's actually kind of maybe an +interesting homework problem perhaps or + + align:start position:0% +interesting homework problem perhaps or + + + align:start position:0% +interesting homework problem perhaps or +some kind of a problem to think about + + align:start position:0% +some kind of a problem to think about + + + align:start position:0% +some kind of a problem to think about +um + + align:start position:0% + + + + align:start position:0% + +so turing machines for fs + + align:start position:0% +so turing machines for fs + + + align:start position:0% +so turing machines for fs +does does f have to be a it's not really + + align:start position:0% +does does f have to be a it's not really + + + align:start position:0% +does does f have to be a it's not really +a decider but it has to be um well yeah + + align:start position:0% +a decider but it has to be um well yeah + + + align:start position:0% +a decider but it has to be um well yeah +i guess it does have to be to start in + + align:start position:0% +i guess it does have to be to start in + + + align:start position:0% +i guess it does have to be to start in +the way it always holds the turing + + align:start position:0% +the way it always holds the turing + + + align:start position:0% +the way it always holds the turing +machines for f has to always hold it + + align:start position:0% +machines for f has to always hold it + + + align:start position:0% +machines for f has to always hold it +always has to have an output so + + align:start position:0% +always has to have an output so + + + align:start position:0% +always has to have an output so +f um + + align:start position:0% +f um + + + align:start position:0% +f um +uh for the computing the function always + + align:start position:0% +uh for the computing the function always + + + align:start position:0% +uh for the computing the function always +always has to + + align:start position:0% +always has to + + + align:start position:0% +always has to +always has to hold + + align:start position:0% +always has to hold + + + align:start position:0% +always has to hold +um + + align:start position:0% + + + + align:start position:0% + +so someone is asking me uh + + align:start position:0% +so someone is asking me uh + + + align:start position:0% +so someone is asking me uh +can i explain uh the the statement that + + align:start position:0% +can i explain uh the the statement that + + + align:start position:0% +can i explain uh the the statement that +if error holds then i'll put the same + + align:start position:0% +if error holds then i'll put the same + + + align:start position:0% +if error holds then i'll put the same +result + + align:start position:0% +result + + + align:start position:0% +result +i just mean that in that previous slide + + align:start position:0% +i just mean that in that previous slide + + + align:start position:0% +i just mean that in that previous slide +um or two slides back if r accepts holds + + align:start position:0% +um or two slides back if r accepts holds + + + align:start position:0% +um or two slides back if r accepts holds +and accepts + + align:start position:0% +and accepts + + + align:start position:0% +and accepts +then we're gonna hold an accept and if r + + align:start position:0% +then we're gonna hold an accept and if r + + + align:start position:0% +then we're gonna hold an accept and if r +holds and rejects then we hold and + + align:start position:0% +holds and rejects then we hold and + + + align:start position:0% +holds and rejects then we hold and +reject um so i can i don't know if this + + align:start position:0% +reject um so i can i don't know if this + + + align:start position:0% +reject um so i can i don't know if this +is a good idea but we can just pull that + + align:start position:0% +is a good idea but we can just pull that + + + align:start position:0% +is a good idea but we can just pull that +back here + + align:start position:0% +back here + + + align:start position:0% +back here +just that was this statement here if our + + align:start position:0% +just that was this statement here if our + + + align:start position:0% +just that was this statement here if our +holds and output the same result i just + + align:start position:0% +holds and output the same result i just + + + align:start position:0% +holds and output the same result i just +mean that s is going to do the same you + + align:start position:0% +mean that s is going to do the same you + + + align:start position:0% +mean that s is going to do the same you +know we're translating + + align:start position:0% +know we're translating + + + align:start position:0% +know we're translating +an a problem to a b problem + + align:start position:0% + + + + align:start position:0% + +and then answering the b problem + + align:start position:0% +and then answering the b problem + + + align:start position:0% +and then answering the b problem +and we're going to give the same + + align:start position:0% +and we're going to give the same + + + align:start position:0% +and we're going to give the same +value the same answer there uh so + + align:start position:0% +value the same answer there uh so + + + align:start position:0% +value the same answer there uh so +whatever r says we're going to say 2. + + align:start position:0% + + + + align:start position:0% + +that's + + align:start position:0% +that's + + + align:start position:0% +that's +helpful + + align:start position:0% +helpful + + + align:start position:0% +helpful +um + + align:start position:0% +um + + + align:start position:0% +um +all right uh + + align:start position:0% +all right uh + + + align:start position:0% +all right uh +well that's a good question here um + + align:start position:0% + + + + align:start position:0% + +you know + + align:start position:0% +you know + + + align:start position:0% +you know +if a is reducible to b uh why can't we + + align:start position:0% +if a is reducible to b uh why can't we + + + align:start position:0% +if a is reducible to b uh why can't we +just get b reducible to a by inverting + + align:start position:0% +just get b reducible to a by inverting + + + align:start position:0% +just get b reducible to a by inverting +the function that's a great question i + + align:start position:0% +the function that's a great question i + + + align:start position:0% +the function that's a great question i +like that question + + align:start position:0% +like that question + + + align:start position:0% +like that question +um + + align:start position:0% +um + + + align:start position:0% +um +the reason is is because um + + align:start position:0% +the reason is is because um + + + align:start position:0% +the reason is is because um +the function that's mapping onto b + + align:start position:0% +the function that's mapping onto b + + + align:start position:0% +the function that's mapping onto b +uh doesn't have to be on to + + align:start position:0% +uh doesn't have to be on to + + + align:start position:0% +uh doesn't have to be on to +surjective i guess um + + align:start position:0% +surjective i guess um + + + align:start position:0% +surjective i guess um +so you can't always you can you're not + + align:start position:0% +so you can't always you can you're not + + + align:start position:0% +so you can't always you can you're not +going to be able to if it was + + align:start position:0% +going to be able to if it was + + + align:start position:0% +going to be able to if it was +um you know onto so if it covered all of + + align:start position:0% +um you know onto so if it covered all of + + + align:start position:0% +um you know onto so if it covered all of +b + + align:start position:0% +b + + + align:start position:0% +b +um + + align:start position:0% +um + + + align:start position:0% +um +then i think then you would get a um an + + align:start position:0% +then i think then you would get a um an + + + align:start position:0% +then i think then you would get a um an +invertible function and it would they + + align:start position:0% +invertible function and it would they + + + align:start position:0% +invertible function and it would they +you would get the + + align:start position:0% +you would get the + + + align:start position:0% +you would get the +reduction going the other way as well um + + align:start position:0% +reduction going the other way as well um + + + align:start position:0% +reduction going the other way as well um +but uh though i'm not sure what happens + + align:start position:0% +but uh though i'm not sure what happens + + + align:start position:0% +but uh though i'm not sure what happens +when you have doesn't matter if you have + + align:start position:0% +when you have doesn't matter if you have + + + align:start position:0% +when you have doesn't matter if you have +collisions + + align:start position:0% +collisions + + + align:start position:0% +collisions +it turns out that's not going to matter + + align:start position:0% +it turns out that's not going to matter + + + align:start position:0% +it turns out that's not going to matter +but anyway let's let's not get it too + + align:start position:0% +but anyway let's let's not get it too + + + align:start position:0% +but anyway let's let's not get it too +complicated here but the the problem + + align:start position:0% +complicated here but the the problem + + + align:start position:0% +complicated here but the the problem +with inverting it is that it's not + + align:start position:0% +with inverting it is that it's not + + + align:start position:0% +with inverting it is that it's not +necessarily on you know onto the whole + + align:start position:0% +necessarily on you know onto the whole + + + align:start position:0% +necessarily on you know onto the whole +range + + align:start position:0% +range + + + align:start position:0% +range +of b + + align:start position:0% +of b + + + align:start position:0% +of b +uh + + align:start position:0% +uh + + + align:start position:0% +uh +okay uh + + align:start position:0% + + + + align:start position:0% + +so we're kind of out of time here um + + align:start position:0% +so we're kind of out of time here um + + + align:start position:0% +so we're kind of out of time here um +is a reducible to a complement let me + + align:start position:0% +is a reducible to a complement let me + + + align:start position:0% +is a reducible to a complement let me +just end with that no not necessarily um + + align:start position:0% +just end with that no not necessarily um + + + align:start position:0% +just end with that no not necessarily um +it's reduceable take okay that's we'll + + align:start position:0% +it's reduceable take okay that's we'll + + + align:start position:0% +it's reduceable take okay that's we'll +get there it's reducible a is reducible + + align:start position:0% +get there it's reducible a is reducible + + + align:start position:0% +get there it's reducible a is reducible +to a complement um + + align:start position:0% +to a complement um + + + align:start position:0% +to a complement um +but not mapping reducible to a + + align:start position:0% +but not mapping reducible to a + + + align:start position:0% +but not mapping reducible to a +complement but a in is general reducible + + align:start position:0% +complement but a in is general reducible + + + align:start position:0% +complement but a in is general reducible +to a complement so we'll actually we'll + + align:start position:0% +to a complement so we'll actually we'll + + + align:start position:0% +to a complement so we'll actually we'll +talk i have a slide on that + + align:start position:0% +talk i have a slide on that + + + align:start position:0% +talk i have a slide on that +uh so let us + + align:start position:0% +uh so let us + + + align:start position:0% +uh so let us +move on + + align:start position:0% +move on + + + align:start position:0% +move on +okay mapping i think it's actually this + + align:start position:0% +okay mapping i think it's actually this + + + align:start position:0% +okay mapping i think it's actually this +slide mapping versus general + + align:start position:0% +slide mapping versus general + + + align:start position:0% +slide mapping versus general +reducibility + + align:start position:0% +reducibility + + + align:start position:0% +reducibility +so we're going to kind of contrast it to + + align:start position:0% +so we're going to kind of contrast it to + + + align:start position:0% +so we're going to kind of contrast it to +a bit + + align:start position:0% +a bit + + + align:start position:0% +a bit +so mapping reducibility which is what + + align:start position:0% +so mapping reducibility which is what + + + align:start position:0% +so mapping reducibility which is what +we've just been talking about has this + + align:start position:0% +we've just been talking about has this + + + align:start position:0% +we've just been talking about has this +picture which is i think a very useful + + align:start position:0% +picture which is i think a very useful + + + align:start position:0% +picture which is i think a very useful +picture to remember um + + align:start position:0% +picture to remember um + + + align:start position:0% +picture to remember um +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +because + + align:start position:0% + + + + align:start position:0% + +the way i like to think of a mapping + + align:start position:0% +the way i like to think of a mapping + + + align:start position:0% +the way i like to think of a mapping +reduction as a problem translator + + align:start position:0% +reduction as a problem translator + + + align:start position:0% +reduction as a problem translator +your problem sort of in the a domain + + align:start position:0% +your problem sort of in the a domain + + + align:start position:0% +your problem sort of in the a domain +and the mapping reduction allows you to + + align:start position:0% +and the mapping reduction allows you to + + + align:start position:0% +and the mapping reduction allows you to +translate that problem into the b domain + + align:start position:0% +translate that problem into the b domain + + + align:start position:0% +translate that problem into the b domain +okay and then if you have a way of + + align:start position:0% +okay and then if you have a way of + + + align:start position:0% +okay and then if you have a way of +solving it in the b domain + + align:start position:0% +solving it in the b domain + + + align:start position:0% +solving it in the b domain +combining that with the reduction you + + align:start position:0% +combining that with the reduction you + + + align:start position:0% +combining that with the reduction you +get a solution to the problem in the a + + align:start position:0% +get a solution to the problem in the a + + + align:start position:0% +get a solution to the problem in the a +domain + + align:start position:0% +domain + + + align:start position:0% +domain +so that's why if a is mapping reducible + + align:start position:0% +so that's why if a is mapping reducible + + + align:start position:0% +so that's why if a is mapping reducible +to b + + align:start position:0% +to b + + + align:start position:0% +to b +and b is solvable + + align:start position:0% +and b is solvable + + + align:start position:0% +and b is solvable +then a is also solvable + + align:start position:0% +then a is also solvable + + + align:start position:0% +then a is also solvable +um + + align:start position:0% +um + + + align:start position:0% +um +so mapping + + align:start position:0% +so mapping + + + align:start position:0% +so mapping +reduction is a special kind of + + align:start position:0% +reduction is a special kind of + + + align:start position:0% +reduction is a special kind of +reducibility as opposed to the general + + align:start position:0% +reducibility as opposed to the general + + + align:start position:0% +reducibility as opposed to the general +notion general reducibility that where + + align:start position:0% +notion general reducibility that where + + + align:start position:0% +notion general reducibility that where +we started + + align:start position:0% +we started + + + align:start position:0% +we started +and it's particularly useful to prove + + align:start position:0% +and it's particularly useful to prove + + + align:start position:0% +and it's particularly useful to prove +touring unrecognizability so when you + + align:start position:0% +touring unrecognizability so when you + + + align:start position:0% +touring unrecognizability so when you +want to prove touring recognizable + + align:start position:0% +want to prove touring recognizable + + + align:start position:0% +want to prove touring recognizable +unrecognizability + + align:start position:0% + + + + align:start position:0% + +as we'll see the general red + + align:start position:0% +as we'll see the general red + + + align:start position:0% +as we'll see the general red +reducibility is not per it's not fine + + align:start position:0% +reducibility is not per it's not fine + + + align:start position:0% +reducibility is not per it's not fine +enough in a way it doesn't sort of um + + align:start position:0% +enough in a way it doesn't sort of um + + + align:start position:0% +enough in a way it doesn't sort of um +differentiate things as well as mapping + + align:start position:0% +differentiate things as well as mapping + + + align:start position:0% +differentiate things as well as mapping +reducibility does + + align:start position:0% +reducibility does + + + align:start position:0% +reducibility does +and and and for that reason it's not + + align:start position:0% +and and and for that reason it's not + + + align:start position:0% +and and and for that reason it's not +always going to be useful to prove + + align:start position:0% +always going to be useful to prove + + + align:start position:0% +always going to be useful to prove +touring unrecognizability it's better + + align:start position:0% +touring unrecognizability it's better + + + align:start position:0% +touring unrecognizability it's better +for proving undecidability + + align:start position:0% + + + + align:start position:0% + +so what we're calling reducibility or + + align:start position:0% +so what we're calling reducibility or + + + align:start position:0% +so what we're calling reducibility or +general reducibility + + align:start position:0% +general reducibility + + + align:start position:0% +general reducibility +is where we just use a a solver for b to + + align:start position:0% +is where we just use a a solver for b to + + + align:start position:0% +is where we just use a a solver for b to +solve a in sort of a more most general + + align:start position:0% +solve a in sort of a more most general + + + align:start position:0% +solve a in sort of a more most general +possible way + + align:start position:0% +possible way + + + align:start position:0% +possible way +so i'm writing that as the picture here + + align:start position:0% +so i'm writing that as the picture here + + + align:start position:0% +so i'm writing that as the picture here +you you want to solve a + + align:start position:0% +you you want to solve a + + + align:start position:0% +you you want to solve a +you're going to use the b solver as a + + align:start position:0% +you're going to use the b solver as a + + + align:start position:0% +you're going to use the b solver as a +subroutine + + align:start position:0% +subroutine + + + align:start position:0% +subroutine +to solve a + + align:start position:0% +to solve a + + + align:start position:0% +to solve a +that's the way we did the whole tm a + + align:start position:0% +that's the way we did the whole tm a + + + align:start position:0% +that's the way we did the whole tm a +reduction at the beginning + + align:start position:0% +reduction at the beginning + + + align:start position:0% +reduction at the beginning +um + + align:start position:0% +um + + + align:start position:0% +um +but we didn't necessarily translate an + + align:start position:0% +but we didn't necessarily translate an + + + align:start position:0% +but we didn't necessarily translate an +atm problem to a whole tm problem + + align:start position:0% +atm problem to a whole tm problem + + + align:start position:0% +atm problem to a whole tm problem +a little slightly different uh so you + + align:start position:0% +a little slightly different uh so you + + + align:start position:0% +a little slightly different uh so you +can go back and look at that + + align:start position:0% +can go back and look at that + + + align:start position:0% +can go back and look at that +um so i find that people struggle more + + align:start position:0% +um so i find that people struggle more + + + align:start position:0% +um so i find that people struggle more +with the mapping reducibility concept + + align:start position:0% +with the mapping reducibility concept + + + align:start position:0% +with the mapping reducibility concept +and that the general reducibility is + + align:start position:0% +and that the general reducibility is + + + align:start position:0% +and that the general reducibility is +what people naturally gravitate towards + + align:start position:0% +what people naturally gravitate towards + + + align:start position:0% +what people naturally gravitate towards +and so in some sense it's conceptually + + align:start position:0% +and so in some sense it's conceptually + + + align:start position:0% +and so in some sense it's conceptually +simpler + + align:start position:0% +simpler + + + align:start position:0% +simpler +and it's useful to proving + + align:start position:0% +and it's useful to proving + + + align:start position:0% +and it's useful to proving +undecidability so but you really have to + + align:start position:0% +undecidability so but you really have to + + + align:start position:0% +undecidability so but you really have to +be comfortable with both and especially + + align:start position:0% +be comfortable with both and especially + + + align:start position:0% +be comfortable with both and especially +in the complexities + + align:start position:0% +in the complexities + + + align:start position:0% +in the complexities +part we're going to be focusing on + + align:start position:0% +part we're going to be focusing on + + + align:start position:0% +part we're going to be focusing on +mapping + + align:start position:0% +mapping + + + align:start position:0% +mapping +reducibility so one noteworthy + + align:start position:0% +reducibility so one noteworthy + + + align:start position:0% +reducibility so one noteworthy +difference here as uh sort of + + align:start position:0% +difference here as uh sort of + + + align:start position:0% +difference here as uh sort of +foreshadowed by uh the + + align:start position:0% +foreshadowed by uh the + + + align:start position:0% +foreshadowed by uh the +person who made this question which is a + + align:start position:0% +person who made this question which is a + + + align:start position:0% +person who made this question which is a +good question + + align:start position:0% +good question + + + align:start position:0% +good question +is that a is all is reducible using a + + align:start position:0% +is that a is all is reducible using a + + + align:start position:0% +is that a is all is reducible using a +general reduction to a complement which + + align:start position:0% +general reduction to a complement which + + + align:start position:0% +general reduction to a complement which +kind of makes sense + + align:start position:0% +kind of makes sense + + + align:start position:0% +kind of makes sense +i mean if i can solve a cop you know if + + align:start position:0% +i mean if i can solve a cop you know if + + + align:start position:0% +i mean if i can solve a cop you know if +i can test whether things are an a + + align:start position:0% +i can test whether things are an a + + + align:start position:0% +i can test whether things are an a +complement well i can test whether + + align:start position:0% +complement well i can test whether + + + align:start position:0% +complement well i can test whether +things are in a you just invert the + + align:start position:0% +things are in a you just invert the + + + align:start position:0% +things are in a you just invert the +answer + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +a may not be mapping reducible to a + + align:start position:0% +a may not be mapping reducible to a + + + align:start position:0% +a may not be mapping reducible to a +complement because there it's a very + + align:start position:0% +complement because there it's a very + + + align:start position:0% +complement because there it's a very +special kind of reduction + + align:start position:0% +special kind of reduction + + + align:start position:0% +special kind of reduction +and you just can't necess you can't you + + align:start position:0% +and you just can't necess you can't you + + + align:start position:0% +and you just can't necess you can't you +have to just translate things in the + + align:start position:0% +have to just translate things in the + + + align:start position:0% +have to just translate things in the +language to things in the language and + + align:start position:0% +language to things in the language and + + + align:start position:0% +language to things in the language and +things out of the language of things out + + align:start position:0% +things out of the language of things out + + + align:start position:0% +things out of the language of things out +of the language and they don't + + align:start position:0% +of the language and they don't + + + align:start position:0% +of the language and they don't +necessarily allow you to do that + + align:start position:0% +necessarily allow you to do that + + + align:start position:0% +necessarily allow you to do that +inversion + + align:start position:0% +inversion + + + align:start position:0% +inversion +so for example atm + + align:start position:0% +so for example atm + + + align:start position:0% +so for example atm +complement + + align:start position:0% +complement + + + align:start position:0% +complement +is not mapping reducible to atm + + align:start position:0% +is not mapping reducible to atm + + + align:start position:0% +is not mapping reducible to atm +because as we pointed out + + align:start position:0% +because as we pointed out + + + align:start position:0% +because as we pointed out +anything that's reducible to a + + align:start position:0% +anything that's reducible to a + + + align:start position:0% +anything that's reducible to a +recognizable + + align:start position:0% +recognizable + + + align:start position:0% +recognizable +language is going to be recognizable + + align:start position:0% +language is going to be recognizable + + + align:start position:0% +language is going to be recognizable +anything mapping reducible to a + + align:start position:0% +anything mapping reducible to a + + + align:start position:0% +anything mapping reducible to a +recognizable languages map is going to + + align:start position:0% +recognizable languages map is going to + + + align:start position:0% +recognizable languages map is going to +be recognizable + + align:start position:0% +be recognizable + + + align:start position:0% +be recognizable +but we know that atm complement is not + + align:start position:0% +but we know that atm complement is not + + + align:start position:0% +but we know that atm complement is not +recognizable we showed that before + + align:start position:0% +recognizable we showed that before + + + align:start position:0% +recognizable we showed that before +so it couldn't be mapping reducible to + + align:start position:0% +so it couldn't be mapping reducible to + + + align:start position:0% +so it couldn't be mapping reducible to +atm + + align:start position:0% + + + + align:start position:0% + +you know coming a little fast i realize + + align:start position:0% +you know coming a little fast i realize + + + align:start position:0% +you know coming a little fast i realize +you're gonna have to uh + + align:start position:0% +you're gonna have to uh + + + align:start position:0% +you're gonna have to uh +digest it so here's the last check-in + + align:start position:0% +digest it so here's the last check-in + + + align:start position:0% +digest it so here's the last check-in +for today + + align:start position:0% +for today + + + align:start position:0% +for today +um + + align:start position:0% + + + + align:start position:0% + +okay we showed that if a is mapping + + align:start position:0% +okay we showed that if a is mapping + + + align:start position:0% +okay we showed that if a is mapping +reducible to b and b is turing + + align:start position:0% +reducible to b and b is turing + + + align:start position:0% +reducible to b and b is turing +recognizable then so is a + + align:start position:0% +recognizable then so is a + + + align:start position:0% +recognizable then so is a +and so let's just say that again + + align:start position:0% +and so let's just say that again + + + align:start position:0% +and so let's just say that again +carefully if a is mapping reducible to b + + align:start position:0% +carefully if a is mapping reducible to b + + + align:start position:0% +carefully if a is mapping reducible to b +and b is turing recognizable + + align:start position:0% +and b is turing recognizable + + + align:start position:0% +and b is turing recognizable +then so is a and here the difference is + + align:start position:0% +then so is a and here the difference is + + + align:start position:0% +then so is a and here the difference is +on recognize the emphasis on turing + + align:start position:0% +on recognize the emphasis on turing + + + align:start position:0% +on recognize the emphasis on turing +recognizable as opposed to decidable + + align:start position:0% + + + + align:start position:0% + +is the same true if we use general + + align:start position:0% +is the same true if we use general + + + align:start position:0% +is the same true if we use general +reducibility instead of mapping + + align:start position:0% +reducibility instead of mapping + + + align:start position:0% +reducibility instead of mapping +reducibility + + align:start position:0% + + + + align:start position:0% + +so you got it so we're saying a is + + align:start position:0% +so you got it so we're saying a is + + + align:start position:0% +so you got it so we're saying a is +mapping reducible to b using this + + align:start position:0% +mapping reducible to b using this + + + align:start position:0% +mapping reducible to b using this +picture over here + + align:start position:0% +picture over here + + + align:start position:0% +picture over here +and we're going to assume that b + + align:start position:0% +and we're going to assume that b + + + align:start position:0% +and we're going to assume that b +is touring recognizable + + align:start position:0% + + + + align:start position:0% + +okay so that we have a + + align:start position:0% +okay so that we have a + + + align:start position:0% +okay so that we have a +machine which + + align:start position:0% +machine which + + + align:start position:0% +machine which +holds an except + + align:start position:0% +holds an except + + + align:start position:0% +holds an except +when you're inside b + + align:start position:0% +when you're inside b + + + align:start position:0% +when you're inside b +and you know is going to reject possibly + + align:start position:0% +and you know is going to reject possibly + + + align:start position:0% +and you know is going to reject possibly +by looping when you're not inside b + + align:start position:0% +by looping when you're not inside b + + + align:start position:0% +by looping when you're not inside b +now that allows you to get + + align:start position:0% +now that allows you to get + + + align:start position:0% +now that allows you to get +a recognizer + + align:start position:0% +a recognizer + + + align:start position:0% +a recognizer +for a + + align:start position:0% +for a + + + align:start position:0% +for a +if you have a mapping reduction + + align:start position:0% +if you have a mapping reduction + + + align:start position:0% +if you have a mapping reduction +does it always work to give you a + + align:start position:0% +does it always work to give you a + + + align:start position:0% +does it always work to give you a +recognizer if you have just a general + + align:start position:0% +recognizer if you have just a general + + + align:start position:0% +recognizer if you have just a general +reduction + + align:start position:0% +reduction + + + align:start position:0% +reduction +if you just have a if you just now + + align:start position:0% +if you just have a if you just now + + + align:start position:0% +if you just have a if you just now +assume you have a b solver + + align:start position:0% +assume you have a b solver + + + align:start position:0% +assume you have a b solver +and you're going to build an a solver + + align:start position:0% +and you're going to build an a solver + + + align:start position:0% +and you're going to build an a solver +out of that + + align:start position:0% +out of that + + + align:start position:0% +out of that +um + + align:start position:0% +um + + + align:start position:0% +um +okay so mull that over while i'm setting + + align:start position:0% +okay so mull that over while i'm setting + + + align:start position:0% +okay so mull that over while i'm setting +this thing up + + align:start position:0% + + + + align:start position:0% + +well the right answer is winning but not + + align:start position:0% +well the right answer is winning but not + + + align:start position:0% +well the right answer is winning but not +by much + + align:start position:0% + + + + align:start position:0% + +i suppose i shouldn't be + + align:start position:0% +i suppose i shouldn't be + + + align:start position:0% +i suppose i shouldn't be +uh + + align:start position:0% +uh + + + align:start position:0% +uh +laughing about it uh but + + align:start position:0% +laughing about it uh but + + + align:start position:0% +laughing about it uh but +i i knew that this is going to be + + align:start position:0% +i i knew that this is going to be + + + align:start position:0% +i i knew that this is going to be +challenging so i think it's the kind of + + align:start position:0% +challenging so i think it's the kind of + + + align:start position:0% +challenging so i think it's the kind of +thing you're going to have to + + align:start position:0% +thing you're going to have to + + + align:start position:0% +thing you're going to have to +uh work at + + align:start position:0% +uh work at + + + align:start position:0% +uh work at +um so let's see we're almost done here + + align:start position:0% +um so let's see we're almost done here + + + align:start position:0% +um so let's see we're almost done here +um + + align:start position:0% +um + + + align:start position:0% +um +five seconds to go + + align:start position:0% +five seconds to go + + + align:start position:0% +five seconds to go +better answered i i could see a few of + + align:start position:0% +better answered i i could see a few of + + + align:start position:0% +better answered i i could see a few of +you either you've left the + + align:start position:0% +you either you've left the + + + align:start position:0% +you either you've left the +room + + align:start position:0% +room + + + align:start position:0% +room +or you're uh + + align:start position:0% +or you're uh + + + align:start position:0% +or you're uh +okay two seconds + + align:start position:0% +okay two seconds + + + align:start position:0% +okay two seconds +one two three + + align:start position:0% +one two three + + + align:start position:0% +one two three +somebody hasn't answered it + + align:start position:0% + + + + align:start position:0% + +there we go so this is the correct + + align:start position:0% +there we go so this is the correct + + + align:start position:0% +there we go so this is the correct +answer is b + + align:start position:0% +answer is b + + + align:start position:0% +answer is b +it's not the same + + align:start position:0% +it's not the same + + + align:start position:0% +it's not the same +you're not going the reason is that in a + + align:start position:0% +you're not going the reason is that in a + + + align:start position:0% +you're not going the reason is that in a +general word i mean the picture's right + + align:start position:0% +general word i mean the picture's right + + + align:start position:0% +general word i mean the picture's right +here + + align:start position:0% +here + + + align:start position:0% +here +i mean so you mean you know this is + + align:start position:0% +i mean so you mean you know this is + + + align:start position:0% +i mean so you mean you know this is +um + + align:start position:0% +um + + + align:start position:0% +um +let's see + + align:start position:0% +let's see + + + align:start position:0% +let's see +uh + + align:start position:0% + + + + align:start position:0% + +you know + + align:start position:0% + + + + align:start position:0% + +um how do i explain this so + + align:start position:0% +um how do i explain this so + + + align:start position:0% +um how do i explain this so +uh + + align:start position:0% + + + + align:start position:0% + +we know that + + align:start position:0% +we know that + + + align:start position:0% +we know that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +a language is going to be um + + align:start position:0% +a language is going to be um + + + align:start position:0% +a language is going to be um +okay if we're using general reducibility + + align:start position:0% +okay if we're using general reducibility + + + align:start position:0% +okay if we're using general reducibility +and a is it's just reducible to b + + align:start position:0% +and a is it's just reducible to b + + + align:start position:0% +and a is it's just reducible to b +um + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so + + align:start position:0% +so + + + align:start position:0% +so +we know that + + align:start position:0% +we know that + + + align:start position:0% +we know that +a language is always always reducible to + + align:start position:0% +a language is always always reducible to + + + align:start position:0% +a language is always always reducible to +its complement in the using general + + align:start position:0% +its complement in the using general + + + align:start position:0% +its complement in the using general +reducibility + + align:start position:0% +reducibility + + + align:start position:0% +reducibility +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so if this were true + + align:start position:0% +so if this were true + + + align:start position:0% +so if this were true +um + + align:start position:0% +um + + + align:start position:0% +um +then + + align:start position:0% + + + + align:start position:0% + +then we would have here + + align:start position:0% +then we would have here + + + align:start position:0% +then we would have here +um + + align:start position:0% +um + + + align:start position:0% +um +um + + align:start position:0% +um + + + align:start position:0% +um +so um + + align:start position:0% +so um + + + align:start position:0% +so um +if this were true when + + align:start position:0% +if this were true when + + + align:start position:0% +if this were true when +um a + + align:start position:0% +um a + + + align:start position:0% +um a +uh when a language is reducible to its + + align:start position:0% +uh when a language is reducible to its + + + align:start position:0% +uh when a language is reducible to its +complement if the complement were + + align:start position:0% +complement if the complement were + + + align:start position:0% +complement if the complement were +recognizable the language would also be + + align:start position:0% +recognizable the language would also be + + + align:start position:0% +recognizable the language would also be +recognizable + + align:start position:0% +recognizable + + + align:start position:0% +recognizable +that clearly isn't is not going to be + + align:start position:0% +that clearly isn't is not going to be + + + align:start position:0% +that clearly isn't is not going to be +the case because + + align:start position:0% +the case because + + + align:start position:0% +the case because +you know atm is reducible to the you + + align:start position:0% +you know atm is reducible to the you + + + align:start position:0% +you know atm is reducible to the you +know atm complement is reducible to atm + + align:start position:0% +know atm complement is reducible to atm + + + align:start position:0% +know atm complement is reducible to atm +using general reducibility + + align:start position:0% +using general reducibility + + + align:start position:0% +using general reducibility +uh but um + + align:start position:0% +uh but um + + + align:start position:0% +uh but um +atm complement is not recognizable even + + align:start position:0% +atm complement is not recognizable even + + + align:start position:0% +atm complement is not recognizable even +though atm is recognizable so we kind of + + align:start position:0% +though atm is recognizable so we kind of + + + align:start position:0% +though atm is recognizable so we kind of +have a proof that this has to be no + + align:start position:0% +have a proof that this has to be no + + + align:start position:0% +have a proof that this has to be no +but as you can see i'm even getting + + align:start position:0% +but as you can see i'm even getting + + + align:start position:0% +but as you can see i'm even getting +myself confused so um + + align:start position:0% +myself confused so um + + + align:start position:0% +myself confused so um +you have to you have to stare at it um + + align:start position:0% +you have to you have to stare at it um + + + align:start position:0% +you have to you have to stare at it um +so let's let me see we can try to take a + + align:start position:0% +so let's let me see we can try to take a + + + align:start position:0% +so let's let me see we can try to take a +couple of questions see if i can clear + + align:start position:0% +couple of questions see if i can clear + + + align:start position:0% +couple of questions see if i can clear +up people's confusion + + align:start position:0% +up people's confusion + + + align:start position:0% +up people's confusion +why again okay so why again is a + + align:start position:0% +why again okay so why again is a + + + align:start position:0% +why again okay so why again is a +reducible to its complement in the + + align:start position:0% +reducible to its complement in the + + + align:start position:0% +reducible to its complement in the +general sense + + align:start position:0% +general sense + + + align:start position:0% +general sense +so i'm saying + + align:start position:0% +so i'm saying + + + align:start position:0% +so i'm saying +if you have a solver if you have a + + align:start position:0% +if you have a solver if you have a + + + align:start position:0% +if you have a solver if you have a +decider for for for a complement it + + align:start position:0% +decider for for for a complement it + + + align:start position:0% +decider for for for a complement it +gives you a solver for a + + align:start position:0% +gives you a solver for a + + + align:start position:0% +gives you a solver for a +you just ask the solver + + align:start position:0% +you just ask the solver + + + align:start position:0% +you just ask the solver +you know is the string in the language + + align:start position:0% +you know is the string in the language + + + align:start position:0% +you know is the string in the language +or not + + align:start position:0% +or not + + + align:start position:0% +or not +and now um + + align:start position:0% +and now um + + + align:start position:0% +and now um +you just give the opposite answer if you + + align:start position:0% +you just give the opposite answer if you + + + align:start position:0% +you just give the opposite answer if you +want to + + align:start position:0% +want to + + + align:start position:0% +want to +solve the the complementary problem so + + align:start position:0% +solve the the complementary problem so + + + align:start position:0% +solve the the complementary problem so +the a complement is reduced + + align:start position:0% +the a complement is reduced + + + align:start position:0% +the a complement is reduced +reducible to a + + align:start position:0% +reducible to a + + + align:start position:0% +reducible to a +you just invert the answer for whatever + + align:start position:0% +you just invert the answer for whatever + + + align:start position:0% +you just invert the answer for whatever +the solver is doing for a but you can't + + align:start position:0% +the solver is doing for a but you can't + + + align:start position:0% +the solver is doing for a but you can't +just do that inversion when you have a + + align:start position:0% +just do that inversion when you have a + + + align:start position:0% +just do that inversion when you have a +mapping reduction + + align:start position:0% +mapping reduction + + + align:start position:0% +mapping reduction +it's a much more + + align:start position:0% +it's a much more + + + align:start position:0% +it's a much more +um + + align:start position:0% +um + + + align:start position:0% +um +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +specific + + align:start position:0% +specific + + + align:start position:0% +specific +translation that's allowed + + align:start position:0% +translation that's allowed + + + align:start position:0% +translation that's allowed +um + + align:start position:0% +um + + + align:start position:0% +um +so i mean the fundamental difference + + align:start position:0% +so i mean the fundamental difference + + + align:start position:0% +so i mean the fundamental difference +between german disability mapping + + align:start position:0% +between german disability mapping + + + align:start position:0% +between german disability mapping +disability i'm trying to bring it out + + align:start position:0% +disability i'm trying to bring it out + + + align:start position:0% +disability i'm trying to bring it out +here it's just + + align:start position:0% +here it's just + + + align:start position:0% +here it's just +it's just a difference in the nature of + + align:start position:0% +it's just a difference in the nature of + + + align:start position:0% +it's just a difference in the nature of +the way things are used mapping + + align:start position:0% +the way things are used mapping + + + align:start position:0% +the way things are used mapping +reducibility is a special kind of + + align:start position:0% +reducibility is a special kind of + + + align:start position:0% +reducibility is a special kind of +general reducibility so you know to + + align:start position:0% +general reducibility so you know to + + + align:start position:0% +general reducibility so you know to +answer the question about what's the + + align:start position:0% +answer the question about what's the + + + align:start position:0% +answer the question about what's the +fundamental difference + + align:start position:0% +fundamental difference + + + align:start position:0% +fundamental difference +you know one is using the + + align:start position:0% +you know one is using the + + + align:start position:0% +you know one is using the +the problem as a subroutine and the one + + align:start position:0% +the problem as a subroutine and the one + + + align:start position:0% +the problem as a subroutine and the one +is using it as a um + + align:start position:0% +is using it as a um + + + align:start position:0% +is using it as a um +as a + + align:start position:0% +as a + + + align:start position:0% +as a +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +um + + align:start position:0% + + + + align:start position:0% + +anyway i think we're going to have to uh + + align:start position:0% +anyway i think we're going to have to uh + + + align:start position:0% +anyway i think we're going to have to uh +move on here and i'm going to have a + + align:start position:0% +move on here and i'm going to have a + + + align:start position:0% +move on here and i'm going to have a +couple of examples which may help + + align:start position:0% +couple of examples which may help + + + align:start position:0% +couple of examples which may help +and then uh + + align:start position:0% +and then uh + + + align:start position:0% +and then uh +uh there are also there's office hours + + align:start position:0% +uh there are also there's office hours + + + align:start position:0% +uh there are also there's office hours +too after after the after the lecture + + align:start position:0% +too after after the after the lecture + + + align:start position:0% +too after after the after the lecture +um + + align:start position:0% +um + + + align:start position:0% +um +okay oh yeah so i wanted to again to + + align:start position:0% +okay oh yeah so i wanted to again to + + + align:start position:0% +okay oh yeah so i wanted to again to +help you + + align:start position:0% +help you + + + align:start position:0% +help you +you know i'm putting these down as sort + + align:start position:0% +you know i'm putting these down as sort + + + align:start position:0% +you know i'm putting these down as sort +of templates for how do you use + + align:start position:0% +of templates for how do you use + + + align:start position:0% +of templates for how do you use +reduceability um + + align:start position:0% +reduceability um + + + align:start position:0% +reduceability um +i'm not saying you should just + + align:start position:0% +i'm not saying you should just + + + align:start position:0% +i'm not saying you should just +uh + + align:start position:0% +uh + + + align:start position:0% +uh +apply things blindly but i think it's + + align:start position:0% +apply things blindly but i think it's + + + align:start position:0% +apply things blindly but i think it's +sometimes good just to see the pattern + + align:start position:0% +sometimes good just to see the pattern + + + align:start position:0% +sometimes good just to see the pattern +and then to understand how the pattern + + align:start position:0% +and then to understand how the pattern + + + align:start position:0% +and then to understand how the pattern +works once you see that once you just + + align:start position:0% +works once you see that once you just + + + align:start position:0% +works once you see that once you just +start to understand the pattern of how + + align:start position:0% +start to understand the pattern of how + + + align:start position:0% +start to understand the pattern of how +things are used + + align:start position:0% +things are used + + + align:start position:0% +things are used +so to show um a language is undecidable + + align:start position:0% +so to show um a language is undecidable + + + align:start position:0% +so to show um a language is undecidable +just + + align:start position:0% +just + + + align:start position:0% +just +to prove a language b is undecidable + + align:start position:0% +to prove a language b is undecidable + + + align:start position:0% +to prove a language b is undecidable +show undecidable language is reducible + + align:start position:0% +show undecidable language is reducible + + + align:start position:0% +show undecidable language is reducible +to be + + align:start position:0% +to be + + + align:start position:0% +to be +using just a general reduction is going + + align:start position:0% +using just a general reduction is going + + + align:start position:0% +using just a general reduction is going +to be good enough + + align:start position:0% +to be good enough + + + align:start position:0% +to be good enough +um + + align:start position:0% +um + + + align:start position:0% +um +and and the template for that is assume + + align:start position:0% +and and the template for that is assume + + + align:start position:0% +and and the template for that is assume +we have r deciding b + + align:start position:0% +we have r deciding b + + + align:start position:0% +we have r deciding b +which you then can use as a subroutine + + align:start position:0% +which you then can use as a subroutine + + + align:start position:0% +which you then can use as a subroutine +when you make a machine uh turing + + align:start position:0% +when you make a machine uh turing + + + align:start position:0% +when you make a machine uh turing +machine or + + align:start position:0% +machine or + + + align:start position:0% +machine or +s deciding a + + align:start position:0% +s deciding a + + + align:start position:0% +s deciding a +and that's going to be your + + align:start position:0% +and that's going to be your + + + align:start position:0% +and that's going to be your +contradiction if a was + + align:start position:0% +contradiction if a was + + + align:start position:0% +contradiction if a was +originally shown to be known to be + + align:start position:0% +originally shown to be known to be + + + align:start position:0% +originally shown to be known to be +undecidable + + align:start position:0% +undecidable + + + align:start position:0% +undecidable +um + + align:start position:0% +um + + + align:start position:0% +um +but now to prove something + + align:start position:0% +but now to prove something + + + align:start position:0% +but now to prove something +unrecognizable + + align:start position:0% +unrecognizable + + + align:start position:0% +unrecognizable +this kind of reduction is not going to + + align:start position:0% +this kind of reduction is not going to + + + align:start position:0% +this kind of reduction is not going to +be is not in a sense um + + align:start position:0% +be is not in a sense um + + + align:start position:0% +be is not in a sense um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it's it's not + + align:start position:0% +it's it's not + + + align:start position:0% +it's it's not +uh as enough + + align:start position:0% +uh as enough + + + align:start position:0% +uh as enough +um because this kind of reduction allows + + align:start position:0% +um because this kind of reduction allows + + + align:start position:0% +um because this kind of reduction allows +for complementation + + align:start position:0% +for complementation + + + align:start position:0% +for complementation +which is not going to be + + align:start position:0% +which is not going to be + + + align:start position:0% +which is not going to be +uh satisfactory when you're trying to + + align:start position:0% +uh satisfactory when you're trying to + + + align:start position:0% +uh satisfactory when you're trying to +prove touring unrecognizable so you're + + align:start position:0% +prove touring unrecognizable so you're + + + align:start position:0% +prove touring unrecognizable so you're +gonna have to prohibit + + align:start position:0% +gonna have to prohibit + + + align:start position:0% +gonna have to prohibit +that complementation and that's really + + align:start position:0% +that complementation and that's really + + + align:start position:0% +that complementation and that's really +one of the effects of the mapping + + align:start position:0% +one of the effects of the mapping + + + align:start position:0% +one of the effects of the mapping +reducibility if that's sort of getting + + align:start position:0% +reducibility if that's sort of getting + + + align:start position:0% +reducibility if that's sort of getting +at the essence of it + + align:start position:0% +at the essence of it + + + align:start position:0% +at the essence of it +um + + align:start position:0% +um + + + align:start position:0% +um +so we're going to show an on turing + + align:start position:0% +so we're going to show an on turing + + + align:start position:0% +so we're going to show an on turing +unrecognizable a is mapping reducible to + + align:start position:0% +unrecognizable a is mapping reducible to + + + align:start position:0% +unrecognizable a is mapping reducible to +b + + align:start position:0% +b + + + align:start position:0% +b +often you start off with the complement + + align:start position:0% +often you start off with the complement + + + align:start position:0% +often you start off with the complement +of atm which is a language we know is + + align:start position:0% +of atm which is a language we know is + + + align:start position:0% +of atm which is a language we know is +touring uh + + align:start position:0% +touring uh + + + align:start position:0% +touring uh +unrecognizable as we showed before + + align:start position:0% +unrecognizable as we showed before + + + align:start position:0% +unrecognizable as we showed before +um + + align:start position:0% + + + + align:start position:0% + +okay here the template is you give the + + align:start position:0% +okay here the template is you give the + + + align:start position:0% +okay here the template is you give the +reduction function f + + align:start position:0% +reduction function f + + + align:start position:0% +reduction function f +that computable function + + align:start position:0% +that computable function + + + align:start position:0% +that computable function +um + + align:start position:0% +um + + + align:start position:0% +um +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um + + align:start position:0% +um + + + align:start position:0% +um +so here are going to be two examples one + + align:start position:0% +so here are going to be two examples one + + + align:start position:0% +so here are going to be two examples one +showing that etm is touring + + align:start position:0% +showing that etm is touring + + + align:start position:0% +showing that etm is touring +unrecognizable we showed it was + + align:start position:0% +unrecognizable we showed it was + + + align:start position:0% +unrecognizable we showed it was +undecidable before + + align:start position:0% +undecidable before + + + align:start position:0% +undecidable before +now we're going to show it's + + align:start position:0% +now we're going to show it's + + + align:start position:0% +now we're going to show it's +even + + align:start position:0% +even + + + align:start position:0% +even +in a sense worse it's not even + + align:start position:0% +in a sense worse it's not even + + + align:start position:0% +in a sense worse it's not even +recognizable + + align:start position:0% + + + + align:start position:0% + +and the way we'll do that is to reduce a + + align:start position:0% + + + + align:start position:0% + +a known + + align:start position:0% +a known + + + align:start position:0% +a known +unrecognizable language to etm + + align:start position:0% +unrecognizable language to etm + + + align:start position:0% +unrecognizable language to etm +in the emptiness + + align:start position:0% +in the emptiness + + + align:start position:0% +in the emptiness +language + + align:start position:0% +language + + + align:start position:0% +language +um + + align:start position:0% +um + + + align:start position:0% +um +so here is the picture + + align:start position:0% +so here is the picture + + + align:start position:0% +so here is the picture +that we have when we're doing mapping + + align:start position:0% +that we have when we're doing mapping + + + align:start position:0% +that we have when we're doing mapping +reductions + + align:start position:0% +reductions + + + align:start position:0% +reductions +we're going to map strings that are in + + align:start position:0% + + + + align:start position:0% + +the complement of atm so strings that + + align:start position:0% +the complement of atm so strings that + + + align:start position:0% +the complement of atm so strings that +are outside of atm if you wish to + + align:start position:0% +are outside of atm if you wish to + + + align:start position:0% +are outside of atm if you wish to +strings where + + align:start position:0% +strings where + + + align:start position:0% +strings where +the language is empty + + align:start position:0% +the language is empty + + + align:start position:0% +the language is empty +to machines with the language is empty + + align:start position:0% +to machines with the language is empty + + + align:start position:0% +to machines with the language is empty +and here + + align:start position:0% +and here + + + align:start position:0% +and here +um + + align:start position:0% +um + + + align:start position:0% +um +strings describing machines which + + align:start position:0% +strings describing machines which + + + align:start position:0% +strings describing machines which +language is empty and here we're going + + align:start position:0% +language is empty and here we're going + + + align:start position:0% +language is empty and here we're going +to take um + + align:start position:0% +to take um + + + align:start position:0% +to take um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +atm problems + + align:start position:0% +atm problems + + + align:start position:0% +atm problems +so and map them to + + align:start position:0% +so and map them to + + + align:start position:0% +so and map them to +machines where the language + + align:start position:0% +machines where the language + + + align:start position:0% +machines where the language +is not empty + + align:start position:0% +is not empty + + + align:start position:0% +is not empty +and the thing that's going to do the + + align:start position:0% +and the thing that's going to do the + + + align:start position:0% +and the thing that's going to do the +trick is going to be that same + + align:start position:0% +trick is going to be that same + + + align:start position:0% +trick is going to be that same +reduction function that we saw earlier + + align:start position:0% +reduction function that we saw earlier + + + align:start position:0% +reduction function that we saw earlier +um + + align:start position:0% +um + + + align:start position:0% +um +you know we're going to take that + + align:start position:0% +you know we're going to take that + + + align:start position:0% +you know we're going to take that +machine w from before the machine that + + align:start position:0% +machine w from before the machine that + + + align:start position:0% +machine w from before the machine that +filters out all the non w + + align:start position:0% +filters out all the non w + + + align:start position:0% +filters out all the non w +all the non w's + + align:start position:0% +all the non w's + + + align:start position:0% +all the non w's +and we're going to take mw + + align:start position:0% +and we're going to take mw + + + align:start position:0% +and we're going to take mw +which is + + align:start position:0% +which is + + + align:start position:0% +which is +a + + align:start position:0% +a + + + align:start position:0% +a +you know um + + align:start position:0% +you know um + + + align:start position:0% +you know um +an atm complement problem + + align:start position:0% +an atm complement problem + + + align:start position:0% +an atm complement problem +so the so + + align:start position:0% +so the so + + + align:start position:0% +so the so +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so if m + + align:start position:0% +so if m + + + align:start position:0% +so if m +rejects w then it's in the complement of + + align:start position:0% +rejects w then it's in the complement of + + + align:start position:0% +rejects w then it's in the complement of +atm + + align:start position:0% +atm + + + align:start position:0% +atm +and that's supposed to + + align:start position:0% +and that's supposed to + + + align:start position:0% +and that's supposed to +map to a string a machine which is + + align:start position:0% + + + + align:start position:0% + +uh where + + align:start position:0% + + + + align:start position:0% + +the the language is empty okay so if mw + + align:start position:0% +the the language is empty okay so if mw + + + align:start position:0% +the the language is empty okay so if mw +is in the complement of atm so m rejects + + align:start position:0% +is in the complement of atm so m rejects + + + align:start position:0% +is in the complement of atm so m rejects +w then mw's language is going to be + + align:start position:0% +w then mw's language is going to be + + + align:start position:0% +w then mw's language is going to be +empty which is what + + align:start position:0% +empty which is what + + + align:start position:0% +empty which is what +you want to have happen + + align:start position:0% +you want to have happen + + + align:start position:0% +you want to have happen +um + + align:start position:0% +um + + + align:start position:0% +um +let me move on to my last i mean this + + align:start position:0% +let me move on to my last i mean this + + + align:start position:0% +let me move on to my last i mean this +example is in a way kind of similar to + + align:start position:0% +example is in a way kind of similar to + + + align:start position:0% +example is in a way kind of similar to +the one we did before and i i really + + align:start position:0% +the one we did before and i i really + + + align:start position:0% +the one we did before and i i really +want to get to my the last example here + + align:start position:0% +want to get to my the last example here + + + align:start position:0% +want to get to my the last example here +um + + align:start position:0% +um + + + align:start position:0% +um +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +uh we'll have to just talk through this + + align:start position:0% +uh we'll have to just talk through this + + + align:start position:0% +uh we'll have to just talk through this +uh rather than having it uh uh build um + + align:start position:0% +uh rather than having it uh uh build um + + + align:start position:0% +uh rather than having it uh uh build um +let's take eqtm + + align:start position:0% +let's take eqtm + + + align:start position:0% +let's take eqtm +that's the equivalence + + align:start position:0% +that's the equivalence + + + align:start position:0% +that's the equivalence +problem for turing machines + + align:start position:0% +problem for turing machines + + + align:start position:0% +problem for turing machines +do they uh + + align:start position:0% +do they uh + + + align:start position:0% +do they uh +um recognize the same language + + align:start position:0% +um recognize the same language + + + align:start position:0% +um recognize the same language +um so + + align:start position:0% +um so + + + align:start position:0% +um so +this is a this is a an + + align:start position:0% +this is a this is a an + + + align:start position:0% +this is a this is a an +a language of a new kind for us this is + + align:start position:0% +a language of a new kind for us this is + + + align:start position:0% +a language of a new kind for us this is +a language where neither it nor its + + align:start position:0% +a language where neither it nor its + + + align:start position:0% +a language where neither it nor its +complement are going to be recognizable + + align:start position:0% +complement are going to be recognizable + + + align:start position:0% +complement are going to be recognizable +to recognizable + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +so the way we get that is + + align:start position:0% +so the way we get that is + + + align:start position:0% +so the way we get that is +um + + align:start position:0% +um + + + align:start position:0% +um +we're going to reduce the complement the + + align:start position:0% +we're going to reduce the complement the + + + align:start position:0% +we're going to reduce the complement the +way we show problems are not + + align:start position:0% +way we show problems are not + + + align:start position:0% +way we show problems are not +recognizable is re + + align:start position:0% +recognizable is re + + + align:start position:0% +recognizable is re +mapping reduce + + align:start position:0% +mapping reduce + + + align:start position:0% +mapping reduce +a non-recognizable language to a + + align:start position:0% +a non-recognizable language to a + + + align:start position:0% +a non-recognizable language to a +typically the complement of atm so we're + + align:start position:0% +typically the complement of atm so we're + + + align:start position:0% +typically the complement of atm so we're +going to mapping reduce the complement + + align:start position:0% +going to mapping reduce the complement + + + align:start position:0% +going to mapping reduce the complement +of atm + + align:start position:0% +of atm + + + align:start position:0% +of atm +to + + align:start position:0% +to + + + align:start position:0% +to +both + + align:start position:0% +both + + + align:start position:0% +both +eqtm and to the complement of eqtm to + + align:start position:0% +eqtm and to the complement of eqtm to + + + align:start position:0% +eqtm and to the complement of eqtm to +show that both of those are not + + align:start position:0% +show that both of those are not + + + align:start position:0% +show that both of those are not +recognizable + + align:start position:0% +recognizable + + + align:start position:0% +recognizable +and here we're going to introduce a new + + align:start position:0% +and here we're going to introduce a new + + + align:start position:0% +and here we're going to introduce a new +uh machine that we're going to be + + align:start position:0% +uh machine that we're going to be + + + align:start position:0% +uh machine that we're going to be +building inside the reduction function + + align:start position:0% + + + + align:start position:0% + +and that's going to be a + + align:start position:0% +and that's going to be a + + + align:start position:0% +and that's going to be a +machine i'm going to call t w + + align:start position:0% +machine i'm going to call t w + + + align:start position:0% +machine i'm going to call t w +and t w is a machine + + align:start position:0% +and t w is a machine + + + align:start position:0% +and t w is a machine +that + + align:start position:0% +that + + + align:start position:0% +that +always behaves the way m behaves on w + + align:start position:0% +always behaves the way m behaves on w + + + align:start position:0% +always behaves the way m behaves on w +for every input + + align:start position:0% +for every input + + + align:start position:0% +for every input +so if m accepts w + + align:start position:0% +so if m accepts w + + + align:start position:0% +so if m accepts w +t is going to accept everything + + align:start position:0% +t is going to accept everything + + + align:start position:0% +t is going to accept everything +if m rejects w t is going to reject + + align:start position:0% +if m rejects w t is going to reject + + + align:start position:0% +if m rejects w t is going to reject +everything + + align:start position:0% +everything + + + align:start position:0% +everything +so it copies the behavior of m on w onto + + align:start position:0% +so it copies the behavior of m on w onto + + + align:start position:0% +so it copies the behavior of m on w onto +all inputs and the way i describe that + + align:start position:0% +all inputs and the way i describe that + + + align:start position:0% +all inputs and the way i describe that +machine tw is it ignores its input + + align:start position:0% +machine tw is it ignores its input + + + align:start position:0% +machine tw is it ignores its input +whatever the input is it just simulates + + align:start position:0% +whatever the input is it just simulates + + + align:start position:0% +whatever the input is it just simulates +m on w + + align:start position:0% + + + + align:start position:0% + +you could easily given m + + align:start position:0% +you could easily given m + + + align:start position:0% +you could easily given m +and w you can build the machine tw + + align:start position:0% +and w you can build the machine tw + + + align:start position:0% +and w you can build the machine tw +it just always runs mmw no matter what + + align:start position:0% +it just always runs mmw no matter what + + + align:start position:0% +it just always runs mmw no matter what +input it gets + + align:start position:0% + + + + align:start position:0% + +and so now we're going to give a + + align:start position:0% +and so now we're going to give a + + + align:start position:0% +and so now we're going to give a +function which maps atm problems which + + align:start position:0% +function which maps atm problems which + + + align:start position:0% +function which maps atm problems which +have the form mw so it's a atm + + align:start position:0% +have the form mw so it's a atm + + + align:start position:0% +have the form mw so it's a atm +complement problem so this is we want to + + align:start position:0% +complement problem so this is we want to + + + align:start position:0% +complement problem so this is we want to +test if this if m accepts w or not so + + align:start position:0% +test if this if m accepts w or not so + + + align:start position:0% +test if this if m accepts w or not so +that's an atm complement type problem + + align:start position:0% +that's an atm complement type problem + + + align:start position:0% +that's an atm complement type problem +and i want to map that to an eqtm + + align:start position:0% +and i want to map that to an eqtm + + + align:start position:0% +and i want to map that to an eqtm +problem of the form + + align:start position:0% +problem of the form + + + align:start position:0% +problem of the form +you know eqtm problems are pairs of + + align:start position:0% +you know eqtm problems are pairs of + + + align:start position:0% +you know eqtm problems are pairs of +machines + + align:start position:0% +machines + + + align:start position:0% +machines +now and where we're going to be testing + + align:start position:0% +now and where we're going to be testing + + + align:start position:0% +now and where we're going to be testing +equivalents so i'm just trying to give + + align:start position:0% +equivalents so i'm just trying to give + + + align:start position:0% +equivalents so i'm just trying to give +you the form of the output of the + + align:start position:0% +you the form of the output of the + + + align:start position:0% +you the form of the output of the +reduction function f + + align:start position:0% +reduction function f + + + align:start position:0% +reduction function f +and specifically what it's going to look + + align:start position:0% +and specifically what it's going to look + + + align:start position:0% +and specifically what it's going to look +like is + + align:start position:0% +like is + + + align:start position:0% +like is +when we have + + align:start position:0% +when we have + + + align:start position:0% +when we have +m is f is processing on mw + + align:start position:0% +m is f is processing on mw + + + align:start position:0% +m is f is processing on mw +it's going to produce two machines one + + align:start position:0% +it's going to produce two machines one + + + align:start position:0% +it's going to produce two machines one +of them is going to be tw + + align:start position:0% + + + + align:start position:0% + +which always behaves the way m behaves + + align:start position:0% +which always behaves the way m behaves + + + align:start position:0% +which always behaves the way m behaves +on w + + align:start position:0% +on w + + + align:start position:0% +on w +but + + align:start position:0% +but + + + align:start position:0% +but +expanded to all inputs + + align:start position:0% +expanded to all inputs + + + align:start position:0% +expanded to all inputs +and then and then + + align:start position:0% +and then and then + + + align:start position:0% +and then and then +and a machine i'm going to call t reject + + align:start position:0% +and a machine i'm going to call t reject + + + align:start position:0% +and a machine i'm going to call t reject +which just is designed to reject + + align:start position:0% +which just is designed to reject + + + align:start position:0% +which just is designed to reject +everything + + align:start position:0% + + + + align:start position:0% + +now look at just walk through the logic + + align:start position:0% +now look at just walk through the logic + + + align:start position:0% +now look at just walk through the logic +with me + + align:start position:0% +with me + + + align:start position:0% +with me +if m rejects w + + align:start position:0% +if m rejects w + + + align:start position:0% +if m rejects w +tw rejects everything + + align:start position:0% +tw rejects everything + + + align:start position:0% +tw rejects everything +and so will be equivalent to the machine + + align:start position:0% +and so will be equivalent to the machine + + + align:start position:0% +and so will be equivalent to the machine +t reject + + align:start position:0% +t reject + + + align:start position:0% +t reject +that's what we want + + align:start position:0% +that's what we want + + + align:start position:0% +that's what we want +if m rejects w + + align:start position:0% +if m rejects w + + + align:start position:0% +if m rejects w +so we're in the language atm complement + + align:start position:0% +so we're in the language atm complement + + + align:start position:0% +so we're in the language atm complement +then these two machines that i produce + + align:start position:0% +then these two machines that i produce + + + align:start position:0% +then these two machines that i produce +for you are going to be in + + align:start position:0% +for you are going to be in + + + align:start position:0% +for you are going to be in +the eqtm language + + align:start position:0% +the eqtm language + + + align:start position:0% +the eqtm language +that's what i want to have happen + + align:start position:0% +that's what i want to have happen + + + align:start position:0% +that's what i want to have happen +for a reduction from atm complement to + + align:start position:0% +for a reduction from atm complement to + + + align:start position:0% +for a reduction from atm complement to +eqtm + + align:start position:0% + + + + align:start position:0% + +similarly + + align:start position:0% +similarly + + + align:start position:0% +similarly +to do part two + + align:start position:0% +to do part two + + + align:start position:0% +to do part two +i'm going to use make here a different f + + align:start position:0% +i'm going to use make here a different f + + + align:start position:0% +i'm going to use make here a different f +maybe i should call it f prime + + align:start position:0% +maybe i should call it f prime + + + align:start position:0% +maybe i should call it f prime +all right and you know f1 and f2 for the + + align:start position:0% +all right and you know f1 and f2 for the + + + align:start position:0% +all right and you know f1 and f2 for the +two different parts so these are two + + align:start position:0% +two different parts so these are two + + + align:start position:0% +two different parts so these are two +different f's i'm going to make f here + + align:start position:0% +different f's i'm going to make f here + + + align:start position:0% +different f's i'm going to make f here +on + + align:start position:0% +on + + + align:start position:0% +on +instead of generating + + align:start position:0% +instead of generating + + + align:start position:0% +instead of generating +t w and t reject i'm going to have t w + + align:start position:0% +t w and t reject i'm going to have t w + + + align:start position:0% +t w and t reject i'm going to have t w +and t accept which is a turing machine + + align:start position:0% +and t accept which is a turing machine + + + align:start position:0% +and t accept which is a turing machine +that always accepts its input + + align:start position:0% +that always accepts its input + + + align:start position:0% +that always accepts its input +now + + align:start position:0% +now + + + align:start position:0% +now +if m rejects w + + align:start position:0% +if m rejects w + + + align:start position:0% +if m rejects w +it's an atm complement + + align:start position:0% +it's an atm complement + + + align:start position:0% +it's an atm complement +then tw + + align:start position:0% +then tw + + + align:start position:0% +then tw +is going to reject everything and it's + + align:start position:0% +is going to reject everything and it's + + + align:start position:0% +is going to reject everything and it's +going to be different from + + align:start position:0% +going to be different from + + + align:start position:0% +going to be different from +it's companion here t accept + + align:start position:0% +it's companion here t accept + + + align:start position:0% +it's companion here t accept +and so won't it'll be in it won't be an + + align:start position:0% +and so won't it'll be in it won't be an + + + align:start position:0% +and so won't it'll be in it won't be an +eqtm complement + + align:start position:0% +eqtm complement + + + align:start position:0% +eqtm complement +but if m accepts w + + align:start position:0% +but if m accepts w + + + align:start position:0% +but if m accepts w +then tw is going to accept everything + + align:start position:0% +then tw is going to accept everything + + + align:start position:0% +then tw is going to accept everything +and they're going to be equivalent to + + align:start position:0% +and they're going to be equivalent to + + + align:start position:0% +and they're going to be equivalent to +t except and you will be + + align:start position:0% +t except and you will be + + + align:start position:0% +t except and you will be +uh + + align:start position:0% +uh + + + align:start position:0% +uh +equivalent so the here is where we're + + align:start position:0% +equivalent so the here is where we're + + + align:start position:0% +equivalent so the here is where we're +taking + + align:start position:0% +taking + + + align:start position:0% +taking +atm complement and mapping it to the + + align:start position:0% +atm complement and mapping it to the + + + align:start position:0% +atm complement and mapping it to the +complement of + + align:start position:0% +complement of + + + align:start position:0% +complement of +eqtm + + align:start position:0% +eqtm + + + align:start position:0% +eqtm +um + + align:start position:0% +um + + + align:start position:0% +um +too many compliments here i i realize + + align:start position:0% +too many compliments here i i realize + + + align:start position:0% +too many compliments here i i realize +like compliments are confusing but + + align:start position:0% +like compliments are confusing but + + + align:start position:0% +like compliments are confusing but +anyway why don't you mull this over um + + align:start position:0% +anyway why don't you mull this over um + + + align:start position:0% +anyway why don't you mull this over um +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +um + + align:start position:0% +um + + + align:start position:0% +um +just to summarize + + align:start position:0% +just to summarize + + + align:start position:0% +just to summarize +okay yeah + + align:start position:0% +okay yeah + + + align:start position:0% +okay yeah +you know we're out of time here but why + + align:start position:0% +you know we're out of time here but why + + + align:start position:0% +you know we're out of time here but why +do we use reducing when we talk about + + align:start position:0% +do we use reducing when we talk about + + + align:start position:0% +do we use reducing when we talk about +reductions + + align:start position:0% +reductions + + + align:start position:0% +reductions +it's because when we reduce a to b + + align:start position:0% +it's because when we reduce a to b + + + align:start position:0% +it's because when we reduce a to b +we kind of bring a's difficulty down to + + align:start position:0% +we kind of bring a's difficulty down to + + + align:start position:0% +we kind of bring a's difficulty down to +b's difficulty that's where the reducing + + align:start position:0% +b's difficulty that's where the reducing + + + align:start position:0% +b's difficulty that's where the reducing +comes from + + align:start position:0% +comes from + + + align:start position:0% +comes from +um + + align:start position:0% +um + + + align:start position:0% +um +or + + align:start position:0% +or + + + align:start position:0% +or +we bring b's difficulty up to a's + + align:start position:0% +we bring b's difficulty up to a's + + + align:start position:0% +we bring b's difficulty up to a's +difficulty because it's really a + + align:start position:0% +difficulty because it's really a + + + align:start position:0% +difficulty because it's really a +difficulty relative to b that we're + + align:start position:0% +difficulty relative to b that we're + + + align:start position:0% +difficulty relative to b that we're +talking about when we're reducing a to b + + align:start position:0% +talking about when we're reducing a to b + + + align:start position:0% +talking about when we're reducing a to b +so that's why + + align:start position:0% +so that's why + + + align:start position:0% +so that's why +the term reducing seems + + align:start position:0% +the term reducing seems + + + align:start position:0% +the term reducing seems +a little out of place when we're proving + + align:start position:0% +a little out of place when we're proving + + + align:start position:0% +a little out of place when we're proving +things undecidable or unrecognizable but + + align:start position:0% +things undecidable or unrecognizable but + + + align:start position:0% +things undecidable or unrecognizable but +that's where it's coming from + + align:start position:0% +that's where it's coming from + + + align:start position:0% +that's where it's coming from +anyway quick review + + align:start position:0% +anyway quick review + + + align:start position:0% +anyway quick review +um we introduced the ter the + + align:start position:0% +um we introduced the ter the + + + align:start position:0% +um we introduced the ter the +reducibility method + + align:start position:0% +reducibility method + + + align:start position:0% +reducibility method +we defined mapping reducibility as a + + align:start position:0% +we defined mapping reducibility as a + + + align:start position:0% +we defined mapping reducibility as a +special kind of reducibility we showed + + align:start position:0% +special kind of reducibility we showed + + + align:start position:0% +special kind of reducibility we showed +etm is undecidable and unrecognizable + + align:start position:0% +etm is undecidable and unrecognizable + + + align:start position:0% +etm is undecidable and unrecognizable +and that eqtm is both it and its + + align:start position:0% +and that eqtm is both it and its + + + align:start position:0% +and that eqtm is both it and its +complement are unrecognizable + + align:start position:0% +complement are unrecognizable + + + align:start position:0% +complement are unrecognizable +so we're out of time um i will uh shut + + align:start position:0% +so we're out of time um i will uh shut + + + align:start position:0% +so we're out of time um i will uh shut +this down + + align:start position:0% +this down + + + align:start position:0% +this down +but i'll take a few questions here + + align:start position:0% +but i'll take a few questions here + + + align:start position:0% +but i'll take a few questions here +actually you know i'll stick around for + + align:start position:0% +actually you know i'll stick around for + + + align:start position:0% +actually you know i'll stick around for +a few questions and then i'll move to + + align:start position:0% +a few questions and then i'll move to + + + align:start position:0% +a few questions and then i'll move to +the other chat room for office hours + + align:start position:0% +the other chat room for office hours + + + align:start position:0% +the other chat room for office hours +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +question to go over + + align:start position:0% +question to go over + + + align:start position:0% +question to go over +the case for the complement of eqtm + + align:start position:0% +the case for the complement of eqtm + + + align:start position:0% +the case for the complement of eqtm +so i will do that + + align:start position:0% + + + + align:start position:0% + +so that's in this slide here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this is the this is proof part two + + align:start position:0% + + + + align:start position:0% + +um for the person who asked me to go + + align:start position:0% +um for the person who asked me to go + + + align:start position:0% +um for the person who asked me to go +over it but i think it's + + align:start position:0% +over it but i think it's + + + align:start position:0% +over it but i think it's +helpful for for those of you who are + + align:start position:0% +helpful for for those of you who are + + + align:start position:0% +helpful for for those of you who are +might be a little bit uh shaky on this + + align:start position:0% +might be a little bit uh shaky on this + + + align:start position:0% +might be a little bit uh shaky on this +i want a mapping reduce the complement + + align:start position:0% +i want a mapping reduce the complement + + + align:start position:0% +i want a mapping reduce the complement +of atm to the complement of eqtm + + align:start position:0% + + + + align:start position:0% + +by the way i don't know if this is going + + align:start position:0% +by the way i don't know if this is going + + + align:start position:0% +by the way i don't know if this is going +to be helpful + + align:start position:0% +to be helpful + + + align:start position:0% +to be helpful +but as we pointed out in the check-in a + + align:start position:0% +but as we pointed out in the check-in a + + + align:start position:0% +but as we pointed out in the check-in a +while back that's completely equivalent + + align:start position:0% +while back that's completely equivalent + + + align:start position:0% +while back that's completely equivalent +to + + align:start position:0% +to + + + align:start position:0% +to +having a mapping reduction from atm to + + align:start position:0% +having a mapping reduction from atm to + + + align:start position:0% +having a mapping reduction from atm to +eqtm + + align:start position:0% +eqtm + + + align:start position:0% +eqtm +you can + + align:start position:0% +you can + + + align:start position:0% +you can +complement both sides + + align:start position:0% +complement both sides + + + align:start position:0% +complement both sides +and + + align:start position:0% +and + + + align:start position:0% +and +you get an equivalent statement + + align:start position:0% +you get an equivalent statement + + + align:start position:0% +you get an equivalent statement +maybe let's stick with the compliments + + align:start position:0% +maybe let's stick with the compliments + + + align:start position:0% +maybe let's stick with the compliments +here um though + + align:start position:0% +here um though + + + align:start position:0% +here um though +i hope that doesn't make it too + + align:start position:0% +i hope that doesn't make it too + + + align:start position:0% +i hope that doesn't make it too +confusing + + align:start position:0% +confusing + + + align:start position:0% +confusing +okay we're trying to show the complement + + align:start position:0% +okay we're trying to show the complement + + + align:start position:0% +okay we're trying to show the complement +of atm is mapping reducible to the + + align:start position:0% +of atm is mapping reducible to the + + + align:start position:0% +of atm is mapping reducible to the +complement of eqtm what does that mean + + align:start position:0% +complement of eqtm what does that mean + + + align:start position:0% +complement of eqtm what does that mean +so that means when m rejects w + + align:start position:0% +so that means when m rejects w + + + align:start position:0% +so that means when m rejects w +so you're in the complement + + align:start position:0% +so you're in the complement + + + align:start position:0% +so you're in the complement +we want the two turing machines + + align:start position:0% +we want the two turing machines + + + align:start position:0% +we want the two turing machines +to be inequivalent + + align:start position:0% +to be inequivalent + + + align:start position:0% +to be inequivalent +no yeah so we're in the complement of + + align:start position:0% +no yeah so we're in the complement of + + + align:start position:0% +no yeah so we're in the complement of +eqtm + + align:start position:0% + + + + align:start position:0% + +so we're with so in other words we're in + + align:start position:0% +so we're with so in other words we're in + + + align:start position:0% +so we're with so in other words we're in +the complement of atm we want the result + + align:start position:0% +the complement of atm we want the result + + + align:start position:0% +the complement of atm we want the result +of the uh of f to be in + + align:start position:0% +of the uh of f to be in + + + align:start position:0% +of the uh of f to be in +um + + align:start position:0% +um + + + align:start position:0% +um +in the complement of eq dm + + align:start position:0% +in the complement of eq dm + + + align:start position:0% +in the complement of eq dm +so in other words when m rejects w the + + align:start position:0% +so in other words when m rejects w the + + + align:start position:0% +so in other words when m rejects w the +two machines should be in equivalent + + align:start position:0% + + + + align:start position:0% + +right when m accepts w the two machines + + align:start position:0% +right when m accepts w the two machines + + + align:start position:0% +right when m accepts w the two machines +should be equivalent + + align:start position:0% +should be equivalent + + + align:start position:0% +should be equivalent +because when we're + + align:start position:0% +because when we're + + + align:start position:0% +because when we're +not in this language so we're an atm we + + align:start position:0% +not in this language so we're an atm we + + + align:start position:0% +not in this language so we're an atm we +want to be not in that language so we + + align:start position:0% +want to be not in that language so we + + + align:start position:0% +want to be not in that language so we +should we should be an eqtm + + align:start position:0% +should we should be an eqtm + + + align:start position:0% +should we should be an eqtm +so when m accepts w + + align:start position:0% +so when m accepts w + + + align:start position:0% +so when m accepts w +we should be equivalent + + align:start position:0% +we should be equivalent + + + align:start position:0% +we should be equivalent +when m a rejects w we should be inequal + + align:start position:0% +when m a rejects w we should be inequal + + + align:start position:0% +when m a rejects w we should be inequal +that's what we want + + align:start position:0% +that's what we want + + + align:start position:0% +that's what we want +let's go down here + + align:start position:0% +let's go down here + + + align:start position:0% +let's go down here +so if m accepts w + + align:start position:0% + + + + align:start position:0% + +we want + + align:start position:0% +we want + + + align:start position:0% +we want +we want them to so when m accepts w want + + align:start position:0% +we want them to so when m accepts w want + + + align:start position:0% +we want them to so when m accepts w want +them to be equivalent so if wham accepts + + align:start position:0% +them to be equivalent so if wham accepts + + + align:start position:0% +them to be equivalent so if wham accepts +w + + align:start position:0% +w + + + align:start position:0% +w +t w accepts everything and it's + + align:start position:0% +t w accepts everything and it's + + + align:start position:0% +t w accepts everything and it's +equivalent to t except + + align:start position:0% +equivalent to t except + + + align:start position:0% +equivalent to t except +when m rejects w + + align:start position:0% +when m rejects w + + + align:start position:0% +when m rejects w +t w + + align:start position:0% +t w + + + align:start position:0% +t w +um + + align:start position:0% +um + + + align:start position:0% +um +rejects everything and so it's not + + align:start position:0% +rejects everything and so it's not + + + align:start position:0% +rejects everything and so it's not +equivalent to the machine that accepts + + align:start position:0% +equivalent to the machine that accepts + + + align:start position:0% +equivalent to the machine that accepts +everything + + align:start position:0% +everything + + + align:start position:0% +everything +so this + + align:start position:0% +so this + + + align:start position:0% +so this +i hope that's + + align:start position:0% +i hope that's + + + align:start position:0% +i hope that's +just go through it just go through the + + align:start position:0% +just go through it just go through the + + + align:start position:0% +just go through it just go through the +logic yourself you'll see why it's + + align:start position:0% +logic yourself you'll see why it's + + + align:start position:0% +logic yourself you'll see why it's +working + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +all right see bye bye everyone + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/NW7cfJwoFMk.txt b/NW7cfJwoFMk.txt new file mode 100644 index 0000000000000000000000000000000000000000..9092aa999a022a38b2c2ea7eec915d4a16bd5103 --- /dev/null +++ b/NW7cfJwoFMk.txt @@ -0,0 +1,2843 @@ +align:start position:0% + +and uh Juliet, we can't wait to hear + + align:start position:0% +and uh Juliet, we can't wait to hear + + + align:start position:0% +and uh Juliet, we can't wait to hear +about the model, + + align:start position:0% + + + + align:start position:0% + +maybe. + + align:start position:0% +maybe. + + + align:start position:0% +maybe. +>> Oh, okay. That goes a little little too + + align:start position:0% +>> Oh, okay. That goes a little little too + + + align:start position:0% +>> Oh, okay. That goes a little little too +fast. Um, well, hello everyone. My name + + align:start position:0% +fast. Um, well, hello everyone. My name + + + align:start position:0% +fast. Um, well, hello everyone. My name +is Juliet Simpson. I am a researcher at + + align:start position:0% +is Juliet Simpson. I am a researcher at + + + align:start position:0% +is Juliet Simpson. I am a researcher at +ENL. I'm excited to be talking to you + + align:start position:0% +ENL. I'm excited to be talking to you + + + align:start position:0% +ENL. I'm excited to be talking to you +about the modeling work that we've been + + align:start position:0% +about the modeling work that we've been + + + align:start position:0% +about the modeling work that we've been +doing. I know I've gotten a lot of great + + align:start position:0% +doing. I know I've gotten a lot of great + + + align:start position:0% +doing. I know I've gotten a lot of great +feedins from earlier today. Um I will + + align:start position:0% +feedins from earlier today. Um I will + + + align:start position:0% +feedins from earlier today. Um I will +just start by noting that uh this is + + align:start position:0% +just start by noting that uh this is + + + align:start position:0% +just start by noting that uh this is +geared a little bit more towards like + + align:start position:0% +geared a little bit more towards like + + + align:start position:0% +geared a little bit more towards like +teaching people about generally the + + align:start position:0% +teaching people about generally the + + + align:start position:0% +teaching people about generally the +modeling that happens for these systems + + align:start position:0% +modeling that happens for these systems + + + align:start position:0% +modeling that happens for these systems +and a little bit less towards results. + + align:start position:0% +and a little bit less towards results. + + + align:start position:0% +and a little bit less towards results. +So if you're interested in that, feel + + align:start position:0% +So if you're interested in that, feel + + + align:start position:0% +So if you're interested in that, feel +free to talk to me. And also um I'm + + align:start position:0% +free to talk to me. And also um I'm + + + align:start position:0% +free to talk to me. And also um I'm +going to be talking about modeling for + + align:start position:0% +going to be talking about modeling for + + + align:start position:0% +going to be talking about modeling for +these systems within the context of a + + align:start position:0% +these systems within the context of a + + + align:start position:0% +these systems within the context of a +model that we've been building out on + + align:start position:0% +model that we've been building out on + + + align:start position:0% +model that we've been building out on +the legup project. Um, but just know + + align:start position:0% +the legup project. Um, but just know + + + align:start position:0% +the legup project. Um, but just know +that there are a lot of other models out + + align:start position:0% +that there are a lot of other models out + + + align:start position:0% +that there are a lot of other models out +there. Um, each tailored to kind of do + + align:start position:0% +there. Um, each tailored to kind of do + + + align:start position:0% +there. Um, each tailored to kind of do +some slightly different things. Um, and + + align:start position:0% +some slightly different things. Um, and + + + align:start position:0% +some slightly different things. Um, and +a lot of great options. And I'm just + + align:start position:0% +a lot of great options. And I'm just + + + align:start position:0% +a lot of great options. And I'm just +doing this kind of within one context. + + align:start position:0% +doing this kind of within one context. + + + align:start position:0% +doing this kind of within one context. +So to get started, I'm talking + + align:start position:0% +So to get started, I'm talking + + + align:start position:0% +So to get started, I'm talking +specifically today about technoeconomic + + align:start position:0% +specifically today about technoeconomic + + + align:start position:0% +specifically today about technoeconomic +modeling. And that involves two + + align:start position:0% +modeling. And that involves two + + + align:start position:0% +modeling. And that involves two +components if you're not familiar with + + align:start position:0% +components if you're not familiar with + + + align:start position:0% +components if you're not familiar with +it. Um, as you might guess by the name, + + align:start position:0% +it. Um, as you might guess by the name, + + + align:start position:0% +it. Um, as you might guess by the name, +the technical model and the economic + + align:start position:0% +the technical model and the economic + + + align:start position:0% +the technical model and the economic +model. And this is really important + + align:start position:0% +model. And this is really important + + + align:start position:0% +model. And this is really important +because it allows us to think about + + align:start position:0% +because it allows us to think about + + + align:start position:0% +because it allows us to think about +trade-offs between impacts to technical + + align:start position:0% +trade-offs between impacts to technical + + + align:start position:0% +trade-offs between impacts to technical +design, how that impacts operation and + + align:start position:0% +design, how that impacts operation and + + + align:start position:0% +design, how that impacts operation and +performance of a system and then looking + + align:start position:0% +performance of a system and then looking + + + align:start position:0% +performance of a system and then looking +at the costs of that, the economic + + align:start position:0% +at the costs of that, the economic + + + align:start position:0% +at the costs of that, the economic +impact. + + align:start position:0% + + + + align:start position:0% + +Now, why does all of this modeling uh + + align:start position:0% +Now, why does all of this modeling uh + + + align:start position:0% +Now, why does all of this modeling uh +why is it matter? Why is it important? + + align:start position:0% +why is it matter? Why is it important? + + + align:start position:0% +why is it matter? Why is it important? +This really helps us to answer a lot of + + align:start position:0% +This really helps us to answer a lot of + + + align:start position:0% +This really helps us to answer a lot of +questions without having to go dig holes + + align:start position:0% +questions without having to go dig holes + + + align:start position:0% +questions without having to go dig holes +in the ground. um we can start to think + + align:start position:0% +in the ground. um we can start to think + + + align:start position:0% +in the ground. um we can start to think +a little more critically ahead of time + + align:start position:0% +a little more critically ahead of time + + + align:start position:0% +a little more critically ahead of time +before the design and before the build. + + align:start position:0% +before the design and before the build. + + + align:start position:0% +before the design and before the build. +We can think about what communities does + + align:start position:0% +We can think about what communities does + + + align:start position:0% +We can think about what communities does +the geothermal network make sense in. Uh + + align:start position:0% +the geothermal network make sense in. Uh + + + align:start position:0% +the geothermal network make sense in. Uh +does it make sense to just go for + + align:start position:0% +does it make sense to just go for + + + align:start position:0% +does it make sense to just go for +geothermal bore holes or should we pull + + align:start position:0% +geothermal bore holes or should we pull + + + align:start position:0% +geothermal bore holes or should we pull +in some of the other thermal resources + + align:start position:0% +in some of the other thermal resources + + + align:start position:0% +in some of the other thermal resources +that have been mentioned today? What + + align:start position:0% +that have been mentioned today? What + + + align:start position:0% +that have been mentioned today? What +kind of monthly payment might be + + align:start position:0% +kind of monthly payment might be + + + align:start position:0% +kind of monthly payment might be +required from customers or what expected + + align:start position:0% +required from customers or what expected + + + align:start position:0% +required from customers or what expected +total costs might there be? There's lots + + align:start position:0% +total costs might there be? There's lots + + + align:start position:0% +total costs might there be? There's lots +of questions on that side of the + + align:start position:0% +of questions on that side of the + + + align:start position:0% +of questions on that side of the +economics as well. Um, so having + + align:start position:0% +economics as well. Um, so having + + + align:start position:0% +economics as well. Um, so having +something that can help um, people start + + align:start position:0% +something that can help um, people start + + + align:start position:0% +something that can help um, people start +to think about the finance side as well. + + align:start position:0% +to think about the finance side as well. + + + align:start position:0% +to think about the finance side as well. +And then after you build, what would + + align:start position:0% +And then after you build, what would + + + align:start position:0% +And then after you build, what would +happen if you added one more house to + + align:start position:0% +happen if you added one more house to + + + align:start position:0% +happen if you added one more house to +the loop or what would happen if you + + align:start position:0% +the loop or what would happen if you + + + align:start position:0% +the loop or what would happen if you +wanted to change a little bit the + + align:start position:0% +wanted to change a little bit the + + + align:start position:0% +wanted to change a little bit the +performance set point for the + + align:start position:0% +performance set point for the + + + align:start position:0% +performance set point for the +temperatures or the operation or the + + align:start position:0% +temperatures or the operation or the + + + align:start position:0% +temperatures or the operation or the +speeds of the loop. Um, so being able to + + align:start position:0% +speeds of the loop. Um, so being able to + + + align:start position:0% +speeds of the loop. Um, so being able to +work with some sort of um, modeling + + align:start position:0% +work with some sort of um, modeling + + + align:start position:0% +work with some sort of um, modeling +option, digital twin, something that + + align:start position:0% +option, digital twin, something that + + + align:start position:0% +option, digital twin, something that +lets you change those parameters before + + align:start position:0% +lets you change those parameters before + + + align:start position:0% +lets you change those parameters before +going out and impacting your customers + + align:start position:0% +going out and impacting your customers + + + align:start position:0% +going out and impacting your customers +in the real world. + + align:start position:0% + + + + align:start position:0% + +Couple of components that I'm then going + + align:start position:0% +Couple of components that I'm then going + + + align:start position:0% +Couple of components that I'm then going +to talk through in a minute. um both on + + align:start position:0% +to talk through in a minute. um both on + + + align:start position:0% +to talk through in a minute. um both on +the physical system side, a lot of the + + align:start position:0% +the physical system side, a lot of the + + + align:start position:0% +the physical system side, a lot of the +major components that we've already + + align:start position:0% +major components that we've already + + + align:start position:0% +major components that we've already +mentioned today, understanding your + + align:start position:0% +mentioned today, understanding your + + + align:start position:0% +mentioned today, understanding your +building loads, knowing um when they're + + align:start position:0% +building loads, knowing um when they're + + + align:start position:0% +building loads, knowing um when they're +going to need heating and cooling + + align:start position:0% +going to need heating and cooling + + + align:start position:0% +going to need heating and cooling +throughout the year and how much of it. + + align:start position:0% +throughout the year and how much of it. + + + align:start position:0% +throughout the year and how much of it. +Understanding your opportunities for + + align:start position:0% +Understanding your opportunities for + + + align:start position:0% +Understanding your opportunities for +thermal resources in an area. Um + + align:start position:0% +thermal resources in an area. Um + + + align:start position:0% +thermal resources in an area. Um +capturing the distribution system + + align:start position:0% +capturing the distribution system + + + align:start position:0% +capturing the distribution system +correctly. That could include knowing + + align:start position:0% +correctly. That could include knowing + + + align:start position:0% +correctly. That could include knowing +whether you want to go for a one pipe + + align:start position:0% +whether you want to go for a one pipe + + + align:start position:0% +whether you want to go for a one pipe +system or two pipes. How big is the pipe + + align:start position:0% +system or two pipes. How big is the pipe + + + align:start position:0% +system or two pipes. How big is the pipe +going to be? How much thermal inertia is + + align:start position:0% +going to be? How much thermal inertia is + + + align:start position:0% +going to be? How much thermal inertia is +there in the water or whatever working + + align:start position:0% +there in the water or whatever working + + + align:start position:0% +there in the water or whatever working +fluid you have moving in that pipe? How + + align:start position:0% +fluid you have moving in that pipe? How + + + align:start position:0% +fluid you have moving in that pipe? How +well are your heat pumps going to + + align:start position:0% +well are your heat pumps going to + + + align:start position:0% +well are your heat pumps going to +perform? What's their coefficient of + + align:start position:0% +perform? What's their coefficient of + + + align:start position:0% +perform? What's their coefficient of +performance look like with different + + align:start position:0% +performance look like with different + + + align:start position:0% +performance look like with different +entering temperatures? + + align:start position:0% +entering temperatures? + + + align:start position:0% +entering temperatures? +And then something we've discussed a + + align:start position:0% +And then something we've discussed a + + + align:start position:0% +And then something we've discussed a +little less today, the economic side. + + align:start position:0% +little less today, the economic side. + + + align:start position:0% +little less today, the economic side. +Um, estimating capital cost, operating + + align:start position:0% +Um, estimating capital cost, operating + + + align:start position:0% +Um, estimating capital cost, operating +cost, maintenance is all really + + align:start position:0% +cost, maintenance is all really + + + align:start position:0% +cost, maintenance is all really +difficult. It's something that we we + + align:start position:0% +difficult. It's something that we we + + + align:start position:0% +difficult. It's something that we we +certainly struggle with, but it's really + + align:start position:0% +certainly struggle with, but it's really + + + align:start position:0% +certainly struggle with, but it's really +important to these systems. And then + + align:start position:0% +important to these systems. And then + + + align:start position:0% +important to these systems. And then +also thinking about the finance plan. + + align:start position:0% +also thinking about the finance plan. + + + align:start position:0% +also thinking about the finance plan. +what's your cost recovery look like? Um, + + align:start position:0% +what's your cost recovery look like? Um, + + + align:start position:0% +what's your cost recovery look like? Um, +who is paying for it? It's probably + + align:start position:0% +who is paying for it? It's probably + + + align:start position:0% +who is paying for it? It's probably +going to have a big impact on that. Um, + + align:start position:0% +going to have a big impact on that. Um, + + + align:start position:0% +going to have a big impact on that. Um, +but that then has an impact at the end + + align:start position:0% +but that then has an impact at the end + + + align:start position:0% +but that then has an impact at the end +of the day on what customer payments + + align:start position:0% +of the day on what customer payments + + + align:start position:0% +of the day on what customer payments +look like as well. + + align:start position:0% + + + + align:start position:0% + +Now, we've tried to put both halves of + + align:start position:0% +Now, we've tried to put both halves of + + + align:start position:0% +Now, we've tried to put both halves of +those models into something we're + + align:start position:0% +those models into something we're + + + align:start position:0% +those models into something we're +working on at ENL called heat nets. This + + align:start position:0% +working on at ENL called heat nets. This + + + align:start position:0% +working on at ENL called heat nets. This +stands for heat and economic analysis + + align:start position:0% +stands for heat and economic analysis + + + align:start position:0% +stands for heat and economic analysis +tool for network thermal systems. ENL + + align:start position:0% +tool for network thermal systems. ENL + + + align:start position:0% +tool for network thermal systems. ENL +has been building out this tool in + + align:start position:0% +has been building out this tool in + + + align:start position:0% +has been building out this tool in +collaboration with heat as part of the + + align:start position:0% +collaboration with heat as part of the + + + align:start position:0% +collaboration with heat as part of the +legup project. And so we're really + + align:start position:0% +legup project. And so we're really + + + align:start position:0% +legup project. And so we're really +excited to have both halves of it up and + + align:start position:0% +excited to have both halves of it up and + + + align:start position:0% +excited to have both halves of it up and +running now. So we have this code that + + align:start position:0% +running now. So we have this code that + + + align:start position:0% +running now. So we have this code that +is written in Python. It's intended to + + align:start position:0% +is written in Python. It's intended to + + + align:start position:0% +is written in Python. It's intended to +long-term be open source and we're + + align:start position:0% +long-term be open source and we're + + + align:start position:0% +long-term be open source and we're +working towards having that being a + + align:start position:0% +working towards having that being a + + + align:start position:0% +working towards having that being a +public GitHub repository. The first half + + align:start position:0% +public GitHub repository. The first half + + + align:start position:0% +public GitHub repository. The first half +is the physics-based model. That's a + + align:start position:0% +is the physics-based model. That's a + + + align:start position:0% +is the physics-based model. That's a +reduced order model. As Isbel mentioned + + align:start position:0% +reduced order model. As Isbel mentioned + + + align:start position:0% +reduced order model. As Isbel mentioned +earlier, the idea there is that it's a + + align:start position:0% +earlier, the idea there is that it's a + + + align:start position:0% +earlier, the idea there is that it's a +little bit more uh high level. It really + + align:start position:0% +little bit more uh high level. It really + + + align:start position:0% +little bit more uh high level. It really +builds on a lot of other more detailed + + align:start position:0% +builds on a lot of other more detailed + + + align:start position:0% +builds on a lot of other more detailed +models to capture the energy flow around + + align:start position:0% +models to capture the energy flow around + + + align:start position:0% +models to capture the energy flow around +the network and the use of electricity + + align:start position:0% +the network and the use of electricity + + + align:start position:0% +the network and the use of electricity +over time. + + align:start position:0% +over time. + + + align:start position:0% +over time. +The second model is the economic model + + align:start position:0% +The second model is the economic model + + + align:start position:0% +The second model is the economic model +used to calculate uh economic metrics of + + align:start position:0% +used to calculate uh economic metrics of + + + align:start position:0% +used to calculate uh economic metrics of +the system as well. + + align:start position:0% + + + + align:start position:0% + +So I'm going to give a little bit of + + align:start position:0% +So I'm going to give a little bit of + + + align:start position:0% +So I'm going to give a little bit of +highle information about both of those + + align:start position:0% +highle information about both of those + + + align:start position:0% +highle information about both of those +models before talking about what kind of + + align:start position:0% +models before talking about what kind of + + + align:start position:0% +models before talking about what kind of +questions we can answer with them. So + + align:start position:0% +questions we can answer with them. So + + + align:start position:0% +questions we can answer with them. So +first on the reduced order side, this is + + align:start position:0% +first on the reduced order side, this is + + + align:start position:0% +first on the reduced order side, this is +for capturing the physics of what's + + align:start position:0% +for capturing the physics of what's + + + align:start position:0% +for capturing the physics of what's +actually happening on the loop. Where is + + align:start position:0% +actually happening on the loop. Where is + + + align:start position:0% +actually happening on the loop. Where is +heat moving over time? Where is water + + align:start position:0% +heat moving over time? Where is water + + + align:start position:0% +heat moving over time? Where is water +moving? Uh how much electricity is being + + align:start position:0% +moving? Uh how much electricity is being + + + align:start position:0% +moving? Uh how much electricity is being +used for that whole process. The major + + align:start position:0% +used for that whole process. The major + + + align:start position:0% +used for that whole process. The major +components that we're capturing are + + align:start position:0% +components that we're capturing are + + + align:start position:0% +components that we're capturing are +shown here in this simple diagram, but + + align:start position:0% +shown here in this simple diagram, but + + + align:start position:0% +shown here in this simple diagram, but +know that this is showing one building + + align:start position:0% +know that this is showing one building + + + align:start position:0% +know that this is showing one building +when you might have 50. And these are + + align:start position:0% +when you might have 50. And these are + + + align:start position:0% +when you might have 50. And these are +just going to be um repeated over time. + + align:start position:0% +just going to be um repeated over time. + + + align:start position:0% +just going to be um repeated over time. +The main backbone of this model is the + + align:start position:0% +The main backbone of this model is the + + + align:start position:0% +The main backbone of this model is the +ambient temperature loop. So, a lot of + + align:start position:0% +ambient temperature loop. So, a lot of + + + align:start position:0% +ambient temperature loop. So, a lot of +the modeling effort here goes into the + + align:start position:0% +the modeling effort here goes into the + + + align:start position:0% +the modeling effort here goes into the +effort of capturing how does heat move + + align:start position:0% +effort of capturing how does heat move + + + align:start position:0% +effort of capturing how does heat move +physically around this loop. How much + + align:start position:0% +physically around this loop. How much + + + align:start position:0% +physically around this loop. How much +thermal inertia is in there? So if you + + align:start position:0% +thermal inertia is in there? So if you + + + align:start position:0% +thermal inertia is in there? So if you +dump in some heat, how quickly is it + + align:start position:0% +dump in some heat, how quickly is it + + + align:start position:0% +dump in some heat, how quickly is it +going to change temperature and how + + align:start position:0% +going to change temperature and how + + + align:start position:0% +going to change temperature and how +quickly is that going to then propagate + + align:start position:0% +quickly is that going to then propagate + + + align:start position:0% +quickly is that going to then propagate +around the loop and affect all of the + + align:start position:0% +around the loop and affect all of the + + + align:start position:0% +around the loop and affect all of the +customers? + + align:start position:0% +customers? + + + align:start position:0% +customers? +Then plugging in and exchanging heat + + align:start position:0% +Then plugging in and exchanging heat + + + align:start position:0% +Then plugging in and exchanging heat +with that we have all of the buildings. + + align:start position:0% +with that we have all of the buildings. + + + align:start position:0% +with that we have all of the buildings. +Um so that requires doing some building + + align:start position:0% +Um so that requires doing some building + + + align:start position:0% +Um so that requires doing some building +modeling, understanding their loads over + + align:start position:0% +modeling, understanding their loads over + + + align:start position:0% +modeling, understanding their loads over +time, understanding how the heat pumps + + align:start position:0% +time, understanding how the heat pumps + + + align:start position:0% +time, understanding how the heat pumps +are going to perform given different + + align:start position:0% +are going to perform given different + + + align:start position:0% +are going to perform given different +entering temperatures um from that main + + align:start position:0% +entering temperatures um from that main + + + align:start position:0% +entering temperatures um from that main +thermal loop. There's also all of your + + align:start position:0% +thermal loop. There's also all of your + + + align:start position:0% +thermal loop. There's also all of your +thermal sources and syncs. So in this + + align:start position:0% +thermal sources and syncs. So in this + + + align:start position:0% +thermal sources and syncs. So in this +case we're mostly focused on borehole + + align:start position:0% +case we're mostly focused on borehole + + + align:start position:0% +case we're mostly focused on borehole +fields. Um but there could be other ones + + align:start position:0% +fields. Um but there could be other ones + + + align:start position:0% +fields. Um but there could be other ones +as well. Um this modeling is being done + + align:start position:0% +as well. Um this modeling is being done + + + align:start position:0% +as well. Um this modeling is being done +um like I mentioned at a reduced order + + align:start position:0% +um like I mentioned at a reduced order + + + align:start position:0% +um like I mentioned at a reduced order +level. So we're relying on collaborators + + align:start position:0% +level. So we're relying on collaborators + + + align:start position:0% +level. So we're relying on collaborators +who are doing some more detailed + + align:start position:0% +who are doing some more detailed + + + align:start position:0% +who are doing some more detailed +modeling including models that we're + + align:start position:0% +modeling including models that we're + + + align:start position:0% +modeling including models that we're +getting from Lawrence Berkeley National + + align:start position:0% +getting from Lawrence Berkeley National + + + align:start position:0% +getting from Lawrence Berkeley National +Labs um to be able to look at what is + + align:start position:0% +Labs um to be able to look at what is + + + align:start position:0% +Labs um to be able to look at what is +our bore hole bore hole performance look + + align:start position:0% +our bore hole bore hole performance look + + + align:start position:0% +our bore hole bore hole performance look +like over time. + + align:start position:0% +like over time. + + + align:start position:0% +like over time. +And then finally, having some sort of + + align:start position:0% +And then finally, having some sort of + + + align:start position:0% +And then finally, having some sort of +central control control station. Um, + + align:start position:0% +central control control station. Um, + + + align:start position:0% +central control control station. Um, +being able to model the circulation + + align:start position:0% +being able to model the circulation + + + align:start position:0% +being able to model the circulation +pumps to move the fluid around. Um, in + + align:start position:0% +pumps to move the fluid around. Um, in + + + align:start position:0% +pumps to move the fluid around. Um, in +our models right now, we always account + + align:start position:0% +our models right now, we always account + + + align:start position:0% +our models right now, we always account +for the option of an auxiliary heating + + align:start position:0% +for the option of an auxiliary heating + + + align:start position:0% +for the option of an auxiliary heating +and cooling system. And that allows us + + align:start position:0% +and cooling system. And that allows us + + + align:start position:0% +and cooling system. And that allows us +to really play with our temperature + + align:start position:0% +to really play with our temperature + + + align:start position:0% +to really play with our temperature +bounds and um, how many buildings we + + align:start position:0% +bounds and um, how many buildings we + + + align:start position:0% +bounds and um, how many buildings we +have on the loop. And then having a + + align:start position:0% +have on the loop. And then having a + + + align:start position:0% +have on the loop. And then having a +control decision architecture that + + align:start position:0% +control decision architecture that + + + align:start position:0% +control decision architecture that +determines how do all of these pieces + + align:start position:0% +determines how do all of these pieces + + + align:start position:0% +determines how do all of these pieces +run together. + + align:start position:0% + + + + align:start position:0% + +Just as a quick example of some of the + + align:start position:0% +Just as a quick example of some of the + + + align:start position:0% +Just as a quick example of some of the +outputs we can get from that. On the + + align:start position:0% +outputs we can get from that. On the + + + align:start position:0% +outputs we can get from that. On the +left we're showing one that shows uh + + align:start position:0% +left we're showing one that shows uh + + + align:start position:0% +left we're showing one that shows uh +spatial trends. So as you move around + + align:start position:0% +spatial trends. So as you move around + + + align:start position:0% +spatial trends. So as you move around +the loop, this is done in a straight + + align:start position:0% +the loop, this is done in a straight + + + align:start position:0% +the loop, this is done in a straight +line. We can imagine the end feeds back + + align:start position:0% +line. We can imagine the end feeds back + + + align:start position:0% +line. We can imagine the end feeds back +into the beginning. Um this relates back + + align:start position:0% +into the beginning. Um this relates back + + + align:start position:0% +into the beginning. Um this relates back +to what Isbel was saying earlier that + + align:start position:0% +to what Isbel was saying earlier that + + + align:start position:0% +to what Isbel was saying earlier that +you see changes in temperature as you + + align:start position:0% +you see changes in temperature as you + + + align:start position:0% +you see changes in temperature as you +move around the loop. And then you also + + align:start position:0% +move around the loop. And then you also + + + align:start position:0% +move around the loop. And then you also +see things happen over time. So the one + + align:start position:0% +see things happen over time. So the one + + + align:start position:0% +see things happen over time. So the one +on the right hand side is showing uh + + align:start position:0% +on the right hand side is showing uh + + + align:start position:0% +on the right hand side is showing uh +every hour throughout a year how is heat + + align:start position:0% +every hour throughout a year how is heat + + + align:start position:0% +every hour throughout a year how is heat +being exchanged with the loop. So in + + align:start position:0% +being exchanged with the loop. So in + + + align:start position:0% +being exchanged with the loop. So in +this case we're showing building loads + + align:start position:0% +this case we're showing building loads + + + align:start position:0% +this case we're showing building loads +and bore hole loads um in blue and green + + align:start position:0% +and bore hole loads um in blue and green + + + align:start position:0% +and bore hole loads um in blue and green +and those are generally opposites. So in + + align:start position:0% +and those are generally opposites. So in + + + align:start position:0% +and those are generally opposites. So in +the wintertime buildings take heat out + + align:start position:0% +the wintertime buildings take heat out + + + align:start position:0% +the wintertime buildings take heat out +of the loop and the borehole field puts + + align:start position:0% +of the loop and the borehole field puts + + + align:start position:0% +of the loop and the borehole field puts +heat in. We see the opposite trend in + + align:start position:0% +heat in. We see the opposite trend in + + + align:start position:0% +heat in. We see the opposite trend in +the summertime + + align:start position:0% +the summertime + + + align:start position:0% +the summertime +and then some additional auxiliary heat + + align:start position:0% +and then some additional auxiliary heat + + + align:start position:0% +and then some additional auxiliary heat +in this model. Um, and so you could see + + align:start position:0% +in this model. Um, and so you could see + + + align:start position:0% +in this model. Um, and so you could see +maybe where there's areas uh that you + + align:start position:0% +maybe where there's areas uh that you + + + align:start position:0% +maybe where there's areas uh that you +need um you might need some additional + + align:start position:0% +need um you might need some additional + + + align:start position:0% +need um you might need some additional +heat and you can consider trade-offs for + + align:start position:0% +heat and you can consider trade-offs for + + + align:start position:0% +heat and you can consider trade-offs for +is it worthwhile to have some sort of + + align:start position:0% +is it worthwhile to have some sort of + + + align:start position:0% +is it worthwhile to have some sort of +electric boiler provide that or to drill + + align:start position:0% +electric boiler provide that or to drill + + + align:start position:0% +electric boiler provide that or to drill +more bore holes. And again, this comes + + align:start position:0% +more bore holes. And again, this comes + + + align:start position:0% +more bore holes. And again, this comes +down to a lot of trade-offs. + + align:start position:0% +down to a lot of trade-offs. + + + align:start position:0% +down to a lot of trade-offs. +The other half of this model is + + align:start position:0% +The other half of this model is + + + align:start position:0% +The other half of this model is +economic. + + align:start position:0% +economic. + + + align:start position:0% +economic. +Um I will warn you that this is the side + + align:start position:0% +Um I will warn you that this is the side + + + align:start position:0% +Um I will warn you that this is the side +that I spend a little bit less time on + + align:start position:0% +that I spend a little bit less time on + + + align:start position:0% +that I spend a little bit less time on +um at work but um this takes in a lot of + + align:start position:0% +um at work but um this takes in a lot of + + + align:start position:0% +um at work but um this takes in a lot of +inputs from um the physicsbased model. + + align:start position:0% +inputs from um the physicsbased model. + + + align:start position:0% +inputs from um the physicsbased model. +So the physics based model will tell you + + align:start position:0% +So the physics based model will tell you + + + align:start position:0% +So the physics based model will tell you +how much electricity are all the + + align:start position:0% +how much electricity are all the + + + align:start position:0% +how much electricity are all the +components using over time also what + + align:start position:0% +components using over time also what + + + align:start position:0% +components using over time also what +were the design specs you chose for the + + align:start position:0% +were the design specs you chose for the + + + align:start position:0% +were the design specs you chose for the +system and then you have to give it some + + align:start position:0% +system and then you have to give it some + + + align:start position:0% +system and then you have to give it some +additional information. So what + + align:start position:0% +additional information. So what + + + align:start position:0% +additional information. So what +financial assumptions are you putting in + + align:start position:0% +financial assumptions are you putting in + + + align:start position:0% +financial assumptions are you putting in +um how much of this project uh how much + + align:start position:0% +um how much of this project uh how much + + + align:start position:0% +um how much of this project uh how much +is financed with debt? How much is + + align:start position:0% +is financed with debt? How much is + + + align:start position:0% +is financed with debt? How much is +upfront? um what kind of assumptions are + + align:start position:0% +upfront? um what kind of assumptions are + + + align:start position:0% +upfront? um what kind of assumptions are +you making on incentives you might + + align:start position:0% +you making on incentives you might + + + align:start position:0% +you making on incentives you might +received? That all comes together into a + + align:start position:0% +received? That all comes together into a + + + align:start position:0% +received? That all comes together into a +variety of outputs that we can look at. + + align:start position:0% +variety of outputs that we can look at. + + + align:start position:0% +variety of outputs that we can look at. +One that we're particularly excited + + align:start position:0% +One that we're particularly excited + + + align:start position:0% +One that we're particularly excited +about right now is something we're + + align:start position:0% +about right now is something we're + + + align:start position:0% +about right now is something we're +calling um LCO X. Um this builds off of + + align:start position:0% +calling um LCO X. Um this builds off of + + + align:start position:0% +calling um LCO X. Um this builds off of +the standard levelized cost of energy + + align:start position:0% +the standard levelized cost of energy + + + align:start position:0% +the standard levelized cost of energy +equation, but here we're allowing for + + align:start position:0% +equation, but here we're allowing for + + + align:start position:0% +equation, but here we're allowing for +pulling in multiple energy flows. Um so + + align:start position:0% +pulling in multiple energy flows. Um so + + + align:start position:0% +pulling in multiple energy flows. Um so +it's no longer just energy. um our costs + + align:start position:0% +it's no longer just energy. um our costs + + + align:start position:0% +it's no longer just energy. um our costs +are including both capital cost and the + + align:start position:0% +are including both capital cost and the + + + align:start position:0% +are including both capital cost and the +cost of the electricity to operate the + + align:start position:0% +cost of the electricity to operate the + + + align:start position:0% +cost of the electricity to operate the +system and then our thing that we're + + align:start position:0% +system and then our thing that we're + + + align:start position:0% +system and then our thing that we're +producing in this case is heating and + + align:start position:0% +producing in this case is heating and + + + align:start position:0% +producing in this case is heating and +cooling to buildings. Um right now we're + + align:start position:0% +cooling to buildings. Um right now we're + + + align:start position:0% +cooling to buildings. Um right now we're +looking at that as just the absolute + + align:start position:0% +looking at that as just the absolute + + + align:start position:0% +looking at that as just the absolute +values of them. How much total um you + + align:start position:0% +values of them. How much total um you + + + align:start position:0% +values of them. How much total um you +know uh help are you putting into these + + align:start position:0% +know uh help are you putting into these + + + align:start position:0% +know uh help are you putting into these +buildings to maintain their climate. Um + + align:start position:0% +buildings to maintain their climate. Um + + + align:start position:0% +buildings to maintain their climate. Um +so heat and cool are equally valued at + + align:start position:0% +so heat and cool are equally valued at + + + align:start position:0% +so heat and cool are equally valued at +the moment. + + align:start position:0% +the moment. + + + align:start position:0% +the moment. +And we can then get more granular with + + align:start position:0% +And we can then get more granular with + + + align:start position:0% +And we can then get more granular with +those outputs as well. So just an + + align:start position:0% +those outputs as well. So just an + + + align:start position:0% +those outputs as well. So just an +example of something that you could look + + align:start position:0% +example of something that you could look + + + align:start position:0% +example of something that you could look +at. Um this is just using + + align:start position:0% +at. Um this is just using + + + align:start position:0% +at. Um this is just using +not random numbers but uh example + + align:start position:0% +not random numbers but uh example + + + align:start position:0% +not random numbers but uh example +numbers for some example building. You + + align:start position:0% +numbers for some example building. You + + + align:start position:0% +numbers for some example building. You +could start to look at how much energy + + align:start position:0% +could start to look at how much energy + + + align:start position:0% +could start to look at how much energy +consumption do you expect throughout a + + align:start position:0% +consumption do you expect throughout a + + + align:start position:0% +consumption do you expect throughout a +year? How does that then trickle down + + align:start position:0% +year? How does that then trickle down + + + align:start position:0% +year? How does that then trickle down +into what might that user depending on + + align:start position:0% +into what might that user depending on + + + align:start position:0% +into what might that user depending on +um what cost recovery is being used? + + align:start position:0% +um what cost recovery is being used? + + + align:start position:0% +um what cost recovery is being used? +What might their monthly bill payment + + align:start position:0% +What might their monthly bill payment + + + align:start position:0% +What might their monthly bill payment +look like? Things like that. So now we + + align:start position:0% +look like? Things like that. So now we + + + align:start position:0% +look like? Things like that. So now we +can start to go all the way from design + + align:start position:0% +can start to go all the way from design + + + align:start position:0% +can start to go all the way from design +decisions down to monthly bills for um + + align:start position:0% +decisions down to monthly bills for um + + + align:start position:0% +decisions down to monthly bills for um +individual homes. + + align:start position:0% + + + + align:start position:0% + +So just kind of to wrap up that this + + align:start position:0% +So just kind of to wrap up that this + + + align:start position:0% +So just kind of to wrap up that this +idea um showing how the data flows all + + align:start position:0% +idea um showing how the data flows all + + + align:start position:0% +idea um showing how the data flows all +together. We have first this reduced + + align:start position:0% +together. We have first this reduced + + + align:start position:0% +together. We have first this reduced +order model. This is physics-based. We + + align:start position:0% +order model. This is physics-based. We + + + align:start position:0% +order model. This is physics-based. We +have a lot of different inputs that come + + align:start position:0% +have a lot of different inputs that come + + + align:start position:0% +have a lot of different inputs that come +into this. It really relies on highle + + align:start position:0% +into this. It really relies on highle + + + align:start position:0% +into this. It really relies on highle +modeling done elsewhere that all can + + align:start position:0% +modeling done elsewhere that all can + + + align:start position:0% +modeling done elsewhere that all can +come together. + + align:start position:0% +come together. + + + align:start position:0% +come together. +And a major output from that is the time + + align:start position:0% +And a major output from that is the time + + + align:start position:0% +And a major output from that is the time +series electricity consumption. + + align:start position:0% +series electricity consumption. + + + align:start position:0% +series electricity consumption. +There's some other inputs that we're + + align:start position:0% +There's some other inputs that we're + + + align:start position:0% +There's some other inputs that we're +going to need to get to the economic + + align:start position:0% +going to need to get to the economic + + + align:start position:0% +going to need to get to the economic +model. So we start to have to think + + align:start position:0% +model. So we start to have to think + + + align:start position:0% +model. So we start to have to think +about component cost, estimating those, + + align:start position:0% +about component cost, estimating those, + + + align:start position:0% +about component cost, estimating those, +knowing what our financial assumptions + + align:start position:0% +knowing what our financial assumptions + + + align:start position:0% +knowing what our financial assumptions +are, and then eventually feeding that + + align:start position:0% +are, and then eventually feeding that + + + align:start position:0% +are, and then eventually feeding that +all into an economic model where we can + + align:start position:0% +all into an economic model where we can + + + align:start position:0% +all into an economic model where we can +get outputs like that LCOX value I was + + align:start position:0% +get outputs like that LCOX value I was + + + align:start position:0% +get outputs like that LCOX value I was +mentioning, also net pleasant value, + + align:start position:0% +mentioning, also net pleasant value, + + + align:start position:0% +mentioning, also net pleasant value, +internal rate of return, um, and + + align:start position:0% +internal rate of return, um, and + + + align:start position:0% +internal rate of return, um, and +something we're calling thermal energy + + align:start position:0% +something we're calling thermal energy + + + align:start position:0% +something we're calling thermal energy +price. + + align:start position:0% + + + + align:start position:0% + +And then you get to answer the fun + + align:start position:0% +And then you get to answer the fun + + + align:start position:0% +And then you get to answer the fun +questions. So this is what we're really + + align:start position:0% +questions. So this is what we're really + + + align:start position:0% +questions. So this is what we're really +here for. We build out all of this + + align:start position:0% +here for. We build out all of this + + + align:start position:0% +here for. We build out all of this +modeling so that we can start to answer + + align:start position:0% +modeling so that we can start to answer + + + align:start position:0% +modeling so that we can start to answer +interesting questions. So I have two + + align:start position:0% +interesting questions. So I have two + + + align:start position:0% +interesting questions. So I have two +quick examples here to wrap up. The + + align:start position:0% +quick examples here to wrap up. The + + + align:start position:0% +quick examples here to wrap up. The +first is what if you change the minimum + + align:start position:0% +first is what if you change the minimum + + + align:start position:0% +first is what if you change the minimum +loop temperature. Um so in this case + + align:start position:0% +loop temperature. Um so in this case + + + align:start position:0% +loop temperature. Um so in this case +we're assuming with the way our control + + align:start position:0% +we're assuming with the way our control + + + align:start position:0% +we're assuming with the way our control +system that we've built is set up um you + + align:start position:0% +system that we've built is set up um you + + + align:start position:0% +system that we've built is set up um you +have to decide uh when do the pumps ramp + + align:start position:0% +have to decide uh when do the pumps ramp + + + align:start position:0% +have to decide uh when do the pumps ramp +up, when does the borehole get used, + + align:start position:0% +up, when does the borehole get used, + + + align:start position:0% +up, when does the borehole get used, +when does auxiliary heat turn on in + + align:start position:0% +when does auxiliary heat turn on in + + + align:start position:0% +when does auxiliary heat turn on in +order to maintain some minimum + + align:start position:0% +order to maintain some minimum + + + align:start position:0% +order to maintain some minimum +temperature. + + align:start position:0% +temperature. + + + align:start position:0% +temperature. +In this case study that we did, we found + + align:start position:0% +In this case study that we did, we found + + + align:start position:0% +In this case study that we did, we found +that as you increase that minimum loop + + align:start position:0% +that as you increase that minimum loop + + + align:start position:0% +that as you increase that minimum loop +temperature, the cost to the utility + + align:start position:0% +temperature, the cost to the utility + + + align:start position:0% +temperature, the cost to the utility +goes up greatly. This makes sense. + + align:start position:0% +goes up greatly. This makes sense. + + + align:start position:0% +goes up greatly. This makes sense. +They're having to work really hard to + + align:start position:0% +They're having to work really hard to + + + align:start position:0% +They're having to work really hard to +maintain a higher temperature, but the + + align:start position:0% +maintain a higher temperature, but the + + + align:start position:0% +maintain a higher temperature, but the +cost of the consumer goes down slightly + + align:start position:0% +cost of the consumer goes down slightly + + + align:start position:0% +cost of the consumer goes down slightly +because their heat pump is working more + + align:start position:0% +because their heat pump is working more + + + align:start position:0% +because their heat pump is working more +efficiently now. So, you see this + + align:start position:0% +efficiently now. So, you see this + + + align:start position:0% +efficiently now. So, you see this +trade-off here. Well, in this case, + + align:start position:0% +trade-off here. Well, in this case, + + + align:start position:0% +trade-off here. Well, in this case, +we're talking about annual electricity + + align:start position:0% +we're talking about annual electricity + + + align:start position:0% +we're talking about annual electricity +costs, not considering capital cost that + + align:start position:0% +costs, not considering capital cost that + + + align:start position:0% +costs, not considering capital cost that +goes into that. But um we have to think + + align:start position:0% +goes into that. But um we have to think + + + align:start position:0% +goes into that. But um we have to think +about how benefits are shared to all + + align:start position:0% +about how benefits are shared to all + + + align:start position:0% +about how benefits are shared to all +parties involved in a geothermal + + align:start position:0% +parties involved in a geothermal + + + align:start position:0% +parties involved in a geothermal +network. + + align:start position:0% +network. + + + align:start position:0% +network. +And as one final example, you can also + + align:start position:0% +And as one final example, you can also + + + align:start position:0% +And as one final example, you can also +think about what happens as you change + + align:start position:0% +think about what happens as you change + + + align:start position:0% +think about what happens as you change +the number and location of bore holes + + align:start position:0% +the number and location of bore holes + + + align:start position:0% +the number and location of bore holes +around the loop. And here we see that if + + align:start position:0% +around the loop. And here we see that if + + + align:start position:0% +around the loop. And here we see that if +you just think about electricity system + + align:start position:0% +you just think about electricity system + + + align:start position:0% +you just think about electricity system +costs, electricity usage, um more bore + + align:start position:0% +costs, electricity usage, um more bore + + + align:start position:0% +costs, electricity usage, um more bore +holes means less energy is used. um in + + align:start position:0% +holes means less energy is used. um in + + + align:start position:0% +holes means less energy is used. um in +this case because we're not needing any + + align:start position:0% +this case because we're not needing any + + + align:start position:0% +this case because we're not needing any +sort of auxiliary electric boiler. Uh + + align:start position:0% +sort of auxiliary electric boiler. Uh + + + align:start position:0% +sort of auxiliary electric boiler. Uh +but you have to consider that weight + + align:start position:0% +but you have to consider that weight + + + align:start position:0% +but you have to consider that weight +against economic impacts. So how much + + align:start position:0% +against economic impacts. So how much + + + align:start position:0% +against economic impacts. So how much +did they cost? Was that cost worth it? + + align:start position:0% +did they cost? Was that cost worth it? + + + align:start position:0% +did they cost? Was that cost worth it? +What's your trade-off look like there? + + align:start position:0% +What's your trade-off look like there? + + + align:start position:0% +What's your trade-off look like there? +So thank you all for listening to me + + align:start position:0% +So thank you all for listening to me + + + align:start position:0% +So thank you all for listening to me +talk about modeling. I think that + + align:start position:0% +talk about modeling. I think that + + + align:start position:0% +talk about modeling. I think that +modeling can really help us to answer a + + align:start position:0% +modeling can really help us to answer a + + + align:start position:0% +modeling can really help us to answer a +lot of key questions as we move forwards + + align:start position:0% +lot of key questions as we move forwards + + + align:start position:0% +lot of key questions as we move forwards +with building out geothermal networks. + + align:start position:0% +with building out geothermal networks. + + + align:start position:0% +with building out geothermal networks. +Um, one model that we're excited about + + align:start position:0% +Um, one model that we're excited about + + + align:start position:0% +Um, one model that we're excited about +for it is heat nets, which I've talked + + align:start position:0% +for it is heat nets, which I've talked + + + align:start position:0% +for it is heat nets, which I've talked +through some examples of today. Um, but + + align:start position:0% +through some examples of today. Um, but + + + align:start position:0% +through some examples of today. Um, but +again, a lot of great modeling going on + + align:start position:0% +again, a lot of great modeling going on + + + align:start position:0% +again, a lot of great modeling going on +in the space that we're excited for. Um, + + align:start position:0% +in the space that we're excited for. Um, + + + align:start position:0% +in the space that we're excited for. Um, +but we're looking forward to the + + align:start position:0% +but we're looking forward to the + + + align:start position:0% +but we're looking forward to the +opportunity to think about the um, + + align:start position:0% +opportunity to think about the um, + + + align:start position:0% +opportunity to think about the um, +analysis of how these design and + + align:start position:0% +analysis of how these design and + + + align:start position:0% +analysis of how these design and +operational decisions impact both + + align:start position:0% +operational decisions impact both + + + align:start position:0% +operational decisions impact both +performance and economics of these + + align:start position:0% +performance and economics of these + + + align:start position:0% +performance and economics of these +systems. + + align:start position:0% +systems. + + + align:start position:0% +systems. +Thank you. \ No newline at end of file diff --git a/Nn8nBPyzzQ0.txt b/Nn8nBPyzzQ0.txt new file mode 100644 index 0000000000000000000000000000000000000000..5459a54cff4c70822eab98abb26a1a21d66d9cfb --- /dev/null +++ b/Nn8nBPyzzQ0.txt @@ -0,0 +1,9952 @@ +align:start position:0% + +okay uh can people hear me in the back + + align:start position:0% +okay uh can people hear me in the back + + + align:start position:0% +okay uh can people hear me in the back +we good okay nice let's uh let's get + + align:start position:0% +we good okay nice let's uh let's get + + + align:start position:0% +we good okay nice let's uh let's get +started so uh last week uh last week yes + + align:start position:0% +started so uh last week uh last week yes + + + align:start position:0% +started so uh last week uh last week yes +last week uh we started talking about uh + + align:start position:0% +last week uh we started talking about uh + + + align:start position:0% +last week uh we started talking about uh +our number Theory unit and in particular + + align:start position:0% +our number Theory unit and in particular + + + align:start position:0% +our number Theory unit and in particular +Vis visibility uh and we saw a very + + align:start position:0% +Vis visibility uh and we saw a very + + + align:start position:0% +Vis visibility uh and we saw a very +exciting uh you know application of of + + align:start position:0% +exciting uh you know application of of + + + align:start position:0% +exciting uh you know application of of +divisibility saving New York City uh + + align:start position:0% +divisibility saving New York City uh + + + align:start position:0% +divisibility saving New York City uh +today we're going to look at an even + + align:start position:0% +today we're going to look at an even + + + align:start position:0% +today we're going to look at an even +more exciting example um modular + + align:start position:0% +more exciting example um modular + + + align:start position:0% +more exciting example um modular +arithmetic uh so + + align:start position:0% + + + + align:start position:0% + +recall so uh we saw bit's identity and + + align:start position:0% +recall so uh we saw bit's identity and + + + align:start position:0% +recall so uh we saw bit's identity and +uh the + + align:start position:0% +uh the + + + align:start position:0% +uh the +pulverizer so I'll just write that up + + align:start position:0% +pulverizer so I'll just write that up + + + align:start position:0% +pulverizer so I'll just write that up +here so for all + + align:start position:0% +here so for all + + + align:start position:0% +here so for all +integers + + align:start position:0% + + + + align:start position:0% + +uh a + + align:start position:0% + + + + align:start position:0% + +B uh there exists s and + + align:start position:0% +B uh there exists s and + + + align:start position:0% +B uh there exists s and +t whoops such + + align:start position:0% +t whoops such + + + align:start position:0% +t whoops such +that uh that's a little bit confusing + + align:start position:0% +that uh that's a little bit confusing + + + align:start position:0% +that uh that's a little bit confusing +sorry uh + + align:start position:0% +sorry uh + + + align:start position:0% +sorry uh +gcd of a comma b equals a s + b t okay + + align:start position:0% +gcd of a comma b equals a s + b t okay + + + align:start position:0% +gcd of a comma b equals a s + b t okay +and uh moreover we can compute these uh + + align:start position:0% +and uh moreover we can compute these uh + + + align:start position:0% +and uh moreover we can compute these uh +efficiently using the uh the pulverizer + + align:start position:0% +efficiently using the uh the pulverizer + + + align:start position:0% +efficiently using the uh the pulverizer +the extended ukan algorithm + + align:start position:0% +the extended ukan algorithm + + + align:start position:0% +the extended ukan algorithm +uh then the other useful fact that we're + + align:start position:0% +uh then the other useful fact that we're + + + align:start position:0% +uh then the other useful fact that we're +going to make use of + + align:start position:0% +going to make use of + + + align:start position:0% +going to make use of +today + + align:start position:0% + + + + align:start position:0% + +uh every + + align:start position:0% +uh every + + + align:start position:0% +uh every +number + + align:start position:0% +number + + + align:start position:0% +number +uh can be + + align:start position:0% + + + + align:start position:0% + +written as an + + align:start position:0% +written as an + + + align:start position:0% +written as an +ilc of A and B if and only + + align:start position:0% +ilc of A and B if and only + + + align:start position:0% +ilc of A and B if and only +if it is divisible by their gcd + + align:start position:0% + + + + align:start position:0% + +okay so we are going + + align:start position:0% +okay so we are going + + + align:start position:0% +okay so we are going +to make use of these two facts so do not + + align:start position:0% +to make use of these two facts so do not + + + align:start position:0% +to make use of these two facts so do not +forget + + align:start position:0% + + + + align:start position:0% + +okay oh sorry + + align:start position:0% + + + + align:start position:0% + +okay so let's start talking about + + align:start position:0% +okay so let's start talking about + + + align:start position:0% +okay so let's start talking about +modular arithmetic then um I expect that + + align:start position:0% +modular arithmetic then um I expect that + + + align:start position:0% +modular arithmetic then um I expect that +at least in some form it is something + + align:start position:0% +at least in some form it is something + + + align:start position:0% +at least in some form it is something +that's you know fairly familiar to all + + align:start position:0% +that's you know fairly familiar to all + + + align:start position:0% +that's you know fairly familiar to all +of you uh so presumably you learned back + + align:start position:0% +of you uh so presumably you learned back + + + align:start position:0% +of you uh so presumably you learned back +in grade school like what what is the + + align:start position:0% +in grade school like what what is the + + + align:start position:0% +in grade school like what what is the +sum of an even integer and an odd + + align:start position:0% +sum of an even integer and an odd + + + align:start position:0% +sum of an even integer and an odd +integer what what do you know about + + align:start position:0% + + + + align:start position:0% + +it did people not learn this oh yeah + + align:start position:0% +it did people not learn this oh yeah + + + align:start position:0% +it did people not learn this oh yeah +yeah it's odd okay so first example even + + align:start position:0% +yeah it's odd okay so first example even + + + align:start position:0% +yeah it's odd okay so first example even +plus odd is + + align:start position:0% + + + + align:start position:0% + +odd even plus + + align:start position:0% +odd even plus + + + align:start position:0% +odd even plus +odd is + + align:start position:0% +odd is + + + align:start position:0% +odd is +odd okay uh what is the last digit of uh + + align:start position:0% +odd okay uh what is the last digit of uh + + + align:start position:0% +odd okay uh what is the last digit of uh +say + + align:start position:0% +say + + + align:start position:0% +say +357 by + + align:start position:0% + + + + align:start position:0% + +994 yeah eight yeah so ends in eight + + align:start position:0% + + + + align:start position:0% + +okay why is + + align:start position:0% + + + + align:start position:0% + +that yeah you can you can basically + + align:start position:0% +that yeah you can you can basically + + + align:start position:0% +that yeah you can you can basically +ignore everything except the uh the last + + align:start position:0% +ignore everything except the uh the last + + + align:start position:0% +ignore everything except the uh the last +two digits uh you multiply those + + align:start position:0% +two digits uh you multiply those + + + align:start position:0% +two digits uh you multiply those +together you get 28 that ends in an + + align:start position:0% +together you get 28 that ends in an + + + align:start position:0% +together you get 28 that ends in an +eight so this is also going to end in an + + align:start position:0% +eight so this is also going to end in an + + + align:start position:0% +eight so this is also going to end in an +eight okay uh it's currently 2:39 p.m. + + align:start position:0% +eight okay uh it's currently 2:39 p.m. + + + align:start position:0% +eight okay uh it's currently 2:39 p.m. +what time will it be in 49 + + align:start position:0% + + + + align:start position:0% + +hours 330 yeah about + + align:start position:0% + + + + align:start position:0% + +339 in 49 hours and why is + + align:start position:0% + + + + align:start position:0% + +that yeah uh is that an + + align:start position:0% +that yeah uh is that an + + + align:start position:0% +that yeah uh is that an +answer how how are we getting to that + + align:start position:0% +answer how how are we getting to that + + + align:start position:0% +answer how how are we getting to that +yeah yeah so 49 hours is one hour more + + align:start position:0% +yeah yeah so 49 hours is one hour more + + + align:start position:0% +yeah yeah so 49 hours is one hour more +than two full days we can kind of forget + + align:start position:0% +than two full days we can kind of forget + + + align:start position:0% +than two full days we can kind of forget +about those two days and just add an + + align:start position:0% +about those two days and just add an + + + align:start position:0% +about those two days and just add an +hour onto the current time okay uh what + + align:start position:0% +hour onto the current time okay uh what + + + align:start position:0% +hour onto the current time okay uh what +day of the week will it be 100 days from + + align:start position:0% + + + + align:start position:0% + +now Thursday yeah 100 days is uh two + + align:start position:0% +now Thursday yeah 100 days is uh two + + + align:start position:0% +now Thursday yeah 100 days is uh two +days more than uh 14 weeks right so we + + align:start position:0% +days more than uh 14 weeks right so we + + + align:start position:0% +days more than uh 14 weeks right so we +can forget about those 14 weeks add + + align:start position:0% +can forget about those 14 weeks add + + + align:start position:0% +can forget about those 14 weeks add +those two days and we get Thursday okay + + align:start position:0% +those two days and we get Thursday okay + + + align:start position:0% +those two days and we get Thursday okay +so these are all you know fairly + + align:start position:0% +so these are all you know fairly + + + align:start position:0% +so these are all you know fairly +familiar examples to to most of you + + align:start position:0% +familiar examples to to most of you + + + align:start position:0% +familiar examples to to most of you +hopefully of uh modular arithmetic and + + align:start position:0% +hopefully of uh modular arithmetic and + + + align:start position:0% +hopefully of uh modular arithmetic and +the the theme is kind of that when + + align:start position:0% +the the theme is kind of that when + + + align:start position:0% +the the theme is kind of that when +you're when you're working modulo n uh + + align:start position:0% +you're when you're working modulo n uh + + + align:start position:0% +you're when you're working modulo n uh +you're just ignoring all multiples of N + + align:start position:0% +you're just ignoring all multiples of N + + + align:start position:0% +you're just ignoring all multiples of N +and only focusing on remainders okay so + + align:start position:0% +and only focusing on remainders okay so + + + align:start position:0% +and only focusing on remainders okay so +even and odd this is the remainder when + + align:start position:0% +even and odd this is the remainder when + + + align:start position:0% +even and odd this is the remainder when +dividing by two days of the week we + + align:start position:0% +dividing by two days of the week we + + + align:start position:0% +dividing by two days of the week we +divide by seven look at the remainder uh + + align:start position:0% +divide by seven look at the remainder uh + + + align:start position:0% +divide by seven look at the remainder uh +last digit this is you know remainder + + align:start position:0% +last digit this is you know remainder + + + align:start position:0% +last digit this is you know remainder +when we divide by 10 uh our remainder + + align:start position:0% +when we divide by 10 uh our remainder + + + align:start position:0% +when we divide by 10 uh our remainder +when we divide by 12 or 24 depending on + + align:start position:0% +when we divide by 12 or 24 depending on + + + align:start position:0% +when we divide by 12 or 24 depending on +whether you care about AM or + + align:start position:0% +whether you care about AM or + + + align:start position:0% +whether you care about AM or +PM uh and so we often call Modular + + align:start position:0% +PM uh and so we often call Modular + + + align:start position:0% +PM uh and so we often call Modular +arithmetic clock arithmetic for for this + + align:start position:0% +arithmetic clock arithmetic for for this + + + align:start position:0% +arithmetic clock arithmetic for for this +reason uh because it's something that + + align:start position:0% +reason uh because it's something that + + + align:start position:0% +reason uh because it's something that +people are are familiar within that + + align:start position:0% +people are are familiar within that + + + align:start position:0% +people are are familiar within that +context + + align:start position:0% +context + + + align:start position:0% +context +okay so let's define what we mean + + align:start position:0% +okay so let's define what we mean + + + align:start position:0% +okay so let's define what we mean +actually why don't we use a new board + + align:start position:0% +actually why don't we use a new board + + + align:start position:0% +actually why don't we use a new board +for + + align:start position:0% + + + + align:start position:0% + +this so we're going to say that a is + + align:start position:0% +this so we're going to say that a is + + + align:start position:0% +this so we're going to say that a is +congruent n to B so this can be uh that + + align:start position:0% +congruent n to B so this can be uh that + + + align:start position:0% +congruent n to B so this can be uh that +this will usually be pronounced uh a is + + align:start position:0% +this will usually be pronounced uh a is + + + align:start position:0% +this will usually be pronounced uh a is +congruent to b modulo + + align:start position:0% +congruent to b modulo + + + align:start position:0% +congruent to b modulo +n uh if and only + + align:start position:0% + + + + align:start position:0% + +if uh n divides a minus B + + align:start position:0% + + + + align:start position:0% + +okay so you might also see this written + + align:start position:0% +okay so you might also see this written + + + align:start position:0% +okay so you might also see this written +as uh a congruent to + + align:start position:0% +as uh a congruent to + + + align:start position:0% +as uh a congruent to +B mod n who has seen this notation + + align:start position:0% +B mod n who has seen this notation + + + align:start position:0% +B mod n who has seen this notation +before okay many who has seen this + + align:start position:0% +before okay many who has seen this + + + align:start position:0% +before okay many who has seen this +notation uh couple not quite as many + + align:start position:0% +notation uh couple not quite as many + + + align:start position:0% +notation uh couple not quite as many +okay so uh for the purposes of this + + align:start position:0% +okay so uh for the purposes of this + + + align:start position:0% +okay so uh for the purposes of this +class um we're going to you know + + align:start position:0% +class um we're going to you know + + + align:start position:0% +class um we're going to you know +generally be using this notation we're + + align:start position:0% +generally be using this notation we're + + + align:start position:0% +generally be using this notation we're +going to try not to use the the right + + align:start position:0% +going to try not to use the the right + + + align:start position:0% +going to try not to use the the right +one + + align:start position:0% +one + + + align:start position:0% +one +right yes right um and I will explain + + align:start position:0% +right yes right um and I will explain + + + align:start position:0% +right yes right um and I will explain +why in in a few minutes uh the the right + + align:start position:0% +why in in a few minutes uh the the right + + + align:start position:0% +why in in a few minutes uh the the right +one even for people who think they're + + align:start position:0% +one even for people who think they're + + + align:start position:0% +one even for people who think they're +familiar it uh often leads to some uh + + align:start position:0% +familiar it uh often leads to some uh + + + align:start position:0% +familiar it uh often leads to some uh +some confusion okay so let's let's try + + align:start position:0% +some confusion okay so let's let's try + + + align:start position:0% +some confusion okay so let's let's try +and stick with this one until you like + + align:start position:0% +and stick with this one until you like + + + align:start position:0% +and stick with this one until you like +really know what you're doing okay but + + align:start position:0% +really know what you're doing okay but + + + align:start position:0% +really know what you're doing okay but +uh you know for future reference if you + + align:start position:0% +uh you know for future reference if you + + + align:start position:0% +uh you know for future reference if you +see the the right one it means the same + + align:start position:0% +see the the right one it means the same + + + align:start position:0% +see the the right one it means the same +thing + + align:start position:0% +thing + + + align:start position:0% +thing +okay so basically we would like to + + align:start position:0% +okay so basically we would like to + + + align:start position:0% +okay so basically we would like to +consider a and b to be you know the same + + align:start position:0% +consider a and b to be you know the same + + + align:start position:0% +consider a and b to be you know the same +like you can think of this roughly + + align:start position:0% +like you can think of this roughly + + + align:start position:0% +like you can think of this roughly +speaking as + + align:start position:0% +speaking as + + + align:start position:0% +speaking as +equals uh if n divides their + + align:start position:0% +equals uh if n divides their + + + align:start position:0% +equals uh if n divides their +difference okay so for example if we're + + align:start position:0% +difference okay so for example if we're + + + align:start position:0% +difference okay so for example if we're +working modulo 5 there are only you know + + align:start position:0% +working modulo 5 there are only you know + + + align:start position:0% +working modulo 5 there are only you know +five different kind of distinct values + + align:start position:0% +five different kind of distinct values + + + align:start position:0% +five different kind of distinct values +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we're going to notate them like + + align:start position:0% +so we're going to notate them like + + + align:start position:0% +so we're going to notate them like +this so uh that this is uh the + + align:start position:0% +this so uh that this is uh the + + + align:start position:0% +this so uh that this is uh the +congruence class of of Z modu of 5 so + + align:start position:0% +congruence class of of Z modu of 5 so + + + align:start position:0% +congruence class of of Z modu of 5 so +everything that's congruent to to zero + + align:start position:0% +everything that's congruent to to zero + + + align:start position:0% +everything that's congruent to to zero +okay so this is going to be 0 plus orus + + align:start position:0% +okay so this is going to be 0 plus orus + + + align:start position:0% +okay so this is going to be 0 plus orus +5 plus or minus 10 + + align:start position:0% +5 plus or minus 10 + + + align:start position:0% +5 plus or minus 10 +Etc okay so that's you know one set of + + align:start position:0% +Etc okay so that's you know one set of + + + align:start position:0% +Etc okay so that's you know one set of +of values that are the + + align:start position:0% +of values that are the + + + align:start position:0% +of values that are the +same got a second one represented by one + + align:start position:0% +same got a second one represented by one + + + align:start position:0% +same got a second one represented by one +okay and this is going to be you know 1 + + align:start position:0% +okay and this is going to be you know 1 + + + align:start position:0% +okay and this is going to be you know 1 +6 11 uh - 4 - 9 + + align:start position:0% + + + + align:start position:0% + +okay so everything that's equivalent to + + align:start position:0% +okay so everything that's equivalent to + + + align:start position:0% +okay so everything that's equivalent to +one modu + + align:start position:0% + + + + align:start position:0% + +5 and then we've + + align:start position:0% + + + + align:start position:0% + +got three more okay defined + + align:start position:0% +got three more okay defined + + + align:start position:0% +got three more okay defined +analogously okay and so for a general K + + align:start position:0% +analogously okay and so for a general K + + + align:start position:0% +analogously okay and so for a general K +which of these five groups is it going + + align:start position:0% +which of these five groups is it going + + + align:start position:0% +which of these five groups is it going +to belong to like how how would we + + align:start position:0% +to belong to like how how would we + + + align:start position:0% +to belong to like how how would we +figure it + + align:start position:0% + + + + align:start position:0% + +out yeah + + align:start position:0% + + + + align:start position:0% + +yeah so uh the answer was we're going to + + align:start position:0% +yeah so uh the answer was we're going to + + + align:start position:0% +yeah so uh the answer was we're going to +divide it by the the modulus five and + + align:start position:0% +divide it by the the modulus five and + + + align:start position:0% +divide it by the the modulus five and +look at the remainder okay + + align:start position:0% +look at the remainder okay + + + align:start position:0% +look at the remainder okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so a general K is going to be an element + + align:start position:0% +so a general K is going to be an element + + + align:start position:0% +so a general K is going to be an element +of the remainder when we divide K by + + align:start position:0% +of the remainder when we divide K by + + + align:start position:0% +of the remainder when we divide K by +five okay does that make sense to + + align:start position:0% +five okay does that make sense to + + + align:start position:0% +five okay does that make sense to +everybody okay so in particular if we + + align:start position:0% +everybody okay so in particular if we + + + align:start position:0% +everybody okay so in particular if we +write uh you + + align:start position:0% +write uh you + + + align:start position:0% +write uh you +know K = 5 q + r where R is + + align:start position:0% +know K = 5 q + r where R is + + + align:start position:0% +know K = 5 q + r where R is +between + + align:start position:0% +between + + + align:start position:0% +between +zero and five then K is going to be an + + align:start position:0% +zero and five then K is going to be an + + + align:start position:0% +zero and five then K is going to be an +element + + align:start position:0% +element + + + align:start position:0% +element +of this set + + align:start position:0% +of this set + + + align:start position:0% +of this set +okay so that makes sense to + + align:start position:0% +okay so that makes sense to + + + align:start position:0% +okay so that makes sense to +everybody Rec simply happy with + + align:start position:0% +everybody Rec simply happy with + + + align:start position:0% +everybody Rec simply happy with +this okay + + align:start position:0% + + + + align:start position:0% + +so more generally recall the division + + align:start position:0% + + + + align:start position:0% + +theorem okay so the division theorem + + align:start position:0% +theorem okay so the division theorem + + + align:start position:0% +theorem okay so the division theorem +says uh for all pairs um n comma D + + align:start position:0% + + + + align:start position:0% + +with d greater than + + align:start position:0% +with d greater than + + + align:start position:0% +with d greater than +zero there exists a unique pair of + + align:start position:0% +zero there exists a unique pair of + + + align:start position:0% +zero there exists a unique pair of +integers + + align:start position:0% +integers + + + align:start position:0% +integers +uh q and + + align:start position:0% +uh q and + + + align:start position:0% +uh q and +R with uh zero less than or equal to R + + align:start position:0% +R with uh zero less than or equal to R + + + align:start position:0% +R with uh zero less than or equal to R +less than + + align:start position:0% + + + + align:start position:0% + +d uh such + + align:start position:0% +d uh such + + + align:start position:0% +d uh such +that uh n equals QD + r + + align:start position:0% +that uh n equals QD + r + + + align:start position:0% +that uh n equals QD + r +okay uh and we say that Q here is the + + align:start position:0% +okay uh and we say that Q here is the + + + align:start position:0% +okay uh and we say that Q here is the +quotient + + align:start position:0% + + + + align:start position:0% + +and we sometimes denote this as uh div n + + align:start position:0% +and we sometimes denote this as uh div n + + + align:start position:0% +and we sometimes denote this as uh div n +comma D or sometimes we might write this + + align:start position:0% +comma D or sometimes we might write this + + + align:start position:0% +comma D or sometimes we might write this +in infix notation and + + align:start position:0% +in infix notation and + + + align:start position:0% +in infix notation and +div D okay and R is the remainder so + + align:start position:0% +div D okay and R is the remainder so + + + align:start position:0% +div D okay and R is the remainder so +this is going to be uh + + align:start position:0% +this is going to be uh + + + align:start position:0% +this is going to be uh +REM n comma + + align:start position:0% +REM n comma + + + align:start position:0% +REM n comma +D or sometimes we also write this as n + + align:start position:0% +D or sometimes we also write this as n + + + align:start position:0% +D or sometimes we also write this as n +REM + + align:start position:0% +REM + + + align:start position:0% +REM +D okay + + align:start position:0% +D okay + + + align:start position:0% +D okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +sorry oh uh the exclamation after the + + align:start position:0% +sorry oh uh the exclamation after the + + + align:start position:0% +sorry oh uh the exclamation after the +exists this means there exists a unique + + align:start position:0% +exists this means there exists a unique + + + align:start position:0% +exists this means there exists a unique +pair uh so not only does there exist + + align:start position:0% +pair uh so not only does there exist + + + align:start position:0% +pair uh so not only does there exist +some pair but there's only one of them + + align:start position:0% + + + + align:start position:0% + +okay so when working modulo n uh a + + align:start position:0% +okay so when working modulo n uh a + + + align:start position:0% +okay so when working modulo n uh a +number is always going to be equivalent + + align:start position:0% +number is always going to be equivalent + + + align:start position:0% +number is always going to be equivalent +to its remainder sometimes we'll also + + align:start position:0% +to its remainder sometimes we'll also + + + align:start position:0% +to its remainder sometimes we'll also +call this its its residue + + align:start position:0% +call this its its residue + + + align:start position:0% +call this its its residue +okay and you know just as we saw up here + + align:start position:0% +okay and you know just as we saw up here + + + align:start position:0% +okay and you know just as we saw up here +uh these residue + + align:start position:0% +uh these residue + + + align:start position:0% +uh these residue +classes uh form a partition of all of + + align:start position:0% +classes uh form a partition of all of + + + align:start position:0% +classes uh form a partition of all of +the uh of all of the integers okay so oh + + align:start position:0% +the uh of all of the integers okay so oh + + + align:start position:0% +the uh of all of the integers okay so oh +sorry so the the numbers zero up through + + align:start position:0% +sorry so the the numbers zero up through + + + align:start position:0% +sorry so the the numbers zero up through +n minus + + align:start position:0% +n minus + + + align:start position:0% +n minus +one uh these represent you know all of + + align:start position:0% +one uh these represent you know all of + + + align:start position:0% +one uh these represent you know all of +the possible groupings uh modulo n okay + + align:start position:0% + + + + align:start position:0% + +does that make sense to + + align:start position:0% + + + + align:start position:0% + +everybody + + align:start position:0% + + + + align:start position:0% + +okay so the following + + align:start position:0% +okay so the following + + + align:start position:0% +okay so the following +theorem is quite + + align:start position:0% +theorem is quite + + + align:start position:0% +theorem is quite +useful + + align:start position:0% + + + + align:start position:0% + +so A and B are congruent modulo n + + align:start position:0% +so A and B are congruent modulo n + + + align:start position:0% +so A and B are congruent modulo n +if and only + + align:start position:0% + + + + align:start position:0% + +if remainder of a comma + + align:start position:0% +if remainder of a comma + + + align:start position:0% +if remainder of a comma +n is equal to the remainder when you + + align:start position:0% +n is equal to the remainder when you + + + align:start position:0% +n is equal to the remainder when you +divide B by + + align:start position:0% +divide B by + + + align:start position:0% +divide B by +n + + align:start position:0% + + + + align:start position:0% + +okay so how might we prove this + + align:start position:0% +okay so how might we prove this + + + align:start position:0% +okay so how might we prove this +rigorously any ideas + + align:start position:0% + + + + align:start position:0% + +somebody volunteers + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +okay yeah so we're we're going to use + + align:start position:0% +okay yeah so we're we're going to use + + + align:start position:0% +okay yeah so we're we're going to use +the division theorem right the if if we + + align:start position:0% +the division theorem right the if if we + + + align:start position:0% +the division theorem right the if if we +apply the division theorem to to both A + + align:start position:0% +apply the division theorem to to both A + + + align:start position:0% +apply the division theorem to to both A +and B we're going to get the same R okay + + align:start position:0% +and B we're going to get the same R okay + + + align:start position:0% +and B we're going to get the same R okay +I'm going to back up a step first uh at + + align:start position:0% +I'm going to back up a step first uh at + + + align:start position:0% +I'm going to back up a step first uh at +a very high level what do we need to do + + align:start position:0% +a very high level what do we need to do + + + align:start position:0% +a very high level what do we need to do +in order to prove a statement like + + align:start position:0% +in order to prove a statement like + + + align:start position:0% +in order to prove a statement like +this we're trying to prove an if and + + align:start position:0% +this we're trying to prove an if and + + + align:start position:0% +this we're trying to prove an if and +only if we have to prove implications in + + align:start position:0% +only if we have to prove implications in + + + align:start position:0% +only if we have to prove implications in +both directions okay so first + + align:start position:0% +both directions okay so first + + + align:start position:0% +both directions okay so first +direction if uh REM a comma n equals REM + + align:start position:0% +direction if uh REM a comma n equals REM + + + align:start position:0% +direction if uh REM a comma n equals REM +B comma + + align:start position:0% +B comma + + + align:start position:0% +B comma +n then + + align:start position:0% + + + + align:start position:0% + +uh a is congruent mod n to B + + align:start position:0% +uh a is congruent mod n to B + + + align:start position:0% +uh a is congruent mod n to B +okay so we're going to + + align:start position:0% +okay so we're going to + + + align:start position:0% +okay so we're going to +assume that these are equal right so + + align:start position:0% +assume that these are equal right so + + + align:start position:0% +assume that these are equal right so +then the the r that we get from the + + align:start position:0% +then the the r that we get from the + + + align:start position:0% +then the the r that we get from the +division theorem is the same in both + + align:start position:0% +division theorem is the same in both + + + align:start position:0% +division theorem is the same in both +cases so a = q n + r b = q Prime n + + + align:start position:0% +cases so a = q n + r b = q Prime n + + + + align:start position:0% +cases so a = q n + r b = q Prime n + +r + + align:start position:0% +r + + + align:start position:0% +r +okay now what happens when we subtract + + align:start position:0% +okay now what happens when we subtract + + + align:start position:0% +okay now what happens when we subtract +them well then we get a minus b = n * Q + + align:start position:0% +them well then we get a minus b = n * Q + + + align:start position:0% +them well then we get a minus b = n * Q +- Q + + align:start position:0% +- Q + + + align:start position:0% +- Q +prime plus r - R and this is + + align:start position:0% +prime plus r - R and this is + + + align:start position:0% +prime plus r - R and this is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay so now the difference is a multiple + + align:start position:0% +okay so now the difference is a multiple + + + align:start position:0% +okay so now the difference is a multiple +of n so by our definition A and A and B + + align:start position:0% +of n so by our definition A and A and B + + + align:start position:0% +of n so by our definition A and A and B +are + + align:start position:0% +are + + + align:start position:0% +are +congruent okay does that make sense to + + align:start position:0% +congruent okay does that make sense to + + + align:start position:0% +congruent okay does that make sense to +everybody + + align:start position:0% + + + + align:start position:0% + +yeah uh oh so some examples of a n and B + + align:start position:0% +yeah uh oh so some examples of a n and B + + + align:start position:0% +yeah uh oh so some examples of a n and B +okay uh so for example uh 17 is + + align:start position:0% +okay uh so for example uh 17 is + + + align:start position:0% +okay uh so for example uh 17 is +congruent mod 5 to + + align:start position:0% +congruent mod 5 to + + + align:start position:0% +congruent mod 5 to +12 okay because five divides the + + align:start position:0% +12 okay because five divides the + + + align:start position:0% +12 okay because five divides the +difference right if you subtract them + + align:start position:0% +difference right if you subtract them + + + align:start position:0% +difference right if you subtract them +you get five uh five is a multiple of + + align:start position:0% +you get five uh five is a multiple of + + + align:start position:0% +you get five uh five is a multiple of +five so they're congruent okay uh + + align:start position:0% +five so they're congruent okay uh + + + align:start position:0% +five so they're congruent okay uh +17 is also congruent to say + + align:start position:0% +17 is also congruent to say + + + align:start position:0% +17 is also congruent to say +32 right if you subtract these you get5 + + align:start position:0% +32 right if you subtract these you get5 + + + align:start position:0% +32 right if you subtract these you get5 +same deal it's not + + align:start position:0% + + + + align:start position:0% + +congruent to + + align:start position:0% + + + + align:start position:0% + +33 okay if you subtract those you get -6 + + align:start position:0% +33 okay if you subtract those you get -6 + + + align:start position:0% +33 okay if you subtract those you get -6 +which is not a multiple of of + + align:start position:0% +which is not a multiple of of + + + align:start position:0% +which is not a multiple of of +five + + align:start position:0% +five + + + align:start position:0% +five +okay any other questions + + align:start position:0% + + + + align:start position:0% + +yeah okay so well this is only half the + + align:start position:0% +yeah okay so well this is only half the + + + align:start position:0% +yeah okay so well this is only half the +proof right we're we're proving One + + align:start position:0% +proof right we're we're proving One + + + align:start position:0% +proof right we're we're proving One +Direction so we are assuming that uh the + + align:start position:0% +Direction so we are assuming that uh the + + + align:start position:0% +Direction so we are assuming that uh the +two remainders are the same okay and + + align:start position:0% +two remainders are the same okay and + + + align:start position:0% +two remainders are the same okay and +we're trying to prove + + align:start position:0% +we're trying to prove + + + align:start position:0% +we're trying to prove +this right so if the two remainders are + + align:start position:0% +this right so if the two remainders are + + + align:start position:0% +this right so if the two remainders are +the same right that's you know from the + + align:start position:0% +the same right that's you know from the + + + align:start position:0% +the same right that's you know from the +division theorem we've got the same R in + + align:start position:0% +division theorem we've got the same R in + + + align:start position:0% +division theorem we've got the same R in +both + + align:start position:0% +both + + + align:start position:0% +both +cases so uh we're going to write them + + align:start position:0% +cases so uh we're going to write them + + + align:start position:0% +cases so uh we're going to write them +we're going to write both numbers in + + align:start position:0% +we're going to write both numbers in + + + align:start position:0% +we're going to write both numbers in +that form okay so a is qn plus r + + align:start position:0% +that form okay so a is qn plus r + + + align:start position:0% +that form okay so a is qn plus r +r b is QPR n plus r Prime but you know + + align:start position:0% +r b is QPR n plus r Prime but you know + + + align:start position:0% +r b is QPR n plus r Prime but you know +we established that R is equal to R + + align:start position:0% +we established that R is equal to R + + + align:start position:0% +we established that R is equal to R +Prime okay so we're just writing that as + + align:start position:0% +Prime okay so we're just writing that as + + + align:start position:0% +Prime okay so we're just writing that as +Q Prime n uh plus r okay and now in + + align:start position:0% +Q Prime n uh plus r okay and now in + + + align:start position:0% +Q Prime n uh plus r okay and now in +order to show that A and B are + + align:start position:0% +order to show that A and B are + + + align:start position:0% +order to show that A and B are +equivalent we have to subtract and and + + align:start position:0% +equivalent we have to subtract and and + + + align:start position:0% +equivalent we have to subtract and and +see whether the difference is a multiple + + align:start position:0% +see whether the difference is a multiple + + + align:start position:0% +see whether the difference is a multiple +of + + align:start position:0% +of + + + align:start position:0% +of +n so in this case when we subtract them + + align:start position:0% +n so in this case when we subtract them + + + align:start position:0% +n so in this case when we subtract them +right the RS + + align:start position:0% +right the RS + + + align:start position:0% +right the RS +cancel uh the N factors out and we get + + align:start position:0% +cancel uh the N factors out and we get + + + align:start position:0% +cancel uh the N factors out and we get +uh n * Q - Q Prime + + align:start position:0% +uh n * Q - Q Prime + + + align:start position:0% +uh n * Q - Q Prime +okay so that is indeed a multiple of N + + align:start position:0% +okay so that is indeed a multiple of N + + + align:start position:0% +okay so that is indeed a multiple of N +and so uh you know n divides the + + align:start position:0% +and so uh you know n divides the + + + align:start position:0% +and so uh you know n divides the +difference so they're + + align:start position:0% +difference so they're + + + align:start position:0% +difference so they're +equivalent + + align:start position:0% +equivalent + + + align:start position:0% +equivalent +congruent okay + + align:start position:0% + + + + align:start position:0% + +yeah uh how we say this a is congruent + + align:start position:0% +yeah uh how we say this a is congruent + + + align:start position:0% +yeah uh how we say this a is congruent +to B mod n or a is congruent mod n to B + + align:start position:0% +to B mod n or a is congruent mod n to B + + + align:start position:0% +to B mod n or a is congruent mod n to B +uh there are you know several different + + align:start position:0% +uh there are you know several different + + + align:start position:0% +uh there are you know several different +ways of of saying it + + align:start position:0% + + + + align:start position:0% + +okay okay what about going in the other + + align:start position:0% + + + + align:start position:0% + +direction + + align:start position:0% + + + + align:start position:0% + +suppose a is congruent mod n to + + align:start position:0% +suppose a is congruent mod n to + + + align:start position:0% +suppose a is congruent mod n to +B now we want to prove that the + + align:start position:0% +B now we want to prove that the + + + align:start position:0% +B now we want to prove that the +remainders uh when you divide by n are + + align:start position:0% +remainders uh when you divide by n are + + + align:start position:0% +remainders uh when you divide by n are +the same how do we do + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +y + + align:start position:0% + + + + align:start position:0% + +okay okay + + align:start position:0% + + + + align:start position:0% + +okay yeah so the the last step here is + + align:start position:0% +okay yeah so the the last step here is + + + align:start position:0% +okay yeah so the the last step here is +now to use the division theorem again + + align:start position:0% +now to use the division theorem again + + + align:start position:0% +now to use the division theorem again +okay so if we apply the division theorem + + align:start position:0% +okay so if we apply the division theorem + + + align:start position:0% +okay so if we apply the division theorem +I guess to B is probably going to be the + + align:start position:0% +I guess to B is probably going to be the + + + align:start position:0% +I guess to B is probably going to be the +most useful right we can write b equals + + align:start position:0% +most useful right we can write b equals + + + align:start position:0% +most useful right we can write b equals +let's do the same form that we had there + + align:start position:0% +let's do the same form that we had there + + + align:start position:0% +let's do the same form that we had there +Q Prime n + + + align:start position:0% +Q Prime n + + + + align:start position:0% +Q Prime n + +r + + align:start position:0% +r + + + align:start position:0% +r +okay now a is B plus k + + align:start position:0% +okay now a is B plus k + + + align:start position:0% +okay now a is B plus k +n so that's going to be Q prime plus + + align:start position:0% +n so that's going to be Q prime plus + + + align:start position:0% +n so that's going to be Q prime plus +K * n plus + + align:start position:0% +K * n plus + + + align:start position:0% +K * n plus +r okay and now the division theorem says + + align:start position:0% +r okay and now the division theorem says + + + align:start position:0% +r okay and now the division theorem says +that this Q prime plus K and R those are + + align:start position:0% +that this Q prime plus K and R those are + + + align:start position:0% +that this Q prime plus K and R those are +unique okay so that Q prime plus K is + + align:start position:0% +unique okay so that Q prime plus K is + + + align:start position:0% +unique okay so that Q prime plus K is +the the Q that we need and the the r is + + align:start position:0% +the the Q that we need and the the r is + + + align:start position:0% +the the Q that we need and the the r is +the same + + align:start position:0% +the same + + + align:start position:0% +the same +okay so both of them have the same + + align:start position:0% + + + + align:start position:0% + +remainder okay do does this make sense + + align:start position:0% +remainder okay do does this make sense + + + align:start position:0% +remainder okay do does this make sense +to everybody + + align:start position:0% + + + + align:start position:0% + +yeah uh a congruent to B mod + + align:start position:0% +yeah uh a congruent to B mod + + + align:start position:0% +yeah uh a congruent to B mod +n uh so what we're trying to prove an if + + align:start position:0% +n uh so what we're trying to prove an if + + + align:start position:0% +n uh so what we're trying to prove an if +and only if here right so for One + + align:start position:0% +and only if here right so for One + + + align:start position:0% +and only if here right so for One +Direction we're assuming one side and + + align:start position:0% +Direction we're assuming one side and + + + align:start position:0% +Direction we're assuming one side and +trying to prove the other and for the + + align:start position:0% +trying to prove the other and for the + + + align:start position:0% +trying to prove the other and for the +other direction like we did the + + align:start position:0% +other direction like we did the + + + align:start position:0% +other direction like we did the +opposite right so this is One Direction + + align:start position:0% +opposite right so this is One Direction + + + align:start position:0% +opposite right so this is One Direction +we're + + align:start position:0% +we're + + + align:start position:0% +we're +assuming that the remainders are the + + align:start position:0% +assuming that the remainders are the + + + align:start position:0% +assuming that the remainders are the +same and we want to prove that they're + + align:start position:0% +same and we want to prove that they're + + + align:start position:0% +same and we want to prove that they're +equivalent they're congruent for the + + align:start position:0% +equivalent they're congruent for the + + + align:start position:0% +equivalent they're congruent for the +other direction we assume that they're + + align:start position:0% +other direction we assume that they're + + + align:start position:0% +other direction we assume that they're +congruent and then we want to prove that + + align:start position:0% +congruent and then we want to prove that + + + align:start position:0% +congruent and then we want to prove that +the remainders are the same okay so kind + + align:start position:0% +the remainders are the same okay so kind + + + align:start position:0% +the remainders are the same okay so kind +of two separate proofs + + align:start position:0% + + + + align:start position:0% + +any other + + align:start position:0% + + + + align:start position:0% + +questions okay so yeah in in some sense + + align:start position:0% +questions okay so yeah in in some sense + + + align:start position:0% +questions okay so yeah in in some sense +we can consider you know the the N + + align:start position:0% +we can consider you know the the N + + + align:start position:0% +we can consider you know the the N +different numbers like 0 through n minus + + align:start position:0% +different numbers like 0 through n minus + + + align:start position:0% +different numbers like 0 through n minus +one to be you know the only numbers we + + align:start position:0% +one to be you know the only numbers we + + + align:start position:0% +one to be you know the only numbers we +care about when when working mod n okay + + align:start position:0% +care about when when working mod n okay + + + align:start position:0% +care about when when working mod n okay +everything else is going to be + + align:start position:0% +everything else is going to be + + + align:start position:0% +everything else is going to be +equivalent to one of those it's going to + + align:start position:0% +equivalent to one of those it's going to + + + align:start position:0% +equivalent to one of those it's going to +be equivalent to its + + align:start position:0% +be equivalent to its + + + align:start position:0% +be equivalent to its +remainder + + align:start position:0% +remainder + + + align:start position:0% +remainder +okay uh so I'm going to take a moment + + align:start position:0% +okay uh so I'm going to take a moment + + + align:start position:0% +okay uh so I'm going to take a moment +here to talk about + + align:start position:0% + + + + align:start position:0% + +notation + + align:start position:0% +notation + + + align:start position:0% +notation +okay uh so the remainder which we've + + align:start position:0% +okay uh so the remainder which we've + + + align:start position:0% +okay uh so the remainder which we've +called uh REM a comma + + align:start position:0% + + + + align:start position:0% + +n uh so + + align:start position:0% +n uh so + + + align:start position:0% +n uh so +our convention right is that uh you know + + align:start position:0% +our convention right is that uh you know + + + align:start position:0% +our convention right is that uh you know +even if n is negative this remainder + + align:start position:0% +even if n is negative this remainder + + + align:start position:0% +even if n is negative this remainder +should always be positive okay not + + align:start position:0% +should always be positive okay not + + + align:start position:0% +should always be positive okay not +everybody uses this convention uh so + + align:start position:0% +everybody uses this convention uh so + + + align:start position:0% +everybody uses this convention uh so +particular in in particular when you're + + align:start position:0% +particular in in particular when you're + + + align:start position:0% +particular in in particular when you're +dealing with uh programming languages um + + align:start position:0% +dealing with uh programming languages um + + + align:start position:0% +dealing with uh programming languages um +most have you know some operation that + + align:start position:0% +most have you know some operation that + + + align:start position:0% +most have you know some operation that +looks like + + align:start position:0% +looks like + + + align:start position:0% +looks like +this uh it may be denoted uh differently + + align:start position:0% +this uh it may be denoted uh differently + + + align:start position:0% +this uh it may be denoted uh differently +in different languages um like sometimes + + align:start position:0% +in different languages um like sometimes + + + align:start position:0% +in different languages um like sometimes +it's a percent sign sometimes it's + + align:start position:0% +it's a percent sign sometimes it's + + + align:start position:0% +it's a percent sign sometimes it's +actually you know rem or mod or + + align:start position:0% +actually you know rem or mod or + + + align:start position:0% +actually you know rem or mod or +something like that and uh sometimes + + align:start position:0% +something like that and uh sometimes + + + align:start position:0% +something like that and uh sometimes +it'll behave the same as as you know how + + align:start position:0% +it'll behave the same as as you know how + + + align:start position:0% +it'll behave the same as as you know how +we def it sometimes it'll be allowed to + + align:start position:0% +we def it sometimes it'll be allowed to + + + align:start position:0% +we def it sometimes it'll be allowed to +be negative so like if n is negative the + + align:start position:0% +be negative so like if n is negative the + + + align:start position:0% +be negative so like if n is negative the +remainder might be negative or something + + align:start position:0% +remainder might be negative or something + + + align:start position:0% +remainder might be negative or something +like that okay and uh some languages + + align:start position:0% +like that okay and uh some languages + + + align:start position:0% +like that okay and uh some languages +have + + align:start position:0% +have + + + align:start position:0% +have +both uh usually with different names + + align:start position:0% +both uh usually with different names + + + align:start position:0% +both uh usually with different names +like uh you know mod versus double + + align:start position:0% +like uh you know mod versus double + + + align:start position:0% +like uh you know mod versus double +mod uh in this class whenever we write + + align:start position:0% +mod uh in this class whenever we write + + + align:start position:0% +mod uh in this class whenever we write +uh RAM m a comma n we always mean the + + align:start position:0% +uh RAM m a comma n we always mean the + + + align:start position:0% +uh RAM m a comma n we always mean the +the positive uh or the the non- negative + + align:start position:0% +the positive uh or the the non- negative + + + align:start position:0% +the positive uh or the the non- negative +remainder so this is always going to be + + align:start position:0% +remainder so this is always going to be + + + align:start position:0% +remainder so this is always going to be +you know between + + align:start position:0% +you know between + + + align:start position:0% +you know between +zero and uh n + + align:start position:0% +zero and uh n + + + align:start position:0% +zero and uh n +okay um and perhaps even more + + align:start position:0% +okay um and perhaps even more + + + align:start position:0% +okay um and perhaps even more +confusing uh sometimes this would be + + align:start position:0% +confusing uh sometimes this would be + + + align:start position:0% +confusing uh sometimes this would be +written + + align:start position:0% +written + + + align:start position:0% +written +as mod of a comma n or even worse an + + align:start position:0% +as mod of a comma n or even worse an + + + align:start position:0% +as mod of a comma n or even worse an +infix not a uh a + + align:start position:0% +infix not a uh a + + + align:start position:0% +infix not a uh a +mod n okay so this is why we don't like + + align:start position:0% +mod n okay so this is why we don't like + + + align:start position:0% +mod n okay so this is why we don't like +to use uh the word mod when talking + + align:start position:0% +to use uh the word mod when talking + + + align:start position:0% +to use uh the word mod when talking +about modular uh + + align:start position:0% +about modular uh + + + align:start position:0% +about modular uh +congruences + + align:start position:0% +congruences + + + align:start position:0% +congruences +um because if you see something like uh + + align:start position:0% +um because if you see something like uh + + + align:start position:0% +um because if you see something like uh +say AAL B mod n what does that mean + + align:start position:0% + + + + align:start position:0% + +who can tell me what that + + align:start position:0% + + + + align:start position:0% + +means + + align:start position:0% + + + + align:start position:0% + +MH yeah do do do you have a uh a + + align:start position:0% + + + + align:start position:0% + +guess okay and what why is that + + align:start position:0% + + + + align:start position:0% + +yeah the answer was that's just the + + align:start position:0% +yeah the answer was that's just the + + + align:start position:0% +yeah the answer was that's just the +definition um yeah so the the the + + align:start position:0% +definition um yeah so the the the + + + align:start position:0% +definition um yeah so the the the +important distinction here is between + + align:start position:0% +important distinction here is between + + + align:start position:0% +important distinction here is between +these two things + + align:start position:0% + + + + align:start position:0% + +right right these are very different + + align:start position:0% +right right these are very different + + + align:start position:0% +right right these are very different +statements okay the mod here is kind of + + align:start position:0% +statements okay the mod here is kind of + + + align:start position:0% +statements okay the mod here is kind of +attached to this uh equivalence uh + + align:start position:0% +attached to this uh equivalence uh + + + align:start position:0% +attached to this uh equivalence uh +sign and uh so this is you know talking + + align:start position:0% +sign and uh so this is you know talking + + + align:start position:0% +sign and uh so this is you know talking +about a relation between A and B okay + + align:start position:0% +about a relation between A and B okay + + + align:start position:0% +about a relation between A and B okay +this is a function written in infix + + align:start position:0% +this is a function written in infix + + + align:start position:0% +this is a function written in infix +notation okay so that this is saying + + align:start position:0% +notation okay so that this is saying + + + align:start position:0% +notation okay so that this is saying +that you know a is actually equal to the + + align:start position:0% +that you know a is actually equal to the + + + align:start position:0% +that you know a is actually equal to the +one value uh that you get when you you + + align:start position:0% +one value uh that you get when you you + + + align:start position:0% +one value uh that you get when you you +know divide B by n and take the + + align:start position:0% +know divide B by n and take the + + + align:start position:0% +know divide B by n and take the +remainder okay so these mean different + + align:start position:0% +remainder okay so these mean different + + + align:start position:0% +remainder okay so these mean different +things it is going to be much less + + align:start position:0% +things it is going to be much less + + + align:start position:0% +things it is going to be much less +confusing if you use uh you know a + + align:start position:0% +confusing if you use uh you know a + + + align:start position:0% +confusing if you use uh you know a +equals B + + align:start position:0% +equals B + + + align:start position:0% +equals B +REM n or you know in prefix notation REM + + align:start position:0% +REM n or you know in prefix notation REM + + + align:start position:0% +REM n or you know in prefix notation REM +B comma n + + align:start position:0% +B comma n + + + align:start position:0% +B comma n +uh for the left one and a congruent mod + + align:start position:0% +uh for the left one and a congruent mod + + + align:start position:0% +uh for the left one and a congruent mod +n to B for the right one okay so it's + + align:start position:0% +n to B for the right one okay so it's + + + align:start position:0% +n to B for the right one okay so it's +hopefully much more obvious what the + + align:start position:0% +hopefully much more obvious what the + + + align:start position:0% +hopefully much more obvious what the +distinction is between you know these + + align:start position:0% +distinction is between you know these + + + align:start position:0% +distinction is between you know these +two things than between these two things + + align:start position:0% +two things than between these two things + + + align:start position:0% +two things than between these two things +so please use the ones on the bottom + + align:start position:0% +so please use the ones on the bottom + + + align:start position:0% +so please use the ones on the bottom +until you are you know very comfortable + + align:start position:0% +until you are you know very comfortable + + + align:start position:0% +until you are you know very comfortable +with with modular arithmetic + + align:start position:0% + + + + align:start position:0% + +okay okay so let's go uh let's go back + + align:start position:0% +okay okay so let's go uh let's go back + + + align:start position:0% +okay okay so let's go uh let's go back +to the actual content now + + align:start position:0% + + + + align:start position:0% + +so as I promised before we're actually + + align:start position:0% +so as I promised before we're actually + + + align:start position:0% +so as I promised before we're actually +going to be talking about arithmetic so + + align:start position:0% +going to be talking about arithmetic so + + + align:start position:0% +going to be talking about arithmetic so +let's let's start on that okay so the + + align:start position:0% +let's let's start on that okay so the + + + align:start position:0% +let's let's start on that okay so the +the simple statement that we wrote up + + align:start position:0% +the simple statement that we wrote up + + + align:start position:0% +the simple statement that we wrote up +there on the on the left even plus odd + + align:start position:0% +there on the on the left even plus odd + + + align:start position:0% +there on the on the left even plus odd +equals uh equals odd in some sense + + align:start position:0% +equals uh equals odd in some sense + + + align:start position:0% +equals uh equals odd in some sense +that's saying something kind of profound + + align:start position:0% +that's saying something kind of profound + + + align:start position:0% +that's saying something kind of profound +right like you know no matter which + + align:start position:0% +right like you know no matter which + + + align:start position:0% +right like you know no matter which +uh even number and which odd number you + + align:start position:0% +uh even number and which odd number you + + + align:start position:0% +uh even number and which odd number you +pick if you add them together you're + + align:start position:0% +pick if you add them together you're + + + align:start position:0% +pick if you add them together you're +always going to get an odd number + + align:start position:0% +always going to get an odd number + + + align:start position:0% +always going to get an odd number +okay uh and you know more generally if + + align:start position:0% +okay uh and you know more generally if + + + align:start position:0% +okay uh and you know more generally if +we take you know any a congruent to + + align:start position:0% +we take you know any a congruent to + + + align:start position:0% +we take you know any a congruent to +let's say 3 mod 5 and any B congruent + + align:start position:0% +let's say 3 mod 5 and any B congruent + + + align:start position:0% +let's say 3 mod 5 and any B congruent +mod 5 to say + + align:start position:0% +mod 5 to say + + + align:start position:0% +mod 5 to say +four right if you add + + align:start position:0% +four right if you add + + + align:start position:0% +four right if you add +them what do you know about it + + align:start position:0% +them what do you know about it + + + align:start position:0% +them what do you know about it +what do you know about their + + align:start position:0% + + + + align:start position:0% + +sum + + align:start position:0% +sum + + + align:start position:0% +sum +yeah + + align:start position:0% + + + + align:start position:0% + +mhm so their sum is always going to be + + align:start position:0% +mhm so their sum is always going to be + + + align:start position:0% +mhm so their sum is always going to be +congruent to two module of five okay or + + align:start position:0% +congruent to two module of five okay or + + + align:start position:0% +congruent to two module of five okay or +perhaps uh an + + align:start position:0% + + + + align:start position:0% + +easier thing to + + align:start position:0% +easier thing to + + + align:start position:0% +easier thing to +see is it's always going to be + + align:start position:0% +see is it's always going to be + + + align:start position:0% +see is it's always going to be +equivalent to s + + align:start position:0% + + + + align:start position:0% + +which is in turn you know congruent to + + align:start position:0% +which is in turn you know congruent to + + + align:start position:0% +which is in turn you know congruent to +two + + align:start position:0% +two + + + align:start position:0% +two +Okay so adding A and B module of 5 like + + align:start position:0% +Okay so adding A and B module of 5 like + + + align:start position:0% +Okay so adding A and B module of 5 like +you you get the same result as if you + + align:start position:0% +you you get the same result as if you + + + align:start position:0% +you you get the same result as if you +you know add these two equivalent + + align:start position:0% +you know add these two equivalent + + + align:start position:0% +you know add these two equivalent +remainders + + align:start position:0% + + + + align:start position:0% + +okay so we have a + + align:start position:0% + + + + align:start position:0% + +theorem suppose + + align:start position:0% + + + + align:start position:0% + +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +A and B are equivalent mod + + align:start position:0% +A and B are equivalent mod + + + align:start position:0% +A and B are equivalent mod +n then for all C we have the + + align:start position:0% +n then for all C we have the + + + align:start position:0% +n then for all C we have the +following uh I have space here so a + + + align:start position:0% +following uh I have space here so a + + + + align:start position:0% +following uh I have space here so a + +C is congruent to B+ + + align:start position:0% +C is congruent to B+ + + + align:start position:0% +C is congruent to B+ +C uh a minus C is congruent to B minus C + + align:start position:0% +C uh a minus C is congruent to B minus C + + + align:start position:0% +C uh a minus C is congruent to B minus C +uh C minus a is congruent to C minus + + align:start position:0% +uh C minus a is congruent to C minus + + + align:start position:0% +uh C minus a is congruent to C minus +b and a * + + align:start position:0% +b and a * + + + align:start position:0% +b and a * +C is congruent to B * + + align:start position:0% +C is congruent to B * + + + align:start position:0% +C is congruent to B * +C + + align:start position:0% + + + + align:start position:0% + +okay so as you might expect you know if + + align:start position:0% +okay so as you might expect you know if + + + align:start position:0% +okay so as you might expect you know if +you want to add subtract or or multiply + + align:start position:0% +you want to add subtract or or multiply + + + align:start position:0% +you want to add subtract or or multiply +modulo n you're kind of allowed to + + align:start position:0% +modulo n you're kind of allowed to + + + align:start position:0% +modulo n you're kind of allowed to +replace things wherever you want with uh + + align:start position:0% +replace things wherever you want with uh + + + align:start position:0% +replace things wherever you want with uh +something it's equivalent to + + align:start position:0% +something it's equivalent to + + + align:start position:0% +something it's equivalent to +okay so at any point during this + + align:start position:0% +okay so at any point during this + + + align:start position:0% +okay so at any point during this +computation you can you know replace uh + + align:start position:0% +computation you can you know replace uh + + + align:start position:0% +computation you can you know replace uh +oh sorry different A and B uh that this + + align:start position:0% +oh sorry different A and B uh that this + + + align:start position:0% +oh sorry different A and B uh that this +this is not relevant for the theorem + + align:start position:0% +this is not relevant for the theorem + + + align:start position:0% +this is not relevant for the theorem +statement like if if a and b are + + align:start position:0% +statement like if if a and b are + + + align:start position:0% +statement like if if a and b are +equivalent then you can you know replace + + align:start position:0% +equivalent then you can you know replace + + + align:start position:0% +equivalent then you can you know replace +A's with B's wherever you want and + + align:start position:0% +A's with B's wherever you want and + + + align:start position:0% +A's with B's wherever you want and +you'll get the same + + align:start position:0% +you'll get the same + + + align:start position:0% +you'll get the same +result okay do does that make sense + + align:start position:0% + + + + align:start position:0% + +uh okay so + + align:start position:0% + + + + align:start position:0% + +question what + + align:start position:0% +question what + + + align:start position:0% +question what +about a to the C and B to the C + + align:start position:0% + + + + align:start position:0% + +so let's assume that uh you know C is + + align:start position:0% +so let's assume that uh you know C is + + + align:start position:0% +so let's assume that uh you know C is +positive for + + align:start position:0% + + + + align:start position:0% + +now can I say anything about + + align:start position:0% +now can I say anything about + + + align:start position:0% +now can I say anything about +exponentiation modu + + align:start position:0% +exponentiation modu + + + align:start position:0% +exponentiation modu +n okay if we assume that uh A and B are + + align:start position:0% +n okay if we assume that uh A and B are + + + align:start position:0% +n okay if we assume that uh A and B are +congruent modu n can we say anything + + align:start position:0% +congruent modu n can we say anything + + + align:start position:0% +congruent modu n can we say anything +about a to the C versus B to the + + align:start position:0% +about a to the C versus B to the + + + align:start position:0% +about a to the C versus B to the +c yeah + + align:start position:0% + + + + align:start position:0% + +yeah so uh let let me rephrase that + + align:start position:0% +yeah so uh let let me rephrase that + + + align:start position:0% +yeah so uh let let me rephrase that +slightly I you can prove it more + + align:start position:0% +slightly I you can prove it more + + + align:start position:0% +slightly I you can prove it more +formally by induction + + align:start position:0% +formally by induction + + + align:start position:0% +formally by induction +okay right so you can repeatedly + + align:start position:0% +okay right so you can repeatedly + + + align:start position:0% +okay right so you can repeatedly +multiply every multiplication is going + + align:start position:0% +multiply every multiplication is going + + + align:start position:0% +multiply every multiplication is going +to give you you know congruent values + + align:start position:0% +to give you you know congruent values + + + align:start position:0% +to give you you know congruent values +okay so by the time you get to to a + + align:start position:0% +okay so by the time you get to to a + + + align:start position:0% +okay so by the time you get to to a +power of C there's still going to be + + align:start position:0% +power of C there's still going to be + + + align:start position:0% +power of C there's still going to be +congruent okay so yes this is true and + + align:start position:0% +congruent okay so yes this is true and + + + align:start position:0% +congruent okay so yes this is true and +proof by + + align:start position:0% + + + + align:start position:0% + +induction on C okay so our base + + align:start position:0% +induction on C okay so our base + + + align:start position:0% +induction on C okay so our base +case is going to be when C equals 1 okay + + align:start position:0% +case is going to be when C equals 1 okay + + + align:start position:0% +case is going to be when C equals 1 okay +in this case you know our assumption is + + align:start position:0% +in this case you know our assumption is + + + align:start position:0% +in this case you know our assumption is +that a is congruent to + + align:start position:0% +that a is congruent to + + + align:start position:0% +that a is congruent to +B right so a to the 1 is congruent to a + + align:start position:0% +B right so a to the 1 is congruent to a + + + align:start position:0% +B right so a to the 1 is congruent to a +well it's equal to a b to the 1 is equal + + align:start position:0% +well it's equal to a b to the 1 is equal + + + align:start position:0% +well it's equal to a b to the 1 is equal +to B so this is + + align:start position:0% +to B so this is + + + align:start position:0% +to B so this is +fine uh our inductive + + align:start position:0% +fine uh our inductive + + + align:start position:0% +fine uh our inductive +step so + + align:start position:0% +step so + + + align:start position:0% +step so +assume that a to the cus one is + + align:start position:0% +assume that a to the cus one is + + + align:start position:0% +assume that a to the cus one is +congruent mod n to B to the + + align:start position:0% +congruent mod n to B to the + + + align:start position:0% +congruent mod n to B to the +cus1 okay now what happens when we uh + + align:start position:0% +cus1 okay now what happens when we uh + + + align:start position:0% +cus1 okay now what happens when we uh +when we increment our exponent + + align:start position:0% + + + + align:start position:0% + +what is a to the + + align:start position:0% + + + + align:start position:0% + +C + + align:start position:0% +C + + + align:start position:0% +C +yeah + + align:start position:0% + + + + align:start position:0% + +mhm okay so we can uh you know strip off + + align:start position:0% +mhm okay so we can uh you know strip off + + + align:start position:0% +mhm okay so we can uh you know strip off +a a a factor of + + align:start position:0% + + + + align:start position:0% + +a now we can replace each of these + + align:start position:0% +a now we can replace each of these + + + align:start position:0% +a now we can replace each of these +factors + + align:start position:0% +factors + + + align:start position:0% +factors +individually + + align:start position:0% +individually + + + align:start position:0% +individually +okay so by our theorem up there this is + + align:start position:0% +okay so by our theorem up there this is + + + align:start position:0% +okay so by our theorem up there this is +congruent to B the cus one * a okay we + + align:start position:0% +congruent to B the cus one * a okay we + + + align:start position:0% +congruent to B the cus one * a okay we +can replace this + + align:start position:0% + + + + align:start position:0% + +factor and now by our uh theorem + + align:start position:0% +factor and now by our uh theorem + + + align:start position:0% +factor and now by our uh theorem +assumption right we can replace this + + align:start position:0% +assumption right we can replace this + + + align:start position:0% +assumption right we can replace this +Factor as well + + align:start position:0% + + + + align:start position:0% + +okay does that make sense to + + align:start position:0% + + + + align:start position:0% + +everybody okay what + + align:start position:0% +everybody okay what + + + align:start position:0% +everybody okay what +about C to the + + align:start position:0% + + + + align:start position:0% + +A and C to the B + + align:start position:0% + + + + align:start position:0% + +so we just saw that when we're working + + align:start position:0% +so we just saw that when we're working + + + align:start position:0% +so we just saw that when we're working +modu n we're allowed to you know replace + + align:start position:0% +modu n we're allowed to you know replace + + + align:start position:0% +modu n we're allowed to you know replace +uh the base of exponents as we like can + + align:start position:0% +uh the base of exponents as we like can + + + align:start position:0% +uh the base of exponents as we like can +we do the same thing with the with the + + align:start position:0% +we do the same thing with the with the + + + align:start position:0% +we do the same thing with the with the +uh exponents + + align:start position:0% + + + + align:start position:0% + +themselves show pounds for + + align:start position:0% + + + + align:start position:0% + +yes show pounds for + + align:start position:0% +yes show pounds for + + + align:start position:0% +yes show pounds for +no okay no it seems like it's winning + + align:start position:0% +no okay no it seems like it's winning + + + align:start position:0% +no okay no it seems like it's winning +out by popular vote but not by much + + align:start position:0% +out by popular vote but not by much + + + align:start position:0% +out by popular vote but not by much +there are a lot of extensions + + align:start position:0% +there are a lot of extensions + + + align:start position:0% +there are a lot of extensions +uh can anybody give me a reason why or + + align:start position:0% +uh can anybody give me a reason why or + + + align:start position:0% +uh can anybody give me a reason why or +why + + align:start position:0% + + + + align:start position:0% + +not + + align:start position:0% + + + + align:start position:0% + +yeah uh 2^2 is not congruent mod 5 to + + align:start position:0% +yeah uh 2^2 is not congruent mod 5 to + + + align:start position:0% +yeah uh 2^2 is not congruent mod 5 to +what 2 + + align:start position:0% +what 2 + + + align:start position:0% +what 2 +cubed + + align:start position:0% +cubed + + + align:start position:0% +cubed +uh okay that is a true statement um does + + align:start position:0% +uh okay that is a true statement um does + + + align:start position:0% +uh okay that is a true statement um does +that uh does + + align:start position:0% + + + + align:start position:0% + +that yeah so you you are correct that we + + align:start position:0% +that yeah so you you are correct that we + + + align:start position:0% +that yeah so you you are correct that we +only need one counter example um is this + + align:start position:0% +only need one counter example um is this + + + align:start position:0% +only need one counter example um is this +a counter + + align:start position:0% + + + + align:start position:0% + +example so let's see so the the the + + align:start position:0% +example so let's see so the the the + + + align:start position:0% +example so let's see so the the the +claim right is that if a is congruent to + + align:start position:0% +claim right is that if a is congruent to + + + align:start position:0% +claim right is that if a is congruent to +B mod n then C to the a is congruent to + + align:start position:0% +B mod n then C to the a is congruent to + + + align:start position:0% +B mod n then C to the a is congruent to +C to the B right we haven't satisfied + + align:start position:0% +C to the B right we haven't satisfied + + + align:start position:0% +C to the B right we haven't satisfied +our precondition here two is not + + align:start position:0% +our precondition here two is not + + + align:start position:0% +our precondition here two is not +congruent to three Mod Five okay so you + + align:start position:0% +congruent to three Mod Five okay so you + + + align:start position:0% +congruent to three Mod Five okay so you +you are you have the uh the right idea + + align:start position:0% +you are you have the uh the right idea + + + align:start position:0% +you are you have the uh the right idea +we do want to find a single counter + + align:start position:0% +we do want to find a single counter + + + align:start position:0% +we do want to find a single counter +example that will suffice to disprove + + align:start position:0% +example that will suffice to disprove + + + align:start position:0% +example that will suffice to disprove +this uh we're going to need a different + + align:start position:0% +this uh we're going to need a different + + + align:start position:0% +this uh we're going to need a different +counter example if we want this to + + align:start position:0% +counter example if we want this to + + + align:start position:0% +counter example if we want this to +work okay does anybody else have an idea + + align:start position:0% +work okay does anybody else have an idea + + + align:start position:0% +work okay does anybody else have an idea +for a counter example or failing that + + align:start position:0% +for a counter example or failing that + + + align:start position:0% +for a counter example or failing that +does any have a + + align:start position:0% + + + + align:start position:0% + +proof + + align:start position:0% + + + + align:start position:0% + +yeah okay uh what are the smaller + + align:start position:0% +yeah okay uh what are the smaller + + + align:start position:0% +yeah okay uh what are the smaller +components like factors of of C + + align:start position:0% +components like factors of of C + + + align:start position:0% +components like factors of of C +yeah okay + + align:start position:0% +yeah okay + + + align:start position:0% +yeah okay +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so what do you want to do with those + + align:start position:0% +so what do you want to do with those + + + align:start position:0% +so what do you want to do with those +factors of + + align:start position:0% +factors of + + + align:start position:0% +factors of +C I suppose we could you know strip off + + align:start position:0% +C I suppose we could you know strip off + + + align:start position:0% +C I suppose we could you know strip off +you know say a is smaller than b we + + align:start position:0% +you know say a is smaller than b we + + + align:start position:0% +you know say a is smaller than b we +could strip off a of + + align:start position:0% + + + + align:start position:0% + +them okay so you want to divide out a + + align:start position:0% +them okay so you want to divide out a + + + align:start position:0% +them okay so you want to divide out a +bunch of factors of uh C and until we + + align:start position:0% +bunch of factors of uh C and until we + + + align:start position:0% +bunch of factors of uh C and until we +get something like + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +okay + + align:start position:0% + + + + align:start position:0% + +um how do you divide modern + + align:start position:0% + + + + align:start position:0% + +okay let's look at a concrete + + align:start position:0% +okay let's look at a concrete + + + align:start position:0% +okay let's look at a concrete +example so let's uh keep trying to to + + align:start position:0% +example so let's uh keep trying to to + + + align:start position:0% +example so let's uh keep trying to to +look at + + align:start position:0% +look at + + + align:start position:0% +look at +five let's say B minus a is also + + align:start position:0% + + + + align:start position:0% + +five is this a true statement + + align:start position:0% + + + + align:start position:0% + +sorry did did somebody + + align:start position:0% + + + + align:start position:0% + +um is this true for all + + align:start position:0% + + + + align:start position:0% + +C so I I claim that minus one is not + + align:start position:0% +C so I I claim that minus one is not + + + align:start position:0% +C so I I claim that minus one is not +going to work + + align:start position:0% + + + + align:start position:0% + +here right yeah + + align:start position:0% + + + + align:start position:0% + +yeah so anything to the zeroth power is + + align:start position:0% +yeah so anything to the zeroth power is + + + align:start position:0% +yeah so anything to the zeroth power is +is one that's that's fine uh the the + + align:start position:0% +is one that's that's fine uh the the + + + align:start position:0% +is one that's that's fine uh the the +problem is uh you know we're + + align:start position:0% +problem is uh you know we're + + + align:start position:0% +problem is uh you know we're +subtracting a from both of these + + align:start position:0% +subtracting a from both of these + + + align:start position:0% +subtracting a from both of these +exponents + + align:start position:0% +exponents + + + align:start position:0% +exponents +right so if say you have b equal 5 plus + + align:start position:0% +right so if say you have b equal 5 plus + + + align:start position:0% +right so if say you have b equal 5 plus +a right you're going to end up with five + + align:start position:0% +a right you're going to end up with five + + + align:start position:0% +a right you're going to end up with five +on on the the right hand + + align:start position:0% +on on the the right hand + + + align:start position:0% +on on the the right hand +side + + align:start position:0% + + + + align:start position:0% + +right so counter example right is going + + align:start position:0% +right so counter example right is going + + + align:start position:0% +right so counter example right is going +to be you + + align:start position:0% +to be you + + + align:start position:0% +to be you +know maybe we could have something like + + align:start position:0% +know maybe we could have something like + + + align:start position:0% +know maybe we could have something like +you know C to the one and C to the 6 and + + align:start position:0% +you know C to the one and C to the 6 and + + + align:start position:0% +you know C to the one and C to the 6 and +in particular we're going to want C to + + align:start position:0% +in particular we're going to want C to + + + align:start position:0% +in particular we're going to want C to +be minus + + align:start position:0% + + + + align:start position:0% + +one okay + + align:start position:0% +one okay + + + align:start position:0% +one okay +uh n was five that's + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +okay so this is our counter example + + align:start position:0% +okay so this is our counter example + + + align:start position:0% +okay so this is our counter example +right we've exhibited a specific a B and + + align:start position:0% +right we've exhibited a specific a B and + + + align:start position:0% +right we've exhibited a specific a B and +N where our you know uh purported + + align:start position:0% +N where our you know uh purported + + + align:start position:0% +N where our you know uh purported +theorem statement + + align:start position:0% +theorem statement + + + align:start position:0% +theorem statement +fails okay it is not the case that minus + + align:start position:0% +fails okay it is not the case that minus + + + align:start position:0% +fails okay it is not the case that minus +1 1 is congruent mod 5 to min-1 6 right + + align:start position:0% +1 1 is congruent mod 5 to min-1 6 right + + + align:start position:0% +1 1 is congruent mod 5 to min-1 6 right +the left hand side isus one the right + + align:start position:0% +the left hand side isus one the right + + + align:start position:0% +the left hand side isus one the right +right hand side is positive + + align:start position:0% + + + + align:start position:0% + +one okay so when exponentiating we have + + align:start position:0% +one okay so when exponentiating we have + + + align:start position:0% +one okay so when exponentiating we have +to be careful we are allowed to replace + + align:start position:0% +to be careful we are allowed to replace + + + align:start position:0% +to be careful we are allowed to replace +the bases of exponents we're not allowed + + align:start position:0% +the bases of exponents we're not allowed + + + align:start position:0% +the bases of exponents we're not allowed +to replace the exponents + + align:start position:0% + + + + align:start position:0% + +themselves + + align:start position:0% + + + + align:start position:0% + +okay so we will see in a little while + + align:start position:0% +okay so we will see in a little while + + + align:start position:0% +okay so we will see in a little while +how we can uh you know get around this + + align:start position:0% +how we can uh you know get around this + + + align:start position:0% +how we can uh you know get around this +to some degree we can do something with + + align:start position:0% +to some degree we can do something with + + + align:start position:0% +to some degree we can do something with +the exponents it's just not + + align:start position:0% +the exponents it's just not + + + align:start position:0% +the exponents it's just not +this + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh why don't we take a look at an + + align:start position:0% +uh why don't we take a look at an + + + align:start position:0% +uh why don't we take a look at an +example + + align:start position:0% +example + + + align:start position:0% +example +first + + align:start position:0% +first + + + align:start position:0% +first +so suppose X is 1 + + align:start position:0% +so suppose X is 1 + + + align:start position:0% +so suppose X is 1 +1335 to the + + align:start position:0% +1335 to the + + + align:start position:0% +1335 to the +11111 uh multiplied by 6 + + + align:start position:0% +11111 uh multiplied by 6 + + + + align:start position:0% +11111 uh multiplied by 6 + +7799 to the 5 + + align:start position:0% + + + + align:start position:0% + +okay uh how might we + + align:start position:0% +okay uh how might we + + + align:start position:0% +okay uh how might we +compute remainder of X after we divide + + align:start position:0% +compute remainder of X after we divide + + + align:start position:0% +compute remainder of X after we divide +by + + align:start position:0% + + + + align:start position:0% + +100 okay how can we use the uh two + + align:start position:0% +100 okay how can we use the uh two + + + align:start position:0% +100 okay how can we use the uh two +theorems that we did prove to compute + + align:start position:0% +theorems that we did prove to compute + + + align:start position:0% +theorems that we did prove to compute +that efficiently + + align:start position:0% + + + + align:start position:0% + +what might our first step + + align:start position:0% + + + + align:start position:0% + +be uh okay so the answer was distribute + + align:start position:0% +be uh okay so the answer was distribute + + + align:start position:0% +be uh okay so the answer was distribute +this uh across this + + align:start position:0% +this uh across this + + + align:start position:0% +this uh across this +addition um I claim that that's going to + + align:start position:0% +addition um I claim that that's going to + + + align:start position:0% +addition um I claim that that's going to +make our lives harder not easier + + align:start position:0% + + + + align:start position:0% + +so what what was the theme of the two + + align:start position:0% +so what what was the theme of the two + + + align:start position:0% +so what what was the theme of the two +theorems that we just + + align:start position:0% +theorems that we just + + + align:start position:0% +theorems that we just +proved if we want to do computations + + align:start position:0% +proved if we want to do computations + + + align:start position:0% +proved if we want to do computations +modul + + align:start position:0% +modul + + + align:start position:0% +modul +n we can replace things by you know + + align:start position:0% +n we can replace things by you know + + + align:start position:0% +n we can replace things by you know +other numbers that are easier to work + + align:start position:0% +other numbers that are easier to work + + + align:start position:0% +other numbers that are easier to work +with uh and which are congruent + + align:start position:0% +with uh and which are congruent + + + align:start position:0% +with uh and which are congruent +okay so Computing the remainder when we + + align:start position:0% +okay so Computing the remainder when we + + + align:start position:0% +okay so Computing the remainder when we +divide by 100 right + + align:start position:0% +divide by 100 right + + + align:start position:0% +divide by 100 right +that's looking for a computation modul + + align:start position:0% +that's looking for a computation modul + + + align:start position:0% +that's looking for a computation modul +100 okay so we can replace these values + + align:start position:0% +100 okay so we can replace these values + + + align:start position:0% +100 okay so we can replace these values +modul 100 and make them easier to work + + align:start position:0% +modul 100 and make them easier to work + + + align:start position:0% +modul 100 and make them easier to work +with + + align:start position:0% +with + + + align:start position:0% +with +Okay are any of these values that I've + + align:start position:0% +Okay are any of these values that I've + + + align:start position:0% +Okay are any of these values that I've +written down uh congruent to anything + + align:start position:0% +written down uh congruent to anything + + + align:start position:0% +written down uh congruent to anything +nice modu 100 + + align:start position:0% + + + + align:start position:0% + +anyone + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah yeah so we can just get rid of + + align:start position:0% +yeah yeah so we can just get rid of + + + align:start position:0% +yeah yeah so we can just get rid of +these right that's congruent to + + align:start position:0% +these right that's congruent to + + + align:start position:0% +these right that's congruent to +35 what else can we + + align:start position:0% +35 what else can we + + + align:start position:0% +35 what else can we +do yeah + + align:start position:0% + + + + align:start position:0% + +uh so we're we're Computing modul 100 + + align:start position:0% +uh so we're we're Computing modul 100 + + + align:start position:0% +uh so we're we're Computing modul 100 +right we're looking for the remainder + + align:start position:0% +right we're looking for the remainder + + + align:start position:0% +right we're looking for the remainder +when we divide by + + align:start position:0% +when we divide by + + + align:start position:0% +when we divide by +100 uh so we know that uh one whoops + + align:start position:0% + + + + align:start position:0% + +1335 is congruent to 35 modul + + align:start position:0% +1335 is congruent to 35 modul + + + align:start position:0% +1335 is congruent to 35 modul + + align:start position:0% + + + align:start position:0% +okay yeah so we're we're getting rid of + + align:start position:0% +okay yeah so we're we're getting rid of + + + align:start position:0% +okay yeah so we're we're getting rid of +the the first three digits and only + + align:start position:0% +the the first three digits and only + + + align:start position:0% +the the first three digits and only +looking at the remainder after we divide + + align:start position:0% +looking at the remainder after we divide + + + align:start position:0% +looking at the remainder after we divide +by 100 + + align:start position:0% +by 100 + + + align:start position:0% +by 100 +okay so basically the the idea is that + + align:start position:0% +okay so basically the the idea is that + + + align:start position:0% +okay so basically the the idea is that +we can do this division you know at + + align:start position:0% +we can do this division you know at + + + align:start position:0% +we can do this division you know at +intermediate + + align:start position:0% +intermediate + + + align:start position:0% +intermediate +steps we we can you know take remainders + + align:start position:0% +steps we we can you know take remainders + + + align:start position:0% +steps we we can you know take remainders +uh in the middle of our computation okay + + align:start position:0% +uh in the middle of our computation okay + + + align:start position:0% +uh in the middle of our computation okay +that's that's what these two theorems + + align:start position:0% +that's that's what these two theorems + + + align:start position:0% +that's that's what these two theorems +are are telling + + align:start position:0% +are are telling + + + align:start position:0% +are are telling +us okay anything else that we can + + align:start position:0% + + + + align:start position:0% + +simplify no does somebody want to do + + align:start position:0% +simplify no does somebody want to do + + + align:start position:0% +simplify no does somebody want to do +that computation by + + align:start position:0% +that computation by + + + align:start position:0% +that computation by +hand no nobody yeah okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay okay yeah we can do the same thing + + align:start position:0% +okay okay yeah we can do the same thing + + + align:start position:0% +okay okay yeah we can do the same thing +here turn that into just + + align:start position:0% +here turn that into just + + + align:start position:0% +here turn that into just + + align:start position:0% + + + align:start position:0% +um I claim that we can take that a step + + align:start position:0% + + + + align:start position:0% + +further 99 is not particularly easy to + + align:start position:0% +further 99 is not particularly easy to + + + align:start position:0% +further 99 is not particularly easy to +work with I claim that there's something + + align:start position:0% +work with I claim that there's something + + + align:start position:0% +work with I claim that there's something +else it's equivalent to that + + align:start position:0% +else it's equivalent to that + + + align:start position:0% +else it's equivalent to that +is + + align:start position:0% +is + + + align:start position:0% +is +yeah uh not zero negative one yeah + + align:start position:0% +yeah uh not zero negative one yeah + + + align:start position:0% +yeah uh not zero negative one yeah +so we can replace the 7799 with negative + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +Okay negative 1 is easy to work + + align:start position:0% +Okay negative 1 is easy to work + + + align:start position:0% +Okay negative 1 is easy to work +with + + align:start position:0% +with + + + align:start position:0% +with +Okay so now what + + align:start position:0% + + + + align:start position:0% + +happens yeah + + align:start position:0% + + + + align:start position:0% + +yeah okay so let's exponentiate this + + align:start position:0% +yeah okay so let's exponentiate this + + + align:start position:0% +yeah okay so let's exponentiate this +negative + + align:start position:0% +negative + + + align:start position:0% +negative +1 so we end up with 6 + 1 which is + + align:start position:0% + + + + align:start position:0% + +7 now what do we do about 35 to the uh + + align:start position:0% + + + + align:start position:0% + +11,111 uh we don't really know how to do + + align:start position:0% +11,111 uh we don't really know how to do + + + align:start position:0% +11,111 uh we don't really know how to do +anything with with exponents + + align:start position:0% +anything with with exponents + + + align:start position:0% +anything with with exponents +right so let's kind of just try to start + + align:start position:0% +right so let's kind of just try to start + + + align:start position:0% +right so let's kind of just try to start +exponentiating it and see what + + align:start position:0% +exponentiating it and see what + + + align:start position:0% +exponentiating it and see what +happens + + align:start position:0% +happens + + + align:start position:0% +happens +okay + + align:start position:0% + + + + align:start position:0% + +so what's 35 + + align:start position:0% + + + + align:start position:0% + +squ that's going to be uh well if we + + align:start position:0% +squ that's going to be uh well if we + + + align:start position:0% +squ that's going to be uh well if we +actually compute it it'll be 1225 right + + align:start position:0% +actually compute it it'll be 1225 right + + + align:start position:0% +actually compute it it'll be 1225 right +I + + align:start position:0% +I + + + align:start position:0% +I +think is that right 1175 + + align:start position:0% + + + + align:start position:0% + +1225 okay so that's going to be + + align:start position:0% +1225 okay so that's going to be + + + align:start position:0% +1225 okay so that's going to be +congruent to + + align:start position:0% +congruent to + + + align:start position:0% +congruent to + + align:start position:0% + + + + align:start position:0% + +okay 35 + + align:start position:0% + + + + align:start position:0% + +cubed well it's going to be 25 * + + align:start position:0% +cubed well it's going to be 25 * + + + align:start position:0% +cubed well it's going to be 25 * +35 okay so that's 875 so that's that's + + align:start position:0% +35 okay so that's 875 so that's that's + + + align:start position:0% +35 okay so that's 875 so that's that's +going to be congruent to 75 + + align:start position:0% + + + + align:start position:0% + +okay 35 to + + align:start position:0% + + + + align:start position:0% + +4th uh 35 to 4th is going to be 35 squar + + align:start position:0% +4th uh 35 to 4th is going to be 35 squar + + + align:start position:0% +4th uh 35 to 4th is going to be 35 squar +squared again so 25 + + align:start position:0% +squared again so 25 + + + align:start position:0% +squared again so 25 +squ okay 25 squ is 625 that also has a + + align:start position:0% +squ okay 25 squ is 625 that also has a + + + align:start position:0% +squ okay 25 squ is 625 that also has a +remainder of + + align:start position:0% + + + + align:start position:0% + +25 so what's going to happen after this + + align:start position:0% +25 so what's going to happen after this + + + align:start position:0% +25 so what's going to happen after this +point + + align:start position:0% +point + + + align:start position:0% +point +what happens is we continue multiplying + + align:start position:0% +what happens is we continue multiplying + + + align:start position:0% +what happens is we continue multiplying +by + + align:start position:0% + + + + align:start position:0% + +35 yeah the answer was it'll alternate + + align:start position:0% +35 yeah the answer was it'll alternate + + + align:start position:0% +35 yeah the answer was it'll alternate +between 75 and 25 right whenever we have + + align:start position:0% +between 75 and 25 right whenever we have + + + align:start position:0% +between 75 and 25 right whenever we have +an odd power as long as it's greater + + align:start position:0% +an odd power as long as it's greater + + + align:start position:0% +an odd power as long as it's greater +than one right uh when we exponentiate + + align:start position:0% +than one right uh when we exponentiate + + + align:start position:0% +than one right uh when we exponentiate +uh 35 it's going to be 75 whenever we + + align:start position:0% +uh 35 it's going to be 75 whenever we + + + align:start position:0% +uh 35 it's going to be 75 whenever we +have an even power it's going to be + + align:start position:0% +have an even power it's going to be + + + align:start position:0% +have an even power it's going to be +25 okay you can you know prove that + + align:start position:0% +25 okay you can you know prove that + + + align:start position:0% +25 okay you can you know prove that +formally by + + align:start position:0% +formally by + + + align:start position:0% +formally by +induction not going to do that here but + + align:start position:0% +induction not going to do that here but + + + align:start position:0% +induction not going to do that here but +the point is 35 we've got an odd + + align:start position:0% +the point is 35 we've got an odd + + + align:start position:0% +the point is 35 we've got an odd +exponent here so we can replace + + align:start position:0% + + + + align:start position:0% + +this with + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +okay and now 75 * + + align:start position:0% +okay and now 75 * + + + align:start position:0% +okay and now 75 * +7 is going to have a remainder of + + align:start position:0% + + + + align:start position:0% + +25 okay + + align:start position:0% + + + + align:start position:0% + +okay so does that make sense to + + align:start position:0% +okay so does that make sense to + + + align:start position:0% +okay so does that make sense to +everybody we perform the computation but + + align:start position:0% +everybody we perform the computation but + + + align:start position:0% +everybody we perform the computation but +instead of just like doing it over the + + align:start position:0% +instead of just like doing it over the + + + align:start position:0% +instead of just like doing it over the +integers and then reducing mod 100 right + + align:start position:0% +integers and then reducing mod 100 right + + + align:start position:0% +integers and then reducing mod 100 right +we're reducing mod 100 you know whenever + + align:start position:0% +we're reducing mod 100 you know whenever + + + align:start position:0% +we're reducing mod 100 you know whenever +we can we're we're always trying to + + align:start position:0% +we can we're we're always trying to + + + align:start position:0% +we can we're we're always trying to +replace intermediate values with things + + align:start position:0% +replace intermediate values with things + + + align:start position:0% +replace intermediate values with things +that are easier to work with okay and + + align:start position:0% +that are easier to work with okay and + + + align:start position:0% +that are easier to work with okay and +that simplifies our computation + + align:start position:0% +that simplifies our computation + + + align:start position:0% +that simplifies our computation +considerably yeah + + align:start position:0% + + + + align:start position:0% + +uh you can perform the computation uh 25 + + align:start position:0% +uh you can perform the computation uh 25 + + + align:start position:0% +uh you can perform the computation uh 25 +by 21 is possibly an easier one to + + align:start position:0% + + + + align:start position:0% + +do + + align:start position:0% + + + + align:start position:0% + +okay okay uh any other + + align:start position:0% +okay okay uh any other + + + align:start position:0% +okay okay uh any other +questions yeah + + align:start position:0% + + + + align:start position:0% + +yes uh so uh we had six plus -1 to the + + align:start position:0% +yes uh so uh we had six plus -1 to the + + + align:start position:0% +yes uh so uh we had six plus -1 to the +5K okay uh so we are you know + + align:start position:0% +5K okay uh so we are you know + + + align:start position:0% +5K okay uh so we are you know +exponentiating this this negative 1 over + + align:start position:0% +exponentiating this this negative 1 over + + + align:start position:0% +exponentiating this this negative 1 over +the integers right negative 1 to uh any + + align:start position:0% +the integers right negative 1 to uh any + + + align:start position:0% +the integers right negative 1 to uh any +even power is going to be + + align:start position:0% +even power is going to be + + + align:start position:0% +even power is going to be +one okay so + + align:start position:0% +one okay so + + + align:start position:0% +one okay so +we + + align:start position:0% +we + + + align:start position:0% +we +sorry oh sorry uh 5K 5,000 + + align:start position:0% +sorry oh sorry uh 5K 5,000 + + + align:start position:0% +sorry oh sorry uh 5K 5,000 +sorry it's it's not actually + + align:start position:0% +sorry it's it's not actually + + + align:start position:0% +sorry it's it's not actually +um yeah my + + align:start position:0% +um yeah my + + + align:start position:0% +um yeah my +bad this this kind of + + align:start position:0% + + + + align:start position:0% + +K + + align:start position:0% +K + + + align:start position:0% +K +okay sorry that's that's that's my bad + + align:start position:0% +okay sorry that's that's that's my bad + + + align:start position:0% +okay sorry that's that's that's my bad +any other + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% + + + + align:start position:0% + +yeah pardon + + align:start position:0% + + + + align:start position:0% + +like oh okay so the the question was is + + align:start position:0% +like oh okay so the the question was is + + + align:start position:0% +like oh okay so the the question was is +there always going to be a pattern like + + align:start position:0% +there always going to be a pattern like + + + align:start position:0% +there always going to be a pattern like +this uh so this is kind of touching on + + align:start position:0% +this uh so this is kind of touching on + + + align:start position:0% +this uh so this is kind of touching on +um stuff that we will see later but yes + + align:start position:0% +um stuff that we will see later but yes + + + align:start position:0% +um stuff that we will see later but yes +there will always be some pattern it may + + align:start position:0% +there will always be some pattern it may + + + align:start position:0% +there will always be some pattern it may +not be this easy to + + align:start position:0% +not be this easy to + + + align:start position:0% +not be this easy to +find right but you know the basic idea + + align:start position:0% +find right but you know the basic idea + + + align:start position:0% +find right but you know the basic idea +right is that there are only 100 + + align:start position:0% +right is that there are only 100 + + + align:start position:0% +right is that there are only 100 +different values that it that it could + + align:start position:0% +different values that it that it could + + + align:start position:0% +different values that it that it could +take you know modul + + align:start position:0% +take you know modul + + + align:start position:0% +take you know modul +100 right so if you have you know more + + align:start position:0% +100 right so if you have you know more + + + align:start position:0% +100 right so if you have you know more +than 100 + + align:start position:0% +than 100 + + + align:start position:0% +than 100 +Powers right something's going to have + + align:start position:0% +Powers right something's going to have + + + align:start position:0% +Powers right something's going to have +to collide okay and you know at that + + align:start position:0% +to collide okay and you know at that + + + align:start position:0% +to collide okay and you know at that +point it'll start + + align:start position:0% +point it'll start + + + align:start position:0% +point it'll start +repeating uh here it you know it it + + align:start position:0% +repeating uh here it you know it it + + + align:start position:0% +repeating uh here it you know it it +happened to be quite nice it started + + align:start position:0% +happened to be quite nice it started + + + align:start position:0% +happened to be quite nice it started +repeating you know very quickly in the + + align:start position:0% +repeating you know very quickly in the + + + align:start position:0% +repeating you know very quickly in the +the period is only two uh that may not + + align:start position:0% +the period is only two uh that may not + + + align:start position:0% +the period is only two uh that may not +always be the case though okay but we we + + align:start position:0% +always be the case though okay but we we + + + align:start position:0% +always be the case though okay but we we +will see in a moment how to uh uh you + + align:start position:0% +will see in a moment how to uh uh you + + + align:start position:0% +will see in a moment how to uh uh you +know something more about uh about what + + align:start position:0% +know something more about uh about what + + + align:start position:0% +know something more about uh about what +we can say about that okay + + align:start position:0% + + + + align:start position:0% + +okay so we we've seen how to add + + align:start position:0% +okay so we we've seen how to add + + + align:start position:0% +okay so we we've seen how to add +subtract multiply how to change the + + align:start position:0% +subtract multiply how to change the + + + align:start position:0% +subtract multiply how to change the +bases of exponents what about + + align:start position:0% +bases of exponents what about + + + align:start position:0% +bases of exponents what about +division okay are we allowed to divide + + align:start position:0% +division okay are we allowed to divide + + + align:start position:0% +division okay are we allowed to divide +modulo n so suppose we + + align:start position:0% +modulo n so suppose we + + + align:start position:0% +modulo n so suppose we +have 3x is + + align:start position:0% +have 3x is + + + align:start position:0% +have 3x is +congruent uh to 3 modul 6 + + align:start position:0% + + + + align:start position:0% + +okay so if we had this over the integers + + align:start position:0% +okay so if we had this over the integers + + + align:start position:0% +okay so if we had this over the integers +say or over the reals right uh I guess + + align:start position:0% +say or over the reals right uh I guess + + + align:start position:0% +say or over the reals right uh I guess +reals are a better example if we just + + align:start position:0% +reals are a better example if we just + + + align:start position:0% +reals are a better example if we just +had you know 3x = 3 how would we solve + + align:start position:0% +had you know 3x = 3 how would we solve + + + align:start position:0% +had you know 3x = 3 how would we solve +this for + + align:start position:0% + + + + align:start position:0% + +X it's it's not a trick question I + + align:start position:0% + + + + align:start position:0% + +promise yeah yeah you just divide both + + align:start position:0% +promise yeah yeah you just divide both + + + align:start position:0% +promise yeah yeah you just divide both +sides by three right you you can cancel + + align:start position:0% +sides by three right you you can cancel + + + align:start position:0% +sides by three right you you can cancel +off this three and you just just get xal + + align:start position:0% +off this three and you just just get xal + + + align:start position:0% +off this three and you just just get xal +1 okay so now the actual question is can + + align:start position:0% +1 okay so now the actual question is can + + + align:start position:0% +1 okay so now the actual question is can +we do that you know modu n can we do + + align:start position:0% +we do that you know modu n can we do + + + align:start position:0% +we do that you know modu n can we do +that modu of 6 are we allowed to just + + align:start position:0% +that modu of 6 are we allowed to just + + + align:start position:0% +that modu of 6 are we allowed to just +cancel these threes and + + align:start position:0% + + + + align:start position:0% + +conclude that uh oops X is congruent to + + align:start position:0% +conclude that uh oops X is congruent to + + + align:start position:0% +conclude that uh oops X is congruent to +one modul + + align:start position:0% +one modul + + + align:start position:0% +one modul + + align:start position:0% + + + + align:start position:0% + +yeah okay uh so the answer is yes + + align:start position:0% +yeah okay uh so the answer is yes + + + align:start position:0% +yeah okay uh so the answer is yes +because it's the same as multiplying by + + align:start position:0% +because it's the same as multiplying by + + + align:start position:0% +because it's the same as multiplying by +1/3 okay uh so remember that 1/3 is not + + align:start position:0% +1/3 okay uh so remember that 1/3 is not + + + align:start position:0% +1/3 okay uh so remember that 1/3 is not +really uh something that we can like it + + align:start position:0% +really uh something that we can like it + + + align:start position:0% +really uh something that we can like it +it doesn't really make sense modulo + + align:start position:0% +it doesn't really make sense modulo + + + align:start position:0% +it doesn't really make sense modulo +modul + + align:start position:0% +modul + + + align:start position:0% +modul +n okay or at least not modul 6 you know + + align:start position:0% +n okay or at least not modul 6 you know + + + align:start position:0% +n okay or at least not modul 6 you know +sometimes it might make sense sometimes + + align:start position:0% +sometimes it might make sense sometimes + + + align:start position:0% +sometimes it might make sense sometimes +it might not we'll see more about that + + align:start position:0% +it might not we'll see more about that + + + align:start position:0% +it might not we'll see more about that +in a + + align:start position:0% +in a + + + align:start position:0% +in a +moment um but like what is a third right + + align:start position:0% +moment um but like what is a third right + + + align:start position:0% +moment um but like what is a third right +we're talking about + + align:start position:0% + + + + align:start position:0% + +integers + + align:start position:0% +integers + + + align:start position:0% +integers +yeah so + + align:start position:0% + + + + align:start position:0% + +sorry so other way around multiply + + align:start position:0% +sorry so other way around multiply + + + align:start position:0% +sorry so other way around multiply +instead of + + align:start position:0% +instead of + + + align:start position:0% +instead of +dividing okay uh so the suggestion was + + align:start position:0% +dividing okay uh so the suggestion was + + + align:start position:0% +dividing okay uh so the suggestion was +instead of dividing by three let's try + + align:start position:0% +instead of dividing by three let's try + + + align:start position:0% +instead of dividing by three let's try +multiplying by something so that we get + + align:start position:0% +multiplying by something so that we get + + + align:start position:0% +multiplying by something so that we get +one + + align:start position:0% +one + + + align:start position:0% +one +here okay so let's you know try to + + align:start position:0% +here okay so let's you know try to + + + align:start position:0% +here okay so let's you know try to +multiply this like you know multiply + + align:start position:0% +multiply this like you know multiply + + + align:start position:0% +multiply this like you know multiply +both sides by some + + align:start position:0% +both sides by some + + + align:start position:0% +both sides by some +a and this should end up being one if we + + align:start position:0% +a and this should end up being one if we + + + align:start position:0% +a and this should end up being one if we +choose our a + + align:start position:0% +choose our a + + + align:start position:0% +choose our a +appropriately + + align:start position:0% +appropriately + + + align:start position:0% +appropriately +okay what a do we + + align:start position:0% + + + + align:start position:0% + +choose does there exist such an + + align:start position:0% + + + + align:start position:0% + +a yeah + + align:start position:0% + + + + align:start position:0% + +yeah okay so the original claim is + + align:start position:0% +yeah okay so the original claim is + + + align:start position:0% +yeah okay so the original claim is +false uh the counter example right is + + align:start position:0% +false uh the counter example right is + + + align:start position:0% +false uh the counter example right is +that we could take X's three here right + + align:start position:0% +that we could take X's three here right + + + align:start position:0% +that we could take X's three here right +3 * 3 is is 9 that is congruent to + + align:start position:0% +3 * 3 is is 9 that is congruent to + + + align:start position:0% +3 * 3 is is 9 that is congruent to +three right but X is not congruent to + + align:start position:0% +three right but X is not congruent to + + + align:start position:0% +three right but X is not congruent to +one + + align:start position:0% +one + + + align:start position:0% +one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the answer I guess to the to the + + align:start position:0% +so the answer I guess to the to the + + + align:start position:0% +so the answer I guess to the to the +follow-up question is that no there is + + align:start position:0% +follow-up question is that no there is + + + align:start position:0% +follow-up question is that no there is +there's no such a right we cannot divide + + align:start position:0% +there's no such a right we cannot divide + + + align:start position:0% +there's no such a right we cannot divide +by three or you know multiply by + + align:start position:0% +by three or you know multiply by + + + align:start position:0% +by three or you know multiply by +something to to uh get one + + align:start position:0% +something to to uh get one + + + align:start position:0% +something to to uh get one +okay and this is you know basically the + + align:start position:0% +okay and this is you know basically the + + + align:start position:0% +okay and this is you know basically the +same thing that we were doing last week + + align:start position:0% +same thing that we were doing last week + + + align:start position:0% +same thing that we were doing last week +right we're looking for a solution to + + align:start position:0% +right we're looking for a solution to + + + align:start position:0% +right we're looking for a solution to +you know 3 a is congruent to 1 modul + + align:start position:0% +you know 3 a is congruent to 1 modul + + + align:start position:0% +you know 3 a is congruent to 1 modul +6 right if we unpack what this uh + + align:start position:0% +6 right if we unpack what this uh + + + align:start position:0% +6 right if we unpack what this uh +actually + + align:start position:0% +actually + + + align:start position:0% +actually +means 6 divides 3 a - + + align:start position:0% +means 6 divides 3 a - + + + align:start position:0% +means 6 divides 3 a - + + align:start position:0% + + + align:start position:0% +okay is there a solution to + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +no + + align:start position:0% + + + + align:start position:0% + +okay so basically that's asking if we + + align:start position:0% +okay so basically that's asking if we + + + align:start position:0% +okay so basically that's asking if we +can uh write one as a linear combination + + align:start position:0% +can uh write one as a linear combination + + + align:start position:0% +can uh write one as a linear combination +of six and three okay + + align:start position:0% +of six and three okay + + + align:start position:0% +of six and three okay +but one is not a multiple of their gcd + + align:start position:0% +but one is not a multiple of their gcd + + + align:start position:0% +but one is not a multiple of their gcd +so we + + align:start position:0% + + + + align:start position:0% + +cannot okay does that make sense to + + align:start position:0% +cannot okay does that make sense to + + + align:start position:0% +cannot okay does that make sense to +everybody so we cannot always + + align:start position:0% +everybody so we cannot always + + + align:start position:0% +everybody so we cannot always +divide are there circumstances under + + align:start position:0% +divide are there circumstances under + + + align:start position:0% +divide are there circumstances under +which we can divide + + align:start position:0% + + + + align:start position:0% + +yeah uh oh okay so the idea was divide + + align:start position:0% +yeah uh oh okay so the idea was divide + + + align:start position:0% +yeah uh oh okay so the idea was divide +to divide the six as well um yeah I + + align:start position:0% +to divide the six as well um yeah I + + + align:start position:0% +to divide the six as well um yeah I +suppose he could do that um but we are + + align:start position:0% +suppose he could do that um but we are + + + align:start position:0% +suppose he could do that um but we are +looking you know we are specifically + + align:start position:0% +looking you know we are specifically + + + align:start position:0% +looking you know we are specifically +trying to do arithmetic modul 6 so that + + align:start position:0% +trying to do arithmetic modul 6 so that + + + align:start position:0% +trying to do arithmetic modul 6 so that +may or may not make sense right um + + align:start position:0% + + + + align:start position:0% + +but I mean yeah I suppose you could say + + align:start position:0% +but I mean yeah I suppose you could say + + + align:start position:0% +but I mean yeah I suppose you could say +you know six divides uh 3x - 3 a and so + + align:start position:0% +you know six divides uh 3x - 3 a and so + + + align:start position:0% +you know six divides uh 3x - 3 a and so +you could you know factor out a three + + align:start position:0% +you could you know factor out a three + + + align:start position:0% +you could you know factor out a three +and say that you know X is at least + + align:start position:0% +and say that you know X is at least + + + align:start position:0% +and say that you know X is at least +all and in fact that that does + + align:start position:0% +all and in fact that that does + + + align:start position:0% +all and in fact that that does +characterize the solutions to the uh to + + align:start position:0% +characterize the solutions to the uh to + + + align:start position:0% +characterize the solutions to the uh to +the original problem it's just that may + + align:start position:0% +the original problem it's just that may + + + align:start position:0% +the original problem it's just that may +or may not you know that may or may not + + align:start position:0% +or may not you know that may or may not + + + align:start position:0% +or may not you know that may or may not +be what you're actually looking for okay + + align:start position:0% + + + + align:start position:0% + +okay so under what circumstances are we + + align:start position:0% +okay so under what circumstances are we + + + align:start position:0% +okay so under what circumstances are we +allowed to + + align:start position:0% + + + + align:start position:0% + +divide so you know we just saw that we + + align:start position:0% +divide so you know we just saw that we + + + align:start position:0% +divide so you know we just saw that we +can't divide here because you know + + align:start position:0% +can't divide here because you know + + + align:start position:0% +can't divide here because you know +there's no uh solution + + align:start position:0% + + + + align:start position:0% + +to this equation okay what if there is a + + align:start position:0% +to this equation okay what if there is a + + + align:start position:0% +to this equation okay what if there is a +solution like what if instead of uh + + align:start position:0% +solution like what if instead of uh + + + align:start position:0% +solution like what if instead of uh +modulo 6 we + + align:start position:0% +modulo 6 we + + + align:start position:0% +modulo 6 we +had uh modulo + + align:start position:0% +had uh modulo + + + align:start position:0% +had uh modulo + + align:start position:0% + + + + align:start position:0% + +okay would we be allowed to divide + + align:start position:0% + + + + align:start position:0% + +here if we have 3 X's congruent to 3 + + align:start position:0% +here if we have 3 X's congruent to 3 + + + align:start position:0% +here if we have 3 X's congruent to 3 +modul 5 can we then + + align:start position:0% +modul 5 can we then + + + align:start position:0% +modul 5 can we then +include x is congruent to one module of + + align:start position:0% +include x is congruent to one module of + + + align:start position:0% +include x is congruent to one module of +5 seeing some nods + + align:start position:0% + + + + align:start position:0% + +why well basically exactly the same + + align:start position:0% +why well basically exactly the same + + + align:start position:0% +why well basically exactly the same +reason right this exactly + + align:start position:0% +reason right this exactly + + + align:start position:0% +reason right this exactly +characterizes when what we described + + align:start position:0% +characterizes when what we described + + + align:start position:0% +characterizes when what we described +will work okay + + align:start position:0% +will work okay + + + align:start position:0% +will work okay +if + + align:start position:0% +if + + + align:start position:0% +if +uh the the modulus and the uh Co + + align:start position:0% +uh the the modulus and the uh Co + + + align:start position:0% +uh the the modulus and the uh Co +efficient we're trying to divide by our + + align:start position:0% +efficient we're trying to divide by our + + + align:start position:0% +efficient we're trying to divide by our +co-prime right if their G gcd is + + align:start position:0% +co-prime right if their G gcd is + + + align:start position:0% +co-prime right if their G gcd is +one then we'll be able to + + align:start position:0% +one then we'll be able to + + + align:start position:0% +one then we'll be able to +divide + + align:start position:0% +divide + + + align:start position:0% +divide +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh so more formally let's write out what + + align:start position:0% +uh so more formally let's write out what + + + align:start position:0% +uh so more formally let's write out what +we + + align:start position:0% +we + + + align:start position:0% +we +mean so let's start with a + + align:start position:0% +mean so let's start with a + + + align:start position:0% +mean so let's start with a +definition so we'll say that uh a + + align:start position:0% +definition so we'll say that uh a + + + align:start position:0% +definition so we'll say that uh a +multiplicative inverse + + align:start position:0% + + + + align:start position:0% + +of let's call it x uh + + align:start position:0% +of let's call it x uh + + + align:start position:0% +of let's call it x uh +modulo + + align:start position:0% +modulo + + + align:start position:0% +modulo +n uh which we will denote uh x to the ne + + align:start position:0% + + + + align:start position:0% + +1 is a + + align:start position:0% + + + + align:start position:0% + +number uh which as you might expect + + align:start position:0% +number uh which as you might expect + + + align:start position:0% +number uh which as you might expect +satisfies the following uh + + align:start position:0% + + + + align:start position:0% + +congruence okay so just as we have + + align:start position:0% +congruence okay so just as we have + + + align:start position:0% +congruence okay so just as we have +multiplicative inverses over the reals + + align:start position:0% +multiplicative inverses over the reals + + + align:start position:0% +multiplicative inverses over the reals +right so x * X inverse should be equal + + align:start position:0% +right so x * X inverse should be equal + + + align:start position:0% +right so x * X inverse should be equal +to one in that case we are defining + + align:start position:0% +to one in that case we are defining + + + align:start position:0% +to one in that case we are defining +something analogous uh when we're + + align:start position:0% +something analogous uh when we're + + + align:start position:0% +something analogous uh when we're +working mod n + + align:start position:0% +working mod n + + + align:start position:0% +working mod n +okay so does that definition make sense + + align:start position:0% +okay so does that definition make sense + + + align:start position:0% +okay so does that definition make sense +to people + + align:start position:0% + + + + align:start position:0% + +so as an example + + align:start position:0% +so as an example + + + align:start position:0% +so as an example +right uh one + + align:start position:0% +right uh one + + + align:start position:0% +right uh one +inverse uh you know so one is a is a + + align:start position:0% +inverse uh you know so one is a is a + + + align:start position:0% +inverse uh you know so one is a is a +multiplicative inverse of one maybe I + + align:start position:0% +multiplicative inverse of one maybe I + + + align:start position:0% +multiplicative inverse of one maybe I +should write it like that + + align:start position:0% + + + + align:start position:0% + +you know + + align:start position:0% +you know + + + align:start position:0% +you know +anything + + align:start position:0% +anything + + + align:start position:0% +anything +okay two is a multiplicative + + align:start position:0% + + + + align:start position:0% + +inverse of + + align:start position:0% +inverse of + + + align:start position:0% +inverse of +three Mod Five okay because 2 * 3 is six + + align:start position:0% +three Mod Five okay because 2 * 3 is six + + + align:start position:0% +three Mod Five okay because 2 * 3 is six +six is congruent to one modul + + align:start position:0% +six is congruent to one modul + + + align:start position:0% +six is congruent to one modul +5 okay so two and three are modul + + align:start position:0% +5 okay so two and three are modul + + + align:start position:0% +5 okay so two and three are modul +inverse modular inverses of each other + + align:start position:0% +inverse modular inverses of each other + + + align:start position:0% +inverse modular inverses of each other +modu of five + + align:start position:0% + + + + align:start position:0% + +the the last part yeah so + + align:start position:0% +the the last part yeah so + + + align:start position:0% +the the last part yeah so +um what this is saying right is that uh + + align:start position:0% +um what this is saying right is that uh + + + align:start position:0% +um what this is saying right is that uh +2 * 3 is congruent to one modulo whoops + + align:start position:0% +2 * 3 is congruent to one modulo whoops + + + align:start position:0% +2 * 3 is congruent to one modulo whoops +I should write it like + + align:start position:0% +I should write it like + + + align:start position:0% +I should write it like +this + + align:start position:0% +this + + + align:start position:0% +this +okay uh so 2 * three is is six right six + + align:start position:0% +okay uh so 2 * three is is six right six + + + align:start position:0% +okay uh so 2 * three is is six right six +is congruent to one module of 5 right + + align:start position:0% +is congruent to one module of 5 right + + + align:start position:0% +is congruent to one module of 5 right +so that means that two and three are + + align:start position:0% +so that means that two and three are + + + align:start position:0% +so that means that two and three are +multiplicative inverses of each other + + align:start position:0% +multiplicative inverses of each other + + + align:start position:0% +multiplicative inverses of each other +module of five okay because when you + + align:start position:0% +module of five okay because when you + + + align:start position:0% +module of five okay because when you +multiply them you get + + align:start position:0% + + + + align:start position:0% + +one okay does that make + + align:start position:0% + + + + align:start position:0% + +sense okay so when do multiplicative + + align:start position:0% +sense okay so when do multiplicative + + + align:start position:0% +sense okay so when do multiplicative +inverses exist + + align:start position:0% + + + + align:start position:0% + +can anybody uh finish this theorem + + align:start position:0% +can anybody uh finish this theorem + + + align:start position:0% +can anybody uh finish this theorem +statement can anybody characterize + + align:start position:0% + + + + align:start position:0% + +this when is a invertible modul n + + align:start position:0% + + + + align:start position:0% + +yeah yeah when the + + align:start position:0% +yeah yeah when the + + + align:start position:0% +yeah yeah when the +gcd of A and N is one + + align:start position:0% + + + + align:start position:0% + +okay and why is that + + align:start position:0% + + + + align:start position:0% + +okay yeah so that's uh that's good + + align:start position:0% +okay yeah so that's uh that's good + + + align:start position:0% +okay yeah so that's uh that's good +intuition if the gcd were not one like + + align:start position:0% +intuition if the gcd were not one like + + + align:start position:0% +intuition if the gcd were not one like +say the the gcd is two right so both A + + align:start position:0% +say the the gcd is two right so both A + + + align:start position:0% +say the the gcd is two right so both A +and N are even right multiplying a by + + align:start position:0% +and N are even right multiplying a by + + + align:start position:0% +and N are even right multiplying a by +anything is going to give you an even + + align:start position:0% +anything is going to give you an even + + + align:start position:0% +anything is going to give you an even +number right that's never going to be + + align:start position:0% +number right that's never going to be + + + align:start position:0% +number right that's never going to be +congruent to one modul another even + + align:start position:0% +congruent to one modul another even + + + align:start position:0% +congruent to one modul another even +number + + align:start position:0% +number + + + align:start position:0% +number +okay so more + + align:start position:0% + + + + align:start position:0% + +formally so a has an + + align:start position:0% + + + + align:start position:0% + +inverse mod n if and only + + align:start position:0% + + + + align:start position:0% + +if uh there exists a b so this is just + + align:start position:0% +if uh there exists a b so this is just + + + align:start position:0% +if uh there exists a b so this is just +the the definition + + align:start position:0% +the the definition + + + align:start position:0% +the the definition +such that a is congruent mod n to + + align:start position:0% +such that a is congruent mod n to + + + align:start position:0% +such that a is congruent mod n to +one + + align:start position:0% +one + + + align:start position:0% +one +okay now how do we characterize when + + align:start position:0% +okay now how do we characterize when + + + align:start position:0% +okay now how do we characterize when +this is + + align:start position:0% + + + + align:start position:0% + +true well let's unpack this definition + + align:start position:0% +true well let's unpack this definition + + + align:start position:0% +true well let's unpack this definition +here okay so this means that n divides + + align:start position:0% +here okay so this means that n divides + + + align:start position:0% +here okay so this means that n divides +their + + align:start position:0% + + + + align:start position:0% + +difference so Oops why don't I write + + align:start position:0% +difference so Oops why don't I write + + + align:start position:0% +difference so Oops why don't I write +this + + align:start position:0% +this + + + align:start position:0% +this +as AB minus + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% +one + + + align:start position:0% +one +okay right so we're saying that n + + align:start position:0% +okay right so we're saying that n + + + align:start position:0% +okay right so we're saying that n +divides a minus one we're looking at + + align:start position:0% +divides a minus one we're looking at + + + align:start position:0% +divides a minus one we're looking at +what that uh division actually looks + + align:start position:0% +what that uh division actually looks + + + align:start position:0% +what that uh division actually looks +like what the uh what the factor of n is + + align:start position:0% +like what the uh what the factor of n is + + + align:start position:0% +like what the uh what the factor of n is +okay so there's some Q such that qn is a + + align:start position:0% +okay so there's some Q such that qn is a + + + align:start position:0% +okay so there's some Q such that qn is a +minus one + + align:start position:0% + + + + align:start position:0% + +okay now we can rewrite + + align:start position:0% +okay now we can rewrite + + + align:start position:0% +okay now we can rewrite +this so 1 equal a minus q + + align:start position:0% + + + + align:start position:0% + +n okay so we're saying there exist B and + + align:start position:0% +n okay so we're saying there exist B and + + + align:start position:0% +n okay so we're saying there exist B and +Q such that 1 equal + + align:start position:0% +Q such that 1 equal + + + align:start position:0% +Q such that 1 equal +AB uh plus minus Q * n okay so this is + + align:start position:0% +AB uh plus minus Q * n okay so this is + + + align:start position:0% +AB uh plus minus Q * n okay so this is +just saying that one is an ilc of a + + align:start position:0% +just saying that one is an ilc of a + + + align:start position:0% +just saying that one is an ilc of a +Ann okay + + align:start position:0% + + + + align:start position:0% + +okay and as we saw before this happens + + align:start position:0% +okay and as we saw before this happens + + + align:start position:0% +okay and as we saw before this happens +if and only if the gcd is + + align:start position:0% + + + + align:start position:0% + +one okay + + align:start position:0% +one okay + + + align:start position:0% +one okay +so does that make sense to + + align:start position:0% + + + + align:start position:0% + +everybody so if two numbers have a gcd + + align:start position:0% +everybody so if two numbers have a gcd + + + align:start position:0% +everybody so if two numbers have a gcd +of one then we can divide by uh by one + + align:start position:0% +of one then we can divide by uh by one + + + align:start position:0% +of one then we can divide by uh by one +when working module of the + + align:start position:0% +when working module of the + + + align:start position:0% +when working module of the +other + + align:start position:0% + + + + align:start position:0% + +okay uh + + align:start position:0% + + + + align:start position:0% + +so if we have say 7x is congruent mod + + align:start position:0% +so if we have say 7x is congruent mod + + + align:start position:0% +so if we have say 7x is congruent mod +30 to + + align:start position:0% +30 to + + + align:start position:0% +30 to + + align:start position:0% + + + align:start position:0% +okay then we are allowed to divide by + + align:start position:0% +okay then we are allowed to divide by + + + align:start position:0% +okay then we are allowed to divide by +both sides because the gcd of 7 and 30 + + align:start position:0% +both sides because the gcd of 7 and 30 + + + align:start position:0% +both sides because the gcd of 7 and 30 +is one so we're allowed to divide both + + align:start position:0% +is one so we're allowed to divide both + + + align:start position:0% +is one so we're allowed to divide both +sides by + + align:start position:0% +sides by + + + align:start position:0% +sides by +seven okay so we are allowed to conclude + + align:start position:0% +seven okay so we are allowed to conclude + + + align:start position:0% +seven okay so we are allowed to conclude +that X is congruent mod 30 to + + align:start position:0% +that X is congruent mod 30 to + + + align:start position:0% +that X is congruent mod 30 to +two Okay I suppose more formally we'd + + align:start position:0% +two Okay I suppose more formally we'd + + + align:start position:0% +two Okay I suppose more formally we'd +want to find a multiplicative inverse of + + align:start position:0% +want to find a multiplicative inverse of + + + align:start position:0% +want to find a multiplicative inverse of +seven okay uh and I think 13 is such an + + align:start position:0% +seven okay uh and I think 13 is such an + + + align:start position:0% +seven okay uh and I think 13 is such an +inverse 7 by 13 91 yeah so if we + + align:start position:0% +inverse 7 by 13 91 yeah so if we + + + align:start position:0% +inverse 7 by 13 91 yeah so if we +multiply both sides by 13 right we'll + + align:start position:0% +multiply both sides by 13 right we'll + + + align:start position:0% +multiply both sides by 13 right we'll +get a coefficient of one over here and + + align:start position:0% +get a coefficient of one over here and + + + align:start position:0% +get a coefficient of one over here and +we'll get we'll get two uh on the right + + align:start position:0% +we'll get we'll get two uh on the right + + + align:start position:0% +we'll get we'll get two uh on the right +hand + + align:start position:0% +hand + + + align:start position:0% +hand +side + + align:start position:0% + + + + align:start position:0% + +okay so sometimes you can divide but not + + align:start position:0% +okay so sometimes you can divide but not + + + align:start position:0% +okay so sometimes you can divide but not +always + + align:start position:0% + + + + align:start position:0% + +okay so let's use that now to figure out + + align:start position:0% +okay so let's use that now to figure out + + + align:start position:0% +okay so let's use that now to figure out +what more we can say about + + align:start position:0% +what more we can say about + + + align:start position:0% +what more we can say about +exponentiation okay so the following is + + align:start position:0% +exponentiation okay so the following is + + + align:start position:0% +exponentiation okay so the following is +a + + align:start position:0% +a + + + align:start position:0% +a +theorem which is attributed to FMA as + + align:start position:0% +theorem which is attributed to FMA as + + + align:start position:0% +theorem which is attributed to FMA as +many things are it's often known as + + align:start position:0% +many things are it's often known as + + + align:start position:0% +many things are it's often known as +fma's little theorem not to be confused + + align:start position:0% +fma's little theorem not to be confused + + + align:start position:0% +fma's little theorem not to be confused +with fma's Last Theorem which + + align:start position:0% +with fma's Last Theorem which + + + align:start position:0% +with fma's Last Theorem which +FMA I I feel like that one should not be + + align:start position:0% +FMA I I feel like that one should not be + + + align:start position:0% +FMA I I feel like that one should not be +attributed to him at all um because he + + align:start position:0% +attributed to him at all um because he + + + align:start position:0% +attributed to him at all um because he +didn't prove it or I think he thought he + + align:start position:0% +didn't prove it or I think he thought he + + + align:start position:0% +didn't prove it or I think he thought he +knew a proof and was like a complete + + align:start position:0% +knew a proof and was like a complete + + + align:start position:0% +knew a proof and was like a complete + up but you know whatever uh f + + align:start position:0% + up but you know whatever uh f + + + align:start position:0% + up but you know whatever uh f +little theorem is a different story it + + align:start position:0% +little theorem is a different story it + + + align:start position:0% +little theorem is a different story it +is uh you know much more Elementary he + + align:start position:0% +is uh you know much more Elementary he + + + align:start position:0% +is uh you know much more Elementary he +did actually prove it um it states the + + align:start position:0% +did actually prove it um it states the + + + align:start position:0% +did actually prove it um it states the +following uh so if p is + + align:start position:0% + + + + align:start position:0% + +Prime and a is not a multiple of P so a + + align:start position:0% +Prime and a is not a multiple of P so a + + + align:start position:0% +Prime and a is not a multiple of P so a +not congruent mod P to + + align:start position:0% +not congruent mod P to + + + align:start position:0% +not congruent mod P to +zero okay + + align:start position:0% +zero okay + + + align:start position:0% +zero okay +then a to the P minus one is congruent + + align:start position:0% +then a to the P minus one is congruent + + + align:start position:0% +then a to the P minus one is congruent +mod P2 + + align:start position:0% + + + + align:start position:0% + +one okay + + align:start position:0% +one okay + + + align:start position:0% +one okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so if you think about what this is + + align:start position:0% +so if you think about what this is + + + align:start position:0% +so if you think about what this is +saying a little bit right um it's + + align:start position:0% +saying a little bit right um it's + + + align:start position:0% +saying a little bit right um it's +similar to what we were trying to do + + align:start position:0% +similar to what we were trying to do + + + align:start position:0% +similar to what we were trying to do +with with exponents + + align:start position:0% +with with exponents + + + align:start position:0% +with with exponents +earlier but instead of getting rid of uh + + align:start position:0% +earlier but instead of getting rid of uh + + + align:start position:0% +earlier but instead of getting rid of uh +you know multiples of of p in an + + align:start position:0% +you know multiples of of p in an + + + align:start position:0% +you know multiples of of p in an +exponent when working working mod P + + align:start position:0% +exponent when working working mod P + + + align:start position:0% +exponent when working working mod P +we're instead going to get rid of + + align:start position:0% +we're instead going to get rid of + + + align:start position:0% +we're instead going to get rid of +multiples of P minus + + align:start position:0% +multiples of P minus + + + align:start position:0% +multiples of P minus +one okay so so basically we can always + + align:start position:0% +one okay so so basically we can always + + + align:start position:0% +one okay so so basically we can always +factor out an a to the P minus + + align:start position:0% +factor out an a to the P minus + + + align:start position:0% +factor out an a to the P minus +one without you know changing uh the end + + align:start position:0% +one without you know changing uh the end + + + align:start position:0% +one without you know changing uh the end +result + + align:start position:0% +result + + + align:start position:0% +result +yeah + + align:start position:0% + + + + align:start position:0% + +sorry thank you Zach I promise I'm + + align:start position:0% +sorry thank you Zach I promise I'm + + + align:start position:0% +sorry thank you Zach I promise I'm +awake yeah if if a is congruent to zero + + align:start position:0% +awake yeah if if a is congruent to zero + + + align:start position:0% +awake yeah if if a is congruent to zero +then um clearly this theorem is false uh + + align:start position:0% +then um clearly this theorem is false uh + + + align:start position:0% +then um clearly this theorem is false uh +yeah a a should not be congruent to zero + + align:start position:0% +yeah a a should not be congruent to zero + + + align:start position:0% +yeah a a should not be congruent to zero +if if a is congruent to zero then a to + + align:start position:0% +if if a is congruent to zero then a to + + + align:start position:0% +if if a is congruent to zero then a to +the pus one is also + + align:start position:0% +the pus one is also + + + align:start position:0% +the pus one is also +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay uh so how could we prove this any + + align:start position:0% + + + + align:start position:0% + +ideas it's a bit of a weird proof idea + + align:start position:0% +ideas it's a bit of a weird proof idea + + + align:start position:0% +ideas it's a bit of a weird proof idea +let's consider the following + + align:start position:0% +let's consider the following + + + align:start position:0% +let's consider the following +Set uh so + + align:start position:0% +Set uh so + + + align:start position:0% +Set uh so +a 2 a 3 a + + align:start position:0% +a 2 a 3 a + + + align:start position:0% +a 2 a 3 a +all the way up to P minus + + align:start position:0% +all the way up to P minus + + + align:start position:0% +all the way up to P minus +one * + + align:start position:0% +one * + + + align:start position:0% +one * +a + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now what can we say about this set if we + + align:start position:0% +now what can we say about this set if we + + + align:start position:0% +now what can we say about this set if we +reduce everything in it modu P + + align:start position:0% + + + + align:start position:0% + +MH yeah so the answer was that you know + + align:start position:0% +MH yeah so the answer was that you know + + + align:start position:0% +MH yeah so the answer was that you know +this is basically equivalent to this is + + align:start position:0% +this is basically equivalent to this is + + + align:start position:0% +this is basically equivalent to this is +abusing notation a + + align:start position:0% + + + + align:start position:0% + +bit + + align:start position:0% +bit + + + align:start position:0% +bit +okay the claim is that all of these are + + align:start position:0% +okay the claim is that all of these are + + + align:start position:0% +okay the claim is that all of these are +distinct modul p and none of them are + + align:start position:0% +distinct modul p and none of them are + + + align:start position:0% +distinct modul p and none of them are +zero okay why is that + + align:start position:0% +zero okay why is that + + + align:start position:0% +zero okay why is that +now first probably the easier part why + + align:start position:0% +now first probably the easier part why + + + align:start position:0% +now first probably the easier part why +is none of these + + align:start position:0% +is none of these + + + align:start position:0% +is none of these +zero that's basically saying why is none + + align:start position:0% +zero that's basically saying why is none + + + align:start position:0% +zero that's basically saying why is none +of them a multiple of + + align:start position:0% + + + + align:start position:0% + +P well all of the coefficients on a are + + align:start position:0% +P well all of the coefficients on a are + + + align:start position:0% +P well all of the coefficients on a are +less than P so P doesn't divide any of + + align:start position:0% +less than P so P doesn't divide any of + + + align:start position:0% +less than P so P doesn't divide any of +those P also doesn't divide a by + + align:start position:0% +those P also doesn't divide a by + + + align:start position:0% +those P also doesn't divide a by +assumption and P is prime so doesn't + + align:start position:0% +assumption and P is prime so doesn't + + + align:start position:0% +assumption and P is prime so doesn't +divide any of these + + align:start position:0% +divide any of these + + + align:start position:0% +divide any of these +products okay so none of these is + + align:start position:0% +products okay so none of these is + + + align:start position:0% +products okay so none of these is +zero why are they all dis in + + align:start position:0% + + + + align:start position:0% + +modul yeah + + align:start position:0% + + + + align:start position:0% + +okay um let me try and rephrase + + align:start position:0% +okay um let me try and rephrase + + + align:start position:0% +okay um let me try and rephrase +that uh so if you look at two different + + align:start position:0% +that uh so if you look at two different + + + align:start position:0% +that uh so if you look at two different +values + + align:start position:0% +values + + + align:start position:0% +values +right like two different coefficients + + align:start position:0% +right like two different coefficients + + + align:start position:0% +right like two different coefficients +you + + align:start position:0% + + + + align:start position:0% + +said so suppose for + + align:start position:0% + + + + align:start position:0% + +contradiction a * I equals a * J right + + align:start position:0% +contradiction a * I equals a * J right + + + align:start position:0% +contradiction a * I equals a * J right +so where we're actually going to use a + + align:start position:0% +so where we're actually going to use a + + + align:start position:0% +so where we're actually going to use a +instead of n + + align:start position:0% +instead of n + + + align:start position:0% +instead of n +okay or sorry this should be + + align:start position:0% + + + + align:start position:0% + +P okay what is this telling + + align:start position:0% + + + + align:start position:0% + +us + + align:start position:0% + + + + align:start position:0% + +yeah that's right + + align:start position:0% +yeah that's right + + + align:start position:0% +yeah that's right +yes yes so the answer was uh p is prime + + align:start position:0% +yes yes so the answer was uh p is prime + + + align:start position:0% +yes yes so the answer was uh p is prime +so A and P are co-prime right so a has + + align:start position:0% +so A and P are co-prime right so a has + + + align:start position:0% +so A and P are co-prime right so a has +an inverse we can consol + + align:start position:0% +an inverse we can consol + + + align:start position:0% +an inverse we can consol +it so this tells us that I is equivalent + + align:start position:0% +it so this tells us that I is equivalent + + + align:start position:0% +it so this tells us that I is equivalent +mod P to + + align:start position:0% +mod P to + + + align:start position:0% +mod P to +J right the two coefficients are + + align:start position:0% +J right the two coefficients are + + + align:start position:0% +J right the two coefficients are +equivalent the two coefficients are + + align:start position:0% +equivalent the two coefficients are + + + align:start position:0% +equivalent the two coefficients are +coming from the set 1 to P minus + + align:start position:0% +coming from the set 1 to P minus + + + align:start position:0% +coming from the set 1 to P minus +one so if they're congruent mod P + + align:start position:0% +one so if they're congruent mod P + + + align:start position:0% +one so if they're congruent mod P +they're actually equal okay + + align:start position:0% + + + + align:start position:0% + +so that means that all of these values + + align:start position:0% +so that means that all of these values + + + align:start position:0% +so that means that all of these values +are going to be distinct modul + + align:start position:0% +are going to be distinct modul + + + align:start position:0% +are going to be distinct modul +P none of them are zero so they're you + + align:start position:0% +P none of them are zero so they're you + + + align:start position:0% +P none of them are zero so they're you +know these particular + + align:start position:0% + + + + align:start position:0% + +values okay what happens when we + + align:start position:0% +values okay what happens when we + + + align:start position:0% +values okay what happens when we +multiply everything in s together + + align:start position:0% + + + + align:start position:0% + +well if we multiply everything in this + + align:start position:0% +well if we multiply everything in this + + + align:start position:0% +well if we multiply everything in this +set what do we + + align:start position:0% + + + + align:start position:0% + +get + + align:start position:0% + + + + align:start position:0% + +yeah yes uh P minus one factorial that's + + align:start position:0% +yeah yes uh P minus one factorial that's + + + align:start position:0% +yeah yes uh P minus one factorial that's +what it's + + align:start position:0% +what it's + + + align:start position:0% +what it's +called + + align:start position:0% +called + + + align:start position:0% +called +so if we take the product of both sides + + align:start position:0% +so if we take the product of both sides + + + align:start position:0% +so if we take the product of both sides +we have you know the product of this or + + align:start position:0% +we have you know the product of this or + + + align:start position:0% +we have you know the product of this or +sorry the product of this one + + align:start position:0% + + + + align:start position:0% + +is going to be equal to P minus one + + align:start position:0% +is going to be equal to P minus one + + + align:start position:0% +is going to be equal to P minus one +factorial + + align:start position:0% +factorial + + + align:start position:0% +factorial +okay what about the other + + align:start position:0% + + + + align:start position:0% + +one well the other one is going to be + + align:start position:0% +one well the other one is going to be + + + align:start position:0% +one well the other one is going to be +the same except we've got a bunch of + + align:start position:0% +the same except we've got a bunch of + + + align:start position:0% +the same except we've got a bunch of +factors of a right how many factors of + + align:start position:0% + + + + align:start position:0% + +a yeah + + align:start position:0% + + + + align:start position:0% + +yeah and so this will be a p + + align:start position:0% +yeah and so this will be a p + + + align:start position:0% +yeah and so this will be a p +minus1 * P + + align:start position:0% +minus1 * P + + + align:start position:0% +minus1 * P +minus1 + + align:start position:0% + + + + align:start position:0% + +factorial + + align:start position:0% +factorial + + + align:start position:0% +factorial +okay so P minus one factorial + + align:start position:0% +okay so P minus one factorial + + + align:start position:0% +okay so P minus one factorial +is equivalent to P minus1 factorial time + + align:start position:0% +is equivalent to P minus1 factorial time + + + align:start position:0% +is equivalent to P minus1 factorial time +a p minus + + align:start position:0% +a p minus + + + align:start position:0% +a p minus +one what does that tell + + align:start position:0% + + + + align:start position:0% + +us + + align:start position:0% + + + + align:start position:0% + +yeah okay so the answer was that because + + align:start position:0% +yeah okay so the answer was that because + + + align:start position:0% +yeah okay so the answer was that because +p is prime + + align:start position:0% +p is prime + + + align:start position:0% +p is prime +none of these + + align:start position:0% +none of these + + + align:start position:0% +none of these +numbers right are a multiple of P so + + align:start position:0% +numbers right are a multiple of P so + + + align:start position:0% +numbers right are a multiple of P so +their product is not a multiple of P so + + align:start position:0% +their product is not a multiple of P so + + + align:start position:0% +their product is not a multiple of P so +P minus one factorial is not a multiple + + align:start position:0% +P minus one factorial is not a multiple + + + align:start position:0% +P minus one factorial is not a multiple +of P so it has an + + align:start position:0% +of P so it has an + + + align:start position:0% +of P so it has an +inverse so that means that we can cancel + + align:start position:0% +inverse so that means that we can cancel + + + align:start position:0% +inverse so that means that we can cancel +it from both + + align:start position:0% +it from both + + + align:start position:0% +it from both +sides and we end up with one is + + align:start position:0% +sides and we end up with one is + + + align:start position:0% +sides and we end up with one is +congruent to a to the P minus + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% + + + + align:start position:0% + +okay so we have uh P minus one factorial + + align:start position:0% +okay so we have uh P minus one factorial + + + align:start position:0% +okay so we have uh P minus one factorial +conent mod P pus1 factorial time a + + align:start position:0% +conent mod P pus1 factorial time a + + + align:start position:0% +conent mod P pus1 factorial time a +pus1 these + + align:start position:0% + + + + align:start position:0% + +canel and we have one is congruent to a + + align:start position:0% +canel and we have one is congruent to a + + + align:start position:0% +canel and we have one is congruent to a +to the P minus + + align:start position:0% +to the P minus + + + align:start position:0% +to the P minus +one + + align:start position:0% +one + + + align:start position:0% +one +okay and that's the uh result that we + + align:start position:0% +okay and that's the uh result that we + + + align:start position:0% +okay and that's the uh result that we +were looking + + align:start position:0% +were looking + + + align:start position:0% +were looking +for okay so if we're working mod n we + + align:start position:0% +for okay so if we're working mod n we + + + align:start position:0% +for okay so if we're working mod n we +cannot generally reduce exponents + + align:start position:0% +cannot generally reduce exponents + + + align:start position:0% +cannot generally reduce exponents +n but if n is prime we can instead + + align:start position:0% +n but if n is prime we can instead + + + align:start position:0% +n but if n is prime we can instead +reduce mod uh nus + + align:start position:0% + + + + align:start position:0% + +one okay do does that uh does that make + + align:start position:0% +one okay do does that uh does that make + + + align:start position:0% +one okay do does that uh does that make +sense to + + align:start position:0% + + + + align:start position:0% + +everybody + + align:start position:0% + + + + align:start position:0% + +so as an + + align:start position:0% +so as an + + + align:start position:0% +so as an +example so if we wanted to say find + + align:start position:0% + + + + align:start position:0% + +uh the remainder of seven to the say uh + + align:start position:0% +uh the remainder of seven to the say uh + + + align:start position:0% +uh the remainder of seven to the say uh +95 uh + + align:start position:0% +95 uh + + + align:start position:0% +95 uh +modulo let's say + + align:start position:0% + + + + align:start position:0% + +13 okay how might we do that + + align:start position:0% + + + + align:start position:0% + +well 13 is + + align:start position:0% +well 13 is + + + align:start position:0% +well 13 is +prime so instead of computing 7 to the + + align:start position:0% +prime so instead of computing 7 to the + + + align:start position:0% +prime so instead of computing 7 to the +95 let's reduce that Mod 13 minus 1 so + + align:start position:0% +95 let's reduce that Mod 13 minus 1 so + + + align:start position:0% +95 let's reduce that Mod 13 minus 1 so +modul + + align:start position:0% +modul + + + align:start position:0% +modul +12 okay so this is going to be the same + + align:start position:0% +12 okay so this is going to be the same + + + align:start position:0% +12 okay so this is going to be the same +as 7 to the what is it + + align:start position:0% + + + + align:start position:0% + +11 13 + + align:start position:0% + + + + align:start position:0% + +okay now what can we + + align:start position:0% + + + + align:start position:0% + +do what is 7 to the + + align:start position:0% + + + + align:start position:0% + +12 H + + align:start position:0% +12 H + + + align:start position:0% +12 H +sorry did did somebody give an answer I + + align:start position:0% +sorry did did somebody give an answer I + + + align:start position:0% +sorry did did somebody give an answer I +I + + align:start position:0% +I + + + align:start position:0% +I +no one yes okay so 7 12 is + + align:start position:0% +no one yes okay so 7 12 is + + + align:start position:0% +no one yes okay so 7 12 is +1 right 7 11 * 7 is 7 to the 12 so this + + align:start position:0% +1 right 7 11 * 7 is 7 to the 12 so this + + + align:start position:0% +1 right 7 11 * 7 is 7 to the 12 so this +is the modular inverse of 7 modular + + align:start position:0% +is the modular inverse of 7 modular + + + align:start position:0% +is the modular inverse of 7 modular +13 okay what can you multiply seven by + + align:start position:0% +13 okay what can you multiply seven by + + + align:start position:0% +13 okay what can you multiply seven by +to get one Mod 13 yeah two + + align:start position:0% + + + + align:start position:0% + +okay so that's all we have time for + + align:start position:0% +okay so that's all we have time for + + + align:start position:0% +okay so that's all we have time for +today um I will see you on Thursday and + + align:start position:0% +today um I will see you on Thursday and + + + align:start position:0% +today um I will see you on Thursday and +if you have any questions you know feel + + align:start position:0% +if you have any questions you know feel + + + align:start position:0% +if you have any questions you know feel +free to come up and ask \ No newline at end of file diff --git a/O-dyKz5dpeY.txt b/O-dyKz5dpeY.txt new file mode 100644 index 0000000000000000000000000000000000000000..50de5afa42e78dee4ef4e5c488863a66b19f28aa --- /dev/null +++ b/O-dyKz5dpeY.txt @@ -0,0 +1,955 @@ +align:start position:0% + +let us now go through an example suppose + + align:start position:0% +let us now go through an example suppose + + + align:start position:0% +let us now go through an example suppose +that we have an unknown random variable + + align:start position:0% +that we have an unknown random variable + + + align:start position:0% +that we have an unknown random variable +theta that has a uniform distribution + + align:start position:0% +theta that has a uniform distribution + + + align:start position:0% +theta that has a uniform distribution +between 4 and 10 we observe some other + + align:start position:0% +between 4 and 10 we observe some other + + + align:start position:0% +between 4 and 10 we observe some other +random variable X that's related to + + align:start position:0% +random variable X that's related to + + + align:start position:0% +random variable X that's related to +theta according to the following model + + align:start position:0% +theta according to the following model + + + align:start position:0% +theta according to the following model +this is the conditional distribution of + + align:start position:0% +this is the conditional distribution of + + + align:start position:0% +this is the conditional distribution of +x given theta for any given value of + + align:start position:0% +x given theta for any given value of + + + align:start position:0% +x given theta for any given value of +theta x is going to take values between + + align:start position:0% +theta x is going to take values between + + + align:start position:0% +theta x is going to take values between +theta minus 1 and theta plus 1 and the + + align:start position:0% +theta minus 1 and theta plus 1 and the + + + align:start position:0% +theta minus 1 and theta plus 1 and the +conditional distribution is uniform on + + align:start position:0% +conditional distribution is uniform on + + + align:start position:0% +conditional distribution is uniform on +that range one way of thinking about + + align:start position:0% +that range one way of thinking about + + + align:start position:0% +that range one way of thinking about +this particular observation model is + + align:start position:0% +this particular observation model is + + + align:start position:0% +this particular observation model is +that what we observe is the true value + + align:start position:0% +that what we observe is the true value + + + align:start position:0% +that what we observe is the true value +of theta plus some noise term and this + + align:start position:0% +of theta plus some noise term and this + + + align:start position:0% +of theta plus some noise term and this +noise term is uniform on the range from + + align:start position:0% +noise term is uniform on the range from + + + align:start position:0% +noise term is uniform on the range from +minus 1 to plus 1 so given a value of + + align:start position:0% +minus 1 to plus 1 so given a value of + + + align:start position:0% +minus 1 to plus 1 so given a value of +theta we may observe anything because of + + align:start position:0% +theta we may observe anything because of + + + align:start position:0% +theta we may observe anything because of +noise that's up to one lower or one + + align:start position:0% +noise that's up to one lower or one + + + align:start position:0% +noise that's up to one lower or one +higher than the true value of theta and + + align:start position:0% +higher than the true value of theta and + + + align:start position:0% +higher than the true value of theta and +if we take this description actually + + align:start position:0% +if we take this description actually + + + align:start position:0% +if we take this description actually +this random variable U has this + + align:start position:0% +this random variable U has this + + + align:start position:0% +this random variable U has this +distribution no matter what theta is + + align:start position:0% +distribution no matter what theta is + + + align:start position:0% +distribution no matter what theta is +and therefore U is independent of theta + + align:start position:0% +and therefore U is independent of theta + + + align:start position:0% +and therefore U is independent of theta +but in any case this particular + + align:start position:0% +but in any case this particular + + + align:start position:0% +but in any case this particular +interpretation will not matter let us + + align:start position:0% +interpretation will not matter let us + + + align:start position:0% +interpretation will not matter let us +see how do we proceed in Bayesian + + align:start position:0% +see how do we proceed in Bayesian + + + align:start position:0% +see how do we proceed in Bayesian +estimation the first step is always to + + align:start position:0% +estimation the first step is always to + + + align:start position:0% +estimation the first step is always to +put our hands on the posterior + + align:start position:0% +put our hands on the posterior + + + align:start position:0% +put our hands on the posterior +distribution of theta and to find the + + align:start position:0% +distribution of theta and to find the + + + align:start position:0% +distribution of theta and to find the +posterior we can start by first finding + + align:start position:0% +posterior we can start by first finding + + + align:start position:0% +posterior we can start by first finding +the joint so let us look at the X theta + + align:start position:0% +the joint so let us look at the X theta + + + align:start position:0% +the joint so let us look at the X theta +plane that's where the joint + + align:start position:0% +plane that's where the joint + + + align:start position:0% +plane that's where the joint +distribution is going to live and our + + align:start position:0% +distribution is going to live and our + + + align:start position:0% +distribution is going to live and our +first step will be to locate those + + align:start position:0% +first step will be to locate those + + + align:start position:0% +first step will be to locate those +values of X and theta that are possible + + align:start position:0% +values of X and theta that are possible + + + align:start position:0% +values of X and theta that are possible +given our description from this model + + align:start position:0% +given our description from this model + + + align:start position:0% +given our description from this model +here we know that theta minus 1 is going + + align:start position:0% +here we know that theta minus 1 is going + + + align:start position:0% +here we know that theta minus 1 is going +to be less than or equal to X and X is + + align:start position:0% +to be less than or equal to X and X is + + + align:start position:0% +to be less than or equal to X and X is +going to be less than or equal to theta + + align:start position:0% +going to be less than or equal to theta + + + align:start position:0% +going to be less than or equal to theta +plus 1 and we translate this into two + + align:start position:0% +plus 1 and we translate this into two + + + align:start position:0% +plus 1 and we translate this into two +inequalities namely that theta is less + + align:start position:0% +inequalities namely that theta is less + + + align:start position:0% +inequalities namely that theta is less +than or equal to X plus 1 + + align:start position:0% +than or equal to X plus 1 + + + align:start position:0% +than or equal to X plus 1 +and from here that theta is larger than + + align:start position:0% +and from here that theta is larger than + + + align:start position:0% +and from here that theta is larger than +or equal to X minus one so these are the + + align:start position:0% +or equal to X minus one so these are the + + + align:start position:0% +or equal to X minus one so these are the +constraints that we have on the possible + + align:start position:0% +constraints that we have on the possible + + + align:start position:0% +constraints that we have on the possible +values of X and theta so here we plot + + align:start position:0% +values of X and theta so here we plot + + + align:start position:0% +values of X and theta so here we plot +the line where theta is equal to X plus + + align:start position:0% +the line where theta is equal to X plus + + + align:start position:0% +the line where theta is equal to X plus +1 and here we plot the line on which + + align:start position:0% +1 and here we plot the line on which + + + align:start position:0% +1 and here we plot the line on which +theta is equal to X minus 1 and these + + align:start position:0% +theta is equal to X minus 1 and these + + + align:start position:0% +theta is equal to X minus 1 and these +two inequalities that we got here tell + + align:start position:0% +two inequalities that we got here tell + + + align:start position:0% +two inequalities that we got here tell +us that we need to live somewhere in + + align:start position:0% +us that we need to live somewhere in + + + align:start position:0% +us that we need to live somewhere in +between those two lines in addition we + + align:start position:0% +between those two lines in addition we + + + align:start position:0% +between those two lines in addition we +have the fact that theta lives between 4 + + align:start position:0% +have the fact that theta lives between 4 + + + align:start position:0% +have the fact that theta lives between 4 +and 10 and that places these two limits + + align:start position:0% +and 10 and that places these two limits + + + align:start position:0% +and 10 and that places these two limits +as well so to summarize this shape here + + align:start position:0% +as well so to summarize this shape here + + + align:start position:0% +as well so to summarize this shape here +is the set of all possible X's and + + align:start position:0% +is the set of all possible X's and + + + align:start position:0% +is the set of all possible X's and +Thetas outside this shape the joint PDF + + align:start position:0% +Thetas outside this shape the joint PDF + + + align:start position:0% +Thetas outside this shape the joint PDF +is going to be 0 what is it going to be + + align:start position:0% +is going to be 0 what is it going to be + + + align:start position:0% +is going to be 0 what is it going to be +inside here well because the prior is + + align:start position:0% +inside here well because the prior is + + + align:start position:0% +inside here well because the prior is +uniform that is it is constant and the + + align:start position:0% +uniform that is it is constant and the + + + align:start position:0% +uniform that is it is constant and the +model is also uniform to obtain the + + align:start position:0% +model is also uniform to obtain the + + + align:start position:0% +model is also uniform to obtain the +joint we multiply these two and since + + align:start position:0% +joint we multiply these two and since + + + align:start position:0% +joint we multiply these two and since +they are constant we obtain a joint + + align:start position:0% +they are constant we obtain a joint + + + align:start position:0% +they are constant we obtain a joint +that's also constant so the joint PDF is + + align:start position:0% +that's also constant so the joint PDF is + + + align:start position:0% +that's also constant so the joint PDF is +equal to a constant over that set we can + + align:start position:0% +equal to a constant over that set we can + + + align:start position:0% +equal to a constant over that set we can +easily calculate the area of this set it + + align:start position:0% +easily calculate the area of this set it + + + align:start position:0% +easily calculate the area of this set it +is 12 so the joint is equal to 1 over 12 + + align:start position:0% +is 12 so the joint is equal to 1 over 12 + + + align:start position:0% +is 12 so the joint is equal to 1 over 12 +inside this set and of course it's 0 + + align:start position:0% +inside this set and of course it's 0 + + + align:start position:0% +inside this set and of course it's 0 +elsewhere so we have a uniform joint PDF + + align:start position:0% +elsewhere so we have a uniform joint PDF + + + align:start position:0% +elsewhere so we have a uniform joint PDF +now let us look at the posterior if I + + align:start position:0% +now let us look at the posterior if I + + + align:start position:0% +now let us look at the posterior if I +tell you that X takes on this specific + + align:start position:0% +tell you that X takes on this specific + + + align:start position:0% +tell you that X takes on this specific +value this means that we now live in + + align:start position:0% +value this means that we now live in + + + align:start position:0% +value this means that we now live in +this universe and it means that all of + + align:start position:0% +this universe and it means that all of + + + align:start position:0% +this universe and it means that all of +those Thetas are possible the posterior + + align:start position:0% +those Thetas are possible the posterior + + + align:start position:0% +those Thetas are possible the posterior +distribution is going to be distribution + + align:start position:0% +distribution is going to be distribution + + + align:start position:0% +distribution is going to be distribution +that tells us the probabilities of these + + align:start position:0% +that tells us the probabilities of these + + + align:start position:0% +that tells us the probabilities of these +different Thetas what kind of + + align:start position:0% +different Thetas what kind of + + + align:start position:0% +different Thetas what kind of +distribution is it well we know that the + + align:start position:0% +distribution is it well we know that the + + + align:start position:0% +distribution is it well we know that the +conditional is just a section out of the + + align:start position:0% +conditional is just a section out of the + + + align:start position:0% +conditional is just a section out of the +joint but keeps otherwise the same shape + + align:start position:0% +joint but keeps otherwise the same shape + + + align:start position:0% +joint but keeps otherwise the same shape +since the joint is constant it's + + align:start position:0% +since the joint is constant it's + + + align:start position:0% +since the joint is constant it's +uniform over that set it means that the + + align:start position:0% +uniform over that set it means that the + + + align:start position:0% +uniform over that set it means that the +posterior or the conditional is also + + align:start position:0% +posterior or the conditional is also + + + align:start position:0% +posterior or the conditional is also +constant over that set so the conclusion + + align:start position:0% +constant over that set so the conclusion + + + align:start position:0% +constant over that set so the conclusion +is that the posterior distribution of + + align:start position:0% +is that the posterior distribution of + + + align:start position:0% +is that the posterior distribution of +theta is a uniform distribution on this + + align:start position:0% +theta is a uniform distribution on this + + + align:start position:0% +theta is a uniform distribution on this +set given this knowledge what is the + + align:start position:0% +set given this knowledge what is the + + + align:start position:0% +set given this knowledge what is the +conditional expectation the conditional + + align:start position:0% +conditional expectation the conditional + + + align:start position:0% +conditional expectation the conditional +expectation of a uniform is just the + + align:start position:0% +expectation of a uniform is just the + + + align:start position:0% +expectation of a uniform is just the +midpoint of that uniform and so this is + + align:start position:0% +midpoint of that uniform and so this is + + + align:start position:0% +midpoint of that uniform and so this is +going to be our estimate of theta the + + align:start position:0% +going to be our estimate of theta the + + + align:start position:0% +going to be our estimate of theta the +conditional expectation of theta given + + align:start position:0% +conditional expectation of theta given + + + align:start position:0% +conditional expectation of theta given +the observation that we have obtained + + align:start position:0% +the observation that we have obtained + + + align:start position:0% +the observation that we have obtained +and then a similar argument applies no + + align:start position:0% +and then a similar argument applies no + + + align:start position:0% +and then a similar argument applies no +matter what X we have obtained for any + + align:start position:0% +matter what X we have obtained for any + + + align:start position:0% +matter what X we have obtained for any +given X our estimate is going to be the + + align:start position:0% +given X our estimate is going to be the + + + align:start position:0% +given X our estimate is going to be the +midpoint of the corresponding interval + + align:start position:0% + + + + align:start position:0% + +so what kind of shape do we get by doing + + align:start position:0% +so what kind of shape do we get by doing + + + align:start position:0% +so what kind of shape do we get by doing +this by joining the midpoints it's going + + align:start position:0% +this by joining the midpoints it's going + + + align:start position:0% +this by joining the midpoints it's going +to be a straight line over this region + + align:start position:0% +to be a straight line over this region + + + align:start position:0% +to be a straight line over this region +it's also going to be a straight line + + align:start position:0% +it's also going to be a straight line + + + align:start position:0% +it's also going to be a straight line +over this region except that because of + + align:start position:0% +over this region except that because of + + + align:start position:0% +over this region except that because of +the change in shape it's going to be a + + align:start position:0% +the change in shape it's going to be a + + + align:start position:0% +the change in shape it's going to be a +straight line with a different slope and + + align:start position:0% +straight line with a different slope and + + + align:start position:0% +straight line with a different slope and +similarly in this region it's also going + + align:start position:0% +similarly in this region it's also going + + + align:start position:0% +similarly in this region it's also going +to be a straight line with a different + + align:start position:0% +to be a straight line with a different + + + align:start position:0% +to be a straight line with a different +slope so what have we plotted here for + + align:start position:0% +slope so what have we plotted here for + + + align:start position:0% +slope so what have we plotted here for +any given value of x we have plotted the + + align:start position:0% +any given value of x we have plotted the + + + align:start position:0% +any given value of x we have plotted the +corresponding conditional expectation of + + align:start position:0% +corresponding conditional expectation of + + + align:start position:0% +corresponding conditional expectation of +theta given that value of x and as a + + align:start position:0% +theta given that value of x and as a + + + align:start position:0% +theta given that value of x and as a +function of X this gives us a certain + + align:start position:0% +function of X this gives us a certain + + + align:start position:0% +function of X this gives us a certain +curve and this blue curve that we have + + align:start position:0% +curve and this blue curve that we have + + + align:start position:0% +curve and this blue curve that we have +calculated is a particular function of X + + align:start position:0% +calculated is a particular function of X + + + align:start position:0% +calculated is a particular function of X +and we can think of this function G as + + align:start position:0% +and we can think of this function G as + + + align:start position:0% +and we can think of this function G as +being our estimator so the way we're + + align:start position:0% +being our estimator so the way we're + + + align:start position:0% +being our estimator so the way we're +going to be processing the data will be + + align:start position:0% +going to be processing the data will be + + + align:start position:0% +going to be processing the data will be +that whenever we obtain an X we apply + + align:start position:0% +that whenever we obtain an X we apply + + + align:start position:0% +that whenever we obtain an X we apply +this particular function G and we come + + align:start position:0% +this particular function G and we come + + + align:start position:0% +this particular function G and we come +up with an estimate \ No newline at end of file diff --git a/O8gzYz51K9I.txt b/O8gzYz51K9I.txt new file mode 100644 index 0000000000000000000000000000000000000000..ac8f2f8717e8931cc31711f3159400158ebe8a45 --- /dev/null +++ b/O8gzYz51K9I.txt @@ -0,0 +1,16867 @@ +align:start position:0% + +for today i'll just talk a little bit + + align:start position:0% +for today i'll just talk a little bit + + + align:start position:0% +for today i'll just talk a little bit +more + + align:start position:0% +more + + + align:start position:0% +more +generally at the beginning about + + align:start position:0% +generally at the beginning about + + + align:start position:0% +generally at the beginning about +a few observations that i've had + + align:start position:0% +a few observations that i've had + + + align:start position:0% +a few observations that i've had +perhaps a little bit about reliability + + align:start position:0% +perhaps a little bit about reliability + + + align:start position:0% +perhaps a little bit about reliability +microarray studies + + align:start position:0% +microarray studies + + + align:start position:0% +microarray studies +i'll talk about classification problem + + align:start position:0% +i'll talk about classification problem + + + align:start position:0% +i'll talk about classification problem +in general and then i'll talk more about + + align:start position:0% +in general and then i'll talk more about + + + align:start position:0% +in general and then i'll talk more about +phenotypes and then review some + + align:start position:0% +phenotypes and then review some + + + align:start position:0% +phenotypes and then review some +literature um + + align:start position:0% +literature um + + + align:start position:0% +literature um +that are well cited + + align:start position:0% +that are well cited + + + align:start position:0% +that are well cited +so i bet you've had some exposure to + + align:start position:0% +so i bet you've had some exposure to + + + align:start position:0% +so i bet you've had some exposure to +that right did anyone + + align:start position:0% +that right did anyone + + + align:start position:0% +that right did anyone +maybe marco or zach or talk about like + + align:start position:0% +maybe marco or zach or talk about like + + + align:start position:0% +maybe marco or zach or talk about like +lymphoma studies and + + align:start position:0% +lymphoma studies and + + + align:start position:0% +lymphoma studies and +what do you remember any other papers + + align:start position:0% +what do you remember any other papers + + + align:start position:0% +what do you remember any other papers +that you covered here + + align:start position:0% +that you covered here + + + align:start position:0% +that you covered here +yeah + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +anything else you remember + + align:start position:0% + + + + align:start position:0% + +okay all right so + + align:start position:0% +okay all right so + + + align:start position:0% +okay all right so +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so maybe the stuff that i have + + align:start position:0% +all right so maybe the stuff that i have + + + align:start position:0% +all right so maybe the stuff that i have +is new okay good + + align:start position:0% +is new okay good + + + align:start position:0% +is new okay good +um so you probably know all this + + align:start position:0% +um so you probably know all this + + + align:start position:0% +um so you probably know all this +um + + align:start position:0% +um + + + align:start position:0% +um +it's actually the so the cdnas are cdna + + align:start position:0% +it's actually the so the cdnas are cdna + + + align:start position:0% +it's actually the so the cdnas are cdna +rates are cheaper right so + + align:start position:0% +rates are cheaper right so + + + align:start position:0% +rates are cheaper right so +um they are used a lot in biological a + + align:start position:0% +um they are used a lot in biological a + + + align:start position:0% +um they are used a lot in biological a +lot of biology labs + + align:start position:0% +lot of biology labs + + + align:start position:0% +lot of biology labs +the ones that i work with for example in + + align:start position:0% +the ones that i work with for example in + + + align:start position:0% +the ones that i work with for example in +the new building they have their own + + align:start position:0% +the new building they have their own + + + align:start position:0% +the new building they have their own +libraries they print their own + + align:start position:0% +libraries they print their own + + + align:start position:0% +libraries they print their own +um affi arrays are + + align:start position:0% +um affi arrays are + + + align:start position:0% +um affi arrays are +i think the consensus that the api + + align:start position:0% +i think the consensus that the api + + + align:start position:0% +i think the consensus that the api +arrays are probably the most accurate at + + align:start position:0% +arrays are probably the most accurate at + + + align:start position:0% +arrays are probably the most accurate at +this point but it's still you know eight + + align:start position:0% +this point but it's still you know eight + + + align:start position:0% +this point but it's still you know eight +two + + align:start position:0% +two + + + align:start position:0% +two +thousand dollars + + align:start position:0% +thousand dollars + + + align:start position:0% +thousand dollars +per array + + align:start position:0% +per array + + + align:start position:0% +per array +a lot of groups are experimenting with + + align:start position:0% +a lot of groups are experimenting with + + + align:start position:0% +a lot of groups are experimenting with +these printed oligonucleotide arrays so + + align:start position:0% +these printed oligonucleotide arrays so + + + align:start position:0% +these printed oligonucleotide arrays so +agilent has + + align:start position:0% +agilent has + + + align:start position:0% +agilent has +uh so there are just whole variety now + + align:start position:0% +uh so there are just whole variety now + + + align:start position:0% +uh so there are just whole variety now +agilent has + + align:start position:0% +agilent has + + + align:start position:0% +agilent has +one + + align:start position:0% +one + + + align:start position:0% +one +type of platform where they actually + + align:start position:0% +type of platform where they actually + + + align:start position:0% +type of platform where they actually +you know + + align:start position:0% +you know + + + align:start position:0% +you know +give you the chips and you have to + + align:start position:0% +give you the chips and you have to + + + align:start position:0% +give you the chips and you have to +basically buy their whole setup + + align:start position:0% +basically buy their whole setup + + + align:start position:0% +basically buy their whole setup +and it's cheaper + + align:start position:0% +and it's cheaper + + + align:start position:0% +and it's cheaper +people seem to like it but you know who + + align:start position:0% +people seem to like it but you know who + + + align:start position:0% +people seem to like it but you know who +knows what's gonna happen in the future + + align:start position:0% +knows what's gonna happen in the future + + + align:start position:0% +knows what's gonna happen in the future +i mean these are it's all um + + align:start position:0% +i mean these are it's all um + + + align:start position:0% +i mean these are it's all um +unclear at this point exactly what + + align:start position:0% +unclear at this point exactly what + + + align:start position:0% +unclear at this point exactly what +platform is the best you know + + align:start position:0% +platform is the best you know + + + align:start position:0% +platform is the best you know +information per dollar spent but there + + align:start position:0% +information per dollar spent but there + + + align:start position:0% +information per dollar spent but there +are other companies that will actually + + align:start position:0% +are other companies that will actually + + + align:start position:0% +are other companies that will actually +make these + + align:start position:0% +make these + + + align:start position:0% +make these +oligonucleotides and then you just buy + + align:start position:0% +oligonucleotides and then you just buy + + + align:start position:0% +oligonucleotides and then you just buy +those and then you print it yourself so + + align:start position:0% +those and then you print it yourself so + + + align:start position:0% +those and then you print it yourself so +you just have those you know spray + + align:start position:0% +you just have those you know spray + + + align:start position:0% +you just have those you know spray +printers and then print those + + align:start position:0% +printers and then print those + + + align:start position:0% +printers and then print those +uh i think those will run + + align:start position:0% +uh i think those will run + + + align:start position:0% +uh i think those will run +like at this point maybe a third of a + + align:start position:0% +like at this point maybe a third of a + + + align:start position:0% +like at this point maybe a third of a +happy cost so + + align:start position:0% +happy cost so + + + align:start position:0% +happy cost so +that's a good option for the future but + + align:start position:0% +that's a good option for the future but + + + align:start position:0% +that's a good option for the future but +it's not clear + + align:start position:0% +it's not clear + + + align:start position:0% +it's not clear +um how good those are so + + align:start position:0% +um how good those are so + + + align:start position:0% +um how good those are so +you know it's cheaper at this point um + + align:start position:0% +you know it's cheaper at this point um + + + align:start position:0% +you know it's cheaper at this point um +but not as good um + + align:start position:0% +but not as good um + + + align:start position:0% +but not as good um +we are actually trying to print that at + + align:start position:0% +we are actually trying to print that at + + + align:start position:0% +we are actually trying to print that at +the heart partner center ourselves + + align:start position:0% +the heart partner center ourselves + + + align:start position:0% +the heart partner center ourselves +um + + align:start position:0% +um + + + align:start position:0% +um +and so if we can get that to work we're + + align:start position:0% +and so if we can get that to work we're + + + align:start position:0% +and so if we can get that to work we're +doing it for human and math at this + + align:start position:0% +doing it for human and math at this + + + align:start position:0% +doing it for human and math at this +point if you can get that work that + + align:start position:0% +point if you can get that work that + + + align:start position:0% +point if you can get that work that +would be you know + + align:start position:0% +would be you know + + + align:start position:0% +would be you know +very very um + + align:start position:0% +very very um + + + align:start position:0% +very very um +good for our investigators + + align:start position:0% +good for our investigators + + + align:start position:0% +good for our investigators +sage is a very accurate way of doing + + align:start position:0% +sage is a very accurate way of doing + + + align:start position:0% +sage is a very accurate way of doing +special data analysis + + align:start position:0% +special data analysis + + + align:start position:0% +special data analysis +it basically involves sequencing every + + align:start position:0% +it basically involves sequencing every + + + align:start position:0% +it basically involves sequencing every +little tag + + align:start position:0% +little tag + + + align:start position:0% +little tag +so advantage is that you get a very even + + align:start position:0% +so advantage is that you get a very even + + + align:start position:0% +so advantage is that you get a very even +for a very small copy number of + + align:start position:0% +for a very small copy number of + + + align:start position:0% +for a very small copy number of +transcripts you can get them accurately + + align:start position:0% +transcripts you can get them accurately + + + align:start position:0% +transcripts you can get them accurately +the upside is of course or the downside + + align:start position:0% +the upside is of course or the downside + + + align:start position:0% +the upside is of course or the downside +is that it's expensive + + align:start position:0% +is that it's expensive + + + align:start position:0% +is that it's expensive +but there are a bunch of groups around + + align:start position:0% +but there are a bunch of groups around + + + align:start position:0% +but there are a bunch of groups around +here that have large libraries + + align:start position:0% +here that have large libraries + + + align:start position:0% +here that have large libraries +so + + align:start position:0% +so + + + align:start position:0% +so +i'm personally interested in the second + + align:start position:0% +i'm personally interested in the second + + + align:start position:0% +i'm personally interested in the second +point + + align:start position:0% +point + + + align:start position:0% +point +which is nowadays called systems biology + + align:start position:0% +which is nowadays called systems biology + + + align:start position:0% +which is nowadays called systems biology +so + + align:start position:0% +so + + + align:start position:0% +so +that is integrating a lot of high + + align:start position:0% +that is integrating a lot of high + + + align:start position:0% +that is integrating a lot of high +throughput technologies + + align:start position:0% +throughput technologies + + + align:start position:0% +throughput technologies +in genomics and proteomics and putting + + align:start position:0% +in genomics and proteomics and putting + + + align:start position:0% +in genomics and proteomics and putting +that together so microarray is where + + align:start position:0% +that together so microarray is where + + + align:start position:0% +that together so microarray is where +everyone started now that all these + + align:start position:0% +everyone started now that all these + + + align:start position:0% +everyone started now that all these +other technologies are getting more + + align:start position:0% +other technologies are getting more + + + align:start position:0% +other technologies are getting more +mature we're all interested in combining + + align:start position:0% +mature we're all interested in combining + + + align:start position:0% +mature we're all interested in combining +all those + + align:start position:0% +all those + + + align:start position:0% +all those +and there are a lot of public and + + align:start position:0% +and there are a lot of public and + + + align:start position:0% +and there are a lot of public and +commercial tools of the + + align:start position:0% +commercial tools of the + + + align:start position:0% +commercial tools of the +tools and databases that you should be + + align:start position:0% +tools and databases that you should be + + + align:start position:0% +tools and databases that you should be +aware of so i think the problem is + + align:start position:0% +aware of so i think the problem is + + + align:start position:0% +aware of so i think the problem is +that + + align:start position:0% +that + + + align:start position:0% +that +even the the best biologists don't know + + align:start position:0% +even the the best biologists don't know + + + align:start position:0% +even the the best biologists don't know +what's out there so the challenge for + + align:start position:0% +what's out there so the challenge for + + + align:start position:0% +what's out there so the challenge for +for me and a lot of other people in + + align:start position:0% +for me and a lot of other people in + + + align:start position:0% +for me and a lot of other people in +similar situations is that + + align:start position:0% +similar situations is that + + + align:start position:0% +similar situations is that +you have to instead of assuming that + + align:start position:0% +you have to instead of assuming that + + + align:start position:0% +you have to instead of assuming that +they know what's out there you have to + + align:start position:0% +they know what's out there you have to + + + align:start position:0% +they know what's out there you have to +kind of tell them what to do you know + + align:start position:0% +kind of tell them what to do you know + + + align:start position:0% +kind of tell them what to do you know +tell the biologists that you know you + + align:start position:0% +tell the biologists that you know you + + + align:start position:0% +tell the biologists that you know you +should try such and such because + + align:start position:0% +should try such and such because + + + align:start position:0% +should try such and such because +they're just unaware of what's going on + + align:start position:0% +they're just unaware of what's going on + + + align:start position:0% +they're just unaware of what's going on +in bioinformatics generally + + align:start position:0% +in bioinformatics generally + + + align:start position:0% +in bioinformatics generally +so in terms of data integration um + + align:start position:0% +so in terms of data integration um + + + align:start position:0% +so in terms of data integration um +initially you know people did a lot of + + align:start position:0% +initially you know people did a lot of + + + align:start position:0% +initially you know people did a lot of +expression data studies there have been + + align:start position:0% +expression data studies there have been + + + align:start position:0% +expression data studies there have been +some + + align:start position:0% + + + + align:start position:0% + +nice programs that link literature um + + align:start position:0% +nice programs that link literature um + + + align:start position:0% +nice programs that link literature um +for example i we just at the center just + + align:start position:0% +for example i we just at the center just + + + align:start position:0% +for example i we just at the center just +got a commercial license to something + + align:start position:0% +got a commercial license to something + + + align:start position:0% +got a commercial license to something +called ingenuity um you basically put + + align:start position:0% +called ingenuity um you basically put + + + align:start position:0% +called ingenuity um you basically put +your expression data into the software + + align:start position:0% +your expression data into the software + + + align:start position:0% +your expression data into the software +and it will generate nice networks + + align:start position:0% +and it will generate nice networks + + + align:start position:0% +and it will generate nice networks +and you can well there are many ways of + + align:start position:0% +and you can well there are many ways of + + + align:start position:0% +and you can well there are many ways of +viewing this data but you can for + + align:start position:0% +viewing this data but you can for + + + align:start position:0% +viewing this data but you can for +example click on links between genes and + + align:start position:0% +example click on links between genes and + + + align:start position:0% +example click on links between genes and +it will bring up + + align:start position:0% +it will bring up + + + align:start position:0% +it will bring up +all literature + + align:start position:0% +all literature + + + align:start position:0% +all literature +related that site that cite those genes + + align:start position:0% +related that site that cite those genes + + + align:start position:0% +related that site that cite those genes +i mean there are lots of programs to + + align:start position:0% +i mean there are lots of programs to + + + align:start position:0% +i mean there are lots of programs to +that do that but this particular program + + align:start position:0% +that do that but this particular program + + + align:start position:0% +that do that but this particular program +does it really well + + align:start position:0% +does it really well + + + align:start position:0% +does it really well +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +you know something like that is + + align:start position:0% +you know something like that is + + + align:start position:0% +you know something like that is +enormously helpful if you know that such + + align:start position:0% +enormously helpful if you know that such + + + align:start position:0% +enormously helpful if you know that such +things are exist and if you have access + + align:start position:0% +things are exist and if you have access + + + align:start position:0% +things are exist and if you have access +to it there are some free ones out there + + align:start position:0% +to it there are some free ones out there + + + align:start position:0% +to it there are some free ones out there +but they're just not as good i mean this + + align:start position:0% +but they're just not as good i mean this + + + align:start position:0% +but they're just not as good i mean this +software they have + + align:start position:0% +software they have + + + align:start position:0% +software they have +tons of people not not tons a lot of + + align:start position:0% +tons of people not not tons a lot of + + + align:start position:0% +tons of people not not tons a lot of +people just sitting there curating + + align:start position:0% +people just sitting there curating + + + align:start position:0% +people just sitting there curating +literature by hand and so they've + + align:start position:0% +literature by hand and so they've + + + align:start position:0% +literature by hand and so they've +accumulated this huge database + + align:start position:0% +accumulated this huge database + + + align:start position:0% +accumulated this huge database +but i think that's + + align:start position:0% +but i think that's + + + align:start position:0% +but i think that's +eventually this is i think how + + align:start position:0% +eventually this is i think how + + + align:start position:0% +eventually this is i think how +a lot of us are going to do research so + + align:start position:0% +a lot of us are going to do research so + + + align:start position:0% +a lot of us are going to do research so +you know these tools will get smarter + + align:start position:0% +you know these tools will get smarter + + + align:start position:0% +you know these tools will get smarter +and smarter + + align:start position:0% +and smarter + + + align:start position:0% +and smarter +so you don't have to you know go through + + align:start position:0% +so you don't have to you know go through + + + align:start position:0% +so you don't have to you know go through +pubmed yourself + + align:start position:0% +pubmed yourself + + + align:start position:0% +pubmed yourself +there are other types of data i don't + + align:start position:0% +there are other types of data i don't + + + align:start position:0% +there are other types of data i don't +know if you've actually covered any of + + align:start position:0% +know if you've actually covered any of + + + align:start position:0% +know if you've actually covered any of +these + + align:start position:0% +these + + + align:start position:0% +these +in class but there's a lot of protein + + align:start position:0% +in class but there's a lot of protein + + + align:start position:0% +in class but there's a lot of protein +dna binding data + + align:start position:0% +dna binding data + + + align:start position:0% +dna binding data +so the most famous data set is from the + + align:start position:0% +so the most famous data set is from the + + + align:start position:0% +so the most famous data set is from the +white head + + align:start position:0% +white head + + + align:start position:0% +white head +from rick + + align:start position:0% +from rick + + + align:start position:0% +from rick +young's lab where + + align:start position:0% +young's lab where + + + align:start position:0% +young's lab where +for east they + + align:start position:0% +for east they + + + align:start position:0% +for east they +basically took all the transcription + + align:start position:0% +basically took all the transcription + + + align:start position:0% +basically took all the transcription +factors about 100 little more than 100 + + align:start position:0% +factors about 100 little more than 100 + + + align:start position:0% +factors about 100 little more than 100 +for yeast + + align:start position:0% +for yeast + + + align:start position:0% +for yeast +and then they found + + align:start position:0% +and then they found + + + align:start position:0% +and then they found +where in the genome these transcription + + align:start position:0% +where in the genome these transcription + + + align:start position:0% +where in the genome these transcription +factors actually bind so in vivo + + align:start position:0% +factors actually bind so in vivo + + + align:start position:0% +factors actually bind so in vivo +so + + align:start position:0% +so + + + align:start position:0% +so +they can't locate you don't have enough + + align:start position:0% +they can't locate you don't have enough + + + align:start position:0% +they can't locate you don't have enough +resolutions to pinpoint exactly where uh + + align:start position:0% +resolutions to pinpoint exactly where uh + + + align:start position:0% +resolutions to pinpoint exactly where uh +you know what base pair there are + + align:start position:0% + + + + align:start position:0% + +binding but you know which + + align:start position:0% +binding but you know which + + + align:start position:0% +binding but you know which +genes are actually using these + + align:start position:0% +genes are actually using these + + + align:start position:0% +genes are actually using these +transcription factors you know for their + + align:start position:0% +transcription factors you know for their + + + align:start position:0% +transcription factors you know for their +regulation um so you know that data is + + align:start position:0% +regulation um so you know that data is + + + align:start position:0% +regulation um so you know that data is +enormously useful i think they're trying + + align:start position:0% +enormously useful i think they're trying + + + align:start position:0% +enormously useful i think they're trying +to do that for humans human genome but i + + align:start position:0% +to do that for humans human genome but i + + + align:start position:0% +to do that for humans human genome but i +don't know how how well that's going + + align:start position:0% +don't know how how well that's going + + + align:start position:0% +don't know how how well that's going +protein microarrays + + align:start position:0% + + + + align:start position:0% + +so that has been has not been as + + align:start position:0% +so that has been has not been as + + + align:start position:0% +so that has been has not been as +successful as people initially thought + + align:start position:0% +successful as people initially thought + + + align:start position:0% +successful as people initially thought +it would be + + align:start position:0% +it would be + + + align:start position:0% +it would be +there are just a lot of difficulties in + + align:start position:0% +there are just a lot of difficulties in + + + align:start position:0% +there are just a lot of difficulties in +just manufacturing + + align:start position:0% +just manufacturing + + + align:start position:0% +just manufacturing +but + + align:start position:0% +but + + + align:start position:0% +but +for example um at the center + + align:start position:0% +for example um at the center + + + align:start position:0% +for example um at the center +harvard partner center uh there's some + + align:start position:0% +harvard partner center uh there's some + + + align:start position:0% +harvard partner center uh there's some +contract with some company + + align:start position:0% +contract with some company + + + align:start position:0% +contract with some company +um + + align:start position:0% +um + + + align:start position:0% +um +that make these protein arrays with + + align:start position:0% +that make these protein arrays with + + + align:start position:0% +that make these protein arrays with +about + + align:start position:0% +about + + + align:start position:0% +about +50 or 60 um + + align:start position:0% +50 or 60 um + + + align:start position:0% +50 or 60 um +just molecules sitting there then + + align:start position:0% +just molecules sitting there then + + + align:start position:0% +just molecules sitting there then +these i guess these are 50 or 60 really + + align:start position:0% +these i guess these are 50 or 60 really + + + align:start position:0% +these i guess these are 50 or 60 really +common uh sort of antibody uh + + align:start position:0% +common uh sort of antibody uh + + + align:start position:0% +common uh sort of antibody uh +detection systems so i think that could + + align:start position:0% +detection systems so i think that could + + + align:start position:0% +detection systems so i think that could +be very uh + + align:start position:0% +be very uh + + + align:start position:0% +be very uh +helpful + + align:start position:0% +helpful + + + align:start position:0% +helpful +but i think that technology is still not + + align:start position:0% +but i think that technology is still not + + + align:start position:0% +but i think that technology is still not +quite there at least not for the price + + align:start position:0% +quite there at least not for the price + + + align:start position:0% +quite there at least not for the price +that's + + align:start position:0% +that's + + + align:start position:0% +that's +reasonable for + + align:start position:0% +reasonable for + + + align:start position:0% +reasonable for +most investigators + + align:start position:0% +most investigators + + + align:start position:0% +most investigators +mass spec that's an enormous area that + + align:start position:0% +mass spec that's an enormous area that + + + align:start position:0% +mass spec that's an enormous area that +has taken off in the past i'd say at + + align:start position:0% +has taken off in the past i'd say at + + + align:start position:0% +has taken off in the past i'd say at +least in terms of informatics maybe just + + align:start position:0% +least in terms of informatics maybe just + + + align:start position:0% +least in terms of informatics maybe just +past year or two uh there are enormous + + align:start position:0% + + + + align:start position:0% + +amounts of data and a lot of informatics + + align:start position:0% +amounts of data and a lot of informatics + + + align:start position:0% +amounts of data and a lot of informatics +challenges and so + + align:start position:0% +challenges and so + + + align:start position:0% +challenges and so +um yeah another another + + align:start position:0% +um yeah another another + + + align:start position:0% +um yeah another another +set of data that could be integrated + + align:start position:0% +set of data that could be integrated + + + align:start position:0% +set of data that could be integrated +into your studies + + align:start position:0% +into your studies + + + align:start position:0% +into your studies +um so there you know when people talk + + align:start position:0% +um so there you know when people talk + + + align:start position:0% +um so there you know when people talk +about systems biology people mean + + align:start position:0% +about systems biology people mean + + + align:start position:0% +about systems biology people mean +different things but generally they + + align:start position:0% +different things but generally they + + + align:start position:0% +different things but generally they +refer to the fact that you have you're + + align:start position:0% +refer to the fact that you have you're + + + align:start position:0% +refer to the fact that you have you're +combining combining all these different + + align:start position:0% +combining combining all these different + + + align:start position:0% +combining combining all these different +types to generate some coherent picture + + align:start position:0% +types to generate some coherent picture + + + align:start position:0% +types to generate some coherent picture +and it's just it's actually really hard + + align:start position:0% +and it's just it's actually really hard + + + align:start position:0% +and it's just it's actually really hard +and i think some of the reasons will be + + align:start position:0% +and i think some of the reasons will be + + + align:start position:0% +and i think some of the reasons will be +clear uh in the next few slides + + align:start position:0% +clear uh in the next few slides + + + align:start position:0% +clear uh in the next few slides +okay so let me just skip that + + align:start position:0% +okay so let me just skip that + + + align:start position:0% +okay so let me just skip that +um + + align:start position:0% +um + + + align:start position:0% +um +so just to give you a funny story on + + align:start position:0% +so just to give you a funny story on + + + align:start position:0% +so just to give you a funny story on +sort of you know + + align:start position:0% +sort of you know + + + align:start position:0% +sort of you know +the necessity for a good analysis with + + align:start position:0% +the necessity for a good analysis with + + + align:start position:0% +the necessity for a good analysis with +all this data there was a well + + align:start position:0% + + + + align:start position:0% + +cited paper + + align:start position:0% +cited paper + + + align:start position:0% +cited paper +in nature genetics in 2001 called + + align:start position:0% +in nature genetics in 2001 called + + + align:start position:0% +in nature genetics in 2001 called +transcriptional regulation and function + + align:start position:0% +transcriptional regulation and function + + + align:start position:0% +transcriptional regulation and function +during the human cell cycle + + align:start position:0% +during the human cell cycle + + + align:start position:0% +during the human cell cycle +so + + align:start position:0% +so + + + align:start position:0% +so +i think it actually came from the group + + align:start position:0% +i think it actually came from the group + + + align:start position:0% +i think it actually came from the group +that did the yeast cell cycle a couple + + align:start position:0% +that did the yeast cell cycle a couple + + + align:start position:0% +that did the yeast cell cycle a couple +years back prior to that and in that + + align:start position:0% +years back prior to that and in that + + + align:start position:0% +years back prior to that and in that +paper they claimed that there were a + + align:start position:0% +paper they claimed that there were a + + + align:start position:0% +paper they claimed that there were a +large number of mammalian genes about + + align:start position:0% +large number of mammalian genes about + + + align:start position:0% +large number of mammalian genes about +700 that had cell cycle specific + + align:start position:0% +700 that had cell cycle specific + + + align:start position:0% +700 that had cell cycle specific +patterns so + + align:start position:0% + + + + align:start position:0% + +i think this was done on um affy data + + align:start position:0% +i think this was done on um affy data + + + align:start position:0% +i think this was done on um affy data +actually + + align:start position:0% +actually + + + align:start position:0% +actually +anyway the next year there's a paper in + + align:start position:0% +anyway the next year there's a paper in + + + align:start position:0% +anyway the next year there's a paper in +pnas + + align:start position:0% +pnas + + + align:start position:0% +pnas +called analysis of cell cycle specific + + align:start position:0% +called analysis of cell cycle specific + + + align:start position:0% +called analysis of cell cycle specific +gene expression in human cells as + + align:start position:0% +gene expression in human cells as + + + align:start position:0% +gene expression in human cells as +determined by microwaves and double + + align:start position:0% +determined by microwaves and double + + + align:start position:0% +determined by microwaves and double +diamidone block synchronization so + + align:start position:0% +diamidone block synchronization so + + + align:start position:0% +diamidone block synchronization so +from the title you can't really tell + + align:start position:0% +from the title you can't really tell + + + align:start position:0% +from the title you can't really tell +what this you know + + align:start position:0% +what this you know + + + align:start position:0% +what this you know +what the subject is but basically what + + align:start position:0% +what the subject is but basically what + + + align:start position:0% +what the subject is but basically what +they did in the 2002 paper is go back + + align:start position:0% +they did in the 2002 paper is go back + + + align:start position:0% +they did in the 2002 paper is go back +and re-analyze the data from 2001 paper + + align:start position:0% +and re-analyze the data from 2001 paper + + + align:start position:0% +and re-analyze the data from 2001 paper +and + + align:start position:0% +and + + + align:start position:0% +and +so if you look at the text here the + + align:start position:0% +so if you look at the text here the + + + align:start position:0% +so if you look at the text here the +original microarray data presented to + + align:start position:0% +original microarray data presented to + + + align:start position:0% +original microarray data presented to +support the existence of + + align:start position:0% +support the existence of + + + align:start position:0% +support the existence of +cyclic or + + align:start position:0% +cyclic or + + + align:start position:0% +cyclic or +gene expression in human cells is now + + align:start position:0% +gene expression in human cells is now + + + align:start position:0% +gene expression in human cells is now +re-examined with a statistical approach + + align:start position:0% +re-examined with a statistical approach + + + align:start position:0% +re-examined with a statistical approach +we find that there is + + align:start position:0% +we find that there is + + + align:start position:0% +we find that there is +internal evidence implying that the + + align:start position:0% +internal evidence implying that the + + + align:start position:0% +internal evidence implying that the +original microarray data do not support + + align:start position:0% +original microarray data do not support + + + align:start position:0% +original microarray data do not support +the proposed patterns of gene expression + + align:start position:0% +the proposed patterns of gene expression + + + align:start position:0% +the proposed patterns of gene expression +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so they + + align:start position:0% +so they + + + align:start position:0% +so they +one of these i think it was the first + + align:start position:0% +one of these i think it was the first + + + align:start position:0% +one of these i think it was the first +author that's a statistician so they + + align:start position:0% +author that's a statistician so they + + + align:start position:0% +author that's a statistician so they +claim that + + align:start position:0% +claim that + + + align:start position:0% +claim that +so to + + align:start position:0% +so to + + + align:start position:0% +so to +uh to study the the cell cycle you need + + align:start position:0% +uh to study the the cell cycle you need + + + align:start position:0% +uh to study the the cell cycle you need +to synchronize at the beginning right + + align:start position:0% +to synchronize at the beginning right + + + align:start position:0% +to synchronize at the beginning right +using some you know one of many methods + + align:start position:0% +using some you know one of many methods + + + align:start position:0% +using some you know one of many methods +then they you know look at this data and + + align:start position:0% +then they you know look at this data and + + + align:start position:0% +then they you know look at this data and +say well you know after randomizing data + + align:start position:0% +say well you know after randomizing data + + + align:start position:0% +say well you know after randomizing data +we still see a bunch of genes that have + + align:start position:0% +we still see a bunch of genes that have + + + align:start position:0% +we still see a bunch of genes that have +cycle cyclic behavior + + align:start position:0% +cycle cyclic behavior + + + align:start position:0% +cycle cyclic behavior +in fact you know if you study carefully + + align:start position:0% +in fact you know if you study carefully + + + align:start position:0% +in fact you know if you study carefully +cells are not even synchronized so they + + align:start position:0% +cells are not even synchronized so they + + + align:start position:0% +cells are not even synchronized so they +claim that the first experiment was just + + align:start position:0% +claim that the first experiment was just + + + align:start position:0% +claim that the first experiment was just +junk right + + align:start position:0% +junk right + + + align:start position:0% +junk right +and the the 700 genes that they observed + + align:start position:0% +and the the 700 genes that they observed + + + align:start position:0% +and the the 700 genes that they observed +was + + align:start position:0% +was + + + align:start position:0% +was +something that just could have come by + + align:start position:0% +something that just could have come by + + + align:start position:0% +something that just could have come by +chance + + align:start position:0% + + + + align:start position:0% + +right because you i mean because you + + align:start position:0% +right because you i mean because you + + + align:start position:0% +right because you i mean because you +have so many genes you're going to see + + align:start position:0% +have so many genes you're going to see + + + align:start position:0% +have so many genes you're going to see +some genes that go in cycles + + align:start position:0% +some genes that go in cycles + + + align:start position:0% +some genes that go in cycles +okay so it came out in pianist and so + + align:start position:0% +okay so it came out in pianist and so + + + align:start position:0% +okay so it came out in pianist and so +since then um + + align:start position:0% +since then um + + + align:start position:0% +since then um +at least yeah they were just back in you + + align:start position:0% +at least yeah they were just back in you + + + align:start position:0% +at least yeah they were just back in you +know exchanges back and forth right so + + align:start position:0% +know exchanges back and forth right so + + + align:start position:0% +know exchanges back and forth right so +the first group you know has a website + + align:start position:0% +the first group you know has a website + + + align:start position:0% +the first group you know has a website +that details like + + align:start position:0% +that details like + + + align:start position:0% +that details like +this is what we did + + align:start position:0% +this is what we did + + + align:start position:0% +this is what we did +this is what the pns paper did and this + + align:start position:0% +this is what the pns paper did and this + + + align:start position:0% +this is what the pns paper did and this +is why they're wrong just you know whole + + align:start position:0% +is why they're wrong just you know whole + + + align:start position:0% +is why they're wrong just you know whole +website and i think this the second guys + + align:start position:0% +website and i think this the second guys + + + align:start position:0% +website and i think this the second guys +also had a rebuttal to that website + + align:start position:0% +also had a rebuttal to that website + + + align:start position:0% +also had a rebuttal to that website +so + + align:start position:0% +so + + + align:start position:0% +so +it would + + align:start position:0% +it would + + + align:start position:0% +it would +right and this is a you know + + align:start position:0% +right and this is a you know + + + align:start position:0% +right and this is a you know +uh + + align:start position:0% +uh + + + align:start position:0% +uh +important + + align:start position:0% +important + + + align:start position:0% +important +uh + + align:start position:0% +uh + + + align:start position:0% +uh +thing to settle right because + + align:start position:0% +thing to settle right because + + + align:start position:0% +thing to settle right because +you know it came out in nature genetics + + align:start position:0% +you know it came out in nature genetics + + + align:start position:0% +you know it came out in nature genetics +a lot of people are using this data but + + align:start position:0% +a lot of people are using this data but + + + align:start position:0% +a lot of people are using this data but +the other group says this is all + + align:start position:0% +the other group says this is all + + + align:start position:0% +the other group says this is all +nonsense + + align:start position:0% +nonsense + + + align:start position:0% +nonsense +and + + align:start position:0% +and + + + align:start position:0% +and +i think i mean so i read through a + + align:start position:0% +i think i mean so i read through a + + + align:start position:0% +i think i mean so i read through a +little bit of that i think what happened + + align:start position:0% +little bit of that i think what happened + + + align:start position:0% +little bit of that i think what happened +was + + align:start position:0% +was + + + align:start position:0% +was +i mean as usual the truth is somewhere + + align:start position:0% +i mean as usual the truth is somewhere + + + align:start position:0% +i mean as usual the truth is somewhere +in between i mean the first group was so + + align:start position:0% +in between i mean the first group was so + + + align:start position:0% +in between i mean the first group was so +you know interested in showing that + + align:start position:0% +you know interested in showing that + + + align:start position:0% +you know interested in showing that +there are lots of genes that are + + align:start position:0% +there are lots of genes that are + + + align:start position:0% +there are lots of genes that are +um cycling that they just + + align:start position:0% +um cycling that they just + + + align:start position:0% +um cycling that they just +you know + + align:start position:0% +you know + + + align:start position:0% +you know +you know + + align:start position:0% +you know + + + align:start position:0% +you know +use methods that will be advantageous to + + align:start position:0% +use methods that will be advantageous to + + + align:start position:0% +use methods that will be advantageous to +them and the second uh + + align:start position:0% +them and the second uh + + + align:start position:0% +them and the second uh +paper they were so interested in showing + + align:start position:0% +paper they were so interested in showing + + + align:start position:0% +paper they were so interested in showing +that the data was wrong that they + + align:start position:0% +that the data was wrong that they + + + align:start position:0% +that the data was wrong that they +defined things in such a way that there + + align:start position:0% +defined things in such a way that there + + + align:start position:0% +defined things in such a way that there +would be no uh + + align:start position:0% +would be no uh + + + align:start position:0% +would be no uh +you know cycling genes so + + align:start position:0% + + + + align:start position:0% + +if you found the same gene + + align:start position:0% +if you found the same gene + + + align:start position:0% +if you found the same gene +yeah + + align:start position:0% + + + + align:start position:0% + +maybe i don't know yeah yeah + + align:start position:0% +maybe i don't know yeah yeah + + + align:start position:0% +maybe i don't know yeah yeah +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +i mean i like that depending on how you + + align:start position:0% +i mean i like that depending on how you + + + align:start position:0% +i mean i like that depending on how you +do it i i would say i would think that + + align:start position:0% +do it i i would say i would think that + + + align:start position:0% +do it i i would say i would think that +you know they would find some overlap + + align:start position:0% +you know they would find some overlap + + + align:start position:0% +you know they would find some overlap +with the first one but not 700 right so + + align:start position:0% +with the first one but not 700 right so + + + align:start position:0% +with the first one but not 700 right so +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so + + align:start position:0% +so + + + align:start position:0% +so +so i guess the lesson is that you should + + align:start position:0% +so i guess the lesson is that you should + + + align:start position:0% +so i guess the lesson is that you should +you know make sure you do things well + + align:start position:0% +you know make sure you do things well + + + align:start position:0% +you know make sure you do things well +before you publish + + align:start position:0% +before you publish + + + align:start position:0% +before you publish +at least in such a way that you know no + + align:start position:0% +at least in such a way that you know no + + + align:start position:0% +at least in such a way that you know no +one can attack you like this + + align:start position:0% +one can attack you like this + + + align:start position:0% +one can attack you like this +and this is just one example there are a + + align:start position:0% +and this is just one example there are a + + + align:start position:0% +and this is just one example there are a +lot of + + align:start position:0% +lot of + + + align:start position:0% +lot of +problems with early + + align:start position:0% +problems with early + + + align:start position:0% +problems with early +studies and i'll actually + + align:start position:0% +studies and i'll actually + + + align:start position:0% +studies and i'll actually +tell you about another problem + + align:start position:0% +tell you about another problem + + + align:start position:0% +tell you about another problem +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +that has been very common + + align:start position:0% + + + + align:start position:0% + +so one thing + + align:start position:0% +so one thing + + + align:start position:0% +so one thing +that i've been interested in with a + + align:start position:0% +that i've been interested in with a + + + align:start position:0% +that i've been interested in with a +student + + align:start position:0% +student + + + align:start position:0% +student +who actually published a paper on this + + align:start position:0% +who actually published a paper on this + + + align:start position:0% +who actually published a paper on this +um before anyone else + + align:start position:0% +um before anyone else + + + align:start position:0% +um before anyone else +so there are substantial differences in + + align:start position:0% +so there are substantial differences in + + + align:start position:0% +so there are substantial differences in +different technologies for microwave + + align:start position:0% +different technologies for microwave + + + align:start position:0% +different technologies for microwave +platforms right so you know cdnas you + + align:start position:0% +platforms right so you know cdnas you + + + align:start position:0% +platforms right so you know cdnas you +know they're very different from affy uh + + align:start position:0% +know they're very different from affy uh + + + align:start position:0% +know they're very different from affy uh +arrays + + align:start position:0% +arrays + + + align:start position:0% +arrays +so you know a lot of the + + align:start position:0% +so you know a lot of the + + + align:start position:0% +so you know a lot of the +one of the common questions is what + + align:start position:0% +one of the common questions is what + + + align:start position:0% +one of the common questions is what +platform should i use right + + align:start position:0% +platform should i use right + + + align:start position:0% +platform should i use right +if something's cheaper does it work as + + align:start position:0% +if something's cheaper does it work as + + + align:start position:0% +if something's cheaper does it work as +well do they agree + + align:start position:0% +well do they agree + + + align:start position:0% +well do they agree +um + + align:start position:0% +um + + + align:start position:0% +um +so which platform is the best and so + + align:start position:0% +so which platform is the best and so + + + align:start position:0% +so which platform is the best and so +there are a bunch of papers on this some + + align:start position:0% +there are a bunch of papers on this some + + + align:start position:0% +there are a bunch of papers on this some +of which are cited in the article um but + + align:start position:0% +of which are cited in the article um but + + + align:start position:0% +of which are cited in the article um but +i mean that's just a very small subset + + align:start position:0% +i mean that's just a very small subset + + + align:start position:0% +i mean that's just a very small subset +and most of them are conflicting um + + align:start position:0% +and most of them are conflicting um + + + align:start position:0% +and most of them are conflicting um +except that you know + + align:start position:0% +except that you know + + + align:start position:0% +except that you know +they agree that they do not agree very + + align:start position:0% +they agree that they do not agree very + + + align:start position:0% +they agree that they do not agree very +well okay so it's they're conflicting in + + align:start position:0% +well okay so it's they're conflicting in + + + align:start position:0% +well okay so it's they're conflicting in +terms of you know which one is better + + align:start position:0% +terms of you know which one is better + + + align:start position:0% +terms of you know which one is better +you know how accurate are they + + align:start position:0% +you know how accurate are they + + + align:start position:0% +you know how accurate are they +um + + align:start position:0% +um + + + align:start position:0% +um +but i think overall it's the overlap is + + align:start position:0% +but i think overall it's the overlap is + + + align:start position:0% +but i think overall it's the overlap is +surprisingly small so if you do your + + align:start position:0% +surprisingly small so if you do your + + + align:start position:0% +surprisingly small so if you do your +experiment with cdna arrays find genes + + align:start position:0% +experiment with cdna arrays find genes + + + align:start position:0% +experiment with cdna arrays find genes +that are different from spiders you + + align:start position:0% +that are different from spiders you + + + align:start position:0% +that are different from spiders you +repeat the experiment with + + align:start position:0% +repeat the experiment with + + + align:start position:0% +repeat the experiment with +acne arrays you get a very different + + align:start position:0% +acne arrays you get a very different + + + align:start position:0% +acne arrays you get a very different +result okay + + align:start position:0% +result okay + + + align:start position:0% +result okay +so that's a big problem right i mean for + + align:start position:0% +so that's a big problem right i mean for + + + align:start position:0% +so that's a big problem right i mean for +one thing you're not sure if the results + + align:start position:0% +one thing you're not sure if the results + + + align:start position:0% +one thing you're not sure if the results +that you get are correct or not + + align:start position:0% +that you get are correct or not + + + align:start position:0% +that you get are correct or not +um + + align:start position:0% +um + + + align:start position:0% +um +and + + align:start position:0% +and + + + align:start position:0% +and +another thing is that eventually you'd + + align:start position:0% +another thing is that eventually you'd + + + align:start position:0% +another thing is that eventually you'd +like to you know combine data from + + align:start position:0% +like to you know combine data from + + + align:start position:0% +like to you know combine data from +different people right so if you if + + align:start position:0% +different people right so if you if + + + align:start position:0% +different people right so if you if +someone else + + align:start position:0% +someone else + + + align:start position:0% +someone else +you know in another school has done + + align:start position:0% +you know in another school has done + + + align:start position:0% +you know in another school has done +um you know very similar experiment + + align:start position:0% +um you know very similar experiment + + + align:start position:0% +um you know very similar experiment +then you don't want to you know and you + + align:start position:0% +then you don't want to you know and you + + + align:start position:0% +then you don't want to you know and you +want to see how your experiment compares + + align:start position:0% +want to see how your experiment compares + + + align:start position:0% +want to see how your experiment compares +with that + + align:start position:0% +with that + + + align:start position:0% +with that +then you don't want to have to repeat + + align:start position:0% +then you don't want to have to repeat + + + align:start position:0% +then you don't want to have to repeat +their experiment you like to just do + + align:start position:0% +their experiment you like to just do + + + align:start position:0% +their experiment you like to just do +your experiment on whatever platform you + + align:start position:0% +your experiment on whatever platform you + + + align:start position:0% +your experiment on whatever platform you +have and compare it against what someone + + align:start position:0% +have and compare it against what someone + + + align:start position:0% +have and compare it against what someone +else has done which may not be on the + + align:start position:0% +else has done which may not be on the + + + align:start position:0% +else has done which may not be on the +same platform + + align:start position:0% +same platform + + + align:start position:0% +same platform +and so + + align:start position:0% +and so + + + align:start position:0% +and so +this is a big issue and i + + align:start position:0% +this is a big issue and i + + + align:start position:0% +this is a big issue and i +it's you know far away from being + + align:start position:0% +it's you know far away from being + + + align:start position:0% +it's you know far away from being +settled just there are so many issues + + align:start position:0% +settled just there are so many issues + + + align:start position:0% +settled just there are so many issues +and + + align:start position:0% +and + + + align:start position:0% +and +problems so that + + align:start position:0% +problems so that + + + align:start position:0% +problems so that +i think it'll be + + align:start position:0% +i think it'll be + + + align:start position:0% +i think it'll be +a while before + + align:start position:0% +a while before + + + align:start position:0% +a while before +these things get sorted out + + align:start position:0% +these things get sorted out + + + align:start position:0% +these things get sorted out +so + + align:start position:0% +so + + + align:start position:0% +so +um as i mentioned affy + + align:start position:0% +um as i mentioned affy + + + align:start position:0% +um as i mentioned affy +arrays appear to have the most + + align:start position:0% +arrays appear to have the most + + + align:start position:0% +arrays appear to have the most +reproducible experiment you know i think + + align:start position:0% +reproducible experiment you know i think + + + align:start position:0% +reproducible experiment you know i think +most people + + align:start position:0% +most people + + + align:start position:0% +most people +that have tried multiple hybridizations + + align:start position:0% +that have tried multiple hybridizations + + + align:start position:0% +that have tried multiple hybridizations +will say that they agree + + align:start position:0% +will say that they agree + + + align:start position:0% +will say that they agree +with correlation of 0.9899 + + align:start position:0% +with correlation of 0.9899 + + + align:start position:0% +with correlation of 0.9899 +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +but one thing i've done with + + align:start position:0% +but one thing i've done with + + + align:start position:0% +but one thing i've done with +steve greenberg which over who whom you + + align:start position:0% +steve greenberg which over who whom you + + + align:start position:0% +steve greenberg which over who whom you +met i think a couple weeks ago + + align:start position:0% +met i think a couple weeks ago + + + align:start position:0% +met i think a couple weeks ago +is um that we've studied how we + + align:start position:0% +is um that we've studied how we + + + align:start position:0% +is um that we've studied how we +reproducible data are between two + + align:start position:0% +reproducible data are between two + + + align:start position:0% +reproducible data are between two +generations of athlete arrays so there + + align:start position:0% +generations of athlete arrays so there + + + align:start position:0% +generations of athlete arrays so there +is + + align:start position:0% +is + + + align:start position:0% +is +a very + + align:start position:0% +a very + + + align:start position:0% +a very +popular set of + + align:start position:0% +popular set of + + + align:start position:0% +popular set of +arrays the first one was u-95 that + + align:start position:0% +arrays the first one was u-95 that + + + align:start position:0% +arrays the first one was u-95 that +that's + + align:start position:0% +that's + + + align:start position:0% +that's +95 refers to the uni uh the version of + + align:start position:0% +95 refers to the uni uh the version of + + + align:start position:0% +95 refers to the uni uh the version of +uh unigine database that they use to + + align:start position:0% +uh unigine database that they use to + + + align:start position:0% +uh unigine database that they use to +um + + align:start position:0% +um + + + align:start position:0% +um +to collect the information about with + + align:start position:0% +to collect the information about with + + + align:start position:0% +to collect the information about with +you know the probes + + align:start position:0% +you know the probes + + + align:start position:0% +you know the probes +so that i think + + align:start position:0% +so that i think + + + align:start position:0% +so that i think +um people used for a couple of years uh + + align:start position:0% +um people used for a couple of years uh + + + align:start position:0% +um people used for a couple of years uh +lots of chips i mean many thousands of + + align:start position:0% +lots of chips i mean many thousands of + + + align:start position:0% +lots of chips i mean many thousands of +chips + + align:start position:0% +chips + + + align:start position:0% +chips +and then u133 is the newer one + + align:start position:0% +and then u133 is the newer one + + + align:start position:0% +and then u133 is the newer one +and there's a + + align:start position:0% +and there's a + + + align:start position:0% +and there's a +so + + align:start position:0% +so + + + align:start position:0% +so +u95 actually came in five chips and u133 + + align:start position:0% +u95 actually came in five chips and u133 + + + align:start position:0% +u95 actually came in five chips and u133 +came in two chips so you know they + + align:start position:0% +came in two chips so you know they + + + align:start position:0% +came in two chips so you know they +do they changed bunch of things so they + + align:start position:0% +do they changed bunch of things so they + + + align:start position:0% +do they changed bunch of things so they +were able to fit into two chips + + align:start position:0% +were able to fit into two chips + + + align:start position:0% +were able to fit into two chips +now there are there is just a single + + align:start position:0% +now there are there is just a single + + + align:start position:0% +now there are there is just a single +chip with all the whole human + + align:start position:0% + + + + align:start position:0% + +genes so + + align:start position:0% +genes so + + + align:start position:0% +genes so +you know from you know five arrays + + align:start position:0% +you know from you know five arrays + + + align:start position:0% +you know from you know five arrays +three four years ago now you have a + + align:start position:0% +three four years ago now you have a + + + align:start position:0% +three four years ago now you have a +single array um + + align:start position:0% +single array um + + + align:start position:0% +single array um +and so a lot of experiments have been + + align:start position:0% +and so a lot of experiments have been + + + align:start position:0% +and so a lot of experiments have been +done um and these are human arrays + + align:start position:0% +done um and these are human arrays + + + align:start position:0% +done um and these are human arrays +just to give you a sense of how many + + align:start position:0% +just to give you a sense of how many + + + align:start position:0% +just to give you a sense of how many +arrays are out there when i was talking + + align:start position:0% +arrays are out there when i was talking + + + align:start position:0% +arrays are out there when i was talking +to someone from juventus + + align:start position:0% +to someone from juventus + + + align:start position:0% +to someone from juventus +pharmaceutical they have a prepared + + align:start position:0% +pharmaceutical they have a prepared + + + align:start position:0% +pharmaceutical they have a prepared +proprietary database with + + align:start position:0% +proprietary database with + + + align:start position:0% +proprietary database with +i think they said about + + align:start position:0% +i think they said about + + + align:start position:0% +i think they said about +i can't remember it was either 20 000 or + + align:start position:0% +i can't remember it was either 20 000 or + + + align:start position:0% +i can't remember it was either 20 000 or +30 000 chips + + align:start position:0% +30 000 chips + + + align:start position:0% +30 000 chips +right + + align:start position:0% +right + + + align:start position:0% +right +of their own right + + align:start position:0% +of their own right + + + align:start position:0% +of their own right +their internal database so 20 000 let's + + align:start position:0% +their internal database so 20 000 let's + + + align:start position:0% +their internal database so 20 000 let's +say times thousand bucks that's 20 + + align:start position:0% +say times thousand bucks that's 20 + + + align:start position:0% +say times thousand bucks that's 20 +million right it's a lot of money + + align:start position:0% +million right it's a lot of money + + + align:start position:0% +million right it's a lot of money +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +anyway so there's a lot of data using + + align:start position:0% +anyway so there's a lot of data using + + + align:start position:0% +anyway so there's a lot of data using +these error i actually i don't know if + + align:start position:0% +these error i actually i don't know if + + + align:start position:0% +these error i actually i don't know if +uh these arrays are not the one you know + + align:start position:0% +uh these arrays are not the one you know + + + align:start position:0% +uh these arrays are not the one you know +they didn't they didn't have 20 000 of + + align:start position:0% +they didn't they didn't have 20 000 of + + + align:start position:0% +they didn't they didn't have 20 000 of +these arrays but they have a lot of + + align:start position:0% +these arrays but they have a lot of + + + align:start position:0% +these arrays but they have a lot of +atheists these are twenty thousand + + align:start position:0% +atheists these are twenty thousand + + + align:start position:0% +atheists these are twenty thousand +accurace + + align:start position:0% +accurace + + + align:start position:0% +accurace +um and that's just one company um + + align:start position:0% +um and that's just one company um + + + align:start position:0% +um and that's just one company um +anyway so + + align:start position:0% +anyway so + + + align:start position:0% +anyway so +what steve and i wanted to do was + + align:start position:0% +what steve and i wanted to do was + + + align:start position:0% +what steve and i wanted to do was +look at how + + align:start position:0% + + + + align:start position:0% + +how the the results would vary depending + + align:start position:0% +how the the results would vary depending + + + align:start position:0% +how the the results would vary depending +on which platform you use + + align:start position:0% +on which platform you use + + + align:start position:0% +on which platform you use +and + + align:start position:0% +and + + + align:start position:0% +and +he actually had done the experiment on + + align:start position:0% +he actually had done the experiment on + + + align:start position:0% +he actually had done the experiment on +u-95 and then + + align:start position:0% +u-95 and then + + + align:start position:0% +u-95 and then +then he had a new grand he had more + + align:start position:0% +then he had a new grand he had more + + + align:start position:0% +then he had a new grand he had more +samples so he wanted to uniformly again + + align:start position:0% +samples so he wanted to uniformly again + + + align:start position:0% +samples so he wanted to uniformly again +and so he did it on u133 + + align:start position:0% +and so he did it on u133 + + + align:start position:0% +and so he did it on u133 +and you know it's not because he had so + + align:start position:0% +and you know it's not because he had so + + + align:start position:0% +and you know it's not because he had so +much money that he just wanted to try + + align:start position:0% +much money that he just wanted to try + + + align:start position:0% +much money that he just wanted to try +this + + align:start position:0% +this + + + align:start position:0% +this +so what he did was he hybridized 14 + + align:start position:0% +so what he did was he hybridized 14 + + + align:start position:0% +so what he did was he hybridized 14 +muscle life samples from + + align:start position:0% +muscle life samples from + + + align:start position:0% +muscle life samples from +with + + align:start position:0% +with + + + align:start position:0% +with +patients with inflammatory myopathies + + align:start position:0% +patients with inflammatory myopathies + + + align:start position:0% +patients with inflammatory myopathies +which is + + align:start position:0% +which is + + + align:start position:0% +which is +his specialty then they were hybridized + + align:start position:0% +his specialty then they were hybridized + + + align:start position:0% +his specialty then they were hybridized +to both chips + + align:start position:0% +to both chips + + + align:start position:0% +to both chips +so i looked at this data we submitted + + align:start position:0% +so i looked at this data we submitted + + + align:start position:0% +so i looked at this data we submitted +the paper just recently um but what we + + align:start position:0% +the paper just recently um but what we + + + align:start position:0% +the paper just recently um but what we +looked at was what happens when we group + + align:start position:0% +looked at was what happens when we group + + + align:start position:0% +looked at was what happens when we group +the arrays using hierarchical clustering + + align:start position:0% +the arrays using hierarchical clustering + + + align:start position:0% +the arrays using hierarchical clustering +which you know by now and when we find + + align:start position:0% +which you know by now and when we find + + + align:start position:0% +which you know by now and when we find +differential expense genes in each case + + align:start position:0% +differential expense genes in each case + + + align:start position:0% +differential expense genes in each case +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +you can't read the labels from there i + + align:start position:0% +you can't read the labels from there i + + + align:start position:0% +you can't read the labels from there i +bet but + + align:start position:0% +bet but + + + align:start position:0% +bet but +so that if you look at the top left one + + align:start position:0% +so that if you look at the top left one + + + align:start position:0% +so that if you look at the top left one +so we basically + + align:start position:0% +so we basically + + + align:start position:0% +so we basically +pulled all the data together and said + + align:start position:0% +pulled all the data together and said + + + align:start position:0% +pulled all the data together and said +okay just can i can i cluster them so + + align:start position:0% +okay just can i can i cluster them so + + + align:start position:0% +okay just can i can i cluster them so +you what you should see is + + align:start position:0% +you what you should see is + + + align:start position:0% +you what you should see is +you know same sample hybridized to 95 + + align:start position:0% +you know same sample hybridized to 95 + + + align:start position:0% +you know same sample hybridized to 95 +133 should be next to each other right + + align:start position:0% +133 should be next to each other right + + + align:start position:0% +133 should be next to each other right +that should be the case for all your + + align:start position:0% +that should be the case for all your + + + align:start position:0% +that should be the case for all your +samples + + align:start position:0% +samples + + + align:start position:0% +samples +um + + align:start position:0% +um + + + align:start position:0% +um +in this clustering + + align:start position:0% +in this clustering + + + align:start position:0% +in this clustering +everything on the left is u133 and + + align:start position:0% +everything on the left is u133 and + + + align:start position:0% +everything on the left is u133 and +everything on the right is u95 + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay so if you cluster + + align:start position:0% +okay so if you cluster + + + align:start position:0% +okay so if you cluster +okay + + align:start position:0% +okay + + + align:start position:0% +okay +it's not the sample characteristics but + + align:start position:0% +it's not the sample characteristics but + + + align:start position:0% +it's not the sample characteristics but +the array type that it's the + + align:start position:0% +the array type that it's the + + + align:start position:0% +the array type that it's the +distinguishing feature + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +well in this case + + align:start position:0% +well in this case + + + align:start position:0% +well in this case +we use pearson correlation so + + align:start position:0% +we use pearson correlation so + + + align:start position:0% +we use pearson correlation so +any linear normalization would not + + align:start position:0% +any linear normalization would not + + + align:start position:0% +any linear normalization would not +affect the result + + align:start position:0% +affect the result + + + align:start position:0% +affect the result +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but no matter what you try it's going to + + align:start position:0% +but no matter what you try it's going to + + + align:start position:0% +but no matter what you try it's going to +turn out this way + + align:start position:0% +turn out this way + + + align:start position:0% +turn out this way +and so this is disturbing right + + align:start position:0% + + + + align:start position:0% + +so there are some ways to fix this so + + align:start position:0% +so there are some ways to fix this so + + + align:start position:0% +so there are some ways to fix this so +in this particular case + + align:start position:0% +in this particular case + + + align:start position:0% +in this particular case +um we + + align:start position:0% +um we + + + align:start position:0% +um we +normalized the genes in a particular way + + align:start position:0% +normalized the genes in a particular way + + + align:start position:0% +normalized the genes in a particular way +and then we were able to actually get + + align:start position:0% +and then we were able to actually get + + + align:start position:0% +and then we were able to actually get +this to line up correctly + + align:start position:0% +this to line up correctly + + + align:start position:0% +this to line up correctly +but what we did in this case + + align:start position:0% +but what we did in this case + + + align:start position:0% +but what we did in this case +um in general you know doesn't work so + + align:start position:0% +um in general you know doesn't work so + + + align:start position:0% +um in general you know doesn't work so +we could only do it here but in general + + align:start position:0% +we could only do it here but in general + + + align:start position:0% +we could only do it here but in general +it doesn't work + + align:start position:0% +it doesn't work + + + align:start position:0% +it doesn't work +so remember this is you know + + align:start position:0% +so remember this is you know + + + align:start position:0% +so remember this is you know +one platform just different generations + + align:start position:0% +one platform just different generations + + + align:start position:0% +one platform just different generations +right so if you were to compare + + align:start position:0% +right so if you were to compare + + + align:start position:0% +right so if you were to compare +different platforms i mean things are + + align:start position:0% +different platforms i mean things are + + + align:start position:0% +different platforms i mean things are +just much harder + + align:start position:0% +just much harder + + + align:start position:0% +just much harder +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and so + + align:start position:0% +and so + + + align:start position:0% +and so +it's just + + align:start position:0% +it's just + + + align:start position:0% +it's just +an idea of of + + align:start position:0% +an idea of of + + + align:start position:0% +an idea of of +that should give you some idea as to how + + align:start position:0% +that should give you some idea as to how + + + align:start position:0% +that should give you some idea as to how +different they are another way + + align:start position:0% +different they are another way + + + align:start position:0% +different they are another way +that we looked at was + + align:start position:0% +that we looked at was + + + align:start position:0% +that we looked at was +for each from each platform we looked at + + align:start position:0% +for each from each platform we looked at + + + align:start position:0% +for each from each platform we looked at +um + + align:start position:0% +um + + + align:start position:0% +um +so the samples were + + align:start position:0% +so the samples were + + + align:start position:0% +so the samples were +naturally divided into two groups so we + + align:start position:0% +naturally divided into two groups so we + + + align:start position:0% +naturally divided into two groups so we +looked at for each platform what genes + + align:start position:0% +looked at for each platform what genes + + + align:start position:0% +looked at for each platform what genes +are differentially expressed so from the + + align:start position:0% +are differentially expressed so from the + + + align:start position:0% +are differentially expressed so from the +95 uh you 95 samples we got you know + + align:start position:0% +95 uh you 95 samples we got you know + + + align:start position:0% +95 uh you 95 samples we got you know +long list + + align:start position:0% +long list + + + align:start position:0% +long list +from 133 you've got a long list okay how + + align:start position:0% +from 133 you've got a long list okay how + + + align:start position:0% +from 133 you've got a long list okay how +much overlap is there + + align:start position:0% +much overlap is there + + + align:start position:0% +much overlap is there +okay that was the question okay does + + align:start position:0% +okay that was the question okay does + + + align:start position:0% +okay that was the question okay does +that make sense okay + + align:start position:0% +that make sense okay + + + align:start position:0% +that make sense okay +so if you look at the dotted line um + + align:start position:0% +so if you look at the dotted line um + + + align:start position:0% +so if you look at the dotted line um +if you look at + + align:start position:0% + + + + align:start position:0% + +how many different right so + + align:start position:0% +how many different right so + + + align:start position:0% +how many different right so +so we had 14 + + align:start position:0% +so we had 14 + + + align:start position:0% +so we had 14 +okay and they were + + align:start position:0% +okay and they were + + + align:start position:0% +okay and they were +basically five of one type and the rest + + align:start position:0% +basically five of one type and the rest + + + align:start position:0% +basically five of one type and the rest +were + + align:start position:0% +were + + + align:start position:0% +were +uh + + align:start position:0% +uh + + + align:start position:0% +uh +could be considered as another type + + align:start position:0% +could be considered as another type + + + align:start position:0% +could be considered as another type +so of the fourth so using those five and + + align:start position:0% +so of the fourth so using those five and + + + align:start position:0% +so of the fourth so using those five and +nine chips we looked at the differential + + align:start position:0% +nine chips we looked at the differential + + + align:start position:0% +nine chips we looked at the differential +expansions okay so we do that separately + + align:start position:0% +expansions okay so we do that separately + + + align:start position:0% +expansions okay so we do that separately +for each one + + align:start position:0% +for each one + + + align:start position:0% +for each one +so i mean they should overlap right and + + align:start position:0% +so i mean they should overlap right and + + + align:start position:0% +so i mean they should overlap right and +just say + + align:start position:0% +just say + + + align:start position:0% +just say +exactly same samples + + align:start position:0% +exactly same samples + + + align:start position:0% +exactly same samples +right we you know we did a lot of + + align:start position:0% +right we you know we did a lot of + + + align:start position:0% +right we you know we did a lot of +analysis to make sure that there wasn't + + align:start position:0% +analysis to make sure that there wasn't + + + align:start position:0% +analysis to make sure that there wasn't +a lot of you know degradation of you + + align:start position:0% +a lot of you know degradation of you + + + align:start position:0% +a lot of you know degradation of you +know rna and such + + align:start position:0% +know rna and such + + + align:start position:0% +know rna and such +but if you look at this so + + align:start position:0% +but if you look at this so + + + align:start position:0% +but if you look at this so +forget the solid line for now if you + + align:start position:0% +forget the solid line for now if you + + + align:start position:0% +forget the solid line for now if you +look at the dotted dashed line + + align:start position:0% +look at the dotted dashed line + + + align:start position:0% +look at the dotted dashed line +out of top 100 + + align:start position:0% +out of top 100 + + + align:start position:0% +out of top 100 +they're about 20 percent less than 20 + + align:start position:0% +they're about 20 percent less than 20 + + + align:start position:0% +they're about 20 percent less than 20 +dead overlap so about 20 + + align:start position:0% +dead overlap so about 20 + + + align:start position:0% +dead overlap so about 20 +genes will show up in both but 80 genes + + align:start position:0% +genes will show up in both but 80 genes + + + align:start position:0% +genes will show up in both but 80 genes +are not in common + + align:start position:0% +are not in common + + + align:start position:0% +are not in common +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +so that's a you know somewhat disturbing + + align:start position:0% +so that's a you know somewhat disturbing + + + align:start position:0% +so that's a you know somewhat disturbing +right i mean if you look at + + align:start position:0% +right i mean if you look at + + + align:start position:0% +right i mean if you look at +top 50 and usually when investigators do + + align:start position:0% +top 50 and usually when investigators do + + + align:start position:0% +top 50 and usually when investigators do +these experiments you know they can't + + align:start position:0% +these experiments you know they can't + + + align:start position:0% +these experiments you know they can't +really look at more than you know top + + align:start position:0% +really look at more than you know top + + + align:start position:0% +really look at more than you know top +you know 20 30 50. + + align:start position:0% +you know 20 30 50. + + + align:start position:0% +you know 20 30 50. +that's it's about 15 that are in common + + align:start position:0% +that's it's about 15 that are in common + + + align:start position:0% +that's it's about 15 that are in common +so 15 + + align:start position:0% +so 15 + + + align:start position:0% +so 15 +that's like 7 or 18 out of 50 so + + align:start position:0% +that's like 7 or 18 out of 50 so + + + align:start position:0% +that's like 7 or 18 out of 50 so +that's somewhat disturbing right + + align:start position:0% +that's somewhat disturbing right + + + align:start position:0% +that's somewhat disturbing right +so we actually um for the paper we + + align:start position:0% +so we actually um for the paper we + + + align:start position:0% +so we actually um for the paper we +actually found some way of fixing this + + align:start position:0% +actually found some way of fixing this + + + align:start position:0% +actually found some way of fixing this +problem in the general case so + + align:start position:0% +problem in the general case so + + + align:start position:0% +problem in the general case so +we could raise the percentages um + + align:start position:0% +we could raise the percentages um + + + align:start position:0% +we could raise the percentages um +a lot + + align:start position:0% +a lot + + + align:start position:0% +a lot +but + + align:start position:0% +but + + + align:start position:0% +but +you know + + align:start position:0% +you know + + + align:start position:0% +you know +most people who will not go through this + + align:start position:0% +most people who will not go through this + + + align:start position:0% +most people who will not go through this +trouble of what we did + + align:start position:0% +trouble of what we did + + + align:start position:0% +trouble of what we did +um + + align:start position:0% +um + + + align:start position:0% +um +should be aware that their list is not + + align:start position:0% +should be aware that their list is not + + + align:start position:0% +should be aware that their list is not +all that + + align:start position:0% +all that + + + align:start position:0% +all that +robust and in some sense this is not + + align:start position:0% +robust and in some sense this is not + + + align:start position:0% +robust and in some sense this is not +surprising although the degree to which + + align:start position:0% +surprising although the degree to which + + + align:start position:0% +surprising although the degree to which +that they disagree is surprising + + align:start position:0% +that they disagree is surprising + + + align:start position:0% +that they disagree is surprising +um generally you have you know several + + align:start position:0% +um generally you have you know several + + + align:start position:0% +um generally you have you know several +hundred + + align:start position:0% +hundred + + + align:start position:0% +hundred +or maybe even thousands of genes that + + align:start position:0% +or maybe even thousands of genes that + + + align:start position:0% +or maybe even thousands of genes that +are differently expressed and there are + + align:start position:0% +are differently expressed and there are + + + align:start position:0% +are differently expressed and there are +you know differential expressed at a + + align:start position:0% +you know differential expressed at a + + + align:start position:0% +you know differential expressed at a +very similar level right so any + + align:start position:0% +very similar level right so any + + + align:start position:0% +very similar level right so any +perturbation that you make to the data + + align:start position:0% +perturbation that you make to the data + + + align:start position:0% +perturbation that you make to the data +things are going to just + + align:start position:0% +things are going to just + + + align:start position:0% +things are going to just +you know + + align:start position:0% +you know + + + align:start position:0% +you know +shuffle and they'll be you know they're + + align:start position:0% +shuffle and they'll be you know they're + + + align:start position:0% +shuffle and they'll be you know they're +generally not very stable so it's not + + align:start position:0% +generally not very stable so it's not + + + align:start position:0% +generally not very stable so it's not +surprising that they don't agree very + + align:start position:0% +surprising that they don't agree very + + + align:start position:0% +surprising that they don't agree very +much but in this case because it was so + + align:start position:0% +much but in this case because it was so + + + align:start position:0% +much but in this case because it was so +tightly controlled i mean because they + + align:start position:0% +tightly controlled i mean because they + + + align:start position:0% +tightly controlled i mean because they +get the same + + align:start position:0% +get the same + + + align:start position:0% +get the same +rna labeled at the same time + + align:start position:0% +rna labeled at the same time + + + align:start position:0% +rna labeled at the same time +they were hybridized in the same + + align:start position:0% +they were hybridized in the same + + + align:start position:0% +they were hybridized in the same +facility + + align:start position:0% +facility + + + align:start position:0% +facility +we expected this to be a little higher + + align:start position:0% +we expected this to be a little higher + + + align:start position:0% +we expected this to be a little higher +but it's not + + align:start position:0% + + + + align:start position:0% + +so this is challenge uh i think + + align:start position:0% +so this is challenge uh i think + + + align:start position:0% +so this is challenge uh i think +and you know it should be a caution uh + + align:start position:0% +and you know it should be a caution uh + + + align:start position:0% +and you know it should be a caution uh +for people doing experiments + + align:start position:0% +for people doing experiments + + + align:start position:0% +for people doing experiments +uh one thing that um so + + align:start position:0% +uh one thing that um so + + + align:start position:0% +uh one thing that um so +one um + + align:start position:0% +one um + + + align:start position:0% +one um +one thing that + + align:start position:0% +one thing that + + + align:start position:0% +one thing that +people should pay more attention to + + align:start position:0% +people should pay more attention to + + + align:start position:0% +people should pay more attention to +therefore is not so much + + align:start position:0% +therefore is not so much + + + align:start position:0% +therefore is not so much +what genes are expressed but what kind + + align:start position:0% +what genes are expressed but what kind + + + align:start position:0% +what genes are expressed but what kind +of genes are expressed so people are now + + align:start position:0% +of genes are expressed so people are now + + + align:start position:0% +of genes are expressed so people are now +thinking of more robust way of looking + + align:start position:0% +thinking of more robust way of looking + + + align:start position:0% +thinking of more robust way of looking +at the list + + align:start position:0% +at the list + + + align:start position:0% +at the list +i mean for example + + align:start position:0% +i mean for example + + + align:start position:0% +i mean for example +you know what kind of goal category + + align:start position:0% +you know what kind of goal category + + + align:start position:0% +you know what kind of goal category +genes are represented at the top now + + align:start position:0% +genes are represented at the top now + + + align:start position:0% +genes are represented at the top now +that kind of thing + + align:start position:0% +that kind of thing + + + align:start position:0% +that kind of thing +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah so that's a good question so we + + align:start position:0% +yeah so that's a good question so we + + + align:start position:0% +yeah so that's a good question so we +looked at that in detail so + + align:start position:0% +looked at that in detail so + + + align:start position:0% +looked at that in detail so +it turns out that if the probes so you + + align:start position:0% +it turns out that if the probes so you + + + align:start position:0% +it turns out that if the probes so you +all know how happy arrays work so if the + + align:start position:0% +all know how happy arrays work so if the + + + align:start position:0% +all know how happy arrays work so if the +probes are exactly the same the + + align:start position:0% +probes are exactly the same the + + + align:start position:0% +probes are exactly the same the +sequences are exactly the same they are + + align:start position:0% +sequences are exactly the same they are + + + align:start position:0% +sequences are exactly the same they are +very reproducible okay so they very they + + align:start position:0% +very reproducible okay so they very they + + + align:start position:0% +very reproducible okay so they very they +they give very good results + + align:start position:0% +they give very good results + + + align:start position:0% +they give very good results +but if they are different + + align:start position:0% +but if they are different + + + align:start position:0% +but if they are different +it's + + align:start position:0% +it's + + + align:start position:0% +it's +i mean i i don't have pictures here to + + align:start position:0% +i mean i i don't have pictures here to + + + align:start position:0% +i mean i i don't have pictures here to +show you but + + align:start position:0% +show you but + + + align:start position:0% +show you but +you know no relationship even even + + align:start position:0% +you know no relationship even even + + + align:start position:0% +you know no relationship even even +though they are supposed to + + align:start position:0% +though they are supposed to + + + align:start position:0% +though they are supposed to +um detect the same transcript + + align:start position:0% +um detect the same transcript + + + align:start position:0% +um detect the same transcript +so basically that i mean the lesson is + + align:start position:0% +so basically that i mean the lesson is + + + align:start position:0% +so basically that i mean the lesson is +that slight changes in the sequence + + align:start position:0% +that slight changes in the sequence + + + align:start position:0% +that slight changes in the sequence +information + + align:start position:0% +information + + + align:start position:0% +information +results in huge changes in your + + align:start position:0% +results in huge changes in your + + + align:start position:0% +results in huge changes in your +expression + + align:start position:0% +expression + + + align:start position:0% +expression +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% + + + + align:start position:0% + +no the length is the same the length + + align:start position:0% +no the length is the same the length + + + align:start position:0% +no the length is the same the length +those are 25 moves and the reason that + + align:start position:0% +those are 25 moves and the reason that + + + align:start position:0% +those are 25 moves and the reason that +they're so there is a debate as to what + + align:start position:0% +they're so there is a debate as to what + + + align:start position:0% +they're so there is a debate as to what +the optimal length is and so people have + + align:start position:0% +the optimal length is and so people have + + + align:start position:0% +the optimal length is and so people have +you know + + align:start position:0% +you know + + + align:start position:0% +you know +so the commercial um suppliers that i + + align:start position:0% +so the commercial um suppliers that i + + + align:start position:0% +so the commercial um suppliers that i +listed earlier they have different + + align:start position:0% +listed earlier they have different + + + align:start position:0% +listed earlier they have different +lengths so there are some 30 30 mers 50 + + align:start position:0% +lengths so there are some 30 30 mers 50 + + + align:start position:0% +lengths so there are some 30 30 mers 50 +meters a lot of people think that the + + align:start position:0% +meters a lot of people think that the + + + align:start position:0% +meters a lot of people think that the +longer + + align:start position:0% + + + + align:start position:0% + +nucleotides or the nucleotides usually + + align:start position:0% +nucleotides or the nucleotides usually + + + align:start position:0% +nucleotides or the nucleotides usually +have seven beamers + + align:start position:0% +have seven beamers + + + align:start position:0% +have seven beamers +or that size + + align:start position:0% +or that size + + + align:start position:0% +or that size +you know are the best + + align:start position:0% +you know are the best + + + align:start position:0% +you know are the best +um but i mean that's still a bit of an + + align:start position:0% +um but i mean that's still a bit of an + + + align:start position:0% +um but i mean that's still a bit of an +open question but athlete we + + align:start position:0% +open question but athlete we + + + align:start position:0% +open question but athlete we +would probably would like to have longer + + align:start position:0% +would probably would like to have longer + + + align:start position:0% +would probably would like to have longer +pros but they're limited by technology + + align:start position:0% +pros but they're limited by technology + + + align:start position:0% +pros but they're limited by technology +so they're built by you know it's the + + align:start position:0% +so they're built by you know it's the + + + align:start position:0% +so they're built by you know it's the +same same technology that you use to + + align:start position:0% +same same technology that you use to + + + align:start position:0% +same same technology that you use to +build semiconductor chips and so you + + align:start position:0% +build semiconductor chips and so you + + + align:start position:0% +build semiconductor chips and so you +can't you know + + align:start position:0% +can't you know + + + align:start position:0% +can't you know +tile so many uh + + align:start position:0% +tile so many uh + + + align:start position:0% +tile so many uh +nucleotides so + + align:start position:0% +nucleotides so + + + align:start position:0% +nucleotides so +um so what they did + + align:start position:0% +um so what they did + + + align:start position:0% +um so what they did +so the reason that affy got better is + + align:start position:0% +so the reason that affy got better is + + + align:start position:0% +so the reason that affy got better is +that + + align:start position:0% +that + + + align:start position:0% +that +this is it's so hard to figure out + + align:start position:0% +this is it's so hard to figure out + + + align:start position:0% +this is it's so hard to figure out +exactly which sequences would give you + + align:start position:0% +exactly which sequences would give you + + + align:start position:0% +exactly which sequences would give you +the best result so basically what affi + + align:start position:0% +the best result so basically what affi + + + align:start position:0% +the best result so basically what affi +has done over the years is that + + align:start position:0% +has done over the years is that + + + align:start position:0% +has done over the years is that +throughout the generations they figured + + align:start position:0% +throughout the generations they figured + + + align:start position:0% +throughout the generations they figured +out just by + + align:start position:0% +out just by + + + align:start position:0% +out just by +trial and error which ones give + + align:start position:0% +trial and error which ones give + + + align:start position:0% +trial and error which ones give +bad results and so they just + + align:start position:0% +bad results and so they just + + + align:start position:0% +bad results and so they just +you know next time the product comes out + + align:start position:0% +you know next time the product comes out + + + align:start position:0% +you know next time the product comes out +they get rid of all the bad ones and + + align:start position:0% +they get rid of all the bad ones and + + + align:start position:0% +they get rid of all the bad ones and +just you know try new ones + + align:start position:0% +just you know try new ones + + + align:start position:0% +just you know try new ones +so by that try and error process in my + + align:start position:0% +so by that try and error process in my + + + align:start position:0% +so by that try and error process in my +view they've gotten pretty good + + align:start position:0% +view they've gotten pretty good + + + align:start position:0% +view they've gotten pretty good +so + + align:start position:0% +so + + + align:start position:0% +so +if you look at you know two three years + + align:start position:0% +if you look at you know two three years + + + align:start position:0% +if you look at you know two three years +ago if you look at + + align:start position:0% +ago if you look at + + + align:start position:0% +ago if you look at +the old chip just how much + + align:start position:0% +the old chip just how much + + + align:start position:0% +the old chip just how much +variation there is on you know among the + + align:start position:0% +variation there is on you know among the + + + align:start position:0% +variation there is on you know among the +probes that are supposed to detect the + + align:start position:0% +probes that are supposed to detect the + + + align:start position:0% +probes that are supposed to detect the +same gene you'd see just things all over + + align:start position:0% +same gene you'd see just things all over + + + align:start position:0% +same gene you'd see just things all over +the place + + align:start position:0% +the place + + + align:start position:0% +the place +just you know maybe half the probes + + align:start position:0% +just you know maybe half the probes + + + align:start position:0% +just you know maybe half the probes +may give you completely different + + align:start position:0% +may give you completely different + + + align:start position:0% +may give you completely different +numbers but now it's it is much better + + align:start position:0% +numbers but now it's it is much better + + + align:start position:0% +numbers but now it's it is much better +uh things so things have certainly + + align:start position:0% +uh things so things have certainly + + + align:start position:0% +uh things so things have certainly +improved + + align:start position:0% +improved + + + align:start position:0% +improved +and i i think affi + + align:start position:0% +and i i think affi + + + align:start position:0% +and i i think affi +is the platform itself has some + + align:start position:0% +is the platform itself has some + + + align:start position:0% +is the platform itself has some +advantages because they are using some + + align:start position:0% +advantages because they are using some + + + align:start position:0% +advantages because they are using some +you know multiple probes + + align:start position:0% +you know multiple probes + + + align:start position:0% +you know multiple probes +other platforms you know they don't have + + align:start position:0% +other platforms you know they don't have + + + align:start position:0% +other platforms you know they don't have +the luxury of doing that right so they + + align:start position:0% +the luxury of doing that right so they + + + align:start position:0% +the luxury of doing that right so they +have single longer probe but they have + + align:start position:0% +have single longer probe but they have + + + align:start position:0% +have single longer probe but they have +no idea what that's correct enough + + align:start position:0% +no idea what that's correct enough + + + align:start position:0% +no idea what that's correct enough +um and i've looked at actually + + align:start position:0% +um and i've looked at actually + + + align:start position:0% +um and i've looked at actually +commercial arrays not affy and compared + + align:start position:0% +commercial arrays not affy and compared + + + align:start position:0% +commercial arrays not affy and compared +that against aphey and you just get + + align:start position:0% +that against aphey and you just get + + + align:start position:0% +that against aphey and you just get +disturbing results + + align:start position:0% +disturbing results + + + align:start position:0% +disturbing results +so + + align:start position:0% + + + + align:start position:0% + +so you know + + align:start position:0% +so you know + + + align:start position:0% +so you know +you probably have heard of a lot of good + + align:start position:0% +you probably have heard of a lot of good + + + align:start position:0% +you probably have heard of a lot of good +things about microwaves and that's + + align:start position:0% +things about microwaves and that's + + + align:start position:0% +things about microwaves and that's +probably true + + align:start position:0% +probably true + + + align:start position:0% +probably true +overall i mean it's + + align:start position:0% +overall i mean it's + + + align:start position:0% +overall i mean it's +but there are some issues that you need + + align:start position:0% +but there are some issues that you need + + + align:start position:0% +but there are some issues that you need +to be careful about + + align:start position:0% +to be careful about + + + align:start position:0% +to be careful about +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so yeah i was a little surprised about + + align:start position:0% +so yeah i was a little surprised about + + + align:start position:0% +so yeah i was a little surprised about +this and um + + align:start position:0% +this and um + + + align:start position:0% +this and um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +i guess the recommendation is that if + + align:start position:0% +i guess the recommendation is that if + + + align:start position:0% +i guess the recommendation is that if +you have different platforms at least + + align:start position:0% +you have different platforms at least + + + align:start position:0% +you have different platforms at least +you know unless you're going to go + + align:start position:0% +you know unless you're going to go + + + align:start position:0% +you know unless you're going to go +through unless you + + align:start position:0% +through unless you + + + align:start position:0% +through unless you +are able to go through what we went + + align:start position:0% +are able to go through what we went + + + align:start position:0% +are able to go through what we went +through um + + align:start position:0% +through um + + + align:start position:0% +through um +not to combine the arrays + + align:start position:0% +not to combine the arrays + + + align:start position:0% +not to combine the arrays +but then that's not a very satisfactory + + align:start position:0% +but then that's not a very satisfactory + + + align:start position:0% +but then that's not a very satisfactory +solution right i mean if you have a + + align:start position:0% +solution right i mean if you have a + + + align:start position:0% +solution right i mean if you have a +database with all these um + + align:start position:0% +database with all these um + + + align:start position:0% +database with all these um +chips that everyone else has done what + + align:start position:0% +chips that everyone else has done what + + + align:start position:0% +chips that everyone else has done what +good use you know what you use it if you + + align:start position:0% +good use you know what you use it if you + + + align:start position:0% +good use you know what you use it if you +can't use them + + align:start position:0% +can't use them + + + align:start position:0% +can't use them +other than + + align:start position:0% +other than + + + align:start position:0% +other than +just you know + + align:start position:0% +just you know + + + align:start position:0% +just you know +each data set in its own um + + align:start position:0% +each data set in its own um + + + align:start position:0% +each data set in its own um +state so + + align:start position:0% +state so + + + align:start position:0% +state so +okay so i don't think we need to talk + + align:start position:0% +okay so i don't think we need to talk + + + align:start position:0% +okay so i don't think we need to talk +about how many chips we need um i don't + + align:start position:0% +about how many chips we need um i don't + + + align:start position:0% +about how many chips we need um i don't +know if you're anyone's planning to do + + align:start position:0% +know if you're anyone's planning to do + + + align:start position:0% +know if you're anyone's planning to do +a right experience you're great + + align:start position:0% +a right experience you're great + + + align:start position:0% +a right experience you're great +experience oh okay + + align:start position:0% +experience oh okay + + + align:start position:0% +experience oh okay +um + + align:start position:0% +um + + + align:start position:0% +um +so generally + + align:start position:0% +so generally + + + align:start position:0% +so generally +i think for most platforms that have + + align:start position:0% +i think for most platforms that have + + + align:start position:0% +i think for most platforms that have +been + + align:start position:0% +been + + + align:start position:0% +been +around for a while + + align:start position:0% +around for a while + + + align:start position:0% +around for a while +most people would agree that biological + + align:start position:0% +most people would agree that biological + + + align:start position:0% +most people would agree that biological +variability dominates technical + + align:start position:0% +variability dominates technical + + + align:start position:0% +variability dominates technical +measurement errors so for affy you don't + + align:start position:0% +measurement errors so for affy you don't + + + align:start position:0% +measurement errors so for affy you don't +want to do + + align:start position:0% +want to do + + + align:start position:0% +want to do +many replicas of the same + + align:start position:0% +many replicas of the same + + + align:start position:0% +many replicas of the same +tissue or sample right + + align:start position:0% + + + + align:start position:0% + +in terms of exactly how many you need + + align:start position:0% +in terms of exactly how many you need + + + align:start position:0% +in terms of exactly how many you need +how many chips you need that's a hard + + align:start position:0% +how many chips you need that's a hard + + + align:start position:0% +how many chips you need that's a hard +question + + align:start position:0% +question + + + align:start position:0% +question +only because you don't know how much + + align:start position:0% +only because you don't know how much + + + align:start position:0% +only because you don't know how much +variability that + + align:start position:0% +variability that + + + align:start position:0% +variability that +you have in your samples so if someone + + align:start position:0% +you have in your samples so if someone + + + align:start position:0% +you have in your samples so if someone +can tell me i have this much variability + + align:start position:0% +can tell me i have this much variability + + + align:start position:0% +can tell me i have this much variability +in my samples + + align:start position:0% +in my samples + + + align:start position:0% +in my samples +you know i want this false positive rate + + align:start position:0% +you know i want this false positive rate + + + align:start position:0% +you know i want this false positive rate +this false negative rate i can give you + + align:start position:0% +this false negative rate i can give you + + + align:start position:0% +this false negative rate i can give you +numbers based on some model + + align:start position:0% +numbers based on some model + + + align:start position:0% +numbers based on some model +but usually people can't give me those + + align:start position:0% +but usually people can't give me those + + + align:start position:0% +but usually people can't give me those +numbers so there's no point in + + align:start position:0% +numbers so there's no point in + + + align:start position:0% +numbers so there's no point in +talking about this um some in generally + + align:start position:0% +talking about this um some in generally + + + align:start position:0% +talking about this um some in generally +speakings if you have data like cancer + + align:start position:0% +speakings if you have data like cancer + + + align:start position:0% +speakings if you have data like cancer +data where you have a lot of variability + + align:start position:0% +data where you have a lot of variability + + + align:start position:0% +data where you have a lot of variability +i think people would say some studies + + align:start position:0% +i think people would say some studies + + + align:start position:0% +i think people would say some studies +have said you know having samples like + + align:start position:0% +have said you know having samples like + + + align:start position:0% +have said you know having samples like +10 to 15 per group for a trigger + + align:start position:0% +10 to 15 per group for a trigger + + + align:start position:0% +10 to 15 per group for a trigger +comparison might give you something like + + align:start position:0% +comparison might give you something like + + + align:start position:0% +comparison might give you something like +75 false positive ray + + align:start position:0% +75 false positive ray + + + align:start position:0% +75 false positive ray +and for detecting genes that are + + align:start position:0% +and for detecting genes that are + + + align:start position:0% +and for detecting genes that are +three-fold + + align:start position:0% +three-fold + + + align:start position:0% +three-fold +variable so + + align:start position:0% +variable so + + + align:start position:0% +variable so +yeah there can be some estimates like + + align:start position:0% +yeah there can be some estimates like + + + align:start position:0% +yeah there can be some estimates like +that + + align:start position:0% +that + + + align:start position:0% +that +for keeping parameters but in general + + align:start position:0% +for keeping parameters but in general + + + align:start position:0% +for keeping parameters but in general +it's hard + + align:start position:0% +it's hard + + + align:start position:0% +it's hard +so um + + align:start position:0% +so um + + + align:start position:0% +so um +yeah let's leave at that + + align:start position:0% +yeah let's leave at that + + + align:start position:0% +yeah let's leave at that +um + + align:start position:0% + + + + align:start position:0% + +i think i'm gonna skip most of these i'm + + align:start position:0% +i think i'm gonna skip most of these i'm + + + align:start position:0% +i think i'm gonna skip most of these i'm +sure you've seen these before + + align:start position:0% +sure you've seen these before + + + align:start position:0% +sure you've seen these before +um + + align:start position:0% +um + + + align:start position:0% +um +have you guys talked about p values + + align:start position:0% +have you guys talked about p values + + + align:start position:0% +have you guys talked about p values +multiple testing + + align:start position:0% + + + + align:start position:0% + +okay so maybe not okay so + + align:start position:0% +okay so maybe not okay so + + + align:start position:0% +okay so maybe not okay so +just to give you + + align:start position:0% +just to give you + + + align:start position:0% +just to give you +one example + + align:start position:0% +one example + + + align:start position:0% +one example +um so suppose you flip a coin 10 times + + align:start position:0% +um so suppose you flip a coin 10 times + + + align:start position:0% +um so suppose you flip a coin 10 times +and get all heads okay + + align:start position:0% +and get all heads okay + + + align:start position:0% +and get all heads okay +this is like a you know + + align:start position:0% +this is like a you know + + + align:start position:0% +this is like a you know +statistics 101 you know problem question + + align:start position:0% +statistics 101 you know problem question + + + align:start position:0% +statistics 101 you know problem question +um what's the probability that you get + + align:start position:0% +um what's the probability that you get + + + align:start position:0% +um what's the probability that you get +all heads okay + + align:start position:0% +all heads okay + + + align:start position:0% +all heads okay +and it turns out it's about + + align:start position:0% + + + + align:start position:0% + +it's + + align:start position:0% + + + + align:start position:0% + +it's about point zero zero one right + + align:start position:0% +it's about point zero zero one right + + + align:start position:0% +it's about point zero zero one right +it's like one over two to the + + align:start position:0% + + + + align:start position:0% + +to the tenth right so + + align:start position:0% +to the tenth right so + + + align:start position:0% +to the tenth right so +yeah so it's about point one percent + + align:start position:0% +yeah so it's about point one percent + + + align:start position:0% +yeah so it's about point one percent +okay so if you if the question is is it + + align:start position:0% +okay so if you if the question is is it + + + align:start position:0% +okay so if you if the question is is it +biased + + align:start position:0% +biased + + + align:start position:0% +biased +say probably right + + align:start position:0% +say probably right + + + align:start position:0% +say probably right +it's pretty unlikely + + align:start position:0% +it's pretty unlikely + + + align:start position:0% +it's pretty unlikely +but what if there are ten thousand + + align:start position:0% +but what if there are ten thousand + + + align:start position:0% +but what if there are ten thousand +people flipping coins and one person + + align:start position:0% +people flipping coins and one person + + + align:start position:0% +people flipping coins and one person +gets 10 heads + + align:start position:0% +gets 10 heads + + + align:start position:0% +gets 10 heads +right + + align:start position:0% +right + + + align:start position:0% +right +so should you be surprised that someone + + align:start position:0% +so should you be surprised that someone + + + align:start position:0% +so should you be surprised that someone +got 10 heads + + align:start position:0% +got 10 heads + + + align:start position:0% +got 10 heads +probably not right + + align:start position:0% +probably not right + + + align:start position:0% +probably not right +so + + align:start position:0% + + + + align:start position:0% + +so you need to adjust for this right + + align:start position:0% +so you need to adjust for this right + + + align:start position:0% +so you need to adjust for this right +this is the same problem that + + align:start position:0% +this is the same problem that + + + align:start position:0% +this is the same problem that +you know that you that i mentioned + + align:start position:0% +you know that you that i mentioned + + + align:start position:0% +you know that you that i mentioned +earlier with the nature genetics paper + + align:start position:0% +earlier with the nature genetics paper + + + align:start position:0% +earlier with the nature genetics paper +you need to adjust for + + align:start position:0% +you need to adjust for + + + align:start position:0% +you need to adjust for +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the fact that there are so many genes + + align:start position:0% +the fact that there are so many genes + + + align:start position:0% +the fact that there are so many genes +in some sense it is somewhat people find + + align:start position:0% +in some sense it is somewhat people find + + + align:start position:0% +in some sense it is somewhat people find +it somewhat + + align:start position:0% +it somewhat + + + align:start position:0% +it somewhat +difficult to understand because i'm + + align:start position:0% +difficult to understand because i'm + + + align:start position:0% +difficult to understand because i'm +interested in one gene but + + align:start position:0% +interested in one gene but + + + align:start position:0% +interested in one gene but +if if um if my probability depends on + + align:start position:0% +if if um if my probability depends on + + + align:start position:0% +if if um if my probability depends on +like what kind of chip i use for example + + align:start position:0% +like what kind of chip i use for example + + + align:start position:0% +like what kind of chip i use for example +if i use a chip with 10 000 genes versus + + align:start position:0% +if i use a chip with 10 000 genes versus + + + align:start position:0% +if i use a chip with 10 000 genes versus +a chip with 30 000 genes + + align:start position:0% +a chip with 30 000 genes + + + align:start position:0% +a chip with 30 000 genes +okay my conclusion will or my + + align:start position:0% +okay my conclusion will or my + + + align:start position:0% +okay my conclusion will or my +probability will be different for for my + + align:start position:0% +probability will be different for for my + + + align:start position:0% +probability will be different for for my +for the gene that i'm interested in so + + align:start position:0% +for the gene that i'm interested in so + + + align:start position:0% +for the gene that i'm interested in so +people find it sometimes without to + + align:start position:0% +people find it sometimes without to + + + align:start position:0% +people find it sometimes without to +understand but some correction has to be + + align:start position:0% +understand but some correction has to be + + + align:start position:0% +understand but some correction has to be +made i think + + align:start position:0% +made i think + + + align:start position:0% +made i think +uh so it's often referred to as multiple + + align:start position:0% +uh so it's often referred to as multiple + + + align:start position:0% +uh so it's often referred to as multiple +testing like you know adjustments + + align:start position:0% +testing like you know adjustments + + + align:start position:0% +testing like you know adjustments +i think there is some consensus now on + + align:start position:0% +i think there is some consensus now on + + + align:start position:0% +i think there is some consensus now on +how to how to do this um so maybe we + + align:start position:0% +how to how to do this um so maybe we + + + align:start position:0% +how to how to do this um so maybe we +won't talk about this here + + align:start position:0% +won't talk about this here + + + align:start position:0% +won't talk about this here +but people generally + + align:start position:0% +but people generally + + + align:start position:0% +but people generally +and i i agree this with i agree with + + align:start position:0% +and i i agree this with i agree with + + + align:start position:0% +and i i agree this with i agree with +this as well uh there's something called + + align:start position:0% +this as well uh there's something called + + + align:start position:0% +this as well uh there's something called +false discovery right that you may have + + align:start position:0% +false discovery right that you may have + + + align:start position:0% +false discovery right that you may have +heard of uh i think that's a very + + align:start position:0% +heard of uh i think that's a very + + + align:start position:0% +heard of uh i think that's a very +reasonable approach exactly how to + + align:start position:0% +reasonable approach exactly how to + + + align:start position:0% +reasonable approach exactly how to +calculate that is not so simple but um + + align:start position:0% +calculate that is not so simple but um + + + align:start position:0% +calculate that is not so simple but um +can be done + + align:start position:0% +can be done + + + align:start position:0% +can be done +all right so let's talk a little more + + align:start position:0% +all right so let's talk a little more + + + align:start position:0% +all right so let's talk a little more +about the subject that i'm interested in + + align:start position:0% +about the subject that i'm interested in + + + align:start position:0% +about the subject that i'm interested in +in terms of application so + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +eventually for people that are + + align:start position:0% +eventually for people that are + + + align:start position:0% +eventually for people that are +interested in + + align:start position:0% +interested in + + + align:start position:0% +interested in +applications + + align:start position:0% +applications + + + align:start position:0% +applications +clinical applications + + align:start position:0% +clinical applications + + + align:start position:0% +clinical applications +of microarray um + + align:start position:0% +of microarray um + + + align:start position:0% +of microarray um +or any other type of uh high throughput + + align:start position:0% +or any other type of uh high throughput + + + align:start position:0% +or any other type of uh high throughput +data is + + align:start position:0% +data is + + + align:start position:0% +data is +that + + align:start position:0% +that + + + align:start position:0% +that +you'd like to use this in you know your + + align:start position:0% +you'd like to use this in you know your + + + align:start position:0% +you'd like to use this in you know your +clinical setting that is you know + + align:start position:0% +clinical setting that is you know + + + align:start position:0% +clinical setting that is you know +treatment related things + + align:start position:0% +treatment related things + + + align:start position:0% +treatment related things +so + + align:start position:0% +so + + + align:start position:0% +so +the challenge is to + + align:start position:0% +the challenge is to + + + align:start position:0% +the challenge is to +you know stop doing these simple sort of + + align:start position:0% +you know stop doing these simple sort of + + + align:start position:0% +you know stop doing these simple sort of +methodological problems at some point + + align:start position:0% +methodological problems at some point + + + align:start position:0% +methodological problems at some point +and move on to real problems that means + + align:start position:0% +and move on to real problems that means + + + align:start position:0% +and move on to real problems that means +incorporating + + align:start position:0% +incorporating + + + align:start position:0% +incorporating +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +large amount of phenotypic data so you + + align:start position:0% +large amount of phenotypic data so you + + + align:start position:0% +large amount of phenotypic data so you +know in a clinical setting typically you + + align:start position:0% +know in a clinical setting typically you + + + align:start position:0% +know in a clinical setting typically you +have lots of other + + align:start position:0% +have lots of other + + + align:start position:0% +have lots of other +types of data + + align:start position:0% +types of data + + + align:start position:0% +types of data +listed here + + align:start position:0% +listed here + + + align:start position:0% +listed here +and we like to find relationships + + align:start position:0% +and we like to find relationships + + + align:start position:0% +and we like to find relationships +between you know genomic data and + + align:start position:0% +between you know genomic data and + + + align:start position:0% +between you know genomic data and +phenotype data phenotypic data + + align:start position:0% +phenotype data phenotypic data + + + align:start position:0% +phenotype data phenotypic data +so you know questions could be what + + align:start position:0% +so you know questions could be what + + + align:start position:0% +so you know questions could be what +genes are variables are correlated with + + align:start position:0% +genes are variables are correlated with + + + align:start position:0% +genes are variables are correlated with +particular phenotype + + align:start position:0% +particular phenotype + + + align:start position:0% +particular phenotype +what should be used as predictors + + align:start position:0% +what should be used as predictors + + + align:start position:0% +what should be used as predictors +um + + align:start position:0% +um + + + align:start position:0% +um +so i'm just introducing the sort of + + align:start position:0% +so i'm just introducing the sort of + + + align:start position:0% +so i'm just introducing the sort of +framework at a basic level and then + + align:start position:0% +framework at a basic level and then + + + align:start position:0% +framework at a basic level and then +we'll look at some papers + + align:start position:0% + + + + align:start position:0% + +so the most simple case + + align:start position:0% +so the most simple case + + + align:start position:0% +so the most simple case +that people have spent a lot of + + align:start position:0% +that people have spent a lot of + + + align:start position:0% +that people have spent a lot of +effort on is the binary case so the + + align:start position:0% +effort on is the binary case so the + + + align:start position:0% +effort on is the binary case so the +phenotypic data + + align:start position:0% +phenotypic data + + + align:start position:0% +phenotypic data +in this case is just a label right 0 1 + + align:start position:0% +in this case is just a label right 0 1 + + + align:start position:0% +in this case is just a label right 0 1 +yes or no disease versus normal + + align:start position:0% +yes or no disease versus normal + + + align:start position:0% +yes or no disease versus normal +and there are + + align:start position:0% +and there are + + + align:start position:0% +and there are +basically every methods out there that + + align:start position:0% +basically every methods out there that + + + align:start position:0% +basically every methods out there that +could be applied to this has been + + align:start position:0% +could be applied to this has been + + + align:start position:0% +could be applied to this has been +applied and there's tons of papers on + + align:start position:0% +applied and there's tons of papers on + + + align:start position:0% +applied and there's tons of papers on +this how to do this better right how do + + align:start position:0% +this how to do this better right how do + + + align:start position:0% +this how to do this better right how do +you pick out genes that are related to + + align:start position:0% +you pick out genes that are related to + + + align:start position:0% +you pick out genes that are related to +the label and how do you do the + + align:start position:0% +the label and how do you do the + + + align:start position:0% +the label and how do you do the +prediction okay + + align:start position:0% +prediction okay + + + align:start position:0% +prediction okay +um have you guys talked about prediction + + align:start position:0% +um have you guys talked about prediction + + + align:start position:0% +um have you guys talked about prediction +like how to + + align:start position:0% +like how to + + + align:start position:0% +like how to +do do you know what leave one out cross + + align:start position:0% +do do you know what leave one out cross + + + align:start position:0% +do do you know what leave one out cross +validation is okay + + align:start position:0% +validation is okay + + + align:start position:0% +validation is okay +all right so good + + align:start position:0% +all right so good + + + align:start position:0% +all right so good +um + + align:start position:0% +um + + + align:start position:0% +um +and then people did uh + + align:start position:0% +and then people did uh + + + align:start position:0% +and then people did uh +multiple subclasses right just not just + + align:start position:0% +multiple subclasses right just not just + + + align:start position:0% +multiple subclasses right just not just +two but multiple cases + + align:start position:0% +two but multiple cases + + + align:start position:0% +two but multiple cases +um + + align:start position:0% +um + + + align:start position:0% +um +no and then in this case it's + + align:start position:0% +no and then in this case it's + + + align:start position:0% +no and then in this case it's +non-ordered right so you have just + + align:start position:0% +non-ordered right so you have just + + + align:start position:0% +non-ordered right so you have just +different subtypes you could have an + + align:start position:0% +different subtypes you could have an + + + align:start position:0% +different subtypes you could have an +ordered uh subclasses that is if you + + align:start position:0% +ordered uh subclasses that is if you + + + align:start position:0% +ordered uh subclasses that is if you +have a rating for severity of disease + + align:start position:0% +have a rating for severity of disease + + + align:start position:0% +have a rating for severity of disease +you know maybe you have one you know one + + align:start position:0% +you know maybe you have one you know one + + + align:start position:0% +you know maybe you have one you know one +through five as your um + + align:start position:0% +through five as your um + + + align:start position:0% +through five as your um +whoops + + align:start position:0% +whoops + + + align:start position:0% +whoops +phenotype + + align:start position:0% +phenotype + + + align:start position:0% +phenotype +um continuous okay + + align:start position:0% +um continuous okay + + + align:start position:0% +um continuous okay +for some reason um + + align:start position:0% +for some reason um + + + align:start position:0% +for some reason um +this hasn't really the last two haven't + + align:start position:0% +this hasn't really the last two haven't + + + align:start position:0% +this hasn't really the last two haven't +been + + align:start position:0% +been + + + align:start position:0% +been +done as + + align:start position:0% +done as + + + align:start position:0% +done as +well as they should have been or they + + align:start position:0% +well as they should have been or they + + + align:start position:0% +well as they should have been or they +should be + + align:start position:0% +should be + + + align:start position:0% +should be +yeah they should that + + align:start position:0% +yeah they should that + + + align:start position:0% +yeah they should that +as well as they should be + + align:start position:0% +as well as they should be + + + align:start position:0% +as well as they should be +but it's certainly in an area where um + + align:start position:0% +but it's certainly in an area where um + + + align:start position:0% +but it's certainly in an area where um +a lot of progress needs to be made so + + align:start position:0% +a lot of progress needs to be made so + + + align:start position:0% +a lot of progress needs to be made so +for example i i did one + + align:start position:0% +for example i i did one + + + align:start position:0% +for example i i did one +um collaboration where the phenotype was + + align:start position:0% +um collaboration where the phenotype was + + + align:start position:0% +um collaboration where the phenotype was +some invasive ability of cells + + align:start position:0% +some invasive ability of cells + + + align:start position:0% +some invasive ability of cells +so what genes predict the ability of + + align:start position:0% +so what genes predict the ability of + + + align:start position:0% +so what genes predict the ability of +these cancer cells + + align:start position:0% +these cancer cells + + + align:start position:0% +these cancer cells +and so how to apply through all this you + + align:start position:0% +and so how to apply through all this you + + + align:start position:0% +and so how to apply through all this you +know finding genes and then finding + + align:start position:0% +know finding genes and then finding + + + align:start position:0% +know finding genes and then finding +predictions uh + + align:start position:0% +predictions uh + + + align:start position:0% +predictions uh +prediction algorithms and then making + + align:start position:0% +prediction algorithms and then making + + + align:start position:0% +prediction algorithms and then making +predictions how to do that optimally is + + align:start position:0% +predictions how to do that optimally is + + + align:start position:0% +predictions how to do that optimally is +not + + align:start position:0% +not + + + align:start position:0% +not +completely + + align:start position:0% +completely + + + align:start position:0% +completely +settled + + align:start position:0% +settled + + + align:start position:0% +settled +and finally the sensor data type + + align:start position:0% +and finally the sensor data type + + + align:start position:0% +and finally the sensor data type +is something that i'm very interested in + + align:start position:0% +is something that i'm very interested in + + + align:start position:0% +is something that i'm very interested in +um + + align:start position:0% +um + + + align:start position:0% +um +and i'll talk a little bit more about + + align:start position:0% +and i'll talk a little bit more about + + + align:start position:0% +and i'll talk a little bit more about +that later okay + + align:start position:0% +that later okay + + + align:start position:0% +that later okay +so it turns out that a lot of these + + align:start position:0% +so it turns out that a lot of these + + + align:start position:0% +so it turns out that a lot of these +phenotypes can be reduced to the binary + + align:start position:0% +phenotypes can be reduced to the binary + + + align:start position:0% +phenotypes can be reduced to the binary +type okay so if you have multiple + + align:start position:0% +type okay so if you have multiple + + + align:start position:0% +type okay so if you have multiple +subclasses you can combine them to two + + align:start position:0% +subclasses you can combine them to two + + + align:start position:0% +subclasses you can combine them to two +if you have continuous data you can say + + align:start position:0% +if you have continuous data you can say + + + align:start position:0% +if you have continuous data you can say +well low invasive versus high if you + + align:start position:0% +well low invasive versus high if you + + + align:start position:0% +well low invasive versus high if you +have severity of disease you can divide + + align:start position:0% +have severity of disease you can divide + + + align:start position:0% +have severity of disease you can divide +into two so you can always turn into + + align:start position:0% +into two so you can always turn into + + + align:start position:0% +into two so you can always turn into +these into a simpler problem and that's + + align:start position:0% +these into a simpler problem and that's + + + align:start position:0% +these into a simpler problem and that's +what people have done in many cases but + + align:start position:0% +what people have done in many cases but + + + align:start position:0% +what people have done in many cases but +you lose a lot of information so you + + align:start position:0% +you lose a lot of information so you + + + align:start position:0% +you lose a lot of information so you +like to preserve that and do that um + + align:start position:0% +like to preserve that and do that um + + + align:start position:0% +like to preserve that and do that um +carry the same procedure out + + align:start position:0% +carry the same procedure out + + + align:start position:0% +carry the same procedure out +um + + align:start position:0% +um + + + align:start position:0% +um +so i mean + + align:start position:0% +so i mean + + + align:start position:0% +so i mean +you probably have seen this before there + + align:start position:0% +you probably have seen this before there + + + align:start position:0% +you probably have seen this before there +are lots of questions that could be + + align:start position:0% +are lots of questions that could be + + + align:start position:0% +are lots of questions that could be +asked um and have been asked + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +just to give you a sort of general + + align:start position:0% +just to give you a sort of general + + + align:start position:0% +just to give you a sort of general +framework so + + align:start position:0% +framework so + + + align:start position:0% +framework so +because um + + align:start position:0% +because um + + + align:start position:0% +because um +there are so many genes and data um + + align:start position:0% +there are so many genes and data um + + + align:start position:0% +there are so many genes and data um +usually there are some type of + + align:start position:0% +usually there are some type of + + + align:start position:0% +usually there are some type of +dimensionality reduction + + align:start position:0% +dimensionality reduction + + + align:start position:0% +dimensionality reduction +even when you have a very good method + + align:start position:0% +even when you have a very good method + + + align:start position:0% +even when you have a very good method +you still need to + + align:start position:0% +you still need to + + + align:start position:0% +you still need to +reduce the data set size + + align:start position:0% +reduce the data set size + + + align:start position:0% +reduce the data set size +sometimes you know unless you have a + + align:start position:0% +sometimes you know unless you have a + + + align:start position:0% +sometimes you know unless you have a +nice computer things may not even fit on + + align:start position:0% +nice computer things may not even fit on + + + align:start position:0% +nice computer things may not even fit on +your data unless you do some sort of + + align:start position:0% +your data unless you do some sort of + + + align:start position:0% +your data unless you do some sort of +reduction so + + align:start position:0% +reduction so + + + align:start position:0% +reduction so +this problem is called feature selection + + align:start position:0% +this problem is called feature selection + + + align:start position:0% +this problem is called feature selection +computer science + + align:start position:0% +computer science + + + align:start position:0% +computer science +so there are lots of different ways of + + align:start position:0% +so there are lots of different ways of + + + align:start position:0% +so there are lots of different ways of +filtering genes you know + + align:start position:0% +filtering genes you know + + + align:start position:0% +filtering genes you know +threshold value for immune expression + + align:start position:0% +threshold value for immune expression + + + align:start position:0% +threshold value for immune expression +variation filtering and so on there are + + align:start position:0% +variation filtering and so on there are + + + align:start position:0% +variation filtering and so on there are +lots of tools for doing the + + align:start position:0% +lots of tools for doing the + + + align:start position:0% +lots of tools for doing the +dimensionality reduction so + + align:start position:0% +dimensionality reduction so + + + align:start position:0% +dimensionality reduction so +typically + + align:start position:0% +typically + + + align:start position:0% +typically +either you + + align:start position:0% +either you + + + align:start position:0% +either you +reduce dimension by just + + align:start position:0% +reduce dimension by just + + + align:start position:0% +reduce dimension by just +um + + align:start position:0% +um + + + align:start position:0% +um +cutting down the number of genes or you + + align:start position:0% +cutting down the number of genes or you + + + align:start position:0% +cutting down the number of genes or you +could actually find some sort of linear + + align:start position:0% +could actually find some sort of linear + + + align:start position:0% +could actually find some sort of linear +combinations of genes + + align:start position:0% +combinations of genes + + + align:start position:0% +combinations of genes +and then + + align:start position:0% +and then + + + align:start position:0% +and then +use those as the reduced dimension so if + + align:start position:0% +use those as the reduced dimension so if + + + align:start position:0% +use those as the reduced dimension so if +you do like principal components you + + align:start position:0% +you do like principal components you + + + align:start position:0% +you do like principal components you +know or single value composition + + align:start position:0% +know or single value composition + + + align:start position:0% +know or single value composition +you reduce the dimension but the + + align:start position:0% +you reduce the dimension but the + + + align:start position:0% +you reduce the dimension but the +dimensions that you have in the end are + + align:start position:0% +dimensions that you have in the end are + + + align:start position:0% +dimensions that you have in the end are +not + + align:start position:0% +not + + + align:start position:0% +not +genes right those are combinations of + + align:start position:0% +genes right those are combinations of + + + align:start position:0% +genes right those are combinations of +genes so there are different ways of + + align:start position:0% +genes so there are different ways of + + + align:start position:0% +genes so there are different ways of +doing this + + align:start position:0% +doing this + + + align:start position:0% +doing this +and with + + align:start position:0% + + + + align:start position:0% + +disadvantages and advantages for each + + align:start position:0% +disadvantages and advantages for each + + + align:start position:0% +disadvantages and advantages for each +one so i won't go through this but you + + align:start position:0% +one so i won't go through this but you + + + align:start position:0% +one so i won't go through this but you +know t-test you probably have heard of + + align:start position:0% +know t-test you probably have heard of + + + align:start position:0% +know t-test you probably have heard of +so let me just spend + + align:start position:0% +so let me just spend + + + align:start position:0% +so let me just spend +maybe two three slides john just one + + align:start position:0% +maybe two three slides john just one + + + align:start position:0% +maybe two three slides john just one +thing that i that a lot of people have + + align:start position:0% +thing that i that a lot of people have + + + align:start position:0% +thing that i that a lot of people have +noticed + + align:start position:0% +noticed + + + align:start position:0% +noticed +this problem has been fixed um + + align:start position:0% +this problem has been fixed um + + + align:start position:0% +this problem has been fixed um +in most cases + + align:start position:0% +in most cases + + + align:start position:0% +in most cases +say starting a year or two ago but if + + align:start position:0% +say starting a year or two ago but if + + + align:start position:0% +say starting a year or two ago but if +you go back to earlier papers + + align:start position:0% +you go back to earlier papers + + + align:start position:0% +you go back to earlier papers +um they're you know they've done a lot + + align:start position:0% +um they're you know they've done a lot + + + align:start position:0% +um they're you know they've done a lot +of um + + align:start position:0% +of um + + + align:start position:0% +of um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +sub-optimal things or in this case just + + align:start position:0% +sub-optimal things or in this case just + + + align:start position:0% +sub-optimal things or in this case just +some you know wrong thing in their study + + align:start position:0% +some you know wrong thing in their study + + + align:start position:0% +some you know wrong thing in their study +so + + align:start position:0% +so + + + align:start position:0% +so +so there are a lot of + + align:start position:0% +so there are a lot of + + + align:start position:0% +so there are a lot of +papers on classifying disease categories + + align:start position:0% +papers on classifying disease categories + + + align:start position:0% +papers on classifying disease categories +right and this has been the primary or + + align:start position:0% +right and this has been the primary or + + + align:start position:0% +right and this has been the primary or +one of the primary applications of + + align:start position:0% +one of the primary applications of + + + align:start position:0% +one of the primary applications of +appi technology or cdna technology + + align:start position:0% +appi technology or cdna technology + + + align:start position:0% +appi technology or cdna technology +of course you know the performance + + align:start position:0% +of course you know the performance + + + align:start position:0% +of course you know the performance +depends on methodology used a lot of + + align:start position:0% +depends on methodology used a lot of + + + align:start position:0% +depends on methodology used a lot of +times you see these + + align:start position:0% +times you see these + + + align:start position:0% +times you see these +machine learning algorithms like + + align:start position:0% +machine learning algorithms like + + + align:start position:0% +machine learning algorithms like +singular + + align:start position:0% +singular + + + align:start position:0% +singular +not singular support vector machines + + align:start position:0% +not singular support vector machines + + + align:start position:0% +not singular support vector machines +neural networks they appear to give + + align:start position:0% +neural networks they appear to give + + + align:start position:0% +neural networks they appear to give +pretty good results often + + align:start position:0% +pretty good results often + + + align:start position:0% +pretty good results often +um + + align:start position:0% +um + + + align:start position:0% +um +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +as you probably know if there are enough + + align:start position:0% +as you probably know if there are enough + + + align:start position:0% +as you probably know if there are enough +samples you want to use sep training and + + align:start position:0% +samples you want to use sep training and + + + align:start position:0% +samples you want to use sep training and +testing such to assess your accuracy + + align:start position:0% +testing such to assess your accuracy + + + align:start position:0% +testing such to assess your accuracy +uh if not use even that cost validation + + align:start position:0% +uh if not use even that cost validation + + + align:start position:0% +uh if not use even that cost validation +it turns out that a lot of papers in + + align:start position:0% +it turns out that a lot of papers in + + + align:start position:0% +it turns out that a lot of papers in +good journals have made mistakes in + + align:start position:0% +good journals have made mistakes in + + + align:start position:0% +good journals have made mistakes in +prediction accuracy + + align:start position:0% + + + + align:start position:0% + +and what they state + + align:start position:0% +and what they state + + + align:start position:0% +and what they state +uh are over estimates of the real + + align:start position:0% +uh are over estimates of the real + + + align:start position:0% +uh are over estimates of the real +accuracy so + + align:start position:0% + + + + align:start position:0% + +um was this this wasn't discussed by + + align:start position:0% +um was this this wasn't discussed by + + + align:start position:0% +um was this this wasn't discussed by +other people right + + align:start position:0% +other people right + + + align:start position:0% +other people right +[Music] + + align:start position:0% + + + + align:start position:0% + +oh he did + + align:start position:0% +oh he did + + + align:start position:0% +oh he did +breast cancer + + align:start position:0% +breast cancer + + + align:start position:0% +breast cancer +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so let me very briefly then so + + align:start position:0% +all right so let me very briefly then so + + + align:start position:0% +all right so let me very briefly then so +let me just talk about this one + + align:start position:0% +let me just talk about this one + + + align:start position:0% +let me just talk about this one +simulation study did he talk about this + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +um there's a rick's + + align:start position:0% +um there's a rick's + + + align:start position:0% +um there's a rick's +rick simon at nih he's a + + align:start position:0% +rick simon at nih he's a + + + align:start position:0% +rick simon at nih he's a +statistician who's done a lot of good + + align:start position:0% +statistician who's done a lot of good + + + align:start position:0% +statistician who's done a lot of good +work he published this paper + + align:start position:0% +work he published this paper + + + align:start position:0% +work he published this paper +actually i think the date is in may may + + align:start position:0% +actually i think the date is in may may + + + align:start position:0% +actually i think the date is in may may +have been 2002. + + align:start position:0% +have been 2002. + + + align:start position:0% +have been 2002. +anyway journal + + align:start position:0% +anyway journal + + + align:start position:0% +anyway journal +national cancer institute so he did a + + align:start position:0% +national cancer institute so he did a + + + align:start position:0% +national cancer institute so he did a +simulation study just to show you what + + align:start position:0% +simulation study just to show you what + + + align:start position:0% +simulation study just to show you what +kind of mistakes could be made + + align:start position:0% +kind of mistakes could be made + + + align:start position:0% +kind of mistakes could be made +so + + align:start position:0% +so + + + align:start position:0% +so +there were + + align:start position:0% +there were + + + align:start position:0% +there were +he generated + + align:start position:0% +he generated + + + align:start position:0% +he generated +simulated data 20 expression profiles + + align:start position:0% +simulated data 20 expression profiles + + + align:start position:0% +simulated data 20 expression profiles +10 randomly assigned to one class the + + align:start position:0% +10 randomly assigned to one class the + + + align:start position:0% +10 randomly assigned to one class the +rest to the other okay + + align:start position:0% +rest to the other okay + + + align:start position:0% +rest to the other okay +so in this case because the data are all + + align:start position:0% +so in this case because the data are all + + + align:start position:0% +so in this case because the data are all +random + + align:start position:0% +random + + + align:start position:0% +random +there's no true underlying differences + + align:start position:0% +there's no true underlying differences + + + align:start position:0% +there's no true underlying differences +and that means whatever prediction you + + align:start position:0% +and that means whatever prediction you + + + align:start position:0% +and that means whatever prediction you +should make you make the error should be + + align:start position:0% +should make you make the error should be + + + align:start position:0% +should make you make the error should be +about half + + align:start position:0% +about half + + + align:start position:0% +about half +right and he averaged this procedure + + align:start position:0% +right and he averaged this procedure + + + align:start position:0% +right and he averaged this procedure +over two thousand datasets okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +resubstitution here means + + align:start position:0% +resubstitution here means + + + align:start position:0% +resubstitution here means +okay so you have 20 samples so you build + + align:start position:0% +okay so you have 20 samples so you build + + + align:start position:0% +okay so you have 20 samples so you build +your model prediction model + + align:start position:0% +your model prediction model + + + align:start position:0% +your model prediction model +based on all 20 okay + + align:start position:0% +based on all 20 okay + + + align:start position:0% +based on all 20 okay +so you have your model and then + + align:start position:0% +so you have your model and then + + + align:start position:0% +so you have your model and then +you test the model on each one okay + + align:start position:0% +you test the model on each one okay + + + align:start position:0% +you test the model on each one okay +so if you do that 98.2 percent of time + + align:start position:0% +so if you do that 98.2 percent of time + + + align:start position:0% +so if you do that 98.2 percent of time +you make no error + + align:start position:0% +you make no error + + + align:start position:0% +you make no error +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you always get the labels correct + + align:start position:0% +you always get the labels correct + + + align:start position:0% +you always get the labels correct +okay cancer or not or whatever labels + + align:start position:0% +okay cancer or not or whatever labels + + + align:start position:0% +okay cancer or not or whatever labels +you might be in a particular study + + align:start position:0% +you might be in a particular study + + + align:start position:0% +you might be in a particular study +that's the label + + align:start position:0% +that's the label + + + align:start position:0% +that's the label +so + + align:start position:0% +so + + + align:start position:0% +so +you know and you know that's clearly a + + align:start position:0% +you know and you know that's clearly a + + + align:start position:0% +you know and you know that's clearly a +wrong thing to do right you can't build + + align:start position:0% +wrong thing to do right you can't build + + + align:start position:0% +wrong thing to do right you can't build +your model based on your data and then + + align:start position:0% +your model based on your data and then + + + align:start position:0% +your model based on your data and then +and then predict the data + + align:start position:0% +and then predict the data + + + align:start position:0% +and then predict the data +but what a lot of people have done in + + align:start position:0% +but what a lot of people have done in + + + align:start position:0% +but what a lot of people have done in +good journals is to + + align:start position:0% +good journals is to + + + align:start position:0% +good journals is to +uh remove the test sample after gene + + align:start position:0% +uh remove the test sample after gene + + + align:start position:0% +uh remove the test sample after gene +selection okay so i have my 20 samples + + align:start position:0% +selection okay so i have my 20 samples + + + align:start position:0% +selection okay so i have my 20 samples +and then i filter the genes + + align:start position:0% +and then i filter the genes + + + align:start position:0% +and then i filter the genes +you know and then i pick the genes that + + align:start position:0% +you know and then i pick the genes that + + + align:start position:0% +you know and then i pick the genes that +are informative of the classes okay + + align:start position:0% +are informative of the classes okay + + + align:start position:0% +are informative of the classes okay +and then + + align:start position:0% +and then + + + align:start position:0% +and then +to predict the model and leave one out + + align:start position:0% +to predict the model and leave one out + + + align:start position:0% +to predict the model and leave one out +or predict the label i'd leave one out + + align:start position:0% +or predict the label i'd leave one out + + + align:start position:0% +or predict the label i'd leave one out +build my model but based on the genes + + align:start position:0% +build my model but based on the genes + + + align:start position:0% +build my model but based on the genes +that i've already selected + + align:start position:0% +that i've already selected + + + align:start position:0% +that i've already selected +and then predict the one that's left out + + align:start position:0% +and then predict the one that's left out + + + align:start position:0% +and then predict the one that's left out +okay then you leave another one out + + align:start position:0% +okay then you leave another one out + + + align:start position:0% +okay then you leave another one out +build a new model to the prediction okay + + align:start position:0% +build a new model to the prediction okay + + + align:start position:0% +build a new model to the prediction okay +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +so you think well you know + + align:start position:0% +so you think well you know + + + align:start position:0% +so you think well you know +that should be okay right + + align:start position:0% +that should be okay right + + + align:start position:0% +that should be okay right +but it's okay if the if the gene + + align:start position:0% +but it's okay if the if the gene + + + align:start position:0% +but it's okay if the if the gene +set that you get is the same every time + + align:start position:0% +set that you get is the same every time + + + align:start position:0% +set that you get is the same every time +you + + align:start position:0% +you + + + align:start position:0% +you +if it were the same every time you + + align:start position:0% +if it were the same every time you + + + align:start position:0% +if it were the same every time you +delete a sample and recalculate okay put + + align:start position:0% +delete a sample and recalculate okay put + + + align:start position:0% +delete a sample and recalculate okay put +it at i mean as we saw earlier i mean + + align:start position:0% +it at i mean as we saw earlier i mean + + + align:start position:0% +it at i mean as we saw earlier i mean +the gene is not very stable + + align:start position:0% +the gene is not very stable + + + align:start position:0% +the gene is not very stable +so + + align:start position:0% +so + + + align:start position:0% +so +if you do that + + align:start position:0% +if you do that + + + align:start position:0% +if you do that +there's a lot of bias + + align:start position:0% +there's a lot of bias + + + align:start position:0% +there's a lot of bias +so if you do that in this simulated data + + align:start position:0% +so if you do that in this simulated data + + + align:start position:0% +so if you do that in this simulated data +set 90 percent of time + + align:start position:0% +set 90 percent of time + + + align:start position:0% +set 90 percent of time +on a random data set you have 90 + + align:start position:0% +on a random data set you have 90 + + + align:start position:0% +on a random data set you have 90 +accuracy + + align:start position:0% +accuracy + + + align:start position:0% +accuracy +right so + + align:start position:0% +right so + + + align:start position:0% +right so +and generally the difference is not this + + align:start position:0% +and generally the difference is not this + + + align:start position:0% +and generally the difference is not this +big but it's substantial it could be + + align:start position:0% +big but it's substantial it could be + + + align:start position:0% +big but it's substantial it could be +substantial depending on say the size of + + align:start position:0% +substantial depending on say the size of + + + align:start position:0% +substantial depending on say the size of +your data set + + align:start position:0% +your data set + + + align:start position:0% +your data set +now if you do it correctly that is you + + align:start position:0% +now if you do it correctly that is you + + + align:start position:0% +now if you do it correctly that is you +remove the data set before selection + + align:start position:0% +remove the data set before selection + + + align:start position:0% +remove the data set before selection +right before second genes you reselect + + align:start position:0% +right before second genes you reselect + + + align:start position:0% +right before second genes you reselect +the genes and you do the prediction and + + align:start position:0% +the genes and you do the prediction and + + + align:start position:0% +the genes and you do the prediction and +so on then the median of you get median + + align:start position:0% +so on then the median of you get median + + + align:start position:0% +so on then the median of you get median +of 11 misclassification okay about so + + align:start position:0% +of 11 misclassification okay about so + + + align:start position:0% +of 11 misclassification okay about so +you should get 10 so you get something + + align:start position:0% +you should get 10 so you get something + + + align:start position:0% +you should get 10 so you get something +close to something close to the same of + + align:start position:0% +close to something close to the same of + + + align:start position:0% +close to something close to the same of +course no one really does it + + align:start position:0% +course no one really does it + + + align:start position:0% +course no one really does it +exactly the way it should be done so the + + align:start position:0% +exactly the way it should be done so the + + + align:start position:0% +exactly the way it should be done so the +way it should be done is + + align:start position:0% +way it should be done is + + + align:start position:0% +way it should be done is +you delete one sample + + align:start position:0% +you delete one sample + + + align:start position:0% +you delete one sample +and then start everything from scratch + + align:start position:0% +and then start everything from scratch + + + align:start position:0% +and then start everything from scratch +like you renormalize + + align:start position:0% +like you renormalize + + + align:start position:0% +like you renormalize +you you know do everything right but no + + align:start position:0% +you you know do everything right but no + + + align:start position:0% +you you know do everything right but no +one really does that right so + + align:start position:0% +one really does that right so + + + align:start position:0% +one really does that right so +they just actually normalize using all + + align:start position:0% +they just actually normalize using all + + + align:start position:0% +they just actually normalize using all +the data + + align:start position:0% +the data + + + align:start position:0% +the data +and then you know + + align:start position:0% +and then you know + + + align:start position:0% +and then you know +nowadays you you move on and then you + + align:start position:0% +nowadays you you move on and then you + + + align:start position:0% +nowadays you you move on and then you +move one to the gene selection and so on + + align:start position:0% +move one to the gene selection and so on + + + align:start position:0% +move one to the gene selection and so on +so + + align:start position:0% +so + + + align:start position:0% +so +i think people probably suspected that + + align:start position:0% +i think people probably suspected that + + + align:start position:0% +i think people probably suspected that +there was a problem with this but + + align:start position:0% +there was a problem with this but + + + align:start position:0% +there was a problem with this but +um + + align:start position:0% +um + + + align:start position:0% +um +not + + align:start position:0% +not + + + align:start position:0% +not +not as big as + + align:start position:0% +not as big as + + + align:start position:0% +not as big as +it is in certain cases + + align:start position:0% + + + + align:start position:0% + +so nowadays like if you see it you know + + align:start position:0% +so nowadays like if you see it you know + + + align:start position:0% +so nowadays like if you see it you know +paper + + align:start position:0% +paper + + + align:start position:0% +paper +in good journals it will have the + + align:start position:0% +in good journals it will have the + + + align:start position:0% +in good journals it will have the +supplementary information they'll talk + + align:start position:0% +supplementary information they'll talk + + + align:start position:0% +supplementary information they'll talk +about what the bias is but they often + + align:start position:0% +about what the bias is but they often + + + align:start position:0% +about what the bias is but they often +report + + align:start position:0% +report + + + align:start position:0% +report +the better rate you know in the paper so + + align:start position:0% +the better rate you know in the paper so + + + align:start position:0% +the better rate you know in the paper so +you know not good + + align:start position:0% +you know not good + + + align:start position:0% +you know not good +okay so let's talk about uh survival + + align:start position:0% +okay so let's talk about uh survival + + + align:start position:0% +okay so let's talk about uh survival +times now um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +how many of you are familiar with like + + align:start position:0% +how many of you are familiar with like + + + align:start position:0% +how many of you are familiar with like +sensor data like + + align:start position:0% +sensor data like + + + align:start position:0% +sensor data like +okay so i won't really talk about the + + align:start position:0% +okay so i won't really talk about the + + + align:start position:0% +okay so i won't really talk about the +basics too much then + + align:start position:0% +basics too much then + + + align:start position:0% +basics too much then +um + + align:start position:0% +um + + + align:start position:0% +um +the censoring rate often is in the order + + align:start position:0% +the censoring rate often is in the order + + + align:start position:0% +the censoring rate often is in the order +of + + align:start position:0% +of + + + align:start position:0% +of +you know it could be like 50 that's not + + align:start position:0% +you know it could be like 50 that's not + + + align:start position:0% +you know it could be like 50 that's not +unusual so you want to make sure that + + align:start position:0% +unusual so you want to make sure that + + + align:start position:0% +unusual so you want to make sure that +you take care of your sensoring + + align:start position:0% +you take care of your sensoring + + + align:start position:0% +you take care of your sensoring +correctly + + align:start position:0% +correctly + + + align:start position:0% +correctly +and generally we talk about the right + + align:start position:0% +and generally we talk about the right + + + align:start position:0% +and generally we talk about the right +censoring right you have a patient a + + align:start position:0% +censoring right you have a patient a + + + align:start position:0% +censoring right you have a patient a +studies terminated before patients die + + align:start position:0% +studies terminated before patients die + + + align:start position:0% +studies terminated before patients die +your patient drops out of study + + align:start position:0% +your patient drops out of study + + + align:start position:0% +your patient drops out of study +um + + align:start position:0% +um + + + align:start position:0% +um +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +as in as in the other um phenotypes the + + align:start position:0% +as in as in the other um phenotypes the + + + align:start position:0% +as in as in the other um phenotypes the +simplest thing you can do is + + align:start position:0% +simplest thing you can do is + + + align:start position:0% +simplest thing you can do is +to use standard uh uni + + align:start position:0% +to use standard uh uni + + + align:start position:0% +to use standard uh uni +variant approach that is i look at my + + align:start position:0% +variant approach that is i look at my + + + align:start position:0% +variant approach that is i look at my +genes one at a time sees the system + + align:start position:0% +genes one at a time sees the system + + + align:start position:0% +genes one at a time sees the system +relates to survival right so there are + + align:start position:0% +relates to survival right so there are + + + align:start position:0% +relates to survival right so there are +many ways of doing that + + align:start position:0% +many ways of doing that + + + align:start position:0% +many ways of doing that +um because i mean it's this problem has + + align:start position:0% +um because i mean it's this problem has + + + align:start position:0% +um because i mean it's this problem has +been around for + + align:start position:0% +been around for + + + align:start position:0% +been around for +decades and so there are good methods + + align:start position:0% +decades and so there are good methods + + + align:start position:0% +decades and so there are good methods +for doing this + + align:start position:0% +for doing this + + + align:start position:0% +for doing this +for example + + align:start position:0% +for example + + + align:start position:0% +for example +you know log rank tests + + align:start position:0% +you know log rank tests + + + align:start position:0% +you know log rank tests +will give you some p value as to how + + align:start position:0% +will give you some p value as to how + + + align:start position:0% +will give you some p value as to how +that gene is + + align:start position:0% +that gene is + + + align:start position:0% +that gene is +correlated with your survival data + + align:start position:0% +correlated with your survival data + + + align:start position:0% +correlated with your survival data +and so a lot of people will do that some + + align:start position:0% +and so a lot of people will do that some + + + align:start position:0% +and so a lot of people will do that some +sort of univariate approach constraint + + align:start position:0% +sort of univariate approach constraint + + + align:start position:0% +sort of univariate approach constraint +was inclined and then they put together + + align:start position:0% +was inclined and then they put together + + + align:start position:0% +was inclined and then they put together +at the end when some some type of voting + + align:start position:0% +at the end when some some type of voting + + + align:start position:0% +at the end when some some type of voting +method so to do a prediction of the + + align:start position:0% +method so to do a prediction of the + + + align:start position:0% +method so to do a prediction of the +patient + + align:start position:0% +patient + + + align:start position:0% +patient +you know you say well + + align:start position:0% +you know you say well + + + align:start position:0% +you know you say well +you know what does my gene one say about + + align:start position:0% +you know what does my gene one say about + + + align:start position:0% +you know what does my gene one say about +this patient what about my what about + + align:start position:0% +this patient what about my what about + + + align:start position:0% +this patient what about my what about +gene two you know what about gene + + align:start position:0% +gene two you know what about gene + + + align:start position:0% +gene two you know what about gene +hundred they sort of add up you know + + align:start position:0% +hundred they sort of add up you know + + + align:start position:0% +hundred they sort of add up you know +um + + align:start position:0% +um + + + align:start position:0% +um +sometimes weighted differently depending + + align:start position:0% +sometimes weighted differently depending + + + align:start position:0% +sometimes weighted differently depending +on how + + align:start position:0% +on how + + + align:start position:0% +on how +good the gene is in predicting or in its + + align:start position:0% +good the gene is in predicting or in its + + + align:start position:0% +good the gene is in predicting or in its +correlation to the phenotype + + align:start position:0% +correlation to the phenotype + + + align:start position:0% +correlation to the phenotype +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so + + align:start position:0% + + + + align:start position:0% + +as i'll talk a little more later + + align:start position:0% +as i'll talk a little more later + + + align:start position:0% +as i'll talk a little more later +this is often not optimal so i mean it's + + align:start position:0% +this is often not optimal so i mean it's + + + align:start position:0% +this is often not optimal so i mean it's +how people do it because it's easy + + align:start position:0% +how people do it because it's easy + + + align:start position:0% +how people do it because it's easy +but it's not optimal + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +let's skip that so let's just do some um + + align:start position:0% + + + + align:start position:0% + +take a look at some examples so + + align:start position:0% +take a look at some examples so + + + align:start position:0% +take a look at some examples so +so eventually so um you'd like to do + + align:start position:0% +so eventually so um you'd like to do + + + align:start position:0% +so eventually so um you'd like to do +your study and then correlate that with + + align:start position:0% +your study and then correlate that with + + + align:start position:0% +your study and then correlate that with +your phenotype and then actually go on + + align:start position:0% +your phenotype and then actually go on + + + align:start position:0% +your phenotype and then actually go on +to show that whatever + + align:start position:0% +to show that whatever + + + align:start position:0% +to show that whatever +you don't want to just show that it's + + align:start position:0% +you don't want to just show that it's + + + align:start position:0% +you don't want to just show that it's +related to the phenotype right you want + + align:start position:0% +related to the phenotype right you want + + + align:start position:0% +related to the phenotype right you want +to show that it's + + align:start position:0% +to show that it's + + + align:start position:0% +to show that it's +show that it's better than what people + + align:start position:0% +show that it's better than what people + + + align:start position:0% +show that it's better than what people +use currently right so this wasn't done + + align:start position:0% +use currently right so this wasn't done + + + align:start position:0% +use currently right so this wasn't done +until you know like say 2001 2002 so + + align:start position:0% +until you know like say 2001 2002 so + + + align:start position:0% +until you know like say 2001 2002 so +people just said oh my expression + + align:start position:0% +people just said oh my expression + + + align:start position:0% +people just said oh my expression +profiles are related to my phenotype + + align:start position:0% +profiles are related to my phenotype + + + align:start position:0% +profiles are related to my phenotype +okay but it's actually better + + align:start position:0% +okay but it's actually better + + + align:start position:0% +okay but it's actually better +so it's actually + + align:start position:0% +so it's actually + + + align:start position:0% +so it's actually +i guess this is a interesting question + + align:start position:0% +i guess this is a interesting question + + + align:start position:0% +i guess this is a interesting question +for debate i mean people have + + align:start position:0% +for debate i mean people have + + + align:start position:0% +for debate i mean people have +published all these papers for + + align:start position:0% +published all these papers for + + + align:start position:0% +published all these papers for +you know two three years but i actually + + align:start position:0% +you know two three years but i actually + + + align:start position:0% +you know two three years but i actually +don't know of any hospital that will do + + align:start position:0% +don't know of any hospital that will do + + + align:start position:0% +don't know of any hospital that will do +the testing and then do prediction + + align:start position:0% +the testing and then do prediction + + + align:start position:0% +the testing and then do prediction +um + + align:start position:0% +um + + + align:start position:0% +um +on the patient right + + align:start position:0% +on the patient right + + + align:start position:0% +on the patient right +i mean there was some report of a plan + + align:start position:0% +i mean there was some report of a plan + + + align:start position:0% +i mean there was some report of a plan +to do this in + + align:start position:0% +to do this in + + + align:start position:0% +to do this in +netherlands + + align:start position:0% +netherlands + + + align:start position:0% +netherlands +but + + align:start position:0% +but + + + align:start position:0% +but +you know this hasn't really + + align:start position:0% +you know this hasn't really + + + align:start position:0% +you know this hasn't really +uh come about + + align:start position:0% +uh come about + + + align:start position:0% +uh come about +so i mean i actually had a good friend + + align:start position:0% +so i mean i actually had a good friend + + + align:start position:0% +so i mean i actually had a good friend +in the pathology department who's + + align:start position:0% +in the pathology department who's + + + align:start position:0% +in the pathology department who's +actually done a lot of erase himself and + + align:start position:0% +actually done a lot of erase himself and + + + align:start position:0% +actually done a lot of erase himself and +so now that he finished his md phd he's + + align:start position:0% +so now that he finished his md phd he's + + + align:start position:0% +so now that he finished his md phd he's +in doing a pathology uh + + align:start position:0% +in doing a pathology uh + + + align:start position:0% +in doing a pathology uh +fellowship he said okay you know maybe + + align:start position:0% +fellowship he said okay you know maybe + + + align:start position:0% +fellowship he said okay you know maybe +i'll try to get this thing + + align:start position:0% +i'll try to get this thing + + + align:start position:0% +i'll try to get this thing +to the clinic + + align:start position:0% +to the clinic + + + align:start position:0% +to the clinic +and it turns out just there's just a lot + + align:start position:0% +and it turns out just there's just a lot + + + align:start position:0% +and it turns out just there's just a lot +of problems right for one thing + + align:start position:0% +of problems right for one thing + + + align:start position:0% +of problems right for one thing +a lot of these heaven studies have not + + align:start position:0% +a lot of these heaven studies have not + + + align:start position:0% +a lot of these heaven studies have not +showed + + align:start position:0% +showed + + + align:start position:0% +showed +that have not shown that + + align:start position:0% +that have not shown that + + + align:start position:0% +that have not shown that +compared to the cost involved that it's + + align:start position:0% +compared to the cost involved that it's + + + align:start position:0% +compared to the cost involved that it's +actually a good deal right so apparently + + align:start position:0% +actually a good deal right so apparently + + + align:start position:0% +actually a good deal right so apparently +there are very simple tests for a lot of + + align:start position:0% +there are very simple tests for a lot of + + + align:start position:0% +there are very simple tests for a lot of +say cancer related uh + + align:start position:0% +say cancer related uh + + + align:start position:0% +say cancer related uh +diagnosis there are very simple tests + + align:start position:0% +diagnosis there are very simple tests + + + align:start position:0% +diagnosis there are very simple tests +that are very cheap and very easy to do + + align:start position:0% +that are very cheap and very easy to do + + + align:start position:0% +that are very cheap and very easy to do +take you know very little time + + align:start position:0% +take you know very little time + + + align:start position:0% +take you know very little time +so + + align:start position:0% +so + + + align:start position:0% +so +he said it's not clear in the clinic + + align:start position:0% +he said it's not clear in the clinic + + + align:start position:0% +he said it's not clear in the clinic +whether + + align:start position:0% +whether + + + align:start position:0% +whether +those tests are actually you know + + align:start position:0% +those tests are actually you know + + + align:start position:0% +those tests are actually you know +less accurate than this it's much + + align:start position:0% +less accurate than this it's much + + + align:start position:0% +less accurate than this it's much +simpler people already do this and so + + align:start position:0% +simpler people already do this and so + + + align:start position:0% +simpler people already do this and so +there's necessary there isn't a great + + align:start position:0% +there's necessary there isn't a great + + + align:start position:0% +there's necessary there isn't a great +incentive to switch to this + + align:start position:0% +incentive to switch to this + + + align:start position:0% +incentive to switch to this +um and probably probably the bigger + + align:start position:0% +um and probably probably the bigger + + + align:start position:0% +um and probably probably the bigger +reason though is + + align:start position:0% +reason though is + + + align:start position:0% +reason though is +money right so + + align:start position:0% +money right so + + + align:start position:0% +money right so +insurance companies these days + + align:start position:0% +insurance companies these days + + + align:start position:0% +insurance companies these days +are paid by + + align:start position:0% +are paid by + + + align:start position:0% +are paid by +um + + align:start position:0% +um + + + align:start position:0% +um +paid per patient right so i forget the + + align:start position:0% +paid per patient right so i forget the + + + align:start position:0% +paid per patient right so i forget the +terminology for this + + align:start position:0% +terminology for this + + + align:start position:0% +terminology for this +but so if the hospital wants to to do an + + align:start position:0% +but so if the hospital wants to to do an + + + align:start position:0% +but so if the hospital wants to to do an +ex you know an extra procedure like this + + align:start position:0% +ex you know an extra procedure like this + + + align:start position:0% +ex you know an extra procedure like this +test + + align:start position:0% +test + + + align:start position:0% +test +basically they don't get reimbursed by + + align:start position:0% +basically they don't get reimbursed by + + + align:start position:0% +basically they don't get reimbursed by +the insurance company unless it can be + + align:start position:0% +the insurance company unless it can be + + + align:start position:0% +the insurance company unless it can be +shown to the insurance company that this + + align:start position:0% +shown to the insurance company that this + + + align:start position:0% +shown to the insurance company that this +is + + align:start position:0% +is + + + align:start position:0% +is +you know a necessary procedure to be + + align:start position:0% +you know a necessary procedure to be + + + align:start position:0% +you know a necessary procedure to be +done on all these patients okay and + + align:start position:0% +done on all these patients okay and + + + align:start position:0% +done on all these patients okay and +that's the difficult thing i mean he so + + align:start position:0% +that's the difficult thing i mean he so + + + align:start position:0% +that's the difficult thing i mean he so +my friend looked into this and it's not + + align:start position:0% +my friend looked into this and it's not + + + align:start position:0% +my friend looked into this and it's not +easy right hospital or insurance + + align:start position:0% +easy right hospital or insurance + + + align:start position:0% +easy right hospital or insurance +companies are not willing to + + align:start position:0% +companies are not willing to + + + align:start position:0% +companies are not willing to +you know shell out money unless it's you + + align:start position:0% +you know shell out money unless it's you + + + align:start position:0% +you know shell out money unless it's you +know proven sorry in a reasonably you + + align:start position:0% +know proven sorry in a reasonably you + + + align:start position:0% +know proven sorry in a reasonably you +know good way + + align:start position:0% +know good way + + + align:start position:0% +know good way +and of course you know when i if i were + + align:start position:0% +and of course you know when i if i were + + + align:start position:0% +and of course you know when i if i were +to for example show them the earlier + + align:start position:0% +to for example show them the earlier + + + align:start position:0% +to for example show them the earlier +results and how + + align:start position:0% +results and how + + + align:start position:0% +results and how +irreducible these are + + align:start position:0% +irreducible these are + + + align:start position:0% +irreducible these are +no one's gonna say i'm gonna pay a + + align:start position:0% +no one's gonna say i'm gonna pay a + + + align:start position:0% +no one's gonna say i'm gonna pay a +thousand dollars per patient + + align:start position:0% +thousand dollars per patient + + + align:start position:0% +thousand dollars per patient +so + + align:start position:0% +so + + + align:start position:0% +so +i + + align:start position:0% +i + + + align:start position:0% +i +so i don't know where you know at what + + align:start position:0% +so i don't know where you know at what + + + align:start position:0% +so i don't know where you know at what +point this is gonna really be done in in + + align:start position:0% +point this is gonna really be done in in + + + align:start position:0% +point this is gonna really be done in in +the clinic so + + align:start position:0% +the clinic so + + + align:start position:0% +the clinic so +um + + align:start position:0% +um + + + align:start position:0% +um +but i think as more + + align:start position:0% +but i think as more + + + align:start position:0% +but i think as more +people + + align:start position:0% +people + + + align:start position:0% +people +publish better papers + + align:start position:0% +publish better papers + + + align:start position:0% +publish better papers +and + + align:start position:0% +and + + + align:start position:0% +and +and do a more comprehensive + + align:start position:0% +and do a more comprehensive + + + align:start position:0% +and do a more comprehensive +cost benefit analysis you know maybe it + + align:start position:0% +cost benefit analysis you know maybe it + + + align:start position:0% +cost benefit analysis you know maybe it +will happen + + align:start position:0% +will happen + + + align:start position:0% +will happen +um i think initially people are very + + align:start position:0% +um i think initially people are very + + + align:start position:0% +um i think initially people are very +excited that this is you know what + + align:start position:0% +excited that this is you know what + + + align:start position:0% +excited that this is you know what +you're gonna do right you walk into + + align:start position:0% +you're gonna do right you walk into + + + align:start position:0% +you're gonna do right you walk into +clinic they do this and you know give + + align:start position:0% +clinic they do this and you know give + + + align:start position:0% +clinic they do this and you know give +you all these diagnoses + + align:start position:0% +you all these diagnoses + + + align:start position:0% +you all these diagnoses +diagnoses but who knows when this is + + align:start position:0% +diagnoses but who knows when this is + + + align:start position:0% +diagnoses but who knows when this is +going to happen um + + align:start position:0% +going to happen um + + + align:start position:0% +going to happen um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so yeah those are some practical issues + + align:start position:0% +so yeah those are some practical issues + + + align:start position:0% +so yeah those are some practical issues +that + + align:start position:0% + + + + align:start position:0% + +that are not so easy to resolve + + align:start position:0% +that are not so easy to resolve + + + align:start position:0% +that are not so easy to resolve +in any way in any case this is um + + align:start position:0% +in any way in any case this is um + + + align:start position:0% +in any way in any case this is um +a paper that came out in nature this is + + align:start position:0% +a paper that came out in nature this is + + + align:start position:0% +a paper that came out in nature this is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i think a group from the netherlands + + align:start position:0% +i think a group from the netherlands + + + align:start position:0% +i think a group from the netherlands +where + + align:start position:0% +where + + + align:start position:0% +where +i think they are more + + align:start position:0% +i think they are more + + + align:start position:0% +i think they are more +at least from a couple + + align:start position:0% +at least from a couple + + + align:start position:0% +at least from a couple +articles that i've read there are more + + align:start position:0% +articles that i've read there are more + + + align:start position:0% +articles that i've read there are more +um closer to actually doing this in + + align:start position:0% +um closer to actually doing this in + + + align:start position:0% +um closer to actually doing this in +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the clinic and one article + + align:start position:0% +the clinic and one article + + + align:start position:0% +the clinic and one article +actually cited this paper the result of + + align:start position:0% +actually cited this paper the result of + + + align:start position:0% +actually cited this paper the result of +this paper as a basis for doing this in + + align:start position:0% +this paper as a basis for doing this in + + + align:start position:0% +this paper as a basis for doing this in +clinic so + + align:start position:0% +clinic so + + + align:start position:0% +clinic so +uh one problem is that i don't think + + align:start position:0% +uh one problem is that i don't think + + + align:start position:0% +uh one problem is that i don't think +what was done in this paper is that + + align:start position:0% +what was done in this paper is that + + + align:start position:0% +what was done in this paper is that +grade so + + align:start position:0% +grade so + + + align:start position:0% +grade so +that's a bit of an issue but at least in + + align:start position:0% +that's a bit of an issue but at least in + + + align:start position:0% +that's a bit of an issue but at least in +this paper they claim that this gene + + align:start position:0% +this paper they claim that this gene + + + align:start position:0% +this paper they claim that this gene +expression profile will outperform all + + align:start position:0% +expression profile will outperform all + + + align:start position:0% +expression profile will outperform all +currently used clinical primers and + + align:start position:0% +currently used clinical primers and + + + align:start position:0% +currently used clinical primers and +predicting disease outcomes certain + + align:start position:0% +predicting disease outcomes certain + + + align:start position:0% +predicting disease outcomes certain +blood cancer so + + align:start position:0% +blood cancer so + + + align:start position:0% +blood cancer so +so is any anyone familiar with this + + align:start position:0% +so is any anyone familiar with this + + + align:start position:0% +so is any anyone familiar with this +paper + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +all right so did you talk about + + align:start position:0% +all right so did you talk about + + + align:start position:0% +all right so did you talk about +methodology as well + + align:start position:0% +methodology as well + + + align:start position:0% +methodology as well +oh okay i've + + align:start position:0% +oh okay i've + + + align:start position:0% +oh okay i've +i must have forgotten did he talk about + + align:start position:0% +i must have forgotten did he talk about + + + align:start position:0% +i must have forgotten did he talk about +this very very well + + align:start position:0% + + + + align:start position:0% + +okay but so you talked about this paper + + align:start position:0% +okay but so you talked about this paper + + + align:start position:0% +okay but so you talked about this paper +but not + + align:start position:0% +but not + + + align:start position:0% +but not +let's see which paper + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +i i apologize i + + align:start position:0% +i i apologize i + + + align:start position:0% +i i apologize i +from i was trying to remember from last + + align:start position:0% +from i was trying to remember from last + + + align:start position:0% +from i was trying to remember from last +year what papers were covered + + align:start position:0% +year what papers were covered + + + align:start position:0% +year what papers were covered +and um + + align:start position:0% +and um + + + align:start position:0% +and um +i knew that the lymphoma papers were + + align:start position:0% +i knew that the lymphoma papers were + + + align:start position:0% +i knew that the lymphoma papers were +covered by zac or somebody + + align:start position:0% +covered by zac or somebody + + + align:start position:0% +covered by zac or somebody +but then i forgot that steve might have + + align:start position:0% +but then i forgot that steve might have + + + align:start position:0% +but then i forgot that steve might have +covered this + + align:start position:0% +covered this + + + align:start position:0% +covered this +um + + align:start position:0% +um + + + align:start position:0% +um +okay anyway so + + align:start position:0% + + + + align:start position:0% + +actually + + align:start position:0% +actually + + + align:start position:0% +actually +there isn't that much time so + + align:start position:0% +there isn't that much time so + + + align:start position:0% +there isn't that much time so +it's good that he covered + + align:start position:0% +it's good that he covered + + + align:start position:0% +it's good that he covered +this so + + align:start position:0% +this so + + + align:start position:0% +this so +so basically the approach is you do some + + align:start position:0% +so basically the approach is you do some + + + align:start position:0% +so basically the approach is you do some +you build some sort of classifier right + + align:start position:0% +you build some sort of classifier right + + + align:start position:0% +you build some sort of classifier right +you pick out the genes + + align:start position:0% +you pick out the genes + + + align:start position:0% +you pick out the genes +build some sort of classifier and then + + align:start position:0% +build some sort of classifier and then + + + align:start position:0% +build some sort of classifier and then +so the way that these papers prove that + + align:start position:0% +so the way that these papers prove that + + + align:start position:0% +so the way that these papers prove that +you know things are good + + align:start position:0% +you know things are good + + + align:start position:0% +you know things are good +or the expression profiles are better + + align:start position:0% +or the expression profiles are better + + + align:start position:0% +or the expression profiles are better +is that + + align:start position:0% +is that + + + align:start position:0% +is that +you do some sort of uh kaplan plot for + + align:start position:0% +you do some sort of uh kaplan plot for + + + align:start position:0% +you do some sort of uh kaplan plot for +each one and then you do a logarithmic + + align:start position:0% +each one and then you do a logarithmic + + + align:start position:0% +each one and then you do a logarithmic +test or some tests like that to show + + align:start position:0% +test or some tests like that to show + + + align:start position:0% +test or some tests like that to show +that there's a big difference right so + + align:start position:0% +that there's a big difference right so + + + align:start position:0% +that there's a big difference right so +um + + align:start position:0% +um + + + align:start position:0% +um +so you they do this for + + align:start position:0% +so you they do this for + + + align:start position:0% +so you they do this for +a variety of + + align:start position:0% +a variety of + + + align:start position:0% +a variety of +strata + + align:start position:0% +strata + + + align:start position:0% +strata +stratified groups so you might take + + align:start position:0% +stratified groups so you might take + + + align:start position:0% +stratified groups so you might take +patients that were + + align:start position:0% +patients that were + + + align:start position:0% +patients that were +assigned + + align:start position:0% +assigned + + + align:start position:0% +assigned +one category of disease by + + align:start position:0% +one category of disease by + + + align:start position:0% +one category of disease by +your typical + + align:start position:0% +your typical + + + align:start position:0% +your typical +um + + align:start position:0% +um + + + align:start position:0% +um +uh prognosis + + align:start position:0% +uh prognosis + + + align:start position:0% +uh prognosis +and then you show that within that group + + align:start position:0% +and then you show that within that group + + + align:start position:0% +and then you show that within that group +there's enough variability so somehow + + align:start position:0% +there's enough variability so somehow + + + align:start position:0% +there's enough variability so somehow +that + + align:start position:0% +that + + + align:start position:0% +that +you know + + align:start position:0% +you know + + + align:start position:0% +you know +there is some information in the + + align:start position:0% +there is some information in the + + + align:start position:0% +there is some information in the +expression data that's not captured by + + align:start position:0% +expression data that's not captured by + + + align:start position:0% +expression data that's not captured by +this + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +um + + align:start position:0% +um + + + align:start position:0% +um +and the next step that + + align:start position:0% +and the next step that + + + align:start position:0% +and the next step that +are in that that are done increasingly + + align:start position:0% +are in that that are done increasingly + + + align:start position:0% +are in that that are done increasingly +now is is after you get this classifier + + align:start position:0% +now is is after you get this classifier + + + align:start position:0% +now is is after you get this classifier +you put that together with all the other + + align:start position:0% +you put that together with all the other + + + align:start position:0% +you put that together with all the other +data right + + align:start position:0% +data right + + + align:start position:0% +data right +so + + align:start position:0% +so + + + align:start position:0% +so +in this case um + + align:start position:0% +in this case um + + + align:start position:0% +in this case um +in this case they have one + + align:start position:0% +in this case they have one + + + align:start position:0% +in this case they have one +uh + + align:start position:0% +uh + + + align:start position:0% +uh +basically out of all the expression uh + + align:start position:0% +basically out of all the expression uh + + + align:start position:0% +basically out of all the expression uh +data that they have they just come up + + align:start position:0% +data that they have they just come up + + + align:start position:0% +data that they have they just come up +with one signature right so yes you know + + align:start position:0% +with one signature right so yes you know + + + align:start position:0% +with one signature right so yes you know +yes + + align:start position:0% +yes + + + align:start position:0% +yes +it looks good versus no it doesn't + + align:start position:0% +it looks good versus no it doesn't + + + align:start position:0% +it looks good versus no it doesn't +and so that becomes just a one + + align:start position:0% +and so that becomes just a one + + + align:start position:0% +and so that becomes just a one +variable in your class in your + + align:start position:0% +variable in your class in your + + + align:start position:0% +variable in your class in your +multivariate model that you have so + + align:start position:0% +multivariate model that you have so + + + align:start position:0% +multivariate model that you have so +typically you just + + align:start position:0% +typically you just + + + align:start position:0% +typically you just +most studies + + align:start position:0% +most studies + + + align:start position:0% +most studies +without expression data will just have a + + align:start position:0% +without expression data will just have a + + + align:start position:0% +without expression data will just have a +multi + + align:start position:0% +multi + + + align:start position:0% +multi +multivariate + + align:start position:0% +multivariate + + + align:start position:0% +multivariate +model cox model sometimes + + align:start position:0% +model cox model sometimes + + + align:start position:0% +model cox model sometimes +so cox model is just a + + align:start position:0% +so cox model is just a + + + align:start position:0% +so cox model is just a +multiple linear regression + + align:start position:0% +multiple linear regression + + + align:start position:0% +multiple linear regression +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +done differently for sensor data + + align:start position:0% +done differently for sensor data + + + align:start position:0% +done differently for sensor data +so for for cost model you fit everything + + align:start position:0% +so for for cost model you fit everything + + + align:start position:0% +so for for cost model you fit everything +and then if you say + + align:start position:0% +and then if you say + + + align:start position:0% +and then if you say +if you see that the p value is small for + + align:start position:0% +if you see that the p value is small for + + + align:start position:0% +if you see that the p value is small for +that + + align:start position:0% +that + + + align:start position:0% +that +um then you say well you know it's a + + align:start position:0% +um then you say well you know it's a + + + align:start position:0% +um then you say well you know it's a +it's a new parameter or new variable + + align:start position:0% +it's a new parameter or new variable + + + align:start position:0% +it's a new parameter or new variable +that you should take into account in + + align:start position:0% +that you should take into account in + + + align:start position:0% +that you should take into account in +your in your study so i think this is a + + align:start position:0% +your in your study so i think this is a + + + align:start position:0% +your in your study so i think this is a +fairly reasonable approach + + align:start position:0% +fairly reasonable approach + + + align:start position:0% +fairly reasonable approach +um + + align:start position:0% +um + + + align:start position:0% +um +there is another study you may have seen + + align:start position:0% +there is another study you may have seen + + + align:start position:0% +there is another study you may have seen +this as well + + align:start position:0% +this as well + + + align:start position:0% +this as well +where they do something they do + + align:start position:0% +where they do something they do + + + align:start position:0% +where they do something they do +something + + align:start position:0% +something + + + align:start position:0% +something +better i think + + align:start position:0% +better i think + + + align:start position:0% +better i think +which is + + align:start position:0% +which is + + + align:start position:0% +which is +um + + align:start position:0% +um + + + align:start position:0% +um +after you get + + align:start position:0% +after you get + + + align:start position:0% +after you get +all your + + align:start position:0% + + + + align:start position:0% + +expression data + + align:start position:0% +expression data + + + align:start position:0% +expression data +they actually + + align:start position:0% +they actually + + + align:start position:0% +they actually +manually go through the top genes + + align:start position:0% +manually go through the top genes + + + align:start position:0% +manually go through the top genes +and then try to come up with new + + align:start position:0% +and then try to come up with new + + + align:start position:0% +and then try to come up with new +variables so i think this + + align:start position:0% +variables so i think this + + + align:start position:0% +variables so i think this +good signature versus bad signature is + + align:start position:0% +good signature versus bad signature is + + + align:start position:0% +good signature versus bad signature is +too crude right it doesn't really give + + align:start position:0% +too crude right it doesn't really give + + + align:start position:0% +too crude right it doesn't really give +you + + align:start position:0% +you + + + align:start position:0% +you +as much information + + align:start position:0% +as much information + + + align:start position:0% +as much information +from the data i think you know you could + + align:start position:0% +from the data i think you know you could + + + align:start position:0% +from the data i think you know you could +get i think a lot of you know more + + align:start position:0% +get i think a lot of you know more + + + align:start position:0% +get i think a lot of you know more +information from your expression data so + + align:start position:0% +information from your expression data so + + + align:start position:0% +information from your expression data so +in this example + + align:start position:0% +in this example + + + align:start position:0% +in this example +they actually have + + align:start position:0% +they actually have + + + align:start position:0% +they actually have +not yes or no score but they actually + + align:start position:0% +not yes or no score but they actually + + + align:start position:0% +not yes or no score but they actually +have a prediction score okay so that's + + align:start position:0% +have a prediction score okay so that's + + + align:start position:0% +have a prediction score okay so that's +you know a continuous variable + + align:start position:0% +you know a continuous variable + + + align:start position:0% +you know a continuous variable +and then they actually classify their + + align:start position:0% +and then they actually classify their + + + align:start position:0% +and then they actually classify their +genes you know depending on their + + align:start position:0% +genes you know depending on their + + + align:start position:0% +genes you know depending on their +expression profiles and their sort of + + align:start position:0% +expression profiles and their sort of + + + align:start position:0% +expression profiles and their sort of +um + + align:start position:0% +um + + + align:start position:0% +um +known annotations into these groups so + + align:start position:0% +known annotations into these groups so + + + align:start position:0% +known annotations into these groups so +in this case they have + + align:start position:0% +in this case they have + + + align:start position:0% +in this case they have +five groups so proliferation signature + + align:start position:0% +five groups so proliferation signature + + + align:start position:0% +five groups so proliferation signature +value this is a you know set of + + align:start position:0% +value this is a you know set of + + + align:start position:0% +value this is a you know set of +genes + + align:start position:0% +genes + + + align:start position:0% +genes +uh bmp + + align:start position:0% +uh bmp + + + align:start position:0% +uh bmp +six that's just one gene that just + + align:start position:0% +six that's just one gene that just + + + align:start position:0% +six that's just one gene that just +happened to be different from all the + + align:start position:0% +happened to be different from all the + + + align:start position:0% +happened to be different from all the +other uh profiles + + align:start position:0% +other uh profiles + + + align:start position:0% +other uh profiles +then they have these signature values so + + align:start position:0% +then they have these signature values so + + + align:start position:0% +then they have these signature values so +i think there's a this is a fairly + + align:start position:0% +i think there's a this is a fairly + + + align:start position:0% +i think there's a this is a fairly +reasonable approach and i think it gives + + align:start position:0% +reasonable approach and i think it gives + + + align:start position:0% +reasonable approach and i think it gives +you a lot more information plus these + + align:start position:0% +you a lot more information plus these + + + align:start position:0% +you a lot more information plus these +coefficients right i think give you + + align:start position:0% +coefficients right i think give you + + + align:start position:0% +coefficients right i think give you +sort of a more robust view of + + align:start position:0% +sort of a more robust view of + + + align:start position:0% +sort of a more robust view of +you know how that expression + + align:start position:0% +you know how that expression + + + align:start position:0% +you know how that expression +that group of genes is + + align:start position:0% +that group of genes is + + + align:start position:0% +that group of genes is +impacting your + + align:start position:0% +impacting your + + + align:start position:0% +impacting your +survival in this case + + align:start position:0% +survival in this case + + + align:start position:0% +survival in this case +okay so you get a prediction score and + + align:start position:0% +okay so you get a prediction score and + + + align:start position:0% +okay so you get a prediction score and +then i guess from here you could do you + + align:start position:0% +then i guess from here you could do you + + + align:start position:0% +then i guess from here you could do you +know + + align:start position:0% +know + + + align:start position:0% +know +you can make + + align:start position:0% +you can make + + + align:start position:0% +you can make +you could put other things other + + align:start position:0% +you could put other things other + + + align:start position:0% +you could put other things other +variables in this setting in the + + align:start position:0% +variables in this setting in the + + + align:start position:0% +variables in this setting in the +regression setting + + align:start position:0% +regression setting + + + align:start position:0% +regression setting +okay actually there's a paper + + align:start position:0% +okay actually there's a paper + + + align:start position:0% +okay actually there's a paper +they came out + + align:start position:0% +they came out + + + align:start position:0% +they came out +this past week right this week so + + align:start position:0% +this past week right this week so + + + align:start position:0% +this past week right this week so +um + + align:start position:0% +um + + + align:start position:0% +um +and + + align:start position:0% +and + + + align:start position:0% +and +you're smiling + + align:start position:0% + + + + align:start position:0% + +oh you know this one okay + + align:start position:0% +oh you know this one okay + + + align:start position:0% +oh you know this one okay +so + + align:start position:0% +so + + + align:start position:0% +so +i i mean i feel like at some point you + + align:start position:0% +i i mean i feel like at some point you + + + align:start position:0% +i i mean i feel like at some point you +know + + align:start position:0% +know + + + align:start position:0% +know +someone can write a software right where + + align:start position:0% +someone can write a software right where + + + align:start position:0% +someone can write a software right where +you enter the data center will just do + + align:start position:0% +you enter the data center will just do + + + align:start position:0% +you enter the data center will just do +all the + + align:start position:0% +all the + + + align:start position:0% +all the +things that that are done because it's + + align:start position:0% +things that that are done because it's + + + align:start position:0% +things that that are done because it's +i think fairly + + align:start position:0% + + + + align:start position:0% + +similar in all the papers um except the + + align:start position:0% +similar in all the papers um except the + + + align:start position:0% +similar in all the papers um except the +algorithms um + + align:start position:0% +algorithms um + + + align:start position:0% +algorithms um +and you know + + align:start position:0% +and you know + + + align:start position:0% +and you know +basically the algorithm the choice of + + align:start position:0% +basically the algorithm the choice of + + + align:start position:0% +basically the algorithm the choice of +algorithms used is like you know who the + + align:start position:0% +algorithms used is like you know who the + + + align:start position:0% +algorithms used is like you know who the +investigator knows right who knows how + + align:start position:0% +investigator knows right who knows how + + + align:start position:0% +investigator knows right who knows how +to do these things right so in this case + + align:start position:0% +to do these things right so in this case + + + align:start position:0% +to do these things right so in this case +there's a + + align:start position:0% +there's a + + + align:start position:0% +there's a +um + + align:start position:0% +um + + + align:start position:0% +um +tip sherani is a statistician at + + align:start position:0% +tip sherani is a statistician at + + + align:start position:0% +tip sherani is a statistician at +stanford and so he he this paper uses + + align:start position:0% +stanford and so he he this paper uses + + + align:start position:0% +stanford and so he he this paper uses +methods that he developed + + align:start position:0% +methods that he developed + + + align:start position:0% +methods that he developed +which i think is a fairly good method + + align:start position:0% +which i think is a fairly good method + + + align:start position:0% +which i think is a fairly good method +so + + align:start position:0% + + + + align:start position:0% + +just to give you a rough idea what what + + align:start position:0% +just to give you a rough idea what what + + + align:start position:0% +just to give you a rough idea what what +they do here is + + align:start position:0% +they do here is + + + align:start position:0% +they do here is +um so + + align:start position:0% +um so + + + align:start position:0% +um so +they make predictions in the end so they + + align:start position:0% +they make predictions in the end so they + + + align:start position:0% +they make predictions in the end so they +select genes by + + align:start position:0% +select genes by + + + align:start position:0% +select genes by +the method that tips ronnie developed + + align:start position:0% +the method that tips ronnie developed + + + align:start position:0% +the method that tips ronnie developed +which is + + align:start position:0% +which is + + + align:start position:0% +which is +actually it's a little complicated to + + align:start position:0% +actually it's a little complicated to + + + align:start position:0% +actually it's a little complicated to +explain but + + align:start position:0% +explain but + + + align:start position:0% +explain but +it basically does + + align:start position:0% +it basically does + + + align:start position:0% +it basically does +a + + align:start position:0% +a + + + align:start position:0% +a +search through all your space of genes + + align:start position:0% + + + + align:start position:0% + +but you can also actually look for + + align:start position:0% +but you can also actually look for + + + align:start position:0% +but you can also actually look for +combinations of genes so + + align:start position:0% +combinations of genes so + + + align:start position:0% +combinations of genes so +remember you know most + + align:start position:0% +remember you know most + + + align:start position:0% +remember you know most +basically all the typical + + align:start position:0% +basically all the typical + + + align:start position:0% +basically all the typical +methods + + align:start position:0% +methods + + + align:start position:0% +methods +we'll look for in a gene that's related + + align:start position:0% +we'll look for in a gene that's related + + + align:start position:0% +we'll look for in a gene that's related +to the phenotype so + + align:start position:0% +to the phenotype so + + + align:start position:0% +to the phenotype so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +if there's any interaction between genes + + align:start position:0% +if there's any interaction between genes + + + align:start position:0% +if there's any interaction between genes +you you basically lose them all okay + + align:start position:0% +you you basically lose them all okay + + + align:start position:0% +you you basically lose them all okay +um + + align:start position:0% +um + + + align:start position:0% +um +so there is some fancy method that he + + align:start position:0% +so there is some fancy method that he + + + align:start position:0% +so there is some fancy method that he +developed where you basically search + + align:start position:0% +developed where you basically search + + + align:start position:0% +developed where you basically search +through all your genes you know it's + + align:start position:0% +through all your genes you know it's + + + align:start position:0% +through all your genes you know it's +like + + align:start position:0% +like + + + align:start position:0% +like +regression + + align:start position:0% +regression + + + align:start position:0% +regression +uh sort of stepwise regression type + + align:start position:0% +uh sort of stepwise regression type + + + align:start position:0% +uh sort of stepwise regression type +where you basically search through your + + align:start position:0% +where you basically search through your + + + align:start position:0% +where you basically search through your +genes you keep the one that gives you + + align:start position:0% +genes you keep the one that gives you + + + align:start position:0% +genes you keep the one that gives you +the best information and then you try + + align:start position:0% +the best information and then you try + + + align:start position:0% +the best information and then you try +next set and then you try combinations + + align:start position:0% +next set and then you try combinations + + + align:start position:0% +next set and then you try combinations +and that kind of thing so they identify + + align:start position:0% +and that kind of thing so they identify + + + align:start position:0% +and that kind of thing so they identify +a bunch of genes + + align:start position:0% +a bunch of genes + + + align:start position:0% +a bunch of genes +then they do a prediction um + + align:start position:0% +then they do a prediction um + + + align:start position:0% +then they do a prediction um +so they had 116 adults + + align:start position:0% +so they had 116 adults + + + align:start position:0% +so they had 116 adults +you have one group a training set with + + align:start position:0% +you have one group a training set with + + + align:start position:0% +you have one group a training set with +59 you do a prediction on 57. the way + + align:start position:0% +59 you do a prediction on 57. the way + + + align:start position:0% +59 you do a prediction on 57. the way +they do the prediction is an algorithm + + align:start position:0% +they do the prediction is an algorithm + + + align:start position:0% +they do the prediction is an algorithm +that was published in pnas a year or two + + align:start position:0% +that was published in pnas a year or two + + + align:start position:0% +that was published in pnas a year or two +ago + + align:start position:0% +ago + + + align:start position:0% +ago +basically you + + align:start position:0% +basically you + + + align:start position:0% +basically you +look at + + align:start position:0% + + + + align:start position:0% + +you take a new sample and then see which + + align:start position:0% +you take a new sample and then see which + + + align:start position:0% +you take a new sample and then see which +of the clusters + + align:start position:0% +of the clusters + + + align:start position:0% +of the clusters +the profile is closest to but they do + + align:start position:0% +the profile is closest to but they do + + + align:start position:0% +the profile is closest to but they do +this in a slightly sort of clever way so + + align:start position:0% +this in a slightly sort of clever way so + + + align:start position:0% +this in a slightly sort of clever way so +you know + + align:start position:0% +you know + + + align:start position:0% +you know +so instead of just looking at + + align:start position:0% +so instead of just looking at + + + align:start position:0% +so instead of just looking at +correlations they you know do something + + align:start position:0% +correlations they you know do something + + + align:start position:0% +correlations they you know do something +a little bit fancier + + align:start position:0% +a little bit fancier + + + align:start position:0% +a little bit fancier +but i i mean the underlying + + align:start position:0% +but i i mean the underlying + + + align:start position:0% +but i i mean the underlying +idea is the same + + align:start position:0% +idea is the same + + + align:start position:0% +idea is the same +and then they do the in the end they do + + align:start position:0% +and then they do the in the end they do + + + align:start position:0% +and then they do the in the end they do +the multivariate analysis + + align:start position:0% +the multivariate analysis + + + align:start position:0% +the multivariate analysis +gene expression predictor was strongly + + align:start position:0% +gene expression predictor was strongly + + + align:start position:0% +gene expression predictor was strongly +an independent prognostic factor + + align:start position:0% +an independent prognostic factor + + + align:start position:0% +an independent prognostic factor +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +uh this is a figure in the paper + + align:start position:0% +uh this is a figure in the paper + + + align:start position:0% +uh this is a figure in the paper +i i guess at this point + + align:start position:0% + + + + align:start position:0% + +we'll skip this um + + align:start position:0% +we'll skip this um + + + align:start position:0% +we'll skip this um +so for the next actually about five ten + + align:start position:0% +so for the next actually about five ten + + + align:start position:0% +so for the next actually about five ten +minutes let me talk about something that + + align:start position:0% +minutes let me talk about something that + + + align:start position:0% +minutes let me talk about something that +i did um + + align:start position:0% +i did um + + + align:start position:0% +i did um +so + + align:start position:0% + + + + align:start position:0% + +most studies uh + + align:start position:0% +most studies uh + + + align:start position:0% +most studies uh +so far used survival curves as a way of + + align:start position:0% +so far used survival curves as a way of + + + align:start position:0% +so far used survival curves as a way of +verifying the result so you you know + + align:start position:0% +verifying the result so you you know + + + align:start position:0% +verifying the result so you you know +basically + + align:start position:0% +basically + + + align:start position:0% +basically +do the uh clustering on supervised + + align:start position:0% +do the uh clustering on supervised + + + align:start position:0% +do the uh clustering on supervised +clustering and then you define groups + + align:start position:0% +clustering and then you define groups + + + align:start position:0% +clustering and then you define groups +and say are they really different + + align:start position:0% +and say are they really different + + + align:start position:0% +and say are they really different +okay so if they're really different + + align:start position:0% +okay so if they're really different + + + align:start position:0% +okay so if they're really different +as + + align:start position:0% +as + + + align:start position:0% +as +verified by + + align:start position:0% +verified by + + + align:start position:0% +verified by +these curves then you say oh that's + + align:start position:0% +these curves then you say oh that's + + + align:start position:0% +these curves then you say oh that's +great okay + + align:start position:0% +great okay + + + align:start position:0% +great okay +but + + align:start position:0% +but + + + align:start position:0% +but +in some sense this is + + align:start position:0% +in some sense this is + + + align:start position:0% +in some sense this is +sort of an indirect way of doing things + + align:start position:0% +sort of an indirect way of doing things + + + align:start position:0% +sort of an indirect way of doing things +right i mean if maybe there is a + + align:start position:0% +right i mean if maybe there is a + + + align:start position:0% +right i mean if maybe there is a +different way of clustering that gives + + align:start position:0% +different way of clustering that gives + + + align:start position:0% +different way of clustering that gives +you a better result who knows right i + + align:start position:0% +you a better result who knows right i + + + align:start position:0% +you a better result who knows right i +mean this is just kind of checking to + + align:start position:0% +mean this is just kind of checking to + + + align:start position:0% +mean this is just kind of checking to +see if your clustering was done + + align:start position:0% +see if your clustering was done + + + align:start position:0% +see if your clustering was done +correctly + + align:start position:0% +correctly + + + align:start position:0% +correctly +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +and another way + + align:start position:0% +and another way + + + align:start position:0% +and another way +another problem with this is that + + align:start position:0% + + + + align:start position:0% + +yeah well i mean so + + align:start position:0% +yeah well i mean so + + + align:start position:0% +yeah well i mean so +so that's i think one way of doing + + align:start position:0% +so that's i think one way of doing + + + align:start position:0% +so that's i think one way of doing +things another way actually to do the + + align:start position:0% +things another way actually to do the + + + align:start position:0% +things another way actually to do the +censoring is as was done in a lot of the + + align:start position:0% +censoring is as was done in a lot of the + + + align:start position:0% +censoring is as was done in a lot of the +other papers + + align:start position:0% +other papers + + + align:start position:0% +other papers +is to turn survival times into binary + + align:start position:0% +is to turn survival times into binary + + + align:start position:0% +is to turn survival times into binary +indicator as i mentioned + + align:start position:0% +indicator as i mentioned + + + align:start position:0% +indicator as i mentioned +um so something that we were interested + + align:start position:0% +um so something that we were interested + + + align:start position:0% +um so something that we were interested +in was whether there is some combination + + align:start position:0% +in was whether there is some combination + + + align:start position:0% +in was whether there is some combination +right so maybe + + align:start position:0% +right so maybe + + + align:start position:0% +right so maybe +maybe it's not really gene a that's + + align:start position:0% +maybe it's not really gene a that's + + + align:start position:0% +maybe it's not really gene a that's +predictive but it's gene a + + align:start position:0% +predictive but it's gene a + + + align:start position:0% +predictive but it's gene a +plus half of gene b plus two times gene + + align:start position:0% +plus half of gene b plus two times gene + + + align:start position:0% +plus half of gene b plus two times gene +c maybe that's you know maybe that's not + + align:start position:0% +c maybe that's you know maybe that's not + + + align:start position:0% +c maybe that's you know maybe that's not +really the most predictive of + + align:start position:0% +really the most predictive of + + + align:start position:0% +really the most predictive of +survival time right so there's no + + align:start position:0% +survival time right so there's no + + + align:start position:0% +survival time right so there's no +otherwise you're just + + align:start position:0% +otherwise you're just + + + align:start position:0% +otherwise you're just +you don't know exactly how to combine + + align:start position:0% +you don't know exactly how to combine + + + align:start position:0% +you don't know exactly how to combine +your genes right + + align:start position:0% +your genes right + + + align:start position:0% +your genes right +if you do some sort of voting method for + + align:start position:0% +if you do some sort of voting method for + + + align:start position:0% +if you do some sort of voting method for +example it's not + + align:start position:0% +example it's not + + + align:start position:0% +example it's not +you could sort of that + + align:start position:0% +you could sort of that + + + align:start position:0% +you could sort of that +you are combining information from all + + align:start position:0% +you are combining information from all + + + align:start position:0% +you are combining information from all +your genes but you're not doing an + + align:start position:0% +your genes but you're not doing an + + + align:start position:0% +your genes but you're not doing an +optimal way so we actually + + align:start position:0% +optimal way so we actually + + + align:start position:0% +optimal way so we actually +thought about this problem and then came + + align:start position:0% +thought about this problem and then came + + + align:start position:0% +thought about this problem and then came +up with what i think is a good solution + + align:start position:0% +up with what i think is a good solution + + + align:start position:0% +up with what i think is a good solution +um of course the the difficulty is that + + align:start position:0% +um of course the the difficulty is that + + + align:start position:0% +um of course the the difficulty is that +um + + align:start position:0% +um + + + align:start position:0% +um +it's too complicated and so + + align:start position:0% +it's too complicated and so + + + align:start position:0% +it's too complicated and so +it's hard to write a software that + + align:start position:0% +it's hard to write a software that + + + align:start position:0% +it's hard to write a software that +someone can use you know to just press a + + align:start position:0% +someone can use you know to just press a + + + align:start position:0% +someone can use you know to just press a +button and + + align:start position:0% +button and + + + align:start position:0% +button and +get a good result so + + align:start position:0% +get a good result so + + + align:start position:0% +get a good result so +and i can't just you know you can't just + + align:start position:0% +and i can't just you know you can't just + + + align:start position:0% +and i can't just you know you can't just +do analysis for other people so + + align:start position:0% +do analysis for other people so + + + align:start position:0% +do analysis for other people so +as in many uh bioinformatics algorithms + + align:start position:0% +as in many uh bioinformatics algorithms + + + align:start position:0% +as in many uh bioinformatics algorithms +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it's uh + + align:start position:0% +it's uh + + + align:start position:0% +it's uh +it's kind of there but + + align:start position:0% +it's kind of there but + + + align:start position:0% +it's kind of there but +we haven't really done as much as we + + align:start position:0% +we haven't really done as much as we + + + align:start position:0% +we haven't really done as much as we +could have done with it + + align:start position:0% +could have done with it + + + align:start position:0% +could have done with it +so just to give you a brief + + align:start position:0% +so just to give you a brief + + + align:start position:0% +so just to give you a brief +overview of this + + align:start position:0% +overview of this + + + align:start position:0% +overview of this +so the the basic problem is that you + + align:start position:0% +so the the basic problem is that you + + + align:start position:0% +so the the basic problem is that you +have too many variables right so + + align:start position:0% +have too many variables right so + + + align:start position:0% +have too many variables right so +we use some method uh it's called + + align:start position:0% +we use some method uh it's called + + + align:start position:0% +we use some method uh it's called +partial least squares it's actually + + align:start position:0% +partial least squares it's actually + + + align:start position:0% +partial least squares it's actually +becoming very popular now + + align:start position:0% +becoming very popular now + + + align:start position:0% +becoming very popular now +and it turns out that it's a compromise + + align:start position:0% +and it turns out that it's a compromise + + + align:start position:0% +and it turns out that it's a compromise +between + + align:start position:0% +between + + + align:start position:0% +between +just doing lead squares like your + + align:start position:0% +just doing lead squares like your + + + align:start position:0% +just doing lead squares like your +regression versus pca so + + align:start position:0% +regression versus pca so + + + align:start position:0% +regression versus pca so +principal component analysis + + align:start position:0% +principal component analysis + + + align:start position:0% +principal component analysis +is good in that you try to maximize + + align:start position:0% +is good in that you try to maximize + + + align:start position:0% +is good in that you try to maximize +information contained in your few + + align:start position:0% +information contained in your few + + + align:start position:0% +information contained in your few +components + + align:start position:0% +components + + + align:start position:0% +components +but it doesn't really have anything to + + align:start position:0% +but it doesn't really have anything to + + + align:start position:0% +but it doesn't really have anything to +do with the phenotype right + + align:start position:0% +do with the phenotype right + + + align:start position:0% +do with the phenotype right +so if you pick variables based on pca + + align:start position:0% +so if you pick variables based on pca + + + align:start position:0% +so if you pick variables based on pca +you do a dimension reduction in some + + align:start position:0% +you do a dimension reduction in some + + + align:start position:0% +you do a dimension reduction in some +optimal way but it may not be related to + + align:start position:0% +optimal way but it may not be related to + + + align:start position:0% +optimal way but it may not be related to +your phenotype + + align:start position:0% +your phenotype + + + align:start position:0% +your phenotype +if you do regression + + align:start position:0% +if you do regression + + + align:start position:0% +if you do regression +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you are picking something that's really + + align:start position:0% +you are picking something that's really + + + align:start position:0% +you are picking something that's really +tightly correlated with your phenotype + + align:start position:0% +tightly correlated with your phenotype + + + align:start position:0% +tightly correlated with your phenotype +but you're not really doing any + + align:start position:0% +but you're not really doing any + + + align:start position:0% +but you're not really doing any +dimension reduction + + align:start position:0% +dimension reduction + + + align:start position:0% +dimension reduction +or you can't do it in an optimal way so + + align:start position:0% +or you can't do it in an optimal way so + + + align:start position:0% +or you can't do it in an optimal way so +there's something called partially + + align:start position:0% +there's something called partially + + + align:start position:0% +there's something called partially +squares that's sort of a compromise + + align:start position:0% +squares that's sort of a compromise + + + align:start position:0% +squares that's sort of a compromise +between the two and it appears to work + + align:start position:0% +between the two and it appears to work + + + align:start position:0% +between the two and it appears to work +really well in + + align:start position:0% +really well in + + + align:start position:0% +really well in +most cases + + align:start position:0% + + + + align:start position:0% + +and it turns out that someone had worked + + align:start position:0% +and it turns out that someone had worked + + + align:start position:0% +and it turns out that someone had worked +this out so they figured out how to do + + align:start position:0% +this out so they figured out how to do + + + align:start position:0% +this out so they figured out how to do +partial least squares for + + align:start position:0% +partial least squares for + + + align:start position:0% +partial least squares for +you know different types of phenotypes + + align:start position:0% +you know different types of phenotypes + + + align:start position:0% +you know different types of phenotypes +continuous and + + align:start position:0% +continuous and + + + align:start position:0% +continuous and +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +binary phenotype + + align:start position:0% +binary phenotype + + + align:start position:0% +binary phenotype +so it gets a little complicated + + align:start position:0% +so it gets a little complicated + + + align:start position:0% +so it gets a little complicated +you know as soon as you + + align:start position:0% +you know as soon as you + + + align:start position:0% +you know as soon as you +have a phenotype that's not binary but + + align:start position:0% +have a phenotype that's not binary but + + + align:start position:0% +have a phenotype that's not binary but +or as soon as it's not continuous but it + + align:start position:0% +or as soon as it's not continuous but it + + + align:start position:0% +or as soon as it's not continuous but it +has been worked out but when you have + + align:start position:0% +has been worked out but when you have + + + align:start position:0% +has been worked out but when you have +censoring um + + align:start position:0% +censoring um + + + align:start position:0% +censoring um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +well again you know if you have a small + + align:start position:0% +well again you know if you have a small + + + align:start position:0% +well again you know if you have a small +number of genes you could use something + + align:start position:0% +number of genes you could use something + + + align:start position:0% +number of genes you could use something +like cox model to correlate + + align:start position:0% +like cox model to correlate + + + align:start position:0% +like cox model to correlate +gene expression to censoring + + align:start position:0% +gene expression to censoring + + + align:start position:0% +gene expression to censoring +but when you have too many genes you + + align:start position:0% +but when you have too many genes you + + + align:start position:0% +but when you have too many genes you +can't do that your standard method trail + + align:start position:0% +can't do that your standard method trail + + + align:start position:0% +can't do that your standard method trail +so the question was can we do this right + + align:start position:0% +so the question was can we do this right + + + align:start position:0% +so the question was can we do this right +can we apply a method that's + + align:start position:0% +can we apply a method that's + + + align:start position:0% +can we apply a method that's +well known to work for regular just + + align:start position:0% +well known to work for regular just + + + align:start position:0% +well known to work for regular just +other simpler phenotype but can we work + + align:start position:0% +other simpler phenotype but can we work + + + align:start position:0% +other simpler phenotype but can we work +can we get this to work for sensor data + + align:start position:0% +can we get this to work for sensor data + + + align:start position:0% +can we get this to work for sensor data +so it turns out that we + + align:start position:0% +so it turns out that we + + + align:start position:0% +so it turns out that we +came up with + + align:start position:0% +came up with + + + align:start position:0% +came up with +it turned a fairly good solution it + + align:start position:0% +it turned a fairly good solution it + + + align:start position:0% +it turned a fairly good solution it +turns out that this was worked out you + + align:start position:0% +turns out that this was worked out you + + + align:start position:0% +turns out that this was worked out you +know many years ago + + align:start position:0% +know many years ago + + + align:start position:0% +know many years ago +we discovered but there was no need they + + align:start position:0% +we discovered but there was no need they + + + align:start position:0% +we discovered but there was no need they +didn't have high throughput data so + + align:start position:0% +didn't have high throughput data so + + + align:start position:0% +didn't have high throughput data so +there was no need to use this it's + + align:start position:0% +there was no need to use this it's + + + align:start position:0% +there was no need to use this it's +actually it was done by a statistician + + align:start position:0% +actually it was done by a statistician + + + align:start position:0% +actually it was done by a statistician +and it's very hard to understand i mean + + align:start position:0% +and it's very hard to understand i mean + + + align:start position:0% +and it's very hard to understand i mean +i can barely understand it myself + + align:start position:0% +i can barely understand it myself + + + align:start position:0% +i can barely understand it myself +so you know it's like just in some + + align:start position:0% +so you know it's like just in some + + + align:start position:0% +so you know it's like just in some +extent it was reinventing the wheel but + + align:start position:0% +extent it was reinventing the wheel but + + + align:start position:0% +extent it was reinventing the wheel but +we do it a little differently and then + + align:start position:0% +we do it a little differently and then + + + align:start position:0% +we do it a little differently and then +we were able to apply this + + align:start position:0% +we were able to apply this + + + align:start position:0% +we were able to apply this +so it turns out that we were actually + + align:start position:0% +so it turns out that we were actually + + + align:start position:0% +so it turns out that we were actually +able to + + align:start position:0% +able to + + + align:start position:0% +able to +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +get some really good results for example + + align:start position:0% +get some really good results for example + + + align:start position:0% +get some really good results for example +if if i use the results of that + + align:start position:0% +if if i use the results of that + + + align:start position:0% +if if i use the results of that +algorithm to divide the patient to + + align:start position:0% +algorithm to divide the patient to + + + align:start position:0% +algorithm to divide the patient to +different groups then it's more + + align:start position:0% +different groups then it's more + + + align:start position:0% +different groups then it's more +significant than using some other method + + align:start position:0% +significant than using some other method + + + align:start position:0% +significant than using some other method +of doing things + + align:start position:0% +of doing things + + + align:start position:0% +of doing things +so there are methods like this + + align:start position:0% +so there are methods like this + + + align:start position:0% +so there are methods like this +um + + align:start position:0% +um + + + align:start position:0% +um +that could be i think that will be + + align:start position:0% +that could be i think that will be + + + align:start position:0% +that could be i think that will be +available and + + align:start position:0% +available and + + + align:start position:0% +available and +and unfortunately it does require some + + align:start position:0% +and unfortunately it does require some + + + align:start position:0% +and unfortunately it does require some +sort of mathematical training but + + align:start position:0% +sort of mathematical training but + + + align:start position:0% +sort of mathematical training but +you know for people here that are + + align:start position:0% +you know for people here that are + + + align:start position:0% +you know for people here that are +interested in this and can invest the + + align:start position:0% +interested in this and can invest the + + + align:start position:0% +interested in this and can invest the +time and energy i mean i think knowing + + align:start position:0% +time and energy i mean i think knowing + + + align:start position:0% +time and energy i mean i think knowing +the you know the better algorithms will + + align:start position:0% +the you know the better algorithms will + + + align:start position:0% +the you know the better algorithms will +give you um + + align:start position:0% +give you um + + + align:start position:0% +give you um +a lot of um + + align:start position:0% +a lot of um + + + align:start position:0% +a lot of um +insights into + + align:start position:0% +insights into + + + align:start position:0% +insights into +into what's going on underneath your + + align:start position:0% +into what's going on underneath your + + + align:start position:0% +into what's going on underneath your +data + + align:start position:0% + + + + align:start position:0% + +random expression + + align:start position:0% + + + + align:start position:0% + +well that's the problem right + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +but not as well right right + + align:start position:0% +but not as well right right + + + align:start position:0% +but not as well right right +yeah but it's actually not that likely + + align:start position:0% +yeah but it's actually not that likely + + + align:start position:0% +yeah but it's actually not that likely +if you actually do the calculation yeah + + align:start position:0% +if you actually do the calculation yeah + + + align:start position:0% +if you actually do the calculation yeah +but um + + align:start position:0% +but um + + + align:start position:0% +but um +yeah yeah you could find some + + align:start position:0% +yeah yeah you could find some + + + align:start position:0% +yeah yeah you could find some +right you could find some combinations + + align:start position:0% +right you could find some combinations + + + align:start position:0% +right you could find some combinations +that will it's it's true for anything + + align:start position:0% +that will it's it's true for anything + + + align:start position:0% +that will it's it's true for anything +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% +um + + + align:start position:0% +um +but even for the binary case right you + + align:start position:0% +but even for the binary case right you + + + align:start position:0% +but even for the binary case right you +know if you have 10 in each group what's + + align:start position:0% +know if you have 10 in each group what's + + + align:start position:0% +know if you have 10 in each group what's +the probability you're gonna find a + + align:start position:0% +the probability you're gonna find a + + + align:start position:0% +the probability you're gonna find a +random predictor + + align:start position:0% +random predictor + + + align:start position:0% +random predictor +that will be lined if it's continuous + + align:start position:0% +that will be lined if it's continuous + + + align:start position:0% +that will be lined if it's continuous +data right they will be lined up exactly + + align:start position:0% +data right they will be lined up exactly + + + align:start position:0% +data right they will be lined up exactly +as in the order of the patients it's not + + align:start position:0% +as in the order of the patients it's not + + + align:start position:0% +as in the order of the patients it's not +that likely yeah so if it's not binary + + align:start position:0% +that likely yeah so if it's not binary + + + align:start position:0% +that likely yeah so if it's not binary +right + + align:start position:0% +right + + + align:start position:0% +right +it's it's much less likely + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah exactly yeah + + align:start position:0% +yeah yeah yeah exactly yeah + + + align:start position:0% +yeah yeah yeah exactly yeah +so + + align:start position:0% +so + + + align:start position:0% +so +that's the problem like even for + + align:start position:0% +that's the problem like even for + + + align:start position:0% +that's the problem like even for +even for these um capital markers that + + align:start position:0% +even for these um capital markers that + + + align:start position:0% +even for these um capital markers that +people show i'm some they need to just + + align:start position:0% +people show i'm some they need to just + + + align:start position:0% +people show i'm some they need to just +for multiple testing in some way + + align:start position:0% +for multiple testing in some way + + + align:start position:0% +for multiple testing in some way +right + + align:start position:0% +right + + + align:start position:0% +right +right so you you you can certainly find + + align:start position:0% +right so you you you can certainly find + + + align:start position:0% +right so you you you can certainly find +genes that will give you a p-value + + align:start position:0% +genes that will give you a p-value + + + align:start position:0% +genes that will give you a p-value +significant p-value even though the data + + align:start position:0% +significant p-value even though the data + + + align:start position:0% +significant p-value even though the data +are random + + align:start position:0% +are random + + + align:start position:0% +are random +um so + + align:start position:0% +um so + + + align:start position:0% +um so +some people do permutation tests to + + align:start position:0% +some people do permutation tests to + + + align:start position:0% +some people do permutation tests to +adjust for the p-value + + align:start position:0% +adjust for the p-value + + + align:start position:0% +adjust for the p-value +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% + + + + align:start position:0% + +conclusions um + + align:start position:0% +conclusions um + + + align:start position:0% +conclusions um +i don't need to go over that here + + align:start position:0% +i don't need to go over that here + + + align:start position:0% +i don't need to go over that here +so + + align:start position:0% +so + + + align:start position:0% +so +um let's see so + + align:start position:0% +um let's see so + + + align:start position:0% +um let's see so +just + + align:start position:0% +just + + + align:start position:0% +just +uh as a final comment um + + align:start position:0% +uh as a final comment um + + + align:start position:0% +uh as a final comment um +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +well to summarize briefly i i would say + + align:start position:0% +well to summarize briefly i i would say + + + align:start position:0% +well to summarize briefly i i would say +that + + align:start position:0% +that + + + align:start position:0% +that +some of the recent papers have have done + + align:start position:0% +some of the recent papers have have done + + + align:start position:0% +some of the recent papers have have done +it pretty well i think analysis i think + + align:start position:0% +it pretty well i think analysis i think + + + align:start position:0% +it pretty well i think analysis i think +that involves not just doing + + align:start position:0% +that involves not just doing + + + align:start position:0% +that involves not just doing +um the typical you know + + align:start position:0% +um the typical you know + + + align:start position:0% +um the typical you know +cluster and then find the + + align:start position:0% +cluster and then find the + + + align:start position:0% +cluster and then find the +pbi for the kaplan-meier curves but + + align:start position:0% +pbi for the kaplan-meier curves but + + + align:start position:0% +pbi for the kaplan-meier curves but +actually + + align:start position:0% +actually + + + align:start position:0% +actually +getting a good + + align:start position:0% +getting a good + + + align:start position:0% +getting a good +sort of score of some sort and then + + align:start position:0% +sort of score of some sort and then + + + align:start position:0% +sort of score of some sort and then +incorporating that into your + + align:start position:0% +incorporating that into your + + + align:start position:0% +incorporating that into your +multivariate model um + + align:start position:0% +multivariate model um + + + align:start position:0% +multivariate model um +and then it's i mean that part is + + align:start position:0% +and then it's i mean that part is + + + align:start position:0% +and then it's i mean that part is +actually not trivial but um + + align:start position:0% +actually not trivial but um + + + align:start position:0% +actually not trivial but um +if you + + align:start position:0% +if you + + + align:start position:0% +if you +if you're familiar with a statistical + + align:start position:0% +if you're familiar with a statistical + + + align:start position:0% +if you're familiar with a statistical +package + + align:start position:0% +package + + + align:start position:0% +package +something like this + + align:start position:0% +something like this + + + align:start position:0% +something like this +it is actually naughty not hard so you + + align:start position:0% +it is actually naughty not hard so you + + + align:start position:0% +it is actually naughty not hard so you +know you should be able to + + align:start position:0% +know you should be able to + + + align:start position:0% +know you should be able to +i think you know if you understand these + + align:start position:0% +i think you know if you understand these + + + align:start position:0% +i think you know if you understand these +papers really well and there are a lot + + align:start position:0% +papers really well and there are a lot + + + align:start position:0% +papers really well and there are a lot +of little steps that you have to worry + + align:start position:0% +of little steps that you have to worry + + + align:start position:0% +of little steps that you have to worry +about + + align:start position:0% +about + + + align:start position:0% +about +you know you should probably be able to + + align:start position:0% +you know you should probably be able to + + + align:start position:0% +you know you should probably be able to +do everything your own i think + + align:start position:0% +do everything your own i think + + + align:start position:0% +do everything your own i think +so without too much difficulty + + align:start position:0% +so without too much difficulty + + + align:start position:0% +so without too much difficulty +so + + align:start position:0% +so + + + align:start position:0% +so +so finally um + + align:start position:0% +so finally um + + + align:start position:0% +so finally um +the software that i use all the time is + + align:start position:0% +the software that i use all the time is + + + align:start position:0% +the software that i use all the time is +r + + align:start position:0% +r + + + align:start position:0% +r +do you guys are you familiar with the + + align:start position:0% +do you guys are you familiar with the + + + align:start position:0% +do you guys are you familiar with the +software okay what + + align:start position:0% +software okay what + + + align:start position:0% +software okay what +what + + align:start position:0% +what + + + align:start position:0% +what +statistics software do you know if any + + align:start position:0% +statistics software do you know if any + + + align:start position:0% +statistics software do you know if any +do you guys know matlab + + align:start position:0% +do you guys know matlab + + + align:start position:0% +do you guys know matlab +okay some matlab a lot of people know so + + align:start position:0% +okay some matlab a lot of people know so + + + align:start position:0% +okay some matlab a lot of people know so +r is + + align:start position:0% +r is + + + align:start position:0% +r is +uh so if you go to statistics department + + align:start position:0% +uh so if you go to statistics department + + + align:start position:0% +uh so if you go to statistics department +they'll use + + align:start position:0% +they'll use + + + align:start position:0% +they'll use +one of two software + + align:start position:0% +one of two software + + + align:start position:0% +one of two software +um one is at sas + + align:start position:0% +um one is at sas + + + align:start position:0% +um one is at sas +a lot of people use that + + align:start position:0% +a lot of people use that + + + align:start position:0% +a lot of people use that +and the other one is s plus so sas is + + align:start position:0% +and the other one is s plus so sas is + + + align:start position:0% +and the other one is s plus so sas is +has been around forever + + align:start position:0% +has been around forever + + + align:start position:0% +has been around forever +it's like 4chan right it's like + + align:start position:0% +it's like 4chan right it's like + + + align:start position:0% +it's like 4chan right it's like +it's been around forever there's a lot + + align:start position:0% +it's been around forever there's a lot + + + align:start position:0% +it's been around forever there's a lot +of people + + align:start position:0% +of people + + + align:start position:0% +of people +that have written good software for it + + align:start position:0% +that have written good software for it + + + align:start position:0% +that have written good software for it +you know that it works but it's very + + align:start position:0% +you know that it works but it's very + + + align:start position:0% +you know that it works but it's very +clumsy right a lot of things that you + + align:start position:0% +clumsy right a lot of things that you + + + align:start position:0% +clumsy right a lot of things that you +want to do you can't do + + align:start position:0% +want to do you can't do + + + align:start position:0% +want to do you can't do +they have a better um + + align:start position:0% +they have a better um + + + align:start position:0% +they have a better um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +windows driven uh package now for sas + + align:start position:0% +windows driven uh package now for sas + + + align:start position:0% +windows driven uh package now for sas +but even just a few years ago like they + + align:start position:0% +but even just a few years ago like they + + + align:start position:0% +but even just a few years ago like they +it will draw plots like using asterisks + + align:start position:0% +it will draw plots like using asterisks + + + align:start position:0% +it will draw plots like using asterisks +on a you know text kind of page way so + + align:start position:0% +on a you know text kind of page way so + + + align:start position:0% +on a you know text kind of page way so +the draw little uh you know + + align:start position:0% +the draw little uh you know + + + align:start position:0% +the draw little uh you know +characters on your screen as a plot um + + align:start position:0% +characters on your screen as a plot um + + + align:start position:0% +characters on your screen as a plot um +but i think the younger sort of + + align:start position:0% +but i think the younger sort of + + + align:start position:0% +but i think the younger sort of +generation that are more computer savvy + + align:start position:0% +generation that are more computer savvy + + + align:start position:0% +generation that are more computer savvy +are more likely to use s plus + + align:start position:0% +are more likely to use s plus + + + align:start position:0% +are more likely to use s plus +unless they have to use sas in their + + align:start position:0% +unless they have to use sas in their + + + align:start position:0% +unless they have to use sas in their +statistics courses so s plus is more + + align:start position:0% +statistics courses so s plus is more + + + align:start position:0% +statistics courses so s plus is more +like matlab so it's + + align:start position:0% +like matlab so it's + + + align:start position:0% +like matlab so it's +fairly + + align:start position:0% +fairly + + + align:start position:0% +fairly +powerful and it gives you a lot of + + align:start position:0% +powerful and it gives you a lot of + + + align:start position:0% +powerful and it gives you a lot of +freedom + + align:start position:0% +freedom + + + align:start position:0% +freedom +and + + align:start position:0% +and + + + align:start position:0% +and +r + + align:start position:0% +r + + + align:start position:0% +r +there's so the reason it's called s plus + + align:start position:0% +there's so the reason it's called s plus + + + align:start position:0% +there's so the reason it's called s plus +is there's there's a statistics language + + align:start position:0% +is there's there's a statistics language + + + align:start position:0% +is there's there's a statistics language +called s + + align:start position:0% +called s + + + align:start position:0% +called s +um i don't know why it's called that's + + align:start position:0% +um i don't know why it's called that's + + + align:start position:0% +um i don't know why it's called that's +in its name y ryc programming language + + align:start position:0% +in its name y ryc programming language + + + align:start position:0% +in its name y ryc programming language +called + + align:start position:0% +called + + + align:start position:0% +called +c and then some + + align:start position:0% +c and then some + + + align:start position:0% +c and then some +and this was developed at bell labs and + + align:start position:0% +and this was developed at bell labs and + + + align:start position:0% +and this was developed at bell labs and +you know some company took the code + + align:start position:0% +you know some company took the code + + + align:start position:0% +you know some company took the code +and then made that as a product and they + + align:start position:0% +and then made that as a product and they + + + align:start position:0% +and then made that as a product and they +called it s plus + + align:start position:0% +called it s plus + + + align:start position:0% +called it s plus +and then now there's a bunch of people a + + align:start position:0% +and then now there's a bunch of people a + + + align:start position:0% +and then now there's a bunch of people a +lot of whom worked on a lot of them a + + align:start position:0% +lot of whom worked on a lot of them a + + + align:start position:0% +lot of whom worked on a lot of them a +lot of whom are familiar with s that + + align:start position:0% +lot of whom are familiar with s that + + + align:start position:0% +lot of whom are familiar with s that +developed r + + align:start position:0% +developed r + + + align:start position:0% +developed r +so actually the guy that wrote + + align:start position:0% +so actually the guy that wrote + + + align:start position:0% +so actually the guy that wrote +one of the two + + align:start position:0% +one of the two + + + align:start position:0% +one of the two +co-authors of the original r is at dana + + align:start position:0% +co-authors of the original r is at dana + + + align:start position:0% +co-authors of the original r is at dana +farber and he's been doing a lot of work + + align:start position:0% +farber and he's been doing a lot of work + + + align:start position:0% +farber and he's been doing a lot of work +um + + align:start position:0% +um + + + align:start position:0% +um +in microwave analysis as well but so the + + align:start position:0% +in microwave analysis as well but so the + + + align:start position:0% +in microwave analysis as well but so the +software r is + + align:start position:0% +software r is + + + align:start position:0% +software r is +uh free + + align:start position:0% +uh free + + + align:start position:0% +uh free +and it's like linux you know people + + align:start position:0% +and it's like linux you know people + + + align:start position:0% +and it's like linux you know people +contribute it's you know it's well + + align:start position:0% +contribute it's you know it's well + + + align:start position:0% +contribute it's you know it's well +tested + + align:start position:0% +tested + + + align:start position:0% +tested +um + + align:start position:0% +um + + + align:start position:0% +um +and very powerful + + align:start position:0% +and very powerful + + + align:start position:0% +and very powerful +um + + align:start position:0% +um + + + align:start position:0% +um +and that's what i use all the time um + + align:start position:0% +and that's what i use all the time um + + + align:start position:0% +and that's what i use all the time um +there are some lot of there are some + + align:start position:0% +there are some lot of there are some + + + align:start position:0% +there are some lot of there are some +issues like you know memory management + + align:start position:0% +issues like you know memory management + + + align:start position:0% +issues like you know memory management +and certain the + + align:start position:0% +and certain the + + + align:start position:0% +and certain the +data types but i think things are + + align:start position:0% +data types but i think things are + + + align:start position:0% +data types but i think things are +improving and so i'm i'm quite happy + + align:start position:0% +improving and so i'm i'm quite happy + + + align:start position:0% +improving and so i'm i'm quite happy +with it and everyone that i've + + align:start position:0% +with it and everyone that i've + + + align:start position:0% +with it and everyone that i've +recommended + + align:start position:0% +recommended + + + align:start position:0% +recommended +to are pretty happy with it + + align:start position:0% +to are pretty happy with it + + + align:start position:0% +to are pretty happy with it +it has a feel of matlab like you don't + + align:start position:0% +it has a feel of matlab like you don't + + + align:start position:0% +it has a feel of matlab like you don't +declare variables you just kind of use + + align:start position:0% +declare variables you just kind of use + + + align:start position:0% +declare variables you just kind of use +them + + align:start position:0% +them + + + align:start position:0% +them +matrix manipulations are very similar + + align:start position:0% +matrix manipulations are very similar + + + align:start position:0% +matrix manipulations are very similar +everything's done in vector form + + align:start position:0% +everything's done in vector form + + + align:start position:0% +everything's done in vector form +i showed this to one guy in + + align:start position:0% +i showed this to one guy in + + + align:start position:0% +i showed this to one guy in +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +in one of the lefts and at the + + align:start position:0% +in one of the lefts and at the + + + align:start position:0% +in one of the lefts and at the +children's hospital as a fellow and then + + align:start position:0% +children's hospital as a fellow and then + + + align:start position:0% +children's hospital as a fellow and then +he was trying to do some + + align:start position:0% +he was trying to do some + + + align:start position:0% +he was trying to do some +microwave data analysis and + + align:start position:0% +microwave data analysis and + + + align:start position:0% +microwave data analysis and +excel like you know doing some sort of + + align:start position:0% +excel like you know doing some sort of + + + align:start position:0% +excel like you know doing some sort of +permutation and i showed him how to do + + align:start position:0% +permutation and i showed him how to do + + + align:start position:0% +permutation and i showed him how to do +this and he said you know this one line + + align:start position:0% +this and he said you know this one line + + + align:start position:0% +this and he said you know this one line +i mean it took me three hours to do this + + align:start position:0% +i mean it took me three hours to do this + + + align:start position:0% +i mean it took me three hours to do this +in excel and this is one line in r right + + align:start position:0% +in excel and this is one line in r right + + + align:start position:0% +in excel and this is one line in r right +he's very happy + + align:start position:0% + + + + align:start position:0% + +matlab has more statistics but i think + + align:start position:0% +matlab has more statistics but i think + + + align:start position:0% +matlab has more statistics but i think +r has more sophisticated statistics so + + align:start position:0% +r has more sophisticated statistics so + + + align:start position:0% +r has more sophisticated statistics so +matlab is more engineering oriented + + align:start position:0% +matlab is more engineering oriented + + + align:start position:0% +matlab is more engineering oriented +it has matlab has better graphics + + align:start position:0% +it has matlab has better graphics + + + align:start position:0% +it has matlab has better graphics +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +it's probably better for solving + + align:start position:0% +it's probably better for solving + + + align:start position:0% +it's probably better for solving +for algorithms like if you want to solve + + align:start position:0% +for algorithms like if you want to solve + + + align:start position:0% +for algorithms like if you want to solve +a large matrix it's probably better in + + align:start position:0% +a large matrix it's probably better in + + + align:start position:0% +a large matrix it's probably better in +matlab + + align:start position:0% +matlab + + + align:start position:0% +matlab +just because a lot more people are + + align:start position:0% +just because a lot more people are + + + align:start position:0% +just because a lot more people are +working with matlab and you know it's a + + align:start position:0% +working with matlab and you know it's a + + + align:start position:0% +working with matlab and you know it's a +big company they spent a lot of money on + + align:start position:0% +big company they spent a lot of money on + + + align:start position:0% +big company they spent a lot of money on +it + + align:start position:0% +it + + + align:start position:0% +it +um + + align:start position:0% +um + + + align:start position:0% +um +but for statistics uh routines i think r + + align:start position:0% +but for statistics uh routines i think r + + + align:start position:0% +but for statistics uh routines i think r +is more + + align:start position:0% +is more + + + align:start position:0% +is more +more sophisticated you have a lot more + + align:start position:0% +more sophisticated you have a lot more + + + align:start position:0% +more sophisticated you have a lot more +options + + align:start position:0% +options + + + align:start position:0% +options +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +yeah so i mean i i used to use matlab + + align:start position:0% +yeah so i mean i i used to use matlab + + + align:start position:0% +yeah so i mean i i used to use matlab +all the time but now i'm happy with r + + align:start position:0% +all the time but now i'm happy with r + + + align:start position:0% +all the time but now i'm happy with r +but if you know one you know it's easy + + align:start position:0% +but if you know one you know it's easy + + + align:start position:0% +but if you know one you know it's easy +to pick up the other + + align:start position:0% +to pick up the other + + + align:start position:0% +to pick up the other +i mean you always get confused as to you + + align:start position:0% +i mean you always get confused as to you + + + align:start position:0% +i mean you always get confused as to you +know how do i comment something out or + + align:start position:0% +know how do i comment something out or + + + align:start position:0% +know how do i comment something out or +you know that sort of thing but you know + + align:start position:0% +you know that sort of thing but you know + + + align:start position:0% +you know that sort of thing but you know +they're basically the same same flavor + + align:start position:0% +they're basically the same same flavor + + + align:start position:0% +they're basically the same same flavor +the same reason that matlab was popular + + align:start position:0% + + + + align:start position:0% + +let's see steep learning curve but + + align:start position:0% +let's see steep learning curve but + + + align:start position:0% +let's see steep learning curve but +worthwhile in the long run um + + align:start position:0% +worthwhile in the long run um + + + align:start position:0% +worthwhile in the long run um +and there's something called + + align:start position:0% +and there's something called + + + align:start position:0% +and there's something called +bioconductor + + align:start position:0% +bioconductor + + + align:start position:0% +bioconductor +i don't know if anyone has heard of this + + align:start position:0% +i don't know if anyone has heard of this + + + align:start position:0% +i don't know if anyone has heard of this +so + + align:start position:0% +so + + + align:start position:0% +so +this is an effort that + + align:start position:0% +this is an effort that + + + align:start position:0% +this is an effort that +that robert gentleman who's at the um + + align:start position:0% +that robert gentleman who's at the um + + + align:start position:0% +that robert gentleman who's at the um +dana farber institute who + + align:start position:0% +dana farber institute who + + + align:start position:0% +dana farber institute who +was one of the founders of r started + + align:start position:0% +was one of the founders of r started + + + align:start position:0% +was one of the founders of r started +when we so i was kind of more + + align:start position:0% +when we so i was kind of more + + + align:start position:0% +when we so i was kind of more +part of it just + + align:start position:0% +part of it just + + + align:start position:0% +part of it just +more part of this project before but and + + align:start position:0% +more part of this project before but and + + + align:start position:0% +more part of this project before but and +we actually he suggested at the very + + align:start position:0% +we actually he suggested at the very + + + align:start position:0% +we actually he suggested at the very +beginning + + align:start position:0% +beginning + + + align:start position:0% +beginning +for the title or for the name of the + + align:start position:0% +for the title or for the name of the + + + align:start position:0% +for the title or for the name of the +project madman like microarray data + + align:start position:0% +project madman like microarray data + + + align:start position:0% +project madman like microarray data +management + + align:start position:0% +management + + + align:start position:0% +management +but in the end you know it was decided + + align:start position:0% +but in the end you know it was decided + + + align:start position:0% +but in the end you know it was decided +that nih would not want to + + align:start position:0% +that nih would not want to + + + align:start position:0% +that nih would not want to +find something called madman so + + align:start position:0% +find something called madman so + + + align:start position:0% +find something called madman so +he came up with biconductor which is a + + align:start position:0% +he came up with biconductor which is a + + + align:start position:0% +he came up with biconductor which is a +much better thing + + align:start position:0% +much better thing + + + align:start position:0% +much better thing +so if you go to buyconnected.org there + + align:start position:0% +so if you go to buyconnected.org there + + + align:start position:0% +so if you go to buyconnected.org there +are packages that you can download so + + align:start position:0% +are packages that you can download so + + + align:start position:0% +are packages that you can download so +what what's happening now is that this i + + align:start position:0% +what what's happening now is that this i + + + align:start position:0% +what what's happening now is that this i +think this package has sort of caught on + + align:start position:0% +think this package has sort of caught on + + + align:start position:0% +think this package has sort of caught on +so that + + align:start position:0% +so that + + + align:start position:0% +so that +if someone writes or comes up with a + + align:start position:0% +if someone writes or comes up with a + + + align:start position:0% +if someone writes or comes up with a +good algorithm they'll write a r routine + + align:start position:0% +good algorithm they'll write a r routine + + + align:start position:0% +good algorithm they'll write a r routine +and deposit it somewhere in this website + + align:start position:0% +and deposit it somewhere in this website + + + align:start position:0% +and deposit it somewhere in this website +so that you can download it and run it + + align:start position:0% +so that you can download it and run it + + + align:start position:0% +so that you can download it and run it +so um and that's been done for a lot of + + align:start position:0% +so um and that's been done for a lot of + + + align:start position:0% +so um and that's been done for a lot of +good algorithms out there so if you want + + align:start position:0% +good algorithms out there so if you want + + + align:start position:0% +good algorithms out there so if you want +to normalize your you see dna data using + + align:start position:0% +to normalize your you see dna data using + + + align:start position:0% +to normalize your you see dna data using +some fancy method it's there + + align:start position:0% +some fancy method it's there + + + align:start position:0% +some fancy method it's there +download it + + align:start position:0% +download it + + + align:start position:0% +download it +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it's pretty easy so and there's a + + align:start position:0% +it's pretty easy so and there's a + + + align:start position:0% +it's pretty easy so and there's a +windows version of this that's pretty + + align:start position:0% +windows version of this that's pretty + + + align:start position:0% +windows version of this that's pretty +easy + + align:start position:0% +easy + + + align:start position:0% +easy +our r comes in linux and windows but + + align:start position:0% +our r comes in linux and windows but + + + align:start position:0% +our r comes in linux and windows but +um it gets uh compiled for + + align:start position:0% +um it gets uh compiled for + + + align:start position:0% +um it gets uh compiled for +um gets ported to windows frequently + + align:start position:0% +um gets ported to windows frequently + + + align:start position:0% +um gets ported to windows frequently +and i i've had no problems with it um + + align:start position:0% +and i i've had no problems with it um + + + align:start position:0% +and i i've had no problems with it um +i think someone was trying to port it to + + align:start position:0% +i think someone was trying to port it to + + + align:start position:0% +i think someone was trying to port it to +apple um + + align:start position:0% +apple um + + + align:start position:0% +apple um +but i don't know how successful it is i + + align:start position:0% +but i don't know how successful it is i + + + align:start position:0% +but i don't know how successful it is i +wouldn't recommend it um + + align:start position:0% +wouldn't recommend it um + + + align:start position:0% +wouldn't recommend it um +but i'm pretty happy with it this is + + align:start position:0% +but i'm pretty happy with it this is + + + align:start position:0% +but i'm pretty happy with it this is +what i use all the time this is what a + + align:start position:0% +what i use all the time this is what a + + + align:start position:0% +what i use all the time this is what a +lot of people use + + align:start position:0% +lot of people use + + + align:start position:0% +lot of people use +um + + align:start position:0% +um + + + align:start position:0% +um +who um do micro analysis + + align:start position:0% + + + + align:start position:0% + +okay so i see that i have i ended three + + align:start position:0% +okay so i see that i have i ended three + + + align:start position:0% +okay so i see that i have i ended three +minutes early so + + align:start position:0% + + + + align:start position:0% + +yeah so the problem with the website + + align:start position:0% +yeah so the problem with the website + + + align:start position:0% +yeah so the problem with the website +yeah there is there is the problem is + + align:start position:0% +yeah there is there is the problem is + + + align:start position:0% +yeah there is there is the problem is +that + + align:start position:0% +that + + + align:start position:0% +that +i i think r is just a bad name because + + align:start position:0% +i i think r is just a bad name because + + + align:start position:0% +i i think r is just a bad name because +you can't really search for r + + align:start position:0% +you can't really search for r + + + align:start position:0% +you can't really search for r +yeah uh you can go to biconductor r and + + align:start position:0% +yeah uh you can go to biconductor r and + + + align:start position:0% +yeah uh you can go to biconductor r and +there's a link back to r + + align:start position:0% +there's a link back to r + + + align:start position:0% +there's a link back to r +or you can do you can do if you do + + align:start position:0% +or you can do you can do if you do + + + align:start position:0% +or you can do you can do if you do +statistical package or + + align:start position:0% + + + + align:start position:0% + +r used to be i mean it used to be hard + + align:start position:0% +r used to be i mean it used to be hard + + + align:start position:0% +r used to be i mean it used to be hard +to um like run these things but + + align:start position:0% +to um like run these things but + + + align:start position:0% +to um like run these things but +robert and his friends have really made + + align:start position:0% +robert and his friends have really made + + + align:start position:0% +robert and his friends have really made +this easy so that + + align:start position:0% +this easy so that + + + align:start position:0% +this easy so that +you basically click the button and it'll + + align:start position:0% +you basically click the button and it'll + + + align:start position:0% +you basically click the button and it'll +install on your + + align:start position:0% +install on your + + + align:start position:0% +install on your +windows so + + align:start position:0% + + + + align:start position:0% + +all right \ No newline at end of file diff --git a/OrK_pnmh_pQ.txt b/OrK_pnmh_pQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..da1908f577c89daaee9c26e8ca9e17d98be8c6db --- /dev/null +++ b/OrK_pnmh_pQ.txt @@ -0,0 +1,13267 @@ +align:start position:0% + +okay so today I want to talk about um + + align:start position:0% +okay so today I want to talk about um + + + align:start position:0% +okay so today I want to talk about um +anden and one uh new method which is the + + align:start position:0% +anden and one uh new method which is the + + + align:start position:0% +anden and one uh new method which is the +method of IND instrumental vibl and or + + align:start position:0% +method of IND instrumental vibl and or + + + align:start position:0% +method of IND instrumental vibl and or +two stag Le + + align:start position:0% +two stag Le + + + align:start position:0% +two stag Le +squares so after our nice interlude of + + align:start position:0% +squares so after our nice interlude of + + + align:start position:0% +squares so after our nice interlude of +machine learning where we didn't think + + align:start position:0% +machine learning where we didn't think + + + align:start position:0% +machine learning where we didn't think +about we didn't have to think about + + align:start position:0% +about we didn't have to think about + + + align:start position:0% +about we didn't have to think about +causality anymore or even about + + align:start position:0% +causality anymore or even about + + + align:start position:0% +causality anymore or even about +coefficients because we were all about + + align:start position:0% +coefficients because we were all about + + + align:start position:0% +coefficients because we were all about +protection I want to bring us back to + + align:start position:0% +protection I want to bring us back to + + + align:start position:0% +protection I want to bring us back to +our efforts to establish + + align:start position:0% +our efforts to establish + + + align:start position:0% +our efforts to establish +causality uh which sometimes is really + + align:start position:0% +causality uh which sometimes is really + + + align:start position:0% +causality uh which sometimes is really +what we are interested + + align:start position:0% +what we are interested + + + align:start position:0% +what we are interested +in uh so suppose that we we start from a + + align:start position:0% +in uh so suppose that we we start from a + + + align:start position:0% +in uh so suppose that we we start from a +model like the one we had uh finished + + align:start position:0% +model like the one we had uh finished + + + align:start position:0% +model like the one we had uh finished +with at the end of um of last uh last uh + + align:start position:0% +with at the end of um of last uh last uh + + + align:start position:0% +with at the end of um of last uh last uh +lecture where we have some X1 variable + + align:start position:0% +lecture where we have some X1 variable + + + align:start position:0% +lecture where we have some X1 variable +that we actually observe we are + + align:start position:0% +that we actually observe we are + + + align:start position:0% +that we actually observe we are +interested in the causal effect of X1 + + align:start position:0% +interested in the causal effect of X1 + + + align:start position:0% +interested in the causal effect of X1 +and then we have some X2 variables that + + align:start position:0% +and then we have some X2 variables that + + + align:start position:0% +and then we have some X2 variables that +uh um we we may or may not observe and + + align:start position:0% +uh um we we may or may not observe and + + + align:start position:0% +uh um we we may or may not observe and +we discussed a bunch of stuff that uh we + + align:start position:0% +we discussed a bunch of stuff that uh we + + + align:start position:0% +we discussed a bunch of stuff that uh we +could do in order to make sure that the + + align:start position:0% +could do in order to make sure that the + + + align:start position:0% +could do in order to make sure that the +coefficient of beta 1 is in fact + + align:start position:0% +coefficient of beta 1 is in fact + + + align:start position:0% +coefficient of beta 1 is in fact +indicating the causal relationship going + + align:start position:0% +indicating the causal relationship going + + + align:start position:0% +indicating the causal relationship going +from X1 to to Y uh but there are + + align:start position:0% +from X1 to to Y uh but there are + + + align:start position:0% +from X1 to to Y uh but there are +occasions where the regression based + + align:start position:0% +occasions where the regression based + + + align:start position:0% +occasions where the regression based +methods that we saw + + align:start position:0% +methods that we saw + + + align:start position:0% +methods that we saw +just controlling for as many X2 as you + + align:start position:0% +just controlling for as many X2 as you + + + align:start position:0% +just controlling for as many X2 as you +as we can or uh difference in different + + align:start position:0% +as we can or uh difference in different + + + align:start position:0% +as we can or uh difference in different +strategies which is another form of + + align:start position:0% +strategies which is another form of + + + align:start position:0% +strategies which is another form of +regression control if you want or even + + align:start position:0% +regression control if you want or even + + + align:start position:0% +regression control if you want or even +regression discontinuity design is just + + align:start position:0% +regression discontinuity design is just + + + align:start position:0% +regression discontinuity design is just +not going to cut it uh because uh we + + align:start position:0% +not going to cut it uh because uh we + + + align:start position:0% +not going to cut it uh because uh we +don't have the control variables for + + align:start position:0% +don't have the control variables for + + + align:start position:0% +don't have the control variables for +example uh because uh uh there is no + + align:start position:0% +example uh because uh uh there is no + + + align:start position:0% +example uh because uh uh there is no +regression discontinuity that we can use + + align:start position:0% +regression discontinuity that we can use + + + align:start position:0% +regression discontinuity that we can use +uh oh because a plausible case can be + + align:start position:0% +uh oh because a plausible case can be + + + align:start position:0% +uh oh because a plausible case can be +made that the variable X2 actually could + + align:start position:0% +made that the variable X2 actually could + + + align:start position:0% +made that the variable X2 actually could +affect y the variable X1 sorry X2 also + + align:start position:0% +affect y the variable X1 sorry X2 also + + + align:start position:0% +affect y the variable X1 sorry X2 also +by the way but here is we interested in + + align:start position:0% +by the way but here is we interested in + + + align:start position:0% +by the way but here is we interested in +causal effect of X1 the variable X1 + + align:start position:0% +causal effect of X1 the variable X1 + + + align:start position:0% +causal effect of X1 the variable X1 +might affect y as well in which case uh + + align:start position:0% +might affect y as well in which case uh + + + align:start position:0% +might affect y as well in which case uh +there is really not an easy control + + align:start position:0% +there is really not an easy control + + + align:start position:0% +there is really not an easy control +approach to that problem because if the + + align:start position:0% +approach to that problem because if the + + + align:start position:0% +approach to that problem because if the +variable X1 affect Y and Y affects the + + align:start position:0% +variable X1 affect Y and Y affects the + + + align:start position:0% +variable X1 affect Y and Y affects the +variable X1 like we there's no way we we + + align:start position:0% +variable X1 like we there's no way we we + + + align:start position:0% +variable X1 like we there's no way we we +can we cannot easily control for them so + + align:start position:0% +can we cannot easily control for them so + + + align:start position:0% +can we cannot easily control for them so +um Sarah gave me a very nice example of + + align:start position:0% +um Sarah gave me a very nice example of + + + align:start position:0% +um Sarah gave me a very nice example of +of of of this uh which is this uh kind + + align:start position:0% +of of of this uh which is this uh kind + + + align:start position:0% +of of of this uh which is this uh kind +of breaking news of a few years ago + + align:start position:0% +of breaking news of a few years ago + + + align:start position:0% +of breaking news of a few years ago +unhappy people watch more TV study an + + align:start position:0% +unhappy people watch more TV study an + + + align:start position:0% +unhappy people watch more TV study an +extensive new research study has found + + align:start position:0% +extensive new research study has found + + + align:start position:0% +extensive new research study has found +that unhappy PE people watch more TV + + align:start position:0% +that unhappy PE people watch more TV + + + align:start position:0% +that unhappy PE people watch more TV +while those who consider themselves + + align:start position:0% +while those who consider themselves + + + align:start position:0% +while those who consider themselves +happy spend more time reading and + + align:start position:0% +happy spend more time reading and + + + align:start position:0% +happy spend more time reading and +socializing now the question is that + + align:start position:0% +socializing now the question is that + + + align:start position:0% +socializing now the question is that +from this typ + + align:start position:0% +from this typ + + + align:start position:0% +from this typ +do you think they're trying to claim + + align:start position:0% +do you think they're trying to claim + + + align:start position:0% +do you think they're trying to claim +that it is TV that make you unhappy or + + align:start position:0% +that it is TV that make you unhappy or + + + align:start position:0% +that it is TV that make you unhappy or +that is uh unhappiness that makes you + + align:start position:0% +that is uh unhappiness that makes you + + + align:start position:0% +that is uh unhappiness that makes you +watch + + align:start position:0% + + + + align:start position:0% + +TV the latter who is voting for the + + align:start position:0% +TV the latter who is voting for the + + + align:start position:0% +TV the latter who is voting for the +former no one so interestingly they are + + align:start position:0% +former no one so interestingly they are + + + align:start position:0% +former no one so interestingly they are +actually + + align:start position:0% +actually + + + align:start position:0% +actually +uh uh thinking about the the + + align:start position:0% +uh uh thinking about the the + + + align:start position:0% +uh uh thinking about the the +forer + + align:start position:0% +forer + + + align:start position:0% +forer +and the + + align:start position:0% +and the + + + align:start position:0% +and the +latter this is a spectacular study that + + align:start position:0% +latter this is a spectacular study that + + + align:start position:0% +latter this is a spectacular study that +actually in the same study which is + + align:start position:0% +actually in the same study which is + + + align:start position:0% +actually in the same study which is +based on + + align:start position:0% +based on + + + align:start position:0% +based on +correlation makes both causal claims TV + + align:start position:0% +correlation makes both causal claims TV + + + align:start position:0% +correlation makes both causal claims TV +do cause people to be less + + align:start position:0% +do cause people to be less + + + align:start position:0% +do cause people to be less +happy in other words the caal order is + + align:start position:0% +happy in other words the caal order is + + + align:start position:0% +happy in other words the caal order is +reversed for people who watch television + + align:start position:0% +reversed for people who watch television + + + align:start position:0% +reversed for people who watch television +unhappiness leads to television viewing + + align:start position:0% +unhappiness leads to television viewing + + + align:start position:0% +unhappiness leads to television viewing +so I think one could actually make a + + align:start position:0% +so I think one could actually make a + + + align:start position:0% +so I think one could actually make a +reasonable case going both ways so it is + + align:start position:0% +reasonable case going both ways so it is + + + align:start position:0% +reasonable case going both ways so it is +not uh it is not a necessarily a stupid + + align:start position:0% +not uh it is not a necessarily a stupid + + + align:start position:0% +not uh it is not a necessarily a stupid +thing to think about uh the problem is + + align:start position:0% +thing to think about uh the problem is + + + align:start position:0% +thing to think about uh the problem is +that intuitively you feel both could not + + align:start position:0% +that intuitively you feel both could not + + + align:start position:0% +that intuitively you feel both could not +very easily being established from the + + align:start position:0% +very easily being established from the + + + align:start position:0% +very easily being established from the +cell caal sem causal regression because + + align:start position:0% +cell caal sem causal regression because + + + align:start position:0% +cell caal sem causal regression because +if I can write the model both + + align:start position:0% +if I can write the model both + + + align:start position:0% +if I can write the model both +ways clearly the coefficient is going to + + align:start position:0% +ways clearly the coefficient is going to + + + align:start position:0% +ways clearly the coefficient is going to +be biased if I attribute if I first + + align:start position:0% +be biased if I attribute if I first + + + align:start position:0% +be biased if I attribute if I first +attribute the entire causal effect on + + align:start position:0% +attribute the entire causal effect on + + + align:start position:0% +attribute the entire causal effect on +X and then I reverse the regression I + + align:start position:0% +X and then I reverse the regression I + + + align:start position:0% +X and then I reverse the regression I +tribute the entire coal effect on y i + + align:start position:0% +tribute the entire coal effect on y i + + + align:start position:0% +tribute the entire coal effect on y i +seems to be giving myself double credit + + align:start position:0% +seems to be giving myself double credit + + + align:start position:0% +seems to be giving myself double credit +so that's the main problem endogenity is + + align:start position:0% +so that's the main problem endogenity is + + + align:start position:0% +so that's the main problem endogenity is +any situation where you they making the + + align:start position:0% +any situation where you they making the + + + align:start position:0% +any situation where you they making the +argument actually sort of a theory + + align:start position:0% +argument actually sort of a theory + + + align:start position:0% +argument actually sort of a theory +argument why um TV cause people to be + + align:start position:0% +argument why um TV cause people to be + + + align:start position:0% +argument why um TV cause people to be +less happy which is the idea that uh uh + + align:start position:0% +less happy which is the idea that uh uh + + + align:start position:0% +less happy which is the idea that uh uh +it's too easy and it's passive and you + + align:start position:0% +it's too easy and it's passive and you + + + align:start position:0% +it's too easy and it's passive and you +don't kind of other activities have more + + align:start position:0% +don't kind of other activities have more + + + align:start position:0% +don't kind of other activities have more +benefits and then the other so that's + + align:start position:0% +benefits and then the other so that's + + + align:start position:0% +benefits and then the other so that's +that why TV might make you unhappy and + + align:start position:0% +that why TV might make you unhappy and + + + align:start position:0% +that why TV might make you unhappy and +in other words the causal effect is + + align:start position:0% +in other words the causal effect is + + + align:start position:0% +in other words the causal effect is +reversed unhappiness leads to television + + align:start position:0% +reversed unhappiness leads to television + + + align:start position:0% +reversed unhappiness leads to television +viewing if you unhappy and not very + + align:start position:0% +viewing if you unhappy and not very + + + align:start position:0% +viewing if you unhappy and not very +energetic you're going to watch TV so + + align:start position:0% +energetic you're going to watch TV so + + + align:start position:0% +energetic you're going to watch TV so +both both channels are plausible and + + align:start position:0% +both both channels are plausible and + + + align:start position:0% +both both channels are plausible and +prior so this is the when we have an + + align:start position:0% +prior so this is the when we have an + + + align:start position:0% +prior so this is the when we have an +endogenity + + align:start position:0% +endogenity + + + align:start position:0% +endogenity +problems so we talk about endogenity + + align:start position:0% +problems so we talk about endogenity + + + align:start position:0% +problems so we talk about endogenity +when there is this Mutual relationship + + align:start position:0% +when there is this Mutual relationship + + + align:start position:0% +when there is this Mutual relationship +uh what are other + + align:start position:0% +uh what are other + + + align:start position:0% +uh what are other +examples you can think about where you'd + + align:start position:0% +examples you can think about where you'd + + + align:start position:0% +examples you can think about where you'd +have it's not an omitted variable Bas is + + align:start position:0% +have it's not an omitted variable Bas is + + + align:start position:0% +have it's not an omitted variable Bas is +that is really the fact that one could + + align:start position:0% +that is really the fact that one could + + + align:start position:0% +that is really the fact that one could +sit down and write a model causal model + + align:start position:0% +sit down and write a model causal model + + + align:start position:0% +sit down and write a model causal model +going either way so can you think of + + align:start position:0% +going either way so can you think of + + + align:start position:0% +going either way so can you think of +other examples that where we would be in + + align:start position:0% +other examples that where we would be in + + + align:start position:0% +other examples that where we would be in +the same + + align:start position:0% + + + + align:start position:0% + +situation yep a lot of conditions + + align:start position:0% +situation yep a lot of conditions + + + align:start position:0% +situation yep a lot of conditions +associated with stfe failure would sort + + align:start position:0% +associated with stfe failure would sort + + + align:start position:0% +associated with stfe failure would sort +have reinforcing effects whether it's + + align:start position:0% +have reinforcing effects whether it's + + + align:start position:0% +have reinforcing effects whether it's +like type of government being to say + + align:start position:0% +like type of government being to say + + + align:start position:0% +like type of government being to say +failure failure sort of being associated + + align:start position:0% +failure failure sort of being associated + + + align:start position:0% +failure failure sort of being associated +to right so for example uh you could + + align:start position:0% +to right so for example uh you could + + + align:start position:0% +to right so for example uh you could +have a that's a great example so you can + + align:start position:0% +have a that's a great example so you can + + + align:start position:0% +have a that's a great example so you can +have huge crisis leading to a govern + + align:start position:0% +have huge crisis leading to a govern + + + align:start position:0% +have huge crisis leading to a govern +like collapsing or you could have the + + align:start position:0% +like collapsing or you could have the + + + align:start position:0% +like collapsing or you could have the +the government collapsing leading to a + + align:start position:0% +the government collapsing leading to a + + + align:start position:0% +the government collapsing leading to a +huge crisis and those two things will + + align:start position:0% +huge crisis and those two things will + + + align:start position:0% +huge crisis and those two things will +will observe them together and what + + align:start position:0% +will observe them together and what + + + align:start position:0% +will observe them together and what +caused what maybe both caused each other + + align:start position:0% +caused what maybe both caused each other + + + align:start position:0% +caused what maybe both caused each other +uh so that's that's that's a great + + align:start position:0% +uh so that's that's that's a great + + + align:start position:0% +uh so that's that's that's a great +example yep any system + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +with right yeah would be for example you + + align:start position:0% +with right yeah would be for example you + + + align:start position:0% +with right yeah would be for example you +say that a low social economic + + align:start position:0% +say that a low social economic + + + align:start position:0% +say that a low social economic +leads to tends to be associated with + + align:start position:0% +leads to tends to be associated with + + + align:start position:0% +leads to tends to be associated with +lower education but lower education is + + align:start position:0% +lower education but lower education is + + + align:start position:0% +lower education but lower education is +also sometimes related to low + + align:start position:0% +also sometimes related to low + + + align:start position:0% +also sometimes related to low +ofcom right so one thing here is that it + + align:start position:0% +ofcom right so one thing here is that it + + + align:start position:0% +ofcom right so one thing here is that it +might not be if you're interesting the + + align:start position:0% +might not be if you're interesting the + + + align:start position:0% +might not be if you're interesting the +the economic status of the of the + + align:start position:0% +the economic status of the of the + + + align:start position:0% +the economic status of the of the +parents might lead to low education of + + align:start position:0% +parents might lead to low education of + + + align:start position:0% +parents might lead to low education of +the kids and then the low education of + + align:start position:0% +the kids and then the low education of + + + align:start position:0% +the kids and then the low education of +the kids will not immediately + + align:start position:0% +the kids will not immediately + + + align:start position:0% +the kids will not immediately +necessarily feed back onto low education + + align:start position:0% +necessarily feed back onto low education + + + align:start position:0% +necessarily feed back onto low education +of the of of the parent so in this in + + align:start position:0% +of the of of the parent so in this in + + + align:start position:0% +of the of of the parent so in this in +that case that might be more of an + + align:start position:0% +that case that might be more of an + + + align:start position:0% +that case that might be more of an +omitted viable Bas but you could think + + align:start position:0% +omitted viable Bas but you could think + + + align:start position:0% +omitted viable Bas but you could think +of version of that for example uh + + align:start position:0% +of version of that for example uh + + + align:start position:0% +of version of that for example uh +um uh older uh teenager running into + + align:start position:0% +um uh older uh teenager running into + + + align:start position:0% +um uh older uh teenager running into +trouble at at school getting kicked out + + align:start position:0% +trouble at at school getting kicked out + + + align:start position:0% +trouble at at school getting kicked out +which only brings them to more trouble + + align:start position:0% +which only brings them to more trouble + + + align:start position:0% +which only brings them to more trouble +which + + align:start position:0% + + + + align:start position:0% + +ex yep practicing something that an + + align:start position:0% +ex yep practicing something that an + + + align:start position:0% +ex yep practicing something that an +instrument makes you better at it and + + align:start position:0% +instrument makes you better at it and + + + align:start position:0% +instrument makes you better at it and +being better at it makes you want + + align:start position:0% +being better at it makes you want + + + align:start position:0% +being better at it makes you want +exactly perfect perfect so these are all + + align:start position:0% +exactly perfect perfect so these are all + + + align:start position:0% +exactly perfect perfect so these are all +great examples so uh related to the + + align:start position:0% +great examples so uh related to the + + + align:start position:0% +great examples so uh related to the +state failure at sort of democracy and + + align:start position:0% +state failure at sort of democracy and + + + align:start position:0% +state failure at sort of democracy and +growth or maybe growth makes it more + + align:start position:0% +growth or maybe growth makes it more + + + align:start position:0% +growth or maybe growth makes it more +plausible that the Democracy takes hold + + align:start position:0% +plausible that the Democracy takes hold + + + align:start position:0% +plausible that the Democracy takes hold +because there is more interest in in a + + align:start position:0% +because there is more interest in in a + + + align:start position:0% +because there is more interest in in a +in a particip process of government on + + align:start position:0% +in a particip process of government on + + + align:start position:0% +in a particip process of government on +the other hand uh maybe democracy is + + align:start position:0% +the other hand uh maybe democracy is + + + align:start position:0% +the other hand uh maybe democracy is +good for GS there is a paper on the + + align:start position:0% +good for GS there is a paper on the + + + align:start position:0% +good for GS there is a paper on the +flashing everywhere in the department + + align:start position:0% +flashing everywhere in the department + + + align:start position:0% +flashing everywhere in the department +these days that makes exactly this claim + + align:start position:0% +these days that makes exactly this claim + + + align:start position:0% +these days that makes exactly this claim +uh health and exercise is another one + + align:start position:0% +uh health and exercise is another one + + + align:start position:0% +uh health and exercise is another one +you could think that you know exercising + + align:start position:0% +you could think that you know exercising + + + align:start position:0% +you could think that you know exercising +regularly keeps you in good shape but if + + align:start position:0% +regularly keeps you in good shape but if + + + align:start position:0% +regularly keeps you in good shape but if +you're in bad shape you you might not + + align:start position:0% +you're in bad shape you you might not + + + align:start position:0% +you're in bad shape you you might not +feel like exercising in um recent one + + align:start position:0% +feel like exercising in um recent one + + + align:start position:0% +feel like exercising in um recent one +that I heard about is that making cross + + align:start position:0% +that I heard about is that making cross + + + align:start position:0% +that I heard about is that making cross +people who do crosswords are less likely + + align:start position:0% +people who do crosswords are less likely + + + align:start position:0% +people who do crosswords are less likely +to to exhibit sign of uh cognitive + + align:start position:0% +to to exhibit sign of uh cognitive + + + align:start position:0% +to to exhibit sign of uh cognitive +decline like pre-dementia on the other + + align:start position:0% +decline like pre-dementia on the other + + + align:start position:0% +decline like pre-dementia on the other +youing that people who have predementia + + align:start position:0% +youing that people who have predementia + + + align:start position:0% +youing that people who have predementia +are not so excited about doing crossw so + + align:start position:0% +are not so excited about doing crossw so + + + align:start position:0% +are not so excited about doing crossw so +that's like that's uh and of course one + + align:start position:0% +that's like that's uh and of course one + + + align:start position:0% +that's like that's uh and of course one +that as economists we love is prices and + + align:start position:0% +that as economists we love is prices and + + + align:start position:0% +that as economists we love is prices and +quantity uh uh when prices are low + + align:start position:0% +quantity uh uh when prices are low + + + align:start position:0% +quantity uh uh when prices are low +people uh uh want less of it on the + + align:start position:0% +people uh uh want less of it on the + + + align:start position:0% +people uh uh want less of it on the +other hand when people want more of + + align:start position:0% +other hand when people want more of + + + align:start position:0% +other hand when people want more of +something the prices tend to go higher + + align:start position:0% +something the prices tend to go higher + + + align:start position:0% +something the prices tend to go higher +so in this case it's it's actually the + + align:start position:0% +so in this case it's it's actually the + + + align:start position:0% +so in this case it's it's actually the +relationship going opposite direction + + align:start position:0% +relationship going opposite direction + + + align:start position:0% +relationship going opposite direction +but there there is also a causality + + align:start position:0% +but there there is also a causality + + + align:start position:0% +but there there is also a causality +running running both ways we can run it + + align:start position:0% +running running both ways we can run it + + + align:start position:0% +running running both ways we can run it +run the equations there's a supply + + align:start position:0% +run the equations there's a supply + + + align:start position:0% +run the equations there's a supply +equation and the demand equation where + + align:start position:0% +equation and the demand equation where + + + align:start position:0% +equation and the demand equation where +price and quantity appear on both + + align:start position:0% +price and quantity appear on both + + + align:start position:0% +price and quantity appear on both +sides so these are uh + + align:start position:0% +sides so these are uh + + + align:start position:0% +sides so these are uh +um examples of endogenity so whenever we + + align:start position:0% +um examples of endogenity so whenever we + + + align:start position:0% +um examples of endogenity so whenever we +have onogen + + align:start position:0% +have onogen + + + align:start position:0% +have onogen +we have a problem it's going to be + + align:start position:0% +we have a problem it's going to be + + + align:start position:0% +we have a problem it's going to be +difficult to come up with a control fun + + align:start position:0% +difficult to come up with a control fun + + + align:start position:0% +difficult to come up with a control fun +with a control coming from out you know + + align:start position:0% +with a control coming from out you know + + + align:start position:0% +with a control coming from out you know +using the strategy of adding a lot of + + align:start position:0% +using the strategy of adding a lot of + + + align:start position:0% +using the strategy of adding a lot of +x2s or even a difference in difference + + align:start position:0% +x2s or even a difference in difference + + + align:start position:0% +x2s or even a difference in difference +once there is + + align:start position:0% +once there is + + + align:start position:0% +once there is +endogenity uh and then there are also + + align:start position:0% +endogenity uh and then there are also + + + align:start position:0% +endogenity uh and then there are also +many cases where there is no strictly + + align:start position:0% +many cases where there is no strictly + + + align:start position:0% +many cases where there is no strictly +speaking onogen but there is just a very + + align:start position:0% +speaking onogen but there is just a very + + + align:start position:0% +speaking onogen but there is just a very +thorny omitted variable B and we know + + align:start position:0% +thorny omitted variable B and we know + + + align:start position:0% +thorny omitted variable B and we know +that there is no data set in which that + + align:start position:0% +that there is no data set in which that + + + align:start position:0% +that there is no data set in which that +data that variable is there it's not + + align:start position:0% +data that variable is there it's not + + + align:start position:0% +data that variable is there it's not +it's not an endogenity we we we would we + + align:start position:0% +it's not an endogenity we we we would we + + + align:start position:0% +it's not an endogenity we we we would we +could name and pinpoint the variable if + + align:start position:0% +could name and pinpoint the variable if + + + align:start position:0% +could name and pinpoint the variable if +we could but we just don't have + + align:start position:0% +we could but we just don't have + + + align:start position:0% +we could but we just don't have +it um and I'll give you one example of + + align:start position:0% +it um and I'll give you one example of + + + align:start position:0% +it um and I'll give you one example of +that that's going to be our sort of + + align:start position:0% +that that's going to be our sort of + + + align:start position:0% +that that's going to be our sort of +running example for + + align:start position:0% +running example for + + + align:start position:0% +running example for +today which is the benefits of Education + + align:start position:0% +today which is the benefits of Education + + + align:start position:0% +today which is the benefits of Education +you exactly the example that you you + + align:start position:0% +you exactly the example that you you + + + align:start position:0% +you exactly the example that you you +mentioned uh we know that there is a + + align:start position:0% +mentioned uh we know that there is a + + + align:start position:0% +mentioned uh we know that there is a +strong correlation between education and + + align:start position:0% +strong correlation between education and + + + align:start position:0% +strong correlation between education and +many outcomes uh of course knowledge + + align:start position:0% +many outcomes uh of course knowledge + + + align:start position:0% +many outcomes uh of course knowledge +earnings uh fertility or that's mostly + + align:start position:0% +earnings uh fertility or that's mostly + + + align:start position:0% +earnings uh fertility or that's mostly +in developing country but Health Etc of + + align:start position:0% +in developing country but Health Etc of + + + align:start position:0% +in developing country but Health Etc of +course if we upset serve uh if we + + align:start position:0% +course if we upset serve uh if we + + + align:start position:0% +course if we upset serve uh if we +interpret if we run a regression of any + + align:start position:0% +interpret if we run a regression of any + + + align:start position:0% +interpret if we run a regression of any +of this outcome on Education Without + + align:start position:0% +of this outcome on Education Without + + + align:start position:0% +of this outcome on Education Without +controlling for a number of stuff they + + align:start position:0% +controlling for a number of stuff they + + + align:start position:0% +controlling for a number of stuff they +might be biased exactly as you pointed + + align:start position:0% +might be biased exactly as you pointed + + + align:start position:0% +might be biased exactly as you pointed +out for example the family background + + align:start position:0% +out for example the family background + + + align:start position:0% +out for example the family background +might affect those outcomes later in + + align:start position:0% +might affect those outcomes later in + + + align:start position:0% +might affect those outcomes later in +life uh people kids who come from poorer + + align:start position:0% +life uh people kids who come from poorer + + + align:start position:0% +life uh people kids who come from poorer +backgrounds may have trouble uh finding + + align:start position:0% +backgrounds may have trouble uh finding + + + align:start position:0% +backgrounds may have trouble uh finding +a job for reasons of nothing to do with + + align:start position:0% +a job for reasons of nothing to do with + + + align:start position:0% +a job for reasons of nothing to do with +education but say because of networks + + align:start position:0% +education but say because of networks + + + align:start position:0% +education but say because of networks +and for this reason they'll have lower + + align:start position:0% +and for this reason they'll have lower + + + align:start position:0% +and for this reason they'll have lower +earnings uh so that's going to uh + + align:start position:0% +earnings uh so that's going to uh + + + align:start position:0% +earnings uh so that's going to uh +create an omitted VI omitted variable bi + + align:start position:0% +create an omitted VI omitted variable bi + + + align:start position:0% +create an omitted VI omitted variable bi +uh and and it might be very difficult to + + align:start position:0% +uh and and it might be very difficult to + + + align:start position:0% +uh and and it might be very difficult to +observe everything we need to know about + + align:start position:0% +observe everything we need to know about + + + align:start position:0% +observe everything we need to know about +the kids another one is just what we + + align:start position:0% +the kids another one is just what we + + + align:start position:0% +the kids another one is just what we +were discussing in case of the applying + + align:start position:0% +were discussing in case of the applying + + + align:start position:0% +were discussing in case of the applying +to college uh sort of spunk and drive + + align:start position:0% +to college uh sort of spunk and drive + + + align:start position:0% +to college uh sort of spunk and drive +and + + align:start position:0% +and + + + align:start position:0% +and +energy uh what Economist sometimes put + + align:start position:0% +energy uh what Economist sometimes put + + + align:start position:0% +energy uh what Economist sometimes put +under ability which you know is a little + + align:start position:0% +under ability which you know is a little + + + align:start position:0% +under ability which you know is a little +bit vague but you know people who are + + align:start position:0% +bit vague but you know people who are + + + align:start position:0% +bit vague but you know people who are +more energetic Etc smarter what not will + + align:start position:0% +more energetic Etc smarter what not will + + + align:start position:0% +more energetic Etc smarter what not will +find it easier to get get an education + + align:start position:0% +find it easier to get get an education + + + align:start position:0% +find it easier to get get an education +they might also do much better in life + + align:start position:0% +they might also do much better in life + + + align:start position:0% +they might also do much better in life +anyway even without the education there + + align:start position:0% +anyway even without the education there + + + align:start position:0% +anyway even without the education there +are cases like the the cases with a + + align:start position:0% +are cases like the the cases with a + + + align:start position:0% +are cases like the the cases with a +college application where we have a + + align:start position:0% +college application where we have a + + + align:start position:0% +college application where we have a +variable that's pretty good proxy for + + align:start position:0% +variable that's pretty good proxy for + + + align:start position:0% +variable that's pretty good proxy for +that but it's rare have to be uh we were + + align:start position:0% +that but it's rare have to be uh we were + + + align:start position:0% +that but it's rare have to be uh we were +quite lucky to have that so in this + + align:start position:0% +quite lucky to have that so in this + + + align:start position:0% +quite lucky to have that so in this +case you know my my first instinct to + + align:start position:0% +case you know my my first instinct to + + + align:start position:0% +case you know my my first instinct to +any such problem is to see whether we + + align:start position:0% +any such problem is to see whether we + + + align:start position:0% +any such problem is to see whether we +could run an RCT but in this case + + align:start position:0% +could run an RCT but in this case + + + align:start position:0% +could run an RCT but in this case +assigning education to people is not + + align:start position:0% +assigning education to people is not + + + align:start position:0% +assigning education to people is not +going to be possible because an + + align:start position:0% +going to be possible because an + + + align:start position:0% +going to be possible because an +education is like is really a choice uh + + align:start position:0% +education is like is really a choice uh + + + align:start position:0% +education is like is really a choice uh +you can't really Force kids to to stay + + align:start position:0% +you can't really Force kids to to stay + + + align:start position:0% +you can't really Force kids to to stay +in school past the point uh you can't uh + + align:start position:0% +in school past the point uh you can't uh + + + align:start position:0% +in school past the point uh you can't uh +and on the other hand you can't force + + align:start position:0% +and on the other hand you can't force + + + align:start position:0% +and on the other hand you can't force +parents not to send kids to school so + + align:start position:0% +parents not to send kids to school so + + + align:start position:0% +parents not to send kids to school so +that's you know it's closely linked to + + align:start position:0% +that's you know it's closely linked to + + + align:start position:0% +that's you know it's closely linked to +your personality and your choice and who + + align:start position:0% +your personality and your choice and who + + + align:start position:0% +your personality and your choice and who +you are so let's say we cannot assign + + align:start position:0% +you are so let's say we cannot assign + + + align:start position:0% +you are so let's say we cannot assign +randomly you get three years you get + + align:start position:0% +randomly you get three years you get + + + align:start position:0% +randomly you get three years you get +five years you get to go to secondary + + align:start position:0% +five years you get to go to secondary + + + align:start position:0% +five years you get to go to secondary +school or not okay we can't really do + + align:start position:0% +school or not okay we can't really do + + + align:start position:0% +school or not okay we can't really do +that + + align:start position:0% +that + + + align:start position:0% +that +easily so what can we + + align:start position:0% +easily so what can we + + + align:start position:0% +easily so what can we +do well instead of trying trying to + + align:start position:0% +do well instead of trying trying to + + + align:start position:0% +do well instead of trying trying to +assign education randomly we could try + + align:start position:0% +assign education randomly we could try + + + align:start position:0% +assign education randomly we could try +and assign students to a program which + + align:start position:0% +and assign students to a program which + + + align:start position:0% +and assign students to a program which +may lead her to get more + + align:start position:0% +may lead her to get more + + + align:start position:0% +may lead her to get more +education so what would be a an example + + align:start position:0% +education so what would be a an example + + + align:start position:0% +education so what would be a an example +of an education like of of an + + align:start position:0% +of an education like of of an + + + align:start position:0% +of an education like of of an +intervention like that that could be + + align:start position:0% +intervention like that that could be + + + align:start position:0% +intervention like that that could be +randomized uh that is going to lead some + + align:start position:0% +randomized uh that is going to lead some + + + align:start position:0% +randomized uh that is going to lead some +people to get on average going to lead + + align:start position:0% +people to get on average going to lead + + + align:start position:0% +people to get on average going to lead +some people who to get more education + + align:start position:0% +some people who to get more education + + + align:start position:0% +some people who to get more education +than if they had not received that + + align:start position:0% +than if they had not received that + + + align:start position:0% +than if they had not received that +particular + + align:start position:0% +particular + + + align:start position:0% +particular +intervention after school programs where + + align:start position:0% +intervention after school programs where + + + align:start position:0% +intervention after school programs where +enrollment is that yes so it could be an + + align:start position:0% +enrollment is that yes so it could be an + + + align:start position:0% +enrollment is that yes so it could be an +after school program for reasons I want + + align:start position:0% +after school program for reasons I want + + + align:start position:0% +after school program for reasons I want +to keep you I want you to keep this s in + + align:start position:0% +to keep you I want you to keep this s in + + + align:start position:0% +to keep you I want you to keep this s in +mind uh because uh for reason we're + + align:start position:0% +mind uh because uh for reason we're + + + align:start position:0% +mind uh because uh for reason we're +going to discuss in a minute it's not + + align:start position:0% +going to discuss in a minute it's not + + + align:start position:0% +going to discuss in a minute it's not +going to be a great + + align:start position:0% +going to be a great + + + align:start position:0% +going to be a great +instrument uh but uh it's still going to + + align:start position:0% +instrument uh but uh it's still going to + + + align:start position:0% +instrument uh but uh it's still going to +it could still affect whether the kids + + align:start position:0% +it could still affect whether the kids + + + align:start position:0% +it could still affect whether the kids +stay in school so let's keep after + + align:start position:0% +stay in school so let's keep after + + + align:start position:0% +stay in school so let's keep after +school education + + align:start position:0% +school education + + + align:start position:0% +school education +yeah free + + align:start position:0% +yeah free + + + align:start position:0% +yeah free +fre right so free something uh would uh + + align:start position:0% +fre right so free something uh would uh + + + align:start position:0% +fre right so free something uh would uh +would would free preschool or whatever + + align:start position:0% +would would free preschool or whatever + + + align:start position:0% +would would free preschool or whatever +level you're interested in free + + align:start position:0% +level you're interested in free + + + align:start position:0% +level you're interested in free +preschool or + + align:start position:0% +preschool or + + + align:start position:0% +preschool or +free school yeah free meals free meals + + align:start position:0% +free school yeah free meals free meals + + + align:start position:0% +free school yeah free meals free meals +exactly so let's keep that in mind as + + align:start position:0% +exactly so let's keep that in mind as + + + align:start position:0% +exactly so let's keep that in mind as +well campaigning and advertising + + align:start position:0% +well campaigning and advertising + + + align:start position:0% +well campaigning and advertising +campaigning information Etc try to + + align:start position:0% +campaigning information Etc try to + + + align:start position:0% +campaigning information Etc try to +convince for example there is quite a + + align:start position:0% +convince for example there is quite a + + + align:start position:0% +convince for example there is quite a +lot of evidence that parents may not be + + align:start position:0% +lot of evidence that parents may not be + + + align:start position:0% +lot of evidence that parents may not be +aware of the benefits of education so + + align:start position:0% +aware of the benefits of education so + + + align:start position:0% +aware of the benefits of education so +letting some people know what the + + align:start position:0% +letting some people know what the + + + align:start position:0% +letting some people know what the +benefits of Education are could be a way + + align:start position:0% +benefits of Education are could be a way + + + align:start position:0% +benefits of Education are could be a way +yeah access to technology like laptop + + align:start position:0% +yeah access to technology like laptop + + + align:start position:0% +yeah access to technology like laptop +program right I want to keep that one in + + align:start position:0% +program right I want to keep that one in + + + align:start position:0% +program right I want to keep that one in +mind because it's also going to create + + align:start position:0% +mind because it's also going to create + + + align:start position:0% +mind because it's also going to create +problems for us but that could affect + + align:start position:0% +problems for us but that could affect + + + align:start position:0% +problems for us but that could affect +education H um I'm not sure if this one + + align:start position:0% +education H um I'm not sure if this one + + + align:start position:0% +education H um I'm not sure if this one +fits and that's what I'm asking but is + + align:start position:0% +fits and that's what I'm asking but is + + + align:start position:0% +fits and that's what I'm asking but is +what about like regular Public School + + align:start position:0% +what about like regular Public School + + + align:start position:0% +what about like regular Public School +versus a charter where you have to get + + align:start position:0% +versus a charter where you have to get + + + align:start position:0% +versus a charter where you have to get +in by Lottery right so that is going to + + align:start position:0% +in by Lottery right so that is going to + + + align:start position:0% +in by Lottery right so that is going to +give us the effect of going to Charter + + align:start position:0% +give us the effect of going to Charter + + + align:start position:0% +give us the effect of going to Charter +School as opposed to the effect of + + align:start position:0% +School as opposed to the effect of + + + align:start position:0% +School as opposed to the effect of +regular Public School uh which is a very + + align:start position:0% +regular Public School uh which is a very + + + align:start position:0% +regular Public School uh which is a very +interesting and important question on + + align:start position:0% +interesting and important question on + + + align:start position:0% +interesting and important question on +its own but would probably be a + + align:start position:0% +its own but would probably be a + + + align:start position:0% +its own but would probably be a +different question but that's not that's + + align:start position:0% +different question but that's not that's + + + align:start position:0% +different question but that's not that's +not exactly because now I'm thinking + + align:start position:0% +not exactly because now I'm thinking + + + align:start position:0% +not exactly because now I'm thinking +about something that's going to vary + + align:start position:0% +about something that's going to vary + + + align:start position:0% +about something that's going to vary +whether you know the years of education + + align:start position:0% +whether you know the years of education + + + align:start position:0% +whether you know the years of education +literally that some kids get yeah + + align:start position:0% +literally that some kids get yeah + + + align:start position:0% +literally that some kids get yeah +rewards for attending school or for high + + align:start position:0% +rewards for attending school or for high + + + align:start position:0% +rewards for attending school or for high +performance right you could give uh you + + align:start position:0% +performance right you could give uh you + + + align:start position:0% +performance right you could give uh you +could give uh uh you could give + + align:start position:0% +could give uh uh you could give + + + align:start position:0% +could give uh uh you could give +incentive there again I want you to keep + + align:start position:0% +incentive there again I want you to keep + + + align:start position:0% +incentive there again I want you to keep +that in mind uh we'll go back to all + + align:start position:0% +that in mind uh we'll go back to all + + + align:start position:0% +that in mind uh we'll go back to all +these instruments so I I hope you can + + align:start position:0% +these instruments so I I hope you can + + + align:start position:0% +these instruments so I I hope you can +maintain a a mental list of all of the + + align:start position:0% +maintain a a mental list of all of the + + + align:start position:0% +maintain a a mental list of all of the +one because I want to go back and and + + align:start position:0% +one because I want to go back and and + + + align:start position:0% +one because I want to go back and and +reevaluate + + align:start position:0% +reevaluate + + + align:start position:0% +reevaluate +them uh the one I want to study today so + + align:start position:0% +them uh the one I want to study today so + + + align:start position:0% +them uh the one I want to study today so +so for for now the one I'm going to keep + + align:start position:0% +so for for now the one I'm going to keep + + + align:start position:0% +so for for now the one I'm going to keep +uh track on immediately is the is + + align:start position:0% +uh track on immediately is the is + + + align:start position:0% +uh track on immediately is the is +leisa's idea of uh of scholarships + + align:start position:0% +leisa's idea of uh of scholarships + + + align:start position:0% +leisa's idea of uh of scholarships +making making education free for some + + align:start position:0% +making making education free for some + + + align:start position:0% +making making education free for some +for some + + align:start position:0% +for some + + + align:start position:0% +for some +people uh so but whatever the + + align:start position:0% +people uh so but whatever the + + + align:start position:0% +people uh so but whatever the +intervention is uh that is going to + + align:start position:0% +intervention is uh that is going to + + + align:start position:0% +intervention is uh that is going to +affect + + align:start position:0% +affect + + + align:start position:0% +affect +education uh if that intervention has no + + align:start position:0% +education uh if that intervention has no + + + align:start position:0% +education uh if that intervention has no +no direct impact on earning if we're + + align:start position:0% +no direct impact on earning if we're + + + align:start position:0% +no direct impact on earning if we're +willing to make the assumption that that + + align:start position:0% +willing to make the assumption that that + + + align:start position:0% +willing to make the assumption that that +that uh that intervention in of its own + + align:start position:0% +that uh that intervention in of its own + + + align:start position:0% +that uh that intervention in of its own +would not affect earnings or cognitive + + align:start position:0% +would not affect earnings or cognitive + + + align:start position:0% +would not affect earnings or cognitive +scores or whatever you look + + align:start position:0% +scores or whatever you look + + + align:start position:0% +scores or whatever you look +at but you see that it affects earning + + align:start position:0% +at but you see that it affects earning + + + align:start position:0% +at but you see that it affects earning +that the people who got the the program + + align:start position:0% +that the people who got the the program + + + align:start position:0% +that the people who got the the program +are have higher cognitive scores or are + + align:start position:0% +are have higher cognitive scores or are + + + align:start position:0% +are have higher cognitive scores or are +have higher earnings or have lower + + align:start position:0% +have higher earnings or have lower + + + align:start position:0% +have higher earnings or have lower +fertility then you can iner that because + + align:start position:0% +fertility then you can iner that because + + + align:start position:0% +fertility then you can iner that because +you you're willing if you're willing to + + align:start position:0% +you you're willing if you're willing to + + + align:start position:0% +you you're willing if you're willing to +make the assumption that it has no + + align:start position:0% +make the assumption that it has no + + + align:start position:0% +make the assumption that it has no +direct effect on education uh then you + + align:start position:0% +direct effect on education uh then you + + + align:start position:0% +direct effect on education uh then you +can infer that it if affected on it has + + align:start position:0% +can infer that it if affected on it has + + + align:start position:0% +can infer that it if affected on it has +to be because it moved + + align:start position:0% +to be because it moved + + + align:start position:0% +to be because it moved +education uh so in other word there is a + + align:start position:0% +education uh so in other word there is a + + + align:start position:0% +education uh so in other word there is a +link between uh the intervention so here + + align:start position:0% +link between uh the intervention so here + + + align:start position:0% +link between uh the intervention so here +I'm going to call it + + align:start position:0% + + + + align:start position:0% + +scholarships affects uh + + align:start position:0% + + + + align:start position:0% + +education which affects uh final + + align:start position:0% +education which affects uh final + + + align:start position:0% +education which affects uh final +outcomes I'm going to write a number of + + align:start position:0% +outcomes I'm going to write a number of + + + align:start position:0% +outcomes I'm going to write a number of +cognitive + + align:start position:0% + + + + align:start position:0% + +score + + align:start position:0% + + + + align:start position:0% + +earnings + + align:start position:0% + + + + align:start position:0% + +attitude + + align:start position:0% +attitude + + + align:start position:0% +attitude +Etc uh suppose that you are willing to + + align:start position:0% +Etc uh suppose that you are willing to + + + align:start position:0% +Etc uh suppose that you are willing to +make the assumption that that link is + + align:start position:0% +make the assumption that that link is + + + align:start position:0% +make the assumption that that link is +not + + align:start position:0% + + + + align:start position:0% + +there and suppose the scholarships were + + align:start position:0% +there and suppose the scholarships were + + + align:start position:0% +there and suppose the scholarships were +randomly assigned such that you can + + align:start position:0% +randomly assigned such that you can + + + align:start position:0% +randomly assigned such that you can +really look at the effect of the + + align:start position:0% +really look at the effect of the + + + align:start position:0% +really look at the effect of the +scholarships on cognitive scores or + + align:start position:0% +scholarships on cognitive scores or + + + align:start position:0% +scholarships on cognitive scores or +earnings or attitude in a way that you + + align:start position:0% +earnings or attitude in a way that you + + + align:start position:0% +earnings or attitude in a way that you +really convince it's a nice causal + + align:start position:0% +really convince it's a nice causal + + + align:start position:0% +really convince it's a nice causal +effect then you can say well I see that + + align:start position:0% +effect then you can say well I see that + + + align:start position:0% +effect then you can say well I see that +scholarship affects earnings that the + + align:start position:0% +scholarship affects earnings that the + + + align:start position:0% +scholarship affects earnings that the +people who got the scholarships have + + align:start position:0% +people who got the scholarships have + + + align:start position:0% +people who got the scholarships have +higher earnings than people who didn't + + align:start position:0% +higher earnings than people who didn't + + + align:start position:0% +higher earnings than people who didn't +I'm willing to assume it's not because + + align:start position:0% +I'm willing to assume it's not because + + + align:start position:0% +I'm willing to assume it's not because +of the scholarship themselves then it + + align:start position:0% +of the scholarship themselves then it + + + align:start position:0% +of the scholarship themselves then it +has to be because of + + align:start position:0% +has to be because of + + + align:start position:0% +has to be because of +education and because of that I can + + align:start position:0% +education and because of that I can + + + align:start position:0% +education and because of that I can +infair what the effect of education is + + align:start position:0% +infair what the effect of education is + + + align:start position:0% +infair what the effect of education is +without really using any uh endogenous + + align:start position:0% +without really using any uh endogenous + + + align:start position:0% +without really using any uh endogenous +variation in + + align:start position:0% +variation in + + + align:start position:0% +variation in +education so that's basically the name + + align:start position:0% +education so that's basically the name + + + align:start position:0% +education so that's basically the name +of the game now I'm going to formalize + + align:start position:0% +of the game now I'm going to formalize + + + align:start position:0% +of the game now I'm going to formalize +this this Insight so if it's if it went + + align:start position:0% +this this Insight so if it's if it went + + + align:start position:0% +this this Insight so if it's if it went +fast don't worry about it we're going to + + align:start position:0% +fast don't worry about it we're going to + + + align:start position:0% +fast don't worry about it we're going to +now go very slowly through this uh we + + align:start position:0% +now go very slowly through this uh we + + + align:start position:0% +now go very slowly through this uh we +are using uh a scholarship as an in + + align:start position:0% +are using uh a scholarship as an in + + + align:start position:0% +are using uh a scholarship as an in +instrument for Education which is + + align:start position:0% +instrument for Education which is + + + align:start position:0% +instrument for Education which is +something that makes education move uh + + align:start position:0% +something that makes education move uh + + + align:start position:0% +something that makes education move uh +that we can exploit in order to look at + + align:start position:0% +that we can exploit in order to look at + + + align:start position:0% +that we can exploit in order to look at +the causal effect of + + align:start position:0% +the causal effect of + + + align:start position:0% +the causal effect of +Education that's the that's the plan uh + + align:start position:0% +Education that's the that's the plan uh + + + align:start position:0% +Education that's the that's the plan uh +so I'll give you uh and we are going to + + align:start position:0% +so I'll give you uh and we are going to + + + align:start position:0% +so I'll give you uh and we are going to +do that with today with an example that + + align:start position:0% +do that with today with an example that + + + align:start position:0% +do that with today with an example that +uh that I worked on with Pascal IND dupa + + align:start position:0% +uh that I worked on with Pascal IND dupa + + + align:start position:0% +uh that I worked on with Pascal IND dupa +and Michael ker where we actually + + align:start position:0% +and Michael ker where we actually + + + align:start position:0% +and Michael ker where we actually +randomly assigned scholarships for + + align:start position:0% +randomly assigned scholarships for + + + align:start position:0% +randomly assigned scholarships for +secondary + + align:start position:0% +secondary + + + align:start position:0% +secondary +school so the question we want to to + + align:start position:0% +school so the question we want to to + + + align:start position:0% +school so the question we want to to +look at is whether education affects uh + + align:start position:0% +look at is whether education affects uh + + + align:start position:0% +look at is whether education affects uh +cognitive scores and wages WR um Yi as + + align:start position:0% +cognitive scores and wages WR um Yi as + + + align:start position:0% +cognitive scores and wages WR um Yi as +the as the outcome for historical reason + + align:start position:0% +the as the outcome for historical reason + + + align:start position:0% +the as the outcome for historical reason +it's I I call AI the + + align:start position:0% +it's I I call AI the + + + align:start position:0% +it's I I call AI the +education uh so that's our education + + align:start position:0% +education uh so that's our education + + + align:start position:0% +education uh so that's our education +outcome so in this case it's going to be + + align:start position:0% +outcome so in this case it's going to be + + + align:start position:0% +outcome so in this case it's going to be +whether the kids attend secondary school + + align:start position:0% +whether the kids attend secondary school + + + align:start position:0% +whether the kids attend secondary school +or not the variable equal one whether + + align:start position:0% +or not the variable equal one whether + + + align:start position:0% +or not the variable equal one whether +the kids attend secondary school or not + + align:start position:0% +the kids attend secondary school or not + + + align:start position:0% +the kids attend secondary school or not +and why is earnings or cognitive scores + + align:start position:0% +and why is earnings or cognitive scores + + + align:start position:0% +and why is earnings or cognitive scores +I'm going to do it do it uh with both + + align:start position:0% +I'm going to do it do it uh with both + + + align:start position:0% +I'm going to do it do it uh with both +cognitive scores and + + align:start position:0% +cognitive scores and + + + align:start position:0% +cognitive scores and +earnings + + align:start position:0% +earnings + + + align:start position:0% +earnings +and uh I'm not willing to make the + + align:start position:0% +and uh I'm not willing to make the + + + align:start position:0% +and uh I'm not willing to make the +assumption that uh the um that Epsilon I + + align:start position:0% +assumption that uh the um that Epsilon I + + + align:start position:0% +assumption that uh the um that Epsilon I +is independent of AI That's the big + + align:start position:0% +is independent of AI That's the big + + + align:start position:0% +is independent of AI That's the big +difference between what we the setting + + align:start position:0% +difference between what we the setting + + + align:start position:0% +difference between what we the setting +we have now and what we looked at before + + align:start position:0% +we have now and what we looked at before + + + align:start position:0% +we have now and what we looked at before +because in there there is an omitted + + align:start position:0% +because in there there is an omitted + + + align:start position:0% +because in there there is an omitted +variable problems I don't have the + + align:start position:0% +variable problems I don't have the + + + align:start position:0% +variable problems I don't have the +variable which is ability or spunk or + + align:start position:0% +variable which is ability or spunk or + + + align:start position:0% +variable which is ability or spunk or +network connections or whatever goes + + align:start position:0% +network connections or whatever goes + + + align:start position:0% +network connections or whatever goes +with the background so in the absence of + + align:start position:0% +with the background so in the absence of + + + align:start position:0% +with the background so in the absence of +that I know that if I estimate dis + + align:start position:0% +that I know that if I estimate dis + + + align:start position:0% +that I know that if I estimate dis +equation would be best uh beta would be + + align:start position:0% +equation would be best uh beta would be + + + align:start position:0% +equation would be best uh beta would be +best uh one + + align:start position:0% +best uh one + + + align:start position:0% +best uh one +note this assumes that the effect of + + align:start position:0% +note this assumes that the effect of + + + align:start position:0% +note this assumes that the effect of +education is the same on all PE on on + + align:start position:0% +education is the same on all PE on on + + + align:start position:0% +education is the same on all PE on on +everybody so there is a coefficient + + align:start position:0% +everybody so there is a coefficient + + + align:start position:0% +everybody so there is a coefficient +better + + align:start position:0% +better + + + align:start position:0% +better +um we may not like this assumption + + align:start position:0% +um we may not like this assumption + + + align:start position:0% +um we may not like this assumption +because education might be more + + align:start position:0% +because education might be more + + + align:start position:0% +because education might be more +effective for some people than some + + align:start position:0% +effective for some people than some + + + align:start position:0% +effective for some people than some +others so we'll discuss how to interpret + + align:start position:0% +others so we'll discuss how to interpret + + + align:start position:0% +others so we'll discuss how to interpret +IV when that assumption is not correct + + align:start position:0% +IV when that assumption is not correct + + + align:start position:0% +IV when that assumption is not correct +uh in a bit later in this + + align:start position:0% +uh in a bit later in this + + + align:start position:0% +uh in a bit later in this +lecture uh but this is otherwise this is + + align:start position:0% +lecture uh but this is otherwise this is + + + align:start position:0% +lecture uh but this is otherwise this is +not this is a model that should be + + align:start position:0% +not this is a model that should be + + + align:start position:0% +not this is a model that should be +familiar after all the econometric Swift + + align:start position:0% +familiar after all the econometric Swift + + + align:start position:0% +familiar after all the econometric Swift +scene and we really interested in a caal + + align:start position:0% +scene and we really interested in a caal + + + align:start position:0% +scene and we really interested in a caal +estimate of + + align:start position:0% + + + + align:start position:0% + +better um so what did we do we uh we + + align:start position:0% +better um so what did we do we uh we + + + align:start position:0% +better um so what did we do we uh we +went to Ghana where um primary in junior + + align:start position:0% +went to Ghana where um primary in junior + + + align:start position:0% +went to Ghana where um primary in junior +high school is are free and there is a + + align:start position:0% +high school is are free and there is a + + + align:start position:0% +high school is are free and there is a +big Gateway exam after junior high + + align:start position:0% +big Gateway exam after junior high + + + align:start position:0% +big Gateway exam after junior high +school and you can only go to secondary + + align:start position:0% +school and you can only go to secondary + + + align:start position:0% +school and you can only go to secondary +school if you qualify but in addition + + align:start position:0% +school if you qualify but in addition + + + align:start position:0% +school if you qualify but in addition +it's very expensive so it goes from you + + align:start position:0% +it's very expensive so it goes from you + + + align:start position:0% +it's very expensive so it goes from you +go from free primary and Junior High to + + align:start position:0% +go from free primary and Junior High to + + + align:start position:0% +go from free primary and Junior High to +very expensive secondary school for + + align:start position:0% +very expensive secondary school for + + + align:start position:0% +very expensive secondary school for +people who + + align:start position:0% +people who + + + align:start position:0% +people who +qualify so what we did is we went to a + + align:start position:0% +qualify so what we did is we went to a + + + align:start position:0% +qualify so what we did is we went to a +bunch of kids who had + + align:start position:0% +bunch of kids who had + + + align:start position:0% +bunch of kids who had +qualified but had not enrolled uh by + + align:start position:0% +qualified but had not enrolled uh by + + + align:start position:0% +qualified but had not enrolled uh by +September and uh we could know that by + + align:start position:0% +September and uh we could know that by + + + align:start position:0% +September and uh we could know that by +looking at by going back to the Jun all + + align:start position:0% +looking at by going back to the Jun all + + + align:start position:0% +looking at by going back to the Jun all +the junior high school where they + + align:start position:0% +the junior high school where they + + + align:start position:0% +the junior high school where they +attended and find out information about + + align:start position:0% +attended and find out information about + + + align:start position:0% +attended and find out information about +them we we had thisare a big set of kids + + align:start position:0% +them we we had thisare a big set of kids + + + align:start position:0% +them we we had thisare a big set of kids +uh who had qualified for secondary + + align:start position:0% +uh who had qualified for secondary + + + align:start position:0% +uh who had qualified for secondary +school but didn't + + align:start position:0% +school but didn't + + + align:start position:0% +school but didn't +go and uh it's pretty common in Ghana to + + align:start position:0% +go and uh it's pretty common in Ghana to + + + align:start position:0% +go and uh it's pretty common in Ghana to +show up late in secondary school to show + + align:start position:0% +show up late in secondary school to show + + + align:start position:0% +show up late in secondary school to show +up in January instead of September + + align:start position:0% +up in January instead of September + + + align:start position:0% +up in January instead of September +because you finally you managed to + + align:start position:0% +because you finally you managed to + + + align:start position:0% +because you finally you managed to +gather the money so what we did is we + + align:start position:0% +gather the money so what we did is we + + + align:start position:0% +gather the money so what we did is we +went to see them in September and say + + align:start position:0% +went to see them in September and say + + + align:start position:0% +went to see them in September and say +hey um so we we we took that a sample of + + align:start position:0% +hey um so we we we took that a sample of + + + align:start position:0% +hey um so we we we took that a sample of +about 3,000 kids and we randomly + + align:start position:0% +about 3,000 kids and we randomly + + + align:start position:0% +about 3,000 kids and we randomly +selected about thousand of them and we + + align:start position:0% +selected about thousand of them and we + + + align:start position:0% +selected about thousand of them and we +went to hey if you want we have a + + align:start position:0% +went to hey if you want we have a + + + align:start position:0% +went to hey if you want we have a +scholarship for you to go to secondary + + align:start position:0% +scholarship for you to go to secondary + + + align:start position:0% +scholarship for you to go to secondary +school for your uh which is going to + + align:start position:0% +school for your uh which is going to + + + align:start position:0% +school for your uh which is going to +cover the the four years of secondary + + align:start position:0% +cover the the four years of secondary + + + align:start position:0% +cover the the four years of secondary +school uh so I want you I don't to call + + align:start position:0% +school uh so I want you I don't to call + + + align:start position:0% +school uh so I want you I don't to call +this variable Z which is D equal to one + + align:start position:0% +this variable Z which is D equal to one + + + align:start position:0% +this variable Z which is D equal to one +if you are assigned to the treatment + + align:start position:0% +if you are assigned to the treatment + + + align:start position:0% +if you are assigned to the treatment +group and we offered the scholarship and + + align:start position:0% +group and we offered the scholarship and + + + align:start position:0% +group and we offered the scholarship and +zero + + align:start position:0% +zero + + + align:start position:0% +zero +otherwise so this Z1 is randomly + + align:start position:0% +otherwise so this Z1 is randomly + + + align:start position:0% +otherwise so this Z1 is randomly +assigned because we randomly selected in + + align:start position:0% +assigned because we randomly selected in + + + align:start position:0% +assigned because we randomly selected in +our little office who we would go with + + align:start position:0% +our little office who we would go with + + + align:start position:0% +our little office who we would go with +saying hi uh can we get collect some + + align:start position:0% +saying hi uh can we get collect some + + + align:start position:0% +saying hi uh can we get collect some +data about you or hi can we collect some + + align:start position:0% +data about you or hi can we collect some + + + align:start position:0% +data about you or hi can we collect some +data about you and then oh by the way we + + align:start position:0% +data about you and then oh by the way we + + + align:start position:0% +data about you and then oh by the way we +have a scholarship for you and then what + + align:start position:0% +have a scholarship for you and then what + + + align:start position:0% +have a scholarship for you and then what +we did is that we followed them because + + align:start position:0% +we did is that we followed them because + + + align:start position:0% +we did is that we followed them because +we did that uh in 2008 and we've been + + align:start position:0% +we did that uh in 2008 and we've been + + + align:start position:0% +we did that uh in 2008 and we've been +following them since then so in first we + + align:start position:0% +following them since then so in first we + + + align:start position:0% +following them since then so in first we +had to wait till they left school uh so + + align:start position:0% +had to wait till they left school uh so + + + align:start position:0% +had to wait till they left school uh so +which they did in 2012 and then since + + align:start position:0% +which they did in 2012 and then since + + + align:start position:0% +which they did in 2012 and then since +2013 we've been interviewing them + + align:start position:0% +2013 we've been interviewing them + + + align:start position:0% +2013 we've been interviewing them +regularly both The Losers of the + + align:start position:0% +regularly both The Losers of the + + + align:start position:0% +regularly both The Losers of the +scholarship the people wouldn't get it + + align:start position:0% +scholarship the people wouldn't get it + + + align:start position:0% +scholarship the people wouldn't get it +and the + + align:start position:0% +and the + + + align:start position:0% +and the +winners so uh getting the scholarship + + align:start position:0% +winners so uh getting the scholarship + + + align:start position:0% +winners so uh getting the scholarship +uh does not translate into a onetoone + + align:start position:0% +uh does not translate into a onetoone + + + align:start position:0% +uh does not translate into a onetoone +relationship between going to school + + align:start position:0% +relationship between going to school + + + align:start position:0% +relationship between going to school +because most of people who got the + + align:start position:0% +because most of people who got the + + + align:start position:0% +because most of people who got the +scholarship did go to secondary school + + align:start position:0% +scholarship did go to secondary school + + + align:start position:0% +scholarship did go to secondary school +but not everyone some of them by that + + align:start position:0% +but not everyone some of them by that + + + align:start position:0% +but not everyone some of them by that +time decided that they were not + + align:start position:0% +time decided that they were not + + + align:start position:0% +time decided that they were not +interested anymore and on the other side + + align:start position:0% +interested anymore and on the other side + + + align:start position:0% +interested anymore and on the other side +a bunch of the kids who didn't get the + + align:start position:0% +a bunch of the kids who didn't get the + + + align:start position:0% +a bunch of the kids who didn't get the +scholarship managed to find some other + + align:start position:0% +scholarship managed to find some other + + + align:start position:0% +scholarship managed to find some other +way to pay for secondary school so they + + align:start position:0% +way to pay for secondary school so they + + + align:start position:0% +way to pay for secondary school so they +got they cobbled their money together or + + align:start position:0% +got they cobbled their money together or + + + align:start position:0% +got they cobbled their money together or +they got some other scholarships or + + align:start position:0% +they got some other scholarships or + + + align:start position:0% +they got some other scholarships or +something like + + align:start position:0% +something like + + + align:start position:0% +something like +that so uh what we have have here and + + align:start position:0% +that so uh what we have have here and + + + align:start position:0% +that so uh what we have have here and +that's going to be the structure of the + + align:start position:0% +that's going to be the structure of the + + + align:start position:0% +that's going to be the structure of the +table for for a lot of today is we are + + align:start position:0% +table for for a lot of today is we are + + + align:start position:0% +table for for a lot of today is we are +looking at uh boys and girls separately + + align:start position:0% +looking at uh boys and girls separately + + + align:start position:0% +looking at uh boys and girls separately +and we're looking at uh um um their um + + align:start position:0% +and we're looking at uh um um their um + + + align:start position:0% +and we're looking at uh um um their um +their outcome so this is the the average + + align:start position:0% +their outcome so this is the the average + + + align:start position:0% +their outcome so this is the the average +the sample average uh in the treatment + + align:start position:0% +the sample average uh in the treatment + + + align:start position:0% +the sample average uh in the treatment +group in the control group the + + align:start position:0% +group in the control group the + + + align:start position:0% +group in the control group the +difference with the standard error are + + align:start position:0% +difference with the standard error are + + + align:start position:0% +difference with the standard error are +the uh sample average for the treatment + + align:start position:0% +the uh sample average for the treatment + + + align:start position:0% +the uh sample average for the treatment +group control group the difference with + + align:start position:0% +group control group the difference with + + + align:start position:0% +group control group the difference with +the standard ER and what you see is that + + align:start position:0% +the standard ER and what you see is that + + + align:start position:0% +the standard ER and what you see is that +so first of all it's not going to mean + + align:start position:0% +so first of all it's not going to mean + + + align:start position:0% +so first of all it's not going to mean +anything to you uh but uh give me a + + align:start position:0% +anything to you uh but uh give me a + + + align:start position:0% +anything to you uh but uh give me a +moment of of admiration for the fact + + align:start position:0% +moment of of admiration for the fact + + + align:start position:0% +moment of of admiration for the fact +that we found back 97% of the kids in + + align:start position:0% +that we found back 97% of the kids in + + + align:start position:0% +that we found back 97% of the kids in +2013 we found back 97% of the kid that + + align:start position:0% +2013 we found back 97% of the kid that + + + align:start position:0% +2013 we found back 97% of the kid that +we had identified in 2008 and remember + + align:start position:0% +we had identified in 2008 and remember + + + align:start position:0% +we had identified in 2008 and remember +adolescents are mobile because this is + + align:start position:0% +adolescents are mobile because this is + + + align:start position:0% +adolescents are mobile because this is +the moment where they will leave and go + + align:start position:0% +the moment where they will leave and go + + + align:start position:0% +the moment where they will leave and go +work elsewhere uh so that was a pretty + + align:start position:0% +work elsewhere uh so that was a pretty + + + align:start position:0% +work elsewhere uh so that was a pretty +good tracking rate it's important + + align:start position:0% +good tracking rate it's important + + + align:start position:0% +good tracking rate it's important +because when you don't track people + + align:start position:0% +because when you don't track people + + + align:start position:0% +because when you don't track people +espe especially not equally the people + + align:start position:0% +espe especially not equally the people + + + align:start position:0% +espe especially not equally the people +who remain are + + align:start position:0% +who remain are + + + align:start position:0% +who remain are +not necessarily representative of the + + align:start position:0% +not necessarily representative of the + + + align:start position:0% +not necessarily representative of the +initial population okay so here we don't + + align:start position:0% +initial population okay so here we don't + + + align:start position:0% +initial population okay so here we don't +have that problem so we can now forget + + align:start position:0% +have that problem so we can now forget + + + align:start position:0% +have that problem so we can now forget +about it uh and then we can see that uh + + align:start position:0% +about it uh and then we can see that uh + + + align:start position:0% +about it uh and then we can see that uh +78% of the treatment group ever enrolled + + align:start position:0% +78% of the treatment group ever enrolled + + + align:start position:0% +78% of the treatment group ever enrolled +to secondary school and only 45% of the + + align:start position:0% +to secondary school and only 45% of the + + + align:start position:0% +to secondary school and only 45% of the +control group of the treatment group are + + align:start position:0% +control group of the treatment group are + + + align:start position:0% +control group of the treatment group are +58% of the treatment group completed + + align:start position:0% +58% of the treatment group completed + + + align:start position:0% +58% of the treatment group completed +Primary School uh 24% of the control + + align:start position:0% +Primary School uh 24% of the control + + + align:start position:0% +Primary School uh 24% of the control +group completed primary school so that + + align:start position:0% +group completed primary school so that + + + align:start position:0% +group completed primary school so that +gives us a difference of about 33% for + + align:start position:0% +gives us a difference of about 33% for + + + align:start position:0% +gives us a difference of about 33% for +the wom and 38% for the for the men uh + + align:start position:0% +the wom and 38% for the for the men uh + + + align:start position:0% +the wom and 38% for the for the men uh +similarly you see that more women didn't + + align:start position:0% +similarly you see that more women didn't + + + align:start position:0% +similarly you see that more women didn't +go even though they got the scholarship + + align:start position:0% +go even though they got the scholarship + + + align:start position:0% +go even though they got the scholarship +than men uh and almost all the boys + + align:start position:0% +than men uh and almost all the boys + + + align:start position:0% +than men uh and almost all the boys +basically took took um took a chance to + + align:start position:0% +basically took took um took a chance to + + + align:start position:0% +basically took took um took a chance to +get the scholarships so we get this uh + + align:start position:0% +get the scholarships so we get this uh + + + align:start position:0% +get the scholarships so we get this uh +this difference and this is really the + + align:start position:0% +this difference and this is really the + + + align:start position:0% +this difference and this is really the +causal effect of getting the scholarship + + align:start position:0% +causal effect of getting the scholarship + + + align:start position:0% +causal effect of getting the scholarship +on going to secondary school because + + align:start position:0% +on going to secondary school because + + + align:start position:0% +on going to secondary school because +that's uh that that was randomly + + align:start position:0% +that's uh that that was randomly + + + align:start position:0% +that's uh that that was randomly +assigned so that's + + align:start position:0% +assigned so that's + + + align:start position:0% +assigned so that's +nice uh now I want to combine uh this + + align:start position:0% +nice uh now I want to combine uh this + + + align:start position:0% +nice uh now I want to combine uh this +equation which is the causal the the my + + align:start position:0% +equation which is the causal the the my + + + align:start position:0% +equation which is the causal the the my +my causal effect model to uh uh uh with + + align:start position:0% +my causal effect model to uh uh uh with + + + align:start position:0% +my causal effect model to uh uh uh with +this data which is the fact that uh uh + + align:start position:0% +this data which is the fact that uh uh + + + align:start position:0% +this data which is the fact that uh uh +the the scholarship did cause some + + align:start position:0% +the the scholarship did cause some + + + align:start position:0% +the the scholarship did cause some +people to be more likely to go to super + + align:start position:0% +people to be more likely to go to super + + + align:start position:0% +people to be more likely to go to super +high school so + + align:start position:0% +high school so + + + align:start position:0% +high school so +uh let's combine the two in the in in + + align:start position:0% +uh let's combine the two in the in in + + + align:start position:0% +uh let's combine the two in the in in +the with the expectation notation that + + align:start position:0% +the with the expectation notation that + + + align:start position:0% +the with the expectation notation that +we introduced when we talked about + + align:start position:0% +we introduced when we talked about + + + align:start position:0% +we introduced when we talked about +causality so the effect of the treatment + + align:start position:0% +causality so the effect of the treatment + + + align:start position:0% +causality so the effect of the treatment +and participation can be measured by the + + align:start position:0% +and participation can be measured by the + + + align:start position:0% +and participation can be measured by the +uh expectation of going to school given + + align:start position:0% +uh expectation of going to school given + + + align:start position:0% +uh expectation of going to school given +that you got the scholarship minus the + + align:start position:0% +that you got the scholarship minus the + + + align:start position:0% +that you got the scholarship minus the +expectation of going to school given + + align:start position:0% +expectation of going to school given + + + align:start position:0% +expectation of going to school given +that you didn't so for example for girls + + align:start position:0% +that you didn't so for example for girls + + + align:start position:0% +that you didn't so for example for girls +what is this difference what is this + + align:start position:0% +what is this difference what is this + + + align:start position:0% +what is this difference what is this +number this difference 33% exactly so uh + + align:start position:0% +number this difference 33% exactly so uh + + + align:start position:0% +number this difference 33% exactly so uh +now we can look at the effect of the + + align:start position:0% +now we can look at the effect of the + + + align:start position:0% +now we can look at the effect of the +treatment on cognitive stest scores or + + align:start position:0% +treatment on cognitive stest scores or + + + align:start position:0% +treatment on cognitive stest scores or +whatever you're interested in I'll show + + align:start position:0% +whatever you're interested in I'll show + + + align:start position:0% +whatever you're interested in I'll show +that to you in a right away uh this is + + align:start position:0% +that to you in a right away uh this is + + + align:start position:0% +that to you in a right away uh this is +no this is still cognitive outcomes + + align:start position:0% +no this is still cognitive outcomes + + + align:start position:0% +no this is still cognitive outcomes +that's cognitive + + align:start position:0% +that's cognitive + + + align:start position:0% +that's cognitive +scores uh total standardized scores over + + align:start position:0% +scores uh total standardized scores over + + + align:start position:0% +scores uh total standardized scores over +here this is standardized to be so it's + + align:start position:0% +here this is standardized to be so it's + + + align:start position:0% +here this is standardized to be so it's +all it's in standard deviation of the + + align:start position:0% +all it's in standard deviation of the + + + align:start position:0% +all it's in standard deviation of the +overall distribution and you can see + + align:start position:0% +overall distribution and you can see + + + align:start position:0% +overall distribution and you can see +that for uh uh uh + + align:start position:0% +that for uh uh uh + + + align:start position:0% +that for uh uh uh +women in the control group they perform + + align:start position:0% +women in the control group they perform + + + align:start position:0% +women in the control group they perform +less well than boys so they they they in + + align:start position:0% +less well than boys so they they they in + + + align:start position:0% +less well than boys so they they they in +the control group they have a standard + + align:start position:0% +the control group they have a standard + + + align:start position:0% +the control group they have a standard +Dev of minus 7 17 uh in the treatment + + align:start position:0% +Dev of minus 7 17 uh in the treatment + + + align:start position:0% +Dev of minus 7 17 uh in the treatment +group it's about zero so the difference + + align:start position:0% +group it's about zero so the difference + + + align:start position:0% +group it's about zero so the difference +between the two is 18 standard deviation + + align:start position:0% +between the two is 18 standard deviation + + + align:start position:0% +between the two is 18 standard deviation +of uh of test scores it's just a unit of + + align:start position:0% +of uh of test scores it's just a unit of + + + align:start position:0% +of uh of test scores it's just a unit of +test scores 18 standard deviation for + + align:start position:0% +test scores 18 standard deviation for + + + align:start position:0% +test scores 18 standard deviation for +the woman and for the men likewise we + + align:start position:0% +the woman and for the men likewise we + + + align:start position:0% +the woman and for the men likewise we +see that the uh the treatment group is + + align:start position:0% +see that the uh the treatment group is + + + align:start position:0% +see that the uh the treatment group is +point 30 standard deviation control mean + + align:start position:0% +point 30 standard deviation control mean + + + align:start position:0% +point 30 standard deviation control mean +is 18 standard so the difference is uh + + align:start position:0% +is 18 standard so the difference is uh + + + align:start position:0% +is 18 standard so the difference is uh +0.125 uh so that gives us the effect of + + align:start position:0% +0.125 uh so that gives us the effect of + + + align:start position:0% +0.125 uh so that gives us the effect of +the scholarship on uh test scores and we + + align:start position:0% +the scholarship on uh test scores and we + + + align:start position:0% +the scholarship on uh test scores and we +know again this is caal effect because + + align:start position:0% +know again this is caal effect because + + + align:start position:0% +know again this is caal effect because +our scholarship are still randomly + + align:start position:0% +our scholarship are still randomly + + + align:start position:0% +our scholarship are still randomly +assigned so this is really is the causal + + align:start position:0% +assigned so this is really is the causal + + + align:start position:0% +assigned so this is really is the causal +effect of winning the scholarship on + + align:start position:0% +effect of winning the scholarship on + + + align:start position:0% +effect of winning the scholarship on +test scores but of course that's not the + + align:start position:0% +test scores but of course that's not the + + + align:start position:0% +test scores but of course that's not the +effect of education on test scores + + align:start position:0% +effect of education on test scores + + + align:start position:0% +effect of education on test scores +because not the difference is not one + + align:start position:0% +because not the difference is not one + + + align:start position:0% +because not the difference is not one +for one between getting a scholarship + + align:start position:0% +for one between getting a scholarship + + + align:start position:0% +for one between getting a scholarship +and U and uh and going to school so we + + align:start position:0% +and U and uh and going to school so we + + + align:start position:0% +and U and uh and going to school so we +could be interested in U in just that + + align:start position:0% +could be interested in U in just that + + + align:start position:0% +could be interested in U in just that +you know if I give people if I go around + + align:start position:0% +you know if I give people if I go around + + + align:start position:0% +you know if I give people if I go around +and offer people scholarships to go to + + align:start position:0% +and offer people scholarships to go to + + + align:start position:0% +and offer people scholarships to go to +secondary school what is going to be the + + align:start position:0% +secondary school what is going to be the + + + align:start position:0% +secondary school what is going to be the +final impact on test scores or wages or + + align:start position:0% +final impact on test scores or wages or + + + align:start position:0% +final impact on test scores or wages or +anything you're interested in sometimes + + align:start position:0% +anything you're interested in sometimes + + + align:start position:0% +anything you're interested in sometimes +that's what we are interested in but it + + align:start position:0% +that's what we are interested in but it + + + align:start position:0% +that's what we are interested in but it +is not necessarily the question of + + align:start position:0% +is not necessarily the question of + + + align:start position:0% +is not necessarily the question of +interest because for example the + + align:start position:0% +interest because for example the + + + align:start position:0% +interest because for example the +government might be interested in other + + align:start position:0% +government might be interested in other + + + align:start position:0% +government might be interested in other +ways to expand access to education for + + align:start position:0% +ways to expand access to education for + + + align:start position:0% +ways to expand access to education for +example uh uh building more schools or + + align:start position:0% +example uh uh building more schools or + + + align:start position:0% +example uh uh building more schools or +making it cheaper Etc so you might be + + align:start position:0% +making it cheaper Etc so you might be + + + align:start position:0% +making it cheaper Etc so you might be +interested in the causal effect of + + align:start position:0% +interested in the causal effect of + + + align:start position:0% +interested in the causal effect of +actually going to schools so now let's + + align:start position:0% +actually going to schools so now let's + + + align:start position:0% +actually going to schools so now let's +see how we can combine the fact that we + + align:start position:0% +see how we can combine the fact that we + + + align:start position:0% +see how we can combine the fact that we +have an effect of scholarship on going + + align:start position:0% +have an effect of scholarship on going + + + align:start position:0% +have an effect of scholarship on going +to school and an effect of scholarship + + align:start position:0% +to school and an effect of scholarship + + + align:start position:0% +to school and an effect of scholarship +on test scores to look at whether we can + + align:start position:0% +on test scores to look at whether we can + + + align:start position:0% +on test scores to look at whether we can +get a good estimate of the causal effect + + align:start position:0% +get a good estimate of the causal effect + + + align:start position:0% +get a good estimate of the causal effect +of going to schools on test scores so + + align:start position:0% +of going to schools on test scores so + + + align:start position:0% +of going to schools on test scores so +for that yeah for that let's combine uh + + align:start position:0% +for that yeah for that let's combine uh + + + align:start position:0% +for that yeah for that let's combine uh +these two expressions with our uh + + align:start position:0% +these two expressions with our uh + + + align:start position:0% +these two expressions with our uh +expression for + + align:start position:0% +expression for + + + align:start position:0% +expression for +yi so we know that uh Y is Alpha plus + + align:start position:0% +yi so we know that uh Y is Alpha plus + + + align:start position:0% +yi so we know that uh Y is Alpha plus +beta a i plus Epsilon I so I'm just + + align:start position:0% +beta a i plus Epsilon I so I'm just + + + align:start position:0% +beta a i plus Epsilon I so I'm just +going to put expectations around that + + align:start position:0% +going to put expectations around that + + + align:start position:0% +going to put expectations around that +for the treatment group so the + + align:start position:0% +for the treatment group so the + + + align:start position:0% +for the treatment group so the +expectation of Yi given z i equal 1 is + + align:start position:0% +expectation of Yi given z i equal 1 is + + + align:start position:0% +expectation of Yi given z i equal 1 is +Alpha plus beta the expectation of a I + + align:start position:0% +Alpha plus beta the expectation of a I + + + align:start position:0% +Alpha plus beta the expectation of a I +given that Z equal 1 plus the + + align:start position:0% +given that Z equal 1 plus the + + + align:start position:0% +given that Z equal 1 plus the +expectation of e Epsilon I given that Z + + align:start position:0% +expectation of e Epsilon I given that Z + + + align:start position:0% +expectation of e Epsilon I given that Z +equal one okay I can do that I'm going + + align:start position:0% +equal one okay I can do that I'm going + + + align:start position:0% +equal one okay I can do that I'm going +to do the same around for uh uh the + + align:start position:0% +to do the same around for uh uh the + + + align:start position:0% +to do the same around for uh uh the +control group so just putting + + align:start position:0% +control group so just putting + + + align:start position:0% +control group so just putting +expectation around the the the + + align:start position:0% +expectation around the the the + + + align:start position:0% +expectation around the the the +structural equation uh e of e i given y + + align:start position:0% +structural equation uh e of e i given y + + + align:start position:0% +structural equation uh e of e i given y +i given Z equal Z is Alpha plus beta e + + align:start position:0% +i given Z equal Z is Alpha plus beta e + + + align:start position:0% +i given Z equal Z is Alpha plus beta e +of a I given Z equal Z Plus e of Epsilon + + align:start position:0% +of a I given Z equal Z Plus e of Epsilon + + + align:start position:0% +of a I given Z equal Z Plus e of Epsilon +I given that Z equal + + align:start position:0% +I given that Z equal + + + align:start position:0% +I given that Z equal +Z okay make sense I'm going to take the + + align:start position:0% +Z okay make sense I'm going to take the + + + align:start position:0% +Z okay make sense I'm going to take the +difference between the two which is + + align:start position:0% +difference between the two which is + + + align:start position:0% +difference between the two which is +going to be our causal effect of test + + align:start position:0% +going to be our causal effect of test + + + align:start position:0% +going to be our causal effect of test +scores what is it equal + + align:start position:0% +scores what is it equal + + + align:start position:0% +scores what is it equal +to is it's equal to Beta time um e of EI + + align:start position:0% +to is it's equal to Beta time um e of EI + + + align:start position:0% +to is it's equal to Beta time um e of EI +given zal 1 minus E of a I given Z equal + + align:start position:0% +given zal 1 minus E of a I given Z equal + + + align:start position:0% +given zal 1 minus E of a I given Z equal +0 plus e of Epsilon I given zal 1 minus + + align:start position:0% +0 plus e of Epsilon I given zal 1 minus + + + align:start position:0% +0 plus e of Epsilon I given zal 1 minus +E of Epsilon I given that Z equal + + align:start position:0% +E of Epsilon I given that Z equal + + + align:start position:0% +E of Epsilon I given that Z equal +0 now I want you to assume that this is + + align:start position:0% +0 now I want you to assume that this is + + + align:start position:0% +0 now I want you to assume that this is +zero and we will comment on this + + align:start position:0% +zero and we will comment on this + + + align:start position:0% +zero and we will comment on this +assumption in a minute whether it's a + + align:start position:0% +assumption in a minute whether it's a + + + align:start position:0% +assumption in a minute whether it's a +good assumption to make or a bad + + align:start position:0% +good assumption to make or a bad + + + align:start position:0% +good assumption to make or a bad +assumption to make but for a minute I + + align:start position:0% +assumption to make but for a minute I + + + align:start position:0% +assumption to make but for a minute I +admit that this might be + + align:start position:0% +admit that this might be + + + align:start position:0% +admit that this might be +zero if that is zero then beta is simply + + align:start position:0% +zero if that is zero then beta is simply + + + align:start position:0% +zero if that is zero then beta is simply +uh the the the ratio between uh the the + + align:start position:0% +uh the the the ratio between uh the the + + + align:start position:0% +uh the the the ratio between uh the the +causal effect of the uh scholarship on + + align:start position:0% +causal effect of the uh scholarship on + + + align:start position:0% +causal effect of the uh scholarship on +the outcome of interest and the causal + + align:start position:0% +the outcome of interest and the causal + + + align:start position:0% +the outcome of interest and the causal +effect of the scholarship on uh the + + align:start position:0% +effect of the scholarship on uh the + + + align:start position:0% +effect of the scholarship on uh the +going to schools so this is what we have + + align:start position:0% +going to schools so this is what we have + + + align:start position:0% +going to schools so this is what we have +here beta hat is uh e of i y i given Z + + align:start position:0% +here beta hat is uh e of i y i given Z + + + align:start position:0% +here beta hat is uh e of i y i given Z +equal 1 minus E of y i given zal 0 + + align:start position:0% +equal 1 minus E of y i given zal 0 + + + align:start position:0% +equal 1 minus E of y i given zal 0 +divided by E of a I given zal 1 minus E + + align:start position:0% +divided by E of a I given zal 1 minus E + + + align:start position:0% +divided by E of a I given zal 1 minus E +of a I given zal Z in other word what + + align:start position:0% +of a I given zal Z in other word what + + + align:start position:0% +of a I given zal Z in other word what +I'm doing is that I'm scaling up the + + align:start position:0% +I'm doing is that I'm scaling up the + + + align:start position:0% +I'm doing is that I'm scaling up the +effect of the scholarship by the fact + + align:start position:0% +effect of the scholarship by the fact + + + align:start position:0% +effect of the scholarship by the fact +that not everybody is induced to go to + + align:start position:0% +that not everybody is induced to go to + + + align:start position:0% +that not everybody is induced to go to +school uh because of the scholarship + + align:start position:0% +school uh because of the scholarship + + + align:start position:0% +school uh because of the scholarship +some would have gone anywhere and some + + align:start position:0% +some would have gone anywhere and some + + + align:start position:0% +some would have gone anywhere and some +didn't go even despite that so in our + + align:start position:0% +didn't go even despite that so in our + + + align:start position:0% +didn't go even despite that so in our +example this could be this would be for + + align:start position:0% +example this could be this would be for + + + align:start position:0% +example this could be this would be for +for woman uh Point uh uh + + align:start position:0% +for woman uh Point uh uh + + + align:start position:0% +for woman uh Point uh uh +0.125 if I remember correctly divide + + align:start position:0% +0.125 if I remember correctly divide + + + align:start position:0% +0.125 if I remember correctly divide +divided by + + align:start position:0% +divided by + + + align:start position:0% +divided by +33% so basically multiplying by three so + + align:start position:0% +33% so basically multiplying by three so + + + align:start position:0% +33% so basically multiplying by three so +it's going to be about 6 for test scores + + align:start position:0% +it's going to be about 6 for test scores + + + align:start position:0% +it's going to be about 6 for test scores +so it's telling me that increasing going + + align:start position:0% +so it's telling me that increasing going + + + align:start position:0% +so it's telling me that increasing going +people who have gone to school have + + align:start position:0% +people who have gone to school have + + + align:start position:0% +people who have gone to school have +cognitive test scores that have about6 + + align:start position:0% +cognitive test scores that have about6 + + + align:start position:0% +cognitive test scores that have about6 +teration higher than than girls who + + align:start position:0% +teration higher than than girls who + + + align:start position:0% +teration higher than than girls who +haven't gone to school okay so the key + + align:start position:0% +haven't gone to school okay so the key + + + align:start position:0% +haven't gone to school okay so the key +of course of all this calculation is + + align:start position:0% +of course of all this calculation is + + + align:start position:0% +of course of all this calculation is +this assumption over here that + + align:start position:0% +this assumption over here that + + + align:start position:0% +this assumption over here that +the expectation of Epsilon I given Z + + align:start position:0% +the expectation of Epsilon I given Z + + + align:start position:0% +the expectation of Epsilon I given Z +equal Z minus the expectation of Epsilon + + align:start position:0% +equal Z minus the expectation of Epsilon + + + align:start position:0% +equal Z minus the expectation of Epsilon +I given that Z equal one is uh uh in + + align:start position:0% +I given that Z equal one is uh uh in + + + align:start position:0% +I given that Z equal one is uh uh in +fact zero so why is that possibly + + align:start position:0% +fact zero so why is that possibly + + + align:start position:0% +fact zero so why is that possibly +true uh and that's going to tell us + + align:start position:0% +true uh and that's going to tell us + + + align:start position:0% +true uh and that's going to tell us +basically for a instrument to be a good + + align:start position:0% +basically for a instrument to be a good + + + align:start position:0% +basically for a instrument to be a good +instrument we need we need two things + + align:start position:0% +instrument we need we need two things + + + align:start position:0% +instrument we need we need two things +this better not be zero otherwise it's + + align:start position:0% +this better not be zero otherwise it's + + + align:start position:0% +this better not be zero otherwise it's +going to this is going to go to infinity + + align:start position:0% +going to this is going to go to infinity + + + align:start position:0% +going to this is going to go to infinity +and with it the standard error we need + + align:start position:0% +and with it the standard error we need + + + align:start position:0% +and with it the standard error we need +something that affects the first stage + + align:start position:0% +something that affects the first stage + + + align:start position:0% +something that affects the first stage +we need a relationship between + + align:start position:0% +we need a relationship between + + + align:start position:0% +we need a relationship between +scholarship and + + align:start position:0% +scholarship and + + + align:start position:0% +scholarship and +education that's easy to check if it's + + align:start position:0% +education that's easy to check if it's + + + align:start position:0% +education that's easy to check if it's +not there you just try for another + + align:start position:0% +not there you just try for another + + + align:start position:0% +not there you just try for another +instrument so that one + + align:start position:0% +instrument so that one + + + align:start position:0% +instrument so that one +is pretty important but uh pretty + + align:start position:0% +is pretty important but uh pretty + + + align:start position:0% +is pretty important but uh pretty +fundamental but easy to + + align:start position:0% +fundamental but easy to + + + align:start position:0% +fundamental but easy to +check the other one is that + + align:start position:0% +check the other one is that + + + align:start position:0% +check the other one is that +um is this assumption that the the + + align:start position:0% +um is this assumption that the the + + + align:start position:0% +um is this assumption that the the +expectation of Epsilon given Z equal 1 + + align:start position:0% +expectation of Epsilon given Z equal 1 + + + align:start position:0% +expectation of Epsilon given Z equal 1 +minus Z equal Z is in fact zero + + align:start position:0% +minus Z equal Z is in fact zero + + + align:start position:0% +minus Z equal Z is in fact zero +and that really can be unpacked in two + + align:start position:0% +and that really can be unpacked in two + + + align:start position:0% +and that really can be unpacked in two +things one is + + align:start position:0% +things one is + + + align:start position:0% +things one is +that uh the effect of Z on Yi can in + + align:start position:0% +that uh the effect of Z on Yi can in + + + align:start position:0% +that uh the effect of Z on Yi can in +fact be estimated well so that's going + + align:start position:0% +fact be estimated well so that's going + + + align:start position:0% +fact be estimated well so that's going +to give be be G in this case it's given + + align:start position:0% +to give be be G in this case it's given + + + align:start position:0% +to give be be G in this case it's given +to you free of charge because the + + align:start position:0% +to you free of charge because the + + + align:start position:0% +to you free of charge because the +instrument is randomly assigned so we do + + align:start position:0% +instrument is randomly assigned so we do + + + align:start position:0% +instrument is randomly assigned so we do +know that the difference between uh the + + align:start position:0% +know that the difference between uh the + + + align:start position:0% +know that the difference between uh the +outcome for Z equal 1 minus Z equal Z is + + align:start position:0% +outcome for Z equal 1 minus Z equal Z is + + + align:start position:0% +outcome for Z equal 1 minus Z equal Z is +in fact the causal effect of going going + + align:start position:0% +in fact the causal effect of going going + + + align:start position:0% +in fact the causal effect of going going +a schol getting a scholarship on on U on + + align:start position:0% +a schol getting a scholarship on on U on + + + align:start position:0% +a schol getting a scholarship on on U on +uh on test scores or the outcomes so + + align:start position:0% +uh on test scores or the outcomes so + + + align:start position:0% +uh on test scores or the outcomes so +that's one aspect when we use + + align:start position:0% +that's one aspect when we use + + + align:start position:0% +that's one aspect when we use +instruments that are not randomly + + align:start position:0% +instruments that are not randomly + + + align:start position:0% +instruments that are not randomly +assigned that are given to us by Nature + + align:start position:0% +assigned that are given to us by Nature + + + align:start position:0% +assigned that are given to us by Nature +by natural experiment or what not it it + + align:start position:0% +by natural experiment or what not it it + + + align:start position:0% +by natural experiment or what not it it +might have to be argued that this is in + + align:start position:0% +might have to be argued that this is in + + + align:start position:0% +might have to be argued that this is in +fact + + align:start position:0% +fact + + + align:start position:0% +fact +true and then there is a second part of + + align:start position:0% +true and then there is a second part of + + + align:start position:0% +true and then there is a second part of +the assumption that is not given to us + + align:start position:0% +the assumption that is not given to us + + + align:start position:0% +the assumption that is not given to us +for free even in randomiz control trials + + align:start position:0% +for free even in randomiz control trials + + + align:start position:0% +for free even in randomiz control trials +and that's very important to remember + + align:start position:0% +and that's very important to remember + + + align:start position:0% +and that's very important to remember +that is that there there is no direct + + align:start position:0% +that is that there there is no direct + + + align:start position:0% +that is that there there is no direct +effect of the scholarship on cognitive + + align:start position:0% +effect of the scholarship on cognitive + + + align:start position:0% +effect of the scholarship on cognitive +test scores otherwise this wouldn't be + + align:start position:0% +test scores otherwise this wouldn't be + + + align:start position:0% +test scores otherwise this wouldn't be +true + + align:start position:0% +true + + + align:start position:0% +true +anymore because part of the effect of + + align:start position:0% +anymore because part of the effect of + + + align:start position:0% +anymore because part of the effect of +the of part of the of the effect of the + + align:start position:0% +the of part of the of the effect of the + + + align:start position:0% +the of part of the of the effect of the +scholarship on the test scores comes not + + align:start position:0% +scholarship on the test scores comes not + + + align:start position:0% +scholarship on the test scores comes not +from education but from uh uh from + + align:start position:0% +from education but from uh uh from + + + align:start position:0% +from education but from uh uh from +another uh channel uh so in other words + + align:start position:0% +another uh channel uh so in other words + + + align:start position:0% +another uh channel uh so in other words +uh in + + align:start position:0% +uh in + + + align:start position:0% +uh in +here if the really belongs to the this + + align:start position:0% + + + + align:start position:0% + +equation um then we would have an + + align:start position:0% +equation um then we would have an + + + align:start position:0% +equation um then we would have an +omitted variable bias if we don't + + align:start position:0% +omitted variable bias if we don't + + + align:start position:0% +omitted variable bias if we don't +include it and therefore Epsilon e of + + align:start position:0% +include it and therefore Epsilon e of + + + align:start position:0% +include it and therefore Epsilon e of +Epsilon I given Z equal one is not going + + align:start position:0% +Epsilon I given Z equal one is not going + + + align:start position:0% +Epsilon I given Z equal one is not going +to be is not going to be zero in this + + align:start position:0% +to be is not going to be zero in this + + + align:start position:0% +to be is not going to be zero in this +model I can't assume that so anything + + align:start position:0% +model I can't assume that so anything + + + align:start position:0% +model I can't assume that so anything +that we need to be able to assume that + + align:start position:0% +that we need to be able to assume that + + + align:start position:0% +that we need to be able to assume that +the scholarship don't affect the final + + align:start position:0% +the scholarship don't affect the final + + + align:start position:0% +the scholarship don't affect the final +outcome you assign the scholarships did + + align:start position:0% +outcome you assign the scholarships did + + + align:start position:0% +outcome you assign the scholarships did +you say that they were randomly + + align:start position:0% +you say that they were randomly + + + align:start position:0% +you say that they were randomly +distributed because I'm just thinking if + + align:start position:0% +distributed because I'm just thinking if + + + align:start position:0% +distributed because I'm just thinking if +a child receives a scholarship they may + + align:start position:0% +a child receives a scholarship they may + + + align:start position:0% +a child receives a scholarship they may +think oh well um I'm receiving this + + align:start position:0% +think oh well um I'm receiving this + + + align:start position:0% +think oh well um I'm receiving this +scholarship because somebody sees + + align:start position:0% +scholarship because somebody sees + + + align:start position:0% +scholarship because somebody sees +potential in me they see potential in + + align:start position:0% +potential in me they see potential in + + + align:start position:0% +potential in me they see potential in +themselves and then they get F yeah + + align:start position:0% +themselves and then they get F yeah + + + align:start position:0% +themselves and then they get F yeah +exactly so uh I believe we did say say + + align:start position:0% +exactly so uh I believe we did say say + + + align:start position:0% +exactly so uh I believe we did say say +so but we were concerned about that + + align:start position:0% +so but we were concerned about that + + + align:start position:0% +so but we were concerned about that +overconfidence spunk Etc that people + + align:start position:0% +overconfidence spunk Etc that people + + + align:start position:0% +overconfidence spunk Etc that people +feel like you know they've been chosen + + align:start position:0% +feel like you know they've been chosen + + + align:start position:0% +feel like you know they've been chosen +somehow uh by us or by God for that + + align:start position:0% +somehow uh by us or by God for that + + + align:start position:0% +somehow uh by us or by God for that +matter or you know and then that would + + align:start position:0% +matter or you know and then that would + + + align:start position:0% +matter or you know and then that would +have an effect independently of + + align:start position:0% +have an effect independently of + + + align:start position:0% +have an effect independently of +scholarship so we did look at uh um we + + align:start position:0% +scholarship so we did look at uh um we + + + align:start position:0% +scholarship so we did look at uh um we +tried to get a that uh but you putting + + align:start position:0% +tried to get a that uh but you putting + + + align:start position:0% +tried to get a that uh but you putting +more generally you're putting your + + align:start position:0% +more generally you're putting your + + + align:start position:0% +more generally you're putting your +finger on + + align:start position:0% +finger on + + + align:start position:0% +finger on +exactly the really hard part with with + + align:start position:0% +exactly the really hard part with with + + + align:start position:0% +exactly the really hard part with with +randomiz with with IV is + + align:start position:0% +randomiz with with IV is + + + align:start position:0% +randomiz with with IV is +that you need to go over any number of + + align:start position:0% +that you need to go over any number of + + + align:start position:0% +that you need to go over any number of +those stories and un + + align:start position:0% +those stories and un + + + align:start position:0% +those stories and un +like the second assumption which in this + + align:start position:0% +like the second assumption which in this + + + align:start position:0% +like the second assumption which in this +case is true by construction or can + + align:start position:0% +case is true by construction or can + + + align:start position:0% +case is true by construction or can +sometimes be checked um uh this this + + align:start position:0% +sometimes be checked um uh this this + + + align:start position:0% +sometimes be checked um uh this this +assumption is like has to be argued so + + align:start position:0% +assumption is like has to be argued so + + + align:start position:0% +assumption is like has to be argued so +and you will never be able to prove it + + align:start position:0% +and you will never be able to prove it + + + align:start position:0% +and you will never be able to prove it +you can just think about all the stories + + align:start position:0% +you can just think about all the stories + + + align:start position:0% +you can just think about all the stories +you could possibly think about and try + + align:start position:0% +you could possibly think about and try + + + align:start position:0% +you could possibly think about and try +to see whether there is evidence for + + align:start position:0% +to see whether there is evidence for + + + align:start position:0% +to see whether there is evidence for +them but you've never so you could prove + + align:start position:0% +them but you've never so you could prove + + + align:start position:0% +them but you've never so you could prove +yourself wrong but you're never going to + + align:start position:0% +yourself wrong but you're never going to + + + align:start position:0% +yourself wrong but you're never going to +be able to prove yourself right so + + align:start position:0% +be able to prove yourself right so + + + align:start position:0% +be able to prove yourself right so +that's exactly that's exactly that uh so + + align:start position:0% +that's exactly that's exactly that uh so + + + align:start position:0% +that's exactly that's exactly that uh so +and this is exactly what we need to + + align:start position:0% +and this is exactly what we need to + + + align:start position:0% +and this is exactly what we need to +never forget to chase both condition + + align:start position:0% +never forget to chase both condition + + + align:start position:0% +never forget to chase both condition +that there is + + align:start position:0% +that there is + + + align:start position:0% +that there is +no that both the the scholarship is + + align:start position:0% +no that both the the scholarship is + + + align:start position:0% +no that both the the scholarship is +randomly assigned or as good as randomly + + align:start position:0% +randomly assigned or as good as randomly + + + align:start position:0% +randomly assigned or as good as randomly +assigned and that there is no direct + + align:start position:0% +assigned and that there is no direct + + + align:start position:0% +assigned and that there is no direct +effect and try to go over in our head + + align:start position:0% +effect and try to go over in our head + + + align:start position:0% +effect and try to go over in our head +over all of this uh + + align:start position:0% +over all of this uh + + + align:start position:0% +over all of this uh +condition the second condition might is + + align:start position:0% +condition the second condition might is + + + align:start position:0% +condition the second condition might is +often not verified even when the first + + align:start position:0% +often not verified even when the first + + + align:start position:0% +often not verified even when the first +example here so you ask the first + + align:start position:0% +example here so you ask the first + + + align:start position:0% +example here so you ask the first +question which is could the scholarship + + align:start position:0% +question which is could the scholarship + + + align:start position:0% +question which is could the scholarship +per se have an an effect on cognitive + + align:start position:0% +per se have an an effect on cognitive + + + align:start position:0% +per se have an an effect on cognitive +score maybe a scholarship make people + + align:start position:0% +score maybe a scholarship make people + + + align:start position:0% +score maybe a scholarship make people +confident or happy give them drive and + + align:start position:0% +confident or happy give them drive and + + + align:start position:0% +confident or happy give them drive and +spun on energy so that would be issue + + align:start position:0% +spun on energy so that would be issue + + + align:start position:0% +spun on energy so that would be issue +what else could could be uh could what + + align:start position:0% +what else could could be uh could what + + + align:start position:0% +what else could could be uh could what +could be another reason why scholarship + + align:start position:0% +could be another reason why scholarship + + + align:start position:0% +could be another reason why scholarship +have a direct impact on test + + align:start position:0% +have a direct impact on test + + + align:start position:0% +have a direct impact on test +scores well actually + + align:start position:0% +scores well actually + + + align:start position:0% +scores well actually +maybe yeah but I was thinking because if + + align:start position:0% +maybe yeah but I was thinking because if + + + align:start position:0% +maybe yeah but I was thinking because if +you if the family has to like scre up + + align:start position:0% +you if the family has to like scre up + + + align:start position:0% +you if the family has to like scre up +money but they have now they have a + + align:start position:0% +money but they have now they have a + + + align:start position:0% +money but they have now they have a +scholarship they can use the money to + + align:start position:0% +scholarship they can use the money to + + + align:start position:0% +scholarship they can use the money to +like for better nutrition for example + + align:start position:0% +like for better nutrition for example + + + align:start position:0% +like for better nutrition for example +yeah exactly so a lot of kids in the + + align:start position:0% +yeah exactly so a lot of kids in the + + + align:start position:0% +yeah exactly so a lot of kids in the +control school went to school anyway and + + align:start position:0% +control school went to school anyway and + + + align:start position:0% +control school went to school anyway and +presumably they had to script the money + + align:start position:0% +presumably they had to script the money + + + align:start position:0% +presumably they had to script the money +so now the control some of the kids have + + align:start position:0% +so now the control some of the kids have + + + align:start position:0% +so now the control some of the kids have +gone to school anywhere but the + + align:start position:0% +gone to school anywhere but the + + + align:start position:0% +gone to school anywhere but the +treatment school didn't have to pay for + + align:start position:0% +treatment school didn't have to pay for + + + align:start position:0% +treatment school didn't have to pay for +it therefore you know that money may not + + align:start position:0% +it therefore you know that money may not + + + align:start position:0% +it therefore you know that money may not +be used for buying books or buying or + + align:start position:0% +be used for buying books or buying or + + + align:start position:0% +be used for buying books or buying or +buying better food or something like + + align:start position:0% +buying better food or something like + + + align:start position:0% +buying better food or something like +that that would be another reason why + + align:start position:0% +that that would be another reason why + + + align:start position:0% +that that would be another reason why +scholarship will affect your test course + + align:start position:0% +scholarship will affect your test course + + + align:start position:0% +scholarship will affect your test course +potentially even if over and above any + + align:start position:0% +potentially even if over and above any + + + align:start position:0% +potentially even if over and above any +effect on Education Direct on years of + + align:start position:0% +effect on Education Direct on years of + + + align:start position:0% +effect on Education Direct on years of +education which is what I'm measuring + + align:start position:0% +education which is what I'm measuring + + + align:start position:0% +education which is what I'm measuring +yeah do we assign + + align:start position:0% +yeah do we assign + + + align:start position:0% +yeah do we assign +any yes exactly the students know that + + align:start position:0% +any yes exactly the students know that + + + align:start position:0% +any yes exactly the students know that +uh you know you scrap exactly one year + + align:start position:0% +uh you know you scrap exactly one year + + + align:start position:0% +uh you know you scrap exactly one year +but you know that you need to keep + + align:start position:0% +but you know that you need to keep + + + align:start position:0% +but you know that you need to keep +thinking about it it might stress you + + align:start position:0% +thinking about it it might stress you + + + align:start position:0% +thinking about it it might stress you +out if you go to sandil sto uh today + + align:start position:0% +out if you go to sandil sto uh today + + + align:start position:0% +out if you go to sandil sto uh today +it's like basically it's all about that + + align:start position:0% +it's like basically it's all about that + + + align:start position:0% +it's like basically it's all about that +that we only have so many so much bond + + align:start position:0% +that we only have so many so much bond + + + align:start position:0% +that we only have so many so much bond +withd to think about things in our life + + align:start position:0% +withd to think about things in our life + + + align:start position:0% +withd to think about things in our life +and therefore if I take some bondway + + align:start position:0% +and therefore if I take some bondway + + + align:start position:0% +and therefore if I take some bondway +away because you're thinking will I ever + + align:start position:0% +away because you're thinking will I ever + + + align:start position:0% +away because you're thinking will I ever +be able to manage the money you have + + align:start position:0% +be able to manage the money you have + + + align:start position:0% +be able to manage the money you have +less bondway to think about making good + + align:start position:0% +less bondway to think about making good + + + align:start position:0% +less bondway to think about making good +grades did any of the kids who didn't + + align:start position:0% +grades did any of the kids who didn't + + + align:start position:0% +grades did any of the kids who didn't +perceive scholarships work while going + + align:start position:0% +perceive scholarships work while going + + + align:start position:0% +perceive scholarships work while going +to school not really no because it's + + align:start position:0% +to school not really no because it's + + + align:start position:0% +to school not really no because it's +like a lot yeah you go to school it's + + align:start position:0% +like a lot yeah you go to school it's + + + align:start position:0% +like a lot yeah you go to school it's +usually it's residential so it's not + + align:start position:0% +usually it's residential so it's not + + + align:start position:0% +usually it's residential so it's not +that you have much of a + + align:start position:0% +that you have much of a + + + align:start position:0% +that you have much of a +choice but if they had then they would + + align:start position:0% +choice but if they had then they would + + + align:start position:0% +choice but if they had then they would +have taken time away from their study + + align:start position:0% +have taken time away from their study + + + align:start position:0% +have taken time away from their study +and that would also be a concern yeah + + align:start position:0% +and that would also be a concern yeah + + + align:start position:0% +and that would also be a concern yeah +what kinds of survey questions have you + + align:start position:0% +what kinds of survey questions have you + + + align:start position:0% +what kinds of survey questions have you +been asking them in order to get at some + + align:start position:0% +been asking them in order to get at some + + + align:start position:0% +been asking them in order to get at some +of these other stories so anything and + + align:start position:0% +of these other stories so anything and + + + align:start position:0% +of these other stories so anything and +everything like as many as possible so + + align:start position:0% +everything like as many as possible so + + + align:start position:0% +everything like as many as possible so +first of all uh I think it's a great + + align:start position:0% +first of all uh I think it's a great + + + align:start position:0% +first of all uh I think it's a great +teaching example but actually in the + + align:start position:0% +teaching example but actually in the + + + align:start position:0% +teaching example but actually in the +paper for a long time we didn't even + + align:start position:0% +paper for a long time we didn't even + + + align:start position:0% +paper for a long time we didn't even +present the IV because we thought there + + align:start position:0% +present the IV because we thought there + + + align:start position:0% +present the IV because we thought there +was a lot of things that one could be + + align:start position:0% +was a lot of things that one could be + + + align:start position:0% +was a lot of things that one could be +worried about uh but since we were + + align:start position:0% +worried about uh but since we were + + + align:start position:0% +worried about uh but since we were +always doing it implicitly we finally + + align:start position:0% +always doing it implicitly we finally + + + align:start position:0% +always doing it implicitly we finally +put it but then we Tred to put a lot of + + align:start position:0% +put it but then we Tred to put a lot of + + + align:start position:0% +put it but then we Tred to put a lot of +stuff to try to get at that so for + + align:start position:0% +stuff to try to get at that so for + + + align:start position:0% +stuff to try to get at that so for +example the other + + align:start position:0% +example the other + + + align:start position:0% +example the other +children uh there the education of the + + align:start position:0% +children uh there the education of the + + + align:start position:0% +children uh there the education of the +other children you know for example it + + align:start position:0% +other children you know for example it + + + align:start position:0% +other children you know for example it +could be that because you went to + + align:start position:0% +could be that because you went to + + + align:start position:0% +could be that because you went to +Secondary School you you uh for free it + + align:start position:0% +Secondary School you you uh for free it + + + align:start position:0% +Secondary School you you uh for free it +it allows the other kids to get educated + + align:start position:0% +it allows the other kids to get educated + + + align:start position:0% +it allows the other kids to get educated +any notion of the budget const of the + + align:start position:0% +any notion of the budget const of the + + + align:start position:0% +any notion of the budget const of the +family being relaxed uh we try to get at + + align:start position:0% +family being relaxed uh we try to get at + + + align:start position:0% +family being relaxed uh we try to get at +the overconfidence question by asking + + align:start position:0% +the overconfidence question by asking + + + align:start position:0% +the overconfidence question by asking +kids in advance uh how of the cognitive + + align:start position:0% +kids in advance uh how of the cognitive + + + align:start position:0% +kids in advance uh how of the cognitive +test how well they think they're going + + align:start position:0% +test how well they think they're going + + + align:start position:0% +test how well they think they're going +to do people are very overconfidence + + align:start position:0% +to do people are very overconfidence + + + align:start position:0% +to do people are very overconfidence +boys more than girls but uh it seems + + align:start position:0% +boys more than girls but uh it seems + + + align:start position:0% +boys more than girls but uh it seems +that the treatment the treatment doesn't + + align:start position:0% +that the treatment the treatment doesn't + + + align:start position:0% +that the treatment the treatment doesn't +affect that um uh we have questions on + + align:start position:0% +affect that um uh we have questions on + + + align:start position:0% +affect that um uh we have questions on +health we have questions + + align:start position:0% +health we have questions + + + align:start position:0% +health we have questions +on uh how people paid for schools + + align:start position:0% +on uh how people paid for schools + + + align:start position:0% +on uh how people paid for schools +Etc so we but this is all kind of always + + align:start position:0% +Etc so we but this is all kind of always + + + align:start position:0% +Etc so we but this is all kind of always +a little bit + + align:start position:0% +a little bit + + + align:start position:0% +a little bit +circumstantial uh so that's the that's + + align:start position:0% +circumstantial uh so that's the that's + + + align:start position:0% +circumstantial uh so that's the that's +the so that's the key yeah so this + + align:start position:0% +the so that's the key yeah so this + + + align:start position:0% +the so that's the key yeah so this +process or this experiment we're testing + + align:start position:0% +process or this experiment we're testing + + + align:start position:0% +process or this experiment we're testing +the + + align:start position:0% +the + + + align:start position:0% +the +ofation on test SC but that's within + + align:start position:0% +ofation on test SC but that's within + + + align:start position:0% +ofation on test SC but that's within +people who were qualified for these + + align:start position:0% +people who were qualified for these + + + align:start position:0% +people who were qualified for these +within in this group exactly does that + + align:start position:0% +within in this group exactly does that + + + align:start position:0% +within in this group exactly does that +mean that we have anytime we use this it + + align:start position:0% +mean that we have anytime we use this it + + + align:start position:0% +mean that we have anytime we use this it +has to be with the caveat that like for + + align:start position:0% +has to be with the caveat that like for + + + align:start position:0% +has to be with the caveat that like for +people who are accepted to high school a + + align:start position:0% +people who are accepted to high school a + + + align:start position:0% +people who are accepted to high school a +way to General generalize to like the + + align:start position:0% +way to General generalize to like the + + + align:start position:0% +way to General generalize to like the +entire student so that's a great + + align:start position:0% +entire student so that's a great + + + align:start position:0% +entire student so that's a great +question strictly speaking no you've + + align:start position:0% +question strictly speaking no you've + + + align:start position:0% +question strictly speaking no you've +done the experiment here among a set of + + align:start position:0% +done the experiment here among a set of + + + align:start position:0% +done the experiment here among a set of +kids who qualified for high school + + align:start position:0% +kids who qualified for high school + + + align:start position:0% +kids who qualified for high school +anywhere so if the government uh is + + align:start position:0% +anywhere so if the government uh is + + + align:start position:0% +anywhere so if the government uh is +thinking about improving uh education by + + align:start position:0% +thinking about improving uh education by + + + align:start position:0% +thinking about improving uh education by +relaxing the requirement instead of + + align:start position:0% +relaxing the requirement instead of + + + align:start position:0% +relaxing the requirement instead of +making it free so this could give us a + + align:start position:0% +making it free so this could give us a + + + align:start position:0% +making it free so this could give us a +good idea of keeping the exact system in + + align:start position:0% +good idea of keeping the exact system in + + + align:start position:0% +good idea of keeping the exact system in +place but making it free or cheaper + + align:start position:0% +place but making it free or cheaper + + + align:start position:0% +place but making it free or cheaper +right that's basically going to cover it + + align:start position:0% +right that's basically going to cover it + + + align:start position:0% +right that's basically going to cover it +pretty much uh what it would not + + align:start position:0% +pretty much uh what it would not + + + align:start position:0% +pretty much uh what it would not +necessarily cover is to say keep the + + align:start position:0% +necessarily cover is to say keep the + + + align:start position:0% +necessarily cover is to say keep the +same amount of money but relax or remove + + align:start position:0% +same amount of money but relax or remove + + + align:start position:0% +same amount of money but relax or remove +the admission requirement then you're + + align:start position:0% +the admission requirement then you're + + + align:start position:0% +the admission requirement then you're +going to get new kids coming in but + + align:start position:0% +going to get new kids coming in but + + + align:start position:0% +going to get new kids coming in but +they're going to be different kids + + align:start position:0% +they're going to be different kids + + + align:start position:0% +they're going to be different kids +compared to this one um so that's that's + + align:start position:0% +compared to this one um so that's that's + + + align:start position:0% +compared to this one um so that's that's +a question of um the external validity + + align:start position:0% +a question of um the external validity + + + align:start position:0% +a question of um the external validity +so here the the estimate is valid for + + align:start position:0% +so here the the estimate is valid for + + + align:start position:0% +so here the the estimate is valid for +this question in this sample but if we + + align:start position:0% +this question in this sample but if we + + + align:start position:0% +this question in this sample but if we +don't + + align:start position:0% +don't + + + align:start position:0% +don't +if if we don't assume that the returns + + align:start position:0% +if if we don't assume that the returns + + + align:start position:0% +if if we don't assume that the returns +to ucation are the same for + + align:start position:0% +to ucation are the same for + + + align:start position:0% +to ucation are the same for +everyone uh they might not tell tell us + + align:start position:0% +everyone uh they might not tell tell us + + + align:start position:0% +everyone uh they might not tell tell us +the effect of another manipulation in + + align:start position:0% +the effect of another manipulation in + + + align:start position:0% +the effect of another manipulation in +another sample and uh in particular for + + align:start position:0% +another sample and uh in particular for + + + align:start position:0% +another sample and uh in particular for +example you could think that the + + align:start position:0% +example you could think that the + + + align:start position:0% +example you could think that the +admitting um less qualified kids would + + align:start position:0% +admitting um less qualified kids would + + + align:start position:0% +admitting um less qualified kids would +uh and they would go to less good + + align:start position:0% +uh and they would go to less good + + + align:start position:0% +uh and they would go to less good +schools might lead to lower returns to + + align:start position:0% +schools might lead to lower returns to + + + align:start position:0% +schools might lead to lower returns to +education so what we did to try to + + align:start position:0% +education so what we did to try to + + + align:start position:0% +education so what we did to try to +address that is that we we have kids + + align:start position:0% +address that is that we we have kids + + + align:start position:0% +address that is that we we have kids +over the entire distribution because we + + align:start position:0% +over the entire distribution because we + + + align:start position:0% +over the entire distribution because we +have kids of admitted students but some + + align:start position:0% +have kids of admitted students but some + + + align:start position:0% +have kids of admitted students but some +kids were at the very bottom and some + + align:start position:0% +kids were at the very bottom and some + + + align:start position:0% +kids were at the very bottom and some +kids are the very best because they were + + align:start position:0% +kids are the very best because they were + + + align:start position:0% +kids are the very best because they were +randomized at all levels + + align:start position:0% +randomized at all levels + + + align:start position:0% +randomized at all levels +so what we look at uh to be able to say + + align:start position:0% +so what we look at uh to be able to say + + + align:start position:0% +so what we look at uh to be able to say +something to that is that the is the + + align:start position:0% +something to that is that the is the + + + align:start position:0% +something to that is that the is the +effect of the scholarship or the effect + + align:start position:0% +effect of the scholarship or the effect + + + align:start position:0% +effect of the scholarship or the effect +of going to school once you have one you + + align:start position:0% +of going to school once you have one you + + + align:start position:0% +of going to school once you have one you +have the other on at all level of the + + align:start position:0% +have the other on at all level of the + + + align:start position:0% +have the other on at all level of the +distribution like does is it the case + + align:start position:0% +distribution like does is it the case + + + align:start position:0% +distribution like does is it the case +that we have lower effects for kids who + + align:start position:0% +that we have lower effects for kids who + + + align:start position:0% +that we have lower effects for kids who +are just qualified versus kids who uh + + align:start position:0% +are just qualified versus kids who uh + + + align:start position:0% +are just qualified versus kids who uh +who who uh who are like well above and + + align:start position:0% +who who uh who are like well above and + + + align:start position:0% +who who uh who are like well above and +we're not finding that we're finding + + align:start position:0% +we're not finding that we're finding + + + align:start position:0% +we're not finding that we're finding +that it seems to be a shift up so that + + align:start position:0% +that it seems to be a shift up so that + + + align:start position:0% +that it seems to be a shift up so that +doesn't necess mean that you would + + align:start position:0% +doesn't necess mean that you would + + + align:start position:0% +doesn't necess mean that you would +extrapolate Beyond but it gives you some + + align:start position:0% +extrapolate Beyond but it gives you some + + + align:start position:0% +extrapolate Beyond but it gives you some +sense that it might Yep this just a + + align:start position:0% +sense that it might Yep this just a + + + align:start position:0% +sense that it might Yep this just a +general question but how do you + + align:start position:0% +general question but how do you + + + align:start position:0% +general question but how do you +synthesize all the information that you + + align:start position:0% +synthesize all the information that you + + + align:start position:0% +synthesize all the information that you +get from surveys when you're + + align:start position:0% +get from surveys when you're + + + align:start position:0% +get from surveys when you're +constructing a model or special or + + align:start position:0% +constructing a model or special or + + + align:start position:0% +constructing a model or special or +something uh so that's a great question + + align:start position:0% +something uh so that's a great question + + + align:start position:0% +something uh so that's a great question +uh generally when you when you conceive + + align:start position:0% +uh generally when you when you conceive + + + align:start position:0% +uh generally when you when you conceive +of a study and if you're going to ask + + align:start position:0% +of a study and if you're going to ask + + + align:start position:0% +of a study and if you're going to ask +questions to people you're putting a lot + + align:start position:0% +questions to people you're putting a lot + + + align:start position:0% +questions to people you're putting a lot +of questions in the + + align:start position:0% +of questions in the + + + align:start position:0% +of questions in the +survey uh and therefore you might have a + + align:start position:0% +survey uh and therefore you might have a + + + align:start position:0% +survey uh and therefore you might have a +lot of although it's less true for us + + align:start position:0% +lot of although it's less true for us + + + align:start position:0% +lot of although it's less true for us +because a lot of the service are done on + + align:start position:0% +because a lot of the service are done on + + + align:start position:0% +because a lot of the service are done on +the phone and have to be kept short but + + align:start position:0% +the phone and have to be kept short but + + + align:start position:0% +the phone and have to be kept short but +one of them is in person and has lots + + align:start position:0% +one of them is in person and has lots + + + align:start position:0% +one of them is in person and has lots +and lots of variables it has all of this + + align:start position:0% +and lots of variables it has all of this + + + align:start position:0% +and lots of variables it has all of this +and then uh and then um a qu very + + align:start position:0% +and then uh and then um a qu very + + + align:start position:0% +and then uh and then um a qu very +legitimate question is what do you + + align:start position:0% +legitimate question is what do you + + + align:start position:0% +legitimate question is what do you +report and the danger being that if you + + align:start position:0% +report and the danger being that if you + + + align:start position:0% +report and the danger being that if you +report many many many many things I + + align:start position:0% +report many many many many things I + + + align:start position:0% +report many many many many things I +think we discussed that if you run + + align:start position:0% +think we discussed that if you run + + + align:start position:0% +think we discussed that if you run +enough test a few of them are going to + + align:start position:0% +enough test a few of them are going to + + + align:start position:0% +enough test a few of them are going to +be significant + + align:start position:0% +be significant + + + align:start position:0% +be significant +anyway so there are kind of two the + + align:start position:0% +anyway so there are kind of two the + + + align:start position:0% +anyway so there are kind of two the +literature is at the moment in general + + align:start position:0% +literature is at the moment in general + + + align:start position:0% +literature is at the moment in general +in economics and in Social s sort of + + align:start position:0% +in economics and in Social s sort of + + + align:start position:0% +in economics and in Social s sort of +grappling up grappling with this + + align:start position:0% +grappling up grappling with this + + + align:start position:0% +grappling up grappling with this +problem uh one way to go is to spec is + + align:start position:0% +problem uh one way to go is to spec is + + + align:start position:0% +problem uh one way to go is to spec is +to you presumably you're running the + + align:start position:0% +to you presumably you're running the + + + align:start position:0% +to you presumably you're running the +experiment because you have a model in + + align:start position:0% +experiment because you have a model in + + + align:start position:0% +experiment because you have a model in +mind you can write it up and therefore + + align:start position:0% +mind you can write it up and therefore + + + align:start position:0% +mind you can write it up and therefore +say in advance what you want to look at + + align:start position:0% +say in advance what you want to look at + + + align:start position:0% +say in advance what you want to look at +so people call that pre-analysis plan or + + align:start position:0% +so people call that pre-analysis plan or + + + align:start position:0% +so people call that pre-analysis plan or +registration so you can say out of this + + align:start position:0% +registration so you can say out of this + + + align:start position:0% +registration so you can say out of this +all big Wells of data I'm going to + + align:start position:0% +all big Wells of data I'm going to + + + align:start position:0% +all big Wells of data I'm going to +really focus on these four five outcomes + + align:start position:0% +really focus on these four five outcomes + + + align:start position:0% +really focus on these four five outcomes +that's what I'm mainly going to look at + + align:start position:0% +that's what I'm mainly going to look at + + + align:start position:0% +that's what I'm mainly going to look at +and the rest is going to sub entiate my + + align:start position:0% +and the rest is going to sub entiate my + + + align:start position:0% +and the rest is going to sub entiate my +case but these are my litmos tests so + + align:start position:0% +case but these are my litmos tests so + + + align:start position:0% +case but these are my litmos tests so +that's that that is one way to go uh and + + align:start position:0% +that's that that is one way to go uh and + + + align:start position:0% +that's that that is one way to go uh and +the the the other is to do the same + + align:start position:0% +the the the other is to do the same + + + align:start position:0% +the the the other is to do the same +exercise but expost which is uh sort of + + align:start position:0% +exercise but expost which is uh sort of + + + align:start position:0% +exercise but expost which is uh sort of +write down a model Expos to justify what + + align:start position:0% +write down a model Expos to justify what + + + align:start position:0% +write down a model Expos to justify what +you're looking at and then try to + + align:start position:0% +you're looking at and then try to + + + align:start position:0% +you're looking at and then try to +organize all of the things that you look + + align:start position:0% +organize all of the things that you look + + + align:start position:0% +organize all of the things that you look +at to make that case for + + align:start position:0% +at to make that case for + + + align:start position:0% +at to make that case for +example in our case we really want to + + align:start position:0% +example in our case we really want to + + + align:start position:0% +example in our case we really want to +basically look at the effect of + + align:start position:0% +basically look at the effect of + + + align:start position:0% +basically look at the effect of +education on a range of outcomes + + align:start position:0% +education on a range of outcomes + + + align:start position:0% +education on a range of outcomes +separately for women and men and then + + align:start position:0% +separately for women and men and then + + + align:start position:0% +separately for women and men and then +all of the rest is going to be + + align:start position:0% +all of the rest is going to be + + + align:start position:0% +all of the rest is going to be +circumstantial that it's really the + + align:start position:0% +circumstantial that it's really the + + + align:start position:0% +circumstantial that it's really the +effect of education so we can check for + + align:start position:0% +effect of education so we can check for + + + align:start position:0% +effect of education so we can check for +possible direct effect of scholarship on + + align:start position:0% +possible direct effect of scholarship on + + + align:start position:0% +possible direct effect of scholarship on +test scor that might not go through + + align:start position:0% +test scor that might not go through + + + align:start position:0% +test scor that might not go through +education s of gives you some discipline + + align:start position:0% +education s of gives you some discipline + + + align:start position:0% +education s of gives you some discipline +for what you want to look at but it's a + + align:start position:0% +for what you want to look at but it's a + + + align:start position:0% +for what you want to look at but it's a +great it's a great + + align:start position:0% +great it's a great + + + align:start position:0% +great it's a great +question uh so so that's it to this this + + align:start position:0% +question uh so so that's it to this this + + + align:start position:0% +question uh so so that's it to this this +uh this thing is called the the Val + + align:start position:0% +uh this thing is called the the Val + + + align:start position:0% +uh this thing is called the the Val +estimate uh the simple division between + + align:start position:0% +estimate uh the simple division between + + + align:start position:0% +estimate uh the simple division between +uh between the effect of the scholarship + + align:start position:0% +uh between the effect of the scholarship + + + align:start position:0% +uh between the effect of the scholarship +on on on the final outcome and the + + align:start position:0% +on on on the final outcome and the + + + align:start position:0% +on on on the final outcome and the +effect of the scholarship on going to + + align:start position:0% +effect of the scholarship on going to + + + align:start position:0% +effect of the scholarship on going to +school uh the first uh + + align:start position:0% +school uh the first uh + + + align:start position:0% +school uh the first uh +the nominator is the first stage + + align:start position:0% +the nominator is the first stage + + + align:start position:0% +the nominator is the first stage +relationship numerator sorry numerator + + align:start position:0% +relationship numerator sorry numerator + + + align:start position:0% +relationship numerator sorry numerator +is the first stage relationship the + + align:start position:0% +is the first stage relationship the + + + align:start position:0% +is the first stage relationship the +denominator is the reduced form + + align:start position:0% +denominator is the reduced form + + + align:start position:0% +denominator is the reduced form +relationship we call it the reduced form + + align:start position:0% +relationship we call it the reduced form + + + align:start position:0% +relationship we call it the reduced form +relationship and the beta hat is the Val + + align:start position:0% +relationship and the beta hat is the Val + + + align:start position:0% +relationship and the beta hat is the Val +is the Val estimate and it's the + + align:start position:0% +is the Val estimate and it's the + + + align:start position:0% +is the Val estimate and it's the +simplest form of an instrumental + + align:start position:0% +simplest form of an instrumental + + + align:start position:0% +simplest form of an instrumental +variable estimate uh where that is is + + align:start position:0% +variable estimate uh where that is is + + + align:start position:0% +variable estimate uh where that is is +our instrument and it's simple because + + align:start position:0% +our instrument and it's simple because + + + align:start position:0% +our instrument and it's simple because +uh that is binary so we can just compare + + align:start position:0% +uh that is binary so we can just compare + + + align:start position:0% +uh that is binary so we can just compare +uh treatment and + + align:start position:0% +uh treatment and + + + align:start position:0% +uh treatment and +control if you have understood this and + + align:start position:0% +control if you have understood this and + + + align:start position:0% +control if you have understood this and +all the subtleties that go with it uh + + align:start position:0% +all the subtleties that go with it uh + + + align:start position:0% +all the subtleties that go with it uh +you you're done in the sense of having + + align:start position:0% +you you're done in the sense of having + + + align:start position:0% +you you're done in the sense of having +understood IV and the rest is kind of + + align:start position:0% +understood IV and the rest is kind of + + + align:start position:0% +understood IV and the rest is kind of +building up on this + + align:start position:0% +building up on this + + + align:start position:0% +building up on this +Insight uh we went through this quickly + + align:start position:0% +Insight uh we went through this quickly + + + align:start position:0% +Insight uh we went through this quickly +but without the benefits of the table + + align:start position:0% +but without the benefits of the table + + + align:start position:0% +but without the benefits of the table +but remember this is the effect for + + align:start position:0% +but remember this is the effect for + + + align:start position:0% +but remember this is the effect for +women for example this is the effect on + + align:start position:0% +women for example this is the effect on + + + align:start position:0% +women for example this is the effect on +having a + + align:start position:0% +having a + + + align:start position:0% +having a +uh completed Secondary School 33 + + align:start position:0% +uh completed Secondary School 33 + + + align:start position:0% +uh completed Secondary School 33 +percentage Point more likely girls are + + align:start position:0% +percentage Point more likely girls are + + + align:start position:0% +percentage Point more likely girls are +33 percentage Point more likely to + + align:start position:0% +33 percentage Point more likely to + + + align:start position:0% +33 percentage Point more likely to +complete secondary school if they + + align:start position:0% +complete secondary school if they + + + align:start position:0% +complete secondary school if they +receive the scholarship then if they + + align:start position:0% +receive the scholarship then if they + + + align:start position:0% +receive the scholarship then if they +don't um this is the effect on cognitive + + align:start position:0% +don't um this is the effect on cognitive + + + align:start position:0% +don't um this is the effect on cognitive +test scores the cognitive test scores of + + align:start position:0% +test scores the cognitive test scores of + + + align:start position:0% +test scores the cognitive test scores of +girls is uh8 standard deviation larger + + align:start position:0% +girls is uh8 standard deviation larger + + + align:start position:0% +girls is uh8 standard deviation larger +if they have received the scholarship + + align:start position:0% +if they have received the scholarship + + + align:start position:0% +if they have received the scholarship +than if they haven't and so all I need + + align:start position:0% +than if they haven't and so all I need + + + align:start position:0% +than if they haven't and so all I need +to do is to divide one by the other uh + + align:start position:0% +to do is to divide one by the other uh + + + align:start position:0% +to do is to divide one by the other uh +to get the to get the effect so I would + + align:start position:0% +to get the to get the effect so I would + + + align:start position:0% +to get the to get the effect so I would +divide + + align:start position:0% +divide + + + align:start position:0% +divide +18 5 divided by 33 and it's going to be + + align:start position:0% + + + + align:start position:0% + +approximately 6 little + + align:start position:0% + + + + align:start position:0% + +less so you can play with that for you + + align:start position:0% +less so you can play with that for you + + + align:start position:0% +less so you can play with that for you +can do it for men you can do you can do + + align:start position:0% +can do it for men you can do you can do + + + align:start position:0% +can do it for men you can do you can do +it for years of schooling instead of uh + + align:start position:0% +it for years of schooling instead of uh + + + align:start position:0% +it for years of schooling instead of uh +completing secondary school you can do + + align:start position:0% +completing secondary school you can do + + + align:start position:0% +completing secondary school you can do +it for earnings uh the tables are all + + align:start position:0% +it for earnings uh the tables are all + + + align:start position:0% +it for earnings uh the tables are all +there in the slides so + + align:start position:0% +there in the slides so + + + align:start position:0% +there in the slides so +you can do anything you're interested + + align:start position:0% +you can do anything you're interested + + + align:start position:0% +you can do anything you're interested +in so we've seen that uh you can see + + align:start position:0% +in so we've seen that uh you can see + + + align:start position:0% +in so we've seen that uh you can see +that even a small violation of ether + + align:start position:0% +that even a small violation of ether + + + align:start position:0% +that even a small violation of ether +condition for the validity of the + + align:start position:0% +condition for the validity of the + + + align:start position:0% +condition for the validity of the +instrument uh can result in a large Bas + + align:start position:0% +instrument uh can result in a large Bas + + + align:start position:0% +instrument uh can result in a large Bas +you can see it in the in the equation + + align:start position:0% +you can see it in the in the equation + + + align:start position:0% +you can see it in the in the equation +it's because it's + + align:start position:0% +it's because it's + + + align:start position:0% +it's because it's +below so if there it's it's divided by + + align:start position:0% +below so if there it's it's divided by + + + align:start position:0% +below so if there it's it's divided by +something which is less than one so any + + align:start position:0% +something which is less than one so any + + + align:start position:0% +something which is less than one so any +small bias in epsilon would be blown up + + align:start position:0% +small bias in epsilon would be blown up + + + align:start position:0% +small bias in epsilon would be blown up +by the side of the first stage so can + + align:start position:0% +by the side of the first stage so can + + + align:start position:0% +by the side of the first stage so can +result in very large bias for beta uh so + + align:start position:0% +result in very large bias for beta uh so + + + align:start position:0% +result in very large bias for beta uh so +it's pretty important to check the + + align:start position:0% +it's pretty important to check the + + + align:start position:0% +it's pretty important to check the +equation and uh + + align:start position:0% +equation and uh + + + align:start position:0% +equation and uh +uh people tend to forget that + + align:start position:0% +uh people tend to forget that + + + align:start position:0% +uh people tend to forget that +actually uh often or they will only look + + align:start position:0% +actually uh often or they will only look + + + align:start position:0% +actually uh often or they will only look +at the first half especially when both + + align:start position:0% +at the first half especially when both + + + align:start position:0% +at the first half especially when both +with people who start from RCS and + + align:start position:0% +with people who start from RCS and + + + align:start position:0% +with people who start from RCS and +people who start from uh naturally + + align:start position:0% +people who start from uh naturally + + + align:start position:0% +people who start from uh naturally +assigned variation we'll be very careful + + align:start position:0% +assigned variation we'll be very careful + + + align:start position:0% +assigned variation we'll be very careful +to say that indeed we really have a good + + align:start position:0% +to say that indeed we really have a good + + + align:start position:0% +to say that indeed we really have a good +in instrument because we have something + + align:start position:0% +in instrument because we have something + + + align:start position:0% +in instrument because we have something +that affects education it it also + + align:start position:0% +that affects education it it also + + + align:start position:0% +that affects education it it also +affects cognitive test sces I'm quite + + align:start position:0% +affects cognitive test sces I'm quite + + + align:start position:0% +affects cognitive test sces I'm quite +confident about the this estimate so I'm + + align:start position:0% +confident about the this estimate so I'm + + + align:start position:0% +confident about the this estimate so I'm +confident that my redu form is well + + align:start position:0% +confident that my redu form is well + + + align:start position:0% +confident that my redu form is well +estimated but then they forget that + + align:start position:0% +estimated but then they forget that + + + align:start position:0% +estimated but then they forget that +intermediate link so what I want to do + + align:start position:0% +intermediate link so what I want to do + + + align:start position:0% +intermediate link so what I want to do +before going to look at formulas is to + + align:start position:0% +before going to look at formulas is to + + + align:start position:0% +before going to look at formulas is to +go over some examples and say whether uh + + align:start position:0% +go over some examples and say whether uh + + + align:start position:0% +go over some examples and say whether uh +it's seems to seems to you to be valid + + align:start position:0% +it's seems to seems to you to be valid + + + align:start position:0% +it's seems to seems to you to be valid +or not valid uh and just to make sure + + align:start position:0% +or not valid uh and just to make sure + + + align:start position:0% +or not valid uh and just to make sure +there is Boo in here there are some that + + align:start position:0% +there is Boo in here there are some that + + + align:start position:0% +there is Boo in here there are some that +I at least I think is are okay and some + + align:start position:0% +I at least I think is are okay and some + + + align:start position:0% +I at least I think is are okay and some +that I think are not okay so here's the + + align:start position:0% +that I think are not okay so here's the + + + align:start position:0% +that I think are not okay so here's the +first example um that's from a real + + align:start position:0% +first example um that's from a real + + + align:start position:0% +first example um that's from a real +paper by hens um doctors are randomly + + align:start position:0% +paper by hens um doctors are randomly + + + align:start position:0% +paper by hens um doctors are randomly +selected to receive advice to remind + + align:start position:0% +selected to receive advice to remind + + + align:start position:0% +selected to receive advice to remind +their patient that it's flu season and + + align:start position:0% +their patient that it's flu season and + + + align:start position:0% +their patient that it's flu season and +they should take a flu shot uh I use it + + align:start position:0% +they should take a flu shot uh I use it + + + align:start position:0% +they should take a flu shot uh I use it +as an instrument for taking the flu shot + + align:start position:0% +as an instrument for taking the flu shot + + + align:start position:0% +as an instrument for taking the flu shot +on S + + align:start position:0% +on S + + + align:start position:0% +on S +days for the impact of taking the flu + + align:start position:0% +days for the impact of taking the flu + + + align:start position:0% +days for the impact of taking the flu +shot on on C so that's um called often + + align:start position:0% +shot on on C so that's um called often + + + align:start position:0% +shot on on C so that's um called often +called an encouragement design basically + + align:start position:0% +called an encouragement design basically + + + align:start position:0% +called an encouragement design basically +my randomized variation is this letter + + align:start position:0% +my randomized variation is this letter + + + align:start position:0% +my randomized variation is this letter +that I sent to the to the doctors and I + + align:start position:0% +that I sent to the to the doctors and I + + + align:start position:0% +that I sent to the to the doctors and I +want to use the receiving letter the + + align:start position:0% +want to use the receiving letter the + + + align:start position:0% +want to use the receiving letter the +doctors received the letter as an + + align:start position:0% +doctors received the letter as an + + + align:start position:0% +doctors received the letter as an +instrument for I have received the flu + + align:start position:0% +instrument for I have received the flu + + + align:start position:0% +instrument for I have received the flu +shot and then my final outcome will be + + align:start position:0% +shot and then my final outcome will be + + + align:start position:0% +shot and then my final outcome will be +six days so is it valid is it a good + + align:start position:0% +six days so is it valid is it a good + + + align:start position:0% +six days so is it valid is it a good +instrument or not a good + + align:start position:0% + + + + align:start position:0% + +instrument if the doctor reminds a + + align:start position:0% +instrument if the doctor reminds a + + + align:start position:0% +instrument if the doctor reminds a +patient to take the flu shot then there + + align:start position:0% +patient to take the flu shot then there + + + align:start position:0% +patient to take the flu shot then there +could be a way that the patient takes + + align:start position:0% +could be a way that the patient takes + + + align:start position:0% +could be a way that the patient takes +less days because they feel confident + + align:start position:0% +less days because they feel confident + + + align:start position:0% +less days because they feel confident +doctor looking after them so that could + + align:start position:0% +doctor looking after them so that could + + + align:start position:0% +doctor looking after them so that could +be one what what would be a less uh less + + align:start position:0% +be one what what would be a less uh less + + + align:start position:0% +be one what what would be a less uh less +stretchy one yeah if if you tell a + + align:start position:0% +stretchy one yeah if if you tell a + + + align:start position:0% +stretchy one yeah if if you tell a +doctor to remind their patient unless + + align:start position:0% +doctor to remind their patient unless + + + align:start position:0% +doctor to remind their patient unless +it's like oh call up the patient is + + align:start position:0% +it's like oh call up the patient is + + + align:start position:0% +it's like oh call up the patient is +there for another reason and they remind + + align:start position:0% +there for another reason and they remind + + + align:start position:0% +there for another reason and they remind +hey flu shop the patient is already sick + + align:start position:0% +hey flu shop the patient is already sick + + + align:start position:0% +hey flu shop the patient is already sick +for reason unrelated to the flu shop + + align:start position:0% +for reason unrelated to the flu shop + + + align:start position:0% +for reason unrelated to the flu shop +because they went to the doctor and find + + align:start position:0% +because they went to the doctor and find + + + align:start position:0% +because they went to the doctor and find +it yeah so that would be fine because it + + align:start position:0% +it yeah so that would be fine because it + + + align:start position:0% +it yeah so that would be fine because it +is still the case that if the patients + + align:start position:0% +is still the case that if the patients + + + align:start position:0% +is still the case that if the patients +have come anywhere and are you know + + align:start position:0% +have come anywhere and are you know + + + align:start position:0% +have come anywhere and are you know +patient that tend to be sick that will + + align:start position:0% +patient that tend to be sick that will + + + align:start position:0% +patient that tend to be sick that will +come anyway it is still randomly a sign + + align:start position:0% +come anyway it is still randomly a sign + + + align:start position:0% +come anyway it is still randomly a sign +whether or not the doctor has the has + + align:start position:0% +whether or not the doctor has the has + + + align:start position:0% +whether or not the doctor has the has +the letter or not so uh that you know + + align:start position:0% +the letter or not so uh that you know + + + align:start position:0% +the letter or not so uh that you know +it's in this pool of reasonably sick + + align:start position:0% +it's in this pool of reasonably sick + + + align:start position:0% +it's in this pool of reasonably sick +people so we at this at the time where + + align:start position:0% +people so we at this at the time where + + + align:start position:0% +people so we at this at the time where +they went to the patient so uh so sick + + align:start position:0% +they went to the patient so uh so sick + + + align:start position:0% +they went to the patient so uh so sick +days for instance would just be the + + align:start position:0% +days for instance would just be the + + + align:start position:0% +days for instance would just be the +people who had gone to the doctor yeah + + align:start position:0% +people who had gone to the doctor yeah + + + align:start position:0% +people who had gone to the doctor yeah +it would be among it would be in the set + + align:start position:0% +it would be among it would be in the set + + + align:start position:0% +it would be among it would be in the set +even if we took the whole set uh the + + align:start position:0% +even if we took the whole set uh the + + + align:start position:0% +even if we took the whole set uh the +instrument might be weak in the sense + + align:start position:0% +instrument might be weak in the sense + + + align:start position:0% +instrument might be weak in the sense +you might not have very high predictive + + align:start position:0% +you might not have very high predictive + + + align:start position:0% +you might not have very high predictive +power because lots of people didn't go + + align:start position:0% +power because lots of people didn't go + + + align:start position:0% +power because lots of people didn't go +but as long as we select a sample where + + align:start position:0% +but as long as we select a sample where + + + align:start position:0% +but as long as we select a sample where +people where there is actually effective + + align:start position:0% +people where there is actually effective + + + align:start position:0% +people where there is actually effective +variation you've gone to the doctor once + + align:start position:0% +variation you've gone to the doctor once + + + align:start position:0% +variation you've gone to the doctor once +but your doctor has that letter or + + align:start position:0% +but your doctor has that letter or + + + align:start position:0% +but your doctor has that letter or +doesn't have that letter so the pool is + + align:start position:0% +doesn't have that letter so the pool is + + + align:start position:0% +doesn't have that letter so the pool is +good comparable I don't know whether if + + align:start position:0% +good comparable I don't know whether if + + + align:start position:0% +good comparable I don't know whether if +you're told oh it's full season you + + align:start position:0% +you're told oh it's full season you + + + align:start position:0% +you're told oh it's full season you +should get your FL shot and you're + + align:start position:0% +should get your FL shot and you're + + + align:start position:0% +should get your FL shot and you're +thinking about calling a SE be like oh + + align:start position:0% +thinking about calling a SE be like oh + + + align:start position:0% +thinking about calling a SE be like oh +it's season so not like Mak more likely + + align:start position:0% +it's season so not like Mak more likely + + + align:start position:0% +it's season so not like Mak more likely +to call like I gu so that could be one I + + align:start position:0% +to call like I gu so that could be one I + + + align:start position:0% +to call like I gu so that could be one I +I would still put it in the stretchy one + + align:start position:0% +I would still put it in the stretchy one + + + align:start position:0% +I would still put it in the stretchy one +but maybe a little less + + align:start position:0% +but maybe a little less + + + align:start position:0% +but maybe a little less +stretchy + + align:start position:0% +stretchy + + + align:start position:0% +stretchy +yeah seon you get a lot of reminders + + align:start position:0% +yeah seon you get a lot of reminders + + + align:start position:0% +yeah seon you get a lot of reminders +anyway yourct wasn't toind + + align:start position:0% +anyway yourct wasn't toind + + + align:start position:0% +anyway yourct wasn't toind +you I + + align:start position:0% +you I + + + align:start position:0% +you I +know so + + align:start position:0% +know so + + + align:start position:0% +know so +that how yes exactly so we might not + + align:start position:0% +that how yes exactly so we might not + + + align:start position:0% +that how yes exactly so we might not +have a first stage so the nice thing is + + align:start position:0% +have a first stage so the nice thing is + + + align:start position:0% +have a first stage so the nice thing is +we're going to be able to see that uh so + + align:start position:0% +we're going to be able to see that uh so + + + align:start position:0% +we're going to be able to see that uh so +if we don't have a first stage we don't + + align:start position:0% +if we don't have a first stage we don't + + + align:start position:0% +if we don't have a first stage we don't +have a first stage so that's yep to be + + align:start position:0% +have a first stage so that's yep to be + + + align:start position:0% +have a first stage so that's yep to be +said about doctors actually following + + align:start position:0% +said about doctors actually following + + + align:start position:0% +said about doctors actually following +your advice like you need to measure + + align:start position:0% +your advice like you need to measure + + + align:start position:0% +your advice like you need to measure +okay how often doctors follow my advice + + align:start position:0% +okay how often doctors follow my advice + + + align:start position:0% +okay how often doctors follow my advice +yes so they might so exactly that that + + align:start position:0% +yes so they might so exactly that that + + + align:start position:0% +yes so they might so exactly that that +will also affect the first stage they + + align:start position:0% +will also affect the first stage they + + + align:start position:0% +will also affect the first stage they +might up might not follow your advice so + + align:start position:0% +might up might not follow your advice so + + + align:start position:0% +might up might not follow your advice so +that's if they don't that which doctors + + align:start position:0% +that's if they don't that which doctors + + + align:start position:0% +that's if they don't that which doctors +are know not to then that would that + + align:start position:0% +are know not to then that would that + + + align:start position:0% +are know not to then that would that +would also make the first stage weaker + + align:start position:0% +would also make the first stage weaker + + + align:start position:0% +would also make the first stage weaker +we'll be able to check that by the first + + align:start position:0% +we'll be able to check that by the first + + + align:start position:0% +we'll be able to check that by the first +stage yeah what I he is what if like the + + align:start position:0% +stage yeah what I he is what if like the + + + align:start position:0% +stage yeah what I he is what if like the +doctors you randomly select you advise + + align:start position:0% +doctors you randomly select you advise + + + align:start position:0% +doctors you randomly select you advise +them to do this like they don't follow + + align:start position:0% +them to do this like they don't follow + + + align:start position:0% +them to do this like they don't follow +your advice anyway like I feel like + + align:start position:0% +your advice anyway like I feel like + + + align:start position:0% +your advice anyway like I feel like +doctors are + + align:start position:0% +doctors are + + + align:start position:0% +doctors are +yes so then you wouldn't have a first + + align:start position:0% +yes so then you wouldn't have a first + + + align:start position:0% +yes so then you wouldn't have a first +stage so for all of this reason it might + + align:start position:0% +stage so for all of this reason it might + + + align:start position:0% +stage so for all of this reason it might +not be such the first stage might not be + + align:start position:0% +not be such the first stage might not be + + + align:start position:0% +not be such the first stage might not be +very large or might not be there at all + + align:start position:0% +very large or might not be there at all + + + align:start position:0% +very large or might not be there at all +so if it's not there at all you just go + + align:start position:0% +so if it's not there at all you just go + + + align:start position:0% +so if it's not there at all you just go +home and do something else but if it's + + align:start position:0% +home and do something else but if it's + + + align:start position:0% +home and do something else but if it's +not very large you might still tempted + + align:start position:0% +not very large you might still tempted + + + align:start position:0% +not very large you might still tempted +to use it and then we really need to + + align:start position:0% +to use it and then we really need to + + + align:start position:0% +to use it and then we really need to +make sure that there is no uh that + + align:start position:0% +make sure that there is no uh that + + + align:start position:0% +make sure that there is no uh that +there's no other + + align:start position:0% + + + + align:start position:0% + +violation so You' you've you you've + + align:start position:0% +violation so You' you've you you've + + + align:start position:0% +violation so You' you've you you've +tried and the stretchy ones are are + + align:start position:0% +tried and the stretchy ones are are + + + align:start position:0% +tried and the stretchy ones are are +stretchy but they had the right idea + + align:start position:0% +stretchy but they had the right idea + + + align:start position:0% +stretchy but they had the right idea +which is is there an effect is there an + + align:start position:0% +which is is there an effect is there an + + + align:start position:0% +which is is there an effect is there an +effect of the letter over and above uh + + align:start position:0% +effect of the letter over and above uh + + + align:start position:0% +effect of the letter over and above uh +over and above the fact that it leads + + align:start position:0% +over and above the fact that it leads + + + align:start position:0% +over and above the fact that it leads +some people to get the vaccines and what + + align:start position:0% +some people to get the vaccines and what + + + align:start position:0% +some people to get the vaccines and what +they sh in that paper is that there is + + align:start position:0% +they sh in that paper is that there is + + + align:start position:0% +they sh in that paper is that there is +an effect of the letter which is the + + align:start position:0% +an effect of the letter which is the + + + align:start position:0% +an effect of the letter which is the +doctors also say by the way it's flu + + align:start position:0% +doctors also say by the way it's flu + + + align:start position:0% +doctors also say by the way it's flu +season remember to take orange juice and + + align:start position:0% +season remember to take orange juice and + + + align:start position:0% +season remember to take orange juice and +uh wash your hands often and all of + + align:start position:0% +uh wash your hands often and all of + + + align:start position:0% +uh wash your hands often and all of +these things so all of these things + + align:start position:0% +these things so all of these things + + + align:start position:0% +these things so all of these things +might make people less + + align:start position:0% +might make people less + + + align:start position:0% +might make people less +sick not just with the flu but with + + align:start position:0% +sick not just with the flu but with + + + align:start position:0% +sick not just with the flu but with +other other things they might be less + + align:start position:0% +other other things they might be less + + + align:start position:0% +other other things they might be less +likely to get the common cold or + + align:start position:0% +likely to get the common cold or + + + align:start position:0% +likely to get the common cold or +pneumonia what not uh that are not the + + align:start position:0% +pneumonia what not uh that are not the + + + align:start position:0% +pneumonia what not uh that are not the +flu and uh any of these thing will will + + align:start position:0% +flu and uh any of these thing will will + + + align:start position:0% +flu and uh any of these thing will will +will affect the outcome six days not + + align:start position:0% +will affect the outcome six days not + + + align:start position:0% +will affect the outcome six days not +through the flu vaccines but through + + align:start position:0% +through the flu vaccines but through + + + align:start position:0% +through the flu vaccines but through +these other things and in particular if + + align:start position:0% +these other things and in particular if + + + align:start position:0% +these other things and in particular if +it's compounded by the fact that the + + align:start position:0% +it's compounded by the fact that the + + + align:start position:0% +it's compounded by the fact that the +first stage is not very large then we + + align:start position:0% +first stage is not very large then we + + + align:start position:0% +first stage is not very large then we +would kind of mistakenly attribute all + + align:start position:0% +would kind of mistakenly attribute all + + + align:start position:0% +would kind of mistakenly attribute all +of this reduction which is due to any + + align:start position:0% +of this reduction which is due to any + + + align:start position:0% +of this reduction which is due to any +number of causes to just a flu shot + + align:start position:0% +number of causes to just a flu shot + + + align:start position:0% +number of causes to just a flu shot +which would be which would lead to + + align:start position:0% +which would be which would lead to + + + align:start position:0% +which would be which would lead to +B uh I want to follow up on that Charter + + align:start position:0% +B uh I want to follow up on that Charter + + + align:start position:0% +B uh I want to follow up on that Charter +School example so um in Boston and many + + align:start position:0% +School example so um in Boston and many + + + align:start position:0% +School example so um in Boston and many +other places uh there are too many kids + + align:start position:0% +other places uh there are too many kids + + + align:start position:0% +other places uh there are too many kids +who want to go to charter school and + + align:start position:0% +who want to go to charter school and + + + align:start position:0% +who want to go to charter school and +they are not enough charter schools so + + align:start position:0% +they are not enough charter schools so + + + align:start position:0% +they are not enough charter schools so +when a kid applies to chapter school and + + align:start position:0% +when a kid applies to chapter school and + + + align:start position:0% +when a kid applies to chapter school and +the schools have to randomize who they + + align:start position:0% +the schools have to randomize who they + + + align:start position:0% +the schools have to randomize who they +take in so some kids uh + + align:start position:0% +take in so some kids uh + + + align:start position:0% +take in so some kids uh +so suppose you want to look at the + + align:start position:0% +so suppose you want to look at the + + + align:start position:0% +so suppose you want to look at the +impact of uh of and then suppose you + + align:start position:0% +impact of uh of and then suppose you + + + align:start position:0% +impact of uh of and then suppose you +want to look at the at the impact of of + + align:start position:0% +want to look at the at the impact of of + + + align:start position:0% +want to look at the at the impact of of +of going to Charter School you could say + + align:start position:0% +of going to Charter School you could say + + + align:start position:0% +of going to Charter School you could say +well I'm going to use I'm going to focus + + align:start position:0% +well I'm going to use I'm going to focus + + + align:start position:0% +well I'm going to use I'm going to focus +on the kids who have applied to this + + align:start position:0% +on the kids who have applied to this + + + align:start position:0% +on the kids who have applied to this +school and and and use the lottery + + align:start position:0% +school and and and use the lottery + + + align:start position:0% +school and and and use the lottery +assume the lottery was well run to look + + align:start position:0% +assume the lottery was well run to look + + + align:start position:0% +assume the lottery was well run to look +at the impact of going to Charter + + align:start position:0% +at the impact of going to Charter + + + align:start position:0% +at the impact of going to Charter +School + + align:start position:0% +School + + + align:start position:0% +School +uh how does that + + align:start position:0% + + + + align:start position:0% + +look you like + + align:start position:0% +look you like + + + align:start position:0% +look you like +it any opposition + + align:start position:0% + + + + align:start position:0% + +any using uh to in Boston for example uh + + align:start position:0% +any using uh to in Boston for example uh + + + align:start position:0% +any using uh to in Boston for example uh +CH schools are over subscribed so they + + align:start position:0% +CH schools are over subscribed so they + + + align:start position:0% +CH schools are over subscribed so they +have to randomize they have to run a + + align:start position:0% +have to randomize they have to run a + + + align:start position:0% +have to randomize they have to run a +lottery and we are using it as an + + align:start position:0% +lottery and we are using it as an + + + align:start position:0% +lottery and we are using it as an +instrument we're using winning the + + align:start position:0% +instrument we're using winning the + + + align:start position:0% +instrument we're using winning the +lottery as an instrument for attending a + + align:start position:0% +lottery as an instrument for attending a + + + align:start position:0% +lottery as an instrument for attending a +particular charter school or Charter + + align:start position:0% +particular charter school or Charter + + + align:start position:0% +particular charter school or Charter +School in + + align:start position:0% +School in + + + align:start position:0% +School in +general + + align:start position:0% +general + + + align:start position:0% +general +YIFY are the two groups you're looking + + align:start position:0% +YIFY are the two groups you're looking + + + align:start position:0% +YIFY are the two groups you're looking +at the kids who wind up at Charter + + align:start position:0% +at the kids who wind up at Charter + + + align:start position:0% +at the kids who wind up at Charter +School enter the lottery but no we are + + align:start position:0% +School enter the lottery but no we are + + + align:start position:0% +School enter the lottery but no we are +going to look at we're going to look + + align:start position:0% +going to look at we're going to look + + + align:start position:0% +going to look at we're going to look +yeah exactly we are going to look at the + + align:start position:0% +yeah exactly we are going to look at the + + + align:start position:0% +yeah exactly we are going to look at the +kids all of the kids who apply to + + align:start position:0% +kids all of the kids who apply to + + + align:start position:0% +kids all of the kids who apply to +charter + + align:start position:0% +charter + + + align:start position:0% +charter +school either think for example at a + + align:start position:0% +school either think for example at a + + + align:start position:0% +school either think for example at a +particular one makes it makes the + + align:start position:0% +particular one makes it makes the + + + align:start position:0% +particular one makes it makes the +thinking easier imagine a particular all + + align:start position:0% +thinking easier imagine a particular all + + + align:start position:0% +thinking easier imagine a particular all +of the kids who appli to Bridge Academy + + align:start position:0% +of the kids who appli to Bridge Academy + + + align:start position:0% +of the kids who appli to Bridge Academy +Bridge Academy is over subscribe every + + align:start position:0% +Bridge Academy is over subscribe every + + + align:start position:0% +Bridge Academy is over subscribe every +year who gets who gets not Bridge um + + align:start position:0% +year who gets who gets not Bridge um + + + align:start position:0% +year who gets who gets not Bridge um +it's called Uh bridge is what the well + + align:start position:0% +it's called Uh bridge is what the well + + + align:start position:0% +it's called Uh bridge is what the well +let's assume Bridge Academy yeah then + + align:start position:0% +let's assume Bridge Academy yeah then + + + align:start position:0% +let's assume Bridge Academy yeah then +all of the kids uh apply then some of + + align:start position:0% +all of the kids uh apply then some of + + + align:start position:0% +all of the kids uh apply then some of +them get in some of them don't get in by + + align:start position:0% +them get in some of them don't get in by + + + align:start position:0% +them get in some of them don't get in by +Lottery and I'm comparing the people who + + align:start position:0% +Lottery and I'm comparing the people who + + + align:start position:0% +Lottery and I'm comparing the people who +win the lottery to people who lose the + + align:start position:0% +win the lottery to people who lose the + + + align:start position:0% +win the lottery to people who lose the +luxury + + align:start position:0% +luxury + + + align:start position:0% +luxury +yeah students who + + align:start position:0% + + + + align:start position:0% + +apply knowledge of theol just gener more + + align:start position:0% +apply knowledge of theol just gener more + + + align:start position:0% +apply knowledge of theol just gener more +confidence that they be able to succeed + + align:start position:0% +confidence that they be able to succeed + + + align:start position:0% +confidence that they be able to succeed +or get in Asos to people from oros to + + align:start position:0% +or get in Asos to people from oros to + + + align:start position:0% +or get in Asos to people from oros to +students from more disadvantage + + align:start position:0% +students from more disadvantage + + + align:start position:0% +students from more disadvantage +background there's no point + + align:start position:0% +background there's no point + + + align:start position:0% +background there's no point +applying yes so this is related to the + + align:start position:0% +applying yes so this is related to the + + + align:start position:0% +applying yes so this is related to the +question we had before if it gives me a + + align:start position:0% +question we had before if it gives me a + + + align:start position:0% +question we had before if it gives me a +causal effect it's going to give me the + + align:start position:0% +causal effect it's going to give me the + + + align:start position:0% +causal effect it's going to give me the +causal effect for the pool of applicant + + align:start position:0% +causal effect for the pool of applicant + + + align:start position:0% +causal effect for the pool of applicant +which may or may not be representative + + align:start position:0% +which may or may not be representative + + + align:start position:0% +which may or may not be representative +of uh of of the larger pool uh that is + + align:start position:0% +of uh of of the larger pool uh that is + + + align:start position:0% +of uh of of the larger pool uh that is +life that's kind of what we have with + + align:start position:0% +life that's kind of what we have with + + + align:start position:0% +life that's kind of what we have with +samples like that's the sample so we + + align:start position:0% +samples like that's the sample so we + + + align:start position:0% +samples like that's the sample so we +we'll just take that as um you know as + + align:start position:0% +we'll just take that as um you know as + + + align:start position:0% +we'll just take that as um you know as +given but that's that's a very good + + align:start position:0% +given but that's that's a very good + + + align:start position:0% +given but that's that's a very good +point and that's you know something that + + align:start position:0% +point and that's you know something that + + + align:start position:0% +point and that's you know something that +has been leveled as a criticism against + + align:start position:0% +has been leveled as a criticism against + + + align:start position:0% +has been leveled as a criticism against +all of these + + align:start position:0% +all of these + + + align:start position:0% +all of these +studies students who lose Lottery there + + align:start position:0% +studies students who lose Lottery there + + + align:start position:0% +studies students who lose Lottery there +might be some psychological effect + + align:start position:0% +might be some psychological effect + + + align:start position:0% +might be some psychological effect +because they didn't get into the school + + align:start position:0% +because they didn't get into the school + + + align:start position:0% +because they didn't get into the school +so then their underperformance in non + + align:start position:0% +so then their underperformance in non + + + align:start position:0% +so then their underperformance in non +charter school isn't the fact that they + + align:start position:0% +charter school isn't the fact that they + + + align:start position:0% +charter school isn't the fact that they +go to Charter School the fact that + + align:start position:0% +go to Charter School the fact that + + + align:start position:0% +go to Charter School the fact that +psycholog yes so this is kind of back to + + align:start position:0% +psycholog yes so this is kind of back to + + + align:start position:0% +psycholog yes so this is kind of back to +exactly what sort of uh the point about + + align:start position:0% +exactly what sort of uh the point about + + + align:start position:0% +exactly what sort of uh the point about +winning the lery might make you happy + + align:start position:0% +winning the lery might make you happy + + + align:start position:0% +winning the lery might make you happy +and in here like losing the ly might + + align:start position:0% +and in here like losing the ly might + + + align:start position:0% +and in here like losing the ly might +make you depressed so that might be that + + align:start position:0% +make you depressed so that might be that + + + align:start position:0% +make you depressed so that might be that +might be a an issue um other than that + + align:start position:0% +might be a an issue um other than that + + + align:start position:0% +might be a an issue um other than that +it seems to me to be a pretty good + + align:start position:0% +it seems to me to be a pretty good + + + align:start position:0% +it seems to me to be a pretty good +instrument uh and actually it's been + + align:start position:0% +instrument uh and actually it's been + + + align:start position:0% +instrument uh and actually it's been +used frequently uh I think that needs to + + align:start position:0% +used frequently uh I think that needs to + + + align:start position:0% +used frequently uh I think that needs to +be uh um taken into consideration and + + align:start position:0% +be uh um taken into consideration and + + + align:start position:0% +be uh um taken into consideration and +the fact that it's a specific set of + + align:start position:0% +the fact that it's a specific set of + + + align:start position:0% +the fact that it's a specific set of +kids also have to be taken into + + align:start position:0% +kids also have to be taken into + + + align:start position:0% +kids also have to be taken into +consideration but I don't see a big + + align:start position:0% +consideration but I don't see a big + + + align:start position:0% +consideration but I don't see a big +issue with with those at + + align:start position:0% +issue with with those at + + + align:start position:0% +issue with with those at +all uh in fact Josh Ang and parak Pak + + align:start position:0% +all uh in fact Josh Ang and parak Pak + + + align:start position:0% +all uh in fact Josh Ang and parak Pak +both from the Departments are working + + align:start position:0% +both from the Departments are working + + + align:start position:0% +both from the Departments are working +with those a + + align:start position:0% +with those a + + + align:start position:0% +with those a +lot um so that one would be I think + + align:start position:0% +lot um so that one would be I think + + + align:start position:0% +lot um so that one would be I think +largely okay with your cat another one + + align:start position:0% +largely okay with your cat another one + + + align:start position:0% +largely okay with your cat another one +is uh kids are in schools that are + + align:start position:0% +is uh kids are in schools that are + + + align:start position:0% +is uh kids are in schools that are +randomly uh kids are in school uh and + + align:start position:0% +randomly uh kids are in school uh and + + + align:start position:0% +randomly uh kids are in school uh and +well the the sentence is not very well + + align:start position:0% +well the the sentence is not very well + + + align:start position:0% +well the the sentence is not very well +con constructed uh so yes kids it's a + + align:start position:0% +con constructed uh so yes kids it's a + + + align:start position:0% +con constructed uh so yes kids it's a +study that is randomized at the school + + align:start position:0% +study that is randomized at the school + + + align:start position:0% +study that is randomized at the school +School + + align:start position:0% +School + + + align:start position:0% +School +level and uh kids are um either in a in + + align:start position:0% +level and uh kids are um either in a in + + + align:start position:0% +level and uh kids are um either in a in +a school that is assigned to receive the + + align:start position:0% +a school that is assigned to receive the + + + align:start position:0% +a school that is assigned to receive the +pill or not but not every kid actually + + align:start position:0% +pill or not but not every kid actually + + + align:start position:0% +pill or not but not every kid actually +gets the peill because they were absent + + align:start position:0% +gets the peill because they were absent + + + align:start position:0% +gets the peill because they were absent +on this day or something like that so + + align:start position:0% +on this day or something like that so + + + align:start position:0% +on this day or something like that so +let's say only some of the kids actually + + align:start position:0% +let's say only some of the kids actually + + + align:start position:0% +let's say only some of the kids actually +get the DW Waring pill and other don't + + align:start position:0% +get the DW Waring pill and other don't + + + align:start position:0% +get the DW Waring pill and other don't +so first I estimate the effect of being + + align:start position:0% +so first I estimate the effect of being + + + align:start position:0% +so first I estimate the effect of being +a dew Waring school on my uh cognitive + + align:start position:0% +a dew Waring school on my uh cognitive + + + align:start position:0% +a dew Waring school on my uh cognitive +scores present in school later on + + align:start position:0% +scores present in school later on + + + align:start position:0% +scores present in school later on +whatever you're interested in but then I + + align:start position:0% +whatever you're interested in but then I + + + align:start position:0% +whatever you're interested in but then I +say well let me actually instrument this + + align:start position:0% +say well let me actually instrument this + + + align:start position:0% +say well let me actually instrument this +is not the effect of being dewed because + + align:start position:0% +is not the effect of being dewed because + + + align:start position:0% +is not the effect of being dewed because +only about half the kids end up being + + align:start position:0% +only about half the kids end up being + + + align:start position:0% +only about half the kids end up being +dewed so let me look let me use the fact + + align:start position:0% +dewed so let me look let me use the fact + + + align:start position:0% +dewed so let me look let me use the fact +that I was in a dew Waring school as an + + align:start position:0% +that I was in a dew Waring school as an + + + align:start position:0% +that I was in a dew Waring school as an +instrument for actually being dewed in + + align:start position:0% +instrument for actually being dewed in + + + align:start position:0% +instrument for actually being dewed in +other words I'm going to multiply all my + + align:start position:0% +other words I'm going to multiply all my + + + align:start position:0% +other words I'm going to multiply all my +estimates by two + + align:start position:0% + + + + align:start position:0% + +yeah for okay if school is the what + + align:start position:0% +yeah for okay if school is the what + + + align:start position:0% +yeah for okay if school is the what +percentage of students are actually that + + align:start position:0% +percentage of students are actually that + + + align:start position:0% +percentage of students are actually that +suppose I know suppose I know it suppose + + align:start position:0% +suppose I know suppose I know it suppose + + + align:start position:0% +suppose I know suppose I know it suppose +I know for every I have an individual + + align:start position:0% +I know for every I have an individual + + + align:start position:0% +I know for every I have an individual +level data set where I know whether the + + align:start position:0% +level data set where I know whether the + + + align:start position:0% +level data set where I know whether the +kid was actually dewed and whether they + + align:start position:0% +kid was actually dewed and whether they + + + align:start position:0% +kid was actually dewed and whether they +are in a dew Waring + + align:start position:0% +are in a dew Waring + + + align:start position:0% +are in a dew Waring +school and I don't so I know so I can + + align:start position:0% +school and I don't so I know so I can + + + align:start position:0% +school and I don't so I know so I can +calculate for each School the fraction + + align:start position:0% +calculate for each School the fraction + + + align:start position:0% +calculate for each School the fraction +of kids who actually was dewed or I can + + align:start position:0% +of kids who actually was dewed or I can + + + align:start position:0% +of kids who actually was dewed or I can +calculate for the entire treatment + + align:start position:0% +calculate for the entire treatment + + + align:start position:0% +calculate for the entire treatment +School how many what fraction of the + + align:start position:0% +School how many what fraction of the + + + align:start position:0% +School how many what fraction of the +treatment kids actually got dewed and + + align:start position:0% +treatment kids actually got dewed and + + + align:start position:0% +treatment kids actually got dewed and +let's say no one got dewed in the non in + + align:start position:0% +let's say no one got dewed in the non in + + + align:start position:0% +let's say no one got dewed in the non in +the control school then I have enough to + + align:start position:0% +the control school then I have enough to + + + align:start position:0% +the control school then I have enough to +do my reduced form and my + + align:start position:0% +do my reduced form and my + + + align:start position:0% +do my reduced form and my +so to clarify like when we say the worm + + align:start position:0% +so to clarify like when we say the worm + + + align:start position:0% +so to clarify like when we say the worm +do we just mean they got the pill or + + align:start position:0% +do we just mean they got the pill or + + + align:start position:0% +do we just mean they got the pill or +they don't have any worms in they got + + align:start position:0% +they don't have any worms in they got + + + align:start position:0% +they don't have any worms in they got +the pill that's the effect suppose + + align:start position:0% +the pill that's the effect suppose + + + align:start position:0% +the pill that's the effect suppose +that's what we are interested we think + + align:start position:0% +that's what we are interested we think + + + align:start position:0% +that's what we are interested we think +which is actually one for one because + + align:start position:0% +which is actually one for one because + + + align:start position:0% +which is actually one for one because +the pill are + + align:start position:0% +the pill are + + + align:start position:0% +the pill are +pretty you get the wor you get the pill + + align:start position:0% +pretty you get the wor you get the pill + + + align:start position:0% +pretty you get the wor you get the pill +and you're deep Worm but you don't + + align:start position:0% +and you're deep Worm but you don't + + + align:start position:0% +and you're deep Worm but you don't +measure it like immediately then and + + align:start position:0% +measure it like immediately then and + + + align:start position:0% +measure it like immediately then and +then some kid who didn't wasn't there + + align:start position:0% +then some kid who didn't wasn't there + + + align:start position:0% +then some kid who didn't wasn't there +that day when they were doing out pills + + align:start position:0% +that day when they were doing out pills + + + align:start position:0% +that day when they were doing out pills +comes back andly contagious see the + + align:start position:0% +comes back andly contagious see the + + + align:start position:0% +comes back andly contagious see the +worms again exactly so that would be the + + align:start position:0% +worms again exactly so that would be the + + + align:start position:0% +worms again exactly so that would be the +problem which is that that and in on the + + align:start position:0% +problem which is that that and in on the + + + align:start position:0% +problem which is that that and in on the +other end even the kids who did not get + + align:start position:0% +other end even the kids who did not get + + + align:start position:0% +other end even the kids who did not get +the + + align:start position:0% +the + + + align:start position:0% +the +pill actually uh uh actually get much + + align:start position:0% +pill actually uh uh actually get much + + + align:start position:0% +pill actually uh uh actually get much +better if they are in a school with + + align:start position:0% +better if they are in a school with + + + align:start position:0% +better if they are in a school with +other kids who get the one simply + + align:start position:0% +other kids who get the one simply + + + align:start position:0% +other kids who get the one simply +because worms are so contagious that if + + align:start position:0% +because worms are so contagious that if + + + align:start position:0% +because worms are so contagious that if +you have worms you'll give them to the + + align:start position:0% +you have worms you'll give them to the + + + align:start position:0% +you have worms you'll give them to the +neighbors and therefore treating being + + align:start position:0% +neighbors and therefore treating being + + + align:start position:0% +neighbors and therefore treating being +in a treatment school as an + + align:start position:0% +in a treatment school as an + + + align:start position:0% +in a treatment school as an +effect irrespective of whether I got + + align:start position:0% +effect irrespective of whether I got + + + align:start position:0% +effect irrespective of whether I got +treated myself because worms are + + align:start position:0% +treated myself because worms are + + + align:start position:0% +treated myself because worms are +contentious so uh that would not be okay + + align:start position:0% +contentious so uh that would not be okay + + + align:start position:0% +contentious so uh that would not be okay +here it's pretty clear it's an example + + align:start position:0% +here it's pretty clear it's an example + + + align:start position:0% +here it's pretty clear it's an example +any example with externalities Etc are + + align:start position:0% +any example with externalities Etc are + + + align:start position:0% +any example with externalities Etc are +example that are going to violate that + + align:start position:0% +example that are going to violate that + + + align:start position:0% +example that are going to violate that +link because there is a direct effect of + + align:start position:0% +link because there is a direct effect of + + + align:start position:0% +link because there is a direct effect of +being in a treatment school on getting + + align:start position:0% +being in a treatment school on getting + + + align:start position:0% +being in a treatment school on getting +the opin Y so you ask me to keep the + + align:start position:0% +the opin Y so you ask me to keep the + + + align:start position:0% +the opin Y so you ask me to keep the +laptop example in mind yes I want to go + + align:start position:0% +laptop example in mind yes I want to go + + + align:start position:0% +laptop example in mind yes I want to go +back to the laptop example uh so uh so + + align:start position:0% +back to the laptop example uh so uh so + + + align:start position:0% +back to the laptop example uh so uh so +uh so now think of the laptop uh think + + align:start position:0% +uh so now think of the laptop uh think + + + align:start position:0% +uh so now think of the laptop uh think +of the laptop example would it be a good + + align:start position:0% +of the laptop example would it be a good + + + align:start position:0% +of the laptop example would it be a good +ex would it be a good instrument + + align:start position:0% +ex would it be a good instrument + + + align:start position:0% +ex would it be a good instrument +providing the + + align:start position:0% +providing the + + + align:start position:0% +providing the +laptops so why would not be a good + + align:start position:0% +laptops so why would not be a good + + + align:start position:0% +laptops so why would not be a good +instrument feels like there are a lot of + + align:start position:0% +instrument feels like there are a lot of + + + align:start position:0% +instrument feels like there are a lot of +external + + align:start position:0% +external + + + align:start position:0% +external +Associated external effects like it's + + align:start position:0% +Associated external effects like it's + + + align:start position:0% +Associated external effects like it's +not just affecting education there's + + align:start position:0% +not just affecting education there's + + + align:start position:0% +not just affecting education there's +also a bunch of effects on like how much + + align:start position:0% +also a bunch of effects on like how much + + + align:start position:0% +also a bunch of effects on like how much +time you spend on laptop as opposed to + + align:start position:0% +time you spend on laptop as opposed to + + + align:start position:0% +time you spend on laptop as opposed to +say exactly other it might make you + + align:start position:0% +say exactly other it might make you + + + align:start position:0% +say exactly other it might make you +spend more time at might be more likely + + align:start position:0% +spend more time at might be more likely + + + align:start position:0% +spend more time at might be more likely +that you actually go to school and stay + + align:start position:0% +that you actually go to school and stay + + + align:start position:0% +that you actually go to school and stay +in school doesn't drop out but also it + + align:start position:0% +in school doesn't drop out but also it + + + align:start position:0% +in school doesn't drop out but also it +might help you study it might hinder + + align:start position:0% +might help you study it might hinder + + + align:start position:0% +might help you study it might hinder +your studies it might do all sorts of + + align:start position:0% +your studies it might do all sorts of + + + align:start position:0% +your studies it might do all sorts of +stuff directly so laptop would not be a + + align:start position:0% +stuff directly so laptop would not be a + + + align:start position:0% +stuff directly so laptop would not be a +great example uh which are the ones that + + align:start position:0% +great example uh which are the ones that + + + align:start position:0% +great example uh which are the ones that +we went + + align:start position:0% +we went + + + align:start position:0% +we went +over that so go ahead go ahead yeah yes + + align:start position:0% +over that so go ahead go ahead yeah yes + + + align:start position:0% +over that so go ahead go ahead yeah yes +oh just if you have a school where only + + align:start position:0% +oh just if you have a school where only + + + align:start position:0% +oh just if you have a school where only +a few kids have laptops they're going to + + align:start position:0% +a few kids have laptops they're going to + + + align:start position:0% +a few kids have laptops they're going to +share them with the other students yeah + + align:start position:0% +share them with the other students yeah + + + align:start position:0% +share them with the other students yeah +they might also be if we if we randomize + + align:start position:0% +they might also be if we if we randomize + + + align:start position:0% +they might also be if we if we randomize +these laptops at the individual level + + align:start position:0% +these laptops at the individual level + + + align:start position:0% +these laptops at the individual level +there might be an effect on the other + + align:start position:0% +there might be an effect on the other + + + align:start position:0% +there might be an effect on the other +kids so that's the that will that will + + align:start position:0% +kids so that's the that will that will + + + align:start position:0% +kids so that's the that will that will +create extra problems yeah so to address + + align:start position:0% +create extra problems yeah so to address + + + align:start position:0% +create extra problems yeah so to address +those two issues what if we just gave + + align:start position:0% +those two issues what if we just gave + + + align:start position:0% +those two issues what if we just gave +them laop really like + + align:start position:0% +them laop really like + + + align:start position:0% +them laop really like +hardcoded functions like you can only do + + align:start position:0% +hardcoded functions like you can only do + + + align:start position:0% +hardcoded functions like you can only do +XYZ on it they're all educational would + + align:start position:0% +XYZ on it they're all educational would + + + align:start position:0% +XYZ on it they're all educational would +that solve some things you now this is + + align:start position:0% +that solve some things you now this is + + + align:start position:0% +that solve some things you now this is +like effect would it or would it not for + + align:start position:0% +like effect would it or would it not for + + + align:start position:0% +like effect would it or would it not for +their effect uh it would make it would + + align:start position:0% +their effect uh it would make it would + + + align:start position:0% +their effect uh it would make it would +make sure it doesn't hurt them but it + + align:start position:0% +make sure it doesn't hurt them but it + + + align:start position:0% +make sure it doesn't hurt them but it +would presumably help + + align:start position:0% +would presumably help + + + align:start position:0% +would presumably help +them in fact the channel through which + + align:start position:0% +them in fact the channel through which + + + align:start position:0% +them in fact the channel through which +you would have kids more likely to stay + + align:start position:0% +you would have kids more likely to stay + + + align:start position:0% +you would have kids more likely to stay +in school is that they will understand + + align:start position:0% +in school is that they will understand + + + align:start position:0% +in school is that they will understand +their lessons better and the like so you + + align:start position:0% +their lessons better and the like so you + + + align:start position:0% +their lessons better and the like so you +will have two effects going on from the + + align:start position:0% +will have two effects going on from the + + + align:start position:0% +will have two effects going on from the +laptop you will have kids in school for + + align:start position:0% +laptop you will have kids in school for + + + align:start position:0% +laptop you will have kids in school for +longer but also if you want the quality + + align:start position:0% +longer but also if you want the quality + + + align:start position:0% +longer but also if you want the quality +of their education improves so it would + + align:start position:0% +of their education improves so it would + + + align:start position:0% +of their education improves so it would +still not be a good instrument it might + + align:start position:0% +still not be a good instrument it might + + + align:start position:0% +still not be a good instrument it might +be a better program but it would still + + align:start position:0% +be a better program but it would still + + + align:start position:0% +be a better program but it would still +not be a good instrument for uh going to + + align:start position:0% +not be a good instrument for uh going to + + + align:start position:0% +not be a good instrument for uh going to +school it might be a fine instrument if + + align:start position:0% +school it might be a fine instrument if + + + align:start position:0% +school it might be a fine instrument if +you're interested in the effect of + + align:start position:0% +you're interested in the effect of + + + align:start position:0% +you're interested in the effect of +cognitive scores on future + + align:start position:0% +cognitive scores on future + + + align:start position:0% +cognitive scores on future +earnings you might say well the laptop + + align:start position:0% +earnings you might say well the laptop + + + align:start position:0% +earnings you might say well the laptop +really the only thing they did is to + + align:start position:0% +really the only thing they did is to + + + align:start position:0% +really the only thing they did is to +increase cognitive scores then you could + + align:start position:0% +increase cognitive scores then you could + + + align:start position:0% +increase cognitive scores then you could +use it as an instrument for cognitive + + align:start position:0% +use it as an instrument for cognitive + + + align:start position:0% +use it as an instrument for cognitive +scores yeah if you talking about me so + + align:start position:0% +scores yeah if you talking about me so + + + align:start position:0% +scores yeah if you talking about me so +in that case meals would also be + + align:start position:0% +in that case meals would also be + + + align:start position:0% +in that case meals would also be +problematic because they might be of + + align:start position:0% +problematic because they might be of + + + align:start position:0% +problematic because they might be of +different nutrition levels than what + + align:start position:0% +different nutrition levels than what + + + align:start position:0% +different nutrition levels than what +kids would get otherwise exactly so + + align:start position:0% +kids would get otherwise exactly so + + + align:start position:0% +kids would get otherwise exactly so +meals is another example that would be + + align:start position:0% +meals is another example that would be + + + align:start position:0% +meals is another example that would be +problematic certainly would bring a lot + + align:start position:0% +problematic certainly would bring a lot + + + align:start position:0% +problematic certainly would bring a lot +of kids to school but it also put + + align:start position:0% +of kids to school but it also put + + + align:start position:0% +of kids to school but it also put +something in their stomach typically the + + align:start position:0% +something in their stomach typically the + + + align:start position:0% +something in their stomach typically the +meals have vitamins and iron and the + + align:start position:0% +meals have vitamins and iron and the + + + align:start position:0% +meals have vitamins and iron and the +like it make the kids more alert uh + + align:start position:0% +like it make the kids more alert uh + + + align:start position:0% +like it make the kids more alert uh +during the school day they will learn + + align:start position:0% +during the school day they will learn + + + align:start position:0% +during the school day they will learn +better and we will have this effect mhed + + align:start position:0% +better and we will have this effect mhed + + + align:start position:0% +better and we will have this effect mhed +up exactly so meals would be would be + + align:start position:0% +up exactly so meals would be would be + + + align:start position:0% +up exactly so meals would be would be +another one thank you that's so in that + + align:start position:0% +another one thank you that's so in that + + + align:start position:0% +another one thank you that's so in that +case could we have a direct estimation + + align:start position:0% +case could we have a direct estimation + + + align:start position:0% +case could we have a direct estimation +of having needs on exactly same thing + + align:start position:0% +of having needs on exactly same thing + + + align:start position:0% +of having needs on exactly same thing +with the laptops by the way nothing + + align:start position:0% +with the laptops by the way nothing + + + align:start position:0% +with the laptops by the way nothing +prevents you from looking at the effect + + align:start position:0% +prevents you from looking at the effect + + + align:start position:0% +prevents you from looking at the effect +of laptop of on test sces but you + + align:start position:0% +of laptop of on test sces but you + + + align:start position:0% +of laptop of on test sces but you +wouldn't want to do the IV all it says + + align:start position:0% +wouldn't want to do the IV all it says + + + align:start position:0% +wouldn't want to do the IV all it says +is that's going to give you a very good + + align:start position:0% +is that's going to give you a very good + + + align:start position:0% +is that's going to give you a very good +estimate of laptop on test course or + + align:start position:0% +estimate of laptop on test course or + + + align:start position:0% +estimate of laptop on test course or +meals on testore that's pretty + + align:start position:0% +meals on testore that's pretty + + + align:start position:0% +meals on testore that's pretty +interesting but you + + align:start position:0% +interesting but you + + + align:start position:0% +interesting but you +can't extrapolate from that that that's + + align:start position:0% +can't extrapolate from that that that's + + + align:start position:0% +can't extrapolate from that that that's +the effect of Education sometimes you + + align:start position:0% +the effect of Education sometimes you + + + align:start position:0% +the effect of Education sometimes you +can sometime you cannot so in this case + + align:start position:0% +can sometime you cannot so in this case + + + align:start position:0% +can sometime you cannot so in this case +I don't think this would be a problem + + align:start position:0% +I don't think this would be a problem + + + align:start position:0% +I don't think this would be a problem +because these are intervention that we + + align:start position:0% +because these are intervention that we + + + align:start position:0% +because these are intervention that we +be interested in + + align:start position:0% +be interested in + + + align:start position:0% +be interested in +anyway uh in other cases uh it might be + + align:start position:0% +anyway uh in other cases uh it might be + + + align:start position:0% +anyway uh in other cases uh it might be +a problem because they're not so + + align:start position:0% +a problem because they're not so + + + align:start position:0% +a problem because they're not so +interesting intervention you use just + + align:start position:0% +interesting intervention you use just + + + align:start position:0% +interesting intervention you use just +use them as a as a way of getting more + + align:start position:0% +use them as a as a way of getting more + + + align:start position:0% +use them as a as a way of getting more +education so but that's always the thing + + align:start position:0% +education so but that's always the thing + + + align:start position:0% +education so but that's always the thing +we have to go + + align:start position:0% +we have to go + + + align:start position:0% +we have to go +through uh so I mentioned at the + + align:start position:0% +through uh so I mentioned at the + + + align:start position:0% +through uh so I mentioned at the +beginning and we already had some sort + + align:start position:0% +beginning and we already had some sort + + + align:start position:0% +beginning and we already had some sort +of circle around this this issue is that + + align:start position:0% +of circle around this this issue is that + + + align:start position:0% +of circle around this this issue is that +in reality the the the often we are not + + align:start position:0% +in reality the the the often we are not + + + align:start position:0% +in reality the the the often we are not +really willing to make the assumption + + align:start position:0% +really willing to make the assumption + + + align:start position:0% +really willing to make the assumption +that the effect of going to school on + + align:start position:0% +that the effect of going to school on + + + align:start position:0% +that the effect of going to school on +test course is constant for example so + + align:start position:0% +test course is constant for example so + + + align:start position:0% +test course is constant for example so +ideally we would like a sort of little + + align:start position:0% +ideally we would like a sort of little + + + align:start position:0% +ideally we would like a sort of little +eye next to the beta beta eye so as we + + align:start position:0% +eye next to the beta beta eye so as we + + + align:start position:0% +eye next to the beta beta eye so as we +know we are not going to be able to + + align:start position:0% +know we are not going to be able to + + + align:start position:0% +know we are not going to be able to +estimate the causal effect for each + + align:start position:0% +estimate the causal effect for each + + + align:start position:0% +estimate the causal effect for each +person if we had if we simply look at + + align:start position:0% +person if we had if we simply look at + + + align:start position:0% +person if we had if we simply look at +the reduced form effect we know the + + align:start position:0% +the reduced form effect we know the + + + align:start position:0% +the reduced form effect we know the +interpretation of it it's still the + + align:start position:0% +interpretation of it it's still the + + + align:start position:0% +interpretation of it it's still the +average treatment + + align:start position:0% +average treatment + + + align:start position:0% +average treatment +effect uh so what the but in this case + + align:start position:0% +effect uh so what the but in this case + + + align:start position:0% +effect uh so what the but in this case +the simple calculation we did to get the + + align:start position:0% +the simple calculation we did to get the + + + align:start position:0% +the simple calculation we did to get the +to to show that + + align:start position:0% +to to show that + + + align:start position:0% +to to show that +that beta is in fact the effect of + + align:start position:0% +that beta is in fact the effect of + + + align:start position:0% +that beta is in fact the effect of +U the effect of uh + + align:start position:0% +U the effect of uh + + + align:start position:0% +U the effect of uh +um going to school on test course + + align:start position:0% +um going to school on test course + + + align:start position:0% +um going to school on test course +doesn't apply anymore so what can we do + + align:start position:0% +doesn't apply anymore so what can we do + + + align:start position:0% +doesn't apply anymore so what can we do +uh so it turned out that the valtim + + align:start position:0% +uh so it turned out that the valtim + + + align:start position:0% +uh so it turned out that the valtim +still as a caal interpretation under a + + align:start position:0% +still as a caal interpretation under a + + + align:start position:0% +still as a caal interpretation under a +fairly additional M + + align:start position:0% +fairly additional M + + + align:start position:0% +fairly additional M +assumption which I'll I'll discuss you + + align:start position:0% +assumption which I'll I'll discuss you + + + align:start position:0% +assumption which I'll I'll discuss you +in a which should show you to you in a + + align:start position:0% +in a which should show you to you in a + + + align:start position:0% +in a which should show you to you in a +moment uh in that case what the Val + + align:start position:0% +moment uh in that case what the Val + + + align:start position:0% +moment uh in that case what the Val +estimate does are the IV estimate when + + align:start position:0% +estimate does are the IV estimate when + + + align:start position:0% +estimate does are the IV estimate when +we go to IV estimate is that it captures + + align:start position:0% +we go to IV estimate is that it captures + + + align:start position:0% +we go to IV estimate is that it captures +the effect of the treatment on those who + + align:start position:0% +the effect of the treatment on those who + + + align:start position:0% +the effect of the treatment on those who +are compelled by the instrument to get + + align:start position:0% +are compelled by the instrument to get + + + align:start position:0% +are compelled by the instrument to get +treated uh so we call that the local + + align:start position:0% +treated uh so we call that the local + + + align:start position:0% +treated uh so we call that the local +average treatment effect or + + align:start position:0% +average treatment effect or + + + align:start position:0% +average treatment effect or +latte uh just in case that is like + + align:start position:0% +latte uh just in case that is like + + + align:start position:0% +latte uh just in case that is like +what uh so what doesn't refer to the lty + + align:start position:0% +what uh so what doesn't refer to the lty + + + align:start position:0% +what uh so what doesn't refer to the lty +thing what refers to what what did I + + align:start position:0% +thing what refers to what what did I + + + align:start position:0% +thing what refers to what what did I +just say uh so let's go back to our + + align:start position:0% +just say uh so let's go back to our + + + align:start position:0% +just say uh so let's go back to our +school example and consider the one zero + + align:start position:0% +school example and consider the one zero + + + align:start position:0% +school example and consider the one zero +decision of going to high school school + + align:start position:0% +decision of going to high school school + + + align:start position:0% +decision of going to high school school +or + + align:start position:0% +or + + + align:start position:0% +or +not in principle you can have four + + align:start position:0% +not in principle you can have four + + + align:start position:0% +not in principle you can have four +groups of + + align:start position:0% +groups of + + + align:start position:0% +groups of +kids uh you can have the kids who would + + align:start position:0% +kids uh you can have the kids who would + + + align:start position:0% +kids uh you can have the kids who would +go to high school anyway so in fact we + + align:start position:0% +go to high school anyway so in fact we + + + align:start position:0% +go to high school anyway so in fact we +know how what fraction we have we have + + align:start position:0% +know how what fraction we have we have + + + align:start position:0% +know how what fraction we have we have +some kids who went + + align:start position:0% +some kids who went + + + align:start position:0% +some kids who went +anywhere uh you have the kids and we are + + align:start position:0% +anywhere uh you have the kids and we are + + + align:start position:0% +anywhere uh you have the kids and we are +going to call those the always take + + align:start position:0% +going to call those the always take + + + align:start position:0% +going to call those the always take +cares they always they will go to school + + align:start position:0% +cares they always they will go to school + + + align:start position:0% +cares they always they will go to school +regardless they'll figure it out + + align:start position:0% +regardless they'll figure it out + + + align:start position:0% +regardless they'll figure it out +okay we're going to we could have the + + align:start position:0% +okay we're going to we could have the + + + align:start position:0% +okay we're going to we could have the +kids who would not go to high school + + align:start position:0% +kids who would not go to high school + + + align:start position:0% +kids who would not go to high school +even when they offered a scholarship so + + align:start position:0% +even when they offered a scholarship so + + + align:start position:0% +even when they offered a scholarship so +this is our bunch there are very few + + align:start position:0% +this is our bunch there are very few + + + align:start position:0% +this is our bunch there are very few +among boys we saw that most of them went + + align:start position:0% +among boys we saw that most of them went + + + align:start position:0% +among boys we saw that most of them went +but among girls there are many people + + align:start position:0% +but among girls there are many people + + + align:start position:0% +but among girls there are many people +who just decline the offer of + + align:start position:0% +who just decline the offer of + + + align:start position:0% +who just decline the offer of +scholarship and don't go let's call this + + align:start position:0% +scholarship and don't go let's call this + + + align:start position:0% +scholarship and don't go let's call this +one the never take carees unless they're + + align:start position:0% +one the never take carees unless they're + + + align:start position:0% +one the never take carees unless they're +not going to take the treatment and then + + align:start position:0% +not going to take the treatment and then + + + align:start position:0% +not going to take the treatment and then +there are a group of kids who would go + + align:start position:0% +there are a group of kids who would go + + + align:start position:0% +there are a group of kids who would go +if they are offered a scholarship but + + align:start position:0% +if they are offered a scholarship but + + + align:start position:0% +if they are offered a scholarship but +they would not go if they are not + + align:start position:0% +they would not go if they are not + + + align:start position:0% +they would not go if they are not +offered a + + align:start position:0% +offered a + + + align:start position:0% +offered a +scholarship call these guys the + + align:start position:0% +scholarship call these guys the + + + align:start position:0% +scholarship call these guys the +compliers they're complying to your + + align:start position:0% +compliers they're complying to your + + + align:start position:0% +compliers they're complying to your +treatment and then we have a first group + + align:start position:0% +treatment and then we have a first group + + + align:start position:0% +treatment and then we have a first group +of kid what is this first group of + + align:start position:0% +of kid what is this first group of + + + align:start position:0% +of kid what is this first group of +kid + + align:start position:0% + + + + align:start position:0% + +don't go yes those who don't go his + + align:start position:0% +don't go yes those who don't go his + + + align:start position:0% +don't go yes those who don't go his +offer but would have gone otherwise who + + align:start position:0% +offer but would have gone otherwise who + + + align:start position:0% +offer but would have gone otherwise who +are kind of who are spiteful so those + + align:start position:0% +are kind of who are spiteful so those + + + align:start position:0% +are kind of who are spiteful so those +who would not go if offered but the but + + align:start position:0% +who would not go if offered but the but + + + align:start position:0% +who would not go if offered but the but +so the opposite if they not go oh oh I + + align:start position:0% +so the opposite if they not go oh oh I + + + align:start position:0% +so the opposite if they not go oh oh I +got not go if offered but go if not + + align:start position:0% +got not go if offered but go if not + + + align:start position:0% +got not go if offered but go if not +offered so please correct that in your + + align:start position:0% +offered so please correct that in your + + + align:start position:0% +offered so please correct that in your +in your notes those are the + + align:start position:0% +in your notes those are the + + + align:start position:0% +in your notes those are the +defiles uh so that group is kind of + + align:start position:0% +defiles uh so that group is kind of + + + align:start position:0% +defiles uh so that group is kind of +weird so + + align:start position:0% +weird so + + + align:start position:0% +weird so +my assumption so the the relatively mild + + align:start position:0% +my assumption so the the relatively mild + + + align:start position:0% +my assumption so the the relatively mild +assumption sometimes it's not mild but + + align:start position:0% +assumption sometimes it's not mild but + + + align:start position:0% +assumption sometimes it's not mild but +uh in most cases it's relatively mild + + align:start position:0% +uh in most cases it's relatively mild + + + align:start position:0% +uh in most cases it's relatively mild +but it's an assumption assume it doesn't + + align:start position:0% +but it's an assumption assume it doesn't + + + align:start position:0% +but it's an assumption assume it doesn't +exist okay assume there are no + + align:start position:0% +exist okay assume there are no + + + align:start position:0% +exist okay assume there are no +defiers in that case uh you can write a + + align:start position:0% +defiers in that case uh you can write a + + + align:start position:0% +defiers in that case uh you can write a +few line of algebra that will spare you + + align:start position:0% +few line of algebra that will spare you + + + align:start position:0% +few line of algebra that will spare you +to prove that the Val estimate is the + + align:start position:0% +to prove that the Val estimate is the + + + align:start position:0% +to prove that the Val estimate is the +effect of the treatment for the + + align:start position:0% +effect of the treatment for the + + + align:start position:0% +effect of the treatment for the +compliers the intuition is very easy and + + align:start position:0% +compliers the intuition is very easy and + + + align:start position:0% +compliers the intuition is very easy and +the trick to the proof is very easy is + + align:start position:0% +the trick to the proof is very easy is + + + align:start position:0% +the trick to the proof is very easy is +that the first stage for the other two + + align:start position:0% +that the first stage for the other two + + + align:start position:0% +that the first stage for the other two +groups are zero + + align:start position:0% +groups are zero + + + align:start position:0% +groups are zero +and you assume that group doesn't exist + + align:start position:0% +and you assume that group doesn't exist + + + align:start position:0% +and you assume that group doesn't exist +so the first stage is entirely kind of + + align:start position:0% +so the first stage is entirely kind of + + + align:start position:0% +so the first stage is entirely kind of +uh moving these guys out and therefore + + align:start position:0% +uh moving these guys out and therefore + + + align:start position:0% +uh moving these guys out and therefore +uh the uh uh we have the effect for them + + align:start position:0% +uh the uh uh we have the effect for them + + + align:start position:0% +uh the uh uh we have the effect for them +so to the point that you and you both + + align:start position:0% +so to the point that you and you both + + + align:start position:0% +so to the point that you and you both +made which is when I look for example at + + align:start position:0% +made which is when I look for example at + + + align:start position:0% +made which is when I look for example at +kids who qualify for secondary school + + align:start position:0% +kids who qualify for secondary school + + + align:start position:0% +kids who qualify for secondary school +anywhere or when I look at kids who + + align:start position:0% +anywhere or when I look at kids who + + + align:start position:0% +anywhere or when I look at kids who +apply to Charter School you have to make + + align:start position:0% +apply to Charter School you have to make + + + align:start position:0% +apply to Charter School you have to make +one additional comment which is + + align:start position:0% +one additional comment which is + + + align:start position:0% +one additional comment which is +important which is within this group I'm + + align:start position:0% +important which is within this group I'm + + + align:start position:0% +important which is within this group I'm +not even looking at I'm not even getting + + align:start position:0% +not even looking at I'm not even getting + + + align:start position:0% +not even looking at I'm not even getting +the causal effect for all of them I'm + + align:start position:0% +the causal effect for all of them I'm + + + align:start position:0% +the causal effect for all of them I'm +getting the causal effect for the type + + align:start position:0% +getting the causal effect for the type + + + align:start position:0% +getting the causal effect for the type +of kids who is moved by me so with a + + align:start position:0% +of kids who is moved by me so with a + + + align:start position:0% +of kids who is moved by me so with a +charter school for example some kids are + + align:start position:0% +charter school for example some kids are + + + align:start position:0% +charter school for example some kids are +very determined and if they don't get in + + align:start position:0% +very determined and if they don't get in + + + align:start position:0% +very determined and if they don't get in +they will Camp their parents or + + align:start position:0% +they will Camp their parents or + + + align:start position:0% +they will Camp their parents or +themselves will camp out next to the + + align:start position:0% +themselves will camp out next to the + + + align:start position:0% +themselves will camp out next to the +principal office andless until they get + + align:start position:0% +principal office andless until they get + + + align:start position:0% +principal office andless until they get +a spot so this most motivated of the + + align:start position:0% +a spot so this most motivated of the + + + align:start position:0% +a spot so this most motivated of the +motivated will get it anywhere and then + + align:start position:0% +motivated will get it anywhere and then + + + align:start position:0% +motivated will get it anywhere and then +they they're not part of it so maybe the + + align:start position:0% +they they're not part of it so maybe the + + + align:start position:0% +they they're not part of it so maybe the +effect is still not for for the most + + align:start position:0% +effect is still not for for the most + + + align:start position:0% +effect is still not for for the most +motivated of the lot uh there are very + + align:start position:0% +motivated of the lot uh there are very + + + align:start position:0% +motivated of the lot uh there are very +few in the case of of of charter school + + align:start position:0% +few in the case of of of charter school + + + align:start position:0% +few in the case of of of charter school +there are very + + align:start position:0% +there are very + + + align:start position:0% +there are very +few never take carees because once + + align:start position:0% +few never take carees because once + + + align:start position:0% +few never take carees because once +people apply presumably they are + + align:start position:0% +people apply presumably they are + + + align:start position:0% +people apply presumably they are +planning to go uh uh in our case it's + + align:start position:0% +planning to go uh uh in our case it's + + + align:start position:0% +planning to go uh uh in our case it's +the same thing the kids who manage to + + align:start position:0% +the same thing the kids who manage to + + + align:start position:0% +the same thing the kids who manage to +scrap the money anywh presumably quite + + align:start position:0% +scrap the money anywh presumably quite + + + align:start position:0% +scrap the money anywh presumably quite +motivated so my group is this kind of + + align:start position:0% +motivated so my group is this kind of + + + align:start position:0% +motivated so my group is this kind of +either the poorest of the kids and so + + align:start position:0% +either the poorest of the kids and so + + + align:start position:0% +either the poorest of the kids and so +the question you have to ask whenever + + align:start position:0% +the question you have to ask whenever + + + align:start position:0% +the question you have to ask whenever +you do an IV is that is it a group that + + align:start position:0% +you do an IV is that is it a group that + + + align:start position:0% +you do an IV is that is it a group that +I'm interested in because you know that + + align:start position:0% +I'm interested in because you know that + + + align:start position:0% +I'm interested in because you know that +exist you know what the fraction you + + align:start position:0% +exist you know what the fraction you + + + align:start position:0% +exist you know what the fraction you +don't know who they are in your sample + + align:start position:0% +don't know who they are in your sample + + + align:start position:0% +don't know who they are in your sample +nothing tells you that someone is an + + align:start position:0% +nothing tells you that someone is an + + + align:start position:0% +nothing tells you that someone is an +always take care or not because you + + align:start position:0% +always take care or not because you + + + align:start position:0% +always take care or not because you +don't know what would have happened to + + align:start position:0% +don't know what would have happened to + + + align:start position:0% +don't know what would have happened to +them if they had not received a + + align:start position:0% +them if they had not received a + + + align:start position:0% +them if they had not received a +scholarship you just know it one way so + + align:start position:0% +scholarship you just know it one way so + + + align:start position:0% +scholarship you just know it one way so +the question is is the group that is in + + align:start position:0% +the question is is the group that is in + + + align:start position:0% +the question is is the group that is in +general of Interest or not + + align:start position:0% +general of Interest or not + + + align:start position:0% +general of Interest or not +particularly uh and uh um and uh that + + align:start position:0% +particularly uh and uh um and uh that + + + align:start position:0% +particularly uh and uh um and uh that +has to be argued in a lot of cases it + + align:start position:0% +has to be argued in a lot of cases it + + + align:start position:0% +has to be argued in a lot of cases it +happens to be the group we are + + align:start position:0% +happens to be the group we are + + + align:start position:0% +happens to be the group we are +interested in with an instrument because + + align:start position:0% +interested in with an instrument because + + + align:start position:0% +interested in with an instrument because +we are sort of the instrument of F of + + align:start position:0% +we are sort of the instrument of F of + + + align:start position:0% +we are sort of the instrument of F of +the form that you are facilitated some + + align:start position:0% +the form that you are facilitated some + + + align:start position:0% +the form that you are facilitated some +group to get the to get the thing so for + + align:start position:0% +group to get the to get the thing so for + + + align:start position:0% +group to get the to get the thing so for +example in the case of + + align:start position:0% +example in the case of + + + align:start position:0% +example in the case of +scholarship there are the people who are + + align:start position:0% +scholarship there are the people who are + + + align:start position:0% +scholarship there are the people who are +moved by my instrument by by having free + + align:start position:0% +moved by my instrument by by having free + + + align:start position:0% +moved by my instrument by by having free +school to actually go to school so + + align:start position:0% +school to actually go to school so + + + align:start position:0% +school to actually go to school so +consider a government what could be + + align:start position:0% +consider a government what could be + + + align:start position:0% +consider a government what could be +their policy to improve Secondary School + + align:start position:0% +their policy to improve Secondary School + + + align:start position:0% +their policy to improve Secondary School +well it could be to make it cheaper so + + align:start position:0% +well it could be to make it cheaper so + + + align:start position:0% +well it could be to make it cheaper so +the type of people who would go to + + align:start position:0% +the type of people who would go to + + + align:start position:0% +the type of people who would go to +school because of that policy would be + + align:start position:0% +school because of that policy would be + + + align:start position:0% +school because of that policy would be +very much like the type of people who go + + align:start position:0% +very much like the type of people who go + + + align:start position:0% +very much like the type of people who go +to school with because of my instrument + + align:start position:0% +to school with because of my instrument + + + align:start position:0% +to school with because of my instrument +so that would be nice but when you're + + align:start position:0% +so that would be nice but when you're + + + align:start position:0% +so that would be nice but when you're +using very exotic instrument which + + align:start position:0% +using very exotic instrument which + + + align:start position:0% +using very exotic instrument which +happens more with using natural + + align:start position:0% +happens more with using natural + + + align:start position:0% +happens more with using natural +variation as source of instrument + + align:start position:0% +variation as source of instrument + + + align:start position:0% +variation as source of instrument +sometimes we like well do we care about + + align:start position:0% +sometimes we like well do we care about + + + align:start position:0% +sometimes we like well do we care about +these people like that doesn't really + + align:start position:0% +these people like that doesn't really + + + align:start position:0% +these people like that doesn't really +you know and is their treatment effect + + align:start position:0% +you know and is their treatment effect + + + align:start position:0% +you know and is their treatment effect +okay I know as I have an + + align:start position:0% +okay I know as I have an + + + align:start position:0% +okay I know as I have an +excellent estimate of the causal effect + + align:start position:0% +excellent estimate of the causal effect + + + align:start position:0% +excellent estimate of the causal effect +for them but that might not be + + align:start position:0% +for them but that might not be + + + align:start position:0% +for them but that might not be +representative of the causal effect for + + align:start position:0% +representative of the causal effect for + + + align:start position:0% +representative of the causal effect for +the rest of the world and I'm not so + + align:start position:0% +the rest of the world and I'm not so + + + align:start position:0% +the rest of the world and I'm not so +interested in them uh so so that's the + + align:start position:0% +interested in them uh so so that's the + + + align:start position:0% +interested in them uh so so that's the +type of question that you have to ask + + align:start position:0% +type of question that you have to ask + + + align:start position:0% +type of question that you have to ask +yourself so I we stop here and then what + + align:start position:0% +yourself so I we stop here and then what + + + align:start position:0% +yourself so I we stop here and then what +we I will take we we'll take up exactly + + align:start position:0% +we I will take we we'll take up exactly + + + align:start position:0% +we I will take we we'll take up exactly +from there on uh on one step before + + align:start position:0% +from there on uh on one step before + + + align:start position:0% +from there on uh on one step before +going to experimental design going over + + align:start position:0% +going to experimental design going over + + + align:start position:0% +going to experimental design going over +the formula linking it to two stely + + align:start position:0% +the formula linking it to two stely + + + align:start position:0% +the formula linking it to two stely +square more generally + + align:start position:0% + + + + align:start position:0% + +okay \ No newline at end of file diff --git a/P3tGiT72APw.txt b/P3tGiT72APw.txt new file mode 100644 index 0000000000000000000000000000000000000000..d6c15da6ac7dab1c502daffd0b763bef63481dc1 --- /dev/null +++ b/P3tGiT72APw.txt @@ -0,0 +1,8843 @@ +align:start position:0% + +all right so today we're going to start + + align:start position:0% +all right so today we're going to start + + + align:start position:0% +all right so today we're going to start +a new chapter on graph limits are so + + align:start position:0% +a new chapter on graph limits are so + + + align:start position:0% +a new chapter on graph limits are so +graph limits is a relatively new subject + + align:start position:0% +graph limits is a relatively new subject + + + align:start position:0% +graph limits is a relatively new subject +in graph theory + + align:start position:0% +in graph theory + + + align:start position:0% +in graph theory +so as the name suggests we're looking at + + align:start position:0% +so as the name suggests we're looking at + + + align:start position:0% +so as the name suggests we're looking at +some kind of an analytic limit of graphs + + align:start position:0% +some kind of an analytic limit of graphs + + + align:start position:0% +some kind of an analytic limit of graphs +which sounds kind of like a strange idea + + align:start position:0% +which sounds kind of like a strange idea + + + align:start position:0% +which sounds kind of like a strange idea +because you think of grass as + + align:start position:0% +because you think of grass as + + + align:start position:0% +because you think of grass as +fundamentally discrete objects but let + + align:start position:0% +fundamentally discrete objects but let + + + align:start position:0% +fundamentally discrete objects but let +me begin with a an example to motivate + + align:start position:0% +me begin with a an example to motivate + + + align:start position:0% +me begin with a an example to motivate +at least pure mathematical motivation + + align:start position:0% +at least pure mathematical motivation + + + align:start position:0% +at least pure mathematical motivation +for graph limits there are several other + + align:start position:0% +for graph limits there are several other + + + align:start position:0% +for graph limits there are several other +ways you can motivate graph limits + + align:start position:0% +ways you can motivate graph limits + + + align:start position:0% +ways you can motivate graph limits +especially coming from more applied + + align:start position:0% +especially coming from more applied + + + align:start position:0% +especially coming from more applied +perspectives but let me stick with the + + align:start position:0% +perspectives but let me stick with the + + + align:start position:0% +perspectives but let me stick with the +the following story suppose okay so + + align:start position:0% +the following story suppose okay so + + + align:start position:0% +the following story suppose okay so +suppose you lived in you know ancient + + align:start position:0% +suppose you lived in you know ancient + + + align:start position:0% +suppose you lived in you know ancient +Greeks and you only knew rational + + align:start position:0% +Greeks and you only knew rational + + + align:start position:0% +Greeks and you only knew rational +numbers you didn't know about real + + align:start position:0% +numbers you didn't know about real + + + align:start position:0% +numbers you didn't know about real +numbers but you understand perfectly + + align:start position:0% +numbers but you understand perfectly + + + align:start position:0% +numbers but you understand perfectly +rational numbers and we wish to maximize + + align:start position:0% + + + + align:start position:0% + +so we wish to minimize the following + + align:start position:0% +so we wish to minimize the following + + + align:start position:0% +so we wish to minimize the following +polynomial X cubed minus X let's say for + + align:start position:0% +polynomial X cubed minus X let's say for + + + align:start position:0% +polynomial X cubed minus X let's say for +X between 0 and 1 okay so you can do + + align:start position:0% +X between 0 and 1 okay so you can do + + + align:start position:0% +X between 0 and 1 okay so you can do +this and so forth also the Greeks knew + + align:start position:0% +this and so forth also the Greeks knew + + + align:start position:0% +this and so forth also the Greeks knew +calculus and take the derivative and all + + align:start position:0% +calculus and take the derivative and all + + + align:start position:0% +calculus and take the derivative and all +of that ok so you find that well you + + align:start position:0% +of that ok so you find that well you + + + align:start position:0% +of that ok so you find that well you +have a problem right because we know + + align:start position:0% +have a problem right because we know + + + align:start position:0% +have a problem right because we know +right so you're given our advanced state + + align:start position:0% +right so you're given our advanced state + + + align:start position:0% +right so you're given our advanced state +of mathematics we know that the maximum + + align:start position:0% +of mathematics we know that the maximum + + + align:start position:0% +of mathematics we know that the maximum +third the minimizer is at x equals to 1 + + align:start position:0% +third the minimizer is at x equals to 1 + + + align:start position:0% +third the minimizer is at x equals to 1 +over root 3 but that number doesn't + + align:start position:0% +over root 3 but that number doesn't + + + align:start position:0% +over root 3 but that number doesn't +exist in the real numbers so how might + + align:start position:0% +exist in the real numbers so how might + + + align:start position:0% +exist in the real numbers so how might +civilization that only knew rational + + align:start position:0% +civilization that only knew rational + + + align:start position:0% +civilization that only knew rational +numbers Express this answer they could + + align:start position:0% +numbers Express this answer they could + + + align:start position:0% +numbers Express this answer they could +say the minimum occurs not in Q so + + align:start position:0% +say the minimum occurs not in Q so + + + align:start position:0% +say the minimum occurs not in Q so +there's not + + align:start position:0% +there's not + + + align:start position:0% +there's not +thank you but not minimized by a single + + align:start position:0% +thank you but not minimized by a single + + + align:start position:0% +thank you but not minimized by a single +number but by a sequence and this is a + + align:start position:0% +number but by a sequence and this is a + + + align:start position:0% +number but by a sequence and this is a +sequence that you know more advanced + + align:start position:0% +sequence that you know more advanced + + + align:start position:0% +sequence that you know more advanced +civilization with no sequence that + + align:start position:0% +civilization with no sequence that + + + align:start position:0% +civilization with no sequence that +converges to 1 over root 3 but I can + + align:start position:0% +converges to 1 over root 3 but I can + + + align:start position:0% +converges to 1 over root 3 but I can +give you the sequence through some other + + align:start position:0% +give you the sequence through some other + + + align:start position:0% +give you the sequence through some other +means and this is you know one of the + + align:start position:0% +means and this is you know one of the + + + align:start position:0% +means and this is you know one of the +ways of defining the complete set of + + align:start position:0% +ways of defining the complete set of + + + align:start position:0% +ways of defining the complete set of +real numbers for instance but you can + + align:start position:0% +real numbers for instance but you can + + + align:start position:0% +real numbers for instance but you can +define explicitly a sequence of real + + align:start position:0% +define explicitly a sequence of real + + + align:start position:0% +define explicitly a sequence of real +numbers that converges ok but of course + + align:start position:0% +numbers that converges ok but of course + + + align:start position:0% +numbers that converges ok but of course +this is all quite cumbersome if you have + + align:start position:0% +this is all quite cumbersome if you have + + + align:start position:0% +this is all quite cumbersome if you have +to actually write down the sequence of + + align:start position:0% +to actually write down the sequence of + + + align:start position:0% +to actually write down the sequence of +real numbers to express the sensor it + + align:start position:0% +real numbers to express the sensor it + + + align:start position:0% +real numbers to express the sensor it +will be much better if we knew the real + + align:start position:0% +will be much better if we knew the real + + + align:start position:0% +will be much better if we knew the real +numbers and we do and the real numbers + + align:start position:0% +numbers and we do and the real numbers + + + align:start position:0% +numbers and we do and the real numbers +in some sense I mean you know in a very + + align:start position:0% +in some sense I mean you know in a very + + + align:start position:0% +in some sense I mean you know in a very +rigorous sense is a completion of the + + align:start position:0% +rigorous sense is a completion of the + + + align:start position:0% +rigorous sense is a completion of the +rational numbers that's the story that + + align:start position:0% +rational numbers that's the story that + + + align:start position:0% +rational numbers that's the story that +we're all familiar with but now let's + + align:start position:0% +we're all familiar with but now let's + + + align:start position:0% +we're all familiar with but now let's +think about graphs which are some kind + + align:start position:0% +think about graphs which are some kind + + + align:start position:0% +think about graphs which are some kind +of a discrete set of objects akin to the + + align:start position:0% +of a discrete set of objects akin to the + + + align:start position:0% +of a discrete set of objects akin to the +rational numbers and the story now is + + align:start position:0% +rational numbers and the story now is + + + align:start position:0% +rational numbers and the story now is +about graphs suppose I have a fixed P + + align:start position:0% +about graphs suppose I have a fixed P + + + align:start position:0% +about graphs suppose I have a fixed P +between 0 & 1 and the problem now is to + + align:start position:0% +between 0 & 1 and the problem now is to + + + align:start position:0% +between 0 & 1 and the problem now is to +minimize the for cycle density among + + align:start position:0% +minimize the for cycle density among + + + align:start position:0% +minimize the for cycle density among +graphs with density with edge density P + + align:start position:0% + + + + align:start position:0% + +so this is some kind of optimization + + align:start position:0% +so this is some kind of optimization + + + align:start position:0% +so this is some kind of optimization +problem so I don't restrict the number + + align:start position:0% +problem so I don't restrict the number + + + align:start position:0% +problem so I don't restrict the number +of vertices you can use as many vertices + + align:start position:0% +of vertices you can use as many vertices + + + align:start position:0% +of vertices you can use as many vertices +as you like and I would like to minimize + + align:start position:0% +as you like and I would like to minimize + + + align:start position:0% +as you like and I would like to minimize +the force cycle density now we saw a few + + align:start position:0% +the force cycle density now we saw a few + + + align:start position:0% +the force cycle density now we saw a few +lectures ago this inequality that tells + + align:start position:0% +lectures ago this inequality that tells + + + align:start position:0% +lectures ago this inequality that tells +us that so we saw a few lectures ago + + align:start position:0% +us that so we saw a few lectures ago + + + align:start position:0% +us that so we saw a few lectures ago +that this density is always at least key + + align:start position:0% +that this density is always at least key + + + align:start position:0% +that this density is always at least key +to the form okay so in the lecture on + + align:start position:0% +to the form okay so in the lecture on + + + align:start position:0% +to the form okay so in the lecture on +quasi randomness so we saw this + + align:start position:0% +quasi randomness so we saw this + + + align:start position:0% +quasi randomness so we saw this +inequality and we also saw that this + + align:start position:0% +inequality and we also saw that this + + + align:start position:0% +inequality and we also saw that this +minimum is approached by a sequence of + + align:start position:0% + + + + align:start position:0% + +quasi random graphs and in some sense + + align:start position:0% +quasi random graphs and in some sense + + + align:start position:0% +quasi random graphs and in some sense +that's so the answer is P to the fourth + + align:start position:0% +that's so the answer is P to the fourth + + + align:start position:0% +that's so the answer is P to the fourth +and there's not a specific graph there's + + align:start position:0% +and there's not a specific graph there's + + + align:start position:0% +and there's not a specific graph there's +no one graph that minimizes this for + + align:start position:0% +no one graph that minimizes this for + + + align:start position:0% +no one graph that minimizes this for +cycle density is minimized by a sequence + + align:start position:0% +cycle density is minimized by a sequence + + + align:start position:0% +cycle density is minimized by a sequence +and just like in the story with rational + + align:start position:0% +and just like in the story with rational + + + align:start position:0% +and just like in the story with rational +numbers and the real numbers it would be + + align:start position:0% +numbers and the real numbers it would be + + + align:start position:0% +numbers and the real numbers it would be +nice if we didn't have to write out the + + align:start position:0% +nice if we didn't have to write out the + + + align:start position:0% +nice if we didn't have to write out the +answer in this cumbersome you know + + align:start position:0% +answer in this cumbersome you know + + + align:start position:0% +answer in this cumbersome you know +sequential way but just have a single + + align:start position:0% +sequential way but just have a single + + + align:start position:0% +sequential way but just have a single +graphical like object that depicts what + + align:start position:0% +graphical like object that depicts what + + + align:start position:0% +graphical like object that depicts what +the minimizer should be and graph limits + + align:start position:0% +the minimizer should be and graph limits + + + align:start position:0% +the minimizer should be and graph limits +provides a language for us to do this + + align:start position:0% +provides a language for us to do this + + + align:start position:0% +provides a language for us to do this +okay so one of the goals of graph limits + + align:start position:0% +okay so one of the goals of graph limits + + + align:start position:0% +okay so one of the goals of graph limits +this gives us a single object for this + + align:start position:0% +this gives us a single object for this + + + align:start position:0% +this gives us a single object for this +minimizer instead of taking a sequence + + align:start position:0% +minimizer instead of taking a sequence + + + align:start position:0% +minimizer instead of taking a sequence +ok so roughly that is the idea that you + + align:start position:0% +ok so roughly that is the idea that you + + + align:start position:0% +ok so roughly that is the idea that you +have a sequence of graphs and I would + + align:start position:0% +have a sequence of graphs and I would + + + align:start position:0% +have a sequence of graphs and I would +like some analytic object to capture the + + align:start position:0% +like some analytic object to capture the + + + align:start position:0% +like some analytic object to capture the +behavior of this sequence in the limit + + align:start position:0% +behavior of this sequence in the limit + + + align:start position:0% +behavior of this sequence in the limit +and these graph limits can be written + + align:start position:0% +and these graph limits can be written + + + align:start position:0% +and these graph limits can be written +actually in the fairly concrete form and + + align:start position:0% +actually in the fairly concrete form and + + + align:start position:0% +actually in the fairly concrete form and +so now let me begin with some + + align:start position:0% +so now let me begin with some + + + align:start position:0% +so now let me begin with some +definitions the main object that we'll + + align:start position:0% +definitions the main object that we'll + + + align:start position:0% +definitions the main object that we'll +look at is something called a graph form + + align:start position:0% +look at is something called a graph form + + + align:start position:0% +look at is something called a graph form +so this is so he merges the two word + + align:start position:0% +so this is so he merges the two word + + + align:start position:0% +so this is so he merges the two word +graph function graph on is by definition + + align:start position:0% +graph function graph on is by definition + + + align:start position:0% +graph function graph on is by definition +a symmetric measurable function often + + align:start position:0% +a symmetric measurable function often + + + align:start position:0% +a symmetric measurable function often +denoted by the letter W from the unit + + align:start position:0% +denoted by the letter W from the unit + + + align:start position:0% +denoted by the letter W from the unit +square 2:01 interval and here being + + align:start position:0% +square 2:01 interval and here being + + + align:start position:0% +square 2:01 interval and here being +symmetric means that if if you exchange + + align:start position:0% +symmetric means that if if you exchange + + + align:start position:0% +symmetric means that if if you exchange +the two argument variables this function + + align:start position:0% +the two argument variables this function + + + align:start position:0% +the two argument variables this function +remains the same okay that's so that's + + align:start position:0% +remains the same okay that's so that's + + + align:start position:0% +remains the same okay that's so that's +the definition of a graph on and these + + align:start position:0% +the definition of a graph on and these + + + align:start position:0% +the definition of a graph on and these +are the objects that will play the role + + align:start position:0% +are the objects that will play the role + + + align:start position:0% +are the objects that will play the role +of limits for sequences of graphs and I + + align:start position:0% +of limits for sequences of graphs and I + + + align:start position:0% +of limits for sequences of graphs and I +will give you lots of examples in a + + align:start position:0% +will give you lots of examples in a + + + align:start position:0% +will give you lots of examples in a +second ok so that's the definition this + + align:start position:0% +second ok so that's the definition this + + + align:start position:0% +second ok so that's the definition this +is the form of the graphing style we'll + + align:start position:0% +is the form of the graphing style we'll + + + align:start position:0% +is the form of the graphing style we'll +be looking at mostly but just to mention + + align:start position:0% +be looking at mostly but just to mention + + + align:start position:0% +be looking at mostly but just to mention +a few remarks that the domain can be + + align:start position:0% +a few remarks that the domain can be + + + align:start position:0% +a few remarks that the domain can be +instead any product of any square of a + + align:start position:0% +instead any product of any square of a + + + align:start position:0% +instead any product of any square of a +probability measure space + + align:start position:0% + + + + align:start position:0% + +okay so instead of taking the 0y + + align:start position:0% +okay so instead of taking the 0y + + + align:start position:0% +okay so instead of taking the 0y +interval I could also use any + + align:start position:0% +interval I could also use any + + + align:start position:0% +interval I could also use any +probability major space so it's only + + align:start position:0% +probability major space so it's only + + + align:start position:0% +probability major space so it's only +slightly more general so there are some + + align:start position:0% +slightly more general so there are some + + + align:start position:0% +slightly more general so there are some +general theorems you measure theory that + + align:start position:0% +general theorems you measure theory that + + + align:start position:0% +general theorems you measure theory that +tells us that in most probability major + + align:start position:0% +tells us that in most probability major + + + align:start position:0% +tells us that in most probability major +spaces if they're nice enough they are + + align:start position:0% +spaces if they're nice enough they are + + + align:start position:0% +spaces if they're nice enough they are +in some sense equivalent no can be + + align:start position:0% +in some sense equivalent no can be + + + align:start position:0% +in some sense equivalent no can be +captured by this interval so I don't + + align:start position:0% +captured by this interval so I don't + + + align:start position:0% +captured by this interval so I don't +want to worry too much about all the + + align:start position:0% +want to worry too much about all the + + + align:start position:0% +want to worry too much about all the +measured wedeck technicalities I think + + align:start position:0% +measured wedeck technicalities I think + + + align:start position:0% +measured wedeck technicalities I think +they're not so important for the + + align:start position:0% +they're not so important for the + + + align:start position:0% +they're not so important for the +discussion of graph limits but you know + + align:start position:0% +discussion of graph limits but you know + + + align:start position:0% +discussion of graph limits but you know +there are some subtle issues like that + + align:start position:0% +there are some subtle issues like that + + + align:start position:0% +there are some subtle issues like that +just lurking behind but I just don't + + align:start position:0% +just lurking behind but I just don't + + + align:start position:0% +just lurking behind but I just don't +want to really talk about it so for the + + align:start position:0% +want to really talk about it so for the + + + align:start position:0% +want to really talk about it so for the +most part we'll be looking at graph ins + + align:start position:0% +most part we'll be looking at graph ins + + + align:start position:0% +most part we'll be looking at graph ins +of this form and also the okay so + + align:start position:0% +of this form and also the okay so + + + align:start position:0% +of this form and also the okay so +instead of the domain so they are the + + align:start position:0% +instead of the domain so they are the + + + align:start position:0% +instead of the domain so they are the +values so instead of 0 my interval you + + align:start position:0% +values so instead of 0 my interval you + + + align:start position:0% +values so instead of 0 my interval you +could also take a more general space for + + align:start position:0% +could also take a more general space for + + + align:start position:0% +could also take a more general space for +example the real numbers or even the + + align:start position:0% +example the real numbers or even the + + + align:start position:0% +example the real numbers or even the +complex numbers I'm going to use the + + align:start position:0% +complex numbers I'm going to use the + + + align:start position:0% +complex numbers I'm going to use the +word graphing to reserve this word for + + align:start position:0% +word graphing to reserve this word for + + + align:start position:0% +word graphing to reserve this word for +when the values are between 0 and 1 and + + align:start position:0% +when the values are between 0 and 1 and + + + align:start position:0% +when the values are between 0 and 1 and +if it's a or let me call this just a + + align:start position:0% +if it's a or let me call this just a + + + align:start position:0% +if it's a or let me call this just a +kernel although that will now come up so + + align:start position:0% +kernel although that will now come up so + + + align:start position:0% +kernel although that will now come up so +much okay so when I say graph um I just + + align:start position:0% +much okay so when I say graph um I just + + + align:start position:0% +much okay so when I say graph um I just +mean the values between 0 & 1 although + + align:start position:0% +mean the values between 0 & 1 although + + + align:start position:0% +mean the values between 0 & 1 although +you know if you do not look up papers in + + align:start position:0% +you know if you do not look up papers in + + + align:start position:0% +you know if you do not look up papers in +the literature sometimes they don't use + + align:start position:0% +the literature sometimes they don't use + + + align:start position:0% +the literature sometimes they don't use +these works so consistently so be + + align:start position:0% +these works so consistently so be + + + align:start position:0% +these works so consistently so be +careful what they mean by a graph on + + align:start position:0% +careful what they mean by a graph on + + + align:start position:0% +careful what they mean by a graph on +alright so that's the definition but now + + align:start position:0% +alright so that's the definition but now + + + align:start position:0% +alright so that's the definition but now +let me give you some examples how do we + + align:start position:0% +let me give you some examples how do we + + + align:start position:0% +let me give you some examples how do we +think of griffons and what do they have + + align:start position:0% +think of griffons and what do they have + + + align:start position:0% +think of griffons and what do they have +to do with graphs so if we start with a + + align:start position:0% +to do with graphs so if we start with a + + + align:start position:0% +to do with graphs so if we start with a +graph I want to show you how to turn it + + align:start position:0% +graph I want to show you how to turn it + + + align:start position:0% +graph I want to show you how to turn it +into a graphing so let's start with this + + align:start position:0% +into a graphing so let's start with this + + + align:start position:0% +into a graphing so let's start with this +graph which you've seen before this is + + align:start position:0% +graph which you've seen before this is + + + align:start position:0% +graph which you've seen before this is +the half graph + + align:start position:0% + + + + align:start position:0% + +so from this graph I can label the + + align:start position:0% +so from this graph I can label the + + + align:start position:0% +so from this graph I can label the +vertices and form an adjacency matrix of + + align:start position:0% +vertices and form an adjacency matrix of + + + align:start position:0% +vertices and form an adjacency matrix of +this graph where I label the rows and + + align:start position:0% +this graph where I label the rows and + + + align:start position:0% +this graph where I label the rows and +columns by the vertices and put in zeros + + align:start position:0% +columns by the vertices and put in zeros + + + align:start position:0% +columns by the vertices and put in zeros +and ones according to whether the edges + + align:start position:0% +and ones according to whether the edges + + + align:start position:0% +and ones according to whether the edges +are adjacent so that's the adjacency + + align:start position:0% +are adjacent so that's the adjacency + + + align:start position:0% +are adjacent so that's the adjacency +matrix and now I want you to view this + + align:start position:0% +matrix and now I want you to view this + + + align:start position:0% +matrix and now I want you to view this +matrix as a black and white picture so I + + align:start position:0% +matrix as a black and white picture so I + + + align:start position:0% +matrix as a black and white picture so I +think one of these pixelated images + + align:start position:0% +think one of these pixelated images + + + align:start position:0% +think one of these pixelated images +where I turn the once into black boxes + + align:start position:0% + + + + align:start position:0% + +where of course on the blackboard black + + align:start position:0% +where of course on the blackboard black + + + align:start position:0% +where of course on the blackboard black +is white and white is black so I turn + + align:start position:0% +is white and white is black so I turn + + + align:start position:0% +is white and white is black so I turn +the ones into black boxes and I leave + + align:start position:0% +the ones into black boxes and I leave + + + align:start position:0% +the ones into black boxes and I leave +the zeros as M key whitespace so I get + + align:start position:0% +the zeros as M key whitespace so I get + + + align:start position:0% +the zeros as M key whitespace so I get +this image and I think of this image as + + align:start position:0% +this image and I think of this image as + + + align:start position:0% +this image and I think of this image as +a function and this is a function going + + align:start position:0% +a function and this is a function going + + + align:start position:0% +a function and this is a function going +from zero one squared to zero one + + align:start position:0% +from zero one squared to zero one + + + align:start position:0% +from zero one squared to zero one +interval taking only zero and one values + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so that's a function on the under + + align:start position:0% +okay so that's a function on the under + + + align:start position:0% +okay so that's a function on the under +square but now so this is a single graph + + align:start position:0% +square but now so this is a single graph + + + align:start position:0% +square but now so this is a single graph +or so for any specific graph I can turn + + align:start position:0% +or so for any specific graph I can turn + + + align:start position:0% +or so for any specific graph I can turn +it into a graph on like this we're now + + align:start position:0% +it into a graph on like this we're now + + + align:start position:0% +it into a graph on like this we're now +imagine of a sequence of graphs in + + align:start position:0% +imagine of a sequence of graphs in + + + align:start position:0% +imagine of a sequence of graphs in +particular consider a sequence of half + + align:start position:0% +particular consider a sequence of half + + + align:start position:0% +particular consider a sequence of half +graphs okay so here is H 3 H n is the + + align:start position:0% +graphs okay so here is H 3 H n is the + + + align:start position:0% +graphs okay so here is H 3 H n is the +general cough graph and you can imagine + + align:start position:0% +general cough graph and you can imagine + + + align:start position:0% +general cough graph and you can imagine +that as n gets large this picture looks + + align:start position:0% +that as n gets large this picture looks + + + align:start position:0% +that as n gets large this picture looks +like instead of the staircase you just + + align:start position:0% +like instead of the staircase you just + + + align:start position:0% +like instead of the staircase you just +have a straight line connecting the two + + align:start position:0% +have a straight line connecting the two + + + align:start position:0% +have a straight line connecting the two +ends and indeed this function here this + + align:start position:0% +ends and indeed this function here this + + + align:start position:0% +ends and indeed this function here this +graph on is the limit of the sequence of + + align:start position:0% +graph on is the limit of the sequence of + + + align:start position:0% +graph on is the limit of the sequence of +1/2 graphs as n goes to infinity so one + + align:start position:0% +1/2 graphs as n goes to infinity so one + + + align:start position:0% +1/2 graphs as n goes to infinity so one +way you can think about griffons is you + + align:start position:0% +way you can think about griffons is you + + + align:start position:0% +way you can think about griffons is you +have a sequence of graphs you look at + + align:start position:0% +have a sequence of graphs you look at + + + align:start position:0% +have a sequence of graphs you look at +their adjacency matrix you view it as a + + align:start position:0% +their adjacency matrix you view it as a + + + align:start position:0% +their adjacency matrix you view it as a +picture a pixelated image black and + + align:start position:0% +picture a pixelated image black and + + + align:start position:0% +picture a pixelated image black and +white according to the zeros and ones in + + align:start position:0% +white according to the zeros and ones in + + + align:start position:0% +white according to the zeros and ones in +the adjacency matrix and as you you know + + align:start position:0% +the adjacency matrix and as you you know + + + align:start position:0% +the adjacency matrix and as you you know +take a sequence kind of you make your + + align:start position:0% +take a sequence kind of you make your + + + align:start position:0% +take a sequence kind of you make your +eyes a little bit blurry and then you + + align:start position:0% +eyes a little bit blurry and then you + + + align:start position:0% +eyes a little bit blurry and then you +think about you know what the sequence + + align:start position:0% +think about you know what the sequence + + + align:start position:0% +think about you know what the sequence +of images converges to okay so the + + align:start position:0% +of images converges to okay so the + + + align:start position:0% +of images converges to okay so the +resulting limit is the limit of this + + align:start position:0% +resulting limit is the limit of this + + + align:start position:0% +resulting limit is the limit of this +sequence of graphs so that's an informal + + align:start position:0% +sequence of graphs so that's an informal + + + align:start position:0% +sequence of graphs so that's an informal +explanation so I haven't done anything + + align:start position:0% +explanation so I haven't done anything + + + align:start position:0% +explanation so I haven't done anything +precisely and in fact one needs to be + + align:start position:0% +precisely and in fact one needs to be + + + align:start position:0% +precisely and in fact one needs to be +somewhat careful with this depiction + + align:start position:0% +somewhat careful with this depiction + + + align:start position:0% +somewhat careful with this depiction +because let me give you another example + + align:start position:0% + + + + align:start position:0% + +suppose I have a sequence of random or + + align:start position:0% +suppose I have a sequence of random or + + + align:start position:0% +suppose I have a sequence of random or +quasi random + + align:start position:0% + + + + align:start position:0% + +with edge density 1/2 so what does this + + align:start position:0% +with edge density 1/2 so what does this + + + align:start position:0% +with edge density 1/2 so what does this +look like again I have this picture here + + align:start position:0% +look like again I have this picture here + + + align:start position:0% +look like again I have this picture here +and I have a lot of so I have a lot of + + align:start position:0% +and I have a lot of so I have a lot of + + + align:start position:0% +and I have a lot of so I have a lot of +but 1/2 of the pixels are black and the + + align:start position:0% +but 1/2 of the pixels are black and the + + + align:start position:0% +but 1/2 of the pixels are black and the +other half pixels are white and you can + + align:start position:0% +other half pixels are white and you can + + + align:start position:0% +other half pixels are white and you can +thing you know from far away + + align:start position:0% +thing you know from far away + + + align:start position:0% +thing you know from far away +I cannot distinguish necessarily which + + align:start position:0% +I cannot distinguish necessarily which + + + align:start position:0% +I cannot distinguish necessarily which +ones your black which ones are white and + + align:start position:0% +ones your black which ones are white and + + + align:start position:0% +ones your black which ones are white and +in the limit it looks like a grayscale + + align:start position:0% +in the limit it looks like a grayscale + + + align:start position:0% +in the limit it looks like a grayscale +image with a grayscale being 1/2 density + + align:start position:0% +image with a grayscale being 1/2 density + + + align:start position:0% +image with a grayscale being 1/2 density +and indeed it converges to the constant + + align:start position:0% +and indeed it converges to the constant + + + align:start position:0% +and indeed it converges to the constant +function 1/2 okay so the limits + + align:start position:0% +function 1/2 okay so the limits + + + align:start position:0% +function 1/2 okay so the limits +represented by this problem up here is + + align:start position:0% +represented by this problem up here is + + + align:start position:0% +represented by this problem up here is +the constant graphing without constant + + align:start position:0% +the constant graphing without constant + + + align:start position:0% +the constant graphing without constant +value P but now let me give you a + + align:start position:0% +value P but now let me give you a + + + align:start position:0% +value P but now let me give you a +different example consider a + + align:start position:0% +different example consider a + + + align:start position:0% +different example consider a +checkerboard okay so here's a + + align:start position:0% +checkerboard okay so here's a + + + align:start position:0% +checkerboard okay so here's a +checkerboard where I color the squares + + align:start position:0% +checkerboard where I color the squares + + + align:start position:0% +checkerboard where I color the squares +according to in this alternating black + + align:start position:0% +according to in this alternating black + + + align:start position:0% +according to in this alternating black +and white manner according to a usual + + align:start position:0% +and white manner according to a usual + + + align:start position:0% +and white manner according to a usual +checkerboard and as the number of + + align:start position:0% +checkerboard and as the number of + + + align:start position:0% +checkerboard and as the number of +squares goes to infinity what should + + align:start position:0% +squares goes to infinity what should + + + align:start position:0% +squares goes to infinity what should +this converge to oh by the story I just + + align:start position:0% +this converge to oh by the story I just + + + align:start position:0% +this converge to oh by the story I just +told you you might think that you know + + align:start position:0% +told you you might think that you know + + + align:start position:0% +told you you might think that you know +if you zoom really zoom out everything + + align:start position:0% +if you zoom really zoom out everything + + + align:start position:0% +if you zoom really zoom out everything +looks like density 1/2 and so you might + + align:start position:0% +looks like density 1/2 and so you might + + + align:start position:0% +looks like density 1/2 and so you might +guess that the image limit is + + align:start position:0% +guess that the image limit is + + + align:start position:0% +guess that the image limit is +one half constant but what is this graph + + align:start position:0% + + + + align:start position:0% + +it's a complete bipartite graph it is a + + align:start position:0% +it's a complete bipartite graph it is a + + + align:start position:0% +it's a complete bipartite graph it is a +complete bipartite graph between the odd + + align:start position:0% +complete bipartite graph between the odd + + + align:start position:0% +complete bipartite graph between the odd +and even rows and there's a different + + align:start position:0% +and even rows and there's a different + + + align:start position:0% +and even rows and there's a different +way to draw the complete bipartite graph + + align:start position:0% +way to draw the complete bipartite graph + + + align:start position:0% +way to draw the complete bipartite graph +namely that picture just by permuting + + align:start position:0% +namely that picture just by permuting + + + align:start position:0% +namely that picture just by permuting +them rows and columns and it's much more + + align:start position:0% +them rows and columns and it's much more + + + align:start position:0% +them rows and columns and it's much more +reasonable that this is the limit of the + + align:start position:0% +reasonable that this is the limit of the + + + align:start position:0% +reasonable that this is the limit of the +sequence of complete bipartite graphs + + align:start position:0% +sequence of complete bipartite graphs + + + align:start position:0% +sequence of complete bipartite graphs +with equal parts so one needs to be very + + align:start position:0% +with equal parts so one needs to be very + + + align:start position:0% +with equal parts so one needs to be very +careful all right so it's not + + align:start position:0% +careful all right so it's not + + + align:start position:0% +careful all right so it's not +necessarily an intuitive definition I + + align:start position:0% +necessarily an intuitive definition I + + + align:start position:0% +necessarily an intuitive definition I +mean that's the the idea that you just + + align:start position:0% +mean that's the the idea that you just + + + align:start position:0% +mean that's the the idea that you just +know squint your eyes and think about + + align:start position:0% +know squint your eyes and think about + + + align:start position:0% +know squint your eyes and think about +what the image becomes that works fine + + align:start position:0% +what the image becomes that works fine + + + align:start position:0% +what the image becomes that works fine +for intuition for some examples but not + + align:start position:0% +for intuition for some examples but not + + + align:start position:0% +for intuition for some examples but not +for others so we do really need to be + + align:start position:0% +for others so we do really need to be + + + align:start position:0% +for others so we do really need to be +careful in giving a precise definition + + align:start position:0% +careful in giving a precise definition + + + align:start position:0% +careful in giving a precise definition +and here the rearrangement of rows and + + align:start position:0% +and here the rearrangement of rows and + + + align:start position:0% +and here the rearrangement of rows and +columns needs to be taken care of okay + + align:start position:0% +columns needs to be taken care of okay + + + align:start position:0% +columns needs to be taken care of okay +so let me be more precise starting with + + align:start position:0% +so let me be more precise starting with + + + align:start position:0% +so let me be more precise starting with +a graph G I can so let me label the + + align:start position:0% +a graph G I can so let me label the + + + align:start position:0% +a graph G I can so let me label the +vertices by one through n I can denote + + align:start position:0% +vertices by one through n I can denote + + + align:start position:0% +vertices by one through n I can denote +by W sub G this function square phone + + align:start position:0% +by W sub G this function square phone + + + align:start position:0% +by W sub G this function square phone +obtained by following procedure + + align:start position:0% + + + + align:start position:0% + +first you partition the interval into + + align:start position:0% + + + + align:start position:0% + +intervals of length exactly 1 over N and + + align:start position:0% +intervals of length exactly 1 over N and + + + align:start position:0% +intervals of length exactly 1 over N and +you set W of X comma Y to be basically + + align:start position:0% +you set W of X comma Y to be basically + + + align:start position:0% +you set W of X comma Y to be basically +what happened in the procedure above if + + align:start position:0% +what happened in the procedure above if + + + align:start position:0% +what happened in the procedure above if +x and y lie in the box + + align:start position:0% +x and y lie in the box + + + align:start position:0% +x and y lie in the box +bye-bye cross I sub J then I put in 1 if + + align:start position:0% +bye-bye cross I sub J then I put in 1 if + + + align:start position:0% +bye-bye cross I sub J then I put in 1 if +I is adjacent to J and 0 otherwise okay + + align:start position:0% +I is adjacent to J and 0 otherwise okay + + + align:start position:0% +I is adjacent to J and 0 otherwise okay +so this picture where we obtained by + + align:start position:0% +so this picture where we obtained by + + + align:start position:0% +so this picture where we obtained by +taking the adjacency matrix and + + align:start position:0% +taking the adjacency matrix and + + + align:start position:0% +taking the adjacency matrix and +transforming it into a pixelated image + + align:start position:0% + + + + align:start position:0% + +what are some of the things that we + + align:start position:0% +what are some of the things that we + + + align:start position:0% +what are some of the things that we +would like to do with graph limits or + + align:start position:0% +would like to do with graph limits or + + + align:start position:0% +would like to do with graph limits or +graphs in general ranges okay so here's + + align:start position:0% +graphs in general ranges okay so here's + + + align:start position:0% +graphs in general ranges okay so here's +our some quantities we're interested in + + align:start position:0% +our some quantities we're interested in + + + align:start position:0% +our some quantities we're interested in +when considering graph limits so given + + align:start position:0% +when considering graph limits so given + + + align:start position:0% +when considering graph limits so given +two graphs G and H we say that a graph + + align:start position:0% +two graphs G and H we say that a graph + + + align:start position:0% +two graphs G and H we say that a graph +homomorphism so a graph homomorphism + + align:start position:0% +homomorphism so a graph homomorphism + + + align:start position:0% +homomorphism so a graph homomorphism +between from G to H is a map of their + + align:start position:0% +between from G to H is a map of their + + + align:start position:0% +between from G to H is a map of their +vertex s + + align:start position:0% + + + + align:start position:0% + +such that the edges are preserved so you + + align:start position:0% +such that the edges are preserved so you + + + align:start position:0% +such that the edges are preserved so you +have so whenever you V is an edge inch + + align:start position:0% +have so whenever you V is an edge inch + + + align:start position:0% +have so whenever you V is an edge inch +their image vertices get mapped to an + + align:start position:0% +their image vertices get mapped to an + + + align:start position:0% +their image vertices get mapped to an +edge of G and we are interested in the + + align:start position:0% +edge of G and we are interested in the + + + align:start position:0% +edge of G and we are interested in the +number of graph homomorphisms so often I + + align:start position:0% +number of graph homomorphisms so often I + + + align:start position:0% +number of graph homomorphisms so often I +use uppercase to denote a set so the set + + align:start position:0% +use uppercase to denote a set so the set + + + align:start position:0% +use uppercase to denote a set so the set +of homomorphisms G to H and lowercase to + + align:start position:0% +of homomorphisms G to H and lowercase to + + + align:start position:0% +of homomorphisms G to H and lowercase to +denote the number so for example the + + align:start position:0% +denote the number so for example the + + + align:start position:0% +denote the number so for example the +number of homomorphisms from a single + + align:start position:0% +number of homomorphisms from a single + + + align:start position:0% +number of homomorphisms from a single +vertex so single vertex with no edge to + + align:start position:0% +vertex so single vertex with no edge to + + + align:start position:0% +vertex so single vertex with no edge to +a graph G that's just the okay what is + + align:start position:0% +a graph G that's just the okay what is + + + align:start position:0% +a graph G that's just the okay what is +this quantity so it's the number of + + align:start position:0% +this quantity so it's the number of + + + align:start position:0% +this quantity so it's the number of +vertices of G what about homomorphisms + + align:start position:0% +vertices of G what about homomorphisms + + + align:start position:0% +vertices of G what about homomorphisms +from an edge to G not quite a number of + + align:start position:0% +from an edge to G not quite a number of + + + align:start position:0% +from an edge to G not quite a number of +edges but twice the number of edges okay + + align:start position:0% +edges but twice the number of edges okay + + + align:start position:0% +edges but twice the number of edges okay +what about the number of homomorphisms + + align:start position:0% +what about the number of homomorphisms + + + align:start position:0% +what about the number of homomorphisms +from a triangle to G + + align:start position:0% + + + + align:start position:0% + +okay so okay you got the idea so the six + + align:start position:0% +okay so okay you got the idea so the six + + + align:start position:0% +okay so okay you got the idea so the six +times the number of triangles okay so + + align:start position:0% +times the number of triangles okay so + + + align:start position:0% +times the number of triangles okay so +now let me ask a slightly more + + align:start position:0% +now let me ask a slightly more + + + align:start position:0% +now let me ask a slightly more +interesting question what about the + + align:start position:0% +interesting question what about the + + + align:start position:0% +interesting question what about the +number of homomorphisms from H to a + + align:start position:0% +number of homomorphisms from H to a + + + align:start position:0% +number of homomorphisms from H to a +triangle what's a different name for + + align:start position:0% +triangle what's a different name for + + + align:start position:0% +triangle what's a different name for +this quantity here + + align:start position:0% + + + + align:start position:0% + +it's a number of proper three colorings + + align:start position:0% + + + + align:start position:0% + +number of okay so there's a number of + + align:start position:0% +number of okay so there's a number of + + + align:start position:0% +number of okay so there's a number of +property coloring the number of proper + + align:start position:0% +property coloring the number of proper + + + align:start position:0% +property coloring the number of proper +colorings of H with three labelled + + align:start position:0% +colorings of H with three labelled + + + align:start position:0% +colorings of H with three labelled +colors red green and blue so think about + + align:start position:0% +colors red green and blue so think about + + + align:start position:0% +colors red green and blue so think about +the three vertices as red green and blue + + align:start position:0% +the three vertices as red green and blue + + + align:start position:0% +the three vertices as red green and blue +and whichever vertex of H get mapped to + + align:start position:0% +and whichever vertex of H get mapped to + + + align:start position:0% +and whichever vertex of H get mapped to +red color that vertex red you see that + + align:start position:0% +red color that vertex red you see that + + + align:start position:0% +red color that vertex red you see that +there's a one-to-one correspondence + + align:start position:0% +there's a one-to-one correspondence + + + align:start position:0% +there's a one-to-one correspondence +between such homomorphisms and proper + + align:start position:0% +between such homomorphisms and proper + + + align:start position:0% +between such homomorphisms and proper +colorings so many important graph + + align:start position:0% +colorings so many important graph + + + align:start position:0% +colorings so many important graph +parameters graph quantities can be + + align:start position:0% +parameters graph quantities can be + + + align:start position:0% +parameters graph quantities can be +encoded in terms of craft hormone + + align:start position:0% +encoded in terms of craft hormone + + + align:start position:0% +encoded in terms of craft hormone +morphisms and these are the ones that + + align:start position:0% +morphisms and these are the ones that + + + align:start position:0% +morphisms and these are the ones that +we're going to be looking at most of the + + align:start position:0% +we're going to be looking at most of the + + + align:start position:0% +we're going to be looking at most of the +time when we're thinking about very + + align:start position:0% +time when we're thinking about very + + + align:start position:0% +time when we're thinking about very +large graphs often it's not a number of + + align:start position:0% +large graphs often it's not a number of + + + align:start position:0% +large graphs often it's not a number of +homomorphisms that concern us but the + + align:start position:0% +homomorphisms that concern us but the + + + align:start position:0% +homomorphisms that concern us but the +density of homomorphisms and the + + align:start position:0% +density of homomorphisms and the + + + align:start position:0% +density of homomorphisms and the +difference between homomorphisms on one + + align:start position:0% +difference between homomorphisms on one + + + align:start position:0% +difference between homomorphisms on one +hand and sub graphs is that + + align:start position:0% + + + + align:start position:0% + +homomorphisms not quite the same as sub + + align:start position:0% +homomorphisms not quite the same as sub + + + align:start position:0% +homomorphisms not quite the same as sub +graphs other than this multiplicity + + align:start position:0% +graphs other than this multiplicity + + + align:start position:0% +graphs other than this multiplicity +because you might have a non injective + + align:start position:0% + + + + align:start position:0% + +homomorphisms but this non injective + + align:start position:0% +homomorphisms but this non injective + + + align:start position:0% +homomorphisms but this non injective +homomorphisms do not end up contributing + + align:start position:0% +homomorphisms do not end up contributing + + + align:start position:0% +homomorphisms do not end up contributing +very much because they only have an to + + align:start position:0% +very much because they only have an to + + + align:start position:0% +very much because they only have an to +the number of vertices of h minus 1 on + + align:start position:0% +the number of vertices of h minus 1 on + + + align:start position:0% +the number of vertices of h minus 1 on +that water where i think of n as the + + align:start position:0% +that water where i think of n as the + + + align:start position:0% +that water where i think of n as the +number of vertices of G so and it's + + align:start position:0% +number of vertices of G so and it's + + + align:start position:0% +number of vertices of G so and it's +supposed to be large so in terms of + + align:start position:0% +supposed to be large so in terms of + + + align:start position:0% +supposed to be large so in terms of +graph limits when n gets large I don't + + align:start position:0% +graph limits when n gets large I don't + + + align:start position:0% +graph limits when n gets large I don't +need to distinguish so much between + + align:start position:0% +need to distinguish so much between + + + align:start position:0% +need to distinguish so much between +homomorphisms and sub graphs we define + + align:start position:0% +homomorphisms and sub graphs we define + + + align:start position:0% +homomorphisms and sub graphs we define +the homomorphism density + + align:start position:0% + + + + align:start position:0% + +denoted by the letter T from H to G by + + align:start position:0% +denoted by the letter T from H to G by + + + align:start position:0% +denoted by the letter T from H to G by +define it to be the fraction of all + + align:start position:0% +define it to be the fraction of all + + + align:start position:0% +define it to be the fraction of all +vertex maps that are homomorphisms so + + align:start position:0% +vertex maps that are homomorphisms so + + + align:start position:0% +vertex maps that are homomorphisms so +this is also equivalent we defined as + + align:start position:0% +this is also equivalent we defined as + + + align:start position:0% +this is also equivalent we defined as +the probability that a uniform random + + align:start position:0% +the probability that a uniform random + + + align:start position:0% +the probability that a uniform random +map from the vertex set of H to the + + align:start position:0% +map from the vertex set of H to the + + + align:start position:0% +map from the vertex set of H to the +vertex set of G is a homomorphism from H + + align:start position:0% +vertex set of G is a homomorphism from H + + + align:start position:0% +vertex set of G is a homomorphism from H +to G so it's a graph homomorphism and + + align:start position:0% +to G so it's a graph homomorphism and + + + align:start position:0% +to G so it's a graph homomorphism and +this quantity turns out to be quite + + align:start position:0% +this quantity turns out to be quite + + + align:start position:0% +this quantity turns out to be quite +important so what can be seen this a lot + + align:start position:0% +important so what can be seen this a lot + + + align:start position:0% +important so what can be seen this a lot +and because of this remark over here in + + align:start position:0% +and because of this remark over here in + + + align:start position:0% +and because of this remark over here in +the limit this quantity on graph + + align:start position:0% +the limit this quantity on graph + + + align:start position:0% +the limit this quantity on graph +homomorphism densities in the limit as + + align:start position:0% +homomorphism densities in the limit as + + + align:start position:0% +homomorphism densities in the limit as +the number of vertices G goes to + + align:start position:0% +the number of vertices G goes to + + + align:start position:0% +the number of vertices G goes to +infinity and H fixed so homomorphism + + align:start position:0% +infinity and H fixed so homomorphism + + + align:start position:0% +infinity and H fixed so homomorphism +densities approaches the same limit as + + align:start position:0% +densities approaches the same limit as + + + align:start position:0% +densities approaches the same limit as +sub graph densities + + align:start position:0% + + + + align:start position:0% + +so you should regard these two + + align:start position:0% +so you should regard these two + + + align:start position:0% +so you should regard these two +quantities as basically the same thing + + align:start position:0% + + + + align:start position:0% + +any questions so far + + align:start position:0% + + + + align:start position:0% + +all right so all of these quantities so + + align:start position:0% +all right so all of these quantities so + + + align:start position:0% +all right so all of these quantities so +far defined are for okay so there + + align:start position:0% +far defined are for okay so there + + + align:start position:0% +far defined are for okay so there +everything is defined so far for graphs + + align:start position:0% +everything is defined so far for graphs + + + align:start position:0% +everything is defined so far for graphs +right so what happens between graphs and + + align:start position:0% +right so what happens between graphs and + + + align:start position:0% +right so what happens between graphs and +graphs so what about for griffons now + + align:start position:0% +graphs so what about for griffons now + + + align:start position:0% +graphs so what about for griffons now +I'll give you this limit object just + + align:start position:0% +I'll give you this limit object just + + + align:start position:0% +I'll give you this limit object just +analytic object I can still define + + align:start position:0% +analytic object I can still define + + + align:start position:0% +analytic object I can still define +densities by integrals now so suppose I + + align:start position:0% +densities by integrals now so suppose I + + + align:start position:0% +densities by integrals now so suppose I +start with a symmetric measurable + + align:start position:0% +start with a symmetric measurable + + + align:start position:0% +start with a symmetric measurable +function for example I'll graph on but I + + align:start position:0% +function for example I'll graph on but I + + + align:start position:0% +function for example I'll graph on but I +can let my range be even more generous + + align:start position:0% +can let my range be even more generous + + + align:start position:0% +can let my range be even more generous +starting with such a function I define + + align:start position:0% +starting with such a function I define + + + align:start position:0% +starting with such a function I define +the graph homomorphism density from a + + align:start position:0% +the graph homomorphism density from a + + + align:start position:0% +the graph homomorphism density from a +fixed graph H to this graph on or kernel + + align:start position:0% +fixed graph H to this graph on or kernel + + + align:start position:0% +fixed graph H to this graph on or kernel +more generally to be the following + + align:start position:0% +more generally to be the following + + + align:start position:0% +more generally to be the following +integral where I'm before I go down the + + align:start position:0% +integral where I'm before I go down the + + + align:start position:0% +integral where I'm before I go down the +full form let me first give you an + + align:start position:0% +full form let me first give you an + + + align:start position:0% +full form let me first give you an +example I think it will be more helpful + + align:start position:0% +example I think it will be more helpful + + + align:start position:0% +example I think it will be more helpful +so if I'm looking at a triangle going to + + align:start position:0% +so if I'm looking at a triangle going to + + + align:start position:0% +so if I'm looking at a triangle going to +W what I would like is integral that + + align:start position:0% +W what I would like is integral that + + + align:start position:0% +W what I would like is integral that +captures the triangle density so this + + align:start position:0% +captures the triangle density so this + + + align:start position:0% +captures the triangle density so this +quantity here if I let XYZ vary over + + align:start position:0% + + + + align:start position:0% + +zero and one zero to one independent in + + align:start position:0% +zero and one zero to one independent in + + + align:start position:0% +zero and one zero to one independent in +uniformly then this quantity here + + align:start position:0% +uniformly then this quantity here + + + align:start position:0% +uniformly then this quantity here +captures the triangle density in W in + + align:start position:0% +captures the triangle density in W in + + + align:start position:0% +captures the triangle density in W in +fact and now state status more precisely + + align:start position:0% +fact and now state status more precisely + + + align:start position:0% +fact and now state status more precisely +in a second if you look at the + + align:start position:0% +in a second if you look at the + + + align:start position:0% +in a second if you look at the +translation from graph to graph on and + + align:start position:0% +translation from graph to graph on and + + + align:start position:0% +translation from graph to graph on and +combine that translation with this + + align:start position:0% +combine that translation with this + + + align:start position:0% +combine that translation with this +definition here you recover the triangle + + align:start position:0% +definition here you recover the triangle + + + align:start position:0% +definition here you recover the triangle +density + + align:start position:0% + + + + align:start position:0% + +more generally 4h instead of a triangle + + align:start position:0% +more generally 4h instead of a triangle + + + align:start position:0% +more generally 4h instead of a triangle +the H density in a graph form is defined + + align:start position:0% +the H density in a graph form is defined + + + align:start position:0% +the H density in a graph form is defined +to be the integral of instead of this + + align:start position:0% +to be the integral of instead of this + + + align:start position:0% +to be the integral of instead of this +product here I take a product + + align:start position:0% +product here I take a product + + + align:start position:0% +product here I take a product +corresponding to the graph structure of + + align:start position:0% +corresponding to the graph structure of + + + align:start position:0% +corresponding to the graph structure of +H one factor for each edge of H and the + + align:start position:0% +H one factor for each edge of H and the + + + align:start position:0% +H one factor for each edge of H and the +variables go over the vertex set of H so + + align:start position:0% +variables go over the vertex set of H so + + + align:start position:0% +variables go over the vertex set of H so +this is the definition of homomorphism + + align:start position:0% +this is the definition of homomorphism + + + align:start position:0% +this is the definition of homomorphism +densities not for graphs before + + align:start position:0% +densities not for graphs before + + + align:start position:0% +densities not for graphs before +symmetric measurable functions in + + align:start position:0% +symmetric measurable functions in + + + align:start position:0% +symmetric measurable functions in +particular for graph owns and we define + + align:start position:0% +particular for graph owns and we define + + + align:start position:0% +particular for graph owns and we define +it this way because and we use the same + + align:start position:0% +it this way because and we use the same + + + align:start position:0% +it this way because and we use the same +symbols because these two definitions + + align:start position:0% +symbols because these two definitions + + + align:start position:0% +symbols because these two definitions +agree if you start with a graph and look + + align:start position:0% +agree if you start with a graph and look + + + align:start position:0% +agree if you start with a graph and look +at the H density in G then this quantity + + align:start position:0% +at the H density in G then this quantity + + + align:start position:0% +at the H density in G then this quantity +here is equal to the H density in the + + align:start position:0% +here is equal to the H density in the + + + align:start position:0% +here is equal to the H density in the +graph on associated to the graph G + + align:start position:0% +graph on associated to the graph G + + + align:start position:0% +graph on associated to the graph G +constructed as we did just now okay so + + align:start position:0% +constructed as we did just now okay so + + + align:start position:0% +constructed as we did just now okay so +make sure you understand why this is + + align:start position:0% +make sure you understand why this is + + + align:start position:0% +make sure you understand why this is +true and why we defined densities this + + align:start position:0% +true and why we defined densities this + + + align:start position:0% +true and why we defined densities this +way any questions so far + + align:start position:0% + + + + align:start position:0% + +what so we've given the definition of + + align:start position:0% +what so we've given the definition of + + + align:start position:0% +what so we've given the definition of +graph homomorphism density and we've + + align:start position:0% +graph homomorphism density and we've + + + align:start position:0% +graph homomorphism density and we've +defined these objects these graphs and I + + align:start position:0% +defined these objects these graphs and I + + + align:start position:0% +defined these objects these graphs and I +mentioned even something about the idea + + align:start position:0% +mentioned even something about the idea + + + align:start position:0% +mentioned even something about the idea +of a limit but in what sense can we have + + align:start position:0% +of a limit but in what sense can we have + + + align:start position:0% +of a limit but in what sense can we have +a limit of graphs so here's an important + + align:start position:0% +a limit of graphs so here's an important + + + align:start position:0% +a limit of graphs so here's an important +definition on the convergence of graphs + + align:start position:0% +definition on the convergence of graphs + + + align:start position:0% +definition on the convergence of graphs +so in what sense + + align:start position:0% +so in what sense + + + align:start position:0% +so in what sense +can we say that a sequence of graphs + + align:start position:0% +can we say that a sequence of graphs + + + align:start position:0% +can we say that a sequence of graphs +converge so we say that sequence graphs + + align:start position:0% + + + + align:start position:0% + +jiseop n graphs or graph ons so these + + align:start position:0% +jiseop n graphs or graph ons so these + + + align:start position:0% +jiseop n graphs or graph ons so these +two definitions are interchangeable for + + align:start position:0% +two definitions are interchangeable for + + + align:start position:0% +two definitions are interchangeable for +the what I'm about to say regarding + + align:start position:0% +the what I'm about to say regarding + + + align:start position:0% +the what I'm about to say regarding +limits so phones in which case I'm going + + align:start position:0% +limits so phones in which case I'm going + + + align:start position:0% +limits so phones in which case I'm going +to denote them by W sub M okay so we say + + align:start position:0% +to denote them by W sub M okay so we say + + + align:start position:0% +to denote them by W sub M okay so we say +the sequence is convergent if the + + align:start position:0% +the sequence is convergent if the + + + align:start position:0% +the sequence is convergent if the +sequence of sub graph densities of + + align:start position:0% +sequence of sub graph densities of + + + align:start position:0% +sequence of sub graph densities of +course if you're looking at griffons + + align:start position:0% +course if you're looking at griffons + + + align:start position:0% +course if you're looking at griffons +then you should look at the graph on sub + + align:start position:0% +then you should look at the graph on sub + + + align:start position:0% +then you should look at the graph on sub +graph density in homomorphism density in + + align:start position:0% +graph density in homomorphism density in + + + align:start position:0% +graph density in homomorphism density in +griffons if this sequence converges and + + align:start position:0% +griffons if this sequence converges and + + + align:start position:0% +griffons if this sequence converges and +goes to infinity for every graph + + align:start position:0% +goes to infinity for every graph + + + align:start position:0% +goes to infinity for every graph +eh okay so that's the definition of what + + align:start position:0% +eh okay so that's the definition of what + + + align:start position:0% +eh okay so that's the definition of what +it means for sequence of graphs to + + align:start position:0% +it means for sequence of graphs to + + + align:start position:0% +it means for sequence of graphs to +converge which so far looks actually + + align:start position:0% +converge which so far looks actually + + + align:start position:0% +converge which so far looks actually +quite different from what we discussed + + align:start position:0% +quite different from what we discussed + + + align:start position:0% +quite different from what we discussed +intuitively but I will state some + + align:start position:0% +intuitively but I will state some + + + align:start position:0% +intuitively but I will state some +theorems towards the end of this lecture + + align:start position:0% +theorems towards the end of this lecture + + + align:start position:0% +theorems towards the end of this lecture +explaining what the connections are + + align:start position:0% +explaining what the connections are + + + align:start position:0% +explaining what the connections are +alright so intuitively what I've said + + align:start position:0% +alright so intuitively what I've said + + + align:start position:0% +alright so intuitively what I've said +earlier is that you have a sequence of + + align:start position:0% +earlier is that you have a sequence of + + + align:start position:0% +earlier is that you have a sequence of +graphs that are convergent if you have + + align:start position:0% +graphs that are convergent if you have + + + align:start position:0% +graphs that are convergent if you have +some vague notion of one image morphing + + align:start position:0% +some vague notion of one image morphing + + + align:start position:0% +some vague notion of one image morphing +into a sequence of images morphing into + + align:start position:0% +into a sequence of images morphing into + + + align:start position:0% +into a sequence of images morphing into +this final image it still hold that + + align:start position:0% +this final image it still hold that + + + align:start position:0% +this final image it still hold that +thought in your mind but that's not a + + align:start position:0% +thought in your mind but that's not a + + + align:start position:0% +thought in your mind but that's not a +rigorous definition yet the definition + + align:start position:0% +rigorous definition yet the definition + + + align:start position:0% +rigorous definition yet the definition +we will use for convergent convergence + + align:start position:0% +we will use for convergent convergence + + + align:start position:0% +we will use for convergent convergence +is if all the subgraph all the + + align:start position:0% +is if all the subgraph all the + + + align:start position:0% +is if all the subgraph all the +homomorphism densities or equivalently + + align:start position:0% +homomorphism densities or equivalently + + + align:start position:0% +homomorphism densities or equivalently +subgraph densities they converge so this + + align:start position:0% +subgraph densities they converge so this + + + align:start position:0% +subgraph densities they converge so this +is the definition it's not required so + + align:start position:0% +is the definition it's not required so + + + align:start position:0% +is the definition it's not required so +this is basically rigorous as stated + + align:start position:0% +this is basically rigorous as stated + + + align:start position:0% +this is basically rigorous as stated +just as a remark it's it's not required + + align:start position:0% +just as a remark it's it's not required + + + align:start position:0% +just as a remark it's it's not required +that the number of vertices goes to + + align:start position:0% +that the number of vertices goes to + + + align:start position:0% +that the number of vertices goes to +infinity although you wouldn't you think + + align:start position:0% +infinity although you wouldn't you think + + + align:start position:0% +infinity although you wouldn't you think +that is the case so just put it out + + align:start position:0% +that is the case so just put it out + + + align:start position:0% +that is the case so just put it out +there something I can have a sequence of + + align:start position:0% +there something I can have a sequence of + + + align:start position:0% +there something I can have a sequence of +constant graphs and they will still be + + align:start position:0% +constant graphs and they will still be + + + align:start position:0% +constant graphs and they will still be +convergent and and that's still okay but + + align:start position:0% +convergent and and that's still okay but + + + align:start position:0% +convergent and and that's still okay but +you should think of the number of + + align:start position:0% +you should think of the number of + + + align:start position:0% +you should think of the number of +vertices going to infinity + + align:start position:0% + + + + align:start position:0% + +thank you any other questions + + align:start position:0% + + + + align:start position:0% + +all right so so there are some questions + + align:start position:0% +all right so so there are some questions + + + align:start position:0% +all right so so there are some questions +that would like to discuss right and + + align:start position:0% +that would like to discuss right and + + + align:start position:0% +that would like to discuss right and +this will occupy the next few lectures + + align:start position:0% +this will occupy the next few lectures + + + align:start position:0% +this will occupy the next few lectures +in terms of proving the following + + align:start position:0% +in terms of proving the following + + + align:start position:0% +in terms of proving the following +statements one is do you always have + + align:start position:0% +statements one is do you always have + + + align:start position:0% +statements one is do you always have +graph limits if you have a convergent + + align:start position:0% +graph limits if you have a convergent + + + align:start position:0% +graph limits if you have a convergent +sequence of graphs do they always + + align:start position:0% +sequence of graphs do they always + + + align:start position:0% +sequence of graphs do they always +approach a limit just because something + + align:start position:0% +approach a limit just because something + + + align:start position:0% +approach a limit just because something +is convergent doesn't mean you can + + align:start position:0% +is convergent doesn't mean you can + + + align:start position:0% +is convergent doesn't mean you can +represent the limit necessarily okay so + + align:start position:0% +represent the limit necessarily okay so + + + align:start position:0% +represent the limit necessarily okay so +it turns out the answer is yes turns out + + align:start position:0% +it turns out the answer is yes turns out + + + align:start position:0% +it turns out the answer is yes turns out +that and this is makes it a good theory + + align:start position:0% +that and this is makes it a good theory + + + align:start position:0% +that and this is makes it a good theory +a good useful theory or easy theory to + + align:start position:0% +a good useful theory or easy theory to + + + align:start position:0% +a good useful theory or easy theory to +use that there's always a limit object + + align:start position:0% +use that there's always a limit object + + + align:start position:0% +use that there's always a limit object +when whenever you have convergence and + + align:start position:0% +when whenever you have convergence and + + + align:start position:0% +when whenever you have convergence and +the other question is well we've + + align:start position:0% +the other question is well we've + + + align:start position:0% +the other question is well we've +described intuitively one notion of + + align:start position:0% +described intuitively one notion of + + + align:start position:0% +described intuitively one notion of +convergence and also defined more + + align:start position:0% +convergence and also defined more + + + align:start position:0% +convergence and also defined more +rigorously another this definition of + + align:start position:0% +rigorously another this definition of + + + align:start position:0% +rigorously another this definition of +convergence are these two notions + + align:start position:0% +convergence are these two notions + + + align:start position:0% +convergence are these two notions +compatible and what does this even mean + + align:start position:0% +compatible and what does this even mean + + + align:start position:0% +compatible and what does this even mean +right this idea of image becoming closer + + align:start position:0% +right this idea of image becoming closer + + + align:start position:0% +right this idea of image becoming closer +and closer to a final image what does + + align:start position:0% +and closer to a final image what does + + + align:start position:0% +and closer to a final image what does +that even mean okay so these are some of + + align:start position:0% +that even mean okay so these are some of + + + align:start position:0% +that even mean okay so these are some of +the questions I would like to address so + + align:start position:0% +the questions I would like to address so + + + align:start position:0% +the questions I would like to address so +in the the next few things I would like + + align:start position:0% +in the the next few things I would like + + + align:start position:0% +in the the next few things I would like +to discuss it first I want to give you a + + align:start position:0% +to discuss it first I want to give you a + + + align:start position:0% +to discuss it first I want to give you a +definition of a distance between two + + align:start position:0% +definition of a distance between two + + + align:start position:0% +definition of a distance between two +graphs or two graphs if I give you two + + align:start position:0% +graphs or two graphs if I give you two + + + align:start position:0% +graphs or two graphs if I give you two +graphs how similar or dissimilar are + + align:start position:0% +graphs how similar or dissimilar are + + + align:start position:0% +graphs how similar or dissimilar are +they so that we have this metric and + + align:start position:0% +they so that we have this metric and + + + align:start position:0% +they so that we have this metric and +then we can talk about convergence in + + align:start position:0% +then we can talk about convergence in + + + align:start position:0% +then we can talk about convergence in +metric spaces + + align:start position:0% + + + + align:start position:0% + +let's take quick let's take a quick + + align:start position:0% +let's take quick let's take a quick + + + align:start position:0% +let's take quick let's take a quick +break + + align:start position:0% +break + + + align:start position:0% +break +okay so given this notion of convergence + + align:start position:0% +okay so given this notion of convergence + + + align:start position:0% +okay so given this notion of convergence +I would like to define a notion of + + align:start position:0% +I would like to define a notion of + + + align:start position:0% +I would like to define a notion of +distance between graphs so that + + align:start position:0% +distance between graphs so that + + + align:start position:0% +distance between graphs so that +convergence corresponds to convergence + + align:start position:0% +convergence corresponds to convergence + + + align:start position:0% +convergence corresponds to convergence +in the metric space sense of distance + + align:start position:0% +in the metric space sense of distance + + + align:start position:0% +in the metric space sense of distance +going to zero so how can we define + + align:start position:0% +going to zero so how can we define + + + align:start position:0% +going to zero so how can we define +distance first let me tell you that + + align:start position:0% +distance first let me tell you that + + + align:start position:0% +distance first let me tell you that +there's a trivial way right so there's a + + align:start position:0% +there's a trivial way right so there's a + + + align:start position:0% +there's a trivial way right so there's a +way which you look at that definition + + align:start position:0% +way which you look at that definition + + + align:start position:0% +way which you look at that definition +and produce a distance out and here's + + align:start position:0% +and produce a distance out and here's + + + align:start position:0% +and produce a distance out and here's +what you can do I can I can convert that + + align:start position:0% +what you can do I can I can convert that + + + align:start position:0% +what you can do I can I can convert that +definition to a metric by setting the + + align:start position:0% +definition to a metric by setting the + + + align:start position:0% +definition to a metric by setting the +distance between two graphs g and g + + align:start position:0% +distance between two graphs g and g + + + align:start position:0% +distance between two graphs g and g +prime to be the following quantity + + align:start position:0% +prime to be the following quantity + + + align:start position:0% +prime to be the following quantity +obtained by well what would i like to do + + align:start position:0% +obtained by well what would i like to do + + + align:start position:0% +obtained by well what would i like to do +i would like to say the distance goes to + + align:start position:0% +i would like to say the distance goes to + + + align:start position:0% +i would like to say the distance goes to +zero if and only if that homomorphism + + align:start position:0% +zero if and only if that homomorphism + + + align:start position:0% +zero if and only if that homomorphism +densities they're all close to each + + align:start position:0% +densities they're all close to each + + + align:start position:0% +densities they're all close to each +other okay so i can sum up all the + + align:start position:0% +other okay so i can sum up all the + + + align:start position:0% +other okay so i can sum up all the +homomorphism densities and look at there + + align:start position:0% +homomorphism densities and look at there + + + align:start position:0% +homomorphism densities and look at there +are differences between g and g prime + + align:start position:0% +are differences between g and g prime + + + align:start position:0% +are differences between g and g prime +and i simply enumerate the list of all + + align:start position:0% +and i simply enumerate the list of all + + + align:start position:0% +and i simply enumerate the list of all +possible graphs + + align:start position:0% + + + + align:start position:0% + +I want to be just slightly more careful + + align:start position:0% +I want to be just slightly more careful + + + align:start position:0% +I want to be just slightly more careful +with this definition here because I want + + align:start position:0% +with this definition here because I want + + + align:start position:0% +with this definition here because I want +something which ok so we write this this + + align:start position:0% +something which ok so we write this this + + + align:start position:0% +something which ok so we write this this +number might be infinite for all pairs G + + align:start position:0% +number might be infinite for all pairs G + + + align:start position:0% +number might be infinite for all pairs G +& G Prime + + align:start position:0% +& G Prime + + + align:start position:0% +& G Prime +so if I just add a scaling factor here + + align:start position:0% +so if I just add a scaling factor here + + + align:start position:0% +so if I just add a scaling factor here +then then this is this is some distance + + align:start position:0% +then then this is this is some distance + + + align:start position:0% +then then this is this is some distance +okay so this is some distance and you + + align:start position:0% +okay so this is some distance and you + + + align:start position:0% +okay so this is some distance and you +see that it matches the definition up + + align:start position:0% +see that it matches the definition up + + + align:start position:0% +see that it matches the definition up +there but it's completely useless right + + align:start position:0% +there but it's completely useless right + + + align:start position:0% +there but it's completely useless right +it might as well might as well not said + + align:start position:0% +it might as well might as well not said + + + align:start position:0% +it might as well might as well not said +anything because it's tautologically the + + align:start position:0% +anything because it's tautologically the + + + align:start position:0% +anything because it's tautologically the +same as what's happened up there and if + + align:start position:0% +same as what's happened up there and if + + + align:start position:0% +same as what's happened up there and if +I give you two graphs you know it + + align:start position:0% +I give you two graphs you know it + + + align:start position:0% +I give you two graphs you know it +doesn't really tell you all that much + + align:start position:0% +doesn't really tell you all that much + + + align:start position:0% +doesn't really tell you all that much +information except to encapsulate that + + align:start position:0% +information except to encapsulate that + + + align:start position:0% +information except to encapsulate that +definition into a single number okay so + + align:start position:0% +definition into a single number okay so + + + align:start position:0% +definition into a single number okay so +I'm just the point of this is just just + + align:start position:0% +I'm just the point of this is just just + + + align:start position:0% +I'm just the point of this is just just +to tell you that you know there's + + align:start position:0% +to tell you that you know there's + + + align:start position:0% +to tell you that you know there's +there's always a trivial way to define + + align:start position:0% +there's always a trivial way to define + + + align:start position:0% +there's always a trivial way to define +distance but we want some more + + align:start position:0% +distance but we want some more + + + align:start position:0% +distance but we want some more +interesting ways okay so what can we do + + align:start position:0% +interesting ways okay so what can we do + + + align:start position:0% +interesting ways okay so what can we do +so here's an attempt which is better + + align:start position:0% +so here's an attempt which is better + + + align:start position:0% +so here's an attempt which is better +than other distance okay so we've seen + + align:start position:0% +than other distance okay so we've seen + + + align:start position:0% +than other distance okay so we've seen +this before when we discuss removal on + + align:start position:0% +this before when we discuss removal on + + + align:start position:0% +this before when we discuss removal on +us the Edit distance is the number of + + align:start position:0% +us the Edit distance is the number of + + + align:start position:0% +us the Edit distance is the number of +edges you need to change to go from one + + align:start position:0% +edges you need to change to go from one + + + align:start position:0% +edges you need to change to go from one +graph to the other graph and it seems + + align:start position:0% +graph to the other graph and it seems + + + align:start position:0% +graph to the other graph and it seems +like a pretty reasonable thing to do and + + align:start position:0% +like a pretty reasonable thing to do and + + + align:start position:0% +like a pretty reasonable thing to do and +it is an important quantity for many + + align:start position:0% +it is an important quantity for many + + + align:start position:0% +it is an important quantity for many +applications but turns out not the right + + align:start position:0% +applications but turns out not the right + + + align:start position:0% +applications but turns out not the right +one for our application and here's the + + align:start position:0% +one for our application and here's the + + + align:start position:0% +one for our application and here's the +reason okay so this is why the Edit + + align:start position:0% +reason okay so this is why the Edit + + + align:start position:0% +reason okay so this is why the Edit +distance is okay so by the distance I + + align:start position:0% +distance is okay so by the distance I + + + align:start position:0% +distance is okay so by the distance I +mean one over the number of vertex + + align:start position:0% +mean one over the number of vertex + + + align:start position:0% +mean one over the number of vertex +squared times the number of changes + + align:start position:0% +squared times the number of changes + + + align:start position:0% +squared times the number of changes +needed okay so there's normalization so + + align:start position:0% +needed okay so there's normalization so + + + align:start position:0% +needed okay so there's normalization so +that the distance is always between zero + + align:start position:0% +that the distance is always between zero + + + align:start position:0% +that the distance is always between zero +and one but this is not a very good + + align:start position:0% +and one but this is not a very good + + + align:start position:0% +and one but this is not a very good +notion for the following reason if I + + align:start position:0% +notion for the following reason if I + + + align:start position:0% +notion for the following reason if I +take two copies of the edit when a + + align:start position:0% +take two copies of the edit when a + + + align:start position:0% +take two copies of the edit when a +random graph GN 1/2 what do you think is + + align:start position:0% +random graph GN 1/2 what do you think is + + + align:start position:0% +random graph GN 1/2 what do you think is +the Edit distance between two such + + align:start position:0% +the Edit distance between two such + + + align:start position:0% +the Edit distance between two such +random graphs + + align:start position:0% + + + + align:start position:0% + +how many edges yep okay okay so yeah so + + align:start position:0% +how many edges yep okay okay so yeah so + + + align:start position:0% +how many edges yep okay okay so yeah so +let me try to rephrase what you're + + align:start position:0% +let me try to rephrase what you're + + + align:start position:0% +let me try to rephrase what you're +saying so suppose I have this G and G + + align:start position:0% +saying so suppose I have this G and G + + + align:start position:0% +saying so suppose I have this G and G +prime both sitting on top of the vertex + + align:start position:0% +prime both sitting on top of the vertex + + + align:start position:0% +prime both sitting on top of the vertex +set and okay so if I'm not allowed to + + align:start position:0% +set and okay so if I'm not allowed to + + + align:start position:0% +set and okay so if I'm not allowed to +you know rearrange the vertices how many + + align:start position:0% +you know rearrange the vertices how many + + + align:start position:0% +you know rearrange the vertices how many +exchanges do I need to go from one to + + align:start position:0% +exchanges do I need to go from one to + + + align:start position:0% +exchanges do I need to go from one to +the other I need about one half one half + + align:start position:0% +the other I need about one half one half + + + align:start position:0% +the other I need about one half one half +the time I'm going to have a wrong edge + + align:start position:0% +the time I'm going to have a wrong edge + + + align:start position:0% +the time I'm going to have a wrong edge +there now you can make this number just + + align:start position:0% +there now you can make this number just + + + align:start position:0% +there now you can make this number just +slightly smaller by permuting the + + align:start position:0% +slightly smaller by permuting the + + + align:start position:0% +slightly smaller by permuting the +vertices but actually you will not + + align:start position:0% +vertices but actually you will not + + + align:start position:0% +vertices but actually you will not +improve that much it's still going to be + + align:start position:0% +improve that much it's still going to be + + + align:start position:0% +improve that much it's still going to be +roughly that edit distance which is + + align:start position:0% +roughly that edit distance which is + + + align:start position:0% +roughly that edit distance which is +quite large I mean this is almost almost + + align:start position:0% +quite large I mean this is almost almost + + + align:start position:0% +quite large I mean this is almost almost +as large as you can possibly get between + + align:start position:0% +as large as you can possibly get between + + + align:start position:0% +as large as you can possibly get between +two arbitrary graphs so if we want to + + align:start position:0% +two arbitrary graphs so if we want to + + + align:start position:0% +two arbitrary graphs so if we want to +say that random graphs they approach + + align:start position:0% +say that random graphs they approach + + + align:start position:0% +say that random graphs they approach +limit a single limit then this is not a + + align:start position:0% +limit a single limit then this is not a + + + align:start position:0% +limit a single limit then this is not a +very good notion because they're quite + + align:start position:0% +very good notion because they're quite + + + align:start position:0% +very good notion because they're quite +far apart for every N okay so this is + + align:start position:0% +far apart for every N okay so this is + + + align:start position:0% +far apart for every N okay so this is +the reason why the more obvious + + align:start position:0% +the reason why the more obvious + + + align:start position:0% +the reason why the more obvious +suggestion of an e d distance might not + + align:start position:0% +suggestion of an e d distance might not + + + align:start position:0% +suggestion of an e d distance might not +be such a great idea so what should I + + align:start position:0% +be such a great idea so what should I + + + align:start position:0% +be such a great idea so what should I +use instead so we should take + + align:start position:0% +use instead so we should take + + + align:start position:0% +use instead so we should take +inspiration from what we discussed in + + align:start position:0% +inspiration from what we discussed in + + + align:start position:0% +inspiration from what we discussed in +plotting randomness yes question okay so + + align:start position:0% +plotting randomness yes question okay so + + + align:start position:0% +plotting randomness yes question okay so +the question is instead of distance only + + align:start position:0% +the question is instead of distance only + + + align:start position:0% +the question is instead of distance only +for two graphs with the same vertex set + + align:start position:0% +for two graphs with the same vertex set + + + align:start position:0% +for two graphs with the same vertex set +let's say yes so we'll see later on you + + align:start position:0% +let's say yes so we'll see later on you + + + align:start position:0% +let's say yes so we'll see later on you +can also compare graphs with different + + align:start position:0% +can also compare graphs with different + + + align:start position:0% +can also compare graphs with different +number of vertices yeah so hold on to + + align:start position:0% +number of vertices yeah so hold on to + + + align:start position:0% +number of vertices yeah so hold on to +that thought + + align:start position:0% +that thought + + + align:start position:0% +that thought +so I would like to come up with a notion + + align:start position:0% +so I would like to come up with a notion + + + align:start position:0% +so I would like to come up with a notion +of distance between graphs that is + + align:start position:0% +of distance between graphs that is + + + align:start position:0% +of distance between graphs that is +inspired by our discussion of quasi + + align:start position:0% +inspired by our discussion of quasi + + + align:start position:0% +inspired by our discussion of quasi +randomness earlier so think about the + + align:start position:0% +randomness earlier so think about the + + + align:start position:0% +randomness earlier so think about the +discussion of quasi randomness quasi + + align:start position:0% +discussion of quasi randomness quasi + + + align:start position:0% +discussion of quasi randomness quasi +random graphs okay in what sense can G + + align:start position:0% +random graphs okay in what sense can G + + + align:start position:0% +random graphs okay in what sense can G +be close to a constant let's say so this + + align:start position:0% +be close to a constant let's say so this + + + align:start position:0% +be close to a constant let's say so this +was the this chunk graham wilson theorem + + align:start position:0% +was the this chunk graham wilson theorem + + + align:start position:0% +was the this chunk graham wilson theorem +that we proved a few lectures ago so in + + align:start position:0% +that we proved a few lectures ago so in + + + align:start position:0% +that we proved a few lectures ago so in +what sense can G be close to P and one + + align:start position:0% +what sense can G be close to P and one + + + align:start position:0% +what sense can G be close to P and one +of those definitions was discrepancy and + + align:start position:0% +of those definitions was discrepancy and + + + align:start position:0% +of those definitions was discrepancy and +discrepancy says that if the following + + align:start position:0% +discrepancy says that if the following + + + align:start position:0% +discrepancy says that if the following +quantity is small for all subsets XY + + align:start position:0% +quantity is small for all subsets XY + + + align:start position:0% +quantity is small for all subsets XY +which are subsets of vertices of G okay + + align:start position:0% +which are subsets of vertices of G okay + + + align:start position:0% +which are subsets of vertices of G okay +so you remember all of you remember this + + align:start position:0% +so you remember all of you remember this + + + align:start position:0% +so you remember all of you remember this +part the discrepancy hypothesis for + + align:start position:0% +part the discrepancy hypothesis for + + + align:start position:0% +part the discrepancy hypothesis for +quasi randomness and this is a kind of + + align:start position:0% +quasi randomness and this is a kind of + + + align:start position:0% +quasi randomness and this is a kind of +definition that we would like to + + align:start position:0% +definition that we would like to + + + align:start position:0% +definition that we would like to +describe when two graphs are similar to + + align:start position:0% +describe when two graphs are similar to + + + align:start position:0% +describe when two graphs are similar to +each other when they are close in this + + align:start position:0% +each other when they are close in this + + + align:start position:0% +each other when they are close in this +discrepancy sense so now instead of a + + align:start position:0% +discrepancy sense so now instead of a + + + align:start position:0% +discrepancy sense so now instead of a +graph and a number what if now I have + + align:start position:0% +graph and a number what if now I have + + + align:start position:0% +graph and a number what if now I have +two graphs I'll give you two graphs G & + + align:start position:0% +two graphs I'll give you two graphs G & + + + align:start position:0% +two graphs I'll give you two graphs G & +G Prime + + align:start position:0% +G Prime + + + align:start position:0% +G Prime +and what I would like to say is that if + + align:start position:0% +and what I would like to say is that if + + + align:start position:0% +and what I would like to say is that if +for now so if they have the same vertex + + align:start position:0% +for now so if they have the same vertex + + + align:start position:0% +for now so if they have the same vertex +set + + align:start position:0% + + + + align:start position:0% + +I want to say that they're close if I + + align:start position:0% +I want to say that they're close if I + + + align:start position:0% +I want to say that they're close if I +have that the number of edges between X + + align:start position:0% +have that the number of edges between X + + + align:start position:0% +have that the number of edges between X +Y and G is very close to the number of + + align:start position:0% +Y and G is very close to the number of + + + align:start position:0% +Y and G is very close to the number of +edges between X and Y and G Prime and I + + align:start position:0% +edges between X and Y and G Prime and I + + + align:start position:0% +edges between X and Y and G Prime and I +normalize by the number of vertices + + align:start position:0% +normalize by the number of vertices + + + align:start position:0% +normalize by the number of vertices +squared and it's number of vertices and + + align:start position:0% +squared and it's number of vertices and + + + align:start position:0% +squared and it's number of vertices and +I would like to find out the worst + + align:start position:0% +I would like to find out the worst + + + align:start position:0% +I would like to find out the worst +possible scenario + + align:start position:0% +possible scenario + + + align:start position:0% +possible scenario +so overall x and y subsets of the vertex + + align:start position:0% +so overall x and y subsets of the vertex + + + align:start position:0% +so overall x and y subsets of the vertex +set if this quantity is small + + align:start position:0% +set if this quantity is small + + + align:start position:0% +set if this quantity is small +I hope then now would like to say that + + align:start position:0% +I hope then now would like to say that + + + align:start position:0% +I hope then now would like to say that +gng prime are close to each other so + + align:start position:0% + + + + align:start position:0% + +this is inspired by this discrepancy + + align:start position:0% +this is inspired by this discrepancy + + + align:start position:0% +this is inspired by this discrepancy +notion can you see anything wrong with + + align:start position:0% +notion can you see anything wrong with + + + align:start position:0% +notion can you see anything wrong with +this definition here yep so permutations + + align:start position:0% +this definition here yep so permutations + + + align:start position:0% +this definition here yep so permutations +of vertices so just like in a + + align:start position:0% +of vertices so just like in a + + + align:start position:0% +of vertices so just like in a +checkerboard example we saw earlier you + + align:start position:0% +checkerboard example we saw earlier you + + + align:start position:0% +checkerboard example we saw earlier you +have two graphs and if they're indeed + + align:start position:0% +have two graphs and if they're indeed + + + align:start position:0% +have two graphs and if they're indeed +labelled graphs in the same labeled + + align:start position:0% +labelled graphs in the same labeled + + + align:start position:0% +labelled graphs in the same labeled +vertex set then this is the definition + + align:start position:0% +vertex set then this is the definition + + + align:start position:0% +vertex set then this is the definition +more or less use how to find it more + + align:start position:0% +more or less use how to find it more + + + align:start position:0% +more or less use how to find it more +precisely in a second but if their own + + align:start position:0% +precisely in a second but if their own + + + align:start position:0% +precisely in a second but if their own +labeled vertices we need to possibly + + align:start position:0% +labeled vertices we need to possibly + + + align:start position:0% +labeled vertices we need to possibly +optimize permute over permutations over + + align:start position:0% +optimize permute over permutations over + + + align:start position:0% +optimize permute over permutations over +rearrangements of vertices + + align:start position:0% + + + + align:start position:0% + +which actually turns out to be quite + + align:start position:0% +which actually turns out to be quite + + + align:start position:0% +which actually turns out to be quite +subtle so I'm going to give precise + + align:start position:0% +subtle so I'm going to give precise + + + align:start position:0% +subtle so I'm going to give precise +definitions in a second but this one + + align:start position:0% +definitions in a second but this one + + + align:start position:0% +definitions in a second but this one +here yeah so think about permuting + + align:start position:0% +here yeah so think about permuting + + + align:start position:0% +here yeah so think about permuting +vertices but it's actually been more + + align:start position:0% +vertices but it's actually been more + + + align:start position:0% +vertices but it's actually been more +subtle than that all right so here are + + align:start position:0% +subtle than that all right so here are + + + align:start position:0% +subtle than that all right so here are +some actual definitions I'm going to + + align:start position:0% +some actual definitions I'm going to + + + align:start position:0% +some actual definitions I'm going to +define this quantity called a cut norm + + align:start position:0% + + + + align:start position:0% + +yeah so this chapter is all going to be + + align:start position:0% +yeah so this chapter is all going to be + + + align:start position:0% +yeah so this chapter is all going to be +somewhat functional analytic in nature + + align:start position:0% +somewhat functional analytic in nature + + + align:start position:0% +somewhat functional analytic in nature +okay used to the analytic language so + + align:start position:0% +okay used to the analytic language so + + + align:start position:0% +okay used to the analytic language so +the cut norm of W is defined to be the + + align:start position:0% +the cut norm of W is defined to be the + + + align:start position:0% +the cut norm of W is defined to be the +following quantity the node by this norm + + align:start position:0% +following quantity the node by this norm + + + align:start position:0% +following quantity the node by this norm +with a box in the subscript which is + + align:start position:0% +with a box in the subscript which is + + + align:start position:0% +with a box in the subscript which is +defined to be if I look at this W and I + + align:start position:0% +defined to be if I look at this W and I + + + align:start position:0% +defined to be if I look at this W and I +integrated over a box and I would like + + align:start position:0% +integrated over a box and I would like + + + align:start position:0% +integrated over a box and I would like +to maximize this quantity here over + + align:start position:0% +to maximize this quantity here over + + + align:start position:0% +to maximize this quantity here over +choices of boxes SMT there are subsets + + align:start position:0% +choices of boxes SMT there are subsets + + + align:start position:0% +choices of boxes SMT there are subsets +of their interval measurable subsets so + + align:start position:0% +of their interval measurable subsets so + + + align:start position:0% +of their interval measurable subsets so +choose your so over all possible choices + + align:start position:0% +choose your so over all possible choices + + + align:start position:0% +choose your so over all possible choices +of measurable subsets s and T if I + + align:start position:0% +of measurable subsets s and T if I + + + align:start position:0% +of measurable subsets s and T if I +integrate W over s cross T what is the + + align:start position:0% +integrate W over s cross T what is the + + + align:start position:0% +integrate W over s cross T what is the +furthest I can get from zero so this is + + align:start position:0% +furthest I can get from zero so this is + + + align:start position:0% +furthest I can get from zero so this is +a definition of cut norm and you can + + align:start position:0% +a definition of cut norm and you can + + + align:start position:0% +a definition of cut norm and you can +already see that it has some relations + + align:start position:0% +already see that it has some relations + + + align:start position:0% +already see that it has some relations +to what were discuss up there but while + + align:start position:0% +to what were discuss up there but while + + + align:start position:0% +to what were discuss up there but while +we're talking about norms let me just + + align:start position:0% +we're talking about norms let me just + + + align:start position:0% +we're talking about norms let me just +mention a few other norms that might + + align:start position:0% +mention a few other norms that might + + + align:start position:0% +mention a few other norms that might +come up later on when we discuss limits + + align:start position:0% +come up later on when we discuss limits + + + align:start position:0% +come up later on when we discuss limits +so there will be a lot of norms + + align:start position:0% +so there will be a lot of norms + + + align:start position:0% +so there will be a lot of norms +throughout so in particular the LP norm + + align:start position:0% +throughout so in particular the LP norm + + + align:start position:0% +throughout so in particular the LP norm +is going to play a frequent role the LP + + align:start position:0% +is going to play a frequent role the LP + + + align:start position:0% +is going to play a frequent role the LP +norm is defined by looking at the pleat + + align:start position:0% +norm is defined by looking at the pleat + + + align:start position:0% +norm is defined by looking at the pleat +norm of the absolute value integrated + + align:start position:0% +norm of the absolute value integrated + + + align:start position:0% +norm of the absolute value integrated +and then raised to 1 over P and + + align:start position:0% + + + + align:start position:0% + +okay so the infinity-norm the our + + align:start position:0% +okay so the infinity-norm the our + + + align:start position:0% +okay so the infinity-norm the our +infinity norm so this is almost but not + + align:start position:0% +infinity norm so this is almost but not + + + align:start position:0% +infinity norm so this is almost but not +quite the same as the soup so almost the + + align:start position:0% +quite the same as the soup so almost the + + + align:start position:0% +quite the same as the soup so almost the +same as the supremum but not quite + + align:start position:0% +same as the supremum but not quite + + + align:start position:0% +same as the supremum but not quite +because i need to ignore subsets of + + align:start position:0% +because i need to ignore subsets of + + + align:start position:0% +because i need to ignore subsets of +measure zero okay so I can write down a + + align:start position:0% +measure zero okay so I can write down a + + + align:start position:0% +measure zero okay so I can write down a +formal definition in a second but I need + + align:start position:0% +formal definition in a second but I need + + + align:start position:0% +formal definition in a second but I need +to if I change W on the subset of + + align:start position:0% +to if I change W on the subset of + + + align:start position:0% +to if I change W on the subset of +measure zero I shouldn't change any of + + align:start position:0% +measure zero I shouldn't change any of + + + align:start position:0% +measure zero I shouldn't change any of +these norms and so the one way to define + + align:start position:0% +these norms and so the one way to define + + + align:start position:0% +these norms and so the one way to define +this essential supremum it's called an + + align:start position:0% +this essential supremum it's called an + + + align:start position:0% +this essential supremum it's called an +essential soup is that it is the largest + + align:start position:0% +essential soup is that it is the largest + + + align:start position:0% +essential soup is that it is the largest +so it is the smallest lambda such that + + align:start position:0% +so it is the smallest lambda such that + + + align:start position:0% +so it is the smallest lambda such that +smallest number M such that the measure + + align:start position:0% +smallest number M such that the measure + + + align:start position:0% +smallest number M such that the measure +of the set taking value bigger than M + + align:start position:0% + + + + align:start position:0% + +the set has measure zero so it's the + + align:start position:0% +the set has measure zero so it's the + + + align:start position:0% +the set has measure zero so it's the +threshold above which you measure zero + + align:start position:0% +threshold above which you measure zero + + + align:start position:0% +threshold above which you measure zero +and the l2 norm will play a particularly + + align:start position:0% +and the l2 norm will play a particularly + + + align:start position:0% +and the l2 norm will play a particularly +special role and for the l2 norm you're + + align:start position:0% +special role and for the l2 norm you're + + + align:start position:0% +special role and for the l2 norm you're +really in a hilbert space in which case + + align:start position:0% +really in a hilbert space in which case + + + align:start position:0% +really in a hilbert space in which case +we are going to have inner products and + + align:start position:0% +we are going to have inner products and + + + align:start position:0% +we are going to have inner products and +we denote inner products using the + + align:start position:0% +we denote inner products using the + + + align:start position:0% +we denote inner products using the +square using these brackets so + + align:start position:0% +square using these brackets so + + + align:start position:0% +square using these brackets so +everything's real I don't have to worry + + align:start position:0% +everything's real I don't have to worry + + + align:start position:0% +everything's real I don't have to worry +about complex conjugates + + align:start position:0% + + + + align:start position:0% + +alright so comparing with a discussion + + align:start position:0% +alright so comparing with a discussion + + + align:start position:0% +alright so comparing with a discussion +up there we see that a sequence of so + + align:start position:0% +up there we see that a sequence of so + + + align:start position:0% +up there we see that a sequence of so +sequence GN quasi random graphs has + + align:start position:0% +sequence GN quasi random graphs has + + + align:start position:0% +sequence GN quasi random graphs has +property that the Associated Guang's + + align:start position:0% +property that the Associated Guang's + + + align:start position:0% +property that the Associated Guang's +converge to P in the cut more ok for + + align:start position:0% +converge to P in the cut more ok for + + + align:start position:0% +converge to P in the cut more ok for +quasi random graphs there's no issue of + + align:start position:0% +quasi random graphs there's no issue of + + + align:start position:0% +quasi random graphs there's no issue of +having to do with permutations because + + align:start position:0% +having to do with permutations because + + + align:start position:0% +having to do with permutations because +the target is invariant upon + + align:start position:0% +the target is invariant upon + + + align:start position:0% +the target is invariant upon +permutations but if I give you two + + align:start position:0% +permutations but if I give you two + + + align:start position:0% +permutations but if I give you two +different graphs then I need to think + + align:start position:0% +different graphs then I need to think + + + align:start position:0% +different graphs then I need to think +about their permutations and to study + + align:start position:0% +about their permutations and to study + + + align:start position:0% +about their permutations and to study +permutations of vertices the right way + + align:start position:0% +permutations of vertices the right way + + + align:start position:0% +permutations of vertices the right way +to do this is to consider measure + + align:start position:0% +to do this is to consider measure + + + align:start position:0% +to do this is to consider measure +preserving transformations so we say + + align:start position:0% +preserving transformations so we say + + + align:start position:0% +preserving transformations so we say +that fee from the interval to the + + align:start position:0% +that fee from the interval to the + + + align:start position:0% +that fee from the interval to the +interval yes is measure preserving first + + align:start position:0% +interval yes is measure preserving first + + + align:start position:0% +interval yes is measure preserving first +of all it has to be a measurable map and + + align:start position:0% +of all it has to be a measurable map and + + + align:start position:0% +of all it has to be a measurable map and +everything I'm going to talk about are + + align:start position:0% +everything I'm going to talk about are + + + align:start position:0% +everything I'm going to talk about are +measurable so on sometimes I will even + + align:start position:0% +measurable so on sometimes I will even + + + align:start position:0% +measurable so on sometimes I will even +admit mentioning it so it is measure + + align:start position:0% +admit mentioning it so it is measure + + + align:start position:0% +admit mentioning it so it is measure +preserving if for all measurable subsets + + align:start position:0% +preserving if for all measurable subsets + + + align:start position:0% +preserving if for all measurable subsets +a of this interval one has that the + + align:start position:0% +a of this interval one has that the + + + align:start position:0% +a of this interval one has that the +pullback of a + + align:start position:0% + + + + align:start position:0% + +has the same measure as a itself let me + + align:start position:0% +has the same measure as a itself let me + + + align:start position:0% +has the same measure as a itself let me +give you an example okay so you have to + + align:start position:0% +give you an example okay so you have to + + + align:start position:0% +give you an example okay so you have to +be also slightly careful with this + + align:start position:0% +be also slightly careful with this + + + align:start position:0% +be also slightly careful with this +definition if you think about the push + + align:start position:0% +definition if you think about the push + + + align:start position:0% +definition if you think about the push +forward that's false it has to be the + + align:start position:0% +forward that's false it has to be the + + + align:start position:0% +forward that's false it has to be the +pullback so for example in so the map + + align:start position:0% + + + + align:start position:0% + +which sends okay so an easy example the + + align:start position:0% +which sends okay so an easy example the + + + align:start position:0% +which sends okay so an easy example the +map which sends X to X plus 1/2 so the + + align:start position:0% +map which sends X to X plus 1/2 so the + + + align:start position:0% +map which sends X to X plus 1/2 so the +thing about the circle as your as your + + align:start position:0% +thing about the circle as your as your + + + align:start position:0% +thing about the circle as your as your +space and here I'm just rotating the + + align:start position:0% +space and here I'm just rotating the + + + align:start position:0% +space and here I'm just rotating the +circle by 1/2 rotation so it's obviously + + align:start position:0% +circle by 1/2 rotation so it's obviously + + + align:start position:0% +circle by 1/2 rotation so it's obviously +a measure preserving I'm not changing + + align:start position:0% +a measure preserving I'm not changing + + + align:start position:0% +a measure preserving I'm not changing +any measures certainly more interesting + + align:start position:0% +any measures certainly more interesting + + + align:start position:0% +any measures certainly more interesting +example quite a bit more interesting + + align:start position:0% +example quite a bit more interesting + + + align:start position:0% +example quite a bit more interesting +example is setting X 2 to X this is also + + align:start position:0% +example is setting X 2 to X this is also + + + align:start position:0% +example is setting X 2 to X this is also +measure preserving and you might be + + align:start position:0% +measure preserving and you might be + + + align:start position:0% +measure preserving and you might be +puzzled for a second why it's measure + + align:start position:0% +puzzled for a second why it's measure + + + align:start position:0% +puzzled for a second why it's measure +preserving because it sounds like it's + + align:start position:0% +preserving because it sounds like it's + + + align:start position:0% +preserving because it sounds like it's +dilating everything by a factor of 2 but + + align:start position:0% +dilating everything by a factor of 2 but + + + align:start position:0% +dilating everything by a factor of 2 but +if you look at the definition so here's + + align:start position:0% +if you look at the definition so here's + + + align:start position:0% +if you look at the definition so here's +again not mod 1 if you look at the + + align:start position:0% +again not mod 1 if you look at the + + + align:start position:0% +again not mod 1 if you look at the +definition if you look at let's say a + + align:start position:0% + + + + align:start position:0% + +subset 8 which is like so what should I + + align:start position:0% + + + + align:start position:0% + +so if that if that is my 8 okay so + + align:start position:0% +so if that if that is my 8 okay so + + + align:start position:0% +so if that if that is my 8 okay so +what's the inverse of a so it's + + align:start position:0% + + + + align:start position:0% + +so the measure is preserved upon this + + align:start position:0% +so the measure is preserved upon this + + + align:start position:0% +so the measure is preserved upon this +pullback okay so if you push forward + + align:start position:0% +pullback okay so if you push forward + + + align:start position:0% +pullback okay so if you push forward +then you might dilate by a factor of two + + align:start position:0% +then you might dilate by a factor of two + + + align:start position:0% +then you might dilate by a factor of two +but when you pull back the measure gets + + align:start position:0% +but when you pull back the measure gets + + + align:start position:0% +but when you pull back the measure gets +preserved so this measure preserving + + align:start position:0% +preserved so this measure preserving + + + align:start position:0% +preserved so this measure preserving +transformations are going to play the + + align:start position:0% +transformations are going to play the + + + align:start position:0% +transformations are going to play the +role of permutations of vertices so it + + align:start position:0% +role of permutations of vertices so it + + + align:start position:0% +role of permutations of vertices so it +turns out that these things are actually + + align:start position:0% +turns out that these things are actually + + + align:start position:0% +turns out that these things are actually +really quite subtle technically and I'm + + align:start position:0% +really quite subtle technically and I'm + + + align:start position:0% +really quite subtle technically and I'm +going to as much as I can ignore some of + + align:start position:0% +going to as much as I can ignore some of + + + align:start position:0% +going to as much as I can ignore some of +the major theoretic technicalities but + + align:start position:0% +the major theoretic technicalities but + + + align:start position:0% +the major theoretic technicalities but +but they are quite subtle so for example + + align:start position:0% +but they are quite subtle so for example + + + align:start position:0% +but they are quite subtle so for example +okay so now let me give you a definition + + align:start position:0% +okay so now let me give you a definition + + + align:start position:0% +okay so now let me give you a definition +for the distance between two griffons I + + align:start position:0% +for the distance between two griffons I + + + align:start position:0% +for the distance between two griffons I +write starting with a major symmetric + + align:start position:0% +write starting with a major symmetric + + + align:start position:0% +write starting with a major symmetric +measurable function W I so I write W + + align:start position:0% +measurable function W I so I write W + + + align:start position:0% +measurable function W I so I write W +superscript C to denote the function + + align:start position:0% +superscript C to denote the function + + + align:start position:0% +superscript C to denote the function +obtained by as follows so I think of + + align:start position:0% +obtained by as follows so I think of + + + align:start position:0% +obtained by as follows so I think of +this as relabeling the vertices of a + + align:start position:0% +this as relabeling the vertices of a + + + align:start position:0% +this as relabeling the vertices of a +graph and now I define this distance so + + align:start position:0% +graph and now I define this distance so + + + align:start position:0% +graph and now I define this distance so +this is going to be called a cut + + align:start position:0% +this is going to be called a cut + + + align:start position:0% +this is going to be called a cut +distance between two symmetric + + align:start position:0% +distance between two symmetric + + + align:start position:0% +distance between two symmetric +measurable functions U and W to be the + + align:start position:0% +measurable functions U and W to be the + + + align:start position:0% +measurable functions U and W to be the +infimum over all major preserving by + + align:start position:0% +infimum over all major preserving by + + + align:start position:0% +infimum over all major preserving by +directions + + align:start position:0% + + + + align:start position:0% + +okay so this is the definition for the + + align:start position:0% +okay so this is the definition for the + + + align:start position:0% +okay so this is the definition for the +distance between two graphics take the + + align:start position:0% +distance between two graphics take the + + + align:start position:0% +distance between two graphics take the +optimal in my question tizzy and looking + + align:start position:0% +optimal in my question tizzy and looking + + + align:start position:0% +optimal in my question tizzy and looking +at if so I haven't told you yet whether + + align:start position:0% +at if so I haven't told you yet whether + + + align:start position:0% +at if so I haven't told you yet whether +you can take a single one and turns out + + align:start position:0% +you can take a single one and turns out + + + align:start position:0% +you can take a single one and turns out +that's a subtle issue and generally it + + align:start position:0% +that's a subtle issue and generally it + + + align:start position:0% +that's a subtle issue and generally it +doesn't exist so but I look over all + + align:start position:0% +doesn't exist so but I look over all + + + align:start position:0% +doesn't exist so but I look over all +major preserving by directions feet and + + align:start position:0% +major preserving by directions feet and + + + align:start position:0% +major preserving by directions feet and +I look at the distance between W and W + + align:start position:0% +I look at the distance between W and W + + + align:start position:0% +I look at the distance between W and W +optimized over the best possible measure + + align:start position:0% +optimized over the best possible measure + + + align:start position:0% +optimized over the best possible measure +preserving bisection so this is really a + + align:start position:0% +preserving bisection so this is really a + + + align:start position:0% +preserving bisection so this is really a +nymph it's not always a pain and + + align:start position:0% +nymph it's not always a pain and + + + align:start position:0% +nymph it's not always a pain and +actually this example here is a great + + align:start position:0% +actually this example here is a great + + + align:start position:0% +actually this example here is a great +example for you can create an example + + align:start position:0% +example for you can create an example + + + align:start position:0% +example for you can create an example +for why infants not always attained from + + align:start position:0% +for why infants not always attained from + + + align:start position:0% +for why infants not always attained from +the discussion over here for example if + + align:start position:0% +the discussion over here for example if + + + align:start position:0% +the discussion over here for example if +if you is the function x times y this is + + align:start position:0% +if you is the function x times y this is + + + align:start position:0% +if you is the function x times y this is +a graph on X Y and W is you see where Z + + align:start position:0% +a graph on X Y and W is you see where Z + + + align:start position:0% +a graph on X Y and W is you see where Z +is the map that sends X 2 to X then you + + align:start position:0% +is the map that sends X 2 to X then you + + + align:start position:0% +is the map that sends X 2 to X then you +know in your mind you should think of + + align:start position:0% +know in your mind you should think of + + + align:start position:0% +know in your mind you should think of +these two as really the same graphics + + align:start position:0% +these two as really the same graphics + + + align:start position:0% +these two as really the same graphics +you're applying the measure preserving + + align:start position:0% +you're applying the measure preserving + + + align:start position:0% +you're applying the measure preserving +transformation it's like doing a + + align:start position:0% +transformation it's like doing a + + + align:start position:0% +transformation it's like doing a +permutation + + align:start position:0% +permutation + + + align:start position:0% +permutation +but because V is not by ejected you + + align:start position:0% +but because V is not by ejected you + + + align:start position:0% +but because V is not by ejected you +cannot putting fie here to get these two + + align:start position:0% +cannot putting fie here to get these two + + + align:start position:0% +cannot putting fie here to get these two +things to be the same okay so it's so + + align:start position:0% +things to be the same okay so it's so + + + align:start position:0% +things to be the same okay so it's so +there's some subtlety so this is really + + align:start position:0% +there's some subtlety so this is really + + + align:start position:0% +there's some subtlety so this is really +an example to just to highlight there's + + align:start position:0% +an example to just to highlight there's + + + align:start position:0% +an example to just to highlight there's +some subtleties here which I'm gonna try + + align:start position:0% +some subtleties here which I'm gonna try + + + align:start position:0% +some subtleties here which I'm gonna try +to ignore as much as possible + + align:start position:0% +to ignore as much as possible + + + align:start position:0% +to ignore as much as possible +and but I always give you correct + + align:start position:0% +and but I always give you correct + + + align:start position:0% +and but I always give you correct +definitions any questions + + align:start position:0% + + + + align:start position:0% + +yep + + align:start position:0% + + + + align:start position:0% + +yeah so question do we expect the + + align:start position:0% +yeah so question do we expect the + + + align:start position:0% +yeah so question do we expect the +contestants between these two to be zero + + align:start position:0% +contestants between these two to be zero + + + align:start position:0% +contestants between these two to be zero +and the answer is yes so we do expect + + align:start position:0% +and the answer is yes so we do expect + + + align:start position:0% +and the answer is yes so we do expect +them to be zero and that they are zero + + align:start position:0% +them to be zero and that they are zero + + + align:start position:0% +them to be zero and that they are zero +that's they are equal to zero I mean let + + align:start position:0% +that's they are equal to zero I mean let + + + align:start position:0% +that's they are equal to zero I mean let +me just tell you one something that is + + align:start position:0% +me just tell you one something that is + + + align:start position:0% +me just tell you one something that is +known and this is one of those + + align:start position:0% +known and this is one of those + + + align:start position:0% +known and this is one of those +statements that has a lot of major + + align:start position:0% +statements that has a lot of major + + + align:start position:0% +statements that has a lot of major +theoretic technicalities for all + + align:start position:0% +theoretic technicalities for all + + + align:start position:0% +theoretic technicalities for all +griffons + + align:start position:0% +griffons + + + align:start position:0% +griffons +U and W it turns out that there exist + + align:start position:0% +U and W it turns out that there exist + + + align:start position:0% +U and W it turns out that there exist +major preserving maps okay so not + + align:start position:0% +major preserving maps okay so not + + + align:start position:0% +major preserving maps okay so not +necessarily by sections but major + + align:start position:0% +necessarily by sections but major + + + align:start position:0% +necessarily by sections but major +preserving maps from zero one interval + + align:start position:0% +preserving maps from zero one interval + + + align:start position:0% +preserving maps from zero one interval +to itself such that the distance between + + align:start position:0% +to itself such that the distance between + + + align:start position:0% +to itself such that the distance between +u and W the cut distance is obtained by + + align:start position:0% +u and W the cut distance is obtained by + + + align:start position:0% +u and W the cut distance is obtained by +the cut norm difference between of the + + align:start position:0% +the cut norm difference between of the + + + align:start position:0% +the cut norm difference between of the +difference between UV and W sigh + + align:start position:0% + + + + align:start position:0% + +don't worry about it okay so so far + + align:start position:0% +don't worry about it okay so so far + + + align:start position:0% +don't worry about it okay so so far +we've defined this notion of a cut + + align:start position:0% +we've defined this notion of a cut + + + align:start position:0% +we've defined this notion of a cut +distance between two graph ons but now + + align:start position:0% +distance between two graph ons but now + + + align:start position:0% +distance between two graph ons but now +I'll give you two graphs so what you do + + align:start position:0% +I'll give you two graphs so what you do + + + align:start position:0% +I'll give you two graphs so what you do +do for two graphs well I can okay great + + align:start position:0% +do for two graphs well I can okay great + + + align:start position:0% +do for two graphs well I can okay great +so take the graphing associated with + + align:start position:0% +so take the graphing associated with + + + align:start position:0% +so take the graphing associated with +these graphs and consider their cut + + align:start position:0% +these graphs and consider their cut + + + align:start position:0% +these graphs and consider their cut +distance so for graph G and G prime and + + align:start position:0% +distance so for graph G and G prime and + + + align:start position:0% +distance so for graph G and G prime and +potentially even different number of + + align:start position:0% +potentially even different number of + + + align:start position:0% +potentially even different number of +vertices I can define the distance the + + align:start position:0% +vertices I can define the distance the + + + align:start position:0% +vertices I can define the distance the +cut distance between these two graphs to + + align:start position:0% +cut distance between these two graphs to + + + align:start position:0% +cut distance between these two graphs to +be the distance between the Associated + + align:start position:0% +be the distance between the Associated + + + align:start position:0% +be the distance between the Associated +graph ohms and similarly if I have a + + align:start position:0% +graph ohms and similarly if I have a + + + align:start position:0% +graph ohms and similarly if I have a +graph and a graph on I can also compare + + align:start position:0% +graph and a graph on I can also compare + + + align:start position:0% +graph and a graph on I can also compare +their distance + + align:start position:0% + + + + align:start position:0% + +so what does this actually mean alright + + align:start position:0% +so what does this actually mean alright + + + align:start position:0% +so what does this actually mean alright +so if I give you two graphs even with + + align:start position:0% +so if I give you two graphs even with + + + align:start position:0% +so if I give you two graphs even with +the same number of vertices it's not + + align:start position:0% +the same number of vertices it's not + + + align:start position:0% +the same number of vertices it's not +quite the same thing as a permutation of + + align:start position:0% +quite the same thing as a permutation of + + + align:start position:0% +quite the same thing as a permutation of +vertices it's a bit more subtle why is + + align:start position:0% +vertices it's a bit more subtle why is + + + align:start position:0% +vertices it's a bit more subtle why is +it more subtle than just permuting the + + align:start position:0% +it more subtle than just permuting the + + + align:start position:0% +it more subtle than just permuting the +vertices so here we're using measure + + align:start position:0% +vertices so here we're using measure + + + align:start position:0% +vertices so here we're using measure +preserving transformations which doesn't + + align:start position:0% +preserving transformations which doesn't + + + align:start position:0% +preserving transformations which doesn't +see your atomic vertices so we might + + align:start position:0% +see your atomic vertices so we might + + + align:start position:0% +see your atomic vertices so we might +split up your vertices so you might take + + align:start position:0% +split up your vertices so you might take + + + align:start position:0% +split up your vertices so you might take +a vertex and then you know chop it in + + align:start position:0% +a vertex and then you know chop it in + + + align:start position:0% +a vertex and then you know chop it in +half and send one half somewhere and + + align:start position:0% +half and send one half somewhere and + + + align:start position:0% +half and send one half somewhere and +another half somewhere else yes these + + align:start position:0% +another half somewhere else yes these + + + align:start position:0% +another half somewhere else yes these +guys they don't care about your vertices + + align:start position:0% +guys they don't care about your vertices + + + align:start position:0% +guys they don't care about your vertices +anymore so it's not quite the same as + + align:start position:0% +anymore so it's not quite the same as + + + align:start position:0% +anymore so it's not quite the same as +commuting vertices but it's some kind of + + align:start position:0% +commuting vertices but it's some kind of + + + align:start position:0% +commuting vertices but it's some kind of +fun so you allow some kind of splitting + + align:start position:0% +fun so you allow some kind of splitting + + + align:start position:0% +fun so you allow some kind of splitting +and rearrangement and overlays so you + + align:start position:0% +and rearrangement and overlays so you + + + align:start position:0% +and rearrangement and overlays so you +can write out this distance in this + + align:start position:0% +can write out this distance in this + + + align:start position:0% +can write out this distance in this +format find out the best way to split an + + align:start position:0% +format find out the best way to split an + + + align:start position:0% +format find out the best way to split an +overlay and to rearrange that way but + + align:start position:0% +overlay and to rearrange that way but + + + align:start position:0% +overlay and to rearrange that way but +it's much cleaner to just define it in + + align:start position:0% +it's much cleaner to just define it in + + + align:start position:0% +it's much cleaner to just define it in +terms of graphics yes okay questions is + + align:start position:0% +terms of graphics yes okay questions is + + + align:start position:0% +terms of graphics yes okay questions is +there why we take my junctions up there + + align:start position:0% +there why we take my junctions up there + + + align:start position:0% +there why we take my junctions up there +and no so up there if I wrote instead + + align:start position:0% +and no so up there if I wrote instead + + + align:start position:0% +and no so up there if I wrote instead +major preserving Maps it's still a + + align:start position:0% +major preserving Maps it's still a + + + align:start position:0% +major preserving Maps it's still a +correct definition and it's the same + + align:start position:0% +correct definition and it's the same + + + align:start position:0% +correct definition and it's the same +definition and the fact that these two + + align:start position:0% +definition and the fact that these two + + + align:start position:0% +definition and the fact that these two +are equivalent goes through some measure + + align:start position:0% +are equivalent goes through some measure + + + align:start position:0% +are equivalent goes through some measure +theory which I want I will not do not + + align:start position:0% +theory which I want I will not do not + + + align:start position:0% +theory which I want I will not do not +want it indulgent + + align:start position:0% + + + + align:start position:0% + +great but the moral of the story is you + + align:start position:0% +great but the moral of the story is you + + + align:start position:0% +great but the moral of the story is you +take two graphics + + align:start position:0% +take two graphics + + + align:start position:0% +take two graphics +I'm rearrange the vertices in some way + + align:start position:0% +I'm rearrange the vertices in some way + + + align:start position:0% +I'm rearrange the vertices in some way +in the best way overlaid them on top of + + align:start position:0% +in the best way overlaid them on top of + + + align:start position:0% +in the best way overlaid them on top of +each other and take the difference and + + align:start position:0% +each other and take the difference and + + + align:start position:0% +each other and take the difference and +look at a cut norm so that's the + + align:start position:0% +look at a cut norm so that's the + + + align:start position:0% +look at a cut norm so that's the +distance all right so I want to finish + + align:start position:0% +distance all right so I want to finish + + + align:start position:0% +distance all right so I want to finish +by stating the main theorems that formed + + align:start position:0% +by stating the main theorems that formed + + + align:start position:0% +by stating the main theorems that formed +graph limit theory and these are + + align:start position:0% +graph limit theory and these are + + + align:start position:0% +graph limit theory and these are +addressed the questions I mentioned + + align:start position:0% +addressed the questions I mentioned + + + align:start position:0% +addressed the questions I mentioned +right before the break so do there exist + + align:start position:0% +right before the break so do there exist + + + align:start position:0% +right before the break so do there exist +limits and do these two different + + align:start position:0% +limits and do these two different + + + align:start position:0% +limits and do these two different +notions of one having to do with + + align:start position:0% +notions of one having to do with + + + align:start position:0% +notions of one having to do with +distance and another having to do with + + align:start position:0% +distance and another having to do with + + + align:start position:0% +distance and another having to do with +homomorphism densities how do they + + align:start position:0% +homomorphism densities how do they + + + align:start position:0% +homomorphism densities how do they +relate to each other are they consistent + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so first theorem one has to do with the + + align:start position:0% +so first theorem one has to do with the + + + align:start position:0% +so first theorem one has to do with the +equivalence of convergence namely that + + align:start position:0% +equivalence of convergence namely that + + + align:start position:0% +equivalence of convergence namely that +if you have a sequence of graphs or + + align:start position:0% +if you have a sequence of graphs or + + + align:start position:0% +if you have a sequence of graphs or +graph owns the sequence is convergent in + + align:start position:0% +graph owns the sequence is convergent in + + + align:start position:0% +graph owns the sequence is convergent in +the sense up there if and only if they + + align:start position:0% +the sense up there if and only if they + + + align:start position:0% +the sense up there if and only if they +are convergent in the sense of in this + + align:start position:0% +are convergent in the sense of in this + + + align:start position:0% +are convergent in the sense of in this +metric space so remember what + + align:start position:0% +metric space so remember what + + + align:start position:0% +metric space so remember what +convergence means in the metric space is + + align:start position:0% +convergence means in the metric space is + + + align:start position:0% +convergence means in the metric space is +that of a Cauchy sequence so if and only + + align:start position:0% +that of a Cauchy sequence so if and only + + + align:start position:0% +that of a Cauchy sequence so if and only +if it is a Cauchy sequence with respect + + align:start position:0% +if it is a Cauchy sequence with respect + + + align:start position:0% +if it is a Cauchy sequence with respect +to this cut distance okay so it just + + align:start position:0% +to this cut distance okay so it just + + + align:start position:0% +to this cut distance okay so it just +before many of you it's been a while + + align:start position:0% +before many of you it's been a while + + + align:start position:0% +before many of you it's been a while +since you took 18100 so I never remind + + align:start position:0% +since you took 18100 so I never remind + + + align:start position:0% +since you took 18100 so I never remind +you a Cauchy sequence in this case it + + align:start position:0% +you a Cauchy sequence in this case it + + + align:start position:0% +you a Cauchy sequence in this case it +means that if I look at the distance + + align:start position:0% +means that if I look at the distance + + + align:start position:0% +means that if I look at the distance +between two graphs a if I look far + + align:start position:0% +between two graphs a if I look far + + + align:start position:0% +between two graphs a if I look far +enough out then I can contain the rest + + align:start position:0% +enough out then I can contain the rest + + + align:start position:0% +enough out then I can contain the rest +of the sequence in an arbitrarily small + + align:start position:0% +of the sequence in an arbitrarily small + + + align:start position:0% +of the sequence in an arbitrarily small +ball so super-positive + + align:start position:0% +ball so super-positive + + + align:start position:0% +ball so super-positive +m of this guy here goes to 0 as n goes + + align:start position:0% +m of this guy here goes to 0 as n goes + + + align:start position:0% +m of this guy here goes to 0 as n goes +to infinity because we we don't know yet + + align:start position:0% +to infinity because we we don't know yet + + + align:start position:0% +to infinity because we we don't know yet +the whether the limit exists so I can't + + align:start position:0% +the whether the limit exists so I can't + + + align:start position:0% +the whether the limit exists so I can't +talk about them getting closer and + + align:start position:0% +talk about them getting closer and + + + align:start position:0% +talk about them getting closer and +closer to a limit but they mutually get + + align:start position:0% +closer to a limit but they mutually get + + + align:start position:0% +closer to a limit but they mutually get +closer to each other + + align:start position:0% + + + + align:start position:0% + +okay so theorem one tells us that these + + align:start position:0% +okay so theorem one tells us that these + + + align:start position:0% +okay so theorem one tells us that these +two notions one having to do with + + align:start position:0% +two notions one having to do with + + + align:start position:0% +two notions one having to do with +homomorphism densities yes + + align:start position:0% +homomorphism densities yes + + + align:start position:0% +homomorphism densities yes +consistent and in fact equivalent to + + align:start position:0% +consistent and in fact equivalent to + + + align:start position:0% +consistent and in fact equivalent to +appropriate notion in the metric space + + align:start position:0% + + + + align:start position:0% + +so now we okay so let's use the symbol + + align:start position:0% +so now we okay so let's use the symbol + + + align:start position:0% +so now we okay so let's use the symbol +so we say that G sub n converges to W + + align:start position:0% +so we say that G sub n converges to W + + + align:start position:0% +so we say that G sub n converges to W +okay so or in the case of sequence of + + align:start position:0% +okay so or in the case of sequence of + + + align:start position:0% +okay so or in the case of sequence of +graph ons + + align:start position:0% +graph ons + + + align:start position:0% +graph ons +okay so we can do that as well so if so + + align:start position:0% +okay so we can do that as well so if so + + + align:start position:0% +okay so we can do that as well so if so +here we say that G sub n converges W if + + align:start position:0% +here we say that G sub n converges W if + + + align:start position:0% +here we say that G sub n converges W if +whenever you look at the f density in G + + align:start position:0% +whenever you look at the f density in G + + + align:start position:0% +whenever you look at the f density in G +sub n this sequence converges to the + + align:start position:0% +sub n this sequence converges to the + + + align:start position:0% +sub n this sequence converges to the +corresponding f density in W for every F + + align:start position:0% +corresponding f density in W for every F + + + align:start position:0% +corresponding f density in W for every F +and similarly if you have a graph on + + align:start position:0% +and similarly if you have a graph on + + + align:start position:0% +and similarly if you have a graph on +instead of a graph so that definition + + align:start position:0% +instead of a graph so that definition + + + align:start position:0% +instead of a graph so that definition +will just know whether sequence is + + align:start position:0% +will just know whether sequence is + + + align:start position:0% +will just know whether sequence is +convergent here's it converges to this + + align:start position:0% +convergent here's it converges to this + + + align:start position:0% +convergent here's it converges to this +graph on W and the question is if you + + align:start position:0% +graph on W and the question is if you + + + align:start position:0% +graph on W and the question is if you +give me a convergent sequence is there a + + align:start position:0% +give me a convergent sequence is there a + + + align:start position:0% +give me a convergent sequence is there a +limit does it converge to some limit and + + align:start position:0% +limit does it converge to some limit and + + + align:start position:0% +limit does it converge to some limit and +the answer is yes and that's the second + + align:start position:0% +the answer is yes and that's the second + + + align:start position:0% +the answer is yes and that's the second +theorem which tells us the existence of + + align:start position:0% +theorem which tells us the existence of + + + align:start position:0% +theorem which tells us the existence of +the limit object the statement is that + + align:start position:0% +the limit object the statement is that + + + align:start position:0% +the limit object the statement is that +every convergent sequence of graph + + align:start position:0% + + + + align:start position:0% + +or griffons has a limit graph alright so + + align:start position:0% +or griffons has a limit graph alright so + + + align:start position:0% +or griffons has a limit graph alright so +now I want you to imagine this space of + + align:start position:0% +now I want you to imagine this space of + + + align:start position:0% +now I want you to imagine this space of +griffons + + align:start position:0% +griffons + + + align:start position:0% +griffons +so have the space containing or the + + align:start position:0% +so have the space containing or the + + + align:start position:0% +so have the space containing or the +Griffons and let me denote this space by + + align:start position:0% +Griffons and let me denote this space by + + + align:start position:0% +Griffons and let me denote this space by +this curly w naught so this not is don't + + align:start position:0% +this curly w naught so this not is don't + + + align:start position:0% +this curly w naught so this not is don't +worry about it is more just convention + + align:start position:0% +worry about it is more just convention + + + align:start position:0% +worry about it is more just convention +but let me also put a tilde on top for + + align:start position:0% +but let me also put a tilde on top for + + + align:start position:0% +but let me also put a tilde on top for +the following reason let this be the + + align:start position:0% +the following reason let this be the + + + align:start position:0% +the following reason let this be the +space of graphing x' where we identify + + align:start position:0% +space of graphing x' where we identify + + + align:start position:0% +space of graphing x' where we identify +graph owns with distance 0 so then this + + align:start position:0% +graph owns with distance 0 so then this + + + align:start position:0% +graph owns with distance 0 so then this +space combined with this metric is a + + align:start position:0% +space combined with this metric is a + + + align:start position:0% +space combined with this metric is a +metric space it is the space of graphics + + align:start position:0% + + + + align:start position:0% + +so the third theorem is that it's the + + align:start position:0% +so the third theorem is that it's the + + + align:start position:0% +so the third theorem is that it's the +compactness of the space of griffons + + align:start position:0% +compactness of the space of griffons + + + align:start position:0% +compactness of the space of griffons +namely that this space is compact + + align:start position:0% + + + + align:start position:0% + +okay because we're in the metric space + + align:start position:0% +okay because we're in the metric space + + + align:start position:0% +okay because we're in the metric space +compactness in the usual sense of every + + align:start position:0% +compactness in the usual sense of every + + + align:start position:0% +compactness in the usual sense of every +open cover has a finite sub cover it's + + align:start position:0% +open cover has a finite sub cover it's + + + align:start position:0% +open cover has a finite sub cover it's +equivalent to slightly more intuitive + + align:start position:0% +equivalent to slightly more intuitive + + + align:start position:0% +equivalent to slightly more intuitive +notion of sequential compactness every + + align:start position:0% +notion of sequential compactness every + + + align:start position:0% +notion of sequential compactness every +sequence has a convergent subsequence + + align:start position:0% +sequence has a convergent subsequence + + + align:start position:0% +sequence has a convergent subsequence +and then it's also limit converges to + + align:start position:0% +and then it's also limit converges to + + + align:start position:0% +and then it's also limit converges to +some limit so how do you how should you + + align:start position:0% +some limit so how do you how should you + + + align:start position:0% +some limit so how do you how should you +think of theorem 3 so it's about + + align:start position:0% +think of theorem 3 so it's about + + + align:start position:0% +think of theorem 3 so it's about +compactness and you know some + + align:start position:0% +compactness and you know some + + + align:start position:0% +compactness and you know some +topological notion but intuitively you + + align:start position:0% +topological notion but intuitively you + + + align:start position:0% +topological notion but intuitively you +should think of compactness saying in + + align:start position:0% +should think of compactness saying in + + + align:start position:0% +should think of compactness saying in +the English word the English meaning of + + align:start position:0% +the English word the English meaning of + + + align:start position:0% +the English word the English meaning of +the word compact is no small if you + + align:start position:0% +the word compact is no small if you + + + align:start position:0% +the word compact is no small if you +think of this space as being quite small + + align:start position:0% +think of this space as being quite small + + + align:start position:0% +think of this space as being quite small +which is rather counterintuitive because + + align:start position:0% +which is rather counterintuitive because + + + align:start position:0% +which is rather counterintuitive because +we're looking at the space of griffons + + align:start position:0% +we're looking at the space of griffons + + + align:start position:0% +we're looking at the space of griffons +you know certainly at least as large as + + align:start position:0% +you know certainly at least as large as + + + align:start position:0% +you know certainly at least as large as +the space of graphs but in really all + + align:start position:0% +the space of graphs but in really all + + + align:start position:0% +the space of graphs but in really all +functions from the square to the + + align:start position:0% +functions from the square to the + + + align:start position:0% +functions from the square to the +interval which seems like a pretty large + + align:start position:0% +interval which seems like a pretty large + + + align:start position:0% +interval which seems like a pretty large +space but this theorem here says that in + + align:start position:0% +space but this theorem here says that in + + + align:start position:0% +space but this theorem here says that in +fact that space is quite small and we + + align:start position:0% +fact that space is quite small and we + + + align:start position:0% +fact that space is quite small and we +have we also seen that philosophy before + + align:start position:0% + + + + align:start position:0% + +so in summary this graph regularity + + align:start position:0% +so in summary this graph regularity + + + align:start position:0% +so in summary this graph regularity +lemma the underlying philosophy there is + + align:start position:0% +lemma the underlying philosophy there is + + + align:start position:0% +lemma the underlying philosophy there is +that even though the possibilities the + + align:start position:0% +that even though the possibilities the + + + align:start position:0% +that even though the possibilities the +space of possibilities for graph is + + align:start position:0% +space of possibilities for graph is + + + align:start position:0% +space of possibilities for graph is +quite large + + align:start position:0% +quite large + + + align:start position:0% +quite large +once you apply similarities regularity + + align:start position:0% +once you apply similarities regularity + + + align:start position:0% +once you apply similarities regularity +lemma and once you are ok with some + + align:start position:0% +lemma and once you are ok with some + + + align:start position:0% +lemma and once you are ok with some +epsilon approximations there's only a + + align:start position:0% +epsilon approximations there's only a + + + align:start position:0% +epsilon approximations there's only a +small description this bounded + + align:start position:0% +small description this bounded + + + align:start position:0% +small description this bounded +description of a graph and you can work + + align:start position:0% +description of a graph and you can work + + + align:start position:0% +description of a graph and you can work +with that description and these two + + align:start position:0% +with that description and these two + + + align:start position:0% +with that description and these two +philosophies it's non coincidence that + + align:start position:0% +philosophies it's non coincidence that + + + align:start position:0% +philosophies it's non coincidence that +they are consistent with each other + + align:start position:0% +they are consistent with each other + + + align:start position:0% +they are consistent with each other +because we will use similarities + + align:start position:0% +because we will use similarities + + + align:start position:0% +because we will use similarities +regularity lemma to prove this + + align:start position:0% +regularity lemma to prove this + + + align:start position:0% +regularity lemma to prove this +compactness in fact we will use a + + align:start position:0% +compactness in fact we will use a + + + align:start position:0% +compactness in fact we will use a +slightly weaker version of similarities + + align:start position:0% +slightly weaker version of similarities + + + align:start position:0% +slightly weaker version of similarities +regularity lemma to prove compactness + + align:start position:0% +regularity lemma to prove compactness + + + align:start position:0% +regularity lemma to prove compactness +and then + + align:start position:0% +and then + + + align:start position:0% +and then +see that from the compactness one can + + align:start position:0% +see that from the compactness one can + + + align:start position:0% +see that from the compactness one can +use properties of the compactness to + + align:start position:0% +use properties of the compactness to + + + align:start position:0% +use properties of the compactness to +boost to a stronger version of + + align:start position:0% +boost to a stronger version of + + + align:start position:0% +boost to a stronger version of +regularity but the underlying philosophy + + align:start position:0% +regularity but the underlying philosophy + + + align:start position:0% +regularity but the underlying philosophy +here is that this compactness is in some + + align:start position:0% +here is that this compactness is in some + + + align:start position:0% +here is that this compactness is in some +sense a quantity is a qualitative + + align:start position:0% + + + + align:start position:0% + +reformulation analytic reformulation of + + align:start position:0% + + + + align:start position:0% + +similarities + + align:start position:0% +similarities + + + align:start position:0% +similarities +graph regularity + + align:start position:0% + + + + align:start position:0% + +okay so so this topic this graph limits + + align:start position:0% +okay so so this topic this graph limits + + + align:start position:0% +okay so so this topic this graph limits +which you know well explore for the next + + align:start position:0% +which you know well explore for the next + + + align:start position:0% +which you know well explore for the next +few lectures including giving you a + + align:start position:0% +few lectures including giving you a + + + align:start position:0% +few lectures including giving you a +proof of oh three of these main theorems + + align:start position:0% +proof of oh three of these main theorems + + + align:start position:0% +proof of oh three of these main theorems +nicely encapsulates the past couple of + + align:start position:0% +nicely encapsulates the past couple of + + + align:start position:0% +nicely encapsulates the past couple of +topics we've done so on one hand + + align:start position:0% +topics we've done so on one hand + + + align:start position:0% +topics we've done so on one hand +similarities regularity lemma or some + + align:start position:0% +similarities regularity lemma or some + + + align:start position:0% +similarities regularity lemma or some +version that will be used in proving the + + align:start position:0% +version that will be used in proving the + + + align:start position:0% +version that will be used in proving the +existence of the element and also the + + align:start position:0% +existence of the element and also the + + + align:start position:0% +existence of the element and also the +compactness and also it's + + align:start position:0% +compactness and also it's + + + align:start position:0% +compactness and also it's +philosophically and in in some sense + + align:start position:0% +philosophically and in in some sense + + + align:start position:0% +philosophically and in in some sense +related very much equivalent in some + + align:start position:0% +related very much equivalent in some + + + align:start position:0% +related very much equivalent in some +sense and related to these notions + + align:start position:0% +sense and related to these notions + + + align:start position:0% +sense and related to these notions +there's also related to quasi randomness + + align:start position:0% +there's also related to quasi randomness + + + align:start position:0% +there's also related to quasi randomness +in particular quasi random graphs that + + align:start position:0% +in particular quasi random graphs that + + + align:start position:0% +in particular quasi random graphs that +we did a few lectures ago where in quasi + + align:start position:0% +we did a few lectures ago where in quasi + + + align:start position:0% +we did a few lectures ago where in quasi +random graphs we are really looking at + + align:start position:0% +random graphs we are really looking at + + + align:start position:0% +random graphs we are really looking at +the constant graph on in this language + + align:start position:0% +the constant graph on in this language + + + align:start position:0% +the constant graph on in this language +and now we expand our horizons and + + align:start position:0% +and now we expand our horizons and + + + align:start position:0% +and now we expand our horizons and +instead of just looking at the constant + + align:start position:0% +instead of just looking at the constant + + + align:start position:0% +instead of just looking at the constant +graph on we can now consider arbitrary + + align:start position:0% +graph on we can now consider arbitrary + + + align:start position:0% +graph on we can now consider arbitrary +graph phones so there this model for a + + align:start position:0% +graph phones so there this model for a + + + align:start position:0% +graph phones so there this model for a +very large graph any questions + + align:start position:0% + + + + align:start position:0% + +questions can we prove theorem three + + align:start position:0% +questions can we prove theorem three + + + align:start position:0% +questions can we prove theorem three +analytically and deduce the regularity + + align:start position:0% +analytically and deduce the regularity + + + align:start position:0% +analytically and deduce the regularity +lemma so you'll see once you see the + + align:start position:0% +lemma so you'll see once you see the + + + align:start position:0% +lemma so you'll see once you see the +proof depends on what you mean by + + align:start position:0% +proof depends on what you mean by + + + align:start position:0% +proof depends on what you mean by +roughly the answer is yes but there's a + + align:start position:0% +roughly the answer is yes but there's a + + + align:start position:0% +roughly the answer is yes but there's a +very important caveat is that because + + align:start position:0% +very important caveat is that because + + + align:start position:0% +very important caveat is that because +we're using compact Ness any argument + + align:start position:0% +we're using compact Ness any argument + + + align:start position:0% +we're using compact Ness any argument +involving compactness gives no + + align:start position:0% +involving compactness gives no + + + align:start position:0% +involving compactness gives no +quantitative bounds so you will have a + + align:start position:0% +quantitative bounds so you will have a + + + align:start position:0% +quantitative bounds so you will have a +proof of the similarity regularity lemma + + align:start position:0% +proof of the similarity regularity lemma + + + align:start position:0% +proof of the similarity regularity lemma +that tells you there is a bound for each + + align:start position:0% +that tells you there is a bound for each + + + align:start position:0% +that tells you there is a bound for each +epsilon but it doesn't tell you what the + + align:start position:0% +epsilon but it doesn't tell you what the + + + align:start position:0% +epsilon but it doesn't tell you what the +bound is + + align:start position:0% + + + + align:start position:0% + +okay does Cote theorem 3 imply theorem 1 + + align:start position:0% +okay does Cote theorem 3 imply theorem 1 + + + align:start position:0% +okay does Cote theorem 3 imply theorem 1 +and the answer is no because theorem 1 + + align:start position:0% +and the answer is no because theorem 1 + + + align:start position:0% +and the answer is no because theorem 1 +the notion of convergence is about + + align:start position:0% +the notion of convergence is about + + + align:start position:0% +the notion of convergence is about +homomorphism densities right so the + + align:start position:0% +homomorphism densities right so the + + + align:start position:0% +homomorphism densities right so the +theorem 1 is about these two different + + align:start position:0% +theorem 1 is about these two different + + + align:start position:0% +theorem 1 is about these two different +notions of convergence and that they're + + align:start position:0% +notions of convergence and that they're + + + align:start position:0% +notions of convergence and that they're +equivalent to each other + + align:start position:0% +equivalent to each other + + + align:start position:0% +equivalent to each other +theorem 3 is just about the metric it's + + align:start position:0% +theorem 3 is just about the metric it's + + + align:start position:0% +theorem 3 is just about the metric it's +about the cut metric so theorem 1 is the + + align:start position:0% +about the cut metric so theorem 1 is the + + + align:start position:0% +about the cut metric so theorem 1 is the +point of theorem 1 is that you have + + align:start position:0% +point of theorem 1 is that you have + + + align:start position:0% +point of theorem 1 is that you have +these two you have these two notions of + + align:start position:0% +these two you have these two notions of + + + align:start position:0% +these two you have these two notions of +convergence 1 having to do with sub + + align:start position:0% +convergence 1 having to do with sub + + + align:start position:0% +convergence 1 having to do with sub +graph densities and the other having to + + align:start position:0% +graph densities and the other having to + + + align:start position:0% +graph densities and the other having to +do with a cut distance and in fact + + align:start position:0% +do with a cut distance and in fact + + + align:start position:0% +do with a cut distance and in fact +they're equivalent notions so all great + + align:start position:0% +they're equivalent notions so all great + + + align:start position:0% +they're equivalent notions so all great +questions and the others a graph or + + align:start position:0% +questions and the others a graph or + + + align:start position:0% +questions and the others a graph or +graph on F is always a graph so in t f w + + align:start position:0% +graph on F is always a graph so in t f w + + + align:start position:0% +graph on F is always a graph so in t f w +it i do not define this quantity for + + align:start position:0% +it i do not define this quantity for + + + align:start position:0% +it i do not define this quantity for +graph on f so this quantity here i'm + + align:start position:0% +graph on f so this quantity here i'm + + + align:start position:0% +graph on f so this quantity here i'm +only allow the second argument to be a + + align:start position:0% +only allow the second argument to be a + + + align:start position:0% +only allow the second argument to be a +graph on the first argument is not + + align:start position:0% +graph on the first argument is not + + + align:start position:0% +graph on the first argument is not +allowed to be a graph on it doesn't make + + align:start position:0% +allowed to be a graph on it doesn't make + + + align:start position:0% +allowed to be a graph on it doesn't make +sense ok questions theorem 1 and theorem + + align:start position:0% +sense ok questions theorem 1 and theorem + + + align:start position:0% +sense ok questions theorem 1 and theorem +2 together + + align:start position:0% +2 together + + + align:start position:0% +2 together +implied theorem 3 so first of all + + align:start position:0% +implied theorem 3 so first of all + + + align:start position:0% +implied theorem 3 so first of all +theorem 1 is is really it's not about + + align:start position:0% +theorem 1 is is really it's not about + + + align:start position:0% +theorem 1 is is really it's not about +compactness right so it's really about + + align:start position:0% +compactness right so it's really about + + + align:start position:0% +compactness right so it's really about +the equivalence of two different notions + + align:start position:0% +the equivalence of two different notions + + + align:start position:0% +the equivalence of two different notions +of convergence it's like you have two + + align:start position:0% +of convergence it's like you have two + + + align:start position:0% +of convergence it's like you have two +different metrics I'm showing that these + + align:start position:0% +different metrics I'm showing that these + + + align:start position:0% +different metrics I'm showing that these +two metrics are equivalent to each other + + align:start position:0% +two metrics are equivalent to each other + + + align:start position:0% +two metrics are equivalent to each other +theorem 2 and theorem 3 are quite + + align:start position:0% +theorem 2 and theorem 3 are quite + + + align:start position:0% +theorem 2 and theorem 3 are quite +intimately related so theorem 2 is about + + align:start position:0% +intimately related so theorem 2 is about + + + align:start position:0% +intimately related so theorem 2 is about +I mean they're - okay so they're quite + + align:start position:0% +I mean they're - okay so they're quite + + + align:start position:0% +I mean they're - okay so they're quite +related but they're not quite the same + + align:start position:0% +related but they're not quite the same + + + align:start position:0% +related but they're not quite the same +so let me just give you the real line + + align:start position:0% +so let me just give you the real line + + + align:start position:0% +so let me just give you the real line +analogy going back to what we said in + + align:start position:0% +analogy going back to what we said in + + + align:start position:0% +analogy going back to what we said in +the beginning or so theorem 2 is kind of + + align:start position:0% +the beginning or so theorem 2 is kind of + + + align:start position:0% +the beginning or so theorem 2 is kind of +like saying that the real numbers is + + align:start position:0% +like saying that the real numbers is + + + align:start position:0% +like saying that the real numbers is +complete so every convergent sequence + + align:start position:0% +complete so every convergent sequence + + + align:start position:0% +complete so every convergent sequence +has a limit + + align:start position:0% +has a limit + + + align:start position:0% +has a limit +so where's theorem three is more than + + align:start position:0% +so where's theorem three is more than + + + align:start position:0% +so where's theorem three is more than +that it's also bounded right in some + + align:start position:0% +that it's also bounded right in some + + + align:start position:0% +that it's also bounded right in some +sense but here if there's no notion of + + align:start position:0% +sense but here if there's no notion of + + + align:start position:0% +sense but here if there's no notion of +bounded it's it's compact so but but the + + align:start position:0% +bounded it's it's compact so but but the + + + align:start position:0% +bounded it's it's compact so but but the +the main I mean you should think of + + align:start position:0% +the main I mean you should think of + + + align:start position:0% +the main I mean you should think of +these two are very much related to each + + align:start position:0% +these two are very much related to each + + + align:start position:0% +these two are very much related to each +other + + align:start position:0% +other + + + align:start position:0% +other +here it's + + align:start position:0% +here it's + + + align:start position:0% +here it's +but but they're not equivalent anything + + align:start position:0% +but but they're not equivalent anything + + + align:start position:0% +but but they're not equivalent anything +else okay great so that's all for today \ No newline at end of file diff --git a/PdyARRNwi7I.txt b/PdyARRNwi7I.txt new file mode 100644 index 0000000000000000000000000000000000000000..6c46123ed9a6922d93e03ac102e725c76bdbd2c7 --- /dev/null +++ b/PdyARRNwi7I.txt @@ -0,0 +1,4269 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of +MIT courses, visit + +mitopencourseware@ocw.mit.edu. + +PROFESSOR: All right, +so let's get started. + +So today we're going to +review local alignment, + +we talked about last time, and +introduce global alignment, + +also talking about +issues related + +to protein sequences, +which include + +some more interesting +scoring matrices. + +So just some info on topic +one, which we are still in. + +So I will have an +overview slide. + +It'll have a blue +background, and there + +will be a review slide +with a purple background + +in every lecture. + +So last time we talked about +local alignment and some + +of the statistics +associated with that, + +and also a little bit about +sequencing, technologies, + +both conventional +Sanger DNA sequencing + +as well as second +generation sequencing. + +And at the beginning of the +local alignment section, + +we introduced a simple +BLAST-like algorithm, + +and then we talked about +statistics, target frequencies, + +mismatched penalties, +that sort of thing. + +So there were a couple questions +at the end which I just + +wanted to briefly answer. + +So I believe it was Joe asked +about how the dye is attached + +to the DNTP in dye +terminator sequencing. + +And it appears +that it's attached + +to the base, sort of the +backside of the base, not + +the Watson-Crick +face, obviously. + +That seems to be the +common way that it's done. + +And then there was +another question + +from somebody in the back. + +I don't remember who asked about +when you're making libraries, + +how do you make sure that +each of your insert sequences + +has the two different adapters, +one adaptor on one side + +and the other adapter +on the other side? + +And there are at least +three ways to do this. + +So simplest is in +RNA ligation, when + +you take advantage of the +different chemistry at the five + +prime and three prime +ends of the small RNA + +that you're trying to clone. + +So you just use the +phosphate and NLH + +to ligate two +different adapters. + +Another more complicated way +occurs in ribosome footprint + +profiling, which is a method for +mapping the precise locations + +of ribosomes along +mRNAs, and involves polyA + +tailing, and then +introducing the adapters + +together, the two adapters, +with a polyT primer + +that primes off the polyA tail. + +And then you circularize, and +then you PCR off the circles. + +And it's a little +bit complicated, + +but you can look it up +in the reference that's + +up here on the slide. + +It's working now. + +And then, finally, +the way that's + +actually most commonly +used for protocols + +like RNA seq and +genomic DNA sequencing + +is that after you make +your double strand DNA, + +there's an enzyme that adds +a single A to the three + +prime end of each strand. + +So now you have a +symmetrical molecule. + +But then you add these funny +Y-shaped adapters that have + +and overhanging T on, +say, the red guy here. + +And so what will happen is +that each of these Y's can + +be ligated here. + +But each of the inserts, +independent of which + +strand it is, will have a red +adapter at the five prime end + +and a blue adaptor at +the three prime end. + +Any questions +about this or about + +sequencing technologies before +we go to local alignments? + +OK, good. + +It was a good question, +and that's the answer. + +So we motivated our +discussion of local alignments + +last time by talking +about this example, + +where you have a non-coding +RNA that you found, inhuman. + +You BLAST it against mouse, +and you get this alignment. + +Is this significant? + +So is this really likely to +be a homologous sequence? + +And how do you find +the alignments? + +And so we said +that, well, there's + +this theory that's +exact, at least + +exact in the asymptotic sense +for large query and database + +sizes that tells us the +statistical significance + +of the highest scoring +ungapped local alignment. + +And it's given by +this formula here, + +which is the extreme value +or Gumbel distribution. + +And then we talked +about the constraints + +or the expected score +has to be negative, + +but positive scores have to +be possible for this theory + +to work. + +And we also talked +about an algorithm. + +But if you remember, the +algorithms was very simple. + +It involved-- this +is zero-- keeping + +track of the cumulative score. + +So we have a mismatch and a +match, mismatch, mismatch, + +mismatch, match, match, match. + +That is a high scoring +segment, et cetera. + +So you keep track of the lowest +point you've ever been to + +as well as the current score. + +And when the current score +exceeds that lowest point + +you've ever been to by more +than we've ever seen before, + +more than this, then that's +your high scoring segment. + +Now it turns out, if this +is not intuitive to you, + +there's another +algorithm which I find, + +personally, more intuitive. + +So I just want to tell you +about that one as well. + +And it's basically +the same thing, + +except whenever you go +negative, you reset to zero. + +So here, we were +going to go negative, + +so we just reset to zero. + +That was on this mismatch here. + +Then we have a match. + +Now we're at plus 1. + +That's fine. + +Now we have a mismatch. + +Now we're down to zero. + +We don't need to do anything. + +Now we have another mismatch. + +Here, we're still at zero. + +Remember, we just stay at zero. + +We were going to go negative, +but we stayed at zero. + +Another mismatch, we +still stay at zero. + +And now we have these +three matches in a row. + +My line is not +staying very flat. + +But this should've +been here flat at zero. + +The point is that now the +highest scoring segment + +is the highest point +you ever reach. + +So it's very simple. + +So this is actually slightly +easier to implement. + +And that's sort +of a little trick. + +So for local alignments, +you can often reset to zero. + +Any questions about that? + +So well, we talked about +computational efficiency, + +this big O notation, +where you consider + +the number of +individual computations + +that are required to run +an algorithm as a function + +of the size of the +input, basically + +the number of units +in the problem base + +pairs, amino acid +residues, whatever. + +So computer scientists look +at the asymptotic worst case + +running time. + +That's either because +they're pessimistic, + +or perhaps because they +want to guarantee things. + +They want to say, it's not +going to be worse than this. + +Maybe it'll be faster, +and then you'll be happy. + +But I can guarantee +you, it's not + +going to be worse than this. + +And so in this case, the +algorithm we talked about + +was order n times +n, where that's + +the lengths of +the two sequences. + +So toward the end +last time, we get + +we talked about this +lambda parameter + +and said that lambda is the +unique positive solution + +to this equation here, +where sij are the scores + +and pi and rj are the +nucleotide frequencies. + +And then there's this +target frequency formula + +that comes up that says that +if you use a scoring system sij + +to apply to sequences, +and then you pull out + +just the high scoring +segments, the ones that + +are unusually high +scoring, they will have + +a frequency of +matching nucleotides + +qij that's given by the +product of the frequencies + +in the two sequences basically +weighted by e to the lambda + +sij. + +So matches will occur more +strongly, because that + +has a positive work, and +mismatches less strongly. + +And that then gives +rise to this notion + +that there's an optimal +mismatch penalty, if you just + +consider scoring systems +that have plus 1 for a match + +and m for a mismatch, some +negative number, that's + +given by this equation +here, and here I've + +worked out a couple of values. + +So the theory says that to find +matches that are 99% identical, + +you should use a mismatched +score of minus 3, + +but for 75% identical, +you should use minus 1. + +And I asked you to think +about does that make sense, + +or how is that true? + +So y is minus 3 +better than minus 1 + +for finding nearly +identical matches. + +Anyone have an idea +or thought on this? + +There's some thoughts +on the slide. + +But can anyone intuitively +explain why this is true? + +Yeah, what's your name? + +AUDIENCE: Eric. + +PROFESSOR: Yeah, go ahead. + +AUDIENCE: With a mismatch +penalty of minus 3, + +you actually need more +steps climbing back up + +to get back to +some local maximum. + +And therefore, you do require +a longer stretch [INAUDIBLE] + +matches in order to +get a significant hit. + +That's my guess as +to why a score of m + +equals minus 3, a +penalty, [INAUDIBLE] + +why it would be +better at finding + +the higher identity matches. + +PROFESSOR: OK, because +the minus 3 makes + +you go down faster, so it +takes longer to recover, + +so you can only find +nearly identical things + +with that kind of +scoring system. + +Is that your point? + +OK, that's a good point. + +So yeah, when would +you want to use + +a mismatched penalty of minus 1? + +AUDIENCE: When you're trying +to look for things that are + +[INAUDIBLE], but +maybe not so close. + +Well, when you're looking +for a [INAUDIBLE], + +you're looking for [INAUDIBLE]. + +That kind of situation. + +PROFESSOR: And so +let's say I'm using + +a mismatch penalty of minus 2. + +Can I find regions +that are 66% identical? + +AUDIENCE: Probably. + +PROFESSOR: Probably. + +AUDIENCE: But not guaranteed. + +PROFESSOR: Anyone else +have a comment on that? + +Match is plus 1. + +Mismatch is minus 2 +regions of 66% identity. + +Yeah, with Levi, yeah. + +AUDIENCE: No, since your +score will just be zero. + +PROFESSOR: Yeah. + +That's correct. + +So Levi's comment is +your score will be zero. + +Well, I'll just say plus for +match, plus, plus, minus, plus, + +plus, minus. + +I mean, it'll be interspersed. + +It doesn't have to be like +this for every triplet. + +But but on average, you'll have +two matches for every match. + +That's what 66% identity means. + +And so these will score +a total of plus 2. + +And this will score minus 2. + +And so you basically will +never rise much above zero. + +And so you you can't really +use that mismatch penalty. + +There's a limit. + +66% is sort of at a point +where you can no longer see. + +You could potentially +see things that + +are 75% identical if +they were incredibly + +long with that kind +of mismatch penalty. + +But you just can't see +anything below 2/3% identity + +with minus 2. + +So to find those low things, +you have to use the lower. + +You have to go down +to minus 1 if you + +want to find the +really weak matches. + +But they will have to be +correspondingly very long + +in order to achieve +statistical significance. + +So correspondingly, the +reason why it's better + +to use a harsher mismatch +penalty of minus 3 + +to find the nearly +identical regions + +is that, in this +equation, when you + +go from having a plus 1, minus +1 scoring system to plus 1, + +minus 3, lambda will change. + +This equation will +no longer satisfied + +so that a new value of +lambda will be relevant. + +And that value will be larger. + +That's not totally +obvious from this equation + +because you sort of +have one term, which + +is either the minus lambda in +one term or either plus lambda. + +But it turns out that +that making the mismatch + +penalty more negative will +lead to a solution that's + +a bigger value of lambda. + +So that means that +the same score, x, + +will lead to a larger +negative exponent here. + +and? + +How will that +affect the p-value? + +Anyone take us through this? + +It's a little bit +convoluted with all + +these negative +exponentials and stuff, + +but can someone explain to us +how that affects the p-value? + +Same x. + +We're going to increase lambda. + +What happens to the p-value? + +This gets bigger, more negative. + +That means this e to the +minus thing gets closer to 0. + +That means that this is +inside an exponential. + +As that thing gets closer +to 0, this whole term + +here gets closer to 1. + +Therefore you're +subtracting it from 1. + +Therefore the p-value +gets smaller, closer to 0, + +more significant. + +Does that made sense? + +So it's good to +just work through + +how this equation works. + +So that's all I wanted +to say about mismatch + +penalties for DNA. + +Any questions about that? + +So how do you actually +use this in practice? + +So if you just +Google "BLAST end," + +you'll get to this website. + +It's been set up at NCBI +for about 20 years or so. + +And of course, it's gone +through various iterations + +and improvements over the years. + +And if you look +down at the bottom, + +there is a place where +you can click and set + +the algorithm parameters. + +And there are a number of +parameters you can set. + +Some of them affect the speed. + +But we're focused here +mostly on parameters + +that will affect the quality, +the nature of the alignments + +that you find. + +And so here, you can set +not arbitrary penalties, + +but you can set within a range +of standard mismatch penalties. + +You can do 1 minus 1, +1 minus 2, et cetera. + +So what about sequences +that code for protein? + +So exons, for example. + +So you can search them with a +nucleotide search, like BLAST. + +But it can often be +the case that you'll + +do better if you first +translate your exon + +into the corresponding +amino acid sequence using + +a genetic code and then +search that peptide. + +Now you may or may not know +the reading frame of your exon + +a priori, or even know +that it is an exon, + +so BLAST automatically will +do this translation for you. + +So for example, with +this DNA sequence, + +it'll translate in all +three of the reading frames, + +leading to essentially +this bag of peptides + +here, where sometimes you'll +hit a stop code on, like right + +here. + +And then it just treats +it as, OK, there's + +a little PR dipeptide there. + +And then there's a longer +peptide here, [INAUDIBLE], + +and so forth. + +So it just makes these bags of +peptides for each reading frame + +and searches all those peptides +against some target, which + +can be approaching +database or a DNA database, + +again, translated in +all the reading frames. + +So the folks at NCBI have made +all these different flavors + +of BLAST available. + +So BLASTP is for proteins. + +N is for nucleotides. + +And then the translating ones +are called things like BLASTX + +for a nucleotide query +against a protein database. + +TBLASTN for a protein query +against a nucleotide database, + +which gets translated in +all frames, or TBLASTX, + +where you translate both +the nucleotide sequences + +in all frames. + +And then there's a number +of other versions of BLAST + +which we probably won't +discuss but that are well + +described in the textbook +and other accessible + +online sources. + +Let me ask you this. + +So remember ESTs. + +So ESTs are segments of cDNAs +that typically correspond + +to one ABI 3700 Sanger +sequenc off of that cDNA, + +so one read, like +600 bases or so. + +So let's say you have +some ESTs from chimp. + +And you don't have +the chimp genome yet. + +So you're going to search +them against human. + +What would you do? + +Would you use a +translating search? + +Or would you use +a BLASTN search? + +Or does it matter? + +Chimp is a 98% identical +human, very high. + +Any ideas? + +Yeah, Tim. + +AUDIENCE: You could use +a translating search, + +because you know that the cDNAs +are at least coding for RNAs. + +And so if you just use +a nucleotide search, + +then you're not going to +have functional significance + +in terms of the alignment. + +But if it's going +for a protein, then-- + +PROFESSOR: You mean you won't +know whether it is the protein + +coding part of the cDNA or not? + +AUDIENCE: So I just +mean that if you're + +looking between +chimp and human, then + +you're expecting some +sort of mismatch. + +But it's possible that it +could be a functional mismatch. + +Then you know that the cDNA +is maybe coding for a protein. + +Therefore, if the +mismatch is between two + +similar amino acids, then +that would be picked up + +by a translating +search, but it would + +be skewed against it +in a nucleotide search. + +PROFESSOR: OK, fair enough. + +But if you assume that +the two genomes are, + +let's say, 97% identical, even +in a non-coding region, which + +they're very high. + +I don't remember the exact +percent, but very high. + +Then if you're searching 600 +nucleotides against the genome, + +even if it's 95% +identical, you'll + +easily find that under either. + +So either answer is +correct, BLASTN or BLASTX. + +And the UTRs could only be found +by-- if it happened that this + +was a sequence from +a three prime UTR, + +you could only find that +by BLASTN typically. + +What if it's a human EST +against the mouse genome? + +So mouse exons are +about 80% identical + +to human exons at the +nucleotide level, typically. + +Any ideas? + +What kind of search +would you do? + +BLASTN, BLASTX, +or something else? + +TBLASTX. + +Yeah, go ahead. + +AUDIENCE: I have +another question. + +What exactly is the +kind of question + +we're trying to answer by +doing this BLAST search? + +PROFESSOR: Oh, +well, I was assuming + +you're just trying to find +the closest homologous cDNA + +or exons in the genome-- exons, +I guess, yeah, the exons. + +of the homologous gene. + +Yeah, that's a good question. + +Exons of a homologous gene. + +We've got a human EST going +against the mouse genome. + +When do we do? + +AUDIENCE: I suggest +BLASTP because-- + +PROFESSOR: Well, +BLASTP, that's protein. + +This is a nucleotide +sequence against nucleotide. + +So we can do BLASTN +or TBLASTX, let's say. + +AUDIENCE: TBLASTX. + +PROFESSOR: TBLASTX. + +You translate your EST, +translate the genome, + +search those peptides. + +TBLASTX, why? + +AUDIENCE: The +nucleotide sequences + +may be only about +80% similarity, + +but the protein +sequences functionally, + +due to the functional +constraints, + +you might actually get +higher similarities there. + +PROFESSOR: Yeah. + +It's exactly right. + +So they are about, on +average, about 80% identical. + +It varies by gene. + +But a lot of those +variations that occur + +are at the third side +of the codon that + +don't effect the amino +acid, because there's + +a lot of constraint +on protein sequence. + +And so you'll do +better, in general, + +with a translating search +than with a nucleotide search. + +Although, they both may work. + +But you may find a +more complete match + +with a translating search. + +That's good. + +Everyone got that? + +Sally, yeah. + +AUDIENCE: Is there a reason +why you wouldn't use BLASTX + +and instead you use TBLASTX? + +PROFESSOR: Yeah, I +just gave the example + +of searching against the genome. + +But you could search against +the mouse proteome as well. + +You might or might not. + +It depends how well +annotated that genome is. + +Mouse is pretty well annotated. + +Almost all the proteins +are probably known. + +So you probably get it. + +But if you were searching +against some more obscure + +organism, the chameleon +genome or something, + +and it wasn't well +annotated, then you + +might do better with searching +against the genome, because you + +could find a new x on there. + +OK, good. + +Question yeah, go ahead. + +AUDIENCE: So when we do these +translations, these nucleotide, + +amino acid things, +do we get all frames? + +Do the algorithms to all frames? + +PROFESSOR: Yeah, all six frames. + +So three frames on the plus +strand, and three frames + +on the reverse strand. + +Yeah. + +All right, great. + +So that's the end of local +alignment, for the moment. + +And we're going to now move +on to global alignment using + +two algorithms. + +For global alignment, +Needleman-Wunch-Sellers, + +and then for gapped local +alignment, Smith-Waterman. + +And toward the end, +we're going to introduce + +the concept of amino acid +substitution matrices. + +So the background for +today, the textbook + +does a pretty good +job on these topics, + +especially the +pages indicated are + +good for introducing the +PAM series of matrices. + +We'll talked a little bit today +and a little bit next time. + +So why would we align +protein sequences? + +So the most obvious reason is to +find homologues that we might, + +then, want to investigate, +or we might, for example, + +if you have a human protein +and you find homologous mouse + +protein, and that mouse +protein has known function from + +a knockout or from some +biochemical studies, + +for example, then you can guess +that the human protein will + +have similar function. + +So we often use this +type of inference + +that sequence similarity implies +similarity in function and/or + +structure. + +So how true is this? + +So it turns out, +from a wide body + +of literature, that this +inference that sequence + +similarity implies functional +and structural similarity + +is almost always true when +the sequence similarity is + +more than about 30% identity +over the whole length + +of a protein, over +300, 400 amino acids. + +That's a good inference. + +Below that, sort of +in the 20% to 30% + +sequence similarity, +that's often + +referred to as +the Twilight Zone, + +where sometimes it's +a good inference, + +and sometimes it's not. + +So you need to be a +little bit careful. + +And below that, it's deeper +into the Twilight Zone, + +where most of the time you +probably shouldn't trust it. + +But occasionally, you can see +these very remote homologies. + +You might want to have +additional information + +to support that +kind of inference. + +And I want to just point out +that the converse is just not + +true in biology. + +So structural +similarity does not + +imply sequence +similarity or even + +derivation from a +common ancestor. + +So you may think, +well, every protein + +has a really complex, elaborate +three dimensional structure, + +and there's no way that +could ever evolve twice. + +And it's true that probably +that exact structure can never + +evolve twice. + +But a very similar structure, +a similar fold even, + +in terms of the topology +of alpha helices + +and beta strands, which +Professor Frank will + +talk about later in the +course, the identical fold + +can involve more than once. + +It's not that hard +to evolve a pattern + +of alpha helices +and beta strands. + +And so this point about +structural similarity + +not implying +sequence similarity, + +the way I think about it +is like this, like here + +are two organisms. + +This is a hummingbird, +you've all seen. + +And some of you +may have seen this. + +This is a hawk moth, +which is an insect that + +is roughly two inches long, +beats its wings very fast, + +has a long tongue that +sips nectar from flowers. + +So it basically occupies +the same ecological niche + +as a hummingbird, and +looks very, very similar + +to a hummingbird at a distance. + +From 10 or more feet, +you often can't tell. + +This is an insect, +and that's a bird. + +The last common +ancestor was something + +that probably lived +500 million years ago, + +and certainly didn't +have wings, and may not + +have had legs or eyes. + +And yet, they've +independently evolved + +eyes and wings and +all these things. + +So when there's +selective pressure + +to evolve something, either +a morphology or a protein + +structure, for +example, evolution + +is flexible enough that it can +evolve it many, many times. + +So here's an example from +the protein structure world. + +This is homophilous +iron binding protein. + +This is just the iron +coordination center. + +And this is now a eukaryotic +protein called lactoferrin. + +Turns out these +guys are homologous. + +But eukaryotes and bacteria +diverged 2 million years + +ago or so, so their ancestry +is very, very ancient. + +And yet, you can see that in +this iron coordination center, + +you have a tyrosine +pointing into the iron here. + +And you have a histidine +up here, and so forth. + +So the geometry has +been highly conserved. + +It's not perfectly conserved. + +Like, here you +have a carboxylate. + +And here you have a phosphate. + +So there's been a +little bit of change. + +But overall, this way +of coordinating iron + +has basically evolved +independently. + +So although these +are homologous, + +the last common +ancestor bound anions-- + +that's known from +[INAUDIBLE] construction. + +So they independently evolved +the ability to bind cations, + +like iron. + +And here is actually +my favorite example. + +So here's a protein called +ribosome recycling factor. + +And that's its shape. + +So it's a very +unusual shaped protein + +that's kind of shaped like an L. + +Does this remind +anyone of anything, + +this particular shape? + +Have you seen this in another +biomolecule at some point? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Something +like [INAUDIBLE]. + +OK, could be. + +Any other guesses? + +How about this? + +That's a tRNA. + +So the 3D structure of +tRNA is almost identical, + +both in terms of +the overall shape + +and in terms of the geometry. + +Sorry, I'm having issues +with my animations here. + +The geometry of these, they're +both about 70 angstroms long. + +So why is that? + +Why would this protein +evolve to have the same three + +dimensional shape as a tRNA? + +Any ideas? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: [INAUDIBLE]. + +Right, exactly. + +It fits into the +ribosome, and it's + +involved, when the +ribosome is stalled, + +and basically +releasing the ribosome. + +So it's mimicking a tRNA +in terms of structure. + +And so the point about +this is that, if you + +were to take a bunch +of biomolecules + +and match them up using +a structure comparison + +algorithm to find similar ones-- +these two are clearly similar. + +And yet, they probably never +had a common ancestor right, + +because one's an RNA +in one's a protein. + +OK. + +So now what we're going to talk +about a few different types + +of alignments. + +So we talked about +local alignments, + +where you don't try to +align the entire sequence + +of your query or your database. + +You just find smaller +regions of high similarity. + +Global alignment, where +you try to align the two + +proteins from end +to end, you assume + +that these two proteins +are homologous, + +and actually that they +haven't had major insertions + +or rearrangements +of their sequence. + +And then semi-global, +which is sort + +of a little twist on global. + +And we'll talk about a few +different scoring systems-- so + +ungapped, which we've been +talking about until now, + +and then we'll introduce +gaps of two types that + +are called linear and affine. + +And the nomenclature is a little +bit confusing, as you'll see. + +They're both linear, in a sense. + +So a common way to represent +sequence alignments, especially + +in the protein alignment-- you +can do it for protein or DNA-- + +is what's called a dot matrix. + +Now we've got two proteins. + +They might be 500 amino +acids long each, let's say. + +You write sequence +one along the x-axis, + +sequence two along the y-axis. + +And then you make a dot +in this matrix whenever + +they have identical residues, +although probably there + +would be a lot +more dots in this. + +So let's say, whenever you have +three residues in a row that + +are identical-- OK, that's +going to occur fairly rarely, + +since there's 20 amino acids. + +And you make that dot. + +And for these two +proteins, you don't + +get any off diagonal dots. + +You just get these three +diagonal lines here. + +So what does that tell you +about the history of these two + +proteins? + +What's that right there? + +Sally. + +AUDIENCE: An +insertion or deletion. + +PROFESSOR: An +insertion or deletion. + +An insertion in which protein? + +AUDIENCE: Sequence two. + +PROFESSOR: Or a deletion in? + +AUDIENCE: One. + +PROFESSOR: OK. + +Everyone got that? + +OK, good. + +There's extra sequence +in sequence two here + +that's not in sequence one. + +You don't know whether it's +an insertion or deletion. + +It could be either one, +based on this information. + +Sometimes you can figure that +out from other information. + +So sometimes you call that an +indel-- insertion or deletion. + +And then, what is +this down here? + +Someone else? + +Insertion, I heard, insertion +in sequence one or deletion + +in sequence two. + +OK, good. + +All right, so what +type of alignment + +would be most appropriate +for this pair sequences, + +a local or a global? + +AUDIENCE: I would do +global, because they're + +very, very similar. [INAUDIBLE]. + +PROFESSOR: Yeah. + +They are quite similar +across their entire lengths, + +just with these +two major indels. + +So that's sort of the +classical case where + +you want to do the +global alignment. + +All right. + +So what about +these two proteins? + +Based on this dot +matrix, what can you + +say about the relation +between these two, + +and what type of +alignment would you + +want to use when comparing +these two proteins? + +Yeah, what's your name? + +AUDIENCE: Sonia. + +PROFESSOR: Go ahead, Sonia. + +AUDIENCE: It looks like they've +got similar domains, maybe. + +So local alignment +might be better. + +PROFESSOR: And why wouldn't +you do a global alignment? + +AUDIENCE: Local, because the +local alignment might actually + +find those domains and +tell you what they are. + +PROFESSOR: So a local +alignment should at least + +find these two guys here. + +And why do these two +parallel diagonal + +lines, what does that tell you? + +AUDIENCE: That the +two different proteins + +have similar sequences, just in +different parts of the protein, + +different areas +relative to the start. + +PROFESSOR: Right. + +Yeah, go ahead. + +AUDIENCE: Doesn't it +just basically mean + +that there's a section +in sequence two + +that's in sequence one twice? + +PROFESSOR: Yeah, exactly. + +So this segment of sequence two, +here-- sorry, having trouble, + +there we go, that apart-- is +present twice in sequence one. + +It's present once from +about here over to here, + +and then it's present once +from here over to here. + +So it's repeated. + +So repeats and +things like that will + +confuse your global alignment. + +The global alignment needs to +align each residue-- or trying + +to align each residue +in protein one + +to each residue in protein two. + +And here, it's ambiguous. + +It's not clear which +part of sequence one + +to align to that +part of sequence two. + +So it'll get confused. + +It'll choose one or the other. + +But that may be +wrong, and that really + +doesn't capture what +actually happens. + +So yeah, so here +a local alignment + +would be more suitable. + +Good. + +So let's talk now about +gaps, again, which + +can be called indels. + +In protein sequence alignments, +or DNA, which many of you + +have probably seen, you +often use maybe just + +a dash to represent a gap. + +So in this alignment +here, you can + +see that's kind of a +reasonable alignment, right? + +You've got pretty good +matching on both sides. + +But there's nothing in +the second sequence that + +matches the RG in +the first sequence. + +So that would be a reasonable +alignment of those two. + +And so what's often +used is what's + +called a linear gap penalty. + +So if you have end gaps, +like in this case two, + +you assign a gap +penalty A, let's say. + +And A is a negative number. + +And then you can just run the +same kinds of algorithms, where + +you add up matches, +penalize mismatches, + +but then you have an +additional penalty + +you apply when you +introduce a gap. + +And typically, +the gap penalty is + +more severe than your +average mismatch. + +But there's really +no theory that + +says exactly how the gap +penalty should be chosen. + +But empirically, +in cases where you + +should know the +answer, where you have, + +for example, a +structural alignment, + +you can often find that +a gap penalty that's + +bigger than your +average mismatch penalty + +is usually the +right thing to do. + +So why would that be? + +Why would a gap penalty-- +why would you want to set it + +larger than a typical mismatch? + +Any ideas? + +Yeah, what's your name? + +AUDIENCE: I'm Chris. + +PROFESSOR: Chris. + +AUDIENCE: Because having +mutations that shift the frame + +or that one insert would +have insertions or deletions + +is far more uncommon than just +having changing [INAUDIBLE]. + +PROFESSOR: Mutations that create +insertions and deletions are + +less common than those that +introduce substitutions + +of residues. + +Everyone got that? + +That's true. + +And do you know by what factor? + +AUDIENCE: Oh, I couldn't +give you a number. + +PROFESSOR: So I mean, +this varies by organism, + +and It varies by what type of +insertion you're looking at. + +But even at the single +nucleotide level, + +having insertions +is about an order + +of magnitude less +common than having + +a substitution in +those lineages. + +And here, in order to get +an amino acid insertion, + +you actually have to have a +triplet insertion, three or six + +or some multiple of +three into the exon. + +And that's quite +a bit less common. + +So they occur less commonly. + +A mutation occurs less commonly, +and therefore the mutation + +is actually accepted by +evolution even less commonly. + +And an alternative is a +so-called affine gap penalty, + +which is defined +as G plus n lambda. + +So n is the number +of gaps, and then G + +is what's called a +gap opening penalty. + +So the idea here is +that basically the gaps + +tend to cluster. + +So having an insertion +is a rare thing. + +You penalize that +with G. But then, + +if you're going to +have an insertion, + +sometimes you'll have a big +insertion of two or three + +or four codons. + +A four codon insertion should +not be penalized twice as much + +as a two codon insertion, +because only one gap actually + +occurred. + +And when you have +this insertion event, + +it can any variety of sizes. + +You still penalize +more for a bigger gap + +than for a smaller gap, +but it's no longer linear. + +I mean, it's still +a linear function, + +just with this +constant thing added. + +So these are the two common +types of gap penalties + +that you'll see +in the literature. + +The affine works a +little bit better, + +but it is a little bit more +complicated to implement. + +So sometimes you'll see both +of them used in practice. + +And then, of course, by changing +your definition of gamma, + +you could have a +G plus n minus 1. + +So that first gap would +be G, and then all + +the subsequent gaps would gamma. + +So you're not going to have +to double score something. + +All right. + +OK. + +You've got two proteins. + +How do you actually find the +optimal global alignment? + +Any ideas on how to do this? + +So we can write one sequence +down one axis, one down + +the other axis. + +We can make this dot plot. + +The dot plot can give us some +ideas about what's going on. + +But how do we actually +find the optimal one + +where we want to start +from the beginning? + +In the end, we're going +to write the two sequences + +one above the other. + +And if the first residue +or the first sequence is n, + +and maybe we'll +align it to here, + +then we have to write +the entire sequence here + +all the way down to the end. + +And below it has to +be either a residue + +in sequence two or a gap. + +And again, we can +have gaps up here. + +So you have to do something. + +You have to make it all the way +from the beginning to the end. + +And we're just going to sum +the scores of all the matching + +residues, of all the mismatching +residues, and of all the gaps. + +How do we find that alignment? + +Chris. + +AUDIENCE: Well, since we're +using dynamic programming, + +I'm guessing that you're +going to have to fill out + +a matrix of some +sort and backtrack. + +PROFESSOR: And so when you see +the term dynamic programming, + +what does that mean to you? + +AUDIENCE: You're going to +find solutions to sub problems + +until you find a +smaller solution. + +Then you'd backtrack +through what + +you've solved so far to +find the global sequence. + +PROFESSOR: Good. + +That's a good way +of describing it. + +So what smaller +problems are you going + +to break this +large problem into? + +AUDIENCE: The smaller +sub-sequences. + +PROFESSOR: Which +smaller sub-sequences? + +Anyone else? + +You are definitely on +the right track here. + +Go ahead. + +AUDIENCE: I mean, it +says at the top there, + +one sequence across the +top and one down the side. + +You could start with just +the gap versus the sequence + +and say your gap will +increase as you move across. + +Basically, each cell there could +be filled out with information + +from some of its neighbors. + +So you want to make +sure that you fill out + +old cells in some +order so that we + +can proceed to the next +level with what we've + +[? written down. ?] + +PROFESSOR: So if +you had precisely + +to find a sub problem where you +could see what the answer is, + +and then a slightly larger sub +problem whose solution would + +build on the solution that first +one, where would you start? + +What would be your +smallest sub problem? + +AUDIENCE: I'd start +with the top row, + +because you could just +the gap versus gap, + +and then move in the row, +because you don't need anything + +above that. + +PROFESSOR: And then what's +the smallest actual problem + +where you actually have +parts of the protein aligned? + +AUDIENCE: One row in +column two, basically. + +If it's a match, +you have some score. + +And if it's a mismatch, +you have some other score. + +And you want the best +possible one in each block. + +PROFESSOR: Yeah, OK. + +Yeah. + +That's good. + +So just to generalize +this-- hopefully this + +is blank-- in general, you +could think about we've got, + +let's say, 1 to n here, +and a sequence 1 to n here. + +You could think about a position +i here and a position j here. + +And we could say finding the +optimal global alignment, + +that's a big problem. + +That's complicated. + +But finding an alignment +of just the sequence from 1 + +to i in the first protein +against the sequence + +from 1 to j in the +second protein, + +that could be pretty easy. + +If i is 2 and j is 2, +you've got a dipeptide + +against a dipeptide. + +You could actually +try all combinations + +and get the optimal +alignment there. + +And so the idea, then, is if you +can record those optimal scores + +here in this matrix, then you +could build out, for example, + +like this, and find +the optimal alignments + +of increasingly +bigger sub problems + +where you add another residue +in each direction, for example. + +Does that makes sense to you? + +The idea of a dynamic +programming algorithm + +is it's a form of +recursive optimization. + +So you first optimize +something small, + +and then you optimize +something bigger + +using the solution you got +from that smaller piece. + +And the way that that's +done for protein sequences + +in Neeleman-Wunsch is +to, as we were saying, + +first consider that there +might be a gap in one aligning + +to a residue in the other. + +So we need to put these +gaps down across the top + +and down the side. + +This is a linear gap +penalty, for example. + +And so here would +be how you start. + +And this is a gap penalty, +obviously, of minus 8. + +So if you're the +optimal solution that + +begins with this V in +the top sequence aligned + +to this gap in the +vertical sequence, + +there's one gap there, +so it's minus 8. + +And then if you want to start +with two gaps against this V + +and D, then it's minus 16. + +So that's how you +would start it. + +So you start with these problems +where there's no options. + +If you have two gaps against +two residues, that's minus 16. + +By our scoring system, +it's unambiguous. + +So you just can fill those in. + +And then you can +start thinking about, + +what do we put right here? + +What score should +we put right there? + +Remember, we're defining +the entries in this matrix + +as the optimal score of the +sub-sequence of the top protein + +up to position i against +the vertical protein up + +to position j. + +So that would be the +top protein position + +one up to the vertical +protein position one. + +What score would that be? + +What's the optical +alignment there + +that ends position +one both sequences? + +It'll depend on +your scoring system. + +But for a reasonable scoring +system, that's a match. + +That's going to get +some positive score. + +That's going to be better than +anything involving a gap in one + +against a gap in the other +or something crazy like that. + +So that's going to get whatever +your VV match score is. + +This is your Sij from +your scoring matrix + +for your different amino acids. + +And then, basically the +way that this is done + +is to consider that when +you're matching that position + +one against position one, you +might have come from a gap + +before in one sequence or a +gap in the other sequence, + +or from a match position +in the other sequence. + +And that leads to +these three arrows. + +I think it gets clear if I write +up the whole algorithm here. + +So Sij is the score of the +optimal alignment ending + +at position i in sequence one +and position j in sequence two. + +Requires that we know +what's above, to the left, + +and diagonally above. + +And you solve it from +the top and left down + +to the bottom and +right, which is often + +called dynamic programming. + +And let's just look at +what the recursion is. + +So Needleman and +Wunsch basically + +observed that you could find +this optimal global alignment + +score by filling in the +matrix by at each point taking + +the maximum of these +three scores here. + +So you take the +maximum of the score + +that you had above and to the +left, so diagonally above, plus + +sigma of xi yj. + +Sigma, in this case, +is the scoring matrix + +that you're using +that's 20 by 20 that + +scores each amino acid against +each other amino acid residue. + +You add that score if you're +going to move diagonally + +to whatever the optimal +score was there, + +or if you're moving to +the right or down, you're + +adding a gap in one +sequence or the other. + +So you have to add A, which +is this gap penalty, which + +is a negative number, to +whatever the optimal alignment + +was before. + +I think it's maybe easier +if we do an example here. + +So here is the PAM250 +scoring matrix. + +So this was actually developed +by Dayhoff back in the '70s. + +This might be an +updated version, + +but it's more or less +the same as the original. + +Notice, it's a +triangular matrix. + +Why is that? + +AUDIENCE: It's symmetric. + +PROFESSOR: It's +symmetric, right. + +So it has a diagonal. + +But then everything +below the diagonal, + +it would be mirrored +above the diagonal, + +because it's symmetric. + +Because you don't know when +you see a valine matched + +to a leucine, it's the same as +a leucine matched to a valine, + +because it's a symmetrical +definition of scoring. + +And here are two +relevant scores. + +So notice that VV has a score +of plus 4 in this matrix. + +And over here, VD has +a score of minus 2. + +So I'll just write those down. + +Anyone notice anything else +interesting about this matrix? + +We haven't said exactly where it +comes from, but we're going to. + +Yeah, what's your name? + +AUDIENCE: Michael. + +PROFESSOR: Go ahead. + +AUDIENCE: Not all the +diagonal values are the same. + +PROFESSOR: Not all +diagonals are the same. + +In fact, there's a pretty +big range, from 2 up to 17, + +so a big range. + +And anything else? + +OK, I'm sorry, go ahead. + +What's your name? + +AUDIENCE: Tagius. + +PROFESSOR: Tagius, yeah. + +Go ahead. + +AUDIENCE: There +are positive values + +for things that +are not the same? + +PROFESSOR: Yeah. + +So all the diagonal +terms are positive. + +So a match of any +particular residue type + +to its identical +residue is always + +scored positively, but +with varying scores. + +And there are also some positive +scores in the off diagonal. + +And where are those +positive scores occurring? + +Notice they tend to +be to nearby residues. + +And notice the order of +residues is not alphabetical. + +So someone who knows a +lot about amino acids, + +what can you see +about these scores? + +Yeah, go ahead. + +AUDIENCE: I think these +amino acids [INAUDIBLE] + +based on their [INAUDIBLE]. + +PROFESSOR: So the comment +was that the residues have + +been grouped by similar +chemistry of their side chains. + +And that's exactly right. + +So the basic residues, +histidine, arginine, + +and lysine, are all together. + +The acidic residues, +aspartate and glutamate, + +are here, along with +asparagine and glutamine. + +And notice that D to E +has a positive score here. + +It's 3. + +It's almost as good as D to D +or E to E, which are plus 4. + +So recognizing that you can +often substitute in evolution + +an aspartate for a glutamate. + +So yeah, so it basically, +to some extent, + +is scoring for +similar chemistry. + +But that doesn't explain +why, on the diagonal, + +you have such a large +range of values. + +Why is a tryptophan +more like a tryptophan + +than a serine is like a serine. + +Tim, you want to comment? + +AUDIENCE: Perhaps it's because +tryptophans occur very rarely + +in all proteins [INAUDIBLE]. + +So if you've got +two [INAUDIBLE], + +that's a lot rarer of an +occurrence and [INAUDIBLE]. + +PROFESSOR: So Tim's point was +that tryptophans occur rarely, + +so when you see two +tryptophans aligned, + +you should take note of it. + +It can anchor your alignment. + +You can be more +confident in that. + +Sally. + +AUDIENCE: Well, tryptophans +are also incredibly bulky, + +and also have the ability to +make electric interactions, + +electro-static interactions. + +PROFESSOR: Not really +electro-static, you would say, + +more-- + +[INTERPOSING VOICES] + +AUDIENCE: Yes. + +But they do have +a lot of abilities + +to interact with +other side chains. + +And cysteines contribute +very, very strongly + +to the three dimensional +structure of the protein. + +PROFESSOR: Why is that? + +AUDIENCE: Well, because +they can form [INAUDIBLE]. + +PROFESSOR: OK. + +Yeah. + +So maybe you don't put your +tryptophans and your cysteines + +into your protein by +chance, or you only + +put them when you +want them, when + +there's enough space +for a tryptophan. + +And when you substitute +something smaller, + +it leaves a gap. + +It leaves a 3D spatial gap. + +And so you don't want that. + +You don't get good packing. + +When you have cysteines, +they form disulfide bonds. + +If you change it to something +that's non-cysteine, + +it can form that anymore. + +That could be disruptive +to the overall fold. + +So those ones tend to be more +conserved in protein sequence + +alignments, absolutely. + +Whereas, for example, if you +look at these hydrophobics, + +the MILV group +down here, they all + +have positive scores +relative to each other. + +And that says that, basically, +most the time when those + +are used-- I mean, +there are sometimes + +when it went really matters. + +But a lot of time, if you just +want a transmembrane segment, + +you can often substitute any one +of those at several positions + +and it'll work equally well +as a transmembrane segment. + +So these are not random at all. + +There's some patterns here. + +So let's go back +to this algorithm. + +So now, if we're going to +implement this recursion, + +so we fill on the top +row and the left column, + +and then we need to +fill in this first. + +I would argue the first +interesting place in the matrix + +is right here. + +And we consider +adding a gap here. + +When you move vertically +or horizontally, + +you're not adding a +match or adding a match. + +So from this position, this is +sort of the beginning point. + +It doesn't actually correspond +to a particular position + +in the protein. + +We're going to add +now the score for VV. + +And we said that VV, you look +it up in that PAM matrix, + +and it's plus 4. + +So we're going to +add 4 there to 0. + +And so that's clearly +bigger than minus 16, + +which is what you get from +coming above or coming + +from the left. + +So you put in the 4. + +And then you also, in addition +to putting that 4 there, + +you also keep the arrow. + +So there's that red arrow. + +We remember where we came +from in this algorithm. + +Because someone said something +about backtracking-- I + +think Chris-- so that's +going to be relevant later. + +So we basically get rid +of those two dotted arrows + +and just keep that red +arrow as well as the score. + +And then we fill in +the next position here. + +And so to fill in +this, now we're + +considering going to the second +position in sequence one, + +but we're still only at the +first position in sequence two. + +So if we match V to V, +then we'd have to add, + +basically, a gap in +one of the sequences. + +Basically it would be +a gap in sequence two. + +And that's going to be minus 8. + +So you take 4, and then plus +minus 8, so it's negative 4. + +Or you could do minus 8 +and then plus negative 2, + +if you want to start +from a gap and then + +add a DV mismatch +there, because minus 2 + +was the score for a DV mismatch. + +Or again, you can start from a +gap and then add another gap. + +OK, does that make sense? + +So what is the +maximum going to be? + +Negative 4. + +And the arrow is going +to be horizontal, + +because we got some bonus +points for that VV match, + +and now it's carrying over. + +We're negative, but that's OK. + +We're going to just keep +the maximum, whatever it is. + +All right, so it's minus 4, +and the horizontal arrow. + +And then here's the +entire matrix filled out. + +And you'll have a chance +to do this for yourself + +on problem set one. + +And I've also filled in arrows. + +I haven't filled +in all the arrows, + +because it gets +kind of cluttered. + +But all the relevant arrows +here are filled in, as well as + +some irrelevant arrows. + +And so then, once +I fill this in, + +what do I do with +this information? + +How do I get an actual +alignment out of this matrix? + +Any ideas? + +Yeah, what's your name? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yeah, so what he said +is start at the bottom right + +corner and go +backwards following + +the red arrows in reverse. + +Is that right? + +So why the bottom right corner? + +What's special about that? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yeah. + +It's a score of the +optimal alignment + +of the entire sequence one +against the entire sequence + +two. + +So that's the answer. + +That's what we define as the +optimal global alignment. + +And then you want to +know how you got there. + +And so how did we get there? + +So the fact that there's +this red arrow here, + +what does that red arrow +correspond to specifically? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Right. + +In this particular case, for +this particular red arrow, + +remember the +diagonals are matches. + +So what match is that? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yeah, that's +a Y to Y match, right? + +Can everyone see that? + +We added Y to Y, +which was plus 10, + +to whatever this +13 was and got 23. + +OK, so now we go back to here. + +And then how do we get here? + +We came from up here by +going this diagonal arrow. + +What is that? + +What match was that? + +That's a +cysteine-cysteine match. + +And then how do +we get to this 1? + +We came vertically. + +And so what does that mean? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: We inserted a +gap, in which sequence? + +The first one. + +The second one? + +What do people think? + +Moving down. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yeah, the top one. + +And so that got us to here. + +Here's a match, plus 2 for +having a serine-serine match. + +Here's a plus 3 for +having a D to E mismatch. + +But remember, that's those +are chemically similar, + +so they get a positive score. + +And then this is the V to V. + +So can you see? + +I think I have the +optimal alignment written + +somewhere here, +hopefully, there. + +That's called the trace back. + +And then that is the alignment. + +OK, we align the Y to +the Y, the C to the C. + +Then we have basically a gap +in this top sequence-- that's + +that purple dash there-- +that's corresponding to that L. + +And you can see why we wanted +to put that gap in there, + +because we want +these S's to match, + +and we want the C's to match. + +And the only way +to connect those + +is to have a gap in the purple. + +And the purple was shorter +than the green sequence + +anyway, so we kind +of knew that there + +was going to be a gap somewhere. + +And good. + +And that's the +optimal alignment. + +So that's just some philosophy +on Needlemen-Wunsch alignments. + +So what is +semi-global alignment? + +You don't see that +that commonly. + +It's not that big a deal. + +I don't want to spend +too much time on it. + +But it is actually +reasonable a lot of times + +that, let's say you +have a protein that + +has a particular +enzymatic activity, + +and you may find that the +whole, the bulk of the protein + +is well conserved +across species. + +But then at the N and +C termini, there's + +a little bit of flutter. + +You can add a few residues or +delete a few residues, and not + +much matters at the +N and C termini. + +Or it may matter not for +the structure but for, + +you know, you're adding a single +peptide so it'll be secreted, + +or you're adding some +localization signal. + +You're adding some +little thing that + +isn't necessarily conserved. + +And so a semi-global +alignment, where + +you use the same +algorithm, except + +that you initialize the edges of +the dynamic programming matrix + +to 0, instead of the minus +8, minus 16 whole gap, + +and go to 0. + +So we're not going to penalize +for gaps of the edges. + +And then, instead of +requiring the trace back + +to begin at the +bottom right, Smn, + +you allow it to +begin at the highest + +score in the bottom row +or the rightmost column. + +And when you do the +trace back as before, + +these two changes basically find +the optimal global alignment + +but allowing arbitrary +numbers of gaps at the ends + +and just finding the core match. + +It has to go basically +to the end of one + +or the other +sequences, but then you + +can have other residues +hanging off the end + +on the other sequence, if +you want, with no penalty. + +And this sometimes will +give a better answer, + +so it's worth knowing about. + +And it's quite +easy to implement. + +Now what about gapped +local alignments? + +So what if you +have two proteins? + +Do you remember +those two proteins + +where we had the two diagonal? + +I guess they were +diagonal lines. + +How where they? + +Something like that. + +Anyway, diagonal +lines like that. + +So where in this protein on the +vertical, there is a sequence + +here that matches two segments +of the horizontal protein. + +So for those two, you don't want +to do this global alignment. + +It'll get confused. + +It doesn't know whether +to match this guy to this + +or this other one +to the sequence. + +So you want to use +a local alignment. + +So how do we modify this +Needleman-Wunsch algorithm + +to do local alignment? + +Any ideas? + +It's not super hard. + +Yeah, go ahead. + +AUDIENCE: If the score +is going to go negative, + +instead of putting a negative +score, you just put 0, + +and you start from where you get +the highest total score, rather + +than the last +column or last row. + +Start your traceback +from the highest score. + +PROFESSOR: So whenever you're +going negative, you reset to 0. + +Now what does that +remind you of? + +That's the same trick +we did write previously + +with ungapped local alignment. + +So you reset to 0. + +And that's as a no +penalty, because if you're + +going negative, it's better +just to throw that stuff away + +and start over. + +We can do that because +we're doing local alignment. + +We don't have to +align the whole thing. + +So that's allowed. + +And then, rather than going +to the bottom right corner, + +you can be anywhere +in the matrix. + +You look for that highest score +and then do the traceback. + +That's exactly right. + +So it's not that different. + +There are a few +constraints, though, + +now on the scoring system. + +So if you think about the +Needleman-Wunsch algorithm, + +we could actually use a matrix +that had all positive scores. + +You could take +the PAM250 matrix. + +And let's say the +most negative score + +there is, I don't know, +like minus 10 or something, + +and you could just add 10, or +even add 20 to all those score. + +So they're all positive now. + +And you could still +run that algorithm. + +And it would still produce +more or less sensible results. + +I mean, they t wouldn't be +as good as the real PAM250, + +but you would still get +a coherent alignment out + +of the other end. + +But that is no +longer true when you + +talk about the +Smith-Waterman algorithm, + +for the same reason that an +ungapped local alignment, + +we had to require that the +expected score be negative, + +because you have to +have this negative drift + +to find small regions +that go in the positive. + +So if you have this rule, this +kind of permissive that says, + +whenever we go negative +we can just reset to 0, + +then you have to have this +negative drift in order + +for positive scoring +stuff to be unusual. + +All right, so that's +another constraint there. + +You have to have negative +values for mismatches-- I mean, + +not all mismatches. + +But if you took two random +residues in alignment, + +the average score +has to be negative. + +I should probably rephrase +that, but more or less. + +And here's an example +of Smith-Waterman. + +So you right zeroes down the +left side and across the top. + +And that's because, +remember, if you go negative, + +you reset to 0. + +So we're doing that. + +And then you take the +maximum of four things. + +So coming from the diagonal and +adding the score of the match, + +that's the same as before. + +Coming from the left and +adding a gap in one sequence, + +coming from above +and adding a gap + +in the other sequence, or 0. + +This "or 0" business +allows us to reset to 0 + +if we ever go negative. + +And when you have a 0, you still +keep track of these arrows. + +But when you have a +0, there's no arrow. + +You're starting it. + +You're starting the +alignment right there. + +So that's Smith-Waterman. + +It's helpful. + +I think on problem +set one, you'll + +have some experience thinking +about both Needleman-Wunsch + +and Smith-Waterman. + +They sort of behave a +little bit differently, + +but they're highly related. + +So it's important to +understand how they're similar, + +how they're different. + +And what I want to focus on for +the remainder of this lecture + +is just introducing the concept +of amino acid similarity + +matrices. + +We saw that PAM matrix, but +where does it come from? + +And what does it mean? + +And does it work well or not, +and are there alternatives? + +So we could use this +identity matrix. + +But as we've heard, +there are a number + +of reasons why that +may not be optimal. + +For example, the cysteines, we +should surely score them more, + +because they're often +involved in disulfide bonds, + +and those have major structural +effects on the protein + +and are likely to be conserved +more than your average leucine + +or alanine or whatever. + +So clearly, scoring +system should + +favor matching identical or +related amino acids, penalize + +poor matches and for gaps. + +And there's also +an argument that + +can be made that it should +have to do with how often one + +residue is substituted for +another during evolution. + +So that commonly +substituted thing + +should have either positive +scores or less negative + +scores than rarely +substituted things. + +And perhaps not +totally obvious, but it + +is if you think +about it for a while, + +is that any scoring system that +you dream up carries with it + +an implicit model of +molecular evolution + +for how often things +are going to be + +substituted for each other. + +So it's going to turn out +that the score is roughly + +proportional to a +[INAUDIBLE] score + +for the occurrence of +that pair of residues, + +divided by how +often it would occur + +by chance, something like that. + +And so that if you assign +positive scores to things, + +to certain pairs +of residues, you're + +basically implying that +those things will commonly + +interchange during evolution. + +And so if you want to have +realistic, useful scores, + +it helps to think about what the +implicit evolutionary model is + +and whether that is a realistic +model for how proteins evolve. + +So I'm going to come to Dayhoff. + +And so unlike +later matrices, she + +had an explicit +evolutionary model, + +like an actual mathematical +model, for how proteins evolve. + +And the idea was +that there are going + +to be alignments +of some proteins. + +And keep in mind, +this was in 1978. + +So the protein database probably +had like 1,000 proteins in it, + +or something. + +It was very, very small. + +But there were some +alignments that were obvious. + +If you see two protein +segments of 50 residues long + +that are 85 identical, there's +no way that occurred by chance. + +You don't even need to +do statistics on that. + +So you're sure. + +So she took these very high +confidence protein sequence + +alignments, and she calculated +the actual residue residue + +substitution frequencies, how +often we have a valine in one + +sequence as a substitute +for a leucine. + +And it's actually +assumed it's symmetrical. + +Again, you don't +know the direction. + +And calculated these +substitution frequencies. + +Basically estimated +what she called + +a PAM1 one matrix, +which is a matrix that + +implies 1% divergence +between proteins. + +So there's, on average, +only a 1% chance + +any given residue will change. + +And the real alignments had +greater divergence than that. + +They had something +like 15% divergence. + +But you can look at +those frequencies + +and reduce them +by a factor of 15, + +and you'll get not exactly +15 but something like 15. + +And you'll get +something where there's + +a 1% chance of substitution. + +And then once you have that +model for what 1% sequence + +substitution looks +like, turns out + +you can just represent +that as a matrix + +and multiply it up to get a +matrix that describes what + +5% sequence substitution looks +like, or 10% or 50% or 250%. + +So that PAM250 matrix that we +talked about before, that's + +a model for what 250% amino +acid substitution looks like. + +How does that even make sense? + +How can you have more than 100%? + +Is anyone with me on this? + +Tim, yeah. + +AUDIENCE: Because +it can go back. + +So it's more likely, in +some cases, that you revert + +rather than [INAUDIBLE]. + +PROFESSOR: Right. + +So a PAM10 matrix means, on +average, 10% of the residues + +have changed. + +But a few of those +residues might + +have actually-- so maybe about +90% won't have changed at all. + +Some will have +changed once, but some + +might have even changed +twice, even at 10%. + +And when you get to +250%, on average, + +every residue has +changed 2 and 1/2 times. + +But again, a few residues +might have remained the same. + +And some residues that +change-- for example, + +if you had an isoleucine +that mutated to a valine, + +it might have actually changed +back already in that time. + +So it basically accounts for +all those sorts of things. + +And if you have commonly +substituted residues, + +you get that type of +evolution happening. + +All right. + +So she took these protein +sequence alignments-- + +it looks something like +this-- and calculated + +these statistics. + +Again, I don't want to +go through this in detail + +during lecture, because +it's very well described + +in the text. + +But what I do want to do +is introduce this concept + +of a Markov chain, +because it's sort + +of what is underlying +these Dayhoff matrices. + +So let's think about it. + +We'll do more on this next time. + +But imagine that you +were able to sequence + +the genomes of +cartoon characters + +with some newly +developed technology + +and you chose to analyze +the complicated genetics + +of the Simpson lineage. + +I'm assuming you all +know these people. + +This is Grandpa and Homer eating +doughnut and his son, Bart. + +So imagine this is +Grandpa's genome + +at the apolipoprotein A locus. + +And a mutation occurred that +he then passed on to Homer. + +So this mutation occurred in the +germ line, passed on to Homer. + +And then when Homer passed +on his genes to Bart, + +another mutation occurred +here, changing this AT pair + +to a GC pair in Bart. + +So this, I would argue, +is a type of Markov chain. + +So what is a Markov chain? + +So it's just a +stochastic process. + +So a stochastic process +is a random process, + +is sort of the general meaning. + +But here we're +going to be dealing + +with discrete stochastic +processes, which is just + +a sequence of random variables. + +So X1 here is a random variable +that represents, for example, + +the genome of an +individual, or it + +could represent the +genotype, in this case, + +at a particular position, +maybe whether it's an A, + +C, G, or T at one particular +position in the genome. + +And now the index here-- one, +two, three, and so forth-- + +is going to represent time. + +So X1 might be the +genotype in Grandpa Simpson + +at a particular position. + +And X2 might be the +genotype of Homer Simpson. + +And X3 would be the genotype +in the next generation, which + +would be Bart Simpson. + +And what a Markov +chain is is it's + +a particular type of +stochastic process + +that arises commonly in +natural sciences, really, + +and other places +all over the place. + +So it's a good one +to know that has + +what's called the +Markov property. + +And that says that +the probability + +that the next +random variable, or + +the genotype at the next +generation, if you will-- so + +Xn plus 1 equals +some value, j, which + +could be any of the +possible values, + +say any of the four bases, +conditional on the values of X1 + +through Xn, that is the entire +history of the process up + +to that time, is equal to +the conditional probability + +that Xn plus 1 equals j given +only that little xn equals + +some particular value. + +So basically what it says +that if I tell you what + +Homer's genotype +was at this locus, + +and I tell you what Grandpa +Simpson's genotype was at that + +locus, you can just +ignore Grandpa Simpson's. + +That's irrelevant. + +It only matters what +Homer's genotype + +was for the purpose of +predicting Bart's genotype. + +Does that make sense? + +So it really doesn't +matter whether that base + +in Homer's genome was the same +as it was in Grandpa Simpson's + +genome, or whether it +was a mutation that's + +specific to Homer, +because Homer is + +the one who passes +on DNA to Bart. + +Does that make sense? + +So you only look +back one generation. + +It's a type of +memoryless process, + +that you only remember +the last generation. + +That's the only thing +that's relevant. + +And so to understand +Markov chains, + +it's very important +that you all review + +your conditional probability. + +So we're going to do a little +bit more on Markov chains + +next time. + +P A given B, what +does that mean? + +If you don't remember, look +it up in the Probability + +and Statistics, because that's +sort of essential to Markov + +chains. + +So next time we're going to +talk about comparative genomics, + +which will involve some +applications of some + +of the alignment methods that +we've been talking about. + +And I may post some examples of +interesting comparative genomic + +research papers, which are +going to be optional reading. + +You may get a little more out +of the lecture if you read them, + +but it's not essential. \ No newline at end of file diff --git a/PgMAfWpOuf0.txt b/PgMAfWpOuf0.txt new file mode 100644 index 0000000000000000000000000000000000000000..bb94f877143fa5d8c5cd5fc488e08268ba084555 --- /dev/null +++ b/PgMAfWpOuf0.txt @@ -0,0 +1,6547 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +where we left off yesterday was + + align:start position:0% +where we left off yesterday was + + + align:start position:0% +where we left off yesterday was +beginning to discuss methods for + + align:start position:0% +beginning to discuss methods for + + + align:start position:0% +beginning to discuss methods for +unnatural and you know asset + + align:start position:0% +unnatural and you know asset + + + align:start position:0% +unnatural and you know asset +incorporation into proteins using the + + align:start position:0% +incorporation into proteins using the + + + align:start position:0% +incorporation into proteins using the +ribosome and the methodology that was + + align:start position:0% +ribosome and the methodology that was + + + align:start position:0% +ribosome and the methodology that was +introduced and where we need to continue + + align:start position:0% +introduced and where we need to continue + + + align:start position:0% +introduced and where we need to continue +today is the shelfs schultz method of + + align:start position:0% +today is the shelfs schultz method of + + + align:start position:0% +today is the shelfs schultz method of +using the native ribosome it could play + + align:start position:0% +using the native ribosome it could play + + + align:start position:0% +using the native ribosome it could play +some tricks and get unnatural amino + + align:start position:0% +some tricks and get unnatural amino + + + align:start position:0% +some tricks and get unnatural amino +acids into proteins so we'll work + + align:start position:0% +acids into proteins so we'll work + + + align:start position:0% +acids into proteins so we'll work +through this further to show how the + + align:start position:0% +through this further to show how the + + + align:start position:0% +through this further to show how the +rest of the machinery was generated and + + align:start position:0% +rest of the machinery was generated and + + + align:start position:0% +rest of the machinery was generated and +then we'll consider some of the + + align:start position:0% +then we'll consider some of the + + + align:start position:0% +then we'll consider some of the +limitations and some of that came up in + + align:start position:0% +limitations and some of that came up in + + + align:start position:0% +limitations and some of that came up in +questions last time and then we'll close + + align:start position:0% +questions last time and then we'll close + + + align:start position:0% +questions last time and then we'll close +with the discussion of one strategy + + align:start position:0% +with the discussion of one strategy + + + align:start position:0% +with the discussion of one strategy +that's a different strategy that uses + + align:start position:0% +that's a different strategy that uses + + + align:start position:0% +that's a different strategy that uses +actually an orthogonal ribosome which is + + align:start position:0% +actually an orthogonal ribosome which is + + + align:start position:0% +actually an orthogonal ribosome which is +really really neat here so where are we + + align:start position:0% +really really neat here so where are we + + + align:start position:0% +really really neat here so where are we +left off last time in terms of this + + align:start position:0% +left off last time in terms of this + + + align:start position:0% +left off last time in terms of this +Shultz method right was that we needed a + + align:start position:0% +Shultz method right was that we needed a + + + align:start position:0% +Shultz method right was that we needed a +unique codon for the unnatural amino + + align:start position:0% +unique codon for the unnatural amino + + + align:start position:0% +unique codon for the unnatural amino +acid right and a stop codon was + + align:start position:0% +acid right and a stop codon was + + + align:start position:0% +acid right and a stop codon was +reassigned + + align:start position:0% + + + + align:start position:0% + +okay so TIG or amber stop and the other + + align:start position:0% +okay so TIG or amber stop and the other + + + align:start position:0% +okay so TIG or amber stop and the other +thing that we need that we'll discuss + + align:start position:0% +thing that we need that we'll discuss + + + align:start position:0% +thing that we need that we'll discuss +now involves the requirement and or of + + align:start position:0% +now involves the requirement and or of + + + align:start position:0% +now involves the requirement and or of +an orthogonal tRNA and amino acyl tRNA + + align:start position:0% +an orthogonal tRNA and amino acyl tRNA + + + align:start position:0% +an orthogonal tRNA and amino acyl tRNA +synthetase pair that can be used in this + + align:start position:0% +synthetase pair that can be used in this + + + align:start position:0% +synthetase pair that can be used in this +method + + align:start position:0% + + + + align:start position:0% + +okay so the question is where does this + + align:start position:0% +okay so the question is where does this + + + align:start position:0% +okay so the question is where does this +come from + + align:start position:0% +come from + + + align:start position:0% +come from +so where do we get a tRNA and an a a RS + + align:start position:0% +so where do we get a tRNA and an a a RS + + + align:start position:0% +so where do we get a tRNA and an a a RS +that can be used for this unnatural + + align:start position:0% +that can be used for this unnatural + + + align:start position:0% +that can be used for this unnatural +amino acid of interest and one way to + + align:start position:0% +amino acid of interest and one way to + + + align:start position:0% +amino acid of interest and one way to +think about this in terms of a search is + + align:start position:0% +think about this in terms of a search is + + + align:start position:0% +think about this in terms of a search is +to think about different tRNA s and a a + + align:start position:0% +to think about different tRNA s and a a + + + align:start position:0% +to think about different tRNA s and a a +RS from different organisms and so + + align:start position:0% +RS from different organisms and so + + + align:start position:0% +RS from different organisms and so +what's found if T RNAs are compared + + align:start position:0% +what's found if T RNAs are compared + + + align:start position:0% +what's found if T RNAs are compared +between bacteria eukaryotes are key + + align:start position:0% +between bacteria eukaryotes are key + + + align:start position:0% +between bacteria eukaryotes are key +there's evolutionary divergence and so + + align:start position:0% +there's evolutionary divergence and so + + + align:start position:0% +there's evolutionary divergence and so +cannot evolutionary divergence be taken + + align:start position:0% +cannot evolutionary divergence be taken + + + align:start position:0% +cannot evolutionary divergence be taken +advantage of and effectively is it + + align:start position:0% +advantage of and effectively is it + + + align:start position:0% +advantage of and effectively is it +possible to find some tRNA and its amino + + align:start position:0% +possible to find some tRNA and its amino + + + align:start position:0% +possible to find some tRNA and its amino +acyl tRNA synthetase from one organism + + align:start position:0% +acyl tRNA synthetase from one organism + + + align:start position:0% +acyl tRNA synthetase from one organism +that's orthogonal to the corresponding + + align:start position:0% +that's orthogonal to the corresponding + + + align:start position:0% +that's orthogonal to the corresponding +tRNA an amino acyl tRNA synthesis case + + align:start position:0% +tRNA an amino acyl tRNA synthesis case + + + align:start position:0% +tRNA an amino acyl tRNA synthesis case +in the organism of interest so + + align:start position:0% +in the organism of interest so + + + align:start position:0% +in the organism of interest so +effectively if we want to use ecoli we + + align:start position:0% +effectively if we want to use ecoli we + + + align:start position:0% +effectively if we want to use ecoli we +want to find a pair from another + + align:start position:0% +want to find a pair from another + + + align:start position:0% +want to find a pair from another +organism that's completely independent + + align:start position:0% +organism that's completely independent + + + align:start position:0% +organism that's completely independent +of the endogenous ecoli machinery so + + align:start position:0% +of the endogenous ecoli machinery so + + + align:start position:0% +of the endogenous ecoli machinery so +what does this mean a lot of trial and + + align:start position:0% +what does this mean a lot of trial and + + + align:start position:0% +what does this mean a lot of trial and +error was done to identify a pair from + + align:start position:0% +error was done to identify a pair from + + + align:start position:0% +error was done to identify a pair from +another organism and where they ended up + + align:start position:0% +another organism and where they ended up + + + align:start position:0% +another organism and where they ended up +finding one is from Ameth antigen some + + align:start position:0% +finding one is from Ameth antigen some + + + align:start position:0% +finding one is from Ameth antigen some +account mechana caucus gin our CI here + + align:start position:0% + + + + align:start position:0% + +okay and this initial pair was for + + align:start position:0% +okay and this initial pair was for + + + align:start position:0% +okay and this initial pair was for +tyrosine and so there's some features of + + align:start position:0% +tyrosine and so there's some features of + + + align:start position:0% +tyrosine and so there's some features of +this pair that are noteworthy to bring + + align:start position:0% +this pair that are noteworthy to bring + + + align:start position:0% +this pair that are noteworthy to bring +up so first if we think about the amino + + align:start position:0% +up so first if we think about the amino + + + align:start position:0% +up so first if we think about the amino +acyl tRNA synthetase here this one has + + align:start position:0% +acyl tRNA synthetase here this one has + + + align:start position:0% +acyl tRNA synthetase here this one has +an unusual feature so when we discussed + + align:start position:0% +an unusual feature so when we discussed + + + align:start position:0% +an unusual feature so when we discussed +these aar s remember we discussed the + + align:start position:0% +these aar s remember we discussed the + + + align:start position:0% +these aar s remember we discussed the +mechanism and we also discussed what + + align:start position:0% +mechanism and we also discussed what + + + align:start position:0% +mechanism and we also discussed what +happens if a wrong amino acid is + + align:start position:0% +happens if a wrong amino acid is + + + align:start position:0% +happens if a wrong amino acid is +selected and we learned that they have + + align:start position:0% +selected and we learned that they have + + + align:start position:0% +selected and we learned that they have +editing function right and that there's + + align:start position:0% +editing function right and that there's + + + align:start position:0% +editing function right and that there's +editing domains what also came up in + + align:start position:0% +editing domains what also came up in + + + align:start position:0% +editing domains what also came up in +those discussions is that we need to + + align:start position:0% +those discussions is that we need to + + + align:start position:0% +those discussions is that we need to +take every one of these enzymes as a + + align:start position:0% +take every one of these enzymes as a + + + align:start position:0% +take every one of these enzymes as a +case-by-case basis and as it turns out + + align:start position:0% +case-by-case basis and as it turns out + + + align:start position:0% +case-by-case basis and as it turns out +this particular enzyme does not have an + + align:start position:0% +this particular enzyme does not have an + + + align:start position:0% +this particular enzyme does not have an +editing domain so then the thing to + + align:start position:0% +editing domain so then the thing to + + + align:start position:0% +editing domain so then the thing to +think about is why would that be useful + + align:start position:0% +think about is why would that be useful + + + align:start position:0% +think about is why would that be useful +from the standpoint of incorporating an + + align:start position:0% +from the standpoint of incorporating an + + + align:start position:0% +from the standpoint of incorporating an +unnatural amino acid so what's the + + align:start position:0% +unnatural amino acid so what's the + + + align:start position:0% +unnatural amino acid so what's the +benefit there + + align:start position:0% + + + + align:start position:0% + +so what does this editing domain do + + align:start position:0% + + + + align:start position:0% + +it's one less than the other domain + + align:start position:0% +it's one less than the other domain + + + align:start position:0% +it's one less than the other domain +we're recognizing hydrolyzed and + + align:start position:0% +we're recognizing hydrolyzed and + + + align:start position:0% +we're recognizing hydrolyzed and +unnatural amino acid that you put in + + align:start position:0% +unnatural amino acid that you put in + + + align:start position:0% +unnatural amino acid that you put in +even if you have the binding site to + + align:start position:0% +even if you have the binding site to + + + align:start position:0% +even if you have the binding site to +recognize it a little bit first finding + + align:start position:0% +recognize it a little bit first finding + + + align:start position:0% +recognize it a little bit first finding +site to recognize it exactly right + + align:start position:0% +site to recognize it exactly right + + + align:start position:0% +site to recognize it exactly right +there's an OB isolation happening so no + + align:start position:0% +there's an OB isolation happening so no + + + align:start position:0% +there's an OB isolation happening so no +hydrolysis so it's just more likely this + + align:start position:0% +hydrolysis so it's just more likely this + + + align:start position:0% +hydrolysis so it's just more likely this +I'm not truly immuno acid can be a + + align:start position:0% +I'm not truly immuno acid can be a + + + align:start position:0% +I'm not truly immuno acid can be a +successful substrate and there's less + + align:start position:0% +successful substrate and there's less + + + align:start position:0% +successful substrate and there's less +engineering that has to be done in terms + + align:start position:0% +engineering that has to be done in terms + + + align:start position:0% +engineering that has to be done in terms +of modifying the enzyme here so another + + align:start position:0% +of modifying the enzyme here so another + + + align:start position:0% +of modifying the enzyme here so another +point in terms of they cone that it does + + align:start position:0% +point in terms of they cone that it does + + + align:start position:0% +point in terms of they cone that it does +not a silly ecoli tRNA okay and that's + + align:start position:0% +not a silly ecoli tRNA okay and that's + + + align:start position:0% +not a silly ecoli tRNA okay and that's +important for trying to use this in + + align:start position:0% +important for trying to use this in + + + align:start position:0% +important for trying to use this in +e.coli here what's the potential problem + + align:start position:0% + + + + align:start position:0% + +so is this going to be specific for the + + align:start position:0% +so is this going to be specific for the + + + align:start position:0% +so is this going to be specific for the +unnatural amino acid of interest no way + + align:start position:0% +unnatural amino acid of interest no way + + + align:start position:0% +unnatural amino acid of interest no way +right it unlikely at least and depending + + align:start position:0% +right it unlikely at least and depending + + + align:start position:0% +right it unlikely at least and depending +on what type of unnatural amino acid + + align:start position:0% +on what type of unnatural amino acid + + + align:start position:0% +on what type of unnatural amino acid +you're thinking about it may definitely + + align:start position:0% +you're thinking about it may definitely + + + align:start position:0% +you're thinking about it may definitely +be in no way right so there's some + + align:start position:0% +be in no way right so there's some + + + align:start position:0% +be in no way right so there's some +experimental work to do to make this + + align:start position:0% +experimental work to do to make this + + + align:start position:0% +experimental work to do to make this +specific for the unnatural amino acid of + + align:start position:0% +specific for the unnatural amino acid of + + + align:start position:0% +specific for the unnatural amino acid of +interest which means there has to be + + align:start position:0% +interest which means there has to be + + + align:start position:0% +interest which means there has to be +some mutagenesis and selection which + + align:start position:0% +some mutagenesis and selection which + + + align:start position:0% +some mutagenesis and selection which +we're not going to talk about in detail + + align:start position:0% +we're not going to talk about in detail + + + align:start position:0% +we're not going to talk about in detail +here so what about the tRNA + + align:start position:0% + + + + align:start position:0% + +so we need to think about the tRNA + + align:start position:0% +so we need to think about the tRNA + + + align:start position:0% +so we need to think about the tRNA +structure right and how tRNAs interact + + align:start position:0% +structure right and how tRNAs interact + + + align:start position:0% +structure right and how tRNAs interact +with a ARS right and recall we had in an + + align:start position:0% +with a ARS right and recall we had in an + + + align:start position:0% +with a ARS right and recall we had in an +earlier lecture one example of a crystal + + align:start position:0% +earlier lecture one example of a crystal + + + align:start position:0% +earlier lecture one example of a crystal +structure of this complex and we saw + + align:start position:0% +structure of this complex and we saw + + + align:start position:0% +structure of this complex and we saw +there's many positions where they + + align:start position:0% +there's many positions where they + + + align:start position:0% +there's many positions where they +interact what was known in this system + + align:start position:0% +interact what was known in this system + + + align:start position:0% +interact what was known in this system +here is that they figured okay and also + + align:start position:0% +here is that they figured okay and also + + + align:start position:0% +here is that they figured okay and also +keep in mind just backing up them and at + + align:start position:0% +keep in mind just backing up them and at + + + align:start position:0% +keep in mind just backing up them and at +this tRNA as we know based on this + + align:start position:0% +this tRNA as we know based on this + + + align:start position:0% +this tRNA as we know based on this +nomenclature has an anticodon for + + align:start position:0% +nomenclature has an anticodon for + + + align:start position:0% +nomenclature has an anticodon for +tyrosine right so that's gonna have to + + align:start position:0% +tyrosine right so that's gonna have to + + + align:start position:0% +tyrosine right so that's gonna have to +be mutated to be the anticodon for the + + align:start position:0% +be mutated to be the anticodon for the + + + align:start position:0% +be mutated to be the anticodon for the +amber stop in order to use in this + + align:start position:0% +amber stop in order to use in this + + + align:start position:0% +amber stop in order to use in this +method right so this is going to have to + + align:start position:0% +method right so this is going to have to + + + align:start position:0% +method right so this is going to have to +be mutated right to give us tRNA CUA + + align:start position:0% +be mutated right to give us tRNA CUA + + + align:start position:0% +be mutated right to give us tRNA CUA +okay where this is indicating the + + align:start position:0% +okay where this is indicating the + + + align:start position:0% +okay where this is indicating the +anticodon here so that mutation we don't + + align:start position:0% +anticodon here so that mutation we don't + + + align:start position:0% +anticodon here so that mutation we don't +want that mutation to disrupt the + + align:start position:0% +want that mutation to disrupt the + + + align:start position:0% +want that mutation to disrupt the +interaction between the tRNA and the + + align:start position:0% +interaction between the tRNA and the + + + align:start position:0% +interaction between the tRNA and the +amino acyl tRNA synthetase right and it + + align:start position:0% +amino acyl tRNA synthetase right and it + + + align:start position:0% +amino acyl tRNA synthetase right and it +turns out there were minimal + + align:start position:0% +turns out there were minimal + + + align:start position:0% +turns out there were minimal +interactions in that area for the native + + align:start position:0% +interactions in that area for the native + + + align:start position:0% +interactions in that area for the native +system so the thinking was that these + + align:start position:0% +system so the thinking was that these + + + align:start position:0% +system so the thinking was that these +mutations could be tolerated here so + + align:start position:0% +mutations could be tolerated here so + + + align:start position:0% +mutations could be tolerated here so +with that said what is the potential + + align:start position:0% +with that said what is the potential + + + align:start position:0% +with that said what is the potential +problem with this tRNA + + align:start position:0% + + + + align:start position:0% + +so if we want to put this trna into + + align:start position:0% +so if we want to put this trna into + + + align:start position:0% +so if we want to put this trna into +e.coli right it can't be recognized by + + align:start position:0% +e.coli right it can't be recognized by + + + align:start position:0% +e.coli right it can't be recognized by +any of the e.coli aar s so all of these + + align:start position:0% +any of the e.coli aar s so all of these + + + align:start position:0% +any of the e.coli aar s so all of these +recognition issues come up + + align:start position:0% +recognition issues come up + + + align:start position:0% +recognition issues come up +so here again with another example where + + align:start position:0% +so here again with another example where + + + align:start position:0% +so here again with another example where +there needed to be some mutagenesis and + + align:start position:0% +there needed to be some mutagenesis and + + + align:start position:0% +there needed to be some mutagenesis and +selection to prevent interactions + + align:start position:0% +selection to prevent interactions + + + align:start position:0% +selection to prevent interactions +between this trna from the meth antigen + + align:start position:0% +between this trna from the meth antigen + + + align:start position:0% +between this trna from the meth antigen +and the aar s sub e coli and effectively + + align:start position:0% +and the aar s sub e coli and effectively + + + align:start position:0% +and the aar s sub e coli and effectively +what they did is to pick eleven + + align:start position:0% +what they did is to pick eleven + + + align:start position:0% +what they did is to pick eleven +positions on the tRNA which I'll just + + align:start position:0% +positions on the tRNA which I'll just + + + align:start position:0% +positions on the tRNA which I'll just +chart out okay so here's our tRNA here's + + align:start position:0% +chart out okay so here's our tRNA here's + + + align:start position:0% +chart out okay so here's our tRNA here's +our CUA anticodon here right and + + align:start position:0% +our CUA anticodon here right and + + + align:start position:0% +our CUA anticodon here right and +effectively these ends are positions + + align:start position:0% +effectively these ends are positions + + + align:start position:0% +effectively these ends are positions +where they randomized and did + + align:start position:0% +where they randomized and did + + + align:start position:0% +where they randomized and did +mutagenesis + + align:start position:0% + + + + align:start position:0% + +okay so they identified these eleven + + align:start position:0% +okay so they identified these eleven + + + align:start position:0% +okay so they identified these eleven +positions okay + + align:start position:0% +positions okay + + + align:start position:0% +positions okay +and these eleven positions do not + + align:start position:0% +and these eleven positions do not + + + align:start position:0% +and these eleven positions do not +interact with the a a RS here of the + + align:start position:0% +interact with the a a RS here of the + + + align:start position:0% +interact with the a a RS here of the +pair right so the idea is to maintain + + align:start position:0% +pair right so the idea is to maintain + + + align:start position:0% +pair right so the idea is to maintain +this interaction but prevent any + + align:start position:0% +this interaction but prevent any + + + align:start position:0% +this interaction but prevent any +interaction of this tRNA with e.coli + + align:start position:0% +interaction of this tRNA with e.coli + + + align:start position:0% +interaction of this tRNA with e.coli +machinery here so effectively they used + + align:start position:0% +machinery here so effectively they used + + + align:start position:0% +machinery here so effectively they used +a method called directed evolution to do + + align:start position:0% + + + + align:start position:0% + +selection and what might happen out of + + align:start position:0% +selection and what might happen out of + + + align:start position:0% +selection and what might happen out of +that right imagine you have some large + + align:start position:0% +that right imagine you have some large + + + align:start position:0% +that right imagine you have some large +pool of mutant tRNAs what might happen + + align:start position:0% +pool of mutant tRNAs what might happen + + + align:start position:0% +pool of mutant tRNAs what might happen +right so here + + align:start position:0% + + + + align:start position:0% + +okay so the end result is that the tRNA + + align:start position:0% + + + + align:start position:0% + +might be non-functional right so the + + align:start position:0% +might be non-functional right so the + + + align:start position:0% +might be non-functional right so the +mutation was not helpful okay it might + + align:start position:0% +mutation was not helpful okay it might + + + align:start position:0% +mutation was not helpful okay it might +be non-orthogonal + + align:start position:0% + + + + align:start position:0% + +okay meaning that is recognized by the + + align:start position:0% +okay meaning that is recognized by the + + + align:start position:0% +okay meaning that is recognized by the +endogenous you call a machinery or it + + align:start position:0% +endogenous you call a machinery or it + + + align:start position:0% +endogenous you call a machinery or it +may be orthogonal here + + align:start position:0% +may be orthogonal here + + + align:start position:0% +may be orthogonal here +okay so recognized only okay and so this + + align:start position:0% +okay so recognized only okay and so this + + + align:start position:0% +okay so recognized only okay and so this +is what we needs to be selected for here + + align:start position:0% +is what we needs to be selected for here + + + align:start position:0% +is what we needs to be selected for here +okay and so assays need to be done that + + align:start position:0% +okay and so assays need to be done that + + + align:start position:0% +okay and so assays need to be done that +allows these to be differentiated here + + align:start position:0% + + + + align:start position:0% + +so the end result is an orthogonal pair + + align:start position:0% +so the end result is an orthogonal pair + + + align:start position:0% +so the end result is an orthogonal pair +but the point is you can't just take + + align:start position:0% +but the point is you can't just take + + + align:start position:0% +but the point is you can't just take +this pair from the other organism if it + + align:start position:0% +this pair from the other organism if it + + + align:start position:0% +this pair from the other organism if it +needs to be further modified so where + + align:start position:0% +needs to be further modified so where + + + align:start position:0% +needs to be further modified so where +does that put us in terms of the cartoon + + align:start position:0% +does that put us in terms of the cartoon + + + align:start position:0% +does that put us in terms of the cartoon +we saw yesterday without some of these + + align:start position:0% +we saw yesterday without some of these + + + align:start position:0% +we saw yesterday without some of these +details right so here we have the tRNA + + align:start position:0% +details right so here we have the tRNA + + + align:start position:0% +details right so here we have the tRNA +that has this amber anticodon so that + + align:start position:0% +that has this amber anticodon so that + + + align:start position:0% +that has this amber anticodon so that +sort of our thuggin old tRNA we have an + + align:start position:0% +sort of our thuggin old tRNA we have an + + + align:start position:0% +sort of our thuggin old tRNA we have an +unnatural amino acid that's able to get + + align:start position:0% +unnatural amino acid that's able to get + + + align:start position:0% +unnatural amino acid that's able to get +into the organism of interest and we + + align:start position:0% +into the organism of interest and we + + + align:start position:0% +into the organism of interest and we +have the orthogonal tRNA synthetase + + align:start position:0% +have the orthogonal tRNA synthetase + + + align:start position:0% +have the orthogonal tRNA synthetase +right so these give us this amino acyl + + align:start position:0% +right so these give us this amino acyl + + + align:start position:0% +right so these give us this amino acyl +tRNA with the unnatural amino acid and + + align:start position:0% +tRNA with the unnatural amino acid and + + + align:start position:0% +tRNA with the unnatural amino acid and +then that can be incorporated into the a + + align:start position:0% +then that can be incorporated into the a + + + align:start position:0% +then that can be incorporated into the a +site of the ribosome right so this is a + + align:start position:0% +site of the ribosome right so this is a + + + align:start position:0% +site of the ribosome right so this is a +case where we have a plasmid DNA here's + + align:start position:0% +case where we have a plasmid DNA here's + + + align:start position:0% +case where we have a plasmid DNA here's +the gene of interest in red and + + align:start position:0% +the gene of interest in red and + + + align:start position:0% +the gene of interest in red and +somewhere in that + + align:start position:0% +somewhere in that + + + align:start position:0% +somewhere in that +and stop codon has been placed to allow + + align:start position:0% +and stop codon has been placed to allow + + + align:start position:0% +and stop codon has been placed to allow +for incorporation of this unnatural + + align:start position:0% +for incorporation of this unnatural + + + align:start position:0% +for incorporation of this unnatural +amino acid somewhere within the + + align:start position:0% +amino acid somewhere within the + + + align:start position:0% +amino acid somewhere within the +polypeptide chain is shown here okay + + align:start position:0% +polypeptide chain is shown here okay + + + align:start position:0% +polypeptide chain is shown here okay +so if we think about the scope of this + + align:start position:0% +so if we think about the scope of this + + + align:start position:0% +so if we think about the scope of this +methodology where does this take us + + align:start position:0% +methodology where does this take us + + + align:start position:0% +methodology where does this take us +so it's quite broad this type of work + + align:start position:0% +so it's quite broad this type of work + + + align:start position:0% +so it's quite broad this type of work +has been applied beyond e.coli so in + + align:start position:0% +has been applied beyond e.coli so in + + + align:start position:0% +has been applied beyond e.coli so in +yeast and mammalian cells at present + + align:start position:0% +yeast and mammalian cells at present + + + align:start position:0% +yeast and mammalian cells at present +there's many many different unnatural + + align:start position:0% +there's many many different unnatural + + + align:start position:0% +there's many many different unnatural +amino acids that can be incorporated and + + align:start position:0% +amino acids that can be incorporated and + + + align:start position:0% +amino acids that can be incorporated and +it's used by many labs so that's + + align:start position:0% +it's used by many labs so that's + + + align:start position:0% +it's used by many labs so that's +something to keep in mind if you're + + align:start position:0% +something to keep in mind if you're + + + align:start position:0% +something to keep in mind if you're +developing a new method you'd really + + align:start position:0% +developing a new method you'd really + + + align:start position:0% +developing a new method you'd really +like other folks in other labs to be + + align:start position:0% +like other folks in other labs to be + + + align:start position:0% +like other folks in other labs to be +able to use your method there's a lot of + + align:start position:0% +able to use your method there's a lot of + + + align:start position:0% +able to use your method there's a lot of +troubleshooting to do experimentally to + + align:start position:0% +troubleshooting to do experimentally to + + + align:start position:0% +troubleshooting to do experimentally to +get it up and running and Joanne's a + + align:start position:0% +get it up and running and Joanne's a + + + align:start position:0% +get it up and running and Joanne's a +wonderful person to talk about that if + + align:start position:0% +wonderful person to talk about that if + + + align:start position:0% +wonderful person to talk about that if +you're curious for details just some + + align:start position:0% +you're curious for details just some + + + align:start position:0% +you're curious for details just some +amino acids scope and you know what + + align:start position:0% +amino acids scope and you know what + + + align:start position:0% +amino acids scope and you know what +maybe we could do so these are some + + align:start position:0% +maybe we could do so these are some + + + align:start position:0% +maybe we could do so these are some +earlier examples of unnatural amino + + align:start position:0% +earlier examples of unnatural amino + + + align:start position:0% +earlier examples of unnatural amino +acids that can be incorporated and what + + align:start position:0% +acids that can be incorporated and what + + + align:start position:0% +acids that can be incorporated and what +are some of the neat things if we look + + align:start position:0% +are some of the neat things if we look + + + align:start position:0% +are some of the neat things if we look +just here for example there's an azide + + align:start position:0% +just here for example there's an azide + + + align:start position:0% +just here for example there's an azide +why might we want an azide you know + + align:start position:0% +why might we want an azide you know + + + align:start position:0% +why might we want an azide you know +click chemistry right some chemistry + + align:start position:0% +click chemistry right some chemistry + + + align:start position:0% +click chemistry right some chemistry +that could be done after protein + + align:start position:0% +that could be done after protein + + + align:start position:0% +that could be done after protein +expression or maybe in a cell here we + + align:start position:0% +expression or maybe in a cell here we + + + align:start position:0% +expression or maybe in a cell here we +have a benzophenone + + align:start position:0% +have a benzophenone + + + align:start position:0% +have a benzophenone +so they're useful for cross-linking + + align:start position:0% +so they're useful for cross-linking + + + align:start position:0% +so they're useful for cross-linking +experiments and will likely talk about + + align:start position:0% +experiments and will likely talk about + + + align:start position:0% +experiments and will likely talk about +and then so phenom cross-linking and + + align:start position:0% +and then so phenom cross-linking and + + + align:start position:0% +and then so phenom cross-linking and +recitation thighs in detail we see some + + align:start position:0% +recitation thighs in detail we see some + + + align:start position:0% +recitation thighs in detail we see some +sugars here this is a downsell group + + align:start position:0% +sugars here this is a downsell group + + + align:start position:0% +sugars here this is a downsell group +that's a fluorophore + + align:start position:0% +that's a fluorophore + + + align:start position:0% +that's a fluorophore +so there's many possibilities here just + + align:start position:0% +so there's many possibilities here just + + + align:start position:0% +so there's many possibilities here just +looking at these molecules what's + + align:start position:0% +looking at these molecules what's + + + align:start position:0% +looking at these molecules what's +something similar about all of them + + align:start position:0% + + + + align:start position:0% + +we think about them compared to to a + + align:start position:0% +we think about them compared to to a + + + align:start position:0% +we think about them compared to to a +native amino-acid they're small okay + + align:start position:0% +native amino-acid they're small okay + + + align:start position:0% +native amino-acid they're small okay +they're quite small so they're sort of + + align:start position:0% +they're quite small so they're sort of + + + align:start position:0% +they're quite small so they're sort of +phenylalanine or tyrosine like right and + + align:start position:0% +phenylalanine or tyrosine like right and + + + align:start position:0% +phenylalanine or tyrosine like right and +does that make sense right from the + + align:start position:0% +does that make sense right from the + + + align:start position:0% +does that make sense right from the +standpoint of using this machinery + + align:start position:0% +standpoint of using this machinery + + + align:start position:0% +standpoint of using this machinery +initially yes right and you can imagine + + align:start position:0% +initially yes right and you can imagine + + + align:start position:0% +initially yes right and you can imagine +looking for other pairs to put in other + + align:start position:0% +looking for other pairs to put in other + + + align:start position:0% +looking for other pairs to put in other +types of unnatural amino acids right so + + align:start position:0% +types of unnatural amino acids right so + + + align:start position:0% +types of unnatural amino acids right so +that's reflective there just as some + + align:start position:0% +that's reflective there just as some + + + align:start position:0% +that's reflective there just as some +further examples so this is another + + align:start position:0% +further examples so this is another + + + align:start position:0% +further examples so this is another +example of using an unnatural amino acid + + align:start position:0% +example of using an unnatural amino acid + + + align:start position:0% +example of using an unnatural amino acid +that can be useful for for click + + align:start position:0% +that can be useful for for click + + + align:start position:0% +that can be useful for for click +chemistry right and I picked this in + + align:start position:0% +chemistry right and I picked this in + + + align:start position:0% +chemistry right and I picked this in +part for one this unnatural amino acid + + align:start position:0% +part for one this unnatural amino acid + + + align:start position:0% +part for one this unnatural amino acid +looks very different than the ones we + + align:start position:0% +looks very different than the ones we + + + align:start position:0% +looks very different than the ones we +saw in the prior slide right but there's + + align:start position:0% +saw in the prior slide right but there's + + + align:start position:0% +saw in the prior slide right but there's +an amino acyl tRNA synthetase and the + + align:start position:0% +an amino acyl tRNA synthetase and the + + + align:start position:0% +an amino acyl tRNA synthetase and the +tRNA for this alkyne and so you can + + align:start position:0% +tRNA for this alkyne and so you can + + + align:start position:0% +tRNA for this alkyne and so you can +imagine expressing a protein with this + + align:start position:0% +imagine expressing a protein with this + + + align:start position:0% +imagine expressing a protein with this +at a specific location and then after + + align:start position:0% +at a specific location and then after + + + align:start position:0% +at a specific location and then after +the fact clicking on a molecule like + + align:start position:0% +the fact clicking on a molecule like + + + align:start position:0% +the fact clicking on a molecule like +this flora for here right so just + + align:start position:0% +this flora for here right so just + + + align:start position:0% +this flora for here right so just +thinking about this process why maybe + + align:start position:0% +thinking about this process why maybe + + + align:start position:0% +thinking about this process why maybe +with this put on later rather than in + + align:start position:0% +with this put on later rather than in + + + align:start position:0% +with this put on later rather than in +the cell + + align:start position:0% + + + + align:start position:0% + +do you mean clicking it on or + + align:start position:0% +do you mean clicking it on or + + + align:start position:0% +do you mean clicking it on or +synthesizer putting that whole thing + + align:start position:0% +synthesizer putting that whole thing + + + align:start position:0% +synthesizer putting that whole thing +yeah right cuz you can imagine someone + + align:start position:0% +yeah right cuz you can imagine someone + + + align:start position:0% +yeah right cuz you can imagine someone +could have thought rather than clicking + + align:start position:0% +could have thought rather than clicking + + + align:start position:0% +could have thought rather than clicking +this on after the fact why not just use + + align:start position:0% +this on after the fact why not just use + + + align:start position:0% +this on after the fact why not just use +this whole moiety here as the unnatural + + align:start position:0% +this whole moiety here as the unnatural + + + align:start position:0% +this whole moiety here as the unnatural +amino acid right so this flora for it + + align:start position:0% +amino acid right so this flora for it + + + align:start position:0% +amino acid right so this flora for it +might be hard to find a synth apace yeah + + align:start position:0% +might be hard to find a synth apace yeah + + + align:start position:0% +might be hard to find a synth apace yeah +I'm just asking you to think about this + + align:start position:0% +I'm just asking you to think about this + + + align:start position:0% +I'm just asking you to think about this +right so you know what what needs to be + + align:start position:0% +right so you know what what needs to be + + + align:start position:0% +right so you know what what needs to be +thought about right so here there's + + align:start position:0% +thought about right so here there's + + + align:start position:0% +thought about right so here there's +still a chemical step after this + + align:start position:0% +still a chemical step after this + + + align:start position:0% +still a chemical step after this +unnatural amino acid was put in and in + + align:start position:0% +unnatural amino acid was put in and in + + + align:start position:0% +unnatural amino acid was put in and in +this case why might that be + + align:start position:0% +this case why might that be + + + align:start position:0% +this case why might that be +right maybe it's a permeability issue + + align:start position:0% +right maybe it's a permeability issue + + + align:start position:0% +right maybe it's a permeability issue +right we don't know if that molecule + + align:start position:0% +right we don't know if that molecule + + + align:start position:0% +right we don't know if that molecule +readily taken up by the organism is it a + + align:start position:0% +readily taken up by the organism is it a + + + align:start position:0% +readily taken up by the organism is it a +size issue that it's hard to get + + align:start position:0% +size issue that it's hard to get + + + align:start position:0% +size issue that it's hard to get +machinery to accommodate this this type + + align:start position:0% +machinery to accommodate this this type + + + align:start position:0% +machinery to accommodate this this type +of molecule there folding + + align:start position:0% + + + + align:start position:0% + +process maybe I'm not stopping because + + align:start position:0% +process maybe I'm not stopping because + + + align:start position:0% +process maybe I'm not stopping because +it's not + + align:start position:0% + + + + align:start position:0% + +right so can the polypeptide reach its + + align:start position:0% +right so can the polypeptide reach its + + + align:start position:0% +right so can the polypeptide reach its +native conformation with this + + align:start position:0% +native conformation with this + + + align:start position:0% +native conformation with this +perturbation just to think about and + + align:start position:0% +perturbation just to think about and + + + align:start position:0% +perturbation just to think about and +here are just some examples of unnatural + + align:start position:0% +here are just some examples of unnatural + + + align:start position:0% +here are just some examples of unnatural +amino acids that can be used for + + align:start position:0% +amino acids that can be used for + + + align:start position:0% +amino acids that can be used for +fluorine NMR as was mentioned last time + + align:start position:0% +fluorine NMR as was mentioned last time + + + align:start position:0% +fluorine NMR as was mentioned last time +ok so this is all really exciting but + + align:start position:0% +ok so this is all really exciting but + + + align:start position:0% +ok so this is all really exciting but +what is the limitation and there's a + + align:start position:0% +what is the limitation and there's a + + + align:start position:0% +what is the limitation and there's a +major limitation of this methodology as + + align:start position:0% +major limitation of this methodology as + + + align:start position:0% +major limitation of this methodology as +it was first described so the major + + align:start position:0% +it was first described so the major + + + align:start position:0% +it was first described so the major +limitation is that the efficiency is low + + align:start position:0% + + + + align:start position:0% + +ok and if we consider wanting to + + align:start position:0% +ok and if we consider wanting to + + + align:start position:0% +ok and if we consider wanting to +incorporate one unnatural amino acid + + align:start position:0% +incorporate one unnatural amino acid + + + align:start position:0% +incorporate one unnatural amino acid +into a polypeptide so there's one Amber + + align:start position:0% +into a polypeptide so there's one Amber + + + align:start position:0% +into a polypeptide so there's one Amber +stop codon put in what was found is that + + align:start position:0% +stop codon put in what was found is that + + + align:start position:0% +stop codon put in what was found is that +about 20 to 30 percent efficiency for + + align:start position:0% +about 20 to 30 percent efficiency for + + + align:start position:0% +about 20 to 30 percent efficiency for +incorporation of one unnatural amino + + align:start position:0% +incorporation of one unnatural amino + + + align:start position:0% +incorporation of one unnatural amino +acid ok and then this value plummeted to + + align:start position:0% +acid ok and then this value plummeted to + + + align:start position:0% +acid ok and then this value plummeted to +less than one percent okay for + + align:start position:0% +less than one percent okay for + + + align:start position:0% +less than one percent okay for +incorporation of two unnatural amino + + align:start position:0% +incorporation of two unnatural amino + + + align:start position:0% +incorporation of two unnatural amino +acids so imagine there's two amber stop + + align:start position:0% +acids so imagine there's two amber stop + + + align:start position:0% +acids so imagine there's two amber stop +codons put within the gene so why is + + align:start position:0% +codons put within the gene so why is + + + align:start position:0% +codons put within the gene so why is +this this is because what's observed is + + align:start position:0% +this this is because what's observed is + + + align:start position:0% +this this is because what's observed is +that only a small amount + + align:start position:0% + + + + align:start position:0% + +if the protein or polypeptide + + align:start position:0% +if the protein or polypeptide + + + align:start position:0% +if the protein or polypeptide +synthesized reaches completion okay and + + align:start position:0% +synthesized reaches completion okay and + + + align:start position:0% +synthesized reaches completion okay and +so how can we think about this imagine + + align:start position:0% +so how can we think about this imagine + + + align:start position:0% +so how can we think about this imagine +here I'm just going to draw some + + align:start position:0% +here I'm just going to draw some + + + align:start position:0% +here I'm just going to draw some +polypeptide chain going from n to C + + align:start position:0% +polypeptide chain going from n to C + + + align:start position:0% +polypeptide chain going from n to C +terminus + + align:start position:0% +terminus + + + align:start position:0% +terminus +okay let's imagine this is 20 kilo + + align:start position:0% +okay let's imagine this is 20 kilo + + + align:start position:0% +okay let's imagine this is 20 kilo +daltons in size and maybe this unnatural + + align:start position:0% +daltons in size and maybe this unnatural + + + align:start position:0% +daltons in size and maybe this unnatural +amino acid is being placed right in the + + align:start position:0% +amino acid is being placed right in the + + + align:start position:0% +amino acid is being placed right in the +middle okay so we want to put an + + align:start position:0% +middle okay so we want to put an + + + align:start position:0% +middle okay so we want to put an +unnatural amino acid here okay so + + align:start position:0% +unnatural amino acid here okay so + + + align:start position:0% +unnatural amino acid here okay so +imagine you make your plasmid DNA to do + + align:start position:0% +imagine you make your plasmid DNA to do + + + align:start position:0% +imagine you make your plasmid DNA to do +this you have the tRNA and the AAA RS + + align:start position:0% +this you have the tRNA and the AAA RS + + + align:start position:0% +this you have the tRNA and the AAA RS +and the unnatural amino acid and you do + + align:start position:0% +and the unnatural amino acid and you do + + + align:start position:0% +and the unnatural amino acid and you do +your expression and then you take a look + + align:start position:0% +your expression and then you take a look + + + align:start position:0% +your expression and then you take a look +by SDS page so gel electrophoresis what + + align:start position:0% +by SDS page so gel electrophoresis what + + + align:start position:0% +by SDS page so gel electrophoresis what +do you see okay right so imagine here we + + align:start position:0% +do you see okay right so imagine here we + + + align:start position:0% +do you see okay right so imagine here we +have 20 10 5 killa Dalton's + + align:start position:0% +have 20 10 5 killa Dalton's + + + align:start position:0% +have 20 10 5 killa Dalton's +here right so we have some molecular + + align:start position:0% +here right so we have some molecular + + + align:start position:0% +here right so we have some molecular +weight markers let's just say here okay + + align:start position:0% +weight markers let's just say here okay + + + align:start position:0% +weight markers let's just say here okay +if you do this say for the native + + align:start position:0% +if you do this say for the native + + + align:start position:0% +if you do this say for the native +sequence so you haven't put in the stop + + align:start position:0% +sequence so you haven't put in the stop + + + align:start position:0% +sequence so you haven't put in the stop +codon right imagine there's your protein + + align:start position:0% +codon right imagine there's your protein + + + align:start position:0% +codon right imagine there's your protein +if we have + + align:start position:0% + + + + align:start position:0% + +the unnatural amino acid what do we see + + align:start position:0% + + + + align:start position:0% + +any something like this so what does + + align:start position:0% +any something like this so what does + + + align:start position:0% +any something like this so what does +this tell you first of all why do you + + align:start position:0% +this tell you first of all why do you + + + align:start position:0% +this tell you first of all why do you +look at the native one + + align:start position:0% + + + + align:start position:0% + +I mean effectively you want some + + align:start position:0% +I mean effectively you want some + + + align:start position:0% +I mean effectively you want some +positive control because if you can't + + align:start position:0% +positive control because if you can't + + + align:start position:0% +positive control because if you can't +express your polypeptide with the native + + align:start position:0% +express your polypeptide with the native + + + align:start position:0% +express your polypeptide with the native +sequence you're not going to want to go + + align:start position:0% +sequence you're not going to want to go + + + align:start position:0% +sequence you're not going to want to go +try to stick in an unnatural amino acid + + align:start position:0% +try to stick in an unnatural amino acid + + + align:start position:0% +try to stick in an unnatural amino acid +right there's a problem + + align:start position:0% +right there's a problem + + + align:start position:0% +right there's a problem +so that's your positive control so we + + align:start position:0% +so that's your positive control so we + + + align:start position:0% +so that's your positive control so we +see in this make-belief gel there's one + + align:start position:0% +see in this make-belief gel there's one + + + align:start position:0% +see in this make-belief gel there's one +band at twenty killer Dalton's right + + align:start position:0% +band at twenty killer Dalton's right + + + align:start position:0% +band at twenty killer Dalton's right +which is the size of that if that ever + + align:start position:0% +which is the size of that if that ever + + + align:start position:0% +which is the size of that if that ever +happens to you you've had an instant + + align:start position:0% +happens to you you've had an instant + + + align:start position:0% +happens to you you've had an instant +gratification protein pack so what about + + align:start position:0% +gratification protein pack so what about + + + align:start position:0% +gratification protein pack so what about +this plane with the unnatural amino acid + + align:start position:0% +this plane with the unnatural amino acid + + + align:start position:0% +this plane with the unnatural amino acid +what do we see and what does this data + + align:start position:0% +what do we see and what does this data + + + align:start position:0% +what do we see and what does this data +tell us Lindsey yeah something happened + + align:start position:0% +tell us Lindsey yeah something happened + + + align:start position:0% +tell us Lindsey yeah something happened +right so early truncation and why are + + align:start position:0% +right so early truncation and why are + + + align:start position:0% +right so early truncation and why are +you saying that right we see two bands + + align:start position:0% +you saying that right we see two bands + + + align:start position:0% +you saying that right we see two bands +there's one band with the expected + + align:start position:0% +there's one band with the expected + + + align:start position:0% +there's one band with the expected +migration to about 20 kilotons and then + + align:start position:0% +migration to about 20 kilotons and then + + + align:start position:0% +migration to about 20 kilotons and then +there's a second band that's coming up + + align:start position:0% +there's a second band that's coming up + + + align:start position:0% +there's a second band that's coming up +around ten kilotons right and based on + + align:start position:0% +around ten kilotons right and based on + + + align:start position:0% +around ten kilotons right and based on +what I sketched out here that unnatural + + align:start position:0% +what I sketched out here that unnatural + + + align:start position:0% +what I sketched out here that unnatural +amino acid is roughly around a ten + + align:start position:0% +amino acid is roughly around a ten + + + align:start position:0% +amino acid is roughly around a ten +kiloton mark okay what about the + + align:start position:0% +kiloton mark okay what about the + + + align:start position:0% +kiloton mark okay what about the +relative intensity of these bands what + + align:start position:0% +relative intensity of these bands what + + + align:start position:0% +relative intensity of these bands what +do we see more of you know we see more + + align:start position:0% +do we see more of you know we see more + + + align:start position:0% +do we see more of you know we see more +of the truncated form right so so what's + + align:start position:0% +of the truncated form right so so what's + + + align:start position:0% +of the truncated form right so so what's +going on right we need to think about + + align:start position:0% + + + + align:start position:0% + +right our ribosome and there's some + + align:start position:0% +right our ribosome and there's some + + + align:start position:0% +right our ribosome and there's some +polypeptide being made right and then + + align:start position:0% +polypeptide being made right and then + + + align:start position:0% +polypeptide being made right and then +what's coming here we either have our + + align:start position:0% +what's coming here we either have our + + + align:start position:0% +what's coming here we either have our +tRNA with the unnatural amino acid or + + align:start position:0% +tRNA with the unnatural amino acid or + + + align:start position:0% +tRNA with the unnatural amino acid or +the release factor right so there's + + align:start position:0% +the release factor right so there's + + + align:start position:0% +the release factor right so there's +going to be competition for binding in + + align:start position:0% +going to be competition for binding in + + + align:start position:0% +going to be competition for binding in +the a site between the tRNA and the + + align:start position:0% +the a site between the tRNA and the + + + align:start position:0% +the a site between the tRNA and the +release factor and so this is getting + + align:start position:0% +release factor and so this is getting + + + align:start position:0% +release factor and so this is getting +back to I believe Max's question from + + align:start position:0% +back to I believe Max's question from + + + align:start position:0% +back to I believe Max's question from +last time about this using the stop + + align:start position:0% +last time about this using the stop + + + align:start position:0% +last time about this using the stop +codon right there's fundamentally a + + align:start position:0% +codon right there's fundamentally a + + + align:start position:0% +codon right there's fundamentally a +problem here so yeah + + align:start position:0% + + + + align:start position:0% + +different for us yes so we discussed + + align:start position:0% +different for us yes so we discussed + + + align:start position:0% +different for us yes so we discussed +that I think in lecture 4 so there's + + align:start position:0% +that I think in lecture 4 so there's + + + align:start position:0% +that I think in lecture 4 so there's +release factor 1 and release factor 2 + + align:start position:0% +release factor 1 and release factor 2 + + + align:start position:0% +release factor 1 and release factor 2 +and there's three different stop codons + + align:start position:0% +and there's three different stop codons + + + align:start position:0% +and there's three different stop codons +so they both recognize one of the same + + align:start position:0% +so they both recognize one of the same + + + align:start position:0% +so they both recognize one of the same +and two different right and in this case + + align:start position:0% +and two different right and in this case + + + align:start position:0% +and two different right and in this case +release factor what one recognizes the + + align:start position:0% +release factor what one recognizes the + + + align:start position:0% +release factor what one recognizes the +amber stop codon here so we're not + + align:start position:0% +amber stop codon here so we're not + + + align:start position:0% +amber stop codon here so we're not +worrying about release factor two + + align:start position:0% +worrying about release factor two + + + align:start position:0% +worrying about release factor two +competing with this stop codon because + + align:start position:0% +competing with this stop codon because + + + align:start position:0% +competing with this stop codon because +it doesn't recognize this stop codon + + align:start position:0% +it doesn't recognize this stop codon + + + align:start position:0% +it doesn't recognize this stop codon +here right so if release factor one goes + + align:start position:0% +here right so if release factor one goes + + + align:start position:0% +here right so if release factor one goes +in right we get premature termination + + align:start position:0% + + + + align:start position:0% + +and that results in truncated protein so + + align:start position:0% +and that results in truncated protein so + + + align:start position:0% +and that results in truncated protein so +is this a problem and how much of a + + align:start position:0% +is this a problem and how much of a + + + align:start position:0% +is this a problem and how much of a +problem is it + + align:start position:0% + + + + align:start position:0% + +recognising the proton that is trying to + + align:start position:0% +recognising the proton that is trying to + + + align:start position:0% +recognising the proton that is trying to +order that originally was a stopper yeah + + align:start position:0% +order that originally was a stopper yeah + + + align:start position:0% +order that originally was a stopper yeah +because the codons still a stop codon + + align:start position:0% +because the codons still a stop codon + + + align:start position:0% +because the codons still a stop codon +but right doing the while said it wasn't + + align:start position:0% +but right doing the while said it wasn't + + + align:start position:0% +but right doing the while said it wasn't +though we replace it I'm like sorry like + + align:start position:0% +though we replace it I'm like sorry like + + + align:start position:0% +though we replace it I'm like sorry like +so we replaced it we just stopped at the + + align:start position:0% +so we replaced it we just stopped at the + + + align:start position:0% +so we replaced it we just stopped at the +stop wasn't there originally and so + + align:start position:0% +stop wasn't there originally and so + + + align:start position:0% +stop wasn't there originally and so +that's why you get old twenty ring right + + align:start position:0% +that's why you get old twenty ring right + + + align:start position:0% +that's why you get old twenty ring right +yes so you had yeah okay continue there + + align:start position:0% +yes so you had yeah okay continue there + + + align:start position:0% +yes so you had yeah okay continue there +is no stop before now there's a stop but + + align:start position:0% +is no stop before now there's a stop but + + + align:start position:0% +is no stop before now there's a stop but +it's not supposed to have like this top + + align:start position:0% +it's not supposed to have like this top + + + align:start position:0% +it's not supposed to have like this top +right right solar is active it depends + + align:start position:0% +right right solar is active it depends + + + align:start position:0% +right right solar is active it depends +what enters the a site so a stop codon + + align:start position:0% +what enters the a site so a stop codon + + + align:start position:0% +what enters the a site so a stop codon +is a stop codon right but the idea is + + align:start position:0% +is a stop codon right but the idea is + + + align:start position:0% +is a stop codon right but the idea is +that this tRNA has been tweaked to allow + + align:start position:0% +that this tRNA has been tweaked to allow + + + align:start position:0% +that this tRNA has been tweaked to allow +a tRNA to recognize the stop but there's + + align:start position:0% +a tRNA to recognize the stop but there's + + + align:start position:0% +a tRNA to recognize the stop but there's +going to be competition right because + + align:start position:0% +going to be competition right because + + + align:start position:0% +going to be competition right because +you have the tRNA that's going to + + align:start position:0% +you have the tRNA that's going to + + + align:start position:0% +you have the tRNA that's going to +deliver the unnatural amino acid but you + + align:start position:0% +deliver the unnatural amino acid but you + + + align:start position:0% +deliver the unnatural amino acid but you +also have release factor right around so + + align:start position:0% +also have release factor right around so + + + align:start position:0% +also have release factor right around so +this release factor one is in the + + align:start position:0% +this release factor one is in the + + + align:start position:0% +this release factor one is in the +endogenous pool so the question is which + + align:start position:0% +endogenous pool so the question is which + + + align:start position:0% +endogenous pool so the question is which +one which one gets there and does the + + align:start position:0% +one which one gets there and does the + + + align:start position:0% +one which one gets there and does the +job right and so what that gel is + + align:start position:0% +job right and so what that gel is + + + align:start position:0% +job right and so what that gel is +telling you is that there's a mixture + + align:start position:0% +telling you is that there's a mixture + + + align:start position:0% +telling you is that there's a mixture +right sometimes the tRNA will get there + + align:start position:0% +right sometimes the tRNA will get there + + + align:start position:0% +right sometimes the tRNA will get there +and translation continues until you get + + align:start position:0% +and translation continues until you get + + + align:start position:0% +and translation continues until you get +to the you know the desired stop where + + align:start position:0% +to the you know the desired stop where + + + align:start position:0% +to the you know the desired stop where +you want translation to stop in terms of + + align:start position:0% +you want translation to stop in terms of + + + align:start position:0% +you want translation to stop in terms of +stopping or if the release factor gets + + align:start position:0% +stopping or if the release factor gets + + + align:start position:0% +stopping or if the release factor gets +there you get termination so you get + + align:start position:0% +there you get termination so you get + + + align:start position:0% +there you get termination so you get +some truncated protein + + align:start position:0% + + + + align:start position:0% + +no I mean just imagine we're just + + align:start position:0% +no I mean just imagine we're just + + + align:start position:0% +no I mean just imagine we're just +looking at protein here I mean I mean + + align:start position:0% +looking at protein here I mean I mean + + + align:start position:0% +looking at protein here I mean I mean +it's like bird this came from so if you + + align:start position:0% +it's like bird this came from so if you + + + align:start position:0% +it's like bird this came from so if you +had a fluorescent and you know acid + + align:start position:0% +had a fluorescent and you know acid + + + align:start position:0% +had a fluorescent and you know acid +you'd see something no because if you + + align:start position:0% +you'd see something no because if you + + + align:start position:0% +you'd see something no because if you +didn't have the unnatural amino acid + + align:start position:0% +didn't have the unnatural amino acid + + + align:start position:0% +didn't have the unnatural amino acid +there what else could be there but what + + align:start position:0% +there what else could be there but what + + + align:start position:0% +there what else could be there but what +native amino acid can be incorporated if + + align:start position:0% +native amino acid can be incorporated if + + + align:start position:0% +native amino acid can be incorporated if +there's a stop yeah right so there has + + align:start position:0% +there's a stop yeah right so there has + + + align:start position:0% +there's a stop yeah right so there has +to be a stop right now that's also + + align:start position:0% +to be a stop right now that's also + + + align:start position:0% +to be a stop right now that's also +backtracking why you need to make sure + + align:start position:0% +backtracking why you need to make sure + + + align:start position:0% +backtracking why you need to make sure +everything's orthogonal because you + + align:start position:0% +everything's orthogonal because you + + + align:start position:0% +everything's orthogonal because you +don't want one of the endogenous + + align:start position:0% +don't want one of the endogenous + + + align:start position:0% +don't want one of the endogenous +aminoacyl trna synthetases to put some + + align:start position:0% +aminoacyl trna synthetases to put some + + + align:start position:0% +aminoacyl trna synthetases to put some +endogenous amino acid on this tRNA okay + + align:start position:0% +endogenous amino acid on this tRNA okay + + + align:start position:0% +endogenous amino acid on this tRNA okay +yeah so either full-length with the + + align:start position:0% +yeah so either full-length with the + + + align:start position:0% +yeah so either full-length with the +unnatural amino acid or truncated + + align:start position:0% +unnatural amino acid or truncated + + + align:start position:0% +unnatural amino acid or truncated +because our f1 came along here right so + + align:start position:0% +because our f1 came along here right so + + + align:start position:0% +because our f1 came along here right so +in terms of how much of a problem this + + align:start position:0% +in terms of how much of a problem this + + + align:start position:0% +in terms of how much of a problem this +is in some respects it depends on what + + align:start position:0% +is in some respects it depends on what + + + align:start position:0% +is in some respects it depends on what +you need and what you want to do right + + align:start position:0% +you need and what you want to do right + + + align:start position:0% +you need and what you want to do right +if you're over expressing protein and + + align:start position:0% +if you're over expressing protein and + + + align:start position:0% +if you're over expressing protein and +you can deal with this mixture and get + + align:start position:0% +you can deal with this mixture and get + + + align:start position:0% +you can deal with this mixture and get +enough full-length right maybe that's + + align:start position:0% +enough full-length right maybe that's + + + align:start position:0% +enough full-length right maybe that's +okay + + align:start position:0% +okay + + + align:start position:0% +okay +if you're doing an experiment in cells + + align:start position:0% +if you're doing an experiment in cells + + + align:start position:0% +if you're doing an experiment in cells +you have to ask what is the consequence + + align:start position:0% +you have to ask what is the consequence + + + align:start position:0% +you have to ask what is the consequence +of also having some truncated protein + + align:start position:0% +of also having some truncated protein + + + align:start position:0% +of also having some truncated protein +around right what does that mean for the + + align:start position:0% +around right what does that mean for the + + + align:start position:0% +around right what does that mean for the +cell what does that mean for your + + align:start position:0% +cell what does that mean for your + + + align:start position:0% +cell what does that mean for your +measurement there for that so how can we + + align:start position:0% +measurement there for that so how can we + + + align:start position:0% +measurement there for that so how can we +get around this problem of our f1 so + + align:start position:0% +get around this problem of our f1 so + + + align:start position:0% +get around this problem of our f1 so +effectively we want to diminish our f1 + + align:start position:0% +effectively we want to diminish our f1 + + + align:start position:0% +effectively we want to diminish our f1 +mediated chain termination what are some + + align:start position:0% +mediated chain termination what are some + + + align:start position:0% +mediated chain termination what are some +possibilities is that feasible okay so + + align:start position:0% +possibilities is that feasible okay so + + + align:start position:0% +possibilities is that feasible okay so +we could do that and we could get a + + align:start position:0% +we could do that and we could get a + + + align:start position:0% +we could do that and we could get a +better yield that'd be great for protein + + align:start position:0% +better yield that'd be great for protein + + + align:start position:0% +better yield that'd be great for protein +over expression if we could minimize + + align:start position:0% +over expression if we could minimize + + + align:start position:0% +over expression if we could minimize +truncated phenotypes that would be great + + align:start position:0% +truncated phenotypes that would be great + + + align:start position:0% +truncated phenotypes that would be great +for an experiment in cells you don't + + align:start position:0% +for an experiment in cells you don't + + + align:start position:0% +for an experiment in cells you don't +need to worry about what this truncated + + align:start position:0% +need to worry about what this truncated + + + align:start position:0% +need to worry about what this truncated +protein might do so what are + + align:start position:0% +protein might do so what are + + + align:start position:0% +protein might do so what are +possibilities + + align:start position:0% +possibilities + + + align:start position:0% +possibilities +so can we knock down or knock out our f1 + + align:start position:0% + + + + align:start position:0% + +yeah so this is a wonderful little story + + align:start position:0% +yeah so this is a wonderful little story + + + align:start position:0% +yeah so this is a wonderful little story +I'll just tell a little bit about we're + + align:start position:0% +I'll just tell a little bit about we're + + + align:start position:0% +I'll just tell a little bit about we're +not gonna go into a huge detail but for + + align:start position:0% +not gonna go into a huge detail but for + + + align:start position:0% +not gonna go into a huge detail but for +quite some time it was thought that our + + align:start position:0% +quite some time it was thought that our + + + align:start position:0% +quite some time it was thought that our +f1 was essential in e.coli so a lot of + + align:start position:0% +f1 was essential in e.coli so a lot of + + + align:start position:0% +f1 was essential in e.coli so a lot of +experiments were done with the coli k12 + + align:start position:0% +experiments were done with the coli k12 + + + align:start position:0% +experiments were done with the coli k12 +and even if you go look on a website + + align:start position:0% +and even if you go look on a website + + + align:start position:0% +and even if you go look on a website +about all the genes in e.coli k12 it + + align:start position:0% +about all the genes in e.coli k12 it + + + align:start position:0% +about all the genes in e.coli k12 it +will tell you our f1 is essential but + + align:start position:0% +will tell you our f1 is essential but + + + align:start position:0% +will tell you our f1 is essential but +then in 2012 the paper came out an ACS + + align:start position:0% +then in 2012 the paper came out an ACS + + + align:start position:0% +then in 2012 the paper came out an ACS +Chemical Biology where they were doing + + align:start position:0% +Chemical Biology where they were doing + + + align:start position:0% +Chemical Biology where they were doing +some work and a different strain of + + align:start position:0% +some work and a different strain of + + + align:start position:0% +some work and a different strain of +e.coli so there's many different eco + + align:start position:0% +e.coli so there's many different eco + + + align:start position:0% +e.coli so there's many different eco +lies and k12 is a laboratory workhorse + + align:start position:0% +lies and k12 is a laboratory workhorse + + + align:start position:0% +lies and k12 is a laboratory workhorse +and there's also strains Ecole IB and + + align:start position:0% +and there's also strains Ecole IB and + + + align:start position:0% +and there's also strains Ecole IB and +they're also laboratory workhorses so + + align:start position:0% +they're also laboratory workhorses so + + + align:start position:0% +they're also laboratory workhorses so +maybe many of you have used like BL 21 + + align:start position:0% +maybe many of you have used like BL 21 + + + align:start position:0% +maybe many of you have used like BL 21 +de 3 cells for protein expression so + + align:start position:0% +de 3 cells for protein expression so + + + align:start position:0% +de 3 cells for protein expression so +this lab was working an equal eye B + + align:start position:0% +this lab was working an equal eye B + + + align:start position:0% +this lab was working an equal eye B +strain and found that our f1 could be + + align:start position:0% +strain and found that our f1 could be + + + align:start position:0% +strain and found that our f1 could be +knocked out that it's not essential so + + align:start position:0% +knocked out that it's not essential so + + + align:start position:0% +knocked out that it's not essential so +then the question is what's going on and + + align:start position:0% +then the question is what's going on and + + + align:start position:0% +then the question is what's going on and +as it turns out the you know + + align:start position:0% +as it turns out the you know + + + align:start position:0% +as it turns out the you know +essentiality of our f1 and e.coli turned + + align:start position:0% +essentiality of our f1 and e.coli turned + + + align:start position:0% +essentiality of our f1 and e.coli turned +out to be due to an issue with our f2 + + align:start position:0% +out to be due to an issue with our f2 + + + align:start position:0% +out to be due to an issue with our f2 +and in the k12 release factor 2 has a + + align:start position:0% +and in the k12 release factor 2 has a + + + align:start position:0% +and in the k12 release factor 2 has a +single point mutation that makes it less + + align:start position:0% +single point mutation that makes it less + + + align:start position:0% +single point mutation that makes it less +able to stop you know what certain stop + + align:start position:0% +able to stop you know what certain stop + + + align:start position:0% +able to stop you know what certain stop +codon so when you had both of those + + align:start position:0% +codon so when you had both of those + + + align:start position:0% +codon so when you had both of those +together it was deleterious so our f1 + + align:start position:0% +together it was deleterious so our f1 + + + align:start position:0% +together it was deleterious so our f1 +can be knocked out would you want to do + + align:start position:0% +can be knocked out would you want to do + + + align:start position:0% +can be knocked out would you want to do +that + + align:start position:0% + + + + align:start position:0% + +you know there are three release factors + + align:start position:0% +you know there are three release factors + + + align:start position:0% +you know there are three release factors +rf3 the gtps right it's a little + + align:start position:0% +rf3 the gtps right it's a little + + + align:start position:0% +rf3 the gtps right it's a little +different there are some redundancies + + align:start position:0% +different there are some redundancies + + + align:start position:0% +different there are some redundancies +right and I mean something to just to + + align:start position:0% +right and I mean something to just to + + + align:start position:0% +right and I mean something to just to +ask is if you can knock it out and this + + align:start position:0% +ask is if you can knock it out and this + + + align:start position:0% +ask is if you can knock it out and this +sells viable viability is different than + + align:start position:0% +sells viable viability is different than + + + align:start position:0% +sells viable viability is different than +normal healthy cell right so those ecoli + + align:start position:0% +normal healthy cell right so those ecoli + + + align:start position:0% +normal healthy cell right so those ecoli +be without RF one will grow but are they + + align:start position:0% +be without RF one will grow but are they + + + align:start position:0% +be without RF one will grow but are they +growing and replicating as well as the + + align:start position:0% +growing and replicating as well as the + + + align:start position:0% +growing and replicating as well as the +wild-type no no but is it good enough + + align:start position:0% +wild-type no no but is it good enough + + + align:start position:0% +wild-type no no but is it good enough +and I think again it just comes down to + + align:start position:0% +and I think again it just comes down to + + + align:start position:0% +and I think again it just comes down to +asking what is it that you want to do so + + align:start position:0% +asking what is it that you want to do so + + + align:start position:0% +asking what is it that you want to do so +maybe if you're over expressing protein + + align:start position:0% +maybe if you're over expressing protein + + + align:start position:0% +maybe if you're over expressing protein +and you're gonna purify that it's not + + align:start position:0% +and you're gonna purify that it's not + + + align:start position:0% +and you're gonna purify that it's not +such a big deal but again if you're + + align:start position:0% +such a big deal but again if you're + + + align:start position:0% +such a big deal but again if you're +looking at some cellular process you're + + align:start position:0% +looking at some cellular process you're + + + align:start position:0% +looking at some cellular process you're +gonna need to think about what's + + align:start position:0% +gonna need to think about what's + + + align:start position:0% +gonna need to think about what's +happening if RF one can't terminate + + align:start position:0% +happening if RF one can't terminate + + + align:start position:0% +happening if RF one can't terminate +translation for you know it's it's + + align:start position:0% +translation for you know it's it's + + + align:start position:0% +translation for you know it's it's +repertoire of proteins and genes there + + align:start position:0% +repertoire of proteins and genes there + + + align:start position:0% +repertoire of proteins and genes there +there will be some consequence of that + + align:start position:0% +there will be some consequence of that + + + align:start position:0% +there will be some consequence of that +that perturbation just to keep in mind + + align:start position:0% +that perturbation just to keep in mind + + + align:start position:0% +that perturbation just to keep in mind +but there's certainly work going on with + + align:start position:0% +but there's certainly work going on with + + + align:start position:0% +but there's certainly work going on with +that now that it was found not to be + + align:start position:0% +that now that it was found not to be + + + align:start position:0% +that now that it was found not to be +essential so in vitro translation just + + align:start position:0% +essential so in vitro translation just + + + align:start position:0% +essential so in vitro translation just +something to think about + + align:start position:0% +something to think about + + + align:start position:0% +something to think about +right if you're going to work in a test + + align:start position:0% +right if you're going to work in a test + + + align:start position:0% +right if you're going to work in a test +tube could you just do this outside of + + align:start position:0% +tube could you just do this outside of + + + align:start position:0% +tube could you just do this outside of +the cell and then the possibility we're + + align:start position:0% +the cell and then the possibility we're + + + align:start position:0% +the cell and then the possibility we're +going to discuss in closing if this one + + align:start position:0% +going to discuss in closing if this one + + + align:start position:0% +going to discuss in closing if this one +of a new ribosome which i think is + + align:start position:0% +of a new ribosome which i think is + + + align:start position:0% +of a new ribosome which i think is +pretty cool so is it possible to have an + + align:start position:0% +pretty cool so is it possible to have an + + + align:start position:0% +pretty cool so is it possible to have an +orthogonal ribosome here to get around + + align:start position:0% +orthogonal ribosome here to get around + + + align:start position:0% +orthogonal ribosome here to get around +this problem right so effectively can we + + align:start position:0% +this problem right so effectively can we + + + align:start position:0% +this problem right so effectively can we +make a new ribosome that only translates + + align:start position:0% +make a new ribosome that only translates + + + align:start position:0% +make a new ribosome that only translates +the message encoded in a plasmid that + + align:start position:0% +the message encoded in a plasmid that + + + align:start position:0% +the message encoded in a plasmid that +has the gene of interest where you want + + align:start position:0% +has the gene of interest where you want + + + align:start position:0% +has the gene of interest where you want +the unnatural amino acid to go okay and + + align:start position:0% +the unnatural amino acid to go okay and + + + align:start position:0% +the unnatural amino acid to go okay and +so thinking about this in cartoon form + + align:start position:0% +so thinking about this in cartoon form + + + align:start position:0% +so thinking about this in cartoon form +imagine we have a coli or some organism + + align:start position:0% +imagine we have a coli or some organism + + + align:start position:0% +imagine we have a coli or some organism +and there's the native ribosome and this + + align:start position:0% +and there's the native ribosome and this + + + align:start position:0% +and there's the native ribosome and this +native ribosome translates all of the + + align:start position:0% +native ribosome translates all of the + + + align:start position:0% +native ribosome translates all of the +native wild-type + + align:start position:0% +native wild-type + + + align:start position:0% +native wild-type +mRNAs and gives synthesis of the + + align:start position:0% +mRNAs and gives synthesis of the + + + align:start position:0% +mRNAs and gives synthesis of the +proteome but then imagine we can put in + + align:start position:0% +proteome but then imagine we can put in + + + align:start position:0% +proteome but then imagine we can put in +orthogonal ribosome into this organism + + align:start position:0% +orthogonal ribosome into this organism + + + align:start position:0% +orthogonal ribosome into this organism +and this orthogonal ribosome only + + align:start position:0% +and this orthogonal ribosome only + + + align:start position:0% +and this orthogonal ribosome only +recognizes an orthogonal mRNA which + + align:start position:0% +recognizes an orthogonal mRNA which + + + align:start position:0% +recognizes an orthogonal mRNA which +means that only translates off of this + + align:start position:0% +means that only translates off of this + + + align:start position:0% +means that only translates off of this +orthogonal mRNA and only gives you + + align:start position:0% +orthogonal mRNA and only gives you + + + align:start position:0% +orthogonal mRNA and only gives you +synthesis of the protein you want with + + align:start position:0% +synthesis of the protein you want with + + + align:start position:0% +synthesis of the protein you want with +the unnatural amino acid so how to think + + align:start position:0% +the unnatural amino acid so how to think + + + align:start position:0% +the unnatural amino acid so how to think +about doing this right need to think + + align:start position:0% +about doing this right need to think + + + align:start position:0% +about doing this right need to think +back about the initiation process right + + align:start position:0% +back about the initiation process right + + + align:start position:0% +back about the initiation process right +and that mRNAs have a ribosome binding + + align:start position:0% +and that mRNAs have a ribosome binding + + + align:start position:0% +and that mRNAs have a ribosome binding +site so effectively it's necessary to + + align:start position:0% +site so effectively it's necessary to + + + align:start position:0% +site so effectively it's necessary to +engineer an mRNA that contains a + + align:start position:0% +engineer an mRNA that contains a + + + align:start position:0% +engineer an mRNA that contains a +ribosome binding site that will not + + align:start position:0% +ribosome binding site that will not + + + align:start position:0% +ribosome binding site that will not +direct translation by the endogenous + + align:start position:0% +direct translation by the endogenous + + + align:start position:0% +direct translation by the endogenous +ribosome so some new ribosome binding + + align:start position:0% +ribosome so some new ribosome binding + + + align:start position:0% +ribosome so some new ribosome binding +site okay and then this orthogonal + + align:start position:0% +site okay and then this orthogonal + + + align:start position:0% +site okay and then this orthogonal +ribosome needs to be engineered such + + align:start position:0% +ribosome needs to be engineered such + + + align:start position:0% +ribosome needs to be engineered such +that it specifically binds to the + + align:start position:0% +that it specifically binds to the + + + align:start position:0% +that it specifically binds to the +orthogonal mRNA and it doesn't bind to + + align:start position:0% +orthogonal mRNA and it doesn't bind to + + + align:start position:0% +orthogonal mRNA and it doesn't bind to +the wild-type mRNAs there right so no + + align:start position:0% +the wild-type mRNAs there right so no + + + align:start position:0% +the wild-type mRNAs there right so no +translation of the cellular message + + align:start position:0% +translation of the cellular message + + + align:start position:0% +translation of the cellular message +because this ribosome binding site and + + align:start position:0% +because this ribosome binding site and + + + align:start position:0% +because this ribosome binding site and +orthogonal ribosome are a match okay so + + align:start position:0% +orthogonal ribosome are a match okay so + + + align:start position:0% +orthogonal ribosome are a match okay so +a unique binding site so in thinking + + align:start position:0% +a unique binding site so in thinking + + + align:start position:0% +a unique binding site so in thinking +about how to do this right you want to + + align:start position:0% +about how to do this right you want to + + + align:start position:0% +about how to do this right you want to +think about the ribosome structure right + + align:start position:0% +think about the ribosome structure right + + + align:start position:0% +think about the ribosome structure right +and we know that the 16s rRNA is + + align:start position:0% +and we know that the 16s rRNA is + + + align:start position:0% +and we know that the 16s rRNA is +involved in binding to the mRNA at the + + align:start position:0% +involved in binding to the mRNA at the + + + align:start position:0% +involved in binding to the mRNA at the +beginning of the initiation step so what + + align:start position:0% +beginning of the initiation step so what + + + align:start position:0% +beginning of the initiation step so what +was done was to mutate the 16s and come + + align:start position:0% +was done was to mutate the 16s and come + + + align:start position:0% +was done was to mutate the 16s and come +up with an orthogonal ribosome okay so + + align:start position:0% +up with an orthogonal ribosome okay so + + + align:start position:0% +up with an orthogonal ribosome okay so +this has been done that's not a solution + + align:start position:0% +this has been done that's not a solution + + + align:start position:0% +this has been done that's not a solution +to the problem of our f1 terminating + + align:start position:0% +to the problem of our f1 terminating + + + align:start position:0% +to the problem of our f1 terminating +translation on its own right so then the + + align:start position:0% +translation on its own right so then the + + + align:start position:0% +translation on its own right so then the +next question is if we can have just + + align:start position:0% +next question is if we can have just + + + align:start position:0% +next question is if we can have just +this orthogonal ribosome an orthogonal + + align:start position:0% +this orthogonal ribosome an orthogonal + + + align:start position:0% +this orthogonal ribosome an orthogonal +mrna can we improve that system to + + align:start position:0% +mrna can we improve that system to + + + align:start position:0% +mrna can we improve that system to +minimize our f1 mediated chain + + align:start position:0% +minimize our f1 mediated chain + + + align:start position:0% +minimize our f1 mediated chain +termination + + align:start position:0% +termination + + + align:start position:0% +termination +okay so effectively what we want to do + + align:start position:0% +okay so effectively what we want to do + + + align:start position:0% +okay so effectively what we want to do +is prevent our f1 from binding to the a + + align:start position:0% +is prevent our f1 from binding to the a + + + align:start position:0% +is prevent our f1 from binding to the a +site of the orthogonal ribosome + + align:start position:0% +site of the orthogonal ribosome + + + align:start position:0% +site of the orthogonal ribosome +but it's still going to do its job for + + align:start position:0% +but it's still going to do its job for + + + align:start position:0% +but it's still going to do its job for +the endogenous ribosome here so what + + align:start position:0% +the endogenous ribosome here so what + + + align:start position:0% +the endogenous ribosome here so what +what needs to happen and we'll go + + align:start position:0% +what needs to happen and we'll go + + + align:start position:0% +what needs to happen and we'll go +through the steps this is just the + + align:start position:0% +through the steps this is just the + + + align:start position:0% +through the steps this is just the +schematic in cartoon form right so + + align:start position:0% +schematic in cartoon form right so + + + align:start position:0% +schematic in cartoon form right so +imagine we're starting with native + + align:start position:0% +imagine we're starting with native + + + align:start position:0% +imagine we're starting with native +ribosomes and orthogonal ribosomes okay + + align:start position:0% +ribosomes and orthogonal ribosomes okay + + + align:start position:0% +ribosomes and orthogonal ribosomes okay +and we have T RNAs and rf1 and nothing's + + align:start position:0% +and we have T RNAs and rf1 and nothing's + + + align:start position:0% +and we have T RNAs and rf1 and nothing's +been done to this orthogonal ribosomes + + align:start position:0% +been done to this orthogonal ribosomes + + + align:start position:0% +been done to this orthogonal ribosomes +so our f1 can still bind there and so we + + align:start position:0% +so our f1 can still bind there and so we + + + align:start position:0% +so our f1 can still bind there and so we +want to have some evolution so + + align:start position:0% +want to have some evolution so + + + align:start position:0% +want to have some evolution so +mutagenesis and selection of the + + align:start position:0% +mutagenesis and selection of the + + + align:start position:0% +mutagenesis and selection of the +orthogonal ribosome such that only the + + align:start position:0% +orthogonal ribosome such that only the + + + align:start position:0% +orthogonal ribosome such that only the +trna goes to the a site and our f1 only + + align:start position:0% +trna goes to the a site and our f1 only + + + align:start position:0% +trna goes to the a site and our f1 only +goes to the wild-type ribosome + + align:start position:0% + + + + align:start position:0% + +so there's other possibilities one + + align:start position:0% +so there's other possibilities one + + + align:start position:0% +so there's other possibilities one +possibility I'll just throw out there is + + align:start position:0% +possibility I'll just throw out there is + + + align:start position:0% +possibility I'll just throw out there is +using rather than a triplet a quadruplet + + align:start position:0% +using rather than a triplet a quadruplet + + + align:start position:0% +using rather than a triplet a quadruplet +code on there which we won't talk about + + align:start position:0% +code on there which we won't talk about + + + align:start position:0% +code on there which we won't talk about +right there's more than one solution to + + align:start position:0% +right there's more than one solution to + + + align:start position:0% +right there's more than one solution to +the problem but where we're gonna focus + + align:start position:0% +the problem but where we're gonna focus + + + align:start position:0% +the problem but where we're gonna focus +on is work done to minimize our f1 and + + align:start position:0% +on is work done to minimize our f1 and + + + align:start position:0% +on is work done to minimize our f1 and +and how to think about doing that from + + align:start position:0% +and how to think about doing that from + + + align:start position:0% +and how to think about doing that from +the standpoint of what we know of + + align:start position:0% +the standpoint of what we know of + + + align:start position:0% +the standpoint of what we know of +ribosome structure and the interaction + + align:start position:0% +ribosome structure and the interaction + + + align:start position:0% +ribosome structure and the interaction +okay so the name of this new a ribosome + + align:start position:0% +okay so the name of this new a ribosome + + + align:start position:0% +okay so the name of this new a ribosome +is ribose and so what did they do they + + align:start position:0% +is ribose and so what did they do they + + + align:start position:0% +is ribose and so what did they do they +started with the orthogonal ribosome + + align:start position:0% + + + + align:start position:0% + +okay and so the first is that there + + align:start position:0% +okay and so the first is that there + + + align:start position:0% +okay and so the first is that there +needs to be some mutation to the + + align:start position:0% +needs to be some mutation to the + + + align:start position:0% +needs to be some mutation to the +ribosome so libraries of mutants + + align:start position:0% + + + + align:start position:0% + +okay there needs to be some selection + + align:start position:0% +okay there needs to be some selection + + + align:start position:0% +okay there needs to be some selection +process okay so effectively there's a + + align:start position:0% +process okay so effectively there's a + + + align:start position:0% +process okay so effectively there's a +requirement for of activity from the + + align:start position:0% +requirement for of activity from the + + + align:start position:0% +requirement for of activity from the +ribosome okay and when there's this + + align:start position:0% +ribosome okay and when there's this + + + align:start position:0% +ribosome okay and when there's this +there needs to be some sequencing okay + + align:start position:0% +there needs to be some sequencing okay + + + align:start position:0% +there needs to be some sequencing okay +or identity determination so where is + + align:start position:0% +or identity determination so where is + + + align:start position:0% +or identity determination so where is +the mutation here and then with some + + align:start position:0% +the mutation here and then with some + + + align:start position:0% +the mutation here and then with some +mutant in hand that looks like it's a + + align:start position:0% +mutant in hand that looks like it's a + + + align:start position:0% +mutant in hand that looks like it's a +good option there needs to be a seis to + + align:start position:0% +good option there needs to be a seis to + + + align:start position:0% +good option there needs to be a seis to +study it okay and we're pretty much + + align:start position:0% +study it okay and we're pretty much + + + align:start position:0% +study it okay and we're pretty much +gonna focus on step four I'll briefly + + align:start position:0% +gonna focus on step four I'll briefly + + + align:start position:0% +gonna focus on step four I'll briefly +say something about steps one two and + + align:start position:0% +say something about steps one two and + + + align:start position:0% +say something about steps one two and +three here so the first thing is if we + + align:start position:0% +three here so the first thing is if we + + + align:start position:0% +three here so the first thing is if we +want to mutate this a ribosome how do we + + align:start position:0% +want to mutate this a ribosome how do we + + + align:start position:0% +want to mutate this a ribosome how do we +think about designing a mutant library + + align:start position:0% +think about designing a mutant library + + + align:start position:0% +think about designing a mutant library +right and so what we need to think about + + align:start position:0% +right and so what we need to think about + + + align:start position:0% +right and so what we need to think about +in this case because the goal is to + + align:start position:0% +in this case because the goal is to + + + align:start position:0% +in this case because the goal is to +minimize RF one mediated chain + + align:start position:0% +minimize RF one mediated chain + + + align:start position:0% +minimize RF one mediated chain +termination and enhance tRNA getting + + align:start position:0% +termination and enhance tRNA getting + + + align:start position:0% +termination and enhance tRNA getting +into this a site right we want to look + + align:start position:0% +into this a site right we want to look + + + align:start position:0% +into this a site right we want to look +at how the ribosome interacts with RF + + align:start position:0% +at how the ribosome interacts with RF + + + align:start position:0% +at how the ribosome interacts with RF +one how it interacts with the tRNA also + + align:start position:0% +one how it interacts with the tRNA also + + + align:start position:0% +one how it interacts with the tRNA also +think about the M R and I they're right + + align:start position:0% +think about the M R and I they're right + + + align:start position:0% +think about the M R and I they're right +and so there's crystal structures + + align:start position:0% +and so there's crystal structures + + + align:start position:0% +and so there's crystal structures +available there might be biochemical + + align:start position:0% +available there might be biochemical + + + align:start position:0% +available there might be biochemical +information available right but really + + align:start position:0% +information available right but really + + + align:start position:0% +information available right but really +to ask where does it make sense to make + + align:start position:0% +to ask where does it make sense to make + + + align:start position:0% +to ask where does it make sense to make +mutations right and so if we think about + + align:start position:0% +mutations right and so if we think about + + + align:start position:0% +mutations right and so if we think about +the stop codon being recognized by the + + align:start position:0% +the stop codon being recognized by the + + + align:start position:0% +the stop codon being recognized by the +tRNA + + align:start position:0% +tRNA + + + align:start position:0% +tRNA +and rf1 in the a-site right somehow we + + align:start position:0% +and rf1 in the a-site right somehow we + + + align:start position:0% +and rf1 in the a-site right somehow we +want to mutate the ribosomal RNA in that + + align:start position:0% +want to mutate the ribosomal RNA in that + + + align:start position:0% +want to mutate the ribosomal RNA in that +region to give us the desired outcome + + align:start position:0% +region to give us the desired outcome + + + align:start position:0% +region to give us the desired outcome +right so what they did is mutate 16s + + align:start position:0% +right so what they did is mutate 16s + + + align:start position:0% +right so what they did is mutate 16s +rRNA to favor suppression of the amber + + align:start position:0% +rRNA to favor suppression of the amber + + + align:start position:0% +rRNA to favor suppression of the amber +stop codon by the tRNA and crystal + + align:start position:0% +stop codon by the tRNA and crystal + + + align:start position:0% +stop codon by the tRNA and crystal +structures guided the library design and + + align:start position:0% +structures guided the library design and + + + align:start position:0% +structures guided the library design and +so they looked at crystal structures + + align:start position:0% +so they looked at crystal structures + + + align:start position:0% +so they looked at crystal structures +where T RNAs are bound to the a site or + + align:start position:0% +where T RNAs are bound to the a site or + + + align:start position:0% +where T RNAs are bound to the a site or +where our f1 is bound to the a site and + + align:start position:0% +where our f1 is bound to the a site and + + + align:start position:0% +where our f1 is bound to the a site and +from these they selected seven different + + align:start position:0% +from these they selected seven different + + + align:start position:0% +from these they selected seven different +positions of the RNA and randomly + + align:start position:0% +positions of the RNA and randomly + + + align:start position:0% +positions of the RNA and randomly +mutated them okay so that gives you some + + align:start position:0% +mutated them okay so that gives you some + + + align:start position:0% +mutated them okay so that gives you some +mutants to study right then there needs + + align:start position:0% +mutants to study right then there needs + + + align:start position:0% +mutants to study right then there needs +to be a selection process so the mutant + + align:start position:0% +to be a selection process so the mutant + + + align:start position:0% +to be a selection process so the mutant +needs to be active right some of these + + align:start position:0% +needs to be active right some of these + + + align:start position:0% +needs to be active right some of these +mutations might cause the ribosome to be + + align:start position:0% +mutations might cause the ribosome to be + + + align:start position:0% +mutations might cause the ribosome to be +inactive and that that won't be very + + align:start position:0% +inactive and that that won't be very + + + align:start position:0% +inactive and that that won't be very +helpful and so they developed an assay + + align:start position:0% +helpful and so they developed an assay + + + align:start position:0% +helpful and so they developed an assay +based on antibiotic resistance to select + + align:start position:0% +based on antibiotic resistance to select + + + align:start position:0% +based on antibiotic resistance to select +okay and effectively an enzyme that + + align:start position:0% +okay and effectively an enzyme that + + + align:start position:0% +okay and effectively an enzyme that +provides resistance to chlorella and + + align:start position:0% +provides resistance to chlorella and + + + align:start position:0% +provides resistance to chlorella and +fennec all which is an antibiotic that + + align:start position:0% +fennec all which is an antibiotic that + + + align:start position:0% +fennec all which is an antibiotic that +blacks translation and was put under the + + align:start position:0% +blacks translation and was put under the + + + align:start position:0% +blacks translation and was put under the +control of the ribosome right so you can + + align:start position:0% +control of the ribosome right so you can + + + align:start position:0% +control of the ribosome right so you can +imagine using antibiotic resistance as a + + align:start position:0% +imagine using antibiotic resistance as a + + + align:start position:0% +imagine using antibiotic resistance as a +selection there okay and then the + + align:start position:0% +selection there okay and then the + + + align:start position:0% +selection there okay and then the +sequencing right once we've selected for + + align:start position:0% +sequencing right once we've selected for + + + align:start position:0% +sequencing right once we've selected for +some mutants we have to ask where is the + + align:start position:0% +some mutants we have to ask where is the + + + align:start position:0% +some mutants we have to ask where is the +mutation and so what they found after + + align:start position:0% +mutation and so what they found after + + + align:start position:0% +mutation and so what they found after +going through this work is that for iOS + + align:start position:0% + + + + align:start position:0% + +it's only a double mutant + + align:start position:0% + + + + align:start position:0% + +in the 16s rRNA so two positions you + + align:start position:0% +in the 16s rRNA so two positions you + + + align:start position:0% +in the 16s rRNA so two positions you +three five three 1g a new five three + + align:start position:0% +three five three 1g a new five three + + + align:start position:0% +three five three 1g a new five three +four a okay so these mutations improved + + align:start position:0% +four a okay so these mutations improved + + + align:start position:0% +four a okay so these mutations improved +suppression of the amber stop codon and + + align:start position:0% +suppression of the amber stop codon and + + + align:start position:0% +suppression of the amber stop codon and +I also point out these mutations are + + align:start position:0% +I also point out these mutations are + + + align:start position:0% +I also point out these mutations are +very unusual so at least at the time of + + align:start position:0% +very unusual so at least at the time of + + + align:start position:0% +very unusual so at least at the time of +this work + + align:start position:0% +this work + + + align:start position:0% +this work +no sequenced natural ribosome had these + + align:start position:0% +no sequenced natural ribosome had these + + + align:start position:0% +no sequenced natural ribosome had these +two mutations here and they're found in + + align:start position:0% +two mutations here and they're found in + + + align:start position:0% +two mutations here and they're found in +very few examples of sequenced rrnas + + align:start position:0% +very few examples of sequenced rrnas + + + align:start position:0% +very few examples of sequenced rrnas +here so I mean just to think about the + + align:start position:0% +here so I mean just to think about the + + + align:start position:0% +here so I mean just to think about the +ribosomes so huge right and just to + + align:start position:0% +ribosomes so huge right and just to + + + align:start position:0% +ribosomes so huge right and just to +point mutations can make this change + + align:start position:0% +point mutations can make this change + + + align:start position:0% +point mutations can make this change +here so what's seen in terms of some + + align:start position:0% +here so what's seen in terms of some + + + align:start position:0% +here so what's seen in terms of some +characterization + + align:start position:0% + + + + align:start position:0% + +what do we need to ask in terms of + + align:start position:0% +what do we need to ask in terms of + + + align:start position:0% +what do we need to ask in terms of +characterization bless you so something + + align:start position:0% +characterization bless you so something + + + align:start position:0% +characterization bless you so something +we want to ask about is fidelity right + + align:start position:0% +we want to ask about is fidelity right + + + align:start position:0% +we want to ask about is fidelity right +here so if we think about identity one + + align:start position:0% +here so if we think about identity one + + + align:start position:0% +here so if we think about identity one +we can ask if we're using this to + + align:start position:0% +we can ask if we're using this to + + + align:start position:0% +we can ask if we're using this to +express some protein + + align:start position:0% +express some protein + + + align:start position:0% +express some protein +what is the protein yield and how does + + align:start position:0% +what is the protein yield and how does + + + align:start position:0% +what is the protein yield and how does +that compare to the native ribosome we + + align:start position:0% +that compare to the native ribosome we + + + align:start position:0% +that compare to the native ribosome we +want it to incorporate amino acids + + align:start position:0% +want it to incorporate amino acids + + + align:start position:0% +want it to incorporate amino acids +correctly right with high fidelity and + + align:start position:0% +correctly right with high fidelity and + + + align:start position:0% +correctly right with high fidelity and +incorporation of the unnatural amino + + align:start position:0% +incorporation of the unnatural amino + + + align:start position:0% +incorporation of the unnatural amino +acid so doesn't miss incorporate amino + + align:start position:0% +acid so doesn't miss incorporate amino + + + align:start position:0% +acid so doesn't miss incorporate amino +acids so that's the question we need to + + align:start position:0% +acids so that's the question we need to + + + align:start position:0% +acids so that's the question we need to +ask okay and then of course we need to + + align:start position:0% +ask okay and then of course we need to + + + align:start position:0% +ask okay and then of course we need to +ask about Amber stop codon to the + + align:start position:0% +ask about Amber stop codon to the + + + align:start position:0% +ask about Amber stop codon to the +pression efficiency + + align:start position:0% + + + + align:start position:0% + +and so in thinking about this what is + + align:start position:0% +and so in thinking about this what is + + + align:start position:0% +and so in thinking about this what is +the point of comparison right so we can + + align:start position:0% +the point of comparison right so we can + + + align:start position:0% +the point of comparison right so we can +imagine in all of these comparing this + + align:start position:0% +imagine in all of these comparing this + + + align:start position:0% +imagine in all of these comparing this +new orthogonal ribosome right Bo X to + + align:start position:0% +new orthogonal ribosome right Bo X to + + + align:start position:0% +new orthogonal ribosome right Bo X to +the starting orthogonal ribosome right + + align:start position:0% +the starting orthogonal ribosome right + + + align:start position:0% +the starting orthogonal ribosome right +here so what are the experiments so + + align:start position:0% +here so what are the experiments so + + + align:start position:0% +here so what are the experiments so +first let's think about protein yield + + align:start position:0% + + + + align:start position:0% + +and I'll just say I have a pet peeve + + align:start position:0% +and I'll just say I have a pet peeve + + + align:start position:0% +and I'll just say I have a pet peeve +when people don't report their protein + + align:start position:0% +when people don't report their protein + + + align:start position:0% +when people don't report their protein +yields and experimental so if you're + + align:start position:0% +yields and experimental so if you're + + + align:start position:0% +yields and experimental so if you're +doing biochemistry I always think about + + align:start position:0% +doing biochemistry I always think about + + + align:start position:0% +doing biochemistry I always think about +doing that there so what they did is an + + align:start position:0% +doing that there so what they did is an + + + align:start position:0% +doing that there so what they did is an +experiment where they made a plasmid so + + align:start position:0% +experiment where they made a plasmid so + + + align:start position:0% +experiment where they made a plasmid so +we have an orthogonal DNA that will give + + align:start position:0% +we have an orthogonal DNA that will give + + + align:start position:0% +we have an orthogonal DNA that will give +orthogonal mRNA + + align:start position:0% + + + + align:start position:0% + +okay so this gets transcribed to give + + align:start position:0% +okay so this gets transcribed to give + + + align:start position:0% +okay so this gets transcribed to give +the orthogonal mRNA and then it gets + + align:start position:0% +the orthogonal mRNA and then it gets + + + align:start position:0% +the orthogonal mRNA and then it gets +translated okay by either the au + + align:start position:0% +translated okay by either the au + + + align:start position:0% +translated okay by either the au +ribosome or ribose X and the result of + + align:start position:0% +ribosome or ribose X and the result of + + + align:start position:0% +ribosome or ribose X and the result of +this is a fusion protein where we have a + + align:start position:0% +this is a fusion protein where we have a + + + align:start position:0% +this is a fusion protein where we have a +protein called GST glutathione s + + align:start position:0% +protein called GST glutathione s + + + align:start position:0% +protein called GST glutathione s +transferase and then MBP which is multi + + align:start position:0% +transferase and then MBP which is multi + + + align:start position:0% +transferase and then MBP which is multi +winding protein and as we move forward + + align:start position:0% +winding protein and as we move forward + + + align:start position:0% +winding protein and as we move forward +it will become clear why they they use + + align:start position:0% +it will become clear why they they use + + + align:start position:0% +it will become clear why they they use +this fusion okay so just the first + + align:start position:0% +this fusion okay so just the first + + + align:start position:0% +this fusion okay so just the first +question is how does the yield of + + align:start position:0% +question is how does the yield of + + + align:start position:0% +question is how does the yield of +protein compare are they doing a similar + + align:start position:0% +protein compare are they doing a similar + + + align:start position:0% +protein compare are they doing a similar +job or were these two mutations + + align:start position:0% +job or were these two mutations + + + align:start position:0% +job or were these two mutations +detrimental okay so here's the result + + align:start position:0% +detrimental okay so here's the result + + + align:start position:0% +detrimental okay so here's the result +from this experiment one looking at + + align:start position:0% +from this experiment one looking at + + + align:start position:0% +from this experiment one looking at +protein yield + + align:start position:0% +protein yield + + + align:start position:0% +protein yield +okay so again we're looking at an SDS + + align:start position:0% +okay so again we're looking at an SDS + + + align:start position:0% +okay so again we're looking at an SDS +page gel that's being stained for for + + align:start position:0% +page gel that's being stained for for + + + align:start position:0% +page gel that's being stained for for +the protein and we see that this GST and + + align:start position:0% +the protein and we see that this GST and + + + align:start position:0% +the protein and we see that this GST and +BP fusion has a molecular weight of 71 + + align:start position:0% +BP fusion has a molecular weight of 71 + + + align:start position:0% +BP fusion has a molecular weight of 71 +kilotons right and what we see up here + + align:start position:0% +kilotons right and what we see up here + + + align:start position:0% +kilotons right and what we see up here +are the components that were in each of + + align:start position:0% +are the components that were in each of + + + align:start position:0% +are the components that were in each of +the experiments for each of the lanes + + align:start position:0% +the experiments for each of the lanes + + + align:start position:0% +the experiments for each of the lanes +right so here in this Lane we have no oh + + align:start position:0% +right so here in this Lane we have no oh + + + align:start position:0% +right so here in this Lane we have no oh +right boom + + align:start position:0% +right boom + + + align:start position:0% +right boom +no Rui Bo the plasmid was included here + + align:start position:0% +no Rui Bo the plasmid was included here + + + align:start position:0% +no Rui Bo the plasmid was included here +we have the orthogonal ribosome in the + + align:start position:0% +we have the orthogonal ribosome in the + + + align:start position:0% +we have the orthogonal ribosome in the +plasmid here Rybak's in the plasmid so + + align:start position:0% +plasmid here Rybak's in the plasmid so + + + align:start position:0% +plasmid here Rybak's in the plasmid so +what do we see + + align:start position:0% + + + + align:start position:0% + +pardon are they all the same yield + + align:start position:0% +pardon are they all the same yield + + + align:start position:0% +pardon are they all the same yield +there's three lanes yeah so no + + align:start position:0% +there's three lanes yeah so no + + + align:start position:0% +there's three lanes yeah so no +orthogonal ribosome no translation and + + align:start position:0% +orthogonal ribosome no translation and + + + align:start position:0% +orthogonal ribosome no translation and +that's a good thing to see right that + + align:start position:0% +that's a good thing to see right that + + + align:start position:0% +that's a good thing to see right that +tells you that this orthogonal mrna is + + align:start position:0% +tells you that this orthogonal mrna is + + + align:start position:0% +tells you that this orthogonal mrna is +not being translated by the endogenous + + align:start position:0% +not being translated by the endogenous + + + align:start position:0% +not being translated by the endogenous +ribosome that that's an important + + align:start position:0% +ribosome that that's an important + + + align:start position:0% +ribosome that that's an important +observation and then I think what you + + align:start position:0% +observation and then I think what you + + + align:start position:0% +observation and then I think what you +meant to say is that in these two lanes + + align:start position:0% +meant to say is that in these two lanes + + + align:start position:0% +meant to say is that in these two lanes +where we have either the starting + + align:start position:0% +where we have either the starting + + + align:start position:0% +where we have either the starting +orthogonal ribosome or ribose + + align:start position:0% +orthogonal ribosome or ribose + + + align:start position:0% +orthogonal ribosome or ribose +we see is what appears to be a very + + align:start position:0% +we see is what appears to be a very + + + align:start position:0% +we see is what appears to be a very +similar amount of protein right so here + + align:start position:0% +similar amount of protein right so here + + + align:start position:0% +similar amount of protein right so here +you know you assume and you look at the + + align:start position:0% +you know you assume and you look at the + + + align:start position:0% +you know you assume and you look at the +experimental the same volumes were + + align:start position:0% +experimental the same volumes were + + + align:start position:0% +experimental the same volumes were +loaded all of these things we're getting + + align:start position:0% +loaded all of these things we're getting + + + align:start position:0% +loaded all of these things we're getting +the same amount of protein yield so + + align:start position:0% +the same amount of protein yield so + + + align:start position:0% +the same amount of protein yield so +that's a great result okay here so + + align:start position:0% +that's a great result okay here so + + + align:start position:0% +that's a great result okay here so +that's good news what's the next + + align:start position:0% +that's good news what's the next + + + align:start position:0% +that's good news what's the next +experiment and we'll close I think on + + align:start position:0% +experiment and we'll close I think on + + + align:start position:0% +experiment and we'll close I think on +this experiment so the next experiment + + align:start position:0% +this experiment so the next experiment + + + align:start position:0% +this experiment so the next experiment +is amino acid missing Corporation so + + align:start position:0% +is amino acid missing Corporation so + + + align:start position:0% +is amino acid missing Corporation so +again what they did is they use this GST + + align:start position:0% +again what they did is they use this GST + + + align:start position:0% +again what they did is they use this GST +MVP fusion protein okay and there's a + + align:start position:0% +MVP fusion protein okay and there's a + + + align:start position:0% +MVP fusion protein okay and there's a +linker region here and in this linker + + align:start position:0% +linker region here and in this linker + + + align:start position:0% +linker region here and in this linker +region they engineered a protease + + align:start position:0% +region they engineered a protease + + + align:start position:0% +region they engineered a protease +cleavage site here + + align:start position:0% + + + + align:start position:0% + +so for thrombin here and why did they do + + align:start position:0% +so for thrombin here and why did they do + + + align:start position:0% +so for thrombin here and why did they do +this to look at them you know acid + + align:start position:0% +this to look at them you know acid + + + align:start position:0% +this to look at them you know acid +incorporation missing corporation + + align:start position:0% +incorporation missing corporation + + + align:start position:0% +incorporation missing corporation +whether that's happening effectively + + align:start position:0% +whether that's happening effectively + + + align:start position:0% +whether that's happening effectively +they took advantage of the fact that GST + + align:start position:0% +they took advantage of the fact that GST + + + align:start position:0% +they took advantage of the fact that GST +contains cysteine whereas multo finding + + align:start position:0% +contains cysteine whereas multo finding + + + align:start position:0% +contains cysteine whereas multo finding +protein has no cysteine okay so their + + align:start position:0% +protein has no cysteine okay so their + + + align:start position:0% +protein has no cysteine okay so their +idea was let's use radio labeled + + align:start position:0% +idea was let's use radio labeled + + + align:start position:0% +idea was let's use radio labeled +cysteine as a probe and monitor for + + align:start position:0% +cysteine as a probe and monitor for + + + align:start position:0% +cysteine as a probe and monitor for +radioactive cysteine and corporation + + align:start position:0% +radioactive cysteine and corporation + + + align:start position:0% +radioactive cysteine and corporation +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so effectively + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +okay okay so effectively what can be + + align:start position:0% +okay okay so effectively what can be + + + align:start position:0% +okay okay so effectively what can be +done is that this can be expressed in + + align:start position:0% +done is that this can be expressed in + + + align:start position:0% +done is that this can be expressed in +purified game the presence of the radio + + align:start position:0% +purified game the presence of the radio + + + align:start position:0% +purified game the presence of the radio +labeled cysteine thrombin can be used to + + align:start position:0% +labeled cysteine thrombin can be used to + + + align:start position:0% +labeled cysteine thrombin can be used to +cleave and then you can look and ask is + + align:start position:0% +cleave and then you can look and ask is + + + align:start position:0% +cleave and then you can look and ask is +there radio activity associated with GST + + align:start position:0% +there radio activity associated with GST + + + align:start position:0% +there radio activity associated with GST +and we hope the answer is yes and is + + align:start position:0% +and we hope the answer is yes and is + + + align:start position:0% +and we hope the answer is yes and is +there radio activity associated with + + align:start position:0% +there radio activity associated with + + + align:start position:0% +there radio activity associated with +maltose binding protein okay and so + + align:start position:0% +maltose binding protein okay and so + + + align:start position:0% +maltose binding protein okay and so +where we'll begin on Friday is looking + + align:start position:0% +where we'll begin on Friday is looking + + + align:start position:0% +where we'll begin on Friday is looking +at the data from this assay but until + + align:start position:0% +at the data from this assay but until + + + align:start position:0% +at the data from this assay but until +then what I'd like you to think about is + + align:start position:0% +then what I'd like you to think about is + + + align:start position:0% +then what I'd like you to think about is +in terms of amino acid miss + + align:start position:0% +in terms of amino acid miss + + + align:start position:0% +in terms of amino acid miss +incorporation kind of strengths and + + align:start position:0% +incorporation kind of strengths and + + + align:start position:0% +incorporation kind of strengths and +limitations of this this assay right so + + align:start position:0% +limitations of this this assay right so + + + align:start position:0% +limitations of this this assay right so +the choice of using one amino acid to + + align:start position:0% +the choice of using one amino acid to + + + align:start position:0% +the choice of using one amino acid to +take a look there okay so I'll see you + + align:start position:0% +take a look there okay so I'll see you + + + align:start position:0% +take a look there okay so I'll see you +Friday + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/PnDtMfyZSIE.txt b/PnDtMfyZSIE.txt new file mode 100644 index 0000000000000000000000000000000000000000..7f5f8de667101a4c0d89307ffcd0c94d12d0474f --- /dev/null +++ b/PnDtMfyZSIE.txt @@ -0,0 +1,14423 @@ +align:start position:0% + +so we ended last time with some + + align:start position:0% +so we ended last time with some + + + align:start position:0% +so we ended last time with some +these element elementary properties that + + align:start position:0% +these element elementary properties that + + + align:start position:0% +these element elementary properties that +you know about the absolute value + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +prove one more theorem about the + + align:start position:0% +prove one more theorem about the + + + align:start position:0% +prove one more theorem about the +absolute value which + + align:start position:0% + + + + align:start position:0% + +maybe you didn't cover + + align:start position:0% +maybe you didn't cover + + + align:start position:0% +maybe you didn't cover +in calculus but + + align:start position:0% +in calculus but + + + align:start position:0% +in calculus but +it's a + + align:start position:0% +it's a + + + align:start position:0% +it's a +fundamental importance + + align:start position:0% + + + + align:start position:0% + +in real analysis which is the triangle + + align:start position:0% +in real analysis which is the triangle + + + align:start position:0% +in real analysis which is the triangle +inequality + + align:start position:0% + + + + align:start position:0% + +which states that for all x y and r + + align:start position:0% +which states that for all x y and r + + + align:start position:0% +which states that for all x y and r +the absolute value of x plus y + + align:start position:0% + + + + align:start position:0% + +is less than or equal to the absolute + + align:start position:0% +is less than or equal to the absolute + + + align:start position:0% +is less than or equal to the absolute +value of x + + align:start position:0% + + + + align:start position:0% + +plus the absolute value of y + + align:start position:0% + + + + align:start position:0% + +okay so why is it called a triangle + + align:start position:0% +okay so why is it called a triangle + + + align:start position:0% +okay so why is it called a triangle +inequality well + + align:start position:0% +inequality well + + + align:start position:0% +inequality well +let me uh + + align:start position:0% +let me uh + + + align:start position:0% +let me uh +instead + + align:start position:0% +instead + + + align:start position:0% +instead +of x and y being real numbers let's + + align:start position:0% +of x and y being real numbers let's + + + align:start position:0% +of x and y being real numbers let's +think of these as as vectors so + + align:start position:0% +think of these as as vectors so + + + align:start position:0% +think of these as as vectors so +um + + align:start position:0% + + + + align:start position:0% + +there's x + + align:start position:0% +there's x + + + align:start position:0% +there's x +let's + + align:start position:0% + + + + align:start position:0% + +say uh + + align:start position:0% + + + + align:start position:0% + +y and then + + align:start position:0% +y and then + + + align:start position:0% +y and then +vector x plus y + + align:start position:0% +vector x plus y + + + align:start position:0% +vector x plus y +is + + align:start position:0% +is + + + align:start position:0% +is +this side + + align:start position:0% + + + + align:start position:0% + +then what this is stating is that the + + align:start position:0% +then what this is stating is that the + + + align:start position:0% +then what this is stating is that the +length + + align:start position:0% +length + + + align:start position:0% +length +of + + align:start position:0% +of + + + align:start position:0% +of +one of these sides of this triangle is + + align:start position:0% +one of these sides of this triangle is + + + align:start position:0% +one of these sides of this triangle is +less than or equal to the sum of the two + + align:start position:0% +less than or equal to the sum of the two + + + align:start position:0% +less than or equal to the sum of the two +sides the sum of the lengths of the + + align:start position:0% +sides the sum of the lengths of the + + + align:start position:0% +sides the sum of the lengths of the +other two sides of the triangle + + align:start position:0% +other two sides of the triangle + + + align:start position:0% +other two sides of the triangle +okay + + align:start position:0% + + + + align:start position:0% + +so that's why it's uh called the + + align:start position:0% +so that's why it's uh called the + + + align:start position:0% +so that's why it's uh called the +triangle inequality + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +proof is not very difficult + + align:start position:0% + + + + align:start position:0% + +although this inequality + + align:start position:0% +although this inequality + + + align:start position:0% +although this inequality +is + + align:start position:0% + + + + align:start position:0% + +probably + + align:start position:0% +probably + + + align:start position:0% +probably +one of the three most useful things + + align:start position:0% +one of the three most useful things + + + align:start position:0% +one of the three most useful things +you'll learn in this class if you go on + + align:start position:0% +you'll learn in this class if you go on + + + align:start position:0% +you'll learn in this class if you go on +to study more analysis + + align:start position:0% +to study more analysis + + + align:start position:0% +to study more analysis +uh the other one being okay so i'm + + align:start position:0% +uh the other one being okay so i'm + + + align:start position:0% +uh the other one being okay so i'm +coming + + align:start position:0% +coming + + + align:start position:0% +coming +uh + + align:start position:0% +uh + + + align:start position:0% +uh +this is knowledge from uh pde so i'm i + + align:start position:0% +this is knowledge from uh pde so i'm i + + + align:start position:0% +this is knowledge from uh pde so i'm i +guess i'm kind of viewing it through + + align:start position:0% +guess i'm kind of viewing it through + + + align:start position:0% +guess i'm kind of viewing it through +that lens of what i find useful in pdes + + align:start position:0% +that lens of what i find useful in pdes + + + align:start position:0% +that lens of what i find useful in pdes +but triangle inequality integration by + + align:start position:0% +but triangle inequality integration by + + + align:start position:0% +but triangle inequality integration by +parts change of variables those three + + align:start position:0% +parts change of variables those three + + + align:start position:0% +parts change of variables those three +power + + align:start position:0% + + + + align:start position:0% + +the analysis machine that i'm most + + align:start position:0% +the analysis machine that i'm most + + + align:start position:0% +the analysis machine that i'm most +familiar with + + align:start position:0% +familiar with + + + align:start position:0% +familiar with +so how to prove the triangle inequality + + align:start position:0% + + + + align:start position:0% + +if x and y is in r + + align:start position:0% +if x and y is in r + + + align:start position:0% +if x and y is in r +then clearly + + align:start position:0% +then clearly + + + align:start position:0% +then clearly +by + + align:start position:0% +by + + + align:start position:0% +by +property number six the abs x is less + + align:start position:0% +property number six the abs x is less + + + align:start position:0% +property number six the abs x is less +than or equal to the absolute value of x + + align:start position:0% +than or equal to the absolute value of x + + + align:start position:0% +than or equal to the absolute value of x +and y is less than or equal to the + + align:start position:0% +and y is less than or equal to the + + + align:start position:0% +and y is less than or equal to the +absolute value of y so their sum is less + + align:start position:0% +absolute value of y so their sum is less + + + align:start position:0% +absolute value of y so their sum is less +than or equal to the absolute value of x + + align:start position:0% +than or equal to the absolute value of x + + + align:start position:0% +than or equal to the absolute value of x +plus y + + align:start position:0% + + + + align:start position:0% + +and not only that + + align:start position:0% +and not only that + + + align:start position:0% +and not only that +i can replace x by minus x and i get + + align:start position:0% +i can replace x by minus x and i get + + + align:start position:0% +i can replace x by minus x and i get +minus x + + align:start position:0% + + + + align:start position:0% + +plus minus y this is less than or equal + + align:start position:0% +plus minus y this is less than or equal + + + align:start position:0% +plus minus y this is less than or equal +to the absolute value of minus x + + align:start position:0% + + + + align:start position:0% + +plus the absolute value of minus y but + + align:start position:0% +plus the absolute value of minus y but + + + align:start position:0% +plus the absolute value of minus y but +this is just + + align:start position:0% +this is just + + + align:start position:0% +this is just +absolute value of x plus y + + align:start position:0% + + + + align:start position:0% + +and both of these therefore imply + + align:start position:0% +and both of these therefore imply + + + align:start position:0% +and both of these therefore imply +so if i just take this and multiply + + align:start position:0% +so if i just take this and multiply + + + align:start position:0% +so if i just take this and multiply +through by minus one + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +this inequality which by number five and + + align:start position:0% +this inequality which by number five and + + + align:start position:0% +this inequality which by number five and +the properties that we + + align:start position:0% +the properties that we + + + align:start position:0% +the properties that we +approved for the absolute value implies + + align:start position:0% +approved for the absolute value implies + + + align:start position:0% +approved for the absolute value implies +that the absolute value of x plus y is + + align:start position:0% +that the absolute value of x plus y is + + + align:start position:0% +that the absolute value of x plus y is +less than or equal to + + align:start position:0% + + + + align:start position:0% + +the absolute value of x + + align:start position:0% +the absolute value of x + + + align:start position:0% +the absolute value of x +plus + + align:start position:0% +plus + + + align:start position:0% +plus +the absolute value of y + + align:start position:0% + + + + align:start position:0% + +so let me just make a + + align:start position:0% +so let me just make a + + + align:start position:0% +so let me just make a +remark about the reverse triangle + + align:start position:0% +remark about the reverse triangle + + + align:start position:0% +remark about the reverse triangle +inequality which + + align:start position:0% + + + + align:start position:0% + +will make an appearance in your + + align:start position:0% +will make an appearance in your + + + align:start position:0% +will make an appearance in your +assignment + + align:start position:0% +assignment + + + align:start position:0% +assignment +and + + align:start position:0% +and + + + align:start position:0% +and +so + + align:start position:0% +so + + + align:start position:0% +so +this involves + + align:start position:0% +this involves + + + align:start position:0% +this involves +the absolute value of x minus y + + align:start position:0% +the absolute value of x minus y + + + align:start position:0% +the absolute value of x minus y +and the absolute value of the difference + + align:start position:0% +and the absolute value of the difference + + + align:start position:0% +and the absolute value of the difference +in the absolute values + + align:start position:0% +in the absolute values + + + align:start position:0% +in the absolute values +why is it reversed because the + + align:start position:0% +why is it reversed because the + + + align:start position:0% +why is it reversed because the +inequality reverses + + align:start position:0% + + + + align:start position:0% + +the absolute value of x minus the + + align:start position:0% +the absolute value of x minus the + + + align:start position:0% +the absolute value of x minus the +absolute value in y + + align:start position:0% +absolute value in y + + + align:start position:0% +absolute value in y +take the absolute value this is less + + align:start position:0% +take the absolute value this is less + + + align:start position:0% +take the absolute value this is less +than or equal to the absolute value of x + + align:start position:0% +than or equal to the absolute value of x + + + align:start position:0% +than or equal to the absolute value of x +minus y and you'll prove this in the + + align:start position:0% +minus y and you'll prove this in the + + + align:start position:0% +minus y and you'll prove this in the +assignment okay + + align:start position:0% +assignment okay + + + align:start position:0% +assignment okay +so these two + + align:start position:0% +so these two + + + align:start position:0% +so these two +so you know this follows from the + + align:start position:0% +so you know this follows from the + + + align:start position:0% +so you know this follows from the +triangle inequality but these two uh + + align:start position:0% +triangle inequality but these two uh + + + align:start position:0% +triangle inequality but these two uh +inequalities get used uh quite a bit and + + align:start position:0% +inequalities get used uh quite a bit and + + + align:start position:0% +inequalities get used uh quite a bit and +we'll use them quite a bit throughout + + align:start position:0% +we'll use them quite a bit throughout + + + align:start position:0% +we'll use them quite a bit throughout +the course + + align:start position:0% +the course + + + align:start position:0% +the course +okay + + align:start position:0% + + + + align:start position:0% + +all right so let me take a minute + + align:start position:0% +all right so let me take a minute + + + align:start position:0% +all right so let me take a minute +to reconnect um + + align:start position:0% +to reconnect um + + + align:start position:0% +to reconnect um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +r with + + align:start position:0% +r with + + + align:start position:0% +r with +what you know and love from calculus + + align:start position:0% +what you know and love from calculus + + + align:start position:0% +what you know and love from calculus +namely decimals + + align:start position:0% +namely decimals + + + align:start position:0% +namely decimals +and + + align:start position:0% +and + + + align:start position:0% +and +we're going to use this fact about r + + align:start position:0% +we're going to use this fact about r + + + align:start position:0% +we're going to use this fact about r +uh to answer you know a natural question + + align:start position:0% +uh to answer you know a natural question + + + align:start position:0% +uh to answer you know a natural question +that maybe + + align:start position:0% +that maybe + + + align:start position:0% +that maybe +you're asking yourself + + align:start position:0% +you're asking yourself + + + align:start position:0% +you're asking yourself +which is the following + + align:start position:0% +which is the following + + + align:start position:0% +which is the following +so let me raise this as a question + + align:start position:0% +so let me raise this as a question + + + align:start position:0% +so let me raise this as a question +um + + align:start position:0% + + + + align:start position:0% + +so this first part is not + + align:start position:0% +so this first part is not + + + align:start position:0% +so this first part is not +a question we've already + + align:start position:0% +a question we've already + + + align:start position:0% +a question we've already +uh addressed this in the first + + align:start position:0% +uh addressed this in the first + + + align:start position:0% +uh addressed this in the first +assignment the fact that + + align:start position:0% +assignment the fact that + + + align:start position:0% +assignment the fact that +the rationals is countable in fact you + + align:start position:0% +the rationals is countable in fact you + + + align:start position:0% +the rationals is countable in fact you +did it for the positive rationals but if + + align:start position:0% +did it for the positive rationals but if + + + align:start position:0% +did it for the positive rationals but if +the positive rationals are countable you + + align:start position:0% +the positive rationals are countable you + + + align:start position:0% +the positive rationals are countable you +can then prove that + + align:start position:0% +can then prove that + + + align:start position:0% +can then prove that +all rationals are countable + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +a natural question is are accountable + + align:start position:0% +a natural question is are accountable + + + align:start position:0% +a natural question is are accountable +okay or is the set of real numbers + + align:start position:0% +okay or is the set of real numbers + + + align:start position:0% +okay or is the set of real numbers +countable + + align:start position:0% +countable + + + align:start position:0% +countable +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% + + + + align:start position:0% + +in the end + + align:start position:0% +in the end + + + align:start position:0% +in the end +i'm not going to leave you in suspense + + align:start position:0% +i'm not going to leave you in suspense + + + align:start position:0% +i'm not going to leave you in suspense +the answer is no + + align:start position:0% + + + + align:start position:0% + +and we're going to prove this but let me + + align:start position:0% +and we're going to prove this but let me + + + align:start position:0% +and we're going to prove this but let me +just make a few remarks about what this + + align:start position:0% +just make a few remarks about what this + + + align:start position:0% +just make a few remarks about what this +says + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +it's the following so + + align:start position:0% + + + + align:start position:0% + +if q + + align:start position:0% +if q + + + align:start position:0% +if q +so this is not a proof of this i'm just + + align:start position:0% +so this is not a proof of this i'm just + + + align:start position:0% +so this is not a proof of this i'm just +going to make a remark based on this + + align:start position:0% +going to make a remark based on this + + + align:start position:0% +going to make a remark based on this +answer + + align:start position:0% +answer + + + align:start position:0% +answer +so + + align:start position:0% + + + + align:start position:0% + +since r + + align:start position:0% + + + + align:start position:0% + +is uncountable + + align:start position:0% + + + + align:start position:0% + +and q + + align:start position:0% + + + + align:start position:0% + +is countable + + align:start position:0% +is countable + + + align:start position:0% +is countable +this implies that + + align:start position:0% + + + + align:start position:0% + +our take away q the set of irrational + + align:start position:0% +our take away q the set of irrational + + + align:start position:0% +our take away q the set of irrational +numbers + + align:start position:0% + + + + align:start position:0% + +is in fact + + align:start position:0% + + + + align:start position:0% + +uncountable + + align:start position:0% +uncountable + + + align:start position:0% +uncountable +why + + align:start position:0% +why + + + align:start position:0% +why +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +so i'm just gonna say in words why this + + align:start position:0% +so i'm just gonna say in words why this + + + align:start position:0% +so i'm just gonna say in words why this +is uh true + + align:start position:0% +is uh true + + + align:start position:0% +is uh true +so + + align:start position:0% +so + + + align:start position:0% +so +suppose otherwise that both the rational + + align:start position:0% +suppose otherwise that both the rational + + + align:start position:0% +suppose otherwise that both the rational +numbers and the irrationals are + + align:start position:0% +numbers and the irrationals are + + + align:start position:0% +numbers and the irrationals are +countable + + align:start position:0% +countable + + + align:start position:0% +countable +then you can map in a bijective fashion + + align:start position:0% +then you can map in a bijective fashion + + + align:start position:0% +then you can map in a bijective fashion +the rationals to the natural numbers + + align:start position:0% +the rationals to the natural numbers + + + align:start position:0% +the rationals to the natural numbers +and the irrationals + + align:start position:0% + + + + align:start position:0% + +also to the natural numbers but then you + + align:start position:0% +also to the natural numbers but then you + + + align:start position:0% +also to the natural numbers but then you +can map those natural numbers to 0 minus + + align:start position:0% +can map those natural numbers to 0 minus + + + align:start position:0% +can map those natural numbers to 0 minus +1 minus 2 minus 3 and so on + + align:start position:0% +1 minus 2 minus 3 and so on + + + align:start position:0% +1 minus 2 minus 3 and so on +so then you find that there is a + + align:start position:0% +so then you find that there is a + + + align:start position:0% +so then you find that there is a +bijection from q to the natural numbers + + align:start position:0% +bijection from q to the natural numbers + + + align:start position:0% +bijection from q to the natural numbers +and the irrationals to + + align:start position:0% +and the irrationals to + + + align:start position:0% +and the irrationals to +the integers less than or equal to 0 and + + align:start position:0% +the integers less than or equal to 0 and + + + align:start position:0% +the integers less than or equal to 0 and +therefore there's a bijection from r to + + align:start position:0% +therefore there's a bijection from r to + + + align:start position:0% +therefore there's a bijection from r to +the integers + + align:start position:0% +the integers + + + align:start position:0% +the integers +but the integers are countable + + align:start position:0% +but the integers are countable + + + align:start position:0% +but the integers are countable +which would contradict the fact that r + + align:start position:0% +which would contradict the fact that r + + + align:start position:0% +which would contradict the fact that r +is uncountable + + align:start position:0% +is uncountable + + + align:start position:0% +is uncountable +therefore the set of irrationals is + + align:start position:0% +therefore the set of irrationals is + + + align:start position:0% +therefore the set of irrationals is +uncountable okay so in short if you + + align:start position:0% +uncountable okay so in short if you + + + align:start position:0% +uncountable okay so in short if you +didn't follow that + + align:start position:0% + + + + align:start position:0% + +the set of irrationals is + + align:start position:0% +the set of irrationals is + + + align:start position:0% +the set of irrationals is +uncountable + + align:start position:0% +uncountable + + + align:start position:0% +uncountable +because otherwise this would force r to + + align:start position:0% +because otherwise this would force r to + + + align:start position:0% +because otherwise this would force r to +be countable okay + + align:start position:0% +be countable okay + + + align:start position:0% +be countable okay +now i haven't proved yet that r is uh is + + align:start position:0% +now i haven't proved yet that r is uh is + + + align:start position:0% +now i haven't proved yet that r is uh is +uncountable we'll do that in just a + + align:start position:0% +uncountable we'll do that in just a + + + align:start position:0% +uncountable we'll do that in just a +minute and we'll use uh + + align:start position:0% +minute and we'll use uh + + + align:start position:0% +minute and we'll use uh +a theorem about decimal uh expansions + + align:start position:0% +a theorem about decimal uh expansions + + + align:start position:0% +a theorem about decimal uh expansions +for + + align:start position:0% +for + + + align:start position:0% +for +or decimal representations of real + + align:start position:0% +or decimal representations of real + + + align:start position:0% +or decimal representations of real +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +so + + align:start position:0% + + + + align:start position:0% + +so now connecting + + align:start position:0% +so now connecting + + + align:start position:0% +so now connecting +you know rationals and irrationals to + + align:start position:0% +you know rationals and irrationals to + + + align:start position:0% +you know rationals and irrationals to +what you've seen since you were + + align:start position:0% +what you've seen since you were + + + align:start position:0% +what you've seen since you were +small so to decimals we simply we + + align:start position:0% +small so to decimals we simply we + + + align:start position:0% +small so to decimals we simply we +typically + + align:start position:0% + + + + align:start position:0% + +we think of rational numbers as + + align:start position:0% + + + + align:start position:0% + +in terms of decimal + + align:start position:0% +in terms of decimal + + + align:start position:0% +in terms of decimal +decimal + + align:start position:0% + + + + align:start position:0% + +representations + + align:start position:0% + + + + align:start position:0% + +what does that mean + + align:start position:0% +what does that mean + + + align:start position:0% +what does that mean +that means we take + + align:start position:0% +that means we take + + + align:start position:0% +that means we take +if x is in + + align:start position:0% + + + + align:start position:0% + +q + + align:start position:0% +q + + + align:start position:0% +q +then we'll write x as + + align:start position:0% +then we'll write x as + + + align:start position:0% +then we'll write x as +some number times + + align:start position:0% +some number times + + + align:start position:0% +some number times +some digit times 10 to the k + + align:start position:0% +some digit times 10 to the k + + + align:start position:0% +some digit times 10 to the k +plus + + align:start position:0% +plus + + + align:start position:0% +plus +ten to the k minus one plus + + align:start position:0% +ten to the k minus one plus + + + align:start position:0% +ten to the k minus one plus +d zero + + align:start position:0% +d zero + + + align:start position:0% +d zero +and then + + align:start position:0% +and then + + + align:start position:0% +and then +uh we go to the tenth spot so d to the + + align:start position:0% +uh we go to the tenth spot so d to the + + + align:start position:0% +uh we go to the tenth spot so d to the +minus + + align:start position:0% +minus + + + align:start position:0% +minus +d minus one ten to the minus 1 plus + + align:start position:0% +d minus one ten to the minus 1 plus + + + align:start position:0% +d minus one ten to the minus 1 plus +so this is discussion i'm not stating + + align:start position:0% +so this is discussion i'm not stating + + + align:start position:0% +so this is discussion i'm not stating +any theorems right now + + align:start position:0% + + + + align:start position:0% + +until we get down to maybe some + + align:start position:0% + + + + align:start position:0% + +last decimal spot + + align:start position:0% +last decimal spot + + + align:start position:0% +last decimal spot +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and with + + align:start position:0% +and with + + + align:start position:0% +and with +these digits + + align:start position:0% + + + + align:start position:0% + +a subset of 0 1 + + align:start position:0% +a subset of 0 1 + + + align:start position:0% +a subset of 0 1 +9. + + align:start position:0% +9. + + + align:start position:0% +9. +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so all i'm saying is typically we think + + align:start position:0% +so all i'm saying is typically we think + + + align:start position:0% +so all i'm saying is typically we think +of x's this way and then we write + + align:start position:0% + + + + align:start position:0% + +x as + + align:start position:0% +x as + + + align:start position:0% +x as +d k + + align:start position:0% +d k + + + align:start position:0% +d k +d k minus 1 + + align:start position:0% +d k minus 1 + + + align:start position:0% +d k minus 1 +d minus 1 d minus 2 + + align:start position:0% +d minus 1 d minus 2 + + + align:start position:0% +d minus 1 d minus 2 +and so on okay + + align:start position:0% +and so on okay + + + align:start position:0% +and so on okay +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +i'm using this notation because i'm + + align:start position:0% +i'm using this notation because i'm + + + align:start position:0% +i'm using this notation because i'm +going to be + + align:start position:0% + + + + align:start position:0% + +this is the notation i need to state the + + align:start position:0% +this is the notation i need to state the + + + align:start position:0% +this is the notation i need to state the +theorem about the real numbers + + align:start position:0% +theorem about the real numbers + + + align:start position:0% +theorem about the real numbers +but + + align:start position:0% + + + + align:start position:0% + +it's quite silly that i'm about to write + + align:start position:0% +it's quite silly that i'm about to write + + + align:start position:0% +it's quite silly that i'm about to write +this down in this setting + + align:start position:0% +this down in this setting + + + align:start position:0% +this down in this setting +you know + + align:start position:0% +you know + + + align:start position:0% +you know +welcome to mit + + align:start position:0% +welcome to mit + + + align:start position:0% +welcome to mit +so + + align:start position:0% +so + + + align:start position:0% +so +for + + align:start position:0% +for + + + align:start position:0% +for +example 1 times 10 + + align:start position:0% + + + + align:start position:0% + +plus 1 + + align:start position:0% + + + + align:start position:0% + +times 10 to the 0 + + align:start position:0% +times 10 to the 0 + + + align:start position:0% +times 10 to the 0 +plus 1 times + + align:start position:0% +plus 1 times + + + align:start position:0% +plus 1 times +10 to the minus 1 + + align:start position:0% +10 to the minus 1 + + + align:start position:0% +10 to the minus 1 +right + + align:start position:0% +right + + + align:start position:0% +right +the this is supposed to represent the + + align:start position:0% +the this is supposed to represent the + + + align:start position:0% +the this is supposed to represent the +number 11.1 + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +which is the rational number + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +it's quite funny that i had to think + + align:start position:0% +it's quite funny that i had to think + + + align:start position:0% +it's quite funny that i had to think +about that for a minute to go from the + + align:start position:0% +about that for a minute to go from the + + + align:start position:0% +about that for a minute to go from the +decimal expansion to the rational + + align:start position:0% +decimal expansion to the rational + + + align:start position:0% +decimal expansion to the rational +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +but um + + align:start position:0% +but um + + + align:start position:0% +but um +you know don't give me too hard of a + + align:start position:0% +you know don't give me too hard of a + + + align:start position:0% +you know don't give me too hard of a +time + + align:start position:0% +time + + + align:start position:0% +time +in + + align:start position:0% +in + + + align:start position:0% +in +a lot of at least pure math + + align:start position:0% +a lot of at least pure math + + + align:start position:0% +a lot of at least pure math +we typically write things in rational + + align:start position:0% +we typically write things in rational + + + align:start position:0% +we typically write things in rational +numbers we don't + + align:start position:0% +numbers we don't + + + align:start position:0% +numbers we don't +write in decimal i haven't had to write + + align:start position:0% +write in decimal i haven't had to write + + + align:start position:0% +write in decimal i haven't had to write +in decimal expansions in quite some time + + align:start position:0% +in decimal expansions in quite some time + + + align:start position:0% +in decimal expansions in quite some time +anyways + + align:start position:0% +anyways + + + align:start position:0% +anyways +now of course not all rational numbers + + align:start position:0% +now of course not all rational numbers + + + align:start position:0% +now of course not all rational numbers +can be written as a finite decimal + + align:start position:0% +can be written as a finite decimal + + + align:start position:0% +can be written as a finite decimal +expansion for example one-third you have + + align:start position:0% +expansion for example one-third you have + + + align:start position:0% +expansion for example one-third you have +to write as + + align:start position:0% +to write as + + + align:start position:0% +to write as +0.33333 + + align:start position:0% +0.33333 + + + align:start position:0% +0.33333 +and so on and so on + + align:start position:0% + + + + align:start position:0% + +you know so that's not necessarily + + align:start position:0% +you know so that's not necessarily + + + align:start position:0% +you know so that's not necessarily +covered under the + + align:start position:0% +covered under the + + + align:start position:0% +covered under the +discussion that i have right here + + align:start position:0% +discussion that i have right here + + + align:start position:0% +discussion that i have right here +um but it will become + + align:start position:0% +um but it will become + + + align:start position:0% +um but it will become +covered um and what i'm about to stay + + align:start position:0% +covered um and what i'm about to stay + + + align:start position:0% +covered um and what i'm about to stay +for the real numbers + + align:start position:0% +for the real numbers + + + align:start position:0% +for the real numbers +um + + align:start position:0% +um + + + align:start position:0% +um +so we could cover a third + + align:start position:0% +so we could cover a third + + + align:start position:0% +so we could cover a third +uh and then we can also cover every real + + align:start position:0% +uh and then we can also cover every real + + + align:start position:0% +uh and then we can also cover every real +number if we allow sort of infinite + + align:start position:0% +number if we allow sort of infinite + + + align:start position:0% +number if we allow sort of infinite +decimal uh representations so i'll use + + align:start position:0% +decimal uh representations so i'll use + + + align:start position:0% +decimal uh representations so i'll use +the word decimal expansions or decimal + + align:start position:0% +the word decimal expansions or decimal + + + align:start position:0% +the word decimal expansions or decimal +representations interchangeably there + + align:start position:0% +representations interchangeably there + + + align:start position:0% +representations interchangeably there +so + + align:start position:0% + + + + align:start position:0% + +make a definition and what i'm going to + + align:start position:0% +make a definition and what i'm going to + + + align:start position:0% +make a definition and what i'm going to +state is about real numbers between 0 + + align:start position:0% +state is about real numbers between 0 + + + align:start position:0% +state is about real numbers between 0 +and 1. + + align:start position:0% +and 1. + + + align:start position:0% +and 1. +of course if you want to talk about real + + align:start position:0% +of course if you want to talk about real + + + align:start position:0% +of course if you want to talk about real +numbers bigger than 1 then you just tack + + align:start position:0% +numbers bigger than 1 then you just tack + + + align:start position:0% +numbers bigger than 1 then you just tack +on 1 to the + + align:start position:0% +on 1 to the + + + align:start position:0% +on 1 to the +if you like to the d0 place + + align:start position:0% +if you like to the d0 place + + + align:start position:0% +if you like to the d0 place +[Applause] + + align:start position:0% + + + + align:start position:0% + +so the infinite part is having to deal + + align:start position:0% +so the infinite part is having to deal + + + align:start position:0% +so the infinite part is having to deal +with what comes after the the decimal + + align:start position:0% +with what comes after the the decimal + + + align:start position:0% +with what comes after the the decimal +point + + align:start position:0% +point + + + align:start position:0% +point +um + + align:start position:0% +um + + + align:start position:0% +um +so the let me make the following so this + + align:start position:0% +so the let me make the following so this + + + align:start position:0% +so the let me make the following so this +is a rigorous definition + + align:start position:0% +is a rigorous definition + + + align:start position:0% +is a rigorous definition +let x in + + align:start position:0% +let x in + + + align:start position:0% +let x in +0 1 excluding 0 + + align:start position:0% + + + + align:start position:0% + +and let + + align:start position:0% +and let + + + align:start position:0% +and let +d + + align:start position:0% +d + + + align:start position:0% +d +minus j be in 0 1 + + align:start position:0% +minus j be in 0 1 + + + align:start position:0% +minus j be in 0 1 +to 9. + + align:start position:0% + + + + align:start position:0% + +for j a natural number + + align:start position:0% + + + + align:start position:0% + +so we say + + align:start position:0% + + + + align:start position:0% + +x is + + align:start position:0% + + + + align:start position:0% + +so what does it mean to say that x is + + align:start position:0% +so what does it mean to say that x is + + + align:start position:0% +so what does it mean to say that x is +given by an infinite decimal expansion + + align:start position:0% +given by an infinite decimal expansion + + + align:start position:0% +given by an infinite decimal expansion +or given by an infinite decimal + + align:start position:0% +or given by an infinite decimal + + + align:start position:0% +or given by an infinite decimal +representation rotation we say x is + + align:start position:0% +representation rotation we say x is + + + align:start position:0% +representation rotation we say x is +represented + + align:start position:0% +represented + + + align:start position:0% +represented +by the digits + + align:start position:0% + + + + align:start position:0% + +and we write + + align:start position:0% + + + + align:start position:0% + +x is equal to + + align:start position:0% +x is equal to + + + align:start position:0% +x is equal to +d minus 1 d minus 2 + + align:start position:0% +d minus 1 d minus 2 + + + align:start position:0% +d minus 1 d minus 2 +minus 3. + + align:start position:0% +minus 3. + + + align:start position:0% +minus 3. +um + + align:start position:0% +um + + + align:start position:0% +um +if so this is a precise meaning of this + + align:start position:0% +if so this is a precise meaning of this + + + align:start position:0% +if so this is a precise meaning of this +if x is equal to the supremum + + align:start position:0% +if x is equal to the supremum + + + align:start position:0% +if x is equal to the supremum +of + + align:start position:0% +of + + + align:start position:0% +of +the set + + align:start position:0% + + + + align:start position:0% + +so i take a finite + + align:start position:0% +so i take a finite + + + align:start position:0% +so i take a finite +decimal expansion + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% +and then + + + align:start position:0% +and then +so i get a number for each in a natural + + align:start position:0% +so i get a number for each in a natural + + + align:start position:0% +so i get a number for each in a natural +number so the first one is just d to + + align:start position:0% +number so the first one is just d to + + + align:start position:0% +number so the first one is just d to +d minus 1 10 to the minus 1 and then for + + align:start position:0% +d minus 1 10 to the minus 1 and then for + + + align:start position:0% +d minus 1 10 to the minus 1 and then for +n equals 2 i tack on next to hundreds + + align:start position:0% +n equals 2 i tack on next to hundreds + + + align:start position:0% +n equals 2 i tack on next to hundreds +place and then the thousands place and + + align:start position:0% +place and then the thousands place and + + + align:start position:0% +place and then the thousands place and +so i get + + align:start position:0% +so i get + + + align:start position:0% +so i get +a set of real numbers + + align:start position:0% +a set of real numbers + + + align:start position:0% +a set of real numbers +if i take it supremum and i get x then i + + align:start position:0% +if i take it supremum and i get x then i + + + align:start position:0% +if i take it supremum and i get x then i +say that x is represented by + + align:start position:0% +say that x is represented by + + + align:start position:0% +say that x is represented by +these digits or that x + + align:start position:0% +these digits or that x + + + align:start position:0% +these digits or that x +or that this gives a decimal + + align:start position:0% +or that this gives a decimal + + + align:start position:0% +or that this gives a decimal +representation of x + + align:start position:0% +representation of x + + + align:start position:0% +representation of x +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that + + align:start position:0% +so that + + + align:start position:0% +so that +you see + + align:start position:0% + + + + align:start position:0% + +this lines up with what + + align:start position:0% + + + + align:start position:0% + +you know + + align:start position:0% + + + + align:start position:0% + +if i look at 0.2500 + + align:start position:0% +if i look at 0.2500 + + + align:start position:0% +if i look at 0.2500 +remember this is now + + align:start position:0% +remember this is now + + + align:start position:0% +remember this is now +the soup of + + align:start position:0% +the soup of + + + align:start position:0% +the soup of +what + + align:start position:0% +what + + + align:start position:0% +what +of a certain set so let me do + + align:start position:0% +of a certain set so let me do + + + align:start position:0% +of a certain set so let me do +first this guy so this is + + align:start position:0% + + + + align:start position:0% + +2 over 10 and then now i add the + + align:start position:0% +2 over 10 and then now i add the + + + align:start position:0% +2 over 10 and then now i add the +hundreds place plus + + align:start position:0% +hundreds place plus + + + align:start position:0% +hundreds place plus +5 up for 100 and then 2 over 10 plus + + align:start position:0% +5 up for 100 and then 2 over 10 plus + + + align:start position:0% +5 up for 100 and then 2 over 10 plus +5 over 100 this is a set remember plus 0 + + align:start position:0% +5 over 100 this is a set remember plus 0 + + + align:start position:0% +5 over 100 this is a set remember plus 0 +over + + align:start position:0% +over + + + align:start position:0% +over +1000 plus so + + align:start position:0% +1000 plus so + + + align:start position:0% +1000 plus so +and + + align:start position:0% +and + + + align:start position:0% +and +at each + + align:start position:0% +at each + + + align:start position:0% +at each +next guy i'm supposed to take this and + + align:start position:0% +next guy i'm supposed to take this and + + + align:start position:0% +next guy i'm supposed to take this and +add on another zero so as a set + + align:start position:0% +add on another zero so as a set + + + align:start position:0% +add on another zero so as a set +this is just + + align:start position:0% + + + + align:start position:0% + +a set containing two elements namely + + align:start position:0% +a set containing two elements namely + + + align:start position:0% +a set containing two elements namely +two + + align:start position:0% +two + + + align:start position:0% +two +tenths and + + align:start position:0% + + + + align:start position:0% + +25 over 100 + + align:start position:0% +25 over 100 + + + align:start position:0% +25 over 100 +and so this is + + align:start position:0% +and so this is + + + align:start position:0% +and so this is +uh bigger than that guy so the supremum + + align:start position:0% +uh bigger than that guy so the supremum + + + align:start position:0% +uh bigger than that guy so the supremum +is 25 over 100 which equals a fourth + + align:start position:0% +is 25 over 100 which equals a fourth + + + align:start position:0% +is 25 over 100 which equals a fourth +okay so all of that to tell you that yes + + align:start position:0% +okay so all of that to tell you that yes + + + align:start position:0% +okay so all of that to tell you that yes +this definition should + + align:start position:0% +this definition should + + + align:start position:0% +this definition should +or at least does + + align:start position:0% +or at least does + + + align:start position:0% +or at least does +ring true with what you were taught that + + align:start position:0% +ring true with what you were taught that + + + align:start position:0% +ring true with what you were taught that +a quarter is equal to 0.25 + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so now we're done with the triangle + + align:start position:0% +so now we're done with the triangle + + + align:start position:0% +so now we're done with the triangle +inequality + + align:start position:0% +inequality + + + align:start position:0% +inequality +i'm going to erase this + + align:start position:0% + + + + align:start position:0% + +and so this is uh the last bit of + + align:start position:0% +and so this is uh the last bit of + + + align:start position:0% +and so this is uh the last bit of +discussion about + + align:start position:0% +discussion about + + + align:start position:0% +discussion about +the elementary properties of the real + + align:start position:0% +the elementary properties of the real + + + align:start position:0% +the elementary properties of the real +numbers next we'll be talking about + + align:start position:0% +numbers next we'll be talking about + + + align:start position:0% +numbers next we'll be talking about +sequences of real numbers + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +all right so i have this definition + + align:start position:0% +all right so i have this definition + + + align:start position:0% +all right so i have this definition +the fundamental theorem about uh + + align:start position:0% +the fundamental theorem about uh + + + align:start position:0% +the fundamental theorem about uh +the real numbers is that every real + + align:start position:0% +the real numbers is that every real + + + align:start position:0% +the real numbers is that every real +number at least uh in the setting + + align:start position:0% +number at least uh in the setting + + + align:start position:0% +number at least uh in the setting +between zero and one can be represented + + align:start position:0% +between zero and one can be represented + + + align:start position:0% +between zero and one can be represented +uh + + align:start position:0% +uh + + + align:start position:0% +uh +by a set of digits or it has a decimal + + align:start position:0% +by a set of digits or it has a decimal + + + align:start position:0% +by a set of digits or it has a decimal +uh representation + + align:start position:0% + + + + align:start position:0% + +in every decimal + + align:start position:0% +in every decimal + + + align:start position:0% +in every decimal +if you like every set of digits + + align:start position:0% +if you like every set of digits + + + align:start position:0% +if you like every set of digits +corresponds to + + align:start position:0% +corresponds to + + + align:start position:0% +corresponds to +a decimal representation of a real + + align:start position:0% +a decimal representation of a real + + + align:start position:0% +a decimal representation of a real +number + + align:start position:0% +number + + + align:start position:0% +number +so let me state + + align:start position:0% +so let me state + + + align:start position:0% +so let me state +the + + align:start position:0% +the + + + align:start position:0% +the +second thing i said first + + align:start position:0% +second thing i said first + + + align:start position:0% +second thing i said first +so + + align:start position:0% + + + + align:start position:0% + +for every set of digits + + align:start position:0% + + + + align:start position:0% + +b minus j + + align:start position:0% + + + + align:start position:0% + +with + + align:start position:0% + + + + align:start position:0% + +each of these d d minus j's in zero up + + align:start position:0% +each of these d d minus j's in zero up + + + align:start position:0% +each of these d d minus j's in zero up +to nine + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +there exists + + align:start position:0% + + + + align:start position:0% + +a unique x + + align:start position:0% +a unique x + + + align:start position:0% +a unique x +in + + align:start position:0% +in + + + align:start position:0% +in +closed interval 0 1 + + align:start position:0% + + + + align:start position:0% + +such that x is equal to + + align:start position:0% + + + + align:start position:0% + +p minus 1 so + + align:start position:0% +p minus 1 so + + + align:start position:0% +p minus 1 so +with this decimal representation + + align:start position:0% +with this decimal representation + + + align:start position:0% +with this decimal representation +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +you give me some digits + + align:start position:0% +you give me some digits + + + align:start position:0% +you give me some digits +and i can find a unique real number that + + align:start position:0% +and i can find a unique real number that + + + align:start position:0% +and i can find a unique real number that +has that decimal uh + + align:start position:0% +has that decimal uh + + + align:start position:0% +has that decimal uh +representation + + align:start position:0% +representation + + + align:start position:0% +representation +now before i state the the second part + + align:start position:0% +now before i state the the second part + + + align:start position:0% +now before i state the the second part +of the theorem + + align:start position:0% +of the theorem + + + align:start position:0% +of the theorem +this says that i give you digits i get a + + align:start position:0% +this says that i give you digits i get a + + + align:start position:0% +this says that i give you digits i get a +unique real number now you ask about the + + align:start position:0% +unique real number now you ask about the + + + align:start position:0% +unique real number now you ask about the +other direction + + align:start position:0% +other direction + + + align:start position:0% +other direction +if i have a real number + + align:start position:0% +if i have a real number + + + align:start position:0% +if i have a real number +do i get a unique set of digits and of + + align:start position:0% +do i get a unique set of digits and of + + + align:start position:0% +do i get a unique set of digits and of +course that is not true + + align:start position:0% +course that is not true + + + align:start position:0% +course that is not true +necessarily because for example + + align:start position:0% + + + + align:start position:0% + +one-half + + align:start position:0% +one-half + + + align:start position:0% +one-half +this is equal to + + align:start position:0% + + + + align:start position:0% + +0.5 + + align:start position:0% +0.5 + + + align:start position:0% +0.5 +0 0 and so on + + align:start position:0% +0 0 and so on + + + align:start position:0% +0 0 and so on +but this is also equal to 0.4999 + + align:start position:0% +but this is also equal to 0.4999 + + + align:start position:0% +but this is also equal to 0.4999 +and so on so + + align:start position:0% +and so on so + + + align:start position:0% +and so on so +yes every + + align:start position:0% +yes every + + + align:start position:0% +yes every +set of digits gives me a unique real + + align:start position:0% +set of digits gives me a unique real + + + align:start position:0% +set of digits gives me a unique real +number + + align:start position:0% +number + + + align:start position:0% +number +so if i gave you these digits they would + + align:start position:0% +so if i gave you these digits they would + + + align:start position:0% +so if i gave you these digits they would +spit out one half and only one half it + + align:start position:0% +spit out one half and only one half it + + + align:start position:0% +spit out one half and only one half it +wouldn't spit out a fourth + + align:start position:0% +wouldn't spit out a fourth + + + align:start position:0% +wouldn't spit out a fourth +but if you give me a real number there + + align:start position:0% +but if you give me a real number there + + + align:start position:0% +but if you give me a real number there +does not necessarily + + align:start position:0% +does not necessarily + + + align:start position:0% +does not necessarily +uh give exist a unique + + align:start position:0% +uh give exist a unique + + + align:start position:0% +uh give exist a unique +set of digits giving + + align:start position:0% +set of digits giving + + + align:start position:0% +set of digits giving +a decimal expansion for that number so i + + align:start position:0% +a decimal expansion for that number so i + + + align:start position:0% +a decimal expansion for that number so i +can have two different decimal + + align:start position:0% +can have two different decimal + + + align:start position:0% +can have two different decimal +expansions i have point five nine point + + align:start position:0% +expansions i have point five nine point + + + align:start position:0% +expansions i have point five nine point +four nine nine nine i will always have + + align:start position:0% +four nine nine nine i will always have + + + align:start position:0% +four nine nine nine i will always have +at least one but it's not necessarily + + align:start position:0% +at least one but it's not necessarily + + + align:start position:0% +at least one but it's not necessarily +unique okay but we can send we can + + align:start position:0% +unique okay but we can send we can + + + align:start position:0% +unique okay but we can send we can +single out one unique + + align:start position:0% +single out one unique + + + align:start position:0% +single out one unique +choice by requiring that + + align:start position:0% +choice by requiring that + + + align:start position:0% +choice by requiring that +some sense uh if i were to truncate it + + align:start position:0% +some sense uh if i were to truncate it + + + align:start position:0% +some sense uh if i were to truncate it +then the decimal expansion would be less + + align:start position:0% +then the decimal expansion would be less + + + align:start position:0% +then the decimal expansion would be less +than the number i'm looking at + + align:start position:0% +than the number i'm looking at + + + align:start position:0% +than the number i'm looking at +wanting to expand so that's the second + + align:start position:0% +wanting to expand so that's the second + + + align:start position:0% +wanting to expand so that's the second +part of this theorem + + align:start position:0% +part of this theorem + + + align:start position:0% +part of this theorem +is that for every x + + align:start position:0% + + + + align:start position:0% + +in 0 1 now excluding 0 + + align:start position:0% + + + + align:start position:0% + +there exists + + align:start position:0% + + + + align:start position:0% + +exist + + align:start position:0% + + + + align:start position:0% + +unique digits + + align:start position:0% + + + + align:start position:0% + +and as before these are in 0 + + align:start position:0% +and as before these are in 0 + + + align:start position:0% +and as before these are in 0 +up to 9 + + align:start position:0% +up to 9 + + + align:start position:0% +up to 9 +such that + + align:start position:0% + + + + align:start position:0% + +x + + align:start position:0% +x + + + align:start position:0% +x +is + + align:start position:0% +is + + + align:start position:0% +is +such that these give a decimal + + align:start position:0% +such that these give a decimal + + + align:start position:0% +such that these give a decimal +representation of x + + align:start position:0% + + + + align:start position:0% + +and so what singles + + align:start position:0% +and so what singles + + + align:start position:0% +and so what singles +out of choice if we're ever + + align:start position:0% +out of choice if we're ever + + + align:start position:0% +out of choice if we're ever +coming up against these two things um + + align:start position:0% +coming up against these two things um + + + align:start position:0% +coming up against these two things um +and + + align:start position:0% + + + + align:start position:0% + +if i truncate + + align:start position:0% +if i truncate + + + align:start position:0% +if i truncate +the decimal expansion + + align:start position:0% +the decimal expansion + + + align:start position:0% +the decimal expansion +so i'm not going to write 0s after that + + align:start position:0% +so i'm not going to write 0s after that + + + align:start position:0% +so i'm not going to write 0s after that +i'm just going to truncate it this + + align:start position:0% +i'm just going to truncate it this + + + align:start position:0% +i'm just going to truncate it this +always is less than x + + align:start position:0% +always is less than x + + + align:start position:0% +always is less than x +and this is less than or equal to + + align:start position:0% + + + + align:start position:0% + +plus + + align:start position:0% +plus + + + align:start position:0% +plus +10 to the minus n + + align:start position:0% +10 to the minus n + + + align:start position:0% +10 to the minus n +okay + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +you know this inequality will always + + align:start position:0% +you know this inequality will always + + + align:start position:0% +you know this inequality will always +hold + + align:start position:0% +hold + + + align:start position:0% +hold +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +and in fact + + align:start position:0% +and in fact + + + align:start position:0% +and in fact +so + + align:start position:0% +so + + + align:start position:0% +so +this inequality will always hold + + align:start position:0% +this inequality will always hold + + + align:start position:0% +this inequality will always hold +and in fact x is always bigger than or + + align:start position:0% +and in fact x is always bigger than or + + + align:start position:0% +and in fact x is always bigger than or +equal to this side like uh no matter + + align:start position:0% +equal to this side like uh no matter + + + align:start position:0% +equal to this side like uh no matter +what if if x is given by + + align:start position:0% +what if if x is given by + + + align:start position:0% +what if if x is given by +a decimal representation so we always + + align:start position:0% +a decimal representation so we always + + + align:start position:0% +a decimal representation so we always +have these two + + align:start position:0% +have these two + + + align:start position:0% +have these two +this is a less than or equal to and this + + align:start position:0% +this is a less than or equal to and this + + + align:start position:0% +this is a less than or equal to and this +is a less than or equal to but we single + + align:start position:0% +is a less than or equal to but we single + + + align:start position:0% +is a less than or equal to but we single +out a unique choice of decimal + + align:start position:0% +out a unique choice of decimal + + + align:start position:0% +out a unique choice of decimal +representation by + + align:start position:0% +representation by + + + align:start position:0% +representation by +choosing this to be a strict less than + + align:start position:0% +choosing this to be a strict less than + + + align:start position:0% +choosing this to be a strict less than +okay so then that forces us to choose + + align:start position:0% +okay so then that forces us to choose + + + align:start position:0% +okay so then that forces us to choose +this guy + + align:start position:0% +this guy + + + align:start position:0% +this guy +over this guy + + align:start position:0% +over this guy + + + align:start position:0% +over this guy +so + + align:start position:0% + + + + align:start position:0% + +for theorem two + + align:start position:0% +for theorem two + + + align:start position:0% +for theorem two +this would say that the represent the + + align:start position:0% +this would say that the represent the + + + align:start position:0% +this would say that the represent the +unique representation + + align:start position:0% +unique representation + + + align:start position:0% +unique representation +that satisfies this for one half is + + align:start position:0% +that satisfies this for one half is + + + align:start position:0% +that satisfies this for one half is +given by 0.4999 + + align:start position:0% +given by 0.4999 + + + align:start position:0% +given by 0.4999 +and for example for one would be just + + align:start position:0% +and for example for one would be just + + + align:start position:0% +and for example for one would be just +0.9999 okay + + align:start position:0% +0.9999 okay + + + align:start position:0% +0.9999 okay +because if i take this representation + + align:start position:0% +because if i take this representation + + + align:start position:0% +because if i take this representation +and cut it off this is actually equal to + + align:start position:0% +and cut it off this is actually equal to + + + align:start position:0% +and cut it off this is actually equal to +one-half + + align:start position:0% +one-half + + + align:start position:0% +one-half +and not less than one-half + + align:start position:0% +and not less than one-half + + + align:start position:0% +and not less than one-half +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that was a lot of discussion about + + align:start position:0% +so that was a lot of discussion about + + + align:start position:0% +so that was a lot of discussion about +the theorem but that was for a reason + + align:start position:0% +the theorem but that was for a reason + + + align:start position:0% +the theorem but that was for a reason +because i'm not actually going to prove + + align:start position:0% +because i'm not actually going to prove + + + align:start position:0% +because i'm not actually going to prove +this theorem um + + align:start position:0% +this theorem um + + + align:start position:0% +this theorem um +it's not uh entirely + + align:start position:0% +it's not uh entirely + + + align:start position:0% +it's not uh entirely +difficult it just uses you know the + + align:start position:0% +difficult it just uses you know the + + + align:start position:0% +difficult it just uses you know the +least upper bound property of the real + + align:start position:0% +least upper bound property of the real + + + align:start position:0% +least upper bound property of the real +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +but it's a little um + + align:start position:0% +but it's a little um + + + align:start position:0% +but it's a little um +clunky to write down and what i'd rather + + align:start position:0% +clunky to write down and what i'd rather + + + align:start position:0% +clunky to write down and what i'd rather +do is just use this theorem + + align:start position:0% +do is just use this theorem + + + align:start position:0% +do is just use this theorem +to prove + + align:start position:0% +to prove + + + align:start position:0% +to prove +uh + + align:start position:0% +uh + + + align:start position:0% +uh +my answer the answer to my question up + + align:start position:0% +my answer the answer to my question up + + + align:start position:0% +my answer the answer to my question up +there on whether r is countable or not + + align:start position:0% +there on whether r is countable or not + + + align:start position:0% +there on whether r is countable or not +okay + + align:start position:0% +okay + + + align:start position:0% +okay +in the textbook there is a proof of this + + align:start position:0% +in the textbook there is a proof of this + + + align:start position:0% +in the textbook there is a proof of this +theorem which you can read + + align:start position:0% +theorem which you can read + + + align:start position:0% +theorem which you can read +okay + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +we're actually going to use this theorem + + align:start position:0% +we're actually going to use this theorem + + + align:start position:0% +we're actually going to use this theorem +to prove + + align:start position:0% + + + + align:start position:0% + +the following theorem due to cantor + + align:start position:0% +the following theorem due to cantor + + + align:start position:0% +the following theorem due to cantor +so we just went from uh absolute values + + align:start position:0% +so we just went from uh absolute values + + + align:start position:0% +so we just went from uh absolute values +which maybe was not too shock and awe + + align:start position:0% +which maybe was not too shock and awe + + + align:start position:0% +which maybe was not too shock and awe +now to this theorem which to me is + + align:start position:0% +now to this theorem which to me is + + + align:start position:0% +now to this theorem which to me is +shocking off is that + + align:start position:0% + + + + align:start position:0% + +following that + + align:start position:0% + + + + align:start position:0% + +the interval 0 1 + + align:start position:0% + + + + align:start position:0% + +is uncountable + + align:start position:0% +is uncountable + + + align:start position:0% +is uncountable +okay + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +so maybe you're asking yourself + + align:start position:0% +so maybe you're asking yourself + + + align:start position:0% +so maybe you're asking yourself +well that's showing this is uncountable + + align:start position:0% +well that's showing this is uncountable + + + align:start position:0% +well that's showing this is uncountable +and + + align:start position:0% +and + + + align:start position:0% +and +that's saying r is + + align:start position:0% +that's saying r is + + + align:start position:0% +that's saying r is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uncountable + + align:start position:0% +uncountable + + + align:start position:0% +uncountable +so where do we go from this to that + + align:start position:0% +so where do we go from this to that + + + align:start position:0% +so where do we go from this to that +well i'll let you think about that but + + align:start position:0% +well i'll let you think about that but + + + align:start position:0% +well i'll let you think about that but +let's assume this was uncountable and r + + align:start position:0% +let's assume this was uncountable and r + + + align:start position:0% +let's assume this was uncountable and r +was countable so i'm just going to say + + align:start position:0% +was countable so i'm just going to say + + + align:start position:0% +was countable so i'm just going to say +this + + align:start position:0% +this + + + align:start position:0% +this +say y out loud + + align:start position:0% +say y out loud + + + align:start position:0% +say y out loud +if this was um + + align:start position:0% +if this was um + + + align:start position:0% +if this was um +uncountable and r was countable + + align:start position:0% +uncountable and r was countable + + + align:start position:0% +uncountable and r was countable +then since this is a subset of r that + + align:start position:0% +then since this is a subset of r that + + + align:start position:0% +then since this is a subset of r that +means + + align:start position:0% +means + + + align:start position:0% +means +this under + + align:start position:0% +this under + + + align:start position:0% +this under +would be + + align:start position:0% +would be + + + align:start position:0% +would be +so + + align:start position:0% +so + + + align:start position:0% +so +let me just write so + + align:start position:0% + + + + align:start position:0% + +why does this imply + + align:start position:0% + + + + align:start position:0% + +and i'm going to give you kind of a fake + + align:start position:0% +and i'm going to give you kind of a fake + + + align:start position:0% +and i'm going to give you kind of a fake +proof but you can actually make this + + align:start position:0% +proof but you can actually make this + + + align:start position:0% +proof but you can actually make this +completely rigorous + + align:start position:0% + + + + align:start position:0% + +fake proof in the sense that i'm just + + align:start position:0% +fake proof in the sense that i'm just + + + align:start position:0% +fake proof in the sense that i'm just +going to write symbols + + align:start position:0% +going to write symbols + + + align:start position:0% +going to write symbols +that + + align:start position:0% +that + + + align:start position:0% +that +imply this so why is + + align:start position:0% +imply this so why is + + + align:start position:0% +imply this so why is +r + + align:start position:0% +r + + + align:start position:0% +r +uncountable then if this is uncountable + + align:start position:0% +uncountable then if this is uncountable + + + align:start position:0% +uncountable then if this is uncountable +well + + align:start position:0% +well + + + align:start position:0% +well +the function that takes an element in + + align:start position:0% +the function that takes an element in + + + align:start position:0% +the function that takes an element in +here just into r + + align:start position:0% +here just into r + + + align:start position:0% +here just into r +this is clearly bijective so just the + + align:start position:0% +this is clearly bijective so just the + + + align:start position:0% +this is clearly bijective so just the +identity map from 0 1 into r + + align:start position:0% +identity map from 0 1 into r + + + align:start position:0% +identity map from 0 1 into r +is injective map + + align:start position:0% +is injective map + + + align:start position:0% +is injective map +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +i clearly have that + + align:start position:0% +i clearly have that + + + align:start position:0% +i clearly have that +cardinality of this set + + align:start position:0% +cardinality of this set + + + align:start position:0% +cardinality of this set +is less than or equal to + + align:start position:0% +is less than or equal to + + + align:start position:0% +is less than or equal to +the cardinality of r + + align:start position:0% +the cardinality of r + + + align:start position:0% +the cardinality of r +okay in fact + + align:start position:0% +okay in fact + + + align:start position:0% +okay in fact +you know maybe you can think about it + + align:start position:0% +you know maybe you can think about it + + + align:start position:0% +you know maybe you can think about it +maybe i'll put on the assignment but + + align:start position:0% +maybe i'll put on the assignment but + + + align:start position:0% +maybe i'll put on the assignment but +in fact one can prove they have the same + + align:start position:0% +in fact one can prove they have the same + + + align:start position:0% +in fact one can prove they have the same +cardinality but + + align:start position:0% + + + + align:start position:0% + +i have that + + align:start position:0% +i have that + + + align:start position:0% +i have that +and this is uncountable therefore its + + align:start position:0% +and this is uncountable therefore its + + + align:start position:0% +and this is uncountable therefore its +cardinality + + align:start position:0% +cardinality + + + align:start position:0% +cardinality +is bigger than the natural numbers + + align:start position:0% + + + + align:start position:0% + +so this should imply that cardinality of + + align:start position:0% +so this should imply that cardinality of + + + align:start position:0% +so this should imply that cardinality of +the natural numbers + + align:start position:0% +the natural numbers + + + align:start position:0% +the natural numbers +is less than the cardinality of r + + align:start position:0% +is less than the cardinality of r + + + align:start position:0% +is less than the cardinality of r +okay + + align:start position:0% +okay + + + align:start position:0% +okay +in other words r is uncountable + + align:start position:0% + + + + align:start position:0% + +all right so let's prove + + align:start position:0% +all right so let's prove + + + align:start position:0% +all right so let's prove +this theorem due to cantor now + + align:start position:0% +this theorem due to cantor now + + + align:start position:0% +this theorem due to cantor now +this other theorem due to cantor that + + align:start position:0% +this other theorem due to cantor that + + + align:start position:0% +this other theorem due to cantor that +the + + align:start position:0% +the + + + align:start position:0% +the +cardinality of + + align:start position:0% +cardinality of + + + align:start position:0% +cardinality of +the power set is bigger than the + + align:start position:0% +the power set is bigger than the + + + align:start position:0% +the power set is bigger than the +cardinality of the set i mean that was + + align:start position:0% + + + + align:start position:0% + +at least the proof + + align:start position:0% +at least the proof + + + align:start position:0% +at least the proof +the first time i saw that was some crazy + + align:start position:0% +the first time i saw that was some crazy + + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +this is also going to be some pretty + + align:start position:0% +this is also going to be some pretty + + + align:start position:0% +this is also going to be some pretty +crazy and clever too + + align:start position:0% +crazy and clever too + + + align:start position:0% +crazy and clever too +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +this is what's referred to as cantor's + + align:start position:0% +this is what's referred to as cantor's + + + align:start position:0% +this is what's referred to as cantor's +diagonalization argument + + align:start position:0% +diagonalization argument + + + align:start position:0% +diagonalization argument +or diagonal argument + + align:start position:0% +or diagonal argument + + + align:start position:0% +or diagonal argument +and it's the following so we're going to + + align:start position:0% +and it's the following so we're going to + + + align:start position:0% +and it's the following so we're going to +prove this by contradiction + + align:start position:0% + + + + align:start position:0% + +so we're going to assume that this is + + align:start position:0% +so we're going to assume that this is + + + align:start position:0% +so we're going to assume that this is +countable so it can't be finite there's + + align:start position:0% +countable so it can't be finite there's + + + align:start position:0% +countable so it can't be finite there's +infinitely many of + + align:start position:0% +infinitely many of + + + align:start position:0% +infinitely many of +elements in here so suppose + + align:start position:0% + + + + align:start position:0% + +uh that in fact it has the cardinality + + align:start position:0% +uh that in fact it has the cardinality + + + align:start position:0% +uh that in fact it has the cardinality +of the natural numbers + + align:start position:0% + + + + align:start position:0% + +and we're going to arrive at a + + align:start position:0% +and we're going to arrive at a + + + align:start position:0% +and we're going to arrive at a +contradiction + + align:start position:0% +contradiction + + + align:start position:0% +contradiction +so then + + align:start position:0% + + + + align:start position:0% + +there exists a function which i'm going + + align:start position:0% +there exists a function which i'm going + + + align:start position:0% +there exists a function which i'm going +to call x + + align:start position:0% +to call x + + + align:start position:0% +to call x +from + + align:start position:0% +from + + + align:start position:0% +from +natural numbers into + + align:start position:0% +natural numbers into + + + align:start position:0% +natural numbers into +0 1 + + align:start position:0% +0 1 + + + align:start position:0% +0 1 +okay which is bijective + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% + + + + align:start position:0% + +so let me + + align:start position:0% +so let me + + + align:start position:0% +so let me +label this inequality star + + align:start position:0% +label this inequality star + + + align:start position:0% +label this inequality star +for each in + + align:start position:0% + + + + align:start position:0% + +we write x + + align:start position:0% +we write x + + + align:start position:0% +we write x +of n so this is an element of 0 1. + + align:start position:0% +of n so this is an element of 0 1. + + + align:start position:0% +of n so this is an element of 0 1. +so this is bijective so every element in + + align:start position:0% +so this is bijective so every element in + + + align:start position:0% +so this is bijective so every element in +0 1 + + align:start position:0% +0 1 + + + align:start position:0% +0 1 +gets mapped onto so + + align:start position:0% +gets mapped onto so + + + align:start position:0% +gets mapped onto so +we write x of n to be in its decimal + + align:start position:0% +we write x of n to be in its decimal + + + align:start position:0% +we write x of n to be in its decimal +representation + + align:start position:0% + + + + align:start position:0% + +i have two + + align:start position:0% +i have two + + + align:start position:0% +i have two +indices now one for the digit + + align:start position:0% +indices now one for the digit + + + align:start position:0% +indices now one for the digit +place and the one for + + align:start position:0% +place and the one for + + + align:start position:0% +place and the one for +which + + align:start position:0% + + + + align:start position:0% + +excuse me + + align:start position:0% +excuse me + + + align:start position:0% +excuse me +at least i sheltered you from that + + align:start position:0% +at least i sheltered you from that + + + align:start position:0% +at least i sheltered you from that +sneeze by putting my hand over the + + align:start position:0% +sneeze by putting my hand over the + + + align:start position:0% +sneeze by putting my hand over the +microphone the microphone's still on + + align:start position:0% +microphone the microphone's still on + + + align:start position:0% +microphone the microphone's still on +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so for each end we write + + align:start position:0% + + + + align:start position:0% + +each x of n in its decimal + + align:start position:0% +each x of n in its decimal + + + align:start position:0% +each x of n in its decimal +representation + + align:start position:0% + + + + align:start position:0% + +satisfying star so each x in here can be + + align:start position:0% +satisfying star so each x in here can be + + + align:start position:0% +satisfying star so each x in here can be +written uniquely + + align:start position:0% + + + + align:start position:0% + +in a given decimal representation + + align:start position:0% +in a given decimal representation + + + align:start position:0% +in a given decimal representation +satisfying this inequality here now what + + align:start position:0% +satisfying this inequality here now what + + + align:start position:0% +satisfying this inequality here now what +we're going to do is we're going to come + + align:start position:0% +we're going to do is we're going to come + + + align:start position:0% +we're going to do is we're going to come +up with + + align:start position:0% +up with + + + align:start position:0% +up with +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +a real number in the interval 0 1 + + align:start position:0% +a real number in the interval 0 1 + + + align:start position:0% +a real number in the interval 0 1 +which x does not map to + + align:start position:0% +which x does not map to + + + align:start position:0% +which x does not map to +which therefore contradicts the fact + + align:start position:0% +which therefore contradicts the fact + + + align:start position:0% +which therefore contradicts the fact +that x is surjective remember bijective + + align:start position:0% +that x is surjective remember bijective + + + align:start position:0% +that x is surjective remember bijective +surjective means + + align:start position:0% +surjective means + + + align:start position:0% +surjective means +um + + align:start position:0% +um + + + align:start position:0% +um +that + + align:start position:0% +that + + + align:start position:0% +that +everything has to get mapped onto this + + align:start position:0% +everything has to get mapped onto this + + + align:start position:0% +everything has to get mapped onto this +onto part + + align:start position:0% +onto part + + + align:start position:0% +onto part +uh + + align:start position:0% +uh + + + align:start position:0% +uh +injective means it maps different things + + align:start position:0% +injective means it maps different things + + + align:start position:0% +injective means it maps different things +to different things + + align:start position:0% +to different things + + + align:start position:0% +to different things +so what's + + align:start position:0% +so what's + + + align:start position:0% +so what's +what's kind of the idea + + align:start position:0% +what's kind of the idea + + + align:start position:0% +what's kind of the idea +of finding this + + align:start position:0% + + + + align:start position:0% + +element that doesn't get mapped onto + + align:start position:0% +element that doesn't get mapped onto + + + align:start position:0% +element that doesn't get mapped onto +so + + align:start position:0% + + + + align:start position:0% + +let me + + align:start position:0% + + + + align:start position:0% + +write down + + align:start position:0% +write down + + + align:start position:0% +write down +just a few + + align:start position:0% + + + + align:start position:0% + +of these decimal expansions + + align:start position:0% +of these decimal expansions + + + align:start position:0% +of these decimal expansions +and i may not want to do a fourth one + + align:start position:0% + + + + align:start position:0% + +and maybe i do + + align:start position:0% + + + + align:start position:0% + +so this is uh again discussion so i'm + + align:start position:0% +so this is uh again discussion so i'm + + + align:start position:0% +so this is uh again discussion so i'm +going to put this in brackets meaning + + align:start position:0% +going to put this in brackets meaning + + + align:start position:0% +going to put this in brackets meaning +this is not part of the proof but this + + align:start position:0% +this is not part of the proof but this + + + align:start position:0% +this is not part of the proof but this +is part of the idea of + + align:start position:0% +is part of the idea of + + + align:start position:0% +is part of the idea of +what's going on and + + align:start position:0% + + + + align:start position:0% + +where's the diagonal part + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +and this should + + align:start position:0% +and this should + + + align:start position:0% +and this should +go off in this direction and the decimal + + align:start position:0% +go off in this direction and the decimal + + + align:start position:0% +go off in this direction and the decimal +expansions march off in that direction + + align:start position:0% +expansions march off in that direction + + + align:start position:0% +expansions march off in that direction +and so somehow + + align:start position:0% +and so somehow + + + align:start position:0% +and so somehow +this list if it kept going in that + + align:start position:0% +this list if it kept going in that + + + align:start position:0% +this list if it kept going in that +direction + + align:start position:0% +direction + + + align:start position:0% +direction +uh would have to contain every real + + align:start position:0% +uh would have to contain every real + + + align:start position:0% +uh would have to contain every real +number between zero and one + + align:start position:0% +number between zero and one + + + align:start position:0% +number between zero and one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so what's uh what's the idea to come + + align:start position:0% +and so what's uh what's the idea to come + + + align:start position:0% +and so what's uh what's the idea to come +up with a real number between zero and + + align:start position:0% +up with a real number between zero and + + + align:start position:0% +up with a real number between zero and +one + + align:start position:0% +one + + + align:start position:0% +one +that + + align:start position:0% +that + + + align:start position:0% +that +is not in this list is + + align:start position:0% +is not in this list is + + + align:start position:0% +is not in this list is +we go down the diagonal + + align:start position:0% + + + + align:start position:0% + +of the decimal expansions + + align:start position:0% + + + + align:start position:0% + +and we + + align:start position:0% +and we + + + align:start position:0% +and we +change + + align:start position:0% +change + + + align:start position:0% +change +each decimal to something else + + align:start position:0% +each decimal to something else + + + align:start position:0% +each decimal to something else +okay then what it is + + align:start position:0% +okay then what it is + + + align:start position:0% +okay then what it is +and so therefore and then i take uh + + align:start position:0% +and so therefore and then i take uh + + + align:start position:0% +and so therefore and then i take uh +my element y + + align:start position:0% +my element y + + + align:start position:0% +my element y +so remember we're trying to find a y + + align:start position:0% + + + + align:start position:0% + +not in this + + align:start position:0% + + + + align:start position:0% + +list + + align:start position:0% +list + + + align:start position:0% +list +and then i would take y to be the real + + align:start position:0% +and then i would take y to be the real + + + align:start position:0% +and then i would take y to be the real +number that i get by changing each of + + align:start position:0% +number that i get by changing each of + + + align:start position:0% +number that i get by changing each of +these + + align:start position:0% + + + + align:start position:0% + +decimal uh + + align:start position:0% + + + + align:start position:0% + +digits okay + + align:start position:0% +digits okay + + + align:start position:0% +digits okay +so you can imagine if y somehow popped + + align:start position:0% +so you can imagine if y somehow popped + + + align:start position:0% +so you can imagine if y somehow popped +up let's say it popped up + + align:start position:0% +up let's say it popped up + + + align:start position:0% +up let's say it popped up +since i don't want to write anymore as + + align:start position:0% +since i don't want to write anymore as + + + align:start position:0% +since i don't want to write anymore as +x4 all right then somehow this number + + align:start position:0% +x4 all right then somehow this number + + + align:start position:0% +x4 all right then somehow this number +would have to be + + align:start position:0% +would have to be + + + align:start position:0% +would have to be +the + + align:start position:0% +the + + + align:start position:0% +the +digit for y + + align:start position:0% +digit for y + + + align:start position:0% +digit for y +but i changed it and therefore it's not + + align:start position:0% +but i changed it and therefore it's not + + + align:start position:0% +but i changed it and therefore it's not +the digit of y + + align:start position:0% +the digit of y + + + align:start position:0% +the digit of y +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +you know that's it in a nutshell + + align:start position:0% +you know that's it in a nutshell + + + align:start position:0% +you know that's it in a nutshell +um + + align:start position:0% +um + + + align:start position:0% +um +if you didn't get that that's fine let + + align:start position:0% +if you didn't get that that's fine let + + + align:start position:0% +if you didn't get that that's fine let +me now write out uh + + align:start position:0% +me now write out uh + + + align:start position:0% +me now write out uh +the details + + align:start position:0% +the details + + + align:start position:0% +the details +so you know it's a little bit simpler to + + align:start position:0% +so you know it's a little bit simpler to + + + align:start position:0% +so you know it's a little bit simpler to +to imagine if let's say all of these + + align:start position:0% +to imagine if let's say all of these + + + align:start position:0% +to imagine if let's say all of these +were zeros and ones so instead of being + + align:start position:0% +were zeros and ones so instead of being + + + align:start position:0% +were zeros and ones so instead of being +base ten i was base two + + align:start position:0% +base ten i was base two + + + align:start position:0% +base ten i was base two +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so instead of + + align:start position:0% +and so instead of + + + align:start position:0% +and so instead of +uh if the digit was a zero i flipped it + + align:start position:0% +uh if the digit was a zero i flipped it + + + align:start position:0% +uh if the digit was a zero i flipped it +to one + + align:start position:0% +to one + + + align:start position:0% +to one +so + + align:start position:0% +so + + + align:start position:0% +so +you can imagine that if y did so and + + align:start position:0% +you can imagine that if y did so and + + + align:start position:0% +you can imagine that if y did so and +then i form + + align:start position:0% +then i form + + + align:start position:0% +then i form +y by flipping the digits okay so if this + + align:start position:0% +y by flipping the digits okay so if this + + + align:start position:0% +y by flipping the digits okay so if this +was 0 0 1 1 + + align:start position:0% +was 0 0 1 1 + + + align:start position:0% +was 0 0 1 1 +then y would start off 1 1 0 0 + + align:start position:0% +then y would start off 1 1 0 0 + + + align:start position:0% +then y would start off 1 1 0 0 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and therefore if y appeared say 4th in + + align:start position:0% +and therefore if y appeared say 4th in + + + align:start position:0% +and therefore if y appeared say 4th in +line + + align:start position:0% + + + + align:start position:0% + +it would have to be 1 and 0 in the same + + align:start position:0% +it would have to be 1 and 0 in the same + + + align:start position:0% +it would have to be 1 and 0 in the same +spot + + align:start position:0% +spot + + + align:start position:0% +spot +okay just by how i've constructed y by + + align:start position:0% +okay just by how i've constructed y by + + + align:start position:0% +okay just by how i've constructed y by +flipping it and therefore y can't be in + + align:start position:0% +flipping it and therefore y can't be in + + + align:start position:0% +flipping it and therefore y can't be in +that list and therefore this map cannot + + align:start position:0% +that list and therefore this map cannot + + + align:start position:0% +that list and therefore this map cannot +be + + align:start position:0% +be + + + align:start position:0% +be +subjective + + align:start position:0% +subjective + + + align:start position:0% +subjective +all right which is our contradiction + + align:start position:0% +all right which is our contradiction + + + align:start position:0% +all right which is our contradiction +so + + align:start position:0% +so + + + align:start position:0% +so +let me make this more precise + + align:start position:0% + + + + align:start position:0% + +let + + align:start position:0% + + + + align:start position:0% + +e j this is going to be one + + align:start position:0% +e j this is going to be one + + + align:start position:0% +e j this is going to be one +if + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +j + + align:start position:0% +j + + + align:start position:0% +j +digit of the j + + align:start position:0% +digit of the j + + + align:start position:0% +digit of the j +x of j + + align:start position:0% +x of j + + + align:start position:0% +x of j +does not equal one + + align:start position:0% +does not equal one + + + align:start position:0% +does not equal one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +two + + align:start position:0% + + + + align:start position:0% + +if the j digit of the j + + align:start position:0% +if the j digit of the j + + + align:start position:0% +if the j digit of the j +guy in that list or x of j + + align:start position:0% + + + + align:start position:0% + +does equal one + + align:start position:0% +does equal one + + + align:start position:0% +does equal one +okay + + align:start position:0% + + + + align:start position:0% + +by + + align:start position:0% +by + + + align:start position:0% +by +part one of the theorem + + align:start position:0% +part one of the theorem + + + align:start position:0% +part one of the theorem +previous theorem + + align:start position:0% +previous theorem + + + align:start position:0% +previous theorem +there exists + + align:start position:0% + + + + align:start position:0% + +a unique y + + align:start position:0% + + + + align:start position:0% + +in zero one without zero why because + + align:start position:0% +in zero one without zero why because + + + align:start position:0% +in zero one without zero why because +some of these did you know these digits + + align:start position:0% +some of these did you know these digits + + + align:start position:0% +some of these did you know these digits +are non-zero it's always either one or + + align:start position:0% +are non-zero it's always either one or + + + align:start position:0% +are non-zero it's always either one or +two + + align:start position:0% +two + + + align:start position:0% +two +okay + + align:start position:0% + + + + align:start position:0% + +such that + + align:start position:0% + + + + align:start position:0% + +y is equal to e minus one e minus 2 and + + align:start position:0% +y is equal to e minus one e minus 2 and + + + align:start position:0% +y is equal to e minus one e minus 2 and +so on ok + + align:start position:0% + + + + align:start position:0% + +so moreover + + align:start position:0% + + + + align:start position:0% + +since all + + align:start position:0% + + + + align:start position:0% + +of these digits + + align:start position:0% + + + + align:start position:0% + +are either one or two + + align:start position:0% + + + + align:start position:0% + +they are + + align:start position:0% + + + + align:start position:0% + +certainly non-zero + + align:start position:0% + + + + align:start position:0% + +so y is given by a decimal expansion + + align:start position:0% +so y is given by a decimal expansion + + + align:start position:0% +so y is given by a decimal expansion +where all of these things are non-zero + + align:start position:0% +where all of these things are non-zero + + + align:start position:0% +where all of these things are non-zero +okay so that means + + align:start position:0% + + + + align:start position:0% + +that for all in a natural number if i + + align:start position:0% +that for all in a natural number if i + + + align:start position:0% +that for all in a natural number if i +take + + align:start position:0% +take + + + align:start position:0% +take +a finite decimal expansion so i cut this + + align:start position:0% +a finite decimal expansion so i cut this + + + align:start position:0% +a finite decimal expansion so i cut this +off at e to the minus n since e to the e + + align:start position:0% +off at e to the minus n since e to the e + + + align:start position:0% +off at e to the minus n since e to the e +minus n plus one + + align:start position:0% +minus n plus one + + + align:start position:0% +minus n plus one +is either one or two that's going to be + + align:start position:0% +is either one or two that's going to be + + + align:start position:0% +is either one or two that's going to be +positive so + + align:start position:0% +positive so + + + align:start position:0% +positive so +that's + + align:start position:0% +that's + + + align:start position:0% +that's +less than y + + align:start position:0% +less than y + + + align:start position:0% +less than y +and this is always the case that this is + + align:start position:0% +and this is always the case that this is + + + align:start position:0% +and this is always the case that this is +less than or equal to + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +because all these digits are positive if + + align:start position:0% +because all these digits are positive if + + + align:start position:0% +because all these digits are positive if +i cut it off if i truncate it then + + align:start position:0% +i cut it off if i truncate it then + + + align:start position:0% +i cut it off if i truncate it then +that number is going to be less than y + + align:start position:0% +that number is going to be less than y + + + align:start position:0% +that number is going to be less than y +okay because i'm missing stuff out in + + align:start position:0% +okay because i'm missing stuff out in + + + align:start position:0% +okay because i'm missing stuff out in +the millions place or whatever + + align:start position:0% +the millions place or whatever + + + align:start position:0% +the millions place or whatever +each time + + align:start position:0% +each time + + + align:start position:0% +each time +for each n okay + + align:start position:0% +for each n okay + + + align:start position:0% +for each n okay +and therefore + + align:start position:0% + + + + align:start position:0% + +this decimal expansion + + align:start position:0% +this decimal expansion + + + align:start position:0% +this decimal expansion +is + + align:start position:0% + + + + align:start position:0% + +the unique + + align:start position:0% + + + + align:start position:0% + +decimal representation + + align:start position:0% + + + + align:start position:0% + +from part two of the theorem okay that i + + align:start position:0% +from part two of the theorem okay that i + + + align:start position:0% +from part two of the theorem okay that i +stated right + + align:start position:0% +stated right + + + align:start position:0% +stated right +every element in zero one has a unique + + align:start position:0% +every element in zero one has a unique + + + align:start position:0% +every element in zero one has a unique +representation satisfying that + + align:start position:0% +representation satisfying that + + + align:start position:0% +representation satisfying that +inequality because all of these digits + + align:start position:0% +inequality because all of these digits + + + align:start position:0% +inequality because all of these digits +are positive + + align:start position:0% +are positive + + + align:start position:0% +are positive +this + + align:start position:0% +this + + + align:start position:0% +this +in fact is a unique representation of + + align:start position:0% +in fact is a unique representation of + + + align:start position:0% +in fact is a unique representation of +this element y which i've constructed by + + align:start position:0% +this element y which i've constructed by + + + align:start position:0% +this element y which i've constructed by +flipping digits + + align:start position:0% +flipping digits + + + align:start position:0% +flipping digits +from this map + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% + + + + align:start position:0% + +x is + + align:start position:0% + + + + align:start position:0% + +surjective + + align:start position:0% +surjective + + + align:start position:0% +surjective +there exists an n natural number um you + + align:start position:0% +there exists an n natural number um you + + + align:start position:0% +there exists an n natural number um you +know this n has nothing to do with that + + align:start position:0% +know this n has nothing to do with that + + + align:start position:0% +know this n has nothing to do with that +n maybe i'll use a different letter + + align:start position:0% +n maybe i'll use a different letter + + + align:start position:0% +n maybe i'll use a different letter +m + + align:start position:0% +m + + + align:start position:0% +m +such that + + align:start position:0% +such that + + + align:start position:0% +such that +y equals x of m + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +let's say i look at + + align:start position:0% + + + + align:start position:0% + +e to the minus m + + align:start position:0% +e to the minus m + + + align:start position:0% +e to the minus m +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so then + + align:start position:0% +so then + + + align:start position:0% +so then +this says that + + align:start position:0% +this says that + + + align:start position:0% +this says that +the m digit which is + + align:start position:0% + + + + align:start position:0% + +should be giving me e to the minus m + + align:start position:0% +should be giving me e to the minus m + + + align:start position:0% +should be giving me e to the minus m +because this is equal to y + + align:start position:0% +because this is equal to y + + + align:start position:0% +because this is equal to y +this + + align:start position:0% +this + + + align:start position:0% +this +remember is equal to + + align:start position:0% +remember is equal to + + + align:start position:0% +remember is equal to +one + + align:start position:0% +one + + + align:start position:0% +one +if + + align:start position:0% + + + + align:start position:0% + +the m + + align:start position:0% + + + + align:start position:0% + +two + + align:start position:0% +two + + + align:start position:0% +two +if dm + + align:start position:0% + + + + align:start position:0% + +equals one + + align:start position:0% +equals one + + + align:start position:0% +equals one +in particular this does not equal + + align:start position:0% +in particular this does not equal + + + align:start position:0% +in particular this does not equal +d + + align:start position:0% +d + + + align:start position:0% +d +m + + align:start position:0% + + + + align:start position:0% + +so i have proven that + + align:start position:0% +so i have proven that + + + align:start position:0% +so i have proven that +this number + + align:start position:0% +this number + + + align:start position:0% +this number +does not equal itself + + align:start position:0% +does not equal itself + + + align:start position:0% +does not equal itself +okay + + align:start position:0% + + + + align:start position:0% + +all right i can never if i can never + + align:start position:0% +all right i can never if i can never + + + align:start position:0% +all right i can never if i can never +have this + + align:start position:0% +have this + + + align:start position:0% +have this +number whatever it is equal to this + + align:start position:0% +number whatever it is equal to this + + + align:start position:0% +number whatever it is equal to this +thing because i'm always changing it if + + align:start position:0% +thing because i'm always changing it if + + + align:start position:0% +thing because i'm always changing it if +this thing is one + + align:start position:0% +this thing is one + + + align:start position:0% +this thing is one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +then + + align:start position:0% +then + + + align:start position:0% +then +this number is two + + align:start position:0% +this number is two + + + align:start position:0% +this number is two +if this number is not one then this + + align:start position:0% +if this number is not one then this + + + align:start position:0% +if this number is not one then this +number is one and therefore it's not + + align:start position:0% +number is one and therefore it's not + + + align:start position:0% +number is one and therefore it's not +equal to that + + align:start position:0% +equal to that + + + align:start position:0% +equal to that +okay + + align:start position:0% + + + + align:start position:0% + +and this is a contradiction + + align:start position:0% + + + + align:start position:0% + +thus uh + + align:start position:0% +thus uh + + + align:start position:0% +thus uh +it shows that + + align:start position:0% + + + + align:start position:0% + +the set is uncountable + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so i hope i explained that uh well + + align:start position:0% +so i hope i explained that uh well + + + align:start position:0% +so i hope i explained that uh well +enough + + align:start position:0% + + + + align:start position:0% + +you know you can also look in the + + align:start position:0% +you know you can also look in the + + + align:start position:0% +you know you can also look in the +textbook for + + align:start position:0% +textbook for + + + align:start position:0% +textbook for +uh + + align:start position:0% +uh + + + align:start position:0% +uh +explanation as well and of course you + + align:start position:0% +explanation as well and of course you + + + align:start position:0% +explanation as well and of course you +can ask me in office hours for + + align:start position:0% + + + + align:start position:0% + +more explanation + + align:start position:0% + + + + align:start position:0% + +let me fuel up real quick + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now we're moving on to a new chapter + + align:start position:0% +now we're moving on to a new chapter + + + align:start position:0% +now we're moving on to a new chapter +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +um we're gonna get to + + align:start position:0% + + + + align:start position:0% + +now we're going to get to the analysis + + align:start position:0% +now we're going to get to the analysis + + + align:start position:0% +now we're going to get to the analysis +part so analysis as i've said before is + + align:start position:0% +part so analysis as i've said before is + + + align:start position:0% +part so analysis as i've said before is +the study of limits real analysis is the + + align:start position:0% +the study of limits real analysis is the + + + align:start position:0% +the study of limits real analysis is the +study of limits that has to deal with + + align:start position:0% +study of limits that has to deal with + + + align:start position:0% +study of limits that has to deal with +real numbers + + align:start position:0% +real numbers + + + align:start position:0% +real numbers +so let's get to + + align:start position:0% +so let's get to + + + align:start position:0% +so let's get to +our first + + align:start position:0% + + + + align:start position:0% + +notion of a limit and that is the limit + + align:start position:0% +notion of a limit and that is the limit + + + align:start position:0% +notion of a limit and that is the limit +of a sequence of real numbers + + align:start position:0% + + + + align:start position:0% + +so now we're moving on to + + align:start position:0% + + + + align:start position:0% + +sequences and + + align:start position:0% + + + + align:start position:0% + +series + + align:start position:0% + + + + align:start position:0% + +okay so what is the precise definition + + align:start position:0% +okay so what is the precise definition + + + align:start position:0% +okay so what is the precise definition +of a sequence of real numbers + + align:start position:0% + + + + align:start position:0% + +a sequence + + align:start position:0% + + + + align:start position:0% + +of real numbers is + + align:start position:0% + + + + align:start position:0% + +precisely a function + + align:start position:0% +precisely a function + + + align:start position:0% +precisely a function +x from + + align:start position:0% +x from + + + align:start position:0% +x from +the natural numbers into r + + align:start position:0% +the natural numbers into r + + + align:start position:0% +the natural numbers into r +okay just a function it doesn't have to + + align:start position:0% +okay just a function it doesn't have to + + + align:start position:0% +okay just a function it doesn't have to +be bijectives or objective injective + + align:start position:0% +be bijectives or objective injective + + + align:start position:0% +be bijectives or objective injective +anything it's just a function from the + + align:start position:0% +anything it's just a function from the + + + align:start position:0% +anything it's just a function from the +natural numbers to r so that's precisely + + align:start position:0% +natural numbers to r so that's precisely + + + align:start position:0% +natural numbers to r so that's precisely +what + + align:start position:0% +what + + + align:start position:0% +what +a sequence of real numbers is uh now we + + align:start position:0% +a sequence of real numbers is uh now we + + + align:start position:0% +a sequence of real numbers is uh now we +typically don't think of a sequence as a + + align:start position:0% +typically don't think of a sequence as a + + + align:start position:0% +typically don't think of a sequence as a +function in fact we don't even use that + + align:start position:0% +function in fact we don't even use that + + + align:start position:0% +function in fact we don't even use that +notation + + align:start position:0% + + + + align:start position:0% + +we denote x of n by + + align:start position:0% +we denote x of n by + + + align:start position:0% +we denote x of n by +x sub n + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +the associated sequence + + align:start position:0% +the associated sequence + + + align:start position:0% +the associated sequence +by + + align:start position:0% + + + + align:start position:0% + +this curly brackets + + align:start position:0% +this curly brackets + + + align:start position:0% +this curly brackets +n equals 1 to infinity + + align:start position:0% +n equals 1 to infinity + + + align:start position:0% +n equals 1 to infinity +or + + align:start position:0% +or + + + align:start position:0% +or +we might not even + + align:start position:0% +we might not even + + + align:start position:0% +we might not even +write the n equals 1 to infinity part + + align:start position:0% +write the n equals 1 to infinity part + + + align:start position:0% +write the n equals 1 to infinity part +or + + align:start position:0% +or + + + align:start position:0% +or +just start listing them + + align:start position:0% +just start listing them + + + align:start position:0% +just start listing them +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +let me + + align:start position:0% +let me + + + align:start position:0% +let me +quickly say that although + + align:start position:0% +quickly say that although + + + align:start position:0% +quickly say that although +so again a sequence + + align:start position:0% + + + + align:start position:0% + +you know unambiguously defined is a + + align:start position:0% +you know unambiguously defined is a + + + align:start position:0% +you know unambiguously defined is a +function from the natural numbers to + + align:start position:0% +function from the natural numbers to + + + align:start position:0% +function from the natural numbers to +real + + align:start position:0% +real + + + align:start position:0% +real +so don't confuse this with a set okay a + + align:start position:0% +so don't confuse this with a set okay a + + + align:start position:0% +so don't confuse this with a set okay a +sequence is not a set + + align:start position:0% +sequence is not a set + + + align:start position:0% +sequence is not a set +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +you know think of a sequence even though + + align:start position:0% +you know think of a sequence even though + + + align:start position:0% +you know think of a sequence even though +again it's defined as a function as just + + align:start position:0% +again it's defined as a function as just + + + align:start position:0% +again it's defined as a function as just +a + + align:start position:0% +a + + + align:start position:0% +a +uh infinite listing + + align:start position:0% +uh infinite listing + + + align:start position:0% +uh infinite listing +of elements of r okay + + align:start position:0% +of elements of r okay + + + align:start position:0% +of elements of r okay +one element the the first element the + + align:start position:0% +one element the the first element the + + + align:start position:0% +one element the the first element the +second element the third element and so + + align:start position:0% +second element the third element and so + + + align:start position:0% +second element the third element and so +on + + align:start position:0% +on + + + align:start position:0% +on +okay and they don't have to be different + + align:start position:0% +okay and they don't have to be different + + + align:start position:0% +okay and they don't have to be different +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +for example + + align:start position:0% + + + + align:start position:0% + +one one one one + + align:start position:0% +one one one one + + + align:start position:0% +one one one one +one + + align:start position:0% +one + + + align:start position:0% +one +that is a perfectly good sequence okay + + align:start position:0% +that is a perfectly good sequence okay + + + align:start position:0% +that is a perfectly good sequence okay +in terms of what is the function this is + + align:start position:0% +in terms of what is the function this is + + + align:start position:0% +in terms of what is the function this is +x of n + + align:start position:0% +x of n + + + align:start position:0% +x of n +equals one + + align:start position:0% +equals one + + + align:start position:0% +equals one +for all n but again i will not think of + + align:start position:0% +for all n but again i will not think of + + + align:start position:0% +for all n but again i will not think of +really a sequence as a function + + align:start position:0% +really a sequence as a function + + + align:start position:0% +really a sequence as a function +just as we never thought about + + align:start position:0% +just as we never thought about + + + align:start position:0% +just as we never thought about +functions as + + align:start position:0% +functions as + + + align:start position:0% +functions as +subsets of as certain subsets of + + align:start position:0% +subsets of as certain subsets of + + + align:start position:0% +subsets of as certain subsets of +the cartesian product of two sets you + + align:start position:0% +the cartesian product of two sets you + + + align:start position:0% +the cartesian product of two sets you +should really think of these as just a + + align:start position:0% +should really think of these as just a + + + align:start position:0% +should really think of these as just a +list of + + align:start position:0% +list of + + + align:start position:0% +list of +real numbers + + align:start position:0% +real numbers + + + align:start position:0% +real numbers +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and when we refer to them we'll either + + align:start position:0% +and when we refer to them we'll either + + + align:start position:0% +and when we refer to them we'll either +write them like that or with curly + + align:start position:0% +write them like that or with curly + + + align:start position:0% +write them like that or with curly +brackets around an expression for x sub + + align:start position:0% +brackets around an expression for x sub + + + align:start position:0% +brackets around an expression for x sub +n + + align:start position:0% + + + + align:start position:0% + +so for example if i were to write + + align:start position:0% +so for example if i were to write + + + align:start position:0% +so for example if i were to write +this + + align:start position:0% +this + + + align:start position:0% +this +this means + + align:start position:0% + + + + align:start position:0% + +this is the sequence + + align:start position:0% +this is the sequence + + + align:start position:0% +this is the sequence +given by one one-half + + align:start position:0% +given by one one-half + + + align:start position:0% +given by one one-half +one-third + + align:start position:0% +one-third + + + align:start position:0% +one-third +one-fourth + + align:start position:0% +one-fourth + + + align:start position:0% +one-fourth +one-fifth and so on + + align:start position:0% +one-fifth and so on + + + align:start position:0% +one-fifth and so on +okay + + align:start position:0% + + + + align:start position:0% + +okay um + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +here's another definition + + align:start position:0% +here's another definition + + + align:start position:0% +here's another definition +so a sequence is bounded + + align:start position:0% +so a sequence is bounded + + + align:start position:0% +so a sequence is bounded +if in some sense it doesn't run off to + + align:start position:0% +if in some sense it doesn't run off to + + + align:start position:0% +if in some sense it doesn't run off to +arbitrarily large values + + align:start position:0% +arbitrarily large values + + + align:start position:0% +arbitrarily large values +so + + align:start position:0% + + + + align:start position:0% + +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +x sub n + + align:start position:0% + + + + align:start position:0% + +bounded + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% + + + + align:start position:0% + +there exists + + align:start position:0% +there exists + + + align:start position:0% +there exists +some real number b bigger than or equal + + align:start position:0% +some real number b bigger than or equal + + + align:start position:0% +some real number b bigger than or equal +to 0 such that + + align:start position:0% + + + + align:start position:0% + +for all + + align:start position:0% +for all + + + align:start position:0% +for all +n in the natural numbers + + align:start position:0% +n in the natural numbers + + + align:start position:0% +n in the natural numbers +x n is less than or equal to b + + align:start position:0% +x n is less than or equal to b + + + align:start position:0% +x n is less than or equal to b +an absolute value okay + + align:start position:0% +an absolute value okay + + + align:start position:0% +an absolute value okay +so + + align:start position:0% + + + + align:start position:0% + +again for example if we take a look back + + align:start position:0% +again for example if we take a look back + + + align:start position:0% +again for example if we take a look back +at both of those two sequences + + align:start position:0% +at both of those two sequences + + + align:start position:0% +at both of those two sequences +one one one + + align:start position:0% +one one one + + + align:start position:0% +one one one +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +and the sequence one over n + + align:start position:0% + + + + align:start position:0% + +are bounded why because every element in + + align:start position:0% +are bounded why because every element in + + + align:start position:0% +are bounded why because every element in +this + + align:start position:0% +this + + + align:start position:0% +this +um and i + + align:start position:0% +um and i + + + align:start position:0% +um and i +uh every i shouldn't say element but + + align:start position:0% +uh every i shouldn't say element but + + + align:start position:0% +uh every i shouldn't say element but +um + + align:start position:0% +um + + + align:start position:0% +um +every entry in this sequence + + align:start position:0% +every entry in this sequence + + + align:start position:0% +every entry in this sequence +is equal to one so it's bounded by one + + align:start position:0% +is equal to one so it's bounded by one + + + align:start position:0% +is equal to one so it's bounded by one +and every entry in this sequence + + align:start position:0% +and every entry in this sequence + + + align:start position:0% +and every entry in this sequence +uh + + align:start position:0% +uh + + + align:start position:0% +uh +is less than or equal to one so it's + + align:start position:0% +is less than or equal to one so it's + + + align:start position:0% +is less than or equal to one so it's +bounded by one in absolute value it's + + align:start position:0% +bounded by one in absolute value it's + + + align:start position:0% +bounded by one in absolute value it's +also positive so they're both bounded + + align:start position:0% +also positive so they're both bounded + + + align:start position:0% +also positive so they're both bounded +another example is the sequence + + align:start position:0% +another example is the sequence + + + align:start position:0% +another example is the sequence +written -1 to the n + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +i'll write + + align:start position:0% +i'll write + + + align:start position:0% +i'll write +equals although this shouldn't this + + align:start position:0% +equals although this shouldn't this + + + align:start position:0% +equals although this shouldn't this +doesn't mean anything i'm just going to + + align:start position:0% +doesn't mean anything i'm just going to + + + align:start position:0% +doesn't mean anything i'm just going to +write it + + align:start position:0% +write it + + + align:start position:0% +write it +write it + + align:start position:0% +write it + + + align:start position:0% +write it +or start listing the the entries minus + + align:start position:0% +or start listing the the entries minus + + + align:start position:0% +or start listing the the entries minus +one one minus one one minus one one + + align:start position:0% + + + + align:start position:0% + +this is also bounded + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% + + + + align:start position:0% + +the absolute value of minus 1 to the n + + align:start position:0% +the absolute value of minus 1 to the n + + + align:start position:0% +the absolute value of minus 1 to the n +is 1 so that's bounded by 1 for all n + + align:start position:0% +is 1 so that's bounded by 1 for all n + + + align:start position:0% +is 1 so that's bounded by 1 for all n +so what's a non-example + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +in + + align:start position:0% +in + + + align:start position:0% +in +in other words this is the sequence one + + align:start position:0% +in other words this is the sequence one + + + align:start position:0% +in other words this is the sequence one +two three four + + align:start position:0% +two three four + + + align:start position:0% +two three four +five + + align:start position:0% +five + + + align:start position:0% +five +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +now precisely why is it + + align:start position:0% +now precisely why is it + + + align:start position:0% +now precisely why is it +un + + align:start position:0% +un + + + align:start position:0% +un +so i should say + + align:start position:0% +so i should say + + + align:start position:0% +so i should say +this is bounded + + align:start position:0% + + + + align:start position:0% + +and otherwise i'll refer to x sub n as + + align:start position:0% +and otherwise i'll refer to x sub n as + + + align:start position:0% +and otherwise i'll refer to x sub n as +unbound + + align:start position:0% + + + + align:start position:0% + +unbounded + + align:start position:0% +unbounded + + + align:start position:0% +unbounded +okay + + align:start position:0% + + + + align:start position:0% + +so why is it unbounded because you know + + align:start position:0% +so why is it unbounded because you know + + + align:start position:0% +so why is it unbounded because you know +the entries are getting larger and + + align:start position:0% +the entries are getting larger and + + + align:start position:0% +the entries are getting larger and +larger in size + + align:start position:0% +larger in size + + + align:start position:0% +larger in size +um but + + align:start position:0% +um but + + + align:start position:0% +um but +you know if i were to ask you to prove + + align:start position:0% +you know if i were to ask you to prove + + + align:start position:0% +you know if i were to ask you to prove +this + + align:start position:0% +this + + + align:start position:0% +this +you would have to show so + + align:start position:0% +you would have to show so + + + align:start position:0% +you would have to show so +and this is also a good first exercise + + align:start position:0% +and this is also a good first exercise + + + align:start position:0% +and this is also a good first exercise +what does it mean to be unbounded + + align:start position:0% +what does it mean to be unbounded + + + align:start position:0% +what does it mean to be unbounded +so i said this at one point + + align:start position:0% +so i said this at one point + + + align:start position:0% +so i said this at one point +that if you come across a + + align:start position:0% +that if you come across a + + + align:start position:0% +that if you come across a +reasonably interesting definition you + + align:start position:0% +reasonably interesting definition you + + + align:start position:0% +reasonably interesting definition you +should look up + + align:start position:0% +should look up + + + align:start position:0% +should look up +or try to come up with examples + + align:start position:0% +or try to come up with examples + + + align:start position:0% +or try to come up with examples +and typically when you do come up with + + align:start position:0% +and typically when you do come up with + + + align:start position:0% +and typically when you do come up with +examples you should come up with + + align:start position:0% +examples you should come up with + + + align:start position:0% +examples you should come up with +non-examples and what that requires you + + align:start position:0% +non-examples and what that requires you + + + align:start position:0% +non-examples and what that requires you +to do + + align:start position:0% +to do + + + align:start position:0% +to do +is negate the definition okay what does + + align:start position:0% +is negate the definition okay what does + + + align:start position:0% +is negate the definition okay what does +it mean for something to not be that + + align:start position:0% +it mean for something to not be that + + + align:start position:0% +it mean for something to not be that +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so for + + align:start position:0% +so for + + + align:start position:0% +so for +so even though + + align:start position:0% +so even though + + + align:start position:0% +so even though +i'm saying that if it's not bounded i + + align:start position:0% +i'm saying that if it's not bounded i + + + align:start position:0% +i'm saying that if it's not bounded i +call it unbounded i haven't actually + + align:start position:0% +call it unbounded i haven't actually + + + align:start position:0% +call it unbounded i haven't actually +written a mathematical statement to this + + align:start position:0% +written a mathematical statement to this + + + align:start position:0% +written a mathematical statement to this +effect on what this means + + align:start position:0% +effect on what this means + + + align:start position:0% +effect on what this means +so let me make this uh right + + align:start position:0% +so let me make this uh right + + + align:start position:0% +so let me make this uh right +here as a remark so + + align:start position:0% +here as a remark so + + + align:start position:0% +here as a remark so +a sequence + + align:start position:0% + + + + align:start position:0% + +is unbounded + + align:start position:0% + + + + align:start position:0% + +so if it doesn't satisfy that definition + + align:start position:0% +so if it doesn't satisfy that definition + + + align:start position:0% +so if it doesn't satisfy that definition +so we need to negate this definition the + + align:start position:0% +so we need to negate this definition the + + + align:start position:0% +so we need to negate this definition the +definition says uh this is bounded if + + align:start position:0% +definition says uh this is bounded if + + + align:start position:0% +definition says uh this is bounded if +there exists a b bigger than or equal to + + align:start position:0% +there exists a b bigger than or equal to + + + align:start position:0% +there exists a b bigger than or equal to +zero such that this holds for all in + + align:start position:0% +zero such that this holds for all in + + + align:start position:0% +zero such that this holds for all in +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now when i negate that there exists that + + align:start position:0% +now when i negate that there exists that + + + align:start position:0% +now when i negate that there exists that +becomes a for all and when i negate a + + align:start position:0% +becomes a for all and when i negate a + + + align:start position:0% +becomes a for all and when i negate a +for all that becomes of their exist + + align:start position:0% +for all that becomes of their exist + + + align:start position:0% +for all that becomes of their exist +and then i negate this condition + + align:start position:0% +and then i negate this condition + + + align:start position:0% +and then i negate this condition +so the sequence is unbounded if + + align:start position:0% + + + + align:start position:0% + +for all b + + align:start position:0% +for all b + + + align:start position:0% +for all b +bigger than or equal to zero there + + align:start position:0% +bigger than or equal to zero there + + + align:start position:0% +bigger than or equal to zero there +exists + + align:start position:0% +exists + + + align:start position:0% +exists +a natural number in n + + align:start position:0% +a natural number in n + + + align:start position:0% +a natural number in n +such that + + align:start position:0% +such that + + + align:start position:0% +such that +x in an absolute value + + align:start position:0% +x in an absolute value + + + align:start position:0% +x in an absolute value +is bigger than b + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now using this so this is if you like + + align:start position:0% +now using this so this is if you like + + + align:start position:0% +now using this so this is if you like +you can take that as a second definition + + align:start position:0% +you can take that as a second definition + + + align:start position:0% +you can take that as a second definition +or it's not really a definition since + + align:start position:0% +or it's not really a definition since + + + align:start position:0% +or it's not really a definition since +it's just the negation of the first + + align:start position:0% +it's just the negation of the first + + + align:start position:0% +it's just the negation of the first +definition + + align:start position:0% +definition + + + align:start position:0% +definition +why + + align:start position:0% +why + + + align:start position:0% +why +does why is this set unbounded because + + align:start position:0% +does why is this set unbounded because + + + align:start position:0% +does why is this set unbounded because +of the archimedean property right so + + align:start position:0% + + + + align:start position:0% + +so now i'm i'm giving you a little short + + align:start position:0% +so now i'm i'm giving you a little short + + + align:start position:0% +so now i'm i'm giving you a little short +proof on why this + + align:start position:0% +proof on why this + + + align:start position:0% +proof on why this +sequence is unbounded + + align:start position:0% +sequence is unbounded + + + align:start position:0% +sequence is unbounded +let b + + align:start position:0% +let b + + + align:start position:0% +let b +be + + align:start position:0% +be + + + align:start position:0% +be +bigger than or equal to zero + + align:start position:0% +bigger than or equal to zero + + + align:start position:0% +bigger than or equal to zero +by + + align:start position:0% +by + + + align:start position:0% +by +our comedian property + + align:start position:0% +our comedian property + + + align:start position:0% +our comedian property +there exists a natural number + + align:start position:0% +there exists a natural number + + + align:start position:0% +there exists a natural number +in + + align:start position:0% +in + + + align:start position:0% +in +such that n + + align:start position:0% +such that n + + + align:start position:0% +such that n +is bigger than b + + align:start position:0% +is bigger than b + + + align:start position:0% +is bigger than b +which is exactly what we wanted to prove + + align:start position:0% +which is exactly what we wanted to prove + + + align:start position:0% +which is exactly what we wanted to prove +because in this case x sub n is in + + align:start position:0% + + + + align:start position:0% + +is unbounded + + align:start position:0% +is unbounded + + + align:start position:0% +is unbounded +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Applause] + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% + + + + align:start position:0% + +what does it mean for + + align:start position:0% +what does it mean for + + + align:start position:0% +what does it mean for +us to have a limit of a sequence what is + + align:start position:0% +us to have a limit of a sequence what is + + + align:start position:0% +us to have a limit of a sequence what is +a limit of a + + align:start position:0% +a limit of a + + + align:start position:0% +a limit of a +sequence mean what does it mean for a + + align:start position:0% +sequence mean what does it mean for a + + + align:start position:0% +sequence mean what does it mean for a +real number to be + + align:start position:0% +real number to be + + + align:start position:0% +real number to be +the limit of a sequence + + align:start position:0% +the limit of a sequence + + + align:start position:0% +the limit of a sequence +um + + align:start position:0% +um + + + align:start position:0% +um +what does it mean for a sequence to + + align:start position:0% +what does it mean for a sequence to + + + align:start position:0% +what does it mean for a sequence to +converge to something so + + align:start position:0% + + + + align:start position:0% + +sequence x of n + + align:start position:0% + + + + align:start position:0% + +converges + + align:start position:0% +converges + + + align:start position:0% +converges +to + + align:start position:0% +to + + + align:start position:0% +to +real number x and r + + align:start position:0% +real number x and r + + + align:start position:0% +real number x and r +if the following condition is satisfied + + align:start position:0% +if the following condition is satisfied + + + align:start position:0% +if the following condition is satisfied +if + + align:start position:0% + + + + align:start position:0% + +for every epsilon positive + + align:start position:0% + + + + align:start position:0% + +there exists a natural number capital m + + align:start position:0% +there exists a natural number capital m + + + align:start position:0% +there exists a natural number capital m +such that + + align:start position:0% + + + + align:start position:0% + +for all n bigger than or equal to + + align:start position:0% +for all n bigger than or equal to + + + align:start position:0% +for all n bigger than or equal to +capital m + + align:start position:0% +capital m + + + align:start position:0% +capital m +x n minus x + + align:start position:0% +x n minus x + + + align:start position:0% +x n minus x +absolute value is less than epsilon okay + + align:start position:0% +absolute value is less than epsilon okay + + + align:start position:0% +absolute value is less than epsilon okay +now remember the absolute value is meant + + align:start position:0% +now remember the absolute value is meant + + + align:start position:0% +now remember the absolute value is meant +to be something like a distance so what + + align:start position:0% +to be something like a distance so what + + + align:start position:0% +to be something like a distance so what +does this statement say it says if i + + align:start position:0% +does this statement say it says if i + + + align:start position:0% +does this statement say it says if i +give you a little bit of tolerance + + align:start position:0% +give you a little bit of tolerance + + + align:start position:0% +give you a little bit of tolerance +epsilon + + align:start position:0% +epsilon + + + align:start position:0% +epsilon +and you go far enough out in the + + align:start position:0% +and you go far enough out in the + + + align:start position:0% +and you go far enough out in the +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +then + + align:start position:0% +then + + + align:start position:0% +then +the distance between that entry in the + + align:start position:0% +the distance between that entry in the + + + align:start position:0% +the distance between that entry in the +sequence and x + + align:start position:0% +sequence and x + + + align:start position:0% +sequence and x +are very close to each other + + align:start position:0% +are very close to each other + + + align:start position:0% +are very close to each other +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +let me finish stating + + align:start position:0% +let me finish stating + + + align:start position:0% +let me finish stating +uh the rest of this definition then + + align:start position:0% +uh the rest of this definition then + + + align:start position:0% +uh the rest of this definition then +we'll we'll do a little more discussion + + align:start position:0% +we'll we'll do a little more discussion + + + align:start position:0% +we'll we'll do a little more discussion +um + + align:start position:0% + + + + align:start position:0% + +if a sequence converges we say it's + + align:start position:0% + + + + align:start position:0% + +convergent + + align:start position:0% + + + + align:start position:0% + +otherwise + + align:start position:0% + + + + align:start position:0% + +we say it's divergent + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +all right let me draw um + + align:start position:0% +all right let me draw um + + + align:start position:0% +all right let me draw um +let me draw a little picture + + align:start position:0% + + + + align:start position:0% + +what this is meant to to be so + + align:start position:0% +what this is meant to to be so + + + align:start position:0% +what this is meant to to be so +um + + align:start position:0% +um + + + align:start position:0% +um +the real + + align:start position:0% +the real + + + align:start position:0% +the real +numbers you know + + align:start position:0% +numbers you know + + + align:start position:0% +numbers you know +it was this uh + + align:start position:0% +it was this uh + + + align:start position:0% +it was this uh +i mean it is this uh + + align:start position:0% +i mean it is this uh + + + align:start position:0% +i mean it is this uh +unique uh ordered field with least upper + + align:start position:0% +unique uh ordered field with least upper + + + align:start position:0% +unique uh ordered field with least upper +bound property but when you think about + + align:start position:0% +bound property but when you think about + + + align:start position:0% +bound property but when you think about +the real numbers + + align:start position:0% +the real numbers + + + align:start position:0% +the real numbers +you know think of it as you've always + + align:start position:0% +you know think of it as you've always + + + align:start position:0% +you know think of it as you've always +thought about it as just the real number + + align:start position:0% +thought about it as just the real number + + + align:start position:0% +thought about it as just the real number +line + + align:start position:0% +line + + + align:start position:0% +line +so + + align:start position:0% +so + + + align:start position:0% +so +what does this definition mean + + align:start position:0% +what does this definition mean + + + align:start position:0% +what does this definition mean +it means that + + align:start position:0% + + + + align:start position:0% + +that a sequence converges to + + align:start position:0% +that a sequence converges to + + + align:start position:0% +that a sequence converges to +some x if + + align:start position:0% +some x if + + + align:start position:0% +some x if +for every epsilon + + align:start position:0% +for every epsilon + + + align:start position:0% +for every epsilon +i can do the following if i look at + + align:start position:0% + + + + align:start position:0% + +if i + + align:start position:0% +if i + + + align:start position:0% +if i +give + + align:start position:0% +give + + + align:start position:0% +give +you an epsilon + + align:start position:0% + + + + align:start position:0% + +and you go on either side of x + + align:start position:0% +and you go on either side of x + + + align:start position:0% +and you go on either side of x +epsilon amount + + align:start position:0% +epsilon amount + + + align:start position:0% +epsilon amount +then + + align:start position:0% +then + + + align:start position:0% +then +you should be able to find a capital m + + align:start position:0% +you should be able to find a capital m + + + align:start position:0% +you should be able to find a capital m +so that + + align:start position:0% +so that + + + align:start position:0% +so that +if + + align:start position:0% +if + + + align:start position:0% +if +you look at + + align:start position:0% +you look at + + + align:start position:0% +you look at +entries in your sequence x sub n for n + + align:start position:0% +entries in your sequence x sub n for n + + + align:start position:0% +entries in your sequence x sub n for n +bigger than or equal to m + + align:start position:0% +bigger than or equal to m + + + align:start position:0% +bigger than or equal to m +they're in this guy so then i should + + align:start position:0% +they're in this guy so then i should + + + align:start position:0% +they're in this guy so then i should +have x of m there + + align:start position:0% +have x of m there + + + align:start position:0% +have x of m there +x of n plus 1 + + align:start position:0% +x of n plus 1 + + + align:start position:0% +x of n plus 1 +x of n plus 2 + + align:start position:0% +x of n plus 2 + + + align:start position:0% +x of n plus 2 +and in general + + align:start position:0% +and in general + + + align:start position:0% +and in general +x sub n should be in there as long as n + + align:start position:0% +x sub n should be in there as long as n + + + align:start position:0% +x sub n should be in there as long as n +is bigger than or equal to m so i should + + align:start position:0% +is bigger than or equal to m so i should + + + align:start position:0% +is bigger than or equal to m so i should +be able to do this um for every epsilon + + align:start position:0% +be able to do this um for every epsilon + + + align:start position:0% +be able to do this um for every epsilon +okay i give + + align:start position:0% +okay i give + + + align:start position:0% +okay i give +so for any amount of tolerance epsilon + + align:start position:0% +so for any amount of tolerance epsilon + + + align:start position:0% +so for any amount of tolerance epsilon +you should be able to go + + align:start position:0% +you should be able to go + + + align:start position:0% +you should be able to go +far enough out in the sequence that all + + align:start position:0% +far enough out in the sequence that all + + + align:start position:0% +far enough out in the sequence that all +entries + + align:start position:0% +entries + + + align:start position:0% +entries +uh in that sequence + + align:start position:0% +uh in that sequence + + + align:start position:0% +uh in that sequence +are within this tolerance + + align:start position:0% +are within this tolerance + + + align:start position:0% +are within this tolerance +of x + + align:start position:0% +of x + + + align:start position:0% +of x +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +you know i mean + + align:start position:0% +you know i mean + + + align:start position:0% +you know i mean +although this is a picture of what the + + align:start position:0% +although this is a picture of what the + + + align:start position:0% +although this is a picture of what the +definition means + + align:start position:0% +definition means + + + align:start position:0% +definition means +how should you + + align:start position:0% +how should you + + + align:start position:0% +how should you +i mean you've probably gotten + + align:start position:0% +i mean you've probably gotten + + + align:start position:0% +i mean you've probably gotten +plenty of + + align:start position:0% + + + + align:start position:0% + +plenty of + + align:start position:0% +plenty of + + + align:start position:0% +plenty of +experience with sequences when you were + + align:start position:0% +experience with sequences when you were + + + align:start position:0% +experience with sequences when you were +doing calculus but what does this mean + + align:start position:0% +doing calculus but what does this mean + + + align:start position:0% +doing calculus but what does this mean +you know kind of loosely it means if i + + align:start position:0% +you know kind of loosely it means if i + + + align:start position:0% +you know kind of loosely it means if i +look close to x + + align:start position:0% +look close to x + + + align:start position:0% +look close to x +some little interval containing x + + align:start position:0% +some little interval containing x + + + align:start position:0% +some little interval containing x +then all of the sequence all of the + + align:start position:0% +then all of the sequence all of the + + + align:start position:0% +then all of the sequence all of the +elements of the sequence should be + + align:start position:0% +elements of the sequence should be + + + align:start position:0% +elements of the sequence should be +eventually in this um + + align:start position:0% + + + + align:start position:0% + +in this little interval + + align:start position:0% +in this little interval + + + align:start position:0% +in this little interval +okay + + align:start position:0% +okay + + + align:start position:0% +okay +or another way to think about it is that + + align:start position:0% + + + + align:start position:0% + +as i go on in the sequence + + align:start position:0% + + + + align:start position:0% + +the entries are getting closer and + + align:start position:0% +the entries are getting closer and + + + align:start position:0% +the entries are getting closer and +closer and closer to x + + align:start position:0% +closer and closer to x + + + align:start position:0% +closer and closer to x +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now the way one makes + + align:start position:0% +now the way one makes + + + align:start position:0% +now the way one makes +kind of these last two um + + align:start position:0% +kind of these last two um + + + align:start position:0% +kind of these last two um +you know intuitive statements precise is + + align:start position:0% +you know intuitive statements precise is + + + align:start position:0% +you know intuitive statements precise is +by this definition okay the closer and + + align:start position:0% +by this definition okay the closer and + + + align:start position:0% +by this definition okay the closer and +closer part is in + + align:start position:0% +closer part is in + + + align:start position:0% +closer part is in +encapsulated in this for all epsilon + + align:start position:0% +encapsulated in this for all epsilon + + + align:start position:0% +encapsulated in this for all epsilon +thought part + + align:start position:0% +thought part + + + align:start position:0% +thought part +and eventually getting closer and closer + + align:start position:0% +and eventually getting closer and closer + + + align:start position:0% +and eventually getting closer and closer +means + + align:start position:0% +means + + + align:start position:0% +means +for all n bigger than or equal to + + align:start position:0% +for all n bigger than or equal to + + + align:start position:0% +for all n bigger than or equal to +capital m as long as i go far enough out + + align:start position:0% +capital m as long as i go far enough out + + + align:start position:0% +capital m as long as i go far enough out +in the sequence they're getting close to + + align:start position:0% +in the sequence they're getting close to + + + align:start position:0% +in the sequence they're getting close to +x + + align:start position:0% +x + + + align:start position:0% +x +okay so i hope that's + + align:start position:0% +okay so i hope that's + + + align:start position:0% +okay so i hope that's +that's pretty clear + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +all right so again we have a definition + + align:start position:0% +all right so again we have a definition + + + align:start position:0% +all right so again we have a definition +we have um + + align:start position:0% + + + + align:start position:0% + +and it's + + align:start position:0% +and it's + + + align:start position:0% +and it's +reasonably interesting so we should do + + align:start position:0% +reasonably interesting so we should do + + + align:start position:0% +reasonably interesting so we should do +examples and then also negate it + + align:start position:0% +examples and then also negate it + + + align:start position:0% +examples and then also negate it +but before i do either of those + + align:start position:0% +but before i do either of those + + + align:start position:0% +but before i do either of those +i do want to just prove a very simple + + align:start position:0% +i do want to just prove a very simple + + + align:start position:0% +i do want to just prove a very simple +fact about + + align:start position:0% + + + + align:start position:0% + +convergent sequences namely that + + align:start position:0% +convergent sequences namely that + + + align:start position:0% +convergent sequences namely that +if i have a sequence which converges to + + align:start position:0% +if i have a sequence which converges to + + + align:start position:0% +if i have a sequence which converges to +x + + align:start position:0% +x + + + align:start position:0% +x +then + + align:start position:0% +then + + + align:start position:0% +then +x is the only thing that sequence can + + align:start position:0% +x is the only thing that sequence can + + + align:start position:0% +x is the only thing that sequence can +converge to all right i cannot have a + + align:start position:0% +converge to all right i cannot have a + + + align:start position:0% +converge to all right i cannot have a +convergent sequence which conver which + + align:start position:0% +convergent sequence which conver which + + + align:start position:0% +convergent sequence which conver which +converges to two different things like i + + align:start position:0% +converges to two different things like i + + + align:start position:0% +converges to two different things like i +said if you go by this intuition that + + align:start position:0% +said if you go by this intuition that + + + align:start position:0% +said if you go by this intuition that +eventually the x + + align:start position:0% +eventually the x + + + align:start position:0% +eventually the x +sub n's are getting closer and closer + + align:start position:0% +sub n's are getting closer and closer + + + align:start position:0% +sub n's are getting closer and closer +and closer to x + + align:start position:0% +and closer to x + + + align:start position:0% +and closer to x +well then there's no way they can be + + align:start position:0% +well then there's no way they can be + + + align:start position:0% +well then there's no way they can be +also getting closer to something other + + align:start position:0% +also getting closer to something other + + + align:start position:0% +also getting closer to something other +than x okay + + align:start position:0% + + + + align:start position:0% + +so i just want to prove that real quick + + align:start position:0% +so i just want to prove that real quick + + + align:start position:0% +so i just want to prove that real quick +and then we'll do examples and the + + align:start position:0% +and then we'll do examples and the + + + align:start position:0% +and then we'll do examples and the +negation of this definition + + align:start position:0% + + + + align:start position:0% + +so following theorem + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +so i'm going to state + + align:start position:0% +so i'm going to state + + + align:start position:0% +so i'm going to state +first the theorem that has nothing to do + + align:start position:0% +first the theorem that has nothing to do + + + align:start position:0% +first the theorem that has nothing to do +with sequences but uh um + + align:start position:0% +with sequences but uh um + + + align:start position:0% +with sequences but uh um +is a nice way if you want to show two + + align:start position:0% +is a nice way if you want to show two + + + align:start position:0% +is a nice way if you want to show two +things are equal + + align:start position:0% +things are equal + + + align:start position:0% +things are equal +you can show they're smaller than + + align:start position:0% +you can show they're smaller than + + + align:start position:0% +you can show they're smaller than +anything so the first theorem that i'm + + align:start position:0% +anything so the first theorem that i'm + + + align:start position:0% +anything so the first theorem that i'm +going to state is uh + + align:start position:0% +going to state is uh + + + align:start position:0% +going to state is uh +if + + align:start position:0% +if + + + align:start position:0% +if +x and y are in r + + align:start position:0% +x and y are in r + + + align:start position:0% +x and y are in r +and + + align:start position:0% +and + + + align:start position:0% +and +all epsilon positive + + align:start position:0% +all epsilon positive + + + align:start position:0% +all epsilon positive +x minus y is less than epsilon + + align:start position:0% +x minus y is less than epsilon + + + align:start position:0% +x minus y is less than epsilon +then + + align:start position:0% + + + + align:start position:0% + +x equals y this is not a surprising + + align:start position:0% +x equals y this is not a surprising + + + align:start position:0% +x equals y this is not a surprising +statement if i have + + align:start position:0% +statement if i have + + + align:start position:0% +statement if i have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +x and y and the distance between them is + + align:start position:0% +x and y and the distance between them is + + + align:start position:0% +x and y and the distance between them is +arbitrarily small then they have to be + + align:start position:0% +arbitrarily small then they have to be + + + align:start position:0% +arbitrarily small then they have to be +the same thing okay + + align:start position:0% +the same thing okay + + + align:start position:0% +the same thing okay +um + + align:start position:0% +um + + + align:start position:0% +um +so what's the proof + + align:start position:0% + + + + align:start position:0% + +suppose x y is in r + + align:start position:0% +suppose x y is in r + + + align:start position:0% +suppose x y is in r +and um + + align:start position:0% +and um + + + align:start position:0% +and um +for all epsilon positive + + align:start position:0% + + + + align:start position:0% + +x minus y is less than epsilon so now i + + align:start position:0% +x minus y is less than epsilon so now i + + + align:start position:0% +x minus y is less than epsilon so now i +want to prove x equals y so let's assume + + align:start position:0% +want to prove x equals y so let's assume + + + align:start position:0% +want to prove x equals y so let's assume +that this does not hold + + align:start position:0% + + + + align:start position:0% + +and arrive at a contradiction so this is + + align:start position:0% +and arrive at a contradiction so this is + + + align:start position:0% +and arrive at a contradiction so this is +a short proof by contradiction suppose x + + align:start position:0% +a short proof by contradiction suppose x + + + align:start position:0% +a short proof by contradiction suppose x +does not equal y + + align:start position:0% +does not equal y + + + align:start position:0% +does not equal y +then + + align:start position:0% + + + + align:start position:0% + +remember we proved that + + align:start position:0% + + + + align:start position:0% + +the absolute value of something is 0 if + + align:start position:0% +the absolute value of something is 0 if + + + align:start position:0% +the absolute value of something is 0 if +and only + + align:start position:0% +and only + + + align:start position:0% +and only +if that thing is equal to zero and it's + + align:start position:0% +if that thing is equal to zero and it's + + + align:start position:0% +if that thing is equal to zero and it's +always non-negative + + align:start position:0% +always non-negative + + + align:start position:0% +always non-negative +so x not equal to y means the absolute + + align:start position:0% +so x not equal to y means the absolute + + + align:start position:0% +so x not equal to y means the absolute +value of x minus y is less than is + + align:start position:0% +value of x minus y is less than is + + + align:start position:0% +value of x minus y is less than is +bigger than zero + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +by this assumption + + align:start position:0% +by this assumption + + + align:start position:0% +by this assumption +for epsilon equal to x minus y over 2 + + align:start position:0% +for epsilon equal to x minus y over 2 + + + align:start position:0% +for epsilon equal to x minus y over 2 +i get + + align:start position:0% + + + + align:start position:0% + +which implies if i just subtract that + + align:start position:0% +which implies if i just subtract that + + + align:start position:0% +which implies if i just subtract that +over + + align:start position:0% +over + + + align:start position:0% +over +x minus y is less than zero so one-half + + align:start position:0% +x minus y is less than zero so one-half + + + align:start position:0% +x minus y is less than zero so one-half +is less than zero + + align:start position:0% +is less than zero + + + align:start position:0% +is less than zero +or + + align:start position:0% + + + + align:start position:0% + +and that's a very false statement we've + + align:start position:0% +and that's a very false statement we've + + + align:start position:0% +and that's a very false statement we've +already proven that the absolute value + + align:start position:0% +already proven that the absolute value + + + align:start position:0% +already proven that the absolute value +is always non-negative + + align:start position:0% +is always non-negative + + + align:start position:0% +is always non-negative +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +if i have two real numbers that are + + align:start position:0% +if i have two real numbers that are + + + align:start position:0% +if i have two real numbers that are +arbitrarily close to each other then + + align:start position:0% +arbitrarily close to each other then + + + align:start position:0% +arbitrarily close to each other then +they have to be the same okay i'm going + + align:start position:0% +they have to be the same okay i'm going + + + align:start position:0% +they have to be the same okay i'm going +to use this theorem to prove that + + align:start position:0% + + + + align:start position:0% + +um i don't know why i put a one there + + align:start position:0% +um i don't know why i put a one there + + + align:start position:0% +um i don't know why i put a one there +uh y + + align:start position:0% +uh y + + + align:start position:0% +uh y +limits + + align:start position:0% +limits + + + align:start position:0% +limits +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and i have not said uh + + align:start position:0% +and i have not said uh + + + align:start position:0% +and i have not said uh +that's what we call x but + + align:start position:0% +that's what we call x but + + + align:start position:0% +that's what we call x but +why a convergent sequence can only + + align:start position:0% +why a convergent sequence can only + + + align:start position:0% +why a convergent sequence can only +converge to one thing + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +here's the statement of the second + + align:start position:0% +here's the statement of the second + + + align:start position:0% +here's the statement of the second +theorem + + align:start position:0% +theorem + + + align:start position:0% +theorem +if + + align:start position:0% + + + + align:start position:0% + +x sub n is a sequence + + align:start position:0% + + + + align:start position:0% + +and it converges to x + + align:start position:0% + + + + align:start position:0% + +and it also converges to y + + align:start position:0% + + + + align:start position:0% + +then x equals y so a convergent sequence + + align:start position:0% +then x equals y so a convergent sequence + + + align:start position:0% +then x equals y so a convergent sequence +can only converge + + align:start position:0% +can only converge + + + align:start position:0% +can only converge +to one thing okay + + align:start position:0% +to one thing okay + + + align:start position:0% +to one thing okay +and again like i said this should be + + align:start position:0% +and again like i said this should be + + + align:start position:0% +and again like i said this should be +clear because + + align:start position:0% +clear because + + + align:start position:0% +clear because +what's happening is + + align:start position:0% + + + + align:start position:0% + +if i have two things that are not equal + + align:start position:0% +if i have two things that are not equal + + + align:start position:0% +if i have two things that are not equal +and x sub n converges to x that means as + + align:start position:0% +and x sub n converges to x that means as + + + align:start position:0% +and x sub n converges to x that means as +long as i go far enough out in the + + align:start position:0% +long as i go far enough out in the + + + align:start position:0% +long as i go far enough out in the +sequence they're supposed to be here in + + align:start position:0% +sequence they're supposed to be here in + + + align:start position:0% +sequence they're supposed to be here in +this small + + align:start position:0% +this small + + + align:start position:0% +this small +interval around x + + align:start position:0% +interval around x + + + align:start position:0% +interval around x +while if they're supposed to be um + + align:start position:0% +while if they're supposed to be um + + + align:start position:0% +while if they're supposed to be um +converging to y + + align:start position:0% +converging to y + + + align:start position:0% +converging to y +if i go far enough out they're also + + align:start position:0% +if i go far enough out they're also + + + align:start position:0% +if i go far enough out they're also +supposed to be over here + + align:start position:0% +supposed to be over here + + + align:start position:0% +supposed to be over here +as long as i go far enough out + + align:start position:0% +as long as i go far enough out + + + align:start position:0% +as long as i go far enough out +but you can't be in two places at once + + align:start position:0% +but you can't be in two places at once + + + align:start position:0% +but you can't be in two places at once +um + + align:start position:0% +um + + + align:start position:0% +um +ever and so that's what that's why x + + align:start position:0% +ever and so that's what that's why x + + + align:start position:0% +ever and so that's what that's why x +must equal y + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +although i suppose that now we're doing + + align:start position:0% +although i suppose that now we're doing + + + align:start position:0% +although i suppose that now we're doing +all the classes online + + align:start position:0% +all the classes online + + + align:start position:0% +all the classes online +some are recorded so you can be two + + align:start position:0% +some are recorded so you can be two + + + align:start position:0% +some are recorded so you can be two +places at once but + + align:start position:0% +places at once but + + + align:start position:0% +places at once but +at least not not in not here + + align:start position:0% +at least not not in not here + + + align:start position:0% +at least not not in not here +um okay so we're going to use this + + align:start position:0% +um okay so we're going to use this + + + align:start position:0% +um okay so we're going to use this +theorem to prove this statement + + align:start position:0% + + + + align:start position:0% + +suppose + + align:start position:0% + + + + align:start position:0% + +converges to + + align:start position:0% + + + + align:start position:0% + +x and y + + align:start position:0% +x and y + + + align:start position:0% +x and y +and i want to verify that for all + + align:start position:0% +and i want to verify that for all + + + align:start position:0% +and i want to verify that for all +epsilon positive the absolute value of x + + align:start position:0% +epsilon positive the absolute value of x + + + align:start position:0% +epsilon positive the absolute value of x +minus y is less than or equal to epsilon + + align:start position:0% +minus y is less than or equal to epsilon + + + align:start position:0% +minus y is less than or equal to epsilon +okay + + align:start position:0% + + + + align:start position:0% + +now remember if i'm proving something + + align:start position:0% +now remember if i'm proving something + + + align:start position:0% +now remember if i'm proving something +for all epsilon + + align:start position:0% +for all epsilon + + + align:start position:0% +for all epsilon +i have to that means i do it for + + align:start position:0% +i have to that means i do it for + + + align:start position:0% +i have to that means i do it for +arbitrarily arbitrary epsilon + + align:start position:0% +arbitrarily arbitrary epsilon + + + align:start position:0% +arbitrarily arbitrary epsilon +you get points just for setting let + + align:start position:0% +you get points just for setting let + + + align:start position:0% +you get points just for setting let +epsilon be positive + + align:start position:0% +epsilon be positive + + + align:start position:0% +epsilon be positive +okay now i want to show the absolute + + align:start position:0% +okay now i want to show the absolute + + + align:start position:0% +okay now i want to show the absolute +value of x minus y is less than or equal + + align:start position:0% +value of x minus y is less than or equal + + + align:start position:0% +value of x minus y is less than or equal +to epsilon and we're basically going to + + align:start position:0% +to epsilon and we're basically going to + + + align:start position:0% +to epsilon and we're basically going to +do the argument that i just erased + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +since x sub n + + align:start position:0% + + + + align:start position:0% + +converges to x + + align:start position:0% + + + + align:start position:0% + +that implies that there exists a natural + + align:start position:0% +that implies that there exists a natural + + + align:start position:0% +that implies that there exists a natural +number m1 + + align:start position:0% + + + + align:start position:0% + +such that + + align:start position:0% +such that + + + align:start position:0% +such that +all n bigger than or equal to m1 + + align:start position:0% +all n bigger than or equal to m1 + + + align:start position:0% +all n bigger than or equal to m1 +x of n minus x is less than + + align:start position:0% +x of n minus x is less than + + + align:start position:0% +x of n minus x is less than +epsilon over two y the epsilon over two + + align:start position:0% +epsilon over two y the epsilon over two + + + align:start position:0% +epsilon over two y the epsilon over two +you'll see magic happens + + align:start position:0% + + + + align:start position:0% + +and since + + align:start position:0% + + + + align:start position:0% + +x sub n converges to y + + align:start position:0% + + + + align:start position:0% + +that's this implies that there exists an + + align:start position:0% +that's this implies that there exists an + + + align:start position:0% +that's this implies that there exists an +m2 natural number + + align:start position:0% +m2 natural number + + + align:start position:0% +m2 natural number +such that + + align:start position:0% + + + + align:start position:0% + +for all n bigger than or equal to m2 + + align:start position:0% +for all n bigger than or equal to m2 + + + align:start position:0% +for all n bigger than or equal to m2 +so again this is the part that says as + + align:start position:0% +so again this is the part that says as + + + align:start position:0% +so again this is the part that says as +long as i go far enough out x of n has + + align:start position:0% +long as i go far enough out x of n has + + + align:start position:0% +long as i go far enough out x of n has +to be close to x now this is the part + + align:start position:0% +to be close to x now this is the part + + + align:start position:0% +to be close to x now this is the part +that says as long as i go far enough out + + align:start position:0% +that says as long as i go far enough out + + + align:start position:0% +that says as long as i go far enough out +x of n has to be close to y + + align:start position:0% +x of n has to be close to y + + + align:start position:0% +x of n has to be close to y +so that for all n bigger than or equal + + align:start position:0% +so that for all n bigger than or equal + + + align:start position:0% +so that for all n bigger than or equal +to m 2 + + align:start position:0% +to m 2 + + + align:start position:0% +to m 2 +x of n minus y + + align:start position:0% +x of n minus y + + + align:start position:0% +x of n minus y +is less than epsilon over 2. + + align:start position:0% +is less than epsilon over 2. + + + align:start position:0% +is less than epsilon over 2. +okay + + align:start position:0% +okay + + + align:start position:0% +okay +then + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% +since + + + align:start position:0% +since +the sum and 1 plus these are both + + align:start position:0% +the sum and 1 plus these are both + + + align:start position:0% +the sum and 1 plus these are both +natural numbers this is bigger than or + + align:start position:0% +natural numbers this is bigger than or + + + align:start position:0% +natural numbers this is bigger than or +equal to m1 + + align:start position:0% +equal to m1 + + + align:start position:0% +equal to m1 +and + + align:start position:0% +and + + + align:start position:0% +and +m2 + + align:start position:0% + + + + align:start position:0% + +this implies now + + align:start position:0% +this implies now + + + align:start position:0% +this implies now +i'm going to use + + align:start position:0% +i'm going to use + + + align:start position:0% +i'm going to use +these two inequalities + + align:start position:0% +these two inequalities + + + align:start position:0% +these two inequalities +and the triangle inequality + + align:start position:0% +and the triangle inequality + + + align:start position:0% +and the triangle inequality +then if i look at the absolute value of + + align:start position:0% +then if i look at the absolute value of + + + align:start position:0% +then if i look at the absolute value of +x minus y this is equal to + + align:start position:0% +x minus y this is equal to + + + align:start position:0% +x minus y this is equal to +the absolute value of x minus x sub n + + align:start position:0% +the absolute value of x minus x sub n + + + align:start position:0% +the absolute value of x minus x sub n +plus + + align:start position:0% +plus + + + align:start position:0% +plus +x of n minus + + align:start position:0% + + + + align:start position:0% + +so let me not x sub n but x sub + + align:start position:0% +so let me not x sub n but x sub + + + align:start position:0% +so let me not x sub n but x sub +m1 plus m2 + + align:start position:0% +m1 plus m2 + + + align:start position:0% +m1 plus m2 +plus + + align:start position:0% +plus + + + align:start position:0% +plus +x sub m1 plus m2 + + align:start position:0% + + + + align:start position:0% + +now by the triangle inequality this is + + align:start position:0% +now by the triangle inequality this is + + + align:start position:0% +now by the triangle inequality this is +less than or equal to x + + align:start position:0% + + + + align:start position:0% + +m2 plus + + align:start position:0% +m2 plus + + + align:start position:0% +m2 plus +m1 plus m2 + + align:start position:0% +m1 plus m2 + + + align:start position:0% +m1 plus m2 +minus y + + align:start position:0% +minus y + + + align:start position:0% +minus y +now + + align:start position:0% +now + + + align:start position:0% +now +this is less than epsilon over 2 because + + align:start position:0% +this is less than epsilon over 2 because + + + align:start position:0% +this is less than epsilon over 2 because +m1 plus m2 is bigger than or equal to m1 + + align:start position:0% + + + + align:start position:0% + +and for the same reason since m1 plus m2 + + align:start position:0% +and for the same reason since m1 plus m2 + + + align:start position:0% +and for the same reason since m1 plus m2 +is bigger than or equal to m2 this is + + align:start position:0% +is bigger than or equal to m2 this is + + + align:start position:0% +is bigger than or equal to m2 this is +less than epsilon over 2. + + align:start position:0% +less than epsilon over 2. + + + align:start position:0% +less than epsilon over 2. +ah now you see why i divided both of + + align:start position:0% +ah now you see why i divided both of + + + align:start position:0% +ah now you see why i divided both of +those by 2 + + align:start position:0% +those by 2 + + + align:start position:0% +those by 2 +because when i add them up i get epsilon + + align:start position:0% +because when i add them up i get epsilon + + + align:start position:0% +because when i add them up i get epsilon +so i've shown that for every epsilon + + align:start position:0% +so i've shown that for every epsilon + + + align:start position:0% +so i've shown that for every epsilon +positive + + align:start position:0% +positive + + + align:start position:0% +positive +the absolute value of x minus y is less + + align:start position:0% +the absolute value of x minus y is less + + + align:start position:0% +the absolute value of x minus y is less +than epsilon + + align:start position:0% + + + + align:start position:0% + +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +by the theorem that i proved a minute + + align:start position:0% +by the theorem that i proved a minute + + + align:start position:0% +by the theorem that i proved a minute +ago + + align:start position:0% +ago + + + align:start position:0% +ago +x equals y + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +why did i + + align:start position:0% +why did i + + + align:start position:0% +why did i +state that theorem because i want to use + + align:start position:0% +state that theorem because i want to use + + + align:start position:0% +state that theorem because i want to use +notation and i want this notation to be + + align:start position:0% +notation and i want this notation to be + + + align:start position:0% +notation and i want this notation to be +already + + align:start position:0% +already + + + align:start position:0% +already +apparent that it's consistent + + align:start position:0% + + + + align:start position:0% + +and i'm going to use terminology + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +this is not really a new definition it's + + align:start position:0% +this is not really a new definition it's + + + align:start position:0% +this is not really a new definition it's +just some terminology + + align:start position:0% + + + + align:start position:0% + +recall x + + align:start position:0% + + + + align:start position:0% + +the limit of the sequence + + align:start position:0% + + + + align:start position:0% + +now the fact that i've shown only + + align:start position:0% +now the fact that i've shown only + + + align:start position:0% +now the fact that i've shown only +um + + align:start position:0% +um + + + align:start position:0% +um +that there's only one guy that a + + align:start position:0% +that there's only one guy that a + + + align:start position:0% +that there's only one guy that a +sequence can converge to is why i get to + + align:start position:0% +sequence can converge to is why i get to + + + align:start position:0% +sequence can converge to is why i get to +use the word d so + + align:start position:0% +use the word d so + + + align:start position:0% +use the word d so +not we call x a limit of x of n we it's + + align:start position:0% +not we call x a limit of x of n we it's + + + align:start position:0% +not we call x a limit of x of n we it's +the limit because there's only one + + align:start position:0% +the limit because there's only one + + + align:start position:0% +the limit because there's only one +uh if one + + align:start position:0% + + + + align:start position:0% + +exists and write + + align:start position:0% + + + + align:start position:0% + +x equals limit as n goes to infinity of + + align:start position:0% +x equals limit as n goes to infinity of + + + align:start position:0% +x equals limit as n goes to infinity of +x sub n + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +so let's pause on negating the + + align:start position:0% +so let's pause on negating the + + + align:start position:0% +so let's pause on negating the +definition of + + align:start position:0% +definition of + + + align:start position:0% +definition of +uh what it means for sequence to be + + align:start position:0% +uh what it means for sequence to be + + + align:start position:0% +uh what it means for sequence to be +convergent and let's let's do a couple + + align:start position:0% +convergent and let's let's do a couple + + + align:start position:0% +convergent and let's let's do a couple +of examples of convergent sequences + + align:start position:0% +of examples of convergent sequences + + + align:start position:0% +of examples of convergent sequences +uh proving that they are convergent + + align:start position:0% +uh proving that they are convergent + + + align:start position:0% +uh proving that they are convergent +sequences and computing what they + + align:start position:0% + + + + align:start position:0% + +and at least proving that these + + align:start position:0% +and at least proving that these + + + align:start position:0% +and at least proving that these +sequences do converge to the limit that + + align:start position:0% +sequences do converge to the limit that + + + align:start position:0% +sequences do converge to the limit that +i'm telling you + + align:start position:0% + + + + align:start position:0% + +so for example + + align:start position:0% +so for example + + + align:start position:0% +so for example +let's look at the constant sequence x of + + align:start position:0% +let's look at the constant sequence x of + + + align:start position:0% +let's look at the constant sequence x of +n equals one + + align:start position:0% +n equals one + + + align:start position:0% +n equals one +for all n so that's uh + + align:start position:0% +for all n so that's uh + + + align:start position:0% +for all n so that's uh +you know the sequence one one one so on + + align:start position:0% +you know the sequence one one one so on + + + align:start position:0% +you know the sequence one one one so on +then + + align:start position:0% + + + + align:start position:0% + +i'm just going to write 1 not x of n + + align:start position:0% +i'm just going to write 1 not x of n + + + align:start position:0% +i'm just going to write 1 not x of n +the limit as n goes to infinity of 1 + + align:start position:0% +the limit as n goes to infinity of 1 + + + align:start position:0% +the limit as n goes to infinity of 1 +equals 1. + + align:start position:0% +equals 1. + + + align:start position:0% +equals 1. +okay this this + + align:start position:0% + + + + align:start position:0% + +proof is not very + + align:start position:0% +proof is not very + + + align:start position:0% +proof is not very +enlightening so but + + align:start position:0% +enlightening so but + + + align:start position:0% +enlightening so but +i'll show you how it goes + + align:start position:0% +i'll show you how it goes + + + align:start position:0% +i'll show you how it goes +so you're supposed to show + + align:start position:0% +so you're supposed to show + + + align:start position:0% +so you're supposed to show +what does this mean this means for every + + align:start position:0% +what does this mean this means for every + + + align:start position:0% +what does this mean this means for every +epsilon positive there exists a natural + + align:start position:0% +epsilon positive there exists a natural + + + align:start position:0% +epsilon positive there exists a natural +number capital m such that if i'm bigger + + align:start position:0% +number capital m such that if i'm bigger + + + align:start position:0% +number capital m such that if i'm bigger +than capital m + + align:start position:0% +than capital m + + + align:start position:0% +than capital m +this minus the limit should be less than + + align:start position:0% +this minus the limit should be less than + + + align:start position:0% +this minus the limit should be less than +epsilon so let epsilon be positive i + + align:start position:0% +epsilon so let epsilon be positive i + + + align:start position:0% +epsilon so let epsilon be positive i +have to now + + align:start position:0% +have to now + + + align:start position:0% +have to now +come up with a capital m so that x of n + + align:start position:0% +come up with a capital m so that x of n + + + align:start position:0% +come up with a capital m so that x of n +minus x is less than epsilon whenever + + align:start position:0% +minus x is less than epsilon whenever + + + align:start position:0% +minus x is less than epsilon whenever +little n is bigger than or equal to + + align:start position:0% +little n is bigger than or equal to + + + align:start position:0% +little n is bigger than or equal to +capital m + + align:start position:0% +capital m + + + align:start position:0% +capital m +so i'm going to choose capital m to be + + align:start position:0% +so i'm going to choose capital m to be + + + align:start position:0% +so i'm going to choose capital m to be +1. i can do that for this sequence + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +if n is bigger than or equal to m + + align:start position:0% +if n is bigger than or equal to m + + + align:start position:0% +if n is bigger than or equal to m +and i look at the + + align:start position:0% + + + + align:start position:0% + +nth uh entry in the sequence well this + + align:start position:0% +nth uh entry in the sequence well this + + + align:start position:0% +nth uh entry in the sequence well this +is just one + + align:start position:0% +is just one + + + align:start position:0% +is just one +minus one equals zero and that's less + + align:start position:0% +minus one equals zero and that's less + + + align:start position:0% +minus one equals zero and that's less +than epsilon + + align:start position:0% +than epsilon + + + align:start position:0% +than epsilon +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +not very enlightening because capital m + + align:start position:0% +not very enlightening because capital m + + + align:start position:0% +not very enlightening because capital m +equals one uh + + align:start position:0% +equals one uh + + + align:start position:0% +equals one uh +is good enough + + align:start position:0% +is good enough + + + align:start position:0% +is good enough +so let's do something a little + + align:start position:0% +so let's do something a little + + + align:start position:0% +so let's do something a little +more so how about the limit as n goes to + + align:start position:0% +more so how about the limit as n goes to + + + align:start position:0% +more so how about the limit as n goes to +infinity + + align:start position:0% +infinity + + + align:start position:0% +infinity +one over n equals zero + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so let's do a proof of this + + align:start position:0% + + + + align:start position:0% + +again how i'm supposed to be proving + + align:start position:0% +again how i'm supposed to be proving + + + align:start position:0% +again how i'm supposed to be proving +this epsilon statement uh + + align:start position:0% +this epsilon statement uh + + + align:start position:0% +this epsilon statement uh +in the definition in order to be able to + + align:start position:0% +in the definition in order to be able to + + + align:start position:0% +in the definition in order to be able to +to + + align:start position:0% +to + + + align:start position:0% +to +state this + + align:start position:0% +state this + + + align:start position:0% +state this +um + + align:start position:0% +um + + + align:start position:0% +um +so which is a for every epsilon + + align:start position:0% +so which is a for every epsilon + + + align:start position:0% +so which is a for every epsilon +statement so i start the proof off would + + align:start position:0% +statement so i start the proof off would + + + align:start position:0% +statement so i start the proof off would +let epsilon be positive now i have to + + align:start position:0% +let epsilon be positive now i have to + + + align:start position:0% +let epsilon be positive now i have to +find i have to tell you how to choose + + align:start position:0% +find i have to tell you how to choose + + + align:start position:0% +find i have to tell you how to choose +capital m + + align:start position:0% +capital m + + + align:start position:0% +capital m +to ensure that little n bigger than or + + align:start position:0% +to ensure that little n bigger than or + + + align:start position:0% +to ensure that little n bigger than or +equal to capital m implies x of n minus + + align:start position:0% +equal to capital m implies x of n minus + + + align:start position:0% +equal to capital m implies x of n minus +0 in this case is less than epsilon so + + align:start position:0% + + + + align:start position:0% + +i will say choose capital m + + align:start position:0% +i will say choose capital m + + + align:start position:0% +i will say choose capital m +natural number + + align:start position:0% +natural number + + + align:start position:0% +natural number +such that + + align:start position:0% +such that + + + align:start position:0% +such that +m is bigger than + + align:start position:0% +m is bigger than + + + align:start position:0% +m is bigger than +one over epsilon okay + + align:start position:0% +one over epsilon okay + + + align:start position:0% +one over epsilon okay +in fact i'm not going to write it that + + align:start position:0% +in fact i'm not going to write it that + + + align:start position:0% +in fact i'm not going to write it that +way + + align:start position:0% +way + + + align:start position:0% +way +i'm going to write it this way + + align:start position:0% + + + + align:start position:0% + +1 over m is less than epsilon + + align:start position:0% +1 over m is less than epsilon + + + align:start position:0% +1 over m is less than epsilon +and why can i do this why can i + + align:start position:0% +and why can i do this why can i + + + align:start position:0% +and why can i do this why can i +find um + + align:start position:0% +find um + + + align:start position:0% +find um +such a natural number that satisfies + + align:start position:0% +such a natural number that satisfies + + + align:start position:0% +such a natural number that satisfies +this + + align:start position:0% +this + + + align:start position:0% +this +you can't just insert statements into + + align:start position:0% +you can't just insert statements into + + + align:start position:0% +you can't just insert statements into +your proof you know + + align:start position:0% +your proof you know + + + align:start position:0% +your proof you know +choose capital m to satisfy the unicorn + + align:start position:0% +choose capital m to satisfy the unicorn + + + align:start position:0% +choose capital m to satisfy the unicorn +property + + align:start position:0% +property + + + align:start position:0% +property +and not + + align:start position:0% +and not + + + align:start position:0% +and not +you know + + align:start position:0% +you know + + + align:start position:0% +you know +clarify why you can + + align:start position:0% +clarify why you can + + + align:start position:0% +clarify why you can +um + + align:start position:0% +um + + + align:start position:0% +um +choose such a natural number that + + align:start position:0% +choose such a natural number that + + + align:start position:0% +choose such a natural number that +satisfies the uniform prop the unicorn + + align:start position:0% +satisfies the uniform prop the unicorn + + + align:start position:0% +satisfies the uniform prop the unicorn +property + + align:start position:0% +property + + + align:start position:0% +property +um i can do this by the archimedean + + align:start position:0% +um i can do this by the archimedean + + + align:start position:0% +um i can do this by the archimedean +property right this is equivalently + + align:start position:0% +property right this is equivalently + + + align:start position:0% +property right this is equivalently +stating that i can find a natural number + + align:start position:0% +stating that i can find a natural number + + + align:start position:0% +stating that i can find a natural number +m so that m is bigger than one over + + align:start position:0% +m so that m is bigger than one over + + + align:start position:0% +m so that m is bigger than one over +epsilon what i had written there + + align:start position:0% +epsilon what i had written there + + + align:start position:0% +epsilon what i had written there +originally + + align:start position:0% +originally + + + align:start position:0% +originally +so let me write it this way + + align:start position:0% + + + + align:start position:0% + +such a m exists by + + align:start position:0% + + + + align:start position:0% + +the archimedean property of the natural + + align:start position:0% +the archimedean property of the natural + + + align:start position:0% +the archimedean property of the natural +numbers okay i'll say that a few times + + align:start position:0% +numbers okay i'll say that a few times + + + align:start position:0% +numbers okay i'll say that a few times +if i have to uh or + + align:start position:0% +if i have to uh or + + + align:start position:0% +if i have to uh or +um to + + align:start position:0% +um to + + + align:start position:0% +um to +clarify why + + align:start position:0% +clarify why + + + align:start position:0% +clarify why +certain natural numbers satisfying + + align:start position:0% +certain natural numbers satisfying + + + align:start position:0% +certain natural numbers satisfying +certain properties exist + + align:start position:0% +certain properties exist + + + align:start position:0% +certain properties exist +and then at one point i'll just stop + + align:start position:0% +and then at one point i'll just stop + + + align:start position:0% +and then at one point i'll just stop +because it should be clear that i've + + align:start position:0% +because it should be clear that i've + + + align:start position:0% +because it should be clear that i've +done it enough times you know how or why + + align:start position:0% +done it enough times you know how or why + + + align:start position:0% +done it enough times you know how or why +something does exist + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +i choose a natural number + + align:start position:0% +i choose a natural number + + + align:start position:0% +i choose a natural number +and a + + align:start position:0% +and a + + + align:start position:0% +and a +natural number m so that i have this + + align:start position:0% +natural number m so that i have this + + + align:start position:0% +natural number m so that i have this +now i need to show you that um + + align:start position:0% +now i need to show you that um + + + align:start position:0% +now i need to show you that um +this number works okay + + align:start position:0% +this number works okay + + + align:start position:0% +this number works okay +so + + align:start position:0% + + + + align:start position:0% + +let n be bigger than capital m + + align:start position:0% +let n be bigger than capital m + + + align:start position:0% +let n be bigger than capital m +then if i look at x sub n minus my + + align:start position:0% +then if i look at x sub n minus my + + + align:start position:0% +then if i look at x sub n minus my +proposed limit which is 0 so i look at 1 + + align:start position:0% +proposed limit which is 0 so i look at 1 + + + align:start position:0% +proposed limit which is 0 so i look at 1 +minus n + + align:start position:0% +minus n + + + align:start position:0% +minus n +0 this is equal to just 1 over n since + + align:start position:0% +0 this is equal to just 1 over n since + + + align:start position:0% +0 this is equal to just 1 over n since +little n is bigger than or equal to + + align:start position:0% +little n is bigger than or equal to + + + align:start position:0% +little n is bigger than or equal to +capital m this is less than or equal to + + align:start position:0% +capital m this is less than or equal to + + + align:start position:0% +capital m this is less than or equal to +capital m + + align:start position:0% +capital m + + + align:start position:0% +capital m +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and which is less than epsilon + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and therefore i've proven + + align:start position:0% +and therefore i've proven + + + align:start position:0% +and therefore i've proven +what i wanted to prove + + align:start position:0% +what i wanted to prove + + + align:start position:0% +what i wanted to prove +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so how do these you know if i just give + + align:start position:0% +so how do these you know if i just give + + + align:start position:0% +so how do these you know if i just give +you a sequence and i ask you to prove + + align:start position:0% +you a sequence and i ask you to prove + + + align:start position:0% +you a sequence and i ask you to prove +that + + align:start position:0% +that + + + align:start position:0% +that +um + + align:start position:0% +um + + + align:start position:0% +um +so this is some discussion + + align:start position:0% +so this is some discussion + + + align:start position:0% +so this is some discussion +you know how do you come up with these + + align:start position:0% +you know how do you come up with these + + + align:start position:0% +you know how do you come up with these +proofs how should the proof typically + + align:start position:0% +proofs how should the proof typically + + + align:start position:0% +proofs how should the proof typically +look + + align:start position:0% +look + + + align:start position:0% +look +if i want to prove + + align:start position:0% + + + + align:start position:0% + +equals l + + align:start position:0% +equals l + + + align:start position:0% +equals l +or x + + align:start position:0% +or x + + + align:start position:0% +or x +um + + align:start position:0% +um + + + align:start position:0% +um +you know what's the proof of that look + + align:start position:0% +you know what's the proof of that look + + + align:start position:0% +you know what's the proof of that look +like it should always + + align:start position:0% +like it should always + + + align:start position:0% +like it should always +so the proof would should be let epsilon + + align:start position:0% +so the proof would should be let epsilon + + + align:start position:0% +so the proof would should be let epsilon +be positive and then maybe you need to + + align:start position:0% +be positive and then maybe you need to + + + align:start position:0% +be positive and then maybe you need to +do some explaining + + align:start position:0% +do some explaining + + + align:start position:0% +do some explaining +um + + align:start position:0% +um + + + align:start position:0% +um +and then you'll say choose + + align:start position:0% +and then you'll say choose + + + align:start position:0% +and then you'll say choose +m + + align:start position:0% + + + + align:start position:0% + +so that something + + align:start position:0% +so that something + + + align:start position:0% +so that something +okay + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +that such a m exists + + align:start position:0% +that such a m exists + + + align:start position:0% +that such a m exists +probably will be explained there + + align:start position:0% +probably will be explained there + + + align:start position:0% +probably will be explained there +okay + + align:start position:0% +okay + + + align:start position:0% +okay +or in the same sentence + + align:start position:0% + + + + align:start position:0% + +and then the next part of the proof + + align:start position:0% +and then the next part of the proof + + + align:start position:0% +and then the next part of the proof +should be showing that this capital m + + align:start position:0% +should be showing that this capital m + + + align:start position:0% +should be showing that this capital m +works + + align:start position:0% +works + + + align:start position:0% +works +all right so then + + align:start position:0% +all right so then + + + align:start position:0% +all right so then +if n is bigger than or equal to capital + + align:start position:0% +if n is bigger than or equal to capital + + + align:start position:0% +if n is bigger than or equal to capital +m + + align:start position:0% +m + + + align:start position:0% +m +then you should show that it works + + align:start position:0% +then you should show that it works + + + align:start position:0% +then you should show that it works +by looking at x of n minus x + + align:start position:0% +by looking at x of n minus x + + + align:start position:0% +by looking at x of n minus x +doing + + align:start position:0% +doing + + + align:start position:0% +doing +calculation or inequalities and it's + + align:start position:0% +calculation or inequalities and it's + + + align:start position:0% +calculation or inequalities and it's +arriving at this being less than epsilon + + align:start position:0% +arriving at this being less than epsilon + + + align:start position:0% +arriving at this being less than epsilon +which is what you're wanting to prove + + align:start position:0% +which is what you're wanting to prove + + + align:start position:0% +which is what you're wanting to prove +right you're wanting in the end to + + align:start position:0% +right you're wanting in the end to + + + align:start position:0% +right you're wanting in the end to +verify this definition + + align:start position:0% +verify this definition + + + align:start position:0% +verify this definition +yeah which says for every epsilon you + + align:start position:0% +yeah which says for every epsilon you + + + align:start position:0% +yeah which says for every epsilon you +can find a capital m + + align:start position:0% +can find a capital m + + + align:start position:0% +can find a capital m +so that i get this all right + + align:start position:0% +so that i get this all right + + + align:start position:0% +so that i get this all right +so in a proof you are carrying that out + + align:start position:0% +so in a proof you are carrying that out + + + align:start position:0% +so in a proof you are carrying that out +you're saying + + align:start position:0% +you're saying + + + align:start position:0% +you're saying +for epsilon positive i choose m so that + + align:start position:0% +for epsilon positive i choose m so that + + + align:start position:0% +for epsilon positive i choose m so that +this happens + + align:start position:0% +this happens + + + align:start position:0% +this happens +okay + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +um + + align:start position:0% +um + + + align:start position:0% +um +you know how do you + + align:start position:0% + + + + align:start position:0% + +how do you come up with such a capital m + + align:start position:0% +how do you come up with such a capital m + + + align:start position:0% +how do you come up with such a capital m +so again this is just discussion and + + align:start position:0% +so again this is just discussion and + + + align:start position:0% +so again this is just discussion and +maybe we won't get to any more examples + + align:start position:0% +maybe we won't get to any more examples + + + align:start position:0% +maybe we won't get to any more examples +i'll just finish this discussion + + align:start position:0% + + + + align:start position:0% + +and then we'll call it a day how do you + + align:start position:0% +and then we'll call it a day how do you + + + align:start position:0% +and then we'll call it a day how do you +come up with such a capital m how did i + + align:start position:0% +come up with such a capital m how did i + + + align:start position:0% +come up with such a capital m how did i +come up with + + align:start position:0% +come up with + + + align:start position:0% +come up with +m + + align:start position:0% +m + + + align:start position:0% +m +why did i choose m in this way you know + + align:start position:0% +why did i choose m in this way you know + + + align:start position:0% +why did i choose m in this way you know +in the end you can see it here + + align:start position:0% +in the end you can see it here + + + align:start position:0% +in the end you can see it here +is that um + + align:start position:0% +is that um + + + align:start position:0% +is that um +i chose it because if i fiddle around + + align:start position:0% +i chose it because if i fiddle around + + + align:start position:0% +i chose it because if i fiddle around +with the thing i want to bound + + align:start position:0% +with the thing i want to bound + + + align:start position:0% +with the thing i want to bound +i ended up with one over m + + align:start position:0% +i ended up with one over m + + + align:start position:0% +i ended up with one over m +which i can + + align:start position:0% +which i can + + + align:start position:0% +which i can +control + + align:start position:0% +control + + + align:start position:0% +control +right and make it smaller than epsilon + + align:start position:0% +right and make it smaller than epsilon + + + align:start position:0% +right and make it smaller than epsilon +okay so typically how do you find + + align:start position:0% +okay so typically how do you find + + + align:start position:0% +okay so typically how do you find +capital m + + align:start position:0% + + + + align:start position:0% + +so this is a + + align:start position:0% +so this is a + + + align:start position:0% +so this is a +discussion i guess within a discussion + + align:start position:0% + + + + align:start position:0% + +typically you'll take x of n minus x + + align:start position:0% +typically you'll take x of n minus x + + + align:start position:0% +typically you'll take x of n minus x +your proposed limit maybe i give you um + + align:start position:0% +your proposed limit maybe i give you um + + + align:start position:0% +your proposed limit maybe i give you um +a + + align:start position:0% +a + + + align:start position:0% +a +a sequence + + align:start position:0% +a sequence + + + align:start position:0% +a sequence +explicitly or maybe it's a + + align:start position:0% +explicitly or maybe it's a + + + align:start position:0% +explicitly or maybe it's a +expression involving some other + + align:start position:0% +expression involving some other + + + align:start position:0% +expression involving some other +sequences + + align:start position:0% +sequences + + + align:start position:0% +sequences +and you fiddle around with it maybe you + + align:start position:0% +and you fiddle around with it maybe you + + + align:start position:0% +and you fiddle around with it maybe you +write it differently or + + align:start position:0% +write it differently or + + + align:start position:0% +write it differently or +add and subtract something or multiply + + align:start position:0% +add and subtract something or multiply + + + align:start position:0% +add and subtract something or multiply +uh by one in a fancy way + + align:start position:0% +uh by one in a fancy way + + + align:start position:0% +uh by one in a fancy way +and + + align:start position:0% +and + + + align:start position:0% +and +you'll get some expression uh + + align:start position:0% +you'll get some expression uh + + + align:start position:0% +you'll get some expression uh +typically involving + + align:start position:0% +typically involving + + + align:start position:0% +typically involving +something involving m + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and as long as + + align:start position:0% +and as long as + + + align:start position:0% +and as long as +this expression involving m is simple + + align:start position:0% +this expression involving m is simple + + + align:start position:0% +this expression involving m is simple +enough + + align:start position:0% +enough + + + align:start position:0% +enough +then you choose capital m + + align:start position:0% +then you choose capital m + + + align:start position:0% +then you choose capital m +so that this thing is less than epsilon + + align:start position:0% +so that this thing is less than epsilon + + + align:start position:0% +so that this thing is less than epsilon +now simple enough for example one over m + + align:start position:0% +now simple enough for example one over m + + + align:start position:0% +now simple enough for example one over m +i can choose capital m so that this is + + align:start position:0% +i can choose capital m so that this is + + + align:start position:0% +i can choose capital m so that this is +less than epsilon by the archimedean + + align:start position:0% +less than epsilon by the archimedean + + + align:start position:0% +less than epsilon by the archimedean +property + + align:start position:0% +property + + + align:start position:0% +property +okay if + + align:start position:0% +okay if + + + align:start position:0% +okay if +for example and that's basically + + align:start position:0% +for example and that's basically + + + align:start position:0% +for example and that's basically +1 over m or 5 over m or something like + + align:start position:0% +1 over m or 5 over m or something like + + + align:start position:0% +1 over m or 5 over m or something like +that + + align:start position:0% +that + + + align:start position:0% +that +that kind of exhausts all the simplest + + align:start position:0% +that kind of exhausts all the simplest + + + align:start position:0% +that kind of exhausts all the simplest +ones + + align:start position:0% +ones + + + align:start position:0% +ones +for now + + align:start position:0% +for now + + + align:start position:0% +for now +but if for example you ended up with 1 + + align:start position:0% +but if for example you ended up with 1 + + + align:start position:0% +but if for example you ended up with 1 +over m squared + + align:start position:0% +over m squared + + + align:start position:0% +over m squared +minus 3m + + align:start position:0% +minus 3m + + + align:start position:0% +minus 3m +minus plus 100 i would not say this is a + + align:start position:0% +minus plus 100 i would not say this is a + + + align:start position:0% +minus plus 100 i would not say this is a +simple enough + + align:start position:0% +simple enough + + + align:start position:0% +simple enough +expression to be able to say choose + + align:start position:0% +expression to be able to say choose + + + align:start position:0% +expression to be able to say choose +capital m so that this is less than + + align:start position:0% +capital m so that this is less than + + + align:start position:0% +capital m so that this is less than +epsilon without more explanation than + + align:start position:0% +epsilon without more explanation than + + + align:start position:0% +epsilon without more explanation than +what i just gave here + + align:start position:0% +what i just gave here + + + align:start position:0% +what i just gave here +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and we'll do some more uh + + align:start position:0% +and we'll do some more uh + + + align:start position:0% +and we'll do some more uh +um + + align:start position:0% +um + + + align:start position:0% +um +examples uh next time to to flesh this + + align:start position:0% +examples uh next time to to flesh this + + + align:start position:0% +examples uh next time to to flesh this +out a little bit more + + align:start position:0% +out a little bit more + + + align:start position:0% +out a little bit more +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so we'll stop there \ No newline at end of file diff --git a/Q148jV9ljPM.txt b/Q148jV9ljPM.txt new file mode 100644 index 0000000000000000000000000000000000000000..b799c6eebedf334627edb301d8dece99936c1d07 --- /dev/null +++ b/Q148jV9ljPM.txt @@ -0,0 +1,2047 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: He ended up last +Thursday's lectures talking + +about Gaussian distributions. + +As he said, one of the +interesting things about a + +Gaussian is it can be fully +characterized by its mean and + +its standard deviation. + +And this concept of being +able to take a curve and + +characterize it with a small +number of parameters is + +something we'll continue to see +as a very important way of + +looking at modeling +physical systems. + +And in fact, that is +the part of the + +term that we've entered. + +And it's a part of the term +we'll spend a lot of time on. + +And the whole issue is, how do +we construct computational + +models that will help us +understand the real world? + +When we can, we love to model +distributions as Gaussians, or + +normal, because they're so +nicely characterized. + +We have nice rules of thumb that +tell us how close things + +lie to the mean, et cetera. + +However, it's important to +understand that if something + +is not actually normally +distributed and we pretend it + +is, we can get very misleading +results out of our model. + +So let's think about the +fact that not all + +distributions are normal. + +So consider rolling +a single die. + +Each of the 6 outcomes +is equally probable. + +So we would not expect to see a +peak, say, at 3 or 4, and a + +trough at 1. + +A 3 or a 4 is the same +probability as 1. + +Similarly, if one thinks about +the Massachusetts state + +lottery, or any fair lottery, +the probability of each number + +coming up is the same. + +So it would be a flat line. + +If you had a million numbers, +the probability of each number + +is 1 over a million. + +And so if you plotted the +probability of each number, + +again, you'd get a flat line. + +Such distributions are +called uniform. + +Each result is equally +probable. + +We can fully characterize a +uniform distribution with a + +single parameter, its range. + +If I tell you it ranges over 1 +to a million, that's all you + +need to know to know what the +distribution looks like. + +So they're even simpler than +normal distributions. + +Uniform distributions occur +quite often in games devised + +by humans, but almost +never in nature. + +And typically they're +not very useful for + +modeling complex systems. + +We have to work hard to invent +something that's normal. + +Most things are not naturally +that way. + +I'm sorry, to invent things +that are uniform. + +Normal, as we saw last time, +occurs all the time in nature. + +The other thing that occurs +quite frequently are + +exponential distributions. + +They're used in a lot +of different ways. + +For example, people who are +trying to plan things like + +highway systems use exponential +distributions to + +model inter-arrival times, how +much time there is between + +each car, say, entering +the Mass Turnpike. + +We'll see many other +examples of them. + +The key thing about them is +they have the property of + +being memoryless. + +They are in fact the only +continuous distributions that + +are memoryless. + +So let's look at an example +with which some of you are + +more familiar than you want to +be, the concentration of a + +drug in the human body. + +For those who are watching on +OpenCourseWare, it's not + +because all the students +are drug users. + +It's because they're working on +a problem set that involves + +modeling drugs in +the human body. + +I don't know how many of you +are drug users, all right? + +Assume that at each time step, +each molecule has a + +probability p of being +cleared by the body. + +The system is memoryless in the +sense that at each step, + +the probability of a particular +molecule being + +cleared is independent +of what happened at + +the previous steps. + +So the fact that a molecule +didn't get cleared at time t + +has no impact on whether +or not it will be + +cleared at time t1. + +The probability doesn't go up +as it doesn't get cleared. + +So it's independent of +the previous steps. + +So at time t equals 1, what's +the probability of the + +molecule still being +in the human body? + +If the probability of being +cleared at each step is p, + +it's 1 minus p, right? + +So if the probability of being +cleared was 0.5 at each time + +step, the time that it still +exists after the first time + +step is 1 minus 0.5-- + +i.e., 0.5. + +So what's the probability of +it still being in the human + +body at time t equals 2? + +Well, it wasn't cleared +at time 1. + +Since it's memoryless, whether +or not it's cleared at time 2 + +is also 1/p. + +And so it existing still after +two steps is going to be 1 + +minus p squared. + +We saw that with independent +probabilities. + +And the nice thing about working +with exponential + +distributions is we know that +the probabilities are + +independent. + +More generally, its still being +in the body at time t is + +going to be 1 minus +p to the t. + +So we have a nice closed-form +solution that will give us the + +probability of each molecule +surviving until time t. + +All right? + +So now let's look at the +question of, suppose that at + +time t equals 0, there +are m0 molecules. + +Now we can ask, how many +molecules are there likely to + +be at any time t? + +Well, let's write a little +program to look at that. + +So that's this program, clear. + +We'll start with n, the number +of molecules, the probability + +of clearing it at each step, +and the number of steps. + +And we'll keep track of +the num remaining. + +So at the beginning, we have +n molecules remaining. + +And then for t in range steps, +we're just going to multiply + +n, the number we started with, +times the probability of each + +molecule still existing. + +And then we'll plot it. + +Does that make sense? + +So this is a tiny bit of code +that basically implements that + +formula over on the board. + +Let's run it. + +And we'll run it starting with +a 1,000 molecules, a + +probability of each being +cleared of 0.01, and we'll + +look at 500 time steps. + +All right. + +This is kind of interesting. + +We're getting a straight line. + +That doesn't look like an +exponential, does it? + +Or does it? + +Why do we have a straight +line here? + +Somebody? + +Because I used a semilog axis. + +So let's look at it +now without that. + +We now see something that +really does look like + +exponential decay. + +It drops very quickly in the +beginning, and then it + +asymptotes towards 0. + +But of course it never +quite gets there in + +a continuous model. + +If we had a discrete model, we +would eventually have to get + +to 0, because that last molecule +would either get + +cleared or not. + +But in a continuous world-- + +which is in this case probably +not a good model, or not a + +perfect model I should say, +because it allows us to have a + +quarter of a molecule there, +which we kind of know is + +physiologically nonsense, +biochemically nonsense. + +But you can see we get this +exponential decay. + +But as we saw previously, if +we plot an exponential on a + +log axis, as the math +would tell us, we + +get a straight line. + +And that, in fact, is a very +simple and nice way to see + +whether you have an exponential +distribution. + +Put it on a log axis, see +if it's straight. + +It's a good trick, and +one we use a lot. + +OK. + +So there, I took the physical +model I described and derived, + +through a little bit of math, +what the result should be, and + +implemented some code +to give us a plot of + +what that told us. + +Let's look at a different +way of doing it. + +I could've instead written a +Monte Carlo simulation to do + +the same kind of thing. + +So here, instead of working out +the probabilities, I just + +tried to write some code that +exactly mimicked the physical + +process that I was +talking about. + +So instead of knowing that I +could just look at 1 minus p + +to the t, at each step, I +cleared some molecules. + +I just used random.random. + +If I came out with something +less than the clear + +probability, I got rid +of that molecule. + +And I did that for each +molecule, deciding whether or + +not it should be cleared. + +For molecule m in range, looking +at all the remaining + +molecules, I either clear +one or I don't. + +And then I can plot that. + +So let's look what happens if +I compare the two results. + +So I'm going to do the original +analytical model of + +clear, and then the simulation +model of clearing, and see + +what I get. + +Well, much to my relief, I get +kind of the same curve. + +Not exactly. + +You'll notice that the blue +curve, the analytical model, + +is a beautiful smooth curve, +whereas the red curve has got + +a little bit of jaggies. + +It's clearly very similar +to the blue + +curve, but not identical. + +It doesn't surprise me. + +There is some randomness +in there. + +And in fact, I could have gotten +unlucky and gotten + +something that didn't look +like the blue curve. + +But given the sample size, that +would have been quite + +surprising. + +Which of these two models +do you like better? + +So we've got two models. + +We've got one I'll call the +analytic model, and one I'll + +call the simulation model. + +Both show exponential decay. + +That is to say the number +of molecules declines + +exponentially, quite quickly. + +But they're not quite +identical. + +So which would we prefer? + +Or which would you prefer? + +There is no right +answer for this. + +Just for fun, I'll +ask for a poll. + +Who prefers the analytical +model? + +Who prefer the simulation? + +All right. + +Somebody who prefers the +analytical, tell me why. + +AUDIENCE: It looks +a lot nicer. + +PROFESSOR: Well, all right. + +It looks a lot nicer. + +That's kind of human +nature, to prefer + +something that looks prettier. + +On the other hand, what we're +really interested in is the + +question of not aesthetics, +but fidelity to the actual + +physical situation. + +A straight line might +look even nicer, but + +it wouldn't be accurate. + +So when we think about +evaluating a model, what we + +really should be asking, I +think, are two questions. + +One is fidelity. + +And another way to think about +that is credibility. + +Typically, we're creating a +model because we don't know + +the actual answer. + +And we're trying to see what +might actually happen if we, + +say, ran a physical +experiment. + +And so we have to ask the +question of, do we believe the + +results the model +are giving us. + +And so that sort of boils down +to not a question of + +mathematics, but a question +of reasoning. + +Can we look at the model +and convince + +ourselves that it is accurate? + +And the other question +is utility. + +And I can think about that as, +in some sense, what questions + +are answerable with the model? + +So the first one is pretty much +a question of personal + +preference. + +And for this particular +simulation, which is pretty + +simple, or this particular +model, it's hard to argue that + +one is more believable +than the other. + +I might argue the second is more +believable, because it's + +a direct implementation of +the physical system. + +I didn't rely on my +math being right. + +But the math is pretty +simple here. + +What's, I think, more apparent +is in this case there is some + +additional utility offered +by the simulation model. + +And it's often true of that, +simulation models, that we can + +ask what-if questions, because +we can easily change the model + +to be slightly different in ways +that is usually harder + +for an analytic model. + +For example, suppose these +drug molecules had this + +peculiar property that every +100 time steps, they could + +clone themselves. + +And so every molecule that was +there became two molecules. + +Unlikely for the drug. + +Not so unlikely for, say, a +bacterium or a virus, as + +you've seen. + +Well, a little hard to figure +out how to do the + +probabilities in the case that +that happens, because we'll no + +longer get this beautiful, +simple exponential decay. + +But quite easy to think about +how we would change the + +simulation model, which is +what I have done here. + +So I said here, if time is not +equal to 0 and time is evenly + +divisible by 100, then I'm +just going to double the + +number of molecules. + +Every living molecule +will clone itself. + +And now we'll see what we get. + +Well, we get this rather +peculiar-looking sawtooth + +distribution. + +We still have, overall, +an exponential decay. + +But we see every once in +while it jumps up, and + +then it comes down. + +It's not so easy to write a +simple closed-form formula + +that describes this, but very +easy to produce a simulation + +model that gives you +some insight to + +what's happening here. + +And that's, I think, one of +the great attractions of + +simulation modeling, is we get +to do this sort of thing. + +Many, many physical systems +exhibit exponential decay or + +exponential growth. + +For example, people in Japan +now are very interested in + +half-life of various radioactive +particles. + +And when we talk about +half-life, we mean that there + +is exponential decay +in radioactivity. + +That's what half-life is. + +So people are looking at what +is the half-life of iodine, + +say, versus other radioactive +particles. + +We also see exponential +growth a lot. + +I used to have a swimming pool +which I had to maintain, and I + +realized if I let the algae +get out of control in the + +pool, it went from having very +little algae to having a lot + +of algae very quickly, +because the algae + +doubles every period. + +And so all of a sudden, +it takes off. + +So exponential growth is-- + +exponential decay are +important things. + +We see them all the time. + +People use the word very +carelessly when they mean + +quick growth. + +They say exponential. + +But of course, it has a +very specific meaning. + +OK. + +We've now, for the moment at +least, finished our short + +venture into probability +and distributions. + +We'll come back to it a little +bit when we talk about how to + +lie with statistics. + +But before we do that, before +we leave probability for a + +while, just for fun, I want to +pose to you one of these + +probability problems that +hurts people's heads. + +It's a very popular one. + +How many people here +have heard of + +the Monty Hall problem? + +OK, a lot of you. + +So as we play the game, those +of you who know the answer, + +I'll ask your forbearance +not to blurt it out. + +So it's a wonderful problem. + +It's so exciting that people +have written books about it. + +So here's how it works. + +This is from a game show called, +I think, Let's Make a + +Deal, with the host, Monty +Hall, who did it forever. + +So the way it works is you +start with three doors. + +Behind one of the doors +is a great prize-- + +for example, an automobile. + +Behind each of the other +doors is a booby + +prize, typically a goat. + +I don't know why people don't +like goats, but apparently + +they don't. + +So the way it works is Monty +invites someone from the + +audience, chosen on the basis of +their outlandish costumes. + +And they come down and they're +told what wonderful prize is + +behind one of the doors. + +And then they're asked +to choose a door. + +So the person might choose a +door and say, I'll choose door + +number one. + +Monty then opens one of +the other two doors. + +He knows which doors have +the goats and which + +door has the car. + +He opens a door with the goat. + +So now there are +two doors left. + +And he asks the contestant, +do you want to switch. + +Do you want to stick with door +one or would you like to + +switch to door two? + +And the Monty Hall problem +is, what should she do? + +And the audience will always +shout out advice. + +So I do have a simulation +of that. + +I'd like to run. + +I need three people to volunteer +to be doors. + +Come on, three doors. + +It's not so hard. + +Come on down. + +And I need one person to +volunteer to be the contest. + +Is anybody in a costume here? + +I don't know. + +Mitch is kind of in one, but-- + +all right. + +These are the contestants. + +All right, you're +door number (2). + +You're door number (1). + +You are door number (3). + +A contestant please. + +There's $1 in one of these. + +You can actually win +something of value. + +All right, we have a contestant +coming down. + +Oh, all right, we have two +contestants coming down. + +All right. + +The aisle wins. + +All right, choose a door. + +You choose door number (2). + +All right, let us open +door number (1). + +And let's see what's +in door number (1). + +Show it to the class. + +It is a goat. + +Now you have a choice. + +You can stick with your original +decision, or you can + +switch to door number (3). + +Suggestions? + +AUDIENCE: Switch. + +AUDIENCE: Switch. + +AUDIENCE: Switch. + +AUDIENCE: Switch. + +AUDIENCE: Lower one. + +AUDIENCE: Don't switch it. + +AUDIENCE: Switch. + +PROFESSOR: All right. + +She is going to stick with +door number (2). + +Let us open door number (2). + +She wins $1. + +It is yours. + +Don't spend it all at once. + +Thank you, everybody. + +All right, now, was she +lucky or was she + +smart, is the question? + +Does it matter? + +This was a subject of enormous +debate in the + +mathematical community. + +In 1991, Parade magazine +published a correct solution + +to the problem, and +approximately 10,000 readers, + +including a 1,000 with PhDs in +mathematics, wrote to Parade + +telling them they had published +the wrong solution. + +And the debate roiled on. + +So who thinks she was lucky +and who thinks it actually + +matters whether you switch? + +Who thinks it matters, those +who don't know the problem? + +Who thinks it doesn't matter? + +All right. + +The doesn't-matters win +by a small margin. + +And in fact, that's what the +readers of Parade thought. + +But they were wrong. + +It matters a lot whether +you switch. + +Let's do the analysis first, +analytically, and then we'll + +do a simulation. + +So the player makes a choice. + +And this is some interesting +ways to think about + +probability. + +And with the probability of 1/3, +the player has chosen the + +correct door. + +All right? + +Now that means that with a +probability of 2 out of 3, the + +car lies behind one of +the other two doors. + +Now here's the key step. + +Monty opens a door that +he knows does + +not contain the prize. + +The key thing to notice here is +the choice of doors is not + +independent of the choice of the +player, because Monty will + +never choose the door that the +player has initially picked. + +Now since the probability of the +prize being behind the two + +remaining doors is 2 out of 3, +the probability of the prize + +being behind one of the doors +that he did not open + +is 2 out of 3 -- + +in fact, behind the +other door. + +In fact, you were +extraordinarily lucky to win + +the dollar, because switching +doubles the odds of winning. + +Because remember, your odds of +winning were 1 out of 3 when + +you first chose the door. + +That left two doors. + +The probability of the car being +behind one of those two + +doors was 2/3. + +Monty opened the one that +didn't contain the car, + +because he knew it +contained a goat. + +So that must mean the +probability of the car being + +behind the remaining +door is 2 out of 3. + +So you double your +odds of winning. + +The logic is kind of clear. + +It didn't stop people from +aggressively debating it for + +the longest of times. + +And I kind of didn't +believe it myself. + +So I did what I usually do, +is I wrote some code. + +And let's look at two +pieces of code here. + +And again, the theme here is +how we can use simulation + +models to understand slightly +complex, or more than slightly + +complex, situations. + +So here's the way +the game works. + +So I've got a simple simulation +that counts the + +number of wins. + +And the way it's done is, for +t in range number of trials, + +the contestant picks 1, +2, or 3 at random. + +I've tried to mimic +exactly the game. + +So the car is behind +one of the doors. + +The contestant guesses a door. + +And then there's this +'choose' function to + +open one of the two. + +And we're going to have +2 ways of choosing + +which door gets opened. + +So the Monty Hall way-- + +Monty chooses. + +He takes the guessed door and +the prize door, and he opens + +the non-guess that contains +the goat. + +So if (1) is the guessed door, +and (1) is not the guessed + +door and it's not the prize +door, then he opens (1). + +Same thing for (2). + +And if (1) or (2) is not the +choice, he opens (3). + +As opposed to the random choose +function, which just + +chooses at random between the +doors that weren't guessed. + +So it might open the car, at +which point the contest is + +told, sorry, you lose, +you don't even + +have a choice anymore. + +We're then going to run the +simulation with Monty choosing + +and random choice, and +see what we get. + +So you've got the code on +the handout to do this. + +I'm not going to go +over the details. + +The thing to notice about it is +it's yet another example of + +how we can use PyLab to do +some interesting plots. + +This time I'm going to print a +pie chart, just to show that + +we can do those. + +And let's see what happens. + +So people understand +what's going on? + +That I've got these two +functions, montyChoose and + +randomChoose. + +I'm using those functions as +parameters, a very convenient + +thing, and running the +simulation each way. + +And let's see what happens. + +All right. + +So what we see here is, when I +run montyChoose, sure enough, + +it comes out to about 2/3 of +the time, you win if you + +change, and only 1/3 of the +time if you don't, pretty + +close to what the +math predicts. + +In fact, sort of astonishingly +close. + +On the other hand, if Monte +had been just choosing at + +random, then we see it really +doesn't matter whether you + +switch or not. + +So again, from a probability +point of view, we see how + +subtle these things can be based +upon whether decisions + +are independent of previous +decisions, or not independent. + +And we also see, in some sense, +that we can write a + +very small piece of code that +actually provides a simulation + +of a real, in this case, game, +and we can have, I think, a + +lot of confidence. + +We can look at the code and say, +is it really the way the + +game is described? + +Yes. + +And then we get nice results +that tell us what to do. + +And in this case it tells us +that, if Monty is choosing + +based upon what he knows, +then by all + +means, you should switch. + +And I'm sorry that it didn't +work out that way when we + +played the game, but that's +the way probabilities are, + +that you didn't switch +and you lucked out. + +So now you're a rich lady. + +All right. + +So that's one thing we can do. + +One more thing I want to talk +about, before we leave the + +subject of Monte Carlo +simulations-- + +it's pretty clear that these +kind of simulations are very + +useful for tackling problems +in which predictive + +non-determinism plays a role. + +And at first blush, you might +think that, OK, that's the + +only time we should use a Monte +Carlo simulation, when + +there's some inherent randomness +in the problem, and + +therefore it's hard to model +analytically, and therefore + +we'll use randomness +in the code. + +Interestingly enough, +particularly in recent years, + +but for quite a while, people +have understood the notion of + +using randomized algorithms +to solve problems in which + +randomness plays no role. + +And that's a little surprising, +but an incredibly + +useful concept to put in your +bag of tricks, the ability to + +use randomization to solve +problems that are not random. + +So let me talk about +an example. + +Consider the concept of pi. + +Pi has been around +for a long time. + +For thousands of years, +people have known + +that there's a constant-- + +called pi since about +the 18th century-- + +associated with circles, such +that the circumference of a + +circle is always going +to be equal to + +pi times the diameter. + +The area of a circle is +always going to be pi + +r-squared, et cetera. + +So for thousands of years, +people knew that there was + +such a constant. + +They just didn't know +what it was. + +And there's a long and beautiful +history of people + +attempting to estimate pi. + +About the earliest estimate +I've found is from the + +Egyptians, in something called +the Rhind Papyrus, from 1650 + +BC, or thereabouts. + +And it estimated pi +to be 4 times-- + +let me get this right-- + +8/9 squared, which is +3.16, more or less. + +That was pretty good. + +About a 1,000 years later, +an estimate of pi + +appears in the Bible. + +Or at least, it's implied by the +Bible in a description of + +one of Solomon's construction +projects. + +It says, "And he made a molten +sea, 10 cubits from the one + +brim to the other. + +It was round all about, and his +height was five cubits. + +And a line of 30 cubits did +compass it round about." + +So you can take that and solve +for pi, because you've given + +the circumference, and other +details, the diameter. + +You can solve for pi. + +And you see, if you do that, pi +comes out to be exactly 3. + +Not quite as accurate +as the Egyptians + +had 1,000 years earlier. + +Now perhaps the Bible +is wrong. + +I don't want to offend +anybody. + +Or perhaps the molten sea wasn't +perfectly circular. + +Or maybe the circumference was +measured from the wall outside + +and the diameter from +the inside. + +Or maybe it was just that was a +good enough number to use in + +construction, because a cubit +was something like the length + +of your forearm. + +Different people have different +length forearms, and + +there was no reason to try +and be more precise. + +Who knows? + +The best estimate of pi in +ancient times was from + +Archimedes of Syracuse. + +And he did something quite +amazing for around 200 BC. + +He didn't give the +value of pi. + +He said, I don't know what the +value is, but I can give you + +an upper bound and +a lower bound. + +And he did this by carefully +constructing a polygon with a + +huge number of tiny little +straight lines that would + +approximate a circle, and then +actually measuring things. + +So he built a polygon with 96 +sides, and concluded that pi + +was somewhere between 223 +divided by 71, and 22/7. + +Very sophisticated at the time, +to be giving upper and + +lower bounds. + +If we look at what the middle +of that is, it's actually + +amazingly good. + +It's 3.1418. + +Not bad. + +All right. + +What does this have to do with +Monte Carlo simulations? + +Many years later-- + +in fact, in the 1700s, two +French mathematicians invented + +another way of computing pi. + +Buffon and Laplace. + +Actually Buffon first +proposed it. + +He got it wrong. + +Laplace corrected it. + +And they said, we can find pi +using a stochastic simulation. + +They didn't use those words, +but that's what + +they basically described. + +And they talked about it in +terms of needle-dropping. + +So think about having a square, +and inscribing in the + +square a circle. + +And you'll excuse my lack +of artistic ability. + +So they put one of those +on the floor. + +And then they dropped needles, +which would get carried around + +by the wind and land in +some random place. + +And they counted the number of +needles that landed in the + +circle, and the number of +needles that landed in the + +square but not in the circle. + +And then they did +a little math. + +Let's assume for the sake of +argument here that the radius + +of the circle is 1. + +They observed the following +equation must hold, that the + +needles in the circle over the +needles in the square should + +be equal to the area of the +circle divided by the area of + +the square. + +It seems logical, if they're +landing at random, that they + +would get distributed +proportional to the area. + +And then they solved for pi, +knowing that the area of the + +circle is pi r-squared. + +They could then say that pi-- + +in fact, in this case, since we +know the radius is 1, and 1 + +squared is 1, that tells us that +the area of the circle + +should be pi, right? + +Pi times 1. + +So they said pi is equal to the +area of the circle, which + +is equal to the area of the +square times the needles in + +the circle, divided by the +needles in the square. + +So they had that formula. + +Unfortunately they couldn't drop +enough needles to get a + +very good estimate. + +So they described +how to do it. + +But this was an experiment. + +They did the math, they +had a nice formula. + +They did not have an +experimental apparatus that + +would actually let them drop +enough needles to get a very + +good estimate. + +It would take a lot +of patience. + +And maybe they wouldn't +land at random. + +Who knows what. + +Fortunately, today, we have a +much easier way to do that. + +So we can write some code that +does the simulation. + +We're going to have +a way to throw the + +needles or drop the needles. + +And then what we're going to +do is we're going to have a + +simulation that we're going +to run, that's going to-- + +I don't know how many +needles to drop. + +I'm going to keep dropping +needles until I get a small + +enough standard deviation that I +can be confident that I have + +a bound on pi with some +confidence interval. + +In fact, I'm going to use 5% +here, and use that rule of + +thumb that Mitch talked about +last time, about standard + +deviations. + +And I say, all right, I'm going +to keep running the + +experiment until the standard +deviation of + +trials is 5% or less. + +Two standard deviations is small +enough that I get my + +answer within some precision. + +I'm going to ask here for +a precision of 0.01. + +And so therefore my standard +deviation should be that + +precision divided by 4, because +I'm looking for 2 + +standard deviations on either +side of the mean, which is why + +I'm dividing by 4 +and not by 2. + +So I divide by 4 and +I see what I get. + +So let's run it. + +And this will take a +little bit of time. + +It will take no time if I don't +uncomment the code to + +actually run the experiment. + +Estimate pi. + +And we'll get some estimates. + +So what we can see here is that +my estimates change as I + +run experiments. + +Every time I run this-- or not +every time, I often get a + +different number of +needles I need. + +But you can see that my first +estimate is not very good. + +My estimates do get +better, though not + +monotonically better. + +But what does get monotonically +better is the + +standard deviation gets smaller +and smaller, which is + +what you would expect. + +So there's no guarantee that by +running a bigger trial, I + +get a more accurate result. + +What there is a guarantee +is that I can have more + +confidence in my result. + +I could have gotten lucky and +run a small number of needles + +and gotten it exactly +right by chance. + +But I would have been wrong to +assume it was right, because + +let's pretend we didn't +know what the value + +of pi was, a priori. + +But what I can say here is since +my standard deviation is + +now 0.002, and if we look at +it, we'll see that these + +things are normally distributed, +I can be pretty + +sure that the true value of pi +is 3.1407 et cetera, plus or + +minus 0.00023, et cetera, +with a 95% confidence. + +So this is using the stuff +that you saw in the last + +lecture to now combine that +statistical background with + +this simulation to compute +a pretty darn + +good estimate of pi. + +And if I ran more needles, if I +wanted to get more precise, + +I can get as precise as I want +to be, as many digits of + +precision as I want. + +So again, what we see here is +that we've been able to solve + +a problem that had nothing +to do with randomness. + +The value of pi is not +a random number. + +And yet we used randomness +to solve it. + +A very common technique. + +And we use some very simple +statistics to know whether or + +not we should believe +our solution. + +And so those are the +two lessons I + +want you to take home. + +Now if you look at your handout, +you'll see that at + +the bottom, I've used the same +technique to do integration. + +If you think about what +integration means, when you + +ask, what is the integral of +some formula, what you learned + +when you first looked at +calculus was that that was the + +area under some curve, right? + +That's what the integral is. + +And you learned all sorts of +complicated mathematics to + +solve complicated integrals. + +Well, you can pose an +integration problem exactly + +analogous to this. + +You draw your curve. + +You drops some needles. + +You count how many fall under +the curve, how many don't fall + +under the curve in +some larger area. + +And you can solve +the integration. + +And that's exactly what I've +done here, where f is the + +function being integrated. + +I won't go through +the details. + +Now in fact, this kind of +simulation is not a good way + +to solve single integrals. + +It's much better to use +something like Simpson's rule, + +whatever that is. + +But in fact, it is frequently +used in practice for more + +complicated things, a double or +triple integration, where + +the mathematics gets +fairly complicated. + +People will often solve those +problems using a Monte Carlo + +simulation. + +It's a practical method +for tackling it. + +And again, in your handout, +you'll see a very simple piece + +of code that does a +double integral. + +All right. + +That's all for today. \ No newline at end of file diff --git a/QBcQJdJk9r8.txt b/QBcQJdJk9r8.txt new file mode 100644 index 0000000000000000000000000000000000000000..5ca022474a29a65114619720c071838f1f8237b1 --- /dev/null +++ b/QBcQJdJk9r8.txt @@ -0,0 +1,1107 @@ +align:start position:0% + +one last bit of housekeeping then we're + + align:start position:0% +one last bit of housekeeping then we're + + + align:start position:0% +one last bit of housekeeping then we're +done what should our Hardware do if for + + align:start position:0% +done what should our Hardware do if for + + + align:start position:0% +done what should our Hardware do if for +some reason an instruction can't be + + align:start position:0% +some reason an instruction can't be + + + align:start position:0% +some reason an instruction can't be +executed for example if a programming + + align:start position:0% +executed for example if a programming + + + align:start position:0% +executed for example if a programming +error has led to trying to execute some + + align:start position:0% +error has led to trying to execute some + + + align:start position:0% +error has led to trying to execute some +piece of data as an instruction and the + + align:start position:0% +piece of data as an instruction and the + + + align:start position:0% +piece of data as an instruction and the +opcode field doesn't correspond to a + + align:start position:0% +opcode field doesn't correspond to a + + + align:start position:0% +opcode field doesn't correspond to a +beta instruction a so-called ill OP or + + align:start position:0% +beta instruction a so-called ill OP or + + + align:start position:0% +beta instruction a so-called ill OP or +illegal operation or maybe the address + + align:start position:0% +illegal operation or maybe the address + + + align:start position:0% +illegal operation or maybe the address +is larger than the actual amount of main + + align:start position:0% +is larger than the actual amount of main + + + align:start position:0% +is larger than the actual amount of main +memory or maybe one of the operand + + align:start position:0% +memory or maybe one of the operand + + + align:start position:0% +memory or maybe one of the operand +values is not acceptable for example if + + align:start position:0% +values is not acceptable for example if + + + align:start position:0% +values is not acceptable for example if +the B operand for a div instruction is + + align:start position:0% +the B operand for a div instruction is + + + align:start position:0% +the B operand for a div instruction is +zero in modern computers the accepted + + align:start position:0% +zero in modern computers the accepted + + + align:start position:0% +zero in modern computers the accepted +strategy is to cease execution of the + + align:start position:0% +strategy is to cease execution of the + + + align:start position:0% +strategy is to cease execution of the +running program and transfer control to + + align:start position:0% +running program and transfer control to + + + align:start position:0% +running program and transfer control to +some error handler code the error + + align:start position:0% +some error handler code the error + + + align:start position:0% +some error handler code the error +handler might store the program state on + + align:start position:0% +handler might store the program state on + + + align:start position:0% +handler might store the program state on +to disk for later debugging or for an + + align:start position:0% +to disk for later debugging or for an + + + align:start position:0% +to disk for later debugging or for an +unimplemented but legal opcode it might + + align:start position:0% +unimplemented but legal opcode it might + + + align:start position:0% +unimplemented but legal opcode it might +emulate the missing instruction and + + align:start position:0% +emulate the missing instruction and + + + align:start position:0% +emulate the missing instruction and +software and resume execution as if the + + align:start position:0% +software and resume execution as if the + + + align:start position:0% +software and resume execution as if the +instruction had been implemented in + + align:start position:0% +instruction had been implemented in + + + align:start position:0% +instruction had been implemented in +hardware there's also the need to deal + + align:start position:0% +hardware there's also the need to deal + + + align:start position:0% +hardware there's also the need to deal +with external events like those + + align:start position:0% +with external events like those + + + align:start position:0% +with external events like those +associated with input and output here + + align:start position:0% +associated with input and output here + + + align:start position:0% +associated with input and output here +we'd like to interrupt the execution of + + align:start position:0% +we'd like to interrupt the execution of + + + align:start position:0% +we'd like to interrupt the execution of +the current program run some code to + + align:start position:0% +the current program run some code to + + + align:start position:0% +the current program run some code to +deal with the external event then resume + + align:start position:0% +deal with the external event then resume + + + align:start position:0% +deal with the external event then resume +execution as if the interrupts had never + + align:start position:0% +execution as if the interrupts had never + + + align:start position:0% +execution as if the interrupts had never +happened to deal with these cases we'll + + align:start position:0% +happened to deal with these cases we'll + + + align:start position:0% +happened to deal with these cases we'll +add hardware to treat exceptions like + + align:start position:0% +add hardware to treat exceptions like + + + align:start position:0% +add hardware to treat exceptions like +forced procedure calls to special code + + align:start position:0% +forced procedure calls to special code + + + align:start position:0% +forced procedure calls to special code +to handle the situation arranging to + + align:start position:0% +to handle the situation arranging to + + + align:start position:0% +to handle the situation arranging to +save the PC plus for value of the + + align:start position:0% +save the PC plus for value of the + + + align:start position:0% +save the PC plus for value of the +interrupted program so that the handler + + align:start position:0% +interrupted program so that the handler + + + align:start position:0% +interrupted program so that the handler +can resume execution if it wishes this + + align:start position:0% +can resume execution if it wishes this + + + align:start position:0% +can resume execution if it wishes this +is a very powerful feature since it + + align:start position:0% +is a very powerful feature since it + + + align:start position:0% +is a very powerful feature since it +allows us to transfer control to + + align:start position:0% +allows us to transfer control to + + + align:start position:0% +allows us to transfer control to +software to handle most any circumstance + + align:start position:0% +software to handle most any circumstance + + + align:start position:0% +software to handle most any circumstance +beyond the capability of our modest + + align:start position:0% +beyond the capability of our modest + + + align:start position:0% +beyond the capability of our modest +hardware as we'll see in part 3 of the + + align:start position:0% +hardware as we'll see in part 3 of the + + + align:start position:0% +hardware as we'll see in part 3 of the +course the exception hardware will be + + align:start position:0% +course the exception hardware will be + + + align:start position:0% +course the exception hardware will be +our key to interfacing running programs + + align:start position:0% +our key to interfacing running programs + + + align:start position:0% +our key to interfacing running programs +to the operating system and to allow the + + align:start position:0% +to the operating system and to allow the + + + align:start position:0% +to the operating system and to allow the +operating system to deal with external + + align:start position:0% +operating system to deal with external + + + align:start position:0% +operating system to deal with external +events without any awareness on the part + + align:start position:0% +events without any awareness on the part + + + align:start position:0% +events without any awareness on the part +of the running program so our plan is to + + align:start position:0% +of the running program so our plan is to + + + align:start position:0% +of the running program so our plan is to +interrupt the running program acting + + align:start position:0% +interrupt the running program acting + + + align:start position:0% +interrupt the running program acting +like the current instruction was + + align:start position:0% +like the current instruction was + + + align:start position:0% +like the current instruction was +actually a procedure call to the handler + + align:start position:0% +actually a procedure call to the handler + + + align:start position:0% +actually a procedure call to the handler +code when it finishes execution + + align:start position:0% +code when it finishes execution + + + align:start position:0% +code when it finishes execution +can if appropriate used the normal + + align:start position:0% +can if appropriate used the normal + + + align:start position:0% +can if appropriate used the normal +procedure return sequence to resume + + align:start position:0% +procedure return sequence to resume + + + align:start position:0% +procedure return sequence to resume +execution of the user program we'll use + + align:start position:0% +execution of the user program we'll use + + + align:start position:0% +execution of the user program we'll use +the term exception to refer to + + align:start position:0% +the term exception to refer to + + + align:start position:0% +the term exception to refer to +exceptions caused by executing the + + align:start position:0% +exceptions caused by executing the + + + align:start position:0% +exceptions caused by executing the +current program such exceptions are + + align:start position:0% +current program such exceptions are + + + align:start position:0% +current program such exceptions are +synchronous in the sense that they are + + align:start position:0% +synchronous in the sense that they are + + + align:start position:0% +synchronous in the sense that they are +triggered by executing a particular + + align:start position:0% +triggered by executing a particular + + + align:start position:0% +triggered by executing a particular +instruction in other words if the + + align:start position:0% +instruction in other words if the + + + align:start position:0% +instruction in other words if the +program was rerun with the same data the + + align:start position:0% +program was rerun with the same data the + + + align:start position:0% +program was rerun with the same data the +same exception would occur we'll use the + + align:start position:0% +same exception would occur we'll use the + + + align:start position:0% +same exception would occur we'll use the +term interrupt to refer to a spur dis + + align:start position:0% +term interrupt to refer to a spur dis + + + align:start position:0% +term interrupt to refer to a spur dis +exceptions resulting from external + + align:start position:0% +exceptions resulting from external + + + align:start position:0% +exceptions resulting from external +events whose timing is unrelated to the + + align:start position:0% +events whose timing is unrelated to the + + + align:start position:0% +events whose timing is unrelated to the +currently running program the + + align:start position:0% +currently running program the + + + align:start position:0% +currently running program the +implementation for both types of + + align:start position:0% +implementation for both types of + + + align:start position:0% +implementation for both types of +exceptions is the same when an exception + + align:start position:0% +exceptions is the same when an exception + + + align:start position:0% +exceptions is the same when an exception +is detected the beta hardware will + + align:start position:0% +is detected the beta hardware will + + + align:start position:0% +is detected the beta hardware will +behave as if the current instruction was + + align:start position:0% +behave as if the current instruction was + + + align:start position:0% +behave as if the current instruction was +a taken branch to either location for + + align:start position:0% +a taken branch to either location for + + + align:start position:0% +a taken branch to either location for +for synchronous exceptions or location 8 + + align:start position:0% +for synchronous exceptions or location 8 + + + align:start position:0% +for synchronous exceptions or location 8 +for asynchronous interrupts presumably + + align:start position:0% +for asynchronous interrupts presumably + + + align:start position:0% +for asynchronous interrupts presumably +the instructions in those locations will + + align:start position:0% +the instructions in those locations will + + + align:start position:0% +the instructions in those locations will +jump to the entry points of the + + align:start position:0% +jump to the entry points of the + + + align:start position:0% +jump to the entry points of the +appropriate handler routines will save + + align:start position:0% +appropriate handler routines will save + + + align:start position:0% +appropriate handler routines will save +the PC plus for value of the interrupted + + align:start position:0% +the PC plus for value of the interrupted + + + align:start position:0% +the PC plus for value of the interrupted +program into R 30 a register dedicated + + align:start position:0% +program into R 30 a register dedicated + + + align:start position:0% +program into R 30 a register dedicated +to that purpose will call that register + + align:start position:0% +to that purpose will call that register + + + align:start position:0% +to that purpose will call that register +xp exception pointer to remind ourselves + + align:start position:0% +xp exception pointer to remind ourselves + + + align:start position:0% +xp exception pointer to remind ourselves +of how we're using it since interrupts + + align:start position:0% +of how we're using it since interrupts + + + align:start position:0% +of how we're using it since interrupts +in particular can happen at any point + + align:start position:0% +in particular can happen at any point + + + align:start position:0% +in particular can happen at any point +during a programs execution thus over + + align:start position:0% +during a programs execution thus over + + + align:start position:0% +during a programs execution thus over +writing the contents of XP at any time + + align:start position:0% +writing the contents of XP at any time + + + align:start position:0% +writing the contents of XP at any time +user programs can't use the XP registers + + align:start position:0% +user programs can't use the XP registers + + + align:start position:0% +user programs can't use the XP registers +to hold values since those values might + + align:start position:0% +to hold values since those values might + + + align:start position:0% +to hold values since those values might +disappear at any moment here's how this + + align:start position:0% +disappear at any moment here's how this + + + align:start position:0% +disappear at any moment here's how this +scheme works suppose we don't include + + align:start position:0% +scheme works suppose we don't include + + + align:start position:0% +scheme works suppose we don't include +hardware to implement the diff + + align:start position:0% +hardware to implement the diff + + + align:start position:0% +hardware to implement the diff +instruction so it's treated as an + + align:start position:0% +instruction so it's treated as an + + + align:start position:0% +instruction so it's treated as an +illegal opcode the exception hardware + + align:start position:0% +illegal opcode the exception hardware + + + align:start position:0% +illegal opcode the exception hardware +forces a procedure call to location for + + align:start position:0% +forces a procedure call to location for + + + align:start position:0% +forces a procedure call to location for +which then branches to the ill OP + + align:start position:0% +which then branches to the ill OP + + + align:start position:0% +which then branches to the ill OP +handler showing here the PC plus 4 value + + align:start position:0% +handler showing here the PC plus 4 value + + + align:start position:0% +handler showing here the PC plus 4 value +of the div instruction has been saved in + + align:start position:0% +of the div instruction has been saved in + + + align:start position:0% +of the div instruction has been saved in +the XP register so the handler can fetch + + align:start position:0% +the XP register so the handler can fetch + + + align:start position:0% +the XP register so the handler can fetch +the illegal instruction and if it can + + align:start position:0% +the illegal instruction and if it can + + + align:start position:0% +the illegal instruction and if it can +emulate its operation and software when + + align:start position:0% +emulate its operation and software when + + + align:start position:0% +emulate its operation and software when +the handler is complete it can resume + + align:start position:0% +the handler is complete it can resume + + + align:start position:0% +the handler is complete it can resume +execution of the original program at the + + align:start position:0% +execution of the original program at the + + + align:start position:0% +execution of the original program at the +instruction following diff by performing + + align:start position:0% +instruction following diff by performing + + + align:start position:0% +instruction following diff by performing +a jump XP + + align:start position:0% +a jump XP + + + align:start position:0% +a jump XP +pretty neat to handle exceptions we all + + align:start position:0% +pretty neat to handle exceptions we all + + + align:start position:0% +pretty neat to handle exceptions we all +need a few simple changes to the data + + align:start position:0% +need a few simple changes to the data + + + align:start position:0% +need a few simple changes to the data +path we've added a MUX controlled by the + + align:start position:0% +path we've added a MUX controlled by the + + + align:start position:0% +path we've added a MUX controlled by the +W a sell signal to choose the right back + + align:start position:0% +W a sell signal to choose the right back + + + align:start position:0% +W a sell signal to choose the right back +address for the register file when W a + + align:start position:0% +address for the register file when W a + + + align:start position:0% +address for the register file when W a +cell is one write back will occur to the + + align:start position:0% +cell is one write back will occur to the + + + align:start position:0% +cell is one write back will occur to the +X P register in other words register 30 + + align:start position:0% +X P register in other words register 30 + + + align:start position:0% +X P register in other words register 30 +when W a cell is 0 write back will occur + + align:start position:0% +when W a cell is 0 write back will occur + + + align:start position:0% +when W a cell is 0 write back will occur +normally in other words to the register + + align:start position:0% +normally in other words to the register + + + align:start position:0% +normally in other words to the register +specified by the RC field of the current + + align:start position:0% +specified by the RC field of the current + + + align:start position:0% +specified by the RC field of the current +instruction the remaining two inputs of + + align:start position:0% +instruction the remaining two inputs of + + + align:start position:0% +instruction the remaining two inputs of +the PC sell MUX are set to the constant + + align:start position:0% +the PC sell MUX are set to the constant + + + align:start position:0% +the PC sell MUX are set to the constant +addresses for the exception handlers in + + align:start position:0% +addresses for the exception handlers in + + + align:start position:0% +addresses for the exception handlers in +our case for for illegal operations and + + align:start position:0% +our case for for illegal operations and + + + align:start position:0% +our case for for illegal operations and +eight for interrupts here's the flow of + + align:start position:0% +eight for interrupts here's the flow of + + + align:start position:0% +eight for interrupts here's the flow of +control during an exception the PC plus + + align:start position:0% +control during an exception the PC plus + + + align:start position:0% +control during an exception the PC plus +4 value for the interrupted instruction + + align:start position:0% +4 value for the interrupted instruction + + + align:start position:0% +4 value for the interrupted instruction +is routed through the WD cell MUX to be + + align:start position:0% +is routed through the WD cell MUX to be + + + align:start position:0% +is routed through the WD cell MUX to be +written into the X P register meanwhile + + align:start position:0% +written into the X P register meanwhile + + + align:start position:0% +written into the X P register meanwhile +the control logic chooses either 3 or 4 + + align:start position:0% +the control logic chooses either 3 or 4 + + + align:start position:0% +the control logic chooses either 3 or 4 +as the value of PC cell to select the + + align:start position:0% +as the value of PC cell to select the + + + align:start position:0% +as the value of PC cell to select the +appropriate next instruction that will + + align:start position:0% +appropriate next instruction that will + + + align:start position:0% +appropriate next instruction that will +initiate the handling of the exception + + align:start position:0% +initiate the handling of the exception + + + align:start position:0% +initiate the handling of the exception +the remaining control signals are forced + + align:start position:0% +the remaining control signals are forced + + + align:start position:0% +the remaining control signals are forced +to their don't care values since we no + + align:start position:0% +to their don't care values since we no + + + align:start position:0% +to their don't care values since we no +longer care about completing the + + align:start position:0% +longer care about completing the + + + align:start position:0% +longer care about completing the +execution of the instruction we had + + align:start position:0% +execution of the instruction we had + + + align:start position:0% +execution of the instruction we had +fetched from main memory at the + + align:start position:0% +fetched from main memory at the + + + align:start position:0% +fetched from main memory at the +beginning of the cycle note that the + + align:start position:0% +beginning of the cycle note that the + + + align:start position:0% +beginning of the cycle note that the +interrupted instruction has not been + + align:start position:0% +interrupted instruction has not been + + + align:start position:0% +interrupted instruction has not been +executed so if the exception handler + + align:start position:0% +executed so if the exception handler + + + align:start position:0% +executed so if the exception handler +wishes to execute the interrupted + + align:start position:0% +wishes to execute the interrupted + + + align:start position:0% +wishes to execute the interrupted +instruction it will have to subtract 4 + + align:start position:0% +instruction it will have to subtract 4 + + + align:start position:0% +instruction it will have to subtract 4 +from the value in the X P register + + align:start position:0% +from the value in the X P register + + + align:start position:0% +from the value in the X P register +before performing a jump X P to resume + + align:start position:0% +before performing a jump X P to resume + + + align:start position:0% +before performing a jump X P to resume +execution of the interrupted program \ No newline at end of file diff --git a/QJ96fO8Eef4.txt b/QJ96fO8Eef4.txt new file mode 100644 index 0000000000000000000000000000000000000000..3ee9731d713f401a0dd1394587e14afe5b35478c --- /dev/null +++ b/QJ96fO8Eef4.txt @@ -0,0 +1,10536 @@ +align:start position:0% + +So um right so to one of the things I + + align:start position:0% +So um right so to one of the things I + + + align:start position:0% +So um right so to one of the things I +want to focus on today and we'll get to + + align:start position:0% +want to focus on today and we'll get to + + + align:start position:0% +want to focus on today and we'll get to +this in just a minute is uh how to write + + align:start position:0% +this in just a minute is uh how to write + + + align:start position:0% +this in just a minute is uh how to write +a proof. So this is going to be + + align:start position:0% +a proof. So this is going to be + + + align:start position:0% +a proof. So this is going to be +uh + + align:start position:0% + + + + align:start position:0% + +how to write uh a mathematical proof. + + align:start position:0% + + + + align:start position:0% + +So how how do you write a proof as + + align:start position:0% +So how how do you write a proof as + + + align:start position:0% +So how how do you write a proof as +opposed to you know how do you think + + align:start position:0% +opposed to you know how do you think + + + align:start position:0% +opposed to you know how do you think +about uh why something should be true, + + align:start position:0% +about uh why something should be true, + + + align:start position:0% +about uh why something should be true, +right? And so this is like one of the + + align:start position:0% +right? And so this is like one of the + + + align:start position:0% +right? And so this is like one of the +important topics for this uh course. So + + align:start position:0% +important topics for this uh course. So + + + align:start position:0% +important topics for this uh course. So +uh you know overall I mean there's a lot + + align:start position:0% +uh you know overall I mean there's a lot + + + align:start position:0% +uh you know overall I mean there's a lot +of uh important concepts that we will + + align:start position:0% +of uh important concepts that we will + + + align:start position:0% +of uh important concepts that we will +talk about right but some of the general + + align:start position:0% +talk about right but some of the general + + + align:start position:0% +talk about right but some of the general +things that we learn is how to prove + + align:start position:0% +things that we learn is how to prove + + + align:start position:0% +things that we learn is how to prove +something but also how to write a proper + + align:start position:0% +something but also how to write a proper + + + align:start position:0% +something but also how to write a proper +mathematical proof right and those + + align:start position:0% +mathematical proof right and those + + + align:start position:0% +mathematical proof right and those +things are a little bit different and + + align:start position:0% +things are a little bit different and + + + align:start position:0% +things are a little bit different and +we'll talk about this in a minute. + + align:start position:0% +we'll talk about this in a minute. + + + align:start position:0% +we'll talk about this in a minute. +Uh I also want to say that so on the + + align:start position:0% +Uh I also want to say that so on the + + + align:start position:0% +Uh I also want to say that so on the +course information the last page of the + + align:start position:0% +course information the last page of the + + + align:start position:0% +course information the last page of the +course several people were asking about + + align:start position:0% +course several people were asking about + + + align:start position:0% +course several people were asking about +this on the last page of course + + align:start position:0% +this on the last page of course + + + align:start position:0% +this on the last page of course +animation + + align:start position:0% +animation + + + align:start position:0% +animation +there is uh there is right so there's a + + align:start position:0% +there is uh there is right so there's a + + + align:start position:0% +there is uh there is right so there's a +notes there's a notes for the class that + + align:start position:0% +notes there's a notes for the class that + + + align:start position:0% +notes there's a notes for the class that +I write uh and I typically I try to + + align:start position:0% +I write uh and I typically I try to + + + align:start position:0% +I write uh and I typically I try to +write them in advance a couple of days + + align:start position:0% +write them in advance a couple of days + + + align:start position:0% +write them in advance a couple of days +in advance and then I try to go over it + + align:start position:0% +in advance and then I try to go over it + + + align:start position:0% +in advance and then I try to go over it +the day uh also to make sure to find + + align:start position:0% +the day uh also to make sure to find + + + align:start position:0% +the day uh also to make sure to find +tbooks and things like that. So that is + + align:start position:0% +tbooks and things like that. So that is + + + align:start position:0% +tbooks and things like that. So that is +more readable. Uh so if I were you, I + + align:start position:0% +more readable. Uh so if I were you, I + + + align:start position:0% +more readable. Uh so if I were you, I +would first read the lecture notes that + + align:start position:0% +would first read the lecture notes that + + + align:start position:0% +would first read the lecture notes that +I post after the lectures. Uh and then + + align:start position:0% +I post after the lectures. Uh and then + + + align:start position:0% +I post after the lectures. Uh and then +there's also on the last page of the + + align:start position:0% +there's also on the last page of the + + + align:start position:0% +there's also on the last page of the +course information there is uh and I try + + align:start position:0% +course information there is uh and I try + + + align:start position:0% +course information there is uh and I try +to do this in advance but it's a little + + align:start position:0% +to do this in advance but it's a little + + + align:start position:0% +to do this in advance but it's a little +bit difficult to do it in advance. So uh + + align:start position:0% +bit difficult to do it in advance. So uh + + + align:start position:0% +bit difficult to do it in advance. So uh +it say the the date and it say the + + align:start position:0% +it say the the date and it say the + + + align:start position:0% +it say the the date and it say the +material some keywords from the lecture + + align:start position:0% +material some keywords from the lecture + + + align:start position:0% +material some keywords from the lecture +uh on that date. So I over the weekend I + + align:start position:0% +uh on that date. So I over the weekend I + + + align:start position:0% +uh on that date. So I over the weekend I +posted for the two lectures for this + + align:start position:0% +posted for the two lectures for this + + + align:start position:0% +posted for the two lectures for this +week + + align:start position:0% +week + + + align:start position:0% +week +but then I go back I will try to go + + align:start position:0% +but then I go back I will try to go + + + align:start position:0% +but then I go back I will try to go +back. So I actually went back this + + align:start position:0% +back. So I actually went back this + + + align:start position:0% +back. So I actually went back this +morning and changed some of it from the + + align:start position:0% +morning and changed some of it from the + + + align:start position:0% +morning and changed some of it from the +second lecture so that it fits more and + + align:start position:0% +second lecture so that it fits more and + + + align:start position:0% +second lecture so that it fits more and +I think I will only uh I give references + + align:start position:0% +I think I will only uh I give references + + + align:start position:0% +I think I will only uh I give references +there to the book but and initially I + + align:start position:0% +there to the book but and initially I + + + align:start position:0% +there to the book but and initially I +was thinking giving both references to + + align:start position:0% +was thinking giving both references to + + + align:start position:0% +was thinking giving both references to +Ruden and to the main textbook. + + align:start position:0% +Ruden and to the main textbook. + + + align:start position:0% +Ruden and to the main textbook. +I think it's probably just uh maybe it's + + align:start position:0% +I think it's probably just uh maybe it's + + + align:start position:0% +I think it's probably just uh maybe it's +I mean I think it's probably smarter + + align:start position:0% +I mean I think it's probably smarter + + + align:start position:0% +I mean I think it's probably smarter +just to give it from the main textbook. + + align:start position:0% +just to give it from the main textbook. + + + align:start position:0% +just to give it from the main textbook. +Okay. But I and uh Rudin is a great book + + align:start position:0% +Okay. But I and uh Rudin is a great book + + + align:start position:0% +Okay. But I and uh Rudin is a great book +um you know this was a book uh that was + + align:start position:0% +um you know this was a book uh that was + + + align:start position:0% +um you know this was a book uh that was +that was um that was created here long + + align:start position:0% +that was um that was created here long + + + align:start position:0% +that was um that was created here long +time ago and it it is like a classic in + + align:start position:0% +time ago and it it is like a classic in + + + align:start position:0% +time ago and it it is like a classic in +the subject. It's a great book. It's + + align:start position:0% +the subject. It's a great book. It's + + + align:start position:0% +the subject. It's a great book. It's +more formal than the other book. So the + + align:start position:0% +more formal than the other book. So the + + + align:start position:0% +more formal than the other book. So the +other book is a little bit more + + align:start position:0% +other book is a little bit more + + + align:start position:0% +other book is a little bit more +accessible. + + align:start position:0% +accessible. + + + align:start position:0% +accessible. +Uh, and so that's why we're using that. + + align:start position:0% +Uh, and so that's why we're using that. + + + align:start position:0% +Uh, and so that's why we're using that. +But but actually Rudin is a fantastic + + align:start position:0% +But but actually Rudin is a fantastic + + + align:start position:0% +But but actually Rudin is a fantastic +book. If if it was just myself, + + align:start position:0% +book. If if it was just myself, + + + align:start position:0% +book. If if it was just myself, +uh, I would just I think Ruden is hard + + align:start position:0% +uh, I would just I think Ruden is hard + + + align:start position:0% +uh, I would just I think Ruden is hard +to beat. But but but the other one is is + + align:start position:0% +to beat. But but but the other one is is + + + align:start position:0% +to beat. But but but the other one is is +more accessible and so it might actually + + align:start position:0% +more accessible and so it might actually + + + align:start position:0% +more accessible and so it might actually +be better the first time you learn it. + + align:start position:0% + + + + align:start position:0% + +And but so I think from here on out, so + + align:start position:0% +And but so I think from here on out, so + + + align:start position:0% +And but so I think from here on out, so +I deleted the references I had to root + + align:start position:0% +I deleted the references I had to root + + + align:start position:0% +I deleted the references I had to root +in. I think I would just give references + + align:start position:0% +in. I think I would just give references + + + align:start position:0% +in. I think I would just give references +to the main textbook + + align:start position:0% +to the main textbook + + + align:start position:0% +to the main textbook +uh and and but but you know I certainly + + align:start position:0% +uh and and but but you know I certainly + + + align:start position:0% +uh and and but but you know I certainly +encourage you to look at root and also I + + align:start position:0% +encourage you to look at root and also I + + + align:start position:0% +encourage you to look at root and also I +also encourage you to look at chapters + + align:start position:0% +also encourage you to look at chapters + + + align:start position:0% +also encourage you to look at chapters +that we will skip uh but there's also + + align:start position:0% +that we will skip uh but there's also + + + align:start position:0% +that we will skip uh but there's also +things that that we initially skip and + + align:start position:0% +things that that we initially skip and + + + align:start position:0% +things that that we initially skip and +then we come back to + + align:start position:0% +then we come back to + + + align:start position:0% +then we come back to +but but again you know you should and + + align:start position:0% +but but again you know you should and + + + align:start position:0% +but but again you know you should and +it's like the when I list the things + + align:start position:0% +it's like the when I list the things + + + align:start position:0% +it's like the when I list the things +that we will cover in the lecture in + + align:start position:0% +that we will cover in the lecture in + + + align:start position:0% +that we will cover in the lecture in +advance it's only sort of approximation + + align:start position:0% +advance it's only sort of approximation + + + align:start position:0% +advance it's only sort of approximation +right so um once I write lecture it + + align:start position:0% +right so um once I write lecture it + + + align:start position:0% +right so um once I write lecture it +might be slightly different + + align:start position:0% +might be slightly different + + + align:start position:0% +might be slightly different +okay so um so we had uh so last time we + + align:start position:0% +okay so um so we had uh so last time we + + + align:start position:0% +okay so um so we had uh so last time we +talked about the theorem we didn't prove + + align:start position:0% +talked about the theorem we didn't prove + + + align:start position:0% +talked about the theorem we didn't prove +it that the real is a complete + + align:start position:0% + + + + align:start position:0% + +uh order field, + + align:start position:0% + + + + align:start position:0% + +right? And so in particular, it was an + + align:start position:0% +right? And so in particular, it was an + + + align:start position:0% +right? And so in particular, it was an +order set uh that was uh also a field + + align:start position:0% +order set uh that was uh also a field + + + align:start position:0% +order set uh that was uh also a field +and it was complete, right? And so + + align:start position:0% +and it was complete, right? And so + + + align:start position:0% +and it was complete, right? And so +again, complete meant so if you had a + + align:start position:0% +again, complete meant so if you had a + + + align:start position:0% +again, complete meant so if you had a +subset a here, which was a subset of of + + align:start position:0% +subset a here, which was a subset of of + + + align:start position:0% +subset a here, which was a subset of of +R, + + align:start position:0% +R, + + + align:start position:0% +R, +then uh A is bounded. + + align:start position:0% + + + + align:start position:0% + +It's bounded from above. + + align:start position:0% +It's bounded from above. + + + align:start position:0% +It's bounded from above. +[Applause] + + align:start position:0% + + + + align:start position:0% + +Uh if there exist + + align:start position:0% + + + + align:start position:0% + +uh m in uh r such that + + align:start position:0% +uh m in uh r such that + + + align:start position:0% +uh m in uh r such that +for all + + align:start position:0% + + + + align:start position:0% + +uh a in a + + align:start position:0% +uh a in a + + + align:start position:0% +uh a in a +a here is less equal to m. So, + + align:start position:0% +a here is less equal to m. So, + + + align:start position:0% +a here is less equal to m. So, +and then if that's the case, then we say + + align:start position:0% +and then if that's the case, then we say + + + align:start position:0% +and then if that's the case, then we say +that and M here + + align:start position:0% +that and M here + + + align:start position:0% +that and M here +is set to be + + align:start position:0% + + + + align:start position:0% + +uh an upper bound. + + align:start position:0% + + + + align:start position:0% + +Likewise, might likewise + + align:start position:0% + + + + align:start position:0% + +uh if um if a here is a subset of r + + align:start position:0% +uh if um if a here is a subset of r + + + align:start position:0% +uh if um if a here is a subset of r +uh uh then we say that + + align:start position:0% + + + + align:start position:0% + +that uh a is bounded from below. + + align:start position:0% + + + + align:start position:0% + +If there exist + + align:start position:0% + + + + align:start position:0% + +uh little m in in R such that + + align:start position:0% +uh little m in in R such that + + + align:start position:0% +uh little m in in R such that +uh m here is less than a for all Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, this is upper and lower bounds. + + align:start position:0% +So, this is upper and lower bounds. + + + align:start position:0% +So, this is upper and lower bounds. +Okay. And several people ask on on Piaza + + align:start position:0% +Okay. And several people ask on on Piaza + + + align:start position:0% +Okay. And several people ask on on Piaza +they ask um you know they were a little + + align:start position:0% +they ask um you know they were a little + + + align:start position:0% +they ask um you know they were a little +unclear about + + align:start position:0% + + + + align:start position:0% + +um you know where does this M capital M + + align:start position:0% +um you know where does this M capital M + + + align:start position:0% +um you know where does this M capital M +where does this have to be in what set + + align:start position:0% +where does this have to be in what set + + + align:start position:0% +where does this have to be in what set +does it have to be? And likewise for + + align:start position:0% +does it have to be? And likewise for + + + align:start position:0% +does it have to be? And likewise for +this little M, right? And so let me try + + align:start position:0% +this little M, right? And so let me try + + + align:start position:0% +this little M, right? And so let me try +to give you some example and I try to do + + align:start position:0% +to give you some example and I try to do + + + align:start position:0% +to give you some example and I try to do +that on P, but let me just uh just + + align:start position:0% +that on P, but let me just uh just + + + align:start position:0% +that on P, but let me just uh just +because several people were asking about + + align:start position:0% +because several people were asking about + + + align:start position:0% +because several people were asking about +it, let me just say again. So that this + + align:start position:0% +it, let me just say again. So that this + + + align:start position:0% +it, let me just say again. So that this +capital M when you have it like this, + + align:start position:0% +capital M when you have it like this, + + + align:start position:0% +capital M when you have it like this, +this capital M does not need to be in + + align:start position:0% +this capital M does not need to be in + + + align:start position:0% +this capital M does not need to be in +the set, right? A is bounded. So here's + + align:start position:0% +the set, right? A is bounded. So here's + + + align:start position:0% +the set, right? A is bounded. So here's +an example. + + align:start position:0% + + + + align:start position:0% + +If you're looking at the set 0 one. So + + align:start position:0% +If you're looking at the set 0 one. So + + + align:start position:0% +If you're looking at the set 0 one. So +this is the interval. This is the + + align:start position:0% +this is the interval. This is the + + + align:start position:0% +this is the interval. This is the +interval but it does not contain zero + + align:start position:0% +interval but it does not contain zero + + + align:start position:0% +interval but it does not contain zero +and it does not contain one but it + + align:start position:0% +and it does not contain one but it + + + align:start position:0% +and it does not contain one but it +contain everything in between zero and + + align:start position:0% +contain everything in between zero and + + + align:start position:0% +contain everything in between zero and +one. + + align:start position:0% +one. + + + align:start position:0% +one. +This one here is bounded. So this if + + align:start position:0% +This one here is bounded. So this if + + + align:start position:0% +This one here is bounded. So this if +this here is a and we think about a here + + align:start position:0% +this here is a and we think about a here + + + align:start position:0% +this here is a and we think about a here +as a subset of r + + align:start position:0% +as a subset of r + + + align:start position:0% +as a subset of r +then a is bounded + + align:start position:0% + + + + align:start position:0% + +and so one usually say it's bounded if + + align:start position:0% +and so one usually say it's bounded if + + + align:start position:0% +and so one usually say it's bounded if +it's it's it's both from above and + + align:start position:0% +it's it's it's both from above and + + + align:start position:0% +it's it's it's both from above and +below. + + align:start position:0% + + + + align:start position:0% + +All right. So if one just say that it's + + align:start position:0% +All right. So if one just say that it's + + + align:start position:0% +All right. So if one just say that it's +bounded then one means that it's bound + + align:start position:0% +bounded then one means that it's bound + + + align:start position:0% +bounded then one means that it's bound +from above and below + + align:start position:0% +from above and below + + + align:start position:0% +from above and below +it's bounded + + align:start position:0% +it's bounded + + + align:start position:0% +it's bounded +and uh right and so because like bounded + + align:start position:0% +and uh right and so because like bounded + + + align:start position:0% +and uh right and so because like bounded +from above + + align:start position:0% + + + + align:start position:0% + +about because you can just you have that + + align:start position:0% +about because you can just you have that + + + align:start position:0% +about because you can just you have that +if x here is in this interval then of + + align:start position:0% +if x here is in this interval then of + + + align:start position:0% +if x here is in this interval then of +course x is lesser or equal to one right + + align:start position:0% +course x is lesser or equal to one right + + + align:start position:0% +course x is lesser or equal to one right +in fact it's strictly less than one + + align:start position:0% +in fact it's strictly less than one + + + align:start position:0% +in fact it's strictly less than one +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +But you see this set here, there is no + + align:start position:0% +But you see this set here, there is no + + + align:start position:0% +But you see this set here, there is no +element in the set that is an upper + + align:start position:0% +element in the set that is an upper + + + align:start position:0% +element in the set that is an upper +bound for this set, right? The upper + + align:start position:0% +bound for this set, right? The upper + + + align:start position:0% +bound for this set, right? The upper +bound is outside the set, but it is an + + align:start position:0% +bound is outside the set, but it is an + + + align:start position:0% +bound is outside the set, but it is an +all of our and that's that's fine, + + align:start position:0% +all of our and that's that's fine, + + + align:start position:0% +all of our and that's that's fine, +right? An upper bound uh is will + + align:start position:0% +right? An upper bound uh is will + + + align:start position:0% +right? An upper bound uh is will +typically just be in a larger set. And + + align:start position:0% +typically just be in a larger set. And + + + align:start position:0% +typically just be in a larger set. And +the same with uh with + + align:start position:0% +the same with uh with + + + align:start position:0% +the same with uh with +with lower bound. + + align:start position:0% +with lower bound. + + + align:start position:0% +with lower bound. +Now these this kind everything on this + + align:start position:0% +Now these this kind everything on this + + + align:start position:0% +Now these this kind everything on this +board except this theorem but you know + + align:start position:0% +board except this theorem but you know + + + align:start position:0% +board except this theorem but you know +this in terms of ordered sets right has + + align:start position:0% +this in terms of ordered sets right has + + + align:start position:0% +this in terms of ordered sets right has +nothing to do you know it's just much + + align:start position:0% +nothing to do you know it's just much + + + align:start position:0% +nothing to do you know it's just much +more general than R. So if you take if S + + align:start position:0% +more general than R. So if you take if S + + + align:start position:0% +more general than R. So if you take if S +here is an ordered set + + align:start position:0% + + + + align:start position:0% + +and A here is a subset + + align:start position:0% + + + + align:start position:0% + +it's a subset. + + align:start position:0% + + + + align:start position:0% + +So it's a ordered set. So so it it's a + + align:start position:0% +So it's a ordered set. So so it it's a + + + align:start position:0% +So it's a ordered set. So so it it's a +set with an ordering. And if a here is a + + align:start position:0% +set with an ordering. And if a here is a + + + align:start position:0% +set with an ordering. And if a here is a +subset of s + + align:start position:0% +subset of s + + + align:start position:0% +subset of s +then again we can say that uh a is + + align:start position:0% +then again we can say that uh a is + + + align:start position:0% +then again we can say that uh a is +bounded from above. + + align:start position:0% + + + + align:start position:0% + +If um if uh there exist + + align:start position:0% + + + + align:start position:0% + +m again m does not have to be an a + + align:start position:0% +m again m does not have to be an a + + + align:start position:0% +m again m does not have to be an a +but it can be just in the larger set so + + align:start position:0% +but it can be just in the larger set so + + + align:start position:0% +but it can be just in the larger set so +that such that + + align:start position:0% +that such that + + + align:start position:0% +that such that +for all + + align:start position:0% +for all + + + align:start position:0% +for all +a in a it's lesser equal to m + + align:start position:0% +a in a it's lesser equal to m + + + align:start position:0% +a in a it's lesser equal to m +Right? So this is just this is like the + + align:start position:0% +Right? So this is just this is like the + + + align:start position:0% +Right? So this is just this is like the +definition in general being bounded + + align:start position:0% +definition in general being bounded + + + align:start position:0% +definition in general being bounded +above if you have a order set and you + + align:start position:0% +above if you have a order set and you + + + align:start position:0% +above if you have a order set and you +have a subset. Right? And now just to + + align:start position:0% +have a subset. Right? And now just to + + + align:start position:0% +have a subset. Right? And now just to +illustrate it. So typically we're going + + align:start position:0% +illustrate it. So typically we're going + + + align:start position:0% +illustrate it. So typically we're going +to think about where the set is with a + + align:start position:0% +to think about where the set is with a + + + align:start position:0% +to think about where the set is with a +usual ordering and you have a subset of + + align:start position:0% +usual ordering and you have a subset of + + + align:start position:0% +usual ordering and you have a subset of +it and you talk about whether it's + + align:start position:0% +it and you talk about whether it's + + + align:start position:0% +it and you talk about whether it's +bounded from above or below. + + align:start position:0% +bounded from above or below. + + + align:start position:0% +bounded from above or below. +But of course, you could also do it in + + align:start position:0% +But of course, you could also do it in + + + align:start position:0% +But of course, you could also do it in +in a more general setting like this, + + align:start position:0% +in a more general setting like this, + + + align:start position:0% +in a more general setting like this, +right? And so here's an example + + align:start position:0% +right? And so here's an example + + + align:start position:0% +right? And so here's an example +that if you look at which maybe is + + align:start position:0% +that if you look at which maybe is + + + align:start position:0% +that if you look at which maybe is +counterintuitive, + + align:start position:0% +counterintuitive, + + + align:start position:0% +counterintuitive, +but if you take if s here is + + align:start position:0% +but if you take if s here is + + + align:start position:0% +but if you take if s here is +is the half line. So it's it's all the + + align:start position:0% +is the half line. So it's it's all the + + + align:start position:0% +is the half line. So it's it's all the +real numbers + + align:start position:0% +real numbers + + + align:start position:0% +real numbers +between + + align:start position:0% +between + + + align:start position:0% +between +uh say zero and infinity. + + align:start position:0% +uh say zero and infinity. + + + align:start position:0% +uh say zero and infinity. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +and um + + align:start position:0% +and um + + + align:start position:0% +and um +and then uh you would have a here is a + + align:start position:0% +and then uh you would have a here is a + + + align:start position:0% +and then uh you would have a here is a +subset + + align:start position:0% +subset + + + align:start position:0% +subset +zero to one. + + align:start position:0% + + + + align:start position:0% + +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +Now a here and the ordering. So this is + + align:start position:0% +Now a here and the ordering. So this is + + + align:start position:0% +Now a here and the ordering. So this is +this is of course a subset of r but you + + align:start position:0% +this is of course a subset of r but you + + + align:start position:0% +this is of course a subset of r but you +should forget about r. I mean you know + + align:start position:0% +should forget about r. I mean you know + + + align:start position:0% +should forget about r. I mean you know +you know the ordering from r but forget + + align:start position:0% +you know the ordering from r but forget + + + align:start position:0% +you know the ordering from r but forget +about it because this is now what you + + align:start position:0% +about it because this is now what you + + + align:start position:0% +about it because this is now what you +think about the set s right? + + align:start position:0% +think about the set s right? + + + align:start position:0% +think about the set s right? +And so if you're looking at A as a + + align:start position:0% +And so if you're looking at A as a + + + align:start position:0% +And so if you're looking at A as a +subset of this then A here A is bounded + + align:start position:0% +subset of this then A here A is bounded + + + align:start position:0% +subset of this then A here A is bounded +from above. + + align:start position:0% + + + + align:start position:0% + +Right? Why? This is just because for all + + align:start position:0% +Right? Why? This is just because for all + + + align:start position:0% +Right? Why? This is just because for all +a in in a you have that A here is + + align:start position:0% +a in in a you have that A here is + + + align:start position:0% +a in in a you have that A here is +strictly less than one. So one here is + + align:start position:0% +strictly less than one. So one here is + + + align:start position:0% +strictly less than one. So one here is +an upper bound for A. Right? But now + + align:start position:0% +an upper bound for A. Right? But now + + + align:start position:0% +an upper bound for A. Right? But now +think about does this set here has a + + align:start position:0% +think about does this set here has a + + + align:start position:0% +think about does this set here has a +lower bound, right? + + align:start position:0% +lower bound, right? + + + align:start position:0% +lower bound, right? +Well, a lower bound have to be inside + + align:start position:0% +Well, a lower bound have to be inside + + + align:start position:0% +Well, a lower bound have to be inside +this set S, right? Because we're + + align:start position:0% +this set S, right? Because we're + + + align:start position:0% +this set S, right? Because we're +thinking about this here as a subset of + + align:start position:0% +thinking about this here as a subset of + + + align:start position:0% +thinking about this here as a subset of +this ordered set. We don't think about + + align:start position:0% +this ordered set. We don't think about + + + align:start position:0% +this ordered set. We don't think about +it as a subset of the real line. But if + + align:start position:0% +it as a subset of the real line. But if + + + align:start position:0% +it as a subset of the real line. But if +you think about it as a subset of this + + align:start position:0% +you think about it as a subset of this + + + align:start position:0% +you think about it as a subset of this +set here, then there is no lower bound, + + align:start position:0% +set here, then there is no lower bound, + + + align:start position:0% +set here, then there is no lower bound, +right? because zero is not in this set + + align:start position:0% +right? because zero is not in this set + + + align:start position:0% +right? because zero is not in this set +and no negative numbers in this set. So + + align:start position:0% +and no negative numbers in this set. So + + + align:start position:0% +and no negative numbers in this set. So +this here so and this seems maybe a + + align:start position:0% +this here so and this seems maybe a + + + align:start position:0% +this here so and this seems maybe a +little bit counterintuitive but a is not + + align:start position:0% +little bit counterintuitive but a is not + + + align:start position:0% +little bit counterintuitive but a is not +is not + + align:start position:0% +is not + + + align:start position:0% +is not +bounded from below + + align:start position:0% + + + + align:start position:0% + +as a subset of + + align:start position:0% + + + + align:start position:0% + +of s. Obviously it is bounded from below + + align:start position:0% +of s. Obviously it is bounded from below + + + align:start position:0% +of s. Obviously it is bounded from below +if you were thinking about it as a + + align:start position:0% +if you were thinking about it as a + + + align:start position:0% +if you were thinking about it as a +subset of real real line. But if you + + align:start position:0% +subset of real real line. But if you + + + align:start position:0% +subset of real real line. But if you +think about it as a subset of S, it's + + align:start position:0% +think about it as a subset of S, it's + + + align:start position:0% +think about it as a subset of S, it's +not bounded from below. + + align:start position:0% +not bounded from below. + + + align:start position:0% +not bounded from below. +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +another person was asking the infinite + + align:start position:0% +another person was asking the infinite + + + align:start position:0% +another person was asking the infinite +and minus infinity those are not uh real + + align:start position:0% +and minus infinity those are not uh real + + + align:start position:0% +and minus infinity those are not uh real +numbers. Okay. + + align:start position:0% +numbers. Okay. + + + align:start position:0% +numbers. Okay. +>> Yeah. + + align:start position:0% + + + + align:start position:0% + +try. + + align:start position:0% +try. + + + align:start position:0% +try. +>> Yeah. + + align:start position:0% + + + + align:start position:0% + +>> Uh + + align:start position:0% +>> Uh + + + align:start position:0% +>> Uh +uh if it's not directly stated that if + + align:start position:0% +uh if it's not directly stated that if + + + align:start position:0% +uh if it's not directly stated that if +that it's not directly stated that + + align:start position:0% +that it's not directly stated that + + + align:start position:0% +that it's not directly stated that +there's a set S + + align:start position:0% +there's a set S + + + align:start position:0% +there's a set S +uh and then it has to be a subset of + + align:start position:0% +uh and then it has to be a subset of + + + align:start position:0% +uh and then it has to be a subset of +that set, right? then it would be + + align:start position:0% +that set, right? then it would be + + + align:start position:0% +that set, right? then it would be +assumed that is a yeah a of course you + + align:start position:0% +assumed that is a yeah a of course you + + + align:start position:0% +assumed that is a yeah a of course you +welcome to to ask on pat is you know I + + align:start position:0% +welcome to to ask on pat is you know I + + + align:start position:0% +welcome to to ask on pat is you know I +don't have the homework here but but but + + align:start position:0% +don't have the homework here but but but + + + align:start position:0% +don't have the homework here but but but +I would say that you're safe if it's if + + align:start position:0% +I would say that you're safe if it's if + + + align:start position:0% +I would say that you're safe if it's if +it's not stated directly what the larger + + align:start position:0% +it's not stated directly what the larger + + + align:start position:0% +it's not stated directly what the larger +set is then you can assume it's are + + align:start position:0% +set is then you can assume it's are + + + align:start position:0% +set is then you can assume it's are +because we're going to concentrate + + align:start position:0% +because we're going to concentrate + + + align:start position:0% +because we're going to concentrate +mostly on our this is another + + align:start position:0% +mostly on our this is another + + + align:start position:0% +mostly on our this is another +distinction between Ruden and and this + + align:start position:0% +distinction between Ruden and and this + + + align:start position:0% +distinction between Ruden and and this +book that is the main textbook ruden is + + align:start position:0% +book that is the main textbook ruden is + + + align:start position:0% +book that is the main textbook ruden is +more abstract than the main textbook we + + align:start position:0% +more abstract than the main textbook we + + + align:start position:0% +more abstract than the main textbook we +are using + + align:start position:0% +are using + + + align:start position:0% +are using +in particular. Um you know the this the + + align:start position:0% +in particular. Um you know the this the + + + align:start position:0% +in particular. Um you know the this the +main textbook here and I'll do the same + + align:start position:0% +main textbook here and I'll do the same + + + align:start position:0% +main textbook here and I'll do the same +in my lectures is that a lot of things + + align:start position:0% +in my lectures is that a lot of things + + + align:start position:0% +in my lectures is that a lot of things +are motivated from R and then you + + align:start position:0% +are motivated from R and then you + + + align:start position:0% +are motivated from R and then you +abstract afterwards. So whereas ruden + + align:start position:0% +abstract afterwards. So whereas ruden + + + align:start position:0% +abstract afterwards. So whereas ruden +starts with abstraction and then it + + align:start position:0% +starts with abstraction and then it + + + align:start position:0% +starts with abstraction and then it +specializes to R and and of course + + align:start position:0% +specializes to R and and of course + + + align:start position:0% +specializes to R and and of course +there's you know there's an argument for + + align:start position:0% +there's you know there's an argument for + + + align:start position:0% +there's you know there's an argument for +maybe starting with a familiar and then + + align:start position:0% +maybe starting with a familiar and then + + + align:start position:0% +maybe starting with a familiar and then +abstract instead of doing the other way + + align:start position:0% +abstract instead of doing the other way + + + align:start position:0% +abstract instead of doing the other way +around. + + align:start position:0% +around. + + + align:start position:0% +around. +Okay so + + align:start position:0% + + + + align:start position:0% + +right and so for a whether it's just a + + align:start position:0% +right and so for a whether it's just a + + + align:start position:0% +right and so for a whether it's just a +order set I mean just in general so so + + align:start position:0% +order set I mean just in general so so + + + align:start position:0% +order set I mean just in general so so +remember that completeness + + align:start position:0% + + + + align:start position:0% + +So completeness. So this is when you + + align:start position:0% +So completeness. So this is when you + + + align:start position:0% +So completeness. So this is when you +have a order set. + + align:start position:0% +have a order set. + + + align:start position:0% +have a order set. +So if you have a order set and a here is + + align:start position:0% +So if you have a order set and a here is + + + align:start position:0% +So if you have a order set and a here is +a subset + + align:start position:0% + + + + align:start position:0% + +uh of s that is bounded from above + + align:start position:0% + + + + align:start position:0% + +from above. + + align:start position:0% + + + + align:start position:0% + +uh then if this if it is complete if S + + align:start position:0% +uh then if this if it is complete if S + + + align:start position:0% +uh then if this if it is complete if S +is complete. So if + + align:start position:0% +is complete. So if + + + align:start position:0% +is complete. So if +S is complete + + align:start position:0% + + + + align:start position:0% + +then any subset that is bounded from + + align:start position:0% +then any subset that is bounded from + + + align:start position:0% +then any subset that is bounded from +above + + align:start position:0% +above + + + align:start position:0% +above +uh has a has a least upper bound. Then + + align:start position:0% +uh has a has a least upper bound. Then + + + align:start position:0% +uh has a has a least upper bound. Then +uh then a has a list + + align:start position:0% + + + + align:start position:0% + +upper bound. + + align:start position:0% + + + + align:start position:0% + +Okay. And that least upper bounds is + + align:start position:0% +Okay. And that least upper bounds is + + + align:start position:0% +Okay. And that least upper bounds is +denoted by the soup + + align:start position:0% +denoted by the soup + + + align:start position:0% +denoted by the soup +of a. Right? So, so this thing here it + + align:start position:0% +of a. Right? So, so this thing here it + + + align:start position:0% +of a. Right? So, so this thing here it +has the property + + align:start position:0% +has the property + + + align:start position:0% +has the property +that uh that a is lesser equal to m for + + align:start position:0% +that uh that a is lesser equal to m for + + + align:start position:0% +that uh that a is lesser equal to m for +all + + align:start position:0% +all + + + align:start position:0% +all +uh a in a and also if + + align:start position:0% +uh a in a and also if + + + align:start position:0% +uh a in a and also if +m_1 is another upper bound + + align:start position:0% +m_1 is another upper bound + + + align:start position:0% +m_1 is another upper bound +upper bound + + align:start position:0% + + + + align:start position:0% + +for a + + align:start position:0% +for a + + + align:start position:0% +for a +then + + align:start position:0% +then + + + align:start position:0% +then +uh m is less or equal to m. + + align:start position:0% + + + + align:start position:0% + +So that's a least ups + + align:start position:0% +So that's a least ups + + + align:start position:0% +So that's a least ups +and the same thing is so similarly + + align:start position:0% +and the same thing is so similarly + + + align:start position:0% +and the same thing is so similarly +when we have a order set and we have a + + align:start position:0% +when we have a order set and we have a + + + align:start position:0% +when we have a order set and we have a +set if it's complete and if we have + + align:start position:0% +set if it's complete and if we have + + + align:start position:0% +set if it's complete and if we have +uh + + align:start position:0% + + + + align:start position:0% + +if uh a here + + align:start position:0% +if uh a here + + + align:start position:0% +if uh a here +is bound from below Boom. + + align:start position:0% + + + + align:start position:0% + +Then uh then + + align:start position:0% +Then uh then + + + align:start position:0% +Then uh then +uh infair + + align:start position:0% +uh infair + + + align:start position:0% +uh infair +of A is the least up is the + + align:start position:0% +of A is the least up is the + + + align:start position:0% +of A is the least up is the +the largest the greatest + + align:start position:0% + + + + align:start position:0% + +uh lower bound + + align:start position:0% + + + + align:start position:0% + +for A right. So this again means that + + align:start position:0% +for A right. So this again means that + + + align:start position:0% +for A right. So this again means that +this number here little M. So M here is + + align:start position:0% +this number here little M. So M here is + + + align:start position:0% +this number here little M. So M here is +lesser equal to A for all + + align:start position:0% +lesser equal to A for all + + + align:start position:0% +lesser equal to A for all +A in A. + + align:start position:0% +A in A. + + + align:start position:0% +A in A. +And if M1 here is another lower bound. + + align:start position:0% + + + + align:start position:0% + +then uh m1 here is less or equal to m. + + align:start position:0% +then uh m1 here is less or equal to m. + + + align:start position:0% +then uh m1 here is less or equal to m. +So this is the symmetric property. + + align:start position:0% +So this is the symmetric property. + + + align:start position:0% +So this is the symmetric property. +And so again r the reals uh is complete. + + align:start position:0% +And so again r the reals uh is complete. + + + align:start position:0% +And so again r the reals uh is complete. +So whenever you take a bounded subset of + + align:start position:0% +So whenever you take a bounded subset of + + + align:start position:0% +So whenever you take a bounded subset of +the real so if it's bounded that means + + align:start position:0% +the real so if it's bounded that means + + + align:start position:0% +the real so if it's bounded that means +that it's bounded from above and below + + align:start position:0% +that it's bounded from above and below + + + align:start position:0% +that it's bounded from above and below +then it has a least upper bound and a + + align:start position:0% +then it has a least upper bound and a + + + align:start position:0% +then it has a least upper bound and a +greatest lower bound. Okay. And those + + align:start position:0% +greatest lower bound. Okay. And those + + + align:start position:0% +greatest lower bound. Okay. And those +are are denoted by soup and if right and + + align:start position:0% +are are denoted by soup and if right and + + + align:start position:0% +are are denoted by soup and if right and +and in general soup and in are not in + + align:start position:0% +and in general soup and in are not in + + + align:start position:0% +and in general soup and in are not in +the set itself in the set a right + + align:start position:0% +the set itself in the set a right + + + align:start position:0% +the set itself in the set a right +I mean they could be but in general they + + align:start position:0% +I mean they could be but in general they + + + align:start position:0% +I mean they could be but in general they +wouldn't be. Yeah. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Yeah. + + align:start position:0% + + + + align:start position:0% + +>> That's as right. Uh so + + align:start position:0% +>> That's as right. Uh so + + + align:start position:0% +>> That's as right. Uh so +uh no so so if you're looking at this + + align:start position:0% +uh no so so if you're looking at this + + + align:start position:0% +uh no so so if you're looking at this +set here right + + align:start position:0% +set here right + + + align:start position:0% +set here right +so suppose that this here is is the set + + align:start position:0% +so suppose that this here is is the set + + + align:start position:0% +so suppose that this here is is the set +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +um + + align:start position:0% +um + + + align:start position:0% +um +uh s then and if you take a here is a + + align:start position:0% +uh s then and if you take a here is a + + + align:start position:0% +uh s then and if you take a here is a +subset of s and a here is bounded from + + align:start position:0% +subset of s and a here is bounded from + + + align:start position:0% +subset of s and a here is bounded from +let's say that a there is bounded from + + align:start position:0% +let's say that a there is bounded from + + + align:start position:0% +let's say that a there is bounded from +below, + + align:start position:0% + + + + align:start position:0% + +right? If it's bounded from below, + + align:start position:0% +right? If it's bounded from below, + + + align:start position:0% +right? If it's bounded from below, +you know, then it couldn't be this set + + align:start position:0% +you know, then it couldn't be this set + + + align:start position:0% +you know, then it couldn't be this set +here. + + align:start position:0% +here. + + + align:start position:0% +here. +This here is not bounded from below, + + align:start position:0% +This here is not bounded from below, + + + align:start position:0% +This here is not bounded from below, +right? So, it sort of means that if it's + + align:start position:0% +right? So, it sort of means that if it's + + + align:start position:0% +right? So, it sort of means that if it's +bounded from below, then a here could + + align:start position:0% +bounded from below, then a here could + + + align:start position:0% +bounded from below, then a here could +not have numbers that was approaching + + align:start position:0% +not have numbers that was approaching + + + align:start position:0% +not have numbers that was approaching +zero. + + align:start position:0% +zero. + + + align:start position:0% +zero. +Right? And so actually if it is bounded + + align:start position:0% +Right? And so actually if it is bounded + + + align:start position:0% +Right? And so actually if it is bounded +from below, + + align:start position:0% +from below, + + + align:start position:0% +from below, +if it's a subset of this and it's + + align:start position:0% +if it's a subset of this and it's + + + align:start position:0% +if it's a subset of this and it's +bounded from below, then actually it + + align:start position:0% +bounded from below, then actually it + + + align:start position:0% +bounded from below, then actually it +would have a least lower bound lower + + align:start position:0% +would have a least lower bound lower + + + align:start position:0% +would have a least lower bound lower +bound, right? You should mean + + align:start position:0% + + + + align:start position:0% + +so it is it is I mean I'm not going to + + align:start position:0% +so it is it is I mean I'm not going to + + + align:start position:0% +so it is it is I mean I'm not going to +prove anything is complete or not + + align:start position:0% +prove anything is complete or not + + + align:start position:0% +prove anything is complete or not +complete but but it's pretty convincing + + align:start position:0% +complete but but it's pretty convincing + + + align:start position:0% +complete but but it's pretty convincing +that it is actually complete. + + align:start position:0% + + + + align:start position:0% + +Um in this sense there's an other sense + + align:start position:0% +Um in this sense there's an other sense + + + align:start position:0% +Um in this sense there's an other sense +that is not complete but but anyway in + + align:start position:0% +that is not complete but but anyway in + + + align:start position:0% +that is not complete but but anyway in +this sense it is complete. Yeah. No it's + + align:start position:0% +this sense it is complete. Yeah. No it's + + + align:start position:0% +this sense it is complete. Yeah. No it's +it's it's a little bit uh it can be + + align:start position:0% +it's it's a little bit uh it can be + + + align:start position:0% +it's it's a little bit uh it can be +confusing. Later on we'll talk about + + align:start position:0% +confusing. Later on we'll talk about + + + align:start position:0% +confusing. Later on we'll talk about +maybe some other notion of completeness + + align:start position:0% +maybe some other notion of completeness + + + align:start position:0% +maybe some other notion of completeness +and then it's not complete but but this + + align:start position:0% +and then it's not complete but but this + + + align:start position:0% +and then it's not complete but but this +notion it is complete. + + align:start position:0% +notion it is complete. + + + align:start position:0% +notion it is complete. +Okay. So, so + + align:start position:0% +Okay. So, so + + + align:start position:0% +Okay. So, so +um the the the next thing I want to get + + align:start position:0% +um the the the next thing I want to get + + + align:start position:0% +um the the the next thing I want to get +to is this with how to write a + + align:start position:0% +to is this with how to write a + + + align:start position:0% +to is this with how to write a +mathematical proof. Okay. And so and and + + align:start position:0% +mathematical proof. Okay. And so and and + + + align:start position:0% +mathematical proof. Okay. And so and and +again + + align:start position:0% +again + + + align:start position:0% +again +I mean that's a super important thing to + + align:start position:0% +I mean that's a super important thing to + + + align:start position:0% +I mean that's a super important thing to +learn in this class. + + align:start position:0% +learn in this class. + + + align:start position:0% +learn in this class. +Uh and and it's not just a + + align:start position:0% +Uh and and it's not just a + + + align:start position:0% +Uh and and it's not just a +it's not just a + + align:start position:0% +it's not just a + + + align:start position:0% +it's not just a +a formal thing. + + align:start position:0% +a formal thing. + + + align:start position:0% +a formal thing. +Uh I mean, you know, it Yeah. I mean, it + + align:start position:0% +Uh I mean, you know, it Yeah. I mean, it + + + align:start position:0% +Uh I mean, you know, it Yeah. I mean, it +may seem like a formal thing, you know, + + align:start position:0% +may seem like a formal thing, you know, + + + align:start position:0% +may seem like a formal thing, you know, +why bother with that? Uh uh but it's + + align:start position:0% +why bother with that? Uh uh but it's + + + align:start position:0% +why bother with that? Uh uh but it's +really really useful and the more + + align:start position:0% +really really useful and the more + + + align:start position:0% +really really useful and the more +complicated things become, the more + + align:start position:0% +complicated things become, the more + + + align:start position:0% +complicated things become, the more +useful it is. + + align:start position:0% +useful it is. + + + align:start position:0% +useful it is. +And so um so I want to illustrate this + + align:start position:0% +And so um so I want to illustrate this + + + align:start position:0% +And so um so I want to illustrate this +with how to write a mathematical proof. + + align:start position:0% +with how to write a mathematical proof. + + + align:start position:0% +with how to write a mathematical proof. +So I going going to illustrate this. So, + + align:start position:0% +So I going going to illustrate this. So, + + + align:start position:0% +So I going going to illustrate this. So, +so we will illustrate it + + align:start position:0% + + + + align:start position:0% + +by by uh proving again by by by uh by + + align:start position:0% +by by uh proving again by by by uh by + + + align:start position:0% +by by uh proving again by by by uh by +writing a + + align:start position:0% + + + + align:start position:0% + +a formal proof + + align:start position:0% + + + + align:start position:0% + +of time + + align:start position:0% + + + + align:start position:0% + +square root of two + + align:start position:0% +square root of two + + + align:start position:0% +square root of two +is a real number. + + align:start position:0% +is a real number. + + + align:start position:0% +is a real number. +So I want to write a a I want to you + + align:start position:0% +So I want to write a a I want to you + + + align:start position:0% +So I want to write a a I want to you +know so last time we talked about that + + align:start position:0% +know so last time we talked about that + + + align:start position:0% +know so last time we talked about that +square root of two was a real number and + + align:start position:0% +square root of two was a real number and + + + align:start position:0% +square root of two was a real number and +but that what we when we proved it it + + align:start position:0% +but that what we when we proved it it + + + align:start position:0% +but that what we when we proved it it +was more like we talked about the idea + + align:start position:0% +was more like we talked about the idea + + + align:start position:0% +was more like we talked about the idea +and so and so then the question is so if + + align:start position:0% +and so and so then the question is so if + + + align:start position:0% +and so and so then the question is so if +you have like you imagine you have a + + align:start position:0% +you have like you imagine you have a + + + align:start position:0% +you have like you imagine you have a +piece of scrap paper what we did last + + align:start position:0% +piece of scrap paper what we did last + + + align:start position:0% +piece of scrap paper what we did last +time was what you would be writing on + + align:start position:0% +time was what you would be writing on + + + align:start position:0% +time was what you would be writing on +the scrap paper. So I want to talk about + + align:start position:0% +the scrap paper. So I want to talk about + + + align:start position:0% +the scrap paper. So I want to talk about +you know if you were handing it in or + + align:start position:0% +you know if you were handing it in or + + + align:start position:0% +you know if you were handing it in or +showing it to something somebody then + + align:start position:0% +showing it to something somebody then + + + align:start position:0% +showing it to something somebody then +you wouldn't do that + + align:start position:0% +you wouldn't do that + + + align:start position:0% +you wouldn't do that +uh you would do what we do now and but + + align:start position:0% +uh you would do what we do now and but + + + align:start position:0% +uh you would do what we do now and but +it doesn't necessarily make for a great + + align:start position:0% +it doesn't necessarily make for a great + + + align:start position:0% +it doesn't necessarily make for a great +a formal proof doesn't necessarily make + + align:start position:0% +a formal proof doesn't necessarily make + + + align:start position:0% +a formal proof doesn't necessarily make +for a great lecture because it's kind of + + align:start position:0% +for a great lecture because it's kind of + + + align:start position:0% +for a great lecture because it's kind of +formal. + + align:start position:0% +formal. + + + align:start position:0% +formal. +So, so, so let me try to explain how you + + align:start position:0% +So, so, so let me try to explain how you + + + align:start position:0% +So, so, so let me try to explain how you +should should write this. And again, + + align:start position:0% +should should write this. And again, + + + align:start position:0% +should should write this. And again, +this is a very simple example. + + align:start position:0% +this is a very simple example. + + + align:start position:0% +this is a very simple example. +Um, but hopefully it will give you an + + align:start position:0% +Um, but hopefully it will give you an + + + align:start position:0% +Um, but hopefully it will give you an +idea of what to do. And again, this is a + + align:start position:0% +idea of what to do. And again, this is a + + + align:start position:0% +idea of what to do. And again, this is a +really important part of this class that + + align:start position:0% +really important part of this class that + + + align:start position:0% +really important part of this class that +you know you you're bound to use in many + + align:start position:0% +you know you you're bound to use in many + + + align:start position:0% +you know you you're bound to use in many +other classes later on. + + align:start position:0% +other classes later on. + + + align:start position:0% +other classes later on. +Okay. So let's first talk about what was + + align:start position:0% +Okay. So let's first talk about what was + + + align:start position:0% +Okay. So let's first talk about what was +square root of two. So square root of + + align:start position:0% +square root of two. So square root of + + + align:start position:0% +square root of two. So square root of +two this here was a number and it was + + align:start position:0% +two this here was a number and it was + + + align:start position:0% +two this here was a number and it was +given by that it has a property that + + align:start position:0% +given by that it has a property that + + + align:start position:0% +given by that it has a property that +it's positive and when you square it + + align:start position:0% +it's positive and when you square it + + + align:start position:0% +it's positive and when you square it +then you get two right that was what + + align:start position:0% +then you get two right that was what + + + align:start position:0% +then you get two right that was what +square root of two was. + + align:start position:0% + + + + align:start position:0% + +Now + + align:start position:0% +Now + + + align:start position:0% +Now +um + + align:start position:0% +um + + + align:start position:0% +um +so we again so we want to prove so this + + align:start position:0% +so we again so we want to prove so this + + + align:start position:0% +so we again so we want to prove so this +is the theorem. So theorem + + align:start position:0% + + + + align:start position:0% + +square root of two is a real number. + + align:start position:0% +square root of two is a real number. + + + align:start position:0% +square root of two is a real number. +So I know maybe I should write it more + + align:start position:0% +So I know maybe I should write it more + + + align:start position:0% +So I know maybe I should write it more +formally. there exist + + align:start position:0% + + + + align:start position:0% + +alpha greater than zero. Uh + + align:start position:0% +alpha greater than zero. Uh + + + align:start position:0% +alpha greater than zero. Uh +there's alpha in r with + + align:start position:0% +there's alpha in r with + + + align:start position:0% +there's alpha in r with +alpha greater than zero and alpha + + align:start position:0% +alpha greater than zero and alpha + + + align:start position:0% +alpha greater than zero and alpha +squared is equal to two. Okay. + + align:start position:0% + + + + align:start position:0% + +Now we look at the set + + align:start position:0% +Now we look at the set + + + align:start position:0% +Now we look at the set +uh A. + + align:start position:0% + + + + align:start position:0% + +The set A is the numbers uh the it's the + + align:start position:0% +The set A is the numbers uh the it's the + + + align:start position:0% +The set A is the numbers uh the it's the +uh X + + align:start position:0% +uh X + + + align:start position:0% +uh X +such that X is positive + + align:start position:0% + + + + align:start position:0% + +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +uh X² + + align:start position:0% +uh X² + + + align:start position:0% +uh X² +is lesser equal to two. + + align:start position:0% + + + + align:start position:0% + +Yeah. So x here and so now I was + + align:start position:0% +Yeah. So x here and so now I was + + + align:start position:0% +Yeah. So x here and so now I was +specialized to the real numbers. So that + + align:start position:0% +specialized to the real numbers. So that + + + align:start position:0% +specialized to the real numbers. So that +was why I didn't actually write it but + + align:start position:0% +was why I didn't actually write it but + + + align:start position:0% +was why I didn't actually write it but +but you're right. Certainly can't hurt. + + align:start position:0% +but you're right. Certainly can't hurt. + + + align:start position:0% +but you're right. Certainly can't hurt. +Uh okay. So that's the theorem and so + + align:start position:0% +Uh okay. So that's the theorem and so + + + align:start position:0% +Uh okay. So that's the theorem and so +now we try to write a formal proof. + + align:start position:0% + + + + align:start position:0% + +Uh observe first + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +um a here is non empty + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% +since + + + align:start position:0% +since +one is in a right one is positive and + + align:start position:0% +one is in a right one is positive and + + + align:start position:0% +one is in a right one is positive and +when you square one you get one so this + + align:start position:0% +when you square one you get one so this + + + align:start position:0% +when you square one you get one so this +is definitely less or equal to two so a + + align:start position:0% +is definitely less or equal to two so a + + + align:start position:0% +is definitely less or equal to two so a +here is non + + align:start position:0% +here is non + + + align:start position:0% +here is non +Um uh next observe + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +uh a here + + align:start position:0% +uh a here + + + align:start position:0% +uh a here +is bounded is bounded from above. + + align:start position:0% + + + + align:start position:0% + +In general, by the way, when you write a + + align:start position:0% +In general, by the way, when you write a + + + align:start position:0% +In general, by the way, when you write a +proof, then you then you really only try + + align:start position:0% +proof, then you then you really only try + + + align:start position:0% +proof, then you then you really only try +to establish the properties that you + + align:start position:0% +to establish the properties that you + + + align:start position:0% +to establish the properties that you +need because otherwise it's confusing. + + align:start position:0% +need because otherwise it's confusing. + + + align:start position:0% +need because otherwise it's confusing. +If you establish all kind of other + + align:start position:0% +If you establish all kind of other + + + align:start position:0% +If you establish all kind of other +property that is not needed, that just + + align:start position:0% +property that is not needed, that just + + + align:start position:0% +property that is not needed, that just +makes it confusing. So it's bounded from + + align:start position:0% +makes it confusing. So it's bounded from + + + align:start position:0% +makes it confusing. So it's bounded from +above + + align:start position:0% + + + + align:start position:0% + +and this is just because + + align:start position:0% +and this is just because + + + align:start position:0% +and this is just because +um since + + align:start position:0% + + + + align:start position:0% + +since uh two is an upper bound + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% +for + + + align:start position:0% +for +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now the next thing here. So now we have + + align:start position:0% +now the next thing here. So now we have + + + align:start position:0% +now the next thing here. So now we have +a non- empty bounded subset. So we set + + align:start position:0% +a non- empty bounded subset. So we set + + + align:start position:0% +a non- empty bounded subset. So we set +so set alpha equal to the soup of a + + align:start position:0% +so set alpha equal to the soup of a + + + align:start position:0% +so set alpha equal to the soup of a +and we we want to prove want to show + + align:start position:0% + + + + align:start position:0% + +that alpha is positive and alpha squ is + + align:start position:0% +that alpha is positive and alpha squ is + + + align:start position:0% +that alpha is positive and alpha squ is +equal to 2. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Well, + + align:start position:0% +Well, + + + align:start position:0% +Well, +[Applause] + + align:start position:0% + + + + align:start position:0% + +right by definition the way we defined + + align:start position:0% +right by definition the way we defined + + + align:start position:0% +right by definition the way we defined +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the way we defined a all the elements in + + align:start position:0% +the way we defined a all the elements in + + + align:start position:0% +the way we defined a all the elements in +a were positive. So by definition + + align:start position:0% + + + + align:start position:0% + +uh uh uh zero is a lower bound. + + align:start position:0% + + + + align:start position:0% + +So so you for sure have that zero here + + align:start position:0% +So so you for sure have that zero here + + + align:start position:0% +So so you for sure have that zero here +is less or equal to well it's actually I + + align:start position:0% +is less or equal to well it's actually I + + + align:start position:0% +is less or equal to well it's actually I +mean even one is a lower bound. So, so + + align:start position:0% +mean even one is a lower bound. So, so + + + align:start position:0% +mean even one is a lower bound. So, so +uh we can also just say that one since + + align:start position:0% +uh we can also just say that one since + + + align:start position:0% +uh we can also just say that one since +one is a lower bound since since one + + align:start position:0% +one is a lower bound since since one + + + align:start position:0% +one is a lower bound since since one +here is in a you also have that this + + align:start position:0% +here is in a you also have that this + + + align:start position:0% +here is in a you also have that this +alpha here must be bigger equal to one + + align:start position:0% +alpha here must be bigger equal to one + + + align:start position:0% +alpha here must be bigger equal to one +because it was supposed to be an upper + + align:start position:0% +because it was supposed to be an upper + + + align:start position:0% +because it was supposed to be an upper +bound for a. So in particular + + align:start position:0% +bound for a. So in particular + + + align:start position:0% +bound for a. So in particular +now um + + align:start position:0% +now um + + + align:start position:0% +now um +and so we have that alpha is less than + + align:start position:0% +and so we have that alpha is less than + + + align:start position:0% +and so we have that alpha is less than +one and it's the least upper bound and + + align:start position:0% +one and it's the least upper bound and + + + align:start position:0% +one and it's the least upper bound and +two was an upper bound. So you are to + + align:start position:0% +two was an upper bound. So you are to + + + align:start position:0% +two was an upper bound. So you are to +have this + + align:start position:0% +have this + + + align:start position:0% +have this +since uh maybe I should write if you + + align:start position:0% +since uh maybe I should write if you + + + align:start position:0% +since uh maybe I should write if you +write write it with this uh since since + + align:start position:0% +write write it with this uh since since + + + align:start position:0% +write write it with this uh since since +one is an a we have + + align:start position:0% + + + + align:start position:0% + +that one here lesser equal to alpha. + + align:start position:0% +that one here lesser equal to alpha. + + + align:start position:0% +that one here lesser equal to alpha. +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +and + + align:start position:0% +and + + + align:start position:0% +and +since + + align:start position:0% +since + + + align:start position:0% +since +alpha is the least of a bound + + align:start position:0% + + + + align:start position:0% + +and true is an upper bound. + + align:start position:0% + + + + align:start position:0% + +We have + + align:start position:0% + + + + align:start position:0% + +that alpha is less than equal to two. + + align:start position:0% +that alpha is less than equal to two. + + + align:start position:0% +that alpha is less than equal to two. +Okay. Now remember I mean we're going to + + align:start position:0% +Okay. Now remember I mean we're going to + + + align:start position:0% +Okay. Now remember I mean we're going to +do it exactly like we did last time but + + align:start position:0% +do it exactly like we did last time but + + + align:start position:0% +do it exactly like we did last time but +we're just going to write it down uh in + + align:start position:0% +we're just going to write it down uh in + + + align:start position:0% +we're just going to write it down uh in +a proper way as a proof. Right? So + + align:start position:0% +a proper way as a proof. Right? So + + + align:start position:0% +a proper way as a proof. Right? So +remember that last time we then divided + + align:start position:0% +remember that last time we then divided + + + align:start position:0% +remember that last time we then divided +the proof into two steps. + + align:start position:0% +the proof into two steps. + + + align:start position:0% +the proof into two steps. +Uh the first step was uh so part one. + + align:start position:0% +Uh the first step was uh so part one. + + + align:start position:0% +Uh the first step was uh so part one. +So, so, so now, so all we need to prove, + + align:start position:0% +So, so, so now, so all we need to prove, + + + align:start position:0% +So, so, so now, so all we need to prove, +maybe I'll just say that all we need to + + align:start position:0% +maybe I'll just say that all we need to + + + align:start position:0% +maybe I'll just say that all we need to +prove + + align:start position:0% + + + + align:start position:0% + +to show + + align:start position:0% +to show + + + align:start position:0% +to show +is that alpha square is equal to two, + + align:start position:0% +is that alpha square is equal to two, + + + align:start position:0% +is that alpha square is equal to two, +right? Because we already have it as + + align:start position:0% +right? Because we already have it as + + + align:start position:0% +right? Because we already have it as +positive now because it's bigger than + + align:start position:0% +positive now because it's bigger than + + + align:start position:0% +positive now because it's bigger than +one, right? + + align:start position:0% +one, right? + + + align:start position:0% +one, right? +And so there was two parts to this to + + align:start position:0% +And so there was two parts to this to + + + align:start position:0% +And so there was two parts to this to +step one and step two or step part one + + align:start position:0% +step one and step two or step part one + + + align:start position:0% +step one and step two or step part one +and part two. + + align:start position:0% +and part two. + + + align:start position:0% +and part two. +The first part was so part one we will + + align:start position:0% +The first part was so part one we will + + + align:start position:0% +The first part was so part one we will +show + + align:start position:0% + + + + align:start position:0% + +that uh alpha squared + + align:start position:0% +that uh alpha squared + + + align:start position:0% +that uh alpha squared +is less or equal to + + align:start position:0% +is less or equal to + + + align:start position:0% +is less or equal to +uh two + + align:start position:0% + + + + align:start position:0% + +and so we prove this. So + + align:start position:0% + + + + align:start position:0% + +assume not + + align:start position:0% + + + + align:start position:0% + +uh we will show that that leads + + align:start position:0% + + + + align:start position:0% + +that. Um + + align:start position:0% +that. Um + + + align:start position:0% +that. Um +this + + align:start position:0% +this + + + align:start position:0% +this +leads to + + align:start position:0% + + + + align:start position:0% + +a contradiction + + align:start position:0% + + + + align:start position:0% + +to that alpha is the least upper bound + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% +for + + + align:start position:0% +for +I mean I'm writing everything out here + + align:start position:0% +I mean I'm writing everything out here + + + align:start position:0% +I mean I'm writing everything out here +right just to illustrate is right as you + + align:start position:0% +right just to illustrate is right as you + + + align:start position:0% +right just to illustrate is right as you +get more and more familiar with this + + align:start position:0% +get more and more familiar with this + + + align:start position:0% +get more and more familiar with this +right then the structure is the same but + + align:start position:0% +right then the structure is the same but + + + align:start position:0% +right then the structure is the same but +you know some of these steps will seem + + align:start position:0% +you know some of these steps will seem + + + align:start position:0% +you know some of these steps will seem +almost too trivial and that's probably + + align:start position:0% +almost too trivial and that's probably + + + align:start position:0% +almost too trivial and that's probably +fine right but of course it's always + + align:start position:0% +fine right but of course it's always + + + align:start position:0% +fine right but of course it's always +good to air on more details than fewer + + align:start position:0% +good to air on more details than fewer + + + align:start position:0% +good to air on more details than fewer +details + + align:start position:0% + + + + align:start position:0% + +okay so so this is what we want to do so + + align:start position:0% +okay so so this is what we want to do so + + + align:start position:0% +okay so so this is what we want to do so +so we assume not so assume + + align:start position:0% +so we assume not so assume + + + align:start position:0% +so we assume not so assume +so assume + + align:start position:0% + + + + align:start position:0% + +that alpha squared is strictly bigger + + align:start position:0% +that alpha squared is strictly bigger + + + align:start position:0% +that alpha squared is strictly bigger +than two. Right? + + align:start position:0% +than two. Right? + + + align:start position:0% +than two. Right? +Then and this is where it sort of + + align:start position:0% +Then and this is where it sort of + + + align:start position:0% +Then and this is where it sort of +deviate more from how we did it last + + align:start position:0% +deviate more from how we did it last + + + align:start position:0% +deviate more from how we did it last +time + + align:start position:0% +time + + + align:start position:0% +time +and that's why you know what we did last + + align:start position:0% +and that's why you know what we did last + + + align:start position:0% +and that's why you know what we did last +time is really what you want to have on + + align:start position:0% +time is really what you want to have on + + + align:start position:0% +time is really what you want to have on +on the scrap paper. I mean that's what + + align:start position:0% +on the scrap paper. I mean that's what + + + align:start position:0% +on the scrap paper. I mean that's what +we did last time was like the idea and + + align:start position:0% +we did last time was like the idea and + + + align:start position:0% +we did last time was like the idea and +then once you see the idea then you try + + align:start position:0% +then once you see the idea then you try + + + align:start position:0% +then once you see the idea then you try +to write it as a formal proof like what + + align:start position:0% +to write it as a formal proof like what + + + align:start position:0% +to write it as a formal proof like what +we do now + + align:start position:0% +we do now + + + align:start position:0% +we do now +and so so so assume not + + align:start position:0% +and so so so assume not + + + align:start position:0% +and so so so assume not +set + + align:start position:0% +set + + + align:start position:0% +set +h equal to so I'm going to set h equ= to + + align:start position:0% +h equal to so I'm going to set h equ= to + + + align:start position:0% +h equal to so I'm going to set h equ= to +alpha^ 2 - 2 over 4 alpha. + + align:start position:0% +alpha^ 2 - 2 over 4 alpha. + + + align:start position:0% +alpha^ 2 - 2 over 4 alpha. +Okay. Right. Obviously, if this was like + + align:start position:0% +Okay. Right. Obviously, if this was like + + + align:start position:0% +Okay. Right. Obviously, if this was like +the first time you would do it, you + + align:start position:0% +the first time you would do it, you + + + align:start position:0% +the first time you would do it, you +wouldn't just come up with this sort of + + align:start position:0% +wouldn't just come up with this sort of + + + align:start position:0% +wouldn't just come up with this sort of +thing, right? I mean, this is coming + + align:start position:0% +thing, right? I mean, this is coming + + + align:start position:0% +thing, right? I mean, this is coming +from the scrap paper that you have, + + align:start position:0% +from the scrap paper that you have, + + + align:start position:0% +from the scrap paper that you have, +right? You're setting h equal to that. + + align:start position:0% +right? You're setting h equal to that. + + + align:start position:0% +right? You're setting h equal to that. +And then you observe + + align:start position:0% + + + + align:start position:0% + +you observe that since since uh + + align:start position:0% +you observe that since since uh + + + align:start position:0% +you observe that since since uh +since alpha here is bigger than one and + + align:start position:0% +since alpha here is bigger than one and + + + align:start position:0% +since alpha here is bigger than one and +uh alpha squared is bigger than two. + + align:start position:0% +uh alpha squared is bigger than two. + + + align:start position:0% +uh alpha squared is bigger than two. +Since that right then the nominator here + + align:start position:0% +Since that right then the nominator here + + + align:start position:0% +Since that right then the nominator here +is positive and the denominator is + + align:start position:0% +is positive and the denominator is + + + align:start position:0% +is positive and the denominator is +positive. So h here is positive right? + + align:start position:0% + + + + align:start position:0% + +You also have that you also have that h + + align:start position:0% +You also have that you also have that h + + + align:start position:0% +You also have that you also have that h +is um + + align:start position:0% +is um + + + align:start position:0% +is um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh right you also have automatically + + align:start position:0% +uh right you also have automatically + + + align:start position:0% +uh right you also have automatically +that uh that h is maybe we don't need + + align:start position:0% +that uh that h is maybe we don't need + + + align:start position:0% +that uh that h is maybe we don't need +that. Let's see if we need that. + + align:start position:0% +that. Let's see if we need that. + + + align:start position:0% +that. Let's see if we need that. +Uh okay. So now uh you def set + + align:start position:0% +Uh okay. So now uh you def set + + + align:start position:0% +Uh okay. So now uh you def set +uh alpha 1 equal to uh alpha + + align:start position:0% +uh alpha 1 equal to uh alpha + + + align:start position:0% +uh alpha 1 equal to uh alpha +minus h. + + align:start position:0% +minus h. + + + align:start position:0% +minus h. +And what I want to prove is so we want + + align:start position:0% +And what I want to prove is so we want + + + align:start position:0% +And what I want to prove is so we want +to show + + align:start position:0% + + + + align:start position:0% + +that uh alpha here alpha 1 is an upper + + align:start position:0% +that uh alpha here alpha 1 is an upper + + + align:start position:0% +that uh alpha here alpha 1 is an upper +bound + + align:start position:0% + + + + align:start position:0% + +for a. + + align:start position:0% +for a. + + + align:start position:0% +for a. +So I want to prove that this is an upper + + align:start position:0% +So I want to prove that this is an upper + + + align:start position:0% +So I want to prove that this is an upper +bound for a the first thing I want to do + + align:start position:0% +bound for a the first thing I want to do + + + align:start position:0% +bound for a the first thing I want to do +if it's an upper bounds it does need to + + align:start position:0% +if it's an upper bounds it does need to + + + align:start position:0% +if it's an upper bounds it does need to +be need to be positive. So let's check + + align:start position:0% +be need to be positive. So let's check + + + align:start position:0% +be need to be positive. So let's check +that. + + align:start position:0% +that. + + + align:start position:0% +that. +So um so since + + align:start position:0% +So um so since + + + align:start position:0% +So um so since +uh since + + align:start position:0% +uh since + + + align:start position:0% +uh since +so since + + align:start position:0% +so since + + + align:start position:0% +so since +we already have that h was positive so + + align:start position:0% +we already have that h was positive so + + + align:start position:0% +we already have that h was positive so +this here was h was positive alpha^ 2 - + + align:start position:0% +this here was h was positive alpha^ 2 - + + + align:start position:0% +this here was h was positive alpha^ 2 - + + align:start position:0% + + + align:start position:0% +over 4 alpha. + + align:start position:0% +over 4 alpha. + + + align:start position:0% +over 4 alpha. +Right? This thing here is less or equal + + align:start position:0% +Right? This thing here is less or equal + + + align:start position:0% +Right? This thing here is less or equal +to I can even forget about the two. So I + + align:start position:0% +to I can even forget about the two. So I + + + align:start position:0% +to I can even forget about the two. So I +can write it as alpha squar over 4 + + align:start position:0% +can write it as alpha squar over 4 + + + align:start position:0% +can write it as alpha squar over 4 +alpha. And so this here is I can just + + align:start position:0% +alpha. And so this here is I can just + + + align:start position:0% +alpha. And so this here is I can just +divide by alpha. So I get alpha over 4. + + align:start position:0% +divide by alpha. So I get alpha over 4. + + + align:start position:0% +divide by alpha. So I get alpha over 4. +So I have since we have that h here is + + align:start position:0% +So I have since we have that h here is + + + align:start position:0% +So I have since we have that h here is +less than alpha over 4 then + + align:start position:0% +less than alpha over 4 then + + + align:start position:0% +less than alpha over 4 then +uh alpha 1 + + align:start position:0% +uh alpha 1 + + + align:start position:0% +uh alpha 1 +is uh is bigger than + + align:start position:0% +is uh is bigger than + + + align:start position:0% +is uh is bigger than +uh is bigger equal to 3/4 + + align:start position:0% +uh is bigger equal to 3/4 + + + align:start position:0% +uh is bigger equal to 3/4 +of uh of alpha right + + align:start position:0% +of uh of alpha right + + + align:start position:0% +of uh of alpha right +because I'm subtracting at most alpha + + align:start position:0% +because I'm subtracting at most alpha + + + align:start position:0% +because I'm subtracting at most alpha +over 4 and so there's still 3/4 of alpha + + align:start position:0% +over 4 and so there's still 3/4 of alpha + + + align:start position:0% +over 4 and so there's still 3/4 of alpha +left right so I have This in particular, + + align:start position:0% +left right so I have This in particular, + + + align:start position:0% +left right so I have This in particular, +this thing here, it's actually bigger + + align:start position:0% +this thing here, it's actually bigger + + + align:start position:0% +this thing here, it's actually bigger +than 3 over 4, but I just need it to be + + align:start position:0% +than 3 over 4, but I just need it to be + + + align:start position:0% +than 3 over 4, but I just need it to be +positive. + + align:start position:0% + + + + align:start position:0% + +So, it's positive. So, + + align:start position:0% +So, it's positive. So, + + + align:start position:0% +So, it's positive. So, +so alpha over alpha 1 is positive. + + align:start position:0% + + + + align:start position:0% + +Now, I'm looking at alpha 1 squared, + + align:start position:0% +Now, I'm looking at alpha 1 squared, + + + align:start position:0% +Now, I'm looking at alpha 1 squared, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +And so alpha 1^ 2 is uh is equal to + + align:start position:0% +And so alpha 1^ 2 is uh is equal to + + + align:start position:0% +And so alpha 1^ 2 is uh is equal to +alpha minus h + + align:start position:0% +alpha minus h + + + align:start position:0% +alpha minus h +squared. + + align:start position:0% + + + + align:start position:0% + +So this here is equal to alpha^ 2 + h^ 2 + + align:start position:0% +So this here is equal to alpha^ 2 + h^ 2 + + + align:start position:0% +So this here is equal to alpha^ 2 + h^ 2 +- 2 alpha h. + + align:start position:0% +- 2 alpha h. + + + align:start position:0% +- 2 alpha h. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And this thing here is less or equal to + + align:start position:0% +And this thing here is less or equal to + + + align:start position:0% +And this thing here is less or equal to +uh alpha squared. + + align:start position:0% +uh alpha squared. + + + align:start position:0% +uh alpha squared. +Uh here h here is uh h is uh so now I + + align:start position:0% +Uh here h here is uh h is uh so now I + + + align:start position:0% +Uh here h here is uh h is uh so now I +like to say that h is lesser equal to + + align:start position:0% +like to say that h is lesser equal to + + + align:start position:0% +like to say that h is lesser equal to +one. + + align:start position:0% +one. + + + align:start position:0% +one. +Uh actually I'm going to use that it's + + align:start position:0% +Uh actually I'm going to use that it's + + + align:start position:0% +Uh actually I'm going to use that it's +less than a half. And why is that the + + align:start position:0% +less than a half. And why is that the + + + align:start position:0% +less than a half. And why is that the +case? It's actually + + align:start position:0% +case? It's actually + + + align:start position:0% +case? It's actually +uh alpha itself. We already know that + + align:start position:0% +uh alpha itself. We already know that + + + align:start position:0% +uh alpha itself. We already know that +alpha was less than two. So you have + + align:start position:0% +alpha was less than two. So you have + + + align:start position:0% +alpha was less than two. So you have +that this thing here is less or equal to + + align:start position:0% +that this thing here is less or equal to + + + align:start position:0% +that this thing here is less or equal to +2 over 4. So this is equal to a half. + + align:start position:0% +2 over 4. So this is equal to a half. + + + align:start position:0% +2 over 4. So this is equal to a half. +Right? + + align:start position:0% + + + + align:start position:0% + +Um so now uh now I have that + + align:start position:0% +Um so now uh now I have that + + + align:start position:0% +Um so now uh now I have that +um now I have that this thing here is + + align:start position:0% +um now I have that this thing here is + + + align:start position:0% +um now I have that this thing here is +less than + + align:start position:0% +less than + + + align:start position:0% +less than +um then plus + + align:start position:0% +um then plus + + + align:start position:0% +um then plus +um here I can here I I just use that + + align:start position:0% +um here I can here I I just use that + + + align:start position:0% +um here I can here I I just use that +it's less than + + align:start position:0% +it's less than + + + align:start position:0% +it's less than +uh this thing here by this here I just I + + align:start position:0% +uh this thing here by this here I just I + + + align:start position:0% +uh this thing here by this here I just I +think it's fine to just use uh h here I + + align:start position:0% +think it's fine to just use uh h here I + + + align:start position:0% +think it's fine to just use uh h here I +could use h over two. Maybe I'll use h + + align:start position:0% +could use h over two. Maybe I'll use h + + + align:start position:0% +could use h over two. Maybe I'll use h +over two. So one of the h I just replace + + align:start position:0% +over two. So one of the h I just replace + + + align:start position:0% +over two. So one of the h I just replace +by a half that is an upper bound and the + + align:start position:0% +by a half that is an upper bound and the + + + align:start position:0% +by a half that is an upper bound and the +other one uh I just keep right. + + align:start position:0% +other one uh I just keep right. + + + align:start position:0% +other one uh I just keep right. +So I have that and then minus 2 alpha h. + + align:start position:0% +So I have that and then minus 2 alpha h. + + + align:start position:0% +So I have that and then minus 2 alpha h. +But if you multiply alpha + + align:start position:0% +But if you multiply alpha + + + align:start position:0% +But if you multiply alpha +by h then it's disappear in the + + align:start position:0% +by h then it's disappear in the + + + align:start position:0% +by h then it's disappear in the +denominator. So you're getting minus 2 + + align:start position:0% +denominator. So you're getting minus 2 + + + align:start position:0% +denominator. So you're getting minus 2 +and then you're getting uh alpha squared + + align:start position:0% +and then you're getting uh alpha squared + + + align:start position:0% +and then you're getting uh alpha squared +- 2 over uh 4 + + align:start position:0% + + + + align:start position:0% + +right and so here you get this here + + align:start position:0% +right and so here you get this here + + + align:start position:0% +right and so here you get this here +becomes uh alpha squared + + align:start position:0% +becomes uh alpha squared + + + align:start position:0% +becomes uh alpha squared +uh plus and here I'm just writing in and + + align:start position:0% +uh plus and here I'm just writing in and + + + align:start position:0% +uh plus and here I'm just writing in and +I think it's at the moment we're sort of + + align:start position:0% +I think it's at the moment we're sort of + + + align:start position:0% +I think it's at the moment we're sort of +overkilling it here. Um, and so I can + + align:start position:0% +overkilling it here. Um, and so I can + + + align:start position:0% +overkilling it here. Um, and so I can +replace this one here. So, uh, right, + + align:start position:0% +replace this one here. So, uh, right, + + + align:start position:0% +replace this one here. So, uh, right, +let me just write it in. Alpha 2 - 2 + + align:start position:0% +let me just write it in. Alpha 2 - 2 + + + align:start position:0% +let me just write it in. Alpha 2 - 2 +over, uh, 2 * 4 * alpha, right? + + align:start position:0% +over, uh, 2 * 4 * alpha, right? + + + align:start position:0% +over, uh, 2 * 4 * alpha, right? +And this thing here is alpha 2 - 2 / 2. + + align:start position:0% +And this thing here is alpha 2 - 2 / 2. + + + align:start position:0% +And this thing here is alpha 2 - 2 / 2. +This two cancel with one of those two. + + align:start position:0% +This two cancel with one of those two. + + + align:start position:0% +This two cancel with one of those two. +So, this is what I have. + + align:start position:0% + + + + align:start position:0% + +Uh and so now I get + + align:start position:0% +Uh and so now I get + + + align:start position:0% +Uh and so now I get +that uh this thing here + + align:start position:0% +that uh this thing here + + + align:start position:0% +that uh this thing here +is so + + align:start position:0% +is so + + + align:start position:0% +is so +so I get that this thing here is uh um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +we adding it here. So this thing here is + + align:start position:0% +we adding it here. So this thing here is + + + align:start position:0% +we adding it here. So this thing here is +uh alpha squared. So, let's just let me + + align:start position:0% +uh alpha squared. So, let's just let me + + + align:start position:0% +uh alpha squared. So, let's just let me +just bring these two together. Let me u + + align:start position:0% +just bring these two together. Let me u + + + align:start position:0% +just bring these two together. Let me u +let me just maybe I'll just uh combine + + align:start position:0% +let me just maybe I'll just uh combine + + + align:start position:0% +let me just maybe I'll just uh combine +all of these. I don't think I need it + + align:start position:0% +all of these. I don't think I need it + + + align:start position:0% +all of these. I don't think I need it +this well. + + align:start position:0% +this well. + + + align:start position:0% +this well. +Um + + align:start position:0% + + + + align:start position:0% + +um right. So, if I if I combine these + + align:start position:0% +um right. So, if I if I combine these + + + align:start position:0% +um right. So, if I if I combine these +two here, I think I'm fine with just + + align:start position:0% +two here, I think I'm fine with just + + + align:start position:0% +two here, I think I'm fine with just +having a a two here. H four, sorry, + + align:start position:0% +having a a two here. H four, sorry, + + + align:start position:0% +having a a two here. H four, sorry, +instead of the two. So if I if I do that + + align:start position:0% +instead of the two. So if I if I do that + + + align:start position:0% +instead of the two. So if I if I do that +then I get alpha squared + + align:start position:0% +then I get alpha squared + + + align:start position:0% +then I get alpha squared +maybe I should just bring it on the + + align:start position:0% +maybe I should just bring it on the + + + align:start position:0% +maybe I should just bring it on the +common denominator. So this here this + + align:start position:0% +common denominator. So this here this + + + align:start position:0% +common denominator. So this here this +alpha sorry I'm get rid of I'm just I'm + + align:start position:0% +alpha sorry I'm get rid of I'm just I'm + + + align:start position:0% +alpha sorry I'm get rid of I'm just I'm +replacing I'm bounding this from above + + align:start position:0% +replacing I'm bounding this from above + + + align:start position:0% +replacing I'm bounding this from above +by alpha squar plus + + align:start position:0% +by alpha squar plus + + + align:start position:0% +by alpha squar plus +and I'm going to I'm going to just make + + align:start position:0% +and I'm going to I'm going to just make + + + align:start position:0% +and I'm going to I'm going to just make +it easy for myself. So I think it's fine + + align:start position:0% +it easy for myself. So I think it's fine + + + align:start position:0% +it easy for myself. So I think it's fine +to just uh use that alpha is bounded by + + align:start position:0% +to just uh use that alpha is bounded by + + + align:start position:0% +to just uh use that alpha is bounded by +one and then you can just bound it by + + align:start position:0% +one and then you can just bound it by + + + align:start position:0% +one and then you can just bound it by +alpha squared minus 2 uh over 4 + + align:start position:0% +alpha squared minus 2 uh over 4 + + + align:start position:0% +alpha squared minus 2 uh over 4 +uh and uh and this in here is uh is + + align:start position:0% +uh and uh and this in here is uh is + + + align:start position:0% +uh and uh and this in here is uh is +alpha squared + + align:start position:0% +alpha squared + + + align:start position:0% +alpha squared +minus 2 over 2 right here again I'm just + + align:start position:0% +minus 2 over 2 right here again I'm just + + + align:start position:0% +minus 2 over 2 right here again I'm just +using that alpha was bigger equal to + + align:start position:0% +using that alpha was bigger equal to + + + align:start position:0% +using that alpha was bigger equal to +one. Uh and um right and then I I just + + align:start position:0% +one. Uh and um right and then I I just + + + align:start position:0% +one. Uh and um right and then I I just +actually ignore this true right. So this + + align:start position:0% +actually ignore this true right. So this + + + align:start position:0% +actually ignore this true right. So this +is definitely an upper bound. + + align:start position:0% + + + + align:start position:0% + +And so now you see that this thing here + + align:start position:0% +And so now you see that this thing here + + + align:start position:0% +And so now you see that this thing here +is equal to alpha squared. This thing + + align:start position:0% +is equal to alpha squared. This thing + + + align:start position:0% +is equal to alpha squared. This thing +here you can think about this thing + + align:start position:0% +here you can think about this thing + + + align:start position:0% +here you can think about this thing +here. You can write this in here if you + + align:start position:0% +here. You can write this in here if you + + + align:start position:0% +here. You can write this in here if you +will as alpha^ 2 + alpha^ 2 - 2 over 4 - + + align:start position:0% +will as alpha^ 2 + alpha^ 2 - 2 over 4 - + + + align:start position:0% +will as alpha^ 2 + alpha^ 2 - 2 over 4 - +2 alpha^ 2 - 2 over over 4. + + align:start position:0% +2 alpha^ 2 - 2 over over 4. + + + align:start position:0% +2 alpha^ 2 - 2 over over 4. +And so what you get is that it's alpha^ + + align:start position:0% +And so what you get is that it's alpha^ + + + align:start position:0% +And so what you get is that it's alpha^ +2 minus alpha^ 2 - 2 over 4. + + align:start position:0% +2 minus alpha^ 2 - 2 over 4. + + + align:start position:0% +2 minus alpha^ 2 - 2 over 4. +Right? And this thing here is now this + + align:start position:0% +Right? And this thing here is now this + + + align:start position:0% +Right? And this thing here is now this +thing here is positive right because + + align:start position:0% +thing here is positive right because + + + align:start position:0% +thing here is positive right because +alpha square was strictly bigger than + + align:start position:0% +alpha square was strictly bigger than + + + align:start position:0% +alpha square was strictly bigger than +two. This is positive. So this is + + align:start position:0% +two. This is positive. So this is + + + align:start position:0% +two. This is positive. So this is +strictly less than alpha square right. + + align:start position:0% +strictly less than alpha square right. + + + align:start position:0% +strictly less than alpha square right. +And so this here would also which is + + align:start position:0% +And so this here would also which is + + + align:start position:0% +And so this here would also which is +still right. This is + + align:start position:0% +still right. This is + + + align:start position:0% +still right. This is +right. So this thing here is also an + + align:start position:0% +right. So this thing here is also an + + + align:start position:0% +right. So this thing here is also an +upper bound. Uh, sorry. Sorry. Oh, I + + align:start position:0% +upper bound. Uh, sorry. Sorry. Oh, I + + + align:start position:0% +upper bound. Uh, sorry. Sorry. Oh, I +need to Oh, sorry. + + align:start position:0% +need to Oh, sorry. + + + align:start position:0% +need to Oh, sorry. +Okay. So, I have this. + + align:start position:0% + + + + align:start position:0% + +No, no, sorry about that. + + align:start position:0% +No, no, sorry about that. + + + align:start position:0% +No, no, sorry about that. +Okay. So, yeah. No, I I sorry. I um + + align:start position:0% + + + + align:start position:0% + +Okay, let let's go over this again. + + align:start position:0% +Okay, let let's go over this again. + + + align:start position:0% +Okay, let let's go over this again. +Sorry. + + align:start position:0% + + + + align:start position:0% + +So what I'm trying to prove here I'm + + align:start position:0% +So what I'm trying to prove here I'm + + + align:start position:0% +So what I'm trying to prove here I'm +trying to write down the formal I mean + + align:start position:0% +trying to write down the formal I mean + + + align:start position:0% +trying to write down the formal I mean +that that's a problem that it got so + + align:start position:0% +that that's a problem that it got so + + + align:start position:0% +that that's a problem that it got so +formal that that I was now in. So what + + align:start position:0% +formal that that I was now in. So what + + + align:start position:0% +formal that that I was now in. So what +I'm trying to prove here is that I want + + align:start position:0% +I'm trying to prove here is that I want + + + align:start position:0% +I'm trying to prove here is that I want +to say this part one is that alpha + + align:start position:0% +to say this part one is that alpha + + + align:start position:0% +to say this part one is that alpha +squared + + align:start position:0% +squared + + + align:start position:0% +squared +is lesser equal to to one. Right? This + + align:start position:0% +is lesser equal to to one. Right? This + + + align:start position:0% +is lesser equal to to one. Right? This +is what less equal to two. That's what I + + align:start position:0% +is what less equal to two. That's what I + + + align:start position:0% +is what less equal to two. That's what I +want to prove. Right? This is part one, + + align:start position:0% +want to prove. Right? This is part one, + + + align:start position:0% +want to prove. Right? This is part one, +right? And so I assume not so I assume + + align:start position:0% +right? And so I assume not so I assume + + + align:start position:0% +right? And so I assume not so I assume +that alpha square was strictly bigger + + align:start position:0% +that alpha square was strictly bigger + + + align:start position:0% +that alpha square was strictly bigger +than two, right? If alpha square was + + align:start position:0% +than two, right? If alpha square was + + + align:start position:0% +than two, right? If alpha square was +strictly bigger than two, here you have + + align:start position:0% +strictly bigger than two, here you have + + + align:start position:0% +strictly bigger than two, here you have +zero. Here you have alpha and now we + + align:start position:0% +zero. Here you have alpha and now we + + + align:start position:0% +zero. Here you have alpha and now we +define this alpha zero. + + align:start position:0% +define this alpha zero. + + + align:start position:0% +define this alpha zero. +Alpha zero was to the left so to speak + + align:start position:0% +Alpha zero was to the left so to speak + + + align:start position:0% +Alpha zero was to the left so to speak +of alpha because it was subtracting a + + align:start position:0% +of alpha because it was subtracting a + + + align:start position:0% +of alpha because it was subtracting a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +and what I want to show is that this + + align:start position:0% +and what I want to show is that this + + + align:start position:0% +and what I want to show is that this +alpha zero I want to show that this + + align:start position:0% +alpha zero I want to show that this + + + align:start position:0% +alpha zero I want to show that this +alpha zero is also an upper bound so I + + align:start position:0% +alpha zero is also an upper bound so I + + + align:start position:0% +alpha zero is also an upper bound so I +want to prove that this square here is + + align:start position:0% +want to prove that this square here is + + + align:start position:0% +want to prove that this square here is +also bigger than two that's what I want + + align:start position:0% +also bigger than two that's what I want + + + align:start position:0% +also bigger than two that's what I want +to prove right + + align:start position:0% +to prove right + + + align:start position:0% +to prove right +so I want to find I want to to find a + + align:start position:0% +so I want to find I want to to find a + + + align:start position:0% +so I want to find I want to to find a +lower bound B and that lower bound + + align:start position:0% +lower bound B and that lower bound + + + align:start position:0% +lower bound B and that lower bound +should be two. Right? So this is not + + align:start position:0% +should be two. Right? So this is not + + + align:start position:0% +should be two. Right? So this is not +exactly what I wanted to do. Okay? So + + align:start position:0% +exactly what I wanted to do. Okay? So + + + align:start position:0% +exactly what I wanted to do. Okay? So +let's just go through it here. Sorry. So + + align:start position:0% +let's just go through it here. Sorry. So + + + align:start position:0% +let's just go through it here. Sorry. So +this here was correct and this here is + + align:start position:0% +this here was correct and this here is + + + align:start position:0% +this here was correct and this here is +for really for the second part. + + align:start position:0% +for really for the second part. + + + align:start position:0% +for really for the second part. +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +okay. + + align:start position:0% +okay. + + + align:start position:0% +okay. +So we define it like this. + + align:start position:0% +So we define it like this. + + + align:start position:0% +So we define it like this. +And now I say that this thing here + + align:start position:0% +And now I say that this thing here + + + align:start position:0% +And now I say that this thing here +is bigger equal to + + align:start position:0% +is bigger equal to + + + align:start position:0% +is bigger equal to +But I want to bound it from below. And + + align:start position:0% +But I want to bound it from below. And + + + align:start position:0% +But I want to bound it from below. And +so then I can ignore the h squ. So it's + + align:start position:0% +so then I can ignore the h squ. So it's + + + align:start position:0% +so then I can ignore the h squ. So it's +bigger than because that's positive just + + align:start position:0% +bigger than because that's positive just + + + align:start position:0% +bigger than because that's positive just +bigger than alpha^ 2 - 2 alpha h. Right? + + align:start position:0% +bigger than alpha^ 2 - 2 alpha h. Right? + + + align:start position:0% +bigger than alpha^ 2 - 2 alpha h. Right? +And this thing here is so this is equal + + align:start position:0% +And this thing here is so this is equal + + + align:start position:0% +And this thing here is so this is equal +to alpha squar minus 2 alpha. I fill in + + align:start position:0% +to alpha squar minus 2 alpha. I fill in + + + align:start position:0% +to alpha squar minus 2 alpha. I fill in +what h was. This here was h + + align:start position:0% +what h was. This here was h + + + align:start position:0% +what h was. This here was h +right + + align:start position:0% +right + + + align:start position:0% +right +and uh and uh then you see that this + + align:start position:0% +and uh and uh then you see that this + + + align:start position:0% +and uh and uh then you see that this +here cancel with that and this here and + + align:start position:0% +here cancel with that and this here and + + + align:start position:0% +here cancel with that and this here and +you're getting that you're getting alpha + + align:start position:0% +you're getting that you're getting alpha + + + align:start position:0% +you're getting that you're getting alpha +squared + + align:start position:0% +squared + + + align:start position:0% +squared +uh uh this is this alpha squar minus + + align:start position:0% +uh uh this is this alpha squar minus + + + align:start position:0% +uh uh this is this alpha squar minus +uh alpha^ 2 - 2 / 2 + + align:start position:0% +uh alpha^ 2 - 2 / 2 + + + align:start position:0% +uh alpha^ 2 - 2 / 2 +And this thing here is equal to this is + + align:start position:0% +And this thing here is equal to this is + + + align:start position:0% +And this thing here is equal to this is +equal to alpha squared over two. This is + + align:start position:0% +equal to alpha squared over two. This is + + + align:start position:0% +equal to alpha squared over two. This is +subtracting that and then you're adding + + align:start position:0% +subtracting that and then you're adding + + + align:start position:0% +subtracting that and then you're adding +right you're adding one. So this is what + + align:start position:0% +right you're adding one. So this is what + + + align:start position:0% +right you're adding one. So this is what +it is right alpha we have already proven + + align:start position:0% +it is right alpha we have already proven + + + align:start position:0% +it is right alpha we have already proven +that alpha here was bigger equal to one. + + align:start position:0% +that alpha here was bigger equal to one. + + + align:start position:0% +that alpha here was bigger equal to one. +So, so using so this here is bigger + + align:start position:0% +So, so using so this here is bigger + + + align:start position:0% +So, so using so this here is bigger +equal to I claim that this here is + + align:start position:0% +equal to I claim that this here is + + + align:start position:0% +equal to I claim that this here is +bigger equal to two using + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +alpha is uh bigger equal to one right + + align:start position:0% +alpha is uh bigger equal to one right + + + align:start position:0% +alpha is uh bigger equal to one right +and so you see that alpha one that is a + + align:start position:0% +and so you see that alpha one that is a + + + align:start position:0% +and so you see that alpha one that is a +smaller number because you're + + align:start position:0% +smaller number because you're + + + align:start position:0% +smaller number because you're +subtracting a positive number from alpha + + align:start position:0% +subtracting a positive number from alpha + + + align:start position:0% +subtracting a positive number from alpha +that is also an upper bound right. So + + align:start position:0% +that is also an upper bound right. So + + + align:start position:0% +that is also an upper bound right. So +this is contradicting. So this + + align:start position:0% +this is contradicting. So this + + + align:start position:0% +this is contradicting. So this +contradict and then one often writes uh + + align:start position:0% +contradict and then one often writes uh + + + align:start position:0% +contradict and then one often writes uh +one often writes this symbol here. This + + align:start position:0% +one often writes this symbol here. This + + + align:start position:0% +one often writes this symbol here. This +is a standard symbol that means this is + + align:start position:0% +is a standard symbol that means this is + + + align:start position:0% +is a standard symbol that means this is +a contradiction. Yeah. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. Then you get two. But that's fine. + + align:start position:0% +>> Yeah. Then you get two. But that's fine. + + + align:start position:0% +>> Yeah. Then you get two. But that's fine. +I just needed to show I all I needed to + + align:start position:0% +I just needed to show I all I needed to + + + align:start position:0% +I just needed to show I all I needed to +do was I needed to prove + + align:start position:0% +do was I needed to prove + + + align:start position:0% +do was I needed to prove +that I I I I have that. So So you see + + align:start position:0% +that I I I I have that. So So you see + + + align:start position:0% +that I I I I have that. So So you see +that I have that I'm assuming that this + + align:start position:0% +that I have that I'm assuming that this + + + align:start position:0% +that I have that I'm assuming that this +thing here is strictly positive and then + + align:start position:0% +thing here is strictly positive and then + + + align:start position:0% +thing here is strictly positive and then +I define alpha 1 but alpha 1 is strictly + + align:start position:0% +I define alpha 1 but alpha 1 is strictly + + + align:start position:0% +I define alpha 1 but alpha 1 is strictly +less than alpha. Right? And then I have + + align:start position:0% +less than alpha. Right? And then I have + + + align:start position:0% +less than alpha. Right? And then I have +that alpha squar alpha squar alpha 1 + + align:start position:0% +that alpha squar alpha squar alpha 1 + + + align:start position:0% +that alpha squar alpha squar alpha 1 +squared is bigger equal to two. This + + align:start position:0% +squared is bigger equal to two. This + + + align:start position:0% +squared is bigger equal to two. This +here means that alpha 1 is also an upper + + align:start position:0% +here means that alpha 1 is also an upper + + + align:start position:0% +here means that alpha 1 is also an upper +bound. This is strictly less than alpha. + + align:start position:0% +bound. This is strictly less than alpha. + + + align:start position:0% +bound. This is strictly less than alpha. +This was supposed to be the least upper + + align:start position:0% +This was supposed to be the least upper + + + align:start position:0% +This was supposed to be the least upper +bound. That's a contradiction. Right? + + align:start position:0% +bound. That's a contradiction. Right? + + + align:start position:0% +bound. That's a contradiction. Right? +And so you see I fell into the trap. I + + align:start position:0% +And so you see I fell into the trap. I + + + align:start position:0% +And so you see I fell into the trap. I +was doing it so formally that I lost + + align:start position:0% +was doing it so formally that I lost + + + align:start position:0% +was doing it so formally that I lost +track of what I was doing. So I was + + align:start position:0% +track of what I was doing. So I was + + + align:start position:0% +track of what I was doing. So I was +actually in a process of proving the I + + align:start position:0% +actually in a process of proving the I + + + align:start position:0% +actually in a process of proving the I +mean that's a danger with but but the + + align:start position:0% +mean that's a danger with but but the + + + align:start position:0% +mean that's a danger with but but the +formal proof is is much easier to read + + align:start position:0% +formal proof is is much easier to read + + + align:start position:0% +formal proof is is much easier to read +afterwards, right? And so you see the + + align:start position:0% +afterwards, right? And so you see the + + + align:start position:0% +afterwards, right? And so you see the +difference here with a formal proof was + + align:start position:0% +difference here with a formal proof was + + + align:start position:0% +difference here with a formal proof was +last time we we sort of did a little + + align:start position:0% +last time we we sort of did a little + + + align:start position:0% +last time we we sort of did a little +calculation and then we try to figure + + align:start position:0% +calculation and then we try to figure + + + align:start position:0% +calculation and then we try to figure +out what should this H be and then it + + align:start position:0% +out what should this H be and then it + + + align:start position:0% +out what should this H be and then it +sort of came at the end. Right? But but + + align:start position:0% +sort of came at the end. Right? But but + + + align:start position:0% +sort of came at the end. Right? But but +when you write down the formal proof + + align:start position:0% +when you write down the formal proof + + + align:start position:0% +when you write down the formal proof +then you would sort of upfront you would + + align:start position:0% +then you would sort of upfront you would + + + align:start position:0% +then you would sort of upfront you would +already have done that little + + align:start position:0% +already have done that little + + + align:start position:0% +already have done that little +calculation and you would up front say + + align:start position:0% +calculation and you would up front say + + + align:start position:0% +calculation and you would up front say +what h was supposed to be and then you + + align:start position:0% +what h was supposed to be and then you + + + align:start position:0% +what h was supposed to be and then you +kind of run through the argument. Right. + + align:start position:0% +kind of run through the argument. Right. + + + align:start position:0% +kind of run through the argument. Right. +Yeah. + + align:start position:0% + + + + align:start position:0% + +>> Sorry. + + align:start position:0% + + + + align:start position:0% + +>> Uh um here. So + + align:start position:0% +>> Uh um here. So + + + align:start position:0% +>> Uh um here. So +uh if I'm I'm I mean of course alpha is + + align:start position:0% +uh if I'm I'm I mean of course alpha is + + + align:start position:0% +uh if I'm I'm I mean of course alpha is +much bigger than one but I'm just using + + align:start position:0% +much bigger than one but I'm just using + + + align:start position:0% +much bigger than one but I'm just using +we already we I'm only need here that + + align:start position:0% +we already we I'm only need here that + + + align:start position:0% +we already we I'm only need here that +alpha is bigger equal to one to say that + + align:start position:0% +alpha is bigger equal to one to say that + + + align:start position:0% +alpha is bigger equal to one to say that +this thing here is bigger equal to two + + align:start position:0% +this thing here is bigger equal to two + + + align:start position:0% +this thing here is bigger equal to two +>> sorry + + align:start position:0% +>> sorry + + + align:start position:0% +>> sorry +>> this is right this is alpha so the the + + align:start position:0% +>> this is right this is alpha so the the + + + align:start position:0% +>> this is right this is alpha so the the +inequality here is that alpha 1 2 is + + align:start position:0% +inequality here is that alpha 1 2 is + + + align:start position:0% +inequality here is that alpha 1 2 is +bigger equal to two and I'm using that + + align:start position:0% +bigger equal to two and I'm using that + + + align:start position:0% +bigger equal to two and I'm using that +alpha + + align:start position:0% +alpha + + + align:start position:0% +alpha +at this stage here to conclude this + + align:start position:0% +at this stage here to conclude this + + + align:start position:0% +at this stage here to conclude this +inequality. I'm using + + align:start position:0% +inequality. I'm using + + + align:start position:0% +inequality. I'm using +uh sorry no no you're right yeah sorry + + align:start position:0% +uh sorry no no you're right yeah sorry + + + align:start position:0% +uh sorry no no you're right yeah sorry +about that you're right I'm using that + + align:start position:0% +about that you're right I'm using that + + + align:start position:0% +about that you're right I'm using that +alpha no I'm not using that I'm using + + align:start position:0% +alpha no I'm not using that I'm using + + + align:start position:0% +alpha no I'm not using that I'm using +that alpha squared is bigger equal to + + align:start position:0% +that alpha squared is bigger equal to + + + align:start position:0% +that alpha squared is bigger equal to +two yeah sorry that was what you meant + + align:start position:0% +two yeah sorry that was what you meant + + + align:start position:0% +two yeah sorry that was what you meant +yeah saying you + + align:start position:0% +yeah saying you + + + align:start position:0% +yeah saying you +okay so that was uh why that was a + + align:start position:0% +okay so that was uh why that was a + + + align:start position:0% +okay so that was uh why that was a +formal proof of uh parts one and then + + align:start position:0% +formal proof of uh parts one and then + + + align:start position:0% +formal proof of uh parts one and then +there's part um + + align:start position:0% +there's part um + + + align:start position:0% +there's part um +part two so the other inequality + + align:start position:0% + + + + align:start position:0% + +So, how do we do that? + + align:start position:0% +So, how do we do that? + + + align:start position:0% +So, how do we do that? +And and and when you write this, + + align:start position:0% + + + + align:start position:0% + +when you write this, it's always good to + + align:start position:0% +when you write this, it's always good to + + + align:start position:0% +when you write this, it's always good to +try to explain + + align:start position:0% +try to explain + + + align:start position:0% +try to explain +um + + align:start position:0% +um + + + align:start position:0% +um +what you're going to do and in in in + + align:start position:0% +what you're going to do and in in in + + + align:start position:0% +what you're going to do and in in in +this case what is going to be the + + align:start position:0% +this case what is going to be the + + + align:start position:0% +this case what is going to be the +contradiction. So let's try to prove + + align:start position:0% +contradiction. So let's try to prove + + + align:start position:0% +contradiction. So let's try to prove +part two and hopefully we get it + + align:start position:0% +part two and hopefully we get it + + + align:start position:0% +part two and hopefully we get it +straight this time. So so part two so I + + align:start position:0% +straight this time. So so part two so I + + + align:start position:0% +straight this time. So so part two so I +want to show that um so we have so part + + align:start position:0% +want to show that um so we have so part + + + align:start position:0% +want to show that um so we have so part +one was establishing that alpha squar + + align:start position:0% +one was establishing that alpha squar + + + align:start position:0% +one was establishing that alpha squar +was lesser + + align:start position:0% +was lesser + + + align:start position:0% +was lesser +equal to true. Now we want to prove so + + align:start position:0% +equal to true. Now we want to prove so + + + align:start position:0% +equal to true. Now we want to prove so +part two + + align:start position:0% +part two + + + align:start position:0% +part two +uh uh want to show + + align:start position:0% + + + + align:start position:0% + +that alpha squar is bigger equal to two. + + align:start position:0% + + + + align:start position:0% + +And so + + align:start position:0% +And so + + + align:start position:0% +And so +uh again we're proving this + + align:start position:0% +uh again we're proving this + + + align:start position:0% +uh again we're proving this +we will show this by contradiction. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +assume + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +alpha squared is strictly less than two. + + align:start position:0% +alpha squared is strictly less than two. + + + align:start position:0% +alpha squared is strictly less than two. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +And now it it's it's it's you know it's + + align:start position:0% +And now it it's it's it's you know it's + + + align:start position:0% +And now it it's it's it's you know it's +it's I think it's helpful. Well, you + + align:start position:0% +it's I think it's helpful. Well, you + + + align:start position:0% +it's I think it's helpful. Well, you +don't necessarily have to do it, but I + + align:start position:0% +don't necessarily have to do it, but I + + + align:start position:0% +don't necessarily have to do it, but I +think it's helpful if you say um maybe + + align:start position:0% +think it's helpful if you say um maybe + + + align:start position:0% +think it's helpful if you say um maybe +it's too, you know, too long, but it's + + align:start position:0% +it's too, you know, too long, but it's + + + align:start position:0% +it's too, you know, too long, but it's +at least helpful to think about uh where + + align:start position:0% +at least helpful to think about uh where + + + align:start position:0% +at least helpful to think about uh where +is the contradiction coming from. So, if + + align:start position:0% +is the contradiction coming from. So, if + + + align:start position:0% +is the contradiction coming from. So, if +alpha square is less than two, + + align:start position:0% +alpha square is less than two, + + + align:start position:0% +alpha square is less than two, +uh in so I I will say it, you don't + + align:start position:0% +uh in so I I will say it, you don't + + + align:start position:0% +uh in so I I will say it, you don't +necessarily have to write it, but indeed + + align:start position:0% +necessarily have to write it, but indeed + + + align:start position:0% +necessarily have to write it, but indeed +we will show + + align:start position:0% + + + + align:start position:0% + +that if this is the case + + align:start position:0% + + + + align:start position:0% + +is the case + + align:start position:0% + + + + align:start position:0% + +then they exist. + + align:start position:0% + + + + align:start position:0% + +uh there exist some numbers alpha 2 + + align:start position:0% +uh there exist some numbers alpha 2 + + + align:start position:0% +uh there exist some numbers alpha 2 +bigger than alpha such that + + align:start position:0% + + + + align:start position:0% + +alpha 2 squared is also less than + + align:start position:0% +alpha 2 squared is also less than + + + align:start position:0% +alpha 2 squared is also less than +two. + + align:start position:0% +two. + + + align:start position:0% +two. +Contradicting + + align:start position:0% + + + + align:start position:0% + +that alpha is an upper bound + + align:start position:0% + + + + align:start position:0% + +for for for the set A we defined. Okay, + + align:start position:0% +for for for the set A we defined. Okay, + + + align:start position:0% +for for for the set A we defined. Okay, +that's what we will prove. Okay. + + align:start position:0% + + + + align:start position:0% + +And so we want to find a a a real number + + align:start position:0% +And so we want to find a a a real number + + + align:start position:0% +And so we want to find a a a real number +that is larger than this + + align:start position:0% +that is larger than this + + + align:start position:0% +that is larger than this +but still uh but still uh the square is + + align:start position:0% +but still uh but still uh the square is + + + align:start position:0% +but still uh but still uh the square is +still less than two. Okay. + + align:start position:0% +still less than two. Okay. + + + align:start position:0% +still less than two. Okay. +And so in this case I'm going to + + align:start position:0% +And so in this case I'm going to + + + align:start position:0% +And so in this case I'm going to +so so + + align:start position:0% + + + + align:start position:0% + +now we sort of do the you know the + + align:start position:0% +now we sort of do the you know the + + + align:start position:0% +now we sort of do the you know the +structure is going to be the same. + + align:start position:0% +structure is going to be the same. + + + align:start position:0% +structure is going to be the same. +you know, we had this little scrap paper + + align:start position:0% +you know, we had this little scrap paper + + + align:start position:0% +you know, we had this little scrap paper +where we sort of outline the argument + + align:start position:0% +where we sort of outline the argument + + + align:start position:0% +where we sort of outline the argument +and figure out what H had to be. And so + + align:start position:0% +and figure out what H had to be. And so + + + align:start position:0% +and figure out what H had to be. And so +I'm going to use this H. So, so we're + + align:start position:0% +I'm going to use this H. So, so we're + + + align:start position:0% +I'm going to use this H. So, so we're +going to again maybe I'll just erase + + align:start position:0% +going to again maybe I'll just erase + + + align:start position:0% +going to again maybe I'll just erase +this here so we don't get confused with + + align:start position:0% +this here so we don't get confused with + + + align:start position:0% +this here so we don't get confused with +the first part and the second part. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. So, + + align:start position:0% +Okay. So, + + + align:start position:0% +Okay. So, +so I'm going to set + + align:start position:0% +so I'm going to set + + + align:start position:0% +so I'm going to set +h again. I'm going to define it very + + align:start position:0% +h again. I'm going to define it very + + + align:start position:0% +h again. I'm going to define it very +similar to what I did before, but now I + + align:start position:0% +similar to what I did before, but now I + + + align:start position:0% +similar to what I did before, but now I +have to remember that I'm assuming that + + align:start position:0% +have to remember that I'm assuming that + + + align:start position:0% +have to remember that I'm assuming that +alpha squar is less than two. So I + + align:start position:0% +alpha squar is less than two. So I + + + align:start position:0% +alpha squar is less than two. So I +define h to be 2 minus alpha squar over + + align:start position:0% +define h to be 2 minus alpha squar over + + + align:start position:0% +define h to be 2 minus alpha squar over +4 alpha. + + align:start position:0% +4 alpha. + + + align:start position:0% +4 alpha. +Okay, this is how I define it. + + align:start position:0% +Okay, this is how I define it. + + + align:start position:0% +Okay, this is how I define it. +uh and then I what I'm interested in is + + align:start position:0% +uh and then I what I'm interested in is + + + align:start position:0% +uh and then I what I'm interested in is +so I have here zero I have this that is + + align:start position:0% +so I have here zero I have this that is + + + align:start position:0% +so I have here zero I have this that is +supposed to be the upper bound but I + + align:start position:0% +supposed to be the upper bound but I + + + align:start position:0% +supposed to be the upper bound but I +want to prove that that really isn't an + + align:start position:0% +want to prove that that really isn't an + + + align:start position:0% +want to prove that that really isn't an +upper bound that's an element in in my + + align:start position:0% +upper bound that's an element in in my + + + align:start position:0% +upper bound that's an element in in my +set A and so this is this alpha 2 so I'm + + align:start position:0% +set A and so this is this alpha 2 so I'm + + + align:start position:0% +set A and so this is this alpha 2 so I'm +defy so I'm setting + + align:start position:0% +defy so I'm setting + + + align:start position:0% +defy so I'm setting +set this and alpha 2 equal to alpha plus + + align:start position:0% +set this and alpha 2 equal to alpha plus + + + align:start position:0% +set this and alpha 2 equal to alpha plus +h + + align:start position:0% +h + + + align:start position:0% +h +this here was just to illustrate you + + align:start position:0% +this here was just to illustrate you + + + align:start position:0% +this here was just to illustrate you +shouldn't you don't necessarily have to + + align:start position:0% +shouldn't you don't necessarily have to + + + align:start position:0% +shouldn't you don't necessarily have to +include that + + align:start position:0% +include that + + + align:start position:0% +include that +okay and I want to show you we want to + + align:start position:0% +okay and I want to show you we want to + + + align:start position:0% +okay and I want to show you we want to +show + + align:start position:0% + + + + align:start position:0% + +I think it's good idea to write what you + + align:start position:0% +I think it's good idea to write what you + + + align:start position:0% +I think it's good idea to write what you +want to show in particular if I really + + align:start position:0% +want to show in particular if I really + + + align:start position:0% +want to show in particular if I really +had written that before uh then I + + align:start position:0% +had written that before uh then I + + + align:start position:0% +had written that before uh then I +wouldn't have been in trouble right + + align:start position:0% +wouldn't have been in trouble right + + + align:start position:0% +wouldn't have been in trouble right +because I was trying to prove something + + align:start position:0% +because I was trying to prove something + + + align:start position:0% +because I was trying to prove something +else uh so you want to prove that alpha + + align:start position:0% +else uh so you want to prove that alpha + + + align:start position:0% +else uh so you want to prove that alpha +squared here + + align:start position:0% + + + + align:start position:0% + +is also less than two. Right? + + align:start position:0% +is also less than two. Right? + + + align:start position:0% +is also less than two. Right? +So this is this is so so we already have + + align:start position:0% +So this is this is so so we already have + + + align:start position:0% +So this is this is so so we already have +that alpha here + + align:start position:0% + + + + align:start position:0% + +uh is is positive. + + align:start position:0% +uh is is positive. + + + align:start position:0% +uh is is positive. +It's + + align:start position:0% + + + + align:start position:0% + +um it's bigger than one. So uh so this + + align:start position:0% +um it's bigger than one. So uh so this + + + align:start position:0% +um it's bigger than one. So uh so this +number here this here we already know is + + align:start position:0% +number here this here we already know is + + + align:start position:0% +number here this here we already know is +bigger than alpha. Okay. + + align:start position:0% + + + + align:start position:0% + +And so if I can prove that so this here + + align:start position:0% +And so if I can prove that so this here + + + align:start position:0% +And so if I can prove that so this here +is so this bigger than alpha if I can + + align:start position:0% +is so this bigger than alpha if I can + + + align:start position:0% +is so this bigger than alpha if I can +prove that the square is less than two + + align:start position:0% +prove that the square is less than two + + + align:start position:0% +prove that the square is less than two +then alpha here alpha here sorry would + + align:start position:0% +then alpha here alpha here sorry would + + + align:start position:0% +then alpha here alpha here sorry would +not be an upper bound right there's + + align:start position:0% +not be an upper bound right there's + + + align:start position:0% +not be an upper bound right there's +another element in the set uh a that is + + align:start position:0% +another element in the set uh a that is + + + align:start position:0% +another element in the set uh a that is +bigger. Okay. + + align:start position:0% +bigger. Okay. + + + align:start position:0% +bigger. Okay. +So I want to prove that. So now I'm + + align:start position:0% +So I want to prove that. So now I'm + + + align:start position:0% +So I want to prove that. So now I'm +looking at alpha + + align:start position:0% +looking at alpha + + + align:start position:0% +looking at alpha +2 squared. So that is alpha plus h. + + align:start position:0% +2 squared. So that is alpha plus h. + + + align:start position:0% +2 squared. So that is alpha plus h. +Right? That's how I define alpha 2 and I + + align:start position:0% +Right? That's how I define alpha 2 and I + + + align:start position:0% +Right? That's how I define alpha 2 and I +square it. + + align:start position:0% + + + + align:start position:0% + +And if I do that then I get alpha + + align:start position:0% +And if I do that then I get alpha + + + align:start position:0% +And if I do that then I get alpha +squared plus h 2 + + align:start position:0% +squared plus h 2 + + + align:start position:0% +squared plus h 2 +uh plus + + align:start position:0% +uh plus + + + align:start position:0% +uh plus +um 2 h + + align:start position:0% +um 2 h + + + align:start position:0% +um 2 h +uh alpha right + + align:start position:0% + + + + align:start position:0% + +and I now uh so now I want an upper + + align:start position:0% +and I now uh so now I want an upper + + + align:start position:0% +and I now uh so now I want an upper +bound right and so we already have that + + align:start position:0% +bound right and so we already have that + + + align:start position:0% +bound right and so we already have that +alpha is this one here h is you see that + + align:start position:0% +alpha is this one here h is you see that + + + align:start position:0% +alpha is this one here h is you see that +h is in this case here. So h is is equal + + align:start position:0% +h is in this case here. So h is is equal + + + align:start position:0% +h is in this case here. So h is is equal +to 2 - alpha^ 2 over 4 alpha. Alpha is + + align:start position:0% +to 2 - alpha^ 2 over 4 alpha. Alpha is + + + align:start position:0% +to 2 - alpha^ 2 over 4 alpha. Alpha is +bigger equal to one. This here the + + align:start position:0% +bigger equal to one. This here the + + + align:start position:0% +bigger equal to one. This here the +denominator is bounded by two. So again + + align:start position:0% +denominator is bounded by two. So again + + + align:start position:0% +denominator is bounded by two. So again +it's 2 over 4. So this is bounded by a + + align:start position:0% +it's 2 over 4. So this is bounded by a + + + align:start position:0% +it's 2 over 4. So this is bounded by a +half. + + align:start position:0% +half. + + + align:start position:0% +half. +So h is positive + + align:start position:0% +So h is positive + + + align:start position:0% +So h is positive +and we have that h is positive and h is + + align:start position:0% +and we have that h is positive and h is + + + align:start position:0% +and we have that h is positive and h is +less than half. + + align:start position:0% +less than half. + + + align:start position:0% +less than half. +And so now uh I this here I can bound I + + align:start position:0% +And so now uh I this here I can bound I + + + align:start position:0% +And so now uh I this here I can bound I +can bound trivially by just using that h + + align:start position:0% +can bound trivially by just using that h + + + align:start position:0% +can bound trivially by just using that h +is bounded by one. So I get this plus h + + align:start position:0% +is bounded by one. So I get this plus h + + + align:start position:0% +is bounded by one. So I get this plus h ++ 2 + + align:start position:0% ++ 2 + + + align:start position:0% ++ 2 +uh and then h * alpha again or 2 h + + align:start position:0% +uh and then h * alpha again or 2 h + + + align:start position:0% +uh and then h * alpha again or 2 h +alpha. This is right when you multiply + + align:start position:0% +alpha. This is right when you multiply + + + align:start position:0% +alpha. This is right when you multiply +this by two alpha then the alpha cancel + + align:start position:0% +this by two alpha then the alpha cancel + + + align:start position:0% +this by two alpha then the alpha cancel +out and the two cancel with one of these + + align:start position:0% +out and the two cancel with one of these + + + align:start position:0% +out and the two cancel with one of these +uh with + + align:start position:0% +uh with + + + align:start position:0% +uh with +two in this form. So you're getting 2 + + align:start position:0% +two in this form. So you're getting 2 + + + align:start position:0% +two in this form. So you're getting 2 +minus alpha squar over two. + + align:start position:0% + + + + align:start position:0% + +Okay. And so now I get that this thing + + align:start position:0% +Okay. And so now I get that this thing + + + align:start position:0% +Okay. And so now I get that this thing +here is bounded by so h here + + align:start position:0% +here is bounded by so h here + + + align:start position:0% +here is bounded by so h here +h is also + + align:start position:0% +h is also + + + align:start position:0% +h is also +a + + align:start position:0% +a + + + align:start position:0% +a +a very rough bound for h is so using + + align:start position:0% +a very rough bound for h is so using + + + align:start position:0% +a very rough bound for h is so using +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +so using so I have that and now using + + align:start position:0% + + + + align:start position:0% + +that h here is equal = to alpha 2 - + + align:start position:0% +that h here is equal = to alpha 2 - + + + align:start position:0% +that h here is equal = to alpha 2 - +alpha^ 2 / 2 / 4 alpha which is less + + align:start position:0% +alpha^ 2 / 2 / 4 alpha which is less + + + align:start position:0% +alpha^ 2 / 2 / 4 alpha which is less +than + + align:start position:0% +than + + + align:start position:0% +than +uh 2 - alpha^ 2 over 2 since + + align:start position:0% +uh 2 - alpha^ 2 over 2 since + + + align:start position:0% +uh 2 - alpha^ 2 over 2 since +alpha here is bigger than one + + align:start position:0% +alpha here is bigger than one + + + align:start position:0% +alpha here is bigger than one +right so I have that right so using that + + align:start position:0% +right so I have that right so using that + + + align:start position:0% +right so I have that right so using that +we have + + align:start position:0% + + + + align:start position:0% + +that alpha 2^ squared is less or equal + + align:start position:0% +that alpha 2^ squared is less or equal + + + align:start position:0% +that alpha 2^ squared is less or equal +to let me just write that line I'm just + + align:start position:0% +to let me just write that line I'm just + + + align:start position:0% +to let me just write that line I'm just +now filling in alpha squared to the h + + align:start position:0% +now filling in alpha squared to the h + + + align:start position:0% +now filling in alpha squared to the h +here I'm using this inequality here 2 - + + align:start position:0% +here I'm using this inequality here 2 - + + + align:start position:0% +here I'm using this inequality here 2 - +alpha^ 2 / 2 and then I have the same + + align:start position:0% +alpha^ 2 / 2 and then I have the same + + + align:start position:0% +alpha^ 2 / 2 and then I have the same +thing again + + align:start position:0% +thing again + + + align:start position:0% +thing again +and so you see that this here it's this + + align:start position:0% +and so you see that this here it's this + + + align:start position:0% +and so you see that this here it's this +here times 2 so this is just alpha^ 2us + + align:start position:0% +here times 2 so this is just alpha^ 2us + + + align:start position:0% +here times 2 so this is just alpha^ 2us +- 2 + 2 - + + align:start position:0% +- 2 + 2 - + + + align:start position:0% +- 2 + 2 - +uh alpha square + + align:start position:0% + + + + align:start position:0% + +and and this inequality here was one of + + align:start position:0% +and and this inequality here was one of + + + align:start position:0% +and and this inequality here was one of +these inequality I should have replaced + + align:start position:0% +these inequality I should have replaced + + + align:start position:0% +these inequality I should have replaced +by a strict inequality. This because h + + align:start position:0% +by a strict inequality. This because h + + + align:start position:0% +by a strict inequality. This because h +is positive and is strictly less than + + align:start position:0% +is positive and is strictly less than + + + align:start position:0% +is positive and is strictly less than +one. So this here is actually a strict + + align:start position:0% +one. So this here is actually a strict + + + align:start position:0% +one. So this here is actually a strict +inequality. So this here is a strict + + align:start position:0% +inequality. So this here is a strict + + + align:start position:0% +inequality. So this here is a strict +inequality. + + align:start position:0% + + + + align:start position:0% + +Okay. But now you see that this thing + + align:start position:0% +Okay. But now you see that this thing + + + align:start position:0% +Okay. But now you see that this thing +here the alpha cancel out and you're + + align:start position:0% +here the alpha cancel out and you're + + + align:start position:0% +here the alpha cancel out and you're +getting two right so you have that alpha + + align:start position:0% +getting two right so you have that alpha + + + align:start position:0% +getting two right so you have that alpha +2 squared is strictly less than two + + align:start position:0% +2 squared is strictly less than two + + + align:start position:0% +2 squared is strictly less than two +that's what we wanted to prove right and + + align:start position:0% +that's what we wanted to prove right and + + + align:start position:0% +that's what we wanted to prove right and +this this this + + align:start position:0% +this this this + + + align:start position:0% +this this this +gives + + align:start position:0% +gives + + + align:start position:0% +gives +that + + align:start position:0% +that + + + align:start position:0% +that +alpha 2 is also in a and yet + + align:start position:0% +alpha 2 is also in a and yet + + + align:start position:0% +alpha 2 is also in a and yet +alpha 2 was bigger bigger than alpha. + + align:start position:0% +alpha 2 was bigger bigger than alpha. + + + align:start position:0% +alpha 2 was bigger bigger than alpha. +And this is the desired contradiction. + + align:start position:0% + + + + align:start position:0% + +Okay. So again, you know, we already did + + align:start position:0% +Okay. So again, you know, we already did + + + align:start position:0% +Okay. So again, you know, we already did +this last time, but but the the point + + align:start position:0% +this last time, but but the the point + + + align:start position:0% +this last time, but but the the point +here is that how do you write down a + + align:start position:0% +here is that how do you write down a + + + align:start position:0% +here is that how do you write down a +formal proof, right? And a formal proof + + align:start position:0% +formal proof, right? And a formal proof + + + align:start position:0% +formal proof, right? And a formal proof +in this case is that you try very + + align:start position:0% +in this case is that you try very + + + align:start position:0% +in this case is that you try very +clearly in this case it was divided into + + align:start position:0% +clearly in this case it was divided into + + + align:start position:0% +clearly in this case it was divided into +two steps. So you you you you try to + + align:start position:0% +two steps. So you you you you try to + + + align:start position:0% +two steps. So you you you you try to +divide it into the two steps and then + + align:start position:0% +divide it into the two steps and then + + + align:start position:0% +divide it into the two steps and then +maybe you have a a last line that say + + align:start position:0% +maybe you have a a last line that say + + + align:start position:0% +maybe you have a a last line that say +that you know part one part one + + align:start position:0% +that you know part one part one + + + align:start position:0% +that you know part one part one +and part two together + + align:start position:0% + + + + align:start position:0% + +show + + align:start position:0% +show + + + align:start position:0% +show +that alpha squ is equal to two. uh + + align:start position:0% +that alpha squ is equal to two. uh + + + align:start position:0% +that alpha squ is equal to two. uh +completing the proof, + + align:start position:0% + + + + align:start position:0% + +right? And again, the point here was + + align:start position:0% +right? And again, the point here was + + + align:start position:0% +right? And again, the point here was +that so we already knew how to prove + + align:start position:0% +that so we already knew how to prove + + + align:start position:0% +that so we already knew how to prove +this, but like how do you write down a + + align:start position:0% +this, but like how do you write down a + + + align:start position:0% +this, but like how do you write down a +formal proof, right? And so in in in for + + align:start position:0% +formal proof, right? And so in in in for + + + align:start position:0% +formal proof, right? And so in in in for +this proof, it was divided into these + + align:start position:0% +this proof, it was divided into these + + + align:start position:0% +this proof, it was divided into these +two steps. So you try to write each step + + align:start position:0% +two steps. So you try to write each step + + + align:start position:0% +two steps. So you try to write each step +separately. + + align:start position:0% +separately. + + + align:start position:0% +separately. +They were both both of the two steps was + + align:start position:0% +They were both both of the two steps was + + + align:start position:0% +They were both both of the two steps was +proven by contradiction. + + align:start position:0% +proven by contradiction. + + + align:start position:0% +proven by contradiction. +And so you would say up front you would + + align:start position:0% +And so you would say up front you would + + + align:start position:0% +And so you would say up front you would +say that you're going to prove it by + + align:start position:0% +say that you're going to prove it by + + + align:start position:0% +say that you're going to prove it by +contradiction. + + align:start position:0% +contradiction. + + + align:start position:0% +contradiction. +And then of course there would be you + + align:start position:0% +And then of course there would be you + + + align:start position:0% +And then of course there would be you +would you know it the statement that you + + align:start position:0% +would you know it the statement that you + + + align:start position:0% +would you know it the statement that you +want to prove since you're proving it by + + align:start position:0% +want to prove since you're proving it by + + + align:start position:0% +want to prove since you're proving it by +contradiction you would assume the + + align:start position:0% +contradiction you would assume the + + + align:start position:0% +contradiction you would assume the +negation + + align:start position:0% +negation + + + align:start position:0% +negation +and then I think if you can and it + + align:start position:0% +and then I think if you can and it + + + align:start position:0% +and then I think if you can and it +doesn't fill too much I think it's very + + align:start position:0% +doesn't fill too much I think it's very + + + align:start position:0% +doesn't fill too much I think it's very +helpful to write what you are trying how + + align:start position:0% +helpful to write what you are trying how + + + align:start position:0% +helpful to write what you are trying how +you are trying to get the contradiction + + align:start position:0% +you are trying to get the contradiction + + + align:start position:0% +you are trying to get the contradiction +right that's what I tried here right and + + align:start position:0% +right that's what I tried here right and + + + align:start position:0% +right that's what I tried here right and +then but and then you see then the big + + align:start position:0% +then but and then you see then the big + + + align:start position:0% +then but and then you see then the big +difference from when we were trying to + + align:start position:0% +difference from when we were trying to + + + align:start position:0% +difference from when we were trying to +figure out how to prove it is that you + + align:start position:0% +figure out how to prove it is that you + + + align:start position:0% +figure out how to prove it is that you +now go ahead and you just define + + align:start position:0% +now go ahead and you just define + + + align:start position:0% +now go ahead and you just define +you define the things. You define H and + + align:start position:0% +you define the things. You define H and + + + align:start position:0% +you define the things. You define H and +alpha 2, right? That sort of seems to + + align:start position:0% +alpha 2, right? That sort of seems to + + + align:start position:0% +alpha 2, right? That sort of seems to +come out of nowhere + + align:start position:0% +come out of nowhere + + + align:start position:0% +come out of nowhere +and then you establish the property that + + align:start position:0% +and then you establish the property that + + + align:start position:0% +and then you establish the property that +you want to prove that that leads to the + + align:start position:0% +you want to prove that that leads to the + + + align:start position:0% +you want to prove that that leads to the +contradiction. Okay, that's sort of the + + align:start position:0% +contradiction. Okay, that's sort of the + + + align:start position:0% +contradiction. Okay, that's sort of the +structure. + + align:start position:0% +structure. + + + align:start position:0% +structure. +Are there any questions to this? + + align:start position:0% +Are there any questions to this? + + + align:start position:0% +Are there any questions to this? +Yeah. + + align:start position:0% + + + + align:start position:0% + +>> So, + + align:start position:0% + + + + align:start position:0% + +>> right. So, we're using a few things. + + align:start position:0% +>> right. So, we're using a few things. + + + align:start position:0% +>> right. So, we're using a few things. +We're using um I mean and and and uh + + align:start position:0% +We're using um I mean and and and uh + + + align:start position:0% +We're using um I mean and and and uh +we're using a few thing uh we're using + + align:start position:0% +we're using a few thing uh we're using + + + align:start position:0% +we're using a few thing uh we're using +that is ordered that is ordered. We're + + align:start position:0% +that is ordered that is ordered. We're + + + align:start position:0% +that is ordered that is ordered. We're +also using uh something about that is a + + align:start position:0% +also using uh something about that is a + + + align:start position:0% +also using uh something about that is a +ordered field. And why? because we're + + align:start position:0% +ordered field. And why? because we're + + + align:start position:0% +ordered field. And why? because we're +using something well we're using + + align:start position:0% +using something well we're using + + + align:start position:0% +using something well we're using +something about multiplication to at all + + align:start position:0% +something about multiplication to at all + + + align:start position:0% +something about multiplication to at all +define square root right and also we're + + align:start position:0% +define square root right and also we're + + + align:start position:0% +define square root right and also we're +using something about that one is bigger + + align:start position:0% +using something about that one is bigger + + + align:start position:0% +using something about that one is bigger +than zero right + + align:start position:0% +than zero right + + + align:start position:0% +than zero right +uh and um + + align:start position:0% +uh and um + + + align:start position:0% +uh and um +and then + + align:start position:0% +and then + + + align:start position:0% +and then +um and then so we're using and then + + align:start position:0% +um and then so we're using and then + + + align:start position:0% +um and then so we're using and then +we're also using of course completeness + + align:start position:0% +we're also using of course completeness + + + align:start position:0% +we're also using of course completeness +in order to define this least upper + + align:start position:0% +in order to define this least upper + + + align:start position:0% +in order to define this least upper +bound right so we're using a bunch of + + align:start position:0% +bound right so we're using a bunch of + + + align:start position:0% +bound right so we're using a bunch of +these things, right? But of course, if + + align:start position:0% +these things, right? But of course, if + + + align:start position:0% +these things, right? But of course, if +you have + + align:start position:0% +you have + + + align:start position:0% +you have +Yeah. I mean, uh I mean, if you're + + align:start position:0% +Yeah. I mean, uh I mean, if you're + + + align:start position:0% +Yeah. I mean, uh I mean, if you're +asking when I mean and that's not really + + align:start position:0% +asking when I mean and that's not really + + + align:start position:0% +asking when I mean and that's not really +I mean you know uh at this stage I mean + + align:start position:0% +I mean you know uh at this stage I mean + + + align:start position:0% +I mean you know uh at this stage I mean +like very very soon um in one of the + + align:start position:0% +like very very soon um in one of the + + + align:start position:0% +like very very soon um in one of the +next few lectures + + align:start position:0% +next few lectures + + + align:start position:0% +next few lectures +things will be in the real numbers. I + + align:start position:0% +things will be in the real numbers. I + + + align:start position:0% +things will be in the real numbers. I +mean we're not going to work on general + + align:start position:0% +mean we're not going to work on general + + + align:start position:0% +mean we're not going to work on general +fields and we're not going to yeah I + + align:start position:0% +fields and we're not going to yeah I + + + align:start position:0% +fields and we're not going to yeah I +mean general fields this is not part of + + align:start position:0% +mean general fields this is not part of + + + align:start position:0% +mean general fields this is not part of +the subject but you but of course it's + + align:start position:0% +the subject but you but of course it's + + + align:start position:0% +the subject but you but of course it's +interesting to ask + + align:start position:0% +interesting to ask + + + align:start position:0% +interesting to ask +and you see and and I think that's your + + align:start position:0% +and you see and and I think that's your + + + align:start position:0% +and you see and and I think that's your +point is like when can you define + + align:start position:0% +point is like when can you define + + + align:start position:0% +point is like when can you define +something like a square root of two in a + + align:start position:0% +something like a square root of two in a + + + align:start position:0% +something like a square root of two in a +field something like that and and + + align:start position:0% +field something like that and and + + + align:start position:0% +field something like that and and +there's a lot of things you're + + align:start position:0% +there's a lot of things you're + + + align:start position:0% +there's a lot of things you're +absolutely right that there's a lot of + + align:start position:0% +absolutely right that there's a lot of + + + align:start position:0% +absolutely right that there's a lot of +these things that was just sort of + + align:start position:0% +these things that was just sort of + + + align:start position:0% +these things that was just sort of +general property but maybe we shouldn't + + align:start position:0% +general property but maybe we shouldn't + + + align:start position:0% +general property but maybe we shouldn't +get too much into + + align:start position:0% + + + + align:start position:0% + +the so I wanted to there's a few more + + align:start position:0% +the so I wanted to there's a few more + + + align:start position:0% +the so I wanted to there's a few more +things I was hoping to do. So I also + + align:start position:0% +things I was hoping to do. So I also + + + align:start position:0% +things I was hoping to do. So I also +wanted to just talk about the + + align:start position:0% +wanted to just talk about the + + + align:start position:0% +wanted to just talk about the +Archimedian property again. And so I + + align:start position:0% +Archimedian property again. And so I + + + align:start position:0% +Archimedian property again. And so I +wanted to again you know just outline + + align:start position:0% + + + + align:start position:0% + +uh how to write a formal proof and again + + align:start position:0% +uh how to write a formal proof and again + + + align:start position:0% +uh how to write a formal proof and again +and the reason of course why I'm + + align:start position:0% +and the reason of course why I'm + + + align:start position:0% +and the reason of course why I'm +illustrating how to write a form the for + + align:start position:0% +illustrating how to write a form the for + + + align:start position:0% +illustrating how to write a form the for +the writing a formal proof is an + + align:start position:0% +the writing a formal proof is an + + + align:start position:0% +the writing a formal proof is an +important part of this class + + align:start position:0% +important part of this class + + + align:start position:0% +important part of this class +and and I'm obviously uh using the syncs + + align:start position:0% +and and I'm obviously uh using the syncs + + + align:start position:0% +and and I'm obviously uh using the syncs +that we already proved last time just so + + align:start position:0% +that we already proved last time just so + + + align:start position:0% +that we already proved last time just so +so that you can kind of focus on how to + + align:start position:0% +so that you can kind of focus on how to + + + align:start position:0% +so that you can kind of focus on how to +not not the proof not the statements why + + align:start position:0% +not not the proof not the statements why + + + align:start position:0% +not not the proof not the statements why +the statement should be true but just + + align:start position:0% +the statement should be true but just + + + align:start position:0% +the statement should be true but just +how to write it. Um and so let's + + align:start position:0% + + + + align:start position:0% + +let's talk about the Archimedian + + align:start position:0% +let's talk about the Archimedian + + + align:start position:0% +let's talk about the Archimedian +property + + align:start position:0% + + + + align:start position:0% + +and so the Archimedian property just + + align:start position:0% +and so the Archimedian property just + + + align:start position:0% +and so the Archimedian property just +saying that so this is the theorem + + align:start position:0% +saying that so this is the theorem + + + align:start position:0% +saying that so this is the theorem +that the natural numbers + + align:start position:0% +that the natural numbers + + + align:start position:0% +that the natural numbers +is not bounded from above. Right? + + align:start position:0% + + + + align:start position:0% + +That's one way of formulating it. Right? + + align:start position:0% +That's one way of formulating it. Right? + + + align:start position:0% +That's one way of formulating it. Right? +You could also say like we did last time + + align:start position:0% +You could also say like we did last time + + + align:start position:0% +You could also say like we did last time +that whenever you take a real there's a + + align:start position:0% +that whenever you take a real there's a + + + align:start position:0% +that whenever you take a real there's a +larger uh natural number than that real, + + align:start position:0% +larger uh natural number than that real, + + + align:start position:0% +larger uh natural number than that real, +right? This but that's the same. + + align:start position:0% +right? This but that's the same. + + + align:start position:0% +right? This but that's the same. +Okay. So now how do we prove this? + + align:start position:0% + + + + align:start position:0% + +So again here we're thinking about + + align:start position:0% +So again here we're thinking about + + + align:start position:0% +So again here we're thinking about +things as being subset of R. We always + + align:start position:0% +things as being subset of R. We always + + + align:start position:0% +things as being subset of R. We always +you know when when we don't really + + align:start position:0% +you know when when we don't really + + + align:start position:0% +you know when when we don't really +mention it then we always think about it + + align:start position:0% +mention it then we always think about it + + + align:start position:0% +mention it then we always think about it +as being subset of R. + + align:start position:0% +as being subset of R. + + + align:start position:0% +as being subset of R. +And so we uh we pro we will show this by + + align:start position:0% +And so we uh we pro we will show this by + + + align:start position:0% +And so we uh we pro we will show this by +contradiction. + + align:start position:0% + + + + align:start position:0% + +by contradiction. + + align:start position:0% + + + + align:start position:0% + +So suppose + + align:start position:0% + + + + align:start position:0% + +alpha is an upper bound + + align:start position:0% + + + + align:start position:0% + +for the natural numbers. + + align:start position:0% + + + + align:start position:0% + +Well, uh we can assume + + align:start position:0% +Well, uh we can assume + + + align:start position:0% +Well, uh we can assume +after replacing + + align:start position:0% + + + + align:start position:0% + +uh alpha by by soup of a. We can assume + + align:start position:0% + + + + align:start position:0% + +that alpha + + align:start position:0% +that alpha + + + align:start position:0% +that alpha +is the least up about + + align:start position:0% + + + + align:start position:0% + +Right. So, and now uh and and then then + + align:start position:0% +Right. So, and now uh and and then then + + + align:start position:0% +Right. So, and now uh and and then then +I think it's nice again uh to to write + + align:start position:0% +I think it's nice again uh to to write + + + align:start position:0% +I think it's nice again uh to to write +where the contradiction is coming from. + + align:start position:0% +where the contradiction is coming from. + + + align:start position:0% +where the contradiction is coming from. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +so + + align:start position:0% + + + + align:start position:0% + +we'll show + + align:start position:0% + + + + align:start position:0% + +We will get the desired contradiction + + align:start position:0% + + + + align:start position:0% + +by showing + + align:start position:0% + + + + align:start position:0% + +that's uh that that's alpha minus one + + align:start position:0% +that's uh that that's alpha minus one + + + align:start position:0% +that's uh that that's alpha minus one +is also + + align:start position:0% +is also + + + align:start position:0% +is also +an upper bound + + align:start position:0% + + + + align:start position:0% + +contradicting + + align:start position:0% + + + + align:start position:0% + +that alpha was the least of + + align:start position:0% + + + + align:start position:0% + +okay and So now uh since + + align:start position:0% + + + + align:start position:0% + +since uh alpha so so so this is what we + + align:start position:0% +since uh alpha so so so this is what we + + + align:start position:0% +since uh alpha so so so this is what we +want to prove that and since + + align:start position:0% +want to prove that and since + + + align:start position:0% +want to prove that and since +alpha is an upper bound + + align:start position:0% + + + + align:start position:0% + +for all + + align:start position:0% +for all + + + align:start position:0% +for all +natural numbers. + + align:start position:0% + + + + align:start position:0% + +Uh if you add one to the natural number, + + align:start position:0% +Uh if you add one to the natural number, + + + align:start position:0% +Uh if you add one to the natural number, +this is also this here is also a natural + + align:start position:0% +this is also this here is also a natural + + + align:start position:0% +this is also this here is also a natural +number, right? N + one is also a natural + + align:start position:0% +number, right? N + one is also a natural + + + align:start position:0% +number, right? N + one is also a natural +number. So n + one must be lesser equal + + align:start position:0% +number. So n + one must be lesser equal + + + align:start position:0% +number. So n + one must be lesser equal +to this upper bound, right? + + align:start position:0% +to this upper bound, right? + + + align:start position:0% +to this upper bound, right? +But this implies + + align:start position:0% + + + + align:start position:0% + +that n subtracting one on both side + + align:start position:0% +that n subtracting one on both side + + + align:start position:0% +that n subtracting one on both side +implies that n is less or equal to alpha + + align:start position:0% +implies that n is less or equal to alpha + + + align:start position:0% +implies that n is less or equal to alpha +minus one. And this which holds for all + + align:start position:0% +minus one. And this which holds for all + + + align:start position:0% +minus one. And this which holds for all +n + + align:start position:0% + + + + align:start position:0% + +are all natural numbers. So, + + align:start position:0% +are all natural numbers. So, + + + align:start position:0% +are all natural numbers. So, +alpha minus one is also an upper one. + + align:start position:0% + + + + align:start position:0% + +Okay. And that's and this is this is the + + align:start position:0% +Okay. And that's and this is this is the + + + align:start position:0% +Okay. And that's and this is this is the +right this this proof gives you this the + + align:start position:0% +right this this proof gives you this the + + + align:start position:0% +right this this proof gives you this the +side contradiction. + + align:start position:0% +side contradiction. + + + align:start position:0% +side contradiction. +Okay. So that's how you would write + + align:start position:0% +Okay. So that's how you would write + + + align:start position:0% +Okay. So that's how you would write +that. + + align:start position:0% +that. + + + align:start position:0% +that. +Let me um talk a little bit about + + align:start position:0% +Let me um talk a little bit about + + + align:start position:0% +Let me um talk a little bit about +sequences and we so this will be a big + + align:start position:0% +sequences and we so this will be a big + + + align:start position:0% +sequences and we so this will be a big +topic. Uh so sequences + + align:start position:0% + + + + align:start position:0% + +so well first so we talked about that a + + align:start position:0% +so well first so we talked about that a + + + align:start position:0% +so well first so we talked about that a +little bit. So if you look at at the So + + align:start position:0% +little bit. So if you look at at the So + + + align:start position:0% +little bit. So if you look at at the So +how do we think about + + align:start position:0% + + + + align:start position:0% + +of of square root two uh on the on the + + align:start position:0% +of of square root two uh on the on the + + + align:start position:0% +of of square root two uh on the on the +real line I mean so the way to think + + align:start position:0% +real line I mean so the way to think + + + align:start position:0% +real line I mean so the way to think +about square root of two is what we did + + align:start position:0% +about square root of two is what we did + + + align:start position:0% +about square root of two is what we did +here that it's this positive thing so + + align:start position:0% +here that it's this positive thing so + + + align:start position:0% +here that it's this positive thing so +that the square is two right but if you + + align:start position:0% +that the square is two right but if you + + + align:start position:0% +that the square is two right but if you +want to place two on the real line + + align:start position:0% +want to place two on the real line + + + align:start position:0% +want to place two on the real line +then uh you could sing about it as one + + align:start position:0% +then uh you could sing about it as one + + + align:start position:0% +then uh you could sing about it as one +as a limit of a sequence. If you take + + align:start position:0% +as a limit of a sequence. If you take + + + align:start position:0% +as a limit of a sequence. If you take +one and then the one is less than 1.4 + + align:start position:0% +one and then the one is less than 1.4 + + + align:start position:0% +one and then the one is less than 1.4 +which is less than 1.4 + + align:start position:0% +which is less than 1.4 + + + align:start position:0% +which is less than 1.4 +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +one + + align:start position:0% +one + + + align:start position:0% +one +which is less than 1.414 + + align:start position:0% +which is less than 1.414 + + + align:start position:0% +which is less than 1.414 +etc. + + align:start position:0% +etc. + + + align:start position:0% +etc. +Right? And so this here is a + + align:start position:0% +Right? And so this here is a + + + align:start position:0% +Right? And so this here is a +sequence. I'll be make that precise in + + align:start position:0% +sequence. I'll be make that precise in + + + align:start position:0% +sequence. I'll be make that precise in +just a minute. But it's a an increasing + + align:start position:0% +just a minute. But it's a an increasing + + + align:start position:0% +just a minute. But it's a an increasing +sequence of numbers. And the limit the + + align:start position:0% +sequence of numbers. And the limit the + + + align:start position:0% +sequence of numbers. And the limit the +limit is square<unk>2. Right? So if you + + align:start position:0% +limit is square<unk>2. Right? So if you + + + align:start position:0% +limit is square<unk>2. Right? So if you +plug it two in on the calculator, it + + align:start position:0% +plug it two in on the calculator, it + + + align:start position:0% +plug it two in on the calculator, it +will bring out a lot of digits, right? + + align:start position:0% +will bring out a lot of digits, right? + + + align:start position:0% +will bring out a lot of digits, right? +And these are the first digits and it + + align:start position:0% +And these are the first digits and it + + + align:start position:0% +And these are the first digits and it +will continue on. And that's how you + + align:start position:0% +will continue on. And that's how you + + + align:start position:0% +will continue on. And that's how you +think about uh square root of two. If + + align:start position:0% +think about uh square root of two. If + + + align:start position:0% +think about uh square root of two. If +you want to think about it on the real + + align:start position:0% +you want to think about it on the real + + + align:start position:0% +you want to think about it on the real +line + + align:start position:0% +line + + + align:start position:0% +line +and so we want to and so square two is + + align:start position:0% +and so we want to and so square two is + + + align:start position:0% +and so we want to and so square two is +going to be the limit of these and we + + align:start position:0% +going to be the limit of these and we + + + align:start position:0% +going to be the limit of these and we +need to make this precise and we also + + align:start position:0% +need to make this precise and we also + + + align:start position:0% +need to make this precise and we also +need to make precise what really a + + align:start position:0% +need to make precise what really a + + + align:start position:0% +need to make precise what really a +sequence is. + + align:start position:0% +sequence is. + + + align:start position:0% +sequence is. +So a sequence + + align:start position:0% + + + + align:start position:0% + +so a sequence + + align:start position:0% + + + + align:start position:0% + +of real numbers. + + align:start position:0% + + + + align:start position:0% + +This is a map. + + align:start position:0% +This is a map. + + + align:start position:0% +This is a map. +It's a function from the natural numbers + + align:start position:0% +It's a function from the natural numbers + + + align:start position:0% +It's a function from the natural numbers +into R. + + align:start position:0% +into R. + + + align:start position:0% +into R. +So for each natural number you get a + + align:start position:0% +So for each natural number you get a + + + align:start position:0% +So for each natural number you get a +real number and and so right so a + + align:start position:0% +real number and and so right so a + + + align:start position:0% +real number and and so right so a +function + + align:start position:0% +function + + + align:start position:0% +function +it is you know a function is is defined + + align:start position:0% +it is you know a function is is defined + + + align:start position:0% +it is you know a function is is defined +by the value at different points. So + + align:start position:0% +by the value at different points. So + + + align:start position:0% +by the value at different points. So +this thing here but if it but if you + + align:start position:0% +this thing here but if it but if you + + + align:start position:0% +this thing here but if it but if you +want to think about it as a sequence + + align:start position:0% +want to think about it as a sequence + + + align:start position:0% +want to think about it as a sequence +then it's common to denote it to denote + + align:start position:0% +then it's common to denote it to denote + + + align:start position:0% +then it's common to denote it to denote +this here like that. So this is how one + + align:start position:0% +this here like that. So this is how one + + + align:start position:0% +this here like that. So this is how one +typically write a sequence where instead + + align:start position:0% +typically write a sequence where instead + + + align:start position:0% +typically write a sequence where instead +of the you know what the the argument is + + align:start position:0% +of the you know what the the argument is + + + align:start position:0% +of the you know what the the argument is +this what what this is inside a bracket + + align:start position:0% +this what what this is inside a bracket + + + align:start position:0% +this what what this is inside a bracket +you write it as a subscript. Okay. + + align:start position:0% +you write it as a subscript. Okay. + + + align:start position:0% +you write it as a subscript. Okay. +So this is a sequence + + align:start position:0% +So this is a sequence + + + align:start position:0% +So this is a sequence +and so uh and so in in the case over + + align:start position:0% +and so uh and so in in the case over + + + align:start position:0% +and so uh and so in in the case over +there if you're thinking about a1 say to + + align:start position:0% +there if you're thinking about a1 say to + + + align:start position:0% +there if you're thinking about a1 say to +be equal to 1 a2 to be equal to 1.4 4 83 + + align:start position:0% +be equal to 1 a2 to be equal to 1.4 4 83 + + + align:start position:0% +be equal to 1 a2 to be equal to 1.4 4 83 +and now I'm thinking about the sequence + + align:start position:0% +and now I'm thinking about the sequence + + + align:start position:0% +and now I'm thinking about the sequence +here as I'm thinking about square root + + align:start position:0% +here as I'm thinking about square root + + + align:start position:0% +here as I'm thinking about square root +of two and I take the number of you know + + align:start position:0% +of two and I take the number of you know + + + align:start position:0% +of two and I take the number of you know +the subscript here I'm just taking the + + align:start position:0% +the subscript here I'm just taking the + + + align:start position:0% +the subscript here I'm just taking the +number of digits in square root two so + + align:start position:0% +number of digits in square root two so + + + align:start position:0% +number of digits in square root two so +now I need three digits here I needed + + align:start position:0% +now I need three digits here I needed + + + align:start position:0% +now I need three digits here I needed +two one 41 + + align:start position:0% +two one 41 + + + align:start position:0% +two one 41 +a4 is 1.414 4 1 4 etc. Right? And so + + align:start position:0% +a4 is 1.414 4 1 4 etc. Right? And so + + + align:start position:0% +a4 is 1.414 4 1 4 etc. Right? And so +so then you have so then a n here is a + + align:start position:0% +so then you have so then a n here is a + + + align:start position:0% +so then you have so then a n here is a +sequence + + align:start position:0% + + + + align:start position:0% + +of real numbers + + align:start position:0% +of real numbers + + + align:start position:0% +of real numbers +and it's actually increasing that the + + align:start position:0% +and it's actually increasing that the + + + align:start position:0% +and it's actually increasing that the +sequence a n is less than a n + one. we + + align:start position:0% +sequence a n is less than a n + one. we + + + align:start position:0% +sequence a n is less than a n + one. we +have this property + + align:start position:0% +have this property + + + align:start position:0% +have this property +and uh and we want to talk about next + + align:start position:0% +and uh and we want to talk about next + + + align:start position:0% +and uh and we want to talk about next +time we want to talk about uh uh what + + align:start position:0% +time we want to talk about uh uh what + + + align:start position:0% +time we want to talk about uh uh what +does a limit mean? + + align:start position:0% +does a limit mean? + + + align:start position:0% +does a limit mean? +What is a limit? + + align:start position:0% + + + + align:start position:0% + +And and so uh square root of two indeed + + align:start position:0% +And and so uh square root of two indeed + + + align:start position:0% +And and so uh square root of two indeed +will be the limit of this sequence and + + align:start position:0% +will be the limit of this sequence and + + + align:start position:0% +will be the limit of this sequence and +the limit you write like this sometimes + + align:start position:0% +the limit you write like this sometimes + + + align:start position:0% +the limit you write like this sometimes +as n goes to infinity of a n. + + align:start position:0% +as n goes to infinity of a n. + + + align:start position:0% +as n goes to infinity of a n. +But we'll talk about this next time. + + align:start position:0% +But we'll talk about this next time. + + + align:start position:0% +But we'll talk about this next time. +Okay. \ No newline at end of file diff --git a/QORX1OUabio.txt b/QORX1OUabio.txt new file mode 100644 index 0000000000000000000000000000000000000000..e86c45dfdf0e3624148d50815ce432c959d3ada2 --- /dev/null +++ b/QORX1OUabio.txt @@ -0,0 +1,1139 @@ +align:start position:0% + +the topic for this video lecture is + + align:start position:0% +the topic for this video lecture is + + + align:start position:0% +the topic for this video lecture is +connected vertices the kind of + + align:start position:0% +connected vertices the kind of + + + align:start position:0% +connected vertices the kind of +connections we can have between + + align:start position:0% +connections we can have between + + + align:start position:0% +connections we can have between +different vertices edges so we're gonna + + align:start position:0% +different vertices edges so we're gonna + + + align:start position:0% +different vertices edges so we're gonna +start by showing that the shortest walk + + align:start position:0% +start by showing that the shortest walk + + + align:start position:0% +start by showing that the shortest walk +between two vertices is a path now we're + + align:start position:0% +between two vertices is a path now we're + + + align:start position:0% +between two vertices is a path now we're +going to prove it by contradiction so + + align:start position:0% +going to prove it by contradiction so + + + align:start position:0% +going to prove it by contradiction so +suppose we have some path from u to B + + align:start position:0% +suppose we have some path from u to B + + + align:start position:0% +suppose we have some path from u to B +and it crosses over itself right so here + + align:start position:0% +and it crosses over itself right so here + + + align:start position:0% +and it crosses over itself right so here +we have U and V and at some point you + + align:start position:0% +we have U and V and at some point you + + + align:start position:0% +we have U and V and at some point you +know you get to C then you go back to C + + align:start position:0% +know you get to C then you go back to C + + + align:start position:0% +know you get to C then you go back to C +and from there you go to V right so + + align:start position:0% +and from there you go to V right so + + + align:start position:0% +and from there you go to V right so +you've gone through the Vord some virtus + + align:start position:0% +you've gone through the Vord some virtus + + + align:start position:0% +you've gone through the Vord some virtus +C twice but if you want to get the + + align:start position:0% +C twice but if you want to get the + + + align:start position:0% +C twice but if you want to get the +shortest path from u to V why would you + + align:start position:0% +shortest path from u to V why would you + + + align:start position:0% +shortest path from u to V why would you +go through this loop why not just keep + + align:start position:0% +go through this loop why not just keep + + + align:start position:0% +go through this loop why not just keep +going straight from C to B so the path + + align:start position:0% +going straight from C to B so the path + + + align:start position:0% +going straight from C to B so the path +with that you know that section that + + align:start position:0% +with that you know that section that + + + align:start position:0% +with that you know that section that +goes from C back to itself also goes + + align:start position:0% +goes from C back to itself also goes + + + align:start position:0% +goes from C back to itself also goes +from u to be and is shorter so if we + + align:start position:0% +from u to be and is shorter so if we + + + align:start position:0% +from u to be and is shorter so if we +have any path that crosses over itself + + align:start position:0% +have any path that crosses over itself + + + align:start position:0% +have any path that crosses over itself +we can just get rid of that part that + + align:start position:0% +we can just get rid of that part that + + + align:start position:0% +we can just get rid of that part that +loops around back into itself and we + + align:start position:0% +loops around back into itself and we + + + align:start position:0% +loops around back into itself and we +still have a a walk from u to V so + + align:start position:0% +still have a a walk from u to V so + + + align:start position:0% +still have a a walk from u to V so +therefore the shortest walk we need to + + align:start position:0% +therefore the shortest walk we need to + + + align:start position:0% +therefore the shortest walk we need to +be is going to be a path so now we're + + align:start position:0% +be is going to be a path so now we're + + + align:start position:0% +be is going to be a path so now we're +going to talk about the length n walk + + align:start position:0% +going to talk about the length n walk + + + align:start position:0% +going to talk about the length n walk +relation what this means is with two + + align:start position:0% +relation what this means is with two + + + align:start position:0% +relation what this means is with two +vertices V and W there is this GN + + align:start position:0% +vertices V and W there is this GN + + + align:start position:0% +vertices V and W there is this GN +relation between V and W if there is + + align:start position:0% +relation between V and W if there is + + + align:start position:0% +relation between V and W if there is +there exists a length and walk from V to + + align:start position:0% +there exists a length and walk from V to + + + align:start position:0% +there exists a length and walk from V to +W and GN is called the length n walk + + align:start position:0% +W and GN is called the length n walk + + + align:start position:0% +W and GN is called the length n walk +relation for G so basically if you can + + align:start position:0% +relation for G so basically if you can + + + align:start position:0% +relation for G so basically if you can +find a way to go from V to W in exactly + + align:start position:0% +find a way to go from V to W in exactly + + + align:start position:0% +find a way to go from V to W in exactly +n steps then GN applies from V to W and + + align:start position:0% +n steps then GN applies from V to W and + + + align:start position:0% +n steps then GN applies from V to W and +G itself when you think about it is the + + align:start position:0% +G itself when you think about it is the + + + align:start position:0% +G itself when you think about it is the +length one walk walk relation you know + + align:start position:0% +length one walk walk relation you know + + + align:start position:0% +length one walk walk relation you know +the graphs define these relations and + + align:start position:0% +the graphs define these relations and + + + align:start position:0% +the graphs define these relations and +there's an edge from one virtus to + + align:start position:0% +there's an edge from one virtus to + + + align:start position:0% +there's an edge from one virtus to +another if there's if there's a length + + align:start position:0% +another if there's if there's a length + + + align:start position:0% +another if there's if there's a length +of one edge from one vertex to another + + align:start position:0% +of one edge from one vertex to another + + + align:start position:0% +of one edge from one vertex to another +you know it is it's tough now this lemma + + align:start position:0% +you know it is it's tough now this lemma + + + align:start position:0% +you know it is it's tough now this lemma +right we say that GM and relational + + align:start position:0% +right we say that GM and relational + + + align:start position:0% +right we say that GM and relational +composition with GN equals G M plus n + + align:start position:0% +composition with GN equals G M plus n + + + align:start position:0% +composition with GN equals G M plus n +let's explain what this means so what + + align:start position:0% +let's explain what this means so what + + + align:start position:0% +let's explain what this means so what +that relational composition means is + + align:start position:0% +that relational composition means is + + + align:start position:0% +that relational composition means is +that that really the relational + + align:start position:0% +that that really the relational + + + align:start position:0% +that that really the relational +composition between the two applies from + + align:start position:0% +composition between the two applies from + + + align:start position:0% +composition between the two applies from +X to Y + + align:start position:0% +X to Y + + + align:start position:0% +X to Y +if there is some virtus Z such that + + align:start position:0% +if there is some virtus Z such that + + + align:start position:0% +if there is some virtus Z such that +there is a path M from X to Z and then a + + align:start position:0% +there is a path M from X to Z and then a + + + align:start position:0% +there is a path M from X to Z and then a +path ñ from Z to one right there's some + + align:start position:0% +path ñ from Z to one right there's some + + + align:start position:0% +path ñ from Z to one right there's some +GN replies from X to Z and GN applies + + align:start position:0% +GN replies from X to Z and GN applies + + + align:start position:0% +GN replies from X to Z and GN applies +from Z to Y and Y this is the same thing + + align:start position:0% +from Z to Y and Y this is the same thing + + + align:start position:0% +from Z to Y and Y this is the same thing +as G and plus in makes sense right if + + align:start position:0% +as G and plus in makes sense right if + + + align:start position:0% +as G and plus in makes sense right if +there's a path length m to Z and on the + + align:start position:0% +there's a path length m to Z and on the + + + align:start position:0% +there's a path length m to Z and on the +path left Glen's end from there to Y you + + align:start position:0% +path left Glen's end from there to Y you + + + align:start position:0% +path left Glen's end from there to Y you +just go from X to Z and M steps then Z 2 + + align:start position:0% +just go from X to Z and M steps then Z 2 + + + align:start position:0% +just go from X to Z and M steps then Z 2 +y n steps and you have n plus n steps + + align:start position:0% +y n steps and you have n plus n steps + + + align:start position:0% +y n steps and you have n plus n steps +from X to Y the length 0 walk relation + + align:start position:0% +from X to Y the length 0 walk relation + + + align:start position:0% +from X to Y the length 0 walk relation +just makes each virtus go back to itself + + align:start position:0% +just makes each virtus go back to itself + + + align:start position:0% +just makes each virtus go back to itself +like it points back to itself the + + align:start position:0% +like it points back to itself the + + + align:start position:0% +like it points back to itself the +individual one and the lemma still true + + align:start position:0% +individual one and the lemma still true + + + align:start position:0% +individual one and the lemma still true +you know G 0 composed with G n is just G + + align:start position:0% +you know G 0 composed with G n is just G + + + align:start position:0% +you know G 0 composed with G n is just G +n which makes sense you know everything + + align:start position:0% +n which makes sense you know everything + + + align:start position:0% +n which makes sense you know everything +itself plus GN just gives you G + + align:start position:0% + + + + align:start position:0% + +let's talk about composition of matrices + + align:start position:0% +let's talk about composition of matrices + + + align:start position:0% +let's talk about composition of matrices +so if we have some adjacency matrix for + + align:start position:0% +so if we have some adjacency matrix for + + + align:start position:0% +so if we have some adjacency matrix for +G then and we do a composition with some + + align:start position:0% +G then and we do a composition with some + + + align:start position:0% +G then and we do a composition with some +H then we can get that by applying this + + align:start position:0% +H then we can get that by applying this + + + align:start position:0% +H then we can get that by applying this +boolean and/or matrix multiplication you + + align:start position:0% +boolean and/or matrix multiplication you + + + align:start position:0% +boolean and/or matrix multiplication you +know these adjacency matrices are ones + + align:start position:0% +know these adjacency matrices are ones + + + align:start position:0% +know these adjacency matrices are ones +and zeros so we do matrix multiplication + + align:start position:0% +and zeros so we do matrix multiplication + + + align:start position:0% +and zeros so we do matrix multiplication +but with boolean operations instead of + + align:start position:0% +but with boolean operations instead of + + + align:start position:0% +but with boolean operations instead of +plusses and multiplications so we can + + align:start position:0% +plusses and multiplications so we can + + + align:start position:0% +plusses and multiplications so we can +compute a G of n by fast matrix + + align:start position:0% +compute a G of n by fast matrix + + + align:start position:0% +compute a G of n by fast matrix +exponentiation how do we do that well + + align:start position:0% +exponentiation how do we do that well + + + align:start position:0% +exponentiation how do we do that well +basically you can do it for G and over + + align:start position:0% +basically you can do it for G and over + + + align:start position:0% +basically you can do it for G and over +to twice and then GN over 4 for each of + + align:start position:0% +to twice and then GN over 4 for each of + + + align:start position:0% +to twice and then GN over 4 for each of +those twice and go doing those boolean + + align:start position:0% +those twice and go doing those boolean + + + align:start position:0% +those twice and go doing those boolean +operations on each right so a G of n + + align:start position:0% +operations on each right so a G of n + + + align:start position:0% +operations on each right so a G of n +equals a G of n over 2 applying this + + align:start position:0% +equals a G of n over 2 applying this + + + align:start position:0% +equals a G of n over 2 applying this +operator to a G n over 2 so you can just + + align:start position:0% +operator to a G n over 2 so you can just + + + align:start position:0% +operator to a G n over 2 so you can just +break it down into each time so we get + + align:start position:0% +break it down into each time so we get + + + align:start position:0% +break it down into each time so we get +logarithmic number of products that we + + align:start position:0% +logarithmic number of products that we + + + align:start position:0% +logarithmic number of products that we +have to do + + align:start position:0% + + + + align:start position:0% + +now let's define another relation g-star + + align:start position:0% +now let's define another relation g-star + + + align:start position:0% +now let's define another relation g-star +is just called the walk relation of G + + align:start position:0% +is just called the walk relation of G + + + align:start position:0% +is just called the walk relation of G +and basically you a G Star applies from + + align:start position:0% +and basically you a G Star applies from + + + align:start position:0% +and basically you a G Star applies from +u to V if there is a walk for me to be + + align:start position:0% +u to V if there is a walk for me to be + + + align:start position:0% +u to V if there is a walk for me to be +no matter how long it is if you can find + + align:start position:0% +no matter how long it is if you can find + + + align:start position:0% +no matter how long it is if you can find +some way to get from u to B then in a + + align:start position:0% +some way to get from u to B then in a + + + align:start position:0% +some way to get from u to B then in a +but if we want to get the walk relation + + align:start position:0% +but if we want to get the walk relation + + + align:start position:0% +but if we want to get the walk relation +you just get everything inside the the + + align:start position:0% +you just get everything inside the the + + + align:start position:0% +you just get everything inside the the +graph and apply self-loop so make every + + align:start position:0% +graph and apply self-loop so make every + + + align:start position:0% +graph and apply self-loop so make every +ad in a edge that points back to itself + + align:start position:0% +ad in a edge that points back to itself + + + align:start position:0% +ad in a edge that points back to itself +for every virtus and we call this G less + + align:start position:0% +for every virtus and we call this G less + + + align:start position:0% +for every virtus and we call this G less +than or equal to and it's basically G + + align:start position:0% +than or equal to and it's basically G + + + align:start position:0% +than or equal to and it's basically G +and then add in these G 0 self birds + + align:start position:0% +and then add in these G 0 self birds + + + align:start position:0% +and then add in these G 0 self birds +self edges and G less than equal to has + + align:start position:0% +self edges and G less than equal to has + + + align:start position:0% +self edges and G less than equal to has +a length and walk if G has a less than + + align:start position:0% +a length and walk if G has a less than + + + align:start position:0% +a length and walk if G has a less than +or equal to n1 now think about that if I + + align:start position:0% +or equal to n1 now think about that if I + + + align:start position:0% +or equal to n1 now think about that if I +can get from virtus x2 virtus y in n + + align:start position:0% +can get from virtus x2 virtus y in n + + + align:start position:0% +can get from virtus x2 virtus y in n +minus 1 or n minus some amount of steps + + align:start position:0% +minus 1 or n minus some amount of steps + + + align:start position:0% +minus 1 or n minus some amount of steps +in G then I can get there in n steps in + + align:start position:0% +in G then I can get there in n steps in + + + align:start position:0% +in G then I can get there in n steps in +G less than or equal to because I can + + align:start position:0% +G less than or equal to because I can + + + align:start position:0% +G less than or equal to because I can +just loop around right if I want to get + + align:start position:0% +just loop around right if I want to get + + + align:start position:0% +just loop around right if I want to get +here from red to blue right I can get + + align:start position:0% +here from red to blue right I can get + + + align:start position:0% +here from red to blue right I can get +there in one step without those self + + align:start position:0% +there in one step without those self + + + align:start position:0% +there in one step without those self +loops but with the self loops I can just + + align:start position:0% +loops but with the self loops I can just + + + align:start position:0% +loops but with the self loops I can just +keep starting from red go around to read + + align:start position:0% +keep starting from red go around to read + + + align:start position:0% +keep starting from red go around to read +as many times as I want n minus 1 times + + align:start position:0% +as many times as I want n minus 1 times + + + align:start position:0% +as many times as I want n minus 1 times +and then do this final step so I can + + align:start position:0% +and then do this final step so I can + + + align:start position:0% +and then do this final step so I can +make it make a n length and walk for any + + align:start position:0% +make it make a n length and walk for any + + + align:start position:0% +make it make a n length and walk for any +value of N greater than me now let's + + align:start position:0% +value of N greater than me now let's + + + align:start position:0% +value of N greater than me now let's +compute the walk relation using what + + align:start position:0% +compute the walk relation using what + + + align:start position:0% +compute the walk relation using what +we've just defined so G has n vertices + + align:start position:0% +we've just defined so G has n vertices + + + align:start position:0% +we've just defined so G has n vertices +so the length of path are gonna be less + + align:start position:0% +so the length of path are gonna be less + + + align:start position:0% +so the length of path are gonna be less +than or equal to n right if you go if we + + align:start position:0% +than or equal to n right if you go if we + + + align:start position:0% +than or equal to n right if you go if we +just go in a straight line from one + + align:start position:0% +just go in a straight line from one + + + align:start position:0% +just go in a straight line from one +thing to another passing through each + + align:start position:0% +thing to another passing through each + + + align:start position:0% +thing to another passing through each +possible produce at most you're gonna + + align:start position:0% +possible produce at most you're gonna + + + align:start position:0% +possible produce at most you're gonna +get n minus 1 length right because + + align:start position:0% +get n minus 1 length right because + + + align:start position:0% +get n minus 1 length right because +you're gonna pass through n vertices so + + align:start position:0% +you're gonna pass through n vertices so + + + align:start position:0% +you're gonna pass through n vertices so +there's n minus 1 edges connected so G + + align:start position:0% +there's n minus 1 edges connected so G + + + align:start position:0% +there's n minus 1 edges connected so G +star which is just the relation if there + + align:start position:0% +star which is just the relation if there + + + align:start position:0% +star which is just the relation if there +is a walk from you to B is going to be + + align:start position:0% +is a walk from you to B is going to be + + + align:start position:0% +is a walk from you to B is going to be +this G less than or equal to 2 the N + + align:start position:0% +this G less than or equal to 2 the N + + + align:start position:0% +this G less than or equal to 2 the N +minus 1 so if we get G less than or + + align:start position:0% +minus 1 so if we get G less than or + + + align:start position:0% +minus 1 so if we get G less than or +equal to add in all these self loops and + + align:start position:0% +equal to add in all these self loops and + + + align:start position:0% +equal to add in all these self loops and +then find all the paths of length + + align:start position:0% +then find all the paths of length + + + align:start position:0% +then find all the paths of length +this one in there which is basically all + + align:start position:0% +this one in there which is basically all + + + align:start position:0% +this one in there which is basically all +paths and a G Star and G less than equal + + align:start position:0% +paths and a G Star and G less than equal + + + align:start position:0% +paths and a G Star and G less than equal +to n minus 1 is all path less than or + + align:start position:0% +to n minus 1 is all path less than or + + + align:start position:0% +to n minus 1 is all path less than or +equal to n minus 1 but since G only has + + align:start position:0% +equal to n minus 1 but since G only has + + + align:start position:0% +equal to n minus 1 but since G only has +passed of less than or equal to n minus + + align:start position:0% +passed of less than or equal to n minus + + + align:start position:0% +passed of less than or equal to n minus +1 that's just all the pads it's just + + align:start position:0% +1 that's just all the pads it's just + + + align:start position:0% +1 that's just all the pads it's just +every single one of the verse and so + + align:start position:0% +every single one of the verse and so + + + align:start position:0% +every single one of the verse and so +we've defined G Star and that's how we + + align:start position:0% +we've defined G Star and that's how we + + + align:start position:0% +we've defined G Star and that's how we +get all connected bird espares and we + + align:start position:0% +get all connected bird espares and we + + + align:start position:0% +get all connected bird espares and we +can do this in n squared log n time + + align:start position:0% +can do this in n squared log n time + + + align:start position:0% +can do this in n squared log n time +using that composition of the Jason C + + align:start position:0% +using that composition of the Jason C + + + align:start position:0% +using that composition of the Jason C +matrices \ No newline at end of file diff --git a/QaOHeMnpnmU.txt b/QaOHeMnpnmU.txt new file mode 100644 index 0000000000000000000000000000000000000000..3e032872cf588f9f631ce9da557a28468bf5b5d0 --- /dev/null +++ b/QaOHeMnpnmU.txt @@ -0,0 +1,495 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so here's um here's some + + align:start position:0% +ocw.mit.edu so here's um here's some + + + align:start position:0% +ocw.mit.edu so here's um here's some +code I'm defining a function function + + align:start position:0% +code I'm defining a function function + + + align:start position:0% +code I'm defining a function function +named SQ + + align:start position:0% +named SQ + + + align:start position:0% +named SQ +and it takes in two + + align:start position:0% +and it takes in two + + + align:start position:0% +and it takes in two +parameters I'm defining a function named + + align:start position:0% +parameters I'm defining a function named + + + align:start position:0% +parameters I'm defining a function named +F takes in one parameter and then I'm + + align:start position:0% +F takes in one parameter and then I'm + + + align:start position:0% +F takes in one parameter and then I'm +doing these two lines the first one is + + align:start position:0% +doing these two lines the first one is + + + align:start position:0% +doing these two lines the first one is +just calling function + + align:start position:0% +just calling function + + + align:start position:0% +just calling function +SQ and the next one is just printing the + + align:start position:0% + + + + align:start position:0% + +value so let's first + + align:start position:0% +value so let's first + + + align:start position:0% +value so let's first +see what uh nice + + align:start position:0% +see what uh nice + + + align:start position:0% +see what uh nice +okay uh let's work through it + + align:start position:0% + + + + align:start position:0% + +so the first things we see here is two + + align:start position:0% +so the first things we see here is two + + + align:start position:0% +so the first things we see here is two +function definitions right so we don't + + align:start position:0% +function definitions right so we don't + + + align:start position:0% +function definitions right so we don't +currently care about what's inside them + + align:start position:0% +currently care about what's inside them + + + align:start position:0% +currently care about what's inside them +right now because we haven't made a + + align:start position:0% +right now because we haven't made a + + + align:start position:0% +right now because we haven't made a +function call yet so the first thing we + + align:start position:0% +function call yet so the first thing we + + + align:start position:0% +function call yet so the first thing we +do is we have the function call calc + + align:start position:0% +do is we have the function call calc + + + align:start position:0% +do is we have the function call calc +equal SQ F and 2 okay so inside + + align:start position:0% +equal SQ F and 2 okay so inside + + + align:start position:0% +equal SQ F and 2 okay so inside +SQ we're going to have + + align:start position:0% +SQ we're going to have + + + align:start position:0% +SQ we're going to have +Funk and X + + align:start position:0% + + + + align:start position:0% + +and Funk is going to get mapped to F and + + align:start position:0% +and Funk is going to get mapped to F and + + + align:start position:0% +and Funk is going to get mapped to F and +X is going to get mapped to two right + + align:start position:0% +X is going to get mapped to two right + + + align:start position:0% +X is going to get mapped to two right +because we're taking the variables in + + align:start position:0% +because we're taking the variables in + + + align:start position:0% +because we're taking the variables in +order and mapping them to those so f is + + align:start position:0% +order and mapping them to those so f is + + + align:start position:0% +order and mapping them to those so f is +Funk is f and X is + + align:start position:0% +Funk is f and X is + + + align:start position:0% +Funk is f and X is +two first thing the function does s q is + + align:start position:0% +two first thing the function does s q is + + + align:start position:0% +two first thing the function does s q is +create this variable Y is equal to + + align:start position:0% +create this variable Y is equal to + + + align:start position:0% +create this variable Y is equal to +x^2 so we're going to have y is equal + + align:start position:0% +x^2 so we're going to have y is equal + + + align:start position:0% +x^2 so we're going to have y is equal +to + + align:start position:0% + + + + align:start position:0% + +4 and then we're going to return Funk + + align:start position:0% +4 and then we're going to return Funk + + + align:start position:0% +4 and then we're going to return Funk +y so Funk of Y this is going to be we're + + align:start position:0% +y so Funk of Y this is going to be we're + + + align:start position:0% +y so Funk of Y this is going to be we're +just replacing the parameters F of + + align:start position:0% +just replacing the parameters F of + + + align:start position:0% +just replacing the parameters F of + + align:start position:0% + + + align:start position:0% +right so now this is another function + + align:start position:0% +right so now this is another function + + + align:start position:0% +right so now this is another function +call we know what f is python this + + align:start position:0% +call we know what f is python this + + + align:start position:0% +call we know what f is python this +program knows what f is f is going to be + + align:start position:0% +program knows what f is f is going to be + + + align:start position:0% +program knows what f is f is going to be +this part right here which returns + + align:start position:0% +this part right here which returns + + + align:start position:0% +this part right here which returns +X2 okay so in + + align:start position:0% + + + + align:start position:0% + +f x gets mapped to whatever variable we + + align:start position:0% +f x gets mapped to whatever variable we + + + align:start position:0% +f x gets mapped to whatever variable we +put in which in this case is + + align:start position:0% + + + + align:start position:0% + +four and we're going to return to + + align:start position:0% +four and we're going to return to + + + align:start position:0% +four and we're going to return to +whoever called us which is over here 4^ + + align:start position:0% +whoever called us which is over here 4^ + + + align:start position:0% +whoever called us which is over here 4^ +squar which is + + align:start position:0% + + + + align:start position:0% + +16 okay so F of four gets replaced with + + align:start position:0% +16 okay so F of four gets replaced with + + + align:start position:0% +16 okay so F of four gets replaced with + + align:start position:0% + + + + align:start position:0% + +and F of four was up here right we're + + align:start position:0% +and F of four was up here right we're + + + align:start position:0% +and F of four was up here right we're +just popping out of Scopes now so F of + + align:start position:0% +just popping out of Scopes now so F of + + + align:start position:0% +just popping out of Scopes now so F of +four was up here so then this that line + + align:start position:0% +four was up here so then this that line + + + align:start position:0% +four was up here so then this that line +there return Funk Y is going to return + + align:start position:0% +there return Funk Y is going to return + + + align:start position:0% +there return Funk Y is going to return +16 and whoever called us was down here + + align:start position:0% +16 and whoever called us was down here + + + align:start position:0% +16 and whoever called us was down here +Cal is equal to 16 and then we're just + + align:start position:0% +Cal is equal to 16 and then we're just + + + align:start position:0% +Cal is equal to 16 and then we're just +printing + + align:start position:0% + + + + align:start position:0% + +Cal so 16 was right + + align:start position:0% +Cal so 16 was right + + + align:start position:0% +Cal so 16 was right +yay \ No newline at end of file diff --git a/QbueCxKUUTo.txt b/QbueCxKUUTo.txt new file mode 100644 index 0000000000000000000000000000000000000000..8d494a5bc0fba4ec9afc73c11e3528be9ebcf7d4 --- /dev/null +++ b/QbueCxKUUTo.txt @@ -0,0 +1,2563 @@ +align:start position:0% + +so while i've argued that there are many + + align:start position:0% +so while i've argued that there are many + + + align:start position:0% +so while i've argued that there are many +ways in which a room can become + + align:start position:0% +ways in which a room can become + + + align:start position:0% +ways in which a room can become +well mixed hopefully well enough to + + align:start position:0% +well mixed hopefully well enough to + + + align:start position:0% +well mixed hopefully well enough to +apply our + + align:start position:0% +apply our + + + align:start position:0% +apply our +well-mixed criterion for airborne + + align:start position:0% +well-mixed criterion for airborne + + + align:start position:0% +well-mixed criterion for airborne +transmission through long-range aerosols + + align:start position:0% +transmission through long-range aerosols + + + align:start position:0% +transmission through long-range aerosols +there is one very important way in which + + align:start position:0% +there is one very important way in which + + + align:start position:0% +there is one very important way in which +the transmission problem + + align:start position:0% +the transmission problem + + + align:start position:0% +the transmission problem +is never well mixed and that is taking + + align:start position:0% +is never well mixed and that is taking + + + align:start position:0% +is never well mixed and that is taking +into account the source of the particles + + align:start position:0% +into account the source of the particles + + + align:start position:0% +into account the source of the particles +which is the exhaling of an infected + + align:start position:0% +which is the exhaling of an infected + + + align:start position:0% +which is the exhaling of an infected +individual + + align:start position:0% +individual + + + align:start position:0% +individual +which leads to a very high concentration + + align:start position:0% +which leads to a very high concentration + + + align:start position:0% +which leads to a very high concentration +of particles leaving the mouth which + + align:start position:0% +of particles leaving the mouth which + + + align:start position:0% +of particles leaving the mouth which +then + + align:start position:0% +then + + + align:start position:0% +then +ends up being dispersed throughout the + + align:start position:0% +ends up being dispersed throughout the + + + align:start position:0% +ends up being dispersed throughout the +room and there is a sort of + + align:start position:0% +room and there is a sort of + + + align:start position:0% +room and there is a sort of +space and time dependence of that + + align:start position:0% +space and time dependence of that + + + align:start position:0% +space and time dependence of that +process which we must consider + + align:start position:0% +process which we must consider + + + align:start position:0% +process which we must consider +uh in looking at other possibilities of + + align:start position:0% +uh in looking at other possibilities of + + + align:start position:0% +uh in looking at other possibilities of +transmission than + + align:start position:0% +transmission than + + + align:start position:0% +transmission than +just the well-mixed background error + + align:start position:0% + + + + align:start position:0% + +so in particular the uh i've already + + align:start position:0% +so in particular the uh i've already + + + align:start position:0% +so in particular the uh i've already +indicated that the flows generated by + + align:start position:0% +indicated that the flows generated by + + + align:start position:0% +indicated that the flows generated by +breathing + + align:start position:0% +breathing + + + align:start position:0% +breathing +tend to be a higher enough reynolds + + align:start position:0% +tend to be a higher enough reynolds + + + align:start position:0% +tend to be a higher enough reynolds +number to generate turbulence + + align:start position:0% +number to generate turbulence + + + align:start position:0% +number to generate turbulence +and in particular they generate a + + align:start position:0% +and in particular they generate a + + + align:start position:0% +and in particular they generate a +turbulent + + align:start position:0% +turbulent + + + align:start position:0% +turbulent +uh jet which ends up taking the form of + + align:start position:0% +uh jet which ends up taking the form of + + + align:start position:0% +uh jet which ends up taking the form of +a cone + + align:start position:0% +a cone + + + align:start position:0% +a cone +not perfectly but approximately a cone + + align:start position:0% +not perfectly but approximately a cone + + + align:start position:0% +not perfectly but approximately a cone +which means that the radius of the jet + + align:start position:0% +which means that the radius of the jet + + + align:start position:0% +which means that the radius of the jet +is + + align:start position:0% +is + + + align:start position:0% +is +alpha times the + + align:start position:0% +alpha times the + + + align:start position:0% +alpha times the +position in the jet here so if i write a + + align:start position:0% +position in the jet here so if i write a + + + align:start position:0% +position in the jet here so if i write a +coordinate system + + align:start position:0% +coordinate system + + + align:start position:0% +coordinate system +you know which z a cylindrical + + align:start position:0% +you know which z a cylindrical + + + align:start position:0% +you know which z a cylindrical +coordinate system where z is the + + align:start position:0% +coordinate system where z is the + + + align:start position:0% +coordinate system where z is the +direction of the flow + + align:start position:0% +direction of the flow + + + align:start position:0% +direction of the flow +and r is the radial coordinate then + + align:start position:0% +and r is the radial coordinate then + + + align:start position:0% +and r is the radial coordinate then +that's the cone and the cone angle is + + align:start position:0% +that's the cone and the cone angle is + + + align:start position:0% +that's the cone and the cone angle is +alpha + + align:start position:0% +alpha + + + align:start position:0% +alpha +the term alpha also has a physical + + align:start position:0% +the term alpha also has a physical + + + align:start position:0% +the term alpha also has a physical +interpretation + + align:start position:0% +interpretation + + + align:start position:0% +interpretation +as the error entrainment coefficient + + align:start position:0% + + + + align:start position:0% + +and for respiratory jets in the air this + + align:start position:0% +and for respiratory jets in the air this + + + align:start position:0% +and for respiratory jets in the air this +coefficient is usually around 0.1 to + + align:start position:0% +coefficient is usually around 0.1 to + + + align:start position:0% +coefficient is usually around 0.1 to +0.15 + + align:start position:0% +0.15 + + + align:start position:0% +0.15 +so that gives you basically the opening + + align:start position:0% +so that gives you basically the opening + + + align:start position:0% +so that gives you basically the opening +angle of the + + align:start position:0% +angle of the + + + align:start position:0% +angle of the +of the cone so + + align:start position:0% +of the cone so + + + align:start position:0% +of the cone so +i will come come to explaining and + + align:start position:0% +i will come come to explaining and + + + align:start position:0% +i will come come to explaining and +deriving + + align:start position:0% +deriving + + + align:start position:0% +deriving +why the jet has the shape of a cone but + + align:start position:0% +why the jet has the shape of a cone but + + + align:start position:0% +why the jet has the shape of a cone but +let's just assume that + + align:start position:0% +let's just assume that + + + align:start position:0% +let's just assume that +and let's continue with the assumption + + align:start position:0% +and let's continue with the assumption + + + align:start position:0% +and let's continue with the assumption +that the flow is at high reynolds number + + align:start position:0% +that the flow is at high reynolds number + + + align:start position:0% +that the flow is at high reynolds number +which means it's dominated by inertia by + + align:start position:0% +which means it's dominated by inertia by + + + align:start position:0% +which means it's dominated by inertia by +kinetic energy + + align:start position:0% +kinetic energy + + + align:start position:0% +kinetic energy +and by the tendency for the fluid to + + align:start position:0% +and by the tendency for the fluid to + + + align:start position:0% +and by the tendency for the fluid to +keep wanting to move in a new direction + + align:start position:0% +keep wanting to move in a new direction + + + align:start position:0% +keep wanting to move in a new direction +now if the fluid coming out of the mouth + + align:start position:0% +now if the fluid coming out of the mouth + + + align:start position:0% +now if the fluid coming out of the mouth +we're just being spit out at a very high + + align:start position:0% +we're just being spit out at a very high + + + align:start position:0% +we're just being spit out at a very high +rate you might imagine a very narrow + + align:start position:0% +rate you might imagine a very narrow + + + align:start position:0% +rate you might imagine a very narrow +kind of uh you know stream of of air + + align:start position:0% +kind of uh you know stream of of air + + + align:start position:0% +kind of uh you know stream of of air +but the reason it's widening is that air + + align:start position:0% +but the reason it's widening is that air + + + align:start position:0% +but the reason it's widening is that air +is actually being entrained + + align:start position:0% +is actually being entrained + + + align:start position:0% +is actually being entrained +is that some of the ambient air is being + + align:start position:0% +is that some of the ambient air is being + + + align:start position:0% +is that some of the ambient air is being +sucked in + + align:start position:0% + + + + align:start position:0% + +and this is making the jet have more and + + align:start position:0% +and this is making the jet have more and + + + align:start position:0% +and this is making the jet have more and +more fluid in it + + align:start position:0% +more fluid in it + + + align:start position:0% +more fluid in it +but then that fluid is sharing the + + align:start position:0% +but then that fluid is sharing the + + + align:start position:0% +but then that fluid is sharing the +momentum it's also spreading and + + align:start position:0% +momentum it's also spreading and + + + align:start position:0% +momentum it's also spreading and +diffusing the particles + + align:start position:0% +diffusing the particles + + + align:start position:0% +diffusing the particles +and the wider it gets the more it slows + + align:start position:0% +and the wider it gets the more it slows + + + align:start position:0% +and the wider it gets the more it slows +down + + align:start position:0% +down + + + align:start position:0% +down +because now that momentum is being + + align:start position:0% +because now that momentum is being + + + align:start position:0% +because now that momentum is being +shared through the sort of turbulent + + align:start position:0% +shared through the sort of turbulent + + + align:start position:0% +shared through the sort of turbulent +uh exchange going on so we can let's do + + align:start position:0% +uh exchange going on so we can let's do + + + align:start position:0% +uh exchange going on so we can let's do +that calculation so we have + + align:start position:0% +that calculation so we have + + + align:start position:0% +that calculation so we have +um so just remind you that we are in a + + align:start position:0% +um so just remind you that we are in a + + + align:start position:0% +um so just remind you that we are in a +situation + + align:start position:0% +situation + + + align:start position:0% +situation +of very high reynolds number typically + + align:start position:0% +of very high reynolds number typically + + + align:start position:0% +of very high reynolds number typically +and we will assume + + align:start position:0% +and we will assume + + + align:start position:0% +and we will assume +that there is roughly + + align:start position:0% + + + + align:start position:0% + +and it's actually a good assumption + + align:start position:0% +and it's actually a good assumption + + + align:start position:0% +and it's actually a good assumption +roughly a constant + + align:start position:0% +roughly a constant + + + align:start position:0% +roughly a constant +momentum flux + + align:start position:0% + + + + align:start position:0% + +what that means if i take a slice here + + align:start position:0% +what that means if i take a slice here + + + align:start position:0% +what that means if i take a slice here +and i look at essentially the kinetic + + align:start position:0% +and i look at essentially the kinetic + + + align:start position:0% +and i look at essentially the kinetic +energy density or the momentum per time + + align:start position:0% +energy density or the momentum per time + + + align:start position:0% +energy density or the momentum per time +that is crossing + + align:start position:0% +that is crossing + + + align:start position:0% +that is crossing +a slice of the jet that that actually + + align:start position:0% +a slice of the jet that that actually + + + align:start position:0% +a slice of the jet that that actually +should be conserved + + align:start position:0% +should be conserved + + + align:start position:0% +should be conserved +and so if i write that momentum flux as + + align:start position:0% +and so if i write that momentum flux as + + + align:start position:0% +and so if i write that momentum flux as +capital k + + align:start position:0% +capital k + + + align:start position:0% +capital k +is the area of the cross section pi r + + align:start position:0% +is the area of the cross section pi r + + + align:start position:0% +is the area of the cross section pi r +squared if i look at a given + + align:start position:0% +squared if i look at a given + + + align:start position:0% +squared if i look at a given +position r here and then i have + + align:start position:0% +position r here and then i have + + + align:start position:0% +position r here and then i have +the the momentum is is the density of + + align:start position:0% +the the momentum is is the density of + + + align:start position:0% +the the momentum is is the density of +the fluid which is the air + + align:start position:0% +the fluid which is the air + + + align:start position:0% +the fluid which is the air +um times uh the the velocity field + + align:start position:0% +um times uh the the velocity field + + + align:start position:0% +um times uh the the velocity field +the velocity and that's so that's + + align:start position:0% +the velocity and that's so that's + + + align:start position:0% +the velocity and that's so that's +momentum momentum flux would be momentum + + align:start position:0% +momentum momentum flux would be momentum + + + align:start position:0% +momentum momentum flux would be momentum +times velocity + + align:start position:0% +times velocity + + + align:start position:0% +times velocity +or rho v squared which is also kinetic + + align:start position:0% +or rho v squared which is also kinetic + + + align:start position:0% +or rho v squared which is also kinetic +energy density + + align:start position:0% +energy density + + + align:start position:0% +energy density +this quantity should be roughly constant + + align:start position:0% + + + + align:start position:0% + +so we can now solve for the average + + align:start position:0% +so we can now solve for the average + + + align:start position:0% +so we can now solve for the average +velocity + + align:start position:0% +velocity + + + align:start position:0% +velocity +v bar which uh would be + + align:start position:0% +v bar which uh would be + + + align:start position:0% +v bar which uh would be +a square root of k + + align:start position:0% +a square root of k + + + align:start position:0% +a square root of k +over pi uh rho a times + + align:start position:0% +over pi uh rho a times + + + align:start position:0% +over pi uh rho a times +1 over r after we take the square root + + align:start position:0% +1 over r after we take the square root + + + align:start position:0% +1 over r after we take the square root +but then because we have a cone + + align:start position:0% +but then because we have a cone + + + align:start position:0% +but then because we have a cone +r is alpha z so this is + + align:start position:0% +r is alpha z so this is + + + align:start position:0% +r is alpha z so this is +square root of k over pi a + + align:start position:0% +square root of k over pi a + + + align:start position:0% +square root of k over pi a +one over alpha z so we can see the + + align:start position:0% +one over alpha z so we can see the + + + align:start position:0% +one over alpha z so we can see the +velocity is decaying like + + align:start position:0% +velocity is decaying like + + + align:start position:0% +velocity is decaying like +one over distance from the mouth so it + + align:start position:0% +one over distance from the mouth so it + + + align:start position:0% +one over distance from the mouth so it +is + + align:start position:0% +is + + + align:start position:0% +is +the jet is slowing down but it's still + + align:start position:0% +the jet is slowing down but it's still + + + align:start position:0% +the jet is slowing down but it's still +of course continuing to advance + + align:start position:0% +of course continuing to advance + + + align:start position:0% +of course continuing to advance +as the momentum is being shared across a + + align:start position:0% +as the momentum is being shared across a + + + align:start position:0% +as the momentum is being shared across a +larger and larger + + align:start position:0% +larger and larger + + + align:start position:0% +larger and larger +area of entrained turbulent flow + + align:start position:0% +area of entrained turbulent flow + + + align:start position:0% +area of entrained turbulent flow +so we can now use this result to + + align:start position:0% +so we can now use this result to + + + align:start position:0% +so we can now use this result to +figure out what is the rate of progress + + align:start position:0% +figure out what is the rate of progress + + + align:start position:0% +figure out what is the rate of progress +of the front so if i call this + + align:start position:0% +of the front so if i call this + + + align:start position:0% +of the front so if i call this +z of the front so let's say when i first + + align:start position:0% +z of the front so let's say when i first + + + align:start position:0% +z of the front so let's say when i first +start exhaling there's kind of a wall + + align:start position:0% +start exhaling there's kind of a wall + + + align:start position:0% +start exhaling there's kind of a wall +of droplets and i can sketch that this + + align:start position:0% +of droplets and i can sketch that this + + + align:start position:0% +of droplets and i can sketch that this +flow is actually full of droplets + + align:start position:0% +flow is actually full of droplets + + + align:start position:0% +flow is actually full of droplets +that we're interested in tracking i'd + + align:start position:0% +that we're interested in tracking i'd + + + align:start position:0% +that we're interested in tracking i'd +like to know you know how those are + + align:start position:0% +like to know you know how those are + + + align:start position:0% +like to know you know how those are +first leaving the mouth + + align:start position:0% +first leaving the mouth + + + align:start position:0% +first leaving the mouth +well i can write that this velocity + + align:start position:0% +well i can write that this velocity + + + align:start position:0% +well i can write that this velocity +is at a given position corresponding to + + align:start position:0% +is at a given position corresponding to + + + align:start position:0% +is at a given position corresponding to +the front is dzf dt + + align:start position:0% +the front is dzf dt + + + align:start position:0% +the front is dzf dt +and if this is the f so i apply this at + + align:start position:0% +and if this is the f so i apply this at + + + align:start position:0% +and if this is the f so i apply this at +the front + + align:start position:0% +the front + + + align:start position:0% +the front +then i can put the zf on the other side + + align:start position:0% +then i can put the zf on the other side + + + align:start position:0% +then i can put the zf on the other side +and i have zf + + align:start position:0% +and i have zf + + + align:start position:0% +and i have zf +z f d t is equal to + + align:start position:0% +z f d t is equal to + + + align:start position:0% +z f d t is equal to +square root of k over pi + + align:start position:0% + + + + align:start position:0% + +rho a and then i've got i guess also + + align:start position:0% +rho a and then i've got i guess also + + + align:start position:0% +rho a and then i've got i guess also +an alpha or one over alpha and then + + align:start position:0% +an alpha or one over alpha and then + + + align:start position:0% +an alpha or one over alpha and then +this expression here can be written as + + align:start position:0% +this expression here can be written as + + + align:start position:0% +this expression here can be written as +one half + + align:start position:0% +one half + + + align:start position:0% +one half +times the derivative of z f + + align:start position:0% +times the derivative of z f + + + align:start position:0% +times the derivative of z f +squared so i can then solve for the + + align:start position:0% +squared so i can then solve for the + + + align:start position:0% +squared so i can then solve for the +position of the front and i find z + + align:start position:0% +position of the front and i find z + + + align:start position:0% +position of the front and i find z +f is equal to + + align:start position:0% +f is equal to + + + align:start position:0% +f is equal to +well let's see what i get i get i put + + align:start position:0% +well let's see what i get i get i put + + + align:start position:0% +well let's see what i get i get i put +the 2 on the other side + + align:start position:0% +the 2 on the other side + + + align:start position:0% +the 2 on the other side +i take a square root so i get 2 over + + align:start position:0% +i take a square root so i get 2 over + + + align:start position:0% +i take a square root so i get 2 over +alpha to the one half + + align:start position:0% +alpha to the one half + + + align:start position:0% +alpha to the one half +i get k over pi rho a + + align:start position:0% +i get k over pi rho a + + + align:start position:0% +i get k over pi rho a +it was a square root and then i take + + align:start position:0% +it was a square root and then i take + + + align:start position:0% +it was a square root and then i take +another square root so i get a 1 + + align:start position:0% +another square root so i get a 1 + + + align:start position:0% +another square root so i get a 1 +quarter and then i get t + + align:start position:0% +quarter and then i get t + + + align:start position:0% +quarter and then i get t +to the one half because when i integrate + + align:start position:0% +to the one half because when i integrate + + + align:start position:0% +to the one half because when i integrate +this equation + + align:start position:0% +this equation + + + align:start position:0% +this equation +i get z f squared is all this stuff + + align:start position:0% +i get z f squared is all this stuff + + + align:start position:0% +i get z f squared is all this stuff +times t okay starting from t equals zero + + align:start position:0% +times t okay starting from t equals zero + + + align:start position:0% +times t okay starting from t equals zero +so we find is that + + align:start position:0% +so we find is that + + + align:start position:0% +so we find is that +initially the uh jet starts to progress + + align:start position:0% +initially the uh jet starts to progress + + + align:start position:0% +initially the uh jet starts to progress +like square root of time and so this + + align:start position:0% +like square root of time and so this + + + align:start position:0% +like square root of time and so this +coefficient here is some kind of like + + align:start position:0% +coefficient here is some kind of like + + + align:start position:0% +coefficient here is some kind of like +has the units of a diffusivity so it's + + align:start position:0% +has the units of a diffusivity so it's + + + align:start position:0% +has the units of a diffusivity so it's +kind of like appears that the jet is + + align:start position:0% +kind of like appears that the jet is + + + align:start position:0% +kind of like appears that the jet is +sort of diffusing + + align:start position:0% +sort of diffusing + + + align:start position:0% +sort of diffusing +um you could call this uh d + + align:start position:0% +um you could call this uh d + + + align:start position:0% +um you could call this uh d +effective you know sort of for for the + + align:start position:0% +effective you know sort of for for the + + + align:start position:0% +effective you know sort of for for the +for the front of the jet + + align:start position:0% +for the front of the jet + + + align:start position:0% +for the front of the jet +okay but that doesn't last forever + + align:start position:0% +okay but that doesn't last forever + + + align:start position:0% +okay but that doesn't last forever +because some point the person + + align:start position:0% +because some point the person + + + align:start position:0% +because some point the person +you know closes their mouth and starts + + align:start position:0% +you know closes their mouth and starts + + + align:start position:0% +you know closes their mouth and starts +breathing in again and maybe even pulls + + align:start position:0% +breathing in again and maybe even pulls + + + align:start position:0% +breathing in again and maybe even pulls +the + + align:start position:0% +the + + + align:start position:0% +the +the fluid back a little bit but not too + + align:start position:0% +the fluid back a little bit but not too + + + align:start position:0% +the fluid back a little bit but not too +much because it has momentum and it + + align:start position:0% +much because it has momentum and it + + + align:start position:0% +much because it has momentum and it +keeps moving forward so when somebody + + align:start position:0% +keeps moving forward so when somebody + + + align:start position:0% +keeps moving forward so when somebody +breathes + + align:start position:0% +breathes + + + align:start position:0% +breathes +it starts out looking like that but then + + align:start position:0% +it starts out looking like that but then + + + align:start position:0% +it starts out looking like that but then +in a later time if i draw the same + + align:start position:0% +in a later time if i draw the same + + + align:start position:0% +in a later time if i draw the same +person again + + align:start position:0% + + + + align:start position:0% + +then in fact actually let me draw him + + align:start position:0% +then in fact actually let me draw him + + + align:start position:0% +then in fact actually let me draw him +with a closed mouth + + align:start position:0% + + + + align:start position:0% + +uh because he's just finished let's say + + align:start position:0% +uh because he's just finished let's say + + + align:start position:0% +uh because he's just finished let's say +exhaling is getting ready for his next + + align:start position:0% +exhaling is getting ready for his next + + + align:start position:0% +exhaling is getting ready for his next +breath + + align:start position:0% +breath + + + align:start position:0% +breath +so now this blob of fluid has kind of + + align:start position:0% +so now this blob of fluid has kind of + + + align:start position:0% +so now this blob of fluid has kind of +worked its way out + + align:start position:0% +worked its way out + + + align:start position:0% +worked its way out +and it's now somewhere out here + + align:start position:0% +and it's now somewhere out here + + + align:start position:0% +and it's now somewhere out here +okay and this is what + + align:start position:0% +okay and this is what + + + align:start position:0% +okay and this is what +we call a puff so if you're smoking for + + align:start position:0% +we call a puff so if you're smoking for + + + align:start position:0% +we call a puff so if you're smoking for +example a cigarette you know that you + + align:start position:0% +example a cigarette you know that you + + + align:start position:0% +example a cigarette you know that you +can + + align:start position:0% +can + + + align:start position:0% +can +create a puff of smoke by just releasing + + align:start position:0% +create a puff of smoke by just releasing + + + align:start position:0% +create a puff of smoke by just releasing +a finite amount of fluid and then it + + align:start position:0% +a finite amount of fluid and then it + + + align:start position:0% +a finite amount of fluid and then it +kind of goes out and it makes + + align:start position:0% +kind of goes out and it makes + + + align:start position:0% +kind of goes out and it makes +some interesting patterns and usually is + + align:start position:0% +some interesting patterns and usually is + + + align:start position:0% +some interesting patterns and usually is +very turbulent unless you're very + + align:start position:0% +very turbulent unless you're very + + + align:start position:0% +very turbulent unless you're very +careful in trying to control it + + align:start position:0% + + + + align:start position:0% + +and of course this contains lots of + + align:start position:0% +and of course this contains lots of + + + align:start position:0% +and of course this contains lots of +these droplets they're interested in + + align:start position:0% +these droplets they're interested in + + + align:start position:0% +these droplets they're interested in +and so then now we could briefly ask how + + align:start position:0% +and so then now we could briefly ask how + + + align:start position:0% +and so then now we could briefly ask how +fast does the puff move well + + align:start position:0% +fast does the puff move well + + + align:start position:0% +fast does the puff move well +you see here the fluid keeps moving + + align:start position:0% +you see here the fluid keeps moving + + + align:start position:0% +you see here the fluid keeps moving +because it's constantly being given + + align:start position:0% +because it's constantly being given + + + align:start position:0% +because it's constantly being given +momentum + + align:start position:0% +momentum + + + align:start position:0% +momentum +so if it's a steady jet as you're + + align:start position:0% +so if it's a steady jet as you're + + + align:start position:0% +so if it's a steady jet as you're +breathing you're pushing pushing pushing + + align:start position:0% +breathing you're pushing pushing pushing + + + align:start position:0% +breathing you're pushing pushing pushing +and so this thing keeps moving on the + + align:start position:0% +and so this thing keeps moving on the + + + align:start position:0% +and so this thing keeps moving on the +square root of + + align:start position:0% +square root of + + + align:start position:0% +square root of +t it keeps entraining more but as soon + + align:start position:0% +t it keeps entraining more but as soon + + + align:start position:0% +t it keeps entraining more but as soon +as you stop giving it more momentum you + + align:start position:0% +as you stop giving it more momentum you + + + align:start position:0% +as you stop giving it more momentum you +gave it just a finite amount of momentum + + align:start position:0% +gave it just a finite amount of momentum + + + align:start position:0% +gave it just a finite amount of momentum +then the puff actually slows down it + + align:start position:0% +then the puff actually slows down it + + + align:start position:0% +then the puff actually slows down it +doesn't keep pushing ahead as quickly it + + align:start position:0% +doesn't keep pushing ahead as quickly it + + + align:start position:0% +doesn't keep pushing ahead as quickly it +also doesn't entrain + + align:start position:0% +also doesn't entrain + + + align:start position:0% +also doesn't entrain +more air as quickly either and we can do + + align:start position:0% +more air as quickly either and we can do + + + align:start position:0% +more air as quickly either and we can do +a very simple argument to see what + + align:start position:0% +a very simple argument to see what + + + align:start position:0% +a very simple argument to see what +happens to the scaling + + align:start position:0% +happens to the scaling + + + align:start position:0% +happens to the scaling +so this momentum flux here was a + + align:start position:0% +so this momentum flux here was a + + + align:start position:0% +so this momentum flux here was a +constant momentum class + + align:start position:0% +constant momentum class + + + align:start position:0% +constant momentum class +flux in the case of a jet but here in + + align:start position:0% +flux in the case of a jet but here in + + + align:start position:0% +flux in the case of a jet but here in +the case of a puff + + align:start position:0% + + + + align:start position:0% + +we could maybe as a very crude estimate + + align:start position:0% +we could maybe as a very crude estimate + + + align:start position:0% +we could maybe as a very crude estimate +just say that the momentum flux + + align:start position:0% +just say that the momentum flux + + + align:start position:0% +just say that the momentum flux +is something now replaced by some you + + align:start position:0% +is something now replaced by some you + + + align:start position:0% +is something now replaced by some you +know kind of + + align:start position:0% +know kind of + + + align:start position:0% +know kind of +constant value that is maintained only + + align:start position:0% +constant value that is maintained only + + + align:start position:0% +constant value that is maintained only +for a time tb which is the time of the + + align:start position:0% +for a time tb which is the time of the + + + align:start position:0% +for a time tb which is the time of the +breath + + align:start position:0% +breath + + + align:start position:0% +breath +and then averaged over a longer period + + align:start position:0% +and then averaged over a longer period + + + align:start position:0% +and then averaged over a longer period +of time so if you think of this as kind + + align:start position:0% +of time so if you think of this as kind + + + align:start position:0% +of time so if you think of this as kind +of like a + + align:start position:0% +of like a + + + align:start position:0% +of like a +you know an average momentum flux we've + + align:start position:0% +you know an average momentum flux we've + + + align:start position:0% +you know an average momentum flux we've +injected some into flux but then we took + + align:start position:0% +injected some into flux but then we took + + + align:start position:0% +injected some into flux but then we took +it away and so if i want to find out the + + align:start position:0% +it away and so if i want to find out the + + + align:start position:0% +it away and so if i want to find out the +average over a period of time t i have + + align:start position:0% +average over a period of time t i have + + + align:start position:0% +average over a period of time t i have +to + + align:start position:0% +to + + + align:start position:0% +to +divide by t so you see if i do that then + + align:start position:0% +divide by t so you see if i do that then + + + align:start position:0% +divide by t so you see if i do that then +i arrive that in the puff case that + + align:start position:0% +i arrive that in the puff case that + + + align:start position:0% +i arrive that in the puff case that +the position of the of the front or of + + align:start position:0% +the position of the of the front or of + + + align:start position:0% +the position of the of the front or of +the puff + + align:start position:0% +the puff + + + align:start position:0% +the puff +is a lot of these same constants here + + align:start position:0% +is a lot of these same constants here + + + align:start position:0% +is a lot of these same constants here +but is now + + align:start position:0% +but is now + + + align:start position:0% +but is now +uh scaling as t to the one quarter + + align:start position:0% +uh scaling as t to the one quarter + + + align:start position:0% +uh scaling as t to the one quarter +because if my k + + align:start position:0% +because if my k + + + align:start position:0% +because if my k +has a one over uh one over t and then + + align:start position:0% +has a one over uh one over t and then + + + align:start position:0% +has a one over uh one over t and then +it's raised to one quarter power then i + + align:start position:0% +it's raised to one quarter power then i + + + align:start position:0% +it's raised to one quarter power then i +end up with zf goes like t to the one + + align:start position:0% +end up with zf goes like t to the one + + + align:start position:0% +end up with zf goes like t to the one +quarter so it slows down so first it was + + align:start position:0% +quarter so it slows down so first it was + + + align:start position:0% +quarter so it slows down so first it was +sort of squared of time + + align:start position:0% +sort of squared of time + + + align:start position:0% +sort of squared of time +now it's becoming more fourth order time + + align:start position:0% +now it's becoming more fourth order time + + + align:start position:0% +now it's becoming more fourth order time +and it starts + + align:start position:0% +and it starts + + + align:start position:0% +and it starts +it's almost just sort of sitting there + + align:start position:0% +it's almost just sort of sitting there + + + align:start position:0% +it's almost just sort of sitting there +it's not progressing that much and then + + align:start position:0% +it's not progressing that much and then + + + align:start position:0% +it's not progressing that much and then +a new breath comes + + align:start position:0% +a new breath comes + + + align:start position:0% +a new breath comes +and so that's what happens next and + + align:start position:0% +and so that's what happens next and + + + align:start position:0% +and so that's what happens next and +especially if one is speaking or singing + + align:start position:0% +especially if one is speaking or singing + + + align:start position:0% +especially if one is speaking or singing +then the exhaling is a much longer and + + align:start position:0% +then the exhaling is a much longer and + + + align:start position:0% +then the exhaling is a much longer and +more continuous process than the + + align:start position:0% +more continuous process than the + + + align:start position:0% +more continuous process than the +inhaling which is very sudden + + align:start position:0% +inhaling which is very sudden + + + align:start position:0% +inhaling which is very sudden +so you talk and take a breath and you + + align:start position:0% +so you talk and take a breath and you + + + align:start position:0% +so you talk and take a breath and you +talk + + align:start position:0% +talk + + + align:start position:0% +talk +and so there's a lot more of this going + + align:start position:0% +and so there's a lot more of this going + + + align:start position:0% +and so there's a lot more of this going +on than this + + align:start position:0% +on than this + + + align:start position:0% +on than this +even in normal speech and in normal + + align:start position:0% +even in normal speech and in normal + + + align:start position:0% +even in normal speech and in normal +breathing to some extent as well but + + align:start position:0% +breathing to some extent as well but + + + align:start position:0% +breathing to some extent as well but +especially when one is speaking + + align:start position:0% +especially when one is speaking + + + align:start position:0% +especially when one is speaking +and so an interesting development then + + align:start position:0% +and so an interesting development then + + + align:start position:0% +and so an interesting development then +is that if we have a person + + align:start position:0% +is that if we have a person + + + align:start position:0% +is that if we have a person +who is speaking + + align:start position:0% + + + + align:start position:0% + +then we can generate uh what has been + + align:start position:0% +then we can generate uh what has been + + + align:start position:0% +then we can generate uh what has been +called + + align:start position:0% +called + + + align:start position:0% +called +a puff train so we have you know here's + + align:start position:0% +a puff train so we have you know here's + + + align:start position:0% +a puff train so we have you know here's +the most recent + + align:start position:0% +the most recent + + + align:start position:0% +the most recent +uh you know new breath you know getting + + align:start position:0% +uh you know new breath you know getting + + + align:start position:0% +uh you know new breath you know getting +exhaled and then the previous one + + align:start position:0% +exhaled and then the previous one + + + align:start position:0% +exhaled and then the previous one +was you know here still kind of floating + + align:start position:0% +was you know here still kind of floating + + + align:start position:0% +was you know here still kind of floating +around and the one ahead of that has + + align:start position:0% +around and the one ahead of that has + + + align:start position:0% +around and the one ahead of that has +dispersed a bit more but it hasn't + + align:start position:0% +dispersed a bit more but it hasn't + + + align:start position:0% +dispersed a bit more but it hasn't +progressed as far + + align:start position:0% +progressed as far + + + align:start position:0% +progressed as far +and so it's a little bit thinner and if + + align:start position:0% +and so it's a little bit thinner and if + + + align:start position:0% +and so it's a little bit thinner and if +we kind of color each breath you know + + align:start position:0% +we kind of color each breath you know + + + align:start position:0% +we kind of color each breath you know +a different way then what we're left + + align:start position:0% +a different way then what we're left + + + align:start position:0% +a different way then what we're left +with is something + + align:start position:0% +with is something + + + align:start position:0% +with is something +that actually looks an awful lot like + + align:start position:0% +that actually looks an awful lot like + + + align:start position:0% +that actually looks an awful lot like +a continuous cone again so this + + align:start position:0% +a continuous cone again so this + + + align:start position:0% +a continuous cone again so this +is a puff train + + align:start position:0% +is a puff train + + + align:start position:0% +is a puff train +this could be for example from speaking + + align:start position:0% +this could be for example from speaking + + + align:start position:0% +this could be for example from speaking +or singing and overall the behavior + + align:start position:0% +or singing and overall the behavior + + + align:start position:0% +or singing and overall the behavior +is quite similar to a jet + + align:start position:0% +is quite similar to a jet + + + align:start position:0% +is quite similar to a jet +just where the k is replaced by the time + + align:start position:0% +just where the k is replaced by the time + + + align:start position:0% +just where the k is replaced by the time +average momentum flux + + align:start position:0% +average momentum flux + + + align:start position:0% +average momentum flux +so i should mention that this way of + + align:start position:0% +so i should mention that this way of + + + align:start position:0% +so i should mention that this way of +thinking here uh + + align:start position:0% +thinking here uh + + + align:start position:0% +thinking here uh +was recently introduced and verified + + align:start position:0% +was recently introduced and verified + + + align:start position:0% +was recently introduced and verified +experimentally in a paper + + align:start position:0% +experimentally in a paper + + + align:start position:0% +experimentally in a paper +by um + + align:start position:0% + + + + align:start position:0% + +bakaranian and howard stone + + align:start position:0% +bakaranian and howard stone + + + align:start position:0% +bakaranian and howard stone +and collaborators + + align:start position:0% + + + + align:start position:0% + +and also introduced this uh notion of + + align:start position:0% +and also introduced this uh notion of + + + align:start position:0% +and also introduced this uh notion of +the scaling and that + + align:start position:0% +the scaling and that + + + align:start position:0% +the scaling and that +showed that actually the puff train has + + align:start position:0% +showed that actually the puff train has + + + align:start position:0% +showed that actually the puff train has +a scaling which is very similar to the + + align:start position:0% +a scaling which is very similar to the + + + align:start position:0% +a scaling which is very similar to the +initial jet with the square root of time + + align:start position:0% +initial jet with the square root of time + + + align:start position:0% +initial jet with the square root of time +uh and so that's an important concept + + align:start position:0% +uh and so that's an important concept + + + align:start position:0% +uh and so that's an important concept +we'll come to now because we want to ask + + align:start position:0% +we'll come to now because we want to ask + + + align:start position:0% +we'll come to now because we want to ask +now what if somebody is speaking + + align:start position:0% +now what if somebody is speaking + + + align:start position:0% +now what if somebody is speaking +and or even just breathing continuously + + align:start position:0% +and or even just breathing continuously + + + align:start position:0% +and or even just breathing continuously +in a certain direction and generating + + align:start position:0% +in a certain direction and generating + + + align:start position:0% +in a certain direction and generating +aerosol particles how does their + + align:start position:0% +aerosol particles how does their + + + align:start position:0% +aerosol particles how does their +concentration evolve + + align:start position:0% +concentration evolve + + + align:start position:0% +concentration evolve +in this sort of a respiratory plume or + + align:start position:0% + + + + align:start position:0% + +jet \ No newline at end of file diff --git a/QleELaAfTd4.txt b/QleELaAfTd4.txt new file mode 100644 index 0000000000000000000000000000000000000000..6445dceee94e247afa932e7c95d1bce72b5f4de5 --- /dev/null +++ b/QleELaAfTd4.txt @@ -0,0 +1,581 @@ +PROFESSOR: Last time we +introduced poles. + +And in particular, we introduced +how to move from + +the manipulation of feed-forward +and feedback + +systems and the geometric +sequence that fell out into + +using the base of that geometric +sequence to attempt + +to predict the long-term +behavior of the system. + +When we're solving for poles and +we're only interested in + +long term behavior, one of the +easiest ways to do so to solve + +for the roots of z, where z is a +substitution for 1 over R in + +the denominator of the +system function. + +Once we've done that, we +have a list of poles. + +From that list of poles, we +would like to select, the + +dominant pole, or the pole with +the greatest magnitude, + +and then based on the magnitude +and period of that + +pole we can determine what the +long term behavior of our + +system looks like. + +Today I'd like to mention +to you some notable + +things about poles. + +If you are interested in this +information or feedback and + +controls in the general sense, +I highly recommend 6.003. + +But here's some information you +should at least be aware + +of as a consequence of 6.01. + +The other thing I would like to +do is just walk through a + +couple of pole problems to +familiarize you, or get you + +more comfortable with the idea +of solving for the poles of a + +system function, or looking at +the unit sample response of a + +system function and then +graphing the poles. + +The first thing that I want +to mention is pole-zero + +cancellation. + +And what do I mean +when I say that? + +I mean that if both the +numerator and the denominator + +have a degree of R in them, then +you're going to have both + +a zero and a pole. + +If the zero and the pole have +the same value associated with + +them, you may be tempted +to cancel them out. + +Unless both the zero and the +pole are equal to 0 -- + +don't do it. + +The reason why is that when you +get to a implementation of + +a real system, it is highly +unlikely that both the zero + +and the pole will be implemented +to a degree of + +accuracy that you will actually +see those two things + +cancel out. + +The only exception to this is +when both the pole and the + +zero are equal to 0, +or in this case. + +This you should feel free +to convert to this. + +In almost any other situation, +don't factor. + +The other thing I want to talk +about is repeated roots. + +If you have a repeated root, +you'll have repeated poles. + +This does get tricky when you're +talking about how to + +add the unit response +of those poles. + +But the long term behavior +of your system is + +going to look the same. + +So if both of these poles are +the dominant pole, then the + +characteristics of both, which +are the same, are going to + +determine what your long term +behavior looks like. + +If they're not, then the +dominant pole is going to + +determine what your long term +behavior looks like. + +The last thing I want to mention +is superposition. + +So far we've only talked about +the unit sample response of a + +system function and how we use +poles to determine what the + +long term behavior of our +system's going to be. + +We can look at the response to +more complicated inputs than + +the unit sample response, +or the delta. + +In fact, one of the things we' +probably end up looking at + +some point is the +step function. + +The thing that you need to know +to go from talking about + +unit sample response to any +other sort of response, is + +that we're still working +with an LTI system. + +What that means is if you take +the summation of your inputs, + +and apply the system function +to that summation, it is the + +same as the output that would +result from inputting all + +those values at once. + +The best way I would like to +explain it is by referring + +again to if your function was +a system function, the same + +property applies. + +Now let's walk through +a pole problem. + +Here I have a second order +system set up. + +We've got two degrees of R. I +have feedback, and I can solve + +for an expression of +y in terms of x. + +In fact, let's do +that right now. + +y is the result of the +summation or a linear + +combination of x plus a delayed +signal of y scaled by + +1.6 in a linear combination with +a delayed value of the + +delayed value of y scaled +by negative 0.63. + +There's my first degree. + +For consistency's sake, there's +my second degree. + +Let's first solve for +the system function. + +If you're confused, I recommend +doing the algebra + +from here to this expression. + +You should get this +fraction out. + +Our second step is to solve +for the roots of z. + +Remember that z is equal to 1 +over R in the denominator of + +the system function. + +In this case, we'll +be working with-- + +all I've done there is taken +every degree of R, substitute + +it in for 1/z. + +and then multiply it out, so +that I'm not working with z in + +the denominator anymore. + +I'm actually just working with +everything in the numerator. + +If I follow this back out, +I get this expression. + +And my poles are going +to be 0.7 and 0.9. + +All right, based on my poles, +what are the properties of the + +unit sample response +in the long term? + +First thing I'm going to do is +look for the dominant pole + +among the poles that I found. + +In this case, I don't even have +to worry about finding + +the length of the distance from +the origin for poles in + +the complex plane. + +All I have to worry about +is the magnitude of + +poles on the real axis. + +0.9 is my dominant pole, because +it's the largest pole. + +0.9 is less than 1. + +So I'm going to end up +with convergence. + +Eventually, my system is +going to converge, or + +tend towards 0. + +The other interesting property +of my system is what is its + +period, how does that relate +to what my function's + +going to look like. + +In this case, we're only working +on the positive real + +axis, so the angle associated +with graphing this pole on the + +complex plane is 0, so there is +no period for our system. + +This means that our system +is going to converge + +monotonically. + +Now let's walk through some unit +sample responses and then + +graph the poles that generated +those unit sample responses on + +the unit circle, where this +is the complex plane. + +Let's look at this +graph first. + +The first thing that I notice +about this graph is that, like + +in the previous example, we have +monotonic convergence. + +We're tending towards 0, and +we're not alternating or + +oscillating about the x-axis. + +So I know I'm going to be +working somewhere along this + +line before the edge +of the unit circle. + +Because at the edge of the unit +circle, the distance from + +the origin is equal to 1. + +If you made me guess, then I +would look at the distance + +here and compare it +to the distance at + +the next time step. + +I realize this is +a blackboard. + +It's not entirely to scale. + +But for the purposes of this +demonstration, I'd like to say + +that the signal at this time +step is 0.5 the signal from + +the previous times. + +Likewise at the next time step, +I would like to say that + +this signal is 0.5 the signal +from the previous time step, + +and so on and so forth. + +Therefore, I'm going to graph +my pole right here. + +Let's take a look +at this graph. + +I've drawn these squiggles to +indicate that the unit sample + +response exceeds the bounds +of the space that I + +gave for this graph. + +So just assume that these values +are much larger than + +I've drawn them. + +The first thing that I notice +about this unit sample + +response graph is the fact that +not only am I increasing + +in a way that does not seem +to change in any way-- + +we're going to end +up diverging-- + +is that I'm actually alternating +about the x-axis. + +And that particularly, that +if I were to call this an + +oscillation, then I +would say it's an + +oscillation with period 2. + +This means that I'm working +with a negative real pole. + +The fact that I'm diverging +means I'm working with a + +negative real pole that has +magnitude greater than 1. + +If you had to make me guess, I +would look at the distance + +associated with this time +step, compare it to the + +distance associated with +this time step. + +And if you had to ask me, I +would say this is about 1.3 + +the value at the +previous step. + +Likewise, if I were to look at +the next time step, I would + +say that this increase +is about 30% of + +the previous value. + +I'm not even going +to try that one. + +But what I'm trying to get +at is that you can use + +comparisons of previous and +future time steps in order to + +attempt to determine the +magnitude of the pole if + +you're working with the +first order system. + +If you're working with the +second order system, then it's + +possible that you'll see +some really interesting + +initialization effects. + +And you should probably ask +one of us what's up. + +But for this example, +we're going to put + +our pole over here. + +Here's the last graph I +want to talk about. + +The first thing that I notice is +that it doesn't seem to be + +diverging, but it doesn't +really seem to + +be converging either. + +If this is the case, then +I'm going to put + +it on the unit circle. + +The second thing that I notice +is that it's not monotonic and + +it's not alternating. + +This is oscillating. + +So in order to determine what +angle I'm going to sign to my + +unit simple response, I'm going +to count out the time + +steps that it takes to cycle +through an entire period and + +then from there figure out what +the angle would have to + +be in order to determine a +period of that length. + +So I start here. + +I'm just going to count 1, +2, 3, 4, 5, 6, 7, 8 -- + +to complete one full +oscillation. + +This means that my +period is 8. + +If I have to divide 2pi by a +particular angle in order to + +get out 8, I want to +divide by pi/4. + +So at this point, I'm working +with a magnitude of about 1, + +and I want this angle +to be about pi/4. + +This concludes my tutorial +on solving poles. + +Next time, we'll end up talking +about circuits. \ No newline at end of file diff --git a/RJhoT5PEf_0.txt b/RJhoT5PEf_0.txt new file mode 100644 index 0000000000000000000000000000000000000000..30ec203ff5dd40d775316882d08ba2df6ab0eae5 --- /dev/null +++ b/RJhoT5PEf_0.txt @@ -0,0 +1,14936 @@ +align:start position:0% + +all right let's get started last lecture + + align:start position:0% +all right let's get started last lecture + + + align:start position:0% +all right let's get started last lecture +we began talking about an entirely new + + align:start position:0% +we began talking about an entirely new + + + align:start position:0% +we began talking about an entirely new +topic in uh computer science and we have + + align:start position:0% +topic in uh computer science and we have + + + align:start position:0% +topic in uh computer science and we have +begun uh learning about how to figure + + align:start position:0% +begun uh learning about how to figure + + + align:start position:0% +begun uh learning about how to figure +out the runtime of our programs right so + + align:start position:0% +out the runtime of our programs right so + + + align:start position:0% +out the runtime of our programs right so +we did um we looked at how to actually + + align:start position:0% +we did um we looked at how to actually + + + align:start position:0% +we did um we looked at how to actually +time the program by figuring out exactly + + align:start position:0% +time the program by figuring out exactly + + + align:start position:0% +time the program by figuring out exactly +how long it takes and then how to count + + align:start position:0% +how long it takes and then how to count + + + align:start position:0% +how long it takes and then how to count +the number of operations in the program + + align:start position:0% +the number of operations in the program + + + align:start position:0% +the number of operations in the program +today we're going to do very same thing + + align:start position:0% +today we're going to do very same thing + + + align:start position:0% +today we're going to do very same thing +uh to begin with so for the first half + + align:start position:0% +uh to begin with so for the first half + + + align:start position:0% +uh to begin with so for the first half +of the lecture we'll time a bunch of + + align:start position:0% +of the lecture we'll time a bunch of + + + align:start position:0% +of the lecture we'll time a bunch of +programs and then we'll count the number + + align:start position:0% +programs and then we'll count the number + + + align:start position:0% +programs and then we'll count the number +of operations just like before but we're + + align:start position:0% +of operations just like before but we're + + + align:start position:0% +of operations just like before but we're +going to do them in the context of + + align:start position:0% +going to do them in the context of + + + align:start position:0% +going to do them in the context of +slightly different slightly more + + align:start position:0% +slightly different slightly more + + + align:start position:0% +slightly different slightly more +interesting programs or functions um + + align:start position:0% +interesting programs or functions um + + + align:start position:0% +interesting programs or functions um +involving just pure numbers as our + + align:start position:0% +involving just pure numbers as our + + + align:start position:0% +involving just pure numbers as our +parameters and then functions that + + align:start position:0% +parameters and then functions that + + + align:start position:0% +parameters and then functions that +involve lists as our + + align:start position:0% +involve lists as our + + + align:start position:0% +involve lists as our +parameters um that'll be the first half + + align:start position:0% +parameters um that'll be the first half + + + align:start position:0% +parameters um that'll be the first half +of the lecture and then from there on + + align:start position:0% +of the lecture and then from there on + + + align:start position:0% +of the lecture and then from there on +we're going to look at the idea of order + + align:start position:0% +we're going to look at the idea of order + + + align:start position:0% +we're going to look at the idea of order +of growth which is kind of what we're + + align:start position:0% +of growth which is kind of what we're + + + align:start position:0% +of growth which is kind of what we're +building up this set of lectures to and + + align:start position:0% +building up this set of lectures to and + + + align:start position:0% +building up this set of lectures to and +then the order of growth um there'll be + + align:start position:0% +then the order of growth um there'll be + + + align:start position:0% +then the order of growth um there'll be +a little bit of math a little bit of + + align:start position:0% +a little bit of math a little bit of + + + align:start position:0% +a little bit of math a little bit of +graphing but not uh not too much and + + align:start position:0% +graphing but not uh not too much and + + + align:start position:0% +graphing but not uh not too much and +then we're just um we're just going to + + align:start position:0% +then we're just um we're just going to + + + align:start position:0% +then we're just um we're just going to +uh see how to actually uh evaluate the + + align:start position:0% +uh see how to actually uh evaluate the + + + align:start position:0% +uh see how to actually uh evaluate the +order of growth of functions from there + + align:start position:0% +order of growth of functions from there + + + align:start position:0% +order of growth of functions from there +on out okay so let's begin by just + + align:start position:0% +on out okay so let's begin by just + + + align:start position:0% +on out okay so let's begin by just +figuring out the runtime of our programs + + align:start position:0% +figuring out the runtime of our programs + + + align:start position:0% +figuring out the runtime of our programs +right this was a really quick and easy + + align:start position:0% +right this was a really quick and easy + + + align:start position:0% +right this was a really quick and easy +way to First to figure out exactly how + + align:start position:0% +way to First to figure out exactly how + + + align:start position:0% +way to First to figure out exactly how +long our programs take so last lecture + + align:start position:0% +long our programs take so last lecture + + + align:start position:0% +long our programs take so last lecture +we imported this time module and we're + + align:start position:0% +we imported this time module and we're + + + align:start position:0% +we imported this time module and we're +doing that again this time but instead + + align:start position:0% +doing that again this time but instead + + + align:start position:0% +doing that again this time but instead +of actually running the um the time + + align:start position:0% +of actually running the um the time + + + align:start position:0% +of actually running the um the time +function that we had seen last lecture + + align:start position:0% +function that we had seen last lecture + + + align:start position:0% +function that we had seen last lecture +um here right uh instead of running the + + align:start position:0% +um here right uh instead of running the + + + align:start position:0% +um here right uh instead of running the +time function which gave us this sort of + + align:start position:0% +time function which gave us this sort of + + + align:start position:0% +time function which gave us this sort of +global uh AB um absolute time since some + + align:start position:0% +global uh AB um absolute time since some + + + align:start position:0% +global uh AB um absolute time since some +some date in the past we're going to run + + align:start position:0% +some date in the past we're going to run + + + align:start position:0% +some date in the past we're going to run +this slightly different function called + + align:start position:0% +this slightly different function called + + + align:start position:0% +this slightly different function called +performance counter and this is what is + + align:start position:0% +performance counter and this is what is + + + align:start position:0% +performance counter and this is what is +typically used in the real world um to + + align:start position:0% +typically used in the real world um to + + + align:start position:0% +typically used in the real world um to +figure out how long an actual program or + + align:start position:0% +figure out how long an actual program or + + + align:start position:0% +figure out how long an actual program or +function takes to run the reason we're + + align:start position:0% +function takes to run the reason we're + + + align:start position:0% +function takes to run the reason we're +using this is because it's more accurate + + align:start position:0% +using this is because it's more accurate + + + align:start position:0% +using this is because it's more accurate +so the time.time function that we used + + align:start position:0% +so the time.time function that we used + + + align:start position:0% +so the time.time function that we used +last lecture gave us um maybe uh + + align:start position:0% +last lecture gave us um maybe uh + + + align:start position:0% +last lecture gave us um maybe uh +Precision to 1 * 103 or something very + + align:start position:0% +Precision to 1 * 103 or something very + + + align:start position:0% +Precision to 1 * 103 or something very +uh very big like that the performance + + align:start position:0% +uh very big like that the performance + + + align:start position:0% +uh very big like that the performance +counter can actually give us Precision + + align:start position:0% +counter can actually give us Precision + + + align:start position:0% +counter can actually give us Precision +to something uh that's a lot lot smaller + + align:start position:0% +to something uh that's a lot lot smaller + + + align:start position:0% +to something uh that's a lot lot smaller +so maybe one * 10 8 or some something + + align:start position:0% +so maybe one * 10 8 or some something + + + align:start position:0% +so maybe one * 10 8 or some something +very small so we'll be able to see uh + + align:start position:0% +very small so we'll be able to see uh + + + align:start position:0% +very small so we'll be able to see uh +the timings uh of some functions that + + align:start position:0% +the timings uh of some functions that + + + align:start position:0% +the timings uh of some functions that +were basically zero in the last lecture + + align:start position:0% +were basically zero in the last lecture + + + align:start position:0% +were basically zero in the last lecture +okay so just a quick review of how we + + align:start position:0% +okay so just a quick review of how we + + + align:start position:0% +okay so just a quick review of how we +actually get the time that a function + + align:start position:0% +actually get the time that a function + + + align:start position:0% +actually get the time that a function +takes to run we run this performance + + align:start position:0% +takes to run we run this performance + + + align:start position:0% +takes to run we run this performance +counter time and this one gives us not a + + align:start position:0% +counter time and this one gives us not a + + + align:start position:0% +counter time and this one gives us not a +absolute time but more of a um a shorter + + align:start position:0% +absolute time but more of a um a shorter + + + align:start position:0% +absolute time but more of a um a shorter +time frame not from some time in the + + align:start position:0% +time frame not from some time in the + + + align:start position:0% +time frame not from some time in the +past and the performance counter is very + + align:start position:0% +past and the performance counter is very + + + align:start position:0% +past and the performance counter is very +useful when we're getting these DTS + + align:start position:0% +useful when we're getting these DTS + + + align:start position:0% +useful when we're getting these DTS +right the difference in times so we're + + align:start position:0% +right the difference in times so we're + + + align:start position:0% +right the difference in times so we're +uh running the performance counter to + + align:start position:0% +uh running the performance counter to + + + align:start position:0% +uh running the performance counter to +get the quote unquote starting time we + + align:start position:0% +get the quote unquote starting time we + + + align:start position:0% +get the quote unquote starting time we +run the function we run the performance + + align:start position:0% +run the function we run the performance + + + align:start position:0% +run the function we run the performance +counter again to get the quote unquote + + align:start position:0% +counter again to get the quote unquote + + + align:start position:0% +counter again to get the quote unquote +stopping time subtract the starting time + + align:start position:0% +stopping time subtract the starting time + + + align:start position:0% +stopping time subtract the starting time +to get the DT okay so uh and then we + + align:start position:0% +to get the DT okay so uh and then we + + + align:start position:0% +to get the DT okay so uh and then we +will'll print that that time to see how + + align:start position:0% +will'll print that that time to see how + + + align:start position:0% +will'll print that that time to see how +long the function actually takes to run + + align:start position:0% +long the function actually takes to run + + + align:start position:0% +long the function actually takes to run +uh yeah that's what I said okay so we're + + align:start position:0% +uh yeah that's what I said okay so we're + + + align:start position:0% +uh yeah that's what I said okay so we're +going to look at two different functions + + align:start position:0% +going to look at two different functions + + + align:start position:0% +going to look at two different functions +uh than than last time but they're going + + align:start position:0% +uh than than last time but they're going + + + align:start position:0% +uh than than last time but they're going +to uh they're going to have sort of the + + align:start position:0% +to uh they're going to have sort of the + + + align:start position:0% +to uh they're going to have sort of the +same uh overarching themes that we saw + + align:start position:0% +same uh overarching themes that we saw + + + align:start position:0% +same uh overarching themes that we saw +last lecture so the first function we're + + align:start position:0% +last lecture so the first function we're + + + align:start position:0% +last lecture so the first function we're +going to look at is called convert to + + align:start position:0% +going to look at is called convert to + + + align:start position:0% +going to look at is called convert to +kilometers taking in some miles and + + align:start position:0% +kilometers taking in some miles and + + + align:start position:0% +kilometers taking in some miles and +Returns the value in kilometers and the + + align:start position:0% +Returns the value in kilometers and the + + + align:start position:0% +Returns the value in kilometers and the +second function is a function named + + align:start position:0% +second function is a function named + + + align:start position:0% +second function is a function named +compound so this one should seem uh very + + align:start position:0% +compound so this one should seem uh very + + + align:start position:0% +compound so this one should seem uh very +familiar it will bring flashbacks to + + align:start position:0% +familiar it will bring flashbacks to + + + align:start position:0% +familiar it will bring flashbacks to +problem set one um it's a function that + + align:start position:0% +problem set one um it's a function that + + + align:start position:0% +problem set one um it's a function that +takes in a monthly investment an + + align:start position:0% +takes in a monthly investment an + + + align:start position:0% +takes in a monthly investment an +interest rate for the month and some + + align:start position:0% +interest rate for the month and some + + + align:start position:0% +interest rate for the month and some +number of months to invest that much and + + align:start position:0% +number of months to invest that much and + + + align:start position:0% +number of months to invest that much and +it returns how much money you've made + + align:start position:0% +it returns how much money you've made + + + align:start position:0% +it returns how much money you've made +over those number of months so you can + + align:start position:0% +over those number of months so you can + + + align:start position:0% +over those number of months so you can +see here you have a total initialized a + + align:start position:0% +see here you have a total initialized a + + + align:start position:0% +see here you have a total initialized a +loop that goes through that many months + + align:start position:0% +loop that goes through that many months + + + align:start position:0% +loop that goes through that many months +and it updates the total based on the + + align:start position:0% +and it updates the total based on the + + + align:start position:0% +and it updates the total based on the +interest rate and how much money you + + align:start position:0% +interest rate and how much money you + + + align:start position:0% +interest rate and how much money you +have there right now plus whatever + + align:start position:0% +have there right now plus whatever + + + align:start position:0% +have there right now plus whatever +you've invested for that month okay so + + align:start position:0% +you've invested for that month okay so + + + align:start position:0% +you've invested for that month okay so +the three questions we're going to + + align:start position:0% +the three questions we're going to + + + align:start position:0% +the three questions we're going to +answer just like we answered last + + align:start position:0% +answer just like we answered last + + + align:start position:0% +answer just like we answered last +lecture is how long in actual seconds + + align:start position:0% +lecture is how long in actual seconds + + + align:start position:0% +lecture is how long in actual seconds +does it take to run these functions + + align:start position:0% +does it take to run these functions + + + align:start position:0% +does it take to run these functions +which input parameters does the function + + align:start position:0% +which input parameters does the function + + + align:start position:0% +which input parameters does the function +actually depend on and do these two + + align:start position:0% +actually depend on and do these two + + + align:start position:0% +actually depend on and do these two +functions actually run at for for + + align:start position:0% +functions actually run at for for + + + align:start position:0% +functions actually run at for for +different amounts of time and and sort + + align:start position:0% +different amounts of time and and sort + + + align:start position:0% +different amounts of time and and sort +of what is that difference right does + + align:start position:0% +of what is that difference right does + + + align:start position:0% +of what is that difference right does +one run in 12 seconds and the other one + + align:start position:0% +one run in 12 seconds and the other one + + + align:start position:0% +one run in 12 seconds and the other one +R run in 0. five sort what what is the + + align:start position:0% +R run in 0. five sort what what is the + + + align:start position:0% +R run in 0. five sort what what is the +the actual time that it takes for them + + align:start position:0% +the actual time that it takes for them + + + align:start position:0% +the actual time that it takes for them +to + + align:start position:0% +to + + + align:start position:0% +to +run so this is our code so these are the + + align:start position:0% +run so this is our code so these are the + + + align:start position:0% +run so this is our code so these are the +two functions um before we go on let me + + align:start position:0% +two functions um before we go on let me + + + align:start position:0% +two functions um before we go on let me +just show you how we're creating the + + align:start position:0% +just show you how we're creating the + + + align:start position:0% +just show you how we're creating the +inputs so just like before we're + + align:start position:0% +inputs so just like before we're + + + align:start position:0% +inputs so just like before we're +creating a list of all of the different + + align:start position:0% +creating a list of all of the different + + + align:start position:0% +creating a list of all of the different +different inputs we're going to run the + + align:start position:0% +different inputs we're going to run the + + + align:start position:0% +different inputs we're going to run the +function with so here I've got this Ln + + align:start position:0% +function with so here I've got this Ln + + + align:start position:0% +function with so here I've got this Ln +that will contain the numbers 1 10 100 a + + align:start position:0% +that will contain the numbers 1 10 100 a + + + align:start position:0% +that will contain the numbers 1 10 100 a +th and so on and these are going to be + + align:start position:0% +th and so on and these are going to be + + + align:start position:0% +th and so on and these are going to be +the parameters to my function one at a + + align:start position:0% +the parameters to my function one at a + + + align:start position:0% +the parameters to my function one at a +time of course and then I've got my Loop + + align:start position:0% +time of course and then I've got my Loop + + + align:start position:0% +time of course and then I've got my Loop +here for each one of those inputs one 10 + + align:start position:0% +here for each one of those inputs one 10 + + + align:start position:0% +here for each one of those inputs one 10 +100 a thousand I'm just going to run my + + align:start position:0% +100 a thousand I'm just going to run my + + + align:start position:0% +100 a thousand I'm just going to run my +function right so here I'm measuring the + + align:start position:0% +function right so here I'm measuring the + + + align:start position:0% +function right so here I'm measuring the +time it takes and then I'm going to + + align:start position:0% +time it takes and then I'm going to + + + align:start position:0% +time it takes and then I'm going to +report the the time that it took to run + + align:start position:0% +report the the time that it took to run + + + align:start position:0% +report the the time that it took to run +the + + align:start position:0% +the + + + align:start position:0% +the +program and just for fun I'm also going + + align:start position:0% +program and just for fun I'm also going + + + align:start position:0% +program and just for fun I'm also going +to report how many times this program + + align:start position:0% +to report how many times this program + + + align:start position:0% +to report how many times this program +could run in one second because for me + + align:start position:0% +could run in one second because for me + + + align:start position:0% +could run in one second because for me +it was a little bit hard to read you + + align:start position:0% +it was a little bit hard to read you + + + align:start position:0% +it was a little bit hard to read you +know one time 10 negative you know 20 + + align:start position:0% +know one time 10 negative you know 20 + + + align:start position:0% +know one time 10 negative you know 20 +you know eight or something like that + + align:start position:0% +you know eight or something like that + + + align:start position:0% +you know eight or something like that +but it was a lot easier for me to see + + align:start position:0% +but it was a lot easier for me to see + + + align:start position:0% +but it was a lot easier for me to see +this big number for how many times that + + align:start position:0% +this big number for how many times that + + + align:start position:0% +this big number for how many times that +function could have run in one + + align:start position:0% +function could have run in one + + + align:start position:0% +function could have run in one +second so here I've + + align:start position:0% +second so here I've + + + align:start position:0% +second so here I've +got uh convert to + + align:start position:0% +got uh convert to + + + align:start position:0% +got uh convert to +kilometers so I'm going to run it + + align:start position:0% +kilometers so I'm going to run it + + + align:start position:0% +kilometers so I'm going to run it +and we're going to see it's this right + + align:start position:0% +and we're going to see it's this right + + + align:start position:0% +and we're going to see it's this right +here how long the function actually took + + align:start position:0% +here how long the function actually took + + + align:start position:0% +here how long the function actually took +so last time we ran a program that was + + align:start position:0% +so last time we ran a program that was + + + align:start position:0% +so last time we ran a program that was +really simple like this all of it + + align:start position:0% +really simple like this all of it + + + align:start position:0% +really simple like this all of it +basically said it took zero seconds + + align:start position:0% +basically said it took zero seconds + + + align:start position:0% +basically said it took zero seconds +right it was just so fast that that + + align:start position:0% +right it was just so fast that that + + + align:start position:0% +right it was just so fast that that +time. time function was wasn't able to + + align:start position:0% +time. time function was wasn't able to + + + align:start position:0% +time. time function was wasn't able to +pick up that precise uh time difference + + align:start position:0% +pick up that precise uh time difference + + + align:start position:0% +pick up that precise uh time difference +but this performance counter can right + + align:start position:0% +but this performance counter can right + + + align:start position:0% +but this performance counter can right +which is a lot nicer so now we see that + + align:start position:0% +which is a lot nicer so now we see that + + + align:start position:0% +which is a lot nicer so now we see that +no matter what the input it looks like + + align:start position:0% +no matter what the input it looks like + + + align:start position:0% +no matter what the input it looks like +the time is pretty much the same right 3 + + align:start position:0% +the time is pretty much the same right 3 + + + align:start position:0% +the time is pretty much the same right 3 +* 10 7 Seconds no matter what the input + + align:start position:0% +* 10 7 Seconds no matter what the input + + + align:start position:0% +* 10 7 Seconds no matter what the input +is right that was + + align:start position:0% +is right that was + + + align:start position:0% +is right that was +expected now what about the count uh the + + align:start position:0% +expected now what about the count uh the + + + align:start position:0% +expected now what about the count uh the +compound + + align:start position:0% +compound + + + align:start position:0% +compound +function this one's going to be a little + + align:start position:0% +function this one's going to be a little + + + align:start position:0% +function this one's going to be a little +bit more interesting because there are + + align:start position:0% +bit more interesting because there are + + + align:start position:0% +bit more interesting because there are +actually three parameters to this + + align:start position:0% +actually three parameters to this + + + align:start position:0% +actually three parameters to this +function right so what we're going to do + + align:start position:0% +function right so what we're going to do + + + align:start position:0% +function right so what we're going to do +is change each one and see which one of + + align:start position:0% +is change each one and see which one of + + + align:start position:0% +is change each one and see which one of +those parameters actually has an effect + + align:start position:0% +those parameters actually has an effect + + + align:start position:0% +those parameters actually has an effect +on the + + align:start position:0% +on the + + + align:start position:0% +on the +runtime so here this bit is going to fix + + align:start position:0% +runtime so here this bit is going to fix + + + align:start position:0% +runtime so here this bit is going to fix +my interest + + align:start position:0% +my interest + + + align:start position:0% +my interest +rate and fix the number of months and + + align:start position:0% +rate and fix the number of months and + + + align:start position:0% +rate and fix the number of months and +I'm going to change the amount I invest + + align:start position:0% +I'm going to change the amount I invest + + + align:start position:0% +I'm going to change the amount I invest +every month okay so if I run that that + + align:start position:0% +every month okay so if I run that that + + + align:start position:0% +every month okay so if I run that that +was pretty fast um again we look at the + + align:start position:0% +was pretty fast um again we look at the + + + align:start position:0% +was pretty fast um again we look at the +results here and no matter how much I + + align:start position:0% +results here and no matter how much I + + + align:start position:0% +results here and no matter how much I +invest every month it looks like the + + align:start position:0% +invest every month it looks like the + + + align:start position:0% +invest every month it looks like the +program doesn't really change how long + + align:start position:0% +program doesn't really change how long + + + align:start position:0% +program doesn't really change how long +it takes to run right it's always about + + align:start position:0% +it takes to run right it's always about + + + align:start position:0% +it takes to run right it's always about +1 time 10 the6 seconds to + + align:start position:0% +1 time 10 the6 seconds to + + + align:start position:0% +1 time 10 the6 seconds to +run all + + align:start position:0% +run all + + + align:start position:0% +run all +right what if I change the interest rate + + align:start position:0% +right what if I change the interest rate + + + align:start position:0% +right what if I change the interest rate +so this one's was a little a little bit + + align:start position:0% +so this one's was a little a little bit + + + align:start position:0% +so this one's was a little a little bit +harder to change but I settled on this + + align:start position:0% +harder to change but I settled on this + + + align:start position:0% +harder to change but I settled on this +as the thing I'm + + align:start position:0% +as the thing I'm + + + align:start position:0% +as the thing I'm +varying uh sorry I'm varying it in this + + align:start position:0% +varying uh sorry I'm varying it in this + + + align:start position:0% +varying uh sorry I'm varying it in this +way so it's going to be 1 Point um 1.1 + + align:start position:0% +way so it's going to be 1 Point um 1.1 + + + align:start position:0% +way so it's going to be 1 Point um 1.1 +or 1.01 or 1.01 that's what I'm going to + + align:start position:0% +or 1.01 or 1.01 that's what I'm going to + + + align:start position:0% +or 1.01 or 1.01 that's what I'm going to +invest uh the interest rate for whatever + + align:start position:0% +invest uh the interest rate for whatever + + + align:start position:0% +invest uh the interest rate for whatever +I'm going to invest in and I'm going to + + align:start position:0% +I'm going to invest in and I'm going to + + + align:start position:0% +I'm going to invest in and I'm going to +fix $10 as my investment per month and + + align:start position:0% +fix $10 as my investment per month and + + + align:start position:0% +fix $10 as my investment per month and +fix the 12 months again so if I run + + align:start position:0% +fix the 12 months again so if I run + + + align:start position:0% +fix the 12 months again so if I run +that same deal it looks like changing + + align:start position:0% +that same deal it looks like changing + + + align:start position:0% +that same deal it looks like changing +this investment isn't really making much + + align:start position:0% +this investment isn't really making much + + + align:start position:0% +this investment isn't really making much +of a difference in how long it takes the + + align:start position:0% +of a difference in how long it takes the + + + align:start position:0% +of a difference in how long it takes the +program to + + align:start position:0% +program to + + + align:start position:0% +program to +run all right one last parameter to try + + align:start position:0% +run all right one last parameter to try + + + align:start position:0% +run all right one last parameter to try +so now I'm going to fix the initial + + align:start position:0% +so now I'm going to fix the initial + + + align:start position:0% +so now I'm going to fix the initial +investment to $10 a month and I'm going + + align:start position:0% +investment to $10 a month and I'm going + + + align:start position:0% +investment to $10 a month and I'm going +to fix my interest rate to this per + + align:start position:0% +to fix my interest rate to this per + + + align:start position:0% +to fix my interest rate to this per +month and I'm going to vary how many + + align:start position:0% +month and I'm going to vary how many + + + align:start position:0% +month and I'm going to vary how many +months I'm going to invest this so again + + align:start position:0% +months I'm going to invest this so again + + + align:start position:0% +months I'm going to invest this so again +this n will be one 10 100 a th000 10,000 + + align:start position:0% +this n will be one 10 100 a th000 10,000 + + + align:start position:0% +this n will be one 10 100 a th000 10,000 +and so on so let's see what this is + + align:start position:0% +and so on so let's see what this is + + + align:start position:0% +and so on so let's see what this is +going to + + align:start position:0% +going to + + + align:start position:0% +going to +do already it's doing something + + align:start position:0% +do already it's doing something + + + align:start position:0% +do already it's doing something +different than the other two because it + + align:start position:0% +different than the other two because it + + + align:start position:0% +different than the other two because it +hasn't finished running yet right so + + align:start position:0% +hasn't finished running yet right so + + + align:start position:0% +hasn't finished running yet right so +it's still working on this last one down + + align:start position:0% +it's still working on this last one down + + + align:start position:0% +it's still working on this last one down +here but we can see that more + + align:start position:0% +here but we can see that more + + + align:start position:0% +here but we can see that more +interesting things are happening now + + align:start position:0% +interesting things are happening now + + + align:start position:0% +interesting things are happening now +right so here I've got um initially it's + + align:start position:0% +right so here I've got um initially it's + + + align:start position:0% +right so here I've got um initially it's +a little bit hard to tell for those + + align:start position:0% +a little bit hard to tell for those + + + align:start position:0% +a little bit hard to tell for those +small numbers which is fine but luckily + + align:start position:0% +small numbers which is fine but luckily + + + align:start position:0% +small numbers which is fine but luckily +we're able to run it for a bunch of uh a + + align:start position:0% +we're able to run it for a bunch of uh a + + + align:start position:0% +we're able to run it for a bunch of uh a +bunch of inputs so starting from about + + align:start position:0% +bunch of inputs so starting from about + + + align:start position:0% +bunch of inputs so starting from about +here right when I when I start investing + + align:start position:0% +here right when I when I start investing + + + align:start position:0% +here right when I when I start investing +a thou sorry when I start investing my + + align:start position:0% +a thou sorry when I start investing my + + + align:start position:0% +a thou sorry when I start investing my +money over a thousand months 10,000 + + align:start position:0% +money over a thousand months 10,000 + + + align:start position:0% +money over a thousand months 10,000 +months 100,000 months and so on it looks + + align:start position:0% +months 100,000 months and so on it looks + + + align:start position:0% +months 100,000 months and so on it looks +like we can kind of see a pattern again + + align:start position:0% +like we can kind of see a pattern again + + + align:start position:0% +like we can kind of see a pattern again +for a thousand months it takes the + + align:start position:0% +for a thousand months it takes the + + + align:start position:0% +for a thousand months it takes the +program takes about 5times 10 to neg 5 + + align:start position:0% +program takes about 5times 10 to neg 5 + + + align:start position:0% +program takes about 5times 10 to neg 5 +Seconds to run if I increase the number + + align:start position:0% +Seconds to run if I increase the number + + + align:start position:0% +Seconds to run if I increase the number +of months by 10 it takes 5 time 10 10 to + + align:start position:0% +of months by 10 it takes 5 time 10 10 to + + + align:start position:0% +of months by 10 it takes 5 time 10 10 to +the4 uh seconds to run and then as my + + align:start position:0% +the4 uh seconds to run and then as my + + + align:start position:0% +the4 uh seconds to run and then as my +input increases by 10 the number of + + align:start position:0% +input increases by 10 the number of + + + align:start position:0% +input increases by 10 the number of +months my time to run seems to increase + + align:start position:0% +months my time to run seems to increase + + + align:start position:0% +months my time to run seems to increase +by 10 as well right so 0.005 + + align:start position:0% +by 10 as well right so 0.005 + + + align:start position:0% +by 10 as well right so 0.005 +0.05 78 something like + + align:start position:0% + + + + align:start position:0% + +that okay so this is from a previous run + + align:start position:0% +that okay so this is from a previous run + + + align:start position:0% +that okay so this is from a previous run +of course each run will be different + + align:start position:0% +of course each run will be different + + + align:start position:0% +of course each run will be different +because we're just calcul we're just + + align:start position:0% +because we're just calcul we're just + + + align:start position:0% +because we're just calcul we're just +purely grabbing the time that the + + align:start position:0% +purely grabbing the time that the + + + align:start position:0% +purely grabbing the time that the +program took to run um so the actual + + align:start position:0% +program took to run um so the actual + + + align:start position:0% +program took to run um so the actual +time will be different but um few things + + align:start position:0% +time will be different but um few things + + + align:start position:0% +time will be different but um few things +to notice so python actually reported + + align:start position:0% +to notice so python actually reported + + + align:start position:0% +to notice so python actually reported +the time it took the program to run in + + align:start position:0% +the time it took the program to run in + + + align:start position:0% +the time it took the program to run in +scientific notation which is kind of + + align:start position:0% +scientific notation which is kind of + + + align:start position:0% +scientific notation which is kind of +cool so this is 4.3 * 10 -6 so it knew + + align:start position:0% +cool so this is 4.3 * 10 -6 so it knew + + + align:start position:0% +cool so this is 4.3 * 10 -6 so it knew +how to show it to me like that so it's + + align:start position:0% +how to show it to me like that so it's + + + align:start position:0% +how to show it to me like that so it's +not uh doesn't have a bunch of zeros in + + align:start position:0% +not uh doesn't have a bunch of zeros in + + + align:start position:0% +not uh doesn't have a bunch of zeros in +there um and then the observation as we + + align:start position:0% +there um and then the observation as we + + + align:start position:0% +there um and then the observation as we +might have you know as you might have + + align:start position:0% +might have you know as you might have + + + align:start position:0% +might have you know as you might have +guessed is uh um for this convert to + + align:start position:0% +guessed is uh um for this convert to + + + align:start position:0% +guessed is uh um for this convert to +kilometers was independent right so this + + align:start position:0% +kilometers was independent right so this + + + align:start position:0% +kilometers was independent right so this +is the kilometers not the compound + + align:start position:0% +is the kilometers not the compound + + + align:start position:0% +is the kilometers not the compound +function but then the compound function + + align:start position:0% +function but then the compound function + + + align:start position:0% +function but then the compound function +here this is again from a previous run + + align:start position:0% +here this is again from a previous run + + + align:start position:0% +here this is again from a previous run +we can make a few + + align:start position:0% +we can make a few + + + align:start position:0% +we can make a few +observations so so the first was that + + align:start position:0% +observations so so the first was that + + + align:start position:0% +observations so so the first was that +the time only change only uh actually + + align:start position:0% +the time only change only uh actually + + + align:start position:0% +the time only change only uh actually +changed with the with the input when we + + align:start position:0% +changed with the with the input when we + + + align:start position:0% +changed with the with the input when we +changed n months right when we changed + + align:start position:0% +changed n months right when we changed + + + align:start position:0% +changed n months right when we changed +the uh initial investment or the + + align:start position:0% +the uh initial investment or the + + + align:start position:0% +the uh initial investment or the +interest rate the program just basically + + align:start position:0% +interest rate the program just basically + + + align:start position:0% +interest rate the program just basically +took the same amount of time to run so + + align:start position:0% +took the same amount of time to run so + + + align:start position:0% +took the same amount of time to run so +it was only nend months that actually + + align:start position:0% +it was only nend months that actually + + + align:start position:0% +it was only nend months that actually +made a difference for + + align:start position:0% +made a difference for + + + align:start position:0% +made a difference for +us second observation again something we + + align:start position:0% +us second observation again something we + + + align:start position:0% +us second observation again something we +noticed is as we increase the number of + + align:start position:0% +noticed is as we increase the number of + + + align:start position:0% +noticed is as we increase the number of +months by 10 the time it takes the + + align:start position:0% +months by 10 the time it takes the + + + align:start position:0% +months by 10 the time it takes the +program to run also increases by 10 + + align:start position:0% +program to run also increases by 10 + + + align:start position:0% +program to run also increases by 10 +again something we've uh we talked about + + align:start position:0% +again something we've uh we talked about + + + align:start position:0% +again something we've uh we talked about +and the last + + align:start position:0% + + + + align:start position:0% + +observation um is that we have this + + align:start position:0% +observation um is that we have this + + + align:start position:0% +observation um is that we have this +relationship very apparent as the input + + align:start position:0% +relationship very apparent as the input + + + align:start position:0% +relationship very apparent as the input +is really big right as the input is + + align:start position:0% +is really big right as the input is + + + align:start position:0% +is really big right as the input is +small I think I mentioned this last time + + align:start position:0% +small I think I mentioned this last time + + + align:start position:0% +small I think I mentioned this last time +if for some reason my computer you know + + align:start position:0% +if for some reason my computer you know + + + align:start position:0% +if for some reason my computer you know +updates or decides to dedicate some time + + align:start position:0% +updates or decides to dedicate some time + + + align:start position:0% +updates or decides to dedicate some time +some resources to do to running an app + + align:start position:0% +some resources to do to running an app + + + align:start position:0% +some resources to do to running an app +in the background for whatever reason as + + align:start position:0% +in the background for whatever reason as + + + align:start position:0% +in the background for whatever reason as +it's trying to figure out the compound + + align:start position:0% +it's trying to figure out the compound + + + align:start position:0% +it's trying to figure out the compound +function with an input of one this + + align:start position:0% +function with an input of one this + + + align:start position:0% +function with an input of one this +number could be changed dramatically + + align:start position:0% +number could be changed dramatically + + + align:start position:0% +number could be changed dramatically +right because 2 * 106 can be affected a + + align:start position:0% +right because 2 * 106 can be affected a + + + align:start position:0% +right because 2 * 106 can be affected a +lot by just a little bit of time + + align:start position:0% +lot by just a little bit of time + + + align:start position:0% +lot by just a little bit of time +dedicated to something else whereas you + + align:start position:0% +dedicated to something else whereas you + + + align:start position:0% +dedicated to something else whereas you +know 4 seconds or 14 seconds if that my + + align:start position:0% +know 4 seconds or 14 seconds if that my + + + align:start position:0% +know 4 seconds or 14 seconds if that my +computer dedicates a little bit of time + + align:start position:0% +computer dedicates a little bit of time + + + align:start position:0% +computer dedicates a little bit of time +to something else that four or 14 won't + + align:start position:0% +to something else that four or 14 won't + + + align:start position:0% +to something else that four or 14 won't +be affected as much right so when the + + align:start position:0% +be affected as much right so when the + + + align:start position:0% +be affected as much right so when the +numbers are big that's when we can see + + align:start position:0% +numbers are big that's when we can see + + + align:start position:0% +numbers are big that's when we can see +the the behavior here of our function a + + align:start position:0% +the the behavior here of our function a + + + align:start position:0% +the the behavior here of our function a +lot more clearly right not when the + + align:start position:0% +lot more clearly right not when the + + + align:start position:0% +lot more clearly right not when the +numbers are + + align:start position:0% +numbers are + + + align:start position:0% +numbers are +small + + align:start position:0% +small + + + align:start position:0% +small +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now I'd like to look at some more + + align:start position:0% +so now I'd like to look at some more + + + align:start position:0% +so now I'd like to look at some more +functions um these functions are going + + align:start position:0% +functions um these functions are going + + + align:start position:0% +functions um these functions are going +to have the input being a list as + + align:start position:0% +to have the input being a list as + + + align:start position:0% +to have the input being a list as +opposed to just numbers right we've seen + + align:start position:0% +opposed to just numbers right we've seen + + + align:start position:0% +opposed to just numbers right we've seen +a bunch of examples with numbers but + + align:start position:0% +a bunch of examples with numbers but + + + align:start position:0% +a bunch of examples with numbers but +let's see what happens when my input is + + align:start position:0% +let's see what happens when my input is + + + align:start position:0% +let's see what happens when my input is +a list so here's a very simple function + + align:start position:0% +a list so here's a very simple function + + + align:start position:0% +a list so here's a very simple function +it takes in a list L and it sums all of + + align:start position:0% +it takes in a list L and it sums all of + + + align:start position:0% +it takes in a list L and it sums all of +the elements in the list l so we've seen + + align:start position:0% +the elements in the list l so we've seen + + + align:start position:0% +the elements in the list l so we've seen +this a bunch of times already we + + align:start position:0% +this a bunch of times already we + + + align:start position:0% +this a bunch of times already we +initialize a total to be zero we iterate + + align:start position:0% +initialize a total to be zero we iterate + + + align:start position:0% +initialize a total to be zero we iterate +through each element in L and we keep + + align:start position:0% +through each element in L and we keep + + + align:start position:0% +through each element in L and we keep +our running total by just adding the + + align:start position:0% +our running total by just adding the + + + align:start position:0% +our running total by just adding the +element to to that total right pretty + + align:start position:0% +element to to that total right pretty + + + align:start position:0% +element to to that total right pretty +simple and we return + + align:start position:0% +simple and we return + + + align:start position:0% +simple and we return +it now how do we actually run this + + align:start position:0% +it now how do we actually run this + + + align:start position:0% +it now how do we actually run this +function with a whole bunch of different + + align:start position:0% +function with a whole bunch of different + + + align:start position:0% +function with a whole bunch of different +inputs well that's what um we're going + + align:start position:0% +inputs well that's what um we're going + + + align:start position:0% +inputs well that's what um we're going +to see next so this bit here is exactly + + align:start position:0% +to see next so this bit here is exactly + + + align:start position:0% +to see next so this bit here is exactly +the same as before it's actually + + align:start position:0% +the same as before it's actually + + + align:start position:0% +the same as before it's actually +creating for us the list of 1 10 100 a + + align:start position:0% +creating for us the list of 1 10 100 a + + + align:start position:0% +creating for us the list of 1 10 100 a +th000 10,000 and so on but clearly the + + align:start position:0% +th000 10,000 and so on but clearly the + + + align:start position:0% +th000 10,000 and so on but clearly the +number 10 cannot be an input to this + + align:start position:0% +number 10 cannot be an input to this + + + align:start position:0% +number 10 cannot be an input to this +function right because this function is + + align:start position:0% +function right because this function is + + + align:start position:0% +function right because this function is +expecting a + + align:start position:0% +expecting a + + + align:start position:0% +expecting a +list right so L cannot be 10 it needs to + + align:start position:0% +list right so L cannot be 10 it needs to + + + align:start position:0% +list right so L cannot be 10 it needs to +be a list with some things in it so + + align:start position:0% +be a list with some things in it so + + + align:start position:0% +be a list with some things in it so +instead what we're going to do out of + + align:start position:0% +instead what we're going to do out of + + + align:start position:0% +instead what we're going to do out of +that number one 10 100 a thousand and so + + align:start position:0% +that number one 10 100 a thousand and so + + + align:start position:0% +that number one 10 100 a thousand and so +on we're actually going to make a list + + align:start position:0% +on we're actually going to make a list + + + align:start position:0% +on we're actually going to make a list +with just some random dummy numbers in + + align:start position:0% +with just some random dummy numbers in + + + align:start position:0% +with just some random dummy numbers in +it I don't actually care what these + + align:start position:0% +it I don't actually care what these + + + align:start position:0% +it I don't actually care what these +numbers are so let's just make them be + + align:start position:0% +numbers are so let's just make them be + + + align:start position:0% +numbers are so let's just make them be +the numbers zero to 9 0 to 99 0 to + + align:start position:0% +the numbers zero to 9 0 to 99 0 to + + + align:start position:0% +the numbers zero to 9 0 to 99 0 to +999 and in effect each one of these + + align:start position:0% +999 and in effect each one of these + + + align:start position:0% +999 and in effect each one of these +lists will then have one element in it + + align:start position:0% +lists will then have one element in it + + + align:start position:0% +lists will then have one element in it +10 elements in it 100 elements in it a + + align:start position:0% +10 elements in it 100 elements in it a + + + align:start position:0% +10 elements in it 100 elements in it a +thousand elements in it and so on all + + align:start position:0% +thousand elements in it and so on all + + + align:start position:0% +thousand elements in it and so on all +right everyone okay with that right so + + align:start position:0% +right everyone okay with that right so + + + align:start position:0% +right everyone okay with that right so +the input is now different it needs to + + align:start position:0% +the input is now different it needs to + + + align:start position:0% +the input is now different it needs to +be a list we're just creating a bunch of + + align:start position:0% +be a list we're just creating a bunch of + + + align:start position:0% +be a list we're just creating a bunch of +lists of varying + + align:start position:0% +lists of varying + + + align:start position:0% +lists of varying +lengths so the Rel relationship between + + align:start position:0% +lengths so the Rel relationship between + + + align:start position:0% +lengths so the Rel relationship between +these lengths are that the lists are 10 + + align:start position:0% +these lengths are that the lists are 10 + + + align:start position:0% +these lengths are that the lists are 10 +times as big as the the previous list + + align:start position:0% +times as big as the the previous list + + + align:start position:0% +times as big as the the previous list +right okay so then now I have my input + + align:start position:0% +right okay so then now I have my input + + + align:start position:0% +right okay so then now I have my input +list here I do the exact same thing as + + align:start position:0% +list here I do the exact same thing as + + + align:start position:0% +list here I do the exact same thing as +before not yet um I run the performance + + align:start position:0% +before not yet um I run the performance + + + align:start position:0% +before not yet um I run the performance +counter uh to I create my starting time + + align:start position:0% +counter uh to I create my starting time + + + align:start position:0% +counter uh to I create my starting time +I run my function and I get the DT and I + + align:start position:0% +I run my function and I get the DT and I + + + align:start position:0% +I run my function and I get the DT and I +report the exact same thing as + + align:start position:0% +report the exact same thing as + + + align:start position:0% +report the exact same thing as +before all right so let's run + + align:start position:0% + + + + align:start position:0% + +that down + + align:start position:0% + + + + align:start position:0% + +here right running running running again + + align:start position:0% +here right running running running again + + + align:start position:0% +here right running running running again +we have to wait a little bit it looks + + align:start position:0% +we have to wait a little bit it looks + + + align:start position:0% +we have to wait a little bit it looks +like it's working but it's just getting + + align:start position:0% +like it's working but it's just getting + + + align:start position:0% +like it's working but it's just getting +slower and slower which is fine so um + + align:start position:0% +slower and slower which is fine so um + + + align:start position:0% +slower and slower which is fine so um +what do we notice so when we had one + + align:start position:0% +what do we notice so when we had one + + + align:start position:0% +what do we notice so when we had one +element in my list it took 1 * 105 + + align:start position:0% +element in my list it took 1 * 105 + + + align:start position:0% +element in my list it took 1 * 105 +seconds to run when I had 10 it took 1 * + + align:start position:0% +seconds to run when I had 10 it took 1 * + + + align:start position:0% +seconds to run when I had 10 it took 1 * +10 -6 seconds to run it was actually + + align:start position:0% +10 -6 seconds to run it was actually + + + align:start position:0% +10 -6 seconds to run it was actually +shorter to have more elements in it see + + align:start position:0% +shorter to have more elements in it see + + + align:start position:0% +shorter to have more elements in it see +this is what I mean when um it's very + + align:start position:0% +this is what I mean when um it's very + + + align:start position:0% +this is what I mean when um it's very +unpredictable for low numbers but as we + + align:start position:0% +unpredictable for low numbers but as we + + + align:start position:0% +unpredictable for low numbers but as we +get to lists of length a th000 10,000 + + align:start position:0% +get to lists of length a th000 10,000 + + + align:start position:0% +get to lists of length a th000 10,000 +100,000 uh a million and so on we can + + align:start position:0% +100,000 uh a million and so on we can + + + align:start position:0% +100,000 uh a million and so on we can +start to see the pattern so with 10,000 + + align:start position:0% +start to see the pattern so with 10,000 + + + align:start position:0% +start to see the pattern so with 10,000 +it took four * 104 seconds to run with + + align:start position:0% +it took four * 104 seconds to run with + + + align:start position:0% +it took four * 104 seconds to run with +100,000 it took four * 103 seconds to + + align:start position:0% +100,000 it took four * 103 seconds to + + + align:start position:0% +100,000 it took four * 103 seconds to +run and then as the input increases by + + align:start position:0% +run and then as the input increases by + + + align:start position:0% +run and then as the input increases by +10 that is the length of my list + + align:start position:0% +10 that is the length of my list + + + align:start position:0% +10 that is the length of my list +increases by 10 it looks like the + + align:start position:0% +increases by 10 it looks like the + + + align:start position:0% +increases by 10 it looks like the +program takes 10 times as long to run + + align:start position:0% +program takes 10 times as long to run + + + align:start position:0% +program takes 10 times as long to run +okay a very similar thing as before so + + align:start position:0% +okay a very similar thing as before so + + + align:start position:0% +okay a very similar thing as before so +the first observation that we can make + + align:start position:0% +the first observation that we can make + + + align:start position:0% +the first observation that we can make +out of this uh this this function is + + align:start position:0% +out of this uh this this function is + + + align:start position:0% +out of this uh this this function is +that um the size of the input obviously + + align:start position:0% +that um the size of the input obviously + + + align:start position:0% +that um the size of the input obviously +is now uh the length of our list right + + align:start position:0% +is now uh the length of our list right + + + align:start position:0% +is now uh the length of our list right +it's not just the number 10 or the + + align:start position:0% +it's not just the number 10 or the + + + align:start position:0% +it's not just the number 10 or the +number a thousand it's a length of + + align:start position:0% +number a thousand it's a length of + + + align:start position:0% +number a thousand it's a length of +length a list of length 10 or a list of + + align:start position:0% +length a list of length 10 or a list of + + + align:start position:0% +length a list of length 10 or a list of +length a + + align:start position:0% +length a + + + align:start position:0% +length a +thousand second observation is that + + align:start position:0% +thousand second observation is that + + + align:start position:0% +thousand second observation is that +again just like in the previous case the + + align:start position:0% +again just like in the previous case the + + + align:start position:0% +again just like in the previous case the +average time uh increases by 10 as the + + align:start position:0% +average time uh increases by 10 as the + + + align:start position:0% +average time uh increases by 10 as the +length of our list increases by + + align:start position:0% +length of our list increases by + + + align:start position:0% +length of our list increases by +10 okay again very good um and just like + + align:start position:0% +10 okay again very good um and just like + + + align:start position:0% +10 okay again very good um and just like +before this relationship between the + + align:start position:0% +before this relationship between the + + + align:start position:0% +before this relationship between the +size and time is more predictable for + + align:start position:0% +size and time is more predictable for + + + align:start position:0% +size and time is more predictable for +large sizes than it was for small sizes + + align:start position:0% +large sizes than it was for small sizes + + + align:start position:0% +large sizes than it was for small sizes +right as we just saw here which little + + align:start position:0% +right as we just saw here which little + + + align:start position:0% +right as we just saw here which little +surpris me a little bit as well is if + + align:start position:0% +surpris me a little bit as well is if + + + align:start position:0% +surpris me a little bit as well is if +for us a list of that's longer it took a + + align:start position:0% +for us a list of that's longer it took a + + + align:start position:0% +for us a list of that's longer it took a +shorter amount of time to run which is + + align:start position:0% +shorter amount of time to run which is + + + align:start position:0% +shorter amount of time to run which is +counterintuitive but again that's + + align:start position:0% +counterintuitive but again that's + + + align:start position:0% +counterintuitive but again that's +probably because my computer did + + align:start position:0% +probably because my computer did + + + align:start position:0% +probably because my computer did +something here to uh take a little bit + + align:start position:0% +something here to uh take a little bit + + + align:start position:0% +something here to uh take a little bit +longer to + + align:start position:0% + + + + align:start position:0% + +run okay and then the last observation + + align:start position:0% +run okay and then the last observation + + + align:start position:0% +run okay and then the last observation +this is uh this is compared to the + + align:start position:0% +this is uh this is compared to the + + + align:start position:0% +this is uh this is compared to the +compound function where we change the + + align:start position:0% +compound function where we change the + + + align:start position:0% +compound function where we change the +number of months it looks like the time + + align:start position:0% +number of months it looks like the time + + + align:start position:0% +number of months it looks like the time +that this program actually takes to run + + align:start position:0% +that this program actually takes to run + + + align:start position:0% +that this program actually takes to run +is pretty comparable just in terms of + + align:start position:0% +is pretty comparable just in terms of + + + align:start position:0% +is pretty comparable just in terms of +pure you know seconds is comparable to + + align:start position:0% +pure you know seconds is comparable to + + + align:start position:0% +pure you know seconds is comparable to +how long it took for the compound to run + + align:start position:0% +how long it took for the compound to run + + + align:start position:0% +how long it took for the compound to run +right so here when my input was 100 + + align:start position:0% +right so here when my input was 100 + + + align:start position:0% +right so here when my input was 100 +million I think yeah 100 million it took + + align:start position:0% +million I think yeah 100 million it took + + + align:start position:0% +million I think yeah 100 million it took +about 8 seconds to run and when my list + + align:start position:0% +about 8 seconds to run and when my list + + + align:start position:0% +about 8 seconds to run and when my list +had 100 million elements in it it took + + align:start position:0% +had 100 million elements in it it took + + + align:start position:0% +had 100 million elements in it it took +about 7 Seconds to run right and then 10 + + align:start position:0% +about 7 Seconds to run right and then 10 + + + align:start position:0% +about 7 Seconds to run right and then 10 +times faster going uh uh when we + + align:start position:0% +times faster going uh uh when we + + + align:start position:0% +times faster going uh uh when we +decreased our input by 10 + + align:start position:0% +decreased our input by 10 + + + align:start position:0% +decreased our input by 10 +okay so already we're starting to see + + align:start position:0% +okay so already we're starting to see + + + align:start position:0% +okay so already we're starting to see +something something that we're going to + + align:start position:0% +something something that we're going to + + + align:start position:0% +something something that we're going to +get yeah go ahead is the of + + align:start position:0% +get yeah go ahead is the of + + + align:start position:0% +get yeah go ahead is the of +function + + align:start position:0% +function + + + align:start position:0% +function +um oh sum of is just this function that + + align:start position:0% +um oh sum of is just this function that + + + align:start position:0% +um oh sum of is just this function that +I wrote here yep that's just yeah I did + + align:start position:0% +I wrote here yep that's just yeah I did + + + align:start position:0% +I wrote here yep that's just yeah I did +I name it something differently in here + + align:start position:0% +I name it something differently in here + + + align:start position:0% +I name it something differently in here +no it was + + align:start position:0% +no it was + + + align:start position:0% +no it was +yeah yeah so already we're starting to + + align:start position:0% +yeah yeah so already we're starting to + + + align:start position:0% +yeah yeah so already we're starting to +get at this idea where I have two uh + + align:start position:0% +get at this idea where I have two uh + + + align:start position:0% +get at this idea where I have two uh +functions that do wildly different + + align:start position:0% +functions that do wildly different + + + align:start position:0% +functions that do wildly different +things right one sums the elements in a + + align:start position:0% +things right one sums the elements in a + + + align:start position:0% +things right one sums the elements in a +list the other one just Loops over some + + align:start position:0% +list the other one just Loops over some + + + align:start position:0% +list the other one just Loops over some +number of months and does some + + align:start position:0% +number of months and does some + + + align:start position:0% +number of months and does some +calculation but it looks like they're + + align:start position:0% +calculation but it looks like they're + + + align:start position:0% +calculation but it looks like they're +sort of in terms of just algorithmically + + align:start position:0% +sort of in terms of just algorithmically + + + align:start position:0% +sort of in terms of just algorithmically +wise they are very similar they take + + align:start position:0% +wise they are very similar they take + + + align:start position:0% +wise they are very similar they take +similar amounts of time they increase at + + align:start position:0% +similar amounts of time they increase at + + + align:start position:0% +similar amounts of time they increase at +the same rate + + align:start position:0% +the same rate + + + align:start position:0% +the same rate +um and basically they just have a for + + align:start position:0% +um and basically they just have a for + + + align:start position:0% +um and basically they just have a for +Loop right or some sort of loop that + + align:start position:0% +Loop right or some sort of loop that + + + align:start position:0% +Loop right or some sort of loop that +iterates through the input and does + + align:start position:0% +iterates through the input and does + + + align:start position:0% +iterates through the input and does +something so algorithmically we want to + + align:start position:0% +something so algorithmically we want to + + + align:start position:0% +something so algorithmically we want to +consider both of these functions the + + align:start position:0% +consider both of these functions the + + + align:start position:0% +consider both of these functions the +same even though they Implement + + align:start position:0% +same even though they Implement + + + align:start position:0% +same even though they Implement +completely different + + align:start position:0% + + + + align:start position:0% + +things other questions before we go on + + align:start position:0% +things other questions before we go on + + + align:start position:0% +things other questions before we go on +to another list + + align:start position:0% +to another list + + + align:start position:0% +to another list +function okay so let's look at a + + align:start position:0% +function okay so let's look at a + + + align:start position:0% +function okay so let's look at a +slightly different uh problem uh dealing + + align:start position:0% +slightly different uh problem uh dealing + + + align:start position:0% +slightly different uh problem uh dealing +with lists so this function or these + + align:start position:0% +with lists so this function or these + + + align:start position:0% +with lists so this function or these +three functions + + align:start position:0% +three functions + + + align:start position:0% +three functions +deal with finding an element in a list + + align:start position:0% +deal with finding an element in a list + + + align:start position:0% +deal with finding an element in a list +and we're going to compare the runtimes + + align:start position:0% +and we're going to compare the runtimes + + + align:start position:0% +and we're going to compare the runtimes +of these three + + align:start position:0% +of these three + + + align:start position:0% +of these three +functions so the first function is going + + align:start position:0% +functions so the first function is going + + + align:start position:0% +functions so the first function is going +to be a very brute forcey method to find + + align:start position:0% +to be a very brute forcey method to find + + + align:start position:0% +to be a very brute forcey method to find +the element in a + + align:start position:0% +the element in a + + + align:start position:0% +the element in a +list it's going was there a question + + align:start position:0% + + + + align:start position:0% + +yeah all right no worries um okay so the + + align:start position:0% +yeah all right no worries um okay so the + + + align:start position:0% +yeah all right no worries um okay so the +the first function will do a brute force + + align:start position:0% +the first function will do a brute force + + + align:start position:0% +the first function will do a brute force +uh search to find find an element X + + align:start position:0% +uh search to find find an element X + + + align:start position:0% +uh search to find find an element X +right here one of my parameters within a + + align:start position:0% +right here one of my parameters within a + + + align:start position:0% +right here one of my parameters within a +list F the other one of my parameters + + align:start position:0% +list F the other one of my parameters + + + align:start position:0% +list F the other one of my parameters +basically given a list of a bunch of + + align:start position:0% +basically given a list of a bunch of + + + align:start position:0% +basically given a list of a bunch of +elements this function will just + + align:start position:0% +elements this function will just + + + align:start position:0% +elements this function will just +painstakingly look at each element one + + align:start position:0% +painstakingly look at each element one + + + align:start position:0% +painstakingly look at each element one +at a time and ask whether that element + + align:start position:0% +at a time and ask whether that element + + + align:start position:0% +at a time and ask whether that element +is the one that I'm looking for right so + + align:start position:0% +is the one that I'm looking for right so + + + align:start position:0% +is the one that I'm looking for right so +starting over here the beginning of my + + align:start position:0% +starting over here the beginning of my + + + align:start position:0% +starting over here the beginning of my +list and going to the end of my list + + align:start position:0% +list and going to the end of my list + + + align:start position:0% +list and going to the end of my list +that's what is in + + align:start position:0% +that's what is in + + + align:start position:0% +that's what is in +does the next one binary search also + + align:start position:0% +does the next one binary search also + + + align:start position:0% +does the next one binary search also +looks for an element in a list making + + align:start position:0% +looks for an element in a list making + + + align:start position:0% +looks for an element in a list making +sure that the list is ordered but the + + align:start position:0% +sure that the list is ordered but the + + + align:start position:0% +sure that the list is ordered but the +way that it's going to do it is in a + + align:start position:0% +way that it's going to do it is in a + + + align:start position:0% +way that it's going to do it is in a +slightly smarter way so I'm actually + + align:start position:0% +slightly smarter way so I'm actually + + + align:start position:0% +slightly smarter way so I'm actually +going to draw my list this + + align:start position:0% +going to draw my list this + + + align:start position:0% +going to draw my list this +way so each one of these is going to be + + align:start position:0% +way so each one of these is going to be + + + align:start position:0% +way so each one of these is going to be +um you know elements in my list so this + + align:start position:0% +um you know elements in my list so this + + + align:start position:0% +um you know elements in my list so this +is going to do a bisection search to + + align:start position:0% +is going to do a bisection search to + + + align:start position:0% +is going to do a bisection search to +find the element in the list so again + + align:start position:0% +find the element in the list so again + + + align:start position:0% +find the element in the list so again +we're looking for element X within this + + align:start position:0% +we're looking for element X within this + + + align:start position:0% +we're looking for element X within this +list + + align:start position:0% +list + + + align:start position:0% +list +L and remember by section search we + + align:start position:0% +L and remember by section search we + + + align:start position:0% +L and remember by section search we +start with a l with a an a beginning end + + align:start position:0% +start with a l with a an a beginning end + + + align:start position:0% +start with a l with a an a beginning end +point and an ending end point and our + + align:start position:0% +point and an ending end point and our + + + align:start position:0% +point and an ending end point and our +first guess for where for the element or + + align:start position:0% +first guess for where for the element or + + + align:start position:0% +first guess for where for the element or +whatever we're looking for is to just + + align:start position:0% +whatever we're looking for is to just + + + align:start position:0% +whatever we're looking for is to just +say what's the is it the middle element + + align:start position:0% +say what's the is it the middle element + + + align:start position:0% +say what's the is it the middle element +right so look at the element in the + + align:start position:0% +right so look at the element in the + + + align:start position:0% +right so look at the element in the +middle and ask are you the one I'm + + align:start position:0% +middle and ask are you the one I'm + + + align:start position:0% +middle and ask are you the one I'm +looking for in this particular case you + + align:start position:0% +looking for in this particular case you + + + align:start position:0% +looking for in this particular case you +look at the element in the middle and + + align:start position:0% +look at the element in the middle and + + + align:start position:0% +look at the element in the middle and +you say are you the X I'm looking for + + align:start position:0% +you say are you the X I'm looking for + + + align:start position:0% +you say are you the X I'm looking for +right good so that's this one right here + + align:start position:0% +right good so that's this one right here + + + align:start position:0% +right good so that's this one right here +so the midpoint calculation is Right + + align:start position:0% +so the midpoint calculation is Right + + + align:start position:0% +so the midpoint calculation is Right +Here Right the reason why we're doing SL + + align:start position:0% +Here Right the reason why we're doing SL + + + align:start position:0% +Here Right the reason why we're doing SL +slash for integer division is in the + + align:start position:0% +slash for integer division is in the + + + align:start position:0% +slash for integer division is in the +case where I have a list where I would + + align:start position:0% +case where I have a list where I would + + + align:start position:0% +case where I have a list where I would +actually you know look at the midpoint + + align:start position:0% +actually you know look at the midpoint + + + align:start position:0% +actually you know look at the midpoint +here right obviously I can't um ask the + + align:start position:0% +here right obviously I can't um ask the + + + align:start position:0% +here right obviously I can't um ask the +I ask python for the element at index + + align:start position:0% +I ask python for the element at index + + + align:start position:0% +I ask python for the element at index +3.5 right it doesn't work like that so + + align:start position:0% +3.5 right it doesn't work like that so + + + align:start position:0% +3.5 right it doesn't work like that so +I'm just going to round down you could + + align:start position:0% +I'm just going to round down you could + + + align:start position:0% +I'm just going to round down you could +also round up if you wanted to I just + + align:start position:0% +also round up if you wanted to I just + + + align:start position:0% +also round up if you wanted to I just +made the choice to round down just so + + align:start position:0% +made the choice to round down just so + + + align:start position:0% +made the choice to round down just so +I'm actually grabbing the element at an + + align:start position:0% +I'm actually grabbing the element at an + + + align:start position:0% +I'm actually grabbing the element at an +uh an integer + + align:start position:0% +uh an integer + + + align:start position:0% +uh an integer +Index right so I've grabbed my middle + + align:start position:0% +Index right so I've grabbed my middle + + + align:start position:0% +Index right so I've grabbed my middle +element and then I ask are you the one + + align:start position:0% +element and then I ask are you the one + + + align:start position:0% +element and then I ask are you the one +I'm looking for and if not I ask whether + + align:start position:0% +I'm looking for and if not I ask whether + + + align:start position:0% +I'm looking for and if not I ask whether +this one is too low or too high and then + + align:start position:0% +this one is too low or too high and then + + + align:start position:0% +this one is too low or too high and then +if it's too low then I know I need to + + align:start position:0% +if it's too low then I know I need to + + + align:start position:0% +if it's too low then I know I need to +search + + align:start position:0% +search + + + align:start position:0% +search +this part of my list and if it's too + + align:start position:0% +this part of my list and if it's too + + + align:start position:0% +this part of my list and if it's too +high I need to search this part of my + + align:start position:0% +high I need to search this part of my + + + align:start position:0% +high I need to search this part of my +list right so that's what this little if + + align:start position:0% +list right so that's what this little if + + + align:start position:0% +list right so that's what this little if +else is doing right and when I make my + + align:start position:0% +else is doing right and when I make my + + + align:start position:0% +else is doing right and when I make my +decision as to which side to look at + + align:start position:0% +decision as to which side to look at + + + align:start position:0% +decision as to which side to look at +then I reset my end + + align:start position:0% +then I reset my end + + + align:start position:0% +then I reset my end +points and I do the process all over + + align:start position:0% +points and I do the process all over + + + align:start position:0% +points and I do the process all over +again by asking the midpoint there are + + align:start position:0% +again by asking the midpoint there are + + + align:start position:0% +again by asking the midpoint there are +you the one I'm looking for so on and so + + align:start position:0% +you the one I'm looking for so on and so + + + align:start position:0% +you the one I'm looking for so on and so +on right so this does a bisection search + + align:start position:0% +on right so this does a bisection search + + + align:start position:0% +on right so this does a bisection search +uh also called binary search for the + + align:start position:0% +uh also called binary search for the + + + align:start position:0% +uh also called binary search for the +element in a + + align:start position:0% +element in a + + + align:start position:0% +element in a +list and the last way for us to search + + align:start position:0% +list and the last way for us to search + + + align:start position:0% +list and the last way for us to search +whether an element is in a list is one + + align:start position:0% +whether an element is in a list is one + + + align:start position:0% +whether an element is in a list is one +that we've already been doing it's this + + align:start position:0% +that we've already been doing it's this + + + align:start position:0% +that we've already been doing it's this +little one liner here is x in L so using + + align:start position:0% +little one liner here is x in L so using + + + align:start position:0% +little one liner here is x in L so using +the keyword + + align:start position:0% +the keyword + + + align:start position:0% +the keyword +in right so that's I call that the the + + align:start position:0% +in right so that's I call that the the + + + align:start position:0% +in right so that's I call that the the +built-in function the built-in operator + + align:start position:0% +built-in function the built-in operator + + + align:start position:0% +built-in function the built-in operator +in + + align:start position:0% +in + + + align:start position:0% +in +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so it would be unfair if we just asked + + align:start position:0% +so it would be unfair if we just asked + + + align:start position:0% +so it would be unfair if we just asked +python to figure out um or to just uh + + align:start position:0% +python to figure out um or to just uh + + + align:start position:0% +python to figure out um or to just uh +pick a random number and ask whether + + align:start position:0% +pick a random number and ask whether + + + align:start position:0% +pick a random number and ask whether +that element was the one we're looking + + align:start position:0% +that element was the one we're looking + + + align:start position:0% +that element was the one we're looking +for Okay so instead what we're going to + + align:start position:0% +for Okay so instead what we're going to + + + align:start position:0% +for Okay so instead what we're going to +do is to kind of take an average for + + align:start position:0% +do is to kind of take an average for + + + align:start position:0% +do is to kind of take an average for +each one of these three functions just + + align:start position:0% +each one of these three functions just + + + align:start position:0% +each one of these three functions just +to make it fair so we're going to say + + align:start position:0% +to make it fair so we're going to say + + + align:start position:0% +to make it fair so we're going to say +when we're searching for an element in + + align:start position:0% +when we're searching for an element in + + + align:start position:0% +when we're searching for an element in +the list I'm going to say that I'm going + + align:start position:0% +the list I'm going to say that I'm going + + + align:start position:0% +the list I'm going to say that I'm going +to take the average of the case when the + + align:start position:0% +to take the average of the case when the + + + align:start position:0% +to take the average of the case when the +element is the first one in the + + align:start position:0% +element is the first one in the + + + align:start position:0% +element is the first one in the +list and I can find it maybe right away + + align:start position:0% +list and I can find it maybe right away + + + align:start position:0% +list and I can find it maybe right away +in this case or maybe not right away in + + align:start position:0% +in this case or maybe not right away in + + + align:start position:0% +in this case or maybe not right away in +this case the average with that plus + + align:start position:0% +this case the average with that plus + + + align:start position:0% +this case the average with that plus +when the element is the last one in the + + align:start position:0% +when the element is the last one in the + + + align:start position:0% +when the element is the last one in the +list and plus when when the element is + + align:start position:0% +list and plus when when the element is + + + align:start position:0% +list and plus when when the element is +the middle one in my list right so in + + align:start position:0% +the middle one in my list right so in + + + align:start position:0% +the middle one in my list right so in +that way we're actually you know kind of + + align:start position:0% +that way we're actually you know kind of + + + align:start position:0% +that way we're actually you know kind of +covering all our bases kind of best case + + align:start position:0% +covering all our bases kind of best case + + + align:start position:0% +covering all our bases kind of best case +worst case medium case + + align:start position:0% +worst case medium case + + + align:start position:0% +worst case medium case +scenarios right so each one of these + + align:start position:0% +scenarios right so each one of these + + + align:start position:0% +scenarios right so each one of these +three functions will be run with + + align:start position:0% +three functions will be run with + + + align:start position:0% +three functions will be run with +that in mind so that's these three + + align:start position:0% +that in mind so that's these three + + + align:start position:0% +that in mind so that's these three +functions so this is my brute force is + + align:start position:0% +functions so this is my brute force is + + + align:start position:0% +functions so this is my brute force is +in this is my binary + + align:start position:0% +in this is my binary + + + align:start position:0% +in this is my binary +search and the in obviously I'm just + + align:start position:0% +search and the in obviously I'm just + + + align:start position:0% +search and the in obviously I'm just +going to type in in when I run + + align:start position:0% +going to type in in when I run + + + align:start position:0% +going to type in in when I run +it so I'll just show you for one of them + + align:start position:0% +it so I'll just show you for one of them + + + align:start position:0% +it so I'll just show you for one of them +so we're going to uncomment this entire + + align:start position:0% +so we're going to uncomment this entire + + + align:start position:0% +so we're going to uncomment this entire +bit + + align:start position:0% + + + + align:start position:0% + +here and run + + align:start position:0% +here and run + + + align:start position:0% +here and run +it um but you can see here so instead of + + align:start position:0% +it um but you can see here so instead of + + + align:start position:0% +it um but you can see here so instead of +just running the performance counter and + + align:start position:0% +just running the performance counter and + + + align:start position:0% +just running the performance counter and +making one function call I'm actually + + align:start position:0% +making one function call I'm actually + + + align:start position:0% +making one function call I'm actually +going to run three function calls + + align:start position:0% +going to run three function calls + + + align:start position:0% +going to run three function calls +iterated over this little Loop where I'm + + align:start position:0% +iterated over this little Loop where I'm + + + align:start position:0% +iterated over this little Loop where I'm +looking for the element at the zeroth + + align:start position:0% +looking for the element at the zeroth + + + align:start position:0% +looking for the element at the zeroth +location the element at the halfway + + align:start position:0% +location the element at the halfway + + + align:start position:0% +location the element at the halfway +location + + align:start position:0% +location + + + align:start position:0% +location +and the element at the end of my list + + align:start position:0% +and the element at the end of my list + + + align:start position:0% +and the element at the end of my list +and I'm just averaging those down here + + align:start position:0% +and I'm just averaging those down here + + + align:start position:0% +and I'm just averaging those down here +the time it takes to find those + + align:start position:0% +the time it takes to find those + + + align:start position:0% +the time it takes to find those +three does that make sense + + align:start position:0% +three does that make sense + + + align:start position:0% +three does that make sense +okay all right so this is a lot to look + + align:start position:0% +okay all right so this is a lot to look + + + align:start position:0% +okay all right so this is a lot to look +at luckily I'm going to summarize it in + + align:start position:0% +at luckily I'm going to summarize it in + + + align:start position:0% +at luckily I'm going to summarize it in +the next few slides so we don't have to + + align:start position:0% +the next few slides so we don't have to + + + align:start position:0% +the next few slides so we don't have to +stare at that uh at that python uh uh + + align:start position:0% +stare at that uh at that python uh uh + + + align:start position:0% +stare at that uh at that python uh uh +screen + + align:start position:0% +screen + + + align:start position:0% +screen +there okay so we had three functions to + + align:start position:0% +there okay so we had three functions to + + + align:start position:0% +there okay so we had three functions to +run let's first look at how each of + + align:start position:0% +run let's first look at how each of + + + align:start position:0% +run let's first look at how each of +these three functions did individually + + align:start position:0% +these three functions did individually + + + align:start position:0% +these three functions did individually +and then we can start comparing them to + + align:start position:0% +and then we can start comparing them to + + + align:start position:0% +and then we can start comparing them to +each other so the first function we ran + + align:start position:0% +each other so the first function we ran + + + align:start position:0% +each other so the first function we ran +was the is in so remember this was The + + align:start position:0% +was the is in so remember this was The + + + align:start position:0% +was the is in so remember this was The +Brute Force One we're painstakingly + + align:start position:0% +Brute Force One we're painstakingly + + + align:start position:0% +Brute Force One we're painstakingly +going through each element and asking if + + align:start position:0% +going through each element and asking if + + + align:start position:0% +going through each element and asking if +it's the one we're looking for so no no + + align:start position:0% +it's the one we're looking for so no no + + + align:start position:0% +it's the one we're looking for so no no +smart way about that just root force + + align:start position:0% +smart way about that just root force + + + align:start position:0% +smart way about that just root force +your way + + align:start position:0% +your way + + + align:start position:0% +your way +through we notice that as the input list + + align:start position:0% +through we notice that as the input list + + + align:start position:0% +through we notice that as the input list +Grows by 10 the time it takes for to + + align:start position:0% +Grows by 10 the time it takes for to + + + align:start position:0% +Grows by 10 the time it takes for to +find find the element in the list + + align:start position:0% +find find the element in the list + + + align:start position:0% +find find the element in the list +whether it's the first one last one or + + align:start position:0% +whether it's the first one last one or + + + align:start position:0% +whether it's the first one last one or +in the middle on average also Grows by + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +okay all + + align:start position:0% +okay all + + + align:start position:0% +okay all +right + + align:start position:0% +right + + + align:start position:0% +right +next let's look at the buil-in function + + align:start position:0% +next let's look at the buil-in function + + + align:start position:0% +next let's look at the buil-in function +we'll worry about the binary one later + + align:start position:0% +we'll worry about the binary one later + + + align:start position:0% +we'll worry about the binary one later +the built-in function so just using the + + align:start position:0% +the built-in function so just using the + + + align:start position:0% +the built-in function so just using the +in operator and you + + align:start position:0% +in operator and you + + + align:start position:0% +in operator and you +see um this was down + + align:start position:0% +see um this was down + + + align:start position:0% +see um this was down +here so this in so basically the + + align:start position:0% +here so this in so basically the + + + align:start position:0% +here so this in so basically the +function I'm running is purely just + + align:start position:0% +function I'm running is purely just + + + align:start position:0% +function I'm running is purely just +asking whether X is in L right and that + + align:start position:0% +asking whether X is in L right and that + + + align:start position:0% +asking whether X is in L right and that +returns true or + + align:start position:0% +returns true or + + + align:start position:0% +returns true or +false so I didn't need to make a + + align:start position:0% +false so I didn't need to make a + + + align:start position:0% +false so I didn't need to make a +function for that but that builtin in + + align:start position:0% +function for that but that builtin in + + + align:start position:0% +function for that but that builtin in +operator also has a very similar Trend + + align:start position:0% +operator also has a very similar Trend + + + align:start position:0% +operator also has a very similar Trend +right as the length of my list increases + + align:start position:0% +right as the length of my list increases + + + align:start position:0% +right as the length of my list increases +by + + align:start position:0% +by + + + align:start position:0% +by +10 the time it takes for my program to + + align:start position:0% +10 the time it takes for my program to + + + align:start position:0% +10 the time it takes for my program to +run is also 10 times as long right I + + align:start position:0% +run is also 10 times as long right I + + + align:start position:0% +run is also 10 times as long right I +went 05 + + align:start position:0% +went 05 + + + align:start position:0% +went 05 +to.5 and the next one would be five and + + align:start position:0% +to.5 and the next one would be five and + + + align:start position:0% +to.5 and the next one would be five and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +right okay so those seem to be doing + + align:start position:0% +right okay so those seem to be doing + + + align:start position:0% +right okay so those seem to be doing +approximately the same sort of they they + + align:start position:0% +approximately the same sort of they they + + + align:start position:0% +approximately the same sort of they they +have the same uh + + align:start position:0% +have the same uh + + + align:start position:0% +have the same uh +performance now what about the bisection + + align:start position:0% +performance now what about the bisection + + + align:start position:0% +performance now what about the bisection +search or binary + + align:start position:0% +search or binary + + + align:start position:0% +search or binary +search well this one is not so clear + + align:start position:0% +search well this one is not so clear + + + align:start position:0% +search well this one is not so clear +right if we look at the input right the + + align:start position:0% +right if we look at the input right the + + + align:start position:0% +right if we look at the input right the +input clearly increases by 10 from here + + align:start position:0% +input clearly increases by 10 from here + + + align:start position:0% +input clearly increases by 10 from here +to + + align:start position:0% +to + + + align:start position:0% +to +here the time increases 9 * 10 -6 to 1.1 + + align:start position:0% +here the time increases 9 * 10 -6 to 1.1 + + + align:start position:0% +here the time increases 9 * 10 -6 to 1.1 +* + + align:start position:0% +* + + + align:start position:0% +* +105 right and so the factor how many + + align:start position:0% +105 right and so the factor how many + + + align:start position:0% +105 right and so the factor how many +more times it took is very unclear + + align:start position:0% +more times it took is very unclear + + + align:start position:0% +more times it took is very unclear +right it's not quite one if it was one + + align:start position:0% +right it's not quite one if it was one + + + align:start position:0% +right it's not quite one if it was one +that meant it's independent right it's + + align:start position:0% +that meant it's independent right it's + + + align:start position:0% +that meant it's independent right it's +constant it doesn't matter what the + + align:start position:0% +constant it doesn't matter what the + + + align:start position:0% +constant it doesn't matter what the +input size is it's always going to give + + align:start position:0% +input size is it's always going to give + + + align:start position:0% +input size is it's always going to give +us this amount uh it's always going to + + align:start position:0% +us this amount uh it's always going to + + + align:start position:0% +us this amount uh it's always going to +run in this amount of time so it's not + + align:start position:0% +run in this amount of time so it's not + + + align:start position:0% +run in this amount of time so it's not +quite one so it's almost independent of + + align:start position:0% +quite one so it's almost independent of + + + align:start position:0% +quite one so it's almost independent of +size but it's not linear right like the + + align:start position:0% +size but it's not linear right like the + + + align:start position:0% +size but it's not linear right like the +other two functions were right it's not + + align:start position:0% +other two functions were right it's not + + + align:start position:0% +other two functions were right it's not +10 when the input Grows by + + align:start position:0% +10 when the input Grows by + + + align:start position:0% +10 when the input Grows by +10 so we're not quite sure what this + + align:start position:0% +10 so we're not quite sure what this + + + align:start position:0% +10 so we're not quite sure what this +function is right but clearly it's not + + align:start position:0% +function is right but clearly it's not + + + align:start position:0% +function is right but clearly it's not +as bad as the other two but not as good + + align:start position:0% +as bad as the other two but not as good + + + align:start position:0% +as bad as the other two but not as good +as no + + align:start position:0% +as no + + + align:start position:0% +as no +relation okay observation that was + + align:start position:0% +relation okay observation that was + + + align:start position:0% +relation okay observation that was +observation three observation four will + + align:start position:0% +observation three observation four will + + + align:start position:0% +observation three observation four will +now compare the function that we wrote + + align:start position:0% +now compare the function that we wrote + + + align:start position:0% +now compare the function that we wrote +the is in this one here to the binary + + align:start position:0% +the is in this one here to the binary + + + align:start position:0% +the is in this one here to the binary +search this one down + + align:start position:0% +search this one down + + + align:start position:0% +search this one down +here + + align:start position:0% +here + + + align:start position:0% +here +well binary search was orders of + + align:start position:0% +well binary search was orders of + + + align:start position:0% +well binary search was orders of +magnitude faster than Brute Force right + + align:start position:0% +magnitude faster than Brute Force right + + + align:start position:0% +magnitude faster than Brute Force right +Brute Force when the input was what is + + align:start position:0% +Brute Force when the input was what is + + + align:start position:0% +Brute Force when the input was what is +this 10 million or 100 million I'm not + + align:start position:0% +this 10 million or 100 million I'm not + + + align:start position:0% +this 10 million or 100 million I'm not +sure um when the input was 100 million + + align:start position:0% +sure um when the input was 100 million + + + align:start position:0% +sure um when the input was 100 million +Brute Force took 1.6 seconds but the + + align:start position:0% +Brute Force took 1.6 seconds but the + + + align:start position:0% +Brute Force took 1.6 seconds but the +bisection search the binary search took + + align:start position:0% +bisection search the binary search took + + + align:start position:0% +bisection search the binary search took +0.0000001 + + align:start position:0% +0.0000001 + + + align:start position:0% +0.0000001 +seconds so it's not like we went from + + align:start position:0% +seconds so it's not like we went from + + + align:start position:0% +seconds so it's not like we went from +1.5 seconds to 1.2 seconds or to.5 + + align:start position:0% +1.5 seconds to 1.2 seconds or to.5 + + + align:start position:0% +1.5 seconds to 1.2 seconds or to.5 +seconds we were orders of magnitude + + align:start position:0% +seconds we were orders of magnitude + + + align:start position:0% +seconds we were orders of magnitude +faster right 10 to + + align:start position:0% +faster right 10 to + + + align:start position:0% +faster right 10 to +the5 right so there's a really big + + align:start position:0% +the5 right so there's a really big + + + align:start position:0% +the5 right so there's a really big +difference between this algorithm the + + align:start position:0% +difference between this algorithm the + + + align:start position:0% +difference between this algorithm the +one that Brute Forces its way through + + align:start position:0% +one that Brute Forces its way through + + + align:start position:0% +one that Brute Forces its way through +and between this algorithm that does + + align:start position:0% +and between this algorithm that does + + + align:start position:0% +and between this algorithm that does +something smart about removing half of + + align:start position:0% +something smart about removing half of + + + align:start position:0% +something smart about removing half of +the search space with each each Loop + + align:start position:0% +the search space with each each Loop + + + align:start position:0% +the search space with each each Loop +right all right so that's important to + + align:start position:0% +right all right so that's important to + + + align:start position:0% +right all right so that's important to +know and last ly just kind of comparing + + align:start position:0% +know and last ly just kind of comparing + + + align:start position:0% +know and last ly just kind of comparing +pure time that it takes these programs + + align:start position:0% +pure time that it takes these programs + + + align:start position:0% +pure time that it takes these programs +to run let's compare the function that + + align:start position:0% +to run let's compare the function that + + + align:start position:0% +to run let's compare the function that +we wrote the one that Loops one at a + + align:start position:0% +we wrote the one that Loops one at a + + + align:start position:0% +we wrote the one that Loops one at a +time through this list and the buil-in + + align:start position:0% +time through this list and the buil-in + + + align:start position:0% +time through this list and the buil-in +in + + align:start position:0% +in + + + align:start position:0% +in +function the built-in in function see + + align:start position:0% +function the built-in in function see + + + align:start position:0% +function the built-in in function see +while it's still the same sort of has + + align:start position:0% +while it's still the same sort of has + + + align:start position:0% +while it's still the same sort of has +the same relationship linear right with + + align:start position:0% +the same relationship linear right with + + + align:start position:0% +the same relationship linear right with +the input size it seems to do a lot + + align:start position:0% +the input size it seems to do a lot + + + align:start position:0% +the input size it seems to do a lot +better consistently by about uh 10 + + align:start position:0% +better consistently by about uh 10 + + + align:start position:0% +better consistently by about uh 10 +second sorry 10 times as fast + + align:start position:0% +second sorry 10 times as fast + + + align:start position:0% +second sorry 10 times as fast +right so when our function took uh 1 + + align:start position:0% +right so when our function took uh 1 + + + align:start position:0% +right so when our function took uh 1 +seconds the built-in one took 0.005 + + align:start position:0% +seconds the built-in one took 0.005 + + + align:start position:0% +seconds the built-in one took 0.005 +seconds where when our function took 1 + + align:start position:0% +seconds where when our function took 1 + + + align:start position:0% +seconds where when our function took 1 +second the built-in function took 0.5 + + align:start position:0% +second the built-in function took 0.5 + + + align:start position:0% +second the built-in function took 0.5 +seconds so consistently it's just faster + + align:start position:0% +seconds so consistently it's just faster + + + align:start position:0% +seconds so consistently it's just faster +to use the built-in in function than to + + align:start position:0% +to use the built-in in function than to + + + align:start position:0% +to use the built-in in function than to +make our own + + align:start position:0% +make our own + + + align:start position:0% +make our own +okay all right questions about any of + + align:start position:0% +okay all right questions about any of + + + align:start position:0% +okay all right questions about any of +these + + align:start position:0% + + + + align:start position:0% + +observations they make + + align:start position:0% +observations they make + + + align:start position:0% +observations they make +sense are they interesting + + align:start position:0% + + + + align:start position:0% + +yeah okay so what do we see just a quick + + align:start position:0% +yeah okay so what do we see just a quick + + + align:start position:0% +yeah okay so what do we see just a quick +recap of those three + + align:start position:0% +recap of those three + + + align:start position:0% +recap of those three +functions right the first one we saw is + + align:start position:0% +functions right the first one we saw is + + + align:start position:0% +functions right the first one we saw is +linear in the size of the argument so + + align:start position:0% +linear in the size of the argument so + + + align:start position:0% +linear in the size of the argument so +when the input list size increases by 10 + + align:start position:0% +when the input list size increases by 10 + + + align:start position:0% +when the input list size increases by 10 +the program takes 10 times as long to + + align:start position:0% +the program takes 10 times as long to + + + align:start position:0% +the program takes 10 times as long to +run but this other one is something less + + align:start position:0% +run but this other one is something less + + + align:start position:0% +run but this other one is something less +than linear but not constant so we're + + align:start position:0% +than linear but not constant so we're + + + align:start position:0% +than linear but not constant so we're +not quite sure what it + + align:start position:0% +not quite sure what it + + + align:start position:0% +not quite sure what it +is all right we'll come back to this in + + align:start position:0% +is all right we'll come back to this in + + + align:start position:0% +is all right we'll come back to this in +a little bit we'll end up plotting some + + align:start position:0% +a little bit we'll end up plotting some + + + align:start position:0% +a little bit we'll end up plotting some +of these uh runtimes so we'll actually + + align:start position:0% +of these uh runtimes so we'll actually + + + align:start position:0% +of these uh runtimes so we'll actually +be able to see the relationship um at uh + + align:start position:0% +be able to see the relationship um at uh + + + align:start position:0% +be able to see the relationship um at uh +in in a few + + align:start position:0% +in in a few + + + align:start position:0% +in in a few +slides the next thing I actually want to + + align:start position:0% +slides the next thing I actually want to + + + align:start position:0% +slides the next thing I actually want to +do is do one more sort of + + align:start position:0% +do is do one more sort of + + + align:start position:0% +do is do one more sort of +function this one is called the diameter + + align:start position:0% +function this one is called the diameter + + + align:start position:0% +function this one is called the diameter +right and I'll explain what it's doing + + align:start position:0% +right and I'll explain what it's doing + + + align:start position:0% +right and I'll explain what it's doing +because it looks a little bit scary but + + align:start position:0% +because it looks a little bit scary but + + + align:start position:0% +because it looks a little bit scary but +suppose we actually have some points in + + align:start position:0% +suppose we actually have some points in + + + align:start position:0% +suppose we actually have some points in +a 2d plane right so it looks like + + align:start position:0% +a 2d plane right so it looks like + + + align:start position:0% +a 2d plane right so it looks like +this basically what this function is + + align:start position:0% +this basically what this function is + + + align:start position:0% +this basically what this function is +going to do is it's going to figure out + + align:start position:0% +going to do is it's going to figure out + + + align:start position:0% +going to do is it's going to figure out +the + + align:start position:0% +the + + + align:start position:0% +the +biggest + + align:start position:0% +biggest + + + align:start position:0% +biggest +distance between all of these points so + + align:start position:0% +distance between all of these points so + + + align:start position:0% +distance between all of these points so +you know the distance between these two + + align:start position:0% +you know the distance between these two + + + align:start position:0% +you know the distance between these two +points is you know something this the + + align:start position:0% +points is you know something this the + + + align:start position:0% +points is you know something this the +distance between these two points is + + align:start position:0% +distance between these two points is + + + align:start position:0% +distance between these two points is +something else which two points yield + + align:start position:0% +something else which two points yield + + + align:start position:0% +something else which two points yield +the biggest distance right that's what + + align:start position:0% +the biggest distance right that's what + + + align:start position:0% +the biggest distance right that's what +this function aims to tell us and what + + align:start position:0% +this function aims to tell us and what + + + align:start position:0% +this function aims to tell us and what +that distance + + align:start position:0% +that distance + + + align:start position:0% +that distance +is so the way it works is it has nested + + align:start position:0% +is so the way it works is it has nested + + + align:start position:0% +is so the way it works is it has nested +for Loops so this is different than what + + align:start position:0% +for Loops so this is different than what + + + align:start position:0% +for Loops so this is different than what +we've seen so far right we saw an + + align:start position:0% +we've seen so far right we saw an + + + align:start position:0% +we've seen so far right we saw an +example of this last lecture but now + + align:start position:0% +example of this last lecture but now + + + align:start position:0% +example of this last lecture but now +we're seeing it in the context of + + align:start position:0% +we're seeing it in the context of + + + align:start position:0% +we're seeing it in the context of +something something actually useful so + + align:start position:0% +something something actually useful so + + + align:start position:0% +something something actually useful so +in this particular case we're going to + + align:start position:0% +in this particular case we're going to + + + align:start position:0% +in this particular case we're going to +create an input list all right + + align:start position:0% +create an input list all right + + + align:start position:0% +create an input list all right +so again our input list will just have + + align:start position:0% +so again our input list will just have + + + align:start position:0% +so again our input list will just have +some dummy values in it I don't actually + + align:start position:0% +some dummy values in it I don't actually + + + align:start position:0% +some dummy values in it I don't actually +care what these numbers are I just want + + align:start position:0% +care what these numbers are I just want + + + align:start position:0% +care what these numbers are I just want +to populate a whole bunch of points in a + + align:start position:0% +to populate a whole bunch of points in a + + + align:start position:0% +to populate a whole bunch of points in a +2d plane so what we're going to do is + + align:start position:0% +2d plane so what we're going to do is + + + align:start position:0% +2d plane so what we're going to do is +pretty much just iterate from number0 to + + align:start position:0% +pretty much just iterate from number0 to + + + align:start position:0% +pretty much just iterate from number0 to +10 sorry 0 to 9 0 to 99 0 to 999 and so + + align:start position:0% +10 sorry 0 to 9 0 to 99 0 to 999 and so + + + align:start position:0% +10 sorry 0 to 9 0 to 99 0 to 999 and so +on just like we did before + + align:start position:0% +on just like we did before + + + align:start position:0% +on just like we did before +and to get us a little + + align:start position:0% +and to get us a little + + + align:start position:0% +and to get us a little +coordinate in the 2D plane based on + + align:start position:0% +coordinate in the 2D plane based on + + + align:start position:0% +coordinate in the 2D plane based on +those numbers I'm just going to take the + + align:start position:0% +those numbers I'm just going to take the + + + align:start position:0% +those numbers I'm just going to take the +cosine of that number comma the sign of + + align:start position:0% +cosine of that number comma the sign of + + + align:start position:0% +cosine of that number comma the sign of +that number so that together so like + + align:start position:0% +that number so that together so like + + + align:start position:0% +that number so that together so like +cosine of you + + align:start position:0% +cosine of you + + + align:start position:0% +cosine of you +know one or whatever sine of one will be + + align:start position:0% +know one or whatever sine of one will be + + + align:start position:0% +know one or whatever sine of one will be +this point here right set up as a tuple + + align:start position:0% +this point here right set up as a tuple + + + align:start position:0% +this point here right set up as a tuple +and then this one might be cosine of + + align:start position:0% +and then this one might be cosine of + + + align:start position:0% +and then this one might be cosine of +five right comma uh s of five something + + align:start position:0% +five right comma uh s of five something + + + align:start position:0% +five right comma uh s of five something +like that so so I'm just making a whole + + align:start position:0% +like that so so I'm just making a whole + + + align:start position:0% +like that so so I'm just making a whole +bunch of coordinates in a 2d plane + + align:start position:0% +bunch of coordinates in a 2d plane + + + align:start position:0% +bunch of coordinates in a 2d plane +ensuring that I have n + + align:start position:0% +ensuring that I have n + + + align:start position:0% +ensuring that I have n +coordinates okay now the + + align:start position:0% +coordinates okay now the + + + align:start position:0% +coordinates okay now the +loop uh sorry there's going to be two + + align:start position:0% +loop uh sorry there's going to be two + + + align:start position:0% +loop uh sorry there's going to be two +Loops the outer loop will basically take + + align:start position:0% +Loops the outer loop will basically take + + + align:start position:0% +Loops the outer loop will basically take +us through each of these + + align:start position:0% +us through each of these + + + align:start position:0% +us through each of these +elements okay I have five in this + + align:start position:0% +elements okay I have five in this + + + align:start position:0% +elements okay I have five in this +particular + + align:start position:0% +particular + + + align:start position:0% +particular +case and the inner loop will go through + + align:start position:0% +case and the inner loop will go through + + + align:start position:0% +case and the inner loop will go through +every other element right but notice it + + align:start position:0% +every other element right but notice it + + + align:start position:0% +every other element right but notice it +starts from I + one and I'll tell you + + align:start position:0% +starts from I + one and I'll tell you + + + align:start position:0% +starts from I + one and I'll tell you +why that is instead of starting from + + align:start position:0% +why that is instead of starting from + + + align:start position:0% +why that is instead of starting from +zero so let's just walk through let's + + align:start position:0% +zero so let's just walk through let's + + + align:start position:0% +zero so let's just walk through let's +say we start out with this element this + + align:start position:0% +say we start out with this element this + + + align:start position:0% +say we start out with this element this +look as our first uh element in our + + align:start position:0% +look as our first uh element in our + + + align:start position:0% +look as our first uh element in our +outer for Loop so right now we've + + align:start position:0% +outer for Loop so right now we've + + + align:start position:0% +outer for Loop so right now we've +grabbed the first element in our our + + align:start position:0% +grabbed the first element in our our + + + align:start position:0% +grabbed the first element in our our +outer for Loop and what we're going to + + align:start position:0% +outer for Loop and what we're going to + + + align:start position:0% +outer for Loop and what we're going to +do is figure out the distance between it + + align:start position:0% +do is figure out the distance between it + + + align:start position:0% +do is figure out the distance between it +and everybody else so now we're + + align:start position:0% +and everybody else so now we're + + + align:start position:0% +and everybody else so now we're +iterating through the inner for Loop + + align:start position:0% +iterating through the inner for Loop + + + align:start position:0% +iterating through the inner for Loop +going through each element except for + + align:start position:0% +going through each element except for + + + align:start position:0% +going through each element except for +myself + + align:start position:0% +myself + + + align:start position:0% +myself +so I'm going to get the distance between + + align:start position:0% +so I'm going to get the distance between + + + align:start position:0% +so I'm going to get the distance between +this one and this one since it's the + + align:start position:0% +this one and this one since it's the + + + align:start position:0% +this one and this one since it's the +first one obviously it's this the + + align:start position:0% +first one obviously it's this the + + + align:start position:0% +first one obviously it's this the +biggest one but then I'm going to get + + align:start position:0% +biggest one but then I'm going to get + + + align:start position:0% +biggest one but then I'm going to get +the distance between this one and this + + align:start position:0% +the distance between this one and this + + + align:start position:0% +the distance between this one and this +one right and I'm going to say are you + + align:start position:0% +one right and I'm going to say are you + + + align:start position:0% +one right and I'm going to say are you +bigger than this one it looks like no so + + align:start position:0% +bigger than this one it looks like no so + + + align:start position:0% +bigger than this one it looks like no so +we're still keeping this one as our + + align:start position:0% +we're still keeping this one as our + + + align:start position:0% +we're still keeping this one as our +longest one then I'm going to grab the + + align:start position:0% +longest one then I'm going to grab the + + + align:start position:0% +longest one then I'm going to grab the +distance between this and this one and + + align:start position:0% +distance between this and this one and + + + align:start position:0% +distance between this and this one and +this and this one and as I'm going + + align:start position:0% +this and this one and as I'm going + + + align:start position:0% +this and this one and as I'm going +through this little if statement here + + align:start position:0% +through this little if statement here + + + align:start position:0% +through this little if statement here +keeps track of the farthest one so the + + align:start position:0% +keeps track of the farthest one so the + + + align:start position:0% +keeps track of the farthest one so the +one that has the biggest magnitude right + + align:start position:0% +one that has the biggest magnitude right + + + align:start position:0% +one that has the biggest magnitude right +in this case that's probably the first + + align:start position:0% +in this case that's probably the first + + + align:start position:0% +in this case that's probably the first +one we looked + + align:start position:0% +one we looked + + + align:start position:0% +one we looked +at and after I've gone through each + + align:start position:0% +at and after I've gone through each + + + align:start position:0% +at and after I've gone through each +element each other element I've + + align:start position:0% +element each other element I've + + + align:start position:0% +element each other element I've +concluded my first iteration in my outer + + align:start position:0% +concluded my first iteration in my outer + + + align:start position:0% +concluded my first iteration in my outer +for + + align:start position:0% +for + + + align:start position:0% +for +Loop okay so now the outer for Loop goes + + align:start position:0% +Loop okay so now the outer for Loop goes + + + align:start position:0% +Loop okay so now the outer for Loop goes +to the next element in the list let's + + align:start position:0% +to the next element in the list let's + + + align:start position:0% +to the next element in the list let's +say it's this one doesn't actually + + align:start position:0% +say it's this one doesn't actually + + + align:start position:0% +say it's this one doesn't actually +matter okay this one we'll look at the + + align:start position:0% +matter okay this one we'll look at the + + + align:start position:0% +matter okay this one we'll look at the +distance between itself and everybody + + align:start position:0% +distance between itself and everybody + + + align:start position:0% +distance between itself and everybody +else except for the one we already + + align:start position:0% +else except for the one we already + + + align:start position:0% +else except for the one we already +looked at because we already know this + + align:start position:0% +looked at because we already know this + + + align:start position:0% +looked at because we already know this +distance right we kept track of it + + align:start position:0% +distance right we kept track of it + + + align:start position:0% +distance right we kept track of it +already when we iterated through this + + align:start position:0% +already when we iterated through this + + + align:start position:0% +already when we iterated through this +one so as I'm going through my outer for + + align:start position:0% +one so as I'm going through my outer for + + + align:start position:0% +one so as I'm going through my outer for +Loop keeping track of this uh this point + + align:start position:0% +Loop keeping track of this uh this point + + + align:start position:0% +Loop keeping track of this uh this point +here it figures out the distance between + + align:start position:0% +here it figures out the distance between + + + align:start position:0% +here it figures out the distance between +this one this one which is suddenly + + align:start position:0% +this one this one which is suddenly + + + align:start position:0% +this one this one which is suddenly +bigger than that one which we had kept + + align:start position:0% +bigger than that one which we had kept + + + align:start position:0% +bigger than that one which we had kept +track of and then this one right here + + align:start position:0% +track of and then this one right here + + + align:start position:0% +track of and then this one right here +right all right good so now we're still + + align:start position:0% +right all right good so now we're still + + + align:start position:0% +right all right good so now we're still +keeping track of the biggest distance + + align:start position:0% +keeping track of the biggest distance + + + align:start position:0% +keeping track of the biggest distance +we've seen it's probably this one here + + align:start position:0% +we've seen it's probably this one here + + + align:start position:0% +we've seen it's probably this one here +and I've concluded the second iteration + + align:start position:0% +and I've concluded the second iteration + + + align:start position:0% +and I've concluded the second iteration +of my outer for Loop and now I go to the + + align:start position:0% +of my outer for Loop and now I go to the + + + align:start position:0% +of my outer for Loop and now I go to the +next element let's say it's this one + + align:start position:0% +next element let's say it's this one + + + align:start position:0% +next element let's say it's this one +doesn't matter again now this one is + + align:start position:0% +doesn't matter again now this one is + + + align:start position:0% +doesn't matter again now this one is +going to get the distance between itself + + align:start position:0% +going to get the distance between itself + + + align:start position:0% +going to get the distance between itself +and everybody else except for the two + + align:start position:0% +and everybody else except for the two + + + align:start position:0% +and everybody else except for the two +that we've already seen this one and + + align:start position:0% +that we've already seen this one and + + + align:start position:0% +that we've already seen this one and +this one right so that's why our inner + + align:start position:0% +this one right so that's why our inner + + + align:start position:0% +this one right so that's why our inner +loop starts at I + one so this one will + + align:start position:0% +loop starts at I + one so this one will + + + align:start position:0% +loop starts at I + one so this one will +get the distance between itself and this + + align:start position:0% +get the distance between itself and this + + + align:start position:0% +get the distance between itself and this +one all the way back there and this one + + align:start position:0% +one all the way back there and this one + + + align:start position:0% +one all the way back there and this one +all the way over here right and then + + align:start position:0% +all the way over here right and then + + + align:start position:0% +all the way over here right and then +next iteration in the outer for Loop + + align:start position:0% +next iteration in the outer for Loop + + + align:start position:0% +next iteration in the outer for Loop +takes a look at this one let's say and + + align:start position:0% +takes a look at this one let's say and + + + align:start position:0% +takes a look at this one let's say and +it finds the distance between itself and + + align:start position:0% +it finds the distance between itself and + + + align:start position:0% +it finds the distance between itself and +everybody else but you know what there's + + align:start position:0% +everybody else but you know what there's + + + align:start position:0% +everybody else but you know what there's +only one left that one there and then + + align:start position:0% +only one left that one there and then + + + align:start position:0% +only one left that one there and then +the last time through this one doesn't + + align:start position:0% +the last time through this one doesn't + + + align:start position:0% +the last time through this one doesn't +even get a chance to find the distance + + align:start position:0% +even get a chance to find the distance + + + align:start position:0% +even get a chance to find the distance +between itself and anybody else because + + align:start position:0% +between itself and anybody else because + + + align:start position:0% +between itself and anybody else because +everybody else already found the + + align:start position:0% +everybody else already found the + + + align:start position:0% +everybody else already found the +distance between + + align:start position:0% +distance between + + + align:start position:0% +distance between +it okay and so in this way we're + + align:start position:0% +it okay and so in this way we're + + + align:start position:0% +it okay and so in this way we're +basically finding all the possible pairs + + align:start position:0% +basically finding all the possible pairs + + + align:start position:0% +basically finding all the possible pairs +of all of these points in this 2D plane + + align:start position:0% +of all of these points in this 2D plane + + + align:start position:0% +of all of these points in this 2D plane +and keeping track of the longest of the + + align:start position:0% +and keeping track of the longest of the + + + align:start position:0% +and keeping track of the longest of the +biggest distance okay so in terms of the + + align:start position:0% +biggest distance okay so in terms of the + + + align:start position:0% +biggest distance okay so in terms of the +list the input list the way that looks + + align:start position:0% +list the input list the way that looks + + + align:start position:0% +list the input list the way that looks +like right this i+1 business here um the + + align:start position:0% +like right this i+1 business here um the + + + align:start position:0% +like right this i+1 business here um the +Loop basically says I'm going to start + + align:start position:0% +Loop basically says I'm going to start + + + align:start position:0% +Loop basically says I'm going to start +with U and I'm going to get the + + align:start position:0% +with U and I'm going to get the + + + align:start position:0% +with U and I'm going to get the +difference between U and the element at + + align:start position:0% +difference between U and the element at + + + align:start position:0% +difference between U and the element at +index one the element at index two and + + align:start position:0% +index one the element at index two and + + + align:start position:0% +index one the element at index two and +the element at index + + align:start position:0% +the element at index + + + align:start position:0% +the element at index +3 this outer for Loop is done next we're + + align:start position:0% +3 this outer for Loop is done next we're + + + align:start position:0% +3 this outer for Loop is done next we're +going to get the difference the distance + + align:start position:0% +going to get the difference the distance + + + align:start position:0% +going to get the difference the distance +between this one and everybody else + + align:start position:0% +between this one and everybody else + + + align:start position:0% +between this one and everybody else +right so obviously not the element index + + align:start position:0% +right so obviously not the element index + + + align:start position:0% +right so obviously not the element index +zero because we already know that + + align:start position:0% +zero because we already know that + + + align:start position:0% +zero because we already know that +distance so we're going to get the + + align:start position:0% +distance so we're going to get the + + + align:start position:0% +distance so we're going to get the +distance between element at index one + + align:start position:0% +distance between element at index one + + + align:start position:0% +distance between element at index one +and index two and index + + align:start position:0% +and index two and index + + + align:start position:0% +and index two and index +3 and then we're done and then the last + + align:start position:0% +3 and then we're done and then the last + + + align:start position:0% +3 and then we're done and then the last +Loop uh outer loop gets the distance + + align:start position:0% +Loop uh outer loop gets the distance + + + align:start position:0% +Loop uh outer loop gets the distance +between element and index two and index + + align:start position:0% +between element and index two and index + + + align:start position:0% +between element and index two and index +three and then it's done right so just + + align:start position:0% +three and then it's done right so just + + + align:start position:0% +three and then it's done right so just +these the two nested Loops just does all + + align:start position:0% +these the two nested Loops just does all + + + align:start position:0% +these the two nested Loops just does all +of this + + align:start position:0% +of this + + + align:start position:0% +of this +um uh until it finds the all all of + + align:start position:0% +um uh until it finds the all all of + + + align:start position:0% +um uh until it finds the all all of +these pairs it basically uh uh pairs up + + align:start position:0% +these pairs it basically uh uh pairs up + + + align:start position:0% +these pairs it basically uh uh pairs up +everybody + + align:start position:0% +everybody + + + align:start position:0% +everybody +together okay so if we run + + align:start position:0% +together okay so if we run + + + align:start position:0% +together okay so if we run +it what are we going to see so my input + + align:start position:0% +it what are we going to see so my input + + + align:start position:0% +it what are we going to see so my input +for this particular function you'll + + align:start position:0% +for this particular function you'll + + + align:start position:0% +for this particular function you'll +notice first of all is going to be much + + align:start position:0% +notice first of all is going to be much + + + align:start position:0% +notice first of all is going to be much +much smaller than the inputs for + + align:start position:0% +much smaller than the inputs for + + + align:start position:0% +much smaller than the inputs for +everything we've done so far right some + + align:start position:0% +everything we've done so far right some + + + align:start position:0% +everything we've done so far right some +of the inputs we had seen in the past + + align:start position:0% +of the inputs we had seen in the past + + + align:start position:0% +of the inputs we had seen in the past +were a million 10 million 100 million in + + align:start position:0% +were a million 10 million 100 million in + + + align:start position:0% +were a million 10 million 100 million in +this particular case I'm only going to + + align:start position:0% +this particular case I'm only going to + + + align:start position:0% +this particular case I'm only going to +go up to 6,000 because it's just going + + align:start position:0% +go up to 6,000 because it's just going + + + align:start position:0% +go up to 6,000 because it's just going +to take way too long to run if I make it + + align:start position:0% +to take way too long to run if I make it + + + align:start position:0% +to take way too long to run if I make it +go for any much any longer than + + align:start position:0% +go for any much any longer than + + + align:start position:0% +go for any much any longer than +that so what do we see already we've got + + align:start position:0% +that so what do we see already we've got + + + align:start position:0% +that so what do we see already we've got +um 100 points so 100 of these right + + align:start position:0% +um 100 points so 100 of these right + + + align:start position:0% +um 100 points so 100 of these right +finding the distance uh finding the + + align:start position:0% +finding the distance uh finding the + + + align:start position:0% +finding the distance uh finding the +maximum distance between a bunch of + + align:start position:0% +maximum distance between a bunch of + + + align:start position:0% +maximum distance between a bunch of +these pairs took about 03 seconds if we + + align:start position:0% +these pairs took about 03 seconds if we + + + align:start position:0% +these pairs took about 03 seconds if we +doubled that to 200 points it took 0.11 + + align:start position:0% +doubled that to 200 points it took 0.11 + + + align:start position:0% +doubled that to 200 points it took 0.11 +seconds if we doubled that to 400 points + + align:start position:0% +seconds if we doubled that to 400 points + + + align:start position:0% +seconds if we doubled that to 400 points +it took 0.005 seconds and so on and so + + align:start position:0% +it took 0.005 seconds and so on and so + + + align:start position:0% +it took 0.005 seconds and so on and so +on so just like before let's take a look + + align:start position:0% +on so just like before let's take a look + + + align:start position:0% +on so just like before let's take a look +at big numbers to see our + + align:start position:0% +at big numbers to see our + + + align:start position:0% +at big numbers to see our +Trend so as the numbers increase right + + align:start position:0% +Trend so as the numbers increase right + + + align:start position:0% +Trend so as the numbers increase right +by two if my put increases by two it + + align:start position:0% +by two if my put increases by two it + + + align:start position:0% +by two if my put increases by two it +looks like the time that it takes for me + + align:start position:0% +looks like the time that it takes for me + + + align:start position:0% +looks like the time that it takes for me +to find out the biggest distance + + align:start position:0% +to find out the biggest distance + + + align:start position:0% +to find out the biggest distance +increases by four right so my input + + align:start position:0% +increases by four right so my input + + + align:start position:0% +increases by four right so my input +increases by two the time increases by + + align:start position:0% +increases by two the time increases by + + + align:start position:0% +increases by two the time increases by +four uh and I'm not going to run this + + align:start position:0% +four uh and I'm not going to run this + + + align:start position:0% +four uh and I'm not going to run this +but you can make a new list on your own + + align:start position:0% +but you can make a new list on your own + + + align:start position:0% +but you can make a new list on your own +and change this to be uh inputs that are + + align:start position:0% +and change this to be uh inputs that are + + + align:start position:0% +and change this to be uh inputs that are +multiple that are uh yeah multiples of + + align:start position:0% +multiple that are uh yeah multiples of + + + align:start position:0% +multiple that are uh yeah multiples of +10 right increasing by 10 each time and + + align:start position:0% +10 right increasing by 10 each time and + + + align:start position:0% +10 right increasing by 10 each time and +you'll see a very similar pattern where + + align:start position:0% +you'll see a very similar pattern where + + + align:start position:0% +you'll see a very similar pattern where +the out where the time it takes to run + + align:start position:0% +the out where the time it takes to run + + + align:start position:0% +the out where the time it takes to run +that program will be about 100 times as + + align:start position:0% +that program will be about 100 times as + + + align:start position:0% +that program will be about 100 times as +slow so the relationship there is a n n + + align:start position:0% +slow so the relationship there is a n n + + + align:start position:0% +slow so the relationship there is a n n +s kind of + + align:start position:0% +s kind of + + + align:start position:0% +s kind of +relationship all right so a few + + align:start position:0% +relationship all right so a few + + + align:start position:0% +relationship all right so a few +observations here as well um first one I + + align:start position:0% +observations here as well um first one I + + + align:start position:0% +observations here as well um first one I +already mentioned is this program just + + align:start position:0% +already mentioned is this program just + + + align:start position:0% +already mentioned is this program just +on just takes a lot longer to run in + + align:start position:0% +on just takes a lot longer to run in + + + align:start position:0% +on just takes a lot longer to run in +general right so here we were able with + + align:start position:0% +general right so here we were able with + + + align:start position:0% +general right so here we were able with +the uh compound and with finding whether + + align:start position:0% +the uh compound and with finding whether + + + align:start position:0% +the uh compound and with finding whether +in elements in the list and getting the + + align:start position:0% +in elements in the list and getting the + + + align:start position:0% +in elements in the list and getting the +sum of all the elements in a list we + + align:start position:0% +sum of all the elements in a list we + + + align:start position:0% +sum of all the elements in a list we +were able to run you know 100 million a + + align:start position:0% +were able to run you know 100 million a + + + align:start position:0% +were able to run you know 100 million a +list with a 100 million elements and it + + align:start position:0% +list with a 100 million elements and it + + + align:start position:0% +list with a 100 million elements and it +still took about you know one one + + align:start position:0% +still took about you know one one + + + align:start position:0% +still took about you know one one +something seconds whereas with this + + align:start position:0% +something seconds whereas with this + + + align:start position:0% +something seconds whereas with this +diameter function we can barely get to + + align:start position:0% +diameter function we can barely get to + + + align:start position:0% +diameter function we can barely get to +you know 6,000 and it's already taking + + align:start position:0% +you know 6,000 and it's already taking + + + align:start position:0% +you know 6,000 and it's already taking +14 seconds so just way way way slower + + align:start position:0% +14 seconds so just way way way slower + + + align:start position:0% +14 seconds so just way way way slower +program in general right and then the + + align:start position:0% +program in general right and then the + + + align:start position:0% +program in general right and then the +relationship seems to be an N squ kind + + align:start position:0% +relationship seems to be an N squ kind + + + align:start position:0% +relationship seems to be an N squ kind +of relationship relating the input to + + align:start position:0% +of relationship relating the input to + + + align:start position:0% +of relationship relating the input to +how long the program + + align:start position:0% +how long the program + + + align:start position:0% +how long the program +takes so let's actually plot well I + + align:start position:0% +takes so let's actually plot well I + + + align:start position:0% +takes so let's actually plot well I +already did this but um here are the + + align:start position:0% +already did this but um here are the + + + align:start position:0% +already did this but um here are the +relationships for these sort of three + + align:start position:0% +relationships for these sort of three + + + align:start position:0% +relationships for these sort of three +types of algorithms that we've seen so + + align:start position:0% +types of algorithms that we've seen so + + + align:start position:0% +types of algorithms that we've seen so +far so the um this is the finding the + + align:start position:0% +far so the um this is the finding the + + + align:start position:0% +far so the um this is the finding the +element in a list those three versions + + align:start position:0% +element in a list those three versions + + + align:start position:0% +element in a list those three versions +sorry those two versions that we saw and + + align:start position:0% +sorry those two versions that we saw and + + + align:start position:0% +sorry those two versions that we saw and +this is the diameter + + align:start position:0% +this is the diameter + + + align:start position:0% +this is the diameter +function so if we uh plot how long it + + align:start position:0% +function so if we uh plot how long it + + + align:start position:0% +function so if we uh plot how long it +takes the program to run when the input + + align:start position:0% +takes the program to run when the input + + + align:start position:0% +takes the program to run when the input +increas when sorry when the input is + + align:start position:0% +increas when sorry when the input is + + + align:start position:0% +increas when sorry when the input is +this size we can see that there is a + + align:start position:0% +this size we can see that there is a + + + align:start position:0% +this size we can see that there is a +linear relationship so the time it takes + + align:start position:0% +linear relationship so the time it takes + + + align:start position:0% +linear relationship so the time it takes +for the program to run is linear in the + + align:start position:0% + + + + align:start position:0% + +input um the diameter we'll talk about + + align:start position:0% +input um the diameter we'll talk about + + + align:start position:0% +input um the diameter we'll talk about +the by binary search in a bit the + + align:start position:0% +the by binary search in a bit the + + + align:start position:0% +the by binary search in a bit the +diameter we again notice this just by + + align:start position:0% +diameter we again notice this just by + + + align:start position:0% +diameter we again notice this just by +looking at the pure numbers but it's a + + align:start position:0% +looking at the pure numbers but it's a + + + align:start position:0% +looking at the pure numbers but it's a +lot easier to see it visually when the + + align:start position:0% +lot easier to see it visually when the + + + align:start position:0% +lot easier to see it visually when the +uh this is on the x-axis the size of the + + align:start position:0% +uh this is on the x-axis the size of the + + + align:start position:0% +uh this is on the x-axis the size of the +problem so how many points we actually + + align:start position:0% +problem so how many points we actually + + + align:start position:0% +problem so how many points we actually +are finding the diameter + + align:start position:0% +are finding the diameter + + + align:start position:0% +are finding the diameter +between and how long it actually takes + + align:start position:0% +between and how long it actually takes + + + align:start position:0% +between and how long it actually takes +the program to run again the + + align:start position:0% +the program to run again the + + + align:start position:0% +the program to run again the +relationship is quadratic now that we + + align:start position:0% +relationship is quadratic now that we + + + align:start position:0% +relationship is quadratic now that we +plot it we clear clearly see the + + align:start position:0% +plot it we clear clearly see the + + + align:start position:0% +plot it we clear clearly see the +quadratic + + align:start position:0% +quadratic + + + align:start position:0% +quadratic +relationship and then this binary search + + align:start position:0% +relationship and then this binary search + + + align:start position:0% +relationship and then this binary search +we were very unsure of what it was right + + align:start position:0% +we were very unsure of what it was right + + + align:start position:0% +we were very unsure of what it was right +it wasn't quite constant it definitely + + align:start position:0% +it wasn't quite constant it definitely + + + align:start position:0% +it wasn't quite constant it definitely +wasn't linear but now that we've plotted + + align:start position:0% +wasn't linear but now that we've plotted + + + align:start position:0% +wasn't linear but now that we've plotted +it so this is the input size and this is + + align:start position:0% +it so this is the input size and this is + + + align:start position:0% +it so this is the input size and this is +how long it actually takes the program + + align:start position:0% +how long it actually takes the program + + + align:start position:0% +how long it actually takes the program +to run you can see it drastically + + align:start position:0% +to run you can see it drastically + + + align:start position:0% +to run you can see it drastically +increases when the uh input size is very + + align:start position:0% +increases when the uh input size is very + + + align:start position:0% +increases when the uh input size is very +small but then it kind of um sort of ASM + + align:start position:0% +small but then it kind of um sort of ASM + + + align:start position:0% +small but then it kind of um sort of ASM +totically reaches some sort of value um + + align:start position:0% +totically reaches some sort of value um + + + align:start position:0% +totically reaches some sort of value um +it's actually a logarithmic + + align:start position:0% +it's actually a logarithmic + + + align:start position:0% +it's actually a logarithmic +relationship okay + + align:start position:0% +relationship okay + + + align:start position:0% +relationship okay +all right um last thing I wanted to + + align:start position:0% +all right um last thing I wanted to + + + align:start position:0% +all right um last thing I wanted to +mention about timing before we move on + + align:start position:0% +mention about timing before we move on + + + align:start position:0% +mention about timing before we move on +to Counting is just pure running just + + align:start position:0% +to Counting is just pure running just + + + align:start position:0% +to Counting is just pure running just +purely running these functions on + + align:start position:0% +purely running these functions on + + + align:start position:0% +purely running these functions on +different computers will just give us + + align:start position:0% +different computers will just give us + + + align:start position:0% +different computers will just give us +different values just right off the bat + + align:start position:0% +different values just right off the bat + + + align:start position:0% +different values just right off the bat +so for my uh on this you know newer is + + align:start position:0% +so for my uh on this you know newer is + + + align:start position:0% +so for my uh on this you know newer is +computer uh how long did it take to run + + align:start position:0% +computer uh how long did it take to run + + + align:start position:0% +computer uh how long did it take to run +this compound well no what it like three + + align:start position:0% +this compound well no what it like three + + + align:start position:0% +this compound well no what it like three +seconds or something 1 point something + + align:start position:0% +seconds or something 1 point something + + + align:start position:0% +seconds or something 1 point something +seconds on an older laptop it took you + + align:start position:0% +seconds on an older laptop it took you + + + align:start position:0% +seconds on an older laptop it took you +know 663 seconds on an even older + + align:start position:0% +know 663 seconds on an even older + + + align:start position:0% +know 663 seconds on an even older +desktop it took + + align:start position:0% +desktop it took + + + align:start position:0% +desktop it took +1226 seconds right so just you're just + + align:start position:0% +1226 seconds right so just you're just + + + align:start position:0% +1226 seconds right so just you're just +purely timing things the machine you're + + align:start position:0% +purely timing things the machine you're + + + align:start position:0% +purely timing things the machine you're +running it on is going to make a + + align:start position:0% +running it on is going to make a + + + align:start position:0% +running it on is going to make a +difference + + align:start position:0% +difference + + + align:start position:0% +difference +okay and then that's fine right it's + + align:start position:0% +okay and then that's fine right it's + + + align:start position:0% +okay and then that's fine right it's +it's important to know how long it takes + + align:start position:0% +it's important to know how long it takes + + + align:start position:0% +it's important to know how long it takes +but if you're just looking at the + + align:start position:0% +but if you're just looking at the + + + align:start position:0% +but if you're just looking at the +relationship between input and how long + + align:start position:0% +relationship between input and how long + + + align:start position:0% +relationship between input and how long +the program takes to run that's the same + + align:start position:0% +the program takes to run that's the same + + + align:start position:0% +the program takes to run that's the same +so it doesn't matter what machine you're + + align:start position:0% +so it doesn't matter what machine you're + + + align:start position:0% +so it doesn't matter what machine you're +running it on when you increase the + + align:start position:0% +running it on when you increase the + + + align:start position:0% +running it on when you increase the +input by 10 the program will take 10 + + align:start position:0% +input by 10 the program will take 10 + + + align:start position:0% +input by 10 the program will take 10 +times as long to run no matter whether + + align:start position:0% +times as long to run no matter whether + + + align:start position:0% +times as long to run no matter whether +you're running on a fast laptop old + + align:start position:0% +you're running on a fast laptop old + + + align:start position:0% +you're running on a fast laptop old +laptop or a super old + + align:start position:0% +laptop or a super old + + + align:start position:0% +laptop or a super old +desktop + + align:start position:0% +desktop + + + align:start position:0% +desktop +okay so just timing a program is really + + align:start position:0% +okay so just timing a program is really + + + align:start position:0% +okay so just timing a program is really +important right you'd like to know + + align:start position:0% +important right you'd like to know + + + align:start position:0% +important right you'd like to know +whether the program you wrote you're + + align:start position:0% +whether the program you wrote you're + + + align:start position:0% +whether the program you wrote you're +going to have to wait you know an a + + align:start position:0% +going to have to wait you know an a + + + align:start position:0% +going to have to wait you know an a +month for it to finish or a couple + + align:start position:0% +month for it to finish or a couple + + + align:start position:0% +month for it to finish or a couple +minutes for it to finish that's an + + align:start position:0% +minutes for it to finish that's an + + + align:start position:0% +minutes for it to finish that's an +important thing to know but what we're + + align:start position:0% +important thing to know but what we're + + + align:start position:0% +important thing to know but what we're +going to get at towards the end of this + + align:start position:0% +going to get at towards the end of this + + + align:start position:0% +going to get at towards the end of this +uh lecture is something that's + + align:start position:0% +uh lecture is something that's + + + align:start position:0% +uh lecture is something that's +complimentary and that's this idea of um + + align:start position:0% +complimentary and that's this idea of um + + + align:start position:0% +complimentary and that's this idea of um +ASM totic complexity so kind of + + align:start position:0% +ASM totic complexity so kind of + + + align:start position:0% +ASM totic complexity so kind of +mathematically saying you know what this + + align:start position:0% +mathematically saying you know what this + + + align:start position:0% +mathematically saying you know what this +program is not going to be that bad to + + align:start position:0% +program is not going to be that bad to + + + align:start position:0% +program is not going to be that bad to +run right it's you're not going to have + + align:start position:0% +run right it's you're not going to have + + + align:start position:0% +run right it's you're not going to have +to wait for it for months to run without + + align:start position:0% +to wait for it for months to run without + + + align:start position:0% +to wait for it for months to run without +actually running it of course so you'd + + align:start position:0% +actually running it of course so you'd + + + align:start position:0% +actually running it of course so you'd +be able to glance at a program and say + + align:start position:0% +be able to glance at a program and say + + + align:start position:0% +be able to glance at a program and say +this one is reasonable to run um and so + + align:start position:0% +this one is reasonable to run um and so + + + align:start position:0% +this one is reasonable to run um and so +we're going to do that in terms of uh + + align:start position:0% +we're going to do that in terms of uh + + + align:start position:0% +we're going to do that in terms of uh +this idea of order of growth which we'll + + align:start position:0% +this idea of order of growth which we'll + + + align:start position:0% +this idea of order of growth which we'll +get at to at in a little + + align:start position:0% +get at to at in a little + + + align:start position:0% +get at to at in a little +bit okay any questions on timing before + + align:start position:0% +bit okay any questions on timing before + + + align:start position:0% +bit okay any questions on timing before +we get to Counting oh + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +yes can you assume that all built-in + + align:start position:0% +yes can you assume that all built-in + + + align:start position:0% +yes can you assume that all built-in +functions are optimal in terms of + + align:start position:0% +functions are optimal in terms of + + + align:start position:0% +functions are optimal in terms of +running time yes certainly more better + + align:start position:0% +running time yes certainly more better + + + align:start position:0% +running time yes certainly more better +than when we when we write them + + align:start position:0% +than when we when we write them + + + align:start position:0% +than when we when we write them +um uh yes in Python and then of course + + align:start position:0% +um uh yes in Python and then of course + + + align:start position:0% +um uh yes in Python and then of course +in other languages you know there would + + align:start position:0% +in other languages you know there would + + + align:start position:0% +in other languages you know there would +be there maybe take advantage of other + + align:start position:0% +be there maybe take advantage of other + + + align:start position:0% +be there maybe take advantage of other +speedups as well like putting things in + + align:start position:0% +speedups as well like putting things in + + + align:start position:0% +speedups as well like putting things in +memory efficiently but yeah generally + + align:start position:0% +memory efficiently but yeah generally + + + align:start position:0% +memory efficiently but yeah generally +it's better to run something that's + + align:start position:0% +it's better to run something that's + + + align:start position:0% +it's better to run something that's +already been made than to make it + + align:start position:0% +already been made than to make it + + + align:start position:0% +already been made than to make it +yourself + + align:start position:0% +yourself + + + align:start position:0% +yourself +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay so now what we're going to do is + + align:start position:0% +okay so now what we're going to do is + + + align:start position:0% +okay so now what we're going to do is +we're going to count operations just + + align:start position:0% +we're going to count operations just + + + align:start position:0% +we're going to count operations just +like we did last lecture clearly timing + + align:start position:0% +like we did last lecture clearly timing + + + align:start position:0% +like we did last lecture clearly timing +is nice but it doesn't give us a nice + + align:start position:0% +is nice but it doesn't give us a nice + + + align:start position:0% +is nice but it doesn't give us a nice +relationship besides us like spotting it + + align:start position:0% +relationship besides us like spotting it + + + align:start position:0% +relationship besides us like spotting it +right um there's no formula there's no + + align:start position:0% +right um there's no formula there's no + + + align:start position:0% +right um there's no formula there's no +relationship that relates the input to + + align:start position:0% +relationship that relates the input to + + + align:start position:0% +relationship that relates the input to +how long it takes the program to run + + align:start position:0% +how long it takes the program to run + + + align:start position:0% +how long it takes the program to run +right counting will get us a little bit + + align:start position:0% +right counting will get us a little bit + + + align:start position:0% +right counting will get us a little bit +closer to that and we saw that last + + align:start position:0% +closer to that and we saw that last + + + align:start position:0% +closer to that and we saw that last +lecture let me remind you the idea of + + align:start position:0% +lecture let me remind you the idea of + + + align:start position:0% +lecture let me remind you the idea of +counting + + align:start position:0% +counting + + + align:start position:0% +counting +so the idea of counting is that we're + + align:start position:0% +so the idea of counting is that we're + + + align:start position:0% +so the idea of counting is that we're +going to take a bunch of these + + align:start position:0% +going to take a bunch of these + + + align:start position:0% +going to take a bunch of these +operations like mathematical operations + + align:start position:0% +operations like mathematical operations + + + align:start position:0% +operations like mathematical operations +comparisons uh indexing into something + + align:start position:0% +comparisons uh indexing into something + + + align:start position:0% +comparisons uh indexing into something +um assigning a value to a variable all + + align:start position:0% +um assigning a value to a variable all + + + align:start position:0% +um assigning a value to a variable all +of these things right when we run them + + align:start position:0% +of these things right when we run them + + + align:start position:0% +of these things right when we run them +yes they might run for different amounts + + align:start position:0% +yes they might run for different amounts + + + align:start position:0% +yes they might run for different amounts +of Time 1 * 10ga 9 versus 2 * 109 + + align:start position:0% +of Time 1 * 10ga 9 versus 2 * 109 + + + align:start position:0% +of Time 1 * 10ga 9 versus 2 * 109 +something like that but that's very + + align:start position:0% +something like that but that's very + + + align:start position:0% +something like that but that's very +that's not a very big difference and so + + align:start position:0% +that's not a very big difference and so + + + align:start position:0% +that's not a very big difference and so +what we're going to say is that every + + align:start position:0% +what we're going to say is that every + + + align:start position:0% +what we're going to say is that every +one of these operations will consider to + + align:start position:0% +one of these operations will consider to + + + align:start position:0% +one of these operations will consider to +be constant right they will take one + + align:start position:0% +be constant right they will take one + + + align:start position:0% +be constant right they will take one +unit of + + align:start position:0% +unit of + + + align:start position:0% +unit of +time so if we say that we can actually + + align:start position:0% +time so if we say that we can actually + + + align:start position:0% +time so if we say that we can actually +come up with a relationship that tells + + align:start position:0% +come up with a relationship that tells + + + align:start position:0% +come up with a relationship that tells +us according to you know that that + + align:start position:0% +us according to you know that that + + + align:start position:0% +us according to you know that that +relates the input to how much this how + + align:start position:0% +relates the input to how much this how + + + align:start position:0% +relates the input to how much this how +many operations this program will will + + align:start position:0% +many operations this program will will + + + align:start position:0% +many operations this program will will +run so here in the convert to kilometers + + align:start position:0% +run so here in the convert to kilometers + + + align:start position:0% +run so here in the convert to kilometers +what do we have we have one + + align:start position:0% +what do we have we have one + + + align:start position:0% +what do we have we have one +multiplication + + align:start position:0% +multiplication + + + align:start position:0% +multiplication +and you know just for the heck of it + + align:start position:0% +and you know just for the heck of it + + + align:start position:0% +and you know just for the heck of it +this lecture let's say the return also + + align:start position:0% +this lecture let's say the return also + + + align:start position:0% +this lecture let's say the return also +counts as an + + align:start position:0% +counts as an + + + align:start position:0% +counts as an +operation so in this convert to colomer + + align:start position:0% +operation so in this convert to colomer + + + align:start position:0% +operation so in this convert to colomer +function we have two operations notice + + align:start position:0% +function we have two operations notice + + + align:start position:0% +function we have two operations notice +that it's not really related to the + + align:start position:0% +that it's not really related to the + + + align:start position:0% +that it's not really related to the +input at all so the the amount of + + align:start position:0% +input at all so the the amount of + + + align:start position:0% +input at all so the the amount of +operations that this program takes to + + align:start position:0% +operations that this program takes to + + + align:start position:0% +operations that this program takes to +run is always two it matches what our + + align:start position:0% +run is always two it matches what our + + + align:start position:0% +run is always two it matches what our +timing said right it basically didn't + + align:start position:0% +timing said right it basically didn't + + + align:start position:0% +timing said right it basically didn't +matter what the input was it always took + + align:start position:0% +matter what the input was it always took + + + align:start position:0% +matter what the input was it always took +approximately the same amount of time to + + align:start position:0% +approximately the same amount of time to + + + align:start position:0% +approximately the same amount of time to +run + + align:start position:0% +run + + + align:start position:0% +run +okay the sum of function so it takes an + + align:start position:0% +okay the sum of function so it takes an + + + align:start position:0% +okay the sum of function so it takes an +an input list and it gets the sum of all + + align:start position:0% +an input list and it gets the sum of all + + + align:start position:0% +an input list and it gets the sum of all +the + + align:start position:0% +the + + + align:start position:0% +the +elements this one will do we'll have one + + align:start position:0% +elements this one will do we'll have one + + + align:start position:0% +elements this one will do we'll have one +operation for doing this assignment + + align:start position:0% +operation for doing this assignment + + + align:start position:0% +operation for doing this assignment +it'll have one operation for grabbing an + + align:start position:0% +it'll have one operation for grabbing an + + + align:start position:0% +it'll have one operation for grabbing an +an uh an element in my list L and + + align:start position:0% +an uh an element in my list L and + + + align:start position:0% +an uh an element in my list L and +assigning it to + + align:start position:0% +assigning it to + + + align:start position:0% +assigning it to +I it'll have two operations for this + + align:start position:0% +I it'll have two operations for this + + + align:start position:0% +I it'll have two operations for this +total plus equals I right remember total + + align:start position:0% +total plus equals I right remember total + + + align:start position:0% +total plus equals I right remember total +plus I on the right hand side is one + + align:start position:0% +plus I on the right hand side is one + + + align:start position:0% +plus I on the right hand side is one +operation and total equals that is my + + align:start position:0% +operation and total equals that is my + + + align:start position:0% +operation and total equals that is my +second operation so that's two + + align:start position:0% +second operation so that's two + + + align:start position:0% +second operation so that's two +operations and then let's not forget our + + align:start position:0% +operations and then let's not forget our + + + align:start position:0% +operations and then let's not forget our +for Loop that's kind of the important + + align:start position:0% +for Loop that's kind of the important + + + align:start position:0% +for Loop that's kind of the important +part of this function how many times + + align:start position:0% +part of this function how many times + + + align:start position:0% +part of this function how many times +will these three operations repeat this + + align:start position:0% +will these three operations repeat this + + + align:start position:0% +will these three operations repeat this +one plus these two well it's going to + + align:start position:0% +one plus these two well it's going to + + + align:start position:0% +one plus these two well it's going to +repeat however many elements I have in L + + align:start position:0% +repeat however many elements I have in L + + + align:start position:0% +repeat however many elements I have in L +so length L + + align:start position:0% +so length L + + + align:start position:0% +so length L +times okay and then again let's say we + + align:start position:0% +times okay and then again let's say we + + + align:start position:0% +times okay and then again let's say we +count the return the return will also be + + align:start position:0% +count the return the return will also be + + + align:start position:0% +count the return the return will also be +one operation so the total number of + + align:start position:0% +one operation so the total number of + + + align:start position:0% +one operation so the total number of +operations for this sum of function will + + align:start position:0% +operations for this sum of function will + + + align:start position:0% +operations for this sum of function will +be one for the total equal Z Plus length + + align:start position:0% +be one for the total equal Z Plus length + + + align:start position:0% +be one for the total equal Z Plus length +of L * 3 because there's three + + align:start position:0% +of L * 3 because there's three + + + align:start position:0% +of L * 3 because there's three +operations being done for each length of + + align:start position:0% +operations being done for each length of + + + align:start position:0% +operations being done for each length of +L plus another one for the return so + + align:start position:0% +L plus another one for the return so + + + align:start position:0% +L plus another one for the return so +that's going to be three length L + + + align:start position:0% +that's going to be three length L + + + + align:start position:0% +that's going to be three length L + +2 that's a nice little formula that + + align:start position:0% +2 that's a nice little formula that + + + align:start position:0% +2 that's a nice little formula that +relates uh how how how many units of + + align:start position:0% +relates uh how how how many units of + + + align:start position:0% +relates uh how how how many units of +time we'll have to wait depending on the + + align:start position:0% +time we'll have to wait depending on the + + + align:start position:0% +time we'll have to wait depending on the +size of the list right that's pretty + + align:start position:0% +size of the list right that's pretty + + + align:start position:0% +size of the list right that's pretty +cool so the way that we're going to + + align:start position:0% +cool so the way that we're going to + + + align:start position:0% +cool so the way that we're going to +count the number of oper options again + + align:start position:0% +count the number of oper options again + + + align:start position:0% +count the number of oper options again +I'm going to do it slightly differently + + align:start position:0% +I'm going to do it slightly differently + + + align:start position:0% +I'm going to do it slightly differently +in the last lecture just to show you + + align:start position:0% +in the last lecture just to show you + + + align:start position:0% +in the last lecture just to show you +that there is another way to do it so + + align:start position:0% +that there is another way to do it so + + + align:start position:0% +that there is another way to do it so +this is our function is in it's going to + + align:start position:0% +this is our function is in it's going to + + + align:start position:0% +this is our function is in it's going to +count how many operations we have and + + align:start position:0% +count how many operations we have and + + + align:start position:0% +count how many operations we have and +I'm going to use something called a + + align:start position:0% +I'm going to use something called a + + + align:start position:0% +I'm going to use something called a +global variable I'll show you again the + + align:start position:0% +global variable I'll show you again the + + + align:start position:0% +global variable I'll show you again the +difference between them so it's just + + align:start position:0% +difference between them so it's just + + + align:start position:0% +difference between them so it's just +these three lines that I + + align:start position:0% +these three lines that I + + + align:start position:0% +these three lines that I +added and you should never ever use + + align:start position:0% +added and you should never ever use + + + align:start position:0% +added and you should never ever use +Global variables in your programs except + + align:start position:0% +Global variables in your programs except + + + align:start position:0% +Global variables in your programs except +in this situation the idea of global + + align:start position:0% +in this situation the idea of global + + + align:start position:0% +in this situation the idea of global +variables is that you can Define + + align:start position:0% +variables is that you can Define + + + align:start position:0% +variables is that you can Define +variables just in the main program + + align:start position:0% +variables just in the main program + + + align:start position:0% +variables just in the main program +outside of any + + align:start position:0% +outside of any + + + align:start position:0% +outside of any +functions and you can access those + + align:start position:0% +functions and you can access those + + + align:start position:0% +functions and you can access those +variables within some function purely by + + align:start position:0% +variables within some function purely by + + + align:start position:0% +variables within some function purely by +saying you know if we defined count out + + align:start position:0% +saying you know if we defined count out + + + align:start position:0% +saying you know if we defined count out +here right before this function + + align:start position:0% +here right before this function + + + align:start position:0% +here right before this function +definition count equals zero or whatever + + align:start position:0% +definition count equals zero or whatever + + + align:start position:0% +definition count equals zero or whatever +inside of any function we can say hey + + align:start position:0% +inside of any function we can say hey + + + align:start position:0% +inside of any function we can say hey +python I would like to access this + + align:start position:0% +python I would like to access this + + + align:start position:0% +python I would like to access this +variable that I defined outside of this + + align:start position:0% +variable that I defined outside of this + + + align:start position:0% +variable that I defined outside of this +function you say that uh you tell python + + align:start position:0% +function you say that uh you tell python + + + align:start position:0% +function you say that uh you tell python +using Global and then the name of that + + align:start position:0% +using Global and then the name of that + + + align:start position:0% +using Global and then the name of that +variable and python will grab that + + align:start position:0% +variable and python will grab that + + + align:start position:0% +variable and python will grab that +variable that's B basically quote + + align:start position:0% +variable that's B basically quote + + + align:start position:0% +variable that's B basically quote +unquote shared across the entire program + + align:start position:0% +unquote shared across the entire program + + + align:start position:0% +unquote shared across the entire program +and modifi that variable right so in + + align:start position:0% +and modifi that variable right so in + + + align:start position:0% +and modifi that variable right so in +there in essence we're basically saying + + align:start position:0% +there in essence we're basically saying + + + align:start position:0% +there in essence we're basically saying +this is now a shared variable if I + + align:start position:0% +this is now a shared variable if I + + + align:start position:0% +this is now a shared variable if I +modify it within this counter within + + align:start position:0% +modify it within this counter within + + + align:start position:0% +modify it within this counter within +this function it'll be you know + + align:start position:0% +this function it'll be you know + + + align:start position:0% +this function it'll be you know +obviously modified for everything + + align:start position:0% +obviously modified for everything + + + align:start position:0% +obviously modified for everything +else it's very tempting to use Global + + align:start position:0% +else it's very tempting to use Global + + + align:start position:0% +else it's very tempting to use Global +variables because you know all the + + align:start position:0% +variables because you know all the + + + align:start position:0% +variables because you know all the +variables you could ever want to create + + align:start position:0% +variables you could ever want to create + + + align:start position:0% +variables you could ever want to create +are going to be accessible by everybody + + align:start position:0% +are going to be accessible by everybody + + + align:start position:0% +are going to be accessible by everybody +right no need to pass in parameters no + + align:start position:0% +right no need to pass in parameters no + + + align:start position:0% +right no need to pass in parameters no +need to do but it's it's very very bad + + align:start position:0% +need to do but it's it's very very bad + + + align:start position:0% +need to do but it's it's very very bad +programming so we won't ever do it + + align:start position:0% +programming so we won't ever do it + + + align:start position:0% +programming so we won't ever do it +except in this particular case because + + align:start position:0% +except in this particular case because + + + align:start position:0% +except in this particular case because +we'd like to keep a counter of things + + align:start position:0% +we'd like to keep a counter of things + + + align:start position:0% +we'd like to keep a counter of things +that are happening or for debugging + + align:start position:0% +that are happening or for debugging + + + align:start position:0% +that are happening or for debugging +purposes and things like + + align:start position:0% +purposes and things like + + + align:start position:0% +purposes and things like +that so the count variable will keep + + align:start position:0% +that so the count variable will keep + + + align:start position:0% +that so the count variable will keep +track of uh it'll just increment in key + + align:start position:0% +track of uh it'll just increment in key + + + align:start position:0% +track of uh it'll just increment in key +places where we have these constant unit + + align:start position:0% +places where we have these constant unit + + + align:start position:0% +places where we have these constant unit +of times happening so I've got count + + align:start position:0% +of times happening so I've got count + + + align:start position:0% +of times happening so I've got count +plus equals 1 here because I've got my + + align:start position:0% +plus equals 1 here because I've got my + + + align:start position:0% +plus equals 1 here because I've got my +return value I've got count plus equals + + align:start position:0% +return value I've got count plus equals + + + align:start position:0% +return value I've got count plus equals +2 here because I grab an element from L + + align:start position:0% +2 here because I grab an element from L + + + align:start position:0% +2 here because I grab an element from L +and I do the equality check here and + + align:start position:0% +and I do the equality check here and + + + align:start position:0% +and I do the equality check here and +then that's it okay oops + + align:start position:0% + + + + align:start position:0% + +Sor so if I run that it's down + + align:start position:0% + + + + align:start position:0% + +here what are we going to + + align:start position:0% +here what are we going to + + + align:start position:0% +here what are we going to +see + + align:start position:0% +see + + + align:start position:0% +see +well I didn't actually do how many how + + align:start position:0% +well I didn't actually do how many how + + + align:start position:0% +well I didn't actually do how many how +much more it ran but we can see the the + + align:start position:0% +much more it ran but we can see the the + + + align:start position:0% +much more it ran but we can see the the +relationship ship right we go 9 to 37 to + + align:start position:0% +relationship ship right we go 9 to 37 to + + + align:start position:0% +relationship ship right we go 9 to 37 to +3007 to 37 to 30,7 and so on so again + + align:start position:0% +3007 to 37 to 30,7 and so on so again + + + align:start position:0% +3007 to 37 to 30,7 and so on so again +the same relationship where we increase + + align:start position:0% +the same relationship where we increase + + + align:start position:0% +the same relationship where we increase +the input by 10 the amount number of + + align:start position:0% +the input by 10 the amount number of + + + align:start position:0% +the input by 10 the amount number of +operations we do is 10 times as more + + align:start position:0% +operations we do is 10 times as more + + + align:start position:0% +operations we do is 10 times as more +exactly like the formula said it would + + align:start position:0% +exactly like the formula said it would + + + align:start position:0% +exactly like the formula said it would +be what about the binary search so again + + align:start position:0% +be what about the binary search so again + + + align:start position:0% +be what about the binary search so again +we're going to use this Global variable + + align:start position:0% +we're going to use this Global variable + + + align:start position:0% +we're going to use this Global variable +and we're going to have the counter keep + + align:start position:0% +and we're going to have the counter keep + + + align:start position:0% +and we're going to have the counter keep +track of all of these operations so this + + align:start position:0% +track of all of these operations so this + + + align:start position:0% +track of all of these operations so this +count uh incrementing by three accounts + + align:start position:0% +count uh incrementing by three accounts + + + align:start position:0% +count uh incrementing by three accounts +for setting the low to zero setting the + + align:start position:0% +for setting the low to zero setting the + + + align:start position:0% +for setting the low to zero setting the +he is this thing and grabbing this + + align:start position:0% +he is this thing and grabbing this + + + align:start position:0% +he is this thing and grabbing this +actual value of + + align:start position:0% +actual value of + + + align:start position:0% +actual value of +length incrementing the count within + + align:start position:0% +length incrementing the count within + + + align:start position:0% +length incrementing the count within +this while loop will keep track of this + + align:start position:0% +this while loop will keep track of this + + + align:start position:0% +this while loop will keep track of this +subtraction as one operation and the + + align:start position:0% +subtraction as one operation and the + + + align:start position:0% +subtraction as one operation and the +test that it's greater than one as + + align:start position:0% +test that it's greater than one as + + + align:start position:0% +test that it's greater than one as +another + + align:start position:0% +another + + + align:start position:0% +another +operation counting uh uh increasing by + + align:start position:0% +operation counting uh uh increasing by + + + align:start position:0% +operation counting uh uh increasing by +three here accounts for high plus low + + align:start position:0% +three here accounts for high plus low + + + align:start position:0% +three here accounts for high plus low +the integer Division and assigning that + + align:start position:0% +the integer Division and assigning that + + + align:start position:0% +the integer Division and assigning that +value back to + + align:start position:0% +value back to + + + align:start position:0% +value back to +Mid count plus three here accounts for + + align:start position:0% +Mid count plus three here accounts for + + + align:start position:0% +Mid count plus three here accounts for +indexing into this l + + align:start position:0% +indexing into this l + + + align:start position:0% +indexing into this l +the less than or equal check and then + + align:start position:0% +the less than or equal check and then + + + align:start position:0% +the less than or equal check and then +either doing this reassignment of low or + + align:start position:0% +either doing this reassignment of low or + + + align:start position:0% +either doing this reassignment of low or +this reassignment of high right so + + align:start position:0% +this reassignment of high right so + + + align:start position:0% +this reassignment of high right so +that's three operations and then lastly + + align:start position:0% +that's three operations and then lastly + + + align:start position:0% +that's three operations and then lastly +count increases by three once more + + align:start position:0% +count increases by three once more + + + align:start position:0% +count increases by three once more +because I've got these operations here + + align:start position:0% +because I've got these operations here + + + align:start position:0% +because I've got these operations here +so indexing into the into low checking + + align:start position:0% +so indexing into the into low checking + + + align:start position:0% +so indexing into the into low checking +for equality and then doing the return + + align:start position:0% +for equality and then doing the return + + + align:start position:0% +for equality and then doing the return +okay so the actual number of operations + + align:start position:0% +okay so the actual number of operations + + + align:start position:0% +okay so the actual number of operations +will be kept track of in right by the + + align:start position:0% +will be kept track of in right by the + + + align:start position:0% +will be kept track of in right by the +counter so all doing is just kind of + + align:start position:0% +counter so all doing is just kind of + + + align:start position:0% +counter so all doing is just kind of +reporting how many uh times how many + + align:start position:0% +reporting how many uh times how many + + + align:start position:0% +reporting how many uh times how many +operations we've done so as we increase + + align:start position:0% +operations we've done so as we increase + + + align:start position:0% +operations we've done so as we increase +the input by 10 uh just like with timing + + align:start position:0% +the input by 10 uh just like with timing + + + align:start position:0% +the input by 10 uh just like with timing +we can't quite tell what the + + align:start position:0% +we can't quite tell what the + + + align:start position:0% +we can't quite tell what the +relationship is right again it's it's + + align:start position:0% +relationship is right again it's it's + + + align:start position:0% +relationship is right again it's it's +like one point something right with each + + align:start position:0% + + + + align:start position:0% + +run all right so this is uh these are + + align:start position:0% +run all right so this is uh these are + + + align:start position:0% +run all right so this is uh these are +the uh the results so the observation + + align:start position:0% +the uh the results so the observation + + + align:start position:0% +the uh the results so the observation +one as I mentioned when we increase the + + align:start position:0% +one as I mentioned when we increase the + + + align:start position:0% +one as I mentioned when we increase the +input by 10 this Brute Force I ered it + + align:start position:0% +input by 10 this Brute Force I ered it + + + align:start position:0% +input by 10 this Brute Force I ered it +but the brute force is in function also + + align:start position:0% +but the brute force is in function also + + + align:start position:0% +but the brute force is in function also +is uh does 10 times as many operations + + align:start position:0% +is uh does 10 times as many operations + + + align:start position:0% +is uh does 10 times as many operations +the binary search again we don't know + + align:start position:0% +the binary search again we don't know + + + align:start position:0% +the binary search again we don't know +what rate it is at but we can plot them + + align:start position:0% +what rate it is at but we can plot them + + + align:start position:0% +what rate it is at but we can plot them +so here I have the plots just like when + + align:start position:0% +so here I have the plots just like when + + + align:start position:0% +so here I have the plots just like when +I plotted the input size versus how long + + align:start position:0% +I plotted the input size versus how long + + + align:start position:0% +I plotted the input size versus how long +the program actually took to run I'm now + + align:start position:0% +the program actually took to run I'm now + + + align:start position:0% +the program actually took to run I'm now +plotting the input size versus actually + + align:start position:0% +plotting the input size versus actually + + + align:start position:0% +plotting the input size versus actually +just the number of operations being done + + align:start position:0% +just the number of operations being done + + + align:start position:0% +just the number of operations being done +so the isin function that Brute Force + + align:start position:0% +so the isin function that Brute Force + + + align:start position:0% +so the isin function that Brute Force +way of finding whether an element is in + + align:start position:0% +way of finding whether an element is in + + + align:start position:0% +way of finding whether an element is in +a list grows linearly no surprise there + + align:start position:0% +a list grows linearly no surprise there + + + align:start position:0% +a list grows linearly no surprise there +and how lucky for us um the binary + + align:start position:0% +and how lucky for us um the binary + + + align:start position:0% +and how lucky for us um the binary +search matches uh the graph matches the + + align:start position:0% +search matches uh the graph matches the + + + align:start position:0% +search matches uh the graph matches the +one that we had for timing right so as I + + align:start position:0% +one that we had for timing right so as I + + + align:start position:0% +one that we had for timing right so as I +increase my size in the binary search + + align:start position:0% +increase my size in the binary search + + + align:start position:0% +increase my size in the binary search +method the number of operations that I + + align:start position:0% +method the number of operations that I + + + align:start position:0% +method the number of operations that I +do is logarithmic in in time just like + + align:start position:0% +do is logarithmic in in time just like + + + align:start position:0% +do is logarithmic in in time just like +we saw in in the actual + + align:start position:0% +we saw in in the actual + + + align:start position:0% +we saw in in the actual +timing + + align:start position:0% +timing + + + align:start position:0% +timing +okay so timing and Counting are really + + align:start position:0% +okay so timing and Counting are really + + + align:start position:0% +okay so timing and Counting are really +nice right timing gives us pure number + + align:start position:0% +nice right timing gives us pure number + + + align:start position:0% +nice right timing gives us pure number +of seconds or you know months or + + align:start position:0% +of seconds or you know months or + + + align:start position:0% +of seconds or you know months or +whatever we need to wait for this + + align:start position:0% +whatever we need to wait for this + + + align:start position:0% +whatever we need to wait for this +program to finish but counting gives us + + align:start position:0% +program to finish but counting gives us + + + align:start position:0% +program to finish but counting gives us +a nice little formula right that relates + + align:start position:0% +a nice little formula right that relates + + + align:start position:0% +a nice little formula right that relates +the input to the number of of of + + align:start position:0% +the input to the number of of of + + + align:start position:0% +the input to the number of of of +operations that you have to do you might + + align:start position:0% +operations that you have to do you might + + + align:start position:0% +operations that you have to do you might +have noticed I briefly touched upon this + + align:start position:0% +have noticed I briefly touched upon this + + + align:start position:0% +have noticed I briefly touched upon this +that throughout this entire lecture and + + align:start position:0% +that throughout this entire lecture and + + + align:start position:0% +that throughout this entire lecture and +last lecture we basically just saw + + align:start position:0% +last lecture we basically just saw + + + align:start position:0% +last lecture we basically just saw +something like you know three different + + align:start position:0% +something like you know three different + + + align:start position:0% +something like you know three different +algorithms right we saw something that's + + align:start position:0% +algorithms right we saw something that's + + + align:start position:0% +algorithms right we saw something that's +constant something that's linear + + align:start position:0% +constant something that's linear + + + align:start position:0% +constant something that's linear +something that's you know quadratic and + + align:start position:0% +something that's you know quadratic and + + + align:start position:0% +something that's you know quadratic and +something that's B uh binary C + + align:start position:0% +something that's B uh binary C + + + align:start position:0% +something that's B uh binary C +logarithmic in this particular case + + align:start position:0% +logarithmic in this particular case + + + align:start position:0% +logarithmic in this particular case +right so that's four different + + align:start position:0% +right so that's four different + + + align:start position:0% +right so that's four different +algorithms but we saw way more functions + + align:start position:0% +algorithms but we saw way more functions + + + align:start position:0% +algorithms but we saw way more functions +run right so what we'd like to do is + + align:start position:0% +run right so what we'd like to do is + + + align:start position:0% +run right so what we'd like to do is +evaluate the algorithms not the + + align:start position:0% +evaluate the algorithms not the + + + align:start position:0% +evaluate the algorithms not the +different implementations right and what + + align:start position:0% +different implementations right and what + + + align:start position:0% +different implementations right and what +we'd like to do is evaluate these + + align:start position:0% +we'd like to do is evaluate these + + + align:start position:0% +we'd like to do is evaluate these +algorithms as the input gets really + + align:start position:0% +algorithms as the input gets really + + + align:start position:0% +algorithms as the input gets really +really big so what we're going to do is + + align:start position:0% +really big so what we're going to do is + + + align:start position:0% +really big so what we're going to do is +figure out a relationship between the + + align:start position:0% +figure out a relationship between the + + + align:start position:0% +figure out a relationship between the +programs run time + + align:start position:0% +programs run time + + + align:start position:0% +programs run time +time and the input but what we're going + + align:start position:0% +time and the input but what we're going + + + align:start position:0% +time and the input but what we're going +to do is focus on the biggest terms that + + align:start position:0% +to do is focus on the biggest terms that + + + align:start position:0% +to do is focus on the biggest terms that +contribute to the program's runtime + + align:start position:0% +contribute to the program's runtime + + + align:start position:0% +contribute to the program's runtime +right so we saw these examples last time + + align:start position:0% +right so we saw these examples last time + + + align:start position:0% +right so we saw these examples last time +right this my sum which basically summed + + align:start position:0% +right this my sum which basically summed + + + align:start position:0% +right this my sum which basically summed +all the elements sorry all the numbers + + align:start position:0% +all the elements sorry all the numbers + + + align:start position:0% +all the elements sorry all the numbers +from 0 to X and this the silly Square + + align:start position:0% +from 0 to X and this the silly Square + + + align:start position:0% +from 0 to X and this the silly Square +function that had nested Loops kind of + + align:start position:0% +function that had nested Loops kind of + + + align:start position:0% +function that had nested Loops kind of +like this diameter one right we were + + align:start position:0% +like this diameter one right we were + + + align:start position:0% +like this diameter one right we were +able to say something like um you know + + align:start position:0% +able to say something like um you know + + + align:start position:0% +able to say something like um you know +when the input increases by 10 + + align:start position:0% +when the input increases by 10 + + + align:start position:0% +when the input increases by 10 +the program is 10 times as long to run + + align:start position:0% +the program is 10 times as long to run + + + align:start position:0% +the program is 10 times as long to run +right so the efficiency of that program + + align:start position:0% +right so the efficiency of that program + + + align:start position:0% +right so the efficiency of that program +was on the order of X when the input + + align:start position:0% +was on the order of X when the input + + + align:start position:0% +was on the order of X when the input +increased by X the program took x times + + align:start position:0% +increased by X the program took x times + + + align:start position:0% +increased by X the program took x times +as long to run the square had a similar + + align:start position:0% +as long to run the square had a similar + + + align:start position:0% +as long to run the square had a similar +we could have said it in a similar way + + align:start position:0% +we could have said it in a similar way + + + align:start position:0% +we could have said it in a similar way +right when the input increases by X the + + align:start position:0% +right when the input increases by X the + + + align:start position:0% +right when the input increases by X the +program took X squ as long to run so I + + align:start position:0% +program took X squ as long to run so I + + + align:start position:0% +program took X squ as long to run so I +don't actually care right about all of + + align:start position:0% +don't actually care right about all of + + + align:start position:0% +don't actually care right about all of +these differences in the exact timings 1 + + align:start position:0% +these differences in the exact timings 1 + + + align:start position:0% +these differences in the exact timings 1 +* 10-6 1.3 * 10 to6 I don't care what I + + align:start position:0% +* 10-6 1.3 * 10 to6 I don't care what I + + + align:start position:0% +* 10-6 1.3 * 10 to6 I don't care what I +do care is the order of growth how does + + align:start position:0% +do care is the order of growth how does + + + align:start position:0% +do care is the order of growth how does +the program run in relation to the input + + align:start position:0% +the program run in relation to the input + + + align:start position:0% +the program run in relation to the input +okay and I care about that when the + + align:start position:0% +okay and I care about that when the + + + align:start position:0% +okay and I care about that when the +input is really really big so what we're + + align:start position:0% +input is really really big so what we're + + + align:start position:0% +input is really really big so what we're +going to do is Express the program's + + align:start position:0% +going to do is Express the program's + + + align:start position:0% +going to do is Express the program's +runtime in an order of not exact kind of + + align:start position:0% +runtime in an order of not exact kind of + + + align:start position:0% +runtime in an order of not exact kind of +relationship so while counting was + + align:start position:0% +relationship so while counting was + + + align:start position:0% +relationship so while counting was +really nice right it told us a nice + + align:start position:0% +really nice right it told us a nice + + + align:start position:0% +really nice right it told us a nice +relationship between the input and the + + align:start position:0% +relationship between the input and the + + + align:start position:0% +relationship between the input and the +number of + + align:start position:0% +number of + + + align:start position:0% +number of +operations when the input is really + + align:start position:0% +operations when the input is really + + + align:start position:0% +operations when the input is really +really big like 3x+ 4 when X is really + + align:start position:0% +really big like 3x+ 4 when X is really + + + align:start position:0% +really big like 3x+ 4 when X is really +really big I don't care that the number + + align:start position:0% +really big I don't care that the number + + + align:start position:0% +really big I don't care that the number +of operations is 3x + 4 right because + + align:start position:0% +of operations is 3x + 4 right because + + + align:start position:0% +of operations is 3x + 4 right because +when X is really really big that plus4 + + align:start position:0% +when X is really really big that plus4 + + + align:start position:0% +when X is really really big that plus4 +might as well be plus Z and that 3x is + + align:start position:0% +might as well be plus Z and that 3x is + + + align:start position:0% +might as well be plus Z and that 3x is +basically like X when the input is + + align:start position:0% +basically like X when the input is + + + align:start position:0% +basically like X when the input is +really really big right so that's what + + align:start position:0% +really really big right so that's what + + + align:start position:0% +really really big right so that's what +we're going to try to do all right now + + align:start position:0% +we're going to try to do all right now + + + align:start position:0% +we're going to try to do all right now +before we do that we need to decide what + + align:start position:0% +before we do that we need to decide what + + + align:start position:0% +before we do that we need to decide what +to measure right because when we write + + align:start position:0% +to measure right because when we write + + + align:start position:0% +to measure right because when we write +functions we're going to have functions + + align:start position:0% +functions we're going to have functions + + + align:start position:0% +functions we're going to have functions +that have a whole bunch of inputs + + align:start position:0% +that have a whole bunch of inputs + + + align:start position:0% +that have a whole bunch of inputs +potentially right so the input could be + + align:start position:0% +potentially right so the input could be + + + align:start position:0% +potentially right so the input could be +an integer like in convert to kilometers + + align:start position:0% +an integer like in convert to kilometers + + + align:start position:0% +an integer like in convert to kilometers +it could be a list in which case we + + align:start position:0% +it could be a list in which case we + + + align:start position:0% +it could be a list in which case we +would be interested in maybe the length + + align:start position:0% +would be interested in maybe the length + + + align:start position:0% +would be interested in maybe the length +of the list and if you have many + + align:start position:0% +of the list and if you have many + + + align:start position:0% +of the list and if you have many +parameters you'd have to decide right + + align:start position:0% +parameters you'd have to decide right + + + align:start position:0% +parameters you'd have to decide right +what is the parameter that contributes + + align:start position:0% +what is the parameter that contributes + + + align:start position:0% +what is the parameter that contributes +to the to the growth of this + + align:start position:0% +to the to the growth of this + + + align:start position:0% +to the to the growth of this +function so here's an example + + align:start position:0% +function so here's an example + + + align:start position:0% +function so here's an example +uh this is our is in function it looks + + align:start position:0% +uh this is our is in function it looks + + + align:start position:0% +uh this is our is in function it looks +for an element e in list L right so + + align:start position:0% +for an element e in list L right so + + + align:start position:0% +for an element e in list L right so +there's two parameters to this + + align:start position:0% +there's two parameters to this + + + align:start position:0% +there's two parameters to this +one we can ask does the program take + + align:start position:0% +one we can ask does the program take + + + align:start position:0% +one we can ask does the program take +longer to run as e increases right it's + + align:start position:0% +longer to run as e increases right it's + + + align:start position:0% +longer to run as e increases right it's +one of the parameters let's see what + + align:start position:0% +one of the parameters let's see what + + + align:start position:0% +one of the parameters let's see what +happens as we make e bigger so we can + + align:start position:0% +happens as we make e bigger so we can + + + align:start position:0% +happens as we make e bigger so we can +look at a little example if we find out + + align:start position:0% +look at a little example if we find out + + + align:start position:0% +look at a little example if we find out +whether zero is in this list containing + + align:start position:0% +whether zero is in this list containing + + + align:start position:0% +whether zero is in this list containing +One Two Three or whether a thousand is + + align:start position:0% +One Two Three or whether a thousand is + + + align:start position:0% +One Two Three or whether a thousand is +in the list 1 two 3 does the program + + align:start position:0% +in the list 1 two 3 does the program + + + align:start position:0% +in the list 1 two 3 does the program +take longer to run no no exactly so e is + + align:start position:0% +take longer to run no no exactly so e is + + + align:start position:0% +take longer to run no no exactly so e is +not really relevant in my runtime sort + + align:start position:0% +not really relevant in my runtime sort + + + align:start position:0% +not really relevant in my runtime sort +of uh calculation here all right well + + align:start position:0% +of uh calculation here all right well + + + align:start position:0% +of uh calculation here all right well +let's consider L + + align:start position:0% +let's consider L + + + align:start position:0% +let's consider L +now when we say l is going to change it + + align:start position:0% +now when we say l is going to change it + + + align:start position:0% +now when we say l is going to change it +could change in two ways right the + + align:start position:0% +could change in two ways right the + + + align:start position:0% +could change in two ways right the +elements in L could have different + + align:start position:0% +elements in L could have different + + + align:start position:0% +elements in L could have different +values right or the list length itself + + align:start position:0% +values right or the list length itself + + + align:start position:0% +values right or the list length itself +could be + + align:start position:0% +could be + + + align:start position:0% +could be +different so in this particular function + + align:start position:0% +different so in this particular function + + + align:start position:0% +different so in this particular function +let's say that the elements in L are + + align:start position:0% +let's say that the elements in L are + + + align:start position:0% +let's say that the elements in L are +small numbers versus big numbers okay + + align:start position:0% +small numbers versus big numbers okay + + + align:start position:0% +small numbers versus big numbers okay +that's certainly something that could + + align:start position:0% +that's certainly something that could + + + align:start position:0% +that's certainly something that could +happen and certainly with some functions + + align:start position:0% +happen and certainly with some functions + + + align:start position:0% +happen and certainly with some functions +that's going to make a difference so + + align:start position:0% +that's going to make a difference so + + + align:start position:0% +that's going to make a difference so +let's say in this particular function if + + align:start position:0% +let's say in this particular function if + + + align:start position:0% +let's say in this particular function if +the elements in L are big versus small + + align:start position:0% +the elements in L are big versus small + + + align:start position:0% +the elements in L are big versus small +is it going to make an impact on my + + align:start position:0% +is it going to make an impact on my + + + align:start position:0% +is it going to make an impact on my +runtime well here's a little example + + align:start position:0% +runtime well here's a little example + + + align:start position:0% +runtime well here's a little example +let's say I'm looking for the number + + align:start position:0% +let's say I'm looking for the number + + + align:start position:0% +let's say I'm looking for the number +zero inside a list with one two three + + align:start position:0% +zero inside a list with one two three + + + align:start position:0% +zero inside a list with one two three +and the number zero inside a list with a + + align:start position:0% +and the number zero inside a list with a + + + align:start position:0% +and the number zero inside a list with a +th 2,000 and + + align:start position:0% +th 2,000 and + + + align:start position:0% +th 2,000 and +3,000 is that going to make a + + align:start position:0% +3,000 is that going to make a + + + align:start position:0% +3,000 is that going to make a +difference no right + + align:start position:0% +difference no right + + + align:start position:0% +difference no right +so the size of the elements themselves + + align:start position:0% +so the size of the elements themselves + + + align:start position:0% +so the size of the elements themselves +don't really + + align:start position:0% +don't really + + + align:start position:0% +don't really +matter and one last thing to ask + + align:start position:0% +matter and one last thing to ask + + + align:start position:0% +matter and one last thing to ask +ourselves is what about the length of + + align:start position:0% +ourselves is what about the length of + + + align:start position:0% +ourselves is what about the length of +the list so if L has different lengths + + align:start position:0% +the list so if L has different lengths + + + align:start position:0% +the list so if L has different lengths +will this make a difference in our + + align:start position:0% +will this make a difference in our + + + align:start position:0% +will this make a difference in our +runtime right so if I'm looking for zero + + align:start position:0% +runtime right so if I'm looking for zero + + + align:start position:0% +runtime right so if I'm looking for zero +and a list with three elements or zero + + align:start position:0% +and a list with three elements or zero + + + align:start position:0% +and a list with three elements or zero +in a list with 10 elements where clearly + + align:start position:0% +in a list with 10 elements where clearly + + + align:start position:0% +in a list with 10 elements where clearly +that zero is nowhere to be found is that + + align:start position:0% +that zero is nowhere to be found is that + + + align:start position:0% +that zero is nowhere to be found is that +length list L going to have a difference + + align:start position:0% +length list L going to have a difference + + + align:start position:0% +length list L going to have a difference +yeah in this case it will exactly so + + align:start position:0% +yeah in this case it will exactly so + + + align:start position:0% +yeah in this case it will exactly so +here in this particular function the + + align:start position:0% +here in this particular function the + + + align:start position:0% +here in this particular function the +input I'd be interested in uh in in sort + + align:start position:0% +input I'd be interested in uh in in sort + + + align:start position:0% +input I'd be interested in uh in in sort +of uh reporting the runtime from is the + + align:start position:0% +of uh reporting the runtime from is the + + + align:start position:0% +of uh reporting the runtime from is the +length of the list right not the + + align:start position:0% +length of the list right not the + + + align:start position:0% +length of the list right not the +elements in the list not e itself but + + align:start position:0% +elements in the list not e itself but + + + align:start position:0% +elements in the list not e itself but +the length of the + + align:start position:0% +the length of the + + + align:start position:0% +the length of the +list okay so the last thing that I'll + + align:start position:0% +list okay so the last thing that I'll + + + align:start position:0% +list okay so the last thing that I'll +mention is for this particular class + + align:start position:0% +mention is for this particular class + + + align:start position:0% +mention is for this particular class +we're going to talk about the worst case + + align:start position:0% +we're going to talk about the worst case + + + align:start position:0% +we're going to talk about the worst case +scenario so you might have noticed in + + align:start position:0% +scenario so you might have noticed in + + + align:start position:0% +scenario so you might have noticed in +this previous example here right I + + align:start position:0% +this previous example here right I + + + align:start position:0% +this previous example here right I +always looked for an element that wasn't + + align:start position:0% +always looked for an element that wasn't + + + align:start position:0% +always looked for an element that wasn't +even in the list right so when you're + + align:start position:0% +even in the list right so when you're + + + align:start position:0% +even in the list right so when you're +faced with a function you ask yourself + + align:start position:0% +faced with a function you ask yourself + + + align:start position:0% +faced with a function you ask yourself +this particular class at least what is + + align:start position:0% +this particular class at least what is + + + align:start position:0% +this particular class at least what is +the worst case scenario and finding out + + align:start position:0% +the worst case scenario and finding out + + + align:start position:0% +the worst case scenario and finding out +whether are functions in the list the + + align:start position:0% +whether are functions in the list the + + + align:start position:0% +whether are functions in the list the +worst case scenario for us is if it's + + align:start position:0% +worst case scenario for us is if it's + + + align:start position:0% +worst case scenario for us is if it's +not in the list at all + + align:start position:0% +not in the list at all + + + align:start position:0% +not in the list at all +right um so that's sort of another um um + + align:start position:0% +right um so that's sort of another um um + + + align:start position:0% +right um so that's sort of another um um +aspect of of runtime that we don't + + align:start position:0% +aspect of of runtime that we don't + + + align:start position:0% +aspect of of runtime that we don't +actually we won't talk about because for + + align:start position:0% +actually we won't talk about because for + + + align:start position:0% +actually we won't talk about because for +us we're always interested in the worst + + align:start position:0% +us we're always interested in the worst + + + align:start position:0% +us we're always interested in the worst +case but there are certain certainly + + align:start position:0% +case but there are certain certainly + + + align:start position:0% +case but there are certain certainly +analyses where you could look at the + + align:start position:0% +analyses where you could look at the + + + align:start position:0% +analyses where you could look at the +best case scenario which is well the + + align:start position:0% +best case scenario which is well the + + + align:start position:0% +best case scenario which is well the +element is the first one in the list + + align:start position:0% +element is the first one in the list + + + align:start position:0% +element is the first one in the list +right in that case you're always going + + align:start position:0% +right in that case you're always going + + + align:start position:0% +right in that case you're always going +to find it right away so it's constant + + align:start position:0% +to find it right away so it's constant + + + align:start position:0% +to find it right away so it's constant +um or an average case scenario which is + + align:start position:0% +um or an average case scenario which is + + + align:start position:0% +um or an average case scenario which is +kind of what people do in the real world + + align:start position:0% +kind of what people do in the real world + + + align:start position:0% +kind of what people do in the real world +right you're not always encountering the + + align:start position:0% +right you're not always encountering the + + + align:start position:0% +right you're not always encountering the +worst case but for us we're going to + + align:start position:0% +worst case but for us we're going to + + + align:start position:0% +worst case but for us we're going to +look at the worst case scenario so our + + align:start position:0% +look at the worst case scenario so our + + + align:start position:0% +look at the worst case scenario so our +goal is going to be to describe how the + + align:start position:0% +goal is going to be to describe how the + + + align:start position:0% +goal is going to be to describe how the +runtime grows as the size of the input + + align:start position:0% +runtime grows as the size of the input + + + align:start position:0% +runtime grows as the size of the input +grows in a really General way so we're + + align:start position:0% +grows in a really General way so we're + + + align:start position:0% +grows in a really General way so we're +not going to be interested in figuring + + align:start position:0% +not going to be interested in figuring + + + align:start position:0% +not going to be interested in figuring +out the exact number of operations no 3x + + align:start position:0% +out the exact number of operations no 3x + + + align:start position:0% +out the exact number of operations no 3x +plus 2 kind of deal here we're just + + align:start position:0% +plus 2 kind of deal here we're just + + + align:start position:0% +plus 2 kind of deal here we're just +going to focus on terms that are really + + align:start position:0% +going to focus on terms that are really + + + align:start position:0% +going to focus on terms that are really +that grow the fastest we're going to + + align:start position:0% +that grow the fastest we're going to + + + align:start position:0% +that grow the fastest we're going to +eliminate any sort of additive + + align:start position:0% +eliminate any sort of additive + + + align:start position:0% +eliminate any sort of additive +multiplicative constants and things like + + align:start position:0% +multiplicative constants and things like + + + align:start position:0% +multiplicative constants and things like +that so we're just going to focus on + + align:start position:0% +that so we're just going to focus on + + + align:start position:0% +that so we're just going to focus on +terms that grow the fastest and that + + align:start position:0% +terms that grow the fastest and that + + + align:start position:0% +terms that grow the fastest and that +will give us our order of growth so the + + align:start position:0% +will give us our order of growth so the + + + align:start position:0% +will give us our order of growth so the +way we're going to denote the order of + + align:start position:0% +way we're going to denote the order of + + + align:start position:0% +way we're going to denote the order of +growth is using this notation called Big + + align:start position:0% +growth is using this notation called Big + + + align:start position:0% +growth is using this notation called Big +O and big Theta okay now warning we're + + align:start position:0% +O and big Theta okay now warning we're + + + align:start position:0% +O and big Theta okay now warning we're +going to have some math coming our way + + align:start position:0% +going to have some math coming our way + + + align:start position:0% +going to have some math coming our way +it's going to be like three slides of + + align:start position:0% +it's going to be like three slides of + + + align:start position:0% +it's going to be like three slides of +just pure math okay you can sit back you + + align:start position:0% +just pure math okay you can sit back you + + + align:start position:0% +just pure math okay you can sit back you +won't need to know it uh won't need to + + align:start position:0% +won't need to know it uh won't need to + + + align:start position:0% +won't need to know it uh won't need to +know the details but it will motivate us + + align:start position:0% +know the details but it will motivate us + + + align:start position:0% +know the details but it will motivate us +to to to kind of give us the idea about + + align:start position:0% +to to to kind of give us the idea about + + + align:start position:0% +to to to kind of give us the idea about +this ASM totic order of + + align:start position:0% +this ASM totic order of + + + align:start position:0% +this ASM totic order of +growth all right so this is the the + + align:start position:0% +growth all right so this is the the + + + align:start position:0% +growth all right so this is the the +mathematical definition of Big O right + + align:start position:0% +mathematical definition of Big O right + + + align:start position:0% +mathematical definition of Big O right +so what we would like to do there will + + align:start position:0% +so what we would like to do there will + + + align:start position:0% +so what we would like to do there will +be a drawing don't worry so what we + + align:start position:0% +be a drawing don't worry so what we + + + align:start position:0% +be a drawing don't worry so what we +would like to do is figure out uh an + + align:start position:0% +would like to do is figure out uh an + + + align:start position:0% +would like to do is figure out uh an +upper Bound for our function so the + + align:start position:0% +upper Bound for our function so the + + + align:start position:0% +upper Bound for our function so the +function might look like this and I know + + align:start position:0% +function might look like this and I know + + + align:start position:0% +function might look like this and I know +this is just an F but we relate this to + + align:start position:0% +this is just an F but we relate this to + + + align:start position:0% +this is just an F but we relate this to +our class by saying you know what if we + + align:start position:0% +our class by saying you know what if we + + + align:start position:0% +our class by saying you know what if we +did the order of calculation sorry the + + align:start position:0% +did the order of calculation sorry the + + + align:start position:0% +did the order of calculation sorry the +number of operations analysis right for + + align:start position:0% +number of operations analysis right for + + + align:start position:0% +number of operations analysis right for +a function we could basically come up + + align:start position:0% +a function we could basically come up + + + align:start position:0% +a function we could basically come up +with something like this right we came + + align:start position:0% +with something like this right we came + + + align:start position:0% +with something like this right we came +up with 3x + 2 we could come up with + + align:start position:0% +up with 3x + 2 we could come up with + + + align:start position:0% +up with 3x + 2 we could come up with +3x^2 + 20x + 1 for some random function + + align:start position:0% +3x^2 + 20x + 1 for some random function + + + align:start position:0% +3x^2 + 20x + 1 for some random function +that we wrote right so that we consider + + align:start position:0% +that we wrote right so that we consider + + + align:start position:0% +that we wrote right so that we consider +the + + align:start position:0% +the + + + align:start position:0% +the +function now the Big O is going to be + + align:start position:0% +function now the Big O is going to be + + + align:start position:0% +function now the Big O is going to be +the upper bound on this function so if I + + align:start position:0% +the upper bound on this function so if I + + + align:start position:0% +the upper bound on this function so if I +plug this function in my in my uh XY AIS + + align:start position:0% +plug this function in my in my uh XY AIS + + + align:start position:0% +plug this function in my in my uh XY AIS +this is what it looks like the Big O + + align:start position:0% +this is what it looks like the Big O + + + align:start position:0% +this is what it looks like the Big O +will be some other function that's going + + align:start position:0% +will be some other function that's going + + + align:start position:0% +will be some other function that's going +to Upper bound this one the blue one + + align:start position:0% +to Upper bound this one the blue one + + + align:start position:0% +to Upper bound this one the blue one +okay and it's going to Upper bound it + + align:start position:0% +okay and it's going to Upper bound it + + + align:start position:0% +okay and it's going to Upper bound it +for all values Beyond some X right so + + align:start position:0% +for all values Beyond some X right so + + + align:start position:0% +for all values Beyond some X right so +for all values Beyond some x uh some + + align:start position:0% +for all values Beyond some x uh some + + + align:start position:0% +for all values Beyond some x uh some +some number on the x axis some crossover + + align:start position:0% +some number on the x axis some crossover + + + align:start position:0% +some number on the x axis some crossover +point this big O of G this G will always + + align:start position:0% +point this big O of G this G will always + + + align:start position:0% +point this big O of G this G will always +be bigger than my f that's the idea here + + align:start position:0% +be bigger than my f that's the idea here + + + align:start position:0% +be bigger than my f that's the idea here +so clearly X is not going to Upper bound + + align:start position:0% +so clearly X is not going to Upper bound + + + align:start position:0% +so clearly X is not going to Upper bound +it right because after this crossover + + align:start position:0% +it right because after this crossover + + + align:start position:0% +it right because after this crossover +point x will be below my function no + + align:start position:0% +point x will be below my function no + + + align:start position:0% +point x will be below my function no +matter how big how big of a constant I + + align:start position:0% +matter how big how big of a constant I + + + align:start position:0% +matter how big how big of a constant I +tack onto that X I could have a + + align:start position:0% +tack onto that X I could have a + + + align:start position:0% +tack onto that X I could have a +THX that's still not going to Upper + + align:start position:0% +THX that's still not going to Upper + + + align:start position:0% +THX that's still not going to Upper +bound my little blue line here so what + + align:start position:0% +bound my little blue line here so what + + + align:start position:0% +bound my little blue line here so what +we're going to do is we're going to + + align:start position:0% +we're going to do is we're going to + + + align:start position:0% +we're going to do is we're going to +increase the the the exponential there + + align:start position:0% +increase the the the exponential there + + + align:start position:0% +increase the the the exponential there +so let's take x s well X squ is getting + + align:start position:0% +so let's take x s well X squ is getting + + + align:start position:0% +so let's take x s well X squ is getting +closer it looks like they're both + + align:start position:0% +closer it looks like they're both + + + align:start position:0% +closer it looks like they're both +quadratics but uh this uh orange line is + + align:start position:0% +quadratics but uh this uh orange line is + + + align:start position:0% +quadratics but uh this uh orange line is +not above the blue line for some + + align:start position:0% +not above the blue line for some + + + align:start position:0% +not above the blue line for some +crossover + + align:start position:0% +crossover + + + align:start position:0% +crossover +Point 2x getting closer 3x getting + + align:start position:0% +Point 2x getting closer 3x getting + + + align:start position:0% +Point 2x getting closer 3x getting +closer + + align:start position:0% +closer + + + align:start position:0% +closer +4X is an upper bound on my f because + + align:start position:0% +4X is an upper bound on my f because + + + align:start position:0% +4X is an upper bound on my f because +after this little crossover Point here + + align:start position:0% +after this little crossover Point here + + + align:start position:0% +after this little crossover Point here +at about 20 my orange line the G will be + + align:start position:0% +at about 20 my orange line the G will be + + + align:start position:0% +at about 20 my orange line the G will be +always + + align:start position:0% +always + + + align:start position:0% +always +above my blue line my f right so far so + + align:start position:0% +above my blue line my f right so far so + + + align:start position:0% +above my blue line my f right so far so +good just visually speaking + + align:start position:0% +good just visually speaking + + + align:start position:0% +good just visually speaking +yeah one below it there do that matter + + align:start position:0% +yeah one below it there do that matter + + + align:start position:0% +yeah one below it there do that matter +yeah the orange one is below it that's + + align:start position:0% +yeah the orange one is below it that's + + + align:start position:0% +yeah the orange one is below it that's +totally fine because what we're + + align:start position:0% +totally fine because what we're + + + align:start position:0% +totally fine because what we're +interested in is the behavior when the + + align:start position:0% +interested in is the behavior when the + + + align:start position:0% +interested in is the behavior when the +input is really big okay so that's why I + + align:start position:0% +input is really big okay so that's why I + + + align:start position:0% +input is really big okay so that's why I +don't care about like weird stuff + + align:start position:0% +don't care about like weird stuff + + + align:start position:0% +don't care about like weird stuff +happening down there all I care about is + + align:start position:0% +happening down there all I care about is + + + align:start position:0% +happening down there all I care about is +when when my X is super + + align:start position:0% +when when my X is super + + + align:start position:0% +when when my X is super +big okay so now I found this G so I can + + align:start position:0% +big okay so now I found this G so I can + + + align:start position:0% +big okay so now I found this G so I can +say + + align:start position:0% +say + + + align:start position:0% +say +that after this point 20 my orange line + + align:start position:0% +that after this point 20 my orange line + + + align:start position:0% +that after this point 20 my orange line +will always be above my blue so I can + + align:start position:0% +will always be above my blue so I can + + + align:start position:0% +will always be above my blue so I can +say that my f is Big O of G is Big O of + + align:start position:0% +say that my f is Big O of G is Big O of + + + align:start position:0% +say that my f is Big O of G is Big O of +X squ okay because I don't care about + + align:start position:0% +X squ okay because I don't care about + + + align:start position:0% +X squ okay because I don't care about +this four so much because it's just a + + align:start position:0% +this four so much because it's just a + + + align:start position:0% +this four so much because it's just a +multiplicative + + align:start position:0% +multiplicative + + + align:start position:0% +multiplicative +constant because this + + align:start position:0% +constant because this + + + align:start position:0% +constant because this +4X is always greater than my function + + align:start position:0% +4X is always greater than my function + + + align:start position:0% +4X is always greater than my function +for all X greater than this crossover + + align:start position:0% +for all X greater than this crossover + + + align:start position:0% +for all X greater than this crossover +Point here right + + align:start position:0% +Point here right + + + align:start position:0% +Point here right +that's it that's the definition right so + + align:start position:0% +that's it that's the definition right so + + + align:start position:0% +that's it that's the definition right so +the G here is basically this function + + align:start position:0% +the G here is basically this function + + + align:start position:0% +the G here is basically this function +without the multiplicative constant in + + align:start position:0% +without the multiplicative constant in + + + align:start position:0% +without the multiplicative constant in +front of + + align:start position:0% +front of + + + align:start position:0% +front of +it okay so I say 3x^2 + 20x + 1 is Big O + + align:start position:0% +it okay so I say 3x^2 + 20x + 1 is Big O + + + align:start position:0% +it okay so I say 3x^2 + 20x + 1 is Big O +of + + align:start position:0% +of + + + align:start position:0% +of +X2 so generally speaking that was just + + align:start position:0% +X2 so generally speaking that was just + + + align:start position:0% +X2 so generally speaking that was just +an example generally speaking the Big O + + align:start position:0% +an example generally speaking the Big O + + + align:start position:0% +an example generally speaking the Big O +is an upper bound on my function okay + + align:start position:0% +is an upper bound on my function okay + + + align:start position:0% +is an upper bound on my function okay +and this is now just using uh variables + + align:start position:0% +and this is now just using uh variables + + + align:start position:0% +and this is now just using uh variables +like constants and things like that but + + align:start position:0% +like constants and things like that but + + + align:start position:0% +like constants and things like that but +it's exactly the same situation that we + + align:start position:0% +it's exactly the same situation that we + + + align:start position:0% +it's exactly the same situation that we +had from before okay so I'm going to try + + align:start position:0% +had from before okay so I'm going to try + + + align:start position:0% +had from before okay so I'm going to try +to map the blue to the blue and the + + align:start position:0% +to map the blue to the blue and the + + + align:start position:0% +to map the blue to the blue and the +orange to the orange and the purple to + + align:start position:0% +orange to the orange and the purple to + + + align:start position:0% +orange to the orange and the purple to +the purple to help you um kind of match + + align:start position:0% +the purple to help you um kind of match + + + align:start position:0% +the purple to help you um kind of match +up what we saw in the previous slide so + + align:start position:0% +up what we saw in the previous slide so + + + align:start position:0% +up what we saw in the previous slide so +basically we say that our function f is + + align:start position:0% +basically we say that our function f is + + + align:start position:0% +basically we say that our function f is +Big O of this Orange G right if we can + + align:start position:0% +Big O of this Orange G right if we can + + + align:start position:0% +Big O of this Orange G right if we can +find some blue constant right where this + + align:start position:0% +find some blue constant right where this + + + align:start position:0% +find some blue constant right where this +constant was this four here where that + + align:start position:0% +constant was this four here where that + + + align:start position:0% +constant was this four here where that +constant multiplied by G the X squar is + + align:start position:0% +constant multiplied by G the X squar is + + + align:start position:0% +constant multiplied by G the X squar is +greater than my function for all uh + + align:start position:0% +greater than my function for all uh + + + align:start position:0% +greater than my function for all uh +values beyond that crossover point right + + align:start position:0% +values beyond that crossover point right + + + align:start position:0% +values beyond that crossover point right +so I found my four because 4x2 is always + + align:start position:0% +so I found my four because 4x2 is always + + + align:start position:0% +so I found my four because 4x2 is always +greater than my function Beyond + + align:start position:0% +greater than my function Beyond + + + align:start position:0% +greater than my function Beyond +21 right that's what we saw in in the + + align:start position:0% +21 right that's what we saw in in the + + + align:start position:0% +21 right that's what we saw in in the +picture right so then we can say that my + + align:start position:0% +picture right so then we can say that my + + + align:start position:0% +picture right so then we can say that my +function f is G is Big O of G of X where + + align:start position:0% +function f is G is Big O of G of X where + + + align:start position:0% +function f is G is Big O of G of X where +that g is X squ just matched + + align:start position:0% +that g is X squ just matched + + + align:start position:0% +that g is X squ just matched +it all right so in terms of the the + + align:start position:0% +it all right so in terms of the the + + + align:start position:0% +it all right so in terms of the the +picture here right this is kind of a + + align:start position:0% +picture here right this is kind of a + + + align:start position:0% +picture here right this is kind of a +little zoom in of what happens Anything + + align:start position:0% +little zoom in of what happens Anything + + + align:start position:0% +little zoom in of what happens Anything +Can Happen down here but beyond the + + align:start position:0% +Can Happen down here but beyond the + + + align:start position:0% +Can Happen down here but beyond the +crossover point which is here in the big + + align:start position:0% +crossover point which is here in the big + + + align:start position:0% +crossover point which is here in the big +picture that crossover Point uh beyond + + align:start position:0% +picture that crossover Point uh beyond + + + align:start position:0% +picture that crossover Point uh beyond +that crossover point my orange is always + + align:start position:0% +that crossover point my orange is always + + + align:start position:0% +that crossover point my orange is always +greater than my + + align:start position:0% +greater than my + + + align:start position:0% +greater than my +blue okay so what does this mean we're + + align:start position:0% +blue okay so what does this mean we're + + + align:start position:0% +blue okay so what does this mean we're +going to talk about this in a few slides + + align:start position:0% +going to talk about this in a few slides + + + align:start position:0% +going to talk about this in a few slides +but you might have thought about this I + + align:start position:0% +but you might have thought about this I + + + align:start position:0% +but you might have thought about this I +can actually pick any function that + + align:start position:0% +can actually pick any function that + + + align:start position:0% +can actually pick any function that +grows faster than uh what is this 3x2 + + align:start position:0% +grows faster than uh what is this 3x2 + + + align:start position:0% +grows faster than uh what is this 3x2 +right I can pick X factorial X factorial + + align:start position:0% +right I can pick X factorial X factorial + + + align:start position:0% +right I can pick X factorial X factorial +grows super fast or 2 to the x that also + + align:start position:0% +grows super fast or 2 to the x that also + + + align:start position:0% +grows super fast or 2 to the x that also +grows super fast all of those functions + + align:start position:0% +grows super fast all of those functions + + + align:start position:0% +grows super fast all of those functions +that grow way faster than mine are also + + align:start position:0% +that grow way faster than mine are also + + + align:start position:0% +that grow way faster than mine are also +upper bounds on this on this + + align:start position:0% +upper bounds on this on this + + + align:start position:0% +upper bounds on this on this +function okay so that's Big O it's just + + align:start position:0% +function okay so that's Big O it's just + + + align:start position:0% +function okay so that's Big O it's just +an upper + + align:start position:0% +an upper + + + align:start position:0% +an upper +bound then what is + + align:start position:0% +bound then what is + + + align:start position:0% +bound then what is +Theta for the reason I just stated right + + align:start position:0% +Theta for the reason I just stated right + + + align:start position:0% +Theta for the reason I just stated right +I said X squ sorry X factorial 2 to the + + align:start position:0% +I said X squ sorry X factorial 2 to the + + + align:start position:0% +I said X squ sorry X factorial 2 to the +X all of these functions that grow much + + align:start position:0% +X all of these functions that grow much + + + align:start position:0% +X all of these functions that grow much +faster than my function are all upper + + align:start position:0% +faster than my function are all upper + + + align:start position:0% +faster than my function are all upper +bounds and that's not really helpful for + + align:start position:0% +bounds and that's not really helpful for + + + align:start position:0% +bounds and that's not really helpful for +us when we say oh this function is Big O + + align:start position:0% +us when we say oh this function is Big O + + + align:start position:0% +us when we say oh this function is Big O +of whatever right because you can just + + align:start position:0% +of whatever right because you can just + + + align:start position:0% +of whatever right because you can just +pick something that's ludicrously fast + + align:start position:0% +pick something that's ludicrously fast + + + align:start position:0% +pick something that's ludicrously fast +that grows ludicrously you know fast and + + align:start position:0% +that grows ludicrously you know fast and + + + align:start position:0% +that grows ludicrously you know fast and +say that that has no meaning so instead + + align:start position:0% +say that that has no meaning so instead + + + align:start position:0% +say that that has no meaning so instead +what we usually report is the Theta + + align:start position:0% +what we usually report is the Theta + + + align:start position:0% +what we usually report is the Theta +which is actually an upper bound and a + + align:start position:0% +which is actually an upper bound and a + + + align:start position:0% +which is actually an upper bound and a +lower Bound for our function right so + + align:start position:0% +lower Bound for our function right so + + + align:start position:0% +lower Bound for our function right so +using the exact same reasoning we're + + align:start position:0% +using the exact same reasoning we're + + + align:start position:0% +using the exact same reasoning we're +going to find some constant tacked onto + + align:start position:0% +going to find some constant tacked onto + + + align:start position:0% +going to find some constant tacked onto +that g of X such that that function + + align:start position:0% +that g of X such that that function + + + align:start position:0% +that g of X such that that function +grows um is is always underneath our + + align:start position:0% +grows um is is always underneath our + + + align:start position:0% +grows um is is always underneath our +function okay so I again I'll put up a a + + align:start position:0% +function okay so I again I'll put up a a + + + align:start position:0% +function okay so I again I'll put up a a +lot of math but basically these first + + align:start position:0% +lot of math but basically these first + + + align:start position:0% +lot of math but basically these first +two lines here this one here there + + align:start position:0% +two lines here this one here there + + + align:start position:0% +two lines here this one here there +exists blah blah blah blah blah that + + align:start position:0% +exists blah blah blah blah blah that + + + align:start position:0% +exists blah blah blah blah blah that +first here this is a is the Big O + + align:start position:0% +first here this is a is the Big O + + + align:start position:0% +first here this is a is the Big O +definition so we've already know what + + align:start position:0% +definition so we've already know what + + + align:start position:0% +definition so we've already know what +that means all we're going to do is tack + + align:start position:0% +that means all we're going to do is tack + + + align:start position:0% +that means all we're going to do is tack +on another condition which is we can + + align:start position:0% +on another condition which is we can + + + align:start position:0% +on another condition which is we can +find another constant for that same + + align:start position:0% +find another constant for that same + + + align:start position:0% +find another constant for that same +G where that function Beyond some + + align:start position:0% +G where that function Beyond some + + + align:start position:0% +G where that function Beyond some +crossover point is always below my blue + + align:start position:0% +crossover point is always below my blue + + + align:start position:0% +crossover point is always below my blue +my blue line so here's an example right + + align:start position:0% +my blue line so here's an example right + + + align:start position:0% +my blue line so here's an example right +4x^2 we saw that it grew faster than + + align:start position:0% +4x^2 we saw that it grew faster than + + + align:start position:0% +4x^2 we saw that it grew faster than +3x^2 Beyond a crossover Point well we + + align:start position:0% +3x^2 Beyond a crossover Point well we + + + align:start position:0% +3x^2 Beyond a crossover Point well we +could say 2x^2 will always grow slower + + align:start position:0% +could say 2x^2 will always grow slower + + + align:start position:0% +could say 2x^2 will always grow slower +than its own crossover + + align:start position:0% + + + + align:start position:0% + +Point okay so the constant four was the + + align:start position:0% +Point okay so the constant four was the + + + align:start position:0% +Point okay so the constant four was the +same as we had seen before but this + + align:start position:0% +same as we had seen before but this + + + align:start position:0% +same as we had seen before but this +constant two now becomes a lower bound + + align:start position:0% +constant two now becomes a lower bound + + + align:start position:0% +constant two now becomes a lower bound +right so I'm basically trying to have + + align:start position:0% +right so I'm basically trying to have + + + align:start position:0% +right so I'm basically trying to have +that same G both upper bind and lower + + align:start position:0% +that same G both upper bind and lower + + + align:start position:0% +that same G both upper bind and lower +bound my blue + + align:start position:0% +bound my blue + + + align:start position:0% +bound my blue +function + + align:start position:0% +function + + + align:start position:0% +function +right and that's the definition of + + align:start position:0% +right and that's the definition of + + + align:start position:0% +right and that's the definition of +theta so now I can no longer say that 2 + + align:start position:0% +theta so now I can no longer say that 2 + + + align:start position:0% +theta so now I can no longer say that 2 +to the X right an exponential both upper + + align:start position:0% +to the X right an exponential both upper + + + align:start position:0% +to the X right an exponential both upper +bounds and lower bounds it because that + + align:start position:0% +bounds and lower bounds it because that + + + align:start position:0% +bounds and lower bounds it because that +2 to the X will grow faster than my + + align:start position:0% +2 to the X will grow faster than my + + + align:start position:0% +2 to the X will grow faster than my +function no matter what constant I + + align:start position:0% +function no matter what constant I + + + align:start position:0% +function no matter what constant I +attack attack onto it okay so now what + + align:start position:0% +attack attack onto it okay so now what + + + align:start position:0% +attack attack onto it okay so now what +we see is that really the G of X is + + align:start position:0% +we see is that really the G of X is + + + align:start position:0% +we see is that really the G of X is +going to be the term that grows the + + align:start position:0% +going to be the term that grows the + + + align:start position:0% +going to be the term that grows the +fastest it's just going to be that term + + align:start position:0% +fastest it's just going to be that term + + + align:start position:0% +fastest it's just going to be that term +here right it's going to be the thing + + align:start position:0% +here right it's going to be the thing + + + align:start position:0% +here right it's going to be the thing +without the fastest growing term in my + + align:start position:0% +without the fastest growing term in my + + + align:start position:0% +without the fastest growing term in my +function without the constant on + + align:start position:0% +function without the constant on + + + align:start position:0% +function without the constant on +it okay so yes we will never remember + + align:start position:0% +it okay so yes we will never remember + + + align:start position:0% +it okay so yes we will never remember +all that but we're going to do a bunch + + align:start position:0% +all that but we're going to do a bunch + + + align:start position:0% +all that but we're going to do a bunch +of exercises and you're going to see + + align:start position:0% +of exercises and you're going to see + + + align:start position:0% +of exercises and you're going to see +just how easy it is to figure out the + + align:start position:0% +just how easy it is to figure out the + + + align:start position:0% +just how easy it is to figure out the +order of growth okay but I will mention + + align:start position:0% +order of growth okay but I will mention + + + align:start position:0% +order of growth okay but I will mention +this just again because it's very + + align:start position:0% +this just again because it's very + + + align:start position:0% +this just again because it's very +important right so when we're talking + + align:start position:0% +important right so when we're talking + + + align:start position:0% +important right so when we're talking +about upper bounds you can pick any + + align:start position:0% +about upper bounds you can pick any + + + align:start position:0% +about upper bounds you can pick any +function that grows faster than yours + + align:start position:0% +function that grows faster than yours + + + align:start position:0% +function that grows faster than yours +right F ofx this 3x s thing is O of x s + + align:start position:0% +right F ofx this 3x s thing is O of x s + + + align:start position:0% +right F ofx this 3x s thing is O of x s +yes but it's also o of X cubed o of x to + + align:start position:0% +yes but it's also o of X cubed o of x to + + + align:start position:0% +yes but it's also o of X cubed o of x to +the 5 O of x to the 100 o of 2 to the x + + align:start position:0% +the 5 O of x to the 100 o of 2 to the x + + + align:start position:0% +the 5 O of x to the 100 o of 2 to the x +o of X factorial all of those things + + align:start position:0% +o of X factorial all of those things + + + align:start position:0% +o of X factorial all of those things +that grow much faster but my f ofx is + + align:start position:0% +that grow much faster but my f ofx is + + + align:start position:0% +that grow much faster but my f ofx is +only one Theta and it's Theta of X2 + + align:start position:0% +only one Theta and it's Theta of X2 + + + align:start position:0% +only one Theta and it's Theta of X2 +right and that's the term that grow + + align:start position:0% +right and that's the term that grow + + + align:start position:0% +right and that's the term that grow +that's the term that grows the fastest + + align:start position:0% +that's the term that grows the fastest + + + align:start position:0% +that's the term that grows the fastest +in my function + + align:start position:0% +in my function + + + align:start position:0% +in my function +here so when we look at a function right + + align:start position:0% +here so when we look at a function right + + + align:start position:0% +here so when we look at a function right +based on the number of operations or + + align:start position:0% +based on the number of operations or + + + align:start position:0% +based on the number of operations or +however you know you know you're given + + align:start position:0% +however you know you know you're given + + + align:start position:0% +however you know you know you're given +the function when we look at the order + + align:start position:0% +the function when we look at the order + + + align:start position:0% +the function when we look at the order +of growth of the function we just focus + + align:start position:0% +of growth of the function we just focus + + + align:start position:0% +of growth of the function we just focus +on the dominant term right so in the + + align:start position:0% +on the dominant term right so in the + + + align:start position:0% +on the dominant term right so in the +first one the input here is n and the + + align:start position:0% +first one the input here is n and the + + + align:start position:0% +first one the input here is n and the +function is n^2 + 2 n + 2 which which + + align:start position:0% +function is n^2 + 2 n + 2 which which + + + align:start position:0% +function is n^2 + 2 n + 2 which which +one of these is the dominant term you + + align:start position:0% +one of these is the dominant term you + + + align:start position:0% +one of these is the dominant term you +tell + + align:start position:0% +tell + + + align:start position:0% +tell +me yes exactly n squ so this function is + + align:start position:0% +me yes exactly n squ so this function is + + + align:start position:0% +me yes exactly n squ so this function is +just going to be Theta of n^2 that's + + align:start position:0% +just going to be Theta of n^2 that's + + + align:start position:0% +just going to be Theta of n^2 that's +it how about in the next one what's the + + align:start position:0% +it how about in the next one what's the + + + align:start position:0% +it how about in the next one what's the +dominant term + + align:start position:0% + + + + align:start position:0% + +here yeah exactly 3x squ even though + + align:start position:0% +here yeah exactly 3x squ even though + + + align:start position:0% +here yeah exactly 3x squ even though +100,000x is going to be huge for a while + + align:start position:0% +100,000x is going to be huge for a while + + + align:start position:0% +100,000x is going to be huge for a while +and this constant is also going to be + + align:start position:0% +and this constant is also going to be + + + align:start position:0% +and this constant is also going to be +huge for a while as X gets really really + + align:start position:0% +huge for a while as X gets really really + + + align:start position:0% +huge for a while as X gets really really +big this 3x and in fact just X2 will + + align:start position:0% +big this 3x and in fact just X2 will + + + align:start position:0% +big this 3x and in fact just X2 will +kind of take over everything else right + + align:start position:0% +kind of take over everything else right + + + align:start position:0% +kind of take over everything else right +so this next one is Al is Theta of + + align:start position:0% +so this next one is Al is Theta of + + + align:start position:0% +so this next one is Al is Theta of +x^2 how about the next + + align:start position:0% +x^2 how about the next + + + align:start position:0% +x^2 how about the next +one what's the term that grows the + + align:start position:0% +one what's the term that grows the + + + align:start position:0% +one what's the term that grows the +fastest + + align:start position:0% + + + + align:start position:0% + +here yeah exactly a right log is is is + + align:start position:0% +here yeah exactly a right log is is is + + + align:start position:0% +here yeah exactly a right log is is is +is slower growth right so this Theta of + + align:start position:0% +is slower growth right so this Theta of + + + align:start position:0% +is slower growth right so this Theta of +this function is just Theta of + + align:start position:0% +this function is just Theta of + + + align:start position:0% +this function is just Theta of +a so notice what we're doing here is + + align:start position:0% +a so notice what we're doing here is + + + align:start position:0% +a so notice what we're doing here is +just focusing on the dominant term we're + + align:start position:0% +just focusing on the dominant term we're + + + align:start position:0% +just focusing on the dominant term we're +going to drop the multiplicative + + align:start position:0% +going to drop the multiplicative + + + align:start position:0% +going to drop the multiplicative +constants drop every other term and + + align:start position:0% +constants drop every other term and + + + align:start position:0% +constants drop every other term and +relate the Theta in terms of the input + + align:start position:0% +relate the Theta in terms of the input + + + align:start position:0% +relate the Theta in terms of the input +right so I don't just use Theta of n all + + align:start position:0% +right so I don't just use Theta of n all + + + align:start position:0% +right so I don't just use Theta of n all +the time right in the previous one it's + + align:start position:0% +the time right in the previous one it's + + + align:start position:0% +the time right in the previous one it's +tempting to say the first one's Theta of + + align:start position:0% +tempting to say the first one's Theta of + + + align:start position:0% +tempting to say the first one's Theta of +n s the next one's Theta of n squ the + + align:start position:0% +n s the next one's Theta of n squ the + + + align:start position:0% +n s the next one's Theta of n squ the +last one's Theta of n but n is not + + align:start position:0% +last one's Theta of n but n is not + + + align:start position:0% +last one's Theta of n but n is not +always the input to your function right + + align:start position:0% +always the input to your function right + + + align:start position:0% +always the input to your function right +if it is great if it's not you always + + align:start position:0% +if it is great if it's not you always + + + align:start position:0% +if it is great if it's not you always +have to relate it according to the input + + align:start position:0% +have to relate it according to the input + + + align:start position:0% +have to relate it according to the input +of the function maybe it's length L + + align:start position:0% +of the function maybe it's length L + + + align:start position:0% +of the function maybe it's length L +maybe it's you know something + + align:start position:0% +maybe it's you know something + + + align:start position:0% +maybe it's you know something +else okay so let's have you try a couple + + align:start position:0% +else okay so let's have you try a couple + + + align:start position:0% +else okay so let's have you try a couple +more what is the Theta of the first one + + align:start position:0% +more what is the Theta of the first one + + + align:start position:0% +more what is the Theta of the first one +here what's the term that grows the + + align:start position:0% +here what's the term that grows the + + + align:start position:0% +here what's the term that grows the +fastest yeah Theta of X next + + align:start position:0% + + + + align:start position:0% + +one n cubed exactly theeta of n Cub I + + align:start position:0% +one n cubed exactly theeta of n Cub I + + + align:start position:0% +one n cubed exactly theeta of n Cub I +told you this is going to be so easy I + + align:start position:0% +told you this is going to be so easy I + + + align:start position:0% +told you this is going to be so easy I +know that math was scary how about the + + align:start position:0% +know that math was scary how about the + + + align:start position:0% +know that math was scary how about the +next + + align:start position:0% + + + + align:start position:0% + +one that's the term that grows the + + align:start position:0% +one that's the term that grows the + + + align:start position:0% +one that's the term that grows the +fastest but then it's Theta of drop any + + align:start position:0% +fastest but then it's Theta of drop any + + + align:start position:0% +fastest but then it's Theta of drop any +multiplicative constants and it's just + + align:start position:0% +multiplicative constants and it's just + + + align:start position:0% +multiplicative constants and it's just +Theta of Y the last one is going to be + + align:start position:0% +Theta of Y the last one is going to be + + + align:start position:0% +Theta of Y the last one is going to be +TR + + align:start position:0% +TR + + + align:start position:0% +TR +what is the Theta if the if the variable + + align:start position:0% +what is the Theta if the if the variable + + + align:start position:0% +what is the Theta if the if the variable +is only + + align:start position:0% + + + + align:start position:0% + +B yeah 2 to the B what about if the + + align:start position:0% +B yeah 2 to the B what about if the + + + align:start position:0% +B yeah 2 to the B what about if the +variable is only + + align:start position:0% +variable is only + + + align:start position:0% +variable is only +a a cubed exactly and if my function is + + align:start position:0% +a a cubed exactly and if my function is + + + align:start position:0% +a a cubed exactly and if my function is +both a function of a and + + align:start position:0% + + + + align:start position:0% + +b and + + align:start position:0% +b and + + + align:start position:0% +b and +a plus 2 uh plus a cubed right because + + align:start position:0% +a plus 2 uh plus a cubed right because + + + align:start position:0% +a plus 2 uh plus a cubed right because +both will contribute to the runtime of + + align:start position:0% +both will contribute to the runtime of + + + align:start position:0% +both will contribute to the runtime of +this function right not just the B right + + align:start position:0% +this function right not just the B right + + + align:start position:0% +this function right not just the B right +so if this function whatever this crazy + + align:start position:0% +so if this function whatever this crazy + + + align:start position:0% +so if this function whatever this crazy +function is that I wrote that takes so + + align:start position:0% +function is that I wrote that takes so + + + align:start position:0% +function is that I wrote that takes so +long to run was uh had both inputs b and + + align:start position:0% +long to run was uh had both inputs b and + + + align:start position:0% +long to run was uh had both inputs b and +a right as its parameters the Theta for + + align:start position:0% +a right as its parameters the Theta for + + + align:start position:0% +a right as its parameters the Theta for +that function is both is in terms of + + align:start position:0% +that function is both is in terms of + + + align:start position:0% +that function is both is in terms of +both BNA right the dominant terms of + + align:start position:0% +both BNA right the dominant terms of + + + align:start position:0% +both BNA right the dominant terms of +each + + align:start position:0% + + + + align:start position:0% + +yeah no no need to worry about negative + + align:start position:0% +yeah no no need to worry about negative + + + align:start position:0% +yeah no no need to worry about negative +coefficients have a yeah + + align:start position:0% +coefficients have a yeah + + + align:start position:0% +coefficients have a yeah +Yeah Yeah + + align:start position:0% + + + + align:start position:0% + +question oh some different param + + align:start position:0% +question oh some different param + + + align:start position:0% +question oh some different param +variable that's not even here yeah if + + align:start position:0% +variable that's not even here yeah if + + + align:start position:0% +variable that's not even here yeah if +the if we were if the parameter the + + align:start position:0% +the if we were if the parameter the + + + align:start position:0% +the if we were if the parameter the +function was C let's say for this last + + align:start position:0% +function was C let's say for this last + + + align:start position:0% +function was C let's say for this last +one but the formula was this then the + + align:start position:0% +one but the formula was this then the + + + align:start position:0% +one but the formula was this then the +Theta would be just constant Theta of + + align:start position:0% +Theta would be just constant Theta of + + + align:start position:0% +Theta would be just constant Theta of +one because it doesn't even depend on + + align:start position:0% +one because it doesn't even depend on + + + align:start position:0% +one because it doesn't even depend on +these variables so these are just + + align:start position:0% +these variables so these are just + + + align:start position:0% +these variables so these are just +considered constant time that's a great + + align:start position:0% +considered constant time that's a great + + + align:start position:0% +considered constant time that's a great +question yeah if the parameter was C or + + align:start position:0% +question yeah if the parameter was C or + + + align:start position:0% +question yeah if the parameter was C or +something + + align:start position:0% +something + + + align:start position:0% +something +else okay so now we can actually look at + + align:start position:0% +else okay so now we can actually look at + + + align:start position:0% +else okay so now we can actually look at +functions that we write and we do the + + align:start position:0% +functions that we write and we do the + + + align:start position:0% +functions that we write and we do the +exact same thing we can first start out + + align:start position:0% +exact same thing we can first start out + + + align:start position:0% +exact same thing we can first start out +with just saying how many operations + + align:start position:0% +with just saying how many operations + + + align:start position:0% +with just saying how many operations +does this function take come up with + + align:start position:0% +does this function take come up with + + + align:start position:0% +does this function take come up with +that relationship and just Theta that + + align:start position:0% +that relationship and just Theta that + + + align:start position:0% +that relationship and just Theta that +right just like we did on the previous + + align:start position:0% +right just like we did on the previous + + + align:start position:0% +right just like we did on the previous +slide so here's a function that uh that + + align:start position:0% +slide so here's a function that uh that + + + align:start position:0% +slide so here's a function that uh that +calculates the + + align:start position:0% +calculates the + + + align:start position:0% +calculates the +factorial what do we have here well + + align:start position:0% +factorial what do we have here well + + + align:start position:0% +factorial what do we have here well +we've got this is constant here right + + align:start position:0% +we've got this is constant here right + + + align:start position:0% +we've got this is constant here right +we've got just one while loop where + + align:start position:0% +we've got just one while loop where + + + align:start position:0% +we've got just one while loop where +there's five things going on here + + align:start position:0% +there's five things going on here + + + align:start position:0% +there's five things going on here +there's the comparison there's this uh + + align:start position:0% +there's the comparison there's this uh + + + align:start position:0% +there's the comparison there's this uh +times equals which is two operations + + align:start position:0% +times equals which is two operations + + + align:start position:0% +times equals which is two operations +this minus equals its two operations so + + align:start position:0% +this minus equals its two operations so + + + align:start position:0% +this minus equals its two operations so +this function is just 5n + 2 by the same + + align:start position:0% +this function is just 5n + 2 by the same + + + align:start position:0% +this function is just 5n + 2 by the same +analysis we did you know a few slides + + align:start position:0% +analysis we did you know a few slides + + + align:start position:0% +analysis we did you know a few slides +ago right so if we say what's the Theta + + align:start position:0% +ago right so if we say what's the Theta + + + align:start position:0% +ago right so if we say what's the Theta +of this function well what's the Theta + + align:start position:0% +of this function well what's the Theta + + + align:start position:0% +of this function well what's the Theta +of this 5 n plus 2 super easy right it's + + align:start position:0% +of this 5 n plus 2 super easy right it's + + + align:start position:0% +of this 5 n plus 2 super easy right it's +just Theta of N and in this case the par + + align:start position:0% +just Theta of N and in this case the par + + + align:start position:0% +just Theta of N and in this case the par +parameter to our function is truly + + align:start position:0% + + + + align:start position:0% + +n um when we have functions that are + + align:start position:0% +n um when we have functions that are + + + align:start position:0% +n um when we have functions that are +slightly more complex and we've got + + align:start position:0% +slightly more complex and we've got + + + align:start position:0% +slightly more complex and we've got +things that are in series like for + + align:start position:0% +things that are in series like for + + + align:start position:0% +things that are in series like for +example here I've got two for Loops one + + align:start position:0% +example here I've got two for Loops one + + + align:start position:0% +example here I've got two for Loops one +right after the other um we basically + + align:start position:0% +right after the other um we basically + + + align:start position:0% +right after the other um we basically +use this law of addition to take care of + + align:start position:0% +use this law of addition to take care of + + + align:start position:0% +use this law of addition to take care of +that so that means we figure out what + + align:start position:0% +that so that means we figure out what + + + align:start position:0% +that so that means we figure out what +the Theta is for the first for Loop the + + align:start position:0% +the Theta is for the first for Loop the + + + align:start position:0% +the Theta is for the first for Loop the +Theta for the next for Loop Loop and we + + align:start position:0% +Theta for the next for Loop Loop and we + + + align:start position:0% +Theta for the next for Loop Loop and we +just add those two uh thetas together + + align:start position:0% +just add those two uh thetas together + + + align:start position:0% +just add those two uh thetas together +okay so the first for Loop here is Theta + + align:start position:0% +okay so the first for Loop here is Theta + + + align:start position:0% +okay so the first for Loop here is Theta +of n because it's something that depends + + align:start position:0% +of n because it's something that depends + + + align:start position:0% +of n because it's something that depends +on parameter n and the next for Loop + + align:start position:0% +on parameter n and the next for Loop + + + align:start position:0% +on parameter n and the next for Loop +here is Theta of n s right and this this + + align:start position:0% +here is Theta of n s right and this this + + + align:start position:0% +here is Theta of n s right and this this +uh because the parameter here is n * n + + align:start position:0% +uh because the parameter here is n * n + + + align:start position:0% +uh because the parameter here is n * n +the stuff inside the for Loops are + + align:start position:0% +the stuff inside the for Loops are + + + align:start position:0% +the stuff inside the for Loops are +constant so they don't contribute + + align:start position:0% +constant so they don't contribute + + + align:start position:0% +constant so they don't contribute +anything to our thetas right there's no + + align:start position:0% +anything to our thetas right there's no + + + align:start position:0% +anything to our thetas right there's no +more things to multiply the complexity + + align:start position:0% +more things to multiply the complexity + + + align:start position:0% +more things to multiply the complexity +there so so the if this is my entire + + align:start position:0% +there so so the if this is my entire + + + align:start position:0% +there so so the if this is my entire +function here the Theta for this + + align:start position:0% +function here the Theta for this + + + align:start position:0% +function here the Theta for this +function is Theta of n plus Theta of n^ + + align:start position:0% +function is Theta of n plus Theta of n^ + + + align:start position:0% +function is Theta of n plus Theta of n^ +2 right and the law of addition just + + align:start position:0% +2 right and the law of addition just + + + align:start position:0% +2 right and the law of addition just +says Theta of n plus Theta of n^ 2 is + + align:start position:0% +says Theta of n plus Theta of n^ 2 is + + + align:start position:0% +says Theta of n plus Theta of n^ 2 is +just Theta of sticking those two inside + + align:start position:0% +just Theta of sticking those two inside + + + align:start position:0% +just Theta of sticking those two inside +as as part of my function n plus n^ s + + align:start position:0% +as as part of my function n plus n^ s + + + align:start position:0% +as as part of my function n plus n^ s +and we know how to do that that just + + align:start position:0% +and we know how to do that that just + + + align:start position:0% +and we know how to do that that just +simplifies to the dominant term which is + + align:start position:0% + + + + align:start position:0% + +n^2 okay so that's the law of addition + + align:start position:0% +n^2 okay so that's the law of addition + + + align:start position:0% +n^2 okay so that's the law of addition +so that's when we have loops or things + + align:start position:0% +so that's when we have loops or things + + + align:start position:0% +so that's when we have loops or things +like that in series what about when we + + align:start position:0% +like that in series what about when we + + + align:start position:0% +like that in series what about when we +have loops that are nested right then we + + align:start position:0% +have loops that are nested right then we + + + align:start position:0% +have loops that are nested right then we +use the law of + + align:start position:0% +use the law of + + + align:start position:0% +use the law of +multiplication because for each one of + + align:start position:0% +multiplication because for each one of + + + align:start position:0% +multiplication because for each one of +these things we're going to have to do + + align:start position:0% +these things we're going to have to do + + + align:start position:0% +these things we're going to have to do +this that many times right so in this + + align:start position:0% +this that many times right so in this + + + align:start position:0% +this that many times right so in this +particular case we need to be careful + + align:start position:0% +particular case we need to be careful + + + align:start position:0% +particular case we need to be careful +the outer for Loop is going to be Theta + + align:start position:0% +the outer for Loop is going to be Theta + + + align:start position:0% +the outer for Loop is going to be Theta +of N and the inner for + + align:start position:0% +of N and the inner for + + + align:start position:0% +of N and the inner for +Loop is also Theta of n even though I'm + + align:start position:0% +Loop is also Theta of n even though I'm + + + align:start position:0% +Loop is also Theta of n even though I'm +dividing n by two right 0.5 * n is still + + align:start position:0% +dividing n by two right 0.5 * n is still + + + align:start position:0% +dividing n by two right 0.5 * n is still +Theta n right that multiplicative + + align:start position:0% +Theta n right that multiplicative + + + align:start position:0% +Theta n right that multiplicative +constant in front of that n is 0.5 which + + align:start position:0% +constant in front of that n is 0.5 which + + + align:start position:0% +constant in front of that n is 0.5 which +is just you know it's just uh it's still + + align:start position:0% +is just you know it's just uh it's still + + + align:start position:0% +is just you know it's just uh it's still +leads me to be Theta of + + align:start position:0% +leads me to be Theta of + + + align:start position:0% +leads me to be Theta of +n the print is constant so there's + + align:start position:0% +n the print is constant so there's + + + align:start position:0% +n the print is constant so there's +nothing else to multiply there so the + + align:start position:0% +nothing else to multiply there so the + + + align:start position:0% +nothing else to multiply there so the +law of multiplication just says Theta of + + align:start position:0% +law of multiplication just says Theta of + + + align:start position:0% +law of multiplication just says Theta of +n * Theta of n is Theta of n^ 2 inside + + align:start position:0% + + + + align:start position:0% + +there okay so let's look at this + + align:start position:0% +there okay so let's look at this + + + align:start position:0% +there okay so let's look at this +program what is the Theta for for + + align:start position:0% +program what is the Theta for for + + + align:start position:0% +program what is the Theta for for +this well we could do it sort of in very + + align:start position:0% +this well we could do it sort of in very + + + align:start position:0% +this well we could do it sort of in very +grave detail we've got X as our + + align:start position:0% +grave detail we've got X as our + + + align:start position:0% +grave detail we've got X as our +parameter so we only count loops and + + align:start position:0% +parameter so we only count loops and + + + align:start position:0% +parameter so we only count loops and +things like that that are a function of + + align:start position:0% +things like that that are a function of + + + align:start position:0% +things like that that are a function of +x if I had a loop that was a function of + + align:start position:0% +x if I had a loop that was a function of + + + align:start position:0% +x if I had a loop that was a function of +I don't know n or something that doesn't + + align:start position:0% +I don't know n or something that doesn't + + + align:start position:0% +I don't know n or something that doesn't +count because it's not a function of my + + align:start position:0% +count because it's not a function of my + + + align:start position:0% +count because it's not a function of my +input so only look at things that are + + align:start position:0% +input so only look at things that are + + + align:start position:0% +input so only look at things that are +function of + + align:start position:0% +function of + + + align:start position:0% +function of +X I've got one outer four Loop that goes + + align:start position:0% +X I've got one outer four Loop that goes + + + align:start position:0% +X I've got one outer four Loop that goes +through x times so that's Theta of x + + align:start position:0% +through x times so that's Theta of x + + + align:start position:0% +through x times so that's Theta of x +I've got an inner for Loop that starts + + align:start position:0% +I've got an inner for Loop that starts + + + align:start position:0% +I've got an inner for Loop that starts +from I and goes to + + align:start position:0% +from I and goes to + + + align:start position:0% +from I and goes to +X that's a little bit tricky but in the + + align:start position:0% +X that's a little bit tricky but in the + + + align:start position:0% +X that's a little bit tricky but in the +end overall it's going to be Theta of X + + align:start position:0% +end overall it's going to be Theta of X + + + align:start position:0% +end overall it's going to be Theta of X +because it's going to be the first time + + align:start position:0% +because it's going to be the first time + + + align:start position:0% +because it's going to be the first time +it's going to go through x times the + + align:start position:0% +it's going to go through x times the + + + align:start position:0% +it's going to go through x times the +next time it's going to go x - one then + + align:start position:0% +next time it's going to go x - one then + + + align:start position:0% +next time it's going to go x - one then +x -2 then x - 3 so we're effectively + + align:start position:0% +x -2 then x - 3 so we're effectively + + + align:start position:0% +x -2 then x - 3 so we're effectively +just kind of adding over all of these + + align:start position:0% +just kind of adding over all of these + + + align:start position:0% +just kind of adding over all of these +runs X plus uh sorry uh 1 plus 2 plus 3 + + align:start position:0% +runs X plus uh sorry uh 1 plus 2 plus 3 + + + align:start position:0% +runs X plus uh sorry uh 1 plus 2 plus 3 +plus 4 plus 5 all the way up to X and + + align:start position:0% +plus 4 plus 5 all the way up to X and + + + align:start position:0% +plus 4 plus 5 all the way up to X and +that's just some function of X right + + align:start position:0% +that's just some function of X right + + + align:start position:0% +that's just some function of X right +it's definitely not going to be constant + + align:start position:0% +it's definitely not going to be constant + + + align:start position:0% +it's definitely not going to be constant +so the inner loop is also Theta of + + align:start position:0% +so the inner loop is also Theta of + + + align:start position:0% +so the inner loop is also Theta of +X um everything else is Theta of one + + align:start position:0% +X um everything else is Theta of one + + + align:start position:0% +X um everything else is Theta of one +right there's nothing else that that + + align:start position:0% +right there's nothing else that that + + + align:start position:0% +right there's nothing else that that +depends on X so this whole function is + + align:start position:0% +depends on X so this whole function is + + + align:start position:0% +depends on X so this whole function is +going to be Theta of one for this uh + + align:start position:0% +going to be Theta of one for this uh + + + align:start position:0% +going to be Theta of one for this uh +assignment here Theta of X time Theta of + + align:start position:0% +assignment here Theta of X time Theta of + + + align:start position:0% +assignment here Theta of X time Theta of +X for this nested Loop here and Theta of + + align:start position:0% +X for this nested Loop here and Theta of + + + align:start position:0% +X for this nested Loop here and Theta of +one for this return down here so overall + + align:start position:0% +one for this return down here so overall + + + align:start position:0% +one for this return down here so overall +it's just going to be Theta of all right + + align:start position:0% +it's just going to be Theta of all right + + + align:start position:0% +it's just going to be Theta of all right +so that's sorry that's that and so + + align:start position:0% +so that's sorry that's that and so + + + align:start position:0% +so that's sorry that's that and so +overall it's just going to be Theta of + + align:start position:0% +overall it's just going to be Theta of + + + align:start position:0% +overall it's just going to be Theta of +x^2 just by the laws of multiplication + + align:start position:0% +x^2 just by the laws of multiplication + + + align:start position:0% +x^2 just by the laws of multiplication +and + + align:start position:0% +and + + + align:start position:0% +and +addition all right think about this and + + align:start position:0% +addition all right think about this and + + + align:start position:0% +addition all right think about this and +then tell me what you think it + + align:start position:0% + + + + align:start position:0% + +is what do you guys think it + + align:start position:0% + + + + align:start position:0% + +is yeah Theta of length of L absolutely + + align:start position:0% +is yeah Theta of length of L absolutely + + + align:start position:0% +is yeah Theta of length of L absolutely +right so this is constant this stuff + + align:start position:0% +right so this is constant this stuff + + + align:start position:0% +right so this is constant this stuff +inside the loop is constant the return + + align:start position:0% +inside the loop is constant the return + + + align:start position:0% +inside the loop is constant the return +is constant and the only thing that + + align:start position:0% +is constant and the only thing that + + + align:start position:0% +is constant and the only thing that +depends on L is the length of the list + + align:start position:0% +depends on L is the length of the list + + + align:start position:0% +depends on L is the length of the list +right this Loop so the answer is Theta + + align:start position:0% +right this Loop so the answer is Theta + + + align:start position:0% +right this Loop so the answer is Theta +length L perfect how about this + + align:start position:0% + + + + align:start position:0% + +one so here we're assuming the Len all + + align:start position:0% +one so here we're assuming the Len all + + + align:start position:0% +one so here we're assuming the Len all +the inputs are the same + + align:start position:0% + + + + align:start position:0% + +length yeah Theta of length of pick your + + align:start position:0% +length yeah Theta of length of pick your + + + align:start position:0% +length yeah Theta of length of pick your +favorite one Theta of length L is + + align:start position:0% +favorite one Theta of length L is + + + align:start position:0% +favorite one Theta of length L is +reasonable you could also say Theta of + + align:start position:0% +reasonable you could also say Theta of + + + align:start position:0% +reasonable you could also say Theta of +length L1 or Theta of length L2 cuz + + align:start position:0% +length L1 or Theta of length L2 cuz + + + align:start position:0% +length L1 or Theta of length L2 cuz +these are uh two Loops that are in + + align:start position:0% +these are uh two Loops that are in + + + align:start position:0% +these are uh two Loops that are in +series right right so this one just + + align:start position:0% +series right right so this one just + + + align:start position:0% +series right right so this one just +Loops through the length of L but inside + + align:start position:0% +Loops through the length of L but inside + + + align:start position:0% +Loops through the length of L but inside +we're not doing anything that costs more + + align:start position:0% +we're not doing anything that costs more + + + align:start position:0% +we're not doing anything that costs more +than just constant time right here we're + + align:start position:0% +than just constant time right here we're + + + align:start position:0% +than just constant time right here we're +just comparing two numbers like three + + align:start position:0% +just comparing two numbers like three + + + align:start position:0% +just comparing two numbers like three +and two we're just assigning something + + align:start position:0% +and two we're just assigning something + + + align:start position:0% +and two we're just assigning something +to true so nothing else really depends + + align:start position:0% +to true so nothing else really depends + + + align:start position:0% +to true so nothing else really depends +on the the lengths of the list so this + + align:start position:0% +on the the lengths of the list so this + + + align:start position:0% +on the the lengths of the list so this +is Theta of length L this is plus Theta + + align:start position:0% +is Theta of length L this is plus Theta + + + align:start position:0% +is Theta of length L this is plus Theta +of length l so that's just Theta of + + align:start position:0% +of length l so that's just Theta of + + + align:start position:0% +of length l so that's just Theta of +length + + align:start position:0% +length + + + align:start position:0% +length +L all right so we saw a bunch of + + align:start position:0% +L all right so we saw a bunch of + + + align:start position:0% +L all right so we saw a bunch of +different algorithms right sorry no we + + align:start position:0% +different algorithms right sorry no we + + + align:start position:0% +different algorithms right sorry no we +didn't say a bunch we saw a bunch of + + align:start position:0% +didn't say a bunch we saw a bunch of + + + align:start position:0% +didn't say a bunch we saw a bunch of +different programs but we could kind of + + align:start position:0% +different programs but we could kind of + + + align:start position:0% +different programs but we could kind of +classify them all into one of these + + align:start position:0% +classify them all into one of these + + + align:start position:0% +classify them all into one of these +categories right and this is all + + align:start position:0% +categories right and this is all + + + align:start position:0% +categories right and this is all +basically all the different algorithms + + align:start position:0% +basically all the different algorithms + + + align:start position:0% +basically all the different algorithms +that you could ever + + align:start position:0% +that you could ever + + + align:start position:0% +that you could ever +write in general right so something + + align:start position:0% +write in general right so something + + + align:start position:0% +write in general right so something +that's constant Theta of one something + + align:start position:0% +that's constant Theta of one something + + + align:start position:0% +that's constant Theta of one something +that's logarithmic is Theta log n + + align:start position:0% +that's logarithmic is Theta log n + + + align:start position:0% +that's logarithmic is Theta log n +something that's linear we saw many of + + align:start position:0% +something that's linear we saw many of + + + align:start position:0% +something that's linear we saw many of +these is Theta of n something that's log + + align:start position:0% +these is Theta of n something that's log + + + align:start position:0% +these is Theta of n something that's log +linear we haven't seen any yet but + + align:start position:0% +linear we haven't seen any yet but + + + align:start position:0% +linear we haven't seen any yet but +that's Theta of n log n Theta of n to + + align:start position:0% +that's Theta of n log n Theta of n to + + + align:start position:0% +that's Theta of n log n Theta of n to +some constant like n s n cubed is + + align:start position:0% +some constant like n s n cubed is + + + align:start position:0% +some constant like n s n cubed is +polinomial and Theta of some constant to + + align:start position:0% +polinomial and Theta of some constant to + + + align:start position:0% +polinomial and Theta of some constant to +the N like 2 to the N 3 to the N is + + align:start position:0% +the N like 2 to the N 3 to the N is + + + align:start position:0% +the N like 2 to the N 3 to the N is +exponential and when we're writing our + + align:start position:0% +exponential and when we're writing our + + + align:start position:0% +exponential and when we're writing our +programs you can do a quick analysis of + + align:start position:0% +programs you can do a quick analysis of + + + align:start position:0% +programs you can do a quick analysis of +the of the program that you just wrote + + align:start position:0% +the of the program that you just wrote + + + align:start position:0% +the of the program that you just wrote +look at the loops look at to see how + + align:start position:0% +look at the loops look at to see how + + + align:start position:0% +look at the loops look at to see how +efficient you wrote it and you could + + align:start position:0% +efficient you wrote it and you could + + + align:start position:0% +efficient you wrote it and you could +basically classify your program into one + + align:start position:0% +basically classify your program into one + + + align:start position:0% +basically classify your program into one +of these categories right if you had + + align:start position:0% +of these categories right if you had + + + align:start position:0% +of these categories right if you had +nested Loops that both depend on the + + align:start position:0% +nested Loops that both depend on the + + + align:start position:0% +nested Loops that both depend on the +input you probably wrote A polinomial + + align:start position:0% +input you probably wrote A polinomial + + + align:start position:0% +input you probably wrote A polinomial +type algorithm if you just had one Loop + + align:start position:0% +type algorithm if you just had one Loop + + + align:start position:0% +type algorithm if you just had one Loop +that depended on the input you probably + + align:start position:0% +that depended on the input you probably + + + align:start position:0% +that depended on the input you probably +wrote a linear type algorithm right and + + align:start position:0% +wrote a linear type algorithm right and + + + align:start position:0% +wrote a linear type algorithm right and +when we write these algorithms at a + + align:start position:0% +when we write these algorithms at a + + + align:start position:0% +when we write these algorithms at a +first pass we want to be somewhere up + + align:start position:0% +first pass we want to be somewhere up + + + align:start position:0% +first pass we want to be somewhere up +here you don't want to do anything + + align:start position:0% +here you don't want to do anything + + + align:start position:0% +here you don't want to do anything +that's polinomial or definitely not + + align:start position:0% +that's polinomial or definitely not + + + align:start position:0% +that's polinomial or definitely not +exponential because things get slow + + align:start position:0% +exponential because things get slow + + + align:start position:0% +exponential because things get slow +really quickly with those numbers right + + align:start position:0% +really quickly with those numbers right + + + align:start position:0% +really quickly with those numbers right +so we never ever want to be in that + + align:start position:0% +so we never ever want to be in that + + + align:start position:0% +so we never ever want to be in that +situation although sometimes it's + + align:start position:0% +situation although sometimes it's + + + align:start position:0% +situation although sometimes it's +unavoidable right so that's all I've got + + align:start position:0% +unavoidable right so that's all I've got + + + align:start position:0% +unavoidable right so that's all I've got +next lecture we will be going through a + + align:start position:0% +next lecture we will be going through a + + + align:start position:0% +next lecture we will be going through a +bunch of those different complexity + + align:start position:0% +bunch of those different complexity + + + align:start position:0% +bunch of those different complexity +classes and looking at different + + align:start position:0% +classes and looking at different + + + align:start position:0% +classes and looking at different +programs that land in the those classes + + align:start position:0% +programs that land in the those classes + + + align:start position:0% +programs that land in the those classes +right especially the the logarithmic and + + align:start position:0% +right especially the the logarithmic and + + + align:start position:0% +right especially the the logarithmic and +the log linear all + + align:start position:0% + + + + align:start position:0% + +right \ No newline at end of file diff --git a/Re2lkF0vgQw.txt b/Re2lkF0vgQw.txt new file mode 100644 index 0000000000000000000000000000000000000000..c9e0d728964f294aea5499b8a5b923c9b839a1f1 --- /dev/null +++ b/Re2lkF0vgQw.txt @@ -0,0 +1,17619 @@ +align:start position:0% + +all right so welcome this is lecture 21 + + align:start position:0% +all right so welcome this is lecture 21 + + + align:start position:0% +all right so welcome this is lecture 21 +of + + align:start position:0% +of + + + align:start position:0% +of +1413 we're going to talk about poverty + + align:start position:0% +1413 we're going to talk about poverty + + + align:start position:0% +1413 we're going to talk about poverty +as seen through the lens of + + align:start position:0% +as seen through the lens of + + + align:start position:0% +as seen through the lens of +psychology uh what are we going to do + + align:start position:0% +psychology uh what are we going to do + + + align:start position:0% +psychology uh what are we going to do +i'm going to give you some broad + + align:start position:0% +i'm going to give you some broad + + + align:start position:0% +i'm going to give you some broad +overview we're going to particularly + + align:start position:0% +overview we're going to particularly + + + align:start position:0% +overview we're going to particularly +talk about this work on + + align:start position:0% +talk about this work on + + + align:start position:0% +talk about this work on +scarcity by mani rao which is the idea + + align:start position:0% +scarcity by mani rao which is the idea + + + align:start position:0% +scarcity by mani rao which is the idea +that + + align:start position:0% +that + + + align:start position:0% +that +um thinking your thoughts about poverty + + align:start position:0% +um thinking your thoughts about poverty + + + align:start position:0% +um thinking your thoughts about poverty +captures people's minds which in turn + + align:start position:0% +captures people's minds which in turn + + + align:start position:0% +captures people's minds which in turn +leaves less capacity + + align:start position:0% +leaves less capacity + + + align:start position:0% +leaves less capacity +in people's minds to do other things and + + align:start position:0% +in people's minds to do other things and + + + align:start position:0% +in people's minds to do other things and +then we're going to talk a little bit + + align:start position:0% +then we're going to talk a little bit + + + align:start position:0% +then we're going to talk a little bit +uh at the end at least briefly about + + align:start position:0% +uh at the end at least briefly about + + + align:start position:0% +uh at the end at least briefly about +other deprivations that poverty entails + + align:start position:0% +other deprivations that poverty entails + + + align:start position:0% +other deprivations that poverty entails +um some of this is work that i have done + + align:start position:0% +um some of this is work that i have done + + + align:start position:0% +um some of this is work that i have done +some of this is worked by others + + align:start position:0% +some of this is worked by others + + + align:start position:0% +some of this is worked by others +okay so i want to start with like a + + align:start position:0% +okay so i want to start with like a + + + align:start position:0% +okay so i want to start with like a +simple observation that i sort of like + + align:start position:0% +simple observation that i sort of like + + + align:start position:0% +simple observation that i sort of like +at the heart of um + + align:start position:0% +at the heart of um + + + align:start position:0% +at the heart of um +a lot of this literature and the + + align:start position:0% +a lot of this literature and the + + + align:start position:0% +a lot of this literature and the +observation is that + + align:start position:0% +observation is that + + + align:start position:0% +observation is that +um when you look around um in the world + + align:start position:0% +um when you look around um in the world + + + align:start position:0% +um when you look around um in the world +and look for evidence and when you work + + align:start position:0% +and look for evidence and when you work + + + align:start position:0% +and look for evidence and when you work +on + + align:start position:0% +on + + + align:start position:0% +on +poverty related issues you'll see um + + align:start position:0% +poverty related issues you'll see um + + + align:start position:0% +poverty related issues you'll see um +observe quite a few um seemingly + + align:start position:0% +observe quite a few um seemingly + + + align:start position:0% +observe quite a few um seemingly +suboptimal behaviors + + align:start position:0% +suboptimal behaviors + + + align:start position:0% +suboptimal behaviors +among the poor this would be things like + + align:start position:0% +among the poor this would be things like + + + align:start position:0% +among the poor this would be things like +lack of investment or taking advantage + + align:start position:0% +lack of investment or taking advantage + + + align:start position:0% +lack of investment or taking advantage +of high return investment opportunities + + align:start position:0% +of high return investment opportunities + + + align:start position:0% +of high return investment opportunities +this would be like investment in + + align:start position:0% +this would be like investment in + + + align:start position:0% +this would be like investment in +fertilizer or + + align:start position:0% +fertilizer or + + + align:start position:0% +fertilizer or +health investments or machines or + + align:start position:0% +health investments or machines or + + + align:start position:0% +health investments or machines or +like um or like low savings + + align:start position:0% +like um or like low savings + + + align:start position:0% +like um or like low savings +in particular things like precautionary + + align:start position:0% +in particular things like precautionary + + + align:start position:0% +in particular things like precautionary +savings like being ready for shocks + + align:start position:0% +savings like being ready for shocks + + + align:start position:0% +savings like being ready for shocks +saving for the future for the retirement + + align:start position:0% +saving for the future for the retirement + + + align:start position:0% +saving for the future for the retirement +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +at the same time with high return uh or + + align:start position:0% +at the same time with high return uh or + + + align:start position:0% +at the same time with high return uh or +high + + align:start position:0% +high + + + align:start position:0% +high +interest rate um credit people take very + + align:start position:0% +interest rate um credit people take very + + + align:start position:0% +interest rate um credit people take very +high + + align:start position:0% +high + + + align:start position:0% +high +interest loans in part what i've shown + + align:start position:0% +interest loans in part what i've shown + + + align:start position:0% +interest loans in part what i've shown +you + + align:start position:0% +you + + + align:start position:0% +you +earlier in the class that's particularly + + align:start position:0% +earlier in the class that's particularly + + + align:start position:0% +earlier in the class that's particularly +prevalent among the poor + + align:start position:0% +prevalent among the poor + + + align:start position:0% +prevalent among the poor +there's some evidence of like um worse + + align:start position:0% +there's some evidence of like um worse + + + align:start position:0% +there's some evidence of like um worse +performance + + align:start position:0% +performance + + + align:start position:0% +performance +of parenting among poor parents + + align:start position:0% +of parenting among poor parents + + + align:start position:0% +of parenting among poor parents +including like things like violence + + align:start position:0% +including like things like violence + + + align:start position:0% +including like things like violence +against children and so on + + align:start position:0% +against children and so on + + + align:start position:0% +against children and so on +there's some evidence of lower + + align:start position:0% +there's some evidence of lower + + + align:start position:0% +there's some evidence of lower +productivity + + align:start position:0% +productivity + + + align:start position:0% +productivity +punctuality lower medical adherence + + align:start position:0% +punctuality lower medical adherence + + + align:start position:0% +punctuality lower medical adherence +for like you know drugs that are sort of + + align:start position:0% +for like you know drugs that are sort of + + + align:start position:0% +for like you know drugs that are sort of +even very high-stakes drugs that are + + align:start position:0% +even very high-stakes drugs that are + + + align:start position:0% +even very high-stakes drugs that are +life-saving + + align:start position:0% +life-saving + + + align:start position:0% +life-saving +there's some evidence of food and drug + + align:start position:0% +there's some evidence of food and drug + + + align:start position:0% +there's some evidence of food and drug +consumption + + align:start position:0% +consumption + + + align:start position:0% +consumption +in terms of like uh healthy eating or um + + align:start position:0% + + + + align:start position:0% + +excessive um drug use and the like all + + align:start position:0% +excessive um drug use and the like all + + + align:start position:0% +excessive um drug use and the like all +of those things + + align:start position:0% +of those things + + + align:start position:0% +of those things +tend to be correlated one other way the + + align:start position:0% +tend to be correlated one other way the + + + align:start position:0% +tend to be correlated one other way the +other with different forms of + + align:start position:0% +other with different forms of + + + align:start position:0% +other with different forms of +income or poverty okay and so now + + align:start position:0% +income or poverty okay and so now + + + align:start position:0% +income or poverty okay and so now +you might sort of say well that's + + align:start position:0% +you might sort of say well that's + + + align:start position:0% +you might sort of say well that's +interesting but now what explains these + + align:start position:0% +interesting but now what explains these + + + align:start position:0% +interesting but now what explains these +behaviors + + align:start position:0% +behaviors + + + align:start position:0% +behaviors +how do we think about this what a + + align:start position:0% +how do we think about this what a + + + align:start position:0% +how do we think about this what a +plausible explanation + + align:start position:0% +plausible explanation + + + align:start position:0% +plausible explanation +kinds of correlations to be very clear + + align:start position:0% +kinds of correlations to be very clear + + + align:start position:0% +kinds of correlations to be very clear +these are correlations + + align:start position:0% +these are correlations + + + align:start position:0% +these are correlations +um uh not causal effects + + align:start position:0% +um uh not causal effects + + + align:start position:0% +um uh not causal effects +so education could explain quite a few + + align:start position:0% +so education could explain quite a few + + + align:start position:0% +so education could explain quite a few +of those things could explain + + align:start position:0% +of those things could explain + + + align:start position:0% +of those things could explain +potentially productivity it could + + align:start position:0% +potentially productivity it could + + + align:start position:0% +potentially productivity it could +explain potentially + + align:start position:0% +explain potentially + + + align:start position:0% +explain potentially +um parenting and to explain some form of + + align:start position:0% +um parenting and to explain some form of + + + align:start position:0% +um parenting and to explain some form of +like + + align:start position:0% +like + + + align:start position:0% +like +um financial investments they could also + + align:start position:0% +um financial investments they could also + + + align:start position:0% +um financial investments they could also +explain things like medical adherence + + align:start position:0% +explain things like medical adherence + + + align:start position:0% +explain things like medical adherence +like for example if you look at + + align:start position:0% +like for example if you look at + + + align:start position:0% +like for example if you look at +um in + + align:start position:0% +um in + + + align:start position:0% +um in +some settings where people have not + + align:start position:0% +some settings where people have not + + + align:start position:0% +some settings where people have not +sort of learned in school any basics of + + align:start position:0% +sort of learned in school any basics of + + + align:start position:0% +sort of learned in school any basics of +medicine or biology and so on and sort + + align:start position:0% +medicine or biology and so on and sort + + + align:start position:0% +medicine or biology and so on and sort +of then it's not obvious that you should + + align:start position:0% +of then it's not obvious that you should + + + align:start position:0% +of then it's not obvious that you should +take + + align:start position:0% +take + + + align:start position:0% +take +medicine from the traditional doctor + + align:start position:0% +medicine from the traditional doctor + + + align:start position:0% +medicine from the traditional doctor +versus from some healer in the village + + align:start position:0% +versus from some healer in the village + + + align:start position:0% +versus from some healer in the village +because you know how would you know + + align:start position:0% +because you know how would you know + + + align:start position:0% +because you know how would you know +what's better and what's worse instead + + align:start position:0% +what's better and what's worse instead + + + align:start position:0% +what's better and what's worse instead +of presumably some of these things you + + align:start position:0% +of presumably some of these things you + + + align:start position:0% +of presumably some of these things you +would learn + + align:start position:0% +would learn + + + align:start position:0% +would learn +um in school so one broad explanatory + + align:start position:0% +um in school so one broad explanatory + + + align:start position:0% +um in school so one broad explanatory +factor is sort of like omitted variables + + align:start position:0% +factor is sort of like omitted variables + + + align:start position:0% +factor is sort of like omitted variables +if you went on one of them + + align:start position:0% +if you went on one of them + + + align:start position:0% +if you went on one of them +is potentially education it's not about + + align:start position:0% +is potentially education it's not about + + + align:start position:0% +is potentially education it's not about +like + + align:start position:0% +like + + + align:start position:0% +like +um committed variable this is about like + + align:start position:0% +um committed variable this is about like + + + align:start position:0% +um committed variable this is about like +um + + align:start position:0% +um + + + align:start position:0% +um +a treatment effect of poverty itself um + + align:start position:0% +a treatment effect of poverty itself um + + + align:start position:0% +a treatment effect of poverty itself um +and i'm gonna be more specific about + + align:start position:0% +and i'm gonna be more specific about + + + align:start position:0% +and i'm gonna be more specific about +that but essentially something about + + align:start position:0% +that but essentially something about + + + align:start position:0% +that but essentially something about +like + + align:start position:0% +like + + + align:start position:0% +like +being in poverty itself uh affects + + align:start position:0% +being in poverty itself uh affects + + + align:start position:0% +being in poverty itself uh affects +people's behaviors that causes them + + align:start position:0% +people's behaviors that causes them + + + align:start position:0% +people's behaviors that causes them +um uh some of these outcomes some of + + align:start position:0% +um uh some of these outcomes some of + + + align:start position:0% +um uh some of these outcomes some of +these things that we've seen here we've + + align:start position:0% +these things that we've seen here we've + + + align:start position:0% +these things that we've seen here we've +talked about that in + + align:start position:0% +talked about that in + + + align:start position:0% +talked about that in +detail but that's exactly right i mean + + align:start position:0% +detail but that's exactly right i mean + + + align:start position:0% +detail but that's exactly right i mean +in some ways like people would say + + align:start position:0% +in some ways like people would say + + + align:start position:0% +in some ways like people would say +even for um like if you take credit for + + align:start position:0% +even for um like if you take credit for + + + align:start position:0% +even for um like if you take credit for +example or for some things you know + + align:start position:0% +example or for some things you know + + + align:start position:0% +example or for some things you know +you probably can't explain but for high + + align:start position:0% +you probably can't explain but for high + + + align:start position:0% +you probably can't explain but for high +return investment you would say wow + + align:start position:0% +return investment you would say wow + + + align:start position:0% +return investment you would say wow +there's uncertainty and there's a good + + align:start position:0% +there's uncertainty and there's a good + + + align:start position:0% +there's uncertainty and there's a good +chance that there might be losses at the + + align:start position:0% +chance that there might be losses at the + + + align:start position:0% +chance that there might be losses at the +end of the day + + align:start position:0% +end of the day + + + align:start position:0% +end of the day +and if you're really close to + + align:start position:0% +and if you're really close to + + + align:start position:0% +and if you're really close to +subsistence you might not want to invest + + align:start position:0% +subsistence you might not want to invest + + + align:start position:0% +subsistence you might not want to invest +in stuff because you know + + align:start position:0% +in stuff because you know + + + align:start position:0% +in stuff because you know +um if a bad shock happens um that's + + align:start position:0% +um if a bad shock happens um that's + + + align:start position:0% +um if a bad shock happens um that's +really bad + + align:start position:0% +really bad + + + align:start position:0% +really bad +um so i think some of that is right in + + align:start position:0% +um so i think some of that is right in + + + align:start position:0% +um so i think some of that is right in +punctuality punctuality for example + + align:start position:0% +punctuality punctuality for example + + + align:start position:0% +punctuality punctuality for example +could + + align:start position:0% +could + + + align:start position:0% +could +could also be in some way uncertainty is + + align:start position:0% +could also be in some way uncertainty is + + + align:start position:0% +could also be in some way uncertainty is +like you tried to take a bus to work and + + align:start position:0% +like you tried to take a bus to work and + + + align:start position:0% +like you tried to take a bus to work and +the bus just comes every + + align:start position:0% +the bus just comes every + + + align:start position:0% +the bus just comes every +hour and then sometimes this comes a + + align:start position:0% +hour and then sometimes this comes a + + + align:start position:0% +hour and then sometimes this comes a +half an hour earlier and sometimes comes + + align:start position:0% +half an hour earlier and sometimes comes + + + align:start position:0% +half an hour earlier and sometimes comes +later and it's really hard to be + + align:start position:0% +later and it's really hard to be + + + align:start position:0% +later and it's really hard to be +actually + + align:start position:0% +actually + + + align:start position:0% +actually +punctual it could just be like people + + align:start position:0% +punctual it could just be like people + + + align:start position:0% +punctual it could just be like people +some people are not productive and + + align:start position:0% +some people are not productive and + + + align:start position:0% +some people are not productive and +they're just bad at doing stuff + + align:start position:0% +they're just bad at doing stuff + + + align:start position:0% +they're just bad at doing stuff +and therefore um they become poorer and + + align:start position:0% +and therefore um they become poorer and + + + align:start position:0% +and therefore um they become poorer and +then they end up being poor + + align:start position:0% +then they end up being poor + + + align:start position:0% +then they end up being poor +because of that so that's essentially i + + align:start position:0% +because of that so that's essentially i + + + align:start position:0% +because of that so that's essentially i +think that we covered pretty much + + align:start position:0% +think that we covered pretty much + + + align:start position:0% +think that we covered pretty much +everything so one is + + align:start position:0% +everything so one is + + + align:start position:0% +everything so one is +it could be sort of environmental + + align:start position:0% +it could be sort of environmental + + + align:start position:0% +it could be sort of environmental +conditions which is you know + + align:start position:0% +conditions which is you know + + + align:start position:0% +conditions which is you know +transportation + + align:start position:0% +transportation + + + align:start position:0% +transportation +it's really hard to get to work on time + + align:start position:0% +it's really hard to get to work on time + + + align:start position:0% +it's really hard to get to work on time +or like you have to communicate for two + + align:start position:0% +or like you have to communicate for two + + + align:start position:0% +or like you have to communicate for two +hours and then you're really tired and + + align:start position:0% +hours and then you're really tired and + + + align:start position:0% +hours and then you're really tired and +that makes you less productive + + align:start position:0% +that makes you less productive + + + align:start position:0% +that makes you less productive +things like predatory lending sort of + + align:start position:0% +things like predatory lending sort of + + + align:start position:0% +things like predatory lending sort of +tricks you want to like lending + + align:start position:0% +tricks you want to like lending + + + align:start position:0% +tricks you want to like lending +there could be some things about + + align:start position:0% +there could be some things about + + + align:start position:0% +there could be some things about +institutional structures which is to say + + align:start position:0% +institutional structures which is to say + + + align:start position:0% +institutional structures which is to say +like you know i told you for example at + + align:start position:0% +like you know i told you for example at + + + align:start position:0% +like you know i told you for example at +mit + + align:start position:0% +mit + + + align:start position:0% +mit +um there's a default um what other + + align:start position:0% +um there's a default um what other + + + align:start position:0% +um there's a default um what other +places there's + + align:start position:0% +places there's + + + align:start position:0% +places there's +defaults for people to save money and + + align:start position:0% +defaults for people to save money and + + + align:start position:0% +defaults for people to save money and +there's a default to like get health + + align:start position:0% +there's a default to like get health + + + align:start position:0% +there's a default to like get health +insurance and there's defaults for all + + align:start position:0% +insurance and there's defaults for all + + + align:start position:0% +insurance and there's defaults for all +sorts of like good behaviors + + align:start position:0% +sorts of like good behaviors + + + align:start position:0% +sorts of like good behaviors +like you know um uh uh + + align:start position:0% +like you know um uh uh + + + align:start position:0% +like you know um uh uh +for vaccinations and so on and so forth + + align:start position:0% +for vaccinations and so on and so forth + + + align:start position:0% +for vaccinations and so on and so forth +where you sort of like essentially + + align:start position:0% +where you sort of like essentially + + + align:start position:0% +where you sort of like essentially +pushed by society + + align:start position:0% +pushed by society + + + align:start position:0% +pushed by society +about the environmental conditions that + + align:start position:0% +about the environmental conditions that + + + align:start position:0% +about the environmental conditions that +you face into doing the right thing + + align:start position:0% +you face into doing the right thing + + + align:start position:0% +you face into doing the right thing +or whatever good behaviors whatever you + + align:start position:0% +or whatever good behaviors whatever you + + + align:start position:0% +or whatever good behaviors whatever you +want to call it and so + + align:start position:0% +want to call it and so + + + align:start position:0% +want to call it and so +um um and so the poor might just not + + align:start position:0% +um um and so the poor might just not + + + align:start position:0% +um um and so the poor might just not +have those things so for example having + + align:start position:0% +have those things so for example having + + + align:start position:0% +have those things so for example having +a bank account + + align:start position:0% +a bank account + + + align:start position:0% +a bank account +might be like if you paid um daily or + + align:start position:0% +might be like if you paid um daily or + + + align:start position:0% +might be like if you paid um daily or +you can buy like trick the rich + + align:start position:0% +you can buy like trick the rich + + + align:start position:0% +you can buy like trick the rich +by trip the big shot drivers that i was + + align:start position:0% +by trip the big shot drivers that i was + + + align:start position:0% +by trip the big shot drivers that i was +showing you earlier in the semester + + align:start position:0% +showing you earlier in the semester + + + align:start position:0% +showing you earlier in the semester +they paid trip by trip and then they + + align:start position:0% +they paid trip by trip and then they + + + align:start position:0% +they paid trip by trip and then they +passed by like the liquor stores + + align:start position:0% +passed by like the liquor stores + + + align:start position:0% +passed by like the liquor stores +uh uh essentially daily and have a bunch + + align:start position:0% +uh uh essentially daily and have a bunch + + + align:start position:0% +uh uh essentially daily and have a bunch +of cash on hand + + align:start position:0% +of cash on hand + + + align:start position:0% +of cash on hand +well that's much trickier to sort of + + align:start position:0% +well that's much trickier to sort of + + + align:start position:0% +well that's much trickier to sort of +resist in some sense if you were + + align:start position:0% +resist in some sense if you were + + + align:start position:0% +resist in some sense if you were +um particularly also prone to physical + + align:start position:0% +um particularly also prone to physical + + + align:start position:0% +um particularly also prone to physical +pain and then sort of uh + + align:start position:0% +pain and then sort of uh + + + align:start position:0% +pain and then sort of uh +to use alcohol as a way to deal with + + align:start position:0% +to use alcohol as a way to deal with + + + align:start position:0% +to use alcohol as a way to deal with +your physical pain + + align:start position:0% +your physical pain + + + align:start position:0% +your physical pain +as opposed to somebody who's paid months + + align:start position:0% +as opposed to somebody who's paid months + + + align:start position:0% +as opposed to somebody who's paid months +late and half of the money goes into + + align:start position:0% +late and half of the money goes into + + + align:start position:0% +late and half of the money goes into +like the rent + + align:start position:0% +like the rent + + + align:start position:0% +like the rent +anyway and like on other expenses and so + + align:start position:0% +anyway and like on other expenses and so + + + align:start position:0% +anyway and like on other expenses and so +on which is much easier to + + align:start position:0% +on which is much easier to + + + align:start position:0% +on which is much easier to +to manage so that's kind of like broadly + + align:start position:0% +to manage so that's kind of like broadly + + + align:start position:0% +to manage so that's kind of like broadly +i haven't summarized it as like + + align:start position:0% +i haven't summarized it as like + + + align:start position:0% +i haven't summarized it as like +environmental conditions then there's + + align:start position:0% +environmental conditions then there's + + + align:start position:0% +environmental conditions then there's +like selection and + + align:start position:0% +like selection and + + + align:start position:0% +like selection and +emitted variables which is them i think + + align:start position:0% +emitted variables which is them i think + + + align:start position:0% +emitted variables which is them i think +jose was mentioning education which is a + + align:start position:0% +jose was mentioning education which is a + + + align:start position:0% +jose was mentioning education which is a +very good one + + align:start position:0% +very good one + + + align:start position:0% +very good one +there's things like um intelligence + + align:start position:0% +there's things like um intelligence + + + align:start position:0% +there's things like um intelligence +talent + + align:start position:0% +talent + + + align:start position:0% +talent +effort mistakes and so on you might say + + align:start position:0% +effort mistakes and so on you might say + + + align:start position:0% +effort mistakes and so on you might say +well like if you are + + align:start position:0% +well like if you are + + + align:start position:0% +well like if you are +um more prone if you're less productive + + align:start position:0% +um more prone if you're less productive + + + align:start position:0% +um more prone if you're less productive +for example if you're prone to making + + align:start position:0% +for example if you're prone to making + + + align:start position:0% +for example if you're prone to making +mistakes and so on + + align:start position:0% +mistakes and so on + + + align:start position:0% +mistakes and so on +well that sort of um leads to worse + + align:start position:0% +well that sort of um leads to worse + + + align:start position:0% +well that sort of um leads to worse +outcome and that means you end up + + align:start position:0% +outcome and that means you end up + + + align:start position:0% +outcome and that means you end up +um being poor and that's really like + + align:start position:0% +um being poor and that's really like + + + align:start position:0% +um being poor and that's really like +sort of like uh + + align:start position:0% +sort of like uh + + + align:start position:0% +sort of like uh +uh in some sense like a right-wing kind + + align:start position:0% +uh in some sense like a right-wing kind + + + align:start position:0% +uh in some sense like a right-wing kind +of you that said like you know people + + align:start position:0% +of you that said like you know people + + + align:start position:0% +of you that said like you know people +are + + align:start position:0% +are + + + align:start position:0% +are +they should do whatever they want to do + + align:start position:0% +they should do whatever they want to do + + + align:start position:0% +they should do whatever they want to do +and like if they end up being poor it's + + align:start position:0% +and like if they end up being poor it's + + + align:start position:0% +and like if they end up being poor it's +sort of their fault + + align:start position:0% +sort of their fault + + + align:start position:0% +sort of their fault +and so on that's of course not what + + align:start position:0% +and so on that's of course not what + + + align:start position:0% +and so on that's of course not what +we're going to argue um here will be + + align:start position:0% +we're going to argue um here will be + + + align:start position:0% +we're going to argue um here will be +interested in or what i'm trying to + + align:start position:0% +interested in or what i'm trying to + + + align:start position:0% +interested in or what i'm trying to +show you some evidence stuff is that + + align:start position:0% +show you some evidence stuff is that + + + align:start position:0% +show you some evidence stuff is that +there's a treatment effect of poverty + + align:start position:0% +there's a treatment effect of poverty + + + align:start position:0% +there's a treatment effect of poverty +um itself potentially which is to say + + align:start position:0% +um itself potentially which is to say + + + align:start position:0% +um itself potentially which is to say +that like being poor itself + + align:start position:0% +that like being poor itself + + + align:start position:0% +that like being poor itself +causes these behaviors and i'm going to + + align:start position:0% +causes these behaviors and i'm going to + + + align:start position:0% +causes these behaviors and i'm going to +show you evidence of like two + + align:start position:0% +show you evidence of like two + + + align:start position:0% +show you evidence of like two +uh and two ways one is + + align:start position:0% +uh and two ways one is + + + align:start position:0% +uh and two ways one is +um by inducing thoughts about money + + align:start position:0% +um by inducing thoughts about money + + + align:start position:0% +um by inducing thoughts about money +essentially thinking about can you pay + + align:start position:0% +essentially thinking about can you pay + + + align:start position:0% +essentially thinking about can you pay +school fees can you pay your rent can + + align:start position:0% +school fees can you pay your rent can + + + align:start position:0% +school fees can you pay your rent can +you get groceries for your children are + + align:start position:0% +you get groceries for your children are + + + align:start position:0% +you get groceries for your children are +your children going to be hungry tonight + + align:start position:0% +your children going to be hungry tonight + + + align:start position:0% +your children going to be hungry tonight +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +these are all kind of thoughts that + + align:start position:0% +these are all kind of thoughts that + + + align:start position:0% +these are all kind of thoughts that +invade people's minds involved + + align:start position:0% +invade people's minds involved + + + align:start position:0% +invade people's minds involved +voluntarily and by doing so um they + + align:start position:0% +voluntarily and by doing so um they + + + align:start position:0% +voluntarily and by doing so um they +capture + + align:start position:0% +capture + + + align:start position:0% +capture +people's attention and then since + + align:start position:0% +people's attention and then since + + + align:start position:0% +people's attention and then since +attention overall is limited + + align:start position:0% +attention overall is limited + + + align:start position:0% +attention overall is limited +and people have less attention available + + align:start position:0% +and people have less attention available + + + align:start position:0% +and people have less attention available +for other things + + align:start position:0% +for other things + + + align:start position:0% +for other things +that sort of one broad um um + + align:start position:0% +that sort of one broad um um + + + align:start position:0% +that sort of one broad um um +theory um and i'll focus on that mostly + + align:start position:0% +theory um and i'll focus on that mostly + + + align:start position:0% +theory um and i'll focus on that mostly +which sort of because people call it + + align:start position:0% +which sort of because people call it + + + align:start position:0% +which sort of because people call it +people refer to under the name of + + align:start position:0% +people refer to under the name of + + + align:start position:0% +people refer to under the name of +scarcity and and then you know there's a + + align:start position:0% +scarcity and and then you know there's a + + + align:start position:0% +scarcity and and then you know there's a +bunch of other + + align:start position:0% +bunch of other + + + align:start position:0% +bunch of other +aspects of poverty as well that might be + + align:start position:0% +aspects of poverty as well that might be + + + align:start position:0% +aspects of poverty as well that might be +uh impeding with people's cognitive + + align:start position:0% +uh impeding with people's cognitive + + + align:start position:0% +uh impeding with people's cognitive +function their attention + + align:start position:0% +function their attention + + + align:start position:0% +function their attention +that tire them out which is like not + + align:start position:0% +that tire them out which is like not + + + align:start position:0% +that tire them out which is like not +sleeping well being in pain + + align:start position:0% +sleeping well being in pain + + + align:start position:0% +sleeping well being in pain +um being exposed to pollution + + align:start position:0% +um being exposed to pollution + + + align:start position:0% +um being exposed to pollution +environmental pollution + + align:start position:0% +environmental pollution + + + align:start position:0% +environmental pollution +uh noise pollution and so on + + align:start position:0% +uh noise pollution and so on + + + align:start position:0% +uh noise pollution and so on +and so forth and so now what's the + + align:start position:0% +and so forth and so now what's the + + + align:start position:0% +and so forth and so now what's the +underlying + + align:start position:0% +underlying + + + align:start position:0% +underlying +sort of idea here while again the lying + + align:start position:0% +sort of idea here while again the lying + + + align:start position:0% +sort of idea here while again the lying +idea is that there might be a + + align:start position:0% +idea is that there might be a + + + align:start position:0% +idea is that there might be a +what's called like people call it + + align:start position:0% +what's called like people call it + + + align:start position:0% +what's called like people call it +behavioral poverty drought + + align:start position:0% +behavioral poverty drought + + + align:start position:0% +behavioral poverty drought +trap and the broad line of argument is + + align:start position:0% +trap and the broad line of argument is + + + align:start position:0% +trap and the broad line of argument is +that poverty affects people's + + align:start position:0% +that poverty affects people's + + + align:start position:0% +that poverty affects people's +cognition decision making of + + align:start position:0% +cognition decision making of + + + align:start position:0% +cognition decision making of +productivity these factors in turn + + align:start position:0% +productivity these factors in turn + + + align:start position:0% +productivity these factors in turn +then influence people's future uh + + align:start position:0% +then influence people's future uh + + + align:start position:0% +then influence people's future uh +poverty because if you're not productive + + align:start position:0% +poverty because if you're not productive + + + align:start position:0% +poverty because if you're not productive +and you can't save money and so on + + align:start position:0% +and you can't save money and so on + + + align:start position:0% +and you can't save money and so on +you're going to be + + align:start position:0% +you're going to be + + + align:start position:0% +you're going to be +more poor in the future and then if + + align:start position:0% +more poor in the future and then if + + + align:start position:0% +more poor in the future and then if +those things are going on there's + + align:start position:0% +those things are going on there's + + + align:start position:0% +those things are going on there's +essentially some form of vicious + + align:start position:0% +essentially some form of vicious + + + align:start position:0% +essentially some form of vicious +cycle going on which makes it difficult + + align:start position:0% +cycle going on which makes it difficult + + + align:start position:0% +cycle going on which makes it difficult +if not + + align:start position:0% +if not + + + align:start position:0% +if not +um impossible for a person to become + + align:start position:0% +um impossible for a person to become + + + align:start position:0% +um impossible for a person to become +rich now notice at the very least that + + align:start position:0% +rich now notice at the very least that + + + align:start position:0% +rich now notice at the very least that +will lower + + align:start position:0% +will lower + + + align:start position:0% +will lower +mobility you know sometimes you're poor + + align:start position:0% +mobility you know sometimes you're poor + + + align:start position:0% +mobility you know sometimes you're poor +and you want to become richer you have + + align:start position:0% +and you want to become richer you have + + + align:start position:0% +and you want to become richer you have +to deal with a bunch of bad stuff that + + align:start position:0% +to deal with a bunch of bad stuff that + + + align:start position:0% +to deal with a bunch of bad stuff that +happens to you um + + align:start position:0% +happens to you um + + + align:start position:0% +happens to you um +every day um but my conscious human + + align:start position:0% +every day um but my conscious human + + + align:start position:0% +every day um but my conscious human +mobility is low it might or it might be + + align:start position:0% +mobility is low it might or it might be + + + align:start position:0% +mobility is low it might or it might be +like actually a trap it's just + + align:start position:0% +like actually a trap it's just + + + align:start position:0% +like actually a trap it's just +next to or actually impossible to become + + align:start position:0% +next to or actually impossible to become + + + align:start position:0% +next to or actually impossible to become +richer because all these forces are too + + align:start position:0% +richer because all these forces are too + + + align:start position:0% +richer because all these forces are too +strong to + + align:start position:0% +strong to + + + align:start position:0% +strong to +overcome them for people um so today + + align:start position:0% +overcome them for people um so today + + + align:start position:0% +overcome them for people um so today +we're going to talk about two + + align:start position:0% +we're going to talk about two + + + align:start position:0% +we're going to talk about two +broad lines of research i'm going to + + align:start position:0% +broad lines of research i'm going to + + + align:start position:0% +broad lines of research i'm going to +first focus mostly on the first one + + align:start position:0% +first focus mostly on the first one + + + align:start position:0% +first focus mostly on the first one +which is monitoring concerns capture + + align:start position:0% +which is monitoring concerns capture + + + align:start position:0% +which is monitoring concerns capture +people's cognitive function + + align:start position:0% +people's cognitive function + + + align:start position:0% +people's cognitive function +i'm going to talk a little bit then + + align:start position:0% +i'm going to talk a little bit then + + + align:start position:0% +i'm going to talk a little bit then +about other poverty-induced depression + + align:start position:0% +about other poverty-induced depression + + + align:start position:0% +about other poverty-induced depression +and behaviors which might have sort of + + align:start position:0% +and behaviors which might have sort of + + + align:start position:0% +and behaviors which might have sort of +similar effects + + align:start position:0% +similar effects + + + align:start position:0% +similar effects +um overall okay so now i want to + + align:start position:0% +um overall okay so now i want to + + + align:start position:0% +um overall okay so now i want to +do like a simple um uh test with you um + + align:start position:0% +do like a simple um uh test with you um + + + align:start position:0% +do like a simple um uh test with you um +so what i'd like you to do is to um + + align:start position:0% +so what i'd like you to do is to um + + + align:start position:0% +so what i'd like you to do is to um +so i don't second actually + + align:start position:0% + + + + align:start position:0% + +ready don't write anything down just try + + align:start position:0% +ready don't write anything down just try + + + align:start position:0% +ready don't write anything down just try +to remember it and then uh try to recall + + align:start position:0% +to remember it and then uh try to recall + + + align:start position:0% +to remember it and then uh try to recall +in a bit + + align:start position:0% +in a bit + + + align:start position:0% +in a bit +okay i'm gonna start reading bed + + align:start position:0% +okay i'm gonna start reading bed + + + align:start position:0% +okay i'm gonna start reading bed +rest dream doze + + align:start position:0% +rest dream doze + + + align:start position:0% +rest dream doze +snore slumber blanket + + align:start position:0% +snore slumber blanket + + + align:start position:0% +snore slumber blanket +snooze wake map + + align:start position:0% +snooze wake map + + + align:start position:0% +snooze wake map +awake tired + + align:start position:0% + + + + align:start position:0% + +okay now please write down the as many + + align:start position:0% +okay now please write down the as many + + + align:start position:0% +okay now please write down the as many +words as you + + align:start position:0% + + + + align:start position:0% + +remember + + align:start position:0% + + + + align:start position:0% + +ten more seconds + + align:start position:0% + + + + align:start position:0% + +all right so done so um uh usually i + + align:start position:0% +all right so done so um uh usually i + + + align:start position:0% +all right so done so um uh usually i +would sort of like have people raise + + align:start position:0% +would sort of like have people raise + + + align:start position:0% +would sort of like have people raise +their hands which is a little tricky but + + align:start position:0% +their hands which is a little tricky but + + + align:start position:0% +their hands which is a little tricky but +so i'm gonna just read you the list of + + align:start position:0% +so i'm gonna just read you the list of + + + align:start position:0% +so i'm gonna just read you the list of +words and you can knock to me i couldn't + + align:start position:0% +words and you can knock to me i couldn't + + + align:start position:0% +words and you can knock to me i couldn't +see some of you at least uh you cannot + + align:start position:0% +see some of you at least uh you cannot + + + align:start position:0% +see some of you at least uh you cannot +and + + align:start position:0% +and + + + align:start position:0% +and +tell me whether you remember um um + + align:start position:0% +tell me whether you remember um um + + + align:start position:0% +tell me whether you remember um um +the the words that i read + + align:start position:0% +the the words that i read + + + align:start position:0% +the the words that i read +okay i'm gonna start bed + + align:start position:0% +okay i'm gonna start bed + + + align:start position:0% +okay i'm gonna start bed +rest pretty good + + align:start position:0% +rest pretty good + + + align:start position:0% +rest pretty good +green doze + + align:start position:0% + + + + align:start position:0% + +snore oh + + align:start position:0% +snore oh + + + align:start position:0% +snore oh +slumber + + align:start position:0% + + + + align:start position:0% + +sleep + + align:start position:0% + + + + align:start position:0% + +blanket snooze + + align:start position:0% + + + + align:start position:0% + +quake nap + + align:start position:0% +quake nap + + + align:start position:0% +quake nap +awake tired + + align:start position:0% + + + + align:start position:0% + +okay so i know this is making everybody + + align:start position:0% +okay so i know this is making everybody + + + align:start position:0% +okay so i know this is making everybody +sleepy and want to take a nap um + + align:start position:0% +sleepy and want to take a nap um + + + align:start position:0% +sleepy and want to take a nap um +me too um so here's a list of words um + + align:start position:0% +me too um so here's a list of words um + + + align:start position:0% +me too um so here's a list of words um +um that + + align:start position:0% +um that + + + align:start position:0% +um that +asked me to remember now um one thing + + align:start position:0% +asked me to remember now um one thing + + + align:start position:0% +asked me to remember now um one thing +that's kind of nice + + align:start position:0% +that's kind of nice + + + align:start position:0% +that's kind of nice +you and me you know like most people + + align:start position:0% +you and me you know like most people + + + align:start position:0% +you and me you know like most people +remember quite a few things um um + + align:start position:0% +remember quite a few things um um + + + align:start position:0% +remember quite a few things um um +and the majority for example remember + + align:start position:0% +and the majority for example remember + + + align:start position:0% +and the majority for example remember +sped and so on and so forth + + align:start position:0% +sped and so on and so forth + + + align:start position:0% +sped and so on and so forth +now what's quite interesting about these + + align:start position:0% +now what's quite interesting about these + + + align:start position:0% +now what's quite interesting about these +words is that + + align:start position:0% +words is that + + + align:start position:0% +words is that +um while i remember i put all these + + align:start position:0% +um while i remember i put all these + + + align:start position:0% +um while i remember i put all these +names up here which is you know + + align:start position:0% +names up here which is you know + + + align:start position:0% +names up here which is you know +um these are the words that i actually + + align:start position:0% +um these are the words that i actually + + + align:start position:0% +um these are the words that i actually +read now one word that's actually + + align:start position:0% +read now one word that's actually + + + align:start position:0% +read now one word that's actually +missing in this list here + + align:start position:0% +missing in this list here + + + align:start position:0% +missing in this list here +is sleep and so um + + align:start position:0% +is sleep and so um + + + align:start position:0% +is sleep and so um +you sort of i snuck this in here i'm + + align:start position:0% +you sort of i snuck this in here i'm + + + align:start position:0% +you sort of i snuck this in here i'm +uh this is why i had to go back um it + + align:start position:0% +uh this is why i had to go back um it + + + align:start position:0% +uh this is why i had to go back um it +turns out i actually didn't read the + + align:start position:0% +turns out i actually didn't read the + + + align:start position:0% +turns out i actually didn't read the +word sleep + + align:start position:0% +word sleep + + + align:start position:0% +word sleep +now quite a few of you were nodding i'm + + align:start position:0% +now quite a few of you were nodding i'm + + + align:start position:0% +now quite a few of you were nodding i'm +happily when i asked you about sleep + + align:start position:0% +happily when i asked you about sleep + + + align:start position:0% +happily when i asked you about sleep +and what's the reason why sleep is why + + align:start position:0% +and what's the reason why sleep is why + + + align:start position:0% +and what's the reason why sleep is why +you remembered sleep + + align:start position:0% +you remembered sleep + + + align:start position:0% +you remembered sleep +so all of these words is like uh um + + align:start position:0% +so all of these words is like uh um + + + align:start position:0% +so all of these words is like uh um +they they all around sleep so like it's + + align:start position:0% +they they all around sleep so like it's + + + align:start position:0% +they they all around sleep so like it's +really like + + align:start position:0% +really like + + + align:start position:0% +really like +uh uh sleep should have been there + + align:start position:0% +uh uh sleep should have been there + + + align:start position:0% +uh uh sleep should have been there +it's kind of the type of thing where + + align:start position:0% +it's kind of the type of thing where + + + align:start position:0% +it's kind of the type of thing where +people would ask you like have you been + + align:start position:0% +people would ask you like have you been + + + align:start position:0% +people would ask you like have you been +to the party + + align:start position:0% +to the party + + + align:start position:0% +to the party +last week where like people just assumed + + align:start position:0% +last week where like people just assumed + + + align:start position:0% +last week where like people just assumed +where essentially all the friends were + + align:start position:0% +where essentially all the friends were + + + align:start position:0% +where essentially all the friends were +there people just assumed that you were + + align:start position:0% +there people just assumed that you were + + + align:start position:0% +there people just assumed that you were +there as well because you're supposed to + + align:start position:0% +there as well because you're supposed to + + + align:start position:0% +there as well because you're supposed to +be there + + align:start position:0% +be there + + + align:start position:0% +be there +it's like sleep is supposed to be in + + align:start position:0% +it's like sleep is supposed to be in + + + align:start position:0% +it's like sleep is supposed to be in +this list but he didn't put it there and + + align:start position:0% +this list but he didn't put it there and + + + align:start position:0% +this list but he didn't put it there and +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +this is what called like false memory + + align:start position:0% +this is what called like false memory + + + align:start position:0% +this is what called like false memory +tests and there's quite a bit of work on + + align:start position:0% +tests and there's quite a bit of work on + + + align:start position:0% +tests and there's quite a bit of work on +actually false memories and people's + + align:start position:0% +actually false memories and people's + + + align:start position:0% +actually false memories and people's +minds essentially make up things + + align:start position:0% +minds essentially make up things + + + align:start position:0% +minds essentially make up things +um in particular stuff that sort of um + + align:start position:0% +um in particular stuff that sort of um + + + align:start position:0% +um in particular stuff that sort of um +or where you have all situations that + + align:start position:0% +or where you have all situations that + + + align:start position:0% +or where you have all situations that +that + + align:start position:0% +that + + + align:start position:0% +that +you think that should be the case you + + align:start position:0% +you think that should be the case you + + + align:start position:0% +you think that should be the case you +can do the same with like man + + align:start position:0% +can do the same with like man + + + align:start position:0% +can do the same with like man +and other lists and so on and now + + align:start position:0% +and other lists and so on and now + + + align:start position:0% +and other lists and so on and now +psychologists have been + + align:start position:0% +psychologists have been + + + align:start position:0% +psychologists have been +doing like um studies um for the rich + + align:start position:0% +doing like um studies um for the rich + + + align:start position:0% +doing like um studies um for the rich +and the poor and so + + align:start position:0% +and the poor and so + + + align:start position:0% +and the poor and so +here's two lists one is about sort of + + align:start position:0% +here's two lists one is about sort of + + + align:start position:0% +here's two lists one is about sort of +money related stuff + + align:start position:0% +money related stuff + + + align:start position:0% +money related stuff +and one is about uh sort of just + + align:start position:0% +and one is about uh sort of just + + + align:start position:0% +and one is about uh sort of just +anything that's related to like i guess + + align:start position:0% +anything that's related to like i guess + + + align:start position:0% +anything that's related to like i guess +man or like um gender in some ways and i + + align:start position:0% +man or like um gender in some ways and i + + + align:start position:0% +man or like um gender in some ways and i +looked at how many people have certain + + align:start position:0% +looked at how many people have certain + + + align:start position:0% +looked at how many people have certain +false memories + + align:start position:0% +false memories + + + align:start position:0% +false memories +and what these studies show it's + + align:start position:0% +and what these studies show it's + + + align:start position:0% +and what these studies show it's +essentially that when you look when you + + align:start position:0% +essentially that when you look when you + + + align:start position:0% +essentially that when you look when you +take this list for a man + + align:start position:0% +take this list for a man + + + align:start position:0% +take this list for a man +can you do this with high and poor high + + align:start position:0% +can you do this with high and poor high + + + align:start position:0% +can you do this with high and poor high +income and low income + + align:start position:0% +income and low income + + + align:start position:0% +income and low income +people the fraction who remember man + + align:start position:0% +people the fraction who remember man + + + align:start position:0% +people the fraction who remember man +wrong way + + align:start position:0% +wrong way + + + align:start position:0% +wrong way +um is about like you know 15 to 20 um + + align:start position:0% +um is about like you know 15 to 20 um + + + align:start position:0% +um is about like you know 15 to 20 um +the fraction among the poor who remember + + align:start position:0% +the fraction among the poor who remember + + + align:start position:0% +the fraction among the poor who remember +money is similarly high among the rich + + align:start position:0% +money is similarly high among the rich + + + align:start position:0% +money is similarly high among the rich +that's not the case now why is that well + + align:start position:0% +that's not the case now why is that well + + + align:start position:0% +that's not the case now why is that well +it seems to be that like for the poor + + align:start position:0% +it seems to be that like for the poor + + + align:start position:0% +it seems to be that like for the poor +when you read lists like groceries + + align:start position:0% +when you read lists like groceries + + + align:start position:0% +when you read lists like groceries +expense spill gas etc + + align:start position:0% +expense spill gas etc + + + align:start position:0% +expense spill gas etc +what they think about is essentially how + + align:start position:0% +what they think about is essentially how + + + align:start position:0% +what they think about is essentially how +i'm going to pay for this and they think + + align:start position:0% +i'm going to pay for this and they think + + + align:start position:0% +i'm going to pay for this and they think +about + + align:start position:0% +about + + + align:start position:0% +about +money when um for the rich and + + align:start position:0% +money when um for the rich and + + + align:start position:0% +money when um for the rich and +instead when you say like groceries or + + align:start position:0% +instead when you say like groceries or + + + align:start position:0% +instead when you say like groceries or +whatever they think about like what i'm + + align:start position:0% +whatever they think about like what i'm + + + align:start position:0% +whatever they think about like what i'm +going to buy for dinner and what are the + + align:start position:0% +going to buy for dinner and what are the + + + align:start position:0% +going to buy for dinner and what are the +nice things i'm going to do + + align:start position:0% +nice things i'm going to do + + + align:start position:0% +nice things i'm going to do +and for them this is really not top of + + align:start position:0% +and for them this is really not top of + + + align:start position:0% +and for them this is really not top of +mind so this is essentially + + align:start position:0% +mind so this is essentially + + + align:start position:0% +mind so this is essentially +at least one piece of evidence that + + align:start position:0% +at least one piece of evidence that + + + align:start position:0% +at least one piece of evidence that +money captures + + align:start position:0% +money captures + + + align:start position:0% +money captures +um the minds of the poor more so than + + align:start position:0% +um the minds of the poor more so than + + + align:start position:0% +um the minds of the poor more so than +for the rich now + + align:start position:0% +for the rich now + + + align:start position:0% +for the rich now +a second study is a study about their + + align:start position:0% +a second study is a study about their + + + align:start position:0% +a second study is a study about their +doctor's visit + + align:start position:0% +doctor's visit + + + align:start position:0% +doctor's visit +so this is a study where they uh + + align:start position:0% +so this is a study where they uh + + + align:start position:0% +so this is a study where they uh +participants were asked about following + + align:start position:0% +participants were asked about following + + + align:start position:0% +participants were asked about following +situation which is + + align:start position:0% +situation which is + + + align:start position:0% +situation which is +imagine that you have been feeling sick + + align:start position:0% +imagine that you have been feeling sick + + + align:start position:0% +imagine that you have been feeling sick +lately and finally decide to go see a + + align:start position:0% +lately and finally decide to go see a + + + align:start position:0% +lately and finally decide to go see a +doctor about it + + align:start position:0% +doctor about it + + + align:start position:0% +doctor about it +the doctor explains to have a serious + + align:start position:0% +the doctor explains to have a serious + + + align:start position:0% +the doctor explains to have a serious +condition that requires immediate + + align:start position:0% +condition that requires immediate + + + align:start position:0% +condition that requires immediate +attention + + align:start position:0% +attention + + + align:start position:0% +attention +the good news however is you are + + align:start position:0% +the good news however is you are + + + align:start position:0% +the good news however is you are +virtually guaranteed to make a full + + align:start position:0% +virtually guaranteed to make a full + + + align:start position:0% +virtually guaranteed to make a full +recovery + + align:start position:0% +recovery + + + align:start position:0% +recovery +the doctor writes several prescriptions + + align:start position:0% +the doctor writes several prescriptions + + + align:start position:0% +the doctor writes several prescriptions +you will also need to make several + + align:start position:0% +you will also need to make several + + + align:start position:0% +you will also need to make several +appointments what would be on your mind + + align:start position:0% +appointments what would be on your mind + + + align:start position:0% +appointments what would be on your mind +on or or how would you feel about when + + align:start position:0% +on or or how would you feel about when + + + align:start position:0% +on or or how would you feel about when +you hear this news + + align:start position:0% +you hear this news + + + align:start position:0% +you hear this news +what are the three things that you think + + align:start position:0% +what are the three things that you think + + + align:start position:0% +what are the three things that you think +about it or + + align:start position:0% +about it or + + + align:start position:0% +about it or +feel you can think about for a second + + align:start position:0% +feel you can think about for a second + + + align:start position:0% +feel you can think about for a second +what is it that you would feel what are + + align:start position:0% +what is it that you would feel what are + + + align:start position:0% +what is it that you would feel what are +you thinking about when you when you see + + align:start position:0% +you thinking about when you when you see + + + align:start position:0% +you thinking about when you when you see +this + + align:start position:0% +this + + + align:start position:0% +this +and what's particularly interesting is + + align:start position:0% +and what's particularly interesting is + + + align:start position:0% +and what's particularly interesting is +now when you look at people's responses + + align:start position:0% +now when you look at people's responses + + + align:start position:0% +now when you look at people's responses +some people say wife son co-worker + + align:start position:0% +some people say wife son co-worker + + + align:start position:0% +some people say wife son co-worker +uh uh some people are scared afraid + + align:start position:0% +uh uh some people are scared afraid + + + align:start position:0% +uh uh some people are scared afraid +worried + + align:start position:0% +worried + + + align:start position:0% +worried +um relief hope joy so like emotions + + align:start position:0% +um relief hope joy so like emotions + + + align:start position:0% +um relief hope joy so like emotions +um uh uh or just relationships and other + + align:start position:0% +um uh uh or just relationships and other + + + align:start position:0% +um uh uh or just relationships and other +people + + align:start position:0% +people + + + align:start position:0% +people +not exactly sure what the co-worker is + + align:start position:0% +not exactly sure what the co-worker is + + + align:start position:0% +not exactly sure what the co-worker is +doing there but anyway um + + align:start position:0% +doing there but anyway um + + + align:start position:0% +doing there but anyway um +uh uh but um what's particularly + + align:start position:0% +uh uh but um what's particularly + + + align:start position:0% +uh uh but um what's particularly +interesting is like the fraction of + + align:start position:0% +interesting is like the fraction of + + + align:start position:0% +interesting is like the fraction of +people who say + + align:start position:0% +people who say + + + align:start position:0% +people who say +costs and as you can imagine um + + align:start position:0% +costs and as you can imagine um + + + align:start position:0% +costs and as you can imagine um +when you do this by low and high income + + align:start position:0% +when you do this by low and high income + + + align:start position:0% +when you do this by low and high income +um when you think about like + + align:start position:0% +um when you think about like + + + align:start position:0% +um when you think about like +um medical conditions + + align:start position:0% +um medical conditions + + + align:start position:0% +um medical conditions +for the rich um this is much more about + + align:start position:0% +for the rich um this is much more about + + + align:start position:0% +for the rich um this is much more about +like emotions about + + align:start position:0% +like emotions about + + + align:start position:0% +like emotions about +about their health about like their + + align:start position:0% +about their health about like their + + + align:start position:0% +about their health about like their +relationships their loved ones and so on + + align:start position:0% +relationships their loved ones and so on + + + align:start position:0% +relationships their loved ones and so on +when the poor think about like health or + + align:start position:0% +when the poor think about like health or + + + align:start position:0% +when the poor think about like health or +health expenditures or health issues + + align:start position:0% +health expenditures or health issues + + + align:start position:0% +health expenditures or health issues +they think very much about health + + align:start position:0% +they think very much about health + + + align:start position:0% +they think very much about health +expenditures and that is essentially + + align:start position:0% +expenditures and that is essentially + + + align:start position:0% +expenditures and that is essentially +what's top of mind + + align:start position:0% +what's top of mind + + + align:start position:0% +what's top of mind +for them and so again when you split the + + align:start position:0% +for them and so again when you split the + + + align:start position:0% +for them and so again when you split the +sample by low and high income people + + align:start position:0% +sample by low and high income people + + + align:start position:0% +sample by low and high income people +the poor have much higher proportions of + + align:start position:0% +the poor have much higher proportions of + + + align:start position:0% +the poor have much higher proportions of +money related thoughts + + align:start position:0% +money related thoughts + + + align:start position:0% +money related thoughts +as reported by these kinds of questions + + align:start position:0% +as reported by these kinds of questions + + + align:start position:0% +as reported by these kinds of questions +compared to the rich + + align:start position:0% +compared to the rich + + + align:start position:0% +compared to the rich +the third study um last study that i'm + + align:start position:0% +the third study um last study that i'm + + + align:start position:0% +the third study um last study that i'm +going to show you is the study that i + + align:start position:0% +going to show you is the study that i + + + align:start position:0% +going to show you is the study that i +showed you very much at the beginning of + + align:start position:0% +showed you very much at the beginning of + + + align:start position:0% +showed you very much at the beginning of +the class which was study about + + align:start position:0% +the class which was study about + + + align:start position:0% +the class which was study about +um imagine you are about to purchase an + + align:start position:0% +um imagine you are about to purchase an + + + align:start position:0% +um imagine you are about to purchase an +ipad for 500. the salesman says + + align:start position:0% +ipad for 500. the salesman says + + + align:start position:0% +ipad for 500. the salesman says +you can get the same ipad exact same + + align:start position:0% +you can get the same ipad exact same + + + align:start position:0% +you can get the same ipad exact same +ipod for 15 + + align:start position:0% +ipod for 15 + + + align:start position:0% +ipod for 15 +off would you walk for uh uh 30 minutes + + align:start position:0% +off would you walk for uh uh 30 minutes + + + align:start position:0% +off would you walk for uh uh 30 minutes +in total for for doing it would you go + + align:start position:0% +in total for for doing it would you go + + + align:start position:0% +in total for for doing it would you go +for the other store + + align:start position:0% +for the other store + + + align:start position:0% +for the other store +and similarly you should do the same + + align:start position:0% +and similarly you should do the same + + + align:start position:0% +and similarly you should do the same +thing for an ipad case + + align:start position:0% +thing for an ipad case + + + align:start position:0% +thing for an ipad case +and sort of the result that we found in + + align:start position:0% +and sort of the result that we found in + + + align:start position:0% +and sort of the result that we found in +this class and like but other studies + + align:start position:0% +this class and like but other studies + + + align:start position:0% +this class and like but other studies +have found is that + + align:start position:0% +have found is that + + + align:start position:0% +have found is that +people are way more likely to report + + align:start position:0% +people are way more likely to report + + + align:start position:0% +people are way more likely to report +than they would walk for the ipad case + + align:start position:0% +than they would walk for the ipad case + + + align:start position:0% +than they would walk for the ipad case +than for the ipad itself and the + + align:start position:0% +than for the ipad itself and the + + + align:start position:0% +than for the ipad itself and the +explanation of course is + + align:start position:0% +explanation of course is + + + align:start position:0% +explanation of course is +um that people evaluate things in + + align:start position:0% +um that people evaluate things in + + + align:start position:0% +um that people evaluate things in +relative terms + + align:start position:0% +relative terms + + + align:start position:0% +relative terms +right so if you think about the ipad + + align:start position:0% +right so if you think about the ipad + + + align:start position:0% +right so if you think about the ipad +case 15 is like + + align:start position:0% +case 15 is like + + + align:start position:0% +case 15 is like +really high relative to like 30 dollars + + align:start position:0% +really high relative to like 30 dollars + + + align:start position:0% +really high relative to like 30 dollars +the ipad cases um value + + align:start position:0% +the ipad cases um value + + + align:start position:0% +the ipad cases um value +well um for the ipad itself 15 compared + + align:start position:0% +well um for the ipad itself 15 compared + + + align:start position:0% +well um for the ipad itself 15 compared +to 500 + + align:start position:0% +to 500 + + + align:start position:0% +to 500 +is like not very much now that's in some + + align:start position:0% +is like not very much now that's in some + + + align:start position:0% +is like not very much now that's in some +sense some form of like money illusion + + align:start position:0% +sense some form of like money illusion + + + align:start position:0% +sense some form of like money illusion +or some form of + + align:start position:0% +or some form of + + + align:start position:0% +or some form of +unit confusion of the leg because at the + + align:start position:0% +unit confusion of the leg because at the + + + align:start position:0% +unit confusion of the leg because at the +end of the day + + align:start position:0% +end of the day + + + align:start position:0% +end of the day +you should just be willing to walk for + + align:start position:0% +you should just be willing to walk for + + + align:start position:0% +you should just be willing to walk for +30 minutes for either 15 + + align:start position:0% +30 minutes for either 15 + + + align:start position:0% +30 minutes for either 15 +or not that's not gonna change depending + + align:start position:0% +or not that's not gonna change depending + + + align:start position:0% +or not that's not gonna change depending +on whether you buy an ipad or an ipad + + align:start position:0% +on whether you buy an ipad or an ipad + + + align:start position:0% +on whether you buy an ipad or an ipad +case now many studies have found this + + align:start position:0% +case now many studies have found this + + + align:start position:0% +case now many studies have found this +kind of patterns including like in this + + align:start position:0% +kind of patterns including like in this + + + align:start position:0% +kind of patterns including like in this +class + + align:start position:0% +class + + + align:start position:0% +class +but once you do that with the poor then + + align:start position:0% +but once you do that with the poor then + + + align:start position:0% +but once you do that with the poor then +much less likely if at all to engage in + + align:start position:0% +much less likely if at all to engage in + + + align:start position:0% +much less likely if at all to engage in +this kind of behavior + + align:start position:0% +this kind of behavior + + + align:start position:0% +this kind of behavior +which seems to sort of suggest that the + + align:start position:0% +which seems to sort of suggest that the + + + align:start position:0% +which seems to sort of suggest that the +poor in fact are less prone to these + + align:start position:0% +poor in fact are less prone to these + + + align:start position:0% +poor in fact are less prone to these +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +labeling or sort of like monetary um uh + + align:start position:0% +labeling or sort of like monetary um uh + + + align:start position:0% +labeling or sort of like monetary um uh +sort of um + + align:start position:0% +sort of um + + + align:start position:0% +sort of um +comparisons um for them essentially a + + align:start position:0% +comparisons um for them essentially a + + + align:start position:0% +comparisons um for them essentially a +dollar is a dollar and they sort of + + align:start position:0% +dollar is a dollar and they sort of + + + align:start position:0% +dollar is a dollar and they sort of +understand that like 15 + + align:start position:0% +understand that like 15 + + + align:start position:0% +understand that like 15 +is valuable regardless of like what is + + align:start position:0% +is valuable regardless of like what is + + + align:start position:0% +is valuable regardless of like what is +surrounding comparisons + + align:start position:0% +surrounding comparisons + + + align:start position:0% +surrounding comparisons +um might be and so if i had to summarize + + align:start position:0% +um might be and so if i had to summarize + + + align:start position:0% +um might be and so if i had to summarize +now what i've just shown you very + + align:start position:0% +now what i've just shown you very + + + align:start position:0% +now what i've just shown you very +quickly is that + + align:start position:0% +quickly is that + + + align:start position:0% +quickly is that +thoughts about money um tend to capture + + align:start position:0% +thoughts about money um tend to capture + + + align:start position:0% +thoughts about money um tend to capture +and + + align:start position:0% +and + + + align:start position:0% +and +take much more space in the poor's minds + + align:start position:0% +take much more space in the poor's minds + + + align:start position:0% +take much more space in the poor's minds +these are the first two studies that + + align:start position:0% +these are the first two studies that + + + align:start position:0% +these are the first two studies that +showed you + + align:start position:0% +showed you + + + align:start position:0% +showed you +that i showed you and second the extra + + align:start position:0% +that i showed you and second the extra + + + align:start position:0% +that i showed you and second the extra +focus on money has actually some + + align:start position:0% +focus on money has actually some + + + align:start position:0% +focus on money has actually some +positive consequences in some sense + + align:start position:0% +positive consequences in some sense + + + align:start position:0% +positive consequences in some sense +in some sense you can say here this is + + align:start position:0% +in some sense you can say here this is + + + align:start position:0% +in some sense you can say here this is +an irrational decision to say + + align:start position:0% +an irrational decision to say + + + align:start position:0% +an irrational decision to say +um yes that you will do it for the ipad + + align:start position:0% +um yes that you will do it for the ipad + + + align:start position:0% +um yes that you will do it for the ipad +case compared to like the ipad or + + align:start position:0% +case compared to like the ipad or + + + align:start position:0% +case compared to like the ipad or +sort of there's some mis-optimization + + align:start position:0% +sort of there's some mis-optimization + + + align:start position:0% +sort of there's some mis-optimization +going on so the poor actually doing + + align:start position:0% +going on so the poor actually doing + + + align:start position:0% +going on so the poor actually doing +better they're less prone to these kinds + + align:start position:0% +better they're less prone to these kinds + + + align:start position:0% +better they're less prone to these kinds +of errors + + align:start position:0% +of errors + + + align:start position:0% +of errors +um um compared to the rich i think + + align:start position:0% +um um compared to the rich i think + + + align:start position:0% +um um compared to the rich i think +that's a good thing people like + + align:start position:0% +that's a good thing people like + + + align:start position:0% +that's a good thing people like +better potentially better monetary + + align:start position:0% +better potentially better monetary + + + align:start position:0% +better potentially better monetary +decisions here + + align:start position:0% +decisions here + + + align:start position:0% +decisions here +um so there's some positive um + + align:start position:0% +um so there's some positive um + + + align:start position:0% +um so there's some positive um +consequences or um + + align:start position:0% +consequences or um + + + align:start position:0% +consequences or um +uh impacts based on that but now um + + align:start position:0% +uh impacts based on that but now um + + + align:start position:0% +uh impacts based on that but now um +and this is we're gonna go as well are + + align:start position:0% +and this is we're gonna go as well are + + + align:start position:0% +and this is we're gonna go as well are +there also some negative effects + + align:start position:0% +there also some negative effects + + + align:start position:0% +there also some negative effects +potentially + + align:start position:0% +potentially + + + align:start position:0% +potentially +the reason being that um if you have a + + align:start position:0% +the reason being that um if you have a + + + align:start position:0% +the reason being that um if you have a +certain amount of attention available + + align:start position:0% +certain amount of attention available + + + align:start position:0% +certain amount of attention available +overall or cognitive resources available + + align:start position:0% +overall or cognitive resources available + + + align:start position:0% +overall or cognitive resources available +if your brain is taking out by + + align:start position:0% +if your brain is taking out by + + + align:start position:0% +if your brain is taking out by +essentially um + + align:start position:0% +essentially um + + + align:start position:0% +essentially um +these thoughts about money then um there + + align:start position:0% +these thoughts about money then um there + + + align:start position:0% +these thoughts about money then um there +will be less available resources for + + align:start position:0% +will be less available resources for + + + align:start position:0% +will be less available resources for +other stuff any questions on + + align:start position:0% +other stuff any questions on + + + align:start position:0% +other stuff any questions on +on this so far + + align:start position:0% + + + + align:start position:0% + +okay so then um let's talk about the + + align:start position:0% +okay so then um let's talk about the + + + align:start position:0% +okay so then um let's talk about the +um uh scarcity work specifically so + + align:start position:0% +um uh scarcity work specifically so + + + align:start position:0% +um uh scarcity work specifically so +scarcity is actually defined + + align:start position:0% +scarcity is actually defined + + + align:start position:0% +scarcity is actually defined +generally here as not having enough + + align:start position:0% +generally here as not having enough + + + align:start position:0% +generally here as not having enough +enough of something + + align:start position:0% +enough of something + + + align:start position:0% +enough of something +this could be money friends hair uh time + + align:start position:0% +this could be money friends hair uh time + + + align:start position:0% +this could be money friends hair uh time +etc it's very general actually + + align:start position:0% +etc it's very general actually + + + align:start position:0% +etc it's very general actually +um and so the idea is just like if you + + align:start position:0% +um and so the idea is just like if you + + + align:start position:0% +um and so the idea is just like if you +have something that you think you don't + + align:start position:0% +have something that you think you don't + + + align:start position:0% +have something that you think you don't +have enough + + align:start position:0% +have enough + + + align:start position:0% +have enough +notice that the definition is pretty + + align:start position:0% +notice that the definition is pretty + + + align:start position:0% +notice that the definition is pretty +vague in the sense of like + + align:start position:0% +vague in the sense of like + + + align:start position:0% +vague in the sense of like +it's not just saying like having low + + align:start position:0% +it's not just saying like having low + + + align:start position:0% +it's not just saying like having low +income but instead of + + align:start position:0% +income but instead of + + + align:start position:0% +income but instead of +thinking that you don't have enough + + align:start position:0% +thinking that you don't have enough + + + align:start position:0% +thinking that you don't have enough +income which could be also like in + + align:start position:0% +income which could be also like in + + + align:start position:0% +income which could be also like in +relative terms and so on + + align:start position:0% +relative terms and so on + + + align:start position:0% +relative terms and so on +and then yet the the hypothesis is that + + align:start position:0% +and then yet the the hypothesis is that + + + align:start position:0% +and then yet the the hypothesis is that +scarcity capture people's + + align:start position:0% +scarcity capture people's + + + align:start position:0% +scarcity capture people's +mental cognitive capacity their + + align:start position:0% +mental cognitive capacity their + + + align:start position:0% +mental cognitive capacity their +bandwidth as they call it + + align:start position:0% +bandwidth as they call it + + + align:start position:0% +bandwidth as they call it +this happens automatically and not + + align:start position:0% +this happens automatically and not + + + align:start position:0% +this happens automatically and not +intentionally that is to say that it's + + align:start position:0% +intentionally that is to say that it's + + + align:start position:0% +intentionally that is to say that it's +not people + + align:start position:0% +not people + + + align:start position:0% +not people +choose to spend a lot of time on uh + + align:start position:0% +choose to spend a lot of time on uh + + + align:start position:0% +choose to spend a lot of time on uh +thinking about money + + align:start position:0% +thinking about money + + + align:start position:0% +thinking about money +but rather um money captures their minds + + align:start position:0% +but rather um money captures their minds + + + align:start position:0% +but rather um money captures their minds +and then they have trouble thinking + + align:start position:0% +and then they have trouble thinking + + + align:start position:0% +and then they have trouble thinking +about other uh + + align:start position:0% +about other uh + + + align:start position:0% +about other uh +things think about this inside would be + + align:start position:0% +things think about this inside would be + + + align:start position:0% +things think about this inside would be +like suppose you have like some + + align:start position:0% +like suppose you have like some + + + align:start position:0% +like suppose you have like some +fights with a good friend of yours or a + + align:start position:0% +fights with a good friend of yours or a + + + align:start position:0% +fights with a good friend of yours or a +partner or the leg + + align:start position:0% +partner or the leg + + + align:start position:0% +partner or the leg +and then you have an important job + + align:start position:0% +and then you have an important job + + + align:start position:0% +and then you have an important job +interview it's really not productive to + + align:start position:0% +interview it's really not productive to + + + align:start position:0% +interview it's really not productive to +think about the fight with your + + align:start position:0% +think about the fight with your + + + align:start position:0% +think about the fight with your +um a friend or + + align:start position:0% +um a friend or + + + align:start position:0% +um a friend or +family member or partner or the like + + align:start position:0% +family member or partner or the like + + + align:start position:0% +family member or partner or the like +during the job interview there's nothing + + align:start position:0% +during the job interview there's nothing + + + align:start position:0% +during the job interview there's nothing +productive about doing that you should + + align:start position:0% +productive about doing that you should + + + align:start position:0% +productive about doing that you should +be focusing on the interview and try to + + align:start position:0% +be focusing on the interview and try to + + + align:start position:0% +be focusing on the interview and try to +do your best + + align:start position:0% +do your best + + + align:start position:0% +do your best +but it might be that like essentially + + align:start position:0% +but it might be that like essentially + + + align:start position:0% +but it might be that like essentially +these thoughts invade your minds and you + + align:start position:0% +these thoughts invade your minds and you + + + align:start position:0% +these thoughts invade your minds and you +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +get really distracted unintentionally + + align:start position:0% +get really distracted unintentionally + + + align:start position:0% +get really distracted unintentionally +and then do worse in those kinds of + + align:start position:0% +and then do worse in those kinds of + + + align:start position:0% +and then do worse in those kinds of +things + + align:start position:0% +things + + + align:start position:0% +things +and that's the idea here uh similarly + + align:start position:0% +and that's the idea here uh similarly + + + align:start position:0% +and that's the idea here uh similarly +here as well + + align:start position:0% +here as well + + + align:start position:0% +here as well +which is um that essentially um there's + + align:start position:0% +which is um that essentially um there's + + + align:start position:0% +which is um that essentially um there's +might be some benefit of like + + align:start position:0% +might be some benefit of like + + + align:start position:0% +might be some benefit of like +figuring out monitoring problems and + + align:start position:0% +figuring out monitoring problems and + + + align:start position:0% +figuring out monitoring problems and +figuring out how to pay the bills and so + + align:start position:0% +figuring out how to pay the bills and so + + + align:start position:0% +figuring out how to pay the bills and so +on and so forth + + align:start position:0% +on and so forth + + + align:start position:0% +on and so forth +but overall um these benefits might be + + align:start position:0% +but overall um these benefits might be + + + align:start position:0% +but overall um these benefits might be +overwhelmed by + + align:start position:0% +overwhelmed by + + + align:start position:0% +overwhelmed by +um taking over people's brain + + align:start position:0% +um taking over people's brain + + + align:start position:0% +um taking over people's brain +that leaves less resources for other + + align:start position:0% +that leaves less resources for other + + + align:start position:0% +that leaves less resources for other +things + + align:start position:0% +things + + + align:start position:0% +things +um the decisions that are productivity + + align:start position:0% +um the decisions that are productivity + + + align:start position:0% +um the decisions that are productivity +that people have to do in life + + align:start position:0% +that people have to do in life + + + align:start position:0% +that people have to do in life +and so uh in particular poverty now so + + align:start position:0% +and so uh in particular poverty now so + + + align:start position:0% +and so uh in particular poverty now so +this is a general introduction now + + align:start position:0% +this is a general introduction now + + + align:start position:0% +this is a general introduction now +poverty specifically makes monetary + + align:start position:0% +poverty specifically makes monetary + + + align:start position:0% +poverty specifically makes monetary +concerns + + align:start position:0% +concerns + + + align:start position:0% +concerns +top of mind today they poor might be + + align:start position:0% +top of mind today they poor might be + + + align:start position:0% +top of mind today they poor might be +acting more rational in some ways + + align:start position:0% +acting more rational in some ways + + + align:start position:0% +acting more rational in some ways +in some sense in financial choices which + + align:start position:0% +in some sense in financial choices which + + + align:start position:0% +in some sense in financial choices which +is kind of what that + + align:start position:0% +is kind of what that + + + align:start position:0% +is kind of what that +the evidence that i just showed you and + + align:start position:0% +the evidence that i just showed you and + + + align:start position:0% +the evidence that i just showed you and +there are several studies to try to make + + align:start position:0% +there are several studies to try to make + + + align:start position:0% +there are several studies to try to make +that point + + align:start position:0% +that point + + + align:start position:0% +that point +um but you know scarcity might then + + align:start position:0% +um but you know scarcity might then + + + align:start position:0% +um but you know scarcity might then +deteriorate performance at other + + align:start position:0% +deteriorate performance at other + + + align:start position:0% +deteriorate performance at other +cognitive tasks + + align:start position:0% +cognitive tasks + + + align:start position:0% +cognitive tasks +now here's sort of a powerpoint version + + align:start position:0% +now here's sort of a powerpoint version + + + align:start position:0% +now here's sort of a powerpoint version +of that which is you know people may + + align:start position:0% +of that which is you know people may + + + align:start position:0% +of that which is you know people may +think about many things in life they + + align:start position:0% +think about many things in life they + + + align:start position:0% +think about many things in life they +might think about rent they might think + + align:start position:0% +might think about rent they might think + + + align:start position:0% +might think about rent they might think +about + + align:start position:0% +about + + + align:start position:0% +about +the kids doing well eating healthy + + align:start position:0% +the kids doing well eating healthy + + + align:start position:0% +the kids doing well eating healthy +utilities uh car payments and so on but + + align:start position:0% +utilities uh car payments and so on but + + + align:start position:0% +utilities uh car payments and so on but +what does scarcity do it magnifies + + align:start position:0% +what does scarcity do it magnifies + + + align:start position:0% +what does scarcity do it magnifies +essentially people's thoughts about rent + + align:start position:0% +essentially people's thoughts about rent + + + align:start position:0% +essentially people's thoughts about rent +car + + align:start position:0% +car + + + align:start position:0% +car +payments and utility bills he's all + + align:start position:0% +payments and utility bills he's all + + + align:start position:0% +payments and utility bills he's all +monetary things that people think about + + align:start position:0% +monetary things that people think about + + + align:start position:0% +monetary things that people think about +a lot + + align:start position:0% +a lot + + + align:start position:0% +a lot +and then it might sort of like drown out + + align:start position:0% +and then it might sort of like drown out + + + align:start position:0% +and then it might sort of like drown out +or like force out other thoughts about + + align:start position:0% +or like force out other thoughts about + + + align:start position:0% +or like force out other thoughts about +other things about eating healthy + + align:start position:0% +other things about eating healthy + + + align:start position:0% +other things about eating healthy +or about uh taking care of their kids in + + align:start position:0% +or about uh taking care of their kids in + + + align:start position:0% +or about uh taking care of their kids in +other + + align:start position:0% +other + + + align:start position:0% +other +ways than paying the bills okay + + align:start position:0% +ways than paying the bills okay + + + align:start position:0% +ways than paying the bills okay +and so now i'm going to show you + + align:start position:0% +and so now i'm going to show you + + + align:start position:0% +and so now i'm going to show you +evidence from two studies that sort of + + align:start position:0% +evidence from two studies that sort of + + + align:start position:0% +evidence from two studies that sort of +support this point the first one is + + align:start position:0% +support this point the first one is + + + align:start position:0% +support this point the first one is +um or the paper is called poverty and + + align:start position:0% +um or the paper is called poverty and + + + align:start position:0% +um or the paper is called poverty and +pete's cognitive function that was the + + align:start position:0% +pete's cognitive function that was the + + + align:start position:0% +pete's cognitive function that was the +reading for today + + align:start position:0% +reading for today + + + align:start position:0% +reading for today +the first one is called them all the + + align:start position:0% +the first one is called them all the + + + align:start position:0% +the first one is called them all the +study so what does a small study do it's + + align:start position:0% +study so what does a small study do it's + + + align:start position:0% +study so what does a small study do it's +a + + align:start position:0% +a + + + align:start position:0% +a +kind of like a lab experiment but it's + + align:start position:0% +kind of like a lab experiment but it's + + + align:start position:0% +kind of like a lab experiment but it's +sort of in some sense like a field + + align:start position:0% +sort of in some sense like a field + + + align:start position:0% +sort of in some sense like a field +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +uh uh so it's in a new jersey mall that + + align:start position:0% +uh uh so it's in a new jersey mall that + + + align:start position:0% +uh uh so it's in a new jersey mall that +um asks shoppers or stops shoppers um + + align:start position:0% +um asks shoppers or stops shoppers um + + + align:start position:0% +um asks shoppers or stops shoppers um +with the median + + align:start position:0% +with the median + + + align:start position:0% +with the median +uh household income of roughly 70 000 + + align:start position:0% +uh household income of roughly 70 000 + + + align:start position:0% +uh household income of roughly 70 000 +um to someone richer than the average + + align:start position:0% +um to someone richer than the average + + + align:start position:0% +um to someone richer than the average +american + + align:start position:0% +american + + + align:start position:0% +american +but with quite a bit of um range of + + align:start position:0% +but with quite a bit of um range of + + + align:start position:0% +but with quite a bit of um range of +income uh overall so they select very + + align:start position:0% +income uh overall so they select very + + + align:start position:0% +income uh overall so they select very +rich people unfairly um poor people + + align:start position:0% +rich people unfairly um poor people + + + align:start position:0% +rich people unfairly um poor people +and then um there's a sequence of um + + align:start position:0% +and then um there's a sequence of um + + + align:start position:0% +and then um there's a sequence of um +three events essentially which is + + align:start position:0% +three events essentially which is + + + align:start position:0% +three events essentially which is +um people are asked hypothetical + + align:start position:0% +um people are asked hypothetical + + + align:start position:0% +um people are asked hypothetical +questions involving money + + align:start position:0% +questions involving money + + + align:start position:0% +questions involving money +some are hard and some are easy and then + + align:start position:0% +some are hard and some are easy and then + + + align:start position:0% +some are hard and some are easy and then +people are asked to do cognitive tests + + align:start position:0% +people are asked to do cognitive tests + + + align:start position:0% +people are asked to do cognitive tests +these are non-verbal + + align:start position:0% +these are non-verbal + + + align:start position:0% +these are non-verbal +tests that sort of measure people's + + align:start position:0% +tests that sort of measure people's + + + align:start position:0% +tests that sort of measure people's +fluid intelligence which is raven's + + align:start position:0% +fluid intelligence which is raven's + + + align:start position:0% +fluid intelligence which is raven's +matrices which you might be um familiar + + align:start position:0% +matrices which you might be um familiar + + + align:start position:0% +matrices which you might be um familiar +with just with iq type + + align:start position:0% +with just with iq type + + + align:start position:0% +with just with iq type +tests and some form of cognitive control + + align:start position:0% +tests and some form of cognitive control + + + align:start position:0% +tests and some form of cognitive control +which essentially is about like are you + + align:start position:0% +which essentially is about like are you + + + align:start position:0% +which essentially is about like are you +able to override + + align:start position:0% +able to override + + + align:start position:0% +able to override +um automatic responses um when making uh + + align:start position:0% + + + + align:start position:0% + +when doing cognitive tasks and then uh + + align:start position:0% +when doing cognitive tasks and then uh + + + align:start position:0% +when doing cognitive tasks and then uh +number three then is like + + align:start position:0% +number three then is like + + + align:start position:0% +number three then is like +people then answer the hypothetical + + align:start position:0% +people then answer the hypothetical + + + align:start position:0% +people then answer the hypothetical +questions so what does this look like + + align:start position:0% +questions so what does this look like + + + align:start position:0% +questions so what does this look like +the hypothetical question is involving + + align:start position:0% +the hypothetical question is involving + + + align:start position:0% +the hypothetical question is involving +money + + align:start position:0% +money + + + align:start position:0% +money +which is the following your car is + + align:start position:0% +which is the following your car is + + + align:start position:0% +which is the following your car is +having some trouble and requires x + + align:start position:0% +having some trouble and requires x + + + align:start position:0% +having some trouble and requires x +dollars to be fixed + + align:start position:0% +dollars to be fixed + + + align:start position:0% +dollars to be fixed +you can pay in full um take a loan or + + align:start position:0% +you can pay in full um take a loan or + + + align:start position:0% +you can pay in full um take a loan or +take a chance and forgo the service at + + align:start position:0% +take a chance and forgo the service at + + + align:start position:0% +take a chance and forgo the service at +the moment + + align:start position:0% +the moment + + + align:start position:0% +the moment +how would you go about making this + + align:start position:0% +how would you go about making this + + + align:start position:0% +how would you go about making this +decision and so then that people ask + + align:start position:0% +decision and so then that people ask + + + align:start position:0% +decision and so then that people ask +this question and they say well you can + + align:start position:0% +this question and they say well you can + + + align:start position:0% +this question and they say well you can +think about this for a while and then + + align:start position:0% +think about this for a while and then + + + align:start position:0% +think about this for a while and then +afterwards i'm going to ask you + + align:start position:0% +afterwards i'm going to ask you + + + align:start position:0% +afterwards i'm going to ask you +um about the answer of that question and + + align:start position:0% +um about the answer of that question and + + + align:start position:0% +um about the answer of that question and +then + + align:start position:0% +then + + + align:start position:0% +then +there's a hard version and an easy + + align:start position:0% +there's a hard version and an easy + + + align:start position:0% +there's a hard version and an easy +version + + align:start position:0% +version + + + align:start position:0% +version +the idea is that the experiment wants to + + align:start position:0% +the idea is that the experiment wants to + + + align:start position:0% +the idea is that the experiment wants to +keep everything + + align:start position:0% +keep everything + + + align:start position:0% +keep everything +the same for like uh across treatments + + align:start position:0% +the same for like uh across treatments + + + align:start position:0% +the same for like uh across treatments +and the idea that that is that 150 for + + align:start position:0% +and the idea that that is that 150 for + + + align:start position:0% +and the idea that that is that 150 for +the average american is not that much + + align:start position:0% +the average american is not that much + + + align:start position:0% +the average american is not that much +money so it's + + align:start position:0% +money so it's + + + align:start position:0% +money so it's +not going to be like a huge problem for + + align:start position:0% +not going to be like a huge problem for + + + align:start position:0% +not going to be like a huge problem for +most people at least in normal times of + + align:start position:0% +most people at least in normal times of + + + align:start position:0% +most people at least in normal times of +their lives + + align:start position:0% +their lives + + + align:start position:0% +their lives +but fifteen hundred dollars is actually + + align:start position:0% +but fifteen hundred dollars is actually + + + align:start position:0% +but fifteen hundred dollars is actually +a lot of money for like a low-income + + align:start position:0% +a lot of money for like a low-income + + + align:start position:0% +a lot of money for like a low-income +person in the us + + align:start position:0% +person in the us + + + align:start position:0% +person in the us +but perhaps not that um big of a deal + + align:start position:0% +but perhaps not that um big of a deal + + + align:start position:0% +but perhaps not that um big of a deal +for rich perks + + align:start position:0% +for rich perks + + + align:start position:0% +for rich perks +like for rich person the 1500 or the 150 + + align:start position:0% +like for rich person the 1500 or the 150 + + + align:start position:0% +like for rich person the 1500 or the 150 +are both fine they're going to have some + + align:start position:0% +are both fine they're going to have some + + + align:start position:0% +are both fine they're going to have some +money in the bank account and they're + + align:start position:0% +money in the bank account and they're + + + align:start position:0% +money in the bank account and they're +going to deal with it somehow it's not a + + align:start position:0% +going to deal with it somehow it's not a + + + align:start position:0% +going to deal with it somehow it's not a +huge issue + + align:start position:0% +huge issue + + + align:start position:0% +huge issue +for the poor person 150 is you know + + align:start position:0% +for the poor person 150 is you know + + + align:start position:0% +for the poor person 150 is you know +not great but not a huge problem or not + + align:start position:0% +not great but not a huge problem or not + + + align:start position:0% +not great but not a huge problem or not +a huge headache but fifteen hundred + + align:start position:0% +a huge headache but fifteen hundred + + + align:start position:0% +a huge headache but fifteen hundred +dollars surely is really bad + + align:start position:0% +dollars surely is really bad + + + align:start position:0% +dollars surely is really bad +that's sort of the idea here and varying + + align:start position:0% +that's sort of the idea here and varying + + + align:start position:0% +that's sort of the idea here and varying +um uh this + + align:start position:0% +um uh this + + + align:start position:0% +um uh this +now what uh the study then finds is that + + align:start position:0% +now what uh the study then finds is that + + + align:start position:0% +now what uh the study then finds is that +and + + align:start position:0% +and + + + align:start position:0% +and +let me walk you through these graphs + + align:start position:0% +let me walk you through these graphs + + + align:start position:0% +let me walk you through these graphs +let's look on the left side um + + align:start position:0% +let's look on the left side um + + + align:start position:0% +let's look on the left side um +on the right side is quite similar + + align:start position:0% +on the right side is quite similar + + + align:start position:0% +on the right side is quite similar +you'll see here + + align:start position:0% +you'll see here + + + align:start position:0% +you'll see here +um always four bars the bars are + + align:start position:0% +um always four bars the bars are + + + align:start position:0% +um always four bars the bars are +um for the dark bars are how people are + + align:start position:0% +um for the dark bars are how people are + + + align:start position:0% +um for the dark bars are how people are +doing after the hard task and the + + align:start position:0% +doing after the hard task and the + + + align:start position:0% +doing after the hard task and the +um the lighter bus bars are after the + + align:start position:0% +um the lighter bus bars are after the + + + align:start position:0% +um the lighter bus bars are after the +easy task + + align:start position:0% +easy task + + + align:start position:0% +easy task +let's um start with the light gray bars + + align:start position:0% +let's um start with the light gray bars + + + align:start position:0% +let's um start with the light gray bars +comparing the poor versus the rich and + + align:start position:0% +comparing the poor versus the rich and + + + align:start position:0% +comparing the poor versus the rich and +what you essentially see is the poor and + + align:start position:0% +what you essentially see is the poor and + + + align:start position:0% +what you essentially see is the poor and +the rich are doing pretty much the same + + align:start position:0% +the rich are doing pretty much the same + + + align:start position:0% +the rich are doing pretty much the same +after doing um the easy task so to be + + align:start position:0% +after doing um the easy task so to be + + + align:start position:0% +after doing um the easy task so to be +clear what's poor versus which is + + align:start position:0% +clear what's poor versus which is + + + align:start position:0% +clear what's poor versus which is +essentially medium split + + align:start position:0% +essentially medium split + + + align:start position:0% +essentially medium split +by the median income so if you're above + + align:start position:0% +by the median income so if you're above + + + align:start position:0% +by the median income so if you're above +the medium you're called + + align:start position:0% +the medium you're called + + + align:start position:0% +the medium you're called +rich if you're below the medium you're + + align:start position:0% +rich if you're below the medium you're + + + align:start position:0% +rich if you're below the medium you're +called poor for the purpose of this + + align:start position:0% +called poor for the purpose of this + + + align:start position:0% +called poor for the purpose of this +study + + align:start position:0% +study + + + align:start position:0% +study +now um for the + + align:start position:0% +now um for the + + + align:start position:0% +now um for the +for the easy task here this is like the + + align:start position:0% +for the easy task here this is like the + + + align:start position:0% +for the easy task here this is like the +rich do essentially as well or as badly + + align:start position:0% +rich do essentially as well or as badly + + + align:start position:0% +rich do essentially as well or as badly +as + + align:start position:0% +as + + + align:start position:0% +as +the poor do they get about forty percent + + align:start position:0% +the poor do they get about forty percent + + + align:start position:0% +the poor do they get about forty percent +uh uh + + align:start position:0% +uh uh + + + align:start position:0% +uh uh +cracked in these these um uh ravens uh + + align:start position:0% +cracked in these these um uh ravens uh + + + align:start position:0% +cracked in these these um uh ravens uh +puzzles and the poor do essentially the + + align:start position:0% +puzzles and the poor do essentially the + + + align:start position:0% +puzzles and the poor do essentially the +same so there's no difference after the + + align:start position:0% +same so there's no difference after the + + + align:start position:0% +same so there's no difference after the +easy task + + align:start position:0% +easy task + + + align:start position:0% +easy task +now after the hard task for the rich + + align:start position:0% +now after the hard task for the rich + + + align:start position:0% +now after the hard task for the rich +essentially it's the same if anything + + align:start position:0% +essentially it's the same if anything + + + align:start position:0% +essentially it's the same if anything +they do a little bit better + + align:start position:0% +they do a little bit better + + + align:start position:0% +they do a little bit better +the this difference is not statistically + + align:start position:0% +the this difference is not statistically + + + align:start position:0% +the this difference is not statistically +significant + + align:start position:0% +significant + + + align:start position:0% +significant +in contrast you see like a clear drop in + + align:start position:0% +in contrast you see like a clear drop in + + + align:start position:0% +in contrast you see like a clear drop in +uh performance among the poor okay they + + align:start position:0% +uh performance among the poor okay they + + + align:start position:0% +uh performance among the poor okay they +do about like + + align:start position:0% +do about like + + + align:start position:0% +do about like +um uh uh twelve percentage points worse + + align:start position:0% +um uh uh twelve percentage points worse + + + align:start position:0% +um uh uh twelve percentage points worse +this is like really like a huge + + align:start position:0% +this is like really like a huge + + + align:start position:0% +this is like really like a huge +difference + + align:start position:0% +difference + + + align:start position:0% +difference +in how well people um so this is for + + align:start position:0% +in how well people um so this is for + + + align:start position:0% +in how well people um so this is for +raymond's matrices this is for + + align:start position:0% +raymond's matrices this is for + + + align:start position:0% +raymond's matrices this is for +um what's called hearts and flowers for + + align:start position:0% +um what's called hearts and flowers for + + + align:start position:0% +um what's called hearts and flowers for +cognitive control which is essentially + + align:start position:0% +cognitive control which is essentially + + + align:start position:0% +cognitive control which is essentially +how good are people + + align:start position:0% +how good are people + + + align:start position:0% +how good are people +at uh controlling their attentional + + align:start position:0% +at uh controlling their attentional + + + align:start position:0% +at uh controlling their attentional +resources and what you see is + + align:start position:0% +resources and what you see is + + + align:start position:0% +resources and what you see is +essentially more or less the same + + align:start position:0% +essentially more or less the same + + + align:start position:0% +essentially more or less the same +pattern + + align:start position:0% +pattern + + + align:start position:0% +pattern +that for the easy task the rich and the + + align:start position:0% +that for the easy task the rich and the + + + align:start position:0% +that for the easy task the rich and the +poor do pretty much the same + + align:start position:0% +poor do pretty much the same + + + align:start position:0% +poor do pretty much the same +the hard task compared to the easy to + + align:start position:0% +the hard task compared to the easy to + + + align:start position:0% +the hard task compared to the easy to +pass does nothing for the rich + + align:start position:0% +pass does nothing for the rich + + + align:start position:0% +pass does nothing for the rich +because essentially uh the performance + + align:start position:0% +because essentially uh the performance + + + align:start position:0% +because essentially uh the performance +is the same or like slightly different + + align:start position:0% +is the same or like slightly different + + + align:start position:0% +is the same or like slightly different +but not statistically significantly so + + align:start position:0% +but not statistically significantly so + + + align:start position:0% +but not statistically significantly so +and for the poor there's a large drop in + + align:start position:0% +and for the poor there's a large drop in + + + align:start position:0% +and for the poor there's a large drop in +performance um + + align:start position:0% +performance um + + + align:start position:0% +performance um +compared to the rich any questions on + + align:start position:0% +compared to the rich any questions on + + + align:start position:0% +compared to the rich any questions on +that + + align:start position:0% + + + + align:start position:0% + +okay so then um i'm going to show you + + align:start position:0% +okay so then um i'm going to show you + + + align:start position:0% +okay so then um i'm going to show you +the second study that + + align:start position:0% +the second study that + + + align:start position:0% +the second study that +uh is related to this so one thing you + + align:start position:0% +uh is related to this so one thing you + + + align:start position:0% +uh is related to this so one thing you +might sort of say well as we already + + align:start position:0% +might sort of say well as we already + + + align:start position:0% +might sort of say well as we already +showed you already a study so why did we + + align:start position:0% +showed you already a study so why did we + + + align:start position:0% +showed you already a study so why did we +need another study whether we did one we + + align:start position:0% +need another study whether we did one we + + + align:start position:0% +need another study whether we did one we +showed you that like + + align:start position:0% +showed you that like + + + align:start position:0% +showed you that like +um poverty is thinking about poverty + + align:start position:0% +um poverty is thinking about poverty + + + align:start position:0% +um poverty is thinking about poverty +affects people's cognition so why would + + align:start position:0% +affects people's cognition so why would + + + align:start position:0% +affects people's cognition so why would +it + + align:start position:0% +it + + + align:start position:0% +it +why do we need more evidence + + align:start position:0% +why do we need more evidence + + + align:start position:0% +why do we need more evidence +that's right so effort is an interesting + + align:start position:0% +that's right so effort is an interesting + + + align:start position:0% +that's right so effort is an interesting +issue that um + + align:start position:0% +issue that um + + + align:start position:0% +issue that um +so there's in fact uh this study has um + + align:start position:0% +so there's in fact uh this study has um + + + align:start position:0% +so there's in fact uh this study has um +and i took this out of the slides + + align:start position:0% +and i took this out of the slides + + + align:start position:0% +and i took this out of the slides +because i have too many + + align:start position:0% +because i have too many + + + align:start position:0% +because i have too many +um there's an incentivized version of + + align:start position:0% +um there's an incentivized version of + + + align:start position:0% +um there's an incentivized version of +this task and uh the authors do find + + align:start position:0% +this task and uh the authors do find + + + align:start position:0% +this task and uh the authors do find +that he wants to incentivize + + align:start position:0% +that he wants to incentivize + + + align:start position:0% +that he wants to incentivize +these tasks uh uh do you find the same + + align:start position:0% +these tasks uh uh do you find the same + + + align:start position:0% +these tasks uh uh do you find the same +patterns + + align:start position:0% +patterns + + + align:start position:0% +patterns +but even there you know the it's a bit + + align:start position:0% +but even there you know the it's a bit + + + align:start position:0% +but even there you know the it's a bit +sort of like a task that is not a task + + align:start position:0% +sort of like a task that is not a task + + + align:start position:0% +sort of like a task that is not a task +that people do in their real life + + align:start position:0% +that people do in their real life + + + align:start position:0% +that people do in their real life +and in a way which is actually not what + + align:start position:0% +and in a way which is actually not what + + + align:start position:0% +and in a way which is actually not what +the harvest study is + + align:start position:0% +the harvest study is + + + align:start position:0% +the harvest study is +addressing um the uh + + align:start position:0% +addressing um the uh + + + align:start position:0% +addressing um the uh +you might wonder kind of does this + + align:start position:0% +you might wonder kind of does this + + + align:start position:0% +you might wonder kind of does this +translate into real world choices and + + align:start position:0% +translate into real world choices and + + + align:start position:0% +translate into real world choices and +decisions + + align:start position:0% +decisions + + + align:start position:0% +decisions +that are actually of consequence for + + align:start position:0% +that are actually of consequence for + + + align:start position:0% +that are actually of consequence for +people's behaviors + + align:start position:0% +people's behaviors + + + align:start position:0% +people's behaviors +to be clear these effects here these + + align:start position:0% +to be clear these effects here these + + + align:start position:0% +to be clear these effects here these +differences in cognitive performances + + align:start position:0% +differences in cognitive performances + + + align:start position:0% +differences in cognitive performances +are very large this is like the order of + + align:start position:0% +are very large this is like the order of + + + align:start position:0% +are very large this is like the order of +nineteen something like 10 iq points + + align:start position:0% +nineteen something like 10 iq points + + + align:start position:0% +nineteen something like 10 iq points +which is really huge + + align:start position:0% +which is really huge + + + align:start position:0% +which is really huge +um so you might sort of argue that you + + align:start position:0% +um so you might sort of argue that you + + + align:start position:0% +um so you might sort of argue that you +know you think that iq etc matters a lot + + align:start position:0% +know you think that iq etc matters a lot + + + align:start position:0% +know you think that iq etc matters a lot +so in some sense + + align:start position:0% +so in some sense + + + align:start position:0% +so in some sense +uh that's what and shift but you know i + + align:start position:0% +uh that's what and shift but you know i + + + align:start position:0% +uh that's what and shift but you know i +agree with you in some sense we would + + align:start position:0% +agree with you in some sense we would + + + align:start position:0% +agree with you in some sense we would +like to see + + align:start position:0% +like to see + + + align:start position:0% +like to see +does this translate into real world + + align:start position:0% +does this translate into real world + + + align:start position:0% +does this translate into real world +choices that + + align:start position:0% +choices that + + + align:start position:0% +choices that +um uh we see in every day + + align:start position:0% +um uh we see in every day + + + align:start position:0% +um uh we see in every day +in people's everyday lives um + + align:start position:0% +in people's everyday lives um + + + align:start position:0% +in people's everyday lives um +now i think we talked about a few of + + align:start position:0% +now i think we talked about a few of + + + align:start position:0% +now i think we talked about a few of +those things so one is + + align:start position:0% +those things so one is + + + align:start position:0% +those things so one is +external validity concerns which is to + + align:start position:0% +external validity concerns which is to + + + align:start position:0% +external validity concerns which is to +say like look we did like to study + + align:start position:0% +say like look we did like to study + + + align:start position:0% +say like look we did like to study +um in the mall which is a little bit of + + align:start position:0% +um in the mall which is a little bit of + + + align:start position:0% +um in the mall which is a little bit of +funny thing to do + + align:start position:0% +funny thing to do + + + align:start position:0% +funny thing to do +and like you hear about the scenario + + align:start position:0% +and like you hear about the scenario + + + align:start position:0% +and like you hear about the scenario +which is kind of weird and maybe it + + align:start position:0% +which is kind of weird and maybe it + + + align:start position:0% +which is kind of weird and maybe it +tricks you out and maybe the poor are + + align:start position:0% +tricks you out and maybe the poor are + + + align:start position:0% +tricks you out and maybe the poor are +more freaked out than the rich + + align:start position:0% +more freaked out than the rich + + + align:start position:0% +more freaked out than the rich +for some reason and like but really um + + align:start position:0% +for some reason and like but really um + + + align:start position:0% +for some reason and like but really um +if you think about like paying back your + + align:start position:0% +if you think about like paying back your + + + align:start position:0% +if you think about like paying back your +your debt or like any sort of school + + align:start position:0% +your debt or like any sort of school + + + align:start position:0% +your debt or like any sort of school +fees or just not having money + + align:start position:0% +fees or just not having money + + + align:start position:0% +fees or just not having money +that's like a repeated exposure of + + align:start position:0% +that's like a repeated exposure of + + + align:start position:0% +that's like a repeated exposure of +something that you know in your real + + align:start position:0% +something that you know in your real + + + align:start position:0% +something that you know in your real +life like for example not having harvest + + align:start position:0% +life like for example not having harvest + + + align:start position:0% +life like for example not having harvest +versus harvest is the thing that you + + align:start position:0% +versus harvest is the thing that you + + + align:start position:0% +versus harvest is the thing that you +experience every year or i'll be like + + align:start position:0% +experience every year or i'll be like + + + align:start position:0% +experience every year or i'll be like +twice a year even and so you think you + + align:start position:0% +twice a year even and so you think you + + + align:start position:0% +twice a year even and so you think you +know some of these things might sort of + + align:start position:0% +know some of these things might sort of + + + align:start position:0% +know some of these things might sort of +go away with repeat exposure + + align:start position:0% +go away with repeat exposure + + + align:start position:0% +go away with repeat exposure +and so we kind of would like to have + + align:start position:0% +and so we kind of would like to have + + + align:start position:0% +and so we kind of would like to have +like a real world setting where like + + align:start position:0% +like a real world setting where like + + + align:start position:0% +like a real world setting where like +we have actually really natural + + align:start position:0% +we have actually really natural + + + align:start position:0% +we have actually really natural +variation or or some experimental + + align:start position:0% +variation or or some experimental + + + align:start position:0% +variation or or some experimental +variation potentially + + align:start position:0% +variation potentially + + + align:start position:0% +variation potentially +as opposed to like the somewhat weird um + + align:start position:0% +as opposed to like the somewhat weird um + + + align:start position:0% +as opposed to like the somewhat weird um +uh feature in like some walls somebody + + align:start position:0% +uh feature in like some walls somebody + + + align:start position:0% +uh feature in like some walls somebody +talks you up and asks you some questions + + align:start position:0% +talks you up and asks you some questions + + + align:start position:0% +talks you up and asks you some questions +uh which people might find funny and + + align:start position:0% +uh which people might find funny and + + + align:start position:0% +uh which people might find funny and +might not be representative for what + + align:start position:0% +might not be representative for what + + + align:start position:0% +might not be representative for what +people do with their lives + + align:start position:0% +people do with their lives + + + align:start position:0% +people do with their lives +um and then the second part is kind of + + align:start position:0% +um and then the second part is kind of + + + align:start position:0% +um and then the second part is kind of +how do we interpret magnitudes right + + align:start position:0% +how do we interpret magnitudes right + + + align:start position:0% +how do we interpret magnitudes right +so i showed you and said like look uh + + align:start position:0% +so i showed you and said like look uh + + + align:start position:0% +so i showed you and said like look uh +these effects are really large + + align:start position:0% +these effects are really large + + + align:start position:0% +these effects are really large +um after the hard task the poor do worse + + align:start position:0% +um after the hard task the poor do worse + + + align:start position:0% +um after the hard task the poor do worse +than the rich + + align:start position:0% +than the rich + + + align:start position:0% +than the rich +but we have like no idea how we should + + align:start position:0% +but we have like no idea how we should + + + align:start position:0% +but we have like no idea how we should +scale this in terms of like + + align:start position:0% +scale this in terms of like + + + align:start position:0% +scale this in terms of like +you know what does it actually mean for + + align:start position:0% +you know what does it actually mean for + + + align:start position:0% +you know what does it actually mean for +our actual effects of poverty + + align:start position:0% +our actual effects of poverty + + + align:start position:0% +our actual effects of poverty +like if you suppose i give somebody a + + align:start position:0% +like if you suppose i give somebody a + + + align:start position:0% +like if you suppose i give somebody a +thousand dollars or ten thousand dollars + + align:start position:0% +thousand dollars or ten thousand dollars + + + align:start position:0% +thousand dollars or ten thousand dollars +what does it do to people's performance + + align:start position:0% +what does it do to people's performance + + + align:start position:0% +what does it do to people's performance +it essentially what this shows is that + + align:start position:0% +it essentially what this shows is that + + + align:start position:0% +it essentially what this shows is that +the poor are more sort of frazzled by + + align:start position:0% +the poor are more sort of frazzled by + + + align:start position:0% +the poor are more sort of frazzled by +these financial questions + + align:start position:0% +these financial questions + + + align:start position:0% +these financial questions +but it gives you essentially and it + + align:start position:0% +but it gives you essentially and it + + + align:start position:0% +but it gives you essentially and it +seems to be important because the + + align:start position:0% +seems to be important because the + + + align:start position:0% +seems to be important because the +magnitude is large in these effects + + align:start position:0% +magnitude is large in these effects + + + align:start position:0% +magnitude is large in these effects +but there's no way to actually scale + + align:start position:0% +but there's no way to actually scale + + + align:start position:0% +but there's no way to actually scale +these effects in some sense and thinking + + align:start position:0% +these effects in some sense and thinking + + + align:start position:0% +these effects in some sense and thinking +about like what does this + + align:start position:0% +about like what does this + + + align:start position:0% +about like what does this +priming intervention actually correspond + + align:start position:0% +priming intervention actually correspond + + + align:start position:0% +priming intervention actually correspond +to in the real world in terms of like + + align:start position:0% +to in the real world in terms of like + + + align:start position:0% +to in the real world in terms of like +dollars or how rich or poor people + + align:start position:0% +dollars or how rich or poor people + + + align:start position:0% +dollars or how rich or poor people +are so that's another sort of reason why + + align:start position:0% +are so that's another sort of reason why + + + align:start position:0% +are so that's another sort of reason why +you might want to do + + align:start position:0% +you might want to do + + + align:start position:0% +you might want to do +another study okay so what is the other + + align:start position:0% +another study okay so what is the other + + + align:start position:0% +another study okay so what is the other +study + + align:start position:0% +study + + + align:start position:0% +study +um as lauren was somebody saying it's + + align:start position:0% +um as lauren was somebody saying it's + + + align:start position:0% +um as lauren was somebody saying it's +it's a study with 464 + + align:start position:0% +it's a study with 464 + + + align:start position:0% +it's a study with 464 +uh sugarcane farmers in 54 um villages + + align:start position:0% +uh sugarcane farmers in 54 um villages + + + align:start position:0% +uh sugarcane farmers in 54 um villages +in tamil nadu + + align:start position:0% +in tamil nadu + + + align:start position:0% +in tamil nadu +these are small scale farmers that earn + + align:start position:0% +these are small scale farmers that earn + + + align:start position:0% +these are small scale farmers that earn +at least um the majority of sixty + + align:start position:0% +at least um the majority of sixty + + + align:start position:0% +at least um the majority of sixty +percent of income + + align:start position:0% +percent of income + + + align:start position:0% +percent of income +from um sugar cane so these are mostly + + align:start position:0% +from um sugar cane so these are mostly + + + align:start position:0% +from um sugar cane so these are mostly +schwokin farmers + + align:start position:0% +schwokin farmers + + + align:start position:0% +schwokin farmers +um and sort of crucially for the study + + align:start position:0% +um and sort of crucially for the study + + + align:start position:0% +um and sort of crucially for the study +the um + + align:start position:0% +the um + + + align:start position:0% +the um +harvest is staggered over three to five + + align:start position:0% +harvest is staggered over three to five + + + align:start position:0% +harvest is staggered over three to five +months period set + + align:start position:0% +months period set + + + align:start position:0% +months period set +by the sugar mills due to capacity + + align:start position:0% +by the sugar mills due to capacity + + + align:start position:0% +by the sugar mills due to capacity +constraints so it's not that some people + + align:start position:0% +constraints so it's not that some people + + + align:start position:0% +constraints so it's not that some people +um harvest earlier + + align:start position:0% +um harvest earlier + + + align:start position:0% +um harvest earlier +than others because they decide to do so + + align:start position:0% +than others because they decide to do so + + + align:start position:0% +than others because they decide to do so +maybe because they need more cash + + align:start position:0% +maybe because they need more cash + + + align:start position:0% +maybe because they need more cash +but it's rather because of capacity + + align:start position:0% +but it's rather because of capacity + + + align:start position:0% +but it's rather because of capacity +constraints the sugar male is + + align:start position:0% +constraints the sugar male is + + + align:start position:0% +constraints the sugar male is +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +deciding who decides who + + align:start position:0% +deciding who decides who + + + align:start position:0% +deciding who decides who +harvest um and who are asleep and so now + + align:start position:0% +harvest um and who are asleep and so now + + + align:start position:0% +harvest um and who are asleep and so now +what the study exploit is that the + + align:start position:0% +what the study exploit is that the + + + align:start position:0% +what the study exploit is that the +sugarcane harvest um cycle takes about + + align:start position:0% +sugarcane harvest um cycle takes about + + + align:start position:0% +sugarcane harvest um cycle takes about +18 months + + align:start position:0% +18 months + + + align:start position:0% +18 months +it's extremely long and as a result + + align:start position:0% +it's extremely long and as a result + + + align:start position:0% +it's extremely long and as a result +um farmers tend to be a relatively poor + + align:start position:0% +um farmers tend to be a relatively poor + + + align:start position:0% +um farmers tend to be a relatively poor +um pre-harvest this is kind of like + + align:start position:0% +um pre-harvest this is kind of like + + + align:start position:0% +um pre-harvest this is kind of like +think about this is like + + align:start position:0% +think about this is like + + + align:start position:0% +think about this is like +um you know grad school or undergrad + + align:start position:0% +um you know grad school or undergrad + + + align:start position:0% +um you know grad school or undergrad +stipends if you have gotten money for + + align:start position:0% +stipends if you have gotten money for + + + align:start position:0% +stipends if you have gotten money for +the month so for the semester or the + + align:start position:0% +the month so for the semester or the + + + align:start position:0% +the month so for the semester or the +like + + align:start position:0% +like + + + align:start position:0% +like +the beginning of the semester is always + + align:start position:0% +the beginning of the semester is always + + + align:start position:0% +the beginning of the semester is always +amazing you have lots of or + + align:start position:0% +amazing you have lots of or + + + align:start position:0% +amazing you have lots of or +months for that matter is always amazing + + align:start position:0% +months for that matter is always amazing + + + align:start position:0% +months for that matter is always amazing +they have lots of cash and um + + align:start position:0% +they have lots of cash and um + + + align:start position:0% +they have lots of cash and um +can do lots of nice things and then + + align:start position:0% +can do lots of nice things and then + + + align:start position:0% +can do lots of nice things and then +towards the end of the + + align:start position:0% +towards the end of the + + + align:start position:0% +towards the end of the +month or semester people tend to run out + + align:start position:0% +month or semester people tend to run out + + + align:start position:0% +month or semester people tend to run out +of um + + align:start position:0% +of um + + + align:start position:0% +of um +cash at least when i was a grad student + + align:start position:0% +cash at least when i was a grad student + + + align:start position:0% +cash at least when i was a grad student +um + + align:start position:0% +um + + + align:start position:0% +um +or student in general similar things are + + align:start position:0% +or student in general similar things are + + + align:start position:0% +or student in general similar things are +true + + align:start position:0% +true + + + align:start position:0% +true +um for like food stamps or other sort of + + align:start position:0% +um for like food stamps or other sort of + + + align:start position:0% +um for like food stamps or other sort of +cash programs + + align:start position:0% +cash programs + + + align:start position:0% +cash programs +there's quite a bit of evidence that + + align:start position:0% +there's quite a bit of evidence that + + + align:start position:0% +there's quite a bit of evidence that +shows at the beginning of the months + + align:start position:0% +shows at the beginning of the months + + + align:start position:0% +shows at the beginning of the months +people are doing + + align:start position:0% +people are doing + + + align:start position:0% +people are doing +a lot better than at the end which sort + + align:start position:0% +a lot better than at the end which sort + + + align:start position:0% +a lot better than at the end which sort +of seems to suggest that + + align:start position:0% +of seems to suggest that + + + align:start position:0% +of seems to suggest that +people have trouble uh smoothing their + + align:start position:0% +people have trouble uh smoothing their + + + align:start position:0% +people have trouble uh smoothing their +um + + align:start position:0% +um + + + align:start position:0% +um +income over time which presumably has to + + align:start position:0% +income over time which presumably has to + + + align:start position:0% +income over time which presumably has to +do with some form of self-control or + + align:start position:0% +do with some form of self-control or + + + align:start position:0% +do with some form of self-control or +other problems + + align:start position:0% +other problems + + + align:start position:0% +other problems +but so for the purpose of the study + + align:start position:0% +but so for the purpose of the study + + + align:start position:0% +but so for the purpose of the study +farmers are relatively poor pre-harvest + + align:start position:0% +farmers are relatively poor pre-harvest + + + align:start position:0% +farmers are relatively poor pre-harvest +and that now allows the authors to look + + align:start position:0% +and that now allows the authors to look + + + align:start position:0% +and that now allows the authors to look +at + + align:start position:0% +at + + + align:start position:0% +at +within personal comparisons of people + + align:start position:0% +within personal comparisons of people + + + align:start position:0% +within personal comparisons of people +sometimes when they're poor and + + align:start position:0% +sometimes when they're poor and + + + align:start position:0% +sometimes when they're poor and +sometimes when they're rich + + align:start position:0% +sometimes when they're rich + + + align:start position:0% +sometimes when they're rich +at looking at their cognitive + + align:start position:0% +at looking at their cognitive + + + align:start position:0% +at looking at their cognitive +performance by looking at people pre and + + align:start position:0% +performance by looking at people pre and + + + align:start position:0% +performance by looking at people pre and +post + + align:start position:0% +post + + + align:start position:0% +post +harvest now first you want to kind of + + align:start position:0% +harvest now first you want to kind of + + + align:start position:0% +harvest now first you want to kind of +like + + align:start position:0% +like + + + align:start position:0% +like +um see some evidence that farmer's + + align:start position:0% +um see some evidence that farmer's + + + align:start position:0% +um see some evidence that farmer's +financial situation is actually worse + + align:start position:0% +financial situation is actually worse + + + align:start position:0% +financial situation is actually worse +pre-harvest + + align:start position:0% +pre-harvest + + + align:start position:0% +pre-harvest +and so there's quite a few um and + + align:start position:0% +and so there's quite a few um and + + + align:start position:0% +and so there's quite a few um and +focused on the first column here + + align:start position:0% +focused on the first column here + + + align:start position:0% +focused on the first column here +quite a few um pieces of evidence people + + align:start position:0% +quite a few um pieces of evidence people + + + align:start position:0% +quite a few um pieces of evidence people +are more likely to have their belongings + + align:start position:0% +are more likely to have their belongings + + + align:start position:0% +are more likely to have their belongings +um + + align:start position:0% +um + + + align:start position:0% +um +pawned um they're more likely to have + + align:start position:0% +pawned um they're more likely to have + + + align:start position:0% +pawned um they're more likely to have +loans outstanding + + align:start position:0% +loans outstanding + + + align:start position:0% +loans outstanding +they also have more loans outstanding um + + align:start position:0% +they also have more loans outstanding um + + + align:start position:0% +they also have more loans outstanding um +then also more likely to say + + align:start position:0% +then also more likely to say + + + align:start position:0% +then also more likely to say +um yes to the question or higher + + align:start position:0% +um yes to the question or higher + + + align:start position:0% +um yes to the question or higher +higher scores to the question about + + align:start position:0% +higher scores to the question about + + + align:start position:0% +higher scores to the question about +their uh uh + + align:start position:0% +their uh uh + + + align:start position:0% +their uh uh +uh ability to cope with ordinary um + + align:start position:0% +uh ability to cope with ordinary um + + + align:start position:0% +uh ability to cope with ordinary um +bills + + align:start position:0% +bills + + + align:start position:0% +bills +in the um uh past 15 days + + align:start position:0% +in the um uh past 15 days + + + align:start position:0% +in the um uh past 15 days +and so uh post harvest and so so all of + + align:start position:0% +and so uh post harvest and so so all of + + + align:start position:0% +and so uh post harvest and so so all of +these things that i was saying + + align:start position:0% +these things that i was saying + + + align:start position:0% +these things that i was saying +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +before harvest people or farmers are + + align:start position:0% +before harvest people or farmers are + + + align:start position:0% +before harvest people or farmers are +like in a financially + + align:start position:0% +like in a financially + + + align:start position:0% +like in a financially +tricky situation and after harvest that + + align:start position:0% +tricky situation and after harvest that + + + align:start position:0% +tricky situation and after harvest that +gets better because they get essentially + + align:start position:0% +gets better because they get essentially + + + align:start position:0% +gets better because they get essentially +a bunch of cash + + align:start position:0% +a bunch of cash + + + align:start position:0% +a bunch of cash +from this harvest because essentially + + align:start position:0% +from this harvest because essentially + + + align:start position:0% +from this harvest because essentially +it's a cash crop you sell you sugarcane + + align:start position:0% +it's a cash crop you sell you sugarcane + + + align:start position:0% +it's a cash crop you sell you sugarcane +and then you get a bunch of money that + + align:start position:0% +and then you get a bunch of money that + + + align:start position:0% +and then you get a bunch of money that +you can use over the next + + align:start position:0% +you can use over the next + + + align:start position:0% +you can use over the next +18 months now then the authors find + + align:start position:0% +18 months now then the authors find + + + align:start position:0% +18 months now then the authors find +again using raven's matrices and some + + align:start position:0% +again using raven's matrices and some + + + align:start position:0% +again using raven's matrices and some +measures of cognitive control + + align:start position:0% +measures of cognitive control + + + align:start position:0% +measures of cognitive control +that people are doing a lot worse + + align:start position:0% +that people are doing a lot worse + + + align:start position:0% +that people are doing a lot worse +pre-harvest compared to post-harvest + + align:start position:0% +pre-harvest compared to post-harvest + + + align:start position:0% +pre-harvest compared to post-harvest +in terms of ravens matrices this is a + + align:start position:0% +in terms of ravens matrices this is a + + + align:start position:0% +in terms of ravens matrices this is a +pure accuracy essentially people + + align:start position:0% +pure accuracy essentially people + + + align:start position:0% +pure accuracy essentially people +do better that like getting more raven's + + align:start position:0% +do better that like getting more raven's + + + align:start position:0% +do better that like getting more raven's +managers these cracks + + align:start position:0% +managers these cracks + + + align:start position:0% +managers these cracks +compared to the control group um + + align:start position:0% +compared to the control group um + + + align:start position:0% +compared to the control group um +they're also doing better in terms of + + align:start position:0% +they're also doing better in terms of + + + align:start position:0% +they're also doing better in terms of +cognitive control + + align:start position:0% +cognitive control + + + align:start position:0% +cognitive control +uh post harvest response times go down + + align:start position:0% +uh post harvest response times go down + + + align:start position:0% +uh post harvest response times go down +which is a good thing + + align:start position:0% +which is a good thing + + + align:start position:0% +which is a good thing +here and um post harvest also like + + align:start position:0% +here and um post harvest also like + + + align:start position:0% +here and um post harvest also like +people's errors go down in these + + align:start position:0% +people's errors go down in these + + + align:start position:0% +people's errors go down in these +measures + + align:start position:0% +measures + + + align:start position:0% +measures +there's a lot of detail related to that + + align:start position:0% +there's a lot of detail related to that + + + align:start position:0% +there's a lot of detail related to that +but in some sense uh + + align:start position:0% +but in some sense uh + + + align:start position:0% +but in some sense uh +that doesn't matter much for you right + + align:start position:0% +that doesn't matter much for you right + + + align:start position:0% +that doesn't matter much for you right +now people + + align:start position:0% +now people + + + align:start position:0% +now people +essentially are doing better um post + + align:start position:0% +essentially are doing better um post + + + align:start position:0% +essentially are doing better um post +harvest when they have + + align:start position:0% +harvest when they have + + + align:start position:0% +harvest when they have +more cash now what + + align:start position:0% +more cash now what + + + align:start position:0% +more cash now what +compounds can you think about what what + + align:start position:0% +compounds can you think about what what + + + align:start position:0% +compounds can you think about what what +what are the potential problems for this + + align:start position:0% +what are the potential problems for this + + + align:start position:0% +what are the potential problems for this +result + + align:start position:0% + + + + align:start position:0% + +like surely this is consistent with uh + + align:start position:0% +like surely this is consistent with uh + + + align:start position:0% +like surely this is consistent with uh +poverty impeding cognitive function but + + align:start position:0% +poverty impeding cognitive function but + + + align:start position:0% +poverty impeding cognitive function but +there could be other things going on and + + align:start position:0% +there could be other things going on and + + + align:start position:0% +there could be other things going on and +what are these other things + + align:start position:0% +what are these other things + + + align:start position:0% +what are these other things +um i think there's some good evidence or + + align:start position:0% +um i think there's some good evidence or + + + align:start position:0% +um i think there's some good evidence or +some one good thing is that like + + align:start position:0% +some one good thing is that like + + + align:start position:0% +some one good thing is that like +it's it would have to be like a very + + align:start position:0% +it's it would have to be like a very + + + align:start position:0% +it's it would have to be like a very +specific jaw shocked it has to do with + + align:start position:0% +specific jaw shocked it has to do with + + + align:start position:0% +specific jaw shocked it has to do with +harvest because there's essentially the + + align:start position:0% +harvest because there's essentially the + + + align:start position:0% +harvest because there's essentially the +harvest period was staggered over + + align:start position:0% +harvest period was staggered over + + + align:start position:0% +harvest period was staggered over +several months so it's not like like you + + align:start position:0% +several months so it's not like like you + + + align:start position:0% +several months so it's not like like you +know + + align:start position:0% +know + + + align:start position:0% +know +at some point the weather got worse and + + align:start position:0% +at some point the weather got worse and + + + align:start position:0% +at some point the weather got worse and +the weather got better because some + + align:start position:0% +the weather got better because some + + + align:start position:0% +the weather got better because some +people actually harvested earlier than + + align:start position:0% +people actually harvested earlier than + + + align:start position:0% +people actually harvested earlier than +others and there's a pre-post comparison + + align:start position:0% +others and there's a pre-post comparison + + + align:start position:0% +others and there's a pre-post comparison +but + + align:start position:0% +but + + + align:start position:0% +but +you know there could be other stuff time + + align:start position:0% +you know there could be other stuff time + + + align:start position:0% +you know there could be other stuff time +friends or something going on at least + + align:start position:0% +friends or something going on at least + + + align:start position:0% +friends or something going on at least +in some + + align:start position:0% +in some + + + align:start position:0% +in some +some ways in a way i think uh uh a + + align:start position:0% +some ways in a way i think uh uh a + + + align:start position:0% +some ways in a way i think uh uh a +confluent or + + align:start position:0% +confluent or + + + align:start position:0% +confluent or +in a way it's also just like a different + + align:start position:0% +in a way it's also just like a different + + + align:start position:0% +in a way it's also just like a different +interpretation perhaps in some ways in + + align:start position:0% +interpretation perhaps in some ways in + + + align:start position:0% +interpretation perhaps in some ways in +the sense of saying like well it's not + + align:start position:0% +the sense of saying like well it's not + + + align:start position:0% +the sense of saying like well it's not +just + + align:start position:0% +just + + + align:start position:0% +just +worries about the level of income but + + align:start position:0% +worries about the level of income but + + + align:start position:0% +worries about the level of income but +it's also + + align:start position:0% +it's also + + + align:start position:0% +it's also +worries about essentially risk or + + align:start position:0% +worries about essentially risk or + + + align:start position:0% +worries about essentially risk or +anxiety essentially and so that's + + align:start position:0% +anxiety essentially and so that's + + + align:start position:0% +anxiety essentially and so that's +slightly different + + align:start position:0% +slightly different + + + align:start position:0% +slightly different +but that anxiety would also sort of + + align:start position:0% +but that anxiety would also sort of + + + align:start position:0% +but that anxiety would also sort of +capture people's minds in some ways + + align:start position:0% +capture people's minds in some ways + + + align:start position:0% +capture people's minds in some ways +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +of course then you would want to see + + align:start position:0% +of course then you would want to see + + + align:start position:0% +of course then you would want to see +something like maybe that's worse for + + align:start position:0% +something like maybe that's worse for + + + align:start position:0% +something like maybe that's worse for +the rich compared to the poor or things + + align:start position:0% +the rich compared to the poor or things + + + align:start position:0% +the rich compared to the poor or things +like that but that's exactly right so + + align:start position:0% +like that but that's exactly right so + + + align:start position:0% +like that but that's exactly right so +there could be essentially + + align:start position:0% +there could be essentially + + + align:start position:0% +there could be essentially +labor costs or any sort of other + + align:start position:0% +labor costs or any sort of other + + + align:start position:0% +labor costs or any sort of other +distractions related to + + align:start position:0% +distractions related to + + + align:start position:0% +distractions related to +the hard rest which which this is kind + + align:start position:0% +the hard rest which which this is kind + + + align:start position:0% +the hard rest which which this is kind +of related to what mania was saying + + align:start position:0% +of related to what mania was saying + + + align:start position:0% +of related to what mania was saying +which is like the harvest itself + + align:start position:0% +which is like the harvest itself + + + align:start position:0% +which is like the harvest itself +might have these kinds of um + + align:start position:0% +might have these kinds of um + + + align:start position:0% +might have these kinds of um +effects okay i think we mentioned most + + align:start position:0% +effects okay i think we mentioned most + + + align:start position:0% +effects okay i think we mentioned most +of the things that i have on my list + + align:start position:0% +of the things that i have on my list + + + align:start position:0% +of the things that i have on my list +so uh so there's a first one is calorie + + align:start position:0% +so uh so there's a first one is calorie + + + align:start position:0% +so uh so there's a first one is calorie +consumption which is sort of the typical + + align:start position:0% +consumption which is sort of the typical + + + align:start position:0% +consumption which is sort of the typical +thing that development economist + + align:start position:0% +thing that development economist + + + align:start position:0% +thing that development economist +economists could study a lot which is to + + align:start position:0% +economists could study a lot which is to + + + align:start position:0% +economists could study a lot which is to +say you know uh + + align:start position:0% +say you know uh + + + align:start position:0% +say you know uh +poor nutrition um might sort of make + + align:start position:0% +poor nutrition um might sort of make + + + align:start position:0% +poor nutrition um might sort of make +people + + align:start position:0% +people + + + align:start position:0% +people +worse it's bad for attention you talked + + align:start position:0% +worse it's bad for attention you talked + + + align:start position:0% +worse it's bad for attention you talked +a little bit about like you know + + align:start position:0% +a little bit about like you know + + + align:start position:0% +a little bit about like you know +shopping on a hungry stomach but also + + align:start position:0% +shopping on a hungry stomach but also + + + align:start position:0% +shopping on a hungry stomach but also +think about like doing + + align:start position:0% +think about like doing + + + align:start position:0% +think about like doing +tests or exams and on your stomach is + + align:start position:0% +tests or exams and on your stomach is + + + align:start position:0% +tests or exams and on your stomach is +probably not a good empty stomach it's + + align:start position:0% +probably not a good empty stomach it's + + + align:start position:0% +probably not a good empty stomach it's +probably not a good idea + + align:start position:0% +probably not a good idea + + + align:start position:0% +probably not a good idea +the authors have some evidence that like + + align:start position:0% +the authors have some evidence that like + + + align:start position:0% +the authors have some evidence that like +the + + align:start position:0% +the + + + align:start position:0% +the +food expenditures are pretty similar + + align:start position:0% +food expenditures are pretty similar + + + align:start position:0% +food expenditures are pretty similar +premium post harvest from like some + + align:start position:0% +premium post harvest from like some + + + align:start position:0% +premium post harvest from like some +other sample + + align:start position:0% +other sample + + + align:start position:0% +other sample +um overall malnutrition doesn't seem to + + align:start position:0% +um overall malnutrition doesn't seem to + + + align:start position:0% +um overall malnutrition doesn't seem to +be like a huge + + align:start position:0% +be like a huge + + + align:start position:0% +be like a huge +uh issue in this area and having said + + align:start position:0% +uh issue in this area and having said + + + align:start position:0% +uh issue in this area and having said +that i think it's + + align:start position:0% +that i think it's + + + align:start position:0% +that i think it's +also reasonable to think that like + + align:start position:0% +also reasonable to think that like + + + align:start position:0% +also reasonable to think that like +pre-imposed harvest would you should + + align:start position:0% +pre-imposed harvest would you should + + + align:start position:0% +pre-imposed harvest would you should +have actually more money and then + + align:start position:0% +have actually more money and then + + + align:start position:0% +have actually more money and then +you've got to spend the money on + + align:start position:0% +you've got to spend the money on + + + align:start position:0% +you've got to spend the money on +something and presumably some of that + + align:start position:0% +something and presumably some of that + + + align:start position:0% +something and presumably some of that +will go on food but anyway so the + + align:start position:0% +will go on food but anyway so the + + + align:start position:0% +will go on food but anyway so the +authors argue that + + align:start position:0% +authors argue that + + + align:start position:0% +authors argue that +nutrition is not a big issue then um + + align:start position:0% +nutrition is not a big issue then um + + + align:start position:0% +nutrition is not a big issue then um +there's sort of two broad issues with i + + align:start position:0% +there's sort of two broad issues with i + + + align:start position:0% +there's sort of two broad issues with i +think was um joseon's and um + + align:start position:0% +think was um joseon's and um + + + align:start position:0% +think was um joseon's and um +catherine's comments which is about the + + align:start position:0% +catherine's comments which is about the + + + align:start position:0% +catherine's comments which is about the +uncertainty of the hardest size + + align:start position:0% +uncertainty of the hardest size + + + align:start position:0% +uncertainty of the hardest size +and some issues related to labor effort + + align:start position:0% +and some issues related to labor effort + + + align:start position:0% +and some issues related to labor effort +and so here the authors have some + + align:start position:0% +and so here the authors have some + + + align:start position:0% +and so here the authors have some +evidence from + + align:start position:0% +evidence from + + + align:start position:0% +evidence from +a post-harvest pre-payment sample what + + align:start position:0% +a post-harvest pre-payment sample what + + + align:start position:0% +a post-harvest pre-payment sample what +does that mean this is a sample that + + align:start position:0% +does that mean this is a sample that + + + align:start position:0% +does that mean this is a sample that +these are people who have um already + + align:start position:0% + + + + align:start position:0% + +harvested already so they've already + + align:start position:0% +harvested already so they've already + + + align:start position:0% +harvested already so they've already +exerted the labor effort and they also + + align:start position:0% +exerted the labor effort and they also + + + align:start position:0% +exerted the labor effort and they also +know already their + + align:start position:0% + + + + align:start position:0% + +approximate payment and + + align:start position:0% + + + + align:start position:0% + +so i was getting confused by this um but + + align:start position:0% +so i was getting confused by this um but + + + align:start position:0% +so i was getting confused by this um but +so these are people who have already + + align:start position:0% +so these are people who have already + + + align:start position:0% +so these are people who have already +done their harvest they have already + + align:start position:0% +done their harvest they have already + + + align:start position:0% +done their harvest they have already +they have done all the work already they + + align:start position:0% +they have done all the work already they + + + align:start position:0% +they have done all the work already they +know already what the harvest size will + + align:start position:0% +know already what the harvest size will + + + align:start position:0% +know already what the harvest size will +be like + + align:start position:0% +be like + + + align:start position:0% +be like +but those people um essentially are + + align:start position:0% +but those people um essentially are + + + align:start position:0% +but those people um essentially are +still + + align:start position:0% +still + + + align:start position:0% +still +not doing better compared to the people + + align:start position:0% +not doing better compared to the people + + + align:start position:0% +not doing better compared to the people +who have received their cash + + align:start position:0% +who have received their cash + + + align:start position:0% +who have received their cash +so that essentially is to say like uh + + align:start position:0% +so that essentially is to say like uh + + + align:start position:0% +so that essentially is to say like uh +even once you've done all the effort and + + align:start position:0% +even once you've done all the effort and + + + align:start position:0% +even once you've done all the effort and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +um that doesn't seem to um + + align:start position:0% +um that doesn't seem to um + + + align:start position:0% +um that doesn't seem to um +uh uh uh help in the sense of you're not + + align:start position:0% +uh uh uh help in the sense of you're not + + + align:start position:0% +uh uh uh help in the sense of you're not +fully doing you're not exhausted from + + align:start position:0% +fully doing you're not exhausted from + + + align:start position:0% +fully doing you're not exhausted from +the work already + + align:start position:0% +the work already + + + align:start position:0% +the work already +you already have all your harvest there + + align:start position:0% +you already have all your harvest there + + + align:start position:0% +you already have all your harvest there +you already know how big your harvest is + + align:start position:0% +you already know how big your harvest is + + + align:start position:0% +you already know how big your harvest is +but you never actually you haven't + + align:start position:0% +but you never actually you haven't + + + align:start position:0% +but you never actually you haven't +really received the money yet + + align:start position:0% +really received the money yet + + + align:start position:0% +really received the money yet +um and you know already what the harvest + + align:start position:0% +um and you know already what the harvest + + + align:start position:0% +um and you know already what the harvest +size is you can't believe you have the + + align:start position:0% +size is you can't believe you have the + + + align:start position:0% +size is you can't believe you have the +anxiety of the harvest size + + align:start position:0% +anxiety of the harvest size + + + align:start position:0% +anxiety of the harvest size +yet if you compare those people to the + + align:start position:0% +yet if you compare those people to the + + + align:start position:0% +yet if you compare those people to the +people that received the money uh you + + align:start position:0% +people that received the money uh you + + + align:start position:0% +people that received the money uh you +should still see differences between uh + + align:start position:0% +should still see differences between uh + + + align:start position:0% +should still see differences between uh +those people and the people who are done + + align:start position:0% +those people and the people who are done + + + align:start position:0% +those people and the people who are done +already + + align:start position:0% +already + + + align:start position:0% +already +the harvest and so that sort of that + + align:start position:0% +the harvest and so that sort of that + + + align:start position:0% +the harvest and so that sort of that +argues that essentially + + align:start position:0% +argues that essentially + + + align:start position:0% +argues that essentially +um it's not about + + align:start position:0% +um it's not about + + + align:start position:0% +um it's not about +anxiety per se about the harvest size + + align:start position:0% +anxiety per se about the harvest size + + + align:start position:0% +anxiety per se about the harvest size +but + + align:start position:0% +but + + + align:start position:0% +but +rather about like just having money in + + align:start position:0% +rather about like just having money in + + + align:start position:0% +rather about like just having money in +your pocket um + + align:start position:0% +your pocket um + + + align:start position:0% +your pocket um +versus not um let me see what the + + align:start position:0% +versus not um let me see what the + + + align:start position:0% +versus not um let me see what the +this the correct graph + + align:start position:0% + + + + align:start position:0% + +i see so this is a little bit + + align:start position:0% +i see so this is a little bit + + + align:start position:0% +i see so this is a little bit +misleadingly um labeled what this is + + align:start position:0% +misleadingly um labeled what this is + + + align:start position:0% +misleadingly um labeled what this is +supposed to say is like + + align:start position:0% +supposed to say is like + + + align:start position:0% +supposed to say is like +this is post-harvest and pre-harvest but + + align:start position:0% +this is post-harvest and pre-harvest but + + + align:start position:0% +this is post-harvest and pre-harvest but +what they mean by post-harvest and + + align:start position:0% +what they mean by post-harvest and + + + align:start position:0% +what they mean by post-harvest and +pre-iris post-hybrid is meant by like + + align:start position:0% +pre-iris post-hybrid is meant by like + + + align:start position:0% +pre-iris post-hybrid is meant by like +you have have received the cash versus + + align:start position:0% +you have have received the cash versus + + + align:start position:0% +you have have received the cash versus +not + + align:start position:0% +not + + + align:start position:0% +not +but both of these are actually both post + + align:start position:0% +but both of these are actually both post + + + align:start position:0% +but both of these are actually both post +harvests in the senate they have been + + align:start position:0% +harvests in the senate they have been + + + align:start position:0% +harvests in the senate they have been +already the + + align:start position:0% +already the + + + align:start position:0% +already the +um uh uh the work + + align:start position:0% +um uh uh the work + + + align:start position:0% +um uh uh the work +anyway sorry that's a bit confusing but + + align:start position:0% +anyway sorry that's a bit confusing but + + + align:start position:0% +anyway sorry that's a bit confusing but +essentially um uh + + align:start position:0% +essentially um uh + + + align:start position:0% +essentially um uh +what they're trying to say is + + align:start position:0% +what they're trying to say is + + + align:start position:0% +what they're trying to say is +essentially what really matters is like + + align:start position:0% +essentially what really matters is like + + + align:start position:0% +essentially what really matters is like +not + + align:start position:0% +not + + + align:start position:0% +not +uh uh the work around the harvest per se + + align:start position:0% +uh uh the work around the harvest per se + + + align:start position:0% +uh uh the work around the harvest per se +or the uncertainty around the harvest + + align:start position:0% +or the uncertainty around the harvest + + + align:start position:0% +or the uncertainty around the harvest +it's really about like + + align:start position:0% +it's really about like + + + align:start position:0% +it's really about like +receiving the cash um versus not and + + align:start position:0% +receiving the cash um versus not and + + + align:start position:0% +receiving the cash um versus not and +then there's like another + + align:start position:0% +then there's like another + + + align:start position:0% +then there's like another +um a problem which you haven't really um + + align:start position:0% +um a problem which you haven't really um + + + align:start position:0% +um a problem which you haven't really um +brought up which is the issue of + + align:start position:0% +brought up which is the issue of + + + align:start position:0% +brought up which is the issue of +learning effects right + + align:start position:0% +learning effects right + + + align:start position:0% +learning effects right +when people do the tasks like um um + + align:start position:0% +when people do the tasks like um um + + + align:start position:0% +when people do the tasks like um um +several times because + + align:start position:0% +several times because + + + align:start position:0% +several times because +we do a test twice you gotta do better + + align:start position:0% +we do a test twice you gotta do better + + + align:start position:0% +we do a test twice you gotta do better +and + + align:start position:0% +and + + + align:start position:0% +and +you know um but to address this issue + + align:start position:0% +you know um but to address this issue + + + align:start position:0% +you know um but to address this issue +they also have like what they call like + + align:start position:0% +they also have like what they call like + + + align:start position:0% +they also have like what they call like +a hold out sample that takes the cargo + + align:start position:0% +a hold out sample that takes the cargo + + + align:start position:0% +a hold out sample that takes the cargo +test for the first time + + align:start position:0% +test for the first time + + + align:start position:0% +test for the first time +post harvest so what i what i showed you + + align:start position:0% +post harvest so what i what i showed you + + + align:start position:0% +post harvest so what i what i showed you +before it was proposed + + align:start position:0% +before it was proposed + + + align:start position:0% +before it was proposed +for both people i've done both of these + + align:start position:0% +for both people i've done both of these + + + align:start position:0% +for both people i've done both of these +tests there's some samples only done + + align:start position:0% +tests there's some samples only done + + + align:start position:0% +tests there's some samples only done +um the tasks like once post harvest and + + align:start position:0% +um the tasks like once post harvest and + + + align:start position:0% +um the tasks like once post harvest and +they don't perform worse than + + align:start position:0% +they don't perform worse than + + + align:start position:0% +they don't perform worse than +people who do the tasks for the second + + align:start position:0% +people who do the tasks for the second + + + align:start position:0% +people who do the tasks for the second +time which seems to say like it's not + + align:start position:0% +time which seems to say like it's not + + + align:start position:0% +time which seems to say like it's not +really about learning + + align:start position:0% +really about learning + + + align:start position:0% +really about learning +having said that that is essentially + + align:start position:0% +having said that that is essentially + + + align:start position:0% +having said that that is essentially +only like a small sub sample + + align:start position:0% +only like a small sub sample + + + align:start position:0% +only like a small sub sample +comparison really seems um mostly + + align:start position:0% +comparison really seems um mostly + + + align:start position:0% +comparison really seems um mostly +underpowered and + + align:start position:0% +underpowered and + + + align:start position:0% +underpowered and +there are some concerns surely about + + align:start position:0% +there are some concerns surely about + + + align:start position:0% +there are some concerns surely about +still um + + align:start position:0% + + + + align:start position:0% + +any questions on these + + align:start position:0% + + + + align:start position:0% + +okay um + + align:start position:0% + + + + align:start position:0% + +so then um so this is a study from like + + align:start position:0% +so then um so this is a study from like + + + align:start position:0% +so then um so this is a study from like +a few years ago so then + + align:start position:0% +a few years ago so then + + + align:start position:0% +a few years ago so then +you know what kind of follow-up is there + + align:start position:0% +you know what kind of follow-up is there + + + align:start position:0% +you know what kind of follow-up is there +um + + align:start position:0% +um + + + align:start position:0% +um +uh that that sort of considers further + + align:start position:0% +uh that that sort of considers further + + + align:start position:0% +uh that that sort of considers further +evidence + + align:start position:0% +evidence + + + align:start position:0% +evidence +so there's one very nice study by + + align:start position:0% +so there's one very nice study by + + + align:start position:0% +so there's one very nice study by +carvalho um in 2015 + + align:start position:0% +carvalho um in 2015 + + + align:start position:0% +carvalho um in 2015 +that looks at the same issue in the us + + align:start position:0% +that looks at the same issue in the us + + + align:start position:0% +that looks at the same issue in the us +and + + align:start position:0% +and + + + align:start position:0% +and +they looked at cognition and decision + + align:start position:0% +they looked at cognition and decision + + + align:start position:0% +they looked at cognition and decision +making of u.s households and + + align:start position:0% +making of u.s households and + + + align:start position:0% +making of u.s households and +um uh paydays and essentially they find + + align:start position:0% +um uh paydays and essentially they find + + + align:start position:0% +um uh paydays and essentially they find +no cognitive effects whatsoever they + + align:start position:0% +no cognitive effects whatsoever they + + + align:start position:0% +no cognitive effects whatsoever they +also find no effects + + align:start position:0% +also find no effects + + + align:start position:0% +also find no effects +on decision-making uh uh as one would + + align:start position:0% +on decision-making uh uh as one would + + + align:start position:0% +on decision-making uh uh as one would +have expected + + align:start position:0% +have expected + + + align:start position:0% +have expected +raises the question about what's going + + align:start position:0% +raises the question about what's going + + + align:start position:0% +raises the question about what's going +on here + + align:start position:0% +on here + + + align:start position:0% +on here +um and what's going on so it could be + + align:start position:0% +um and what's going on so it could be + + + align:start position:0% +um and what's going on so it could be +that this is an external + + align:start position:0% +that this is an external + + + align:start position:0% +that this is an external +issue in some sense in a sense this + + align:start position:0% +issue in some sense in a sense this + + + align:start position:0% +issue in some sense in a sense this +really what what is needed here is + + align:start position:0% +really what what is needed here is + + + align:start position:0% +really what what is needed here is +really like extreme poverty and like + + align:start position:0% +really like extreme poverty and like + + + align:start position:0% +really like extreme poverty and like +really large differences in my people's + + align:start position:0% +really large differences in my people's + + + align:start position:0% +really large differences in my people's +income + + align:start position:0% +income + + + align:start position:0% +income +or like the amount of money that i have + + align:start position:0% +or like the amount of money that i have + + + align:start position:0% +or like the amount of money that i have +available and sort of + + align:start position:0% +available and sort of + + + align:start position:0% +available and sort of +uh when you look at u.s households at + + align:start position:0% +uh when you look at u.s households at + + + align:start position:0% +uh when you look at u.s households at +least the households that were + + align:start position:0% +least the households that were + + + align:start position:0% +least the households that were +considered considered in the kanawha you + + align:start position:0% +considered considered in the kanawha you + + + align:start position:0% +considered considered in the kanawha you +study around paydays where there's + + align:start position:0% +study around paydays where there's + + + align:start position:0% +study around paydays where there's +differences in how much money they have + + align:start position:0% +differences in how much money they have + + + align:start position:0% +differences in how much money they have +cash on hand they have + + align:start position:0% +cash on hand they have + + + align:start position:0% +cash on hand they have +the difference is actually not that huge + + align:start position:0% +the difference is actually not that huge + + + align:start position:0% +the difference is actually not that huge +and so that might just be not + + align:start position:0% +and so that might just be not + + + align:start position:0% +and so that might just be not +sufficiently much expiration uh around + + align:start position:0% +sufficiently much expiration uh around + + + align:start position:0% +sufficiently much expiration uh around +those paydays to be able to generate + + align:start position:0% +those paydays to be able to generate + + + align:start position:0% +those paydays to be able to generate +those types of + + align:start position:0% +those types of + + + align:start position:0% +those types of +um effect it could also be that these + + align:start position:0% +um effect it could also be that these + + + align:start position:0% +um effect it could also be that these +effects don't really um + + align:start position:0% +effects don't really um + + + align:start position:0% +effects don't really um +uh uh replicate in a sense of like + + align:start position:0% +uh uh replicate in a sense of like + + + align:start position:0% +uh uh replicate in a sense of like +there's a replicability issue which + + align:start position:0% +there's a replicability issue which + + + align:start position:0% +there's a replicability issue which +uh uh could be a concern as well + + align:start position:0% +uh uh could be a concern as well + + + align:start position:0% +uh uh could be a concern as well +there's a nice study and this gets to + + align:start position:0% +there's a nice study and this gets to + + + align:start position:0% +there's a nice study and this gets to +the issue that i think um + + align:start position:0% +the issue that i think um + + + align:start position:0% +the issue that i think um +jose mentioned which is uh a study by + + align:start position:0% +jose mentioned which is uh a study by + + + align:start position:0% +jose mentioned which is uh a study by +lee + + align:start position:0% +lee + + + align:start position:0% +lee +is um uh looking at drought insurance + + align:start position:0% +is um uh looking at drought insurance + + + align:start position:0% +is um uh looking at drought insurance +and what they essentially argue is that + + align:start position:0% +and what they essentially argue is that + + + align:start position:0% +and what they essentially argue is that +uh when you put up with insurance so + + align:start position:0% +uh when you put up with insurance so + + + align:start position:0% +uh when you put up with insurance so +usually + + align:start position:0% +usually + + + align:start position:0% +usually +insurance for people would argue + + align:start position:0% +insurance for people would argue + + + align:start position:0% +insurance for people would argue +insurance is used for if a bad + + align:start position:0% +insurance is used for if a bad + + + align:start position:0% +insurance is used for if a bad +state happens in the world you can + + align:start position:0% +state happens in the world you can + + + align:start position:0% +state happens in the world you can +essentially get my get a payment right + + align:start position:0% +essentially get my get a payment right + + + align:start position:0% +essentially get my get a payment right +if i get some health shock or when my + + align:start position:0% +if i get some health shock or when my + + + align:start position:0% +if i get some health shock or when my +harvest is bad or the like + + align:start position:0% +harvest is bad or the like + + + align:start position:0% +harvest is bad or the like +i get some money from the insurance + + align:start position:0% +i get some money from the insurance + + + align:start position:0% +i get some money from the insurance +company and that is good + + align:start position:0% +company and that is good + + + align:start position:0% +company and that is good +because in the bad state of the marginal + + align:start position:0% +because in the bad state of the marginal + + + align:start position:0% +because in the bad state of the marginal +utility is really high of receiving + + align:start position:0% +utility is really high of receiving + + + align:start position:0% +utility is really high of receiving +money + + align:start position:0% +money + + + align:start position:0% +money +and sort of i willing to pay for + + align:start position:0% +and sort of i willing to pay for + + + align:start position:0% +and sort of i willing to pay for +insurance right now + + align:start position:0% +insurance right now + + + align:start position:0% +insurance right now +in the future uh receiving + + align:start position:0% +in the future uh receiving + + + align:start position:0% +in the future uh receiving +so i'm willing to pay for insurance now + + align:start position:0% +so i'm willing to pay for insurance now + + + align:start position:0% +so i'm willing to pay for insurance now +because in the future + + align:start position:0% +because in the future + + + align:start position:0% +because in the future +in a bad state of the world i value that + + align:start position:0% +in a bad state of the world i value that + + + align:start position:0% +in a bad state of the world i value that +money more um than in a good state of + + align:start position:0% +money more um than in a good state of + + + align:start position:0% +money more um than in a good state of +the world + + align:start position:0% +the world + + + align:start position:0% +the world +so in a good state it's willing to pay + + align:start position:0% +so in a good state it's willing to pay + + + align:start position:0% +so in a good state it's willing to pay +for insurance + + align:start position:0% +for insurance + + + align:start position:0% +for insurance +now what lushan denmany instead arguing + + align:start position:0% +now what lushan denmany instead arguing + + + align:start position:0% +now what lushan denmany instead arguing +is well there's an additional value of + + align:start position:0% +is well there's an additional value of + + + align:start position:0% +is well there's an additional value of +insurance which essentially it's helping + + align:start position:0% +insurance which essentially it's helping + + + align:start position:0% +insurance which essentially it's helping +reduce their anxiety and worries about + + align:start position:0% +reduce their anxiety and worries about + + + align:start position:0% +reduce their anxiety and worries about +money ex-ante in all states of the world + + align:start position:0% +money ex-ante in all states of the world + + + align:start position:0% +money ex-ante in all states of the world +that is to say + + align:start position:0% +that is to say + + + align:start position:0% +that is to say +if i'm really worried about like bad + + align:start position:0% +if i'm really worried about like bad + + + align:start position:0% +if i'm really worried about like bad +harvest shocks or other stuff + + align:start position:0% +harvest shocks or other stuff + + + align:start position:0% +harvest shocks or other stuff +health shocks happening in the future + + align:start position:0% +health shocks happening in the future + + + align:start position:0% +health shocks happening in the future +that might really frazzle me and really + + align:start position:0% +that might really frazzle me and really + + + align:start position:0% +that might really frazzle me and really +sort of worry me all the time which + + align:start position:0% +sort of worry me all the time which + + + align:start position:0% +sort of worry me all the time which +in turn might affect people's cognitive + + align:start position:0% +in turn might affect people's cognitive + + + align:start position:0% +in turn might affect people's cognitive +performance well + + align:start position:0% +performance well + + + align:start position:0% +performance well +that's in all states of the world even + + align:start position:0% +that's in all states of the world even + + + align:start position:0% +that's in all states of the world even +when you're doing well right now + + align:start position:0% +when you're doing well right now + + + align:start position:0% +when you're doing well right now +and even if nothing bad ever happens + + align:start position:0% +and even if nothing bad ever happens + + + align:start position:0% +and even if nothing bad ever happens +you're gonna do worse today + + align:start position:0% +you're gonna do worse today + + + align:start position:0% +you're gonna do worse today +because you know you're worried about + + align:start position:0% +because you know you're worried about + + + align:start position:0% +because you know you're worried about +these things and sort of providing + + align:start position:0% +these things and sort of providing + + + align:start position:0% +these things and sort of providing +insurance + + align:start position:0% +insurance + + + align:start position:0% +insurance +therefore might help people do better + + align:start position:0% +therefore might help people do better + + + align:start position:0% +therefore might help people do better +even in good states of the world or in + + align:start position:0% +even in good states of the world or in + + + align:start position:0% +even in good states of the world or in +all states of the world in addition to + + align:start position:0% +all states of the world in addition to + + + align:start position:0% +all states of the world in addition to +sort of having the insurance value of + + align:start position:0% +sort of having the insurance value of + + + align:start position:0% +sort of having the insurance value of +helping people in bad state of the world + + align:start position:0% +helping people in bad state of the world + + + align:start position:0% +helping people in bad state of the world +they don't have + + align:start position:0% +they don't have + + + align:start position:0% +they don't have +some evidence of that there's some mixed + + align:start position:0% +some evidence of that there's some mixed + + + align:start position:0% +some evidence of that there's some mixed +evidence overall but i think the idea of + + align:start position:0% +evidence overall but i think the idea of + + + align:start position:0% +evidence overall but i think the idea of +like + + align:start position:0% +like + + + align:start position:0% +like +insurance being helpful for the poor for + + align:start position:0% +insurance being helpful for the poor for + + + align:start position:0% +insurance being helpful for the poor for +anybody um not just + + align:start position:0% +anybody um not just + + + align:start position:0% +anybody um not just +because it helps in bad states but it + + align:start position:0% +because it helps in bad states but it + + + align:start position:0% +because it helps in bad states but it +helps people worry about bats is a very + + align:start position:0% +helps people worry about bats is a very + + + align:start position:0% +helps people worry about bats is a very +nice one that + + align:start position:0% +nice one that + + + align:start position:0% +nice one that +hopefully will be explored um further + + align:start position:0% +hopefully will be explored um further + + + align:start position:0% +hopefully will be explored um further +now then another question uh um i think + + align:start position:0% +now then another question uh um i think + + + align:start position:0% +now then another question uh um i think +jose was bringing up is to say well + + align:start position:0% +jose was bringing up is to say well + + + align:start position:0% +jose was bringing up is to say well +there are these cognitive tasks well i + + align:start position:0% +there are these cognitive tasks well i + + + align:start position:0% +there are these cognitive tasks well i +showed you so far that these tasks and + + align:start position:0% +showed you so far that these tasks and + + + align:start position:0% +showed you so far that these tasks and +like raven's matrices and cognitive + + align:start position:0% +like raven's matrices and cognitive + + + align:start position:0% +like raven's matrices and cognitive +control + + align:start position:0% +control + + + align:start position:0% +control +and sort of arguably iq tests are + + align:start position:0% +and sort of arguably iq tests are + + + align:start position:0% +and sort of arguably iq tests are +important and helpful and sort of you + + align:start position:0% +important and helpful and sort of you + + + align:start position:0% +important and helpful and sort of you +know + + align:start position:0% +know + + + align:start position:0% +know +we think that's helpful and it maps with + + align:start position:0% +we think that's helpful and it maps with + + + align:start position:0% +we think that's helpful and it maps with +something useful for the world + + align:start position:0% +something useful for the world + + + align:start position:0% +something useful for the world +but it's a little bit hard to tell like + + align:start position:0% +but it's a little bit hard to tell like + + + align:start position:0% +but it's a little bit hard to tell like +does this actually matter for income is + + align:start position:0% +does this actually matter for income is + + + align:start position:0% +does this actually matter for income is +it this is really important or not + + align:start position:0% +it this is really important or not + + + align:start position:0% +it this is really important or not +important and how much does it + + align:start position:0% +important and how much does it + + + align:start position:0% +important and how much does it +um um so in a paper with + + align:start position:0% +um um so in a paper with + + + align:start position:0% +um um so in a paper with +uh a good core + + align:start position:0% +uh a good core + + + align:start position:0% +uh a good core +um we looked at this in a field setting + + align:start position:0% +um we looked at this in a field setting + + + align:start position:0% +um we looked at this in a field setting +with workers + + align:start position:0% +with workers + + + align:start position:0% +with workers +in um orisa and rural uh in rural areas + + align:start position:0% +in um orisa and rural uh in rural areas + + + align:start position:0% +in um orisa and rural uh in rural areas +in + + align:start position:0% +in + + + align:start position:0% +in +india and what we did there is we + + align:start position:0% +india and what we did there is we + + + align:start position:0% +india and what we did there is we +hired people for about two weeks um to + + align:start position:0% +hired people for about two weeks um to + + + align:start position:0% +hired people for about two weeks um to +do a simple + + align:start position:0% +do a simple + + + align:start position:0% +do a simple +um labor task where they were doing uh + + align:start position:0% +um labor task where they were doing uh + + + align:start position:0% +um labor task where they were doing uh +leaf plates was essentially like + + align:start position:0% +leaf plates was essentially like + + + align:start position:0% +leaf plates was essentially like +um uh putting together leaves and chip + + align:start position:0% +um uh putting together leaves and chip + + + align:start position:0% +um uh putting together leaves and chip +plates + + align:start position:0% +plates + + + align:start position:0% +plates +uh which are sort of used in many + + align:start position:0% +uh which are sort of used in many + + + align:start position:0% +uh which are sort of used in many +settings + + align:start position:0% +settings + + + align:start position:0% +settings +by stitching them together using like + + align:start position:0% +by stitching them together using like + + + align:start position:0% +by stitching them together using like +little uh wooden sticks + + align:start position:0% +little uh wooden sticks + + + align:start position:0% +little uh wooden sticks +and um so people are hired for two weeks + + align:start position:0% +and um so people are hired for two weeks + + + align:start position:0% +and um so people are hired for two weeks +and then for + + align:start position:0% +and then for + + + align:start position:0% +and then for +um the sample we buried um when some + + align:start position:0% +um the sample we buried um when some + + + align:start position:0% +um the sample we buried um when some +people were paid + + align:start position:0% +people were paid + + + align:start position:0% +people were paid +earlier often some people heard later + + align:start position:0% +earlier often some people heard later + + + align:start position:0% +earlier often some people heard later +were paid later + + align:start position:0% +were paid later + + + align:start position:0% +were paid later +so everybody was paid exactly the same + + align:start position:0% +so everybody was paid exactly the same + + + align:start position:0% +so everybody was paid exactly the same +conditional on showing up + + align:start position:0% +conditional on showing up + + + align:start position:0% +conditional on showing up +and conditional on how much they + + align:start position:0% +and conditional on how much they + + + align:start position:0% +and conditional on how much they +produced so their piece rates how much + + align:start position:0% +produced so their piece rates how much + + + align:start position:0% +produced so their piece rates how much +they were paid were the same and their + + align:start position:0% +they were paid were the same and their + + + align:start position:0% +they were paid were the same and their +attendance paid for showing up + + align:start position:0% +attendance paid for showing up + + + align:start position:0% +attendance paid for showing up +the only difference was that some people + + align:start position:0% +the only difference was that some people + + + align:start position:0% +the only difference was that some people +were paid earlier and some people were + + align:start position:0% +were paid earlier and some people were + + + align:start position:0% +were paid earlier and some people were +paid later so that allows us then to + + align:start position:0% +paid later so that allows us then to + + + align:start position:0% +paid later so that allows us then to +look at + + align:start position:0% +look at + + + align:start position:0% +look at +how do people the same people how do + + align:start position:0% +how do people the same people how do + + + align:start position:0% +how do people the same people how do +they perform + + align:start position:0% +they perform + + + align:start position:0% +they perform +when they're ready versus not + + align:start position:0% +when they're ready versus not + + + align:start position:0% +when they're ready versus not +compared to another group that is + + align:start position:0% +compared to another group that is + + + align:start position:0% +compared to another group that is +essentially only paid + + align:start position:0% +essentially only paid + + + align:start position:0% +essentially only paid +later and this is a period in the moline + + align:start position:0% +later and this is a period in the moline + + + align:start position:0% +later and this is a period in the moline +period when people are extremely + + align:start position:0% +period when people are extremely + + + align:start position:0% +period when people are extremely +financially constrained + + align:start position:0% +financially constrained + + + align:start position:0% +financially constrained +so people are really short in cash so + + align:start position:0% +so people are really short in cash so + + + align:start position:0% +so people are really short in cash so +you can look at essentially + + align:start position:0% +you can look at essentially + + + align:start position:0% +you can look at essentially +uh really at the impact of transfers + + align:start position:0% +uh really at the impact of transfers + + + align:start position:0% +uh really at the impact of transfers +uh or cash constraints in this setting + + align:start position:0% +uh or cash constraints in this setting + + + align:start position:0% +uh or cash constraints in this setting +what we find is a relatively clear + + align:start position:0% +what we find is a relatively clear + + + align:start position:0% +what we find is a relatively clear +evidence that paying people early makes + + align:start position:0% +evidence that paying people early makes + + + align:start position:0% +evidence that paying people early makes +people + + align:start position:0% +people + + + align:start position:0% +people +a lot more productive and moreover these + + align:start position:0% +a lot more productive and moreover these + + + align:start position:0% +a lot more productive and moreover these +effects are the largest for the poorest + + align:start position:0% +effects are the largest for the poorest + + + align:start position:0% +effects are the largest for the poorest +workers so essentially when you sort of + + align:start position:0% +workers so essentially when you sort of + + + align:start position:0% +workers so essentially when you sort of +divide the sample into + + align:start position:0% +divide the sample into + + + align:start position:0% +divide the sample into +uh among the people who are richer and + + align:start position:0% +uh among the people who are richer and + + + align:start position:0% +uh among the people who are richer and +poorer to start with people who are + + align:start position:0% +poorer to start with people who are + + + align:start position:0% +poorer to start with people who are +particularly poor + + align:start position:0% +particularly poor + + + align:start position:0% +particularly poor +have the largest impacts um in this + + align:start position:0% +have the largest impacts um in this + + + align:start position:0% +have the largest impacts um in this +sample and these are sort of pretty + + align:start position:0% +sample and these are sort of pretty + + + align:start position:0% +sample and these are sort of pretty +large effects it's about five to ten + + align:start position:0% +large effects it's about five to ten + + + align:start position:0% +large effects it's about five to ten +percent of the productivity + + align:start position:0% +percent of the productivity + + + align:start position:0% +percent of the productivity +which is you know it doesn't sound that + + align:start position:0% +which is you know it doesn't sound that + + + align:start position:0% +which is you know it doesn't sound that +large in absolute terms but in relative + + align:start position:0% +large in absolute terms but in relative + + + align:start position:0% +large in absolute terms but in relative +terms or + + align:start position:0% +terms or + + + align:start position:0% +terms or +in terms of like when you double + + align:start position:0% +in terms of like when you double + + + align:start position:0% +in terms of like when you double +people's wages people's um + + align:start position:0% +people's wages people's um + + + align:start position:0% +people's wages people's um +earnings go up only um as much or or not + + align:start position:0% +earnings go up only um as much or or not + + + align:start position:0% +earnings go up only um as much or or not +much more + + align:start position:0% +much more + + + align:start position:0% +much more +so really increasing people's + + align:start position:0% +so really increasing people's + + + align:start position:0% +so really increasing people's +productivity is very very hard in these + + align:start position:0% +productivity is very very hard in these + + + align:start position:0% +productivity is very very hard in these +settings + + align:start position:0% +settings + + + align:start position:0% +settings +and relatively minor interventions such + + align:start position:0% +and relatively minor interventions such + + + align:start position:0% +and relatively minor interventions such +as the one that we did + + align:start position:0% +as the one that we did + + + align:start position:0% +as the one that we did +um had pretty large effects in the real + + align:start position:0% +um had pretty large effects in the real + + + align:start position:0% +um had pretty large effects in the real +world setting for people for whom this + + align:start position:0% +world setting for people for whom this + + + align:start position:0% +world setting for people for whom this +is really + + align:start position:0% +is really + + + align:start position:0% +is really +uh the real jobs in the real life um for + + align:start position:0% +uh the real jobs in the real life um for + + + align:start position:0% +uh the real jobs in the real life um for +about + + align:start position:0% +about + + + align:start position:0% +about +two weeks so suppose you hired somebody + + align:start position:0% +two weeks so suppose you hired somebody + + + align:start position:0% +two weeks so suppose you hired somebody +for a year + + align:start position:0% +for a year + + + align:start position:0% +for a year +should you pay them like daily weekly + + align:start position:0% +should you pay them like daily weekly + + + align:start position:0% +should you pay them like daily weekly +monthly + + align:start position:0% +monthly + + + align:start position:0% +monthly +or or or what and so what am + + align:start position:0% +or or or what and so what am + + + align:start position:0% +or or or what and so what am +i doing or what our evidence shows that + + align:start position:0% +i doing or what our evidence shows that + + + align:start position:0% +i doing or what our evidence shows that +when you hire people for two weeks + + align:start position:0% +when you hire people for two weeks + + + align:start position:0% +when you hire people for two weeks +paying people twice as i'm like paying + + align:start position:0% +paying people twice as i'm like paying + + + align:start position:0% +paying people twice as i'm like paying +people um once after a week and then the + + align:start position:0% +people um once after a week and then the + + + align:start position:0% +people um once after a week and then the +rest at the end + + align:start position:0% +rest at the end + + + align:start position:0% +rest at the end +makes workers more productive than + + align:start position:0% +makes workers more productive than + + + align:start position:0% +makes workers more productive than +paying workers only at the very end + + align:start position:0% +paying workers only at the very end + + + align:start position:0% +paying workers only at the very end +um and assuming you know depending on + + align:start position:0% +um and assuming you know depending on + + + align:start position:0% +um and assuming you know depending on +like the interest rate but that seems to + + align:start position:0% +like the interest rate but that seems to + + + align:start position:0% +like the interest rate but that seems to +be like a thing the company should do + + align:start position:0% +be like a thing the company should do + + + align:start position:0% +be like a thing the company should do +now but of course if you hire people for + + align:start position:0% +now but of course if you hire people for + + + align:start position:0% +now but of course if you hire people for +like + + align:start position:0% +like + + + align:start position:0% +like +a year then paying people weekly versus + + align:start position:0% +a year then paying people weekly versus + + + align:start position:0% +a year then paying people weekly versus +monthly or + + align:start position:0% +monthly or + + + align:start position:0% +monthly or +bi-weekly uh the comparison becomes + + align:start position:0% +bi-weekly uh the comparison becomes + + + align:start position:0% +bi-weekly uh the comparison becomes +quite different because essentially the + + align:start position:0% +quite different because essentially the + + + align:start position:0% +quite different because essentially the +control group that's paid after + + align:start position:0% +control group that's paid after + + + align:start position:0% +control group that's paid after +two weeks now after two weeks of course + + align:start position:0% +two weeks now after two weeks of course + + + align:start position:0% +two weeks now after two weeks of course +they have a lot more money + + align:start position:0% +they have a lot more money + + + align:start position:0% +they have a lot more money +um because they haven't spent it + + align:start position:0% +um because they haven't spent it + + + align:start position:0% +um because they haven't spent it +compared to the treatment group who's + + align:start position:0% +compared to the treatment group who's + + + align:start position:0% +compared to the treatment group who's +paid + + align:start position:0% +paid + + + align:start position:0% +paid +earlier and um i think there essentially + + align:start position:0% +earlier and um i think there essentially + + + align:start position:0% +earlier and um i think there essentially +we can't believe this is we can't really + + align:start position:0% +we can't believe this is we can't really + + + align:start position:0% +we can't believe this is we can't really +speak to that in some sense our our + + align:start position:0% +speak to that in some sense our our + + + align:start position:0% +speak to that in some sense our our +design is just not really + + align:start position:0% +design is just not really + + + align:start position:0% +design is just not really +uh uh set up to do this you would have + + align:start position:0% +uh uh set up to do this you would have + + + align:start position:0% +uh uh set up to do this you would have +to do at least you know you would have + + align:start position:0% +to do at least you know you would have + + + align:start position:0% +to do at least you know you would have +to do + + align:start position:0% +to do + + + align:start position:0% +to do +uh at least another week or two to + + align:start position:0% +uh at least another week or two to + + + align:start position:0% +uh at least another week or two to +measure how the control group now doing + + align:start position:0% +measure how the control group now doing + + + align:start position:0% +measure how the control group now doing +compared to the treatment group or like + + align:start position:0% +compared to the treatment group or like + + + align:start position:0% +compared to the treatment group or like +do it repeatedly there might also be + + align:start position:0% +do it repeatedly there might also be + + + align:start position:0% +do it repeatedly there might also be +some effects on like + + align:start position:0% +some effects on like + + + align:start position:0% +some effects on like +uh over time repeatedly some of these + + align:start position:0% +uh over time repeatedly some of these + + + align:start position:0% +uh over time repeatedly some of these +effects might be going away because + + align:start position:0% +effects might be going away because + + + align:start position:0% +effects might be going away because +workers learn and so on and so forth um + + align:start position:0% +workers learn and so on and so forth um + + + align:start position:0% +workers learn and so on and so forth um +i think of this evidence much more + + align:start position:0% +i think of this evidence much more + + + align:start position:0% +i think of this evidence much more +sense of proof of concept that a + + align:start position:0% +sense of proof of concept that a + + + align:start position:0% +sense of proof of concept that a +providing cash or alleviating cash + + align:start position:0% +providing cash or alleviating cash + + + align:start position:0% +providing cash or alleviating cash +constraints among workers + + align:start position:0% +constraints among workers + + + align:start position:0% +constraints among workers +either through some low interest rate + + align:start position:0% +either through some low interest rate + + + align:start position:0% +either through some low interest rate +loans or some early payments + + align:start position:0% +loans or some early payments + + + align:start position:0% +loans or some early payments +or some form of like ubi or cash + + align:start position:0% +or some form of like ubi or cash + + + align:start position:0% +or some form of like ubi or cash +transfers unconditional + + align:start position:0% +transfers unconditional + + + align:start position:0% +transfers unconditional +additional cash transfers essentially + + align:start position:0% +additional cash transfers essentially + + + align:start position:0% +additional cash transfers essentially +improving workers financial situation in + + align:start position:0% +improving workers financial situation in + + + align:start position:0% +improving workers financial situation in +some ways + + align:start position:0% +some ways + + + align:start position:0% +some ways +can be productive for firms um now how + + align:start position:0% +can be productive for firms um now how + + + align:start position:0% +can be productive for firms um now how +the firm plan actually does that + + align:start position:0% +the firm plan actually does that + + + align:start position:0% +the firm plan actually does that +we don't necessarily know and this is + + align:start position:0% +we don't necessarily know and this is + + + align:start position:0% +we don't necessarily know and this is +sort of too small of a short of an + + align:start position:0% +sort of too small of a short of an + + + align:start position:0% +sort of too small of a short of an +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +uh to show that but it's sort of proof + + align:start position:0% +uh to show that but it's sort of proof + + + align:start position:0% +uh to show that but it's sort of proof +of concept that in a real world setting + + align:start position:0% +of concept that in a real world setting + + + align:start position:0% +of concept that in a real world setting +with very high stakes for workers is + + align:start position:0% +with very high stakes for workers is + + + align:start position:0% +with very high stakes for workers is +there like real earnings + + align:start position:0% +there like real earnings + + + align:start position:0% +there like real earnings +there seem to be these uh uh effects so + + align:start position:0% +there seem to be these uh uh effects so + + + align:start position:0% +there seem to be these uh uh effects so +for firms it might be wealthy + + align:start position:0% +for firms it might be wealthy + + + align:start position:0% +for firms it might be wealthy +to in fact try to improve their uh + + align:start position:0% +to in fact try to improve their uh + + + align:start position:0% +to in fact try to improve their uh +actual situation + + align:start position:0% +actual situation + + + align:start position:0% +actual situation +um or for governments it might be + + align:start position:0% +um or for governments it might be + + + align:start position:0% +um or for governments it might be +valuable + + align:start position:0% +valuable + + + align:start position:0% +valuable +uh to think about cash transfers as a + + align:start position:0% +uh to think about cash transfers as a + + + align:start position:0% +uh to think about cash transfers as a +way to + + align:start position:0% +way to + + + align:start position:0% +way to +so usually when you think about cash + + align:start position:0% +so usually when you think about cash + + + align:start position:0% +so usually when you think about cash +transfers let me actually + + align:start position:0% +transfers let me actually + + + align:start position:0% +transfers let me actually +talk about this for a second and then we + + align:start position:0% +talk about this for a second and then we + + + align:start position:0% +talk about this for a second and then we +can talk about other compounds of the + + align:start position:0% +can talk about other compounds of the + + + align:start position:0% +can talk about other compounds of the +study + + align:start position:0% +study + + + align:start position:0% +study +so usually when you think about the + + align:start position:0% +so usually when you think about the + + + align:start position:0% +so usually when you think about the +public debate about cash transfers and + + align:start position:0% +public debate about cash transfers and + + + align:start position:0% +public debate about cash transfers and +about sort of like welfare programs for + + align:start position:0% +about sort of like welfare programs for + + + align:start position:0% +about sort of like welfare programs for +the poor + + align:start position:0% +the poor + + + align:start position:0% +the poor +often sort of the right-wing response is + + align:start position:0% +often sort of the right-wing response is + + + align:start position:0% +often sort of the right-wing response is +like well the poor are going to be lazy + + align:start position:0% +like well the poor are going to be lazy + + + align:start position:0% +like well the poor are going to be lazy +and they're not going to work and + + align:start position:0% +and they're not going to work and + + + align:start position:0% +and they're not going to work and +they're like you know + + align:start position:0% +they're like you know + + + align:start position:0% +they're like you know +um what about effort and so on and so + + align:start position:0% +um what about effort and so on and so + + + align:start position:0% +um what about effort and so on and so +forth and they get used to the money and + + align:start position:0% +forth and they get used to the money and + + + align:start position:0% +forth and they get used to the money and +then they + + align:start position:0% +then they + + + align:start position:0% +then they +don't work hard enough eventually well + + align:start position:0% +don't work hard enough eventually well + + + align:start position:0% +don't work hard enough eventually well +the evidence that we have here + + align:start position:0% +the evidence that we have here + + + align:start position:0% +the evidence that we have here +in our paper seems to say in fact the + + align:start position:0% +in our paper seems to say in fact the + + + align:start position:0% +in our paper seems to say in fact the +opposite that is to say + + align:start position:0% +opposite that is to say + + + align:start position:0% +opposite that is to say +uh workers when you alleviate the + + align:start position:0% +uh workers when you alleviate the + + + align:start position:0% +uh workers when you alleviate the +financial constraints when you give them + + align:start position:0% +financial constraints when you give them + + + align:start position:0% +financial constraints when you give them +cash to become + + align:start position:0% +cash to become + + + align:start position:0% +cash to become +more productive and they work harder + + align:start position:0% +more productive and they work harder + + + align:start position:0% +more productive and they work harder +than um + + align:start position:0% +than um + + + align:start position:0% +than um +otherwise granted we don't have any + + align:start position:0% +otherwise granted we don't have any + + + align:start position:0% +otherwise granted we don't have any +labor supply response what i'm showing + + align:start position:0% +labor supply response what i'm showing + + + align:start position:0% +labor supply response what i'm showing +you here is essentially productivity + + align:start position:0% +you here is essentially productivity + + + align:start position:0% +you here is essentially productivity +which is you know + + align:start position:0% +which is you know + + + align:start position:0% +which is you know +how hard a worker is working or how much + + align:start position:0% +how hard a worker is working or how much + + + align:start position:0% +how hard a worker is working or how much +our workers producing per + + align:start position:0% +our workers producing per + + + align:start position:0% +our workers producing per +hour work but i think similar things + + align:start position:0% +hour work but i think similar things + + + align:start position:0% +hour work but i think similar things +could be due for + + align:start position:0% +could be due for + + + align:start position:0% +could be due for +two for cash transfers and there's some + + align:start position:0% +two for cash transfers and there's some + + + align:start position:0% +two for cash transfers and there's some +quite interesting evidence on cash + + align:start position:0% +quite interesting evidence on cash + + + align:start position:0% +quite interesting evidence on cash +transfer + + align:start position:0% +transfer + + + align:start position:0% +transfer +programs so both cash transfer + + align:start position:0% +programs so both cash transfer + + + align:start position:0% +programs so both cash transfer +and um in particular um what's called + + align:start position:0% +and um in particular um what's called + + + align:start position:0% +and um in particular um what's called +ultra poor programs which is sort of + + align:start position:0% +ultra poor programs which is sort of + + + align:start position:0% +ultra poor programs which is sort of +these + + align:start position:0% +these + + + align:start position:0% +these +uh multi-faceted uh asset programs + + align:start position:0% +uh multi-faceted uh asset programs + + + align:start position:0% +uh multi-faceted uh asset programs +leads to large and sustained increases + + align:start position:0% +leads to large and sustained increases + + + align:start position:0% +leads to large and sustained increases +in assets savings consumptions etc + + align:start position:0% +in assets savings consumptions etc + + + align:start position:0% +in assets savings consumptions etc +that is to say once you provide people + + align:start position:0% +that is to say once you provide people + + + align:start position:0% +that is to say once you provide people +um with financial resources when they're + + align:start position:0% +um with financial resources when they're + + + align:start position:0% +um with financial resources when they're +very poor + + align:start position:0% +very poor + + + align:start position:0% +very poor +not only do they better in the short run + + align:start position:0% +not only do they better in the short run + + + align:start position:0% +not only do they better in the short run +but in the case of the outdoor poor + + align:start position:0% +but in the case of the outdoor poor + + + align:start position:0% +but in the case of the outdoor poor +programs in the long run + + align:start position:0% +programs in the long run + + + align:start position:0% +programs in the long run +three to five years later people are + + align:start position:0% +three to five years later people are + + + align:start position:0% +three to five years later people are +doing better in terms of like + + align:start position:0% +doing better in terms of like + + + align:start position:0% +doing better in terms of like +having more assets saving more consuming + + align:start position:0% +having more assets saving more consuming + + + align:start position:0% +having more assets saving more consuming +more um + + align:start position:0% +more um + + + align:start position:0% +more um +and so on um and that seems to say that + + align:start position:0% +and so on um and that seems to say that + + + align:start position:0% +and so on um and that seems to say that +uh there might be some things an issue + + align:start position:0% +uh there might be some things an issue + + + align:start position:0% +uh there might be some things an issue +going on + + align:start position:0% +going on + + + align:start position:0% +going on +some form of like a poverty trap going + + align:start position:0% +some form of like a poverty trap going + + + align:start position:0% +some form of like a poverty trap going +on and sort of some of the underlying + + align:start position:0% +on and sort of some of the underlying + + + align:start position:0% +on and sort of some of the underlying +potential channels might be things like + + align:start position:0% +potential channels might be things like + + + align:start position:0% +potential channels might be things like +scarcity stress + + align:start position:0% +scarcity stress + + + align:start position:0% +scarcity stress +mental health and so on i'm going to + + align:start position:0% +mental health and so on i'm going to + + + align:start position:0% +mental health and so on i'm going to +talk a little bit about mental health + + align:start position:0% +talk a little bit about mental health + + + align:start position:0% +talk a little bit about mental health +and stress + + align:start position:0% +and stress + + + align:start position:0% +and stress +in a second but essentially if there are + + align:start position:0% +in a second but essentially if there are + + + align:start position:0% +in a second but essentially if there are +these types of effects going on + + align:start position:0% +these types of effects going on + + + align:start position:0% +these types of effects going on +for the government or any other sort of + + align:start position:0% +for the government or any other sort of + + + align:start position:0% +for the government or any other sort of +public policy + + align:start position:0% +public policy + + + align:start position:0% +public policy +um these kinds of programs conditional + + align:start position:0% +um these kinds of programs conditional + + + align:start position:0% +um these kinds of programs conditional +language conditional cash transfers + + align:start position:0% +language conditional cash transfers + + + align:start position:0% +language conditional cash transfers +um have in addition to having the + + align:start position:0% +um have in addition to having the + + + align:start position:0% +um have in addition to having the +advantage of like you know improving + + align:start position:0% +advantage of like you know improving + + + align:start position:0% +advantage of like you know improving +people's well-being and + + align:start position:0% +people's well-being and + + + align:start position:0% +people's well-being and +having like high you know marginal uh uh + + align:start position:0% +having like high you know marginal uh uh + + + align:start position:0% +having like high you know marginal uh uh +you're telling your money when they're + + align:start position:0% +you're telling your money when they're + + + align:start position:0% +you're telling your money when they're +very poor + + align:start position:0% +very poor + + + align:start position:0% +very poor +it might also in addition make people + + align:start position:0% +it might also in addition make people + + + align:start position:0% +it might also in addition make people +more productive uh as opposed to like + + align:start position:0% +more productive uh as opposed to like + + + align:start position:0% +more productive uh as opposed to like +you know working less + + align:start position:0% +you know working less + + + align:start position:0% +you know working less +um or um the like so i think those two + + align:start position:0% +um or um the like so i think those two + + + align:start position:0% +um or um the like so i think those two +things i think are sort of + + align:start position:0% +things i think are sort of + + + align:start position:0% +things i think are sort of +um um uh uh the the takeaways + + align:start position:0% +um um uh uh the the takeaways + + + align:start position:0% +um um uh uh the the takeaways +if one wanted to understand optimal pace + + align:start position:0% +if one wanted to understand optimal pace + + + align:start position:0% +if one wanted to understand optimal pace +structures one would have to do longer + + align:start position:0% +structures one would have to do longer + + + align:start position:0% +structures one would have to do longer +longer and types of experiments as + + align:start position:0% +longer and types of experiments as + + + align:start position:0% +longer and types of experiments as +natalie um + + align:start position:0% +natalie um + + + align:start position:0% +natalie um +uh pointed out so there's essentially + + align:start position:0% +uh pointed out so there's essentially + + + align:start position:0% +uh pointed out so there's essentially +the way we set this up is um we + + align:start position:0% +the way we set this up is um we + + + align:start position:0% +the way we set this up is um we +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +people i'm sorry this is my slack uh + + align:start position:0% +people i'm sorry this is my slack uh + + + align:start position:0% +people i'm sorry this is my slack uh +pay people to um + + align:start position:0% + + + + align:start position:0% + +uh people through the employer + + align:start position:0% +uh people through the employer + + + align:start position:0% +uh people through the employer +essentially said okay the employer is + + align:start position:0% +essentially said okay the employer is + + + align:start position:0% +essentially said okay the employer is +paying you now earlier versus later + + align:start position:0% +paying you now earlier versus later + + + align:start position:0% +paying you now earlier versus later +and naturally then the worker might just + + align:start position:0% +and naturally then the worker might just + + + align:start position:0% +and naturally then the worker might just +happier doing better financially but + + align:start position:0% +happier doing better financially but + + + align:start position:0% +happier doing better financially but +also like like the employer better say + + align:start position:0% +also like like the employer better say + + + align:start position:0% +also like like the employer better say +like look you just paid me early + + align:start position:0% +like look you just paid me early + + + align:start position:0% +like look you just paid me early +and i trust you more that you're going + + align:start position:0% +and i trust you more that you're going + + + align:start position:0% +and i trust you more that you're going +to be paid me in the future maybe that's + + align:start position:0% +to be paid me in the future maybe that's + + + align:start position:0% +to be paid me in the future maybe that's +some form of gift giving a reciprocity + + align:start position:0% +some form of gift giving a reciprocity + + + align:start position:0% +some form of gift giving a reciprocity +i'm sort of happy about harder um to + + align:start position:0% +i'm sort of happy about harder um to + + + align:start position:0% +i'm sort of happy about harder um to +make the employer happy + + align:start position:0% + + + + align:start position:0% + +several things to get at this and the + + align:start position:0% +several things to get at this and the + + + align:start position:0% +several things to get at this and the +most important part perhaps we also have + + align:start position:0% +most important part perhaps we also have + + + align:start position:0% +most important part perhaps we also have +like + + align:start position:0% +like + + + align:start position:0% +like +uh we announce essentially the structure + + align:start position:0% +uh we announce essentially the structure + + + align:start position:0% +uh we announce essentially the structure +a few days before the actual payment is + + align:start position:0% +a few days before the actual payment is + + + align:start position:0% +a few days before the actual payment is +made that is to say on day five we + + align:start position:0% +made that is to say on day five we + + + align:start position:0% +made that is to say on day five we +announce and say on day eight + + align:start position:0% +announce and say on day eight + + + align:start position:0% +announce and say on day eight +you're going to be paid versus we don't + + align:start position:0% +you're going to be paid versus we don't + + + align:start position:0% +you're going to be paid versus we don't +announce so you say you're going to be + + align:start position:0% +announce so you say you're going to be + + + align:start position:0% +announce so you say you're going to be +paid only later + + align:start position:0% +paid only later + + + align:start position:0% +paid only later +at the end of the study and so if you + + align:start position:0% +at the end of the study and so if you + + + align:start position:0% +at the end of the study and so if you +think you know this is about + + align:start position:0% +think you know this is about + + + align:start position:0% +think you know this is about +reciprocity or like um people being + + align:start position:0% +reciprocity or like um people being + + + align:start position:0% +reciprocity or like um people being +feelings towards the employer + + align:start position:0% +feelings towards the employer + + + align:start position:0% +feelings towards the employer +you would think that then workers should + + align:start position:0% +you would think that then workers should + + + align:start position:0% +you would think that then workers should +then already be working harder + + align:start position:0% +then already be working harder + + + align:start position:0% +then already be working harder +once they're here about when they get + + align:start position:0% +once they're here about when they get + + + align:start position:0% +once they're here about when they get +these kind of announcement um effects + + align:start position:0% +these kind of announcement um effects + + + align:start position:0% +these kind of announcement um effects +and it seems to be the case that there's + + align:start position:0% +and it seems to be the case that there's + + + align:start position:0% +and it seems to be the case that there's +essentially no announcement effect + + align:start position:0% +essentially no announcement effect + + + align:start position:0% +essentially no announcement effect +whatsoever + + align:start position:0% +whatsoever + + + align:start position:0% +whatsoever +uh work uh only become productive + + align:start position:0% +uh work uh only become productive + + + align:start position:0% +uh work uh only become productive +uh pretty much precisely once they've + + align:start position:0% +uh pretty much precisely once they've + + + align:start position:0% +uh pretty much precisely once they've +received their uh + + align:start position:0% +received their uh + + + align:start position:0% +received their uh +cash on hand which is very much + + align:start position:0% +cash on hand which is very much + + + align:start position:0% +cash on hand which is very much +consistent with what i showed you + + align:start position:0% +consistent with what i showed you + + + align:start position:0% +consistent with what i showed you +earlier uh + + align:start position:0% +earlier uh + + + align:start position:0% +earlier uh +the results from money adele um in their + + align:start position:0% +the results from money adele um in their + + + align:start position:0% +the results from money adele um in their +study + + align:start position:0% +study + + + align:start position:0% +study +it seems to really be the case that + + align:start position:0% +it seems to really be the case that + + + align:start position:0% +it seems to really be the case that +knowing that somebody will be paid + + align:start position:0% +knowing that somebody will be paid + + + align:start position:0% +knowing that somebody will be paid +is really not helping workers both from + + align:start position:0% +is really not helping workers both from + + + align:start position:0% +is really not helping workers both from +like or making + + align:start position:0% +like or making + + + align:start position:0% +like or making +workers more productive both in the form + + align:start position:0% +workers more productive both in the form + + + align:start position:0% +workers more productive both in the form +of + + align:start position:0% +of + + + align:start position:0% +of +their relationship or due to their + + align:start position:0% +their relationship or due to their + + + align:start position:0% +their relationship or due to their +relationship with the employer but + + align:start position:0% +relationship with the employer but + + + align:start position:0% +relationship with the employer but +also due to um + + align:start position:0% +also due to um + + + align:start position:0% +also due to um +uh other effects including uh + + align:start position:0% +uh other effects including uh + + + align:start position:0% +uh other effects including uh +sort of like perhaps their their worries + + align:start position:0% +sort of like perhaps their their worries + + + align:start position:0% +sort of like perhaps their their worries +or concerns that they might have about + + align:start position:0% +or concerns that they might have about + + + align:start position:0% +or concerns that they might have about +so it seems to me that similarly from + + align:start position:0% +so it seems to me that similarly from + + + align:start position:0% +so it seems to me that similarly from +the money adult + + align:start position:0% +the money adult + + + align:start position:0% +the money adult +uh paper so like when workers are + + align:start position:0% +uh paper so like when workers are + + + align:start position:0% +uh paper so like when workers are +have done their harvest and you have the + + align:start position:0% +have done their harvest and you have the + + + align:start position:0% +have done their harvest and you have the +harvest in front of you + + align:start position:0% +harvest in front of you + + + align:start position:0% +harvest in front of you +and you know it's worth so many rupees + + align:start position:0% +and you know it's worth so many rupees + + + align:start position:0% +and you know it's worth so many rupees +uh that doesn't seem to increase their + + align:start position:0% +uh that doesn't seem to increase their + + + align:start position:0% +uh that doesn't seem to increase their +cognitive scores that's what i was + + align:start position:0% +cognitive scores that's what i was + + + align:start position:0% +cognitive scores that's what i was +showing you earlier really what it seems + + align:start position:0% +showing you earlier really what it seems + + + align:start position:0% +showing you earlier really what it seems +to be is like you have to be actually + + align:start position:0% +to be is like you have to be actually + + + align:start position:0% +to be is like you have to be actually +paid so once workers + + align:start position:0% +paid so once workers + + + align:start position:0% +paid so once workers +actually have the cash in hand only then + + align:start position:0% +actually have the cash in hand only then + + + align:start position:0% +actually have the cash in hand only then +the cognitive function goes up + + align:start position:0% +the cognitive function goes up + + + align:start position:0% +the cognitive function goes up +uh there seems to be something about + + align:start position:0% +uh there seems to be something about + + + align:start position:0% +uh there seems to be something about +this this + + align:start position:0% + + + + align:start position:0% + +example i have for you is like suppose + + align:start position:0% +example i have for you is like suppose + + + align:start position:0% +example i have for you is like suppose +you have to pay your bills suppose + + align:start position:0% +you have to pay your bills suppose + + + align:start position:0% +you have to pay your bills suppose +you're like sort of like don't have + + align:start position:0% +you're like sort of like don't have + + + align:start position:0% +you're like sort of like don't have +enough money and then you know on the + + align:start position:0% +enough money and then you know on the + + + align:start position:0% +enough money and then you know on the +first the months you're going to be paid + + align:start position:0% +first the months you're going to be paid + + + align:start position:0% +first the months you're going to be paid +your stipend or whatever + + align:start position:0% +your stipend or whatever + + + align:start position:0% +your stipend or whatever +as a student there's something uh uh + + align:start position:0% +as a student there's something uh uh + + + align:start position:0% +as a student there's something uh uh +distinctly different from + + align:start position:0% +distinctly different from + + + align:start position:0% +distinctly different from +having actually been paid the money on + + align:start position:0% +having actually been paid the money on + + + align:start position:0% +having actually been paid the money on +your bank account and having it + + align:start position:0% +your bank account and having it + + + align:start position:0% +your bank account and having it +uh in your possession that is yours or + + align:start position:0% +uh in your possession that is yours or + + + align:start position:0% +uh in your possession that is yours or +being sent a check or whatever + + align:start position:0% +being sent a check or whatever + + + align:start position:0% +being sent a check or whatever +as opposed to knowing it's going to come + + align:start position:0% +as opposed to knowing it's going to come + + + align:start position:0% +as opposed to knowing it's going to come +in two days and you have your + + align:start position:0% +in two days and you have your + + + align:start position:0% +in two days and you have your +outstanding credit card bills + + align:start position:0% +outstanding credit card bills + + + align:start position:0% +outstanding credit card bills +even if you know that you can pay them + + align:start position:0% +even if you know that you can pay them + + + align:start position:0% +even if you know that you can pay them +that's in something from introspection + + align:start position:0% +that's in something from introspection + + + align:start position:0% +that's in something from introspection +the best example i have for you + + align:start position:0% +the best example i have for you + + + align:start position:0% +the best example i have for you +but it seems to be and then be right in + + align:start position:0% +but it seems to be and then be right in + + + align:start position:0% +but it seems to be and then be right in +some sense there could have been some + + align:start position:0% +some sense there could have been some + + + align:start position:0% +some sense there could have been some +effects of just telling workers should + + align:start position:0% +effects of just telling workers should + + + align:start position:0% +effects of just telling workers should +be gonna be paid early versus later + + align:start position:0% +be gonna be paid early versus later + + + align:start position:0% +be gonna be paid early versus later +but it doesn't seem to be the case it + + align:start position:0% +but it doesn't seem to be the case it + + + align:start position:0% +but it doesn't seem to be the case it +really seems to be the case of like + + align:start position:0% +really seems to be the case of like + + + align:start position:0% +really seems to be the case of like +receiving the money having cash in hand + + align:start position:0% +receiving the money having cash in hand + + + align:start position:0% +receiving the money having cash in hand +and then being able to pay the money + + align:start position:0% +and then being able to pay the money + + + align:start position:0% +and then being able to pay the money +lender or pay or essentially some + + align:start position:0% +lender or pay or essentially some + + + align:start position:0% +lender or pay or essentially some +uh person that you owe money some money + + align:start position:0% +uh person that you owe money some money + + + align:start position:0% +uh person that you owe money some money +back seems to be what's quite important + + align:start position:0% +back seems to be what's quite important + + + align:start position:0% +back seems to be what's quite important +for generating those kinds of events + + align:start position:0% + + + + align:start position:0% + +okay so let's move on + + align:start position:0% +okay so let's move on + + + align:start position:0% +okay so let's move on +um i already talked about this + + align:start position:0% +um i already talked about this + + + align:start position:0% +um i already talked about this +essentially yeah so there seems to be + + align:start position:0% +essentially yeah so there seems to be + + + align:start position:0% +essentially yeah so there seems to be +these large effects + + align:start position:0% +these large effects + + + align:start position:0% +these large effects +of uh uh ultra poor programs which + + align:start position:0% +of uh uh ultra poor programs which + + + align:start position:0% +of uh uh ultra poor programs which +seem to say that there might be some um + + align:start position:0% +seem to say that there might be some um + + + align:start position:0% +seem to say that there might be some um +underlying behavioral + + align:start position:0% +underlying behavioral + + + align:start position:0% +underlying behavioral +or other poverty trap going on and sort + + align:start position:0% +or other poverty trap going on and sort + + + align:start position:0% +or other poverty trap going on and sort +of we don't have the answer to that but + + align:start position:0% +of we don't have the answer to that but + + + align:start position:0% +of we don't have the answer to that but +one hypothesis is that some of the + + align:start position:0% +one hypothesis is that some of the + + + align:start position:0% +one hypothesis is that some of the +underlying + + align:start position:0% +underlying + + + align:start position:0% +underlying +psychological issues might be + + align:start position:0% +psychological issues might be + + + align:start position:0% +psychological issues might be +responsible + + align:start position:0% +responsible + + + align:start position:0% +responsible +for that now what are other + + align:start position:0% +for that now what are other + + + align:start position:0% +for that now what are other +poverty so poverty entails a bunch of + + align:start position:0% +poverty so poverty entails a bunch of + + + align:start position:0% +poverty so poverty entails a bunch of +different deprivations beyond money + + align:start position:0% +different deprivations beyond money + + + align:start position:0% +different deprivations beyond money +including malnutrition higher levels of + + align:start position:0% +including malnutrition higher levels of + + + align:start position:0% +including malnutrition higher levels of +stress + + align:start position:0% +stress + + + align:start position:0% +stress +sleep deprivation people's sleeping + + align:start position:0% +sleep deprivation people's sleeping + + + align:start position:0% +sleep deprivation people's sleeping +conditions tend to be terrible + + align:start position:0% +conditions tend to be terrible + + + align:start position:0% +conditions tend to be terrible +uh noise pollution uh the poor more + + align:start position:0% +uh noise pollution uh the poor more + + + align:start position:0% +uh noise pollution uh the poor more +disproportionately + + align:start position:0% +disproportionately + + + align:start position:0% +disproportionately +exposed to noise there's environmental + + align:start position:0% +exposed to noise there's environmental + + + align:start position:0% +exposed to noise there's environmental +pollution + + align:start position:0% +pollution + + + align:start position:0% +pollution +in particular sort of air that the poor + + align:start position:0% +in particular sort of air that the poor + + + align:start position:0% +in particular sort of air that the poor +are much more exposed to + + align:start position:0% +are much more exposed to + + + align:start position:0% +are much more exposed to +heat the poor often don't have access to + + align:start position:0% +heat the poor often don't have access to + + + align:start position:0% +heat the poor often don't have access to +um + + align:start position:0% +um + + + align:start position:0% +um +or heat or temperature more generally + + align:start position:0% +or heat or temperature more generally + + + align:start position:0% +or heat or temperature more generally +the poor heat poor + + align:start position:0% +the poor heat poor + + + align:start position:0% +the poor heat poor +uh have uh are more exposed to high + + align:start position:0% +uh have uh are more exposed to high + + + align:start position:0% +uh have uh are more exposed to high +temperature and don't have access to acs + + align:start position:0% +temperature and don't have access to acs + + + align:start position:0% +temperature and don't have access to acs +often + + align:start position:0% +often + + + align:start position:0% +often +there's also some form of like stigma + + align:start position:0% +there's also some form of like stigma + + + align:start position:0% +there's also some form of like stigma +and exclusion which might have certain + + align:start position:0% +and exclusion which might have certain + + + align:start position:0% +and exclusion which might have certain +cognitive and other effects + + align:start position:0% +cognitive and other effects + + + align:start position:0% +cognitive and other effects +um there's some evidence of + + align:start position:0% +um there's some evidence of + + + align:start position:0% +um there's some evidence of +disproportional + + align:start position:0% +disproportional + + + align:start position:0% +disproportional +uh disproportionate substance abuse that + + align:start position:0% +uh disproportionate substance abuse that + + + align:start position:0% +uh disproportionate substance abuse that +showed you some + + align:start position:0% +showed you some + + + align:start position:0% +showed you some +evidence of increased + + align:start position:0% +evidence of increased + + + align:start position:0% +evidence of increased +excessive drinking and there's also + + align:start position:0% +excessive drinking and there's also + + + align:start position:0% +excessive drinking and there's also +quite a bit of evidence of uh increased + + align:start position:0% +quite a bit of evidence of uh increased + + + align:start position:0% +quite a bit of evidence of uh increased +mental + + align:start position:0% +mental + + + align:start position:0% +mental +uh illness among especially uh among the + + align:start position:0% +uh illness among especially uh among the + + + align:start position:0% +uh illness among especially uh among the +poor so + + align:start position:0% +poor so + + + align:start position:0% +poor so +within any given location the poor are + + align:start position:0% +within any given location the poor are + + + align:start position:0% +within any given location the poor are +disproportionately affected by + + align:start position:0% +disproportionately affected by + + + align:start position:0% +disproportionately affected by +mental illness including things like + + align:start position:0% +mental illness including things like + + + align:start position:0% +mental illness including things like +depression and anxiety + + align:start position:0% +depression and anxiety + + + align:start position:0% +depression and anxiety +but there's a bunch of research in other + + align:start position:0% +but there's a bunch of research in other + + + align:start position:0% +but there's a bunch of research in other +settings that shows that + + align:start position:0% +settings that shows that + + + align:start position:0% +settings that shows that +these factors each of these factors + + align:start position:0% +these factors each of these factors + + + align:start position:0% +these factors each of these factors +affect either health and or cognitive + + align:start position:0% +affect either health and or cognitive + + + align:start position:0% +affect either health and or cognitive +function and so you might wonder you + + align:start position:0% +function and so you might wonder you + + + align:start position:0% +function and so you might wonder you +know how are these factors then + + align:start position:0% +know how are these factors then + + + align:start position:0% +know how are these factors then +affecting people's um + + align:start position:0% +affecting people's um + + + align:start position:0% +affecting people's um +decision making and choices and just to + + align:start position:0% +decision making and choices and just to + + + align:start position:0% +decision making and choices and just to +give you some example of this there's + + align:start position:0% +give you some example of this there's + + + align:start position:0% +give you some example of this there's +some work that we have done in + + align:start position:0% +some work that we have done in + + + align:start position:0% +some work that we have done in +in chennai i also like to do some sense + + align:start position:0% +in chennai i also like to do some sense + + + align:start position:0% +in chennai i also like to do some sense +of what this looks like uh the poor + + align:start position:0% +of what this looks like uh the poor + + + align:start position:0% +of what this looks like uh the poor +essentially tend to have very very + + align:start position:0% +essentially tend to have very very + + + align:start position:0% +essentially tend to have very very +challenging sleeping conditions + + align:start position:0% +challenging sleeping conditions + + + align:start position:0% +challenging sleeping conditions +there's dust noise mosquitoes people + + align:start position:0% +there's dust noise mosquitoes people + + + align:start position:0% +there's dust noise mosquitoes people +sleep in the same room people sleep + + align:start position:0% +sleep in the same room people sleep + + + align:start position:0% +sleep in the same room people sleep +outside + + align:start position:0% +outside + + + align:start position:0% +outside +in the middle of the street and it is + + align:start position:0% +in the middle of the street and it is + + + align:start position:0% +in the middle of the street and it is +it's hot + + align:start position:0% +it's hot + + + align:start position:0% +it's hot +as people sleep on the floor so + + align:start position:0% +as people sleep on the floor so + + + align:start position:0% +as people sleep on the floor so +essentially any challenging sleeping + + align:start position:0% +essentially any challenging sleeping + + + align:start position:0% +essentially any challenging sleeping +condition that you can think of you can + + align:start position:0% +condition that you can think of you can + + + align:start position:0% +condition that you can think of you can +find it among the urban poor so one + + align:start position:0% +find it among the urban poor so one + + + align:start position:0% +find it among the urban poor so one +question you might ask us well then + + align:start position:0% +question you might ask us well then + + + align:start position:0% +question you might ask us well then +does um this lack of sleep of good sleep + + align:start position:0% +does um this lack of sleep of good sleep + + + align:start position:0% +does um this lack of sleep of good sleep +it affect people's + + align:start position:0% + + + + align:start position:0% + +capacity to work on their decision + + align:start position:0% +capacity to work on their decision + + + align:start position:0% +capacity to work on their decision +making and so in our study what we do is + + align:start position:0% +making and so in our study what we do is + + + align:start position:0% +making and so in our study what we do is +we objectively measure sleep + + align:start position:0% +we objectively measure sleep + + + align:start position:0% +we objectively measure sleep +quantity and quality in chennai and + + align:start position:0% +quantity and quality in chennai and + + + align:start position:0% +quantity and quality in chennai and +today document severe sleep deprivation + + align:start position:0% +today document severe sleep deprivation + + + align:start position:0% +today document severe sleep deprivation +and alarmingly + + align:start position:0% +and alarmingly + + + align:start position:0% +and alarmingly +low um quality of sleep in this setting + + align:start position:0% +low um quality of sleep in this setting + + + align:start position:0% +low um quality of sleep in this setting +what do i mean by this + + align:start position:0% +what do i mean by this + + + align:start position:0% +what do i mean by this +people sleep on average about 6.5 hours + + align:start position:0% +people sleep on average about 6.5 hours + + + align:start position:0% +people sleep on average about 6.5 hours +per night + + align:start position:0% +per night + + + align:start position:0% +per night +and the quality of their sleep is low um + + align:start position:0% +and the quality of their sleep is low um + + + align:start position:0% +and the quality of their sleep is low um +which is + + align:start position:0% +which is + + + align:start position:0% +which is +uh one measurement that of that is like + + align:start position:0% +uh one measurement that of that is like + + + align:start position:0% +uh one measurement that of that is like +their uh + + align:start position:0% +their uh + + + align:start position:0% +their uh +fraction of time their sleep uh among + + align:start position:0% +fraction of time their sleep uh among + + + align:start position:0% +fraction of time their sleep uh among +the fraction of + + align:start position:0% +the fraction of + + + align:start position:0% +the fraction of +the time that they spend in bed is about + + align:start position:0% +the time that they spend in bed is about + + + align:start position:0% +the time that they spend in bed is about +70 that's what's referred to as like + + align:start position:0% +70 that's what's referred to as like + + + align:start position:0% +70 that's what's referred to as like +sleep efficiency + + align:start position:0% +sleep efficiency + + + align:start position:0% +sleep efficiency +sleep efficiency is um way higher in + + align:start position:0% +sleep efficiency is um way higher in + + + align:start position:0% +sleep efficiency is um way higher in +which country it's about + + align:start position:0% +which country it's about + + + align:start position:0% +which country it's about +85 to 90 so if the rich spend like + + align:start position:0% +85 to 90 so if the rich spend like + + + align:start position:0% +85 to 90 so if the rich spend like +an hour in bed they spend about like 55 + + align:start position:0% +an hour in bed they spend about like 55 + + + align:start position:0% +an hour in bed they spend about like 55 +or something minutes uh + + align:start position:0% +or something minutes uh + + + align:start position:0% +or something minutes uh +asleep if the poor do that um it's about + + align:start position:0% +asleep if the poor do that um it's about + + + align:start position:0% +asleep if the poor do that um it's about +uh 40 something minutes so essentially + + align:start position:0% +uh 40 something minutes so essentially + + + align:start position:0% +uh 40 something minutes so essentially +there's lots of awakenings + + align:start position:0% +there's lots of awakenings + + + align:start position:0% +there's lots of awakenings +and as a consequence in our sample + + align:start position:0% +and as a consequence in our sample + + + align:start position:0% +and as a consequence in our sample +people sleep about like five and a half + + align:start position:0% +people sleep about like five and a half + + + align:start position:0% +people sleep about like five and a half +hours + + align:start position:0% +hours + + + align:start position:0% +hours +um per night now then uh what we do is + + align:start position:0% +um per night now then uh what we do is + + + align:start position:0% +um per night now then uh what we do is +we have two interventions to increase + + align:start position:0% +we have two interventions to increase + + + align:start position:0% +we have two interventions to increase +sleep + + align:start position:0% +sleep + + + align:start position:0% +sleep +we provide people information sleep + + align:start position:0% +we provide people information sleep + + + align:start position:0% +we provide people information sleep +devices um + + align:start position:0% +devices um + + + align:start position:0% +devices um +and sort of uh which is like mattress + + align:start position:0% +and sort of uh which is like mattress + + + align:start position:0% +and sort of uh which is like mattress +earplugs eye shades and so on + + align:start position:0% +earplugs eye shades and so on + + + align:start position:0% +earplugs eye shades and so on +and we increase sleep by quite a bit for + + align:start position:0% +and we increase sleep by quite a bit for + + + align:start position:0% +and we increase sleep by quite a bit for +about um three weeks and then this + + align:start position:0% +about um three weeks and then this + + + align:start position:0% +about um three weeks and then this +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +we also have an intervention as an avid + + align:start position:0% +we also have an intervention as an avid + + + align:start position:0% +we also have an intervention as an avid +dimension that offers people naps at the + + align:start position:0% +dimension that offers people naps at the + + + align:start position:0% +dimension that offers people naps at the +office + + align:start position:0% +office + + + align:start position:0% +office +which increases both or provides like + + align:start position:0% +which increases both or provides like + + + align:start position:0% +which increases both or provides like +high quality and high + + align:start position:0% +high quality and high + + + align:start position:0% +high quality and high +quality of sleep in that setting now + + align:start position:0% +quality of sleep in that setting now + + + align:start position:0% +quality of sleep in that setting now +what we find then is um somewhat + + align:start position:0% +what we find then is um somewhat + + + align:start position:0% +what we find then is um somewhat +surprisingly that actually increasing + + align:start position:0% +surprisingly that actually increasing + + + align:start position:0% +surprisingly that actually increasing +people's night sleep does + + align:start position:0% +people's night sleep does + + + align:start position:0% +people's night sleep does +very little so like people sleep about + + align:start position:0% +very little so like people sleep about + + + align:start position:0% +very little so like people sleep about +like you know 20 to 30 minutes more + + align:start position:0% +like you know 20 to 30 minutes more + + + align:start position:0% +like you know 20 to 30 minutes more +every night for three weeks + + align:start position:0% +every night for three weeks + + + align:start position:0% +every night for three weeks +and they measure the labor supply we + + align:start position:0% +and they measure the labor supply we + + + align:start position:0% +and they measure the labor supply we +hire them for about that time + + align:start position:0% +hire them for about that time + + + align:start position:0% +hire them for about that time +people are not doing better in any way + + align:start position:0% +people are not doing better in any way + + + align:start position:0% +people are not doing better in any way +in terms of like people not working more + + align:start position:0% +in terms of like people not working more + + + align:start position:0% +in terms of like people not working more +people are not more productive people + + align:start position:0% +people are not more productive people + + + align:start position:0% +people are not more productive people +are not doing better in cognitive tasks + + align:start position:0% +are not doing better in cognitive tasks + + + align:start position:0% +are not doing better in cognitive tasks +they're not happier + + align:start position:0% +they're not happier + + + align:start position:0% +they're not happier +and so on and so forth they also don't + + align:start position:0% +and so on and so forth they also don't + + + align:start position:0% +and so on and so forth they also don't +make different decisions + + align:start position:0% +make different decisions + + + align:start position:0% +make different decisions +and if anything you know they decrease + + align:start position:0% +and if anything you know they decrease + + + align:start position:0% +and if anything you know they decrease +their labor supply they actually work + + align:start position:0% +their labor supply they actually work + + + align:start position:0% +their labor supply they actually work +fewer hours why is that well because + + align:start position:0% +fewer hours why is that well because + + + align:start position:0% +fewer hours why is that well because +people are spending so much more time in + + align:start position:0% +people are spending so much more time in + + + align:start position:0% +people are spending so much more time in +bed + + align:start position:0% +bed + + + align:start position:0% +bed +um they have less time available during + + align:start position:0% +um they have less time available during + + + align:start position:0% +um they have less time available during +the day and some of that time goes into + + align:start position:0% +the day and some of that time goes into + + + align:start position:0% +the day and some of that time goes into +like working + + align:start position:0% +like working + + + align:start position:0% +like working +a few hours um now in contrast an app + + align:start position:0% +a few hours um now in contrast an app + + + align:start position:0% +a few hours um now in contrast an app +treatment um has pretty large effects on + + align:start position:0% +treatment um has pretty large effects on + + + align:start position:0% +treatment um has pretty large effects on +the productivity attention well-being + + align:start position:0% +the productivity attention well-being + + + align:start position:0% +the productivity attention well-being +patients and so on + + align:start position:0% +patients and so on + + + align:start position:0% +patients and so on +so it's not like sleep cannot affect + + align:start position:0% +so it's not like sleep cannot affect + + + align:start position:0% +so it's not like sleep cannot affect +people's outcomes in these settings + + align:start position:0% +people's outcomes in these settings + + + align:start position:0% +people's outcomes in these settings +but rather night sleep as it is does not + + align:start position:0% +but rather night sleep as it is does not + + + align:start position:0% +but rather night sleep as it is does not +really do very much + + align:start position:0% +really do very much + + + align:start position:0% +really do very much +at least the type of night sleep that + + align:start position:0% +at least the type of night sleep that + + + align:start position:0% +at least the type of night sleep that +people are getting + + align:start position:0% +people are getting + + + align:start position:0% +people are getting +and so what we then sort of um uh + + align:start position:0% +and so what we then sort of um uh + + + align:start position:0% +and so what we then sort of um uh +provide some evidence of that like + + align:start position:0% +provide some evidence of that like + + + align:start position:0% +provide some evidence of that like +what's really important here are the + + align:start position:0% +what's really important here are the + + + align:start position:0% +what's really important here are the +reason why people's + + align:start position:0% +reason why people's + + + align:start position:0% +reason why people's +sleep does not do very much in + + align:start position:0% +sleep does not do very much in + + + align:start position:0% +sleep does not do very much in +increasing their + + align:start position:0% +increasing their + + + align:start position:0% +increasing their +productivity or improving their outcomes + + align:start position:0% +productivity or improving their outcomes + + + align:start position:0% +productivity or improving their outcomes +is because the quality of sleep is so + + align:start position:0% +is because the quality of sleep is so + + + align:start position:0% +is because the quality of sleep is so +low + + align:start position:0% +low + + + align:start position:0% +low +so when we sort of look at the sample + + align:start position:0% +so when we sort of look at the sample + + + align:start position:0% +so when we sort of look at the sample +and look at like people who sleep better + + align:start position:0% +and look at like people who sleep better + + + align:start position:0% +and look at like people who sleep better +and worse at baseline at the beginning + + align:start position:0% +and worse at baseline at the beginning + + + align:start position:0% +and worse at baseline at the beginning +of the study + + align:start position:0% +of the study + + + align:start position:0% +of the study +people who sleep better at the beginning + + align:start position:0% +people who sleep better at the beginning + + + align:start position:0% +people who sleep better at the beginning +of the study they actually tend to have + + align:start position:0% +of the study they actually tend to have + + + align:start position:0% +of the study they actually tend to have +reasonably large effects on + + align:start position:0% +reasonably large effects on + + + align:start position:0% +reasonably large effects on +their productivity and contrast people + + align:start position:0% +their productivity and contrast people + + + align:start position:0% +their productivity and contrast people +who have + + align:start position:0% +who have + + + align:start position:0% +who have +bad sleep to start with like for them + + align:start position:0% +bad sleep to start with like for them + + + align:start position:0% +bad sleep to start with like for them +essentially increasing their sleep does + + align:start position:0% +essentially increasing their sleep does + + + align:start position:0% +essentially increasing their sleep does +nothing and potentially makes things + + align:start position:0% +nothing and potentially makes things + + + align:start position:0% +nothing and potentially makes things +um worse so what did we i do not want + + align:start position:0% +um worse so what did we i do not want + + + align:start position:0% +um worse so what did we i do not want +you to take away that like sleeping does + + align:start position:0% +you to take away that like sleeping does + + + align:start position:0% +you to take away that like sleeping does +not do anything + + align:start position:0% +not do anything + + + align:start position:0% +not do anything +uh and my t students are chronically + + align:start position:0% +uh and my t students are chronically + + + align:start position:0% +uh and my t students are chronically +undersleeping and you could be probably + + align:start position:0% +undersleeping and you could be probably + + + align:start position:0% +undersleeping and you could be probably +sleeping uh uh more both all of you or + + align:start position:0% +sleeping uh uh more both all of you or + + + align:start position:0% +sleeping uh uh more both all of you or +most of you + + align:start position:0% +most of you + + + align:start position:0% +most of you +essentially what what we learned from + + align:start position:0% +essentially what what we learned from + + + align:start position:0% +essentially what what we learned from +this is that when people's sleep + + align:start position:0% +this is that when people's sleep + + + align:start position:0% +this is that when people's sleep +conditions are really terrible + + align:start position:0% +conditions are really terrible + + + align:start position:0% +conditions are really terrible +well then um increasing um + + align:start position:0% +well then um increasing um + + + align:start position:0% +well then um increasing um +increasing one's sleep actually doesn't + + align:start position:0% +increasing one's sleep actually doesn't + + + align:start position:0% +increasing one's sleep actually doesn't +do very much the return on sleeping is + + align:start position:0% +do very much the return on sleeping is + + + align:start position:0% +do very much the return on sleeping is +just very very low + + align:start position:0% +just very very low + + + align:start position:0% +just very very low +and so what you learn in some ways that + + align:start position:0% +and so what you learn in some ways that + + + align:start position:0% +and so what you learn in some ways that +the poor at least in this + + align:start position:0% +the poor at least in this + + + align:start position:0% +the poor at least in this +setting the poor are actually doing um + + align:start position:0% +setting the poor are actually doing um + + + align:start position:0% +setting the poor are actually doing um +as well as they could in a sense that + + align:start position:0% +as well as they could in a sense that + + + align:start position:0% +as well as they could in a sense that +they do the best they can + + align:start position:0% +they do the best they can + + + align:start position:0% +they do the best they can +and since sleep is so bad or so terrible + + align:start position:0% +and since sleep is so bad or so terrible + + + align:start position:0% +and since sleep is so bad or so terrible +people sleep really badly + + align:start position:0% +people sleep really badly + + + align:start position:0% +people sleep really badly +um increasing their sleep does not do + + align:start position:0% +um increasing their sleep does not do + + + align:start position:0% +um increasing their sleep does not do +very much + + align:start position:0% +very much + + + align:start position:0% +very much +that's not to say like if you actually + + align:start position:0% +that's not to say like if you actually + + + align:start position:0% +that's not to say like if you actually +fix their sleeping conditions if you + + align:start position:0% +fix their sleeping conditions if you + + + align:start position:0% +fix their sleeping conditions if you +put everybody into like a nice hotel or + + align:start position:0% +put everybody into like a nice hotel or + + + align:start position:0% +put everybody into like a nice hotel or +a nice bedroom and or give them like a + + align:start position:0% +a nice bedroom and or give them like a + + + align:start position:0% +a nice bedroom and or give them like a +nice house + + align:start position:0% +nice house + + + align:start position:0% +nice house +and help them sleep better that wouldn't + + align:start position:0% +and help them sleep better that wouldn't + + + align:start position:0% +and help them sleep better that wouldn't +have potentially large effects + + align:start position:0% +have potentially large effects + + + align:start position:0% +have potentially large effects +but the study that we are we conducted + + align:start position:0% +but the study that we are we conducted + + + align:start position:0% +but the study that we are we conducted +was not doing that study that we + + align:start position:0% +was not doing that study that we + + + align:start position:0% +was not doing that study that we +conducted was essentially saying like + + align:start position:0% +conducted was essentially saying like + + + align:start position:0% +conducted was essentially saying like +take your sleep conditions as given + + align:start position:0% +take your sleep conditions as given + + + align:start position:0% +take your sleep conditions as given +and look at what happens when you + + align:start position:0% +and look at what happens when you + + + align:start position:0% +and look at what happens when you +increase people's um sleep duration for + + align:start position:0% +increase people's um sleep duration for + + + align:start position:0% +increase people's um sleep duration for +given um sleep quality and that doesn't + + align:start position:0% +given um sleep quality and that doesn't + + + align:start position:0% +given um sleep quality and that doesn't +do very much + + align:start position:0% +do very much + + + align:start position:0% +do very much +in contrast as i showed you um or i told + + align:start position:0% +in contrast as i showed you um or i told + + + align:start position:0% +in contrast as i showed you um or i told +you naps + + align:start position:0% +you naps + + + align:start position:0% +you naps +seem to be quite effective in having a + + align:start position:0% +seem to be quite effective in having a + + + align:start position:0% +seem to be quite effective in having a +large a number for + + align:start position:0% +large a number for + + + align:start position:0% +large a number for +range of effects which seems to say that + + align:start position:0% +range of effects which seems to say that + + + align:start position:0% +range of effects which seems to say that +like um sleep can potentially matter + + align:start position:0% +like um sleep can potentially matter + + + align:start position:0% +like um sleep can potentially matter +quite a bit + + align:start position:0% +quite a bit + + + align:start position:0% +quite a bit +but what really is important is try to + + align:start position:0% +but what really is important is try to + + + align:start position:0% +but what really is important is try to +figure out how could we perhaps increase + + align:start position:0% +figure out how could we perhaps increase + + + align:start position:0% +figure out how could we perhaps increase +people's sleep quality + + align:start position:0% +people's sleep quality + + + align:start position:0% +people's sleep quality +which might have an important event so + + align:start position:0% +which might have an important event so + + + align:start position:0% +which might have an important event so +that was a lot of information more than + + align:start position:0% +that was a lot of information more than + + + align:start position:0% +that was a lot of information more than +i perhaps intended + + align:start position:0% +i perhaps intended + + + align:start position:0% +i perhaps intended +any questions on that + + align:start position:0% + + + + align:start position:0% + +okay so then the last um piece which i'm + + align:start position:0% +okay so then the last um piece which i'm + + + align:start position:0% +okay so then the last um piece which i'm +gonna just sort of um + + align:start position:0% +gonna just sort of um + + + align:start position:0% +gonna just sort of um +say a little bit about is um a paper + + align:start position:0% +say a little bit about is um a paper + + + align:start position:0% +say a little bit about is um a paper +um that we just finished on the + + align:start position:0% +um that we just finished on the + + + align:start position:0% +um that we just finished on the +relationship between poverty and mental + + align:start position:0% +relationship between poverty and mental + + + align:start position:0% +relationship between poverty and mental +uh uh common mental disorders as they + + align:start position:0% +uh uh common mental disorders as they + + + align:start position:0% +uh uh common mental disorders as they +refer to which is + + align:start position:0% +refer to which is + + + align:start position:0% +refer to which is +anxiety and depression and + + align:start position:0% +anxiety and depression and + + + align:start position:0% +anxiety and depression and +um what we there sort of argue and uh + + align:start position:0% +um what we there sort of argue and uh + + + align:start position:0% +um what we there sort of argue and uh +it's a pretty short paper + + align:start position:0% +it's a pretty short paper + + + align:start position:0% +it's a pretty short paper +if you're interested um put it on my + + align:start position:0% +if you're interested um put it on my + + + align:start position:0% +if you're interested um put it on my +website um tonight + + align:start position:0% +website um tonight + + + align:start position:0% +website um tonight +um we're gonna look at uh we're looking + + align:start position:0% +um we're gonna look at uh we're looking + + + align:start position:0% +um we're gonna look at uh we're looking +at essentially the relationship between + + align:start position:0% +at essentially the relationship between + + + align:start position:0% +at essentially the relationship between +poverty and these two conditions um and + + align:start position:0% +poverty and these two conditions um and + + + align:start position:0% +poverty and these two conditions um and +what we do is first we show the causal + + align:start position:0% +what we do is first we show the causal + + + align:start position:0% +what we do is first we show the causal +effect in both directions + + align:start position:0% +effect in both directions + + + align:start position:0% +effect in both directions +and so there's quite a bit of evidence + + align:start position:0% +and so there's quite a bit of evidence + + + align:start position:0% +and so there's quite a bit of evidence +that essentially uh + + align:start position:0% +that essentially uh + + + align:start position:0% +that essentially uh +being poor is bad for people's mental + + align:start position:0% +being poor is bad for people's mental + + + align:start position:0% +being poor is bad for people's mental +health these are like causal studies so + + align:start position:0% +health these are like causal studies so + + + align:start position:0% +health these are like causal studies so +for example + + align:start position:0% +for example + + + align:start position:0% +for example +providing people cash transfers improves + + align:start position:0% +providing people cash transfers improves + + + align:start position:0% +providing people cash transfers improves +consistently their mental health + + align:start position:0% +consistently their mental health + + + align:start position:0% +consistently their mental health +so there's a causal effect of not from + + align:start position:0% +so there's a causal effect of not from + + + align:start position:0% +so there's a causal effect of not from +not having money on people's mental + + align:start position:0% +not having money on people's mental + + + align:start position:0% +not having money on people's mental +health and anxiety and depression + + align:start position:0% +health and anxiety and depression + + + align:start position:0% +health and anxiety and depression +at the same time there's a causal effect + + align:start position:0% +at the same time there's a causal effect + + + align:start position:0% +at the same time there's a causal effect +of anxiety and depression + + align:start position:0% +of anxiety and depression + + + align:start position:0% +of anxiety and depression +on people's ability to earn + + align:start position:0% +on people's ability to earn + + + align:start position:0% +on people's ability to earn +income and thus their poverty + + align:start position:0% +income and thus their poverty + + + align:start position:0% +income and thus their poverty +so for example if you provide people + + align:start position:0% +so for example if you provide people + + + align:start position:0% +so for example if you provide people +with cbt or some other forms of + + align:start position:0% +with cbt or some other forms of + + + align:start position:0% +with cbt or some other forms of +psychotherapy that improves their uh uh + + align:start position:0% +psychotherapy that improves their uh uh + + + align:start position:0% +psychotherapy that improves their uh uh +reduces their + + align:start position:0% +reduces their + + + align:start position:0% +reduces their +depression and then in turn it increases + + align:start position:0% +depression and then in turn it increases + + + align:start position:0% +depression and then in turn it increases +their labor supply + + align:start position:0% +their labor supply + + + align:start position:0% +their labor supply +which in turn uh presumably increases + + align:start position:0% +which in turn uh presumably increases + + + align:start position:0% +which in turn uh presumably increases +their ability to earn + + align:start position:0% +their ability to earn + + + align:start position:0% +their ability to earn +income so there's causal effects in both + + align:start position:0% +income so there's causal effects in both + + + align:start position:0% +income so there's causal effects in both +directions from poverty to + + align:start position:0% +directions from poverty to + + + align:start position:0% +directions from poverty to +common mental disorders and from + + align:start position:0% +common mental disorders and from + + + align:start position:0% +common mental disorders and from +continental disorders to + + align:start position:0% +continental disorders to + + + align:start position:0% +continental disorders to +poverty and then what the paperwork does + + align:start position:0% +poverty and then what the paperwork does + + + align:start position:0% +poverty and then what the paperwork does +in a lot more detail is then think about + + align:start position:0% +in a lot more detail is then think about + + + align:start position:0% +in a lot more detail is then think about +what are different mechanisms for + + align:start position:0% +what are different mechanisms for + + + align:start position:0% +what are different mechanisms for +this causal relationship and what + + align:start position:0% +this causal relationship and what + + + align:start position:0% +this causal relationship and what +exactly what evidence do they actually + + align:start position:0% +exactly what evidence do they actually + + + align:start position:0% +exactly what evidence do they actually +have + + align:start position:0% +have + + + align:start position:0% +have +of that and so on the on the side from + + align:start position:0% +of that and so on the on the side from + + + align:start position:0% +of that and so on the on the side from +poverty from economic conditions to + + align:start position:0% +poverty from economic conditions to + + + align:start position:0% +poverty from economic conditions to +mental health + + align:start position:0% +mental health + + + align:start position:0% +mental health +there's a number of different um issues + + align:start position:0% +there's a number of different um issues + + + align:start position:0% +there's a number of different um issues +that could be quite important + + align:start position:0% +that could be quite important + + + align:start position:0% +that could be quite important +ranging from like stresses or just being + + align:start position:0% +ranging from like stresses or just being + + + align:start position:0% +ranging from like stresses or just being +exposed to lots of shocks and therefore + + align:start position:0% +exposed to lots of shocks and therefore + + + align:start position:0% +exposed to lots of shocks and therefore +um worries and uncertainty to + + align:start position:0% +um worries and uncertainty to + + + align:start position:0% +um worries and uncertainty to +environmental conditions in particular + + align:start position:0% +environmental conditions in particular + + + align:start position:0% +environmental conditions in particular +there's quite a bit of emerging evidence + + align:start position:0% +there's quite a bit of emerging evidence + + + align:start position:0% +there's quite a bit of emerging evidence +of pollution being bad for people's + + align:start position:0% +of pollution being bad for people's + + + align:start position:0% +of pollution being bad for people's +mental health + + align:start position:0% +mental health + + + align:start position:0% +mental health +so essentially pollution causing + + align:start position:0% +so essentially pollution causing + + + align:start position:0% +so essentially pollution causing +depression for example + + align:start position:0% +depression for example + + + align:start position:0% +depression for example +um there's some uh potential for + + align:start position:0% +um there's some uh potential for + + + align:start position:0% +um there's some uh potential for +physical health just being in bad health + + align:start position:0% +physical health just being in bad health + + + align:start position:0% +physical health just being in bad health +might sort of bad + + align:start position:0% +might sort of bad + + + align:start position:0% +might sort of bad +it might be bad for your mental health + + align:start position:0% +it might be bad for your mental health + + + align:start position:0% +it might be bad for your mental health +in part because it causes physical pain + + align:start position:0% +in part because it causes physical pain + + + align:start position:0% +in part because it causes physical pain +and other illnesses uh + + align:start position:0% +and other illnesses uh + + + align:start position:0% +and other illnesses uh +there's some evidence of early life + + align:start position:0% +there's some evidence of early life + + + align:start position:0% +there's some evidence of early life +conditions so being + + align:start position:0% +conditions so being + + + align:start position:0% +conditions so being +uh uh growing up in poverty tends to be + + align:start position:0% +uh uh growing up in poverty tends to be + + + align:start position:0% +uh uh growing up in poverty tends to be +bad for people's mental health and + + align:start position:0% +bad for people's mental health and + + + align:start position:0% +bad for people's mental health and +there's some nice evidence of + + align:start position:0% +there's some nice evidence of + + + align:start position:0% +there's some nice evidence of +um shocks to people's uh to mother's + + align:start position:0% +um shocks to people's uh to mother's + + + align:start position:0% +um shocks to people's uh to mother's +father's income + + align:start position:0% +father's income + + + align:start position:0% +father's income +uh might cause uh uh uh mental illness + + align:start position:0% +uh might cause uh uh uh mental illness + + + align:start position:0% +uh might cause uh uh uh mental illness +much later in life for the children + + align:start position:0% +much later in life for the children + + + align:start position:0% +much later in life for the children +um there's quite a bit of evidence of + + align:start position:0% +um there's quite a bit of evidence of + + + align:start position:0% +um there's quite a bit of evidence of +trauma violence and crime with which the + + align:start position:0% +trauma violence and crime with which the + + + align:start position:0% +trauma violence and crime with which the +poor are disproportionately exposed to + + align:start position:0% +poor are disproportionately exposed to + + + align:start position:0% +poor are disproportionately exposed to +affecting people's mental health and + + align:start position:0% +affecting people's mental health and + + + align:start position:0% +affecting people's mental health and +finally social status shame and + + align:start position:0% +finally social status shame and + + + align:start position:0% +finally social status shame and +isolation if you sort of like stigmatize + + align:start position:0% +isolation if you sort of like stigmatize + + + align:start position:0% +isolation if you sort of like stigmatize +and like uh + + align:start position:0% +and like uh + + + align:start position:0% +and like uh +isolate from society that might be bad + + align:start position:0% +isolate from society that might be bad + + + align:start position:0% +isolate from society that might be bad +for your mental health + + align:start position:0% +for your mental health + + + align:start position:0% +for your mental health +particular sort of relative comparisons + + align:start position:0% +particular sort of relative comparisons + + + align:start position:0% +particular sort of relative comparisons +could be quite important + + align:start position:0% +could be quite important + + + align:start position:0% +could be quite important +and then at the same time uh there are + + align:start position:0% +and then at the same time uh there are + + + align:start position:0% +and then at the same time uh there are +effects in the other directions coming + + align:start position:0% +effects in the other directions coming + + + align:start position:0% +effects in the other directions coming +from uh + + align:start position:0% +from uh + + + align:start position:0% +from uh +depression and anxiety um so one + + align:start position:0% +depression and anxiety um so one + + + align:start position:0% +depression and anxiety um so one +profound way in which + + align:start position:0% +profound way in which + + + align:start position:0% +profound way in which +uh depression and anxiety affect + + align:start position:0% +uh depression and anxiety affect + + + align:start position:0% +uh depression and anxiety affect +people's um behaviors cognitive function + + align:start position:0% +people's um behaviors cognitive function + + + align:start position:0% +people's um behaviors cognitive function +the way people think + + align:start position:0% +the way people think + + + align:start position:0% +the way people think +so in contrast to other things such as + + align:start position:0% +so in contrast to other things such as + + + align:start position:0% +so in contrast to other things such as +health um uh + + align:start position:0% +health um uh + + + align:start position:0% +health um uh +depression anxiety affect the way people + + align:start position:0% +depression anxiety affect the way people + + + align:start position:0% +depression anxiety affect the way people +think including their and then that + + align:start position:0% +think including their and then that + + + align:start position:0% +think including their and then that +might sort of affect people's beliefs + + align:start position:0% +might sort of affect people's beliefs + + + align:start position:0% +might sort of affect people's beliefs +their confidence over confidence under + + align:start position:0% +their confidence over confidence under + + + align:start position:0% +their confidence over confidence under +confidence belief + + align:start position:0% +confidence belief + + + align:start position:0% +confidence belief +updating all the stuff that we talked + + align:start position:0% +updating all the stuff that we talked + + + align:start position:0% +updating all the stuff that we talked +about in the class as well as their + + align:start position:0% +about in the class as well as their + + + align:start position:0% +about in the class as well as their +preferences their time purposes + + align:start position:0% +preferences their time purposes + + + align:start position:0% +preferences their time purposes +risk preferences social preferences and + + align:start position:0% +risk preferences social preferences and + + + align:start position:0% +risk preferences social preferences and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +it might affect their labor productivity + + align:start position:0% +it might affect their labor productivity + + + align:start position:0% +it might affect their labor productivity +uh and their labor so apply how much + + align:start position:0% +uh and their labor so apply how much + + + align:start position:0% +uh and their labor so apply how much +people work on how productive they are + + align:start position:0% +people work on how productive they are + + + align:start position:0% +people work on how productive they are +of course um uh people might be very + + align:start position:0% +of course um uh people might be very + + + align:start position:0% +of course um uh people might be very +stigmatized and treated badly + + align:start position:0% +stigmatized and treated badly + + + align:start position:0% +stigmatized and treated badly +um uh because of mental illness which in + + align:start position:0% +um uh because of mental illness which in + + + align:start position:0% +um uh because of mental illness which in +in addition sort of then um uh uh makes + + align:start position:0% +in addition sort of then um uh uh makes + + + align:start position:0% +in addition sort of then um uh uh makes +people less likely to + + align:start position:0% +people less likely to + + + align:start position:0% +people less likely to +seek help potentially because you know + + align:start position:0% +seek help potentially because you know + + + align:start position:0% +seek help potentially because you know +if you're then stigmatized + + align:start position:0% +if you're then stigmatized + + + align:start position:0% +if you're then stigmatized +you might not want to declare to your + + align:start position:0% +you might not want to declare to your + + + align:start position:0% +you might not want to declare to your +employer to anybody else + + align:start position:0% +employer to anybody else + + + align:start position:0% +employer to anybody else +that you're depressed people tend to + + align:start position:0% +that you're depressed people tend to + + + align:start position:0% +that you're depressed people tend to +have worse health conditions + + align:start position:0% +have worse health conditions + + + align:start position:0% +have worse health conditions +um if they're depressed or if they + + align:start position:0% +um if they're depressed or if they + + + align:start position:0% +um if they're depressed or if they +suffer from mental illness or other + + align:start position:0% +suffer from mental illness or other + + + align:start position:0% +suffer from mental illness or other +health conditions tend to get worse + + align:start position:0% +health conditions tend to get worse + + + align:start position:0% +health conditions tend to get worse +health expenditures + + align:start position:0% +health expenditures + + + align:start position:0% +health expenditures +there's also some evidence of uh + + align:start position:0% +there's also some evidence of uh + + + align:start position:0% +there's also some evidence of uh +depression affecting + + align:start position:0% +depression affecting + + + align:start position:0% +depression affecting +uh women's empowerment i think there's + + align:start position:0% +uh women's empowerment i think there's + + + align:start position:0% +uh women's empowerment i think there's +two potential channels here + + align:start position:0% +two potential channels here + + + align:start position:0% +two potential channels here +uh one is that women are in fact + + align:start position:0% +uh one is that women are in fact + + + align:start position:0% +uh one is that women are in fact +disproportionately + + align:start position:0% +disproportionately + + + align:start position:0% +disproportionately +by uh depression anxiety and so on so + + align:start position:0% +by uh depression anxiety and so on so + + + align:start position:0% +by uh depression anxiety and so on so +like the prevalence is + + align:start position:0% +like the prevalence is + + + align:start position:0% +like the prevalence is +the measured prevalence is about twice + + align:start position:0% +the measured prevalence is about twice + + + align:start position:0% +the measured prevalence is about twice +as high um + + align:start position:0% +as high um + + + align:start position:0% +as high um +and so you know to the extent that now + + align:start position:0% +and so you know to the extent that now + + + align:start position:0% +and so you know to the extent that now +you if you improve people's + + align:start position:0% +you if you improve people's + + + align:start position:0% +you if you improve people's +um mental health uh + + align:start position:0% +um mental health uh + + + align:start position:0% +um mental health uh +women will disproportionately benefit + + align:start position:0% +women will disproportionately benefit + + + align:start position:0% +women will disproportionately benefit +from that + + align:start position:0% +from that + + + align:start position:0% +from that +and then there's evidence that once you + + align:start position:0% +and then there's evidence that once you + + + align:start position:0% +and then there's evidence that once you +do that uh women have + + align:start position:0% +do that uh women have + + + align:start position:0% +do that uh women have +a higher bargaining power in the + + align:start position:0% +a higher bargaining power in the + + + align:start position:0% +a higher bargaining power in the +household um + + align:start position:0% +household um + + + align:start position:0% +household um +uh uh more say about resources spent and + + align:start position:0% +uh uh more say about resources spent and + + + align:start position:0% +uh uh more say about resources spent and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +and so forth and then finally uh + + align:start position:0% +and so forth and then finally uh + + + align:start position:0% +and so forth and then finally uh +potentially quite important + + align:start position:0% +potentially quite important + + + align:start position:0% +potentially quite important +is effects on young people this ranges + + align:start position:0% +is effects on young people this ranges + + + align:start position:0% +is effects on young people this ranges +from like + + align:start position:0% +from like + + + align:start position:0% +from like +primary and secondary schooling to like + + align:start position:0% +primary and secondary schooling to like + + + align:start position:0% +primary and secondary schooling to like +college students + + align:start position:0% +college students + + + align:start position:0% +college students +and so on which is to say that a lot of + + align:start position:0% +and so on which is to say that a lot of + + + align:start position:0% +and so on which is to say that a lot of +mental health conditions + + align:start position:0% +mental health conditions + + + align:start position:0% +mental health conditions +appear during adolescence and so those + + align:start position:0% +appear during adolescence and so those + + + align:start position:0% +appear during adolescence and so those +are often when very critical decisions + + align:start position:0% +are often when very critical decisions + + + align:start position:0% +are often when very critical decisions +are made when it comes to education like + + align:start position:0% +are made when it comes to education like + + + align:start position:0% +are made when it comes to education like +do you drop out of school + + align:start position:0% +do you drop out of school + + + align:start position:0% +do you drop out of school +you go to college and so on and so forth + + align:start position:0% +you go to college and so on and so forth + + + align:start position:0% +you go to college and so on and so forth +um it turns out there's actually quite + + align:start position:0% +um it turns out there's actually quite + + + align:start position:0% +um it turns out there's actually quite +uh not not a lot of causal evidence on + + align:start position:0% +uh not not a lot of causal evidence on + + + align:start position:0% +uh not not a lot of causal evidence on +this but it seems very plausible that + + align:start position:0% +this but it seems very plausible that + + + align:start position:0% +this but it seems very plausible that +this could be um quite important instead + + align:start position:0% +this could be um quite important instead + + + align:start position:0% +this could be um quite important instead +of taking these things together it seems + + align:start position:0% +of taking these things together it seems + + + align:start position:0% +of taking these things together it seems +to me that poverty + + align:start position:0% +to me that poverty + + + align:start position:0% +to me that poverty +through like various different channels + + align:start position:0% +through like various different channels + + + align:start position:0% +through like various different channels +including scarcity which i should be at + + align:start position:0% +including scarcity which i should be at + + + align:start position:0% +including scarcity which i should be at +the beginning + + align:start position:0% +the beginning + + + align:start position:0% +the beginning +but also including all these other + + align:start position:0% +but also including all these other + + + align:start position:0% +but also including all these other +conditions might affect profoundly + + align:start position:0% +conditions might affect profoundly + + + align:start position:0% +conditions might affect profoundly +and how they make decisions and how + + align:start position:0% +and how they make decisions and how + + + align:start position:0% +and how they make decisions and how +productive they are at work + + align:start position:0% +productive they are at work + + + align:start position:0% +productive they are at work +which then could reinforce uh uh uh + + align:start position:0% +which then could reinforce uh uh uh + + + align:start position:0% +which then could reinforce uh uh uh +poverty and make it harder for people to + + align:start position:0% +poverty and make it harder for people to + + + align:start position:0% +poverty and make it harder for people to +become richer um this is a lot of + + align:start position:0% +become richer um this is a lot of + + + align:start position:0% +become richer um this is a lot of +information so any questions + + align:start position:0% +information so any questions + + + align:start position:0% +information so any questions +uh i'm happy to discuss or answer any + + align:start position:0% +uh i'm happy to discuss or answer any + + + align:start position:0% +uh i'm happy to discuss or answer any +questions that you would have + + align:start position:0% +questions that you would have + + + align:start position:0% +questions that you would have +i'm not expecting you to remember all of + + align:start position:0% +i'm not expecting you to remember all of + + + align:start position:0% +i'm not expecting you to remember all of +those things i was just + + align:start position:0% +those things i was just + + + align:start position:0% +those things i was just +more elaborating for anybody who might + + align:start position:0% +more elaborating for anybody who might + + + align:start position:0% +more elaborating for anybody who might +be interested you can also read + + align:start position:0% +be interested you can also read + + + align:start position:0% +be interested you can also read +all of these things and the paper um uh + + align:start position:0% +all of these things and the paper um uh + + + align:start position:0% +all of these things and the paper um uh +i'll add to the course website + + align:start position:0% +i'll add to the course website + + + align:start position:0% +i'll add to the course website +as well + + align:start position:0% + + + + align:start position:0% + +all right so um on wednesday we're going + + align:start position:0% +all right so um on wednesday we're going + + + align:start position:0% +all right so um on wednesday we're going +to talk about happiness and mental + + align:start position:0% +to talk about happiness and mental + + + align:start position:0% +to talk about happiness and mental +health + + align:start position:0% +health + + + align:start position:0% +health +um please read the paper by kahneman + + align:start position:0% +um please read the paper by kahneman + + + align:start position:0% +um please read the paper by kahneman +notices i just changed this in the + + align:start position:0% +notices i just changed this in the + + + align:start position:0% +notices i just changed this in the +syllabus so if you have an old version + + align:start position:0% +syllabus so if you have an old version + + + align:start position:0% +syllabus so if you have an old version +of the syllabus + + align:start position:0% +of the syllabus + + + align:start position:0% +of the syllabus +please make sure you read the new paper + + align:start position:0% +please make sure you read the new paper + + + align:start position:0% +please make sure you read the new paper +the paper is very short so it shouldn't + + align:start position:0% +the paper is very short so it shouldn't + + + align:start position:0% +the paper is very short so it shouldn't +be uh + + align:start position:0% +be uh + + + align:start position:0% +be uh +tricky to read essentially it's looking + + align:start position:0% +tricky to read essentially it's looking + + + align:start position:0% +tricky to read essentially it's looking +at what are what is + + align:start position:0% +at what are what is + + + align:start position:0% +at what are what is +what kinds of things uh predict whether + + align:start position:0% +what kinds of things uh predict whether + + + align:start position:0% +what kinds of things uh predict whether +people are happy + + align:start position:0% +people are happy + + + align:start position:0% +people are happy +uh or or not and then on monday we're + + align:start position:0% +uh or or not and then on monday we're + + + align:start position:0% +uh or or not and then on monday we're +going to talk about + + align:start position:0% +going to talk about + + + align:start position:0% +going to talk about +uh policy with with um uh behavioral + + align:start position:0% +uh policy with with um uh behavioral + + + align:start position:0% +uh policy with with um uh behavioral +agents just as a reminder we'll have a + + align:start position:0% +agents just as a reminder we'll have a + + + align:start position:0% +agents just as a reminder we'll have a +guest um + + align:start position:0% +guest um + + + align:start position:0% +guest um +at the end of class uh next time i hope + + align:start position:0% +at the end of class uh next time i hope + + + align:start position:0% +at the end of class uh next time i hope +um the guest will come at 220. i'm + + align:start position:0% +um the guest will come at 220. i'm + + + align:start position:0% +um the guest will come at 220. i'm +hoping for a um + + align:start position:0% +hoping for a um + + + align:start position:0% +hoping for a um +llama to visit us but it could also be a + + align:start position:0% +llama to visit us but it could also be a + + + align:start position:0% +llama to visit us but it could also be a +goat um we'll see how that + + align:start position:0% +goat um we'll see how that + + + align:start position:0% +goat um we'll see how that +goes any questions or comments + + align:start position:0% +goes any questions or comments + + + align:start position:0% +goes any questions or comments +when it comes to depression anxiety + + align:start position:0% +when it comes to depression anxiety + + + align:start position:0% +when it comes to depression anxiety +specifically let me talk about more + + align:start position:0% +specifically let me talk about more + + + align:start position:0% +specifically let me talk about more +generally + + align:start position:0% +generally + + + align:start position:0% +generally +so one of the things i'm working on for + + align:start position:0% +so one of the things i'm working on for + + + align:start position:0% +so one of the things i'm working on for +example is look at + + align:start position:0% +example is look at + + + align:start position:0% +example is look at +looking at the impact of cognitive + + align:start position:0% +looking at the impact of cognitive + + + align:start position:0% +looking at the impact of cognitive +variable therapy or other psychotherapy + + align:start position:0% +variable therapy or other psychotherapy + + + align:start position:0% +variable therapy or other psychotherapy +is to improve + + align:start position:0% +is to improve + + + align:start position:0% +is to improve +people's mental health and then look at + + align:start position:0% +people's mental health and then look at + + + align:start position:0% +people's mental health and then look at +the effects on people's beliefs + + align:start position:0% +the effects on people's beliefs + + + align:start position:0% +the effects on people's beliefs +how confident are they in themselves um + + align:start position:0% +how confident are they in themselves um + + + align:start position:0% +how confident are they in themselves um +how they update their beliefs and + + align:start position:0% +how they update their beliefs and + + + align:start position:0% +how they update their beliefs and +remember we had this stuff on like from + + align:start position:0% +remember we had this stuff on like from + + + align:start position:0% +remember we had this stuff on like from +ireland brow and others about like + + align:start position:0% +ireland brow and others about like + + + align:start position:0% +ireland brow and others about like +asymmetric belief updating + + align:start position:0% +asymmetric belief updating + + + align:start position:0% +asymmetric belief updating +and is that affected for example by + + align:start position:0% +and is that affected for example by + + + align:start position:0% +and is that affected for example by +people's mental health + + align:start position:0% +people's mental health + + + align:start position:0% +people's mental health +moreover we look at preferences which is + + align:start position:0% +moreover we look at preferences which is + + + align:start position:0% +moreover we look at preferences which is +precisely time preferences social + + align:start position:0% +precisely time preferences social + + + align:start position:0% +precisely time preferences social +preferences risk preferences + + align:start position:0% +preferences risk preferences + + + align:start position:0% +preferences risk preferences +and you know once you approve people's + + align:start position:0% +and you know once you approve people's + + + align:start position:0% +and you know once you approve people's +depression + + align:start position:0% +depression + + + align:start position:0% +depression +does that affect people's uh time social + + align:start position:0% +does that affect people's uh time social + + + align:start position:0% +does that affect people's uh time social +interest + + align:start position:0% +interest + + + align:start position:0% +interest +preference more broadly um there's quite + + align:start position:0% +preference more broadly um there's quite + + + align:start position:0% +preference more broadly um there's quite +a few people trying to do studies and i + + align:start position:0% +a few people trying to do studies and i + + + align:start position:0% +a few people trying to do studies and i +went over this fairly quickly + + align:start position:0% +went over this fairly quickly + + + align:start position:0% +went over this fairly quickly +uh to look at these kinds of uh uh types + + align:start position:0% +uh to look at these kinds of uh uh types + + + align:start position:0% +uh to look at these kinds of uh uh types +of effects + + align:start position:0% +of effects + + + align:start position:0% +of effects +which for example um there's some work + + align:start position:0% +which for example um there's some work + + + align:start position:0% +which for example um there's some work +on malnutrition that shows like once you + + align:start position:0% +on malnutrition that shows like once you + + + align:start position:0% +on malnutrition that shows like once you +provide people with more uh + + align:start position:0% +provide people with more uh + + + align:start position:0% +provide people with more uh +calories there's some uh indications + + align:start position:0% +calories there's some uh indications + + + align:start position:0% +calories there's some uh indications +of like less discounting which is kind + + align:start position:0% +of like less discounting which is kind + + + align:start position:0% +of like less discounting which is kind +of what you're + + align:start position:0% +of what you're + + + align:start position:0% +of what you're +uh uh what you're alluding to uh there's + + align:start position:0% +uh uh what you're alluding to uh there's + + + align:start position:0% +uh uh what you're alluding to uh there's +some work on like the relationship + + align:start position:0% +some work on like the relationship + + + align:start position:0% +some work on like the relationship +between stress and discounting there's + + align:start position:0% +between stress and discounting there's + + + align:start position:0% +between stress and discounting there's +actually not that much evidence or less + + align:start position:0% +actually not that much evidence or less + + + align:start position:0% +actually not that much evidence or less +evidence than you would expect + + align:start position:0% +evidence than you would expect + + + align:start position:0% +evidence than you would expect +for sleep deprivation for example we + + align:start position:0% +for sleep deprivation for example we + + + align:start position:0% +for sleep deprivation for example we +find when you when people nap they're + + align:start position:0% +find when you when people nap they're + + + align:start position:0% +find when you when people nap they're +less present biased + + align:start position:0% +less present biased + + + align:start position:0% +less present biased +compared to when they haven't mapped + + align:start position:0% + + + + align:start position:0% + +i find for example for outdoor + + align:start position:0% +i find for example for outdoor + + + align:start position:0% +i find for example for outdoor +consumption i do find that people save + + align:start position:0% +consumption i do find that people save + + + align:start position:0% +consumption i do find that people save +more and it seems to be not driven by + + align:start position:0% +more and it seems to be not driven by + + + align:start position:0% +more and it seems to be not driven by +having more money so again that seems to + + align:start position:0% +having more money so again that seems to + + + align:start position:0% +having more money so again that seems to +be consistent with people's time + + align:start position:0% +be consistent with people's time + + + align:start position:0% +be consistent with people's time +preferences in some way affected by + + align:start position:0% +preferences in some way affected by + + + align:start position:0% +preferences in some way affected by +these conditions + + align:start position:0% +these conditions + + + align:start position:0% +these conditions +um overall there's quite a bit of + + align:start position:0% +um overall there's quite a bit of + + + align:start position:0% +um overall there's quite a bit of +evidence so far on + + align:start position:0% +evidence so far on + + + align:start position:0% +evidence so far on +productivity so papers essentially show + + align:start position:0% +productivity so papers essentially show + + + align:start position:0% +productivity so papers essentially show +that when you're disproportionately + + align:start position:0% +that when you're disproportionately + + + align:start position:0% +that when you're disproportionately +exposed by to heat + + align:start position:0% +exposed by to heat + + + align:start position:0% +exposed by to heat +people are less productive people learn + + align:start position:0% +people are less productive people learn + + + align:start position:0% +people are less productive people learn +less when you're exposed to noise people + + align:start position:0% +less when you're exposed to noise people + + + align:start position:0% +less when you're exposed to noise people +are less productive + + align:start position:0% +are less productive + + + align:start position:0% +are less productive +when people are have less nutrition + + align:start position:0% +when people are have less nutrition + + + align:start position:0% +when people are have less nutrition +they're less productive + + align:start position:0% +they're less productive + + + align:start position:0% +they're less productive +and so on and so forth um there's less + + align:start position:0% +and so on and so forth um there's less + + + align:start position:0% +and so on and so forth um there's less +evidence so far on decision making and + + align:start position:0% +evidence so far on decision making and + + + align:start position:0% +evidence so far on decision making and +sort of preferences overall + + align:start position:0% +sort of preferences overall + + + align:start position:0% +sort of preferences overall +that's what people are currently working + + align:start position:0% +that's what people are currently working + + + align:start position:0% +that's what people are currently working +on that is exactly the question can be + + align:start position:0% +on that is exactly the question can be + + + align:start position:0% +on that is exactly the question can be +sort of explained potentially + + align:start position:0% +sort of explained potentially + + + align:start position:0% +sort of explained potentially +some of the stuff that i was mentioning + + align:start position:0% +some of the stuff that i was mentioning + + + align:start position:0% +some of the stuff that i was mentioning +at the very beginning of the lecture + + align:start position:0% +at the very beginning of the lecture + + + align:start position:0% +at the very beginning of the lecture +can explain potentially certain + + align:start position:0% +can explain potentially certain + + + align:start position:0% +can explain potentially certain +behavioral biases or certain + + align:start position:0% +behavioral biases or certain + + + align:start position:0% +behavioral biases or certain +deviations from the neoclassical model + + align:start position:0% +deviations from the neoclassical model + + + align:start position:0% +deviations from the neoclassical model +by + + align:start position:0% +by + + + align:start position:0% +by +alleviating some of the or addressing + + align:start position:0% +alleviating some of the or addressing + + + align:start position:0% +alleviating some of the or addressing +some of the psychological + + align:start position:0% +some of the psychological + + + align:start position:0% +some of the psychological +um we have don't have a lot of evidence + + align:start position:0% +um we have don't have a lot of evidence + + + align:start position:0% +um we have don't have a lot of evidence +and we hope to have some more um + + align:start position:0% + + + + align:start position:0% + +but that's exactly what people are + + align:start position:0% +but that's exactly what people are + + + align:start position:0% +but that's exactly what people are +working on + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/RizM3cD3XSA.txt b/RizM3cD3XSA.txt new file mode 100644 index 0000000000000000000000000000000000000000..7fbc8afeed3ccc722077be2e66a22c1b0a10aa79 --- /dev/null +++ b/RizM3cD3XSA.txt @@ -0,0 +1,2699 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right I'll go ahead and + + align:start position:0% +ocw.mit.edu all right I'll go ahead and + + + align:start position:0% +ocw.mit.edu all right I'll go ahead and +get started in the interest of time um + + align:start position:0% +get started in the interest of time um + + + align:start position:0% +get started in the interest of time um +we're talking about holographic + + align:start position:0% +we're talking about holographic + + + align:start position:0% +we're talking about holographic +tomography and uh next slide please so + + align:start position:0% +tomography and uh next slide please so + + + align:start position:0% +tomography and uh next slide please so +we can uh just glance at the outline but + + align:start position:0% +we can uh just glance at the outline but + + + align:start position:0% +we can uh just glance at the outline but +again we'll speed through this I know + + align:start position:0% +again we'll speed through this I know + + + align:start position:0% +again we'll speed through this I know +everybody's got class so what is + + align:start position:0% +everybody's got class so what is + + + align:start position:0% +everybody's got class so what is +tomography George I think Tomos means + + align:start position:0% +tomography George I think Tomos means + + + align:start position:0% +tomography George I think Tomos means +slice in Greek is that correct so it's + + align:start position:0% +slice in Greek is that correct so it's + + + align:start position:0% +slice in Greek is that correct so it's +basically reconstructing an image from a + + align:start position:0% +basically reconstructing an image from a + + + align:start position:0% +basically reconstructing an image from a +cross-sectional projections and this is + + align:start position:0% +cross-sectional projections and this is + + + align:start position:0% +cross-sectional projections and this is +an example of a fan projections this is + + align:start position:0% +an example of a fan projections this is + + + align:start position:0% +an example of a fan projections this is +parallel projection data and next + + align:start position:0% +parallel projection data and next + + + align:start position:0% +parallel projection data and next +slide so uh one of the key elements in + + align:start position:0% +slide so uh one of the key elements in + + + align:start position:0% +slide so uh one of the key elements in +tomography is uh forming this radon + + align:start position:0% +tomography is uh forming this radon + + + align:start position:0% +tomography is uh forming this radon +transform property and that's for any + + align:start position:0% +transform property and that's for any + + + align:start position:0% +transform property and that's for any +projection given normal to an angle + + align:start position:0% +projection given normal to an angle + + + align:start position:0% +projection given normal to an angle +Theta uh it's defined as the integral + + align:start position:0% +Theta uh it's defined as the integral + + + align:start position:0% +Theta uh it's defined as the integral +over the path length um gives you the + + align:start position:0% +over the path length um gives you the + + + align:start position:0% +over the path length um gives you the +projection intensity of your object so + + align:start position:0% +projection intensity of your object so + + + align:start position:0% +projection intensity of your object so +next slide please uh that's related to + + align:start position:0% +next slide please uh that's related to + + + align:start position:0% +next slide please uh that's related to +the F slice theem where again if that + + align:start position:0% +the F slice theem where again if that + + + align:start position:0% +the F slice theem where again if that +projection is done at an angle mapped + + align:start position:0% +projection is done at an angle mapped + + + align:start position:0% +projection is done at an angle mapped +into the frequency domain that Maps + + align:start position:0% +into the frequency domain that Maps + + + align:start position:0% +into the frequency domain that Maps +along a straight line in the non-rating + + align:start position:0% +along a straight line in the non-rating + + + align:start position:0% +along a straight line in the non-rating +case so because of that and the + + align:start position:0% +case so because of that and the + + + align:start position:0% +case so because of that and the +linearity of the forer uh slice theorem + + align:start position:0% +linearity of the forer uh slice theorem + + + align:start position:0% +linearity of the forer uh slice theorem +we can reconstruct an entire image and + + align:start position:0% +we can reconstruct an entire image and + + + align:start position:0% +we can reconstruct an entire image and +get a map in the frequency domain with + + align:start position:0% +get a map in the frequency domain with + + + align:start position:0% +get a map in the frequency domain with +discret points due our discret sampling + + align:start position:0% +discret points due our discret sampling + + + align:start position:0% +discret points due our discret sampling +size of the projections so you can + + align:start position:0% +size of the projections so you can + + + align:start position:0% +size of the projections so you can +notice from this though that it's very + + align:start position:0% +notice from this though that it's very + + + align:start position:0% +notice from this though that it's very +highly sampled in the the DC region and + + align:start position:0% +highly sampled in the the DC region and + + + align:start position:0% +highly sampled in the the DC region and +out in the The High Frequency region + + align:start position:0% +out in the The High Frequency region + + + align:start position:0% +out in the The High Frequency region +there's few data points so what happens + + align:start position:0% +there's few data points so what happens + + + align:start position:0% +there's few data points so what happens +this is the ideal case where we like + + align:start position:0% +this is the ideal case where we like + + + align:start position:0% +this is the ideal case where we like +even sampling throughout the + + align:start position:0% +even sampling throughout the + + + align:start position:0% +even sampling throughout the +distribution this is actually what we + + align:start position:0% +distribution this is actually what we + + + align:start position:0% +distribution this is actually what we +collect with a discrete number of pixels + + align:start position:0% +collect with a discrete number of pixels + + + align:start position:0% +collect with a discrete number of pixels +this is our filter so there's different + + align:start position:0% +this is our filter so there's different + + + align:start position:0% +this is our filter so there's different +filter types and what they do is they + + align:start position:0% +filter types and what they do is they + + + align:start position:0% +filter types and what they do is they +try to weight the higher frequency + + align:start position:0% +try to weight the higher frequency + + + align:start position:0% +try to weight the higher frequency +regions so we'd end up with a nicely uh + + align:start position:0% +regions so we'd end up with a nicely uh + + + align:start position:0% +regions so we'd end up with a nicely uh +reconstructed image without a lot of + + align:start position:0% +reconstructed image without a lot of + + + align:start position:0% +reconstructed image without a lot of +blurring due to the high dependence of + + align:start position:0% +blurring due to the high dependence of + + + align:start position:0% +blurring due to the high dependence of +the the DC terms so the different filter + + align:start position:0% +the the DC terms so the different filter + + + align:start position:0% +the the DC terms so the different filter +types the most common is a ramp filter + + align:start position:0% +types the most common is a ramp filter + + + align:start position:0% +types the most common is a ramp filter +which just weights it in this wedge + + align:start position:0% +which just weights it in this wedge + + + align:start position:0% +which just weights it in this wedge +fashion there's a shef Logan filter it's + + align:start position:0% +fashion there's a shef Logan filter it's + + + align:start position:0% +fashion there's a shef Logan filter it's +kind of like a snc form cosine and a + + align:start position:0% +kind of like a snc form cosine and a + + + align:start position:0% +kind of like a snc form cosine and a +Hamming pay attention to this cosine + + align:start position:0% +Hamming pay attention to this cosine + + + align:start position:0% +Hamming pay attention to this cosine +filter because it uh drops off to zero + + align:start position:0% +filter because it uh drops off to zero + + + align:start position:0% +filter because it uh drops off to zero +at the high frequencies you'll see that + + align:start position:0% +at the high frequencies you'll see that + + + align:start position:0% +at the high frequencies you'll see that +coming up so uh this example with this + + align:start position:0% +coming up so uh this example with this + + + align:start position:0% +coming up so uh this example with this +complicated image basically we turn it + + align:start position:0% +complicated image basically we turn it + + + align:start position:0% +complicated image basically we turn it +into a transmission image where black + + align:start position:0% +into a transmission image where black + + + align:start position:0% +into a transmission image where black +represents an opaque white is + + align:start position:0% +represents an opaque white is + + + align:start position:0% +represents an opaque white is +transparent that's the standard 2D Foria + + align:start position:0% +transparent that's the standard 2D Foria + + + align:start position:0% +transparent that's the standard 2D Foria +transform if we do projection mapping + + align:start position:0% +transform if we do projection mapping + + + align:start position:0% +transform if we do projection mapping +and these are different scan angles you + + align:start position:0% +and these are different scan angles you + + + align:start position:0% +and these are different scan angles you +can see that looking from the bottom up + + align:start position:0% +can see that looking from the bottom up + + + align:start position:0% +can see that looking from the bottom up +you can almost pick out the image the + + align:start position:0% +you can almost pick out the image the + + + align:start position:0% +you can almost pick out the image the +the MIT comes through it you know + + align:start position:0% +the MIT comes through it you know + + + align:start position:0% +the MIT comes through it you know +sideways that's a projection you get and + + align:start position:0% +sideways that's a projection you get and + + + align:start position:0% +sideways that's a projection you get and +at 45 degrees those are mapped directly + + align:start position:0% +at 45 degrees those are mapped directly + + + align:start position:0% +at 45 degrees those are mapped directly +to the frequency domain as I depicted + + align:start position:0% +to the frequency domain as I depicted + + + align:start position:0% +to the frequency domain as I depicted +with the for slice serum so next + + align:start position:0% +with the for slice serum so next + + + align:start position:0% +with the for slice serum so next +uh that radon transfer then you can map + + align:start position:0% +uh that radon transfer then you can map + + + align:start position:0% +uh that radon transfer then you can map +for every projection angle that's here + + align:start position:0% +for every projection angle that's here + + + align:start position:0% +for every projection angle that's here +from 0 to 180 and mat lab even has a + + align:start position:0% +from 0 to 180 and mat lab even has a + + + align:start position:0% +from 0 to 180 and mat lab even has a +color scale bone which kind of looks + + align:start position:0% +color scale bone which kind of looks + + + align:start position:0% +color scale bone which kind of looks +like an x-ray go figure so next one next + + align:start position:0% +like an x-ray go figure so next one next + + + align:start position:0% +like an x-ray go figure so next one next +slide please so now we can reconstruct + + align:start position:0% +slide please so now we can reconstruct + + + align:start position:0% +slide please so now we can reconstruct +for a limited number of projections so + + align:start position:0% +for a limited number of projections so + + + align:start position:0% +for a limited number of projections so +you can see in the case where we take 10 + + align:start position:0% +you can see in the case where we take 10 + + + align:start position:0% +you can see in the case where we take 10 +projection reconstruct our image there's + + align:start position:0% +projection reconstruct our image there's + + + align:start position:0% +projection reconstruct our image there's +a lot of artifacts these are streaking a + + align:start position:0% +a lot of artifacts these are streaking a + + + align:start position:0% +a lot of artifacts these are streaking a +lot of uh Noise Within the image and as + + align:start position:0% +lot of uh Noise Within the image and as + + + align:start position:0% +lot of uh Noise Within the image and as +you go up in projection number you get a + + align:start position:0% +you go up in projection number you get a + + + align:start position:0% +you go up in projection number you get a +closer and closer more accurate + + align:start position:0% +closer and closer more accurate + + + align:start position:0% +closer and closer more accurate +reconstruction of your original image + + align:start position:0% +reconstruction of your original image + + + align:start position:0% +reconstruction of your original image +and then with a different filter types + + align:start position:0% +and then with a different filter types + + + align:start position:0% +and then with a different filter types +this is the ramp on top cosine on the + + align:start position:0% +this is the ramp on top cosine on the + + + align:start position:0% +this is the ramp on top cosine on the +bottom you notice that I mentioned the + + align:start position:0% +bottom you notice that I mentioned the + + + align:start position:0% +bottom you notice that I mentioned the +cosine filter kind of attenuates the + + align:start position:0% +cosine filter kind of attenuates the + + + align:start position:0% +cosine filter kind of attenuates the +high frequency terms and you notice that + + align:start position:0% +high frequency terms and you notice that + + + align:start position:0% +high frequency terms and you notice that +with a blurred image in the final + + align:start position:0% +with a blurred image in the final + + + align:start position:0% +with a blurred image in the final +reconstruction so next um we can also + + align:start position:0% +reconstruction so next um we can also + + + align:start position:0% +reconstruction so next um we can also +simulate noise in the projection like + + align:start position:0% +simulate noise in the projection like + + + align:start position:0% +simulate noise in the projection like +one might get in a um a real application + + align:start position:0% +one might get in a um a real application + + + align:start position:0% +one might get in a um a real application +so that's noise in the radon transfer + + align:start position:0% +so that's noise in the radon transfer + + + align:start position:0% +so that's noise in the radon transfer +plots + + align:start position:0% +plots + + + align:start position:0% +plots +um right on transform and then that + + align:start position:0% +um right on transform and then that + + + align:start position:0% +um right on transform and then that +reconstructed image with different kind + + align:start position:0% +reconstructed image with different kind + + + align:start position:0% +reconstructed image with different kind +of standard deviation values for the + + align:start position:0% +of standard deviation values for the + + + align:start position:0% +of standard deviation values for the +noise you can see your reconstruction is + + align:start position:0% +noise you can see your reconstruction is + + + align:start position:0% +noise you can see your reconstruction is +noisier and noisier up to the point + + align:start position:0% +noisier and noisier up to the point + + + align:start position:0% +noisier and noisier up to the point +where it's virtually indistinguishable + + align:start position:0% +where it's virtually indistinguishable + + + align:start position:0% +where it's virtually indistinguishable +for high values and noise + + align:start position:0% +for high values and noise + + + align:start position:0% +for high values and noise +next so another interesting problem + + align:start position:0% +next so another interesting problem + + + align:start position:0% +next so another interesting problem +arises is uh how many objects can you + + align:start position:0% +arises is uh how many objects can you + + + align:start position:0% +arises is uh how many objects can you +detect with very limited projection data + + align:start position:0% +detect with very limited projection data + + + align:start position:0% +detect with very limited projection data +you can see with the simple Square uh + + align:start position:0% +you can see with the simple Square uh + + + align:start position:0% +you can see with the simple Square uh +the radon transform which is also called + + align:start position:0% +the radon transform which is also called + + + align:start position:0% +the radon transform which is also called +a cogram I forgot to mention that but um + + align:start position:0% +a cogram I forgot to mention that but um + + + align:start position:0% +a cogram I forgot to mention that but um +it's pretty uni throughout but if you + + align:start position:0% +it's pretty uni throughout but if you + + + align:start position:0% +it's pretty uni throughout but if you +have four objects you know if you take a + + align:start position:0% +have four objects you know if you take a + + + align:start position:0% +have four objects you know if you take a +limited projection view it might look + + align:start position:0% +limited projection view it might look + + + align:start position:0% +limited projection view it might look +like two or three even so that's + + align:start position:0% +like two or three even so that's + + + align:start position:0% +like two or three even so that's +something in a applications that you + + align:start position:0% +something in a applications that you + + + align:start position:0% +something in a applications that you +need to take um increased number + + align:start position:0% +need to take um increased number + + + align:start position:0% +need to take um increased number +projections ta to resolve your your kind + + align:start position:0% +projections ta to resolve your your kind + + + align:start position:0% +projections ta to resolve your your kind +of defects next so that brings us to a + + align:start position:0% +of defects next so that brings us to a + + + align:start position:0% +of defects next so that brings us to a +standard object and uh this is a head + + align:start position:0% +standard object and uh this is a head + + + align:start position:0% +standard object and uh this is a head +MRI scan or CAT scan I think um and + + align:start position:0% +MRI scan or CAT scan I think um and + + + align:start position:0% +MRI scan or CAT scan I think um and +that's a standard Shep Logan head + + align:start position:0% +that's a standard Shep Logan head + + + align:start position:0% +that's a standard Shep Logan head +Phantom which is actually implemented in + + align:start position:0% +Phantom which is actually implemented in + + + align:start position:0% +Phantom which is actually implemented in +mat lab and you can uh construct a radon + + align:start position:0% +mat lab and you can uh construct a radon + + + align:start position:0% +mat lab and you can uh construct a radon +trans transform of that image next you + + align:start position:0% +trans transform of that image next you + + + align:start position:0% +trans transform of that image next you +can actually look at how many + + align:start position:0% +can actually look at how many + + + align:start position:0% +can actually look at how many +projections you need to get in order to + + align:start position:0% +projections you need to get in order to + + + align:start position:0% +projections you need to get in order to +get accuracy in this accuracy profile we + + align:start position:0% +get accuracy in this accuracy profile we + + + align:start position:0% +get accuracy in this accuracy profile we +defined as um the difference in the + + align:start position:0% +defined as um the difference in the + + + align:start position:0% +defined as um the difference in the +actual reconstructed image per pixel + + align:start position:0% +actual reconstructed image per pixel + + + align:start position:0% +actual reconstructed image per pixel +that magnitude Square divided by the + + align:start position:0% +that magnitude Square divided by the + + + align:start position:0% +that magnitude Square divided by the +number of pixels and then normalize that + + align:start position:0% +number of pixels and then normalize that + + + align:start position:0% +number of pixels and then normalize that +with a um in relation to the actual + + align:start position:0% +with a um in relation to the actual + + + align:start position:0% +with a um in relation to the actual +image so you can see right around 36 + + align:start position:0% +image so you can see right around 36 + + + align:start position:0% +image so you can see right around 36 +projections you get a pretty good + + align:start position:0% +projections you get a pretty good + + + align:start position:0% +projections you get a pretty good +reconstruction you don't need a huge uh + + align:start position:0% +reconstruction you don't need a huge uh + + + align:start position:0% +reconstruction you don't need a huge uh +collection of data for this simple + + align:start position:0% +collection of data for this simple + + + align:start position:0% +collection of data for this simple +Phantom but in real life you obviously + + align:start position:0% +Phantom but in real life you obviously + + + align:start position:0% +Phantom but in real life you obviously +want to maximize your projections that + + align:start position:0% +want to maximize your projections that + + + align:start position:0% +want to maximize your projections that +you can + + align:start position:0% +you can + + + align:start position:0% +you can +collect I did he was going to talk about + + align:start position:0% +collect I did he was going to talk about + + + align:start position:0% +collect I did he was going to talk about +defraction yeah so uh I just touch up a + + align:start position:0% +defraction yeah so uh I just touch up a + + + align:start position:0% +defraction yeah so uh I just touch up a +bit upon the defraction tomography + + align:start position:0% +bit upon the defraction tomography + + + align:start position:0% +bit upon the defraction tomography +before we move on to experimental + + align:start position:0% +before we move on to experimental + + + align:start position:0% +before we move on to experimental +results uh so uh right up to now we've + + align:start position:0% +results uh so uh right up to now we've + + + align:start position:0% +results uh so uh right up to now we've +just considered uh a plane wave uh just + + align:start position:0% +just considered uh a plane wave uh just + + + align:start position:0% +just considered uh a plane wave uh just +passing through an object and we're not + + align:start position:0% +passing through an object and we're not + + + align:start position:0% +passing through an object and we're not +considering defraction at all but uh + + align:start position:0% +considering defraction at all but uh + + + align:start position:0% +considering defraction at all but uh +light rays do not behave uh that way so + + align:start position:0% +light rays do not behave uh that way so + + + align:start position:0% +light rays do not behave uh that way so +a pro projection that we have uh is + + align:start position:0% +a pro projection that we have uh is + + + align:start position:0% +a pro projection that we have uh is +quite different than just uh just the + + align:start position:0% +quite different than just uh just the + + + align:start position:0% +quite different than just uh just the +line integral which which effectively is + + align:start position:0% +line integral which which effectively is + + + align:start position:0% +line integral which which effectively is +the radon transform so uh to the next uh + + align:start position:0% +the radon transform so uh to the next uh + + + align:start position:0% +the radon transform so uh to the next uh +so uh analogous to what we have in the + + align:start position:0% +so uh analogous to what we have in the + + + align:start position:0% +so uh analogous to what we have in the +earlier case which was the forer slice + + align:start position:0% +earlier case which was the forer slice + + + align:start position:0% +earlier case which was the forer slice +theorem instead of uh mapping a + + align:start position:0% +theorem instead of uh mapping a + + + align:start position:0% +theorem instead of uh mapping a +projection at a particular angle uh + + align:start position:0% +projection at a particular angle uh + + + align:start position:0% +projection at a particular angle uh +where we are eliminating it with + + align:start position:0% +where we are eliminating it with + + + align:start position:0% +where we are eliminating it with +incident plane wave uh in the forer uh + + align:start position:0% +incident plane wave uh in the forer uh + + + align:start position:0% +incident plane wave uh in the forer uh +domain uh the transform of the + + align:start position:0% +domain uh the transform of the + + + align:start position:0% +domain uh the transform of the +projection + + align:start position:0% +projection + + + align:start position:0% +projection +maps onto a semicircular Arc instead of + + align:start position:0% +maps onto a semicircular Arc instead of + + + align:start position:0% +maps onto a semicircular Arc instead of +instead of mapping to a straight line uh + + align:start position:0% +instead of mapping to a straight line uh + + + align:start position:0% +instead of mapping to a straight line uh +next + + align:start position:0% +next + + + align:start position:0% +next +pie and uh and the radius of the + + align:start position:0% +pie and uh and the radius of the + + + align:start position:0% +pie and uh and the radius of the +semicircular Arc is proportional to the + + align:start position:0% +semicircular Arc is proportional to the + + + align:start position:0% +semicircular Arc is proportional to the +wave number that's uh the uh so it's + + align:start position:0% +wave number that's uh the uh so it's + + + align:start position:0% +wave number that's uh the uh so it's +it's in a way dependent upon the uh + + align:start position:0% +it's in a way dependent upon the uh + + + align:start position:0% +it's in a way dependent upon the uh +illumination uh + + align:start position:0% +illumination uh + + + align:start position:0% +illumination uh +characteristics uh so uh just to okay uh + + align:start position:0% +characteristics uh so uh just to okay uh + + + align:start position:0% +characteristics uh so uh just to okay uh +just to show uh so once we moving uh + + align:start position:0% +just to show uh so once we moving uh + + + align:start position:0% +just to show uh so once we moving uh +towards lower wavelength U we just uh + + align:start position:0% +towards lower wavelength U we just uh + + + align:start position:0% +towards lower wavelength U we just uh +going towards the earlier case where + + align:start position:0% +going towards the earlier case where + + + align:start position:0% +going towards the earlier case where +where in the the fer domain we're + + align:start position:0% +where in the the fer domain we're + + + align:start position:0% +where in the the fer domain we're +mapping the projection onto a straight + + align:start position:0% +mapping the projection onto a straight + + + align:start position:0% +mapping the projection onto a straight +line + + align:start position:0% +line + + + align:start position:0% +line +uh okay so uh like I just mentioned + + align:start position:0% +uh okay so uh like I just mentioned + + + align:start position:0% +uh okay so uh like I just mentioned +earlier so if you change the uh in the + + align:start position:0% +earlier so if you change the uh in the + + + align:start position:0% +earlier so if you change the uh in the +earlier case we just changed the + + align:start position:0% +earlier case we just changed the + + + align:start position:0% +earlier case we just changed the +orientation of the uh projections I mean + + align:start position:0% +orientation of the uh projections I mean + + + align:start position:0% +orientation of the uh projections I mean +we changing the direction from which we + + align:start position:0% +we changing the direction from which we + + + align:start position:0% +we changing the direction from which we +are recording the projections and uh if + + align:start position:0% +are recording the projections and uh if + + + align:start position:0% +are recording the projections and uh if +also we change the frequency of the + + align:start position:0% +also we change the frequency of the + + + align:start position:0% +also we change the frequency of the +illumination we what we're doing is + + align:start position:0% +illumination we what we're doing is + + + align:start position:0% +illumination we what we're doing is +we're trying to uh map the uh + + align:start position:0% +we're trying to uh map the uh + + + align:start position:0% +we're trying to uh map the uh +information of the object in the fer + + align:start position:0% +information of the object in the fer + + + align:start position:0% +information of the object in the fer +domain along uh along certain + + align:start position:0% +domain along uh along certain + + + align:start position:0% +domain along uh along certain +frequencies and the semicircular Arc uh + + align:start position:0% +frequencies and the semicircular Arc uh + + + align:start position:0% +frequencies and the semicircular Arc uh +in a way uh uh it's as you uh can see + + align:start position:0% +in a way uh uh it's as you uh can see + + + align:start position:0% +in a way uh uh it's as you uh can see +it's uh we mapping it along a smaller + + align:start position:0% +it's uh we mapping it along a smaller + + + align:start position:0% +it's uh we mapping it along a smaller +disk so it's like a low pass version of + + align:start position:0% +disk so it's like a low pass version of + + + align:start position:0% +disk so it's like a low pass version of +the original object um and uh uh so from + + align:start position:0% +the original object um and uh uh so from + + + align:start position:0% +the original object um and uh uh so from +from this for domain we can just do a + + align:start position:0% +from this for domain we can just do a + + + align:start position:0% +from this for domain we can just do a +inverse transform to to get the + + align:start position:0% +inverse transform to to get the + + + align:start position:0% +inverse transform to to get the +information about the real + + align:start position:0% +information about the real + + + align:start position:0% +information about the real +object and yeah so we'll just move on to + + align:start position:0% +object and yeah so we'll just move on to + + + align:start position:0% +object and yeah so we'll just move on to +the fun part I guess + + align:start position:0% +the fun part I guess + + + align:start position:0% +the fun part I guess +sure okay so we did a few experiments + + align:start position:0% +sure okay so we did a few experiments + + + align:start position:0% +sure okay so we did a few experiments +this first one is with this little + + align:start position:0% +this first one is with this little + + + align:start position:0% +this first one is with this little +keychain object and uh what I did was + + align:start position:0% +keychain object and uh what I did was + + + align:start position:0% +keychain object and uh what I did was +just suspend it and spin it and from + + align:start position:0% +just suspend it and spin it and from + + + align:start position:0% +just suspend it and spin it and from +that simple video uh we grab some frames + + align:start position:0% +that simple video uh we grab some frames + + + align:start position:0% +that simple video uh we grab some frames +just assuming it's a constant rotation + + align:start position:0% +just assuming it's a constant rotation + + + align:start position:0% +just assuming it's a constant rotation +profile which is wrong I know that but + + align:start position:0% +profile which is wrong I know that but + + + align:start position:0% +profile which is wrong I know that but +um from that we created simple uh + + align:start position:0% +um from that we created simple uh + + + align:start position:0% +um from that we created simple uh +threshold image values that were + + align:start position:0% +threshold image values that were + + + align:start position:0% +threshold image values that were +equivalent to a transmission data and + + align:start position:0% +equivalent to a transmission data and + + + align:start position:0% +equivalent to a transmission data and +next slide so from that we can digitally + + align:start position:0% +next slide so from that we can digitally + + + align:start position:0% +next slide so from that we can digitally +reconstruct from these uh kind of + + align:start position:0% +reconstruct from these uh kind of + + + align:start position:0% +reconstruct from these uh kind of +vertical + + align:start position:0% +vertical + + + align:start position:0% +vertical +cross-sections uh 3D slices of the um + + align:start position:0% +cross-sections uh 3D slices of the um + + + align:start position:0% +cross-sections uh 3D slices of the um +projected image and and construct a + + align:start position:0% +projected image and and construct a + + + align:start position:0% +projected image and and construct a +three-dimensional uh Topography of our + + align:start position:0% +three-dimensional uh Topography of our + + + align:start position:0% +three-dimensional uh Topography of our +image next slide so this is our + + align:start position:0% +image next slide so this is our + + + align:start position:0% +image next slide so this is our +reconstruction of little keychain and + + align:start position:0% +reconstruction of little keychain and + + + align:start position:0% +reconstruction of little keychain and +what's interesting I don't know if the + + align:start position:0% +what's interesting I don't know if the + + + align:start position:0% +what's interesting I don't know if the +camera can zoom in on + + align:start position:0% +camera can zoom in on + + + align:start position:0% +camera can zoom in on +this where is + + align:start position:0% +this where is + + + align:start position:0% +this where is +he okay well if Singapore can't see it + + align:start position:0% +he okay well if Singapore can't see it + + + align:start position:0% +he okay well if Singapore can't see it +um there's a little white face and some + + align:start position:0% +um there's a little white face and some + + + align:start position:0% +um there's a little white face and some +white artifacts on this image those come + + align:start position:0% +white artifacts on this image those come + + + align:start position:0% +white artifacts on this image those come +up on our reconstruction as the holes + + align:start position:0% +up on our reconstruction as the holes + + + align:start position:0% +up on our reconstruction as the holes +just due to the fact that the threshold + + align:start position:0% +just due to the fact that the threshold + + + align:start position:0% +just due to the fact that the threshold +values were set such that you know dark + + align:start position:0% +values were set such that you know dark + + + align:start position:0% +values were set such that you know dark +images were set to be um transmissive so + + align:start position:0% +images were set to be um transmissive so + + + align:start position:0% +images were set to be um transmissive so +another experiment we did with the help + + align:start position:0% +another experiment we did with the help + + + align:start position:0% +another experiment we did with the help +of Laura in her lab was uh looking at + + align:start position:0% +of Laura in her lab was uh looking at + + + align:start position:0% +of Laura in her lab was uh looking at +transmission + + align:start position:0% +transmission + + + align:start position:0% +transmission +tomography um in the lab using a plain + + align:start position:0% +tomography um in the lab using a plain + + + align:start position:0% +tomography um in the lab using a plain +Wave light source or white light source + + align:start position:0% +Wave light source or white light source + + + align:start position:0% +Wave light source or white light source +and we have in this little test tube + + align:start position:0% +and we have in this little test tube + + + align:start position:0% +and we have in this little test tube +some uh translucent gummy candy and then + + align:start position:0% +some uh translucent gummy candy and then + + + align:start position:0% +some uh translucent gummy candy and then +surrounded by a sugar trying to get + + align:start position:0% +surrounded by a sugar trying to get + + + align:start position:0% +surrounded by a sugar trying to get +index matching um that was like a red + + align:start position:0% +index matching um that was like a red + + + align:start position:0% +index matching um that was like a red +fruit drink I think then all that's in a + + align:start position:0% +fruit drink I think then all that's in a + + + align:start position:0% +fruit drink I think then all that's in a +in a water tank and the stage rotates to + + align:start position:0% +in a water tank and the stage rotates to + + + align:start position:0% +in a water tank and the stage rotates to +the next + + align:start position:0% +the next + + + align:start position:0% +the next +slide so from that we collected 36 + + align:start position:0% +slide so from that we collected 36 + + + align:start position:0% +slide so from that we collected 36 +projections one every 5° around + + align:start position:0% +projections one every 5° around + + + align:start position:0% +projections one every 5° around +360° + + align:start position:0% +360° + + + align:start position:0% +360° +yeah so that or no around 180° I'm sorry + + align:start position:0% +yeah so that or no around 180° I'm sorry + + + align:start position:0% +yeah so that or no around 180° I'm sorry +so these are our collected images and uh + + align:start position:0% +so these are our collected images and uh + + + align:start position:0% +so these are our collected images and uh +add's got a little video it might not + + align:start position:0% +add's got a little video it might not + + + align:start position:0% +add's got a little video it might not +work no okay so anyways uh next slide we + + align:start position:0% +work no okay so anyways uh next slide we + + + align:start position:0% +work no okay so anyways uh next slide we +can reconstruct that as well and get + + align:start position:0% +can reconstruct that as well and get + + + align:start position:0% +can reconstruct that as well and get +these um uh horizontal slices of a + + align:start position:0% +these um uh horizontal slices of a + + + align:start position:0% +these um uh horizontal slices of a +reconstructed image this is a different + + align:start position:0% +reconstructed image this is a different + + + align:start position:0% +reconstructed image this is a different +color map that's the mat lab's color mat + + align:start position:0% +color map that's the mat lab's color mat + + + align:start position:0% +color map that's the mat lab's color mat +Jet and uh that's similar to what an MRI + + align:start position:0% +Jet and uh that's similar to what an MRI + + + align:start position:0% +Jet and uh that's similar to what an MRI +operator might see looking at at slices + + align:start position:0% +operator might see looking at at slices + + + align:start position:0% +operator might see looking at at slices +through somebody's body that's our + + align:start position:0% +through somebody's body that's our + + + align:start position:0% +through somebody's body that's our +reconstructed fan of um uh projection + + align:start position:0% +reconstructed fan of um uh projection + + + align:start position:0% +reconstructed fan of um uh projection +data next and here's our 3D + + align:start position:0% +data next and here's our 3D + + + align:start position:0% +data next and here's our 3D +reconstruction and what's interesting to + + align:start position:0% +reconstruction and what's interesting to + + + align:start position:0% +reconstruction and what's interesting to +note is that we're able to reconstruct + + align:start position:0% +note is that we're able to reconstruct + + + align:start position:0% +note is that we're able to reconstruct +actually not only the gummy object but + + align:start position:0% +actually not only the gummy object but + + + align:start position:0% +actually not only the gummy object but +the little air bubbles that don't really + + align:start position:0% +the little air bubbles that don't really + + + align:start position:0% +the little air bubbles that don't really +resolve in this picture so we thought + + align:start position:0% +resolve in this picture so we thought + + + align:start position:0% +resolve in this picture so we thought +that was really + + align:start position:0% +that was really + + + align:start position:0% +that was really +interesting and uh do you want to talk + + align:start position:0% +interesting and uh do you want to talk + + + align:start position:0% +interesting and uh do you want to talk +about application oh sure okay so the + + align:start position:0% +about application oh sure okay so the + + + align:start position:0% +about application oh sure okay so the +main use for this obviously is medical + + align:start position:0% +main use for this obviously is medical + + + align:start position:0% +main use for this obviously is medical +and biological uh CAT scan computer + + align:start position:0% +and biological uh CAT scan computer + + + align:start position:0% +and biological uh CAT scan computer +axial tomography and then other uses + + align:start position:0% +axial tomography and then other uses + + + align:start position:0% +axial tomography and then other uses +this is actually a cell where they're + + align:start position:0% +this is actually a cell where they're + + + align:start position:0% +this is actually a cell where they're +looking at the internal structure on the + + align:start position:0% +looking at the internal structure on the + + + align:start position:0% +looking at the internal structure on the +um I guess nanoc scale next + + align:start position:0% +um I guess nanoc scale next + + + align:start position:0% +um I guess nanoc scale next +slide and then uh in the material + + align:start position:0% +slide and then uh in the material + + + align:start position:0% +slide and then uh in the material +science field they're using this more + + align:start position:0% +science field they're using this more + + + align:start position:0% +science field they're using this more +and more this is electron tomography + + align:start position:0% +and more this is electron tomography + + + align:start position:0% +and more this is electron tomography +looking at the PN doping of a silicon + + align:start position:0% +looking at the PN doping of a silicon + + + align:start position:0% +looking at the PN doping of a silicon +cell and then that's a materials + + align:start position:0% +cell and then that's a materials + + + align:start position:0% +cell and then that's a materials +crystallography exercise looking at the + + align:start position:0% +crystallography exercise looking at the + + + align:start position:0% +crystallography exercise looking at the +kind of Nano structure materials and uh + + align:start position:0% +kind of Nano structure materials and uh + + + align:start position:0% +kind of Nano structure materials and uh +last slide so the defraction effects we + + align:start position:0% +last slide so the defraction effects we + + + align:start position:0% +last slide so the defraction effects we +really get to experiment with because + + align:start position:0% +really get to experiment with because + + + align:start position:0% +really get to experiment with because +that's somewhat difficult it's kind of a + + align:start position:0% +that's somewhat difficult it's kind of a + + + align:start position:0% +that's somewhat difficult it's kind of a +Cutting Edge and that becomes an effect + + align:start position:0% +Cutting Edge and that becomes an effect + + + align:start position:0% +Cutting Edge and that becomes an effect +as Addie mentioned when the material + + align:start position:0% +as Addie mentioned when the material + + + align:start position:0% +as Addie mentioned when the material +you're trying to resolve is on the same + + align:start position:0% +you're trying to resolve is on the same + + + align:start position:0% +you're trying to resolve is on the same +order of the wavelength that you're + + align:start position:0% +order of the wavelength that you're + + + align:start position:0% +order of the wavelength that you're +Illuminating with so you can see for + + align:start position:0% +Illuminating with so you can see for + + + align:start position:0% +Illuminating with so you can see for +these different projections going across + + align:start position:0% +these different projections going across + + + align:start position:0% +these different projections going across +and then over they're different um + + align:start position:0% +and then over they're different um + + + align:start position:0% +and then over they're different um +distances projection distances of the + + align:start position:0% +distances projection distances of the + + + align:start position:0% +distances projection distances of the +receiving end of their apparatus so you + + align:start position:0% +receiving end of their apparatus so you + + + align:start position:0% +receiving end of their apparatus so you +can see more and more defraction as you + + align:start position:0% +can see more and more defraction as you + + + align:start position:0% +can see more and more defraction as you +propagate further and uh similarly with + + align:start position:0% +propagate further and uh similarly with + + + align:start position:0% +propagate further and uh similarly with +the upper right case that's a little + + align:start position:0% +the upper right case that's a little + + + align:start position:0% +the upper right case that's a little +tungsten wire so the Reconstruction + + align:start position:0% +tungsten wire so the Reconstruction + + + align:start position:0% +tungsten wire so the Reconstruction +takes into account digitally the defract + + align:start position:0% +takes into account digitally the defract + + + align:start position:0% +takes into account digitally the defract +pattern and subtracts that out so with + + align:start position:0% +pattern and subtracts that out so with + + + align:start position:0% +pattern and subtracts that out so with +that uh any + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +sure in the gummy bear picture why was + + align:start position:0% +sure in the gummy bear picture why was + + + align:start position:0% +sure in the gummy bear picture why was +so much of it + + align:start position:0% +so much of it + + + align:start position:0% +so much of it +missing well can you go back to that + + align:start position:0% +missing well can you go back to that + + + align:start position:0% +missing well can you go back to that +yeah the gummy be would stay the shape + + align:start position:0% +yeah the gummy be would stay the shape + + + align:start position:0% +yeah the gummy be would stay the shape +of the gummy be would uh would stay + + align:start position:0% +of the gummy be would uh would stay + + + align:start position:0% +of the gummy be would uh would stay +constant so what we did was uh we just + + align:start position:0% +constant so what we did was uh we just + + + align:start position:0% +constant so what we did was uh we just +we just had two lumps of uh candy placed + + align:start position:0% +we just had two lumps of uh candy placed + + + align:start position:0% +we just had two lumps of uh candy placed +at two different places and that's what + + align:start position:0% +at two different places and that's what + + + align:start position:0% +at two different places and that's what +we're trying to yeah we we hardly wanted + + align:start position:0% +we're trying to yeah we we hardly wanted + + + align:start position:0% +we're trying to yeah we we hardly wanted +to uh get the original shape of the G + + align:start position:0% +to uh get the original shape of the G + + + align:start position:0% +to uh get the original shape of the G +but uh it w't stay the same so yeah it + + align:start position:0% +but uh it w't stay the same so yeah it + + + align:start position:0% +but uh it w't stay the same so yeah it +was actually broken up there so it was + + align:start position:0% +was actually broken up there so it was + + + align:start position:0% +was actually broken up there so it was +broken up to fit of the test tube and + + align:start position:0% +broken up to fit of the test tube and + + + align:start position:0% +broken up to fit of the test tube and +also it was it took some time to create + + align:start position:0% +also it was it took some time to create + + + align:start position:0% +also it was it took some time to create +the projections so it started dissolving + + align:start position:0% +the projections so it started dissolving + + + align:start position:0% +the projections so it started dissolving +in the sugar water almost digesting also + + align:start position:0% +in the sugar water almost digesting also + + + align:start position:0% +in the sugar water almost digesting also +there's a problem of it floating in the + + align:start position:0% +there's a problem of it floating in the + + + align:start position:0% +there's a problem of it floating in the +the + + align:start position:0% +the + + + align:start position:0% +the +medium there's a problem of it floating + + align:start position:0% +medium there's a problem of it floating + + + align:start position:0% +medium there's a problem of it floating +in the medium so we just we just tuck it + + align:start position:0% +in the medium so we just we just tuck it + + + align:start position:0% +in the medium so we just we just tuck it +to the sides of the test tube + + align:start position:0% +to the sides of the test tube + + + align:start position:0% +to the sides of the test tube +so + + align:start position:0% +so + + + align:start position:0% +so +yeah why did you have to put it in water + + align:start position:0% +yeah why did you have to put it in water + + + align:start position:0% +yeah why did you have to put it in water +or was it just to show like what you + + align:start position:0% +or was it just to show like what you + + + align:start position:0% +or was it just to show like what you +would do in a medical application or uh + + align:start position:0% +would do in a medical application or uh + + + align:start position:0% +would do in a medical application or uh +that sure Laura suggested that we use + + align:start position:0% +that sure Laura suggested that we use + + + align:start position:0% +that sure Laura suggested that we use +try to use an index matching fluid so we + + align:start position:0% +try to use an index matching fluid so we + + + align:start position:0% +try to use an index matching fluid so we +don't get the lensing effect and go back + + align:start position:0% +don't get the lensing effect and go back + + + align:start position:0% +don't get the lensing effect and go back +to the projections really quick of that + + align:start position:0% +to the projections really quick of that + + + align:start position:0% +to the projections really quick of that +you can sort of see right here that it + + align:start position:0% +you can sort of see right here that it + + + align:start position:0% +you can sort of see right here that it +was forming cos stics within the candy + + align:start position:0% +was forming cos stics within the candy + + + align:start position:0% +was forming cos stics within the candy +so we were getting kind of a spherical + + align:start position:0% +so we were getting kind of a spherical + + + align:start position:0% +so we were getting kind of a spherical +lens formation Al we were Illuminating + + align:start position:0% +lens formation Al we were Illuminating + + + align:start position:0% +lens formation Al we were Illuminating +it with a a green light we were uh + + align:start position:0% +it with a a green light we were uh + + + align:start position:0% +it with a a green light we were uh +Illuminating it with a different uh + + align:start position:0% +Illuminating it with a different uh + + + align:start position:0% +Illuminating it with a different uh +color light so that's what that's one + + align:start position:0% +color light so that's what that's one + + + align:start position:0% +color light so that's what that's one +reason as well there was a green filter + + align:start position:0% +reason as well there was a green filter + + + align:start position:0% +reason as well there was a green filter +on the white light Flor and we put it in + + align:start position:0% +on the white light Flor and we put it in + + + align:start position:0% +on the white light Flor and we put it in +red fluid to get Max in + + align:start position:0% + + + + align:start position:0% + +cont + + align:start position:0% +cont + + + align:start position:0% +cont +okay thank + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/RjdAI2ycYhI.txt b/RjdAI2ycYhI.txt new file mode 100644 index 0000000000000000000000000000000000000000..dbc3cf1ccdc01b900d52e89122535aca502d01a7 --- /dev/null +++ b/RjdAI2ycYhI.txt @@ -0,0 +1,7899 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu like to try to cover two + + align:start position:0% +ocw.mit.edu like to try to cover two + + + align:start position:0% +ocw.mit.edu like to try to cover two +chapters of the book + + align:start position:0% +chapters of the book + + + align:start position:0% +chapters of the book +today not too much uh more the + + align:start position:0% +today not too much uh more the + + + align:start position:0% +today not too much uh more the +sociobiology book but some pretty + + align:start position:0% +sociobiology book but some pretty + + + align:start position:0% +sociobiology book but some pretty +interesting things still to talk + + align:start position:0% +interesting things still to talk + + + align:start position:0% +interesting things still to talk +about so what does what's the brain to a + + align:start position:0% +about so what does what's the brain to a + + + align:start position:0% +about so what does what's the brain to a +sociobiologist they say it's a + + align:start position:0% +sociobiologist they say it's a + + + align:start position:0% +sociobiologist they say it's a +reproductive organ you know just like + + align:start position:0% +reproductive organ you know just like + + + align:start position:0% +reproductive organ you know just like +every + + align:start position:0% +every + + + align:start position:0% +every +organ that any living things born with + + align:start position:0% +organ that any living things born with + + + align:start position:0% +organ that any living things born with +because they evolve by the processes of + + align:start position:0% +because they evolve by the processes of + + + align:start position:0% +because they evolve by the processes of +natural selection + + align:start position:0% +natural selection + + + align:start position:0% +natural selection +largely and that's based on the maximal + + align:start position:0% +largely and that's based on the maximal + + + align:start position:0% +largely and that's based on the maximal +transmission of change so that's + + align:start position:0% + + + + align:start position:0% + +uh what they + + align:start position:0% +uh what they + + + align:start position:0% +uh what they +assume so what would be the long range + + align:start position:0% +assume so what would be the long range + + + align:start position:0% +assume so what would be the long range +evolutionary outcome if most people + + align:start position:0% +evolutionary outcome if most people + + + align:start position:0% +evolutionary outcome if most people +really had Blank Slate brains at + + align:start position:0% +really had Blank Slate brains at + + + align:start position:0% +really had Blank Slate brains at +Birth you know what would + + align:start position:0% +Birth you know what would + + + align:start position:0% +Birth you know what would +happen if you take a society where + + align:start position:0% +happen if you take a society where + + + align:start position:0% +happen if you take a society where +everybody had + + align:start position:0% +everybody had + + + align:start position:0% +everybody had +blank blank slaves think everything was + + align:start position:0% +blank blank slaves think everything was + + + align:start position:0% +blank blank slaves think everything was +learned a common assumption and people + + align:start position:0% +learned a common assumption and people + + + align:start position:0% +learned a common assumption and people +have + + align:start position:0% +have + + + align:start position:0% +have +babies and + + align:start position:0% +babies and + + + align:start position:0% +babies and +uh so alcot goes through a little + + align:start position:0% +uh so alcot goes through a little + + + align:start position:0% +uh so alcot goes through a little +thought + + align:start position:0% +thought + + + align:start position:0% +thought +experiment and + + align:start position:0% +experiment and + + + align:start position:0% +experiment and +uh he argues I + + align:start position:0% +uh he argues I + + + align:start position:0% +uh he argues I +think pretty well that they'd be taken + + align:start position:0% +think pretty well that they'd be taken + + + align:start position:0% +think pretty well that they'd be taken +advantage of they'd be exploited by + + align:start position:0% +advantage of they'd be exploited by + + + align:start position:0% +advantage of they'd be exploited by +variants who had more targeted brains + + align:start position:0% +variants who had more targeted brains + + + align:start position:0% +variants who had more targeted brains +evolved to basically be more selfish and + + align:start position:0% +evolved to basically be more selfish and + + + align:start position:0% +evolved to basically be more selfish and +so forth and uh + + align:start position:0% +so forth and uh + + + align:start position:0% +so forth and uh +so with genetic variation the totally + + align:start position:0% +so with genetic variation the totally + + + align:start position:0% +so with genetic variation the totally +Blank Slate individuals would decrease + + align:start position:0% +Blank Slate individuals would decrease + + + align:start position:0% +Blank Slate individuals would decrease +and disappear he talks + + align:start position:0% +and disappear he talks + + + align:start position:0% +and disappear he talks +about how that would happen why it would + + align:start position:0% +about how that would happen why it would + + + align:start position:0% +about how that would happen why it would +happen and he quotes Nome chsky there + + align:start position:0% +happen and he quotes Nome chsky there + + + align:start position:0% +happen and he quotes Nome chsky there +the blank slate brain is a dictator's + + align:start position:0% + + + + align:start position:0% + +dream yes you would have dictators arise + + align:start position:0% +dream yes you would have dictators arise + + + align:start position:0% +dream yes you would have dictators arise +and take advantage of such people just + + align:start position:0% +and take advantage of such people just + + + align:start position:0% +and take advantage of such people just +educate them the way you want all right + + align:start position:0% +educate them the way you want all right + + + align:start position:0% +educate them the way you want all right +so let's go back to a topic from Scott's + + align:start position:0% +so let's go back to a topic from Scott's + + + align:start position:0% +so let's go back to a topic from Scott's +book about conditional strategies and I + + align:start position:0% +book about conditional strategies and I + + + align:start position:0% +book about conditional strategies and I +say they're common in + + align:start position:0% +say they're common in + + + align:start position:0% +say they're common in +humans do you remember a conditional + + align:start position:0% +humans do you remember a conditional + + + align:start position:0% +humans do you remember a conditional +strategy in an insect that Scott I think + + align:start position:0% +strategy in an insect that Scott I think + + + align:start position:0% +strategy in an insect that Scott I think +Scott talked about this + + align:start position:0% +Scott talked about this + + + align:start position:0% +Scott talked about this +one no it maybe he talked about a + + align:start position:0% +one no it maybe he talked about a + + + align:start position:0% +one no it maybe he talked about a +different one this one Alcock talks + + align:start position:0% +different one this one Alcock talks + + + align:start position:0% +different one this one Alcock talks +about the dung a dung + + align:start position:0% +about the dung a dung + + + align:start position:0% +about the dung a dung +beetle it shows that it's not the + + align:start position:0% +beetle it shows that it's not the + + + align:start position:0% +beetle it shows that it's not the +pre-programming of behavior is not rigid + + align:start position:0% +pre-programming of behavior is not rigid + + + align:start position:0% +pre-programming of behavior is not rigid +it can be + + align:start position:0% +it can be + + + align:start position:0% +it can be +conditional uh so he he talks about the + + align:start position:0% +conditional uh so he he talks about the + + + align:start position:0% +conditional uh so he he talks about the +RO + + align:start position:0% +RO + + + align:start position:0% +RO +Beetle that he actually did some studies + + align:start position:0% +Beetle that he actually did some studies + + + align:start position:0% +Beetle that he actually did some studies +of he went to Costa ricao with another + + align:start position:0% +of he went to Costa ricao with another + + + align:start position:0% +of he went to Costa ricao with another +scientist and did these + + align:start position:0% +scientist and did these + + + align:start position:0% +scientist and did these +studies it feeds on + + align:start position:0% +studies it feeds on + + + align:start position:0% +studies it feeds on +flies that collect at dong on the forest + + align:start position:0% +flies that collect at dong on the forest + + + align:start position:0% +flies that collect at dong on the forest +floor the large males are territorial + + align:start position:0% +floor the large males are territorial + + + align:start position:0% +floor the large males are territorial +they have very big jaws and the smaller + + align:start position:0% +they have very big jaws and the smaller + + + align:start position:0% +they have very big jaws and the smaller +males would seem like they couldn't + + align:start position:0% +males would seem like they couldn't + + + align:start position:0% +males would seem like they couldn't +wouldn't stand a chance the they can't + + align:start position:0% +wouldn't stand a chance the they can't + + + align:start position:0% +wouldn't stand a chance the they can't +really fight with those big + + align:start position:0% +really fight with those big + + + align:start position:0% +really fight with those big +males uh so what they do is they mimic + + align:start position:0% +males uh so what they do is they mimic + + + align:start position:0% +males uh so what they do is they mimic +female behavior and they're actually + + align:start position:0% +female behavior and they're actually + + + align:start position:0% +female behavior and they're actually +corded by those big males and while + + align:start position:0% +corded by those big males and while + + + align:start position:0% +corded by those big males and while +they're being corded they catch flies + + align:start position:0% +they're being corded they catch flies + + + align:start position:0% +they're being corded they catch flies +and mate with + + align:start position:0% +and mate with + + + align:start position:0% +and mate with +females the very same males though as + + align:start position:0% +females the very same males though as + + + align:start position:0% +females the very same males though as +they get bigger uh can change their + + align:start position:0% +they get bigger uh can change their + + + align:start position:0% +they get bigger uh can change their +behavior they can change to male + + align:start position:0% +behavior they can change to male + + + align:start position:0% +behavior they can change to male +Behavior so it depends on the situation + + align:start position:0% +Behavior so it depends on the situation + + + align:start position:0% +Behavior so it depends on the situation +in other + + align:start position:0% +in other + + + align:start position:0% +in other +words they're programmed the same way + + align:start position:0% +words they're programmed the same way + + + align:start position:0% +words they're programmed the same way +but but it's conditional upon how big + + align:start position:0% +but but it's conditional upon how big + + + align:start position:0% +but but it's conditional upon how big +they are how much they've grown and + + align:start position:0% +they are how much they've grown and + + + align:start position:0% +they are how much they've grown and +we've seen that in iguana we've seen + + align:start position:0% +we've seen that in iguana we've seen + + + align:start position:0% +we've seen that in iguana we've seen +that in uh other beetles this is the + + align:start position:0% +that in uh other beetles this is the + + + align:start position:0% +that in uh other beetles this is the +road + + align:start position:0% +road + + + align:start position:0% +road +Beetle you can see the dung beetles are + + align:start position:0% +Beetle you can see the dung beetles are + + + align:start position:0% +Beetle you can see the dung beetles are +very appropriate they look like a piece + + align:start position:0% +very appropriate they look like a piece + + + align:start position:0% +very appropriate they look like a piece +of dung the one on the left + + align:start position:0% +of dung the one on the left + + + align:start position:0% +of dung the one on the left +especially okay + + align:start position:0% +especially okay + + + align:start position:0% +especially okay +but they're called that of course + + align:start position:0% +but they're called that of course + + + align:start position:0% +but they're called that of course +because that's how they feed they feed + + align:start position:0% +because that's how they feed they feed + + + align:start position:0% +because that's how they feed they feed +on the flies that come to the dung + + align:start position:0% + + + + align:start position:0% + +okay so this is just what we said now + + align:start position:0% +okay so this is just what we said now + + + align:start position:0% +okay so this is just what we said now +what about learning + + align:start position:0% +what about learning + + + align:start position:0% +what about learning +mechanisms people like to think we learn + + align:start position:0% +mechanisms people like to think we learn + + + align:start position:0% +mechanisms people like to think we learn +everything but learning mechanisms + + align:start position:0% +everything but learning mechanisms + + + align:start position:0% +everything but learning mechanisms +themselves have + + align:start position:0% +themselves have + + + align:start position:0% +themselves have +evolved in order to increase + + align:start position:0% + + + + align:start position:0% + +Fitness and so as a + + align:start position:0% +Fitness and so as a + + + align:start position:0% +Fitness and so as a +result there's many different kinds of + + align:start position:0% +result there's many different kinds of + + + align:start position:0% +result there's many different kinds of +learning and they've evolved too + + align:start position:0% +learning and they've evolved too + + + align:start position:0% +learning and they've evolved too +and we can give examples of a kind + + align:start position:0% +and we can give examples of a kind + + + align:start position:0% +and we can give examples of a kind +that's + + align:start position:0% +that's + + + align:start position:0% +that's +uh that has evolved it's very different + + align:start position:0% +uh that has evolved it's very different + + + align:start position:0% +uh that has evolved it's very different +from other kinds this was the again in + + align:start position:0% +from other kinds this was the again in + + + align:start position:0% +from other kinds this was the again in +Scott's book it's called + + align:start position:0% +Scott's book it's called + + + align:start position:0% +Scott's book it's called +the it's called conditional taste + + align:start position:0% +the it's called conditional taste + + + align:start position:0% +the it's called conditional taste +aversion or the poison bait + + align:start position:0% +aversion or the poison bait + + + align:start position:0% +aversion or the poison bait +effect + + align:start position:0% +effect + + + align:start position:0% +effect +uh it just proved and it actually was + + align:start position:0% +uh it just proved and it actually was + + + align:start position:0% +uh it just proved and it actually was +very caught a lot of attention when + + align:start position:0% +very caught a lot of attention when + + + align:start position:0% +very caught a lot of attention when +Garcia who lived in California and made + + align:start position:0% +Garcia who lived in California and made + + + align:start position:0% +Garcia who lived in California and made +this discovery when it was first + + align:start position:0% +this discovery when it was first + + + align:start position:0% +this discovery when it was first +discovered uh reported in the literature + + align:start position:0% +discovered uh reported in the literature + + + align:start position:0% +discovered uh reported in the literature +because it showed that you know + + align:start position:0% +because it showed that you know + + + align:start position:0% +because it showed that you know +Skinner's universal laws of + + align:start position:0% +Skinner's universal laws of + + + align:start position:0% +Skinner's universal laws of +reinforcement learning are + + align:start position:0% +reinforcement learning are + + + align:start position:0% +reinforcement learning are +violated it just doesn't work the way + + align:start position:0% +violated it just doesn't work the way + + + align:start position:0% +violated it just doesn't work the way +other kinds of learning you should know + + align:start position:0% +other kinds of learning you should know + + + align:start position:0% +other kinds of learning you should know +how it's + + align:start position:0% +how it's + + + align:start position:0% +how it's +different + + align:start position:0% +different + + + align:start position:0% +different +uh they don't the unconditional response + + align:start position:0% +uh they don't the unconditional response + + + align:start position:0% +uh they don't the unconditional response +is they're getting ill from the effects + + align:start position:0% +is they're getting ill from the effects + + + align:start position:0% +is they're getting ill from the effects +of the + + align:start position:0% +of the + + + align:start position:0% +of the +poison you know and uh it doesn't have + + align:start position:0% +poison you know and uh it doesn't have + + + align:start position:0% +poison you know and uh it doesn't have +to occur right away whereas in the + + align:start position:0% +to occur right away whereas in the + + + align:start position:0% +to occur right away whereas in the +experiments skinners and other people + + align:start position:0% +experiments skinners and other people + + + align:start position:0% +experiments skinners and other people +that did research on this it has to + + align:start position:0% +that did research on this it has to + + + align:start position:0% +that did research on this it has to +occur quite + + align:start position:0% +occur quite + + + align:start position:0% +occur quite +quickly and one way to show that is that + + align:start position:0% +quickly and one way to show that is that + + + align:start position:0% +quickly and one way to show that is that +there's different kinds of negative + + align:start position:0% +there's different kinds of negative + + + align:start position:0% +there's different kinds of negative +reinforcement or negative reward that + + align:start position:0% +reinforcement or negative reward that + + + align:start position:0% +reinforcement or negative reward that +can have very different consequences on + + align:start position:0% +can have very different consequences on + + + align:start position:0% +can have very different consequences on +the learning of food + + align:start position:0% +the learning of food + + + align:start position:0% +the learning of food +preferences so if every time they ingest + + align:start position:0% +preferences so if every time they ingest + + + align:start position:0% +preferences so if every time they ingest +something you give them an electric + + align:start position:0% +something you give them an electric + + + align:start position:0% +something you give them an electric +shock you should be able to create a + + align:start position:0% +shock you should be able to create a + + + align:start position:0% +shock you should be able to create a +food version + + align:start position:0% +food version + + + align:start position:0% +food version +right it actually has doesn't have very + + align:start position:0% +right it actually has doesn't have very + + + align:start position:0% +right it actually has doesn't have very +much effect on their future preferences + + align:start position:0% +much effect on their future preferences + + + align:start position:0% +much effect on their future preferences +but if you take the same food a neutral + + align:start position:0% +but if you take the same food a neutral + + + align:start position:0% +but if you take the same food a neutral +food something that they normally would + + align:start position:0% +food something that they normally would + + + align:start position:0% +food something that they normally would +eat but you then expose them to x-rays + + align:start position:0% +eat but you then expose them to x-rays + + + align:start position:0% +eat but you then expose them to x-rays +that make them feel + + align:start position:0% +that make them feel + + + align:start position:0% +that make them feel +sick you do that after they eat or drink + + align:start position:0% +sick you do that after they eat or drink + + + align:start position:0% +sick you do that after they eat or drink +something it results in avoidance of + + align:start position:0% +something it results in avoidance of + + + align:start position:0% +something it results in avoidance of +that substance subsequently very + + align:start position:0% +that substance subsequently very + + + align:start position:0% +that substance subsequently very +different effects it's that feeling of + + align:start position:0% +different effects it's that feeling of + + + align:start position:0% +different effects it's that feeling of +not + + align:start position:0% +not + + + align:start position:0% +not +AIA okay the feeling of illness that and + + align:start position:0% +AIA okay the feeling of illness that and + + + align:start position:0% +AIA okay the feeling of illness that and +which doesn't have to occur immediately + + align:start position:0% +which doesn't have to occur immediately + + + align:start position:0% +which doesn't have to occur immediately +that makes them + + align:start position:0% +that makes them + + + align:start position:0% +that makes them +avoid that + + align:start position:0% +avoid that + + + align:start position:0% +avoid that +food works best if it's a novel food + + align:start position:0% +food works best if it's a novel food + + + align:start position:0% +food works best if it's a novel food +okay and we talked about that when we + + align:start position:0% +okay and we talked about that when we + + + align:start position:0% +okay and we talked about that when we +were discussing the Scott book so we + + align:start position:0% +were discussing the Scott book so we + + + align:start position:0% +were discussing the Scott book so we +want other examples of channeled nature + + align:start position:0% +want other examples of channeled nature + + + align:start position:0% +want other examples of channeled nature +of learning abilities specific for + + align:start position:0% +of learning abilities specific for + + + align:start position:0% +of learning abilities specific for +humans and and see if they're similar + + align:start position:0% +humans and and see if they're similar + + + align:start position:0% +humans and and see if they're similar +Animals by Channel we mean specific + + align:start position:0% +Animals by Channel we mean specific + + + align:start position:0% +Animals by Channel we mean specific +kinds of learning that have evolved in + + align:start position:0% +kinds of learning that have evolved in + + + align:start position:0% +kinds of learning that have evolved in +the species and these are the ones I + + align:start position:0% +the species and these are the ones I + + + align:start position:0% +the species and these are the ones I +could think + + align:start position:0% +could think + + + align:start position:0% +could think +of uh some of them are very obvious + + align:start position:0% +of uh some of them are very obvious + + + align:start position:0% +of uh some of them are very obvious +language + + align:start position:0% +language + + + align:start position:0% +language +acquisition our ability to anticipate + + align:start position:0% +acquisition our ability to anticipate + + + align:start position:0% +acquisition our ability to anticipate +the actions of + + align:start position:0% +the actions of + + + align:start position:0% +the actions of +others with a sense of others intentions + + align:start position:0% +others with a sense of others intentions + + + align:start position:0% +others with a sense of others intentions +based on what we attend to and learn uh + + align:start position:0% +based on what we attend to and learn uh + + + align:start position:0% +based on what we attend to and learn uh +often studied in this department by + + align:start position:0% +often studied in this department by + + + align:start position:0% +often studied in this department by +Laura Schultz and other people learning + + align:start position:0% +Laura Schultz and other people learning + + + align:start position:0% +Laura Schultz and other people learning +of faces for later recognition + + align:start position:0% +of faces for later recognition + + + align:start position:0% +of faces for later recognition +yes it's very special in humans and + + align:start position:0% +yes it's very special in humans and + + + align:start position:0% +yes it's very special in humans and +we've evolved a special part of the + + align:start position:0% +we've evolved a special part of the + + + align:start position:0% +we've evolved a special part of the +brain that specializes in face + + align:start position:0% +brain that specializes in face + + + align:start position:0% +brain that specializes in face +learning so do we share these abilities + + align:start position:0% +learning so do we share these abilities + + + align:start position:0% +learning so do we share these abilities +well language + + align:start position:0% +well language + + + align:start position:0% +well language +acquisition the only animals we know + + align:start position:0% +acquisition the only animals we know + + + align:start position:0% +acquisition the only animals we know +that have something similar as bird in + + align:start position:0% +that have something similar as bird in + + + align:start position:0% +that have something similar as bird in +their birds in the song birds in their + + align:start position:0% +their birds in the song birds in their + + + align:start position:0% +their birds in the song birds in their +learning of singing of + + align:start position:0% +learning of singing of + + + align:start position:0% +learning of singing of +songs uh and that's not the kind of + + align:start position:0% +songs uh and that's not the kind of + + + align:start position:0% +songs uh and that's not the kind of +language we're talking about we talk + + align:start position:0% +language we're talking about we talk + + + align:start position:0% +language we're talking about we talk +about humans but it does have some + + align:start position:0% +about humans but it does have some + + + align:start position:0% +about humans but it does have some +similarities in the nature of brain + + align:start position:0% +similarities in the nature of brain + + + align:start position:0% +similarities in the nature of brain +mechanisms hemispheric dominance for + + align:start position:0% +mechanisms hemispheric dominance for + + + align:start position:0% +mechanisms hemispheric dominance for +example uh what about this ability to + + align:start position:0% +example uh what about this ability to + + + align:start position:0% +example uh what about this ability to +anticipate the actions of others + + align:start position:0% +anticipate the actions of others + + + align:start position:0% +anticipate the actions of others +particularly important in social + + align:start position:0% +particularly important in social + + + align:start position:0% +particularly important in social +life uh we have a sense of what other + + align:start position:0% +life uh we have a sense of what other + + + align:start position:0% +life uh we have a sense of what other +people are intending to do are other + + align:start position:0% +people are intending to do are other + + + align:start position:0% +people are intending to do are other +animals like that well certainly the + + align:start position:0% +animals like that well certainly the + + + align:start position:0% +animals like that well certainly the +other primates the social primates and + + align:start position:0% +other primates the social primates and + + + align:start position:0% +other primates the social primates and +apes uh are able to to do that very + + align:start position:0% +apes uh are able to to do that very + + + align:start position:0% +apes uh are able to to do that very +well uh and there's some evidence that + + align:start position:0% +well uh and there's some evidence that + + + align:start position:0% +well uh and there's some evidence that +in fact many other mammals can do + + align:start position:0% +in fact many other mammals can do + + + align:start position:0% +in fact many other mammals can do +that but it does seem + + align:start position:0% +that but it does seem + + + align:start position:0% +that but it does seem +to it does require neocortex or in Birds + + align:start position:0% +to it does require neocortex or in Birds + + + align:start position:0% +to it does require neocortex or in Birds +the neocortical equivalent chromologist + + align:start position:0% +the neocortical equivalent chromologist + + + align:start position:0% +the neocortical equivalent chromologist +structures the hyper palum and the + + align:start position:0% +structures the hyper palum and the + + + align:start position:0% +structures the hyper palum and the +nidopallium + + align:start position:0% + + + + align:start position:0% + +okay and learning of + + align:start position:0% +okay and learning of + + + align:start position:0% +okay and learning of +faces there have been studies now of us + + align:start position:0% +faces there have been studies now of us + + + align:start position:0% +faces there have been studies now of us +particular areas of the primate + + align:start position:0% +particular areas of the primate + + + align:start position:0% +particular areas of the primate +infratemporal cortex seem to be involved + + align:start position:0% +infratemporal cortex seem to be involved + + + align:start position:0% +infratemporal cortex seem to be involved +in face learning learning human faces + + align:start position:0% +in face learning learning human faces + + + align:start position:0% +in face learning learning human faces +and monkey + + align:start position:0% + + + + align:start position:0% + +faces there's other specific abilities + + align:start position:0% +faces there's other specific abilities + + + align:start position:0% +faces there's other specific abilities +that have evolved much more in some + + align:start position:0% +that have evolved much more in some + + + align:start position:0% +that have evolved much more in some +animals than others bird song is one + + align:start position:0% +animals than others bird song is one + + + align:start position:0% +animals than others bird song is one +example uh in The Sparrows and + + align:start position:0% +example uh in The Sparrows and + + + align:start position:0% +example uh in The Sparrows and +finches + + align:start position:0% +finches + + + align:start position:0% +finches +uh some birds that cash their food and + + align:start position:0% +uh some birds that cash their food and + + + align:start position:0% +uh some birds that cash their food and +have to remember where they put it + + align:start position:0% +have to remember where they put it + + + align:start position:0% +have to remember where they put it +that's evolved very differently in + + align:start position:0% +that's evolved very differently in + + + align:start position:0% +that's evolved very differently in +different bird groups even in the same + + align:start position:0% +different bird groups even in the same + + + align:start position:0% +different bird groups even in the same +genus you find the birds some do are + + align:start position:0% +genus you find the birds some do are + + + align:start position:0% +genus you find the birds some do are +very good at it some are not and they + + align:start position:0% +very good at it some are not and they + + + align:start position:0% +very good at it some are not and they +don't do it uh in + + align:start position:0% +don't do it uh in + + + align:start position:0% +don't do it uh in +their food + + align:start position:0% +their food + + + align:start position:0% +their food +foraging and they have their brains are + + align:start position:0% +foraging and they have their brains are + + + align:start position:0% +foraging and they have their brains are +different hippocampus in particular is + + align:start position:0% +different hippocampus in particular is + + + align:start position:0% +different hippocampus in particular is +different you could say maze learning in + + align:start position:0% +different you could say maze learning in + + + align:start position:0% +different you could say maze learning in +rats is something they're they've + + align:start position:0% +rats is something they're they've + + + align:start position:0% +rats is something they're they've +adapted specifically Ally for so well + + align:start position:0% +adapted specifically Ally for so well + + + align:start position:0% +adapted specifically Ally for so well +that they often + + align:start position:0% +that they often + + + align:start position:0% +that they often +outperform college + + align:start position:0% +outperform college + + + align:start position:0% +outperform college +students in maze + + align:start position:0% + + + + align:start position:0% + +learning and they just have that pretty + + align:start position:0% +learning and they just have that pretty + + + align:start position:0% +learning and they just have that pretty +small little + + align:start position:0% +small little + + + align:start position:0% +small little +brain + + align:start position:0% + + + + align:start position:0% + +okay okay so why do humans engage in + + align:start position:0% +okay okay so why do humans engage in + + + align:start position:0% +okay okay so why do humans engage in +behaviors that seem to reduce Fitness + + align:start position:0% +behaviors that seem to reduce Fitness + + + align:start position:0% +behaviors that seem to reduce Fitness +and this has led to a lot of arguments + + align:start position:0% +and this has led to a lot of arguments + + + align:start position:0% +and this has led to a lot of arguments +some of them against are taken to AR + + align:start position:0% +some of them against are taken to AR + + + align:start position:0% +some of them against are taken to AR +they take the arguments to be against + + align:start position:0% +they take the arguments to be against + + + align:start position:0% +they take the arguments to be against +all of sociobiology but remember we + + align:start position:0% +all of sociobiology but remember we + + + align:start position:0% +all of sociobiology but remember we +talked about these things as darwinian + + align:start position:0% +talked about these things as darwinian + + + align:start position:0% +talked about these things as darwinian +puzzles and that's one of the things + + align:start position:0% +puzzles and that's one of the things + + + align:start position:0% +puzzles and that's one of the things +sociobiologists have done a lot of + + align:start position:0% +sociobiologists have done a lot of + + + align:start position:0% +sociobiologists have done a lot of +research + + align:start position:0% +research + + + align:start position:0% +research +on uh assuming that they did evolve to + + align:start position:0% +on uh assuming that they did evolve to + + + align:start position:0% +on uh assuming that they did evolve to +increase Fitness but they may no longer + + align:start position:0% +increase Fitness but they may no longer + + + align:start position:0% +increase Fitness but they may no longer +do so in the current environments + + align:start position:0% +do so in the current environments + + + align:start position:0% +do so in the current environments +because we didn't evolve the major + + align:start position:0% +because we didn't evolve the major + + + align:start position:0% +because we didn't evolve the major +period of our Evolution was very + + align:start position:0% +period of our Evolution was very + + + align:start position:0% +period of our Evolution was very +different + + align:start position:0% +different + + + align:start position:0% +different +from uh Modern Life and we talked about + + align:start position:0% +from uh Modern Life and we talked about + + + align:start position:0% +from uh Modern Life and we talked about +pet love previously + + align:start position:0% +pet love previously + + + align:start position:0% +pet love previously +uh what about alcoholism you know + + align:start position:0% +uh what about alcoholism you know + + + align:start position:0% +uh what about alcoholism you know +why do so many people have a propensity + + align:start position:0% +why do so many people have a propensity + + + align:start position:0% +why do so many people have a propensity +to overindulge in alcohol not everybody + + align:start position:0% +to overindulge in alcohol not everybody + + + align:start position:0% +to overindulge in alcohol not everybody +does and it is there are genetic + + align:start position:0% +does and it is there are genetic + + + align:start position:0% +does and it is there are genetic +differences in the people that have the + + align:start position:0% +differences in the people that have the + + + align:start position:0% +differences in the people that have the +tendency to become alcoholic but why + + align:start position:0% +tendency to become alcoholic but why + + + align:start position:0% +tendency to become alcoholic but why +would that have evolved why would there + + align:start position:0% +would that have evolved why would there + + + align:start position:0% +would that have evolved why would there +be a gene that affects + + align:start position:0% +be a gene that affects + + + align:start position:0% +be a gene that affects +it it must have had an Adaptive + + align:start position:0% +it it must have had an Adaptive + + + align:start position:0% +it it must have had an Adaptive +function well alcohol didn't used to be + + align:start position:0% +function well alcohol didn't used to be + + + align:start position:0% +function well alcohol didn't used to be +available in concentrated doses that you + + align:start position:0% +available in concentrated doses that you + + + align:start position:0% +available in concentrated doses that you +can go down to a liquor store and buy it + + align:start position:0% +can go down to a liquor store and buy it + + + align:start position:0% +can go down to a liquor store and buy it +or even at your grocery store those + + align:start position:0% +or even at your grocery store those + + + align:start position:0% +or even at your grocery store those +weren't the conditions that were present + + align:start position:0% +weren't the conditions that were present + + + align:start position:0% +weren't the conditions that were present +in most of our Evolution and what did + + align:start position:0% +in most of our Evolution and what did + + + align:start position:0% +in most of our Evolution and what did +alcohol mean to those people in living + + align:start position:0% +alcohol mean to those people in living + + + align:start position:0% +alcohol mean to those people in living +in small groups and during you know + + align:start position:0% +in small groups and during you know + + + align:start position:0% +in small groups and during you know +hundreds of thousands of years well it + + align:start position:0% +hundreds of thousands of years well it + + + align:start position:0% +hundreds of thousands of years well it +meant ripe + + align:start position:0% +meant ripe + + + align:start position:0% +meant ripe +fruit that produced some alcohol so they + + align:start position:0% +fruit that produced some alcohol so they + + + align:start position:0% +fruit that produced some alcohol so they +ripen it it means sugar and and ripe + + align:start position:0% +ripen it it means sugar and and ripe + + + align:start position:0% +ripen it it means sugar and and ripe +fruit that's provides good calories and + + align:start position:0% +fruit that's provides good calories and + + + align:start position:0% +fruit that's provides good calories and +energy U altruism of course is we talked + + align:start position:0% +energy U altruism of course is we talked + + + align:start position:0% +energy U altruism of course is we talked +about studied by triers and Alexander + + align:start position:0% +about studied by triers and Alexander + + + align:start position:0% +about studied by triers and Alexander +and other people especially they talk + + align:start position:0% +and other people especially they talk + + + align:start position:0% +and other people especially they talk +about reciprocal altruism which gives a + + align:start position:0% +about reciprocal altruism which gives a + + + align:start position:0% +about reciprocal altruism which gives a +reason why it would evolve + + align:start position:0% +reason why it would evolve + + + align:start position:0% +reason why it would evolve +supporting especially reciprocal + + align:start position:0% +supporting especially reciprocal + + + align:start position:0% +supporting especially reciprocal +altruism in genetic related people but + + align:start position:0% +altruism in genetic related people but + + + align:start position:0% +altruism in genetic related people but +in unrelated people too because and + + align:start position:0% +in unrelated people too because and + + + align:start position:0% +in unrelated people too because and +that's why the + + align:start position:0% +that's why the + + + align:start position:0% +that's why the +reciprocity seems to have evolved + + align:start position:0% +reciprocity seems to have evolved + + + align:start position:0% +reciprocity seems to have evolved +because people that benefit from others + + align:start position:0% +because people that benefit from others + + + align:start position:0% +because people that benefit from others +heal are more likely to return that + + align:start position:0% +heal are more likely to return that + + + align:start position:0% +heal are more likely to return that +later and also there's a value and + + align:start position:0% +later and also there's a value and + + + align:start position:0% +later and also there's a value and +reputation for being charitable what + + align:start position:0% +reputation for being charitable what + + + align:start position:0% +reputation for being charitable what +about use of spices and but an even more + + align:start position:0% +about use of spices and but an even more + + + align:start position:0% +about use of spices and but an even more +difficult one reductions in family size + + align:start position:0% +difficult one reductions in family size + + + align:start position:0% +difficult one reductions in family size +something we call the demographic + + align:start position:0% +something we call the demographic + + + align:start position:0% +something we call the demographic +transition where fertility rates have + + align:start position:0% +transition where fertility rates have + + + align:start position:0% +transition where fertility rates have +declined and some countries since the + + align:start position:0% +declined and some countries since the + + + align:start position:0% +declined and some countries since the +late 1800s and some since the early + + align:start position:0% +late 1800s and some since the early + + + align:start position:0% +late 1800s and some since the early +1900s so let's talk about those two + + align:start position:0% +1900s so let's talk about those two + + + align:start position:0% +1900s so let's talk about those two +things + + align:start position:0% + + + + align:start position:0% + +many people thought for a long time that + + align:start position:0% +many people thought for a long time that + + + align:start position:0% +many people thought for a long time that +spices seem to be a human luxury was + + align:start position:0% +spices seem to be a human luxury was + + + align:start position:0% +spices seem to be a human luxury was +treated that way and yet they're used + + align:start position:0% +treated that way and yet they're used + + + align:start position:0% +treated that way and yet they're used +they have such a widespread use and + + align:start position:0% +they have such a widespread use and + + + align:start position:0% +they have such a widespread use and +people place great value on spices so + + align:start position:0% +people place great value on spices so + + + align:start position:0% +people place great value on spices so +much that it led to some of the early + + align:start position:0% +much that it led to some of the early + + + align:start position:0% +much that it led to some of the early +trade routes between East and + + align:start position:0% +trade routes between East and + + + align:start position:0% +trade routes between East and +West it was treated as a darwinian + + align:start position:0% +West it was treated as a darwinian + + + align:start position:0% +West it was treated as a darwinian +puzzle but then studies were made and + + align:start position:0% +puzzle but then studies were made and + + + align:start position:0% +puzzle but then studies were made and +there's a table a nice figure figure in + + align:start position:0% +there's a table a nice figure figure in + + + align:start position:0% +there's a table a nice figure figure in +your book that shows their antimicrobial + + align:start position:0% +your book that shows their antimicrobial + + + align:start position:0% +your book that shows their antimicrobial +properties it's a a very interesting + + align:start position:0% +properties it's a a very interesting + + + align:start position:0% +properties it's a a very interesting +table you see on page + + align:start position:0% +table you see on page + + + align:start position:0% +table you see on page +179 you + + align:start position:0% +179 you + + + align:start position:0% +179 you +know huge numbers of spices that all + + align:start position:0% +know huge numbers of spices that all + + + align:start position:0% +know huge numbers of spices that all +have anti some of them kill Almost 100% + + align:start position:0% +have anti some of them kill Almost 100% + + + align:start position:0% +have anti some of them kill Almost 100% +the bacteria they're you know the one at + + align:start position:0% +the bacteria they're you know the one at + + + align:start position:0% +the bacteria they're you know the one at +the top of the list is garlic you kill + + align:start position:0% +the top of the list is garlic you kill + + + align:start position:0% +the top of the list is garlic you kill +everything in the + + align:start position:0% +everything in the + + + align:start position:0% +everything in the +food it's as good as cooking so if you + + align:start position:0% +food it's as good as cooking so if you + + + align:start position:0% +food it's as good as cooking so if you +cook and add garlic you don't have to + + align:start position:0% +cook and add garlic you don't have to + + + align:start position:0% +cook and add garlic you don't have to +worry about bacteria but there's many + + align:start position:0% +worry about bacteria but there's many + + + align:start position:0% +worry about bacteria but there's many +others that are pretty high on the list + + align:start position:0% +others that are pretty high on the list + + + align:start position:0% +others that are pretty high on the list +there and 's at least a dozen that are + + align:start position:0% +there and 's at least a dozen that are + + + align:start position:0% +there and 's at least a dozen that are +above kill more than 75% of the bacteria + + align:start position:0% +above kill more than 75% of the bacteria + + + align:start position:0% +above kill more than 75% of the bacteria +in studies that have been done I just + + align:start position:0% +in studies that have been done I just + + + align:start position:0% +in studies that have been done I just +wanted to point out there's other things + + align:start position:0% +wanted to point out there's other things + + + align:start position:0% +wanted to point out there's other things +besides antibacterial + + align:start position:0% +besides antibacterial + + + align:start position:0% +besides antibacterial +actions uh of things that people consume + + align:start position:0% +actions uh of things that people consume + + + align:start position:0% +actions uh of things that people consume +that are additives nevertheless and not + + align:start position:0% +that are additives nevertheless and not + + + align:start position:0% +that are additives nevertheless and not +necessary to get energy from the food uh + + align:start position:0% +necessary to get energy from the food uh + + + align:start position:0% +necessary to get energy from the food uh +the the Masai and batini uh tribal + + align:start position:0% +the the Masai and batini uh tribal + + + align:start position:0% +the the Masai and batini uh tribal +peoples in East Africa use + + align:start position:0% +peoples in East Africa use + + + align:start position:0% +peoples in East Africa use +additives that lower + + align:start position:0% +additives that lower + + + align:start position:0% +additives that lower +cholesterol they add ponents and + + align:start position:0% +cholesterol they add ponents and + + + align:start position:0% +cholesterol they add ponents and +phenolics that reduce their cholesterol + + align:start position:0% +phenolics that reduce their cholesterol + + + align:start position:0% +phenolics that reduce their cholesterol +and reduce that harmful side effect of + + align:start position:0% +and reduce that harmful side effect of + + + align:start position:0% +and reduce that harmful side effect of +the very high fat diet that they + + align:start position:0% +the very high fat diet that they + + + align:start position:0% +the very high fat diet that they +eat all right so let's talk about the + + align:start position:0% +eat all right so let's talk about the + + + align:start position:0% +eat all right so let's talk about the +other problem the greater one really the + + align:start position:0% +other problem the greater one really the + + + align:start position:0% +other problem the greater one really the +demographic transition it was a big + + align:start position:0% +demographic transition it was a big + + + align:start position:0% +demographic transition it was a big +darwinian puzzle there's been a lot of + + align:start position:0% +darwinian puzzle there's been a lot of + + + align:start position:0% +darwinian puzzle there's been a lot of +arguments big literature on it it's the + + align:start position:0% +arguments big literature on it it's the + + + align:start position:0% +arguments big literature on it it's the +decline in + + align:start position:0% +decline in + + + align:start position:0% +decline in +fertility + + align:start position:0% +fertility + + + align:start position:0% +fertility +uh they've looked at a number of + + align:start position:0% +uh they've looked at a number of + + + align:start position:0% +uh they've looked at a number of +different European countries that have + + align:start position:0% +different European countries that have + + + align:start position:0% +different European countries that have +been keeping + + align:start position:0% +been keeping + + + align:start position:0% +been keeping +records + + align:start position:0% +records + + + align:start position:0% +records +uh of their of + + align:start position:0% +uh of their of + + + align:start position:0% +uh of their of +births uh and their whole + + align:start position:0% +births uh and their whole + + + align:start position:0% +births uh and their whole +population in census taking for a long + + align:start position:0% +population in census taking for a long + + + align:start position:0% +population in census taking for a long +long time and the interesting thing + + align:start position:0% +long time and the interesting thing + + + align:start position:0% +long time and the interesting thing +about the demographic transition is it + + align:start position:0% +about the demographic transition is it + + + align:start position:0% +about the demographic transition is it +is that that change to reduce fertility + + align:start position:0% +is that that change to reduce fertility + + + align:start position:0% +is that that change to reduce fertility +began well before birth control modern + + align:start position:0% +began well before birth control modern + + + align:start position:0% +began well before birth control modern +birth control methods developed it's not + + align:start position:0% +birth control methods developed it's not + + + align:start position:0% +birth control methods developed it's not +that there were no birth control methods + + align:start position:0% +that there were no birth control methods + + + align:start position:0% +that there were no birth control methods +they were available in ancient times + + align:start position:0% +they were available in ancient times + + + align:start position:0% +they were available in ancient times +there were herbs that could be effective + + align:start position:0% +there were herbs that could be effective + + + align:start position:0% +there were herbs that could be effective +but the availability of all the + + align:start position:0% +but the availability of all the + + + align:start position:0% +but the availability of all the +convenient ways we have for birth + + align:start position:0% +convenient ways we have for birth + + + align:start position:0% +convenient ways we have for birth +control did not develop and yet we still + + align:start position:0% +control did not develop and yet we still + + + align:start position:0% +control did not develop and yet we still +had this population + + align:start position:0% +had this population + + + align:start position:0% +had this population +decline uh so this is the way people + + align:start position:0% +decline uh so this is the way people + + + align:start position:0% +decline uh so this is the way people +have tried to deal with that + + align:start position:0% +have tried to deal with that + + + align:start position:0% +have tried to deal with that +sociobiologists there were evolutionary + + align:start position:0% +sociobiologists there were evolutionary + + + align:start position:0% +sociobiologists there were evolutionary +advantages of timing of + + align:start position:0% +advantages of timing of + + + align:start position:0% +advantages of timing of +pregnancies having getting pregnant too + + align:start position:0% +pregnancies having getting pregnant too + + + align:start position:0% +pregnancies having getting pregnant too +soon after a birth could reduce the + + align:start position:0% +soon after a birth could reduce the + + + align:start position:0% +soon after a birth could reduce the +chances of survival of the of the + + align:start position:0% +chances of survival of the of the + + + align:start position:0% +chances of survival of the of the +earlier born individual and uh spacing + + align:start position:0% +earlier born individual and uh spacing + + + align:start position:0% +earlier born individual and uh spacing +had a great + + align:start position:0% +had a great + + + align:start position:0% +had a great +advantage and of course there were + + align:start position:0% +advantage and of course there were + + + align:start position:0% +advantage and of course there were +advantages of acquiring wealth to pass + + align:start position:0% +advantages of acquiring wealth to pass + + + align:start position:0% +advantages of acquiring wealth to pass +on to children and grandchildren it + + align:start position:0% +on to children and grandchildren it + + + align:start position:0% +on to children and grandchildren it +increased their chances their genetic + + align:start position:0% +increased their chances their genetic + + + align:start position:0% +increased their chances their genetic +fitness + + align:start position:0% +fitness + + + align:start position:0% +fitness +um their chances of of surviving and + + align:start position:0% +um their chances of of surviving and + + + align:start position:0% +um their chances of of surviving and +reproducing um alog doesn't deal at all + + align:start position:0% +reproducing um alog doesn't deal at all + + + align:start position:0% +reproducing um alog doesn't deal at all +with effects of overcrowding and there's + + align:start position:0% +with effects of overcrowding and there's + + + align:start position:0% +with effects of overcrowding and there's +a lot of overcrowding in these at least + + align:start position:0% +a lot of overcrowding in these at least + + + align:start position:0% +a lot of overcrowding in these at least +parts of these countries that he's + + align:start position:0% +parts of these countries that he's + + + align:start position:0% +parts of these countries that he's +talking about and uh certainly the + + align:start position:0% +talking about and uh certainly the + + + align:start position:0% +talking about and uh certainly the +animal studies of that which have not + + align:start position:0% +animal studies of that which have not + + + align:start position:0% +animal studies of that which have not +been common the best studies were done + + align:start position:0% +been common the best studies were done + + + align:start position:0% +been common the best studies were done +many years ago on rats that showed um + + align:start position:0% +many years ago on rats that showed um + + + align:start position:0% +many years ago on rats that showed um +very clear reductions in + + align:start position:0% +very clear reductions in + + + align:start position:0% +very clear reductions in +fertility U and effects on the immune + + align:start position:0% +fertility U and effects on the immune + + + align:start position:0% +fertility U and effects on the immune +system General so that they had more + + align:start position:0% +system General so that they had more + + + align:start position:0% +system General so that they had more +illness and also I think it's probably + + align:start position:0% +illness and also I think it's probably + + + align:start position:0% +illness and also I think it's probably +important to realize that humans evolve + + align:start position:0% +important to realize that humans evolve + + + align:start position:0% +important to realize that humans evolve +under conditions of limited + + align:start position:0% +under conditions of limited + + + align:start position:0% +under conditions of limited +communication relatively small group + + align:start position:0% +communication relatively small group + + + align:start position:0% +communication relatively small group +sizes so with the coming of Rapid + + align:start position:0% +sizes so with the coming of Rapid + + + align:start position:0% +sizes so with the coming of Rapid +longdistance communication and awareness + + align:start position:0% +longdistance communication and awareness + + + align:start position:0% +longdistance communication and awareness +of population sizes and their + + align:start position:0% +of population sizes and their + + + align:start position:0% +of population sizes and their +consequences uh which has happened only + + align:start position:0% +consequences uh which has happened only + + + align:start position:0% +consequences uh which has happened only +very recently in evolutionary times time + + align:start position:0% +very recently in evolutionary times time + + + align:start position:0% +very recently in evolutionary times time +may it certainly in Highly Educated + + align:start position:0% +may it certainly in Highly Educated + + + align:start position:0% +may it certainly in Highly Educated +people has an effect or at least could + + align:start position:0% +people has an effect or at least could + + + align:start position:0% +people has an effect or at least could +have + + align:start position:0% +have + + + align:start position:0% +have +uh then he elcot goes into another area + + align:start position:0% +uh then he elcot goes into another area + + + align:start position:0% +uh then he elcot goes into another area +that's been really controversy stirred + + align:start position:0% +that's been really controversy stirred + + + align:start position:0% +that's been really controversy stirred +up a lot of anger and everything the way + + align:start position:0% +up a lot of anger and everything the way + + + align:start position:0% +up a lot of anger and everything the way +sociobiologists have studied + + align:start position:0% +sociobiologists have studied + + + align:start position:0% +sociobiologists have studied +rape and this is an appendix + + align:start position:0% +rape and this is an appendix + + + align:start position:0% +rape and this is an appendix +question and he he + + align:start position:0% +question and he he + + + align:start position:0% +question and he he +quotes an argument against so bi + + align:start position:0% +quotes an argument against so bi + + + align:start position:0% +quotes an argument against so bi +biological ideas that rape is not very + + align:start position:0% +biological ideas that rape is not very + + + align:start position:0% +biological ideas that rape is not very +common but it's common enough to assume + + align:start position:0% +common but it's common enough to assume + + + align:start position:0% +common but it's common enough to assume +there has to be some adaptive value or + + align:start position:0% +there has to be some adaptive value or + + + align:start position:0% +there has to be some adaptive value or +it would not exist at all so this person + + align:start position:0% +it would not exist at all so this person + + + align:start position:0% +it would not exist at all so this person +argues that a substantial proportion of + + align:start position:0% +argues that a substantial proportion of + + + align:start position:0% +argues that a substantial proportion of +rapists fail to ejaculate in the victim + + align:start position:0% +rapists fail to ejaculate in the victim + + + align:start position:0% +rapists fail to ejaculate in the victim +so does that refute sociobiological + + align:start position:0% +so does that refute sociobiological + + + align:start position:0% +so does that refute sociobiological +explanations of + + align:start position:0% +explanations of + + + align:start position:0% +explanations of +rape this uh this is a feminist barbar + + align:start position:0% +rape this uh this is a feminist barbar + + + align:start position:0% +rape this uh this is a feminist barbar +aronri she says that children sired by + + align:start position:0% +aronri she says that children sired by + + + align:start position:0% +aronri she says that children sired by +rapists in the past uh surely were more + + align:start position:0% +rapists in the past uh surely were more + + + align:start position:0% +rapists in the past uh surely were more +likely to die than those of paternal + + align:start position:0% +likely to die than those of paternal + + + align:start position:0% +likely to die than those of paternal +non- rapists so rape cannot possibly be + + align:start position:0% +non- rapists so rape cannot possibly be + + + align:start position:0% +non- rapists so rape cannot possibly be +an Evol evolved + + align:start position:0% +an Evol evolved + + + align:start position:0% +an Evol evolved +adaptation she was quoted in the popular + + align:start position:0% +adaptation she was quoted in the popular + + + align:start position:0% +adaptation she was quoted in the popular +press for that so is she right and why + + align:start position:0% +press for that so is she right and why + + + align:start position:0% +press for that so is she right and why +would she make such a + + align:start position:0% +would she make such a + + + align:start position:0% +would she make such a +claim well actually well think of the + + align:start position:0% +claim well actually well think of the + + + align:start position:0% +claim well actually well think of the +2/3 that don't fail to eject + + align:start position:0% +2/3 that don't fail to eject + + + align:start position:0% +2/3 that don't fail to eject +speculate so it's certain that argument + + align:start position:0% +speculate so it's certain that argument + + + align:start position:0% +speculate so it's certain that argument +certainly does the argument that a third + + align:start position:0% +certainly does the argument that a third + + + align:start position:0% +certainly does the argument that a third +of them don't doesn't refute + + align:start position:0% +of them don't doesn't refute + + + align:start position:0% +of them don't doesn't refute +sociobiological explanations at all + + align:start position:0% +sociobiological explanations at all + + + align:start position:0% +sociobiological explanations at all +um and as far as Aaron reich's comments + + align:start position:0% +um and as far as Aaron reich's comments + + + align:start position:0% +um and as far as Aaron reich's comments +uh the fact is many of them do + + align:start position:0% +uh the fact is many of them do + + + align:start position:0% +uh the fact is many of them do +survive she may be making the claim + + align:start position:0% +survive she may be making the claim + + + align:start position:0% +survive she may be making the claim +because she does not want anyone to + + align:start position:0% +because she does not want anyone to + + + align:start position:0% +because she does not want anyone to +consider rape As Natural so we'll deal + + align:start position:0% +consider rape As Natural so we'll deal + + + align:start position:0% +consider rape As Natural so we'll deal +with that what does it mean to say + + align:start position:0% +with that what does it mean to say + + + align:start position:0% +with that what does it mean to say +something is natural and this is that + + align:start position:0% +something is natural and this is that + + + align:start position:0% +something is natural and this is that +any argument is that any moral argument + + align:start position:0% +any argument is that any moral argument + + + align:start position:0% +any argument is that any moral argument +we'll certainly argue that it is + + align:start position:0% +we'll certainly argue that it is + + + align:start position:0% +we'll certainly argue that it is +not okay of course it depends on what + + align:start position:0% +not okay of course it depends on what + + + align:start position:0% +not okay of course it depends on what +you consider natural or + + align:start position:0% +you consider natural or + + + align:start position:0% +you consider natural or +not so first of + + align:start position:0% +not so first of + + + align:start position:0% +not so first of +all it's not a natural behavior in that + + align:start position:0% +all it's not a natural behavior in that + + + align:start position:0% +all it's not a natural behavior in that +it's common it's practiced by only a + + align:start position:0% +it's common it's practiced by only a + + + align:start position:0% +it's common it's practiced by only a +small minority of men usually men + + align:start position:0% +small minority of men usually men + + + align:start position:0% +small minority of men usually men +occasional women hence it's not natural + + align:start position:0% +occasional women hence it's not natural + + + align:start position:0% +occasional women hence it's not natural +in the usual sense if by natural we mean + + align:start position:0% +in the usual sense if by natural we mean + + + align:start position:0% +in the usual sense if by natural we mean +common in a species in some species + + align:start position:0% +common in a species in some species + + + align:start position:0% +common in a species in some species +force culation is very + + align:start position:0% +force culation is very + + + align:start position:0% +force culation is very +widespread and in fact some some of the + + align:start position:0% +widespread and in fact some some of the + + + align:start position:0% +widespread and in fact some some of the +literature on this does call this uh + + align:start position:0% +literature on this does call this uh + + + align:start position:0% +literature on this does call this uh +rape we talked about that Force + + align:start position:0% +rape we talked about that Force + + + align:start position:0% +rape we talked about that Force +copulation uh and traumatic culation in + + align:start position:0% +copulation uh and traumatic culation in + + + align:start position:0% +copulation uh and traumatic culation in +many + + align:start position:0% +many + + + align:start position:0% +many +animals but I also note and alock notes + + align:start position:0% +animals but I also note and alock notes + + + align:start position:0% +animals but I also note and alock notes +that it becomes more common in humans + + align:start position:0% +that it becomes more common in humans + + + align:start position:0% +that it becomes more common in humans +and under certain conditions like + + align:start position:0% +and under certain conditions like + + + align:start position:0% +and under certain conditions like +wartime wartime + + align:start position:0% +wartime wartime + + + align:start position:0% +wartime wartime +conquests so it could in that sense be + + align:start position:0% +conquests so it could in that sense be + + + align:start position:0% +conquests so it could in that sense be +considered a conditional strategy + + align:start position:0% +considered a conditional strategy + + + align:start position:0% +considered a conditional strategy +however in horen that may seem all right + + align:start position:0% +however in horen that may seem all right + + + align:start position:0% +however in horen that may seem all right +so another issue is another appendix + + align:start position:0% +so another issue is another appendix + + + align:start position:0% +so another issue is another appendix +question if men and women differ in how + + align:start position:0% +question if men and women differ in how + + + align:start position:0% +question if men and women differ in how +much they invest in Parental + + align:start position:0% +much they invest in Parental + + + align:start position:0% +much they invest in Parental +care is it strictly because of the + + align:start position:0% +care is it strictly because of the + + + align:start position:0% +care is it strictly because of the +nature of societal influences they + + align:start position:0% +nature of societal influences they + + + align:start position:0% +nature of societal influences they +experienced when young which is what has + + align:start position:0% +experienced when young which is what has + + + align:start position:0% +experienced when young which is what has +been argued hasn't that shaped their + + align:start position:0% +been argued hasn't that shaped their + + + align:start position:0% +been argued hasn't that shaped their +view of appr sex roles well how would + + align:start position:0% +view of appr sex roles well how would + + + align:start position:0% +view of appr sex roles well how would +you test + + align:start position:0% +you test + + + align:start position:0% +you test +it you know this is what you'd have to + + align:start position:0% +it you know this is what you'd have to + + + align:start position:0% +it you know this is what you'd have to +do for one thing you could do + + align:start position:0% +do for one thing you could do + + + align:start position:0% +do for one thing you could do +uh we want to know if all male female + + align:start position:0% +uh we want to know if all male female + + + align:start position:0% +uh we want to know if all male female +differences in Parental care are learned + + align:start position:0% +differences in Parental care are learned + + + align:start position:0% +differences in Parental care are learned +because the statistics are overwhelming + + align:start position:0% +because the statistics are overwhelming + + + align:start position:0% +because the statistics are overwhelming +you know + + align:start position:0% +you know + + + align:start position:0% +you know +women spend much more of their time uh + + align:start position:0% +women spend much more of their time uh + + + align:start position:0% +women spend much more of their time uh +in Parental + + align:start position:0% +in Parental + + + align:start position:0% +in Parental +care cross-cultural studies why is it + + align:start position:0% +care cross-cultural studies why is it + + + align:start position:0% +care cross-cultural studies why is it +that nearly all cultures are similar in + + align:start position:0% +that nearly all cultures are similar in + + + align:start position:0% +that nearly all cultures are similar in +this I didn't say all but most okay + + align:start position:0% +this I didn't say all but most okay + + + align:start position:0% +this I didn't say all but most okay +there are a few + + align:start position:0% +there are a few + + + align:start position:0% +there are a few +exceptions what about twin + + align:start position:0% +exceptions what about twin + + + align:start position:0% +exceptions what about twin +studies are variations in Parental care + + align:start position:0% +studies are variations in Parental care + + + align:start position:0% +studies are variations in Parental care +genetically influenced see I don't know + + align:start position:0% +genetically influenced see I don't know + + + align:start position:0% +genetically influenced see I don't know +the answer to that + + align:start position:0% +the answer to that + + + align:start position:0% +the answer to that +one uh and there also in fact this has + + align:start position:0% +one uh and there also in fact this has + + + align:start position:0% +one uh and there also in fact this has +occurred in scientists there's a + + align:start position:0% +occurred in scientists there's a + + + align:start position:0% +occurred in scientists there's a +deliberate attempts by caregivers to + + align:start position:0% +deliberate attempts by caregivers to + + + align:start position:0% +deliberate attempts by caregivers to +influence children you know to be care + + align:start position:0% +influence children you know to be care + + + align:start position:0% +influence children you know to be care +more about taking care of children and + + align:start position:0% +more about taking care of children and + + + align:start position:0% +more about taking care of children and +so + + align:start position:0% +so + + + align:start position:0% +so +forth what do you think the outcome has + + align:start position:0% +forth what do you think the outcome has + + + align:start position:0% +forth what do you think the outcome has +been it actually doesn't make much + + align:start position:0% +been it actually doesn't make much + + + align:start position:0% +been it actually doesn't make much +difference you know there's still a big + + align:start position:0% +difference you know there's still a big + + + align:start position:0% +difference you know there's still a big +M male female + + align:start position:0% + + + + align:start position:0% + +difference okay another appendix + + align:start position:0% +difference okay another appendix + + + align:start position:0% +difference okay another appendix +question + + align:start position:0% +question + + + align:start position:0% +question +uh the sociobiological the reactions + + align:start position:0% +uh the sociobiological the reactions + + + align:start position:0% +uh the sociobiological the reactions +against the hypothesis that men have a + + align:start position:0% +against the hypothesis that men have a + + + align:start position:0% +against the hypothesis that men have a +predisposition to seek out multiple sex + + align:start position:0% +predisposition to seek out multiple sex + + + align:start position:0% +predisposition to seek out multiple sex +partners of high fertility and lanon + + align:start position:0% +partners of high fertility and lanon + + + align:start position:0% +partners of high fertility and lanon +he + + align:start position:0% +he + + + align:start position:0% +he +simply gives his his own example I'm a + + align:start position:0% +simply gives his his own example I'm a + + + align:start position:0% +simply gives his his own example I'm a +man I don't go around screwing young + + align:start position:0% +man I don't go around screwing young + + + align:start position:0% +man I don't go around screwing young +girls I'm human so I have to be + + align:start position:0% +girls I'm human so I have to be + + + align:start position:0% +girls I'm human so I have to be +explained so what does a sociobiologist + + align:start position:0% +explained so what does a sociobiologist + + + align:start position:0% +explained so what does a sociobiologist +say it's not about exceptions it's about + + align:start position:0% +say it's not about exceptions it's about + + + align:start position:0% +say it's not about exceptions it's about +the the more general + + align:start position:0% +the the more general + + + align:start position:0% +the the more general +rule and some men claim loudly that they + + align:start position:0% +rule and some men claim loudly that they + + + align:start position:0% +rule and some men claim loudly that they +are + + align:start position:0% + + + + align:start position:0% + +monogamous how do you deal with + + align:start position:0% +monogamous how do you deal with + + + align:start position:0% +monogamous how do you deal with +that we are dealt with lean and + + align:start position:0% +that we are dealt with lean and + + + align:start position:0% +that we are dealt with lean and +uh why might he do this well he can that + + align:start position:0% +uh why might he do this well he can that + + + align:start position:0% +uh why might he do this well he can that +can have be helpful to him it can + + align:start position:0% +can have be helpful to him it can + + + align:start position:0% +can have be helpful to him it can +convince his mate to be monogamous too + + align:start position:0% +convince his mate to be monogamous too + + + align:start position:0% +convince his mate to be monogamous too +he wants to have only she'll have only + + align:start position:0% +he wants to have only she'll have only + + + align:start position:0% +he wants to have only she'll have only +his kids it may give the man more + + align:start position:0% +his kids it may give the man more + + + align:start position:0% +his kids it may give the man more +influence or power in social groups and + + align:start position:0% +influence or power in social groups and + + + align:start position:0% +influence or power in social groups and +when he people that talk loudly about it + + align:start position:0% +when he people that talk loudly about it + + + align:start position:0% +when he people that talk loudly about it +you begin to get + + align:start position:0% +you begin to get + + + align:start position:0% +you begin to get +suspicious so and we see examples of + + align:start position:0% +suspicious so and we see examples of + + + align:start position:0% +suspicious so and we see examples of +this in the news too often you know they + + align:start position:0% +this in the news too often you know they + + + align:start position:0% +this in the news too often you know they +do it because they're covering for + + align:start position:0% +do it because they're covering for + + + align:start position:0% +do it because they're covering for +something they actually are doing okay + + align:start position:0% + + + + align:start position:0% + +uh I know some of these things would be + + align:start position:0% +uh I know some of these things would be + + + align:start position:0% +uh I know some of these things would be +nice to explore a little further but I + + align:start position:0% +nice to explore a little further but I + + + align:start position:0% +nice to explore a little further but I +want to go through both + + align:start position:0% +want to go through both + + + align:start position:0% +want to go through both +chapters so let's deal with a few of the + + align:start position:0% +chapters so let's deal with a few of the + + + align:start position:0% +chapters so let's deal with a few of the +Practical issues in thinking about and + + align:start position:0% +Practical issues in thinking about and + + + align:start position:0% +Practical issues in thinking about and +collecting data on + + align:start position:0% + + + + align:start position:0% + +adaptations let's talk let's first talk + + align:start position:0% +adaptations let's talk let's first talk + + + align:start position:0% +adaptations let's talk let's first talk +about the misuse of scientific findings + + align:start position:0% +about the misuse of scientific findings + + + align:start position:0% +about the misuse of scientific findings +or claims and service of political + + align:start position:0% +or claims and service of political + + + align:start position:0% +or claims and service of political +goals including things concerning + + align:start position:0% +goals including things concerning + + + align:start position:0% +goals including things concerning +sociobiology or darwinian Theory + + align:start position:0% +sociobiology or darwinian Theory + + + align:start position:0% +sociobiology or darwinian Theory +okay and sociobiologists of course are + + align:start position:0% +okay and sociobiologists of course are + + + align:start position:0% +okay and sociobiologists of course are +darwinian theorists or using darwinian + + align:start position:0% +darwinian theorists or using darwinian + + + align:start position:0% +darwinian theorists or using darwinian +Theory as their Major + + align:start position:0% +Theory as their Major + + + align:start position:0% +Theory as their Major +Tool so we have the Eugenics argument + + align:start position:0% +Tool so we have the Eugenics argument + + + align:start position:0% +Tool so we have the Eugenics argument +uh the Nazis claim that their racism and + + align:start position:0% +uh the Nazis claim that their racism and + + + align:start position:0% +uh the Nazis claim that their racism and +even Genesis was based on + + align:start position:0% + + + + align:start position:0% + +genetics and then in the 19th century + + align:start position:0% +genetics and then in the 19th century + + + align:start position:0% +genetics and then in the 19th century +there was social Darwinism a lot written + + align:start position:0% +there was social Darwinism a lot written + + + align:start position:0% +there was social Darwinism a lot written +about it it was used to justify + + align:start position:0% +about it it was used to justify + + + align:start position:0% +about it it was used to justify +dominance and superiority of the + + align:start position:0% + + + + align:start position:0% + +Rich and then of course the claim that + + align:start position:0% +Rich and then of course the claim that + + + align:start position:0% +Rich and then of course the claim that +infidelity is natural therefore + + align:start position:0% +infidelity is natural therefore + + + align:start position:0% +infidelity is natural therefore +understandable therefore justifiable + + align:start position:0% +understandable therefore justifiable + + + align:start position:0% +understandable therefore justifiable +we'll come back to that similarly claims + + align:start position:0% +we'll come back to that similarly claims + + + align:start position:0% +we'll come back to that similarly claims +justifying the subjugation of women all + + align:start position:0% +justifying the subjugation of women all + + + align:start position:0% +justifying the subjugation of women all +of these arguments have been made using + + align:start position:0% +of these arguments have been made using + + + align:start position:0% +of these arguments have been made using +scientific + + align:start position:0% +scientific + + + align:start position:0% +scientific +findings but the arguments have always + + align:start position:0% +findings but the arguments have always + + + align:start position:0% +findings but the arguments have always +been flawed so let's talk about a little + + align:start position:0% +been flawed so let's talk about a little + + + align:start position:0% +been flawed so let's talk about a little +more about this first of all I want you + + align:start position:0% +more about this first of all I want you + + + align:start position:0% +more about this first of all I want you +to be able to see that just the way + + align:start position:0% +to be able to see that just the way + + + align:start position:0% +to be able to see that just the way +things are stated makes a big + + align:start position:0% +things are stated makes a big + + + align:start position:0% +things are stated makes a big +difference let's summarize + + align:start position:0% +difference let's summarize + + + align:start position:0% +difference let's summarize +sociobiological + + align:start position:0% +sociobiological + + + align:start position:0% +sociobiological +findings uh stating first of + + align:start position:0% +findings uh stating first of + + + align:start position:0% +findings uh stating first of +all make it sound like people ought to + + align:start position:0% +all make it sound like people ought to + + + align:start position:0% +all make it sound like people ought to +behave in a certain way and then restate + + align:start position:0% +behave in a certain way and then restate + + + align:start position:0% +behave in a certain way and then restate +the finding in a more objective way + + align:start position:0% +the finding in a more objective way + + + align:start position:0% +the finding in a more objective way +because there's there's more objective + + align:start position:0% +because there's there's more objective + + + align:start position:0% +because there's there's more objective +and less objective ways to State these + + align:start position:0% + + + + align:start position:0% + +findings so for example take this + + align:start position:0% +findings so for example take this + + + align:start position:0% +findings so for example take this +statement it is natural to being male + + align:start position:0% +statement it is natural to being male + + + align:start position:0% +statement it is natural to being male +for men to want to have power and + + align:start position:0% +for men to want to have power and + + + align:start position:0% +for men to want to have power and +dominance over others including women + + align:start position:0% +dominance over others including women + + + align:start position:0% +dominance over others including women +you say it like that it sounds like it's + + align:start position:0% +you say it like that it sounds like it's + + + align:start position:0% +you say it like that it sounds like it's +approval you proove of that or justify + + align:start position:0% +approval you proove of that or justify + + + align:start position:0% +approval you proove of that or justify +it in some way but you can restate the + + align:start position:0% +it in some way but you can restate the + + + align:start position:0% +it in some way but you can restate the +actual finding men more than women have + + align:start position:0% +actual finding men more than women have + + + align:start position:0% +actual finding men more than women have +a tendency on average to strive for + + align:start position:0% +a tendency on average to strive for + + + align:start position:0% +a tendency on average to strive for +positions of power and dominance + + align:start position:0% +positions of power and dominance + + + align:start position:0% +positions of power and dominance +perfectly true okay but now it doesn't + + align:start position:0% +perfectly true okay but now it doesn't + + + align:start position:0% +perfectly true okay but now it doesn't +sound like you're you're you're being + + align:start position:0% +sound like you're you're you're being + + + align:start position:0% +sound like you're you're you're being +neutral you're presenting a + + align:start position:0% +neutral you're presenting a + + + align:start position:0% +neutral you're presenting a +finding + + align:start position:0% + + + + align:start position:0% + +okay a related thing using equating + + align:start position:0% +okay a related thing using equating + + + align:start position:0% +okay a related thing using equating +natural and + + align:start position:0% +natural and + + + align:start position:0% +natural and +good I often tell my kids you go through + + align:start position:0% +good I often tell my kids you go through + + + align:start position:0% +good I often tell my kids you go through +a supermarket and you read these big + + align:start position:0% +a supermarket and you read these big + + + align:start position:0% +a supermarket and you read these big +letters all natural natural that doesn't + + align:start position:0% +letters all natural natural that doesn't + + + align:start position:0% +letters all natural natural that doesn't +make it good you + + align:start position:0% +make it good you + + + align:start position:0% +make it good you +know all right + + align:start position:0% +know all right + + + align:start position:0% +know all right +uh well the evolved traits have helped + + align:start position:0% +uh well the evolved traits have helped + + + align:start position:0% +uh well the evolved traits have helped +keep certain genes in the gene pool not + + align:start position:0% +keep certain genes in the gene pool not + + + align:start position:0% +keep certain genes in the gene pool not +because it was good for the individual + + align:start position:0% +because it was good for the individual + + + align:start position:0% +because it was good for the individual +good for the group or good for the + + align:start position:0% +good for the group or good for the + + + align:start position:0% +good for the group or good for the +species as a whole but just because + + align:start position:0% +species as a whole but just because + + + align:start position:0% +species as a whole but just because +possession of these traits happened to + + align:start position:0% +possession of these traits happened to + + + align:start position:0% +possession of these traits happened to +be correlated with success and Gene + + align:start position:0% +be correlated with success and Gene + + + align:start position:0% +be correlated with success and Gene +propagation so no more lessons can be + + align:start position:0% +propagation so no more lessons can be + + + align:start position:0% +propagation so no more lessons can be +drawn from the unfeeling blind process + + align:start position:0% +drawn from the unfeeling blind process + + + align:start position:0% +drawn from the unfeeling blind process +of natural + + align:start position:0% +of natural + + + align:start position:0% +of natural +selection + + align:start position:0% + + + + align:start position:0% + +come back to that one too medical + + align:start position:0% +come back to that one too medical + + + align:start position:0% +come back to that one too medical +issues an + + align:start position:0% +issues an + + + align:start position:0% +issues an +example of medical issue medical issues + + align:start position:0% +example of medical issue medical issues + + + align:start position:0% +example of medical issue medical issues +that can be illumined by soci + + align:start position:0% +that can be illumined by soci + + + align:start position:0% +that can be illumined by soci +sociobiological ideas take an adaptation + + align:start position:0% +sociobiological ideas take an adaptation + + + align:start position:0% +sociobiological ideas take an adaptation +approach and these are things I can + + align:start position:0% +approach and these are things I can + + + align:start position:0% +approach and these are things I can +think of uh galok discusses morning + + align:start position:0% +think of uh galok discusses morning + + + align:start position:0% +think of uh galok discusses morning +sickness and there it's probably a + + align:start position:0% +sickness and there it's probably a + + + align:start position:0% +sickness and there it's probably a +little easier to understand how that + + align:start position:0% +little easier to understand how that + + + align:start position:0% +little easier to understand how that +could be adaptive it seems horrible why + + align:start position:0% +could be adaptive it seems horrible why + + + align:start position:0% +could be adaptive it seems horrible why +should a woman get pregnant and have to + + align:start position:0% +should a woman get pregnant and have to + + + align:start position:0% +should a woman get pregnant and have to +go through this horrible sickness it's + + align:start position:0% +go through this horrible sickness it's + + + align:start position:0% +go through this horrible sickness it's +much greater in some women than in + + align:start position:0% +much greater in some women than in + + + align:start position:0% +much greater in some women than in +others but when they get morning + + align:start position:0% +others but when they get morning + + + align:start position:0% +others but when they get morning +sickness for most of them it's in the + + align:start position:0% +sickness for most of them it's in the + + + align:start position:0% +sickness for most of them it's in the +early period when that fetus is most + + align:start position:0% +early period when that fetus is most + + + align:start position:0% +early period when that fetus is most +vulnerable to things she's eating and + + align:start position:0% +vulnerable to things she's eating and + + + align:start position:0% +vulnerable to things she's eating and +this keeps her from eating a lot any + + align:start position:0% +this keeps her from eating a lot any + + + align:start position:0% +this keeps her from eating a lot any +really strange foods or particular kinds + + align:start position:0% +really strange foods or particular kinds + + + align:start position:0% +really strange foods or particular kinds +of foods they also have very particular + + align:start position:0% +of foods they also have very particular + + + align:start position:0% +of foods they also have very particular +taste it probably signals some + + align:start position:0% +taste it probably signals some + + + align:start position:0% +taste it probably signals some +nutritional + + align:start position:0% +nutritional + + + align:start position:0% +nutritional +need okay so that's the first + + align:start position:0% +need okay so that's the first + + + align:start position:0% +need okay so that's the first +one uh and there have been studies of + + align:start position:0% +one uh and there have been studies of + + + align:start position:0% +one uh and there have been studies of +this that indicate that this is true + + align:start position:0% +this that indicate that this is true + + + align:start position:0% +this that indicate that this is true +what about fever and + + align:start position:0% +what about fever and + + + align:start position:0% +what about fever and +pain first of all there have been some + + align:start position:0% +pain first of all there have been some + + + align:start position:0% +pain first of all there have been some +studies of + + align:start position:0% +studies of + + + align:start position:0% +studies of +fever uh I mean we get fever when we + + align:start position:0% +fever uh I mean we get fever when we + + + align:start position:0% +fever uh I mean we get fever when we +have an infection + + align:start position:0% +have an infection + + + align:start position:0% +have an infection +right is that benefiting the body there + + align:start position:0% +right is that benefiting the body there + + + align:start position:0% +right is that benefiting the body there +is some evidence there have been some + + align:start position:0% +is some evidence there have been some + + + align:start position:0% +is some evidence there have been some +studies that in fact it does improve a + + align:start position:0% +studies that in fact it does improve a + + + align:start position:0% +studies that in fact it does improve a +bit ability of the body to fight disease + + align:start position:0% +bit ability of the body to fight disease + + + align:start position:0% +bit ability of the body to fight disease +but yes it can get out of hand what + + align:start position:0% +but yes it can get out of hand what + + + align:start position:0% +but yes it can get out of hand what +happens say if a child gets a fever that + + align:start position:0% +happens say if a child gets a fever that + + + align:start position:0% +happens say if a child gets a fever that +runs up to 105 and + + align:start position:0% + + + + align:start position:0% + +higher you know what can happen I used + + align:start position:0% +higher you know what can happen I used + + + align:start position:0% +higher you know what can happen I used +to run fevers really high and every time + + align:start position:0% +to run fevers really high and every time + + + align:start position:0% +to run fevers really high and every time +I got sick when I was a little child + + align:start position:0% +I got sick when I was a little child + + + align:start position:0% +I got sick when I was a little child +what did my parents do well they start + + align:start position:0% +what did my parents do well they start + + + align:start position:0% +what did my parents do well they start +putting coal packs on my head they tried + + align:start position:0% +putting coal packs on my head they tried + + + align:start position:0% +putting coal packs on my head they tried +to cool me + + align:start position:0% +to cool me + + + align:start position:0% +to cool me +down and they I don't think they realize + + align:start position:0% +down and they I don't think they realize + + + align:start position:0% +down and they I don't think they realize +why they did it they did it because it + + align:start position:0% +why they did it they did it because it + + + align:start position:0% +why they did it they did it because it +was a tradition in their families do + + align:start position:0% +was a tradition in their families do + + + align:start position:0% +was a tradition in their families do +this you got very high fever but what + + align:start position:0% +this you got very high fever but what + + + align:start position:0% +this you got very high fever but what +can happen SE seizures febril fits okay + + align:start position:0% +can happen SE seizures febril fits okay + + + align:start position:0% +can happen SE seizures febril fits okay +and febril fits in the very young can + + align:start position:0% +and febril fits in the very young can + + + align:start position:0% +and febril fits in the very young can +cause brain damage okay they can wipe + + align:start position:0% +cause brain damage okay they can wipe + + + align:start position:0% +cause brain damage okay they can wipe +out part of the temple load the amydala + + align:start position:0% +out part of the temple load the amydala + + + align:start position:0% +out part of the temple load the amydala +in particular okay so they can be they + + align:start position:0% +in particular okay so they can be they + + + align:start position:0% +in particular okay so they can be they +get dangerous but they fever did evolve + + align:start position:0% +get dangerous but they fever did evolve + + + align:start position:0% +get dangerous but they fever did evolve +for biological adaptive reasons what + + align:start position:0% +for biological adaptive reasons what + + + align:start position:0% +for biological adaptive reasons what +about pain why do we have to suffer so + + align:start position:0% +about pain why do we have to suffer so + + + align:start position:0% +about pain why do we have to suffer so +much pain can be horrible right well + + align:start position:0% +much pain can be horrible right well + + + align:start position:0% +much pain can be horrible right well +take someone who has a con congenital + + align:start position:0% +take someone who has a con congenital + + + align:start position:0% +take someone who has a con congenital +absence of pain what do they like they + + align:start position:0% +absence of pain what do they like they + + + align:start position:0% +absence of pain what do they like they +usually don't even survive to your + + align:start position:0% +usually don't even survive to your + + + align:start position:0% +usually don't even survive to your +age because they keep getting injured + + align:start position:0% +age because they keep getting injured + + + align:start position:0% +age because they keep getting injured +they they don't even change positions + + align:start position:0% +they they don't even change positions + + + align:start position:0% +they they don't even change positions +they don't become uncomfortable enough + + align:start position:0% +they don't become uncomfortable enough + + + align:start position:0% +they don't become uncomfortable enough +to change positions when they're sitting + + align:start position:0% +to change positions when they're sitting + + + align:start position:0% +to change positions when they're sitting +or lying down so they end up with + + align:start position:0% +or lying down so they end up with + + + align:start position:0% +or lying down so they end up with +circulation problems one after + + align:start position:0% +circulation problems one after + + + align:start position:0% +circulation problems one after +another okay it takes a lot of extra + + align:start position:0% +another okay it takes a lot of extra + + + align:start position:0% +another okay it takes a lot of extra +care and help from others to survive + + align:start position:0% +care and help from others to survive + + + align:start position:0% +care and help from others to survive +that condition the absence of pain it + + align:start position:0% +that condition the absence of pain it + + + align:start position:0% +that condition the absence of pain it +serves very useful + + align:start position:0% + + + + align:start position:0% + +functions I wonder sometimes when it + + align:start position:0% +functions I wonder sometimes when it + + + align:start position:0% +functions I wonder sometimes when it +comes to tooth + + align:start position:0% +comes to tooth + + + align:start position:0% +comes to tooth +pain pain in general is very adaptive + + align:start position:0% +pain pain in general is very adaptive + + + align:start position:0% +pain pain in general is very adaptive +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so + + align:start position:0% +so + + + align:start position:0% +so +let's talk about how studies of we + + align:start position:0% +let's talk about how studies of we + + + align:start position:0% +let's talk about how studies of we +brought this up before comp how to + + align:start position:0% +brought this up before comp how to + + + align:start position:0% +brought this up before comp how to +comparative studies help us understand + + align:start position:0% +comparative studies help us understand + + + align:start position:0% +comparative studies help us understand +some of these issues why are studies of + + align:start position:0% +some of these issues why are studies of + + + align:start position:0% +some of these issues why are studies of +the behavior of the white fronted bee + + align:start position:0% +the behavior of the white fronted bee + + + align:start position:0% +the behavior of the white fronted bee +eaters Birds relevant to human behavior + + align:start position:0% +eaters Birds relevant to human behavior + + + align:start position:0% +eaters Birds relevant to human behavior +these are birds that have helpers at the + + align:start position:0% +these are birds that have helpers at the + + + align:start position:0% +these are birds that have helpers at the +nest they both both species have + + align:start position:0% +nest they both both species have + + + align:start position:0% +nest they both both species have +families that persist over long time + + align:start position:0% +families that persist over long time + + + align:start position:0% +families that persist over long time +periods so they they've had similar + + align:start position:0% +periods so they they've had similar + + + align:start position:0% +periods so they they've had similar +selective + + align:start position:0% +selective + + + align:start position:0% +selective +pressures helping by help helping + + align:start position:0% +pressures helping by help helping + + + align:start position:0% +pressures helping by help helping +helpers at the nest is by Offspring + + align:start position:0% +helpers at the nest is by Offspring + + + align:start position:0% +helpers at the nest is by Offspring +usually full siblings sharing about 50% + + align:start position:0% +usually full siblings sharing about 50% + + + align:start position:0% +usually full siblings sharing about 50% +of the genes with the ones that they're + + align:start position:0% +of the genes with the ones that they're + + + align:start position:0% +of the genes with the ones that they're +helping take care + + align:start position:0% +helping take care + + + align:start position:0% +helping take care +of so they are improving their genetic + + align:start position:0% +of so they are improving their genetic + + + align:start position:0% +of so they are improving their genetic +fitness in that + + align:start position:0% +fitness in that + + + align:start position:0% +fitness in that +sense so we can ask questions like well + + align:start position:0% +sense so we can ask questions like well + + + align:start position:0% +sense so we can ask questions like well +how beneficial is the helping and this + + align:start position:0% +how beneficial is the helping and this + + + align:start position:0% +how beneficial is the helping and this +has been studied extensively in the + + align:start position:0% +has been studied extensively in the + + + align:start position:0% +has been studied extensively in the +white fronted be eaters and in that + + align:start position:0% +white fronted be eaters and in that + + + align:start position:0% +white fronted be eaters and in that +species because of the habitat they live + + align:start position:0% +species because of the habitat they live + + + align:start position:0% +species because of the habitat they live +at there's a figure on page 98 that goes + + align:start position:0% +at there's a figure on page 98 that goes + + + align:start position:0% +at there's a figure on page 98 that goes +through + + align:start position:0% +through + + + align:start position:0% +through +this uh just to get one surviving chick + + align:start position:0% +this uh just to get one surviving chick + + + align:start position:0% +this uh just to get one surviving chick +it takes three adults to bring enough + + align:start position:0% +it takes three adults to bring enough + + + align:start position:0% +it takes three adults to bring enough +food for it because you know the adults + + align:start position:0% +food for it because you know the adults + + + align:start position:0% +food for it because you know the adults +have to feed themselves too so they + + align:start position:0% +have to feed themselves too so they + + + align:start position:0% +have to feed themselves too so they +don't have much extra to give the baby + + align:start position:0% +don't have much extra to give the baby + + + align:start position:0% +don't have much extra to give the baby +and that's why two adults usually can't + + align:start position:0% +and that's why two adults usually can't + + + align:start position:0% +and that's why two adults usually can't +succeed in keeping one chick alive and + + align:start position:0% +succeed in keeping one chick alive and + + + align:start position:0% +succeed in keeping one chick alive and +it takes five adults on average to have + + align:start position:0% +it takes five adults on average to have + + + align:start position:0% +it takes five adults on average to have +two surviving + + align:start position:0% + + + + align:start position:0% + +chicks all right so + + align:start position:0% +chicks all right so + + + align:start position:0% +chicks all right so +two and a half for one that means + + align:start position:0% +two and a half for one that means + + + align:start position:0% +two and a half for one that means +three okay but there's conflicts that + + align:start position:0% +three okay but there's conflicts that + + + align:start position:0% +three okay but there's conflicts that +arise and this happens in the birds it + + align:start position:0% +arise and this happens in the birds it + + + align:start position:0% +arise and this happens in the birds it +happens in + + align:start position:0% +happens in + + + align:start position:0% +happens in +humans the fathers have conflicts with + + align:start position:0% +humans the fathers have conflicts with + + + align:start position:0% +humans the fathers have conflicts with +the male offspring that are helpers at + + align:start position:0% +the male offspring that are helpers at + + + align:start position:0% +the male offspring that are helpers at +the nest uh and this can vary a lot but + + align:start position:0% +the nest uh and this can vary a lot but + + + align:start position:0% +the nest uh and this can vary a lot but +it does happen and what happens if the + + align:start position:0% +it does happen and what happens if the + + + align:start position:0% +it does happen and what happens if the +female mate + + align:start position:0% +female mate + + + align:start position:0% +female mate +dies and there's a helper at the nest + + align:start position:0% +dies and there's a helper at the nest + + + align:start position:0% +dies and there's a helper at the nest +well if the male gets another female + + align:start position:0% +well if the male gets another female + + + align:start position:0% +well if the male gets another female +made what does his male how does his + + align:start position:0% +made what does his male how does his + + + align:start position:0% +made what does his male how does his +male respond well you continue to take + + align:start position:0% +male respond well you continue to take + + + align:start position:0% +male respond well you continue to take +care of chicks if there's there there're + + align:start position:0% +care of chicks if there's there there're + + + align:start position:0% +care of chicks if there's there there're +still is full siblings but when he + + align:start position:0% +still is full siblings but when he + + + align:start position:0% +still is full siblings but when he +starts having + + align:start position:0% +starts having + + + align:start position:0% +starts having +more it's very common for that male + + align:start position:0% +more it's very common for that male + + + align:start position:0% +more it's very common for that male +helper at the nest to leave and go off + + align:start position:0% +helper at the nest to leave and go off + + + align:start position:0% +helper at the nest to leave and go off +and form its own + + align:start position:0% +and form its own + + + align:start position:0% +and form its own +nest they generally don't like to take + + align:start position:0% +nest they generally don't like to take + + + align:start position:0% +nest they generally don't like to take +care of U on average they don't stay + + align:start position:0% +care of U on average they don't stay + + + align:start position:0% +care of U on average they don't stay +around to take care of siblings that + + align:start position:0% +around to take care of siblings that + + + align:start position:0% +around to take care of siblings that +were they share less than half the genes + + align:start position:0% +were they share less than half the genes + + + align:start position:0% +were they share less than half the genes +because it goes down like 25% if they're + + align:start position:0% +because it goes down like 25% if they're + + + align:start position:0% +because it goes down like 25% if they're +their step brothers and + + align:start position:0% +their step brothers and + + + align:start position:0% +their step brothers and +sisters so the answers to all of these + + align:start position:0% +sisters so the answers to all of these + + + align:start position:0% +sisters so the answers to all of these +questions have parallels in human + + align:start position:0% +questions have parallels in human + + + align:start position:0% +questions have parallels in human +behavior + + align:start position:0% +behavior + + + align:start position:0% +behavior +uh and one of the ways I think you'll be + + align:start position:0% +uh and one of the ways I think you'll be + + + align:start position:0% +uh and one of the ways I think you'll be +interested in the studies of human + + align:start position:0% +interested in the studies of human + + + align:start position:0% +interested in the studies of human +marriage and step + + align:start position:0% +marriage and step + + + align:start position:0% +marriage and step +families + + align:start position:0% +families + + + align:start position:0% +families +U predictions from the kind of thinking + + align:start position:0% +U predictions from the kind of thinking + + + align:start position:0% +U predictions from the kind of thinking +we've been using + + align:start position:0% +we've been using + + + align:start position:0% +we've been using +and uh these are the C they found that + + align:start position:0% +and uh these are the C they found that + + + align:start position:0% +and uh these are the C they found that +for example there's more conflict within + + align:start position:0% +for example there's more conflict within + + + align:start position:0% +for example there's more conflict within +step families a lot less + + align:start position:0% +step families a lot less + + + align:start position:0% +step families a lot less +stability uh at least in the cases when + + align:start position:0% +stability uh at least in the cases when + + + align:start position:0% +stability uh at least in the cases when +children are invol in + + align:start position:0% +children are invol in + + + align:start position:0% +children are invol in +involved um they're not saying there's + + align:start position:0% +involved um they're not saying there's + + + align:start position:0% +involved um they're not saying there's +generally more conflict but when + + align:start position:0% +generally more conflict but when + + + align:start position:0% +generally more conflict but when +children are involved there's generally + + align:start position:0% +children are involved there's generally + + + align:start position:0% +children are involved there's generally +more + + align:start position:0% +more + + + align:start position:0% +more +conflict + + align:start position:0% +conflict + + + align:start position:0% +conflict +uh the most dramatic thing I think is + + align:start position:0% +uh the most dramatic thing I think is + + + align:start position:0% +uh the most dramatic thing I think is +studies of child + + align:start position:0% + + + + align:start position:0% + +abuse sociobiologists have examined the + + align:start position:0% +abuse sociobiologists have examined the + + + align:start position:0% +abuse sociobiologists have examined the +records of people uh in families where + + align:start position:0% +records of people uh in families where + + + align:start position:0% +records of people uh in families where +child abuse has + + align:start position:0% +child abuse has + + + align:start position:0% +child abuse has +occurred and they've looked at the + + align:start position:0% +occurred and they've looked at the + + + align:start position:0% +occurred and they've looked at the +frequency of criminal child abuse in + + align:start position:0% +frequency of criminal child abuse in + + + align:start position:0% +frequency of criminal child abuse in +families so if you separate then the + + align:start position:0% +families so if you separate then the + + + align:start position:0% +families so if you separate then the +child abuse in families where the + + align:start position:0% +child abuse in families where the + + + align:start position:0% +child abuse in families where the +children are the genetic offspring of + + align:start position:0% +children are the genetic offspring of + + + align:start position:0% +children are the genetic offspring of +both parents and ones where only one + + align:start position:0% +both parents and ones where only one + + + align:start position:0% +both parents and ones where only one +parent they're they're related to only + + align:start position:0% +parent they're they're related to only + + + align:start position:0% +parent they're they're related to only +one + + align:start position:0% +one + + + align:start position:0% +one +parent + + align:start position:0% +parent + + + align:start position:0% +parent +um so they have a step parent there's + + align:start position:0% +um so they have a step parent there's + + + align:start position:0% +um so they have a step parent there's +much greater child abuse by stepparents + + align:start position:0% +much greater child abuse by stepparents + + + align:start position:0% +much greater child abuse by stepparents +and there it's mostly by + + align:start position:0% +and there it's mostly by + + + align:start position:0% +and there it's mostly by +stepfathers the you'd have to look at + + align:start position:0% +stepfathers the you'd have to look at + + + align:start position:0% +stepfathers the you'd have to look at +the curve there on page the the bar + + align:start position:0% +the curve there on page the the bar + + + align:start position:0% +the curve there on page the the bar +graph on page 202 because the + + align:start position:0% +graph on page 202 because the + + + align:start position:0% +graph on page 202 because the +differences are really dramatic they're + + align:start position:0% +differences are really dramatic they're + + + align:start position:0% +differences are really dramatic they're +huge + + align:start position:0% +huge + + + align:start position:0% +huge +okay and then finally and you can look + + align:start position:0% +okay and then finally and you can look + + + align:start position:0% +okay and then finally and you can look +at divorce records and uh the more the + + align:start position:0% +at divorce records and uh the more the + + + align:start position:0% +at divorce records and uh the more the +more step children there are the greater + + align:start position:0% +more step children there are the greater + + + align:start position:0% +more step children there are the greater +the divorce rate so these are just + + align:start position:0% +the divorce rate so these are just + + + align:start position:0% +the divorce rate so these are just +things you can collect by doing + + align:start position:0% +things you can collect by doing + + + align:start position:0% +things you can collect by doing +statistics on these records and these + + align:start position:0% +statistics on these records and these + + + align:start position:0% +statistics on these records and these +are the + + align:start position:0% + + + + align:start position:0% + +findings Alcock also goes through male + + align:start position:0% +findings Alcock also goes through male + + + align:start position:0% +findings Alcock also goes through male +female differences in various + + align:start position:0% +female differences in various + + + align:start position:0% +female differences in various +abilities and uh I'm asking here what + + align:start position:0% +abilities and uh I'm asking here what + + + align:start position:0% +abilities and uh I'm asking here what +differences aren't mentioned by elcock + + align:start position:0% +differences aren't mentioned by elcock + + + align:start position:0% +differences aren't mentioned by elcock +so I just want to mention a few of these + + align:start position:0% +so I just want to mention a few of these + + + align:start position:0% +so I just want to mention a few of these +uh differences in verbal abilities where + + align:start position:0% +uh differences in verbal abilities where + + + align:start position:0% +uh differences in verbal abilities where +women tend to have greater verbal + + align:start position:0% +women tend to have greater verbal + + + align:start position:0% +women tend to have greater verbal +ability on average spatial abilities um + + align:start position:0% +ability on average spatial abilities um + + + align:start position:0% +ability on average spatial abilities um +and again you're going to find clear + + align:start position:0% +and again you're going to find clear + + + align:start position:0% +and again you're going to find clear +exceptions but they on average they're + + align:start position:0% +exceptions but they on average they're + + + align:start position:0% +exceptions but they on average they're +greater in + + align:start position:0% +greater in + + + align:start position:0% +greater in +males linear logic quantitative + + align:start position:0% +males linear logic quantitative + + + align:start position:0% +males linear logic quantitative +analysis computer programming tend to be + + align:start position:0% +analysis computer programming tend to be + + + align:start position:0% +analysis computer programming tend to be +greater in males + + align:start position:0% +greater in males + + + align:start position:0% +greater in males +is's a nice study at MIT of this because + + align:start position:0% +is's a nice study at MIT of this because + + + align:start position:0% +is's a nice study at MIT of this because +about the study of female programmers + + align:start position:0% +about the study of female programmers + + + align:start position:0% +about the study of female programmers +compared with men and they examine the + + align:start position:0% +compared with men and they examine the + + + align:start position:0% +compared with men and they examine the +programs in detail and they found out + + align:start position:0% +programs in detail and they found out + + + align:start position:0% +programs in detail and they found out +that yeah that women don't write use + + align:start position:0% +that yeah that women don't write use + + + align:start position:0% +that yeah that women don't write use +quite the same logic so forth and their + + align:start position:0% +quite the same logic so forth and their + + + align:start position:0% +quite the same logic so forth and their +programs but their programs work just as + + align:start position:0% +programs but their programs work just as + + + align:start position:0% +programs but their programs work just as +well okay and then + + align:start position:0% +well okay and then + + + align:start position:0% +well okay and then +differences between social and emotional + + align:start position:0% +differences between social and emotional + + + align:start position:0% +differences between social and emotional +intelligence and other kinds of + + align:start position:0% +intelligence and other kinds of + + + align:start position:0% +intelligence and other kinds of +intelligence + + align:start position:0% +intelligence + + + align:start position:0% +intelligence +generally social and emotional + + align:start position:0% +generally social and emotional + + + align:start position:0% +generally social and emotional +intelligence and sensitivities are + + align:start position:0% +intelligence and sensitivities are + + + align:start position:0% +intelligence and sensitivities are +greater in + + align:start position:0% +greater in + + + align:start position:0% +greater in +women I've talked about that briefly + + align:start position:0% +women I've talked about that briefly + + + align:start position:0% +women I've talked about that briefly +we'll talk about it again when we talk + + align:start position:0% +we'll talk about it again when we talk + + + align:start position:0% +we'll talk about it again when we talk +about primate social + + align:start position:0% +about primate social + + + align:start position:0% +about primate social +life so what is the naturalistic fallacy + + align:start position:0% +life so what is the naturalistic fallacy + + + align:start position:0% +life so what is the naturalistic fallacy +I alluded to it earlier today um is + + align:start position:0% +I alluded to it earlier today um is + + + align:start position:0% +I alluded to it earlier today um is +often made by people including some + + align:start position:0% +often made by people including some + + + align:start position:0% +often made by people including some +scientists who are opposed to + + align:start position:0% + + + + align:start position:0% + +sociobiology there the naturalistic fact + + align:start position:0% +sociobiology there the naturalistic fact + + + align:start position:0% +sociobiology there the naturalistic fact +fallacy is when they assume that an + + align:start position:0% +fallacy is when they assume that an + + + align:start position:0% +fallacy is when they assume that an +evolved tendency is natural and + + align:start position:0% +evolved tendency is natural and + + + align:start position:0% +evolved tendency is natural and +therefore it's acceptable and + + align:start position:0% +therefore it's acceptable and + + + align:start position:0% +therefore it's acceptable and +justifiable and that is a clear fallacy + + align:start position:0% +justifiable and that is a clear fallacy + + + align:start position:0% +justifiable and that is a clear fallacy +that we've already mentioned and you can + + align:start position:0% +that we've already mentioned and you can + + + align:start position:0% +that we've already mentioned and you can +you need you should think of clear + + align:start position:0% +you need you should think of clear + + + align:start position:0% +you need you should think of clear +examples of that because it's very + + align:start position:0% +examples of that because it's very + + + align:start position:0% +examples of that because it's very +common in the way we talk things we + + align:start position:0% +common in the way we talk things we + + + align:start position:0% +common in the way we talk things we +discuss with in our families and so + + align:start position:0% +discuss with in our families and so + + + align:start position:0% +discuss with in our families and so +forth + + align:start position:0% + + + + align:start position:0% + +okay and related thing is this is we + + align:start position:0% +okay and related thing is this is we + + + align:start position:0% +okay and related thing is this is we +talked about rape but here's + + align:start position:0% +talked about rape but here's + + + align:start position:0% +talked about rape but here's +what particularly feminists have argued + + align:start position:0% +what particularly feminists have argued + + + align:start position:0% +what particularly feminists have argued +and you hear it all the time you still + + align:start position:0% +and you hear it all the time you still + + + align:start position:0% +and you hear it all the time you still +hear this on the + + align:start position:0% +hear this on the + + + align:start position:0% +hear this on the +TV all rape is an exercise in power it's + + align:start position:0% +TV all rape is an exercise in power it's + + + align:start position:0% +TV all rape is an exercise in power it's +not about sex it's not about sexual + + align:start position:0% +not about sex it's not about sexual + + + align:start position:0% +not about sex it's not about sexual +desires it was first argued strongly in + + align:start position:0% +desires it was first argued strongly in + + + align:start position:0% +desires it was first argued strongly in +this book by Susan Brown Miller in 75 + + align:start position:0% +this book by Susan Brown Miller in 75 + + + align:start position:0% +this book by Susan Brown Miller in 75 +called against our will the whole book + + align:start position:0% +called against our will the whole book + + + align:start position:0% +called against our will the whole book +was on rape and her views became very + + align:start position:0% +was on rape and her views became very + + + align:start position:0% +was on rape and her views became very +widespread they've been taught to + + align:start position:0% +widespread they've been taught to + + + align:start position:0% +widespread they've been taught to +students at many universities even in + + align:start position:0% +students at many universities even in + + + align:start position:0% +students at many universities even in +the high + + align:start position:0% +the high + + + align:start position:0% +the high +schools it's led to perpetuation of + + align:start position:0% +schools it's led to perpetuation of + + + align:start position:0% +schools it's led to perpetuation of +various myths about + + align:start position:0% +various myths about + + + align:start position:0% +various myths about +rape so is it true that all rape is an + + align:start position:0% +rape so is it true that all rape is an + + + align:start position:0% +rape so is it true that all rape is an +exercise in power not about sexual + + align:start position:0% +exercise in power not about sexual + + + align:start position:0% +exercise in power not about sexual +desires it's not + + align:start position:0% +desires it's not + + + align:start position:0% +desires it's not +true it's also widespread among animals + + align:start position:0% +true it's also widespread among animals + + + align:start position:0% +true it's also widespread among animals +anal so certainly not in all species + + align:start position:0% +anal so certainly not in all species + + + align:start position:0% +anal so certainly not in all species +it's used quite successfully in many + + align:start position:0% +it's used quite successfully in many + + + align:start position:0% +it's used quite successfully in many +animals so what are the some of the + + align:start position:0% +animals so what are the some of the + + + align:start position:0% +animals so what are the some of the +actual findings of studies that have + + align:start position:0% +actual findings of studies that have + + + align:start position:0% +actual findings of studies that have +collected real data on this and he gives + + align:start position:0% +collected real data on this and he gives + + + align:start position:0% +collected real data on this and he gives +elot + + align:start position:0% +elot + + + align:start position:0% +elot +gives them on these pages in the book + + align:start position:0% +gives them on these pages in the book + + + align:start position:0% +gives them on these pages in the book +and he's got a figure on it we here's + + align:start position:0% +and he's got a figure on it we here's + + + align:start position:0% +and he's got a figure on it we here's +the age just for example age + + align:start position:0% +the age just for example age + + + align:start position:0% +the age just for example age +distribution of rate victims it differs + + align:start position:0% +distribution of rate victims it differs + + + align:start position:0% +distribution of rate victims it differs +very significantly from homicide victims + + align:start position:0% +very significantly from homicide victims + + + align:start position:0% +very significantly from homicide victims +just take uh rape victims and homicide + + align:start position:0% +just take uh rape victims and homicide + + + align:start position:0% +just take uh rape victims and homicide +victims female in both cases the peak + + align:start position:0% +victims female in both cases the peak + + + align:start position:0% +victims female in both cases the peak +age for rape victims was 22 to 23 the + + align:start position:0% +age for rape victims was 22 to 23 the + + + align:start position:0% +age for rape victims was 22 to 23 the +peak age for murder victims was 32 to 33 + + align:start position:0% +peak age for murder victims was 32 to 33 + + + align:start position:0% +peak age for murder victims was 32 to 33 +and the distribution of that in that + + align:start position:0% +and the distribution of that in that + + + align:start position:0% +and the distribution of that in that +curve falls off with age a lot less + + align:start position:0% +curve falls off with age a lot less + + + align:start position:0% +curve falls off with age a lot less +steeply than for rape + + align:start position:0% +steeply than for rape + + + align:start position:0% +steeply than for rape +victims that's just one of the pieces of + + align:start position:0% +victims that's just one of the pieces of + + + align:start position:0% +victims that's just one of the pieces of +data that have supported this and we + + align:start position:0% +data that have supported this and we + + + align:start position:0% +data that have supported this and we +gave some of the earlier finding + + align:start position:0% + + + + align:start position:0% + +before + + align:start position:0% +before + + + align:start position:0% +before +okay we mentioned this also maternal + + align:start position:0% +okay we mentioned this also maternal + + + align:start position:0% +okay we mentioned this also maternal +instincts are in instincts being greater + + align:start position:0% +instincts are in instincts being greater + + + align:start position:0% +instincts are in instincts being greater +than paternal instincts instincts on the + + align:start position:0% +than paternal instincts instincts on the + + + align:start position:0% +than paternal instincts instincts on the +average + + align:start position:0% + + + + align:start position:0% + +uh is the sociobiologist being + + align:start position:0% +uh is the sociobiologist being + + + align:start position:0% +uh is the sociobiologist being +irresponsible since people may misuse + + align:start position:0% +irresponsible since people may misuse + + + align:start position:0% +irresponsible since people may misuse +his conclusions it's been argued that + + align:start position:0% +his conclusions it's been argued that + + + align:start position:0% +his conclusions it's been argued that +they should shut up about this U but + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% +I + + + align:start position:0% +I +like to make this very clear and I'm + + align:start position:0% +like to make this very clear and I'm + + + align:start position:0% +like to make this very clear and I'm +going to go to page 25 to make sure you + + align:start position:0% +going to go to page 25 to make sure you + + + align:start position:0% +going to go to page 25 to make sure you +understand what + + align:start position:0% +understand what + + + align:start position:0% +understand what +sociobiologists themselves actually + + align:start position:0% +sociobiologists themselves actually + + + align:start position:0% +sociobiologists themselves actually +believe about their science and about + + align:start position:0% +believe about their science and about + + + align:start position:0% +believe about their science and about +their morality and so + + align:start position:0% +their morality and so + + + align:start position:0% +their morality and so +forth + + align:start position:0% +forth + + + align:start position:0% +forth +uh Richard Dawkin says say my own + + align:start position:0% +uh Richard Dawkin says say my own + + + align:start position:0% +uh Richard Dawkin says say my own +philosophy of life begins with an + + align:start position:0% +philosophy of life begins with an + + + align:start position:0% +philosophy of life begins with an +explicit rejection of Darwinism as a + + align:start position:0% +explicit rejection of Darwinism as a + + + align:start position:0% +explicit rejection of Darwinism as a +normative principle for living even + + align:start position:0% +normative principle for living even + + + align:start position:0% +normative principle for living even +while I extol it as the explanatory + + align:start position:0% +while I extol it as the explanatory + + + align:start position:0% +while I extol it as the explanatory +principle for + + align:start position:0% +principle for + + + align:start position:0% +principle for +life it's not about morality it's + + align:start position:0% +life it's not about morality it's + + + align:start position:0% +life it's not about morality it's +about the way Evolution + + align:start position:0% +about the way Evolution + + + align:start position:0% +about the way Evolution +occurs remember George C Williams wrote + + align:start position:0% +occurs remember George C Williams wrote + + + align:start position:0% +occurs remember George C Williams wrote +the paper in 1966 that led + + align:start position:0% +the paper in 1966 that led + + + align:start position:0% +the paper in 1966 that led +to basically a revolution in the + + align:start position:0% +to basically a revolution in the + + + align:start position:0% +to basically a revolution in the +thinking about the + + align:start position:0% +thinking about the + + + align:start position:0% +thinking about the +nature of natural selection and + + align:start position:0% +nature of natural selection and + + + align:start position:0% +nature of natural selection and +evolution he's even more + + align:start position:0% +evolution he's even more + + + align:start position:0% +evolution he's even more +emphatic with what other than + + align:start position:0% +emphatic with what other than + + + align:start position:0% +emphatic with what other than +condemnation is a person with any moral + + align:start position:0% +condemnation is a person with any moral + + + align:start position:0% +condemnation is a person with any moral +sense to respond to a system in which + + align:start position:0% +sense to respond to a system in which + + + align:start position:0% +sense to respond to a system in which +the ultimate purpose in life is to be + + align:start position:0% +the ultimate purpose in life is to be + + + align:start position:0% +the ultimate purpose in life is to be +better than your neighbor at getting + + align:start position:0% +better than your neighbor at getting + + + align:start position:0% +better than your neighbor at getting +genes into future + + align:start position:0% + + + + align:start position:0% + +generations and we and uh he goes on and + + align:start position:0% +generations and we and uh he goes on and + + + align:start position:0% +generations and we and uh he goes on and +has very strong statements about + + align:start position:0% + + + + align:start position:0% + +that the fact that interactions among + + align:start position:0% +that the fact that interactions among + + + align:start position:0% +that the fact that interactions among +the members of the same species are also + + align:start position:0% +the members of the same species are also + + + align:start position:0% +the members of the same species are also +Guided by adaptations of various sorts + + align:start position:0% +Guided by adaptations of various sorts + + + align:start position:0% +Guided by adaptations of various sorts +is no guarantee of happiness and Harmony + + align:start position:0% +is no guarantee of happiness and Harmony + + + align:start position:0% +is no guarantee of happiness and Harmony +as dysfunctional step families and + + align:start position:0% +as dysfunctional step families and + + + align:start position:0% +as dysfunctional step families and +couples in sexual conflict demonstrate + + align:start position:0% +couples in sexual conflict demonstrate + + + align:start position:0% +couples in sexual conflict demonstrate +all too clearly this is Alcock now he + + align:start position:0% +all too clearly this is Alcock now he + + + align:start position:0% +all too clearly this is Alcock now he +says if if if more people realized how + + align:start position:0% +says if if if more people realized how + + + align:start position:0% +says if if if more people realized how +our naturally selected brain acts in the + + align:start position:0% +our naturally selected brain acts in the + + + align:start position:0% +our naturally selected brain acts in the +service of our genes then perhaps they + + align:start position:0% +service of our genes then perhaps they + + + align:start position:0% +service of our genes then perhaps they +would be less inclined to endure the + + align:start position:0% +would be less inclined to endure the + + + align:start position:0% +would be less inclined to endure the +consequences of natural selection a + + align:start position:0% +consequences of natural selection a + + + align:start position:0% +consequences of natural selection a +blind process that cares not a wit about + + align:start position:0% +blind process that cares not a wit about + + + align:start position:0% +blind process that cares not a wit about +human beings or anything + + align:start position:0% +human beings or anything + + + align:start position:0% +human beings or anything +else in fact he proposes a he would like + + align:start position:0% +else in fact he proposes a he would like + + + align:start position:0% +else in fact he proposes a he would like +to see the establishment of a sex + + align:start position:0% +to see the establishment of a sex + + + align:start position:0% +to see the establishment of a sex +education class and he argues how this + + align:start position:0% +education class and he argues how this + + + align:start position:0% +education class and he argues how this +could be + + align:start position:0% +could be + + + align:start position:0% +could be +effective and uh + + align:start position:0% +effective and uh + + + align:start position:0% +effective and uh +the so I'm asking here this + + align:start position:0% +the so I'm asking here this + + + align:start position:0% +the so I'm asking here this +question it's based on socio biology and + + align:start position:0% +question it's based on socio biology and + + + align:start position:0% +question it's based on socio biology and +I think it's a fantasy would it actually + + align:start position:0% +I think it's a fantasy would it actually + + + align:start position:0% +I think it's a fantasy would it actually +work and this is what I think I think it + + align:start position:0% +work and this is what I think I think it + + + align:start position:0% +work and this is what I think I think it +would work only for True intellectuals + + align:start position:0% +would work only for True intellectuals + + + align:start position:0% +would work only for True intellectuals +are very rare because those are people + + align:start position:0% +are very rare because those are people + + + align:start position:0% +are very rare because those are people +whose knowledge and reasoning actually + + align:start position:0% +whose knowledge and reasoning actually + + + align:start position:0% +whose knowledge and reasoning actually +influences their behavioral choices in + + align:start position:0% +influences their behavioral choices in + + + align:start position:0% +influences their behavioral choices in +their social life uh they're very rare + + align:start position:0% +their social life uh they're very rare + + + align:start position:0% +their social life uh they're very rare +they're sort of like Sheldon on The Big + + align:start position:0% +they're sort of like Sheldon on The Big + + + align:start position:0% +they're sort of like Sheldon on The Big +Bang the all right and uh so I think the + + align:start position:0% +Bang the all right and uh so I think the + + + align:start position:0% +Bang the all right and uh so I think the +class would most likely be a failure at + + align:start position:0% +class would most likely be a failure at + + + align:start position:0% +class would most likely be a failure at +most schools if not + + align:start position:0% +most schools if not + + + align:start position:0% +most schools if not +all that that's the way I will leave it + + align:start position:0% +all that that's the way I will leave it + + + align:start position:0% +all that that's the way I will leave it +with + + align:start position:0% +with + + + align:start position:0% +with +Sheldon all + + align:start position:0% +Sheldon all + + + align:start position:0% +Sheldon all +right that's all I want to say today I'd + + align:start position:0% +right that's all I want to say today I'd + + + align:start position:0% +right that's all I want to say today I'd +like to know if anybody has any + + align:start position:0% +like to know if anybody has any + + + align:start position:0% +like to know if anybody has any +questions about what you've been working + + align:start position:0% +questions about what you've been working + + + align:start position:0% +questions about what you've been working +on there only a few people I think who + + align:start position:0% +on there only a few people I think who + + + align:start position:0% +on there only a few people I think who +are not here because they had other + + align:start position:0% +are not here because they had other + + + align:start position:0% +are not here because they had other +things that we let them delay their + + align:start position:0% +things that we let them delay their + + + align:start position:0% +things that we let them delay their +turning into their topics most of you + + align:start position:0% +turning into their topics most of you + + + align:start position:0% +turning into their topics most of you +had the topics a week ago but many of + + align:start position:0% +had the topics a week ago but many of + + + align:start position:0% +had the topics a week ago but many of +you didn't + + align:start position:0% +you didn't + + + align:start position:0% +you didn't +so does anybody have any questions if + + align:start position:0% +so does anybody have any questions if + + + align:start position:0% +so does anybody have any questions if +you don't want to make it public then + + align:start position:0% +you don't want to make it public then + + + align:start position:0% +you don't want to make it public then +please come to me after class I will + + align:start position:0% +please come to me after class I will + + + align:start position:0% +please come to me after class I will +stay here and talk to you about it do + + align:start position:0% +stay here and talk to you about it do + + + align:start position:0% +stay here and talk to you about it do +you all have a qu do you all have a + + align:start position:0% +you all have a qu do you all have a + + + align:start position:0% +you all have a qu do you all have a +topic you all know what you're going to + + align:start position:0% +topic you all know what you're going to + + + align:start position:0% +topic you all know what you're going to +do for + + align:start position:0% +do for + + + align:start position:0% +do for +sure because now you've only got until + + align:start position:0% +sure because now you've only got until + + + align:start position:0% +sure because now you've only got until +just before Thanksgiving to get that + + align:start position:0% +just before Thanksgiving to get that + + + align:start position:0% +just before Thanksgiving to get that +report okay + + align:start position:0% + + + + align:start position:0% + +yes oh yeah if you we will we will look + + align:start position:0% +yes oh yeah if you we will we will look + + + align:start position:0% +yes oh yeah if you we will we will look +at all those you know and if we have a + + align:start position:0% +at all those you know and if we have a + + + align:start position:0% +at all those you know and if we have a +strong opinion about your choice we will + + align:start position:0% +strong opinion about your choice we will + + + align:start position:0% +strong opinion about your choice we will +let you know in most cases you know if + + align:start position:0% +let you know in most cases you know if + + + align:start position:0% +let you know in most cases you know if +you have a good understanding of that + + align:start position:0% +you have a good understanding of that + + + align:start position:0% +you have a good understanding of that +assignment there won't be a + + align:start position:0% +assignment there won't be a + + + align:start position:0% +assignment there won't be a +problem I don't want a neuroscience + + align:start position:0% +problem I don't want a neuroscience + + + align:start position:0% +problem I don't want a neuroscience +paper you know remember that this has + + align:start position:0% +paper you know remember that this has + + + align:start position:0% +paper you know remember that this has +got to be focused on the topics of the + + align:start position:0% +got to be focused on the topics of the + + + align:start position:0% +got to be focused on the topics of the +class we will go a little further in the + + align:start position:0% +class we will go a little further in the + + + align:start position:0% +class we will go a little further in the +class mostly ly with um primate social + + align:start position:0% +class mostly ly with um primate social + + + align:start position:0% +class mostly ly with um primate social +behavior and with Conrad Lawrence's view + + align:start position:0% +behavior and with Conrad Lawrence's view + + + align:start position:0% +behavior and with Conrad Lawrence's view +of learning which is much broader in + + align:start position:0% +of learning which is much broader in + + + align:start position:0% +of learning which is much broader in +than modern studies and Neuroscience and + + align:start position:0% +than modern studies and Neuroscience and + + + align:start position:0% +than modern studies and Neuroscience and +in Behavioral Studies too of learning so + + align:start position:0% +in Behavioral Studies too of learning so + + + align:start position:0% +in Behavioral Studies too of learning so +I would like to go over some of that + + align:start position:0% +I would like to go over some of that + + + align:start position:0% +I would like to go over some of that +with you so just a few more topics like + + align:start position:0% +with you so just a few more topics like + + + align:start position:0% +with you so just a few more topics like +this and then it will be your turn and + + align:start position:0% +this and then it will be your turn and + + + align:start position:0% +this and then it will be your turn and +uh I do expect people to come and hear + + align:start position:0% +uh I do expect people to come and hear + + + align:start position:0% +uh I do expect people to come and hear +these talks even though you'll only hear + + align:start position:0% +these talks even though you'll only hear + + + align:start position:0% +these talks even though you'll only hear +a third of them and because will be + + align:start position:0% +a third of them and because will be + + + align:start position:0% +a third of them and because will be +major + + align:start position:0% +major + + + align:start position:0% +major +points uh and uh I generally figure out + + align:start position:0% +points uh and uh I generally figure out + + + align:start position:0% +points uh and uh I generally figure out +some way to ask you about that a little + + align:start position:0% +some way to ask you about that a little + + + align:start position:0% +some way to ask you about that a little +bit on the final exam just to make sure + + align:start position:0% +bit on the final exam just to make sure + + + align:start position:0% +bit on the final exam just to make sure +you you paid attention if you come to + + align:start position:0% +you you paid attention if you come to + + + align:start position:0% +you you paid attention if you come to +the talks and read the slides uh you + + align:start position:0% +the talks and read the slides uh you + + + align:start position:0% +the talks and read the slides uh you +won't have any trouble with that \ No newline at end of file diff --git a/RmbJBq9kpbI.txt b/RmbJBq9kpbI.txt new file mode 100644 index 0000000000000000000000000000000000000000..ba7429bd6c016e43d6526ebb08dd2f23ad6f4cee --- /dev/null +++ b/RmbJBq9kpbI.txt @@ -0,0 +1,1467 @@ +align:start position:0% + +welcome back to 8701 + + align:start position:0% +welcome back to 8701 + + + align:start position:0% +welcome back to 8701 +um our second part of the chapter and + + align:start position:0% +um our second part of the chapter and + + + align:start position:0% +um our second part of the chapter and +qcd is on elastic + + align:start position:0% +qcd is on elastic + + + align:start position:0% +qcd is on elastic +electron proton scattering + + align:start position:0% + + + + align:start position:0% + +so elastic or electron proton scattering + + align:start position:0% +so elastic or electron proton scattering + + + align:start position:0% +so elastic or electron proton scattering +in general has a long history + + align:start position:0% +in general has a long history + + + align:start position:0% +in general has a long history +going back into the 1960s you know + + align:start position:0% +going back into the 1960s you know + + + align:start position:0% +going back into the 1960s you know +famous examples are the mit slack or + + align:start position:0% +famous examples are the mit slack or + + + align:start position:0% +famous examples are the mit slack or +flag mit experiment which led to the + + align:start position:0% +flag mit experiment which led to the + + + align:start position:0% +flag mit experiment which led to the +nobel prize in physics for + + align:start position:0% +nobel prize in physics for + + + align:start position:0% +nobel prize in physics for +jerry friedman henry kendall and richard + + align:start position:0% +jerry friedman henry kendall and richard + + + align:start position:0% +jerry friedman henry kendall and richard +taylor + + align:start position:0% +taylor + + + align:start position:0% +taylor +on 1990 and + + align:start position:0% +on 1990 and + + + align:start position:0% +on 1990 and +the most recent and highest energetic + + align:start position:0% +the most recent and highest energetic + + + align:start position:0% +the most recent and highest energetic +electron positron experiments were + + align:start position:0% +electron positron experiments were + + + align:start position:0% +electron positron experiments were +conducted at daisy in hamburg + + align:start position:0% +conducted at daisy in hamburg + + + align:start position:0% +conducted at daisy in hamburg +at the so-called hera ring + + align:start position:0% + + + + align:start position:0% + +and we'll go back into those experiments + + align:start position:0% +and we'll go back into those experiments + + + align:start position:0% +and we'll go back into those experiments +they're famous for + + align:start position:0% +they're famous for + + + align:start position:0% +they're famous for +not just elastic electron positron + + align:start position:0% +not just elastic electron positron + + + align:start position:0% +not just elastic electron positron +scattering but inelastic and deep + + align:start position:0% +scattering but inelastic and deep + + + align:start position:0% +scattering but inelastic and deep +inelastic electron poisson polytron + + align:start position:0% +inelastic electron poisson polytron + + + align:start position:0% +inelastic electron poisson polytron +scattering which + + align:start position:0% +scattering which + + + align:start position:0% +scattering which +is going to be subject of future + + align:start position:0% +is going to be subject of future + + + align:start position:0% +is going to be subject of future +lectures + + align:start position:0% +lectures + + + align:start position:0% +lectures +um what we're trying to do here even + + align:start position:0% +um what we're trying to do here even + + + align:start position:0% +um what we're trying to do here even +you know you might still wonder why this + + align:start position:0% +you know you might still wonder why this + + + align:start position:0% +you know you might still wonder why this +is topic of a qcd lecture + + align:start position:0% +is topic of a qcd lecture + + + align:start position:0% +is topic of a qcd lecture +um what you're trying to do is study the + + align:start position:0% +um what you're trying to do is study the + + + align:start position:0% +um what you're trying to do is study the +structure of protons and the way to look + + align:start position:0% +structure of protons and the way to look + + + align:start position:0% +structure of protons and the way to look +at this + + align:start position:0% +at this + + + align:start position:0% +at this +is in this uh climate diagram is we're + + align:start position:0% +is in this uh climate diagram is we're + + + align:start position:0% +is in this uh climate diagram is we're +using this photon here + + align:start position:0% +using this photon here + + + align:start position:0% +using this photon here +to broke into the structure of the + + align:start position:0% +to broke into the structure of the + + + align:start position:0% +to broke into the structure of the +proton + + align:start position:0% +proton + + + align:start position:0% +proton +um you know we can start from from this + + align:start position:0% +um you know we can start from from this + + + align:start position:0% +um you know we can start from from this +scattering process which we + + align:start position:0% +scattering process which we + + + align:start position:0% +scattering process which we +already calculated and we derived the + + align:start position:0% +already calculated and we derived the + + + align:start position:0% +already calculated and we derived the +mod scattering cross section formula + + align:start position:0% +mod scattering cross section formula + + + align:start position:0% +mod scattering cross section formula +um but we really want to consider this + + align:start position:0% +um but we really want to consider this + + + align:start position:0% +um but we really want to consider this +proton now as a blob + + align:start position:0% +proton now as a blob + + + align:start position:0% +proton now as a blob +in elastic scattering we are not + + align:start position:0% +in elastic scattering we are not + + + align:start position:0% +in elastic scattering we are not +destroying the proton so we + + align:start position:0% +destroying the proton so we + + + align:start position:0% +destroying the proton so we +leave the proton intact in the + + align:start position:0% +leave the proton intact in the + + + align:start position:0% +leave the proton intact in the +scattering process + + align:start position:0% + + + + align:start position:0% + +we do know that the proton is not a + + align:start position:0% +we do know that the proton is not a + + + align:start position:0% +we do know that the proton is not a +point length particle so if you want to + + align:start position:0% +point length particle so if you want to + + + align:start position:0% +point length particle so if you want to +now + + align:start position:0% +now + + + align:start position:0% +now +study the proton we have to take into + + align:start position:0% +study the proton we have to take into + + + align:start position:0% +study the proton we have to take into +account that it's built out of + + align:start position:0% +account that it's built out of + + + align:start position:0% +account that it's built out of +constituents + + align:start position:0% +constituents + + + align:start position:0% +constituents +and that it has an extension it's not + + align:start position:0% +and that it has an extension it's not + + + align:start position:0% +and that it has an extension it's not +point like anymore + + align:start position:0% +point like anymore + + + align:start position:0% +point like anymore +and one way to do this is by analyzing + + align:start position:0% +and one way to do this is by analyzing + + + align:start position:0% +and one way to do this is by analyzing +the fourier transform of the charge + + align:start position:0% +the fourier transform of the charge + + + align:start position:0% +the fourier transform of the charge +density + + align:start position:0% +density + + + align:start position:0% +density +functions remember the photon couples to + + align:start position:0% +functions remember the photon couples to + + + align:start position:0% +functions remember the photon couples to +charge particles and so when we use a + + align:start position:0% +charge particles and so when we use a + + + align:start position:0% +charge particles and so when we use a +photon to probe + + align:start position:0% +photon to probe + + + align:start position:0% +photon to probe +a proton it probes a charge distribution + + align:start position:0% +a proton it probes a charge distribution + + + align:start position:0% +a proton it probes a charge distribution +inside the proton so we build a fourier + + align:start position:0% +inside the proton so we build a fourier + + + align:start position:0% +inside the proton so we build a fourier +transform + + align:start position:0% +transform + + + align:start position:0% +transform +of the charge distribution um + + align:start position:0% +of the charge distribution um + + + align:start position:0% +of the charge distribution um +and uh and and + + align:start position:0% +and uh and and + + + align:start position:0% +and uh and and +then can extend the cross section uh + + align:start position:0% +then can extend the cross section uh + + + align:start position:0% +then can extend the cross section uh +from a point like cross section + + align:start position:0% +from a point like cross section + + + align:start position:0% +from a point like cross section +we are this fourier transform of the + + align:start position:0% +we are this fourier transform of the + + + align:start position:0% +we are this fourier transform of the +charge distribution + + align:start position:0% +charge distribution + + + align:start position:0% +charge distribution +great in electron position scattering + + align:start position:0% +great in electron position scattering + + + align:start position:0% +great in electron position scattering +there is another point it's not just the + + align:start position:0% +there is another point it's not just the + + + align:start position:0% +there is another point it's not just the +extension of the proton + + align:start position:0% +extension of the proton + + + align:start position:0% +extension of the proton +but also the fact that the proton + + align:start position:0% +but also the fact that the proton + + + align:start position:0% +but also the fact that the proton +carries recoil + + align:start position:0% +carries recoil + + + align:start position:0% +carries recoil +and so we uh need to use two form + + align:start position:0% +and so we uh need to use two form + + + align:start position:0% +and so we uh need to use two form +factors in order to describe the + + align:start position:0% +factors in order to describe the + + + align:start position:0% +factors in order to describe the +cross-section + + align:start position:0% +cross-section + + + align:start position:0% +cross-section +um fully um so let's have a look at the + + align:start position:0% +um fully um so let's have a look at the + + + align:start position:0% +um fully um so let's have a look at the +amplitude again we can + + align:start position:0% +amplitude again we can + + + align:start position:0% +amplitude again we can +start from where we left off with the + + align:start position:0% +start from where we left off with the + + + align:start position:0% +start from where we left off with the +electron + + align:start position:0% +electron + + + align:start position:0% +electron +positron scattering or electron electron + + align:start position:0% +positron scattering or electron electron + + + align:start position:0% +positron scattering or electron electron +neuron scattering + + align:start position:0% +neuron scattering + + + align:start position:0% +neuron scattering +and write down our matrix elements and + + align:start position:0% +and write down our matrix elements and + + + align:start position:0% +and write down our matrix elements and +just now for the proton + + align:start position:0% +just now for the proton + + + align:start position:0% +just now for the proton +what we do here is we modify the vertex + + align:start position:0% +what we do here is we modify the vertex + + + align:start position:0% +what we do here is we modify the vertex +of the proton + + align:start position:0% +of the proton + + + align:start position:0% +of the proton +and the modification is parametrized in + + align:start position:0% +and the modification is parametrized in + + + align:start position:0% +and the modification is parametrized in +those two factors + + align:start position:0% +those two factors + + + align:start position:0% +those two factors +describing describing the the cross + + align:start position:0% +describing describing the the cross + + + align:start position:0% +describing describing the the cross +section or the matrix elements amplitude + + align:start position:0% +section or the matrix elements amplitude + + + align:start position:0% +section or the matrix elements amplitude +with two form factors + + align:start position:0% +with two form factors + + + align:start position:0% +with two form factors +one which just looks like a modification + + align:start position:0% +one which just looks like a modification + + + align:start position:0% +one which just looks like a modification +of our spin + + align:start position:0% +of our spin + + + align:start position:0% +of our spin +half particle you remember there's a + + align:start position:0% +half particle you remember there's a + + + align:start position:0% +half particle you remember there's a +scammer factor + + align:start position:0% +scammer factor + + + align:start position:0% +scammer factor +and then you know this is going to be a + + align:start position:0% +and then you know this is going to be a + + + align:start position:0% +and then you know this is going to be a +number + + align:start position:0% +number + + + align:start position:0% +number +and the other one is a little bit more + + align:start position:0% +and the other one is a little bit more + + + align:start position:0% +and the other one is a little bit more +complicated there is a + + align:start position:0% +complicated there is a + + + align:start position:0% +complicated there is a +powder matrix here and another number + + align:start position:0% +powder matrix here and another number + + + align:start position:0% +powder matrix here and another number +and it's normalized by the mass of the + + align:start position:0% +and it's normalized by the mass of the + + + align:start position:0% +and it's normalized by the mass of the +proton all right so this is just the + + align:start position:0% +proton all right so this is just the + + + align:start position:0% +proton all right so this is just the +parametrization we haven't done much + + align:start position:0% +parametrization we haven't done much + + + align:start position:0% +parametrization we haven't done much +physics here we have just parametrized + + align:start position:0% +physics here we have just parametrized + + + align:start position:0% +physics here we have just parametrized +the distribution um if you then use this + + align:start position:0% +the distribution um if you then use this + + + align:start position:0% +the distribution um if you then use this +we can as i just described um + + align:start position:0% +we can as i just described um + + + align:start position:0% +we can as i just described um +calculate the cross section again using + + align:start position:0% +calculate the cross section again using + + + align:start position:0% +calculate the cross section again using +those this very same parametrization and + + align:start position:0% +those this very same parametrization and + + + align:start position:0% +those this very same parametrization and +get + + align:start position:0% +get + + + align:start position:0% +get +to this formula here in the laboratory + + align:start position:0% +to this formula here in the laboratory + + + align:start position:0% +to this formula here in the laboratory +frame + + align:start position:0% +frame + + + align:start position:0% +frame +um this looks rather complicated but + + align:start position:0% +um this looks rather complicated but + + + align:start position:0% +um this looks rather complicated but +if you uh go back to our form factor + + align:start position:0% +if you uh go back to our form factor + + + align:start position:0% +if you uh go back to our form factor +definitions + + align:start position:0% +definitions + + + align:start position:0% +definitions +and set this one the zero and this one + + align:start position:0% +and set this one the zero and this one + + + align:start position:0% +and set this one the zero and this one +to one you get back in the same here + + align:start position:0% +to one you get back in the same here + + + align:start position:0% +to one you get back in the same here +you said get back to our uh much + + align:start position:0% +you said get back to our uh much + + + align:start position:0% +you said get back to our uh much +scattering result which we had before so + + align:start position:0% +scattering result which we had before so + + + align:start position:0% +scattering result which we had before so +really extended + + align:start position:0% +really extended + + + align:start position:0% +really extended +the discussion to extended extended + + align:start position:0% +the discussion to extended extended + + + align:start position:0% +the discussion to extended extended +objects + + align:start position:0% +objects + + + align:start position:0% +objects +and considering the charge distribution + + align:start position:0% +and considering the charge distribution + + + align:start position:0% +and considering the charge distribution +and also the recall in the quarter + + align:start position:0% +and also the recall in the quarter + + + align:start position:0% +and also the recall in the quarter +so this is great um historically + + align:start position:0% +so this is great um historically + + + align:start position:0% +so this is great um historically +so this is not a new idea this has been + + align:start position:0% +so this is not a new idea this has been + + + align:start position:0% +so this is not a new idea this has been +done for generations + + align:start position:0% +done for generations + + + align:start position:0% +done for generations +historically the parametrization was + + align:start position:0% +historically the parametrization was + + + align:start position:0% +historically the parametrization was +done slightly different + + align:start position:0% +done slightly different + + + align:start position:0% +done slightly different +and so we introduced the linear + + align:start position:0% +and so we introduced the linear + + + align:start position:0% +and so we introduced the linear +combination of those form factors and + + align:start position:0% +combination of those form factors and + + + align:start position:0% +combination of those form factors and +those are + + align:start position:0% +those are + + + align:start position:0% +those are +typically referred to as the electric + + align:start position:0% +typically referred to as the electric + + + align:start position:0% +typically referred to as the electric +and the magnetic four factors the ge and + + align:start position:0% +and the magnetic four factors the ge and + + + align:start position:0% +and the magnetic four factors the ge and +gm + + align:start position:0% +gm + + + align:start position:0% +gm +this formula here and this is just + + align:start position:0% +this formula here and this is just + + + align:start position:0% +this formula here and this is just +algebra going from + + align:start position:0% +algebra going from + + + align:start position:0% +algebra going from +previous formula to this it's called the + + align:start position:0% +previous formula to this it's called the + + + align:start position:0% +previous formula to this it's called the +rosen + + align:start position:0% +rosen + + + align:start position:0% +rosen +blues thousand blues + + align:start position:0% +blues thousand blues + + + align:start position:0% +blues thousand blues +um cross-section formula all right so + + align:start position:0% +um cross-section formula all right so + + + align:start position:0% +um cross-section formula all right so +this is just if you find this in his in + + align:start position:0% +this is just if you find this in his in + + + align:start position:0% +this is just if you find this in his in +in + + align:start position:0% +in + + + align:start position:0% +in +particle physics booklets or nuclear + + align:start position:0% +particle physics booklets or nuclear + + + align:start position:0% +particle physics booklets or nuclear +physics booklet + + align:start position:0% +physics booklet + + + align:start position:0% +physics booklet +this is what's meant by this the only + + align:start position:0% +this is what's meant by this the only + + + align:start position:0% +this is what's meant by this the only +thing we did here is + + align:start position:0% +thing we did here is + + + align:start position:0% +thing we did here is +i extended the rosen the mod scattering + + align:start position:0% +i extended the rosen the mod scattering + + + align:start position:0% +i extended the rosen the mod scattering +formula + + align:start position:0% +formula + + + align:start position:0% +formula +using extended objects extend the charge + + align:start position:0% +using extended objects extend the charge + + + align:start position:0% +using extended objects extend the charge +distribution to the + + align:start position:0% +distribution to the + + + align:start position:0% +distribution to the +formula all right but + + align:start position:0% +formula all right but + + + align:start position:0% +formula all right but +we have done that by using a full + + align:start position:0% +we have done that by using a full + + + align:start position:0% +we have done that by using a full +transform of the charge distribution so + + align:start position:0% +transform of the charge distribution so + + + align:start position:0% +transform of the charge distribution so +if we now measure the cross section + + align:start position:0% +if we now measure the cross section + + + align:start position:0% +if we now measure the cross section +we can infer the charge distribution of + + align:start position:0% +we can infer the charge distribution of + + + align:start position:0% +we can infer the charge distribution of +the total + + align:start position:0% +the total + + + align:start position:0% +the total +and with that the radius the charge + + align:start position:0% +and with that the radius the charge + + + align:start position:0% +and with that the radius the charge +radius of the proton this has been done + + align:start position:0% +radius of the proton this has been done + + + align:start position:0% +radius of the proton this has been done +and we find that the rms the root mean + + align:start position:0% +and we find that the rms the root mean + + + align:start position:0% +and we find that the rms the root mean +square of the proton charge is 0.81 + + align:start position:0% +square of the proton charge is 0.81 + + + align:start position:0% +square of the proton charge is 0.81 +femtometers uh so that's the charge and + + align:start position:0% +femtometers uh so that's the charge and + + + align:start position:0% +femtometers uh so that's the charge and +this is + + align:start position:0% +this is + + + align:start position:0% +this is +this measured charge is still today uh a + + align:start position:0% +this measured charge is still today uh a + + + align:start position:0% +this measured charge is still today uh a +hot topic in particle physics because + + align:start position:0% +hot topic in particle physics because + + + align:start position:0% +hot topic in particle physics because +it's measured distributions do not quite + + align:start position:0% +it's measured distributions do not quite + + + align:start position:0% +it's measured distributions do not quite +agree with + + align:start position:0% +agree with + + + align:start position:0% +agree with +the theory predictions so you see this + + align:start position:0% +the theory predictions so you see this + + + align:start position:0% +the theory predictions so you see this +here parametrized + + align:start position:0% +here parametrized + + + align:start position:0% +here parametrized +for this value of the put in charge the + + align:start position:0% +for this value of the put in charge the + + + align:start position:0% +for this value of the put in charge the +theory and the global fit to the data + + align:start position:0% +theory and the global fit to the data + + + align:start position:0% +theory and the global fit to the data +don't quite agree + + align:start position:0% +don't quite agree + + + align:start position:0% +don't quite agree +you would have to go to slightly higher + + align:start position:0% +you would have to go to slightly higher + + + align:start position:0% +you would have to go to slightly higher +values of the proton radius in order to + + align:start position:0% +values of the proton radius in order to + + + align:start position:0% +values of the proton radius in order to +have + + align:start position:0% +have + + + align:start position:0% +have +theory the previous experiments + + align:start position:0% +theory the previous experiments + + + align:start position:0% +theory the previous experiments +so i leave it here the next lecture now + + align:start position:0% +so i leave it here the next lecture now + + + align:start position:0% +so i leave it here the next lecture now +i + + align:start position:0% +i + + + align:start position:0% +i +split this lecture in two parts the + + align:start position:0% +split this lecture in two parts the + + + align:start position:0% +split this lecture in two parts the +elastic and the inelastic scattering the + + align:start position:0% +elastic and the inelastic scattering the + + + align:start position:0% +elastic and the inelastic scattering the +next lecture will be + + align:start position:0% +next lecture will be + + + align:start position:0% +next lecture will be +on inelastic scattering where we will + + align:start position:0% +on inelastic scattering where we will + + + align:start position:0% +on inelastic scattering where we will +break the proton apart and learn about + + align:start position:0% +break the proton apart and learn about + + + align:start position:0% +break the proton apart and learn about +the structure of the proton + + align:start position:0% +the structure of the proton + + + align:start position:0% +the structure of the proton +you \ No newline at end of file diff --git a/SJI-SAs1Rnk.txt b/SJI-SAs1Rnk.txt new file mode 100644 index 0000000000000000000000000000000000000000..b8fdab338947ce5f319eab768592743629d351e6 --- /dev/null +++ b/SJI-SAs1Rnk.txt @@ -0,0 +1,2923 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Some funny things +happened on the way to the + +moon, as a takeoff of Funny +Things Happened on + +the Way to the Forum. + +And probably not too +many people in this + +audience know that. + +Also, in particular, a thing +that's happening this year is + +the 40th anniversary of +the lunar landing. + +And we're going to +talk a little bit + +about how MIT got involved. + +And let's see if we can +move this along. + +Sputnik was about the size of a +large, maybe oversized beach + +ball, or a basketball. + +And it was launched in +June, of 1957, or + +later, maybe not June. + +I thought I had it +on the screen. + +But anyhow, if it hadn't been +for Sputnik, I doubt if + +anything would have happened in +terms of the United States + +getting interested in +the space program. + +So we have to have a lot of +gratitude for the Russians for + +doing this. + +I remember Wernher von Braun in +a meeting was asked, this + +was after maybe six months of +the program, says, "Wouldn't + +we do a lot better if we +collaborated with the + +Russians?" And he, without +hesitation, said, "If there + +were collaboration with the +Russians, there wouldn't be a + +program in either country." So +it had all to do with the + +race, the race for the moon. + +It was October 4, +I'm sorry, 1957. + +Right after the lunar landing, +Dave Hoag and I were invited + +to the Soviet Union as their +guests, all expenses paid. + +It was really quite +an experience. + +And they gave us a good show. + +Everywhere we went-- + +we had some movies of +the lunar landing. + +And as soon as they knew we had +movies, they wanted to-- + +they took them and set +up their screen. + +If the didn't have a screen, +they'd put up a bed sheet. + +And they oohed and aahed in all +of the right places for + +the landing. + +And it was really quite +an experience. + +And also they asked us, when +will the Americans go to the + +moon again? + +Well that was Apollo 14. + +And the date was sometime +in November. + +And I was always grateful that +it went on time and on that + +date, because the Russians never +gave any indication of + +what they were planning on doing +until it was all over. + +And then they would +take bows, or they + +would hide the results. + +But anyhow, I happened to +buy this little device. + +It's actually a music box. + +It plays the Russian +national anthem. + +It used to, but it's all rusted +out in there now. + +It's been around a long time. + +And when we were in Moscow, +we went to the + +GUM department store. + +And I saw this there +and bought it. + +I'm so glad that I did. + +And I brought it home. + +1957 is particularly interesting +to me, it's + +because my son, my youngest son, +was born in that year. + +And so he really became-- + +everything that happened in +space, he was right there to + +watch it on TV, or whatever +news there was. + +And he's still much +like that today. + +This the MIT Instrumentation +Laboratory responded to-- + +we're going to go into space, +so why don't we design a + +spacecraft which will indeed +take us, not to the moon-- we + +aren't going to think about the +moon-- but actually into + +interplanetary space. + +In 1957, when the Sputnik +was flying, the MIT + +Instrumentation Laboratory +was-- + +that building on the +right is the + +Whittemore Shoe Polish factory. + +And the one on the left is the +old Hood's Milk factory. + +And the railroad tracks there +are the same tracks that cross + +Mass Avenue today. + +The buildings, of course, +are gone. + +And Doc Draper's office is +indicated as a little, the + +corner of these warehouses. + +So we didn't really have +plush surroundings. + +The thing we wanted to do was +to build a Mars probe. + +We would like to launch +this spacecraft. + +And it would coast to Mars and +pass close by, take a picture, + +and then return to Earth so we +could collect the photograph, + +not a whole series of +photographs, just one picture, + +because we didn't want to have +all that time and effort + +invested and find that the +wheel which would change + +pictures was screwed up. + +So it was just the simplest +thing to do, would be to just + +have it open the shutter +and close it. + +And that was the only thing +that had to be done. + +And we'd do that at the point +of closest approach to Mars. + +The round trip from Earth to +Mars and return, there it is. + +We were serious about this. + +We were thinking of launching +it in December of 1962. + +And we would intercept +Mars on February 15. + +And then we would pass +by the planet. + +It's not a two-dimensional +problem. + +This is the relative motion of +the spacecraft with respect to + +the planet during the +planetary contact. + +Then after that, we have to +get back to the earth. + +And unfortunately, we had to +make two trips around the sun + +to get back. + +And so the total trip time was +more than three years. + +That did not play very well with +those who are interested + +in getting some attention +for the work that the + +laboratory was doing. + +But they did get some. + +This is a picture from +the newspaper. + +And I'm on the right hand side, +a younger version of me. + +And there's Hal Laning and Milt +Trageser, all of whom + +were involved in this program. + +And it said, this project +may solve the + +life on Mars mystery. + +But it didn't. + +In fact, it did do +a lot of things. + +But it never flew. + +The Mars probe involved always +a three year round trip to + +photograph the planet. + +And we had to have onboard, +self-contained navigation. + +For three years, this little +vehicle was going to be + +cruising and making measurements +to determine + +where it was and when to make +velocity corrections, all done + +on board the spacecraft -- + +unheard of at that time. + +And after the three-year trip, +it would splash down in the + +Gulf of Mexico. + +And this little model, which is +a good size, is hanging in + +the Draper Laboratory. + +I used to know where it was, +but then they moved it. + +But they said, it's somewhere +in the building. + +So if you want to take a look +at it, and you can get into + +the Draper Lab building, +then you can see this. + +The big red, that's the entry +vehicle, which was, in it was + +the film of the picture +that we took of Mars. + +The major problem was how to +design a small computer and + +its memory in 1960 to survive +a three year round trip to + +Mars, with no data uplink +and no inflight service. + +That doesn't mean +what you think. + +Inflight service means +if something breaks, + +you can't fix it. + +It's got to be perfect. + +But then came 1961. + +Alan Shepard was ready +to fly the + +Mercury-Redstone on May 5 of 1961. + +It was the first American in +space, not the first human + +being in space, the +first American. + +The Russians had already +capitalized on their Sputnik, + +and they had a man in space +somewhat before we did. + +And you look at the picture, +there's the blockhouse. + +It looks like about the +size of a garage. + +And the space vehicle, not very +big, all it was going to + +do was just fly a 20-minute +flight and land in the ocean + +and be fished out. + +That was what we were going to +do, when in fact, the Russians + +were already putting +men in orbit. + +Now, I will never be as amazed +that three weeks after Alan + +Shepard made his flight, that +John F. Kennedy said that he + +believed that this nation +should commit itself to + +achieve the goal, before this +decade is out, of landing a + +man on the moon and returning +him safely to Earth. + +Now, that's pretty gutsy to do +when your only success is a + +20-minute splashdown in +the Atlantic with one + +person at the helm. + +Now, 1961, let's look at some +of the other things. + +Alan Shepard's flight on May 5; +May 25, President Kennedy's + +message to the Congress +and to the world. + +And then on August 10, MIT is +awarded the first NASA Prime + +Contract for Apollo. + +NASA had just barely +been created. + +And in response to President +Kennedy's "we're going to go + +to the moon," they gave +the job to MIT. + +That's pretty amazing when +you think about it. + +And we'll say a word more +about that in a minute. + +The Mars probe never flew, but +the onboard computer did + +evolve into becoming the Apollo +guidance computer. + +There was a computer that we +had to have in our little + +space probe, and that did +evolve into the guidance + +computer, the Apollo +onboard computer, + +for the lunar mission. + +We moved into better quarters. + +This is the home of the Apollo +project from 1962 on. + +That building no +longer exists. + +It was originally a storage +warehouse for underwear. + +And we took over the whole +building, refurbished it, and + +my office was on the other +side of the building. + +And it was on the corner. + +It was a nice office. + +Here's what the place +looks like today. + +This is the luxury waterfront +condominiums that they made + +long after the space +program ended. + +And the underwear factory or +underwear warehouse was + +replaced by these +condominiums. + +Now, MIT was chosen for the +GN&C. And quite a big question + +is "Why?" Well, Jim Webb, who +was the administrator of NASA, + +knew Doc Draper. + +And this is Doc's version +of what happened. + +Jim Webb called Doc Draper on +the telephone, says, "Doc," he + +says, "Can you develop the +guidance and navigation system + +for Apollo?" + +What would you say if +you were Doc Draper. + +You would say, "Yes, +of course. + +We'll do that." "When will it +be ready?" "Well, when you + +need it." (Laughter) That's +a good schedule. + +"And how do I know it will +work?" And you say, "I will go + +along and operate it for you." + +Now that's the story that +Doc always told. + +And I believe it, because +he did know Jim Webb. + +Jim Webb was not a scientist. +Jim Webb was good at getting + +money out of Congress. + +He was a lawyer. + +And his job was to make sure +that the Apollo program was + +adequately funded. + +Now, was it Doc Draper's phone +call from Jim Webb, or was it + +Bob Chilton's memo? + +Bob Chilton worked for +NASA all of his life. + +He's retired. + +He lives down in Texas, at Texas +A&M. And I hear from him + +once a year. + +And here's what Bob +Chilton did. + +He wrote this memo to the Chief +of the Flight Systems + +Division in November 7, 1960. + +He said, "Development of the +onboard capability to + +determine position and velocity +by optical means is + +important to the principle of +onboard command for Apollo. + +The Instrumentation Laboratory +of MIT has shown a strong + +interest in the problem of +self-contained navigation. + +The position and velocity +determination schemes proposed + +in the reference report by +Battin and Laning called A + +Recoverable Interplanetary Space +Probe in 1959 are alike + +in principle to that desired +for Apollo." + +At the time, Bob Chilton was +the head of the Flight + +Dynamics Branch at +Langley Field. + +Bob Chilton's memo, the memo +was stamped Confidential. + +Everything was classified in +those days, and Bob gave me + +his original carbon copy, +which I still treasure. + +Here we are sending men to the +moon, and we had not even + +invented a good copy machine. + +Why was onboard navigation +a basic requirement? + +Well, one of the reasons would +be that the Russians + +might not play fair. + +They might jam the communication +links and we + +would not be able to communicate +with our + +spacecraft. + +1961 was a long time ago. + +We had to use typewriters +and carbon paper. + +Xerox had not been invented. + +You could watch TV, +but not in color. + +There were just black +and white TVs and + +not very good quality. + +You could do calculations +using electromechanical + +machines, no personal computers +or even pocket + +calculators. + +These things would cost about +$800 to $1,000, and all the + +would do is add and subtract +and divide. + +If you spent $500 more, +you could get one + +that did square root. + +And that was a pretty amazing +thing, because every day, just + +about, the repairman would be +there to fix it, because it + +was such a complicated +piece of equipment. + +When we'd go on business +trips, no jets. + +We had propeller-driven +aircraft. + +And the per diem rates +were $12 a day. + +With that $12, I was supposed +to pay for my hotel bill and + +buy three meals, and do +it for $12 a day. + +And that was plenty +good enough. + +In fact, if you just said, give +me the $12, and then if + +you didn't spend it, you could +keep the dollar or + +two which was left. + +Those were different days +than they are today. + +Now let's look at, this came +about only relatively + +recently, the numerology +of 1961. + +It's an invertible number. + +That is, if you turn it +upside-down, it's still 1961. + +Earlier invertible years, +1001, 1111, 1691, 1881. + +When will the next invertible +year take place? + +6009. + +You've got a long wait for +the next invertible year. + +OK, that's one thing. + +But there's more. + +President Kennedy's +Special Message to + +Congress was 5/25/61. + +5 plus 25 plus 6 plus 1 is 37, +which is a prime factor of + +1961, which is only +interesting. + +But if you take the prime +factor, which is 37, there's + +only one other prime factor, +and that's 53. + +So 53 times 37 is 1961. + +If you take 53, and you get the +month of August, 5 plus 3 + +is 8, and the 10th, 3 plus 7 +is 10, and it's all written + +there forever that MIT would +get the Apollo contract on + +August 10 of 1961. + +Isn't that-- that's +pretty amazing. + +I was going to give +a talk on Apollo. + +And I had it in the afternoon. + +And I was fiddling around, +and I came up with this. + +And I was really impressed. + +And so were the audiences when +they realized that this was, + +as I pointed out, this +is not an accident. + +This is the way it was all +planned ahead of time. + +Now also, Apollo is +Greek mythology. + +Apollo is America's Program for +Orbital and Lunar Landing + +Operations, so even the Greeks +knew that we were + +going to do the job. + +1961 was a vintage year. + +A lot of things happened then. + +There they are. + +In January 26, the first +multiple fly-by orbit of the + +planets was determined, +by going from + +Earth to Mars via Venus. + +You go from Earth to Venus to +Mars and back to Earth, all in + +one launch. + +And that was discovered by +me in January 26 of 1961. + +I have to emphasize that that +date is very important. + +Because there was a lawsuit by +somebody whose name I must not + +mention, who brought suit +against me, because he said he + +did it first. But he +didn't really. + +In the spring of that year, the +first offering, that is + +the first class in Astronautical +Guidance, is + +what my course used to be called +until it was changed to + +Astrodynamics. + +On April 12, Yuri Gagarin flew +three orbits of the earth. + +And then to respond to that, on +May 5, Alan Shepard did a + +quarter-orbit flight. + +And then, three weeks later, +President Kennedy commits us + +to going to the moon. + +And in August, Gherman Titov +flies 16 orbits of the Earth. + +And MIT is awarded the first +Apollo contract. + +In October 13, the American +Rocket Society had a meeting, + +because Kennedy said he +wanted to know what + +progress had been made. + +And so we had a spaceflight +report to the nation of all + +the stuff that we were doing. + +Later, on November 21, Draper, +who had said to Jim Webb that + +yes, he would make sure it +worked, because he'd fly it, + +he volunteered formally +to be an astronaut. + +And then, I thought of this much +later, December 23 was + +Christina Shue's [?] + +100th birthday. + +Who in the world was Christina +Shue [?] ? + +My grandmother. + +So in 1961, a lot of +things happened. + +Here is the first round +trip to Venus. + +We were a little discouraged by +taking three years to get + +to Mars and back home. + +So we said, maybe we could +go to Venus and + +return in less time. + +And as a matter of +fact, you can. + +If you see the launch, and you +go past Venus, and then you're + +coming back to Earth. + +But look, you're almost out +to the Martian border. + +And wouldn't it be nice +if Mars were there? + +And that was what we did. + +We had a Venus fly-by. + +And then following that is +the return to Earth. + +And it is all done in just +a little over a year. + +And we visit two planets for +the price of one, first to + +Venus and then to Mars, and +then back to Earth. + +And this was the very +first one of these + +that was ever done. + +We do that all the time today, +using fly-bys of planets to + +change the velocity to get to +another location to accomplish + +something else. + +But this was the first time it +was ever done on a computer. + +Now saying that the first +offering of astronautical + +guidance, it's kind +of interesting. + +Because there are the people +who took that course, Buzz + +Aldrin, who flew in 1961, in +Apollo 11, and then Dave + +Scott, who flew Apollo 15, in +1962, and Ed Mitchell, who was + +on Apollo 14 in 1963. + +Each of these gentlemen, and +they're all still alive and + +well, they walked on the moon. + +And they took astronautical +guidance. + +Apollo 14, I always thought that +Ed Mitchell, it had more + +people watching that launch than +any time in the past or + +the future. + +Why? + +Why? + +It was Apollo 14. + +What was the flight +before that? + +Apollo 13. + +And that was pretty serious. + +We almost didn't +get them home. + +And then to be a crew for the +next flight, I think, took a + +little gutsy. + +Here's the textbook for +the graduate course in + +astronautical guidance. + +The book is Astronautical +Guidance. + +The diagram, if you take my +course, you'll find out how to + +navigate in space by making +measurements of angles between + +stars and near bodies. + +And so that little diagram was +on the flyleaf, and was also + +on the inside of the +book in color. + +Now when the book came out, we +were having a heavy load of + +important visitors. + +And Doc, he took my book, and he +said, "Battin," he says, "I + +want you to buy a +lot of these. + +And I want you to +autograph them. + +We're going to have important +people here." And sure enough, + +let's see who the important +people are. + +Well, there's Doc. + +And then there's Kurt Debus. + +He was the head of the Space +Center in Florida. + +Wernher von Braun needs +no introduction. + +Bob Gilruth, who was the head of +the NASA team in Texas, and + +then me, looking smug. + +And everybody, you see, has +got a copy of the book in + +front of them. + +And I was pretty excited +about that. + +There was an unauthorized +version of the book, + +Astronautical Guidance, +in Russian. + +And this was about +four years later. + +And everything is in Russian. + +There is Battin in Russian. + +And the diagram is exactly +the same diagram + +that appeared on-- + +but it's an unauthorized, that +is, they didn't ask permission + +to do this or give +us any royalties. + +But they did give us an all +expenses paid, round trip + +visit to Moscow and Leningrad +and Tbilisi after the Apollo + +11 landing. + +MIT awarded the first +Apollo contract, and + +here was the team. + +We have Jim Webb, the +one in the center. + +And to the left is +Hugh Dryden. + +He was the deputy administrator, +but he passed + +away in December of 1965. + +And then there's Bob Seamans, +the associate administrator. + +He was promoted to deputy +administrator. + +And Bob Seamans, as you are +well aware, passed away. + +I was very happy that when I +give this talk at this time + +last year, Bob Seamans came. + +He had not heard it before. + +But he came and listened. + +And I was so pleased +that he was there. + +But he passed away shortly +thereafter. + +MIT was chosen. + +Why? + +Well, Bob Seaman's book, Aiming +at Targets, says, it + +doesn't give you much +information. + +It just says, "When the decision +was made to go to the + +moon, the Draper Lab got the +contract for the navigation + +system." + +He really knew why, but he +didn't want to put in print. + +Because after all, he was +from MIT Instrumentation + +Laboratory. + +Doc headed the laboratory. + +And then all of a sudden, +we get the job for + +the GN&C for Apollo. + +But we deserved it. + +And we performed well. + +So was it Doc Draper's +phone call, or was it + +Bob Chilton's memo? + +I guess I got this +in there twice. + +I shouldn't. + +I have to do a little +surgery on this. + +Doc Draper volunteers +to be an astronaut. + +He really did. + +And he had a letter. + +This is part of his letter. + +"I would like formally to +volunteer as a crew member on + +the Apollo mission to the moon, +and also for whatever + +sub-orbital and orbital flights +that may be made in + +preparation for this +lunar trip. + +I realize that my age of 60 +years is a negative factor in + +considering my request, but +General Flickinger tells me + +that this is no sure bar to my +selection as a crew member." + +And we had a system, a real +system, put on the roof of one + +of the buildings on the river, +where you could practice + +navigating. + +And there's Doc Draper making +a navigational fix. + +And you can recognize the Boston +skyline, or what the + +Boston skyline looked +like in those days. + +Some buildings are missing. + +And you could actually make +measurements, and the computer + +would calculate where it was +on the basis of that. + +And the result was always the +particular spot on the roof of + +the building, even though you +could start off with very bad + +guesses of where you were. + +And then by utilizing the +navigation algorithm, you + +could to get a navigation fix. + +The guidance navigation +laboratory system, you could + +see that today, if you get +somebody to take you through + +the Draper Lab. + +This is actual-- + +it's not a mock up. + +It's really the equipment. + +And you have the means of +communicating with the + +computer on the right, +that was the DSKY, + +the display and keyboard. + +where you could get information, +and you could + +also call up different +things that you + +wanted to do in flight. + +For navigation purposes, we had +a scanning telescope and a + +good sextant to make +these measurements. + +You could get a view of the +stars and the planets through + +the sextant and then make +the actual measurements. + +You'd try to line them up, +line up these two images, + +press a button to get +information to the computer. + +In fact, what we have here does +not show behind, where + +the ball for getting information +with respect to + +attitude and velocity, all done +on the back side of the-- + +but this is the front side, is +this what the astronauts saw + +and used in their flights. + +There's the Apollo guidance +computer. + +The fact that it's approximately +one cubic foot, + +it's a really interesting +story. + +When the spacecraft contractor +was chosen, you got a phone + +call from them, saying, "Oh, I +understand that you're going + +to have a computer on board. + +How big is it?" + +Well, we had no idea. + +All we could see was +all this equipment + +that was on the wall. + +And somehow or other, we were +going to have to package this + +down to something that would +fit in the spacecraft. + +So they said, "Well, we've got +to give him a number." And so + +I said, "Well, just tell +him it's a cubic foot." + +And it was. + +We were able to squeeze it. + +You couldn't make it two cubic +feet, because that's all they + +had room for, planned for. + +It was a computer +of that size. + +And it weighed about 70 pounds, +consumed 55 watts, + +which, that's pretty good. + +And then this up close is the +display and keyboard. + +The core rope memory was a-- + +we're not going to spend much +time dwelling on it. + +But it was an invention of Hal +Laning, primarily Hal and + +others, that you could have a +memory system which you would + +wire in place, so that if you +lost electricity, you wouldn't + +lose your memory. + +And there is the way +it was done. + +Each core would store a word. + +In fact, we got it down to +where a single core could + +store 12 words, and each word +was 16 bits or 2 bytes. + +And to read, to get information +out, all you have + +to do was select the +core and switch it. + +And then all of the sense wires +that went through the + +core would produce 1s, and those +that did not go through + +the core would produce 0s. + +And lo and behold, this +was our system. + +The trouble is that you had +to make these things. + +You had to manufacture them. + +And after you've made it, and +if there was a mistake, you + +couldn't change it. + +Here's the speed in kilobytes. + +For our Mars probe, it had +eight read only memory + +kilobytes, and change, this +would be Random Access Memory, + +is a half of a kilobyte. + +The Apollo Guidance Computer +had 74 ROMs and 4 read and + +write memory, and it was +actually a little slower in + +speed than the Mars probe. + +Now today, the kind of memory +that we're talking about, you + +can carry around +in your pocket. + +In fact, I do have it in my +pocket for this talk. + +And it's just absolutely amazing +that first of all, + +that they had the idea that +this was the way to do it, + +because in Apollo 12, the +spacecraft was struck by + +lightning on the way up. + +And all of the read and +write memory vanished. + +They had to put that +back in by hand. + +But the read-only +memory was fine. + +There was no trouble +with it whatsoever. + +Here's a photograph of the core +rope memory up close. + +And how would you manufacture +something like that? + +Well, we used the LOL method, +the Little Old Lady method, + +which I'll show you +in a second. + +The computers and the memory +were manufactured by Raytheon. + +The flight software was written +and tested at the + +Instrumentation Laboratory. + +The core ropes required six +weeks to build, and you + +couldn't make any last-minute +changes. + +And there's one of the women +who's wiring this thing. + +It was set up to be like a +weaving machine that the + +computer would tell you where +you're supposed to + +put the next wire. + +In fact, it would set it up for +you so that you could put + +the wire through +the right core. + +And all this was done +at Raytheon. + +And it must have been very +tedious for these women to do + +that kind of work. + +But they were always so proud +when the astronauts + +would come and visit. + +Oh, it gave them the feeling +that we can't screw up. + +We have to do this right, +because we just met the men + +whose whole lives depend upon. + +How many computers? + +Well, we wound up with one for +the Command Module and one for + +the Lunar Module. + +And there would be no +inflight repair. + +There would be no built-in +redundancy. + +That is, if one of the circuits +fails, that's it. + +There would be no uplink +from the ground. + +And there were many possible +single-point failures, but + +none of them ever happened. + +The quality control people +couldn't calculate the mean + +time between failures, because +they never had any failure of + +the AGC at all. + +Software, the early NASA +manned flights. + +The first one was +Mercury flight. + +There were 6 Mercury flights. + +And there were 10 +Gemini flights. + +The first one was May 5. + +We've already seen Shepard's. + +And the last one of the Mercury +group was May in 1963. + +Then there were Gemini flights, +where there were two + +astronauts in a capsule, +rather than just one. + +And there were 10 of those, +from '65 to '66. + +George Mueller was the Associate +Administrator for + +Manned Spaceflight. + +And he was a NASA person. + +And he was very much concerned +with the computer software. + +In fact, he was in charge of the +software for the Mariner 1 + +spacecraft to Venus, which +was launched in 1962. + +And it went off course due +to a software error. + +There was a missing minus +sign in the code. + +He had this minus sign framed +and hanging in his office. + +Do not take for granted. + +That you've got to check +everything to make sure that + +it's going to work. + +The astronauts used to +come and visit us. + +And in the fall of 1966, +we had six astronauts. + +There were all sitting down +there in the front row. + +And we had them autograph +these. + +And then the people in the back +were the ones that were + +working on the job. + +There is me. + +And there is Dave Hoag, and +there's a whole bunch of other + +people all there to be +photographed with the + +astronauts. + +This is a very sad picture, +because Virgil Grissom and + +Roger Chaffee and Ed White, +who where in that picture, + +were in Apollo 1. + +What happened to Apollo 1? + +It burned up on the ground. + +And so those guys, next to them +was Dave Scott, who was + +one of my students, and Jim +McDivitt and Russell + +Schweickart. + +Russell Schweickart was +an MIT student, but he + +didn't take my course. + +And they flew on Apollo 9. + +Apollo 9 was the first flight +using the Lunar Module. + +Apollo 8. + +This was the round trip +trajectory to the moon. + +And you notice you're going from +Earth to moon, go around + +the moon and back. + +And of course, what you want +to do is to go on an orbit + +which is going to arrive at the +lunar orbit ahead of the + +moon, and then we'll go +around and then be + +swept back to Earth. + +Instead, if you had gone behind +the moon, then the + +energy exchange would have been +such that you would go + +off into the solar +system someplace. + +You had to do this just right +in order to get on an orbit + +back to the Earth. + +This picture is also +in my book. + +And you can look at it. + +And they made a big deal out +of the fact that it is a + +figure eight. + +And Apollo 8 was the +first manned flight + +away from the Earth. + +And so Apollo 8, which was the +Christmas flight, you may + +remember that, maybe +you don't know. + +You don't have to remember it. + +But it was the time when the +astronauts were for the first + +time in orbit around the moon. + +And they were in this +particular mission. + +Of course, you always worry +about, what if the engine + +doesn't work. + +You're going to stay +there forever. + +You're not going to come +back to the Earth. + +There's nothing the ground +could do to help you out. + +And this design for the Apollo 8 +is really a Earth around the + +moon, just as the real +mission showed. + +Here's the crew. + +Frank Borman was +the commander. + +And Bill Landers was the +Lunar Module pilot. + +Even though we didn't +have a Lunar Module, + +they had work to do. + +And Jim Lovell was the +Command Module pilot. + +And he was the one that +did the navigation. + +He did all the measurements to +do the orbit determination, + +the navigation, for the first +time, on a flight to the moon. + +And what he had to do, this is +the navigator measuring an + +angle between a star +and a landmark. + +And you would put a mark in +the computer, which would + +register the time and the +direction of each of these, + +and then it would calculate the +angle, the shaft angle and + +trunnion angle, or two angles. + +And you'd get one piece +of information. + +But when you added all these +different measurements + +together, separated in time and +position, you were able to + +do a very credible job of +navigating to the moon. + +As a matter of fact, it was so +close that it was decided that + +we didn't need an update +from the ground. + +In the rule book, it said, +before you make any velocity + +change, you have to get your +state vector information from + +the ground. + +And Chris Kraft said, he +couldn't see any difference. + +The onboard computer and the +ground were almost identical. + +But they did have to follow +the rules and make the + +correction. + +And Jim Lovell navigated +all the way back. + +So he was the very first person +to ever navigate a + +spacecraft by making telescopic + +measurements on board. + +Jim Lovell, he trained +at MIT using the + +Earth horizon simulator. + +He was calibrated. + +That is, he would tell you where +he thought the horizon + +was, and it would be different +than what the computer thought + +the horizon was. + +And so eventually, at least +he was consistent. + +And so he had demonstrated that +his consistency was such + +that we would calibrate him. + +That is, when he looked at the +horizon, and there was a + +little difference, that +that particular offset + +would be Jim Lovell. + +And other astronauts would +have their own. + +And it says here that Jim was +the first to demonstrate that + +man could navigate +in space without + +assistance from the ground. + +He wrote a book called +Lost Moon. + +This was the Apollo 13 book. + +And he was the Command Module +navigator on Apollo 8. + +There he is when +he was younger. + +And that's just kind of sad, +because on Apollo 8 + +navigational measurements, he +said, "After leaving Earth + +orbit, the astronauts took a few +rapturous sightings of the + +receding planet, and then turn +their spacecraft around to fly + +in a proper, nose-forward +attitude." That always, + +whenever I see that, it's +sort of upsetting. + +We went to all kinds +of trouble. + +And he was the navigator. + +And when he wrote the book, he +didn't mention anything about + +how he did this. + +He just took some rapturous +sightings of + +the receding planet. + +Oh, well. + +Here are the flights. + +Apollo 1 was destroyed +by the fire. + +Then there was Apollo 7, +which was to try it + +out in Earth orbit. + +Apollo 8 went to the moon. + +Apollo 9 was a flight for that +the first time, the lunar + +module flew in Earth orbit. + +Apollo 10 was a dress rehearsal +to fly to the moon. + +You do everything except land. + +And then Apollo 11, you land. + +Then there were a bunch of +others, as you can see. + +12, 13 was, it took a while +before they were ready, over a + +year and a half, to go +from Apollo 13 to 14. + +And at the very end, +they had Apollo 17. + +But there were 18, 19, and 20. + +The rockets were there. + +The spacecraft were there. + +They could have flown. + +But I think that probably the +reason was that with all these + +successes, why don't we +quit when we're ahead? + +And there's another reason why +you might want to quit. + +And that is numerology, again, +more numerology. + +1 plus 9 plus 6 plus 1 is 17. + +And Alan Shepard's flight was +on 5/5/61, which is 17. + +So Apollo 17 was going to be the +last flight to the moon, + +all set by the very beginning. + +But not only that, 17 is +an important number. + +It's a Fermat number. + +It's a Fermat prime. + +Fermat numbers are 2 to the 2 to +the, and so on up the line. + +And Fermat had suggested +that all such + +numbers would be prime. + +And they're not. + +In fact, the only numbers which +are known to be Fermat + +primes are the ones at the +bottom 6, or 0, 1, 2, 3, and 4 + +are the only known primes, and +F2, which is 2 to the 2 to the + +2 plus 1 is seventeen. + +And so it is one of the +only known primes + +generated by this formula. + +So obviously, 17 had to be the +last flight to the moon. + +Then Apollo 11. + +Here are the guys that +flew Apollo 11. + +There's Neil Armstrong. + +And there's Buzz Aldrin. + +These pictures were taken +when they were young. + +They don't look like +that anymore. + +And Mike Collins stayed in +orbit while Neil and Buzz + +landed on the moon. + +And there is a picture +of, this is the arm + +patch for Apollo 11. + +It's the Eagle. + +The spacecraft, the Lunar +Module was the Eagle. + +And there it is, landing +on the moon. + +Now, in the aftermath of Apollo +11, this is Newton's + +tomb in Westminster Abbey. + +And I recently went to +Westminster Abbey to see, + +again, Newton's tomb. + +And they wouldn't let +you go up to it. + +Before, you could +walk up to it. + +And you could pat the-- + +but now you couldn't. + +And I was talking to one +of the guides there. + +And I told them what had +happened in Apollo 11. + +I said, there was a +message left on + +Newton's tomb with flowers. + +And it said, "The Eagle +has landed." + +And his eyes just lit up. + +He said, "I was here +when that happened. + +This was my job. + +And I saw the symbol, +the flowers. + +And I saw the note at that +time." He said, "It really did + +happen." And there it is. + +There is Newton's tomb. + +It's a huge thing. + +If you stand in front +of it, you're no + +taller than the base. + +And so that was the story about +Westminster Abbey and + +"Sir Isaac, the Eagle +has landed." + +It was Howard Johnson +who knew about this. + +Howard Johnson was president +of MIT not too long ago. + +And a friend of his was killing +time between flights. + +And he went to Westminster +Abbey, and he saw this note. + +And he told Howard +Johnson about it. + +And Howard Johnson told me. + +And it's very, very-- brings +tears to your eye when you + +think that they were able +to actually do this. + +And I'm still pretty +emotional. + +"Sir Isaac, the Eagle has +landed." So thank you. + +[APPLAUSE] + +If you have any questions, +fire away. + +If you don't have any questions, +I had a good time. + +I hope you did, too. + +AUDIENCE: First of all, on the +numerology, was that all your + +personal touch? + +Or was that an active +discussion topic? + +PROFESSOR: No, that was just +me talking to nobody. + +No, I was really struck by the +factoring 1961 and getting the + +date out of that. + +That just didn't seem like it +should be, unless somebody was + +moving the hands, and we were +able to get the job. + +And the number 17, I was just +fiddling around one day, and I + +said, oh, maybe that's why 17 +was the last flight to the + +moon, because there's only +one other prime Fermat + +number beyond 17. + +And if you used that number, +it'd be much too big for + +having anything to do with the +number of the flights. + +AUDIENCE: I have a question +about the orbital mechanics + +that you were looking at +of that early period. + +I was in high school several +weeks ago, and somewhere + +around 1951 or 1952, in an +advanced math class, we were + +doing celestial orbital +mechanics. + +And we were doing it from +a small textbook + +imported from England. + +And it was written by somebody +who I didn't recognize as a + +mathematician that year, +Arthur C. Clarke. + +PROFESSOR: Oh yes, of course. + +He just passed away recently. + +AUDIENCE: Yeah, and now I've got +to go home and find out if + +multiple body orbits +were in it or not. + +PROFESSOR: No, he didn't-- + +you mean the one I +was showing you? + +No, he said he was not impressed +at all by that. + +I didn't send it to him. + +Somebody else did. + +And he said, well, that's +not a problem. + +Well, it's not a problem +until you try to do it. + +So he was just not interested. + +AUDIENCE: Work it on the +blackboard for him. + +Thank you. + +PROFESSOR: OK. + +Yes? + +AUDIENCE: Where were you +when Neil Armstrong + +walked on the moon? + +PROFESSOR: I was in Houston. + +And I was in the center there. + +And we were all wringing +our hands. + +The alarm that came off just +before landing, none of us + +knew, except the one person who +had to know, and that was + +the, what's his name. + +I can't think of his name. + +But he was the one who said, he +knew what the alarms were. + +Forget it. + +They're OK. + +Because everyone else, if he +hadn't spoken up, they were + +ready to scrub it, because they + +didn't know what happened. + +And they would have just +decided to play it + +safe and not land. + +But it was not a problem. + +Actually, what was happening +was that the computer had a + +lot of jobs to do +simultaneously. + +It can only do one +thing at a time. + +But it would do a piece of a +job, and then it would switch + +to another one. + +And all the time, it had to be +reading the accelerometer + +information and calculating what +the x-acceleration was, + +lots of things to do. + +And it had more to do than +it had time to do it. + +And the reason was that +somebody, and Buzz Aldrin has + +admitted to it now, that he put +on the ascent radar, just + +in case they were told to not +land but leave, they'd be all + +set with their radar. + +And by leaving that on, which +the computer would do, if they + +were actually launching to +the moon, it was just an + +additional task which was +not supposed to be + +done at that time. + +And so fortunately, the guy who +was in charge knew that + +that was what the problem was, +and he just said forget it. + +Let's go. + +It's one of those things that +you don't want to be + +responsible for. + +You don't want to have to be +the one who says, go ahead, + +and then have it smashed into +the surface of the moon. + +You'd be very serious about +what you would do with the + +rest of your life. + +Any other questions? + +AUDIENCE: Dr. Battin? + +On your left. + +I worked at the lab on +the guidance system. + +And I think the astronaut +students, your old students, + +might be interested knowing, +it wasn't just one program. + +But the Lunar Module and the +Command Module were very + +different, because of the +ascent and landing. + +And also, the lunar +module was a very + +early digital autopilot. + +It worked on a phase plane to +decide when to fire its jets. + +And for ascent, it didn't have a +"gimbal-able" engine, so the + +whole scheme for controlling +it was very different. + +PROFESSOR: Well, the interesting +thing about the + +LEM computer was that the people +who were responsible + +for the LEM said, "OK, well, +we'll put a computer in. + +We'll do our own." And we kept +saying, and NASA kept saying, + +why do we want to do that? + +I mean, if the Command Module +computer will functionally do + +the same things that the Lunar +Module computer is supposed to + +do, then let's do it. + +Let's just change the program. + +Let's don't reinvent a new +computer for that job. + +And fortunately, the decision +was that there would only be + +one computer. + +We had two sets of software to +design, but we didn't do it + +for two different computers. + +Actually, the Lunar +Module had, I + +forget what it's called. + +But it was a little computer +which could do basic things. + +And if you couldn't do +anything with the big + +computer, at least with +that, it could run + +the engine, for example. + +It may not calculate what the +result's supposed to be. + +You'd just give it +to the astronaut. + +And the simple jobs that you +expected the computer to do, + +you would do. + +And again, they never, +ever had to do that. + +They never had to use it. + +But it was always there. + +And they were always +trained for it. + +But it didn't ever +have to be used. + +Yes? + +AUDIENCE: I had hear +about Draper + +attempting to be an astronaut. + +Whatever happened with that? + +Did they just decide-- + +PROFESSOR: Draper what? + +AUDIENCE: Wanting to +be an astronaut. + +Did they just determine-- + +PROFESSOR: Oh, well, +I mean ha ha. + +Actually, Draper would have gone +if they had picked him. + +The Instrumentation Laboratory +existed before Apollo. + +And he personally designed +instruments for aircraft. + +And then he would test-fly +them in the plane, and he + +would be the pilot. + +So he was a test pilot +in that sense. + +But the fact that he was 60 +years old, that's unheard of. + +I remember when I was +60 years old. + +It was a while ago. + +But no, I don't know whether +he was actually + +serious about it. + +He did write a letter to Bob +Seamans saying that he would + +like to be considered. + +And they could say, well, we +considered you, but you + +couldn't do it, physically +couldn't do it. + +AUDIENCE: Also, in those days, +all of the astronauts were + +military pilots. + +PROFESSOR: And there +weren't any women. + +There weren't any women, because +there weren't any + +women test pilots. + +Had there been women test +pilots, that'd be OK. + +Janice Voss was the first female +astronaut from MIT. + +And she helped me +with my course. + +She was really a very +good student. + +And when she graduated, she +applied to be an astronaut. + +And she was turned down once, +twice, and she was turned down + +three times. + +The fourth time, she +was selected. + +And so she says, don't +ever give up. + +If you want to do something, +make sure that + +you don't give up. + +It may not come right away, but +it could come eventually. + +So she was very excited +about that. + +And she was actually the first +female astronaut from MIT. + +We've had other-- + +well, you just saw some of the +guys who went to the moon were + +all MIT students. + +Incidentally, when Buzz Aldrin +was a student, he did not have + +a label on saying I'm going +to be flying to the moon. + +He was a military pilot. + +And he was interested in, +I guess they had begun + +to talk about it. + +He was interested in doing +some of the rendezvous + +calculations. + +But he was not representing +NASA. + +He was just there to get +a Master's degree. + +And all the other astronauts, +none of them arrived and said, + +I am an astronaut, and I want +to [UNINTELLIGIBLE]. + +They were all just students. + +Mostly, they were from +the military. + +They might be from the +Air Force Academy, + +that sort of thing. + +But it was only afterwards that +they got an assignment, + +actually being an astronaut. + +Yes? + +AUDIENCE: Can I ask your +opinion on the + +Constellation program? + +I imagine you think it's long +overdue, but are they doing it + +the right way? + +Do we still have the skills +to go back to the moon? + +PROFESSOR: I don't know. + +I really don't know. + +They're doing so many things +which are just unbelievable, + +the Messenger program +of getting a + +spacecraft to Mercury. + +And they did that by at least +a dozen or more fly-bys of + +Earth and/or Venus in order to +get the energy lowered down to + +where you could actually contact +Venus and maybe go + +around, orbit it, or take +pictures of it, + +or what have you. + +But I don't know any more about +that today than anybody + +who reads the paper. + +The Constellation is, +I'm not sure. + +Is this is a new program +or what? + +AUDIENCE: No, that's the return +to the moon, and then + +to continue on to Mars. + +PROFESSOR: They got a +name for it now, oh. + +Well, I think it's certainly a +great idea to do what we did. + +And it would be wonderful to +be able to do it again. + +And I had a student, +she was actually a + +freshman at the time. + +And she was Japanese. + +And I was a freshman advisor. + +We were going around to ask, +what would you like to do? + +What would you like? + +And it got to her. + +She said, I would like to be +the first woman on Mars. + +And she was serious. + +I want to be an astronaut. + +The fact that I'm Japanese +shouldn't have any problem. + +I said, well, that's great. + +I'll be there to cheer you on. + +But the Japanese do seem to be +getting more interested in + +space, as are the Chinese. + +And the only thing that's +going to get us really + +interested is when it looks like +they're going to do it, + +and we're going to be left in +the dust. If as von Braun + +said, if you had tried to +cooperate with the Russians, + +there wouldn't be a program. + +What was I going to say? + +I've forgotten what I +was going to say. + +But anyhow, there are so many +opportunities that we + +hopefully will not ignore, just +because there isn't any + +particular competition. + +The whole business of Apollo, +we learned how to make these + +computer chips. + +And the chips were manufactured +by Raytheon for + +Apollo, and the largest number +of computer chips that were + +being made were the +ones for Apollo. + +There were very few +applications. + +And so you might say that the +Apollo computer really was the + +original device that +we have here. + +And I think that that is true, +that with an application, + +demand, you're going +to learn how to do + +it better and cheaper. + +OK. + +[APPLAUSE] + +Thank you for coming. + +[APPLAUSE] \ No newline at end of file diff --git a/SV08nmxzdAU.txt b/SV08nmxzdAU.txt new file mode 100644 index 0000000000000000000000000000000000000000..cec96041c4d884e33225684cd7a0f792982a5cb6 --- /dev/null +++ b/SV08nmxzdAU.txt @@ -0,0 +1,3320 @@ +PROFESSOR: So we're slightly +into chapter seven, which is + +the algebra chapter. + +We're talking about a number of +algebraic objects, starting + +with integers and groups +and fields. + +Polynomials. + +Our objective in this chapter +is simply to get to finite + +fields so that you have some +sense what they are, how they + +can be constructed, what their +parameters are, how you can + +operate with them by addition, +multiplication, so forth, as + +you would expect in a field. + +Subtraction, division. + +And that's really all +we're aiming to do. + +I'm trying to give you a short +course in algebra, really, in + +two lectures or fewer. + +And clearly I'm going to +miss a lot of things. + +In particular, I'm not going +to cover even everything + +that's in chapter seven, which +itself is a highly compressed + +introduction to finite fields. + +I'm trying to do this while +remaining faithful to the + +philosophy of this course and +other courses at MIT, which is + +that you should really prove +everything and show why things + +are true, and not simply +make assertions. + +So it's a little tough and it +forces me to go a little fast, + +but I hope that you can keep +up, and especially with the + +assistance of the notes or the +many possible other things you + +could read on this subject, +which are listed in the notes, + +you'll be able to keep up. + +And some of you, of course, have +seen this in other places + +in more extended form. + +Now, this will get us in a +position to start to talk + +about Reed-Solomon codes, which +are the single major + +accomplishment of the field of +algebraic coding theory. + +Certainly for getting to +capacity on the additive white + +Gaussian noise channel and for +lots of other things, they're + +an extremely useful and widely +implemented class of codes. + +And we'll be able to maybe just +get to the beginning of + +that by Wednesday. + +And then I won't be here again +next week, but fortunately we + +have an expert on campus who is +far more expert than I in + +Reed-Solomon codes, their +decoding algorithms, who has + +agreed to talk for two lectures, +maybe one more + +focused on Reed-Solomon codes +and one, I hope, on his whole + +philosophy of life. + +Perhaps. + +I don't know how it's going to +come out, but I'll see it on + +TV when I get back. + +Anyway, Ralf Koetter will be +lecturer for Monday and + +Wednesday next week. + +I think you'll enjoy +the change of pace. + +OK. + +So where are we in +chapter seven? + +We're not very far. + +We're talking about these +various algebraic objects. + +We've started with integers +just to get you + +into the feel of it. + +We mainly talked about integer +factorization, the Euclidean + +division algorithm, things that +you've known for a very + +long time, basically here +because A, we're going to be + +using integers as we go along, +and their factorization + +properties, B, it's a model for +polynomials, which behave + +very much the same way as +integers because they're both + +principal ideal domains. + +In particular, we looked at the +integers mod n with the + +rules of mod n arithmetic, which +we're going to call Zn. + +This is simply 0 through n +minus 1 with the mod n + +arithmetic rules. + +And then we went on to groups. + +We first gave the standard +axioms for groups, and then I + +gave you an alternative set of +axioms which focused on this + +permutation property. + +If you add, I'm calling the +group operation addition, + +because essentially all the +groups we talk about are going + +to be abelian -- + +if we add a group element +to the group, + +what do we get back? + +We get the whole group again. + +It's permuted, it's the +entire group, it's + +in a different order. + +All right? + +And with this and the identity, +this plus the + +identity and the associativity +axiom are also a sufficient + +set of axioms for the group. + +And I think this is really the +most useful thing to think + +about with a group. + +We've also called it the +group property when we + +talked about codes. + +You know, if you add the code +word to all the elements in + +the code, you get +the code back. + +And you saw how useful that +was for seeing certain + +symmetry properties of minor +linear block codes. + +So we even talked about cyclic +groups, specifically finite + +cyclic groups. + +And we showed that all +them basically are + +isomorphic to z mod n. + +A cyclic group is defined +by a single generator. + +If we identify that generator +with one, G plus G is + +identified with 2, and so forth, +then we get an addition + +table which is exactly the same +addition table as Zn. + +And that's what we mean when +we say two groups are + +isomorphic. + +So all finite cyclic groups +look like Zn. + +You can think of them as +being images of Zn. + +All right? + +It's the only one you +need to know about. + +OK. + +So that's where we are any +questions on this material? + +Pretty easy, I think. + +Terribly easy if you've ever +seen any of this before. + +Probably takes a little +absorbing if you haven't. + +OK. + +Now the next natural subject +to talk about is subgroups. + +And what is a subgroup? + +A subgroup simply a subset of +elements in the group which, + +together with the group +operation already specified in + +G, which we're calling circle +plus, is itself a group. + +What does that mean? + +Well, associativity comes for +free, because we already have + +that property for circle plus +in G. Obviously H has to + +include the identity in order +to satisfy the group axioms. + +And finally, the third group +axiom is this permutation or + +group property that if we add +any element of the subgroup to + +itself, we have to stay within +the subgroup and ultimately + +generate the whole subgroup. + +That means that subtraction, + +cancellation hold in the subgroup. + +All right? + +So that's clear. + +What's an example +of a subgroup? + +If we have -- + +we talked about Z10 +as the group. + +What would be a subgroup? + +Anybody? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: 0 to 4. + +OK. + +So you're proposing that H is +the elements 0, 1, 2, 3, 4 out + +of G. Does that work? + +This doesn't include 0. + +But suppose I add 3 and 4? + +AUDIENCE: I assume that you +have modules for a reason. + +PROFESSOR: No. + +In this group, the group +operations modulo 10 addition. + +Subgroup has to have the +same operation as the + +group it came from. + +What you've got here is you've +already got, in essence, a + +quotient group. + +Or at least that's where +you're headed. + +So this is not a subgroup. + +Thank you for the suggestion. + +Fails. + +Anyone else? + +What? + +AUDIENCE: 0,1? + +PROFESSOR: 0,1. + +OK. + +Let's try that. + +And it contains the identity +0 plus 1 is + +certainly in the group. + +How about 1 plus 1? + +It's not in the group. + +0 and 5? + +That sounds more promising. + +Now, 0 plus -- what's the +addition table of this? + +0, 5, 0, 5, 0, 5. + +What's 5 plus 5? + +It's 10. + +But mod-10 , that's 0. + +So it seems we do +have a group. + +And in fact, this is a finite +cyclic group generated by 5, + +and has two elements, so +it's isomorphic to Z2. + +In other words, the addition +table looks just like the + +addition table of Z2 +with a relabeling. + +OK. + +Any other subgroups of Z10? + +The even integers. + +There. + +Now we're really smoking. + +H equals 0,2,4,6,8. + +Those are all the even +integers in Z10. + +And again, evens plus +evens equal evens. + +So we get a group of five +elements, satisfies is the + +group property, and it's +isomorphic to what? + +Z5 -- + +yeah. + +This is obviously the same group +is 0, 1, 2, 3, 4, just + +doubling everything. + +Operates the same way. + +So it's change of labels. + +OK. + +So there are some examples +of subgroups. + +Let's take another +good example. + +Let's just take the set +of all integers. + +That's an infinite group. + +Mathematicians call it cyclic, +even though it doesn't cycle. + +What's a subgroup of that? + +AUDIENCE: Even integers. + +PROFESSOR: All even integers! + +Very good. + +Check. + +Does that include 0? + +Yes. + +Does it have the group +property, even + +plus even is even? + +Clearly subtraction holds, +and so forth. + +So this is the subgroup. + +Interestingly, there's a +one-to-one correspondence + +between Z and 2Z, so the +subgroup is as big as the + +group itself. + +You get into the whole issue +of transfinite numbers. + +But that's not where +we're headed here. + +OK. + +We'll just keep that +in mind for now. + +Obviously 3Z, 4Z, 5Z, and all +the multiples of n are going + +to be a subgroup of the integers +for any integer n. + +So more generally, we could +take H equals nZ. + +What's a coset? + +Coset is also, in the abelian +case, called a + +translate of a subgroup. + +A coset, for instance, is in the +form H plus G for some G + +in the group, not +in the subgroup. + +Now if G is in the subgroup, +we get nothing. + +The coset is just H again by +the group property of H. So + +the interesting cases are where +G is not in H. Let me + +give you some examples. + +Let's take G equals Z10 and +H equals 0,2,4,6,8. + +You might call that 2Z10 It's +the set of all elements which + +are twice the elements in Z10. + +OK. + +What is a coset? + +If I add any element in +this group to H -- + +let's add one, for instance. + +So H plus 1 consists of the +elements 1,3,5,7,9. + +Well, that's interesting. + +That seems to exhaust all +of the elements of Z10. + +Let's take the Z equals the Z10, +and H simply equal to 0 + +and 5, which we might +call 5Z10. + +And all right. + +Now H plus 0, H plus 5 is +just equal to itself. + +H plus 1 is equal to 1,6. + +H plus 2 is equal to 2,7. + +H plus 3 is equal to 3, 8. + +H plus 4 is equal to 4,9. + +So we begin to see some +properties of cosets here for + +which proofs are given +in the notes. + +First of all is that +two cosets are + +either the same or disjoint. + +H plus 2 is the same as H. H +plus 1 is completely disjoint + +from H. Same over here. + +If I had H plus 5, that would +be the same as H. H plus 6 + +would be completely disjoint +from H and would be the same + +as H plus 1. + +In fact, I can take any of the +elements of a coset as its + +representative, and I'm going +to get the same coset, take + +any element outside the coset, +and I'll get a completely + +distinct coset. + +This follows just very +easily from the + +cancellation property. + +All right? + +So the cosets, the distinct +cosets, form a disjoint + +partition of G. We certainly +have a coset that contains + +every element of G. Just take H +plus that element G. That's + +going to contain G because +H contains 0. + +So there is a coset that +contains every element of G. + +Any two cosets, distinct cosets, +are disjoint, so + +that's what we mean by +a disjoint partition. + +We list all the elements +of G in this way. + +And in the finite case, that +gives us a early famous + +theorem attributed +to Lagrange. + +What does that mean? + +This means that H has to divide +G. If G has size 1,10 + +and all the cosets have the same +size, by the way, again + +by the cancellation +property -- + +this means that G has to consist +of an integer number + +of cosets, all of which have +the size of H. OK? + +And therefore some integer times +H is equal to H, which + +is the same thing as +H divides G. OK? + +If G is a finite group, I mean +by this kind of determinant + +notation, the size of H. The +size of H divides the size of + +G. Or more elegantly, the +cardinality of H divides the + +cardinality of G. But +why say cardinality + +when you can say size? + +I shouldn't have put it here. + +Where H is any subgroup, any +subgroup, of course, that's + +finite is itself +a finite group. + +So that's going to turn out to +be quite a powerful theorem. + +And it just follows this +little exercise. + +And we see it's satisfied, +certainly, + +by these two examples. + +In fact, it's pretty easy to see +that the subgroups of Zm + +are going to correspond to the +divisors of m in the same way. + +We're going to get a subgroup +for every divisor of m, and in + +the case of cyclic groups, +this is the way it's + +going to come out. + +Just pick any divisor. + +You get a subgroup +isomorphic to Zd. + +Again, this is done with +more care in the notes. + +Suppose we have the infinite +case here. + +Suppose we have Z and 2Z. + +So let me draw that case. + +G equals Z. H equals 2Z. + +And all right. + +What's H? + +H is the set dot dot dot minus +2,0,2,4, dot dot dot. + +So this is H. And what's H plus +1, or in fact, plus any + +odd number? + +It's going to be the +odd integers. + +H equals minus 1,1,3,5, +and so forth. + +So again, this works in the +infinite case, that the + +distinct cosets form a disjoint +partition of an + +infinite group G. But of +course, we don't get + +Lagrange's theorem as a +corollary, because I already + +said, there's a one-to-one +correspondence between Z and + +2Z, paradoxically. + +So the cardinality of Z +and 2Z are the same. + +More elegant language. + +Nonetheless, you see, this +is a useful partition and + +standard partition +into the even + +integers and the odd integers. + +And we could also write this as +2Z and this is 2Z plus 1. + +So we can divide the +integers into even + +integers and odd integers. + +All right. + +Now we can actually add cosets, +subtract cosets. + +In these cases, we can +even multiply cosets. + +But let's just talk +about staying + +within the group operation. + +Given any abelian -- + +let's continue to say +G is abelian -- + +how would you add two cosets? + +Coset addition is defined +as follows. + +H plus G -- + +we want to have some addition +operation, which I'll just + +indicate by plus -- + +H plus G prime, what's +going to equal? + +We define that to equal +H plus G plus G prime. + +And that makes sense. + +I mean, if we really write all +this out, we get H plus H plus + +G plus G prime. + +H plus H is just H again. + +So it's sort of a +proof of that. + +If you go through in detail, any +element of this coset plus + +any element of this coset +is going to be an + +element of this coset. + +So this itself is a coset. + +So we now have an addition +table for cosets. + +So in fact, it's easy to show +that the cosets themselves + +form a group called +a quotient group. + +Start over here. + +Cosets of H in G under +coset addition -- + +that's going to be Z -- + +form a group. + +We just defined coset +addition. + +And it's easy to check that they +themselves form a group + +called the quotient group. + +Usually written G slash H and +pronounced G mod H. And we can + +can mod out anything. + +We do the arithmetic in these +quotient groups by modding out + +any elements of H. + +And let's take an example. + +Here's a good one. + +For example, the cosets +of 2Z in Z, namely, + +2Z and 2Z plus 1. + +Under coset addition. + +What is coset addition here? + +If I add any even integer to +any even integer, I get an + +even integer. + +Any odd to even, I get +an odd integer. + +Odd to odd gives that. + +I mean, odd to even gives that, +and odd to odd gives me + +back evens again. + +So that's the addition table. + +The subgroup itself, +x is the identity. + +This is clearly isomorphic to +Z2 with this addition table. + +In fact, this is a very good way +of constructing the cyclic + +group Z2, or more +generally, Zn. + +So this would be called +Z mod 2Z. + +And it's isomorphic to Z2, or +in general, Z mod nZ is + +isomorphic to Zn. + +A very good way of thinking of +Zn is as residue classes or + +equivalence classes, modulo n. + +The cosets of nZ. + +are nZ itself, nZ plus 1, +nZ plus 2, up to nZ + +plus n minus 1. + +And if you add them together, +they follow the rules of mod n + +arithmetic. + +If you just add the residues +together and + +then reduce mod n. + +So we can think of +Zn as being -- + +a coset is an equivalence +class. + +It's all the elements of the +group that are equivalent, + +modular of the subgroup H. Or in +the case of integers, it's + +all integers that are +equivalent modulo + +the subgroup nZ. + +They have the same remainder +after division by n. + +They have the same residue. + +These are all equivalence +class notions. + +And how do you add them? + +You add them in the ordinary +way, and then you take + +everything modulo m. + +In other words, you do +mod-m arithmetic. + +OK. + +So I didn't quite go to quotient +groups in the notes, + +but perhaps I should have. + +Probably I should have, because +this is maybe the most + +powerful idea in group theory, +and certainly closely related + +to this little bit of number +theory that we're doing in the + +integers mod n. + +And of course, it has +vastly greater + +applications than just that. + +OK. + +And you could do the same +thing over here. + +This is basically doing the +same kind of thing. + +But I won't take time +to do that. + +So here's another view of the +integers mod-n that may be + +helpful as we go forward. + +All right. + +I think that's all I want +to say about that. + +Yeah. + +Good. + +All right. + +Here would be a good place +to start on fields. + +OK. + +Fields. + +Obviously very important +in algebra. + +Fields are like groups, +only more so. + +Groups are a set of elements +with a single operation, which + +we've been calling addition. + +A field is a set of elements +with two operations, which + +we'll call addition and +multiplication. + +So what do we have? + +We have a set of elements F. +We're going to be particularly + +interested where the +set is finite. + +Those are called +finite fields. + +And we're going to have two +operations, which I'll + +continue to write addition by +simple plus and multiplication + +with an asterisk, just to +be very explicit about + +everything. + +And after a while, you can +write these things as you + +would in ordinary arithmetic, +with just ordinary plus and + +juxtaposition for +multiplication. + +And what are the axioms +of a field? + +They're presented in an elegant +way in the notes, + +which obviously go back a long +way, but I got from Bob + +Gallager, and I like. + +All right. + +Under addition -- + +so let's write it this way. + +Now, just considering the +addition operation is an + +abelian group. + +Commutative group. + +Which means it has an identity, +and we will continue + +to call that identity 0. + +Just as we do in the real +field, let's say. + +OK. + +Think of the real field, if you +like, as a model for all + +fields here. + +All right. + +So that's axiom one. + +Axiom two. + +If we take the non-zero elements +of the field, which I + +write by F star, explicitly +that's F not including 0 -- + +not a very good notation, +but I'll use it -- + +and the multiplication +operation, that, too is an + +abelian group. + +So this, of course, is why we +spent a little time on groups, + +abelian groups, so we'd +eventually be able to deal + +with fields. + +And its identity is called 1. + +Meaning that under +multiplication, 1 times + +anything is equal to itself. + +And then we have something +about how the operations + +distribute, the usual +distributive law that A times + +B plus C is equal to A times B +plus D times C, where I've + +written out all of these. + +So this is how addition and +multiplication interact again + +in a way that you're accustomed +to, and after a + +while, you don't need to write +all these parentheses. + +OK. + +So that's actually almost a +simpler set of axioms than for + +groups, once we understand +the group axioms. + +And so let's check. + +Is the real field, is the set +of all real numbers under + +ordinary real addition and + +multiplication, is that a field? + +What do we have to check? + +We have to check that under +addition, we're going to take + +the additive identity +as being equal to 0. + +Under our reduced set of group +axioms, the main thing we have + +to check is if we add any real +number to the reals, we get + +the reals again and the +one-to-one correspondence is + +the permutation. + +Is that correct? + +Yes, it is. + +And so this is OK. + +Now under multiplication, if +we take the non-zero real + +numbers, here's the question. + +If I have some alpha not equal +to 0, is alpha times the + +reals, not including 0 -- the +non-zero real numbers -- + +equal to R star? + +And here I'm really implying a +one-to-one correspondence. + +So I might write it +more that way. + +I pose this question rather +abstractly, but you can easily + +convince yourself +that it's true. + +Any non-zero number, if I +multiply it by any non-zero + +number, I get a non-zero +number. + +Is the correspondence +one to one? + +Yes, because I can divide out +this number and get alpha. + +So alpha x on R star by +multiplication to give R star + +again, and this is a one-to-one +correspondence. + +But it's obvious why I have +to leave out 0, right? + +0 times any real number is 0. + +So at O, R star is simply +equal to zero set. + +So we always have to leave out +0 from multiplication. + +0 doesn't have an inverse. + +Everything else does +have an inverse. + +Under the standard group +operations, that's what we + +have to check. + +That would be the alternate +question, does every non-zero + +real number have an inverse? + +That's easier to see, +the answer is yes. + +Multiplicative inverse. + +Inverse of alpha is +1 over alpha. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Yes. + +I've used the alternative set +of axioms, including the + +permutation property. + +To check whether there's an +abelian group, I've asked if + +alpha R star is the permutation +of R star. + +And without going through +details, I claim it is. + +Thank you. + +All right. + +So we checked that. + +Of course, the distributive +law holds. + +So the real field is a field, +which you probably were + +willing to accept on +faith, anyway. + +Similarly, you go through +exactly the same arguments for + +the complex field. + +What about the binary field? + +We think we understand +that by now. + +Here the operations are mod-2 +addition and mod-2 + +multiplication. + +I've written down explicitly +the addition and + +multiplication tables. + +Under addition, we simply +have Z2 again. + +F2. + +The additive group of +F2 is simply Z2. + +We forget about multiplication. + +We've seen quite a few times +now that that's a group. + +Under multiplication, what are +the non-zero elements of F2? + +Just one element. one. + +This includes the identity? + +Yes. + +Is it a group? + +Yeah. + +It's a trivial group. + +1 times 1 equals 1. + +1 under multiplication is +isomorphic to the trivial + +group 0 under addition. + +Its group table is +1 times 1 is 1. + +Sure enough. + +That's the identity +permutation. + +Sometimes when things get +too trivial, it's a + +little hard to check. + +But yes. + +And distributive is +easy to check. + +OK? + +So that's all it takes +to define a field. + +Of course, by the inverse +property, when we have + +addition, this also implies an +inverse and a subtraction + +operation and a cancellation +and additive identities. + +We have a field element on both +sides of a plus b equals + +a plus c, then b plus +b equals c. + +That's what I mean +by cancellation. + +Similarly under multiplication, +we get a + +multiplicative inverse. + +1 over alpha, for any alpha in +F. We, therefore, are able to + +define division. + +And we have cancellation for +multiplicative identity. + +So we immediately get a lot from +these group properties. + +We get all the properties +you expect of fields. + +You can add, subtract, multiply, +or divide, all in + +the usual way that we do +over the real field. + +OK. + +Let's stay over here. + +I think my next topic +is prime fields. + +Yes. + +So prime fields. + +When we talked about the +factorization properties of + +the integers, we talked +about primes p. + +And now I'm going to talk about +Fp is going to be a + +field with a finite number +of elements where + +the number is a prime. + +So what are the elements in +this field going to be? + +Are they simply going to be 0, +1 up through p minus 1 again, + +the same elements as were in +the cyclic group with p + +elements where I'm restricting +m now to be a prime p? + +And for my addition operation +and my multiplication + +operation, I'm going to just +let these be mod-p addition + +and multiplication now. + +And I claim that this +is a field. + +So actually, the proof follows +very close to what I + +just did for F2. + +F2 is a model for this. + +But it's a little harder +to check this. + +Under a, under the addition +operation, Fp really is just + +Zp again, so that's OK. + +That's an abelian group. + +Zmod-p. + +Or the quotient group, +Zmod-pZ. + +We can also again think of this +as Zmod-pZ, if we want. + +So everything is going to become +mod-Z. That's a very + +useful way of thinking of it. + +So we're really thinking of +these as remainders or + +representatives of the residue +classes of pZ in Z. This is + +pZ, this is pZ plus 1 up +to Z minus 1, up to pZ + +plus p minus 1. + +This is the same +as pZ minus 1. + +OK. + +The real question is, if we take +the non-zero elements of + +Fp, is this closed? + +And does every element +have an inverse? + +Or equivalently, when we +multiply by a particular + +element, do we just get +a permutation of this? + +The reason that p has +to be a prime -- + +let's suppose we take two of +these things, a and b, and we + +multiply them. + +What's the multiplicative +rule? + +a times b is just ab mod-p. + +That's what I defined +multiplication as. + +Now the question is, could +that possibly be 0? + +Which is the same as saying, +could a times b be a multiple + +of p, where a and b are taken +from the non-zero + +elements of the field? + +And here, because p is a prime, +it's clear that you + +can't multiply two non-zero +numbers which are less than p + +and get a multiple +of the prime p. + +If p were not a prime, +then you could. + +If we took n equals 10 again, +let's say, and we multiplied 2 + +times 5 from the 10 elements +of these residue classes, 2 + +times 5 is, in fact, equal to +0 mod-10, and therefore Fp + +star, or F10 star, would +not be closed under + +multiplication. + +We would get a 0. + +But in this case, we easily +prove, because it's a prime, + +that it's not equal to 0. + +And therefore it's in Fp star, +so it is closed under + +multiplication. + +And the other thing we have to +check is that it's one-to-one. + +In other words, can a star b +equal to a star c, and by the + +cancellation property, +which holds in -- + +Sorry. + +We've got to establish the +cancellation property holds + +under mod-b arithmetic, but +it does, and so we get the + +cancellation property, that +this is true if and + +only if b equals c. + +So in other words, as we run +through all of these multiples + +for any particular alpha, +we're going to get a + +permutation. + +We need to get the +same set back. + +Everything is finite. + +We're going to get a bunch of +distinct elements of the same + +size as the set itself. + +Therefore, it has to +be the set again. + +I haven't said that +very well again. + +That's why we have notes. + +It's written up correctly +in the notes. + +But we have basically checked +everything that we need to + +check, showed that Fp star +is an abelian group under + +multiplication when p is a +prime, and clearly not when p + +is not a prime. + +AUDIENCE: [INAUDIBLE] + +the inverse, there +is inverse of a? + +PROFESSOR: Yes. + +But basically, we have to prove +that if I take any of + +these, if I take a particular +one, say, alpha, and multiply + +times all of them in Fp star, +that I'm just going to get Fp + +star again. + +And to prove that, I have to +prove that alpha times a is + +not equal to alpha times +b if a not equal to b. + +That's all I need +to prove, right? + +And that comes from the +properties of mod-p + +arithmetic. + +That is what is to be proved. + +I need to use mod-p arithmetic +to prove that. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Oh. + +I have to check the identity +is in here. + +The identity is in here. + +It has one. + +I'm sorry. + +I should have checked +that, too. + +But 1 is the identity +for multiplication. + +And then from this property, +since we multiply alpha p + +star, we get Fp star again. + +That includes one. + +All right? + +So it's got to be one of these +guys which, times alpha, gives + +1, and that shows the existence +of an inverse. + +So you can do it any +way you want. + +But the key to the proof is to +prove this, and that's why I + +focused on the permutation +property. + +Permutation property is +really what you prove + +to demonstrate this. + +OK? + +Good. + +Everyone seems to be following +closely here. + +Any further questions? + +This is important, because +we've got our + +first finite field. + +The integers mod-p are a finite +field of size p for any + +prime state. + +We've got F2, F3, F5, +F7, and so forth. + +OK. + +Further on this subject. + +We have two closely related +propositions. + +One, every finite field with +prime p elements is + +isomorphic to Fp. + +So if you give me a finite +field, you tell me it has p + +elements, I'll show you that +it basically has the same + +addition and multiplication +tables with relabeling. + +And secondly, every finite field +with an arbitrary number + +of elements, for every finite +field, the integers of the + +field form a prime field for +some P. You understand my + +abbreviations. + +And the proofs of these are +very closely related. + +What do I mean by the integers +of a field, of a finite field? + +OK. + +Well, let's start from the +very most basic thing. + +What do we know? + +We know that the field contains +0 and 1, and those + +are going to be two of the +integers of the field. + +So 0 and 1 are in F. + +Let's use the closure +under addition. + +Clearly 1 plus 1 is in F. We're +going to call that 2. + +1 plus 1 plus 1 is in F. We're +going to call that 3. + +And so forth. + +And of course, since the field +is finite, eventually this is + +going to have to repeat. + +And from the fact it repeats, +you're basically going to show + +that at some point, one +of these is going + +to be equal to 0. + +So there's going to be some n. + +The first repeat is +going to be n + +equal to 0 in F. OK. + +So that's what I mean +by the integers. + +The integers clearly form a +subgroup of the additive group + +of F, to form a subgroup +under addition. + +And in fact, a cyclic +subgroup. + +I'm skipping over some of the +details here, but that's a + +claim at this point that I +haven't really demonstrated. + +But just from a subgroup +property, let's attack number + +one up here. + +Suppose we have a field with p +elements, and the additive + +group of the field +has p elements. + +It consists of the +same elements. + +And by Lagrange's theorem, what +are the possible orders + +of that subgroup? + +What are the possible number of +elements in that subgroup, + +the sizes of the subgroup? + +The order of a group +is its size. + +Well, it has to divide p. + +There aren't many things +that divide a prime p. + +There's 1 and there's p. + +OK? + +So the subgroup either has +a single element or + +it's all of the group. + +If there's a single element +-- let's to keep an + +open mind here -- + +then what that means is that +if I take G and I add it to + +itself, since it's a subgroup, +it has to give an + +element of the group. + +But there is only one element +of the group. + +Let's say G is the single +element in this subgroup. + +I guess it could only be 1. + +Let's start out with one. + +So suppose one is the only +element of the subgroup. + +Then I get the equation 1 plus +1 equals 1, which by + +cancellation implies +that 1 equals 0. + +OK, well, that can't be true. + +In a field the multiplicative +identity is not + +the additive identity. + +So that can't be true. + +That would only be true if we +had a field with one element, + +and fields implicitly always +have at least two + +elements, 0 and 1. + +F2 is the smallest +finite field. + +I suppose we could set up a +single element that sort of + +satisfies all these axioms, +but then, what is the + +multiplicative group? + +All right. + +So this can't happen. + +So that means this subgroup +has to have p elements. + +It has to consist of all the +elements of the field. + +So that means the integers are +all the elements of the field. + +But now the isomorphism, then, +is that this is isomorphic Fp + +under the isomorphism. + +This corresponds to 2, this +corresponds to 3, and so + +forth, in Fp. + +You can see, you know, 2 is 1 +plus 1, 3 is 1 plus 1 plus 1, + +so 2 plus 3 is going +to be 5 1's. + +Mod size the field, whenever +this cycles. + +So this is going to +have to be p, and + +basically, that shows -- + +AUDIENCE: [INAUDIBLE] + +to prove that it is isomorphical +[UNINTELLIGIBLE] + +multiplying 1 plus 1 into +1 plus 1 plus 1. + +But it is typical -- + +PROFESSOR: I really +have only used the + +additive property here. + +I don't think multiplication +enters into it. + +OK, here's where the +multiplicative + +property adds in. + +I have to prove not only that +this is isomorphic to Fp as an + +additive group, but the +multiplication tables are + +isomorphic under the +same relabeling. + +So for that, I have to show +that 2 times 3, when I've + +defined 3 and 3 this way, gives +me the same result as + +multiplying 2 and +3 in F p mod-p. + +But again, I could do this just +because sort of mod-p + +commutes with addition +and multiplication. + +If I multiply 1 plus 1, two 1's +times three 1's, so I'm + +going to get six 1's, and that's +exactly what I get in + +Fp, reducing everything mod-p. + +So I have to check that also +to prove this isomorphism. + +And this is done carefully +in the notes. + +The distributive law holds +because the distributive law + +holds for sums of n 1's. + +1 plus 1 times 1 plus 1 plus 1 +plus 1, it's going to be the + +same regardless of where you +put it in, how you put the + +parentheses. + +OK. + +So with some sorry hand-waving +here, we've basically given + +the idea of how to prove this. + +It's basically Lagrange that the +additive subgroup has to + +be of size 1 or p, and we prove +quickly that actually p + +is the only case that works. + +And then we extend all the +arithmetic properties by just + +observing they'll hold +for 1 plus 1 plus 1. + +Yeah? + +AUDIENCE: [INAUDIBLE] + +the line 1 plus 1 plus +1 like that? + +Might we [UNINTELLIGIBLE PHRASE] + +1 is equal to 0. + +What is actually +[UNINTELLIGIBLE PHRASE]? + +Should we state that 1 has +to be different than 0? + +PROFESSOR: Yeah. + +I guess I could simply get +around that by stating that + +the multiplicative identity has +to be different from the + +additive identity. + +It clearly follows from this, +and I think I put it as an + +exercise, 0 times any group +element has got + +to be equal to 0. + +So this is how 0 behaves under + +multiplication from these axioms. + +But 1, as the multiplicative +identity, has to satisfy that + +rule, so clearly, 0 +cannot equal to 1. + +Unless, in some trivial sense, +there is only one element in + +the groups if there's any +non-zero element. + +So this implies that 0 +is not equal to 1. + +Just could have included +that as an axiom. + +Yeah? + +AUDIENCE: Assume a +and b [INAUDIBLE] + +PROFESSOR: Excuse me? + +AUDIENCE: Assume a and +b, [UNINTELLIGIBLE] + +does not include 0? + +PROFESSOR: Correct. + +Yeah, you're right. + +OK. + +So it follows from this +that 1 is not 0. + +Yeah. + +I'm sorry I don't personally +have a lot of patience for + +these fine details. + +For mathematicians, +it's important to + +keep them all in mind. + +But my effort is to make these +propositions plausible enough + +so that you can believe them, +and you can go back and read a + +real proof and see that the +proof must be correct + +intuitively, without just +mechanically checking it. + +OK. + +Let me just again outline +how this works. + +It's very similar. + +Again, given any finite field, +if we define the integers of + +the field in this way, we show +that eventually they form a + +cyclic group. + +Their cyclic group +is something that + +has a single generator. + +The generator is 1. + +So eventually it has to cycle +for some number n. + +Now could n be a non-prime? + +No, because this is a field, and +if n were non-prime, then + +we would be able to find two +integers that multiplied + +together gave 0. + +And that's forbidden by the +axioms of the field. + +So the only possibility is that +n is a prime, and in that + +case, we have found what's +called a subfield, a subset of + +the elements of the field which +itself is a field under + +the field axioms. + +And the field has p elements, +and we already know that every + +finite field with p elements +is isomorphic to Fp. + +So it can only be that the set +of integers is a subfield + +which is isomorphic to +Fp for some prime p. + +OK? + +So within any finite field, +we're always going to find, + +just by writing out the integers +and seeing how they + +behave under the additive +property that there are + +exactly p of them. + +So every finite field has +a prime called the + +characteristic. + +The prime characteristic +of the field. + +This is defined as the +characteristic. + +The size of the integer subfield +is the characteristic + +of the field. + +And it has an interesting +property, a + +very important property. + +Suppose we take this p and we +multiply it by any field + +element called data +in the field. + +By the distributive law, +this is just equal to + +1 plus 1 plus -- + +so what do I mean by this? + +I mean beta -- + +whenever I write an integer +times a field element, I mean + +beta plus beta plus +so forth, p times. + +But this is equal to 1 plus 1, +so forth, by the distributive + +law, I guess, times +theta, p times. + +And what is this equal to? + +This is equal to 0. + +So this is equal to 0 times +beta, which fortunately I just + +told you always must equal 0. + +OK. + +So the conclusion is that if +we add any field element to + +itself p times, we're going to +get 0 for all beta in the + +field where p is the +characteristic of the field. + +Now in digital communications, +we're almost always dealing + +with a case where the +characteristic of the field is + +going to be 2. + +The prime subfield is just +going to be the two + +elements 0 and 1. + +1 plus 1 is going to +be equal to 0. + +So subtraction will be +the same as addition. + +And in that particular case, we +will have that the sum beta + +plus beta of any 2 field +elements in a field of + +characteristic two is going +to be equal to 0. + +Just as we had for code words +in binary linear codes. + +Binary linear codes are not +fields, they're vector spaces, + +but it's a similar +property here. + +You add any element of field of +characteristic 2 to itself, + +and you're going to get 0. + +So this shows that addition is +the same as subtraction. + +Beta equals minus beta in a +field of characteristic 0. + +Which is a little bit +more general. + +OK. + +So we have some fields now, and +we find these fields are + +the only field of prime size, +and that every finite field + +has an important subfield +and a prime subfield. + +And that has important +properties, consequences for + +the field itself. + +All right. + +I think that's everything +I want to + +say about prime fields. + +Now we go on to the next +important algebraic object, + +polynomials. + +And again, it's hard to know +just how detailed to be, + +because of course you've all +seen polynomials, and you + +intuitively or formally know +something about their + +algebraic properties, +their factorization + +properties, and so forth. + +So I'm going to go pretty +quickly, and this will be in + +the nature of a review. + +A polynomial -- + +maybe the simplest way -- + +how do you define +a polynomial? + +What does it look like? + +It looks like this. + +F0 plus F1 times x plus F2 times +x squared, so forth, + +plus Fm times x to the m. + +That's what it looks like if +it's a non-zero polynomial. + +Or even if it's just -- + +you could consider all 0 +coefficients to be the zero + +polynomial. + +But in general, the convention +is, we write f of x equal to + +that if x is non-zero. + +What are these f's? + +These are called the +coefficients of the + +polynomial. + +And where do they live? + +We need the coefficients to +be in some common field. + +You've often seen these in the +real or complex field. + +Here they're going to +be in finite fields. + +In particular, very +shortly, they're + +going to be prime fields. + +But in general, we'll just +say these f's have + +to be in some field. + +So we're talking about a +polynomial over F where F is + +some field. + +So there's always some +underlying field if there + +isn't a vector space. + +Some similarities between +this and vector spaces. + +And we usually adopt the +convention that Fm is not + +equal to 0. + +All right? + +So we only write the polynomial +out to its last + +non-zero coefficient. + +In general, this could go up +to an arbitrary degree, but + +well, a polynomial, by +definition has a finite + +degree, which means it has +a finite m for which the + +polynomial can be written +in this way. + +And if the Fm is the highest +non-zero coefficient, then we + +say the degree of f of x is m. + +So all polynomials have a finite +degrees, except for 1. + +There is the zero polynomial, +which we have + +to account for somehow. + +And here we'll just call +it f of x equals 0. + +Informally, it's a polynomial, +all of those + +coefficients are 0. + +But we'll just define it +by its properties. + +Zero polynomial plus any other +polynomial is equal to the + +identity under addition +for the polynomials? + +What's the degree of the +zero polynomial? + +Anyone have a definition for +the degree of the zero + +polynomial? + +Is this well-defined? + +Undefined? + +OK. + +Well, I'll suggest to you +that it should be + +defined as minus infinity. + +This actually makes a lot of +things come out nicely, but it + +is on the other hand, you +don't have to do this. + +If you like, you can define +the degree of + +0 to be minus infinity. + +It's just a convention. + +OK. + +So the set of all polynomials +over F0. + +What's x here? + +I've got this thing x. + +What should I think +of this as being? + +Is this an element of a field, +or is it something else? + +In math, it's usually called +an indeterminate. + +It's just a placeholder. + +It's something else we stick +in order to define the + +polynomial. + +It doesn't have a value, +in principle. + +A comment is made in the notes +that with real and complex + +polynomials, you often think +of x as being a real or + +complex number. + +In other words, you evaluate the +polynomial at some alpha + +in the real or the complex field +by just substituting + +alpha for x. + +And in fact, two polynomials are +equal if they evaluate to + +the same value for all the +alphas and they're + +unequal if not true. + +When we get to finite fields, +it's important this be an + +indeterminate. + +Because consider x and x squared +as polynomials over + +the binary field F2. + +What are the values of these? + +We'll call this F1 of x equals +x, F2 of x equals x squared. + +Then F1 of 0 is 0 and +F1 of 1 is 1. + +Right? + +If I evaluate these at field +elements, the two field + +elements, I get 0 and 1. + +F2 of 0 is equal to 0, and +F2 of 1 is equal to 1. + +But these are not the same +polynomial, all right? + +So x is not to be considered +as a field element. + +It's to be considered just as +a placeholder, a way of + +holding up these polynomials. + +It's actually most important +in multiplication. + +But we gather common +terms in x. + +This is the multiplication +rule. + +But it's just something we +introduce to define the + +polynomial. + +All right. + +So the set of all polynomials +over F in x, or in x over F, + +is simply written as F +square brackets of x. + +That's the convention. + +So that's what I will write +when I mean that. + +And it includes all sequences +like this of finite degree, + +starting at 0, ending +somewhere. + +And also the zero polynomial. + +How do you add polynomials? + +Let's talk about the arithmetic +properties of + +polynomials. + +You know how to do this. + +If you have F0 plus F1 plus F2 +and so forth, you have some + +other polynomial doesn't have +to be the same degree -- + +G of x is G0 plus G1 +x, up there -- + +how do you add these together? + +Component-wise. + +Sum is F0 plus G0 plus +F1 plus G1 x plus 2x + +squared and so forth. + +That's an example. + +So you basically insert dummy +0's out here above the highest + +degree term in G. You add +them up component-wise. + +The addition operation +is where? + +In this field, you have addition +operation in that + +failed field, so you +can do this. + +And you get some result which +is clearly itself a + +polynomial. + +If all the coefficients are +0, you declare that + +the result is 0. + +Otherwise the result +has some degree. + +If you add two polynomials with +different degree, the + +degree of the resulting +polynomial is going to be the + +higher degree. + +If they have the same degree, +you could get cancellation in + +the highest order term, and get +a result which is of lower + +degree, all the way down to 0. + +All right? + +So addition is component-wise +the degree of the result is + +less than or equal to the max +degree of the components. + +So we do addition. + +How do we do multiplication? + +You all know how to do +polynomial multiplication. + +Example. + +F0 plus F1 of x times +G0 plus G1 of x. + +What do you do? + +You just multiply it +out term by term. + +F0 G0 plus F1 G0 x plus F0 G1 +x plus F1 G1 x squared. + +You can combine these +two together. + +And that's your answer, which +clearly is a polynomial. + +So that's one way of doing it, +is multiply out term by term, + +collect the terms. + +The result of this is that what +you get is a convolution + +for each of the coefficients +in the new polynomial. + +You convolve, just by the +ordinary rules of polynomial + +addition, you can basically turn +this around, you convolve + +it, and you'll get these +coefficients. + +This is written out +in the notes. + +So we know how to do polynomial +multiplication. + +What are some of +its properties? + +How is this defined +again in F? + +We see we're now going to need +the multiplicative of + +properties of our field F. +All of these products and + +ultimately convolutions are +performed in F. That's why we + +did these coefficients to be in +a field, so we can do all + +these things. + +All right. + +What are some of +the properties? + +What is the degree of the +product of two polynomials? + +It's going to be the sum +of the degrees, right? + +Provided that both the +polynomials are not 0. + +The highest non-zero term is +clearly going to be a term of + +this kind, and it's going to be +a coefficient of x to the + +sum of the degrees. + +And since F1 and G1 are both +non-zero, by the way we write + +polynomials, them this +highest order term + +is going to be non-zero. + +But we also have to basically +have another rule that 0 times + +f of x is equal to 0. + +So that's the way we +multiply by 0. + +And how does the degree formula +work in this case? + +Well, this is why I defined +the degree of + +0 to be minus infinity. + +So the degree of the product +0 times f of x is -- + +I've defined this to be the +degree of 0 plus the + +degree of f of x. + +This is finite. + +This is minus infinity. + +So the sum is minus infinity, +and so it holds. + +OK? + +That's why we defined +the degree of + +0 to be minus infinity. + +We don't have to, but it's just +so that the sum of the + +degrees formula continues +to work, even if we're + +multiplying by 0. + +Is there a multiplicative +identity for polynomials? + +Yeah. + +What is the multiplicative +identity? + +1. + +OK. + +So one times f of x is +equal to f of x. + +So that's one of the properties +of a field. + +Gee. + +The set of all polynomials over +F in x, is this a field? + +Let's go back and check +our field axioms. + +Under addition, does f of +x form an abelian group? + +Does it have the +group property? + +If we add two polynomials, do +we get another polynomial? + +Do we have cancellation, if F1 +plus F2 equals F1 plus F3, is + +it necessarily true +that F2 equals F3? + +Yeah, it is. + +In fact, this looks very +much under addition. + +These look like vectors. + +If we confine ourselves to the +set of all polynomials of + +degree m or less, +we can add them. + +And it looks very much like the +vector space f to the m. + +Set of all polynomials of degree +m or less corresponds + +to the vector space Fm, which +does have the group property + +under addition. + +So in fact, for f of x, yes. + +It is an abelian group under +addition with identity being + +the 0 polynomial. + +And all of f of x is an infinite +abelian group. + +If we just take polynomials of +degree m or less and restrict + +Fp to be a finite group, then +there are only p to the m + +elements, and we would have +a finite abelian group. + +OK. + +Well. + +Are the polynomials an abelian +group under multiplication? + +It has an identity. + +It has all the arithmetic +properties you might expect. + +It's commutative. + +f of x times g of x is equal +to g of x times f of x. + +So it's abelian. + +It has cancellation. + +f of x g of x is equal +to f of x h of x. + +That's true if and only if g +of x is equal to h of x. + +Is it missing anything? + +Inverse, right? + +Very good. + +Just like the integers. + +Not all the polynomials +have inverses. + +Which are the polynomials +that do have inverses? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: No. + +There are more than that. + +So now we're getting into +polynomial factorization. + +And the particular topic +is units, which are the + +invertible polynomials. + +And what are they? + +Does the 0 polynomial +have an inverse? + +We're a little unsure, are we? + +What could it possibly be? + +If it had an inverse, +this would mean 0 + +times f of x is -- + +well, 0 times f of x would have +to be a one-to-one map to + +all of f of x. + +But it isn't. + +It simply maps to 0. + +Doesn't have an inverse. + +What about the non-zero +polynomials + +that have degree 0? + +In other words, the degree +0 polynomial, is simply + +something that looks like this. +fx equals f0, where f0 + +is not equal to 0. + +Is that invertible? + +Yeah, because f0 is in the +field, and it has an inverse. + +So this has inverse 1 over f of +x, if you like, equals just + +f0 minus 1. + +1 over f0. + +By the rules, you multiply +these two + +things, and you get 1. + +OK. + +So the units in this -- + +well, I'm sorry. + +Take a degree 1 or a higher +polynomial -- + +does that have an inverse? + +Let's suppose we take a +degree 1 polynomial -- + +say, F0 plus F1 x -- + +and what I want to find +is its inverse. + +Let's call it g of x. + +Is it possible to find a g of +x such that the product of + +these two is 1? + +Clearly not, because by our +degree rule, what is the + +degree of this product +going to be? + +The degree is going to be the +sum of this degree plus this + +degree, the degree of f plus +the degree of g, which is + +going to have to +be at least 1. + +Provided that g of x is not 0, +but clearly g of x is not the + +solution we're looking +for here, either. + +So this can't be true, and the +invertible polynomials are the + +degree 0 polynomials, which +means they're basically the + +non-zero elements of F. Yes. + +Considered as polynomials. + +AUDIENCE: And how are the +[UNINTELLIGIBLE PHRASE]? + +PROFESSOR: Yes, indeed. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Ah, no. + +We haven't introduced modulo +polynomials and right. + +The powers and the indices are +the integers from 0 up to some + +finite number. + +OK. + +It's time to quit. + +We'll finish this. + +We'll, I believe, to be able +to certainly finish chapter + +seven, maybe get a little bit +into chapter eight, next time, + +on Wednesday. + +And we'll see you then. \ No newline at end of file diff --git a/SW5Zfs97wSw.txt b/SW5Zfs97wSw.txt new file mode 100644 index 0000000000000000000000000000000000000000..e73ee75534e5f3c54d3137f5dee8c40694d18ff3 --- /dev/null +++ b/SW5Zfs97wSw.txt @@ -0,0 +1,6304 @@ +FEMALE SPEAKER: The following +content is provided under a + +Creative Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or to view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK, so my name is Ben +Olken and we're going to + +be talking about how to think +about sample size for + +randomized evaluations. + +And more generally that the +point of this lecture is not + +just about sample size but we've +spent a lot of time, + +like in last lecture, for +example, thinking about the + +data we're going to collect. + +Then the question is, well, +what are we going to + +do with that data? + +And so it's about sample size +but also more generally, we're + +going to talk about how do we +analyze data in the context of + +an experiment. + +OK. + +So as I said, where we're going +to end up at the end of + +this lecture is, how big +a sample do we need? + +But in order to think about how +big a sample we need, we + +need to understand a little more +about how do we actually + +analyze this data. + +When we say, how large does a +sample need to be to credibly + +detect a given treatment effect, +we're going to need to + +be a little more precise about +what we mean by credibly and + +particularly think a little bit +about the statistics that + +are involved in thinking +through-- + +evaluate-- + +understanding these +experiments. + +And particularly, when we say +something that's credibly + +different, what we mean is +that we can be reasonably + +sure, and I'll be a little bit +more precise about what we + +mean by that, that the +difference between the two + +different groups-- the treatment +and control group-- + +didn't just occur by random +chance, right? + +That there's really something +that we'll call statistically + +significantly different between +these two groups, OK? + +And when we think about +randomizing, right? + +So we've talked about which +groups get the treatment and + +which get the control, that's +going to mean that we expect + +the two groups to be similar +if there was no treatment + +effect because the only +difference between them is + +that they were randomized. + +But there's going to be some +variation in the outcomes + +between the two different +groups, OK? + +And so randomization is going +to remove the bias. + +It's going to mean that the +groups-- we expect the two + +different groups to be +the same, but there + +still could be noise. + +So in some sense, another way of +thinking about this lecture + +is that this lecture is +all about the noise. + +And how big a sample do we +need for the noise to be + +sufficiently small for us to +actually credibly detect the + +differences between the two +different groups, OK? + +So that's what we're going to +talk about is basically, how + +large is large so we can +get rid of the noise? + +And let me say, by the way, that +we've got an hour and a + +half, but you should feel free +to interrupt with questions or + +whatever if I say something +that's not clear because + +there's a lot of material that +we're going to be going + +through pretty quickly. + +OK. + +So when we think about how big +our sample means to be-- + +remember, the whole point is how +big does our sample have + +to be remove the noise that's +going to be in our data? + +And when we think about that, we +think essentially about how + +noisy our data is, right? + +So how big a sample we need is +going to be determined by how + +noisy is the data and also how +big an effect we're looking + +for, right? + +So if the data is really noisy +but the effect is enormous, + +then we don't need as +big of a sample. + +But if the effect we're looking +for is really small + +relative to the noise in the +data, we're going to need a + +bigger sample. + +So actually, sometimes it's +the comparison between the + +effect size and how +noisy the data is. + +It's the ratio between +these things + +that's really important. + +Other factors that we're going +to talk about are, did we do a + +baseline survey before +we started? + +Because a baseline can +essentially help us reduce the + +noise in some sense. + +We're going to talk about +whether individual responses + +are correlated with +each other. + +So for example, if we were to +randomize a whole group of + +people into a given treatment, +that group might be similar in + +lots of other respects. + +So you can't really count that +whole group as if they were + +all independent observations +because they might be + +correlated. + +For example, you all just +took my lecture. + +So if you all were put in the +same treatment group, you all + +were exposed to the treatment +but you also all were exposed + +to my lecture and so you're not + +necessarily independent events. + +And there are some other issues +in terms of the design + +of the experiment that we'll +talk about that can help + +affect samples as well, like +stratification, control + +variables, baseline data, et +cetera, which we're going to + +talk about, OK? + +So the way we're going to go in +this lecture is, I'm going + +to start off with some basics +about, what does it mean to + +test a hypothesis +statistically? + +And then when we get into +hypothesis testing, there are + +two different types of +errors that we're + +going to talk about. + +They're helpfully named type +I and type II errors. + +And you have to be careful not +to make a type III error, + +which is to confuse a type +I and a type II error. + +So we'll talk about +what those are. + +Then we'll talk about standard +errors and significance, which + +is, how do we think about more +formally what these different + +types of errors are? + +We'll talk about power. + +We'll talk about the +effect size. + +And then, finally, the factors +that influence power, OK? + +So this is all the stuff +we're going to go + +through, all right? + +So in order to understand +the basic concepts of-- + +when we're talking about +hypothesis testing, we need to + +think a little about +probabilities, OK? + +Because all this comes down, +essentially, to some basic + +analysis about probability. + +So for example, suppose you had +a professional-- and the + +intuition here is that the more +observations we get, the + +more we can understand the +true probability that + +something occurred-- + +whether the true probability +that something occurred was + +due to a real difference in +the underlying process or + +whether it was just +random chance. + +So for example, consider +the following example. + +So suppose you're faced with a +professional gambler who told + +you that she could get heads +most of the time. + +OK, so you might think this is +a reasonable claim or an + +unreasonable claim, but this is +what they're claiming and + +you want to see if +this is true. + +So they toss the coin and +they get heads, right? + +So can we learn anything +from that? + +Well, probably not because +anyone, even with a fair coin, + +50% of the time, they would get +heads if they tossed it. + +So we're really can't infer +anything from this one. + +What you saw that they did five +times and they got heads, + +heads, tails, heads, heads. + +Well, can you infer anything +about that? + +Well, maybe. + +You can start to say, well, this +seems less likely to have + +occurred just by +random chance. + +But you know there's +only five tosses. + +What's the chance that someone +with an even coin + +can get four heads? + +Well, we could calculate that if +we knew the probabilities. + +And it's certainly not +impossible that this could + +occur, right? + +And now, what if they got +20 tosses, right? + +Well, now you're starting to get +information, although in + +this particular example, +it was closer to 50-50. + +So now you have 12 +versus eight. + +Could that have occurred +by random chance? + +Well, maybe it could +have, right? + +Because it's pretty +close to 50-50. + +And now, suppose you had 100 +tosses or suppose you had + +1,000 tosses with 609 heads +and 391 tails, right? + +So as you're getting more and +more data, right, you're much + +more likely to say something +is meaningful. + +So if you saw this data, for +example, the odds that could + +occur by random chance +are pretty high. + +But if you saw this data with +609 heads and 391 tails out of + +1,000 tosses, it's actually +pretty unlikely that this + +would occur just by +random chance, OK? + +And so this shows you, as you +get more data you can actually + +say, how likely was this outcome +to have occurred by + +random chance? + +And the more data you have, the +more likely you're going + +to be able to conclude that +actually, this difference you + +observed was actually due to +something that the person was + +doing and not just due to what +would happen randomly. + +And in some sense, all of +statistics is basically this + +intuition, which is, you take +the data you observe and you + +calculate what is the chance +that the data I observe could + +have occurred just +by random chance. + +And if the chance that the data +I observed could have + +happened just by random chance +is really unlikely, then you + +say, well then it must've been +that your program actually had + +an effect, OK? + +Does that make sense? + +That's the basic idea, +essentially, of all of + +statistics is, what's the +probability that this thing + +could have happened randomly? + +And if it's unlikely, then +probably there was something + +else going on. + +Here's another example. + +So what this example shows is, +now suppose you have a second + +gambler who had 1,000 tosses +and they had 530 + +heads and 470 tails. + +What this shows is that-- and +that's really a lot of data. + +But in some sense, what we can +learn about this data depends + +on what hypothesis we're +interested in. + +So if the gambler claimed they +obtained heads 70% of the + +time, we could probably say, no, +I don't think so, right? + +This is enough data that the +odds that you would get this + +data pattern if you had heads +70% of the time are really, + +really small, right? + +So we could say, I can +reject this claim. + +But suppose they said that +they claim they could get + +heads 54% of the time, OK? + +And you observe they got +heads 53% of the time. + +Well, you probably couldn't +reject this claim, right? + +Because this is similar enough +to this that if this was the + +truth, this could have occurred +by random chance. + +So in some sense, what we can +say based on the data depends + +on how far the data is from our +hypothesis and how much + +data we have. + +Does that make sense as +some basic intuition? + +OK. + +So how do we apply this +to an experiment? + +Well, at the end of the +experiment, what we're going + +to do is we're going +to compare the + +two different groups. + +We're going to compare +the treatment + +and the control group. + +And we're going to say-- + +we're going to take a look at +the average, just like we were + +doing in the gambling example. + +We'll compare the average in +the treatment group and the + +average in the control, OK? + +And the difference is +the effect size. + +So for example, in this +particular case, in the + +Panchayat case, you'd look at, +for example, the mean number + +of wells you've got in the +village with the female + +leaders versus the mean number +of wells in the villages with + +the male leaders, OK? + +So that's in some sense our +estimate of how big the + +difference is. + +And the question is going to be, +how likely would we have + +been to observe this difference +between the + +treatment and the control group +if it was just due to + +random chance, OK? + +And that's what we need the +statistics to figure out. + +Now one of the reasons-- + +so where does the +noise come from? + +In some sense, we're not going +to observe an infinite number + +of villages. + +Or we're not going to observe +all possible villages. + +In fact, even if we observe all +the villages that exist, + +we're not going to observe, +in some sense, all of the + +possible villages that could've +hypothetically + +existed if the villages were +replicated millions and + +millions of times. + +We're just going +to observe some + +finite number of villages. + +And so we're going to estimate +this mean by computing the + +mean in the villages that +we observed, OK? + +And if there are very few +villages, that mean that we're + +going to calculate is going to +be imprecise because if you + +took a different sample of +villages, you would get a + +slightly different mean, OK? + +If you sample an infinite number +of villages, you get + +the same thing every time. + +But suppose you only sampled +one village. + +Or suppose there was a million +villages out there and you + +sampled two, right? + +And you took the average, OK? + +If you sampled a different two +villages, just by random + +chance, you would get +a different average. + +And sometimes that's where the +part of the noise in our data + +is coming from. + +So for example-- + +sorry. + +So in some sense, what we need +to know is, we need to know if + +these two groups-- it sort of +goes back to the same as + +before, if these two groups were +the same and I sampled + +them, what are the chances I +would get the difference that + +I observed by random chance? + +So for example, suppose +you observed these two + +distributions, OK? + +So this is your control +group and this is + +your treatment group. + +Now you can see there is some +noise in the data, right? + +This one is a mean of 50 and +this one is a mean of 60. + +And there's some-- + +these are histograms, right? + +So this is the distribution of +the number of villages that + +you observed for each +possible outcome. + +So you can see here that there's +some noise, right? + +It's not that everyone here was +exactly 50 and everyone + +here was exactly 60. + +Some people were 45. + +Some were 55 or whatever. + +But if you look at these two +distributions, you could say + +it's pretty unlikely that if +these were actually drawn from + +the same distribution of +villages, all of the blue ones + +would be over here and +all the yellow ones + +would be over here. + +It's very unlikely that if these +were actually the same + +and you draw randomly, you get +this real bifurcation of these + +villages, OK? + +And where are we basing that +idea, that conclusion on? + +We're basing the conclusion on +the fact that there's not a + +lot of overlap, in some sense, +between these two groups. + +But now, what if you saw +this picture, right? + +What would you be able +to conclude? + +Well, it's a little +less clear. + +The mean is still the same. + +All the yellows still have an +average of 60 and all the + +blues have an average of 50. + +But there's a lot more +overlap between them. + +Now if we look at this, we can +sort of eyeball it and say, + +well, there's really a pretty +big difference even relative + +to the distributions there. + +So maybe we could conclude that + +they were really different. + +Maybe not. + +And what if we saw +this, right? + +This is still the same means. + +The yellows have a mean +of 60 and the blues + +have a mean of 50. + +But now they're so +interspersed that + +is harder to know-- + +it's possible, if you saw +pictures like this, you would + +say, well, yes, the yellows are +higher, but maybe this was + +just due to random chance, OK? + +So what the purpose of these +graphs are, is to show you is + +that in order-- so in both +cases, we the same difference + +in the mean outcomes. + +It was 60 versus 50 in all +three cases, right? + +But when you saw this graph, it +was quite clear that these + +two groups were really +different. + +When you saw this graph, is was +much harder to figure out + +if these two were really +different or if this was just + +due to random chance, OK? + +Does that make sense of +where we're going? + +And so, just to come back to +the same theme, all the + +statistics are going to do in +our case is going to help us + +figure out, are these +differences big enough, given + +the distribution of data we +have, how likely is it that + +the difference we observed +could have + +happened by random chance. + +And so intuitively, we can +look at this one and say, + +definitely different. + +And this one, maybe not sure. + +But if we want to be a little +more precise about that, + +that's where we need the +added statistics. + +AUDIENCE: Is the sample size +the same in both examples? + +PROFESSOR: Yeah, the sample +size is the same. + +Yeah, sample size is +exactly the same. + +So you can see that the numbers +go down because it's + +more spread out. + +All right. + +So in some sense, what are the +ingredients that we've talked + +about in terms of thinking +about whether you have a + +statistically significant +difference? + +If you think back to the gambler +example, we talked + +about the sample size +matters, right? + +So if we saw 1,000 tosses, we +had much more precision about + +our estimates than if we had +10 tosses or five tosses. + +The hypothesis you're testing +matters, right? + +Because the smaller an effect +size we're trying to detect, + +the more tosses we need in +the gambler example. + +If you're trying to detect a +really small difference, you + +need a ton of data, whereas if +you're trying to detect really + +extreme differences, you can +do it with less data, OK? + +And the third thing we saw is +the variability of the outcome + +matters, right? + +So the more noisy the outcome +is, the harder it is to know + +whether the differences that +we observe are due just to + +random chance or if they're +really due some difference in + +the treatment versus +the control group. + +OK, so does this makes sense? + +Before I go on, these are the +three ingredients that we're + +going to be playing with. + +Do these make sense? + +Do you have questions on this? + +OK. + +So you may have heard of +a confidence interval. + +How many of you guys +have heard of + +a confidence interval? + +OK. + +How many of you can state +the definition of + +a confidence interval? + +Thanks, Dan. + +I'm glad that you can. + +So what do we mean when we +say confidence interval? + +What we mean by a confidence +interval-- + +so let's just go through what's +on the slide and then + +we can talk about it +a little more. + +So we're going to measure, +say, 100 people and we're + +going to come up with an +average length of 53 + +centimeters. + +So we want to be able to say +something about how precise + +our estimate is. + +So we say the average +is 53 centimeters. + +How confident are we or how +precise are we that it's 53%? + +And that's what a conference +interval is trying to say. + +And a confidence interval, +essentially, tells us that + +with 95% probability-- + +so we have a confidence interval +of 50-56 says that + +with 95% probability, the +true average length lies + +between 50 and 56. + +And so the precise definition +is that if you had a + +hypothesis that the true average +length was in this + +range with-- + +no, I'm going to get it wrong. + +It says that if you had a +hypothesis that the true + +average was in here, it's within +95% probability that + +you would get the data +that you observe, OK? + +A converse way of saying it is +that the truth is somewhere in + +this range, right? + +You can be 95% certain that the +truth is somewhere within + +this range, So if you did 20 of +these tests, only one out + +of 20 times would the truth +be outside your confidence + +interval, OK? + +And so an approximate +interpretation of a confidence + +interval is-- + +so we know that the point +estimate of 43, we have some + +uncertainty about +that estimate. + +We think the average is 53, but +there's some uncertainty. + +And the confidence interval +says, well, it's 95% likely + +that the true answer is between +50 and 56, if that was + +the confidence interval, OK? + +So why is that useful for us? + +Well, our goal is +to figure out-- + +we don't care, actually, what +our estimate of the + +program's effect is. + +We care what the true effect +of a program is, right? + +So we did some intervention. + +Like, for example, we had a +female Panchayat leader + +instead of a male Panchayat +leader and we want to figure + +out what the actual difference +that that intervention made is + +in the world. + +We're going to observe some +sample of Panchayats and we'll + +look at the difference +in that sample. + +And we want to know how much +can we learn about the true + +program effect from +what we estimated. + +And the confidence interval +basically tells us that with + +95% probability, the true +program effect is somewhere in + +the confidence interval, OK? + +Does that makes sense? + +How many of you guys have heard +of the standard error? + +OK. + +So a standard error is related +to the confidence interval in + +that a standard error says that +if we have some estimate, + +you could imagine that if we +did the experiment again, + +essentially, with a new sample +of people that looked like the + +original sample of people, we +might get a slightly different + +point estimate because it's +a different sample. + +The standard error basically +says, what's the distribution + +of those possible estimates +that you could get, OK? + +So it says that basically, if +I did this experiment again, + +maybe i wouldn't get +53, I'd get 54. + +If I did it again, +maybe I'd get 52. + +If I did it again, +I might get 53. + +The standard error is +essentially the standard + +deviation of those possible +estimates that you could get. + +What that means in practice +is that-- + +well, in practice, the standard +error is very related + +to the confidence interval. + +And basically, a good rule of +thumb is that a 95% confidence + +interval is about two +standard errors. + +So if you ever see an estimate +of the standard error, you can + +calculate the confidence +interval, essentially, by + +going up or down two standard +errors from the point + +estimate, OK? + +And the confidence interval +and standard error, + +essentially, are capturing +the same thing. + +They're both capturing-- + +when I said we need statistics +to basically compute, how + +likely is it that we would get +these differences by random + +chance, those are all coming out +in the standard error and + +the confidence interval, +right? + +They're computed by both looking +at how noisy our data + +is, which is the variability +of the outcome, and how big + +our sample is, right? + +Because from these two things, +you can basically calculate + +how uncertain your estimate +would be. + +This is a lot of terminology +very quickly, but does this + +all make sense? + +Any questions on this? + +OK. + +So for example. + +So suppose we saw the sampled +women Pradhans had 7.13 years + +of education and the men had +9.92 years of education, OK? + +And you want to know, is the +truth that men have more + +education than women or is this +just a random artifact of + +our sample? + +So suppose you calculated that +the difference was 2.59. + +That's easy to calculate. + +And the standard error was 0.54 +and the standard error + +was going to be calculated based +on both how much data + +you had and how noisy +the data was. + +You would compute that the 95% +confidence interval is between + +1.53 and 3.64, OK? + +So this means that with 95% +probability, the true + +difference in education rates +between men and women is + +between 1.53 and 3.64. + +So if you were interested in +testing the hypothesis that, + +in fact, men and women are the +same in education, you could + +say that I can reject +that hypothesis. + +With 95% probability, the +true difference is + +between 1.53 and 3.64-- + +so zero is not in this +confidence interval, right? + +So we can reject the hypothesis +that there's no + +difference between +these two groups. + +Does that makes sense? + +So doing another example. + +So in this example, suppose +that we saw that control + +children had an average test +score of 2.45 and the + +treatment had an average +test score of 2.5. + +So we saw a difference of +0.05 and the standard + +error was 0.26, OK? + +So in this case, you would say +well, the 95% confidence + +interval is minus 0.55. + +This is approximately two. + +It's not exactly two. + +Minus 0.55-- + +oh, no, it is exactly +two in this example. + +Minus 0.55 to 0.46, OK? + +And here, you would say that +if we were introducing the + +hypothesis that the null +hypothesis is that the + +treatment had no effect on test +scores, you could not + +reject that null hypothesis, +right? + +Because an effect of zero +is within the confidence + +interval, OK? + +So that's basically how we +use confidence intervals. + +Yeah. + +AUDIENCE: Shouldn't the two +points of that confidence + +interval be equidistant +from 2.59? + +PROFESSOR: From 0.05 you mean? + +Yeah. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Yeah, I think-- + +oh, over here? + +AUDIENCE: Yeah. + +PROFESSOR: So they actually +don't always have-- + +so you raise a good point. + +So there may be some +math errors here. + +I think a more reasonable +estimate, by the way, is that + +this would have to be minus +0.05 for you to get + +something like this. + +AUDIENCE: But in the first +example, if 2.59 is the mean, + +is the difference-- + +PROFESSOR: So it's +approximately + +the same, isn't it? + +AUDIENCE: I think it's +a little skewed-- + +PROFESSOR: Yeah. + +AUDIENCE: On that side, +it is 2.64. + +PROFESSOR: OK. + +Yeah, so you raise +a good point. + +So when I said that a rule +of thumb is two times the + +standard error, that's +a rule of thumb. + +And in particular cases, you can +sometimes get asymmetric + +confidence intervals. + +So you're right that usually +they should be symmetric and + +probably, for simplicity, we +should have put up symmetric + +ones, but it can occur that +confidence intervals are + +asymmetric. + +For example, if you had a-- + +yeah, depending on the +estimation, if you have + +truncation at zero-- + +if you know for sure that there +can never be an outcome + +below zero, for example, then +you can get asymmetric + +confidence intervals. + +AUDIENCE: When the distribution +is not normal? + +PROFESSOR: Yeah. + +Exactly. + +But for most things that you'll +be investigating, + +usually they're going to be-- + +AUDIENCE: Normal. + +PROFESSOR: Yeah, for outcomes +that are zero. + +One [UNINTELLIGIBLE] + +get non-normal, but +yes, in general, + +they are pretty symmetric. + +But they might not be +exactly symmetric. + +OK. + +So as I sort of was suggesting +as we were going through these + +examples, we're often interested +in testing the + +hypothesis that the effect size +is equal to zero, right? + +The classic hypothesis the you +typically want to know is, did + +my program do anything, right? + +And so, how do you test the +hypothesis that my program-- + +so we want to know, did +my program have + +any effect at all? + +And so what we technically want +to do is we want to test + +what's called the null +hypothesis, that the program + +had an effect of nothing, +against an alternative + +hypothesis that the program +had some effect. + +So this is the typical test +that we want to do. + +Now you could say, actually, +I don't care about zero. + +I want to say that I know-- +for example, this is the + +standard thing that we would do +in most policy evaluations + +that we're going to be doing. + +It doesn't have to be zero. + +Suppose you were doing a drug +trial and you knew that the + +best existing treatment +out there already have + +an effect of one. + +And so instead of comparing +to zero, you might be + +comparing to one. + +Is it actually better than the +best existing treatment? + +In most cases, we're usually +comparing to zero, OK? + +And usually, we have the +alternative hypothesis that + +the effect is just not zero. + +We're interested in anything +other than zero. + +Sometimes you can specify other +alternative hypotheses, + +that the effect is always +positive or always negative, + +but usually this is the classic +case, which is we're + +saying, we think this thing +had-- the null is no effect. + +We want to say, did this program +have an effect and + +we're interested in any +possible effect, OK? + +And hypothesis testing says, +when can I reject this null + +hypothesis in favor of +this alternative, OK? + +And as we saw, essentially, +the confidence interval is + +giving you a way to do that. + +It's saying, if the null is +outside the confidence + +interval, then I can +reject the null. + +Yeah. + +AUDIENCE: Surely, if we're +trying to assess the impact of + +an intervention, we're always +going to think it's positive. + +Or in general, because-- + +I gave someone some money to +increase their income or not. + +We've got a pretty good idea +it's going to be positive. + +The probability it's negative +is pretty-- + +PROFESSOR: Why do you-- + +AUDIENCE: Yeah, why +do we change our + +significance level-- + +[INTERPOSING VOICES] + +PROFESSOR: You ask +a great question. + +And I have to say this is +a bit of a source of + +frustration of mine. + +Let me give you a couple +different answers to that. + +Here's the thing. + +If you did that-- + +if I said I can commit, before +I look at the data, that I + +only think it could be positive, +that would mean that + +if it's negative, no matter how +negative, you're going to + +say that was random +chance, OK? + +So it would require a fair +amount of commitment on you, + +on your part, as the +experimenter to say, if I get + +a negative result, no matter how +crazy that negative result + +is, I'm going to say that's +random chance, OK? + +And typically, what often +happens ex post is that people + +can't commit to actually +doing that. + +So suppose you did your +program and you-- + +so I actually have a program +right now that I'm working on + +in Indonesia that's supposed to + +improve health and education. + +And it seems to be making +education worse. + +Now, we have no theory for why +this program should be making + +education worse, OK? + +But it certainly seems to +be there in the data. + +Now, if we had adopted your +approach, we wouldn't be + +entertaining the hypothesis that +it made education worse. + +We would say, even though it's +looking like this program is + +making education worse, +that must be random + +noise in the data. + +We're not going to treat that as +something potentially real. + +Ex post, though, you see this in +the data and you're likely + +to say, gee, man, that's a +really negative effect. + +Maybe the program was doing +something that I + +didn't think about. + +And in our case, actually, we're +starting to investigate + +and maybe it's because it was +health and education and we're + +sort of sucking resources away +from education into health. + +So it requires a lot of +commitment on your part, as + +the researcher, that if you get +these negative effects, to + +treat them as random noise. + +And I think that, because most +researchers, even though they + +would like to say they're +going to do that, if it + +happens that they get a really +negative effect, they're going + +to want to say, gee, that looks +like a negative effect. + +We're going to want +to investigate + +that, take that seriously. + +Because most people do that ex +post, the convention is that + +in most cases, to say we're +going to test against either + +hypothesis in either +direction. + +AUDIENCE: Except that +the approach-- + +PROFESSOR: Does that +makes sense? + +AUDIENCE: Your issue is do +I do this program or not. + +So it doesn't matter whether the +impact of the program is + +zero or negative. + +Even if it's zero, you're +saying that it's-- + +PROFESSOR: You're absolutely +right. + +So if you were strict about it +and said, I'm going to do it + +if it's positive and not if it's +zero, then I think you + +were correct that, strictly +speaking, a one-sided + +hypothesis test will be correct +and it would give you + +some more power. + +AUDIENCE: So it would +give you power. + +PROFESSOR: Yeah, it would +give you more power. + +AUDIENCE: [UNINTELLIGIBLE] + +PROFESSOR: Right. + +And the reason it gives you +power is, remember, how does + +hypothesis testing work? + +It says, well, what is the +chance this outcome could have + +occurred 95-- + +what would have occurred by +chance 95% of the time? + +When you do a two-sided +test, you say, OK-- + +where's my chalkboard? + +Here. + +You imagine a normal +distribution of outcomes. + +You're going to say, well, the +95% is in the middle and + +anything in the tails is the +stuff that I'm going to + +[UNINTELLIGIBLE] by +non-random chance. + +Well, what you're doing with a +one-sided test is you're going + +to say, I'm going to take +that negative stuff-- + +way out there negative stuff-- +and I'm going to say that's + +also random chance. + +So I'm going to pick my 95% +all the way to the left. + +And that means that the 5% +that's not random chance is a + +little more to the right. + +Do you see what I'm saying? + +But it requires that if-- + +you're committing to, even if +you get really negative + +outcomes, asserting that they're +random chance, which + +is really, often, kind +of unbelievable. + +The other thing is that, +although this is technically + +the way hypothesis testing +is set up, the norms and + +conventions are that we all use +two-sided tests for these + +reasons I talked about. + +And so I can just tell you that, +practically speaking, I + +think if you do a one-sided +test, people are going to be + +skeptical because it may be that +you, actually, would do + +that, but I think most of +the time, people can't + +commit to do that. + +And so the standard has become +two-sided tests. + +But I certainly agree +with you. + +It's very frustrating because +one should be able to + +articulate one-sided +hypotheses. + +That's sort of a long answer, +but does that make sense? + +It's OK. + +OK, now, for those of you on +this side of the board, you + +won't be able to see, but +maybe if I need to write + +something on the board +it will be better. + +OK. + +So now we're going to talk +about type I and type II + +errors, which, as I mentioned, +are not helpfully named. + +OK. + +A type I error-- + +so this is all about +probability, so nothing we can + +ever say for sure. + +We can always say that this +is more or less likely. + +And there's two different types +of errors we can make + +when we're doing these +probabilities or doing these + +assessments. + +The first error, and it's called +type I error, is we can + +conclude that there was an +effect when, in fact, there + +was no effect, OK? + +So when I said the 95% +confidence interval, that 95% + +is coming from our choice +about type 1 errors. + +So for example-- + +a significance level is the +probability that you're going + +to falsely conclude the program +had an effect when, in + +fact, there was no effect, OK? + +And that's related to when you +say a 95% confidence interval, + +the remaining 5% is what we're +talking about here. + +That's the probability of making +a type I error, OK? + +And why is that? + +Well, we said there's a 95% +chance that it's going to be + +within this range. + +That means that just by random +chance, there's some chance it + +could be outside that +range, right? + +So if your confidence interval +was over here and zero was + +over here, you would say, well, +with 95% conference, I'm + +going to assume the program had +an effect because zero is + +not within my confidence +interval. + +However, 5% of the time, the +true effect could be over here + +outside your confidence +interval. + +That's what a 95% confidence +interval means. + +So in some sense, that's +what we mean by a-- + +so that's in some sense what +a type I error is. + +A type I error is the +probability that you're going + +to detect an effect when, +in fact, there's not. + +And so the typical levels that +you may see are 5%, 1% or 10% + +significance levels. + +And the way to think about those +significance levels is, + +if you see something that's +significant at the 10% level, + +that means it 10% of the time, +an effect of that size + +could've been just due +to random chance. + +Might not actually +be a true effect. + +And if you've heard of a +p-value, a p-value is exactly + +this number. + +A p-value basically says, what +is the probability that an + +effect this size or larger could +have occurred just by + +random chance, OK? + +So that's what's called +a type I error. + +And typically, there's no deep +reason why 5% is the normal + +level of type I errors that we +use, but it's kind of the + +convention. + +It's what everyone else uses. + +If you use something different, +people are going to + +look at you a little funny. + +So the conventions are we have +5%, 10%, and 1%, as these + +significance levels. + +And you might say, gee, 5% +or 10% seems pretty low. + +Maybe I would want +a bigger one. + +But on the other hand, if you +start thinking about it, that + +means that if you use 10% +significance, that means that + +one out of every 10 studies +is going to be wrong. + +Or if you had 10 different +outcomes in your data set, one + +out of every 10 would be +significant even just by + +random chance. + +So the other type of error is +what's called, as I said, + +helpfully, a type II error. + +And a type II error says that +you fail to reject that the + +program had no effect when, in +fact, there was an effect, OK? + +So this is, the program did +something, but I can't pick it + +up in the data, OK? + +And we talk about the +power of a test. + +The power is basically the +opposite of a type II error. + +A power just says, what's the +probability that I will be + +able to find an effect +given that the actual + +effect is there, OK? + +So when we talk about how big +a sample size we need, what + +we're basically talking about +is, how much power are we + +going to have to detect +an effect? + +Or what's the probability that +given that a true effect is + +there, we're going to pick +it up in the data, OK? + +So here's an example of how +to think about power. + +If I ran the experiment 100 +times-- not 100 samples, but + +if I ran the whole +thing 100 times-- + +what percentage of the time and +in how many these cases + +would I be able to say, reject +the hypothesis that men and + +women have the same education +at the 5% level if, in fact, + +they're different, OK? + +So this is a helpful graph +which basically plots the + +truth and what you're going +to conclude based + +on your data, OK? + +So suppose the truth is that +you had no effect and you + +conclude your no effect, OK? + +Then you're happy. + +If there was an effect and you +conclude there was an effect, + +you're happy. + +So you want to be in one +of these two boxes. + +And the two types of errors you +can make-- so one type of + +error is over here, right? + +So if the truth is there was no +effect, but you concluded + +there was an effect, that +would be making a + +type I error, OK? + +And this is what we +talked about size. + +So this one, we normally +fix this one at 5%. + +So it's only 5% of the time-- + +if there's no effect, 5% of the +time you're going to end + +up here and 95% of the time +you're going to end up here. + +That's what a 95% confidence +interval is telling you. + +And the other thing is, suppose +that the thing had an + +effect but you couldn't find +it in the data, OK? + +That's what's called +a type II error. + +And that's, when we design our +experiments, we want to make + +sure that our samples are +sufficiently large that the + +probability you end up in this +box is not too big, OK? + +So that's a sense of what we +mean by the different types of + +mistakes or errors +you could make. + +Yeah. + +AUDIENCE: It's kind of +a stupid question. + +So power is the probability +that you are not + +making a type II error? + +PROFESSOR: Yes. + +AUDIENCE: So then power is the +probability that you're in the + +smiley face box, +that you are-- + +[INTERPOSING VOICES] + +PROFESSOR: Yes. + +Power is the probability +you're over here. + +Yeah, we say power is related +to type II errors. + +Power is over here. + +This is the power. + +Power is conditional on +there being an effect. + +What's the probability you're +in this box, not this box? + +Probably should say one minus +power to be clearer. + +OK? + +Does that makes sense? + +All right. + +So when we're designing +experiments, we typically fix + +this at conventional levels. + +And we choose our sample size +so that we get this, the + +power, or the probability that +you're in the happy face box + +over here to a reasonable level +given the effect size + +that we think we're +likely to get, OK? + +OK. + +Now, in some sense, the next two +things, standard errors, + +are about this box, size. + +And power is about this +box, or these boxes. + +Yeah. + +AUDIENCE: Why is power not also +the probability that you + +end up in the bottom right box +as opposed to the bottom left? + +PROFESSOR: Because +that's size. + +AUDIENCE: Isn't size also linked +to-- or power also + +linked to-- + +PROFESSOR: No, they're all +related, but we typically-- + +they're related in the +following way. + +We assert a size because when +we calculate our standard + +error-- our confidence +intervals, we pick how big or + +small we want the confidence +intervals to be. + +When we say a 95% confidence +interval, we're + +picking the size, OK? + +So this one, we get to choose. + +AUDIENCE: So it's not sample +size, it's size of the + +confidence interval? + +PROFESSOR: No. + +Yeah, this is size is a-- + +yeah, it's the size of the +confidence interval. + +That's right. + +Sorry, it's not the +sample size. + +That's right. + +It's called the size of the +test in yet more confusing + +terminology. + +That's right. + +This is the size of the +confidence interval, + +essentially. + +And this one you pick, +and this one is + +determined by your data. + +OK? + +All right. + +OK, so now let's talk about this +part, which is standard + +errors and significance. + +It's all kind of related. + +All right, so we're going +to estimate the + +effect of our program. + +And we typically call that +beta, or beta hat. + +So the convention is that things +that are estimated, we + +put a little hat +over them, OK? + +So beta hat is going to be our +estimate of the program's + +effectiveness. + +This is our best guess as to the +difference between these + +two groups. + +So for example, this is the +average treatment test score + +minus the average control +test score. + +And then we're also going to +calculate our estimate of the + +standard error of +beta hat, right? + +And remember that the confidence +interval is about + +two times the standard error. + +So the standard error is going +to say how precise our + +estimate of beta hat is, which +is, remember, if we ran the + +experiment 100 times, what will +be the distributions of + +beta hats that we +would get, OK? + +And this depends on the sample +size and the noise in the + +data, right? + +And remember we went through +this already that here, in + +this case, the standard error of +how confident we would be-- + +so the beta hat, in this case, +is going to be 10, and in this + +case, it's also going +to be 10, right? + +But here, these two things are +really precisely estimated, so + +our standard error of beta hat +is going to be very small + +because we're going to say we +have a very precise estimate + +of the difference +between them. + +And so the confidence +interval is also + +going to be very small. + +And here, there's lots of noise +in the data, so our + +estimate of the standard error +is going to be larger. + +So in both cases, beta +hat is the same. + +It's 10 in both cases. + +But the standard error +is very big here and + +very small here, OK? + +Now, when we calculate the +statistical significance, we + +use something called +a t-ratio. + +And the t-ratio-- + +it's actually often called the +student's t-ratio, which I + +thought was because +students used it. + +But it's actually named +after Mr. Student. + +It's the ratio of beta hat +to the standard error + +of beta hat, OK? + +And the reason that we happen to +use this ratio is that, if + +there is no effect, if beta hat +is actually zero, we know + +that this thing has a normal +distribution, so we can + +calculate the probabilities that +this thing is really or + +really small, OK? + +So we calculate this ratio of +beta hat over the standard + +error of beta hat. + +It turns out that +if t is greater + +than, in absolute value-- + +sorry, if the absolute value of +t, I should say, is greater + +than 1.96-- + +so essentially, if it's bigger +than 2 or less than minus 2, + +we're going to reject the +hypothesis of a quality at a + +5% significance level. + +And why is that? + +It's because it turns out, from +statistics, that if the + +truth is zero, OK? + +So if we're in the no effect +box and the truth is zero, + +this ratio, it turns out, will +have a normal distribution. + +And it just turns out from a +normal distribution that the + +probability that the 5% +confidence interval is 1.96 + +away from zero if you have +a normal distribution. + +That's just a fact about normal +distributions, OK? + +So if we calculate this ratio +and we say it's greater in + +absolute value than 1.96, we're +going to reject the + +hypothesis of a quality +at the 5% level, OK? + +So we can reject zero. + +Zero is going to be outside of +our confidence interval. + +And if it's less than 1.96, +we're going to fail to reject + +it because zero is going to +be inside our confidence + +interval, OK? + +So in this case, for example, +the difference was 2.59. + +The standard error was 0.54. + +The t-ratio is about seven. + +No, it's about five. + +So we're definitely going +to be able to + +reject in this case. + +So we have a t-ratio +of about five, OK? + +So you may see this terminology +and this is where + +it's coming from. + +Now, there's an important point +to note here, which will + +come up later when we talk +about power calculations, + +which is, in some sense, that +the power that we have is + +determined by this ratio of +the point estimate to our + +standard error. + +And so this says, for example, +that if we kind of look at + +this a little more, that if you +have bigger betas, you can + +still detect effects for +a given standard-- + +so if you fix the standard +error but you made beta + +bigger, you're more likely +to conclude there was a + +difference, right? + +So what's going to increase your +being able to conclude + +there was a difference? + +Either your effect size is +bigger or your standard error + +is smaller, mechanically. + +OK. + +So that's how we are going to +calculate being in this box. + +So how do we think about +power, which is the + +probability that we're +in this box? + +We had an effect and we're able +to detect that-- sorry, + +power's in this box-- that +we had an effect, OK? + +So when we're planning an +experiment, we can do some + +calculations to help us figure +out what that power is. + +What's the probability, if the +truth is a certain level, that + +we're going to be able to +pick it up in the data? + +And what do we need +to do that? + +We're going to have to specify +a null hypothesis, which is + +usually zero. + +We're going to be testing that +something's different than + +zero, the two groups are +the same, for example. + +We're going to have to pick our + +significance level, our size. + +And that, we almost +always pick at 5%. + +We're going to have to +pick an effect size. + +And we'll talk about what +exactly this means in a couple + +more slides. + +But when we calculate a power, +a power is for a given + +effect size, OK? + +And then we'll calculate +the power. + +So for example, suppose +that we did this + +and a power was 80%. + +That would mean that if we did +this experiment 100 times-- + +not 100 times, but actually +repeated the whole experiment + +100 times, 80% of the times we +did this experiment, if the + +hypothesis is, in fact, false, +and instead, the truth is + +this, we would be able to reject +the null and conclude + +there was a true effect +80% of the time, OK? + +That's a little bit complicated, +but does that + +make sense, what we're going to +be trying to do with power? + +So we're going to fix +the effect size. + +So remember, we fix +the bottom box. + +When we calculate power, we +have to speculate not just + +effect versus no effect. + +We have to postulate just how +effective the program is. + +So we're going to say, suppose +that the effect size is 5%. + +The truth is 0.2, right? + +How big a sample would we need +to be in this box 80% + +of the time, OK? + +So when we say power, +that's what we mean. + +And when we calculate the size +of the experiments, you have + +to make a judgment call of how +big a power do you want. + +The typical powers that we use +when we do power calculations, + +are either 80% or 90%. + +So what does this mean? + +This means-- suppose +you did 80%. + +Or [UNINTELLIGIBLE] this. + +If you did 80%, that would +mean that if you ran your + +experiment 100 times and the +true effect was 0.2 in this + +case, you would be able +to pick up an effect, + +statistically 80 out +of those 100 times. + +20 out of 100 times, +you wouldn't. + +And the bigger your sample size, +the larger your power is + +going to be, OK? + +Does that make sense so far? + +OK. + +Suppose you wanted to calculate +what our power is + +going to be. + +What are the things you +would need to know? + +You would need to know +your significance + +level of your size. + +And as I said, this, +we just assume, OK? + +This is that bottom box. + +We're just going to assume +that it's 5%. + +And the lower it is, +the larger sample + +you're going to need. + +But this one is sort +of picked for you. + +We almost always use 5% because +that's the convention. + +That's what everyone +uses, essentially. + +The second thing you need to +know is the mean and the + +variance of the outcome in +the comparison group. + +So you need to know-- + +so remember, all this power +calculation is going to depend + +on whether your sample looks +like this, really tight, or + +looks like this and +is very noisy. + +Because you obviously +need a much bigger + +sample here than here. + +So in order to do a power +calculation, you need to know, + +well, just what does the outcome +look like, right? + +Does the outcome really have +very narrow variance? + +Is everyone almost exactly the +same, in which case it's going + +to be very easy to +detect effects? + +Or is there are huge range of +people, in which case you're + +going to need bigger effects. + +Now, how do we get this? + +So this one, we just +conventionally set. + +This one, we have to +get somewhere. + +And we usually have to get it +from some other survey. + +So we have to find someone +that collected data in a + +similar population. + +Or sometimes we'll go and +collect data ourselves in that + +same population. + +Just a very small survey just +to get a sense of what this + +variable looks like, OK? + +And if the variability is big, +we're going to need a really + +big sample. + +And if the variability is really +small, we're going to + +need a small sample. + +And it's really important to do +this because you don't want + +to spend all your time and money +running an experiment + +only to turn out that there was +no hope of ever finding an + +effect because the power +was too small, right? + +Yeah. + +AUDIENCE: And this is in the +entire population, not just + +the comparison group, right? + +It says-- -- + +PROFESSOR: Yeah, but before +you do your treatment, the + +comparison and the treatment +are the same. + +AUDIENCE: They are the same. + +PROFESSOR: Doesn't matter. + +AUDIENCE: So it's a baseline +population. + +PROFESSOR: Baseline +would be fine. + +Yeah. + +Before you do your treatment, +they're the same. + +So it doesn't matter, OK? + +And the first thing you need +is, you need to make an + +assumption about what effect +size you want to detect. + +And this one-- + +sometimes you also have +to supply this. + +And the best way to think about +what effect size you + +want to put in here is you +want to say, what's the + +smallest effect that would +prompt a policy response, OK? + +So one could think about this, +for example, by doing a + +cost-benefit calculation, +right? + +You could say that we do a +cost-benefit calculation. + +This thing costs $100. + +If we don't get an effective +0.1, it's just + +not worth $100, right? + +So that would be a good way of +coming up with how big an + +effect size you want here. + +And the idea, then, is if the +effect is any smaller than + +this, it's just not interesting +to distinguish it + +from zero, right? + +Suppose that the thing had a +true effect of 0.001, right? + +But if it was that small of an +effect, it could be completely + +cost effective. + +So say the thing happens +at an effect of 0.001. + +Who cares, right? + +So you want to be thinking +about, from a policy + +perspective is, what's the +smallest effect size you want + +to know, from a policy +perspective, in order to set + +your power calculations? + +Yeah. + +AUDIENCE: I have a question +back at the mean + +and variance thing. + +PROFESSOR: Oh, here. + +Yeah. + +AUDIENCE: Yeah. + +So in terms of the baseline +thing that you would collect-- + +so I'm on the implementation +side of this, right? + +So we do projects. + +We collect baseline data. + +Now, the case that I'm thinking +of, the baseline data + +that we would collect might not +be exactly the same kind + +of data that we are looking +for in terms of our study. + +What kind of base-- how-- + +PROFESSOR: Right, OK. + +So when we say baseline, there's +two different things + +we mean by baseline. + +For this case, this is not +strictly a baseline. + +This is just something about +what's your variable + +going to look like. + +Let me come back to +that in a sec. + +We also sometimes talk about +baselines that we are going to + +use of actually collecting the +actual outcome variable before + +we start the intervention, +right? + +Those are also useful, and we'll +talk about those in a + +couple slides. + +And those, one wants them to be +more similar, probably, to + +the actual variable you're +going to use. + +Now, for your case, +we often don't-- + +the accuracy of your power +calculation depends pretty + +critically on how close this +mean and variance are to what + +you're going to actually +get in your data. + +And when you start in the +example that you guys are + +going to work on or that maybe +you've already started working + +on, you're going to +find that it's + +actually pretty sensitive. + +Turns out it's pretty +sensitive. + +So getting these wrong is +going to mean your power + +calculation is going +to be wrong. + +So that's sort of an argument +for saying you want this to be + +as good as possible. + +Now the flip side of that, +though, is you're going to + +find that these power +calculations are fairly + +sensitive to what effect size +you choose as well. + +So you're going to find that if +you go from a effect size + +of 0.2 to an effect size of 0.1, +you're going to need four + +times the sample. + +That's just the way the +math works out. + +By which I'm going to mean that +I think that these power + +calculations are useful for +making sure you're in the + +right ballpark, but not +necessarily going to nail an + +exact number for you. + +All that's by way of saying that +you want to get-- because + +these things are so sensitive, +you want to get as close as + +possible to what's actually +going to be there. + +On the other hand you're going +to find the results are also + +so sensitive to the effect size +you want to detect that + +if this was a little bit off, +that might be a tradeoff you + +would be willing to live +with in practice. + +AUDIENCE: So, from my-- + +PROFESSOR: Does that +make sense? + +AUDIENCE: Yeah, but it seems +like the effect size-- your + +estimate of your effect +size is this kind of-- + +we've got all this science for +the calculation and yet your + +estimate of your effect +size is based on-- + +PROFESSOR: You're absolutely +right. + +AUDIENCE: --getting that-- + +PROFESSOR: Hold on, though. + +Let me back up a little +bit, though. + +You're right, except the-- + +in some sense, the best way to +get estimates for your effect + +size is to look at similar +programs, OK? + +So now there are lots +of programs in + +education, for example. + +And they tend to find effect-- + +I've now seen a bazillion things +that work on improving + +test scores. + +And I can tell you that +they tend to get-- + +standardized effect size is the +effect size divided by the + +standard deviation. + +And they tend to get effect +sizes in the 0.1, 0.15, 0.2 + +range, right? + +So you can look at those and +say, well, I think that most + +other comparable interventions +are getting 0.1, so I'm going + +to use 0.1 as my effect size. + +So you're right if you're +just trying to sit here + +introspectful-- + +what my effect size is going +to be, it's very hard. + +But if you use comparable +studies to get a sense, then + +you can get a sense. + +And the other thing I mentioned +is, you can do + +cost-benefit analysis and +say, well, look-- + +which is sort of another way +of saying it, If there are + +other things out there which +cost $100 per kid and get 0.1, + +then my thing, presumably, has +got to do at least as well as + +0.1 for $100-- suppose the other +thing also costs $100 a + +kid, I've got to do at +last as well as 0.1. + +Otherwise, I'd rather +do this other thing. + +So it's another way of getting +at the effect size. + +AUDIENCE: Could you, then, also +look at existing data in + +the literature for the mean +and variance thing, + +or do you have to-- + +PROFESSOR: You could, but this +one is going to be more + +sensitive to your population. + +AUDIENCE: So it would just have +to be very well-matched + +to be able to use it. + +PROFESSOR: Right. + +I mean, look, if you don't have +it, you could do it to + +get a sense, but this is +one where the different + +populations are going to be +very different in terms of + +their mean and variance. + +In order to get an estimate of +this, you need a much, much, + +much smaller sample size than +you need to get an estimate of + +the overall treatment effect +of the program. + +So you can often do +a small survey-- + +much, much, smaller than your +big survey, but a small survey + +just to get a sense of what +these things look like. + +And that can often be a very +worthwhile thing to do. + +AUDIENCE: I have a +related question. + +How often do you see-- + +PROFESSOR: Oh, sorry. + +I just wanted to do one +other thing on this. + +I've had this come up in my +own experience, where I've + +done this small survey, and +found that the baseline + +situation was such that +the whole experiment + +didn't make any sense. + +And we just canceled +the experiment. + +And it can be really useful. + +If you say, if I do this and +my power is 0.01, for + +reasonable effect sizes, +this is pointless. + +So it can be worth it. + +Sorry. + +Go ahead. + +AUDIENCE: So to estimate the +effect size, have you seen + +people run small pilots in +different populations than + +they're eventually going to do +their impact evaluation to get + +a sense of what effect size are +they seeing with that same + +intervention? + +PROFESSOR: Not usually, because +you can't do a small + +pilot to get the effect +size, right? + +AUDIENCE: You're going +to see something-- + +PROFESSOR: You've got to +do the whole thing. + +AUDIENCE: Yeah, yeah. + +PROFESSOR: Right? + +That's the whole point of the +power calculations is, in + +order to detect an effect of +that size, you need to do the + +whole sample. + +So a small pilot won't +really do it. + +AUDIENCE: OK. + +PROFESSOR: So it's not really +going to-- you could get a-- + +no, I guess you really can't get +a sense because you would + +need the whole experiment to +detect the effect size. + +AUDIENCE: Don't you think that +there should be a lot more + +conversation about effect size +before things start? + +Because if you've got a +treatment, if you've got a + +program, and you can't have a +very-- and you've struggled to + +have a good conversation about +what is actually going to + +happen to the kids or what's +going to happen to the health + +or what's going to happen to +the income as a result of + +this, it really may be quite +telling that you really don't + +know what you're doing. + +That there isn't enough of +a theory behind your-- or + +practice or science or anything +behind what your + +program is. + +If people are not pretty +sure, what-- + +PROFESSOR: I mean, +yes and no-- + +AUDIENCE: And then, also, on +the resource allocation. + +Resource allocation, it just +seems to me, most of the time, + +if your ultimate client +is really probably the + +government, right? + +Because the government is the +one that's going to make the + +big resource allocations-- + +PROFESSOR: It depends on who +you're working with. + +It could be an NGO, whoever. + +But yes. + +AUDIENCE: No, but an NGO is +doing something, usually, as a + +demonstration that, in fact, +if it works, then the + +government should do it. + +PROFESSOR: Not always, but +there's someone who, + +presumably, is going +to scale up. + +AUDIENCE: Right. + +And yes, businesses, +maybe, right? + +But I would say, 90% of the +time, it's going to be, + +ultimately, the government +needs to-- + +PROFESSOR: Often, it's +the government. + +In India, for example, there +are NGOs who are-- + +I don't know who's worked on +the Pratham reading thing. + +They're trying to teach-- + +NGOs trying to teach millions +of kids to read, as an NGO. + +So sometimes NGOs +scale up too. + +But anyway, you're right that +there's an ultimate client + +who's interested in this. + +AUDIENCE: So then, having +a conversation + +very early on about-- + +PROFESSOR: Yeah. + +Could be very useful. + +That's absolutely right. + +That's absolutely right. + +AUDIENCE: Because-- + +PROFESSOR: Now, in terms of +your point about theory, + +though, yes and no. + +So I can design an experiment +that's supposed to teach kids + +how to read. + +I know the theory says it should +affect reading but I + +have no idea how much. + +And so-- + +AUDIENCE: Wouldn't you say that +a significant percentage + +of the time, if it's a good +theory about reading, it + +actually should tell you? + +PROFESSOR: Not always. + +I mean-- + +AUDIENCE: Well, then I'd +say it's not such a + +great theory, right? + +Wouldn't you-- + +PROFESSOR: It's a little bit +semantic, but I think that a + +lot of times, I can-- + +say I'm going to teach kids to +read a paragraph or whatever. + +But what percentage of the kids +is it going to work for? + +What percentage of the kids +are going to be affected? + +I think that using theory +to calculate how-- + +I think theory can tell +you a lot what + +variables should be affected. + +And that's what we talked about +in the last lecture. + +I think theory can tell you what +the sign of those effects + +likely to be. + +I think it's often putting a lot +of demands on your theory + +to have them tell you +the magnitude. + +And that's why you want +to do the experiment. + +AUDIENCE: And you just told me +that even beyond the theory, + +you say, well, but we did this +in one school and we saw it + +had this great thing, +but you're saying-- + +[INTERPOSING VOICES] + +PROFESSOR: But your confidence +interval is going to be-- + +well, it's not nothing. + +It's going to tell you +something, but your confidence + +interval is going +to be enormous. + +AUDIENCE: Right, nothing +that you could + +rely on to set a good-- + +[INTERPOSING VOICES] + +PROFESSOR: Right, it gives you +a data point, but it's going + +to have a huge conference +interval. + +AUDIENCE: I don't want to +belabor this, but if you think + +about it in business +terms, right? + +I want to go out and +raise some money. + +PROFESSOR: Yes, absolutely. + +[INTERPOSING VOICES] + +AUDIENCE: --something. + +And so, in order to raise that +money, I have to tell you + +that, in fact, you're going +to make this much money. + +PROFESSOR: Right. + +AUDIENCE: And, of course, it +could turn out to be wrong. + +But I have to tell you you're +going to get a 25% return on + +your money. + +And that means I have to +explain to you why this + +business is going to successful, +how many people + +are going to buy it, how I'm +going to manage my costs down. + +So it's always curious to me +that, when you're talking + +about social interventions, that +I'm not having to make + +that same argument with that +same level of specificity, + +which means I've talked +about the effect size. + +Because I can't raise money if I +tell you, look, I might only + +make you 5% or we might shoot +the moon and make 100%. + +You'll say, thank +you very much. + +This person doesn't know +what their business is. + +I'm not going to give +them my money. + +PROFESSOR: Right. + +So you actually hit on exactly +what's on the next slide. + +Which is exactly what I was +going to say, which is, what + +you want to think about with +your effect size is exactly + +this thing. + +What's the cost of this +program versus + +the benefit it brings? + +And sometimes, what's the cost +vis-a-vis alternative uses of + +the money, right? + +And that's going to be a +conversation you're going to + +have with your client, which is +going to say, if the effect + +size was 0.1, I would do it. + +And then you say, OK, I'm going +to design an experiment + +to see if it's 0.1 +or bigger, right? + +So I'm totally on +board with that. + +Because, as I was saying, if +the effect size is smaller + +than that, it still could be +positive, but if your client + +doesn't care, if it's not worth +the money at that level, + +then why do we need to design +a big experiment + +to pick that up? + +It's also worth noting this +is not your expected + +effect size, right? + +I could expect this thing to +have an effect of 0.2 but even + +if it was as low as 0.1, +it would still be + +worth doing, OK? + +And in that case, I might want +to design an experiment of + +0.1, right? + +Conversely, you guys can all +imagine the opposite, which is + +you could say, I expect +this thing to be 0.1, + +but maybe it's 0.2. + +Maybe it's actually-- + +I'm not sure how good it is. + +I think it's OK. + +But maybe it could +be really great. + +And if it was really great, I +would want to adopt it, so I + +would design an experiment +to 0.2. + +So it's not the expected effect +size, it's what you + +would use to adopt +the program. + +When we talk about +effect sizes, we + +often talk about them-- + +we talk about what we call +standardized effect size, OK? + +As I mentioned, how large an +effect you can detect depends + +on how variable your +sample is. + +So if everyone's the +same, it's very + +easy to pick up effects. + +And we often talk about +standardized effects are the + +effect size divided by the +standard deviation of the + +outcome, OK? + +So standard deviation of outcome +is the measure of how + +variable your outcome is. + +So we often express our effect +sizes relative to the standard + +deviation of the outcome, OK? + +And so when I was talking +about test scores, for + +example, test scores are usually +normalized to have a + +standard deviation of one. + +So this is actually how we +normally express things in + +terms of test scores, but we +could do it for anything. + +And so effect sizes of +0.1, 0.2 are small. + +0.4 are medium. + +0.5 are large. + +Now what do we mean by that? + +This is actually a very helpful +way of thinking about + +what a standardized effect +size is telling you. + +So a standardized effect size of +0.2, which is what we were + +saying was a modest one, means +that the average person in the + +treatment group, the median +or the mean person of the + +treatment group, had a better +outcome than 58% of the people + +in the control group. + +So remember, if it was zero, +it would be 50-50. + +It would be 50%, right? + +If there was no effect, the +distributions would line up + +and this person's in the +treatment group-- + +the median person in the +treatment group would be + +better than 50% of the people +in the control group. + +So this is saying, instead of +lining up at exactly 50-50, + +it's lining up 58%-50%, OK? + +If you get an effect size of +0.5, which we were saying was + +a large effect, that means that +69% of the people in the + +treatment group are going to +be bigger than the median + +person in the control group. + +Sorry, it's the other +way around. + +The average member of the +intervention group is better + +than 69% of people in +the control group. + +So the distributions are +still overlapping. + +But now there's-- + +the middle of the treatment +distribution is at the 69th + +percentile of the control. + +And a large effect of 0.8 would +mean that the median + +person in the treatment group +is at the 79th percentile of + +the control. + +That just gives you a sense of +when we're talking about + +standardized effect sizes, how +big we're talking about. + +And so you can see that +0.2, is actually-- + +you can imagine is going to be +pretty hard to detect, right? + +If the median person in the +treatment group looks like the + +58th percentile of the control +group, that's going to be a + +case where those distributions +have a lot of overlap, right? + +And so this is going to be much +harder to detect than + +this case when the overlap +is much smaller. + +Yeah. + +AUDIENCE: So in your experience, +what do most + +people think their +effect size is? + +Where do they settle? + +They probably wouldn't +settle at 0.2? + +PROFESSOR: Actually, a lot of +people in a lot of educational + +interventions-- + +AUDIENCE: That's enough +for them? + +PROFESSOR: Yeah. + +I would say the typical +intervention that people study + +that I've seen in education, +the effect size is in the + +0.15, 0.2 range. + +It turns out it's really hard +to move test scores. + +AUDIENCE: Yeah. + +PROFESSOR: So yeah, I +would say a lot of-- + +but you'll see when you do the +power calculations, that to + +detect 0.2, you often need +a pretty big sample. + +Look, it depends a lot on what +your intervention is, but I've + +seen a lot in that range. + +And I'm just trying to think +of an experiment I did. + +I can't think of it off hand. + +But yeah, I would say +a lot in this range. + +AUDIENCE: So would the converse +be true, that in + +fact, you don't see too +many that have a real + +large effect size? + +PROFESSOR: I would say it's +pretty rare that I see + +interventions that are 0.8. + +Yeah. + +AUDIENCE: Do you think it's +valuable that just because + +you're setting a low effect +size in designing your + +experiment, you're being +conservative. + +You can still pick up a +[UNINTELLIGIBLE] effect size-- + +PROFESSOR: Of course. + +AUDIENCE: It's just in +the design process-- + +[INTERPOSING VOICES] + +PROFESSOR: Right. + +This is the minimum thing +you could pick up. + +That's absolutely right. + +That's right. + +So right, if you design for 0.2 +but, in fact, your thing + +is amazing and does 0.8, well, +there's no problem at all. + +You'll have a p-value +of 0.00 something. + +You'll have a very strong +[INAUDIBLE]. + +It's a good point. + +OK. + +So how do we actually +calculate our power? + +So there's actually a very nice +software package, which, + +have you guys started +using this yet? + +Yeah? + +OK. + +AUDIENCE: I have a question. + +Can you just clarify something +before you go on? + +PROFESSOR: Yeah. + +AUDIENCE: So by rejecting a null +hypothesis, you won't be + +able to say what the expected +effect is, so you won't be + +able to necessarily quantify +the impact. + +PROFESSOR: No, that's +not quite right. + +AUDIENCE: OK. + +PROFESSOR: So you're going +to estimate your-- + +you run your experiment, you're +going to get a beta, + +which is your estimate, +And you're going to + +get a standard error. + +You reject the null, which +means you say with 95% + +probability, I'm in my +confidence interval. + +So you know you're somewhere +in the confidence interval. + +And then beyond that, you have +an estimate of where in the + +confidence interval you are. + +And your best estimate for +where you are on the + +confidence interval is +your point estimate. + +Does that make sense? + +So in terms of thinking through +the cost-benefit or + +whatever, your best guess of the +effect of the program is + +your point estimate, +is your beta. + +If you wanted to be a little +more precise about it, you + +could say-- + +so this is your estimate, this +is your beta hat, this is your + +confidence interval, right? + +Zero is over here, so you can +reject zero in this case. + +But, in fact, there's a +distribution of where your + +estimates are likely to be. + +And when we said it was 95% +confidence interval, that's + +because the probability of +being over here is 95%. + +But this says you're most likely +to be right here, but + +there's some probability +over here. + +You're more likely to be near +beta then you are to be very-- + +it's not that you're equally +likely to be anywhere in your + +confidence interval. + +You're most likely to be right +near your point estimate. + +So, in fact, if you actually +cared about the range, you + +could say, well, what's the +probability I'm over here? + +And calculate that. + +What's the probability +I'm over here? + +And you could average them to +calculate the average benefit + +of your program. + +Usually, though, we don't bother +to do this and usually + +what we do is we say our best +estimate is that you're right + +at beta hat. + +That is our best estimate and +we calculate our estimate + +based on that. + +But in theory, you could use +the whole distribution + +[INAUDIBLE]. + +OK. + +OK, so suppose we want-- + +so how do we actually calculate +some of these? + +So using the software helps get +a sense, intuitively, of + +what these tradeoffs are +going to look like. + +And I don't know that I'll have +time to go through all + +this, but we'll go through +most of it, OK? + +So for example, so if you run +the software and look at power + +versus number of clusters-- + +hold on. + +So how would you set this +up in the software? + +So we'll talk about clustered +effects in a sec. + +As we discussed, you have to +pick a significance level. + +You have to pick a standardized +effect size. + +That's what delta is +in the software. + +So we use 0.2, OK? + +In the software, it's always +a standardized effect size. + +You just divide by +your standard + +deviation of your outcome. + +That's why you know your +actual outcome variable + +because you know-- +but I think the + +actual effect is whatever-- + +people get one centimeter +longer in order to get a + +standardized effect size, I +need to know the standard + +deviation of my outcome +variable. + +And the program is going to +give you the power as a + +function of your sample +size, OK? + +And one of the things that you +can see is that this is not + +necessarily a linear +relationship, right? + +So for example, here, we've +plotted a delta of-- + +effect size of 0.2 and here's +an effect size of 0.4. + +So this says that with about 200 +clusters, you're going to + +get to a power of 0.8 with the +effect size of 0.4, but you're + +still going to be at a +power of 0.2 with an + +effect size of 0.2. + +So the formulas are +complicated. + +They're not necessarily a linear +function of your power. + +When we think about power, we've +talked about a couple of + +things that influence our power +in terms of the variance + +of our outcome, right? + +The variance of our outcome, +how big our effect size is. + +And those are the basic +things that are going + +to affect our power. + +But there are things that we +can do in our experiment-- + +in the way we design our +experiment that are also going + +to make our experiment more +or less powerful. + +And here are some of the +things that we can do. + +One thing that we can +do is we can think + +about having a cluster-- + +so whether we whether randomize +at the individual + +level or in clusters, whether we +have a baseline, whether we + +use control variables or +stratification, and the type + +hypothesis being tested. + +All four of these are things +that we're going to do that + +for a given outcome variable +and a given effect size, in + +some sense, are going to +affect how powerful our + +experiment is. + +In some sense-- + +given that I may not have time +to finish everything, the one + +that I want to focus on is +the clustering issue. + +This is the one that is the +biggest for designing + +experiments, and it often +makes a big difference. + +So the intuition for clustering +is that-- + +so what is clustering? + +Clustering is, instead of +randomizing-- suppose I want + +to do an experiment on whether +the J-PAL executive ed class + +improves your ability to-- + +whether you took this lecture +improves your understanding of + +power calculation, OK? + +Suppose I randomly sampled this +half of the room and gave + +you my lecture and this half +was the control group. + +And I flipped a coin so I split +you in halves down the + +middle and I said, OK, I'm going +to flip a coin, which is + +control, which is treatment. + +You guys, presumably you all +sat with your friends, OK? + +So people on this side of the +room are going to be more like + +each other then people on that +side of the room, OK? + +So I didn't get an independent +sample, right? + +This group, their outcomes are +going to be correlated because + +some of you are friends +and have similar + +backgrounds and skills. + +And this group is going +to be correlated. + +On the other hand, suppose I had +gone through everyone and + +randomly flipped a coin for +every person and said, + +treatment or control, treatment +or control, + +treatment or control? + +In that case, I would've flipped +the coin 60 times and + +there would be no correlation +between who is in the control + +group and who is in the +treatment group because I + +wouldn't have been randomizing +you into the same groups + +together, OK? + +By doing the cluster design, +splitting you in half and then + +randomizing treatment versus +control or splitting you into + +groups of 10-- + +you five, you 10, you 10. + +You 10, you 10, you 10, and +then flipping the coin. + +I have less variation, in some +sense, than if I had flipped + +the coin in individual-- + +person by person-- + +because those groups are +going to be correlated. + +They're going to have +similar outcomes. + +So the basic point is that your +power is going to be-- + +the more times you flip the coin +to randomize treatment + +and control, essentially, the +more power you're going to + +have because the more your +different groups are going to + +be independent, OK? + +So to go through this again, +suppose you wanted to know-- + +this is, in general, +about clustering. + +Suppose you wanted to know how +the outcome of the national + +elections are going to be. + +So you could either randomly +sample 50 people from the + +entire Indian population, or +you randomly pick five + +families and you ask 10 +people per family what + +their opinions are. + +Clearly, this is going to give +you more information than this + +is because those family members +are going to be + +correlated, right? + +I have views like my wife and +like my father, et cetera. + +So we're not getting independent +views, whereas + +here, you're getting, really, +50 independent data points. + +And that's the same as +what we were talking + +about with the class. + +So this approach is going to +have more power than this + +approach because of the way +you did the sample. + +Yeah. + +AUDIENCE: So is the only reason +that you would cluster, + +then, just because you had to +because you had no choice-- + +PROFESSOR: Yes. + +AUDIENCE: --for political +reasons or just feasibility. + +PROFESSOR: And cost. + +AUDIENCE: And cost. + +PROFESSOR: Yeah. + +AUDIENCE: Well, and the +level of intervention. + +PROFESSOR: Exactly. + +And we'll talk about that. + +There are lots of +reasons people-- + +given this issue, people have +lots of good reasons for + +clustering, but the point is +that there are negative + +tradeoffs for sample size. + +AUDIENCE: About the clusters. + +If you flip the coin for all of +the class and then after, + +you decide that you will select +among the people that + +you have assigned, you will +select those seated-- + +you will select half of those +seated on the left. + +Will that solve the problem-- + +PROFESSOR: You select half of +the ones seated on the left? + +AUDIENCE: Yeah. + +PROFESSOR: Well, it's +a different issue. + +Suppose I first select the left +and now I go one by one, + +flip a coin of the people +on the left. + +I don't have the clustering +issue because I flipped the + +coin per person. + +But I have a different issue, +which is that the people I + +selected are not necessarily +representative of the whole + +population because I didn't pick +a representative sample. + +I picked the ones who happened +to sit over here. + +AUDIENCE: My question-- + +PROFESSOR: So there's two +different issues. + +One is, essentially, how many +times you flip a coin is how + +much power you have, how +independent you're thing is. + +The other issue is, is this +group here representative of + +the entire population? + +You might think that people who +sit near the window like + +to look at the river are +daydreamers and they're not as + +good at math as people who don't +sit near the window. + +And so I would get the effect of +my treatment on people who + +like to sit near the window and +aren't as good at math. + +And that might be a different +treatment effect than if I had + +done it over the whole room. + +So it's a different issue. + +AUDIENCE: Yeah, but my question +was you first draw a + +random number of people that you +assign to the treatment or + +to the control. + +And after that, within that +people, you now say, I will + +take half of those people-- + +I will take half that are seated +on the left and half + +that are seated on the right. + +PROFESSOR: I'm not sure-- + +let me come back to +your question. + +I'm not sure I fully understand +what you're saying. + +Maybe we can talk about +it afterwards. + +I think what you're saying may +be about stratification. + +Why don't we talk +about it later? + +Because we're running a +little short on time. + +In fact, can I borrow +somone's handouts? + +Because I want to make sure I +cover the most important stuff + +in the lecture. + +Let me just see where we are. + +OK. + +AUDIENCE: And if you +need to, you can + +take ten extra minutes. + +PROFESSOR: I may do that. + +I was going to ask you, +Mark, for permission. + +I just wanted to see +what I had left. + +OK. + +So where were we? + +Right. + +OK. + +Right. + +So as I was saying, when +possible, it's better to run + +clustered design. + +And so a cluster randomized +trial is one in which the + +units that are randomized are +clusters of units rather than + +the individual units. + +So I randomized a whole cluster +at a time rather than + +individual person by person. + +And there are lots of common +examples of this. + +So the PROGRESA program, for +example, in Mexico was a + +conditional cash transfer +program. + +They randomized village. + +Some villages were in, some +villages were out. + +If a village was in, +everybody was in. + +In the panchayat case +we talked about, it + +was basically a village. + +It was a panchayat. + +So the whole panchayat +was in or the whole + +panchayat was not in. + +In a lot of education +experiments, we randomize at + +the level of a school. + +Either the whole school is in +or the whole school is out. + +Sometimes you do +it as a class. + +A whole class in a school is +in [UNINTELLIGIBLE] is out. + +In this iron supplementation +example, it was by the family. + +So there's lots of cases where +you would do this kind of + +clustering. + +And there are lots of good +reasons, as I've mentioned, + +for doing clustering. + +So one reason is you're +worried about + +contamination, right? + +So for example, when they're +interested in deworming, worms + +are very easily-- + +there's a lot of +cross-contamination. + +If one kid has worms, the next +kid who's also in school with + +him is likely to get worms. + +So if I just deworm half the +kids in the school, that's + +going to have very little effect +because my control- + +they're going to get +recontaminated by the kids who + +weren't dewormed, right? + +Or it could be the +other way around. + +It could be that if I deworm +half the kids, that's enough + +to knock worms out of +the population. + +The control group is +also affected. + +So you need to choose a level +of randomization where your + +treatment is going to affect +the treatment group and not + +affect the control group. + +So that's a very important +reason for cluster + +randomizing. + +Another reason is this +feasibility consideration. + +So it's often just for a +variety of reasons not + +feasible to give some people the +treatment and not others. + +Sometimes within a village, it's +hard to make some people + +eligible for a program +and others not. + +It's just sometimes hard to +treat people in the same place + +differently. + +And so that's often a reason +why we do cluster + +randomization. + +And some experiments naturally +just occur at a cluster level. + +So for example, if I want to do +something that affects an + +entire classroom, +like give out-- + +suppose I want to train +a teacher, right? + +That obviously affects all the +kids in the teacher's class. + +There's no way to have that only +affect half the kids in + +the teacher's class. + +It's just a fact of life. + +So there are lots of good +reasons why we do cluster + +randomized designs even though +they have negative + +impacts on our power. + +So as I mentioned, the reason +the cluster has a negative + +impact on your power is +because the groups are + +correlated. + +The outcomes for the individuals +are correlated. + +So, for example, if all of the +villagers are exposed to the + +same weather, right? + +All villagers are exposed +to the same weather. + +So it could be that +the weather was + +really bad in this village. + +So all those people are going +to have a lower outcome, for + +example, than if the +weather was good. + +And so, in some sense, even if +there are 1,000 people in that + +village, they all got this +common shock, which is the + +negative weather, you don't +actually have 1,000 + +independent observations in that +village because they have + +this common correlated +component, OK? + +And this common correlated +component we denote by the + +Greek letter rho, which is the +correlation of the units + +within the same cluster. + +So rho measures the correlation +between units in + +the same cluster. + +If rho is zero, then people in +the same cluster are just as + +if they were independent. + +There's no correlation. + +Just as if they had been not +in the same cluster. + +If rho is one, they're perfectly +correlated and it + +means it they all have exactly +the same outcome, OK? + +So it's somewhere between +zero and one. + +And the lower the rho is, the +better you are if you're doing + +a cluster randomized design. + +And why is that? + +It's because the problem within +a clustered randomized + +design is, as I was saying, if +people were all exposed to the + +same weather, it's not as if +you had 1,000 independent + +people in that village. + +You effectively had fewer than +1,000 because they were + +correlated. + +And rho captures that effect-- + +how much smaller, effectively, +is your sample, OK? + +And the bigger rho is, the +smaller your effective sample + +size is, OK? + +And once again, when you do the +power calculations, you + +can play with this and you'll +note that small differences in + +rho make very big differences +in your power. + +And I'll show you the +formula in a sec. + +So often it's low, but it +can be substantial. + +So in some of these test score +cases, for example, it's + +between 0.2 and 0.6, which, +0.6 means that most of the + +differences are coming between +groups, not within groups. + +So the groups, really, are much +closer to one object. + +Yeah. + +AUDIENCE: What does +the 0.5 mean? + +Are you saying that in +Madagascar, the scores on math + +and language-- + +PROFESSOR: It's the correlation + +coefficient, which is the-- + +technically, I believe it's the +between variation divided + +by the total variation. + +I think that's the formula. + +Dan's shaking his head. + +Good. + +Excellent. + +A for me. + +It's what share of the variation +is coming between + +groups divided by the total +share of variation. + +So 0.5 means that, in some +sense, half of the variation + +in your sample is coming +between groups. + +AUDIENCE: Okay. + +PROFESSOR: What? + +AUDIENCE: Isn't it within +[INAUDIBLE]? + +If a rho is-- + +PROFESSOR: No, it's between. + +Because if rho is one, then +each group is one. + +Yeah, it's between. + +If it was zero, then they're +independent and it's saying + +that it's all coming +from within. + +Yeah. + +AUDIENCE: But here it's between +math and language + +scores of one kid or between +math plus language scores of + +two kids in the same group. + +AUDIENCE: Or is it math and +language scores in Madagascar + +are explained by-- + +PROFESSOR: This says +the following. + +This was in Madagascar, they +sampled math and language + +schools by-- + +they took math and language +scores for each kid by + +classroom-- + +or by school. + +I think it was by school in +this particular case. + +Then they said, looking over +the whole sample that they + +looked at in Madagascar, what +percentage of the variation in + +test scores came +between schools + +relative to within schools. + +And they're saying +that half of the + +variation was between schools. + +OK. + +So how much does this hurt +us, essentially? + +So we need to adjust our +standard errors, given the + +fact that these things +are correlated. + +And this is the formula, which +is that for a given total + +sample size, if we have clusters +of size m-- so say we + +have 100 kids per school-- + +and intercorrelation coefficient +should be a rho, + +the size of the smallest effect +we can detect increases + +by this formula compared to +a non-clustered design. + +So this shows you what +this looks like, OK? + +So suppose you had 100 +kids per school, OK? + +Suppose you had 100 kids per +school and you randomized at + +the school level rather +the individual level. + +If your correlation coefficient +was zero, it would + +be the same as if we randomized +at the individual + +level because they're totally +uncorrelated. + +Suppose your correlation +coefficient was 0.1-- + +rho was 0.1. + +Then the smallest effect size +you could have would be 3.3 + +times larger than if you had +done an individual design. + +So does that make sense +how to interpret this? + +And so this illustrates that, +even with very mild + +correlation coefficients-- and +we saw examples of those math + +test scores that +were like 0.5. + +This is only 0.1, but it already +means, in some sense, + +that your experiment +can detect things-- + +if you had been able to +individually randomize, you + +would be able to detect things +that were three times as + +small, right? + +Now that's a combination of +the fact that you have the + +correlation coefficient +and the number + +of people per cluster. + +AUDIENCE: Then in the previous +slide, 0.5 does not mean half? + +PROFESSOR: No, 0.5 is the +correlation-- it's rho. + +AUDIENCE: No, in the + +PROFESSOR: It's rho. + +AUDIENCE: Then it does not mean +half of the difference-- + +PROFESSOR: No, it's half +of the variance. + +Let me move on. + +We can talk about the +formula for that. + +OK. + +So what this means is, if the +experimental design is + +clustered, we now not only need +to consider all the other + +factors we talked about before, +we also need to + +consider this factor rho when +doing our power calculations. + +And rho is yet another thing we +can try to estimate based + +on our little survey of our +population to get a sense of + +what this rho is likely to be. + +And given this clustering issue, +it's very important not + +just that you have a big +enough number of people + +involved in your experiment, but +that you randomize across + +a big enough number +of groups, right? + +And the way I like to think +about is, how many times did + +you flip the coin as to who +should be treatment and who + +should be control? + +And, in fact, it's usually the +case that the number of groups + +you have is often more important +than the total + +number of individuals that you +have because the individuals + +are correlated within +a group, OK? + +So moving on. + +So I'm going to flip +through this. + +This is mostly going over some +of this if you were doing the + +exercise quickly. + +OK. + +And so this chart-- + +in your exercise shows you some +of the tradeoffs that you + +should think about when you're +trying to decide how you + +should trade off the number of +groups you have versus the + +number of people within +a group, OK? + +So in this particular case, a +group was a gram panchayat, + +and within a group there +were villages, OK? + +And there were different costs +involved in doing these + +different things, right? + +So going to the place involved +transportation costs to get to + +the gram panchayat. + +That, say, was a +couple of days. + +And then it took, like, half a +day, say, for every village + +you interviewed. + +So that said, there's some +cost of adding a new gram + +panchayat, but also some +marginal cost of adding + +additional village per +gram panchayat, OK? + +So you could calculate, based +on all your parameters and + +power of 80% and whatever the +intercluster correlation is in + +this particular case, you could +say, well, if we had + +this many villages per gram +panchayat, how many gram + +panchayats would we need +and how many villages + +would we need, OK? + +So you can do this +set of exercises + +and you can say that-- + +and you'll note, for example, +that as we reduce the number + +of gram panchayats we go to-- +another way, as we add more + +villages per gram panchayat, the +total number of villages + +we need to survey goes up. + +And in this particular case, it +doesn't go up by that much + +because the intercluster +correlation is not that high. + +And you could actually do this +type of calculation and you + +could say, well I know +my costs are, right? + +I know what my costs of +going this place are. + +And I can calculate which of +these designs is the cheapest + +design given what I +want to achieve. + +The other thing is, in this +case, the experiment was + +happening everywhere and +they were just trying + +to design the survey. + +But often when we're doing this, +we also need to pay for + +the intervention itself. + +And, at least in a lot of the +cases that I've worked with, + +the cost of actually doing the +intervention is much bigger + +than the cost of doing +the survey. + +And so, in that case, if you +always have to treat every + +village in the gram panchayat, +you can actually save a ton of + +money by going down in the +number of gram panchayats and + +surveying a lot more villages. + +But the whole point is there +are these tradeoffs and you + +need to, in deciding how you're +going to structure your + +experiment and how you're +going to structure your + +survey, you need to think +through what these tradeoffs + +are, make sure you have enough +power, given your estimates of + +your intercluster correlation +and sort of do the cost + +minimizing thing. + +OK, so in the last five minutes +or so, let me just + +highlight a couple of the other +issues that come up in + +thinking about power +calculations. + +So as I mentioned, the cluster +design is one of the most + +important ones. + +And the key thing is making +sure you have enough + +independent groups, where you +flip the coin to randomize + +betwee treatment and control +enough times. + +Some other things that matter +are baselines, control + +variables, and the hypothesis +being tested. + +So one minute on +each of those. + +A baseline has two uses-- + +main uses. + +One use of a baseline is that it +lets you check whether the + +treatment and control +group look the + +same before you started. + +And if you randomized properly, +we know they should + +look similar. + +But you want to make sure that +your randomization was + +actually carried out the way it +was supposed to be and that + +it wasn't the case that people +were pulling out of the hat + +until they got a treatment or +something, that they were + +actually randomizing the way +they were supposed to. + +And having a baseline conducted +before you start can + +allow you to test that your +randomization is actually + +truly random and your groups +look balanced. + +The other thing is, the baseline +can actually help + +reduce your survey size needed +because, but it requires you + +to a survey before you start +the intervention, right? + +And the reason it can reduce +your sample size is that now, + +instead of just looking at, say, +test scores across kids, + +I can look at the change in test +scores from before versus + +after the experiment started. + +And if people are really +persistent, like if the people + +who did really well on the test +this year are likely to + +do really well on the test +next year, that can + +essentially reduce the variance +of your outcome. + +It can be that the variance of +difference in test scores can + +be a lot lower than the variance +in test scores. + +And having a baseline can help +you for that reason. + +And as this slide points out, +your evaluation costs + +basically double because you +have to do two surveys, not + +one survey, but the costs of +the intervention go down + +because you can have a slightly +smaller sample. + +So if your intervention is +really expensive relative to + +your survey, this can +make a lot of sense. + +If your survey is really +expensive relative to your + +intervention, you might +not want to do this. + +And to figure out how this is +going to affect your power, + +you need to know yet another +fact, which is how correlated + +are people's outcomes +over time, right? + +What's the correlation between +how well I do on a test today + +and how well I do on +a test tomorrow? + +And some things are really +correlated and some things are + +not that correlated. + +And a baseline really helps you +on things that are really + +correlated. + +Another thing that can help +you is stratification. + +So what stratification can do +is, stratification says, + +suppose I-- + +in some ways, it's conceptually +a little bit like + +a baseline, which is, suppose I +know that all of the people + +who live in this village tend +to have similar outcomes and + +all of the people who live in +this village tend to have + +similar outcomes. + +And all of the people who live +in this village tend to have + +similar outcomes. + +If I can then randomize by +village, I can compare the + +people in each village +to each other, OK? + +So if I'm looking within +village, if people in villages + +tend to be similar and I can +randomize within village, if I + +look within villages, the +difference between the + +treatment and the +control group is + +going to be less noisy. + +So stratifying is basically a +way of saying I'm going to + +make sure my sample is balanced +across the treatment + +and control groups within +certain subgroups of the + +population. + +And then I'm going to compare +within those subgroups of the + +population when I +do my analysis. + +And once again, we can +think this as a + +way of reducing noise. + +That if people in similar +villages tend to be similar, + +if I only compare treatmet and +control within the same + +village, the noise there +is going to be smaller. + +So in some sense, +it's similar. + +So some things we tend to +stratify by, if we know the + +baseline value of the outcome, +we can sometimes stratify by + +that because we know that the +effects are going to be + +similar for people who have very +similar baseline values. + +Or often, I think, +geographically we often tend + +to do that. + +So basically, we think that +people in certain areas tend + +to be similar so we're going +to make sure our treatments + +and controls are balanced in +those areas as a way of + +reducing noise. + +And the final thing we want to +mention is the hypothesis + +being tested, which is, the more +things you want to test, + +the bigger your sample is +going to need to be. + +So for example, are we +interested in the difference + +between two treatments +as well as the + +treatment versus control? + +If so, we need a much bigger +sample because we not only + +need to be able to tell the +treatment versus the control + +but we also need to be able to +tell the two treatments from + +each other, right? + +So suppose you have two +different treatments. + +Are you interested in just the +overall effect of each of the + +two treatments? + +Or are you interested in +whether the treatments + +interact produces a different +effect if they happen + +together, right? + +The more things you're +interested in, the bigger your + +sample needs to be because you +need to design your sample to + +be big enough to answer each of +these different questions. + +Another thing, for example, you +were interested in testing + +whether the effect is different +in different + +subpopulations. + +Do you just want to know the +average effect of your program + +or do you want to know if it was +different in rural areas + +versus urban areas? + +If you want to know if it's +different in rural versus + +urban areas, you're going to +need a big enough sample in + +rural areas and a big enough +sample in urban areas that you + +can compare the difference +between them. + +So the more different things +that you want to test, + +obviously, the bigger +your experiment's + +going to need to be. + +And a lot of times, in actually +designing the + +experiment, this is something +that comes up all the time, + +that you will very quickly +figure out that the number of + +questions you would like to +answer is far bigger than the + +sample size you can afford. + +And one of the really important +conversations you + +need to have as you're +starting to design an + +experiment are, which are the +really critical questions that + +I really need to know +the answer to? + +So for example, in a project +I was recently doing in + +Indonesia, it turned out that +the government really wanted + +to know whether this program +would work differently in + +urban versus rural areas because +they had a view that + +urban areas are really +different. + +And they were willing to do +different programs in urban + +versus rural areas. + +So we designed our whole sample +to make sure we had + +enough sampled in urban areas +and in rural areas that we + +could test those two +things apart. + +That almost doubled the size +of the experiment, but the + +government thought that was +important enough that they + +really wanted to do that. + +The point here is that-- + +that was the one they +wanted to focus on. + +There was a million +other things we + +could have done instead. + +And so it's really important +to think about, before you + +design the experiment, what the +few key things you want to + +test are because, as I said, net +you're never going to have + +enough money to test all +things you want. + +That's sort of a universal +truth. + +So just to conclude, we've talk +about in this lecture-- + +going back to the basic +statistics of how you're going + +to analyze the experiment, +thinking about how noisy your + +outcome is going to be and how +you're going to compute your + +confidence intervals, +how big your effect + +size is going to be. + +That's all what goes into doing +a power calculation. + +You also need to do some +guess work, right? + +The power calculation is going +to require you to estimate how + +big your sample is +going to be-- + +sorry, how much variance there's +going to be, what your + +effect size is going to be. + +You have to make some +assumptions. + +And a little bit of pilot +testing before the experiment + +begins can be really useful, +I think, mostly + +for thinking about-- + +just collecting some data +can be useful to + +estimate these variances. + +The power calculations can +help you think about this + +question of how many treatments +you can afford to + +have, and can I afford to do +three different versions of + +the program or do I really need +to just pick one or two? + +How do I make this tradeoff of +more clusters versus more + +observations per cluster? + +The power calculation can +be very helpful here. + +And the other thing, and in some +sense, the place I find + +power calculations the most +useful, especially because + +there is a bit of guesswork in +power calculations and you get + +rough rules of thumb. + +You don't get precise answers +because it depends on the + +assumptions. + +But what I find this is really +useful for is whether this is + +feasible or not, right? + +Is this something where I'm +kind of in the right range + +where I think I can get +estimates, or where there's no + +chance, no matter how successful +this program is, + +that I'm going to be able to +pick it up in my data because + +the variable is just +way too noisy. + +And it's really important that +you do the power calculation, + +particularly-- + +both for structuring how to +design the experiment, but + +particularly to make sure you're +not going to waste a + +lot of time and money doing +something where you're going + +to have no hope of +picking it up. + +Because a study which is +underpowered is going to waste + +a lot of everyone's time and +you're very frustrated. + +Very frustrating for +everyone involved. + +So you want to make sure you do +this right before you start + +because otherwise, you're going +to end up spending a lot + +of time, money, and effort on +an experiment and ending up + +not being able to conclude +much of anything. + +OK. + +Thanks very much. \ No newline at end of file diff --git a/U4x-hzhohB8.txt b/U4x-hzhohB8.txt new file mode 100644 index 0000000000000000000000000000000000000000..73603a23413207441fa980851a78187e4f6325b5 --- /dev/null +++ b/U4x-hzhohB8.txt @@ -0,0 +1,579 @@ +align:start position:0% + +hi I'm Eric Dain and I'm a professor of + + align:start position:0% +hi I'm Eric Dain and I'm a professor of + + + align:start position:0% +hi I'm Eric Dain and I'm a professor of +computer science uh here at MIT and I'm + + align:start position:0% +computer science uh here at MIT and I'm + + + align:start position:0% +computer science uh here at MIT and I'm +one of three professors in charge of + + align:start position:0% +one of three professors in charge of + + + align:start position:0% +one of three professors in charge of +this class this semester 6046 so I + + align:start position:0% +this class this semester 6046 so I + + + align:start position:0% +this class this semester 6046 so I +taught about half of the lectures in the + + align:start position:0% +taught about half of the lectures in the + + + align:start position:0% +taught about half of the lectures in the +class sereny taught the other half and + + align:start position:0% +class sereny taught the other half and + + + align:start position:0% +class sereny taught the other half and +Nancy uh prepared new problem sets um + + align:start position:0% +Nancy uh prepared new problem sets um + + + align:start position:0% +Nancy uh prepared new problem sets um +and we all worked together on everything + + align:start position:0% +and we all worked together on everything + + + align:start position:0% +and we all worked together on everything +in the class pretty much we had I think + + align:start position:0% +in the class pretty much we had I think + + + align:start position:0% +in the class pretty much we had I think +10 T so and then uh another five graders + + align:start position:0% +10 T so and then uh another five graders + + + align:start position:0% +10 T so and then uh another five graders +so it's a big uh teaching infrastructure + + align:start position:0% +so it's a big uh teaching infrastructure + + + align:start position:0% +so it's a big uh teaching infrastructure +to deliver algorithms to 300 + + align:start position:0% +to deliver algorithms to 300 + + + align:start position:0% +to deliver algorithms to 300 +students my my entire career at MIT all + + align:start position:0% +students my my entire career at MIT all + + + align:start position:0% +students my my entire career at MIT all +I have done is taught different forms of + + align:start position:0% +I have done is taught different forms of + + + align:start position:0% +I have done is taught different forms of +algorithms uh so 6046 holds a place + + align:start position:0% +algorithms uh so 6046 holds a place + + + align:start position:0% +algorithms uh so 6046 holds a place +particularly dear to my heart um it's + + align:start position:0% +particularly dear to my heart um it's + + + align:start position:0% +particularly dear to my heart um it's +it's a class that's evolved over time so + + align:start position:0% +it's a class that's evolved over time so + + + align:start position:0% +it's a class that's evolved over time so +there's an older version of 6046 on ocw + + align:start position:0% +there's an older version of 6046 on ocw + + + align:start position:0% +there's an older version of 6046 on ocw +uh for a uh when algorithms in the + + align:start position:0% +uh for a uh when algorithms in the + + + align:start position:0% +uh for a uh when algorithms in the +undergraduate level was all taught in + + align:start position:0% +undergraduate level was all taught in + + + align:start position:0% +undergraduate level was all taught in +one semester uh which was exciting but + + align:start position:0% +one semester uh which was exciting but + + + align:start position:0% +one semester uh which was exciting but +also pretty intense and didn't really go + + align:start position:0% +also pretty intense and didn't really go + + + align:start position:0% +also pretty intense and didn't really go +into a lot of depth um so uh several + + align:start position:0% +into a lot of depth um so uh several + + + align:start position:0% +into a lot of depth um so uh several +years ago we split that class into two + + align:start position:0% +years ago we split that class into two + + + align:start position:0% +years ago we split that class into two +66 which is introductory algorithms and + + align:start position:0% +66 which is introductory algorithms and + + + align:start position:0% +66 which is introductory algorithms and +the new 6046 which is this class um + + align:start position:0% +the new 6046 which is this class um + + + align:start position:0% +the new 6046 which is this class um +which is intermediate algorithms beyond + + align:start position:0% +which is intermediate algorithms beyond + + + align:start position:0% +which is intermediate algorithms beyond +what you could Implement in an hour uh + + align:start position:0% +what you could Implement in an hour uh + + + align:start position:0% +what you could Implement in an hour uh +things that you have to think more about + + align:start position:0% +things that you have to think more about + + + align:start position:0% +things that you have to think more about +and proof theorems about so 6046 is sort + + align:start position:0% +and proof theorems about so 6046 is sort + + + align:start position:0% +and proof theorems about so 6046 is sort +of the more theoretical counterpart and + + align:start position:0% +of the more theoretical counterpart and + + + align:start position:0% +of the more theoretical counterpart and +gets into much more uh deeper algorithms + + align:start position:0% +gets into much more uh deeper algorithms + + + align:start position:0% +gets into much more uh deeper algorithms +than it's exciting um and my whole all + + align:start position:0% +than it's exciting um and my whole all + + + align:start position:0% +than it's exciting um and my whole all +of my research is also around algorithms + + align:start position:0% +of my research is also around algorithms + + + align:start position:0% +of my research is also around algorithms +so this is like this is me living the + + align:start position:0% +so this is like this is me living the + + + align:start position:0% +so this is like this is me living the +dream teaching the topic that I love um + + align:start position:0% +dream teaching the topic that I love um + + + align:start position:0% +dream teaching the topic that I love um +and uh it's an exciting class um this is + + align:start position:0% +and uh it's an exciting class um this is + + + align:start position:0% +and uh it's an exciting class um this is +an undergraduate class so the material + + align:start position:0% +an undergraduate class so the material + + + align:start position:0% +an undergraduate class so the material +is stuff that I should know really well + + align:start position:0% +is stuff that I should know really well + + + align:start position:0% +is stuff that I should know really well +but every time I teach it I find that I + + align:start position:0% +but every time I teach it I find that I + + + align:start position:0% +but every time I teach it I find that I +learn it at an even deeper level and + + align:start position:0% +learn it at an even deeper level and + + + align:start position:0% +learn it at an even deeper level and +understand it better also because I try + + align:start position:0% +understand it better also because I try + + + align:start position:0% +understand it better also because I try +to add in new topics that I don't know + + align:start position:0% +to add in new topics that I don't know + + + align:start position:0% +to add in new topics that I don't know +so well so I learn them even better um + + align:start position:0% +so well so I learn them even better um + + + align:start position:0% +so well so I learn them even better um +and that in turn influences my research + + align:start position:0% +and that in turn influences my research + + + align:start position:0% +and that in turn influences my research +so now I once I understand the basics + + align:start position:0% +so now I once I understand the basics + + + align:start position:0% +so now I once I understand the basics +really well I can apply them in new and + + align:start position:0% +really well I can apply them in new and + + + align:start position:0% +really well I can apply them in new and +interesting ways to solve problems I + + align:start position:0% +interesting ways to solve problems I + + + align:start position:0% +interesting ways to solve problems I +didn't know how to solve before + + align:start position:0% +didn't know how to solve before + + + align:start position:0% +didn't know how to solve before +algorithms are just so much fun + + align:start position:0% +algorithms are just so much fun + + + align:start position:0% +algorithms are just so much fun +sometimes I start the class with I'm + + align:start position:0% +sometimes I start the class with I'm + + + align:start position:0% +sometimes I start the class with I'm +Eric Dain and I love + + align:start position:0% +Eric Dain and I love + + + align:start position:0% +Eric Dain and I love +algorithms um it's it's just such a it's + + align:start position:0% +algorithms um it's it's just such a it's + + + align:start position:0% +algorithms um it's it's just such a it's +it's really fun material it's uh it's + + align:start position:0% +it's really fun material it's uh it's + + + align:start position:0% +it's really fun material it's uh it's +very creative it's almost like an art + + align:start position:0% +very creative it's almost like an art + + + align:start position:0% +very creative it's almost like an art +form to come up with a beautiful + + align:start position:0% +form to come up with a beautiful + + + align:start position:0% +form to come up with a beautiful +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +and uh this class teaches so many + + align:start position:0% +and uh this class teaches so many + + + align:start position:0% +and uh this class teaches so many +different algorithms that others have + + align:start position:0% +different algorithms that others have + + + align:start position:0% +different algorithms that others have +developed it's kind of like the cream of + + align:start position:0% +developed it's kind of like the cream of + + + align:start position:0% +developed it's kind of like the cream of +the crop there's zillions out there so + + align:start position:0% +the crop there's zillions out there so + + + align:start position:0% +the crop there's zillions out there so +we can't cover all of them so we take + + align:start position:0% +we can't cover all of them so we take + + + align:start position:0% +we can't cover all of them so we take +out representative examples and find + + align:start position:0% +out representative examples and find + + + align:start position:0% +out representative examples and find +really cool really interesting or really + + align:start position:0% +really cool really interesting or really + + + align:start position:0% +really cool really interesting or really +beautiful algorithms and it's it's it's + + align:start position:0% +beautiful algorithms and it's it's it's + + + align:start position:0% +beautiful algorithms and it's it's it's +really fun to to cover them all and and + + align:start position:0% +really fun to to cover them all and and + + + align:start position:0% +really fun to to cover them all and and +to share that beauty with the students I + + align:start position:0% +to share that beauty with the students I + + + align:start position:0% +to share that beauty with the students I +think I've taught this class 10 times in + + align:start position:0% +think I've taught this class 10 times in + + + align:start position:0% +think I've taught this class 10 times in +some some version so uh it's it's been + + align:start position:0% +some some version so uh it's it's been + + + align:start position:0% +some some version so uh it's it's been +an adventure every time is different and + + align:start position:0% +an adventure every time is different and + + + align:start position:0% +an adventure every time is different and +uh of course the last time is always the + + align:start position:0% +uh of course the last time is always the + + + align:start position:0% +uh of course the last time is always the +best but uh next time will be even + + align:start position:0% +best but uh next time will be even + + + align:start position:0% +best but uh next time will be even +better hopefully \ No newline at end of file diff --git a/UF94OiDYgBY.txt b/UF94OiDYgBY.txt new file mode 100644 index 0000000000000000000000000000000000000000..287603c8238ab21c65369fa3819789f0fda4cd06 --- /dev/null +++ b/UF94OiDYgBY.txt @@ -0,0 +1,8312 @@ +align:start position:0% + +i this is unbelievable uh so whoever uh + + align:start position:0% +i this is unbelievable uh so whoever uh + + + align:start position:0% +i this is unbelievable uh so whoever uh +so you're i i just learned that yfn + + align:start position:0% +so you're i i just learned that yfn + + + align:start position:0% +so you're i i just learned that yfn +means your friendly neighborhood right + + align:start position:0% +means your friendly neighborhood right + + + align:start position:0% +means your friendly neighborhood right +okay uh hackers so uh and look we + + align:start position:0% +okay uh hackers so uh and look we + + + align:start position:0% +okay uh hackers so uh and look we +brought it with us unbelievable this is + + align:start position:0% +brought it with us unbelievable this is + + + align:start position:0% +brought it with us unbelievable this is +making my day this is making my week + + align:start position:0% +making my day this is making my week + + + align:start position:0% +making my day this is making my week +this is incredible and uh and i really i + + align:start position:0% +this is incredible and uh and i really i + + + align:start position:0% +this is incredible and uh and i really i +i i don't know what to say uh this is + + align:start position:0% +i i don't know what to say uh this is + + + align:start position:0% +i i don't know what to say uh this is +amazing so so whoever you are thank you + + align:start position:0% +amazing so so whoever you are thank you + + + align:start position:0% +amazing so so whoever you are thank you +this is this is awesome so like + + align:start position:0% +this is this is awesome so like + + + align:start position:0% +this is this is awesome so like +you know + + align:start position:0% +you know + + + align:start position:0% +you know +uh + + align:start position:0% +uh + + + align:start position:0% +uh +where's laura so laura uh next year i + + align:start position:0% +where's laura so laura uh next year i + + + align:start position:0% +where's laura so laura uh next year i +think we should give every student one + + align:start position:0% +think we should give every student one + + + align:start position:0% +think we should give every student one +of these + + align:start position:0% +of these + + + align:start position:0% +of these +right this will be in our in our so + + align:start position:0% +right this will be in our in our so + + + align:start position:0% +right this will be in our in our so +we've got some candy we've got t-shirts + + align:start position:0% +we've got some candy we've got t-shirts + + + align:start position:0% +we've got some candy we've got t-shirts +um we'll get to those + + align:start position:0% +um we'll get to those + + + align:start position:0% +um we'll get to those +um + + align:start position:0% +um + + + align:start position:0% +um +we've got welcome to the last lecture oh + + align:start position:0% +we've got welcome to the last lecture oh + + + align:start position:0% +we've got welcome to the last lecture oh +there's some t-shirts we're gonna let + + align:start position:0% +there's some t-shirts we're gonna let + + + align:start position:0% +there's some t-shirts we're gonna let +tas throw them out + + align:start position:0% +tas throw them out + + + align:start position:0% +tas throw them out +we're gonna let ta throw them out um and + + align:start position:0% +we're gonna let ta throw them out um and + + + align:start position:0% +we're gonna let ta throw them out um and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and and but but uh + + align:start position:0% +and and but but uh + + + align:start position:0% +and and but but uh +we're getting + + align:start position:0% +we're getting + + + align:start position:0% +we're getting +yeah + + align:start position:0% + + + + align:start position:0% + +you guys gotta uh now + + align:start position:0% +you guys gotta uh now + + + align:start position:0% +you guys gotta uh now +um + + align:start position:0% + + + + align:start position:0% + +so we got a little bit more to cover um + + align:start position:0% +so we got a little bit more to cover um + + + align:start position:0% +so we got a little bit more to cover um +on diffusion + + align:start position:0% +on diffusion + + + align:start position:0% +on diffusion +i got my i gotta why this matters and + + align:start position:0% +i got my i gotta why this matters and + + + align:start position:0% +i got my i gotta why this matters and +then i got a couple things i want to say + + align:start position:0% +then i got a couple things i want to say + + + align:start position:0% +then i got a couple things i want to say +um and and then we'll conclude and like + + align:start position:0% +um and and then we'll conclude and like + + + align:start position:0% +um and and then we'll conclude and like +i said uh the plan today is to conclude + + align:start position:0% +i said uh the plan today is to conclude + + + align:start position:0% +i said uh the plan today is to conclude +a little early + + align:start position:0% +a little early + + + align:start position:0% +a little early +to give you time to fill out the course + + align:start position:0% +to give you time to fill out the course + + + align:start position:0% +to give you time to fill out the course +evaluations + + align:start position:0% +evaluations + + + align:start position:0% +evaluations +we + + align:start position:0% +we + + + align:start position:0% +we +really take this seriously we really + + align:start position:0% +really take this seriously we really + + + align:start position:0% +really take this seriously we really +value uh any and all input that you have + + align:start position:0% +value uh any and all input that you have + + + align:start position:0% +value uh any and all input that you have +um + + align:start position:0% +um + + + align:start position:0% +um +and and so please do if you haven't done + + align:start position:0% +and and so please do if you haven't done + + + align:start position:0% +and and so please do if you haven't done +it already please use the last 15 + + align:start position:0% +it already please use the last 15 + + + align:start position:0% +it already please use the last 15 +minutes that we'll give you in the class + + align:start position:0% +minutes that we'll give you in the class + + + align:start position:0% +minutes that we'll give you in the class +to fill those out um it means a lot to + + align:start position:0% +to fill those out um it means a lot to + + + align:start position:0% +to fill those out um it means a lot to +us + + align:start position:0% +us + + + align:start position:0% +us +um + + align:start position:0% +um + + + align:start position:0% +um +okay i i kind of can't this is still uh + + align:start position:0% +okay i i kind of can't this is still uh + + + align:start position:0% +okay i i kind of can't this is still uh +it's hitting me right here it's slowing + + align:start position:0% +it's hitting me right here it's slowing + + + align:start position:0% +it's hitting me right here it's slowing +me down + + align:start position:0% +me down + + + align:start position:0% +me down +okay i'm gonna get i can do it i'm gonna + + align:start position:0% +okay i'm gonna get i can do it i'm gonna + + + align:start position:0% +okay i'm gonna get i can do it i'm gonna +get through it + + align:start position:0% + + + + align:start position:0% + +so we were talking about fixed laws and + + align:start position:0% +so we were talking about fixed laws and + + + align:start position:0% +so we were talking about fixed laws and +uh and you're only going to be tested on + + align:start position:0% +uh and you're only going to be tested on + + + align:start position:0% +uh and you're only going to be tested on +the first one + + align:start position:0% +the first one + + + align:start position:0% +the first one +okay but i do want to tell you about the + + align:start position:0% +okay but i do want to tell you about the + + + align:start position:0% +okay but i do want to tell you about the +second one + + align:start position:0% +second one + + + align:start position:0% +second one +um + + align:start position:0% +um + + + align:start position:0% +um +you are not going to be tested on the + + align:start position:0% +you are not going to be tested on the + + + align:start position:0% +you are not going to be tested on the +second one that is correct + + align:start position:0% +second one that is correct + + + align:start position:0% +second one that is correct +unlike last year this year because we + + align:start position:0% +unlike last year this year because we + + + align:start position:0% +unlike last year this year because we +didn't have time to get the lecture in + + align:start position:0% +didn't have time to get the lecture in + + + align:start position:0% +didn't have time to get the lecture in +on the second law before the recitation + + align:start position:0% +on the second law before the recitation + + + align:start position:0% +on the second law before the recitation +which was yesterday and so look you'll + + align:start position:0% +which was yesterday and so look you'll + + + align:start position:0% +which was yesterday and so look you'll +there'll probably be a diffusion problem + + align:start position:0% +there'll probably be a diffusion problem + + + align:start position:0% +there'll probably be a diffusion problem +um + + align:start position:0% +um + + + align:start position:0% +um +but uh but not on the second law but i + + align:start position:0% +but uh but not on the second law but i + + + align:start position:0% +but uh but not on the second law but i +still + + align:start position:0% +still + + + align:start position:0% +still +i do want to finish the example um and i + + align:start position:0% +i do want to finish the example um and i + + + align:start position:0% +i do want to finish the example um and i +won't go through it in detail but i want + + align:start position:0% +won't go through it in detail but i want + + + align:start position:0% +won't go through it in detail but i want +to set it up and just show it to you so + + align:start position:0% +to set it up and just show it to you so + + + align:start position:0% +to set it up and just show it to you so +you have a sense of what fixed second + + align:start position:0% +you have a sense of what fixed second + + + align:start position:0% +you have a sense of what fixed second +log lets you do + + align:start position:0% +log lets you do + + + align:start position:0% +log lets you do +um and we you know we ended with the + + align:start position:0% +um and we you know we ended with the + + + align:start position:0% +um and we you know we ended with the +first law and i wrote the second law + + align:start position:0% +first law and i wrote the second law + + + align:start position:0% +first law and i wrote the second law +down now the first law that is something + + align:start position:0% +down now the first law that is something + + + align:start position:0% +down now the first law that is something +i want you to know about and so remember + + align:start position:0% +i want you to know about and so remember + + + align:start position:0% +i want you to know about and so remember +you know with the first law so if we're + + align:start position:0% +you know with the first law so if we're + + + align:start position:0% +you know with the first law so if we're +uh let me go over here + + align:start position:0% +uh let me go over here + + + align:start position:0% +uh let me go over here +so you have a whole board to my + + align:start position:0% +so you have a whole board to my + + + align:start position:0% +so you have a whole board to my +to use so in in fixed first law + + align:start position:0% +to use so in in fixed first law + + + align:start position:0% +to use so in in fixed first law +uh what that meant was + + align:start position:0% +uh what that meant was + + + align:start position:0% +uh what that meant was +it's it's a law that describes + + align:start position:0% +it's it's a law that describes + + + align:start position:0% +it's it's a law that describes +uh the steady state + + align:start position:0% +uh the steady state + + + align:start position:0% +uh the steady state +so um fixed first law was steady state + + align:start position:0% +so um fixed first law was steady state + + + align:start position:0% +so um fixed first law was steady state +and and this is now you know this is now + + align:start position:0% +and and this is now you know this is now + + + align:start position:0% +and and this is now you know this is now +bringing back memories from two days ago + + align:start position:0% +bringing back memories from two days ago + + + align:start position:0% +bringing back memories from two days ago +so steady state which means uh + + align:start position:0% +so steady state which means uh + + + align:start position:0% +so steady state which means uh +no + + align:start position:0% +no + + + align:start position:0% +no +time dependence + + align:start position:0% +time dependence + + + align:start position:0% +time dependence +no time + + align:start position:0% +no time + + + align:start position:0% +no time +dependence okay + + align:start position:0% +dependence okay + + + align:start position:0% +dependence okay +and so we had you know some examples of + + align:start position:0% +and so we had you know some examples of + + + align:start position:0% +and so we had you know some examples of +that and the law itself i'll write it + + align:start position:0% +that and the law itself i'll write it + + + align:start position:0% +that and the law itself i'll write it +down here was that the flux um is equal + + align:start position:0% +down here was that the flux um is equal + + + align:start position:0% +down here was that the flux um is equal +to minus + + align:start position:0% +to minus + + + align:start position:0% +to minus +this diffusion constant times the change + + align:start position:0% +this diffusion constant times the change + + + align:start position:0% +this diffusion constant times the change +in concentration over some difference + + align:start position:0% +in concentration over some difference + + + align:start position:0% +in concentration over some difference +over some distance + + align:start position:0% +over some distance + + + align:start position:0% +over some distance +over some distance and and so we had + + align:start position:0% +over some distance and and so we had + + + align:start position:0% +over some distance and and so we had +this example of um + + align:start position:0% +this example of um + + + align:start position:0% +this example of um +of a membrane right and so so you could + + align:start position:0% +of a membrane right and so so you could + + + align:start position:0% +of a membrane right and so so you could +imagine like some you know we had the + + align:start position:0% +imagine like some you know we had the + + + align:start position:0% +imagine like some you know we had the +glove right it was the remember the + + align:start position:0% +glove right it was the remember the + + + align:start position:0% +glove right it was the remember the +butyl glove + + align:start position:0% +butyl glove + + + align:start position:0% +butyl glove +and and so we had some distance maybe + + align:start position:0% +and and so we had some distance maybe + + + align:start position:0% +and and so we had some distance maybe +this is like a + + align:start position:0% +this is like a + + + align:start position:0% +this is like a +a delta x + + align:start position:0% +a delta x + + + align:start position:0% +a delta x +and and there was some concentration up + + align:start position:0% +and and there was some concentration up + + + align:start position:0% +and and there was some concentration up +here right c + + align:start position:0% +here right c + + + align:start position:0% +here right c +one and some concentration down here c2 + + align:start position:0% +one and some concentration down here c2 + + + align:start position:0% +one and some concentration down here c2 +and now in the key in fixed laws you're + + align:start position:0% +and now in the key in fixed laws you're + + + align:start position:0% +and now in the key in fixed laws you're +going to hold these concentrations + + align:start position:0% +going to hold these concentrations + + + align:start position:0% +going to hold these concentrations +constant + + align:start position:0% +constant + + + align:start position:0% +constant +at the source right at each of these + + align:start position:0% +at the source right at each of these + + + align:start position:0% +at the source right at each of these +points and so you can imagine that it's + + align:start position:0% +points and so you can imagine that it's + + + align:start position:0% +points and so you can imagine that it's +going to change as you go down the hill + + align:start position:0% +going to change as you go down the hill + + + align:start position:0% +going to change as you go down the hill +and we frame this in terms of brownian + + align:start position:0% +and we frame this in terms of brownian + + + align:start position:0% +and we frame this in terms of brownian +motion now you're able to understand why + + align:start position:0% +motion now you're able to understand why + + + align:start position:0% +motion now you're able to understand why +concentration why diffusion happens down + + align:start position:0% +concentration why diffusion happens down + + + align:start position:0% +concentration why diffusion happens down +a concentration gradient right + + align:start position:0% +a concentration gradient right + + + align:start position:0% +a concentration gradient right +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +and so and that gets and now that that + + align:start position:0% +and so and that gets and now that that + + + align:start position:0% +and so and that gets and now that that +flux that flux right remember so j + + align:start position:0% +flux that flux right remember so j + + + align:start position:0% +flux that flux right remember so j +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +j + + align:start position:0% +j + + + align:start position:0% +j +is an amount + + align:start position:0% +is an amount + + + align:start position:0% +is an amount +divided by an area + + align:start position:0% +divided by an area + + + align:start position:0% +divided by an area +times time + + align:start position:0% +times time + + + align:start position:0% +times time +right that's j that's the flux through + + align:start position:0% +right that's j that's the flux through + + + align:start position:0% +right that's j that's the flux through +the membrane + + align:start position:0% +the membrane + + + align:start position:0% +the membrane +and that is + + align:start position:0% +and that is + + + align:start position:0% +and that is +uh also going to be uh + + align:start position:0% +uh also going to be uh + + + align:start position:0% +uh also going to be uh +constant now the + + align:start position:0% +constant now the + + + align:start position:0% +constant now the +the d + + align:start position:0% +the d + + + align:start position:0% +the d +what we assumed in the d + + align:start position:0% +what we assumed in the d + + + align:start position:0% +what we assumed in the d +is that + + align:start position:0% +is that + + + align:start position:0% +is that +it's a constant so in the fixed first + + align:start position:0% +it's a constant so in the fixed first + + + align:start position:0% +it's a constant so in the fixed first +law of problems we often assume d + + align:start position:0% +law of problems we often assume d + + + align:start position:0% +law of problems we often assume d +doesn't depend on concentration + + align:start position:0% +doesn't depend on concentration + + + align:start position:0% +doesn't depend on concentration +right so that means that if i'm over + + align:start position:0% +right so that means that if i'm over + + + align:start position:0% +right so that means that if i'm over +here at a high concentration i'm at over + + align:start position:0% +here at a high concentration i'm at over + + + align:start position:0% +here at a high concentration i'm at over +here at a low concentration well then + + align:start position:0% +here at a low concentration well then + + + align:start position:0% +here at a low concentration well then +by the way this would be like + + align:start position:0% + + + + align:start position:0% + +you like some candy i would like some + + align:start position:0% +you like some candy i would like some + + + align:start position:0% +you like some candy i would like some +candy thank you very much + + align:start position:0% +candy thank you very much + + + align:start position:0% +candy thank you very much +up and down not at all no + + align:start position:0% +up and down not at all no + + + align:start position:0% +up and down not at all no +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +that's awesome + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +i uh + + align:start position:0% + + + + align:start position:0% + +this is just getting better + + align:start position:0% +this is just getting better + + + align:start position:0% +this is just getting better +i'm feeling less and less like talking + + align:start position:0% +i'm feeling less and less like talking + + + align:start position:0% +i'm feeling less and less like talking +about fixed law but + + align:start position:0% +about fixed law but + + + align:start position:0% +about fixed law but +but here we are + + align:start position:0% +but here we are + + + align:start position:0% +but here we are +i'll go fast but okay now uh + + align:start position:0% + + + + align:start position:0% + +now the thing is you know look + + align:start position:0% +now the thing is you know look + + + align:start position:0% +now the thing is you know look +um + + align:start position:0% +um + + + align:start position:0% +um +so this this is x + + align:start position:0% +so this this is x + + + align:start position:0% +so this this is x +this is x um i by the way i really want + + align:start position:0% +this is x um i by the way i really want + + + align:start position:0% +this is x um i by the way i really want +to know where they got the the costumes + + align:start position:0% +to know where they got the the costumes + + + align:start position:0% +to know where they got the the costumes +um from but this is x and this would be + + align:start position:0% +um from but this is x and this would be + + + align:start position:0% +um from but this is x and this would be +like the concentration right + + align:start position:0% + + + + align:start position:0% + +and um and now d okay look d could + + align:start position:0% +and um and now d okay look d could + + + align:start position:0% +and um and now d okay look d could +depend on concentration by the way it's + + align:start position:0% +depend on concentration by the way it's + + + align:start position:0% +depend on concentration by the way it's +actually quite interesting it does + + align:start position:0% +actually quite interesting it does + + + align:start position:0% +actually quite interesting it does +have a small dependence on concentration + + align:start position:0% +have a small dependence on concentration + + + align:start position:0% +have a small dependence on concentration +we often don't don't include it so this + + align:start position:0% +we often don't don't include it so this + + + align:start position:0% +we often don't don't include it so this +would be like a straight line + + align:start position:0% +would be like a straight line + + + align:start position:0% +would be like a straight line +you know but if it did + + align:start position:0% +you know but if it did + + + align:start position:0% +you know but if it did +if it did depend on concentration then + + align:start position:0% +if it did depend on concentration then + + + align:start position:0% +if it did depend on concentration then +you might have a deviation right you + + align:start position:0% +you might have a deviation right you + + + align:start position:0% +you might have a deviation right you +could have something like this + + align:start position:0% +could have something like this + + + align:start position:0% +could have something like this +right you could have something like that + + align:start position:0% +right you could have something like that + + + align:start position:0% +right you could have something like that +you don't need to have a straight line + + align:start position:0% +you don't need to have a straight line + + + align:start position:0% +you don't need to have a straight line +to use fixed law but in a lot of the + + align:start position:0% +to use fixed law but in a lot of the + + + align:start position:0% +to use fixed law but in a lot of the +problems that we do we assume d is just + + align:start position:0% +problems that we do we assume d is just + + + align:start position:0% +problems that we do we assume d is just +independent of concentration it's a + + align:start position:0% +independent of concentration it's a + + + align:start position:0% +independent of concentration it's a +constant + + align:start position:0% +constant + + + align:start position:0% +constant +right + + align:start position:0% +right + + + align:start position:0% +right +i mean if it did depend you know so i'm + + align:start position:0% +i mean if it did depend you know so i'm + + + align:start position:0% +i mean if it did depend you know so i'm +adding more and more carbon and iron + + align:start position:0% +adding more and more carbon and iron + + + align:start position:0% +adding more and more carbon and iron +does the diffusion of the carbon now + + align:start position:0% +does the diffusion of the carbon now + + + align:start position:0% +does the diffusion of the carbon now +depend on how much i added well yeah it + + align:start position:0% +depend on how much i added well yeah it + + + align:start position:0% +depend on how much i added well yeah it +might a little bit + + align:start position:0% +might a little bit + + + align:start position:0% +might a little bit +by the way that doesn't mean that it + + align:start position:0% +by the way that doesn't mean that it + + + align:start position:0% +by the way that doesn't mean that it +depends on time + + align:start position:0% +depends on time + + + align:start position:0% +depends on time +that's the distinction i want to make + + align:start position:0% +that's the distinction i want to make + + + align:start position:0% +that's the distinction i want to make +right so again + + align:start position:0% +right so again + + + align:start position:0% +right so again +you know in the problems we do with + + align:start position:0% +you know in the problems we do with + + + align:start position:0% +you know in the problems we do with +fixed law we'll assume + + align:start position:0% +fixed law we'll assume + + + align:start position:0% +fixed law we'll assume +d doesn't depend on concentration we'll + + align:start position:0% +d doesn't depend on concentration we'll + + + align:start position:0% +d doesn't depend on concentration we'll +just assume it's a constant but the main + + align:start position:0% +just assume it's a constant but the main + + + align:start position:0% +just assume it's a constant but the main +determining factor to see if it's a + + align:start position:0% +determining factor to see if it's a + + + align:start position:0% +determining factor to see if it's a +fixed second law or a fixed first law + + align:start position:0% +fixed second law or a fixed first law + + + align:start position:0% +fixed second law or a fixed first law +problem + + align:start position:0% +problem + + + align:start position:0% +problem +isn't whether d changes with + + align:start position:0% +isn't whether d changes with + + + align:start position:0% +isn't whether d changes with +concentration no it's whether there's a + + align:start position:0% +concentration no it's whether there's a + + + align:start position:0% +concentration no it's whether there's a +time dependence + + align:start position:0% +time dependence + + + align:start position:0% +time dependence +it's whether there's a time dependence + + align:start position:0% +it's whether there's a time dependence + + + align:start position:0% +it's whether there's a time dependence +and that was the problem that we left + + align:start position:0% +and that was the problem that we left + + + align:start position:0% +and that was the problem that we left +off on + + align:start position:0% +off on + + + align:start position:0% +off on +on um + + align:start position:0% +on um + + + align:start position:0% +on um +on + + align:start position:0% +on + + + align:start position:0% +on +monday right we say well you got to do + + align:start position:0% +monday right we say well you got to do + + + align:start position:0% +monday right we say well you got to do +this thing called case hardening to a + + align:start position:0% +this thing called case hardening to a + + + align:start position:0% +this thing called case hardening to a +lot of materials you make the outside + + align:start position:0% +lot of materials you make the outside + + + align:start position:0% +lot of materials you make the outside +harder the inside has to stay ductile + + align:start position:0% +harder the inside has to stay ductile + + + align:start position:0% +harder the inside has to stay ductile +otherwise either it's not strong enough + + align:start position:0% +otherwise either it's not strong enough + + + align:start position:0% +otherwise either it's not strong enough +or it's it's too ductile right it just + + align:start position:0% +or it's it's too ductile right it just + + + align:start position:0% +or it's it's too ductile right it just +breaks down either way + + align:start position:0% +breaks down either way + + + align:start position:0% +breaks down either way +or it's too brittle so you want to case + + align:start position:0% +or it's too brittle so you want to case + + + align:start position:0% +or it's too brittle so you want to case +harden and that was our fixed second law + + align:start position:0% +harden and that was our fixed second law + + + align:start position:0% +harden and that was our fixed second law +problem and and and again + + align:start position:0% +problem and and and again + + + align:start position:0% +problem and and and again +i'm just going to kind of set it up i'm + + align:start position:0% +i'm just going to kind of set it up i'm + + + align:start position:0% +i'm just going to kind of set it up i'm +not going to go through it all but in + + align:start position:0% +not going to go through it all but in + + + align:start position:0% +not going to go through it all but in +the in the second law + + align:start position:0% +the in the second law + + + align:start position:0% +the in the second law +in the second law what you have is an + + align:start position:0% +in the second law what you have is an + + + align:start position:0% +in the second law what you have is an +ability now to look at the time + + align:start position:0% +ability now to look at the time + + + align:start position:0% +ability now to look at the time +dependence so you can imagine if i have + + align:start position:0% +dependence so you can imagine if i have + + + align:start position:0% +dependence so you can imagine if i have +position x + + align:start position:0% +position x + + + align:start position:0% +position x +and concentration + + align:start position:0% +and concentration + + + align:start position:0% +and concentration +c and i start somewhere here so i have + + align:start position:0% +c and i start somewhere here so i have + + + align:start position:0% +c and i start somewhere here so i have +some + + align:start position:0% +some + + + align:start position:0% +some +some source that's why we call it cs + + align:start position:0% +some source that's why we call it cs + + + align:start position:0% +some source that's why we call it cs +right so what did we do we took this + + align:start position:0% +right so what did we do we took this + + + align:start position:0% +right so what did we do we took this +piece of steel + + align:start position:0% +piece of steel + + + align:start position:0% +piece of steel +and we asked a question right i've got + + align:start position:0% +and we asked a question right i've got + + + align:start position:0% +and we asked a question right i've got +i've got i'm case hardening the steel so + + align:start position:0% +i've got i'm case hardening the steel so + + + align:start position:0% +i've got i'm case hardening the steel so +this is iron with carbon and i and i + + align:start position:0% +this is iron with carbon and i and i + + + align:start position:0% +this is iron with carbon and i and i +want to put carbon into it but only up + + align:start position:0% +want to put carbon into it but only up + + + align:start position:0% +want to put carbon into it but only up +to a certain point + + align:start position:0% +to a certain point + + + align:start position:0% +to a certain point +right in a certain a certain amount how + + align:start position:0% +right in a certain a certain amount how + + + align:start position:0% +right in a certain a certain amount how +do i know how long to put it in the oven + + align:start position:0% +do i know how long to put it in the oven + + + align:start position:0% +do i know how long to put it in the oven +that's a fixed second law problem + + align:start position:0% +that's a fixed second law problem + + + align:start position:0% +that's a fixed second law problem +because it's a time dependent process + + align:start position:0% +because it's a time dependent process + + + align:start position:0% +because it's a time dependent process +and i want to know about concentrations + + align:start position:0% +and i want to know about concentrations + + + align:start position:0% +and i want to know about concentrations +into the piece of iron into the piece of + + align:start position:0% +into the piece of iron into the piece of + + + align:start position:0% +into the piece of iron into the piece of +steel as a function of time so you can + + align:start position:0% +steel as a function of time so you can + + + align:start position:0% +steel as a function of time so you can +answer questions like this with fixed + + align:start position:0% +answer questions like this with fixed + + + align:start position:0% +answer questions like this with fixed +second law so i had it at 0.25 weight + + align:start position:0% +second law so i had it at 0.25 weight + + + align:start position:0% +second law so i had it at 0.25 weight +percent carbon and i carburized the + + align:start position:0% +percent carbon and i carburized the + + + align:start position:0% +percent carbon and i carburized the +surface i carborized only a certain + + align:start position:0% +surface i carborized only a certain + + + align:start position:0% +surface i carborized only a certain +amount of it i case harden it right + + align:start position:0% +amount of it i case harden it right + + + align:start position:0% +amount of it i case harden it right +how long should you keep it in the oven + + align:start position:0% +how long should you keep it in the oven + + + align:start position:0% +how long should you keep it in the oven +and and by the way also like how much + + align:start position:0% +and and by the way also like how much + + + align:start position:0% +and and by the way also like how much +what should your carbon your + + align:start position:0% +what should your carbon your + + + align:start position:0% +what should your carbon your +concentration of source be + + align:start position:0% +concentration of source be + + + align:start position:0% +concentration of source be +on the outside right and all these + + align:start position:0% +on the outside right and all these + + + align:start position:0% +on the outside right and all these +things kind of go in and and so you + + align:start position:0% +things kind of go in and and so you + + + align:start position:0% +things kind of go in and and so you +could imagine if the source is there and + + align:start position:0% +could imagine if the source is there and + + + align:start position:0% +could imagine if the source is there and +i'm holding maybe i've got some constant + + align:start position:0% +i'm holding maybe i've got some constant + + + align:start position:0% +i'm holding maybe i've got some constant +c naught right that's the point too + + align:start position:0% +c naught right that's the point too + + + align:start position:0% +c naught right that's the point too +that's the piece of material i started + + align:start position:0% +that's the piece of material i started + + + align:start position:0% +that's the piece of material i started +with + + align:start position:0% +with + + + align:start position:0% +with +right + + align:start position:0% +right + + + align:start position:0% +right +then well you can imagine at t zero + + align:start position:0% +then well you can imagine at t zero + + + align:start position:0% +then well you can imagine at t zero +you've got + + align:start position:0% +you've got + + + align:start position:0% +you've got +you've got this so this would be like + + align:start position:0% +you've got this so this would be like + + + align:start position:0% +you've got this so this would be like +time equals + + align:start position:0% +time equals + + + align:start position:0% +time equals +t naught and then as soon as i expose + + align:start position:0% +t naught and then as soon as i expose + + + align:start position:0% +t naught and then as soon as i expose +this to this uh this higher + + align:start position:0% +this to this uh this higher + + + align:start position:0% +this to this uh this higher +concentration of carbon you might have + + align:start position:0% +concentration of carbon you might have + + + align:start position:0% +concentration of carbon you might have +something like this so now you've got t1 + + align:start position:0% +something like this so now you've got t1 + + + align:start position:0% +something like this so now you've got t1 +and now i wait a little bit longer and + + align:start position:0% +and now i wait a little bit longer and + + + align:start position:0% +and now i wait a little bit longer and +it's going to be able to penetrate more + + align:start position:0% +it's going to be able to penetrate more + + + align:start position:0% +it's going to be able to penetrate more +in so the concentration + + align:start position:0% +in so the concentration + + + align:start position:0% +in so the concentration +inside the material changes as a + + align:start position:0% +inside the material changes as a + + + align:start position:0% +inside the material changes as a +function of time + + align:start position:0% +function of time + + + align:start position:0% +function of time +and so forth + + align:start position:0% +and so forth + + + align:start position:0% +and so forth +right + + align:start position:0% +right + + + align:start position:0% +right +that's what fixed second law tells us + + align:start position:0% +that's what fixed second law tells us + + + align:start position:0% +that's what fixed second law tells us +and it's the the second law is basically + + align:start position:0% +and it's the the second law is basically + + + align:start position:0% +and it's the the second law is basically +a heat equation + + align:start position:0% +a heat equation + + + align:start position:0% +a heat equation +which somebody + + align:start position:0% +which somebody + + + align:start position:0% +which somebody +uh + + align:start position:0% +uh + + + align:start position:0% +uh +noticed after a lecture yesterday and + + align:start position:0% +noticed after a lecture yesterday and + + + align:start position:0% +noticed after a lecture yesterday and +you know you can um + + align:start position:0% +you know you can um + + + align:start position:0% +you know you can um +uh let's see dx squared so this is a + + align:start position:0% +uh let's see dx squared so this is a + + + align:start position:0% +uh let's see dx squared so this is a +this is a partial differential equation + + align:start position:0% +this is a partial differential equation + + + align:start position:0% +this is a partial differential equation +and um + + align:start position:0% +and um + + + align:start position:0% +and um +and but but solving it is is just is + + align:start position:0% +and but but solving it is is just is + + + align:start position:0% +and but but solving it is is just is +just you know talking to our + + align:start position:0% +just you know talking to our + + + align:start position:0% +just you know talking to our +mathematician friends + + align:start position:0% +mathematician friends + + + align:start position:0% +mathematician friends +right and they come back and say oh + + align:start position:0% +right and they come back and say oh + + + align:start position:0% +right and they come back and say oh +that's an error function + + align:start position:0% +that's an error function + + + align:start position:0% +that's an error function +and an error function is just a function + + align:start position:0% +and an error function is just a function + + + align:start position:0% +and an error function is just a function +and it gives us a solution + + align:start position:0% +and it gives us a solution + + + align:start position:0% +and it gives us a solution +c the concentration at any position and + + align:start position:0% +c the concentration at any position and + + + align:start position:0% +c the concentration at any position and +at any time minus the + + align:start position:0% +at any time minus the + + + align:start position:0% +at any time minus the +initial concentration divided by this + + align:start position:0% +initial concentration divided by this + + + align:start position:0% +initial concentration divided by this +difference + + align:start position:0% +difference + + + align:start position:0% +difference +in + + align:start position:0% +in + + + align:start position:0% +in +concentrations between the source and + + align:start position:0% +concentrations between the source and + + + align:start position:0% +concentrations between the source and +the initial + + align:start position:0% +the initial + + + align:start position:0% +the initial +is going to equal oh boy + + align:start position:0% + + + + align:start position:0% + +you'd think i'd have learned + + align:start position:0% +you'd think i'd have learned + + + align:start position:0% +you'd think i'd have learned +36 lectures + + align:start position:0% +36 lectures + + + align:start position:0% +36 lectures +and i still worked my way into a corner + + align:start position:0% + + + + align:start position:0% + +i'm going to do the equals this way + + align:start position:0% +i'm going to do the equals this way + + + align:start position:0% +i'm going to do the equals this way +1 minus error function + + align:start position:0% +1 minus error function + + + align:start position:0% +1 minus error function +of + + align:start position:0% +of + + + align:start position:0% +of +x over + + align:start position:0% +x over + + + align:start position:0% +x over + + align:start position:0% + + + align:start position:0% +root d + + align:start position:0% +root d + + + align:start position:0% +root d +t + + align:start position:0% + + + + align:start position:0% + +that is + + align:start position:0% +that is + + + align:start position:0% +that is +what you get + + align:start position:0% +what you get + + + align:start position:0% +what you get +when you solve fixed second law + + align:start position:0% +when you solve fixed second law + + + align:start position:0% +when you solve fixed second law +that is what you get when you solve + + align:start position:0% +that is what you get when you solve + + + align:start position:0% +that is what you get when you solve +fixed second law + + align:start position:0% +fixed second law + + + align:start position:0% +fixed second law +and um and now the error function is + + align:start position:0% +and um and now the error function is + + + align:start position:0% +and um and now the error function is +just a function it's not you know + + align:start position:0% +just a function it's not you know + + + align:start position:0% +just a function it's not you know +you don't need to worry about uh about + + align:start position:0% +you don't need to worry about uh about + + + align:start position:0% +you don't need to worry about uh about +the details of this you can think about + + align:start position:0% +the details of this you can think about + + + align:start position:0% +the details of this you can think about +it as any as like any other function + + align:start position:0% +it as any as like any other function + + + align:start position:0% +it as any as like any other function +and but one thing that i want to share + + align:start position:0% +and but one thing that i want to share + + + align:start position:0% +and but one thing that i want to share +with you about the error function is + + align:start position:0% +with you about the error function is + + + align:start position:0% +with you about the error function is +and this is something that + + align:start position:0% +and this is something that + + + align:start position:0% +and this is something that +yeah you're not going to need it on on + + align:start position:0% +yeah you're not going to need it on on + + + align:start position:0% +yeah you're not going to need it on on +the exam but you might need this in life + + align:start position:0% +the exam but you might need this in life + + + align:start position:0% +the exam but you might need this in life +you might get an error function in life + + align:start position:0% +you might get an error function in life + + + align:start position:0% +you might get an error function in life +and earth + + align:start position:0% +and earth + + + align:start position:0% +and earth +and if you get an earth + + align:start position:0% +and if you get an earth + + + align:start position:0% +and if you get an earth +i don't want you to panic because an + + align:start position:0% +i don't want you to panic because an + + + align:start position:0% +i don't want you to panic because an +earth is just a function and it just + + align:start position:0% +earth is just a function and it just + + + align:start position:0% +earth is just a function and it just +looks like this + + align:start position:0% +looks like this + + + align:start position:0% +looks like this +okay it just looks like it's a linear + + align:start position:0% +okay it just looks like it's a linear + + + align:start position:0% +okay it just looks like it's a linear +plot roughly + + align:start position:0% +plot roughly + + + align:start position:0% +plot roughly +up to about 0.6 this trick and then it + + align:start position:0% +up to about 0.6 this trick and then it + + + align:start position:0% +up to about 0.6 this trick and then it +kind of goes up to one + + align:start position:0% +kind of goes up to one + + + align:start position:0% +kind of goes up to one +right it's just a function is that one + + align:start position:0% +right it's just a function is that one + + + align:start position:0% +right it's just a function is that one +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +and and so if it's if z is less than + + align:start position:0% +and and so if it's if z is less than + + + align:start position:0% +and and so if it's if z is less than +than 0.6 then the error function of z + + align:start position:0% +than 0.6 then the error function of z + + + align:start position:0% +than 0.6 then the error function of z +is roughly z + + align:start position:0% +is roughly z + + + align:start position:0% +is roughly z +talk about a valuable + + align:start position:0% +talk about a valuable + + + align:start position:0% +talk about a valuable +thing to learn + + align:start position:0% +thing to learn + + + align:start position:0% +thing to learn +and that saves you a lot of time by the + + align:start position:0% +and that saves you a lot of time by the + + + align:start position:0% +and that saves you a lot of time by the +way yeah but but it's just a function + + align:start position:0% +way yeah but but it's just a function + + + align:start position:0% +way yeah but but it's just a function +and it's it's a solution to fix second + + align:start position:0% +and it's it's a solution to fix second + + + align:start position:0% +and it's it's a solution to fix second +law so again + + align:start position:0% +law so again + + + align:start position:0% +law so again +this is this is uh + + align:start position:0% +this is this is uh + + + align:start position:0% +this is this is uh +uh this is how we solve time dependent + + align:start position:0% +uh this is how we solve time dependent + + + align:start position:0% +uh this is how we solve time dependent +diffusion problems and this is how you + + align:start position:0% +diffusion problems and this is how you + + + align:start position:0% +diffusion problems and this is how you +could solve this one right here and what + + align:start position:0% +could solve this one right here and what + + + align:start position:0% +could solve this one right here and what +i'm gonna do is i'm not going to + + align:start position:0% +i'm gonna do is i'm not going to + + + align:start position:0% +i'm gonna do is i'm not going to +actually solve it i'm going to give you + + align:start position:0% +actually solve it i'm going to give you + + + align:start position:0% +actually solve it i'm going to give you +the answer + + align:start position:0% +the answer + + + align:start position:0% +the answer +to + + align:start position:0% +to + + + align:start position:0% +to +that question + + align:start position:0% +that question + + + align:start position:0% +that question +so the time + + align:start position:0% +so the time + + + align:start position:0% +so the time +is + + align:start position:0% +is + + + align:start position:0% +is +seven hours + + align:start position:0% +seven hours + + + align:start position:0% +seven hours +that's the answer and i'm also going to + + align:start position:0% +that's the answer and i'm also going to + + + align:start position:0% +that's the answer and i'm also going to +leave you with the with oh there's error + + align:start position:0% +leave you with the with oh there's error + + + align:start position:0% +leave you with the with oh there's error +function tables oh + + align:start position:0% +function tables oh + + + align:start position:0% +function tables oh +look at that error function tables + + align:start position:0% +look at that error function tables + + + align:start position:0% +look at that error function tables +and and there's the setup of the problem + + align:start position:0% +and and there's the setup of the problem + + + align:start position:0% +and and there's the setup of the problem +so i'm going to leave you actually with + + align:start position:0% +so i'm going to leave you actually with + + + align:start position:0% +so i'm going to leave you actually with +the sketch of the setup and again you + + align:start position:0% +the sketch of the setup and again you + + + align:start position:0% +the sketch of the setup and again you +know + + align:start position:0% +know + + + align:start position:0% +know +this isn't something + + align:start position:0% +this isn't something + + + align:start position:0% +this isn't something +we'll have on the exam but i want you to + + align:start position:0% +we'll have on the exam but i want you to + + + align:start position:0% +we'll have on the exam but i want you to +have this kind of problem at your at + + align:start position:0% +have this kind of problem at your at + + + align:start position:0% +have this kind of problem at your at +your at your service + + align:start position:0% +your at your service + + + align:start position:0% +your at your service +right so you would have this these are + + align:start position:0% +right so you would have this these are + + + align:start position:0% +right so you would have this these are +all embedded in the question there's + + align:start position:0% +all embedded in the question there's + + + align:start position:0% +all embedded in the question there's +your cs + + align:start position:0% +your cs + + + align:start position:0% +your cs +there's your c naught + + align:start position:0% +there's your c naught + + + align:start position:0% +there's your c naught +right at this distance this is what the + + align:start position:0% +right at this distance this is what the + + + align:start position:0% +right at this distance this is what the +question asks this is the concentration + + align:start position:0% +question asks this is the concentration + + + align:start position:0% +question asks this is the concentration +we want we know we look up the diffusion + + align:start position:0% +we want we know we look up the diffusion + + + align:start position:0% +we want we know we look up the diffusion +of carbon + + align:start position:0% +of carbon + + + align:start position:0% +of carbon +we assume it's not dependent on + + align:start position:0% +we assume it's not dependent on + + + align:start position:0% +we assume it's not dependent on +concentration + + align:start position:0% +concentration + + + align:start position:0% +concentration +that d + + align:start position:0% +that d + + + align:start position:0% +that d +and so we just use a constant and then + + align:start position:0% +and so we just use a constant and then + + + align:start position:0% +and so we just use a constant and then +we plug it in and we get a time you + + align:start position:0% +we plug it in and we get a time you + + + align:start position:0% +we plug it in and we get a time you +better believe that this is really + + align:start position:0% +better believe that this is really + + + align:start position:0% +better believe that this is really +important + + align:start position:0% +important + + + align:start position:0% +important +this is really really important + + align:start position:0% +this is really really important + + + align:start position:0% +this is really really important +this is how we make stuff this is how we + + align:start position:0% +this is how we make stuff this is how we + + + align:start position:0% +this is how we make stuff this is how we +make stuff that we make our world out of + + align:start position:0% +make stuff that we make our world out of + + + align:start position:0% +make stuff that we make our world out of +right and and so so that's the picture i + + align:start position:0% +right and and so so that's the picture i + + + align:start position:0% +right and and so so that's the picture i +showed you + + align:start position:0% +showed you + + + align:start position:0% +showed you +all right and this gets me now to + + align:start position:0% +all right and this gets me now to + + + align:start position:0% +all right and this gets me now to +oh + + align:start position:0% +oh + + + align:start position:0% +oh +our last why this matters + + align:start position:0% +our last why this matters + + + align:start position:0% +our last why this matters +right do i need them all i + + align:start position:0% +right do i need them all i + + + align:start position:0% +right do i need them all i +and i'm doing it on the backdrop of this + + align:start position:0% +and i'm doing it on the backdrop of this + + + align:start position:0% +and i'm doing it on the backdrop of this +beautiful periodic table + + align:start position:0% +beautiful periodic table + + + align:start position:0% +beautiful periodic table +right so so + + align:start position:0% + + + + align:start position:0% + +that's a lot of energy + + align:start position:0% +that's a lot of energy + + + align:start position:0% +that's a lot of energy +by the way + + align:start position:0% +by the way + + + align:start position:0% +by the way +you know first you had to make these + + align:start position:0% +you know first you had to make these + + + align:start position:0% +you know first you had to make these +iron pipes and now you gotta you gotta + + align:start position:0% +iron pipes and now you gotta you gotta + + + align:start position:0% +iron pipes and now you gotta you gotta +case harden them + + align:start position:0% +case harden them + + + align:start position:0% +case harden them +right or maybe you gotta put even more + + align:start position:0% +right or maybe you gotta put even more + + + align:start position:0% +right or maybe you gotta put even more +iron in look at the oven 900c is really + + align:start position:0% +iron in look at the oven 900c is really + + + align:start position:0% +iron in look at the oven 900c is really +hot + + align:start position:0% +hot + + + align:start position:0% +hot +how much energy do we + + align:start position:0% +how much energy do we + + + align:start position:0% +how much energy do we +take to make stuff as simple as + + align:start position:0% +take to make stuff as simple as + + + align:start position:0% +take to make stuff as simple as +as concrete + + align:start position:0% +as concrete + + + align:start position:0% +as concrete +right + + align:start position:0% +right + + + align:start position:0% +right +doesn't it just liquid stone didn't you + + align:start position:0% +doesn't it just liquid stone didn't you + + + align:start position:0% +doesn't it just liquid stone didn't you +just grind some stones down or something + + align:start position:0% +just grind some stones down or something + + + align:start position:0% +just grind some stones down or something +and then pour it out + + align:start position:0% +and then pour it out + + + align:start position:0% +and then pour it out +right + + align:start position:0% +right + + + align:start position:0% +right +actually if you think about concrete and + + align:start position:0% +actually if you think about concrete and + + + align:start position:0% +actually if you think about concrete and +other materials like steel right the use + + align:start position:0% +other materials like steel right the use + + + align:start position:0% +other materials like steel right the use +of them + + align:start position:0% +of them + + + align:start position:0% +of them +is going is skyrocketing + + align:start position:0% +is going is skyrocketing + + + align:start position:0% +is going is skyrocketing +right this is how much we're making + + align:start position:0% +right this is how much we're making + + + align:start position:0% +right this is how much we're making +okay so this uh so look at this the + + align:start position:0% +okay so this uh so look at this the + + + align:start position:0% +okay so this uh so look at this the +millions of tons um there's + + align:start position:0% +millions of tons um there's + + + align:start position:0% +millions of tons um there's +uh let's see there's steel + + align:start position:0% +uh let's see there's steel + + + align:start position:0% +uh let's see there's steel +and there's cement look at that there's + + align:start position:0% +and there's cement look at that there's + + + align:start position:0% +and there's cement look at that there's +the world population right there and + + align:start position:0% +the world population right there and + + + align:start position:0% +the world population right there and +this only runs out this runs out in 29 + + align:start position:0% +this only runs out this runs out in 29 + + + align:start position:0% +this only runs out this runs out in 29 +2010 11 + + align:start position:0% +2010 11 + + + align:start position:0% +2010 11 +but it's continuing + + align:start position:0% +but it's continuing + + + align:start position:0% +but it's continuing +it's continuing + + align:start position:0% +it's continuing + + + align:start position:0% +it's continuing +because + + align:start position:0% +because + + + align:start position:0% +because +because it's not just that the + + align:start position:0% +because it's not just that the + + + align:start position:0% +because it's not just that the +population is growing it's that the + + align:start position:0% +population is growing it's that the + + + align:start position:0% +population is growing it's that the +places that the population is growing + + align:start position:0% +places that the population is growing + + + align:start position:0% +places that the population is growing +the most are also industrializing + + align:start position:0% +the most are also industrializing + + + align:start position:0% +the most are also industrializing +and that means building + + align:start position:0% +and that means building + + + align:start position:0% +and that means building +you go to some of these places and + + align:start position:0% +you go to some of these places and + + + align:start position:0% +you go to some of these places and +there's a new building literally every + + align:start position:0% +there's a new building literally every + + + align:start position:0% +there's a new building literally every +block there's a new building being built + + align:start position:0% +block there's a new building being built + + + align:start position:0% +block there's a new building being built +that takes + + align:start position:0% +that takes + + + align:start position:0% +that takes +that takes + + align:start position:0% +that takes + + + align:start position:0% +that takes +this stuff + + align:start position:0% +this stuff + + + align:start position:0% +this stuff +that takes a lot of ovens + + align:start position:0% +that takes a lot of ovens + + + align:start position:0% +that takes a lot of ovens +and a lot of really high temperatures + + align:start position:0% +and a lot of really high temperatures + + + align:start position:0% +and a lot of really high temperatures +the the + + align:start position:0% +the the + + + align:start position:0% +the the +just the cement alone + + align:start position:0% + + + + align:start position:0% + +is is accounting for seven percent of + + align:start position:0% +is is accounting for seven percent of + + + align:start position:0% +is is accounting for seven percent of +all co2 emissions all co2 emissions on + + align:start position:0% +all co2 emissions all co2 emissions on + + + align:start position:0% +all co2 emissions all co2 emissions on +the planet + + align:start position:0% +the planet + + + align:start position:0% +the planet +seven percent of that goes into simply + + align:start position:0% +seven percent of that goes into simply + + + align:start position:0% +seven percent of that goes into simply +making this liquid this magic liquid + + align:start position:0% +making this liquid this magic liquid + + + align:start position:0% +making this liquid this magic liquid +stone this powder + + align:start position:0% +stone this powder + + + align:start position:0% +stone this powder +and at the core of it what is at the + + align:start position:0% +and at the core of it what is at the + + + align:start position:0% +and at the core of it what is at the +core of it it's chemistry + + align:start position:0% +core of it it's chemistry + + + align:start position:0% +core of it it's chemistry +it's clinker it's called a clinker what + + align:start position:0% +it's clinker it's called a clinker what + + + align:start position:0% +it's clinker it's called a clinker what +is a clinker it's this thing it's simply + + align:start position:0% +is a clinker it's this thing it's simply + + + align:start position:0% +is a clinker it's this thing it's simply +a calcium silicate group + + align:start position:0% +a calcium silicate group + + + align:start position:0% +a calcium silicate group +making that is what takes all this + + align:start position:0% +making that is what takes all this + + + align:start position:0% +making that is what takes all this +energy it takes half of it at least + + align:start position:0% +energy it takes half of it at least + + + align:start position:0% +energy it takes half of it at least +making that right + + align:start position:0% + + + + align:start position:0% + +and and it's it's as always the + + align:start position:0% +and and it's it's as always the + + + align:start position:0% +and and it's it's as always the +chemistry gives us + + align:start position:0% +chemistry gives us + + + align:start position:0% +chemistry gives us +the the chance to get out of our + + align:start position:0% +the the chance to get out of our + + + align:start position:0% +the the chance to get out of our +constrained optimization + + align:start position:0% +constrained optimization + + + align:start position:0% +constrained optimization +right and so so you've got to make this + + align:start position:0% +right and so so you've got to make this + + + align:start position:0% +right and so so you've got to make this +mixture of of different types of + + align:start position:0% +mixture of of different types of + + + align:start position:0% +mixture of of different types of +synthetic rock you've got to make + + align:start position:0% +synthetic rock you've got to make + + + align:start position:0% +synthetic rock you've got to make +mixtures of allied and ballet they have + + align:start position:0% +mixtures of allied and ballet they have + + + align:start position:0% +mixtures of allied and ballet they have +different names + + align:start position:0% + + + + align:start position:0% + +and and and you might be able to make + + align:start position:0% +and and and you might be able to make + + + align:start position:0% +and and and you might be able to make +more bellite which takes less energy you + + align:start position:0% +more bellite which takes less energy you + + + align:start position:0% +more bellite which takes less energy you +can you can cool your oven down by 300 c + + align:start position:0% +can you can cool your oven down by 300 c + + + align:start position:0% +can you can cool your oven down by 300 c +to make bellite compared to allied + + align:start position:0% +to make bellite compared to allied + + + align:start position:0% +to make bellite compared to allied +yeah but then even though it's + + align:start position:0% +yeah but then even though it's + + + align:start position:0% +yeah but then even though it's +structurally okay it takes 90 days to + + align:start position:0% +structurally okay it takes 90 days to + + + align:start position:0% +structurally okay it takes 90 days to +dry + + align:start position:0% +dry + + + align:start position:0% +dry +so you can't do that so you got to spend + + align:start position:0% +so you can't do that so you got to spend + + + align:start position:0% +so you can't do that so you got to spend +the 300 extra uh celsius to make more + + align:start position:0% +the 300 extra uh celsius to make more + + + align:start position:0% +the 300 extra uh celsius to make more +allied why + + align:start position:0% +allied why + + + align:start position:0% +allied why +it's all the count it's in the chemistry + + align:start position:0% +it's all the count it's in the chemistry + + + align:start position:0% +it's all the count it's in the chemistry +right it's in the chemistry + + align:start position:0% +right it's in the chemistry + + + align:start position:0% +right it's in the chemistry +and and and understanding + + align:start position:0% +and and and understanding + + + align:start position:0% +and and and understanding +what seems like not a very interesting + + align:start position:0% +what seems like not a very interesting + + + align:start position:0% +what seems like not a very interesting +you know cement is it really that + + align:start position:0% +you know cement is it really that + + + align:start position:0% +you know cement is it really that +interesting you bet it is + + align:start position:0% +interesting you bet it is + + + align:start position:0% +interesting you bet it is +seven percent + + align:start position:0% +seven percent + + + align:start position:0% +seven percent +of all co2 emissions it's just making + + align:start position:0% +of all co2 emissions it's just making + + + align:start position:0% +of all co2 emissions it's just making +this one material + + align:start position:0% +this one material + + + align:start position:0% +this one material +and we're making a lot of it + + align:start position:0% +and we're making a lot of it + + + align:start position:0% +and we're making a lot of it +we're making a lot of it there's a tower + + align:start position:0% +we're making a lot of it there's a tower + + + align:start position:0% +we're making a lot of it there's a tower +164 tower in dubai that opened in 2010 + + align:start position:0% +164 tower in dubai that opened in 2010 + + + align:start position:0% +164 tower in dubai that opened in 2010 +that took a billion + + align:start position:0% +that took a billion + + + align:start position:0% +that took a billion +kilograms + + align:start position:0% +kilograms + + + align:start position:0% +kilograms +of this stuff + + align:start position:0% +of this stuff + + + align:start position:0% +of this stuff +right + + align:start position:0% +right + + + align:start position:0% +right +so um now this makes a lot of co2 and + + align:start position:0% +so um now this makes a lot of co2 and + + + align:start position:0% +so um now this makes a lot of co2 and +i've talked about co2 throughout the + + align:start position:0% +i've talked about co2 throughout the + + + align:start position:0% +i've talked about co2 throughout the +semester right and and so + + align:start position:0% +semester right and and so + + + align:start position:0% +semester right and and so +so one thing i wanted to leave you with + + align:start position:0% +so one thing i wanted to leave you with + + + align:start position:0% +so one thing i wanted to leave you with +was also some things that we're doing + + align:start position:0% +was also some things that we're doing + + + align:start position:0% +was also some things that we're doing +about it what do we do about co2 + + align:start position:0% +about it what do we do about co2 + + + align:start position:0% +about it what do we do about co2 +so how is carbon capture and + + align:start position:0% +so how is carbon capture and + + + align:start position:0% +so how is carbon capture and +sequestration going + + align:start position:0% +sequestration going + + + align:start position:0% +sequestration going +right could we take it all out + + align:start position:0% +right could we take it all out + + + align:start position:0% +right could we take it all out +we put it in could we take it out + + align:start position:0% +we put it in could we take it out + + + align:start position:0% +we put it in could we take it out +um and so i'll share a couple of things + + align:start position:0% +um and so i'll share a couple of things + + + align:start position:0% +um and so i'll share a couple of things +so you know one of the problems with co2 + + align:start position:0% +so you know one of the problems with co2 + + + align:start position:0% +so you know one of the problems with co2 +capture + + align:start position:0% +capture + + + align:start position:0% +capture +is that if you don't do it right where + + align:start position:0% +is that if you don't do it right where + + + align:start position:0% +is that if you don't do it right where +you make it + + align:start position:0% +you make it + + + align:start position:0% +you make it +then you have to transport it and it + + align:start position:0% +then you have to transport it and it + + + align:start position:0% +then you have to transport it and it +turns out that's actually really it's + + align:start position:0% +turns out that's actually really it's + + + align:start position:0% +turns out that's actually really it's +really hard to transport co2 and there's + + align:start position:0% +really hard to transport co2 and there's + + + align:start position:0% +really hard to transport co2 and there's +a lot of problems that have happened + + align:start position:0% +a lot of problems that have happened + + + align:start position:0% +a lot of problems that have happened +over the years in the 80s uh there was a + + align:start position:0% +over the years in the 80s uh there was a + + + align:start position:0% +over the years in the 80s uh there was a +leak that killed thousands of people um + + align:start position:0% +leak that killed thousands of people um + + + align:start position:0% +leak that killed thousands of people um +there have been massive leaks in in + + align:start position:0% +there have been massive leaks in in + + + align:start position:0% +there have been massive leaks in in +canada in transporting this material so + + align:start position:0% +canada in transporting this material so + + + align:start position:0% +canada in transporting this material so +transporting is actually really hard to + + align:start position:0% +transporting is actually really hard to + + + align:start position:0% +transporting is actually really hard to +do + + align:start position:0% +do + + + align:start position:0% +do +um + + align:start position:0% +um + + + align:start position:0% +um +there's metal pipe corrosion this is a + + align:start position:0% +there's metal pipe corrosion this is a + + + align:start position:0% +there's metal pipe corrosion this is a +great chemistry problem + + align:start position:0% +great chemistry problem + + + align:start position:0% +great chemistry problem +unsolved um and and then + + align:start position:0% +unsolved um and and then + + + align:start position:0% +unsolved um and and then +the next part of co2 sequestration so + + align:start position:0% +the next part of co2 sequestration so + + + align:start position:0% +the next part of co2 sequestration so +one is transporting it that's + + align:start position:0% +one is transporting it that's + + + align:start position:0% +one is transporting it that's +challenging and the other is storing it + + align:start position:0% +challenging and the other is storing it + + + align:start position:0% +challenging and the other is storing it +what do you do with it let's suppose we + + align:start position:0% +what do you do with it let's suppose we + + + align:start position:0% +what do you do with it let's suppose we +could capture it + + align:start position:0% +could capture it + + + align:start position:0% +could capture it +well then what + + align:start position:0% +well then what + + + align:start position:0% +well then what +and and there's there's ideas around + + align:start position:0% +and and there's there's ideas around + + + align:start position:0% +and and there's there's ideas around +this right so you could pump it maybe + + align:start position:0% +this right so you could pump it maybe + + + align:start position:0% +this right so you could pump it maybe +underground geosequestration maybe that + + align:start position:0% +underground geosequestration maybe that + + + align:start position:0% +underground geosequestration maybe that +that that's + + align:start position:0% +that that's + + + align:start position:0% +that that's +that's not a sure thing we don't know we + + align:start position:0% +that's not a sure thing we don't know we + + + align:start position:0% +that's not a sure thing we don't know we +don't understand at those scales exactly + + align:start position:0% +don't understand at those scales exactly + + + align:start position:0% +don't understand at those scales exactly +how well we can encase this material and + + align:start position:0% +how well we can encase this material and + + + align:start position:0% +how well we can encase this material and +how long it will last there's a lot of + + align:start position:0% +how long it will last there's a lot of + + + align:start position:0% +how long it will last there's a lot of +questions with that there's a whole line + + align:start position:0% +questions with that there's a whole line + + + align:start position:0% +questions with that there's a whole line +of thinking + + align:start position:0% +of thinking + + + align:start position:0% +of thinking +on putting it in the ocean + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +really + + align:start position:0% +really + + + align:start position:0% +really +so so you want to + + align:start position:0% +so so you want to + + + align:start position:0% +so so you want to +fix the co2 problem by by acidifying the + + align:start position:0% +fix the co2 problem by by acidifying the + + + align:start position:0% +fix the co2 problem by by acidifying the +oceans even faster + + align:start position:0% +oceans even faster + + + align:start position:0% +oceans even faster +okay + + align:start position:0% +okay + + + align:start position:0% +okay +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +right + + align:start position:0% +right + + + align:start position:0% +right +um um so so so so transport and + + align:start position:0% +um um so so so so transport and + + + align:start position:0% +um um so so so so transport and +sequestration is is a big problem but + + align:start position:0% +sequestration is is a big problem but + + + align:start position:0% +sequestration is is a big problem but +what about technologies where you simply + + align:start position:0% +what about technologies where you simply + + + align:start position:0% +what about technologies where you simply +sequester it right there where you make + + align:start position:0% +sequester it right there where you make + + + align:start position:0% +sequester it right there where you make +it like clean coal + + align:start position:0% +it like clean coal + + + align:start position:0% +it like clean coal +right you might have heard of clean coal + + align:start position:0% +right you might have heard of clean coal + + + align:start position:0% +right you might have heard of clean coal +right so clean coal so so i'm going to + + align:start position:0% +right so clean coal so so i'm going to + + + align:start position:0% +right so clean coal so so i'm going to +look at a case study of a clean coal + + align:start position:0% +look at a case study of a clean coal + + + align:start position:0% +look at a case study of a clean coal +project in the u.s in 2005 i got really + + align:start position:0% +project in the u.s in 2005 i got really + + + align:start position:0% +project in the u.s in 2005 i got really +excited because eight companies joined + + align:start position:0% +excited because eight companies joined + + + align:start position:0% +excited because eight companies joined +and it was called futuregen and the us + + align:start position:0% +and it was called futuregen and the us + + + align:start position:0% +and it was called futuregen and the us +government was going to put a lot of + + align:start position:0% +government was going to put a lot of + + + align:start position:0% +government was going to put a lot of +money into it they were going to capture + + align:start position:0% +money into it they were going to capture + + + align:start position:0% +money into it they were going to capture +90 of the co2 you get a little bit less + + align:start position:0% +90 of the co2 you get a little bit less + + + align:start position:0% +90 of the co2 you get a little bit less +efficiency depending on how you think + + align:start position:0% +efficiency depending on how you think + + + align:start position:0% +efficiency depending on how you think +about it it could be 30 percent less + + align:start position:0% +about it it could be 30 percent less + + + align:start position:0% +about it it could be 30 percent less +efficiency i mean less power out of the + + align:start position:0% +efficiency i mean less power out of the + + + align:start position:0% +efficiency i mean less power out of the +plant but you sequester the co2 + + align:start position:0% +plant but you sequester the co2 + + + align:start position:0% +plant but you sequester the co2 +and in 2009 construction was planned in + + align:start position:0% +and in 2009 construction was planned in + + + align:start position:0% +and in 2009 construction was planned in +illinois in 2010 it was canceled in 2010 + + align:start position:0% +illinois in 2010 it was canceled in 2010 + + + align:start position:0% +illinois in 2010 it was canceled in 2010 +it was restarted in 2012 um + + align:start position:0% +it was restarted in 2012 um + + + align:start position:0% +it was restarted in 2012 um +there was all sorts of uh of discussions + + align:start position:0% +there was all sorts of uh of discussions + + + align:start position:0% +there was all sorts of uh of discussions +with the doe that agreed to pay 1.1 + + align:start position:0% +with the doe that agreed to pay 1.1 + + + align:start position:0% +with the doe that agreed to pay 1.1 +billion dollars + + align:start position:0% +billion dollars + + + align:start position:0% +billion dollars +it was all located and then the + + align:start position:0% +it was all located and then the + + + align:start position:0% +it was all located and then the +companies dropped out and the doe + + align:start position:0% +companies dropped out and the doe + + + align:start position:0% +companies dropped out and the doe +canceled the project so that was 10 + + align:start position:0% +canceled the project so that was 10 + + + align:start position:0% +canceled the project so that was 10 +years 10 years and 200 million dollars + + align:start position:0% +years 10 years and 200 million dollars + + + align:start position:0% +years 10 years and 200 million dollars +of taxpayer dollars and absolutely + + align:start position:0% +of taxpayer dollars and absolutely + + + align:start position:0% +of taxpayer dollars and absolutely +nothing has come out of it um so so one + + align:start position:0% +nothing has come out of it um so so one + + + align:start position:0% +nothing has come out of it um so so one +of the you know the things i want to + + align:start position:0% +of the you know the things i want to + + + align:start position:0% +of the you know the things i want to +point out about this direction + + align:start position:0% +point out about this direction + + + align:start position:0% +point out about this direction +and i'm not saying that it's it's not a + + align:start position:0% +and i'm not saying that it's it's not a + + + align:start position:0% +and i'm not saying that it's it's not a +good direction to keep pursuing + + align:start position:0% +good direction to keep pursuing + + + align:start position:0% +good direction to keep pursuing +but the time scales are long + + align:start position:0% +but the time scales are long + + + align:start position:0% +but the time scales are long +so we need to be able to make decisions + + align:start position:0% +so we need to be able to make decisions + + + align:start position:0% +so we need to be able to make decisions +that can cover longer time scales that's + + align:start position:0% +that can cover longer time scales that's + + + align:start position:0% +that can cover longer time scales that's +a huge part of the challenge with this + + align:start position:0% +a huge part of the challenge with this + + + align:start position:0% +a huge part of the challenge with this +it's a policy challenge as much as it is + + align:start position:0% +it's a policy challenge as much as it is + + + align:start position:0% +it's a policy challenge as much as it is +a technical one um + + align:start position:0% +a technical one um + + + align:start position:0% +a technical one um +there is and tying this back + + align:start position:0% +there is and tying this back + + + align:start position:0% +there is and tying this back +to the cement + + align:start position:0% +to the cement + + + align:start position:0% +to the cement +um + + align:start position:0% +um + + + align:start position:0% +um +there is some really interesting + + align:start position:0% +there is some really interesting + + + align:start position:0% +there is some really interesting +research + + align:start position:0% +research + + + align:start position:0% +research +that's going on + + align:start position:0% +that's going on + + + align:start position:0% +that's going on +in actually instead of okay so you've + + align:start position:0% +in actually instead of okay so you've + + + align:start position:0% +in actually instead of okay so you've +got the co2 it comes out when you make + + align:start position:0% +got the co2 it comes out when you make + + + align:start position:0% +got the co2 it comes out when you make +it because the ovens and you're burning + + align:start position:0% +it because the ovens and you're burning + + + align:start position:0% +it because the ovens and you're burning +stuff and and but what if you could take + + align:start position:0% +stuff and and but what if you could take + + + align:start position:0% +stuff and and but what if you could take +that co2 and just put it into the thing + + align:start position:0% +that co2 and just put it into the thing + + + align:start position:0% +that co2 and just put it into the thing +you're making + + align:start position:0% +you're making + + + align:start position:0% +you're making +and and by the way if you're if what + + align:start position:0% +and and by the way if you're if what + + + align:start position:0% +and and by the way if you're if what +you're making is a huge scale like + + align:start position:0% +you're making is a huge scale like + + + align:start position:0% +you're making is a huge scale like +cement + + align:start position:0% +cement + + + align:start position:0% +cement +then maybe you could put a lot of it in + + align:start position:0% +then maybe you could put a lot of it in + + + align:start position:0% +then maybe you could put a lot of it in +right and maybe that could have a real + + align:start position:0% +right and maybe that could have a real + + + align:start position:0% +right and maybe that could have a real +global impact so there's a lot of + + align:start position:0% +global impact so there's a lot of + + + align:start position:0% +global impact so there's a lot of +interest in uh + + align:start position:0% +interest in uh + + + align:start position:0% +interest in uh +substantial okay so here substantial + + align:start position:0% +substantial okay so here substantial + + + align:start position:0% +substantial okay so here substantial +global carbon uptake by cement + + align:start position:0% +global carbon uptake by cement + + + align:start position:0% +global carbon uptake by cement +carbonation so maybe you could get some + + align:start position:0% +carbonation so maybe you could get some + + + align:start position:0% +carbonation so maybe you could get some +of it in the cement i like this paper + + align:start position:0% +of it in the cement i like this paper + + + align:start position:0% +of it in the cement i like this paper +i'm pointing it out because + + align:start position:0% +i'm pointing it out because + + + align:start position:0% +i'm pointing it out because +they say that they use fixed diffusion + + align:start position:0% +they say that they use fixed diffusion + + + align:start position:0% +they say that they use fixed diffusion +law + + align:start position:0% +law + + + align:start position:0% +law +they modeled the carbon uptake by + + align:start position:0% +they modeled the carbon uptake by + + + align:start position:0% +they modeled the carbon uptake by +applying fixed diffusion law yeah + + align:start position:0% +applying fixed diffusion law yeah + + + align:start position:0% +applying fixed diffusion law yeah +it actually matters + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +you can do this too now + + align:start position:0% +you can do this too now + + + align:start position:0% +you can do this too now +and just a few weeks ago on cnn there + + align:start position:0% +and just a few weeks ago on cnn there + + + align:start position:0% +and just a few weeks ago on cnn there +was no this concrete yes concrete is + + align:start position:0% +was no this concrete yes concrete is + + + align:start position:0% +was no this concrete yes concrete is +going high-tech why because this company + + align:start position:0% +going high-tech why because this company + + + align:start position:0% +going high-tech why because this company +has managed to figure out how to put a + + align:start position:0% +has managed to figure out how to put a + + + align:start position:0% +has managed to figure out how to put a +bunch of co2 into the concrete while + + align:start position:0% +bunch of co2 into the concrete while + + + align:start position:0% +bunch of co2 into the concrete while +they make it and it doesn't change the + + align:start position:0% +they make it and it doesn't change the + + + align:start position:0% +they make it and it doesn't change the +mechanical integrity of the concrete + + align:start position:0% +mechanical integrity of the concrete + + + align:start position:0% +mechanical integrity of the concrete +and it's in there it's actually in there + + align:start position:0% +and it's in there it's actually in there + + + align:start position:0% +and it's in there it's actually in there +right this is all chemistry + + align:start position:0% +right this is all chemistry + + + align:start position:0% +right this is all chemistry +this is all chemistry so this is i think + + align:start position:0% +this is all chemistry so this is i think + + + align:start position:0% +this is all chemistry so this is i think +another very interesting direction + + align:start position:0% +another very interesting direction + + + align:start position:0% +another very interesting direction +uh where technology can play a vital + + align:start position:0% +uh where technology can play a vital + + + align:start position:0% +uh where technology can play a vital +role in in this particular global + + align:start position:0% +role in in this particular global + + + align:start position:0% +role in in this particular global +challenge + + align:start position:0% +challenge + + + align:start position:0% +challenge +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and now + + align:start position:0% +and now + + + align:start position:0% +and now +oh + + align:start position:0% +oh + + + align:start position:0% +oh +i'm putting the chalk down + + align:start position:0% +i'm putting the chalk down + + + align:start position:0% +i'm putting the chalk down +and i come to the conclusion i can't + + align:start position:0% +and i come to the conclusion i can't + + + align:start position:0% +and i come to the conclusion i can't +look there i'm going to get sad you're + + align:start position:0% +look there i'm going to get sad you're + + + align:start position:0% +look there i'm going to get sad you're +making me i + + align:start position:0% + + + + align:start position:0% + +the first thing about this that i got to + + align:start position:0% +the first thing about this that i got to + + + align:start position:0% +the first thing about this that i got to +do + + align:start position:0% +do + + + align:start position:0% +do +is i got to think + + align:start position:0% +is i got to think + + + align:start position:0% +is i got to think +i got to thank people + + align:start position:0% +i got to thank people + + + align:start position:0% +i got to thank people +at first i got to thank the concepts + + align:start position:0% +at first i got to thank the concepts + + + align:start position:0% +at first i got to thank the concepts +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +you got to thank the material + + align:start position:0% +you got to thank the material + + + align:start position:0% +you got to thank the material +this is what we have talked about all + + align:start position:0% +this is what we have talked about all + + + align:start position:0% +this is what we have talked about all +semester + + align:start position:0% +semester + + + align:start position:0% +semester +this is what we have learned + + align:start position:0% +this is what we have learned + + + align:start position:0% +this is what we have learned +this is + + align:start position:0% +this is + + + align:start position:0% +this is +this is underneath the hood + + align:start position:0% +this is underneath the hood + + + align:start position:0% +this is underneath the hood +of so much and i hope that i've conveyed + + align:start position:0% +of so much and i hope that i've conveyed + + + align:start position:0% +of so much and i hope that i've conveyed +that to you + + align:start position:0% +that to you + + + align:start position:0% +that to you +this is a starting point for so much + + align:start position:0% +this is a starting point for so much + + + align:start position:0% +this is a starting point for so much +right what have we learned well we've + + align:start position:0% +right what have we learned well we've + + + align:start position:0% +right what have we learned well we've +learned how to go back and forth this is + + align:start position:0% +learned how to go back and forth this is + + + align:start position:0% +learned how to go back and forth this is +what i showed you on day one and now + + align:start position:0% +what i showed you on day one and now + + + align:start position:0% +what i showed you on day one and now +what have we done we have filled this + + align:start position:0% +what have we done we have filled this + + + align:start position:0% +what have we done we have filled this +out we filled it out with balancing + + align:start position:0% +out we filled it out with balancing + + + align:start position:0% +out we filled it out with balancing +reactions we filled it out with the + + align:start position:0% +reactions we filled it out with the + + + align:start position:0% +reactions we filled it out with the +periodic table that one + + align:start position:0% +periodic table that one + + + align:start position:0% +periodic table that one +we filled it out with electrons bore + + align:start position:0% +we filled it out with electrons bore + + + align:start position:0% +we filled it out with electrons bore +model schrodinger atomic orbitals + + align:start position:0% +model schrodinger atomic orbitals + + + align:start position:0% +model schrodinger atomic orbitals +molecular orbitals ionic solids lewis + + align:start position:0% +molecular orbitals ionic solids lewis + + + align:start position:0% +molecular orbitals ionic solids lewis +dots vesper van der waals london h-bonds + + align:start position:0% +dots vesper van der waals london h-bonds + + + align:start position:0% +dots vesper van der waals london h-bonds +all sorts of intermolecular forces + + align:start position:0% +all sorts of intermolecular forces + + + align:start position:0% +all sorts of intermolecular forces +metallic bonds semiconductors bands + + align:start position:0% +metallic bonds semiconductors bands + + + align:start position:0% +metallic bonds semiconductors bands +crystal symmetry lattices planes x-rays + + align:start position:0% +crystal symmetry lattices planes x-rays + + + align:start position:0% +crystal symmetry lattices planes x-rays +x-ray diffraction defects amorphous + + align:start position:0% +x-ray diffraction defects amorphous + + + align:start position:0% +x-ray diffraction defects amorphous +glassy materials reaction rates rate + + align:start position:0% +glassy materials reaction rates rate + + + align:start position:0% +glassy materials reaction rates rate +laws diffusion solubility uranius acids + + align:start position:0% +laws diffusion solubility uranius acids + + + align:start position:0% +laws diffusion solubility uranius acids +and bases polymers and their properties + + align:start position:0% + + + + align:start position:0% + +that's you guys + + align:start position:0% + + + + align:start position:0% + +that's you guys that have learned that + + align:start position:0% +that's you guys that have learned that + + + align:start position:0% +that's you guys that have learned that +material + + align:start position:0% + + + + align:start position:0% + +i it blows me away + + align:start position:0% +i it blows me away + + + align:start position:0% +i it blows me away +that's a lot of stuff and we've learned + + align:start position:0% +that's a lot of stuff and we've learned + + + align:start position:0% +that's a lot of stuff and we've learned +it all and we've we've we've integrated + + align:start position:0% +it all and we've we've we've integrated + + + align:start position:0% +it all and we've we've we've integrated +it into our lives + + align:start position:0% +it into our lives + + + align:start position:0% +it into our lives +but you couldn't have learned any of + + align:start position:0% +but you couldn't have learned any of + + + align:start position:0% +but you couldn't have learned any of +this we couldn't have done any of this + + align:start position:0% +this we couldn't have done any of this + + + align:start position:0% +this we couldn't have done any of this +without + + align:start position:0% +without + + + align:start position:0% +without +some people + + align:start position:0% +some people + + + align:start position:0% +some people +so now we thank the subjects we thank + + align:start position:0% +so now we thank the subjects we thank + + + align:start position:0% +so now we thank the subjects we thank +the people laura would you stand up + + align:start position:0% +the people laura would you stand up + + + align:start position:0% +the people laura would you stand up +please because + + align:start position:0% + + + + align:start position:0% + +many of you have interacted with laura + + align:start position:0% +many of you have interacted with laura + + + align:start position:0% +many of you have interacted with laura +and you know and now sometimes you might + + align:start position:0% +and you know and now sometimes you might + + + align:start position:0% +and you know and now sometimes you might +get a short answer you might get a not a + + align:start position:0% +get a short answer you might get a not a + + + align:start position:0% +get a short answer you might get a not a +short answer + + align:start position:0% +short answer + + + align:start position:0% +short answer +because but why is that it's because + + align:start position:0% +because but why is that it's because + + + align:start position:0% +because but why is that it's because +laura cares + + align:start position:0% +laura cares + + + align:start position:0% +laura cares +deeply + + align:start position:0% +deeply + + + align:start position:0% +deeply +deeply about you all and about your + + align:start position:0% +deeply about you all and about your + + + align:start position:0% +deeply about you all and about your +learning and your experience in this + + align:start position:0% +learning and your experience in this + + + align:start position:0% +learning and your experience in this +class and at mit she cares deeply and + + align:start position:0% +class and at mit she cares deeply and + + + align:start position:0% +class and at mit she cares deeply and +that's the kind of thing that makes this + + align:start position:0% +that's the kind of thing that makes this + + + align:start position:0% +that's the kind of thing that makes this +class what it is we wouldn't have any + + align:start position:0% +class what it is we wouldn't have any + + + align:start position:0% +class what it is we wouldn't have any +shot at it without laura um so laura + + align:start position:0% +shot at it without laura um so laura + + + align:start position:0% +shot at it without laura um so laura +thank you uh very much you know it's + + align:start position:0% +thank you uh very much you know it's + + + align:start position:0% +thank you uh very much you know it's +sort of like there's like when you drop + + align:start position:0% +sort of like there's like when you drop + + + align:start position:0% +sort of like there's like when you drop +your kids off at if they go to sleep way + + align:start position:0% +your kids off at if they go to sleep way + + + align:start position:0% +your kids off at if they go to sleep way +camp there's like the camp parent you + + align:start position:0% +camp there's like the camp parent you + + + align:start position:0% +camp there's like the camp parent you +know who makes sure that your kids it's + + align:start position:0% +know who makes sure that your kids it's + + + align:start position:0% +know who makes sure that your kids it's +like they make sure that your kids will + + align:start position:0% +like they make sure that your kids will + + + align:start position:0% +like they make sure that your kids will +you know + + align:start position:0% +you know + + + align:start position:0% +you know +brush their teeth get to bed uh have a + + align:start position:0% +brush their teeth get to bed uh have a + + + align:start position:0% +brush their teeth get to bed uh have a +plate you know have a blanket and and + + align:start position:0% +plate you know have a blanket and and + + + align:start position:0% +plate you know have a blanket and and +they check in on your kids all the time + + align:start position:0% +they check in on your kids all the time + + + align:start position:0% +they check in on your kids all the time +and i feel like you know + + align:start position:0% +and i feel like you know + + + align:start position:0% +and i feel like you know +we have that for this class + + align:start position:0% +we have that for this class + + + align:start position:0% +we have that for this class +it's laura + + align:start position:0% +it's laura + + + align:start position:0% +it's laura +so thank you laura but now okay now the + + align:start position:0% +so thank you laura but now okay now the + + + align:start position:0% +so thank you laura but now okay now the +thing is now the other now i introduce + + align:start position:0% +thing is now the other now i introduce + + + align:start position:0% +thing is now the other now i introduce +these people to you + + align:start position:0% +these people to you + + + align:start position:0% +these people to you +isaac i still don't have your picture + + align:start position:0% +isaac i still don't have your picture + + + align:start position:0% +isaac i still don't have your picture +but um + + align:start position:0% +but um + + + align:start position:0% +but um +can the tas please stand up + + align:start position:0% +can the tas please stand up + + + align:start position:0% +can the tas please stand up +can the ta stand up come on + + align:start position:0% + + + + align:start position:0% + +thank you + + align:start position:0% + + + + align:start position:0% + +thank you thank you + + align:start position:0% + + + + align:start position:0% + +i am so incredibly lucky + + align:start position:0% +i am so incredibly lucky + + + align:start position:0% +i am so incredibly lucky +to have this + + align:start position:0% +to have this + + + align:start position:0% +to have this +quality people this quality of staff + + align:start position:0% +quality people this quality of staff + + + align:start position:0% +quality people this quality of staff +these these + + align:start position:0% +these these + + + align:start position:0% +these these +kind caring passionate amazing people as + + align:start position:0% +kind caring passionate amazing people as + + + align:start position:0% +kind caring passionate amazing people as +our tas for this class + + align:start position:0% +our tas for this class + + + align:start position:0% +our tas for this class +and and i have i have i am so lucky i + + align:start position:0% +and and i have i have i am so lucky i + + + align:start position:0% +and and i have i have i am so lucky i +get to meet with them every week + + align:start position:0% +get to meet with them every week + + + align:start position:0% +get to meet with them every week +to talk about you guys + + align:start position:0% +to talk about you guys + + + align:start position:0% +to talk about you guys +it's always good don't worry + + align:start position:0% +it's always good don't worry + + + align:start position:0% +it's always good don't worry +it's always good + + align:start position:0% +it's always good + + + align:start position:0% +it's always good +um and and interact even much more than + + align:start position:0% +um and and interact even much more than + + + align:start position:0% +um and and interact even much more than +that about education about teaching + + align:start position:0% +that about education about teaching + + + align:start position:0% +that about education about teaching +about how to make this + + align:start position:0% +about how to make this + + + align:start position:0% +about how to make this +uh + + align:start position:0% +uh + + + align:start position:0% +uh +a fantastic experience for all of you + + align:start position:0% +a fantastic experience for all of you + + + align:start position:0% +a fantastic experience for all of you +so thanks to the tas and then that's why + + align:start position:0% +so thanks to the tas and then that's why + + + align:start position:0% +so thanks to the tas and then that's why +i want the tas to um + + align:start position:0% +i want the tas to um + + + align:start position:0% +i want the tas to um +to throw the t-shirts out and we'll do + + align:start position:0% +to throw the t-shirts out and we'll do + + + align:start position:0% +to throw the t-shirts out and we'll do +that in a minute um what a couple + + align:start position:0% +that in a minute um what a couple + + + align:start position:0% +that in a minute um what a couple +minutes no i one yeah and uh but now + + align:start position:0% +minutes no i one yeah and uh but now + + + align:start position:0% +minutes no i one yeah and uh but now +okay but see it's the tas that have been + + align:start position:0% +okay but see it's the tas that have been + + + align:start position:0% +okay but see it's the tas that have been +here for you + + align:start position:0% +here for you + + + align:start position:0% +here for you +but it's also you all there's you + + align:start position:0% +but it's also you all there's you + + + align:start position:0% +but it's also you all there's you +so right + + align:start position:0% +so right + + + align:start position:0% +so right +oh it's you all that have been here for + + align:start position:0% +oh it's you all that have been here for + + + align:start position:0% +oh it's you all that have been here for +each other + + align:start position:0% +each other + + + align:start position:0% +each other +and so and so i i see it because i talk + + align:start position:0% +and so and so i i see it because i talk + + + align:start position:0% +and so and so i i see it because i talk +to some of you i don't talk to all of + + align:start position:0% +to some of you i don't talk to all of + + + align:start position:0% +to some of you i don't talk to all of +you but i see the community that forms + + align:start position:0% +you but i see the community that forms + + + align:start position:0% +you but i see the community that forms +and i am very appreciative that and i'd + + align:start position:0% +and i am very appreciative that and i'd + + + align:start position:0% +and i am very appreciative that and i'd +like you to be appreciate that so let's + + align:start position:0% +like you to be appreciate that so let's + + + align:start position:0% +like you to be appreciate that so let's +thank each other here for just a minute + + align:start position:0% +thank each other here for just a minute + + + align:start position:0% +thank each other here for just a minute +it's really pretty + + align:start position:0% +it's really pretty + + + align:start position:0% +it's really pretty +i + + align:start position:0% + + + + align:start position:0% + +this is actually getting me revved up a + + align:start position:0% +this is actually getting me revved up a + + + align:start position:0% +this is actually getting me revved up a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +okay now i skipped over i wanna that the + + align:start position:0% +okay now i skipped over i wanna that the + + + align:start position:0% +okay now i skipped over i wanna that the +goodie bags are amazing and so i'm + + align:start position:0% +goodie bags are amazing and so i'm + + + align:start position:0% +goodie bags are amazing and so i'm +thankful to the goody bags and to the + + align:start position:0% +thankful to the goody bags and to the + + + align:start position:0% +thankful to the goody bags and to the +department if anyone's hearing from the + + align:start position:0% +department if anyone's hearing from the + + + align:start position:0% +department if anyone's hearing from the +department for helping us support these + + align:start position:0% +department for helping us support these + + + align:start position:0% +department for helping us support these +goodie bags thank you + + align:start position:0% + + + + align:start position:0% + +thank you + + align:start position:0% +thank you + + + align:start position:0% +thank you +okay yeah thank you yeah that's good + + align:start position:0% +okay yeah thank you yeah that's good + + + align:start position:0% +okay yeah thank you yeah that's good +okay so so i'm i'm very grateful uh to + + align:start position:0% +okay so so i'm i'm very grateful uh to + + + align:start position:0% +okay so so i'm i'm very grateful uh to +that i'm grateful to all of you and and + + align:start position:0% +that i'm grateful to all of you and and + + + align:start position:0% +that i'm grateful to all of you and and +you know last um + + align:start position:0% +you know last um + + + align:start position:0% +you know last um +but not + + align:start position:0% +but not + + + align:start position:0% +but not +i guess just last + + align:start position:0% +i guess just last + + + align:start position:0% +i guess just last +i am thankful to harvard + + align:start position:0% +i am thankful to harvard + + + align:start position:0% +i am thankful to harvard +i was going to say something else but um + + align:start position:0% + + + + align:start position:0% + +anyway i'm thankful to all of these uh + + align:start position:0% +anyway i'm thankful to all of these uh + + + align:start position:0% +anyway i'm thankful to all of these uh +resources that we have used + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and and now okay so + + align:start position:0% +and and now okay so + + + align:start position:0% +and and now okay so +i'm i'm gonna give you some some closing + + align:start position:0% +i'm i'm gonna give you some some closing + + + align:start position:0% +i'm i'm gonna give you some some closing +comments + + align:start position:0% +comments + + + align:start position:0% +comments +i started this semester off in the first + + align:start position:0% +i started this semester off in the first + + + align:start position:0% +i started this semester off in the first +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +and um + + align:start position:0% +and um + + + align:start position:0% +and um +and i asked you all a question + + align:start position:0% +and i asked you all a question + + + align:start position:0% +and i asked you all a question +and the question was why are you here + + align:start position:0% +and the question was why are you here + + + align:start position:0% +and the question was why are you here +right + + align:start position:0% +right + + + align:start position:0% +right +i said like you know really really + + align:start position:0% +i said like you know really really + + + align:start position:0% +i said like you know really really +really why are you here + + align:start position:0% +really why are you here + + + align:start position:0% +really why are you here +why did you come to mit and i asked you + + align:start position:0% +why did you come to mit and i asked you + + + align:start position:0% +why did you come to mit and i asked you +you know did you come here + + align:start position:0% +you know did you come here + + + align:start position:0% +you know did you come here +so you can just phone it in + + align:start position:0% +so you can just phone it in + + + align:start position:0% +so you can just phone it in +get a stamp in four years and go out + + align:start position:0% +get a stamp in four years and go out + + + align:start position:0% +get a stamp in four years and go out +right did you come here so you can walk + + align:start position:0% +right did you come here so you can walk + + + align:start position:0% +right did you come here so you can walk +around some place of privilege and look + + align:start position:0% +around some place of privilege and look + + + align:start position:0% +around some place of privilege and look +down on other people + + align:start position:0% +down on other people + + + align:start position:0% +down on other people +that is not why you're here + + align:start position:0% +that is not why you're here + + + align:start position:0% +that is not why you're here +that is not why you came to mit + + align:start position:0% +that is not why you came to mit + + + align:start position:0% +that is not why you came to mit +right you came to mit because + + align:start position:0% +right you came to mit because + + + align:start position:0% +right you came to mit because +you know that this is where we will make + + align:start position:0% +you know that this is where we will make + + + align:start position:0% +you know that this is where we will make +the transition + + align:start position:0% +the transition + + + align:start position:0% +the transition +from being able to answer any question + + align:start position:0% +from being able to answer any question + + + align:start position:0% +from being able to answer any question +to knowing which question to ask that's + + align:start position:0% +to knowing which question to ask that's + + + align:start position:0% +to knowing which question to ask that's +the transition from student to scholar + + align:start position:0% +the transition from student to scholar + + + align:start position:0% +the transition from student to scholar +and and you know that you came here + + align:start position:0% +and and you know that you came here + + + align:start position:0% +and and you know that you came here +because you have a passion + + align:start position:0% +because you have a passion + + + align:start position:0% +because you have a passion +and and you want to come to a place + + align:start position:0% +and and you want to come to a place + + + align:start position:0% +and and you want to come to a place +where you can take that passion and you + + align:start position:0% +where you can take that passion and you + + + align:start position:0% +where you can take that passion and you +can try to solve really hard problems + + align:start position:0% +can try to solve really hard problems + + + align:start position:0% +can try to solve really hard problems +together to make the world a better + + align:start position:0% +together to make the world a better + + + align:start position:0% +together to make the world a better +place those are reasons why you came + + align:start position:0% +place those are reasons why you came + + + align:start position:0% +place those are reasons why you came +here you came here because you know + + align:start position:0% +here you came here because you know + + + align:start position:0% +here you came here because you know +that progress does not happen + + align:start position:0% +that progress does not happen + + + align:start position:0% +that progress does not happen +because of success it doesn't + + align:start position:0% +because of success it doesn't + + + align:start position:0% +because of success it doesn't +it happens entirely because of what you + + align:start position:0% +it happens entirely because of what you + + + align:start position:0% +it happens entirely because of what you +choose to do with failure + + align:start position:0% +choose to do with failure + + + align:start position:0% +choose to do with failure +that's mit + + align:start position:0% +that's mit + + + align:start position:0% +that's mit +that's the mit way and that's why you're + + align:start position:0% +that's the mit way and that's why you're + + + align:start position:0% +that's the mit way and that's why you're +here + + align:start position:0% +here + + + align:start position:0% +here +and i asked you to think about that on + + align:start position:0% +and i asked you to think about that on + + + align:start position:0% +and i asked you to think about that on +the first lecture + + align:start position:0% +the first lecture + + + align:start position:0% +the first lecture +and then i i gave you a whole lot of + + align:start position:0% +and then i i gave you a whole lot of + + + align:start position:0% +and then i i gave you a whole lot of +examples throughout the class i tried to + + align:start position:0% +examples throughout the class i tried to + + + align:start position:0% +examples throughout the class i tried to +connect our learning in solid state + + align:start position:0% +connect our learning in solid state + + + align:start position:0% +connect our learning in solid state +chemistry to global challenges + + align:start position:0% +chemistry to global challenges + + + align:start position:0% +chemistry to global challenges +right to global challenges that we face + + align:start position:0% +right to global challenges that we face + + + align:start position:0% +right to global challenges that we face +and um + + align:start position:0% +and um + + + align:start position:0% +and um +and i tried to do that you know so i had + + align:start position:0% +and i tried to do that you know so i had + + + align:start position:0% +and i tried to do that you know so i had +36 opportunities there's many more so i + + align:start position:0% +36 opportunities there's many more so i + + + align:start position:0% +36 opportunities there's many more so i +had to pick and choose carefully + + align:start position:0% +had to pick and choose carefully + + + align:start position:0% +had to pick and choose carefully +try to try to give you a sense of some + + align:start position:0% +try to try to give you a sense of some + + + align:start position:0% +try to try to give you a sense of some +of these things + + align:start position:0% +of these things + + + align:start position:0% +of these things +um + + align:start position:0% +um + + + align:start position:0% +um +and and and the thing is about these + + align:start position:0% +and and and the thing is about these + + + align:start position:0% +and and and the thing is about these +challenges the one i just talked about + + align:start position:0% +challenges the one i just talked about + + + align:start position:0% +challenges the one i just talked about +and many others + + align:start position:0% +and many others + + + align:start position:0% +and many others +these are not + + align:start position:0% +these are not + + + align:start position:0% +these are not +you know it's not that these are things + + align:start position:0% +you know it's not that these are things + + + align:start position:0% +you know it's not that these are things +that + + align:start position:0% +that + + + align:start position:0% +that +we need to do soon + + align:start position:0% +we need to do soon + + + align:start position:0% +we need to do soon +there there is an urgency of now about + + align:start position:0% +there there is an urgency of now about + + + align:start position:0% +there there is an urgency of now about +these things there is an urgency of now + + align:start position:0% +these things there is an urgency of now + + + align:start position:0% +these things there is an urgency of now +there's no more time + + align:start position:0% +there's no more time + + + align:start position:0% +there's no more time +to talk about it right + + align:start position:0% +to talk about it right + + + align:start position:0% +to talk about it right +um and and so and and these challenges + + align:start position:0% +um and and so and and these challenges + + + align:start position:0% +um and and so and and these challenges +you know they're also not it's not + + align:start position:0% +you know they're also not it's not + + + align:start position:0% +you know they're also not it's not +because it happens over here + + align:start position:0% +because it happens over here + + + align:start position:0% +because it happens over here +it happens over there + + align:start position:0% +it happens over there + + + align:start position:0% +it happens over there +these are planetary challenges these + + align:start position:0% +these are planetary challenges these + + + align:start position:0% +these are planetary challenges these +cover the whole thing + + align:start position:0% +cover the whole thing + + + align:start position:0% +cover the whole thing +so it's + + align:start position:0% +so it's + + + align:start position:0% +so it's +you know it's all on the table + + align:start position:0% +you know it's all on the table + + + align:start position:0% +you know it's all on the table +right it's all on the line + + align:start position:0% + + + + align:start position:0% + +and by the way if it's a planetary + + align:start position:0% +and by the way if it's a planetary + + + align:start position:0% +and by the way if it's a planetary +challenge it means the challenge doesn't + + align:start position:0% +challenge it means the challenge doesn't + + + align:start position:0% +challenge it means the challenge doesn't +care if you're in a blue state or a red + + align:start position:0% +care if you're in a blue state or a red + + + align:start position:0% +care if you're in a blue state or a red +state or if you live in europe or africa + + align:start position:0% +state or if you live in europe or africa + + + align:start position:0% +state or if you live in europe or africa +or here it doesn't care + + align:start position:0% +or here it doesn't care + + + align:start position:0% +or here it doesn't care +so we better figure out how to get our + + align:start position:0% +so we better figure out how to get our + + + align:start position:0% +so we better figure out how to get our +act together and work together to solve + + align:start position:0% +act together and work together to solve + + + align:start position:0% +act together and work together to solve +these very hard problems + + align:start position:0% +these very hard problems + + + align:start position:0% +these very hard problems +and that's why you're here + + align:start position:0% +and that's why you're here + + + align:start position:0% +and that's why you're here +right that's why you're here + + align:start position:0% +right that's why you're here + + + align:start position:0% +right that's why you're here +and so you know on the first lecture i + + align:start position:0% +and so you know on the first lecture i + + + align:start position:0% +and so you know on the first lecture i +asked you to think about why you're here + + align:start position:0% +asked you to think about why you're here + + + align:start position:0% +asked you to think about why you're here +and on you know in this very last + + align:start position:0% +and on you know in this very last + + + align:start position:0% +and on you know in this very last +lecture i'm asking you + + align:start position:0% +lecture i'm asking you + + + align:start position:0% +lecture i'm asking you +to think about what you want to do about + + align:start position:0% +to think about what you want to do about + + + align:start position:0% +to think about what you want to do about +that what do you want to do about that + + align:start position:0% +that what do you want to do about that + + + align:start position:0% +that what do you want to do about that +and um + + align:start position:0% +and um + + + align:start position:0% +and um +and you know there's a lot of things you + + align:start position:0% +and you know there's a lot of things you + + + align:start position:0% +and you know there's a lot of things you +can do + + align:start position:0% +can do + + + align:start position:0% +can do +i don't mean + + align:start position:0% +i don't mean + + + align:start position:0% +i don't mean +that + + align:start position:0% +that + + + align:start position:0% +that +that you have to work on one of these + + align:start position:0% +that you have to work on one of these + + + align:start position:0% +that you have to work on one of these +things we've talked about in this class + + align:start position:0% +things we've talked about in this class + + + align:start position:0% +things we've talked about in this class +that's not what i mean i mean think + + align:start position:0% +that's not what i mean i mean think + + + align:start position:0% +that's not what i mean i mean think +about what it is that you really want to + + align:start position:0% +about what it is that you really want to + + + align:start position:0% +about what it is that you really want to +do and how you want to do it + + align:start position:0% +do and how you want to do it + + + align:start position:0% +do and how you want to do it +and then go for it + + align:start position:0% +and then go for it + + + align:start position:0% +and then go for it +right + + align:start position:0% +right + + + align:start position:0% +right +um you might have figured that out + + align:start position:0% +um you might have figured that out + + + align:start position:0% +um you might have figured that out +before you came here + + align:start position:0% +before you came here + + + align:start position:0% +before you came here +you may know because in tight + + align:start position:0% +you may know because in tight + + + align:start position:0% +you may know because in tight +already way before you got here you may + + align:start position:0% +already way before you got here you may + + + align:start position:0% +already way before you got here you may +be figuring it out right now + + align:start position:0% +be figuring it out right now + + + align:start position:0% +be figuring it out right now +you may have no clue + + align:start position:0% +you may have no clue + + + align:start position:0% +you may have no clue +what you want to do when you graduate + + align:start position:0% +what you want to do when you graduate + + + align:start position:0% +what you want to do when you graduate +all of those are fine + + align:start position:0% +all of those are fine + + + align:start position:0% +all of those are fine +all of those are fine + + align:start position:0% +all of those are fine + + + align:start position:0% +all of those are fine +yeah but but what i want to leave you + + align:start position:0% +yeah but but what i want to leave you + + + align:start position:0% +yeah but but what i want to leave you +with + + align:start position:0% +with + + + align:start position:0% +with +is a framework + + align:start position:0% +is a framework + + + align:start position:0% +is a framework +and some thinking that i can what can i + + align:start position:0% +and some thinking that i can what can i + + + align:start position:0% +and some thinking that i can what can i +leave you with as as a suggestion as a + + align:start position:0% +leave you with as as a suggestion as a + + + align:start position:0% +leave you with as as a suggestion as a +framework and it really comes down to + + align:start position:0% +framework and it really comes down to + + + align:start position:0% +framework and it really comes down to +three ingredients + + align:start position:0% +three ingredients + + + align:start position:0% +three ingredients +three ingredients that i'm asking you to + + align:start position:0% +three ingredients that i'm asking you to + + + align:start position:0% +three ingredients that i'm asking you to +think about + + align:start position:0% +think about + + + align:start position:0% +think about +when you go off and do + + align:start position:0% +when you go off and do + + + align:start position:0% +when you go off and do +when you leave here when you go off and + + align:start position:0% +when you leave here when you go off and + + + align:start position:0% +when you leave here when you go off and +do what are you gonna do how are you + + align:start position:0% +do what are you gonna do how are you + + + align:start position:0% +do what are you gonna do how are you +gonna frame this and and so the first + + align:start position:0% +gonna frame this and and so the first + + + align:start position:0% +gonna frame this and and so the first +ingredient + + align:start position:0% +ingredient + + + align:start position:0% +ingredient +is kindness now okay + + align:start position:0% +is kindness now okay + + + align:start position:0% +is kindness now okay +bear with me because you're all thinking + + align:start position:0% +bear with me because you're all thinking + + + align:start position:0% +bear with me because you're all thinking +what is he talking about this is a + + align:start position:0% +what is he talking about this is a + + + align:start position:0% +what is he talking about this is a +chemistry class + + align:start position:0% +chemistry class + + + align:start position:0% +chemistry class +and you're talking about kindness + + align:start position:0% + + + + align:start position:0% + +and and you know but + + align:start position:0% +and and you know but + + + align:start position:0% +and and you know but +see the thing is i'm trying to think + + align:start position:0% +see the thing is i'm trying to think + + + align:start position:0% +see the thing is i'm trying to think +about what is a framework that if you + + align:start position:0% +about what is a framework that if you + + + align:start position:0% +about what is a framework that if you +follow it you will do good + + align:start position:0% +follow it you will do good + + + align:start position:0% +follow it you will do good +you will help change this world for the + + align:start position:0% +you will help change this world for the + + + align:start position:0% +you will help change this world for the +better which is what we do at mit it's + + align:start position:0% +better which is what we do at mit it's + + + align:start position:0% +better which is what we do at mit it's +how we think + + align:start position:0% +how we think + + + align:start position:0% +how we think +and and the thing is i don't care if you + + align:start position:0% +and and the thing is i don't care if you + + + align:start position:0% +and and the thing is i don't care if you +define kindness as love or as helping + + align:start position:0% +define kindness as love or as helping + + + align:start position:0% +define kindness as love or as helping +someone + + align:start position:0% +someone + + + align:start position:0% +someone +or as community + + align:start position:0% +or as community + + + align:start position:0% +or as community +or as you know on one of those dates + + align:start position:0% +or as you know on one of those dates + + + align:start position:0% +or as you know on one of those dates +when the candle was in the room and you + + align:start position:0% +when the candle was in the room and you + + + align:start position:0% +when the candle was in the room and you +did the calculation and you saved the + + align:start position:0% +did the calculation and you saved the + + + align:start position:0% +did the calculation and you saved the +day + + align:start position:0% +day + + + align:start position:0% +day +because you knew oxygen was going to run + + align:start position:0% +because you knew oxygen was going to run + + + align:start position:0% +because you knew oxygen was going to run +out that's all kindness + + align:start position:0% +out that's all kindness + + + align:start position:0% +out that's all kindness +all of that is kindness but the thing is + + align:start position:0% +all of that is kindness but the thing is + + + align:start position:0% +all of that is kindness but the thing is +that if you have kindness in what you do + + align:start position:0% +that if you have kindness in what you do + + + align:start position:0% +that if you have kindness in what you do +it's really hard to do bad + + align:start position:0% +it's really hard to do bad + + + align:start position:0% +it's really hard to do bad +right is that is that under the hood + + align:start position:0% +right is that is that under the hood + + + align:start position:0% +right is that is that under the hood +is there an element of kindness you + + align:start position:0% +is there an element of kindness you + + + align:start position:0% +is there an element of kindness you +can't have too much of it we need that + + align:start position:0% +can't have too much of it we need that + + + align:start position:0% +can't have too much of it we need that +vector + + align:start position:0% +vector + + + align:start position:0% +vector +right we need that vector in this world + + align:start position:0% +right we need that vector in this world + + + align:start position:0% +right we need that vector in this world +so that's one ingredient and the second + + align:start position:0% +so that's one ingredient and the second + + + align:start position:0% +so that's one ingredient and the second +ingredient is knowledge now what i mean + + align:start position:0% +ingredient is knowledge now what i mean + + + align:start position:0% +ingredient is knowledge now what i mean +by this is acquisition of knowledge and + + align:start position:0% +by this is acquisition of knowledge and + + + align:start position:0% +by this is acquisition of knowledge and +we have done a lot of that here in this + + align:start position:0% +we have done a lot of that here in this + + + align:start position:0% +we have done a lot of that here in this +class and you do a lot of that at mit + + align:start position:0% +class and you do a lot of that at mit + + + align:start position:0% +class and you do a lot of that at mit +and we celebrate these acquisitions + + align:start position:0% +and we celebrate these acquisitions + + + align:start position:0% +and we celebrate these acquisitions +what i'm asking you to do is think about + + align:start position:0% +what i'm asking you to do is think about + + + align:start position:0% +what i'm asking you to do is think about +this as you go forward how are you + + align:start position:0% +this as you go forward how are you + + + align:start position:0% +this as you go forward how are you +acquiring knowledge how are you learning + + align:start position:0% +acquiring knowledge how are you learning + + + align:start position:0% +acquiring knowledge how are you learning +that sounds cliche you always learn + + align:start position:0% +that sounds cliche you always learn + + + align:start position:0% +that sounds cliche you always learn +you guys have to keep doing that you + + align:start position:0% +you guys have to keep doing that you + + + align:start position:0% +you guys have to keep doing that you +have to keep doing that because for you + + align:start position:0% +have to keep doing that because for you + + + align:start position:0% +have to keep doing that because for you +it's nourishment + + align:start position:0% +it's nourishment + + + align:start position:0% +it's nourishment +and it's another one of these vectors + + align:start position:0% +and it's another one of these vectors + + + align:start position:0% +and it's another one of these vectors +you can't do any harm by learning you + + align:start position:0% +you can't do any harm by learning you + + + align:start position:0% +you can't do any harm by learning you +can only do good + + align:start position:0% +can only do good + + + align:start position:0% +can only do good +for yourself and for everyone that you + + align:start position:0% +for yourself and for everyone that you + + + align:start position:0% +for yourself and for everyone that you +care about + + align:start position:0% +care about + + + align:start position:0% +care about +so keep doing it + + align:start position:0% +so keep doing it + + + align:start position:0% +so keep doing it +the rate might change if learning + + align:start position:0% +the rate might change if learning + + + align:start position:0% +the rate might change if learning +acquisition is a reaction the rate + + align:start position:0% +acquisition is a reaction the rate + + + align:start position:0% +acquisition is a reaction the rate +constant might be lower we know places + + align:start position:0% +constant might be lower we know places + + + align:start position:0% +constant might be lower we know places +where that's already the case + + align:start position:0% +where that's already the case + + + align:start position:0% +where that's already the case +and + + align:start position:0% + + + + align:start position:0% + +and that's okay + + align:start position:0% +and that's okay + + + align:start position:0% +and that's okay +maybe the order is lower too down there + + align:start position:0% +maybe the order is lower too down there + + + align:start position:0% +maybe the order is lower too down there +and and the + + align:start position:0% +and and the + + + align:start position:0% +and and the +but i think you know they probably are + + align:start position:0% +but i think you know they probably are + + + align:start position:0% +but i think you know they probably are +learning something + + align:start position:0% + + + + align:start position:0% + +keep keep that going + + align:start position:0% +keep keep that going + + + align:start position:0% +keep keep that going +and the last thing is passion + + align:start position:0% +and the last thing is passion + + + align:start position:0% +and the last thing is passion +and this involves your talents right you + + align:start position:0% +and this involves your talents right you + + + align:start position:0% +and this involves your talents right you +all have talents already + + align:start position:0% +all have talents already + + + align:start position:0% +all have talents already +you all have them because that's part of + + align:start position:0% +you all have them because that's part of + + + align:start position:0% +you all have them because that's part of +who you are and why you're here + + align:start position:0% +who you are and why you're here + + + align:start position:0% +who you are and why you're here +those are things that you bring a + + align:start position:0% +those are things that you bring a + + + align:start position:0% +those are things that you bring a +passion + + align:start position:0% +passion + + + align:start position:0% +passion +to what are those talents + + align:start position:0% +to what are those talents + + + align:start position:0% +to what are those talents +maybe some of them are hidden + + align:start position:0% +maybe some of them are hidden + + + align:start position:0% +maybe some of them are hidden +but work on them and pursue them do + + align:start position:0% +but work on them and pursue them do + + + align:start position:0% +but work on them and pursue them do +things that you literally are so excited + + align:start position:0% +things that you literally are so excited + + + align:start position:0% +things that you literally are so excited +about you can't sleep sometimes because + + align:start position:0% +about you can't sleep sometimes because + + + align:start position:0% +about you can't sleep sometimes because +of the excitement + + align:start position:0% +of the excitement + + + align:start position:0% +of the excitement +that's what i'm talking about + + align:start position:0% +that's what i'm talking about + + + align:start position:0% +that's what i'm talking about +follow that + + align:start position:0% +follow that + + + align:start position:0% +follow that +feed it + + align:start position:0% + + + + align:start position:0% + +and while you do + + align:start position:0% +and while you do + + + align:start position:0% +and while you do +you know + + align:start position:0% +you know + + + align:start position:0% +you know +lose + + align:start position:0% +lose + + + align:start position:0% +lose +lose the fear + + align:start position:0% +lose the fear + + + align:start position:0% +lose the fear +right avoid greed + + align:start position:0% +right avoid greed + + + align:start position:0% +right avoid greed +and embrace challenge that's what that's + + align:start position:0% +and embrace challenge that's what that's + + + align:start position:0% +and embrace challenge that's what that's +what mit is that's why we're here + + align:start position:0% +what mit is that's why we're here + + + align:start position:0% +what mit is that's why we're here +right that's why we're here + + align:start position:0% +right that's why we're here + + + align:start position:0% +right that's why we're here +so so i i feel like these three + + align:start position:0% +so so i i feel like these three + + + align:start position:0% +so so i i feel like these three +ingredients you know i've thought about + + align:start position:0% +ingredients you know i've thought about + + + align:start position:0% +ingredients you know i've thought about +this and i've thought about these three + + align:start position:0% +this and i've thought about these three + + + align:start position:0% +this and i've thought about these three +ingredients and i've thought about + + align:start position:0% +ingredients and i've thought about + + + align:start position:0% +ingredients and i've thought about +we have these already + + align:start position:0% +we have these already + + + align:start position:0% +we have these already +you all have these ingredients because + + align:start position:0% +you all have these ingredients because + + + align:start position:0% +you all have these ingredients because +that is also mit + + align:start position:0% +that is also mit + + + align:start position:0% +that is also mit +and you are here and you are mit + + align:start position:0% +and you are here and you are mit + + + align:start position:0% +and you are here and you are mit +and so what i'm asking you to do is to + + align:start position:0% +and so what i'm asking you to do is to + + + align:start position:0% +and so what i'm asking you to do is to +hold on to them + + align:start position:0% +hold on to them + + + align:start position:0% +hold on to them +and keep thinking about that + + align:start position:0% +and keep thinking about that + + + align:start position:0% +and keep thinking about that +that's it there's a lot of reasons why + + align:start position:0% +that's it there's a lot of reasons why + + + align:start position:0% +that's it there's a lot of reasons why +i love to teach + + align:start position:0% +i love to teach + + + align:start position:0% +i love to teach +and but but but one of the big ones is + + align:start position:0% +and but but but one of the big ones is + + + align:start position:0% +and but but but one of the big ones is +when i think about the challenges that i + + align:start position:0% +when i think about the challenges that i + + + align:start position:0% +when i think about the challenges that i +share with you guys + + align:start position:0% +share with you guys + + + align:start position:0% +share with you guys +and and i have 36 chances to look up in + + align:start position:0% +and and i have 36 chances to look up in + + + align:start position:0% +and and i have 36 chances to look up in +the room and i think about those + + align:start position:0% +the room and i think about those + + + align:start position:0% +the room and i think about those +challenges and i think about these + + align:start position:0% +challenges and i think about these + + + align:start position:0% +challenges and i think about these +ingredients and i think about + + align:start position:0% +ingredients and i think about + + + align:start position:0% +ingredients and i think about +all of you i actually feel like we have + + align:start position:0% +all of you i actually feel like we have + + + align:start position:0% +all of you i actually feel like we have +a shot + + align:start position:0% +a shot + + + align:start position:0% +a shot +i actually feel that + + align:start position:0% +i actually feel that + + + align:start position:0% +i actually feel that +and so so with that + + align:start position:0% +and so so with that + + + align:start position:0% +and so so with that +good luck on the final and have a + + align:start position:0% +good luck on the final and have a + + + align:start position:0% +good luck on the final and have a +fantastic break + + align:start position:0% + + + + align:start position:0% + +thank you so much + + align:start position:0% +thank you so much + + + align:start position:0% +thank you so much +thank you + + align:start position:0% +thank you + + + align:start position:0% +thank you +thank you guys + + align:start position:0% +thank you guys + + + align:start position:0% +thank you guys +thank you guys + + align:start position:0% +thank you guys + + + align:start position:0% +thank you guys +thank you thank you thank you so much + + align:start position:0% +thank you thank you thank you so much + + + align:start position:0% +thank you thank you thank you so much +thank you + + align:start position:0% + + + + align:start position:0% + +you guys are amazing + + align:start position:0% + + + + align:start position:0% + +thank you thank you + + align:start position:0% + + + + align:start position:0% + +thank you all so much i i i'm gonna have + + align:start position:0% +thank you all so much i i i'm gonna have + + + align:start position:0% +thank you all so much i i i'm gonna have +to leave here or i'm gonna get really + + align:start position:0% +to leave here or i'm gonna get really + + + align:start position:0% +to leave here or i'm gonna get really +emotional i've also i've clearly got a + + align:start position:0% +emotional i've also i've clearly got a + + + align:start position:0% +emotional i've also i've clearly got a +lot of other dance moves the tas have + + align:start position:0% +lot of other dance moves the tas have + + + align:start position:0% +lot of other dance moves the tas have +have uh have helped me + + align:start position:0% +have uh have helped me + + + align:start position:0% +have uh have helped me +so i can practice those uh thank you so + + align:start position:0% +so i can practice those uh thank you so + + + align:start position:0% +so i can practice those uh thank you so +much that that's just incredible uh you + + align:start position:0% +much that that's just incredible uh you + + + align:start position:0% +much that that's just incredible uh you +guys are all incredible and this has + + align:start position:0% +guys are all incredible and this has + + + align:start position:0% +guys are all incredible and this has +been incredible so um uh we do have uh + + align:start position:0% +been incredible so um uh we do have uh + + + align:start position:0% +been incredible so um uh we do have uh +ten minutes uh they're gonna throw i'm + + align:start position:0% +ten minutes uh they're gonna throw i'm + + + align:start position:0% +ten minutes uh they're gonna throw i'm +gonna leave so you guys can fill + + align:start position:0% +gonna leave so you guys can fill + + + align:start position:0% +gonna leave so you guys can fill +evaluations out without me being in the + + align:start position:0% +evaluations out without me being in the + + + align:start position:0% +evaluations out without me being in the +room and uh and and so you can say + + align:start position:0% +room and uh and and so you can say + + + align:start position:0% +room and uh and and so you can say +whatever you want um again don't let the + + align:start position:0% +whatever you want um again don't let the + + + align:start position:0% +whatever you want um again don't let the +free t-shirts be being thrown at you + + align:start position:0% +free t-shirts be being thrown at you + + + align:start position:0% +free t-shirts be being thrown at you +influence your + + align:start position:0% +influence your + + + align:start position:0% +influence your +opinion + + align:start position:0% +opinion + + + align:start position:0% +opinion +or the free candy + + align:start position:0% +or the free candy + + + align:start position:0% +or the free candy +but uh but thanks everyone + + align:start position:0% +but uh but thanks everyone + + + align:start position:0% +but uh but thanks everyone +for a fantastic semester + + align:start position:0% + + + + align:start position:0% + +thank you + + align:start position:0% + + + + align:start position:0% + +that was amazing you guys + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/UroprmQHTLc.txt b/UroprmQHTLc.txt new file mode 100644 index 0000000000000000000000000000000000000000..2a59dfcd4660aad36bc3ba161dc4430471614046 --- /dev/null +++ b/UroprmQHTLc.txt @@ -0,0 +1,2011 @@ +align:start position:0% + +the logic of predicates is a basic + + align:start position:0% +the logic of predicates is a basic + + + align:start position:0% +the logic of predicates is a basic +concept in mathematical language as well + + align:start position:0% +concept in mathematical language as well + + + align:start position:0% +concept in mathematical language as well +as being a topic on its own in + + align:start position:0% +as being a topic on its own in + + + align:start position:0% +as being a topic on its own in +particular I'm going to talk now about + + align:start position:0% +particular I'm going to talk now about + + + align:start position:0% +particular I'm going to talk now about +the idea that two so-called quantifiers + + align:start position:0% +the idea that two so-called quantifiers + + + align:start position:0% +the idea that two so-called quantifiers +for all that's the upside down a and + + align:start position:0% +for all that's the upside down a and + + + align:start position:0% +for all that's the upside down a and +exists that's the backward e so what's a + + align:start position:0% +exists that's the backward e so what's a + + + align:start position:0% +exists that's the backward e so what's a +predicate basically a predicate is a + + align:start position:0% +predicate basically a predicate is a + + + align:start position:0% +predicate basically a predicate is a +proposition except it's got variables in + + align:start position:0% +proposition except it's got variables in + + + align:start position:0% +proposition except it's got variables in +it here's an example P of X Y is the + + align:start position:0% +it here's an example P of X Y is the + + + align:start position:0% +it here's an example P of X Y is the +predicate that depends on x and y and + + align:start position:0% +predicate that depends on x and y and + + + align:start position:0% +predicate that depends on x and y and +let's say it's defined to be X plus 2 + + align:start position:0% +let's say it's defined to be X plus 2 + + + align:start position:0% +let's say it's defined to be X plus 2 +equals Y now in order to figure out + + align:start position:0% +equals Y now in order to figure out + + + align:start position:0% +equals Y now in order to figure out +whether or not a predicate is true I + + align:start position:0% +whether or not a predicate is true I + + + align:start position:0% +whether or not a predicate is true I +need to know the values of the variables + + align:start position:0% +need to know the values of the variables + + + align:start position:0% +need to know the values of the variables +in this case x and y so if I tell you + + align:start position:0% +in this case x and y so if I tell you + + + align:start position:0% +in this case x and y so if I tell you +that X is 1 and that Y is 3 guess what P + + align:start position:0% +that X is 1 and that Y is 3 guess what P + + + align:start position:0% +that X is 1 and that Y is 3 guess what P +of 1 in 3 P of x + y when x is 1 and Y + + align:start position:0% +of 1 in 3 P of x + y when x is 1 and Y + + + align:start position:0% +of 1 in 3 P of x + y when x is 1 and Y +is 3 is true because in fact 1 plus 2 is + + align:start position:0% +is 3 is true because in fact 1 plus 2 is + + + align:start position:0% +is 3 is true because in fact 1 plus 2 is +equal to 3 if I tell you if it X is 1 + + align:start position:0% +equal to 3 if I tell you if it X is 1 + + + align:start position:0% +equal to 3 if I tell you if it X is 1 +and Y is 4 then since 1 plus 2 is not + + align:start position:0% +and Y is 4 then since 1 plus 2 is not + + + align:start position:0% +and Y is 4 then since 1 plus 2 is not +equal to 4 P of 1 + 4 is false on the + + align:start position:0% +equal to 4 P of 1 + 4 is false on the + + + align:start position:0% +equal to 4 P of 1 + 4 is false on the +other hand since P of 1/4 is false that + + align:start position:0% +other hand since P of 1/4 is false that + + + align:start position:0% +other hand since P of 1/4 is false that +makes not P of 1 + 4 true that's the + + align:start position:0% +makes not P of 1 + 4 true that's the + + + align:start position:0% +makes not P of 1 + 4 true that's the +easy part + + align:start position:0% +easy part + + + align:start position:0% +easy part +now the quantifiers are read as for all + + align:start position:0% +now the quantifiers are read as for all + + + align:start position:0% +now the quantifiers are read as for all +and exists but they control a variable + + align:start position:0% +and exists but they control a variable + + + align:start position:0% +and exists but they control a variable +so I write for all X it means 4 and it's + + align:start position:0% +so I write for all X it means 4 and it's + + + align:start position:0% +so I write for all X it means 4 and it's +sorry I write upside down a X and I read + + align:start position:0% +sorry I write upside down a X and I read + + + align:start position:0% +sorry I write upside down a X and I read +it as for all X I'm so used to reading + + align:start position:0% +it as for all X I'm so used to reading + + + align:start position:0% +it as for all X I'm so used to reading +it that I forgot that I needed to read + + align:start position:0% +it that I forgot that I needed to read + + + align:start position:0% +it that I forgot that I needed to read +symbols literally and backwards E Y is + + align:start position:0% +symbols literally and backwards E Y is + + + align:start position:0% +symbols literally and backwards E Y is +read as there exists some Y so let's see + + align:start position:0% +read as there exists some Y so let's see + + + align:start position:0% +read as there exists some Y so let's see +how that would work + + align:start position:0% +how that would work + + + align:start position:0% +how that would work +the upside-down a for all acts like an + + align:start position:0% +the upside-down a for all acts like an + + + align:start position:0% +the upside-down a for all acts like an +end and to understand what it means + + align:start position:0% +end and to understand what it means + + + align:start position:0% +end and to understand what it means +let's look at this example let's let a + + align:start position:0% +let's look at this example let's let a + + + align:start position:0% +let's look at this example let's let a +variable s range over the staff members + + align:start position:0% +variable s range over the staff members + + + align:start position:0% +variable s range over the staff members +in 604 2 at this term which whom there + + align:start position:0% +in 604 2 at this term which whom there + + + align:start position:0% +in 604 2 at this term which whom there +are about 30 counting the graders let's + + align:start position:0% +are about 30 counting the graders let's + + + align:start position:0% +are about 30 counting the graders let's +define a predicate that depends on the + + align:start position:0% +define a predicate that depends on the + + + align:start position:0% +define a predicate that depends on the +variable s called P of s that says that + + align:start position:0% +variable s called P of s that says that + + + align:start position:0% +variable s called P of s that says that +s is pumped about 604 - there + + align:start position:0% +s is pumped about 604 - there + + + align:start position:0% +s is pumped about 604 - there +Susy astok about being on the staff okay + + align:start position:0% +Susy astok about being on the staff okay + + + align:start position:0% +Susy astok about being on the staff okay +if I tell you for all s P of s that's + + align:start position:0% +if I tell you for all s P of s that's + + + align:start position:0% +if I tell you for all s P of s that's +exactly the same as saying that P of + + align:start position:0% +exactly the same as saying that P of + + + align:start position:0% +exactly the same as saying that P of +Drew is true and P of Peter is true and + + align:start position:0% +Drew is true and P of Peter is true and + + + align:start position:0% +Drew is true and P of Peter is true and +P of Kesha is true and a whole bunch + + align:start position:0% +P of Kesha is true and a whole bunch + + + align:start position:0% +P of Kesha is true and a whole bunch +more ends the enthalpy of Michaela + + align:start position:0% +more ends the enthalpy of Michaela + + + align:start position:0% +more ends the enthalpy of Michaela +there'll be twenty nine as if there are + + align:start position:0% +there'll be twenty nine as if there are + + + align:start position:0% +there'll be twenty nine as if there are +thirty staff members + + align:start position:0% + + + + align:start position:0% + +similarly the backwards either exists + + align:start position:0% +similarly the backwards either exists + + + align:start position:0% +similarly the backwards either exists +acts like an or if I tell you that T is + + align:start position:0% +acts like an or if I tell you that T is + + + align:start position:0% +acts like an or if I tell you that T is +now ranging over the 604 to staff just + + align:start position:0% +now ranging over the 604 to staff just + + + align:start position:0% +now ranging over the 604 to staff just +as s was and I write B of T the + + align:start position:0% +as s was and I write B of T the + + + align:start position:0% +as s was and I write B of T the +predicate of T that means T the staff + + align:start position:0% +predicate of T that means T the staff + + + align:start position:0% +predicate of T that means T the staff +member t took 604 two before then if I + + align:start position:0% +member t took 604 two before then if I + + + align:start position:0% +member t took 604 two before then if I +tell you that there exists a TB of T + + align:start position:0% +tell you that there exists a TB of T + + + align:start position:0% +tell you that there exists a TB of T +what I'm telling you is that B of Drew + + align:start position:0% +what I'm telling you is that B of Drew + + + align:start position:0% +what I'm telling you is that B of Drew +either drew took it before or Peter took + + align:start position:0% +either drew took it before or Peter took + + + align:start position:0% +either drew took it before or Peter took +it before or Kesha took it before or + + align:start position:0% +it before or Kesha took it before or + + + align:start position:0% +it before or Kesha took it before or +Michaela took it before this statement + + align:start position:0% +Michaela took it before this statement + + + align:start position:0% +Michaela took it before this statement +is true because in fact several of the + + align:start position:0% +is true because in fact several of the + + + align:start position:0% +is true because in fact several of the +staff members took 604 two from me + + align:start position:0% +staff members took 604 two from me + + + align:start position:0% +staff members took 604 two from me +before and I like to think that the + + align:start position:0% +before and I like to think that the + + + align:start position:0% +before and I like to think that the +previous one that everybody's pumped up + + align:start position:0% +previous one that everybody's pumped up + + + align:start position:0% +previous one that everybody's pumped up +on the staff is true although I can't + + align:start position:0% +on the staff is true although I can't + + + align:start position:0% +on the staff is true although I can't +guarantee that so let's do a little + + align:start position:0% +guarantee that so let's do a little + + + align:start position:0% +guarantee that so let's do a little +practice with existential quantifiers + + align:start position:0% +practice with existential quantifiers + + + align:start position:0% +practice with existential quantifiers +so let's agree that the variables x and + + align:start position:0% +so let's agree that the variables x and + + + align:start position:0% +so let's agree that the variables x and +y will range for this example over the + + align:start position:0% +y will range for this example over the + + + align:start position:0% +y will range for this example over the +non-negative integers and let's consider + + align:start position:0% +non-negative integers and let's consider + + + align:start position:0% +non-negative integers and let's consider +the following predicate about why it + + align:start position:0% +the following predicate about why it + + + align:start position:0% +the following predicate about why it +says that there's some X that's less + + align:start position:0% +says that there's some X that's less + + + align:start position:0% +says that there's some X that's less +than Y Q of Y is there exists an X that + + align:start position:0% +than Y Q of Y is there exists an X that + + + align:start position:0% +than Y Q of Y is there exists an X that +X is less than Y let's see what happens + + align:start position:0% +X is less than Y let's see what happens + + + align:start position:0% +X is less than Y let's see what happens +well what about Q of three the Q of + + align:start position:0% +well what about Q of three the Q of + + + align:start position:0% +well what about Q of three the Q of +three is saying that there is an X such + + align:start position:0% +three is saying that there is an X such + + + align:start position:0% +three is saying that there is an X such +that X is less than three + + align:start position:0% +that X is less than three + + + align:start position:0% +that X is less than three +well an example of such an X is 1 so + + align:start position:0% +well an example of such an X is 1 so + + + align:start position:0% +well an example of such an X is 1 so +that means there is an X that's less + + align:start position:0% +that means there is an X that's less + + + align:start position:0% +that means there is an X that's less +than three because one is and so that + + align:start position:0% +than three because one is and so that + + + align:start position:0% +than three because one is and so that +makes this Q true all right what about Q + + align:start position:0% +makes this Q true all right what about Q + + + align:start position:0% +makes this Q true all right what about Q +of 1 well again there's an X that's a + + align:start position:0% +of 1 well again there's an X that's a + + + align:start position:0% +of 1 well again there's an X that's a +non-negative integer namely 0 that's + + align:start position:0% +non-negative integer namely 0 that's + + + align:start position:0% +non-negative integer namely 0 that's +less than 1 and therefore Q of 1 is true + + align:start position:0% +less than 1 and therefore Q of 1 is true + + + align:start position:0% +less than 1 and therefore Q of 1 is true +on the other hand Q of 0 is false + + align:start position:0% +on the other hand Q of 0 is false + + + align:start position:0% +on the other hand Q of 0 is false +because there is no + + align:start position:0% +because there is no + + + align:start position:0% +because there is no +non-negative integer that's less than + + align:start position:0% +non-negative integer that's less than + + + align:start position:0% +non-negative integer that's less than +zero and so there's no value that you + + align:start position:0% +zero and so there's no value that you + + + align:start position:0% +zero and so there's no value that you +can assign to X that's a non-negative + + align:start position:0% +can assign to X that's a non-negative + + + align:start position:0% +can assign to X that's a non-negative +integer that will make it less than zero + + align:start position:0% +integer that will make it less than zero + + + align:start position:0% +integer that will make it less than zero +okay that one's not so bad I hope + + align:start position:0% +okay that one's not so bad I hope + + + align:start position:0% +okay that one's not so bad I hope +let's look at the same example with a + + align:start position:0% +let's look at the same example with a + + + align:start position:0% +let's look at the same example with a +universal quantifier this time we'll say + + align:start position:0% +universal quantifier this time we'll say + + + align:start position:0% +universal quantifier this time we'll say +that R of Y means that for every X X is + + align:start position:0% +that R of Y means that for every X X is + + + align:start position:0% +that R of Y means that for every X X is +less than Y well R of one is false and + + align:start position:0% +less than Y well R of one is false and + + + align:start position:0% +less than Y well R of one is false and +the reason is that five is a counter + + align:start position:0% +the reason is that five is a counter + + + align:start position:0% +the reason is that five is a counter +example five is not less than one and so + + align:start position:0% +example five is not less than one and so + + + align:start position:0% +example five is not less than one and so +it's not true that every X is less than + + align:start position:0% +it's not true that every X is less than + + + align:start position:0% +it's not true that every X is less than +one hour of eight is false because 12 is + + align:start position:0% +one hour of eight is false because 12 is + + + align:start position:0% +one hour of eight is false because 12 is +not less than eight and therefore not + + align:start position:0% +not less than eight and therefore not + + + align:start position:0% +not less than eight and therefore not +every X is less than eight R of a googol + + align:start position:0% +every X is less than eight R of a googol + + + align:start position:0% +every X is less than eight R of a googol +10 to the 100th is false because if you + + align:start position:0% +10 to the 100th is false because if you + + + align:start position:0% +10 to the 100th is false because if you +let X be a googol it's not less than a + + align:start position:0% +let X be a googol it's not less than a + + + align:start position:0% +let X be a googol it's not less than a +googol and so it's an example of the + + align:start position:0% +googol and so it's an example of the + + + align:start position:0% +googol and so it's an example of the +fact that this doesn't hold for all X's + + align:start position:0% +fact that this doesn't hold for all X's + + + align:start position:0% +fact that this doesn't hold for all X's +that part's obvious okay the thing that + + align:start position:0% +that part's obvious okay the thing that + + + align:start position:0% +that part's obvious okay the thing that +tends to confuse people in the beginning + + align:start position:0% +tends to confuse people in the beginning + + + align:start position:0% +tends to confuse people in the beginning +is what happens when you start mixing up + + align:start position:0% +is what happens when you start mixing up + + + align:start position:0% +is what happens when you start mixing up +quantifiers so let's look at an + + align:start position:0% +quantifiers so let's look at an + + + align:start position:0% +quantifiers so let's look at an +intuitive example first it might help + + align:start position:0% +intuitive example first it might help + + + align:start position:0% +intuitive example first it might help +you remember what happens when you have + + align:start position:0% +you remember what happens when you have + + + align:start position:0% +you remember what happens when you have +an a followed by an e and then we'll + + align:start position:0% +an a followed by an e and then we'll + + + align:start position:0% +an a followed by an e and then we'll +look at an e followed by an a so suppose + + align:start position:0% +look at an e followed by an a so suppose + + + align:start position:0% +look at an e followed by an a so suppose +I look at this statement this time I'm + + align:start position:0% +I look at this statement this time I'm + + + align:start position:0% +I look at this statement this time I'm +gonna tell you that V ranges over the + + align:start position:0% +gonna tell you that V ranges over the + + + align:start position:0% +gonna tell you that V ranges over the +possible computer viruses not biological + + align:start position:0% +possible computer viruses not biological + + + align:start position:0% +possible computer viruses not biological +viruses the range is over Spa antivirus + + align:start position:0% +viruses the range is over Spa antivirus + + + align:start position:0% +viruses the range is over Spa antivirus +software defenses against viruses and I + + align:start position:0% +software defenses against viruses and I + + + align:start position:0% +software defenses against viruses and I +want to look at the predicate that says + + align:start position:0% +want to look at the predicate that says + + + align:start position:0% +want to look at the predicate that says +for every virus there is a defense such + + align:start position:0% +for every virus there is a defense such + + + align:start position:0% +for every virus there is a defense such +that D protects against V this defense + + align:start position:0% +that D protects against V this defense + + + align:start position:0% +that D protects against V this defense +is good against that virus all right + + align:start position:0% +is good against that virus all right + + + align:start position:0% +is good against that virus all right +so each virus I have a defense for so an + + align:start position:0% +so each virus I have a defense for so an + + + align:start position:0% +so each virus I have a defense for so an +example would be these are by the way + + align:start position:0% +example would be these are by the way + + + align:start position:0% +example would be these are by the way +dated viruses but that's when the slides + + align:start position:0% +dated viruses but that's when the slides + + + align:start position:0% +dated viruses but that's when the slides +were made so against the mydoom virus + + align:start position:0% +were made so against the mydoom virus + + + align:start position:0% +were made so against the mydoom virus +you could use a defender a microsoft + + align:start position:0% +you could use a defender a microsoft + + + align:start position:0% +you could use a defender a microsoft +defender against the i-love-you virus + + align:start position:0% +defender against the i-love-you virus + + + align:start position:0% +defender against the i-love-you virus +you could use Norton against Bob less + + align:start position:0% +you could use Norton against Bob less + + + align:start position:0% +you could use Norton against Bob less +virus you could use zone alarm well is + + align:start position:0% +virus you could use zone alarm well is + + + align:start position:0% +virus you could use zone alarm well is +that what we want + + align:start position:0% +that what we want + + + align:start position:0% +that what we want +it's expensive it means that for every + + align:start position:0% +it's expensive it means that for every + + + align:start position:0% +it's expensive it means that for every +different virus I need a different + + align:start position:0% +different virus I need a different + + + align:start position:0% +different virus I need a different +defense I have to spend a fortune on + + align:start position:0% +defense I have to spend a fortune on + + + align:start position:0% +defense I have to spend a fortune on +software this is not what we want so + + align:start position:0% +software this is not what we want so + + + align:start position:0% +software this is not what we want so +that's when for every virus there's a + + align:start position:0% +that's when for every virus there's a + + + align:start position:0% +that's when for every virus there's a +defense but the quantifiers are in the + + align:start position:0% +defense but the quantifiers are in the + + + align:start position:0% +defense but the quantifiers are in the +wrong order let's reverse them suppose I + + align:start position:0% +wrong order let's reverse them suppose I + + + align:start position:0% +wrong order let's reverse them suppose I +tell you that there's one defense that's + + align:start position:0% +tell you that there's one defense that's + + + align:start position:0% +tell you that there's one defense that's +good for all viruses there is a defense + + align:start position:0% +good for all viruses there is a defense + + + align:start position:0% +good for all viruses there is a defense +such that for every virus the protects + + align:start position:0% +such that for every virus the protects + + + align:start position:0% +such that for every virus the protects +against V for example if thee is MIT + + align:start position:0% +against V for example if thee is MIT + + + align:start position:0% +against V for example if thee is MIT +virus scan then it would only be would + + align:start position:0% +virus scan then it would only be would + + + align:start position:0% +virus scan then it would only be would +be wonderful it was true that D protects + + align:start position:0% +be wonderful it was true that D protects + + + align:start position:0% +be wonderful it was true that D protects +against all viruses there's one defense + + align:start position:0% +against all viruses there's one defense + + + align:start position:0% +against all viruses there's one defense +good against every attack that's what we + + align:start position:0% +good against every attack that's what we + + + align:start position:0% +good against every attack that's what we +want + + align:start position:0% +want + + + align:start position:0% +want +because it's a lot cheaper all right + + align:start position:0% +because it's a lot cheaper all right + + + align:start position:0% +because it's a lot cheaper all right +let's start looking at a a concrete + + align:start position:0% +let's start looking at a a concrete + + + align:start position:0% +let's start looking at a a concrete +mathematical example that and I hope + + align:start position:0% +mathematical example that and I hope + + + align:start position:0% +mathematical example that and I hope +that that preload with the viruses will + + align:start position:0% +that that preload with the viruses will + + + align:start position:0% +that that preload with the viruses will +help you decipher how the quantifiers + + align:start position:0% +help you decipher how the quantifiers + + + align:start position:0% +help you decipher how the quantifiers +behave so let's look at this prayer this + + align:start position:0% +behave so let's look at this prayer this + + + align:start position:0% +behave so let's look at this prayer this +predicate now sorry this is a + + align:start position:0% +predicate now sorry this is a + + + align:start position:0% +predicate now sorry this is a +proposition it really doesn't depend on + + align:start position:0% +proposition it really doesn't depend on + + + align:start position:0% +proposition it really doesn't depend on +the values of x and y it's asking about + + align:start position:0% +the values of x and y it's asking about + + + align:start position:0% +the values of x and y it's asking about +all possible X's in all possible Y's + + align:start position:0% +all possible X's in all possible Y's + + + align:start position:0% +all possible X's in all possible Y's +whether there is one in order to figure + + align:start position:0% +whether there is one in order to figure + + + align:start position:0% +whether there is one in order to figure +out whether a proposition like G is true + + align:start position:0% +out whether a proposition like G is true + + + align:start position:0% +out whether a proposition like G is true +actually I do need to know what x and y + + align:start position:0% +actually I do need to know what x and y + + + align:start position:0% +actually I do need to know what x and y +are ranging over cuz as you'll see + + align:start position:0% +are ranging over cuz as you'll see + + + align:start position:0% +are ranging over cuz as you'll see +whether or not G comes out to be true + + align:start position:0% +whether or not G comes out to be true + + + align:start position:0% +whether or not G comes out to be true +will depend on that so I'm gonna look at + + align:start position:0% +will depend on that so I'm gonna look at + + + align:start position:0% +will depend on that so I'm gonna look at +the domain of deep discourse that x and + + align:start position:0% +the domain of deep discourse that x and + + + align:start position:0% +the domain of deep discourse that x and +y range over and we'll suppose that the + + align:start position:0% +y range over and we'll suppose that the + + + align:start position:0% +y range over and we'll suppose that the +domain is the non-negative integers so + + align:start position:0% +domain is the non-negative integers so + + + align:start position:0% +domain is the non-negative integers so +now what G is saying is that if you give + + align:start position:0% +now what G is saying is that if you give + + + align:start position:0% +now what G is saying is that if you give +me a non-negative integer X there is a y + + align:start position:0% +me a non-negative integer X there is a y + + + align:start position:0% +me a non-negative integer X there is a y +that's greater than X I in other words I + + align:start position:0% +that's greater than X I in other words I + + + align:start position:0% +that's greater than X I in other words I +can find another non-negative integer + + align:start position:0% +can find another non-negative integer + + + align:start position:0% +can find another non-negative integer +that's bigger than X well that's + + align:start position:0% +that's bigger than X well that's + + + align:start position:0% +that's bigger than X well that's +certainly true there's a simple recipe + + align:start position:0% +certainly true there's a simple recipe + + + align:start position:0% +certainly true there's a simple recipe +for finding Y give me X let's choose Y + + align:start position:0% +for finding Y give me X let's choose Y + + + align:start position:0% +for finding Y give me X let's choose Y +to be X plus 1 or X plus 2 but I don't + + align:start position:0% +to be X plus 1 or X plus 2 but I don't + + + align:start position:0% +to be X plus 1 or X plus 2 but I don't +necessarily need a recipe + + align:start position:0% +necessarily need a recipe + + + align:start position:0% +necessarily need a recipe +somewhere out there there's a why that's + + align:start position:0% +somewhere out there there's a why that's + + + align:start position:0% +somewhere out there there's a why that's +bigger than X this is true so G is true + + align:start position:0% +bigger than X this is true so G is true + + + align:start position:0% +bigger than X this is true so G is true +when the domain of discourse is the + + align:start position:0% +when the domain of discourse is the + + + align:start position:0% +when the domain of discourse is the +non-negative integers on the other hand + + align:start position:0% +non-negative integers on the other hand + + + align:start position:0% +non-negative integers on the other hand +when I change the domain of discourse + + align:start position:0% +when I change the domain of discourse + + + align:start position:0% +when I change the domain of discourse +different things can happen so let's + + align:start position:0% +different things can happen so let's + + + align:start position:0% +different things can happen so let's +look at the negative integers the + + align:start position:0% +look at the negative integers the + + + align:start position:0% +look at the negative integers the +integer is less than zero and asked is + + align:start position:0% +integer is less than zero and asked is + + + align:start position:0% +integer is less than zero and asked is +it true that for every X there's a y + + align:start position:0% +it true that for every X there's a y + + + align:start position:0% +it true that for every X there's a y +that's greater than X well for a lot of + + align:start position:0% +that's greater than X well for a lot of + + + align:start position:0% +that's greater than X well for a lot of +them there is if X is minus 3 then minus + + align:start position:0% +them there is if X is minus 3 then minus + + + align:start position:0% +them there is if X is minus 3 then minus +2 is bigger than X if X is minus 2 then + + align:start position:0% +2 is bigger than X if X is minus 2 then + + + align:start position:0% +2 is bigger than X if X is minus 2 then +minus 1 is bigger than X but then I'm in + + align:start position:0% +minus 1 is bigger than X but then I'm in + + + align:start position:0% +minus 1 is bigger than X but then I'm in +trouble + + align:start position:0% +trouble + + + align:start position:0% +trouble +if X is minus 1 there's no negative + + align:start position:0% +if X is minus 1 there's no negative + + + align:start position:0% +if X is minus 1 there's no negative +integer that's bigger than X and so G is + + align:start position:0% +integer that's bigger than X and so G is + + + align:start position:0% +integer that's bigger than X and so G is +false + + align:start position:0% +false + + + align:start position:0% +false +when the domain of this course is the + + align:start position:0% +when the domain of this course is the + + + align:start position:0% +when the domain of this course is the +negative integers well let's shift again + + align:start position:0% +negative integers well let's shift again + + + align:start position:0% +negative integers well let's shift again +the point being here both were looking + + align:start position:0% +the point being here both were looking + + + align:start position:0% +the point being here both were looking +at alternating quantifiers and we're + + align:start position:0% +at alternating quantifiers and we're + + + align:start position:0% +at alternating quantifiers and we're +understanding that the meaning of a or + + align:start position:0% +understanding that the meaning of a or + + + align:start position:0% +understanding that the meaning of a or +the truth of a proposition with + + align:start position:0% +the truth of a proposition with + + + align:start position:0% +the truth of a proposition with +quantifiers depends crucially on the + + align:start position:0% +quantifiers depends crucially on the + + + align:start position:0% +quantifiers depends crucially on the +domain of discourse if we let the domain + + align:start position:0% +domain of discourse if we let the domain + + + align:start position:0% +domain of discourse if we let the domain +of this course be the negative reals + + align:start position:0% +of this course be the negative reals + + + align:start position:0% +of this course be the negative reals +then what this is saying is that for + + align:start position:0% +then what this is saying is that for + + + align:start position:0% +then what this is saying is that for +every negative real there's a bigger + + align:start position:0% +every negative real there's a bigger + + + align:start position:0% +every negative real there's a bigger +negative real and that of course is true + + align:start position:0% +negative real and that of course is true + + + align:start position:0% +negative real and that of course is true +because if you give me a negative real + + align:start position:0% +because if you give me a negative real + + + align:start position:0% +because if you give me a negative real +are then are over 2 because it's + + align:start position:0% +are then are over 2 because it's + + + align:start position:0% +are then are over 2 because it's +negative is actually bigger than are and + + align:start position:0% +negative is actually bigger than are and + + + align:start position:0% +negative is actually bigger than are and +it will not be positive if our isn't + + align:start position:0% +it will not be positive if our isn't + + + align:start position:0% +it will not be positive if our isn't +positive so sure enough G in this case + + align:start position:0% +positive so sure enough G in this case + + + align:start position:0% +positive so sure enough G in this case +is true all right let's reverse the + + align:start position:0% +is true all right let's reverse the + + + align:start position:0% +is true all right let's reverse the +quantifiers and see what happens it's + + align:start position:0% +quantifiers and see what happens it's + + + align:start position:0% +quantifiers and see what happens it's +worth thinking about so let's call H the + + align:start position:0% +worth thinking about so let's call H the + + + align:start position:0% +worth thinking about so let's call H the +assertion that for every Y sorry that + + align:start position:0% +assertion that for every Y sorry that + + + align:start position:0% +assertion that for every Y sorry that +there exists a Y such that for every X X + + align:start position:0% +there exists a Y such that for every X X + + + align:start position:0% +there exists a Y such that for every X X +is less than Y so intuitively what this + + align:start position:0% +is less than Y so intuitively what this + + + align:start position:0% +is less than Y so intuitively what this +is saying is there's a biggest element Y + + align:start position:0% +is saying is there's a biggest element Y + + + align:start position:0% +is saying is there's a biggest element Y +is bigger than everything well if the + + align:start position:0% +is bigger than everything well if the + + + align:start position:0% +is bigger than everything well if the +domain is the non-negative integers then + + align:start position:0% +domain is the non-negative integers then + + + align:start position:0% +domain is the non-negative integers then +H is false because there's no biggest + + align:start position:0% +H is false because there's no biggest + + + align:start position:0% +H is false because there's no biggest +non-negative integer + + align:start position:0% +non-negative integer + + + align:start position:0% +non-negative integer +if it's the negative integers it's false + + align:start position:0% +if it's the negative integers it's false + + + align:start position:0% +if it's the negative integers it's false +because there's no biggest negative + + align:start position:0% +because there's no biggest negative + + + align:start position:0% +because there's no biggest negative +integer if it's the negative reals it's + + align:start position:0% +integer if it's the negative reals it's + + + align:start position:0% +integer if it's the negative reals it's +false because there's no biggest + + align:start position:0% +false because there's no biggest + + + align:start position:0% +false because there's no biggest +negative real but the truth is that this + + align:start position:0% +negative real but the truth is that this + + + align:start position:0% +negative real but the truth is that this +thing is going to be false in any domain + + align:start position:0% +thing is going to be false in any domain + + + align:start position:0% +thing is going to be false in any domain +of discourse in which less than is + + align:start position:0% +of discourse in which less than is + + + align:start position:0% +of discourse in which less than is +behaving as it should because of any y + + align:start position:0% +behaving as it should because of any y + + + align:start position:0% +behaving as it should because of any y +is not gonna be bigger than itself + + align:start position:0% +is not gonna be bigger than itself + + + align:start position:0% +is not gonna be bigger than itself +so you can't possibly find a biggest Y + + align:start position:0% +so you can't possibly find a biggest Y + + + align:start position:0% +so you can't possibly find a biggest Y +it would have to be bigger than itself + + align:start position:0% +it would have to be bigger than itself + + + align:start position:0% +it would have to be bigger than itself +this is going to be false in all of + + align:start position:0% +this is going to be false in all of + + + align:start position:0% +this is going to be false in all of +these sensible domains where less than + + align:start position:0% +these sensible domains where less than + + + align:start position:0% +these sensible domains where less than +behaves as we would expect so let's make + + align:start position:0% +behaves as we would expect so let's make + + + align:start position:0% +behaves as we would expect so let's make +this slightly more interesting and make + + align:start position:0% +this slightly more interesting and make + + + align:start position:0% +this slightly more interesting and make +the Y a less than area that it would + + align:start position:0% +the Y a less than area that it would + + + align:start position:0% +the Y a less than area that it would +make that less than a less than or equal + + align:start position:0% +make that less than a less than or equal + + + align:start position:0% +make that less than a less than or equal +to so now it's actually possible that + + align:start position:0% +to so now it's actually possible that + + + align:start position:0% +to so now it's actually possible that +there could be a a biggest element that + + align:start position:0% +there could be a a biggest element that + + + align:start position:0% +there could be a a biggest element that +is greater than or equal to everything + + align:start position:0% +is greater than or equal to everything + + + align:start position:0% +is greater than or equal to everything +including itself and if you look at + + align:start position:0% +including itself and if you look at + + + align:start position:0% +including itself and if you look at +these domains well there isn't any + + align:start position:0% +these domains well there isn't any + + + align:start position:0% +these domains well there isn't any +greatest non-negative integer because + + align:start position:0% +greatest non-negative integer because + + + align:start position:0% +greatest non-negative integer because +for any X X plus 1 is bigger there isn't + + align:start position:0% +for any X X plus 1 is bigger there isn't + + + align:start position:0% +for any X X plus 1 is bigger there isn't +any biggest negative real same reasoning + + align:start position:0% +any biggest negative real same reasoning + + + align:start position:0% +any biggest negative real same reasoning +for any R R over 2 is gonna be bigger + + align:start position:0% +for any R R over 2 is gonna be bigger + + + align:start position:0% +for any R R over 2 is gonna be bigger +but for the negative integers there is a + + align:start position:0% +but for the negative integers there is a + + + align:start position:0% +but for the negative integers there is a +biggest why namely minus 1 its greater + + align:start position:0% +biggest why namely minus 1 its greater + + + align:start position:0% +biggest why namely minus 1 its greater +than or equal to every other negative + + align:start position:0% +than or equal to every other negative + + + align:start position:0% +than or equal to every other negative +integer \ No newline at end of file diff --git a/UySc4jxbqi4.txt b/UySc4jxbqi4.txt new file mode 100644 index 0000000000000000000000000000000000000000..5947d87fb885d1f58623f4addeb393286a84560c --- /dev/null +++ b/UySc4jxbqi4.txt @@ -0,0 +1,14235 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +and that brings us to today's lecture + + align:start position:0% +and that brings us to today's lecture + + + align:start position:0% +and that brings us to today's lecture +which is also something I was not as + + align:start position:0% +which is also something I was not as + + + align:start position:0% +which is also something I was not as +familiar with right so sort of a + + align:start position:0% +familiar with right so sort of a + + + align:start position:0% +familiar with right so sort of a +disclaimer I might have gotten little + + align:start position:0% +disclaimer I might have gotten little + + + align:start position:0% +disclaimer I might have gotten little +things wrong it might not be quite as + + align:start position:0% +things wrong it might not be quite as + + + align:start position:0% +things wrong it might not be quite as +clear but do ask questions so if it's + + align:start position:0% +clear but do ask questions so if it's + + + align:start position:0% +clear but do ask questions so if it's +stuff like lightning Network or discrete + + align:start position:0% +stuff like lightning Network or discrete + + + align:start position:0% +stuff like lightning Network or discrete +log contracts well for me that's sort of + + align:start position:0% +log contracts well for me that's sort of + + + align:start position:0% +log contracts well for me that's sort of +easy because I know it really well this + + align:start position:0% +easy because I know it really well this + + + align:start position:0% +easy because I know it really well this +stuff is things I've known about but I + + align:start position:0% +stuff is things I've known about but I + + + align:start position:0% +stuff is things I've known about but I +never really went as into the details so + + align:start position:0% +never really went as into the details so + + + align:start position:0% +never really went as into the details so +it's a little bit like okay figure it + + align:start position:0% +it's a little bit like okay figure it + + + align:start position:0% +it's a little bit like okay figure it +out enough well enough to explain it + + align:start position:0% +out enough well enough to explain it + + + align:start position:0% +out enough well enough to explain it +rather than just well enough to sort of + + align:start position:0% +rather than just well enough to sort of + + + align:start position:0% +rather than just well enough to sort of +understand how it works so the basic + + align:start position:0% +understand how it works so the basic + + + align:start position:0% +understand how it works so the basic +idea is you want to hide the output + + align:start position:0% +idea is you want to hide the output + + + align:start position:0% +idea is you want to hide the output +amounts so we saw last week how looking + + align:start position:0% +amounts so we saw last week how looking + + + align:start position:0% +amounts so we saw last week how looking +at output amounts can be anonymized and + + align:start position:0% +at output amounts can be anonymized and + + + align:start position:0% +at output amounts can be anonymized and +let you link a lot of different things + + align:start position:0% +let you link a lot of different things + + + align:start position:0% +let you link a lot of different things +and so we'll look at how to do that how + + align:start position:0% +and so we'll look at how to do that how + + + align:start position:0% +and so we'll look at how to do that how +do we hide out them when output amounts + + align:start position:0% +do we hide out them when output amounts + + + align:start position:0% +do we hide out them when output amounts +and so we'll talk about commitments so + + align:start position:0% +and so we'll talk about commitments so + + + align:start position:0% +and so we'll talk about commitments so +first we'll talk about the reasons why + + align:start position:0% +first we'll talk about the reasons why + + + align:start position:0% +first we'll talk about the reasons why +and how to do it then we'll talk about + + align:start position:0% +and how to do it then we'll talk about + + + align:start position:0% +and how to do it then we'll talk about +sort of the definition of commitments + + align:start position:0% +sort of the definition of commitments + + + align:start position:0% +sort of the definition of commitments +like what is a commitment in + + align:start position:0% +like what is a commitment in + + + align:start position:0% +like what is a commitment in +cryptography and then we'll talk about + + align:start position:0% +cryptography and then we'll talk about + + + align:start position:0% +cryptography and then we'll talk about +Peterson commitments and then we'll talk + + align:start position:0% +Peterson commitments and then we'll talk + + + align:start position:0% +Peterson commitments and then we'll talk +about range proofs and put it together + + align:start position:0% +about range proofs and put it together + + + align:start position:0% +about range proofs and put it together +to get what's called confidential + + align:start position:0% +to get what's called confidential + + + align:start position:0% +to get what's called confidential +transactions which is a sort of vaguely + + align:start position:0% +transactions which is a sort of vaguely + + + align:start position:0% +transactions which is a sort of vaguely +non financial transactions it just means + + align:start position:0% +non financial transactions it just means + + + align:start position:0% +non financial transactions it just means +the output amounts are secret okay + + align:start position:0% +the output amounts are secret okay + + + align:start position:0% +the output amounts are secret okay +so yeah interrupt with any questions any + + align:start position:0% +so yeah interrupt with any questions any + + + align:start position:0% +so yeah interrupt with any questions any +point of the way if something is not + + align:start position:0% +point of the way if something is not + + + align:start position:0% +point of the way if something is not +clear + + align:start position:0% +clear + + + align:start position:0% +clear +okay so coin joint last time we talked + + align:start position:0% +okay so coin joint last time we talked + + + align:start position:0% +okay so coin joint last time we talked +about combining transactions with other + + align:start position:0% +about combining transactions with other + + + align:start position:0% +about combining transactions with other +people where you have your input they + + align:start position:0% +people where you have your input they + + + align:start position:0% +people where you have your input they +have their input if your output they + + align:start position:0% +have their input if your output they + + + align:start position:0% +have their input if your output they +have their output and if you sort of + + align:start position:0% +have their output and if you sort of + + + align:start position:0% +have their output and if you sort of +shuffle the ordering of the inputs and + + align:start position:0% +shuffle the ordering of the inputs and + + + align:start position:0% +shuffle the ordering of the inputs and +outputs it might not be clear who's + + align:start position:0% +outputs it might not be clear who's + + + align:start position:0% +outputs it might not be clear who's +sending what where right you're just + + align:start position:0% +sending what where right you're just + + + align:start position:0% +sending what where right you're just +sort of aggregating it and in the + + align:start position:0% +sort of aggregating it and in the + + + align:start position:0% +sort of aggregating it and in the +process you're losing information + + align:start position:0% +process you're losing information + + + align:start position:0% +process you're losing information +because no one gets to see the sort of + + align:start position:0% +because no one gets to see the sort of + + + align:start position:0% +because no one gets to see the sort of +border lines between hey this is one + + align:start position:0% +border lines between hey this is one + + + align:start position:0% +border lines between hey this is one +transaction this is another transaction + + align:start position:0% +transaction this is another transaction + + + align:start position:0% +transaction this is another transaction +it's all in the same transaction so you + + align:start position:0% +it's all in the same transaction so you + + + align:start position:0% +it's all in the same transaction so you +can't really tell but one issue and a + + align:start position:0% +can't really tell but one issue and a + + + align:start position:0% +can't really tell but one issue and a +really big issue was that the output + + align:start position:0% +really big issue was that the output + + + align:start position:0% +really big issue was that the output +amounts can often reveal who's sending + + align:start position:0% +amounts can often reveal who's sending + + + align:start position:0% +amounts can often reveal who's sending +what where so like in this example well + + align:start position:0% +what where so like in this example well + + + align:start position:0% +what where so like in this example well +maybe I don't know who's a but who's B + + align:start position:0% +maybe I don't know who's a but who's B + + + align:start position:0% +maybe I don't know who's a but who's B +who CUSD these all just look like + + align:start position:0% +who CUSD these all just look like + + + align:start position:0% +who CUSD these all just look like +uniformly random addresses or pub keys + + align:start position:0% +uniformly random addresses or pub keys + + + align:start position:0% +uniformly random addresses or pub keys +but if I see an input with ten coins and + + align:start position:0% +but if I see an input with ten coins and + + + align:start position:0% +but if I see an input with ten coins and +input with two coins and an output with + + align:start position:0% +input with two coins and an output with + + + align:start position:0% +input with two coins and an output with +two coins and output with ten coins + + align:start position:0% +two coins and output with ten coins + + + align:start position:0% +two coins and output with ten coins +well there's probably something like + + align:start position:0% +well there's probably something like + + + align:start position:0% +well there's probably something like +this going on right why why else would + + align:start position:0% +this going on right why why else would + + + align:start position:0% +this going on right why why else would +you do this right if you were actually + + align:start position:0% +you do this right if you were actually + + + align:start position:0% +you do this right if you were actually +trying to send two coins somewhere why + + align:start position:0% +trying to send two coins somewhere why + + + align:start position:0% +trying to send two coins somewhere why +even involve this 10 coin input why not + + align:start position:0% +even involve this 10 coin input why not + + + align:start position:0% +even involve this 10 coin input why not +just say two coins the two coins and + + align:start position:0% +just say two coins the two coins and + + + align:start position:0% +just say two coins the two coins and +you're done so if it's if the goal is to + + align:start position:0% +you're done so if it's if the goal is to + + + align:start position:0% +you're done so if it's if the goal is to +you know obscure the transaction graph + + align:start position:0% +you know obscure the transaction graph + + + align:start position:0% +you know obscure the transaction graph +and make have better anonymity because + + align:start position:0% +and make have better anonymity because + + + align:start position:0% +and make have better anonymity because +no one can tell which what's going where + + align:start position:0% +no one can tell which what's going where + + + align:start position:0% +no one can tell which what's going where +well this doesn't really work I think + + align:start position:0% +well this doesn't really work I think + + + align:start position:0% +well this doesn't really work I think +it's going like that and then I showed + + align:start position:0% +it's going like that and then I showed + + + align:start position:0% +it's going like that and then I showed +that there is a way to do it whereas if + + align:start position:0% +that there is a way to do it whereas if + + + align:start position:0% +that there is a way to do it whereas if +you have you know two to eight then the + + align:start position:0% +you have you know two to eight then the + + + align:start position:0% +you have you know two to eight then the +eight is obviously from the person with + + align:start position:0% +eight is obviously from the person with + + + align:start position:0% +eight is obviously from the person with +ten but the two different to coin + + align:start position:0% +ten but the two different to coin + + + align:start position:0% +ten but the two different to coin +outputs are unlink able so that helps + + align:start position:0% +outputs are unlink able so that helps + + + align:start position:0% +outputs are unlink able so that helps +but it's not not great + + align:start position:0% +but it's not not great + + + align:start position:0% +but it's not not great +and then for things like the aggregate + + align:start position:0% +and then for things like the aggregate + + + align:start position:0% +and then for things like the aggregate +signatures maybe you can get people to + + align:start position:0% +signatures maybe you can get people to + + + align:start position:0% +signatures maybe you can get people to +aggregate their transactions together + + align:start position:0% +aggregate their transactions together + + + align:start position:0% +aggregate their transactions together +because it's cheaper and smaller but in + + align:start position:0% +because it's cheaper and smaller but in + + + align:start position:0% +because it's cheaper and smaller but in +general they'll have totally different + + align:start position:0% +general they'll have totally different + + + align:start position:0% +general they'll have totally different +input sizes totally different output + + align:start position:0% +input sizes totally different output + + + align:start position:0% +input sizes totally different output +sizes and it won't really give you any + + align:start position:0% +sizes and it won't really give you any + + + align:start position:0% +sizes and it won't really give you any +anonymity and it won't give you any + + align:start position:0% +anonymity and it won't give you any + + + align:start position:0% +anonymity and it won't give you any +privacy and it hurts fungibility so how + + align:start position:0% +privacy and it hurts fungibility so how + + + align:start position:0% +privacy and it hurts fungibility so how +can we do this wouldn't it be great if + + align:start position:0% +can we do this wouldn't it be great if + + + align:start position:0% +can we do this wouldn't it be great if +we could just hide the output amounts + + align:start position:0% +we could just hide the output amounts + + + align:start position:0% +we could just hide the output amounts +that would be really cool so instead of + + align:start position:0% +that would be really cool so instead of + + + align:start position:0% +that would be really cool so instead of +having it like this it's just you don't + + align:start position:0% +having it like this it's just you don't + + + align:start position:0% +having it like this it's just you don't +see how many coins there are why don't + + align:start position:0% +see how many coins there are why don't + + + align:start position:0% +see how many coins there are why don't +we just delete the output amounts + + align:start position:0% +we just delete the output amounts + + + align:start position:0% +we just delete the output amounts +entirely why even it saves eight bytes + + align:start position:0% +entirely why even it saves eight bytes + + + align:start position:0% +entirely why even it saves eight bytes +right so we can't we can't just delete + + align:start position:0% +right so we can't we can't just delete + + + align:start position:0% +right so we can't we can't just delete +it right so what does this actually mean + + align:start position:0% +it right so what does this actually mean + + + align:start position:0% +it right so what does this actually mean +this would this would be really cool + + align:start position:0% +this would this would be really cool + + + align:start position:0% +this would this would be really cool +though right if we could just sort of + + align:start position:0% +though right if we could just sort of + + + align:start position:0% +though right if we could just sort of +somehow obscure this so that no one can + + align:start position:0% +somehow obscure this so that no one can + + + align:start position:0% +somehow obscure this so that no one can +tell what the amounts are and I guess + + align:start position:0% +tell what the amounts are and I guess + + + align:start position:0% +tell what the amounts are and I guess +initially so they're sort of gonna be + + align:start position:0% +initially so they're sort of gonna be + + + align:start position:0% +initially so they're sort of gonna be +some transition right since Bitcoin + + align:start position:0% +some transition right since Bitcoin + + + align:start position:0% +some transition right since Bitcoin +wasn't built with this from the get-go + + align:start position:0% +wasn't built with this from the get-go + + + align:start position:0% +wasn't built with this from the get-go +at some point there will be a + + align:start position:0% +at some point there will be a + + + align:start position:0% +at some point there will be a +transaction where you can see the input + + align:start position:0% +transaction where you can see the input + + + align:start position:0% +transaction where you can see the input +amounts but then you can't see the + + align:start position:0% +amounts but then you can't see the + + + align:start position:0% +amounts but then you can't see the +output amounts but then you can sort of + + align:start position:0% +output amounts but then you can sort of + + + align:start position:0% +output amounts but then you can sort of +have bounds and say well this neither of + + align:start position:0% +have bounds and say well this neither of + + + align:start position:0% +have bounds and say well this neither of +these can be more than twelve right and + + align:start position:0% +these can be more than twelve right and + + + align:start position:0% +these can be more than twelve right and +then as it goes forward and if the + + align:start position:0% +then as it goes forward and if the + + + align:start position:0% +then as it goes forward and if the +transaction graph gets bigger those + + align:start position:0% +transaction graph gets bigger those + + + align:start position:0% +transaction graph gets bigger those +bounds start getting really wide because + + align:start position:0% +bounds start getting really wide because + + + align:start position:0% +bounds start getting really wide because +you're like well this might have been + + align:start position:0% +you're like well this might have been + + + align:start position:0% +you're like well this might have been +like eleven and it's fine event one and + + align:start position:0% +like eleven and it's fine event one and + + + align:start position:0% +like eleven and it's fine event one and +then the next transaction if it's mixed + + align:start position:0% +then the next transaction if it's mixed + + + align:start position:0% +then the next transaction if it's mixed +in with a bunch of things that have a + + align:start position:0% +in with a bunch of things that have a + + + align:start position:0% +in with a bunch of things that have a +pretty wide range you sort of have to + + align:start position:0% +pretty wide range you sort of have to + + + align:start position:0% +pretty wide range you sort of have to +take the max + + align:start position:0% +take the max + + + align:start position:0% +take the max +and then of all those things the min is + + align:start position:0% +and then of all those things the min is + + + align:start position:0% +and then of all those things the min is +always gonna be like zero so it works + + align:start position:0% +always gonna be like zero so it works + + + align:start position:0% +always gonna be like zero so it works +pretty well even with this trans session + + align:start position:0% +pretty well even with this trans session + + + align:start position:0% +pretty well even with this trans session +oh you could also think of a new system + + align:start position:0% +oh you could also think of a new system + + + align:start position:0% +oh you could also think of a new system +where you start with well you know + + align:start position:0% +where you start with well you know + + + align:start position:0% +where you start with well you know +either you start with obscured amounts + + align:start position:0% +either you start with obscured amounts + + + align:start position:0% +either you start with obscured amounts +or the first mining amounts or not + + align:start position:0% +or the first mining amounts or not + + + align:start position:0% +or the first mining amounts or not +obscured and then you mix them anyway + + align:start position:0% +obscured and then you mix them anyway + + + align:start position:0% +obscured and then you mix them anyway +so this seems like it'd be really useful + + align:start position:0% +so this seems like it'd be really useful + + + align:start position:0% +so this seems like it'd be really useful +because it would allow you to combine + + align:start position:0% +because it would allow you to combine + + + align:start position:0% +because it would allow you to combine +transactions and get better privacy also + + align:start position:0% +transactions and get better privacy also + + + align:start position:0% +transactions and get better privacy also +just really nice in general right even + + align:start position:0% +just really nice in general right even + + + align:start position:0% +just really nice in general right even +if you're not trying to combine with + + align:start position:0% +if you're not trying to combine with + + + align:start position:0% +if you're not trying to combine with +anyone else it's really cool that people + + align:start position:0% +anyone else it's really cool that people + + + align:start position:0% +anyone else it's really cool that people +can't see how much money you have if + + align:start position:0% +can't see how much money you have if + + + align:start position:0% +can't see how much money you have if +people can see how many coins you have + + align:start position:0% +people can see how many coins you have + + + align:start position:0% +people can see how many coins you have +they can try to charge you more they can + + align:start position:0% +they can try to charge you more they can + + + align:start position:0% +they can try to charge you more they can +try to rob you there's all sorts of + + align:start position:0% +try to rob you there's all sorts of + + + align:start position:0% +try to rob you there's all sorts of +reasons why people don't usually say how + + align:start position:0% +reasons why people don't usually say how + + + align:start position:0% +reasons why people don't usually say how +much money they're carrying around right + + align:start position:0% +much money they're carrying around right + + + align:start position:0% +much money they're carrying around right +or how much they make or how you know + + align:start position:0% +or how much they make or how you know + + + align:start position:0% +or how much they make or how you know +things like that people are sort of + + align:start position:0% +things like that people are sort of + + + align:start position:0% +things like that people are sort of +sensitive about pricing information and + + align:start position:0% +sensitive about pricing information and + + + align:start position:0% +sensitive about pricing information and +some of its just sort of societal taboo + + align:start position:0% +some of its just sort of societal taboo + + + align:start position:0% +some of its just sort of societal taboo +but also a lot of its like I don't want + + align:start position:0% +but also a lot of its like I don't want + + + align:start position:0% +but also a lot of its like I don't want +people to know how much money I have and + + align:start position:0% +people to know how much money I have and + + + align:start position:0% +people to know how much money I have and +I think there's like I read recently + + align:start position:0% +I think there's like I read recently + + + align:start position:0% +I think there's like I read recently +like uber sort of doing this thing where + + align:start position:0% +like uber sort of doing this thing where + + + align:start position:0% +like uber sort of doing this thing where +they they're like oh you're rich we're + + align:start position:0% +they they're like oh you're rich we're + + + align:start position:0% +they they're like oh you're rich we're +gonna charge you more and people people + + align:start position:0% +gonna charge you more and people people + + + align:start position:0% +gonna charge you more and people people +don't like that like it has been + + align:start position:0% +don't like that like it has been + + + align:start position:0% +don't like that like it has been +historically doable like people you know + + align:start position:0% +historically doable like people you know + + + align:start position:0% +historically doable like people you know +companies segment things but often the + + align:start position:0% +companies segment things but often the + + + align:start position:0% +companies segment things but often the +way they do is they're like okay well + + align:start position:0% +way they do is they're like okay well + + + align:start position:0% +way they do is they're like okay well +we're gonna make like you know + + align:start position:0% +we're gonna make like you know + + + align:start position:0% +we're gonna make like you know +first-class seats and then economy seats + + align:start position:0% +first-class seats and then economy seats + + + align:start position:0% +first-class seats and then economy seats +and the first-class seats don't take up + + align:start position:0% +and the first-class seats don't take up + + + align:start position:0% +and the first-class seats don't take up +the space of ten economy seats they take + + align:start position:0% +the space of ten economy seats they take + + + align:start position:0% +the space of ten economy seats they take +up the space of maybe two but they cost + + align:start position:0% +up the space of maybe two but they cost + + + align:start position:0% +up the space of maybe two but they cost +like 10x and the idea is well if you're + + align:start position:0% +like 10x and the idea is well if you're + + + align:start position:0% +like 10x and the idea is well if you're +rich we're gonna charge you more you can + + align:start position:0% +rich we're gonna charge you more you can + + + align:start position:0% +rich we're gonna charge you more you can +have the fancy stuff and you know we're + + align:start position:0% +have the fancy stuff and you know we're + + + align:start position:0% +have the fancy stuff and you know we're +gonna make more profit off of that + + align:start position:0% +gonna make more profit off of that + + + align:start position:0% +gonna make more profit off of that +that's sort of more okay I guess but if + + align:start position:0% +that's sort of more okay I guess but if + + + align:start position:0% +that's sort of more okay I guess but if +it's just know you're getting the same + + align:start position:0% +it's just know you're getting the same + + + align:start position:0% +it's just know you're getting the same +economy seat but we know you're rich so + + align:start position:0% +economy seat but we know you're rich so + + + align:start position:0% +economy seat but we know you're rich so +we're gonna charge you more that I don't + + align:start position:0% +we're gonna charge you more that I don't + + + align:start position:0% +we're gonna charge you more that I don't +know yeah and we're sort of getting into + + align:start position:0% +know yeah and we're sort of getting into + + + align:start position:0% +know yeah and we're sort of getting into +that future where there's enough data + + align:start position:0% +that future where there's enough data + + + align:start position:0% +that future where there's enough data +that a lot of companies can do this and + + align:start position:0% +that a lot of companies can do this and + + + align:start position:0% +that a lot of companies can do this and +some people probably myself included is + + align:start position:0% +some people probably myself included is + + + align:start position:0% +some people probably myself included is +like wait no I don't like that I like + + align:start position:0% +like wait no I don't like that I like + + + align:start position:0% +like wait no I don't like that I like +the way it was before where companies + + align:start position:0% +the way it was before where companies + + + align:start position:0% +the way it was before where companies +didn't really know that much about me so + + align:start position:0% +didn't really know that much about me so + + + align:start position:0% +didn't really know that much about me so +this is sort of an effort to try to keep + + align:start position:0% +this is sort of an effort to try to keep + + + align:start position:0% +this is sort of an effort to try to keep +things obscure try to keep the customer + + align:start position:0% +things obscure try to keep the customer + + + align:start position:0% +things obscure try to keep the customer +a bit more anonymous with respect to + + align:start position:0% +a bit more anonymous with respect to + + + align:start position:0% +a bit more anonymous with respect to +merchants so that they don't have as + + align:start position:0% +merchants so that they don't have as + + + align:start position:0% +merchants so that they don't have as +much information to sort of charge more + + align:start position:0% +much information to sort of charge more + + + align:start position:0% +much information to sort of charge more +and then rob you it that's maybe more + + align:start position:0% +and then rob you it that's maybe more + + + align:start position:0% +and then rob you it that's maybe more +Bitcoin specific where like + + align:start position:0% +Bitcoin specific where like + + + align:start position:0% +Bitcoin specific where like +yeah I mean if you walk around in a you + + align:start position:0% +yeah I mean if you walk around in a you + + + align:start position:0% +yeah I mean if you walk around in a you +know area that's sort of high crime with + + align:start position:0% +know area that's sort of high crime with + + + align:start position:0% +know area that's sort of high crime with +a bunch of money hanging out of your + + align:start position:0% +a bunch of money hanging out of your + + + align:start position:0% +a bunch of money hanging out of your +pocket that's a bad idea the Internet is + + align:start position:0% +pocket that's a bad idea the Internet is + + + align:start position:0% +pocket that's a bad idea the Internet is +sort of a high crime area especially + + align:start position:0% +sort of a high crime area especially + + + align:start position:0% +sort of a high crime area especially +with respect to Bitcoin and it's really + + align:start position:0% +with respect to Bitcoin and it's really + + + align:start position:0% +with respect to Bitcoin and it's really +easy to see how much people have and so + + align:start position:0% +easy to see how much people have and so + + + align:start position:0% +easy to see how much people have and so +like it's people you know you the + + align:start position:0% +like it's people you know you the + + + align:start position:0% +like it's people you know you the +hackers know who to target especially if + + align:start position:0% +hackers know who to target especially if + + + align:start position:0% +hackers know who to target especially if +it's like an exchange there they're + + align:start position:0% +it's like an exchange there they're + + + align:start position:0% +it's like an exchange there they're +pretty clear okay this exchange has tons + + align:start position:0% +pretty clear okay this exchange has tons + + + align:start position:0% +pretty clear okay this exchange has tons +money so it might not help the exchange + + align:start position:0% +money so it might not help the exchange + + + align:start position:0% +money so it might not help the exchange +is that much it's sort of obvious they + + align:start position:0% +is that much it's sort of obvious they + + + align:start position:0% +is that much it's sort of obvious they +have a lot of money but anyway okay so + + align:start position:0% +have a lot of money but anyway okay so + + + align:start position:0% +have a lot of money but anyway okay so +this would be really cool to do I think + + align:start position:0% +this would be really cool to do I think + + + align:start position:0% +this would be really cool to do I think +people sort of agree this would be + + align:start position:0% +people sort of agree this would be + + + align:start position:0% +people sort of agree this would be +really cool right like this is this is a + + align:start position:0% +really cool right like this is this is a + + + align:start position:0% +really cool right like this is this is a +nice thing to have + + align:start position:0% +nice thing to have + + + align:start position:0% +nice thing to have +okay so yeah we can it also helps with + + align:start position:0% +okay so yeah we can it also helps with + + + align:start position:0% +okay so yeah we can it also helps with +privacy right you're trying to make it + + align:start position:0% +privacy right you're trying to make it + + + align:start position:0% +privacy right you're trying to make it +hard to link different outputs to each + + align:start position:0% +hard to link different outputs to each + + + align:start position:0% +hard to link different outputs to each +other or link the outputs to a specific + + align:start position:0% +other or link the outputs to a specific + + + align:start position:0% +other or link the outputs to a specific +person and hiding the amounts makes them + + align:start position:0% +person and hiding the amounts makes them + + + align:start position:0% +person and hiding the amounts makes them +really hard to distinguish right so if + + align:start position:0% +really hard to distinguish right so if + + + align:start position:0% +really hard to distinguish right so if +you don't know the amounts they become + + align:start position:0% +you don't know the amounts they become + + + align:start position:0% +you don't know the amounts they become +sort of you completely uniform where + + align:start position:0% +sort of you completely uniform where + + + align:start position:0% +sort of you completely uniform where +this is just a completely random address + + align:start position:0% +this is just a completely random address + + + align:start position:0% +this is just a completely random address +I have no idea how many coins there are + + align:start position:0% +I have no idea how many coins there are + + + align:start position:0% +I have no idea how many coins there are +like I have very little way to + + align:start position:0% +like I have very little way to + + + align:start position:0% +like I have very little way to +distinguish between these of these + + align:start position:0% +distinguish between these of these + + + align:start position:0% +distinguish between these of these +outputs I can sort of try to trace the + + align:start position:0% +outputs I can sort of try to trace the + + + align:start position:0% +outputs I can sort of try to trace the +graph and say okay well this came from + + align:start position:0% +graph and say okay well this came from + + + align:start position:0% +graph and say okay well this came from +here this came from here but they all + + align:start position:0% +here this came from here but they all + + + align:start position:0% +here this came from here but they all +look the same so I've just got this big + + align:start position:0% +look the same so I've just got this big + + + align:start position:0% +look the same so I've just got this big +graph with like no real information + + align:start position:0% +graph with like no real information + + + align:start position:0% +graph with like no real information +other than the links between the notes + + align:start position:0% +other than the links between the notes + + + align:start position:0% +other than the links between the notes +which is still information right but + + align:start position:0% +which is still information right but + + + align:start position:0% +which is still information right but +it's much harder to tell what's going on + + align:start position:0% +it's much harder to tell what's going on + + + align:start position:0% +it's much harder to tell what's going on +okay so we're sold how do we do it okay + + align:start position:0% +okay so we're sold how do we do it okay + + + align:start position:0% +okay so we're sold how do we do it okay +first we need to define what are what + + align:start position:0% +first we need to define what are what + + + align:start position:0% +first we need to define what are what +exactly are we're trying to do right + + align:start position:0% +exactly are we're trying to do right + + + align:start position:0% +exactly are we're trying to do right +whoo what are we hiding from whom who + + align:start position:0% +whoo what are we hiding from whom who + + + align:start position:0% +whoo what are we hiding from whom who +knows what when kind of thing so the + + align:start position:0% +knows what when kind of thing so the + + + align:start position:0% +knows what when kind of thing so the +long-term state of the system no wooden + + align:start position:0% +long-term state of the system no wooden + + + align:start position:0% +long-term state of the system no wooden +can see anything in it no no one can see + + align:start position:0% +can see anything in it no no one can see + + + align:start position:0% +can see anything in it no no one can see +it in the mouse it's just okay a a sign + + align:start position:0% +it in the mouse it's just okay a a sign + + + align:start position:0% +it in the mouse it's just okay a a sign +you know signature from key a signature + + align:start position:0% +you know signature from key a signature + + + align:start position:0% +you know signature from key a signature +from key be some amount of coins you + + align:start position:0% +from key be some amount of coins you + + + align:start position:0% +from key be some amount of coins you +don't see it you don't see any of this + + align:start position:0% +don't see it you don't see any of this + + + align:start position:0% +don't see it you don't see any of this +okay so that's the long-term State but + + align:start position:0% +okay so that's the long-term State but + + + align:start position:0% +okay so that's the long-term State but +wait people receiving the payments + + align:start position:0% +wait people receiving the payments + + + align:start position:0% +wait people receiving the payments +should probably hum know how much + + align:start position:0% +should probably hum know how much + + + align:start position:0% +should probably hum know how much +they're receiving right and they should + + align:start position:0% +they're receiving right and they should + + + align:start position:0% +they're receiving right and they should +probably know how much they have if you + + align:start position:0% +probably know how much they have if you + + + align:start position:0% +probably know how much they have if you +don't know how much money you're getting + + align:start position:0% +don't know how much money you're getting + + + align:start position:0% +don't know how much money you're getting +that's not a very useful payment system + + align:start position:0% +that's not a very useful payment system + + + align:start position:0% +that's not a very useful payment system +people sending should they should also + + align:start position:0% +people sending should they should also + + + align:start position:0% +people sending should they should also +know how much money they're sending + + align:start position:0% +know how much money they're sending + + + align:start position:0% +know how much money they're sending +right if the + + align:start position:0% +right if the + + + align:start position:0% +right if the +can be completely determined by the + + align:start position:0% +can be completely determined by the + + + align:start position:0% +can be completely determined by the +receiver that's also not a good payment + + align:start position:0% +receiver that's also not a good payment + + + align:start position:0% +receiver that's also not a good payment +system I'm just gonna take lots of money + + align:start position:0% +system I'm just gonna take lots of money + + + align:start position:0% +system I'm just gonna take lots of money +so we can have two views right we can + + align:start position:0% +so we can have two views right we can + + + align:start position:0% +so we can have two views right we can +said okay only the sender and receiver + + align:start position:0% +said okay only the sender and receiver + + + align:start position:0% +said okay only the sender and receiver +know the amounts how about that + + align:start position:0% +know the amounts how about that + + + align:start position:0% +know the amounts how about that +we're from the network's point of view + + align:start position:0% +we're from the network's point of view + + + align:start position:0% +we're from the network's point of view +so if I'm just the third party looking + + align:start position:0% +so if I'm just the third party looking + + + align:start position:0% +so if I'm just the third party looking +at this transaction I don't see any of + + align:start position:0% +at this transaction I don't see any of + + + align:start position:0% +at this transaction I don't see any of +the amounts I just see there's no I have + + align:start position:0% +the amounts I just see there's no I have + + + align:start position:0% +the amounts I just see there's no I have +no idea how many coins are being sent + + align:start position:0% +no idea how many coins are being sent + + + align:start position:0% +no idea how many coins are being sent +but from the sender's view the sender + + align:start position:0% +but from the sender's view the sender + + + align:start position:0% +but from the sender's view the sender +says okay I know I have two coins here + + align:start position:0% +says okay I know I have two coins here + + + align:start position:0% +says okay I know I have two coins here +seven coins I changed it from two + + align:start position:0% +seven coins I changed it from two + + + align:start position:0% +seven coins I changed it from two +intended well anyway + + align:start position:0% +intended well anyway + + + align:start position:0% +intended well anyway +two coins here seven coins here and I'm + + align:start position:0% +two coins here seven coins here and I'm + + + align:start position:0% +two coins here seven coins here and I'm +sending seven coins here in two coins + + align:start position:0% +sending seven coins here in two coins + + + align:start position:0% +sending seven coins here in two coins +there so the sender knows the whole + + align:start position:0% +there so the sender knows the whole + + + align:start position:0% +there so the sender knows the whole +thing because they're the ones creating + + align:start position:0% +thing because they're the ones creating + + + align:start position:0% +thing because they're the ones creating +this transaction and then maybe the + + align:start position:0% +this transaction and then maybe the + + + align:start position:0% +this transaction and then maybe the +receiver maybe the receiver doesn't see + + align:start position:0% +receiver maybe the receiver doesn't see + + + align:start position:0% +receiver maybe the receiver doesn't see +everything right maybe the sender can + + align:start position:0% +everything right maybe the sender can + + + align:start position:0% +everything right maybe the sender can +prove to the receiver a single amount + + align:start position:0% +prove to the receiver a single amount + + + align:start position:0% +prove to the receiver a single amount +but hide everything else that would be + + align:start position:0% +but hide everything else that would be + + + align:start position:0% +but hide everything else that would be +ideal right so the the receiver only + + align:start position:0% +ideal right so the the receiver only + + + align:start position:0% +ideal right so the the receiver only +sees oh i'm receiving two coins but i + + align:start position:0% +sees oh i'm receiving two coins but i + + + align:start position:0% +sees oh i'm receiving two coins but i +actually don't know if i know this then + + align:start position:0% +actually don't know if i know this then + + + align:start position:0% +actually don't know if i know this then +i can sort of figure out what these are + + align:start position:0% +i can sort of figure out what these are + + + align:start position:0% +i can sort of figure out what these are +or at least the sum of them but if i + + align:start position:0% +or at least the sum of them but if i + + + align:start position:0% +or at least the sum of them but if i +don't know any of these things i don't + + align:start position:0% +don't know any of these things i don't + + + align:start position:0% +don't know any of these things i don't +know how much the person sending me + + align:start position:0% +know how much the person sending me + + + align:start position:0% +know how much the person sending me +money has i just know oh i got two coins + + align:start position:0% +money has i just know oh i got two coins + + + align:start position:0% +money has i just know oh i got two coins +cool that's what I wanted but I don't + + align:start position:0% +cool that's what I wanted but I don't + + + align:start position:0% +cool that's what I wanted but I don't +learn anything about their inputs or + + align:start position:0% +learn anything about their inputs or + + + align:start position:0% +learn anything about their inputs or +their other outputs within the + + align:start position:0% +their other outputs within the + + + align:start position:0% +their other outputs within the +transaction so that would be ideal if we + + align:start position:0% +transaction so that would be ideal if we + + + align:start position:0% +transaction so that would be ideal if we +can do that right so what we want is the + + align:start position:0% +can do that right so what we want is the + + + align:start position:0% +can do that right so what we want is the +system where network doesn't see any of + + align:start position:0% +system where network doesn't see any of + + + align:start position:0% +system where network doesn't see any of +the amounts the sender presumably sees + + align:start position:0% +the amounts the sender presumably sees + + + align:start position:0% +the amounts the sender presumably sees +all of it now there could be cases where + + align:start position:0% +all of it now there could be cases where + + + align:start position:0% +all of it now there could be cases where +there's multiple senders right and there + + align:start position:0% +there's multiple senders right and there + + + align:start position:0% +there's multiple senders right and there +are two people working together to make + + align:start position:0% +are two people working together to make + + + align:start position:0% +are two people working together to make +a transaction and maybe we don't see + + align:start position:0% +a transaction and maybe we don't see + + + align:start position:0% +a transaction and maybe we don't see +each other's inputs but we'll keep it + + align:start position:0% +each other's inputs but we'll keep it + + + align:start position:0% +each other's inputs but we'll keep it +simple for now where there's a single + + align:start position:0% +simple for now where there's a single + + + align:start position:0% +simple for now where there's a single +sender and then the receiver only sees + + align:start position:0% +sender and then the receiver only sees + + + align:start position:0% +sender and then the receiver only sees +their own output so that would be a + + align:start position:0% +their own output so that would be a + + + align:start position:0% +their own output so that would be a +really powerful system then the receiver + + align:start position:0% +really powerful system then the receiver + + + align:start position:0% +really powerful system then the receiver +would only know they're getting the + + align:start position:0% +would only know they're getting the + + + align:start position:0% +would only know they're getting the +right amount and not learn anything else + + align:start position:0% +right amount and not learn anything else + + + align:start position:0% +right amount and not learn anything else +about the sender's coins okay so yeah we + + align:start position:0% +about the sender's coins okay so yeah we + + + align:start position:0% +about the sender's coins okay so yeah we +might want to like I'm saying you might + + align:start position:0% +might want to like I'm saying you might + + + align:start position:0% +might want to like I'm saying you might +want to hide per output so if you have + + align:start position:0% +want to hide per output so if you have + + + align:start position:0% +want to hide per output so if you have +it if it's just a sort of global like + + align:start position:0% +it if it's just a sort of global like + + + align:start position:0% +it if it's just a sort of global like +either you see everything or you see you + + align:start position:0% +either you see everything or you see you + + + align:start position:0% +either you see everything or you see you +know like you see nothing or you see + + align:start position:0% +know like you see nothing or you see + + + align:start position:0% +know like you see nothing or you see +everything that's still pretty good + + align:start position:0% +everything that's still pretty good + + + align:start position:0% +everything that's still pretty good +right that's still + + align:start position:0% +right that's still + + + align:start position:0% +right that's still +than what we have when everyone sees + + align:start position:0% +than what we have when everyone sees + + + align:start position:0% +than what we have when everyone sees +everything but it it is better if you + + align:start position:0% +everything but it it is better if you + + + align:start position:0% +everything but it it is better if you +can hide it hide the rest of these three + + align:start position:0% +can hide it hide the rest of these three + + + align:start position:0% +can hide it hide the rest of these three +things from the receiver so any ideas + + align:start position:0% +things from the receiver so any ideas + + + align:start position:0% +things from the receiver so any ideas +some kind of encryption hide the amounts + + align:start position:0% +some kind of encryption hide the amounts + + + align:start position:0% +some kind of encryption hide the amounts +of the only people with the right + + align:start position:0% +of the only people with the right + + + align:start position:0% +of the only people with the right +private key can see the numbers right so + + align:start position:0% +private key can see the numbers right so + + + align:start position:0% +private key can see the numbers right so +you encrypt I mean okay so actually I + + align:start position:0% +you encrypt I mean okay so actually I + + + align:start position:0% +you encrypt I mean okay so actually I +don't think I've even talked about + + align:start position:0% +don't think I've even talked about + + + align:start position:0% +don't think I've even talked about +encryption ever in this class because + + align:start position:0% +encryption ever in this class because + + + align:start position:0% +encryption ever in this class because +there's no encryption in blockchain so + + align:start position:0% +there's no encryption in blockchain so + + + align:start position:0% +there's no encryption in blockchain so +which is something you like if you read + + align:start position:0% +which is something you like if you read + + + align:start position:0% +which is something you like if you read +something about blockchain and you like + + align:start position:0% +something about blockchain and you like + + + align:start position:0% +something about blockchain and you like +blockchain is encrypted right now no + + align:start position:0% +blockchain is encrypted right now no + + + align:start position:0% +blockchain is encrypted right now no +they don't know what I'm talking about + + align:start position:0% +they don't know what I'm talking about + + + align:start position:0% +they don't know what I'm talking about +so I haven't actually defined encryption + + align:start position:0% +so I haven't actually defined encryption + + + align:start position:0% +so I haven't actually defined encryption +but encryption is generally you have + + align:start position:0% +but encryption is generally you have + + + align:start position:0% +but encryption is generally you have +some kind of private key you take a + + align:start position:0% +some kind of private key you take a + + + align:start position:0% +some kind of private key you take a +clear text you apply you know you do + + align:start position:0% +clear text you apply you know you do + + + align:start position:0% +clear text you apply you know you do +some so so like I had what signatures + + align:start position:0% +some so so like I had what signatures + + + align:start position:0% +some so so like I had what signatures +you have so a set of functions so + + align:start position:0% +you have so a set of functions so + + + align:start position:0% +you have so a set of functions so +encryption is just okay you've got some + + align:start position:0% +encryption is just okay you've got some + + + align:start position:0% +encryption is just okay you've got some +encryption function which takes a key + + align:start position:0% +encryption function which takes a key + + + align:start position:0% +encryption function which takes a key +and a message and outputs a ciphertext + + align:start position:0% +and a message and outputs a ciphertext + + + align:start position:0% +and a message and outputs a ciphertext +and then you've got some kind of + + align:start position:0% +and then you've got some kind of + + + align:start position:0% +and then you've got some kind of +decryption function which takes often in + + align:start position:0% +decryption function which takes often in + + + align:start position:0% +decryption function which takes often in +the same key or something and then the + + align:start position:0% +the same key or something and then the + + + align:start position:0% +the same key or something and then the +ciphertext and outputs the same message + + align:start position:0% +ciphertext and outputs the same message + + + align:start position:0% +ciphertext and outputs the same message +this is symmetric encryption because + + align:start position:0% +this is symmetric encryption because + + + align:start position:0% +this is symmetric encryption because +you're using the same key you can also + + align:start position:0% +you're using the same key you can also + + + align:start position:0% +you're using the same key you can also +have a symmetric equipt encryption where + + align:start position:0% +have a symmetric equipt encryption where + + + align:start position:0% +have a symmetric equipt encryption where +this could be a public key and this + + align:start position:0% +this could be a public key and this + + + align:start position:0% +this could be a public key and this +could be a private key so in order to + + align:start position:0% +could be a private key so in order to + + + align:start position:0% +could be a private key so in order to +decrypt you need the private key but in + + align:start position:0% +decrypt you need the private key but in + + + align:start position:0% +decrypt you need the private key but in +order to encrypt you only need someone's + + align:start position:0% +order to encrypt you only need someone's + + + align:start position:0% +order to encrypt you only need someone's +public key so in practice the all the + + align:start position:0% +public key so in practice the all the + + + align:start position:0% +public key so in practice the all the +things that people in practice usually + + align:start position:0% +things that people in practice usually + + + align:start position:0% +things that people in practice usually +stage it so you have an asymmetric + + align:start position:0% +stage it so you have an asymmetric + + + align:start position:0% +stage it so you have an asymmetric +algorithm to agree on a key and then you + + align:start position:0% +algorithm to agree on a key and then you + + + align:start position:0% +algorithm to agree on a key and then you +just use this symmetric encryption and + + align:start position:0% +just use this symmetric encryption and + + + align:start position:0% +just use this symmetric encryption and +decryption where the keys are the same + + align:start position:0% +decryption where the keys are the same + + + align:start position:0% +decryption where the keys are the same +because it's like way faster so you can + + align:start position:0% +because it's like way faster so you can + + + align:start position:0% +because it's like way faster so you can +you can do this operation on the order + + align:start position:0% +you can do this operation on the order + + + align:start position:0% +you can do this operation on the order +of like hundreds of megabytes a second + + align:start position:0% +of like hundreds of megabytes a second + + + align:start position:0% +of like hundreds of megabytes a second +whereas the asymmetric ones are slow + + align:start position:0% +whereas the asymmetric ones are slow + + + align:start position:0% +whereas the asymmetric ones are slow +they're sort of it's sort of like + + align:start position:0% +they're sort of it's sort of like + + + align:start position:0% +they're sort of it's sort of like +signing in to it later but yeah it's + + align:start position:0% +signing in to it later but yeah it's + + + align:start position:0% +signing in to it later but yeah it's +it's if you understand all the signing + + align:start position:0% +it's if you understand all the signing + + + align:start position:0% +it's if you understand all the signing +and stuff it's actually not not too bad + + align:start position:0% +and stuff it's actually not not too bad + + + align:start position:0% +and stuff it's actually not not too bad +but so maybe we could say okay well + + align:start position:0% +but so maybe we could say okay well + + + align:start position:0% +but so maybe we could say okay well +there's some kind of private key that + + align:start position:0% +there's some kind of private key that + + + align:start position:0% +there's some kind of private key that +the sender creates encrypts the amounts + + align:start position:0% +the sender creates encrypts the amounts + + + align:start position:0% +the sender creates encrypts the amounts +and then they put the encrypted amounts + + align:start position:0% +and then they put the encrypted amounts + + + align:start position:0% +and then they put the encrypted amounts +in the in the transact + + align:start position:0% +in the in the transact + + + align:start position:0% +in the in the transact +and they reveal the key to the receiver + + align:start position:0% +and they reveal the key to the receiver + + + align:start position:0% +and they reveal the key to the receiver +and potentially you could have different + + align:start position:0% +and potentially you could have different + + + align:start position:0% +and potentially you could have different +keys for each amount right that would + + align:start position:0% +keys for each amount right that would + + + align:start position:0% +keys for each amount right that would +work any problems with that idea you can + + align:start position:0% +work any problems with that idea you can + + + align:start position:0% +work any problems with that idea you can +encrypt everything yeah yeah yeah okay + + align:start position:0% +encrypt everything yeah yeah yeah okay + + + align:start position:0% +encrypt everything yeah yeah yeah okay +so that's that is a sort of no problem + + align:start position:0% +so that's that is a sort of no problem + + + align:start position:0% +so that's that is a sort of no problem +it's a limit but that that limit will + + align:start position:0% +it's a limit but that that limit will + + + align:start position:0% +it's a limit but that that limit will +carry forward to the stuff we actually + + align:start position:0% +carry forward to the stuff we actually + + + align:start position:0% +carry forward to the stuff we actually +do so yeah you're gonna have to right + + align:start position:0% +do so yeah you're gonna have to right + + + align:start position:0% +do so yeah you're gonna have to right +now in Bitcoin you can just sort of find + + align:start position:0% +now in Bitcoin you can just sort of find + + + align:start position:0% +now in Bitcoin you can just sort of find +someone's address send them the coins + + align:start position:0% +someone's address send them the coins + + + align:start position:0% +someone's address send them the coins +you're good with this system there will + + align:start position:0% +you're good with this system there will + + + align:start position:0% +you're good with this system there will +be more interactivity between sender and + + align:start position:0% +be more interactivity between sender and + + + align:start position:0% +be more interactivity between sender and +receiver so that's not great but not a + + align:start position:0% +receiver so that's not great but not a + + + align:start position:0% +receiver so that's not great but not a +deal breaker right so yeah we will need + + align:start position:0% +deal breaker right so yeah we will need + + + align:start position:0% +deal breaker right so yeah we will need +to do that other problem yeah the actual + + align:start position:0% +to do that other problem yeah the actual + + + align:start position:0% +to do that other problem yeah the actual +solution gets it's kind of big so that's + + align:start position:0% +solution gets it's kind of big so that's + + + align:start position:0% +solution gets it's kind of big so that's +that's not great either but the one that + + align:start position:0% +that's not great either but the one that + + + align:start position:0% +that's not great either but the one that +really screws it up because they can't + + align:start position:0% +really screws it up because they can't + + + align:start position:0% +really screws it up because they can't +see anything + + align:start position:0% +see anything + + + align:start position:0% +see anything +well I can just do that right like well + + align:start position:0% +well I can just do that right like well + + + align:start position:0% +well I can just do that right like well +how about I just make 70 coins and 2000 + + align:start position:0% +how about I just make 70 coins and 2000 + + + align:start position:0% +how about I just make 70 coins and 2000 +coin like I can just make as many coins + + align:start position:0% +coin like I can just make as many coins + + + align:start position:0% +coin like I can just make as many coins +as I want no one can see anything + + align:start position:0% +as I want no one can see anything + + + align:start position:0% +as I want no one can see anything +because the network just sees mmm + + align:start position:0% +because the network just sees mmm + + + align:start position:0% +because the network just sees mmm +nothing + + align:start position:0% +nothing + + + align:start position:0% +nothing +I have no idea how many coins are being + + align:start position:0% +I have no idea how many coins are being + + + align:start position:0% +I have no idea how many coins are being +sent but I'm like hey I'm just making + + align:start position:0% +sent but I'm like hey I'm just making + + + align:start position:0% +sent but I'm like hey I'm just making +more coins all over the place + + align:start position:0% +more coins all over the place + + + align:start position:0% +more coins all over the place +and this this doesn't work right because + + align:start position:0% +and this this doesn't work right because + + + align:start position:0% +and this this doesn't work right because +if I can just send coins to myself and + + align:start position:0% +if I can just send coins to myself and + + + align:start position:0% +if I can just send coins to myself and +multiply them indefinitely and like it's + + align:start position:0% +multiply them indefinitely and like it's + + + align:start position:0% +multiply them indefinitely and like it's +hidden so I'm like so to some extent + + align:start position:0% +hidden so I'm like so to some extent + + + align:start position:0% +hidden so I'm like so to some extent +you're like well maybe the network + + align:start position:0% +you're like well maybe the network + + + align:start position:0% +you're like well maybe the network +doesn't care right because well I'm + + align:start position:0% +doesn't care right because well I'm + + + align:start position:0% +doesn't care right because well I'm +making them but they're only my own + + align:start position:0% +making them but they're only my own + + + align:start position:0% +making them but they're only my own +coins but if the network doesn't see + + align:start position:0% +coins but if the network doesn't see + + + align:start position:0% +coins but if the network doesn't see +anything it's easy to create the coins + + align:start position:0% +anything it's easy to create the coins + + + align:start position:0% +anything it's easy to create the coins +and if those coins are later used I + + align:start position:0% +and if those coins are later used I + + + align:start position:0% +and if those coins are later used I +can't tell if they were made up or not + + align:start position:0% +can't tell if they were made up or not + + + align:start position:0% +can't tell if they were made up or not +so if I'm accepting so if I actually see + + align:start position:0% +so if I'm accepting so if I actually see + + + align:start position:0% +so if I'm accepting so if I actually see +this right and someone's like hey here's + + align:start position:0% +this right and someone's like hey here's + + + align:start position:0% +this right and someone's like hey here's +2000 coins I'm like dude this is you're + + align:start position:0% +2000 coins I'm like dude this is you're + + + align:start position:0% +2000 coins I'm like dude this is you're +just making them up you can't just like + + align:start position:0% +just making them up you can't just like + + + align:start position:0% +just making them up you can't just like +write extra zeros on a hundred dollar + + align:start position:0% +write extra zeros on a hundred dollar + + + align:start position:0% +write extra zeros on a hundred dollar +bill like you + + align:start position:0% +bill like you + + + align:start position:0% +bill like you +like this is come on no one's gonna no + + align:start position:0% +like this is come on no one's gonna no + + + align:start position:0% +like this is come on no one's gonna no +one's gonna accept these later right + + align:start position:0% +one's gonna accept these later right + + + align:start position:0% +one's gonna accept these later right +except I and and I won't even know + + align:start position:0% +except I and and I won't even know + + + align:start position:0% +except I and and I won't even know +did you actually even have seven does + + align:start position:0% +did you actually even have seven does + + + align:start position:0% +did you actually even have seven does +this seven coins come from something + + align:start position:0% +this seven coins come from something + + + align:start position:0% +this seven coins come from something +where you did this same kind of thing + + align:start position:0% +where you did this same kind of thing + + + align:start position:0% +where you did this same kind of thing +before so basically if we do that where + + align:start position:0% +before so basically if we do that where + + + align:start position:0% +before so basically if we do that where +we completely obscure the amounts from + + align:start position:0% +we completely obscure the amounts from + + + align:start position:0% +we completely obscure the amounts from +the network and from all third parties + + align:start position:0% +the network and from all third parties + + + align:start position:0% +the network and from all third parties +then any time I'm going to accept this + + align:start position:0% +then any time I'm going to accept this + + + align:start position:0% +then any time I'm going to accept this +I'm gonna have to enforce the rules + + align:start position:0% +I'm gonna have to enforce the rules + + + align:start position:0% +I'm gonna have to enforce the rules +myself and then like retro actively + + align:start position:0% +myself and then like retro actively + + + align:start position:0% +myself and then like retro actively +enforced the rules for all transactions + + align:start position:0% +enforced the rules for all transactions + + + align:start position:0% +enforced the rules for all transactions +beforehand to make sure nothing like + + align:start position:0% +beforehand to make sure nothing like + + + align:start position:0% +beforehand to make sure nothing like +this happened so we could do that we + + align:start position:0% +this happened so we could do that we + + + align:start position:0% +this happened so we could do that we +could say okay it's all obscured the + + align:start position:0% +could say okay it's all obscured the + + + align:start position:0% +could say okay it's all obscured the +third party the network doesn't see + + align:start position:0% +third party the network doesn't see + + + align:start position:0% +third party the network doesn't see +anything and it's up to the participants + + align:start position:0% +anything and it's up to the participants + + + align:start position:0% +anything and it's up to the participants +themselves to say well if you're gonna + + align:start position:0% +themselves to say well if you're gonna + + + align:start position:0% +themselves to say well if you're gonna +send me coins since I know if I'm + + align:start position:0% +send me coins since I know if I'm + + + align:start position:0% +send me coins since I know if I'm +sending it to someone later I'm gonna + + align:start position:0% +sending it to someone later I'm gonna + + + align:start position:0% +sending it to someone later I'm gonna +have to provide some kind of proof that + + align:start position:0% +have to provide some kind of proof that + + + align:start position:0% +have to provide some kind of proof that +this kind of nonsense didn't happen I'm + + align:start position:0% +this kind of nonsense didn't happen I'm + + + align:start position:0% +this kind of nonsense didn't happen I'm +also gonna need proof that all of the + + align:start position:0% +also gonna need proof that all of the + + + align:start position:0% +also gonna need proof that all of the +ancestor transactions that led to these + + align:start position:0% +ancestor transactions that led to these + + + align:start position:0% +ancestor transactions that led to these +two and seven coins I'm gonna need those + + align:start position:0% +two and seven coins I'm gonna need those + + + align:start position:0% +two and seven coins I'm gonna need those +amounts and so yeah you could maybe do + + align:start position:0% +amounts and so yeah you could maybe do + + + align:start position:0% +amounts and so yeah you could maybe do +that right you could provide the + + align:start position:0% +that right you could provide the + + + align:start position:0% +that right you could provide the +decryption keys for all previous amounts + + align:start position:0% +decryption keys for all previous amounts + + + align:start position:0% +decryption keys for all previous amounts +but that basically gets you back to + + align:start position:0% +but that basically gets you back to + + + align:start position:0% +but that basically gets you back to +where we are right now right not not + + align:start position:0% +where we are right now right not not + + + align:start position:0% +where we are right now right not not +quite but pretty close + + align:start position:0% +quite but pretty close + + + align:start position:0% +quite but pretty close +hey guys yeah either you allow people to + + align:start position:0% +hey guys yeah either you allow people to + + + align:start position:0% +hey guys yeah either you allow people to +create coins or you basically are + + align:start position:0% +create coins or you basically are + + + align:start position:0% +create coins or you basically are +revealing close to all previous amounts + + align:start position:0% +revealing close to all previous amounts + + + align:start position:0% +revealing close to all previous amounts +eventually to everyone right because as + + align:start position:0% +eventually to everyone right because as + + + align:start position:0% +eventually to everyone right because as +that transaction graph gets bigger and + + align:start position:0% +that transaction graph gets bigger and + + + align:start position:0% +that transaction graph gets bigger and +bigger I'm gonna start having all these + + align:start position:0% +bigger I'm gonna start having all these + + + align:start position:0% +bigger I'm gonna start having all these +like thousands and thousands of an + + align:start position:0% +like thousands and thousands of an + + + align:start position:0% +like thousands and thousands of an +ancestor transactions that I'm gonna + + align:start position:0% +ancestor transactions that I'm gonna + + + align:start position:0% +ancestor transactions that I'm gonna +have to require proof for you know I'm + + align:start position:0% +have to require proof for you know I'm + + + align:start position:0% +have to require proof for you know I'm +gonna require all those decryption keys + + align:start position:0% +gonna require all those decryption keys + + + align:start position:0% +gonna require all those decryption keys +to make sure nothing like this happened + + align:start position:0% +to make sure nothing like this happened + + + align:start position:0% +to make sure nothing like this happened +and then eventually all the people + + align:start position:0% +and then eventually all the people + + + align:start position:0% +and then eventually all the people +receiving money will be able to see + + align:start position:0% +receiving money will be able to see + + + align:start position:0% +receiving money will be able to see +everything we're not quite everything + + align:start position:0% +everything we're not quite everything + + + align:start position:0% +everything we're not quite everything +but a lot so it's like well third + + align:start position:0% +but a lot so it's like well third + + + align:start position:0% +but a lot so it's like well third +parties you know the miners or maybe + + align:start position:0% +parties you know the miners or maybe + + + align:start position:0% +parties you know the miners or maybe +people who are just looking at the + + align:start position:0% +people who are just looking at the + + + align:start position:0% +people who are just looking at the +blockchain who aren't really receiving + + align:start position:0% +blockchain who aren't really receiving + + + align:start position:0% +blockchain who aren't really receiving +any funds maybe it's it's hidden from + + align:start position:0% +any funds maybe it's it's hidden from + + + align:start position:0% +any funds maybe it's it's hidden from +them but once you start actually using + + align:start position:0% +them but once you start actually using + + + align:start position:0% +them but once you start actually using +the system you're gonna basically be + + align:start position:0% +the system you're gonna basically be + + + align:start position:0% +the system you're gonna basically be +able to see everything so that's not + + align:start position:0% +able to see everything so that's not + + + align:start position:0% +able to see everything so that's not +great and it would also be like really + + align:start position:0% +great and it would also be like really + + + align:start position:0% +great and it would also be like really +annoying because then when you have to + + align:start position:0% +annoying because then when you have to + + + align:start position:0% +annoying because then when you have to +like receive coins you have to like go + + align:start position:0% +like receive coins you have to like go + + + align:start position:0% +like receive coins you have to like go +back through thousands of transactions + + align:start position:0% +back through thousands of transactions + + + align:start position:0% +back through thousands of transactions +to make sure that didn't happen + + align:start position:0% +to make sure that didn't happen + + + align:start position:0% +to make sure that didn't happen +so we need to prevent coin creation + + align:start position:0% +so we need to prevent coin creation + + + align:start position:0% +so we need to prevent coin creation +while still keeping the amounts secret + + align:start position:0% +while still keeping the amounts secret + + + align:start position:0% +while still keeping the amounts secret +this is a tricky problem right + + align:start position:0% +this is a tricky problem right + + + align:start position:0% +this is a tricky problem right +any general ideas here yeah so wouldn't + + align:start position:0% +any general ideas here yeah so wouldn't + + + align:start position:0% +any general ideas here yeah so wouldn't +it be cool if we could do this where you + + align:start position:0% +it be cool if we could do this where you + + + align:start position:0% +it be cool if we could do this where you +sort of the network sees okay + + align:start position:0% +sort of the network sees okay + + + align:start position:0% +sort of the network sees okay +there's W coins here there's X coins + + align:start position:0% +there's W coins here there's X coins + + + align:start position:0% +there's W coins here there's X coins +here and there's Y coins here there's + + align:start position:0% +here and there's Y coins here there's + + + align:start position:0% +here and there's Y coins here there's +equals here and then we have a proof W + + align:start position:0% +equals here and then we have a proof W + + + align:start position:0% +equals here and then we have a proof W +plus X equals y plus C without telling + + align:start position:0% +plus X equals y plus C without telling + + + align:start position:0% +plus X equals y plus C without telling +you what w XY and z are cool okay let's + + align:start position:0% +you what w XY and z are cool okay let's + + + align:start position:0% +you what w XY and z are cool okay let's +do it + + align:start position:0% +do it + + + align:start position:0% +do it +any ideas + + align:start position:0% + + + + align:start position:0% + +so yeah this seems like this would be + + align:start position:0% +so yeah this seems like this would be + + + align:start position:0% +so yeah this seems like this would be +this would work right this would this + + align:start position:0% +this would work right this would this + + + align:start position:0% +this would work right this would this +would do it in that if we can reveal + + align:start position:0% +would do it in that if we can reveal + + + align:start position:0% +would do it in that if we can reveal +like say hey the person I'm you know + + align:start position:0% +like say hey the person I'm you know + + + align:start position:0% +like say hey the person I'm you know +person D Z is 2 okay cool + + align:start position:0% +person D Z is 2 okay cool + + + align:start position:0% +person D Z is 2 okay cool +so I got two coins and they can also + + align:start position:0% +so I got two coins and they can also + + + align:start position:0% +so I got two coins and they can also +verify that these amounts are correct + + align:start position:0% +verify that these amounts are correct + + + align:start position:0% +verify that these amounts are correct +and then if you you could either keep + + align:start position:0% +and then if you you could either keep + + + align:start position:0% +and then if you you could either keep +this proof only to the receiver but then + + align:start position:0% +this proof only to the receiver but then + + + align:start position:0% +this proof only to the receiver but then +you'd have to give proofs to all the pre + + align:start position:0% +you'd have to give proofs to all the pre + + + align:start position:0% +you'd have to give proofs to all the pre +about all the previous transactions or + + align:start position:0% +about all the previous transactions or + + + align:start position:0% +about all the previous transactions or +you can just say no the whole network + + align:start position:0% +you can just say no the whole network + + + align:start position:0% +you can just say no the whole network +enforces these proofs right this is now + + align:start position:0% +enforces these proofs right this is now + + + align:start position:0% +enforces these proofs right this is now +a consensus rule where if you want you + + align:start position:0% +a consensus rule where if you want you + + + align:start position:0% +a consensus rule where if you want you +know even if it's not your transaction + + align:start position:0% +know even if it's not your transaction + + + align:start position:0% +know even if it's not your transaction +it might be a parent of your transaction + + align:start position:0% +it might be a parent of your transaction + + + align:start position:0% +it might be a parent of your transaction +someday so you have to verify it if + + align:start position:0% +someday so you have to verify it if + + + align:start position:0% +someday so you have to verify it if +you're gonna accept the block verify + + align:start position:0% +you're gonna accept the block verify + + + align:start position:0% +you're gonna accept the block verify +these proofs for every transaction so + + align:start position:0% +these proofs for every transaction so + + + align:start position:0% +these proofs for every transaction so +that would work yeah + + align:start position:0% + + + + align:start position:0% + +yeah a minor or or yeah the miners would + + align:start position:0% +yeah a minor or or yeah the miners would + + + align:start position:0% +yeah a minor or or yeah the miners would +do it and also the full notes you know + + align:start position:0% +do it and also the full notes you know + + + align:start position:0% +do it and also the full notes you know +if you're running an ode well I'm not + + align:start position:0% +if you're running an ode well I'm not + + + align:start position:0% +if you're running an ode well I'm not +receiving anything here but I just still + + align:start position:0% +receiving anything here but I just still + + + align:start position:0% +receiving anything here but I just still +need to make sure this is a valid + + align:start position:0% +need to make sure this is a valid + + + align:start position:0% +need to make sure this is a valid +transaction in order to accept it if the + + align:start position:0% +transaction in order to accept it if the + + + align:start position:0% +transaction in order to accept it if the +miners receipt like miner is D and + + align:start position:0% +miners receipt like miner is D and + + + align:start position:0% +miners receipt like miner is D and +receiving this coin then they'll they'll + + align:start position:0% +receiving this coin then they'll they'll + + + align:start position:0% +receiving this coin then they'll they'll +know they they'll both get the proof + + align:start position:0% +know they they'll both get the proof + + + align:start position:0% +know they they'll both get the proof +which is sort of redundant for them and + + align:start position:0% +which is sort of redundant for them and + + + align:start position:0% +which is sort of redundant for them and +they'll also get the actual amount C + + align:start position:0% +they'll also get the actual amount C + + + align:start position:0% +they'll also get the actual amount C +like so they'll know ok this is - yeah + + align:start position:0% +like so they'll know ok this is - yeah + + + align:start position:0% +like so they'll know ok this is - yeah +so that miner would know more but that's + + align:start position:0% +so that miner would know more but that's + + + align:start position:0% +so that miner would know more but that's +okay I guess other miners wouldn't where + + align:start position:0% +okay I guess other miners wouldn't where + + + align:start position:0% +okay I guess other miners wouldn't where +others nodes wouldn't yeah if you're + + align:start position:0% +others nodes wouldn't yeah if you're + + + align:start position:0% +others nodes wouldn't yeah if you're +participating + + align:start position:0% +participating + + + align:start position:0% +participating +you'll potentially know more but the + + align:start position:0% +you'll potentially know more but the + + + align:start position:0% +you'll potentially know more but the +idea is third parties just see a proof + + align:start position:0% +idea is third parties just see a proof + + + align:start position:0% +idea is third parties just see a proof +and don't see the mounts okay so it's + + align:start position:0% +and don't see the mounts okay so it's + + + align:start position:0% +and don't see the mounts okay so it's +already have no idea how many coins are + + align:start position:0% +already have no idea how many coins are + + + align:start position:0% +already have no idea how many coins are +coming in on the inputs because they + + align:start position:0% +coming in on the inputs because they + + + align:start position:0% +coming in on the inputs because they +don't have aut Exocet and the coin you + + align:start position:0% +don't have aut Exocet and the coin you + + + align:start position:0% +don't have aut Exocet and the coin you +know so if you see an input you just see + + align:start position:0% +know so if you see an input you just see + + + align:start position:0% +know so if you see an input you just see +okay it's pointing to some TX ID I don't + + align:start position:0% +okay it's pointing to some TX ID I don't + + + align:start position:0% +okay it's pointing to some TX ID I don't +know how many coins there are I would + + align:start position:0% +know how many coins there are I would + + + align:start position:0% +know how many coins there are I would +have to you could you know you could + + align:start position:0% +have to you could you know you could + + + align:start position:0% +have to you could you know you could +provide a proof to an SP V wallet that + + align:start position:0% +provide a proof to an SP V wallet that + + + align:start position:0% +provide a proof to an SP V wallet that +hey there were you know I can give you + + align:start position:0% +hey there were you know I can give you + + + align:start position:0% +hey there were you know I can give you +that previous transaction and you can + + align:start position:0% +that previous transaction and you can + + + align:start position:0% +that previous transaction and you can +see how many coins but then what about + + align:start position:0% +see how many coins but then what about + + + align:start position:0% +see how many coins but then what about +the one before that so generally svv + + align:start position:0% +the one before that so generally svv + + + align:start position:0% +the one before that so generally svv +wallets can't enforce that amounts are + + align:start position:0% +wallets can't enforce that amounts are + + + align:start position:0% +wallets can't enforce that amounts are +correct or verify signatures because + + align:start position:0% +correct or verify signatures because + + + align:start position:0% +correct or verify signatures because +they don't know enough about these + + align:start position:0% +they don't know enough about these + + + align:start position:0% +they don't know enough about these +inputs whereas full nodes once you see + + align:start position:0% +inputs whereas full nodes once you see + + + align:start position:0% +inputs whereas full nodes once you see +okay when you tell me input zero I know + + align:start position:0% +okay when you tell me input zero I know + + + align:start position:0% +okay when you tell me input zero I know +how much I know what keys things like + + align:start position:0% +how much I know what keys things like + + + align:start position:0% +how much I know what keys things like +that + + align:start position:0% +that + + + align:start position:0% +that +yeah so svv can't well ya know there's + + align:start position:0% +yeah so svv can't well ya know there's + + + align:start position:0% +yeah so svv can't well ya know there's +there's maybe some way to make the SBB + + align:start position:0% +there's maybe some way to make the SBB + + + align:start position:0% +there's maybe some way to make the SBB +have it so that SBB proofs are + + align:start position:0% +have it so that SBB proofs are + + + align:start position:0% +have it so that SBB proofs are +compatible with this but it's sort of + + align:start position:0% +compatible with this but it's sort of + + + align:start position:0% +compatible with this but it's sort of +you already don't have that so I don't + + align:start position:0% +you already don't have that so I don't + + + align:start position:0% +you already don't have that so I don't +think there's much idea you know there's + + align:start position:0% +think there's much idea you know there's + + + align:start position:0% +think there's much idea you know there's +much much research into how to make this + + align:start position:0% +much much research into how to make this + + + align:start position:0% +much much research into how to make this +SP be compatible but yeah that's a good + + align:start position:0% +SP be compatible but yeah that's a good + + + align:start position:0% +SP be compatible but yeah that's a good +question okay other basic idea okay so + + align:start position:0% +question okay other basic idea okay so + + + align:start position:0% +question okay other basic idea okay so +how do we do this so this will take a + + align:start position:0% +how do we do this so this will take a + + + align:start position:0% +how do we do this so this will take a +little little like the actual way to do + + align:start position:0% +little little like the actual way to do + + + align:start position:0% +little little like the actual way to do +this we'll take the rest of the class + + align:start position:0% +this we'll take the rest of the class + + + align:start position:0% +this we'll take the rest of the class +because it's there's a lot of + + align:start position:0% +because it's there's a lot of + + + align:start position:0% +because it's there's a lot of +it's like okay that seems like it'll + + align:start position:0% +it's like okay that seems like it'll + + + align:start position:0% +it's like okay that seems like it'll +work it's like oh no it doesn't and this + + align:start position:0% +work it's like oh no it doesn't and this + + + align:start position:0% +work it's like oh no it doesn't and this +is sort of replaying the ideas from + + align:start position:0% +is sort of replaying the ideas from + + + align:start position:0% +is sort of replaying the ideas from +several years of people trying to do + + align:start position:0% +several years of people trying to do + + + align:start position:0% +several years of people trying to do +this so how will we do this so there's + + align:start position:0% +this so how will we do this so there's + + + align:start position:0% +this so how will we do this so there's +an idea called commitments and the + + align:start position:0% +an idea called commitments and the + + + align:start position:0% +an idea called commitments and the +simplest form of commitment is you + + align:start position:0% +simplest form of commitment is you + + + align:start position:0% +simplest form of commitment is you +commit to some value you output it call + + align:start position:0% +commit to some value you output it call + + + align:start position:0% +commit to some value you output it call +it see and then you reveal the value and + + align:start position:0% +it see and then you reveal the value and + + + align:start position:0% +it see and then you reveal the value and +then someone can verify okay well given + + align:start position:0% +then someone can verify okay well given + + + align:start position:0% +then someone can verify okay well given +C and the value you just revealed did + + align:start position:0% +C and the value you just revealed did + + + align:start position:0% +C and the value you just revealed did +what is that a correct commitment right + + align:start position:0% +what is that a correct commitment right + + + align:start position:0% +what is that a correct commitment right +so I say okay I'm committing to the + + align:start position:0% +so I say okay I'm committing to the + + + align:start position:0% +so I say okay I'm committing to the +value too + + align:start position:0% +value too + + + align:start position:0% +value too +I'm outputting something C and then + + align:start position:0% +I'm outputting something C and then + + + align:start position:0% +I'm outputting something C and then +revealing oh it was - I was like okay + + align:start position:0% +revealing oh it was - I was like okay + + + align:start position:0% +revealing oh it was - I was like okay +let me throw this into my function - and + + align:start position:0% +let me throw this into my function - and + + + align:start position:0% +let me throw this into my function - and +C does that does those match oh it's + + align:start position:0% +C does that does those match oh it's + + + align:start position:0% +C does that does those match oh it's +true okay we're good + + align:start position:0% + + + + align:start position:0% + +and then there's certain properties + + align:start position:0% +and then there's certain properties + + + align:start position:0% +and then there's certain properties +you'd want like you don't want people + + align:start position:0% +you'd want like you don't want people + + + align:start position:0% +you'd want like you don't want people +that well okay well I think I have + + align:start position:0% +that well okay well I think I have + + + align:start position:0% +that well okay well I think I have +slides about that so a hash function is + + align:start position:0% +slides about that so a hash function is + + + align:start position:0% +slides about that so a hash function is +a commitment right I can say the hash of + + align:start position:0% +a commitment right I can say the hash of + + + align:start position:0% +a commitment right I can say the hash of +5 is 6 8 ft whatever and then I commit + + align:start position:0% +5 is 6 8 ft whatever and then I commit + + + align:start position:0% +5 is 6 8 ft whatever and then I commit +to 6 8 something I publish this I tell + + align:start position:0% +to 6 8 something I publish this I tell + + + align:start position:0% +to 6 8 something I publish this I tell +everyone + + align:start position:0% +everyone + + + align:start position:0% +everyone +ok I'm committing to something I'm not + + align:start position:0% +ok I'm committing to something I'm not + + + align:start position:0% +ok I'm committing to something I'm not +gonna tell you what I'm committing to + + align:start position:0% +gonna tell you what I'm committing to + + + align:start position:0% +gonna tell you what I'm committing to +exactly but here's this 6 8 ft 0 b7 + + align:start position:0% +exactly but here's this 6 8 ft 0 b7 + + + align:start position:0% +exactly but here's this 6 8 ft 0 b7 +someone hash output and then I reveal + + align:start position:0% +someone hash output and then I reveal + + + align:start position:0% +someone hash output and then I reveal +you know days later hey my my the thing + + align:start position:0% +you know days later hey my my the thing + + + align:start position:0% +you know days later hey my my the thing +I was committing to that was 5 and then + + align:start position:0% +I was committing to that was 5 and then + + + align:start position:0% +I was committing to that was 5 and then +everyone can check well let me throw 5 + + align:start position:0% +everyone can check well let me throw 5 + + + align:start position:0% +everyone can check well let me throw 5 +into my hash function it was this ok + + align:start position:0% +into my hash function it was this ok + + + align:start position:0% +into my hash function it was this ok +true so that's a commitment scheme right + + align:start position:0% +true so that's a commitment scheme right + + + align:start position:0% +true so that's a commitment scheme right +it is binding so there's like binding + + align:start position:0% +it is binding so there's like binding + + + align:start position:0% +it is binding so there's like binding +and hiding and there's different + + align:start position:0% +and hiding and there's different + + + align:start position:0% +and hiding and there's different +properties of commitment schemes so this + + align:start position:0% +properties of commitment schemes so this + + + align:start position:0% +properties of commitment schemes so this +we could say is a binding + + align:start position:0% +we could say is a binding + + + align:start position:0% +we could say is a binding +computationally binding commitments game + + align:start position:0% +computationally binding commitments game + + + align:start position:0% +computationally binding commitments game +and that I'm not gonna be able to once + + align:start position:0% +and that I'm not gonna be able to once + + + align:start position:0% +and that I'm not gonna be able to once +I've committed to this I'm not gonna be + + align:start position:0% +I've committed to this I'm not gonna be + + + align:start position:0% +I've committed to this I'm not gonna be +able to find another number so I'm not + + align:start position:0% +able to find another number so I'm not + + + align:start position:0% +able to find another number so I'm not +gonna be able to say oh actually it was + + align:start position:0% +gonna be able to say oh actually it was + + + align:start position:0% +gonna be able to say oh actually it was +6 and then get the same commitment now + + align:start position:0% +6 and then get the same commitment now + + + align:start position:0% +6 and then get the same commitment now +right so I'm not gonna so in practice + + align:start position:0% +right so I'm not gonna so in practice + + + align:start position:0% +right so I'm not gonna so in practice +this is really long right this is like a + + align:start position:0% +this is really long right this is like a + + + align:start position:0% +this is really long right this is like a +shot to output I didn't want to write + + align:start position:0% +shot to output I didn't want to write + + + align:start position:0% +shot to output I didn't want to write +the whole thing but it like goes to here + + align:start position:0% +the whole thing but it like goes to here + + + align:start position:0% +the whole thing but it like goes to here +or two lines so the idea is I can't find + + align:start position:0% +or two lines so the idea is I can't find + + + align:start position:0% +or two lines so the idea is I can't find +another number + + align:start position:0% +another number + + + align:start position:0% +another number +especially another exactly the number I + + align:start position:0% +especially another exactly the number I + + + align:start position:0% +especially another exactly the number I +want but I can't find any other number + + align:start position:0% +want but I can't find any other number + + + align:start position:0% +want but I can't find any other number +that will get me to that same house a + + align:start position:0% +that will get me to that same house a + + + align:start position:0% +that will get me to that same house a +hash output right that's a collision and + + align:start position:0% +hash output right that's a collision and + + + align:start position:0% +hash output right that's a collision and +I'm gonna have to try it well wait so + + align:start position:0% +I'm gonna have to try it well wait so + + + align:start position:0% +I'm gonna have to try it well wait so +for a specific number I'd have to try to + + align:start position:0% +for a specific number I'd have to try to + + + align:start position:0% +for a specific number I'd have to try to +do the 256 for any collision I only have + + align:start position:0% +do the 256 for any collision I only have + + + align:start position:0% +do the 256 for any collision I only have +to do to the 128 but still both of those + + align:start position:0% +to do to the 128 but still both of those + + + align:start position:0% +to do to the 128 but still both of those +are really big numbers I can't do it so + + align:start position:0% +are really big numbers I can't do it so + + + align:start position:0% +are really big numbers I can't do it so +it's computationally binding right if I + + align:start position:0% +it's computationally binding right if I + + + align:start position:0% +it's computationally binding right if I +had some amazing computer that could you + + align:start position:0% +had some amazing computer that could you + + + align:start position:0% +had some amazing computer that could you +know perform infinite calculation I + + align:start position:0% +know perform infinite calculation I + + + align:start position:0% +know perform infinite calculation I +could actually find a collision so + + align:start position:0% +could actually find a collision so + + + align:start position:0% +could actually find a collision so +there's there's the distinction between + + align:start position:0% +there's there's the distinction between + + + align:start position:0% +there's there's the distinction between +like computationally and information + + align:start position:0% +like computationally and information + + + align:start position:0% +like computationally and information +theoretically information theoretically + + align:start position:0% +theoretically information theoretically + + + align:start position:0% +theoretically information theoretically +is like stronger where even if I had + + align:start position:0% +is like stronger where even if I had + + + align:start position:0% +is like stronger where even if I had +like the most powerful computer I still + + align:start position:0% +like the most powerful computer I still + + + align:start position:0% +like the most powerful computer I still +couldn't do this where as binding in + + align:start position:0% +couldn't do this where as binding in + + + align:start position:0% +couldn't do this where as binding in +this case it's computationally binding + + align:start position:0% +this case it's computationally binding + + + align:start position:0% +this case it's computationally binding +computationally is good enough + + align:start position:0% +computationally is good enough + + + align:start position:0% +computationally is good enough +everything in Bitcoin is already + + align:start position:0% +everything in Bitcoin is already + + + align:start position:0% +everything in Bitcoin is already +everything in all these systems is + + align:start position:0% +everything in all these systems is + + + align:start position:0% +everything in all these systems is +already basically computationally there + + align:start position:0% +already basically computationally there + + + align:start position:0% +already basically computationally there +are some schemes which are not + + align:start position:0% +are some schemes which are not + + + align:start position:0% +are some schemes which are not +computationally bound so one of the + + align:start position:0% +computationally bound so one of the + + + align:start position:0% +computationally bound so one of the +parts here and like the Petersons + + align:start position:0% +parts here and like the Petersons + + + align:start position:0% +parts here and like the Petersons +commitments are not actually + + align:start position:0% +commitments are not actually + + + align:start position:0% +commitments are not actually +computationally and things like severe + + align:start position:0% +computationally and things like severe + + + align:start position:0% +computationally and things like severe +secret sharing and a couple other things + + align:start position:0% +secret sharing and a couple other things + + + align:start position:0% +secret sharing and a couple other things +where it's like hey this is not + + align:start position:0% +where it's like hey this is not + + + align:start position:0% +where it's like hey this is not +dependent on processing power even if + + align:start position:0% +dependent on processing power even if + + + align:start position:0% +dependent on processing power even if +you have infinite processing power you + + align:start position:0% +you have infinite processing power you + + + align:start position:0% +you have infinite processing power you +just can't figure out what the values + + align:start position:0% +just can't figure out what the values + + + align:start position:0% +just can't figure out what the values +are which is you know cooler but it's + + align:start position:0% +are which is you know cooler but it's + + + align:start position:0% +are which is you know cooler but it's +nice to have it's not a requirement for + + align:start position:0% +nice to have it's not a requirement for + + + align:start position:0% +nice to have it's not a requirement for +our systems okay so this is binding any + + align:start position:0% +our systems okay so this is binding any + + + align:start position:0% +our systems okay so this is binding any +ideas of what this is not why this is + + align:start position:0% +ideas of what this is not why this is + + + align:start position:0% +ideas of what this is not why this is +would not be a good commitment scheme + + align:start position:0% +would not be a good commitment scheme + + + align:start position:0% +would not be a good commitment scheme +you want to commit to a value and then + + align:start position:0% +you want to commit to a value and then + + + align:start position:0% +you want to commit to a value and then +later reveal it you don't want the + + align:start position:0% +later reveal it you don't want the + + + align:start position:0% +later reveal it you don't want the +person who's committing to be able to + + align:start position:0% +person who's committing to be able to + + + align:start position:0% +person who's committing to be able to +change their commitment what else might + + align:start position:0% +change their commitment what else might + + + align:start position:0% +change their commitment what else might +you want but this probably doesn't + + align:start position:0% +you want but this probably doesn't + + + align:start position:0% +you want but this probably doesn't +provide + + align:start position:0% + + + + align:start position:0% + +yeah okay so you want to be able to do + + align:start position:0% +yeah okay so you want to be able to do + + + align:start position:0% +yeah okay so you want to be able to do +fancy stuff the commitments before we + + align:start position:0% +fancy stuff the commitments before we + + + align:start position:0% +fancy stuff the commitments before we +even get there that's in like five or + + align:start position:0% +even get there that's in like five or + + + align:start position:0% +even get there that's in like five or +six slides before we get there this + + align:start position:0% +six slides before we get there this + + + align:start position:0% +six slides before we get there this +doesn't satisfy something else we want + + align:start position:0% + + + + align:start position:0% + +so if I'm committing to a number I'm + + align:start position:0% +so if I'm committing to a number I'm + + + align:start position:0% +so if I'm committing to a number I'm +just like okay I'm gonna commit to the + + align:start position:0% +just like okay I'm gonna commit to the + + + align:start position:0% +just like okay I'm gonna commit to the +number of pizzas I'm ordering at my + + align:start position:0% +number of pizzas I'm ordering at my + + + align:start position:0% +number of pizzas I'm ordering at my +party and everyone's like wondering like + + align:start position:0% +party and everyone's like wondering like + + + align:start position:0% +party and everyone's like wondering like +how many pieces you gonna order well I + + align:start position:0% +how many pieces you gonna order well I + + + align:start position:0% +how many pieces you gonna order well I +just kind of try things right it's + + align:start position:0% +just kind of try things right it's + + + align:start position:0% +just kind of try things right it's +binding but it's not hiding so oops + + align:start position:0% +binding but it's not hiding so oops + + + align:start position:0% +binding but it's not hiding so oops +verifier can easily guess and check the + + align:start position:0% +verifier can easily guess and check the + + + align:start position:0% +verifier can easily guess and check the +committed value right so okay for I + + align:start position:0% +committed value right so okay for I + + + align:start position:0% +committed value right so okay for I +equals zero just keep trying different + + align:start position:0% +equals zero just keep trying different + + + align:start position:0% +equals zero just keep trying different +eyes and see if the hash matches six 8ft + + align:start position:0% +eyes and see if the hash matches six 8ft + + + align:start position:0% +eyes and see if the hash matches six 8ft +you and this will take very little time + + align:start position:0% +you and this will take very little time + + + align:start position:0% +you and this will take very little time +because five is gonna happen pretty + + align:start position:0% +because five is gonna happen pretty + + + align:start position:0% +because five is gonna happen pretty +quick and then everyone will know okay + + align:start position:0% +quick and then everyone will know okay + + + align:start position:0% +quick and then everyone will know okay +he's ordering five pizzas sounds like a + + align:start position:0% +he's ordering five pizzas sounds like a + + + align:start position:0% +he's ordering five pizzas sounds like a +decent party but not really worth going + + align:start position:0% +decent party but not really worth going + + + align:start position:0% +decent party but not really worth going +out of my way to go to if it was ffffff + + align:start position:0% +out of my way to go to if it was ffffff + + + align:start position:0% +out of my way to go to if it was ffffff +pizzas that would be something else + + align:start position:0% +pizzas that would be something else + + + align:start position:0% +pizzas that would be something else +okay so solution pretty pretty + + align:start position:0% +okay so solution pretty pretty + + + align:start position:0% +okay so solution pretty pretty +straightforward solution add a blinding + + align:start position:0% +straightforward solution add a blinding + + + align:start position:0% +straightforward solution add a blinding +factor so we're gonna call that our I + + align:start position:0% +factor so we're gonna call that our I + + + align:start position:0% +factor so we're gonna call that our I +guess our is random yeah so let's say + + align:start position:0% +guess our is random yeah so let's say + + + align:start position:0% +guess our is random yeah so let's say +okay our is be a PC seven five seven + + align:start position:0% +okay our is be a PC seven five seven + + + align:start position:0% +okay our is be a PC seven five seven +nine and now I'm gonna take the hash of + + align:start position:0% +nine and now I'm gonna take the hash of + + + align:start position:0% +nine and now I'm gonna take the hash of +five and concatenate our and say okay + + align:start position:0% +five and concatenate our and say okay + + + align:start position:0% +five and concatenate our and say okay +now this is a different hash and now to + + align:start position:0% +now this is a different hash and now to + + + align:start position:0% +now this is a different hash and now to +reveal Mike you know reveal what I was + + align:start position:0% +reveal Mike you know reveal what I was + + + align:start position:0% +reveal Mike you know reveal what I was +committing to you reveal both v and r + + align:start position:0% +committing to you reveal both v and r + + + align:start position:0% +committing to you reveal both v and r +and then sort of you need you know you + + align:start position:0% +and then sort of you need you know you + + + align:start position:0% +and then sort of you need you know you +need to tell people what order you're + + align:start position:0% +need to tell people what order you're + + + align:start position:0% +need to tell people what order you're +doing things in you need the system + + align:start position:0% +doing things in you need the system + + + align:start position:0% +doing things in you need the system +needs to be predefined right you can't + + align:start position:0% +needs to be predefined right you can't + + + align:start position:0% +needs to be predefined right you can't +sort of when you're committing you also + + align:start position:0% +sort of when you're committing you also + + + align:start position:0% +sort of when you're committing you also +have to sort of commit to the algorithms + + align:start position:0% +have to sort of commit to the algorithms + + + align:start position:0% +have to sort of commit to the algorithms +or have pre agreed-upon algorithms + + align:start position:0% +or have pre agreed-upon algorithms + + + align:start position:0% +or have pre agreed-upon algorithms +because otherwise yeah you could do + + align:start position:0% +because otherwise yeah you could do + + + align:start position:0% +because otherwise yeah you could do +something like no I committed to r5 was + + align:start position:0% +something like no I committed to r5 was + + + align:start position:0% +something like no I committed to r5 was +my blinding factor you know so you need + + align:start position:0% +my blinding factor you know so you need + + + align:start position:0% +my blinding factor you know so you need +you need to have sort of protocols set + + align:start position:0% +you need to have sort of protocols set + + + align:start position:0% +you need to have sort of protocols set +up beforehand which you never know that + + align:start position:0% +up beforehand which you never know that + + + align:start position:0% +up beforehand which you never know that +could be some you know if you just say + + align:start position:0% +could be some you know if you just say + + + align:start position:0% +could be some you know if you just say +hey I'm committing here's this value + + align:start position:0% +hey I'm committing here's this value + + + align:start position:0% +hey I'm committing here's this value +you're like okay well how are you + + align:start position:0% +you're like okay well how are you + + + align:start position:0% +you're like okay well how are you +committing what hash fun + + align:start position:0% +committing what hash fun + + + align:start position:0% +committing what hash fun +what you know what are you doing but + + align:start position:0% +what you know what are you doing but + + + align:start position:0% +what you know what are you doing but +that's sort of I don't know obvious it + + align:start position:0% +that's sort of I don't know obvious it + + + align:start position:0% +that's sort of I don't know obvious it +might not be super obvious so you have + + align:start position:0% +might not be super obvious so you have + + + align:start position:0% +might not be super obvious so you have +to be careful mother okay so this is now + + align:start position:0% +to be careful mother okay so this is now + + + align:start position:0% +to be careful mother okay so this is now +blinding and you know it's it's hidden + + align:start position:0% +blinding and you know it's it's hidden + + + align:start position:0% +blinding and you know it's it's hidden +and it's it's still binding right you + + align:start position:0% +and it's it's still binding right you + + + align:start position:0% +and it's it's still binding right you +can't change it to like six I think + + align:start position:0% +can't change it to like six I think + + + align:start position:0% +can't change it to like six I think +that's the next lightweight okay yeah so + + align:start position:0% +that's the next lightweight okay yeah so + + + align:start position:0% +that's the next lightweight okay yeah so +you can't change this to six and change + + align:start position:0% +you can't change this to six and change + + + align:start position:0% +you can't change this to six and change +to a different are I mean you could but + + align:start position:0% +to a different are I mean you could but + + + align:start position:0% +to a different are I mean you could but +you'd have to do you still have to do a + + align:start position:0% +you'd have to do you still have to do a + + + align:start position:0% +you'd have to do you still have to do a +lot of computation and this is now + + align:start position:0% +lot of computation and this is now + + + align:start position:0% +lot of computation and this is now +actually some things get easier right so + + align:start position:0% +actually some things get easier right so + + + align:start position:0% +actually some things get easier right so +before if you really wanted to reveal + + align:start position:0% +before if you really wanted to reveal + + + align:start position:0% +before if you really wanted to reveal +that it was six basically can write + + align:start position:0% +that it was six basically can write + + + align:start position:0% +that it was six basically can write +because there's a single output for six + + align:start position:0% +because there's a single output for six + + + align:start position:0% +because there's a single output for six +and it just doesn't match this so + + align:start position:0% +and it just doesn't match this so + + + align:start position:0% +and it just doesn't match this so +there's not like if you if you have a + + align:start position:0% +there's not like if you if you have a + + + align:start position:0% +there's not like if you if you have a +single chosen value that you want to + + align:start position:0% +single chosen value that you want to + + + align:start position:0% +single chosen value that you want to +reveal that's not the one that you + + align:start position:0% +reveal that's not the one that you + + + align:start position:0% +reveal that's not the one that you +committed to you're basically stuck + + align:start position:0% +committed to you're basically stuck + + + align:start position:0% +committed to you're basically stuck +there's no way to get around it even + + align:start position:0% +there's no way to get around it even + + + align:start position:0% +there's no way to get around it even +computationally with this that's not + + align:start position:0% +computationally with this that's not + + + align:start position:0% +computationally with this that's not +true right it's like I really want to + + align:start position:0% +true right it's like I really want to + + + align:start position:0% +true right it's like I really want to +reveal six well I can come up with a + + align:start position:0% +reveal six well I can come up with a + + + align:start position:0% +reveal six well I can come up with a +different R such that the hash of six + + align:start position:0% +different R such that the hash of six + + + align:start position:0% +different R such that the hash of six +and our prime is that and then that's + + align:start position:0% +and our prime is that and then that's + + + align:start position:0% +and our prime is that and then that's +now computational slight distinction + + align:start position:0% +now computational slight distinction + + + align:start position:0% +now computational slight distinction +right it's it's still it's still binding + + align:start position:0% +right it's it's still it's still binding + + + align:start position:0% +right it's it's still it's still binding +computationally but before chosen values + + align:start position:0% +computationally but before chosen values + + + align:start position:0% +computationally but before chosen values +may not have been yeah so that's I guess + + align:start position:0% +may not have been yeah so that's I guess + + + align:start position:0% +may not have been yeah so that's I guess +the difference right it's it's + + align:start position:0% +the difference right it's it's + + + align:start position:0% +the difference right it's it's +computationally binding for any value + + align:start position:0% +computationally binding for any value + + + align:start position:0% +computationally binding for any value +but for a specific value it might be + + align:start position:0% +but for a specific value it might be + + + align:start position:0% +but for a specific value it might be +sort of in from not information + + align:start position:0% +sort of in from not information + + + align:start position:0% +sort of in from not information +theoretic but you just can't do it + + align:start position:0% +theoretic but you just can't do it + + + align:start position:0% +theoretic but you just can't do it +because they're the hash function + + align:start position:0% +because they're the hash function + + + align:start position:0% +because they're the hash function +doesn't help you there okay so what else + + align:start position:0% +doesn't help you there okay so what else + + + align:start position:0% +doesn't help you there okay so what else +do we want to do oh you're saying we + + align:start position:0% +do we want to do oh you're saying we + + + align:start position:0% +do we want to do oh you're saying we +need more we want to be able to prove + + align:start position:0% +need more we want to be able to prove + + + align:start position:0% +need more we want to be able to prove +things about the commitments so we need + + align:start position:0% +things about the commitments so we need + + + align:start position:0% +things about the commitments so we need +some kind of homomorphic commitments and + + align:start position:0% +some kind of homomorphic commitments and + + + align:start position:0% +some kind of homomorphic commitments and +we've seen the homomorphic properties of + + align:start position:0% +we've seen the homomorphic properties of + + + align:start position:0% +we've seen the homomorphic properties of +these elliptic curve points which are + + align:start position:0% +these elliptic curve points which are + + + align:start position:0% +these elliptic curve points which are +really nice right where you can add + + align:start position:0% +really nice right where you can add + + + align:start position:0% +really nice right where you can add +private keys or add scalars and that's + + align:start position:0% +private keys or add scalars and that's + + + align:start position:0% +private keys or add scalars and that's +the same as adding these points on a + + align:start position:0% +the same as adding these points on a + + + align:start position:0% +the same as adding these points on a +curve so let's try that we want + + align:start position:0% +curve so let's try that we want + + + align:start position:0% +curve so let's try that we want +something like this we want a commit to + + align:start position:0% +something like this we want a commit to + + + align:start position:0% +something like this we want a commit to +X commit to Y and get these commitments + + align:start position:0% +X commit to Y and get these commitments + + + align:start position:0% +X commit to Y and get these commitments +a and B and then we were on to reveal Z + + align:start position:0% +a and B and then we were on to reveal Z + + + align:start position:0% +a and B and then we were on to reveal Z +which is X plus y + + align:start position:0% + + + + align:start position:0% + +and then we want the verify function + + align:start position:0% +and then we want the verify function + + + align:start position:0% +and then we want the verify function +that's put Z in and a and B either a + + align:start position:0% +that's put Z in and a and B either a + + + align:start position:0% +that's put Z in and a and B either a +plus B or a and B separately and return + + align:start position:0% +plus B or a and B separately and return + + + align:start position:0% +plus B or a and B separately and return +true right so we don't want to reveal x + + align:start position:0% +true right so we don't want to reveal x + + + align:start position:0% +true right so we don't want to reveal x +and y separately we will reveal the sum + + align:start position:0% +and y separately we will reveal the sum + + + align:start position:0% +and y separately we will reveal the sum +of x plus y and then we will reveal you + + align:start position:0% +of x plus y and then we will reveal you + + + align:start position:0% +of x plus y and then we will reveal you +know and then we'll just have the + + align:start position:0% +know and then we'll just have the + + + align:start position:0% +know and then we'll just have the +commitments themselves so you know if + + align:start position:0% +commitments themselves so you know if + + + align:start position:0% +commitments themselves so you know if +since these are the same operator it be + + align:start position:0% +since these are the same operator it be + + + align:start position:0% +since these are the same operator it be +cool if that worked this is what we want + + align:start position:0% +cool if that worked this is what we want + + + align:start position:0% +cool if that worked this is what we want +right and ok so that's actually not that + + align:start position:0% +right and ok so that's actually not that + + + align:start position:0% +right and ok so that's actually not that +bad but we also want all those + + align:start position:0% +bad but we also want all those + + + align:start position:0% +bad but we also want all those +properties where it's hiding and it's + + align:start position:0% +properties where it's hiding and it's + + + align:start position:0% +properties where it's hiding and it's +binding and things like that so what + + align:start position:0% +binding and things like that so what + + + align:start position:0% +binding and things like that so what +should we try first idea is yeah ok this + + align:start position:0% +should we try first idea is yeah ok this + + + align:start position:0% +should we try first idea is yeah ok this +would be useful how can we build this we + + align:start position:0% +would be useful how can we build this we + + + align:start position:0% +would be useful how can we build this we +want to you know we can reveal sums + + align:start position:0% +want to you know we can reveal sums + + + align:start position:0% +want to you know we can reveal sums +without revealing individual parts that + + align:start position:0% +without revealing individual parts that + + + align:start position:0% +without revealing individual parts that +we've committed to so probably the first + + align:start position:0% +we've committed to so probably the first + + + align:start position:0% +we've committed to so probably the first +idea is let's just use private keys and + + align:start position:0% +idea is let's just use private keys and + + + align:start position:0% +idea is let's just use private keys and +public keys right let's use you know a + + align:start position:0% +public keys right let's use you know a + + + align:start position:0% +public keys right let's use you know a +times G and that kind of thing oh and I + + align:start position:0% +times G and that kind of thing oh and I + + + align:start position:0% +times G and that kind of thing oh and I +forgot the joke G how can we build this + + align:start position:0% +forgot the joke G how can we build this + + + align:start position:0% +forgot the joke G how can we build this +G G so yeah you want a commitment to X + + align:start position:0% +G G so yeah you want a commitment to X + + + align:start position:0% +G G so yeah you want a commitment to X +you want to commitment to why you want + + align:start position:0% +you want to commitment to why you want + + + align:start position:0% +you want to commitment to why you want +to reveal Z as X plus y so what if you + + align:start position:0% +to reveal Z as X plus y so what if you + + + align:start position:0% +to reveal Z as X plus y so what if you +did this you said okay I'm gonna make a + + align:start position:0% +did this you said okay I'm gonna make a + + + align:start position:0% +did this you said okay I'm gonna make a +point on the curve X which is just my + + align:start position:0% +point on the curve X which is just my + + + align:start position:0% +point on the curve X which is just my +value x times G point on the curve Y + + align:start position:0% +value x times G point on the curve Y + + + align:start position:0% +value x times G point on the curve Y +which is my value y times G this does + + align:start position:0% +which is my value y times G this does + + + align:start position:0% +which is my value y times G this does +have that homomorphic property right but + + align:start position:0% +have that homomorphic property right but + + + align:start position:0% +have that homomorphic property right but +is this binding okay it is yeah well + + align:start position:0% +is this binding okay it is yeah well + + + align:start position:0% +is this binding okay it is yeah well +yeah I can't come up with a different X + + align:start position:0% +yeah I can't come up with a different X + + + align:start position:0% +yeah I can't come up with a different X +that gets me to that point right so so + + align:start position:0% +that gets me to that point right so so + + + align:start position:0% +that gets me to that point right so so +multiplying by the generator point is + + align:start position:0% +multiplying by the generator point is + + + align:start position:0% +multiplying by the generator point is +sort of like a hash function in that + + align:start position:0% +sort of like a hash function in that + + + align:start position:0% +sort of like a hash function in that +you're not gonna be able to find + + align:start position:0% +you're not gonna be able to find + + + align:start position:0% +you're not gonna be able to find +collisions right so you can't find two + + align:start position:0% +collisions right so you can't find two + + + align:start position:0% +collisions right so you can't find two +different private keys that give you the + + align:start position:0% +different private keys that give you the + + + align:start position:0% +different private keys that give you the +same public key sometimes you can so I + + align:start position:0% +same public key sometimes you can so I + + + align:start position:0% +same public key sometimes you can so I +don't like in this specific case this + + align:start position:0% +don't like in this specific case this + + + align:start position:0% +don't like in this specific case this +binding there's a bunch of asterisks is + + align:start position:0% +binding there's a bunch of asterisks is + + + align:start position:0% +binding there's a bunch of asterisks is +there I probably shouldn't yeah it gets + + align:start position:0% +there I probably shouldn't yeah it gets + + + align:start position:0% +there I probably shouldn't yeah it gets +complicated there are some curves where + + align:start position:0% +complicated there are some curves where + + + align:start position:0% +complicated there are some curves where +it's not and some systems where it's not + + align:start position:0% +it's not and some systems where it's not + + + align:start position:0% +it's not and some systems where it's not +and there have been problems and + + align:start position:0% +and there have been problems and + + + align:start position:0% +and there have been problems and +currencies where people assume that this + + align:start position:0% +currencies where people assume that this + + + align:start position:0% +currencies where people assume that this +is the case I think in Manero but yeah + + align:start position:0% + + + + align:start position:0% + +the curves the curve for Bitcoin I think + + align:start position:0% +the curves the curve for Bitcoin I think + + + align:start position:0% +the curves the curve for Bitcoin I think +it's Y Q no y squared equals x cubed + + align:start position:0% +it's Y Q no y squared equals x cubed + + + align:start position:0% +it's Y Q no y squared equals x cubed +plus or minus minus seven I think that's + + align:start position:0% +plus or minus minus seven I think that's + + + align:start position:0% +plus or minus minus seven I think that's +it it looks sort of like this it's + + align:start position:0% +it it looks sort of like this it's + + + align:start position:0% +it it looks sort of like this it's +symmetric which that isn't I think I had + + align:start position:0% +symmetric which that isn't I think I had + + + align:start position:0% +symmetric which that isn't I think I had +it in like an earlier one and then the + + align:start position:0% +it in like an earlier one and then the + + + align:start position:0% +it in like an earlier one and then the +x-axis is like like this is the origin + + align:start position:0% +x-axis is like like this is the origin + + + align:start position:0% +x-axis is like like this is the origin +ish and then the idea is you know you + + align:start position:0% +ish and then the idea is you know you + + + align:start position:0% +ish and then the idea is you know you +have points and you can so the sum is + + align:start position:0% +have points and you can so the sum is + + + align:start position:0% +have points and you can so the sum is +you know if you have well the sum + + align:start position:0% +you know if you have well the sum + + + align:start position:0% +you know if you have well the sum +there's gonna be like here except it's + + align:start position:0% +there's gonna be like here except it's + + + align:start position:0% +there's gonna be like here except it's +like here the idea is three any any line + + align:start position:0% +like here the idea is three any any line + + + align:start position:0% +like here the idea is three any any line +you draw more or less will intersect at + + align:start position:0% +you draw more or less will intersect at + + + align:start position:0% +you draw more or less will intersect at +three points unless it intersects at a + + align:start position:0% +three points unless it intersects at a + + + align:start position:0% +three points unless it intersects at a +tangent or if it's straight up then you + + align:start position:0% +tangent or if it's straight up then you + + + align:start position:0% +tangent or if it's straight up then you +say it intersects at the point at + + align:start position:0% +say it intersects at the point at + + + align:start position:0% +say it intersects at the point at +infinity right so but any you know any + + align:start position:0% +infinity right so but any you know any + + + align:start position:0% +infinity right so but any you know any +random line you make will probably + + align:start position:0% +random line you make will probably + + + align:start position:0% +random line you make will probably +intersect in three different points and + + align:start position:0% +intersect in three different points and + + + align:start position:0% +intersect in three different points and +so then you can say okay well if this is + + align:start position:0% +so then you can say okay well if this is + + + align:start position:0% +so then you can say okay well if this is +a B and C we define a plus B plus C to + + align:start position:0% +a B and C we define a plus B plus C to + + + align:start position:0% +a B and C we define a plus B plus C to +be zero so then we would define B plus C + + align:start position:0% +be zero so then we would define B plus C + + + align:start position:0% +be zero so then we would define B plus C +to be here negative a and the negation + + align:start position:0% +to be here negative a and the negation + + + align:start position:0% +to be here negative a and the negation +is you just flip it over the x-axis so + + align:start position:0% +is you just flip it over the x-axis so + + + align:start position:0% +is you just flip it over the x-axis so +yeah there there I talked about this a + + align:start position:0% +yeah there there I talked about this a + + + align:start position:0% +yeah there there I talked about this a +little bit before but the idea is you've + + align:start position:0% +little bit before but the idea is you've + + + align:start position:0% +little bit before but the idea is you've +still got this nice property where you + + align:start position:0% +still got this nice property where you + + + align:start position:0% +still got this nice property where you +pick a point on here G just everyone + + align:start position:0% +pick a point on here G just everyone + + + align:start position:0% +pick a point on here G just everyone +picks a random point and it's a + + align:start position:0% +picks a random point and it's a + + + align:start position:0% +picks a random point and it's a +generator because if you keep adding so + + align:start position:0% +generator because if you keep adding so + + + align:start position:0% +generator because if you keep adding so +if you say okay here's G sorry I take + + align:start position:0% +if you say okay here's G sorry I take + + + align:start position:0% +if you say okay here's G sorry I take +the tangent fine this is to G take the + + align:start position:0% +the tangent fine this is to G take the + + + align:start position:0% +the tangent fine this is to G take the +tangent here + + align:start position:0% +tangent here + + + align:start position:0% +tangent here +maybe goes here to 3G take the tangent + + align:start position:0% +maybe goes here to 3G take the tangent + + + align:start position:0% +maybe goes here to 3G take the tangent +here or no that would be 4G sorry this + + align:start position:0% +here or no that would be 4G sorry this + + + align:start position:0% +here or no that would be 4G sorry this +will be H II so you can keep adding the + + align:start position:0% +will be H II so you can keep adding the + + + align:start position:0% +will be H II so you can keep adding the +G and you'll eventually cover the entire + + align:start position:0% +G and you'll eventually cover the entire + + + align:start position:0% +G and you'll eventually cover the entire +curve so and get back to G so that's why + + align:start position:0% +curve so and get back to G so that's why + + + align:start position:0% +curve so and get back to G so that's why +it's sort of a generator because it like + + align:start position:0% +it's sort of a generator because it like + + + align:start position:0% +it's sort of a generator because it like +lets you get to every point by just + + align:start position:0% +lets you get to every point by just + + + align:start position:0% +lets you get to every point by just +multiplying so the nice property here is + + align:start position:0% +multiplying so the nice property here is + + + align:start position:0% +multiplying so the nice property here is +if you have some regular x times G and + + align:start position:0% +if you have some regular x times G and + + + align:start position:0% +if you have some regular x times G and +some number y times G you can also do X + + align:start position:0% +some number y times G you can also do X + + + align:start position:0% +some number y times G you can also do X +plus y times G and that equals x g plus + + align:start position:0% +plus y times G and that equals x g plus + + + align:start position:0% +plus y times G and that equals x g plus +y g right so you can add the points and + + align:start position:0% +y g right so you can add the points and + + + align:start position:0% +y g right so you can add the points and +that's the same as adding the scalars + + align:start position:0% +that's the same as adding the scalars + + + align:start position:0% +that's the same as adding the scalars +before you multiply by G and that's what + + align:start position:0% +before you multiply by G and that's what + + + align:start position:0% +before you multiply by G and that's what +basically we use for everything and then + + align:start position:0% +basically we use for everything and then + + + align:start position:0% +basically we use for everything and then +the idea is you can't go back right + + align:start position:0% +the idea is you can't go back right + + + align:start position:0% +the idea is you can't go back right +given a point let's say we call this big + + align:start position:0% +given a point let's say we call this big + + + align:start position:0% +given a point let's say we call this big +X give it a point big X which is little + + align:start position:0% +X give it a point big X which is little + + + align:start position:0% +X give it a point big X which is little +X times G you can't figure out what X is + + align:start position:0% +X times G you can't figure out what X is + + + align:start position:0% +X times G you can't figure out what X is +so you can't divide by a point right you + + align:start position:0% +so you can't divide by a point right you + + + align:start position:0% +so you can't divide by a point right you +can't say Oh given X I want to do X + + align:start position:0% +can't say Oh given X I want to do X + + + align:start position:0% +can't say Oh given X I want to do X +divided by G which is little X + + align:start position:0% +divided by G which is little X + + + align:start position:0% +divided by G which is little X +I can't divide so I'm stuck right I can + + align:start position:0% +I can't divide so I'm stuck right I can + + + align:start position:0% +I can't divide so I'm stuck right I can +multiply by just repeatedly adding what + + align:start position:0% +multiply by just repeatedly adding what + + + align:start position:0% +multiply by just repeatedly adding what +division is not defined okay so this is + + align:start position:0% +division is not defined okay so this is + + + align:start position:0% +division is not defined okay so this is +binding but I don't want it there's + + align:start position:0% +binding but I don't want it there's + + + align:start position:0% +binding but I don't want it there's +asterisks is there but it's not blinded + + align:start position:0% +asterisks is there but it's not blinded + + + align:start position:0% +asterisks is there but it's not blinded +right so the same problem is just the + + align:start position:0% +right so the same problem is just the + + + align:start position:0% +right so the same problem is just the +the raw hash based commitment where if I + + align:start position:0% +the raw hash based commitment where if I + + + align:start position:0% +the raw hash based commitment where if I +want to commit to the number five and I + + align:start position:0% +want to commit to the number five and I + + + align:start position:0% +want to commit to the number five and I +just say okay five times G and that's my + + align:start position:0% +just say okay five times G and that's my + + + align:start position:0% +just say okay five times G and that's my +point that I'm gonna use for my + + align:start position:0% +point that I'm gonna use for my + + + align:start position:0% +point that I'm gonna use for my +commitment you know same same problem + + align:start position:0% +commitment you know same same problem + + + align:start position:0% +commitment you know same same problem +for loop will pretty quickly show you + + align:start position:0% +for loop will pretty quickly show you + + + align:start position:0% +for loop will pretty quickly show you +that was five okay how about this seems + + align:start position:0% +that was five okay how about this seems + + + align:start position:0% +that was five okay how about this seems +like a good idea I should say unless + + align:start position:0% +like a good idea I should say unless + + + align:start position:0% +like a good idea I should say unless +obviously it's not a good idea way + + align:start position:0% + + + + align:start position:0% + +so why don't we say okay put a add a + + align:start position:0% +so why don't we say okay put a add a + + + align:start position:0% +so why don't we say okay put a add a +blinding factor + + align:start position:0% +blinding factor + + + align:start position:0% +blinding factor +what would this what would the problem + + align:start position:0% +what would this what would the problem + + + align:start position:0% +what would this what would the problem +be here I'm saying okay I'm gonna you + + align:start position:0% +be here I'm saying okay I'm gonna you + + + align:start position:0% +be here I'm saying okay I'm gonna you +know I want to commit to five I'm gonna + + align:start position:0% +know I want to commit to five I'm gonna + + + align:start position:0% +know I want to commit to five I'm gonna +add some random number R and then + + align:start position:0% +add some random number R and then + + + align:start position:0% +add some random number R and then +multiply that that sum by G and then + + align:start position:0% +multiply that that sum by G and then + + + align:start position:0% +multiply that that sum by G and then +when I want to reveal that my I was + + align:start position:0% +when I want to reveal that my I was + + + align:start position:0% +when I want to reveal that my I was +committed to five I reveal a five in are + + align:start position:0% + + + + align:start position:0% + +no but I can say look the first well + + align:start position:0% +no but I can say look the first well + + + align:start position:0% +no but I can say look the first well +yeah you get the problem is addition is + + align:start position:0% +yeah you get the problem is addition is + + + align:start position:0% +yeah you get the problem is addition is +easy to break right I can just say well + + align:start position:0% +easy to break right I can just say well + + + align:start position:0% +easy to break right I can just say well +when I committed to five plus R it + + align:start position:0% +when I committed to five plus R it + + + align:start position:0% +when I committed to five plus R it +revealed 5 and R but it's not binding + + align:start position:0% +revealed 5 and R but it's not binding + + + align:start position:0% +revealed 5 and R but it's not binding +right I can just find our prime which is + + align:start position:0% +right I can just find our prime which is + + + align:start position:0% +right I can just find our prime which is +5 plus R minus 6 and then 6 plus that R + + align:start position:0% +5 plus R minus 6 and then 6 plus that R + + + align:start position:0% +5 plus R minus 6 and then 6 plus that R +prime is gonna be 6 plus 5 plus or minus + + align:start position:0% +prime is gonna be 6 plus 5 plus or minus + + + align:start position:0% +prime is gonna be 6 plus 5 plus or minus +6 you know like I can just compute + + align:start position:0% +6 you know like I can just compute + + + align:start position:0% +6 you know like I can just compute +whatever our prime I want and whatever + + align:start position:0% +whatever our prime I want and whatever + + + align:start position:0% +whatever our prime I want and whatever +number I want to reveal later so this is + + align:start position:0% +number I want to reveal later so this is + + + align:start position:0% +number I want to reveal later so this is +a binding anymore right I'm now adding a + + align:start position:0% +a binding anymore right I'm now adding a + + + align:start position:0% +a binding anymore right I'm now adding a +random thing in and I'm committing to + + align:start position:0% +random thing in and I'm committing to + + + align:start position:0% +random thing in and I'm committing to +the sum of the thing I want and a random + + align:start position:0% +the sum of the thing I want and a random + + + align:start position:0% +the sum of the thing I want and a random +thing but it's not binding because that + + align:start position:0% +thing but it's not binding because that + + + align:start position:0% +thing but it's not binding because that +addition I can I can play with so how + + align:start position:0% +addition I can I can play with so how + + + align:start position:0% +addition I can I can play with so how +about this I'll hash five and + + align:start position:0% +about this I'll hash five and + + + align:start position:0% +about this I'll hash five and +concatenate R and then multiply that + + align:start position:0% +concatenate R and then multiply that + + + align:start position:0% +concatenate R and then multiply that +hashed output by G maybe but then it's + + align:start position:0% +hashed output by G maybe but then it's + + + align:start position:0% +hashed output by G maybe but then it's +no longer homomorphic right then I can't + + align:start position:0% +no longer homomorphic right then I can't + + + align:start position:0% +no longer homomorphic right then I can't +add so if I have you know like the hash + + align:start position:0% +add so if I have you know like the hash + + + align:start position:0% +add so if I have you know like the hash +of 5 and R 1 times G and then the hash + + align:start position:0% +of 5 and R 1 times G and then the hash + + + align:start position:0% +of 5 and R 1 times G and then the hash +of 7 and r2 times G I can't add these + + align:start position:0% +of 7 and r2 times G I can't add these + + + align:start position:0% +of 7 and r2 times G I can't add these +anymore and then have the the fives and + + align:start position:0% +anymore and then have the the fives and + + + align:start position:0% +anymore and then have the the fives and +sevens add up to 12 or it won't work + + align:start position:0% +sevens add up to 12 or it won't work + + + align:start position:0% +sevens add up to 12 or it won't work +because now it's a hash and I've just + + align:start position:0% +because now it's a hash and I've just + + + align:start position:0% +because now it's a hash and I've just +got these hashes adding and you don't + + align:start position:0% +got these hashes adding and you don't + + + align:start position:0% +got these hashes adding and you don't +really get any meaning there so that + + align:start position:0% +really get any meaning there so that + + + align:start position:0% +really get any meaning there so that +doesn't work either so we're stuck yeah + + align:start position:0% +doesn't work either so we're stuck yeah + + + align:start position:0% +doesn't work either so we're stuck yeah +then the way you actually do it is + + align:start position:0% +then the way you actually do it is + + + align:start position:0% +then the way you actually do it is +totally non obvious and introducing G's + + align:start position:0% +totally non obvious and introducing G's + + + align:start position:0% +totally non obvious and introducing G's +for eternal twin H + + align:start position:0% + + + + align:start position:0% + +you make another point on the curve and + + align:start position:0% +you make another point on the curve and + + + align:start position:0% +you make another point on the curve and +you just call it H which is the letter + + align:start position:0% +you just call it H which is the letter + + + align:start position:0% +you just call it H which is the letter +after G yeah it's another generator + + align:start position:0% +after G yeah it's another generator + + + align:start position:0% +after G yeah it's another generator +point distinct from G so you just pick + + align:start position:0% +point distinct from G so you just pick + + + align:start position:0% +point distinct from G so you just pick +one you say okay here's here's H you + + align:start position:0% +one you say okay here's here's H you + + + align:start position:0% +one you say okay here's here's H you +also need to make sure that nobody knows + + align:start position:0% +also need to make sure that nobody knows + + + align:start position:0% +also need to make sure that nobody knows +n such that M times G equals H that n + + align:start position:0% +n such that M times G equals H that n + + + align:start position:0% +n such that M times G equals H that n +might exist but you want to be sure that + + align:start position:0% +might exist but you want to be sure that + + + align:start position:0% +might exist but you want to be sure that +no one knows what it is + + align:start position:0% +no one knows what it is + + + align:start position:0% +no one knows what it is +because if you know how to sort of move + + align:start position:0% +because if you know how to sort of move + + + align:start position:0% +because if you know how to sort of move +between G and H then that'll break this + + align:start position:0% +between G and H then that'll break this + + + align:start position:0% +between G and H then that'll break this +um but if you take two random points you + + align:start position:0% +um but if you take two random points you + + + align:start position:0% +um but if you take two random points you +know G was sort of randomly chosen and + + align:start position:0% +know G was sort of randomly chosen and + + + align:start position:0% +know G was sort of randomly chosen and +you chose a random H this shouldn't be + + align:start position:0% +you chose a random H this shouldn't be + + + align:start position:0% +you chose a random H this shouldn't be +possible right that would be breaking + + align:start position:0% +possible right that would be breaking + + + align:start position:0% +possible right that would be breaking +the discrete log problem so I shouldn't + + align:start position:0% +the discrete log problem so I shouldn't + + + align:start position:0% +the discrete log problem so I shouldn't +be able to compute okay well what is H + + align:start position:0% +be able to compute okay well what is H + + + align:start position:0% +be able to compute okay well what is H +divided by G well you shouldn't be able + + align:start position:0% +divided by G well you shouldn't be able + + + align:start position:0% +divided by G well you shouldn't be able +to compute that and so I think in a lot + + align:start position:0% +to compute that and so I think in a lot + + + align:start position:0% +to compute that and so I think in a lot +of cases they'll define H as like take + + align:start position:0% +of cases they'll define H as like take + + + align:start position:0% +of cases they'll define H as like take +the hash of G's x-coordinate and then + + align:start position:0% +the hash of G's x-coordinate and then + + + align:start position:0% +the hash of G's x-coordinate and then +assign that to the x-coordinate for H + + align:start position:0% +assign that to the x-coordinate for H + + + align:start position:0% +assign that to the x-coordinate for H +something like that so it looks pretty + + align:start position:0% +something like that so it looks pretty + + + align:start position:0% +something like that so it looks pretty +random should be able to find it okay so + + align:start position:0% +random should be able to find it okay so + + + align:start position:0% +random should be able to find it okay so +we've got another another arbitrary + + align:start position:0% +we've got another another arbitrary + + + align:start position:0% +we've got another another arbitrary +point on the curve that we're gonna + + align:start position:0% +point on the curve that we're gonna + + + align:start position:0% +point on the curve that we're gonna +start use using for multiplying things + + align:start position:0% +start use using for multiplying things + + + align:start position:0% +start use using for multiplying things +okay and so this is basically a Peterson + + align:start position:0% +okay and so this is basically a Peterson + + + align:start position:0% +okay and so this is basically a Peterson +commitment which sounds involved and it + + align:start position:0% +commitment which sounds involved and it + + + align:start position:0% +commitment which sounds involved and it +gets involved but really it's not it on + + align:start position:0% +gets involved but really it's not it on + + + align:start position:0% +gets involved but really it's not it on +it's you know at its core it's not too + + align:start position:0% +it's you know at its core it's not too + + + align:start position:0% +it's you know at its core it's not too +bad it's saying we're gonna have a + + align:start position:0% +bad it's saying we're gonna have a + + + align:start position:0% +bad it's saying we're gonna have a +blinding factor and the actual value + + align:start position:0% +blinding factor and the actual value + + + align:start position:0% +blinding factor and the actual value +we're committing to and so now I'm + + align:start position:0% +we're committing to and so now I'm + + + align:start position:0% +we're committing to and so now I'm +multiplying the blinding factor by G and + + align:start position:0% +multiplying the blinding factor by G and + + + align:start position:0% +multiplying the blinding factor by G and +the actual value by H and I'm just + + align:start position:0% +the actual value by H and I'm just + + + align:start position:0% +the actual value by H and I'm just +adding those two up right so you know + + align:start position:0% +adding those two up right so you know + + + align:start position:0% +adding those two up right so you know +how we can do that we can just say okay + + align:start position:0% +how we can do that we can just say okay + + + align:start position:0% +how we can do that we can just say okay +if if my actual value is 5 I take five H + + align:start position:0% +if if my actual value is 5 I take five H + + + align:start position:0% +if if my actual value is 5 I take five H +by taking the tangent getting to H + + align:start position:0% +by taking the tangent getting to H + + + align:start position:0% +by taking the tangent getting to H +taking the tangent again getting for H + + align:start position:0% +taking the tangent again getting for H + + + align:start position:0% +taking the tangent again getting for H +and then adding for H and H by drawing a + + align:start position:0% +and then adding for H and H by drawing a + + + align:start position:0% +and then adding for H and H by drawing a +line between them I'll get five H and + + align:start position:0% +line between them I'll get five H and + + + align:start position:0% +line between them I'll get five H and +then I'll also get our R's gonna be some + + align:start position:0% +then I'll also get our R's gonna be some + + + align:start position:0% +then I'll also get our R's gonna be some +giant random thing right ours not gonna + + align:start position:0% +giant random thing right ours not gonna + + + align:start position:0% +giant random thing right ours not gonna +be like five ours gonna be like a + + align:start position:0% +be like five ours gonna be like a + + + align:start position:0% +be like five ours gonna be like a +256-bit random number and that will + + align:start position:0% +256-bit random number and that will + + + align:start position:0% +256-bit random number and that will +obscure what H was what sorry what V was + + align:start position:0% +obscure what H was what sorry what V was + + + align:start position:0% +obscure what H was what sorry what V was +because I add them together so this is + + align:start position:0% +because I add them together so this is + + + align:start position:0% +because I add them together so this is +by + + align:start position:0% +by + + + align:start position:0% +by +unless I know the ratio right unless I + + align:start position:0% +unless I know the ratio right unless I + + + align:start position:0% +unless I know the ratio right unless I +know H over G or or G or H whatever same + + align:start position:0% +know H over G or or G or H whatever same + + + align:start position:0% +know H over G or or G or H whatever same +thing or I can't come up with another R + + align:start position:0% +thing or I can't come up with another R + + + align:start position:0% +thing or I can't come up with another R +and V pair that gets me back to X so I + + align:start position:0% +and V pair that gets me back to X so I + + + align:start position:0% +and V pair that gets me back to X so I +can try like there there are there is + + align:start position:0% +can try like there there are there is + + + align:start position:0% +can try like there there are there is +one right there's all I there's probably + + align:start position:0% +one right there's all I there's probably + + + align:start position:0% +one right there's all I there's probably +bazillions of well if I could find a + + align:start position:0% +bazillions of well if I could find a + + + align:start position:0% +bazillions of well if I could find a +different R I could then reveal that V + + align:start position:0% +different R I could then reveal that V + + + align:start position:0% +different R I could then reveal that V +was 8 instead of 7 but I can't find that + + align:start position:0% +was 8 instead of 7 but I can't find that + + + align:start position:0% +was 8 instead of 7 but I can't find that +art because I need to know some way to + + align:start position:0% +art because I need to know some way to + + + align:start position:0% +art because I need to know some way to +get between G and H like some factor n + + align:start position:0% +get between G and H like some factor n + + + align:start position:0% +get between G and H like some factor n +where n times G equals H if I don't know + + align:start position:0% +where n times G equals H if I don't know + + + align:start position:0% +where n times G equals H if I don't know +that I can't do this I'm you know it is + + align:start position:0% +that I can't do this I'm you know it is + + + align:start position:0% +that I can't do this I'm you know it is +binding it's also hiding right so you + + align:start position:0% +binding it's also hiding right so you + + + align:start position:0% +binding it's also hiding right so you +might successfully guess I might commit + + align:start position:0% +might successfully guess I might commit + + + align:start position:0% +might successfully guess I might commit +V equals 5 do some random number R times + + align:start position:0% +V equals 5 do some random number R times + + + align:start position:0% +V equals 5 do some random number R times +G Plus 5 H and you might guess correctly + + align:start position:0% +G Plus 5 H and you might guess correctly + + + align:start position:0% +G Plus 5 H and you might guess correctly +but oh this should have been G oops + + align:start position:0% +but oh this should have been G oops + + + align:start position:0% +but oh this should have been G oops +sorry this is G but if I have some + + align:start position:0% +sorry this is G but if I have some + + + align:start position:0% +sorry this is G but if I have some +really long random number times G it's + + align:start position:0% +really long random number times G it's + + + align:start position:0% +really long random number times G it's +also in X and you're not gonna be able + + align:start position:0% +also in X and you're not gonna be able + + + align:start position:0% +also in X and you're not gonna be able +to guess that so this is also hiding and + + align:start position:0% +to guess that so this is also hiding and + + + align:start position:0% +to guess that so this is also hiding and +it's homomorphic so what we can do is we + + align:start position:0% +it's homomorphic so what we can do is we + + + align:start position:0% +it's homomorphic so what we can do is we +can say okay + + align:start position:0% +can say okay + + + align:start position:0% +can say okay +X is R 1 G Plus v1 h y is r 2 G Plus V 2 + + align:start position:0% +X is R 1 G Plus v1 h y is r 2 G Plus V 2 + + + align:start position:0% +X is R 1 G Plus v1 h y is r 2 G Plus V 2 +H and what if I want to prove that Z is + + align:start position:0% +H and what if I want to prove that Z is + + + align:start position:0% +H and what if I want to prove that Z is +value 1 plus value 2 without revealing + + align:start position:0% +value 1 plus value 2 without revealing + + + align:start position:0% +value 1 plus value 2 without revealing +them individually can you see how I + + align:start position:0% +them individually can you see how I + + + align:start position:0% +them individually can you see how I +could do that well I can reveal I can + + align:start position:0% +could do that well I can reveal I can + + + align:start position:0% +could do that well I can reveal I can +actually reveal both R's individually + + align:start position:0% +actually reveal both R's individually + + + align:start position:0% +actually reveal both R's individually +well no sorry I cannot reveal both R's + + align:start position:0% +well no sorry I cannot reveal both R's + + + align:start position:0% +well no sorry I cannot reveal both R's +individually because then you might be + + align:start position:0% +individually because then you might be + + + align:start position:0% +individually because then you might be +able to yeah you'd be able to figure out + + align:start position:0% +able to yeah you'd be able to figure out + + + align:start position:0% +able to yeah you'd be able to figure out +the values but I can reveal the sum of + + align:start position:0% +the values but I can reveal the sum of + + + align:start position:0% +the values but I can reveal the sum of +the ARS and the sum of the meats right + + align:start position:0% +the ARS and the sum of the meats right + + + align:start position:0% +the ARS and the sum of the meats right +so I can say okay well I'm gonna define + + align:start position:0% +so I can say okay well I'm gonna define + + + align:start position:0% +so I can say okay well I'm gonna define +a point Z which is point X plus point y + + align:start position:0% +a point Z which is point X plus point y + + + align:start position:0% +a point Z which is point X plus point y +and that's just going to be the sum of + + align:start position:0% +and that's just going to be the sum of + + + align:start position:0% +and that's just going to be the sum of +the R values those some of those random + + align:start position:0% +the R values those some of those random + + + align:start position:0% +the R values those some of those random +values times G plus the sum of the + + align:start position:0% +values times G plus the sum of the + + + align:start position:0% +values times G plus the sum of the +actual values I've committed 2 times H + + align:start position:0% +actual values I've committed 2 times H + + + align:start position:0% +actual values I've committed 2 times H +and then I reveal just the sums right + + align:start position:0% +and then I reveal just the sums right + + + align:start position:0% +and then I reveal just the sums right +this I reveal that and then the verifier + + align:start position:0% +this I reveal that and then the verifier + + + align:start position:0% +this I reveal that and then the verifier +can do the math themselves and say okay + + align:start position:0% +can do the math themselves and say okay + + + align:start position:0% +can do the math themselves and say okay +well is this are they don't so it's a + + align:start position:0% +well is this are they don't so it's a + + + align:start position:0% +well is this are they don't so it's a +little hard I'm revealing R and V which + + align:start position:0% +little hard I'm revealing R and V which + + + align:start position:0% +little hard I'm revealing R and V which +is equal to this but I'm not revealing + + align:start position:0% +is equal to this but I'm not revealing + + + align:start position:0% +is equal to this but I'm not revealing +these separately right I only reveal the + + align:start position:0% +these separately right I only reveal the + + + align:start position:0% +these separately right I only reveal the +songs and then the verifier can check + + align:start position:0% +songs and then the verifier can check + + + align:start position:0% +songs and then the verifier can check +okay is this are they gave times J plus + + align:start position:0% +okay is this are they gave times J plus + + + align:start position:0% +okay is this are they gave times J plus +this V they gave times H equal to these + + align:start position:0% +this V they gave times H equal to these + + + align:start position:0% +this V they gave times H equal to these +two points added together and if it is + + align:start position:0% +two points added together and if it is + + + align:start position:0% +two points added together and if it is +they've sort of proven okay the song so + + align:start position:0% +they've sort of proven okay the song so + + + align:start position:0% +they've sort of proven okay the song so +for example yeah it's finding hiding and + + align:start position:0% +for example yeah it's finding hiding and + + + align:start position:0% +for example yeah it's finding hiding and +home morphic so this would allow us to + + align:start position:0% +home morphic so this would allow us to + + + align:start position:0% +home morphic so this would allow us to +make proofs right yeah Oh more pick you + + align:start position:0% +make proofs right yeah Oh more pick you + + + align:start position:0% +make proofs right yeah Oh more pick you +revealed of some of the R's you reveal + + align:start position:0% +revealed of some of the R's you reveal + + + align:start position:0% +revealed of some of the R's you reveal +the some of the V's works so basically + + align:start position:0% +the some of the V's works so basically + + + align:start position:0% +the some of the V's works so basically +now instead of coin amounts which are + + align:start position:0% +now instead of coin amounts which are + + + align:start position:0% +now instead of coin amounts which are +like eight byte you entered there in 64 + + align:start position:0% +like eight byte you entered there in 64 + + + align:start position:0% +like eight byte you entered there in 64 +s I just provide elliptic curve points + + align:start position:0% +s I just provide elliptic curve points + + + align:start position:0% +s I just provide elliptic curve points +which are 33 bytes so it's you know a + + align:start position:0% +which are 33 bytes so it's you know a + + + align:start position:0% +which are 33 bytes so it's you know a +bit bigger not a huge deal I can put + + align:start position:0% +bit bigger not a huge deal I can put + + + align:start position:0% +bit bigger not a huge deal I can put +another you know 20-something bytes in + + align:start position:0% +another you know 20-something bytes in + + + align:start position:0% +another you know 20-something bytes in +my outputs no big deal + + align:start position:0% +my outputs no big deal + + + align:start position:0% +my outputs no big deal +and then I just provide a proof by + + align:start position:0% +and then I just provide a proof by + + + align:start position:0% +and then I just provide a proof by +revealing these sums each time right so + + align:start position:0% +revealing these sums each time right so + + + align:start position:0% +revealing these sums each time right so +I prove that W plus X equals y plus C + + align:start position:0% +I prove that W plus X equals y plus C + + + align:start position:0% +I prove that W plus X equals y plus C +and everyone can see okay this actually + + align:start position:0% +and everyone can see okay this actually + + + align:start position:0% +and everyone can see okay this actually +little W amount of coins there's + + align:start position:0% +little W amount of coins there's + + + align:start position:0% +little W amount of coins there's +actually Y coins there's actually X + + align:start position:0% +actually Y coins there's actually X + + + align:start position:0% +actually Y coins there's actually X +coins there's actually Z coins and + + align:start position:0% +coins there's actually Z coins and + + + align:start position:0% +coins there's actually Z coins and +there's a blinding factor that all the + + align:start position:0% +there's a blinding factor that all the + + + align:start position:0% +there's a blinding factor that all the +participants have to keep track of so + + align:start position:0% +participants have to keep track of so + + + align:start position:0% +participants have to keep track of so +the receivers view is they learn their + + align:start position:0% +the receivers view is they learn their + + + align:start position:0% +the receivers view is they learn their +own V and R right so the receiver when + + align:start position:0% +own V and R right so the receiver when + + + align:start position:0% +own V and R right so the receiver when +when someone sends they would have to + + align:start position:0% +when someone sends they would have to + + + align:start position:0% +when someone sends they would have to +tell the receiver hey here's our for the + + align:start position:0% +tell the receiver hey here's our for the + + + align:start position:0% +tell the receiver hey here's our for the +sender makes up our for and they can + + align:start position:0% +sender makes up our for and they can + + + align:start position:0% +sender makes up our for and they can +just compute let's you know make a + + align:start position:0% +just compute let's you know make a + + + align:start position:0% +just compute let's you know make a +random R 3 and then compute R 4 such + + align:start position:0% +random R 3 and then compute R 4 such + + + align:start position:0% +random R 3 and then compute R 4 such +that our + + align:start position:0% +that our + + + align:start position:0% +that our +or plus r3 equals r1 plus r2 right they + + align:start position:0% +or plus r3 equals r1 plus r2 right they + + + align:start position:0% +or plus r3 equals r1 plus r2 right they +need to make sure that the randomness is + + align:start position:0% +need to make sure that the randomness is + + + align:start position:0% +need to make sure that the randomness is +add up which is easy because they're + + align:start position:0% +add up which is easy because they're + + + align:start position:0% +add up which is easy because they're +just regular scalars and the the sender + + align:start position:0% +just regular scalars and the the sender + + + align:start position:0% +just regular scalars and the the sender +has full control over r3 and r4 so + + align:start position:0% +has full control over r3 and r4 so + + + align:start position:0% +has full control over r3 and r4 so +basically make random ones until you get + + align:start position:0% +basically make random ones until you get + + + align:start position:0% +basically make random ones until you get +to the last one and then make the last + + align:start position:0% +to the last one and then make the last + + + align:start position:0% +to the last one and then make the last +one such that they all add up to the + + align:start position:0% +one such that they all add up to the + + + align:start position:0% +one such that they all add up to the +right number and then the sender can say + + align:start position:0% +right number and then the sender can say + + + align:start position:0% +right number and then the sender can say +okay well here's your r4 and here's to + + align:start position:0% +okay well here's your r4 and here's to + + + align:start position:0% +okay well here's your r4 and here's to +you know you're getting two coins and + + align:start position:0% +you know you're getting two coins and + + + align:start position:0% +you know you're getting two coins and +the receiver gets those two numbers and + + align:start position:0% +the receiver gets those two numbers and + + + align:start position:0% +the receiver gets those two numbers and +says okay cool + + align:start position:0% +says okay cool + + + align:start position:0% +says okay cool +I can see that this transaction commits + + align:start position:0% +I can see that this transaction commits + + + align:start position:0% +I can see that this transaction commits +to Z a point and you gave me an R and a + + align:start position:0% +to Z a point and you gave me an R and a + + + align:start position:0% +to Z a point and you gave me an R and a +V that that you know when I do the + + align:start position:0% +V that that you know when I do the + + + align:start position:0% +V that that you know when I do the +operation I get Z so I know that you + + align:start position:0% +operation I get Z so I know that you + + + align:start position:0% +operation I get Z so I know that you +successfully you know you've revealed + + align:start position:0% +successfully you know you've revealed + + + align:start position:0% +successfully you know you've revealed +that these are actually two coins and I + + align:start position:0% +that these are actually two coins and I + + + align:start position:0% +that these are actually two coins and I +can use these values later when I want + + align:start position:0% +can use these values later when I want + + + align:start position:0% +can use these values later when I want +to send my own coins so this works but + + align:start position:0% +to send my own coins so this works but + + + align:start position:0% +to send my own coins so this works but +there's more problems any idea what the + + align:start position:0% +there's more problems any idea what the + + + align:start position:0% +there's more problems any idea what the +next big problem is I mean there's sort + + align:start position:0% +next big problem is I mean there's sort + + + align:start position:0% +next big problem is I mean there's sort +of no way around that right if there's + + align:start position:0% +of no way around that right if there's + + + align:start position:0% +of no way around that right if there's +only one input or wait well only and the + + align:start position:0% +only one input or wait well only and the + + + align:start position:0% +only one input or wait well only and the +receiver learnt so if the receiver + + align:start position:0% +receiver learnt so if the receiver + + + align:start position:0% +receiver learnt so if the receiver +learns these they will be able to this + + align:start position:0% +learns these they will be able to this + + + align:start position:0% +learns these they will be able to this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +if you know the total amount of inputs + + align:start position:0% +if you know the total amount of inputs + + + align:start position:0% +if you know the total amount of inputs +and there's only one other you can just + + align:start position:0% +and there's only one other you can just + + + align:start position:0% +and there's only one other you can just +subtract and figure it out right so + + align:start position:0% +subtract and figure it out right so + + + align:start position:0% +subtract and figure it out right so +there's there's all sorts of things if + + align:start position:0% +there's there's all sorts of things if + + + align:start position:0% +there's there's all sorts of things if +there's only one output that person + + align:start position:0% +there's only one output that person + + + align:start position:0% +there's only one output that person +knows it's the sum of all the inputs + + align:start position:0% + + + + align:start position:0% + +right in this case you don't you don't + + align:start position:0% +right in this case you don't you don't + + + align:start position:0% +right in this case you don't you don't +have to they don't have to reveal to you + + align:start position:0% +have to they don't have to reveal to you + + + align:start position:0% +have to they don't have to reveal to you +the V they just have to reveal that two + + align:start position:0% +the V they just have to reveal that two + + + align:start position:0% +the V they just have to reveal that two +plus y equals W plus X so you don't have + + align:start position:0% +plus y equals W plus X so you don't have + + + align:start position:0% +plus y equals W plus X so you don't have +to you don't have to learn their input + + align:start position:0% +to you don't have to learn their input + + + align:start position:0% +to you don't have to learn their input +amounts yeah if there's only one output + + align:start position:0% +amounts yeah if there's only one output + + + align:start position:0% +amounts yeah if there's only one output +then you learn like okay well if this is + + align:start position:0% +then you learn like okay well if this is + + + align:start position:0% +then you learn like okay well if this is +to these must have added up to two but I + + align:start position:0% +to these must have added up to two but I + + + align:start position:0% +to these must have added up to two but I +don't learn it exactly which so this is + + align:start position:0% +don't learn it exactly which so this is + + + align:start position:0% +don't learn it exactly which so this is +useful there's still a big problem yeah + + align:start position:0% +useful there's still a big problem yeah + + + align:start position:0% +useful there's still a big problem yeah +okay sorry for you can prove W plus X + + align:start position:0% +okay sorry for you can prove W plus X + + + align:start position:0% +okay sorry for you can prove W plus X +equals y plus Z it works it's great + + align:start position:0% + + + + align:start position:0% + +nodes only just need nodes can just + + align:start position:0% +nodes only just need nodes can just + + + align:start position:0% +nodes only just need nodes can just +compute these numbers and they're good + + align:start position:0% +compute these numbers and they're good + + + align:start position:0% +compute these numbers and they're good +right so so one thing you could do here + + align:start position:0% +right so so one thing you could do here + + + align:start position:0% +right so so one thing you could do here +okay wait so so there's one thing that + + align:start position:0% +okay wait so so there's one thing that + + + align:start position:0% +okay wait so so there's one thing that +you could do to break it but it's + + align:start position:0% +you could do to break it but it's + + + align:start position:0% +you could do to break it but it's +actually not a big deal and then there's + + align:start position:0% +actually not a big deal and then there's + + + align:start position:0% +actually not a big deal and then there's +another thing you can do to break it + + align:start position:0% +another thing you can do to break it + + + align:start position:0% +another thing you can do to break it +it's a really big deal yeah + + align:start position:0% + + + + align:start position:0% + +kind of well your yeah but how exactly + + align:start position:0% +kind of well your yeah but how exactly + + + align:start position:0% +kind of well your yeah but how exactly +so one thing you could do is I think I + + align:start position:0% +so one thing you could do is I think I + + + align:start position:0% +so one thing you could do is I think I +said so so basically you can verify it + + align:start position:0% +said so so basically you can verify it + + + align:start position:0% +said so so basically you can verify it +and put in the outputs add up all the + + align:start position:0% +and put in the outputs add up all the + + + align:start position:0% +and put in the outputs add up all the +points make sure they're equal you + + align:start position:0% +points make sure they're equal you + + + align:start position:0% +points make sure they're equal you +reveal our D to the person receiving and + + align:start position:0% +reveal our D to the person receiving and + + + align:start position:0% +reveal our D to the person receiving and +you don't want to forget our if you are + + align:start position:0% +you don't want to forget our if you are + + + align:start position:0% +you don't want to forget our if you are +a sort of now a private key + + align:start position:0% +a sort of now a private key + + + align:start position:0% +a sort of now a private key +if you forget our you're stuck you can't + + align:start position:0% +if you forget our you're stuck you can't + + + align:start position:0% +if you forget our you're stuck you can't +prove anything anymore you can make + + align:start position:0% +prove anything anymore you can make + + + align:start position:0% +prove anything anymore you can make +invalid output which are just points + + align:start position:0% +invalid output which are just points + + + align:start position:0% +invalid output which are just points +with no known R and V but nobody should + + align:start position:0% +with no known R and V but nobody should + + + align:start position:0% +with no known R and V but nobody should +accept those right so you can just do + + align:start position:0% +accept those right so you can just do + + + align:start position:0% +accept those right so you can just do +this where I have no idea what's like + + align:start position:0% +this where I have no idea what's like + + + align:start position:0% +this where I have no idea what's like +there is no commitment here maybe these + + align:start position:0% +there is no commitment here maybe these + + + align:start position:0% +there is no commitment here maybe these +have valid commitments but this is just + + align:start position:0% +have valid commitments but this is just + + + align:start position:0% +have valid commitments but this is just +a point which is w plus X minus y and + + align:start position:0% +a point which is w plus X minus y and + + + align:start position:0% +a point which is w plus X minus y and +there's no known our values or Z or or V + + align:start position:0% +there's no known our values or Z or or V + + + align:start position:0% +there's no known our values or Z or or V +values for these things and from the + + align:start position:0% +values for these things and from the + + + align:start position:0% +values for these things and from the +network's point of view this will still + + align:start position:0% +network's point of view this will still + + + align:start position:0% +network's point of view this will still +be valid right the networks are saying + + align:start position:0% +be valid right the networks are saying + + + align:start position:0% +be valid right the networks are saying +well W plus x equals y plus Z we're good + + align:start position:0% +well W plus x equals y plus Z we're good + + + align:start position:0% +well W plus x equals y plus Z we're good +but then anyone accepting that + + align:start position:0% +but then anyone accepting that + + + align:start position:0% +but then anyone accepting that +transaction you're not going to be able + + align:start position:0% +transaction you're not going to be able + + + align:start position:0% +transaction you're not going to be able +to give them in our value and so they're + + align:start position:0% +to give them in our value and so they're + + + align:start position:0% +to give them in our value and so they're +not going to say this is actual money so + + align:start position:0% +not going to say this is actual money so + + + align:start position:0% +not going to say this is actual money so +this is possible but it's not a huge + + align:start position:0% +this is possible but it's not a huge + + + align:start position:0% +this is possible but it's not a huge +problem because well you can destroy + + align:start position:0% +problem because well you can destroy + + + align:start position:0% +problem because well you can destroy +your own money you can already do that + + align:start position:0% +your own money you can already do that + + + align:start position:0% +your own money you can already do that +in a million different ways in Bitcoin + + align:start position:0% +in a million different ways in Bitcoin + + + align:start position:0% +in a million different ways in Bitcoin +but yeah if you send to it to an output + + align:start position:0% +but yeah if you send to it to an output + + + align:start position:0% +but yeah if you send to it to an output +amount that doesn't have an actual R and + + align:start position:0% +amount that doesn't have an actual R and + + + align:start position:0% +amount that doesn't have an actual R and +V value no that doesn't have a valid + + align:start position:0% +V value no that doesn't have a valid + + + align:start position:0% +V value no that doesn't have a valid +Petersons commitment those coins can + + align:start position:0% +Petersons commitment those coins can + + + align:start position:0% +Petersons commitment those coins can +essentially be destroyed because no + + align:start position:0% +essentially be destroyed because no + + + align:start position:0% +essentially be destroyed because no +one's gonna be able to figure out ours + + align:start position:0% +one's gonna be able to figure out ours + + + align:start position:0% +one's gonna be able to figure out ours +and stuff for here so that's that's one + + align:start position:0% +and stuff for here so that's that's one + + + align:start position:0% +and stuff for here so that's that's one +issue not a big issue right it's just + + align:start position:0% +issue not a big issue right it's just + + + align:start position:0% +issue not a big issue right it's just +don't do that right don't don't ruin + + align:start position:0% +don't do that right don't don't ruin + + + align:start position:0% +don't do that right don't don't ruin +your own money make sure you always have + + align:start position:0% +your own money make sure you always have + + + align:start position:0% +your own money make sure you always have +valid commitments and when you're + + align:start position:0% +valid commitments and when you're + + + align:start position:0% +valid commitments and when you're +accepting payments always make sure that + + align:start position:0% +accepting payments always make sure that + + + align:start position:0% +accepting payments always make sure that +you're given the you know the values in + + align:start position:0% +you're given the you know the values in + + + align:start position:0% +you're given the you know the values in +the random the random blinding factors + + align:start position:0% +the random the random blinding factors + + + align:start position:0% +the random the random blinding factors +so that's one little risk but not the + + align:start position:0% +so that's one little risk but not the + + + align:start position:0% +so that's one little risk but not the +big problem + + align:start position:0% +big problem + + + align:start position:0% +big problem +anyone have idea about the big problem + + align:start position:0% +anyone have idea about the big problem + + + align:start position:0% +anyone have idea about the big problem +so as a hint all of these things and I + + align:start position:0% +so as a hint all of these things and I + + + align:start position:0% +so as a hint all of these things and I +haven't written it because it gets + + align:start position:0% +haven't written it because it gets + + + align:start position:0% +haven't written it because it gets +really redundant all of these things are + + align:start position:0% +really redundant all of these things are + + + align:start position:0% +really redundant all of these things are +like mod P right which is some giant + + align:start position:0% +like mod P right which is some giant + + + align:start position:0% +like mod P right which is some giant +prime number that's like + + align:start position:0% +prime number that's like + + + align:start position:0% +prime number that's like +- to the 256 - 17 or not it's it's not + + align:start position:0% +- to the 256 - 17 or not it's it's not + + + align:start position:0% +- to the 256 - 17 or not it's it's not +in some in the curvy d25 509 it's 2 to + + align:start position:0% +in some in the curvy d25 509 it's 2 to + + + align:start position:0% +in some in the curvy d25 509 it's 2 to +the 2 5 5 - 19 + + align:start position:0% +the 2 5 5 - 19 + + + align:start position:0% +the 2 5 5 - 19 +so that's like an easy one to remember + + align:start position:0% +so that's like an easy one to remember + + + align:start position:0% +so that's like an easy one to remember +so that's why they call it curve - 5 5 1 + + align:start position:0% +so that's why they call it curve - 5 5 1 + + + align:start position:0% +so that's why they call it curve - 5 5 1 +9 in Bitcoin it's 2 to the 256 - some + + align:start position:0% +9 in Bitcoin it's 2 to the 256 - some + + + align:start position:0% +9 in Bitcoin it's 2 to the 256 - some +numbers that are like not too huge so + + align:start position:0% +numbers that are like not too huge so + + + align:start position:0% +numbers that are like not too huge so +since all of these things are modulo + + align:start position:0% +since all of these things are modulo + + + align:start position:0% +since all of these things are modulo +some big prime number what's the + + align:start position:0% +some big prime number what's the + + + align:start position:0% +some big prime number what's the +potential problem here it's a big + + align:start position:0% +potential problem here it's a big + + + align:start position:0% +potential problem here it's a big +problem or in some ways the opposite of + + align:start position:0% +problem or in some ways the opposite of + + + align:start position:0% +problem or in some ways the opposite of +a big problem not a small problem the + + align:start position:0% +a big problem not a small problem the + + + align:start position:0% +a big problem not a small problem the +opposite of a big problem but not small + + align:start position:0% + + + + align:start position:0% + +being negative problem you can basically + + align:start position:0% +being negative problem you can basically + + + align:start position:0% +being negative problem you can basically +commit to negative values right so I + + align:start position:0% +commit to negative values right so I + + + align:start position:0% +commit to negative values right so I +just said negative 99 coins here + + align:start position:0% +just said negative 99 coins here + + + align:start position:0% +just said negative 99 coins here +positive 108 points here the numbers all + + align:start position:0% +positive 108 points here the numbers all + + + align:start position:0% +positive 108 points here the numbers all +work out so you don't actually have + + align:start position:0% +work out so you don't actually have + + + align:start position:0% +work out so you don't actually have +negative usually if you're doing like + + align:start position:0% +negative usually if you're doing like + + + align:start position:0% +negative usually if you're doing like +mod mod some integer you don't think of + + align:start position:0% +mod mod some integer you don't think of + + + align:start position:0% +mod mod some integer you don't think of +it as negative but you can think of + + align:start position:0% +it as negative but you can think of + + + align:start position:0% +it as negative but you can think of +being almost right at the top of that + + align:start position:0% +being almost right at the top of that + + + align:start position:0% +being almost right at the top of that +modulo range as being equivalent to + + align:start position:0% +modulo range as being equivalent to + + + align:start position:0% +modulo range as being equivalent to +being you know negative 1 so if you say + + align:start position:0% +being you know negative 1 so if you say + + + align:start position:0% +being you know negative 1 so if you say +okay I'm gonna I'm gonna have P minus 1 + + align:start position:0% +okay I'm gonna I'm gonna have P minus 1 + + + align:start position:0% +okay I'm gonna I'm gonna have P minus 1 +well that's some huge number that's + + align:start position:0% +well that's some huge number that's + + + align:start position:0% +well that's some huge number that's +within the you know allowable range but + + align:start position:0% +within the you know allowable range but + + + align:start position:0% +within the you know allowable range but +it also will let you treat it as a + + align:start position:0% +it also will let you treat it as a + + + align:start position:0% +it also will let you treat it as a +negative 1 for operations like addition + + align:start position:0% +negative 1 for operations like addition + + + align:start position:0% +negative 1 for operations like addition +and multiplication so this would work + + align:start position:0% +and multiplication so this would work + + + align:start position:0% +and multiplication so this would work +and you can you can calculate what + + align:start position:0% +and you can you can calculate what + + + align:start position:0% +and you can you can calculate what +negative 99 is that's just gonna be you + + align:start position:0% +negative 99 is that's just gonna be you + + + align:start position:0% +negative 99 is that's just gonna be you +know P minus 99 or minus 100 I always am + + align:start position:0% +know P minus 99 or minus 100 I always am + + + align:start position:0% +know P minus 99 or minus 100 I always am +off by 1 when I do these things anyway + + align:start position:0% +off by 1 when I do these things anyway + + + align:start position:0% +off by 1 when I do these things anyway +so so you can calculate okay it's not + + align:start position:0% +so so you can calculate okay it's not + + + align:start position:0% +so so you can calculate okay it's not +really minus 99 right it's some big + + align:start position:0% +really minus 99 right it's some big + + + align:start position:0% +really minus 99 right it's some big +number that's gonna be 32 bytes long + + align:start position:0% +number that's gonna be 32 bytes long + + + align:start position:0% +number that's gonna be 32 bytes long +that's modulo you know modulo P it + + align:start position:0% +that's modulo you know modulo P it + + + align:start position:0% +that's modulo you know modulo P it +doesn't change but it's equivalent to + + align:start position:0% +doesn't change but it's equivalent to + + + align:start position:0% +doesn't change but it's equivalent to +minus 99 so that if I do add these to + + align:start position:0% +minus 99 so that if I do add these to + + + align:start position:0% +minus 99 so that if I do add these to +the skew + + align:start position:0% +the skew + + + align:start position:0% +the skew +Plus this other small number it sort of + + align:start position:0% +Plus this other small number it sort of + + + align:start position:0% +Plus this other small number it sort of +loops over that modulo and then gets + + align:start position:0% +loops over that modulo and then gets + + + align:start position:0% +loops over that modulo and then gets +back to what nine right so this Plus + + align:start position:0% +back to what nine right so this Plus + + + align:start position:0% +back to what nine right so this Plus +this is gonna be nine even though this + + align:start position:0% +this is gonna be nine even though this + + + align:start position:0% +this is gonna be nine even though this +is some you know really long number this + + align:start position:0% +is some you know really long number this + + + align:start position:0% +is some you know really long number this +Plus this is gonna be nine and then it + + align:start position:0% +Plus this is gonna be nine and then it + + + align:start position:0% +Plus this is gonna be nine and then it +all adds up and then I've got this + + align:start position:0% +all adds up and then I've got this + + + align:start position:0% +all adds up and then I've got this +either negative or implausibly large + + align:start position:0% +either negative or implausibly large + + + align:start position:0% +either negative or implausibly large +value that I've committed to but I can + + align:start position:0% +value that I've committed to but I can + + + align:start position:0% +value that I've committed to but I can +just ignore that right I can get rid of + + align:start position:0% +just ignore that right I can get rid of + + + align:start position:0% +just ignore that right I can get rid of +that yeah I'm negative output will be + + align:start position:0% +that yeah I'm negative output will be + + + align:start position:0% +that yeah I'm negative output will be +hidden right no one will see that I've + + align:start position:0% +hidden right no one will see that I've + + + align:start position:0% +hidden right no one will see that I've +got this negative 99 here and then I can + + align:start position:0% +got this negative 99 here and then I can + + + align:start position:0% +got this negative 99 here and then I can +just toss it and end up with a whole + + align:start position:0% +just toss it and end up with a whole + + + align:start position:0% +just toss it and end up with a whole +bunch of negative values that are like + + align:start position:0% +bunch of negative values that are like + + + align:start position:0% +bunch of negative values that are like +anti coins and a whole bunch of more new + + align:start position:0% +anti coins and a whole bunch of more new + + + align:start position:0% +anti coins and a whole bunch of more new +coins and later on I can prove I've got + + align:start position:0% +coins and later on I can prove I've got + + + align:start position:0% +coins and later on I can prove I've got +valid proofs all these you know w plus x + + align:start position:0% +valid proofs all these you know w plus x + + + align:start position:0% +valid proofs all these you know w plus x +equals y plus z proofs worked the whole + + align:start position:0% +equals y plus z proofs worked the whole + + + align:start position:0% +equals y plus z proofs worked the whole +time shoot so we're kind of stuck we + + align:start position:0% +time shoot so we're kind of stuck we + + + align:start position:0% +time shoot so we're kind of stuck we +need more than a proof that the sums are + + align:start position:0% +need more than a proof that the sums are + + + align:start position:0% +need more than a proof that the sums are +equal it was working really well but + + align:start position:0% +equal it was working really well but + + + align:start position:0% +equal it was working really well but +just a proof that the sums are equal is + + align:start position:0% +just a proof that the sums are equal is + + + align:start position:0% +just a proof that the sums are equal is +not enough because we're we're modulo + + align:start position:0% +not enough because we're we're modulo + + + align:start position:0% +not enough because we're we're modulo +this big prime number and so you can + + align:start position:0% +this big prime number and so you can + + + align:start position:0% +this big prime number and so you can +sort of make these negations we also + + align:start position:0% +sort of make these negations we also + + + align:start position:0% +sort of make these negations we also +need a proof that they're non-negative + + align:start position:0% +need a proof that they're non-negative + + + align:start position:0% +need a proof that they're non-negative +and not just not negative right because + + align:start position:0% +and not just not negative right because + + + align:start position:0% +and not just not negative right because +that that negative 99 is actually + + align:start position:0% +that that negative 99 is actually + + + align:start position:0% +that that negative 99 is actually +essentially you know P minus 99 which is + + align:start position:0% +essentially you know P minus 99 which is + + + align:start position:0% +essentially you know P minus 99 which is +some huge it's like 2 to the 256 - 99 + + align:start position:0% +some huge it's like 2 to the 256 - 99 + + + align:start position:0% +some huge it's like 2 to the 256 - 99 +ish so it's not just that the non + + align:start position:0% +ish so it's not just that the non + + + align:start position:0% +ish so it's not just that the non +negative we have to prove that they're + + align:start position:0% +negative we have to prove that they're + + + align:start position:0% +negative we have to prove that they're +reasonably sized but they're fairly + + align:start position:0% +reasonably sized but they're fairly + + + align:start position:0% +reasonably sized but they're fairly +small so if you could prove okay this + + align:start position:0% +small so if you could prove okay this + + + align:start position:0% +small so if you could prove okay this +number is non-negative and it's less + + align:start position:0% +number is non-negative and it's less + + + align:start position:0% +number is non-negative and it's less +than 2 to the 64 that would be cool how + + align:start position:0% +than 2 to the 64 that would be cool how + + + align:start position:0% +than 2 to the 64 that would be cool how +can we prove something about the number + + align:start position:0% +can we prove something about the number + + + align:start position:0% +can we prove something about the number +itself without revealing it so now this + + align:start position:0% +itself without revealing it so now this + + + align:start position:0% +itself without revealing it so now this +is an even trickier problem because + + align:start position:0% +is an even trickier problem because + + + align:start position:0% +is an even trickier problem because +before we wanted to prove a sum right we + + align:start position:0% +before we wanted to prove a sum right we + + + align:start position:0% +before we wanted to prove a sum right we +wanted to prove that ok z equals x plus + + align:start position:0% +wanted to prove that ok z equals x plus + + + align:start position:0% +wanted to prove that ok z equals x plus +y but i don't want to tell you what X + + align:start position:0% +y but i don't want to tell you what X + + + align:start position:0% +y but i don't want to tell you what X +plus y is but I'll tell you what sees + + align:start position:0% +plus y is but I'll tell you what sees + + + align:start position:0% +plus y is but I'll tell you what sees +that was reprove proving a relation + + align:start position:0% +that was reprove proving a relation + + + align:start position:0% +that was reprove proving a relation +between these numbers this is just + + align:start position:0% +between these numbers this is just + + + align:start position:0% +between these numbers this is just +proving something about that number + + align:start position:0% +proving something about that number + + + align:start position:0% +proving something about that number +itself individually right we have to + + align:start position:0% +itself individually right we have to + + + align:start position:0% +itself individually right we have to +prove + + align:start position:0% +prove + + + align:start position:0% +prove +individual numbers ranges so we have to + + align:start position:0% +individual numbers ranges so we have to + + + align:start position:0% +individual numbers ranges so we have to +say okay this 2h there's a 2h in there I + + align:start position:0% +say okay this 2h there's a 2h in there I + + + align:start position:0% +say okay this 2h there's a 2h in there I +don't I can't show you it because I'm + + align:start position:0% +don't I can't show you it because I'm + + + align:start position:0% +don't I can't show you it because I'm +just committing 2w but I want to somehow + + align:start position:0% +just committing 2w but I want to somehow + + + align:start position:0% +just committing 2w but I want to somehow +show you that the the the V here which + + align:start position:0% +show you that the the the V here which + + + align:start position:0% +show you that the the the V here which +happens to be two but I can tell you the + + align:start position:0% +happens to be two but I can tell you the + + + align:start position:0% +happens to be two but I can tell you the +V there is within a small range without + + align:start position:0% +V there is within a small range without + + + align:start position:0% +V there is within a small range without +telling you what it is without revealing + + align:start position:0% +telling you what it is without revealing + + + align:start position:0% +telling you what it is without revealing +it tricky okay so so what you can try to + + align:start position:0% +it tricky okay so so what you can try to + + + align:start position:0% +it tricky okay so so what you can try to +do is sign with the points somehow this + + align:start position:0% +do is sign with the points somehow this + + + align:start position:0% +do is sign with the points somehow this +is what'll get us there + + align:start position:0% +is what'll get us there + + + align:start position:0% +is what'll get us there +the idea of okay well we've got these + + align:start position:0% +the idea of okay well we've got these + + + align:start position:0% +the idea of okay well we've got these +Peterson commitments we've got these + + align:start position:0% +Peterson commitments we've got these + + + align:start position:0% +Peterson commitments we've got these +points on a curve those are sort of + + align:start position:0% +points on a curve those are sort of + + + align:start position:0% +points on a curve those are sort of +public keys or that's how we used to + + align:start position:0% +public keys or that's how we used to + + + align:start position:0% +public keys or that's how we used to +usually think of them can we like sign + + align:start position:0% +usually think of them can we like sign + + + align:start position:0% +usually think of them can we like sign +we know the private keys we know r1 we + + align:start position:0% +we know the private keys we know r1 we + + + align:start position:0% +we know the private keys we know r1 we +know - can we make signature somehow and + + align:start position:0% +know - can we make signature somehow and + + + align:start position:0% +know - can we make signature somehow and +like somehow use that to reveal some + + align:start position:0% +like somehow use that to reveal some + + + align:start position:0% +like somehow use that to reveal some +information about H but not too much so + + align:start position:0% +information about H but not too much so + + + align:start position:0% +information about H but not too much so +the signature equation s you know they + + align:start position:0% +the signature equation s you know they + + + align:start position:0% +the signature equation s you know they +didn't really review it as much but + + align:start position:0% +didn't really review it as much but + + + align:start position:0% +didn't really review it as much but +we've talked about this a couple times + + align:start position:0% +we've talked about this a couple times + + + align:start position:0% +we've talked about this a couple times +come up with a random value k take the + + align:start position:0% +come up with a random value k take the + + + align:start position:0% +come up with a random value k take the +hash of K times G and the message to be + + align:start position:0% +hash of K times G and the message to be + + + align:start position:0% +hash of K times G and the message to be +signed times your private key that's + + align:start position:0% +signed times your private key that's + + + align:start position:0% +signed times your private key that's +your signature s the problem is X Y or + + align:start position:0% +your signature s the problem is X Y or + + + align:start position:0% +your signature s the problem is X Y or +your value that you've got committed to + + align:start position:0% +your value that you've got committed to + + + align:start position:0% +your value that you've got committed to +here it's r 2g plus a 7h what's your + + align:start position:0% +here it's r 2g plus a 7h what's your + + + align:start position:0% +here it's r 2g plus a 7h what's your +private key here what's our two plus + + align:start position:0% +private key here what's our two plus + + + align:start position:0% +private key here what's our two plus +seven but no because you know the + + align:start position:0% +seven but no because you know the + + + align:start position:0% +seven but no because you know the +private scalars here but there's two + + align:start position:0% +private scalars here but there's two + + + align:start position:0% +private scalars here but there's two +points involved in this key so you can't + + align:start position:0% +points involved in this key so you can't + + + align:start position:0% +points involved in this key so you can't +make a signature you generally + + align:start position:0% +make a signature you generally + + + align:start position:0% +make a signature you generally +signatures are with respect to a single + + align:start position:0% +signatures are with respect to a single + + + align:start position:0% +signatures are with respect to a single +generator point right the way to verify + + align:start position:0% +generator point right the way to verify + + + align:start position:0% +generator point right the way to verify +this is multiply both sides by G right s + + align:start position:0% +this is multiply both sides by G right s + + + align:start position:0% +this is multiply both sides by G right s +times G should be K times G minus the + + align:start position:0% +times G should be K times G minus the + + + align:start position:0% +times G should be K times G minus the +hash occasion of G message times a times + + align:start position:0% +hash occasion of G message times a times + + + align:start position:0% +hash occasion of G message times a times +G which is a public key that works but + + align:start position:0% +G which is a public key that works but + + + align:start position:0% +G which is a public key that works but +now you've got H in here so we're stuck + + align:start position:0% + + + + align:start position:0% + +we could try to define another signature + + align:start position:0% +we could try to define another signature + + + align:start position:0% +we could try to define another signature +thing with like both a Sanji but that + + align:start position:0% +thing with like both a Sanji but that + + + align:start position:0% +thing with like both a Sanji but that +doesn't work but what we can show it's + + align:start position:0% +doesn't work but what we can show it's + + + align:start position:0% +doesn't work but what we can show it's +kind of interesting well what if V is + + align:start position:0% +kind of interesting well what if V is + + + align:start position:0% +kind of interesting well what if V is +then X is are two times G Plus zero H + + align:start position:0% +then X is are two times G Plus zero H + + + align:start position:0% +then X is are two times G Plus zero H +which is just are 2 times G right like + + align:start position:0% +which is just are 2 times G right like + + + align:start position:0% +which is just are 2 times G right like +this is this is nothing there's no H + + align:start position:0% +this is this is nothing there's no H + + + align:start position:0% +this is this is nothing there's no H +here and that means my private key is + + align:start position:0% +here and that means my private key is + + + align:start position:0% +here and that means my private key is +just gonna be our two well now I can + + align:start position:0% +just gonna be our two well now I can + + + align:start position:0% +just gonna be our two well now I can +sign now I can resign with respect to G + + align:start position:0% +sign now I can resign with respect to G + + + align:start position:0% +sign now I can resign with respect to G +with this point X that I've committed to + + align:start position:0% +with this point X that I've committed to + + + align:start position:0% +with this point X that I've committed to +because the value is zero right the + + align:start position:0% +because the value is zero right the + + + align:start position:0% +because the value is zero right the +value the thing that I'm multiplying by + + align:start position:0% +value the thing that I'm multiplying by + + + align:start position:0% +value the thing that I'm multiplying by +H is zero so I don't so it'll work for a + + align:start position:0% +H is zero so I don't so it'll work for a + + + align:start position:0% +H is zero so I don't so it'll work for a +signature system like the same regular + + align:start position:0% +signature system like the same regular + + + align:start position:0% +signature system like the same regular +old signature equation that we use I can + + align:start position:0% +old signature equation that we use I can + + + align:start position:0% +old signature equation that we use I can +sign a message with key big X and so + + align:start position:0% +sign a message with key big X and so + + + align:start position:0% +sign a message with key big X and so +this is a proof of a zero value I'll + + align:start position:0% +this is a proof of a zero value I'll + + + align:start position:0% +this is a proof of a zero value I'll +just sign with my own key so if X is you + + align:start position:0% +just sign with my own key so if X is you + + + align:start position:0% +just sign with my own key so if X is you +know some random some random binding + + align:start position:0% +know some random some random binding + + + align:start position:0% +know some random some random binding +factor times G plus zero times H where V + + align:start position:0% +factor times G plus zero times H where V + + + align:start position:0% +factor times G plus zero times H where V +the V the value are committing to is + + align:start position:0% +the V the value are committing to is + + + align:start position:0% +the V the value are committing to is +zero well that means that the signature + + align:start position:0% +zero well that means that the signature + + + align:start position:0% +zero well that means that the signature +is just and what do you so the question + + align:start position:0% +is just and what do you so the question + + + align:start position:0% +is just and what do you so the question +is what message do you sign well maybe + + align:start position:0% +is what message do you sign well maybe + + + align:start position:0% +is what message do you sign well maybe +sign the message which is the pump key + + align:start position:0% +sign the message which is the pump key + + + align:start position:0% +sign the message which is the pump key +itself you sort of don't need to sign a + + align:start position:0% +itself you sort of don't need to sign a + + + align:start position:0% +itself you sort of don't need to sign a +message but throw that in there and then + + align:start position:0% +message but throw that in there and then + + + align:start position:0% +message but throw that in there and then +this will work right and someone can say + + align:start position:0% +this will work right and someone can say + + + align:start position:0% +this will work right and someone can say +hey here's a signature from key X and + + align:start position:0% +hey here's a signature from key X and + + + align:start position:0% +hey here's a signature from key X and +the signatures arbitrary can be a + + align:start position:0% +the signatures arbitrary can be a + + + align:start position:0% +the signatures arbitrary can be a +signature of any message you want but + + align:start position:0% +signature of any message you want but + + + align:start position:0% +signature of any message you want but +the fact that they are able to produce a + + align:start position:0% +the fact that they are able to produce a + + + align:start position:0% +the fact that they are able to produce a +signature reveals to you that V is 0 so + + align:start position:0% +signature reveals to you that V is 0 so + + + align:start position:0% +signature reveals to you that V is 0 so +that's kind of cool + + align:start position:0% +that's kind of cool + + + align:start position:0% +that's kind of cool +it's actually not that cool right + + align:start position:0% +it's actually not that cool right + + + align:start position:0% +it's actually not that cool right +because well I just revealed my value + + align:start position:0% +because well I just revealed my value + + + align:start position:0% +because well I just revealed my value +and it revealed to be 0 but I did it + + align:start position:0% +and it revealed to be 0 but I did it + + + align:start position:0% +and it revealed to be 0 but I did it +without revealing R so that is kind of + + align:start position:0% +without revealing R so that is kind of + + + align:start position:0% +without revealing R so that is kind of +cool right I could do it by just saying + + align:start position:0% +cool right I could do it by just saying + + + align:start position:0% +cool right I could do it by just saying +hey here's my R and V values multiply + + align:start position:0% +hey here's my R and V values multiply + + + align:start position:0% +hey here's my R and V values multiply +them and add them up to see that it gets + + align:start position:0% +them and add them up to see that it gets + + + align:start position:0% +them and add them up to see that it gets +to the point I committed to but I can + + align:start position:0% +to the point I committed to but I can + + + align:start position:0% +to the point I committed to but I can +now prove that I can prove something + + align:start position:0% +now prove that I can prove something + + + align:start position:0% +now prove that I can prove something +about V without revealing anything about + + align:start position:0% +about V without revealing anything about + + + align:start position:0% +about V without revealing anything about +R right before we were saying the way + + align:start position:0% +R right before we were saying the way + + + align:start position:0% +R right before we were saying the way +you reveal these commitments is you + + align:start position:0% +you reveal these commitments is you + + + align:start position:0% +you reveal these commitments is you +reveal the blinding factor and you + + align:start position:0% +reveal the blinding factor and you + + + align:start position:0% +reveal the blinding factor and you +reveal the value itself well now I can + + align:start position:0% +reveal the value itself well now I can + + + align:start position:0% +reveal the value itself well now I can +keep the blinding factor secret and + + align:start position:0% +keep the blinding factor secret and + + + align:start position:0% +keep the blinding factor secret and +reveal a little bit of information about + + align:start position:0% +reveal a little bit of information about + + + align:start position:0% +reveal a little bit of information about +V + + align:start position:0% +V + + + align:start position:0% +V +this works and you can't sign if H is + + align:start position:0% +this works and you can't sign if H is + + + align:start position:0% +this works and you can't sign if H is +nonzero right you're not gonna be able + + align:start position:0% +nonzero right you're not gonna be able + + + align:start position:0% +nonzero right you're not gonna be able +to you know you're not going to be able + + align:start position:0% +to you know you're not going to be able + + + align:start position:0% +to you know you're not going to be able +to calculate any valid signature unless + + align:start position:0% +to calculate any valid signature unless + + + align:start position:0% +to calculate any valid signature unless +V is V so you can also do this with a + + align:start position:0% +V is V so you can also do this with a + + + align:start position:0% +V is V so you can also do this with a +proof of V equals 1 again sign your own + + align:start position:0% +proof of V equals 1 again sign your own + + + align:start position:0% +proof of V equals 1 again sign your own +key so you define X prime to be just X + + align:start position:0% +key so you define X prime to be just X + + + align:start position:0% +key so you define X prime to be just X +minus H and then you can say well look + + align:start position:0% +minus H and then you can say well look + + + align:start position:0% +minus H and then you can say well look +I'm gonna prove to you that I'm gonna + + align:start position:0% +I'm gonna prove to you that I'm gonna + + + align:start position:0% +I'm gonna prove to you that I'm gonna +prove to you that V is 1 and the way I + + align:start position:0% +prove to you that V is 1 and the way I + + + align:start position:0% +prove to you that V is 1 and the way I +do that is take the point I've committed + + align:start position:0% +do that is take the point I've committed + + + align:start position:0% +do that is take the point I've committed +to X subtract H from it and I'll provide + + align:start position:0% +to X subtract H from it and I'll provide + + + align:start position:0% +to X subtract H from it and I'll provide +a signature on that new point and I + + align:start position:0% +a signature on that new point and I + + + align:start position:0% +a signature on that new point and I +can't do that unless V is 1 right so if + + align:start position:0% +can't do that unless V is 1 right so if + + + align:start position:0% +can't do that unless V is 1 right so if +I have this and then I subtract H then I + + align:start position:0% +I have this and then I subtract H then I + + + align:start position:0% +I have this and then I subtract H then I +get back to our times G I can now + + align:start position:0% +get back to our times G I can now + + + align:start position:0% +get back to our times G I can now +provide a signature of just using R + + align:start position:0% +provide a signature of just using R + + + align:start position:0% +provide a signature of just using R +it'll work so what does this get us we + + align:start position:0% +it'll work so what does this get us we + + + align:start position:0% +it'll work so what does this get us we +can prove that V is 0 or it can prove + + align:start position:0% +can prove that V is 0 or it can prove + + + align:start position:0% +can prove that V is 0 or it can prove +that V is 1 or really we can prove that + + align:start position:0% +that V is 1 or really we can prove that + + + align:start position:0% +that V is 1 or really we can prove that +V is anything just subtract a whole + + align:start position:0% +V is anything just subtract a whole + + + align:start position:0% +V is anything just subtract a whole +bunch of H's right say hey subtract + + align:start position:0% +bunch of H's right say hey subtract + + + align:start position:0% +bunch of H's right say hey subtract +7,000 H and now I'll provide a signature + + align:start position:0% +7,000 H and now I'll provide a signature + + + align:start position:0% +7,000 H and now I'll provide a signature +and that proves that V was 7,000 but + + align:start position:0% +and that proves that V was 7,000 but + + + align:start position:0% +and that proves that V was 7,000 but +wait we just revealed V so what's the + + align:start position:0% +wait we just revealed V so what's the + + + align:start position:0% +wait we just revealed V so what's the +point right did that really get us + + align:start position:0% +point right did that really get us + + + align:start position:0% +point right did that really get us +anywhere if if we can make a signature + + align:start position:0% +anywhere if if we can make a signature + + + align:start position:0% +anywhere if if we can make a signature +that reveals the value we've committed + + align:start position:0% +that reveals the value we've committed + + + align:start position:0% +that reveals the value we've committed +to with hiding the rest of the stuff + + align:start position:0% +to with hiding the rest of the stuff + + + align:start position:0% +to with hiding the rest of the stuff +it's that useful right like if it's kind + + align:start position:0% +it's that useful right like if it's kind + + + align:start position:0% +it's that useful right like if it's kind +of cool but what can we do with this any + + align:start position:0% +of cool but what can we do with this any + + + align:start position:0% +of cool but what can we do with this any +ideas ok so there's another part that I + + align:start position:0% +ideas ok so there's another part that I + + + align:start position:0% +ideas ok so there's another part that I +yeah what didn't have time to introduce + + align:start position:0% +yeah what didn't have time to introduce + + + align:start position:0% +yeah what didn't have time to introduce +but maybe we'll at some point and you + + align:start position:0% +but maybe we'll at some point and you + + + align:start position:0% +but maybe we'll at some point and you +can read about it it's really cool ring + + align:start position:0% +can read about it it's really cool ring + + + align:start position:0% +can read about it it's really cool ring +signatures a ring signature is similar + + align:start position:0% +signatures a ring signature is similar + + + align:start position:0% +signatures a ring signature is similar +to a normal signature you've got you + + align:start position:0% +to a normal signature you've got you + + + align:start position:0% +to a normal signature you've got you +know key pairs + + align:start position:0% +know key pairs + + + align:start position:0% +know key pairs +you've got sign verify but there's a set + + align:start position:0% +you've got sign verify but there's a set + + + align:start position:0% +you've got sign verify but there's a set +of public keys during the signing and + + align:start position:0% +of public keys during the signing and + + + align:start position:0% +of public keys during the signing and +verification process so the basic idea + + align:start position:0% +verification process so the basic idea + + + align:start position:0% +verification process so the basic idea +is I sign a message with one of the + + align:start position:0% +is I sign a message with one of the + + + align:start position:0% +is I sign a message with one of the +public keys + + align:start position:0% +public keys + + + align:start position:0% +public keys +but I don't tell you which one and you + + align:start position:0% +but I don't tell you which one and you + + + align:start position:0% +but I don't tell you which one and you +verify that yep there was a signature + + align:start position:0% +verify that yep there was a signature + + + align:start position:0% +verify that yep there was a signature +here I'm not quite sure who signed it + + align:start position:0% +here I'm not quite sure who signed it + + + align:start position:0% +here I'm not quite sure who signed it +there's possibly three or four different + + align:start position:0% +there's possibly three or four different + + + align:start position:0% +there's possibly three or four different +people who may have signed it but I know + + align:start position:0% +people who may have signed it but I know + + + align:start position:0% +people who may have signed it but I know +one of them signed it but not which so + + align:start position:0% +one of them signed it but not which so + + + align:start position:0% +one of them signed it but not which so +basically it's the the key generation + + align:start position:0% +basically it's the the key generation + + + align:start position:0% +basically it's the the key generation +step same as before right + + align:start position:0% +step same as before right + + + align:start position:0% +step same as before right +you have some kind of key Jen takes in + + align:start position:0% +you have some kind of key Jen takes in + + + align:start position:0% +you have some kind of key Jen takes in +some randomness and it spits out a + + align:start position:0% +some randomness and it spits out a + + + align:start position:0% +some randomness and it spits out a +private key and a public key for you you + + align:start position:0% +private key and a public key for you you + + + align:start position:0% +private key and a public key for you you +can use those later sign on the other + + align:start position:0% +can use those later sign on the other + + + align:start position:0% +can use those later sign on the other +hand sign function used to just have the + + align:start position:0% +hand sign function used to just have the + + + align:start position:0% +hand sign function used to just have the +message to sign in your private key and + + align:start position:0% +message to sign in your private key and + + + align:start position:0% +message to sign in your private key and +would output a signature in ring + + align:start position:0% +would output a signature in ring + + + align:start position:0% +would output a signature in ring +signatures you sign with the message you + + align:start position:0% +signatures you sign with the message you + + + align:start position:0% +signatures you sign with the message you +want to sign your private key and then + + align:start position:0% +want to sign your private key and then + + + align:start position:0% +want to sign your private key and then +pick a list of other people's public + + align:start position:0% +pick a list of other people's public + + + align:start position:0% +pick a list of other people's public +keys and this list can be you know just + + align:start position:0% +keys and this list can be you know just + + + align:start position:0% +keys and this list can be you know just +a single one it can be a thousand you + + align:start position:0% +a single one it can be a thousand you + + + align:start position:0% +a single one it can be a thousand you +pick a bunch of other people's public + + align:start position:0% +pick a bunch of other people's public + + + align:start position:0% +pick a bunch of other people's public +keys and you generate a signature and + + align:start position:0% +keys and you generate a signature and + + + align:start position:0% +keys and you generate a signature and +then verify you use the signature to it + + align:start position:0% +then verify you use the signature to it + + + align:start position:0% +then verify you use the signature to it +you know you take the signature in the + + align:start position:0% +you know you take the signature in the + + + align:start position:0% +you know you take the signature in the +message that's been signed and that list + + align:start position:0% +message that's been signed and that list + + + align:start position:0% +message that's been signed and that list +of pub keys and it outputs a boolean of + + align:start position:0% +of pub keys and it outputs a boolean of + + + align:start position:0% +of pub keys and it outputs a boolean of +yep that signature worked or no it + + align:start position:0% +yep that signature worked or no it + + + align:start position:0% +yep that signature worked or no it +didn't but it doesn't tell you which of + + align:start position:0% +didn't but it doesn't tell you which of + + + align:start position:0% +didn't but it doesn't tell you which of +the public keys signed so this is a + + align:start position:0% +the public keys signed so this is a + + + align:start position:0% +the public keys signed so this is a +really cool idea I think the initial + + align:start position:0% +really cool idea I think the initial + + + align:start position:0% +really cool idea I think the initial +paper was how to leak a secret which was + + align:start position:0% +paper was how to leak a secret which was + + + align:start position:0% +paper was how to leak a secret which was +and then there's different papers about + + align:start position:0% +and then there's different papers about + + + align:start position:0% +and then there's different papers about +different more efficient rigged + + align:start position:0% +different more efficient rigged + + + align:start position:0% +different more efficient rigged +signatures but this is a really cool + + align:start position:0% +signatures but this is a really cool + + + align:start position:0% +signatures but this is a really cool +thing to have to use I think this could + + align:start position:0% +thing to have to use I think this could + + + align:start position:0% +thing to have to use I think this could +be really cool for a lot of different + + align:start position:0% +be really cool for a lot of different + + + align:start position:0% +be really cool for a lot of different +things if people actually had public + + align:start position:0% +things if people actually had public + + + align:start position:0% +things if people actually had public +keys that they were associated with and + + align:start position:0% +keys that they were associated with and + + + align:start position:0% +keys that they were associated with and +like wrote them on their business cards + + align:start position:0% +like wrote them on their business cards + + + align:start position:0% +like wrote them on their business cards +and stuff like I do you could then have + + align:start position:0% +and stuff like I do you could then have + + + align:start position:0% +and stuff like I do you could then have +like you know leaking information that's + + align:start position:0% +like you know leaking information that's + + + align:start position:0% +like you know leaking information that's +more credible so instead of just the + + align:start position:0% +more credible so instead of just the + + + align:start position:0% +more credible so instead of just the +newspaper saying you know sources close + + align:start position:0% +newspaper saying you know sources close + + + align:start position:0% +newspaper saying you know sources close +to the matter said X Y Z or you know a + + align:start position:0% +to the matter said X Y Z or you know a + + + align:start position:0% +to the matter said X Y Z or you know a +top official at the White House said + + align:start position:0% +top official at the White House said + + + align:start position:0% +top official at the White House said +this you could actually have it being + + align:start position:0% +this you could actually have it being + + + align:start position:0% +this you could actually have it being +signed and it's like okay well we've got + + align:start position:0% +signed and it's like okay well we've got + + + align:start position:0% +signed and it's like okay well we've got +all these different White House + + align:start position:0% +all these different White House + + + align:start position:0% +all these different White House +officials public keys one of them signed + + align:start position:0% +officials public keys one of them signed + + + align:start position:0% +officials public keys one of them signed +this message so either there was a key + + align:start position:0% +this message so either there was a key + + + align:start position:0% +this message so either there was a key +compromised and they all lost their keys + + align:start position:0% +compromised and they all lost their keys + + + align:start position:0% +compromised and they all lost their keys +which is in practice probably more + + align:start position:0% +which is in practice probably more + + + align:start position:0% +which is in practice probably more +likely in that case or one of these + + align:start position:0% +likely in that case or one of these + + + align:start position:0% +likely in that case or one of these +people actually find this message and I + + align:start position:0% +people actually find this message and I + + + align:start position:0% +people actually find this message and I +know it's one of them but it doesn't + + align:start position:0% +know it's one of them but it doesn't + + + align:start position:0% +know it's one of them but it doesn't +reveal anything about + + align:start position:0% +reveal anything about + + + align:start position:0% +reveal anything about +of the public keys that's pretty cool + + align:start position:0% +of the public keys that's pretty cool + + + align:start position:0% +of the public keys that's pretty cool +okay so you can verify from it's from a + + align:start position:0% +okay so you can verify from it's from a + + + align:start position:0% +okay so you can verify from it's from a +key in the array of public keys but not + + align:start position:0% +key in the array of public keys but not + + + align:start position:0% +key in the array of public keys but not +which so let's put these together I can + + align:start position:0% +which so let's put these together I can + + + align:start position:0% +which so let's put these together I can +sign with X to prove that V is zero I + + align:start position:0% +sign with X to prove that V is zero I + + + align:start position:0% +sign with X to prove that V is zero I +could also sign with X prime which I'm + + align:start position:0% +could also sign with X prime which I'm + + + align:start position:0% +could also sign with X prime which I'm +defining is X minus H to prove that V is + + align:start position:0% +defining is X minus H to prove that V is + + + align:start position:0% +defining is X minus H to prove that V is +one well what if I have a ring signature + + align:start position:0% +one well what if I have a ring signature + + + align:start position:0% +one well what if I have a ring signature +where I say I'm gonna produce a + + align:start position:0% +where I say I'm gonna produce a + + + align:start position:0% +where I say I'm gonna produce a +signature from both of these pumps you + + align:start position:0% +signature from both of these pumps you + + + align:start position:0% +signature from both of these pumps you +know from one of these two public keys + + align:start position:0% +know from one of these two public keys + + + align:start position:0% +know from one of these two public keys +and that would prove that V is either 0 + + align:start position:0% +and that would prove that V is either 0 + + + align:start position:0% +and that would prove that V is either 0 +or 1 but it doesn't prove which right + + align:start position:0% +or 1 but it doesn't prove which right + + + align:start position:0% +or 1 but it doesn't prove which right +makes sense so the idea is I can make + + align:start position:0% +makes sense so the idea is I can make + + + align:start position:0% +makes sense so the idea is I can make +these signatures that essentially reveal + + align:start position:0% +these signatures that essentially reveal + + + align:start position:0% +these signatures that essentially reveal +what V is right they they indirectly + + align:start position:0% +what V is right they they indirectly + + + align:start position:0% +what V is right they they indirectly +reveal what V is by saying there's no + + align:start position:0% +reveal what V is by saying there's no + + + align:start position:0% +reveal what V is by saying there's no +way I could have made this signature + + align:start position:0% +way I could have made this signature + + + align:start position:0% +way I could have made this signature +unless V was zero or unless V was one + + align:start position:0% +unless V was zero or unless V was one + + + align:start position:0% +unless V was zero or unless V was one +because you're you know you're you know + + align:start position:0% +because you're you know you're you know + + + align:start position:0% +because you're you know you're you know +that the H component right V is the + + align:start position:0% +that the H component right V is the + + + align:start position:0% +that the H component right V is the +coefficient for H so you need to know + + align:start position:0% +coefficient for H so you need to know + + + align:start position:0% +coefficient for H so you need to know +that I don't have an H component in + + align:start position:0% +that I don't have an H component in + + + align:start position:0% +that I don't have an H component in +there if I'm gonna make a signature with + + align:start position:0% +there if I'm gonna make a signature with + + + align:start position:0% +there if I'm gonna make a signature with +respect to G and I can make any number + + align:start position:0% +respect to G and I can make any number + + + align:start position:0% +respect to G and I can make any number +of you know I can I can make any number + + align:start position:0% +of you know I can I can make any number + + + align:start position:0% +of you know I can I can make any number +of different sort of X Prime's by + + align:start position:0% +of different sort of X Prime's by + + + align:start position:0% +of different sort of X Prime's by +subtracting different amounts of H but a + + align:start position:0% +subtracting different amounts of H but a + + + align:start position:0% +subtracting different amounts of H but a +single signature would just reveal what + + align:start position:0% +single signature would just reveal what + + + align:start position:0% +single signature would just reveal what +V was which isn't useful but a ring + + align:start position:0% +V was which isn't useful but a ring + + + align:start position:0% +V was which isn't useful but a ring +signature whereas I can say okay well + + align:start position:0% +signature whereas I can say okay well + + + align:start position:0% +signature whereas I can say okay well +there's two different pump keys right + + align:start position:0% +there's two different pump keys right + + + align:start position:0% +there's two different pump keys right +one of those X one of them's X Prime you + + align:start position:0% +one of those X one of them's X Prime you + + + align:start position:0% +one of those X one of them's X Prime you +subtract H and I'm gonna provide a ring + + align:start position:0% +subtract H and I'm gonna provide a ring + + + align:start position:0% +subtract H and I'm gonna provide a ring +signature from one of these to pub keys + + align:start position:0% +signature from one of these to pub keys + + + align:start position:0% +signature from one of these to pub keys +now I've proven to you okay well V is + + align:start position:0% +now I've proven to you okay well V is + + + align:start position:0% +now I've proven to you okay well V is +either 0 or 1 I can't offer you can't be + + align:start position:0% +either 0 or 1 I can't offer you can't be + + + align:start position:0% +either 0 or 1 I can't offer you can't be +both any but it can't be - it can't be 3 + + align:start position:0% +both any but it can't be - it can't be 3 + + + align:start position:0% +both any but it can't be - it can't be 3 +it's got to be one of those two values + + align:start position:0% +it's got to be one of those two values + + + align:start position:0% +it's got to be one of those two values +so does this make sense + + align:start position:0% +so does this make sense + + + align:start position:0% +so does this make sense +questions on this yes + + align:start position:0% + + + + align:start position:0% + +oh well the original scheme it's kind of + + align:start position:0% +oh well the original scheme it's kind of + + + align:start position:0% +oh well the original scheme it's kind of +complicated that the one used in + + align:start position:0% +complicated that the one used in + + + align:start position:0% +complicated that the one used in +confidential transactions is boramy n' + + align:start position:0% +confidential transactions is boramy n' + + + align:start position:0% +confidential transactions is boramy n' +ring signatures yeah it's it's you do a + + align:start position:0% +ring signatures yeah it's it's you do a + + + align:start position:0% +ring signatures yeah it's it's you do a +bunch of like hash functions that like I + + align:start position:0% +bunch of like hash functions that like I + + + align:start position:0% +bunch of like hash functions that like I +can't I don't know it I don't even + + align:start position:0% +can't I don't know it I don't even + + + align:start position:0% +can't I don't know it I don't even +really know it well enough myself to + + align:start position:0% +really know it well enough myself to + + + align:start position:0% +really know it well enough myself to +really be able to explain it in like a + + align:start position:0% +really be able to explain it in like a + + + align:start position:0% +really be able to explain it in like a +minute but basically you compute + + align:start position:0% +minute but basically you compute + + + align:start position:0% +minute but basically you compute +something on all of the pomp keys and + + align:start position:0% +something on all of the pomp keys and + + + align:start position:0% +something on all of the pomp keys and +then verify the signature on like the + + align:start position:0% +then verify the signature on like the + + + align:start position:0% +then verify the signature on like the +aggregate pub key kind of is a way to + + align:start position:0% +aggregate pub key kind of is a way to + + + align:start position:0% +aggregate pub key kind of is a way to +think about it the signatures can that + + align:start position:0% +think about it the signatures can that + + + align:start position:0% +think about it the signatures can that +the computing time gets big with with + + align:start position:0% +the computing time gets big with with + + + align:start position:0% +the computing time gets big with with +the number of pub keys right so if you + + align:start position:0% +the number of pub keys right so if you + + + align:start position:0% +the number of pub keys right so if you +have like millions of fum keys that + + align:start position:0% +have like millions of fum keys that + + + align:start position:0% +have like millions of fum keys that +could possibly be signing this is the + + align:start position:0% +could possibly be signing this is the + + + align:start position:0% +could possibly be signing this is the +verification algorithm gets really + + align:start position:0% +verification algorithm gets really + + + align:start position:0% +verification algorithm gets really +time-consuming so yeah so yeah I can + + align:start position:0% +time-consuming so yeah so yeah I can + + + align:start position:0% +time-consuming so yeah so yeah I can +maybe go into rigged signatures another + + align:start position:0% +maybe go into rigged signatures another + + + align:start position:0% +maybe go into rigged signatures another +time but yeah + + align:start position:0% + + + + align:start position:0% + +well you know these are good so we've + + align:start position:0% +well you know these are good so we've + + + align:start position:0% +well you know these are good so we've +just proven that we've done quite a bit + + align:start position:0% +just proven that we've done quite a bit + + + align:start position:0% +just proven that we've done quite a bit +more than the proof it's not negative + + align:start position:0% +more than the proof it's not negative + + + align:start position:0% +more than the proof it's not negative +we've proved that it's exactly zero or + + align:start position:0% +we've proved that it's exactly zero or + + + align:start position:0% +we've proved that it's exactly zero or +exactly one yeah we might want more + + align:start position:0% +exactly one yeah we might want more + + + align:start position:0% +exactly one yeah we might want more +values so make a rigged signature from a + + align:start position:0% +values so make a rigged signature from a + + + align:start position:0% +values so make a rigged signature from a +million different public keys where the + + align:start position:0% +million different public keys where the + + + align:start position:0% +million different public keys where the +table n is just pumping when is one when + + align:start position:0% +table n is just pumping when is one when + + + align:start position:0% +table n is just pumping when is one when +it's H right and then I just prove that + + align:start position:0% +it's H right and then I just prove that + + + align:start position:0% +it's H right and then I just prove that +V is somewhere in the range from zero to + + align:start position:0% +V is somewhere in the range from zero to + + + align:start position:0% +V is somewhere in the range from zero to +no no no no no no it goes up the best is + + align:start position:0% +no no no no no no it goes up the best is + + + align:start position:0% +no no no no no no it goes up the best is +linear or no there might be sorry + + align:start position:0% +linear or no there might be sorry + + + align:start position:0% +linear or no there might be sorry +there's probably sublinear now but yeah + + align:start position:0% +there's probably sublinear now but yeah + + + align:start position:0% +there's probably sublinear now but yeah +this is not feasible this would that the + + align:start position:0% +this is not feasible this would that the + + + align:start position:0% +this is not feasible this would that the +traditional ring signatures are linear + + align:start position:0% +traditional ring signatures are linear + + + align:start position:0% +traditional ring signatures are linear +with the number of public keys to be + + align:start position:0% +with the number of public keys to be + + + align:start position:0% +with the number of public keys to be +verified so if you did this + + align:start position:0% +verified so if you did this + + + align:start position:0% +verified so if you did this +yeah well all even then you'd have to + + align:start position:0% +yeah well all even then you'd have to + + + align:start position:0% +yeah well all even then you'd have to +you'd have to sort of throw though + + align:start position:0% +you'd have to sort of throw though + + + align:start position:0% +you'd have to sort of throw though +because you have to at least throw the + + align:start position:0% +because you have to at least throw the + + + align:start position:0% +because you have to at least throw the +public key into the verification + + align:start position:0% +public key into the verification + + + align:start position:0% +public key into the verification +function right and so that means you + + align:start position:0% +function right and so that means you + + + align:start position:0% +function right and so that means you +need to compute a million pub keys throw + + align:start position:0% +need to compute a million pub keys throw + + + align:start position:0% +need to compute a million pub keys throw +it into that function it's gonna take a + + align:start position:0% +it into that function it's gonna take a + + + align:start position:0% +it into that function it's gonna take a +long time so this is not itself gonna + + align:start position:0% +long time so this is not itself gonna + + + align:start position:0% +long time so this is not itself gonna +work right did you yes Manero uses + + align:start position:0% +work right did you yes Manero uses + + + align:start position:0% +work right did you yes Manero uses +rigged signatures for for a different + + align:start position:0% +rigged signatures for for a different + + + align:start position:0% +rigged signatures for for a different +reason + + align:start position:0% +reason + + + align:start position:0% +reason +well now they use it for this kind of + + align:start position:0% +well now they use it for this kind of + + + align:start position:0% +well now they use it for this kind of +thing too the Monaro ring signature was + + align:start position:0% +thing too the Monaro ring signature was + + + align:start position:0% +thing too the Monaro ring signature was +initially used for not hiding the + + align:start position:0% +initially used for not hiding the + + + align:start position:0% +initially used for not hiding the +amounts but hiding which outputs were + + align:start position:0% +amounts but hiding which outputs were + + + align:start position:0% +amounts but hiding which outputs were +being spent so in Bitcoin you have you + + align:start position:0% +being spent so in Bitcoin you have you + + + align:start position:0% +being spent so in Bitcoin you have you +know everyone should sew in Bitcoin + + align:start position:0% + + + + align:start position:0% + +so in Bitcoin if you have a transaction + + align:start position:0% +so in Bitcoin if you have a transaction + + + align:start position:0% +so in Bitcoin if you have a transaction +you say okay here's my input here's my + + align:start position:0% +you say okay here's my input here's my + + + align:start position:0% +you say okay here's my input here's my +output and the simplest one it's just + + align:start position:0% +output and the simplest one it's just + + + align:start position:0% +output and the simplest one it's just +like okay this points to you know TX + + align:start position:0% +like okay this points to you know TX + + + align:start position:0% +like okay this points to you know TX +five or something and my output is + + align:start position:0% +five or something and my output is + + + align:start position:0% +five or something and my output is +address maybe you know address its + + align:start position:0% +address maybe you know address its + + + align:start position:0% +address maybe you know address its +address B and it's got seven coins + + align:start position:0% +address B and it's got seven coins + + + align:start position:0% +address B and it's got seven coins +everyone can see what you're spending + + align:start position:0% +everyone can see what you're spending + + + align:start position:0% +everyone can see what you're spending +the idea in one arrow is I don't point + + align:start position:0% +the idea in one arrow is I don't point + + + align:start position:0% +the idea in one arrow is I don't point +to an input I just provide a signature + + align:start position:0% +to an input I just provide a signature + + + align:start position:0% +to an input I just provide a signature +and it's up to you to figure out where + + align:start position:0% +and it's up to you to figure out where + + + align:start position:0% +and it's up to you to figure out where +that signatures like so I provide a + + align:start position:0% +that signatures like so I provide a + + + align:start position:0% +that signatures like so I provide a +signature and a list of pub keys pub a + + align:start position:0% +signature and a list of pub keys pub a + + + align:start position:0% +signature and a list of pub keys pub a +pub B so the smallest would be two and + + align:start position:0% +pub B so the smallest would be two and + + + align:start position:0% +pub B so the smallest would be two and +then I'd you know provide a key you know + + align:start position:0% +then I'd you know provide a key you know + + + align:start position:0% +then I'd you know provide a key you know +so the idea is instead of thinking of it + + align:start position:0% +so the idea is instead of thinking of it + + + align:start position:0% +so the idea is instead of thinking of it +as outputs you just sort of think as pub + + align:start position:0% +as outputs you just sort of think as pub + + + align:start position:0% +as outputs you just sort of think as pub +keys have associated values so you don't + + align:start position:0% +keys have associated values so you don't + + + align:start position:0% +keys have associated values so you don't +look at the transactions themselves say + + align:start position:0% +look at the transactions themselves say + + + align:start position:0% +look at the transactions themselves say +okay this is key C and there previously + + align:start position:0% +okay this is key C and there previously + + + align:start position:0% +okay this is key C and there previously +have been pub key a and pub key B have + + align:start position:0% +have been pub key a and pub key B have + + + align:start position:0% +have been pub key a and pub key B have +had values you know seven coins sent to + + align:start position:0% +had values you know seven coins sent to + + + align:start position:0% +had values you know seven coins sent to +them and I can now say look I'm gonna + + align:start position:0% +them and I can now say look I'm gonna + + + align:start position:0% +them and I can now say look I'm gonna +provide a ring signature from either + + align:start position:0% +provide a ring signature from either + + + align:start position:0% +provide a ring signature from either +pokey a or pub key be and I'm not gonna + + align:start position:0% +pokey a or pub key be and I'm not gonna + + + align:start position:0% +pokey a or pub key be and I'm not gonna +tell you which but you can see that both + + align:start position:0% +tell you which but you can see that both + + + align:start position:0% +tell you which but you can see that both +pub key a and pub TB have received seven + + align:start position:0% +pub key a and pub TB have received seven + + + align:start position:0% +pub key a and pub TB have received seven +coins in the past I want to send seven + + align:start position:0% +coins in the past I want to send seven + + + align:start position:0% +coins in the past I want to send seven +coins over here I'm gonna prove that I + + align:start position:0% +coins over here I'm gonna prove that I + + + align:start position:0% +coins over here I'm gonna prove that I +own one of those two and then you can + + align:start position:0% +own one of those two and then you can + + + align:start position:0% +own one of those two and then you can +validate that the transactions valid and + + align:start position:0% +validate that the transactions valid and + + + align:start position:0% +validate that the transactions valid and +then if later you see another + + align:start position:0% +then if later you see another + + + align:start position:0% +then if later you see another +transaction with a ring signature from + + align:start position:0% +transaction with a ring signature from + + + align:start position:0% +transaction with a ring signature from +pub a but B also sending you know two + + align:start position:0% +pub a but B also sending you know two + + + align:start position:0% +pub a but B also sending you know two +key d7 coins okay now I can believe pub + + align:start position:0% +key d7 coins okay now I can believe pub + + + align:start position:0% +key d7 coins okay now I can believe pub +infamy right I don't know which this you + + align:start position:0% +infamy right I don't know which this you + + + align:start position:0% +infamy right I don't know which this you +know so in transaction one I don't know + + align:start position:0% +know so in transaction one I don't know + + + align:start position:0% +know so in transaction one I don't know +whether a or b a was spent but one of + + align:start position:0% +whether a or b a was spent but one of + + + align:start position:0% +whether a or b a was spent but one of +those two was and then transaction - I + + align:start position:0% +those two was and then transaction - I + + + align:start position:0% +those two was and then transaction - I +don't know whether a or beers went one + + align:start position:0% +don't know whether a or beers went one + + + align:start position:0% +don't know whether a or beers went one +of them was but anyway they both went + + align:start position:0% +of them was but anyway they both went + + + align:start position:0% +of them was but anyway they both went +spent now and so I can you know delete + + align:start position:0% +spent now and so I can you know delete + + + align:start position:0% +spent now and so I can you know delete +them from my storage but the ring + + align:start position:0% +them from my storage but the ring + + + align:start position:0% +them from my storage but the ring +signatures in one era were to use to + + align:start position:0% +signatures in one era were to use to + + + align:start position:0% +signatures in one era were to use to +obscure the transaction graph itself + + align:start position:0% +obscure the transaction graph itself + + + align:start position:0% +obscure the transaction graph itself +where you can see that there's a bunch + + align:start position:0% +where you can see that there's a bunch + + + align:start position:0% +where you can see that there's a bunch +of different keys that have you know + + align:start position:0% +of different keys that have you know + + + align:start position:0% +of different keys that have you know +money associated with them and I'm gonna + + align:start position:0% +money associated with them and I'm gonna + + + align:start position:0% +money associated with them and I'm gonna +provide a signature that I own one of + + align:start position:0% +provide a signature that I own one of + + + align:start position:0% +provide a signature that I own one of +them but I don't tell you which and now + + align:start position:0% +them but I don't tell you which and now + + + align:start position:0% +them but I don't tell you which and now +they also do confidential transactions + + align:start position:0% +they also do confidential transactions + + + align:start position:0% +they also do confidential transactions +to obscure the outputs using rigged + + align:start position:0% +to obscure the outputs using rigged + + + align:start position:0% +to obscure the outputs using rigged +signatures as well so yeah I don't + + align:start position:0% +signatures as well so yeah I don't + + + align:start position:0% +signatures as well so yeah I don't +what are is interesting I I haven't + + align:start position:0% +what are is interesting I I haven't + + + align:start position:0% +what are is interesting I I haven't +looked at it as that closely so I know + + align:start position:0% +looked at it as that closely so I know + + + align:start position:0% +looked at it as that closely so I know +that's the basic idea but there's a lot + + align:start position:0% +that's the basic idea but there's a lot + + + align:start position:0% +that's the basic idea but there's a lot +of sort of subtle details involved in + + align:start position:0% +of sort of subtle details involved in + + + align:start position:0% +of sort of subtle details involved in +how that works that I'm not super + + align:start position:0% +how that works that I'm not super + + + align:start position:0% +how that works that I'm not super +familiar with okay so I gotta finish up + + align:start position:0% +familiar with okay so I gotta finish up + + + align:start position:0% +familiar with okay so I gotta finish up +yeah so the way to actually make this + + align:start position:0% +yeah so the way to actually make this + + + align:start position:0% +yeah so the way to actually make this +practical is let's say you have a rigged + + align:start position:0% +practical is let's say you have a rigged + + + align:start position:0% +practical is let's say you have a rigged +signature for each bit so you're gonna + + align:start position:0% +signature for each bit so you're gonna + + + align:start position:0% +signature for each bit so you're gonna +have to have a different signature for + + align:start position:0% +have to have a different signature for + + + align:start position:0% +have to have a different signature for +each bit in your value so the pub key + + align:start position:0% +each bit in your value so the pub key + + + align:start position:0% +each bit in your value so the pub key +for you know funky x0 well I'm gonna + + align:start position:0% +for you know funky x0 well I'm gonna + + + align:start position:0% +for you know funky x0 well I'm gonna +have a rig signature where I prove that + + align:start position:0% +have a rig signature where I prove that + + + align:start position:0% +have a rig signature where I prove that +it's either 0 or 1 and here I'm gonna + + align:start position:0% +it's either 0 or 1 and here I'm gonna + + + align:start position:0% +it's either 0 or 1 and here I'm gonna +prove it's either a 0 or 2 here I'm + + align:start position:0% +prove it's either a 0 or 2 here I'm + + + align:start position:0% +prove it's either a 0 or 2 here I'm +gonna prove it's either 0 or 4 and so if + + align:start position:0% +gonna prove it's either 0 or 4 and so if + + + align:start position:0% +gonna prove it's either 0 or 4 and so if +I have say 32 signatures I can now prove + + align:start position:0% +I have say 32 signatures I can now prove + + + align:start position:0% +I have say 32 signatures I can now prove +a 32-bit number each of those + + align:start position:0% +a 32-bit number each of those + + + align:start position:0% +a 32-bit number each of those +individuals signatures only has 2 public + + align:start position:0% +individuals signatures only has 2 public + + + align:start position:0% +individuals signatures only has 2 public +keys associated with it so that's now + + align:start position:0% +keys associated with it so that's now + + + align:start position:0% +keys associated with it so that's now +more feasible right I can say okay well + + align:start position:0% +more feasible right I can say okay well + + + align:start position:0% +more feasible right I can say okay well +there's a total of 32 public keys 32 + + align:start position:0% +there's a total of 32 public keys 32 + + + align:start position:0% +there's a total of 32 public keys 32 +signatures not the end of the world + + align:start position:0% +signatures not the end of the world + + + align:start position:0% +signatures not the end of the world +still kind of ugly but and then there's + + align:start position:0% +still kind of ugly but and then there's + + + align:start position:0% +still kind of ugly but and then there's +optimizations where since these pub keys + + align:start position:0% +optimizations where since these pub keys + + + align:start position:0% +optimizations where since these pub keys +are all the same right the sort of zero + + align:start position:0% +are all the same right the sort of zero + + + align:start position:0% +are all the same right the sort of zero +value for that bit we can we can squish + + align:start position:0% +value for that bit we can we can squish + + + align:start position:0% +value for that bit we can we can squish +them together and stuff to make it a + + align:start position:0% +them together and stuff to make it a + + + align:start position:0% +them together and stuff to make it a +little bit smaller so yeah so you have a + + align:start position:0% +little bit smaller so yeah so you have a + + + align:start position:0% +little bit smaller so yeah so you have a +signature per bit of your output if your + + align:start position:0% +signature per bit of your output if your + + + align:start position:0% +signature per bit of your output if your +values are not too big this works right + + align:start position:0% +values are not too big this works right + + + align:start position:0% +values are not too big this works right +if you say okay we're gonna limit it to + + align:start position:0% +if you say okay we're gonna limit it to + + + align:start position:0% +if you say okay we're gonna limit it to +32 bits so from 0 to 4 billion now you + + align:start position:0% +32 bits so from 0 to 4 billion now you + + + align:start position:0% +32 bits so from 0 to 4 billion now you +can prove that you know each bit was + + align:start position:0% +can prove that you know each bit was + + + align:start position:0% +can prove that you know each bit was +either a 0 or 1 essentially without + + align:start position:0% +either a 0 or 1 essentially without + + + align:start position:0% +either a 0 or 1 essentially without +revealing whether it was a 0 or 1 and + + align:start position:0% +revealing whether it was a 0 or 1 and + + + align:start position:0% +revealing whether it was a 0 or 1 and +then you know it's a couple kilobytes + + align:start position:0% +then you know it's a couple kilobytes + + + align:start position:0% +then you know it's a couple kilobytes +for output so that's a little bit it + + align:start position:0% +for output so that's a little bit it + + + align:start position:0% +for output so that's a little bit it +used to be 8 bytes you just sort of said + + align:start position:0% +used to be 8 bytes you just sort of said + + + align:start position:0% +used to be 8 bytes you just sort of said +hey I've got 37 coins also these 8 bytes + + align:start position:0% +hey I've got 37 coins also these 8 bytes + + + align:start position:0% +hey I've got 37 coins also these 8 bytes +are very sparse in that they're rarely + + align:start position:0% +are very sparse in that they're rarely + + + align:start position:0% +are very sparse in that they're rarely +exceed 4 bytes and there so you can sort + + align:start position:0% +exceed 4 bytes and there so you can sort + + + align:start position:0% +exceed 4 bytes and there so you can sort +of come back + + align:start position:0% +of come back + + + align:start position:0% +of come back +two down and on disk so this is a little + + align:start position:0% +two down and on disk so this is a little + + + align:start position:0% +two down and on disk so this is a little +you know scalability wise it's an issue + + align:start position:0% +you know scalability wise it's an issue + + + align:start position:0% +you know scalability wise it's an issue +right you're now going from what used to + + align:start position:0% +right you're now going from what used to + + + align:start position:0% +right you're now going from what used to +be eight bytes is now a couple kilobytes + + align:start position:0% +be eight bytes is now a couple kilobytes + + + align:start position:0% +be eight bytes is now a couple kilobytes +I think they've got it down to like two + + align:start position:0% +I think they've got it down to like two + + + align:start position:0% +I think they've got it down to like two +kilobytes but still that's two kilobytes + + align:start position:0% +kilobytes but still that's two kilobytes + + + align:start position:0% +kilobytes but still that's two kilobytes +and it's it's takes a bit more CPU time + + align:start position:0% +and it's it's takes a bit more CPU time + + + align:start position:0% +and it's it's takes a bit more CPU time +to verify right because now instead of + + align:start position:0% +to verify right because now instead of + + + align:start position:0% +to verify right because now instead of +verifying one signature to see that the + + align:start position:0% +verifying one signature to see that the + + + align:start position:0% +verifying one signature to see that the +coins are moving to the right place + + align:start position:0% +coins are moving to the right place + + + align:start position:0% +coins are moving to the right place +you're verifying like 30 something you + + align:start position:0% +you're verifying like 30 something you + + + align:start position:0% +you're verifying like 30 something you +know 30 plus signatures for every input + + align:start position:0% +know 30 plus signatures for every input + + + align:start position:0% +know 30 plus signatures for every input +and output also the real problem is it's + + align:start position:0% +and output also the real problem is it's + + + align:start position:0% +and output also the real problem is it's +not really compatible with Bitcoin this + + align:start position:0% +not really compatible with Bitcoin this + + + align:start position:0% +not really compatible with Bitcoin this +would be a really tricky fork to + + align:start position:0% +would be a really tricky fork to + + + align:start position:0% +would be a really tricky fork to +implement how do you implement this such + + align:start position:0% +implement how do you implement this such + + + align:start position:0% +implement how do you implement this such +that the old software on the network is + + align:start position:0% +that the old software on the network is + + + align:start position:0% +that the old software on the network is +okay with these transactions where you + + align:start position:0% +okay with these transactions where you + + + align:start position:0% +okay with these transactions where you +know what they're expecting a + + align:start position:0% +know what they're expecting a + + + align:start position:0% +know what they're expecting a +transaction that has a value right how + + align:start position:0% +transaction that has a value right how + + + align:start position:0% +transaction that has a value right how +here's how many coins are being moved if + + align:start position:0% +here's how many coins are being moved if + + + align:start position:0% +here's how many coins are being moved if +you sort of say no I'm not gonna tell + + align:start position:0% +you sort of say no I'm not gonna tell + + + align:start position:0% +you sort of say no I'm not gonna tell +you any more old software doesn't know + + align:start position:0% +you any more old software doesn't know + + + align:start position:0% +you any more old software doesn't know +how to deal with this and by default + + align:start position:0% +how to deal with this and by default + + + align:start position:0% +how to deal with this and by default +will reject these transactions so + + align:start position:0% +will reject these transactions so + + + align:start position:0% +will reject these transactions so +there's there's ways to do it that + + align:start position:0% +there's there's ways to do it that + + + align:start position:0% +there's there's ways to do it that +doesn't break compatibility but they're + + align:start position:0% +doesn't break compatibility but they're + + + align:start position:0% +doesn't break compatibility but they're +pretty ugly the ways to do it is to say + + align:start position:0% +pretty ugly the ways to do it is to say + + + align:start position:0% +pretty ugly the ways to do it is to say +like one of the ways is to say okay from + + align:start position:0% +like one of the ways is to say okay from + + + align:start position:0% +like one of the ways is to say okay from +now on all these transactions all output + + align:start position:0% +now on all these transactions all output + + + align:start position:0% +now on all these transactions all output +values have to be 0 so the old software + + align:start position:0% +values have to be 0 so the old software + + + align:start position:0% +values have to be 0 so the old software +will still work but it'll be pretty + + align:start position:0% +will still work but it'll be pretty + + + align:start position:0% +will still work but it'll be pretty +confused and say like I see all these + + align:start position:0% +confused and say like I see all these + + + align:start position:0% +confused and say like I see all these +values you know I see thousands of + + align:start position:0% +values you know I see thousands of + + + align:start position:0% +values you know I see thousands of +transactions no one seems to be sending + + align:start position:0% +transactions no one seems to be sending + + + align:start position:0% +transactions no one seems to be sending +anyone any money they saw they seemed to + + align:start position:0% +anyone any money they saw they seemed to + + + align:start position:0% +anyone any money they saw they seemed to +be pointless and then there's this like + + align:start position:0% +be pointless and then there's this like + + + align:start position:0% +be pointless and then there's this like +hidden value that's in like a different + + align:start position:0% +hidden value that's in like a different + + + align:start position:0% +hidden value that's in like a different +data structure it would look something + + align:start position:0% +data structure it would look something + + + align:start position:0% +data structure it would look something +like Segway and like cycle it was a + + align:start position:0% +like Segway and like cycle it was a + + + align:start position:0% +like Segway and like cycle it was a +little bit ugly this would be real ugly + + align:start position:0% +little bit ugly this would be real ugly + + + align:start position:0% +little bit ugly this would be real ugly +those are the trade-offs we're dealing + + align:start position:0% +those are the trade-offs we're dealing + + + align:start position:0% +those are the trade-offs we're dealing +with here + + align:start position:0% +with here + + + align:start position:0% +with here +tricky Fork yeah ok but you get this + + align:start position:0% +tricky Fork yeah ok but you get this + + + align:start position:0% +tricky Fork yeah ok but you get this +like this is what you get when you use + + align:start position:0% +like this is what you get when you use + + + align:start position:0% +like this is what you get when you use +confidential transactions you we got it + + align:start position:0% +confidential transactions you we got it + + + align:start position:0% +confidential transactions you we got it +right we have private unlikeable amounts + + align:start position:0% +right we have private unlikeable amounts + + + align:start position:0% +right we have private unlikeable amounts +where the network can verify ok let me + + align:start position:0% +where the network can verify ok let me + + + align:start position:0% +where the network can verify ok let me +verify the w+ x equals y plus c that's + + align:start position:0% +verify the w+ x equals y plus c that's + + + align:start position:0% +verify the w+ x equals y plus c that's +actually the easy part + + align:start position:0% +actually the easy part + + + align:start position:0% +actually the easy part +now let me verify for every individual w + + align:start position:0% +now let me verify for every individual w + + + align:start position:0% +now let me verify for every individual w +x y and z that it is within the range of + + align:start position:0% +x y and z that it is within the range of + + + align:start position:0% +x y and z that it is within the range of +0 to sues the 2 to the third 0 to 2 2 to + + align:start position:0% +0 to sues the 2 to the third 0 to 2 2 to + + + align:start position:0% +0 to sues the 2 to the third 0 to 2 2 to +30 to toaster by verifying all these + + align:start position:0% +30 to toaster by verifying all these + + + align:start position:0% +30 to toaster by verifying all these +separate ring signatures for each bit of + + align:start position:0% +separate ring signatures for each bit of + + + align:start position:0% +separate ring signatures for each bit of +the amount + + align:start position:0% +the amount + + + align:start position:0% +the amount +so but you can do it right you can + + align:start position:0% +so but you can do it right you can + + + align:start position:0% +so but you can do it right you can +verify okay input amounts equals output + + align:start position:0% +verify okay input amounts equals output + + + align:start position:0% +verify okay input amounts equals output +amounts all these input amounts and + + align:start position:0% +amounts all these input amounts and + + + align:start position:0% +amounts all these input amounts and +output amounts are normal looking + + align:start position:0% +output amounts are normal looking + + + align:start position:0% +output amounts are normal looking +numbers that aren't too big that aren't + + align:start position:0% +numbers that aren't too big that aren't + + + align:start position:0% +numbers that aren't too big that aren't +right up near the modulus to wrap around + + align:start position:0% +right up near the modulus to wrap around + + + align:start position:0% +right up near the modulus to wrap around +and it works just kind of big and slow + + align:start position:0% +and it works just kind of big and slow + + + align:start position:0% +and it works just kind of big and slow +we're trying to make that faster so + + align:start position:0% +we're trying to make that faster so + + + align:start position:0% +we're trying to make that faster so +probably not gonna go if you're + + align:start position:0% +probably not gonna go if you're + + + align:start position:0% +probably not gonna go if you're +interested in this though there's a lot + + align:start position:0% +interested in this though there's a lot + + + align:start position:0% +interested in this though there's a lot +of research about this kind of thing + + align:start position:0% +of research about this kind of thing + + + align:start position:0% +of research about this kind of thing +right now + + align:start position:0% +right now + + + align:start position:0% +right now +it's a really cool like getting in a + + align:start position:0% +it's a really cool like getting in a + + + align:start position:0% +it's a really cool like getting in a +crazy interesting math so there's bullet + + align:start position:0% +crazy interesting math so there's bullet + + + align:start position:0% +crazy interesting math so there's bullet +proofs which was benedict at stanford he + + align:start position:0% +proofs which was benedict at stanford he + + + align:start position:0% +proofs which was benedict at stanford he +wrote up i mean a bunch of people wrote + + align:start position:0% +wrote up i mean a bunch of people wrote + + + align:start position:0% +wrote up i mean a bunch of people wrote +it but i think it was sort of his idea + + align:start position:0% +it but i think it was sort of his idea + + + align:start position:0% +it but i think it was sort of his idea +or his thing working with other people + + align:start position:0% +or his thing working with other people + + + align:start position:0% +or his thing working with other people +too that's more efficient range proofs i + + align:start position:0% +too that's more efficient range proofs i + + + align:start position:0% +too that's more efficient range proofs i +do not know how well it works work I + + align:start position:0% +do not know how well it works work I + + + align:start position:0% +do not know how well it works work I +sort of tried to read the paper and got + + align:start position:0% +sort of tried to read the paper and got + + + align:start position:0% +sort of tried to read the paper and got +like two pages in it but just take me a + + align:start position:0% +like two pages in it but just take me a + + + align:start position:0% +like two pages in it but just take me a +long time and then the boramy and rig + + align:start position:0% +long time and then the boramy and rig + + + align:start position:0% +long time and then the boramy and rig +signatures sort of the more efficient + + align:start position:0% +signatures sort of the more efficient + + + align:start position:0% +signatures sort of the more efficient +ring signatures that can compact a lot + + align:start position:0% +ring signatures that can compact a lot + + + align:start position:0% +ring signatures that can compact a lot +of data so that you're not so you know + + align:start position:0% +of data so that you're not so you know + + + align:start position:0% +of data so that you're not so you know +so you get it down to like two kilobytes + + align:start position:0% +so you get it down to like two kilobytes + + + align:start position:0% +so you get it down to like two kilobytes +for these range proofs in confidential + + align:start position:0% +for these range proofs in confidential + + + align:start position:0% +for these range proofs in confidential +transactions and then I may try to give + + align:start position:0% +transactions and then I may try to give + + + align:start position:0% +transactions and then I may try to give +a class about this in like a week or two + + align:start position:0% +a class about this in like a week or two + + + align:start position:0% +a class about this in like a week or two +minimal the idea is that when all of the + + align:start position:0% +minimal the idea is that when all of the + + + align:start position:0% +minimal the idea is that when all of the +transactions in the network are like + + align:start position:0% +transactions in the network are like + + + align:start position:0% +transactions in the network are like +this and they have confidential inputs + + align:start position:0% +this and they have confidential inputs + + + align:start position:0% +this and they have confidential inputs +and outputs amounts the transactions can + + align:start position:0% +and outputs amounts the transactions can + + + align:start position:0% +and outputs amounts the transactions can +be canceled out in an interesting way + + align:start position:0% +be canceled out in an interesting way + + + align:start position:0% +be canceled out in an interesting way +because the amount the output amounts + + align:start position:0% +because the amount the output amounts + + + align:start position:0% +because the amount the output amounts +are unique right they have these binding + + align:start position:0% +are unique right they have these binding + + + align:start position:0% +are unique right they have these binding +factors they have these range proofs and + + align:start position:0% +factors they have these range proofs and + + + align:start position:0% +factors they have these range proofs and +so if you're in a block so just a hint + + align:start position:0% +so if you're in a block so just a hint + + + align:start position:0% +so if you're in a block so just a hint +about middle limbal the idea is if you + + align:start position:0% +about middle limbal the idea is if you + + + align:start position:0% +about middle limbal the idea is if you +have a transaction and it says okay + + align:start position:0% +have a transaction and it says okay + + + align:start position:0% +have a transaction and it says okay +amounts are all obscured right but a is + + align:start position:0% +amounts are all obscured right but a is + + + align:start position:0% +amounts are all obscured right but a is +being consumed B is being consumed see + + align:start position:0% +being consumed B is being consumed see + + + align:start position:0% +being consumed B is being consumed see +it's being created D is being created + + align:start position:0% +it's being created D is being created + + + align:start position:0% +it's being created D is being created +right these these are amounts and then I + + align:start position:0% +right these these are amounts and then I + + + align:start position:0% +right these these are amounts and then I +see later in the block there's another + + align:start position:0% +see later in the block there's another + + + align:start position:0% +see later in the block there's another +transaction which spends d coins and + + align:start position:0% +transaction which spends d coins and + + + align:start position:0% +transaction which spends d coins and +sends to equines I can just I don't have + + align:start position:0% +sends to equines I can just I don't have + + + align:start position:0% +sends to equines I can just I don't have +to actually verify that like a plus B + + align:start position:0% +to actually verify that like a plus B + + + align:start position:0% +to actually verify that like a plus B +equals C plus D + + align:start position:0% +equals C plus D + + + align:start position:0% +equals C plus D +and the equals the kind of thing I can + + align:start position:0% +and the equals the kind of thing I can + + + align:start position:0% +and the equals the kind of thing I can +just cross these out and I can sort of + + align:start position:0% +just cross these out and I can sort of + + + align:start position:0% +just cross these out and I can sort of +verify at a block level instead of a + + align:start position:0% +verify at a block level instead of a + + + align:start position:0% +verify at a block level instead of a +transaction level that the input amounts + + align:start position:0% +transaction level that the input amounts + + + align:start position:0% +transaction level that the input amounts +in output amounts all matched up right + + align:start position:0% +in output amounts all matched up right + + + align:start position:0% +in output amounts all matched up right +because I don't know what D is but + + align:start position:0% +because I don't know what D is but + + + align:start position:0% +because I don't know what D is but +anyway it was on an output side and on + + align:start position:0% +anyway it was on an output side and on + + + align:start position:0% +anyway it was on an output side and on +an input side within the same block so + + align:start position:0% +an input side within the same block so + + + align:start position:0% +an input side within the same block so +anyway it's gone right it's being it's + + align:start position:0% +anyway it's gone right it's being it's + + + align:start position:0% +anyway it's gone right it's being it's +being added to and subtracted in this + + align:start position:0% +being added to and subtracted in this + + + align:start position:0% +being added to and subtracted in this +block so I can sort of do that and I can + + align:start position:0% +block so I can sort of do that and I can + + + align:start position:0% +block so I can sort of do that and I can +do that over multiple blocks and I can + + align:start position:0% +do that over multiple blocks and I can + + + align:start position:0% +do that over multiple blocks and I can +basically keep a tally of how many coins + + align:start position:0% +basically keep a tally of how many coins + + + align:start position:0% +basically keep a tally of how many coins +are in the system and sort of cancel + + align:start position:0% +are in the system and sort of cancel + + + align:start position:0% +are in the system and sort of cancel +things out so that actually lets you do + + align:start position:0% +things out so that actually lets you do + + + align:start position:0% +things out so that actually lets you do +some really cool things where you can + + align:start position:0% +some really cool things where you can + + + align:start position:0% +some really cool things where you can +skip a lot of verification at no loss of + + align:start position:0% +skip a lot of verification at no loss of + + + align:start position:0% +skip a lot of verification at no loss of +security so that's the idea of minimal + + align:start position:0% +security so that's the idea of minimal + + + align:start position:0% +security so that's the idea of minimal +Wimble which is really a fun paper + + align:start position:0% +Wimble which is really a fun paper + + + align:start position:0% +Wimble which is really a fun paper +because it was written by Lord Voldemort + + align:start position:0% +because it was written by Lord Voldemort + + + align:start position:0% +because it was written by Lord Voldemort +it was just sort of someone posted like + + align:start position:0% +it was just sort of someone posted like + + + align:start position:0% +it was just sort of someone posted like +a pastebin link on IRC and like who + + align:start position:0% +a pastebin link on IRC and like who + + + align:start position:0% +a pastebin link on IRC and like who +knows who wrote this Lord Voldemort + + align:start position:0% +knows who wrote this Lord Voldemort + + + align:start position:0% +knows who wrote this Lord Voldemort +except it was Lord Voldemort the French + + align:start position:0% +except it was Lord Voldemort the French + + + align:start position:0% +except it was Lord Voldemort the French +word for Lord world war so like when + + align:start position:0% +word for Lord world war so like when + + + align:start position:0% +word for Lord world war so like when +they hare translated Harry Potter into + + align:start position:0% +they hare translated Harry Potter into + + + align:start position:0% +they hare translated Harry Potter into +French they changed the names around I + + align:start position:0% +French they changed the names around I + + + align:start position:0% +French they changed the names around I +guess and it was the French equivalent + + align:start position:0% +guess and it was the French equivalent + + + align:start position:0% +guess and it was the French equivalent +of Lord Voldemort and so now there's a + + align:start position:0% +of Lord Voldemort and so now there's a + + + align:start position:0% +of Lord Voldemort and so now there's a +bunch of people programming memorable + + align:start position:0% +bunch of people programming memorable + + + align:start position:0% +bunch of people programming memorable +and implementing it and they all use + + align:start position:0% +and implementing it and they all use + + + align:start position:0% +and implementing it and they all use +like Harry Potter Nate not all of them + + align:start position:0% +like Harry Potter Nate not all of them + + + align:start position:0% +like Harry Potter Nate not all of them +but a lot of them use Harry Potter names + + align:start position:0% +but a lot of them use Harry Potter names + + + align:start position:0% +but a lot of them use Harry Potter names +on github so it's kind of it's kind of + + align:start position:0% +on github so it's kind of it's kind of + + + align:start position:0% +on github so it's kind of it's kind of +funny it's also really funny that like + + align:start position:0% +funny it's also really funny that like + + + align:start position:0% +funny it's also really funny that like +it was sort of one of the most I would + + align:start position:0% +it was sort of one of the most I would + + + align:start position:0% +it was sort of one of the most I would +say the most like whoa kind of paper of + + align:start position:0% +say the most like whoa kind of paper of + + + align:start position:0% +say the most like whoa kind of paper of +2016 now and so it's just sort of + + align:start position:0% +2016 now and so it's just sort of + + + align:start position:0% +2016 now and so it's just sort of +interesting indicator of the space we're + + align:start position:0% +interesting indicator of the space we're + + + align:start position:0% +interesting indicator of the space we're +working in that like you know you've got + + align:start position:0% +working in that like you know you've got + + + align:start position:0% +working in that like you know you've got +IBM and all these big companies and + + align:start position:0% +IBM and all these big companies and + + + align:start position:0% +IBM and all these big companies and +they're working on like blockchain + + align:start position:0% +they're working on like blockchain + + + align:start position:0% +they're working on like blockchain +research and like honestly not a ton of + + align:start position:0% +research and like honestly not a ton of + + + align:start position:0% +research and like honestly not a ton of +awesome stuff whereas like whoa middle + + align:start position:0% +awesome stuff whereas like whoa middle + + + align:start position:0% +awesome stuff whereas like whoa middle +limbal okay Lord Voldemort he like + + align:start position:0% +limbal okay Lord Voldemort he like + + + align:start position:0% +limbal okay Lord Voldemort he like +really should ever so it's kind of fun + + align:start position:0% +really should ever so it's kind of fun + + + align:start position:0% +really should ever so it's kind of fun +that it's like still very sort of out + + align:start position:0% +that it's like still very sort of out + + + align:start position:0% +that it's like still very sort of out +there hacker he kind of system okay so + + align:start position:0% +there hacker he kind of system okay so + + + align:start position:0% +there hacker he kind of system okay so +that's hopefully most people got most of + + align:start position:0% +that's hopefully most people got most of + + + align:start position:0% +that's hopefully most people got most of +the idea it's it's a little bit fast to + + align:start position:0% +the idea it's it's a little bit fast to + + + align:start position:0% +the idea it's it's a little bit fast to +sort of explain all the Petersons + + align:start position:0% +sort of explain all the Petersons + + + align:start position:0% +sort of explain all the Petersons +commitments and range proofs and + + align:start position:0% +commitments and range proofs and + + + align:start position:0% +commitments and range proofs and +everything in a little bit of time but I + + align:start position:0% +everything in a little bit of time but I + + + align:start position:0% +everything in a little bit of time but I +think you got the idea and if you're + + align:start position:0% +think you got the idea and if you're + + + align:start position:0% +think you got the idea and if you're +interested in it there's a lot of + + align:start position:0% +interested in it there's a lot of + + + align:start position:0% +interested in it there's a lot of +current research on this and people + + align:start position:0% +current research on this and people + + + align:start position:0% +current research on this and people +implementing it and there's a lot of + + align:start position:0% +implementing it and there's a lot of + + + align:start position:0% +implementing it and there's a lot of +cool things you can do with it \ No newline at end of file diff --git a/VUGsZgQaAZs.txt b/VUGsZgQaAZs.txt new file mode 100644 index 0000000000000000000000000000000000000000..2496a6cf7903e2699af3c277f91742461c11188e --- /dev/null +++ b/VUGsZgQaAZs.txt @@ -0,0 +1,7107 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +ribosome called Rybak's and experiments + + align:start position:0% +ribosome called Rybak's and experiments + + + align:start position:0% +ribosome called Rybak's and experiments +that were done to characterize it and + + align:start position:0% +that were done to characterize it and + + + align:start position:0% +that were done to characterize it and +determine whether it did a better job at + + align:start position:0% +determine whether it did a better job at + + + align:start position:0% +determine whether it did a better job at +allowing the tRNA to suppress the Amber + + align:start position:0% +allowing the tRNA to suppress the Amber + + + align:start position:0% +allowing the tRNA to suppress the Amber +stop codon and then we'll be + + align:start position:0% +stop codon and then we'll be + + + align:start position:0% +stop codon and then we'll be +transitioning into module 2 so we'll be + + align:start position:0% +transitioning into module 2 so we'll be + + + align:start position:0% +transitioning into module 2 so we'll be +starting protein folding today and be + + align:start position:0% +starting protein folding today and be + + + align:start position:0% +starting protein folding today and be +spending the next couple of days on that + + align:start position:0% +spending the next couple of days on that + + + align:start position:0% +spending the next couple of days on that +area and thinking about some of the + + align:start position:0% +area and thinking about some of the + + + align:start position:0% +area and thinking about some of the +macro molecular machines and other + + align:start position:0% +macro molecular machines and other + + + align:start position:0% +macro molecular machines and other +proteins involved so just as a recap + + align:start position:0% +proteins involved so just as a recap + + + align:start position:0% +proteins involved so just as a recap +where we left off last time was thinking + + align:start position:0% +where we left off last time was thinking + + + align:start position:0% +where we left off last time was thinking +about incorporating unnatural amino + + align:start position:0% +about incorporating unnatural amino + + + align:start position:0% +about incorporating unnatural amino +acids using a new ribosome and so we + + align:start position:0% +acids using a new ribosome and so we + + + align:start position:0% +acids using a new ribosome and so we +discussed how an orthogonal ribosome was + + align:start position:0% +discussed how an orthogonal ribosome was + + + align:start position:0% +discussed how an orthogonal ribosome was +designed that binds two orthogonal mRNA + + align:start position:0% +designed that binds two orthogonal mRNA + + + align:start position:0% +designed that binds two orthogonal mRNA +and then the idea was can this + + align:start position:0% +and then the idea was can this + + + align:start position:0% +and then the idea was can this +orthogonal ribosome be improved the + + align:start position:0% +orthogonal ribosome be improved the + + + align:start position:0% +orthogonal ribosome be improved the +immuno genesis and selection to get a + + align:start position:0% +immuno genesis and selection to get a + + + align:start position:0% +immuno genesis and selection to get a +new orthogonal ribosome wear suppression + + align:start position:0% +new orthogonal ribosome wear suppression + + + align:start position:0% +new orthogonal ribosome wear suppression +of the amber stop codon by the tRNA is + + align:start position:0% +of the amber stop codon by the tRNA is + + + align:start position:0% +of the amber stop codon by the tRNA is +favored over termination by release + + align:start position:0% +favored over termination by release + + + align:start position:0% +favored over termination by release +factor one so we talked about this issue + + align:start position:0% +factor one so we talked about this issue + + + align:start position:0% +factor one so we talked about this issue +with release factor one causing + + align:start position:0% +with release factor one causing + + + align:start position:0% +with release factor one causing +truncated protein phenotypes right and + + align:start position:0% +truncated protein phenotypes right and + + + align:start position:0% +truncated protein phenotypes right and +so where we left off was in a series of + + align:start position:0% +so where we left off was in a series of + + + align:start position:0% +so where we left off was in a series of +three types of experiments to look at + + align:start position:0% +three types of experiments to look at + + + align:start position:0% +three types of experiments to look at +how well this ribose works so we looked + + align:start position:0% +how well this ribose works so we looked + + + align:start position:0% +how well this ribose works so we looked +at protein yield to ask is it + + align:start position:0% +at protein yield to ask is it + + + align:start position:0% +at protein yield to ask is it +translating polypeptide as well as the + + align:start position:0% +translating polypeptide as well as the + + + align:start position:0% +translating polypeptide as well as the +starting orthogonal ribosome and then + + align:start position:0% +starting orthogonal ribosome and then + + + align:start position:0% +starting orthogonal ribosome and then +the next experiment we were looking at + + align:start position:0% +the next experiment we were looking at + + + align:start position:0% +the next experiment we were looking at +and where we left off with was + + align:start position:0% +and where we left off with was + + + align:start position:0% +and where we left off with was +experiment 2 which was the question of + + align:start position:0% +experiment 2 which was the question of + + + align:start position:0% +experiment 2 which was the question of +amino acid miss or incorporation + + align:start position:0% + + + + align:start position:0% + +okay and so what was done just in recap + + align:start position:0% +okay and so what was done just in recap + + + align:start position:0% +okay and so what was done just in recap +is that a GST maltose binding protein + + align:start position:0% +is that a GST maltose binding protein + + + align:start position:0% +is that a GST maltose binding protein +and the P fusion protein was designed + + align:start position:0% +and the P fusion protein was designed + + + align:start position:0% +and the P fusion protein was designed +okay and recall that this protein had a + + align:start position:0% +okay and recall that this protein had a + + + align:start position:0% +okay and recall that this protein had a +protease cleavage site okay and that the + + align:start position:0% +protease cleavage site okay and that the + + + align:start position:0% +protease cleavage site okay and that the +GST portion contained cysteine and MBP + + align:start position:0% +GST portion contained cysteine and MBP + + + align:start position:0% +GST portion contained cysteine and MBP +does not contain cysteine okay so the + + align:start position:0% +does not contain cysteine okay so the + + + align:start position:0% +does not contain cysteine okay so the +idea was to use radio labeled cysteine + + align:start position:0% +idea was to use radio labeled cysteine + + + align:start position:0% +idea was to use radio labeled cysteine +as a probe for miss incorporation of + + align:start position:0% +as a probe for miss incorporation of + + + align:start position:0% +as a probe for miss incorporation of +cysteine and Tamil toast binding protein + + align:start position:0% +cysteine and Tamil toast binding protein + + + align:start position:0% +cysteine and Tamil toast binding protein +okay so in terms of the actual + + align:start position:0% +okay so in terms of the actual + + + align:start position:0% +okay so in terms of the actual +experiment what was done right imagine + + align:start position:0% +experiment what was done right imagine + + + align:start position:0% +experiment what was done right imagine +that we express this fusion okay in the + + align:start position:0% +that we express this fusion okay in the + + + align:start position:0% +that we express this fusion okay in the +presence of the radio label cysteine we + + align:start position:0% +presence of the radio label cysteine we + + + align:start position:0% +presence of the radio label cysteine we +use a protease okay and in this case it + + align:start position:0% +use a protease okay and in this case it + + + align:start position:0% +use a protease okay and in this case it +was thrombin this protease gives us two + + align:start position:0% +was thrombin this protease gives us two + + + align:start position:0% +was thrombin this protease gives us two +fragments GST plus MVP okay and these + + align:start position:0% +fragments GST plus MVP okay and these + + + align:start position:0% +fragments GST plus MVP okay and these +two proteins have different size so we + + align:start position:0% +two proteins have different size so we + + + align:start position:0% +two proteins have different size so we +can separate ok so just doing SDS page + + align:start position:0% + + + + align:start position:0% + +okay and ask where do the proteins + + align:start position:0% +okay and ask where do the proteins + + + align:start position:0% +okay and ask where do the proteins +migrate on the gel and then where do we + + align:start position:0% +migrate on the gel and then where do we + + + align:start position:0% +migrate on the gel and then where do we +see radioactivity okay and so the data + + align:start position:0% +see radioactivity okay and so the data + + + align:start position:0% +see radioactivity okay and so the data +are shown here that were reported by the + + align:start position:0% +are shown here that were reported by the + + + align:start position:0% +are shown here that were reported by the +authors so what are we looking at we're + + align:start position:0% +authors so what are we looking at we're + + + align:start position:0% +authors so what are we looking at we're +looking at on the left the Coomassie + + align:start position:0% +looking at on the left the Coomassie + + + align:start position:0% +looking at on the left the Coomassie +stain for total protein and then on the + + align:start position:0% +stain for total protein and then on the + + + align:start position:0% +stain for total protein and then on the +right we're looking at radioactivity + + align:start position:0% +right we're looking at radioactivity + + + align:start position:0% +right we're looking at radioactivity +here okay so what do we have here in + + align:start position:0% +here okay so what do we have here in + + + align:start position:0% +here okay so what do we have here in +terms of the lanes they've done some + + align:start position:0% +terms of the lanes they've done some + + + align:start position:0% +terms of the lanes they've done some +labeling to help us so they'll toast + + align:start position:0% +labeling to help us so they'll toast + + + align:start position:0% +labeling to help us so they'll toast +binding protein is running up here GST + + align:start position:0% +binding protein is running up here GST + + + align:start position:0% +binding protein is running up here GST +is running down here and we have four + + align:start position:0% +is running down here and we have four + + + align:start position:0% +is running down here and we have four +different conditions okay + + align:start position:0% +different conditions okay + + + align:start position:0% +different conditions okay +what do we see we have in lane one + + align:start position:0% +what do we see we have in lane one + + + align:start position:0% +what do we see we have in lane one +ryback's is what's used in lane two we + + align:start position:0% +ryback's is what's used in lane two we + + + align:start position:0% +ryback's is what's used in lane two we +have a system where it's the initial + + align:start position:0% +have a system where it's the initial + + + align:start position:0% +have a system where it's the initial +orthogonal ribosome that was not evolved + + align:start position:0% +orthogonal ribosome that was not evolved + + + align:start position:0% +orthogonal ribosome that was not evolved +right so that's our point of comparison + + align:start position:0% +right so that's our point of comparison + + + align:start position:0% +right so that's our point of comparison +in lane three we have the native + + align:start position:0% +in lane three we have the native + + + align:start position:0% +in lane three we have the native +ribosome only and in the four lane for a + + align:start position:0% +ribosome only and in the four lane for a + + + align:start position:0% +ribosome only and in the four lane for a +control for no gene so what do we see + + align:start position:0% + + + + align:start position:0% + +don't know change translate yes so why + + align:start position:0% +don't know change translate yes so why + + + align:start position:0% +don't know change translate yes so why +do we come to that conclusion they're + + align:start position:0% +do we come to that conclusion they're + + + align:start position:0% +do we come to that conclusion they're +all doing the same thing right what we + + align:start position:0% +all doing the same thing right what we + + + align:start position:0% +all doing the same thing right what we +see on the left here and the Coomassie + + align:start position:0% +see on the left here and the Coomassie + + + align:start position:0% +see on the left here and the Coomassie +stain is that in lanes one through three + + align:start position:0% +stain is that in lanes one through three + + + align:start position:0% +stain is that in lanes one through three +we see a band for MVP and they're all + + align:start position:0% +we see a band for MVP and they're all + + + align:start position:0% +we see a band for MVP and they're all +similar in terms of intensity and + + align:start position:0% +similar in terms of intensity and + + + align:start position:0% +similar in terms of intensity and +likewise for GST we see a band all + + align:start position:0% +likewise for GST we see a band all + + + align:start position:0% +likewise for GST we see a band all +similar intensity so it looks like in + + align:start position:0% +similar intensity so it looks like in + + + align:start position:0% +similar intensity so it looks like in +all cases a similar amount of protein is + + align:start position:0% +all cases a similar amount of protein is + + + align:start position:0% +all cases a similar amount of protein is +being synthesized and that this protease + + align:start position:0% +being synthesized and that this protease + + + align:start position:0% +being synthesized and that this protease +cleavage worked in a comparable manner + + align:start position:0% + + + + align:start position:0% + +the native ribosome is not going to bind + + align:start position:0% +the native ribosome is not going to bind + + + align:start position:0% +the native ribosome is not going to bind +to the orthogonal mrna so you need to + + align:start position:0% +to the orthogonal mrna so you need to + + + align:start position:0% +to the orthogonal mrna so you need to +give a plasmid that has a ribosome + + align:start position:0% +give a plasmid that has a ribosome + + + align:start position:0% +give a plasmid that has a ribosome +binding site compatible with the native + + align:start position:0% +binding site compatible with the native + + + align:start position:0% +binding site compatible with the native +ribosome and yes it's possible that + + align:start position:0% +ribosome and yes it's possible that + + + align:start position:0% +ribosome and yes it's possible that +native ribosome won't work as well or + + align:start position:0% +native ribosome won't work as well or + + + align:start position:0% +native ribosome won't work as well or +reverse I say reverse is more likely + + align:start position:0% +reverse I say reverse is more likely + + + align:start position:0% +reverse I say reverse is more likely +that one of these mutants won't work as + + align:start position:0% +that one of these mutants won't work as + + + align:start position:0% +that one of these mutants won't work as +well + + align:start position:0% +well + + + align:start position:0% +well +but that doesn't appear to be the case + + align:start position:0% +but that doesn't appear to be the case + + + align:start position:0% +but that doesn't appear to be the case +here so what does the gel on the right + + align:start position:0% +here so what does the gel on the right + + + align:start position:0% +here so what does the gel on the right +show so where do we see radioactivity + + align:start position:0% + + + + align:start position:0% + +mostly at GST but + + align:start position:0% +mostly at GST but + + + align:start position:0% +mostly at GST but +do we expect background or make the + + align:start position:0% +do we expect background or make the + + + align:start position:0% +do we expect background or make the +background comfort right so we see a + + align:start position:0% +background comfort right so we see a + + + align:start position:0% +background comfort right so we see a +strong band here right and this is at + + align:start position:0% +strong band here right and this is at + + + align:start position:0% +strong band here right and this is at +the same places where we see GST so + + align:start position:0% +the same places where we see GST so + + + align:start position:0% +the same places where we see GST so +that's a good indication right we know + + align:start position:0% +that's a good indication right we know + + + align:start position:0% +that's a good indication right we know +that there cysteines in GST so we should + + align:start position:0% +that there cysteines in GST so we should + + + align:start position:0% +that there cysteines in GST so we should +see a band here so what about background + + align:start position:0% +see a band here so what about background + + + align:start position:0% +see a band here so what about background +and what about MVP have some of this + + align:start position:0% +and what about MVP have some of this + + + align:start position:0% +and what about MVP have some of this +incorporation identity is very much must + + align:start position:0% +incorporation identity is very much must + + + align:start position:0% +incorporation identity is very much must +compare with just you but a little bit + + align:start position:0% +compare with just you but a little bit + + + align:start position:0% +compare with just you but a little bit +an MDP participation okay is that band + + align:start position:0% +an MDP participation okay is that band + + + align:start position:0% +an MDP participation okay is that band +MVP dude do we know that definitively in + + align:start position:0% +MVP dude do we know that definitively in + + + align:start position:0% +MVP dude do we know that definitively in +this gel there's many species in these + + align:start position:0% +this gel there's many species in these + + + align:start position:0% +this gel there's many species in these +gels right there aren't it isn't just + + align:start position:0% +gels right there aren't it isn't just + + + align:start position:0% +gels right there aren't it isn't just +two bands one for GST and one from MVP + + align:start position:0% +two bands one for GST and one from MVP + + + align:start position:0% +two bands one for GST and one from MVP +right so where do these other bands come + + align:start position:0% +right so where do these other bands come + + + align:start position:0% +right so where do these other bands come +from right could it be from the initial + + align:start position:0% +from right could it be from the initial + + + align:start position:0% +from right could it be from the initial +protein purification and there's some + + align:start position:0% +protein purification and there's some + + + align:start position:0% +protein purification and there's some +contaminants could it be a result of the + + align:start position:0% +contaminants could it be a result of the + + + align:start position:0% +contaminants could it be a result of the +thrombin cleavage and maybe thrombin cut + + align:start position:0% +thrombin cleavage and maybe thrombin cut + + + align:start position:0% +thrombin cleavage and maybe thrombin cut +at some places other than just this + + align:start position:0% +at some places other than just this + + + align:start position:0% +at some places other than just this +cleavage site so that's preferred but + + align:start position:0% +cleavage site so that's preferred but + + + align:start position:0% +cleavage site so that's preferred but +maybe it can cut some other places right + + align:start position:0% +maybe it can cut some other places right + + + align:start position:0% +maybe it can cut some other places right +so there's other species in the gel and + + align:start position:0% +so there's other species in the gel and + + + align:start position:0% +so there's other species in the gel and +cysteine comes up in other proteins so + + align:start position:0% +cysteine comes up in other proteins so + + + align:start position:0% +cysteine comes up in other proteins so +it makes sense that there'd be some + + align:start position:0% +it makes sense that there'd be some + + + align:start position:0% +it makes sense that there'd be some +background just say this protein wasn't + + align:start position:0% +background just say this protein wasn't + + + align:start position:0% +background just say this protein wasn't +99 100 percent pure right or maybe from + + align:start position:0% +99 100 percent pure right or maybe from + + + align:start position:0% +99 100 percent pure right or maybe from +cleavage there in terms of this little + + align:start position:0% +cleavage there in terms of this little + + + align:start position:0% +cleavage there in terms of this little +band is that MVP or not a little hard to + + align:start position:0% +band is that MVP or not a little hard to + + + align:start position:0% +band is that MVP or not a little hard to +say where they place the arrow indicates + + align:start position:0% +say where they place the arrow indicates + + + align:start position:0% +say where they place the arrow indicates +maybe not right but what could you do to + + align:start position:0% +maybe not right but what could you do to + + + align:start position:0% +maybe not right but what could you do to +find that out + + align:start position:0% + + + + align:start position:0% + +yeah so maybe a Western blot if there's + + align:start position:0% +yeah so maybe a Western blot if there's + + + align:start position:0% +yeah so maybe a Western blot if there's +an antibody you could run something less + + align:start position:0% +an antibody you could run something less + + + align:start position:0% +an antibody you could run something less +concentrated you could do mass spec you + + align:start position:0% +concentrated you could do mass spec you + + + align:start position:0% +concentrated you could do mass spec you +know there's options if you wanted to + + align:start position:0% +know there's options if you wanted to + + + align:start position:0% +know there's options if you wanted to +track that down but the bottom line is + + align:start position:0% +track that down but the bottom line is + + + align:start position:0% +track that down but the bottom line is +if we compare the radioactivity here to + + align:start position:0% +if we compare the radioactivity here to + + + align:start position:0% +if we compare the radioactivity here to +what's seen here there's much more with + + align:start position:0% +what's seen here there's much more with + + + align:start position:0% +what's seen here there's much more with +GST which is what we would expect and so + + align:start position:0% +GST which is what we would expect and so + + + align:start position:0% +GST which is what we would expect and so +through some further analysis they + + align:start position:0% +through some further analysis they + + + align:start position:0% +through some further analysis they +conclude the error frequency is less + + align:start position:0% +conclude the error frequency is less + + + align:start position:0% +conclude the error frequency is less +than one in ten to the three for Raible + + align:start position:0% +than one in ten to the three for Raible + + + align:start position:0% +than one in ten to the three for Raible +X at least for cysteine right so what's + + align:start position:0% +X at least for cysteine right so what's + + + align:start position:0% +X at least for cysteine right so what's +the limitation of this experiment from + + align:start position:0% +the limitation of this experiment from + + + align:start position:0% +the limitation of this experiment from +the standpoint of missing Corporation + + align:start position:0% +the standpoint of missing Corporation + + + align:start position:0% +the standpoint of missing Corporation +which is what I asked you to think about + + align:start position:0% +which is what I asked you to think about + + + align:start position:0% +which is what I asked you to think about +in closing last time only testing for + + align:start position:0% +in closing last time only testing for + + + align:start position:0% +in closing last time only testing for +sistemas incorporation so we don't + + align:start position:0% +sistemas incorporation so we don't + + + align:start position:0% +sistemas incorporation so we don't +really know about other amino acids + + align:start position:0% +really know about other amino acids + + + align:start position:0% +really know about other amino acids +right so this is good news but there's + + align:start position:0% +right so this is good news but there's + + + align:start position:0% +right so this is good news but there's +other information we're not getting from + + align:start position:0% +other information we're not getting from + + + align:start position:0% +other information we're not getting from +this experiment there so is it possible + + align:start position:0% +this experiment there so is it possible + + + align:start position:0% +this experiment there so is it possible +that other amino acids are Mis + + align:start position:0% +that other amino acids are Mis + + + align:start position:0% +that other amino acids are Mis +incorporated it would take some + + align:start position:0% +incorporated it would take some + + + align:start position:0% +incorporated it would take some +additional experiments to get at that so + + align:start position:0% +additional experiments to get at that so + + + align:start position:0% +additional experiments to get at that so +the last experiment we're going to look + + align:start position:0% +the last experiment we're going to look + + + align:start position:0% +the last experiment we're going to look +at is asking the question does ribose + + align:start position:0% +at is asking the question does ribose + + + align:start position:0% +at is asking the question does ribose +actually do a better job than the + + align:start position:0% +actually do a better job than the + + + align:start position:0% +actually do a better job than the +progenitor or a ribosome so what we want + + align:start position:0% +progenitor or a ribosome so what we want + + + align:start position:0% +progenitor or a ribosome so what we want +to look is at the efficiency of + + align:start position:0% +to look is at the efficiency of + + + align:start position:0% +to look is at the efficiency of +suppression of the amber stop codon + + align:start position:0% + + + + align:start position:0% + +right so last time we talked about how + + align:start position:0% +right so last time we talked about how + + + align:start position:0% +right so last time we talked about how +one limitation of the Shultz method is + + align:start position:0% +one limitation of the Shultz method is + + + align:start position:0% +one limitation of the Shultz method is +that there's a truncated phenotype right + + align:start position:0% +that there's a truncated phenotype right + + + align:start position:0% +that there's a truncated phenotype right +because our f1 enters the a state rather + + align:start position:0% +because our f1 enters the a state rather + + + align:start position:0% +because our f1 enters the a state rather +than the tRNA so in order to look at + + align:start position:0% +than the tRNA so in order to look at + + + align:start position:0% +than the tRNA so in order to look at +this they continued to use this type of + + align:start position:0% +this they continued to use this type of + + + align:start position:0% +this they continued to use this type of +fusion but instead of having a protease + + align:start position:0% +fusion but instead of having a protease + + + align:start position:0% +fusion but instead of having a protease +cleavage site here they stuck the amber + + align:start position:0% +cleavage site here they stuck the amber + + + align:start position:0% +cleavage site here they stuck the amber +stop codon in between GST and MBP okay + + align:start position:0% +stop codon in between GST and MBP okay + + + align:start position:0% +stop codon in between GST and MBP okay +so they made two different class modes + + align:start position:0% +so they made two different class modes + + + align:start position:0% +so they made two different class modes +so GST a plasmid encoding GST the stop + + align:start position:0% +so GST a plasmid encoding GST the stop + + + align:start position:0% +so GST a plasmid encoding GST the stop +and Maui so this is the gene name for + + align:start position:0% +and Maui so this is the gene name for + + + align:start position:0% +and Maui so this is the gene name for +MVP so if this gets translated the + + align:start position:0% +MVP so if this gets translated the + + + align:start position:0% +MVP so if this gets translated the +question is do we get the GST MVP fusion + + align:start position:0% +question is do we get the GST MVP fusion + + + align:start position:0% +question is do we get the GST MVP fusion +or GST right because if the tRNA does + + align:start position:0% +or GST right because if the tRNA does + + + align:start position:0% +or GST right because if the tRNA does +its job polypeptide synthesis will + + align:start position:0% +its job polypeptide synthesis will + + + align:start position:0% +its job polypeptide synthesis will +continue and we'll get the fusion + + align:start position:0% +continue and we'll get the fusion + + + align:start position:0% +continue and we'll get the fusion +protein if release factor one ends up + + align:start position:0% +protein if release factor one ends up + + + align:start position:0% +protein if release factor one ends up +here at this position we get termination + + align:start position:0% +here at this position we get termination + + + align:start position:0% +here at this position we get termination +and only GST and they also made an + + align:start position:0% +and only GST and they also made an + + + align:start position:0% +and only GST and they also made an +additional construct so in addition to + + align:start position:0% +additional construct so in addition to + + + align:start position:0% +additional construct so in addition to +asking what happens if there is a codon + + align:start position:0% +asking what happens if there is a codon + + + align:start position:0% +asking what happens if there is a codon +for one natural amino acid what happens + + align:start position:0% +for one natural amino acid what happens + + + align:start position:0% +for one natural amino acid what happens +if there's - so recall with the Shultz + + align:start position:0% +if there's - so recall with the Shultz + + + align:start position:0% +if there's - so recall with the Shultz +method what we saw last time is that + + align:start position:0% +method what we saw last time is that + + + align:start position:0% +method what we saw last time is that +when an attempts were made to + + align:start position:0% +when an attempts were made to + + + align:start position:0% +when an attempts were made to +incorporate two unnatural amino acids + + align:start position:0% +incorporate two unnatural amino acids + + + align:start position:0% +incorporate two unnatural amino acids +than one polypeptide the efficiency went + + align:start position:0% +than one polypeptide the efficiency went + + + align:start position:0% +than one polypeptide the efficiency went +down to below one percent there so what + + align:start position:0% +down to below one percent there so what + + + align:start position:0% +down to below one percent there so what +if two of these + + align:start position:0% + + + + align:start position:0% + +are here again the question is these get + + align:start position:0% +are here again the question is these get + + + align:start position:0% +are here again the question is these get +translated do we get GST MBP or GST okay + + align:start position:0% +translated do we get GST MBP or GST okay + + + align:start position:0% +translated do we get GST MBP or GST okay +and as we can see from the jel we can + + align:start position:0% +and as we can see from the jel we can + + + align:start position:0% +and as we can see from the jel we can +differentiate pieces by size okay so in + + align:start position:0% +differentiate pieces by size okay so in + + + align:start position:0% +differentiate pieces by size okay so in +addition to comparing these what was + + align:start position:0% +addition to comparing these what was + + + align:start position:0% +addition to comparing these what was +done is in both sets of experiments + + align:start position:0% +done is in both sets of experiments + + + align:start position:0% +done is in both sets of experiments +there was a comparison of the Schultz + + align:start position:0% +there was a comparison of the Schultz + + + align:start position:0% +there was a comparison of the Schultz +method we discussed first and Rybak's + + align:start position:0% +method we discussed first and Rybak's + + + align:start position:0% +method we discussed first and Rybak's +here okay and just in terms of size so + + align:start position:0% +here okay and just in terms of size so + + + align:start position:0% +here okay and just in terms of size so +GST MBP is about 70 kilotons okay and + + align:start position:0% +GST MBP is about 70 kilotons okay and + + + align:start position:0% +GST MBP is about 70 kilotons okay and +GST is about 20 kilotons 26 so easy to + + align:start position:0% +GST is about 20 kilotons 26 so easy to + + + align:start position:0% +GST is about 20 kilotons 26 so easy to +separate on the gel so what are the data + + align:start position:0% +separate on the gel so what are the data + + + align:start position:0% +separate on the gel so what are the data +and we'll just and what was the + + align:start position:0% +and we'll just and what was the + + + align:start position:0% +and we'll just and what was the +unnatural amino acid employed so they + + align:start position:0% +unnatural amino acid employed so they + + + align:start position:0% +unnatural amino acid employed so they +ended up using an unnatural amino acid + + align:start position:0% +ended up using an unnatural amino acid + + + align:start position:0% +ended up using an unnatural amino acid +called BPA which is a benzophenone + + align:start position:0% +called BPA which is a benzophenone + + + align:start position:0% +called BPA which is a benzophenone +still a cross linker + + align:start position:0% + + + + align:start position:0% + +okay and so I'm going to write up some + + align:start position:0% +okay and so I'm going to write up some + + + align:start position:0% +okay and so I'm going to write up some +details that came out from the jela and + + align:start position:0% +details that came out from the jela and + + + align:start position:0% +details that came out from the jela and +the board because there's a lot of + + align:start position:0% + + + + align:start position:0% + +things to navigate in that gel okay okay + + align:start position:0% +things to navigate in that gel okay okay + + + align:start position:0% +things to navigate in that gel okay okay +so effectively what are the comparisons + + align:start position:0% +so effectively what are the comparisons + + + align:start position:0% +so effectively what are the comparisons +we want to make so in lane three the + + align:start position:0% +we want to make so in lane three the + + + align:start position:0% +we want to make so in lane three the +method we have is the Schultz method + + align:start position:0% + + + + align:start position:0% + +there's one codon for incorporating one + + align:start position:0% +there's one codon for incorporating one + + + align:start position:0% +there's one codon for incorporating one +unnatural amino acid and what they see + + align:start position:0% +unnatural amino acid and what they see + + + align:start position:0% +unnatural amino acid and what they see +is they get about 24% efficiency of full + + align:start position:0% +is they get about 24% efficiency of full + + + align:start position:0% +is they get about 24% efficiency of full +length fusion protein in Lane five we + + align:start position:0% +length fusion protein in Lane five we + + + align:start position:0% +length fusion protein in Lane five we +have the Schultz method with two here + + align:start position:0% +have the Schultz method with two here + + + align:start position:0% +have the Schultz method with two here +and we get about one percent efficiency + + align:start position:0% +and we get about one percent efficiency + + + align:start position:0% +and we get about one percent efficiency +in Lane seven analyzing the orthogonal + + align:start position:0% +in Lane seven analyzing the orthogonal + + + align:start position:0% +in Lane seven analyzing the orthogonal +ribosome Rybak's + + align:start position:0% +ribosome Rybak's + + + align:start position:0% +ribosome Rybak's +and one and what seen is sixty-four + + align:start position:0% +and one and what seen is sixty-four + + + align:start position:0% +and one and what seen is sixty-four +percent efficiency so quite an + + align:start position:0% +percent efficiency so quite an + + + align:start position:0% +percent efficiency so quite an +improvement there and then in Lane nine + + align:start position:0% +improvement there and then in Lane nine + + + align:start position:0% +improvement there and then in Lane nine +what we have is ribose with two and an + + align:start position:0% +what we have is ribose with two and an + + + align:start position:0% +what we have is ribose with two and an +efficiency of twenty-two percent here + + align:start position:0% +efficiency of twenty-two percent here + + + align:start position:0% +efficiency of twenty-two percent here +okay so here we're looking at the + + align:start position:0% +okay so here we're looking at the + + + align:start position:0% +okay so here we're looking at the +wild-type ribosome okay and here we're + + align:start position:0% +wild-type ribosome okay and here we're + + + align:start position:0% +wild-type ribosome okay and here we're +looking at the orthogonal ribosome + + align:start position:0% + + + + align:start position:0% + +orthogonal mRNA okay with the two + + align:start position:0% +orthogonal mRNA okay with the two + + + align:start position:0% +orthogonal mRNA okay with the two +mutations we saw before so these values + + align:start position:0% +mutations we saw before so these values + + + align:start position:0% +mutations we saw before so these values +come up from quantification of the data + + align:start position:0% +come up from quantification of the data + + + align:start position:0% +come up from quantification of the data +here right so you can convince yourself + + align:start position:0% +here right so you can convince yourself + + + align:start position:0% +here right so you can convince yourself +by comparing the band's for GST so + + align:start position:0% +by comparing the band's for GST so + + + align:start position:0% +by comparing the band's for GST so +resulting from + + align:start position:0% +resulting from + + + align:start position:0% +resulting from +Shadid phenotype translation termination + + align:start position:0% +Shadid phenotype translation termination + + + align:start position:0% +Shadid phenotype translation termination +and the bands for the fusion protein GST + + align:start position:0% +and the bands for the fusion protein GST + + + align:start position:0% +and the bands for the fusion protein GST +MVP okay + + align:start position:0% +MVP okay + + + align:start position:0% +MVP okay +so showing that there was successful + + align:start position:0% +so showing that there was successful + + + align:start position:0% +so showing that there was successful +suppression of the amber stop codon here + + align:start position:0% +suppression of the amber stop codon here + + + align:start position:0% +suppression of the amber stop codon here +right so what are the major conclusions + + align:start position:0% +right so what are the major conclusions + + + align:start position:0% +right so what are the major conclusions +right the major conclusion is that at + + align:start position:0% +right the major conclusion is that at + + + align:start position:0% +right the major conclusion is that at +least with this system what we see is + + align:start position:0% +least with this system what we see is + + + align:start position:0% +least with this system what we see is +that ribose has minimized this truncated + + align:start position:0% +that ribose has minimized this truncated + + + align:start position:0% +that ribose has minimized this truncated +peptide phenotype compared to the wild + + align:start position:0% +peptide phenotype compared to the wild + + + align:start position:0% +peptide phenotype compared to the wild +type ribosome okay and then it's been + + align:start position:0% +type ribosome okay and then it's been + + + align:start position:0% +type ribosome okay and then it's been +possible to basically diverge the + + align:start position:0% +possible to basically diverge the + + + align:start position:0% +possible to basically diverge the +decoding properties of the orthogonal + + align:start position:0% +decoding properties of the orthogonal + + + align:start position:0% +decoding properties of the orthogonal +ribosome from the endogenous cellular + + align:start position:0% +ribosome from the endogenous cellular + + + align:start position:0% +ribosome from the endogenous cellular +machinery so this percent here it that's + + align:start position:0% +machinery so this percent here it that's + + + align:start position:0% +machinery so this percent here it that's +the percent of the total Express protein + + align:start position:0% +the percent of the total Express protein + + + align:start position:0% +the percent of the total Express protein +let's delete the other you know 99% + + align:start position:0% +let's delete the other you know 99% + + + align:start position:0% +let's delete the other you know 99% +would have been the GST on the year yeah + + align:start position:0% +would have been the GST on the year yeah + + + align:start position:0% +would have been the GST on the year yeah +I mean so here for instance if we take a + + align:start position:0% +I mean so here for instance if we take a + + + align:start position:0% +I mean so here for instance if we take a +look at lane let's compare lanes three + + align:start position:0% +look at lane let's compare lanes three + + + align:start position:0% +look at lane let's compare lanes three +in lane five right so here's lane three + + align:start position:0% +in lane five right so here's lane three + + + align:start position:0% +in lane five right so here's lane three +and what do we see so in here we have + + align:start position:0% +and what do we see so in here we have + + + align:start position:0% +and what do we see so in here we have +one incorporation of one natural amino + + align:start position:0% +one incorporation of one natural amino + + + align:start position:0% +one incorporation of one natural amino +acid and we see that there's a band for + + align:start position:0% +acid and we see that there's a band for + + + align:start position:0% +acid and we see that there's a band for +the fusion protein and there's a band + + align:start position:0% +the fusion protein and there's a band + + + align:start position:0% +the fusion protein and there's a band +let me make sure I'm in the right lane I + + align:start position:0% +let me make sure I'm in the right lane I + + + align:start position:0% +let me make sure I'm in the right lane I +mean three and a band for GST itself + + align:start position:0% +mean three and a band for GST itself + + + align:start position:0% +mean three and a band for GST itself +right and the intensity of this band is + + align:start position:0% +right and the intensity of this band is + + + align:start position:0% +right and the intensity of this band is +greater than the intensity of that band + + align:start position:0% +greater than the intensity of that band + + + align:start position:0% +greater than the intensity of that band +and you can imagine doing quantitation + + align:start position:0% +and you can imagine doing quantitation + + + align:start position:0% +and you can imagine doing quantitation +whereas if we look at Lane five where + + align:start position:0% +whereas if we look at Lane five where + + + align:start position:0% +whereas if we look at Lane five where +we're trying to incorporate two by this + + align:start position:0% +we're trying to incorporate two by this + + + align:start position:0% +we're trying to incorporate two by this +method we see a band for GST and what do + + align:start position:0% +method we see a band for GST and what do + + + align:start position:0% +method we see a band for GST and what do +we see up here very little okay if we + + align:start position:0% +we see up here very little okay if we + + + align:start position:0% +we see up here very little okay if we +look at Lane seven we're seeing 64% Lane + + align:start position:0% +look at Lane seven we're seeing 64% Lane + + + align:start position:0% +look at Lane seven we're seeing 64% Lane +seven here right we see that we have + + align:start position:0% +seven here right we see that we have + + + align:start position:0% +seven here right we see that we have +this band for the GST MVP fusion and a + + align:start position:0% +this band for the GST MVP fusion and a + + + align:start position:0% +this band for the GST MVP fusion and a +weaker band for GST alone there so + + align:start position:0% +weaker band for GST alone there so + + + align:start position:0% +weaker band for GST alone there so +percent efficiency percent percent of + + align:start position:0% +percent efficiency percent percent of + + + align:start position:0% +percent efficiency percent percent of +the total + + align:start position:0% +the total + + + align:start position:0% +the total +so there's other things happening in + + align:start position:0% +so there's other things happening in + + + align:start position:0% +so there's other things happening in +this field so the schulz method and + + align:start position:0% +this field so the schulz method and + + + align:start position:0% +this field so the schulz method and +these orthogonal ribosomes are two + + align:start position:0% +these orthogonal ribosomes are two + + + align:start position:0% +these orthogonal ribosomes are two +examples and one thing that came up + + align:start position:0% +examples and one thing that came up + + + align:start position:0% +examples and one thing that came up +after this work with Rybak's was to + + align:start position:0% +after this work with Rybak's was to + + + align:start position:0% +after this work with Rybak's was to +design ribosomes that can use quadruplet + + align:start position:0% +design ribosomes that can use quadruplet + + + align:start position:0% +design ribosomes that can use quadruplet +codons rather than triplets so a lot of + + align:start position:0% +codons rather than triplets so a lot of + + + align:start position:0% +codons rather than triplets so a lot of +creativity + + align:start position:0% +creativity + + + align:start position:0% +creativity +and things to look up if you're curious + + align:start position:0% +and things to look up if you're curious + + + align:start position:0% +and things to look up if you're curious +but with that we're gonna close the + + align:start position:0% +but with that we're gonna close the + + + align:start position:0% +but with that we're gonna close the +translation module we will not leave the + + align:start position:0% +translation module we will not leave the + + + align:start position:0% +translation module we will not leave the +ribosome it will keep popping up + + align:start position:0% +ribosome it will keep popping up + + + align:start position:0% +ribosome it will keep popping up +throughout modules two and three but + + align:start position:0% +throughout modules two and three but + + + align:start position:0% +throughout modules two and three but +we're gonna move into what happens to a + + align:start position:0% +we're gonna move into what happens to a + + + align:start position:0% +we're gonna move into what happens to a +polypeptide as as its leaves the + + align:start position:0% +polypeptide as as its leaves the + + + align:start position:0% +polypeptide as as its leaves the +ribosome so how does it get its native + + align:start position:0% +ribosome so how does it get its native + + + align:start position:0% +ribosome so how does it get its native +fold and so what happens to nascent + + align:start position:0% +fold and so what happens to nascent + + + align:start position:0% +fold and so what happens to nascent +polypeptides you know emerging from the + + align:start position:0% +polypeptides you know emerging from the + + + align:start position:0% +polypeptides you know emerging from the +ribosome and how do polypeptides fold + + align:start position:0% +ribosome and how do polypeptides fold + + + align:start position:0% +ribosome and how do polypeptides fold +and so there's reading posted for module + + align:start position:0% +and so there's reading posted for module + + + align:start position:0% +and so there's reading posted for module +2 on stellar and listed here one + + align:start position:0% +2 on stellar and listed here one + + + align:start position:0% +2 on stellar and listed here one +required paper which is a really + + align:start position:0% +required paper which is a really + + + align:start position:0% +required paper which is a really +wonderful review that came out about two + + align:start position:0% +wonderful review that came out about two + + + align:start position:0% +wonderful review that came out about two +years ago so let's think about folding + + align:start position:0% +years ago so let's think about folding + + + align:start position:0% +years ago so let's think about folding +and as a point to thinking about that + + align:start position:0% +and as a point to thinking about that + + + align:start position:0% +and as a point to thinking about that +let's think about our ribosome okay and + + align:start position:0% +let's think about our ribosome okay and + + + align:start position:0% +let's think about our ribosome okay and +there's some emerging polypeptide chain + + align:start position:0% +there's some emerging polypeptide chain + + + align:start position:0% +there's some emerging polypeptide chain +so the nación polypeptide so what + + align:start position:0% +so the nación polypeptide so what + + + align:start position:0% +so the nación polypeptide so what +happens to this polypeptide and the + + align:start position:0% +happens to this polypeptide and the + + + align:start position:0% +happens to this polypeptide and the +first thing to keep in mind is something + + align:start position:0% +first thing to keep in mind is something + + + align:start position:0% +first thing to keep in mind is something +we need to think about is where is this + + align:start position:0% +we need to think about is where is this + + + align:start position:0% +we need to think about is where is this +polypeptide destined to go is this a + + align:start position:0% +polypeptide destined to go is this a + + + align:start position:0% +polypeptide destined to go is this a +polypeptide that will be in the + + align:start position:0% +polypeptide that will be in the + + + align:start position:0% +polypeptide that will be in the +cytoplasm is this a polypeptide that + + align:start position:0% +cytoplasm is this a polypeptide that + + + align:start position:0% +cytoplasm is this a polypeptide that +will become a membrane protein or part + + align:start position:0% +will become a membrane protein or part + + + align:start position:0% +will become a membrane protein or part +of the secretory system and so we can + + align:start position:0% +of the secretory system and so we can + + + align:start position:0% +of the secretory system and so we can +think about cytoplasmic protein ok + + align:start position:0% +think about cytoplasmic protein ok + + + align:start position:0% +think about cytoplasmic protein ok +versus membrane + + align:start position:0% + + + + align:start position:0% + +proteins or in eukaryotes the secretory + + align:start position:0% + + + + align:start position:0% + +here and so we're going to focus this + + align:start position:0% +here and so we're going to focus this + + + align:start position:0% +here and so we're going to focus this +module in terms of thinking about what's + + align:start position:0% +module in terms of thinking about what's + + + align:start position:0% +module in terms of thinking about what's +happening in the cytoplasm we might + + align:start position:0% +happening in the cytoplasm we might + + + align:start position:0% +happening in the cytoplasm we might +touch upon this if there's time but I + + align:start position:0% +touch upon this if there's time but I + + + align:start position:0% +touch upon this if there's time but I +think there won't be so the cytoplasmic + + align:start position:0% +think there won't be so the cytoplasmic + + + align:start position:0% +think there won't be so the cytoplasmic +proteins are folded by chaperones that + + align:start position:0% +proteins are folded by chaperones that + + + align:start position:0% +proteins are folded by chaperones that +they can come into contact with as + + align:start position:0% +they can come into contact with as + + + align:start position:0% +they can come into contact with as +they're emerging from the ribosome or + + align:start position:0% +they're emerging from the ribosome or + + + align:start position:0% +they're emerging from the ribosome or +also after the polypeptide is released + + align:start position:0% +also after the polypeptide is released + + + align:start position:0% +also after the polypeptide is released +to extracellular matrix proteins + + align:start position:0% +to extracellular matrix proteins + + + align:start position:0% +to extracellular matrix proteins +these categories I actually don't know + + align:start position:0% +these categories I actually don't know + + + align:start position:0% +these categories I actually don't know +Joanne weird to extracellular matrix + + align:start position:0% +Joanne weird to extracellular matrix + + + align:start position:0% +Joanne weird to extracellular matrix +proteins will they think of me inside + + align:start position:0% +proteins will they think of me inside + + + align:start position:0% +proteins will they think of me inside +the so mean and they can shut so do you + + align:start position:0% +the so mean and they can shut so do you + + + align:start position:0% +the so mean and they can shut so do you +should go talk to man shoulders you look + + align:start position:0% +should go talk to man shoulders you look + + + align:start position:0% +should go talk to man shoulders you look +at collagen put in your play yeah okay + + align:start position:0% +at collagen put in your play yeah okay + + + align:start position:0% +at collagen put in your play yeah okay +so these interact with a player called + + align:start position:0% +so these interact with a player called + + + align:start position:0% +so these interact with a player called +signal recognition particle which allows + + align:start position:0% +signal recognition particle which allows + + + align:start position:0% +signal recognition particle which allows +for targeting to the membrane or + + align:start position:0% +for targeting to the membrane or + + + align:start position:0% +for targeting to the membrane or +endoplasmic reticulum and eukaryotes + + align:start position:0% +endoplasmic reticulum and eukaryotes + + + align:start position:0% +endoplasmic reticulum and eukaryotes +okay and then folding folding can happen + + align:start position:0% +okay and then folding folding can happen + + + align:start position:0% +okay and then folding folding can happen +here so we're gonna be focused in the + + align:start position:0% +here so we're gonna be focused in the + + + align:start position:0% +here so we're gonna be focused in the +cytoplasm just realize there's other + + align:start position:0% +cytoplasm just realize there's other + + + align:start position:0% +cytoplasm just realize there's other +machineries involved for membrane + + align:start position:0% +machineries involved for membrane + + + align:start position:0% +machineries involved for membrane +proteins so here's just another view of + + align:start position:0% +proteins so here's just another view of + + + align:start position:0% +proteins so here's just another view of +our ribosome we saw this early on in the + + align:start position:0% +our ribosome we saw this early on in the + + + align:start position:0% +our ribosome we saw this early on in the +ribosome unit and want to think about + + align:start position:0% +ribosome unit and want to think about + + + align:start position:0% +ribosome unit and want to think about +this exit tunnel and the emerging + + align:start position:0% +this exit tunnel and the emerging + + + align:start position:0% +this exit tunnel and the emerging +polypeptide chain okay so it's the 50s + + align:start position:0% +polypeptide chain okay so it's the 50s + + + align:start position:0% +polypeptide chain okay so it's the 50s +subunit and as we discussed before this + + align:start position:0% +subunit and as we discussed before this + + + align:start position:0% +subunit and as we discussed before this +exit tunnel is long and it's also quite + + align:start position:0% +exit tunnel is long and it's also quite + + + align:start position:0% +exit tunnel is long and it's also quite +narrow and it's lined by both ribosomal + + align:start position:0% +narrow and it's lined by both ribosomal + + + align:start position:0% +narrow and it's lined by both ribosomal +RNA and proteins and I note a few of you + + align:start position:0% +RNA and proteins and I note a few of you + + + align:start position:0% +RNA and proteins and I note a few of you +asked about the hydrophobic residues of + + align:start position:0% +asked about the hydrophobic residues of + + + align:start position:0% +asked about the hydrophobic residues of +proteins that line this tunnel after + + align:start position:0% +proteins that line this tunnel after + + + align:start position:0% +proteins that line this tunnel after +lecture two and the thing to keep in + + align:start position:0% +lecture two and the thing to keep in + + + align:start position:0% +lecture two and the thing to keep in +mind is that it's not all hydrophobic + + align:start position:0% +mind is that it's not all hydrophobic + + + align:start position:0% +mind is that it's not all hydrophobic +there's also RNA there there will also + + align:start position:0% +there's also RNA there there will also + + + align:start position:0% +there's also RNA there there will also +be other residues and something just to + + align:start position:0% +be other residues and something just to + + + align:start position:0% +be other residues and something just to +think about like can water molecules get + + align:start position:0% +think about like can water molecules get + + + align:start position:0% +think about like can water molecules get +in there as well so we see for instance + + align:start position:0% +in there as well so we see for instance + + + align:start position:0% +in there as well so we see for instance +there's two proteins L 4 and L 22 that + + align:start position:0% +there's two proteins L 4 and L 22 that + + + align:start position:0% +there's two proteins L 4 and L 22 that +line part of the tunnel we have protein + + align:start position:0% +line part of the tunnel we have protein + + + align:start position:0% +line part of the tunnel we have protein +L 23 at the exit but there's also a lot + + align:start position:0% +L 23 at the exit but there's also a lot + + + align:start position:0% +L 23 at the exit but there's also a lot +of RNA there so don't don't forget that + + align:start position:0% +of RNA there so don't don't forget that + + + align:start position:0% +of RNA there so don't don't forget that +so a question just to address early on + + align:start position:0% +so a question just to address early on + + + align:start position:0% +so a question just to address early on +teen folding occur in the exit tunnel + + align:start position:0% +teen folding occur in the exit tunnel + + + align:start position:0% +teen folding occur in the exit tunnel +and I'd say this has been a bit of a + + align:start position:0% +and I'd say this has been a bit of a + + + align:start position:0% +and I'd say this has been a bit of a +controversial question over the years + + align:start position:0% +controversial question over the years + + + align:start position:0% +controversial question over the years +and there's been camps arguing both + + align:start position:0% +and there's been camps arguing both + + + align:start position:0% +and there's been camps arguing both +possibilities yes or no I think the + + align:start position:0% +possibilities yes or no I think the + + + align:start position:0% +possibilities yes or no I think the +thing to keep in mind is that the + + align:start position:0% +thing to keep in mind is that the + + + align:start position:0% +thing to keep in mind is that the +dimensions are limited right and + + align:start position:0% +dimensions are limited right and + + + align:start position:0% +dimensions are limited right and +although we can imagine some + + align:start position:0% +although we can imagine some + + + align:start position:0% +although we can imagine some +conformational flexibility and dynamics + + align:start position:0% +conformational flexibility and dynamics + + + align:start position:0% +conformational flexibility and dynamics +in this exit tunnel it can't undergo + + align:start position:0% +in this exit tunnel it can't undergo + + + align:start position:0% +in this exit tunnel it can't undergo +some tremendous change to say + + align:start position:0% +some tremendous change to say + + + align:start position:0% +some tremendous change to say +accommodate something like ubiquitin + + align:start position:0% +accommodate something like ubiquitin + + + align:start position:0% +accommodate something like ubiquitin +that you saw early on right that that + + align:start position:0% +that you saw early on right that that + + + align:start position:0% +that you saw early on right that that +doesn't just make sense so is it + + align:start position:0% +doesn't just make sense so is it + + + align:start position:0% +doesn't just make sense so is it +possible for some alpha helical fold to + + align:start position:0% +possible for some alpha helical fold to + + + align:start position:0% +possible for some alpha helical fold to +occur in this exit tunnel presumably + + align:start position:0% +occur in this exit tunnel presumably + + + align:start position:0% +occur in this exit tunnel presumably +there is some work that indicates + + align:start position:0% +there is some work that indicates + + + align:start position:0% +there is some work that indicates +there's folding zones and the exit + + align:start position:0% +there's folding zones and the exit + + + align:start position:0% +there's folding zones and the exit +tunnel so maybe some folding happens + + align:start position:0% +tunnel so maybe some folding happens + + + align:start position:0% +tunnel so maybe some folding happens +there but really the main conclusion is + + align:start position:0% +there but really the main conclusion is + + + align:start position:0% +there but really the main conclusion is +that most folding occurs outside of the + + align:start position:0% +that most folding occurs outside of the + + + align:start position:0% +that most folding occurs outside of the +ribosome and after the polypeptide + + align:start position:0% +ribosome and after the polypeptide + + + align:start position:0% +ribosome and after the polypeptide +emerges from the 50s here okay so if + + align:start position:0% +emerges from the 50s here okay so if + + + align:start position:0% +emerges from the 50s here okay so if +we're thinking about most folding of + + align:start position:0% +we're thinking about most folding of + + + align:start position:0% +we're thinking about most folding of +polypeptides as occurring in the + + align:start position:0% +polypeptides as occurring in the + + + align:start position:0% +polypeptides as occurring in the +cytoplasm for cytoplasmic proteins what + + align:start position:0% +cytoplasm for cytoplasmic proteins what + + + align:start position:0% +cytoplasm for cytoplasmic proteins what +we need to think about is that + + align:start position:0% +we need to think about is that + + + align:start position:0% +we need to think about is that +environment and we learned in the + + align:start position:0% +environment and we learned in the + + + align:start position:0% +environment and we learned in the +introductory lectures or had a reminder + + align:start position:0% +introductory lectures or had a reminder + + + align:start position:0% +introductory lectures or had a reminder +that the cellular environment is very + + align:start position:0% +that the cellular environment is very + + + align:start position:0% +that the cellular environment is very +crowded right so we have this issue of + + align:start position:0% +crowded right so we have this issue of + + + align:start position:0% +crowded right so we have this issue of +macromolecular crowding and in thinking + + align:start position:0% +macromolecular crowding and in thinking + + + align:start position:0% +macromolecular crowding and in thinking +about that we need to ask the question + + align:start position:0% +about that we need to ask the question + + + align:start position:0% +about that we need to ask the question +how does this emerging polypeptide fold + + align:start position:0% +how does this emerging polypeptide fold + + + align:start position:0% +how does this emerging polypeptide fold +to its native form in this type of + + align:start position:0% +to its native form in this type of + + + align:start position:0% +to its native form in this type of +environment what type of machinery is + + align:start position:0% +environment what type of machinery is + + + align:start position:0% +environment what type of machinery is +there to help protect it how is Miss + + align:start position:0% +there to help protect it how is Miss + + + align:start position:0% +there to help protect it how is Miss +folding avoided and intermolecular + + align:start position:0% +folding avoided and intermolecular + + + align:start position:0% +folding avoided and intermolecular +interactions that are non-productive + + align:start position:0% +interactions that are non-productive + + + align:start position:0% +interactions that are non-productive +avoided so where are we going to go in + + align:start position:0% +avoided so where are we going to go in + + + align:start position:0% +avoided so where are we going to go in +this module we're going to look at + + align:start position:0% +this module we're going to look at + + + align:start position:0% +this module we're going to look at +protein folding from both the in vitro + + align:start position:0% +protein folding from both the in vitro + + + align:start position:0% +protein folding from both the in vitro +test tube perspective and also from in + + align:start position:0% +test tube perspective and also from in + + + align:start position:0% +test tube perspective and also from in +the cell and so in thinking about + + align:start position:0% +the cell and so in thinking about + + + align:start position:0% +the cell and so in thinking about +protein folding in vitro we'll discuss + + align:start position:0% +protein folding in vitro we'll discuss + + + align:start position:0% +protein folding in vitro we'll discuss +some of the seminal study so Anthon + + align:start position:0% +some of the seminal study so Anthon + + + align:start position:0% +some of the seminal study so Anthon +scens hypothesis and folding of + + align:start position:0% +scens hypothesis and folding of + + + align:start position:0% +scens hypothesis and folding of +ribonuclease a + + align:start position:0% +ribonuclease a + + + align:start position:0% +ribonuclease a +eleven fellas paradox which brings us to + + align:start position:0% +eleven fellas paradox which brings us to + + + align:start position:0% +eleven fellas paradox which brings us to +thinking about energy landscapes and + + align:start position:0% +thinking about energy landscapes and + + + align:start position:0% +thinking about energy landscapes and +also touch upon some of the experimental + + align:start position:0% +also touch upon some of the experimental + + + align:start position:0% +also touch upon some of the experimental +methods that are employed and then in + + align:start position:0% +methods that are employed and then in + + + align:start position:0% +methods that are employed and then in +terms of machines we'll think about + + align:start position:0% +terms of machines we'll think about + + + align:start position:0% +terms of machines we'll think about +largely post-translational protein + + align:start position:0% +largely post-translational protein + + + align:start position:0% +largely post-translational protein +folding in the cytoplasm so grow al grow + + align:start position:0% +folding in the cytoplasm so grow al grow + + + align:start position:0% +folding in the cytoplasm so grow al grow +yes DNA k and j we'll also talk about a + + align:start position:0% +yes DNA k and j we'll also talk about a + + + align:start position:0% +yes DNA k and j we'll also talk about a +protein called trigger factor that + + align:start position:0% +protein called trigger factor that + + + align:start position:0% +protein called trigger factor that +associates with the ribosome and those + + align:start position:0% +associates with the ribosome and those + + + align:start position:0% +associates with the ribosome and those +nascent polypeptide chains okay so these + + align:start position:0% +nascent polypeptide chains okay so these + + + align:start position:0% +nascent polypeptide chains okay so these +machineries fold soluble proteins not + + align:start position:0% +machineries fold soluble proteins not + + + align:start position:0% +machineries fold soluble proteins not +membrane proteins and I'd also like to + + align:start position:0% +membrane proteins and I'd also like to + + + align:start position:0% +membrane proteins and I'd also like to +point out and again we may or may not + + align:start position:0% +point out and again we may or may not + + + align:start position:0% +point out and again we may or may not +get to these systems depending on time + + align:start position:0% +get to these systems depending on time + + + align:start position:0% +get to these systems depending on time +but in addition to these chaperones and + + align:start position:0% +but in addition to these chaperones and + + + align:start position:0% +but in addition to these chaperones and +macro molecular machines involved in + + align:start position:0% +macro molecular machines involved in + + + align:start position:0% +macro molecular machines involved in +folding there are classical enzymes that + + align:start position:0% +folding there are classical enzymes that + + + align:start position:0% +folding there are classical enzymes that +are really important and these include + + align:start position:0% +are really important and these include + + + align:start position:0% +are really important and these include +enzymes that say isomerize prolene also + + align:start position:0% +enzymes that say isomerize prolene also + + + align:start position:0% +enzymes that say isomerize prolene also +dial oxidases and isomerases there so + + align:start position:0% +dial oxidases and isomerases there so + + + align:start position:0% +dial oxidases and isomerases there so +what are our questions for this module + + align:start position:0% +what are our questions for this module + + + align:start position:0% +what are our questions for this module +so why and how our proteins folded and + + align:start position:0% +so why and how our proteins folded and + + + align:start position:0% +so why and how our proteins folded and +in terms of how in the lab versus in the + + align:start position:0% +in terms of how in the lab versus in the + + + align:start position:0% +in terms of how in the lab versus in the +cell classical enzymes and macro + + align:start position:0% +cell classical enzymes and macro + + + align:start position:0% +cell classical enzymes and macro +molecular machines what happens when + + align:start position:0% +molecular machines what happens when + + + align:start position:0% +molecular machines what happens when +proteins are Mis folded how does protein + + align:start position:0% +proteins are Mis folded how does protein + + + align:start position:0% +proteins are Mis folded how does protein +folding relate to disease what methods + + align:start position:0% +folding relate to disease what methods + + + align:start position:0% +folding relate to disease what methods +are employed to study these phenomenon + + align:start position:0% +are employed to study these phenomenon + + + align:start position:0% +are employed to study these phenomenon +and for the case studies we'll look at + + align:start position:0% +and for the case studies we'll look at + + + align:start position:0% +and for the case studies we'll look at +in terms of cytoplasmic players we want + + align:start position:0% +in terms of cytoplasmic players we want + + + align:start position:0% +in terms of cytoplasmic players we want +to understand really what are the + + align:start position:0% +to understand really what are the + + + align:start position:0% +to understand really what are the +structural properties of these different + + align:start position:0% +structural properties of these different + + + align:start position:0% +structural properties of these different +chaperones and their partners how do + + align:start position:0% +chaperones and their partners how do + + + align:start position:0% +chaperones and their partners how do +their structures relate to function how + + align:start position:0% +their structures relate to function how + + + align:start position:0% +their structures relate to function how +do they help peptides obtain the native + + align:start position:0% +do they help peptides obtain the native + + + align:start position:0% +do they help peptides obtain the native +fold and how good is our understanding + + align:start position:0% +fold and how good is our understanding + + + align:start position:0% +fold and how good is our understanding +of these systems will see in the case of + + align:start position:0% +of these systems will see in the case of + + + align:start position:0% +of these systems will see in the case of +DNA KJ it's actually pretty difficult to + + align:start position:0% +DNA KJ it's actually pretty difficult to + + + align:start position:0% +DNA KJ it's actually pretty difficult to +know what they're actually doing here + + align:start position:0% +know what they're actually doing here + + + align:start position:0% +know what they're actually doing here +and really what is the experimental + + align:start position:0% +and really what is the experimental + + + align:start position:0% +and really what is the experimental +basis for our understanding + + align:start position:0% + + + + align:start position:0% + +if we just take an overview of folding + + align:start position:0% +if we just take an overview of folding + + + align:start position:0% +if we just take an overview of folding +and misfolding and this is diagram for a + + align:start position:0% +and misfolding and this is diagram for a + + + align:start position:0% +and misfolding and this is diagram for a +eukaryotic cell and from many many + + align:start position:0% +eukaryotic cell and from many many + + + align:start position:0% +eukaryotic cell and from many many +different types of studies what do we + + align:start position:0% +different types of studies what do we + + + align:start position:0% +different types of studies what do we +see so we see that some sort of bio + + align:start position:0% +see so we see that some sort of bio + + + align:start position:0% +see so we see that some sort of bio +molecule called chaperon keeps coming up + + align:start position:0% +molecule called chaperon keeps coming up + + + align:start position:0% +molecule called chaperon keeps coming up +again and again so these are proteins + + align:start position:0% +again and again so these are proteins + + + align:start position:0% +again and again so these are proteins +that assist with folding or unfolding + + align:start position:0% +that assist with folding or unfolding + + + align:start position:0% +that assist with folding or unfolding +disaggregation right there's many + + align:start position:0% +disaggregation right there's many + + + align:start position:0% +disaggregation right there's many +possibilities for the trajectory of a + + align:start position:0% +possibilities for the trajectory of a + + + align:start position:0% +possibilities for the trajectory of a +protein here right so here we see a + + align:start position:0% +protein here right so here we see a + + + align:start position:0% +protein here right so here we see a +nascent polypeptide emerging from the + + align:start position:0% +nascent polypeptide emerging from the + + + align:start position:0% +nascent polypeptide emerging from the +ribosome and imagine that some folding + + align:start position:0% +ribosome and imagine that some folding + + + align:start position:0% +ribosome and imagine that some folding +intermediate is released so this is not + + align:start position:0% +intermediate is released so this is not + + + align:start position:0% +intermediate is released so this is not +fully at the native fold but it's + + align:start position:0% +fully at the native fold but it's + + + align:start position:0% +fully at the native fold but it's +somewhere along that pathway what might + + align:start position:0% +somewhere along that pathway what might + + + align:start position:0% +somewhere along that pathway what might +happen right here what we see is some + + align:start position:0% +happen right here what we see is some + + + align:start position:0% +happen right here what we see is some +chaperones allow this intermediate to + + align:start position:0% +chaperones allow this intermediate to + + + align:start position:0% +chaperones allow this intermediate to +form a native protein right but look + + align:start position:0% +form a native protein right but look + + + align:start position:0% +form a native protein right but look +there can also be unfolding and this + + align:start position:0% +there can also be unfolding and this + + + align:start position:0% +there can also be unfolding and this +could work its way back this native + + align:start position:0% +could work its way back this native + + + align:start position:0% +could work its way back this native +protein could unfold to a Miss folded + + align:start position:0% +protein could unfold to a Miss folded + + + align:start position:0% +protein could unfold to a Miss folded +state right we can think about + + align:start position:0% +state right we can think about + + + align:start position:0% +state right we can think about +remodeling and maybe there's chaperones + + align:start position:0% +remodeling and maybe there's chaperones + + + align:start position:0% +remodeling and maybe there's chaperones +involved in taking this miss folded + + align:start position:0% +involved in taking this miss folded + + + align:start position:0% +involved in taking this miss folded +state back to an intermediate that's on + + align:start position:0% +state back to an intermediate that's on + + + align:start position:0% +state back to an intermediate that's on +a productive path way what happens here + + align:start position:0% +a productive path way what happens here + + + align:start position:0% +a productive path way what happens here +maybe there's some trouble and rather + + align:start position:0% +maybe there's some trouble and rather + + + align:start position:0% +maybe there's some trouble and rather +than reaching its native fold this + + align:start position:0% +than reaching its native fold this + + + align:start position:0% +than reaching its native fold this +intermediate ends up aggregating okay it + + align:start position:0% +intermediate ends up aggregating okay it + + + align:start position:0% +intermediate ends up aggregating okay it +forms some sort of protein aggregate and + + align:start position:0% +forms some sort of protein aggregate and + + + align:start position:0% +forms some sort of protein aggregate and +maybe that can form oligomers or some + + align:start position:0% +maybe that can form oligomers or some + + + align:start position:0% +maybe that can form oligomers or some +sort of amyloid fibril like what we hear + + align:start position:0% +sort of amyloid fibril like what we hear + + + align:start position:0% +sort of amyloid fibril like what we hear +about with alzheimer's disease + + align:start position:0% +about with alzheimer's disease + + + align:start position:0% +about with alzheimer's disease +here we see their chaperones that can be + + align:start position:0% +here we see their chaperones that can be + + + align:start position:0% +here we see their chaperones that can be +involved in having disaggregates + + align:start position:0% +involved in having disaggregates + + + align:start position:0% +involved in having disaggregates +activity and they can help in breaking + + align:start position:0% +activity and they can help in breaking + + + align:start position:0% +activity and they can help in breaking +down these aggregates and getting back + + align:start position:0% +down these aggregates and getting back + + + align:start position:0% +down these aggregates and getting back +to to some productive place here okay so + + align:start position:0% +to to some productive place here okay so + + + align:start position:0% +to to some productive place here okay so +there's inherent complexity here and + + align:start position:0% +there's inherent complexity here and + + + align:start position:0% +there's inherent complexity here and +many players and relationships between + + align:start position:0% +many players and relationships between + + + align:start position:0% +many players and relationships between +protein misfolding and disease just to + + align:start position:0% +protein misfolding and disease just to + + + align:start position:0% +protein misfolding and disease just to +be aware of right so we typically think + + align:start position:0% +be aware of right so we typically think + + + align:start position:0% +be aware of right so we typically think +about the protein fold providing + + align:start position:0% +about the protein fold providing + + + align:start position:0% +about the protein fold providing +function and protein misfolding can + + align:start position:0% +function and protein misfolding can + + + align:start position:0% +function and protein misfolding can +result in improper function and there's + + align:start position:0% +result in improper function and there's + + + align:start position:0% +result in improper function and there's +many different types of improper + + align:start position:0% +many different types of improper + + + align:start position:0% +many different types of improper +function right it could be lots of fun + + align:start position:0% +function right it could be lots of fun + + + align:start position:0% +function right it could be lots of fun +it could be gain-of-function it could be + + align:start position:0% +it could be gain-of-function it could be + + + align:start position:0% +it could be gain-of-function it could be +formation of some sort of aggregate + + align:start position:0% +formation of some sort of aggregate + + + align:start position:0% +formation of some sort of aggregate +that's deleterious to the cell for one + + align:start position:0% +that's deleterious to the cell for one + + + align:start position:0% +that's deleterious to the cell for one +reason or another and if we just take a + + align:start position:0% +reason or another and if we just take a + + + align:start position:0% +reason or another and if we just take a +look in terms of human diseases that are + + align:start position:0% +look in terms of human diseases that are + + + align:start position:0% +look in terms of human diseases that are +associated with protein misfolding what + + align:start position:0% +associated with protein misfolding what + + + align:start position:0% +associated with protein misfolding what +do we see so there's examples out there + + align:start position:0% +do we see so there's examples out there + + + align:start position:0% +do we see so there's examples out there +like Alzheimer's Parkinson's familial + + align:start position:0% +like Alzheimer's Parkinson's familial + + + align:start position:0% +like Alzheimer's Parkinson's familial +ALS and mad cow + + align:start position:0% +ALS and mad cow + + + align:start position:0% +ALS and mad cow +so Alzheimer's disease is associated + + align:start position:0% +so Alzheimer's disease is associated + + + align:start position:0% +so Alzheimer's disease is associated +with formation of a beta plaques in the + + align:start position:0% +with formation of a beta plaques in the + + + align:start position:0% +with formation of a beta plaques in the +brain in Parkinson's there's a peptide + + align:start position:0% +brain in Parkinson's there's a peptide + + + align:start position:0% +brain in Parkinson's there's a peptide +called alpha synuclein that aggregates + + align:start position:0% +called alpha synuclein that aggregates + + + align:start position:0% +called alpha synuclein that aggregates +in familial ALS also called Lou Gehrig's + + align:start position:0% +in familial ALS also called Lou Gehrig's + + + align:start position:0% +in familial ALS also called Lou Gehrig's +disease there are single point mutations + + align:start position:0% +disease there are single point mutations + + + align:start position:0% +disease there are single point mutations +in an enzyme called superoxide dismutase + + align:start position:0% +in an enzyme called superoxide dismutase + + + align:start position:0% +in an enzyme called superoxide dismutase +that results in Mis folding and some + + align:start position:0% +that results in Mis folding and some + + + align:start position:0% +that results in Mis folding and some +negative consequences there and then Mis + + align:start position:0% +negative consequences there and then Mis + + + align:start position:0% +negative consequences there and then Mis +folding of the prion protein so a lot of + + align:start position:0% +folding of the prion protein so a lot of + + + align:start position:0% +folding of the prion protein so a lot of +these in terms of neurological disorders + + align:start position:0% +these in terms of neurological disorders + + + align:start position:0% +these in terms of neurological disorders +so in addition to fundamental studies + + align:start position:0% +so in addition to fundamental studies + + + align:start position:0% +so in addition to fundamental studies +there's significant interest in + + align:start position:0% +there's significant interest in + + + align:start position:0% +there's significant interest in +understanding protein misfolding + + align:start position:0% +understanding protein misfolding + + + align:start position:0% +understanding protein misfolding +from the standpoint of disease and + + align:start position:0% +from the standpoint of disease and + + + align:start position:0% +from the standpoint of disease and +prevention and I'll just note sometimes + + align:start position:0% +prevention and I'll just note sometimes + + + align:start position:0% +prevention and I'll just note sometimes +questions about natively unfolded + + align:start position:0% +questions about natively unfolded + + + align:start position:0% +questions about natively unfolded +proteins come up and those are outside + + align:start position:0% +proteins come up and those are outside + + + align:start position:0% +proteins come up and those are outside +of the scope of our discussions today + + align:start position:0% +of the scope of our discussions today + + + align:start position:0% +of the scope of our discussions today +but be aware there are proteins that are + + align:start position:0% +but be aware there are proteins that are + + + align:start position:0% +but be aware there are proteins that are +natively unfolded you saw a little bit + + align:start position:0% +natively unfolded you saw a little bit + + + align:start position:0% +natively unfolded you saw a little bit +about of that with some of the ribosomal + + align:start position:0% +about of that with some of the ribosomal + + + align:start position:0% +about of that with some of the ribosomal +proteins right that had those unfolded + + align:start position:0% +proteins right that had those unfolded + + + align:start position:0% +proteins right that had those unfolded +extensions going into the interior so in + + align:start position:0% +extensions going into the interior so in + + + align:start position:0% +extensions going into the interior so in +terms of thinking about protein folding + + align:start position:0% +terms of thinking about protein folding + + + align:start position:0% +terms of thinking about protein folding +in the test tube where we're going to + + align:start position:0% +in the test tube where we're going to + + + align:start position:0% +in the test tube where we're going to +begin is with anthem fins hypothesis and + + align:start position:0% +begin is with anthem fins hypothesis and + + + align:start position:0% +begin is with anthem fins hypothesis and +his seminal experiment on protein + + align:start position:0% +his seminal experiment on protein + + + align:start position:0% +his seminal experiment on protein +folding + + align:start position:0% + + + + align:start position:0% + +so anthen sin is responsible for the + + align:start position:0% +so anthen sin is responsible for the + + + align:start position:0% +so anthen sin is responsible for the +thermodynamic hypothesis of protein + + align:start position:0% +thermodynamic hypothesis of protein + + + align:start position:0% +thermodynamic hypothesis of protein +folding and he performed seminal + + align:start position:0% +folding and he performed seminal + + + align:start position:0% +folding and he performed seminal +experiments on a protein an enzyme + + align:start position:0% +experiments on a protein an enzyme + + + align:start position:0% +experiments on a protein an enzyme +called ribonuclease a and so what + + align:start position:0% +called ribonuclease a and so what + + + align:start position:0% +called ribonuclease a and so what +Amundsen hypothesized is that in terms + + align:start position:0% +Amundsen hypothesized is that in terms + + + align:start position:0% +Amundsen hypothesized is that in terms +of a protein shape or fold it's the + + align:start position:0% +of a protein shape or fold it's the + + + align:start position:0% +of a protein shape or fold it's the +primary sequence so the sequence of + + align:start position:0% +primary sequence so the sequence of + + + align:start position:0% +primary sequence so the sequence of +amino acids that dictates this final + + align:start position:0% +amino acids that dictates this final + + + align:start position:0% +amino acids that dictates this final +shape in aqueous solution so whatever + + align:start position:0% +shape in aqueous solution so whatever + + + align:start position:0% +shape in aqueous solution so whatever +that primary sequence is it dictates + + align:start position:0% +that primary sequence is it dictates + + + align:start position:0% +that primary sequence is it dictates +basically the array of possibilities and + + align:start position:0% +basically the array of possibilities and + + + align:start position:0% +basically the array of possibilities and +the thermodynamically most favorable + + align:start position:0% +the thermodynamically most favorable + + + align:start position:0% +the thermodynamically most favorable +result so what was the experiment and + + align:start position:0% +result so what was the experiment and + + + align:start position:0% +result so what was the experiment and +FinCEN did to probe this + + align:start position:0% + + + + align:start position:0% + +here what he did is look at denaturation + + align:start position:0% +here what he did is look at denaturation + + + align:start position:0% +here what he did is look at denaturation +and refolding of ribonuclease a okay so + + align:start position:0% +and refolding of ribonuclease a okay so + + + align:start position:0% +and refolding of ribonuclease a okay so +this enzyme Queens RNA single-stranded + + align:start position:0% + + + + align:start position:0% + +it's a hundred and twenty four amino + + align:start position:0% +it's a hundred and twenty four amino + + + align:start position:0% +it's a hundred and twenty four amino +acids in length and in the native form + + align:start position:0% +acids in length and in the native form + + + align:start position:0% +acids in length and in the native form +it contains four disulfide bonds here + + align:start position:0% +it contains four disulfide bonds here + + + align:start position:0% +it contains four disulfide bonds here +okay and since there's four disulfide + + align:start position:0% +okay and since there's four disulfide + + + align:start position:0% +okay and since there's four disulfide +bonds there's eight fifteens in the + + align:start position:0% +bonds there's eight fifteens in the + + + align:start position:0% +bonds there's eight fifteens in the +primary sequence right so two cysteine + + align:start position:0% +primary sequence right so two cysteine + + + align:start position:0% +primary sequence right so two cysteine +side chains can come together to form a + + align:start position:0% +side chains can come together to form a + + + align:start position:0% +side chains can come together to form a +disulfide + + align:start position:0% + + + + align:start position:0% + +okay and so if we think about a + + align:start position:0% +okay and so if we think about a + + + align:start position:0% +okay and so if we think about a +cysteines forming for disulfide bonds + + align:start position:0% +cysteines forming for disulfide bonds + + + align:start position:0% +cysteines forming for disulfide bonds +there's many possibilities in terms of + + align:start position:0% +there's many possibilities in terms of + + + align:start position:0% +there's many possibilities in terms of +how those cysteines are matched in the + + align:start position:0% +how those cysteines are matched in the + + + align:start position:0% +how those cysteines are matched in the +linkages so different regio isomers + + align:start position:0% +linkages so different regio isomers + + + align:start position:0% +linkages so different regio isomers +right over a hundred possible + + align:start position:0% +right over a hundred possible + + + align:start position:0% +right over a hundred possible +combinations of these eight cysteine to + + align:start position:0% +combinations of these eight cysteine to + + + align:start position:0% +combinations of these eight cysteine to +give four disulfides okay and only one + + align:start position:0% +give four disulfides okay and only one + + + align:start position:0% +give four disulfides okay and only one +regio isomer so one of these + + align:start position:0% +regio isomer so one of these + + + align:start position:0% +regio isomer so one of these +combinations is the native form here so + + align:start position:0% +combinations is the native form here so + + + align:start position:0% +combinations is the native form here so +one out of over a hundred so these + + align:start position:0% +one out of over a hundred so these + + + align:start position:0% +one out of over a hundred so these +native disulfide linkages that are + + align:start position:0% +native disulfide linkages that are + + + align:start position:0% +native disulfide linkages that are +formed endogenous li are required for + + align:start position:0% +formed endogenous li are required for + + + align:start position:0% +formed endogenous li are required for +activity so what was anthem sins + + align:start position:0% +activity so what was anthem sins + + + align:start position:0% +activity so what was anthem sins +experiment the experiment he did was to + + align:start position:0% +experiment the experiment he did was to + + + align:start position:0% +experiment the experiment he did was to +take native ribonuclease a and I'm gonna + + align:start position:0% +take native ribonuclease a and I'm gonna + + + align:start position:0% +take native ribonuclease a and I'm gonna +just sketch that + + align:start position:0% + + + + align:start position:0% + +so imagine we have the four disulfides + + align:start position:0% + + + + align:start position:0% + +okay here so first step one he reduced + + align:start position:0% +okay here so first step one he reduced + + + align:start position:0% +okay here so first step one he reduced +it so he added a reducing agent to + + align:start position:0% +it so he added a reducing agent to + + + align:start position:0% +it so he added a reducing agent to +reduce these disulfides we'll talk a + + align:start position:0% +reduce these disulfides we'll talk a + + + align:start position:0% +reduce these disulfides we'll talk a +little bit about more what that might be + + align:start position:0% +little bit about more what that might be + + + align:start position:0% +little bit about more what that might be +in a minute and so the end result is + + align:start position:0% + + + + align:start position:0% + +rather than having these disulfides we + + align:start position:0% +rather than having these disulfides we + + + align:start position:0% +rather than having these disulfides we +have eight free cysteines so free + + align:start position:0% +have eight free cysteines so free + + + align:start position:0% +have eight free cysteines so free +meaning not in a disulfide indicated by + + align:start position:0% +meaning not in a disulfide indicated by + + + align:start position:0% +meaning not in a disulfide indicated by +sh okay so this is reduced + + align:start position:0% + + + + align:start position:0% + +okay and so over the course of this + + align:start position:0% +okay and so over the course of this + + + align:start position:0% +okay and so over the course of this +Anthon s'en developed some assays to + + align:start position:0% +Anthon s'en developed some assays to + + + align:start position:0% +Anthon s'en developed some assays to +monitor for activity of this enzyme and + + align:start position:0% +monitor for activity of this enzyme and + + + align:start position:0% +monitor for activity of this enzyme and +what was found is that there is a loss + + align:start position:0% +what was found is that there is a loss + + + align:start position:0% +what was found is that there is a loss +of activity next step okay how did in + + align:start position:0% +of activity next step okay how did in + + + align:start position:0% +of activity next step okay how did in +nature in okay so at nature in is some + + align:start position:0% +nature in okay so at nature in is some + + + align:start position:0% +nature in okay so at nature in is some +chemical like urea or guanidinium that + + align:start position:0% +chemical like urea or guanidinium that + + + align:start position:0% +chemical like urea or guanidinium that +is going to disrupt the fold of the + + align:start position:0% +is going to disrupt the fold of the + + + align:start position:0% +is going to disrupt the fold of the +protein okay and in this case he used + + align:start position:0% +protein okay and in this case he used + + + align:start position:0% +protein okay and in this case he used +urea right so as this is sketched this + + align:start position:0% +urea right so as this is sketched this + + + align:start position:0% +urea right so as this is sketched this +is still folded but the dye sulfites are + + align:start position:0% +is still folded but the dye sulfites are + + + align:start position:0% +is still folded but the dye sulfites are +gone okay so what's the result here we + + align:start position:0% +gone okay so what's the result here we + + + align:start position:0% +gone okay so what's the result here we +get some unfolded polypeptide with the + + align:start position:0% +get some unfolded polypeptide with the + + + align:start position:0% +get some unfolded polypeptide with the +cysteine somewhere so this is denatured + + align:start position:0% + + + + align:start position:0% + +so we have no disulfides no native fold + + align:start position:0% + + + + align:start position:0% + +okay and inactive it can't cleave the + + align:start position:0% +okay and inactive it can't cleave the + + + align:start position:0% +okay and inactive it can't cleave the +single-stranded RNA + + align:start position:0% +single-stranded RNA + + + align:start position:0% +single-stranded RNA +okay so we've succeeded in destroying + + align:start position:0% +okay so we've succeeded in destroying + + + align:start position:0% +okay so we've succeeded in destroying +activity and destroying the fold of this + + align:start position:0% +activity and destroying the fold of this + + + align:start position:0% +activity and destroying the fold of this +protein what did he do next so the next + + align:start position:0% +protein what did he do next so the next + + + align:start position:0% +protein what did he do next so the next +experiment steps in this experiment was + + align:start position:0% +experiment steps in this experiment was + + + align:start position:0% +experiment steps in this experiment was +to ask okay if we start with this + + align:start position:0% +to ask okay if we start with this + + + align:start position:0% +to ask okay if we start with this +unfolded polypeptide that's completely + + align:start position:0% +unfolded polypeptide that's completely + + + align:start position:0% +unfolded polypeptide that's completely +denatured and there's no disulfides can + + align:start position:0% +denatured and there's no disulfides can + + + align:start position:0% +denatured and there's no disulfides can +it return to this native form by removal + + align:start position:0% +it return to this native form by removal + + + align:start position:0% +it return to this native form by removal +of the removal of the denature int and + + align:start position:0% +of the removal of the denature int and + + + align:start position:0% +of the removal of the denature int and +then allowing it to oxidize so imagine + + align:start position:0% +then allowing it to oxidize so imagine + + + align:start position:0% +then allowing it to oxidize so imagine +here we work backwards and step 3 you + + align:start position:0% +here we work backwards and step 3 you + + + align:start position:0% +here we work backwards and step 3 you +know remove + + align:start position:0% + + + + align:start position:0% + +remove the de nature and so how that + + align:start position:0% +remove the de nature and so how that + + + align:start position:0% +remove the de nature and so how that +might be done dialysis is a way to die + + align:start position:0% +might be done dialysis is a way to die + + + align:start position:0% +might be done dialysis is a way to die +Eliza way the de nature in and then what + + align:start position:0% +Eliza way the de nature in and then what + + + align:start position:0% +Eliza way the de nature in and then what +happens if we allow this to oxidize so + + align:start position:0% +happens if we allow this to oxidize so + + + align:start position:0% +happens if we allow this to oxidize so +for instance air oxidation here so what + + align:start position:0% +for instance air oxidation here so what + + + align:start position:0% +for instance air oxidation here so what +he found is that in this order of steps + + align:start position:0% +he found is that in this order of steps + + + align:start position:0% +he found is that in this order of steps +so that nature and sri moved and then + + align:start position:0% +so that nature and sri moved and then + + + align:start position:0% +so that nature and sri moved and then +the protein is allowed to oxidize that + + align:start position:0% +the protein is allowed to oxidize that + + + align:start position:0% +the protein is allowed to oxidize that +greater than 90% of the enzymatic + + align:start position:0% +greater than 90% of the enzymatic + + + align:start position:0% +greater than 90% of the enzymatic +activity was restored so you have this + + align:start position:0% +activity was restored so you have this + + + align:start position:0% +activity was restored so you have this +you know denatured polypeptide and + + align:start position:0% +you know denatured polypeptide and + + + align:start position:0% +you know denatured polypeptide and +dilute aqueous solution and work your + + align:start position:0% +dilute aqueous solution and work your + + + align:start position:0% +dilute aqueous solution and work your +way back and you can restore this + + align:start position:0% +way back and you can restore this + + + align:start position:0% +way back and you can restore this +activity question is still the same or + + align:start position:0% +activity question is still the same or + + + align:start position:0% +activity question is still the same or +similar and results in terms activity + + align:start position:0% +similar and results in terms activity + + + align:start position:0% +similar and results in terms activity +for that very yeah so how do we how + + align:start position:0% +for that very yeah so how do we how + + + align:start position:0% +for that very yeah so how do we how +could we confirm if the fold is + + align:start position:0% +could we confirm if the fold is + + + align:start position:0% +could we confirm if the fold is +perturbed what might be a method to do + + align:start position:0% +perturbed what might be a method to do + + + align:start position:0% +perturbed what might be a method to do +that circular dichroism so that's one + + align:start position:0% +that circular dichroism so that's one + + + align:start position:0% +that circular dichroism so that's one +possibility did he have that available + + align:start position:0% +possibility did he have that available + + + align:start position:0% +possibility did he have that available +that's another question that right that + + align:start position:0% +that's another question that right that + + + align:start position:0% +that's another question that right that +will give you a readout on Alpha helix + + align:start position:0% +will give you a readout on Alpha helix + + + align:start position:0% +will give you a readout on Alpha helix +II or beta sheet and that's one one + + align:start position:0% +II or beta sheet and that's one one + + + align:start position:0% +II or beta sheet and that's one one +possibility right you can imagine other + + align:start position:0% +possibility right you can imagine other + + + align:start position:0% +possibility right you can imagine other +possibilities maybe it would run + + align:start position:0% +possibilities maybe it would run + + + align:start position:0% +possibilities maybe it would run +differently on you know some form of + + align:start position:0% +differently on you know some form of + + + align:start position:0% +differently on you know some form of +column there as a possibility there was + + align:start position:0% +column there as a possibility there was + + + align:start position:0% +column there as a possibility there was +a loss of activity here yeah was it a + + align:start position:0% +a loss of activity here yeah was it a + + + align:start position:0% +a loss of activity here yeah was it a +hundred percent or less than a hundred + + align:start position:0% +hundred percent or less than a hundred + + + align:start position:0% +hundred percent or less than a hundred +percent I'm not sure about that detail + + align:start position:0% +percent I'm not sure about that detail + + + align:start position:0% +percent I'm not sure about that detail +Joanne jus + + align:start position:0% +Joanne jus + + + align:start position:0% +Joanne jus +you should before they deuce it's down + + align:start position:0% +you should before they deuce it's down + + + align:start position:0% +you should before they deuce it's down +there wait protein with a lot of + + align:start position:0% +there wait protein with a lot of + + + align:start position:0% +there wait protein with a lot of +disulfides in it they may not be + + align:start position:0% +disulfides in it they may not be + + + align:start position:0% +disulfides in it they may not be +accessible to read Upton mm-hmm I mean + + align:start position:0% +accessible to read Upton mm-hmm I mean + + + align:start position:0% +accessible to read Upton mm-hmm I mean +often it's done + + align:start position:0% +often it's done + + + align:start position:0% +often it's done +you add them together to get here right + + align:start position:0% +you add them together to get here right + + + align:start position:0% +you add them together to get here right +and he did a lot of experiments as well + + align:start position:0% +and he did a lot of experiments as well + + + align:start position:0% +and he did a lot of experiments as well +with additives so and then definitely in + + align:start position:0% +with additives so and then definitely in + + + align:start position:0% +with additives so and then definitely in +this direction + + align:start position:0% +this direction + + + align:start position:0% +this direction +my understanding is he performed this + + align:start position:0% +my understanding is he performed this + + + align:start position:0% +my understanding is he performed this +both ways so effectively if the denature + + align:start position:0% +both ways so effectively if the denature + + + align:start position:0% +both ways so effectively if the denature +it's removed first and then it oxidizes + + align:start position:0% +it's removed first and then it oxidizes + + + align:start position:0% +it's removed first and then it oxidizes +versus oxidizing it and then removing + + align:start position:0% +versus oxidizing it and then removing + + + align:start position:0% +versus oxidizing it and then removing +them in nature it and when it was that + + align:start position:0% +them in nature it and when it was that + + + align:start position:0% +them in nature it and when it was that +later scenario that the dye sulfites are + + align:start position:0% +later scenario that the dye sulfites are + + + align:start position:0% +later scenario that the dye sulfites are +allowed to form first the end result was + + align:start position:0% +allowed to form first the end result was + + + align:start position:0% +allowed to form first the end result was +a sample that had negligible activity + + align:start position:0% +a sample that had negligible activity + + + align:start position:0% +a sample that had negligible activity +less than 1% right and so from that you + + align:start position:0% +less than 1% right and so from that you + + + align:start position:0% +less than 1% right and so from that you +can imagine why because if this was + + align:start position:0% +can imagine why because if this was + + + align:start position:0% +can imagine why because if this was +allowed to oxidize right it's not + + align:start position:0% +allowed to oxidize right it's not + + + align:start position:0% +allowed to oxidize right it's not +pre-folded to allow the correct + + align:start position:0% +pre-folded to allow the correct + + + align:start position:0% +pre-folded to allow the correct +disulfides to form here entirely on its + + align:start position:0% +disulfides to form here entirely on its + + + align:start position:0% +disulfides to form here entirely on its +own + + align:start position:0% +own + + + align:start position:0% +own +yes oh isn't that incredible + + align:start position:0% + + + + align:start position:0% + +for this case I don't know and depending + + align:start position:0% +for this case I don't know and depending + + + align:start position:0% +for this case I don't know and depending +on the polypeptide it can vary you know + + align:start position:0% +on the polypeptide it can vary you know + + + align:start position:0% +on the polypeptide it can vary you know +from a short period of time we have + + align:start position:0% +from a short period of time we have + + + align:start position:0% +from a short period of time we have +examples in my lab where maybe in 30 + + align:start position:0% +examples in my lab where maybe in 30 + + + align:start position:0% +examples in my lab where maybe in 30 +minutes you can see the properly folded + + align:start position:0% +minutes you can see the properly folded + + + align:start position:0% +minutes you can see the properly folded +form today's or even faster than that + + align:start position:0% +form today's or even faster than that + + + align:start position:0% +form today's or even faster than that +depending like seconds two days + + align:start position:0% +depending like seconds two days + + + align:start position:0% +depending like seconds two days +depending on on the protein and the size + + align:start position:0% +depending on on the protein and the size + + + align:start position:0% +depending on on the protein and the size +yeah but that's what's really incredible + + align:start position:0% +yeah but that's what's really incredible + + + align:start position:0% +yeah but that's what's really incredible +about this experiment just beyond the + + align:start position:0% +about this experiment just beyond the + + + align:start position:0% +about this experiment just beyond the +details of the ordering and what + + align:start position:0% +details of the ordering and what + + + align:start position:0% +details of the ordering and what +happened is the fact that he could take + + align:start position:0% +happened is the fact that he could take + + + align:start position:0% +happened is the fact that he could take +this 124 residue polypeptide that needs + + align:start position:0% +this 124 residue polypeptide that needs + + + align:start position:0% +this 124 residue polypeptide that needs +to have four specific disulfides and + + align:start position:0% +to have four specific disulfides and + + + align:start position:0% +to have four specific disulfides and +just in dilute aqueous solution without + + align:start position:0% +just in dilute aqueous solution without + + + align:start position:0% +just in dilute aqueous solution without +any help you know - they're here + + align:start position:0% +any help you know - they're here + + + align:start position:0% +any help you know - they're here +it could come to its native fold right + + align:start position:0% +it could come to its native fold right + + + align:start position:0% +it could come to its native fold right +so this was support of this hypothesis + + align:start position:0% +so this was support of this hypothesis + + + align:start position:0% +so this was support of this hypothesis +that it's you know the primary sequence + + align:start position:0% +that it's you know the primary sequence + + + align:start position:0% +that it's you know the primary sequence +of a polypeptide that can dictate shape + + align:start position:0% +of a polypeptide that can dictate shape + + + align:start position:0% +of a polypeptide that can dictate shape +and if these polypeptides are allowed to + + align:start position:0% +and if these polypeptides are allowed to + + + align:start position:0% +and if these polypeptides are allowed to +fold under dilute conditions where + + align:start position:0% +fold under dilute conditions where + + + align:start position:0% +fold under dilute conditions where +intermolecular interactions aren't a + + align:start position:0% +intermolecular interactions aren't a + + + align:start position:0% +intermolecular interactions aren't a +problem they can achieve the + + align:start position:0% +problem they can achieve the + + + align:start position:0% +problem they can achieve the +thermodynamically most favorable result + + align:start position:0% + + + + align:start position:0% + +and he did plenty of additional + + align:start position:0% +and he did plenty of additional + + + align:start position:0% +and he did plenty of additional +experiments - in terms of putting + + align:start position:0% +experiments - in terms of putting + + + align:start position:0% +experiments - in terms of putting +additives in and asking how do these + + align:start position:0% +additives in and asking how do these + + + align:start position:0% +additives in and asking how do these +perturb the results here so what did he + + align:start position:0% +perturb the results here so what did he + + + align:start position:0% +perturb the results here so what did he +actually have to say from his experiment + + align:start position:0% +actually have to say from his experiment + + + align:start position:0% +actually have to say from his experiment +in his words the results suggest that + + align:start position:0% +in his words the results suggest that + + + align:start position:0% +in his words the results suggest that +the most that the native molecule is the + + align:start position:0% +the most that the native molecule is the + + + align:start position:0% +the most that the native molecule is the +most stable configuration + + align:start position:0% +most stable configuration + + + align:start position:0% +most stable configuration +thermodynamically speaking and the major + + align:start position:0% +thermodynamically speaking and the major + + + align:start position:0% +thermodynamically speaking and the major +force and the correct pairing of South + + align:start position:0% +force and the correct pairing of South + + + align:start position:0% +force and the correct pairing of South +hydral groups and disulfide linkages is + + align:start position:0% +hydral groups and disulfide linkages is + + + align:start position:0% +hydral groups and disulfide linkages is +the concerted interaction of sidechain + + align:start position:0% +the concerted interaction of sidechain + + + align:start position:0% +the concerted interaction of sidechain +functional groups distributed along the + + align:start position:0% +functional groups distributed along the + + + align:start position:0% +functional groups distributed along the +primary sequence so this primary + + align:start position:0% +primary sequence so this primary + + + align:start position:0% +primary sequence so this primary +sequence dictates the array of + + align:start position:0% +sequence dictates the array of + + + align:start position:0% +sequence dictates the array of +possibilities so in thinking about that + + align:start position:0% +possibilities so in thinking about that + + + align:start position:0% +possibilities so in thinking about that +that brings us to the paradox of the + + align:start position:0% +that brings us to the paradox of the + + + align:start position:0% +that brings us to the paradox of the +menthol here so he was thinking about + + align:start position:0% +menthol here so he was thinking about + + + align:start position:0% +menthol here so he was thinking about +this problem of protein folding and just + + align:start position:0% +this problem of protein folding and just + + + align:start position:0% +this problem of protein folding and just +thought well imagine we have one + + align:start position:0% +thought well imagine we have one + + + align:start position:0% +thought well imagine we have one +polypeptide with + + align:start position:0% +polypeptide with + + + align:start position:0% +polypeptide with +hundred amino acids so smaller than + + align:start position:0% +hundred amino acids so smaller than + + + align:start position:0% +hundred amino acids so smaller than +ribonuclease a what if each amino acid + + align:start position:0% +ribonuclease a what if each amino acid + + + align:start position:0% +ribonuclease a what if each amino acid +had only two possible confirmations what + + align:start position:0% +had only two possible confirmations what + + + align:start position:0% +had only two possible confirmations what +does that mean in terms of possibilities + + align:start position:0% +does that mean in terms of possibilities + + + align:start position:0% +does that mean in terms of possibilities +we have two to the 100th here so if that + + align:start position:0% +we have two to the 100th here so if that + + + align:start position:0% +we have two to the 100th here so if that +polypeptide were to sample every + + align:start position:0% +polypeptide were to sample every + + + align:start position:0% +polypeptide were to sample every +possible conformation during folding + + align:start position:0% +possible conformation during folding + + + align:start position:0% +possible conformation during folding +taking just a picosecond per transition + + align:start position:0% +taking just a picosecond per transition + + + align:start position:0% +taking just a picosecond per transition +the time required to fold the protein + + align:start position:0% +the time required to fold the protein + + + align:start position:0% +the time required to fold the protein +would be what and based on his + + align:start position:0% +would be what and based on his + + + align:start position:0% +would be what and based on his +back-of-the-envelope work here it would + + align:start position:0% +back-of-the-envelope work here it would + + + align:start position:0% +back-of-the-envelope work here it would +be ridiculous larger than the time of + + align:start position:0% +be ridiculous larger than the time of + + + align:start position:0% +be ridiculous larger than the time of +the universe right and that tells us + + align:start position:0% +the universe right and that tells us + + + align:start position:0% +the universe right and that tells us +that just can't be in terms of how we + + align:start position:0% +that just can't be in terms of how we + + + align:start position:0% +that just can't be in terms of how we +think about this here right so each + + align:start position:0% +think about this here right so each + + + align:start position:0% +think about this here right so each +amino acid can't adopt its shape + + align:start position:0% +amino acid can't adopt its shape + + + align:start position:0% +amino acid can't adopt its shape +independently that's just not working on + + align:start position:0% +independently that's just not working on + + + align:start position:0% +independently that's just not working on +a biological time scale so how do we + + align:start position:0% +a biological time scale so how do we + + + align:start position:0% +a biological time scale so how do we +think about this we can use energy and + + align:start position:0% +think about this we can use energy and + + + align:start position:0% +think about this we can use energy and +landscapes here so thinking about + + align:start position:0% +landscapes here so thinking about + + + align:start position:0% +landscapes here so thinking about +tumbling through hoes and valleys and so + + align:start position:0% +tumbling through hoes and valleys and so + + + align:start position:0% +tumbling through hoes and valleys and so +basically we can depict protein folding + + align:start position:0% +basically we can depict protein folding + + + align:start position:0% +basically we can depict protein folding +and this is an example say in a test + + align:start position:0% +and this is an example say in a test + + + align:start position:0% +and this is an example say in a test +tube where there's some ensemble of + + align:start position:0% +tube where there's some ensemble of + + + align:start position:0% +tube where there's some ensemble of +starting unfolded or partially folded + + align:start position:0% +starting unfolded or partially folded + + + align:start position:0% +starting unfolded or partially folded +structures and these are of higher + + align:start position:0% +structures and these are of higher + + + align:start position:0% +structures and these are of higher +energy and there'll be some sort of + + align:start position:0% +energy and there'll be some sort of + + + align:start position:0% +energy and there'll be some sort of +stochastic search and basically these + + align:start position:0% +stochastic search and basically these + + + align:start position:0% +stochastic search and basically these +forms will give us an ensemble of + + align:start position:0% +forms will give us an ensemble of + + + align:start position:0% +forms will give us an ensemble of +partially folded structures and + + align:start position:0% +partially folded structures and + + + align:start position:0% +partially folded structures and +ultimately converge to a native + + align:start position:0% +ultimately converge to a native + + + align:start position:0% +ultimately converge to a native +structure here that's of lower energy + + align:start position:0% +structure here that's of lower energy + + + align:start position:0% +structure here that's of lower energy +here for that okay so we have an + + align:start position:0% +here for that okay so we have an + + + align:start position:0% +here for that okay so we have an +ensemble of many denatured proteins that + + align:start position:0% +ensemble of many denatured proteins that + + + align:start position:0% +ensemble of many denatured proteins that +needs to make its way to the native form + + align:start position:0% +needs to make its way to the native form + + + align:start position:0% +needs to make its way to the native form +and just looking ahead a bit to our + + align:start position:0% +and just looking ahead a bit to our + + + align:start position:0% +and just looking ahead a bit to our +discussions of chaperones these proteins + + align:start position:0% +discussions of chaperones these proteins + + + align:start position:0% +discussions of chaperones these proteins +that assist in folding this is another + + align:start position:0% +that assist in folding this is another + + + align:start position:0% +that assist in folding this is another +view of an energy landscape but it's + + align:start position:0% +view of an energy landscape but it's + + + align:start position:0% +view of an energy landscape but it's +taking chaperones into account so we + + align:start position:0% +taking chaperones into account so we + + + align:start position:0% +taking chaperones into account so we +have energy here and this depiction is + + align:start position:0% +have energy here and this depiction is + + + align:start position:0% +have energy here and this depiction is +from the assigned reading it basically + + align:start position:0% +from the assigned reading it basically + + + align:start position:0% +from the assigned reading it basically +divides things up in terms of like + + align:start position:0% +divides things up in terms of like + + + align:start position:0% +divides things up in terms of like +productive intramolecular contacts + + align:start position:0% +productive intramolecular contacts + + + align:start position:0% +productive intramolecular contacts +versus intermolecular contacts + + align:start position:0% +versus intermolecular contacts + + + align:start position:0% +versus intermolecular contacts +lead to situations like oligomers and + + align:start position:0% +lead to situations like oligomers and + + + align:start position:0% +lead to situations like oligomers and +aggregates and fibrils so up here at + + align:start position:0% +aggregates and fibrils so up here at + + + align:start position:0% +aggregates and fibrils so up here at +high energy we have unfolded or + + align:start position:0% +high energy we have unfolded or + + + align:start position:0% +high energy we have unfolded or +partially folded species and what we see + + align:start position:0% +partially folded species and what we see + + + align:start position:0% +partially folded species and what we see +here bless you is that these chaperones + + align:start position:0% +here bless you is that these chaperones + + + align:start position:0% +here bless you is that these chaperones +are helping to allow these partially + + align:start position:0% +are helping to allow these partially + + + align:start position:0% +are helping to allow these partially +folded States to reach a native state by + + align:start position:0% +folded States to reach a native state by + + + align:start position:0% +folded States to reach a native state by +helping getting over these these + + align:start position:0% +helping getting over these these + + + align:start position:0% +helping getting over these these +barriers and the chaperones do not want + + align:start position:0% +barriers and the chaperones do not want + + + align:start position:0% +barriers and the chaperones do not want +to have the proteins going in this + + align:start position:0% +to have the proteins going in this + + + align:start position:0% +to have the proteins going in this +direction here two species that are + + align:start position:0% +direction here two species that are + + + align:start position:0% +direction here two species that are +potentially deleterious and result from + + align:start position:0% +potentially deleterious and result from + + + align:start position:0% +potentially deleterious and result from +intermolecular contact so oligomers + + align:start position:0% +intermolecular contact so oligomers + + + align:start position:0% +intermolecular contact so oligomers +fibrils and aggregates here what are + + align:start position:0% +fibrils and aggregates here what are + + + align:start position:0% +fibrils and aggregates here what are +some methods in terms of experimental + + align:start position:0% +some methods in terms of experimental + + + align:start position:0% +some methods in terms of experimental +methods for folding there are many that + + align:start position:0% +methods for folding there are many that + + + align:start position:0% +methods for folding there are many that +can be employed so you just need to take + + align:start position:0% +can be employed so you just need to take + + + align:start position:0% +can be employed so you just need to take +studies by a case-by-case basis commonly + + align:start position:0% +studies by a case-by-case basis commonly + + + align:start position:0% +studies by a case-by-case basis commonly +used fluorescence whether that be native + + align:start position:0% +used fluorescence whether that be native + + + align:start position:0% +used fluorescence whether that be native +emission from a protein so if you + + align:start position:0% +emission from a protein so if you + + + align:start position:0% +emission from a protein so if you +imagine you have say a tryptophan + + align:start position:0% +imagine you have say a tryptophan + + + align:start position:0% +imagine you have say a tryptophan +emission can vary depending on where it + + align:start position:0% +emission can vary depending on where it + + + align:start position:0% +emission can vary depending on where it +is in a protein methods like fret we + + align:start position:0% +is in a protein methods like fret we + + + align:start position:0% +is in a protein methods like fret we +just heard about circular dichroism + + align:start position:0% +just heard about circular dichroism + + + align:start position:0% +just heard about circular dichroism +which tells us about secondary structure + + align:start position:0% +which tells us about secondary structure + + + align:start position:0% +which tells us about secondary structure +NMR FTIR stop flow and there's a large + + align:start position:0% +NMR FTIR stop flow and there's a large + + + align:start position:0% +NMR FTIR stop flow and there's a large +field and computation in theory looking + + align:start position:0% +field and computation in theory looking + + + align:start position:0% +field and computation in theory looking +at protein folding as well what are some + + align:start position:0% +at protein folding as well what are some + + + align:start position:0% +at protein folding as well what are some +methods to denature a protein so here we + + align:start position:0% +methods to denature a protein so here we + + + align:start position:0% +methods to denature a protein so here we +saw urea used there's many others + + align:start position:0% +saw urea used there's many others + + + align:start position:0% +saw urea used there's many others +whether that be heat or pH and denatured + + align:start position:0% +whether that be heat or pH and denatured + + + align:start position:0% +whether that be heat or pH and denatured +protein means unfolded protein in the + + align:start position:0% +protein means unfolded protein in the + + + align:start position:0% +protein means unfolded protein in the +context of the lectures in this course + + align:start position:0% +context of the lectures in this course + + + align:start position:0% +context of the lectures in this course +so often studies in vitro start from + + align:start position:0% +so often studies in vitro start from + + + align:start position:0% +so often studies in vitro start from +using an unfolded protein sample and + + align:start position:0% +using an unfolded protein sample and + + + align:start position:0% +using an unfolded protein sample and +then you look at how folding progresses + + align:start position:0% +then you look at how folding progresses + + + align:start position:0% +then you look at how folding progresses +what are some lessons from in-vitro + + align:start position:0% +what are some lessons from in-vitro + + + align:start position:0% +what are some lessons from in-vitro +folding studies just to keep in mind one + + align:start position:0% +folding studies just to keep in mind one + + + align:start position:0% +folding studies just to keep in mind one +every proteins different - and even + + align:start position:0% +every proteins different - and even + + + align:start position:0% +every proteins different - and even +proteins that seem similar are very + + align:start position:0% +proteins that seem similar are very + + + align:start position:0% +proteins that seem similar are very +different you know so maybe they have + + align:start position:0% +different you know so maybe they have + + + align:start position:0% +different you know so maybe they have +the same secondary or tertiary structure + + align:start position:0% +the same secondary or tertiary structure + + + align:start position:0% +the same secondary or tertiary structure +some small peptide but when you try to + + align:start position:0% +some small peptide but when you try to + + + align:start position:0% +some small peptide but when you try to +fold them they may require different + + align:start position:0% +fold them they may require different + + + align:start position:0% +fold them they may require different +there are multi-dimensional energy + + align:start position:0% +there are multi-dimensional energy + + + align:start position:0% +there are multi-dimensional energy +landscapes like what we saw on the prior + + align:start position:0% +landscapes like what we saw on the prior + + + align:start position:0% +landscapes like what we saw on the prior +slides you can often see intermediates + + align:start position:0% +slides you can often see intermediates + + + align:start position:0% +slides you can often see intermediates +along the folding process and in dilute + + align:start position:0% +along the folding process and in dilute + + + align:start position:0% +along the folding process and in dilute +aqueous solution as anfinsen hypothesize + + align:start position:0% +aqueous solution as anfinsen hypothesize + + + align:start position:0% +aqueous solution as anfinsen hypothesize +primary sequence dictates fold just to + + align:start position:0% +primary sequence dictates fold just to + + + align:start position:0% +primary sequence dictates fold just to +note to anyone doing experimental work + + align:start position:0% +note to anyone doing experimental work + + + align:start position:0% +note to anyone doing experimental work +why do we like to use the ice bucket in + + align:start position:0% +why do we like to use the ice bucket in + + + align:start position:0% +why do we like to use the ice bucket in +the cold room when working with proteins + + align:start position:0% +the cold room when working with proteins + + + align:start position:0% +the cold room when working with proteins +and enzymes many native proteins are + + align:start position:0% +and enzymes many native proteins are + + + align:start position:0% +and enzymes many native proteins are +only marginally stable under + + align:start position:0% +only marginally stable under + + + align:start position:0% +only marginally stable under +physiological conditions so we can think + + align:start position:0% +physiological conditions so we can think + + + align:start position:0% +physiological conditions so we can think +about a delta g of denaturation per + + align:start position:0% +about a delta g of denaturation per + + + align:start position:0% +about a delta g of denaturation per +amino acid right so what this means is + + align:start position:0% +amino acid right so what this means is + + + align:start position:0% +amino acid right so what this means is +use your ice bucket and the cold room + + align:start position:0% +use your ice bucket and the cold room + + + align:start position:0% +use your ice bucket and the cold room +when working with your samples just + + align:start position:0% +when working with your samples just + + + align:start position:0% +when working with your samples just +closing thinking about protein folding + + align:start position:0% +closing thinking about protein folding + + + align:start position:0% +closing thinking about protein folding +in vitro verses and vivo do studies and + + align:start position:0% +in vitro verses and vivo do studies and + + + align:start position:0% +in vitro verses and vivo do studies and +vitro really enhance our understanding + + align:start position:0% +vitro really enhance our understanding + + + align:start position:0% +vitro really enhance our understanding +of what's happening in the cell just + + align:start position:0% +of what's happening in the cell just + + + align:start position:0% +of what's happening in the cell just +some observations to keep in mind so on + + align:start position:0% +some observations to keep in mind so on + + + align:start position:0% +some observations to keep in mind so on +the bench top folding can occur over a + + align:start position:0% +the bench top folding can occur over a + + + align:start position:0% +the bench top folding can occur over a +tremendous time skill from nanoseconds + + align:start position:0% +tremendous time skill from nanoseconds + + + align:start position:0% +tremendous time skill from nanoseconds +to hours I have here it can can be days + + align:start position:0% +to hours I have here it can can be days + + + align:start position:0% +to hours I have here it can can be days +depending on your peptide and conditions + + align:start position:0% +depending on your peptide and conditions + + + align:start position:0% +depending on your peptide and conditions +here the studies are generally performed + + align:start position:0% +here the studies are generally performed + + + align:start position:0% +here the studies are generally performed +in dilute buffer and in the absence of + + align:start position:0% +in dilute buffer and in the absence of + + + align:start position:0% +in dilute buffer and in the absence of +any additional protein so you have some + + align:start position:0% +any additional protein so you have some + + + align:start position:0% +any additional protein so you have some +pure polypeptide that you want to fold + + align:start position:0% +pure polypeptide that you want to fold + + + align:start position:0% +pure polypeptide that you want to fold +or study and that's what you work with + + align:start position:0% +or study and that's what you work with + + + align:start position:0% +or study and that's what you work with +and it's found that small proteins will + + align:start position:0% +and it's found that small proteins will + + + align:start position:0% +and it's found that small proteins will +often fold without assistance here so + + align:start position:0% +often fold without assistance here so + + + align:start position:0% +often fold without assistance here so +they don't need helpers in the cell how + + align:start position:0% +they don't need helpers in the cell how + + + align:start position:0% +they don't need helpers in the cell how +do we think about the rate of folding so + + align:start position:0% +do we think about the rate of folding so + + + align:start position:0% +do we think about the rate of folding so +from one point of view the rate of + + align:start position:0% +from one point of view the rate of + + + align:start position:0% +from one point of view the rate of +folding is limited by the rate of + + align:start position:0% +folding is limited by the rate of + + + align:start position:0% +folding is limited by the rate of +polypeptide biosynthesis and how quickly + + align:start position:0% +polypeptide biosynthesis and how quickly + + + align:start position:0% +polypeptide biosynthesis and how quickly +that polypeptide is emerging from the + + align:start position:0% +that polypeptide is emerging from the + + + align:start position:0% +that polypeptide is emerging from the +ribosome right if you're thinking about + + align:start position:0% +ribosome right if you're thinking about + + + align:start position:0% +ribosome right if you're thinking about +a nascent chain and we can think about + + align:start position:0% +a nascent chain and we can think about + + + align:start position:0% +a nascent chain and we can think about +the concentration of peptide coming off + + align:start position:0% +the concentration of peptide coming off + + + align:start position:0% +the concentration of peptide coming off +the ribosome which is often quoted as + + align:start position:0% +the ribosome which is often quoted as + + + align:start position:0% +the ribosome which is often quoted as +low micromolar + + align:start position:0% +low micromolar + + + align:start position:0% +low micromolar +and as I mentioned earlier we really + + align:start position:0% +and as I mentioned earlier we really + + + align:start position:0% +and as I mentioned earlier we really +need to keep in mind that this cellular + + align:start position:0% +need to keep in mind that this cellular + + + align:start position:0% +need to keep in mind that this cellular +environment is very crowded with many + + align:start position:0% +environment is very crowded with many + + + align:start position:0% +environment is very crowded with many +different biomolecules and player + + align:start position:0% +different biomolecules and player + + + align:start position:0% +different biomolecules and player +okay and as a consequence of this + + align:start position:0% +okay and as a consequence of this + + + align:start position:0% +okay and as a consequence of this +crowding there's many proteins that help + + align:start position:0% +crowding there's many proteins that help + + + align:start position:0% +crowding there's many proteins that help +in folding especially the chaperones + + align:start position:0% +in folding especially the chaperones + + + align:start position:0% +in folding especially the chaperones +we'll see that a number of these + + align:start position:0% +we'll see that a number of these + + + align:start position:0% +we'll see that a number of these +chaperones protect the polypeptide that + + align:start position:0% +chaperones protect the polypeptide that + + + align:start position:0% +chaperones protect the polypeptide that +needs to be folded from this environment + + align:start position:0% +needs to be folded from this environment + + + align:start position:0% +needs to be folded from this environment +here so a take-home is that just + + align:start position:0% +here so a take-home is that just + + + align:start position:0% +here so a take-home is that just +spontaneous protein folding in the cell + + align:start position:0% +spontaneous protein folding in the cell + + + align:start position:0% +spontaneous protein folding in the cell +is error-prone if it were to happen and + + align:start position:0% +is error-prone if it were to happen and + + + align:start position:0% +is error-prone if it were to happen and +that inter and intra molecular + + align:start position:0% +that inter and intra molecular + + + align:start position:0% +that inter and intra molecular +interactions are a big issue and so + + align:start position:0% +interactions are a big issue and so + + + align:start position:0% +interactions are a big issue and so +these chaperones are available to help + + align:start position:0% +these chaperones are available to help + + + align:start position:0% +these chaperones are available to help +overcome these issues here so where + + align:start position:0% +overcome these issues here so where + + + align:start position:0% +overcome these issues here so where +we'll begin on Monday is looking at + + align:start position:0% +we'll begin on Monday is looking at + + + align:start position:0% +we'll begin on Monday is looking at +trigger factors grow L grow yes and DNA + + align:start position:0% +trigger factors grow L grow yes and DNA + + + align:start position:0% +trigger factors grow L grow yes and DNA +KJ as an overview and then we'll work + + align:start position:0% +KJ as an overview and then we'll work + + + align:start position:0% +KJ as an overview and then we'll work +our way through these different systems + + align:start position:0% +our way through these different systems + + + align:start position:0% +our way through these different systems +for protein folding in the cytoplasm + + align:start position:0% +for protein folding in the cytoplasm + + + align:start position:0% +for protein folding in the cytoplasm +there + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/VkbtIDSHfSc.txt b/VkbtIDSHfSc.txt new file mode 100644 index 0000000000000000000000000000000000000000..dcd8c49aead1cd23326a7485e635aa6c1c68c0a4 --- /dev/null +++ b/VkbtIDSHfSc.txt @@ -0,0 +1,10771 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay so I hope you can hear me welcome + + align:start position:0% +okay so I hope you can hear me welcome + + + align:start position:0% +okay so I hope you can hear me welcome +back everybody + + align:start position:0% +back everybody + + + align:start position:0% +back everybody +I hope you have the full energy back + + align:start position:0% +I hope you have the full energy back + + + align:start position:0% +I hope you have the full energy back +from Thanksgiving vacation everybody + + align:start position:0% +from Thanksgiving vacation everybody + + + align:start position:0% +from Thanksgiving vacation everybody +welcome back + + align:start position:0% +welcome back + + + align:start position:0% +welcome back +so before we start talk about where we + + align:start position:0% +so before we start talk about where we + + + align:start position:0% +so before we start talk about where we +are now so this is actually the goal + + align:start position:0% +are now so this is actually the goal + + + align:start position:0% +are now so this is actually the goal +which we set for l3 at the beginning so + + align:start position:0% +which we set for l3 at the beginning so + + + align:start position:0% +which we set for l3 at the beginning so +what we have what we have been + + align:start position:0% +what we have what we have been + + + align:start position:0% +what we have what we have been +discussing is to learn about how to + + align:start position:0% +discussing is to learn about how to + + + align:start position:0% +discussing is to learn about how to +translate physical situations into + + align:start position:0% +translate physical situations into + + + align:start position:0% +translate physical situations into +mathematics see simple harmonic + + align:start position:0% +mathematics see simple harmonic + + + align:start position:0% +mathematics see simple harmonic +oscillator coupled oscillators etc and + + align:start position:0% +oscillator coupled oscillators etc and + + + align:start position:0% +oscillator coupled oscillators etc and +we try to put together infinite number + + align:start position:0% +we try to put together infinite number + + + align:start position:0% +we try to put together infinite number +of oscillators and we found waves from + + align:start position:0% +of oscillators and we found waves from + + + align:start position:0% +of oscillators and we found waves from +this this interesting exercise and of + + align:start position:0% +this this interesting exercise and of + + + align:start position:0% +this this interesting exercise and of +course we learned about food year + + align:start position:0% +course we learned about food year + + + align:start position:0% +course we learned about food year +decompositions of waves and also learned + + align:start position:0% +decompositions of waves and also learned + + + align:start position:0% +decompositions of waves and also learned +about how to put together physical + + align:start position:0% +about how to put together physical + + + align:start position:0% +about how to put together physical +systems in order to do that you need to + + align:start position:0% +systems in order to do that you need to + + + align:start position:0% +systems in order to do that you need to +define boundary conditions and those + + align:start position:0% +define boundary conditions and those + + + align:start position:0% +define boundary conditions and those +conditions need to be satisfied so that + + align:start position:0% +conditions need to be satisfied so that + + + align:start position:0% +conditions need to be satisfied so that +you can describe multiple physical + + align:start position:0% +you can describe multiple physical + + + align:start position:0% +you can describe multiple physical +systems all together and the third part + + align:start position:0% +systems all together and the third part + + + align:start position:0% +systems all together and the third part +of the course we have been focusing on + + align:start position:0% +of the course we have been focusing on + + + align:start position:0% +of the course we have been focusing on +many many applications for instance + + align:start position:0% +many many applications for instance + + + align:start position:0% +many many applications for instance +phenomena related to electromagnetic + + align:start position:0% +phenomena related to electromagnetic + + + align:start position:0% +phenomena related to electromagnetic +waves and those are many practical + + align:start position:0% +waves and those are many practical + + + align:start position:0% +waves and those are many practical +applications and optics and the pretty + + align:start position:0% +applications and optics and the pretty + + + align:start position:0% +applications and optics and the pretty +we are critical to the discussion + + align:start position:0% +we are critical to the discussion + + + align:start position:0% +we are critical to the discussion +between waves and vibrations and the + + align:start position:0% +between waves and vibrations and the + + + align:start position:0% +between waves and vibrations and the +future course which is there for the + + align:start position:0% +future course which is there for the + + + align:start position:0% +future course which is there for the +connections to quantum mechanics and if + + align:start position:0% +connections to quantum mechanics and if + + + align:start position:0% +connections to quantum mechanics and if +we have time we will talk about + + align:start position:0% +we have time we will talk about + + + align:start position:0% +we have time we will talk about +gravitational waves if we manage to do + + align:start position:0% +gravitational waves if we manage to do + + + align:start position:0% +gravitational waves if we manage to do +that okay it depends on how fast we + + align:start position:0% +that okay it depends on how fast we + + + align:start position:0% +that okay it depends on how fast we +travel okay so so let's start the + + align:start position:0% +travel okay so so let's start the + + + align:start position:0% +travel okay so so let's start the +lecture today so first we will give you + + align:start position:0% +lecture today so first we will give you + + + align:start position:0% +lecture today so first we will give you +a short review before the Thanksgiving + + align:start position:0% +a short review before the Thanksgiving + + + align:start position:0% +a short review before the Thanksgiving +we're talking about polarizer filters + + align:start position:0% +we're talking about polarizer filters + + + align:start position:0% +we're talking about polarizer filters +and we have been researching how to make + + align:start position:0% +and we have been researching how to make + + + align:start position:0% +and we have been researching how to make +a very good photo so that you can post + + align:start position:0% +a very good photo so that you can post + + + align:start position:0% +a very good photo so that you can post +Facebook right so that's essentially + + align:start position:0% +Facebook right so that's essentially + + + align:start position:0% +Facebook right so that's essentially +what we learned so if you want to take a + + align:start position:0% +what we learned so if you want to take a + + + align:start position:0% +what we learned so if you want to take a +picture of the sky which is the proo + + align:start position:0% +picture of the sky which is the proo + + + align:start position:0% +picture of the sky which is the proo +then you need to use the polarizer and + + align:start position:0% +then you need to use the polarizer and + + + align:start position:0% +then you need to use the polarizer and +the reason we also understand that this + + align:start position:0% +the reason we also understand that this + + + align:start position:0% +the reason we also understand that this +because if you do get the sky which is + + align:start position:0% +because if you do get the sky which is + + + align:start position:0% +because if you do get the sky which is +actually roughly 45 to 90 degrees away + + align:start position:0% +actually roughly 45 to 90 degrees away + + + align:start position:0% +actually roughly 45 to 90 degrees away +from the direction of the Sun basically + + align:start position:0% +from the direction of the Sun basically + + + align:start position:0% +from the direction of the Sun basically +what you get is you start all those as + + align:start position:0% +what you get is you start all those as + + + align:start position:0% +what you get is you start all those as +light from scattered in between the + + align:start position:0% +light from scattered in between the + + + align:start position:0% +light from scattered in between the +sunlight and the molecule or dito dust + + align:start position:0% +sunlight and the molecule or dito dust + + + align:start position:0% +sunlight and the molecule or dito dust +in the in the sky become polarized light + + align:start position:0% +in the in the sky become polarized light + + + align:start position:0% +in the in the sky become polarized light +therefore you can issue a filter then + + align:start position:0% +therefore you can issue a filter then + + + align:start position:0% +therefore you can issue a filter then +using the polarizer okay of course you + + align:start position:0% +using the polarizer okay of course you + + + align:start position:0% +using the polarizer okay of course you +have to tune your polarizer carefully so + + align:start position:0% +have to tune your polarizer carefully so + + + align:start position:0% +have to tune your polarizer carefully so +that you can issue the minimized the + + align:start position:0% +that you can issue the minimized the + + + align:start position:0% +that you can issue the minimized the +light from the sky so that you get + + align:start position:0% +light from the sky so that you get + + + align:start position:0% +light from the sky so that you get +sharper image photo and also we + + align:start position:0% +sharper image photo and also we + + + align:start position:0% +sharper image photo and also we +discussed about okay with polarizer + + align:start position:0% +discussed about okay with polarizer + + + align:start position:0% +discussed about okay with polarizer +polarization filter we can issue filter + + align:start position:0% +polarization filter we can issue filter + + + align:start position:0% +polarization filter we can issue filter +out also the refracted light for example + + align:start position:0% +out also the refracted light for example + + + align:start position:0% +out also the refracted light for example +from from the water or from the from the + + align:start position:0% +from from the water or from the from the + + + align:start position:0% +from from the water or from the from the +from the window car and that is because + + align:start position:0% +from the window car and that is because + + + align:start position:0% +from the window car and that is because +something which is closely related to + + align:start position:0% +something which is closely related to + + + align:start position:0% +something which is closely related to +the boundary condition which we learned + + align:start position:0% +the boundary condition which we learned + + + align:start position:0% +the boundary condition which we learned +about from Maxwell's equation in matter + + align:start position:0% +about from Maxwell's equation in matter + + + align:start position:0% +about from Maxwell's equation in matter +and this is actually the four equations + + align:start position:0% +and this is actually the four equations + + + align:start position:0% +and this is actually the four equations +which we discussed last time and the DA + + align:start position:0% +which we discussed last time and the DA + + + align:start position:0% +which we discussed last time and the DA +HD we were using that to explain the in + + align:start position:0% +HD we were using that to explain the in + + + align:start position:0% +HD we were using that to explain the in +certain light when from from air at were + + align:start position:0% +certain light when from from air at were + + + align:start position:0% +certain light when from from air at were +something which is denser for example + + align:start position:0% +something which is denser for example + + + align:start position:0% +something which is denser for example +that glass and we found that if we start + + align:start position:0% +that glass and we found that if we start + + + align:start position:0% +that glass and we found that if we start +with unpolarized light okay this + + align:start position:0% +with unpolarized light okay this + + + align:start position:0% +with unpolarized light okay this +incident wave is a polarized light what + + align:start position:0% +incident wave is a polarized light what + + + align:start position:0% +incident wave is a polarized light what +we found is that the transmitted wave + + align:start position:0% +we found is that the transmitted wave + + + align:start position:0% +we found is that the transmitted wave +which is actually in the pattern of this + + align:start position:0% +which is actually in the pattern of this + + + align:start position:0% +which is actually in the pattern of this +diagram essentially still kind of pretty + + align:start position:0% +diagram essentially still kind of pretty + + + align:start position:0% +diagram essentially still kind of pretty +close to a polarized light but the + + align:start position:0% +close to a polarized light but the + + + align:start position:0% +close to a polarized light but the +sightly polarized because of the + + align:start position:0% +sightly polarized because of the + + + align:start position:0% +sightly polarized because of the +transmission and the boundary condition + + align:start position:0% +transmission and the boundary condition + + + align:start position:0% +transmission and the boundary condition +and that the refracted light is actually + + align:start position:0% +and that the refracted light is actually + + + align:start position:0% +and that the refracted light is actually +something very interesting happen is + + align:start position:0% +something very interesting happen is + + + align:start position:0% +something very interesting happen is +that only the component which is + + align:start position:0% +that only the component which is + + + align:start position:0% +that only the component which is +actually polarizing the direction which + + align:start position:0% +actually polarizing the direction which + + + align:start position:0% +actually polarizing the direction which +such that the + + align:start position:0% +such that the + + + align:start position:0% +such that the +electric field is oscillating in a + + align:start position:0% +electric field is oscillating in a + + + align:start position:0% +electric field is oscillating in a +direction perpendicular to the surface + + align:start position:0% +direction perpendicular to the surface + + + align:start position:0% +direction perpendicular to the surface +of this of the slide was survive and + + align:start position:0% +of this of the slide was survive and + + + align:start position:0% +of this of the slide was survive and +that actually give you polarized light + + align:start position:0% +that actually give you polarized light + + + align:start position:0% +that actually give you polarized light +which researchers refracted from the + + align:start position:0% +which researchers refracted from the + + + align:start position:0% +which researchers refracted from the +surface and this interesting phenomenon + + align:start position:0% +surface and this interesting phenomenon + + + align:start position:0% +surface and this interesting phenomenon +reached the Maxima that you get to + + align:start position:0% +reached the Maxima that you get to + + + align:start position:0% +reached the Maxima that you get to +depolarize a light when you actually set + + align:start position:0% +depolarize a light when you actually set + + + align:start position:0% +depolarize a light when you actually set +the incident angle of the unpolarized + + align:start position:0% +the incident angle of the unpolarized + + + align:start position:0% +the incident angle of the unpolarized +tide at so called Brewster's angle and + + align:start position:0% +tide at so called Brewster's angle and + + + align:start position:0% +tide at so called Brewster's angle and +this process Ango is happening when the + + align:start position:0% +this process Ango is happening when the + + + align:start position:0% +this process Ango is happening when the +refracted light and the transmitted + + align:start position:0% +refracted light and the transmitted + + + align:start position:0% +refracted light and the transmitted +light direction actually they are + + align:start position:0% +light direction actually they are + + + align:start position:0% +light direction actually they are +orthogonal to each other and that should + + align:start position:0% +orthogonal to each other and that should + + + align:start position:0% +orthogonal to each other and that should +be give you the Maxima in fact we are + + align:start position:0% +be give you the Maxima in fact we are + + + align:start position:0% +be give you the Maxima in fact we are +looking for okay so that's actually what + + align:start position:0% +looking for okay so that's actually what + + + align:start position:0% +looking for okay so that's actually what +we have learned from electromagnetic + + align:start position:0% +we have learned from electromagnetic + + + align:start position:0% +we have learned from electromagnetic +wave in matter and also matching the + + align:start position:0% +wave in matter and also matching the + + + align:start position:0% +wave in matter and also matching the +boundary conditions between meetings + + align:start position:0% +boundary conditions between meetings + + + align:start position:0% +boundary conditions between meetings +between the electromagnetic waves inside + + align:start position:0% +between the electromagnetic waves inside + + + align:start position:0% +between the electromagnetic waves inside +the material and in the air such a we + + align:start position:0% +the material and in the air such a we + + + align:start position:0% +the material and in the air such a we +actually learn about all those intrusive + + align:start position:0% +actually learn about all those intrusive + + + align:start position:0% +actually learn about all those intrusive +when am not and basically we have + + align:start position:0% +when am not and basically we have + + + align:start position:0% +when am not and basically we have +learned how to describe electromagnetic + + align:start position:0% +learned how to describe electromagnetic + + + align:start position:0% +learned how to describe electromagnetic +waves how to add electromagnetic waves + + align:start position:0% +waves how to add electromagnetic waves + + + align:start position:0% +waves how to add electromagnetic waves +together how they propagate okay from + + align:start position:0% +together how they propagate okay from + + + align:start position:0% +together how they propagate okay from +one position to the other position and + + align:start position:0% +one position to the other position and + + + align:start position:0% +one position to the other position and +how the boundary condition works in the + + align:start position:0% +how the boundary condition works in the + + + align:start position:0% +how the boundary condition works in the +equation of motion etc and something + + align:start position:0% +equation of motion etc and something + + + align:start position:0% +equation of motion etc and something +related to dielectrics material and + + align:start position:0% +related to dielectrics material and + + + align:start position:0% +related to dielectrics material and +today what we are going to do is to put + + align:start position:0% +today what we are going to do is to put + + + align:start position:0% +today what we are going to do is to put +all the things we have learned together + + align:start position:0% +all the things we have learned together + + + align:start position:0% +all the things we have learned together +and see if we can actually explain a + + align:start position:0% +and see if we can actually explain a + + + align:start position:0% +and see if we can actually explain a +very interesting phenomena so before I + + align:start position:0% +very interesting phenomena so before I + + + align:start position:0% +very interesting phenomena so before I +start I will show you a demonstration + + align:start position:0% +start I will show you a demonstration + + + align:start position:0% +start I will show you a demonstration +which I'm not sure if I was a that would + + align:start position:0% +which I'm not sure if I was a that would + + + align:start position:0% +which I'm not sure if I was a that would +be successful it's very difficult + + align:start position:0% +be successful it's very difficult + + + align:start position:0% +be successful it's very difficult +actually and of course during the break + + align:start position:0% +actually and of course during the break + + + align:start position:0% +actually and of course during the break +you can come you are welcome to come + + align:start position:0% +you can come you are welcome to come + + + align:start position:0% +you can come you are welcome to come +over and I pray with all those demos and + + align:start position:0% +over and I pray with all those demos and + + + align:start position:0% +over and I pray with all those demos and +here I have two sticks and I am going to + + align:start position:0% +here I have two sticks and I am going to + + + align:start position:0% +here I have two sticks and I am going to +create a soap bubble okay + + align:start position:0% +create a soap bubble okay + + + align:start position:0% +create a soap bubble okay +from this soap cutter and they see if I + + align:start position:0% +from this soap cutter and they see if I + + + align:start position:0% +from this soap cutter and they see if I +will be I will make it or not + + align:start position:0% +will be I will make it or not + + + align:start position:0% +will be I will make it or not +so basically I put this into the soap + + align:start position:0% +so basically I put this into the soap + + + align:start position:0% +so basically I put this into the soap +soapy water and I would try and to try + + align:start position:0% +soapy water and I would try and to try + + + align:start position:0% +soapy water and I would try and to try +to open it and to see if I can create a + + align:start position:0% +to open it and to see if I can create a + + + align:start position:0% +to open it and to see if I can create a +bubble yeah you can see we you can see + + align:start position:0% +bubble yeah you can see we you can see + + + align:start position:0% +bubble yeah you can see we you can see +that there's a colorful soap bubble + + align:start position:0% +that there's a colorful soap bubble + + + align:start position:0% +that there's a colorful soap bubble +created oh you can see that it's not + + align:start position:0% +created oh you can see that it's not + + + align:start position:0% +created oh you can see that it's not +always easy who is getting very messy + + align:start position:0% +always easy who is getting very messy + + + align:start position:0% +always easy who is getting very messy +now I'm trying to destroy the classroom + + align:start position:0% +now I'm trying to destroy the classroom + + + align:start position:0% +now I'm trying to destroy the classroom +but it's okay because we are an IT you + + align:start position:0% +but it's okay because we are an IT you + + + align:start position:0% +but it's okay because we are an IT you +can see that it's really beautiful + + align:start position:0% +can see that it's really beautiful + + + align:start position:0% +can see that it's really beautiful +it's colorful okay ready for a while + + align:start position:0% +it's colorful okay ready for a while + + + align:start position:0% +it's colorful okay ready for a while +then then it breaks okay and of course + + align:start position:0% +then then it breaks okay and of course + + + align:start position:0% +then then it breaks okay and of course +during the break you are welcome to to + + align:start position:0% +during the break you are welcome to to + + + align:start position:0% +during the break you are welcome to to +do this and this actually non-trivial to + + align:start position:0% +do this and this actually non-trivial to + + + align:start position:0% +do this and this actually non-trivial to +create this size of wow okay so the + + align:start position:0% +create this size of wow okay so the + + + align:start position:0% +create this size of wow okay so the +success rate is like 50 percent okay so + + align:start position:0% +success rate is like 50 percent okay so + + + align:start position:0% +success rate is like 50 percent okay so +as you can see from this demonstration + + align:start position:0% + + + + align:start position:0% + +we see something really beautiful this + + align:start position:0% +we see something really beautiful this + + + align:start position:0% +we see something really beautiful this +bubble is colorful right and and I + + align:start position:0% +bubble is colorful right and and I + + + align:start position:0% +bubble is colorful right and and I +didn't shine this but this so purple by + + align:start position:0% +didn't shine this but this so purple by + + + align:start position:0% +didn't shine this but this so purple by +all kinds of different preset colors + + align:start position:0% +all kinds of different preset colors + + + align:start position:0% +all kinds of different preset colors +right so so it appear automatically I am + + align:start position:0% +right so so it appear automatically I am + + + align:start position:0% +right so so it appear automatically I am +just shining it with all kinds of + + align:start position:0% +just shining it with all kinds of + + + align:start position:0% +just shining it with all kinds of +different + + align:start position:0% +different + + + align:start position:0% +different +whyever wavelengths I'd get from you you + + align:start position:0% +whyever wavelengths I'd get from you you + + + align:start position:0% +whyever wavelengths I'd get from you you +don't find life set in here okay pretty + + align:start position:0% +don't find life set in here okay pretty + + + align:start position:0% +don't find life set in here okay pretty +bright light on my face and you can see + + align:start position:0% +bright light on my face and you can see + + + align:start position:0% +bright light on my face and you can see +that it becomes colorful and we are + + align:start position:0% +that it becomes colorful and we are + + + align:start position:0% +that it becomes colorful and we are +going to understand what is going on and + + align:start position:0% +going to understand what is going on and + + + align:start position:0% +going to understand what is going on and +what where this color is coming coming + + align:start position:0% +what where this color is coming coming + + + align:start position:0% +what where this color is coming coming +from okay and and the good news is that + + align:start position:0% +from okay and and the good news is that + + + align:start position:0% +from okay and and the good news is that +based on the knowledge we have learned + + align:start position:0% +based on the knowledge we have learned + + + align:start position:0% +based on the knowledge we have learned +we can we are in a very good position to + + align:start position:0% +we can we are in a very good position to + + + align:start position:0% +we can we are in a very good position to +understand this phenomena + + align:start position:0% +understand this phenomena + + + align:start position:0% +understand this phenomena +so before we start to explain this + + align:start position:0% +so before we start to explain this + + + align:start position:0% +so before we start to explain this +phenomena I would like to talk about a + + align:start position:0% +phenomena I would like to talk about a + + + align:start position:0% +phenomena I would like to talk about a +phenomena so called interference okay + + align:start position:0% +phenomena so called interference okay + + + align:start position:0% +phenomena so called interference okay +so suppose we have to electromagnetic + + align:start position:0% +so suppose we have to electromagnetic + + + align:start position:0% +so suppose we have to electromagnetic +wave we can actually add them together + + align:start position:0% +wave we can actually add them together + + + align:start position:0% +wave we can actually add them together +because of superposition principle so + + align:start position:0% +because of superposition principle so + + + align:start position:0% +because of superposition principle so +what we can do is that suppose I have to + + align:start position:0% +what we can do is that suppose I have to + + + align:start position:0% +what we can do is that suppose I have to +in electro electric field e1 is actually + + align:start position:0% +in electro electric field e1 is actually + + + align:start position:0% +in electro electric field e1 is actually +a is defined as a1 cosine Omega t minus + + align:start position:0% +a is defined as a1 cosine Omega t minus + + + align:start position:0% +a is defined as a1 cosine Omega t minus +KZ plus Phi 1 in the X direction so by + + align:start position:0% +KZ plus Phi 1 in the X direction so by + + + align:start position:0% +KZ plus Phi 1 in the X direction so by +now you should know that this is a + + align:start position:0% +now you should know that this is a + + + align:start position:0% +now you should know that this is a +should electro electric field + + align:start position:0% +should electro electric field + + + align:start position:0% +should electro electric field +propagating at the angular frequency + + align:start position:0% +propagating at the angular frequency + + + align:start position:0% +propagating at the angular frequency +Omega with web with number K going to + + align:start position:0% +Omega with web with number K going to + + + align:start position:0% +Omega with web with number K going to +work positive Z direction we and the + + align:start position:0% +work positive Z direction we and the + + + align:start position:0% +work positive Z direction we and the +electric field is perpendicular to the + + align:start position:0% +electric field is perpendicular to the + + + align:start position:0% +electric field is perpendicular to the +direction of propagation in the current + + align:start position:0% +direction of propagation in the current + + + align:start position:0% +direction of propagation in the current +in the X direction and the wire and also + + align:start position:0% +in the X direction and the wire and also + + + align:start position:0% +in the X direction and the wire and also +this is edge of my electric field have a + + align:start position:0% +this is edge of my electric field have a + + + align:start position:0% +this is edge of my electric field have a +face of Phi 1 okay so that's it should + + align:start position:0% +face of Phi 1 okay so that's it should + + + align:start position:0% +face of Phi 1 okay so that's it should +be what we know already by now what does + + align:start position:0% +be what we know already by now what does + + + align:start position:0% +be what we know already by now what does +this mean this expression me and this + + align:start position:0% +this mean this expression me and this + + + align:start position:0% +this mean this expression me and this +issue the harmonic also dating electric + + align:start position:0% +issue the harmonic also dating electric + + + align:start position:0% +issue the harmonic also dating electric +electric field and of course since I am + + align:start position:0% +electric field and of course since I am + + + align:start position:0% +electric field and of course since I am +talking about interference basically I + + align:start position:0% +talking about interference basically I + + + align:start position:0% +talking about interference basically I +can add this the first electric field at + + align:start position:0% +can add this the first electric field at + + + align:start position:0% +can add this the first electric field at +and the fact a second user to feel + + align:start position:0% +and the fact a second user to feel + + + align:start position:0% +and the fact a second user to feel +together and see what happened so now if + + align:start position:0% +together and see what happened so now if + + + align:start position:0% +together and see what happened so now if +I define the second electric field to be + + align:start position:0% +I define the second electric field to be + + + align:start position:0% +I define the second electric field to be +a 2 which is the amplitude cosine Omega + + align:start position:0% +a 2 which is the amplitude cosine Omega + + + align:start position:0% +a 2 which is the amplitude cosine Omega +t minus KZ basically did lie helpless + + align:start position:0% +t minus KZ basically did lie helpless + + + align:start position:0% +t minus KZ basically did lie helpless +and wavelengths and also the angular + + align:start position:0% +and wavelengths and also the angular + + + align:start position:0% +and wavelengths and also the angular +frequency plus Phi 2 but they have + + align:start position:0% +frequency plus Phi 2 but they have + + + align:start position:0% +frequency plus Phi 2 but they have +different phase and of course they in + + align:start position:0% +different phase and of course they in + + + align:start position:0% +different phase and of course they in +this set I asked them to be pointing to + + align:start position:0% +this set I asked them to be pointing to + + + align:start position:0% +this set I asked them to be pointing to +the same direction which the X direction + + align:start position:0% +the same direction which the X direction + + + align:start position:0% +the same direction which the X direction +okay so we were wondering what is going + + align:start position:0% +okay so we were wondering what is going + + + align:start position:0% +okay so we were wondering what is going +to happen if I super if I consider the + + align:start position:0% +to happen if I super if I consider the + + + align:start position:0% +to happen if I super if I consider the +superposition of this two electric field + + align:start position:0% +superposition of this two electric field + + + align:start position:0% +superposition of this two electric field +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and the total electric field which is + + align:start position:0% +and the total electric field which is + + + align:start position:0% +and the total electric field which is +called the e vector is I should the e1 + + align:start position:0% +called the e vector is I should the e1 + + + align:start position:0% +called the e vector is I should the e1 +plus e2 + + align:start position:0% +plus e2 + + + align:start position:0% +plus e2 +okay so before that I would like to + + align:start position:0% +okay so before that I would like to + + + align:start position:0% +okay so before that I would like to +remind you about pointing vector and + + align:start position:0% +remind you about pointing vector and + + + align:start position:0% +remind you about pointing vector and +also the the so called intensity so + + align:start position:0% +also the the so called intensity so + + + align:start position:0% +also the the so called intensity so +pointing vector is actually defined as + + align:start position:0% +pointing vector is actually defined as + + + align:start position:0% +pointing vector is actually defined as +this X vector pointing vector is equal + + align:start position:0% +this X vector pointing vector is equal + + + align:start position:0% +this X vector pointing vector is equal +to 1 over mu 0 equals P all right so + + align:start position:0% +to 1 over mu 0 equals P all right so + + + align:start position:0% +to 1 over mu 0 equals P all right so +this is actually the directional flux of + + align:start position:0% +this is actually the directional flux of + + + align:start position:0% +this is actually the directional flux of +energy per unit area right so that this + + align:start position:0% +energy per unit area right so that this + + + align:start position:0% +energy per unit area right so that this +issue the the the pointing vector which + + align:start position:0% +issue the the the pointing vector which + + + align:start position:0% +issue the the the pointing vector which +we have been using for for a while and + + align:start position:0% +we have been using for for a while and + + + align:start position:0% +we have been using for for a while and +also a another reminder is that given + + align:start position:0% +also a another reminder is that given + + + align:start position:0% +also a another reminder is that given +the electric field electric field which + + align:start position:0% +the electric field electric field which + + + align:start position:0% +the electric field electric field which +is a show the harmonic purple focusing + + align:start position:0% +is a show the harmonic purple focusing + + + align:start position:0% +is a show the harmonic purple focusing +wave the corresponding P field will be + + align:start position:0% +wave the corresponding P field will be + + + align:start position:0% +wave the corresponding P field will be +equal to a 1 over V V is actually the + + align:start position:0% +equal to a 1 over V V is actually the + + + align:start position:0% +equal to a 1 over V V is actually the +speed of the light in some specific + + align:start position:0% +speed of the light in some specific + + + align:start position:0% +speed of the light in some specific +material and K says K hat is actually + + align:start position:0% +material and K says K hat is actually + + + align:start position:0% +material and K says K hat is actually +the direction of propagation cause this + + align:start position:0% +the direction of propagation cause this + + + align:start position:0% +the direction of propagation cause this +will give you that the magnitude and + + align:start position:0% +will give you that the magnitude and + + + align:start position:0% +will give you that the magnitude and +also the direction of the magnetic + + align:start position:0% +also the direction of the magnetic + + + align:start position:0% +also the direction of the magnetic +responding magnetic field for the + + align:start position:0% +responding magnetic field for the + + + align:start position:0% +responding magnetic field for the +electromagnetic waves okay so so now I'm + + align:start position:0% +electromagnetic waves okay so so now I'm + + + align:start position:0% +electromagnetic waves okay so so now I'm +interested in what will be the resulting + + align:start position:0% +interested in what will be the resulting + + + align:start position:0% +interested in what will be the resulting +intensity if I try to superpose these to + + align:start position:0% +intensity if I try to superpose these to + + + align:start position:0% +intensity if I try to superpose these to +try to put together these two electric + + align:start position:0% +try to put together these two electric + + + align:start position:0% +try to put together these two electric +field okay as you can see that these two + + align:start position:0% +field okay as you can see that these two + + + align:start position:0% +field okay as you can see that these two +electric field have different phase the + + align:start position:0% +electric field have different phase the + + + align:start position:0% +electric field have different phase the +first one I have faced by one the second + + align:start position:0% +first one I have faced by one the second + + + align:start position:0% +first one I have faced by one the second +one have faced by two okay so this means + + align:start position:0% +one have faced by two okay so this means + + + align:start position:0% +one have faced by two okay so this means +that they may reach maxima or minima a + + align:start position:0% +that they may reach maxima or minima a + + + align:start position:0% +that they may reach maxima or minima a +different position in space in this case + + align:start position:0% +different position in space in this case + + + align:start position:0% +different position in space in this case +is in the Z direction and while I'm + + align:start position:0% +is in the Z direction and while I'm + + + align:start position:0% +is in the Z direction and while I'm +actually defining here is actually two + + align:start position:0% +actually defining here is actually two + + + align:start position:0% +actually defining here is actually two +prang waves okay and so it really + + align:start position:0% +prang waves okay and so it really + + + align:start position:0% +prang waves okay and so it really +depends on what would be the relative + + align:start position:0% +depends on what would be the relative + + + align:start position:0% +depends on what would be the relative +face for the first and second + + align:start position:0% +face for the first and second + + + align:start position:0% +face for the first and second +electromagnetic wave okay in order to + + align:start position:0% +electromagnetic wave okay in order to + + + align:start position:0% +electromagnetic wave okay in order to +quantify how much they cancel each other + + align:start position:0% +quantify how much they cancel each other + + + align:start position:0% +quantify how much they cancel each other +or how much they enhance each other what + + align:start position:0% +or how much they enhance each other what + + + align:start position:0% +or how much they enhance each other what +I'm going to do is to evaluate the + + align:start position:0% +I'm going to do is to evaluate the + + + align:start position:0% +I'm going to do is to evaluate the +intensity of the of the resulting + + align:start position:0% +intensity of the of the resulting + + + align:start position:0% +intensity of the of the resulting +electromagnetic waves and what is actual + + align:start position:0% +electromagnetic waves and what is actual + + + align:start position:0% +electromagnetic waves and what is actual +intensity intensity is actually the + + align:start position:0% +intensity intensity is actually the + + + align:start position:0% +intensity intensity is actually the +amplitude of the pointing vector so I + + align:start position:0% +amplitude of the pointing vector so I + + + align:start position:0% +amplitude of the pointing vector so I +write this as the length of the S vector + + align:start position:0% +write this as the length of the S vector + + + align:start position:0% +write this as the length of the S vector +pointing vector and I can of course CAC + + align:start position:0% +pointing vector and I can of course CAC + + + align:start position:0% +pointing vector and I can of course CAC +need a well be the the value of this or + + align:start position:0% +need a well be the the value of this or + + + align:start position:0% +need a well be the the value of this or +say the length of the pointing vector + + align:start position:0% +say the length of the pointing vector + + + align:start position:0% +say the length of the pointing vector +this will be equal to 1 over B 0 okay + + align:start position:0% +this will be equal to 1 over B 0 okay + + + align:start position:0% +this will be equal to 1 over B 0 okay +face on this equation here just a + + align:start position:0% +face on this equation here just a + + + align:start position:0% +face on this equation here just a +reminder and I would like to know what + + align:start position:0% +reminder and I would like to know what + + + align:start position:0% +reminder and I would like to know what +be the length of the e cross P feel that + + align:start position:0% +be the length of the e cross P feel that + + + align:start position:0% +be the length of the e cross P feel that +will give you the length of the pointing + + align:start position:0% +will give you the length of the pointing + + + align:start position:0% +will give you the length of the pointing +vector and basically what you're going + + align:start position:0% +vector and basically what you're going + + + align:start position:0% +vector and basically what you're going +to get is that you are going to get 1 + + align:start position:0% +to get is that you are going to get 1 + + + align:start position:0% +to get is that you are going to get 1 +over mu zero times sings the B field is + + align:start position:0% +over mu zero times sings the B field is + + + align:start position:0% +over mu zero times sings the B field is +actually highly related to the electric + + align:start position:0% +actually highly related to the electric + + + align:start position:0% +actually highly related to the electric +field and it takes a heat of funnel-web + + align:start position:0% +field and it takes a heat of funnel-web + + + align:start position:0% +field and it takes a heat of funnel-web +up 1 over V right okay in terms of the + + align:start position:0% +up 1 over V right okay in terms of the + + + align:start position:0% +up 1 over V right okay in terms of the +size of the amplitude so basically you + + align:start position:0% +size of the amplitude so basically you + + + align:start position:0% +size of the amplitude so basically you +are going to get 1 over V + + align:start position:0% + + + + align:start position:0% + +okay and and the discourse Prada + + align:start position:0% +okay and and the discourse Prada + + + align:start position:0% +okay and and the discourse Prada +actually is okay because if we come in + + align:start position:0% +actually is okay because if we come in + + + align:start position:0% +actually is okay because if we come in +square because II feel and if you are + + align:start position:0% +square because II feel and if you are + + + align:start position:0% +square because II feel and if you are +always orthogonal to each other and we + + align:start position:0% +always orthogonal to each other and we + + + align:start position:0% +always orthogonal to each other and we +can now rewrite this V V is actually the + + align:start position:0% +can now rewrite this V V is actually the + + + align:start position:0% +can now rewrite this V V is actually the +velocity of the speed of the light + + align:start position:0% +velocity of the speed of the light + + + align:start position:0% +velocity of the speed of the light +you matter so basically what I can + + align:start position:0% +you matter so basically what I can + + + align:start position:0% +you matter so basically what I can +rewrite is that this book can see 1 over + + align:start position:0% +rewrite is that this book can see 1 over + + + align:start position:0% +rewrite is that this book can see 1 over +V word we can see over N which is - with + + align:start position:0% +V word we can see over N which is - with + + + align:start position:0% +V word we can see over N which is - with +the the the refractive index of a + + align:start position:0% +the the the refractive index of a + + + align:start position:0% +the the the refractive index of a +specific material I still I have this + + align:start position:0% +specific material I still I have this + + + align:start position:0% +specific material I still I have this +question ok finally I can rewrite see + + align:start position:0% +question ok finally I can rewrite see + + + align:start position:0% +question ok finally I can rewrite see +this formula sings C is equal to square + + align:start position:0% +this formula sings C is equal to square + + + align:start position:0% +this formula sings C is equal to square +root of 1 over square root of mu 0 + + align:start position:0% +root of 1 over square root of mu 0 + + + align:start position:0% +root of 1 over square root of mu 0 +epsilon 0 right therefore I can rewrite + + align:start position:0% +epsilon 0 right therefore I can rewrite + + + align:start position:0% +epsilon 0 right therefore I can rewrite +this expression ok + + align:start position:0% +this expression ok + + + align:start position:0% +this expression ok +in terms of epsilon 0 and what I'm going + + align:start position:0% +in terms of epsilon 0 and what I'm going + + + align:start position:0% +in terms of epsilon 0 and what I'm going +to get this C times kinds epsilon 0 + + align:start position:0% +to get this C times kinds epsilon 0 + + + align:start position:0% +to get this C times kinds epsilon 0 +square so basically what I do is that I + + align:start position:0% +square so basically what I do is that I + + + align:start position:0% +square so basically what I do is that I +multiply both numerator and the + + align:start position:0% +multiply both numerator and the + + + align:start position:0% +multiply both numerator and the +denominator by I see and also I ride a + + align:start position:0% +denominator by I see and also I ride a + + + align:start position:0% +denominator by I see and also I ride a +bike and actually I use this expression + + align:start position:0% +bike and actually I use this expression + + + align:start position:0% +bike and actually I use this expression +the night Ranieri cancel the MU 0 and + + align:start position:0% +the night Ranieri cancel the MU 0 and + + + align:start position:0% +the night Ranieri cancel the MU 0 and +write everything in terms of C and + + align:start position:0% +write everything in terms of C and + + + align:start position:0% +write everything in terms of C and +epsilon 0 okay so so until here they + + align:start position:0% +epsilon 0 okay so so until here they + + + align:start position:0% +epsilon 0 okay so so until here they +were basically no metric basically it's + + align:start position:0% +were basically no metric basically it's + + + align:start position:0% +were basically no metric basically it's +just rewriting the this the length of + + align:start position:0% +just rewriting the this the length of + + + align:start position:0% +just rewriting the this the length of +the the pointing vector in terms of M + + align:start position:0% +the the pointing vector in terms of M + + + align:start position:0% +the the pointing vector in terms of M +and also the electric field so now what + + align:start position:0% +and also the electric field so now what + + + align:start position:0% +and also the electric field so now what +I'm going to do is to practice this + + align:start position:0% +I'm going to do is to practice this + + + align:start position:0% +I'm going to do is to practice this +expression into that formula okay and + + align:start position:0% +expression into that formula okay and + + + align:start position:0% +expression into that formula okay and +see what we are going to get so that me + + align:start position:0% +see what we are going to get so that me + + + align:start position:0% +see what we are going to get so that me +by the way will be the Y square the + + align:start position:0% +by the way will be the Y square the + + + align:start position:0% +by the way will be the Y square the +length of the e square so basically the + + align:start position:0% +length of the e square so basically the + + + align:start position:0% +length of the e square so basically the +definition of the e + + align:start position:0% +definition of the e + + + align:start position:0% +definition of the e +showing here is a superposition of e1 + + align:start position:0% +showing here is a superposition of e1 + + + align:start position:0% +showing here is a superposition of e1 +and e2 therefore I can now quickly write + + align:start position:0% +and e2 therefore I can now quickly write + + + align:start position:0% +and e2 therefore I can now quickly write +down will be e square here okay so so + + align:start position:0% +down will be e square here okay so so + + + align:start position:0% +down will be e square here okay so so +basically the first basically you are + + align:start position:0% +basically the first basically you are + + + align:start position:0% +basically the first basically you are +going to get a 1 square for sine square + + align:start position:0% +going to get a 1 square for sine square + + + align:start position:0% +going to get a 1 square for sine square +Omega t minus KZ us by one basically + + align:start position:0% +Omega t minus KZ us by one basically + + + align:start position:0% +Omega t minus KZ us by one basically +that is coming from a 1 times C 1 right + + align:start position:0% +that is coming from a 1 times C 1 right + + + align:start position:0% +that is coming from a 1 times C 1 right +the second term which I am going to get + + align:start position:0% +the second term which I am going to get + + + align:start position:0% +the second term which I am going to get +is actually e 2 times e 2 e 2 tai situ + + align:start position:0% +is actually e 2 times e 2 e 2 tai situ + + + align:start position:0% +is actually e 2 times e 2 e 2 tai situ +you are going to get a 2 square cosine + + align:start position:0% +you are going to get a 2 square cosine + + + align:start position:0% +you are going to get a 2 square cosine +square Omega t minus KZ a spike right + + align:start position:0% +square Omega t minus KZ a spike right + + + align:start position:0% +square Omega t minus KZ a spike right +basically based on this equation and I + + align:start position:0% +basically based on this equation and I + + + align:start position:0% +basically based on this equation and I +square it and then basically I get the + + align:start position:0% +square it and then basically I get the + + + align:start position:0% +square it and then basically I get the +second thank you okay and finally what I + + align:start position:0% +second thank you okay and finally what I + + + align:start position:0% +second thank you okay and finally what I +am going to get is the third term which + + align:start position:0% +am going to get is the third term which + + + align:start position:0% +am going to get is the third term which +is actually e 1 times e 2 so basically + + align:start position:0% +is actually e 1 times e 2 so basically + + + align:start position:0% +is actually e 1 times e 2 so basically +what I am going to get this a 1 + + align:start position:0% +what I am going to get this a 1 + + + align:start position:0% +what I am going to get this a 1 +basically you are going to get 2 times a + + align:start position:0% +basically you are going to get 2 times a + + + align:start position:0% +basically you are going to get 2 times a +1 a 2 cosine Omega t minus K G by 1 + + align:start position:0% +1 a 2 cosine Omega t minus K G by 1 + + + align:start position:0% +1 a 2 cosine Omega t minus K G by 1 +cosine Omega t minus KZ by 2 which is + + align:start position:0% +cosine Omega t minus KZ by 2 which is + + + align:start position:0% +cosine Omega t minus KZ by 2 which is +actually the first tenth of this e + + align:start position:0% +actually the first tenth of this e + + + align:start position:0% +actually the first tenth of this e +vector squared okay and the question is + + align:start position:0% +vector squared okay and the question is + + + align:start position:0% +vector squared okay and the question is +so far okay I hope this is the forward + + align:start position:0% +so far okay I hope this is the forward + + + align:start position:0% +so far okay I hope this is the forward +to you and of course I can now rewrite + + align:start position:0% +to you and of course I can now rewrite + + + align:start position:0% +to you and of course I can now rewrite +this product is 2 cosine cosine has + + align:start position:0% +this product is 2 cosine cosine has + + + align:start position:0% +this product is 2 cosine cosine has +cosine right basically I can rewrite + + align:start position:0% +cosine right basically I can rewrite + + + align:start position:0% +cosine right basically I can rewrite +this using the formula which we have + + align:start position:0% +this using the formula which we have + + + align:start position:0% +this using the formula which we have +related cosine times cosine basically I + + align:start position:0% +related cosine times cosine basically I + + + align:start position:0% +related cosine times cosine basically I +can rewrite this as a 1/2 cosine 2 Omega + + align:start position:0% +can rewrite this as a 1/2 cosine 2 Omega + + + align:start position:0% +can rewrite this as a 1/2 cosine 2 Omega +t minus 2 KD plus PI 1 + + align:start position:0% +t minus 2 KD plus PI 1 + + + align:start position:0% +t minus 2 KD plus PI 1 +right press 1 over 2 cosine Phi 1 minus + + align:start position:0% +right press 1 over 2 cosine Phi 1 minus + + + align:start position:0% +right press 1 over 2 cosine Phi 1 minus +Phi 2 + + align:start position:0% +Phi 2 + + + align:start position:0% +Phi 2 +so basically the first time is they + + align:start position:0% +so basically the first time is they + + + align:start position:0% +so basically the first time is they +should be collecting the content of the + + align:start position:0% +should be collecting the content of the + + + align:start position:0% +should be collecting the content of the +2 cosine and L lengths together the + + align:start position:0% +2 cosine and L lengths together the + + + align:start position:0% +2 cosine and L lengths together the +second term is they should be us + + align:start position:0% +second term is they should be us + + + align:start position:0% +second term is they should be us +calculating the difference between the + + align:start position:0% +calculating the difference between the + + + align:start position:0% +calculating the difference between the +content of the cosine function and what + + align:start position:0% +content of the cosine function and what + + + align:start position:0% +content of the cosine function and what +I am going to get it says should be by 1 + + align:start position:0% +I am going to get it says should be by 1 + + + align:start position:0% +I am going to get it says should be by 1 +minus Phi 2 + + align:start position:0% +minus Phi 2 + + + align:start position:0% +minus Phi 2 +okay now based on this definition + + align:start position:0% +okay now based on this definition + + + align:start position:0% +okay now based on this definition +intensity I is actually equal to the + + align:start position:0% +intensity I is actually equal to the + + + align:start position:0% +intensity I is actually equal to the +magnitude of the pointing vector so + + align:start position:0% +magnitude of the pointing vector so + + + align:start position:0% +magnitude of the pointing vector so +remember what our goal is to evaluate + + align:start position:0% +remember what our goal is to evaluate + + + align:start position:0% +remember what our goal is to evaluate +what will be the resulting average + + align:start position:0% +what will be the resulting average + + + align:start position:0% +what will be the resulting average +intensity so now I can calculate will be + + align:start position:0% +intensity so now I can calculate will be + + + align:start position:0% +intensity so now I can calculate will be +the average intensity over one period + + align:start position:0% +the average intensity over one period + + + align:start position:0% +the average intensity over one period +okay so this will be equal to 1 over T + + align:start position:0% +okay so this will be equal to 1 over T + + + align:start position:0% +okay so this will be equal to 1 over T +in the equation over 0 to t 1 period and + + align:start position:0% +in the equation over 0 to t 1 period and + + + align:start position:0% +in the equation over 0 to t 1 period and +the instantaneous intensity I Pete ok + + align:start position:0% +the instantaneous intensity I Pete ok + + + align:start position:0% +the instantaneous intensity I Pete ok +and what I am going to get is that okay + + align:start position:0% +and what I am going to get is that okay + + + align:start position:0% +and what I am going to get is that okay +so we have three trends the first one is + + align:start position:0% +so we have three trends the first one is + + + align:start position:0% +so we have three trends the first one is +here which is a she a Y squared cosine + + align:start position:0% +here which is a she a Y squared cosine + + + align:start position:0% +here which is a she a Y squared cosine +square something related to Omega T and + + align:start position:0% +square something related to Omega T and + + + align:start position:0% +square something related to Omega T and +the second x here is also proportional + + align:start position:0% +the second x here is also proportional + + + align:start position:0% +the second x here is also proportional +to cosine square Omega T and finally we + + align:start position:0% +to cosine square Omega T and finally we + + + align:start position:0% +to cosine square Omega T and finally we +have two turns here which is actually + + align:start position:0% +have two turns here which is actually + + + align:start position:0% +have two turns here which is actually +proportional to cosine 2 Omega T and + + align:start position:0% +proportional to cosine 2 Omega T and + + + align:start position:0% +proportional to cosine 2 Omega T and +finally the last time is actually + + align:start position:0% +finally the last time is actually + + + align:start position:0% +finally the last time is actually +independent of time okay so what what + + align:start position:0% +independent of time okay so what what + + + align:start position:0% +independent of time okay so what what +why what I'm going to do is to evaluate + + align:start position:0% +why what I'm going to do is to evaluate + + + align:start position:0% +why what I'm going to do is to evaluate +individual turn so the first time basis + + align:start position:0% +individual turn so the first time basis + + + align:start position:0% +individual turn so the first time basis +the a 1 squared cosine square Omega T so + + align:start position:0% +the a 1 squared cosine square Omega T so + + + align:start position:0% +the a 1 squared cosine square Omega T so +by now you should be pretty + + align:start position:0% +by now you should be pretty + + + align:start position:0% +by now you should be pretty +straightforward for you if I integrate + + align:start position:0% +straightforward for you if I integrate + + + align:start position:0% +straightforward for you if I integrate +cosine squared over one period of time + + align:start position:0% +cosine squared over one period of time + + + align:start position:0% +cosine squared over one period of time +basically what you are going to get this + + align:start position:0% +basically what you are going to get this + + + align:start position:0% +basically what you are going to get this +1/2 right okay so that is a sweet are + + align:start position:0% +1/2 right okay so that is a sweet are + + + align:start position:0% +1/2 right okay so that is a sweet are +several times in + + align:start position:0% +several times in + + + align:start position:0% +several times in +pset so basically what you're going to + + align:start position:0% +pset so basically what you're going to + + + align:start position:0% +pset so basically what you're going to +get is so I'm going to collect all those + + align:start position:0% +get is so I'm going to collect all those + + + align:start position:0% +get is so I'm going to collect all those +constants from here and copy here + + align:start position:0% +constants from here and copy here + + + align:start position:0% +constants from here and copy here +so you basically you have C times an x + + align:start position:0% +so you basically you have C times an x + + + align:start position:0% +so you basically you have C times an x +from zero okay which is a Sudeep coming + + align:start position:0% +from zero okay which is a Sudeep coming + + + align:start position:0% +from zero okay which is a Sudeep coming +from the definition of intensity and + + align:start position:0% +from the definition of intensity and + + + align:start position:0% +from the definition of intensity and +then this is actually for the first time + + align:start position:0% +then this is actually for the first time + + + align:start position:0% +then this is actually for the first time +what I'm going to get is a 1 squared + + align:start position:0% +what I'm going to get is a 1 squared + + + align:start position:0% +what I'm going to get is a 1 squared +divided by 2 this 1/2 is actually just + + align:start position:0% +divided by 2 this 1/2 is actually just + + + align:start position:0% +divided by 2 this 1/2 is actually just +integral related to cosine square + + align:start position:0% +integral related to cosine square + + + align:start position:0% +integral related to cosine square +similarly you are going to get the same + + align:start position:0% +similarly you are going to get the same + + + align:start position:0% +similarly you are going to get the same +result very similar with out for a + + align:start position:0% +result very similar with out for a + + + align:start position:0% +result very similar with out for a +second term the second term is going to + + align:start position:0% +second term the second term is going to + + + align:start position:0% +second term the second term is going to +give you a square divided by 2 all right + + align:start position:0% +give you a square divided by 2 all right + + + align:start position:0% +give you a square divided by 2 all right +ok finally you can have the third time + + align:start position:0% +ok finally you can have the third time + + + align:start position:0% +ok finally you can have the third time +the third term is going to be give you + + align:start position:0% +the third term is going to be give you + + + align:start position:0% +the third term is going to be give you +what value can somebody help me yes zero + + align:start position:0% +what value can somebody help me yes zero + + + align:start position:0% +what value can somebody help me yes zero +fact because this is actually cosine 2 + + align:start position:0% +fact because this is actually cosine 2 + + + align:start position:0% +fact because this is actually cosine 2 +Omega T right so if you do integrate + + align:start position:0% +Omega T right so if you do integrate + + + align:start position:0% +Omega T right so if you do integrate +over one period you are going to get + + align:start position:0% +over one period you are going to get + + + align:start position:0% +over one period you are going to get +zero plus zero each period you keep your + + align:start position:0% +zero plus zero each period you keep your + + + align:start position:0% +zero plus zero each period you keep your +zero right so your first zero is zero so + + align:start position:0% +zero right so your first zero is zero so + + + align:start position:0% +zero right so your first zero is zero so +therefore you can't do very good how + + align:start position:0% +therefore you can't do very good how + + + align:start position:0% +therefore you can't do very good how +about the last time the last time + + align:start position:0% +about the last time the last time + + + align:start position:0% +about the last time the last time +anybody can help me that's right right + + align:start position:0% +anybody can help me that's right right + + + align:start position:0% +anybody can help me that's right right +because this is constant okay so every + + align:start position:0% +because this is constant okay so every + + + align:start position:0% +because this is constant okay so every +Java constant is a constant which is + + align:start position:0% +Java constant is a constant which is + + + align:start position:0% +Java constant is a constant which is +they should be giving you 1 over 2 times + + align:start position:0% +they should be giving you 1 over 2 times + + + align:start position:0% +they should be giving you 1 over 2 times +a 2 times a 1 times 8 cosine Phi 1 minus + + align:start position:0% +a 2 times a 1 times 8 cosine Phi 1 minus + + + align:start position:0% +a 2 times a 1 times 8 cosine Phi 1 minus +PI of course I can cancel this 1/2 which + + align:start position:0% +PI of course I can cancel this 1/2 which + + + align:start position:0% +PI of course I can cancel this 1/2 which +is as you're coming from here and a 2 + + align:start position:0% +is as you're coming from here and a 2 + + + align:start position:0% +is as you're coming from here and a 2 +and basically you are getting a 1 a 2 + + align:start position:0% +and basically you are getting a 1 a 2 + + + align:start position:0% +and basically you are getting a 1 a 2 +cosine Phi 1 minus Phi 2 + + align:start position:0% +cosine Phi 1 minus Phi 2 + + + align:start position:0% +cosine Phi 1 minus Phi 2 +okay and I need to close + + align:start position:0% + + + + align:start position:0% + +any questions so far + + align:start position:0% +any questions so far + + + align:start position:0% +any questions so far +okay so what we have been doing is that + + align:start position:0% +okay so what we have been doing is that + + + align:start position:0% +okay so what we have been doing is that +I evaluate the total electric field if I + + align:start position:0% +I evaluate the total electric field if I + + + align:start position:0% +I evaluate the total electric field if I +had super basically calculate the + + align:start position:0% +had super basically calculate the + + + align:start position:0% +had super basically calculate the +superposition of the two field and then + + align:start position:0% +superposition of the two field and then + + + align:start position:0% +superposition of the two field and then +I am interested in what would be the + + align:start position:0% +I am interested in what would be the + + + align:start position:0% +I am interested in what would be the +average intensity coming from this field + + align:start position:0% +average intensity coming from this field + + + align:start position:0% +average intensity coming from this field +and I write down each square + + align:start position:0% +and I write down each square + + + align:start position:0% +and I write down each square +explicitly there are four times and on + + align:start position:0% +explicitly there are four times and on + + + align:start position:0% +explicitly there are four times and on +this tree of that which way of the + + align:start position:0% +this tree of that which way of the + + + align:start position:0% +this tree of that which way of the +energy survive and the basically the + + align:start position:0% +energy survive and the basically the + + + align:start position:0% +energy survive and the basically the +expression I am getting is it's like + + align:start position:0% +expression I am getting is it's like + + + align:start position:0% +expression I am getting is it's like +this basically you have some constant + + align:start position:0% +this basically you have some constant + + + align:start position:0% +this basically you have some constant +multiplied by a 1 squared over 2 plus a + + align:start position:0% +multiplied by a 1 squared over 2 plus a + + + align:start position:0% +multiplied by a 1 squared over 2 plus a +2 squared over 2 plus a 1 a 2 cosine Phi + + align:start position:0% +2 squared over 2 plus a 1 a 2 cosine Phi + + + align:start position:0% +2 squared over 2 plus a 1 a 2 cosine Phi +1 minus Phi 2 you can see that the + + align:start position:0% +1 minus Phi 2 you can see that the + + + align:start position:0% +1 minus Phi 2 you can see that the +intensity depends on Phi 1 and Phi 2 + + align:start position:0% +intensity depends on Phi 1 and Phi 2 + + + align:start position:0% +intensity depends on Phi 1 and Phi 2 +right so so this actually would change + + align:start position:0% +right so so this actually would change + + + align:start position:0% +right so so this actually would change +the resulting intensity okay to in order + + align:start position:0% +the resulting intensity okay to in order + + + align:start position:0% +the resulting intensity okay to in order +to get some ideas about what does that + + align:start position:0% +to get some ideas about what does that + + + align:start position:0% +to get some ideas about what does that +mean and also how does the intensity the + + align:start position:0% +mean and also how does the intensity the + + + align:start position:0% +mean and also how does the intensity the +average intensity change as a function + + align:start position:0% +average intensity change as a function + + + align:start position:0% +average intensity change as a function +of Phi 1 minus Phi 2 what I'm going to + + align:start position:0% +of Phi 1 minus Phi 2 what I'm going to + + + align:start position:0% +of Phi 1 minus Phi 2 what I'm going to +do is to define Phi 1 minus Phi 2 to be + + align:start position:0% +do is to define Phi 1 minus Phi 2 to be + + + align:start position:0% +do is to define Phi 1 minus Phi 2 to be +Delta okay which I will call it phase + + align:start position:0% +Delta okay which I will call it phase + + + align:start position:0% +Delta okay which I will call it phase +difference okay then I would like to + + align:start position:0% +difference okay then I would like to + + + align:start position:0% +difference okay then I would like to +plot for everything intensity I as a + + align:start position:0% +plot for everything intensity I as a + + + align:start position:0% +plot for everything intensity I as a +function not dope okay + + align:start position:0% + + + + align:start position:0% + +so this is actually the result so if I + + align:start position:0% +so this is actually the result so if I + + + align:start position:0% +so this is actually the result so if I +have the x-axis to be Delta which is + + align:start position:0% +have the x-axis to be Delta which is + + + align:start position:0% +have the x-axis to be Delta which is +actually Phi 1 minus Phi - okay and the + + align:start position:0% +actually Phi 1 minus Phi - okay and the + + + align:start position:0% +actually Phi 1 minus Phi - okay and the +y-axis is intensity + + align:start position:0% +y-axis is intensity + + + align:start position:0% +y-axis is intensity +okay of course I would like to take out + + align:start position:0% +okay of course I would like to take out + + + align:start position:0% +okay of course I would like to take out +the constant which is C times n times + + align:start position:0% +the constant which is C times n times + + + align:start position:0% +the constant which is C times n times +epsilon 0 so I am parting the y-axis is + + align:start position:0% +epsilon 0 so I am parting the y-axis is + + + align:start position:0% +epsilon 0 so I am parting the y-axis is +average intensity divided by C times n + + align:start position:0% +average intensity divided by C times n + + + align:start position:0% +average intensity divided by C times n +times epsilon 0 ok what I'm going to get + + align:start position:0% +times epsilon 0 ok what I'm going to get + + + align:start position:0% +times epsilon 0 ok what I'm going to get +the something which is actually + + align:start position:0% +the something which is actually + + + align:start position:0% +the something which is actually +oscillating up and down like this + + align:start position:0% +oscillating up and down like this + + + align:start position:0% +oscillating up and down like this +ok + + align:start position:0% +ok + + + align:start position:0% +ok +so the maximum value happens the maximum + + align:start position:0% +so the maximum value happens the maximum + + + align:start position:0% +so the maximum value happens the maximum +value happens when Delta is equal to + + align:start position:0% +value happens when Delta is equal to + + + align:start position:0% +value happens when Delta is equal to +zero right when Delta is equal to zero + + align:start position:0% +zero right when Delta is equal to zero + + + align:start position:0% +zero right when Delta is equal to zero +what is going to happen + + align:start position:0% +what is going to happen + + + align:start position:0% +what is going to happen +this means that cosine Delta is equal to + + align:start position:0% +this means that cosine Delta is equal to + + + align:start position:0% +this means that cosine Delta is equal to +what right therefore what you are going + + align:start position:0% +what right therefore what you are going + + + align:start position:0% +what right therefore what you are going +to get is a 1 squared over 2 plus a 2 + + align:start position:0% +to get is a 1 squared over 2 plus a 2 + + + align:start position:0% +to get is a 1 squared over 2 plus a 2 +squared over 2 plus a 1 a 2 okay okay + + align:start position:0% +squared over 2 plus a 1 a 2 okay okay + + + align:start position:0% +squared over 2 plus a 1 a 2 okay okay +this is a shape when Delta is equal to 0 + + align:start position:0% +this is a shape when Delta is equal to 0 + + + align:start position:0% +this is a shape when Delta is equal to 0 +and the intensity actually reach maximum + + align:start position:0% +and the intensity actually reach maximum + + + align:start position:0% +and the intensity actually reach maximum +and the maximum value is actually 1 over + + align:start position:0% +and the maximum value is actually 1 over + + + align:start position:0% +and the maximum value is actually 1 over +2 a 1 plus a 2 squared all right based + + align:start position:0% +2 a 1 plus a 2 squared all right based + + + align:start position:0% +2 a 1 plus a 2 squared all right based +on this calculation ok and the other + + align:start position:0% +on this calculation ok and the other + + + align:start position:0% +on this calculation ok and the other +hand you can actually expect that the + + align:start position:0% +hand you can actually expect that the + + + align:start position:0% +hand you can actually expect that the +intensity reach a minimum when Delta is + + align:start position:0% +intensity reach a minimum when Delta is + + + align:start position:0% +intensity reach a minimum when Delta is +equal to which value anybody can help me + + align:start position:0% + + + + align:start position:0% + +yes right when Delta is PI what is going + + align:start position:0% +yes right when Delta is PI what is going + + + align:start position:0% +yes right when Delta is PI what is going +to happen cosine pi is minus 1 so + + align:start position:0% +to happen cosine pi is minus 1 so + + + align:start position:0% +to happen cosine pi is minus 1 so +therefore what you are getting is 1 over + + align:start position:0% +therefore what you are getting is 1 over + + + align:start position:0% +therefore what you are getting is 1 over +2 a 1 square plus a 2 square minus 2 a 1 + + align:start position:0% +2 a 1 square plus a 2 square minus 2 a 1 + + + align:start position:0% +2 a 1 square plus a 2 square minus 2 a 1 +a 2 and that will give you 1 over 2 a 1 + + align:start position:0% +a 2 and that will give you 1 over 2 a 1 + + + align:start position:0% +a 2 and that will give you 1 over 2 a 1 +minus a 2 you can see that when the + + align:start position:0% +minus a 2 you can see that when the + + + align:start position:0% +minus a 2 you can see that when the +Delta is equal to 0 or when the tota is + + align:start position:0% +Delta is equal to 0 or when the tota is + + + align:start position:0% +Delta is equal to 0 or when the tota is +equal to 2 pi for example okay if you + + align:start position:0% +equal to 2 pi for example okay if you + + + align:start position:0% +equal to 2 pi for example okay if you +increase that the phase difference large + + align:start position:0% +increase that the phase difference large + + + align:start position:0% +increase that the phase difference large +enough or the Delta is actually 4 PI all + + align:start position:0% +enough or the Delta is actually 4 PI all + + + align:start position:0% +enough or the Delta is actually 4 PI all +those number will give you Maxima + + align:start position:0% +those number will give you Maxima + + + align:start position:0% +those number will give you Maxima +constructive interference okay so what + + align:start position:0% +constructive interference okay so what + + + align:start position:0% +constructive interference okay so what +does that mean that means you are adding + + align:start position:0% +does that mean that means you are adding + + + align:start position:0% +does that mean that means you are adding +these two electric field + + align:start position:0% +these two electric field + + + align:start position:0% +these two electric field +the most efficient way okay on the other + + align:start position:0% +the most efficient way okay on the other + + + align:start position:0% +the most efficient way okay on the other +hand when the value of the Delta is + + align:start position:0% +hand when the value of the Delta is + + + align:start position:0% +hand when the value of the Delta is +equal to PI or equal to 3 PI or equal to + + align:start position:0% +equal to PI or equal to 3 PI or equal to + + + align:start position:0% +equal to PI or equal to 3 PI or equal to +5 PI Osetra okay the intensity the + + align:start position:0% +5 PI Osetra okay the intensity the + + + align:start position:0% +5 PI Osetra okay the intensity the +average intensity reach a minimum okay + + align:start position:0% +average intensity reach a minimum okay + + + align:start position:0% +average intensity reach a minimum okay +that means actually instead of adding + + align:start position:0% +that means actually instead of adding + + + align:start position:0% +that means actually instead of adding +then you are actually cancelling them + + align:start position:0% +then you are actually cancelling them + + + align:start position:0% +then you are actually cancelling them +you are cancelling the electric field of + + align:start position:0% +you are cancelling the electric field of + + + align:start position:0% +you are cancelling the electric field of +the of the first and the second + + align:start position:0% +the of the first and the second + + + align:start position:0% +the of the first and the second +electromagnetic wave okay and now will + + align:start position:0% +electromagnetic wave okay and now will + + + align:start position:0% +electromagnetic wave okay and now will +give you a maxima intensity which is 1 + + align:start position:0% +give you a maxima intensity which is 1 + + + align:start position:0% +give you a maxima intensity which is 1 +over 2 a 1 minus a 2 squared just as a + + align:start position:0% +over 2 a 1 minus a 2 squared just as a + + + align:start position:0% +over 2 a 1 minus a 2 squared just as a +reminder this a 1 and a 2 is actually + + align:start position:0% +reminder this a 1 and a 2 is actually + + + align:start position:0% +reminder this a 1 and a 2 is actually +the amplitude of the first and second + + align:start position:0% +the amplitude of the first and second + + + align:start position:0% +the amplitude of the first and second +electric field okay so what will happen + + align:start position:0% +electric field okay so what will happen + + + align:start position:0% +electric field okay so what will happen +if I set a 1 equal to a 2 if I set a 1 2 + + align:start position:0% +if I set a 1 equal to a 2 if I set a 1 2 + + + align:start position:0% +if I set a 1 equal to a 2 if I set a 1 2 +equal to a 2 that means the minima will + + align:start position:0% +equal to a 2 that means the minima will + + + align:start position:0% +equal to a 2 that means the minima will +be equal to what 0 + + align:start position:0% +be equal to what 0 + + + align:start position:0% +be equal to what 0 +yeah very good how about the Maxima will + + align:start position:0% +yeah very good how about the Maxima will + + + align:start position:0% +yeah very good how about the Maxima will +be a 1 plus a 2 right so basically you + + align:start position:0% +be a 1 plus a 2 right so basically you + + + align:start position:0% +be a 1 plus a 2 right so basically you +are going to get 4 times larger value + + align:start position:0% +are going to get 4 times larger value + + + align:start position:0% +are going to get 4 times larger value +come here to the intensity before you + + align:start position:0% +come here to the intensity before you + + + align:start position:0% +come here to the intensity before you +add them together so individual + + align:start position:0% +add them together so individual + + + align:start position:0% +add them together so individual +intensity is I and after adding them + + align:start position:0% +intensity is I and after adding them + + + align:start position:0% +intensity is I and after adding them +together with Delta equal to 0 you are + + align:start position:0% +together with Delta equal to 0 you are + + + align:start position:0% +together with Delta equal to 0 you are +going to get 4 times larger intensity if + + align:start position:0% +going to get 4 times larger intensity if + + + align:start position:0% +going to get 4 times larger intensity if +the amplitude of the first and second + + align:start position:0% +the amplitude of the first and second + + + align:start position:0% +the amplitude of the first and second +units it actually feel is the same okay + + align:start position:0% +units it actually feel is the same okay + + + align:start position:0% +units it actually feel is the same okay +so very good so so that's issued resolve + + align:start position:0% +so very good so so that's issued resolve + + + align:start position:0% +so very good so so that's issued resolve +the calculation and you can see that the + + align:start position:0% +the calculation and you can see that the + + + align:start position:0% +the calculation and you can see that the +amount of intensive weakly we can get + + align:start position:0% +amount of intensive weakly we can get + + + align:start position:0% +amount of intensive weakly we can get +out of this highly depends on the Delta + + align:start position:0% +out of this highly depends on the Delta + + + align:start position:0% +out of this highly depends on the Delta +which is actually the phase difference + + align:start position:0% +which is actually the phase difference + + + align:start position:0% +which is actually the phase difference +between the first and the second + + align:start position:0% +between the first and the second + + + align:start position:0% +between the first and the second +electric field okay can we as you get + + align:start position:0% +electric field okay can we as you get + + + align:start position:0% +electric field okay can we as you get +some more feeling about this addition + + align:start position:0% +some more feeling about this addition + + + align:start position:0% +some more feeling about this addition +okay so what I'm going to do is to again + + align:start position:0% +okay so what I'm going to do is to again + + + align:start position:0% +okay so what I'm going to do is to again +write everything + + align:start position:0% +write everything + + + align:start position:0% +write everything +down in terms of imaginary number horse + + align:start position:0% +down in terms of imaginary number horse + + + align:start position:0% +down in terms of imaginary number horse +a complex number + + align:start position:0% +a complex number + + + align:start position:0% +a complex number +okay so if I have a we write the + + align:start position:0% +okay so if I have a we write the + + + align:start position:0% +okay so if I have a we write the +electric field e1 is a real part of a 1 + + align:start position:0% +electric field e1 is a real part of a 1 + + + align:start position:0% +electric field e1 is a real part of a 1 +exponential I Phi 1 exponential I Omega + + align:start position:0% +exponential I Phi 1 exponential I Omega + + + align:start position:0% +exponential I Phi 1 exponential I Omega +t minus KZ okay in the X direction and I + + align:start position:0% +t minus KZ okay in the X direction and I + + + align:start position:0% +t minus KZ okay in the X direction and I +can also rewrite the expression for the + + align:start position:0% +can also rewrite the expression for the + + + align:start position:0% +can also rewrite the expression for the +second electric field to be the real + + align:start position:0% +second electric field to be the real + + + align:start position:0% +second electric field to be the real +part of a 2 exponential I Phi 2 + + align:start position:0% +part of a 2 exponential I Phi 2 + + + align:start position:0% +part of a 2 exponential I Phi 2 +exponential I Omega T again ok so if I + + align:start position:0% +exponential I Omega T again ok so if I + + + align:start position:0% +exponential I Omega T again ok so if I +add these two field together what I am + + align:start position:0% +add these two field together what I am + + + align:start position:0% +add these two field together what I am +doing is like in the complex prayer I + + align:start position:0% +doing is like in the complex prayer I + + + align:start position:0% +doing is like in the complex prayer I +have imaging and the number contribution + + align:start position:0% +have imaging and the number contribution + + + align:start position:0% +have imaging and the number contribution +in the Y direction and the real part is + + align:start position:0% +in the Y direction and the real part is + + + align:start position:0% +in the Y direction and the real part is +actually in the X direction okay suppose + + align:start position:0% +actually in the X direction okay suppose + + + align:start position:0% +actually in the X direction okay suppose +Omega t minus K Z is zero okay at some + + align:start position:0% +Omega t minus K Z is zero okay at some + + + align:start position:0% +Omega t minus K Z is zero okay at some +instant of time Omega t minus KZ is + + align:start position:0% +instant of time Omega t minus KZ is + + + align:start position:0% +instant of time Omega t minus KZ is +equal to 0 so why I am doing is that ok + + align:start position:0% +equal to 0 so why I am doing is that ok + + + align:start position:0% +equal to 0 so why I am doing is that ok +I have the first vector which is + + align:start position:0% +I have the first vector which is + + + align:start position:0% +I have the first vector which is +actually presenting the the contribution + + align:start position:0% +actually presenting the the contribution + + + align:start position:0% +actually presenting the the contribution +of the first electric field and if this + + align:start position:0% +of the first electric field and if this + + + align:start position:0% +of the first electric field and if this +in that you feel is going to be Phi one + + align:start position:0% +in that you feel is going to be Phi one + + + align:start position:0% +in that you feel is going to be Phi one +pointing to a direction Phi one away + + align:start position:0% +pointing to a direction Phi one away + + + align:start position:0% +pointing to a direction Phi one away +from the real axis okay with amplitude + + align:start position:0% +from the real axis okay with amplitude + + + align:start position:0% +from the real axis okay with amplitude +equal to a-1 right this is as you what + + align:start position:0% +equal to a-1 right this is as you what + + + align:start position:0% +equal to a-1 right this is as you what +we learned or different from the first + + align:start position:0% +we learned or different from the first + + + align:start position:0% +we learned or different from the first +lecture and if I add the second electric + + align:start position:0% +lecture and if I add the second electric + + + align:start position:0% +lecture and if I add the second electric +field what I am going to get is that I'm + + align:start position:0% +field what I am going to get is that I'm + + + align:start position:0% +field what I am going to get is that I'm +going to get another vector ok which is + + align:start position:0% +going to get another vector ok which is + + + align:start position:0% +going to get another vector ok which is +actually a two in glands and the angle + + align:start position:0% +actually a two in glands and the angle + + + align:start position:0% +actually a two in glands and the angle +is Phi 2 here okay so what I'm going + + align:start position:0% +is Phi 2 here okay so what I'm going + + + align:start position:0% +is Phi 2 here okay so what I'm going +getting the resulting amplitude is + + align:start position:0% +getting the resulting amplitude is + + + align:start position:0% +getting the resulting amplitude is +actually when I + + align:start position:0% +actually when I + + + align:start position:0% +actually when I +the real part of the first and second + + align:start position:0% +the real part of the first and second + + + align:start position:0% +the real part of the first and second +expression adding them together okay + + align:start position:0% +expression adding them together okay + + + align:start position:0% +expression adding them together okay +patiently I am taking a projection to + + align:start position:0% +patiently I am taking a projection to + + + align:start position:0% +patiently I am taking a projection to +the real axis and that is actually the + + align:start position:0% +the real axis and that is actually the + + + align:start position:0% +the real axis and that is actually the +resulting amplitude of the electric + + align:start position:0% +resulting amplitude of the electric + + + align:start position:0% +resulting amplitude of the electric +field which is actually the + + align:start position:0% +field which is actually the + + + align:start position:0% +field which is actually the +superposition of the first and second + + align:start position:0% +superposition of the first and second + + + align:start position:0% +superposition of the first and second +field okay + + align:start position:0% +field okay + + + align:start position:0% +field okay +so you can see that when when Phi 1 and + + align:start position:0% +so you can see that when when Phi 1 and + + + align:start position:0% +so you can see that when when Phi 1 and +Phi 2 when Phi 1 is equal to Phi 2 okay + + align:start position:0% +Phi 2 when Phi 1 is equal to Phi 2 okay + + + align:start position:0% +Phi 2 when Phi 1 is equal to Phi 2 okay +what is going to happen is the bowing so + + align:start position:0% +what is going to happen is the bowing so + + + align:start position:0% +what is going to happen is the bowing so +basically what you are going to get is + + align:start position:0% +basically what you are going to get is + + + align:start position:0% +basically what you are going to get is +that the you are increasing the length + + align:start position:0% +that the you are increasing the length + + + align:start position:0% +that the you are increasing the length +of the the routing vector which is + + align:start position:0% +of the the routing vector which is + + + align:start position:0% +of the the routing vector which is +addition of the two vectors you are + + align:start position:0% +addition of the two vectors you are + + + align:start position:0% +addition of the two vectors you are +actually getting a maximum at out of + + align:start position:0% +actually getting a maximum at out of + + + align:start position:0% +actually getting a maximum at out of +this addition right because Phi is equal + + align:start position:0% +this addition right because Phi is equal + + + align:start position:0% +this addition right because Phi is equal +to Phi 2 therefore these two vectors + + align:start position:0% +to Phi 2 therefore these two vectors + + + align:start position:0% +to Phi 2 therefore these two vectors +form a straight line okay therefore you + + align:start position:0% +form a straight line okay therefore you + + + align:start position:0% +form a straight line okay therefore you +can issue the ad and get the maximum + + align:start position:0% +can issue the ad and get the maximum + + + align:start position:0% +can issue the ad and get the maximum +amount of MP 2 out of this okay on the + + align:start position:0% +amount of MP 2 out of this okay on the + + + align:start position:0% +amount of MP 2 out of this okay on the +other hand when Phi 1 minus Phi 2 is is + + align:start position:0% +other hand when Phi 1 minus Phi 2 is is + + + align:start position:0% +other hand when Phi 1 minus Phi 2 is is +back okay could you say should be which + + align:start position:0% +back okay could you say should be which + + + align:start position:0% +back okay could you say should be which +I define as Delta okay when this + + align:start position:0% +I define as Delta okay when this + + + align:start position:0% +I define as Delta okay when this +happened what is going to happen is that + + align:start position:0% +happened what is going to happen is that + + + align:start position:0% +happened what is going to happen is that +what we are doing is like addition of + + align:start position:0% +what we are doing is like addition of + + + align:start position:0% +what we are doing is like addition of +two vectors in the complex plane but + + align:start position:0% +two vectors in the complex plane but + + + align:start position:0% +two vectors in the complex plane but +they are pointing to the opposite + + align:start position:0% +they are pointing to the opposite + + + align:start position:0% +they are pointing to the opposite +direction okay so the first one will be + + align:start position:0% +direction okay so the first one will be + + + align:start position:0% +direction okay so the first one will be +like this and the second one like that + + align:start position:0% +like this and the second one like that + + + align:start position:0% +like this and the second one like that +and they are actually trying to cancel + + align:start position:0% +and they are actually trying to cancel + + + align:start position:0% +and they are actually trying to cancel +each other okay so that's actually how + + align:start position:0% +each other okay so that's actually how + + + align:start position:0% +each other okay so that's actually how +you can actually understand what is + + align:start position:0% +you can actually understand what is + + + align:start position:0% +you can actually understand what is +happening with different Delta value in + + align:start position:0% +happening with different Delta value in + + + align:start position:0% +happening with different Delta value in +this case Delta is equal to 0 the phase + + align:start position:0% +this case Delta is equal to 0 the phase + + + align:start position:0% +this case Delta is equal to 0 the phase +difference is equal to 0 and in the + + align:start position:0% +difference is equal to 0 and in the + + + align:start position:0% +difference is equal to 0 and in the +second case phase difference it + + align:start position:0% +second case phase difference it + + + align:start position:0% +second case phase difference it +two pi and what happened in between is + + align:start position:0% +two pi and what happened in between is + + + align:start position:0% +two pi and what happened in between is +like this right you are adding them sort + + align:start position:0% +like this right you are adding them sort + + + align:start position:0% +like this right you are adding them sort +of together but not in the most + + align:start position:0% +of together but not in the most + + + align:start position:0% +of together but not in the most +efficient way or the most destructive + + align:start position:0% +efficient way or the most destructive + + + align:start position:0% +efficient way or the most destructive +way and you are actually evaluating what + + align:start position:0% +way and you are actually evaluating what + + + align:start position:0% +way and you are actually evaluating what +would be the resulting amplitude by + + align:start position:0% +would be the resulting amplitude by + + + align:start position:0% +would be the resulting amplitude by +looking at the vector sum of the first + + align:start position:0% +looking at the vector sum of the first + + + align:start position:0% +looking at the vector sum of the first +and second film okay so I hope that this + + align:start position:0% +and second film okay so I hope that this + + + align:start position:0% +and second film okay so I hope that this +will give you some more intuition about + + align:start position:0% +will give you some more intuition about + + + align:start position:0% +will give you some more intuition about +what we have been doing okay any + + align:start position:0% +what we have been doing okay any + + + align:start position:0% +what we have been doing okay any +questions so far + + align:start position:0% + + + + align:start position:0% + +all right so now we are actually in a + + align:start position:0% +all right so now we are actually in a + + + align:start position:0% +all right so now we are actually in a +very good position once we actually + + align:start position:0% +very good position once we actually + + + align:start position:0% +very good position once we actually +understand this superposition of the two + + align:start position:0% +understand this superposition of the two + + + align:start position:0% +understand this superposition of the two +electric field and interference + + align:start position:0% +electric field and interference + + + align:start position:0% +electric field and interference +basically the size of the resulting + + align:start position:0% +basically the size of the resulting + + + align:start position:0% +basically the size of the resulting +intensity will be highly dependent on + + align:start position:0% +intensity will be highly dependent on + + + align:start position:0% +intensity will be highly dependent on +the phase difference between the two + + align:start position:0% +the phase difference between the two + + + align:start position:0% +the phase difference between the two +field then we are in a very good + + align:start position:0% +field then we are in a very good + + + align:start position:0% +field then we are in a very good +position to discuss the phenomena which + + align:start position:0% +position to discuss the phenomena which + + + align:start position:0% +position to discuss the phenomena which +we just see okay so before I actually + + align:start position:0% +we just see okay so before I actually + + + align:start position:0% +we just see okay so before I actually +perform the calculation and they give + + align:start position:0% +perform the calculation and they give + + + align:start position:0% +perform the calculation and they give +you the explanation I would like to take + + align:start position:0% +you the explanation I would like to take + + + align:start position:0% +you the explanation I would like to take +a voter's of usual okay so the question + + align:start position:0% +a voter's of usual okay so the question + + + align:start position:0% +a voter's of usual okay so the question +we are asking is in addition to what we + + align:start position:0% +we are asking is in addition to what we + + + align:start position:0% +we are asking is in addition to what we +see in the demo we see a colorful bubble + + align:start position:0% +see in the demo we see a colorful bubble + + + align:start position:0% +see in the demo we see a colorful bubble +okay how thick is a soft film such that + + align:start position:0% +okay how thick is a soft film such that + + + align:start position:0% +okay how thick is a soft film such that +you can see color from the refracted + + align:start position:0% +you can see color from the refracted + + + align:start position:0% +you can see color from the refracted +light the first option is maybe is like + + align:start position:0% +light the first option is maybe is like + + + align:start position:0% +light the first option is maybe is like +one millimeter which is possible right + + align:start position:0% +one millimeter which is possible right + + + align:start position:0% +one millimeter which is possible right +and there is a ball the size of the head + + align:start position:0% +and there is a ball the size of the head + + + align:start position:0% +and there is a ball the size of the head +of a pin okay or it can be 100 micron so + + align:start position:0% +of a pin okay or it can be 100 micron so + + + align:start position:0% +of a pin okay or it can be 100 micron so +that says you about the size the + + align:start position:0% +that says you about the size the + + + align:start position:0% +that says you about the size the +signatures power the size of the human + + align:start position:0% +signatures power the size of the human + + + align:start position:0% +signatures power the size of the human +hair or 100 nanometer which is the size + + align:start position:0% +hair or 100 nanometer which is the size + + + align:start position:0% +hair or 100 nanometer which is the size +of the virus okay how many of you think + + align:start position:0% +of the virus okay how many of you think + + + align:start position:0% +of the virus okay how many of you think +the sickness is roughly one millimeter + + align:start position:0% +the sickness is roughly one millimeter + + + align:start position:0% +the sickness is roughly one millimeter +in raise your hand nobody thinks oh + + align:start position:0% +in raise your hand nobody thinks oh + + + align:start position:0% +in raise your hand nobody thinks oh +really + + align:start position:0% +really + + + align:start position:0% +really +okay they say nobody you think that's + + align:start position:0% +okay they say nobody you think that's + + + align:start position:0% +okay they say nobody you think that's +the case how about 100 micron how many + + align:start position:0% +the case how about 100 micron how many + + + align:start position:0% +the case how about 100 micron how many +of you think so how about 100 nanometer + + align:start position:0% +of you think so how about 100 nanometer + + + align:start position:0% +of you think so how about 100 nanometer +I mean of you okay so that is actually + + align:start position:0% +I mean of you okay so that is actually + + + align:start position:0% +I mean of you okay so that is actually +the boat and we are going to know that + + align:start position:0% +the boat and we are going to know that + + + align:start position:0% +the boat and we are going to know that +is a very soon and how about the rest + + align:start position:0% +is a very soon and how about the rest + + + align:start position:0% +is a very soon and how about the rest +okay cool so now we are going to solve + + align:start position:0% +okay cool so now we are going to solve + + + align:start position:0% +okay cool so now we are going to solve +the puzzle so just a quick reminder + + align:start position:0% +the puzzle so just a quick reminder + + + align:start position:0% +the puzzle so just a quick reminder +about what we have learned from the last + + align:start position:0% +about what we have learned from the last + + + align:start position:0% +about what we have learned from the last +lecture okay so there is a reason why we + + align:start position:0% +lecture okay so there is a reason why we + + + align:start position:0% +lecture okay so there is a reason why we +have the lecture first on the refraction + + align:start position:0% +have the lecture first on the refraction + + + align:start position:0% +have the lecture first on the refraction +of the electromagnetic wave before we + + align:start position:0% +of the electromagnetic wave before we + + + align:start position:0% +of the electromagnetic wave before we +discuss the color of the what of the top + + align:start position:0% +discuss the color of the what of the top + + + align:start position:0% +discuss the color of the what of the top +bubble so from the last lecture suppose + + align:start position:0% +bubble so from the last lecture suppose + + + align:start position:0% +bubble so from the last lecture suppose +I have two material which form a + + align:start position:0% +I have two material which form a + + + align:start position:0% +I have two material which form a +interface between the material number + + align:start position:0% +interface between the material number + + + align:start position:0% +interface between the material number +one with refractive index and one and + + align:start position:0% +one with refractive index and one and + + + align:start position:0% +one with refractive index and one and +the second material have refractive + + align:start position:0% +the second material have refractive + + + align:start position:0% +the second material have refractive +index and - okay if I have an incident + + align:start position:0% +index and - okay if I have an incident + + + align:start position:0% +index and - okay if I have an incident +wave in certain electro magnetic prang + + align:start position:0% +wave in certain electro magnetic prang + + + align:start position:0% +wave in certain electro magnetic prang +wave and the incident angle is actually + + align:start position:0% +wave and the incident angle is actually + + + align:start position:0% +wave and the incident angle is actually +in this case zero so that means this + + align:start position:0% +in this case zero so that means this + + + align:start position:0% +in this case zero so that means this +incident a pram wave is actually + + align:start position:0% +incident a pram wave is actually + + + align:start position:0% +incident a pram wave is actually +propagating in the direction which is + + align:start position:0% +propagating in the direction which is + + + align:start position:0% +propagating in the direction which is +actually hitting the surface directive + + align:start position:0% +actually hitting the surface directive + + + align:start position:0% +actually hitting the surface directive +okay so if the initial amplitude is a + + align:start position:0% +okay so if the initial amplitude is a + + + align:start position:0% +okay so if the initial amplitude is a +okay what we have learned from last time + + align:start position:0% +okay what we have learned from last time + + + align:start position:0% +okay what we have learned from last time +is that there will be refracted wave + + align:start position:0% +is that there will be refracted wave + + + align:start position:0% +is that there will be refracted wave +which is actually R times a + + align:start position:0% +which is actually R times a + + + align:start position:0% +which is actually R times a +are essentially the refractive in + + align:start position:0% +are essentially the refractive in + + + align:start position:0% +are essentially the refractive in +coefficient okay refraction coefficient + + align:start position:0% +coefficient okay refraction coefficient + + + align:start position:0% +coefficient okay refraction coefficient +and then finally you you have also the + + align:start position:0% +and then finally you you have also the + + + align:start position:0% +and then finally you you have also the +transmitted wave which actually I have + + align:start position:0% +transmitted wave which actually I have + + + align:start position:0% +transmitted wave which actually I have +okay now I call it P times a and where T + + align:start position:0% +okay now I call it P times a and where T + + + align:start position:0% +okay now I call it P times a and where T +is the transmission coefficient okay + + align:start position:0% +is the transmission coefficient okay + + + align:start position:0% +is the transmission coefficient okay +from the exercise which we actually + + align:start position:0% +from the exercise which we actually + + + align:start position:0% +from the exercise which we actually +already done last time R is equal to n1 + + align:start position:0% +already done last time R is equal to n1 + + + align:start position:0% +already done last time R is equal to n1 +minus n2 divided by n1 plus n2 and while + + align:start position:0% +minus n2 divided by n1 plus n2 and while + + + align:start position:0% +minus n2 divided by n1 plus n2 and while +the transmission coefficient essentially + + align:start position:0% +the transmission coefficient essentially + + + align:start position:0% +the transmission coefficient essentially +T equal to 2 and 1 divided by 1 plus and + + align:start position:0% +T equal to 2 and 1 divided by 1 plus and + + + align:start position:0% +T equal to 2 and 1 divided by 1 plus and +okay so basically what I'm actually + + align:start position:0% +okay so basically what I'm actually + + + align:start position:0% +okay so basically what I'm actually +talking about here is a conclusion from + + align:start position:0% +talking about here is a conclusion from + + + align:start position:0% +talking about here is a conclusion from +the exercise we have done in a last last + + align:start position:0% +the exercise we have done in a last last + + + align:start position:0% +the exercise we have done in a last last +lecture okay just a quick reminder all + + align:start position:0% +lecture okay just a quick reminder all + + + align:start position:0% +lecture okay just a quick reminder all +right so I would like to discuss with + + align:start position:0% +right so I would like to discuss with + + + align:start position:0% +right so I would like to discuss with +you various of situation related to our + + align:start position:0% +you various of situation related to our + + + align:start position:0% +you various of situation related to our +value okay so the N 1 and n 2 are + + align:start position:0% +value okay so the N 1 and n 2 are + + + align:start position:0% +value okay so the N 1 and n 2 are +related to the property of the first + + align:start position:0% +related to the property of the first + + + align:start position:0% +related to the property of the first +median and the second media right so it + + align:start position:0% +median and the second media right so it + + + align:start position:0% +median and the second media right so it +could be that N 1 and n 2 like N 1 is + + align:start position:0% +could be that N 1 and n 2 like N 1 is + + + align:start position:0% +could be that N 1 and n 2 like N 1 is +actually greater than n 2 okay so if N 1 + + align:start position:0% +actually greater than n 2 okay so if N 1 + + + align:start position:0% +actually greater than n 2 okay so if N 1 +is greater than n 2 in the experimental + + align:start position:0% +is greater than n 2 in the experimental + + + align:start position:0% +is greater than n 2 in the experimental +setup so that means the R will be + + align:start position:0% +setup so that means the R will be + + + align:start position:0% +setup so that means the R will be +greater than 0 right ok because R is + + align:start position:0% +greater than 0 right ok because R is + + + align:start position:0% +greater than 0 right ok because R is +your n 1 minus n 2 divided by the son of + + align:start position:0% +your n 1 minus n 2 divided by the son of + + + align:start position:0% +your n 1 minus n 2 divided by the son of +a man - right therefore what I am going + + align:start position:0% +a man - right therefore what I am going + + + align:start position:0% +a man - right therefore what I am going +to get this + + align:start position:0% +to get this + + + align:start position:0% +to get this +so basically I'm going to happen in + + align:start position:0% +so basically I'm going to happen in + + + align:start position:0% +so basically I'm going to happen in +certain wave like this or say I use the + + align:start position:0% +certain wave like this or say I use the + + + align:start position:0% +certain wave like this or say I use the +notation pointing upward okay once they + + align:start position:0% +notation pointing upward okay once they + + + align:start position:0% +notation pointing upward okay once they +can't refract it it is a should be still + + align:start position:0% +can't refract it it is a should be still + + + align:start position:0% +can't refract it it is a should be still +like this pointing upward because the R + + align:start position:0% +like this pointing upward because the R + + + align:start position:0% +like this pointing upward because the R +is issued equator than 0 there is no + + align:start position:0% +is issued equator than 0 there is no + + + align:start position:0% +is issued equator than 0 there is no +change in sign in the amplitude right + + align:start position:0% +change in sign in the amplitude right + + + align:start position:0% +change in sign in the amplitude right +therefore there's no Philippe if the + + align:start position:0% +therefore there's no Philippe if the + + + align:start position:0% +therefore there's no Philippe if the +unwind is as requested and - okay on the + + align:start position:0% +unwind is as requested and - okay on the + + + align:start position:0% +unwind is as requested and - okay on the +other hand the transmitted wave if you + + align:start position:0% +other hand the transmitted wave if you + + + align:start position:0% +other hand the transmitted wave if you +look at the functional form of the + + align:start position:0% +look at the functional form of the + + + align:start position:0% +look at the functional form of the +transmitted wave transmission + + align:start position:0% +transmitted wave transmission + + + align:start position:0% +transmitted wave transmission +coefficient T is actually equal to 2 and + + align:start position:0% +coefficient T is actually equal to 2 and + + + align:start position:0% +coefficient T is actually equal to 2 and +1 divided by n1 plus n2 okay it's always + + align:start position:0% +1 divided by n1 plus n2 okay it's always + + + align:start position:0% +1 divided by n1 plus n2 okay it's always +positive right therefore will be any + + align:start position:0% +positive right therefore will be any + + + align:start position:0% +positive right therefore will be any +possibility to free plus sign no right + + align:start position:0% +possibility to free plus sign no right + + + align:start position:0% +possibility to free plus sign no right +you're absolutely right + + align:start position:0% +you're absolutely right + + + align:start position:0% +you're absolutely right +so therefore what is going to happen is + + align:start position:0% +so therefore what is going to happen is + + + align:start position:0% +so therefore what is going to happen is +that I will use this little arrow to + + align:start position:0% +that I will use this little arrow to + + + align:start position:0% +that I will use this little arrow to +keep track of the sign change basically + + align:start position:0% +keep track of the sign change basically + + + align:start position:0% +keep track of the sign change basically +you see that after I pass through the + + align:start position:0% +you see that after I pass through the + + + align:start position:0% +you see that after I pass through the +boundary there will be no change in sign + + align:start position:0% +boundary there will be no change in sign + + + align:start position:0% +boundary there will be no change in sign +in amplitude okay no matter what + + align:start position:0% +in amplitude okay no matter what + + + align:start position:0% +in amplitude okay no matter what +happened and the other hand if I have + + align:start position:0% +happened and the other hand if I have + + + align:start position:0% +happened and the other hand if I have +the situation and one smoother than n2 + + align:start position:0% +the situation and one smoother than n2 + + + align:start position:0% +the situation and one smoother than n2 +what is going to happen if you calculate + + align:start position:0% +what is going to happen if you calculate + + + align:start position:0% +what is going to happen if you calculate +the R value you will be negative right + + align:start position:0% +the R value you will be negative right + + + align:start position:0% +the R value you will be negative right +in this case I will be smaller than J so + + align:start position:0% +in this case I will be smaller than J so + + + align:start position:0% +in this case I will be smaller than J so +what is going to happen is that if + + align:start position:0% +what is going to happen is that if + + + align:start position:0% +what is going to happen is that if +initially you have something which is + + align:start position:0% +initially you have something which is + + + align:start position:0% +initially you have something which is +they should be the incident wave have + + align:start position:0% +they should be the incident wave have + + + align:start position:0% +they should be the incident wave have +amplitude positive amplitude and I keep + + align:start position:0% +amplitude positive amplitude and I keep + + + align:start position:0% +amplitude positive amplitude and I keep +track of the sign of this amplitude by + + align:start position:0% +track of the sign of this amplitude by + + + align:start position:0% +track of the sign of this amplitude by +this arrow pointing up okay + + align:start position:0% +this arrow pointing up okay + + + align:start position:0% +this arrow pointing up okay +because the eye is actually smaller than + + align:start position:0% +because the eye is actually smaller than + + + align:start position:0% +because the eye is actually smaller than +zero therefore there is a strip in sign + + align:start position:0% +zero therefore there is a strip in sign + + + align:start position:0% +zero therefore there is a strip in sign +in the amplitude okay so what is going + + align:start position:0% +in the amplitude okay so what is going + + + align:start position:0% +in the amplitude okay so what is going +to happen so the refractive wave will + + align:start position:0% +to happen so the refractive wave will + + + align:start position:0% +to happen so the refractive wave will +look like this and I use this arrow to + + align:start position:0% +look like this and I use this arrow to + + + align:start position:0% +look like this and I use this arrow to +keep track of the sleep in amplitude and + + align:start position:0% +keep track of the sleep in amplitude and + + + align:start position:0% +keep track of the sleep in amplitude and +finally as I mentioned before the + + align:start position:0% +finally as I mentioned before the + + + align:start position:0% +finally as I mentioned before the +transmitted wave the T is always + + align:start position:0% +transmitted wave the T is always + + + align:start position:0% +transmitted wave the T is always +positive therefore there will be no + + align:start position:0% +positive therefore there will be no + + + align:start position:0% +positive therefore there will be no +change in size in amplitude okay finally + + align:start position:0% +change in size in amplitude okay finally + + + align:start position:0% +change in size in amplitude okay finally +the third example is if I have somehow + + align:start position:0% +the third example is if I have somehow + + + align:start position:0% +the third example is if I have somehow +two different material but they have the + + align:start position:0% +two different material but they have the + + + align:start position:0% +two different material but they have the +same refractive index what is going to + + align:start position:0% +same refractive index what is going to + + + align:start position:0% +same refractive index what is going to +happen is that there will be no + + align:start position:0% +happen is that there will be no + + + align:start position:0% +happen is that there will be no +refraction and everything goes through + + align:start position:0% +refraction and everything goes through + + + align:start position:0% +refraction and everything goes through +okay even if you have two different + + align:start position:0% +okay even if you have two different + + + align:start position:0% +okay even if you have two different +kinds of material but if they have the + + align:start position:0% +kinds of material but if they have the + + + align:start position:0% +kinds of material but if they have the +same refractive index then what is going + + align:start position:0% +same refractive index then what is going + + + align:start position:0% +same refractive index then what is going +to happen is that every single pass + + align:start position:0% +to happen is that every single pass + + + align:start position:0% +to happen is that every single pass +through and what you are going to get is + + align:start position:0% +through and what you are going to get is + + + align:start position:0% +through and what you are going to get is +that how you have no refracted light + + align:start position:0% +that how you have no refracted light + + + align:start position:0% +that how you have no refracted light +meaning R is actually equal to zero + + align:start position:0% +meaning R is actually equal to zero + + + align:start position:0% +meaning R is actually equal to zero +any questions so far okay + + align:start position:0% +any questions so far okay + + + align:start position:0% +any questions so far okay +I would like to make sure that everybody + + align:start position:0% +I would like to make sure that everybody + + + align:start position:0% +I would like to make sure that everybody +understand the consequence of this + + align:start position:0% +understand the consequence of this + + + align:start position:0% +understand the consequence of this +calculation so if I introduce no flip in + + align:start position:0% +calculation so if I introduce no flip in + + + align:start position:0% +calculation so if I introduce no flip in +amplitude this means that this + + align:start position:0% +amplitude this means that this + + + align:start position:0% +amplitude this means that this +contribution will introduce Delta equal + + align:start position:0% +contribution will introduce Delta equal + + + align:start position:0% +contribution will introduce Delta equal +to zero so basically there will be no + + align:start position:0% +to zero so basically there will be no + + + align:start position:0% +to zero so basically there will be no +change in the face right because there's + + align:start position:0% +change in the face right because there's + + + align:start position:0% +change in the face right because there's +no flip in amplitude and the other hand + + align:start position:0% +no flip in amplitude and the other hand + + + align:start position:0% +no flip in amplitude and the other hand +if this changing sign in amplitude what + + align:start position:0% +if this changing sign in amplitude what + + + align:start position:0% +if this changing sign in amplitude what +would be the resulting Delta value can + + align:start position:0% +would be the resulting Delta value can + + + align:start position:0% +would be the resulting Delta value can +somebody as you tell me you will be PI + + align:start position:0% +somebody as you tell me you will be PI + + + align:start position:0% +somebody as you tell me you will be PI +right very good so that means you are + + align:start position:0% +right very good so that means you are + + + align:start position:0% +right very good so that means you are +getting hit by a phase difference of Pi + + align:start position:0% +getting hit by a phase difference of Pi + + + align:start position:0% +getting hit by a phase difference of Pi +therefore the amplitude change by factor + + align:start position:0% +therefore the amplitude change by factor + + + align:start position:0% +therefore the amplitude change by factor +of cosine PI which is minus one okay + + align:start position:0% +of cosine PI which is minus one okay + + + align:start position:0% +of cosine PI which is minus one okay +so that is actually something pretty + + align:start position:0% +so that is actually something pretty + + + align:start position:0% +so that is actually something pretty +important when we have the discussion of + + align:start position:0% +important when we have the discussion of + + + align:start position:0% +important when we have the discussion of +the of the soap soap apple refraction + + align:start position:0% +the of the soap soap apple refraction + + + align:start position:0% +the of the soap soap apple refraction +all right so let me give you a quick + + align:start position:0% +all right so let me give you a quick + + + align:start position:0% +all right so let me give you a quick +example about what is actually the + + align:start position:0% +example about what is actually the + + + align:start position:0% +example about what is actually the +amount of the refracted light and also + + align:start position:0% +amount of the refracted light and also + + + align:start position:0% +amount of the refracted light and also +what is the amount of the transmitted + + align:start position:0% +what is the amount of the transmitted + + + align:start position:0% +what is the amount of the transmitted +light okay let me give you a concrete + + align:start position:0% +light okay let me give you a concrete + + + align:start position:0% +light okay let me give you a concrete +example for example if I have n1 equal + + align:start position:0% +example for example if I have n1 equal + + + align:start position:0% +example for example if I have n1 equal +to 1 which is actually the refractive + + align:start position:0% +to 1 which is actually the refractive + + + align:start position:0% +to 1 which is actually the refractive +index of the air and unto equal to 1.5 + + align:start position:0% +index of the air and unto equal to 1.5 + + + align:start position:0% +index of the air and unto equal to 1.5 +okay if that happens what is going to + + align:start position:0% +okay if that happens what is going to + + + align:start position:0% +okay if that happens what is going to +what is the resulting intensity okay + + align:start position:0% +what is the resulting intensity okay + + + align:start position:0% +what is the resulting intensity okay +just a quick reminder every G I the the + + align:start position:0% +just a quick reminder every G I the the + + + align:start position:0% +just a quick reminder every G I the the +intensity average intensity will be + + align:start position:0% +intensity average intensity will be + + + align:start position:0% +intensity average intensity will be +equal to C times and as epsilon 0 X + + align:start position:0% +equal to C times and as epsilon 0 X + + + align:start position:0% +equal to C times and as epsilon 0 X +square divided by 2 where a is the + + align:start position:0% +square divided by 2 where a is the + + + align:start position:0% +square divided by 2 where a is the +amplitude of the electric field okay + + align:start position:0% +amplitude of the electric field okay + + + align:start position:0% +amplitude of the electric field okay +just a quick reminder and this a 1 over + + align:start position:0% +just a quick reminder and this a 1 over + + + align:start position:0% +just a quick reminder and this a 1 over +2 is coming from the time average okay + + align:start position:0% +2 is coming from the time average okay + + + align:start position:0% +2 is coming from the time average okay +just a reminder all right so now I can + + align:start position:0% +just a reminder all right so now I can + + + align:start position:0% +just a reminder all right so now I can +go ahead and use this to formula R and P + + align:start position:0% +go ahead and use this to formula R and P + + + align:start position:0% +go ahead and use this to formula R and P +to calculate the refractive refraction + + align:start position:0% +to calculate the refractive refraction + + + align:start position:0% +to calculate the refractive refraction +coefficient and the transmission + + align:start position:0% +coefficient and the transmission + + + align:start position:0% +coefficient and the transmission +coefficient so R will be equal to 1 + + align:start position:0% +coefficient so R will be equal to 1 + + + align:start position:0% +coefficient so R will be equal to 1 +minus 1 point 5 divided by 1 plus 1 + + align:start position:0% +minus 1 point 5 divided by 1 plus 1 + + + align:start position:0% +minus 1 point 5 divided by 1 plus 1 +point 5 so basically you get minus 0.5 + + align:start position:0% +point 5 so basically you get minus 0.5 + + + align:start position:0% +point 5 so basically you get minus 0.5 +divided by 0.5 okay and that this is + + align:start position:0% +divided by 0.5 okay and that this is + + + align:start position:0% +divided by 0.5 okay and that this is +actually going to give you minus 0.2 + + align:start position:0% +actually going to give you minus 0.2 + + + align:start position:0% +actually going to give you minus 0.2 +right of course I can also calculate + + align:start position:0% +right of course I can also calculate + + + align:start position:0% +right of course I can also calculate +will be the T which will be a 2 divided + + align:start position:0% +will be the T which will be a 2 divided + + + align:start position:0% +will be the T which will be a 2 divided +by 2.5 so basically what you are getting + + align:start position:0% +by 2.5 so basically what you are getting + + + align:start position:0% +by 2.5 so basically what you are getting +is 0.8 okay so I can now calculate what + + align:start position:0% +is 0.8 okay so I can now calculate what + + + align:start position:0% +is 0.8 okay so I can now calculate what +will be the resulting intensity of the + + align:start position:0% +will be the resulting intensity of the + + + align:start position:0% +will be the resulting intensity of the +reflected light okay everybody's + + align:start position:0% +reflected light okay everybody's + + + align:start position:0% +reflected light okay everybody's +following right so what would be the + + align:start position:0% +following right so what would be the + + + align:start position:0% +following right so what would be the +intensity of the refracted light + + align:start position:0% +intensity of the refracted light + + + align:start position:0% +intensity of the refracted light +okay this will be equal to minus 0.2 + + align:start position:0% +okay this will be equal to minus 0.2 + + + align:start position:0% +okay this will be equal to minus 0.2 +squared right because the average + + align:start position:0% +squared right because the average + + + align:start position:0% +squared right because the average +intensity is proportional to a square + + align:start position:0% +intensity is proportional to a square + + + align:start position:0% +intensity is proportional to a square +right a is actually the amplitude of the + + align:start position:0% +right a is actually the amplitude of the + + + align:start position:0% +right a is actually the amplitude of the +electric field okay ah as you tell you + + align:start position:0% +electric field okay ah as you tell you + + + align:start position:0% +electric field okay ah as you tell you +what is actually the relative amplitude + + align:start position:0% +what is actually the relative amplitude + + + align:start position:0% +what is actually the relative amplitude +between the refracted light and the Tran + + align:start position:0% +between the refracted light and the Tran + + + align:start position:0% +between the refracted light and the Tran +and the incident light right okay + + align:start position:0% +and the incident light right okay + + + align:start position:0% +and the incident light right okay +therefore you are getting hit by 0.2 + + align:start position:0% +therefore you are getting hit by 0.2 + + + align:start position:0% +therefore you are getting hit by 0.2 +squared multiplied by the initial + + align:start position:0% + + + + align:start position:0% + +intensity okay basically what you are + + align:start position:0% +intensity okay basically what you are + + + align:start position:0% +intensity okay basically what you are +going to get is your point 0 4 I initial + + align:start position:0% +going to get is your point 0 4 I initial + + + align:start position:0% +going to get is your point 0 4 I initial +intensity okay so basically 4 percent of + + align:start position:0% +intensity okay so basically 4 percent of + + + align:start position:0% +intensity okay so basically 4 percent of +the light is refracted okay let me + + align:start position:0% +the light is refracted okay let me + + + align:start position:0% +the light is refracted okay let me +surprise you a bit right because when + + align:start position:0% +surprise you a bit right because when + + + align:start position:0% +surprise you a bit right because when +you see for example the the soap bubble + + align:start position:0% +you see for example the the soap bubble + + + align:start position:0% +you see for example the the soap bubble +you see that is still pretty bright + + align:start position:0% +you see that is still pretty bright + + + align:start position:0% +you see that is still pretty bright +right but in reality only 4 percent of + + align:start position:0% +right but in reality only 4 percent of + + + align:start position:0% +right but in reality only 4 percent of +the light or 4 percent of the intensity + + align:start position:0% +the light or 4 percent of the intensity + + + align:start position:0% +the light or 4 percent of the intensity +Chiropractic okay that is because your + + align:start position:0% +Chiropractic okay that is because your + + + align:start position:0% +Chiropractic okay that is because your +eyes as you had in that linear you're + + align:start position:0% +eyes as you had in that linear you're + + + align:start position:0% +eyes as you had in that linear you're +responsible the UI response to the Orsay + + align:start position:0% +responsible the UI response to the Orsay + + + align:start position:0% +responsible the UI response to the Orsay +receiving or interpretating the the + + align:start position:0% +receiving or interpretating the the + + + align:start position:0% +receiving or interpretating the the +intensity is really highly nonlinear + + align:start position:0% +intensity is really highly nonlinear + + + align:start position:0% +intensity is really highly nonlinear +okay so basically you get four percent + + align:start position:0% +okay so basically you get four percent + + + align:start position:0% +okay so basically you get four percent +refracted and the rest issue the ghost + + align:start position:0% +refracted and the rest issue the ghost + + + align:start position:0% +refracted and the rest issue the ghost +true and and just to convince you that + + align:start position:0% +true and and just to convince you that + + + align:start position:0% +true and and just to convince you that +the total intensity is a hundred percent + + align:start position:0% +the total intensity is a hundred percent + + + align:start position:0% +the total intensity is a hundred percent +we can calculate well the the intensity + + align:start position:0% +we can calculate well the the intensity + + + align:start position:0% +we can calculate well the the intensity +of the transmitted light this will be + + align:start position:0% +of the transmitted light this will be + + + align:start position:0% +of the transmitted light this will be +equal to one point five is actually from + + align:start position:0% +equal to one point five is actually from + + + align:start position:0% +equal to one point five is actually from +related to and - okay right because the + + align:start position:0% +related to and - okay right because the + + + align:start position:0% +related to and - okay right because the +intensity is proportional to C and + + align:start position:0% +intensity is proportional to C and + + + align:start position:0% +intensity is proportional to C and +epsilon 0 a square over 2 + + align:start position:0% +epsilon 0 a square over 2 + + + align:start position:0% +epsilon 0 a square over 2 +okay times T Square so basically you + + align:start position:0% +okay times T Square so basically you + + + align:start position:0% +okay times T Square so basically you +have point a red right and the I initial + + align:start position:0% +have point a red right and the I initial + + + align:start position:0% +have point a red right and the I initial +okay and if I calculate this value + + align:start position:0% +okay and if I calculate this value + + + align:start position:0% +okay and if I calculate this value +basically you are going to get 96 + + align:start position:0% +basically you are going to get 96 + + + align:start position:0% +basically you are going to get 96 +percent intensity so 96 percent of the + + align:start position:0% +percent intensity so 96 percent of the + + + align:start position:0% +percent intensity so 96 percent of the +initial intensity and show the pass + + align:start position:0% +initial intensity and show the pass + + + align:start position:0% +initial intensity and show the pass +through the the boundary and and the + + align:start position:0% +through the the boundary and and the + + + align:start position:0% +through the the boundary and and the +continue and propagate in the second + + align:start position:0% +continue and propagate in the second + + + align:start position:0% +continue and propagate in the second +medium which is actually in this case is + + align:start position:0% +medium which is actually in this case is + + + align:start position:0% +medium which is actually in this case is +the soap all right so the picture is the + + align:start position:0% +the soap all right so the picture is the + + + align:start position:0% +the soap all right so the picture is the +part when hundred percent of light okay + + align:start position:0% +part when hundred percent of light okay + + + align:start position:0% +part when hundred percent of light okay +intensity going to work the boundary + + align:start position:0% +intensity going to work the boundary + + + align:start position:0% +intensity going to work the boundary +what is going to happen is that 4 + + align:start position:0% +what is going to happen is that 4 + + + align:start position:0% +what is going to happen is that 4 +percent of the light refracted four + + align:start position:0% +percent of the light refracted four + + + align:start position:0% +percent of the light refracted four +percent of the intensity Chiropractic + + align:start position:0% +percent of the intensity Chiropractic + + + align:start position:0% +percent of the intensity Chiropractic +and also because N 1 is smaller than and + + align:start position:0% +and also because N 1 is smaller than and + + + align:start position:0% +and also because N 1 is smaller than and +2 therefore there is a rip inside in the + + align:start position:0% +2 therefore there is a rip inside in the + + + align:start position:0% +2 therefore there is a rip inside in the +intensity + + align:start position:0% +intensity + + + align:start position:0% +intensity +also in the in the amputee MMP - and the + + align:start position:0% +also in the in the amputee MMP - and the + + + align:start position:0% +also in the in the amputee MMP - and the +rest continue 96 percent of them and + + align:start position:0% +rest continue 96 percent of them and + + + align:start position:0% +rest continue 96 percent of them and +there is no flippin sign in the + + align:start position:0% +there is no flippin sign in the + + + align:start position:0% +there is no flippin sign in the +amplitude any questions so far + + align:start position:0% +amplitude any questions so far + + + align:start position:0% +amplitude any questions so far +well really pretty close + + align:start position:0% +well really pretty close + + + align:start position:0% +well really pretty close +okay so now we are in a position to + + align:start position:0% +okay so now we are in a position to + + + align:start position:0% +okay so now we are in a position to +discuss what is actually really + + align:start position:0% +discuss what is actually really + + + align:start position:0% +discuss what is actually really +happening to this soap bubble okay so so + + align:start position:0% +happening to this soap bubble okay so so + + + align:start position:0% +happening to this soap bubble okay so so +I'm going to keep this formula this + + align:start position:0% +I'm going to keep this formula this + + + align:start position:0% +I'm going to keep this formula this +result here and I will now discuss a + + align:start position:0% +result here and I will now discuss a + + + align:start position:0% +result here and I will now discuss a +situation which you have three as a two + + align:start position:0% +situation which you have three as a two + + + align:start position:0% +situation which you have three as a two +interface so suppose I do need during an + + align:start position:0% +interface so suppose I do need during an + + + align:start position:0% +interface so suppose I do need during an +Union + + align:start position:0% +Union + + + align:start position:0% +Union +this is so pop oh okay and put it on the + + align:start position:0% +this is so pop oh okay and put it on the + + + align:start position:0% +this is so pop oh okay and put it on the +porn okay + + align:start position:0% +porn okay + + + align:start position:0% +porn okay +so this is I should be the soft soap all + + align:start position:0% +so this is I should be the soft soap all + + + align:start position:0% +so this is I should be the soft soap all +right + + align:start position:0% +right + + + align:start position:0% +right +and I have now but in certain wave which + + align:start position:0% +and I have now but in certain wave which + + + align:start position:0% +and I have now but in certain wave which +is actually going into this pub with + + align:start position:0% +is actually going into this pub with + + + align:start position:0% +is actually going into this pub with +this bubble okay so now I have hundred + + align:start position:0% +this bubble okay so now I have hundred + + + align:start position:0% +this bubble okay so now I have hundred +percent which is actually going to work + + align:start position:0% +percent which is actually going to work + + + align:start position:0% +percent which is actually going to work +this dispute so after this light the + + align:start position:0% +this dispute so after this light the + + + align:start position:0% +this dispute so after this light the +supreme wave heat the room what is going + + align:start position:0% +supreme wave heat the room what is going + + + align:start position:0% +supreme wave heat the room what is going +to happen the first thing which happened + + align:start position:0% +to happen the first thing which happened + + + align:start position:0% +to happen the first thing which happened +is that there will be four percent of + + align:start position:0% +is that there will be four percent of + + + align:start position:0% +is that there will be four percent of +the light double fractal right okay n2 + + align:start position:0% +the light double fractal right okay n2 + + + align:start position:0% +the light double fractal right okay n2 +is equal to 125 is the same setup just + + align:start position:0% +is equal to 125 is the same setup just + + + align:start position:0% +is equal to 125 is the same setup just +to make sure so four percent of the + + align:start position:0% +to make sure so four percent of the + + + align:start position:0% +to make sure so four percent of the +light card refracted of course the sign + + align:start position:0% +light card refracted of course the sign + + + align:start position:0% +light card refracted of course the sign +changed + + align:start position:0% + + + + align:start position:0% + +96% of the intensity as you continue and + + align:start position:0% +96% of the intensity as you continue and + + + align:start position:0% +96% of the intensity as you continue and +what is actually happening is that there + + align:start position:0% +what is actually happening is that there + + + align:start position:0% +what is actually happening is that there +will be no changing everything inside + + align:start position:0% +will be no changing everything inside + + + align:start position:0% +will be no changing everything inside +okay and this is not the end of the + + align:start position:0% +okay and this is not the end of the + + + align:start position:0% +okay and this is not the end of the +story right because the light will + + align:start position:0% +story right because the light will + + + align:start position:0% +story right because the light will +continue and the continue to propagate + + align:start position:0% +continue and the continue to propagate + + + align:start position:0% +continue and the continue to propagate +what is going to happen is that it would + + align:start position:0% +what is going to happen is that it would + + + align:start position:0% +what is going to happen is that it would +reach another boundary where essentially + + align:start position:0% +reach another boundary where essentially + + + align:start position:0% +reach another boundary where essentially +coming the in certain life is as she's + + align:start position:0% +coming the in certain life is as she's + + + align:start position:0% +coming the in certain life is as she's +traveling from and two refractive index + + align:start position:0% +traveling from and two refractive index + + + align:start position:0% +traveling from and two refractive index +material to n1 which is actually okay + + align:start position:0% +material to n1 which is actually okay + + + align:start position:0% +material to n1 which is actually okay +now I have a situation where the light + + align:start position:0% +now I have a situation where the light + + + align:start position:0% +now I have a situation where the light +is actually going through the boundary + + align:start position:0% +is actually going through the boundary + + + align:start position:0% +is actually going through the boundary +and going out of the air okay + + align:start position:0% +and going out of the air okay + + + align:start position:0% +and going out of the air okay +that means the light is actually going + + align:start position:0% +that means the light is actually going + + + align:start position:0% +that means the light is actually going +into the bubble okay so this ratio + + align:start position:0% +into the bubble okay so this ratio + + + align:start position:0% +into the bubble okay so this ratio +inside inside the bubble alright so what + + align:start position:0% +inside inside the bubble alright so what + + + align:start position:0% +inside inside the bubble alright so what +is going to happen is the power + + align:start position:0% +is going to happen is the power + + + align:start position:0% +is going to happen is the power +basically the calculation is the same + + align:start position:0% +basically the calculation is the same + + + align:start position:0% +basically the calculation is the same +except that now the are essentially + + align:start position:0% +except that now the are essentially + + + align:start position:0% +except that now the are essentially +point - instead of - point 2 right + + align:start position:0% +point - instead of - point 2 right + + + align:start position:0% +point - instead of - point 2 right +because now art and to my son - is point + + align:start position:0% +because now art and to my son - is point + + + align:start position:0% +because now art and to my son - is point +5 point 5 divided by 2 point 5 positive + + align:start position:0% +5 point 5 divided by 2 point 5 positive + + + align:start position:0% +5 point 5 divided by 2 point 5 positive +point - all right so basically what you + + align:start position:0% +point - all right so basically what you + + + align:start position:0% +point - all right so basically what you +are going to get is a refracted light + + align:start position:0% +are going to get is a refracted light + + + align:start position:0% +are going to get is a refracted light +which is a 2d doesn't change doesn't + + align:start position:0% +which is a 2d doesn't change doesn't + + + align:start position:0% +which is a 2d doesn't change doesn't +change the sign of the amplitude and + + align:start position:0% +change the sign of the amplitude and + + + align:start position:0% +change the sign of the amplitude and +what is actually the the intensity the + + align:start position:0% +what is actually the the intensity the + + + align:start position:0% +what is actually the the intensity the +intensity will be 96 percent kinds 4 + + align:start position:0% +intensity will be 96 percent kinds 4 + + + align:start position:0% +intensity will be 96 percent kinds 4 +percent right because only 4 percent of + + align:start position:0% +percent right because only 4 percent of + + + align:start position:0% +percent right because only 4 percent of +the light card you practice and of + + align:start position:0% +the light card you practice and of + + + align:start position:0% +the light card you practice and of +course a large fraction of the light as + + align:start position:0% +course a large fraction of the light as + + + align:start position:0% +course a large fraction of the light as +you pass through the bubble 96 percent + + align:start position:0% +you pass through the bubble 96 percent + + + align:start position:0% +you pass through the bubble 96 percent +eyes 96 percent and this will be again + + align:start position:0% +eyes 96 percent and this will be again + + + align:start position:0% +eyes 96 percent and this will be again +pointing upward because T is always + + align:start position:0% +pointing upward because T is always + + + align:start position:0% +pointing upward because T is always +positive okay any questions so far + + align:start position:0% +positive okay any questions so far + + + align:start position:0% +positive okay any questions so far +okay you can see that this is really + + align:start position:0% +okay you can see that this is really + + + align:start position:0% +okay you can see that this is really +interesting because most of the light is + + align:start position:0% +interesting because most of the light is + + + align:start position:0% +interesting because most of the light is +you pass through the bubble right okay + + align:start position:0% +you pass through the bubble right okay + + + align:start position:0% +you pass through the bubble right okay +so now since you already one thing we + + align:start position:0% +so now since you already one thing we + + + align:start position:0% +so now since you already one thing we +learn from this exercise now what is + + align:start position:0% +learn from this exercise now what is + + + align:start position:0% +learn from this exercise now what is +going to happen to this light if I + + align:start position:0% +going to happen to this light if I + + + align:start position:0% +going to happen to this light if I +continue and increase the time what is + + align:start position:0% +continue and increase the time what is + + + align:start position:0% +continue and increase the time what is +going to happen is that this reflected + + align:start position:0% +going to happen is that this reflected + + + align:start position:0% +going to happen is that this reflected +light from the second surface or second + + align:start position:0% +light from the second surface or second + + + align:start position:0% +light from the second surface or second +boundary okay + + align:start position:0% +boundary okay + + + align:start position:0% +boundary okay +well go backward and the path to the + + align:start position:0% +well go backward and the path to the + + + align:start position:0% +well go backward and the path to the +first boundary okay okay so that is + + align:start position:0% +first boundary okay okay so that is + + + align:start position:0% +first boundary okay okay so that is +going to what is going to happen is the + + align:start position:0% +going to what is going to happen is the + + + align:start position:0% +going to what is going to happen is the +powering so basically we are going to + + align:start position:0% +powering so basically we are going to + + + align:start position:0% +powering so basically we are going to +get again transmitted light and then + + align:start position:0% +get again transmitted light and then + + + align:start position:0% +get again transmitted light and then +refracting light + + align:start position:0% +refracting light + + + align:start position:0% +refracting light +okay the refracted light will be the + + align:start position:0% +okay the refracted light will be the + + + align:start position:0% +okay the refracted light will be the +sign of the refracted light for well the + + align:start position:0% +sign of the refracted light for well the + + + align:start position:0% +sign of the refracted light for well the +arrow pointing up or down up yeah very + + align:start position:0% +arrow pointing up or down up yeah very + + + align:start position:0% +arrow pointing up or down up yeah very +good right now if you are bored then + + align:start position:0% +good right now if you are bored then + + + align:start position:0% +good right now if you are bored then +that means I am very successful + + align:start position:0% +that means I am very successful + + + align:start position:0% +that means I am very successful +all right so that means I'm getting four + + align:start position:0% +all right so that means I'm getting four + + + align:start position:0% +all right so that means I'm getting four +percent times 96 percent times four + + align:start position:0% +percent times 96 percent times four + + + align:start position:0% +percent times 96 percent times four +percent okay won't be the sign for the + + align:start position:0% +percent okay won't be the sign for the + + + align:start position:0% +percent okay won't be the sign for the +transmitted light pointing up or down up + + align:start position:0% +transmitted light pointing up or down up + + + align:start position:0% +transmitted light pointing up or down up +very good everybody right and the 96 + + align:start position:0% +very good everybody right and the 96 + + + align:start position:0% +very good everybody right and the 96 +percent pasture 96 percent times 96 + + align:start position:0% +percent pasture 96 percent times 96 + + + align:start position:0% +percent pasture 96 percent times 96 +percent times opposite okay okay and of + + align:start position:0% +percent times opposite okay okay and of + + + align:start position:0% +percent times opposite okay okay and of +course I can now continue and continue + + align:start position:0% +course I can now continue and continue + + + align:start position:0% +course I can now continue and continue +what is going to happen is that now you + + align:start position:0% +what is going to happen is that now you + + + align:start position:0% +what is going to happen is that now you +would have learned a or tree you will + + align:start position:0% +would have learned a or tree you will + + + align:start position:0% +would have learned a or tree you will +see that this is a crazy phenomena right + + align:start position:0% +see that this is a crazy phenomena right + + + align:start position:0% +see that this is a crazy phenomena right +what is going to happen is that there + + align:start position:0% +what is going to happen is that there + + + align:start position:0% +what is going to happen is that there +will be a tiny fraction of a light which + + align:start position:0% +will be a tiny fraction of a light which + + + align:start position:0% +will be a tiny fraction of a light which +is trapped forever between the two + + align:start position:0% +is trapped forever between the two + + + align:start position:0% +is trapped forever between the two +surface you are going to be bouncing + + align:start position:0% +surface you are going to be bouncing + + + align:start position:0% +surface you are going to be bouncing +back and forth OOP OOP OOP OOP OOP OOP + + align:start position:0% +back and forth OOP OOP OOP OOP OOP OOP + + + align:start position:0% +back and forth OOP OOP OOP OOP OOP OOP +forever okay of course that the fraction + + align:start position:0% +forever okay of course that the fraction + + + align:start position:0% +forever okay of course that the fraction +of the intensity is really really small + + align:start position:0% +of the intensity is really really small + + + align:start position:0% +of the intensity is really really small +okay is because every time you've got + + align:start position:0% +okay is because every time you've got + + + align:start position:0% +okay is because every time you've got +the refraction actually happened you + + align:start position:0% +the refraction actually happened you + + + align:start position:0% +the refraction actually happened you +take a hit of four percent right but + + align:start position:0% +take a hit of four percent right but + + + align:start position:0% +take a hit of four percent right but +since we are talking of + + align:start position:0% +since we are talking of + + + align:start position:0% +since we are talking of +our theoretical physics so theoretical + + align:start position:0% +our theoretical physics so theoretical + + + align:start position:0% +our theoretical physics so theoretical +dduba continue forever okay that's + + align:start position:0% +dduba continue forever okay that's + + + align:start position:0% +dduba continue forever okay that's +actually pretty interesting and going + + align:start position:0% +actually pretty interesting and going + + + align:start position:0% +actually pretty interesting and going +back to practical situation basically I + + align:start position:0% +back to practical situation basically I + + + align:start position:0% +back to practical situation basically I +can safely ignore any further refraction + + align:start position:0% +can safely ignore any further refraction + + + align:start position:0% +can safely ignore any further refraction +because they are heat is so hard because + + align:start position:0% +because they are heat is so hard because + + + align:start position:0% +because they are heat is so hard because +they're made every time I get the 4% + + align:start position:0% +they're made every time I get the 4% + + + align:start position:0% +they're made every time I get the 4% +heat right therefore I can ignore all + + align:start position:0% +heat right therefore I can ignore all + + + align:start position:0% +heat right therefore I can ignore all +the other contributions and the what we + + align:start position:0% +the other contributions and the what we + + + align:start position:0% +the other contributions and the what we +are actually seeing is what our IDs here + + align:start position:0% +are actually seeing is what our IDs here + + + align:start position:0% +are actually seeing is what our IDs here +okay we see the contribution of the + + align:start position:0% +okay we see the contribution of the + + + align:start position:0% +okay we see the contribution of the +first pass which actually refracted from + + align:start position:0% +first pass which actually refracted from + + + align:start position:0% +first pass which actually refracted from +the first surface the second pass is a + + align:start position:0% +the first surface the second pass is a + + + align:start position:0% +the first surface the second pass is a +token a pass through the first service + + align:start position:0% +token a pass through the first service + + + align:start position:0% +token a pass through the first service +because refracted from the second + + align:start position:0% +because refracted from the second + + + align:start position:0% +because refracted from the second +boundary and pass through the first + + align:start position:0% +boundary and pass through the first + + + align:start position:0% +boundary and pass through the first +boundary in that in the second round and + + align:start position:0% +boundary in that in the second round and + + + align:start position:0% +boundary in that in the second round and +then also reach in you are okay so what + + align:start position:0% +then also reach in you are okay so what + + + align:start position:0% +then also reach in you are okay so what +are we looking at we are looking at the + + align:start position:0% +are we looking at we are looking at the + + + align:start position:0% +are we looking at we are looking at the +superposition of two electromagnetic + + align:start position:0% +superposition of two electromagnetic + + + align:start position:0% +superposition of two electromagnetic +wave coming from one which is like this + + align:start position:0% +wave coming from one which is like this + + + align:start position:0% +wave coming from one which is like this +and two which is actually like this okay + + align:start position:0% +and two which is actually like this okay + + + align:start position:0% +and two which is actually like this okay +the question now is what is the sickness + + align:start position:0% +the question now is what is the sickness + + + align:start position:0% +the question now is what is the sickness +of the the film which now I can define + + align:start position:0% +of the the film which now I can define + + + align:start position:0% +of the the film which now I can define +the sickness or say the width of this + + align:start position:0% +the sickness or say the width of this + + + align:start position:0% +the sickness or say the width of this +film + + align:start position:0% +film + + + align:start position:0% +film +to be deep okay now the question we are + + align:start position:0% +to be deep okay now the question we are + + + align:start position:0% +to be deep okay now the question we are +actually asking is what would be the + + align:start position:0% +actually asking is what would be the + + + align:start position:0% +actually asking is what would be the +sickness fee okay which is needed such + + align:start position:0% +sickness fee okay which is needed such + + + align:start position:0% +sickness fee okay which is needed such +that I can have constructive + + align:start position:0% +that I can have constructive + + + align:start position:0% +that I can have constructive +interference okay now the question + + align:start position:0% +interference okay now the question + + + align:start position:0% +interference okay now the question +becomes really good year and the weekend + + align:start position:0% +becomes really good year and the weekend + + + align:start position:0% +becomes really good year and the weekend +HD calculate that by evaluating the + + align:start position:0% +HD calculate that by evaluating the + + + align:start position:0% +HD calculate that by evaluating the +phase difference between the past number + + align:start position:0% +phase difference between the past number + + + align:start position:0% +phase difference between the past number +one and the past number two okay so now + + align:start position:0% +one and the past number two okay so now + + + align:start position:0% +one and the past number two okay so now +what I need in order to have + + align:start position:0% +what I need in order to have + + + align:start position:0% +what I need in order to have +constructive interference + + align:start position:0% +constructive interference + + + align:start position:0% +constructive interference +I need a specific phase difference but + + align:start position:0% +I need a specific phase difference but + + + align:start position:0% +I need a specific phase difference but +before that I need to calculate the + + align:start position:0% +before that I need to calculate the + + + align:start position:0% +before that I need to calculate the +phase difference first between one test + + align:start position:0% +phase difference first between one test + + + align:start position:0% +phase difference first between one test +number one in the past number two okay + + align:start position:0% +number one in the past number two okay + + + align:start position:0% +number one in the past number two okay +what would be the past phase phase + + align:start position:0% +what would be the past phase phase + + + align:start position:0% +what would be the past phase phase +difference the phase difference there + + align:start position:0% +difference the phase difference there + + + align:start position:0% +difference the phase difference there +that will be equal to of course PI this + + align:start position:0% +that will be equal to of course PI this + + + align:start position:0% +that will be equal to of course PI this +pi contribution is coming from the flip + + align:start position:0% +pi contribution is coming from the flip + + + align:start position:0% +pi contribution is coming from the flip +of the amplitude right now actually give + + align:start position:0% +of the amplitude right now actually give + + + align:start position:0% +of the amplitude right now actually give +you a HR PI phase difference the second + + align:start position:0% +you a HR PI phase difference the second + + + align:start position:0% +you a HR PI phase difference the second +phase difference is coming from the + + align:start position:0% +phase difference is coming from the + + + align:start position:0% +phase difference is coming from the +difference in the optical past lens you + + align:start position:0% +difference in the optical past lens you + + + align:start position:0% +difference in the optical past lens you +can see that the first pass it doesn't + + align:start position:0% +can see that the first pass it doesn't + + + align:start position:0% +can see that the first pass it doesn't +go into the film okay it had refracted + + align:start position:0% +go into the film okay it had refracted + + + align:start position:0% +go into the film okay it had refracted +directly and the second pass which is + + align:start position:0% +directly and the second pass which is + + + align:start position:0% +directly and the second pass which is +passed number two it takes more effort + + align:start position:0% +passed number two it takes more effort + + + align:start position:0% +passed number two it takes more effort +or more time for this foot for the light + + align:start position:0% +or more time for this foot for the light + + + align:start position:0% +or more time for this foot for the light +to go back and the rituai okay how big + + align:start position:0% +to go back and the rituai okay how big + + + align:start position:0% +to go back and the rituai okay how big +is the the past-tense difference the the + + align:start position:0% +is the the past-tense difference the the + + + align:start position:0% +is the the past-tense difference the the +size of the path length difference is + + align:start position:0% +size of the path length difference is + + + align:start position:0% +size of the path length difference is +two times D right + + align:start position:0% +two times D right + + + align:start position:0% +two times D right +all right of course I need to actually + + align:start position:0% +all right of course I need to actually + + + align:start position:0% +all right of course I need to actually +translate that back to the LaFace right + + align:start position:0% +translate that back to the LaFace right + + + align:start position:0% +translate that back to the LaFace right +so so - so first I need to actually + + align:start position:0% +so so - so first I need to actually + + + align:start position:0% +so so - so first I need to actually +calculate how many period so the length + + align:start position:0% +calculate how many period so the length + + + align:start position:0% +calculate how many period so the length +divided by lambda will be the period + + align:start position:0% +divided by lambda will be the period + + + align:start position:0% +divided by lambda will be the period +right so lambda is a should be lambda is + + align:start position:0% +right so lambda is a should be lambda is + + + align:start position:0% +right so lambda is a should be lambda is +actually the wave length of the incident + + align:start position:0% +actually the wave length of the incident + + + align:start position:0% +actually the wave length of the incident +light okay but I am missing a factor + + align:start position:0% +light okay but I am missing a factor + + + align:start position:0% +light okay but I am missing a factor +here okay and can somebody help me + + align:start position:0% +here okay and can somebody help me + + + align:start position:0% +here okay and can somebody help me +because this lambda is actually inside + + align:start position:0% +because this lambda is actually inside + + + align:start position:0% +because this lambda is actually inside +the material right so which factor I'm + + align:start position:0% +the material right so which factor I'm + + + align:start position:0% +the material right so which factor I'm +missing and - right yeah thank you very + + align:start position:0% +missing and - right yeah thank you very + + + align:start position:0% +missing and - right yeah thank you very +much + + align:start position:0% +much + + + align:start position:0% +much +so basically inside the material since + + align:start position:0% +so basically inside the material since + + + align:start position:0% +so basically inside the material since +the speed of light is 1.5 times smaller + + align:start position:0% +the speed of light is 1.5 times smaller + + + align:start position:0% +the speed of light is 1.5 times smaller +than the speed of light in vacuum + + align:start position:0% +than the speed of light in vacuum + + + align:start position:0% +than the speed of light in vacuum +therefore the speed let us say that the + + align:start position:0% +therefore the speed let us say that the + + + align:start position:0% +therefore the speed let us say that the +wavelength is actually done - D by D by + + align:start position:0% +wavelength is actually done - D by D by + + + align:start position:0% +wavelength is actually done - D by D by +and - okay and this is actually the + + align:start position:0% +and - okay and this is actually the + + + align:start position:0% +and - okay and this is actually the +number of period and now I need to + + align:start position:0% +number of period and now I need to + + + align:start position:0% +number of period and now I need to +translate that to phase difference + + align:start position:0% +translate that to phase difference + + + align:start position:0% +translate that to phase difference +therefore I multiply this by 2 pi okay + + align:start position:0% +therefore I multiply this by 2 pi okay + + + align:start position:0% +therefore I multiply this by 2 pi okay +so you can see that now I have + + align:start position:0% +so you can see that now I have + + + align:start position:0% +so you can see that now I have +successfully evaluated or quantify the + + align:start position:0% +successfully evaluated or quantify the + + + align:start position:0% +successfully evaluated or quantify the +phase difference between past number 1 + + align:start position:0% +phase difference between past number 1 + + + align:start position:0% +phase difference between past number 1 +and 2 that is there are two contribution + + align:start position:0% +and 2 that is there are two contribution + + + align:start position:0% +and 2 that is there are two contribution +the first one is PI is related to the + + align:start position:0% +the first one is PI is related to the + + + align:start position:0% +the first one is PI is related to the +flip in amplitude okay the second + + align:start position:0% +flip in amplitude okay the second + + + align:start position:0% +flip in amplitude okay the second +contribution the blue one is actually + + align:start position:0% +contribution the blue one is actually + + + align:start position:0% +contribution the blue one is actually +coming from the optical path length + + align:start position:0% +coming from the optical path length + + + align:start position:0% +coming from the optical path length +difference okay and of course you can + + align:start position:0% +difference okay and of course you can + + + align:start position:0% +difference okay and of course you can +evaluate that really precisely therefore + + align:start position:0% +evaluate that really precisely therefore + + + align:start position:0% +evaluate that really precisely therefore +we can now quickly conclude that in + + align:start position:0% +we can now quickly conclude that in + + + align:start position:0% +we can now quickly conclude that in +order to have constructive in + + align:start position:0% +order to have constructive in + + + align:start position:0% +order to have constructive in +constructive interference + + align:start position:0% + + + + align:start position:0% + +okay I need to have Delta equal to two + + align:start position:0% +okay I need to have Delta equal to two + + + align:start position:0% +okay I need to have Delta equal to two +pi where n is an integer + + align:start position:0% +pi where n is an integer + + + align:start position:0% +pi where n is an integer +okay and in order to have destructive + + align:start position:0% +okay and in order to have destructive + + + align:start position:0% +okay and in order to have destructive +interference I need to have I need to + + align:start position:0% +interference I need to have I need to + + + align:start position:0% +interference I need to have I need to +have Delta equal to 2 n plus 1 which we + + align:start position:0% +have Delta equal to 2 n plus 1 which we + + + align:start position:0% +have Delta equal to 2 n plus 1 which we +said should be the result of the + + align:start position:0% +said should be the result of the + + + align:start position:0% +said should be the result of the +calculation which we have done I think + + align:start position:0% +calculation which we have done I think + + + align:start position:0% +calculation which we have done I think +so this is actually based on the + + align:start position:0% +so this is actually based on the + + + align:start position:0% +so this is actually based on the +calculation we have done in the + + align:start position:0% +calculation we have done in the + + + align:start position:0% +calculation we have done in the +beginning ok so we are really close so + + align:start position:0% +beginning ok so we are really close so + + + align:start position:0% +beginning ok so we are really close so +now we have this result Delta is equal + + align:start position:0% +now we have this result Delta is equal + + + align:start position:0% +now we have this result Delta is equal +to PI plus 2d divided times 2 pi divided + + align:start position:0% +to PI plus 2d divided times 2 pi divided + + + align:start position:0% +to PI plus 2d divided times 2 pi divided +by lambda divided by 1/2 right so this + + align:start position:0% +by lambda divided by 1/2 right so this + + + align:start position:0% +by lambda divided by 1/2 right so this +complicated formula now we are in the + + align:start position:0% +complicated formula now we are in the + + + align:start position:0% +complicated formula now we are in the +position to evaluate what would be the + + align:start position:0% +position to evaluate what would be the + + + align:start position:0% +position to evaluate what would be the +the face to face so the first thing + + align:start position:0% +the face to face so the first thing + + + align:start position:0% +the face to face so the first thing +which I would like to discuss is that + + align:start position:0% +which I would like to discuss is that + + + align:start position:0% +which I would like to discuss is that +when T goes to 0 what is actually the + + align:start position:0% +when T goes to 0 what is actually the + + + align:start position:0% +when T goes to 0 what is actually the +limit the demon is that when does the + + align:start position:0% +limit the demon is that when does the + + + align:start position:0% +limit the demon is that when does the +width of the table film is really really + + align:start position:0% +width of the table film is really really + + + align:start position:0% +width of the table film is really really +small goes to 0 okay what is going to + + align:start position:0% +small goes to 0 okay what is going to + + + align:start position:0% +small goes to 0 okay what is going to +happen you are going to have destructive + + align:start position:0% + + + + align:start position:0% + +that is because even when you have T + + align:start position:0% +that is because even when you have T + + + align:start position:0% +that is because even when you have T +equal to 0 the Delta is path because of + + align:start position:0% +equal to 0 the Delta is path because of + + + align:start position:0% +equal to 0 the Delta is path because of +the flip inside in the first pass + + align:start position:0% +the flip inside in the first pass + + + align:start position:0% +the flip inside in the first pass +numbers number 1 ok + + align:start position:0% +numbers number 1 ok + + + align:start position:0% +numbers number 1 ok +the second thing is that now I can + + align:start position:0% +the second thing is that now I can + + + align:start position:0% +the second thing is that now I can +calculate what will be the constructive + + align:start position:0% +calculate what will be the constructive + + + align:start position:0% +calculate what will be the constructive +interference with + + align:start position:0% + + + + align:start position:0% + +okay so this will happen when T is equal + + align:start position:0% +okay so this will happen when T is equal + + + align:start position:0% +okay so this will happen when T is equal +to 2 m minus 1 and divided by 4 and 2 so + + align:start position:0% +to 2 m minus 1 and divided by 4 and 2 so + + + align:start position:0% +to 2 m minus 1 and divided by 4 and 2 so +basically you can use that formula there + + align:start position:0% +basically you can use that formula there + + + align:start position:0% +basically you can use that formula there +ok and solve B then basically that's the + + align:start position:0% +ok and solve B then basically that's the + + + align:start position:0% +ok and solve B then basically that's the +formula we are going to get and I will + + align:start position:0% +formula we are going to get and I will + + + align:start position:0% +formula we are going to get and I will +not go into detail this ok any questions + + align:start position:0% +not go into detail this ok any questions + + + align:start position:0% +not go into detail this ok any questions +so far + + align:start position:0% + + + + align:start position:0% + +ok so now if I so the self conclusion is + + align:start position:0% +ok so now if I so the self conclusion is + + + align:start position:0% +ok so now if I so the self conclusion is +that if I fix if I fix T and land and + + align:start position:0% +that if I fix if I fix T and land and + + + align:start position:0% +that if I fix if I fix T and land and +and the change ladder + + align:start position:0% + + + + align:start position:0% + +ok so that is actually the practical + + align:start position:0% +ok so that is actually the practical + + + align:start position:0% +ok so that is actually the practical +situation right because I have the soft + + align:start position:0% +situation right because I have the soft + + + align:start position:0% +situation right because I have the soft +bubble and we have a well defined ways + + align:start position:0% +bubble and we have a well defined ways + + + align:start position:0% +bubble and we have a well defined ways +which is D ok and what is happening is + + align:start position:0% +which is D ok and what is happening is + + + align:start position:0% +which is D ok and what is happening is +that I am trying to shine this soap + + align:start position:0% +that I am trying to shine this soap + + + align:start position:0% +that I am trying to shine this soap +bubble with light with different + + align:start position:0% +bubble with light with different + + + align:start position:0% +bubble with light with different +wavelengths right ok so so that's + + align:start position:0% +wavelengths right ok so so that's + + + align:start position:0% +wavelengths right ok so so that's +essentially the third situation if I fix + + align:start position:0% +essentially the third situation if I fix + + + align:start position:0% +essentially the third situation if I fix +the ways of the view and change the wave + + align:start position:0% +the ways of the view and change the wave + + + align:start position:0% +the ways of the view and change the wave +length lambda okay + + align:start position:0% +length lambda okay + + + align:start position:0% +length lambda okay +why I am going to get this that the + + align:start position:0% +why I am going to get this that the + + + align:start position:0% +why I am going to get this that the +lambda max which is the wavelength + + align:start position:0% +lambda max which is the wavelength + + + align:start position:0% +lambda max which is the wavelength +needed to have constructive interference + + align:start position:0% +needed to have constructive interference + + + align:start position:0% +needed to have constructive interference +okay + + align:start position:0% + + + + align:start position:0% + +okay lambda max will be equal to 4t + 2 + + align:start position:0% +okay lambda max will be equal to 4t + 2 + + + align:start position:0% +okay lambda max will be equal to 4t + 2 +divided by 2 n minus 1 so basically I + + align:start position:0% +divided by 2 n minus 1 so basically I + + + align:start position:0% +divided by 2 n minus 1 so basically I +can solve the lambda if I'm given a + + align:start position:0% +can solve the lambda if I'm given a + + + align:start position:0% +can solve the lambda if I'm given a +debug okay so actually we already get + + align:start position:0% +debug okay so actually we already get + + + align:start position:0% +debug okay so actually we already get +the answer we are asking in the + + align:start position:0% +the answer we are asking in the + + + align:start position:0% +the answer we are asking in the +beginning okay the first question is why + + align:start position:0% +beginning okay the first question is why + + + align:start position:0% +beginning okay the first question is why +do we see color the second question is + + align:start position:0% +do we see color the second question is + + + align:start position:0% +do we see color the second question is +when I see color what is actually the + + align:start position:0% +when I see color what is actually the + + + align:start position:0% +when I see color what is actually the +width of the soap film we are going to + + align:start position:0% +width of the soap film we are going to + + + align:start position:0% +width of the soap film we are going to +know that we saw in the moment so now I + + align:start position:0% +know that we saw in the moment so now I + + + align:start position:0% +know that we saw in the moment so now I +have this formula in hand if I have T + + align:start position:0% +have this formula in hand if I have T + + + align:start position:0% +have this formula in hand if I have T +okay roughly equal to 100 nanometer okay + + align:start position:0% +okay roughly equal to 100 nanometer okay + + + align:start position:0% +okay roughly equal to 100 nanometer okay +which is the second option which we were + + align:start position:0% +which is the second option which we were + + + align:start position:0% +which is the second option which we were +discussing okay so I thought which is + + align:start position:0% +discussing okay so I thought which is + + + align:start position:0% +discussing okay so I thought which is +the the third option we were discussing + + align:start position:0% +the the third option we were discussing + + + align:start position:0% +the the third option we were discussing +okay all right if T is roughly 100 + + align:start position:0% +okay all right if T is roughly 100 + + + align:start position:0% +okay all right if T is roughly 100 +nanometer okay so that is going to give + + align:start position:0% +nanometer okay so that is going to give + + + align:start position:0% +nanometer okay so that is going to give +you lambda maxima equal to four kinds + + align:start position:0% +you lambda maxima equal to four kinds + + + align:start position:0% +you lambda maxima equal to four kinds +100 nanometer times 1.5 and 2 is 1 point + + align:start position:0% +100 nanometer times 1.5 and 2 is 1 point + + + align:start position:0% +100 nanometer times 1.5 and 2 is 1 point +5 divided by 2 minus 1 okay so that is + + align:start position:0% +5 divided by 2 minus 1 okay so that is + + + align:start position:0% +5 divided by 2 minus 1 okay so that is +actually 600 nanometer divided by 2 + + align:start position:0% +actually 600 nanometer divided by 2 + + + align:start position:0% +actually 600 nanometer divided by 2 +minus 1 okay suppose I have n equal to 1 + + align:start position:0% +minus 1 okay suppose I have n equal to 1 + + + align:start position:0% +minus 1 okay suppose I have n equal to 1 +basically I getting 400 also at 600 + + align:start position:0% +basically I getting 400 also at 600 + + + align:start position:0% +basically I getting 400 also at 600 +nanometer suppose I have n equal to 2 + + align:start position:0% +nanometer suppose I have n equal to 2 + + + align:start position:0% +nanometer suppose I have n equal to 2 +okay 2 and minus 1 is e to the 4 minus 1 + + align:start position:0% +okay 2 and minus 1 is e to the 4 minus 1 + + + align:start position:0% +okay 2 and minus 1 is e to the 4 minus 1 +is 3 therefore you get 200 nanometer and + + align:start position:0% +is 3 therefore you get 200 nanometer and + + + align:start position:0% +is 3 therefore you get 200 nanometer and +120 parameter + + align:start position:0% +120 parameter + + + align:start position:0% +120 parameter +which other required the wavelength okay + + align:start position:0% +which other required the wavelength okay + + + align:start position:0% +which other required the wavelength okay +in order to have constructive + + align:start position:0% +in order to have constructive + + + align:start position:0% +in order to have constructive +interference between pests number one + + align:start position:0% +interference between pests number one + + + align:start position:0% +interference between pests number one +and the past number two okay everybody + + align:start position:0% +and the past number two okay everybody + + + align:start position:0% +and the past number two okay everybody +is following alright if I plot the + + align:start position:0% +is following alright if I plot the + + + align:start position:0% +is following alright if I plot the +spectra of this lambda max assuming T is + + align:start position:0% +spectra of this lambda max assuming T is + + + align:start position:0% +spectra of this lambda max assuming T is +100 nanometer okay what I am getting is + + align:start position:0% +100 nanometer okay what I am getting is + + + align:start position:0% +100 nanometer okay what I am getting is +like this okay so this is a situation of + + align:start position:0% +like this okay so this is a situation of + + + align:start position:0% +like this okay so this is a situation of +very seen you okay so this is that okay + + align:start position:0% +very seen you okay so this is that okay + + + align:start position:0% +very seen you okay so this is that okay +what I'm getting is that okay there + + align:start position:0% +what I'm getting is that okay there + + + align:start position:0% +what I'm getting is that okay there +would be a Maxima here could you say + + align:start position:0% +would be a Maxima here could you say + + + align:start position:0% +would be a Maxima here could you say +should be 600 nanometer okay red color + + align:start position:0% +should be 600 nanometer okay red color + + + align:start position:0% +should be 600 nanometer okay red color +it says should be roughly 600 650 narrow + + align:start position:0% +it says should be roughly 600 650 narrow + + + align:start position:0% +it says should be roughly 600 650 narrow +meter it's a red light and that this + + align:start position:0% +meter it's a red light and that this + + + align:start position:0% +meter it's a red light and that this +issue is roughly the range of the + + align:start position:0% +issue is roughly the range of the + + + align:start position:0% +issue is roughly the range of the +visible light okay which is a cheap + + align:start position:0% +visible light okay which is a cheap + + + align:start position:0% +visible light okay which is a cheap +between lambda equal to lambda violet + + align:start position:0% +between lambda equal to lambda violet + + + align:start position:0% +between lambda equal to lambda violet +okay by all that is equal to 400 all + + align:start position:0% +okay by all that is equal to 400 all + + + align:start position:0% +okay by all that is equal to 400 all +right so you can see that the first + + align:start position:0% +right so you can see that the first + + + align:start position:0% +right so you can see that the first +Maxima Landa Maxima where you have + + align:start position:0% +Maxima Landa Maxima where you have + + + align:start position:0% +Maxima Landa Maxima where you have +constructive interference is at 600 + + align:start position:0% +constructive interference is at 600 + + + align:start position:0% +constructive interference is at 600 +nanometer okay so that means you are + + align:start position:0% +nanometer okay so that means you are + + + align:start position:0% +nanometer okay so that means you are +going to see what kind of color in your + + align:start position:0% +going to see what kind of color in your + + + align:start position:0% +going to see what kind of color in your +soap bubble you're going to see is red + + align:start position:0% +soap bubble you're going to see is red + + + align:start position:0% +soap bubble you're going to see is red +right and then the sick the next + + align:start position:0% +right and then the sick the next + + + align:start position:0% +right and then the sick the next +wavelengths which you can have + + align:start position:0% +wavelengths which you can have + + + align:start position:0% +wavelengths which you can have +constructive interference is 200 + + align:start position:0% +constructive interference is 200 + + + align:start position:0% +constructive interference is 200 +nanometer not is a should be shorter + + align:start position:0% +nanometer not is a should be shorter + + + align:start position:0% +nanometer not is a should be shorter +then the wavelengths of the violet light + + align:start position:0% +then the wavelengths of the violet light + + + align:start position:0% +then the wavelengths of the violet light +is out of the range of the visible light + + align:start position:0% +is out of the range of the visible light + + + align:start position:0% +is out of the range of the visible light +okay what is going to happen your eye + + align:start position:0% +okay what is going to happen your eye + + + align:start position:0% +okay what is going to happen your eye +will not see it right all right so that + + align:start position:0% +will not see it right all right so that + + + align:start position:0% +will not see it right all right so that +the next one would be here there's a + + align:start position:0% +the next one would be here there's a + + + align:start position:0% +the next one would be here there's a +wire bra bra bra bra which I don't care + + align:start position:0% +wire bra bra bra bra which I don't care + + + align:start position:0% +wire bra bra bra bra which I don't care +because they are so short in worthless + + align:start position:0% +because they are so short in worthless + + + align:start position:0% +because they are so short in worthless +and you cannot see + + align:start position:0% +and you cannot see + + + align:start position:0% +and you cannot see +okay so you can see that if I have a + + align:start position:0% +okay so you can see that if I have a + + + align:start position:0% +okay so you can see that if I have a +wish which is roughly hundred nanometer + + align:start position:0% +wish which is roughly hundred nanometer + + + align:start position:0% +wish which is roughly hundred nanometer +very same situation what is going to + + align:start position:0% +very same situation what is going to + + + align:start position:0% +very same situation what is going to +happen what is going to happen is that + + align:start position:0% +happen what is going to happen is that + + + align:start position:0% +happen what is going to happen is that +you are going to get only one Maxima in + + align:start position:0% +you are going to get only one Maxima in + + + align:start position:0% +you are going to get only one Maxima in +the visible light range and therefore + + align:start position:0% +the visible light range and therefore + + + align:start position:0% +the visible light range and therefore +you can see color okay any questions so + + align:start position:0% +you can see color okay any questions so + + + align:start position:0% +you can see color okay any questions so +far + + align:start position:0% +far + + + align:start position:0% +far +okay now what I'm going to do is take + + align:start position:0% +okay now what I'm going to do is take + + + align:start position:0% +okay now what I'm going to do is take +the same formula here but now I would + + align:start position:0% +the same formula here but now I would + + + align:start position:0% +the same formula here but now I would +like to change the this T so now I would + + align:start position:0% +like to change the this T so now I would + + + align:start position:0% +like to change the this T so now I would +like to change the D to consider a + + align:start position:0% +like to change the D to consider a + + + align:start position:0% +like to change the D to consider a +situation where you have a very thick + + align:start position:0% +situation where you have a very thick + + + align:start position:0% +situation where you have a very thick +layer okay so now I would like to change + + align:start position:0% +layer okay so now I would like to change + + + align:start position:0% +layer okay so now I would like to change +the situation + + align:start position:0% +the situation + + + align:start position:0% +the situation +to a very thick layer so maybe I need to + + align:start position:0% +to a very thick layer so maybe I need to + + + align:start position:0% +to a very thick layer so maybe I need to +erase this part of the board make some + + align:start position:0% +erase this part of the board make some + + + align:start position:0% +erase this part of the board make some +space so now if I have T equal to 100 + + align:start position:0% +space so now if I have T equal to 100 + + + align:start position:0% +space so now if I have T equal to 100 +micron okay what is going to happen so I + + align:start position:0% +micron okay what is going to happen so I + + + align:start position:0% +micron okay what is going to happen so I +can now still use this formula to + + align:start position:0% +can now still use this formula to + + + align:start position:0% +can now still use this formula to +calculate what will be the lambda Maxima + + align:start position:0% +calculate what will be the lambda Maxima + + + align:start position:0% +calculate what will be the lambda Maxima +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so lambda maximum will be equal to 600 + + align:start position:0% +so lambda maximum will be equal to 600 + + + align:start position:0% +so lambda maximum will be equal to 600 +micron which is when you have an equal + + align:start position:0% +micron which is when you have an equal + + + align:start position:0% +micron which is when you have an equal +to work okay but this wavelength is way + + align:start position:0% +to work okay but this wavelength is way + + + align:start position:0% +to work okay but this wavelength is way +way large much much larger than the + + align:start position:0% +way large much much larger than the + + + align:start position:0% +way large much much larger than the +wavelength of the visible light okay so + + align:start position:0% +wavelength of the visible light okay so + + + align:start position:0% +wavelength of the visible light okay so +it's not going to work okay therefore + + align:start position:0% +it's not going to work okay therefore + + + align:start position:0% +it's not going to work okay therefore +you have to be patient you have to + + align:start position:0% +you have to be patient you have to + + + align:start position:0% +you have to be patient you have to +increase the value until then is equal + + align:start position:0% +increase the value until then is equal + + + align:start position:0% +increase the value until then is equal +to 500 so I am calculating one two three + + align:start position:0% +to 500 so I am calculating one two three + + + align:start position:0% +to 500 so I am calculating one two three +four five six until 500 we are in the + + align:start position:0% +four five six until 500 we are in the + + + align:start position:0% +four five six until 500 we are in the +visible light range right + + align:start position:0% +visible light range right + + + align:start position:0% +visible light range right +okay now 500 will give you 600 point six + + align:start position:0% +okay now 500 will give you 600 point six + + + align:start position:0% +okay now 500 will give you 600 point six +nanometre suddenly you I can see it + + align:start position:0% +nanometre suddenly you I can see it + + + align:start position:0% +nanometre suddenly you I can see it +okay very good that's me nice right so I + + align:start position:0% +okay very good that's me nice right so I + + + align:start position:0% +okay very good that's me nice right so I +can now put it in my diagram okay this + + align:start position:0% +can now put it in my diagram okay this + + + align:start position:0% +can now put it in my diagram okay this +is issue the wavelength again and I get + + align:start position:0% +is issue the wavelength again and I get + + + align:start position:0% +is issue the wavelength again and I get +one like here okay how about the next + + align:start position:0% +one like here okay how about the next + + + align:start position:0% +one like here okay how about the next +one + + align:start position:0% +one + + + align:start position:0% +one +earn equal to 501 I'm going to get PI + + align:start position:0% +earn equal to 501 I'm going to get PI + + + align:start position:0% +earn equal to 501 I'm going to get PI +99.4 nanometer it's pretty close to this + + align:start position:0% +99.4 nanometer it's pretty close to this + + + align:start position:0% +99.4 nanometer it's pretty close to this +one and then the next one would be five + + align:start position:0% +one and then the next one would be five + + + align:start position:0% +one and then the next one would be five +nine nine three five nine eight point + + align:start position:0% +nine nine three five nine eight point + + + align:start position:0% +nine nine three five nine eight point +two nanometer if n is equal to phi2 and + + align:start position:0% +two nanometer if n is equal to phi2 and + + + align:start position:0% +two nanometer if n is equal to phi2 and +what you are getting is you can see that + + align:start position:0% +what you are getting is you can see that + + + align:start position:0% +what you are getting is you can see that +no things are not going very well + + align:start position:0% +no things are not going very well + + + align:start position:0% +no things are not going very well +right they are spectra all the very very + + align:start position:0% +right they are spectra all the very very + + + align:start position:0% +right they are spectra all the very very +narrow they may be large number of + + align:start position:0% +narrow they may be large number of + + + align:start position:0% +narrow they may be large number of +wetlands can give you constructive + + align:start position:0% +wetlands can give you constructive + + + align:start position:0% +wetlands can give you constructive +interference so what is going to happen + + align:start position:0% +interference so what is going to happen + + + align:start position:0% +interference so what is going to happen +what is going to happen is that you will + + align:start position:0% +what is going to happen is that you will + + + align:start position:0% +what is going to happen is that you will +I will see refraction with all kinds of + + align:start position:0% +I will see refraction with all kinds of + + + align:start position:0% +I will see refraction with all kinds of +different wavelengths and what color is + + align:start position:0% +different wavelengths and what color is + + + align:start position:0% +different wavelengths and what color is +done + + align:start position:0% +done + + + align:start position:0% +done +why'd you are going to see something + + align:start position:0% +why'd you are going to see something + + + align:start position:0% +why'd you are going to see something +which is white okay so that is actually + + align:start position:0% +which is white okay so that is actually + + + align:start position:0% +which is white okay so that is actually +the answer to our question + + align:start position:0% +the answer to our question + + + align:start position:0% +the answer to our question +so what would be the required the + + align:start position:0% +so what would be the required the + + + align:start position:0% +so what would be the required the +sickness that require the sleepiness is + + align:start position:0% +sickness that require the sleepiness is + + + align:start position:0% +sickness that require the sleepiness is +something like 100 nanometer so you can + + align:start position:0% +something like 100 nanometer so you can + + + align:start position:0% +something like 100 nanometer so you can +see how thin is the water bubble okay + + align:start position:0% +see how thin is the water bubble okay + + + align:start position:0% +see how thin is the water bubble okay +that may surprise some of you right most + + align:start position:0% +that may surprise some of you right most + + + align:start position:0% +that may surprise some of you right most +of you actually didn't think that says + + align:start position:0% +of you actually didn't think that says + + + align:start position:0% +of you actually didn't think that says +you that see okay + + align:start position:0% +you that see okay + + + align:start position:0% +you that see okay +secondly if T equal to zero you are + + align:start position:0% +secondly if T equal to zero you are + + + align:start position:0% +secondly if T equal to zero you are +going to have destructive interference + + align:start position:0% +going to have destructive interference + + + align:start position:0% +going to have destructive interference +that means there will be no refracted + + align:start position:0% +that means there will be no refracted + + + align:start position:0% +that means there will be no refracted +light everything is going to pass + + align:start position:0% +light everything is going to pass + + + align:start position:0% +light everything is going to pass +through and the bubble is like + + align:start position:0% +through and the bubble is like + + + align:start position:0% +through and the bubble is like +transparent okay finally when the bubble + + align:start position:0% +transparent okay finally when the bubble + + + align:start position:0% +transparent okay finally when the bubble +is really sick okay + + align:start position:0% +is really sick okay + + + align:start position:0% +is really sick okay +you are going to see what okay so lemme + + align:start position:0% +you are going to see what okay so lemme + + + align:start position:0% +you are going to see what okay so lemme +have finished this + + align:start position:0% +have finished this + + + align:start position:0% +have finished this +with demonstration here first before I + + align:start position:0% +with demonstration here first before I + + + align:start position:0% +with demonstration here first before I +turn off the light I would like to turn + + align:start position:0% +turn off the light I would like to turn + + + align:start position:0% +turn off the light I would like to turn +this on okay so what I have here is it's + + align:start position:0% +this on okay so what I have here is it's + + + align:start position:0% +this on okay so what I have here is it's +a very complicated machine it's not a + + align:start position:0% +a very complicated machine it's not a + + + align:start position:0% +a very complicated machine it's not a +complicated HUD so basically I have a + + align:start position:0% +complicated HUD so basically I have a + + + align:start position:0% +complicated HUD so basically I have a +light source here which emit light with + + align:start position:0% +light source here which emit light with + + + align:start position:0% +light source here which emit light with +all kinds of different paths oh all + + align:start position:0% +all kinds of different paths oh all + + + align:start position:0% +all kinds of different paths oh all +kinds of different wavelengths + + align:start position:0% +kinds of different wavelengths + + + align:start position:0% +kinds of different wavelengths +okay and I have this little device here + + align:start position:0% +okay and I have this little device here + + + align:start position:0% +okay and I have this little device here +there's so solution inside and I can + + align:start position:0% +there's so solution inside and I can + + + align:start position:0% +there's so solution inside and I can +actually rotate from outside you see how + + align:start position:0% +actually rotate from outside you see how + + + align:start position:0% +actually rotate from outside you see how +sweet is this setup okay and I can let + + align:start position:0% +sweet is this setup okay and I can let + + + align:start position:0% +sweet is this setup okay and I can let +you create a soap film out of this okay + + align:start position:0% +you create a soap film out of this okay + + + align:start position:0% +you create a soap film out of this okay +you can see that and rotating and trying + + align:start position:0% +you can see that and rotating and trying + + + align:start position:0% +you can see that and rotating and trying +to actually put yet the result you can + + align:start position:0% +to actually put yet the result you can + + + align:start position:0% +to actually put yet the result you can +see that initially there is nothing + + align:start position:0% +see that initially there is nothing + + + align:start position:0% +see that initially there is nothing +really striking in the beginning you can + + align:start position:0% +really striking in the beginning you can + + + align:start position:0% +really striking in the beginning you can +see that the light is which color it's + + align:start position:0% +see that the light is which color it's + + + align:start position:0% +see that the light is which color it's +white right okay + + align:start position:0% +white right okay + + + align:start position:0% +white right okay +remember there's a there's a because of + + align:start position:0% +remember there's a there's a because of + + + align:start position:0% +remember there's a there's a because of +the optical setup there's this this + + align:start position:0% +the optical setup there's this this + + + align:start position:0% +the optical setup there's this this +image is actually upside down okay so so + + align:start position:0% +image is actually upside down okay so so + + + align:start position:0% +image is actually upside down okay so so +the upper edge is actually the upper + + align:start position:0% +the upper edge is actually the upper + + + align:start position:0% +the upper edge is actually the upper +edge of that image is actually the lower + + align:start position:0% +edge of that image is actually the lower + + + align:start position:0% +edge of that image is actually the lower +edge of my setup okay which I could it's + + align:start position:0% +edge of my setup okay which I could it's + + + align:start position:0% +edge of my setup okay which I could it's +the lower edge of my soft view + + align:start position:0% +the lower edge of my soft view + + + align:start position:0% +the lower edge of my soft view +okay so perfume okay and the due to + + align:start position:0% +okay so perfume okay and the due to + + + align:start position:0% +okay so perfume okay and the due to +gravity right we have gravity right so + + align:start position:0% +gravity right we have gravity right so + + + align:start position:0% +gravity right we have gravity right so +that I can walk around right due to + + align:start position:0% +that I can walk around right due to + + + align:start position:0% +that I can walk around right due to +gravity you can see that there will be + + align:start position:0% +gravity you can see that there will be + + + align:start position:0% +gravity you can see that there will be +more and more seeker you form seeker and + + align:start position:0% +more and more seeker you form seeker and + + + align:start position:0% +more and more seeker you form seeker and +a thicker layer in the pattern of my + + align:start position:0% +a thicker layer in the pattern of my + + + align:start position:0% +a thicker layer in the pattern of my +experimental setup or in the upper edge + + align:start position:0% +experimental setup or in the upper edge + + + align:start position:0% +experimental setup or in the upper edge +of the image and the other hand due to + + align:start position:0% +of the image and the other hand due to + + + align:start position:0% +of the image and the other hand due to +gravity the upper edge or the lower edge + + align:start position:0% +gravity the upper edge or the lower edge + + + align:start position:0% +gravity the upper edge or the lower edge +of the + + align:start position:0% +of the + + + align:start position:0% +of the +of the image will become sinner and a + + align:start position:0% +of the image will become sinner and a + + + align:start position:0% +of the image will become sinner and a +sinner as a function of time at some + + align:start position:0% +sinner as a function of time at some + + + align:start position:0% +sinner as a function of time at some +point the color will start to show up as + + align:start position:0% +point the color will start to show up as + + + align:start position:0% +point the color will start to show up as +you can see now since we wait long + + align:start position:0% +you can see now since we wait long + + + align:start position:0% +you can see now since we wait long +enough they are more like that the + + align:start position:0% +enough they are more like that the + + + align:start position:0% +enough they are more like that the +sodium becomes thinner and thinner and + + align:start position:0% +sodium becomes thinner and thinner and + + + align:start position:0% +sodium becomes thinner and thinner and +you can see that their color popping up + + align:start position:0% +you can see that their color popping up + + + align:start position:0% +you can see that their color popping up +right it's like rainbow why is that + + align:start position:0% +right it's like rainbow why is that + + + align:start position:0% +right it's like rainbow why is that +because we I am bear eating the + + align:start position:0% +because we I am bear eating the + + + align:start position:0% +because we I am bear eating the +thickness of the film as a function of + + align:start position:0% +thickness of the film as a function of + + + align:start position:0% +thickness of the film as a function of +the vertical distance right so therefore + + align:start position:0% +the vertical distance right so therefore + + + align:start position:0% +the vertical distance right so therefore +you can see that this is a she's showing + + align:start position:0% +you can see that this is a she's showing + + + align:start position:0% +you can see that this is a she's showing +you that different T value will give you + + align:start position:0% +you that different T value will give you + + + align:start position:0% +you that different T value will give you +very different color and if we wait long + + align:start position:0% +very different color and if we wait long + + + align:start position:0% +very different color and if we wait long +enough basically what we are going to + + align:start position:0% +enough basically what we are going to + + + align:start position:0% +enough basically what we are going to +get is that the the the whole film will + + align:start position:0% +get is that the the the whole film will + + + align:start position:0% +get is that the the the whole film will +become more and more colorful and I + + align:start position:0% +become more and more colorful and I + + + align:start position:0% +become more and more colorful and I +ensure that up to this class you can + + align:start position:0% +ensure that up to this class you can + + + align:start position:0% +ensure that up to this class you can +walk out of the classroom and explain to + + align:start position:0% +walk out of the classroom and explain to + + + align:start position:0% +walk out of the classroom and explain to +your friend that why the soap purple is + + align:start position:0% +your friend that why the soap purple is + + + align:start position:0% +your friend that why the soap purple is +colorful thank you very much and if you + + align:start position:0% +colorful thank you very much and if you + + + align:start position:0% +colorful thank you very much and if you +have any questions I will be around and + + align:start position:0% +have any questions I will be around and + + + align:start position:0% +have any questions I will be around and +of course if you want to make your own + + align:start position:0% +of course if you want to make your own + + + align:start position:0% +of course if you want to make your own +soap type of you can actually go ahead + + align:start position:0% +soap type of you can actually go ahead + + + align:start position:0% +soap type of you can actually go ahead +and uh play the demo + + align:start position:0% + + + + align:start position:0% + +okay so hello everybody so we are going + + align:start position:0% +okay so hello everybody so we are going + + + align:start position:0% +okay so hello everybody so we are going +to show you a demonstration which we can + + align:start position:0% +to show you a demonstration which we can + + + align:start position:0% +to show you a demonstration which we can +see a colorful interference pattern from + + align:start position:0% +see a colorful interference pattern from + + + align:start position:0% +see a colorful interference pattern from +a soft film so so basically we the + + align:start position:0% +a soft film so so basically we the + + + align:start position:0% +a soft film so so basically we the +experimental setup is like this + + align:start position:0% +experimental setup is like this + + + align:start position:0% +experimental setup is like this +especially we have light which is trying + + align:start position:0% +especially we have light which is trying + + + align:start position:0% +especially we have light which is trying +to shine this same layer of salt film + + align:start position:0% +to shine this same layer of salt film + + + align:start position:0% +to shine this same layer of salt film +and and and this the results as you + + align:start position:0% +and and and this the results as you + + + align:start position:0% +and and and this the results as you +projected on the screen and you can see + + align:start position:0% +projected on the screen and you can see + + + align:start position:0% +projected on the screen and you can see +at first you don't really see a lot of + + align:start position:0% +at first you don't really see a lot of + + + align:start position:0% +at first you don't really see a lot of +colorful pattern because the thickness + + align:start position:0% +colorful pattern because the thickness + + + align:start position:0% +colorful pattern because the thickness +of the film is still read large where + + align:start position:0% +of the film is still read large where + + + align:start position:0% +of the film is still read large where +the seek therefore you don't really see + + align:start position:0% +the seek therefore you don't really see + + + align:start position:0% +the seek therefore you don't really see +a lot of pattern but as a function of + + align:start position:0% +a lot of pattern but as a function of + + + align:start position:0% +a lot of pattern but as a function of +time you can see that this pattern is + + align:start position:0% +time you can see that this pattern is + + + align:start position:0% +time you can see that this pattern is +changing because of gravitational force + + align:start position:0% +changing because of gravitational force + + + align:start position:0% +changing because of gravitational force +you will be able to see that the the the + + align:start position:0% +you will be able to see that the the the + + + align:start position:0% +you will be able to see that the the the +lower part of the film becomes seeker + + align:start position:0% +lower part of the film becomes seeker + + + align:start position:0% +lower part of the film becomes seeker +and the seeker and the upper part of the + + align:start position:0% +and the seeker and the upper part of the + + + align:start position:0% +and the seeker and the upper part of the +film which you see the upside down on + + align:start position:0% +film which you see the upside down on + + + align:start position:0% +film which you see the upside down on +the screen essentially becoming sinner + + align:start position:0% +the screen essentially becoming sinner + + + align:start position:0% +the screen essentially becoming sinner +and the sinner when as we actually + + align:start position:0% +and the sinner when as we actually + + + align:start position:0% +and the sinner when as we actually +discussed during the class when the soft + + align:start position:0% +discussed during the class when the soft + + + align:start position:0% +discussed during the class when the soft +film is seen enough there will be only + + align:start position:0% +film is seen enough there will be only + + + align:start position:0% +film is seen enough there will be only +one or only a few + + align:start position:0% +one or only a few + + + align:start position:0% +one or only a few +maxime mass in the interference pattern + + align:start position:0% +maxime mass in the interference pattern + + + align:start position:0% +maxime mass in the interference pattern +as a function of wavelength which + + align:start position:0% +as a function of wavelength which + + + align:start position:0% +as a function of wavelength which +happened to be inside the visible light + + align:start position:0% +happened to be inside the visible light + + + align:start position:0% +happened to be inside the visible light +range and then you can see that now + + align:start position:0% +range and then you can see that now + + + align:start position:0% +range and then you can see that now +really this colorful pattern radiates + + align:start position:0% +really this colorful pattern radiates + + + align:start position:0% +really this colorful pattern radiates +abandoned is really beautiful and and + + align:start position:0% +abandoned is really beautiful and and + + + align:start position:0% +abandoned is really beautiful and and +you can see that the normal part of the + + align:start position:0% +you can see that the normal part of the + + + align:start position:0% +you can see that the normal part of the +experiment already have a Fanta color + + align:start position:0% +experiment already have a Fanta color + + + align:start position:0% +experiment already have a Fanta color +because there are multiple Maximas + + align:start position:0% +because there are multiple Maximas + + + align:start position:0% +because there are multiple Maximas +in the visible light range on the other + + align:start position:0% +in the visible light range on the other + + + align:start position:0% +in the visible light range on the other +hand in the upper part of the film you + + align:start position:0% +hand in the upper part of the film you + + + align:start position:0% +hand in the upper part of the film you +typically have + + align:start position:0% +typically have + + + align:start position:0% +typically have +the little number of Maximas were only + + align:start position:0% +the little number of Maximas were only + + + align:start position:0% +the little number of Maximas were only +have one maximum mass in the visible + + align:start position:0% +have one maximum mass in the visible + + + align:start position:0% +have one maximum mass in the visible +light range as a function of wavelength + + align:start position:0% +light range as a function of wavelength + + + align:start position:0% +light range as a function of wavelength +therefore you see we need indeed + + align:start position:0% +therefore you see we need indeed + + + align:start position:0% +therefore you see we need indeed +romantic and very very colorful patterns + + align:start position:0% +romantic and very very colorful patterns + + + align:start position:0% +romantic and very very colorful patterns +divided from this experiment + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/W3TqFzVh_rE.txt b/W3TqFzVh_rE.txt new file mode 100644 index 0000000000000000000000000000000000000000..22567b267d3ae36430ed58033282665b06bcbf99 --- /dev/null +++ b/W3TqFzVh_rE.txt @@ -0,0 +1,523 @@ +align:start position:0% + +let's consider the motion of a single + + align:start position:0% +let's consider the motion of a single + + + align:start position:0% +let's consider the motion of a single +particle moving with the velocity V in a + + align:start position:0% +particle moving with the velocity V in a + + + align:start position:0% +particle moving with the velocity V in a +ground reference frame say recall that + + align:start position:0% +ground reference frame say recall that + + + align:start position:0% +ground reference frame say recall that +we defined the momentum of this object + + align:start position:0% +we defined the momentum of this object + + + align:start position:0% +we defined the momentum of this object +as MV and we know that Newton's second + + align:start position:0% +as MV and we know that Newton's second + + + align:start position:0% +as MV and we know that Newton's second +law can be written in terms of the + + align:start position:0% +law can be written in terms of the + + + align:start position:0% +law can be written in terms of the +change of momentum dp/dt and when we + + align:start position:0% +change of momentum dp/dt and when we + + + align:start position:0% +change of momentum dp/dt and when we +integrated newton's second law for + + align:start position:0% +integrated newton's second law for + + + align:start position:0% +integrated newton's second law for +impulse causes the integral of DP from + + align:start position:0% +impulse causes the integral of DP from + + + align:start position:0% +impulse causes the integral of DP from +some time T prime equals zero to some + + align:start position:0% +some time T prime equals zero to some + + + align:start position:0% +some time T prime equals zero to some +time T so we're integrating T Prime and + + align:start position:0% +time T so we're integrating T Prime and + + + align:start position:0% +time T so we're integrating T Prime and +here we're taking our momentum from some + + align:start position:0% +here we're taking our momentum from some + + + align:start position:0% +here we're taking our momentum from some +initial momentum to some momentum at + + align:start position:0% +initial momentum to some momentum at + + + align:start position:0% +initial momentum to some momentum at +time T we have that the impulse causes + + align:start position:0% +time T we have that the impulse causes + + + align:start position:0% +time T we have that the impulse causes +the momentum of this single particle to + + align:start position:0% +the momentum of this single particle to + + + align:start position:0% +the momentum of this single particle to +change and in particular this is what we + + align:start position:0% +change and in particular this is what we + + + align:start position:0% +change and in particular this is what we +call impulse and if the impulse is zero + + align:start position:0% +call impulse and if the impulse is zero + + + align:start position:0% +call impulse and if the impulse is zero +so as an example if the impulse F DT + + align:start position:0% +so as an example if the impulse F DT + + + align:start position:0% +so as an example if the impulse F DT +prime equals zero that tells us that the + + align:start position:0% +prime equals zero that tells us that the + + + align:start position:0% +prime equals zero that tells us that the +momentum of our particle has not changed + + align:start position:0% +momentum of our particle has not changed + + + align:start position:0% +momentum of our particle has not changed +now let's consider our same thing for + + align:start position:0% +now let's consider our same thing for + + + align:start position:0% +now let's consider our same thing for +angular momentum the only difference is + + align:start position:0% +angular momentum the only difference is + + + align:start position:0% +angular momentum the only difference is +that we choose some point s and we'll + + align:start position:0% +that we choose some point s and we'll + + + align:start position:0% +that we choose some point s and we'll +write the vector RS to where the object + + align:start position:0% +write the vector RS to where the object + + + align:start position:0% +write the vector RS to where the object +is and our angular momentum we defined + + align:start position:0% +is and our angular momentum we defined + + + align:start position:0% +is and our angular momentum we defined +about the point as was the vector from s + + align:start position:0% +about the point as was the vector from s + + + align:start position:0% +about the point as was the vector from s +and we can indicate maybe to the mass M + + align:start position:0% +and we can indicate maybe to the mass M + + + align:start position:0% +and we can indicate maybe to the mass M +so it's a vector from s to where the + + align:start position:0% +so it's a vector from s to where the + + + align:start position:0% +so it's a vector from s to where the +object is located cross the momentum of + + align:start position:0% +object is located cross the momentum of + + + align:start position:0% +object is located cross the momentum of +the object and this is how we define the + + align:start position:0% +the object and this is how we define the + + + align:start position:0% +the object and this is how we define the +angular momentum and recall that our + + align:start position:0% +angular momentum and recall that our + + + align:start position:0% +angular momentum and recall that our +basic concept is that the torque about s + + align:start position:0% +basic concept is that the torque about s + + + align:start position:0% +basic concept is that the torque about s +causes the angular momentum about s to + + align:start position:0% +causes the angular momentum about s to + + + align:start position:0% +causes the angular momentum about s to +change for this single particle now + + align:start position:0% +change for this single particle now + + + align:start position:0% +change for this single particle now +torque is if there's a force acting on + + align:start position:0% +torque is if there's a force acting on + + + align:start position:0% +torque is if there's a force acting on +the particle so for instance if the + + align:start position:0% +the particle so for instance if the + + + align:start position:0% +the particle so for instance if the +force were acting at some angle not only + + align:start position:0% +force were acting at some angle not only + + + align:start position:0% +force were acting at some angle not only +does the force change the book cause the + + align:start position:0% +does the force change the book cause the + + + align:start position:0% +does the force change the book cause the +momentum to change but we know that if + + align:start position:0% +momentum to change but we know that if + + + align:start position:0% +momentum to change but we know that if +there's a torque about s it will cause + + align:start position:0% +there's a torque about s it will cause + + + align:start position:0% +there's a torque about s it will cause +the angular momentum of the particle to + + align:start position:0% +the angular momentum of the particle to + + + align:start position:0% +the angular momentum of the particle to +change too now let's talk about the + + align:start position:0% +change too now let's talk about the + + + align:start position:0% +change too now let's talk about the +angular + + align:start position:0% +angular + + + align:start position:0% +angular +pulse which is integrating the torque + + align:start position:0% +pulse which is integrating the torque + + + align:start position:0% +pulse which is integrating the torque +from say some time T prime equals zero + + align:start position:0% +from say some time T prime equals zero + + + align:start position:0% +from say some time T prime equals zero +to some time T and that's the integral + + align:start position:0% +to some time T and that's the integral + + + align:start position:0% +to some time T and that's the integral +of the angular momentum about s and now + + align:start position:0% +of the angular momentum about s and now + + + align:start position:0% +of the angular momentum about s and now +we're integrating this from some initial + + align:start position:0% +we're integrating this from some initial + + + align:start position:0% +we're integrating this from some initial +angular momentum to some final angular + + align:start position:0% +angular momentum to some final angular + + + align:start position:0% +angular momentum to some final angular +momentum and just as before we have that + + align:start position:0% +momentum and just as before we have that + + + align:start position:0% +momentum and just as before we have that +the angular impulse will result in a + + align:start position:0% +the angular impulse will result in a + + + align:start position:0% +the angular impulse will result in a +change of angular momentum and in + + align:start position:0% +change of angular momentum and in + + + align:start position:0% +change of angular momentum and in +particular if our angular impulse is + + align:start position:0% +particular if our angular impulse is + + + align:start position:0% +particular if our angular impulse is +zero that implies that the angular + + align:start position:0% +zero that implies that the angular + + + align:start position:0% +zero that implies that the angular +momentum of this particle is constant + + align:start position:0% +momentum of this particle is constant + + + align:start position:0% +momentum of this particle is constant +and so you can see the analogies the + + align:start position:0% +and so you can see the analogies the + + + align:start position:0% +and so you can see the analogies the +important fact to realize is that in the + + align:start position:0% +important fact to realize is that in the + + + align:start position:0% +important fact to realize is that in the +reference frame momentum does not depend + + align:start position:0% +reference frame momentum does not depend + + + align:start position:0% +reference frame momentum does not depend +on any point but our angular momentum + + align:start position:0% +on any point but our angular momentum + + + align:start position:0% +on any point but our angular momentum +does depend on the choice of the point s + + align:start position:0% +does depend on the choice of the point s + + + align:start position:0% +does depend on the choice of the point s +and in particular in terms of the + + align:start position:0% +and in particular in terms of the + + + align:start position:0% +and in particular in terms of the +impulse the torque about S is also a + + align:start position:0% +impulse the torque about S is also a + + + align:start position:0% +impulse the torque about S is also a +quantity that depends on s and so that's + + align:start position:0% +quantity that depends on s and so that's + + + align:start position:0% +quantity that depends on s and so that's +the analogy between momentum of a single + + align:start position:0% +the analogy between momentum of a single + + + align:start position:0% +the analogy between momentum of a single +particle and angular momentum of a + + align:start position:0% +particle and angular momentum of a + + + align:start position:0% +particle and angular momentum of a +single particle \ No newline at end of file diff --git a/WCKuWTVJMko.txt b/WCKuWTVJMko.txt new file mode 100644 index 0000000000000000000000000000000000000000..f8a0a1ae6db53629e5337cab16a590206af89de5 --- /dev/null +++ b/WCKuWTVJMko.txt @@ -0,0 +1,8867 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu the weekend is over we're + + align:start position:0% +ocw.mit.edu the weekend is over we're + + + align:start position:0% +ocw.mit.edu the weekend is over we're +now in + + align:start position:0% +now in + + + align:start position:0% +now in +3091 so uh + + align:start position:0% +3091 so uh + + + align:start position:0% +3091 so uh +announcement this Wednesday there'll be + + align:start position:0% +announcement this Wednesday there'll be + + + align:start position:0% +announcement this Wednesday there'll be +no lecture instead celebration of + + align:start position:0% +no lecture instead celebration of + + + align:start position:0% +no lecture instead celebration of +learning test number two + + align:start position:0% +learning test number two + + + align:start position:0% +learning test number two +um these are the uh room assignments we + + align:start position:0% +um these are the uh room assignments we + + + align:start position:0% +um these are the uh room assignments we +uh move them just a little bit uh move + + align:start position:0% +uh move them just a little bit uh move + + + align:start position:0% +uh move them just a little bit uh move +the dividing lines rather it's the same + + align:start position:0% +the dividing lines rather it's the same + + + align:start position:0% +the dividing lines rather it's the same +rooms but uh we wanted to make uh a + + align:start position:0% +rooms but uh we wanted to make uh a + + + align:start position:0% +rooms but uh we wanted to make uh a +little more room in here and in Walker + + align:start position:0% +little more room in here and in Walker + + + align:start position:0% +little more room in here and in Walker +gym so there are more people being uh + + align:start position:0% +gym so there are more people being uh + + + align:start position:0% +gym so there are more people being uh +asked to go to room 1-1 190 + + align:start position:0% +asked to go to room 1-1 190 + + + align:start position:0% +asked to go to room 1-1 190 +and then this is the group to go to the + + align:start position:0% +and then this is the group to go to the + + + align:start position:0% +and then this is the group to go to the +Walker gym third floor of the Walker + + align:start position:0% +Walker gym third floor of the Walker + + + align:start position:0% +Walker gym third floor of the Walker +memorial building and then the front + + align:start position:0% +memorial building and then the front + + + align:start position:0% +memorial building and then the front +half of the alphabet uh please report + + align:start position:0% +half of the alphabet uh please report + + + align:start position:0% +half of the alphabet uh please report +here and if you take the test at 1:00 + + align:start position:0% +here and if you take the test at 1:00 + + + align:start position:0% +here and if you take the test at 1:00 +don't go to + + align:start position:0% +don't go to + + + align:start position:0% +don't go to +6120 because we won't be there we're + + align:start position:0% +6120 because we won't be there we're + + + align:start position:0% +6120 because we won't be there we're +we're putting everybody in 26100 that + + align:start position:0% +we're putting everybody in 26100 that + + + align:start position:0% +we're putting everybody in 26100 that +way there are plenty of vacancies so + + align:start position:0% +way there are plenty of vacancies so + + + align:start position:0% +way there are plenty of vacancies so +it's good so I'm just going to go + + align:start position:0% +it's good so I'm just going to go + + + align:start position:0% +it's good so I'm just going to go +quickly over the the um uh comments that + + align:start position:0% +quickly over the the um uh comments that + + + align:start position:0% +quickly over the the um uh comments that +I give before for every test just to put + + align:start position:0% +I give before for every test just to put + + + align:start position:0% +I give before for every test just to put +everybody in the right frame of mind uh + + align:start position:0% +everybody in the right frame of mind uh + + + align:start position:0% +everybody in the right frame of mind uh +the coverage is lectures 7 through + + align:start position:0% +the coverage is lectures 7 through + + + align:start position:0% +the coverage is lectures 7 through +17 uh so that'll start with ionics and + + align:start position:0% +17 uh so that'll start with ionics and + + + align:start position:0% +17 uh so that'll start with ionics and +go through the generation of x-rays but + + align:start position:0% +go through the generation of x-rays but + + + align:start position:0% +go through the generation of x-rays but +not uh brags law or anything like that + + align:start position:0% +not uh brags law or anything like that + + + align:start position:0% +not uh brags law or anything like that +um so remember you got to bring five + + align:start position:0% +um so remember you got to bring five + + + align:start position:0% +um so remember you got to bring five +things with you your periodic table + + align:start position:0% +things with you your periodic table + + + align:start position:0% +things with you your periodic table +table of constants something to write + + align:start position:0% +table of constants something to write + + + align:start position:0% +table of constants something to write +with uh a calculator and your age sheet + + align:start position:0% +with uh a calculator and your age sheet + + + align:start position:0% +with uh a calculator and your age sheet +and you know I'm going to make a bold + + align:start position:0% +and you know I'm going to make a bold + + + align:start position:0% +and you know I'm going to make a bold +suggestion for some of you why don't you + + align:start position:0% +suggestion for some of you why don't you + + + align:start position:0% +suggestion for some of you why don't you +write your recitation instructor's name + + align:start position:0% +write your recitation instructor's name + + + align:start position:0% +write your recitation instructor's name +on your age sheet because I'm going to + + align:start position:0% +on your age sheet because I'm going to + + + align:start position:0% +on your age sheet because I'm going to +tell you what I'm going to do if I don't + + align:start position:0% +tell you what I'm going to do if I don't + + + align:start position:0% +tell you what I'm going to do if I don't +have a recitation instructor's name on + + align:start position:0% +have a recitation instructor's name on + + + align:start position:0% +have a recitation instructor's name on +the exam I'm not going to grade it you + + align:start position:0% +the exam I'm not going to grade it you + + + align:start position:0% +the exam I'm not going to grade it you +know why because I got 630 of these if + + align:start position:0% +know why because I got 630 of these if + + + align:start position:0% +know why because I got 630 of these if +you don't put the recitation + + align:start position:0% +you don't put the recitation + + + align:start position:0% +you don't put the recitation +instructor's name on the exam it means + + align:start position:0% +instructor's name on the exam it means + + + align:start position:0% +instructor's name on the exam it means +you're in no hurry to get it back and + + align:start position:0% +you're in no hurry to get it back and + + + align:start position:0% +you're in no hurry to get it back and +that'll save me time we'll just take all + + align:start position:0% +that'll save me time we'll just take all + + + align:start position:0% +that'll save me time we'll just take all +those we just put them aside and we'll + + align:start position:0% +those we just put them aside and we'll + + + align:start position:0% +those we just put them aside and we'll +just grade the ones for the people who + + align:start position:0% +just grade the ones for the people who + + + align:start position:0% +just grade the ones for the people who +really want to get them back the next + + align:start position:0% +really want to get them back the next + + + align:start position:0% +really want to get them back the next +day and we'll get around to the other + + align:start position:0% +day and we'll get around to the other + + + align:start position:0% +day and we'll get around to the other +ones I + + align:start position:0% +ones I + + + align:start position:0% +ones I +mean + + align:start position:0% +mean + + + align:start position:0% +mean +someday so uh I think after after two + + align:start position:0% +someday so uh I think after after two + + + align:start position:0% +someday so uh I think after after two +months it's not unreasonable for us to + + align:start position:0% +months it's not unreasonable for us to + + + align:start position:0% +months it's not unreasonable for us to +expect you to put the recitation + + align:start position:0% +expect you to put the recitation + + + align:start position:0% +expect you to put the recitation +instructor's name on the uh exam um the + + align:start position:0% +instructor's name on the uh exam um the + + + align:start position:0% +instructor's name on the uh exam um the +purpose of the test is to provide you + + align:start position:0% +purpose of the test is to provide you + + + align:start position:0% +purpose of the test is to provide you +with feedback so we want to just tell + + align:start position:0% +with feedback so we want to just tell + + + align:start position:0% +with feedback so we want to just tell +you are you mastering the material are + + align:start position:0% +you are you mastering the material are + + + align:start position:0% +you are you mastering the material are +you is your study habits are your study + + align:start position:0% +you is your study habits are your study + + + align:start position:0% +you is your study habits are your study +habits effective or not it's all we're + + align:start position:0% +habits effective or not it's all we're + + + align:start position:0% +habits effective or not it's all we're +trying to do so this is not an aptitude + + align:start position:0% +trying to do so this is not an aptitude + + + align:start position:0% +trying to do so this is not an aptitude +test it's it's not an admissions test I + + align:start position:0% +test it's it's not an admissions test I + + + align:start position:0% +test it's it's not an admissions test I +just want to see if you're mastering the + + align:start position:0% +just want to see if you're mastering the + + + align:start position:0% +just want to see if you're mastering the +material and if you are I'm going to say + + align:start position:0% +material and if you are I'm going to say + + + align:start position:0% +material and if you are I'm going to say +congratulations keep up the good work + + align:start position:0% +congratulations keep up the good work + + + align:start position:0% +congratulations keep up the good work +and if you're not I'm going to send you + + align:start position:0% +and if you're not I'm going to send you + + + align:start position:0% +and if you're not I'm going to send you +a message saying you keep up at this + + align:start position:0% +a message saying you keep up at this + + + align:start position:0% +a message saying you keep up at this +level you're going to fail this class + + align:start position:0% +level you're going to fail this class + + + align:start position:0% +level you're going to fail this class +you need to get that information on a + + align:start position:0% +you need to get that information on a + + + align:start position:0% +you need to get that information on a +timely basis uh what are the test taking + + align:start position:0% +timely basis uh what are the test taking + + + align:start position:0% +timely basis uh what are the test taking +strategies read the paper first identify + + align:start position:0% +strategies read the paper first identify + + + align:start position:0% +strategies read the paper first identify +the easy questions work on your schedule + + align:start position:0% +the easy questions work on your schedule + + + align:start position:0% +the easy questions work on your schedule +don't do number one because I made it + + align:start position:0% +don't do number one because I made it + + + align:start position:0% +don't do number one because I made it +number one do number one only because + + align:start position:0% +number one do number one only because + + + align:start position:0% +number one do number one only because +it's the easiest one for you it'll be a + + align:start position:0% +it's the easiest one for you it'll be a + + + align:start position:0% +it's the easiest one for you it'll be a +confidence Builder sooth the nerves and + + align:start position:0% +confidence Builder sooth the nerves and + + + align:start position:0% +confidence Builder sooth the nerves and +so on show your work show your work + + align:start position:0% +so on show your work show your work + + + align:start position:0% +so on show your work show your work +don't write cryptic answers because if + + align:start position:0% +don't write cryptic answers because if + + + align:start position:0% +don't write cryptic answers because if +you get them wrong uh we can't give you + + align:start position:0% +you get them wrong uh we can't give you + + + align:start position:0% +you get them wrong uh we can't give you +part score but if you give us lots of uh + + align:start position:0% +part score but if you give us lots of uh + + + align:start position:0% +part score but if you give us lots of uh +information I don't mean volumes of + + align:start position:0% +information I don't mean volumes of + + + align:start position:0% +information I don't mean volumes of +information but if you give us a few + + align:start position:0% +information but if you give us a few + + + align:start position:0% +information but if you give us a few +ideas as to how you're approaching the + + align:start position:0% +ideas as to how you're approaching the + + + align:start position:0% +ideas as to how you're approaching the +problem then we can give you partial + + align:start position:0% +problem then we can give you partial + + + align:start position:0% +problem then we can give you partial +credit work parametrically try not to + + align:start position:0% +credit work parametrically try not to + + + align:start position:0% +credit work parametrically try not to +immediately start going for your + + align:start position:0% +immediately start going for your + + + align:start position:0% +immediately start going for your +calculator and please bring something to + + align:start position:0% +calculator and please bring something to + + + align:start position:0% +calculator and please bring something to +compute with I was astonished in the + + align:start position:0% +compute with I was astonished in the + + + align:start position:0% +compute with I was astonished in the +first test the number of people that had + + align:start position:0% +first test the number of people that had + + + align:start position:0% +first test the number of people that had +no calculator or um the calculator was + + align:start position:0% +no calculator or um the calculator was + + + align:start position:0% +no calculator or um the calculator was +uh not working and so + + align:start position:0% +uh not working and so + + + align:start position:0% +uh not working and so +on we have a few but this is a large + + align:start position:0% +on we have a few but this is a large + + + align:start position:0% +on we have a few but this is a large +class I don't have enough calculators + + align:start position:0% +class I don't have enough calculators + + + align:start position:0% +class I don't have enough calculators +for + + align:start position:0% +for + + + align:start position:0% +for +everybody and don't grade the test right + + align:start position:0% +everybody and don't grade the test right + + + align:start position:0% +everybody and don't grade the test right +if you're if you feel you're not doing + + align:start position:0% +if you're if you feel you're not doing + + + align:start position:0% +if you're if you feel you're not doing +as well as you'd like don't give up just + + align:start position:0% +as well as you'd like don't give up just + + + align:start position:0% +as well as you'd like don't give up just +you just leave the grading to us and + + align:start position:0% +you just leave the grading to us and + + + align:start position:0% +you just leave the grading to us and +you're not competing with your + + align:start position:0% +you're not competing with your + + + align:start position:0% +you're not competing with your +classmates 50 is a p pass everybody can + + align:start position:0% +classmates 50 is a p pass everybody can + + + align:start position:0% +classmates 50 is a p pass everybody can +pass there's no no success coming at the + + align:start position:0% +pass there's no no success coming at the + + + align:start position:0% +pass there's no no success coming at the +expense of a of a classmate and as + + align:start position:0% +expense of a of a classmate and as + + + align:start position:0% +expense of a of a classmate and as +always do your own work you've got an AG + + align:start position:0% +always do your own work you've got an AG + + + align:start position:0% +always do your own work you've got an AG +sheet you've got your tables of constant + + align:start position:0% +sheet you've got your tables of constant + + + align:start position:0% +sheet you've got your tables of constant +you've got your periodic tables there's + + align:start position:0% +you've got your periodic tables there's + + + align:start position:0% +you've got your periodic tables there's +no reason to resort to any kind of + + align:start position:0% +no reason to resort to any kind of + + + align:start position:0% +no reason to resort to any kind of +intellectual dishonesty and our goal is + + align:start position:0% +intellectual dishonesty and our goal is + + + align:start position:0% +intellectual dishonesty and our goal is +to have them back to you on Thursday in + + align:start position:0% +to have them back to you on Thursday in + + + align:start position:0% +to have them back to you on Thursday in +recitation + + align:start position:0% +recitation + + + align:start position:0% +recitation +so uh good luck I want you just to show + + align:start position:0% +so uh good luck I want you just to show + + + align:start position:0% +so uh good luck I want you just to show +me what you know and I think it's + + align:start position:0% +me what you know and I think it's + + + align:start position:0% +me what you know and I think it's +appropriate that we don't have a week + + align:start position:0% +appropriate that we don't have a week + + + align:start position:0% +appropriate that we don't have a week +test tomorrow so I know there's a lot of + + align:start position:0% +test tomorrow so I know there's a lot of + + + align:start position:0% +test tomorrow so I know there's a lot of +disappointment when I say this but there + + align:start position:0% +disappointment when I say this but there + + + align:start position:0% +disappointment when I say this but there +will be no weekly test tomorrow so we'll + + align:start position:0% +will be no weekly test tomorrow so we'll + + + align:start position:0% +will be no weekly test tomorrow so we'll +we'll catch up + + align:start position:0% +we'll catch up + + + align:start position:0% +we'll catch up +afterwards okay so last day we looked at + + align:start position:0% +afterwards okay so last day we looked at + + + align:start position:0% +afterwards okay so last day we looked at +the selection rules for reflection and + + align:start position:0% +the selection rules for reflection and + + + align:start position:0% +the selection rules for reflection and +cubic crystals and saw that we could + + align:start position:0% +cubic crystals and saw that we could + + + align:start position:0% +cubic crystals and saw that we could +identify distinguish different crystals + + align:start position:0% +identify distinguish different crystals + + + align:start position:0% +identify distinguish different crystals +from one another on the basis of the + + align:start position:0% +from one another on the basis of the + + + align:start position:0% +from one another on the basis of the +patterns in the line Spectrum towards + + align:start position:0% +patterns in the line Spectrum towards + + + align:start position:0% +patterns in the line Spectrum towards +the end we talked about Symmetry and uh + + align:start position:0% +the end we talked about Symmetry and uh + + + align:start position:0% +the end we talked about Symmetry and uh +I think I gave you the the uh the page + + align:start position:0% +I think I gave you the the uh the page + + + align:start position:0% +I think I gave you the the uh the page +here of the um the uh lab book of Danny + + align:start position:0% +here of the um the uh lab book of Danny + + + align:start position:0% +here of the um the uh lab book of Danny +sheckman when he first started to see + + align:start position:0% +sheckman when he first started to see + + + align:start position:0% +sheckman when he first started to see +that he's got five-fold Symmetry and uh + + align:start position:0% +that he's got five-fold Symmetry and uh + + + align:start position:0% +that he's got five-fold Symmetry and uh +uh so the music at the beginning I was + + align:start position:0% +uh so the music at the beginning I was + + + align:start position:0% +uh so the music at the beginning I was +playing take five by Dave Breck I was + + align:start position:0% +playing take five by Dave Breck I was + + + align:start position:0% +playing take five by Dave Breck I was +looking for songs in 54 time so I had + + align:start position:0% +looking for songs in 54 time so I had + + + align:start position:0% +looking for songs in 54 time so I had +this one as + + align:start position:0% +this one as + + + align:start position:0% +this one as +well remember this + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +one count it 1 2 3 4 5 1 2 3 four 2 + + align:start position:0% +one count it 1 2 3 4 5 1 2 3 four 2 + + + align:start position:0% +one count it 1 2 3 4 5 1 2 3 four 2 +three four five but then they wimp out + + align:start position:0% +three four five but then they wimp out + + + align:start position:0% +three four five but then they wimp out +and they go into four four here + + align:start position:0% +and they go into four four here + + + align:start position:0% +and they go into four four here +listen now it's a disco + + align:start position:0% +listen now it's a disco + + + align:start position:0% +listen now it's a disco +song I guess they feel that people can't + + align:start position:0% +song I guess they feel that people can't + + + align:start position:0% +song I guess they feel that people can't +dance to 54 time and it had to be + + align:start position:0% +dance to 54 time and it had to be + + + align:start position:0% +dance to 54 time and it had to be +danceable or else it wouldn't be + + align:start position:0% +danceable or else it wouldn't be + + + align:start position:0% +danceable or else it wouldn't be +marketable but that's 54 very strange + + align:start position:0% +marketable but that's 54 very strange + + + align:start position:0% +marketable but that's 54 very strange +time + + align:start position:0% +time + + + align:start position:0% +time +54 okay today we're going to uh move on + + align:start position:0% +54 okay today we're going to uh move on + + + align:start position:0% +54 okay today we're going to uh move on +our discussion of solids ordered solids + + align:start position:0% +our discussion of solids ordered solids + + + align:start position:0% +our discussion of solids ordered solids +up until now I've been treating crystals + + align:start position:0% +up until now I've been treating crystals + + + align:start position:0% +up until now I've been treating crystals +as though they're perfect + + align:start position:0% +as though they're perfect + + + align:start position:0% +as though they're perfect +I've been treating crystals as though + + align:start position:0% +I've been treating crystals as though + + + align:start position:0% +I've been treating crystals as though +they're perfect in two ways + + align:start position:0% +they're perfect in two ways + + + align:start position:0% +they're perfect in two ways +um perfect crystals in terms of chemical + + align:start position:0% + + + + align:start position:0% + +composition perfection in terms of + + align:start position:0% +composition perfection in terms of + + + align:start position:0% +composition perfection in terms of +chemical + + align:start position:0% + + + + align:start position:0% + +composition and + + align:start position:0% +composition and + + + align:start position:0% +composition and +that that's to say that we're looking at + + align:start position:0% +that that's to say that we're looking at + + + align:start position:0% +that that's to say that we're looking at +pure materials and also perfection in + + align:start position:0% +pure materials and also perfection in + + + align:start position:0% +pure materials and also perfection in +terms of atomic + + align:start position:0% + + + + align:start position:0% + +Arrangement and so that means we're uh + + align:start position:0% +Arrangement and so that means we're uh + + + align:start position:0% +Arrangement and so that means we're uh +treating them as though they're defect + + align:start position:0% + + + + align:start position:0% + +free two types of perfection see we're + + align:start position:0% +free two types of perfection see we're + + + align:start position:0% +free two types of perfection see we're +talking about chemical composition and + + align:start position:0% +talking about chemical composition and + + + align:start position:0% +talking about chemical composition and +we're talking about Atomic Arrangement + + align:start position:0% +we're talking about Atomic Arrangement + + + align:start position:0% +we're talking about Atomic Arrangement +both are critical in determining the + + align:start position:0% +both are critical in determining the + + + align:start position:0% +both are critical in determining the +performance of material but real + + align:start position:0% +performance of material but real + + + align:start position:0% +performance of material but real +engineering materials are not perfect + + align:start position:0% +engineering materials are not perfect + + + align:start position:0% +engineering materials are not perfect +they contain impur impurities and we've + + align:start position:0% +they contain impur impurities and we've + + + align:start position:0% +they contain impur impurities and we've +seen that there are desirable impurities + + align:start position:0% +seen that there are desirable impurities + + + align:start position:0% +seen that there are desirable impurities +such as dopants and there are + + align:start position:0% +such as dopants and there are + + + align:start position:0% +such as dopants and there are +undesirable impurities such as + + align:start position:0% +undesirable impurities such as + + + align:start position:0% +undesirable impurities such as +contaminants and part of what we were + + align:start position:0% +contaminants and part of what we were + + + align:start position:0% +contaminants and part of what we were +doing in the last unit was studying how + + align:start position:0% +doing in the last unit was studying how + + + align:start position:0% +doing in the last unit was studying how +to manage impurities in such a way as to + + align:start position:0% +to manage impurities in such a way as to + + + align:start position:0% +to manage impurities in such a way as to +get desirable + + align:start position:0% +get desirable + + + align:start position:0% +get desirable +properties well the same thing happens + + align:start position:0% +properties well the same thing happens + + + align:start position:0% +properties well the same thing happens +with + + align:start position:0% +with + + + align:start position:0% +with +defects in some cases we have atoms not + + align:start position:0% +defects in some cases we have atoms not + + + align:start position:0% +defects in some cases we have atoms not +always found at their lattice points + + align:start position:0% +always found at their lattice points + + + align:start position:0% +always found at their lattice points +Adams sometimes misbehave they don't go + + align:start position:0% +Adams sometimes misbehave they don't go + + + align:start position:0% +Adams sometimes misbehave they don't go +where they're + + align:start position:0% +where they're + + + align:start position:0% +where they're +told and that can lead to consequences + + align:start position:0% +told and that can lead to consequences + + + align:start position:0% +told and that can lead to consequences +mechanical + + align:start position:0% +mechanical + + + align:start position:0% +mechanical +failure but if we're clever about it if + + align:start position:0% +failure but if we're clever about it if + + + align:start position:0% +failure but if we're clever about it if +we learn how to manage defects we can + + align:start position:0% +we learn how to manage defects we can + + + align:start position:0% +we learn how to manage defects we can +engineer performance that is minimally + + align:start position:0% +engineer performance that is minimally + + + align:start position:0% +engineer performance that is minimally +damaging and in some cases we can + + align:start position:0% +damaging and in some cases we can + + + align:start position:0% +damaging and in some cases we can +enhance the performance of material so + + align:start position:0% +enhance the performance of material so + + + align:start position:0% +enhance the performance of material so +we're going to get tailored properties + + align:start position:0% +we're going to get tailored properties + + + align:start position:0% +we're going to get tailored properties +through defect engineering defect + + align:start position:0% +through defect engineering defect + + + align:start position:0% +through defect engineering defect +engineering right so that's what I want + + align:start position:0% +engineering right so that's what I want + + + align:start position:0% +engineering right so that's what I want +to introduce today so we're going to go + + align:start position:0% +to introduce today so we're going to go + + + align:start position:0% +to introduce today so we're going to go +through the handout because there's a + + align:start position:0% +through the handout because there's a + + + align:start position:0% +through the handout because there's a +lot of taxonomy here and sort of + + align:start position:0% +lot of taxonomy here and sort of + + + align:start position:0% +lot of taxonomy here and sort of +definitions and so I thought we' just + + align:start position:0% +definitions and so I thought we' just + + + align:start position:0% +definitions and so I thought we' just +read along together so the defects are + + align:start position:0% +read along together so the defects are + + + align:start position:0% +read along together so the defects are +classified on the basis of + + align:start position:0% +classified on the basis of + + + align:start position:0% +classified on the basis of +dimensionality so we're going to look at + + align:start position:0% +dimensionality so we're going to look at + + + align:start position:0% +dimensionality so we're going to look at +Zero Dimensional Point defects then + + align:start position:0% +Zero Dimensional Point defects then + + + align:start position:0% +Zero Dimensional Point defects then +we'll go to onedimensional line two- + + align:start position:0% +we'll go to onedimensional line two- + + + align:start position:0% +we'll go to onedimensional line two- +dimensional interfacial + + align:start position:0% +dimensional interfacial + + + align:start position:0% +dimensional interfacial +three-dimensional bulk defects so the + + align:start position:0% +three-dimensional bulk defects so the + + + align:start position:0% +three-dimensional bulk defects so the +first thing is point defects and start + + align:start position:0% +first thing is point defects and start + + + align:start position:0% +first thing is point defects and start +at zero Dimension and these are + + align:start position:0% +at zero Dimension and these are + + + align:start position:0% +at zero Dimension and these are +localized disruptions in the regularity + + align:start position:0% +localized disruptions in the regularity + + + align:start position:0% +localized disruptions in the regularity +of the lattice how local at the level of + + align:start position:0% +of the lattice how local at the level of + + + align:start position:0% +of the lattice how local at the level of +one lattice site at the level of one + + align:start position:0% +one lattice site at the level of one + + + align:start position:0% +one lattice site at the level of one +lattice site and so there's three types + + align:start position:0% +lattice site and so there's three types + + + align:start position:0% +lattice site and so there's three types +I'm going to look at the first one is + + align:start position:0% +I'm going to look at the first one is + + + align:start position:0% +I'm going to look at the first one is +the substitutional impurity and that if + + align:start position:0% +the substitutional impurity and that if + + + align:start position:0% +the substitutional impurity and that if +you flip flip over on the back side I've + + align:start position:0% +you flip flip over on the back side I've + + + align:start position:0% +you flip flip over on the back side I've +I've uh uh copied this cartoon and so + + align:start position:0% +I've uh uh copied this cartoon and so + + + align:start position:0% +I've uh uh copied this cartoon and so +here's a substitutional impurity atom + + align:start position:0% +here's a substitutional impurity atom + + + align:start position:0% +here's a substitutional impurity atom +it's we've seen this already when we put + + align:start position:0% +it's we've seen this already when we put + + + align:start position:0% +it's we've seen this already when we put +phosphorus into silicon one example it + + align:start position:0% +phosphorus into silicon one example it + + + align:start position:0% +phosphorus into silicon one example it +occupies a normal lattice site occupies + + align:start position:0% +occupies a normal lattice site occupies + + + align:start position:0% +occupies a normal lattice site occupies +a normal lce site so there's the dopent + + align:start position:0% +a normal lce site so there's the dopent + + + align:start position:0% +a normal lce site so there's the dopent +that we've seen before and I'll show you + + align:start position:0% +that we've seen before and I'll show you + + + align:start position:0% +that we've seen before and I'll show you +towards the end of the lecture uh Boron + + align:start position:0% +towards the end of the lecture uh Boron + + + align:start position:0% +towards the end of the lecture uh Boron +and Diamond substitution actually sits + + align:start position:0% +and Diamond substitution actually sits + + + align:start position:0% +and Diamond substitution actually sits +at the normal uh carbon lce site there + + align:start position:0% +at the normal uh carbon lce site there + + + align:start position:0% +at the normal uh carbon lce site there +are also alloying ments such as + + align:start position:0% +are also alloying ments such as + + + align:start position:0% +are also alloying ments such as +magnesium and aluminum there are very + + align:start position:0% +magnesium and aluminum there are very + + + align:start position:0% +magnesium and aluminum there are very +few metals that are used in Commerce in + + align:start position:0% +few metals that are used in Commerce in + + + align:start position:0% +few metals that are used in Commerce in +pure form most metals are used in the + + align:start position:0% +pure form most metals are used in the + + + align:start position:0% +pure form most metals are used in the +form of Alloys that is to say solid + + align:start position:0% +form of Alloys that is to say solid + + + align:start position:0% +form of Alloys that is to say solid +Solutions so for example this aluminum + + align:start position:0% +Solutions so for example this aluminum + + + align:start position:0% +Solutions so for example this aluminum +can is dominantly aluminum it contains a + + align:start position:0% +can is dominantly aluminum it contains a + + + align:start position:0% +can is dominantly aluminum it contains a +certain amount of magnesium and a + + align:start position:0% +certain amount of magnesium and a + + + align:start position:0% +certain amount of magnesium and a +certain amount of silicon and this is + + align:start position:0% +certain amount of silicon and this is + + + align:start position:0% +certain amount of silicon and this is +designed to give it the properties that + + align:start position:0% +designed to give it the properties that + + + align:start position:0% +designed to give it the properties that +it needs one of the main properties that + + align:start position:0% +it needs one of the main properties that + + + align:start position:0% +it needs one of the main properties that +we need in this can stock is the ability + + align:start position:0% +we need in this can stock is the ability + + + align:start position:0% +we need in this can stock is the ability +to have very very rapid glass side of + + align:start position:0% +to have very very rapid glass side of + + + align:start position:0% +to have very very rapid glass side of +the atoms this if you look carefully + + align:start position:0% +the atoms this if you look carefully + + + align:start position:0% +the atoms this if you look carefully +there's no seam on the bottom of this + + align:start position:0% +there's no seam on the bottom of this + + + align:start position:0% +there's no seam on the bottom of this +can this is made out of a a single sheet + + align:start position:0% +can this is made out of a a single sheet + + + align:start position:0% +can this is made out of a a single sheet +of aluminum and so the sheet moves over + + align:start position:0% +of aluminum and so the sheet moves over + + + align:start position:0% +of aluminum and so the sheet moves over +a a d press punches down up down and + + align:start position:0% +a a d press punches down up down and + + + align:start position:0% +a a d press punches down up down and +forms the u-shaped right circular + + align:start position:0% +forms the u-shaped right circular + + + align:start position:0% +forms the u-shaped right circular +cylinder and then a second piece is + + align:start position:0% +cylinder and then a second piece is + + + align:start position:0% +cylinder and then a second piece is +crimped onto the top you can imagine the + + align:start position:0% +crimped onto the top you can imagine the + + + align:start position:0% +crimped onto the top you can imagine the +high speed at which the atoms are + + align:start position:0% +high speed at which the atoms are + + + align:start position:0% +high speed at which the atoms are +Gliding Over one another and part of + + align:start position:0% +Gliding Over one another and part of + + + align:start position:0% +Gliding Over one another and part of +what gives us the ability to deform is + + align:start position:0% +what gives us the ability to deform is + + + align:start position:0% +what gives us the ability to deform is +the alloy so magnesium is is purposely + + align:start position:0% +the alloy so magnesium is is purposely + + + align:start position:0% +the alloy so magnesium is is purposely +added to aluminum we've seen uh colored + + align:start position:0% +added to aluminum we've seen uh colored + + + align:start position:0% +added to aluminum we've seen uh colored +Golds and one example is nickel going + + align:start position:0% +Golds and one example is nickel going + + + align:start position:0% +Golds and one example is nickel going +into gold which will turn it from its + + align:start position:0% +into gold which will turn it from its + + + align:start position:0% +into gold which will turn it from its +very buttery uh almost buttery ductility + + align:start position:0% +very buttery uh almost buttery ductility + + + align:start position:0% +very buttery uh almost buttery ductility +into something that's got a little bit + + align:start position:0% +into something that's got a little bit + + + align:start position:0% +into something that's got a little bit +of strength to it I mean you don't want + + align:start position:0% +of strength to it I mean you don't want + + + align:start position:0% +of strength to it I mean you don't want +to ring that if you put it down on the + + align:start position:0% +to ring that if you put it down on the + + + align:start position:0% +to ring that if you put it down on the +on the dresser it starts to deform so we + + align:start position:0% +on the dresser it starts to deform so we + + + align:start position:0% +on the dresser it starts to deform so we +have to give it some strength and in + + align:start position:0% +have to give it some strength and in + + + align:start position:0% +have to give it some strength and in +this case we can alter its color so this + + align:start position:0% +this case we can alter its color so this + + + align:start position:0% +this case we can alter its color so this +is nickel atom sitting on the FCC site + + align:start position:0% +is nickel atom sitting on the FCC site + + + align:start position:0% +is nickel atom sitting on the FCC site +normally occupied by gold again a + + align:start position:0% +normally occupied by gold again a + + + align:start position:0% +normally occupied by gold again a +substitutional impurity and here's the + + align:start position:0% +substitutional impurity and here's the + + + align:start position:0% +substitutional impurity and here's the +last one we learned about seven up and + + align:start position:0% +last one we learned about seven up and + + + align:start position:0% +last one we learned about seven up and +the lithium citrate and seven up suppose + + align:start position:0% +the lithium citrate and seven up suppose + + + align:start position:0% +the lithium citrate and seven up suppose +you're uh on call and you're + + align:start position:0% +you're uh on call and you're + + + align:start position:0% +you're uh on call and you're +administering saline in the uh in the + + align:start position:0% +administering saline in the uh in the + + + align:start position:0% +administering saline in the uh in the +hospital and it's supposed to be 5% + + align:start position:0% +hospital and it's supposed to be 5% + + + align:start position:0% +hospital and it's supposed to be 5% +sodium chloride in water but if there's + + align:start position:0% +sodium chloride in water but if there's + + + align:start position:0% +sodium chloride in water but if there's +a lithium imp Purity substituting for + + align:start position:0% +a lithium imp Purity substituting for + + + align:start position:0% +a lithium imp Purity substituting for +sodium in the sodium chloride lattice + + align:start position:0% +sodium in the sodium chloride lattice + + + align:start position:0% +sodium in the sodium chloride lattice +it's going to dissolve and if you've got + + align:start position:0% +it's going to dissolve and if you've got + + + align:start position:0% +it's going to dissolve and if you've got +some sodium deficient patient you give + + align:start position:0% +some sodium deficient patient you give + + + align:start position:0% +some sodium deficient patient you give +them some lithium chloride it's going to + + align:start position:0% +them some lithium chloride it's going to + + + align:start position:0% +them some lithium chloride it's going to +be a bad day at the office so you you + + align:start position:0% +be a bad day at the office so you you + + + align:start position:0% +be a bad day at the office so you you +know substitutional impurities can have + + align:start position:0% +know substitutional impurities can have + + + align:start position:0% +know substitutional impurities can have +uh deleterious effects so those are + + align:start position:0% +uh deleterious effects so those are + + + align:start position:0% +uh deleterious effects so those are +examples of substitutional impurities + + align:start position:0% +examples of substitutional impurities + + + align:start position:0% +examples of substitutional impurities +the second type is the in interstitial + + align:start position:0% +the second type is the in interstitial + + + align:start position:0% +the second type is the in interstitial +impurity and it occupies the position + + align:start position:0% +impurity and it occupies the position + + + align:start position:0% +impurity and it occupies the position +between the Lites if you go to the + + align:start position:0% +between the Lites if you go to the + + + align:start position:0% +between the Lites if you go to the +cartoon you'll see this highlighted and + + align:start position:0% +cartoon you'll see this highlighted and + + + align:start position:0% +cartoon you'll see this highlighted and +the interstitial impurity obviously this + + align:start position:0% +the interstitial impurity obviously this + + + align:start position:0% +the interstitial impurity obviously this +atom is small it has to fit into the + + align:start position:0% +atom is small it has to fit into the + + + align:start position:0% +atom is small it has to fit into the +void space between the atoms so we did + + align:start position:0% +void space between the atoms so we did + + + align:start position:0% +void space between the atoms so we did +the calculations we know that a + + align:start position:0% +the calculations we know that a + + + align:start position:0% +the calculations we know that a +close-packed FCC lattice is 74 + + align:start position:0% +close-packed FCC lattice is 74 + + + align:start position:0% +close-packed FCC lattice is 74 +4% matter and 26% void well that 26% + + align:start position:0% +4% matter and 26% void well that 26% + + + align:start position:0% +4% matter and 26% void well that 26% +void is not just randomly distributed it + + align:start position:0% +void is not just randomly distributed it + + + align:start position:0% +void is not just randomly distributed it +is the nothing in between the atoms so I + + align:start position:0% +is the nothing in between the atoms so I + + + align:start position:0% +is the nothing in between the atoms so I +could take all the atoms away and I + + align:start position:0% +could take all the atoms away and I + + + align:start position:0% +could take all the atoms away and I +could give you a latus comprising the + + align:start position:0% +could give you a latus comprising the + + + align:start position:0% +could give you a latus comprising the +interstitial + + align:start position:0% +interstitial + + + align:start position:0% +interstitial +sites you understand the concept the + + align:start position:0% +sites you understand the concept the + + + align:start position:0% +sites you understand the concept the +lattice is simply points in space so + + align:start position:0% +lattice is simply points in space so + + + align:start position:0% +lattice is simply points in space so +instead of putting gold atoms there + + align:start position:0% +instead of putting gold atoms there + + + align:start position:0% +instead of putting gold atoms there +let's put the space between the gold + + align:start position:0% +let's put the space between the gold + + + align:start position:0% +let's put the space between the gold +atoms and imagine what we can do so + + align:start position:0% +atoms and imagine what we can do so + + + align:start position:0% +atoms and imagine what we can do so +here's an example of an interstitial + + align:start position:0% +here's an example of an interstitial + + + align:start position:0% +here's an example of an interstitial +atom it's small and it's obviously an + + align:start position:0% +atom it's small and it's obviously an + + + align:start position:0% +atom it's small and it's obviously an +impurity because it's different from the + + align:start position:0% +impurity because it's different from the + + + align:start position:0% +impurity because it's different from the +composition of the parent um material + + align:start position:0% +composition of the parent um material + + + align:start position:0% +composition of the parent um material +and so there are desirable and + + align:start position:0% +and so there are desirable and + + + align:start position:0% +and so there are desirable and +undesirable so an example of a desirable + + align:start position:0% +undesirable so an example of a desirable + + + align:start position:0% +undesirable so an example of a desirable +uh element is carbon in Iron carbon and + + align:start position:0% +uh element is carbon in Iron carbon and + + + align:start position:0% +uh element is carbon in Iron carbon and +iron is the basis for steel without + + align:start position:0% +iron is the basis for steel without + + + align:start position:0% +iron is the basis for steel without +carbon in Iron we wouldn't have steel + + align:start position:0% +carbon in Iron we wouldn't have steel + + + align:start position:0% +carbon in Iron we wouldn't have steel +and the interesting thing about carbon + + align:start position:0% +and the interesting thing about carbon + + + align:start position:0% +and the interesting thing about carbon +and iron is is that the radius the + + align:start position:0% +and iron is is that the radius the + + + align:start position:0% +and iron is is that the radius the +radius of the carbon atom is actually + + align:start position:0% +radius of the carbon atom is actually + + + align:start position:0% +radius of the carbon atom is actually +greater than the radius of the + + align:start position:0% +greater than the radius of the + + + align:start position:0% +greater than the radius of the +interstitial sight in + + align:start position:0% +interstitial sight in + + + align:start position:0% +interstitial sight in +Iron greater than the radius of the + + align:start position:0% +Iron greater than the radius of the + + + align:start position:0% +Iron greater than the radius of the +interstitial sight in Iron so therefore + + align:start position:0% +interstitial sight in Iron so therefore + + + align:start position:0% +interstitial sight in Iron so therefore +when the carbon goes into that + + align:start position:0% +when the carbon goes into that + + + align:start position:0% +when the carbon goes into that +interstitial site it actually distorts + + align:start position:0% +interstitial site it actually distorts + + + align:start position:0% +interstitial site it actually distorts +the lattice it presses back on the + + align:start position:0% +the lattice it presses back on the + + + align:start position:0% +the lattice it presses back on the +parent iron lattice and through this + + align:start position:0% +parent iron lattice and through this + + + align:start position:0% +parent iron lattice and through this +Distortion uh strengthens the + + align:start position:0% +Distortion uh strengthens the + + + align:start position:0% +Distortion uh strengthens the +material another example is hydrogen and + + align:start position:0% +material another example is hydrogen and + + + align:start position:0% +material another example is hydrogen and +lanum Nickel 5 it goes into the + + align:start position:0% +lanum Nickel 5 it goes into the + + + align:start position:0% +lanum Nickel 5 it goes into the +interstices in this compound lanum + + align:start position:0% +interstices in this compound lanum + + + align:start position:0% +interstices in this compound lanum +Nickel + + align:start position:0% +Nickel + + + align:start position:0% +Nickel +5 has voids that are large enough to + + align:start position:0% +5 has voids that are large enough to + + + align:start position:0% +5 has voids that are large enough to +accommodate hydrogen and hydrogen can go + + align:start position:0% +accommodate hydrogen and hydrogen can go + + + align:start position:0% +accommodate hydrogen and hydrogen can go +in this acts as a sponge and hydrogen at + + align:start position:0% +in this acts as a sponge and hydrogen at + + + align:start position:0% +in this acts as a sponge and hydrogen at +Peak loading can go in at this level we + + align:start position:0% +Peak loading can go in at this level we + + + align:start position:0% +Peak loading can go in at this level we +have huge amount of hydrogen going in + + align:start position:0% +have huge amount of hydrogen going in + + + align:start position:0% +have huge amount of hydrogen going in +here the density of hydrogen lanthum + + align:start position:0% +here the density of hydrogen lanthum + + + align:start position:0% +here the density of hydrogen lanthum +Nickel 5 at saturation is greater than + + align:start position:0% +Nickel 5 at saturation is greater than + + + align:start position:0% +Nickel 5 at saturation is greater than +liquid hydrogen itself and this material + + align:start position:0% +liquid hydrogen itself and this material + + + align:start position:0% +liquid hydrogen itself and this material +is under investigation along with others + + align:start position:0% +is under investigation along with others + + + align:start position:0% +is under investigation along with others +like it in the context of uh hydrogen + + align:start position:0% +like it in the context of uh hydrogen + + + align:start position:0% +like it in the context of uh hydrogen +powered vehicles if we're going to put + + align:start position:0% +powered vehicles if we're going to put + + + align:start position:0% +powered vehicles if we're going to put +hydrogen on cars if at some point fuel + + align:start position:0% +hydrogen on cars if at some point fuel + + + align:start position:0% +hydrogen on cars if at some point fuel +cells become practical what is going to + + align:start position:0% +cells become practical what is going to + + + align:start position:0% +cells become practical what is going to +be the mode of storing hydrogen do we + + align:start position:0% +be the mode of storing hydrogen do we + + + align:start position:0% +be the mode of storing hydrogen do we +want compressed hydrogen we're going to + + align:start position:0% +want compressed hydrogen we're going to + + + align:start position:0% +want compressed hydrogen we're going to +have to have all sorts of protection in + + align:start position:0% +have to have all sorts of protection in + + + align:start position:0% +have to have all sorts of protection in +the case of a a collision well this + + align:start position:0% +the case of a a collision well this + + + align:start position:0% +the case of a a collision well this +might be a safer way of putting hydrogen + + align:start position:0% +might be a safer way of putting hydrogen + + + align:start position:0% +might be a safer way of putting hydrogen +on the vehicle so interstitial packing + + align:start position:0% +on the vehicle so interstitial packing + + + align:start position:0% +on the vehicle so interstitial packing +is advantageous in this case but if we + + align:start position:0% +is advantageous in this case but if we + + + align:start position:0% +is advantageous in this case but if we +get wires crossed and instead of putting + + align:start position:0% +get wires crossed and instead of putting + + + align:start position:0% +get wires crossed and instead of putting +hydrogen and lanum Nickel 5 we put + + align:start position:0% +hydrogen and lanum Nickel 5 we put + + + align:start position:0% +hydrogen and lanum Nickel 5 we put +hydrogen in iron that leads to + + align:start position:0% +hydrogen in iron that leads to + + + align:start position:0% +hydrogen in iron that leads to +deleterious effects hydrogen and iron + + align:start position:0% +deleterious effects hydrogen and iron + + + align:start position:0% +deleterious effects hydrogen and iron +and brittles iron and it loses its + + align:start position:0% +and brittles iron and it loses its + + + align:start position:0% +and brittles iron and it loses its +ductility it becomes very brittle and + + align:start position:0% +ductility it becomes very brittle and + + + align:start position:0% +ductility it becomes very brittle and +can fail prematurely and this is also + + align:start position:0% +can fail prematurely and this is also + + + align:start position:0% +can fail prematurely and this is also +Germain to the hydrogen economy in this + + align:start position:0% +Germain to the hydrogen economy in this + + + align:start position:0% +Germain to the hydrogen economy in this +country we can deliver energy through + + align:start position:0% +country we can deliver energy through + + + align:start position:0% +country we can deliver energy through +the electric grid and we can deliver gas + + align:start position:0% +the electric grid and we can deliver gas + + + align:start position:0% +the electric grid and we can deliver gas +through gas pipelines you cannot send + + align:start position:0% +through gas pipelines you cannot send + + + align:start position:0% +through gas pipelines you cannot send +hydrogen through the gas pipelines + + align:start position:0% +hydrogen through the gas pipelines + + + align:start position:0% +hydrogen through the gas pipelines +because the gas pipelines are stay + + align:start position:0% +because the gas pipelines are stay + + + align:start position:0% +because the gas pipelines are stay +stable with hydrocarbon contents but not + + align:start position:0% +stable with hydrocarbon contents but not + + + align:start position:0% +stable with hydrocarbon contents but not +stable with hydrogen hydrogen Under + + align:start position:0% +stable with hydrogen hydrogen Under + + + align:start position:0% +stable with hydrogen hydrogen Under +Pressure will embrittle those pipelines + + align:start position:0% +Pressure will embrittle those pipelines + + + align:start position:0% +Pressure will embrittle those pipelines +that means that we would have to build a + + align:start position:0% +that means that we would have to build a + + + align:start position:0% +that means that we would have to build a +new infrastructure to pipe hydrogen over + + align:start position:0% +new infrastructure to pipe hydrogen over + + + align:start position:0% +new infrastructure to pipe hydrogen over +long distances and that infrastructure + + align:start position:0% +long distances and that infrastructure + + + align:start position:0% +long distances and that infrastructure +cannot be made out of + + align:start position:0% +cannot be made out of + + + align:start position:0% +cannot be made out of +steel because seal will be embrittled + + align:start position:0% +steel because seal will be embrittled + + + align:start position:0% +steel because seal will be embrittled +it's not going to be cheap it's not + + align:start position:0% +it's not going to be cheap it's not + + + align:start position:0% +it's not going to be cheap it's not +going to be cheap these are cost issues + + align:start position:0% +going to be cheap these are cost issues + + + align:start position:0% +going to be cheap these are cost issues +you need to know this because people are + + align:start position:0% +you need to know this because people are + + + align:start position:0% +you need to know this because people are +going to ask you you're from MIT they're + + align:start position:0% +going to ask you you're from MIT they're + + + align:start position:0% +going to ask you you're from MIT they're +going to ask you to help make policy you + + align:start position:0% +going to ask you to help make policy you + + + align:start position:0% +going to ask you to help make policy you +can't just get on board and say well + + align:start position:0% +can't just get on board and say well + + + align:start position:0% +can't just get on board and say well +we'll fix it somehow uh-uh hydrogen's + + align:start position:0% +we'll fix it somehow uh-uh hydrogen's + + + align:start position:0% +we'll fix it somehow uh-uh hydrogen's +very small it goes places where it's not + + align:start position:0% +very small it goes places where it's not + + + align:start position:0% +very small it goes places where it's not +supposed to be okay then the third the + + align:start position:0% +supposed to be okay then the third the + + + align:start position:0% +supposed to be okay then the third the +third the third type of defect is called + + align:start position:0% +third the third type of defect is called + + + align:start position:0% +third the third type of defect is called +the vacancy and that's simply an + + align:start position:0% +the vacancy and that's simply an + + + align:start position:0% +the vacancy and that's simply an +unoccupied lce site different from the + + align:start position:0% +unoccupied lce site different from the + + + align:start position:0% +unoccupied lce site different from the +interstitial it's a site that's not + + align:start position:0% +interstitial it's a site that's not + + + align:start position:0% +interstitial it's a site that's not +occupied and so here's the cartoon you + + align:start position:0% +occupied and so here's the cartoon you + + + align:start position:0% +occupied and so here's the cartoon you +see this is a regular atom that hasn't + + align:start position:0% +see this is a regular atom that hasn't + + + align:start position:0% +see this is a regular atom that hasn't +been uh placed on its proper site we + + align:start position:0% +been uh placed on its proper site we + + + align:start position:0% +been uh placed on its proper site we +have a vacancy + + align:start position:0% +have a vacancy + + + align:start position:0% +have a vacancy +in in that location and so there's two + + align:start position:0% +in in that location and so there's two + + + align:start position:0% +in in that location and so there's two +types of vacancy formations the first is + + align:start position:0% +types of vacancy formations the first is + + + align:start position:0% +types of vacancy formations the first is +when the material is being solidified + + align:start position:0% +when the material is being solidified + + + align:start position:0% +when the material is being solidified +whether it's solidifying from the liquid + + align:start position:0% +whether it's solidifying from the liquid + + + align:start position:0% +whether it's solidifying from the liquid +whether it's vapor deposition or whether + + align:start position:0% +whether it's vapor deposition or whether + + + align:start position:0% +whether it's vapor deposition or whether +it's a solid solid transformation so in + + align:start position:0% +it's a solid solid transformation so in + + + align:start position:0% +it's a solid solid transformation so in +some instances all of the sites don't + + align:start position:0% +some instances all of the sites don't + + + align:start position:0% +some instances all of the sites don't +get filled and then there's an extreme + + align:start position:0% +get filled and then there's an extreme + + + align:start position:0% +get filled and then there's an extreme +case such as U the wall of a nuclear + + align:start position:0% +case such as U the wall of a nuclear + + + align:start position:0% +case such as U the wall of a nuclear +reactor vessel where under high + + align:start position:0% +reactor vessel where under high + + + align:start position:0% +reactor vessel where under high +bombardment of uh Neutron flux over time + + align:start position:0% +bombardment of uh Neutron flux over time + + + align:start position:0% +bombardment of uh Neutron flux over time +atoms are literally dislodged from their + + align:start position:0% +atoms are literally dislodged from their + + + align:start position:0% +atoms are literally dislodged from their +latus positions and you put this on a + + align:start position:0% +latus positions and you put this on a + + + align:start position:0% +latus positions and you put this on a +regular maintenance schedule because as + + align:start position:0% +regular maintenance schedule because as + + + align:start position:0% +regular maintenance schedule because as +you can imagine over a certain period of + + align:start position:0% +you can imagine over a certain period of + + + align:start position:0% +you can imagine over a certain period of +time the material starts to look at the + + align:start position:0% +time the material starts to look at the + + + align:start position:0% +time the material starts to look at the +atomic level more nearly like swiss + + align:start position:0% +atomic level more nearly like swiss + + + align:start position:0% +atomic level more nearly like swiss +cheese and so that's not good so + + align:start position:0% +cheese and so that's not good so + + + align:start position:0% +cheese and so that's not good so +vacancies + + align:start position:0% +vacancies + + + align:start position:0% +vacancies +are present and + + align:start position:0% +are present and + + + align:start position:0% +are present and +uh they're always going to be present + + align:start position:0% +uh they're always going to be present + + + align:start position:0% +uh they're always going to be present +tom do you think we could uh switch the + + align:start position:0% +tom do you think we could uh switch the + + + align:start position:0% +tom do you think we could uh switch the +video over to the document camera please + + align:start position:0% +video over to the document camera please + + + align:start position:0% +video over to the document camera please +okay what I've got here is is a um well + + align:start position:0% +okay what I've got here is is a um well + + + align:start position:0% +okay what I've got here is is a um well +actually it's an object of art this uh + + align:start position:0% +actually it's an object of art this uh + + + align:start position:0% +actually it's an object of art this uh +this was made by an artiste in Montreal + + align:start position:0% +this was made by an artiste in Montreal + + + align:start position:0% +this was made by an artiste in Montreal +back in the + + align:start position:0% +back in the + + + align:start position:0% +back in the +1960s and all it is is uh um two pieces + + align:start position:0% +1960s and all it is is uh um two pieces + + + align:start position:0% +1960s and all it is is uh um two pieces +of polymethyl methacrylate that have + + align:start position:0% +of polymethyl methacrylate that have + + + align:start position:0% +of polymethyl methacrylate that have +been milled and uh joined and in between + + align:start position:0% +been milled and uh joined and in between + + + align:start position:0% +been milled and uh joined and in between +here are 2,000 ball bearings so we just + + align:start position:0% +here are 2,000 ball bearings so we just + + + align:start position:0% +here are 2,000 ball bearings so we just +have 2,000 uh ball bearings and uh I'm + + align:start position:0% +have 2,000 uh ball bearings and uh I'm + + + align:start position:0% +have 2,000 uh ball bearings and uh I'm +going to try Illuminating from the + + align:start position:0% +going to try Illuminating from the + + + align:start position:0% +going to try Illuminating from the +bottom see if that makes things better + + align:start position:0% +bottom see if that makes things better + + + align:start position:0% +bottom see if that makes things better +better ah much better and now if I + + align:start position:0% +better ah much better and now if I + + + align:start position:0% +better ah much better and now if I +learned how to + + align:start position:0% +learned how to + + + align:start position:0% +learned how to +focus okay good and now we're going to + + align:start position:0% + + + + align:start position:0% + +zoom okay so now what do you see you see + + align:start position:0% +zoom okay so now what do you see you see + + + align:start position:0% +zoom okay so now what do you see you see +atoms packing these are hard spheres and + + align:start position:0% +atoms packing these are hard spheres and + + + align:start position:0% +atoms packing these are hard spheres and +they're packing in ways that indicate + + align:start position:0% +they're packing in ways that indicate + + + align:start position:0% +they're packing in ways that indicate +the way atoms would pack you see here's + + align:start position:0% +the way atoms would pack you see here's + + + align:start position:0% +the way atoms would pack you see here's +regular Crystal erase here's some + + align:start position:0% +regular Crystal erase here's some + + + align:start position:0% +regular Crystal erase here's some +disorder oh this is even the gas phase + + align:start position:0% +disorder oh this is even the gas phase + + + align:start position:0% +disorder oh this is even the gas phase +look at this see we have everything okay + + align:start position:0% +look at this see we have everything okay + + + align:start position:0% +look at this see we have everything okay +so now what I'm going to do is I'm going + + align:start position:0% +so now what I'm going to do is I'm going + + + align:start position:0% +so now what I'm going to do is I'm going +to anal so I'm going to lift this up and + + align:start position:0% +to anal so I'm going to lift this up and + + + align:start position:0% +to anal so I'm going to lift this up and +analing would be the equivalent of + + align:start position:0% +analing would be the equivalent of + + + align:start position:0% +analing would be the equivalent of +tapping this okay I'm giving thermal + + align:start position:0% +tapping this okay I'm giving thermal + + + align:start position:0% +tapping this okay I'm giving thermal +energy to this because thermal energy + + align:start position:0% +energy to this because thermal energy + + + align:start position:0% +energy to this because thermal energy +causes atom + + align:start position:0% + + + + align:start position:0% + +motion look at the impact I have + + align:start position:0% +motion look at the impact I have + + + align:start position:0% +motion look at the impact I have +annealed out so much of the uh defects + + align:start position:0% +annealed out so much of the uh defects + + + align:start position:0% +annealed out so much of the uh defects +and now look at large large regular + + align:start position:0% +and now look at large large regular + + + align:start position:0% +and now look at large large regular +regions there's the surface see see a + + align:start position:0% +regions there's the surface see see a + + + align:start position:0% +regions there's the surface see see a +few gas atoms up there and look vac V + + align:start position:0% +few gas atoms up there and look vac V + + + align:start position:0% +few gas atoms up there and look vac V +ancies vacancies there will always be + + align:start position:0% +ancies vacancies there will always be + + + align:start position:0% +ancies vacancies there will always be +vacancies above zero Kelvin there will + + align:start position:0% +vacancies above zero Kelvin there will + + + align:start position:0% +vacancies above zero Kelvin there will +always be vacancies above Zer Kelvin you + + align:start position:0% +always be vacancies above Zer Kelvin you + + + align:start position:0% +always be vacancies above Zer Kelvin you +can come to my office anytime you want I + + align:start position:0% +can come to my office anytime you want I + + + align:start position:0% +can come to my office anytime you want I +defy I challenge anyone to anneal all of + + align:start position:0% +defy I challenge anyone to anneal all of + + + align:start position:0% +defy I challenge anyone to anneal all of +the vacancies out there will always be a + + align:start position:0% +the vacancies out there will always be a + + + align:start position:0% +the vacancies out there will always be a +few vacancies in + + align:start position:0% + + + + align:start position:0% + +here and sometimes vacancies coales + + align:start position:0% +here and sometimes vacancies coales + + + align:start position:0% +here and sometimes vacancies coales +there's a die + + align:start position:0% +there's a die + + + align:start position:0% +there's a die +vacancy there's another die vacancy well + + align:start position:0% +vacancy there's another die vacancy well + + + align:start position:0% +vacancy there's another die vacancy well +it's a good day for die vacancies the + + align:start position:0% +it's a good day for die vacancies the + + + align:start position:0% +it's a good day for die vacancies the +Red Sox are in the World Series a lot of + + align:start position:0% +Red Sox are in the World Series a lot of + + + align:start position:0% +Red Sox are in the World Series a lot of +unusual things are happen happening here + + align:start position:0% +unusual things are happen happening here + + + align:start position:0% +unusual things are happen happening here +so okay so let's take a look uh there is + + align:start position:0% +so okay so let's take a look uh there is + + + align:start position:0% +so okay so let's take a look uh there is +an expression for the vacancy population + + align:start position:0% +an expression for the vacancy population + + + align:start position:0% +an expression for the vacancy population +in any Crystal so what I'm showing you + + align:start position:0% +in any Crystal so what I'm showing you + + + align:start position:0% +in any Crystal so what I'm showing you +this is what's going on in steel this is + + align:start position:0% +this is what's going on in steel this is + + + align:start position:0% +this is what's going on in steel this is +what's going on in that aluminum + + align:start position:0% +what's going on in that aluminum + + + align:start position:0% +what's going on in that aluminum +beverage container this is what's going + + align:start position:0% +beverage container this is what's going + + + align:start position:0% +beverage container this is what's going +on in the airplane wings that you look + + align:start position:0% +on in the airplane wings that you look + + + align:start position:0% +on in the airplane wings that you look +out over when you fly vacancies okay so + + align:start position:0% +out over when you fly vacancies okay so + + + align:start position:0% +out over when you fly vacancies okay so +what's the population of vacancies and + + align:start position:0% +what's the population of vacancies and + + + align:start position:0% +what's the population of vacancies and +the calculation the calculation of + + align:start position:0% +the calculation the calculation of + + + align:start position:0% +the calculation the calculation of +vacancy population involves + + align:start position:0% +vacancy population involves + + + align:start position:0% +vacancy population involves +uh what I'm going to give as a + + align:start position:0% +uh what I'm going to give as a + + + align:start position:0% +uh what I'm going to give as a +equilibrium equilibrium meaning it's an + + align:start position:0% +equilibrium equilibrium meaning it's an + + + align:start position:0% +equilibrium equilibrium meaning it's an +equilibrium with the surroundings in + + align:start position:0% +equilibrium with the surroundings in + + + align:start position:0% +equilibrium with the surroundings in +terms of temperature it's a thermal + + align:start position:0% +terms of temperature it's a thermal + + + align:start position:0% +terms of temperature it's a thermal +equilibrium equilibrium + + align:start position:0% + + + + align:start position:0% + +population of + + align:start position:0% + + + + align:start position:0% + +vacancies and this is in a crystal and + + align:start position:0% +vacancies and this is in a crystal and + + + align:start position:0% +vacancies and this is in a crystal and +so what we're going to do is it's a + + align:start position:0% +so what we're going to do is it's a + + + align:start position:0% +so what we're going to do is it's a +comparison of The Binding energy compar + + align:start position:0% +comparison of The Binding energy compar + + + align:start position:0% +comparison of The Binding energy compar +of The Binding energy to the energy of + + align:start position:0% +of The Binding energy to the energy of + + + align:start position:0% +of The Binding energy to the energy of +disruption energy of disruption because + + align:start position:0% +disruption energy of disruption because + + + align:start position:0% +disruption energy of disruption because +you can imagine The Binding energy of an + + align:start position:0% +you can imagine The Binding energy of an + + + align:start position:0% +you can imagine The Binding energy of an +atom is the negative of the energy to + + align:start position:0% +atom is the negative of the energy to + + + align:start position:0% +atom is the negative of the energy to +form a vacancy how do you form a vacancy + + align:start position:0% +form a vacancy how do you form a vacancy + + + align:start position:0% +form a vacancy how do you form a vacancy +you can imagine you're going with atomic + + align:start position:0% +you can imagine you're going with atomic + + + align:start position:0% +you can imagine you're going with atomic +tweezers and you pull an atom out and + + align:start position:0% +tweezers and you pull an atom out and + + + align:start position:0% +tweezers and you pull an atom out and +what bonds do you have to break the + + align:start position:0% +what bonds do you have to break the + + + align:start position:0% +what bonds do you have to break the +bonds that bonded that atom to others so + + align:start position:0% +bonds that bonded that atom to others so + + + align:start position:0% +bonds that bonded that atom to others so +this is the this is minus the energy of + + align:start position:0% +this is the this is minus the energy of + + + align:start position:0% +this is the this is minus the energy of +vacancy + + align:start position:0% + + + + align:start position:0% + +formation and the disruptive energy is + + align:start position:0% +formation and the disruptive energy is + + + align:start position:0% +formation and the disruptive energy is +in our case a thermal energy and so + + align:start position:0% +in our case a thermal energy and so + + + align:start position:0% +in our case a thermal energy and so +there's a way of expressing this and + + align:start position:0% +there's a way of expressing this and + + + align:start position:0% +there's a way of expressing this and +we're going to say it's given by the + + align:start position:0% +we're going to say it's given by the + + + align:start position:0% +we're going to say it's given by the +following we're going to compare these + + align:start position:0% +following we're going to compare these + + + align:start position:0% +following we're going to compare these +two in an exponential not unlike the one + + align:start position:0% +two in an exponential not unlike the one + + + align:start position:0% +two in an exponential not unlike the one +you saw + + align:start position:0% +you saw + + + align:start position:0% +you saw +earlier in the course so I'm going to + + align:start position:0% +earlier in the course so I'm going to + + + align:start position:0% +earlier in the course so I'm going to +define the fraction the fraction of + + align:start position:0% +define the fraction the fraction of + + + align:start position:0% +define the fraction the fraction of +sites that are unoccupied which will be + + align:start position:0% +sites that are unoccupied which will be + + + align:start position:0% +sites that are unoccupied which will be +the ratio of the number of vacancies per + + align:start position:0% +the ratio of the number of vacancies per + + + align:start position:0% +the ratio of the number of vacancies per +unit volume to the number of sites per + + align:start position:0% +unit volume to the number of sites per + + + align:start position:0% +unit volume to the number of sites per +unit volume so the NV is number of + + align:start position:0% +unit volume so the NV is number of + + + align:start position:0% +unit volume so the NV is number of +vacancies per unit + + align:start position:0% +vacancies per unit + + + align:start position:0% +vacancies per unit +volume and big n is the number of atomic + + align:start position:0% +volume and big n is the number of atomic + + + align:start position:0% +volume and big n is the number of atomic +sites number of atomic sites per unit + + align:start position:0% + + + + align:start position:0% + +volume okay and that's going to be given + + align:start position:0% +volume okay and that's going to be given + + + align:start position:0% +volume okay and that's going to be given +by the + + align:start position:0% +by the + + + align:start position:0% +by the +ratio mediate through this exponential + + align:start position:0% +ratio mediate through this exponential + + + align:start position:0% +ratio mediate through this exponential +of the energy and I I Loosely move + + align:start position:0% +of the energy and I I Loosely move + + + align:start position:0% +of the energy and I I Loosely move +energy in enthalpy back and forth this + + align:start position:0% +energy in enthalpy back and forth this + + + align:start position:0% +energy in enthalpy back and forth this +is the enthalpy + + align:start position:0% +is the enthalpy + + + align:start position:0% +is the enthalpy +of vacancy + + align:start position:0% +of vacancy + + + align:start position:0% +of vacancy +formation vacancy formation + + align:start position:0% + + + + align:start position:0% + +energy vacancy formation + + align:start position:0% +energy vacancy formation + + + align:start position:0% +energy vacancy formation +energy over the thermal energy and how + + align:start position:0% +energy over the thermal energy and how + + + align:start position:0% +energy over the thermal energy and how +do we get a rough measure of the thermal + + align:start position:0% +do we get a rough measure of the thermal + + + align:start position:0% +do we get a rough measure of the thermal +energy product of the boltzman constant + + align:start position:0% +energy product of the boltzman constant + + + align:start position:0% +energy product of the boltzman constant +and absolute + + align:start position:0% +and absolute + + + align:start position:0% +and absolute +temperature so what are we doing we're + + align:start position:0% +temperature so what are we doing we're + + + align:start position:0% +temperature so what are we doing we're +taking this onto the temperature + + align:start position:0% +taking this onto the temperature + + + align:start position:0% +taking this onto the temperature +distribution and we're saying where is + + align:start position:0% +distribution and we're saying where is + + + align:start position:0% +distribution and we're saying where is +this required energy in relation to the + + align:start position:0% +this required energy in relation to the + + + align:start position:0% +this required energy in relation to the +average energy of the system and in + + align:start position:0% +average energy of the system and in + + + align:start position:0% +average energy of the system and in +particular the high-end tail the highend + + align:start position:0% +particular the high-end tail the highend + + + align:start position:0% +particular the high-end tail the highend +tail so and then it has a preactor a and + + align:start position:0% +tail so and then it has a preactor a and + + + align:start position:0% +tail so and then it has a preactor a and +a is just an entropic + + align:start position:0% + + + + align:start position:0% + +prefactor and it's not equal to one a + + align:start position:0% +prefactor and it's not equal to one a + + + align:start position:0% +prefactor and it's not equal to one a +Will T take values between uh a tenth up + + align:start position:0% +Will T take values between uh a tenth up + + + align:start position:0% +Will T take values between uh a tenth up +to about 10 it's typically on the order + + align:start position:0% +to about 10 it's typically on the order + + + align:start position:0% +to about 10 it's typically on the order +of oh four five something like this but + + align:start position:0% +of oh four five something like this but + + + align:start position:0% +of oh four five something like this but +in some some cases it can even be uh + + align:start position:0% +in some some cases it can even be uh + + + align:start position:0% +in some some cases it can even be uh +less than one so this is a relationship + + align:start position:0% +less than one so this is a relationship + + + align:start position:0% +less than one so this is a relationship +that tells us what the fraction of + + align:start position:0% +that tells us what the fraction of + + + align:start position:0% +that tells us what the fraction of +unoccupied sites is as a function of + + align:start position:0% +unoccupied sites is as a function of + + + align:start position:0% +unoccupied sites is as a function of +temperature so we could go in and and + + align:start position:0% +temperature so we could go in and and + + + align:start position:0% +temperature so we could go in and and +calculate what the eff of bond energy is + + align:start position:0% +calculate what the eff of bond energy is + + + align:start position:0% +calculate what the eff of bond energy is +because we know what the thermal energy + + align:start position:0% +because we know what the thermal energy + + + align:start position:0% +because we know what the thermal energy +is so we could work backwards and + + align:start position:0% +is so we could work backwards and + + + align:start position:0% +is so we could work backwards and +calculate that so I did a sample + + align:start position:0% +calculate that so I did a sample + + + align:start position:0% +calculate that so I did a sample +calculation I was wondering you know + + align:start position:0% +calculation I was wondering you know + + + align:start position:0% +calculation I was wondering you know +what what should be the vacancy + + align:start position:0% +what what should be the vacancy + + + align:start position:0% +what what should be the vacancy +population in say a a piece of copper so + + align:start position:0% +population in say a a piece of copper so + + + align:start position:0% +population in say a a piece of copper so +I said all right copper uh happens that + + align:start position:0% +I said all right copper uh happens that + + + align:start position:0% +I said all right copper uh happens that +the enthalpy of formation of a vacancy + + align:start position:0% +the enthalpy of formation of a vacancy + + + align:start position:0% +the enthalpy of formation of a vacancy +is + + align:start position:0% +is + + + align:start position:0% +is +1.29 electron volts per atom and the + + align:start position:0% +1.29 electron volts per atom and the + + + align:start position:0% +1.29 electron volts per atom and the +preactor is equal to 4.5 I had to look + + align:start position:0% +preactor is equal to 4.5 I had to look + + + align:start position:0% +preactor is equal to 4.5 I had to look +this up in tables this is not from uh + + align:start position:0% +this up in tables this is not from uh + + + align:start position:0% +this up in tables this is not from uh +first principal's calculation so I said + + align:start position:0% +first principal's calculation so I said + + + align:start position:0% +first principal's calculation so I said +okay let's look at room + + align:start position:0% +okay let's look at room + + + align:start position:0% +okay let's look at room +temperature at room temperature I + + align:start position:0% +temperature at room temperature I + + + align:start position:0% +temperature at room temperature I +plugged these numbers in and I got um + + align:start position:0% +plugged these numbers in and I got um + + + align:start position:0% +plugged these numbers in and I got um +the fraction of vacant sites as 10 Theus + + align:start position:0% +the fraction of vacant sites as 10 Theus + + + align:start position:0% +the fraction of vacant sites as 10 Theus +21 10us 21 well if you multiply by the + + align:start position:0% +21 10us 21 well if you multiply by the + + + align:start position:0% +21 10us 21 well if you multiply by the +density of copper that turns out to be + + align:start position:0% +density of copper that turns out to be + + + align:start position:0% +density of copper that turns out to be +85 vacancies 85 vacancies per cubic + + align:start position:0% +85 vacancies 85 vacancies per cubic + + + align:start position:0% +85 vacancies 85 vacancies per cubic +centimeter I mean this is vanishingly + + align:start position:0% +centimeter I mean this is vanishingly + + + align:start position:0% +centimeter I mean this is vanishingly +small this is vanishingly small this is + + align:start position:0% +small this is vanishingly small this is + + + align:start position:0% +small this is vanishingly small this is +almost the inverse this is almost none + + align:start position:0% +almost the inverse this is almost none + + + align:start position:0% +almost the inverse this is almost none +right because we have a roughly avagadro + + align:start position:0% +right because we have a roughly avagadro + + + align:start position:0% +right because we have a roughly avagadro +number of atoms per cubic centimeter for + + align:start position:0% +number of atoms per cubic centimeter for + + + align:start position:0% +number of atoms per cubic centimeter for +condensed matter so this is really + + align:start position:0% +condensed matter so this is really + + + align:start position:0% +condensed matter so this is really +really low and 10 of the 21 10 of the 23 + + align:start position:0% +really low and 10 of the 21 10 of the 23 + + + align:start position:0% +really low and 10 of the 21 10 of the 23 +there's 100 difference and sure enough + + align:start position:0% +there's 100 difference and sure enough + + + align:start position:0% +there's 100 difference and sure enough +there it is 85 there's so few you could + + align:start position:0% +there it is 85 there's so few you could + + + align:start position:0% +there it is 85 there's so few you could +give each of them a name uh and then so + + align:start position:0% +give each of them a name uh and then so + + + align:start position:0% +give each of them a name uh and then so +then I said well what happens if we go + + align:start position:0% +then I said well what happens if we go + + + align:start position:0% +then I said well what happens if we go +to the melting point at the melting + + align:start position:0% +to the melting point at the melting + + + align:start position:0% +to the melting point at the melting +point of copper okay I'm not going to + + align:start position:0% +point of copper okay I'm not going to + + + align:start position:0% +point of copper okay I'm not going to +melt the copper it's like ice at 0° C + + align:start position:0% +melt the copper it's like ice at 0° C + + + align:start position:0% +melt the copper it's like ice at 0° C +it's Copper at the threshold of Mel + + align:start position:0% +it's Copper at the threshold of Mel + + + align:start position:0% +it's Copper at the threshold of Mel +melting but still solid if you do the + + align:start position:0% +melting but still solid if you do the + + + align:start position:0% +melting but still solid if you do the +calculation at the melting point of + + align:start position:0% +calculation at the melting point of + + + align:start position:0% +calculation at the melting point of +copper you get + + align:start position:0% +copper you get + + + align:start position:0% +copper you get +7.35 * 10- + + align:start position:0% +7.35 * 10- + + + align:start position:0% +7.35 * 10- +5 which now turns out to be about 70 + + align:start position:0% +5 which now turns out to be about 70 + + + align:start position:0% +5 which now turns out to be about 70 +parts per million on an atom basis so + + align:start position:0% +parts per million on an atom basis so + + + align:start position:0% +parts per million on an atom basis so +for every million copper sites you can + + align:start position:0% +for every million copper sites you can + + + align:start position:0% +for every million copper sites you can +expect about 70 of them to be unoccupied + + align:start position:0% +expect about 70 of them to be unoccupied + + + align:start position:0% +expect about 70 of them to be unoccupied +so now we're starting to get up to to + + align:start position:0% +so now we're starting to get up to to + + + align:start position:0% +so now we're starting to get up to to +real numbers because that would give us + + align:start position:0% +real numbers because that would give us + + + align:start position:0% +real numbers because that would give us +a vacancy population of 6 * 10 to the + + align:start position:0% +a vacancy population of 6 * 10 to the + + + align:start position:0% +a vacancy population of 6 * 10 to the +18th + + align:start position:0% +18th + + + align:start position:0% +18th +per cubic centimeter that's substantial + + align:start position:0% +per cubic centimeter that's substantial + + + align:start position:0% +per cubic centimeter that's substantial +that's substantial this is the kind of + + align:start position:0% +that's substantial this is the kind of + + + align:start position:0% +that's substantial this is the kind of +stuff that would be perceptible if this + + align:start position:0% +stuff that would be perceptible if this + + + align:start position:0% +stuff that would be perceptible if this +was ad doent this were a dopen + + align:start position:0% +was ad doent this were a dopen + + + align:start position:0% +was ad doent this were a dopen +concentration this would alter the + + align:start position:0% +concentration this would alter the + + + align:start position:0% +concentration this would alter the +electrical properties of silicon and + + align:start position:0% +electrical properties of silicon and + + + align:start position:0% +electrical properties of silicon and +here's the way to look at this what's + + align:start position:0% +here's the way to look at this what's + + + align:start position:0% +here's the way to look at this what's +going on here what's going on is this + + align:start position:0% +going on here what's going on is this + + + align:start position:0% +going on here what's going on is this +critical ratio this this is so important + + align:start position:0% +critical ratio this this is so important + + + align:start position:0% +critical ratio this this is so important +the ratio of The Binding energy to the + + align:start position:0% +the ratio of The Binding energy to the + + + align:start position:0% +the ratio of The Binding energy to the +thermal energy The Binding energy to the + + align:start position:0% +thermal energy The Binding energy to the + + + align:start position:0% +thermal energy The Binding energy to the +thermal energy at room temperature this + + align:start position:0% +thermal energy at room temperature this + + + align:start position:0% +thermal energy at room temperature this +ratio is about 50 to one it's about 50 + + align:start position:0% +ratio is about 50 to one it's about 50 + + + align:start position:0% +ratio is about 50 to one it's about 50 +to one at the melting point it's about + + align:start position:0% +to one at the melting point it's about + + + align:start position:0% +to one at the melting point it's about +10 to one and that's what's going on + + align:start position:0% +10 to one and that's what's going on + + + align:start position:0% +10 to one and that's what's going on +you're Shifting the the distribution way + + align:start position:0% +you're Shifting the the distribution way + + + align:start position:0% +you're Shifting the the distribution way +over and giving yourself the ability to + + align:start position:0% +over and giving yourself the ability to + + + align:start position:0% +over and giving yourself the ability to +rip the copper atoms out of their out of + + align:start position:0% +rip the copper atoms out of their out of + + + align:start position:0% +rip the copper atoms out of their out of +their sites so that's that's interesting + + align:start position:0% +their sites so that's that's interesting + + + align:start position:0% +their sites so that's that's interesting +to know okay Tom may we go back to the + + align:start position:0% +to know okay Tom may we go back to the + + + align:start position:0% +to know okay Tom may we go back to the +computer please for + + align:start position:0% + + + + align:start position:0% + +graphics thank you okay so now I want to + + align:start position:0% +graphics thank you okay so now I want to + + + align:start position:0% +graphics thank you okay so now I want to +talk about Point defects in ionic + + align:start position:0% +talk about Point defects in ionic + + + align:start position:0% +talk about Point defects in ionic +crystals because there's a a special + + align:start position:0% +crystals because there's a a special + + + align:start position:0% +crystals because there's a a special +twist here with with an ionic Crystal if + + align:start position:0% +twist here with with an ionic Crystal if + + + align:start position:0% +twist here with with an ionic Crystal if +you've got sodium chloride you can't + + align:start position:0% +you've got sodium chloride you can't + + + align:start position:0% +you've got sodium chloride you can't +just remove a sodium ion because you + + align:start position:0% +just remove a sodium ion because you + + + align:start position:0% +just remove a sodium ion because you +violate charge neutrality so when you + + align:start position:0% +violate charge neutrality so when you + + + align:start position:0% +violate charge neutrality so when you +make vacancies in an ionic Crystal you + + align:start position:0% +make vacancies in an ionic Crystal you + + + align:start position:0% +make vacancies in an ionic Crystal you +have to take them out you have to make + + align:start position:0% +have to take them out you have to make + + + align:start position:0% +have to take them out you have to make +those vacancies by removing atoms in + + align:start position:0% +those vacancies by removing atoms in + + + align:start position:0% +those vacancies by removing atoms in +neutral units so let's look at the + + align:start position:0% +neutral units so let's look at the + + + align:start position:0% +neutral units so let's look at the +various uh types the first one is called + + align:start position:0% +various uh types the first one is called + + + align:start position:0% +various uh types the first one is called +shoty imperfection and it's the + + align:start position:0% +shoty imperfection and it's the + + + align:start position:0% +shoty imperfection and it's the +formation of equivalent not equal but + + align:start position:0% +formation of equivalent not equal but + + + align:start position:0% +formation of equivalent not equal but +equivalent equivalent numbers of + + align:start position:0% +equivalent equivalent numbers of + + + align:start position:0% +equivalent equivalent numbers of +cationic and anionic vacancies and + + align:start position:0% +cationic and anionic vacancies and + + + align:start position:0% +cationic and anionic vacancies and +there's the other cartoon on the back + + align:start position:0% +there's the other cartoon on the back + + + align:start position:0% +there's the other cartoon on the back +side of the handout so here's the shaki + + align:start position:0% +side of the handout so here's the shaki + + + align:start position:0% +side of the handout so here's the shaki +imperfection where you see uh the the + + align:start position:0% +imperfection where you see uh the the + + + align:start position:0% +imperfection where you see uh the the +video graphic is not so good if you uh + + align:start position:0% +video graphic is not so good if you uh + + + align:start position:0% +video graphic is not so good if you uh +squint just a little bit you'll see + + align:start position:0% +squint just a little bit you'll see + + + align:start position:0% +squint just a little bit you'll see +these this is not just an array of dark + + align:start position:0% +these this is not just an array of dark + + + align:start position:0% +these this is not just an array of dark +spheres but there are light spheres in + + align:start position:0% +spheres but there are light spheres in + + + align:start position:0% +spheres but there are light spheres in +between the dark spheres and the light + + align:start position:0% +between the dark spheres and the light + + + align:start position:0% +between the dark spheres and the light +spheres represent the Anon ions and the + + align:start position:0% +spheres represent the Anon ions and the + + + align:start position:0% +spheres represent the Anon ions and the +dark spheres represent the cats and what + + align:start position:0% +dark spheres represent the cats and what + + + align:start position:0% +dark spheres represent the cats and what +you're seeing here is the pair we're + + align:start position:0% +you're seeing here is the pair we're + + + align:start position:0% +you're seeing here is the pair we're +missing both the anion here in the midst + + align:start position:0% +missing both the anion here in the midst + + + align:start position:0% +missing both the anion here in the midst +of four catons and uh the the cat IR + + align:start position:0% +of four catons and uh the the cat IR + + + align:start position:0% +of four catons and uh the the cat IR +over here in order to preserve charge + + align:start position:0% +over here in order to preserve charge + + + align:start position:0% +over here in order to preserve charge +neutrality now they don't necessarily + + align:start position:0% +neutrality now they don't necessarily + + + align:start position:0% +neutrality now they don't necessarily +have to be Side by each I mean the + + align:start position:0% +have to be Side by each I mean the + + + align:start position:0% +have to be Side by each I mean the +cation vacancy can be way over here and + + align:start position:0% +cation vacancy can be way over here and + + + align:start position:0% +cation vacancy can be way over here and +the anion vacancy can be way over here + + align:start position:0% +the anion vacancy can be way over here + + + align:start position:0% +the anion vacancy can be way over here +but globally it's the the same number + + align:start position:0% +but globally it's the the same number + + + align:start position:0% +but globally it's the the same number +and so let's look at how that works one + + align:start position:0% +and so let's look at how that works one + + + align:start position:0% +and so let's look at how that works one +way to one way to describe that is to + + align:start position:0% +way to one way to describe that is to + + + align:start position:0% +way to one way to describe that is to +think about um the instead of removing + + align:start position:0% +think about um the instead of removing + + + align:start position:0% +think about um the instead of removing +the cation and anion the other way to + + align:start position:0% +the cation and anion the other way to + + + align:start position:0% +the cation and anion the other way to +think about this mathematically is to + + align:start position:0% +think about this mathematically is to + + + align:start position:0% +think about this mathematically is to +say suppose I take here's nothing I'm + + align:start position:0% +say suppose I take here's nothing I'm + + + align:start position:0% +say suppose I take here's nothing I'm +going to take some nothing but it's not + + align:start position:0% +going to take some nothing but it's not + + + align:start position:0% +going to take some nothing but it's not +any old nothing it's FCC nothing and I'm + + align:start position:0% +any old nothing it's FCC nothing and I'm + + + align:start position:0% +any old nothing it's FCC nothing and I'm +going to dissolve the FCC nothing into + + align:start position:0% +going to dissolve the FCC nothing into + + + align:start position:0% +going to dissolve the FCC nothing into +sodium chloride so let's do that you'll + + align:start position:0% +sodium chloride so let's do that you'll + + + align:start position:0% +sodium chloride so let's do that you'll +get you'll get the idea conceptually + + align:start position:0% +get you'll get the idea conceptually + + + align:start position:0% +get you'll get the idea conceptually +it's so cool so how do I make I want to + + align:start position:0% +it's so cool so how do I make I want to + + + align:start position:0% +it's so cool so how do I make I want to +make a sodium chloride vacancy pair + + align:start position:0% +make a sodium chloride vacancy pair + + + align:start position:0% +make a sodium chloride vacancy pair +vacancy pair so what I do is instead of + + align:start position:0% +vacancy pair so what I do is instead of + + + align:start position:0% +vacancy pair so what I do is instead of +ripping out a sodium and ripping out a a + + align:start position:0% +ripping out a sodium and ripping out a a + + + align:start position:0% +ripping out a sodium and ripping out a a +chloride what I do is I take nothing + + align:start position:0% +chloride what I do is I take nothing + + + align:start position:0% +chloride what I do is I take nothing +which I represent as + + align:start position:0% +which I represent as + + + align:start position:0% +which I represent as +null and I dissolve it so I'm going to + + align:start position:0% +null and I dissolve it so I'm going to + + + align:start position:0% +null and I dissolve it so I'm going to +take nothing but I'm going to I'm going + + align:start position:0% +take nothing but I'm going to I'm going + + + align:start position:0% +take nothing but I'm going to I'm going +to have some nothing that goes to the + + align:start position:0% +to have some nothing that goes to the + + + align:start position:0% +to have some nothing that goes to the +cationic site and nothing that goes to + + align:start position:0% +cationic site and nothing that goes to + + + align:start position:0% +cationic site and nothing that goes to +the anionic site so this is V is a + + align:start position:0% +the anionic site so this is V is a + + + align:start position:0% +the anionic site so this is V is a +vacancy on a sodium site and a vacancy + + align:start position:0% +vacancy on a sodium site and a vacancy + + + align:start position:0% +vacancy on a sodium site and a vacancy +on a Chlor oride site so this is charge + + align:start position:0% +on a Chlor oride site so this is charge + + + align:start position:0% +on a Chlor oride site so this is charge +neutral now okay we said well it's only + + align:start position:0% +neutral now okay we said well it's only + + + align:start position:0% +neutral now okay we said well it's only +nothing anyways well let's think about + + align:start position:0% +nothing anyways well let's think about + + + align:start position:0% +nothing anyways well let's think about +it um if you look at uh sodium vacancy + + align:start position:0% +it um if you look at uh sodium vacancy + + + align:start position:0% +it um if you look at uh sodium vacancy +sodium vacancy is charge zero but it's + + align:start position:0% +sodium vacancy is charge zero but it's + + + align:start position:0% +sodium vacancy is charge zero but it's +on a can iic sublattice it's zero but + + align:start position:0% +on a can iic sublattice it's zero but + + + align:start position:0% +on a can iic sublattice it's zero but +everywhere around it it's got neighbors + + align:start position:0% +everywhere around it it's got neighbors + + + align:start position:0% +everywhere around it it's got neighbors +of comparable + + align:start position:0% +of comparable + + + align:start position:0% +of comparable +charge + + align:start position:0% +charge + + + align:start position:0% +charge +except this is in a Land of plus one for + + align:start position:0% +except this is in a Land of plus one for + + + align:start position:0% +except this is in a Land of plus one for +V + + align:start position:0% +V + + + align:start position:0% +V +sodium so it this means it has an + + align:start position:0% +sodium so it this means it has an + + + align:start position:0% +sodium so it this means it has an +apparent I'm going to put quotation + + align:start position:0% +apparent I'm going to put quotation + + + align:start position:0% +apparent I'm going to put quotation +marks here it has an apparent charge of + + align:start position:0% +marks here it has an apparent charge of + + + align:start position:0% +marks here it has an apparent charge of +minus one apparent charge of minus one + + align:start position:0% +minus one apparent charge of minus one + + + align:start position:0% +minus one apparent charge of minus one +zero in a Land of plus one is relatively + + align:start position:0% +zero in a Land of plus one is relatively + + + align:start position:0% +zero in a Land of plus one is relatively +negative and what about the chloride the + + align:start position:0% +negative and what about the chloride the + + + align:start position:0% +negative and what about the chloride the +chloride vacancy is zero in a Land of + + align:start position:0% +chloride vacancy is zero in a Land of + + + align:start position:0% +chloride vacancy is zero in a Land of +minus one so a zero in a Land of minus + + align:start position:0% +minus one so a zero in a Land of minus + + + align:start position:0% +minus one so a zero in a Land of minus +one is effectively A+ one so let's put + + align:start position:0% +one is effectively A+ one so let's put + + + align:start position:0% +one is effectively A+ one so let's put +that down so this is I'm going to put + + align:start position:0% +that down so this is I'm going to put + + + align:start position:0% +that down so this is I'm going to put +here this indicates it's this is + + align:start position:0% +here this indicates it's this is + + + align:start position:0% +here this indicates it's this is +locally locally minus and this indicates + + align:start position:0% +locally locally minus and this indicates + + + align:start position:0% +locally locally minus and this indicates +it's locally + + align:start position:0% +it's locally + + + align:start position:0% +it's locally +plus the way I remember these is this + + align:start position:0% +plus the way I remember these is this + + + align:start position:0% +plus the way I remember these is this +this slash reminds me of a minus sign + + align:start position:0% +this slash reminds me of a minus sign + + + align:start position:0% +this slash reminds me of a minus sign +and the plus is sort of like the + + align:start position:0% +and the plus is sort of like the + + + align:start position:0% +and the plus is sort of like the +crosshairs of a of the plus sign that's + + align:start position:0% +crosshairs of a of the plus sign that's + + + align:start position:0% +crosshairs of a of the plus sign that's +how I remember okay and we can do the + + align:start position:0% +how I remember okay and we can do the + + + align:start position:0% +how I remember okay and we can do the +same as we did for the vacancy fraction + + align:start position:0% +same as we did for the vacancy fraction + + + align:start position:0% +same as we did for the vacancy fraction +and compute a shock key fraction what's + + align:start position:0% +and compute a shock key fraction what's + + + align:start position:0% +and compute a shock key fraction what's +the fraction of shocky defects it's + + align:start position:0% +the fraction of shocky defects it's + + + align:start position:0% +the fraction of shocky defects it's +going to be the number of shocky defects + + align:start position:0% +going to be the number of shocky defects + + + align:start position:0% +going to be the number of shocky defects +divided by the total number of sites and + + align:start position:0% +divided by the total number of sites and + + + align:start position:0% +divided by the total number of sites and +it'll be an equation of this form some + + align:start position:0% +it'll be an equation of this form some + + + align:start position:0% +it'll be an equation of this form some +pre-exponential times the exponential of + + align:start position:0% +pre-exponential times the exponential of + + + align:start position:0% +pre-exponential times the exponential of +the ratio of the energy to form the shot + + align:start position:0% +the ratio of the energy to form the shot + + + align:start position:0% +the ratio of the energy to form the shot +key uh defect divided by the product of + + align:start position:0% +key uh defect divided by the product of + + + align:start position:0% +key uh defect divided by the product of +the boltman constant in temperature and + + align:start position:0% +the boltman constant in temperature and + + + align:start position:0% +the boltman constant in temperature and +for sodium chloride the shocky energy is + + align:start position:0% +for sodium chloride the shocky energy is + + + align:start position:0% +for sodium chloride the shocky energy is +on the order of about + + align:start position:0% +on the order of about + + + align:start position:0% +on the order of about +2.5 electron volts and that's about + + align:start position:0% +2.5 electron volts and that's about + + + align:start position:0% +2.5 electron volts and that's about +double what it is for copper so and that + + align:start position:0% +double what it is for copper so and that + + + align:start position:0% +double what it is for copper so and that +makes sense it should take more energy + + align:start position:0% +makes sense it should take more energy + + + align:start position:0% +makes sense it should take more energy +to to make a vacancy pair than it does + + align:start position:0% +to to make a vacancy pair than it does + + + align:start position:0% +to to make a vacancy pair than it does +to make a vacancy and kulic forces of + + align:start position:0% +to make a vacancy and kulic forces of + + + align:start position:0% +to make a vacancy and kulic forces of +attraction in ionic crystals are more + + align:start position:0% +attraction in ionic crystals are more + + + align:start position:0% +attraction in ionic crystals are more +intense than metallic bonding forces in + + align:start position:0% +intense than metallic bonding forces in + + + align:start position:0% +intense than metallic bonding forces in +metal crystals I want to show you one + + align:start position:0% +metal crystals I want to show you one + + + align:start position:0% +metal crystals I want to show you one +other one this is what's going on in the + + align:start position:0% +other one this is what's going on in the + + + align:start position:0% +other one this is what's going on in the +oxygen sensor of your car it's zirconia + + align:start position:0% +oxygen sensor of your car it's zirconia + + + align:start position:0% +oxygen sensor of your car it's zirconia +zironia and I'm going to show you later + + align:start position:0% +zironia and I'm going to show you later + + + align:start position:0% +zironia and I'm going to show you later +how you manage the defects in zirconia + + align:start position:0% +how you manage the defects in zirconia + + + align:start position:0% +how you manage the defects in zirconia +to Advantage so how do I make a vacancy + + align:start position:0% +to Advantage so how do I make a vacancy + + + align:start position:0% +to Advantage so how do I make a vacancy +in zironia the dominant vacancy is shaki + + align:start position:0% +in zironia the dominant vacancy is shaki + + + align:start position:0% +in zironia the dominant vacancy is shaki +and how do we I'm going to write again + + align:start position:0% +and how do we I'm going to write again + + + align:start position:0% +and how do we I'm going to write again +null I'm going to dissolve nothing into + + align:start position:0% +null I'm going to dissolve nothing into + + + align:start position:0% +null I'm going to dissolve nothing into +zirconia so I'm going to make a + + align:start position:0% +zirconia so I'm going to make a + + + align:start position:0% +zirconia so I'm going to make a +zirconium vacancy a zirconium + + align:start position:0% +zirconium vacancy a zirconium + + + align:start position:0% +zirconium vacancy a zirconium +vacancy + + align:start position:0% +vacancy + + + align:start position:0% +vacancy +and two oxygen vacancies I have to + + align:start position:0% +and two oxygen vacancies I have to + + + align:start position:0% +and two oxygen vacancies I have to +preserve the stochiometry of nothing + + align:start position:0% +preserve the stochiometry of nothing + + + align:start position:0% +preserve the stochiometry of nothing +nothing counts here okay because what's + + align:start position:0% +nothing counts here okay because what's + + + align:start position:0% +nothing counts here okay because what's +the local charge this is zero in a Land + + align:start position:0% +the local charge this is zero in a Land + + + align:start position:0% +the local charge this is zero in a Land +of plus4 so it's apparent ently Min -4 + + align:start position:0% +of plus4 so it's apparent ently Min -4 + + + align:start position:0% +of plus4 so it's apparent ently Min -4 +and every oxygen is a zero in a Land of + + align:start position:0% +and every oxygen is a zero in a Land of + + + align:start position:0% +and every oxygen is a zero in a Land of +min-2 all of the oxide ions are minus + + align:start position:0% +min-2 all of the oxide ions are minus + + + align:start position:0% +min-2 all of the oxide ions are minus +two this oxide ion vacancy is zero zero + + align:start position:0% +two this oxide ion vacancy is zero zero + + + align:start position:0% +two this oxide ion vacancy is zero zero +in a Land of minus two is plus two + + align:start position:0% +in a Land of minus two is plus two + + + align:start position:0% +in a Land of minus two is plus two +apparently so I have Min -4 apparent 2 * + + align:start position:0% +apparently so I have Min -4 apparent 2 * + + + align:start position:0% +apparently so I have Min -4 apparent 2 * +Min -2 apparent charge neutrality and + + align:start position:0% +Min -2 apparent charge neutrality and + + + align:start position:0% +Min -2 apparent charge neutrality and +this is now + + align:start position:0% + + + + align:start position:0% + +equalent + + align:start position:0% +equalent + + + align:start position:0% +equalent +equivalent + + align:start position:0% +equivalent + + + align:start position:0% +equivalent +numbers of + + align:start position:0% +numbers of + + + align:start position:0% +numbers of +cation and anion + + align:start position:0% +cation and anion + + + align:start position:0% +cation and anion +vacancies very cool okay so there's + + align:start position:0% +vacancies very cool okay so there's + + + align:start position:0% +vacancies very cool okay so there's +another way though there's another way + + align:start position:0% +another way though there's another way + + + align:start position:0% +another way though there's another way +to make uh vacancies and that's called + + align:start position:0% +to make uh vacancies and that's called + + + align:start position:0% +to make uh vacancies and that's called +the Frankle the Frankle imperfection and + + align:start position:0% +the Frankle the Frankle imperfection and + + + align:start position:0% +the Frankle the Frankle imperfection and +it's the formation of an ion vacancy and + + align:start position:0% +it's the formation of an ion vacancy and + + + align:start position:0% +it's the formation of an ion vacancy and +iron interstitial so that's shown over + + align:start position:0% +iron interstitial so that's shown over + + + align:start position:0% +iron interstitial so that's shown over +here where the little cation you see the + + align:start position:0% +here where the little cation you see the + + + align:start position:0% +here where the little cation you see the +cation see this cat's gone over to + + align:start position:0% +cation see this cat's gone over to + + + align:start position:0% +cation see this cat's gone over to +another uh cation over in this there's a + + align:start position:0% +another uh cation over in this there's a + + + align:start position:0% +another uh cation over in this there's a +there's a there's an inter icial in here + + align:start position:0% +there's a there's an inter icial in here + + + align:start position:0% +there's a there's an inter icial in here +you see the little cat IR cat IR left + + align:start position:0% +you see the little cat IR cat IR left + + + align:start position:0% +you see the little cat IR cat IR left +and went over here yeah but see it + + align:start position:0% +and went over here yeah but see it + + + align:start position:0% +and went over here yeah but see it +didn't leave it didn't leave the crystal + + align:start position:0% +didn't leave it didn't leave the crystal + + + align:start position:0% +didn't leave it didn't leave the crystal +it moved to another place in the crystal + + align:start position:0% +it moved to another place in the crystal + + + align:start position:0% +it moved to another place in the crystal +so I don't have to worry about + + align:start position:0% +so I don't have to worry about + + + align:start position:0% +so I don't have to worry about +compensating with the ion of opposite + + align:start position:0% +compensating with the ion of opposite + + + align:start position:0% +compensating with the ion of opposite +charge because the total cat iron + + align:start position:0% +charge because the total cat iron + + + align:start position:0% +charge because the total cat iron +population hasn't changed but I have + + align:start position:0% +population hasn't changed but I have + + + align:start position:0% +population hasn't changed but I have +created a Caton vacancy you know this is + + align:start position:0% +created a Caton vacancy you know this is + + + align:start position:0% +created a Caton vacancy you know this is +this is what the issue is here and so + + align:start position:0% +this is what the issue is here and so + + + align:start position:0% +this is what the issue is here and so +with Frankle clearly with Frankle um + + align:start position:0% +with Frankle clearly with Frankle um + + + align:start position:0% +with Frankle clearly with Frankle um +Frankle occurs in crystals where you + + align:start position:0% +Frankle occurs in crystals where you + + + align:start position:0% +Frankle occurs in crystals where you +have wide variations in the radi so for + + align:start position:0% +have wide variations in the radi so for + + + align:start position:0% +have wide variations in the radi so for +Frankle the condition is that the radius + + align:start position:0% +Frankle the condition is that the radius + + + align:start position:0% +Frankle the condition is that the radius +of the cation must be either + + align:start position:0% +of the cation must be either + + + align:start position:0% +of the cation must be either +substantially larger than the radius of + + align:start position:0% +substantially larger than the radius of + + + align:start position:0% +substantially larger than the radius of +the annion or it must be substantially + + align:start position:0% +the annion or it must be substantially + + + align:start position:0% +the annion or it must be substantially +smaller than the radius of the annion if + + align:start position:0% +smaller than the radius of the annion if + + + align:start position:0% +smaller than the radius of the annion if +you have ions that are roughly nearly + + align:start position:0% +you have ions that are roughly nearly + + + align:start position:0% +you have ions that are roughly nearly +equal in dimension the interstitial site + + align:start position:0% +equal in dimension the interstitial site + + + align:start position:0% +equal in dimension the interstitial site +isn't big enough to take + + align:start position:0% +isn't big enough to take + + + align:start position:0% +isn't big enough to take +the uh to take the iron so let's look at + + align:start position:0% +the uh to take the iron so let's look at + + + align:start position:0% +the uh to take the iron so let's look at +that one a good example this is silver + + align:start position:0% +that one a good example this is silver + + + align:start position:0% +that one a good example this is silver +bromide silver bromide forms frankal + + align:start position:0% +bromide silver bromide forms frankal + + + align:start position:0% +bromide silver bromide forms frankal +because as you know bromine is Big + + align:start position:0% +because as you know bromine is Big + + + align:start position:0% +because as you know bromine is Big +bromide is huge and silver is small and + + align:start position:0% +bromide is huge and silver is small and + + + align:start position:0% +bromide is huge and silver is small and +when it lose an electron it's smaller so + + align:start position:0% +when it lose an electron it's smaller so + + + align:start position:0% +when it lose an electron it's smaller so +I got a small cation and a honking big + + align:start position:0% +I got a small cation and a honking big + + + align:start position:0% +I got a small cation and a honking big +annion and so there's lots of room in + + align:start position:0% +annion and so there's lots of room in + + + align:start position:0% +annion and so there's lots of room in +there and here's the way we'd write that + + align:start position:0% +there and here's the way we'd write that + + + align:start position:0% +there and here's the way we'd write that +silver sitting on a silver site silver + + align:start position:0% +silver sitting on a silver site silver + + + align:start position:0% +silver sitting on a silver site silver +sitting on a silver site now wants to + + align:start position:0% +sitting on a silver site now wants to + + + align:start position:0% +sitting on a silver site now wants to +move and see it's neutral because silver + + align:start position:0% +move and see it's neutral because silver + + + align:start position:0% +move and see it's neutral because silver +is+ one in a Land of plus one so I can + + align:start position:0% +is+ one in a Land of plus one so I can + + + align:start position:0% +is+ one in a Land of plus one so I can +even put a little X there to show that + + align:start position:0% +even put a little X there to show that + + + align:start position:0% +even put a little X there to show that +it's neutral so silver on a silver site + + align:start position:0% +it's neutral so silver on a silver site + + + align:start position:0% +it's neutral so silver on a silver site +now becomes silver on um interstitial + + align:start position:0% +now becomes silver on um interstitial + + + align:start position:0% +now becomes silver on um interstitial +site silver on an interstitial + + align:start position:0% +site silver on an interstitial + + + align:start position:0% +site silver on an interstitial +site and an interstitial site is zero + + align:start position:0% +site and an interstitial site is zero + + + align:start position:0% +site and an interstitial site is zero +and silver is plus one so now it's + + align:start position:0% +and silver is plus one so now it's + + + align:start position:0% +and silver is plus one so now it's +apparently uh plus one and what's it + + align:start position:0% +apparently uh plus one and what's it + + + align:start position:0% +apparently uh plus one and what's it +going to do to charge compens at it's + + align:start position:0% +going to do to charge compens at it's + + + align:start position:0% +going to do to charge compens at it's +going to leave behind a vacancy + + align:start position:0% +going to leave behind a vacancy + + + align:start position:0% +going to leave behind a vacancy +obviously it jumped off this site so + + align:start position:0% +obviously it jumped off this site so + + + align:start position:0% +obviously it jumped off this site so +there is a vacancy and that vacancy is + + align:start position:0% +there is a vacancy and that vacancy is + + + align:start position:0% +there is a vacancy and that vacancy is +what the vacancy is zero and a land of + + align:start position:0% +what the vacancy is zero and a land of + + + align:start position:0% +what the vacancy is zero and a land of +plus + + align:start position:0% +plus + + + align:start position:0% +plus +one so zero and a land of plus one is + + align:start position:0% +one so zero and a land of plus one is + + + align:start position:0% +one so zero and a land of plus one is +apparently minus this thing makes sense + + align:start position:0% +apparently minus this thing makes sense + + + align:start position:0% +apparently minus this thing makes sense +it's consistent it's consistent and + + align:start position:0% +it's consistent it's consistent and + + + align:start position:0% +it's consistent it's consistent and +likewise we can write a formula for the + + align:start position:0% +likewise we can write a formula for the + + + align:start position:0% +likewise we can write a formula for the +fraction of Frankle sites in a crystal + + align:start position:0% +fraction of Frankle sites in a crystal + + + align:start position:0% +fraction of Frankle sites in a crystal +would be the number of Frankl divided by + + align:start position:0% +would be the number of Frankl divided by + + + align:start position:0% +would be the number of Frankl divided by +the total number of atomic sites for + + align:start position:0% +the total number of atomic sites for + + + align:start position:0% +the total number of atomic sites for +that which then will equal a times some + + align:start position:0% +that which then will equal a times some + + + align:start position:0% +that which then will equal a times some +exponential expression of the ratio of + + align:start position:0% +exponential expression of the ratio of + + + align:start position:0% +exponential expression of the ratio of +the formation energy for the Frankle + + align:start position:0% +the formation energy for the Frankle + + + align:start position:0% +the formation energy for the Frankle +defect divided by the product of the + + align:start position:0% +defect divided by the product of the + + + align:start position:0% +defect divided by the product of the +boltzman constant in temperature and the + + align:start position:0% +boltzman constant in temperature and the + + + align:start position:0% +boltzman constant in temperature and the +Frankle + + align:start position:0% +Frankle + + + align:start position:0% +Frankle +energy what do you think it's going to + + align:start position:0% +energy what do you think it's going to + + + align:start position:0% +energy what do you think it's going to +be closer to that of the uh shocky + + align:start position:0% +be closer to that of the uh shocky + + + align:start position:0% +be closer to that of the uh shocky +energy or closer to that of the single + + align:start position:0% +energy or closer to that of the single + + + align:start position:0% +energy or closer to that of the single +ion excuse me single atom + + align:start position:0% + + + + align:start position:0% + +vacancy it's about one electron it's + + align:start position:0% +vacancy it's about one electron it's + + + align:start position:0% +vacancy it's about one electron it's +closer to that of the the single atom + + align:start position:0% +closer to that of the the single atom + + + align:start position:0% +closer to that of the the single atom +and it's typically the cats it's + + align:start position:0% +and it's typically the cats it's + + + align:start position:0% +and it's typically the cats it's +typically the cats because normally the + + align:start position:0% +typically the cats because normally the + + + align:start position:0% +typically the cats because normally the +anions are the big ones fluoride is the + + align:start position:0% +anions are the big ones fluoride is the + + + align:start position:0% +anions are the big ones fluoride is the +is one exception okay but generally it's + + align:start position:0% +is one exception okay but generally it's + + + align:start position:0% +is one exception okay but generally it's +the cats that are going to go + + align:start position:0% +the cats that are going to go + + + align:start position:0% +the cats that are going to go +interstitially the last one is the F + + align:start position:0% +interstitially the last one is the F + + + align:start position:0% +interstitially the last one is the F +Center the f- center they don't talk + + align:start position:0% +Center the f- center they don't talk + + + align:start position:0% +Center the f- center they don't talk +about in your books but it's a really + + align:start position:0% +about in your books but it's a really + + + align:start position:0% +about in your books but it's a really +cool one I like this one the f- center + + align:start position:0% +cool one I like this one the f- center + + + align:start position:0% +cool one I like this one the f- center +f- Center occurs in non- stok ometry + + align:start position:0% + + + + align:start position:0% + +non + + align:start position:0% +non + + + align:start position:0% +non +stochiometry um it may surprise you but + + align:start position:0% +stochiometry um it may surprise you but + + + align:start position:0% +stochiometry um it may surprise you but +it's possible to have sodium chloride + + align:start position:0% +it's possible to have sodium chloride + + + align:start position:0% +it's possible to have sodium chloride +that isn't one toone sodium and chlorine + + align:start position:0% +that isn't one toone sodium and chlorine + + + align:start position:0% +that isn't one toone sodium and chlorine +it's possible to have um something that + + align:start position:0% +it's possible to have um something that + + + align:start position:0% +it's possible to have um something that +is chlorine deficient so let's see what + + align:start position:0% +is chlorine deficient so let's see what + + + align:start position:0% +is chlorine deficient so let's see what +would happen if we were to dissolve + + align:start position:0% +would happen if we were to dissolve + + + align:start position:0% +would happen if we were to dissolve +excess sodium I'm going to dissolve + + align:start position:0% +excess sodium I'm going to dissolve + + + align:start position:0% +excess sodium I'm going to dissolve +excess sodium into sodium chloride well + + align:start position:0% +excess sodium into sodium chloride well + + + align:start position:0% +excess sodium into sodium chloride well +I can't dissolve a neutral sodium + + align:start position:0% +I can't dissolve a neutral sodium + + + align:start position:0% +I can't dissolve a neutral sodium +chloride will not accept the neutral so + + align:start position:0% +chloride will not accept the neutral so + + + align:start position:0% +chloride will not accept the neutral so +what's the only way I can make sodium + + align:start position:0% +what's the only way I can make sodium + + + align:start position:0% +what's the only way I can make sodium +soluble in sodium chloride I have to + + align:start position:0% +soluble in sodium chloride I have to + + + align:start position:0% +soluble in sodium chloride I have to +convert it into sodium ion so I'm going + + align:start position:0% +convert it into sodium ion so I'm going + + + align:start position:0% +convert it into sodium ion so I'm going +to make a sodium + + align:start position:0% +to make a sodium + + + align:start position:0% +to make a sodium +ion and I'm going to be left with an + + align:start position:0% +ion and I'm going to be left with an + + + align:start position:0% +ion and I'm going to be left with an +electron what am I going to do with that + + align:start position:0% +electron what am I going to do with that + + + align:start position:0% +electron what am I going to do with that +electron where's that electron going to + + align:start position:0% +electron where's that electron going to + + + align:start position:0% +electron where's that electron going to +go think you know you've got veilance + + align:start position:0% +go think you know you've got veilance + + + align:start position:0% +go think you know you've got veilance +bands that are filled you see a parallel + + align:start position:0% +bands that are filled you see a parallel + + + align:start position:0% +bands that are filled you see a parallel +between this and putting phosphorus into + + align:start position:0% +between this and putting phosphorus into + + + align:start position:0% +between this and putting phosphorus into +silicon you've got this extra electron + + align:start position:0% +silicon you've got this extra electron + + + align:start position:0% +silicon you've got this extra electron +this thing has bonding capability this + + align:start position:0% +this thing has bonding capability this + + + align:start position:0% +this thing has bonding capability this +is a fifth wheel doesn't know what to do + + align:start position:0% +is a fifth wheel doesn't know what to do + + + align:start position:0% +is a fifth wheel doesn't know what to do +so one way to model this is I'm going to + + align:start position:0% +so one way to model this is I'm going to + + + align:start position:0% +so one way to model this is I'm going to +now give you the the the full notation + + align:start position:0% +now give you the the the full notation + + + align:start position:0% +now give you the the the full notation +is to put sodium on a sodium site so now + + align:start position:0% +is to put sodium on a sodium site so now + + + align:start position:0% +is to put sodium on a sodium site so now +this is sodium plus I've got an + + align:start position:0% +this is sodium plus I've got an + + + align:start position:0% +this is sodium plus I've got an +electron and + + align:start position:0% +electron and + + + align:start position:0% +electron and +what I have to make a vacancy on a + + align:start position:0% +what I have to make a vacancy on a + + + align:start position:0% +what I have to make a vacancy on a +chloride site in order to compensate for + + align:start position:0% +chloride site in order to compensate for + + + align:start position:0% +chloride site in order to compensate for +this excess electron and now let's look + + align:start position:0% +this excess electron and now let's look + + + align:start position:0% +this excess electron and now let's look +at the way this thing is going to + + align:start position:0% +at the way this thing is going to + + + align:start position:0% +at the way this thing is going to +operate I've got sodium ions and some + + align:start position:0% +operate I've got sodium ions and some + + + align:start position:0% +operate I've got sodium ions and some +FCC lattice here's a chloride vacancy + + align:start position:0% +FCC lattice here's a chloride vacancy + + + align:start position:0% +FCC lattice here's a chloride vacancy +that's been created to compensate here + + align:start position:0% +that's been created to compensate here + + + align:start position:0% +that's been created to compensate here +so this is VC and where's this electron + + align:start position:0% +so this is VC and where's this electron + + + align:start position:0% +so this is VC and where's this electron +going to be this electron is it's not + + align:start position:0% +going to be this electron is it's not + + + align:start position:0% +going to be this electron is it's not +attached to any one of these sodiums so + + align:start position:0% +attached to any one of these sodiums so + + + align:start position:0% +attached to any one of these sodiums so +I'm just going to put the electron here + + align:start position:0% +I'm just going to put the electron here + + + align:start position:0% +I'm just going to put the electron here +do you know of another example where um + + align:start position:0% +do you know of another example where um + + + align:start position:0% +do you know of another example where um +you ended up with something that was + + align:start position:0% +you ended up with something that was + + + align:start position:0% +you ended up with something that was +apparently positive and Motionless in a + + align:start position:0% +apparently positive and Motionless in a + + + align:start position:0% +apparently positive and Motionless in a +crystal with an extra electron that was + + align:start position:0% +crystal with an extra electron that was + + + align:start position:0% +crystal with an extra electron that was +attracted by IC + + align:start position:0% + + + + align:start position:0% + +forces if you had to model this + + align:start position:0% +forces if you had to model this + + + align:start position:0% +forces if you had to model this +operation what model might you choose + + align:start position:0% +operation what model might you choose + + + align:start position:0% +operation what model might you choose +you could use a modified bore model to + + align:start position:0% +you could use a modified bore model to + + + align:start position:0% +you could use a modified bore model to +model the electron motion around the + + align:start position:0% +model the electron motion around the + + + align:start position:0% +model the electron motion around the +vacancy in an F + + align:start position:0% +vacancy in an F + + + align:start position:0% +vacancy in an F +Center yeah this is really cool this is + + align:start position:0% +Center yeah this is really cool this is + + + align:start position:0% +Center yeah this is really cool this is +really cool it's called f- Center + + align:start position:0% +really cool it's called f- Center + + + align:start position:0% +really cool it's called f- Center +because it comes from the + + align:start position:0% +because it comes from the + + + align:start position:0% +because it comes from the +German farba which means color these + + align:start position:0% +German farba which means color these + + + align:start position:0% +German farba which means color these +form color centers because the the if + + align:start position:0% +form color centers because the the if + + + align:start position:0% +form color centers because the the if +you go through the bore model the energy + + align:start position:0% +you go through the bore model the energy + + + align:start position:0% +you go through the bore model the energy +levels in here are in the visible and so + + align:start position:0% +levels in here are in the visible and so + + + align:start position:0% +levels in here are in the visible and so +the different different uh crystals we + + align:start position:0% +the different different uh crystals we + + + align:start position:0% +the different different uh crystals we +can identify if you take sodium chloride + + align:start position:0% +can identify if you take sodium chloride + + + align:start position:0% +can identify if you take sodium chloride +lithium chloride potassium chloride + + align:start position:0% +lithium chloride potassium chloride + + + align:start position:0% +lithium chloride potassium chloride +they're all white salts but if we create + + align:start position:0% +they're all white salts but if we create + + + align:start position:0% +they're all white salts but if we create +vacancies by injecting energy say in the + + align:start position:0% +vacancies by injecting energy say in the + + + align:start position:0% +vacancies by injecting energy say in the +form of a an electrical shock we will + + align:start position:0% +form of a an electrical shock we will + + + align:start position:0% +form of a an electrical shock we will +dope the crystal different colors and + + align:start position:0% +dope the crystal different colors and + + + align:start position:0% +dope the crystal different colors and +the colors change with + + align:start position:0% +the colors change with + + + align:start position:0% +the colors change with +the identity of the crystal because the + + align:start position:0% +the identity of the crystal because the + + + align:start position:0% +the identity of the crystal because the +the energies are going to to be + + align:start position:0% +the energies are going to to be + + + align:start position:0% +the energies are going to to be +different okay good so that's the end of + + align:start position:0% +different okay good so that's the end of + + + align:start position:0% +different okay good so that's the end of +uh that's the end of uh Point defects + + align:start position:0% +uh that's the end of uh Point defects + + + align:start position:0% +uh that's the end of uh Point defects +now let's look at line defects line + + align:start position:0% +now let's look at line defects line + + + align:start position:0% +now let's look at line defects line +defects line defects are very important + + align:start position:0% +defects line defects are very important + + + align:start position:0% +defects line defects are very important +because they answer this + + align:start position:0% +because they answer this + + + align:start position:0% +because they answer this +question data data made line defects + + align:start position:0% +question data data made line defects + + + align:start position:0% +question data data made line defects +necessary people in the early part of + + align:start position:0% +necessary people in the early part of + + + align:start position:0% +necessary people in the early part of +the 20th century were trying to figure + + align:start position:0% +the 20th century were trying to figure + + + align:start position:0% +the 20th century were trying to figure +out what the ultimate yield strength + + align:start position:0% +out what the ultimate yield strength + + + align:start position:0% +out what the ultimate yield strength +yield strength of a metal is yield + + align:start position:0% +yield strength of a metal is yield + + + align:start position:0% +yield strength of a metal is yield +strength of a metal so let's take a look + + align:start position:0% +strength of a metal so let's take a look + + + align:start position:0% +strength of a metal so let's take a look +at say two planes of + + align:start position:0% +at say two planes of + + + align:start position:0% +at say two planes of +atoms and I'm just going to for + + align:start position:0% +atoms and I'm just going to for + + + align:start position:0% +atoms and I'm just going to for +Simplicity connect these with little + + align:start position:0% +Simplicity connect these with little + + + align:start position:0% +Simplicity connect these with little +with little uh struts to indicate that + + align:start position:0% +with little uh struts to indicate that + + + align:start position:0% +with little uh struts to indicate that +there's some bonding going on here and I + + align:start position:0% +there's some bonding going on here and I + + + align:start position:0% +there's some bonding going on here and I +want to ask the question what is the + + align:start position:0% +want to ask the question what is the + + + align:start position:0% +want to ask the question what is the +sheer strength the magnitude of the + + align:start position:0% +sheer strength the magnitude of the + + + align:start position:0% +sheer strength the magnitude of the +sheer strength necessary to cause these + + align:start position:0% +sheer strength necessary to cause these + + + align:start position:0% +sheer strength necessary to cause these +two planes to slide over one another + + align:start position:0% +two planes to slide over one another + + + align:start position:0% +two planes to slide over one another +this is what's going to be involved in + + align:start position:0% +this is what's going to be involved in + + + align:start position:0% +this is what's going to be involved in +the yield of a of a crystal well one way + + align:start position:0% +the yield of a of a crystal well one way + + + align:start position:0% +the yield of a of a crystal well one way +of doing this calculation is to say + + align:start position:0% +of doing this calculation is to say + + + align:start position:0% +of doing this calculation is to say +let's look at say bond + + align:start position:0% +let's look at say bond + + + align:start position:0% +let's look at say bond +strength let's look at bond strength + + align:start position:0% +strength let's look at bond strength + + + align:start position:0% +strength let's look at bond strength +between Pairs of atoms so look at pair + + align:start position:0% +between Pairs of atoms so look at pair + + + align:start position:0% +between Pairs of atoms so look at pair +bond strength times the bond density + + align:start position:0% +bond strength times the bond density + + + align:start position:0% +bond strength times the bond density +right times Bond density if we take pair + + align:start position:0% +right times Bond density if we take pair + + + align:start position:0% +right times Bond density if we take pair +strength times Bond density that should + + align:start position:0% +strength times Bond density that should + + + align:start position:0% +strength times Bond density that should +give us some round number that would be + + align:start position:0% +give us some round number that would be + + + align:start position:0% +give us some round number that would be +representative of how much energy it + + align:start position:0% +representative of how much energy it + + + align:start position:0% +representative of how much energy it +takes for us to be able to Shear the + + align:start position:0% +takes for us to be able to Shear the + + + align:start position:0% +takes for us to be able to Shear the +material and this quantity that we're + + align:start position:0% +material and this quantity that we're + + + align:start position:0% +material and this quantity that we're +looking for is the yield strength + + align:start position:0% +looking for is the yield strength + + + align:start position:0% +looking for is the yield strength +denoted Sigma suby and what we find is + + align:start position:0% +denoted Sigma suby and what we find is + + + align:start position:0% +denoted Sigma suby and what we find is +that the measured value the measured + + align:start position:0% +that the measured value the measured + + + align:start position:0% +that the measured value the measured +value of the yield strength is on the + + align:start position:0% +value of the yield strength is on the + + + align:start position:0% +value of the yield strength is on the +order of only about one tenth only about + + align:start position:0% +order of only about one tenth only about + + + align:start position:0% +order of only about one tenth only about +one tenth of the yield strength as + + align:start position:0% +one tenth of the yield strength as + + + align:start position:0% +one tenth of the yield strength as +determined by + + align:start position:0% +determined by + + + align:start position:0% +determined by +Theory something's way wrong something's + + align:start position:0% +Theory something's way wrong something's + + + align:start position:0% +Theory something's way wrong something's +way wrong well this was solved by + + align:start position:0% +way wrong well this was solved by + + + align:start position:0% +way wrong well this was solved by +Oran Oran was a a professor in Budapest + + align:start position:0% +Oran Oran was a a professor in Budapest + + + align:start position:0% +Oran Oran was a a professor in Budapest +in the 1930s after World War II he ended + + align:start position:0% +in the 1930s after World War II he ended + + + align:start position:0% +in the 1930s after World War II he ended +up here at MIT and he finished his + + align:start position:0% +up here at MIT and he finished his + + + align:start position:0% +up here at MIT and he finished his +career in the mechanical engineering + + align:start position:0% +career in the mechanical engineering + + + align:start position:0% +career in the mechanical engineering +department was a brilliant uh + + align:start position:0% +department was a brilliant uh + + + align:start position:0% +department was a brilliant uh +theoretician in the area of strength of + + align:start position:0% +theoretician in the area of strength of + + + align:start position:0% +theoretician in the area of strength of +metals failure in metals so the story + + align:start position:0% +metals failure in metals so the story + + + align:start position:0% +metals failure in metals so the story +goes this is a apocryphal story is that + + align:start position:0% +goes this is a apocryphal story is that + + + align:start position:0% +goes this is a apocryphal story is that +Oran came home one day from uh the + + align:start position:0% +Oran came home one day from uh the + + + align:start position:0% +Oran came home one day from uh the +university he went up to his uh + + align:start position:0% +university he went up to his uh + + + align:start position:0% +university he went up to his uh +apartment and there was a long hallway + + align:start position:0% +apartment and there was a long hallway + + + align:start position:0% +apartment and there was a long hallway +and a a runner a carpet a long carpet + + align:start position:0% +and a a runner a carpet a long carpet + + + align:start position:0% +and a a runner a carpet a long carpet +along the hallway and the chambermaid + + align:start position:0% +along the hallway and the chambermaid + + + align:start position:0% +along the hallway and the chambermaid +was just finishing cleaning and she was + + align:start position:0% +was just finishing cleaning and she was + + + align:start position:0% +was just finishing cleaning and she was +going to put the carpet back she moved + + align:start position:0% +going to put the carpet back she moved + + + align:start position:0% +going to put the carpet back she moved +it out of the way and she was going to + + align:start position:0% +it out of the way and she was going to + + + align:start position:0% +it out of the way and she was going to +move it back and so he came up and + + align:start position:0% +move it back and so he came up and + + + align:start position:0% +move it back and so he came up and +offered to help her uh move the carpet + + align:start position:0% +offered to help her uh move the carpet + + + align:start position:0% +offered to help her uh move the carpet +and she told him to get out of the way + + align:start position:0% +and she told him to get out of the way + + + align:start position:0% +and she told him to get out of the way +and instead what she did is rather than + + align:start position:0% +and instead what she did is rather than + + + align:start position:0% +and instead what she did is rather than +drag the carpet in order to displace it + + align:start position:0% +drag the carpet in order to displace it + + + align:start position:0% +drag the carpet in order to displace it +what she did is she went to the far end + + align:start position:0% +what she did is she went to the far end + + + align:start position:0% +what she did is she went to the far end +of the + + align:start position:0% +of the + + + align:start position:0% +of the +carpet and made a little + + align:start position:0% +carpet and made a little + + + align:start position:0% +carpet and made a little +Kink made a little kink in the carpet + + align:start position:0% +Kink made a little kink in the carpet + + + align:start position:0% +Kink made a little kink in the carpet +stamped their foot and propagated the + + align:start position:0% +stamped their foot and propagated the + + + align:start position:0% +stamped their foot and propagated the +Kink all the way down and then made a + + align:start position:0% +Kink all the way down and then made a + + + align:start position:0% +Kink all the way down and then made a +second Kink stamped their foot and + + align:start position:0% +second Kink stamped their foot and + + + align:start position:0% +second Kink stamped their foot and +propagated the carpet all the way down + + align:start position:0% +propagated the carpet all the way down + + + align:start position:0% +propagated the carpet all the way down +so what's the difference what's the + + align:start position:0% +so what's the difference what's the + + + align:start position:0% +so what's the difference what's the +difference well with Oran if we if we + + align:start position:0% +difference well with Oran if we if we + + + align:start position:0% +difference well with Oran if we if we +stand at this end and pull we've got the + + align:start position:0% +stand at this end and pull we've got the + + + align:start position:0% +stand at this end and pull we've got the +coefficient of friction along the entire + + align:start position:0% +coefficient of friction along the entire + + + align:start position:0% +coefficient of friction along the entire +length of the carpet takes a huge amount + + align:start position:0% +length of the carpet takes a huge amount + + + align:start position:0% +length of the carpet takes a huge amount +of energy If instead we invest a little + + align:start position:0% +of energy If instead we invest a little + + + align:start position:0% +of energy If instead we invest a little +bit of energy to make the Kink and then + + align:start position:0% +bit of energy to make the Kink and then + + + align:start position:0% +bit of energy to make the Kink and then +propagate the Kink we can move the + + align:start position:0% +propagate the Kink we can move the + + + align:start position:0% +propagate the Kink we can move the +carpet in these small amounts so what + + align:start position:0% +carpet in these small amounts so what + + + align:start position:0% +carpet in these small amounts so what +we've done is now all we have to come up + + align:start position:0% +we've done is now all we have to come up + + + align:start position:0% +we've done is now all we have to come up +with is the amount of energy to lift off + + align:start position:0% +with is the amount of energy to lift off + + + align:start position:0% +with is the amount of energy to lift off +that little patch of carpet and it'll + + align:start position:0% +that little patch of carpet and it'll + + + align:start position:0% +that little patch of carpet and it'll +propagate very easily he looked at this + + align:start position:0% +propagate very easily he looked at this + + + align:start position:0% +propagate very easily he looked at this +and he said that could explain what's + + align:start position:0% +and he said that could explain what's + + + align:start position:0% +and he said that could explain what's +going on here so I've got a little + + align:start position:0% +going on here so I've got a little + + + align:start position:0% +going on here so I've got a little +cartoon that shows actually showing the + + align:start position:0% +cartoon that shows actually showing the + + + align:start position:0% +cartoon that shows actually showing the +caterpillar moving here but can you + + align:start position:0% +caterpillar moving here but can you + + + align:start position:0% +caterpillar moving here but can you +imagine if this is the plane of atoms + + align:start position:0% +imagine if this is the plane of atoms + + + align:start position:0% +imagine if this is the plane of atoms +such that there's an extra plane + + align:start position:0% +such that there's an extra plane + + + align:start position:0% +such that there's an extra plane +sandwiched in here that ends and now if + + align:start position:0% +sandwiched in here that ends and now if + + + align:start position:0% +sandwiched in here that ends and now if +I want to share the top three rows of + + align:start position:0% +I want to share the top three rows of + + + align:start position:0% +I want to share the top three rows of +atoms versus the bottom three rows + + align:start position:0% +atoms versus the bottom three rows + + + align:start position:0% +atoms versus the bottom three rows +instead of having to break every one of + + align:start position:0% +instead of having to break every one of + + + align:start position:0% +instead of having to break every one of +these bonds I have to break them all I + + align:start position:0% +these bonds I have to break them all I + + + align:start position:0% +these bonds I have to break them all I +have to break them all look at here all + + align:start position:0% +have to break them all look at here all + + + align:start position:0% +have to break them all look at here all +I do is I break this one and then I + + align:start position:0% +I do is I break this one and then I + + + align:start position:0% +I do is I break this one and then I +break this one and then I break this one + + align:start position:0% +break this one and then I break this one + + + align:start position:0% +break this one and then I break this one +and then I break this one and so what I + + align:start position:0% +and then I break this one and so what I + + + align:start position:0% +and then I break this one and so what I +do is I break one Bond and just keep + + align:start position:0% +do is I break one Bond and just keep + + + align:start position:0% +do is I break one Bond and just keep +propagating + + align:start position:0% +propagating + + + align:start position:0% +propagating +it and that's the dislocation that's the + + align:start position:0% + + + + align:start position:0% + +dislocation it's a line defect that + + align:start position:0% +dislocation it's a line defect that + + + align:start position:0% +dislocation it's a line defect that +involves the + + align:start position:0% + + + + align:start position:0% + +this it allows us the ability to deform + + align:start position:0% +this it allows us the ability to deform + + + align:start position:0% +this it allows us the ability to deform +Metals at values substantially below + + align:start position:0% +Metals at values substantially below + + + align:start position:0% +Metals at values substantially below +those of the um of the entire Crystal + + align:start position:0% +those of the um of the entire Crystal + + + align:start position:0% +those of the um of the entire Crystal +and makes sense now so here's another + + align:start position:0% +and makes sense now so here's another + + + align:start position:0% +and makes sense now so here's another +cartoon showing the same + + align:start position:0% +cartoon showing the same + + + align:start position:0% +cartoon showing the same +thing and how do these dislocations move + + align:start position:0% +thing and how do these dislocations move + + + align:start position:0% +thing and how do these dislocations move +these dislocations Move + + align:start position:0% +these dislocations Move + + + align:start position:0% +these dislocations Move +Along close packed planes in close- + + align:start position:0% +Along close packed planes in close- + + + align:start position:0% +Along close packed planes in close- +packed directions Tom may we go back to + + align:start position:0% +packed directions Tom may we go back to + + + align:start position:0% +packed directions Tom may we go back to +the um document camera + + align:start position:0% + + + + align:start position:0% + +please okay so here is I'm going to now + + align:start position:0% +please okay so here is I'm going to now + + + align:start position:0% +please okay so here is I'm going to now +go to top view top lamp ah look at this + + align:start position:0% +go to top view top lamp ah look at this + + + align:start position:0% +go to top view top lamp ah look at this +this is face centered cubic face + + align:start position:0% +this is face centered cubic face + + + align:start position:0% +this is face centered cubic face +centered cubic where are the bonds going + + align:start position:0% +centered cubic where are the bonds going + + + align:start position:0% +centered cubic where are the bonds going +to be strongest this is going to be like + + align:start position:0% +to be strongest this is going to be like + + + align:start position:0% +to be strongest this is going to be like +rafts of atoms moving where are the + + align:start position:0% +rafts of atoms moving where are the + + + align:start position:0% +rafts of atoms moving where are the +bonds going to be strongest they're + + align:start position:0% +bonds going to be strongest they're + + + align:start position:0% +bonds going to be strongest they're +going to be strongest in the plane with + + align:start position:0% +going to be strongest in the plane with + + + align:start position:0% +going to be strongest in the plane with +the most bonds so that's going to be the + + align:start position:0% +the most bonds so that's going to be the + + + align:start position:0% +the most bonds so that's going to be the +111 plane because the 111 if you look at + + align:start position:0% +111 plane because the 111 if you look at + + + align:start position:0% +111 plane because the 111 if you look at +this atom here can you see the hexagon + + align:start position:0% +this atom here can you see the hexagon + + + align:start position:0% +this atom here can you see the hexagon +starting here's the hexagon if you train + + align:start position:0% +starting here's the hexagon if you train + + + align:start position:0% +starting here's the hexagon if you train +your eye on this one 1 2 3 4 and then + + align:start position:0% +your eye on this one 1 2 3 4 and then + + + align:start position:0% +your eye on this one 1 2 3 4 and then +there'll be five six so this is a close- + + align:start position:0% +there'll be five six so this is a close- + + + align:start position:0% +there'll be five six so this is a close- +packed plane it's got six nearest + + align:start position:0% +packed plane it's got six nearest + + + align:start position:0% +packed plane it's got six nearest +Neighbors in the plane three above and + + align:start position:0% +Neighbors in the plane three above and + + + align:start position:0% +Neighbors in the plane three above and +three below this is the 111 plane it + + align:start position:0% +three below this is the 111 plane it + + + align:start position:0% +three below this is the 111 plane it +goes up the the diagonal see goes up the + + align:start position:0% +goes up the the diagonal see goes up the + + + align:start position:0% +goes up the the diagonal see goes up the +diagonal so this is the the plane that + + align:start position:0% +diagonal so this is the the plane that + + + align:start position:0% +diagonal so this is the the plane that +has the most bonds if if there are the + + align:start position:0% +has the most bonds if if there are the + + + align:start position:0% +has the most bonds if if there are the +most Bonds in the plane that's the plane + + align:start position:0% +most Bonds in the plane that's the plane + + + align:start position:0% +most Bonds in the plane that's the plane +that has the greatest strength and will + + align:start position:0% +that has the greatest strength and will + + + align:start position:0% +that has the greatest strength and will +not + + align:start position:0% +not + + + align:start position:0% +not +give and doesn't it go axiomatically + + align:start position:0% +give and doesn't it go axiomatically + + + align:start position:0% +give and doesn't it go axiomatically +that if I have the most Bonds in the + + align:start position:0% +that if I have the most Bonds in the + + + align:start position:0% +that if I have the most Bonds in the +plane then normal to the plane I'm going + + align:start position:0% +plane then normal to the plane I'm going + + + align:start position:0% +plane then normal to the plane I'm going +to have weakest bonding so we have these + + align:start position:0% +to have weakest bonding so we have these + + + align:start position:0% +to have weakest bonding so we have these +strong rafts of one1 planes that want to + + align:start position:0% +strong rafts of one1 planes that want to + + + align:start position:0% +strong rafts of one1 planes that want to +to + + align:start position:0% +to + + + align:start position:0% +to +slide now within the plane how does + + align:start position:0% +slide now within the plane how does + + + align:start position:0% +slide now within the plane how does +something move this is like pushing the + + align:start position:0% +something move this is like pushing the + + + align:start position:0% +something move this is like pushing the +wet noodle question okay so if I'm in + + align:start position:0% +wet noodle question okay so if I'm in + + + align:start position:0% +wet noodle question okay so if I'm in +this 111 plane which which direction am + + align:start position:0% +this 111 plane which which direction am + + + align:start position:0% +this 111 plane which which direction am +I going to + + align:start position:0% +I going to + + + align:start position:0% +I going to +move I'm going to move along the + + align:start position:0% +move I'm going to move along the + + + align:start position:0% +move I'm going to move along the +direction where I have the greatest + + align:start position:0% +direction where I have the greatest + + + align:start position:0% +direction where I have the greatest +strength the greatest rigidity and that + + align:start position:0% +strength the greatest rigidity and that + + + align:start position:0% +strength the greatest rigidity and that +means along the direction where I have + + align:start position:0% +means along the direction where I have + + + align:start position:0% +means along the direction where I have +the greatest number of bonds so this is + + align:start position:0% +the greatest number of bonds so this is + + + align:start position:0% +the greatest number of bonds so this is +along the 111 direction see excuse me + + align:start position:0% +along the 111 direction see excuse me + + + align:start position:0% +along the 111 direction see excuse me +the 011 Direction I'm going along this + + align:start position:0% +the 011 Direction I'm going along this + + + align:start position:0% +the 011 Direction I'm going along this +I'm in the red plane and this is across + + align:start position:0% +I'm in the red plane and this is across + + + align:start position:0% +I'm in the red plane and this is across +the diagonal of the face so I'm moving + + align:start position:0% +the diagonal of the face so I'm moving + + + align:start position:0% +the diagonal of the face so I'm moving +in the close pack Direction in the + + align:start position:0% +in the close pack Direction in the + + + align:start position:0% +in the close pack Direction in the +close-packed plane because that's where + + align:start position:0% +close-packed plane because that's where + + + align:start position:0% +close-packed plane because that's where +the bonds are most dense most dense so + + align:start position:0% +the bonds are most dense most dense so + + + align:start position:0% +the bonds are most dense most dense so +Tom may we go back to the uh computer + + align:start position:0% +Tom may we go back to the uh computer + + + align:start position:0% +Tom may we go back to the uh computer +video please so here's the set of + + align:start position:0% +video please so here's the set of + + + align:start position:0% +video please so here's the set of +directions I just showed you FCC the + + align:start position:0% +directions I just showed you FCC the + + + align:start position:0% +directions I just showed you FCC the +highest density plane is 111 and the + + align:start position:0% +highest density plane is 111 and the + + + align:start position:0% +highest density plane is 111 and the +close pack Direction that's the + + align:start position:0% +close pack Direction that's the + + + align:start position:0% +close pack Direction that's the +direction where the atoms touch you know + + align:start position:0% +direction where the atoms touch you know + + + align:start position:0% +direction where the atoms touch you know +this they touch along 011 in BCC it's + + align:start position:0% +this they touch along 011 in BCC it's + + + align:start position:0% +this they touch along 011 in BCC it's +the complement the highest density plane + + align:start position:0% +the complement the highest density plane + + + align:start position:0% +the complement the highest density plane +is the cube diagonal that contains that + + align:start position:0% +is the cube diagonal that contains that + + + align:start position:0% +is the cube diagonal that contains that +Central atom and the highest the closest + + align:start position:0% +Central atom and the highest the closest + + + align:start position:0% +Central atom and the highest the closest +packed direction is the body diagonal + + align:start position:0% +packed direction is the body diagonal + + + align:start position:0% +packed direction is the body diagonal +that's where the atoms touch the simple + + align:start position:0% +that's where the atoms touch the simple + + + align:start position:0% +that's where the atoms touch the simple +cubic it's the face in the face so this + + align:start position:0% +cubic it's the face in the face so this + + + align:start position:0% +cubic it's the face in the face so this +is now the origin of mechanical Behavior + + align:start position:0% +is now the origin of mechanical Behavior + + + align:start position:0% +is now the origin of mechanical Behavior +Behavior this is the origin of + + align:start position:0% +Behavior this is the origin of + + + align:start position:0% +Behavior this is the origin of +mechanical Behavior I can look at this + + align:start position:0% +mechanical Behavior I can look at this + + + align:start position:0% +mechanical Behavior I can look at this +and I can tell you how the material will + + align:start position:0% +and I can tell you how the material will + + + align:start position:0% +and I can tell you how the material will +deform so if I take the set of close + + align:start position:0% +deform so if I take the set of close + + + align:start position:0% +deform so if I take the set of close +packed close packed + + align:start position:0% +packed close packed + + + align:start position:0% +packed close packed +planes moving in close packed + + align:start position:0% +planes moving in close packed + + + align:start position:0% +planes moving in close packed +directions in close packed + + align:start position:0% +directions in close packed + + + align:start position:0% +directions in close packed +directions together this + + align:start position:0% +directions together this + + + align:start position:0% +directions together this +represents the slip system the slip + + align:start position:0% +represents the slip system the slip + + + align:start position:0% +represents the slip system the slip +system and this is how the material + + align:start position:0% +system and this is how the material + + + align:start position:0% +system and this is how the material +deforms and so we'll come back to that + + align:start position:0% +deforms and so we'll come back to that + + + align:start position:0% +deforms and so we'll come back to that +uh uh next day I see we're getting close + + align:start position:0% +uh uh next day I see we're getting close + + + align:start position:0% +uh uh next day I see we're getting close +to the end of the hour so let me Jump + + align:start position:0% +to the end of the hour so let me Jump + + + align:start position:0% +to the end of the hour so let me Jump +Ahead here uh we'll jump through this + + align:start position:0% +Ahead here uh we'll jump through this + + + align:start position:0% +Ahead here uh we'll jump through this +I'll go through that that I'll show you + + align:start position:0% +I'll go through that that I'll show you + + + align:start position:0% +I'll go through that that I'll show you +that another time all right I talked to + + align:start position:0% +that another time all right I talked to + + + align:start position:0% +that another time all right I talked to +you about defects and crystals I talked + + align:start position:0% +you about defects and crystals I talked + + + align:start position:0% +you about defects and crystals I talked +to you about boron you know what happens + + align:start position:0% +to you about boron you know what happens + + + align:start position:0% +to you about boron you know what happens +if you dope silicon with Boron you end + + align:start position:0% +if you dope silicon with Boron you end + + + align:start position:0% +if you dope silicon with Boron you end +up with something that is + + align:start position:0% +up with something that is + + + align:start position:0% +up with something that is +a ptype semiconductor it's shy one + + align:start position:0% +a ptype semiconductor it's shy one + + + align:start position:0% +a ptype semiconductor it's shy one +electron generates a + + align:start position:0% +electron generates a + + + align:start position:0% +electron generates a +hole this is the Hope Diamond the Hope + + align:start position:0% +hole this is the Hope Diamond the Hope + + + align:start position:0% +hole this is the Hope Diamond the Hope +Diamond what makes the Hope Diamond so + + align:start position:0% +Diamond what makes the Hope Diamond so + + + align:start position:0% +Diamond what makes the Hope Diamond so +uh precious is not only its size but + + align:start position:0% +uh precious is not only its size but + + + align:start position:0% +uh precious is not only its size but +it's blue and how did it get to be blue + + align:start position:0% +it's blue and how did it get to be blue + + + align:start position:0% +it's blue and how did it get to be blue +it got to be blue + + align:start position:0% + + + + align:start position:0% + +by Boron + + align:start position:0% +by Boron + + + align:start position:0% +by Boron +doping it's Boron doping at around um + + align:start position:0% +doping it's Boron doping at around um + + + align:start position:0% +doping it's Boron doping at around um +one part per + + align:start position:0% +one part per + + + align:start position:0% +one part per +million one part per million and what + + align:start position:0% +million one part per million and what + + + align:start position:0% +million one part per million and what +this does is it + + align:start position:0% +this does is it + + + align:start position:0% +this does is it +puts it puts a acceptor + + align:start position:0% +puts it puts a acceptor + + + align:start position:0% +puts it puts a acceptor +level it puts an acceptor level about + + align:start position:0% +level it puts an acceptor level about + + + align:start position:0% +level it puts an acceptor level about +0.4 EV + + align:start position:0% +0.4 EV + + + align:start position:0% +0.4 EV +above the veence band and with this + + align:start position:0% +above the veence band and with this + + + align:start position:0% +above the veence band and with this +donor level excuse me the acceptor level + + align:start position:0% +donor level excuse me the acceptor level + + + align:start position:0% +donor level excuse me the acceptor level +about uh 4 EV above the veilance band we + + align:start position:0% +about uh 4 EV above the veilance band we + + + align:start position:0% +about uh 4 EV above the veilance band we +now have transitions that give us this + + align:start position:0% +now have transitions that give us this + + + align:start position:0% +now have transitions that give us this +beautiful blue color so what you're + + align:start position:0% +beautiful blue color so what you're + + + align:start position:0% +beautiful blue color so what you're +looking at is these are not hope + + align:start position:0% +looking at is these are not hope + + + align:start position:0% +looking at is these are not hope +diamonds this is just some oh you know + + align:start position:0% +diamonds this is just some oh you know + + + align:start position:0% +diamonds this is just some oh you know +51 little units by Cartier and this is + + align:start position:0% +51 little units by Cartier and this is + + + align:start position:0% +51 little units by Cartier and this is +the rest this is in the uh um + + align:start position:0% +the rest this is in the uh um + + + align:start position:0% +the rest this is in the uh um +Smithsonian so if you're in Washington + + align:start position:0% +Smithsonian so if you're in Washington + + + align:start position:0% +Smithsonian so if you're in Washington +sometime and you want to study uh Boron + + align:start position:0% +sometime and you want to study uh Boron + + + align:start position:0% +sometime and you want to study uh Boron +doping well you can go and see this at + + align:start position:0% +doping well you can go and see this at + + + align:start position:0% +doping well you can go and see this at +the national gem collection and uh you + + align:start position:0% +the national gem collection and uh you + + + align:start position:0% +the national gem collection and uh you +can stand with your uh contemporaries + + align:start position:0% +can stand with your uh contemporaries + + + align:start position:0% +can stand with your uh contemporaries +and explain to them the Boron doping and + + align:start position:0% +and explain to them the Boron doping and + + + align:start position:0% +and explain to them the Boron doping and +how it makes the thing blue all right + + align:start position:0% +how it makes the thing blue all right + + + align:start position:0% +how it makes the thing blue all right +good luck on Wednesday \ No newline at end of file diff --git a/WTyLg_I1oFY.txt b/WTyLg_I1oFY.txt new file mode 100644 index 0000000000000000000000000000000000000000..2e0605e138abf82da63cad2093f79d8eca763351 --- /dev/null +++ b/WTyLg_I1oFY.txt @@ -0,0 +1,1683 @@ +align:start position:0% + +the probability axioms are the basic + + align:start position:0% +the probability axioms are the basic + + + align:start position:0% +the probability axioms are the basic +rules of probability theory and they are + + align:start position:0% +rules of probability theory and they are + + + align:start position:0% +rules of probability theory and they are +surprisingly few but they imply many + + align:start position:0% +surprisingly few but they imply many + + + align:start position:0% +surprisingly few but they imply many +interesting properties that we will now + + align:start position:0% +interesting properties that we will now + + + align:start position:0% +interesting properties that we will now +explore first we will see that what you + + align:start position:0% +explore first we will see that what you + + + align:start position:0% +explore first we will see that what you +might think of as missing axioms are + + align:start position:0% +might think of as missing axioms are + + + align:start position:0% +might think of as missing axioms are +actually implied by the axioms already + + align:start position:0% +actually implied by the axioms already + + + align:start position:0% +actually implied by the axioms already +in place for example we have an axiom + + align:start position:0% +in place for example we have an axiom + + + align:start position:0% +in place for example we have an axiom +that probabilities are non-negative we + + align:start position:0% +that probabilities are non-negative we + + + align:start position:0% +that probabilities are non-negative we +will show that probabilities are also + + align:start position:0% +will show that probabilities are also + + + align:start position:0% +will show that probabilities are also +less than or equal to one we have + + align:start position:0% +less than or equal to one we have + + + align:start position:0% +less than or equal to one we have +another axiom that says that the + + align:start position:0% +another axiom that says that the + + + align:start position:0% +another axiom that says that the +probability of the entire sample space + + align:start position:0% +probability of the entire sample space + + + align:start position:0% +probability of the entire sample space +is one we will show a counterpart that + + align:start position:0% +is one we will show a counterpart that + + + align:start position:0% +is one we will show a counterpart that +the probability of the empty set is + + align:start position:0% +the probability of the empty set is + + + align:start position:0% +the probability of the empty set is +equal to zero this makes perfect sense + + align:start position:0% +equal to zero this makes perfect sense + + + align:start position:0% +equal to zero this makes perfect sense +the empty set has no elements so it is + + align:start position:0% +the empty set has no elements so it is + + + align:start position:0% +the empty set has no elements so it is +impossible there is zero probability + + align:start position:0% +impossible there is zero probability + + + align:start position:0% +impossible there is zero probability +that the outcome of the experiment would + + align:start position:0% +that the outcome of the experiment would + + + align:start position:0% +that the outcome of the experiment would +lie in the empty set we also have + + align:start position:0% +lie in the empty set we also have + + + align:start position:0% +lie in the empty set we also have +another intuitive property the + + align:start position:0% +another intuitive property the + + + align:start position:0% +another intuitive property the +probability that an event happens plus + + align:start position:0% +probability that an event happens plus + + + align:start position:0% +probability that an event happens plus +the probability that the event does not + + align:start position:0% +the probability that the event does not + + + align:start position:0% +the probability that the event does not +happen exhaust all possibilities and + + align:start position:0% +happen exhaust all possibilities and + + + align:start position:0% +happen exhaust all possibilities and +these two probabilities together should + + align:start position:0% +these two probabilities together should + + + align:start position:0% +these two probabilities together should +add to 1 for instance if the probability + + align:start position:0% +add to 1 for instance if the probability + + + align:start position:0% +add to 1 for instance if the probability +of heads is 0.6 then the probability of + + align:start position:0% +of heads is 0.6 then the probability of + + + align:start position:0% +of heads is 0.6 then the probability of +tails should be 0.4 finally we can + + align:start position:0% +tails should be 0.4 finally we can + + + align:start position:0% +tails should be 0.4 finally we can +generalize the activity axiom which was + + align:start position:0% +generalize the activity axiom which was + + + align:start position:0% +generalize the activity axiom which was +originally given for the case of two + + align:start position:0% +originally given for the case of two + + + align:start position:0% +originally given for the case of two +disjoint events to the case where we're + + align:start position:0% +disjoint events to the case where we're + + + align:start position:0% +disjoint events to the case where we're +dealing with the union of several + + align:start position:0% +dealing with the union of several + + + align:start position:0% +dealing with the union of several +disjoint events by this joint here we + + align:start position:0% +disjoint events by this joint here we + + + align:start position:0% +disjoint events by this joint here we +mean that the intersection of any two of + + align:start position:0% +mean that the intersection of any two of + + + align:start position:0% +mean that the intersection of any two of +these events is the empty set + + align:start position:0% +these events is the empty set + + + align:start position:0% +these events is the empty set +we will prove this for the case of three + + align:start position:0% +we will prove this for the case of three + + + align:start position:0% +we will prove this for the case of three +events and then the argument generalizes + + align:start position:0% +events and then the argument generalizes + + + align:start position:0% +events and then the argument generalizes +for the case where where we're taking + + align:start position:0% +for the case where where we're taking + + + align:start position:0% +for the case where where we're taking +the union of K disjoint events where K + + align:start position:0% +the union of K disjoint events where K + + + align:start position:0% +the union of K disjoint events where K +is any finite number so the intuition of + + align:start position:0% +is any finite number so the intuition of + + + align:start position:0% +is any finite number so the intuition of +this result is the same as for the case + + align:start position:0% +this result is the same as for the case + + + align:start position:0% +this result is the same as for the case +of two events but we will derive it + + align:start position:0% +of two events but we will derive it + + + align:start position:0% +of two events but we will derive it +formally and we will also use it to come + + align:start position:0% +formally and we will also use it to come + + + align:start position:0% +formally and we will also use it to come +up with a way of calculating the + + align:start position:0% +up with a way of calculating the + + + align:start position:0% +up with a way of calculating the +probability of a finite set by simply + + align:start position:0% +probability of a finite set by simply + + + align:start position:0% +probability of a finite set by simply +adding the probabilities of its in + + align:start position:0% +adding the probabilities of its in + + + align:start position:0% +adding the probabilities of its in +visual elements all of these statements + + align:start position:0% +visual elements all of these statements + + + align:start position:0% +visual elements all of these statements +that we were that we just presented are + + align:start position:0% +that we were that we just presented are + + + align:start position:0% +that we were that we just presented are +intuitive and you do not really need to + + align:start position:0% +intuitive and you do not really need to + + + align:start position:0% +intuitive and you do not really need to +be convinced about their validity + + align:start position:0% +be convinced about their validity + + + align:start position:0% +be convinced about their validity +nevertheless it is instructive to see + + align:start position:0% +nevertheless it is instructive to see + + + align:start position:0% +nevertheless it is instructive to see +how these statements follow from the + + align:start position:0% +how these statements follow from the + + + align:start position:0% +how these statements follow from the +axioms that we have put in place so we + + align:start position:0% +axioms that we have put in place so we + + + align:start position:0% +axioms that we have put in place so we +will now present the arguments based + + align:start position:0% +will now present the arguments based + + + align:start position:0% +will now present the arguments based +only on the three axioms that we have + + align:start position:0% +only on the three axioms that we have + + + align:start position:0% +only on the three axioms that we have +available and in order to be able to + + align:start position:0% +available and in order to be able to + + + align:start position:0% +available and in order to be able to +refer to these axioms let us give them + + align:start position:0% +refer to these axioms let us give them + + + align:start position:0% +refer to these axioms let us give them +some names call them axioms a B and C we + + align:start position:0% +some names call them axioms a B and C we + + + align:start position:0% +some names call them axioms a B and C we +start as follows let us look at a sample + + align:start position:0% +start as follows let us look at a sample + + + align:start position:0% +start as follows let us look at a sample +space and a subset of that sample space + + align:start position:0% +space and a subset of that sample space + + + align:start position:0% +space and a subset of that sample space +call it a and consider the complement of + + align:start position:0% +call it a and consider the complement of + + + align:start position:0% +call it a and consider the complement of +that subset the complement is the set of + + align:start position:0% +that subset the complement is the set of + + + align:start position:0% +that subset the complement is the set of +all elements that do not belong to the + + align:start position:0% +all elements that do not belong to the + + + align:start position:0% +all elements that do not belong to the +set a so a set together with its + + align:start position:0% +set a so a set together with its + + + align:start position:0% +set a so a set together with its +complement make up everything which is + + align:start position:0% +complement make up everything which is + + + align:start position:0% +complement make up everything which is +the entire sample space on the other + + align:start position:0% +the entire sample space on the other + + + align:start position:0% +the entire sample space on the other +hand if an element belongs to a set a it + + align:start position:0% +hand if an element belongs to a set a it + + + align:start position:0% +hand if an element belongs to a set a it +does not belong to its complement so the + + align:start position:0% +does not belong to its complement so the + + + align:start position:0% +does not belong to its complement so the +intersection of a set with its + + align:start position:0% +intersection of a set with its + + + align:start position:0% +intersection of a set with its +complement is the empty set now we argue + + align:start position:0% +complement is the empty set now we argue + + + align:start position:0% +complement is the empty set now we argue +as follows we have that the probability + + align:start position:0% +as follows we have that the probability + + + align:start position:0% +as follows we have that the probability +of the entire sample space is equal to 1 + + align:start position:0% +of the entire sample space is equal to 1 + + + align:start position:0% +of the entire sample space is equal to 1 +this is true by our second axiom now the + + align:start position:0% +this is true by our second axiom now the + + + align:start position:0% +this is true by our second axiom now the +sample space as we just discussed can be + + align:start position:0% +sample space as we just discussed can be + + + align:start position:0% +sample space as we just discussed can be +written as the union of an event and the + + align:start position:0% +written as the union of an event and the + + + align:start position:0% +written as the union of an event and the +complement of that event this is just a + + align:start position:0% +complement of that event this is just a + + + align:start position:0% +complement of that event this is just a +set theoretic relation and next since + + align:start position:0% +set theoretic relation and next since + + + align:start position:0% +set theoretic relation and next since +the a set and it's complement are + + align:start position:0% +the a set and it's complement are + + + align:start position:0% +the a set and it's complement are +disjoint this means that we can apply + + align:start position:0% +disjoint this means that we can apply + + + align:start position:0% +disjoint this means that we can apply +the additivity axiom and write this + + align:start position:0% +the additivity axiom and write this + + + align:start position:0% +the additivity axiom and write this +probability as the sum of the + + align:start position:0% +probability as the sum of the + + + align:start position:0% +probability as the sum of the +probability of event a with the + + align:start position:0% +probability of event a with the + + + align:start position:0% +probability of event a with the +probability of the complement of a this + + align:start position:0% +probability of the complement of a this + + + align:start position:0% +probability of the complement of a this +is one of the relations that we had + + align:start position:0% +is one of the relations that we had + + + align:start position:0% +is one of the relations that we had +claimed and which we have now + + align:start position:0% +claimed and which we have now + + + align:start position:0% +claimed and which we have now +established based on this relation we + + align:start position:0% +established based on this relation we + + + align:start position:0% +established based on this relation we +can also write that the probability of + + align:start position:0% +can also write that the probability of + + + align:start position:0% +can also write that the probability of +an event + + align:start position:0% +an event + + + align:start position:0% +an event +a is equal to one minus the probability + + align:start position:0% +a is equal to one minus the probability + + + align:start position:0% +a is equal to one minus the probability +of the complement of that event and + + align:start position:0% +of the complement of that event and + + + align:start position:0% +of the complement of that event and +because by the non-negativity axiom this + + align:start position:0% +because by the non-negativity axiom this + + + align:start position:0% +because by the non-negativity axiom this +quantity here is non-negative 1 minus + + align:start position:0% +quantity here is non-negative 1 minus + + + align:start position:0% +quantity here is non-negative 1 minus +something non-negative is less than or + + align:start position:0% +something non-negative is less than or + + + align:start position:0% +something non-negative is less than or +equal to 1 we're using here the non + + align:start position:0% +equal to 1 we're using here the non + + + align:start position:0% +equal to 1 we're using here the non +negativity axiom and we have established + + align:start position:0% +negativity axiom and we have established + + + align:start position:0% +negativity axiom and we have established +another property namely that + + align:start position:0% +another property namely that + + + align:start position:0% +another property namely that +probabilities are always less than or + + align:start position:0% +probabilities are always less than or + + + align:start position:0% +probabilities are always less than or +equal to 1 + + align:start position:0% +equal to 1 + + + align:start position:0% +equal to 1 +finally let us note that 1 is the + + align:start position:0% +finally let us note that 1 is the + + + align:start position:0% +finally let us note that 1 is the +probability always of a set plus the + + align:start position:0% +probability always of a set plus the + + + align:start position:0% +probability always of a set plus the +probability of a complement of that set + + align:start position:0% +probability of a complement of that set + + + align:start position:0% +probability of a complement of that set +and let us use this property for the + + align:start position:0% +and let us use this property for the + + + align:start position:0% +and let us use this property for the +case where the set of interest is the + + align:start position:0% +case where the set of interest is the + + + align:start position:0% +case where the set of interest is the +entire sample space now the probability + + align:start position:0% +entire sample space now the probability + + + align:start position:0% +entire sample space now the probability +of the entire sample space is itself + + align:start position:0% +of the entire sample space is itself + + + align:start position:0% +of the entire sample space is itself +equal to 1 and what is the complement of + + align:start position:0% +equal to 1 and what is the complement of + + + align:start position:0% +equal to 1 and what is the complement of +the entire sample space the complement + + align:start position:0% +the entire sample space the complement + + + align:start position:0% +the entire sample space the complement +of the entire sample space consists of + + align:start position:0% +of the entire sample space consists of + + + align:start position:0% +of the entire sample space consists of +all elements that do not belong to the + + align:start position:0% +all elements that do not belong to the + + + align:start position:0% +all elements that do not belong to the +sample space but since the sample space + + align:start position:0% +sample space but since the sample space + + + align:start position:0% +sample space but since the sample space +is supposed to come to contain all + + align:start position:0% +is supposed to come to contain all + + + align:start position:0% +is supposed to come to contain all +possible elements its complement is just + + align:start position:0% +possible elements its complement is just + + + align:start position:0% +possible elements its complement is just +the empty set and from this relation we + + align:start position:0% +the empty set and from this relation we + + + align:start position:0% +the empty set and from this relation we +get the implication that the probability + + align:start position:0% +get the implication that the probability + + + align:start position:0% +get the implication that the probability +of the empty set is equal to 0 this + + align:start position:0% +of the empty set is equal to 0 this + + + align:start position:0% +of the empty set is equal to 0 this +establishes yet one more of the + + align:start position:0% +establishes yet one more of the + + + align:start position:0% +establishes yet one more of the +properties that we had just claimed a + + align:start position:0% +properties that we had just claimed a + + + align:start position:0% +properties that we had just claimed a +little earlier we finally come to the + + align:start position:0% +little earlier we finally come to the + + + align:start position:0% +little earlier we finally come to the +proof of the generalization of our + + align:start position:0% +proof of the generalization of our + + + align:start position:0% +proof of the generalization of our +additivity axiom from the case of two + + align:start position:0% +additivity axiom from the case of two + + + align:start position:0% +additivity axiom from the case of two +disjoint events to the case of three + + align:start position:0% +disjoint events to the case of three + + + align:start position:0% +disjoint events to the case of three +disjoint events so we have our sample + + align:start position:0% +disjoint events so we have our sample + + + align:start position:0% +disjoint events so we have our sample +space and within that sample space we + + align:start position:0% +space and within that sample space we + + + align:start position:0% +space and within that sample space we +have three events three subsets and + + align:start position:0% +have three events three subsets and + + + align:start position:0% +have three events three subsets and +these subsets are disjoint in the sense + + align:start position:0% +these subsets are disjoint in the sense + + + align:start position:0% +these subsets are disjoint in the sense +that any two of those subsets have no + + align:start position:0% +that any two of those subsets have no + + + align:start position:0% +that any two of those subsets have no +elements in common and we're interested + + align:start position:0% +elements in common and we're interested + + + align:start position:0% +elements in common and we're interested +in the probability of the union of a B + + align:start position:0% +in the probability of the union of a B + + + align:start position:0% +in the probability of the union of a B +and C how do we make progress we have an + + align:start position:0% +and C how do we make progress we have an + + + align:start position:0% +and C how do we make progress we have an +additive 'ti axiom in our hands which + + align:start position:0% +additive 'ti axiom in our hands which + + + align:start position:0% +additive 'ti axiom in our hands which +applies to the case of the union of two + + align:start position:0% +applies to the case of the union of two + + + align:start position:0% +applies to the case of the union of two +disjoint + + align:start position:0% +disjoint + + + align:start position:0% +disjoint +here we have three of them but we can do + + align:start position:0% +here we have three of them but we can do + + + align:start position:0% +here we have three of them but we can do +the following trick we can think of the + + align:start position:0% +the following trick we can think of the + + + align:start position:0% +the following trick we can think of the +union of a B and C as consisting of the + + align:start position:0% +union of a B and C as consisting of the + + + align:start position:0% +union of a B and C as consisting of the +union of this blue set with that green + + align:start position:0% +union of this blue set with that green + + + align:start position:0% +union of this blue set with that green +set formally what we're doing is that + + align:start position:0% +set formally what we're doing is that + + + align:start position:0% +set formally what we're doing is that +we're expressing the union of these + + align:start position:0% +we're expressing the union of these + + + align:start position:0% +we're expressing the union of these +three sets as follows we form one set by + + align:start position:0% +three sets as follows we form one set by + + + align:start position:0% +three sets as follows we form one set by +taking the union of a with B and before + + align:start position:0% +taking the union of a with B and before + + + align:start position:0% +taking the union of a with B and before +we have the other set C and the overall + + align:start position:0% +we have the other set C and the overall + + + align:start position:0% +we have the other set C and the overall +Union can be thought of as the union of + + align:start position:0% +Union can be thought of as the union of + + + align:start position:0% +Union can be thought of as the union of +these two sets now + + align:start position:0% +these two sets now + + + align:start position:0% +these two sets now +since the three sets are disjoint this + + align:start position:0% +since the three sets are disjoint this + + + align:start position:0% +since the three sets are disjoint this +implies that the blue set is disjoint + + align:start position:0% +implies that the blue set is disjoint + + + align:start position:0% +implies that the blue set is disjoint +from the green set and so we can use the + + align:start position:0% +from the green set and so we can use the + + + align:start position:0% +from the green set and so we can use the +add activity axiom here + + align:start position:0% +add activity axiom here + + + align:start position:0% +add activity axiom here +to write this probability as the + + align:start position:0% +to write this probability as the + + + align:start position:0% +to write this probability as the +probability of a union B plus the + + align:start position:0% +probability of a union B plus the + + + align:start position:0% +probability of a union B plus the +probability of C and now we can use the + + align:start position:0% +probability of C and now we can use the + + + align:start position:0% +probability of C and now we can use the +additive 'ti axiom once more since the + + align:start position:0% +additive 'ti axiom once more since the + + + align:start position:0% +additive 'ti axiom once more since the +set a and B are disjoint to write the + + align:start position:0% +set a and B are disjoint to write the + + + align:start position:0% +set a and B are disjoint to write the +first term as probability of a plus + + align:start position:0% +first term as probability of a plus + + + align:start position:0% +first term as probability of a plus +probability of B we carry over the last + + align:start position:0% +probability of B we carry over the last + + + align:start position:0% +probability of B we carry over the last +term and we have the relation that we + + align:start position:0% +term and we have the relation that we + + + align:start position:0% +term and we have the relation that we +wanted to prove this is the proof for + + align:start position:0% +wanted to prove this is the proof for + + + align:start position:0% +wanted to prove this is the proof for +the case of three events you should be + + align:start position:0% +the case of three events you should be + + + align:start position:0% +the case of three events you should be +able to follow this line of proof to + + align:start position:0% +able to follow this line of proof to + + + align:start position:0% +able to follow this line of proof to +write an argument for the case of four + + align:start position:0% +write an argument for the case of four + + + align:start position:0% +write an argument for the case of four +events and so on and you might want to + + align:start position:0% +events and so on and you might want to + + + align:start position:0% +events and so on and you might want to +continue by induction and eventually you + + align:start position:0% +continue by induction and eventually you + + + align:start position:0% +continue by induction and eventually you +should be able to prove that if the sets + + align:start position:0% +should be able to prove that if the sets + + + align:start position:0% +should be able to prove that if the sets +a 1 up to a K are disjoint then the + + align:start position:0% +a 1 up to a K are disjoint then the + + + align:start position:0% +a 1 up to a K are disjoint then the +probability of the union of those sets + + align:start position:0% + + + + align:start position:0% + +is going to be equal to the sum of their + + align:start position:0% +is going to be equal to the sum of their + + + align:start position:0% +is going to be equal to the sum of their +individual probabilities so this is the + + align:start position:0% +individual probabilities so this is the + + + align:start position:0% +individual probabilities so this is the +generalization to the case where we're + + align:start position:0% +generalization to the case where we're + + + align:start position:0% +generalization to the case where we're +dealing with the union of finitely many + + align:start position:0% +dealing with the union of finitely many + + + align:start position:0% +dealing with the union of finitely many +disjoint events a very useful + + align:start position:0% +disjoint events a very useful + + + align:start position:0% +disjoint events a very useful +application of this comes in the case + + align:start position:0% +application of this comes in the case + + + align:start position:0% +application of this comes in the case +where we want to calculate the + + align:start position:0% +where we want to calculate the + + + align:start position:0% +where we want to calculate the +probability of a finite set so here we + + align:start position:0% +probability of a finite set so here we + + + align:start position:0% +probability of a finite set so here we +have a sample space + + align:start position:0% +have a sample space + + + align:start position:0% +have a sample space +and within that sample space we have + + align:start position:0% +and within that sample space we have + + + align:start position:0% +and within that sample space we have +some particular elements as well as to + + align:start position:0% +some particular elements as well as to + + + align:start position:0% +some particular elements as well as to +up to sk8 K of them and these elements + + align:start position:0% +up to sk8 K of them and these elements + + + align:start position:0% +up to sk8 K of them and these elements +together form a finite set what can we + + align:start position:0% +together form a finite set what can we + + + align:start position:0% +together form a finite set what can we +say about the probability of this finite + + align:start position:0% +say about the probability of this finite + + + align:start position:0% +say about the probability of this finite +set the idea is to take this finite set + + align:start position:0% +set the idea is to take this finite set + + + align:start position:0% +set the idea is to take this finite set +that consists of K elements and think of + + align:start position:0% +that consists of K elements and think of + + + align:start position:0% +that consists of K elements and think of +it as the union of several little sets + + align:start position:0% +it as the union of several little sets + + + align:start position:0% +it as the union of several little sets +that contain one element each so set + + align:start position:0% +that contain one element each so set + + + align:start position:0% +that contain one element each so set +theoretically what we're doing is that + + align:start position:0% +theoretically what we're doing is that + + + align:start position:0% +theoretically what we're doing is that +we're taking this set with K elements + + align:start position:0% +we're taking this set with K elements + + + align:start position:0% +we're taking this set with K elements +and we write it as the union of a set + + align:start position:0% +and we write it as the union of a set + + + align:start position:0% +and we write it as the union of a set +that contains just as one set that + + align:start position:0% +that contains just as one set that + + + align:start position:0% +that contains just as one set that +contains just the second element as two + + align:start position:0% +contains just the second element as two + + + align:start position:0% +contains just the second element as two +and so on up to the cave element we're + + align:start position:0% +and so on up to the cave element we're + + + align:start position:0% +and so on up to the cave element we're +assuming of course that these elements + + align:start position:0% +assuming of course that these elements + + + align:start position:0% +assuming of course that these elements +are all different from each other so in + + align:start position:0% +are all different from each other so in + + + align:start position:0% +are all different from each other so in +that case these sets these single + + align:start position:0% +that case these sets these single + + + align:start position:0% +that case these sets these single +element sets are all disjoint so using + + align:start position:0% +element sets are all disjoint so using + + + align:start position:0% +element sets are all disjoint so using +the additivity property for a union of K + + align:start position:0% +the additivity property for a union of K + + + align:start position:0% +the additivity property for a union of K +disjoint sets we can write this as the + + align:start position:0% +disjoint sets we can write this as the + + + align:start position:0% +disjoint sets we can write this as the +sum of the probabilities of the + + align:start position:0% +sum of the probabilities of the + + + align:start position:0% +sum of the probabilities of the +different single element sets at this + + align:start position:0% +different single element sets at this + + + align:start position:0% +different single element sets at this +point it is usual to start abusing or + + align:start position:0% +point it is usual to start abusing or + + + align:start position:0% +point it is usual to start abusing or +rather simplifying notation a little bit + + align:start position:0% +rather simplifying notation a little bit + + + align:start position:0% +rather simplifying notation a little bit +probabilities are assigned two sets so + + align:start position:0% +probabilities are assigned two sets so + + + align:start position:0% +probabilities are assigned two sets so +here we're talking about the probability + + align:start position:0% +here we're talking about the probability + + + align:start position:0% +here we're talking about the probability +of a set that contains a single element + + align:start position:0% +of a set that contains a single element + + + align:start position:0% +of a set that contains a single element +but intuitively we can also talk as just + + align:start position:0% +but intuitively we can also talk as just + + + align:start position:0% +but intuitively we can also talk as just +the probability of that particular + + align:start position:0% +the probability of that particular + + + align:start position:0% +the probability of that particular +element and use this simpler notation so + + align:start position:0% +element and use this simpler notation so + + + align:start position:0% +element and use this simpler notation so +when using the simpler notation we will + + align:start position:0% +when using the simpler notation we will + + + align:start position:0% +when using the simpler notation we will +be talking about the probabilities of + + align:start position:0% +be talking about the probabilities of + + + align:start position:0% +be talking about the probabilities of +individual elements although in terms of + + align:start position:0% +individual elements although in terms of + + + align:start position:0% +individual elements although in terms of +formal mathematics what we really mean + + align:start position:0% +formal mathematics what we really mean + + + align:start position:0% +formal mathematics what we really mean +is the probability of this event that's + + align:start position:0% +is the probability of this event that's + + + align:start position:0% +is the probability of this event that's +comprised only of a particular element s + + align:start position:0% +comprised only of a particular element s + + + align:start position:0% +comprised only of a particular element s +one and so on \ No newline at end of file diff --git a/WbE2USh7RKI.txt b/WbE2USh7RKI.txt new file mode 100644 index 0000000000000000000000000000000000000000..d67f2547c4a7685c4d4369da5ecd2675a6afddb6 --- /dev/null +++ b/WbE2USh7RKI.txt @@ -0,0 +1,2770 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +JON GRUBER: All right, so today +we are going to continue + +with our discussion of +producer theory. + +And today we're going to move +beyond the unrealistic case of + +perfect competition to the +somewhat more realistic case + +of monopoly. + +Now, we've been discussing +perfect competition thus far + +as a form of market +organization, and that makes + +sense in some context like fast +food and other things. + +But in most contexts, we think +perfect composition is not the + +way the world works. + +There's some limits +on competition. + +And we think that markets-- + +many markets, many of the goods +we consume have only a + +few firms. Operating systems or +cars or a lot of things we + +consume, typically have only +a few firms in them. + +So the most realistic model of +markets would be one which + +accounts for the fact that +there's less than an infinite + +number of firms, there's +only a few firms. + +That turns out also to +be the hardest model. + +So what we do is we sort +of iterate there. + +We started with one extreme, +which is a competitive market + +where there's an infinite number +of firms, that allows + +us to draw some interesting +conclusions. + +Now we're going to reverse field +and talk about the other + +extreme, monopoly, which +is only one firm. + +We'll talk about monopoly +markets with only one firm. + +Then we'll talk about oligopoly, +that middle case, + +which is multiple firms. + +So let's talk about monopoly, +a market where + +there's only one firm. + +The key thing to remember for +monopolies is they're no + +longer price takers, they're +now price makers. + +Competitive firms are +price takers. + +They were given a price +by the market and + +they reacted to that. + +And as we saw in the long run, +that price settled at the + +minimum of average cost. So +basically, they were given the + +price which dictated production +efficiency. + +They reacted to that in how +much they produced. + +You got a flat long +run supply curve. + +However, in a monopoly market, +we don't meet the conditions + +for perfect competition. + +In particular, one condition was +that consumers had perfect + +substitutes between your +good and other + +goods they could buy. + +That's not true in a +monopoly market. + +So if we think about that era, +sort of maybe, I don't know, I + +don't have my computer history +isn't as good. + +Maybe 10 years ago when Macs +were sort of at the nadir of + +their popularity. + +And really you had to be a +pretty high tech guy to be + +using Linux and things +like that. + +That Windows had virtually a +monopoly on operating systems. + +Not really, but virtually. + +Certainly unless you were a +high tech guy who could do + +Linux and things like that, +pretty much if you wanted an + +operating system, +you got Windows. + +Windows pretty much +had a monopoly. + +And that's may be as close as +we've come in the modern + +economy to thinking about +an example of monopoly. + +In that case, Bill Gates +had to decide-- + +wasn't given a price, he had to +decide how much to charge + +for Windows. + +And that decision determined +in turn how + +much he would produce. + +And that's exactly what we'll +talk about today, is how does + +a monopolist decide both what +to charge and how much to + +produce of their good? + +So to do that, we're going +to turn to a new concept. + +Well, not a new concept, but a +different way of looking at + +something we've talked +about before, + +which is marginal revenue. + +If you remember, the profit +maximizing condition that we + +derived when we started our +competition lectures was that + +marginal revenue equals marginal +cost. That was our + +profit maximizing condition, +was that marginal revenue + +equals marginal cost. + +Now we're going go to-- + +in perfect competition. + +And the way we thought about +this marginal revenue equals + +marginal cost, remember the +logic was this notion of + +climbing this profit hill. + +You want to produce any unit. + +Think of yourself as climbing +this profit hill. + +You're deciding, do I produce +the next unit? + +And I produce the next unit as +long as the money I make off + +that unit exceeds what it cost +to produce that unit. + +So I climb that profit hill. + +If marginal revenue is greater +than marginal cost, + +I keep going up. + +At the peak, marginal revenue +will equal marginal cost. Once + +I go beyond that peak, marginal +revenue will fall + +down below marginal cost and +I'll stop producing. + +So the notion is I climb this +hill, which in the peak is + +dictated by marginal revenue +equals marginal cost. + +Now for a competitive firm, +we said marginal + +revenue was just price. + +So in perfect competition, the +rule was set price equal to + +marginal cost. But that +was a particular + +case of marginal revenue. + +So for example, to see that, +let's look at Figure 14-1. + +This is another way. + +Probably next year when I teach +this, I'll put this in + +the lecture on competition. + +Just a way to think about how +marginal revenue is priced. + +Remember, a perfectly +competitive firm faces a + +perfectly elastic +demand curve. + +They face a perfectly elastic +demand curve. + +So they have to think about what +the implications are of + +the marginal unit they sell. + +Well if they sell little q +units, their revenue's a. + +If they sell one more unit, +their revenue is b. + +And the marginal revenue is the +height of that rectangle B + +times the base. + +The base is 1 because it +goes from q plus 1. + +The height is p. + +So the marginal revenue +is price. + +This is a pretty +basic diagram. + +So marginal revenue +is price for the + +perfectly competitive firm. + +Now let's look at the +monopoly case. + +The difference with a +monopolist, as you see in + +Figure 14-2, is they no longer +face a perfectly elastic + +demand curve. + +They now face a downward-sloping +demand curve. + +Why is that? + +Well remember, this is the +graph for little q. + +The reason the graph for little +q was perfectly elastic + +with a perfectly competitive +case was not that we said the + +demand for the entire good +was perfectly elastic. + +It's just that the residual +demand facing anyway one firm + +was perfectly elastic. + +Well now, a monopolist is the +only firm in the market. + +So their residual demand +equals total demand. + +Their residual demand +equals total demand. + +So as long as total demand is +downward-sloping, as we + +typically think it is, +then they'll face a + +downward-sloping demand curve. + +So unlike a perfectly +competitive firm, which faces + +a perfectly elastic residual +demand curve, a monopoly firm + +will face a downward-sloping +market demand curve. + +They face the entire market +demand curve. + +So this is demand curve. + +Now we're talking about big Q's +not little q's anymore. + +Or we could say little +q equals big Q. + +There's only one firm. + +So little q's and the big +Q's are the same. + +So now the firm reacts not to +its residual firm demand + +curve, which is flat, but +the downward-sloping + +market demand curve. + +Now, we're going to make +one assumption + +here that's very important. + +We'll come back to this at +the end of the lecture. + +We're going to assume that the +monopolist can only charge one + +price for their good +to all consumers. + +So most of this lecture we're +going to assume a non-price + +discriminating monopolist. We're +going to say that Bill + +Gates can't look at you and say, +look, you look like you + +really want Windows. + +I'm going to charge +you more than her. + +He can't do that. + +He has one price. + +He sells it to the stores +at one price. + +So it's a non-price +discriminating monopolist + +we're going to work with for the +first 2/3 of this lecture. + +That monopolist has +to set one price. + +Now, for that monopolist, for +Bill Gates with Windows circa + +10 years ago, let's think about +his decision to produce + +another unit. + +He's originally producing at +Q, big Q at a price p1. + +He's originally producing +a big Q at a price p1. + +If he wants to sell one more +unit, he's going to have to + +lower the price. + +Because he now faces a +downward-sloping demand curve. + +So if he wants to sell one more +unit, he's going to have + +to lower the price to P2. + +I have a big cockatoo at home. + +This is his feather. + +So he's going to have to +lower the price to P2. + +What's that going to do? + +Well, on the one hand, what +that's going to do is that's + +going to mean on that next unit +he's going to make p2. + +So he's going to get the +rectangle B. On the other + +hand, on all the units he was +selling at p1, he now gets a + +lower price p2. + +So he loses the rectangle C. +So the marginal revenue for + +this monopolist, the marginal +revenue is equal to the + +rectangle B minus the rectangle +C. The marginal + +revenue is rectangle B +minus rectangle C. + +Or alternatively, you could say +that if we just write that + +out, write out what that +is, that's p2 minus p1 + +minus p2 times Q1. + +Or rewriting, we could rewrite +this then as marginal revenue + +equals p plus delta p delta q, +how much the price changes + +when you change the quantity, +times the + +original quantity Q1. + +Or one more time, for those of +you who prefer calculus. + +If revenue equals p times q, and +q is a function of p, then + +marginal revenue, +differentiating that, is p + +plus dp dq times Q. So marginal +revenue is the price + +plus the change in price from +selling another unit times the + +initial quantity. + +Once again, the graphics +are in this graph. + +The math is here. + +We just differentiate the +revenue equation. + +This term is positive. + +Price is always greater +than 0. + +But this term is negative +because demand + +curves slope down. + +So there's now two effects. + +There's a positive effect, which +is if I sell another + +unit, I make money on +that other unit. + +There's a negative effect, which +is to sell that other + +unit, I have to lower the +price because I face + +downward-sloping demand. + +So there's two effects a +monopolist as he thinks about + +wanting to sell another unit. + +There's the money from that +unit, but the lower + +willingness to pay for +all previous units. + +And that's what makes a +monopolist a little more + +interesting. + +We basically think of the +monopolist as basically having + +to work down the demand curve. + +With a perfectly competitive +firm, they don't have to work + +down the demand curve. + +The demand's flat to them. + +They can sell as much as they +want at that price because + +they don't affect the price. + +They want to sell 10 of that +price or a million at that + +price, it doesn't matter. + +Their demand curve's flat. + +Not true for the monopolist. + +If the monopolist wants to sell +more, he has to face the + +wrath of the market. + +And the wrath of the market is +such that if he wants to sell + +more, he's going to have to +lower the price to do so. + +Remember, once again assuming +he has to charge the same + +price to everyone. + +Assuming he's going to charge +the same price to everyone, if + +he wants to sell more, he's +going to have to lower the + +price to do so. + +There's different ways +of [UNINTELLIGIBLE] + +intuition on this. + +I like to call this the +poisoning effect. + +That's how I like to +think about it. + +That basically, if I want to +sell another unit, I'm going + +to poison the money I made +on all previous units. + +Because if I want to sell +another unit, I have + +to lower the price. + +That's going to take away from +the money I was making on my + +previous units. + +So it's sort of a poisoning +effect is how I like + +to think about it. + +But you can have your own +intuition for it. + +And basicallly, this poisoning +effect did not exist for the + +perfectly competitive firm +because they couldn't affect + +the price with their action. + +They could sell however many +units they wanted at that flat + +price and their actions did +not affect that price. + +The poisoning effect only +exists with monopolists + +because to sell that next +unit, they have + +to lower the price. + +Now, basically what that means +is to find equilibrium for a + +monopolist, it's going to be +a little bit trickier. + +And so let's go to Figure +14-3 and slowly walk + +through Figure 14-3. + +And we'll start walking +through. + +What the monopolist is going +to want to do is draw a + +marginal revenue curve. + +With the perfectly competitive +firm, marginal revenue curve + +was just a price, it +was given to them. + +There was no marginal +revenue curve. + +For a monopolist, there is +a marginal revenue curve. + +So here I have a demand curve. + +The demand curve I've drawn +here in this example. + +The demand curve I've drawn here +is q equals 24 minus p. + +That's a typical demand curve, +downward-sloping. + +As the price goes up, people +want less of it. + +And now we're in +market demands. + +Because remember, little +q equals pq. + +There's only one firm +in the market. + +Now, here's the trick with +monopoly: mathematics. + +The first thing you're going to +want to do is you're going + +to want to invert this. + +You're going to want say, OK, +that takes q, but what takes + +the price a monopolist +is going to charge? + +The price a monopolist is going +to charge is therefore + +going to be 24 minus q. + +That's going to be the +price that the + +monopolist is going to charge. + +Therefore, revenues, pq, +is 24q minus q squared. + +So we inverted the +demand equation. + +We do this because we want to +write down a revenue equation. + +So that's the trick. + +This is the mathematical trick +here is to invert this, so + +then you can write down +a revenue equation. + +We then differentiate this +revenue equation to get that + +marginal revenues equals +24 minus 2q. + +That's marginal revenues. + +The next unit you sell, you +make 24 minus 2 times the + +amount you're now selling. + +And that's the marginal revenue +curve graphed here. + +Now, basically what you see is +in this case the marginal + +revenue curve starts at the same +point as the demand curve + +on the y-axis and +lies everywhere + +below the demand curve. + +Now that first fact, that it +starts at the same intercept, + +is not always true. + +That is true because in this +case we assumed a linear + +demand curve. + +With a nonlinear demand curve, +marginal revenue curves can + +start at different points +on the y-axis. + +The second point about the +marginal revenue curve always + +being below the demand curve is +always true regardless of + +the function. + +The marginal revenue is +always below demand. + +Marginal revenue is always +below demand. + +So that marginal revenue curve +will always be below the + +demand curve because of +this poisoning effect. + +Now, what I want to highlight +here is this means there's a + +very important relationship +between marginal revenue and + +the elasticity of demand. + +So let's take our marginal +revenue equation and put it + +back in change terms. p plus +delta p over delta q times Q. + +And let's multiply +and divide by p. + +So marginal revenue you can +rewrite as p plus p times + +delta p over delta +q times Q over p. + +So I just took this second term, +multiplied and divided + +by p, the second term. + +I just multiplied and +divided by p. + +The reason I did that is because +that means you can + +rewrite this. + +This now starts to look like +an elasticity expression. + +Remember the expression +for elasticity. + +This looks like the inverse of +an elasticity expression. + +Remember what elasticity of +demand was, delta q delta p + +times p over Q. So that's +the inverse to + +the elasticity demand. + +So we can rewrite this as +marginal revenue equals p + +times 1 plus 1 over the +elasticity of demand. + +Marginal revenue equals p +times 1 plus 1 over the + +elasticity of demand. + +Think about what this +means for a second. + +What is the marginal +revenue in a + +perfectly competitive firm? + +Well, as a perfectly competitive +firm, what's the + +elasticity of demand facing a +perfectly competitive firm? + +Infinity. + +Perfectly elastic. + +So marginal revenue by +L'Hopital's rule equals p. + +So for a perfectly competitive +firm where elasticity is + +infinity, marginal +revenue equals p. + +Now instead, if we took a firm +where the elasticity of demand + +was minus 1, the electricity +demand was minus 1, the + +marginal revenue would be 0. + +Why is that? + +What that says is, if you're +a monopolist facing an + +elasticity of demand of minus +1, then you make no money by + +selling the next unit. + +Because these two effects +exactly cancel. + +It turns out with elasticity of +demand of negative 1, these + +two effects exactly cancel. + +Exactly what you make by selling +one more unit is + +offset by how much you have to +lower the price on all your + +previous units. + +So an elasticity of demand +of minus 1, marginal + +revenue equals 0. + +And as you can see as the +elasticity of demand gets + +below minus 1, as it approaches +0 from below. + +As the elasticity of demand +approaches 0 from below-- + +OK, I should have said perfect +competition, I'm sorry, was + +negative infinity, +not infinity. + +Negative infinity. + +As the elasticity of demand +approaches 0 from below, then + +you're going to see that +the marginal revenue-- + +as you approach 0 from below, +marginal revenue is going to + +become negative. + +So for example, if the +elasticity of demand equals + +minus 0.5, then the marginal +revenue equals minus p. + +So if this is minus 0.5, then +this becomes minus 2. + +So marginal revenue +equals minus p. + +You lose money. + +So as that elasticity of demand +approaches 0, you're + +going to have a negative +marginal revenue from selling + +the next unit. + +And why is that? + +With a very inelastic good, +you have to push the price + +down so much to sell the next +unit that you lose money. + +Think about a very elastic +versus very inelastic good. + +With a very elastically demanded +good, to sell another + +unit you don't have to change +the price much. + +Because the demand curve's +very flat. + +So there's not much of +a poisoning effect. + +dp dq is small, or +dq dp is big. + +OK, this is the inverse. + +So dq dp is big with elasticity, +so dp dq is small. + +With a very inelastically +demanded good, to sell one + +more unit you're going to lower +the price a ton, which + +is going to poison the revenues +you get from selling + +that extra unit. + +So that's why marginal revenue +will be higher, or will be a + +larger fraction of p +as this elasticity + +becomes more negative. + +Yeah. + +AUDIENCE: +[UNINTELLIGIBLE PHRASE] + +elastic that means +[UNINTELLIGIBLE PHRASE] + +irrespective of the price. + +So couldn't you just charge a +higher price and get marginal + +revenue [UNINTELLIGIBLE]. + +JON GRUBER: No, because +here's the thing. + +You should have already been +charging that high price. + +The point this is the margin. + +So you go into a market +for insulin. + +You say, look, these guys are +going to die without it. + +I'm going to charge +$500,000 a shot. + +But now the question we're +asking about marginal revenue. + +And at $500,000, you sell to +everyone who can afford it and + +everyone else dies. + +Now you want to ask, what's the +marginal revenue as you're + +trying to sell that 500,000 +and first unit? + +Well to sell that, since it's +inelastically demanded, if + +that person could afford +anything like $500,000, they + +would have bought it already. + +They can't. + +They can only afford $400,000. + +We have to lower the +price to $400,000. + +You're going to sell one more +unit at $400,000 but lose + +$500,000 on all those other +units you were going to sell + +at $500,000. + +The point is it's about the +margin not the level. + +Yes, monopolists make a huge +profit when it's inelastic. + +I'll talk about that +in a minute. + +But that next unit they're +going to lose money on. + +So that's actually a good point +to segue to now, let's + +talk about with this in place, +let's talk about how + +monopolists maximize profits. + +Let's talk about monopoly +profit maximization. + +Let's go to Figure 14-4. + +Profit Maximization +for a Monopolist. + +Now, this is a lot more +confusing than perfectly + +competitive firms, so let's +follow along here. + +This is a case the cost +function here + +is 12 plus q squared. + +So I'm doing the cost +function, which + +is 12 plus q squared. + +That's the cost function. + +And the demand function, +as before, is Q + +equals 24 minus p. + +So that's what's graphed here. + +Now, recall the rule that profit +is maximized where + +marginal revenue equals marginal +cost. Well, we know + +marginal revenue. + +We know marginal revenue-- + +we derived that above-- + +is 24 minus 2Q. + +What's marginal cost with +this expression? + +Well, marginal cost, +differentiation of the cost + +equation, which is 2Q. + +So the optimization term for a +monopolist is going to where + +marginal revenue, which is 24 +minus 2Q, equals marginal + +cost, which is 2Q. + +Or Q equals 6. + +That's going to be the optimal +production level for the + +monopolist. + +So we can see that graphically +that's where the marginal cost + +curve hits the marginal +revenue curve. + +If you go downward from that +point, you get that the sales + +are 6 units. + +So marginal revenue equals +marginal cost at 6. + +You should be able to see that +graphically, it's just where + +the curves intersect. + +Mathematically I just +did it here. + +It's actually pretty +straightforward. + +Here's the hard part. + +What's the price? + +We might say, well, gee, +marginal cost and marginal + +revenue intersect at 6. + +I'm going to draw the +dashed line over. + +That means the price +is going to be 12. + +Why can that not be the price? + +Why is that wrong? + +What would that violate +if the price was 12? + +If you tried to sell +6 at a price of 12? + +Yeah. + +AUDIENCE: [INAUDIBLE]. + +JON GRUBER: It's not on +the the demand curve. + +The monopolist still has to +respect the demand curve. + +So monopolists in setting +their quantity, gets the + +intersection of marginal revenue +and marginal cost. But + +then in setting the price, they +still have to read off + +the demand curve. + +They can't change +consumer tastes. + +So they charge a price of 18. + +That's where you sell +a quantity of 6. + +So monopolists it's a little +bit trickier in a perfectly + +competitive firm. + +You set marginal revenue equal +marginal cost to derive Q. But + +then to get p, you've got to go +back and plug that into the + +demand curve. + +So with a Q of 6, I +have my Q of 6. + +Well, what's the p? + +Well, to get that p, I've +got to go back and + +plug this in here. + +At Q equals 6, p is +24 minus q, or 18. + +So I've got to respect +the demand curve. + +The monopolist has to respect +the demand curve. + +The monopolist picks both price +and quantity, but he has + +to pick them such that you get +a point on the demand curve. + +And the way we solve it, is +the monopolist chooses a + +quantity to set marginal revenue +equal to marginal + +cost, and then chooses the price +that's consistent with + +demand for that quantity. + +Questions about that? + +Now one last thing. + +In the short run, we still have +another condition for + +profit maximization, which +is the shutdown rule. + +Remember the shutdown rule +we talked about perfectly + +competitive firms in the short +run, which is even if profits + +are negative, you might +not shut down. + +You only shut down if price is +less than average variable + +cost. So there's still +the shutdown rule. + +So you only shutd own if price +is less than average variable + +cost. + +Now in this case, what's +the monopolist profits? + +Well, the monopolist made +a profit of 60. + +How do we see that? + +Well that's graphically the box, +the rectangle, that's the + +difference between the average +cost curve and + +the price they get. + +So they're charging 18. + +Now once again, marginal +revenue is gone. + +Think about marginal revenue +like an imaginary concept. + +Marginal revenue isn't something +that actually exists + +in the market. + +Marginal revenue is just +something the monopolist draws + +to pick what they're +going to do. + +But then it disappears. + +What the monopolist cares +about then is price. + +They're charging 18. + +Their average cost for +that unit is only 8. + +So they're making a profit of +10 per unit on 6 units. + +So they're making +a profit of 60. + +And what you can see, what you +should be able to demonstrate + +to yourself is, if a monopolist +sold 5 units. + +I'm sorry, selling 6 units. + +If the monopoly sold that +seventh unit, what you'll be + +able to see is they would lose +money on the seventh unit. + +Because yes, if they sold that +seventh unit, what happened if + +they sold the seventh unit? + +Well then their price would have +to be what if they wanted + +to sell a seventh unit? + +The price would have to be 17. + +The price would have to be 17. + +So to sell a seventh unit, +they'd have to + +have a price of 17. + +So basically at a price of +17, the price was 17. + +Then what would happen? + +Well, they'd sell one +more unit at 17. + +That'd be good. + +But they'd lose $1 +on the previous 6 + +units, which is bad. + +So how much revenues +would they make? + +What would be their +marginal revenue? + +Well, the marginal revenue would +be they make 17 minus + +the 6 poisoning effect. + +So marginal revenue equals 11. + +What's their marginal cost? + +Their marginal cost is 2Q. + +Marginal cost is 14. + +So they lose money. + +So you should be able +to walk through + +this exercise yourself. + +You might say, gee, the marginal +cost of that next + +unit is only 14. + +They sell it for 17. + +Gosh, they should do it. + +What you're missing is by +selling it for 17, they've + +lost the dollar extra +they make on each of + +the previous 6 units. + +And that poisoning +effect makes it + +unprofitable to do this. + +And that's why the monopolists +stop short of what would be + +the perfectly competitive +outcome. + +What would the perfectly +competitive firm do? + +The perfectly competitive +firm would set marginal + +cost equal to demand. + +And they would end up producing +where marginal cost + +equals demand. + +So demand here is 24 minus p. + +Marginal cost is 2Q. + +So they would end up producing +where marginal cost equals + +demand at a much higher +level charging a + +slightly lower price. + +So what you see is the +monopolist ends up selling + +fewer units at a higher price. + +Questions about that? + +Yeah. + +AUDIENCE: How does this work +for Microsoft where their + +marginal costs are very +low or nonexistent? + +JON GRUBER: Well, then what +would happen, if their + +marginal costs were very +low or nonexistent. + +Think of that marginal +cost curve then as + +being much, much flatter. + +It would intersect demand at +a much higher quantity. + +Or it'd intersect marginal +revenue at a + +somewhat higher quantity. + +Not that much higher. + +So if marginal cost is very +low, they produce more but + +they make even more profits. + +So it's a good question +actually, a good comparative + +statics exercise. + +You bring that marginal +cost curve down, + +what's going to happen? + +Quantity is going to go up, but +not as quickly as profits + +are going to go up. + +That's why Bill Gates is the +richest man in the world. + +That's what happens. + +You get really rich. + +So basically, when you're a +monopoly, low marginal cost + +you get really rich. + +But that's a great thought +exercise to understand how + +this monopoly example works. + +Other questions about that? + +So this is a good opportunity +to introduce an important + +concept with monopolists, the +concept of market power. + +What monopolists have, what Bill +Gates has that my local + +McDonald's does not +is market power. + +Or what he had, has less of +now, is market power. + +Market power is the ability to +charge price above marginal + +cost. The summary statistic of +how much power a monopolist + +has is how much they can drive +their price above marginal + +cost. + +When Bill Gates marginal cost +dwindles to 0, his market + +power gets bigger. + +Price above marginal cost. + +Now to think about this, +remember the condition for + +profit maximization. + +It was that marginal revenue, +which we wrote as p times 1 + +plus 1 over epsilon equals +marginal cost. So we can + +rewrite this as marginal cost +over price equals 1 plus 1 + +over epsilon. + +Now let's define the markup. + +Let's define the markup as price +minus marginal cost, how + +much money you make +on the next unit. + +You sell for p, you get marginal +cost. It's money you + +make the next unit. + +If you define the markup, p +minus MC over p, that's the + +percentage markup. + +It's how much you make +on the next unit, + +the percentage markup. + +Then you can see that +that markup equals + +minus 1 over epsilon. + +So the markup for a monopoly +firm equals + +minus 1 over epsilon. + +This comes to the question +before about the insulin + +example's sort of confusing. + +Here we see your intuition +on insulin. + +The lower its elasticity, the +more the monopolists can mark + +up their price. + +So your intuition +is shown here. + +Yes, the monopolist +will charge an + +incredible price for insulin. + +They'll still lose a lot of +money if they try to raise + +that price, if they try +to sell one more unit. + +But the first initial price +they'll set will + +be incredibly high. + +Basically, what is the +constraint on Bill Gates? + +What is the constraint +on Bill Gates? + +It's Steve Jobs. + +It's substitutes. + +The only constraint on a +monopolist is the extent to + +which people can sub-- + +actually, let me go back, that's +not a good example. + +Let's [UNINTELLIGIBLE] + +Bill Gates circa 10 years ago. + +The constraint on Bill Gates +circa 10 years ago was a + +mainframe or some other form +of doing a set of-- + +or 20 years ago it +was a typewriter. + +It was basically the fact that +there was some other way to do + +what Bill Gates was +letting you do. + +If there was no other way to do +what Bill Gates was letting + +you do, he would charge +an infinite price. + +Clearly if there's +some other way-- + +and also, elasticity of course, +comes from substitutes + +or one substitute is just +not to compute. + +So if Bill Gates tried to charge +infinity for Windows, + +people just wouldn't +own computers. + +So the reason Bill Gates can't +charge infinity, and the + +reason he can't charge infinity +for insulin is that + +there's some elasticity +of demand. + +People at some point will +just stop buying. + +Either because they'll choose to +use a typewriter instead or + +they just won't compute. + +They'll write by hand +or something. + +So basically at some point, +there is some elasticity + +because there's a market +demand curve. + +And basically what's going to +determine how much market + +power the monopolist has is +going to be how elastic it is. + +Basically, how close the +substitutes are for that good. + +If there's close substitutes, +the monopolist won't be able + +to charge a very high markup. + +If there's not close substitutes +as of Window circa + +10 years ago, the monopolist can +charge a very high markup + +and become very, very rich. + +Yeah. + +AUDIENCE: But if there are +substitutes for the market, + +then it's not a monopoly +anymore. + +JON GRUBER: No, no, this +is the key thing. + +Substitutes for that producer. + +So basically, that's why +I said Steve Jobs + +is not a good example. + +Because then it's not +a monopoly anymore. + +But the typewriter is +a good example. + +That's a different good, that's +a different market, + +different good that +substitutes. + +So my point is any given good, +insulin being an exception, + +but any good there's always +something you can do instead. + +Insulin there is something +you can do + +instead, you can be sick. + +There's always something +you can do instead. + +We don't have only one +thing in life. + +So the elasticity of demand is +never perfectly inelastic. + +It seems silly 10 years ago, but +20 years ago it actually + +was a legitimate decision +whether to have a PC or not. + +A lot of people just didn't +have computers. + +You could always just +not have one. + +That gives you inelasticity +of demand. + +So basically, it's important +to recognize when we talk + +about substitutes, I'm talking +about here not substitutes + +within the market, but +substitutable activities, + +other things you could +do with your money. + +And the more other things are +you could do with your money, + +the less markup that Bill Gates +can make on his Windows + +operating system. + +Questions about that? + +OK, now we can ask, OK, gee, +John, this is all good and + +interesting, but why did you +just waste the last lecture + +and a half teaching us about +welfare if you're just going + +to go back to producer theory? + +Well, the reason is because +now we come to what the + +welfare effects of monopoly. + +And ask, what effects do +monopoly have on society? + +And in fact, we can show you +that there's a deadweight loss + +on society imposed +by monopoly. + +To see that, let's go +to Figure 14-5. + +And here we can show the +deadweight loss of monopoly. + +And here's the same example +we were using. + +Demand is Q equals 24 minus p. + +Marginal cost is 2Q. + +The cost function is +12 plus Q squared. + +So marginal cost is 2Q. + +As we saw before, the monopolist +chose to sell 6 + +units at a price of 18. + +6 units at a price of 18. + +The perfectly competitive firm +sets demand, which is 24 minus + +Q, sets price, I'm sorry, equal +to marginal cost. Well, + +price comes to demand +curve as 24 minus Q. + +Marginal cost is 2Q. + +So the perfectly competitive +firm sets Q equal to 8. + +The perfectly competitive +firm sets q equal to 8. + +They choose to sell 8 units +at a price of 16. + +So you get the competitive +quantity Q sub c is eight and + +the competitive price +piece p sub c is 16. + +That's where graphically demand +equals marginal cost. + +Or price equals marginal cost. + +The monopoly firm sells 6 +units at a price of 18. + +So what is the welfare +effects of monopoly? + +What we see is we know +that the competitive + +firm maximizes welfare. + +We learned that last time. + +We know that the best you can +do is to sell 8 units at a + +price of 16. + +What happens when you sell +6 units at a price of 18? + +What happens is consumer surplus +falls from A plus B + +plus C. So with perfect +competition, consumer surplus + +is A plus B plus C. With a +monopoly, consumer surplus + +falls to the area A. So you lose +B plus C with monopoly. + +Producer surplus under perfect +competition was the area D + +plus E. Now under a monopolist, +the producer + +surplus is equal to D plus E +plus B. The monopolist , in + +this case, gained the rectangle +B, but gave up the + +rectangle E. The consumer lost +the rectangle B, that was a + +transfer to the monopolist. So +there was a transfer of the + +rectangle B from the consumer to +the monopolist. But C plus + +E have disappeared. + +They're a deadweight loss. + +They're deadweight loss because +in the perfectly + +competitive equilibrium these +are trades that would have + +made both parties better off. + +That is, these are trades which +socially should happen. + +They are trades where the value +to the consumer exceeds + +the cost of producing +that unit. + +Those seventh and eighth +units are units-- + +so take the seventh unit. + +What's that worth to someone? + +Well, it's worth 17. + +We can read that off +the demand curve. + +That's a willingness +to pay curve. + +People are willing to pay 17 +for that seventh unit. + +What's it cost to produce? + +It cost 14. + +So you have a unit which people +want more than it costs + +to produce, yet it's +not getting sold. + +That's deadweight loss. + +So monopolists induce deadweight +loss because units + +that people value above +their marginal + +cost doesn't get sold. + +Units people value above their +marginal cost don't get sold. + +And that's because this +poisoning effect. + +Because while it's socially +optimal to sell those units, + +while society is better off, +it's privately sub-optimal. + +From the monopolist's +perspective, it's bad to sell + +that unit because of this +poisoning effect. + +So basically, the monopolist +is underselling, + +underproducing. + +In general, monopolists will +underproduce goods. + +They'll sell too few goods +because to sell the right + +amount would not be +profit maximizing. + +Because remember, what's the +profits for the perfectly + +competitive firm? + +Profits for the perfectly +competitive firm? + +Well, we know the profits of +perfectly competitive firm. + +We know cost if they +sell 8 units. + +We know the cost function +is, the cost here + +is 12 plus Q squared. + +So if they sell 8 units, their +costs are 12 plus 64, + +which equals 76. + +Their revenues if they sell 8 +units are 8 units times the + +price of 16. + +8 units time the price +of 16, which is 128. + +So what are their profits? + +Their profits are 52. + +So their profits are 52. + +The monopolist's +profits are 60. + +So the monopolist is +better off than the + +competitive firm would be. + +The competitive firm would +only make profits of 52. + +Obviously the short run. + +The long run they +make no profits. + +But in the short run they +make profits of 52. + +The monopolist makes +profits of 60. + +So the monopolist is better off +than the competitive firm. + +The difference of course, is to +do so they cause a social + +deadweight loss. + +Questions about that? + +Yeah. + +AUDIENCE: Is that what the +OPEC is doing right now? + +JON GRUBER: I'm going to +come to that actually. + +Time out on that. + +Because OPEC is more +of an oligopoly. + +And we'll come to that when +we talk about that + +in a couple of lectures. + +But I want to talk about one +more thing before we stop, + +which is I want to talk about +the key assumption we made + +here, which was the monopolist +could only charge + +one price to everyone. + +In fact, we know that's +not true. + +In fact, we know in the world, +there's a large amount of what + +we call price discrimination. + +There's a large amount of +price discrimination. + +We know that for many goods, +different prices get charged + +to different consumers. + +If you ever tried to book an +airline ticket the last + +minute, you know exactly +what I mean. + +Basically, different prices +in many, many contexts get + +charged different consumers. + +Everything from discounts for +senior citizens, to higher + +price last-minute flights, to + +specials, two for one specials. + +People who buy two get +a special price on + +the third, et cetera. + +There's all sorts of price +discrimination just out there + +in the world. + +And in fact, there's very +few goods that are + +sold at just one price. + +McDonald's hamburger +is typically + +sold at just one price. + +They don't say like, fat people +got to pay more for + +McDonald's hamburgers +or something. + +But many, many goods we buy in +the real world are sold at + +many prices. + +And that's an example of a +price-discriminating firm. + +And here's the crazy part. + +Here's the crazy part. + +It turns out that a +price-discriminating + +monopolist maximizes +social welfare. + +A price-discriminating +monopolist is as good as a + +competitive outcome. + +How can that be? + +Let's go to Figure 14-6. + +Here's the price-discriminating + +monopolist. Now, the +price-discriminating + +monopolist, what does he do? + +This is a perfectly +price-discriminating + +monopolist, someone who can +charge a different price to + +every single consumer. + +Well, if you were a +price-discriminating + +monopolist, perfectly +price-discriminating + +monopolist and you could charge +a different price to + +every consumer, what do you +charge the first consumer? + +24. + +What do you charge the +second consumer? + +23. + +Third consumer, 22. + +You literally charge them their +willingness to pay. + +If you're perfectly +price-discriminating, then + +what you do is literally charge +every consumer exactly + +their willingness to pay. + +You say look, I know your +willingness to pay function. + +Your willingness pay function +is p is 24 minus Q. That's + +your willingness to +pay function. + +So I'm going to literally +charge you that. + +I know that about you, it's +stamped on your head. + +So I'm going to say, ah, you're +willing to pay 24 for + +the first unit, 23 for the +second, et cetera. + +In that case, what will the +perfectly price-discriminating + +monopolist do? + +Will they stop at 6 units? + +No, they won't. + +Because for that guy, there's +no poisoning effect. + +There's no reason to +stop at 6 units. + +That seventh unit, as we just +did the math, there's money to + +be made on that seventh unit. + +Because that seventh unit is +worth 17, but it only costs 14 + +to produce. + +So the perfectly discriminating +monopolist will + +sell it at 17. + +Likewise the eighth unit, people +willing to pay 16 and + +it cost 16 to produce. + +So they'll sell it or not. + +They're basically indifferent. + +So we typically say +they'll sell it. + +The point is, the perfectly +price-discriminating + +monopolist will work all the way +down the demand curve to + +the competitive outcome. + +They will move to the +competitive market outcome + +because there's no +poisoning effect. + +There's no reason not to. + +No reason not to sell +as many units. + +No reason not to climb the same +hill the competitive firm + +climbs and sell any unit where +the price exceeds the marginal + +cost. + +Well, what's interesting is +let's ask what's happened to + +social welfare with this +perfectly price-discriminating + +monopolist. Well, consumer +surplus is what? + +What's consumer surplus +with the perfectly + +price-discriminating +monopolist? + +Somebody raised their hand. + +Yeah. + +AUDIENCE: Zero. + +JON GRUBER: Zero. + +Why is it zero? + +AUDIENCE: Because they're +charged exactly + +how the value is. + +JON GRUBER: Exactly. + +Consumer surplus is defined +as willingness + +to pay minus price. + +But your price is set equal to +your willingness to pay. + +So by definition, consumer +surplus is 0. + +With a perfectly +price-discriminating + +monopolist, there's no +consumer surplus. + +But what's producer surplus? + +Same person, what's +producer surplus? + +AUDIENCE: Everything else. + +JON GRUBER: Everything else. + +A plus B plus C plus D plus E. +There's no deadweight loss. + +You get exactly the same social +welfare as you got with + +perfect competition. + +It's just divided differently. + +With perfect competition, +consumers got A plus B plus C. + +Producers got D plus E. + +With a perfectly +price-discriminating + +monopolist, the monopolist +gets everything. + +But the total shaded +area is the same. + +So really fascinating because +here we have the ultimate + +screw on consumers. + +We think about competition +as being the + +best thing for consumers. + +Lots of firms selling goods at a +competitive market where you + +can shop and do what's +best for you. + +It's not surprising intuitively +that that's the + +best thing for society. + +What's very surprising +intuitively is having a + +producer who can screw every +single consumer out of every + +penny they value something is +equally good for society. + +And why is that? + +That's because we've made a +particular assumption, which + +is social welfare is the sum +of producer surplus and + +consumer surplus. + +The linear sum. + +Since it's is sum, we don't care +in that function who gets + +the dollars. + +We just care about the total +amount of dollars, the total + +size of the pie. + +We don't care who gets what +slice of the pie, we just care + +about the total size +of the pie. + +And the total size of the pie +is the same with a perfectly + +price-discriminating +monopolist and + +a competitive firm. + +What this highlights is that +that's a pretty stupid way to + +think about social welfare. + +Clearly, we don't feel the same +way about a market where + +people get everything +they want and a + +market where people-- + +all they're willing to pay is +sucked out of them by a greedy + +monopolist. Clearly we don't. + +And that's why we're going to +need to think more richly + +about equity and think more +richly about the division of + +resources in society. + +Because it turns out that you +can have equally good outcomes + +from an efficiency perspective +that are very, very different + +from an equity perspective. + +And this is the first example +we'll see of that. + +What we'll do when we get +towards the end of the course + +lectures, like 23, 24, lectures +like that, we're + +going to start talking +about equity. + +And what are different rules we +can think of for dividing + +this pie that might give +us a different answer? + +OK, questions about that? + +All right. + +OK, so anyway, we'll +stop here then. + +Let's remember that perfectly +price-discriminating + +monopolist is obviously also +a silly concept just like a + +perfectly competitive firm's +a silly concept. + +What we're going to do next +time is come back and talk + +about price discrimination in +reality and what firms do to + +try to approximate this +golden outcome. \ No newline at end of file diff --git a/WfEQabCGAqI.txt b/WfEQabCGAqI.txt new file mode 100644 index 0000000000000000000000000000000000000000..e7e6ab994e49f632ef5af5a8414a4e57b6c2c969 --- /dev/null +++ b/WfEQabCGAqI.txt @@ -0,0 +1,7610 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu yesterday we've learned + + align:start position:0% +ocw.mit.edu yesterday we've learned + + + align:start position:0% +ocw.mit.edu yesterday we've learned +about flux and we've seen the first few + + align:start position:0% +about flux and we've seen the first few + + + align:start position:0% +about flux and we've seen the first few +examples of how to set up and compute + + align:start position:0% +examples of how to set up and compute + + + align:start position:0% +examples of how to set up and compute +integrals for flux of a vector field + + align:start position:0% +integrals for flux of a vector field + + + align:start position:0% +integrals for flux of a vector field +through a + + align:start position:0% +through a + + + align:start position:0% +through a +surface so remember the + + align:start position:0% +surface so remember the + + + align:start position:0% +surface so remember the +flux of a vector field + + align:start position:0% +flux of a vector field + + + align:start position:0% +flux of a vector field +F + + align:start position:0% +F + + + align:start position:0% +F +through a surface + + align:start position:0% + + + + align:start position:0% + +s is defined by taking the double + + align:start position:0% +s is defined by taking the double + + + align:start position:0% +s is defined by taking the double +integral on the + + align:start position:0% +integral on the + + + align:start position:0% +integral on the +surface of f. n DS where n is the unit + + align:start position:0% +surface of f. n DS where n is the unit + + + align:start position:0% +surface of f. n DS where n is the unit +normal to the surface and DS is the area + + align:start position:0% +normal to the surface and DS is the area + + + align:start position:0% +normal to the surface and DS is the area +element on the surface + + align:start position:0% +element on the surface + + + align:start position:0% +element on the surface +so as we've seen for various surfaces we + + align:start position:0% +so as we've seen for various surfaces we + + + align:start position:0% +so as we've seen for various surfaces we +have various formulas telling us what + + align:start position:0% +have various formulas telling us what + + + align:start position:0% +have various formulas telling us what +the normal Vector is and what the area + + align:start position:0% +the normal Vector is and what the area + + + align:start position:0% +the normal Vector is and what the area +element becomes for example on spheres + + align:start position:0% +element becomes for example on spheres + + + align:start position:0% +element becomes for example on spheres +we typically integrate with respect to + + align:start position:0% +we typically integrate with respect to + + + align:start position:0% +we typically integrate with respect to +Fe and Theta the latitude and longitude + + align:start position:0% +Fe and Theta the latitude and longitude + + + align:start position:0% +Fe and Theta the latitude and longitude +angles on a horizontal plane we would + + align:start position:0% +angles on a horizontal plane we would + + + align:start position:0% +angles on a horizontal plane we would +just end up integrating DX Dy and so on + + align:start position:0% +just end up integrating DX Dy and so on + + + align:start position:0% +just end up integrating DX Dy and so on +so at the end of lecture we saw a + + align:start position:0% +so at the end of lecture we saw a + + + align:start position:0% +so at the end of lecture we saw a +formula and a lot of you asked me how + + align:start position:0% +formula and a lot of you asked me how + + + align:start position:0% +formula and a lot of you asked me how +did we get it well we didn't get it yet + + align:start position:0% +did we get it well we didn't get it yet + + + align:start position:0% +did we get it well we didn't get it yet +so we going to try to explain where it + + align:start position:0% +so we going to try to explain where it + + + align:start position:0% +so we going to try to explain where it +comes from and why it + + align:start position:0% +comes from and why it + + + align:start position:0% +comes from and why it +works okay so the case we want to look + + align:start position:0% +works okay so the case we want to look + + + align:start position:0% +works okay so the case we want to look +at is if s is the + + align:start position:0% +at is if s is the + + + align:start position:0% +at is if s is the +graph of a + + align:start position:0% + + + + align:start position:0% + +function so you know it's given by Z + + align:start position:0% +function so you know it's given by Z + + + align:start position:0% +function so you know it's given by Z +equals some function in terms of X and Y + + align:start position:0% + + + + align:start position:0% + +so our surface is out + + align:start position:0% +so our surface is out + + + align:start position:0% +so our surface is out +here Z is a function of X and Y and X + + align:start position:0% +here Z is a function of X and Y and X + + + align:start position:0% +here Z is a function of X and Y and X +and + + align:start position:0% +and + + + align:start position:0% +and +Y will range over some domain in the XY + + align:start position:0% +Y will range over some domain in the XY + + + align:start position:0% +Y will range over some domain in the XY +plane namely well the region that's the + + align:start position:0% + + + + align:start position:0% + +shadow + + align:start position:0% +shadow + + + align:start position:0% +shadow +of the surface on the XY plane + + align:start position:0% + + + + align:start position:0% + +so I said that we'll have a formula for + + align:start position:0% +so I said that we'll have a formula for + + + align:start position:0% +so I said that we'll have a formula for +NDS which will end up being plusus minus + + align:start position:0% +NDS which will end up being plusus minus + + + align:start position:0% +NDS which will end up being plusus minus +f subx - F suby 1 DX d + + align:start position:0% +f subx - F suby 1 DX d + + + align:start position:0% +f subx - F suby 1 DX d +y so that we will set up and evaluate + + align:start position:0% +y so that we will set up and evaluate + + + align:start position:0% +y so that we will set up and evaluate +the integral in terms of X and Y + + align:start position:0% +the integral in terms of X and Y + + + align:start position:0% +the integral in terms of X and Y +replacing every time we see Z we will + + align:start position:0% +replacing every time we see Z we will + + + align:start position:0% +replacing every time we see Z we will +replace it by F of XY whatever the + + align:start position:0% +replace it by F of XY whatever the + + + align:start position:0% +replace it by F of XY whatever the +formula for f might + + align:start position:0% +formula for f might + + + align:start position:0% +formula for f might +be so by the way I mean see if actually + + align:start position:0% +be so by the way I mean see if actually + + + align:start position:0% +be so by the way I mean see if actually +if we look at a very easy case where + + align:start position:0% +if we look at a very easy case where + + + align:start position:0% +if we look at a very easy case where +this is just a horizontal plane so Z + + align:start position:0% +this is just a horizontal plane so Z + + + align:start position:0% +this is just a horizontal plane so Z +equals constant the function is just a + + align:start position:0% +equals constant the function is just a + + + align:start position:0% +equals constant the function is just a +constant well the partial derivatives + + align:start position:0% +constant well the partial derivatives + + + align:start position:0% +constant well the partial derivatives +become just zero you get 0 0 1 DX Dy + + align:start position:0% +become just zero you get 0 0 1 DX Dy + + + align:start position:0% +become just zero you get 0 0 1 DX Dy +that's what you would expect for a + + align:start position:0% +that's what you would expect for a + + + align:start position:0% +that's what you would expect for a +horizontal plane just from common sense + + align:start position:0% +horizontal plane just from common sense + + + align:start position:0% +horizontal plane just from common sense +so this is more interesting of course if + + align:start position:0% +so this is more interesting of course if + + + align:start position:0% +so this is more interesting of course if +a function is more + + align:start position:0% +a function is more + + + align:start position:0% +a function is more +interesting so how do we get that where + + align:start position:0% +interesting so how do we get that where + + + align:start position:0% +interesting so how do we get that where +does this come + + align:start position:0% + + + + align:start position:0% + +from so so we need to figure out for a + + align:start position:0% +from so so we need to figure out for a + + + align:start position:0% +from so so we need to figure out for a +small piece of our surface what will be + + align:start position:0% +small piece of our surface what will be + + + align:start position:0% +small piece of our surface what will be +n Delta s if you + + align:start position:0% +n Delta s if you + + + align:start position:0% +n Delta s if you +want so let's say that we + + align:start position:0% +want so let's say that we + + + align:start position:0% +want so let's say that we +take a small rectangle in + + align:start position:0% +take a small rectangle in + + + align:start position:0% +take a small rectangle in +here corresponding + + align:start position:0% + + + + align:start position:0% + +to sides Delta X + + align:start position:0% +to sides Delta X + + + align:start position:0% +to sides Delta X +and Delta Y and we look at the piece of + + align:start position:0% +and Delta Y and we look at the piece of + + + align:start position:0% +and Delta Y and we look at the piece of +surface that's above + + align:start position:0% +surface that's above + + + align:start position:0% +surface that's above +that well the question we have now is + + align:start position:0% +that well the question we have now is + + + align:start position:0% +that well the question we have now is +what is the area of this little piece of + + align:start position:0% +what is the area of this little piece of + + + align:start position:0% +what is the area of this little piece of +surface and what is its normal + + align:start position:0% +surface and what is its normal + + + align:start position:0% +surface and what is its normal +Vector so observe this little piece up + + align:start position:0% +Vector so observe this little piece up + + + align:start position:0% +Vector so observe this little piece up +here if it's small enough it will look + + align:start position:0% +here if it's small enough it will look + + + align:start position:0% +here if it's small enough it will look +like a parallelogram Ian it might be + + align:start position:0% +like a parallelogram Ian it might be + + + align:start position:0% +like a parallelogram Ian it might be +slightly curvy but roughly it looks like + + align:start position:0% +slightly curvy but roughly it looks like + + + align:start position:0% +slightly curvy but roughly it looks like +a parallelogram in space and so we've + + align:start position:0% +a parallelogram in space and so we've + + + align:start position:0% +a parallelogram in space and so we've +seen how to find the area of a + + align:start position:0% +seen how to find the area of a + + + align:start position:0% +seen how to find the area of a +parallelogram in space using cross + + align:start position:0% +parallelogram in space using cross + + + align:start position:0% +parallelogram in space using cross +product right if we can figure out what + + align:start position:0% +product right if we can figure out what + + + align:start position:0% +product right if we can figure out what +are the vectors for this side and that + + align:start position:0% +are the vectors for this side and that + + + align:start position:0% +are the vectors for this side and that +side then taking the cross product will + + align:start position:0% +side then taking the cross product will + + + align:start position:0% +side then taking the cross product will +give us and taking the magnitude of the + + align:start position:0% +give us and taking the magnitude of the + + + align:start position:0% +give us and taking the magnitude of the +cross product will give us the area more + + align:start position:0% +cross product will give us the area more + + + align:start position:0% +cross product will give us the area more +the cross product also gives us the + + align:start position:0% +the cross product also gives us the + + + align:start position:0% +the cross product also gives us the +normal Direction so in fact the cross + + align:start position:0% +normal Direction so in fact the cross + + + align:start position:0% +normal Direction so in fact the cross +product gives us two in one it gives us + + align:start position:0% +product gives us two in one it gives us + + + align:start position:0% +product gives us two in one it gives us +the normal Direction and the area + + align:start position:0% +the normal Direction and the area + + + align:start position:0% +the normal Direction and the area +element and that's why I say that we + + align:start position:0% +element and that's why I say that we + + + align:start position:0% +element and that's why I say that we +will have an easy formula for n DS while + + align:start position:0% +will have an easy formula for n DS while + + + align:start position:0% +will have an easy formula for n DS while +n and DS taken separately are more + + align:start position:0% +n and DS taken separately are more + + + align:start position:0% +n and DS taken separately are more +complicated because you'd have to + + align:start position:0% +complicated because you'd have to + + + align:start position:0% +complicated because you'd have to +actually take the length of the + + align:start position:0% +actually take the length of the + + + align:start position:0% +actually take the length of the +direction of this + + align:start position:0% +direction of this + + + align:start position:0% +direction of this +gy okay so let's carry out this program + + align:start position:0% + + + + align:start position:0% + +so let's + + align:start position:0% +so let's + + + align:start position:0% +so let's +say I'm going to + + align:start position:0% +say I'm going to + + + align:start position:0% +say I'm going to +look at a small piece + + align:start position:0% +look at a small piece + + + align:start position:0% +look at a small piece +of the XZ plane the sorry the XY plane + + align:start position:0% +of the XZ plane the sorry the XY plane + + + align:start position:0% +of the XZ plane the sorry the XY plane +so here I have Delta X I have Delta + + align:start position:0% +so here I have Delta X I have Delta + + + align:start position:0% +so here I have Delta X I have Delta +Y and I'm starting at some point XY now + + align:start position:0% +Y and I'm starting at some point XY now + + + align:start position:0% +Y and I'm starting at some point XY now +above that I will have a parallelogram + + align:start position:0% +above that I will have a parallelogram + + + align:start position:0% +above that I will have a parallelogram +on my Surface + + align:start position:0% + + + + align:start position:0% + +I need to figure out so this point here + + align:start position:0% +I need to figure out so this point here + + + align:start position:0% +I need to figure out so this point here +the point where I start I know what it + + align:start position:0% +the point where I start I know what it + + + align:start position:0% +the point where I start I know what it +is it's just x y and well Z is f of x + + align:start position:0% +is it's just x y and well Z is f of x + + + align:start position:0% +is it's just x y and well Z is f of x +y so now what I want to find actually is + + align:start position:0% +y so now what I want to find actually is + + + align:start position:0% +y so now what I want to find actually is +what are these two vectors let's call + + align:start position:0% +what are these two vectors let's call + + + align:start position:0% +what are these two vectors let's call +them u and + + align:start position:0% +them u and + + + align:start position:0% +them u and +v that correspond to moving a bit in the + + align:start position:0% +v that correspond to moving a bit in the + + + align:start position:0% +v that correspond to moving a bit in the +X direction or in the y direction and + + align:start position:0% +X direction or in the y direction and + + + align:start position:0% +X direction or in the y direction and +then U cross V + + align:start position:0% + + + + align:start position:0% + +will be well in terms of the magnitude + + align:start position:0% +will be well in terms of the magnitude + + + align:start position:0% +will be well in terms of the magnitude +of this guy will just be the little + + align:start position:0% +of this guy will just be the little + + + align:start position:0% +of this guy will just be the little +piece of surface area Delta + + align:start position:0% +piece of surface area Delta + + + align:start position:0% +piece of surface area Delta +s and in terms of Direction it will be + + align:start position:0% +s and in terms of Direction it will be + + + align:start position:0% +s and in terms of Direction it will be +normal to the surface so it will be my + + align:start position:0% +normal to the surface so it will be my + + + align:start position:0% +normal to the surface so it will be my +actually I will get just Delta s times + + align:start position:0% +actually I will get just Delta s times + + + align:start position:0% +actually I will get just Delta s times +my normal + + align:start position:0% +my normal + + + align:start position:0% +my normal +V well up to sign because depending on + + align:start position:0% +V well up to sign because depending on + + + align:start position:0% +V well up to sign because depending on +whether I do U cross V or V cross U I + + align:start position:0% +whether I do U cross V or V cross U I + + + align:start position:0% +whether I do U cross V or V cross U I +might get the normal Vector in the + + align:start position:0% +might get the normal Vector in the + + + align:start position:0% +might get the normal Vector in the +direction I want or in the opposite + + align:start position:0% +direction I want or in the opposite + + + align:start position:0% +direction I want or in the opposite +direction but we'll take care of that + + align:start position:0% +direction but we'll take care of that + + + align:start position:0% +direction but we'll take care of that +later up to + + align:start position:0% +later up to + + + align:start position:0% +later up to +sign okay so let's find u and v in case + + align:start position:0% +sign okay so let's find u and v in case + + + align:start position:0% +sign okay so let's find u and v in case +you have trouble with that small picture + + align:start position:0% +you have trouble with that small picture + + + align:start position:0% +you have trouble with that small picture +then I have a better one + + align:start position:0% + + + + align:start position:0% + +here let's keep it just in case you know + + align:start position:0% +here let's keep it just in case you know + + + align:start position:0% +here let's keep it just in case you know +in case this one gets really too + + align:start position:0% +in case this one gets really too + + + align:start position:0% +in case this one gets really too +cluttered um it really represents the + + align:start position:0% +cluttered um it really represents the + + + align:start position:0% +cluttered um it really represents the +same + + align:start position:0% +same + + + align:start position:0% +same +thing okay so let's try to figure out + + align:start position:0% +thing okay so let's try to figure out + + + align:start position:0% +thing okay so let's try to figure out +these vectors u and v + + align:start position:0% + + + + align:start position:0% + +so the vector U starts at the point x y + + align:start position:0% +so the vector U starts at the point x y + + + align:start position:0% +so the vector U starts at the point x y +f of x + + align:start position:0% + + + + align:start position:0% + +y and it goes two whereas its head well + + align:start position:0% +y and it goes two whereas its head well + + + align:start position:0% +y and it goes two whereas its head well +I'll have moved X by Delta X so X Plus + + align:start position:0% +I'll have moved X by Delta X so X Plus + + + align:start position:0% +I'll have moved X by Delta X so X Plus +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +X Y doesn't change and of course the Z + + align:start position:0% +X Y doesn't change and of course the Z + + + align:start position:0% +X Y doesn't change and of course the Z +coordinate has to change it becomes f of + + align:start position:0% +coordinate has to change it becomes f of + + + align:start position:0% +coordinate has to change it becomes f of +x plus Delta X X and + + align:start position:0% +x plus Delta X X and + + + align:start position:0% +x plus Delta X X and +Y now how does f change if I change x a + + align:start position:0% +Y now how does f change if I change x a + + + align:start position:0% +Y now how does f change if I change x a +little bit well we've seen that it's + + align:start position:0% +little bit well we've seen that it's + + + align:start position:0% +little bit well we've seen that it's +given by the partial derivative F subx + + align:start position:0% +given by the partial derivative F subx + + + align:start position:0% +given by the partial derivative F subx +so this is approximately equal to f ofx + + align:start position:0% +so this is approximately equal to f ofx + + + align:start position:0% +so this is approximately equal to f ofx +y plus Delta x * F subx at the given + + align:start position:0% +y plus Delta x * F subx at the given + + + align:start position:0% +y plus Delta x * F subx at the given +point XY I'm not going to add it because + + align:start position:0% +point XY I'm not going to add it because + + + align:start position:0% +point XY I'm not going to add it because +you know notation is already long + + align:start position:0% +you know notation is already long + + + align:start position:0% +you know notation is already long +enough so that means my Vector U is well + + align:start position:0% +enough so that means my Vector U is well + + + align:start position:0% +enough so that means my Vector U is well +approximately because I'm using this + + align:start position:0% +approximately because I'm using this + + + align:start position:0% +approximately because I'm using this +linear + + align:start position:0% +linear + + + align:start position:0% +linear +approximation Delta x z and F subx time + + align:start position:0% +approximation Delta x z and F subx time + + + align:start position:0% +approximation Delta x z and F subx time +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +X okay is that okay with + + align:start position:0% +X okay is that okay with + + + align:start position:0% +X okay is that okay with +everyone + + align:start position:0% + + + + align:start position:0% + +good now what about V well V works the + + align:start position:0% +good now what about V well V works the + + + align:start position:0% +good now what about V well V works the +same way okay so I'm not going to do all + + align:start position:0% +same way okay so I'm not going to do all + + + align:start position:0% +same way okay so I'm not going to do all +the details when I move from here to + + align:start position:0% +the details when I move from here to + + + align:start position:0% +the details when I move from here to +here well X doesn't change and Y changes + + align:start position:0% +here well X doesn't change and Y changes + + + align:start position:0% +here well X doesn't change and Y changes +by Delta y + + align:start position:0% +by Delta y + + + align:start position:0% +by Delta y +so X component nothing + + align:start position:0% +so X component nothing + + + align:start position:0% +so X component nothing +happens y component changes by Delta + + align:start position:0% +happens y component changes by Delta + + + align:start position:0% +happens y component changes by Delta +Y what about the Z component well F + + align:start position:0% +Y what about the Z component well F + + + align:start position:0% +Y what about the Z component well F +changes by F sub y * Delta y That's How + + align:start position:0% +changes by F sub y * Delta y That's How + + + align:start position:0% +changes by F sub y * Delta y That's How +F changes if I increase y by Delta + + align:start position:0% + + + + align:start position:0% + +y okay so I have my two sides now I can + + align:start position:0% +y okay so I have my two sides now I can + + + align:start position:0% +y okay so I have my two sides now I can +can take a cross + + align:start position:0% + + + + align:start position:0% + +product well maybe I will first sorry + + align:start position:0% +product well maybe I will first sorry + + + align:start position:0% +product well maybe I will first sorry +Factor something + + align:start position:0% +Factor something + + + align:start position:0% +Factor something +out see I can rewrite this as 1 f subx * + + align:start position:0% +out see I can rewrite this as 1 f subx * + + + align:start position:0% +out see I can rewrite this as 1 f subx * +Delta X and this one I will reite as 01 + + align:start position:0% +Delta X and this one I will reite as 01 + + + align:start position:0% +Delta X and this one I will reite as 01 +F sub y Delta Y and so now the cross + + align:start position:0% +F sub y Delta Y and so now the cross + + + align:start position:0% +F sub y Delta Y and so now the cross +product so n Delta s up to sign it's + + align:start position:0% +product so n Delta s up to sign it's + + + align:start position:0% +product so n Delta s up to sign it's +going to be U CR v u V well so we'll + + align:start position:0% +going to be U CR v u V well so we'll + + + align:start position:0% +going to be U CR v u V well so we'll +have to do the cross product and we'll + + align:start position:0% +have to do the cross product and we'll + + + align:start position:0% +have to do the cross product and we'll +have a Delta X Delta y coming out okay + + align:start position:0% +have a Delta X Delta y coming out okay + + + align:start position:0% +have a Delta X Delta y coming out okay +I'm just you know saving myself a + + align:start position:0% +I'm just you know saving myself a + + + align:start position:0% +I'm just you know saving myself a +trouble of writing a lot of Delta X and + + align:start position:0% +trouble of writing a lot of Delta X and + + + align:start position:0% +trouble of writing a lot of Delta X and +Delta y's but if you prefer you can just + + align:start position:0% +Delta y's but if you prefer you can just + + + align:start position:0% +Delta y's but if you prefer you can just +do directly this cross product + + align:start position:0% + + + + align:start position:0% + +there okay so let's compute this cross + + align:start position:0% +there okay so let's compute this cross + + + align:start position:0% +there okay so let's compute this cross +product well the I component is 0 minus + + align:start position:0% +product well the I component is 0 minus + + + align:start position:0% +product well the I component is 0 minus +F + + align:start position:0% +F + + + align:start position:0% +F +subx the Y component is going to be well + + align:start position:0% +subx the Y component is going to be well + + + align:start position:0% +subx the Y component is going to be well +F sub y minus 0 but with a minus sign in + + align:start position:0% +F sub y minus 0 but with a minus sign in + + + align:start position:0% +F sub y minus 0 but with a minus sign in +front of everything so negative f sub y + + align:start position:0% +front of everything so negative f sub y + + + align:start position:0% +front of everything so negative f sub y +and the Z component will be just one + + align:start position:0% +and the Z component will be just one + + + align:start position:0% +and the Z component will be just one +times Delta X Delta + + align:start position:0% + + + + align:start position:0% + +y okay does that make sense + + align:start position:0% +y okay does that make sense + + + align:start position:0% +y okay does that make sense +for + + align:start position:0% +for + + + align:start position:0% +for +yes very + + align:start position:0% +yes very + + + align:start position:0% +yes very +good and so now when we just take you + + align:start position:0% +good and so now when we just take you + + + align:start position:0% +good and so now when we just take you +know we shrink this rectangle we shrink + + align:start position:0% +know we shrink this rectangle we shrink + + + align:start position:0% +know we shrink this rectangle we shrink +Delta X and Delta y to zero that's how + + align:start position:0% +Delta X and Delta y to zero that's how + + + align:start position:0% +Delta X and Delta y to zero that's how +we get this formula for NDS equals FX + + align:start position:0% +we get this formula for NDS equals FX + + + align:start position:0% +we get this formula for NDS equals FX +negative fy1 DX d + + align:start position:0% +negative fy1 DX d + + + align:start position:0% +negative fy1 DX d +y well plus minus because it's it's up + + align:start position:0% +y well plus minus because it's it's up + + + align:start position:0% +y well plus minus because it's it's up +to us to choose whether we want to take + + align:start position:0% +to us to choose whether we want to take + + + align:start position:0% +to us to choose whether we want to take +the normal Vector pointing up or down so + + align:start position:0% +the normal Vector pointing up or down so + + + align:start position:0% +the normal Vector pointing up or down so +see if you take this + + align:start position:0% +see if you take this + + + align:start position:0% +see if you take this +convention then the Z component of NDS + + align:start position:0% +convention then the Z component of NDS + + + align:start position:0% +convention then the Z component of NDS +is positive so that corresponds to + + align:start position:0% +is positive so that corresponds to + + + align:start position:0% +is positive so that corresponds to +normal Vector pointing up + + align:start position:0% +normal Vector pointing up + + + align:start position:0% +normal Vector pointing up +if you take the opposite signs then the + + align:start position:0% +if you take the opposite signs then the + + + align:start position:0% +if you take the opposite signs then the +Z component will be negative that means + + align:start position:0% +Z component will be negative that means + + + align:start position:0% +Z component will be negative that means +your normal Vector points + + align:start position:0% +your normal Vector points + + + align:start position:0% +your normal Vector points +down Okay so this one is with and + + align:start position:0% +down Okay so this one is with and + + + align:start position:0% +down Okay so this one is with and +pointing + + align:start position:0% + + + + align:start position:0% + +up I mean when I say up of course it's + + align:start position:0% +up I mean when I say up of course it's + + + align:start position:0% +up I mean when I say up of course it's +still perpendicular to the surface you + + align:start position:0% +still perpendicular to the surface you + + + align:start position:0% +still perpendicular to the surface you +know the surface is really has a big + + align:start position:0% +know the surface is really has a big + + + align:start position:0% +know the surface is really has a big +slope then it's it's not really going to + + align:start position:0% +slope then it's it's not really going to + + + align:start position:0% +slope then it's it's not really going to +go all that much up but more up than + + align:start position:0% + + + + align:start position:0% + +down okay + + align:start position:0% +down okay + + + align:start position:0% +down okay +so that's how we get that formula any + + align:start position:0% + + + + align:start position:0% + +questions no okay so that's a really + + align:start position:0% +questions no okay so that's a really + + + align:start position:0% +questions no okay so that's a really +useful formula so you don't really need + + align:start position:0% +useful formula so you don't really need + + + align:start position:0% +useful formula so you don't really need +to remember all the details of how we + + align:start position:0% +to remember all the details of how we + + + align:start position:0% +to remember all the details of how we +got it but please remember that + + align:start position:0% + + + + align:start position:0% + +formula Let's do an example actually + + align:start position:0% + + + + align:start position:0% + +so let's say I want to find the flux of + + align:start position:0% +so let's say I want to find the flux of + + + align:start position:0% +so let's say I want to find the flux of +the vector field Z * K so it's a + + align:start position:0% +the vector field Z * K so it's a + + + align:start position:0% +the vector field Z * K so it's a +vertical Vector + + align:start position:0% +vertical Vector + + + align:start position:0% +vertical Vector +field + + align:start position:0% +field + + + align:start position:0% +field +through the + + align:start position:0% + + + + align:start position:0% + +portion of the + + align:start position:0% + + + + align:start position:0% + +paraboloid zal X2 + + + align:start position:0% +paraboloid zal X2 + + + + align:start position:0% +paraboloid zal X2 + +y^2 that lives above the unit + + align:start position:0% + + + + align:start position:0% + +dis okay so what does that + + align:start position:0% +dis okay so what does that + + + align:start position:0% +dis okay so what does that +mean z = x² + y^2 well we've seen it + + align:start position:0% +mean z = x² + y^2 well we've seen it + + + align:start position:0% +mean z = x² + y^2 well we've seen it +many times okay it's this parabol + + align:start position:0% +many times okay it's this parabol + + + align:start position:0% +many times okay it's this parabol +pointing + + align:start position:0% +pointing + + + align:start position:0% +pointing +up above the unit dis means I only care + + align:start position:0% +up above the unit dis means I only care + + + align:start position:0% +up above the unit dis means I only care +about I don't care about this infinite + + align:start position:0% +about I don't care about this infinite + + + align:start position:0% +about I don't care about this infinite +surface I will actually stop when I + + align:start position:0% +surface I will actually stop when I + + + align:start position:0% +surface I will actually stop when I +hit a radius of one away from the Z + + align:start position:0% +hit a radius of one away from the Z + + + align:start position:0% +hit a radius of one away from the Z +AIS + + align:start position:0% +AIS + + + align:start position:0% +AIS +and so now I have my Vector field which + + align:start position:0% +and so now I have my Vector field which + + + align:start position:0% +and so now I have my Vector field which +is going to point over all up + + align:start position:0% + + + + align:start position:0% + +because well it's Z * K so the more Z is + + align:start position:0% +because well it's Z * K so the more Z is + + + align:start position:0% +because well it's Z * K so the more Z is +positive the more your vector field goes + + align:start position:0% +positive the more your vector field goes + + + align:start position:0% +positive the more your vector field goes +up of course if Z were negative then it + + align:start position:0% +up of course if Z were negative then it + + + align:start position:0% +up of course if Z were negative then it +would Point down but we live + + align:start position:0% +would Point down but we live + + + align:start position:0% +would Point down but we live +above so actually a quick opinion poll + + align:start position:0% +above so actually a quick opinion poll + + + align:start position:0% +above so actually a quick opinion poll +what do you think the flux should be + + align:start position:0% +what do you think the flux should be + + + align:start position:0% +what do you think the flux should be +should be positive zero negative we + + align:start position:0% +should be positive zero negative we + + + align:start position:0% +should be positive zero negative we +don't know + + align:start position:0% + + + + align:start position:0% + +okay so I see some I don't know I see + + align:start position:0% +okay so I see some I don't know I see + + + align:start position:0% +okay so I see some I don't know I see +some negative and I see some positive so + + align:start position:0% +some negative and I see some positive so + + + align:start position:0% +some negative and I see some positive so +of course I didn't tell you which way + + align:start position:0% +of course I didn't tell you which way + + + align:start position:0% +of course I didn't tell you which way +I'm orienting my paraboloid so so far + + align:start position:0% +I'm orienting my paraboloid so so far + + + align:start position:0% +I'm orienting my paraboloid so so far +both answers are correct the only one + + align:start position:0% +both answers are correct the only one + + + align:start position:0% +both answers are correct the only one +that's probably not correct is zero + + align:start position:0% +that's probably not correct is zero + + + align:start position:0% +that's probably not correct is zero +because no matter which way you choose + + align:start position:0% +because no matter which way you choose + + + align:start position:0% +because no matter which way you choose +to orient it you should get something + + align:start position:0% +to orient it you should get something + + + align:start position:0% +to orient it you should get something +it's not it's not looking like it will + + align:start position:0% +it's not it's not looking like it will + + + align:start position:0% +it's not it's not looking like it will +be zero so let's say that I'm going to + + align:start position:0% +be zero so let's say that I'm going to + + + align:start position:0% +be zero so let's say that I'm going to +do it with a normal pointing upwards + + align:start position:0% + + + + align:start position:0% + +so second + + align:start position:0% + + + + align:start position:0% + +chance okay I see some people changing + + align:start position:0% +chance okay I see some people changing + + + align:start position:0% +chance okay I see some people changing +back and forth between one and two um + + align:start position:0% +back and forth between one and two um + + + align:start position:0% +back and forth between one and two um +okay so let's draw a picture which one + + align:start position:0% +okay so let's draw a picture which one + + + align:start position:0% +okay so let's draw a picture which one +is pointing upwards well let's look at + + align:start position:0% +is pointing upwards well let's look at + + + align:start position:0% +is pointing upwards well let's look at +the bottom point the normal Vector + + align:start position:0% +the bottom point the normal Vector + + + align:start position:0% +the bottom point the normal Vector +pointing up here we know what it means + + align:start position:0% +pointing up here we know what it means + + + align:start position:0% +pointing up here we know what it means +it's this guy and so if you continue to + + align:start position:0% +it's this guy and so if you continue to + + + align:start position:0% +it's this guy and so if you continue to +follow your normal Vector see they're + + align:start position:0% +follow your normal Vector see they're + + + align:start position:0% +follow your normal Vector see they're +actually pointing up and into the + + align:start position:0% +actually pointing up and into the + + + align:start position:0% +actually pointing up and into the +paraboloid okay and I claim that the + + align:start position:0% +paraboloid okay and I claim that the + + + align:start position:0% +paraboloid okay and I claim that the +answer should be positive because the + + align:start position:0% +answer should be positive because the + + + align:start position:0% +answer should be positive because the +vector field is crossing our paraboloid + + align:start position:0% +vector field is crossing our paraboloid + + + align:start position:0% +vector field is crossing our paraboloid +going upwards going from the outside out + + align:start position:0% +going upwards going from the outside out + + + align:start position:0% +going upwards going from the outside out +and Below to the inside and up side so + + align:start position:0% +and Below to the inside and up side so + + + align:start position:0% +and Below to the inside and up side so +in the direction that we're counting + + align:start position:0% + + + + align:start position:0% + +positively well we'll see how it turns + + align:start position:0% +positively well we'll see how it turns + + + align:start position:0% +positively well we'll see how it turns +out when we do the calculation + + align:start position:0% + + + + align:start position:0% + +Okay so we have to + + align:start position:0% +Okay so we have to + + + align:start position:0% +Okay so we have to +compute the integral for + + align:start position:0% +compute the integral for + + + align:start position:0% +compute the integral for +flux double integral of the surface of + + align:start position:0% +flux double integral of the surface of + + + align:start position:0% +flux double integral of the surface of +f. n + + align:start position:0% +f. n + + + align:start position:0% +f. n +DS is going to be okay so what are we + + align:start position:0% +DS is going to be okay so what are we + + + align:start position:0% +DS is going to be okay so what are we +going to + + align:start position:0% +going to + + + align:start position:0% +going to +do well F we said is 0 0 + + align:start position:0% +do well F we said is 0 0 + + + align:start position:0% +do well F we said is 0 0 +Z what is NDS well let's use our brand + + align:start position:0% +Z what is NDS well let's use our brand + + + align:start position:0% +Z what is NDS well let's use our brand +new + + align:start position:0% +new + + + align:start position:0% +new +formula so it says f subx F sub y 1 DX d + + align:start position:0% +formula so it says f subx F sub y 1 DX d + + + align:start position:0% +formula so it says f subx F sub y 1 DX d +y what what is little F in + + align:start position:0% +y what what is little F in + + + align:start position:0% +y what what is little F in +here it's X2 + y^2 okay so when we're + + align:start position:0% +here it's X2 + y^2 okay so when we're + + + align:start position:0% +here it's X2 + y^2 okay so when we're +using this formula we need to know + + align:start position:0% +using this formula we need to know + + + align:start position:0% +using this formula we need to know +what's the you know what little F stands + + align:start position:0% +what's the you know what little F stands + + + align:start position:0% +what's the you know what little F stands +for is whatever the formula is for Z as + + align:start position:0% +for is whatever the formula is for Z as + + + align:start position:0% +for is whatever the formula is for Z as +a function of X and + + align:start position:0% + + + + align:start position:0% + +Y so we + + align:start position:0% +Y so we + + + align:start position:0% +Y so we +take x² + y^ 2 and we take the partial + + align:start position:0% +take x² + y^ 2 and we take the partial + + + align:start position:0% +take x² + y^ 2 and we take the partial +derivatives with minus signs we get -2X + + align:start position:0% +derivatives with minus signs we get -2X + + + align:start position:0% +derivatives with minus signs we get -2X +-2 y and one DX Dy well of course here + + align:start position:0% +-2 y and one DX Dy well of course here + + + align:start position:0% +-2 y and one DX Dy well of course here +it didn't really matter because we're + + align:start position:0% +it didn't really matter because we're + + + align:start position:0% +it didn't really matter because we're +going to dot them with zero so actually + + align:start position:0% +going to dot them with zero so actually + + + align:start position:0% +going to dot them with zero so actually +even if we had make you know if even if + + align:start position:0% +even if we had make you know if even if + + + align:start position:0% +even if we had make you know if even if +we had made a mistake we somehow + + align:start position:0% +we had made a mistake we somehow + + + align:start position:0% +we had made a mistake we somehow +wouldn't have had to pay the price but + + align:start position:0% +wouldn't have had to pay the price but + + + align:start position:0% +wouldn't have had to pay the price but +still okay so we'll end up with double + + align:start position:0% +still okay so we'll end up with double + + + align:start position:0% +still okay so we'll end up with double +integral on S of Z DX + + align:start position:0% +integral on S of Z DX + + + align:start position:0% +integral on S of Z DX +Dy now what do we do with that well we + + align:start position:0% +Dy now what do we do with that well we + + + align:start position:0% +Dy now what do we do with that well we +have too many things we need to get rid + + align:start position:0% +have too many things we need to get rid + + + align:start position:0% +have too many things we need to get rid +of Z so let's use zal = x + y sare once + + align:start position:0% + + + + align:start position:0% + +more okay + + align:start position:0% + + + + align:start position:0% + +so that becomes double integral of X2 + + + align:start position:0% +so that becomes double integral of X2 + + + + align:start position:0% +so that becomes double integral of X2 + +y^2 DX d y and here see we're using the + + align:start position:0% +y^2 DX d y and here see we're using the + + + align:start position:0% +y^2 DX d y and here see we're using the +fact that we're only looking at things + + align:start position:0% +fact that we're only looking at things + + + align:start position:0% +fact that we're only looking at things +that are on the surface it's not like in + + align:start position:0% +that are on the surface it's not like in + + + align:start position:0% +that are on the surface it's not like in +triple integral you could never do that + + align:start position:0% +triple integral you could never do that + + + align:start position:0% +triple integral you could never do that +because Z X and Y are independent here + + align:start position:0% +because Z X and Y are independent here + + + align:start position:0% +because Z X and Y are independent here +they're related by the equation of a + + align:start position:0% +they're related by the equation of a + + + align:start position:0% +they're related by the equation of a +surface sorry if I sound like I'm you + + align:start position:0% +surface sorry if I sound like I'm you + + + align:start position:0% +surface sorry if I sound like I'm you +know renting + + align:start position:0% +know renting + + + align:start position:0% +know renting +but I know from experience this is where + + align:start position:0% +but I know from experience this is where + + + align:start position:0% +but I know from experience this is where +you know one of the most sticky and + + align:start position:0% +you know one of the most sticky and + + + align:start position:0% +you know one of the most sticky and +tricky points is actually + + align:start position:0% +tricky points is actually + + + align:start position:0% +tricky points is actually +that's okay so now how will we actually + + align:start position:0% +that's okay so now how will we actually + + + align:start position:0% +that's okay so now how will we actually +integrate that well now that we have + + align:start position:0% +integrate that well now that we have + + + align:start position:0% +integrate that well now that we have +just X and Y we should figure out what's + + align:start position:0% +just X and Y we should figure out what's + + + align:start position:0% +just X and Y we should figure out what's +the range for X and Y well the range for + + align:start position:0% +the range for X and Y well the range for + + + align:start position:0% +the range for X and Y well the range for +X and Y is going to be the shadow of our + + align:start position:0% +X and Y is going to be the shadow of our + + + align:start position:0% +X and Y is going to be the shadow of our +region it's going to be this unit disc + + align:start position:0% + + + + align:start position:0% + +okay so let me just do that for + + align:start position:0% + + + + align:start position:0% + +now and see here this is finally where + + align:start position:0% +now and see here this is finally where + + + align:start position:0% +now and see here this is finally where +I've left a world of surface integrals + + align:start position:0% +I've left a world of surface integrals + + + align:start position:0% +I've left a world of surface integrals +to go back to a usual double integral + + align:start position:0% +to go back to a usual double integral + + + align:start position:0% +to go back to a usual double integral +and now I have to set it up well I can + + align:start position:0% +and now I have to set it up well I can + + + align:start position:0% +and now I have to set it up well I can +do it this way with dxdy but it looks + + align:start position:0% +do it this way with dxdy but it looks + + + align:start position:0% +do it this way with dxdy but it looks +like there's a smarter thing to do okay + + align:start position:0% +like there's a smarter thing to do okay + + + align:start position:0% +like there's a smarter thing to do okay +I'm going to use actually polar + + align:start position:0% +I'm going to use actually polar + + + align:start position:0% +I'm going to use actually polar +coordinates so in fact I'm going to say + + align:start position:0% +coordinates so in fact I'm going to say + + + align:start position:0% +coordinates so in fact I'm going to say +this is double integral of R 2 * Rd D + + align:start position:0% +this is double integral of R 2 * Rd D + + + align:start position:0% +this is double integral of R 2 * Rd D +Theta I'm on the unit dis so R goes 0 to + + align:start position:0% +Theta I'm on the unit dis so R goes 0 to + + + align:start position:0% +Theta I'm on the unit dis so R goes 0 to +1 Theta goes 0 to 2 pi and if you do the + + align:start position:0% +1 Theta goes 0 to 2 pi and if you do the + + + align:start position:0% +1 Theta goes 0 to 2 pi and if you do the +calculation you'll find that this is + + align:start position:0% +calculation you'll find that this is + + + align:start position:0% +calculation you'll find that this is +going to be Pi / + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +okay any questions about the example + + align:start position:0% + + + + align:start position:0% + +yes okay how do I get how did I get this + + align:start position:0% +yes okay how do I get how did I get this + + + align:start position:0% +yes okay how do I get how did I get this +-2X and2 y so I want to use my formula + + align:start position:0% +-2X and2 y so I want to use my formula + + + align:start position:0% +-2X and2 y so I want to use my formula +for NDS okay my Surface is given by the + + align:start position:0% +for NDS okay my Surface is given by the + + + align:start position:0% +for NDS okay my Surface is given by the +graph of a function it's the graph of a + + align:start position:0% +graph of a function it's the graph of a + + + align:start position:0% +graph of a function it's the graph of a +function X2 + y^2 so I will use this + + align:start position:0% +function X2 + y^2 so I will use this + + + align:start position:0% +function X2 + y^2 so I will use this +formula that's up here I will take the + + align:start position:0% +formula that's up here I will take the + + + align:start position:0% +formula that's up here I will take the +function x s + y^2 and I will take its + + align:start position:0% +function x s + y^2 and I will take its + + + align:start position:0% +function x s + y^2 and I will take its +partial derivatives so if I take the + + align:start position:0% +partial derivatives so if I take the + + + align:start position:0% +partial derivatives so if I take the +partial of f so of X2 + y sare respect + + align:start position:0% +partial of f so of X2 + y sare respect + + + align:start position:0% +partial of f so of X2 + y sare respect +to X I get 2x so I put -2X and then same + + align:start position:0% +to X I get 2x so I put -2X and then same + + + align:start position:0% +to X I get 2x so I put -2X and then same +thing -2 y 1 DX d y yes + + align:start position:0% + + + + align:start position:0% + +uh which K hat Oh you mean the vector + + align:start position:0% +uh which K hat Oh you mean the vector + + + align:start position:0% +uh which K hat Oh you mean the vector +field well so it's a different part of + + align:start position:0% +field well so it's a different part of + + + align:start position:0% +field well so it's a different part of +the story okay so whenever you do a + + align:start position:0% +the story okay so whenever you do a + + + align:start position:0% +the story okay so whenever you do a +surface integral for flux you have two + + align:start position:0% +surface integral for flux you have two + + + align:start position:0% +surface integral for flux you have two +parts of the story one is the vector + + align:start position:0% +parts of the story one is the vector + + + align:start position:0% +parts of the story one is the vector +field whose flux you're taking the other + + align:start position:0% +field whose flux you're taking the other + + + align:start position:0% +field whose flux you're taking the other +one is the surface through which you + + align:start position:0% +one is the surface through which you + + + align:start position:0% +one is the surface through which you +will be taking + + align:start position:0% +will be taking + + + align:start position:0% +will be taking +flux so the vector field only comes as + + align:start position:0% +flux so the vector field only comes as + + + align:start position:0% +flux so the vector field only comes as +you know this F in the notation and + + align:start position:0% +you know this F in the notation and + + + align:start position:0% +you know this F in the notation and +everything else the bounce on the double + + align:start position:0% +everything else the bounce on the double + + + align:start position:0% +everything else the bounce on the double +integral and and the NDS they all come + + align:start position:0% +integral and and the NDS they all come + + + align:start position:0% +integral and and the NDS they all come +from the surface that we're looking at + + align:start position:0% +from the surface that we're looking at + + + align:start position:0% +from the surface that we're looking at +okay so basically in all of this + + align:start position:0% +okay so basically in all of this + + + align:start position:0% +okay so basically in all of this +calculation this is coming from FAL ZK + + align:start position:0% +calculation this is coming from FAL ZK + + + align:start position:0% +calculation this is coming from FAL ZK +everything else comes from the + + align:start position:0% +everything else comes from the + + + align:start position:0% +everything else comes from the +information paraboloid z x + y squ above + + align:start position:0% +information paraboloid z x + y squ above + + + align:start position:0% +information paraboloid z x + y squ above +the unit + + align:start position:0% +the unit + + + align:start position:0% +the unit +dis + + align:start position:0% + + + + align:start position:0% + +okay so in particular if we wanted to + + align:start position:0% +okay so in particular if we wanted to + + + align:start position:0% +okay so in particular if we wanted to +Now find you know the flux of any other + + align:start position:0% +Now find you know the flux of any other + + + align:start position:0% +Now find you know the flux of any other +Vector field through the same paraboloid + + align:start position:0% +Vector field through the same paraboloid + + + align:start position:0% +Vector field through the same paraboloid +well all we have to do is just replace + + align:start position:0% +well all we have to do is just replace + + + align:start position:0% +well all we have to do is just replace +this guy by whatever the new Vector + + align:start position:0% +this guy by whatever the new Vector + + + align:start position:0% +this guy by whatever the new Vector +field is we've learned how to set up + + align:start position:0% +field is we've learned how to set up + + + align:start position:0% +field is we've learned how to set up +flux integrals for this + + align:start position:0% + + + + align:start position:0% + +paraboloid not that you should remember + + align:start position:0% +paraboloid not that you should remember + + + align:start position:0% +paraboloid not that you should remember +this one by heart I mean there's many + + align:start position:0% +this one by heart I mean there's many + + + align:start position:0% +this one by heart I mean there's many +paraboloids in life and other surfaces + + align:start position:0% +paraboloids in life and other surfaces + + + align:start position:0% +paraboloids in life and other surfaces +too so it's better to remember the + + align:start position:0% +too so it's better to remember the + + + align:start position:0% +too so it's better to remember the +general + + align:start position:0% + + + + align:start position:0% + +method okay any other + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +no okay let's see more ways of tech L + + align:start position:0% +no okay let's see more ways of tech L + + + align:start position:0% +no okay let's see more ways of tech L +flux + + align:start position:0% +flux + + + align:start position:0% +flux +integrals but just to reassure you at + + align:start position:0% +integrals but just to reassure you at + + + align:start position:0% +integrals but just to reassure you at +this point we've seen the most important + + align:start position:0% +this point we've seen the most important + + + align:start position:0% +this point we've seen the most important +ones you know 90% of the problems that + + align:start position:0% +ones you know 90% of the problems that + + + align:start position:0% +ones you know 90% of the problems that +will be looking at we can do with what + + align:start position:0% +will be looking at we can do with what + + + align:start position:0% +will be looking at we can do with what +we've seen so far last time and this and + + align:start position:0% +we've seen so far last time and this and + + + align:start position:0% +we've seen so far last time and this and +this + + align:start position:0% +this + + + align:start position:0% +this +formula but let's look a little bit + + align:start position:0% +formula but let's look a little bit + + + align:start position:0% +formula but let's look a little bit +at a more General + + align:start position:0% + + + + align:start position:0% + +situation let's say that my Surface is + + align:start position:0% +situation let's say that my Surface is + + + align:start position:0% +situation let's say that my Surface is +so complicated that I can't actually + + align:start position:0% +so complicated that I can't actually + + + align:start position:0% +so complicated that I can't actually +Express Z as a function of X and Y but + + align:start position:0% +Express Z as a function of X and Y but + + + align:start position:0% +Express Z as a function of X and Y but +let's say that actually I know how to + + align:start position:0% +let's say that actually I know how to + + + align:start position:0% +let's say that actually I know how to +parameterize it so I have parametric + + align:start position:0% +parameterize it so I have parametric + + + align:start position:0% +parameterize it so I have parametric +equation for my Surface that means I can + + align:start position:0% +equation for my Surface that means I can + + + align:start position:0% +equation for my Surface that means I can +express X Y and Z in terms of any two + + align:start position:0% +express X Y and Z in terms of any two + + + align:start position:0% +express X Y and Z in terms of any two +parameter variables that might be + + align:start position:0% +parameter variables that might be + + + align:start position:0% +parameter variables that might be +relevant for + + align:start position:0% +relevant for + + + align:start position:0% +relevant for +me so if you want this one here is the + + align:start position:0% +me so if you want this one here is the + + + align:start position:0% +me so if you want this one here is the +special case where you can parameterize + + align:start position:0% +special case where you can parameterize + + + align:start position:0% +special case where you can parameterize +things in terms of X and Y as your two + + align:start position:0% +things in terms of X and Y as your two + + + align:start position:0% +things in terms of X and Y as your two +variables so how would you do it in the + + align:start position:0% +variables so how would you do it in the + + + align:start position:0% +variables so how would you do it in the +fully General case in a way that will + + align:start position:0% +fully General case in a way that will + + + align:start position:0% +fully General case in a way that will +answer your question + + align:start position:0% +answer your question + + + align:start position:0% +answer your question +I think one of you I forgot asked + + align:start position:0% +I think one of you I forgot asked + + + align:start position:0% +I think one of you I forgot asked +yesterday how would I do it in general + + align:start position:0% +yesterday how would I do it in general + + + align:start position:0% +yesterday how would I do it in general +is there a formula like MDX plus ndy + + align:start position:0% +is there a formula like MDX plus ndy + + + align:start position:0% +is there a formula like MDX plus ndy +well that's going to be the general + + align:start position:0% +well that's going to be the general + + + align:start position:0% +well that's going to be the general +formula and you'll see it's a little bit + + align:start position:0% +formula and you'll see it's a little bit + + + align:start position:0% +formula and you'll see it's a little bit +too complicated so the really useful + + align:start position:0% +too complicated so the really useful + + + align:start position:0% +too complicated so the really useful +ones are actually the special + + align:start position:0% +ones are actually the special + + + align:start position:0% +ones are actually the special +ones so let's say that we are given a + + align:start position:0% +ones so let's say that we are given a + + + align:start position:0% +ones so let's say that we are given a +parametric + + align:start position:0% + + + + align:start position:0% + +description of a surface s so that means + + align:start position:0% +description of a surface s so that means + + + align:start position:0% +description of a surface s so that means +means we can describe + + align:start position:0% +means we can describe + + + align:start position:0% +means we can describe +s by formulas saying X is some function + + align:start position:0% +s by formulas saying X is some function + + + align:start position:0% +s by formulas saying X is some function +of two parameter variables I'm going to + + align:start position:0% +of two parameter variables I'm going to + + + align:start position:0% +of two parameter variables I'm going to +call them u and v hope you don't mind + + align:start position:0% +call them u and v hope you don't mind + + + align:start position:0% +call them u and v hope you don't mind +you can call them T1 and T2 you can call + + align:start position:0% +you can call them T1 and T2 you can call + + + align:start position:0% +you can call them T1 and T2 you can call +them whatever you + + align:start position:0% + + + + align:start position:0% + +want okay so one of the basic properties + + align:start position:0% +want okay so one of the basic properties + + + align:start position:0% +want okay so one of the basic properties +of a surface is because I have only two + + align:start position:0% +of a surface is because I have only two + + + align:start position:0% +of a surface is because I have only two +independent directions to move on I + + align:start position:0% +independent directions to move on I + + + align:start position:0% +independent directions to move on I +should be able to express X Y and Z in + + align:start position:0% +should be able to express X Y and Z in + + + align:start position:0% +should be able to express X Y and Z in +terms of two + + align:start position:0% +terms of two + + + align:start position:0% +terms of two +variables so now let's say that I know + + align:start position:0% +variables so now let's say that I know + + + align:start position:0% +variables so now let's say that I know +how to do + + align:start position:0% +how to do + + + align:start position:0% +how to do +that or maybe I should instead think of + + align:start position:0% +that or maybe I should instead think of + + + align:start position:0% +that or maybe I should instead think of +it in terms of a position Vector if that + + align:start position:0% +it in terms of a position Vector if that + + + align:start position:0% +it in terms of a position Vector if that +helps you the position Vector so that's + + align:start position:0% +helps you the position Vector so that's + + + align:start position:0% +helps you the position Vector so that's +just the vector with components XYZ is + + align:start position:0% +just the vector with components XYZ is + + + align:start position:0% +just the vector with components XYZ is +given as a function of u and v okay so + + align:start position:0% +given as a function of u and v okay so + + + align:start position:0% +given as a function of u and v okay so +it's it works like a parametric curve + + align:start position:0% +it's it works like a parametric curve + + + align:start position:0% +it's it works like a parametric curve +but with two + + align:start position:0% +but with two + + + align:start position:0% +but with two +parameters so now how will we actually + + align:start position:0% +parameters so now how will we actually + + + align:start position:0% +parameters so now how will we actually +set up a flux integral on such a surface + + align:start position:0% +set up a flux integral on such a surface + + + align:start position:0% +set up a flux integral on such a surface +well because we're locating ourselves in + + align:start position:0% +well because we're locating ourselves in + + + align:start position:0% +well because we're locating ourselves in +terms of u and v we will end up with an + + align:start position:0% +terms of u and v we will end up with an + + + align:start position:0% +terms of u and v we will end up with an +integral du DV so we need to figure out + + align:start position:0% +integral du DV so we need to figure out + + + align:start position:0% +integral du DV so we need to figure out +how to express NDS in terms of du and + + align:start position:0% + + + + align:start position:0% + +DV okay so NDS should be + + align:start position:0% +DV okay so NDS should be + + + align:start position:0% +DV okay so NDS should be +something duv how do we do + + align:start position:0% +something duv how do we do + + + align:start position:0% +something duv how do we do +that well we can use the same + + align:start position:0% +that well we can use the same + + + align:start position:0% +that well we can use the same +method that we've actually used over + + align:start position:0% +method that we've actually used over + + + align:start position:0% +method that we've actually used over +here because if you think for a second + + align:start position:0% +here because if you think for a second + + + align:start position:0% +here because if you think for a second +you know here we used of course a + + align:start position:0% +you know here we used of course a + + + align:start position:0% +you know here we used of course a +rectangle in the XY plane and we lifted + + align:start position:0% +rectangle in the XY plane and we lifted + + + align:start position:0% +rectangle in the XY plane and we lifted +it to a parallelogram and so on but more + + align:start position:0% +it to a parallelogram and so on but more + + + align:start position:0% +it to a parallelogram and so on but more +generally you can think what happens if + + align:start position:0% +generally you can think what happens if + + + align:start position:0% +generally you can think what happens if +I change U by Delta U keeping V constant + + align:start position:0% +I change U by Delta U keeping V constant + + + align:start position:0% +I change U by Delta U keeping V constant +or the other way + + align:start position:0% +or the other way + + + align:start position:0% +or the other way +around you know you will get some sort + + align:start position:0% +around you know you will get some sort + + + align:start position:0% +around you know you will get some sort +of mesh grid on your surface and you + + align:start position:0% +of mesh grid on your surface and you + + + align:start position:0% +of mesh grid on your surface and you +will look at a little parallelogram + + align:start position:0% +will look at a little parallelogram + + + align:start position:0% +will look at a little parallelogram +that's an elementary piece of that mesh + + align:start position:0% +that's an elementary piece of that mesh + + + align:start position:0% +that's an elementary piece of that mesh +and figure out what is its area and + + align:start position:0% +and figure out what is its area and + + + align:start position:0% +and figure out what is its area and +normal Vector well that will again be + + align:start position:0% +normal Vector well that will again be + + + align:start position:0% +normal Vector well that will again be +given by the normal by the cross product + + align:start position:0% +given by the normal by the cross product + + + align:start position:0% +given by the normal by the cross product +of the two sides + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let's think a little bit about what + + align:start position:0% +so let's think a little bit about what + + + align:start position:0% +so let's think a little bit about what +happens when I move a little + + align:start position:0% +happens when I move a little + + + align:start position:0% +happens when I move a little +bit on my Surface so you know I'm taking + + align:start position:0% +bit on my Surface so you know I'm taking + + + align:start position:0% +bit on my Surface so you know I'm taking +actually a grid on my Surface given by + + align:start position:0% +actually a grid on my Surface given by + + + align:start position:0% +actually a grid on my Surface given by +the u and v directions and if I take a + + align:start position:0% +the u and v directions and if I take a + + + align:start position:0% +the u and v directions and if I take a +piece of + + align:start position:0% + + + + align:start position:0% + +that corresponding to small changes + + align:start position:0% +that corresponding to small changes + + + align:start position:0% +that corresponding to small changes +Delta U and Delta V + + align:start position:0% + + + + align:start position:0% + +what's going to be going on here well I + + align:start position:0% +what's going to be going on here well I + + + align:start position:0% +what's going to be going on here well I +have to deal with two + + align:start position:0% +have to deal with two + + + align:start position:0% +have to deal with two +vectors one corresponding to changing U + + align:start position:0% +vectors one corresponding to changing U + + + align:start position:0% +vectors one corresponding to changing U +one corresponding to changing V if I + + align:start position:0% +one corresponding to changing V if I + + + align:start position:0% +one corresponding to changing V if I +change U how does my point change while + + align:start position:0% +change U how does my point change while + + + align:start position:0% +change U how does my point change while +that's given by the derivative of this + + align:start position:0% +that's given by the derivative of this + + + align:start position:0% +that's given by the derivative of this +with respect to + + align:start position:0% +with respect to + + + align:start position:0% +with respect to +U okay so this Vector here I will + + align:start position:0% +U okay so this Vector here I will + + + align:start position:0% +U okay so this Vector here I will +call so the + + align:start position:0% +call so the + + + align:start position:0% +call so the +sides are given by + + align:start position:0% +sides are given by + + + align:start position:0% +sides are given by +let me say partial R over partial U time + + align:start position:0% +let me say partial R over partial U time + + + align:start position:0% +let me say partial R over partial U time +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +U if you prefer maybe I should write it + + align:start position:0% +U if you prefer maybe I should write it + + + align:start position:0% +U if you prefer maybe I should write it +as partial X partial U Delta U partial y + + align:start position:0% +as partial X partial U Delta U partial y + + + align:start position:0% +as partial X partial U Delta U partial y +well it's just too boring to write + + align:start position:0% +well it's just too boring to write + + + align:start position:0% +well it's just too boring to write +so um and so on okay it means just you + + align:start position:0% +so um and so on okay it means just you + + + align:start position:0% +so um and so on okay it means just you +know if I change youu a little bit keep + + align:start position:0% +know if I change youu a little bit keep + + + align:start position:0% +know if I change youu a little bit keep +V constant then how X changes is given + + align:start position:0% +V constant then how X changes is given + + + align:start position:0% +V constant then how X changes is given +by partial X partial U time Delta U same + + align:start position:0% +by partial X partial U time Delta U same + + + align:start position:0% +by partial X partial U time Delta U same +thing with Y same thing with z and I'm + + align:start position:0% +thing with Y same thing with z and I'm + + + align:start position:0% +thing with Y same thing with z and I'm +just using Vector notation to do it this + + align:start position:0% +just using Vector notation to do it this + + + align:start position:0% +just using Vector notation to do it this +way if you want that's you know that's + + align:start position:0% +way if you want that's you know that's + + + align:start position:0% +way if you want that's you know that's +the analogue of when I + + align:start position:0% +the analogue of when I + + + align:start position:0% +the analogue of when I +say Delta R for line integrals along a + + align:start position:0% +say Delta R for line integrals along a + + + align:start position:0% +say Delta R for line integrals along a +curve Vector Delta R is the velocity + + align:start position:0% +curve Vector Delta R is the velocity + + + align:start position:0% +curve Vector Delta R is the velocity +Vector drdt time delta + + align:start position:0% + + + + align:start position:0% + +T okay now if I look at the other side + + align:start position:0% + + + + align:start position:0% + +the other okay so sorry so let me start + + align:start position:0% +the other okay so sorry so let me start + + + align:start position:0% +the other okay so sorry so let me start +again and out of space one side is + + align:start position:0% +again and out of space one side is + + + align:start position:0% +again and out of space one side is +partial R partial U * Delta U and the + + align:start position:0% +partial R partial U * Delta U and the + + + align:start position:0% +partial R partial U * Delta U and the +other one would be partial R partial V + + align:start position:0% +other one would be partial R partial V + + + align:start position:0% +other one would be partial R partial V +time Delta V because that's how the + + align:start position:0% +time Delta V because that's how the + + + align:start position:0% +time Delta V because that's how the +position of your point changes if you + + align:start position:0% +position of your point changes if you + + + align:start position:0% +position of your point changes if you +just change U or V and not the other + + align:start position:0% +just change U or V and not the other + + + align:start position:0% +just change U or V and not the other +one so now to find + + align:start position:0% + + + + align:start position:0% + +the surface element together with a + + align:start position:0% +the surface element together with a + + + align:start position:0% +the surface element together with a +normal Vector I would just take the + + align:start position:0% +normal Vector I would just take the + + + align:start position:0% +normal Vector I would just take the +cross product between these + + align:start position:0% + + + + align:start position:0% + +guys so if you prefer that's the cross + + align:start position:0% +guys so if you prefer that's the cross + + + align:start position:0% +guys so if you prefer that's the cross +product of partial R partial U with + + align:start position:0% +product of partial R partial U with + + + align:start position:0% +product of partial R partial U with +partial R partial + + align:start position:0% +partial R partial + + + align:start position:0% +partial R partial +V Delta U Delta + + align:start position:0% +V Delta U Delta + + + align:start position:0% +V Delta U Delta +V and so so n DS is this cross product + + align:start position:0% +V and so so n DS is this cross product + + + align:start position:0% +V and so so n DS is this cross product +time D + + align:start position:0% +time D + + + align:start position:0% +time D +DV up to + + align:start position:0% + + + + align:start position:0% + +sign I mean also here depends on which + + align:start position:0% +sign I mean also here depends on which + + + align:start position:0% +sign I mean also here depends on which +choice I make for my normal Vector of + + align:start position:0% + + + + align:start position:0% + +course okay + + align:start position:0% +course okay + + + align:start position:0% +course okay +now if + + align:start position:0% +now if + + + align:start position:0% +now if +you you know that of course is a + + align:start position:0% +you you know that of course is a + + + align:start position:0% +you you know that of course is a +slightly confusing equation to think of + + align:start position:0% +slightly confusing equation to think of + + + align:start position:0% +slightly confusing equation to think of +so a good exercise if you want to really + + align:start position:0% +so a good exercise if you want to really + + + align:start position:0% +so a good exercise if you want to really +understand what's going on try this in + + align:start position:0% +understand what's going on try this in + + + align:start position:0% +understand what's going on try this in +two good examples to look at one good + + align:start position:0% +two good examples to look at one good + + + align:start position:0% +two good examples to look at one good +example to look at is the previous one + + align:start position:0% +example to look at is the previous one + + + align:start position:0% +example to look at is the previous one +what is it it's when u and v are just X + + align:start position:0% +what is it it's when u and v are just X + + + align:start position:0% +what is it it's when u and v are just X +and Y okay so the parametric equations + + align:start position:0% +and Y okay so the parametric equations + + + align:start position:0% +and Y okay so the parametric equations +are just xal X yal Y and Z is f of XY + + align:start position:0% +are just xal X yal Y and Z is f of XY + + + align:start position:0% +are just xal X yal Y and Z is f of XY +you should end up with the same formula + + align:start position:0% +you should end up with the same formula + + + align:start position:0% +you should end up with the same formula +that we had over there + + align:start position:0% +that we had over there + + + align:start position:0% +that we had over there +and and you should see why because see + + align:start position:0% +and and you should see why because see + + + align:start position:0% +and and you should see why because see +it's both of them are given by a cross + + align:start position:0% +it's both of them are given by a cross + + + align:start position:0% +it's both of them are given by a cross +product the other case you can look at + + align:start position:0% +product the other case you can look at + + + align:start position:0% +product the other case you can look at +just to convince your C even further so + + align:start position:0% +just to convince your C even further so + + + align:start position:0% +just to convince your C even further so +we don't need to do that because we've + + align:start position:0% +we don't need to do that because we've + + + align:start position:0% +we don't need to do that because we've +seen the formula before but in the case + + align:start position:0% +seen the formula before but in the case + + + align:start position:0% +seen the formula before but in the case +of a sphere we've seen the formula for n + + align:start position:0% +of a sphere we've seen the formula for n + + + align:start position:0% +of a sphere we've seen the formula for n +and for DS + + align:start position:0% +and for DS + + + align:start position:0% +and for DS +separately so we know what n DS are in + + align:start position:0% +separately so we know what n DS are in + + + align:start position:0% +separately so we know what n DS are in +terms of d d + + align:start position:0% +terms of d d + + + align:start position:0% +terms of d d +Theta well you could parameterize a + + align:start position:0% +Theta well you could parameterize a + + + align:start position:0% +Theta well you could parameterize a +sphere in terms of Fe and Theta namely + + align:start position:0% +sphere in terms of Fe and Theta namely + + + align:start position:0% +sphere in terms of Fe and Theta namely +the formulas would be xal a sin cosine + + align:start position:0% +the formulas would be xal a sin cosine + + + align:start position:0% +the formulas would be xal a sin cosine +Theta y = a sin F sin Theta Z equals a + + align:start position:0% +Theta y = a sin F sin Theta Z equals a + + + align:start position:0% +Theta y = a sin F sin Theta Z equals a +cosine the formulas for spherical + + align:start position:0% +cosine the formulas for spherical + + + align:start position:0% +cosine the formulas for spherical +coordinates setting row equals a so + + align:start position:0% +coordinates setting row equals a so + + + align:start position:0% +coordinates setting row equals a so +that's a parametric equation for the + + align:start position:0% +that's a parametric equation for the + + + align:start position:0% +that's a parametric equation for the +sphere and then if you try to use this + + align:start position:0% +sphere and then if you try to use this + + + align:start position:0% +sphere and then if you try to use this +formula here you should end up with the + + align:start position:0% +formula here you should end up with the + + + align:start position:0% +formula here you should end up with the +same things we've already seen for NDS + + align:start position:0% +same things we've already seen for NDS + + + align:start position:0% +same things we've already seen for NDS +just with a lot more pain to actually + + align:start position:0% +just with a lot more pain to actually + + + align:start position:0% +just with a lot more pain to actually +get there because your cross product is + + align:start position:0% +get there because your cross product is + + + align:start position:0% +get there because your cross product is +going to be a bit complicated + + align:start position:0% + + + + align:start position:0% + +okay but you know we're seeing all of + + align:start position:0% +okay but you know we're seeing all of + + + align:start position:0% +okay but you know we're seeing all of +these formulas they all fit together + + align:start position:0% +these formulas they all fit together + + + align:start position:0% +these formulas they all fit together +somehow it's always the same question + + align:start position:0% +somehow it's always the same question + + + align:start position:0% +somehow it's always the same question +just we have different angles of attack + + align:start position:0% +just we have different angles of attack + + + align:start position:0% +just we have different angles of attack +on this General + + align:start position:0% + + + + align:start position:0% + +problem okay + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +no okay let's look at yet another last + + align:start position:0% +no okay let's look at yet another last + + + align:start position:0% +no okay let's look at yet another last +way of finding NDS + + align:start position:0% + + + + align:start position:0% + +and then I promise we'll switch to + + align:start position:0% +and then I promise we'll switch to + + + align:start position:0% +and then I promise we'll switch to +something else because I can feel that + + align:start position:0% +something else because I can feel that + + + align:start position:0% +something else because I can feel that +you're getting a bit overwhelmed by all + + align:start position:0% +you're getting a bit overwhelmed by all + + + align:start position:0% +you're getting a bit overwhelmed by all +these formulas for + + align:start position:0% + + + + align:start position:0% + +NDS + + align:start position:0% + + + + align:start position:0% + +so okay so what happens very often is we + + align:start position:0% +so okay so what happens very often is we + + + align:start position:0% +so okay so what happens very often is we +don't actually know how to parameterize + + align:start position:0% +don't actually know how to parameterize + + + align:start position:0% +don't actually know how to parameterize +our surface maybe we don't know how to + + align:start position:0% +our surface maybe we don't know how to + + + align:start position:0% +our surface maybe we don't know how to +solve for Z as a function of X and Y but + + align:start position:0% +solve for Z as a function of X and Y but + + + align:start position:0% +solve for Z as a function of X and Y but +our surface is given by some + + align:start position:0% +our surface is given by some + + + align:start position:0% +our surface is given by some +equation you know + + align:start position:0% +equation you know + + + align:start position:0% +equation you know +and so what that means is actually maybe + + align:start position:0% +and so what that means is actually maybe + + + align:start position:0% +and so what that means is actually maybe +what we + + align:start position:0% +what we + + + align:start position:0% +what we +know is not really these kinds of + + align:start position:0% +know is not really these kinds of + + + align:start position:0% +know is not really these kinds of +formulas but maybe we know a normal + + align:start position:0% + + + + align:start position:0% + +vector and I'm going to call this one + + align:start position:0% +vector and I'm going to call this one + + + align:start position:0% +vector and I'm going to call this one +capital N + + align:start position:0% +capital N + + + align:start position:0% +capital N +because I don't even need it to be a + + align:start position:0% +because I don't even need it to be a + + + align:start position:0% +because I don't even need it to be a +unit Vector you will + + align:start position:0% +unit Vector you will + + + align:start position:0% +unit Vector you will +see it can be a normal Vector of any + + align:start position:0% +see it can be a normal Vector of any + + + align:start position:0% +see it can be a normal Vector of any +length you want to the surfaces + + align:start position:0% + + + + align:start position:0% + +so why would we ever know a normal + + align:start position:0% +so why would we ever know a normal + + + align:start position:0% +so why would we ever know a normal +Vector well for example if our surface + + align:start position:0% +Vector well for example if our surface + + + align:start position:0% +Vector well for example if our surface +is a plane you know say it's a slanted + + align:start position:0% +is a plane you know say it's a slanted + + + align:start position:0% +is a plane you know say it's a slanted +plane given by some equation ax plus b y + + align:start position:0% +plane given by some equation ax plus b y + + + align:start position:0% +plane given by some equation ax plus b y +plus CZ equals D well you know the + + align:start position:0% +plus CZ equals D well you know the + + + align:start position:0% +plus CZ equals D well you know the +normal Vector it's a c of course you + + align:start position:0% +normal Vector it's a c of course you + + + align:start position:0% +normal Vector it's a c of course you +could solve for Z and then go back to + + align:start position:0% +could solve for Z and then go back to + + + align:start position:0% +could solve for Z and then go back to +that case which is why I said that that + + align:start position:0% +that case which is why I said that that + + + align:start position:0% +that case which is why I said that that +one is really useful but you can also + + align:start position:0% +one is really useful but you can also + + + align:start position:0% +one is really useful but you can also +just stay with a normal Vector why why + + align:start position:0% +just stay with a normal Vector why why + + + align:start position:0% +just stay with a normal Vector why why +would you know a normal Vector well + + align:start position:0% +would you know a normal Vector well + + + align:start position:0% +would you know a normal Vector well +let's say that you know an equation + + align:start position:0% +let's say that you know an equation + + + align:start position:0% +let's say that you know an equation +that's of the form G of XYZ equals + + align:start position:0% +that's of the form G of XYZ equals + + + align:start position:0% +that's of the form G of XYZ equals +z well then you know that the gradient + + align:start position:0% +z well then you know that the gradient + + + align:start position:0% +z well then you know that the gradient +of G is perpendicular to the level + + align:start position:0% +of G is perpendicular to the level + + + align:start position:0% +of G is perpendicular to the level +surface okay so let me just give + + align:start position:0% +surface okay so let me just give + + + align:start position:0% +surface okay so let me just give +you two + + align:start position:0% + + + + align:start position:0% + +examples if you have a plane ax + b + + align:start position:0% +examples if you have a plane ax + b + + + align:start position:0% +examples if you have a plane ax + b +y plus C zal D then the normal Vector + + align:start position:0% +y plus C zal D then the normal Vector + + + align:start position:0% +y plus C zal D then the normal Vector +would just be ABC + + align:start position:0% +would just be ABC + + + align:start position:0% +would just be ABC +if you + + align:start position:0% +if you + + + align:start position:0% +if you +have a surface + + align:start position:0% +have a surface + + + align:start position:0% +have a surface +s given by an + + align:start position:0% +s given by an + + + align:start position:0% +s given by an +equation G of XYZ equal + + align:start position:0% +equation G of XYZ equal + + + align:start position:0% +equation G of XYZ equal +Z then you can take the normal Vector to + + align:start position:0% +Z then you can take the normal Vector to + + + align:start position:0% +Z then you can take the normal Vector to +be the gradient of G we've seen that the + + align:start position:0% +be the gradient of G we've seen that the + + + align:start position:0% +be the gradient of G we've seen that the +gradient is perpendicular to the level + + align:start position:0% +gradient is perpendicular to the level + + + align:start position:0% +gradient is perpendicular to the level +surface now of course we don't + + align:start position:0% +surface now of course we don't + + + align:start position:0% +surface now of course we don't +necessarily have to follow what's going + + align:start position:0% +necessarily have to follow what's going + + + align:start position:0% +necessarily have to follow what's going +to come because if we could solve for Z + + align:start position:0% +to come because if we could solve for Z + + + align:start position:0% +to come because if we could solve for Z +then we might be better off doing what + + align:start position:0% +then we might be better off doing what + + + align:start position:0% +then we might be better off doing what +we did over there + + align:start position:0% +we did over there + + + align:start position:0% +we did over there +but let's say that we want to do it this + + align:start position:0% +but let's say that we want to do it this + + + align:start position:0% +but let's say that we want to do it this +way so then what can we + + align:start position:0% +way so then what can we + + + align:start position:0% +way so then what can we +do well I'm going to give you another + + align:start position:0% +do well I'm going to give you another + + + align:start position:0% +do well I'm going to give you another +way to think + + align:start position:0% +way to think + + + align:start position:0% +way to think +geometrically about NDS + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so okay so let's start by thinking about + + align:start position:0% +so okay so let's start by thinking about + + + align:start position:0% +so okay so let's start by thinking about +a slanted plane okay so let's say that + + align:start position:0% +a slanted plane okay so let's say that + + + align:start position:0% +a slanted plane okay so let's say that +my Surface is just a slanted plane so my + + align:start position:0% +my Surface is just a slanted plane so my + + + align:start position:0% +my Surface is just a slanted plane so my +normal Vector would be maybe somewhere + + align:start position:0% +normal Vector would be maybe somewhere + + + align:start position:0% +normal Vector would be maybe somewhere +here and let's say that I'm going to try + + align:start position:0% +here and let's say that I'm going to try + + + align:start position:0% +here and let's say that I'm going to try +you know I need of course some handle on + + align:start position:0% +you know I need of course some handle on + + + align:start position:0% +you know I need of course some handle on +how to set up my integral so maybe I'm + + align:start position:0% +how to set up my integral so maybe I'm + + + align:start position:0% +how to set up my integral so maybe I'm +going to express things in terms of X + + align:start position:0% +going to express things in terms of X + + + align:start position:0% +going to express things in terms of X +and Y okay so I have my + + align:start position:0% +and Y okay so I have my + + + align:start position:0% +and Y okay so I have my +coordinates and I'll try to use X and Y + + align:start position:0% +coordinates and I'll try to use X and Y + + + align:start position:0% +coordinates and I'll try to use X and Y +so then I would like to relate Delta s + + align:start position:0% +so then I would like to relate Delta s + + + align:start position:0% +so then I would like to relate Delta s +DS to the area in the XY plane so that + + align:start position:0% +DS to the area in the XY plane so that + + + align:start position:0% +DS to the area in the XY plane so that +means you know I want maybe to look at + + align:start position:0% +means you know I want maybe to look at + + + align:start position:0% +means you know I want maybe to look at +the projection of this guy onto a + + align:start position:0% +the projection of this guy onto a + + + align:start position:0% +the projection of this guy onto a +horizontal plane let's squish it + + align:start position:0% + + + + align:start position:0% + +horizontally + + align:start position:0% +horizontally + + + align:start position:0% +horizontally +so then you have here another + + align:start position:0% +so then you have here another + + + align:start position:0% +so then you have here another +area Okay so the guy on the slanted + + align:start position:0% +area Okay so the guy on the slanted + + + align:start position:0% +area Okay so the guy on the slanted +plane let's call that Delta s and let's + + align:start position:0% +plane let's call that Delta s and let's + + + align:start position:0% +plane let's call that Delta s and let's +call this guy down here Delta + + align:start position:0% +call this guy down here Delta + + + align:start position:0% +call this guy down here Delta +a so the question and you know Delta a + + align:start position:0% +a so the question and you know Delta a + + + align:start position:0% +a so the question and you know Delta a +would become ultimately maybe Delta X + + align:start position:0% +would become ultimately maybe Delta X + + + align:start position:0% +would become ultimately maybe Delta X +Delta y or something like that the + + align:start position:0% +Delta y or something like that the + + + align:start position:0% +Delta y or something like that the +question is how do we find the + + align:start position:0% +question is how do we find the + + + align:start position:0% +question is how do we find the +conversion rate between these two areas + + align:start position:0% +conversion rate between these two areas + + + align:start position:0% +conversion rate between these two areas +see I mean they're not the same visually + + align:start position:0% +see I mean they're not the same visually + + + align:start position:0% +see I mean they're not the same visually +I hope it's clear to you that if my + + align:start position:0% +I hope it's clear to you that if my + + + align:start position:0% +I hope it's clear to you that if my +plane is actually horizontal then of + + align:start position:0% +plane is actually horizontal then of + + + align:start position:0% +plane is actually horizontal then of +course they're the same but the more + + align:start position:0% +course they're the same but the more + + + align:start position:0% +course they're the same but the more +slanted it becomes the more Delta a + + align:start position:0% +slanted it becomes the more Delta a + + + align:start position:0% +slanted it becomes the more Delta a +becomes smaller than Delta s right I + + align:start position:0% +becomes smaller than Delta s right I + + + align:start position:0% +becomes smaller than Delta s right I +mean if you buy you know if you buy land + + align:start position:0% +mean if you buy you know if you buy land + + + align:start position:0% +mean if you buy you know if you buy land +and it's on the side of a cliff well + + align:start position:0% +and it's on the side of a cliff well + + + align:start position:0% +and it's on the side of a cliff well +whether you look at it on a map or + + align:start position:0% +whether you look at it on a map or + + + align:start position:0% +whether you look at it on a map or +whether you look at it on the actual + + align:start position:0% +whether you look at it on the actual + + + align:start position:0% +whether you look at it on the actual +Cliff the area is going to be very + + align:start position:0% +Cliff the area is going to be very + + + align:start position:0% +Cliff the area is going to be very +different um I'm not sure if that's a + + align:start position:0% +different um I'm not sure if that's a + + + align:start position:0% +different um I'm not sure if that's a +wise thing to do if you want to build a + + align:start position:0% +wise thing to do if you want to build a + + + align:start position:0% +wise thing to do if you want to build a +house there but I'm I've been told you + + align:start position:0% +house there but I'm I've been told you + + + align:start position:0% +house there but I'm I've been told you +can get really cheap + + align:start position:0% +can get really cheap + + + align:start position:0% +can get really cheap +land + + align:start position:0% +land + + + align:start position:0% +land +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +anyway okay so Delta s versus delta a + + align:start position:0% +anyway okay so Delta s versus delta a + + + align:start position:0% +anyway okay so Delta s versus delta a +depends on how slanted things are and + + align:start position:0% +depends on how slanted things are and + + + align:start position:0% +depends on how slanted things are and +let's try to make that more precise by + + align:start position:0% +let's try to make that more precise by + + + align:start position:0% +let's try to make that more precise by +looking at the angle that our plane + + align:start position:0% +looking at the angle that our plane + + + align:start position:0% +looking at the angle that our plane +makes with a horizontal + + align:start position:0% +makes with a horizontal + + + align:start position:0% +makes with a horizontal +Direction okay + + align:start position:0% +Direction okay + + + align:start position:0% +Direction okay +so let's call this angle Alpha the angle + + align:start position:0% +so let's call this angle Alpha the angle + + + align:start position:0% +so let's call this angle Alpha the angle +that our plane makes with the horizontal + + align:start position:0% + + + + align:start position:0% + +direction see it's all coming together + + align:start position:0% +direction see it's all coming together + + + align:start position:0% +direction see it's all coming together +now the first unit about cross products + + align:start position:0% +now the first unit about cross products + + + align:start position:0% +now the first unit about cross products +normal vectors and so on + + align:start position:0% +normal vectors and so on + + + align:start position:0% +normal vectors and so on +is actually useful + + align:start position:0% +is actually useful + + + align:start position:0% +is actually useful +now + + align:start position:0% + + + + align:start position:0% + +so I claim that the surface element is + + align:start position:0% +so I claim that the surface element is + + + align:start position:0% +so I claim that the surface element is +related to the area in the plane by + + align:start position:0% +related to the area in the plane by + + + align:start position:0% +related to the area in the plane by +Delta a equals Delta s time the cosine + + align:start position:0% +Delta a equals Delta s time the cosine + + + align:start position:0% +Delta a equals Delta s time the cosine +of + + align:start position:0% +of + + + align:start position:0% +of +alpha why is + + align:start position:0% +alpha why is + + + align:start position:0% +alpha why is +that well let's look at this small + + align:start position:0% +that well let's look at this small + + + align:start position:0% +that well let's look at this small +rectangle with one horizontal side and + + align:start position:0% +rectangle with one horizontal side and + + + align:start position:0% +rectangle with one horizontal side and +one slanted + + align:start position:0% +one slanted + + + align:start position:0% +one slanted +side well when you project this side + + align:start position:0% +side well when you project this side + + + align:start position:0% +side well when you project this side +doesn't + + align:start position:0% +doesn't + + + align:start position:0% +doesn't +change but this side gets shortened by a + + align:start position:0% +change but this side gets shortened by a + + + align:start position:0% +change but this side gets shortened by a +factor of cosine Alpha whatever this + + align:start position:0% +factor of cosine Alpha whatever this + + + align:start position:0% +factor of cosine Alpha whatever this +length was this length here is that one + + align:start position:0% +length was this length here is that one + + + align:start position:0% +length was this length here is that one +time cosine Alpha so that's why the area + + align:start position:0% +time cosine Alpha so that's why the area + + + align:start position:0% +time cosine Alpha so that's why the area +gets shrunk by cosine Alpha in One + + align:start position:0% +gets shrunk by cosine Alpha in One + + + align:start position:0% +gets shrunk by cosine Alpha in One +Direction nothing happens in the other + + align:start position:0% +Direction nothing happens in the other + + + align:start position:0% +Direction nothing happens in the other +direction you squish by cosine + + align:start position:0% +direction you squish by cosine + + + align:start position:0% +direction you squish by cosine +Alpha + + align:start position:0% +Alpha + + + align:start position:0% +Alpha +so what that means + + align:start position:0% +so what that means + + + align:start position:0% +so what that means +is + + align:start position:0% +is + + + align:start position:0% +is +that + + align:start position:0% +that + + + align:start position:0% +that +well okay so we'll have to deal with + + align:start position:0% +well okay so we'll have to deal with + + + align:start position:0% +well okay so we'll have to deal with +this and of course the one we'll care + + align:start position:0% +this and of course the one we'll care + + + align:start position:0% +this and of course the one we'll care +about actually is Delta s expressed in + + align:start position:0% +about actually is Delta s expressed in + + + align:start position:0% +about actually is Delta s expressed in +terms of Delta a but what are we going + + align:start position:0% +terms of Delta a but what are we going + + + align:start position:0% +terms of Delta a but what are we going +to do with this cosine you know it's not + + align:start position:0% +to do with this cosine you know it's not + + + align:start position:0% +to do with this cosine you know it's not +very convenient to have a cosine left in + + align:start position:0% +very convenient to have a cosine left in + + + align:start position:0% +very convenient to have a cosine left in +here so remember the angle between two + + align:start position:0% +here so remember the angle between two + + + align:start position:0% +here so remember the angle between two +planes it's the same thing as the angle + + align:start position:0% +planes it's the same thing as the angle + + + align:start position:0% +planes it's the same thing as the angle +between their normal vectors so if you + + align:start position:0% +between their normal vectors so if you + + + align:start position:0% +between their normal vectors so if you +want to see this angle Alpha elsewhere + + align:start position:0% +want to see this angle Alpha elsewhere + + + align:start position:0% +want to see this angle Alpha elsewhere +what you can do is you can just take the + + align:start position:0% +what you can do is you can just take the + + + align:start position:0% +what you can do is you can just take the +vertical Direction Let's Take k + + align:start position:0% +vertical Direction Let's Take k + + + align:start position:0% +vertical Direction Let's Take k +a then here we have our angle Alpha + + align:start position:0% + + + + align:start position:0% + +again + + align:start position:0% +again + + + align:start position:0% +again +well so in particular cosine of + + align:start position:0% +well so in particular cosine of + + + align:start position:0% +well so in particular cosine of +alpha I can get well we know how to find + + align:start position:0% +alpha I can get well we know how to find + + + align:start position:0% +alpha I can get well we know how to find +the angle between two vectors right so + + align:start position:0% +the angle between two vectors right so + + + align:start position:0% +the angle between two vectors right so +if we have our normal Vector + + align:start position:0% + + + + align:start position:0% + +n we'll do n. K and we divide by length + + align:start position:0% +n we'll do n. K and we divide by length + + + align:start position:0% +n we'll do n. K and we divide by length +n length K well length K is one that's + + align:start position:0% +n length K well length K is one that's + + + align:start position:0% +n length K well length K is one that's +one easy + + align:start position:0% +one easy + + + align:start position:0% +one easy +guy okay so that's how we find the + + align:start position:0% +guy okay so that's how we find the + + + align:start position:0% +guy okay so that's how we find the +angle so now I'm going to say + + align:start position:0% + + + + align:start position:0% + +well Delta s is going to be 1 / cosine + + align:start position:0% +well Delta s is going to be 1 / cosine + + + align:start position:0% +well Delta s is going to be 1 / cosine +Alpha Delta a and I can rewrite that as + + align:start position:0% +Alpha Delta a and I can rewrite that as + + + align:start position:0% +Alpha Delta a and I can rewrite that as +length of n divided by n. k + + align:start position:0% + + + + align:start position:0% + +time Delta + + align:start position:0% + + + + align:start position:0% + +a now let's multiply that by the unit + + align:start position:0% +a now let's multiply that by the unit + + + align:start position:0% +a now let's multiply that by the unit +normal Vector because what we care about + + align:start position:0% +normal Vector because what we care about + + + align:start position:0% +normal Vector because what we care about +is not so + + align:start position:0% +is not so + + + align:start position:0% +is not so +much DS but actually + + align:start position:0% + + + + align:start position:0% + +NDS so n Delta s will be I'm just going + + align:start position:0% +NDS so n Delta s will be I'm just going + + + align:start position:0% +NDS so n Delta s will be I'm just going +to multiply by + + align:start position:0% + + + + align:start position:0% + +n well let's think for a second what + + align:start position:0% +n well let's think for a second what + + + align:start position:0% +n well let's think for a second what +happens if I take the unit normal n and + + align:start position:0% +happens if I take the unit normal n and + + + align:start position:0% +happens if I take the unit normal n and +I multiply it by the length of my other + + align:start position:0% +I multiply it by the length of my other + + + align:start position:0% +I multiply it by the length of my other +normal Big N well I get big n again + + align:start position:0% +normal Big N well I get big n again + + + align:start position:0% +normal Big N well I get big n again +right this is a normal Vector of the + + align:start position:0% +right this is a normal Vector of the + + + align:start position:0% +right this is a normal Vector of the +same length as n well up to sign but + + align:start position:0% +same length as n well up to sign but + + + align:start position:0% +same length as n well up to sign but +yeah actually maybe I should the only + + align:start position:0% +yeah actually maybe I should the only + + + align:start position:0% +yeah actually maybe I should the only +thing I don't know is whether this guy + + align:start position:0% +thing I don't know is whether this guy + + + align:start position:0% +thing I don't know is whether this guy +will be going in the same direction as + + align:start position:0% +will be going in the same direction as + + + align:start position:0% +will be going in the same direction as +big n or in the opposite + + align:start position:0% +big n or in the opposite + + + align:start position:0% +big n or in the opposite +direction right say that for example my + + align:start position:0% +direction right say that for example my + + + align:start position:0% +direction right say that for example my +capital N has length I don't know length + + align:start position:0% +capital N has length I don't know length + + + align:start position:0% +capital N has length I don't know length +three for + + align:start position:0% +three for + + + align:start position:0% +three for +example then the unit normal Vector + + align:start position:0% +example then the unit normal Vector + + + align:start position:0% +example then the unit normal Vector +might be this guy in which case indeed + + align:start position:0% +might be this guy in which case indeed + + + align:start position:0% +might be this guy in which case indeed +three * little n will be big n or it + + align:start position:0% +three * little n will be big n or it + + + align:start position:0% +three * little n will be big n or it +might be this one in which case three * + + align:start position:0% +might be this one in which case three * + + + align:start position:0% +might be this one in which case three * +little n will be negative + + align:start position:0% +little n will be negative + + + align:start position:0% +little n will be negative +B but up to sign it's n + + align:start position:0% +B but up to sign it's n + + + align:start position:0% +B but up to sign it's n +and then I will have n / n. K Delta a + + align:start position:0% +and then I will have n / n. K Delta a + + + align:start position:0% +and then I will have n / n. K Delta a +and + + align:start position:0% +and + + + align:start position:0% +and +so the final formula the one that + + align:start position:0% +so the final formula the one that + + + align:start position:0% +so the final formula the one that +actually we care about you know in case + + align:start position:0% +actually we care about you know in case + + + align:start position:0% +actually we care about you know in case +you don't really like my explanations of + + align:start position:0% +you don't really like my explanations of + + + align:start position:0% +you don't really like my explanations of +how we get there is + + align:start position:0% +how we get there is + + + align:start position:0% +how we get there is +that DS n DS sorry is plus or + + align:start position:0% +that DS n DS sorry is plus or + + + align:start position:0% +that DS n DS sorry is plus or +minus n / n.k DX + + align:start position:0% +minus n / n.k DX + + + align:start position:0% +minus n / n.k DX +Dy that one is actually kind of useful + + align:start position:0% +Dy that one is actually kind of useful + + + align:start position:0% +Dy that one is actually kind of useful +so let's box it + + align:start position:0% + + + + align:start position:0% + +now just in case you're + + align:start position:0% +now just in case you're + + + align:start position:0% +now just in case you're +wondering of course if you didn't want + + align:start position:0% +wondering of course if you didn't want + + + align:start position:0% +wondering of course if you didn't want +to project to XY you would have maybe + + align:start position:0% +to project to XY you would have maybe + + + align:start position:0% +to project to XY you would have maybe +preferred to project to say the plane of + + align:start position:0% +preferred to project to say the plane of + + + align:start position:0% +preferred to project to say the plane of +a Blackboard YZ well you can do the same + + align:start position:0% +a Blackboard YZ well you can do the same + + + align:start position:0% +a Blackboard YZ well you can do the same +thing okay to express NDS in terms of + + align:start position:0% +thing okay to express NDS in terms of + + + align:start position:0% +thing okay to express NDS in terms of +dydz you do the same argument and simply + + align:start position:0% +dydz you do the same argument and simply + + + align:start position:0% +dydz you do the same argument and simply +the only thing that changes instead of + + align:start position:0% +the only thing that changes instead of + + + align:start position:0% +the only thing that changes instead of +using the vertical vector k you use the + + align:start position:0% +using the vertical vector k you use the + + + align:start position:0% +using the vertical vector k you use the +normal Vector I so you would be doing n/ + + align:start position:0% +normal Vector I so you would be doing n/ + + + align:start position:0% +normal Vector I so you would be doing n/ +n i Dy DZ + + align:start position:0% +n i Dy DZ + + + align:start position:0% +n i Dy DZ +and same thing okay so just you know + + align:start position:0% +and same thing okay so just you know + + + align:start position:0% +and same thing okay so just you know +keep an open mind that this also works + + align:start position:0% +keep an open mind that this also works + + + align:start position:0% +keep an open mind that this also works +with other + + align:start position:0% + + + + align:start position:0% + +variables but anyway so that's how you + + align:start position:0% +variables but anyway so that's how you + + + align:start position:0% +variables but anyway so that's how you +can basically project the vector surface + + align:start position:0% +can basically project the vector surface + + + align:start position:0% +can basically project the vector surface +area element onto the XY plane in a + + align:start position:0% + + + + align:start position:0% + +way + + align:start position:0% + + + + align:start position:0% + +okay so let's look at the special case + + align:start position:0% +okay so let's look at the special case + + + align:start position:0% +okay so let's look at the special case +just to see how this fits with stuff + + align:start position:0% +just to see how this fits with stuff + + + align:start position:0% +just to see how this fits with stuff +we've seen before + + align:start position:0% + + + + align:start position:0% + +let's do a special + + align:start position:0% + + + + align:start position:0% + +example where our surface is given by + + align:start position:0% +example where our surface is given by + + + align:start position:0% +example where our surface is given by +the + + align:start position:0% +the + + + align:start position:0% +the +equation Z minus F of XY equal + + align:start position:0% +equation Z minus F of XY equal + + + align:start position:0% +equation Z minus F of XY equal +Z okay that's a strange way to write the + + align:start position:0% +Z okay that's a strange way to write the + + + align:start position:0% +Z okay that's a strange way to write the +equation Z equals F of XY that we saw + + align:start position:0% +equation Z equals F of XY that we saw + + + align:start position:0% +equation Z equals F of XY that we saw +before but now you know it looks like + + align:start position:0% +before but now you know it looks like + + + align:start position:0% +before but now you know it looks like +well some function of XYZ equals z so + + align:start position:0% +well some function of XYZ equals z so + + + align:start position:0% +well some function of XYZ equals z so +let's try to use this new method + + align:start position:0% +let's try to use this new method + + + align:start position:0% +let's try to use this new method +okay so let's call this guy G of + + align:start position:0% + + + + align:start position:0% + +XYZ well so now let's look at the normal + + align:start position:0% +XYZ well so now let's look at the normal + + + align:start position:0% +XYZ well so now let's look at the normal +Vector the normal Vector would be the + + align:start position:0% +Vector the normal Vector would be the + + + align:start position:0% +Vector the normal Vector would be the +gradient of G we + + align:start position:0% +gradient of G we + + + align:start position:0% +gradient of G we +said what's the gradient of this + + align:start position:0% +said what's the gradient of this + + + align:start position:0% +said what's the gradient of this +function so gradient of G well partial G + + align:start position:0% +function so gradient of G well partial G + + + align:start position:0% +function so gradient of G well partial G +partial X that's just negative partial F + + align:start position:0% +partial X that's just negative partial F + + + align:start position:0% +partial X that's just negative partial F +partial + + align:start position:0% +partial + + + align:start position:0% +partial +X gradient G sorry the Y component + + align:start position:0% +X gradient G sorry the Y component + + + align:start position:0% +X gradient G sorry the Y component +partial G partial Y is going to be + + align:start position:0% +partial G partial Y is going to be + + + align:start position:0% +partial G partial Y is going to be +negative f sub y + + align:start position:0% +negative f sub y + + + align:start position:0% +negative f sub y +and G subz is just + + align:start position:0% + + + + align:start position:0% + +one so now if you take n/ n. + + align:start position:0% +one so now if you take n/ n. + + + align:start position:0% +one so now if you take n/ n. +K DX + + align:start position:0% +K DX + + + align:start position:0% +K DX +Dy well it looks like that's going to + + align:start position:0% +Dy well it looks like that's going to + + + align:start position:0% +Dy well it looks like that's going to +be negative f subx negative f sub y 1 + + align:start position:0% +be negative f subx negative f sub y 1 + + + align:start position:0% +be negative f subx negative f sub y 1 +divided by well what's n. K if you do + + align:start position:0% +divided by well what's n. K if you do + + + align:start position:0% +divided by well what's n. K if you do +that with K you'll get just + + align:start position:0% +that with K you'll get just + + + align:start position:0% +that with K you'll get just +one so I'm not going to write it DX + + align:start position:0% + + + + align:start position:0% + +Dy see that's again our favorite + + align:start position:0% +Dy see that's again our favorite + + + align:start position:0% +Dy see that's again our favorite +formula so this one is actually more + + align:start position:0% +formula so this one is actually more + + + align:start position:0% +formula so this one is actually more +General because you don't need to solve + + align:start position:0% +General because you don't need to solve + + + align:start position:0% +General because you don't need to solve +for Z but if you can solve for Z then + + align:start position:0% +for Z but if you can solve for Z then + + + align:start position:0% +for Z but if you can solve for Z then +it's the same as + + align:start position:0% + + + + align:start position:0% + +before + + align:start position:0% +before + + + align:start position:0% +before +okay I think that's enough formulas for + + align:start position:0% +okay I think that's enough formulas for + + + align:start position:0% +okay I think that's enough formulas for +NDS so + + align:start position:0% + + + + align:start position:0% + +after spending a lot of time telling you + + align:start position:0% +after spending a lot of time telling you + + + align:start position:0% +after spending a lot of time telling you +how to compute surface integrals now I'm + + align:start position:0% +how to compute surface integrals now I'm + + + align:start position:0% +how to compute surface integrals now I'm +going to try to tell you how to avoid + + align:start position:0% +going to try to tell you how to avoid + + + align:start position:0% +going to try to tell you how to avoid +Computing + + align:start position:0% + + + + align:start position:0% + +them and that is called the Divergence + + align:start position:0% +them and that is called the Divergence + + + align:start position:0% +them and that is called the Divergence +theem + + align:start position:0% + + + + align:start position:0% + +and we'll see the proof and everything + + align:start position:0% +and we'll see the proof and everything + + + align:start position:0% +and we'll see the proof and everything +and applications on Tuesday but I want + + align:start position:0% +and applications on Tuesday but I want + + + align:start position:0% +and applications on Tuesday but I want +to at least State the theorem and see + + align:start position:0% +to at least State the theorem and see + + + align:start position:0% +to at least State the theorem and see +how it works in one + + align:start position:0% +how it works in one + + + align:start position:0% +how it works in one +example it's also known as the G grain + + align:start position:0% +example it's also known as the G grain + + + align:start position:0% +example it's also known as the G grain +theorem or just the G theorem depending + + align:start position:0% +theorem or just the G theorem depending + + + align:start position:0% +theorem or just the G theorem depending +on who you talk to + + align:start position:0% +on who you talk to + + + align:start position:0% +on who you talk to +so the green here is the same green as + + align:start position:0% +so the green here is the same green as + + + align:start position:0% +so the green here is the same green as +in green theorum okay because that's + + align:start position:0% +in green theorum okay because that's + + + align:start position:0% +in green theorum okay because that's +somehow that's a space version of green + + align:start position:0% +somehow that's a space version of green + + + align:start position:0% +somehow that's a space version of green +spum so what does it say it + + align:start position:0% +spum so what does it say it + + + align:start position:0% +spum so what does it say it +says so it's 3D + + align:start position:0% +says so it's 3D + + + align:start position:0% +says so it's 3D +analog of grain for + + align:start position:0% + + + + align:start position:0% + +flux what it says is if + + align:start position:0% +flux what it says is if + + + align:start position:0% +flux what it says is if +s is a closed surface okay so remember + + align:start position:0% +s is a closed surface okay so remember + + + align:start position:0% +s is a closed surface okay so remember +it's the same as with green theorem we + + align:start position:0% +it's the same as with green theorem we + + + align:start position:0% +it's the same as with green theorem we +need to have something that's completely + + align:start position:0% +need to have something that's completely + + + align:start position:0% +need to have something that's completely +enclosed so you have a surface + + align:start position:0% +enclosed so you have a surface + + + align:start position:0% +enclosed so you have a surface +and there's somehow no gaps in it + + align:start position:0% +and there's somehow no gaps in it + + + align:start position:0% +and there's somehow no gaps in it +there's no boundary to it it's really + + align:start position:0% +there's no boundary to it it's really + + + align:start position:0% +there's no boundary to it it's really +completely enclosing a region in space + + align:start position:0% +completely enclosing a region in space + + + align:start position:0% +completely enclosing a region in space +that I will call + + align:start position:0% + + + + align:start position:0% + +D and I need to choose my orientation so + + align:start position:0% +D and I need to choose my orientation so + + + align:start position:0% +D and I need to choose my orientation so +the orientation that will work for this + + align:start position:0% +the orientation that will work for this + + + align:start position:0% +the orientation that will work for this +theorem is choosing the normal Vector to + + align:start position:0% +theorem is choosing the normal Vector to + + + align:start position:0% +theorem is choosing the normal Vector to +point outwards + + align:start position:0% + + + + align:start position:0% + +okay so n needs to be + + align:start position:0% + + + + align:start position:0% + +outwards so that's one part of a puzzle + + align:start position:0% +outwards so that's one part of a puzzle + + + align:start position:0% +outwards so that's one part of a puzzle +the other part is a vector field I need + + align:start position:0% +the other part is a vector field I need + + + align:start position:0% +the other part is a vector field I need +to have a vector field that's defined + + align:start position:0% +to have a vector field that's defined + + + align:start position:0% +to have a vector field that's defined +and + + align:start position:0% + + + + align:start position:0% + +differentiable everywhere in D + + align:start position:0% + + + + align:start position:0% + +so same restrictions as + + align:start position:0% +so same restrictions as + + + align:start position:0% +so same restrictions as +usual + + align:start position:0% + + + + align:start position:0% + +then I don't have actually to compute + + align:start position:0% +then I don't have actually to compute + + + align:start position:0% +then I don't have actually to compute +the flux + + align:start position:0% +the flux + + + align:start position:0% +the flux +integral double integral of f. n DS over + + align:start position:0% +integral double integral of f. n DS over + + + align:start position:0% +integral double integral of f. n DS over +a closed surface s I'm going to put a + + align:start position:0% +a closed surface s I'm going to put a + + + align:start position:0% +a closed surface s I'm going to put a +circle just to remind you it's got to be + + align:start position:0% +circle just to remind you it's got to be + + + align:start position:0% +circle just to remind you it's got to be +a closed surface okay that's just + + align:start position:0% +a closed surface okay that's just + + + align:start position:0% +a closed surface okay that's just +notation to remind us closed surface I + + align:start position:0% +notation to remind us closed surface I + + + align:start position:0% +notation to remind us closed surface I +can replace that by the triple integral + + align:start position:0% +can replace that by the triple integral + + + align:start position:0% +can replace that by the triple integral +of the region inside of Divergence of f + + align:start position:0% +of the region inside of Divergence of f + + + align:start position:0% +of the region inside of Divergence of f +DV now I need to tell you what's the + + align:start position:0% +DV now I need to tell you what's the + + + align:start position:0% +DV now I need to tell you what's the +Divergence of a 3D Vector + + align:start position:0% +Divergence of a 3D Vector + + + align:start position:0% +Divergence of a 3D Vector +field well you'll see it's not much + + align:start position:0% +field well you'll see it's not much + + + align:start position:0% +field well you'll see it's not much +harder than in the 2D case what you do + + align:start position:0% +harder than in the 2D case what you do + + + align:start position:0% +harder than in the 2D case what you do +is + + align:start position:0% + + + + align:start position:0% + +just so say that your vector field has + + align:start position:0% +just so say that your vector field has + + + align:start position:0% +just so say that your vector field has +components p q and + + align:start position:0% + + + + align:start position:0% + +R then you will take P subx plus Q sub y + + align:start position:0% +R then you will take P subx plus Q sub y + + + align:start position:0% +R then you will take P subx plus Q sub y +plus r subz okay so that's the + + align:start position:0% +plus r subz okay so that's the + + + align:start position:0% +plus r subz okay so that's the +definition it's pretty easy to remember + + align:start position:0% +definition it's pretty easy to remember + + + align:start position:0% +definition it's pretty easy to remember +you take the X component parti respect + + align:start position:0% +you take the X component parti respect + + + align:start position:0% +you take the X component parti respect +to X Plus partial respect to Y of the Y + + align:start position:0% +to X Plus partial respect to Y of the Y + + + align:start position:0% +to X Plus partial respect to Y of the Y +component plus partial respect to Z of + + align:start position:0% +component plus partial respect to Z of + + + align:start position:0% +component plus partial respect to Z of +the Z + + align:start position:0% +the Z + + + align:start position:0% +the Z +component + + align:start position:0% +component + + + align:start position:0% +component +okay so for example + + align:start position:0% + + + + align:start position:0% + +last time we + + align:start position:0% + + + + align:start position:0% + +saw that the flux of the vector field ZK + + align:start position:0% + + + + align:start position:0% + +through Sphere for a sphere of radius + + align:start position:0% + + + + align:start position:0% + +a was 4/3 a cubed by Computing the + + align:start position:0% +a was 4/3 a cubed by Computing the + + + align:start position:0% +a was 4/3 a cubed by Computing the +surface + + align:start position:0% +surface + + + align:start position:0% +surface +integral well if we do it more + + align:start position:0% +integral well if we do it more + + + align:start position:0% +integral well if we do it more +efficiently Now by Green theorem so + + align:start position:0% +efficiently Now by Green theorem so + + + align:start position:0% +efficiently Now by Green theorem so +we're going to use green + + align:start position:0% +we're going to use green + + + align:start position:0% +we're going to use green +spum for this this sphere because weing + + align:start position:0% +spum for this this sphere because weing + + + align:start position:0% +spum for this this sphere because weing +the whole sphere it's fine it's a closed + + align:start position:0% +the whole sphere it's fine it's a closed + + + align:start position:0% +the whole sphere it's fine it's a closed +surface we couldn't do it for say a + + align:start position:0% +surface we couldn't do it for say a + + + align:start position:0% +surface we couldn't do it for say a +hemisphere or something like that we + + align:start position:0% +hemisphere or something like that we + + + align:start position:0% +hemisphere or something like that we +need to well I mean for the hemisphere + + align:start position:0% +need to well I mean for the hemisphere + + + align:start position:0% +need to well I mean for the hemisphere +we need to add maybe the flat face at + + align:start position:0% +we need to add maybe the flat face at + + + align:start position:0% +we need to add maybe the flat face at +the bottom or something like that + + align:start position:0% +the bottom or something like that + + + align:start position:0% +the bottom or something like that +so GRE theorum + + align:start position:0% +so GRE theorum + + + align:start position:0% +so GRE theorum +says + + align:start position:0% + + + + align:start position:0% + +that our flux integral can be actually + + align:start position:0% +that our flux integral can be actually + + + align:start position:0% +that our flux integral can be actually +replaced by the tri integral over the + + align:start position:0% +replaced by the tri integral over the + + + align:start position:0% +replaced by the tri integral over the +solid bow of radius a of the Divergence + + align:start position:0% +solid bow of radius a of the Divergence + + + align:start position:0% +solid bow of radius a of the Divergence +of ZK DV but now what's the Divergence + + align:start position:0% +of ZK DV but now what's the Divergence + + + align:start position:0% +of ZK DV but now what's the Divergence +of this field well so you have 0 0 Z so + + align:start position:0% +of this field well so you have 0 0 Z so + + + align:start position:0% +of this field well so you have 0 0 Z so +you get 0 + 0 + + + align:start position:0% + + + + align:start position:0% + +1 looks like it will be one so if you do + + align:start position:0% +1 looks like it will be one so if you do + + + align:start position:0% +1 looks like it will be one so if you do +the triple integral of 1 DV you will get + + align:start position:0% +the triple integral of 1 DV you will get + + + align:start position:0% +the triple integral of 1 DV you will get +just the volume + + align:start position:0% + + + + align:start position:0% + +of Orion inside which is 43 Pi a + + align:start position:0% +of Orion inside which is 43 Pi a + + + align:start position:0% +of Orion inside which is 43 Pi a +cub and so it was no accident in fact + + align:start position:0% +cub and so it was no accident in fact + + + align:start position:0% +cub and so it was no accident in fact +before that we looked at also x i + y j + + align:start position:0% +before that we looked at also x i + y j + + + align:start position:0% +before that we looked at also x i + y j +plus ZK and we found three times the + + align:start position:0% +plus ZK and we found three times the + + + align:start position:0% +plus ZK and we found three times the +volume that's because the diverence of + + align:start position:0% +volume that's because the diverence of + + + align:start position:0% +volume that's because the diverence of +that field was actually + + align:start position:0% +that field was actually + + + align:start position:0% +that field was actually +three so very quickly let me just say + + align:start position:0% +three so very quickly let me just say + + + align:start position:0% +three so very quickly let me just say +what this means + + align:start position:0% +what this means + + + align:start position:0% +what this means +physically + + align:start position:0% +physically + + + align:start position:0% +physically +physically see this guy on the left is + + align:start position:0% +physically see this guy on the left is + + + align:start position:0% +physically see this guy on the left is +the amount of stuff that goes out of the + + align:start position:0% +the amount of stuff that goes out of the + + + align:start position:0% +the amount of stuff that goes out of the +region per unit + + align:start position:0% +region per unit + + + align:start position:0% +region per unit +time + + align:start position:0% +time + + + align:start position:0% +time +so I want to figure out how much stuff + + align:start position:0% +so I want to figure out how much stuff + + + align:start position:0% +so I want to figure out how much stuff +comes out of there what does the + + align:start position:0% +comes out of there what does the + + + align:start position:0% +comes out of there what does the +Divergence mean the Divergence means + + align:start position:0% +Divergence mean the Divergence means + + + align:start position:0% +Divergence mean the Divergence means +well it measures how much the flow is + + align:start position:0% +well it measures how much the flow is + + + align:start position:0% +well it measures how much the flow is +expanding things it measures how much I + + align:start position:0% +expanding things it measures how much I + + + align:start position:0% +expanding things it measures how much I +I said probably when we understood 2D + + align:start position:0% +I said probably when we understood 2D + + + align:start position:0% +I said probably when we understood 2D +Divergence it measures the amount of + + align:start position:0% +Divergence it measures the amount of + + + align:start position:0% +Divergence it measures the amount of +sources or sinks that you have inside + + align:start position:0% +sources or sinks that you have inside + + + align:start position:0% +sources or sinks that you have inside +your fluid so you know now it becomes + + align:start position:0% +your fluid so you know now it becomes + + + align:start position:0% +your fluid so you know now it becomes +common sense if you take a region of + + align:start position:0% +common sense if you take a region of + + + align:start position:0% +common sense if you take a region of +space + + align:start position:0% +space + + + align:start position:0% +space +the total amount of water that flows out + + align:start position:0% +the total amount of water that flows out + + + align:start position:0% +the total amount of water that flows out +of it is the total amount of sources + + align:start position:0% +of it is the total amount of sources + + + align:start position:0% +of it is the total amount of sources +that you have in there minus the + + align:start position:0% +that you have in there minus the + + + align:start position:0% +that you have in there minus the +sinks okay I mean in spite of this + + align:start position:0% +sinks okay I mean in spite of this + + + align:start position:0% +sinks okay I mean in spite of this +Common Sense explanation I mean we're + + align:start position:0% +Common Sense explanation I mean we're + + + align:start position:0% +Common Sense explanation I mean we're +going to see actually how to prove this + + align:start position:0% +going to see actually how to prove this + + + align:start position:0% +going to see actually how to prove this +and we'll see how it works and what it + + align:start position:0% +and we'll see how it works and what it + + + align:start position:0% +and we'll see how it works and what it +says \ No newline at end of file diff --git a/WwMz2fJwUCg.txt b/WwMz2fJwUCg.txt new file mode 100644 index 0000000000000000000000000000000000000000..3fa4ebb26dc1cecf3dec1974d2978025247e3bfa --- /dev/null +++ b/WwMz2fJwUCg.txt @@ -0,0 +1,3611 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +SRINIVAS DEVADAS: Good +morning, everyone. + +So we have a singleton lecture +today on linear programming, + +which is general purpose +optimization technique that you + +can use to solve a +whole bunch of problems, + +including ones that we've seen +in 6.046 and previously in 006. + +And most recently, we +looked at max flow. + +We wouldn't have had +to go through all + +of that pain we went through +to derive a max flow algorithm + +if you had a linear +programming package handy + +and all you wanted to do was +find the optimum solution. + +You could have just +run the linear program + +with an appropriate +input, of course, that is + +derived from the flow network. + +And you'd get your +optimal solution. + +And we'll spend a couple +of minutes on that + +as we look at the power of +linear programming in today's + +lecture. + +But it's not just max flow. + +You could do shortest paths. + +You could do multi +commodity max flow, + +which is more complicated +than max flow and a variety + +of other problems. + +So that's that good news. + +The bad news is +that the algorithms + +for linear programming are a +heck of a lot more complicated + +than max flow. + +And you can imagine that that +would be the case, because it's + +a more general purpose and +more powerful technique. + +The history really is that +it was an open problem. + +Up until 1979, people did not +know if linear programming was + +polynomial-time solvable +until Khachiyan came up + +with this ellipsoid +method, and then there's + +been progress sense. + +But the algorithm we're going +to describe today and execute + +on a example input is +a simplex algorithm-- + +the simplex algorithm-- +that runs in worst case + +exponential time. + +But it's a very +efficient in practice. + +And it's held its ground, +even with the advent + +of more efficient, from +a theoretical sense, + +polynomial-time algorithms, +namely the ellipsoid method, + +which actually is not +that efficient in practice + +and new interior point methods. + +So a little bit +of context, let's + +just dive into an +example of optimization + +in the context of +politics and see + +how you could formulate +this particular problem + +as a linear program. + +So how does politics work? + +You buy elections, right? + +So you don't want to +spend a lot of money, + +so you want to minimize +the amount of money that + +is required to buy an election. + +And the way you buy an +election is, well, campaign, + +but you advertise. + +And it doesn't matter +facts that are relevant. + +As long as you get to the right +demographic with the right + +message, let's +assume that you're + +going to win the election. + +So that's our mathematical +abstraction pf campaigning + +and politics all in 30 seconds. + +So how to campaign +to win an election. + +And as I said, we're +going to advertise. + +But you do have a little +bit of work to do here. + +That's why you need +your campaign manager. + +And this manager is +going to estimate votes + +obtained per dollar spent. + +But that dollar is spent +advertising in support + +of a particular case, +or a particular issue. + +And contradictions are allowed. + +As long as you're sending +different messages + +to different demographics, +you're all good, right? + +You're assuming +that people don't + +watch more than one channel. + +So you're a Fox News guy +or you're a MSNB guy. + +You don't do both. + +So now, we get at this estimate. + +And it turns into a table. + +And so you have your policy, +and you've got your demographic. + +So you got urban, now +think Detroit, suburban, + +I guess, you could +Lexington where you live, + +and rural-- I really don't +have any idea what that means. + +But presumably, there's places. + +And here's our policy. + +You want to build +roads-- kind of boring, + +but some people are interested +in roads-- gun control, + +of very sensitive, +farm subsidies-- + +you know who's interested +in that-- and gasoline tax-- + +kind of more, this +hits your pocket, + +so more or less everybody's +interested in that. + +So you tell the urban guys +you want to build roads, + +and they don't like you. + +So you get a minus 2 there. + +So this can go, you +advertise, and it hurts you. + +You lose votes. + +Tell the suburban +people-- well, typically, + +it's a situation where +you have these nice cars, + +and you don't like +potholes, so you like roads + +if you live in suburbia. + +Rural people have 4-by-4's. + +They don't particularly care. + +They don't care as much. + +Gun control-- well, you can +imagine that urban people + +like that. + +Suburban people +are, hm, OK, meh. + +And the rural people +hate it, right? + +You do not want to advertise on +gun control in the rural areas. + +Farm subsidies-- so like, +don't want to deal with that. + +What is a farm? + +And the rural people +love it, right? + +And then gasoline tax, well, +urban people are commuting. + +And, well, they typically +don't have a lot of money. + +So there you go. + +And those are the numbers. + +I'm not going to justify +every number here. + +But you could put whatever +numbers you what, I mean. + +So let's move on. + +This is just a table. + +It could have positive numbers. + +It could have negative numbers. + +And you still want +to win this election. + +Regardless of how +crazy the demographics + +are, how crazy +your electorate is, + +you want to win the election. + +So as long as you +have a great campaign + +manager, who can +get you this table, + +it's all mathematical +here on out. + +You've just got +to figure out how + +you're going to win a majority. + +And you could argue that all +you want is to win the election. + +We're going to do something +slightly different, which + +is something that's obviously +going to guarantee victory. + +But you want to win a +majority in every demographic. + +As the tables may be off by +little, you want to be careful. + +So the last thing, +of course, in order + +to estimate how much money you +need is the population here. + +So that's votes obtained +per dollar spent. + +So you're getting-- it's +$10 a vote, it's $5 a vote, + +et cetera. + +And so we need to +translate that to votes, + +because that's the dollars. + +And you got your population +here corresponding + +to each of these areas. + +And that's what you got here. + +Majority, we'll assume you +win in the case of ties, + +just to keep these numbers easy, +so that's just divided by 2. + +So that's what you got so far. + +And you want to win by spending +the minimum amount of money. + +So that's our +optimization problem. + +So we can take this, +and we can convert it + +to a set of linear equations. + +And that's going to create +our linear program-- + +our first linear program. + +And this is our algebraic setup. + +And so let-- we need +some variables here, + +so let x1, x2, x3, x4 denote +the dollars spent per issue. + +So you got those +four issues up there. + +So let me write that out. + +It's important to +make sure you know + +what I'm talking about with +respect to a particular issue. + +So those are our four issues. + +And those are our +four variables. + +So this linear program +has four variables. + +You're trying to discover +the values of these variables + +to optimize, minimize +your cost function. + +The second thing that +a linear program has-- + +and pretty much the only other +thing a linear program has-- + +are constraints. + +And these constraints +are also linear. + +It gets much more complicated if +you have quadratic constraints, + +and we won't go there. + +These constraints that I'm +going to write correspond + +to this statement here that +says you want to majority + +in each demographic. + +So you can imagine that because +you have three demographics, + +you're going to have +three constraints. + +You could have written +this differently. + +There's just any number +of variants here. + +And you'll get the sense of +that as we go to other examples. + +But we'll just stick +to one variant here. + +So now, I want to +translate everything + +that I've written in English +over there into algebra. + +And so I got my minimization +criterion-- minimize x1 plus x2 + +plus x3 plus x4-- subject to +minus 2x1 plus 8x2 plus 0x3 + +plus 10x4 greater than +or equal to 50,000. + +And this represents +the requirement + +that I want a majority in +the first demographic, namely + +the urban demographic. + +And so I want at least +50,000 votes there. + +And I need to spend +the money corresponding + +to the values of x1 +through x4 in such a way + +that I get those 50,000 votes. + +And that represents +that, and it's just + +reading off the minus 2, 8, 0, +and 10 from the urban column. + +So those numbers that you see +here correspond to the column, + +because I'm talking about +the urban demographic. + +And you can imagine +that the next constraint + +is going to correspond to the +middle column, and the third + +to the third. + +So I'll just write that out. + +I will call this constraint +the constraint number + +1-- I might refer to it +later-- 5x1, plus 2x2 plus 0x3, + +plus 0x4 greater than +or equal to 100,000. + +Call this number two. + +And then finally, 3x1 +minus 5x2 plus 10x3. + +And that's our set +of constraints, + +but there's one +more little issue + +that we have to be careful +about, if you're being precise, + +and that is that there's no +notion of un-advertising. + +And so you're going to +spend positive dollars. + +And so x1 through x4 is +greater than or equal to 0. + +So that's our first +linear program. + +And it came from this +particular problem. + +It'd be wonderful-- +and that's exactly what + +we're going to do for +the rest of the lecture-- + +if we could solve +this linear program + +and any possible linear +program in an efficient way. + +And so the number of +variables is small n. + +And you can imagine that the +number of constraints here, + +just talking about these +constraints, are m constraints. + +And you certainly want at run +time that is polynomial in n. + +That's our goal here. + +And as I mentioned +early on, it was unclear + +for the longest time-- well, +at least not until 1979, + +but people had been +thinking about it + +for a long time before +that-- as to whether there + +was a general algorithm that +would solve any linear program + +in time-polynomial in n. + +And that was resolved +in '79 by Khachiyan. + +We'll look at a algorithm as +simplex that in the worst case + +runs exponentially in n +but is simpler to describe + +and is very efficient +in practice. + +So in our particular problem, +this one, it turns out you-- + +and I'm actually going to come +back to this in a second-- + +but I will just tell +you that the optimum + +for this particular +linear program + +with these particular numbers +correspond to these numbers + +here. + +So you want to spend something +of the order of $20,000 + +for-- so there's 100 +here, so take away the two + +0's-- so spend something of the +order of $20,000 for the first + +issue, building roads, spend +a bit of money for the second + +issue, ignore the third +corresponding to farm + +subsidies, and spend a bit +of money for the gasoline tax + +issue. + +And these numbers aren't +important, other than the fact + +that they happen to be optimum. + +So if you add up these numbers, +then x1 plus x2 plus x3 plus x4 + +is something of the +order of $21,000-- + +$27,000, excuse me, +though I'm writing it out + +as this fraction. + +So important consideration +here is that these values xi + +are real numbers. + +That's it. + +It's not that they +have to be integral. + +Clearly, there +were fractions here + +for the optimum, +some of them anyway. + +But in general, +linear programming + +says the variable +values are real. + +There's also integer +linear programming, + +which is NP complete, which +adds the additional constraint + +that the xi values are integral. + +So it turns into +a harder problem. + +You got polynomial-time +solvable if the xi are real. + +You got NP complete, +which Eric is + +going to talk about on +Thursday, if the values are + +forced to be integral. + +So this extra constraint makes +things worse from a complexity + +standpoint. + +We won't talk about ILP anymore +for the rest of this lecture. + +So I will come back to this. + +And I'll talk about +how we can show + +that this is optimum +without actually going + +into a deep algorithmic dive. + +But what I want to +do just before that + +is to give you the +general formulation + +of a linear program. + +It's called the standard +form in CLRS, also called + +the general form. + +In some cases, we'll look +at the standard form for LP. + +And I want to pop up a +level about this example + +and give you the +general setting. + +And we'll focus in on the +general setting for the most + +part. + +But what I have here is +I can either minimize + +or maximize-- we +had a minimization + +problem-- for the +political problem, + +minimize the linear +objective function + +subject to linear +inequalities or equations. + +And the variables, +think of x as a vector, + +it's a column vector, or +x1, x2, all the way to xn. + +And the objective function is +c times x, so that's c1x1 dot, + +dot, dot, cnxn. + +And we just had all the +coefficients being a 1 + +over there. + +And the inequalities, +they're the fun part, + +you can represent +them as a matrix A, + +so A times x less +than or equal to b. + +And notice that this +is the standard form + +that I'm talking about. + +And now, I have +diverged from what + +I had here, because +I had greater + +than or equal to over here. + +So it turns out, you'll +see linear programs + +in different settings. + +Sometimes, you'll +have minimization. + +Sometimes, you'll +have maximization. + +Sometimes, you'll have +less than constraints, + +less than or equal +to constraints. + +Sometimes, you'll have greater +than or equal to constraints. + +Sometimes, you'll have +equality constraints. + +We'll spend a little +bit of time talking + +about how you can transform +any given linear program + +into a standard form. + +So our standard form is going +to be something that maximizes + +the objective function. + +So these are our +inequalities, and they're + +represented as less +than or equal to. + +That's the standard form. + +And you want to maximize +c times x-- again, + +max for standard-- such that +these set of inequalities + +told Ax less than or equal +to b and x greater than + +or equal to 0. + +So for each of the values that +correspond to the variables, + +you want these variables +to be non-negative + +in the standard form. + +And you want less than +or equal to corresponding + +to each of the +inequalities-- not equal to, + +not greater than or equal to, +but less than or equal to. + +And you have this +linear cost function, + +where you could have +arbitrary coefficients, + +but you're maximizing it. + +So that's it. + +So it's all about polarities, +not much more than that. + +It's just about polarities. + +And if you get a linear program, +a specific linear program that + +doesn't conform to this-- we'll +spend a few minutes talking + +about conversions-- +and it's going + +to be fairly straightforward. + +May not be immediately +obvious, but we'll get to that. + +Any questions so far? + +So I want to go +back to this claim + +here, where I said +this is optimum. + +Now without actually +describing an algorithm to you, + +I'm going to be able +to show you, convince + +you, that this value +here corresponding + +to whatever it is, 3 +million, 3.1 million, + +is in fact optimum. + +And this is +something I could do, + +because linear programming +has this powerful notion + +of duality. + +So what is that? + +Well, let's just first look +at our specific example here. + +And I'll give you a very +specific observation. + +I'm going to give +you what you can + +think of as a certificate +of optimality. + +I'm going to give you a +certificate of optimality + +for that set of numbers. + +And here's how I'm +going to do it. + +So is there a short certificate? + +I can imagine giving +you a long proof + +that a particular linear +programming algorithm always + +gives you the minimum +answer, the optimum answer, + +walk through that, +executive that algorithm + +on this particular +example, and then you're + +convinced, of course, +that the solution is + +going to be optimum. + +But for this specific example, I +want to give you a certificate. + +This certificate isn't going +to work for other examples. + +It's going to short, because it +only works with this example. + +But it won't work +for other ones. + +And so how do I do that? + +So the answer is, +in fact, there is + +a certificate that shows that +the LP solution is optimal. + +And consider that I compute this +particular algebraic quantity, + +where all I've done is I've +taken these three equations + +and I've multiplied them +by these magical constants. + +And so I'm not going +to tell you how we get + +this certificate of optimality. + +But I'm going to give +you the certificate. + +And it's going to +be clear that it's + +a certificate of optimality. + +And if I take these three +equations here, 1, 2, and 3-- + +actually, I refer to 1, 2, and +3, they refer to the equations. + +These are equations +or constraints. + +And so I take that. + +And obviously, if I have +a bunch of equations + +and I multiply them out, I +can certainly add them up, + +and I get another +equation at the end of it. + +And it's all going to be linear. + +And if I do that, +I get x1 plus x2 + +plus 140 divided by +222 times x3 plus x4. + +So that's what happens +to the left hand side. + +And the right hand +side is-- you'll + +recognize this quantity-- +five 0's divided by 111. + +That's what you get. + +So now, can someone tell me +why in the last step, why + +this is a certificate +of optimality-- + +the fact that obviously, this +is all algebra, once I've + +discovered the coefficients-- +so now that I've done this, + +why have I just shown you that +3.1 million divided by 111 + +is, in fact, optimum? + +Can someone tell me this? + +Look at what you have +on the left hand side. + +No? + +Yeah. + +AUDIENCE: Any other +solution would cost more + +than the amount put in spent. + +SRINIVAS DEVADAS: +Any other solution, + +but I want you to relate +that to-- what am I spending? + +AUDIENCE: You're +spending 3,100,000-- + +like, it's the same thing. + +SRINIVAS DEVADAS: Yeah, but +I mean, this was a claim. + +This was a claim-- and at +this point, an unproven claim. + +It was an unproven claim. + +Yeah, go ahead. + +AUDIENCE: You know that the left +hand side of that inequality + +is less than or equal to +x1 plus x2 plus x3 plus x4. + +SRINIVAS DEVADAS: Correct. + +And what is x1 plus x2 plus +x3 plus x4, to be clear? + +AUDIENCE: The thing +you're trying to minimize? + +SRINIVAS DEVADAS: Yeah, +exactly, the thing + +you're trying to minimize. + +Exactly. + +You're almost there. + +but the key observation here is +that x1 plus x2 plus x3 plus x4 + +is greater than or equal to x1 +plus x2-- because all of these + +are positive quantities, +remember-- 140 divided by 222, + +that's less than 1, +x3 plus x4, correct? + +So given that, I can say that +this is greater than our equal + +to 3,100,000 111. + +It's because of this +observation that it's + +a certificate of optimality. + +She has her head down, OK. + +Great. + +So that's pretty cool. + +Just cooked up these +coefficients from somewhere, + +pulled them out of +a hat, you're all + +convinced now that the +value we got was optimum. + +Did not run an algorithm. + +Maybe I ran an +algorithm-- of course, + +you ran an algorithm to get +those coefficients, right? + +Well, how did those +coefficients appear? + +So we're not going to spend +a whole lot of time on this. + +You'll see this +likely in a problem + +set or perhaps in section. + +But in general, I won't +worry too much about duality, + +other than knowing the concept. + +And this notion of LP +duality essentially + +says that what just happened +wasn't a coincidence. + +You can do this all the time. + +There will always be, +for a linear program, + +a short certificate +of optimality + +that corresponds to +some set of coefficients + +that you can do this +particular math with by taking + +these linear constraints, +multiplying them out, adding + +them up together, and showing +that you have a lower bound + +on-- in the case of this +problem-- you can't get lower + +than this. + +And therefore, for a +minimization problem, + +when you reach that, you +clearly found the optimum. + +And that's the +notion of LP duality. + +And the basic theorem-- and +this is really more as an FYI, + +we won't prove this +theorem-- is that if you + +had the standard form for the +LP, which I'm just writing down + +again here, where you had +Ax less than b, x vector + +greater than or equal to 0. + +So that's identically what +I had up here, or done here, + +corresponding to the +standard LP form. + +Well, there's a dual-- this is +what's called the primal form. + +Usually, if you +don't say it, you + +think of it as the primal form. + +And if it's dual, +you call it a dual. + +And this is primal form of LP. + +This is a dual form +of LP, or dual LP. + +And the dual LP +flips everything. + +And it's not just +negation, but transposed, + +and the actual variables +also swap functionalities. + +So it's really pretty cool. + +So your max turns into a min. + +The c gets replaced by the +b, which is on the right hand + +side of the inequalities. + +And your constraints +are A transpose, + +y greater than or equal to c. + +So there's a flip there as well. + +And y is greater +than or equal to 0. + +So there's a bunch of +things that's going on here. + +And these two problems +end up being equivalent-- + +the primal and the dual, +you can always do this. + +And essentially, what +is happening here + +is that you're solving these +two problems simultaneously. + +And there's lots +of algorithms that + +keep flipping between these +two forms for efficiency. + +But ultimately, what +ends up happening is + +you see that the actual +constraints that you had here + +corresponding to the b +constraints turn into-- the b + +ends up in the +cost function here. + +And that's essentially +what's happening out here + +with respect to multiplying +these equations out + +with particular coefficients. + +So as I said, this is +really more as an FYI. + +This is an obviously interesting +and an interesting proof + +of optimality, which is +a different kind of proof + +from proving an +algorithm correct + +and applying that proof +to a particular instance. + +That's the kind of +thing that happens + +in LP, especially when you flip +from primal and dual forms. + +So I'll leave it at that. + +What I'd like to do +is give you a sense + +of how we can convert +to standard form, + +so you can apply an algorithm +that-- for example, you + +have a program and it only +requires standard form. + +It runs on standard form. + +Let's go over it really quickly. + +This is not going to take +very long-- a translation + +from different kinds of LPs-- +and we had a slightly different + +here for our political problem +that had a minimization-- + +and how would we convert +that to standard form. + +So it's probably just one +conversion here that's tricky. + +So suppose I want to +minimize minus 2x1 plus 3x2, + +and I want to convert +it to standard formal. + +All I have is a +standard LP solver. + +What do I do? + +It should be easy. + +What do I do if I had a +solver that was maximizing, + +but I want to +minimize a quantity? + +Just switch the signs, right? + +So negate to 2x1 minus +3x2 and maximize. + +So that was easy. + +This is a tricky one. + +Suppose xj does not have a +non-negativity constraint. + +So it just happens to be the +case that it's not dollars + +but it's some other quantity +that can go negative. + +It might be profit or loss. + +So that quantity +represents profit and loss, + +so it could go +negative if it's loss. + +So I don't have this constraint +in my original problem + +specification. + +But my standard form +and my LP solver + +requires this entire +vector to be non-negative. + +So I got a problem here. + +I can't use my standard +solver, because + +of this non-negativity +constraint. + +So how do I fix that? + +How do I turn it into a problem +that allows the standard solver + +to be used? + +Yeah, go ahead. + +AUDIENCE: You can break +it up into two variables, + +like xj1 and xj2, so +xj1 minus xj2 equals xj, + +and both could have [INAUDIBLE]. + +SRINIVAS DEVADAS: Perfect, +great, that's good. + +Here you go. + +So what you do here is take +xj and replace it with, + +let's say, xj prime +minus xj double prime. + +And you have xj prime +greater than or equal to 0, + +xj double prime greater +than or equal to 0. + +But depending on the +particular values + +in whatever solution +you're exploring + +are the final solution, you +may have an actual xj value + +that's negative or positive. + +So you added an extra variable +here to your linear program. + +And a couple more +real quick, suppose + +that I have an equality +constraint corresponding + +to x1 plus x2 equals 7. + +What do I do with an +equality constraint + +where I have x1 +plus x2 equals 7? + +Yeah, go ahead. + +AUDIENCE: You can say x1 plus x2 +is greater than or equal to 7, + +and x1 plus x2 is less +than or equal to 7. + +SRINIVAS DEVADAS: No, you +can't do less than or equal to. + +AUDIENCE: But then you +can flip the signs to-- + +SRINIVAS DEVADAS: Ah, then +you could flip the signs. + +So you have two +steps there, good. + +So your less than or equal +to needs another multiplier. + +So what you end up doing is +something like x1 plus x2 + +greater than or equal to 7. + +And then you need-- if you +do what the gentleman just + +said-- and flip the sign, +you get minus x1 minus x2 + +greater than or +equal to minus 7. + +Is that right? + +No? + +I messed up? + +Oh, I want less +than or equal to. + +You're right, you're right. + +So I need less than or equal +to-- that's right, of course, + +thank you. + +So I need less than or +equal to in both places. + +So that's the standard form. + +I needed less than or equal to. + +Good. + +What you've done is increased +the number of constraints + +by one. + +Did I get this right +the second time? + +All right. + +So that's pretty much it. + +The last thing, which I +won't really write out, + +is, which we've done here +already, greater than + +or equal to constraint +translated-- I won't give you + +an example of this; +we have this already-- + +translates to less than or +equal to by minus 1 multiplied. + +So we have to +invoke that in order + +to do the equality anyway. + +So you're in business. + +If you have a +standard LP solver, + +you can take pretty much any +optimization problem that + +is linear in terms of +its objective function + +and has linear constraints, and +you can transform it into LP. + +If you had non-linear +constraints, + +there's lots of +work that goes on + +in linearizing those constraints +and using LP solvers. + +It's a very practical +thing to do. + +It may be something you'll +end up doing, invoking + +these powerful LP solvers-- +typically, they're commercially + +available; the best +ones are commercial-- + +and use it to solve +your particular problem. + +It turns your algorithm design +problem into a reduction. + +And so you'll spend really +the next couple of weeks + +thinking about reductions. + +We'll start that +up right now, where + +we'll take existing +combinatorial + +problems, for which we +already know algorithms for, + +and you're going to +reduce them to LP. + +Just to give you a sense +of what the power of LP + +is, but this notion of +reduction is very powerful, + +you can use it to do +complexity proofs. + +Here, we're just using it as a +convenience in today's lecture + +to use our LP hammer. + +So let's say that I have +our favorite problem + +of the week, namely max flow. + +And I want to +convert that to LP. + +So go back a week ago, and right +about this time a week ago, + +and we'd set up the +max flow problem. + +And let's assume that +we went back there. + +And we didn't talk +about augmenting paths, + +and we didn't talk about +residual capacities or min-cut + +or anything like that, +but we knew LP already. + +And we just want to +solve max flow using LP. + +So let's do that. + +So this is maximum flow. + +I'm not going to bother with +converting to standard form. + +We know how to do that, +given what we just + +did here, over there. + +So I'll just do whatever I +want to keep things simple. + +Max flow is obviously +a maximization problem. + +And using the same +notation we've used, + +it's not going to +look like Ax and b, + +just because I want you to +recall what max flow is. + +And we're going +to translate that. + +And the values of +these variables-- + +or the names of these variables, +whether they're x or f, + +it should really matter. + +We know how to do LP +at this point-- we + +know how to formulate LP, I +should say, at this point. + +And we're assuming that +we have an LP solver. + +So what I want to do here +with the maximum flow problem + +is maximizing the flow value. + +And it's simply, +you grab the source, + +you have a variable associated +with the flow from the source + +to every other vertex of v. +And you have to maximize that. + +So that was the +setup for max flow. + +I'm not changing that. + +What do you think the three +constraints, or whatever + +set of constraints +that we have here, + +are going to +correspond to the LP? + +You spent a week +on max flow, looked + +at the problem set, +what constraints am I + +going to have to put up there? + +I'm going to have to put +up capacity constraints. + +That's an obvious one. + +What is another one? + +Conservation constraints. + +All flow entering a node that +is not the source or the sink + +has to leave it. + +In the original +network, is there + +a concept of negative flow? + +No, you will define it going +in the other direction. + +So we did talk about +negative numbers, et cetera, + +but you're going to have +positive quantities, especially + +if you look at net flow, +the version of the flow + +that we zoomed in on in the +Tuesday lecture from last week. + +And you also have-- in +the general setting, + +you're going to have these skew +symmetry constraints as well. + +So the three things +that you need here + +are skew symmetry, +conservation, and capacity. + +So you have such that f u, v +equals minus f v, u for all u, + +v belonging to V. + +And depending on the kind +of network that you have, + +if you constrain +it to a sudden type + +that you don't have +these two-way edges, + +you could certainly +remove some, if not all, + +of these skew +symmetry constraints. + +Important ones are +conservation and capacity. + +And this should seem +pretty familiar to you. + +But the key-- the reason +I'm writing these all out + +is primarily to ensure that you +understand that these are all + +linear constraints. + +So that's pretty +much the only thing + +that you need to observe here. + +Obviously, these +constraints you've + +seen many a time from the +two lectures last week. + +But notice that +they're all linear. + +And finally, this one is f u, +v less than or equal to c of u, + +v for all u, v +belonging to cap V. + +So this is f. + +That's a variable that's +less than another constant, + +clearly linear. + +Doing a bunch of sums here. + +I could obviously have +multipliers, scalar + +multipliers. + +In this case, for +conservation, I + +don't have scalar multipliers, +but clearly linear. + +Skew symmetry, got +two variables in here. + +One of them is a negation of +the other, clearly linear, + +so that's why this is an LP. + +And so you might say, +well, I know better, + +max flow is much more +efficient than any LP + +solver that's out there. + +And you would be right. + +If you have a max flow +problem of this variety, + +it's difficult to +imagine that you + +would get performance, empirical +performance from running an LP + +solver. + +But this generalization +of max flow + +that's a multi-commodity max +flow, where you just don't have + +one commodity flowing through. + +You may be counting cars +and trucks on a road, + +or there's two different +kinds of liquid + +flowing through the same +pipe, whatever, gas or liquid. + +And so when you have +multiple commodities, + +you may have a linear but +more complicated cost function + +that's a function of the flow +of each of the commodities. + +And they may have a certain +weight associated with them. + +So there's a lot of +things that could + +be more general-- there could +be more general settings + +corresponding to max flow. + +And I'll just leave +you with the thought + +that you could simply +have two commodities. + +And we'll just +call them 1 and 2. + +And so now, you have the f1's +and the c1's and the f2's and + +the c2's. + +Each commodity has +to be conserved. + +But what about the capacity? + +What do you think happens +with the capacity? + +Let's just assume these are +two different kinds of cars. + +So what would the capacity +constraint look like? + +Yeah. + +AUDIENCE: You can +say either c1 or f1 + +plus f2 is-- for each edge, +you can add them together + +or you might take the +linear [INAUDIBLE]. + +SRINIVAS DEVADAS: +Exactly, that's right. + +So good point. + +It may be the case that I +have distinct capacities. + +And in fact, if you have +completely disjoint problems, + +you're right in that you +can solve them separately. + +But actually, the +more interesting case + +would be that you have +a single capacity c, + +so you'll have-- let me +just write this out here. + +If in fact you had +two distinct things, + +so if you had f1, c1, +f1, c2, the question + +is, do you have two distinct, +disjoint optimizations, + +in which case you just +use max flow twice. + +On other hand, what's +more interesting really-- + +and I should've used this +example for starters-- + +but here's a better one. + +You have two commodities +and a single capacity. + +So the road is a good example. + +Both the cars and the +trucks share the same road. + +It has a certain capacity. + +And now, your +capacity constraint + +is looking like f1 +plus f2 over here. + +And that's the flow through +the particular edge uv. + +So you have something +like f1 u, v plus f2 u, + +v is less than or equal to c +u, v for this total capacity. + +And that's pretty much it. + +So that is linear. + +The nice thing is +that it's linear. + +You could put weights on it. + +If you wanted to claim +that a particular commodity + +1 uses up-- because +it's a truck, + +it uses up more +space on the road. + +And you can accommodate +fewer of them. + +You could put a +multiplier in there. + +Still say it's linear. + +So that's the power of +by having an LP engine. + +You could translate +problems that + +are not exactly max flow, +that are multi-commodity flow. + +You may have additional linear +constraints that you could add, + +and you could still +use your LP package. + +So that's the reason why this +is interesting and powerful. + +So that is kind of an obvious, +corresponding to max flow. + +Let's look at something +that's a little less obvious. + +And it's going to be a little +tricky to convert the shortest + +path problem to LP, +not a lot of work + +but one little +observation that's + +going to be important to make +in order for the whole thing + +to flow through or +actually work out. + +So we all know the +shortest path problem. + +We want to find-- let's just +call it the single source + +shortest path problem. + +You have a specific source. + +That's going to turn into +the point from which you're + +going to start +computing the distance. + +That's what Dijkstra does, +and that's Bellman-Ford does. + +And so this is from vertex +x-- s, excuse me, s. + +And what I want to do here +is obviously set it up + +as a set of linear constraints. + +If I have dv corresponding to +the distance from the source-- + +so dv represents the +distance from the source-- + +and eventually I want +dv to be the shortest + +distance from the source. + +That's our notation +for shortest paths. + +dv represents an existing +path-- it may not + +be the shortest path-- from +s to v, the value of that. + +But dv monotonically +decreases as you run through. + +It's initially +infinity in Dijkstra + +going back to Dijkstra. + +And then we shrink it through +a process of relaxation. + +Now I want to try and model +that-- I want to try and model + +all of this as an LP. + +So it's not +immediately obvious-- + +the thing that the +flow networks had, + +where we had these constraints. + +We have capacity constraints +and conservation constraints. + +And we could turn that +constraint into an inequality. + +And it was pretty smooth. + +It's pretty easy. + +So what I need to do +here with shortest paths + +is something that's +a little more subtle. + +So what basic constraint do +I have in a shortest path + +algorithm? + +What's an inequality-- +you remember an inequality + +from shortest paths that +we kept talking about? + +The triangle inequality. + +So we're going to have to go +with the triangle inequality + +and take the triangle inequality +and use that to create an LP + +formulation of shortest paths. + +In particular, what +we have here is + +that I could write +dv minus du is + +less than or equal to w u, v +for all u, v belonging to E. + +And that's the +triangle inequality. + +And I'm going to +have d of s equals 0. + +That's the only thing +that I start with. + +And so what's happening +out here is simply + +that there's different +ways of getting + +to v. And my shortest path +is going to be the best + +way of getting to +v. So in particular, + +the way you want to think about +this is that if I have a v + +and I can get to it from, +let's just say, u1 and u2. + +And maybe the +source is over here. + +And these are the only two +edges that can get to v. + +So I'm just looking at a +fairly limited setting. + +u1 and u2 are going to have +to be the two vertices. + +One of these two is +going to get me to v. + +And I got w u1, v here. + +And I got w u2, v over here. + +And so what this +is saying is, I'm + +going to have to write this +out for each of these edges. + +For each of these edges, I'm +going to have this constraint. + +And that's says that the dv +value, if I want the shortest + +path, should obey both +of these constraints. + +And if I want to obey both of +these constraints, one of them + +is going to be my +limiting constraint. + +And I'm going to get +the min of those two. + +Correct? + +So in effect what +this translates to + +is that it's an AND, right? + +So dv have minus du1 is +less than or equal to w u1, + +v. dv minus du2 is less than +or equal to w u2, v. That's + +an AND, because I'm putting both +of those constraints in here. + +And that essentially +means that dv + +is going to be the min +of the two quantities-- + +the du1 quantity +plus the w u1, v, + +and the du2 quantity plus +the w u2, v. That make sense? + +Ask me questions +if this is unclear. + +So that simply +corresponds to the fact + +that I'm doing an AND over here. + +I'm adding all of these +constraints in there. + +So I'm applying the triangle +inequality to every edge, + +to every relationship +between a vertex that + +has a path ending at it. + +And you're pushing it +forward to this vertex v, + +all the different ways that +you can get to v. In this case, + +there is two sets of ways-- +one from u1 and one from u2. + +And the last step is +a minimization step. + +So you think you're +done or we're done, + +but we're not quite +done, because what's + +missing here in terms +of my formulation of LP? + +What else do I have to do here? + +Well, sure, non-negative-- +let's do that. + +Sorry? + +AUDIENCE: Objective. + +SRINIVAS DEVADAS: Objective, +who said objective? + +You again? + +So we are missing an +objective function. + +Now shortest path is what +kind of problem again? + +Short means minimum? + +Minimum, height whatever. + +So do I put a-- what happens +if I put a minimum in here? + +And let's say that I +do something like sigma + +over V, cap V, dv, because +I want to minimize-- + +or I could pick +a particular one. + +I could pick a particular single +source, single destination, + +and I put a minimum there. + +What happens? + +Does this work? + +What's the solution +to this problem, + +if I minimize the distance? + +0, because the zero +value is going to work. + +So there's something-- I +haven't put in the constraint + +that I do want a path. + +I do want a path from +s to v for any v that + +matches one of the +quantities in the min, + +because the min says +I have equality. + +The big issue here is, this +is a less than or equal to, + +and that's why the min doesn't +work in the objective function. + +It's a less than or equal to. + +But this min over here, which +is the definition of a shortest + +path, is saying that it's +either equal to this quantity + +or equal to that quantity. + +There's an equality over here +that is missing from this side. + +And that's the key observation. + +Once you observe that, +that need equality + +for one of these constituent +quantities of the min, + +then you'll see that +what you have to do + +is simply change +this min to a max. + +So you say, well, +how the heck did + +a min get changed into a max? + +And I'm not sure I'm going +to convince every on of you + +in the next minute or so. + +But the bottom line +is, it comes down + +to I do have a min already +in my inequalities, + +because I'm ANDing each +of these inequalities, + +and I'm putting down each of +those inequalities in there. + +So each of them is going to +force me to find the best + +solution, because they're +going to constrain me to not + +go via u2 if u1 is better, +because the other constraint + +corresponding to u1 is +going to force me down. + +So there's an +additional min in there, + +because the ANDing of the +less than or equal tos. + +And then in order to actually +force the equality for one + +of those, I need to push +up as hard as I can, + +or as high as I can. + +So think about it. + +Play around with a +couple of examples. + +Choose a simple +example for starters. + +And you'll see that this +is the correct formulation. + +So you can see that it's not +completely clear in some cases + +how to transform problems to LP. + +But even in those cases, +sometimes you can. + +So there's just a ton +of different problems, + +a good skill to have +to be able to take + +combinatorial +optimization engines, + +like LP or even max flow, and +be able to translate problems + +to them. + +It's something that +you'll probably + +do if you stick to +algorithms in your careers + +or exploiting available +algorithm packages. + +So the last thing I want to do +here for the rest of the time + +is to give you some sense for +how an LP program is actually + +optimized. + +How can you possibly take +the standard LP formulation, + +which is a general setting. + +You know nothing +about shortest paths, + +let's assume, nothing +about max flow. + +It's not about a +specific problem. + +It's about the general setting. + +How can we solve +the general setting, + +because that was the +theme here anyway. + +You had this engine, and +you want to use this engine. + +But now, how do you +build this engine? + +So what we're going to do is +look at a fairly simple example + +of the simplex algorithm. + +And this algorithm +is in the textbook. + +And it'll be in my notes. + +So I'll get as far as I can. + +It's not that complicated +to describe, especially + +from an example standpoint. + +But I may not get +through all of the steps + +to get you the optimum for +this particular example + +given how much time we have. + +The most important +concept in simplex + +is yet another form +of representation + +for simplex, which says that +you can represent the LP, not + +in standard form, +but in slack form. + +So I'm going to tell +you what slack form is. + +And then what we're +going to do is, + +the flow of simplex, +algorithmic flow, + +is to convert one slack +form into and equivalent. + +Obviously, you don't want to +do something that's incorrect, + +but it has to be +an equivalent slack + +form, whose objective value has +not decreased and has likely + +increased. + +So you're guaranteed that +the objective value has not + +decreased. + +You're not guaranteed +that it's increased. + +And then we're going to keep +going till the optimal solution + +becomes obvious. + +And you might say, +how is this obvious? + +That's the reason why I talked +about the short certificate + +of optimality. + +It's definitely a relationship +between the termination + +of simplex and the fact +that you can now say, + +hey, I know I'm done +here, it's kind of obvious + +that I can't do any better. + +And hopefully, you'll see that +by the end of this lecture + +in this simple example. + +So that's it. + +It's an iterative algorithm. + +It's exponential, +unfortunately, because this + +takes m plus n, choose n +iterations in the worst case, + +where n is the +number of variables + +and m is the number +of constraints. + +Most of the time, it +does a lot better, + +but that's the only bound +that you can actually + +prove in the worst case. + +And so you're stuck with +an exponential algorithm + +if you're using +simplex worst case. + +We won't actually do +much analysis on simplex. + +It's really out of scope for +046 in terms of the analysis. + +The actual algorithm is +certainly within scope. + +So what I want to do is +give you some sense for what + +the slack form looks like. + +And we'll do a couple of +iterations of simplex. + +And we'll get as far as we can +before the end the lecture. + +So we'll take a +different example + +from our political example. + +It's similar in size. + +And I want to explain to +you what the slack form is + +and why it's interesting. + +So what I want to do is maximize +3x1 plus x2 plus x3 subject + +to the constraints that +x1 plus x2 plus 3x2 + +is less than or equal to +30, 2x1 plus 2x2 plus 5x3 is + +less than or equal to 24, +4x1 plus x2 plus 2x3 less + +than or equal to 36, and then +non-negativity constraints, + +x1, x2, x3 greater +than or equal to 0. + +So that's our example problem. + +I'll leave it up there. + +You're going to convert +this to slack form. + +And so what is the slack form? + +We're going to introduce an +additional number of variables + +that correspond to the number +of equations that we have. + +So we're going to introduce, +in this case, three new labels, + +because I have three equations. + +And the slack for this +problem looks like this. + +I'm going to have z +equals 3x1 plus x2 + +plus x3, same as before. + +And then I'm going +to have variables + +that represent-- these are +called basic variables. + +And the original variables are +called non-basic variables. + +So I'm going to add three +basic labels, x4, x5, + +and x6, corresponding to +these three constraints. + +And they're going to +represent slack in the sense + +that they're going to +correspond to how much slack you + +have in the +inequalities that you + +have in the original problem. + +So if x4 happens to be +0, then you're jammed up. + +You have no slack, because x1 +plus x2 plus 3x3 equals 30. + +And increasing any one of them +will violate the constraint. + +So that's just simply +the notion of slack. + +It's how much room do you have. + +x5 is 24 minus 2x1 +minus 2x2 minus 5x3. + +And the last one +is 36 minus 4x1. + +This is very mechanical +up to this point. + +And so I'll call this set +of equations, equation I. + +And what I'm going +to do is I'm going + +to now work on a space that +corresponds to x1, x2, x3, x4, + +x5, x6. + +So I'm going to have +these solutions that + +now have six values +associated with them, + +as opposed to just three +values, because I've + +added three variables, the basic +variables, to my non-basic set. + +So the original +variables are non-basic, + +just to differentiate. + +So so far it's just +set up its definitions. + +We can think about up running +through iterations of simplex. + +It takes about three +iterations here + +in order to get to the point +where the optimum is obvious. + +So you're going to convert +through three slack forms. + +And then finally, when you +get to this fourth slack form, + +you see that you have +an optimal solution. + +And how does that work? + +You're going to have the notion +of a basic solution, where + +we set all non-basic +variables to 0. + +So in this case, what +we're going to have-- + +and then we're going to compute +values of the basic variables. + +So our objective function +here is going to be 3 times + +0 plus 1 times 0 plus 2 times +0, which is obviously 0. + +And the values x4, +of course, is going + +to be-- because all of these +are 0-- is going to be 30. + +x5 is going to be 24. + +And x6 is going to be 36. + +So this is kind of a +trivial starting point. + +So you can think +of this as 0, 0, 0, + +the solution that you're +looking at, 30 24, and 36. + +So that's our starting +point, which doesn't really + +tell you much. + +But now comes the +key step, where + +we're going to do something +that's called pivoting. + +And in pivoting, +you're going to swap + +a basic able with a +non-basic variable. + +It is a step that requires +some intelligence. + +But the basic step is a swap. + +So one of the basic +variables is going + +to become a non-basic +variable and vice versa. + +And how do we select this? + +Initially, you can kind of +do this in an arbitrary way. + +It gets a little more +subtle as you go along. + +You don't want to do +things in a random way. + +But let's just start with +what pivoting actually + +does in a more generic setting. + +The basic step is select a +non-basic variable-- let's + +call it x sub e-- who's +coefficient in the objective + +function is positive. + +You can always redefine things +if you can't find something + +like that. + +But we won't go there. + +And then what we're +going to do is + +we're going to increase the +value of x as much as possible. + +And we always have +constraints, of course. + +So we can do that +without violating + +any of the constraints. + +And then at this point, +variable xe becomes basic. + +So it's going to turn +into the left hand side. + +It's going to move over. + +You're going to swap-- the x1 +might be over here, over here, + +and you got to rewrite these +equations so the x1 becomes + +basic, for example, over +to the left hand side, + +and the variable +that it replaced + +goes over to the +right hand side. + +So you can think of this +as Gaussian elimination, + +except with inequalities. + +There's definitely +relationships there, + +if you recall your +Gaussian elimination. + +If you don't, don't +worry about it. + +So xe becomes basic, +and some other variable + +becomes non-basic. + +The values of other +basic variables + +and the objective +function may change. + +So we'll do one +pivot step at least, + +so you get a sense for +the algebra involved. + +And it becomes a +little more concrete. + +To motivate you +further, you'll be + +doing this in problem set +8 on a different example. + +So what did I do +here is we're going + +to select a non-basic variable. + +So let's just select +x1, lexicographic order + +or numeric order, let's +select x1 is selected. + +That's the non-basic variable. + +And what I want to do is +increase the value of x1. + +So I want to increase it +without violating constraints. + +Now, which of these +constraints do you think + +is going to cause trouble +first with respect + +to increasing the value of x1? + +x1 is now 0. + +We're at ground level, we have +all 0, things are feasible. + +Now, as I start +increasing x1, remember, + +you have non-negativity +constraints + +associated with each of +the x4 values as well. + +That's what these basic +variables represent. + +So don't forget the fact that +the constraints are violated. + +You need all the xi's to be +greater than or equal to 0. + +That was true for the +non-basic variables. + +It's also true for +the basic variables. + +So a violation of a +constraint implies + +that one of the currently +basic variables goes negative. + +That's exactly equivalent +to the original inequality + +not being satisfied. + +So which of these +constraints, do you think, + +is going to cause trouble here? + +Just look at it, and should +be able to look at the three + +equations and tell me, as +I increase the value of x1, + +where am I going +to hit my limit? + +x6, yes, absolutely correct. + +So that's because +of the minus 4 here. + +This is a big multiplier. + +I got a minus 1 here, a minus +2 here, and a minus 4 here. + +And if we just look at 4, the +magnitudes, 4 is bigger than 2 + +and is bigger than +1, so it's going + +to be that third constraint. + +So third constraint-- +you can obviously + +compute this numerically +or mechanically. + +It was just easier to do this in +this example by eyeballing it. + +And so third constraint +is the tightest one. + +And it limits how much +we can increase x1. + +So I'm going to +do my second step + +up there, which +corresponds to rewriting + +x1 as these other variables. + +And now, I got x1 on the +left hand side and x6 + +on the right hand side. + +And now, it's just merely +a matter of substitution. + +Once I've done this, I'm just +going to jam through and go in + +and I'm going to rewrite +the other equations with x6 + +on the right hand side. + +And that is, I'm +going to replace x1 + +with the eyeball equation. + +And that's really a +simple substitution. + +So at this point, +what's happened + +is, because the third +constraint representing x6 + +was the one that was +chosen, what's happened + +is that x1 and x6 are +going to interchange roles. + +x1 was non-basic, it's +going to become basic. + +x6 was basic and is going +to become non-basic. + +And that's basically the essence +of the simplex algorithm. + +The iteration and then the +convergence and all of that + +is, as I mentioned, going to +require getting to a point + +where the optimality +is obvious, but we + +won't be doing any +proofs corresponding + +to conversions for simplex +or any other specific LP + +techniques in this class. + +Maybe some constraint +techniques, + +I take back what I said, but +certainly not for simplex. + +But I just want to give you +a sense for the flow here. + +And so let's just go through +this last thing here in terms + +of finishing off the pivot xi's. + +And I want to show you what +the equations look like. + +And if you just keep doing that, +at some point, you'll converge. + +And so what happens +here is you have z + +equals 27 plus x2 divided +by 4 plus x3 divided + +by 2 minus 3x6 divided by 4. + +x1 equals-- so there's +a bunch of algebra + +here that I'm obviously skipping +over, but it's simple algebra. + +And I have x4 over +here, 21 minus 3x2 + +divided by 4 minus 5x3 divided +by 2 plus x6 divided by 4, + +and then one last thing here. + +So that's my pivot step, +that I've flipped x1 and x6. + +So now you ask, +what was the point? + +What was the point of this? + +Well, the point of this was +that you actually increased + +the objective function value +and, in this particular case, + +quite significantly, while +maintaining correctness. + +And so let me just make these +observations and conclude here, + +because then that gets us to +the point where you've seen + +the details of one pivot step. + +And you can imagine applying it +over and over to a convergence. + +And let's just look at the +original basic solution, + +which as you recall was +0, 0, 0, 30, 24, and 36. + +And this is simply +x1 through x6. + +This original basic +solution suddenly + +satisfies these +equations-- equations II, + +if you just put them in there. + +And it makes sense that it will +have the objective value of 0, + +given equivalents, +but you can verify + +that by saying +that you have 27-- + +the original had the +objective value of 0, + +because all the x +sub 1, x2, x3 were 0, + +so that was an easy check in the +set of equations corresponding + +to the first set, which +I've erased at this point. + +But no matter. + +And if you look at what I +have here, I have 36 equals 0. + +So the objective +value here is 0. + +It matches what you had before. + +But the basic +solution for II, I'm + +going to set the +non-basic values. + +So what is a solution here? + +The non-basic values are 0. + +So the solution is going to +be 9, because 9 is non-basic. + +x1 is now non-basic. + +x2 and x3 are still basic. + +And then I have 21 and 6. + +And x6 now has become basic. + +So the way I get this solution +is simply by plugging in 0's + +on this aside. + +And I get 9, 21, and 6, +because I just plugged + +in 0's on the right hand side. + +So that's how I +got a new solution. + +And if you look at the +objective value for this, + +the objective value, you can +look at this objective value + +simply by looking at +the original problem. + +And the original problem +had 3x1 plus x2 plus x3 + +as the objective value. + +And so if you go off and you +see, well, that you had 0's + +for the other ones, +but you have 3 times 9, + +so we have an +objective value of 27. + +So this flip of +our pivot basically + +got you from an +objective value of 0, + +while maintaining correctness, +to an objective value of 27. + +And you can look at this +in the notes or in CLRS, + +but you have to do two +more pivots corresponding + +to two other variables-- +the same grungy + +stuff that I went through here, +substitution after selection. + +And the objective value +is going to increase. + +And you might ask, how +do I know that I'm done? + +And so that was the +last thing here, + +which is increase the value +until it becomes obvious-- no, + +this was pivoting, I'm sorry-- +increase the value pivot + +until it becomes obvious +what the optimum is. + +And what ends up +happening is you end up + +with an objective function. + +In this case, the objective +function mind you, + +this thing over here is +the objective function. + +And notice that it has +a negative coefficient + +on the variable +that was actually + +the part of the first pivot. + +So x1 and x6 were a +part of the first pivot. + +And this got a +negative coefficient. + +So what ends up happening here +is you end up getting something + +like 30 minus something +minus something + +minus something, where you +have xi values over here. + +And when you set these to be +0, that's the best you can do, + +because these are all +negative quantities. + +So I'll just leave +you with that. + +Hopefully, you understood +how we do the pivoting-- + +sub through it three +times, and then + +you get that objective function, +and the optimum value is 30. + +See you next time. \ No newline at end of file diff --git a/X-4how4KkPQ.txt b/X-4how4KkPQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..752f7921ac5236d03d4bc0d908195afd1c477cd8 --- /dev/null +++ b/X-4how4KkPQ.txt @@ -0,0 +1,11347 @@ +align:start position:0% + +All right. Well, last class we started + + align:start position:0% +All right. Well, last class we started + + + align:start position:0% +All right. Well, last class we started +to talk about the forier method in + + align:start position:0% +to talk about the forier method in + + + align:start position:0% +to talk about the forier method in +uklidian space in R2. And the big goal + + align:start position:0% +uklidian space in R2. And the big goal + + + align:start position:0% +uklidian space in R2. And the big goal +for the class is to to digest the forier + + align:start position:0% +for the class is to to digest the forier + + + align:start position:0% +for the class is to to digest the forier +method, finish that story, but also just + + align:start position:0% +method, finish that story, but also just + + + align:start position:0% +method, finish that story, but also just +to digest it in general. Um and then + + align:start position:0% +to digest it in general. Um and then + + + align:start position:0% +to digest it in general. Um and then +after that if there's time we'll start + + align:start position:0% +after that if there's time we'll start + + + align:start position:0% +after that if there's time we'll start +to introduce civ theory which has a + + align:start position:0% +to introduce civ theory which has a + + + align:start position:0% +to introduce civ theory which has a +extremely parallel story um that but + + align:start position:0% +extremely parallel story um that but + + + align:start position:0% +extremely parallel story um that but +that was developed by a different group + + align:start position:0% +that was developed by a different group + + + align:start position:0% +that was developed by a different group +of people and with with somewhat + + align:start position:0% +of people and with with somewhat + + + align:start position:0% +of people and with with somewhat +different goals. + + align:start position:0% +different goals. + + + align:start position:0% +different goals. +Um okay so to digest the 4A method I + + align:start position:0% +Um okay so to digest the 4A method I + + + align:start position:0% +Um okay so to digest the 4A method I +wanted to go back for a second to the + + align:start position:0% +wanted to go back for a second to the + + + align:start position:0% +wanted to go back for a second to the +finite field 4A method where everything + + align:start position:0% +finite field 4A method where everything + + + align:start position:0% +finite field 4A method where everything +is a little bit cleaner and to make a + + align:start position:0% +is a little bit cleaner and to make a + + + align:start position:0% +is a little bit cleaner and to make a +point about it. + + align:start position:0% + + + + align:start position:0% + +Okay. So, + + align:start position:0% + + + + align:start position:0% + +so our main lema in the finite field + + align:start position:0% +so our main lema in the finite field + + + align:start position:0% +so our main lema in the finite field +case was like this. If you have a set of + + align:start position:0% +case was like this. If you have a set of + + + align:start position:0% +case was like this. If you have a set of +lines um in FQ2 + + align:start position:0% +lines um in FQ2 + + + align:start position:0% +lines um in FQ2 +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +and then you add up their characteristic + + align:start position:0% +and then you add up their characteristic + + + align:start position:0% +and then you add up their characteristic +functions + + align:start position:0% + + + + align:start position:0% + +then it has a a big constant part and + + align:start position:0% +then it has a a big constant part and + + + align:start position:0% +then it has a a big constant part and +then a small high frequency part. + + align:start position:0% +then a small high frequency part. + + + align:start position:0% +then a small high frequency part. +And then the conclusion is that f is f + + align:start position:0% +And then the conclusion is that f is f + + + align:start position:0% +And then the conclusion is that f is f +plus f high + + align:start position:0% +plus f high + + + align:start position:0% +plus f high +where um fnot is a constant function. + + align:start position:0% +where um fnot is a constant function. + + + align:start position:0% +where um fnot is a constant function. +It's the number of lines over q and from + + align:start position:0% +It's the number of lines over q and from + + + align:start position:0% +It's the number of lines over q and from +that you can compute its l2 norm. + + align:start position:0% +that you can compute its l2 norm. + + + align:start position:0% +that you can compute its l2 norm. +Um l2 squared is number of lines + + align:start position:0% +Um l2 squared is number of lines + + + align:start position:0% +Um l2 squared is number of lines +squared. + + align:start position:0% +squared. + + + align:start position:0% +squared. +Um and uh fi is has mean zero and we + + align:start position:0% +Um and uh fi is has mean zero and we + + + align:start position:0% +Um and uh fi is has mean zero and we +have a bound for its alorm. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, um, so one thing that you can get + + align:start position:0% +So, um, so one thing that you can get + + + align:start position:0% +So, um, so one thing that you can get +out of this is a bound for the L2 norm + + align:start position:0% +out of this is a bound for the L2 norm + + + align:start position:0% +out of this is a bound for the L2 norm +of f. If you add these together, you get + + align:start position:0% +of f. If you add these together, you get + + + align:start position:0% +of f. If you add these together, you get +a bound for the L2 norm of f. Um, and + + align:start position:0% +a bound for the L2 norm of f. Um, and + + + align:start position:0% +a bound for the L2 norm of f. Um, and +it's worth saying that that bound for + + align:start position:0% +it's worth saying that that bound for + + + align:start position:0% +it's worth saying that that bound for +the L2 norm of f has a elementary proof + + align:start position:0% +the L2 norm of f has a elementary proof + + + align:start position:0% +the L2 norm of f has a elementary proof +that's really simpler than this. Um, let + + align:start position:0% +that's really simpler than this. Um, let + + + align:start position:0% +that's really simpler than this. Um, let +me let me show it for comparison. + + align:start position:0% +me let me show it for comparison. + + + align:start position:0% +me let me show it for comparison. +to help put this in perspective. + + align:start position:0% +to help put this in perspective. + + + align:start position:0% +to help put this in perspective. +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So let's call this elementary L2 bound. + + align:start position:0% + + + + align:start position:0% + +Okay. So there's a first lema that if + + align:start position:0% +Okay. So there's a first lema that if + + + align:start position:0% +Okay. So there's a first lema that if +you have two different lines + + align:start position:0% +you have two different lines + + + align:start position:0% +you have two different lines +and then you take the sum over x + + align:start position:0% +and then you take the sum over x + + + align:start position:0% +and then you take the sum over x +l1 of x l2 of x uh this is at most one + + align:start position:0% +l1 of x l2 of x uh this is at most one + + + align:start position:0% +l1 of x l2 of x uh this is at most one +could do that. Uh it's just saying that + + align:start position:0% +could do that. Uh it's just saying that + + + align:start position:0% +could do that. Uh it's just saying that +two two lines intersect in at most one + + align:start position:0% +two two lines intersect in at most one + + + align:start position:0% +two two lines intersect in at most one +point. + + align:start position:0% +point. + + + align:start position:0% +point. +Okay. And we can use this to make an L2 + + align:start position:0% +Okay. And we can use this to make an L2 + + + align:start position:0% +Okay. And we can use this to make an L2 +estimate. So here's the L2 estimate. + + align:start position:0% + + + + align:start position:0% + +Um + + align:start position:0% +Um + + + align:start position:0% +Um +if f is the sum l and l of l of x + + align:start position:0% +if f is the sum l and l of l of x + + + align:start position:0% +if f is the sum l and l of l of x +then + + align:start position:0% +then + + + align:start position:0% +then +f l2 is bounded by the number the number + + align:start position:0% +f l2 is bounded by the number the number + + + align:start position:0% +f l2 is bounded by the number the number +of lines squared plus number of lines + + align:start position:0% +of lines squared plus number of lines + + + align:start position:0% +of lines squared plus number of lines +times q. + + align:start position:0% +times q. + + + align:start position:0% +times q. +Um here's the proof. + + align:start position:0% +Um here's the proof. + + + align:start position:0% +Um here's the proof. +So f L2^2 + + align:start position:0% +So f L2^2 + + + align:start position:0% +So f L2^2 +is the sum over L1 and L2 of sum on X L1 + + align:start position:0% +is the sum over L1 and L2 of sum on X L1 + + + align:start position:0% +is the sum over L1 and L2 of sum on X L1 +of X L2 of X. + + align:start position:0% + + + + align:start position:0% + +Okay. And now each one of these sums we + + align:start position:0% +Okay. And now each one of these sums we + + + align:start position:0% +Okay. And now each one of these sums we +can control with this lema. All right. + + align:start position:0% +can control with this lema. All right. + + + align:start position:0% +can control with this lema. All right. +But we have to be a little bit careful. + + align:start position:0% +But we have to be a little bit careful. + + + align:start position:0% +But we have to be a little bit careful. +If L1 is equal to L2, that's a different + + align:start position:0% +If L1 is equal to L2, that's a different + + + align:start position:0% +If L1 is equal to L2, that's a different +situation. A line intersects itself in a + + align:start position:0% +situation. A line intersects itself in a + + + align:start position:0% +situation. A line intersects itself in a +lot of points. So we're going to split + + align:start position:0% +lot of points. So we're going to split + + + align:start position:0% +lot of points. So we're going to split +up this sum. So it's the sum L1 equals + + align:start position:0% +up this sum. So it's the sum L1 equals + + + align:start position:0% +up this sum. So it's the sum L1 equals +L2 + + align:start position:0% +L2 + + + align:start position:0% +L2 +plus the sum L1 did not equal L2. + + align:start position:0% +plus the sum L1 did not equal L2. + + + align:start position:0% +plus the sum L1 did not equal L2. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So here we have um only L choices for L1 + + align:start position:0% +So here we have um only L choices for L1 + + + align:start position:0% +So here we have um only L choices for L1 +or only L choices appear in this sum and + + align:start position:0% +or only L choices appear in this sum and + + + align:start position:0% +or only L choices appear in this sum and +each one of them contributes Q. + + align:start position:0% + + + + align:start position:0% + +And then over here we have L squar + + align:start position:0% +And then over here we have L squar + + + align:start position:0% +And then over here we have L squar +choices for the lines but each one of + + align:start position:0% +choices for the lines but each one of + + + align:start position:0% +choices for the lines but each one of +them contributes one. + + align:start position:0% + + + + align:start position:0% + +So that's the + + align:start position:0% +So that's the + + + align:start position:0% +So that's the +all right so if you compare this with + + align:start position:0% +all right so if you compare this with + + + align:start position:0% +all right so if you compare this with +this it looks something looks kind of + + align:start position:0% +this it looks something looks kind of + + + align:start position:0% +this it looks something looks kind of +similar right we get an L2 bound up + + align:start position:0% +similar right we get an L2 bound up + + + align:start position:0% +similar right we get an L2 bound up +there of L^2 + LQ that matches L^2 + LQ + + align:start position:0% +there of L^2 + LQ that matches L^2 + LQ + + + align:start position:0% +there of L^2 + LQ that matches L^2 + LQ +that we get here with this quite simple + + align:start position:0% +that we get here with this quite simple + + + align:start position:0% +that we get here with this quite simple +argument. + + align:start position:0% +argument. + + + align:start position:0% +argument. +Okay, but the main lema has more + + align:start position:0% +Okay, but the main lema has more + + + align:start position:0% +Okay, but the main lema has more +information than that. Um, + + align:start position:0% +information than that. Um, + + + align:start position:0% +information than that. Um, +well, there's actually a really two + + align:start position:0% +well, there's actually a really two + + + align:start position:0% +well, there's actually a really two +cases. If Q uh is bigger than the number + + align:start position:0% +cases. If Q uh is bigger than the number + + + align:start position:0% +cases. If Q uh is bigger than the number +of lines, then this term dominates here + + align:start position:0% +of lines, then this term dominates here + + + align:start position:0% +of lines, then this term dominates here +and this term dominates here. And in + + align:start position:0% +and this term dominates here. And in + + + align:start position:0% +and this term dominates here. And in +that situation, the main lema doesn't + + align:start position:0% +that situation, the main lema doesn't + + + align:start position:0% +that situation, the main lema doesn't +really have much more information than + + align:start position:0% +really have much more information than + + + align:start position:0% +really have much more information than +this because the function fh is not that + + align:start position:0% +this because the function fh is not that + + + align:start position:0% +this because the function fh is not that +special. But the other regime is that + + align:start position:0% +special. But the other regime is that + + + align:start position:0% +special. But the other regime is that +the number of lines is much bigger than + + align:start position:0% +the number of lines is much bigger than + + + align:start position:0% +the number of lines is much bigger than +Q. So this dominates that + + align:start position:0% +Q. So this dominates that + + + align:start position:0% +Q. So this dominates that +and in that situation most of the L2 + + align:start position:0% +and in that situation most of the L2 + + + align:start position:0% +and in that situation most of the L2 +norm is coming from F knot which is very + + align:start position:0% +norm is coming from F knot which is very + + + align:start position:0% +norm is coming from F knot which is very +special because it's constant. + + align:start position:0% +special because it's constant. + + + align:start position:0% +special because it's constant. +Um so so the um + + align:start position:0% +Um so so the um + + + align:start position:0% +Um so so the um +so the main lema has an important piece + + align:start position:0% +so the main lema has an important piece + + + align:start position:0% +so the main lema has an important piece +of information beyond this that when we + + align:start position:0% +of information beyond this that when we + + + align:start position:0% +of information beyond this that when we +have many lines this sum is almost + + align:start position:0% +have many lines this sum is almost + + + align:start position:0% +have many lines this sum is almost +constant and and then it's a constant + + align:start position:0% +constant and and then it's a constant + + + align:start position:0% +constant and and then it's a constant +plus something that's much smaller. + + align:start position:0% +plus something that's much smaller. + + + align:start position:0% +plus something that's much smaller. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +so that uh that is also true in spirit + + align:start position:0% +so that uh that is also true in spirit + + + align:start position:0% +so that uh that is also true in spirit +for the main lema in the real case, but + + align:start position:0% +for the main lema in the real case, but + + + align:start position:0% +for the main lema in the real case, but +the main lemon in the real case is a + + align:start position:0% +the main lemon in the real case is a + + + align:start position:0% +the main lemon in the real case is a +little bit more complicated. So I wanted + + align:start position:0% +little bit more complicated. So I wanted + + + align:start position:0% +little bit more complicated. So I wanted +to do this first and then we could look + + align:start position:0% +to do this first and then we could look + + + align:start position:0% +to do this first and then we could look +for the analogous thing in the more + + align:start position:0% +for the analogous thing in the more + + + align:start position:0% +for the analogous thing in the more +complicated real case. + + align:start position:0% +complicated real case. + + + align:start position:0% +complicated real case. +Okay. So what did the main lema say in + + align:start position:0% +Okay. So what did the main lema say in + + + align:start position:0% +Okay. So what did the main lema say in +the real case? + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Main lema in the real case. + + align:start position:0% +Main lema in the real case. + + + align:start position:0% +Main lema in the real case. +So now we have t is a set of 1 by r + + align:start position:0% +So now we have t is a set of 1 by r + + + align:start position:0% +So now we have t is a set of 1 by r +rectangles + + align:start position:0% + + + + align:start position:0% + +and um uh s t is a smooth approximation + + align:start position:0% + + + + align:start position:0% + +of the characteristic function of t and + + align:start position:0% +of the characteristic function of t and + + + align:start position:0% +of the characteristic function of t and +the exact meaning of that is explained + + align:start position:0% +the exact meaning of that is explained + + + align:start position:0% +the exact meaning of that is explained +in agonizing detail on the homework. + + align:start position:0% +in agonizing detail on the homework. + + + align:start position:0% +in agonizing detail on the homework. +Um okay and then we have a function + + align:start position:0% +Um okay and then we have a function + + + align:start position:0% +Um okay and then we have a function +which is the sum over all the t and t of + + align:start position:0% +which is the sum over all the t and t of + + + align:start position:0% +which is the sum over all the t and t of +this smoothed characteristic function of + + align:start position:0% +this smoothed characteristic function of + + + align:start position:0% +this smoothed characteristic function of +t. + + align:start position:0% +t. + + + align:start position:0% +t. +Okay. Now our bounds are going to depend + + align:start position:0% +Okay. Now our bounds are going to depend + + + align:start position:0% +Okay. Now our bounds are going to depend +on how these tubes are clustered. + + align:start position:0% +on how these tubes are clustered. + + + align:start position:0% +on how these tubes are clustered. +So n subt of r + + align:start position:0% +So n subt of r + + + align:start position:0% +So n subt of r +is the maximum where t tilda is a two + + align:start position:0% +is the maximum where t tilda is a two + + + align:start position:0% +is the maximum where t tilda is a two +little r by two big r a rectangle or + + align:start position:0% +little r by two big r a rectangle or + + + align:start position:0% +little r by two big r a rectangle or +tube of the number of tubes in there. + + align:start position:0% + + + + align:start position:0% + +So picture is we have this tilda and we + + align:start position:0% +So picture is we have this tilda and we + + + align:start position:0% +So picture is we have this tilda and we +see how many middle tubes are in tilda. + + align:start position:0% + + + + align:start position:0% + +Okay so that those are the hypotheses of + + align:start position:0% +Okay so that those are the hypotheses of + + + align:start position:0% +Okay so that those are the hypotheses of +the main lema and then the conclusion is + + align:start position:0% +the main lema and then the conclusion is + + + align:start position:0% +the main lema and then the conclusion is +that you can write f uh you can break it + + align:start position:0% +that you can write f uh you can break it + + + align:start position:0% +that you can write f uh you can break it +up into pieces of different frequencies. + + align:start position:0% +up into pieces of different frequencies. + + + align:start position:0% +up into pieces of different frequencies. +So the pieces are labeled by a sort of a + + align:start position:0% +So the pieces are labeled by a sort of a + + + align:start position:0% +So the pieces are labeled by a sort of a +width parameter little r which is a + + align:start position:0% +width parameter little r which is a + + + align:start position:0% +width parameter little r which is a +diatic number between scale one and + + align:start position:0% +diatic number between scale one and + + + align:start position:0% +diatic number between scale one and +scale capital r + + align:start position:0% +scale capital r + + + align:start position:0% +scale capital r +of f sub little r + + align:start position:0% +of f sub little r + + + align:start position:0% +of f sub little r +where the f sub little r has two good + + align:start position:0% +where the f sub little r has two good + + + align:start position:0% +where the f sub little r has two good +properties. It has a frequency support. + + align:start position:0% +properties. It has a frequency support. + + + align:start position:0% +properties. It has a frequency support. +The support of f little r hat is + + align:start position:0% +The support of f little r hat is + + + align:start position:0% +The support of f little r hat is +contained in the ball of radius 1 / r + + align:start position:0% +contained in the ball of radius 1 / r + + + align:start position:0% +contained in the ball of radius 1 / r +and it has an l2 norm uh bound f sub + + align:start position:0% +and it has an l2 norm uh bound f sub + + + align:start position:0% +and it has an l2 norm uh bound f sub +little r l2 2 is bounded by um the + + align:start position:0% +little r l2 2 is bounded by um the + + + align:start position:0% +little r l2 2 is bounded by um the +number of tubes times this + + align:start position:0% +number of tubes times this + + + align:start position:0% +number of tubes times this +um packing clustering uh parameter at at + + align:start position:0% +um packing clustering uh parameter at at + + + align:start position:0% +um packing clustering uh parameter at at +the scale little r um times big r + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Okay. Now, one thing you could take away + + align:start position:0% +Okay. Now, one thing you could take away + + + align:start position:0% +Okay. Now, one thing you could take away +from this is you could take away from it + + align:start position:0% +from this is you could take away from it + + + align:start position:0% +from this is you could take away from it +a bound for the L2 norm of F by just + + align:start position:0% +a bound for the L2 norm of F by just + + + align:start position:0% +a bound for the L2 norm of F by just +adding up all of these. And like before, + + align:start position:0% +adding up all of these. And like before, + + + align:start position:0% +adding up all of these. And like before, +that bound for the L2 norm of F has a + + align:start position:0% +that bound for the L2 norm of F has a + + + align:start position:0% +that bound for the L2 norm of F has a +simpler proof. Um, and for context for + + align:start position:0% +simpler proof. Um, and for context for + + + align:start position:0% +simpler proof. Um, and for context for +understanding this, I'm going to show + + align:start position:0% +understanding this, I'm going to show + + + align:start position:0% +understanding this, I'm going to show +you this simpler proof. + + align:start position:0% +you this simpler proof. + + + align:start position:0% +you this simpler proof. +>> Yes. FR is orthogonal. + + align:start position:0% +>> Yes. FR is orthogonal. + + + align:start position:0% +>> Yes. FR is orthogonal. +>> The FRS uh the FRS are orthogonal. Um + + align:start position:0% +>> The FRS uh the FRS are orthogonal. Um + + + align:start position:0% +>> The FRS uh the FRS are orthogonal. Um +yeah, the FRS are orthogonal. Um if we + + align:start position:0% +yeah, the FRS are orthogonal. Um if we + + + align:start position:0% +yeah, the FRS are orthogonal. Um if we +didn't know they were orthogonal, we + + align:start position:0% +didn't know they were orthogonal, we + + + align:start position:0% +didn't know they were orthogonal, we +would lose a little bit when we we'd + + align:start position:0% +would lose a little bit when we we'd + + + align:start position:0% +would lose a little bit when we we'd +have to do Koshy Schwarz to compute the + + align:start position:0% +have to do Koshy Schwarz to compute the + + + align:start position:0% +have to do Koshy Schwarz to compute the +L2 of F. Um but the amount that we would + + align:start position:0% +L2 of F. Um but the amount that we would + + + align:start position:0% +L2 of F. Um but the amount that we would +lose would be like a log R, which is + + align:start position:0% +lose would be like a log R, which is + + + align:start position:0% +lose would be like a log R, which is +relatively minor. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. So, let's do an elementary L2 + + align:start position:0% +Okay. So, let's do an elementary L2 + + + align:start position:0% +Okay. So, let's do an elementary L2 +bound. + + align:start position:0% + + + + align:start position:0% + +All right. So, like before we when we + + align:start position:0% +All right. So, like before we when we + + + align:start position:0% +All right. So, like before we when we +expand out the L2 norm, we'll have to + + align:start position:0% +expand out the L2 norm, we'll have to + + + align:start position:0% +expand out the L2 norm, we'll have to +estimate the integral of one tube times + + align:start position:0% +estimate the integral of one tube times + + + align:start position:0% +estimate the integral of one tube times +another tube. Um, but one tube times + + align:start position:0% +another tube. Um, but one tube times + + + align:start position:0% +another tube. Um, but one tube times +another tube is a little bit more + + align:start position:0% +another tube is a little bit more + + + align:start position:0% +another tube is a little bit more +complicated than one line times another + + align:start position:0% +complicated than one line times another + + + align:start position:0% +complicated than one line times another +line. Two lines always intersect in a + + align:start position:0% +line. Two lines always intersect in a + + + align:start position:0% +line. Two lines always intersect in a +point, but two tubes intersect in a + + align:start position:0% +point, but two tubes intersect in a + + + align:start position:0% +point, but two tubes intersect in a +different amount of area depending upon + + align:start position:0% +different amount of area depending upon + + + align:start position:0% +different amount of area depending upon +the angle between them. So, we're going + + align:start position:0% +the angle between them. So, we're going + + + align:start position:0% +the angle between them. So, we're going +to keep track of that. + + align:start position:0% +to keep track of that. + + + align:start position:0% +to keep track of that. +All right. So, let's make a definition. + + align:start position:0% +All right. So, let's make a definition. + + + align:start position:0% +All right. So, let's make a definition. +the um width r in between t1 and t2 + + align:start position:0% +the um width r in between t1 and t2 + + + align:start position:0% +the um width r in between t1 and t2 +is the minimum uh r so that there exists + + align:start position:0% +is the minimum uh r so that there exists + + + align:start position:0% +is the minimum uh r so that there exists +a two r two little r by two big r + + align:start position:0% +a two r two little r by two big r + + + align:start position:0% +a two r two little r by two big r +rectangle tilda that contains them both. + + align:start position:0% + + + + align:start position:0% + +So if this is t1 and this is t2 + + align:start position:0% + + + + align:start position:0% + +then um + + align:start position:0% +then um + + + align:start position:0% +then um +that would be t tilda and that would be + + align:start position:0% +that would be t tilda and that would be + + + align:start position:0% +that would be t tilda and that would be +r. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So now + + align:start position:0% +So now + + + align:start position:0% +So now +if I want to integrate t1 of x t2 of x + + align:start position:0% +if I want to integrate t1 of x t2 of x + + + align:start position:0% +if I want to integrate t1 of x t2 of x +dx + + align:start position:0% +dx + + + align:start position:0% +dx +that's going to be about big r over the + + align:start position:0% +that's going to be about big r over the + + + align:start position:0% +that's going to be about big r over the +little r associated to these two tubes. + + align:start position:0% +little r associated to these two tubes. + + + align:start position:0% +little r associated to these two tubes. +Why? Well the integral is the area of + + align:start position:0% +Why? Well the integral is the area of + + + align:start position:0% +Why? Well the integral is the area of +their overlap. + + align:start position:0% +their overlap. + + + align:start position:0% +their overlap. +And if I I'll sort of sketch their + + align:start position:0% +And if I I'll sort of sketch their + + + align:start position:0% +And if I I'll sort of sketch their +overlap over here. Um not a great + + align:start position:0% +overlap over here. Um not a great + + + align:start position:0% +overlap over here. Um not a great +picture. Um this is around one because + + align:start position:0% +picture. Um this is around one because + + + align:start position:0% +picture. Um this is around one because +it's contained in one of the tubes. And + + align:start position:0% +it's contained in one of the tubes. And + + + align:start position:0% +it's contained in one of the tubes. And +this axis here is uh like big r over + + align:start position:0% +this axis here is uh like big r over + + + align:start position:0% +this axis here is uh like big r over +little r. + + align:start position:0% +little r. + + + align:start position:0% +little r. +As little r gets smaller, they overlap + + align:start position:0% +As little r gets smaller, they overlap + + + align:start position:0% +As little r gets smaller, they overlap +more and more. + + align:start position:0% + + + + align:start position:0% + +Okay, good. Um so now we can make it L2 + + align:start position:0% +Okay, good. Um so now we can make it L2 + + + align:start position:0% +Okay, good. Um so now we can make it L2 +bound. + + align:start position:0% + + + + align:start position:0% + +Let's say that the integral of f2 + + align:start position:0% +Let's say that the integral of f2 + + + align:start position:0% +Let's say that the integral of f2 +bounded by the sum uh sum over little + + align:start position:0% +bounded by the sum uh sum over little + + + align:start position:0% +bounded by the sum uh sum over little +ratic + + align:start position:0% +ratic + + + align:start position:0% +ratic +of + + align:start position:0% +of + + + align:start position:0% +of +t * n subt of little r * big r over + + align:start position:0% +t * n subt of little r * big r over + + + align:start position:0% +t * n subt of little r * big r over +little r. + + align:start position:0% +little r. + + + align:start position:0% +little r. +Okay. And the proof is that we'll just + + align:start position:0% +Okay. And the proof is that we'll just + + + align:start position:0% +Okay. And the proof is that we'll just +break up this sum as a bunch of sums + + align:start position:0% +break up this sum as a bunch of sums + + + align:start position:0% +break up this sum as a bunch of sums +bunch of integrals like this. group them + + align:start position:0% +bunch of integrals like this. group them + + + align:start position:0% +bunch of integrals like this. group them +according to the value of little r and + + align:start position:0% +according to the value of little r and + + + align:start position:0% +according to the value of little r and +we'll see what happens. This is what's + + align:start position:0% +we'll see what happens. This is what's + + + align:start position:0% +we'll see what happens. This is what's +going to fall out. + + align:start position:0% +going to fall out. + + + align:start position:0% +going to fall out. +So here's the proof. Um so the integral + + align:start position:0% +So here's the proof. Um so the integral + + + align:start position:0% +So here's the proof. Um so the integral +of f2 is the sum t1 and t2 in our set of + + align:start position:0% +of f2 is the sum t1 and t2 in our set of + + + align:start position:0% +of f2 is the sum t1 and t2 in our set of +tubes integral of t1 of x t2x. + + align:start position:0% + + + + align:start position:0% + +Now this integral here depends on the + + align:start position:0% +Now this integral here depends on the + + + align:start position:0% +Now this integral here depends on the +value of little r. So let's group these + + align:start position:0% +value of little r. So let's group these + + + align:start position:0% +value of little r. So let's group these +by the value of little r. So that's the + + align:start position:0% +by the value of little r. So that's the + + + align:start position:0% +by the value of little r. So that's the +sum over little ratic + + align:start position:0% +sum over little ratic + + + align:start position:0% +sum over little ratic +sum over t1 and t2 with that value. + + align:start position:0% +sum over t1 and t2 with that value. + + + align:start position:0% +sum over t1 and t2 with that value. +So the r associated to t1 and t2 would + + align:start position:0% +So the r associated to t1 and t2 would + + + align:start position:0% +So the r associated to t1 and t2 would +be about this r + + align:start position:0% +be about this r + + + align:start position:0% +be about this r +and then I have this integral which I + + align:start position:0% +and then I have this integral which I + + + align:start position:0% +and then I have this integral which I +can bound by the lema. So I get big r + + align:start position:0% +can bound by the lema. So I get big r + + + align:start position:0% +can bound by the lema. So I get big r +over little r. + + align:start position:0% + + + + align:start position:0% + +Okay. Now I need to know how many pairs + + align:start position:0% +Okay. Now I need to know how many pairs + + + align:start position:0% +Okay. Now I need to know how many pairs +of tubes are in this list here. Well, I + + align:start position:0% +of tubes are in this list here. Well, I + + + align:start position:0% +of tubes are in this list here. Well, I +can choose T1 and T1 as far as I know + + align:start position:0% +can choose T1 and T1 as far as I know + + + align:start position:0% +can choose T1 and T1 as far as I know +could be anything. So I have number of + + align:start position:0% +could be anything. So I have number of + + + align:start position:0% +could be anything. So I have number of +tubes choices for T1. But once I choose + + align:start position:0% +tubes choices for T1. But once I choose + + + align:start position:0% +tubes choices for T1. But once I choose +T1, I choose need to choose another tube + + align:start position:0% +T1, I choose need to choose another tube + + + align:start position:0% +T1, I choose need to choose another tube +T2 that fits into the same rectangle + + align:start position:0% +T2 that fits into the same rectangle + + + align:start position:0% +T2 that fits into the same rectangle +with T1. So the number of choices for + + align:start position:0% +with T1. So the number of choices for + + + align:start position:0% +with T1. So the number of choices for +that is about N subt R. It's what it's + + align:start position:0% +that is about N subt R. It's what it's + + + align:start position:0% +that is about N subt R. It's what it's +measured. + + align:start position:0% +measured. + + + align:start position:0% +measured. +So this is bounded by sum over r diatic + + align:start position:0% +So this is bounded by sum over r diatic + + + align:start position:0% +So this is bounded by sum over r diatic +of um + + align:start position:0% +of um + + + align:start position:0% +of um +number of tubes + + align:start position:0% +number of tubes + + + align:start position:0% +number of tubes +and n subt of r big r over little. + + align:start position:0% + + + + align:start position:0% + +Okay, great. + + align:start position:0% +Okay, great. + + + align:start position:0% +Okay, great. +So let's compare this with this. + + align:start position:0% +So let's compare this with this. + + + align:start position:0% +So let's compare this with this. +This is exactly what we get by just + + align:start position:0% +This is exactly what we get by just + + + align:start position:0% +This is exactly what we get by just +adding up all those L2 norms uh for the + + align:start position:0% +adding up all those L2 norms uh for the + + + align:start position:0% +adding up all those L2 norms uh for the +for the F subr. + + align:start position:0% +for the F subr. + + + align:start position:0% +for the F subr. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +so this proof is a lot easier than the + + align:start position:0% +so this proof is a lot easier than the + + + align:start position:0% +so this proof is a lot easier than the +proof of the main lama that we did last + + align:start position:0% +proof of the main lama that we did last + + + align:start position:0% +proof of the main lama that we did last +time. Um let's compare the L2 bound in + + align:start position:0% +time. Um let's compare the L2 bound in + + + align:start position:0% +time. Um let's compare the L2 bound in +the main lama. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +If I were to erase this information in + + align:start position:0% +If I were to erase this information in + + + align:start position:0% +If I were to erase this information in +the main lema, then all that would be + + align:start position:0% +the main lema, then all that would be + + + align:start position:0% +the main lema, then all that would be +left is the L2 bound. + + align:start position:0% +left is the L2 bound. + + + align:start position:0% +left is the L2 bound. +But there is this information and this + + align:start position:0% +But there is this information and this + + + align:start position:0% +But there is this information and this +is helpful. This is telling us something + + align:start position:0% +is helpful. This is telling us something + + + align:start position:0% +is helpful. This is telling us something +more. Um, okay. Now, depending upon what + + align:start position:0% +more. Um, okay. Now, depending upon what + + + align:start position:0% +more. Um, okay. Now, depending upon what +we know about this thing here, different + + align:start position:0% +we know about this thing here, different + + + align:start position:0% +we know about this thing here, different +terms might dominate this sum. + + align:start position:0% +terms might dominate this sum. + + + align:start position:0% +terms might dominate this sum. +If it so happens that the term little r + + align:start position:0% +If it so happens that the term little r + + + align:start position:0% +If it so happens that the term little r +equals 1 uh has the biggest contribution + + align:start position:0% +equals 1 uh has the biggest contribution + + + align:start position:0% +equals 1 uh has the biggest contribution +here um then we don't learn very much + + align:start position:0% +here um then we don't learn very much + + + align:start position:0% +here um then we don't learn very much +because the our information about the + + align:start position:0% +because the our information about the + + + align:start position:0% +because the our information about the +support of f1 hat is is the same as the + + align:start position:0% +support of f1 hat is is the same as the + + + align:start position:0% +support of f1 hat is is the same as the +information we already had about the + + align:start position:0% +information we already had about the + + + align:start position:0% +information we already had about the +support of fhat. So we'd have nothing + + align:start position:0% +support of fhat. So we'd have nothing + + + align:start position:0% +support of fhat. So we'd have nothing +new. uh but it may well happen that the + + align:start position:0% +new. uh but it may well happen that the + + + align:start position:0% +new. uh but it may well happen that the +that the the term where this is biggest + + align:start position:0% +that the the term where this is biggest + + + align:start position:0% +that the the term where this is biggest +is has little r much larger + + align:start position:0% +is has little r much larger + + + align:start position:0% +is has little r much larger +and then f little r has this frequency + + align:start position:0% +and then f little r has this frequency + + + align:start position:0% +and then f little r has this frequency +support condition. It gives it some + + align:start position:0% +support condition. It gives it some + + + align:start position:0% +support condition. It gives it some +structure some extra information there + + align:start position:0% +structure some extra information there + + + align:start position:0% +structure some extra information there +that's going to help us. + + align:start position:0% + + + + align:start position:0% + +So let's talk about what what does it + + align:start position:0% +So let's talk about what what does it + + + align:start position:0% +So let's talk about what what does it +mean about the function f little r that + + align:start position:0% +mean about the function f little r that + + + align:start position:0% +mean about the function f little r that +it's frequency is supported there. + + align:start position:0% + + + + align:start position:0% + +Okay. So uh intuition + + align:start position:0% + + + + align:start position:0% + +we call this the the locally constant + + align:start position:0% +we call this the the locally constant + + + align:start position:0% +we call this the the locally constant +intuition + + align:start position:0% + + + + align:start position:0% + +says that if I have some function g and + + align:start position:0% +says that if I have some function g and + + + align:start position:0% +says that if I have some function g and +the support of g hat is contained in the + + align:start position:0% +the support of g hat is contained in the + + + align:start position:0% +the support of g hat is contained in the +ball of radius 1 / r um then + + align:start position:0% +ball of radius 1 / r um then + + + align:start position:0% +ball of radius 1 / r um then +the function g is approximately constant + + align:start position:0% +the function g is approximately constant + + + align:start position:0% +the function g is approximately constant +on balls of radius plus. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +um you know if the support of Ghat is in + + align:start position:0% +um you know if the support of Ghat is in + + + align:start position:0% +um you know if the support of Ghat is in +the ball of radius 1 / r then ghat is a + + align:start position:0% +the ball of radius 1 / r then ghat is a + + + align:start position:0% +the ball of radius 1 / r then ghat is a +combination of waves cosine waves where + + align:start position:0% +combination of waves cosine waves where + + + align:start position:0% +combination of waves cosine waves where +all of the cosine waves have have + + align:start position:0% +all of the cosine waves have have + + + align:start position:0% +all of the cosine waves have have +frequency at most one over r. So each + + align:start position:0% +frequency at most one over r. So each + + + align:start position:0% +frequency at most one over r. So each +one of those cosine waves is not + + align:start position:0% +one of those cosine waves is not + + + align:start position:0% +one of those cosine waves is not +changing very much on balls of radius R. + + align:start position:0% +changing very much on balls of radius R. + + + align:start position:0% +changing very much on balls of radius R. +So it's sort of intuitively plausible + + align:start position:0% +So it's sort of intuitively plausible + + + align:start position:0% +So it's sort of intuitively plausible +that after we add them up also we'll get + + align:start position:0% +that after we add them up also we'll get + + + align:start position:0% +that after we add them up also we'll get +something that is roughly constant on + + align:start position:0% +something that is roughly constant on + + + align:start position:0% +something that is roughly constant on +balls of radius R. + + align:start position:0% +balls of radius R. + + + align:start position:0% +balls of radius R. +We'll come back in a little while and + + align:start position:0% +We'll come back in a little while and + + + align:start position:0% +We'll come back in a little while and +make a precise statement about this. + + align:start position:0% + + + + align:start position:0% + +Okay. So based on this, let me make a + + align:start position:0% +Okay. So based on this, let me make a + + + align:start position:0% +Okay. So based on this, let me make a +picture illustrating main lama R + + align:start position:0% + + + + align:start position:0% + +main + + align:start position:0% +main + + + align:start position:0% +main +and then + + align:start position:0% + + + + align:start position:0% + +okay. Um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +okay so th this will be well so this + + align:start position:0% +okay so th this will be well so this + + + align:start position:0% +okay so th this will be well so this +will be like a uh each one of those + + align:start position:0% +will be like a uh each one of those + + + align:start position:0% +will be like a uh each one of those +lines is going to be a one by R tube. + + align:start position:0% +lines is going to be a one by R tube. + + + align:start position:0% +lines is going to be a one by R tube. +So, I may have a whole bunch of them + + align:start position:0% +So, I may have a whole bunch of them + + + align:start position:0% +So, I may have a whole bunch of them +over here, sort of like this. And a + + align:start position:0% +over here, sort of like this. And a + + + align:start position:0% +over here, sort of like this. And a +whole bunch of them + + align:start position:0% +whole bunch of them + + + align:start position:0% +whole bunch of them +over here, sort of like this. + + align:start position:0% +over here, sort of like this. + + + align:start position:0% +over here, sort of like this. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +And over over in this part of the board, + + align:start position:0% +And over over in this part of the board, + + + align:start position:0% +And over over in this part of the board, +I might have some that are not uh so + + align:start position:0% +I might have some that are not uh so + + + align:start position:0% +I might have some that are not uh so +clumped into thick tubes. It might look + + align:start position:0% +clumped into thick tubes. It might look + + + align:start position:0% +clumped into thick tubes. It might look +sort of like this. + + align:start position:0% + + + + align:start position:0% + +All right. So over here what the picture + + align:start position:0% +All right. So over here what the picture + + + align:start position:0% +All right. So over here what the picture +I wanted to to give you is that I put so + + align:start position:0% +I wanted to to give you is that I put so + + + align:start position:0% +I wanted to to give you is that I put so +many thin strokes of chalk one by our + + align:start position:0% +many thin strokes of chalk one by our + + + align:start position:0% +many thin strokes of chalk one by our +rectangles that they sort of smooshed on + + align:start position:0% +rectangles that they sort of smooshed on + + + align:start position:0% +rectangles that they sort of smooshed on +top of each other and they produced with + + align:start position:0% +top of each other and they produced with + + + align:start position:0% +top of each other and they produced with +like a thick stroke. + + align:start position:0% + + + + align:start position:0% + +Um and so this part over here might be + + align:start position:0% +Um and so this part over here might be + + + align:start position:0% +Um and so this part over here might be +dominated by f of r. So maybe this scale + + align:start position:0% +dominated by f of r. So maybe this scale + + + align:start position:0% +dominated by f of r. So maybe this scale +might be R and F subr + + align:start position:0% +might be R and F subr + + + align:start position:0% +might be R and F subr +be sort of the sum of this blob and that + + align:start position:0% +be sort of the sum of this blob and that + + + align:start position:0% +be sort of the sum of this blob and that +blob + + align:start position:0% + + + + align:start position:0% + +and on the other so this so this over + + align:start position:0% +and on the other so this so this over + + + align:start position:0% +and on the other so this so this over +here in blue would be f subr + + align:start position:0% +here in blue would be f subr + + + align:start position:0% +here in blue would be f subr +and on the other hand this over here + + align:start position:0% +and on the other hand this over here + + + align:start position:0% +and on the other hand this over here +would be f sub f sub one all of this + + align:start position:0% +would be f sub f sub one all of this + + + align:start position:0% +would be f sub f sub one all of this +stuff uh is pretty high frequency + + align:start position:0% + + + + align:start position:0% + +Okay. And notice that this f subar is + + align:start position:0% +Okay. And notice that this f subar is + + + align:start position:0% +Okay. And notice that this f subar is +kind of roughly constant on any ball of + + align:start position:0% +kind of roughly constant on any ball of + + + align:start position:0% +kind of roughly constant on any ball of +radius r. And so if I were to visualize + + align:start position:0% +radius r. And so if I were to visualize + + + align:start position:0% +radius r. And so if I were to visualize +the set where f is big. + + align:start position:0% + + + + align:start position:0% + +Um well there might be some bits in here + + align:start position:0% +Um well there might be some bits in here + + + align:start position:0% +Um well there might be some bits in here +where f is big + + align:start position:0% +where f is big + + + align:start position:0% +where f is big +but then there also might be some piece + + align:start position:0% +but then there also might be some piece + + + align:start position:0% +but then there also might be some piece +in here where f is big. + + align:start position:0% + + + + align:start position:0% + +Okay. Um so over here this is where f + + align:start position:0% +Okay. Um so over here this is where f + + + align:start position:0% +Okay. Um so over here this is where f +sub1 is big and over here this is where + + align:start position:0% +sub1 is big and over here this is where + + + align:start position:0% +sub1 is big and over here this is where +fub r is big. + + align:start position:0% + + + + align:start position:0% + +All right. And and now the kind of + + align:start position:0% +All right. And and now the kind of + + + align:start position:0% +All right. And and now the kind of +trade-off that happens is we might have + + align:start position:0% +trade-off that happens is we might have + + + align:start position:0% +trade-off that happens is we might have +like a very strong bound for the L2 norm + + align:start position:0% +like a very strong bound for the L2 norm + + + align:start position:0% +like a very strong bound for the L2 norm +of F1. And so that bound tells me that + + align:start position:0% +of F1. And so that bound tells me that + + + align:start position:0% +of F1. And so that bound tells me that +this set where F1 is big is small. + + align:start position:0% +this set where F1 is big is small. + + + align:start position:0% +this set where F1 is big is small. +And then we have a bound for the L2 norm + + align:start position:0% +And then we have a bound for the L2 norm + + + align:start position:0% +And then we have a bound for the L2 norm +of FR. It might not be such a good + + align:start position:0% +of FR. It might not be such a good + + + align:start position:0% +of FR. It might not be such a good +bound. It might be bigger. But on the + + align:start position:0% +bound. It might be bigger. But on the + + + align:start position:0% +bound. It might be bigger. But on the +other hand, FR has this nice structure + + align:start position:0% +other hand, FR has this nice structure + + + align:start position:0% +other hand, FR has this nice structure +that it is constant on balls. So the set + + align:start position:0% +that it is constant on balls. So the set + + + align:start position:0% +that it is constant on balls. So the set +where FR is big is is group is clumped + + align:start position:0% +where FR is big is is group is clumped + + + align:start position:0% +where FR is big is is group is clumped +into these big balls. And so that gives + + align:start position:0% +into these big balls. And so that gives + + + align:start position:0% +into these big balls. And so that gives +us so the area might be larger than this + + align:start position:0% +us so the area might be larger than this + + + align:start position:0% +us so the area might be larger than this +area. But the fact that it's clumped + + align:start position:0% +area. But the fact that it's clumped + + + align:start position:0% +area. But the fact that it's clumped +gives us some other geometric + + align:start position:0% +gives us some other geometric + + + align:start position:0% +gives us some other geometric +information about it. It's kind of + + align:start position:0% +information about it. It's kind of + + + align:start position:0% +information about it. It's kind of +simpler. + + align:start position:0% + + + + align:start position:0% + +Okay. So let's pause there. I was uh + + align:start position:0% +Okay. So let's pause there. I was uh + + + align:start position:0% +Okay. So let's pause there. I was uh +recapping the main lema in the real case + + align:start position:0% +recapping the main lema in the real case + + + align:start position:0% +recapping the main lema in the real case +and um I sort of tried to have a picture + + align:start position:0% +and um I sort of tried to have a picture + + + align:start position:0% +and um I sort of tried to have a picture +of what it's telling us. + + align:start position:0% +of what it's telling us. + + + align:start position:0% +of what it's telling us. +Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. So the next thing that we should + + align:start position:0% +Okay. So the next thing that we should + + + align:start position:0% +Okay. So the next thing that we should +do is this is sort of nice but it is not + + align:start position:0% +do is this is sort of nice but it is not + + + align:start position:0% +do is this is sort of nice but it is not +a actual precise math statement. So in + + align:start position:0% +a actual precise math statement. So in + + + align:start position:0% +a actual precise math statement. So in +order to really make use of this idea, + + align:start position:0% +order to really make use of this idea, + + + align:start position:0% +order to really make use of this idea, +we need to now replace this intuition by + + align:start position:0% +we need to now replace this intuition by + + + align:start position:0% +we need to now replace this intuition by +by uh an actual precise thing. So let's + + align:start position:0% +by uh an actual precise thing. So let's + + + align:start position:0% +by uh an actual precise thing. So let's +let's do that. + + align:start position:0% + + + + align:start position:0% + +So here's a precise + + align:start position:0% +So here's a precise + + + align:start position:0% +So here's a precise +version + + align:start position:0% + + + + align:start position:0% + +of the intuition. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. So um + + align:start position:0% + + + + align:start position:0% + +okay. So how do we use + + align:start position:0% + + + + align:start position:0% + +the fact that the support of g hat is + + align:start position:0% +the fact that the support of g hat is + + + align:start position:0% +the fact that the support of g hat is +contained in something like v of 1 / r. + + align:start position:0% + + + + align:start position:0% + +There's a a + + align:start position:0% +There's a a + + + align:start position:0% +There's a a +nice trick for for doing this for using + + align:start position:0% +nice trick for for doing this for using + + + align:start position:0% +nice trick for for doing this for using +this which goes like this. So suppose I + + align:start position:0% +this which goes like this. So suppose I + + + align:start position:0% +this which goes like this. So suppose I +have a function + + align:start position:0% +have a function + + + align:start position:0% +have a function +um ADA + + align:start position:0% +um ADA + + + align:start position:0% +um ADA +so that ADA of C is one for all the C in + + align:start position:0% +so that ADA of C is one for all the C in + + + align:start position:0% +so that ADA of C is one for all the C in +the ball of radius 1 / R. + + align:start position:0% +the ball of radius 1 / R. + + + align:start position:0% +the ball of radius 1 / R. +There are many such functions ADA and + + align:start position:0% +There are many such functions ADA and + + + align:start position:0% +There are many such functions ADA and +and you probably the mo the most useful + + align:start position:0% +and you probably the mo the most useful + + + align:start position:0% +and you probably the mo the most useful +kind is to suppose that ADA is also + + align:start position:0% +kind is to suppose that ADA is also + + + align:start position:0% +kind is to suppose that ADA is also +smooth and compactly supported. + + align:start position:0% + + + + align:start position:0% + +Okay. So g hat is equal to g hat * a + + align:start position:0% +Okay. So g hat is equal to g hat * a + + + align:start position:0% +Okay. So g hat is equal to g hat * a +ghat is supported on this ball and aa is + + align:start position:0% +ghat is supported on this ball and aa is + + + align:start position:0% +ghat is supported on this ball and aa is +one on this ball. + + align:start position:0% +one on this ball. + + + align:start position:0% +one on this ball. +And now I can take the inverse for a + + align:start position:0% +And now I can take the inverse for a + + + align:start position:0% +And now I can take the inverse for a +transform of this and I get that g is g + + align:start position:0% +transform of this and I get that g is g + + + align:start position:0% +transform of this and I get that g is g +convolved with a to check. + + align:start position:0% + + + + align:start position:0% + +Okay. Um so this uh follows from and is + + align:start position:0% +Okay. Um so this uh follows from and is + + + align:start position:0% +Okay. Um so this uh follows from and is +almost equivalent to this but it's often + + align:start position:0% +almost equivalent to this but it's often + + + align:start position:0% +almost equivalent to this but it's often +a little bit easier to work with. + + align:start position:0% +a little bit easier to work with. + + + align:start position:0% +a little bit easier to work with. +So next to work with this we should + + align:start position:0% +So next to work with this we should + + + align:start position:0% +So next to work with this we should +figure out a little bit uh what this + + align:start position:0% +figure out a little bit uh what this + + + align:start position:0% +figure out a little bit uh what this +function a check is like. + + align:start position:0% + + + + align:start position:0% + +So properties of a check. + + align:start position:0% + + + + align:start position:0% + +Okay. So for one thing a check of x is + + align:start position:0% +Okay. So for one thing a check of x is + + + align:start position:0% +Okay. So for one thing a check of x is +less than + + align:start position:0% +less than + + + align:start position:0% +less than +um r the minus2 in the plane + + align:start position:0% + + + + align:start position:0% + +that just follows from the triangle + + align:start position:0% +that just follows from the triangle + + + align:start position:0% +that just follows from the triangle +inequality to compute a check. We + + align:start position:0% +inequality to compute a check. We + + + align:start position:0% +inequality to compute a check. We +integrate ada times a complex + + align:start position:0% +integrate ada times a complex + + + align:start position:0% +integrate ada times a complex +exponential and ada has size one and + + align:start position:0% +exponential and ada has size one and + + + align:start position:0% +exponential and ada has size one and +it's supported on this ball. + + align:start position:0% +it's supported on this ball. + + + align:start position:0% +it's supported on this ball. +So we get this + + align:start position:0% +So we get this + + + align:start position:0% +So we get this +um but in addition to that if if x is + + align:start position:0% +um but in addition to that if if x is + + + align:start position:0% +um but in addition to that if if x is +large then we get cancellation so the + + align:start position:0% +large then we get cancellation so the + + + align:start position:0% +large then we get cancellation so the +next thing is that + + align:start position:0% +next thing is that + + + align:start position:0% +next thing is that +aa check of x um decays rapidly so I'll + + align:start position:0% +aa check of x um decays rapidly so I'll + + + align:start position:0% +aa check of x um decays rapidly so I'll +I'll write something precise in a second + + align:start position:0% +I'll write something precise in a second + + + align:start position:0% +I'll write something precise in a second +decays rapidly + + align:start position:0% +decays rapidly + + + align:start position:0% +decays rapidly +if x is bigger than one and so the + + align:start position:0% +if x is bigger than one and so the + + + align:start position:0% +if x is bigger than one and so the +reason for that is aa check of x is the + + align:start position:0% +reason for that is aa check of x is the + + + align:start position:0% +reason for that is aa check of x is the +integral of c e 2 pi iix xc dx c and um + + align:start position:0% +integral of c e 2 pi iix xc dx c and um + + + align:start position:0% +integral of c e 2 pi iix xc dx c and um +we can bound this integral by + + align:start position:0% +we can bound this integral by + + + align:start position:0% +we can bound this integral by +integrating by parts um and uh this is a + + align:start position:0% +integrating by parts um and uh this is a + + + align:start position:0% +integrating by parts um and uh this is a +nice and smooth thing and if x is bigger + + align:start position:0% +nice and smooth thing and if x is bigger + + + align:start position:0% +nice and smooth thing and if x is bigger +than this we integrate by parts many + + align:start position:0% +than this we integrate by parts many + + + align:start position:0% +than this we integrate by parts many +times we get a strong estimate from this + + align:start position:0% +times we get a strong estimate from this + + + align:start position:0% +times we get a strong estimate from this +okay the estimate has the following + + align:start position:0% +okay the estimate has the following + + + align:start position:0% +okay the estimate has the following +shape I start with an r to the minus2 + + align:start position:0% +shape I start with an r to the minus2 + + + align:start position:0% +shape I start with an r to the minus2 +just to compare to what I had there and + + align:start position:0% +just to compare to what I had there and + + + align:start position:0% +just to compare to what I had there and +then I have um + + align:start position:0% +then I have um + + + align:start position:0% +then I have um +uh x over r and I can put here + + align:start position:0% +uh x over r and I can put here + + + align:start position:0% +uh x over r and I can put here +I can put here any exponent I like but + + align:start position:0% +I can put here any exponent I like but + + + align:start position:0% +I can put here any exponent I like but +negative a th000 will be fine for us. + + align:start position:0% + + + + align:start position:0% + +So if x is more than teeny bit bigger + + align:start position:0% +So if x is more than teeny bit bigger + + + align:start position:0% +So if x is more than teeny bit bigger +than r this thing is very small. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +All + + align:start position:0% + + + + align:start position:0% + +right. + + align:start position:0% +right. + + + align:start position:0% +right. +So now let me set um C subR to be the + + align:start position:0% +So now let me set um C subR to be the + + + align:start position:0% +So now let me set um C subR to be the +norm of A check. + + align:start position:0% +norm of A check. + + + align:start position:0% +norm of A check. +And so C subR has bounds that we just + + align:start position:0% +And so C subR has bounds that we just + + + align:start position:0% +And so C subR has bounds that we just +computed. + + align:start position:0% +computed. + + + align:start position:0% +computed. +So C subar of X is bounded by R the + + align:start position:0% +So C subar of X is bounded by R the + + + align:start position:0% +So C subar of X is bounded by R the +minus2 and it's rapidly decaying + + align:start position:0% + + + + align:start position:0% + +if X is much bigger than R. + + align:start position:0% +if X is much bigger than R. + + + align:start position:0% +if X is much bigger than R. +Um and now we can state a lema. + + align:start position:0% +Um and now we can state a lema. + + + align:start position:0% +Um and now we can state a lema. +So if the support of g hat is contained + + align:start position:0% +So if the support of g hat is contained + + + align:start position:0% +So if the support of g hat is contained +in the ball of radius 1 / r + + align:start position:0% +in the ball of radius 1 / r + + + align:start position:0% +in the ball of radius 1 / r +um then + + align:start position:0% +um then + + + align:start position:0% +um then +the norm of g of x is bounded by + + align:start position:0% +the norm of g of x is bounded by + + + align:start position:0% +the norm of g of x is bounded by +the norm of g convolved with cr x. + + align:start position:0% + + + + align:start position:0% + +And the proof is is + + align:start position:0% +And the proof is is + + + align:start position:0% +And the proof is is +basically just what just what we what we + + align:start position:0% +basically just what just what we what we + + + align:start position:0% +basically just what just what we what we +have. So we we started with G hat is + + align:start position:0% +have. So we we started with G hat is + + + align:start position:0% +have. So we we started with G hat is +Ghat time ADA and so G is G convolved + + align:start position:0% +Ghat time ADA and so G is G convolved + + + align:start position:0% +Ghat time ADA and so G is G convolved +with ADA check. + + align:start position:0% + + + + align:start position:0% + +Now take the triangle inequality. The + + align:start position:0% +Now take the triangle inequality. The + + + align:start position:0% +Now take the triangle inequality. The +norm of G is less than or equal to the + + align:start position:0% +norm of G is less than or equal to the + + + align:start position:0% +norm of G is less than or equal to the +norm of G convolved with the norm of A + + align:start position:0% +norm of G convolved with the norm of A + + + align:start position:0% +norm of G convolved with the norm of A +check. And that's the proof. The norm of + + align:start position:0% +check. And that's the proof. The norm of + + + align:start position:0% +check. And that's the proof. The norm of +A check is called CR. + + align:start position:0% + + + + align:start position:0% + +Okay. And um since we're going to + + align:start position:0% +Okay. And um since we're going to + + + align:start position:0% +Okay. And um since we're going to +eventually be thinking about L2 norms, + + align:start position:0% +eventually be thinking about L2 norms, + + + align:start position:0% +eventually be thinking about L2 norms, +it is helpful to have a tiny variant of + + align:start position:0% +it is helpful to have a tiny variant of + + + align:start position:0% +it is helpful to have a tiny variant of +this lema where we have the norm of G + + align:start position:0% +this lema where we have the norm of G + + + align:start position:0% +this lema where we have the norm of G +squar instead of the norm of G. And it's + + align:start position:0% +squar instead of the norm of G. And it's + + + align:start position:0% +squar instead of the norm of G. And it's +sort of convenient to prove it ahead of + + align:start position:0% +sort of convenient to prove it ahead of + + + align:start position:0% +sort of convenient to prove it ahead of +time instead of in the middle of what's + + align:start position:0% +time instead of in the middle of what's + + + align:start position:0% +time instead of in the middle of what's +coming. So uh lambda 2 + + align:start position:0% + + + + align:start position:0% + +if the support of g hat is contained in + + align:start position:0% +if the support of g hat is contained in + + + align:start position:0% +if the support of g hat is contained in +the ball of radius 1 / r then the norm + + align:start position:0% +the ball of radius 1 / r then the norm + + + align:start position:0% +the ball of radius 1 / r then the norm +of g ^2 is bounded by the norm of g ^2 + + align:start position:0% +of g ^2 is bounded by the norm of g ^2 + + + align:start position:0% +of g ^2 is bounded by the norm of g ^2 +convolved with cr. + + align:start position:0% + + + + align:start position:0% + +Okay. So be before we do the the + + align:start position:0% +Okay. So be before we do the the + + + align:start position:0% +Okay. So be before we do the the +rigorous proof, let me say something + + align:start position:0% +rigorous proof, let me say something + + + align:start position:0% +rigorous proof, let me say something +about how I think about this. Um, so + + align:start position:0% +about how I think about this. Um, so + + + align:start position:0% +about how I think about this. Um, so +this here says that the norm of G is + + align:start position:0% +this here says that the norm of G is + + + align:start position:0% +this here says that the norm of G is +bounded by this is sort of like taking + + align:start position:0% +bounded by this is sort of like taking + + + align:start position:0% +bounded by this is sort of like taking +an average. It's like the norm of G is + + align:start position:0% +an average. It's like the norm of G is + + + align:start position:0% +an average. It's like the norm of G is +bounded by the average value of the norm + + align:start position:0% +bounded by the average value of the norm + + + align:start position:0% +bounded by the average value of the norm +of G on a ball of radius R. + + align:start position:0% +of G on a ball of radius R. + + + align:start position:0% +of G on a ball of radius R. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +and then if you had that by Koshy + + align:start position:0% +and then if you had that by Koshy + + + align:start position:0% +and then if you had that by Koshy +Schwarz you would also have that the + + align:start position:0% +Schwarz you would also have that the + + + align:start position:0% +Schwarz you would also have that the +norm of G squ was bounded by the average + + align:start position:0% +norm of G squ was bounded by the average + + + align:start position:0% +norm of G squ was bounded by the average +of uh the the norm of G squ on the ball. + + align:start position:0% +of uh the the norm of G squ on the ball. + + + align:start position:0% +of uh the the norm of G squ on the ball. +Okay. So that so that's what we'll write + + align:start position:0% +Okay. So that so that's what we'll write + + + align:start position:0% +Okay. So that so that's what we'll write +down now. So the norm of g + + align:start position:0% +down now. So the norm of g + + + align:start position:0% +down now. So the norm of g +of x squared + + align:start position:0% +of x squared + + + align:start position:0% +of x squared +is bounded by the first lema by the norm + + align:start position:0% +is bounded by the first lema by the norm + + + align:start position:0% +is bounded by the first lema by the norm +uh by the norm of g convolved with cr at + + align:start position:0% +uh by the norm of g convolved with cr at + + + align:start position:0% +uh by the norm of g convolved with cr at +x + + align:start position:0% +x + + + align:start position:0% +x +squared. + + align:start position:0% +squared. + + + align:start position:0% +squared. +If I write out what this convolution is, + + align:start position:0% +If I write out what this convolution is, + + + align:start position:0% +If I write out what this convolution is, +it's the integral norm of g of x - y + + align:start position:0% +it's the integral norm of g of x - y + + + align:start position:0% +it's the integral norm of g of x - y +cr of y d y all squared. + + align:start position:0% +cr of y d y all squared. + + + align:start position:0% +cr of y d y all squared. +And now I can do a koshy schwarz. Um I + + align:start position:0% +And now I can do a koshy schwarz. Um I + + + align:start position:0% +And now I can do a koshy schwarz. Um I +want to do a koshy schwarz to get this + + align:start position:0% +want to do a koshy schwarz to get this + + + align:start position:0% +want to do a koshy schwarz to get this +guy squared with one of those. So when I + + align:start position:0% +guy squared with one of those. So when I + + + align:start position:0% +guy squared with one of those. So when I +do my koshi schwarz + + align:start position:0% +do my koshi schwarz + + + align:start position:0% +do my koshi schwarz +my first factor will be integral norm of + + align:start position:0% +my first factor will be integral norm of + + + align:start position:0% +my first factor will be integral norm of +g ^2 x - y cr of y + + align:start position:0% + + + + align:start position:0% + +and my second factor will just be the + + align:start position:0% +and my second factor will just be the + + + align:start position:0% +and my second factor will just be the +integral cr of y dy. + + align:start position:0% + + + + align:start position:0% + +So you could to see that this is a valid + + align:start position:0% +So you could to see that this is a valid + + + align:start position:0% +So you could to see that this is a valid +Koshy Schwarz. The sort of total number + + align:start position:0% +Koshy Schwarz. The sort of total number + + + align:start position:0% +Koshy Schwarz. The sort of total number +of exponents of G is two. Total number + + align:start position:0% +of exponents of G is two. Total number + + + align:start position:0% +of exponents of G is two. Total number +of exponents of C is two. That matches + + align:start position:0% +of exponents of C is two. That matches + + + align:start position:0% +of exponents of C is two. That matches +what's on the other side. + + align:start position:0% +what's on the other side. + + + align:start position:0% +what's on the other side. +Okay. And now um this thing here is + + align:start position:0% +Okay. And now um this thing here is + + + align:start position:0% +Okay. And now um this thing here is +bounded by one which follows by follows + + align:start position:0% +bounded by one which follows by follows + + + align:start position:0% +bounded by one which follows by follows +from our bounds for how it behaves and + + align:start position:0% +from our bounds for how it behaves and + + + align:start position:0% +from our bounds for how it behaves and +which goes along with the intuition that + + align:start position:0% +which goes along with the intuition that + + + align:start position:0% +which goes along with the intuition that +um you know that this integral is one. + + align:start position:0% +um you know that this integral is one. + + + align:start position:0% +um you know that this integral is one. +And so this convolution is like doing an + + align:start position:0% +And so this convolution is like doing an + + + align:start position:0% +And so this convolution is like doing an +average. + + align:start position:0% +average. + + + align:start position:0% +average. +Okay. And this thing here is just the + + align:start position:0% +Okay. And this thing here is just the + + + align:start position:0% +Okay. And this thing here is just the +right hand side. This is G ^2 involved + + align:start position:0% +right hand side. This is G ^2 involved + + + align:start position:0% +right hand side. This is G ^2 involved +with VC. + + align:start position:0% + + + + align:start position:0% + +Okay. So this is the way we will + + align:start position:0% +Okay. So this is the way we will + + + align:start position:0% +Okay. So this is the way we will +rigorously make use of the fact that FR + + align:start position:0% +rigorously make use of the fact that FR + + + align:start position:0% +rigorously make use of the fact that FR +has frequency in there. + + align:start position:0% + + + + align:start position:0% + +Um and it corresponds visually to this + + align:start position:0% +Um and it corresponds visually to this + + + align:start position:0% +Um and it corresponds visually to this +picture that I think I'll erase now + + align:start position:0% +picture that I think I'll erase now + + + align:start position:0% +picture that I think I'll erase now +that FR looks sort of like this. And the + + align:start position:0% +that FR looks sort of like this. And the + + + align:start position:0% +that FR looks sort of like this. And the +places where it's big are consists of + + align:start position:0% +places where it's big are consists of + + + align:start position:0% +places where it's big are consists of +some blobs with balls of radius r. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +so now we can use our main lama to prove + + align:start position:0% +so now we can use our main lama to prove + + + align:start position:0% +so now we can use our main lama to prove +some projection theory estimates. + + align:start position:0% + + + + align:start position:0% + +All right. So our setup + + align:start position:0% +All right. So our setup + + + align:start position:0% +All right. So our setup +is that we have X is a set of unit balls + + align:start position:0% + + + + align:start position:0% + +in the two-dimensional ball of radius R. + + align:start position:0% +in the two-dimensional ball of radius R. + + + align:start position:0% +in the two-dimensional ball of radius R. +D is a set of directions. So it's a + + align:start position:0% +D is a set of directions. So it's a + + + align:start position:0% +D is a set of directions. So it's a +subset of S1, which is 1 / R separated. + + align:start position:0% +subset of S1, which is 1 / R separated. + + + align:start position:0% +subset of S1, which is 1 / R separated. +and s measures the size of the biggest + + align:start position:0% +and s measures the size of the biggest + + + align:start position:0% +and s measures the size of the biggest +projection of x in here. So it's the + + align:start position:0% +projection of x in here. So it's the + + + align:start position:0% +projection of x in here. So it's the +maximum over all the thetas in my + + align:start position:0% +maximum over all the thetas in my + + + align:start position:0% +maximum over all the thetas in my +direction set of the theta projection of + + align:start position:0% +direction set of the theta projection of + + + align:start position:0% +direction set of the theta projection of +x. + + align:start position:0% + + + + align:start position:0% + +So that's our setup and we're going to + + align:start position:0% +So that's our setup and we're going to + + + align:start position:0% +So that's our setup and we're going to +try to bound these different quantities + + align:start position:0% +try to bound these different quantities + + + align:start position:0% +try to bound these different quantities +in terms of how the directions and how + + align:start position:0% +in terms of how the directions and how + + + align:start position:0% +in terms of how the directions and how +the spheres are clustered. So remember + + align:start position:0% +the spheres are clustered. So remember + + + align:start position:0% +the spheres are clustered. So remember +nx of r is the maximum overall possible + + align:start position:0% +nx of r is the maximum overall possible + + + align:start position:0% +nx of r is the maximum overall possible +center c of the amount of x in the ball + + align:start position:0% +center c of the amount of x in the ball + + + align:start position:0% +center c of the amount of x in the ball +of radius c of center c and radius r. + + align:start position:0% +of radius c of center c and radius r. + + + align:start position:0% +of radius c of center c and radius r. +And similarly n subd of row is the + + align:start position:0% +And similarly n subd of row is the + + + align:start position:0% +And similarly n subd of row is the +maximum + + align:start position:0% +maximum + + + align:start position:0% +maximum +over arcs in s1 of length row of the + + align:start position:0% +over arcs in s1 of length row of the + + + align:start position:0% +over arcs in s1 of length row of the +number of directions in the ark. + + align:start position:0% +number of directions in the ark. + + + align:start position:0% +number of directions in the ark. +So that's our setup + + align:start position:0% + + + + align:start position:0% + +and the projection theory estimate that + + align:start position:0% +and the projection theory estimate that + + + align:start position:0% +and the projection theory estimate that +comes from this method I'll call it + + align:start position:0% +comes from this method I'll call it + + + align:start position:0% +comes from this method I'll call it +theorem 2 r theorem 2 in the real case + + align:start position:0% +theorem 2 r theorem 2 in the real case + + + align:start position:0% +theorem 2 r theorem 2 in the real case +says that uh if we have the setup + + align:start position:0% + + + + align:start position:0% + +then the number of directions is bounded + + align:start position:0% +then the number of directions is bounded + + + align:start position:0% +then the number of directions is bounded +I + + align:start position:0% + + + + align:start position:0% + +s big R / X times the maximum over + + align:start position:0% +s big R / X times the maximum over + + + align:start position:0% +s big R / X times the maximum over +little R of um NX of little R and D of + + align:start position:0% +little R of um NX of little R and D of + + + align:start position:0% +little R of um NX of little R and D of +little R over big R over little R 2. + + align:start position:0% + + + + align:start position:0% + +Okay, so this is a little bit messy. Um, + + align:start position:0% +Okay, so this is a little bit messy. Um, + + + align:start position:0% +Okay, so this is a little bit messy. Um, +and we'll eventually make some + + align:start position:0% +and we'll eventually make some + + + align:start position:0% +and we'll eventually make some +hypotheses that allow to simplify it. + + align:start position:0% +hypotheses that allow to simplify it. + + + align:start position:0% +hypotheses that allow to simplify it. +Um, but just notice for now that this + + align:start position:0% +Um, but just notice for now that this + + + align:start position:0% +Um, but just notice for now that this +estimate takes account of how the set of + + align:start position:0% +estimate takes account of how the set of + + + align:start position:0% +estimate takes account of how the set of +directions is clustered and it takes + + align:start position:0% +directions is clustered and it takes + + + align:start position:0% +directions is clustered and it takes +account of how sorry it takes account of + + align:start position:0% +account of how sorry it takes account of + + + align:start position:0% +account of how sorry it takes account of +how the set x of unit balls is clustered + + align:start position:0% +how the set x of unit balls is clustered + + + align:start position:0% +how the set x of unit balls is clustered +and it takes account of how the set of + + align:start position:0% +and it takes account of how the set of + + + align:start position:0% +and it takes account of how the set of +directions is clustered. + + align:start position:0% + + + + align:start position:0% + +Okay, so the proof uh follows the uh + + align:start position:0% +Okay, so the proof uh follows the uh + + + align:start position:0% +Okay, so the proof uh follows the uh +idea of the proof we did in finite + + align:start position:0% +idea of the proof we did in finite + + + align:start position:0% +idea of the proof we did in finite +fields and and makes use of the main + + align:start position:0% +fields and and makes use of the main + + + align:start position:0% +fields and and makes use of the main +lema. And here's our setup. So for every + + align:start position:0% +lema. And here's our setup. So for every + + + align:start position:0% +lema. And here's our setup. So for every +direction in our direction set, let's + + align:start position:0% +direction in our direction set, let's + + + align:start position:0% +direction in our direction set, let's +say t theta is a set of at most s we + + align:start position:0% +say t theta is a set of at most s we + + + align:start position:0% +say t theta is a set of at most s we +could say exactly s one by r tubes t + + align:start position:0% +could say exactly s one by r tubes t + + + align:start position:0% +could say exactly s one by r tubes t +that cover s. + + align:start position:0% + + + + align:start position:0% + +So if this projection has size s then + + align:start position:0% +So if this projection has size s then + + + align:start position:0% +So if this projection has size s then +looking at the fibers of the projections + + align:start position:0% +looking at the fibers of the projections + + + align:start position:0% +looking at the fibers of the projections +I get s tubes that cover my set x. + + align:start position:0% +I get s tubes that cover my set x. + + + align:start position:0% +I get s tubes that cover my set x. +Okay. Then um t my master set of tubes + + align:start position:0% +Okay. Then um t my master set of tubes + + + align:start position:0% +Okay. Then um t my master set of tubes +will be the union over all the + + align:start position:0% +will be the union over all the + + + align:start position:0% +will be the union over all the +directions t theta and f is going to be + + align:start position:0% +directions t theta and f is going to be + + + align:start position:0% +directions t theta and f is going to be +the sum over all these tubes of the + + align:start position:0% +the sum over all these tubes of the + + + align:start position:0% +the sum over all these tubes of the +smoothed approx uh smoothed um + + align:start position:0% +smoothed approx uh smoothed um + + + align:start position:0% +smoothed approx uh smoothed um +characteristic function of the tube. + + align:start position:0% +characteristic function of the tube. + + + align:start position:0% +characteristic function of the tube. +Okay. So we observe that for every x in + + align:start position:0% +Okay. So we observe that for every x in + + + align:start position:0% +Okay. So we observe that for every x in +x um + + align:start position:0% +x um + + + align:start position:0% +x um +f ofx is at least the number of + + align:start position:0% +f ofx is at least the number of + + + align:start position:0% +f ofx is at least the number of +directions. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +So now we now we use our main lama and + + align:start position:0% +So now we now we use our main lama and + + + align:start position:0% +So now we now we use our main lama and +we break up f into these different frs. + + align:start position:0% +we break up f into these different frs. + + + align:start position:0% +we break up f into these different frs. +use main lema. + + align:start position:0% + + + + align:start position:0% + +Um, and I there are only logarithmically + + align:start position:0% +Um, and I there are only logarithmically + + + align:start position:0% +Um, and I there are only logarithmically +many different choices of R. And so one + + align:start position:0% +many different choices of R. And so one + + + align:start position:0% +many different choices of R. And so one +of them has to make a pretty big + + align:start position:0% +of them has to make a pretty big + + + align:start position:0% +of them has to make a pretty big +contribution at each of these points. + + align:start position:0% +contribution at each of these points. + + + align:start position:0% +contribution at each of these points. +And so I can I can choose R. + + align:start position:0% + + + + align:start position:0% + +So that all right. So so I have X * D^2 + + align:start position:0% +So that all right. So so I have X * D^2 + + + align:start position:0% +So that all right. So so I have X * D^2 +that's smaller than the integral X of + + align:start position:0% +that's smaller than the integral X of + + + align:start position:0% +that's smaller than the integral X of +F2. + + align:start position:0% +F2. + + + align:start position:0% +F2. +And now there are only a few Rs. So that + + align:start position:0% +And now there are only a few Rs. So that + + + align:start position:0% +And now there are only a few Rs. So that +should be somewhat smaller than a like a + + align:start position:0% +should be somewhat smaller than a like a + + + align:start position:0% +should be somewhat smaller than a like a +log times the integral over X of R 2. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +[Applause] + + align:start position:0% + + + + align:start position:0% + +Now the first thing I might try here is + + align:start position:0% +Now the first thing I might try here is + + + align:start position:0% +Now the first thing I might try here is +if if you look at the statement of the + + align:start position:0% +if if you look at the statement of the + + + align:start position:0% +if if you look at the statement of the +main lama it has an upper bound for the + + align:start position:0% +main lama it has an upper bound for the + + + align:start position:0% +main lama it has an upper bound for the +L2 norm of FR and I could plug in that + + align:start position:0% +L2 norm of FR and I could plug in that + + + align:start position:0% +L2 norm of FR and I could plug in that +that upper bound and I would bound this + + align:start position:0% +that upper bound and I would bound this + + + align:start position:0% +that upper bound and I would bound this +I would get something out of it + + align:start position:0% + + + + align:start position:0% + +but that's not the optimal thing to do + + align:start position:0% +but that's not the optimal thing to do + + + align:start position:0% +but that's not the optimal thing to do +here. Um dep well depending on what we + + align:start position:0% +here. Um dep well depending on what we + + + align:start position:0% +here. Um dep well depending on what we +know about X depending on what we know + + align:start position:0% +know about X depending on what we know + + + align:start position:0% +know about X depending on what we know +about this. So to get some intuition, + + align:start position:0% +about this. So to get some intuition, + + + align:start position:0% +about this. So to get some intuition, +let's look at this picture that I + + align:start position:0% +let's look at this picture that I + + + align:start position:0% +let's look at this picture that I +haven't managed to erase yet. + + align:start position:0% +haven't managed to erase yet. + + + align:start position:0% +haven't managed to erase yet. +[Applause] + + align:start position:0% + + + + align:start position:0% + +So we're trying to understand this + + align:start position:0% +So we're trying to understand this + + + align:start position:0% +So we're trying to understand this +thing, the integral overx of fr 2. So + + align:start position:0% +thing, the integral overx of fr 2. So + + + align:start position:0% +thing, the integral overx of fr 2. So +let's add an x to our picture. Uh do I + + align:start position:0% +let's add an x to our picture. Uh do I + + + align:start position:0% +let's add an x to our picture. Uh do I +have any more colors? + + align:start position:0% + + + + align:start position:0% + +So x in this picture is going to be + + align:start position:0% +So x in this picture is going to be + + + align:start position:0% +So x in this picture is going to be +yellow. + + align:start position:0% +yellow. + + + align:start position:0% +yellow. +And x may look something like this + + align:start position:0% + + + + align:start position:0% + +depends a little bit on nx of r. If nx + + align:start position:0% +depends a little bit on nx of r. If nx + + + align:start position:0% +depends a little bit on nx of r. If nx +of r the biggest that nx of r could be + + align:start position:0% +of r the biggest that nx of r could be + + + align:start position:0% +of r the biggest that nx of r could be +is r 2. If it's that big then x could + + align:start position:0% +is r 2. If it's that big then x could + + + align:start position:0% +is r 2. If it's that big then x could +fill in this whole thing. But if nx of r + + align:start position:0% +fill in this whole thing. But if nx of r + + + align:start position:0% +fill in this whole thing. But if nx of r +is smaller than r^ 2 then it's sort of + + align:start position:0% +is smaller than r^ 2 then it's sort of + + + align:start position:0% +is smaller than r^ 2 then it's sort of +like the picture that I drew when x is + + align:start position:0% +like the picture that I drew when x is + + + align:start position:0% +like the picture that I drew when x is +only a small fraction of this ball. + + align:start position:0% +only a small fraction of this ball. + + + align:start position:0% +only a small fraction of this ball. +And in this picture it would be lossy to + + align:start position:0% +And in this picture it would be lossy to + + + align:start position:0% +And in this picture it would be lossy to +estimate the integral over just x of fr + + align:start position:0% +estimate the integral over just x of fr + + + align:start position:0% +estimate the integral over just x of fr +2 by the global integral of fr which + + align:start position:0% +2 by the global integral of fr which + + + align:start position:0% +2 by the global integral of fr which +would include the whole orteal. + + align:start position:0% + + + + align:start position:0% + +Okay. Um so we're going to try to do a + + align:start position:0% +Okay. Um so we're going to try to do a + + + align:start position:0% +Okay. Um so we're going to try to do a +bit better than that by using our lemas. + + align:start position:0% +bit better than that by using our lemas. + + + align:start position:0% +bit better than that by using our lemas. +uh about the about the locally constant + + align:start position:0% +uh about the about the locally constant + + + align:start position:0% +uh about the about the locally constant +property of the function fr. + + align:start position:0% + + + + align:start position:0% + +All right. So I'm going to erase this + + align:start position:0% +All right. So I'm going to erase this + + + align:start position:0% +All right. So I'm going to erase this +but I'm going to leave this picture here + + align:start position:0% +but I'm going to leave this picture here + + + align:start position:0% +but I'm going to leave this picture here +for our intuition. + + align:start position:0% + + + + align:start position:0% + +All right. So we have the integral overx + + align:start position:0% +All right. So we have the integral overx + + + align:start position:0% +All right. So we have the integral overx +of fr 2 that is I'll just rewrite it as + + align:start position:0% +of fr 2 that is I'll just rewrite it as + + + align:start position:0% +of fr 2 that is I'll just rewrite it as +the integral of 1x + + align:start position:0% +the integral of 1x + + + align:start position:0% +the integral of 1x +fr. + + align:start position:0% + + + + align:start position:0% + +Okay. Now if I want to use the locally + + align:start position:0% +Okay. Now if I want to use the locally + + + align:start position:0% +Okay. Now if I want to use the locally +constant property of fr 2 it means I + + align:start position:0% +constant property of fr 2 it means I + + + align:start position:0% +constant property of fr 2 it means I +should I could use these lemas and in + + align:start position:0% +should I could use these lemas and in + + + align:start position:0% +should I could use these lemas and in +particular I can use lema 2 which is + + align:start position:0% +particular I can use lema 2 which is + + + align:start position:0% +particular I can use lema 2 which is +sort of well set up to deal with a + + align:start position:0% +sort of well set up to deal with a + + + align:start position:0% +sort of well set up to deal with a +square. So this is bounded by the + + align:start position:0% +square. So this is bounded by the + + + align:start position:0% +square. So this is bounded by the +integral of 1x * + + align:start position:0% +integral of 1x * + + + align:start position:0% +integral of 1x * +fr 2 convolved with uh cr + + align:start position:0% + + + + align:start position:0% + +and um if you write out what this is and + + align:start position:0% +and um if you write out what this is and + + + align:start position:0% +and um if you write out what this is and +do fubini this is the same as the + + align:start position:0% +do fubini this is the same as the + + + align:start position:0% +do fubini this is the same as the +integral of fr 2 times the + + align:start position:0% +integral of fr 2 times the + + + align:start position:0% +integral of fr 2 times the +characteristic function of x involved + + align:start position:0% +characteristic function of x involved + + + align:start position:0% +characteristic function of x involved +with E R + + align:start position:0% + + + + align:start position:0% + +does that step something you see that + + align:start position:0% +does that step something you see that + + + align:start position:0% +does that step something you see that +yeah okay let's do it so the algebra is + + align:start position:0% +yeah okay let's do it so the algebra is + + + align:start position:0% +yeah okay let's do it so the algebra is +like this I have the integral 1x of x + + align:start position:0% +like this I have the integral 1x of x + + + align:start position:0% +like this I have the integral 1x of x +and then I have this convolution which + + align:start position:0% +and then I have this convolution which + + + align:start position:0% +and then I have this convolution which +is the integral fr of x - y cr of y d y + + align:start position:0% + + + + align:start position:0% + +No, let me do it the other way. + + align:start position:0% + + + + align:start position:0% + +Okay. So now what happens if I fubini + + align:start position:0% +Okay. So now what happens if I fubini + + + align:start position:0% +Okay. So now what happens if I fubini +that + + align:start position:0% +that + + + align:start position:0% +that +um that's the integral + + align:start position:0% +um that's the integral + + + align:start position:0% +um that's the integral +fr of y integral of 1 + + align:start position:0% +fr of y integral of 1 + + + align:start position:0% +fr of y integral of 1 +x of x c of x - y dy + + align:start position:0% + + + + align:start position:0% + +okay it doesn't look quite right yet and + + align:start position:0% +okay it doesn't look quite right yet and + + + align:start position:0% +okay it doesn't look quite right yet and +it actually reminds me that there's a + + align:start position:0% +it actually reminds me that there's a + + + align:start position:0% +it actually reminds me that there's a +little something else that's helpful to + + align:start position:0% +little something else that's helpful to + + + align:start position:0% +little something else that's helpful to +say about cr Um + + align:start position:0% +say about cr Um + + + align:start position:0% +say about cr Um +uh so you can also add here that CR is + + align:start position:0% +uh so you can also add here that CR is + + + align:start position:0% +uh so you can also add here that CR is +radial. It implies that it's symmetric. + + align:start position:0% +radial. It implies that it's symmetric. + + + align:start position:0% +radial. It implies that it's symmetric. +Yeah, I should probably have mentioned + + align:start position:0% +Yeah, I should probably have mentioned + + + align:start position:0% +Yeah, I should probably have mentioned +that earlier in my plan. Uh so the + + align:start position:0% +that earlier in my plan. Uh so the + + + align:start position:0% +that earlier in my plan. Uh so the +reason you can do that remember CR was + + align:start position:0% +reason you can do that remember CR was + + + align:start position:0% +reason you can do that remember CR was +the 4A transform of some bump function + + align:start position:0% +the 4A transform of some bump function + + + align:start position:0% +the 4A transform of some bump function +ADA. If your bump function ADA is + + align:start position:0% +ADA. If your bump function ADA is + + + align:start position:0% +ADA. If your bump function ADA is +radial, it for a transform will be + + align:start position:0% +radial, it for a transform will be + + + align:start position:0% +radial, it for a transform will be +radial. So so this guy is radial and + + align:start position:0% +radial. So so this guy is radial and + + + align:start position:0% +radial. So so this guy is radial and +symmetric. Okay. And then because that's + + align:start position:0% +symmetric. Okay. And then because that's + + + align:start position:0% +symmetric. Okay. And then because that's +symmetric, + + align:start position:0% +symmetric, + + + align:start position:0% +symmetric, +I can switch those. So that's the + + align:start position:0% +I can switch those. So that's the + + + align:start position:0% +I can switch those. So that's the +integral fr of y integral 1x of x c of y + + align:start position:0% +integral fr of y integral 1x of x c of y + + + align:start position:0% +integral fr of y integral 1x of x c of y +- x uh sorry this one is this one is dx. + + align:start position:0% + + + + align:start position:0% + +Uh so that's the integral of r of y 1x + + align:start position:0% +Uh so that's the integral of r of y 1x + + + align:start position:0% +Uh so that's the integral of r of y 1x +involved with cr of y. + + align:start position:0% + + + + align:start position:0% + +I feel like there also should be a nice + + align:start position:0% +I feel like there also should be a nice + + + align:start position:0% +I feel like there also should be a nice +image of what's going on in this + + align:start position:0% +image of what's going on in this + + + align:start position:0% +image of what's going on in this +integral. + + align:start position:0% +integral. + + + align:start position:0% +integral. +um like we have this imagine for a + + align:start position:0% +um like we have this imagine for a + + + align:start position:0% +um like we have this imagine for a +second that this was the characteristic + + align:start position:0% +second that this was the characteristic + + + align:start position:0% +second that this was the characteristic +function of a set. It's not quite true, + + align:start position:0% +function of a set. It's not quite true, + + + align:start position:0% +function of a set. It's not quite true, +but it's not far off either. So I have + + align:start position:0% +but it's not far off either. So I have + + + align:start position:0% +but it's not far off either. So I have +one set and I have another set. + + align:start position:0% +one set and I have another set. + + + align:start position:0% +one set and I have another set. +But before I multiply them together, + + align:start position:0% +But before I multiply them together, + + + align:start position:0% +But before I multiply them together, +which would mean intersecting the sets, + + align:start position:0% +which would mean intersecting the sets, + + + align:start position:0% +which would mean intersecting the sets, +I fatten out this set here by a distance + + align:start position:0% +I fatten out this set here by a distance + + + align:start position:0% +I fatten out this set here by a distance +r. So I take this this call this set y. + + align:start position:0% +r. So I take this this call this set y. + + + align:start position:0% +r. So I take this this call this set y. +I take y, I fatten it out by r, and I + + align:start position:0% +I take y, I fatten it out by r, and I + + + align:start position:0% +I take y, I fatten it out by r, and I +intersect it with x. + + align:start position:0% +intersect it with x. + + + align:start position:0% +intersect it with x. +And that's kind of the same thing as + + align:start position:0% +And that's kind of the same thing as + + + align:start position:0% +And that's kind of the same thing as +taking X and fattening it out by R and + + align:start position:0% +taking X and fattening it out by R and + + + align:start position:0% +taking X and fattening it out by R and +intersecting it with Y because I could + + align:start position:0% +intersecting it with Y because I could + + + align:start position:0% +intersecting it with Y because I could +describe both of them like this. I'm + + align:start position:0% +describe both of them like this. I'm + + + align:start position:0% +describe both of them like this. I'm +looking for pairs of points, one in X + + align:start position:0% +looking for pairs of points, one in X + + + align:start position:0% +looking for pairs of points, one in X +and one in Y. The distance between them + + align:start position:0% +and one in Y. The distance between them + + + align:start position:0% +and one in Y. The distance between them +is at most R. If I say it that way, it's + + align:start position:0% +is at most R. If I say it that way, it's + + + align:start position:0% +is at most R. If I say it that way, it's +symmetric. + + align:start position:0% +symmetric. + + + align:start position:0% +symmetric. +And and that's what's going on here. + + align:start position:0% + + + + align:start position:0% + +I guess that's a fancy way of saying I + + align:start position:0% +I guess that's a fancy way of saying I + + + align:start position:0% +I guess that's a fancy way of saying I +just took this integral and I wrote it + + align:start position:0% +just took this integral and I wrote it + + + align:start position:0% +just took this integral and I wrote it +like this. + + align:start position:0% +like this. + + + align:start position:0% +like this. +And now remember that the function CR is + + align:start position:0% +And now remember that the function CR is + + + align:start position:0% +And now remember that the function CR is +symmetric. Now the whole thing is + + align:start position:0% +symmetric. Now the whole thing is + + + align:start position:0% +symmetric. Now the whole thing is +symmetric symmetric in in exchanging + + align:start position:0% +symmetric symmetric in in exchanging + + + align:start position:0% +symmetric symmetric in in exchanging +these two functions. + + align:start position:0% + + + + align:start position:0% + +Okay, cool. + + align:start position:0% +Okay, cool. + + + align:start position:0% +Okay, cool. +Okay, so now we've written it this way + + align:start position:0% +Okay, so now we've written it this way + + + align:start position:0% +Okay, so now we've written it this way +and the intuitive meaning of this is + + align:start position:0% +and the intuitive meaning of this is + + + align:start position:0% +and the intuitive meaning of this is +I've averaged the characteristic + + align:start position:0% +I've averaged the characteristic + + + align:start position:0% +I've averaged the characteristic +function of X over balls of radius R. + + align:start position:0% +function of X over balls of radius R. + + + align:start position:0% +function of X over balls of radius R. +Um and so uh this is bounded by + + align:start position:0% +Um and so uh this is bounded by + + + align:start position:0% +Um and so uh this is bounded by +nx of r / r 2. So this is the integral + + align:start position:0% +nx of r / r 2. So this is the integral + + + align:start position:0% +nx of r / r 2. So this is the integral +of that guy over a ball of radius r + + align:start position:0% +of that guy over a ball of radius r + + + align:start position:0% +of that guy over a ball of radius r +and then I'm picking the average. So I + + align:start position:0% +and then I'm picking the average. So I + + + align:start position:0% +and then I'm picking the average. So I +divide by the area of the ball of radius + + align:start position:0% +divide by the area of the ball of radius + + + align:start position:0% +divide by the area of the ball of radius +r. + + align:start position:0% +r. + + + align:start position:0% +r. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um so to check this a little bit more + + align:start position:0% +Um so to check this a little bit more + + + align:start position:0% +Um so to check this a little bit more +carefully we have to use the bounds that + + align:start position:0% +carefully we have to use the bounds that + + + align:start position:0% +carefully we have to use the bounds that +we have for this CR thing which are over + + align:start position:0% +we have for this CR thing which are over + + + align:start position:0% +we have for this CR thing which are over +here. + + align:start position:0% + + + + align:start position:0% + +So it's bounded by 1 / r^ 2 on the ball + + align:start position:0% +So it's bounded by 1 / r^ 2 on the ball + + + align:start position:0% +So it's bounded by 1 / r^ 2 on the ball +of radius r that would give the average. + + align:start position:0% +of radius r that would give the average. + + + align:start position:0% +of radius r that would give the average. +Then it also has this rapidly decaying + + align:start position:0% +Then it also has this rapidly decaying + + + align:start position:0% +Then it also has this rapidly decaying +tail which to be careful we should take + + align:start position:0% +tail which to be careful we should take + + + align:start position:0% +tail which to be careful we should take +account of. Um but what what it + + align:start position:0% +account of. Um but what what it + + + align:start position:0% +account of. Um but what what it +contributes is is uh is smaller than the + + align:start position:0% +contributes is is uh is smaller than the + + + align:start position:0% +contributes is is uh is smaller than the +first term the main term. + + align:start position:0% + + + + align:start position:0% + +Okay. So that's how we bound this. This + + align:start position:0% +Okay. So that's how we bound this. This + + + align:start position:0% +Okay. So that's how we bound this. This +is now a number. So we can take it out + + align:start position:0% +is now a number. So we can take it out + + + align:start position:0% +is now a number. So we can take it out +of the integral and we just have left + + align:start position:0% +of the integral and we just have left + + + align:start position:0% +of the integral and we just have left +the L2 norm of fr 2. So we plug in our + + align:start position:0% +the L2 norm of fr 2. So we plug in our + + + align:start position:0% +the L2 norm of fr 2. So we plug in our +bound for that. So we have it's bounded + + align:start position:0% +bound for that. So we have it's bounded + + + align:start position:0% +bound for that. So we have it's bounded +by nx of r / r 2. You can think of this + + align:start position:0% +by nx of r / r 2. You can think of this + + + align:start position:0% +by nx of r / r 2. You can think of this +thing as the density of x at scale r + + align:start position:0% +thing as the density of x at scale r + + + align:start position:0% +thing as the density of x at scale r +times the integral of f_sub_r 2. Okay. + + align:start position:0% +times the integral of f_sub_r 2. Okay. + + + align:start position:0% +times the integral of f_sub_r 2. Okay. +And then I just plug in the the bound + + align:start position:0% +And then I just plug in the the bound + + + align:start position:0% +And then I just plug in the the bound +for the integral of fr 2. And we'll + + align:start position:0% +for the integral of fr 2. And we'll + + + align:start position:0% +for the integral of fr 2. And we'll +write that out. So um okay, we have + + align:start position:0% +write that out. So um okay, we have + + + align:start position:0% +write that out. So um okay, we have +number of tubes. We have big r over + + align:start position:0% +number of tubes. We have big r over + + + align:start position:0% +number of tubes. We have big r over +little r. We have nt of r. That's this + + align:start position:0% +little r. We have nt of r. That's this + + + align:start position:0% +little r. We have nt of r. That's this +thing. Then we have n x of r + + align:start position:0% +thing. Then we have n x of r + + + align:start position:0% +thing. Then we have n x of r +and then we have r square. + + align:start position:0% + + + + align:start position:0% + +Okay, we are almost done. Um but what + + align:start position:0% +Okay, we are almost done. Um but what + + + align:start position:0% +Okay, we are almost done. Um but what +what we have here is number of tubes in + + align:start position:0% +what we have here is number of tubes in + + + align:start position:0% +what we have here is number of tubes in +a little r by big r guy and the + + align:start position:0% +a little r by big r guy and the + + + align:start position:0% +a little r by big r guy and the +information we want to be using is the + + align:start position:0% +information we want to be using is the + + + align:start position:0% +information we want to be using is the +number of directions. + + align:start position:0% +number of directions. + + + align:start position:0% +number of directions. +So the last step is that the number of + + align:start position:0% +So the last step is that the number of + + + align:start position:0% +So the last step is that the number of +tubes in a little r by big r tube is + + align:start position:0% +tubes in a little r by big r tube is + + + align:start position:0% +tubes in a little r by big r tube is +bounded by the number of directions in a + + align:start position:0% +bounded by the number of directions in a + + + align:start position:0% +bounded by the number of directions in a +little r over big r uh angle times + + align:start position:0% +little r over big r uh angle times + + + align:start position:0% +little r over big r uh angle times +little r. So here's a picture. + + align:start position:0% +little r. So here's a picture. + + + align:start position:0% +little r. So here's a picture. +Here's our um little r by big r tube. + + align:start position:0% +Here's our um little r by big r tube. + + + align:start position:0% +Here's our um little r by big r tube. +Inside of it, I can fit in some tubes in + + align:start position:0% +Inside of it, I can fit in some tubes in + + + align:start position:0% +Inside of it, I can fit in some tubes in +different directions. So if I pick one + + align:start position:0% +different directions. So if I pick one + + + align:start position:0% +different directions. So if I pick one +direction, I can pick little r of them. + + align:start position:0% +direction, I can pick little r of them. + + + align:start position:0% +direction, I can pick little r of them. +Um, that's this little r. But they don't + + align:start position:0% +Um, that's this little r. But they don't + + + align:start position:0% +Um, that's this little r. But they don't +have to go that way. I could also have + + align:start position:0% +have to go that way. I could also have + + + align:start position:0% +have to go that way. I could also have +them go may maybe the most extreme + + align:start position:0% +them go may maybe the most extreme + + + align:start position:0% +them go may maybe the most extreme +direction is I could have them go that + + align:start position:0% +direction is I could have them go that + + + align:start position:0% +direction is I could have them go that +way. + + align:start position:0% +way. + + + align:start position:0% +way. +And this angle here is uh little r. The + + align:start position:0% +And this angle here is uh little r. The + + + align:start position:0% +And this angle here is uh little r. The +angle there is little r big. + + align:start position:0% +angle there is little r big. + + + align:start position:0% +angle there is little r big. +So all of the different tubes that + + align:start position:0% +So all of the different tubes that + + + align:start position:0% +So all of the different tubes that +appear here um there are they have to + + align:start position:0% +appear here um there are they have to + + + align:start position:0% +appear here um there are they have to +have an angle in a within a range of + + align:start position:0% +have an angle in a within a range of + + + align:start position:0% +have an angle in a within a range of +little r over big r. So the number of + + align:start position:0% +little r over big r. So the number of + + + align:start position:0% +little r over big r. So the number of +directions is like that. And then for + + align:start position:0% +directions is like that. And then for + + + align:start position:0% +directions is like that. And then for +each direction then the number of + + align:start position:0% +each direction then the number of + + + align:start position:0% +each direction then the number of +possible tubes is at most little r. + + align:start position:0% +possible tubes is at most little r. + + + align:start position:0% +possible tubes is at most little r. +Okay. So if you substitute this for that + + align:start position:0% +Okay. So if you substitute this for that + + + align:start position:0% +Okay. So if you substitute this for that +um then this expression becomes the + + align:start position:0% +um then this expression becomes the + + + align:start position:0% +um then this expression becomes the +right hand side of the two. + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +>> Are you able to kind of use the fact + + align:start position:0% +>> Are you able to kind of use the fact + + + align:start position:0% +>> Are you able to kind of use the fact +that the tubes that are at an angle like + + align:start position:0% +that the tubes that are at an angle like + + + align:start position:0% +that the tubes that are at an angle like +you can fit less of them in? Does that + + align:start position:0% +you can fit less of them in? Does that + + + align:start position:0% +you can fit less of them in? Does that +change the bound or do anything + + align:start position:0% +change the bound or do anything + + + align:start position:0% +change the bound or do anything +different? + + align:start position:0% +different? + + + align:start position:0% +different? +>> Yeah. Okay. So the question was um if we + + align:start position:0% +>> Yeah. Okay. So the question was um if we + + + align:start position:0% +>> Yeah. Okay. So the question was um if we +knew that in a given direction these + + align:start position:0% +knew that in a given direction these + + + align:start position:0% +knew that in a given direction these +tubes um were had to have some spacing. + + align:start position:0% +tubes um were had to have some spacing. + + + align:start position:0% +tubes um were had to have some spacing. +So we could so we could also measure the + + align:start position:0% +So we could so we could also measure the + + + align:start position:0% +So we could so we could also measure the +clustering of the tubes in a given + + align:start position:0% +clustering of the tubes in a given + + + align:start position:0% +clustering of the tubes in a given +direction. So if we add some information + + align:start position:0% +direction. So if we add some information + + + align:start position:0% +direction. So if we add some information +about that then maybe this would have to + + align:start position:0% +about that then maybe this would have to + + + align:start position:0% +about that then maybe this would have to +be smaller than little r. + + align:start position:0% +be smaller than little r. + + + align:start position:0% +be smaller than little r. +So in our setup + + align:start position:0% +So in our setup + + + align:start position:0% +So in our setup +so our setup involves three things but + + align:start position:0% +so our setup involves three things but + + + align:start position:0% +so our setup involves three things but +we only thought about the clustering of + + align:start position:0% +we only thought about the clustering of + + + align:start position:0% +we only thought about the clustering of +two of them. Our setup involves set of + + align:start position:0% +two of them. Our setup involves set of + + + align:start position:0% +two of them. Our setup involves set of +unit balls X and we looked at how it's + + align:start position:0% +unit balls X and we looked at how it's + + + align:start position:0% +unit balls X and we looked at how it's +clustered NX of R set of directions D + + align:start position:0% +clustered NX of R set of directions D + + + align:start position:0% +clustered NX of R set of directions D +and we looked at how it's clustered ND + + align:start position:0% +and we looked at how it's clustered ND + + + align:start position:0% +and we looked at how it's clustered ND +of row and also a set of projections + + align:start position:0% +of row and also a set of projections + + + align:start position:0% +of row and also a set of projections +which each have size at most S but we + + align:start position:0% +which each have size at most S but we + + + align:start position:0% +which each have size at most S but we +didn't say anything about how they were + + align:start position:0% +didn't say anything about how they were + + + align:start position:0% +didn't say anything about how they were +clustered. + + align:start position:0% +clustered. + + + align:start position:0% +clustered. +So you could add to this setup something + + align:start position:0% +So you could add to this setup something + + + align:start position:0% +So you could add to this setup something +about how each projection is clustered + + align:start position:0% +about how each projection is clustered + + + align:start position:0% +about how each projection is clustered +and you could then use that to improve + + align:start position:0% +and you could then use that to improve + + + align:start position:0% +and you could then use that to improve +this thing here. + + align:start position:0% +this thing here. + + + align:start position:0% +this thing here. +Yeah. So, that could be a little + + align:start position:0% +Yeah. So, that could be a little + + + align:start position:0% +Yeah. So, that could be a little +homework project if anyone is interested + + align:start position:0% +homework project if anyone is interested + + + align:start position:0% +homework project if anyone is interested +in doing it. + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Good. Any other questions or comments? + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um Okay. So one uh so this the theorem + + align:start position:0% +Um Okay. So one uh so this the theorem + + + align:start position:0% +Um Okay. So one uh so this the theorem +sort of naturally falls out from using + + align:start position:0% +sort of naturally falls out from using + + + align:start position:0% +sort of naturally falls out from using +the fora method um but it's a little + + align:start position:0% +the fora method um but it's a little + + + align:start position:0% +the fora method um but it's a little +messy looking and the the the thing + + align:start position:0% +messy looking and the the the thing + + + align:start position:0% +messy looking and the the the thing +that's particularly messy looking is + + align:start position:0% +that's particularly messy looking is + + + align:start position:0% +that's particularly messy looking is +this maximum over little rx and d and + + align:start position:0% +this maximum over little rx and d and + + + align:start position:0% +this maximum over little rx and d and +there's a a fairly general situation + + align:start position:0% +there's a a fairly general situation + + + align:start position:0% +there's a a fairly general situation +that we mentioned last time where that + + align:start position:0% +that we mentioned last time where that + + + align:start position:0% +that we mentioned last time where that +that messy bit gets a lot cleaner. Um, I + + align:start position:0% +that messy bit gets a lot cleaner. Um, I + + + align:start position:0% +that messy bit gets a lot cleaner. Um, I +don't know that that's so + + align:start position:0% +don't know that that's so + + + align:start position:0% +don't know that that's so +philosophically important, but it's I + + align:start position:0% +philosophically important, but it's I + + + align:start position:0% +philosophically important, but it's I +think it's worth mentioning and that + + align:start position:0% +think it's worth mentioning and that + + + align:start position:0% +think it's worth mentioning and that +this is the way this the results usually + + align:start position:0% +this is the way this the results usually + + + align:start position:0% +this is the way this the results usually +appear in the literature. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% + + + + align:start position:0% + +And and this will allow us to to you + + align:start position:0% +And and this will allow us to to you + + + align:start position:0% +And and this will allow us to to you +know finally prove the result that we + + align:start position:0% +know finally prove the result that we + + + align:start position:0% +know finally prove the result that we +stated last time. + + align:start position:0% + + + + align:start position:0% + +All right. So um so definition we say x + + align:start position:0% +All right. So um so definition we say x + + + align:start position:0% +All right. So um so definition we say x +is housedorf + + align:start position:0% +is housedorf + + + align:start position:0% +is housedorf +or housedorf spacing + + align:start position:0% + + + + align:start position:0% + +if nx of r to the beta is bounded by + + align:start position:0% +if nx of r to the beta is bounded by + + + align:start position:0% +if nx of r to the beta is bounded by +around x to the beta for all beta + + align:start position:0% +around x to the beta for all beta + + + align:start position:0% +around x to the beta for all beta +between zero and one. + + align:start position:0% +between zero and one. + + + align:start position:0% +between zero and one. +So when beta is one this is trivial. Um + + align:start position:0% +So when beta is one this is trivial. Um + + + align:start position:0% +So when beta is one this is trivial. Um +this is always true but this is saying + + align:start position:0% +this is always true but this is saying + + + align:start position:0% +this is always true but this is saying +that at at smaller scales beta this x is + + align:start position:0% +that at at smaller scales beta this x is + + + align:start position:0% +that at at smaller scales beta this x is +not too clumped compared to how it is at + + align:start position:0% +not too clumped compared to how it is at + + + align:start position:0% +not too clumped compared to how it is at +the uh the top scale. Yeah. + + align:start position:0% +the uh the top scale. Yeah. + + + align:start position:0% +the uh the top scale. Yeah. +>> How does the appear there? + + align:start position:0% + + + + align:start position:0% + +>> Ah sorry thanks. There was one uh yeah + + align:start position:0% +>> Ah sorry thanks. There was one uh yeah + + + align:start position:0% +>> Ah sorry thanks. There was one uh yeah +there was one other thing I forgot to + + align:start position:0% +there was one other thing I forgot to + + + align:start position:0% +there was one other thing I forgot to +do. Um okay sorry thanks. So, okay. So, + + align:start position:0% +do. Um okay sorry thanks. So, okay. So, + + + align:start position:0% +do. Um okay sorry thanks. So, okay. So, +the question is um how did we actually + + align:start position:0% +the question is um how did we actually + + + align:start position:0% +the question is um how did we actually +do all this algebra and get the equation + + align:start position:0% +do all this algebra and get the equation + + + align:start position:0% +do all this algebra and get the equation +that the inequality that's actually + + align:start position:0% +that the inequality that's actually + + + align:start position:0% +that the inequality that's actually +stated in theorem 2 and thank you for + + align:start position:0% +stated in theorem 2 and thank you for + + + align:start position:0% +stated in theorem 2 and thank you for +the question because I left out some of + + align:start position:0% +the question because I left out some of + + + align:start position:0% +the question because I left out some of +the steps. + + align:start position:0% +the steps. + + + align:start position:0% +the steps. +Okay. Um + + align:start position:0% +Okay. Um + + + align:start position:0% +Okay. Um +so now that we have done the main ideas + + align:start position:0% +so now that we have done the main ideas + + + align:start position:0% +so now that we have done the main ideas +we're just talking about the algebra I + + align:start position:0% +we're just talking about the algebra I + + + align:start position:0% +we're just talking about the algebra I +will erase this + + align:start position:0% + + + + align:start position:0% + +and um so what do we have so far? If you + + align:start position:0% +and um so what do we have so far? If you + + + align:start position:0% +and um so what do we have so far? If you +put together the inequalities we have so + + align:start position:0% +put together the inequalities we have so + + + align:start position:0% +put together the inequalities we have so +far, we have x times the number of + + align:start position:0% +far, we have x times the number of + + + align:start position:0% +far, we have x times the number of +directions squared. That's where we + + align:start position:0% +directions squared. That's where we + + + align:start position:0% +directions squared. That's where we +started over here. Then we did some + + align:start position:0% +started over here. Then we did some + + + align:start position:0% +started over here. Then we did some +stuff and we ended up here. So that's + + align:start position:0% +stuff and we ended up here. So that's + + + align:start position:0% +stuff and we ended up here. So that's +bounded by number of tubes time big r + + align:start position:0% +bounded by number of tubes time big r + + + align:start position:0% +bounded by number of tubes time big r +over little r + + align:start position:0% +over little r + + + align:start position:0% +over little r +um times + + align:start position:0% +um times + + + align:start position:0% +um times +um + + align:start position:0% +um + + + align:start position:0% +um +md little r over big r * r. That was + + align:start position:0% +md little r over big r * r. That was + + + align:start position:0% +md little r over big r * r. That was +this thing for there. + + align:start position:0% +this thing for there. + + + align:start position:0% +this thing for there. +n x of r over little r 2 and we can + + align:start position:0% +n x of r over little r 2 and we can + + + align:start position:0% +n x of r over little r 2 and we can +cross those guys. + + align:start position:0% +cross those guys. + + + align:start position:0% +cross those guys. +Now we still have this number of tubes. + + align:start position:0% +Now we still have this number of tubes. + + + align:start position:0% +Now we still have this number of tubes. +What's that? Well, we have s tubes in + + align:start position:0% +What's that? Well, we have s tubes in + + + align:start position:0% +What's that? Well, we have s tubes in +each direction. We have d directions. + + align:start position:0% +each direction. We have d directions. + + + align:start position:0% +each direction. We have d directions. +So this is s * d. + + align:start position:0% +So this is s * d. + + + align:start position:0% +So this is s * d. +Okay. So now I've gotten rid of all the + + align:start position:0% +Okay. So now I've gotten rid of all the + + + align:start position:0% +Okay. So now I've gotten rid of all the +extra letters and we only have left the + + align:start position:0% +extra letters and we only have left the + + + align:start position:0% +extra letters and we only have left the +letters that appear in the inequality we + + align:start position:0% +letters that appear in the inequality we + + + align:start position:0% +letters that appear in the inequality we +want. And then the last thing you do is + + align:start position:0% +want. And then the last thing you do is + + + align:start position:0% +want. And then the last thing you do is +you get D by itself. + + align:start position:0% + + + + align:start position:0% + +So I take one factor of D and bring it + + align:start position:0% +So I take one factor of D and bring it + + + align:start position:0% +So I take one factor of D and bring it +over there and cancel the two. And I'll + + align:start position:0% +over there and cancel the two. And I'll + + + align:start position:0% +over there and cancel the two. And I'll +take the X and bring it over here. And + + align:start position:0% +take the X and bring it over here. And + + + align:start position:0% +take the X and bring it over here. And +then what's what's left is what's there? + + align:start position:0% + + + + align:start position:0% + +>> Yeah. Can that inequality be made shown + + align:start position:0% +>> Yeah. Can that inequality be made shown + + + align:start position:0% +>> Yeah. Can that inequality be made shown +in any scenario + + align:start position:0% +in any scenario + + + align:start position:0% +in any scenario +like + + align:start position:0% +like + + + align:start position:0% +like +any choice of like s x? + + align:start position:0% + + + + align:start position:0% + +Um yeah. + + align:start position:0% + + + + align:start position:0% + +Yes. Okay. So, so the question is is + + align:start position:0% +Yes. Okay. So, so the question is is + + + align:start position:0% +Yes. Okay. So, so the question is is +this inequality ever sharp? And uh it is + + align:start position:0% +this inequality ever sharp? And uh it is + + + align:start position:0% +this inequality ever sharp? And uh it is +uh sometimes sharp although not super + + align:start position:0% +uh sometimes sharp although not super + + + align:start position:0% +uh sometimes sharp although not super +often. And um and the cases that I have + + align:start position:0% +often. And um and the cases that I have + + + align:start position:0% +often. And um and the cases that I have +worked out so far when it's sharp are + + align:start position:0% +worked out so far when it's sharp are + + + align:start position:0% +worked out so far when it's sharp are +within this houseorf setting. So let's + + align:start position:0% +within this houseorf setting. So let's + + + align:start position:0% +within this houseorf setting. So let's +maybe do that. It'll all get a lot + + align:start position:0% +maybe do that. It'll all get a lot + + + align:start position:0% +maybe do that. It'll all get a lot +simpler and then I can say what the + + align:start position:0% +simpler and then I can say what the + + + align:start position:0% +simpler and then I can say what the +cases I know are. + + align:start position:0% + + + + align:start position:0% + +Okay. So the house spacing is uh bound + + align:start position:0% +Okay. So the house spacing is uh bound + + + align:start position:0% +Okay. So the house spacing is uh bound +on nx of of little r in terms of the + + align:start position:0% +on nx of of little r in terms of the + + + align:start position:0% +on nx of of little r in terms of the +size of x that looks like this. And I I + + align:start position:0% +size of x that looks like this. And I I + + + align:start position:0% +size of x that looks like this. And I I +coined the term housedorf spacing + + align:start position:0% +coined the term housedorf spacing + + + align:start position:0% +coined the term housedorf spacing +because it sort of comes up naturally + + align:start position:0% +because it sort of comes up naturally + + + align:start position:0% +because it sort of comes up naturally +when you talk about housedorf measures + + align:start position:0% +when you talk about housedorf measures + + + align:start position:0% +when you talk about housedorf measures +and things like that. + + align:start position:0% +and things like that. + + + align:start position:0% +and things like that. +Okay. And it's useful in our setting + + align:start position:0% +Okay. And it's useful in our setting + + + align:start position:0% +Okay. And it's useful in our setting +because + + align:start position:0% +because + + + align:start position:0% +because +if X and D have housed dorf spacing, + + align:start position:0% + + + + align:start position:0% + +then when you take the maximum + + align:start position:0% +then when you take the maximum + + + align:start position:0% +then when you take the maximum +of actually many expressions, but the + + align:start position:0% +of actually many expressions, but the + + + align:start position:0% +of actually many expressions, but the +one that comes up for us here is this. + + align:start position:0% + + + + align:start position:0% + +Okay, what happens? So, so I assume that + + align:start position:0% +Okay, what happens? So, so I assume that + + + align:start position:0% +Okay, what happens? So, so I assume that +both X and D have housed dorf spacing. + + align:start position:0% +both X and D have housed dorf spacing. + + + align:start position:0% +both X and D have housed dorf spacing. +It's important to have both of them. + + align:start position:0% +It's important to have both of them. + + + align:start position:0% +It's important to have both of them. +Then each one of these things get + + align:start position:0% +Then each one of these things get + + + align:start position:0% +Then each one of these things get +replaced by some power of X or D. + + align:start position:0% +replaced by some power of X or D. + + + align:start position:0% +replaced by some power of X or D. +And um once you have a power law, so the + + align:start position:0% +And um once you have a power law, so the + + + align:start position:0% +And um once you have a power law, so the +whole the whole expression will be um + + align:start position:0% +whole the whole expression will be um + + + align:start position:0% +whole the whole expression will be um +will be uh or another way to look at is + + align:start position:0% +will be uh or another way to look at is + + + align:start position:0% +will be uh or another way to look at is +the whole expression will be some power + + align:start position:0% +the whole expression will be some power + + + align:start position:0% +the whole expression will be some power +of little r. Power could be positive or + + align:start position:0% +of little r. Power could be positive or + + + align:start position:0% +of little r. Power could be positive or +negative. the maximum will occur either + + align:start position:0% +negative. the maximum will occur either + + + align:start position:0% +negative. the maximum will occur either +at one or at big r. + + align:start position:0% +at one or at big r. + + + align:start position:0% +at one or at big r. +So this guy basically is equal to what + + align:start position:0% +So this guy basically is equal to what + + + align:start position:0% +So this guy basically is equal to what +happens at one. Uh nx of one is always + + align:start position:0% +happens at one. Uh nx of one is always + + + align:start position:0% +happens at one. Uh nx of one is always +one. Nd of 1 / r is always one. So we + + align:start position:0% +one. Nd of 1 / r is always one. So we + + + align:start position:0% +one. Nd of 1 / r is always one. So we +just get one. And when little r is big + + align:start position:0% +just get one. And when little r is big + + + align:start position:0% +just get one. And when little r is big +r, nx of big r is all the points. Nd of + + align:start position:0% +r, nx of big r is all the points. Nd of + + + align:start position:0% +r, nx of big r is all the points. Nd of +one is all the directions. And we have + + align:start position:0% +one is all the directions. And we have + + + align:start position:0% +one is all the directions. And we have +that. + + align:start position:0% + + + + align:start position:0% + +So it's less nasty. And so we get the + + align:start position:0% +So it's less nasty. And so we get the + + + align:start position:0% +So it's less nasty. And so we get the +following corlary. + + align:start position:0% +following corlary. + + + align:start position:0% +following corlary. +So correlary says if we have our setup + + align:start position:0% +So correlary says if we have our setup + + + align:start position:0% +So correlary says if we have our setup +and X and D have high direct spacing + + align:start position:0% + + + + align:start position:0% + +then the number of directions is bounded + + align:start position:0% +then the number of directions is bounded + + + align:start position:0% +then the number of directions is bounded +by + + align:start position:0% +by + + + align:start position:0% +by +uh + + align:start position:0% +uh + + + align:start position:0% +uh +S SR overX * 1 plus SRX * this thing. So + + align:start position:0% +S SR overX * 1 plus SRX * this thing. So + + + align:start position:0% +S SR overX * 1 plus SRX * this thing. So +s d uh over r. + + align:start position:0% + + + + align:start position:0% + +Okay. Now this one has an + + align:start position:0% +Okay. Now this one has an + + + align:start position:0% +Okay. Now this one has an +interpretation. If this term dominates, + + align:start position:0% +interpretation. If this term dominates, + + + align:start position:0% +interpretation. If this term dominates, +you can cancel the d's and it tells you + + align:start position:0% +you can cancel the d's and it tells you + + + align:start position:0% +you can cancel the d's and it tells you +that s is almost r. + + align:start position:0% +that s is almost r. + + + align:start position:0% +that s is almost r. +So we get either + + align:start position:0% +So we get either + + + align:start position:0% +So we get either +s is almost as big as r. r is the + + align:start position:0% +s is almost as big as r. r is the + + + align:start position:0% +s is almost as big as r. r is the +biggest it could possibly be. So s is + + align:start position:0% +biggest it could possibly be. So s is + + + align:start position:0% +biggest it could possibly be. So s is +almost as big as it could possibly be + + align:start position:0% +almost as big as it could possibly be + + + align:start position:0% +almost as big as it could possibly be +or d is bounded by srx. + + align:start position:0% +or d is bounded by srx. + + + align:start position:0% +or d is bounded by srx. +So that's what we stated last time. The + + align:start position:0% +So that's what we stated last time. The + + + align:start position:0% +So that's what we stated last time. The +formula is not as nasty as the general + + align:start position:0% +formula is not as nasty as the general + + + align:start position:0% +formula is not as nasty as the general +formula. + + align:start position:0% +formula. + + + align:start position:0% +formula. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> There's also a factor of log in the two. + + align:start position:0% +>> There's also a factor of log in the two. + + + align:start position:0% +>> There's also a factor of log in the two. +>> Yep. Thanks. + + align:start position:0% +>> Yep. Thanks. + + + align:start position:0% +>> Yep. Thanks. +[Applause] + + align:start position:0% + + + + align:start position:0% + +So the point from the audience was that + + align:start position:0% +So the point from the audience was that + + + align:start position:0% +So the point from the audience was that +I I there was an extra factor of logar + + align:start position:0% +I I there was an extra factor of logar + + + align:start position:0% +I I there was an extra factor of logar +that I forgot to write down. So I'll put + + align:start position:0% +that I forgot to write down. So I'll put + + + align:start position:0% +that I forgot to write down. So I'll put +this to represent that. Yeah. Thanks. + + align:start position:0% + + + + align:start position:0% + +Okay. So this relatively clean estimate, + + align:start position:0% +Okay. So this relatively clean estimate, + + + align:start position:0% +Okay. So this relatively clean estimate, +it exactly matches our theorem to + + align:start position:0% +it exactly matches our theorem to + + + align:start position:0% +it exactly matches our theorem to +infinite fields. Um I won't write it + + align:start position:0% +infinite fields. Um I won't write it + + + align:start position:0% +infinite fields. Um I won't write it +down, but the the numerology is the + + align:start position:0% +down, but the the numerology is the + + + align:start position:0% +down, but the the numerology is the +same. Um and it it's a little nicer to + + align:start position:0% +same. Um and it it's a little nicer to + + + align:start position:0% +same. Um and it it's a little nicer to +look at. It still takes some digesting + + align:start position:0% +look at. It still takes some digesting + + + align:start position:0% +look at. It still takes some digesting +and um this is sharp in some cases. Um + + align:start position:0% +and um this is sharp in some cases. Um + + + align:start position:0% +and um this is sharp in some cases. Um +it's sharp in the case that s is pretty + + align:start position:0% +it's sharp in the case that s is pretty + + + align:start position:0% +it's sharp in the case that s is pretty +close to r. So because I I need this the + + align:start position:0% +close to r. So because I I need this the + + + align:start position:0% +close to r. So because I I need this the +smallest I could make s would be + + align:start position:0% +smallest I could make s would be + + + align:start position:0% +smallest I could make s would be +something like r / log r and if you take + + align:start position:0% +something like r / log r and if you take + + + align:start position:0% +something like r / log r and if you take +s around that r log r 1 - epsilon then + + align:start position:0% +s around that r log r 1 - epsilon then + + + align:start position:0% +s around that r log r 1 - epsilon then +this is sharp in the example of a grid + + align:start position:0% +this is sharp in the example of a grid + + + align:start position:0% +this is sharp in the example of a grid +of points grid of unit balls. + + align:start position:0% + + + + align:start position:0% + +Yeah. So that's the main interesting + + align:start position:0% +Yeah. So that's the main interesting + + + align:start position:0% +Yeah. So that's the main interesting +example when it that is the main example + + align:start position:0% +example when it that is the main example + + + align:start position:0% +example when it that is the main example +that I know when it's when it's sharp + + align:start position:0% +that I know when it's when it's sharp + + + align:start position:0% +that I know when it's when it's sharp +and there are plenty of examples where + + align:start position:0% +and there are plenty of examples where + + + align:start position:0% +and there are plenty of examples where +it's not sharp but that great example is + + align:start position:0% +it's not sharp but that great example is + + + align:start position:0% +it's not sharp but that great example is +is important. + + align:start position:0% +is important. + + + align:start position:0% +is important. +Yeah. Um okay I guess it's also a + + align:start position:0% +Yeah. Um okay I guess it's also a + + + align:start position:0% +Yeah. Um okay I guess it's also a +natural question if we go to the regime + + align:start position:0% +natural question if we go to the regime + + + align:start position:0% +natural question if we go to the regime +that's not housedorf. + + align:start position:0% +that's not housedorf. + + + align:start position:0% +that's not housedorf. +um this theorem added some + + align:start position:0% +um this theorem added some + + + align:start position:0% +um this theorem added some +junk here to account for for this for + + align:start position:0% +junk here to account for for this for + + + align:start position:0% +junk here to account for for this for +things being more clustered and it's a + + align:start position:0% +things being more clustered and it's a + + + align:start position:0% +things being more clustered and it's a +natural question is there any scenario + + align:start position:0% +natural question is there any scenario + + + align:start position:0% +natural question is there any scenario +where this junk is is exactly sharp um + + align:start position:0% +where this junk is is exactly sharp um + + + align:start position:0% +where this junk is is exactly sharp um +and I wondered about that when I was + + align:start position:0% +and I wondered about that when I was + + + align:start position:0% +and I wondered about that when I was +working on this lecture but I don't know + + align:start position:0% +working on this lecture but I don't know + + + align:start position:0% +working on this lecture but I don't know +the answer yet so if anybody wants to + + align:start position:0% +the answer yet so if anybody wants to + + + align:start position:0% +the answer yet so if anybody wants to +try that's also a nice little project. + + align:start position:0% + + + + align:start position:0% + +Cool. + + align:start position:0% +Cool. + + + align:start position:0% +Cool. +Okay. So, that was the meat of the class + + align:start position:0% +Okay. So, that was the meat of the class + + + align:start position:0% +Okay. So, that was the meat of the class +and that was the the the the thing that + + align:start position:0% +and that was the the the the thing that + + + align:start position:0% +and that was the the the the thing that +um you know + + align:start position:0% +um you know + + + align:start position:0% +um you know +my my my discussion that I planned about + + align:start position:0% +my my my discussion that I planned about + + + align:start position:0% +my my my discussion that I planned about +the 4A method in the real case. So, it's + + align:start position:0% +the 4A method in the real case. So, it's + + + align:start position:0% +the 4A method in the real case. So, it's +another good moment to um see if see if + + align:start position:0% +another good moment to um see if see if + + + align:start position:0% +another good moment to um see if see if +you have questions to digest + + align:start position:0% +you have questions to digest + + + align:start position:0% +you have questions to digest +and we'll start something a little + + align:start position:0% +and we'll start something a little + + + align:start position:0% +and we'll start something a little +different. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. Um for the the maximum term, could + + align:start position:0% +>> Yeah. Um for the the maximum term, could + + + align:start position:0% +>> Yeah. Um for the the maximum term, could +you explain why only like it has to be a + + align:start position:0% +you explain why only like it has to be a + + + align:start position:0% +you explain why only like it has to be a +maximum and it's like the part of the + + align:start position:0% +maximum and it's like the part of the + + + align:start position:0% +maximum and it's like the part of the +proof that requires taking maximum over + + align:start position:0% +proof that requires taking maximum over + + + align:start position:0% +proof that requires taking maximum over +R instead of any given R. + + align:start position:0% +R instead of any given R. + + + align:start position:0% +R instead of any given R. +>> Um so I think the question is why do we + + align:start position:0% +>> Um so I think the question is why do we + + + align:start position:0% +>> Um so I think the question is why do we +have a maximum over R instead of maybe + + align:start position:0% +have a maximum over R instead of maybe + + + align:start position:0% +have a maximum over R instead of maybe +like a sum over R? + + align:start position:0% +like a sum over R? + + + align:start position:0% +like a sum over R? +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Where does maximum come from? + + align:start position:0% +>> Where does maximum come from? + + + align:start position:0% +>> Where does maximum come from? +>> Yeah. Um so you you could put sum over + + align:start position:0% +>> Yeah. Um so you you could put sum over + + + align:start position:0% +>> Yeah. Um so you you could put sum over +little r and the difference isn't very + + align:start position:0% +little r and the difference isn't very + + + align:start position:0% +little r and the difference isn't very +important because the number of terms is + + align:start position:0% +important because the number of terms is + + + align:start position:0% +important because the number of terms is +only log of r and the log of r is is got + + align:start position:0% +only log of r and the log of r is is got + + + align:start position:0% +only log of r and the log of r is is got +absorbed here. But where did this come + + align:start position:0% +absorbed here. But where did this come + + + align:start position:0% +absorbed here. But where did this come +from at all? Well, we had this um + + align:start position:0% +from at all? Well, we had this um + + + align:start position:0% +from at all? Well, we had this um +function that's the sum of all these + + align:start position:0% +function that's the sum of all these + + + align:start position:0% +function that's the sum of all these +tubes which describes our projection + + align:start position:0% +tubes which describes our projection + + + align:start position:0% +tubes which describes our projection +situation. And then we are the key thing + + align:start position:0% +situation. And then we are the key thing + + + align:start position:0% +situation. And then we are the key thing +is that we applied the main lema to this + + align:start position:0% +is that we applied the main lema to this + + + align:start position:0% +is that we applied the main lema to this +function. And the main lema said you + + align:start position:0% +function. And the main lema said you + + + align:start position:0% +function. And the main lema said you +could break up this function into a few. + + align:start position:0% +could break up this function into a few. + + + align:start position:0% +could break up this function into a few. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +>> Yeah. And so one of those pieces is sort + + align:start position:0% +>> Yeah. And so one of those pieces is sort + + + align:start position:0% +>> Yeah. And so one of those pieces is sort +of the important one and that's the one + + align:start position:0% +of the important one and that's the one + + + align:start position:0% +of the important one and that's the one +that appears in the maximum. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. Yeah. + + align:start position:0% +>> Yeah. Yeah. + + + align:start position:0% +>> Yeah. Yeah. +>> Wondering. So in the proof we have to + + align:start position:0% +>> Wondering. So in the proof we have to + + + align:start position:0% +>> Wondering. So in the proof we have to +keep track of all the Rs. + + align:start position:0% +keep track of all the Rs. + + + align:start position:0% +keep track of all the Rs. +Um in the hos spacing case it seems like + + align:start position:0% +Um in the hos spacing case it seems like + + + align:start position:0% +Um in the hos spacing case it seems like +we just there's only two cases. So I'm + + align:start position:0% +we just there's only two cases. So I'm + + + align:start position:0% +we just there's only two cases. So I'm +wondering if if you do have positive + + align:start position:0% +wondering if if you do have positive + + + align:start position:0% +wondering if if you do have positive +spacing is it really necessary? Is it + + align:start position:0% +spacing is it really necessary? Is it + + + align:start position:0% +spacing is it really necessary? Is it +still important to do the static + + align:start position:0% +still important to do the static + + + align:start position:0% +still important to do the static +division? + + align:start position:0% +division? + + + align:start position:0% +division? +>> Okay. So the question is in the house + + align:start position:0% +>> Okay. So the question is in the house + + + align:start position:0% +>> Okay. So the question is in the house +dorf spacing case it turned out at the + + align:start position:0% +dorf spacing case it turned out at the + + + align:start position:0% +dorf spacing case it turned out at the +end of the day that only two values of + + align:start position:0% +end of the day that only two values of + + + align:start position:0% +end of the day that only two values of +little r mattered in the final + + align:start position:0% +little r mattered in the final + + + align:start position:0% +little r mattered in the final +inequality namely one and capital r and + + align:start position:0% +inequality namely one and capital r and + + + align:start position:0% +inequality namely one and capital r and +the question was would it be possible to + + align:start position:0% +the question was would it be possible to + + + align:start position:0% +the question was would it be possible to +write the proof so that only those two + + align:start position:0% +write the proof so that only those two + + + align:start position:0% +write the proof so that only those two +appeared and we didn't have all this you + + align:start position:0% +appeared and we didn't have all this you + + + align:start position:0% +appeared and we didn't have all this you +know rather complicated business of + + align:start position:0% +know rather complicated business of + + + align:start position:0% +know rather complicated business of +keeping track of all the intermediate + + align:start position:0% +keeping track of all the intermediate + + + align:start position:0% +keeping track of all the intermediate +little rs. Um I don't know any way to do + + align:start position:0% +little rs. Um I don't know any way to do + + + align:start position:0% +little rs. Um I don't know any way to do +that. I I think the only way I + + align:start position:0% +that. I I think the only way I + + + align:start position:0% +that. I I think the only way I +understand it is to keep track of all + + align:start position:0% +understand it is to keep track of all + + + align:start position:0% +understand it is to keep track of all +the little Rs and then notice that under + + align:start position:0% +the little Rs and then notice that under + + + align:start position:0% +the little Rs and then notice that under +these hypotheses, the intermediate Rs uh + + align:start position:0% +these hypotheses, the intermediate Rs uh + + + align:start position:0% +these hypotheses, the intermediate Rs uh +are bounded by the extreme ones. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Okay. So, I thought I would say a a + + align:start position:0% +Okay. So, I thought I would say a a + + + align:start position:0% +Okay. So, I thought I would say a a +little bit about the history of these + + align:start position:0% +little bit about the history of these + + + align:start position:0% +little bit about the history of these +ideas. I did haven't been putting names + + align:start position:0% +ideas. I did haven't been putting names + + + align:start position:0% +ideas. I did haven't been putting names +next to the theorems and the reason is + + align:start position:0% +next to the theorems and the reason is + + + align:start position:0% +next to the theorems and the reason is +that these theorems are small variations + + align:start position:0% +that these theorems are small variations + + + align:start position:0% +that these theorems are small variations +of theorems from the literature and + + align:start position:0% +of theorems from the literature and + + + align:start position:0% +of theorems from the literature and +there are many kind of related theorems + + align:start position:0% +there are many kind of related theorems + + + align:start position:0% +there are many kind of related theorems +from the literature but so but but let + + align:start position:0% +from the literature but so but but let + + + align:start position:0% +from the literature but so but but let +me tell you a little bit about the + + align:start position:0% +me tell you a little bit about the + + + align:start position:0% +me tell you a little bit about the +history I think it's interesting I think + + align:start position:0% +history I think it's interesting I think + + + align:start position:0% +history I think it's interesting I think +these are kind of fundamental ideas and + + align:start position:0% +these are kind of fundamental ideas and + + + align:start position:0% +these are kind of fundamental ideas and +they were discovered uh independently or + + align:start position:0% +they were discovered uh independently or + + + align:start position:0% +they were discovered uh independently or +somewhat independently by different + + align:start position:0% +somewhat independently by different + + + align:start position:0% +somewhat independently by different +people working on different problems + + align:start position:0% +people working on different problems + + + align:start position:0% +people working on different problems +Um + + align:start position:0% + + + + align:start position:0% + +so the thing that we have been calling + + align:start position:0% +so the thing that we have been calling + + + align:start position:0% +so the thing that we have been calling +the forier method. + + align:start position:0% +the forier method. + + + align:start position:0% +the forier method. +So let's call this history. + + align:start position:0% + + + + align:start position:0% + +The thing that we are calling the forier + + align:start position:0% +The thing that we are calling the forier + + + align:start position:0% +The thing that we are calling the forier +method appears in a bunch places + + align:start position:0% +method appears in a bunch places + + + align:start position:0% +method appears in a bunch places +including the following. Um the earliest + + align:start position:0% +including the following. Um the earliest + + + align:start position:0% +including the following. Um the earliest +that I am aware of is Linux work in civ + + align:start position:0% +that I am aware of is Linux work in civ + + + align:start position:0% +that I am aware of is Linux work in civ +theory + + align:start position:0% + + + + align:start position:0% + +which I will introduce civ theory and + + align:start position:0% +which I will introduce civ theory and + + + align:start position:0% +which I will introduce civ theory and +tell you what this work was uh in the + + align:start position:0% +tell you what this work was uh in the + + + align:start position:0% +tell you what this work was uh in the +today. So that was in the 1940s. + + align:start position:0% +today. So that was in the 1940s. + + + align:start position:0% +today. So that was in the 1940s. +uh a second place the second place I'm + + align:start position:0% +uh a second place the second place I'm + + + align:start position:0% +uh a second place the second place I'm +aware of is Roth's work on the Hybrron + + align:start position:0% +aware of is Roth's work on the Hybrron + + + align:start position:0% +aware of is Roth's work on the Hybrron +triangle problem + + align:start position:0% +triangle problem + + + align:start position:0% +triangle problem +which at some point in the class + + align:start position:0% +which at some point in the class + + + align:start position:0% +which at some point in the class +probably we'll talk about a little bit + + align:start position:0% +probably we'll talk about a little bit + + + align:start position:0% +probably we'll talk about a little bit +in the 70s. + + align:start position:0% +in the 70s. + + + align:start position:0% +in the 70s. +Um Roth was uh he he he knew civ theory + + align:start position:0% +Um Roth was uh he he he knew civ theory + + + align:start position:0% +Um Roth was uh he he he knew civ theory +he knew Linux work well and he'd worked + + align:start position:0% +he knew Linux work well and he'd worked + + + align:start position:0% +he knew Linux work well and he'd worked +on it but in in this problem he did + + align:start position:0% +on it but in in this problem he did + + + align:start position:0% +on it but in in this problem he did +something similar that's in uklidian + + align:start position:0% +something similar that's in uklidian + + + align:start position:0% +something similar that's in uklidian +space and the setup is kind of different + + align:start position:0% +space and the setup is kind of different + + + align:start position:0% +space and the setup is kind of different +and any so I put it on the list then it + + align:start position:0% +and any so I put it on the list then it + + + align:start position:0% +and any so I put it on the list then it +was something like this was done by + + align:start position:0% +was something like this was done by + + + align:start position:0% +was something like this was done by +falconer in geometric measure theory + + align:start position:0% + + + + align:start position:0% + +so falconer essentially proved um uh the + + align:start position:0% +so falconer essentially proved um uh the + + + align:start position:0% +so falconer essentially proved um uh the +correlary that I just erosed and that + + align:start position:0% +correlary that I just erosed and that + + + align:start position:0% +correlary that I just erosed and that +was around 1980. + + align:start position:0% +was around 1980. + + + align:start position:0% +was around 1980. +Um, and then it was done by Van in the + + align:start position:0% +Um, and then it was done by Van in the + + + align:start position:0% +Um, and then it was done by Van in the +setting of finite fields. So, lines in + + align:start position:0% +setting of finite fields. So, lines in + + + align:start position:0% +setting of finite fields. So, lines in +FQ2 + + align:start position:0% + + + + align:start position:0% + +and I'm not positive about this, but I + + align:start position:0% +and I'm not positive about this, but I + + + align:start position:0% +and I'm not positive about this, but I +think that many of these people were not + + align:start position:0% +think that many of these people were not + + + align:start position:0% +think that many of these people were not +fully aware of others of these people. + + align:start position:0% +fully aware of others of these people. + + + align:start position:0% +fully aware of others of these people. +Okay. Um, we also mentioned the double + + align:start position:0% +Okay. Um, we also mentioned the double + + + align:start position:0% +Okay. Um, we also mentioned the double +counting method. + + align:start position:0% + + + + align:start position:0% + +and the double counting method um that + + align:start position:0% +and the double counting method um that + + + align:start position:0% +and the double counting method um that +that we did. So is it was done by + + align:start position:0% +that we did. So is it was done by + + + align:start position:0% +that we did. So is it was done by +Calfman + + align:start position:0% +Calfman + + + align:start position:0% +Calfman +in the context of geometric measure + + align:start position:0% +in the context of geometric measure + + + align:start position:0% +in the context of geometric measure +theory + + align:start position:0% + + + + align:start position:0% + +in the 1960s. + + align:start position:0% +in the 1960s. + + + align:start position:0% +in the 1960s. +Um and it was done by Gallagher + + align:start position:0% +Um and it was done by Gallagher + + + align:start position:0% +Um and it was done by Gallagher +in the context of civ theory + + align:start position:0% +in the context of civ theory + + + align:start position:0% +in the context of civ theory +I think also in the 1960s. + + align:start position:0% +I think also in the 1960s. + + + align:start position:0% +I think also in the 1960s. +I'm pretty sure that these two people + + align:start position:0% +I'm pretty sure that these two people + + + align:start position:0% +I'm pretty sure that these two people +did not know what the other one was + + align:start position:0% +did not know what the other one was + + + align:start position:0% +did not know what the other one was +doing. + + align:start position:0% +doing. + + + align:start position:0% +doing. +Um, and I guess it was probably also + + align:start position:0% +Um, and I guess it was probably also + + + align:start position:0% +Um, and I guess it was probably also +done in the setting of lines and finite + + align:start position:0% +done in the setting of lines and finite + + + align:start position:0% +done in the setting of lines and finite +fields in the 60s or 70s, but I don't + + align:start position:0% +fields in the 60s or 70s, but I don't + + + align:start position:0% +fields in the 60s or 70s, but I don't +know. I don't quite have I don't have a + + align:start position:0% +know. I don't quite have I don't have a + + + align:start position:0% +know. I don't quite have I don't have a +reference. + + align:start position:0% +reference. + + + align:start position:0% +reference. +And those people probably didn't know + + align:start position:0% +And those people probably didn't know + + + align:start position:0% +And those people probably didn't know +about either of these. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um, so now let me tell you what civ + + align:start position:0% +Um, so now let me tell you what civ + + + align:start position:0% +Um, so now let me tell you what civ +theory is and how it is analogous to + + align:start position:0% +theory is and how it is analogous to + + + align:start position:0% +theory is and how it is analogous to +what we have been doing. + + align:start position:0% +what we have been doing. + + + align:start position:0% +what we have been doing. +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So cif theory takes place over the + + align:start position:0% +So cif theory takes place over the + + + align:start position:0% +So cif theory takes place over the +integers and the main character in civ + + align:start position:0% +integers and the main character in civ + + + align:start position:0% +integers and the main character in civ +theory is taking the integers and + + align:start position:0% +theory is taking the integers and + + + align:start position:0% +theory is taking the integers and +reducing it modulo q for different bases + + align:start position:0% +reducing it modulo q for different bases + + + align:start position:0% +reducing it modulo q for different bases +q + + align:start position:0% +q + + + align:start position:0% +q +um okay so z of course is the integers + + align:start position:0% +um okay so z of course is the integers + + + align:start position:0% +um okay so z of course is the integers +I'm going to write zq for some people + + align:start position:0% +I'm going to write zq for some people + + + align:start position:0% +I'm going to write zq for some people +write z mod qz this is the the integers + + align:start position:0% +write z mod qz this is the the integers + + + align:start position:0% +write z mod qz this is the the integers +modulo q + + align:start position:0% +modulo q + + + align:start position:0% +modulo q +and there's a basic map pi subq z 2 Z + + align:start position:0% +and there's a basic map pi subq z 2 Z + + + align:start position:0% +and there's a basic map pi subq z 2 Z +cub which takes an integer and reduces + + align:start position:0% +cub which takes an integer and reduces + + + align:start position:0% +cub which takes an integer and reduces +it modulo Q. + + align:start position:0% + + + + align:start position:0% + +Okay, this map is going to play the role + + align:start position:0% +Okay, this map is going to play the role + + + align:start position:0% +Okay, this map is going to play the role +of our projections. So let me mention + + align:start position:0% +of our projections. So let me mention + + + align:start position:0% +of our projections. So let me mention +what is analogous. + + align:start position:0% +what is analogous. + + + align:start position:0% +what is analogous. +So we've been talking about maps pi + + align:start position:0% +So we've been talking about maps pi + + + align:start position:0% +So we've been talking about maps pi +theta that go from R2 to R or a + + align:start position:0% +theta that go from R2 to R or a + + + align:start position:0% +theta that go from R2 to R or a +one-dimensional subspace or from FQ2 to + + align:start position:0% +one-dimensional subspace or from FQ2 to + + + align:start position:0% +one-dimensional subspace or from FQ2 to +FQ. + + align:start position:0% +FQ. + + + align:start position:0% +FQ. +Um, and now we're talking about the map + + align:start position:0% +Um, and now we're talking about the map + + + align:start position:0% +Um, and now we're talking about the map +pi Q that goes from Z to Z mod Q. Um, + + align:start position:0% +pi Q that goes from Z to Z mod Q. Um, + + + align:start position:0% +pi Q that goes from Z to Z mod Q. Um, +what do all these things have in common? + + align:start position:0% +what do all these things have in common? + + + align:start position:0% +what do all these things have in common? +They are all group homorphisms between a + + align:start position:0% +They are all group homorphisms between a + + + align:start position:0% +They are all group homorphisms between a +billion groups. + + align:start position:0% + + + + align:start position:0% + +Okay. Um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so what we're going to do in civ theory + + align:start position:0% +so what we're going to do in civ theory + + + align:start position:0% +so what we're going to do in civ theory +is take a take a set which is going to + + align:start position:0% +is take a take a set which is going to + + + align:start position:0% +is take a take a set which is going to +be now a set of integers and think about + + align:start position:0% +be now a set of integers and think about + + + align:start position:0% +be now a set of integers and think about +all the different projections of its + + align:start position:0% +all the different projections of its + + + align:start position:0% +all the different projections of its +integer of the set and think about how + + align:start position:0% +integer of the set and think about how + + + align:start position:0% +integer of the set and think about how +they're all related to each other and + + align:start position:0% +they're all related to each other and + + + align:start position:0% +they're all related to each other and +how they're all related to the original + + align:start position:0% +how they're all related to the original + + + align:start position:0% +how they're all related to the original +set. + + align:start position:0% +set. + + + align:start position:0% +set. +Um so I have another little piece of + + align:start position:0% +Um so I have another little piece of + + + align:start position:0% +Um so I have another little piece of +notation. So this thing is the numbers + + align:start position:0% +notation. So this thing is the numbers + + + align:start position:0% +notation. So this thing is the numbers +from one up to n which is a subset of + + align:start position:0% +from one up to n which is a subset of + + + align:start position:0% +from one up to n which is a subset of +the integers. + + align:start position:0% +the integers. + + + align:start position:0% +the integers. +Um and let me illustrate projection + + align:start position:0% +Um and let me illustrate projection + + + align:start position:0% +Um and let me illustrate projection +theory. Let me illustrate civ theory + + align:start position:0% +theory. Let me illustrate civ theory + + + align:start position:0% +theory. Let me illustrate civ theory +with an interesting example of a set + + align:start position:0% +with an interesting example of a set + + + align:start position:0% +with an interesting example of a set +whose projections behave in kind of a + + align:start position:0% +whose projections behave in kind of a + + + align:start position:0% +whose projections behave in kind of a +funny way. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +Okay. So do an example. + + align:start position:0% +Okay. So do an example. + + + align:start position:0% +Okay. So do an example. +Our example is going to be basically the + + align:start position:0% +Our example is going to be basically the + + + align:start position:0% +Our example is going to be basically the +set of square numbers. It's going to be + + align:start position:0% +set of square numbers. It's going to be + + + align:start position:0% +set of square numbers. It's going to be +the set of little n^ squ where little n + + align:start position:0% +the set of little n^ squ where little n + + + align:start position:0% +the set of little n^ squ where little n +goes from one up to big n to the 1/2. So + + align:start position:0% +goes from one up to big n to the 1/2. So + + + align:start position:0% +goes from one up to big n to the 1/2. So +it's a subset of the integers from 1 to + + align:start position:0% +it's a subset of the integers from 1 to + + + align:start position:0% +it's a subset of the integers from 1 to +n and the cardality is about the square + + align:start position:0% +n and the cardality is about the square + + + align:start position:0% +n and the cardality is about the square +root of n. + + align:start position:0% +root of n. + + + align:start position:0% +root of n. +What happens when I reduce this set + + align:start position:0% +What happens when I reduce this set + + + align:start position:0% +What happens when I reduce this set +modulo p? + + align:start position:0% +modulo p? + + + align:start position:0% +modulo p? +Um so if p is prime + + align:start position:0% +Um so if p is prime + + + align:start position:0% +Um so if p is prime +when I take pi p of x I get the + + align:start position:0% +when I take pi p of x I get the + + + align:start position:0% +when I take pi p of x I get the +quadratic residues and the number of + + align:start position:0% +quadratic residues and the number of + + + align:start position:0% +quadratic residues and the number of +quadratic residues is p + 1 over two. So + + align:start position:0% +quadratic residues is p + 1 over two. So + + + align:start position:0% +quadratic residues is p + 1 over two. So +about half of that. + + align:start position:0% +about half of that. + + + align:start position:0% +about half of that. +So that's kind of an interesting and + + align:start position:0% +So that's kind of an interesting and + + + align:start position:0% +So that's kind of an interesting and +surprising fact. Um, of course if P is + + align:start position:0% +surprising fact. Um, of course if P is + + + align:start position:0% +surprising fact. Um, of course if P is +bigger than square root of N, obviously + + align:start position:0% +bigger than square root of N, obviously + + + align:start position:0% +bigger than square root of N, obviously +the size of this projection is smaller + + align:start position:0% +the size of this projection is smaller + + + align:start position:0% +the size of this projection is smaller +than X. Um, so I might not even hit all + + align:start position:0% +than X. Um, so I might not even hit all + + + align:start position:0% +than X. Um, so I might not even hit all +the quadratic residues if I take a big + + align:start position:0% +the quadratic residues if I take a big + + + align:start position:0% +the quadratic residues if I take a big +P. Uh, that's not surprising. But I + + align:start position:0% +P. Uh, that's not surprising. But I + + + align:start position:0% +P. Uh, that's not surprising. But I +could take P significantly less than the + + align:start position:0% +could take P significantly less than the + + + align:start position:0% +could take P significantly less than the +square root of N. + + align:start position:0% +square root of N. + + + align:start position:0% +square root of N. +And then um I when I do this projection + + align:start position:0% +And then um I when I do this projection + + + align:start position:0% +And then um I when I do this projection +I only hit half of the elements in Z my + + align:start position:0% +I only hit half of the elements in Z my + + + align:start position:0% +I only hit half of the elements in Z my +P and I hit each of those many times. + + align:start position:0% +P and I hit each of those many times. + + + align:start position:0% +P and I hit each of those many times. +That's you know it's not something + + align:start position:0% +That's you know it's not something + + + align:start position:0% +That's you know it's not something +that's likely to happen randomly. It's + + align:start position:0% +that's likely to happen randomly. It's + + + align:start position:0% +that's likely to happen randomly. It's +kind of striking. + + align:start position:0% +kind of striking. + + + align:start position:0% +kind of striking. +So one sample question from civ theory + + align:start position:0% +So one sample question from civ theory + + + align:start position:0% +So one sample question from civ theory +is um uh + + align:start position:0% +is um uh + + + align:start position:0% +is um uh +how big could a set X be and have all of + + align:start position:0% +how big could a set X be and have all of + + + align:start position:0% +how big could a set X be and have all of +its projections be small like this? + + align:start position:0% +its projections be small like this? + + + align:start position:0% +its projections be small like this? +And uh what examples are there? How many + + align:start position:0% +And uh what examples are there? How many + + + align:start position:0% +And uh what examples are there? How many +sets like this can you find? + + align:start position:0% +sets like this can you find? + + + align:start position:0% +sets like this can you find? +All right. Um so using the using his + + align:start position:0% +All right. Um so using the using his + + + align:start position:0% +All right. Um so using the using his +ideas about civ theory, one of the + + align:start position:0% +ideas about civ theory, one of the + + + align:start position:0% +ideas about civ theory, one of the +things that Linick did was to answer + + align:start position:0% +things that Linick did was to answer + + + align:start position:0% +things that Linick did was to answer +this answer some of this question. So + + align:start position:0% +this answer some of this question. So + + + align:start position:0% +this answer some of this question. So +theorem of lin + + align:start position:0% +theorem of lin + + + align:start position:0% +theorem of lin +in the 1940s uh it says um if I have a + + align:start position:0% +in the 1940s uh it says um if I have a + + + align:start position:0% +in the 1940s uh it says um if I have a +subset of the integers from 1 to n and + + align:start position:0% +subset of the integers from 1 to n and + + + align:start position:0% +subset of the integers from 1 to n and +if pi p of x is at most p + 1 / 2 for + + align:start position:0% +if pi p of x is at most p + 1 / 2 for + + + align:start position:0% +if pi p of x is at most p + 1 / 2 for +every p. Um so there's nothing so + + align:start position:0% +every p. Um so there's nothing so + + + align:start position:0% +every p. Um so there's nothing so +special about this. We could put other + + align:start position:0% +special about this. We could put other + + + align:start position:0% +special about this. We could put other +things here but I'm just using this to + + align:start position:0% +things here but I'm just using this to + + + align:start position:0% +things here but I'm just using this to +compare with the squares. + + align:start position:0% +compare with the squares. + + + align:start position:0% +compare with the squares. +Um then the conclusion is that the size + + align:start position:0% +Um then the conclusion is that the size + + + align:start position:0% +Um then the conclusion is that the size +of x is at most around n^ the 1/2. + + align:start position:0% + + + + align:start position:0% + +So it says that the square numbers are + + align:start position:0% +So it says that the square numbers are + + + align:start position:0% +So it says that the square numbers are +just about the biggest set with this + + align:start position:0% +just about the biggest set with this + + + align:start position:0% +just about the biggest set with this +property. + + align:start position:0% + + + + align:start position:0% + +Cool. So we will give two proofs of + + align:start position:0% +Cool. So we will give two proofs of + + + align:start position:0% +Cool. So we will give two proofs of +this. We'll give a proof using double + + align:start position:0% +this. We'll give a proof using double + + + align:start position:0% +this. We'll give a proof using double +counting and we'll give a proof using + + align:start position:0% +counting and we'll give a proof using + + + align:start position:0% +counting and we'll give a proof using +the 4A method. + + align:start position:0% +the 4A method. + + + align:start position:0% +the 4A method. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +there are lots of hard open problems in + + align:start position:0% +there are lots of hard open problems in + + + align:start position:0% +there are lots of hard open problems in +civ theory and one of them is to + + align:start position:0% +civ theory and one of them is to + + + align:start position:0% +civ theory and one of them is to +understand uh what the examples are. So + + align:start position:0% +understand uh what the examples are. So + + + align:start position:0% +understand uh what the examples are. So +the only known examples + + align:start position:0% + + + + align:start position:0% + +only known examples + + align:start position:0% +only known examples + + + align:start position:0% +only known examples +where where this theorem is roughly + + align:start position:0% +where where this theorem is roughly + + + align:start position:0% +where where this theorem is roughly +tight + + align:start position:0% + + + + align:start position:0% + +are the square numbers and close + + align:start position:0% +are the square numbers and close + + + align:start position:0% +are the square numbers and close +cousins. + + align:start position:0% + + + + align:start position:0% + +So sorry it's messy the square numbers + + align:start position:0% +So sorry it's messy the square numbers + + + align:start position:0% +So sorry it's messy the square numbers +and close cousins of the square numbers + + align:start position:0% +and close cousins of the square numbers + + + align:start position:0% +and close cousins of the square numbers +like you can you could replace this with + + align:start position:0% +like you can you could replace this with + + + align:start position:0% +like you can you could replace this with +another degree 2 polinomial in little n + + align:start position:0% +another degree 2 polinomial in little n + + + align:start position:0% +another degree 2 polinomial in little n +and it's not hard to see it's it's kind + + align:start position:0% +and it's not hard to see it's it's kind + + + align:start position:0% +and it's not hard to see it's it's kind +of equivalent and those are all the + + align:start position:0% +of equivalent and those are all the + + + align:start position:0% +of equivalent and those are all the +examples + + align:start position:0% + + + + align:start position:0% + +okay but people know basically nothing + + align:start position:0% +okay but people know basically nothing + + + align:start position:0% +okay but people know basically nothing +in about classifying the examples. + + align:start position:0% + + + + align:start position:0% + +Cool. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, um, so we'll give two proofs of + + align:start position:0% +So, um, so we'll give two proofs of + + + align:start position:0% +So, um, so we'll give two proofs of +this. One based on double counting and + + align:start position:0% +this. One based on double counting and + + + align:start position:0% +this. One based on double counting and +one based on the 4A method. Double + + align:start position:0% +one based on the 4A method. Double + + + align:start position:0% +one based on the 4A method. Double +counting I think we can do today and the + + align:start position:0% +counting I think we can do today and the + + + align:start position:0% +counting I think we can do today and the +4A method we'll do next time, next week. + + align:start position:0% +4A method we'll do next time, next week. + + + align:start position:0% +4A method we'll do next time, next week. +And first of all, I think that these + + align:start position:0% +And first of all, I think that these + + + align:start position:0% +And first of all, I think that these +results are pretty cool. But I also hope + + align:start position:0% +results are pretty cool. But I also hope + + + align:start position:0% +results are pretty cool. But I also hope +that you see that they're really + + align:start position:0% +that you see that they're really + + + align:start position:0% +that you see that they're really +extremely parallel to the results in + + align:start position:0% +extremely parallel to the results in + + + align:start position:0% +extremely parallel to the results in +geometric measure theory that we've just + + align:start position:0% +geometric measure theory that we've just + + + align:start position:0% +geometric measure theory that we've just +been talking. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Okay, let me make a little remark before + + align:start position:0% +Okay, let me make a little remark before + + + align:start position:0% +Okay, let me make a little remark before +we start. Um, so, so I'm going to focus + + align:start position:0% +we start. Um, so, so I'm going to focus + + + align:start position:0% +we start. Um, so, so I'm going to focus +on projections mod p where p is a prime. + + align:start position:0% +on projections mod p where p is a prime. + + + align:start position:0% +on projections mod p where p is a prime. +You could also reduce mod q where q is + + align:start position:0% +You could also reduce mod q where q is + + + align:start position:0% +You could also reduce mod q where q is +not a prime. And all of the ideas still + + align:start position:0% +not a prime. And all of the ideas still + + + align:start position:0% +not a prime. And all of the ideas still +work. It's a little bit more complicated + + align:start position:0% +work. It's a little bit more complicated + + + align:start position:0% +work. It's a little bit more complicated +because if you take two numbers Q1 and + + align:start position:0% +because if you take two numbers Q1 and + + + align:start position:0% +because if you take two numbers Q1 and +Q2 that share a common factor, then + + align:start position:0% +Q2 that share a common factor, then + + + align:start position:0% +Q2 that share a common factor, then +reducing mod Q1 and reducing mod Q2 are + + align:start position:0% +reducing mod Q1 and reducing mod Q2 are + + + align:start position:0% +reducing mod Q1 and reducing mod Q2 are +kind of related to each other. And so if + + align:start position:0% +kind of related to each other. And so if + + + align:start position:0% +kind of related to each other. And so if +you write everything down, you have to + + align:start position:0% +you write everything down, you have to + + + align:start position:0% +you write everything down, you have to +keep track of that. That's just an extra + + align:start position:0% +keep track of that. That's just an extra + + + align:start position:0% +keep track of that. That's just an extra +thing to keep track of. And not so + + align:start position:0% +thing to keep track of. And not so + + + align:start position:0% +thing to keep track of. And not so +difficult, but it it uh it makes + + align:start position:0% +difficult, but it it uh it makes + + + align:start position:0% +difficult, but it it uh it makes +everything a little longer and more + + align:start position:0% +everything a little longer and more + + + align:start position:0% +everything a little longer and more +complicated. Sometimes you might want to + + align:start position:0% +complicated. Sometimes you might want to + + + align:start position:0% +complicated. Sometimes you might want to +do that, but uh in applications, but + + align:start position:0% +do that, but uh in applications, but + + + align:start position:0% +do that, but uh in applications, but +just to show the ideas, I'm going to + + align:start position:0% +just to show the ideas, I'm going to + + + align:start position:0% +just to show the ideas, I'm going to +focus on my P. + + align:start position:0% +focus on my P. + + + align:start position:0% +focus on my P. +Okay. + + align:start position:0% + + + + align:start position:0% + +All right. So, here's the double + + align:start position:0% +All right. So, here's the double + + + align:start position:0% +All right. So, here's the double +counting method. + + align:start position:0% + + + + align:start position:0% + +U so I'll call it theorem 1 s. + + align:start position:0% +U so I'll call it theorem 1 s. + + + align:start position:0% +U so I'll call it theorem 1 s. +Um so it says if x is a subset of the + + align:start position:0% +Um so it says if x is a subset of the + + + align:start position:0% +Um so it says if x is a subset of the +numbers from 1 to n and d is a set of + + align:start position:0% +numbers from 1 to n and d is a set of + + + align:start position:0% +numbers from 1 to n and d is a set of +primes + + align:start position:0% + + + + align:start position:0% + +uh less than or equal to n. + + align:start position:0% +uh less than or equal to n. + + + align:start position:0% +uh less than or equal to n. +Um + + align:start position:0% + + + + align:start position:0% + +and for every p in our set of primes, pi + + align:start position:0% +and for every p in our set of primes, pi + + + align:start position:0% +and for every p in our set of primes, pi +subp of x is less than equal to s. Um + + align:start position:0% +subp of x is less than equal to s. Um + + + align:start position:0% +subp of x is less than equal to s. Um +then we get a conclusion. Um + + align:start position:0% + + + + align:start position:0% + +either + + align:start position:0% +either + + + align:start position:0% +either +x is bounded by 2s or the number of + + align:start position:0% +x is bounded by 2s or the number of + + + align:start position:0% +x is bounded by 2s or the number of +directions is bounded roughly by us. + + align:start position:0% + + + + align:start position:0% + +So I guess this is most interesting if + + align:start position:0% +So I guess this is most interesting if + + + align:start position:0% +So I guess this is most interesting if +the number of directions is + + align:start position:0% +the number of directions is + + + align:start position:0% +the number of directions is +significantly bigger than s. + + align:start position:0% +significantly bigger than s. + + + align:start position:0% +significantly bigger than s. +So if we look at the squares + + align:start position:0% +So if we look at the squares + + + align:start position:0% +So if we look at the squares +uh so suppose I know that pi p of x is + + align:start position:0% +uh so suppose I know that pi p of x is + + + align:start position:0% +uh so suppose I know that pi p of x is +bounded by uh p + 1 / 2. So that's my s + + align:start position:0% +bounded by uh p + 1 / 2. So that's my s + + + align:start position:0% +bounded by uh p + 1 / 2. So that's my s +um and I need to do this. + + align:start position:0% +um and I need to do this. + + + align:start position:0% +um and I need to do this. +Yeah, that's + + align:start position:0% +Yeah, that's + + + align:start position:0% +Yeah, that's +um + + align:start position:0% + + + + align:start position:0% + +Oh, this may not quite work for this. + + align:start position:0% + + + + align:start position:0% + +Actually, I'm not sure if this will + + align:start position:0% +Actually, I'm not sure if this will + + + align:start position:0% +Actually, I'm not sure if this will +imply Linux theorem. Lin proved his + + align:start position:0% +imply Linux theorem. Lin proved his + + + align:start position:0% +imply Linux theorem. Lin proved his +theorem with the forier method. Um, + + align:start position:0% +theorem with the forier method. Um, + + + align:start position:0% +theorem with the forier method. Um, +let's come back to that next time. I + + align:start position:0% +let's come back to that next time. I + + + align:start position:0% +let's come back to that next time. I +think we have just enough time to do the + + align:start position:0% +think we have just enough time to do the + + + align:start position:0% +think we have just enough time to do the +nice double counting argument and uh and + + align:start position:0% +nice double counting argument and uh and + + + align:start position:0% +nice double counting argument and uh and +then do the the for the next. + + align:start position:0% +then do the the for the next. + + + align:start position:0% +then do the the for the next. +Okay. Um so proof we're going to count + + align:start position:0% +Okay. Um so proof we're going to count + + + align:start position:0% +Okay. Um so proof we're going to count +uh coincidences. + + align:start position:0% +uh coincidences. + + + align:start position:0% +uh coincidences. +That's the set of x1 and x2 and x and p + + align:start position:0% +That's the set of x1 and x2 and x and p + + + align:start position:0% +That's the set of x1 and x2 and x and p +in our set of directions or set of + + align:start position:0% +in our set of directions or set of + + + align:start position:0% +in our set of directions or set of +primes. So that pi p of x1 equals pi p + + align:start position:0% +primes. So that pi p of x1 equals pi p + + + align:start position:0% +primes. So that pi p of x1 equals pi p +of x2. + + align:start position:0% + + + + align:start position:0% + +Okay. So we'll count this two different + + align:start position:0% +Okay. So we'll count this two different + + + align:start position:0% +Okay. So we'll count this two different +ways. One is a lower bound. So star is + + align:start position:0% +ways. One is a lower bound. So star is + + + align:start position:0% +ways. One is a lower bound. So star is +at least for every direction. + + align:start position:0% +at least for every direction. + + + align:start position:0% +at least for every direction. +When I do this projection, there are + + align:start position:0% +When I do this projection, there are + + + align:start position:0% +When I do this projection, there are +only s images. So a typical image has x + + align:start position:0% +only s images. So a typical image has x + + + align:start position:0% +only s images. So a typical image has x +over s pre-im images. square that for my + + align:start position:0% +over s pre-im images. square that for my + + + align:start position:0% +over s pre-im images. square that for my +choice of x1 and x2 and then multiply by + + align:start position:0% +choice of x1 and x2 and then multiply by + + + align:start position:0% +choice of x1 and x2 and then multiply by +s for the number of choices of the + + align:start position:0% +s for the number of choices of the + + + align:start position:0% +s for the number of choices of the +projection. So that's um x^2 d s of + + align:start position:0% +projection. So that's um x^2 d s of + + + align:start position:0% +projection. So that's um x^2 d s of +okay now what's our upper bound? + + align:start position:0% + + + + align:start position:0% + +So now I going to fix imagine fixing x1 + + align:start position:0% +So now I going to fix imagine fixing x1 + + + align:start position:0% +So now I going to fix imagine fixing x1 +and x2 and think about how many ps can + + align:start position:0% +and x2 and think about how many ps can + + + align:start position:0% +and x2 and think about how many ps can +satisfy this. + + align:start position:0% + + + + align:start position:0% + +Oh um so + + align:start position:0% +Oh um so + + + align:start position:0% +Oh um so +um + + align:start position:0% +um + + + align:start position:0% +um +so if I have pi p of x1 is equal to pi p + + align:start position:0% +so if I have pi p of x1 is equal to pi p + + + align:start position:0% +so if I have pi p of x1 is equal to pi p +of x2 + + align:start position:0% +of x2 + + + align:start position:0% +of x2 +that tells us that p divides x2 - x1 + + align:start position:0% + + + + align:start position:0% + +and there can't be that many different + + align:start position:0% +and there can't be that many different + + + align:start position:0% +and there can't be that many different +primes that divide x2 - x1. x2 - x1 has + + align:start position:0% +primes that divide x2 - x1. x2 - x1 has + + + align:start position:0% +primes that divide x2 - x1. x2 - x1 has +size uh n. So it could be at most log of + + align:start position:0% +size uh n. So it could be at most log of + + + align:start position:0% +size uh n. So it could be at most log of +n that do this. Um so star is + + align:start position:0% +n that do this. Um so star is + + + align:start position:0% +n that do this. Um so star is +upperbounded by + + align:start position:0% +upperbounded by + + + align:start position:0% +upperbounded by +um okay so so there is a case where x1 + + align:start position:0% +um okay so so there is a case where x1 + + + align:start position:0% +um okay so so there is a case where x1 +equals x2. So that gives me x times the + + align:start position:0% +equals x2. So that gives me x times the + + + align:start position:0% +equals x2. So that gives me x times the +number of directions. + + align:start position:0% +number of directions. + + + align:start position:0% +number of directions. +And then if x1 is not equal to x2, I + + align:start position:0% +And then if x1 is not equal to x2, I + + + align:start position:0% +And then if x1 is not equal to x2, I +have x squar choices for x1 and x2. But + + align:start position:0% +have x squar choices for x1 and x2. But + + + align:start position:0% +have x squar choices for x1 and x2. But +I have only log of n choices for the + + align:start position:0% +I have only log of n choices for the + + + align:start position:0% +I have only log of n choices for the +direction. + + align:start position:0% + + + + align:start position:0% + +Okay. And now I'll compare these to each + + align:start position:0% +Okay. And now I'll compare these to each + + + align:start position:0% +Okay. And now I'll compare these to each +other. + + align:start position:0% + + + + align:start position:0% + +Okay. So I have uh x^2 * d * s inverse + + align:start position:0% +Okay. So I have uh x^2 * d * s inverse + + + align:start position:0% +Okay. So I have uh x^2 * d * s inverse +is less than x * d plus uh x^2 * log. + + align:start position:0% +is less than x * d plus uh x^2 * log. + + + align:start position:0% +is less than x * d plus uh x^2 * log. +So there are two cases. If this one + + align:start position:0% +So there are two cases. If this one + + + align:start position:0% +So there are two cases. If this one +dominates um then I would have that x is + + align:start position:0% +dominates um then I would have that x is + + + align:start position:0% +dominates um then I would have that x is +bounded by 2s + + align:start position:0% +bounded by 2s + + + align:start position:0% +bounded by 2s +or if this one dominates then the x's + + align:start position:0% +or if this one dominates then the x's + + + align:start position:0% +or if this one dominates then the x's +disappear and I get that d is bounded by + + align:start position:0% +disappear and I get that d is bounded by + + + align:start position:0% +disappear and I get that d is bounded by +log of n * s and and that's the that's + + align:start position:0% +log of n * s and and that's the that's + + + align:start position:0% +log of n * s and and that's the that's +the theorem. + + align:start position:0% + + + + align:start position:0% + +Okay. So let me give you an example of + + align:start position:0% +Okay. So let me give you an example of + + + align:start position:0% +Okay. So let me give you an example of +this and argue that this is uh well let + + align:start position:0% +this and argue that this is uh well let + + + align:start position:0% +this and argue that this is uh well let +me give you an example flavor of what + + align:start position:0% +me give you an example flavor of what + + + align:start position:0% +me give you an example flavor of what +this is telling us. So suppose that pi p + + align:start position:0% +this is telling us. So suppose that pi p + + + align:start position:0% +this is telling us. So suppose that pi p +of x is bounded by n^ the 2/3 + + align:start position:0% +of x is bounded by n^ the 2/3 + + + align:start position:0% +of x is bounded by n^ the 2/3 +for um 10 log n + + align:start position:0% +for um 10 log n + + + align:start position:0% +for um 10 log n +* n^ 2/3 different p + + align:start position:0% + + + + align:start position:0% + +um so if that's true then the theorem + + align:start position:0% +um so if that's true then the theorem + + + align:start position:0% +um so if that's true then the theorem +tells us that x is bounded by n^ X. + + align:start position:0% + + + + align:start position:0% + +So these primes might have size around + + align:start position:0% +So these primes might have size around + + + align:start position:0% +So these primes might have size around +this big or a bit bigger. So these + + align:start position:0% +this big or a bit bigger. So these + + + align:start position:0% +this big or a bit bigger. So these +primes are much less than n. So each + + align:start position:0% +primes are much less than n. So each + + + align:start position:0% +primes are much less than n. So each +projection the fact that each projection + + align:start position:0% +projection the fact that each projection + + + align:start position:0% +projection the fact that each projection +one at a time is small, it's not that + + align:start position:0% +one at a time is small, it's not that + + + align:start position:0% +one at a time is small, it's not that +convincing in terms of x being small. + + align:start position:0% +convincing in terms of x being small. + + + align:start position:0% +convincing in terms of x being small. +But knowing that all of these + + align:start position:0% +But knowing that all of these + + + align:start position:0% +But knowing that all of these +projections are this large number of + + align:start position:0% +projections are this large number of + + + align:start position:0% +projections are this large number of +projections is small. It means that x is + + align:start position:0% +projections is small. It means that x is + + + align:start position:0% +projections is small. It means that x is +really that small. \ No newline at end of file diff --git a/XV7YjOer7HE.txt b/XV7YjOer7HE.txt new file mode 100644 index 0000000000000000000000000000000000000000..d9356042752a4e518d12c2c89083a4b13e752160 --- /dev/null +++ b/XV7YjOer7HE.txt @@ -0,0 +1,379 @@ +align:start position:0% + +okay please tell me uh the name of your + + align:start position:0% +okay please tell me uh the name of your + + + align:start position:0% +okay please tell me uh the name of your +team and introduce the members + + align:start position:0% +team and introduce the members + + + align:start position:0% +team and introduce the members +please two guys two girls in an + + align:start position:0% +please two guys two girls in an + + + align:start position:0% +please two guys two girls in an +airplane + + align:start position:0% +airplane + + + align:start position:0% +airplane +I'm joyart + + align:start position:0% +I'm joyart + + + align:start position:0% +I'm joyart +nango uh Tor M all right well you made + + align:start position:0% +nango uh Tor M all right well you made + + + align:start position:0% +nango uh Tor M all right well you made +it this far how are you guys + + align:start position:0% +it this far how are you guys + + + align:start position:0% +it this far how are you guys +feeling nervous nervous yeah sleepy yeah + + align:start position:0% +feeling nervous nervous yeah sleepy yeah + + + align:start position:0% +feeling nervous nervous yeah sleepy yeah +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +definitely uh what's your strategy for + + align:start position:0% +definitely uh what's your strategy for + + + align:start position:0% +definitely uh what's your strategy for +winning today's competition um well our + + align:start position:0% +winning today's competition um well our + + + align:start position:0% +winning today's competition um well our +strategy is to minimize the work that + + align:start position:0% +strategy is to minimize the work that + + + align:start position:0% +strategy is to minimize the work that +the battery has to do so that we the + + align:start position:0% +the battery has to do so that we the + + + align:start position:0% +the battery has to do so that we the +endurance will last the longest so we + + align:start position:0% +endurance will last the longest so we + + + align:start position:0% +endurance will last the longest so we +focused on making the aircraft as light + + align:start position:0% +focused on making the aircraft as light + + + align:start position:0% +focused on making the aircraft as light +as possible and creating as much lift so + + align:start position:0% +as possible and creating as much lift so + + + align:start position:0% +as possible and creating as much lift so +that we can fly sewer and stay up + + align:start position:0% +that we can fly sewer and stay up + + + align:start position:0% +that we can fly sewer and stay up +longer so uh to achieve that what's the + + align:start position:0% +longer so uh to achieve that what's the + + + align:start position:0% +longer so uh to achieve that what's the +most notable design + + align:start position:0% +most notable design + + + align:start position:0% +most notable design +feature say the wind probably since it's + + align:start position:0% +feature say the wind probably since it's + + + align:start position:0% +feature say the wind probably since it's +a very high lift Wing um maybe even too + + align:start position:0% +a very high lift Wing um maybe even too + + + align:start position:0% +a very high lift Wing um maybe even too +much + + align:start position:0% +much + + + align:start position:0% +much +lift saying but um yeah we put a lot of + + align:start position:0% +lift saying but um yeah we put a lot of + + + align:start position:0% +lift saying but um yeah we put a lot of +work into that so so you think that'll + + align:start position:0% +work into that so so you think that'll + + + align:start position:0% +work into that so so you think that'll +give you an advantage uh you've been + + align:start position:0% +give you an advantage uh you've been + + + align:start position:0% +give you an advantage uh you've been +working on this uh project as a team for + + align:start position:0% +working on this uh project as a team for + + + align:start position:0% +working on this uh project as a team for +most of the semester what's been the + + align:start position:0% +most of the semester what's been the + + + align:start position:0% +most of the semester what's been the +most enjoyable part of the + + align:start position:0% +most enjoyable part of the + + + align:start position:0% +most enjoyable part of the +process I think seeing it Fly just like + + align:start position:0% +process I think seeing it Fly just like + + + align:start position:0% +process I think seeing it Fly just like +something that we made that took so much + + align:start position:0% +something that we made that took so much + + + align:start position:0% +something that we made that took so much +time and so much effort and finally + + align:start position:0% +time and so much effort and finally + + + align:start position:0% +time and so much effort and finally +seeing it any other thoughts uh finally + + align:start position:0% +seeing it any other thoughts uh finally + + + align:start position:0% +seeing it any other thoughts uh finally +getting it to fly like as a pilot had a + + align:start position:0% +getting it to fly like as a pilot had a + + + align:start position:0% +getting it to fly like as a pilot had a +lot of trouble originally but now I can + + align:start position:0% +lot of trouble originally but now I can + + + align:start position:0% +lot of trouble originally but now I can +sort of make it fly like we want it so + + align:start position:0% +sort of make it fly like we want it so + + + align:start position:0% +sort of make it fly like we want it so +that's good so you had some control + + align:start position:0% +that's good so you had some control + + + align:start position:0% +that's good so you had some control +issues + + align:start position:0% +issues + + + align:start position:0% +issues +um + + align:start position:0% +um + + + align:start position:0% +um +yeah too good what what was the toughest + + align:start position:0% +yeah too good what what was the toughest + + + align:start position:0% +yeah too good what what was the toughest +part about engineering this + + align:start position:0% +part about engineering this + + + align:start position:0% +part about engineering this +system I since it's so lightweight it + + align:start position:0% +system I since it's so lightweight it + + + align:start position:0% +system I since it's so lightweight it +breaks really easily so even like a + + align:start position:0% +breaks really easily so even like a + + + align:start position:0% +breaks really easily so even like a +little bit of rough landing something + + align:start position:0% +little bit of rough landing something + + + align:start position:0% +little bit of rough landing something +will break off we have to go back + + align:start position:0% +will break off we have to go back + + + align:start position:0% +will break off we have to go back +rebuild it come back just I think a time + + align:start position:0% +rebuild it come back just I think a time + + + align:start position:0% +rebuild it come back just I think a time +more than anything + + align:start position:0% +more than anything + + + align:start position:0% +more than anything +stability well good luck with the flight + + align:start position:0% +stability well good luck with the flight + + + align:start position:0% +stability well good luck with the flight +thanks for talking to us \ No newline at end of file diff --git a/Y-eEV6WqAwg.txt b/Y-eEV6WqAwg.txt new file mode 100644 index 0000000000000000000000000000000000000000..2cb9950bb053ef6aee6322af95df31b63291a983 --- /dev/null +++ b/Y-eEV6WqAwg.txt @@ -0,0 +1,8856 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu first of all welcome to the + + align:start position:0% +ocw.mit.edu first of all welcome to the + + + align:start position:0% +ocw.mit.edu first of all welcome to the +families it's family weekend so welcome + + align:start position:0% +families it's family weekend so welcome + + + align:start position:0% +families it's family weekend so welcome +to the parents CBS and other members of + + align:start position:0% +to the parents CBS and other members of + + + align:start position:0% +to the parents CBS and other members of +extended family hope you have a lovely + + align:start position:0% +extended family hope you have a lovely + + + align:start position:0% +extended family hope you have a lovely +weekend on campus and uh especially + + align:start position:0% +weekend on campus and uh especially + + + align:start position:0% +weekend on campus and uh especially +welcome to + + align:start position:0% +welcome to + + + align:start position:0% +welcome to + + align:start position:0% + + + align:start position:0% +um I have nothing special planned today + + align:start position:0% +um I have nothing special planned today + + + align:start position:0% +um I have nothing special planned today +just a run-of-the-mill lecture so you + + align:start position:0% +just a run-of-the-mill lecture so you + + + align:start position:0% +just a run-of-the-mill lecture so you +get a sense of what it's like to be um + + align:start position:0% +get a sense of what it's like to be um + + + align:start position:0% +get a sense of what it's like to be um +sitting in one of these seats that + + align:start position:0% +sitting in one of these seats that + + + align:start position:0% +sitting in one of these seats that +you've paid so dearly for um I hope we + + align:start position:0% +you've paid so dearly for um I hope we + + + align:start position:0% +you've paid so dearly for um I hope we +can convince you that you've made a + + align:start position:0% +can convince you that you've made a + + + align:start position:0% +can convince you that you've made a +smart decision in putting your son or + + align:start position:0% +smart decision in putting your son or + + + align:start position:0% +smart decision in putting your son or +daughter on this campus uh you'll come + + align:start position:0% +daughter on this campus uh you'll come + + + align:start position:0% +daughter on this campus uh you'll come +to the quick conclusion it's not because + + align:start position:0% +to the quick conclusion it's not because + + + align:start position:0% +to the quick conclusion it's not because +of the facilities facilities here are + + align:start position:0% +of the facilities facilities here are + + + align:start position:0% +of the facilities facilities here are +nothing special + + align:start position:0% +nothing special + + + align:start position:0% +nothing special +uh the classrooms the labs and so on um + + align:start position:0% +uh the classrooms the labs and so on um + + + align:start position:0% +uh the classrooms the labs and so on um +it's the peer group it's not the faculty + + align:start position:0% +it's the peer group it's not the faculty + + + align:start position:0% +it's the peer group it's not the faculty +faculty are okay but I think the I think + + align:start position:0% +faculty are okay but I think the I think + + + align:start position:0% +faculty are okay but I think the I think +it's the peer group I think it's the the + + align:start position:0% +it's the peer group I think it's the the + + + align:start position:0% +it's the peer group I think it's the the +students that are going to be the the + + align:start position:0% +students that are going to be the the + + + align:start position:0% +students that are going to be the the +friends and uh colleagues that uh is + + align:start position:0% +friends and uh colleagues that uh is + + + align:start position:0% +friends and uh colleagues that uh is +makes it a special experience here + + align:start position:0% +makes it a special experience here + + + align:start position:0% +makes it a special experience here +um I'm teaching freshman chemistry but + + align:start position:0% +um I'm teaching freshman chemistry but + + + align:start position:0% +um I'm teaching freshman chemistry but +it's uh taught from the Department of + + align:start position:0% +it's uh taught from the Department of + + + align:start position:0% +it's uh taught from the Department of +material science and engineering and uh + + align:start position:0% +material science and engineering and uh + + + align:start position:0% +material science and engineering and uh +I just want to make one little plug uh + + align:start position:0% +I just want to make one little plug uh + + + align:start position:0% +I just want to make one little plug uh +if if you walk up and down the infinite + + align:start position:0% +if if you walk up and down the infinite + + + align:start position:0% +if if you walk up and down the infinite +Corridor by and large it's ugly because + + align:start position:0% +Corridor by and large it's ugly because + + + align:start position:0% +Corridor by and large it's ugly because +it's uh uh decorated with administrative + + align:start position:0% +it's uh uh decorated with administrative + + + align:start position:0% +it's uh uh decorated with administrative +offices with one exception as you get to + + align:start position:0% +offices with one exception as you get to + + + align:start position:0% +offices with one exception as you get to +the East end it looks like an + + align:start position:0% +the East end it looks like an + + + align:start position:0% +the East end it looks like an +engineering school because there are + + align:start position:0% +engineering school because there are + + + align:start position:0% +engineering school because there are +Labs associated with the Department of + + align:start position:0% +Labs associated with the Department of + + + align:start position:0% +Labs associated with the Department of +material science and engineering and if + + align:start position:0% +material science and engineering and if + + + align:start position:0% +material science and engineering and if +you ever wonder what's going on in those + + align:start position:0% +you ever wonder what's going on in those + + + align:start position:0% +you ever wonder what's going on in those +labs it's your chance to find out so + + align:start position:0% +labs it's your chance to find out so + + + align:start position:0% +labs it's your chance to find out so +this afternoon from 3:30 to 5: it will + + align:start position:0% +this afternoon from 3:30 to 5: it will + + + align:start position:0% +this afternoon from 3:30 to 5: it will +be possible to tour the undergraduate + + align:start position:0% +be possible to tour the undergraduate + + + align:start position:0% +be possible to tour the undergraduate +laboratory which is on the uh south side + + align:start position:0% +laboratory which is on the uh south side + + + align:start position:0% +laboratory which is on the uh south side +and the nanomechanics lab on the north + + align:start position:0% +and the nanomechanics lab on the north + + + align:start position:0% +and the nanomechanics lab on the north +side so if you're you're finding uh + + align:start position:0% +side so if you're you're finding uh + + + align:start position:0% +side so if you're you're finding uh +uncomfortable silence uh with your son + + align:start position:0% +uncomfortable silence uh with your son + + + align:start position:0% +uncomfortable silence uh with your son +or daughter and things are kind of + + align:start position:0% +or daughter and things are kind of + + + align:start position:0% +or daughter and things are kind of +dragging on walk down to the East End of + + align:start position:0% +dragging on walk down to the East End of + + + align:start position:0% +dragging on walk down to the East End of +the infinite Corridor and you can see + + align:start position:0% +the infinite Corridor and you can see + + + align:start position:0% +the infinite Corridor and you can see +some interesting things they're going to + + align:start position:0% +some interesting things they're going to + + + align:start position:0% +some interesting things they're going to +have some demos and and whatnot um and + + align:start position:0% +have some demos and and whatnot um and + + + align:start position:0% +have some demos and and whatnot um and +for the other announcement is that on + + align:start position:0% +for the other announcement is that on + + + align:start position:0% +for the other announcement is that on +Tuesday uh we will have quiz six based + + align:start position:0% +Tuesday uh we will have quiz six based + + + align:start position:0% +Tuesday uh we will have quiz six based +on homework six but there's a few + + align:start position:0% +on homework six but there's a few + + + align:start position:0% +on homework six but there's a few +questions on homework six uh touching + + align:start position:0% +questions on homework six uh touching + + + align:start position:0% +questions on homework six uh touching +upon X-rays and at the rate we're going + + align:start position:0% +upon X-rays and at the rate we're going + + + align:start position:0% +upon X-rays and at the rate we're going +we will not have covered that material + + align:start position:0% +we will not have covered that material + + + align:start position:0% +we will not have covered that material +so ignore the questions on x-rays but + + align:start position:0% +so ignore the questions on x-rays but + + + align:start position:0% +so ignore the questions on x-rays but +the rest I think you should be familiar + + align:start position:0% +the rest I think you should be familiar + + + align:start position:0% +the rest I think you should be familiar +with and uh we'll test at the end of the + + align:start position:0% +with and uh we'll test at the end of the + + + align:start position:0% +with and uh we'll test at the end of the +period instead of the beginning that way + + align:start position:0% +period instead of the beginning that way + + + align:start position:0% +period instead of the beginning that way +you'll have some uh time to interact + + align:start position:0% +you'll have some uh time to interact + + + align:start position:0% +you'll have some uh time to interact +with the recitation + + align:start position:0% +with the recitation + + + align:start position:0% +with the recitation +instructor so what I want to do today is + + align:start position:0% +instructor so what I want to do today is + + + align:start position:0% +instructor so what I want to do today is +uh something really important and it's + + align:start position:0% +uh something really important and it's + + + align:start position:0% +uh something really important and it's +uh fitting that the parents are here up + + align:start position:0% +uh fitting that the parents are here up + + + align:start position:0% +uh fitting that the parents are here up +until now by and large perhaps with the + + align:start position:0% +until now by and large perhaps with the + + + align:start position:0% +until now by and large perhaps with the +exception of some of the band Gap + + align:start position:0% +exception of some of the band Gap + + + align:start position:0% +exception of some of the band Gap +material would we've been covering you + + align:start position:0% +material would we've been covering you + + + align:start position:0% +material would we've been covering you +could have seen bits and pieces of that + + align:start position:0% +could have seen bits and pieces of that + + + align:start position:0% +could have seen bits and pieces of that +in high school and if you've taken a lot + + align:start position:0% +in high school and if you've taken a lot + + + align:start position:0% +in high school and if you've taken a lot +of high school chemistry might be + + align:start position:0% +of high school chemistry might be + + + align:start position:0% +of high school chemistry might be +familiar with it well starting today say + + align:start position:0% +familiar with it well starting today say + + + align:start position:0% +familiar with it well starting today say +goodbye to high school this is solid + + align:start position:0% +goodbye to high school this is solid + + + align:start position:0% +goodbye to high school this is solid +state chemistry now that's why we have + + align:start position:0% +state chemistry now that's why we have + + + align:start position:0% +state chemistry now that's why we have +the crystal models up here and what + + align:start position:0% +the crystal models up here and what + + + align:start position:0% +the crystal models up here and what +we're going to do is we're going to + + align:start position:0% +we're going to do is we're going to + + + align:start position:0% +we're going to do is we're going to +begin with a little bit of a uh review + + align:start position:0% +begin with a little bit of a uh review + + + align:start position:0% +begin with a little bit of a uh review +and so if you'll take a look at the + + align:start position:0% +and so if you'll take a look at the + + + align:start position:0% +and so if you'll take a look at the +handout that's going around this will of + + align:start position:0% +handout that's going around this will of + + + align:start position:0% +handout that's going around this will of +course be posted on the web afterwards + + align:start position:0% +course be posted on the web afterwards + + + align:start position:0% +course be posted on the web afterwards +but uh just to follow along I know the + + align:start position:0% +but uh just to follow along I know the + + + align:start position:0% +but uh just to follow along I know the +par parents are here it gives them some + + align:start position:0% +par parents are here it gives them some + + + align:start position:0% +par parents are here it gives them some +comfort factor to hold a piece of paper + + align:start position:0% +comfort factor to hold a piece of paper + + + align:start position:0% +comfort factor to hold a piece of paper +in their hand so that's your lonus + + align:start position:0% +in their hand so that's your lonus + + + align:start position:0% +in their hand so that's your lonus +blanket for this morning so I want to + + align:start position:0% +blanket for this morning so I want to + + + align:start position:0% +blanket for this morning so I want to +give the big picture and the big picture + + align:start position:0% +give the big picture and the big picture + + + align:start position:0% +give the big picture and the big picture +is that the thesis of 3091 is that + + align:start position:0% +is that the thesis of 3091 is that + + + align:start position:0% +is that the thesis of 3091 is that +electronic structure informs bonding + + align:start position:0% +electronic structure informs bonding + + + align:start position:0% +electronic structure informs bonding +which then informs state of aggregation + + align:start position:0% +which then informs state of aggregation + + + align:start position:0% +which then informs state of aggregation +and just to remind you we started back + + align:start position:0% +and just to remind you we started back + + + align:start position:0% +and just to remind you we started back +uh at the beginning of September with + + align:start position:0% +uh at the beginning of September with + + + align:start position:0% +uh at the beginning of September with +the bore model of the atom and saw that + + align:start position:0% +the bore model of the atom and saw that + + + align:start position:0% +the bore model of the atom and saw that +it was inadequate sommerfeld put in a + + align:start position:0% +it was inadequate sommerfeld put in a + + + align:start position:0% +it was inadequate sommerfeld put in a +few patches came quantum numbers Alf bow + + align:start position:0% +few patches came quantum numbers Alf bow + + + align:start position:0% +few patches came quantum numbers Alf bow +principle multi- electron atoms then we + + align:start position:0% +principle multi- electron atoms then we + + + align:start position:0% +principle multi- electron atoms then we +could explain the patterns in the + + align:start position:0% +could explain the patterns in the + + + align:start position:0% +could explain the patterns in the +periodic table and then we posited octet + + align:start position:0% +periodic table and then we posited octet + + + align:start position:0% +periodic table and then we posited octet +stability as something that atams strive + + align:start position:0% +stability as something that atams strive + + + align:start position:0% +stability as something that atams strive +for and that gave + + align:start position:0% +for and that gave + + + align:start position:0% +for and that gave +to first of all just inert gases explain + + align:start position:0% +to first of all just inert gases explain + + + align:start position:0% +to first of all just inert gases explain +them but then we said you know things + + align:start position:0% +them but then we said you know things + + + align:start position:0% +them but then we said you know things +might engage an electron transfer we + + align:start position:0% +might engage an electron transfer we + + + align:start position:0% +might engage an electron transfer we +could describe ionic uh compounds then + + align:start position:0% +could describe ionic uh compounds then + + + align:start position:0% +could describe ionic uh compounds then +electron sharing Cove valent compounds + + align:start position:0% +electron sharing Cove valent compounds + + + align:start position:0% +electron sharing Cove valent compounds +then we talked about Metals which is 75% + + align:start position:0% +then we talked about Metals which is 75% + + + align:start position:0% +then we talked about Metals which is 75% +of the periodic table and on rout saw + + align:start position:0% +of the periodic table and on rout saw + + + align:start position:0% +of the periodic table and on rout saw +the vander's bonds as a fourth type of + + align:start position:0% +the vander's bonds as a fourth type of + + + align:start position:0% +the vander's bonds as a fourth type of +primary bonding and then we looked at + + align:start position:0% +primary bonding and then we looked at + + + align:start position:0% +primary bonding and then we looked at +secondary bonding which is prevalent in + + align:start position:0% +secondary bonding which is prevalent in + + + align:start position:0% +secondary bonding which is prevalent in +coent compounds and we saw these three + + align:start position:0% +coent compounds and we saw these three + + + align:start position:0% +coent compounds and we saw these three +types dipole dipole London dispersion + + align:start position:0% +types dipole dipole London dispersion + + + align:start position:0% +types dipole dipole London dispersion +and hydrogen bonding and ultimately that + + align:start position:0% +and hydrogen bonding and ultimately that + + + align:start position:0% +and hydrogen bonding and ultimately that +allowed us to decide whether something's + + align:start position:0% +allowed us to decide whether something's + + + align:start position:0% +allowed us to decide whether something's +a solid or liquid or a gas at a + + align:start position:0% +a solid or liquid or a gas at a + + + align:start position:0% +a solid or liquid or a gas at a +particular temperature and we're + + align:start position:0% +particular temperature and we're + + + align:start position:0% +particular temperature and we're +particularly interested in 3091 since + + align:start position:0% +particularly interested in 3091 since + + + align:start position:0% +particularly interested in 3091 since +this is solid state chemistry the + + align:start position:0% +this is solid state chemistry the + + + align:start position:0% +this is solid state chemistry the +circumstances under which something is a + + align:start position:0% +circumstances under which something is a + + + align:start position:0% +circumstances under which something is a +solid so up until now I think you're + + align:start position:0% +solid so up until now I think you're + + + align:start position:0% +solid so up until now I think you're +comfortable with classifying materials + + align:start position:0% +comfortable with classifying materials + + + align:start position:0% +comfortable with classifying materials +on the basis of their bonding type in + + align:start position:0% +on the basis of their bonding type in + + + align:start position:0% +on the basis of their bonding type in +other words it's a Cove valent solid or + + align:start position:0% +other words it's a Cove valent solid or + + + align:start position:0% +other words it's a Cove valent solid or +an ionic solid or a metal but I want to + + align:start position:0% +an ionic solid or a metal but I want to + + + align:start position:0% +an ionic solid or a metal but I want to +show you a little more interesting way + + align:start position:0% +show you a little more interesting way + + + align:start position:0% +show you a little more interesting way +of classify because we're going to + + align:start position:0% +of classify because we're going to + + + align:start position:0% +of classify because we're going to +classify things according to Atomic + + align:start position:0% +classify things according to Atomic + + + align:start position:0% +classify things according to Atomic +Arrangement and so if you flip over the + + align:start position:0% +Arrangement and so if you flip over the + + + align:start position:0% +Arrangement and so if you flip over the +sheet we'll talk about Atomic + + align:start position:0% +sheet we'll talk about Atomic + + + align:start position:0% +sheet we'll talk about Atomic +Arrangement and how it plays into + + align:start position:0% +Arrangement and how it plays into + + + align:start position:0% +Arrangement and how it plays into +classification of solids by the way + + align:start position:0% +classification of solids by the way + + + align:start position:0% +classification of solids by the way +solid let's let's define solid solid is + + align:start position:0% +solid let's let's define solid solid is + + + align:start position:0% +solid let's let's define solid solid is +something that is dimensionally stable + + align:start position:0% +something that is dimensionally stable + + + align:start position:0% +something that is dimensionally stable +it doesn't flow under its own + + align:start position:0% +it doesn't flow under its own + + + align:start position:0% +it doesn't flow under its own +weight has a volume of its own whereas a + + align:start position:0% +weight has a volume of its own whereas a + + + align:start position:0% +weight has a volume of its own whereas a +a fluid either a liquid or a gas takes + + align:start position:0% +a fluid either a liquid or a gas takes + + + align:start position:0% +a fluid either a liquid or a gas takes +the volume of its container the fluid + + align:start position:0% +the volume of its container the fluid + + + align:start position:0% +the volume of its container the fluid +goes to the walls of the contain + + align:start position:0% +goes to the walls of the contain + + + align:start position:0% +goes to the walls of the contain +container the liquid in a gravity field + + align:start position:0% +container the liquid in a gravity field + + + align:start position:0% +container the liquid in a gravity field +sinks to the lowest point in the + + align:start position:0% +sinks to the lowest point in the + + + align:start position:0% +sinks to the lowest point in the +container but the container determines + + align:start position:0% +container but the container determines + + + align:start position:0% +container but the container determines +the shape a solid retains its shape so + + align:start position:0% +the shape a solid retains its shape so + + + align:start position:0% +the shape a solid retains its shape so +now I want to classify solids by atomic + + align:start position:0% +now I want to classify solids by atomic + + + align:start position:0% +now I want to classify solids by atomic +Arrangement so I don't care if they're + + align:start position:0% +Arrangement so I don't care if they're + + + align:start position:0% +Arrangement so I don't care if they're +metals or ionic compounds or calent + + align:start position:0% +metals or ionic compounds or calent + + + align:start position:0% +metals or ionic compounds or calent +compounds there's two classes ordered + + align:start position:0% +compounds there's two classes ordered + + + align:start position:0% +compounds there's two classes ordered +and disordered so isn't it nice when you + + align:start position:0% +and disordered so isn't it nice when you + + + align:start position:0% +and disordered so isn't it nice when you +can take things and classify them you + + align:start position:0% +can take things and classify them you + + + align:start position:0% +can take things and classify them you +know just bifurcate it's one or the + + align:start position:0% +know just bifurcate it's one or the + + + align:start position:0% +know just bifurcate it's one or the +other one or the other and just move + + align:start position:0% +other one or the other and just move + + + align:start position:0% +other one or the other and just move +through that decision tree so let's look + + align:start position:0% +through that decision tree so let's look + + + align:start position:0% +through that decision tree so let's look +at ordered solids ordered solids have a + + align:start position:0% +at ordered solids ordered solids have a + + + align:start position:0% +at ordered solids ordered solids have a +regular Atomic Arrangement whereas + + align:start position:0% +regular Atomic Arrangement whereas + + + align:start position:0% +regular Atomic Arrangement whereas +disordered solids have a random + + align:start position:0% +disordered solids have a random + + + align:start position:0% +disordered solids have a random +arrangement I put an asterisk next to + + align:start position:0% +arrangement I put an asterisk next to + + + align:start position:0% +arrangement I put an asterisk next to +random because it's not totally random + + align:start position:0% +random because it's not totally random + + + align:start position:0% +random because it's not totally random +there's some local order but there's no + + align:start position:0% +there's some local order but there's no + + + align:start position:0% +there's some local order but there's no +long range + + align:start position:0% +long range + + + align:start position:0% +long range +order + + align:start position:0% +order + + + align:start position:0% +order +so the order is short range and what do + + align:start position:0% +so the order is short range and what do + + + align:start position:0% +so the order is short range and what do +we call such solids the ordered solids + + align:start position:0% +we call such solids the ordered solids + + + align:start position:0% +we call such solids the ordered solids +are called crystallin solids and we have + + align:start position:0% +are called crystallin solids and we have + + + align:start position:0% +are called crystallin solids and we have +a plain word everyday word for such an + + align:start position:0% +a plain word everyday word for such an + + + align:start position:0% +a plain word everyday word for such an +ordered solid it's called a crystal and + + align:start position:0% +ordered solid it's called a crystal and + + + align:start position:0% +ordered solid it's called a crystal and +I've been using that term a lot I talked + + align:start position:0% +I've been using that term a lot I talked + + + align:start position:0% +I've been using that term a lot I talked +about Davidson and germ radiating a + + align:start position:0% +about Davidson and germ radiating a + + + align:start position:0% +about Davidson and germ radiating a +nickel crystal that's to distinguish the + + align:start position:0% +nickel crystal that's to distinguish the + + + align:start position:0% +nickel crystal that's to distinguish the +material from something that's + + align:start position:0% +material from something that's + + + align:start position:0% +material from something that's +disordered if it's disordered we say + + align:start position:0% +disordered if it's disordered we say + + + align:start position:0% +disordered if it's disordered we say +that the atomic Arrangement is a + + align:start position:0% +that the atomic Arrangement is a + + + align:start position:0% +that the atomic Arrangement is a +morphous and there's a simple + + align:start position:0% +morphous and there's a simple + + + align:start position:0% +morphous and there's a simple +Anglo-Saxon word for an amorphous solid + + align:start position:0% +Anglo-Saxon word for an amorphous solid + + + align:start position:0% +Anglo-Saxon word for an amorphous solid +glass a glass is an amorphous solid you + + align:start position:0% +glass a glass is an amorphous solid you + + + align:start position:0% +glass a glass is an amorphous solid you +might think glass has to do with whether + + align:start position:0% +might think glass has to do with whether + + + align:start position:0% +might think glass has to do with whether +something is transparent or not and I + + align:start position:0% +something is transparent or not and I + + + align:start position:0% +something is transparent or not and I +want to disabuse you of that we've + + align:start position:0% +want to disabuse you of that we've + + + align:start position:0% +want to disabuse you of that we've +talked about transparency we've talked + + align:start position:0% +talked about transparency we've talked + + + align:start position:0% +talked about transparency we've talked +about transparency and what do we know + + align:start position:0% +about transparency and what do we know + + + align:start position:0% +about transparency and what do we know +about transparency if we want to talk + + align:start position:0% +about transparency if we want to talk + + + align:start position:0% +about transparency if we want to talk +about transparency if something is + + align:start position:0% +about transparency if something is + + + align:start position:0% +about transparency if something is +transparent transparent what do we do we + + align:start position:0% +transparent transparent what do we do we + + + align:start position:0% +transparent transparent what do we do we +ask ourselves is the band Gap in that + + align:start position:0% +ask ourselves is the band Gap in that + + + align:start position:0% +ask ourselves is the band Gap in that +material greater than three electron + + align:start position:0% +material greater than three electron + + + align:start position:0% +material greater than three electron +volts if the answer is yes it's + + align:start position:0% +volts if the answer is yes it's + + + align:start position:0% +volts if the answer is yes it's +transparent if it's less than three + + align:start position:0% +transparent if it's less than three + + + align:start position:0% +transparent if it's less than three +electron volts that's an absorber so + + align:start position:0% +electron volts that's an absorber so + + + align:start position:0% +electron volts that's an absorber so +then what does glass mean glass glass + + align:start position:0% +then what does glass mean glass glass + + + align:start position:0% +then what does glass mean glass glass +means no long range + + align:start position:0% +means no long range + + + align:start position:0% +means no long range +order no long range order let me give + + align:start position:0% +order no long range order let me give + + + align:start position:0% +order no long range order let me give +you some examples um we could say for + + align:start position:0% +you some examples um we could say for + + + align:start position:0% +you some examples um we could say for +example we've got + + align:start position:0% +example we've got + + + align:start position:0% +example we've got +diamond diamond diamond is + + align:start position:0% +diamond diamond diamond is + + + align:start position:0% +diamond diamond diamond is +crystallin Diamond is a is crystallin + + align:start position:0% +crystallin Diamond is a is crystallin + + + align:start position:0% +crystallin Diamond is a is crystallin +and yet it's + + align:start position:0% +and yet it's + + + align:start position:0% +and yet it's +transparent it's transparent why is it + + align:start position:0% +transparent it's transparent why is it + + + align:start position:0% +transparent it's transparent why is it +transparent band Gap is about 5.4 + + align:start position:0% +transparent band Gap is about 5.4 + + + align:start position:0% +transparent band Gap is about 5.4 +electron volts + + align:start position:0% +electron volts + + + align:start position:0% +electron volts +obsidian obsidian + + align:start position:0% +obsidian obsidian + + + align:start position:0% +obsidian obsidian +this is a glassy Rock glassy + + align:start position:0% +this is a glassy Rock glassy + + + align:start position:0% +this is a glassy Rock glassy +Rock it's got no long range + + align:start position:0% +Rock it's got no long range + + + align:start position:0% +Rock it's got no long range +order it's an amorphous material and it + + align:start position:0% +order it's an amorphous material and it + + + align:start position:0% +order it's an amorphous material and it +is + + align:start position:0% +is + + + align:start position:0% +is +opaque obsidian is opaque so here's an + + align:start position:0% +opaque obsidian is opaque so here's an + + + align:start position:0% +opaque obsidian is opaque so here's an +example of an opaque glass and a + + align:start position:0% +example of an opaque glass and a + + + align:start position:0% +example of an opaque glass and a +transparent Crystal so as of now I want + + align:start position:0% +transparent Crystal so as of now I want + + + align:start position:0% +transparent Crystal so as of now I want +to make sure that nobody in 3091 from + + align:start position:0% +to make sure that nobody in 3091 from + + + align:start position:0% +to make sure that nobody in 3091 from +this day forward ever ever says glass is + + align:start position:0% +this day forward ever ever says glass is + + + align:start position:0% +this day forward ever ever says glass is +transparent I will show you before the + + align:start position:0% +transparent I will show you before the + + + align:start position:0% +transparent I will show you before the +end of the month metallic glass + + align:start position:0% +end of the month metallic glass + + + align:start position:0% +end of the month metallic glass +metallic glass how can it be a metal and + + align:start position:0% +metallic glass how can it be a metal and + + + align:start position:0% +metallic glass how can it be a metal and +glassy well it must mean that there are + + align:start position:0% +glassy well it must mean that there are + + + align:start position:0% +glassy well it must mean that there are +metallic bond there's metallic bonding + + align:start position:0% +metallic bond there's metallic bonding + + + align:start position:0% +metallic bond there's metallic bonding +operative but the atoms are not in a + + align:start position:0% +operative but the atoms are not in a + + + align:start position:0% +operative but the atoms are not in a +regular Arrangement and that material is + + align:start position:0% +regular Arrangement and that material is + + + align:start position:0% +regular Arrangement and that material is +not transparent visible light because + + align:start position:0% +not transparent visible light because + + + align:start position:0% +not transparent visible light because +you know that metals have no band Gap + + align:start position:0% +you know that metals have no band Gap + + + align:start position:0% +you know that metals have no band Gap +whatsoever so something's something + + align:start position:0% +whatsoever so something's something + + + align:start position:0% +whatsoever so something's something +important here something important here + + align:start position:0% +important here something important here + + + align:start position:0% +important here something important here +to retain + + align:start position:0% +to retain + + + align:start position:0% +to retain +so this parents will now learn what the + + align:start position:0% +so this parents will now learn what the + + + align:start position:0% +so this parents will now learn what the +students have learned when we go into a + + align:start position:0% +students have learned when we go into a + + + align:start position:0% +students have learned when we go into a +new new unit we begin with a history + + align:start position:0% +new new unit we begin with a history + + + align:start position:0% +new new unit we begin with a history +lesson so let's go back in the Wayback + + align:start position:0% +lesson so let's go back in the Wayback + + + align:start position:0% +lesson so let's go back in the Wayback +machine we'll go back to early efforts + + align:start position:0% +machine we'll go back to early efforts + + + align:start position:0% +machine we'll go back to early efforts +at trying to describe ordered solids so + + align:start position:0% +at trying to describe ordered solids so + + + align:start position:0% +at trying to describe ordered solids so +that's why crystallography is the study + + align:start position:0% +that's why crystallography is the study + + + align:start position:0% +that's why crystallography is the study +of ordered solids Crystal comes from the + + align:start position:0% +of ordered solids Crystal comes from the + + + align:start position:0% +of ordered solids Crystal comes from the +Greek Crystal comes from the + + align:start position:0% +Greek Crystal comes from the + + + align:start position:0% +Greek Crystal comes from the +Greek uh chrystos which is one of the + + align:start position:0% +Greek uh chrystos which is one of the + + + align:start position:0% +Greek uh chrystos which is one of the +terms that might refer to ice it's a + + align:start position:0% +terms that might refer to ice it's a + + + align:start position:0% +terms that might refer to ice it's a +certain form of ice but anyways it's + + align:start position:0% +certain form of ice but anyways it's + + + align:start position:0% +certain form of ice but anyways it's +that's the origin so let's go back to + + align:start position:0% +that's the origin so let's go back to + + + align:start position:0% +that's the origin so let's go back to +the first first uh marking point in + + align:start position:0% +the first first uh marking point in + + + align:start position:0% +the first first uh marking point in +history uh Robert Hook Robert Hook back + + align:start position:0% +history uh Robert Hook Robert Hook back + + + align:start position:0% +history uh Robert Hook Robert Hook back +in 1660 was studying cannonballs they + + align:start position:0% +in 1660 was studying cannonballs they + + + align:start position:0% +in 1660 was studying cannonballs they +were doing military research already + + align:start position:0% +were doing military research already + + + align:start position:0% +were doing military research already +back then what do you think H and he + + align:start position:0% +back then what do you think H and he + + + align:start position:0% +back then what do you think H and he +posited that a crystal must owe its + + align:start position:0% +posited that a crystal must owe its + + + align:start position:0% +posited that a crystal must owe its +regular shape to the packing of + + align:start position:0% +regular shape to the packing of + + + align:start position:0% +regular shape to the packing of +spherical particles packing of spherical + + align:start position:0% +spherical particles packing of spherical + + + align:start position:0% +spherical particles packing of spherical +particles so if you pack regularly + + align:start position:0% +particles so if you pack regularly + + + align:start position:0% +particles so if you pack regularly +you'll get longrange order and then + + align:start position:0% +you'll get longrange order and then + + + align:start position:0% +you'll get longrange order and then +about a decade later there was Neil + + align:start position:0% +about a decade later there was Neil + + + align:start position:0% +about a decade later there was Neil +steensen who was a Dane spent most of + + align:start position:0% +steensen who was a Dane spent most of + + + align:start position:0% +steensen who was a Dane spent most of +his scientific career in Italy and he + + align:start position:0% +his scientific career in Italy and he + + + align:start position:0% +his scientific career in Italy and he +observed that quartz + + align:start position:0% +observed that quartz + + + align:start position:0% +observed that quartz +crystals had the same angles between + + align:start position:0% +crystals had the same angles between + + + align:start position:0% +crystals had the same angles between +corresponding faces regardless of their + + align:start position:0% +corresponding faces regardless of their + + + align:start position:0% +corresponding faces regardless of their +size and see what they were looking for + + align:start position:0% +size and see what they were looking for + + + align:start position:0% +size and see what they were looking for +is trying to make a connection between + + align:start position:0% +is trying to make a connection between + + + align:start position:0% +is trying to make a connection between +the macroscopic and the atomic World in + + align:start position:0% +the macroscopic and the atomic World in + + + align:start position:0% +the macroscopic and the atomic World in +other words here's a simple question if + + align:start position:0% +other words here's a simple question if + + + align:start position:0% +other words here's a simple question if +I see something has a macroscopic shape + + align:start position:0% +I see something has a macroscopic shape + + + align:start position:0% +I see something has a macroscopic shape +very regular and cubic can I infer from + + align:start position:0% +very regular and cubic can I infer from + + + align:start position:0% +very regular and cubic can I infer from +that that if I divide divide divide + + align:start position:0% +that that if I divide divide divide + + + align:start position:0% +that that if I divide divide divide +divide divide if I get down to Atomic + + align:start position:0% +divide divide if I get down to Atomic + + + align:start position:0% +divide divide if I get down to Atomic +Dimensions there will be some cubic + + align:start position:0% +Dimensions there will be some cubic + + + align:start position:0% +Dimensions there will be some cubic +repeat unit yes or no that's the + + align:start position:0% +repeat unit yes or no that's the + + + align:start position:0% +repeat unit yes or no that's the +question they were wrestling with and + + align:start position:0% +question they were wrestling with and + + + align:start position:0% +question they were wrestling with and +then around the end of the century + + align:start position:0% +then around the end of the century + + + align:start position:0% +then around the end of the century +Christian hyans in 1690 studying calite + + align:start position:0% +Christian hyans in 1690 studying calite + + + align:start position:0% +Christian hyans in 1690 studying calite +crystals made drawings of atomic packing + + align:start position:0% +crystals made drawings of atomic packing + + + align:start position:0% +crystals made drawings of atomic packing +and bulk shape and here's a drawing from + + align:start position:0% +and bulk shape and here's a drawing from + + + align:start position:0% +and bulk shape and here's a drawing from +his book in 1690 and Tom if I could have + + align:start position:0% +his book in 1690 and Tom if I could have + + + align:start position:0% +his book in 1690 and Tom if I could have +the if you could switch the video over + + align:start position:0% +the if you could switch the video over + + + align:start position:0% +the if you could switch the video over +to the U uh document projector I've got + + align:start position:0% +to the U uh document projector I've got + + + align:start position:0% +to the U uh document projector I've got +a calite crystal here here's the calite + + align:start position:0% + + + + align:start position:0% + +Crystal all right and now + + align:start position:0% +Crystal all right and now + + + align:start position:0% +Crystal all right and now +autofocus autofocus is off autofocus is + + align:start position:0% +autofocus autofocus is off autofocus is + + + align:start position:0% +autofocus autofocus is off autofocus is +on okay so now you can see this is look + + align:start position:0% +on okay so now you can see this is look + + + align:start position:0% +on okay so now you can see this is look +at the regularity of this imagine you're + + align:start position:0% +at the regularity of this imagine you're + + + align:start position:0% +at the regularity of this imagine you're +looking at this is all you have to work + + align:start position:0% +looking at this is all you have to work + + + align:start position:0% +looking at this is all you have to work +with there's no scanny electron + + align:start position:0% +with there's no scanny electron + + + align:start position:0% +with there's no scanny electron +microscope there's no nanoscope nothing + + align:start position:0% +microscope there's no nanoscope nothing + + + align:start position:0% +microscope there's no nanoscope nothing +that's what you've got to work with and + + align:start position:0% +that's what you've got to work with and + + + align:start position:0% +that's what you've got to work with and +what he comes up with Tom if we could go + + align:start position:0% +what he comes up with Tom if we could go + + + align:start position:0% +what he comes up with Tom if we could go +back to the U um computer video please + + align:start position:0% +back to the U um computer video please + + + align:start position:0% +back to the U um computer video please +so so starting with that Crystal this is + + align:start position:0% +so so starting with that Crystal this is + + + align:start position:0% +so so starting with that Crystal this is +what he posits that's not bad remember + + align:start position:0% +what he posits that's not bad remember + + + align:start position:0% +what he posits that's not bad remember +this hyans is the same one that gave us + + align:start position:0% +this hyans is the same one that gave us + + + align:start position:0% +this hyans is the same one that gave us +Optics you see these people were + + align:start position:0% +Optics you see these people were + + + align:start position:0% +Optics you see these people were +polymaths they weren't narrow + + align:start position:0% +polymaths they weren't narrow + + + align:start position:0% +polymaths they weren't narrow +Specialists they were generalists and + + align:start position:0% +Specialists they were generalists and + + + align:start position:0% +Specialists they were generalists and +they made substantial contributions in + + align:start position:0% +they made substantial contributions in + + + align:start position:0% +they made substantial contributions in +more than one field Tom let's go back to + + align:start position:0% +more than one field Tom let's go back to + + + align:start position:0% +more than one field Tom let's go back to +uh to the document camera let's go back + + align:start position:0% +uh to the document camera let's go back + + + align:start position:0% +uh to the document camera let's go back +to the document camera Let's uh here's + + align:start position:0% +to the document camera Let's uh here's + + + align:start position:0% +to the document camera Let's uh here's +here's a piece of + + align:start position:0% +here's a piece of + + + align:start position:0% +here's a piece of +10 all right so I mean if I had to draw + + align:start position:0% +10 all right so I mean if I had to draw + + + align:start position:0% +10 all right so I mean if I had to draw +this piece of 10 I might draw a + + align:start position:0% +this piece of 10 I might draw a + + + align:start position:0% +this piece of 10 I might draw a +different drawing from what hyan Drew + + align:start position:0% +different drawing from what hyan Drew + + + align:start position:0% +different drawing from what hyan Drew +because you can see the angles are + + align:start position:0% +because you can see the angles are + + + align:start position:0% +because you can see the angles are +different here look at these are right + + align:start position:0% + + + + align:start position:0% + +angles well here's a piece of barrel + + align:start position:0% +angles well here's a piece of barrel + + + align:start position:0% +angles well here's a piece of barrel +this is a brillium aluminum silicate + + align:start position:0% +this is a brillium aluminum silicate + + + align:start position:0% +this is a brillium aluminum silicate +look at that that's a hexagon on end + + align:start position:0% +look at that that's a hexagon on end + + + align:start position:0% +look at that that's a hexagon on end +almost H so what's going on here's a + + align:start position:0% +almost H so what's going on here's a + + + align:start position:0% +almost H so what's going on here's a +piece of cry + + align:start position:0% + + + + align:start position:0% + +light looks at somebody borrowed it and + + align:start position:0% +light looks at somebody borrowed it and + + + align:start position:0% +light looks at somebody borrowed it and +dropped it look at that see see back + + align:start position:0% +dropped it look at that see see back + + + align:start position:0% +dropped it look at that see see back +data imagine drawing that see that's + + align:start position:0% +data imagine drawing that see that's + + + align:start position:0% +data imagine drawing that see that's +what happens they give you lousy samples + + align:start position:0% +what happens they give you lousy samples + + + align:start position:0% +what happens they give you lousy samples +they expect you to do Cutting Edge + + align:start position:0% +they expect you to do Cutting Edge + + + align:start position:0% +they expect you to do Cutting Edge +research what do + + align:start position:0% +research what do + + + align:start position:0% +research what do +you okay Tom let's go back to the uh + + align:start position:0% +you okay Tom let's go back to the uh + + + align:start position:0% +you okay Tom let's go back to the uh +computer before I digress all right so + + align:start position:0% +computer before I digress all right so + + + align:start position:0% +computer before I digress all right so +here we are here's here's another + + align:start position:0% +here we are here's here's another + + + align:start position:0% +here we are here's here's another +example I couldn't bring this one in + + align:start position:0% +example I couldn't bring this one in + + + align:start position:0% +example I couldn't bring this one in +these are big chunks of bay salt off the + + align:start position:0% +these are big chunks of bay salt off the + + + align:start position:0% +these are big chunks of bay salt off the +coast of Iceland and you can see they + + align:start position:0% +coast of Iceland and you can see they + + + align:start position:0% +coast of Iceland and you can see they +have they have other uh forms all right + + align:start position:0% +have they have other uh forms all right + + + align:start position:0% +have they have other uh forms all right +so so far so good now let's go into the + + align:start position:0% +so so far so good now let's go into the + + + align:start position:0% +so so far so good now let's go into the +about years later over to France this is + + align:start position:0% +about years later over to France this is + + + align:start position:0% +about years later over to France this is +renei and he's studying at uh sorban and + + align:start position:0% +renei and he's studying at uh sorban and + + + align:start position:0% +renei and he's studying at uh sorban and +he's studying the cleavage of calite + + align:start position:0% +he's studying the cleavage of calite + + + align:start position:0% +he's studying the cleavage of calite +basically what he does is he comes into + + align:start position:0% +basically what he does is he comes into + + + align:start position:0% +basically what he does is he comes into +work every day and he breaks things okay + + align:start position:0% +work every day and he breaks things okay + + + align:start position:0% +work every day and he breaks things okay +and he breaks the cleav he breaks the + + align:start position:0% +and he breaks the cleav he breaks the + + + align:start position:0% +and he breaks the cleav he breaks the +calite and he looks at the little pieces + + align:start position:0% +calite and he looks at the little pieces + + + align:start position:0% +calite and he looks at the little pieces +of calite and what he observes is that + + align:start position:0% +of calite and what he observes is that + + + align:start position:0% +of calite and what he observes is that +all shards are rhomedal doesn't matter + + align:start position:0% +all shards are rhomedal doesn't matter + + + align:start position:0% +all shards are rhomedal doesn't matter +how small he breaks the calide crystal + + align:start position:0% +how small he breaks the calide crystal + + + align:start position:0% +how small he breaks the calide crystal +down he always gets rhomedal shards so + + align:start position:0% +down he always gets rhomedal shards so + + + align:start position:0% +down he always gets rhomedal shards so +then he says I'm going to deposit that + + align:start position:0% +then he says I'm going to deposit that + + + align:start position:0% +then he says I'm going to deposit that +that's the base unit of celite and + + align:start position:0% +that's the base unit of celite and + + + align:start position:0% +that's the base unit of celite and +furthermore because he's a Frenchman and + + align:start position:0% +furthermore because he's a Frenchman and + + + align:start position:0% +furthermore because he's a Frenchman and +they're steeped in mathematical + + align:start position:0% +they're steeped in mathematical + + + align:start position:0% +they're steeped in mathematical +tradition he decides to ma to model this + + align:start position:0% +tradition he decides to ma to model this + + + align:start position:0% +tradition he decides to ma to model this +mathematically and he says okay we we + + align:start position:0% +mathematically and he says okay we we + + + align:start position:0% +mathematically and he says okay we we +all know that if we wanted to fill three + + align:start position:0% +all know that if we wanted to fill three + + + align:start position:0% +all know that if we wanted to fill three +space with the same unit we could choose + + align:start position:0% +space with the same unit we could choose + + + align:start position:0% +space with the same unit we could choose +a number of shapes right we could start + + align:start position:0% +a number of shapes right we could start + + + align:start position:0% +a number of shapes right we could start +with a cube and I could fill this room + + align:start position:0% +with a cube and I could fill this room + + + align:start position:0% +with a cube and I could fill this room +with cubes of identical size I can fill + + align:start position:0% +with cubes of identical size I can fill + + + align:start position:0% +with cubes of identical size I can fill +this room with sort of uh orthorombic + + align:start position:0% +this room with sort of uh orthorombic + + + align:start position:0% +this room with sort of uh orthorombic +boxes you know sort of rectangular but + + align:start position:0% +boxes you know sort of rectangular but + + + align:start position:0% +boxes you know sort of rectangular but +Square cross-section I could have + + align:start position:0% +Square cross-section I could have + + + align:start position:0% +Square cross-section I could have +something that's rectangular with a + + align:start position:0% +something that's rectangular with a + + + align:start position:0% +something that's rectangular with a +rectangular cross-section I could use + + align:start position:0% +rectangular cross-section I could use + + + align:start position:0% +rectangular cross-section I could use +something that's romedal how do I know + + align:start position:0% +something that's romedal how do I know + + + align:start position:0% +something that's romedal how do I know +look at the Crystal I don't see any + + align:start position:0% +look at the Crystal I don't see any + + + align:start position:0% +look at the Crystal I don't see any +holes here okay so what what uh AI did + + align:start position:0% +holes here okay so what what uh AI did + + + align:start position:0% +holes here okay so what what uh AI did +is he said mathematically I want to + + align:start position:0% +is he said mathematically I want to + + + align:start position:0% +is he said mathematically I want to +determine what is the maximum number of + + align:start position:0% +determine what is the maximum number of + + + align:start position:0% +determine what is the maximum number of +distinguishable shapes that will fill + + align:start position:0% +distinguishable shapes that will fill + + + align:start position:0% +distinguishable shapes that will fill +three space I call this the milk carton + + align:start position:0% +three space I call this the milk carton + + + align:start position:0% +three space I call this the milk carton +problem how many different shapes of + + align:start position:0% +problem how many different shapes of + + + align:start position:0% +problem how many different shapes of +milk cartons could you make that would + + align:start position:0% +milk cartons could you make that would + + + align:start position:0% +milk cartons could you make that would +you be able to fill the truck perfectly + + align:start position:0% +you be able to fill the truck perfectly + + + align:start position:0% +you be able to fill the truck perfectly +and he came up with seven of them seven + + align:start position:0% +and he came up with seven of them seven + + + align:start position:0% +and he came up with seven of them seven +of them and uh I'm getting ahead of + + align:start position:0% +of them and uh I'm getting ahead of + + + align:start position:0% +of them and uh I'm getting ahead of +myself there the seven of them are shown + + align:start position:0% +myself there the seven of them are shown + + + align:start position:0% +myself there the seven of them are shown +here this is in your in your notes and + + align:start position:0% +here this is in your in your notes and + + + align:start position:0% +here this is in your in your notes and +these are the labels for them and here's + + align:start position:0% +these are the labels for them and here's + + + align:start position:0% +these are the labels for them and here's +the basic unit so you have three lengths + + align:start position:0% +the basic unit so you have three lengths + + + align:start position:0% +the basic unit so you have three lengths +ABC and you have three angles alpha beta + + align:start position:0% +ABC and you have three angles alpha beta + + + align:start position:0% +ABC and you have three angles alpha beta +and gamma and depending on which mix you + + align:start position:0% +and gamma and depending on which mix you + + + align:start position:0% +and gamma and depending on which mix you +choose for example the cube is here AAL + + align:start position:0% +choose for example the cube is here AAL + + + align:start position:0% +choose for example the cube is here AAL +b equals c so three uh edges all normal + + align:start position:0% +b equals c so three uh edges all normal + + + align:start position:0% +b equals c so three uh edges all normal +to one another and then here's the + + align:start position:0% +to one another and then here's the + + + align:start position:0% +to one another and then here's the +orthorombic they're not equal to each + + align:start position:0% +orthorombic they're not equal to each + + + align:start position:0% +orthorombic they're not equal to each +other and so on so seven basic + + align:start position:0% +other and so on so seven basic + + + align:start position:0% +other and so on so seven basic +shapes and here they are drawn for you + + align:start position:0% +shapes and here they are drawn for you + + + align:start position:0% +shapes and here they are drawn for you +and this is taken out of the lecture + + align:start position:0% +and this is taken out of the lecture + + + align:start position:0% +and this is taken out of the lecture +notes the archival lecture notes so this + + align:start position:0% +notes the archival lecture notes so this + + + align:start position:0% +notes the archival lecture notes so this +is analogous to the tiling problem just + + align:start position:0% +is analogous to the tiling problem just + + + align:start position:0% +is analogous to the tiling problem just +to drive home the point so if you want + + align:start position:0% +to drive home the point so if you want + + + align:start position:0% +to drive home the point so if you want +to do the tiling problem how many + + align:start position:0% +to do the tiling problem how many + + + align:start position:0% +to do the tiling problem how many +distinct shapes of tile are there in two + + align:start position:0% +distinct shapes of tile are there in two + + + align:start position:0% +distinct shapes of tile are there in two +space right so I think we can agree we + + align:start position:0% +space right so I think we can agree we + + + align:start position:0% +space right so I think we can agree we +can go with square + + align:start position:0% +can go with square + + + align:start position:0% +can go with square +tiles or we could go with rectangular + + align:start position:0% +tiles or we could go with rectangular + + + align:start position:0% +tiles or we could go with rectangular +tiles what other tiles do we have + + align:start position:0% +tiles what other tiles do we have + + + align:start position:0% +tiles what other tiles do we have +Triangle Well triangle is actually it's + + align:start position:0% +Triangle Well triangle is actually it's + + + align:start position:0% +Triangle Well triangle is actually it's +not a basic unit because I can't it + + align:start position:0% +not a basic unit because I can't it + + + align:start position:0% +not a basic unit because I can't it +doesn't observe translational symmetry + + align:start position:0% +doesn't observe translational symmetry + + + align:start position:0% +doesn't observe translational symmetry +but if I close the triangle like this + + align:start position:0% +but if I close the triangle like this + + + align:start position:0% +but if I close the triangle like this +and have a 60° so this will become the + + align:start position:0% +and have a 60° so this will become the + + + align:start position:0% +and have a 60° so this will become the +basic repeat unit okay then there's a + + align:start position:0% +basic repeat unit okay then there's a + + + align:start position:0% +basic repeat unit okay then there's a +regular uh parallel a pipid where this + + align:start position:0% +regular uh parallel a pipid where this + + + align:start position:0% +regular uh parallel a pipid where this +unit angle rather is not equal to 60° + + align:start position:0% +unit angle rather is not equal to 60° + + + align:start position:0% +unit angle rather is not equal to 60° +and this in fact is the basic unit that + + align:start position:0% +and this in fact is the basic unit that + + + align:start position:0% +and this in fact is the basic unit that +Frank Gary uses in building his if you + + align:start position:0% +Frank Gary uses in building his if you + + + align:start position:0% +Frank Gary uses in building his if you +go over to the the status Center you + + align:start position:0% +go over to the the status Center you + + + align:start position:0% +go over to the the status Center you +will see that the basic unit that's used + + align:start position:0% +will see that the basic unit that's used + + + align:start position:0% +will see that the basic unit that's used +to make those irregular shapes is this + + align:start position:0% +to make those irregular shapes is this + + + align:start position:0% +to make those irregular shapes is this +well this is space filling and all of + + align:start position:0% +well this is space filling and all of + + + align:start position:0% +well this is space filling and all of +these are labeled and so on this is the + + align:start position:0% +these are labeled and so on this is the + + + align:start position:0% +these are labeled and so on this is the +clothing problem well how do you cut a + + align:start position:0% +clothing problem well how do you cut a + + + align:start position:0% +clothing problem well how do you cut a +two-dimensional piece of cloth to fit + + align:start position:0% +two-dimensional piece of cloth to fit + + + align:start position:0% +two-dimensional piece of cloth to fit +over a three-dimensional shape it's not + + align:start position:0% +over a three-dimensional shape it's not + + + align:start position:0% +over a three-dimensional shape it's not +trivial problem that's why most clothes + + align:start position:0% +trivial problem that's why most clothes + + + align:start position:0% +trivial problem that's why most clothes +don't fit because it's very simple + + align:start position:0% +don't fit because it's very simple + + + align:start position:0% +don't fit because it's very simple +fashion designers don't understand the + + align:start position:0% +fashion designers don't understand the + + + align:start position:0% +fashion designers don't understand the +simple + + align:start position:0% +simple + + + align:start position:0% +simple +geometry you and we have how do we + + align:start position:0% +geometry you and we have how do we + + + align:start position:0% +geometry you and we have how do we +describe size you know for for men at + + align:start position:0% +describe size you know for for men at + + + align:start position:0% +describe size you know for for men at +least they take a chest size and a + + align:start position:0% +least they take a chest size and a + + + align:start position:0% +least they take a chest size and a +sleeve size for women they just go oh + + align:start position:0% +sleeve size for women they just go oh + + + align:start position:0% +sleeve size for women they just go oh +she's an eight well an eight one number + + align:start position:0% +she's an eight well an eight one number + + + align:start position:0% +she's an eight well an eight one number +you know this is why things don't fit + + align:start position:0% +you know this is why things don't fit + + + align:start position:0% +you know this is why things don't fit +you know you have to get down to the + + align:start position:0% +you know you have to get down to the + + + align:start position:0% +you know you have to get down to the +unit + + align:start position:0% +unit + + + align:start position:0% +unit +cell here's one that won't work the + + align:start position:0% +cell here's one that won't work the + + + align:start position:0% +cell here's one that won't work the +Pentagon won't work and I'm not trying + + align:start position:0% +Pentagon won't work and I'm not trying + + + align:start position:0% +Pentagon won't work and I'm not trying +to make a political statement I'm simply + + align:start position:0% +to make a political statement I'm simply + + + align:start position:0% +to make a political statement I'm simply +saying that so here's what you can do is + + align:start position:0% +saying that so here's what you can do is + + + align:start position:0% +saying that so here's what you can do is +if you here's what happens if you try to + + align:start position:0% +if you here's what happens if you try to + + + align:start position:0% +if you here's what happens if you try to +fill two space with a pentagon you see + + align:start position:0% +fill two space with a pentagon you see + + + align:start position:0% +fill two space with a pentagon you see +it won't butt up there's these white + + align:start position:0% +it won't butt up there's these white + + + align:start position:0% +it won't butt up there's these white +gaps the Reds touch the Reds but it + + align:start position:0% +gaps the Reds touch the Reds but it + + + align:start position:0% +gaps the Reds touch the Reds but it +won't fill so this is how o worked in + + align:start position:0% +won't fill so this is how o worked in + + + align:start position:0% +won't fill so this is how o worked in +three space and determine that certain + + align:start position:0% +three space and determine that certain + + + align:start position:0% +three space and determine that certain +units will not butt up against one + + align:start position:0% +units will not butt up against one + + + align:start position:0% +units will not butt up against one +another and fill three space perfectly + + align:start position:0% +another and fill three space perfectly + + + align:start position:0% +another and fill three space perfectly +okay so we're we're clicking things are + + align:start position:0% +okay so we're we're clicking things are + + + align:start position:0% +okay so we're we're clicking things are +going well but we still haven't got + + align:start position:0% +going well but we still haven't got + + + align:start position:0% +going well but we still haven't got +Atomic Arrangements all we've got is + + align:start position:0% +Atomic Arrangements all we've got is + + + align:start position:0% +Atomic Arrangements all we've got is +milk cartons so far so now let's think + + align:start position:0% +milk cartons so far so now let's think + + + align:start position:0% +milk cartons so far so now let's think +about the next uh The Next Step The Next + + align:start position:0% +about the next uh The Next Step The Next + + + align:start position:0% +about the next uh The Next Step The Next +Step came uh about 50 years later uh + + align:start position:0% +Step came uh about 50 years later uh + + + align:start position:0% +Step came uh about 50 years later uh +1848 which was an auspicious year in in + + align:start position:0% +1848 which was an auspicious year in in + + + align:start position:0% +1848 which was an auspicious year in in +Europe it was another Frenchman Aus bra + + align:start position:0% +Europe it was another Frenchman Aus bra + + + align:start position:0% +Europe it was another Frenchman Aus bra +and uh he proved mathematically that + + align:start position:0% +and uh he proved mathematically that + + + align:start position:0% +and uh he proved mathematically that +there are 14 distinct ways to arrange + + align:start position:0% +there are 14 distinct ways to arrange + + + align:start position:0% +there are 14 distinct ways to arrange +points in space and what do I mean by + + align:start position:0% +points in space and what do I mean by + + + align:start position:0% +points in space and what do I mean by +that here's a cartoon that shows uh the + + align:start position:0% +that here's a cartoon that shows uh the + + + align:start position:0% +that here's a cartoon that shows uh the +cube we've agreed that the cube is a + + align:start position:0% +cube we've agreed that the cube is a + + + align:start position:0% +cube we've agreed that the cube is a +cookie cutter that will fill three space + + align:start position:0% +cookie cutter that will fill three space + + + align:start position:0% +cookie cutter that will fill three space +but when I start putting atoms in the + + align:start position:0% +but when I start putting atoms in the + + + align:start position:0% +but when I start putting atoms in the +cube I have three distinguishable + + align:start position:0% +cube I have three distinguishable + + + align:start position:0% +cube I have three distinguishable +arrangements so here on the left I have + + align:start position:0% +arrangements so here on the left I have + + + align:start position:0% +arrangements so here on the left I have +something where I put atoms only on the + + align:start position:0% +something where I put atoms only on the + + + align:start position:0% +something where I put atoms only on the +corners and the second one I put atoms + + align:start position:0% +corners and the second one I put atoms + + + align:start position:0% +corners and the second one I put atoms +on the corners and one in the center now + + align:start position:0% +on the corners and one in the center now + + + align:start position:0% +on the corners and one in the center now +think look at the one in the center that + + align:start position:0% +think look at the one in the center that + + + align:start position:0% +think look at the one in the center that +one in the center sees eight nearest + + align:start position:0% +one in the center sees eight nearest + + + align:start position:0% +one in the center sees eight nearest +neighbors each one of these see only six + + align:start position:0% +neighbors each one of these see only six + + + align:start position:0% +neighbors each one of these see only six +nearest neighbors so these atoms have a + + align:start position:0% +nearest neighbors so these atoms have a + + + align:start position:0% +nearest neighbors so these atoms have a +different atom Arrangement a different + + align:start position:0% +different atom Arrangement a different + + + align:start position:0% +different atom Arrangement a different +atom environment from the atoms in this + + align:start position:0% +atom environment from the atoms in this + + + align:start position:0% +atom environment from the atoms in this +Arrangement so the left one is called + + align:start position:0% +Arrangement so the left one is called + + + align:start position:0% +Arrangement so the left one is called +Simple cubic the center one is called + + align:start position:0% +Simple cubic the center one is called + + + align:start position:0% +Simple cubic the center one is called +body centered cubic because there's an + + align:start position:0% +body centered cubic because there's an + + + align:start position:0% +body centered cubic because there's an +atom in the center and it doesn't matter + + align:start position:0% +atom in the center and it doesn't matter + + + align:start position:0% +atom in the center and it doesn't matter +I can arbitrarily shift the center up to + + align:start position:0% +I can arbitrarily shift the center up to + + + align:start position:0% +I can arbitrarily shift the center up to +this corner and this corner atom sees + + align:start position:0% +this corner and this corner atom sees + + + align:start position:0% +this corner and this corner atom sees +the same nearest Neighbors in the same + + align:start position:0% +the same nearest Neighbors in the same + + + align:start position:0% +the same nearest Neighbors in the same +Arrangement relative to the center + + align:start position:0% +Arrangement relative to the center + + + align:start position:0% +Arrangement relative to the center +here's body centered cubic + + align:start position:0% +here's body centered cubic + + + align:start position:0% +here's body centered cubic +choose any one of those if I sit here in + + align:start position:0% +choose any one of those if I sit here in + + + align:start position:0% +choose any one of those if I sit here in +the center I've got 1 2 3 4 5 6 7even + + align:start position:0% +the center I've got 1 2 3 4 5 6 7even + + + align:start position:0% +the center I've got 1 2 3 4 5 6 7even +eight or I can go to this one over here + + align:start position:0% +eight or I can go to this one over here + + + align:start position:0% +eight or I can go to this one over here +and it sees one two 3 four and then you + + align:start position:0% +and it sees one two 3 four and then you + + + align:start position:0% +and it sees one two 3 four and then you +just keep going it's going to see the + + align:start position:0% +just keep going it's going to see the + + + align:start position:0% +just keep going it's going to see the +same Arrangement and yet the the cookie + + align:start position:0% +same Arrangement and yet the the cookie + + + align:start position:0% +same Arrangement and yet the the cookie +cutter that fills space is the cube and + + align:start position:0% +cutter that fills space is the cube and + + + align:start position:0% +cutter that fills space is the cube and +yet there's one other possibility and + + align:start position:0% +yet there's one other possibility and + + + align:start position:0% +yet there's one other possibility and +that's face centered cubic face centered + + align:start position:0% +that's face centered cubic face centered + + + align:start position:0% +that's face centered cubic face centered +cubic is here where you have the this + + align:start position:0% +cubic is here where you have the this + + + align:start position:0% +cubic is here where you have the this +the square face and then an atom in the + + align:start position:0% +the square face and then an atom in the + + + align:start position:0% +the square face and then an atom in the +center of each face and that's + + align:start position:0% +center of each face and that's + + + align:start position:0% +center of each face and that's +distinguishable that's the + + align:start position:0% +distinguishable that's the + + + align:start position:0% +distinguishable that's the +distinguishable so bra again Frenchman + + align:start position:0% +distinguishable so bra again Frenchman + + + align:start position:0% +distinguishable so bra again Frenchman +steeped in math goes into the + + align:start position:0% +steeped in math goes into the + + + align:start position:0% +steeped in math goes into the +mathematics and asks how many different + + align:start position:0% +mathematics and asks how many different + + + align:start position:0% +mathematics and asks how many different +ways can I put atoms into these seven + + align:start position:0% +ways can I put atoms into these seven + + + align:start position:0% +ways can I put atoms into these seven +Crystal systems that AI has specified + + align:start position:0% +Crystal systems that AI has specified + + + align:start position:0% +Crystal systems that AI has specified +and get distinguishable Point + + align:start position:0% +and get distinguishable Point + + + align:start position:0% +and get distinguishable Point +environments and the answer is 14 the + + align:start position:0% +environments and the answer is 14 the + + + align:start position:0% +environments and the answer is 14 the +answer is 14 14 ways to arrange points + + align:start position:0% +answer is 14 14 ways to arrange points + + + align:start position:0% +answer is 14 14 ways to arrange points +in space so now we're getting somewhere + + align:start position:0% +in space so now we're getting somewhere + + + align:start position:0% +in space so now we're getting somewhere +now we're getting somewhere and by the + + align:start position:0% +now we're getting somewhere and by the + + + align:start position:0% +now we're getting somewhere and by the +way if you look at this uh you here are + + align:start position:0% +way if you look at this uh you here are + + + align:start position:0% +way if you look at this uh you here are +the 14 uh different bra laes and they're + + align:start position:0% +the 14 uh different bra laes and they're + + + align:start position:0% +the 14 uh different bra laes and they're +showing this is also from the lecture + + align:start position:0% +showing this is also from the lecture + + + align:start position:0% +showing this is also from the lecture +notes and all we're putting here is one + + align:start position:0% +notes and all we're putting here is one + + + align:start position:0% +notes and all we're putting here is one +dot at each lattice point but it doesn't + + align:start position:0% +dot at each lattice point but it doesn't + + + align:start position:0% +dot at each lattice point but it doesn't +have to be a DOT okay what I'm going to + + align:start position:0% +have to be a DOT okay what I'm going to + + + align:start position:0% +have to be a DOT okay what I'm going to +show you in a second is I can put sets + + align:start position:0% +show you in a second is I can put sets + + + align:start position:0% +show you in a second is I can put sets +of atoms groups of atoms in other words + + align:start position:0% +of atoms groups of atoms in other words + + + align:start position:0% +of atoms groups of atoms in other words +if I wanted to describe uh the positions + + align:start position:0% +if I wanted to describe uh the positions + + + align:start position:0% +if I wanted to describe uh the positions +of every Apple in an orchard what I + + align:start position:0% +of every Apple in an orchard what I + + + align:start position:0% +of every Apple in an orchard what I +could do is say that the um that the bra + + align:start position:0% +could do is say that the um that the bra + + + align:start position:0% +could do is say that the um that the bra +lattice is telling me the planting of + + align:start position:0% +lattice is telling me the planting of + + + align:start position:0% +lattice is telling me the planting of +the trees and then I can hang different + + align:start position:0% +the trees and then I can hang different + + + align:start position:0% +the trees and then I can hang different +different types of apple Arrangements at + + align:start position:0% +different types of apple Arrangements at + + + align:start position:0% +different types of apple Arrangements at +each point so this is what we're getting + + align:start position:0% +each point so this is what we're getting + + + align:start position:0% +each point so this is what we're getting +to we're trying to break this down + + align:start position:0% +to we're trying to break this down + + + align:start position:0% +to we're trying to break this down +otherwise we're going to have a + + align:start position:0% +otherwise we're going to have a + + + align:start position:0% +otherwise we're going to have a +gazillion different Atomic arrangements + + align:start position:0% +gazillion different Atomic arrangements + + + align:start position:0% +gazillion different Atomic arrangements +and what we're able to do is confine + + align:start position:0% +and what we're able to do is confine + + + align:start position:0% +and what we're able to do is confine +everything to a simple set of + + align:start position:0% +everything to a simple set of + + + align:start position:0% +everything to a simple set of +14 so what I want to do now is show that + + align:start position:0% +14 so what I want to do now is show that + + + align:start position:0% +14 so what I want to do now is show that +we can look at different uh sets of + + align:start position:0% +we can look at different uh sets of + + + align:start position:0% +we can look at different uh sets of +elements at these at these points so + + align:start position:0% +elements at these at these points so + + + align:start position:0% +elements at these at these points so +let's let's see what happens if we look + + align:start position:0% +let's let's see what happens if we look + + + align:start position:0% +let's let's see what happens if we look +at face centered cubic and put different + + align:start position:0% +at face centered cubic and put different + + + align:start position:0% +at face centered cubic and put different +Atomic groupings at at each point so + + align:start position:0% +Atomic groupings at at each point so + + + align:start position:0% +Atomic groupings at at each point so +ultimately what I'm in search of is the + + align:start position:0% +ultimately what I'm in search of is the + + + align:start position:0% +ultimately what I'm in search of is the +crystal + + align:start position:0% +crystal + + + align:start position:0% +crystal +structure the crystal structure and the + + align:start position:0% +structure the crystal structure and the + + + align:start position:0% +structure the crystal structure and the +crystal structure is the atomic + + align:start position:0% +crystal structure is the atomic + + + align:start position:0% +crystal structure is the atomic +arrangement in three space Atomic + + align:start position:0% +arrangement in three space Atomic + + + align:start position:0% +arrangement in three space Atomic +Arrangement and the crystal structure is + + align:start position:0% +Arrangement and the crystal structure is + + + align:start position:0% +Arrangement and the crystal structure is +the sum of two components first is the + + align:start position:0% +the sum of two components first is the + + + align:start position:0% +the sum of two components first is the +brav + + align:start position:0% + + + + align:start position:0% + +lattice the brav lattice and what the + + align:start position:0% +lattice the brav lattice and what the + + + align:start position:0% +lattice the brav lattice and what the +bra ltis is it's really just a point + + align:start position:0% +bra ltis is it's really just a point + + + align:start position:0% +bra ltis is it's really just a point +environment it's a point + + align:start position:0% +environment it's a point + + + align:start position:0% +environment it's a point +environment and I can put anything I + + align:start position:0% +environment and I can put anything I + + + align:start position:0% +environment and I can put anything I +want at the point including nothing I + + align:start position:0% +want at the point including nothing I + + + align:start position:0% +want at the point including nothing I +mean I can make this the equivalent of a + + align:start position:0% +mean I can make this the equivalent of a + + + align:start position:0% +mean I can make this the equivalent of a +John Cage piano piece you know it's just + + align:start position:0% +John Cage piano piece you know it's just + + + align:start position:0% +John Cage piano piece you know it's just +a bunch of rests of different time + + align:start position:0% +a bunch of rests of different time + + + align:start position:0% +a bunch of rests of different time +signature you know I'm talking about + + align:start position:0% +signature you know I'm talking about + + + align:start position:0% +signature you know I'm talking about +listen that's rest in four four time see + + align:start position:0% +listen that's rest in four four time see + + + align:start position:0% +listen that's rest in four four time see +okay see this that's a simple cubic + + align:start position:0% +okay see this that's a simple cubic + + + align:start position:0% +okay see this that's a simple cubic +lattice it's a set of points in + + align:start position:0% + + + + align:start position:0% + +space okay so it's a point environment + + align:start position:0% +space okay so it's a point environment + + + align:start position:0% +space okay so it's a point environment +but let's hang something on the points + + align:start position:0% +but let's hang something on the points + + + align:start position:0% +but let's hang something on the points +and what we hang on the points is called + + align:start position:0% +and what we hang on the points is called + + + align:start position:0% +and what we hang on the points is called +the basis the basis and this is the atom + + align:start position:0% +the basis the basis and this is the atom + + + align:start position:0% +the basis the basis and this is the atom +grouping the atom + + align:start position:0% +grouping the atom + + + align:start position:0% +grouping the atom +grouping at each lattice + + align:start position:0% +grouping at each lattice + + + align:start position:0% +grouping at each lattice +point this all become + + align:start position:0% +point this all become + + + align:start position:0% +point this all become +clear I assure you with a few + + align:start position:0% +clear I assure you with a few + + + align:start position:0% +clear I assure you with a few +examples so let's look at some examples + + align:start position:0% +examples so let's look at some examples + + + align:start position:0% +examples so let's look at some examples +we let's look at example say for face + + align:start position:0% +we let's look at example say for face + + + align:start position:0% +we let's look at example say for face +Center cubic let's see what we can do + + align:start position:0% +Center cubic let's see what we can do + + + align:start position:0% +Center cubic let's see what we can do +with face Center cub so I'm going to + + align:start position:0% +with face Center cub so I'm going to + + + align:start position:0% +with face Center cub so I'm going to +choose in in all cases the bra + + align:start position:0% +choose in in all cases the bra + + + align:start position:0% +choose in in all cases the bra +lattice the brav lattice is is + + align:start position:0% +lattice the brav lattice is is + + + align:start position:0% +lattice the brav lattice is is +FCC so that's showing up there on the + + align:start position:0% +FCC so that's showing up there on the + + + align:start position:0% +FCC so that's showing up there on the +right side only what you're seeing here + + align:start position:0% +right side only what you're seeing here + + + align:start position:0% +right side only what you're seeing here +is the drawing with just a single atom + + align:start position:0% +is the drawing with just a single atom + + + align:start position:0% +is the drawing with just a single atom +at each lattice Point single atom at + + align:start position:0% +at each lattice Point single atom at + + + align:start position:0% +at each lattice Point single atom at +each lattice point so if the basis is + + align:start position:0% +each lattice point so if the basis is + + + align:start position:0% +each lattice point so if the basis is +something just a single atom so that + + align:start position:0% +something just a single atom so that + + + align:start position:0% +something just a single atom so that +could be a metal so an example for that + + align:start position:0% +could be a metal so an example for that + + + align:start position:0% +could be a metal so an example for that +might be gold see this is gold this is a + + align:start position:0% +might be gold see this is gold this is a + + + align:start position:0% +might be gold see this is gold this is a +brav FCC brav a lattice with one atom at + + align:start position:0% +brav FCC brav a lattice with one atom at + + + align:start position:0% +brav FCC brav a lattice with one atom at +each lattice Point how do I know it's + + align:start position:0% +each lattice Point how do I know it's + + + align:start position:0% +each lattice Point how do I know it's +gold look at the color it's obviously + + align:start position:0% +gold look at the color it's obviously + + + align:start position:0% +gold look at the color it's obviously +it's gold that's how I know that's FCC + + align:start position:0% +it's gold that's how I know that's FCC + + + align:start position:0% +it's gold that's how I know that's FCC +gold but there's a whole bunch of metals + + align:start position:0% +gold but there's a whole bunch of metals + + + align:start position:0% +gold but there's a whole bunch of metals +that are face centered cubic including + + align:start position:0% +that are face centered cubic including + + + align:start position:0% +that are face centered cubic including +aluminum copper Platinum these are all + + align:start position:0% +aluminum copper Platinum these are all + + + align:start position:0% +aluminum copper Platinum these are all +FCC Metals okay and so in this case we + + align:start position:0% +FCC Metals okay and so in this case we + + + align:start position:0% +FCC Metals okay and so in this case we +would call the crystal structure the + + align:start position:0% +would call the crystal structure the + + + align:start position:0% +would call the crystal structure the +crystal structure is also FCC because + + align:start position:0% +crystal structure is also FCC because + + + align:start position:0% +crystal structure is also FCC because +the you've only got one atom per lattice + + align:start position:0% +the you've only got one atom per lattice + + + align:start position:0% +the you've only got one atom per lattice +point so the lattice point and the the a + + align:start position:0% +point so the lattice point and the the a + + + align:start position:0% +point so the lattice point and the the a +lattice and the crystal structure are + + align:start position:0% +lattice and the crystal structure are + + + align:start position:0% +lattice and the crystal structure are +the same face centered cubic I could put + + align:start position:0% +the same face centered cubic I could put + + + align:start position:0% +the same face centered cubic I could put +a + + align:start position:0% +a + + + align:start position:0% +a +molecule I could put a molecule at each + + align:start position:0% +molecule I could put a molecule at each + + + align:start position:0% +molecule I could put a molecule at each +lattice points for example methane I + + align:start position:0% +lattice points for example methane I + + + align:start position:0% +lattice points for example methane I +could put the five atoms carbon and the + + align:start position:0% +could put the five atoms carbon and the + + + align:start position:0% +could put the five atoms carbon and the +four hydrogens at each Lattis point and + + align:start position:0% +four hydrogens at each Lattis point and + + + align:start position:0% +four hydrogens at each Lattis point and +if one of you goes is the first human to + + align:start position:0% +if one of you goes is the first human to + + + align:start position:0% +if one of you goes is the first human to +go to Jupiter when you get to Jupiter + + align:start position:0% +go to Jupiter when you get to Jupiter + + + align:start position:0% +go to Jupiter when you get to Jupiter +and you see solid methane you'll be + + align:start position:0% +and you see solid methane you'll be + + + align:start position:0% +and you see solid methane you'll be +heartened to know that it will be in the + + align:start position:0% +heartened to know that it will be in the + + + align:start position:0% +heartened to know that it will be in the +FCC crystal structure it has to be even + + align:start position:0% +FCC crystal structure it has to be even + + + align:start position:0% +FCC crystal structure it has to be even +prot even even DNA if it partially + + align:start position:0% +prot even even DNA if it partially + + + align:start position:0% +prot even even DNA if it partially +crystallizes is going to crystallize in + + align:start position:0% +crystallizes is going to crystallize in + + + align:start position:0% +crystallizes is going to crystallize in +one of those 14 brav laes it has + + align:start position:0% +one of those 14 brav laes it has + + + align:start position:0% +one of those 14 brav laes it has +to so solid methane and this will also + + align:start position:0% +to so solid methane and this will also + + + align:start position:0% +to so solid methane and this will also +be + + align:start position:0% +be + + + align:start position:0% +be +FCC we can put a an ion pair an ion pair + + align:start position:0% +FCC we can put a an ion pair an ion pair + + + align:start position:0% +FCC we can put a an ion pair an ion pair +for example A cation and an anion at + + align:start position:0% +for example A cation and an anion at + + + align:start position:0% +for example A cation and an anion at +each lattice point and that would give + + align:start position:0% +each lattice point and that would give + + + align:start position:0% +each lattice point and that would give +us sodium chloride and sodium chloride + + align:start position:0% +us sodium chloride and sodium chloride + + + align:start position:0% +us sodium chloride and sodium chloride +gives us something that's called called + + align:start position:0% +gives us something that's called called + + + align:start position:0% +gives us something that's called called +the rock salt crystal structure and this + + align:start position:0% +the rock salt crystal structure and this + + + align:start position:0% +the rock salt crystal structure and this +model here is sodium chloride where the + + align:start position:0% +model here is sodium chloride where the + + + align:start position:0% +model here is sodium chloride where the +greens are sodi uh the greens are + + align:start position:0% +greens are sodi uh the greens are + + + align:start position:0% +greens are sodi uh the greens are +chlorine and the the golds here are + + align:start position:0% +chlorine and the the golds here are + + + align:start position:0% +chlorine and the the golds here are +sodium and what you do is you might say + + align:start position:0% +sodium and what you do is you might say + + + align:start position:0% +sodium and what you do is you might say +well look they describe a square so why + + align:start position:0% +well look they describe a square so why + + + align:start position:0% +well look they describe a square so why +don't we just call this simple cubic but + + align:start position:0% +don't we just call this simple cubic but + + + align:start position:0% +don't we just call this simple cubic but +if we call it simple cubic I have + + align:start position:0% +if we call it simple cubic I have + + + align:start position:0% +if we call it simple cubic I have +different atoms at different lattice + + align:start position:0% +different atoms at different lattice + + + align:start position:0% +different atoms at different lattice +points so that won't work instead if you + + align:start position:0% +points so that won't work instead if you + + + align:start position:0% +points so that won't work instead if you +can just train your eye to look at the + + align:start position:0% +can just train your eye to look at the + + + align:start position:0% +can just train your eye to look at the +the greens look it one 2 3 4 five + + align:start position:0% +the greens look it one 2 3 4 five + + + align:start position:0% +the greens look it one 2 3 4 five +there's a fifth Green in the center of a + + align:start position:0% +there's a fifth Green in the center of a + + + align:start position:0% +there's a fifth Green in the center of a +square then train your eye to look at + + align:start position:0% +square then train your eye to look at + + + align:start position:0% +square then train your eye to look at +the golds 1 2 3 4 make a square five in + + align:start position:0% +the golds 1 2 3 4 make a square five in + + + align:start position:0% +the golds 1 2 3 4 make a square five in +the center so instead say let's look at + + align:start position:0% +the center so instead say let's look at + + + align:start position:0% +the center so instead say let's look at +the pairs green and gold one green and + + align:start position:0% +the pairs green and gold one green and + + + align:start position:0% +the pairs green and gold one green and +gold two green and gold three green and + + align:start position:0% +gold two green and gold three green and + + + align:start position:0% +gold two green and gold three green and +gold four and green and gold five in the + + align:start position:0% +gold four and green and gold five in the + + + align:start position:0% +gold four and green and gold five in the +center make a simple cubic excuse me a + + align:start position:0% +center make a simple cubic excuse me a + + + align:start position:0% +center make a simple cubic excuse me a +face centered cubic lattice with a rock + + align:start position:0% +face centered cubic lattice with a rock + + + align:start position:0% +face centered cubic lattice with a rock +salt crystal structure that's shown here + + align:start position:0% +salt crystal structure that's shown here + + + align:start position:0% +salt crystal structure that's shown here +in this cartoon so whether you count the + + align:start position:0% +in this cartoon so whether you count the + + + align:start position:0% +in this cartoon so whether you count the +greens or you count the blues it does + + align:start position:0% +greens or you count the blues it does + + + align:start position:0% +greens or you count the blues it does +doesn't matter but it's the ion pair so + + align:start position:0% +doesn't matter but it's the ion pair so + + + align:start position:0% +doesn't matter but it's the ion pair so +that means I this is a derivative from + + align:start position:0% +that means I this is a derivative from + + + align:start position:0% +that means I this is a derivative from +the FCC bra latice and then there's one + + align:start position:0% +the FCC bra latice and then there's one + + + align:start position:0% +the FCC bra latice and then there's one +other one there's one other one I can + + align:start position:0% +other one there's one other one I can + + + align:start position:0% +other one there's one other one I can +put an atom + + align:start position:0% +put an atom + + + align:start position:0% +put an atom +pair I can put an atom pair here I put + + align:start position:0% +pair I can put an atom pair here I put + + + align:start position:0% +pair I can put an atom pair here I put +five atoms a molecule here I'm going to + + align:start position:0% +five atoms a molecule here I'm going to + + + align:start position:0% +five atoms a molecule here I'm going to +put an atom pair and the example I'm + + align:start position:0% +put an atom pair and the example I'm + + + align:start position:0% +put an atom pair and the example I'm +going to give you is two + + align:start position:0% +going to give you is two + + + align:start position:0% +going to give you is two +carbons at + + align:start position:0% +carbons at + + + align:start position:0% +carbons at +109° and what will that give me that's + + align:start position:0% +109° and what will that give me that's + + + align:start position:0% +109° and what will that give me that's +that's an example of + + align:start position:0% +that's an example of + + + align:start position:0% +that's an example of +diamond of diamond or silic + + align:start position:0% +diamond of diamond or silic + + + align:start position:0% +diamond of diamond or silic +or geranium and here's diamond right + + align:start position:0% +or geranium and here's diamond right + + + align:start position:0% +or geranium and here's diamond right +here this is Diamond if you train if you + + align:start position:0% +here this is Diamond if you train if you + + + align:start position:0% +here this is Diamond if you train if you +train your eye the the atom that I'm + + align:start position:0% +train your eye the the atom that I'm + + + align:start position:0% +train your eye the the atom that I'm +holding has four struts coming out of it + + align:start position:0% +holding has four struts coming out of it + + + align:start position:0% +holding has four struts coming out of it +that's the sp3 hybridized four struts + + align:start position:0% +that's the sp3 hybridized four struts + + + align:start position:0% +that's the sp3 hybridized four struts +coming out of a single carbon every + + align:start position:0% +coming out of a single carbon every + + + align:start position:0% +coming out of a single carbon every +carbon has four struts coming out of it + + align:start position:0% +carbon has four struts coming out of it + + + align:start position:0% +carbon has four struts coming out of it +but watch this when I when I lie this + + align:start position:0% +but watch this when I when I lie this + + + align:start position:0% +but watch this when I when I lie this +down in a single plane and I bring it up + + align:start position:0% +down in a single plane and I bring it up + + + align:start position:0% +down in a single plane and I bring it up +you see where I've got the poits look at + + align:start position:0% +you see where I've got the poits look at + + + align:start position:0% +you see where I've got the poits look at +how the potit described 1 2 3 4 five + + align:start position:0% +how the potit described 1 2 3 4 five + + + align:start position:0% +how the potit described 1 2 3 4 five +face centered cubic and with each + + align:start position:0% +face centered cubic and with each + + + align:start position:0% +face centered cubic and with each +lattice point I take two carbons two + + align:start position:0% +lattice point I take two carbons two + + + align:start position:0% +lattice point I take two carbons two +carbons here two carbons here two + + align:start position:0% +carbons here two carbons here two + + + align:start position:0% +carbons here two carbons here two +carbons here and I go all the way + + align:start position:0% +carbons here and I go all the way + + + align:start position:0% +carbons here and I go all the way +through the lattice and I end up with + + align:start position:0% +through the lattice and I end up with + + + align:start position:0% +through the lattice and I end up with +diamond cubic crystal structure as a bra + + align:start position:0% +diamond cubic crystal structure as a bra + + + align:start position:0% +diamond cubic crystal structure as a bra +lattice with + + align:start position:0% +lattice with + + + align:start position:0% +lattice with +an a basis of the atom pair and this is + + align:start position:0% +an a basis of the atom pair and this is + + + align:start position:0% +an a basis of the atom pair and this is +Diamond cubic so Diamond cubic is the + + align:start position:0% +Diamond cubic so Diamond cubic is the + + + align:start position:0% +Diamond cubic so Diamond cubic is the +crystal structure but it's derived from + + align:start position:0% +crystal structure but it's derived from + + + align:start position:0% +crystal structure but it's derived from +an FCC lce so again the the the + + align:start position:0% +an FCC lce so again the the the + + + align:start position:0% +an FCC lce so again the the the +overarching theme Here is the integral + + align:start position:0% +overarching theme Here is the integral + + + align:start position:0% +overarching theme Here is the integral +of the brav lattice this is the set of + + align:start position:0% +of the brav lattice this is the set of + + + align:start position:0% +of the brav lattice this is the set of +points right this is the point set point + + align:start position:0% +points right this is the point set point + + + align:start position:0% +points right this is the point set point +set in three space the bra lattice and + + align:start position:0% +set in three space the bra lattice and + + + align:start position:0% +set in three space the bra lattice and +then what you put at each point gives + + align:start position:0% +then what you put at each point gives + + + align:start position:0% +then what you put at each point gives +you the crystal structure and you can go + + align:start position:0% +you the crystal structure and you can go + + + align:start position:0% +you the crystal structure and you can go +on and on and on you can have a ball + + align:start position:0% +on and on and on you can have a ball + + + align:start position:0% +on and on and on you can have a ball +with this + + align:start position:0% +with this + + + align:start position:0% +with this +stuff oh here this is to show you in two + + align:start position:0% +stuff oh here this is to show you in two + + + align:start position:0% +stuff oh here this is to show you in two +space this is an interesting this is a + + align:start position:0% +space this is an interesting this is a + + + align:start position:0% +space this is an interesting this is a +eer print this is a dogs so what's the + + align:start position:0% +eer print this is a dogs so what's the + + + align:start position:0% +eer print this is a dogs so what's the +crystal structure here so let's start + + align:start position:0% +crystal structure here so let's start + + + align:start position:0% +crystal structure here so let's start +looking or you might go one 1 2 3 4 five + + align:start position:0% +looking or you might go one 1 2 3 4 five + + + align:start position:0% +looking or you might go one 1 2 3 4 five +you might say well this looks like + + align:start position:0% +you might say well this looks like + + + align:start position:0% +you might say well this looks like +simple uh face centered cubic actually + + align:start position:0% +simple uh face centered cubic actually + + + align:start position:0% +simple uh face centered cubic actually +face centered and body centered are the + + align:start position:0% +face centered and body centered are the + + + align:start position:0% +face centered and body centered are the +same in topace right the body is you + + align:start position:0% +same in topace right the body is you + + + align:start position:0% +same in topace right the body is you +know so how do how do you describe a + + align:start position:0% +know so how do how do you describe a + + + align:start position:0% +know so how do how do you describe a +sponge in + + align:start position:0% +sponge in + + + align:start position:0% +sponge in +topace think about it okay the trouble + + align:start position:0% +topace think about it okay the trouble + + + align:start position:0% +topace think about it okay the trouble +is this dog's facing in the other + + align:start position:0% +is this dog's facing in the other + + + align:start position:0% +is this dog's facing in the other +direction so that won't work so instead + + align:start position:0% +direction so that won't work so instead + + + align:start position:0% +direction so that won't work so instead +all these dogs are facing the same way + + align:start position:0% +all these dogs are facing the same way + + + align:start position:0% +all these dogs are facing the same way +and now if you look carefully take as + + align:start position:0% +and now if you look carefully take as + + + align:start position:0% +and now if you look carefully take as +the basis see those those could be + + align:start position:0% +the basis see those those could be + + + align:start position:0% +the basis see those those could be +lattice points the bra lattice is the + + align:start position:0% +lattice points the bra lattice is the + + + align:start position:0% +lattice points the bra lattice is the +dots the basis is the set of four dogs + + align:start position:0% +dots the basis is the set of four dogs + + + align:start position:0% +dots the basis is the set of four dogs +the two facing the right and these two + + align:start position:0% +the two facing the right and these two + + + align:start position:0% +the two facing the right and these two +facing the left now two right two left + + align:start position:0% +facing the left now two right two left + + + align:start position:0% +facing the left now two right two left +two right two left so it's the four dog + + align:start position:0% +two right two left so it's the four dog + + + align:start position:0% +two right two left so it's the four dog +set you know those four dogs are the + + align:start position:0% +set you know those four dogs are the + + + align:start position:0% +set you know those four dogs are the +bases so bingo so now what do we have we + + align:start position:0% +bases so bingo so now what do we have we + + + align:start position:0% +bases so bingo so now what do we have we +have SIMPLE cubic this is SCP simple + + align:start position:0% +have SIMPLE cubic this is SCP simple + + + align:start position:0% +have SIMPLE cubic this is SCP simple +cubic puppy that's a two space all right + + align:start position:0% +cubic puppy that's a two space all right + + + align:start position:0% +cubic puppy that's a two space all right +look at this + + align:start position:0% + + + + align:start position:0% + +one I put the dot here on the abdomen of + + align:start position:0% +one I put the dot here on the abdomen of + + + align:start position:0% +one I put the dot here on the abdomen of +this uh + + align:start position:0% +this uh + + + align:start position:0% +this uh +creature okay so what do you got this is + + align:start position:0% +creature okay so what do you got this is + + + align:start position:0% +creature okay so what do you got this is +a + + align:start position:0% +a + + + align:start position:0% +a +rhombus or some of you might initially + + align:start position:0% +rhombus or some of you might initially + + + align:start position:0% +rhombus or some of you might initially +have called this the triangle but you + + align:start position:0% +have called this the triangle but you + + + align:start position:0% +have called this the triangle but you +see that when you put the two of them + + align:start position:0% +see that when you put the two of them + + + align:start position:0% +see that when you put the two of them +together this has translational Symmetry + + align:start position:0% +together this has translational Symmetry + + + align:start position:0% +together this has translational Symmetry +and in fact look at how many uh of these + + align:start position:0% +and in fact look at how many uh of these + + + align:start position:0% +and in fact look at how many uh of these +uh entities belong to that ltis point + + align:start position:0% +uh entities belong to that ltis point + + + align:start position:0% +uh entities belong to that ltis point +all of this all of this all of this + + align:start position:0% +all of this all of this all of this + + + align:start position:0% +all of this all of this all of this +because the tail to this is up here so + + align:start position:0% +because the tail to this is up here so + + + align:start position:0% +because the tail to this is up here so +the repeat doesn't start until down here + + align:start position:0% +the repeat doesn't start until down here + + + align:start position:0% +the repeat doesn't start until down here +you could cut it this way I don't care + + align:start position:0% +you could cut it this way I don't care + + + align:start position:0% +you could cut it this way I don't care +but the point is this is the concept of + + align:start position:0% +but the point is this is the concept of + + + align:start position:0% +but the point is this is the concept of +the basis the basis is many many units + + align:start position:0% +the basis the basis is many many units + + + align:start position:0% +the basis the basis is many many units +that are repeatable and can be + + align:start position:0% +that are repeatable and can be + + + align:start position:0% +that are repeatable and can be +positioned at each lattice + + align:start position:0% +positioned at each lattice + + + align:start position:0% +positioned at each lattice +point so now what I want to do is talk a + + align:start position:0% +point so now what I want to do is talk a + + + align:start position:0% +point so now what I want to do is talk a +little bit more about the cubic system + + align:start position:0% +little bit more about the cubic system + + + align:start position:0% +little bit more about the cubic system +because we're going to focus on a cubic + + align:start position:0% +because we're going to focus on a cubic + + + align:start position:0% +because we're going to focus on a cubic +system in 3091 largely because it has a + + align:start position:0% +system in 3091 largely because it has a + + + align:start position:0% +system in 3091 largely because it has a +simple geometry most of the periodic + + align:start position:0% +simple geometry most of the periodic + + + align:start position:0% +simple geometry most of the periodic +table you find is in uh cubic system FCC + + align:start position:0% +table you find is in uh cubic system FCC + + + align:start position:0% +table you find is in uh cubic system FCC +or BCC and then the math is simple + + align:start position:0% +or BCC and then the math is simple + + + align:start position:0% +or BCC and then the math is simple +because you can you're in coordinate + + align:start position:0% +because you can you're in coordinate + + + align:start position:0% +because you can you're in coordinate +cartisian coordinates so let's take a + + align:start position:0% +cartisian coordinates so let's take a + + + align:start position:0% +cartisian coordinates so let's take a +look at uh at what we've got going for + + align:start position:0% +look at uh at what we've got going for + + + align:start position:0% +look at uh at what we've got going for +us here um I want to look at the + + align:start position:0% +us here um I want to look at the + + + align:start position:0% +us here um I want to look at the +properties of cubic crystals so here we + + align:start position:0% +properties of cubic crystals so here we + + + align:start position:0% +properties of cubic crystals so here we +are this is a table out of your lecture + + align:start position:0% +are this is a table out of your lecture + + + align:start position:0% +are this is a table out of your lecture +notes and uh I'm going to work through + + align:start position:0% +notes and uh I'm going to work through + + + align:start position:0% +notes and uh I'm going to work through +this table and I urge you to get uh + + align:start position:0% +this table and I urge you to get uh + + + align:start position:0% +this table and I urge you to get uh +friendly and comfortable with this table + + align:start position:0% +friendly and comfortable with this table + + + align:start position:0% +friendly and comfortable with this table +so that you understand the properties + + align:start position:0% +so that you understand the properties + + + align:start position:0% +so that you understand the properties +and why why am I making you learn this + + align:start position:0% +and why why am I making you learn this + + + align:start position:0% +and why why am I making you learn this +stuff because I think it stands to + + align:start position:0% +stuff because I think it stands to + + + align:start position:0% +stuff because I think it stands to +reason that if you look in this Crystal + + align:start position:0% +reason that if you look in this Crystal + + + align:start position:0% +reason that if you look in this Crystal +you see that atoms touch along certain + + align:start position:0% +you see that atoms touch along certain + + + align:start position:0% +you see that atoms touch along certain +directions and atoms are far apart along + + align:start position:0% +directions and atoms are far apart along + + + align:start position:0% +directions and atoms are far apart along +other directions well we've already seen + + align:start position:0% +other directions well we've already seen + + + align:start position:0% +other directions well we've already seen +in 3091 that there's a correlation + + align:start position:0% +in 3091 that there's a correlation + + + align:start position:0% +in 3091 that there's a correlation +between atomic contact and bonding and + + align:start position:0% +between atomic contact and bonding and + + + align:start position:0% +between atomic contact and bonding and +bonding is related to a whole host of + + align:start position:0% +bonding is related to a whole host of + + + align:start position:0% +bonding is related to a whole host of +other properties for example mechanical + + align:start position:0% +other properties for example mechanical + + + align:start position:0% +other properties for example mechanical +strength there are people in this room + + align:start position:0% +strength there are people in this room + + + align:start position:0% +strength there are people in this room +that are thinking about being mechanical + + align:start position:0% +that are thinking about being mechanical + + + align:start position:0% +that are thinking about being mechanical +engineers aeroastro Engineers nuclear + + align:start position:0% +engineers aeroastro Engineers nuclear + + + align:start position:0% +engineers aeroastro Engineers nuclear +Engineers you need to understand the + + align:start position:0% +Engineers you need to understand the + + + align:start position:0% +Engineers you need to understand the +relationship between the crystal + + align:start position:0% +relationship between the crystal + + + align:start position:0% +relationship between the crystal +structure and the strength of the + + align:start position:0% +structure and the strength of the + + + align:start position:0% +structure and the strength of the +material obviously if I look down an + + align:start position:0% +material obviously if I look down an + + + align:start position:0% +material obviously if I look down an +atom direction if I look down an atom + + align:start position:0% +atom direction if I look down an atom + + + align:start position:0% +atom direction if I look down an atom +Direction where I have a high density of + + align:start position:0% +Direction where I have a high density of + + + align:start position:0% +Direction where I have a high density of +atoms that's going to be a direction of + + align:start position:0% +atoms that's going to be a direction of + + + align:start position:0% +atoms that's going to be a direction of +strength if I look down a direction that + + align:start position:0% +strength if I look down a direction that + + + align:start position:0% +strength if I look down a direction that +has a low population of atoms that's + + align:start position:0% +has a low population of atoms that's + + + align:start position:0% +has a low population of atoms that's +going to be a direction of weakness and + + align:start position:0% +going to be a direction of weakness and + + + align:start position:0% +going to be a direction of weakness and +then subsequently if I want to cleave a + + align:start position:0% +then subsequently if I want to cleave a + + + align:start position:0% +then subsequently if I want to cleave a +crystal then where am I going to cleave + + align:start position:0% +crystal then where am I going to cleave + + + align:start position:0% +crystal then where am I going to cleave +it I have to understand the + + align:start position:0% +it I have to understand the + + + align:start position:0% +it I have to understand the +crystallography the electrical + + align:start position:0% +crystallography the electrical + + + align:start position:0% +crystallography the electrical +properties the optical properties what's + + align:start position:0% +properties the optical properties what's + + + align:start position:0% +properties the optical properties what's +the index of refraction it's the Ben of + + align:start position:0% +the index of refraction it's the Ben of + + + align:start position:0% +the index of refraction it's the Ben of +light in response to the field set up by + + align:start position:0% +light in response to the field set up by + + + align:start position:0% +light in response to the field set up by +the + + align:start position:0% +the + + + align:start position:0% +the +bonds if you want to go into opto + + align:start position:0% +bonds if you want to go into opto + + + align:start position:0% +bonds if you want to go into opto +Electronics you better know this stuff + + align:start position:0% +Electronics you better know this stuff + + + align:start position:0% +Electronics you better know this stuff +everybody has to know this stuff because + + align:start position:0% +everybody has to know this stuff because + + + align:start position:0% +everybody has to know this stuff because +chemistry is Central to everything it's + + align:start position:0% +chemistry is Central to everything it's + + + align:start position:0% +chemistry is Central to everything it's +all chemistry this conversation is + + align:start position:0% +all chemistry this conversation is + + + align:start position:0% +all chemistry this conversation is +brought to you by secondary + + align:start position:0% +brought to you by secondary + + + align:start position:0% +brought to you by secondary +bonding it's + + align:start position:0% +bonding it's + + + align:start position:0% +bonding it's +all that's it so let's look at this one + + align:start position:0% +all that's it so let's look at this one + + + align:start position:0% +all that's it so let's look at this one +in in some detail and what I want to do + + align:start position:0% +in in some detail and what I want to do + + + align:start position:0% +in in some detail and what I want to do +first of all is the unit cell let's look + + align:start position:0% +first of all is the unit cell let's look + + + align:start position:0% +first of all is the unit cell let's look +at the unit cell so so here's + + align:start position:0% +at the unit cell so so here's + + + align:start position:0% +at the unit cell so so here's +FCC face centered cubic so there's the + + align:start position:0% +FCC face centered cubic so there's the + + + align:start position:0% +FCC face centered cubic so there's the +lattice and now what I'm going to use is + + align:start position:0% +lattice and now what I'm going to use is + + + align:start position:0% +lattice and now what I'm going to use is +a hard sphere model so I'm going to make + + align:start position:0% +a hard sphere model so I'm going to make + + + align:start position:0% +a hard sphere model so I'm going to make +the Spheres the atoms so big that they + + align:start position:0% +the Spheres the atoms so big that they + + + align:start position:0% +the Spheres the atoms so big that they +actually touch along + + align:start position:0% +actually touch along + + + align:start position:0% +actually touch along +their + + align:start position:0% +their + + + align:start position:0% +their +principal axis of contact so face + + align:start position:0% +principal axis of contact so face + + + align:start position:0% +principal axis of contact so face +centered cubic the atoms touch along + + align:start position:0% +centered cubic the atoms touch along + + + align:start position:0% +centered cubic the atoms touch along +that face diagonal and the unit cell + + align:start position:0% +that face diagonal and the unit cell + + + align:start position:0% +that face diagonal and the unit cell +this is called the unit cell this is the + + align:start position:0% +this is called the unit cell this is the + + + align:start position:0% +this is called the unit cell this is the +repeat unit this is the the unit cell is + + align:start position:0% +repeat unit this is the the unit cell is + + + align:start position:0% +repeat unit this is the the unit cell is +that which repeats in three space in + + align:start position:0% +that which repeats in three space in + + + align:start position:0% +that which repeats in three space in +fills three space it's it's the it's the + + align:start position:0% +fills three space it's it's the it's the + + + align:start position:0% +fills three space it's it's the it's the +basic unit of the crystal system and the + + align:start position:0% +basic unit of the crystal system and the + + + align:start position:0% +basic unit of the crystal system and the +edge of the unit cell is given the + + align:start position:0% +edge of the unit cell is given the + + + align:start position:0% +edge of the unit cell is given the +dimension + + align:start position:0% +dimension + + + align:start position:0% +dimension +a so the edge of the unit cell and this + + align:start position:0% +a so the edge of the unit cell and this + + + align:start position:0% +a so the edge of the unit cell and this +is a a cube so it's all the same Edge so + + align:start position:0% +is a a cube so it's all the same Edge so + + + align:start position:0% +is a a cube so it's all the same Edge so +the volume of the unit cell is equal to + + align:start position:0% +the volume of the unit cell is equal to + + + align:start position:0% +the volume of the unit cell is equal to +a cub that's trivial so we got that oh + + align:start position:0% +a cub that's trivial so we got that oh + + + align:start position:0% +a cub that's trivial so we got that oh +lattice points per unit cell lattice + + align:start position:0% +lattice points per unit cell lattice + + + align:start position:0% +lattice points per unit cell lattice +points per unit cell let's look at that + + align:start position:0% +points per unit cell let's look at that + + + align:start position:0% +points per unit cell let's look at that +let's look at this uh this red one how + + align:start position:0% +let's look at this uh this red one how + + + align:start position:0% +let's look at this uh this red one how +many lattice points well we can count + + align:start position:0% +many lattice points well we can count + + + align:start position:0% +many lattice points well we can count +lce points by Counting atoms if you see + + align:start position:0% +lce points by Counting atoms if you see + + + align:start position:0% +lce points by Counting atoms if you see +there's eight Corner atoms and how much + + align:start position:0% +there's eight Corner atoms and how much + + + align:start position:0% +there's eight Corner atoms and how much +of each of those Corner atoms lies + + align:start position:0% +of each of those Corner atoms lies + + + align:start position:0% +of each of those Corner atoms lies +within the bounds of this unit cell it's + + align:start position:0% +within the bounds of this unit cell it's + + + align:start position:0% +within the bounds of this unit cell it's +18 okay so lattice lattice points per + + align:start position:0% +18 okay so lattice lattice points per + + + align:start position:0% +18 okay so lattice lattice points per +unit cell per unit cell is going to + + align:start position:0% +unit cell per unit cell is going to + + + align:start position:0% +unit cell per unit cell is going to +equal 8 * 1/8 this is the + + align:start position:0% +equal 8 * 1/8 this is the + + + align:start position:0% +equal 8 * 1/8 this is the +corners this is the corners and then + + align:start position:0% +corners this is the corners and then + + + align:start position:0% +corners this is the corners and then +we've got these face atoms 8 * an e is + + align:start position:0% +we've got these face atoms 8 * an e is + + + align:start position:0% +we've got these face atoms 8 * an e is +one and you see these blue ones these + + align:start position:0% +one and you see these blue ones these + + + align:start position:0% +one and you see these blue ones these +blue ones are half inside this unit cell + + align:start position:0% +blue ones are half inside this unit cell + + + align:start position:0% +blue ones are half inside this unit cell +and half inside the adjacent unit cell + + align:start position:0% +and half inside the adjacent unit cell + + + align:start position:0% +and half inside the adjacent unit cell +and I got 1 2 3 four five six of them + + align:start position:0% +and I got 1 2 3 four five six of them + + + align:start position:0% +and I got 1 2 3 four five six of them +two in this direction three principal + + align:start position:0% +two in this direction three principal + + + align:start position:0% +two in this direction three principal +directions and two times so that's 6 * + + align:start position:0% +directions and two times so that's 6 * + + + align:start position:0% +directions and two times so that's 6 * +12 which is this is the face face atoms + + align:start position:0% +12 which is this is the face face atoms + + + align:start position:0% +12 which is this is the face face atoms +okay 6 * a half is three so 3 + 1 is + + align:start position:0% +okay 6 * a half is three so 3 + 1 is + + + align:start position:0% +okay 6 * a half is three so 3 + 1 is +four so I have effectively four lattice + + align:start position:0% +four so I have effectively four lattice + + + align:start position:0% +four so I have effectively four lattice +points per unit cell I'm not saying + + align:start position:0% +points per unit cell I'm not saying + + + align:start position:0% +points per unit cell I'm not saying +atoms because I could replace each of + + align:start position:0% +atoms because I could replace each of + + + align:start position:0% +atoms because I could replace each of +these single atoms with a methane + + align:start position:0% +these single atoms with a methane + + + align:start position:0% +these single atoms with a methane +molecule so then I'd have five atoms per + + align:start position:0% +molecule so then I'd have five atoms per + + + align:start position:0% +molecule so then I'd have five atoms per +point so that's why I'm being a little + + align:start position:0% +point so that's why I'm being a little + + + align:start position:0% +point so that's why I'm being a little +bit fastidious here lattice points per + + align:start position:0% +bit fastidious here lattice points per + + + align:start position:0% +bit fastidious here lattice points per +unit cell uh what else are we looking at + + align:start position:0% +unit cell uh what else are we looking at + + + align:start position:0% +unit cell uh what else are we looking at +oh number uh oh nearest neighbor + + align:start position:0% +oh number uh oh nearest neighbor + + + align:start position:0% +oh number uh oh nearest neighbor +distance well nearest neighbor distance + + align:start position:0% +distance well nearest neighbor distance + + + align:start position:0% +distance well nearest neighbor distance +that's that's kind of obvious this here + + align:start position:0% +that's that's kind of obvious this here + + + align:start position:0% +that's that's kind of obvious this here +there's a here's a drawing this is a + + align:start position:0% +there's a here's a drawing this is a + + + align:start position:0% +there's a here's a drawing this is a +this is a and that distance is uh < tk2 + + align:start position:0% +this is a and that distance is uh < tk2 + + + align:start position:0% +this is a and that distance is uh < tk2 +time a and this is half of root2 so + + align:start position:0% +time a and this is half of root2 so + + + align:start position:0% +time a and this is half of root2 so +that's given here a over < tk2 nearest + + align:start position:0% +that's given here a over < tk2 nearest + + + align:start position:0% +that's given here a over < tk2 nearest +neighbors well you can see that nearest + + align:start position:0% +neighbors well you can see that nearest + + + align:start position:0% +neighbors well you can see that nearest +Neighbors let's count from this one it's + + align:start position:0% +Neighbors let's count from this one it's + + + align:start position:0% +Neighbors let's count from this one it's +got four at the corners right and it's + + align:start position:0% +got four at the corners right and it's + + + align:start position:0% +got four at the corners right and it's +got three in this plane and three in the + + align:start position:0% +got three in this plane and three in the + + + align:start position:0% +got three in this plane and three in the +other plane so that's going to add up 4+ + + align:start position:0% +other plane so that's going to add up 4+ + + + align:start position:0% +other plane so that's going to add up 4+ +4 + 4 is nearest neighbors is equal to + + align:start position:0% +4 + 4 is nearest neighbors is equal to + + + align:start position:0% +4 + 4 is nearest neighbors is equal to +12 some people call this the + + align:start position:0% +12 some people call this the + + + align:start position:0% +12 some people call this the +coordination number coordination number + + align:start position:0% +coordination number coordination number + + + align:start position:0% +coordination number coordination number +and this has got the highest this has + + align:start position:0% +and this has got the highest this has + + + align:start position:0% +and this has got the highest this has +got the highest number of nearest + + align:start position:0% +got the highest number of nearest + + + align:start position:0% +got the highest number of nearest +Neighbors when you have hard spheres of + + align:start position:0% +Neighbors when you have hard spheres of + + + align:start position:0% +Neighbors when you have hard spheres of +equal dimension of any uh Crystal system + + align:start position:0% +equal dimension of any uh Crystal system + + + align:start position:0% +equal dimension of any uh Crystal system +you can see here in body centered cubic + + align:start position:0% +you can see here in body centered cubic + + + align:start position:0% +you can see here in body centered cubic +it has eight nearest neighbors whereas + + align:start position:0% +it has eight nearest neighbors whereas + + + align:start position:0% +it has eight nearest neighbors whereas +simple cubic only has six nearest + + align:start position:0% +simple cubic only has six nearest + + + align:start position:0% +simple cubic only has six nearest +neighbors oops I don't want to look at + + align:start position:0% +neighbors oops I don't want to look at + + + align:start position:0% +neighbors oops I don't want to look at +that anymore all right and then the + + align:start position:0% +that anymore all right and then the + + + align:start position:0% +that anymore all right and then the +packing density I want to show you the + + align:start position:0% +packing density I want to show you the + + + align:start position:0% +packing density I want to show you the +packing density that's an interesting + + align:start position:0% +packing density that's an interesting + + + align:start position:0% +packing density that's an interesting +calculation what the packing density + + align:start position:0% +calculation what the packing density + + + align:start position:0% +calculation what the packing density +indicates is how much going back to + + align:start position:0% +indicates is how much going back to + + + align:start position:0% +indicates is how much going back to +democratus if we model if we model the + + align:start position:0% +democratus if we model if we model the + + + align:start position:0% +democratus if we model if we model the +FCC uh Crystal as hard spheres touching + + align:start position:0% +FCC uh Crystal as hard spheres touching + + + align:start position:0% +FCC uh Crystal as hard spheres touching +how much of this is matter and how much + + align:start position:0% +how much of this is matter and how much + + + align:start position:0% +how much of this is matter and how much +of it is free space that's given by the + + align:start position:0% +of it is free space that's given by the + + + align:start position:0% +of it is free space that's given by the +packing + + align:start position:0% +packing + + + align:start position:0% +packing +density packing density and that's equal + + align:start position:0% +density packing density and that's equal + + + align:start position:0% +density packing density and that's equal +to the volume of the + + align:start position:0% +to the volume of the + + + align:start position:0% +to the volume of the +atoms divided by total + + align:start position:0% +atoms divided by total + + + align:start position:0% +atoms divided by total +volume total volume so if we choose the + + align:start position:0% +volume total volume so if we choose the + + + align:start position:0% +volume total volume so if we choose the +unit cell as the basis so we've got + + align:start position:0% +unit cell as the basis so we've got + + + align:start position:0% +unit cell as the basis so we've got +something to count on let's let's go + + align:start position:0% +something to count on let's let's go + + + align:start position:0% +something to count on let's let's go +back so we know that the let's go to the + + align:start position:0% +back so we know that the let's go to the + + + align:start position:0% +back so we know that the let's go to the +other one I like this one it's a cuter + + align:start position:0% +other one I like this one it's a cuter + + + align:start position:0% +other one I like this one it's a cuter +drawing okay so the volume of the atoms + + align:start position:0% +drawing okay so the volume of the atoms + + + align:start position:0% +drawing okay so the volume of the atoms +well I know I've got four atoms + + align:start position:0% +well I know I've got four atoms + + + align:start position:0% +well I know I've got four atoms +equivalent of four atoms and what's the + + align:start position:0% +equivalent of four atoms and what's the + + + align:start position:0% +equivalent of four atoms and what's the +volume of an atom it's going to be 4/3 * + + align:start position:0% +volume of an atom it's going to be 4/3 * + + + align:start position:0% +volume of an atom it's going to be 4/3 * +pi * the radius of the atom + + align:start position:0% +pi * the radius of the atom + + + align:start position:0% +pi * the radius of the atom +cubed and what's the uh volume of that + + align:start position:0% +cubed and what's the uh volume of that + + + align:start position:0% +cubed and what's the uh volume of that +unit cell that unit cell is a cubed and + + align:start position:0% +unit cell that unit cell is a cubed and + + + align:start position:0% +unit cell that unit cell is a cubed and +now I need to know the relationship + + align:start position:0% +now I need to know the relationship + + + align:start position:0% +now I need to know the relationship +between A and R so I can convert one to + + align:start position:0% +between A and R so I can convert one to + + + align:start position:0% +between A and R so I can convert one to +the other and then I'll have a + + align:start position:0% +the other and then I'll have a + + + align:start position:0% +the other and then I'll have a +dimensionless group here so there you + + align:start position:0% +dimensionless group here so there you + + + align:start position:0% +dimensionless group here so there you +can see the relationship between A and R + + align:start position:0% +can see the relationship between A and R + + + align:start position:0% +can see the relationship between A and R +A 2 + a squ is uh the the 16 R squ so if + + align:start position:0% +A 2 + a squ is uh the the 16 R squ so if + + + align:start position:0% +A 2 + a squ is uh the the 16 R squ so if +you go through all that you can convince + + align:start position:0% +you go through all that you can convince + + + align:start position:0% +you go through all that you can convince +yourself that a = 2 roots of 2 R in F CC + + align:start position:0% +yourself that a = 2 roots of 2 R in F CC + + + align:start position:0% +yourself that a = 2 roots of 2 R in F CC +so plug that into there and you'll end + + align:start position:0% +so plug that into there and you'll end + + + align:start position:0% +so plug that into there and you'll end +up with the packing density will be + + align:start position:0% +up with the packing density will be + + + align:start position:0% +up with the packing density will be +equal to Pi ID 3 * theare < TK of two + + align:start position:0% +equal to Pi ID 3 * theare < TK of two + + + align:start position:0% +equal to Pi ID 3 * theare < TK of two +which is a value of + + align:start position:0% +which is a value of + + + align:start position:0% +which is a value of +0.74 so that means in face centered + + align:start position:0% +0.74 so that means in face centered + + + align:start position:0% +0.74 so that means in face centered +cubic uh in a face centered cubic + + align:start position:0% +cubic uh in a face centered cubic + + + align:start position:0% +cubic uh in a face centered cubic +lattice you have + + align:start position:0% +lattice you have + + + align:start position:0% +lattice you have +74% matter this is assuming hard sphere + + align:start position:0% +74% matter this is assuming hard sphere + + + align:start position:0% +74% matter this is assuming hard sphere +model hard sphere model spheres so big + + align:start position:0% +model hard sphere model spheres so big + + + align:start position:0% +model hard sphere model spheres so big +that they touch + + align:start position:0% +that they touch + + + align:start position:0% +that they touch +so that's 26% + + align:start position:0% +so that's 26% + + + align:start position:0% +so that's 26% +void 26% void and you can go through and + + align:start position:0% +void 26% void and you can go through and + + + align:start position:0% +void 26% void and you can go through and +you can see that as you look at this + + align:start position:0% +you can see that as you look at this + + + align:start position:0% +you can see that as you look at this +table that the packing decreases in the + + align:start position:0% +table that the packing decreases in the + + + align:start position:0% +table that the packing decreases in the +case of body centered cubic there's a + + align:start position:0% +case of body centered cubic there's a + + + align:start position:0% +case of body centered cubic there's a +little more open space it's 68% and in + + align:start position:0% +little more open space it's 68% and in + + + align:start position:0% +little more open space it's 68% and in +case of um in the case of uh simple + + align:start position:0% +case of um in the case of uh simple + + + align:start position:0% +case of um in the case of uh simple +cubic it's only about half packed so + + align:start position:0% +cubic it's only about half packed so + + + align:start position:0% +cubic it's only about half packed so +this table here is a is something that + + align:start position:0% +this table here is a is something that + + + align:start position:0% +this table here is a is something that +you want to get good and friendly with + + align:start position:0% +you want to get good and friendly with + + + align:start position:0% +you want to get good and friendly with +other thing I need to show you is a + + align:start position:0% +other thing I need to show you is a + + + align:start position:0% +other thing I need to show you is a +crystallographic notation and uh what I + + align:start position:0% +crystallographic notation and uh what I + + + align:start position:0% +crystallographic notation and uh what I +think I'm going to do is is uh uh invite + + align:start position:0% +think I'm going to do is is uh uh invite + + + align:start position:0% +think I'm going to do is is uh uh invite +you to to look at the website this this + + align:start position:0% +you to to look at the website this this + + + align:start position:0% +you to to look at the website this this +will give you the um the the nature of + + align:start position:0% +will give you the um the the nature of + + + align:start position:0% +will give you the um the the nature of +the crystallographic notation position + + align:start position:0% +the crystallographic notation position + + + align:start position:0% +the crystallographic notation position +is basically as it is in in in your math + + align:start position:0% +is basically as it is in in in your math + + + align:start position:0% +is basically as it is in in in your math +classes the only difference is we don't + + align:start position:0% +classes the only difference is we don't + + + align:start position:0% +classes the only difference is we don't +put uh enclosures there's no parenthesis + + align:start position:0% +put uh enclosures there's no parenthesis + + + align:start position:0% +put uh enclosures there's no parenthesis +around a point so if the origin is 00 0 + + align:start position:0% +around a point so if the origin is 00 0 + + + align:start position:0% +around a point so if the origin is 00 0 +but don't put parenthesis around it so a + + align:start position:0% +but don't put parenthesis around it so a + + + align:start position:0% +but don't put parenthesis around it so a +point is simply written as + + align:start position:0% +point is simply written as + + + align:start position:0% +point is simply written as +follows so origin for a point z0 Z + + align:start position:0% +follows so origin for a point z0 Z + + + align:start position:0% +follows so origin for a point z0 Z +that's all there is to it in the case of + + align:start position:0% +that's all there is to it in the case of + + + align:start position:0% +that's all there is to it in the case of +uh directions uh this is going to take a + + align:start position:0% +uh directions uh this is going to take a + + + align:start position:0% +uh directions uh this is going to take a +little more time than I have set aside + + align:start position:0% +little more time than I have set aside + + + align:start position:0% +little more time than I have set aside +because I've got a few uh items of + + align:start position:0% +because I've got a few uh items of + + + align:start position:0% +because I've got a few uh items of +business that I need to take care of so + + align:start position:0% +business that I need to take care of so + + + align:start position:0% +business that I need to take care of so +I think I'm going to uh I think I'm + + align:start position:0% +I think I'm going to uh I think I'm + + + align:start position:0% +I think I'm going to uh I think I'm +going to uh hold at this point and we'll + + align:start position:0% +going to uh hold at this point and we'll + + + align:start position:0% +going to uh hold at this point and we'll +jump ahead to this is see I always have + + align:start position:0% +jump ahead to this is see I always have + + + align:start position:0% +jump ahead to this is see I always have +a few things up my sleeve okay so let's + + align:start position:0% +a few things up my sleeve okay so let's + + + align:start position:0% +a few things up my sleeve okay so let's +let's go back to the the beginning um + + align:start position:0% +let's go back to the the beginning um + + + align:start position:0% +let's go back to the the beginning um +when people came in as is the custom we + + align:start position:0% +when people came in as is the custom we + + + align:start position:0% +when people came in as is the custom we +have music playing and um what was the + + align:start position:0% +have music playing and um what was the + + + align:start position:0% +have music playing and um what was the +music + + align:start position:0% +music + + + align:start position:0% +music +today yeah the talking heads and the + + align:start position:0% +today yeah the talking heads and the + + + align:start position:0% +today yeah the talking heads and the +song + + align:start position:0% +song + + + align:start position:0% +song +was Burning Down The House so why would + + align:start position:0% +was Burning Down The House so why would + + + align:start position:0% +was Burning Down The House so why would +I be playing Burning Down The House in a + + align:start position:0% +I be playing Burning Down The House in a + + + align:start position:0% +I be playing Burning Down The House in a +lecture about + + align:start position:0% +lecture about + + + align:start position:0% +lecture about +crystallography well uh what inspired me + + align:start position:0% +crystallography well uh what inspired me + + + align:start position:0% +crystallography well uh what inspired me +to play to choose that piece of music + + align:start position:0% +to play to choose that piece of music + + + align:start position:0% +to play to choose that piece of music +was this painting the houses at leack + + align:start position:0% +was this painting the houses at leack + + + align:start position:0% +was this painting the houses at leack +this was painted by George bra in 1908 L + + align:start position:0% +this was painted by George bra in 1908 L + + + align:start position:0% +this was painted by George bra in 1908 L +stack is a community down in the + + align:start position:0% +stack is a community down in the + + + align:start position:0% +stack is a community down in the +southern part of France and uh when + + align:start position:0% +southern part of France and uh when + + + align:start position:0% +southern part of France and uh when +Brack painted this he outraged the + + align:start position:0% +Brack painted this he outraged the + + + align:start position:0% +Brack painted this he outraged the +critics of the salon in Paris who + + align:start position:0% +critics of the salon in Paris who + + + align:start position:0% +critics of the salon in Paris who +condemned this painting they said look + + align:start position:0% +condemned this painting they said look + + + align:start position:0% +condemned this painting they said look +it it doesn't have a common perspective + + align:start position:0% +it it doesn't have a common perspective + + + align:start position:0% +it it doesn't have a common perspective +the the the houses in the back the it + + align:start position:0% +the the the houses in the back the it + + + align:start position:0% +the the the houses in the back the it +looks as though the lighting is coming + + align:start position:0% +looks as though the lighting is coming + + + align:start position:0% +looks as though the lighting is coming +from here but then the lighting over + + align:start position:0% +from here but then the lighting over + + + align:start position:0% +from here but then the lighting over +here is coming from another angle uh he + + align:start position:0% +here is coming from another angle uh he + + + align:start position:0% +here is coming from another angle uh he +broke all sorts of artistic conventions + + align:start position:0% +broke all sorts of artistic conventions + + + align:start position:0% +broke all sorts of artistic conventions +and one critic um ultimately condemned + + align:start position:0% +and one critic um ultimately condemned + + + align:start position:0% +and one critic um ultimately condemned +this painting of houses as nothing but a + + align:start position:0% +this painting of houses as nothing but a + + + align:start position:0% +this painting of houses as nothing but a +stack of huge cubes and from this came + + align:start position:0% +stack of huge cubes and from this came + + + align:start position:0% +stack of huge cubes and from this came +the term cubism and since we've been + + align:start position:0% +the term cubism and since we've been + + + align:start position:0% +the term cubism and since we've been +talking about the properties of cubic + + align:start position:0% +talking about the properties of cubic + + + align:start position:0% +talking about the properties of cubic +crystals I thought the connection was + + align:start position:0% +crystals I thought the connection was + + + align:start position:0% +crystals I thought the connection was +pretty + + align:start position:0% + + + + align:start position:0% + +obvious okay I did all right um what I + + align:start position:0% +obvious okay I did all right um what I + + + align:start position:0% +obvious okay I did all right um what I +we have a we have a contest every year + + align:start position:0% +we have a we have a contest every year + + + align:start position:0% +we have a we have a contest every year +in 3091 the contest involves um + + align:start position:0% +in 3091 the contest involves um + + + align:start position:0% +in 3091 the contest involves um +developing a neonic device for the + + align:start position:0% +developing a neonic device for the + + + align:start position:0% +developing a neonic device for the +certain groups in the periodic table the + + align:start position:0% +certain groups in the periodic table the + + + align:start position:0% +certain groups in the periodic table the +Lesser known actinides and lanthanides + + align:start position:0% +Lesser known actinides and lanthanides + + + align:start position:0% +Lesser known actinides and lanthanides +and so um I'm going to announce the + + align:start position:0% +and so um I'm going to announce the + + + align:start position:0% +and so um I'm going to announce the +winners today and we'll see if they come + + align:start position:0% +winners today and we'll see if they come + + + align:start position:0% +winners today and we'll see if they come +to class but in their defense there's a + + align:start position:0% +to class but in their defense there's a + + + align:start position:0% +to class but in their defense there's a +second lecture so if they're not here we + + align:start position:0% +second lecture so if they're not here we + + + align:start position:0% +second lecture so if they're not here we +assume that they're at the second + + align:start position:0% +assume that they're at the second + + + align:start position:0% +assume that they're at the second +lecture right so anyway so here's one + + align:start position:0% +lecture right so anyway so here's one + + + align:start position:0% +lecture right so anyway so here's one +this was uh for the Lites this was a a + + align:start position:0% +this was uh for the Lites this was a a + + + align:start position:0% +this was uh for the Lites this was a a +an Elizabethan sonnet uh that was + + align:start position:0% +an Elizabethan sonnet uh that was + + + align:start position:0% +an Elizabethan sonnet uh that was +written by Allison Burke is Allison + + align:start position:0% +written by Allison Burke is Allison + + + align:start position:0% +written by Allison Burke is Allison +here she obviously goes to the second + + align:start position:0% +here she obviously goes to the second + + + align:start position:0% +here she obviously goes to the second +lecture okay so just so you you'll see + + align:start position:0% +lecture okay so just so you you'll see + + + align:start position:0% +lecture okay so just so you you'll see +in a minute what the what the prizes are + + align:start position:0% +in a minute what the what the prizes are + + + align:start position:0% +in a minute what the what the prizes are +okay next one uh Eddie Fagan is Eddie + + align:start position:0% + + + + align:start position:0% + +here you have to come down and claim + + align:start position:0% +here you have to come down and claim + + + align:start position:0% +here you have to come down and claim +your prize come on + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +down okay so he has a choice of two two + + align:start position:0% +down okay so he has a choice of two two + + + align:start position:0% +down okay so he has a choice of two two +items one is the + + align:start position:0% +items one is the + + + align:start position:0% +items one is the +uh congratulations okay but I haven't + + align:start position:0% +uh congratulations okay but I haven't + + + align:start position:0% +uh congratulations okay but I haven't +shown you everything first here's his uh + + align:start position:0% +shown you everything first here's his uh + + + align:start position:0% +shown you everything first here's his uh +pneumonic verse but this was really hot + + align:start position:0% +pneumonic verse but this was really hot + + + align:start position:0% +pneumonic verse but this was really hot +look one of the things that we learn is + + align:start position:0% +look one of the things that we learn is + + + align:start position:0% +look one of the things that we learn is +the born exponent + + align:start position:0% + + + + align:start position:0% + +and but what's really cute is I mean I + + align:start position:0% +and but what's really cute is I mean I + + + align:start position:0% +and but what's really cute is I mean I +didn't notice this the first time I just + + align:start position:0% +didn't notice this the first time I just + + + align:start position:0% +didn't notice this the first time I just +caught it last night so this of course + + align:start position:0% +caught it last night so this of course + + + align:start position:0% +caught it last night so this of course +is a a punt on the born identity but + + align:start position:0% +is a a punt on the born identity but + + + align:start position:0% +is a a punt on the born identity but +down here it's uh 3091 pictures is in + + align:start position:0% +down here it's uh 3091 pictures is in + + + align:start position:0% +down here it's uh 3091 pictures is in +the corner here very sweet very sweet + + align:start position:0% +the corner here very sweet very sweet + + + align:start position:0% +the corner here very sweet very sweet +okay so you have a choice of you have a + + align:start position:0% +okay so you have a choice of you have a + + + align:start position:0% +okay so you have a choice of you have a +choice of uh the hot neck tie from the + + align:start position:0% +choice of uh the hot neck tie from the + + + align:start position:0% +choice of uh the hot neck tie from the +American Chemical Society or or this is + + align:start position:0% +American Chemical Society or or this is + + + align:start position:0% +American Chemical Society or or this is +a beautiful uh this is a lady's um scarf + + align:start position:0% +a beautiful uh this is a lady's um scarf + + + align:start position:0% +a beautiful uh this is a lady's um scarf +don't know you don't know what's going + + align:start position:0% +don't know you don't know what's going + + + align:start position:0% +don't know you don't know what's going +on in his personal life what are you + + align:start position:0% +on in his personal life what are you + + + align:start position:0% +on in his personal life what are you +talking about come + + align:start position:0% +talking about come + + + align:start position:0% +talking about come +on but you know what I'm going to do + + align:start position:0% +on but you know what I'm going to do + + + align:start position:0% +on but you know what I'm going to do +you're not going to make the choice + + align:start position:0% +you're not going to make the choice + + + align:start position:0% +you're not going to make the choice +right here in front of all of these + + align:start position:0% +right here in front of all of these + + + align:start position:0% +right here in front of all of these +people you're going to talk to me + + align:start position:0% +people you're going to talk to me + + + align:start position:0% +people you're going to talk to me +afterwards and they're not going to know + + align:start position:0% +afterwards and they're not going to know + + + align:start position:0% +afterwards and they're not going to know +what you chose perfect okay + + align:start position:0% + + + + align:start position:0% + +okay so the one that the one that I'm + + align:start position:0% +okay so the one that the one that I'm + + + align:start position:0% +okay so the one that the one that I'm +choosing is the winner I've I've had uh + + align:start position:0% +choosing is the winner I've I've had uh + + + align:start position:0% +choosing is the winner I've I've had uh +all sorts of things given to me over the + + align:start position:0% +all sorts of things given to me over the + + + align:start position:0% +all sorts of things given to me over the +years the Elizabeth and sonnet is one uh + + align:start position:0% +years the Elizabeth and sonnet is one uh + + + align:start position:0% +years the Elizabeth and sonnet is one uh +but this is the one that takes the cake + + align:start position:0% +but this is the one that takes the cake + + + align:start position:0% +but this is the one that takes the cake +this one uh this is a musical uh + + align:start position:0% +this one uh this is a musical uh + + + align:start position:0% +this one uh this is a musical uh +departure a riff on the Nat King Cole uh + + align:start position:0% +departure a riff on the Nat King Cole uh + + + align:start position:0% +departure a riff on the Nat King Cole uh +song Love and and this this this is a an + + align:start position:0% +song Love and and this this this is a an + + + align:start position:0% +song Love and and this this this is a an +image of the CD she she turned in the CD + + align:start position:0% +image of the CD she she turned in the CD + + + align:start position:0% +image of the CD she she turned in the CD +to me at minutes before 5:00 on the + + align:start position:0% +to me at minutes before 5:00 on the + + + align:start position:0% +to me at minutes before 5:00 on the +deadline date okay so I have this this + + align:start position:0% +deadline date okay so I have this this + + + align:start position:0% +deadline date okay so I have this this +is the image and um there's the + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +words listen to this phrase here + + align:start position:0% + + + + align:start position:0% + +it's imitates very very in the song it's + + align:start position:0% +it's imitates very very in the song it's + + + align:start position:0% +it's imitates very very in the song it's +beautiful + + align:start position:0% + + + + align:start position:0% + +yeah so it's really good all right + + align:start position:0% +yeah so it's really good all right + + + align:start position:0% +yeah so it's really good all right +[Applause] + + align:start position:0% + + + + align:start position:0% + +is is Miss Gabriel here please come + + align:start position:0% +is is Miss Gabriel here please come + + + align:start position:0% +is is Miss Gabriel here please come +down she obviously is also she's either + + align:start position:0% +down she obviously is also she's either + + + align:start position:0% +down she obviously is also she's either +here or she's shy or she goes to the + + align:start position:0% +here or she's shy or she goes to the + + + align:start position:0% +here or she's shy or she goes to the +1:00 class anyways I wanted you to see + + align:start position:0% +1:00 class anyways I wanted you to see + + + align:start position:0% +1:00 class anyways I wanted you to see +and I I want you to understand that this + + align:start position:0% +and I I want you to understand that this + + + align:start position:0% +and I I want you to understand that this +is part and parcel of what makes this uh + + align:start position:0% +is part and parcel of what makes this uh + + + align:start position:0% +is part and parcel of what makes this uh +student body uh unique I mean I submit + + align:start position:0% +student body uh unique I mean I submit + + + align:start position:0% +student body uh unique I mean I submit +that this kind of thing would not happen + + align:start position:0% +that this kind of thing would not happen + + + align:start position:0% +that this kind of thing would not happen +at + + align:start position:0% +at + + + align:start position:0% +at +[Applause] + + align:start position:0% + + + + align:start position:0% + +Harvard okay couple more things Tom + + align:start position:0% +Harvard okay couple more things Tom + + + align:start position:0% +Harvard okay couple more things Tom +could I get back to the document camera + + align:start position:0% +could I get back to the document camera + + + align:start position:0% +could I get back to the document camera +I want to show some other crystals and + + align:start position:0% +I want to show some other crystals and + + + align:start position:0% +I want to show some other crystals and +make the point about Symmetry and so on + + align:start position:0% +make the point about Symmetry and so on + + + align:start position:0% +make the point about Symmetry and so on +so this Crystal I'm going to show you is + + align:start position:0% +so this Crystal I'm going to show you is + + + align:start position:0% +so this Crystal I'm going to show you is +cryolite and cryolite is B refringent + + align:start position:0% +cryolite and cryolite is B refringent + + + align:start position:0% +cryolite and cryolite is B refringent +I'm sorry I'm going to have to ask you + + align:start position:0% +I'm sorry I'm going to have to ask you + + + align:start position:0% +I'm sorry I'm going to have to ask you +to go back to the thing I'm I needed to + + align:start position:0% +to go back to the thing I'm I needed to + + + align:start position:0% +to go back to the thing I'm I needed to +show this one thing please Tom can we go + + align:start position:0% +show this one thing please Tom can we go + + + align:start position:0% +show this one thing please Tom can we go +back to the + + align:start position:0% +back to the + + + align:start position:0% +back to the +computer thanks uh okay so what I'm + + align:start position:0% +computer thanks uh okay so what I'm + + + align:start position:0% +computer thanks uh okay so what I'm +going to show you is something that's B + + align:start position:0% +going to show you is something that's B + + + align:start position:0% +going to show you is something that's B +refringent the crystal symmetry has + + align:start position:0% +refringent the crystal symmetry has + + + align:start position:0% +refringent the crystal symmetry has +atoms Just In Parallel a little bit off + + align:start position:0% +atoms Just In Parallel a little bit off + + + align:start position:0% +atoms Just In Parallel a little bit off +axis from one another and what that does + + align:start position:0% +axis from one another and what that does + + + align:start position:0% +axis from one another and what that does +is it gives rise to two indices of + + align:start position:0% +is it gives rise to two indices of + + + align:start position:0% +is it gives rise to two indices of +refraction and so if you have a light + + align:start position:0% +refraction and so if you have a light + + + align:start position:0% +refraction and so if you have a light +Ray entering the crystal off the + + align:start position:0% +Ray entering the crystal off the + + + align:start position:0% +Ray entering the crystal off the +alignment of the optical axis the the + + align:start position:0% +alignment of the optical axis the the + + + align:start position:0% +alignment of the optical axis the the +light will split into two so you'll get + + align:start position:0% +light will split into two so you'll get + + + align:start position:0% +light will split into two so you'll get +an ordinary Ray and an extraordinary Ray + + align:start position:0% +an ordinary Ray and an extraordinary Ray + + + align:start position:0% +an ordinary Ray and an extraordinary Ray +and the separation of these two rays is + + align:start position:0% +and the separation of these two rays is + + + align:start position:0% +and the separation of these two rays is +related to the difference in the indices + + align:start position:0% +related to the difference in the indices + + + align:start position:0% +related to the difference in the indices +of refraction now if you're an opto + + align:start position:0% +of refraction now if you're an opto + + + align:start position:0% +of refraction now if you're an opto +electronics and you're making a splice + + align:start position:0% +electronics and you're making a splice + + + align:start position:0% +electronics and you're making a splice +and you got a material that's B + + align:start position:0% +and you got a material that's B + + + align:start position:0% +and you got a material that's B +refringent you better know this because + + align:start position:0% +refringent you better know this because + + + align:start position:0% +refringent you better know this because +all of a sudden you got your light going + + align:start position:0% +all of a sudden you got your light going + + + align:start position:0% +all of a sudden you got your light going +off to to the side or maybe this is what + + align:start position:0% +off to to the side or maybe this is what + + + align:start position:0% +off to to the side or maybe this is what +you want see so what I'm going to show + + align:start position:0% +you want see so what I'm going to show + + + align:start position:0% +you want see so what I'm going to show +you is now we can go to this this is a + + align:start position:0% +you is now we can go to this this is a + + + align:start position:0% +you is now we can go to this this is a +piece of cryolite and it's by refringent + + align:start position:0% +piece of cryolite and it's by refringent + + + align:start position:0% +piece of cryolite and it's by refringent +and what I'm going to do is show you how + + align:start position:0% +and what I'm going to do is show you how + + + align:start position:0% +and what I'm going to do is show you how +it will will act on if we can go to this + + align:start position:0% +it will will act on if we can go to this + + + align:start position:0% +it will will act on if we can go to this +where am I okay I'm here good let's see + + align:start position:0% +where am I okay I'm here good let's see + + + align:start position:0% +where am I okay I'm here good let's see +can I zoom in anymore good and now what + + align:start position:0% +can I zoom in anymore good and now what + + + align:start position:0% +can I zoom in anymore good and now what +we'll see is as I turn this you see now + + align:start position:0% +we'll see is as I turn this you see now + + + align:start position:0% +we'll see is as I turn this you see now +I've lined up so do you see this line + + align:start position:0% +I've lined up so do you see this line + + + align:start position:0% +I've lined up so do you see this line +here appears as a line everything's as + + align:start position:0% +here appears as a line everything's as + + + align:start position:0% +here appears as a line everything's as +it should be but then as I turn + + align:start position:0% +it should be but then as I turn + + + align:start position:0% +it should be but then as I turn +this cool see that separation and I can + + align:start position:0% +this cool see that separation and I can + + + align:start position:0% +this cool see that separation and I can +bring it back + + align:start position:0% + + + + align:start position:0% + +so that's by refringence and this is + + align:start position:0% +so that's by refringence and this is + + + align:start position:0% +so that's by refringence and this is +another example of what you get with the + + align:start position:0% +another example of what you get with the + + + align:start position:0% +another example of what you get with the +crystal that is a + + align:start position:0% +crystal that is a + + + align:start position:0% +crystal that is a +um has a particular uh crystal structure + + align:start position:0% +um has a particular uh crystal structure + + + align:start position:0% +um has a particular uh crystal structure +uh one of the RH rhomedal types uh back + + align:start position:0% +uh one of the RH rhomedal types uh back + + + align:start position:0% +uh one of the RH rhomedal types uh back +to the computer Tom I got to set up one + + align:start position:0% +to the computer Tom I got to set up one + + + align:start position:0% +to the computer Tom I got to set up one +other thing + + align:start position:0% +other thing + + + align:start position:0% +other thing +here okay so this gives you an + + align:start position:0% +here okay so this gives you an + + + align:start position:0% +here okay so this gives you an +indication of some of the materials that + + align:start position:0% +indication of some of the materials that + + + align:start position:0% +indication of some of the materials that +you may know that are obviously calite + + align:start position:0% +you may know that are obviously calite + + + align:start position:0% +you may know that are obviously calite +um ice is B refringent not terribly so + + align:start position:0% +um ice is B refringent not terribly so + + + align:start position:0% +um ice is B refringent not terribly so +roual very much uh titanium dioxide one + + align:start position:0% +roual very much uh titanium dioxide one + + + align:start position:0% +roual very much uh titanium dioxide one +of the forms of titanium dioxide quartz + + align:start position:0% +of the forms of titanium dioxide quartz + + + align:start position:0% +of the forms of titanium dioxide quartz +just mildly so okay now I want to show + + align:start position:0% +just mildly so okay now I want to show + + + align:start position:0% +just mildly so okay now I want to show +some some very strange FCC uh this is + + align:start position:0% +some some very strange FCC uh this is + + + align:start position:0% +some some very strange FCC uh this is +colored Golds you know uh you know what + + align:start position:0% +colored Golds you know uh you know what + + + align:start position:0% +colored Golds you know uh you know what +gold looks like uh it's a very malleable + + align:start position:0% +gold looks like uh it's a very malleable + + + align:start position:0% +gold looks like uh it's a very malleable +it's an + + align:start position:0% +it's an + + + align:start position:0% +it's an +FCC uh Crystal and yellow uh by alloying + + align:start position:0% +FCC uh Crystal and yellow uh by alloying + + + align:start position:0% +FCC uh Crystal and yellow uh by alloying +with different elements you can change + + align:start position:0% +with different elements you can change + + + align:start position:0% +with different elements you can change +color right but these are all FCC you + + align:start position:0% +color right but these are all FCC you + + + align:start position:0% +color right but these are all FCC you +see nickel nickel's FCC aluminum IS F CC + + align:start position:0% +see nickel nickel's FCC aluminum IS F CC + + + align:start position:0% +see nickel nickel's FCC aluminum IS F CC +and uh indium so on what I'm going to + + align:start position:0% +and uh indium so on what I'm going to + + + align:start position:0% +and uh indium so on what I'm going to +show you is uh the alloying of indium + + align:start position:0% +show you is uh the alloying of indium + + + align:start position:0% +show you is uh the alloying of indium +with uh yellow gold to give something + + align:start position:0% +with uh yellow gold to give something + + + align:start position:0% +with uh yellow gold to give something +that is uh 12 karat gold so Tom may we + + align:start position:0% +that is uh 12 karat gold so Tom may we + + + align:start position:0% +that is uh 12 karat gold so Tom may we +switch to the document + + align:start position:0% +switch to the document + + + align:start position:0% +switch to the document +camera okay let's get the cry light out + + align:start position:0% +camera okay let's get the cry light out + + + align:start position:0% +camera okay let's get the cry light out +of the way this is gold this is the gold + + align:start position:0% +of the way this is gold this is the gold + + + align:start position:0% +of the way this is gold this is the gold +foil that Rutherford would have used in + + align:start position:0% +foil that Rutherford would have used in + + + align:start position:0% +foil that Rutherford would have used in +his famous + + align:start position:0% +his famous + + + align:start position:0% +his famous +experiment okay and now this is Indian + + align:start position:0% +experiment okay and now this is Indian + + + align:start position:0% +experiment okay and now this is Indian +gold + + align:start position:0% + + + + align:start position:0% + +it's a very soft sort of a Dove's egg + + align:start position:0% +it's a very soft sort of a Dove's egg + + + align:start position:0% +it's a very soft sort of a Dove's egg +blue + + align:start position:0% +blue + + + align:start position:0% +blue +color very um lovely + + align:start position:0% +color very um lovely + + + align:start position:0% +color very um lovely +color so you might ask yourself what + + align:start position:0% +color so you might ask yourself what + + + align:start position:0% +color so you might ask yourself what +could you do with something like this + + align:start position:0% +could you do with something like this + + + align:start position:0% +could you do with something like this +because it's somewhat brittle you can + + align:start position:0% +because it's somewhat brittle you can + + + align:start position:0% +because it's somewhat brittle you can +see here's the Machining that gives you + + align:start position:0% +see here's the Machining that gives you + + + align:start position:0% +see here's the Machining that gives you +a better sense of it just a little bit + + align:start position:0% +a better sense of it just a little bit + + + align:start position:0% +a better sense of it just a little bit +off right so what I was thinking is what + + align:start position:0% +off right so what I was thinking is what + + + align:start position:0% +off right so what I was thinking is what +if we were to do something like this we + + align:start position:0% +if we were to do something like this we + + + align:start position:0% +if we were to do something like this we +could take a watch like so see this and + + align:start position:0% +could take a watch like so see this and + + + align:start position:0% +could take a watch like so see this and +then what we could do is put something + + align:start position:0% +then what we could do is put something + + + align:start position:0% +then what we could do is put something +like that here see and then we put + + align:start position:0% +like that here see and then we put + + + align:start position:0% +like that here see and then we put +quartz movement underneath and we put + + align:start position:0% +quartz movement underneath and we put + + + align:start position:0% +quartz movement underneath and we put +some numbers on the front here and some + + align:start position:0% +some numbers on the front here and some + + + align:start position:0% +some numbers on the front here and some +hands this thing's this thing's solid 12 + + align:start position:0% +hands this thing's this thing's solid 12 + + + align:start position:0% +hands this thing's this thing's solid 12 +karat gold we could sell this thing for + + align:start position:0% +karat gold we could sell this thing for + + + align:start position:0% +karat gold we could sell this thing for +about $10,000 a + + align:start position:0% + + + + align:start position:0% + +pizza and then there's all those other + + align:start position:0% +pizza and then there's all those other + + + align:start position:0% +pizza and then there's all those other +colored Golds we could do all of this as + + align:start position:0% +colored Golds we could do all of this as + + + align:start position:0% +colored Golds we could do all of this as +well so I think this gives you a a sense + + align:start position:0% +well so I think this gives you a a sense + + + align:start position:0% +well so I think this gives you a a sense +of what happens when you understand + + align:start position:0% +of what happens when you understand + + + align:start position:0% +of what happens when you understand +crystallography + + align:start position:0% +crystallography + + + align:start position:0% +crystallography +and I think with that we're going to go + + align:start position:0% +and I think with that we're going to go + + + align:start position:0% +and I think with that we're going to go +go for an early dismissal and wish you a + + align:start position:0% +go for an early dismissal and wish you a + + + align:start position:0% +go for an early dismissal and wish you a +good weekend \ No newline at end of file diff --git a/YQ26hzI4OJk.txt b/YQ26hzI4OJk.txt new file mode 100644 index 0000000000000000000000000000000000000000..9be8b26d05804efd1a0b6247a1d13ea130a12232 --- /dev/null +++ b/YQ26hzI4OJk.txt @@ -0,0 +1,995 @@ +align:start position:0% + +let us now revisit the variants and see + + align:start position:0% +let us now revisit the variants and see + + + align:start position:0% +let us now revisit the variants and see +what happens in the case of independence + + align:start position:0% +what happens in the case of independence + + + align:start position:0% +what happens in the case of independence +variances have some general properties + + align:start position:0% +variances have some general properties + + + align:start position:0% +variances have some general properties +that we have already seen however since + + align:start position:0% +that we have already seen however since + + + align:start position:0% +that we have already seen however since +we often add random variables we would + + align:start position:0% +we often add random variables we would + + + align:start position:0% +we often add random variables we would +like to be able to say something about + + align:start position:0% +like to be able to say something about + + + align:start position:0% +like to be able to say something about +the variance of the sum of two random + + align:start position:0% +the variance of the sum of two random + + + align:start position:0% +the variance of the sum of two random +variables unfortunately the situation is + + align:start position:0% +variables unfortunately the situation is + + + align:start position:0% +variables unfortunately the situation is +not so simple and in general the + + align:start position:0% +not so simple and in general the + + + align:start position:0% +not so simple and in general the +variance of the sum is not the same as + + align:start position:0% +variance of the sum is not the same as + + + align:start position:0% +variance of the sum is not the same as +the sum of the variances we will see an + + align:start position:0% +the sum of the variances we will see an + + + align:start position:0% +the sum of the variances we will see an +example shortly on the other hand when x + + align:start position:0% +example shortly on the other hand when x + + + align:start position:0% +example shortly on the other hand when x +and y are independent the variance of + + align:start position:0% +and y are independent the variance of + + + align:start position:0% +and y are independent the variance of +the sum is equal to the sum of the + + align:start position:0% +the sum is equal to the sum of the + + + align:start position:0% +the sum is equal to the sum of the +variances and this is a very useful fact + + align:start position:0% +variances and this is a very useful fact + + + align:start position:0% +variances and this is a very useful fact +let us go through the derivation of this + + align:start position:0% +let us go through the derivation of this + + + align:start position:0% +let us go through the derivation of this +property but to keep things simple let + + align:start position:0% +property but to keep things simple let + + + align:start position:0% +property but to keep things simple let +us assume just for the sake of the + + align:start position:0% +us assume just for the sake of the + + + align:start position:0% +us assume just for the sake of the +derivation that the two random variables + + align:start position:0% +derivation that the two random variables + + + align:start position:0% +derivation that the two random variables +have zero mean so in that case the + + align:start position:0% +have zero mean so in that case the + + + align:start position:0% +have zero mean so in that case the +variance of the sum is just the expected + + align:start position:0% +variance of the sum is just the expected + + + align:start position:0% +variance of the sum is just the expected +value of the square of the sum and we + + align:start position:0% +value of the square of the sum and we + + + align:start position:0% +value of the square of the sum and we +can expand the quadratic and write this + + align:start position:0% +can expand the quadratic and write this + + + align:start position:0% +can expand the quadratic and write this +as expectation of x squared plus 2xy + + align:start position:0% +as expectation of x squared plus 2xy + + + align:start position:0% +as expectation of x squared plus 2xy +plus y squared then we use linearity of + + align:start position:0% +plus y squared then we use linearity of + + + align:start position:0% +plus y squared then we use linearity of +expectations to write this as expected + + align:start position:0% +expectations to write this as expected + + + align:start position:0% +expectations to write this as expected +value of x squared plus twice the + + align:start position:0% +value of x squared plus twice the + + + align:start position:0% +value of x squared plus twice the +expected value of x times y and then + + align:start position:0% +expected value of x times y and then + + + align:start position:0% +expected value of x times y and then +plus the expected value of y squared now + + align:start position:0% +plus the expected value of y squared now + + + align:start position:0% +plus the expected value of y squared now +the first term is just the variance of X + + align:start position:0% +the first term is just the variance of X + + + align:start position:0% +the first term is just the variance of X +because we have assumed that we have + + align:start position:0% +because we have assumed that we have + + + align:start position:0% +because we have assumed that we have +zero mean the last term is similarly the + + align:start position:0% +zero mean the last term is similarly the + + + align:start position:0% +zero mean the last term is similarly the +variance of Y how about the middle term + + align:start position:0% +variance of Y how about the middle term + + + align:start position:0% +variance of Y how about the middle term +because of independence the expected + + align:start position:0% +because of independence the expected + + + align:start position:0% +because of independence the expected +value of the product + + align:start position:0% +value of the product + + + align:start position:0% +value of the product +is the same as the product of the + + align:start position:0% +is the same as the product of the + + + align:start position:0% +is the same as the product of the +expected values and the expected values + + align:start position:0% +expected values and the expected values + + + align:start position:0% +expected values and the expected values +are zero in our case so this term + + align:start position:0% +are zero in our case so this term + + + align:start position:0% +are zero in our case so this term +because of independence this term is + + align:start position:0% +because of independence this term is + + + align:start position:0% +because of independence this term is +going to be equal to zero in particular + + align:start position:0% +going to be equal to zero in particular + + + align:start position:0% +going to be equal to zero in particular +what we have is that the expected value + + align:start position:0% +what we have is that the expected value + + + align:start position:0% +what we have is that the expected value +of XY equals the expected value of x + + align:start position:0% +of XY equals the expected value of x + + + align:start position:0% +of XY equals the expected value of x +times the expected value of y equal to + + align:start position:0% +times the expected value of y equal to + + + align:start position:0% +times the expected value of y equal to +zero and so we have verified that indeed + + align:start position:0% +zero and so we have verified that indeed + + + align:start position:0% +zero and so we have verified that indeed +the variance of the sum is equal to the + + align:start position:0% +the variance of the sum is equal to the + + + align:start position:0% +the variance of the sum is equal to the +sum of the variances let us now look at + + align:start position:0% +sum of the variances let us now look at + + + align:start position:0% +sum of the variances let us now look at +some examples suppose that X is the same + + align:start position:0% +some examples suppose that X is the same + + + align:start position:0% +some examples suppose that X is the same +random variable as Y clearly this is a + + align:start position:0% +random variable as Y clearly this is a + + + align:start position:0% +random variable as Y clearly this is a +case where independence fails to hold if + + align:start position:0% +case where independence fails to hold if + + + align:start position:0% +case where independence fails to hold if +I tell you the value of X then you know + + align:start position:0% +I tell you the value of X then you know + + + align:start position:0% +I tell you the value of X then you know +the value of y so in this case the + + align:start position:0% +the value of y so in this case the + + + align:start position:0% +the value of y so in this case the +variance of the sum is the same as the + + align:start position:0% +variance of the sum is the same as the + + + align:start position:0% +variance of the sum is the same as the +variance of twice X since X is the same + + align:start position:0% +variance of twice X since X is the same + + + align:start position:0% +variance of twice X since X is the same +as Y X plus y is 2 times X and then + + align:start position:0% +as Y X plus y is 2 times X and then + + + align:start position:0% +as Y X plus y is 2 times X and then +using this property for the variance + + align:start position:0% +using this property for the variance + + + align:start position:0% +using this property for the variance +what happens when we multiply by a + + align:start position:0% +what happens when we multiply by a + + + align:start position:0% +what happens when we multiply by a +constant this is going to be 4 times the + + align:start position:0% +constant this is going to be 4 times the + + + align:start position:0% +constant this is going to be 4 times the +variance of X in another example suppose + + align:start position:0% +variance of X in another example suppose + + + align:start position:0% +variance of X in another example suppose +that X is the negative of Y in that case + + align:start position:0% +that X is the negative of Y in that case + + + align:start position:0% +that X is the negative of Y in that case +X plus y is identically equal to 0 so + + align:start position:0% +X plus y is identically equal to 0 so + + + align:start position:0% +X plus y is identically equal to 0 so +we're dealing with a random variable + + align:start position:0% +we're dealing with a random variable + + + align:start position:0% +we're dealing with a random variable +that takes a constant value in + + align:start position:0% +that takes a constant value in + + + align:start position:0% +that takes a constant value in +particular it is always equal to its + + align:start position:0% +particular it is always equal to its + + + align:start position:0% +particular it is always equal to its +mean and so the difference from the mean + + align:start position:0% +mean and so the difference from the mean + + + align:start position:0% +mean and so the difference from the mean +is always equal to 0 and so the variance + + align:start position:0% +is always equal to 0 and so the variance + + + align:start position:0% +is always equal to 0 and so the variance +will also evaluate to 0 so we see that + + align:start position:0% +will also evaluate to 0 so we see that + + + align:start position:0% +will also evaluate to 0 so we see that +the variance of the sum can take quite + + align:start position:0% +the variance of the sum can take quite + + + align:start position:0% +the variance of the sum can take quite +different values depending on the sort + + align:start position:0% +different values depending on the sort + + + align:start position:0% +different values depending on the sort +of inter relation that we have between + + align:start position:0% +of inter relation that we have between + + + align:start position:0% +of inter relation that we have between +the two random variables so these two + + align:start position:0% +the two random variables so these two + + + align:start position:0% +the two random variables so these two +examples indicate that knowing the + + align:start position:0% +examples indicate that knowing the + + + align:start position:0% +examples indicate that knowing the +variance of each one of the random + + align:start position:0% +variance of each one of the random + + + align:start position:0% +variance of each one of the random +variables is not enough to say much + + align:start position:0% +variables is not enough to say much + + + align:start position:0% +variables is not enough to say much +about the variance of the sum the answer + + align:start position:0% +about the variance of the sum the answer + + + align:start position:0% +about the variance of the sum the answer +will generally depend on how the two + + align:start position:0% +will generally depend on how the two + + + align:start position:0% +will generally depend on how the two +random variables are related to each + + align:start position:0% +random variables are related to each + + + align:start position:0% +random variables are related to each +other and what kind of dependencies they + + align:start position:0% +other and what kind of dependencies they + + + align:start position:0% +other and what kind of dependencies they +have as the last example suppose now + + align:start position:0% +have as the last example suppose now + + + align:start position:0% +have as the last example suppose now +that x and y are independent x is + + align:start position:0% +that x and y are independent x is + + + align:start position:0% +that x and y are independent x is +independent from + + align:start position:0% +independent from + + + align:start position:0% +independent from +why and therefore X is also independent + + align:start position:0% +why and therefore X is also independent + + + align:start position:0% +why and therefore X is also independent +from minus three-y therefore this + + align:start position:0% +from minus three-y therefore this + + + align:start position:0% +from minus three-y therefore this +variance is equal to the sum of the + + align:start position:0% +variance is equal to the sum of the + + + align:start position:0% +variance is equal to the sum of the +variances of X and of minus 3y and using + + align:start position:0% +variances of X and of minus 3y and using + + + align:start position:0% +variances of X and of minus 3y and using +the fact that we already know this is + + align:start position:0% +the fact that we already know this is + + + align:start position:0% +the fact that we already know this is +going to be equal to the variance of X + + align:start position:0% +going to be equal to the variance of X + + + align:start position:0% +going to be equal to the variance of X +plus 9 times the variance of Y as an + + align:start position:0% +plus 9 times the variance of Y as an + + + align:start position:0% +plus 9 times the variance of Y as an +illustration of the usefulness of the + + align:start position:0% +illustration of the usefulness of the + + + align:start position:0% +illustration of the usefulness of the +property of the variance that we have + + align:start position:0% +property of the variance that we have + + + align:start position:0% +property of the variance that we have +just established we will now use it to + + align:start position:0% +just established we will now use it to + + + align:start position:0% +just established we will now use it to +calculate the variance of a binomial + + align:start position:0% +calculate the variance of a binomial + + + align:start position:0% +calculate the variance of a binomial +random variable remember that a binomial + + align:start position:0% +random variable remember that a binomial + + + align:start position:0% +random variable remember that a binomial +with parameters N and P corresponds to + + align:start position:0% +with parameters N and P corresponds to + + + align:start position:0% +with parameters N and P corresponds to +the number of successes in n independent + + align:start position:0% +the number of successes in n independent + + + align:start position:0% +the number of successes in n independent +trials we use indicator variables this + + align:start position:0% +trials we use indicator variables this + + + align:start position:0% +trials we use indicator variables this +is the same trick that we use to + + align:start position:0% +is the same trick that we use to + + + align:start position:0% +is the same trick that we use to +calculate the expected value of the + + align:start position:0% +calculate the expected value of the + + + align:start position:0% +calculate the expected value of the +binomial so the random variable X sub I + + align:start position:0% +binomial so the random variable X sub I + + + align:start position:0% +binomial so the random variable X sub I +is equal to 1 if the eyes trial is a + + align:start position:0% +is equal to 1 if the eyes trial is a + + + align:start position:0% +is equal to 1 if the eyes trial is a +success in this is 0 otherwise and as we + + align:start position:0% +success in this is 0 otherwise and as we + + + align:start position:0% +success in this is 0 otherwise and as we +did before we note that X the total + + align:start position:0% +did before we note that X the total + + + align:start position:0% +did before we note that X the total +number of successes is the sum of those + + align:start position:0% +number of successes is the sum of those + + + align:start position:0% +number of successes is the sum of those +indicator variables each success makes + + align:start position:0% +indicator variables each success makes + + + align:start position:0% +indicator variables each success makes +one of those variables equal to 1 so by + + align:start position:0% +one of those variables equal to 1 so by + + + align:start position:0% +one of those variables equal to 1 so by +adding those indicator variables were + + align:start position:0% +adding those indicator variables were + + + align:start position:0% +adding those indicator variables were +just counting the number of successes + + align:start position:0% +just counting the number of successes + + + align:start position:0% +just counting the number of successes +the key point to note is that the + + align:start position:0% +the key point to note is that the + + + align:start position:0% +the key point to note is that the +assumption of Independence that we're + + align:start position:0% +assumption of Independence that we're + + + align:start position:0% +assumption of Independence that we're +making is essentially the assumption + + align:start position:0% +making is essentially the assumption + + + align:start position:0% +making is essentially the assumption +that these random variables X I are + + align:start position:0% +that these random variables X I are + + + align:start position:0% +that these random variables X I are +independent of each other so we're + + align:start position:0% +independent of each other so we're + + + align:start position:0% +independent of each other so we're +dealing with a situation where we have a + + align:start position:0% +dealing with a situation where we have a + + + align:start position:0% +dealing with a situation where we have a +sum of independent random variables and + + align:start position:0% +sum of independent random variables and + + + align:start position:0% +sum of independent random variables and +according to what we have shown the + + align:start position:0% +according to what we have shown the + + + align:start position:0% +according to what we have shown the +variance of X is going to be the sum of + + align:start position:0% +variance of X is going to be the sum of + + + align:start position:0% +variance of X is going to be the sum of +the variances of the x i's + + align:start position:0% + + + + align:start position:0% + +now the X eyes all have the same + + align:start position:0% +now the X eyes all have the same + + + align:start position:0% +now the X eyes all have the same +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +so all these variances will be the same + + align:start position:0% +so all these variances will be the same + + + align:start position:0% +so all these variances will be the same +it suffices to consider one of them now + + align:start position:0% +it suffices to consider one of them now + + + align:start position:0% +it suffices to consider one of them now +x1 is a Bernoulli random variable with + + align:start position:0% +x1 is a Bernoulli random variable with + + + align:start position:0% +x1 is a Bernoulli random variable with +parameter P we know what it's variance + + align:start position:0% +parameter P we know what it's variance + + + align:start position:0% +parameter P we know what it's variance +is it is P times 1 minus P and therefore + + align:start position:0% +is it is P times 1 minus P and therefore + + + align:start position:0% +is it is P times 1 minus P and therefore +this is the formula for the variance of + + align:start position:0% +this is the formula for the variance of + + + align:start position:0% +this is the formula for the variance of +a binomial random variable \ No newline at end of file diff --git a/Z8jR--1_2e4.txt b/Z8jR--1_2e4.txt new file mode 100644 index 0000000000000000000000000000000000000000..555297f57e9125aca00d31329cd135e308e9a27c --- /dev/null +++ b/Z8jR--1_2e4.txt @@ -0,0 +1,287 @@ +Now would be a good time to take a moment +to look at the documentation for the library + +of logic gates we'll use for our designs. + +Look for "The Standard Cell Library" handout +in the Updates & Handouts tab, which is next + +to the Courseware tab. + +The information on this slide is taken from +there. + +The library has both inverting gates (such +as inverters, NANDs and NORs) and non-inverting + +gates (such as buffers, ANDs and ORs). + +Why bother to include both types of gates? + +Didn't we just learn we can build any circuit +using only NAND or NOR? + +Good questions! + +We get some insight into the answers if we +look at these three implementations for a + +4-input AND function. + +The upper circuit is a direct implementation +using the 4-input AND gate available in the + +library. + +The tPD of the gate is 160 picoseconds and +its size is 20 square microns. + +Don't worry too much about the actual numbers, +what matters on this slide is how the numbers + +compare between designs. + +The middle circuit implements the same function, +this time using a 4-INPUT NAND gate hooked + +to an inverter to produce the AND functionality +we want. + +The tPD of this circuit is 90 picoseconds, +considerably faster than the single gate above. + +The tradeoff is that the size is somewhat +larger. + +How can this be? + +Especially since we know the AND gate implementation +is the NAND/INVERTER pair shown in the middle + +circuit. + +The answer is that the creators of the library +decided to make the non-inverting gates small + +but slow by using MOSFETs with much smaller +widths than used in the inverting logic gates, + +which were designed to be fast. + +Why would we ever want to use a slow gate? + +Remember that the propagation delay of a circuit +is set by the longest path in terms of delay + +from inputs to outputs. + +In a complex circuit, there are many input/output +paths, but it's only the components on the + +longest path that need to be fast in order +to achieve the best possible overall tPD. + +The components on the other, shorter paths, +can potentially be a bit slower. + +And the components on short input/output paths +can be very slow indeed. + +So for the portions of the circuit that aren't +speed sensitive, it's a good tradeoff to use + +slower but smaller gates. + +The overall performance isn't affected, but +the total size is improved. + +So for faster performance we'll design with +inverting gates, and for smallest size we'll + +design with non-inverting gates. + +The creators of the gate library designed +the available gates with this tradeoff in + +mind. + +The 4-input inverting gates are also designed +with this tradeoff in mind. + +For the ultimate in performance, we want to +use a tree circuit of 2-input gates, as shown + +in the lower circuit. + +This implementation shaves 10 picoseconds +off the tPD, while costing us a bit more in + +size. + +Take a closer look at the lower circuit. + +This tree circuit uses two NAND gates whose +outputs are combined with a NOR gate. + +Does this really compute the AND of A, B, +C, and D? + +Yup, as you can verify by building the truth +table for this combinational system using + +the truth tables for NAND and NOR. + +This circuit is a good example of the application +of a particular Boolean identity known as + +Demorgan's Law. + +There are two forms of Demorgan's law, both +of which are shown here. + +The top form is the one we're interested in +for analyzing the lower circuit. + +It tells us that the NOR of A with B is equivalent +to the AND of (NOT A) with (NOT B). + +So the 2-input NOR gate can be thought of +as a 2-input AND gate with inverting inputs. + +How does this help? + +We can now see that the lower circuit is actually +a tree of AND gates, where the inverting outputs + +of the first layer match up with the inverting +inputs of the second layer. + +It's a little confusing the first time you +see it, but with practice you'll be comfortable + +using Demorgan's law when building trees or +chains of inverting logic. + +Using Demorgan's Law we can answer the question +of how to build NANDs and NORs with large + +numbers of inputs. + +Our gate library includes inverting gates +with up to 4 inputs. + +Why stop there? + +Well, the pulldown chain of a 4-input NAND +gate has 4 NFETs in series and the resistance + +of the conducting channels is starting to +add up. + +We could make the NFETs wider to compensate, +but then the gate gets much larger and the + +wider NFETs impose a higher capacitive load +on the input signals. + +The number of possible tradeoffs between size +and speed grows rapidly with the number of + +inputs, so it's usually just best for the +library designer to stop at 4-input gates + +and let the circuit designer take it from +there. + +Happily, Demorgan's law shows us how build +trees of alternating NANDs and NORs to build + +inverting logic with a large number of inputs. + +Here we see schematics for an 8-input NAND +and an 8-input NOR gate. + +Think of the middle layer of NOR gates in +the left circuit as AND gates with inverting + +inputs and then it's easy to see that the +circuit is a tree of ANDs with an inverting + +output. + +Similarly, think of the middle layer of NAND +gates in the right circuit as OR gates with + +inverting inputs and see that we really have +a tree of OR gates with an inverting output. + +Now let's see how to build sum-of-products +circuits using inverting logic. + +The two circuits shown here implement the +same sum-of-products logic function. + +The one on the top uses two layers of NAND +gates, the one on the bottom, two layers of + +NOR gates. + +Let's visualize Demorgan's Law in action on +the top circuit. + +The NAND gate with Y on its output can be +transformed by Demorgan's Law into an OR gate + +with inverting inputs. + +So we can redraw the circuit on the top left +as the circuit shown on the top right. + +Now, notice that the inverting outputs of +the first layer are cancelled by the inverting + +inputs of the second layer, a step we can +show visually by removing matching inversions. + +And, voila, we see the NAND/NAND circuit in +sum-of-products form: a layer of inverters, + +a layer of AND gates, and an OR gate to combine +the product terms. + +We can use a similar visualization to transform +the output gate of the bottom circuit, giving + +us the circuit on the bottom right. + +Match up the bubbles and we see that we have +the same logic function as above. + +Looking at the NOR/NOR circuit on the bottom +left, we see it has 4 inverters, whereas the + +NAND/NAND circuit only has one. + +Why would we ever use the NOR/NOR implementation? + +It has to do with the loading on the inputs. + +In the top circuit, the input A connects to +a total of four MOSFET switches. + +In the bottom circuit, it connects to only +the two MOSFET switches in the inverter. + +So, the bottom circuit imposes half the capacitive +load on the A signal. + +This might be significant if the signal A +connected to many such circuits. + +The bottom line: when you find yourself needing +a fast implementation for the AND/OR circuitry + +for a sum-of-products expression, try using +the NAND/NAND implementation. + +It'll be noticeably faster than using AND/OR. \ No newline at end of file diff --git a/ZjVicrRxFtM.txt b/ZjVicrRxFtM.txt new file mode 100644 index 0000000000000000000000000000000000000000..020b296dc110fc8c6f1c537e830e5297d733f5e5 --- /dev/null +++ b/ZjVicrRxFtM.txt @@ -0,0 +1,2765 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So again, this +is one more question on + +hybridization. + +This is the last question you'll +get on hybridization + +before you see the exam. + +So now we're talking about +hybridization of two different + +atoms in a molecule. + +So we're looking at +this carbon atom + +here and this nitrogen. + +So using the rules that we've +learned in terms of doing this + +quickly, let's see if you can +get these answers in quick. + +So let's go ahead and just take +10 more seconds on this + +question here. + +Your parents are free to help +if they're here with you. + +OK. + +Excellent. excellent +job, 98% of you. + +You're a lot louder with the +parents here, so let's make + +sure we're still listening. + +OK, so let's go over what we +just we just established here. + +Carbon a is going to be +s p 3 hybridized. + +What is the geometry, what's +the vsper geometry there? + +Good, it's tetrahedral. + +And this nitrogen b here, that's +s p 3 hybrid as well. + +What's the geometry around +that nitrogen? + +Trigonal pyramidal, right. + +We have to take into account +the fact that there's that + +lone pair there. + +All right, so let's go ahead and +switch over to the lecture + +notes and see what +we just did here. + +And essentially actually what +we just did was I had you + +identify two of four components +that make up what's + +called the morphine rule. + +And the morphine rule is a set +of structural elements that + +are responsible for the +biological activity of + +morphine and other morphine-like +drugs that have + +a similar pharmacological +activity in terms of how + +they're active. + +So specifically, the morphine +rule is a set of four + +components, which start with the +phenyl ring here, so, an + +aromatic ring. + +The second thing you identified, +which is an s p 3 + +hybrid carbon. + +And then following that we have +a c h 2 c h 2 group here. + +And the last part of the +rule is this s p + +3 hybridized nitrogen. + +So, in terms of thinking about +what this means, I said this + +is responsible for the + +biological activity of morphine. + +If we take a look at the +morphine molecule here, what + +you can see is that it's a +little bit more complicated + +than this structure that +we see right here. + +But if I go ahead and highlight +the residues in + +purple, you can see that it, +in fact, does follow the + +morphine rule. + +And what this means is this +is what allows morphine to + +actually bind into its receptor, +which is a pain + +receptor and block the +feeling of pain. + +So that's a very important thing +in terms of thinking + +about hybridization in geometry, +because we've + +actually established a very +important structure and shape, + +which is this morphine rule +here, that if it's found in a + +molecule, as long as there +aren't other parts of the + +molecule that are messing up +that interaction, we can + +actually form a very +tight binder + +into these pain receptors. + +So morphine, as you know, is +a very potent pain killer. + +But you also, I'm sure, know +that it's also very addictive, + +so it's only used sparingly in +terms of treating pain in a + +general sense, and it's always +used in very closely-monitored + +situations in terms +of hospital care. + +But what's interesting to take +note of is that the bioaction + +of morphine is very similar to +endorphins that we naturally + +biosynthesize. + +Endorphins have a structure +that's very similar to this + +structure up here -- endorphins +are small peptide + +molecules that we biosynthesize +and have in very + +low concentrations +in our brain. + +They bind to pain receptors and + +block those pain receptors. + +So, when someone talks about an +endorphin high, which you + +sometimes get -- one example +would be the runners' high, if + +you run for a long way running +fast, eventually you'll hit + +that runner's high where you get +this burst of endorphins. + +All of a sudden your feet don't +hurt, your shins don't + +hurt, the pain goes +away and you got + +this feeling of eurphoria. + +It's the exact same interaction +and it's because + +of that structure there. + +It's not exactly the morphine +rule in endorphins but it's + +very similar. + +So, if we look at other +derivatives of morphine, such + +as codeine and diacetylmorphine, +these also + +you can see have this morphin +rule within them, this + +structure that you've identified +using your vsper + +rules and thinking about +hybridization. + +Codeine, as you may know, is +less of a potent pain killer + +compared to morphine, but it's +also less addictive. + +So for that reason it's +prescribed with + +slightly less oversight. + +So if you get your wisdom teeth +removed or something + +like that, some of you might +have had taken codeine before, + +and now you can think about by +looking at the structure, a + +little bit more about how +that worked in terms of + +blocking your pain. + +One that I just want to mention +because it's so + +interesting is this derivative, +which is + +diacetylmorphine. + +The only difference between +morphine and diacetylmorphine + +is the changing of an alcohol +group, or two actually, two + +acetyl groups here. + +This was synthesized by the +company Bayer, and you + +probably know Bayer from +Bayer's aspirin. + +Bayer had a huge success with +aspirin where they took + +salicylic acid and replaced an o +h group with an acetyl group + +here, and made acetylsalicylic +acid. + +Does anyone know the common +name for that? + +Yup. + +So that's aspirin, and we often + +think of Bayer's aspirin. + +We associate it really +closely. + +They worked really hard in +marketing to make that really + +close association and with +copywriting, so that when we + +think about aspirin we +think about Bayers. + +Bayers also made this change +here, and they did find that + +diacetylmorphine is much, much +more potent than morphine is. + +They could use just a tiny, tiny +amount of this compound + +and get the same pain-killing +properties that + +they saw with morphine. + +The problem is that this +masked some of the side + +effects that they didn't realize +initially, which was + +the extreme, extreme ability for +you to become addicted to + +diacetylmorphine. + +And this was first thought of as +a hero drug because it was + +such a strong pain killer, +and this was + +called a Bayer's heroin. + +We don't usually associate the +name Bayers with heroin, like + +we did with aspirin -- that's +because Bayers did not work so + +hard to keep that association +there. + +But it's an interesting story +from the history of drugs. + +One more example I want to show +you is demerol, which is + +used clinically quite often. + +Demerol, if we look at the +structure here, actually looks + +nothing like morphine at all. + +So to an untrained eye, +you might not see the + +relationship there. + +But because you all know some +of these basic principles of + +chemistry, you should be able to +pick out that morphine rule + +right in the middle +of demerol. + +And, in fact, demerol is +a pain killer, it's an + +alternative to using morphine. + +Again, not quite as strong as +morphine in terms of pain + +killing abilities, but also not +as addictive either, and + +there are some other side +effects, such as nausea that + +are limited with demerol +compared to morphine. + +Demerol has its own set of +problems, so it's not the + +perfect solution to a different +alternative to + +morphine, but you do see it +used in certain cases. + +All right, so that's thinking +about vsper theory, and that's + +thinking about hybridization. + +We're now going to shift gears +to talking about some new + +topics today. + +So, we ended in Wednesday's +lecture with giving that set + +of rules to very quickly +determine hybridization. + +And then after we'd established +that, we moved on + +to starting to talk about a +little bit of thermochemistry. + +Specifically what we were +talking about is the + +enthalpies of chemical +reactions, so either the + +amount of heat that's released, +or the amount of + +heat that's required +in order to have a + +chemical reaction go. + +And we'd established so far two +ways to think about how we + +can measure what the overall +enthalpy of a reaction is. + +And I just wanted to introduced +one more technique + +that we can use to do that. + +And this relies on the fact +that when we talk about + +enthalpy or we talk about the +heat change of a reaction, + +this is a state function, and +any time we're talking about + +state function, it's independent +of path. + +So essentially, all that we're +worried about is the state + +that we started in. + +So, for example, when we were +talking about the oxidation of + +glucose, the state that we start +in are the reactants, so + +it's glucose plus oxygen. + +And what we ended up with were +six moles each of carbon + +dioxide and water. + +So, we don't care how we get +there in terms of making this + +calculation, all we're +interested in is the + +difference between those two +states, to think about the + +overall change in enthalpy. + +So, for example, when we talked +about how we could + +calculate this, one way that we +can do it, and we'll look + +at these numbers even more +specifically in a second, is + +thinking about instead of going +straight down here, + +which we might not have the +numbers available to us to + +calculate directly, we can think +about well, what happens + +if instead we break apart this +glucose molecule and decompose + +it into its elements, because +using tables in the back of + +our book, for example, we can +figure out what the change in + +enthalpy is of this +reaction here. + +That doesn't quite get us to +where we need to go though, so + +then we can think about the +enthalpy of formation of six + +carbon dioxide molecules. + +And then we can go one step +further and think about the + +enthalpy of formation for +six water molecules. + +So this is just a round +about way of going + +from here to here. + +Instead we went up and then +down and then down, but + +because it's a state function, +we're absolutely + +allowed to do this. + +And to formalize this, we can +talk about what's called + +Hess's law. + +And Hess's law just tell us that +if we have two or three + +or any number of chemical +reactions that we can add + +together in order to get the +chemical equation that we're + +actually interested in, we can +figure out the change in + +enthalpy of that reaction that +we're interested in, just by + +adding together all of the other +enthalpies of reaction + +for every other reaction that +we had to add together in + +order to get there. + +So, let's take a look at what +we're talking about here. + +So when I just showed you that +example graphically, I'm just + +writing it out more like an +equation here, because the + +nice thing about Hess's law, +is it allows you to think + +about chemical reactions kind +of as if they're algebraic + +expressions. + +So we can just add all of these +different expressions + +together, and if we're thinking +about algebra, we can + +just think about crossing things +out that are in the + +reactants versus in +the products. + +So if we do this, what we end +up getting is the reaction + +that we're interested in, the +oxidation of glucose to form + +carbon dioxide in water. + +So let's look pretty carefully +at exactly the fact that these + +all cancel out to give us the +reaction I say we get. + +So, for example, we can think +about the oxygen molecules -- + +we can cancel out 6 here and 6 +here, as long as we multiply + +this whole reaction by 6. + +Again, we can get rid of those +last 3 oxygen molecules there. + +Similarly, we can cross out +our 6 hydrogens from the + +products with 6 molecular +hydrogens from the reactants. + +And then the last thing we can +cancel out are our carbon + +atoms -- we have 6 in the +products, and we have 6 in the + +reactants here. + +So you'll see that the only +things that are not canceled + +out is what's left in +our bottom reaction. + +So we can go ahead and just add +up all of these different + +reaction enthalpies. + +In the first case what we're +going to have is an enthalpy + +of 1260, and that's in + +kilojoules per mole of glucose. + +And the reason that this is +positive is because it's + +essentially the reverse reaction +of the change in + +enthalpy of formation. + +So it's going to be a positive +number there. + +We add to that the enthalpy for +this reaction here, which + +is negative 393 . + +5, but we need to remember to +multiply that by 6, because + +we're actually adding +together six of + +those individual reactions. + +And lastly, we also add together +six of this final + +reaction here, which has +an enthalpy change of + +negative 285 . + +8. + +So if we go ahead and just add +up all of our individual + +enthalpy changes, what we're +going to end up with for our + +entire reaction here, is a +change in enthalpy of negative + +2816, and that's kilojoules +per mole of glucose. + +Does anyone remember from +Wednesday's class, does this + +match what we had seen +experimentally? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Yeah, so this is +the exact number that we + +calculated when we used heats +of formation, and it's also + +the exact number that's seen +in terms of experimental. + +All right. + +So there's actually three ways +we now have to calculate heats + +of the change in enthalpy +of an overall reaction. + +So, we have these in our notes +from last time and from + +finishing the end of this unit +right now, but I'm just going + +to summarize them for you on the +board, because there are a + +couple things that can get +confusing that I want to make + +sure no one is confusing, +particularly in + +the upcoming exam. + +So what was the first way that +we learned to think about + +calculating enthalpies +of reaction? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Um-hmm. + +So, it's talking about +bond enthalpies. + +And when we talk about bond +enthalpy, the symbol that we + +see for a bond enthalpy +is usually delta h. + +And this is where all the +confusion starts, because + +everything's delta h, it just +depends on the subscript here, + +right, what kind of delta +h we're talking about. + +In the case of bond enthalpy +often you'll see no + +subscript at all. + +But sometimes you do see a +subscript, which would then + +just be delta h sub b here. + +So if we're trying to do this +calculation based on bond + +enthalpies, for the delta h for +an overall reaction, what + +we want to do is take the +sum of all of those bond + +enthalpies of our bonds that are +broken, and what we want + +to do is subtract from that +the sum of all our bond + +enthalpies of our bonds +that are formed. + +All right, so let's think a +little bit more about what + +this means. + +So, if we're talking about bonds +broken, are we talking + +about reactants or products? + +STUDENT: [INAUDIBLE] + +PROFESSOR: . + +Reactants. + +So, essentially we're summing +up the bond enthalpy of + +reactants and subtracting +it from the products. + +All right, great. + +So that's our first +strategy there. + +The second strategy that we +learned is thinking about bond + +enthalpies of reaction by using +the enthalpy change in + +terms of the enthalpy +of formation. + +So this one is sometimes a +little bit more intuitive, + +because we're talking about the +enthalpy change it takes + +in order to form a +given molecule. + +So, if we're trying to do a +calculation using enthalpies + +of formation, what we find is +that delta h of the reaction + +is equal to the sum of the +delta h of formation of + +products or reactants? + +STUDENT: Products. + +PROFESSOR: Products, good. + +Of products minus the delta h of +formation, and this is the + +sum again of reactants. + +All right, and our third +strategy is what we just + +talked about, which is Hess's +law, and in fact, both one and + +two are applications of Hess's +law -- specific applications, + +but any application of Hess's +law you can use any way of + +adding up different equations +to get the final enthalpy of + +the reaction. + +The reason I wanted to put these +two strategies, however, + +on the board right next to each +other, is so we can just + +confront a point of confusion +that happens a lot with + +students, which is why in the +first case do we have + +reactants minus product, and +in the second case we have + +products minus reactants. + +So, you need to keep these two +straight when you're doing + +your calculations in terms of +enthalpies, and the reason is + +because the definition of a +bond enthalpy when we're + +talking about bonds, is the +enthalpy that it takes in + +order to break the bond, the +amount of heat that goes in to + +breaking a bond. + +So it's typically a positive +number, because if you have a + +stable bond you have to +put heat into it in + +order to break it. + +So you end up having a positive +bond enthalpy here. + +In contrast, when we're talking +about enthalpies of + +formation, now we're talking +about is the change of + +enthalpy in order to +form a molecule. + +So, for example, if we have a +nice stable molecule with + +strong bonds in it, what we're +going to find is that the + +delta h of formation, would that +be positive or negative? + +So it's negative. + +So you'd end up with a negative +delta h of formation. + +So because you're talking about +a term that's negative + +here where it would be positive +in the first case, + +you end up flipping signs +to have it work out. + +So, if this doesn't make sense +as I'm saying it right now, + +just go back in your notes and +look through and make sure + +that you aren't going to get +mixed up when you're using + +bond enthalpies versus +enthalpies of formation here. + +All right, so that's pretty +much all we're + +going to say on enthalpy. + +So I really just want to stress, +this is going to be + +the end of exam 2 material +here, I said I'd be clear + +about it in class today. + +This is it. + +It's also written in +your notes when + +you go ahead to study. + +So remember, in terms of exam 2, +which I'll remind you is on + +Wednesday, it's going to be all +the way from the material + +on lecture 10 up to +this point here. + +So only through enthalpy, and +it's also going to be on + +problem-sets four and five, +and I'll mention that this + +afternoon, as I said, I'll post +a bunch of extra practice + +problems, which are more review +of these same concepts, + +so you can get even more +practice this weekend and + +early next week to prepare. + +All right, so that's enthalpy, +that's the + +end of exam 2 material. + +But there's actually another +really important concept that + +we need to talk about -- we +really don't want to stop with + +enthalpy, luckily it's exam 2 +and not the end of the class, + +because a really important +concept to think about is + +spontaneous change. + +So thinking about whether a +reaction is spontaneous or + +non-spontaneous. + +And when we think about a +spontaneous reaction, I think + +this is a term many of you are +familiar with, spontaneous + +just means that the reactions +going to proceed in the + +forward direction without any +kind of outside intervention. + +So thinking of a spontaneous +process, can talk about a + +chemical reaction, but you +could just picture, for + +example, putting a round rock +on the top of a hill -- it + +will spontaneously just roll +right down that hill. + +So a spontaneous process also +has direction, right, because + +the rock won't spontaneously +roll back up the hill without + +putting in work. + +So essentially we're talking +about a spontaneous process + +when something's going to happen +without actually having + +to do anything else to +force it to happen. + +So let's think about in terms +of chemistry what we're + +talking about is a spontaneous +reaction -- that's the + +specific type of spontaneous +process that + +we're interested in. + +So let's think about a few +different types of spontaneous + +reactions, and see if we can +come up with some idea of + +what's going to cause them +to be spontaneous. + +So one spontaneous reaction is +written here, so this is just + +the oxidation of iron, or the +formation of rust. This turns + +out to also be an exothermic +reaction, it has a negative + +delta h of 824 kilojoules +per mole. + +Another spontaneous reaction +is written here, the + +combination of an acid +and a base, which + +neutralizes each other. + +So we have a hydronium ion and a +hydroxide ion interacting to + +form water. + +This is spontaneous, and +again, it's exothermic. + +So, its delta h is +negative 55 . + +9 kilojoules per mole. + +Let's think about some +really relevant + +reactions in our bodies. + +So one incredibly important +reaction, of course, is ATP + +hydrolysis where we have +adenosine here, a + +triphosphate, so we have three +phosphate groups here. + +That's called ATP. + +It has a total charge +of minus four. + +So if we hydrolize this, one +of the phosphate bonds here + +and lose a phosphate, we end up +with adenosine diphosphate + +or ADP and that has a charge +of minus three. + +Yup? + +STUDENT: On our notes, this +equation [INAUDIBLE]. + +PROFESSOR: Oh, no. + +OK, thank you. + +Which equation are +we talking about? + +STUDENT: [INAUDIBLE] + +PROFESSOR: I'm sorry, what +page are you on? + +Page two. + +So the one with h 3 -- + +OK. + +All right, let's go +back to that. + +OK, so if you can fix this +reaction in your notes here. + +I'll also fix it on the website, +so if you don't want + +to fix it now I'll just +re-post the notes. + +So it should be four irons plus +three oxygens is two f e + +2 o 3 solid. + +Thanks for pointing that out. + +All right, does everyone +have that down? + +I know you had to flip +a page there. + +All right, so I'll post +it in the notes if you + +didn't get it there. + +Let's go back to ATP +hydrolysis here. + +So we're going from ATP to ADP, +and that is a spontaneous + +process, and it's an exothermic +reaction as well. + +So we find that it's negative +24 kilojoules per mole in + +terms of the change +in enthalpy there. + +All right, so at this point +I just showed you three + +reactions where we have +something that's spontaneous + +and it's also exothermic. + +And I could show you a countless +number of other + +reactions where it's +the same thing. + +It's actually quite common +if you have an exothermic + +reaction that it's also +spontaneous at room + +temperature. + +So we might start to draw the +conclusion that, in fact, it's + +enthalpy that's responsible for +whether or not a reaction + +is spontaneous or +non-spontaneous. + +So it's very easy to get that +impression, but let me show + +you a few more reactions +before we draw any + +conclusions. + +Let me show you some more +spontaneous reactions. + +So, for example, the conversion +of solid h 2 o to + +liquid h 2 o at room +temperature, I think we all + +know this is spontaneous. + +Ice melts at room temperature, +but it turns out that the + +enthalpy change is positive, +it's 7 kilojoules per mole. + +Similarly, if we look at this +reaction here, which is + +ammonium nitrate. + +This is a very commonly used +fertilizer, a very commonly + +used nitrogen source +in agriculture. + +If we think about solvating this +and forming the two ions, + +ammonium ion and nitrate ion. + +Again, this is a spontaneous +reaction, but what we find + +here is that delta h again +is positive, it's also + +endothermic. + +So thinking about all of this, +would you say that enthalpy is + +the key to spontaneity? + +STUDENT: No. + +PROFESSOR: No, it's definitely +not the key to spontaneity. + +It tends to correlate in many +cases at room temperature, but + +it is not the key +to spontaneity. + +And the key to spontaneity is +instead something called Gibbs + +free energy or delta g. + +And if we think about what delta +g is, we can relate it + +to enthalpy, and this will sort +of show us why there's + +often this correlation, because +delta g is equal delta + +h minus this term here, which +is temperature, and that's + +temperature times a +change in entropy. + +And we'll talk very in-depth +in just a few minutes about + +what entropy actually is, but +for now I just want you to + +think about the fact that in +addition to thinking about + +enthalpy there's this +other term here + +that comes into play. + +So when we're talking about what +the sign about delta g is + +or free energy is, some of you +might already be familiar with + +this, when we're talking about +a negative delta g, is this + +spontaneous or non-spontaneous. + +So, maybe not so familiar, +which is totally fine. + +So in terms of thinking about +a negative delta g, that's + +going to be a spontaneous +process. + +Any time you see a negative free +energy, which just like + +when we talk about entropy, it's +a similar idea, it means + +that free energy is released +as the reaction progresses. + +That's going to be a spontaneous +process. + +So that means that if delta g +is greater than zero, then + +what we're going to see a +non-spontaneous process. + +And finally in the case where +delta g is equal to zero, at + +this point we're at equilibrium, +which basically + +means that there's no net change +in either the forward + +or the reverse reaction in +terms of thinking about + +whether something's +spontaneous or not + +spontaneous, it's just +at equilibrium + +we see no net change. + +And something I want to point +out is that this reaction is + +valid only when where at +constant temperature and + +pressure, which we will be +throughout the discussions in + +this class in terms of +using this equation. + +And also, it turns out that +when you do most chemical + +equations, you are, in fact, +at a pretty constant + +temperature, and a constant +pressure in terms of most + +things are done in the open +atmosphere, so that's really + +not going to change. + +All right, so let's just talk +very briefly about why it is + +that free energy is what +determines spontaneity, and + +not this enthalpy here, +not what the + +change in enthalpy is. + +And it really comes in terms +remembering it in terms of the + +definition. + +When we think about delta g, +what that is is that it's + +energy that's released or used +in the reaction, but if it is + +released, that it can directly +be used to do work. + +It's what we call free +energy -- it's + +free to do other things. + +Whereas when we were talking +about enthalpy here, well, + +this is the amount of heat +that's released when we break + +and form the bonds +in the reaction. + +But some of it actually gets +stuck in the molecules, and + +this is just a way to think +about it, this term here is + +one way we can think about it, +it's just some energy that's + +getting stuck. + +So, for example, molecules, +which we don't really go into + +in this class, have vibrational +movements, they + +have rotational movements, +there's energy associated with + +that that can sort of get stuck, +as we could say, some + +of the enthalpy that's released +in terms of forming + +and breaking the bonds +in a reaction. + +So that's our case where we +could see that we have a + +negative delta h, but we +still end up with a + +positive delta g. + +And again, I haven't really gone +into what entropy is here + +yet, and we will just +in a few minutes. + +But first, I want to take a look +at one of the examples + +that we talked about, which is +the conversion of ammonium + +nitrate when its solvated, +breaking up into its ions. + +So what I had told you is +that, in fact, this is a + +positive delta h, but still +that the reaction is + +spontaneous. + +So let's just do this +calculation and see if we can + +confirm that in terms +of delta g. + +So the reaction again that we're +going to use is delta g + +equals delta h minus +t delta s. + +So if we're talking about room +temperature here, so we're + +going to say that delta g in +this case is going to be equal + +to 28 kilojoules per mole, +minus -- we're at room + +temperature or 298 kelvin -- in +this reaction, you always + +put temperature into kelvin. + +And then we need to multiply +it by the entropy, which is + +109 joules per kelvin mole. + +I want to point out that entropy +tends to be a much + +smaller value than enthalpy, +so it's reported in joules + +instead of kilojoules. + +When you solve these problems, +it's really important to + +convert it into kilojoules so +that your units work out and + +you don't get a completely +crazy answer. + +So we want to convert +this to 0 . + +109 kilojoules per +kelvin mole. + +So we can just re-write this, +so we have 28 kilojoules per + +mole, then this term +here will be 32 . + +5 kilojoules per mole. + +So what we end up with our delta +g for this reaction is + +going to be negative 4 +kilojoules per mole. + +All right, so talking about this +as a negative delta g, + +would you say this is +a spontaneous or + +non-spontaneous reaction. + +Yeah, it's spontaneous. + +So what we're going to see is +delta g is negative 4, so this + +reaction is spontaneous +even though our + +enthalpy change was positive. + +Let's take a look at one more +reaction since we spent so + +much time discussing the +oxidation of glucose. + +So again, what we know about +this reaction, we've already + +calculated the delta +h is negative 2816 + +kilojoules per mole. + +And you could look up and +we'll figure out how to + +calculate it soon, the change in +entropy, which is plus 233 + +joules per k mole. + +So before we actually do this +calculation, let's go to a + +clicker question and I want +you to think about what's + +happening here. + +So if you're thinking about the +oxidation of glucose and + +what the sign is of the change +in enthalpy and the change in + +entropy, which of these +statements is true. + +Is it going to be spontaneous +at all temperatures, + +non-spontaneous at all +temperatures, or will it + +depend on the temperature +whether this reaction is + +spontaneous or not +spontaneous? + +So, remember this is our +relationship here. + +So let's go ahead and just take +10 seconds on this one. + +OK, so we have a pretty +mixed response here. + +So this could have made or broke +the chances of your team + +on the competition today, but +they'll be a few more left to + +redeem yourselves if you +got it incorrect. + +So what we're going to find is +that it's spontaneous at all + +temperatures, and we can +actually just look at this + +equation here to figure +out why that is. + +If our reaction is spontaneous, +that means that + +delta g is negative. + +So in terms of delta h being +negative, well, that's going + +to always contribute to delta +g being negative no matter + +what the temperature is. + +And if delta s is positive, +since it's minus t delta s, + +and our temperature is always +positive because we're on the + +kelvin scale, so it starts +at zero there, then this + +component here is always going +to be negative as well. + +So we're always going to have +two negative numbers so that + +our combination, our delta g's +always going to be negative, + +it's always going to +be spontaneous. + +All right, so let's make sure +that's what we do see when we + +calculate this for the oxidation +of glucose here. + +So if we do this and we plug +in our numbers, we see that + +delta g is going to be equal +to negative 2816 times the + +temperature, room temperature, +times again, + +remember to put 0. + +233, because we need to +convert from joules to + +kilojoules for our +entropy term. + +So what we find out is that this +reaction has a delta g of + +negative 2885 kilojoules +per mole. + +This is a spontaneous +reaction. + +All right, so let's get back +to that entropy term. + +I introduced it without +explaining at all + +what it really is. + +So let's take a few moments +and think about entropy. + +Entropy is actually a very easy +concept to think about, + +it's a measure of disorder. + +I think most of us have a very +good concept of how things + +tend to go to disorder, so +it's something we can + +conceptualize just in an +infinite number of ways. + +And entropy is simply +a measure of the + +disorder of a system. + +And when we're talking about +chemical reactions, what we're + +talking about is a change +in entropy. + +So whether, as a reaction goes +forward, are we becoming more + +ordered or are we becoming +more disordered? + +So just like we saw for +enthalpy, entropy also is a + +state function, so it doesn't +matter in terms of path how we + +got from point a to point b. + +All we need to worry about is +the current state of our + +system, what the current +entropy is and take the + +difference. + +So, an example that I like to +use in terms of conceptually + +thinking about what's going on +in terms of disorder, and + +which is especially relevant +in New England is thinking + +about stone wall. + +So you can think about a stone +wall in terms of being very, + +very ordered, right. + +If you just built your stone +wall, every stone is in place, + +it has a high degree of order. + +So in other words, the +disorder is very low. + +So it has a low entropy, a +low level of disorder. + +But if we're looking at a New +England stone wall, which are + +typically found if you're hiking +in the woods you see + +ones that are just ancient and +are completely crumbling down, + +you'll find that the stone wall +is no longer quite so + +ordered as it was. + +In fact, let's say there's a +few stones that have fallen + +off, our disorder has increased, +so we end up + +increasing the entropy. + +And I do just want to point out +with this analogy that it + +is a state function. + +So for thinking about the change +in entropy, which is + +this distance right here, we +can either calculate it + +directly from here to here. but +it also doesn't matter, + +let's say the wall crumbled down +completely and we ended + +up having a very high degree of +disorder, if then someone + +put most of the stones back in +place and we went back down to + +this degree of disorder here, +it doesn't matter, it's a + +state function, all we care +about is the actual difference + +between our starting point +and our ending point. + +And I just can't resist putting +in a little quote, + +"something there is that doesn't +love a wall." Does + +anybody know where this quote +is from -- very famous poem, + +very famous poet. + +Good guesses, parents +can help with this. + +Yes, excellent. + +I've never heard the correct +answer this question before. + +Excellent. + +So this is Robert Frost +in The Mending Wall. + +He talks about, it sounds like +a lot of you did know this, + +this makes me full of joy. +"Something there is that + +doesn't love a wall," there's +many interpretations for this + +poem, but maybe it's +about entropy. + +Entropy doesn't love a wall, +we're going from order to + +disorder, that wall wants +to come down. + +All right. + +So let's formalize these +thoughts on entropy and in + +terms of what we're +talking about. + +Again, what I said on that's +chart there is as we increase + +entropy, we're increasing +disorder. + +So if you saw a positive +change in entropy in a + +reaction, would you think about +that as being more or + +less ordered? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Yeah, so it's +actually going to be less + +ordered, and, in fact, I should +stop saying order, I + +should be just saying disorder +because disorder's actually + +what we're measuring, and +there's an increase in + +disorder here when we have a +positive change in enthalpy. + +So if we have a negative change +in enthalpy, we're + +going to see a decrease +in disorder. + +So in terms of considering +different types of states that + +we can be in, whether we're in +a gas state or a liquid state + +or a solid state for any given +molecule or any given + +compound, we can think about +how much order or disorder + +these states have. So which of +these three states would you + +call the most disordered? + +STUDENT: Gas. + +PROFESSOR: Yeah, it's +the gas state. + +So it turns out that the +disorder gas is greater than + +liquid., which is greater +than solid. + +This makes sense and the gas +molecules are free to bounce + +around, go wherever they want. + +Once you're in a liquid, they +have a little bit more + +limitation, they can't +go anywhere. + +But the molecules can still +slide all around + +and pass each other. + +Once you're in a solid state, +this molecule is not going to + +flip places with the other +molecules there. + +It's going to be kind of stuck +in its place within the solid. + +So, just understanding this +explanation of entropy that + +we're going to have an increase +in entropy if we have + +an increase in disorder, allows +us to make predictions + +about reactions even without +doing any calculations, and we + +always like when that happens, +because then once we do + +calculations, we can check our +calculations and make sure + +they make sense with what +we would be predicting. + +So before we talk about how to +actually do a calculation, + +let's go to a clicker question +here and make sure everyone is + +on the same page in terms of +thinking about changes in + +entropy or changes or delta +s for the reaction. + +So let's say we're talking about +the decomposition of + +hydrogen peroxide into +water and oxygen. + +I want you to tell me if you +think it's going to have a + +positive delta s, a negative, +or zero, or maybe this will + +change with temperature +as well. + +All right, so let's go +ahead and take 10 + +seconds on this one. + +OK, excellent. + +Great job with the +questions today. + +So we are actually going to see +a positive delta s. this + +should be very clear because +we're going from two moles of + +liquid, to now having two moles +of liquid, plus a mole + +of gas, so we're going to be +increasing the disorder of our + +system here. + +All right, so let's think about +how we actually can + +calculate, though, delta s. + +So far I've just been giving +you the delta s's for the + +reactions, but, as I'm sure you +can guess, you won't be + +given that information, for +example, on upcoming + +problem-sets, you'll actually +need to calculate the entropy. + +So what we can do is we can +actually calculate the entropy + +of a reaction from absolute +entropies of individual + +molecules that we're +discussing. + +So this is very similar to how +we calculated the enthalpy of + +a reaction by taking the +change of enthalpy of + +formation, except we don't even +have to worry about a + +change in entropy because we can +talk about entropy as an + +absolute value. + +There's an absolute zero in +terms of entropy where there + +is no disorder at all. + +And this is described for any +molecule as being its perfect + +crystal at absolute zero. + +So this is what we're going to +say there's absolute complete + +order, there's no disorder +at all in this system. + +So what we can take to calculate +the entropy in a + +reaction, is just to take the +sum of the entropy of all the + +products, and subtract from that +the entropy from all of + +the reactants. + +So let's try this for the +example that you just did on + +the clicker question, and make +sure that our calculation + +matches up with our +prediction here. + +So again, we're just going to +take the sum of the entropy of + +the products minus out +of the reactants. + +So if we talk about this, +we're starting with our + +product, so our first +product is water. + +And what I want to point out is +you need to make sure you + +multiply this by 2, because, in +fact, we have two moles of + +water that are formed here. + +STUDENT: [INAUDIBLE] + +PROFESSOR: OK, I'm so sorry. + +Yeah, so yikes, this +should be water. + +You know what, let's just +write this on the board. + +So we're going to talk about +delta s of the reaction. + +So that's to be sum of the +entropy of the products. + +So we're going to be talking +about 2 times entropy of + +water, and we'll add to that +our other product, which is + +molecular oxygen here, and we +don't need to put a number out + +here because it's +just one mole. + +So that's of o 2, and we'll +subtract from that, the + +entropy of hydrogen +peroxide here. + +And do we need to put anything +out here for this? + +STUDENT: 2. + +PROFESSOR: So, yeah, because +there's two moles there. + +So water plus oxygen minus +hydrogen peroxide. + +Let's hope I at least got +the values right. + +Yeah, and actually I think this +is right, I believe this + +is the entropy of water. + +So OK, so the actual numbers +are right here for what is + +written on the board and +hopefully in your notes. + +So what we find out is that the +entropy of this reaction + +here, the change in entropy, the +delta s, is 125 joules per + +k per mole. + +All right, so we can also -- +well, first, we already + +thought about why delta +s is positive. + +Delta s is positive because +we're going from a liquid to a + +liquid and a gas -- we're +increasing our disorder. + +So let's think about whether +this reaction is spontaneous + +or not, and to do that, we +actually need to go ahead and + +completely calculate delta g. + +So to do this, we can take our +values here, and delta g is + +equal to delta h minus +t delta s. + +So if we plug all of this in, +we have our delta h is + +negative 196 kilojoules per +mole, minus our temperature, + +and I wanted you to write this +again, because I want to make + +sure you get in the habit of +converting our joules to + +kilojoules. + +It's 0 . + +125 kilojoules per +kelvin mole. + +So we end up with a delta +g of negative 233 + +kilojoules per mole. + +Is that spontaneous or +non-spontaneous? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Great. + +So the reaction here +is spontaneous. + +So actually, this is probably +a reaction that you're + +familiar with because a lot of +us do have hydrogen peroxide + +just in our medicine cabinet. + +And if you go and look at the +expiration date on your + +hydrogen peroxide, you +will see that it + +does, in fact, expire. + +And you might think oh no, what +happens when it expires, + +when it goes bad? + +All that's happening is it's +turning into water. + +So I wouldn't drink it after +its expiration date, but + +probably there's more +water than hydrogen + +peroxide at that point. + +But it also actually brings out +a really important point + +about thermodynamics, which is +that thermodynamics, in fact, + +tells us if a reaction happening +in the forward + +direction is spontaneous +or non-spontaneous. + +So, for example, we see +that yes, it is + +a spontaneous reaction. + +But you'll note that +thermodynamics tells us + +absolutely nothing about the +timeframe of that reaction. + +So some reactions that are +spontaneous take place in a + +matter of seconds or +microseconds or less. + +Other reactions, such as this, +to have an appreciable amount + +of that reaction go forward, +it actually takes years. + +You'll notice that it's not +just one day before that + +hydrogen peroxide expires. + +It's takes a really long time to +get a significant amount of + +this reaction to go. + +So just make sure, we will get +to talking about kinetics, + +which does tell us about the + +timeframe of chemical reactions. + +But don't confuse +thermochemistry or + +thermodynamics with kinetics. + +It doesn't matter how huge our +delta g is in terms of being + +if it's negative two or if it's +negative two million, + +that still doesn't tell +us how fast the + +reaction's going to go. + +All right. + +So let's think about one more +example here in terms of + +thinking about entropy. + +So another example we talked +about was the melting of ice + +at room temperature. + +I think all of us agree that +this is spontaneous, but that + +the enthalpy change +is positive, it's + +an endothermic reaction. + +So we can think about +calculating the entropy here, + +and I'm happy to see that I did, +in fact, put the products + +h 2 o here as a liquid, +subtracting the reactant, + +which is h 2 o as a solid. + +If we go ahead and plug in those +values here, what we end + +up with is a delta s of +this reaction of 28 . + +59 joules. + +This makes sense because we're +increasing the disorder of the + +system, we're seeing a positive +delta s here. + +And I just answered that +question for you. + +We're going why is +delta s positive? + +We're going from a +solid to liquid, + +we're increasing disorder. + +So, we can calculate delta g as +well, and if we do this we + +plug in these numbers here. + +What we end up with is that +delta g equals negative 1 . + +57 kilojoules per mole. + +So it is spontaneous, delta +g is just barely negative. + +And what actually is the case, +which we'll talk about more on + +Monday and thinking more and +more about how temperature + +actually affects these +reactions, but what we know + +about melting of ice is that +it is, in fact, temperature + +dependent, right. + +Ice doesn't melt at just +any old temperature. + +So that's where temperature +actually comes into play here. + +All right. + +So we have a case -- +spontaneous, even though delta + +h is positive. + +All right, so let's think also +about how we can go about + +calculating the free energy +of formation. + +So we know that we can use the +equation that we saw in terms + +of the free energy the reaction, +but what if we're + +actually thinking about the free +energy of the formation + +of a particular molecule? + +So that's actually completely +analogous to thinking about + +the enthalpy of formation, or +it's basically the standard + +Gibbs free energy +of formation. + +So this is talking about forming +a mole of a compound + +from its most stable elements, +from its elements in their + +most stable states at pressure +of one bar and at room + +temperature. + +So we know that we can tabulate +it must like we + +tabulated delta h formation, +but we can also tabulate it + +from this reaction here, which +it looks like I already told + +you this reaction, which I did +but I told you a more general + +form, which was for the free +energy of a reaction. + +This is the free energy of +a reaction, which is the + +formation of a certain compound, +and this is the free + +energy of formation equals +the enthalpy of formation + +minus t delta s. + +So let's think about why it is +important to be thinking about + +these changes of free energy +in terms of forming a + +molecule, and it's important +because the delta g + +information is actually a +measure of how stable or + +unstable a molecule is relative +to its element. + +So, for example, if something +is really stable relative to + +its elements, we can think +about whether delta g of + +formation should be negative +or positive. + +So let's have you do one last +clicker question here, and + +tell me what do you think, if +delta g of formation, of + +actually forming a molecule is +going to be negative, would + +you say that the compound is +going to be stable or unstable + +relative to the elements that +that compound is made up of? + +All right, let's take +10 seconds on this. + +OK, interesting. + +So this is going to be another +tie breaker for us. + +So let's go back to the notes +and think about this. + +So it turns out that it's going +to be stable, relative + +to its -- the compound +is stable + +relative to its elements. + +And the reason for this is if +you think of the reaction of + +the elements forming the +compound, if the delta g of + +that reaction is negative, +that means it's going to + +spontaneously form +the compound. + +It's going to go -- release +energy when it actually forms + +that compound. + +So that's another way of telling +us that the compound + +is more stable than +its elements. + +So conversely, if we have delta +g of formation being + +greater than zero, so delta g +of formation is just delta g + +of the reaction where the +compound is formed, then what + +we find is that it's +thermodynamically unstable + +relative to its elements, +because instead of releasing + +energy in that reaction, you +actually have to put energy + +into that reaction in order +to make it happen. + +So, delta g of formation can +give us an indication of + +whether we have a stable or +an unstable compound. \ No newline at end of file diff --git a/_CovlKXmuWo.txt b/_CovlKXmuWo.txt new file mode 100644 index 0000000000000000000000000000000000000000..8d8cfd1c19e6f6b4c727021bec142ae5ea27f4dc --- /dev/null +++ b/_CovlKXmuWo.txt @@ -0,0 +1,1323 @@ +OK. So today we're going to spend a little bit of time on some + +elementary chemistry just to develop our language that we use with one + +another. And so when I say hydrogen bond, you don't stare blankly at me + +and scratch your heads. Many of you have had this already. + +For many of you this is a review, but it's a useful review. + +We believe here at MIT of teaching things two or three times often, + +the same subject matter, but at increasing levels of sophistication. + +So I do this without apology. Our first issue here is how are + +atoms and molecules held together? And the most familiar way by which + +atoms and molecules are held together is, of course, + +the covalent bonds. And covalent bonds have an energy of roughly 80 + +kilocalories per mole. And that's a rather strong energy to + +hold together two atoms because the energy, the thermal energy, + +that is the energy at, let's say, body temperature is about 0.6 + +kilocalories per mole. And, therefore, if you had a bond, + +if there was something holding things together that was in this + +range or two or three or four times higher then the simple thermal + +energy at room temperature or at body temperature would be sufficient + +to break apart such a bond. But, in fact, this energy, + +the energy of a covalent bond is so much higher that it's highly + +unlikely that thermal energy is going to break apart a preexisting + +covalent bond. And I was just reading yesterday + +about how people were analyzing the mitochondrial DNA from some + +Neanderthal bones which were dug up. The last Neanderthal lived around + +30,000 years ago, our recently demised cousins. + +And they were analyzing the DNA sequences. And they got out of + +those analyses stretches of DNA that were 200, 300 nucleotides long. + +And that really is stunning testimonial to the fact that under + +very difficult conditions, nonetheless, complex biological + +molecules are able to survive over astounding periods of time, + +indeed those that are held together by the covalent bonds like this. + +Of course, you remember the film Jurassic Park where they used PCR + +reaction to resurrect the DNA of dinosaurs. That's a bit of a + +fantasy since dinosaurs left us, I guess, about 150 million years ago, + +something like that. There's a big difference, + +obviously, between 300,000 and 150 million year ago. + +Now, the fact is if you look at the way that molecules are actually + +hooked up, for instance, let's look at a water molecule here. + +Ideally there should be no charge on this molecule. + +And, in fact, there is no net charge. But the truth of the matter + +is, if one wants to get frank, that oxygen molecules, and we always + +are here, that oxygen molecules have a greater affinity for electrons + +than do hydrogen atoms, i.e., they are electronegative. + +And, therefore, what this means is that the swarms of electrons that + +are holding all this together at the orbitals are drawn more closely to + +the oxygen and the hydrogen atoms, i.e., the protons are relatively + +willing to give up their electrons. And what this means is that there's + +an unequal distribution. And, as a consequence, there is a + +fraction of a negative charge here at this end of the molecule and + +there are fractions of positive charges here because it's not as if + +they've totally given up the electrons, but the electrons are + +shifted more in this direction. And this molecule is therefore + +called a polar molecule by virtue of the fact that here it has a positive + +pole and here it has a negative pole. There are other pairs of molecules + +which are relatively equally electronegative. + +For example, here, if we have a carbon and a hydrogen, + +these two atoms are roughly equally matched in terms of their ability to + +pull electrons away, one from the other. And, + +as a consequence, there is no net shifting of charge. + +And keep in mind that this delta I show here is only a fraction of an + +electronic charge. It's not the entire electronic + +charge moved over. But this has important consequences + +for the entire biochemistry that we're about to get into both today + +and on Monday. Important because polar molecules, + +such as water like this, are able to dissolve certain compounds. + +And nonpolar molecules, which have large arrays of these kinds of bonds + +or carbon-carbon bonds, these are relatively insoluble in + +water, and that has important consequences for the organization of + +biological membranes. We might have a carbonyl bond here, + +that is a C going to an O via a double bond. And here we have, + +once again, a situation where the oxygen is far more avid in terms of + +its willingness and interest in pulling electrons toward itself. + +And, therefore, the carbon gives up a little bit of the electron cloud + +and it becomes slightly electropositive. + +Whereas, the oxygen atom becomes slightly electronegative. + +Now, the fact of the matter is that there are also other bonds that are + +noncovalent and are much less energetic. For example, + +let's talk for a moment about a hydrogen bond. + +And it's perhaps easiest to demonstrate a hydrogen bond by + +looking at the structure of two neighboring water molecules in a + +solution of water of all things. And, the fact of the matter is, + +let's say we draw one water molecule down here and one water molecule + +down here. What will happen is that this oxygen atom over here by virtue + +of its electronegativity will have a certain affinity for pulling this + +hydrogen atom toward itself. And, in fact, what actually happens + +in real life, whatever that is at the molecular level, + +is that this hydrogen atom may actually be bouncing back and forth + +between these two oxygens. It may be rapidly an interchange + +between them. This interchange causes a strong association between + +two neighboring water molecules. And, indeed, represents the reason + +why water does not vaporize at room temperature because the water + +molecules have a strong affinity or an avidity for one another. + +And, therefore, just to take some illustrations out of the book, + +this is the way it's illustrated in the book. + +Probably good to have a screen down. And here you can see the way that + +water molecules are actually arrayed in water. This is the lower + +illustration here. Just to indicate to you that the + +hydrogen atoms are not really the possession, the ownership of one + +molecule of water. They're just constantly being + +exchanged back and forth. And this back and forth exchange, + +this sharing of a hydrogen atom is what enables a hydrogen bond of + +roughly 5 kilocalories of energy per mole to hold things together. + +5 kilocalories is not much. It's only one order of magnitude + +above 0.6 rather than being two orders of magnitude. + +And, therefore, if one raises the temperature to the level of boiling, + +if the temperature is high enough, the thermal energy is high enough to + +rip apart these kinds of associations. + +Now, if we were to go back here to look at this carbonyl atom we would + +find the following sort of situation. Here we have this unequal sharing + +of electropositive and electronegative bonds. + +Let's put an acidic group like this. This is a carboxylic acid right + +here. Here we see a carbon bond to a hydroxyl here via + +this oxygen atom. Here, once again, + +we have an electronegative atom. And, in fact, if we talk about an + +ionized acid, normally in the absence of ionization there would be + +a net zero charge right here. But at neutral pH it may well be + +the case that the association, for various reasons, between this + +oxygen and this hydrogen will allow the hydrogen, or rather the proton, + +the nucleus of the hydrogen atom to just wander away. + +And, therefore, we can imagine there could be a net negative + +charge here. A whole, this has one full electron, + +electronegative charge here, the charge of one electron, + +and this proton will have ionized, will have left the carboxylic group + +in which it originated, and now we have an ionized acid + +group. Either before or even after this ionization, + +there is a strong affinity of the carboxyl group with the water around + +it because let's look at what happened before the ionization + +occurred. This carbon here is strong and + +electronegative. And, therefore, it will participate + +in hydrogen bonding to the water solvent here, i. + +., this proton will be shared a bit between the oxygen of the water + +molecule and the oxygen right here. Similarly, here this oxygen will be + +slightly electronegative for the reasons I've just described. + +And here, once again, there may be some weak hydrogen bonding going on. + +Although, not as effective as over here where we have a double-bond + +where we have a lot of concentration of a cloud of electrons pulled + +towards the oxygen atom. And this begins to give us clues as + +to why certain molecules are soluble in water and others are insoluble. + +For example, if we look at aliphatic compounds. + +Let's look at a compound that's structured like this. + + I guess most people would call this + +pentane. And we can call it that, too. And this has no + +electronegativity or positivity by virtue of the equal affinities of + +these two kinds of atoms, that is the hydrogen and the carbons + +for electrons. And as a consequence, + +this will not be able to form any hydrogen bonds with a solvent around + +it if the solvent happens to be water. + +So there's not good bonding here. And this will, in fact, also if one + +puts this in a solution of water, this will cause all the water + +molecules to line up in a certain way, almost a quasi-crystal around + +the aliphatic molecule. They'll be ordered in a certain + +layer around the aliphatic molecule without being able to form any + +strong hydrogen bonds with them. And this ordering represents a loss + +of chaos, a loss of entropy. Entropy is chaos. It's disorder. + +It's what happens, let's say, at 10:55 when we all leave the room, + +all of a sudden order becomes chaotic. And here, + +before this lining up occurred, the water molecules were chaotically + +arrayed throughout the solvent. After this lining up occurred there + +was a loss of entropy, there was a loss of chaos. + +And thermodynamics tells us that generally the ordering of molecules + +is disfavored. And consequently we now have two + +reasons why this molecule doesn't like to be in the midst of water. + +First of all, it's unable to form hydrogen bonds with the solvent. + +And second of all there is a decrease in the entropy, + +in the chaos that occurs when this molecule directly confronts water. + +And because of those two reasons it turns out that this molecule doesn't + +like to be in water. The aliphatic molecule, + +as one would call this in organic chemistry, doesn't like to be in + +water. And a dislike of water is often called its hydrophobicity, + +or we often call it hydro, might as well spell it right, + +hydrophobic, i.e., it really hates to be in water. + +In fact, class, there's a second meaning for + +hydrophobia, or hydrophobic has a second meaning. + +Every five years I ask a class to see who knows what the second + +meaning of hydrophobia is. This is really obscure. Sorry? + +Rabies, right. The TAs aren't allowed to answer that. + +If somebody has rabies, at one stage of rabies, almost near + +the terminal stage, the individual becomes hydrophobic + +because he or she doesn't like to drink water, for reasons that are + +obscure at least to me. Now, conversely, + +molecules that have carboxyl group on it would be called hydrophilic. + +And, as we'll see over this lecture and the next one, + +these hydrophobic and hydrophilic tendencies tend to have great + +affects on the overall behavior of molecules. Let's, + +for example, imagine a situation where we have a long aliphatic tail + +like this. In fact, these tails can go on in certain + +aliphatic compounds. They can go on for 20 or even 30 + +carbons. And at the end of this, let's just put arbitrarily a + +carboxyl group. And let's say we ionized it. + +So here's an acidic group that's ionized. It's shed its proton. + +It's actually acquired a negative charge. And now we have something, + +this molecule is a bit schizoid. Because on one end of it, + +it loves to be in water, the other end of it hates to be in water. + +And this has strong affects. It's sometimes called amphipathic, + +but we don't need to worry about that word. And, + +therefore, this carboxyl head loves to stick its head, + +to immerse its head in water. And these things, the aliphatic + +portion hates to be in water. Now, as a consequence of these + +rather conflicted feelings that these molecules have about water, + +we can ask the question what happens when we put such molecules + +actually into water? And what we see here is the + +following. That if we were to construct, for example, + +a molecule of the sort that has here, in this case we're talking about a + +molecule that has two hydrophobic tails. We'll get into its detailed + +structure shortly, but just imagine for a moment two + +long hydrophobic tails out here ended with a hydrophilic head. + +And under such situations, if we put thousands of these or + +millions of these molecules into a solution of water, + +what we will then see is, no pointer? All right. Pointer? + +All right. What we will then see is that the hydrophilic head groups, + +which are here depicted in red, will point their way outwards, + +they will want to stick their heads in water. + +And conversely the hydrophobic tails fleeing from the water will actually + +associate one with the other. And so you have a structure that's + +called, in this case, an a micelle where you form this + +little globular sphere where the lipid tails are tucked inside. + +And, therefore, are actually being shielded from any direct exposure to + +water. This structure down here, the lipid bilayer, is actually, as + +we will discuss in greater detail shortly, the overall topology of the + +way most biological membranes are organized. + +In fact, virtually all of them. Why is that? Because biological + +membranes separate two hydrophilic or two aqueous spaces. + +Thank you, sir. A gentleman you are. So here is an aqueous space + +and here is an aqueous space. And as we see the hydrophilic heads + +are immersed or sticking their heads into the hydrophilic space. + +This is called a lipid bilayer. And, obviously, it's highly + +effective for separately these two aqueous compartments. + +In eukaryotic cells, as I mentioned last time, there is an enormous + +premium placed on separating and segregating different aqueous + +compartments which is invariably achieved through the device of + +constructing these lipid bilayers. Here's a vesicle. A vesicle is + +more complicated than a micelle. Because if you look at the membrane + +lining the vesicle, you see it's actually a lipid + +bilayer, but one that in 3-dimensional space is actually a + +sphere. And in the case of this vesicle, we can well imagine that on + +the inside of the vesicle water is kept, can be stored, + +and on the outside of the vesicle water can be stored. + +And many of the membranes that we see within the cytoplasms themselves + +are actually constructed on this kind of design. + +So when we draw, for example, in this case the Golgi + +apparatus, which I mentioned to you in passing last time we met, + +each one of these membranes here, it's obviously drawn as a double + +line, but whenever you see a membrane indicated, + +implicit in that drawing is the fact that each one of these membranes is + +actually a bilayer. There are never any monolayers of + +lipids in living cells. Each one of these vesicles you see + +here is actually a lipid bilayer with an aqueous inside and, + +once again, aqueous on the outside. Again, much of the thermodynamic + +stability that allows these vesicles to remain intact rather than just + +diffuse apart is created by these hydrophilic and hydrophobic forces + +which tie such molecules together or will rip them apart. + +Now, in truth there are yet other kinds of forces that govern the + +affinity of molecules to one another. For example, let's imagine a + +situation where we have an ionized acid group of the sort we just + +talked about before. Now, by the way, + +here, let's say I'll draw the negative charge on one of these two + +oxygens, if you can see that. But the truth is that the electrons + +are swarming back and forth, and so the negative charge is shared + +equally, the negative one electron charge is shared equally between + +these two oxygen atoms. And this is obviously an area of + +great electronegativity. Independent of that, + +let's imagine up here we have a basic group, let's say an amine + +group over here. And, the fact of the matter is, + +amine groups, NH2 groups, that's what an amine is, + +here's an amine group. This is a carboxylic group. + +And the amine group, which is used very often in biochemistry, + +actually has an affinity. It has an unpaired set of electrons on the + +nitrogen, and so it likes to attract protons to it, + +which makes it, causes it to be called basic. + +And this attraction, the scavenging of protons, + +perhaps from the water, will obviously give this whole group here + +a net positive charge, a charge equal to the charge of one + +proton. Here, once again, we can imagine this is + +hydrophilic because this charge group can once again also associate + +quite intimately with aqueous solvent. + +Now, independent of any other forces that might exist here, + +indeed one could imagine situations where there is a sharing of a proton. + +And, therefore, a hydrogen bond formed between these + +two. Independent of that is the simple electrostatic interaction of + +these two groups. That is the mutual attraction of + +positive and negative groups, one to the other. And the + +electrostatic interactions, you cannot quantify exactly how many + +kilocalories a mole there is because the energetic value in electrostatic + +interaction is equal to one over r squared where r is the distance + +between these two charged groups. And obviously the further apart you + +get the weaker the attraction with one another. There are also what + +are called van der Walls interactions. There are largely of + +interest to a very small community of biochemists. + +You probably will never, you may never hear this term again + +in your life. And van der Waals interactions come + +from the fact that if we were to have, for example, + +two molecules over here which are not normally charged in any way, + +let's just talk about two aliphatic chains again. And I won't put in + +all the protons and everything, but just imagine a situation like + +this. What will happen is that because of the fluctuations of + +electrons, because the electrons are swimming around here all the time, + +moving from one area to the next they're never equally distributed + +homogenously over a long period of time, there will be brief instance + +in time, microseconds or even nanoseconds when there happens to be + +more electrons over here than right here. + +Just by chance. And this area of unequal + +distribution of electrons will in turn induce the opposite kind of + +electron shift in a neighboring molecule down here. + +Obviously, depending on the distance between them. + +But the negative here will repel electrons down here. + +The positive here will attract electrons down here. + +And so you will have these two quasi-polar arrangements here and + +here, very ephemeral, that is lasting for a very short + +transient period of time. But, nonetheless, sufficient to + +give a very weak interaction between these two molecules which may + +persist only for a microsecond and then be dissipated because the + +charges then redistributed once again. + +And, as a consequence of that, one has very weak interactions which, + +in the great scheme of things, play only a very minor role in the + +overall energy which holds molecules together. Now, + +with that background in mind, let's begin to elaborate on it, + +on how we can make molecules that have interesting properties that + +enable them, among other things, to participate in the construction + +of lipid bilayers, which will be the first object of + +our attentions today in terms of actual biochemistry. + +So here's a fatty acid. We see that up here. I, + +in effect, drew you the structure of a fatty acid up here already once + +before. And what we can see is through a linkage known as + +esterification we can create this molecule. So what do I + +mean by esterification? Well, in this case we're talking + +about a situation here where we have a carbon atom over here like this + +with a hydroxyl group. You see it over here. And what + +we're doing is we're dehydrating this, we're pulling out one net + +molecule of water. And each time we do that, + +on three separate occasions, what we end up doing is to create + +instead of this is to create a covalent bond between these two. + +And so the end product of dehydrating this, + +pulling out one net molecule of water is that we end up with a + +structure that looks like this. + +And you see that happening on at least three different occasions, + +here, here and here. Well, actually, I should put a carbon over here. + +So here we have three esterifications. + +The hydroxyl group in each case is reacting with a carboxyl group here + +pulling out one water, and each case creating what's called + +triacylglyercol or triglyceride. Triglyceride refers to the fact + +that we started here with a glycerol and we have now esterified it. + +Now, in fact, there are two directions here in this + +kind of reaction. Esterification is the kind of + +linkage that we just showed here. And the truth is that vast numbers + +of biochemical linkages are made by esterification reactions and + +reversed by reactions that are called simply hydrolysis. + +And, in this case, what we're referring to is the fact that if one + +were to reintroduce a water molecule into each of these three linkages, + +one, two and three, we would break the bond and cause this entire + +structure to revert to the two precursors that existed or + +preexisted prior to these three esterification reactions. + +And time and again you'll see, over the next weeks, that + +esterification reactions are important for constructing different + +kinds of molecules. Now, the fact of the matter is we + +can do other kinds of modifications of a glycerol like this. + +Here what we've done, instead of adding a third fatty acid, + +note what was done here. Here through an esterification, + +let's look up at this one here, instead of adding a third fatty acid, + +we've saved, we've reserved one of the three groups of the glycerol. + +Here's what we saw just before. We've saved one of the three groups + +of the glycerol and put on instead this highly hydrophilic phosphate + +group, once again through a dehydration reaction, an + +esterification reaction. And now what we've done is add + +insult to injury because in the absence of this phosphate it would + +have a hydroxyl here which is mildly hydrophilic. But now look how + +strongly charged this is. Here are two negative charges, + +one electron each. And this is already a bit electronegative. + +So here we have an extremely potent hydrophilic entity. + +And here the degree of schizophrenia between one end of the + +molecule and the other is greatly exaggerated. Here, + +in fact, this is extremely hydrophilic. + +And, as a consequence of that, this really likes to stick its head + +inside water. And when we therefore talk about, we draw the images of + +different kinds of membranes, like this I showed you before the + +two tails. Here you saw the two tails I drew before in that diagram. + +Here's what we can imagine they actually look like in more real + +molecular terms. And the hydrophilic heads sticking + +in the water, this is just repeating what we saw before, + +become even more hydrophilic if we look at a molecule like this. + +Let's look at this thing here. Here's a very long hydrophobic tail. + +Here are the two glycerols once again. Here is the phosphate. + +And keep in mind that phosphate obviously has these extra oxygens. + +Phosphate can react with more than just one partner, + +the glycerol down here. In this case we've added this group + +up here. And this group up here is, once again, this happens to be a + +serine which is an amino acid, this also happens to be quite + +hydrophilic. Here's our old friend the basic + +amino group. Here's the carboxyl group. This is a bit hydrophobic, + +CH2. And then we once again have the hydrophilic head here. + +And, therefore, we imagine, if we look at what's called a + +space-filling model, and a space-filling model really is + +intended to show us what one imagines if one had this vision, + +which we don't have, how much space each of these atoms would actually + +take up if one were able to see them. + +And here we see this space filling model. This lipid molecule here is + +actually slightly kinked with its hydrophilic head tucked into the + +water space. And so here's actually the way that many biological + +membranes look in terms of the way that they are constructed. + +Now, the fact of the matter is this also affords the cell the ability to + +segregate contents on one or the other side of whatever lipid bilayer + +it happens to have constructed. And here we can see about the + +semi-permeability, how permeable these membranes are to + +different kinds of molecules. Permeability obviously refers to + +the ability of this membrane to obstruct or to allow the migration + +of molecules from one side to the other. + +Ions, and these ions we see right here are obviously highly + +hydrophilic by virtue of their charge. That's explains, + +in fact, why, for example, table salt goes so readily into + +solution, because it readily ionizes into sodium, NA and CL, + +which then are avidly taken up by the water molecules. + +So these are highly hydrophilic ions. And the questions is, + +can they go from one side of the membrane to the other? + +And the answer is absolutely not or highly improbably. Why? + +Because these are so highly hydrophilic, the water molecules + +love to gather around them and form hydrogen bonds and electrostatic + +bonds with them. And if one of these ions ventures + +over here, it's going from an area where it's warmly embraced by the + +solvent molecules to an area where these molecules intensely dislike + +these ions. And, therefore, thermodynamically the + +entrance of any one of these ions into the membrane, + +into the hydrophobic portion of the membrane is highly disfavored, + +which makes the membrane essentially, for all practical purposes, + +impermeable. The same can be said of glucose + +which happens to be a carbohydrate. We'll talk about it shortly. But + +it's also nicely hydrophilic. It also can go in water. In fact, + +it can go through. And it's actually the case, + +to my knowledge, that one doesn't really understand to this day why + +lipid bilayers are reasonably permeable to water. + +You would say, well, water shouldn't be able to go + +through. It clearly doesn't have to have a + +net positive or negative charge, but the physical chemist, if you + +asked them why does water, why is water able to go through + +lipid bilayers? They'll say, well, + +we've been working on that and we'll get you an answer in the next five + +or ten years. And they said that 40 years ago and 30 years ago, + +and they're still saying it. And we don't really understand why + +water goes through, which is an embarrassment because + +here's one of the fundamental biochemical properties of living + +matter that is poorly understood. Gases can go right through. + +And amino acids, ATP, glucose 6 phosphate, + +highly hydrophilic, can also not go through. Now, + +the advantage of this is that a cell can accumulate large concentrations + +of these molecules either on the inside or it can pump them to the + +outside. In other words, it can create great gradients in the + +concentrations of different kinds of ions. For example, + +in many cells, the concentration of calcium, CA++ is a thousand times + +higher on the outside of the cell than on the inside of the cell which + +is a testimonial to how impermeable these lipid bilayer membranes are. + +The fact of the matter is I'm fudging a little bit here because in + +the lipid bilayers of the plasma membrane of the cell, + +the outer membrane of the cell that we talked about in passing last time, + +there are ion pumps which are constantly working away pumping ions + +from one side to the other overcomes the little bit of leakage which may + +have occurred if a calcium ion happens to have snuck through in one + +direction or the other. And we end up expending a lot of + +energy to keep these ion gradients in appropriate concentrations on the + +outside and the inside. In fact, virtually all the energy + +that is expended in our brain, almost all of it is expended to + +power the ion pumps which are constantly insuring that the + +concentrations of certain ions on the outside and the inside of + +neurons are kept at their proper respective levels. + +It could therefore be that actually more than half of our metabolic + +burden every day is expended just keeping the ions segregated on the + +outside and inside of cells. For example, potassium is at high + +levels inside cells, sodium is at high levels outside + +cells, just to site some arbitrary examples. There are also, + +by the way, as I mentioned last time, channels. + +And channels are actually just little doughnut shaped objects which + +are placed, inserted into lipid bilayers in the plasma membranes and + +just allow for the passive diffusion of an ion through them, + +through the doughnut hole enabling an ion, so if here's the lipid + +bilayer, not showing its two things, these kinds of doughnut shaped + +protein aggregates will allow the passage of ions in one + +direction or another. And here energy is not being + +expended to enable this passage. It may just be through diffusion. + +If there's a higher concentration of ion on side of the lipid bilayer + +and a lower one on this side, this diffusion will allow the ion to + +migrate through the bore of the ion channel from one side to the other. + +In fact, even though this does not involve the expenditure of energy on + +the part of the cell, the cell may actually use a gating + +mechanism to open or close these channels. + +When the channels are closed then the ions cannot move through. + +When the channels are gated open then diffusion can take over and + +insure the transfer, the transportation of ions from one + +side to the other. Now, having said that, + +we can begin to look at yet other higher level structures. + +Here, by the way, is a better drawing than the one I provided you. + +This comes from your book of what a vesicle looks like. + +Here's what it looks like under the electron microscope and here's what + +it looks like when a talented rather than hapless and hopeless artist + +like myself tries to draw it. So let's just say that's our intro + +into lipids and membranes. And let's move onto the next layer + +of complexity. And the next layer of complexity in + +terms of molecules represents carbohydrates. + +And when we talk about a carbohydrate amongst ourselves we're + +talking about a molecule which, roughly speaking, has one carbon + +atom for every water molecule. And we'll shortly indulge ourselves + +in talking about all kinds of different carbohydrate molecules. + +Here is really one of the most important carbohydrate molecules, + +glucose. And what should we note about glucose? + +Well, the first thing you should see is that glucose has six carbon + +atoms. And, therefore, as a consequence it's called a + +hexose. We're going to talk about pentoses + +very shortly. They only have five, to state the obvious. Glycerol, + +which we talked about before, is also considered in one sense a + +carbohydrate, but it's been called by some people a triose. + +It only has three carbon atoms. And you can imagine, therefore, in + +principal that there are certain biochemical mechanisms which indeed + +exist which enable one to join two glycerol molecules, + +one to the other, to create something like a hexose, glucose. + +In fact, what we see from this drawing, expertly drawn by yours + +truly, is that the hexose molecule isn't really a linear molecule in + +solution. What happens is that because of various steric and + +thermodynamic forces it likes to cyclize. So let me just mention, + +I've just used two words that are useful to know about. + +Steric or stereochemistry refers to the 3-dimensional structure of a + +molecule. And, obviously, the stereochemistry of a + +molecule is dictated by the flexibility with which participating + +atoms can form bonds, whether we have a trivalent atom + +like nitrogen or a tetravalent atom like carbon or a monovalent + +like hydrogen. And these structures, + +the stereochemistry is dictated both by what atoms are present here and + +by thermodynamic considerations which cause this particular hexose, + +indeed virtually all hexoses, to cyclize. When I say cyclize, + +obviously I mean to form a circular structure. Here we note one thing. + +You can see how the hydroxyl here actually attacks the positively + +charged carbon here in order to form this cyclic structure. + +You see one of the six points on this hexagonal structure here is + +oxygen. It's not carbon at all. So there is one oxygen and five + +carbons. And one of the carbons is relegated, is exiled to outside of + +the circle. It's sometimes called an extracyclic because it's sticking + +out from the actual circle. And this is the structure in which + +glucose actually exists inside cells. And, in fact, + +there is, in truth, two alternative ways by which + +glucose can cyclize, whether the oxygen attacks the + +carbon on the carbonyl group underneath or on top. + +And you see that gives us two alternative structures. + +What's different about them? Well, if we think about this hexose + +as existing in a plane, or the hexagon is in a plane + +In this case the oxygen is above the plane and the hydrogen is below the + +plane. With equal probability you can have these two atoms reversed + +where hydrogen is now above the plane and hydroxyl is below the + +plane. And both of these structures, these alternative structures can + +fairly be considered to be glucose. Now, let's get a little bit more + +complicated. Here we have fructose and we have galactose. + +And what we see here is, by the way, that we have exactly the + +same number of carbon atoms and hydrogen atoms and oxygen atoms but + +they're hooked up slightly differently. And here now we begin + +to get very picky about the disposition, the orientation of + +these different kinds of hydroxyls and hydrogens. + +And note, by the way, here that in many cases one doesn't + +even put in the H for the hydrogen. It's just implied by the end of + +this line. And here, if you were to look at + +this, you'll see here now we have two extra cyclic carbons. + +Here's galactose which is yet another hexose. + +These are all hexoses, but their stereochemistry creates + +quite different kinds of structures. And it turns out that this + +stereochemistry is extremely important. These molecules function + +very differently, one from the other. + +And, for example, to the extent that glucose is used + +in different kinds of energy metabolism and to the extent that + +galactose is not, there must be certain biochemical + +mechanisms in which one has catalysts, the catalysts that we + +call enzymes that ensure that one can convert one of these hexoses + +through an enzyme into, let's say a less useful one into a + +more useful one, glucose, which can readily be burnt + +up by the energy-generating machinery. Here we've gone yet + +another order of magnitude more complex because we've gone from a + +monosaccharide, i.e., one or another hexose, + +to a disaccharide. And here's common table sugar. + +And here you see that it's formed once again through an esterification + +reaction, i.e. there is a dehydration reaction + +between this hydroxyl here and this hydroxyl here. + +And biochemists take the orientation of these hydroxyl and + +hydrogen groups very seriously. Now, you can say they're a bit + +obsessive. Indeed they probably are. + +But, nonetheless, we can admit that the specific + +orientations of all these things dictate very importantly the + +difference between here, in this case sucrose, and in this + +case lactose. Why is this important? Well, this is the sugar in milk + +sugar. This is the dominant sugar in milk sugar, + +lactose. And half the world, as adults, cannot absorb this. + +All kinds of unpleasant things happen when they actually + +drink milk. How many people here are lactose + +intolerant? It's nothing to be ashamed of. I'm married to a very + +lactose intolerant person. She's otherwise very nice. + +The fact is that the enzyme to break down lactose, + +it's an enzyme which is called lactase. And here we have yet + +another nomenclature item. So lactase is the enzyme which + +breaks down lactose. And, by the way, + +this is just the harbinger of many other enzymes we're going to talk + +about in the future that end in A-S-E. Whereas, + +carbohydrates, many of them end in O-S-E, as you've already sensed. + +So it turns out that the enzyme lactase is made in large amounts by + +most mammals very early in life. Why? To be able to breakdown the + +milk sugar that comes in their mother's milk. + +But once mammals are weaned there's no reason on earth for them to + +continue to make lactase, in their stomach for example. + +And, as a consequence, in most mammals the production of lactase is + +shut down later in life. And for some weird quirk of human + +history, a significant proportion of humanity has learned how to retain + +the ability to make lactose through adulthood. And, + +as a consequence, people can go and have ice cream + +until the age of 70, 80 or 90 without becoming very + +bloated. And we don't need to get into all + +the details, but you can begin to imagine. And what happens is, + +therefore, the lactase enzyme is shut down in their stomach. + +It depends. Sometimes they lose it at the age of 10 or 15 or 20. + +And then, for the rest of their lives, whenever they have a milk + +containing product, in fact, my son is also lactose + +intolerant. I'm surrounded by these people. Again, + +he is otherwise a tolerant person but he's lactose intolerant. + +So this lactose molecule will go into the stomach, + +it will remain undigested, it will remain a disaccharide + +instead of being cleaved into two monosaccharides. + +The two monosaccharides are no problem because they can readily be + +interconverted. The galactose can be readily + +converted into glucose, and glucose is the universal + +currency of carbohydrate energy. And so this disaccharide passes + +through the stomach unaltered and it gets into the intestines, + +in the small intestine and the large intestine. + +And it turns out we have more bacterial cells in our gut than we + +have our own cells in the rest of the body. Imagine that. + +And there are a lot of bacteria that are waiting around in the gut + +for just a little gulp of lactose. And they never get it because most + +people break down their lactose long before it gets into the intestine. + +But here we have these lactose intolerant people. + +The disaccharide gets into the gut and the bacteria go to town. + +They've been waiting around for years, decades for a little bit of + +lactose. And now it finally arrives and they go to town, + +ad they start metabolizing it and they ferment and they produce lots + +of gas and other kinds of byproducts. And, as a consequence, + +this makes people very uncomfortable. Just to show you, + +now, the fact is that lactose intolerance people can perfectly + +well break down sucrose, obviously. This is one of the great + +energy sources from plants. But they cannot break this down. + +And I emphasize that point to indicate that the stereochemical + +differences between different kinds of carbohydrates makes a very + +important difference. An enzyme like sucrase will break + +down the sucrose but it will not touch lactose. + +So there's a high degree of stereospecificity as it's called in + +the trade. Here we now go to another step forward that we're + +going to pursue in much greater detail next time. + +Because here, for the first time, we talk about polymerization. We're + +making polymers. Where the large number of hydroxyl + +groups on these monosaccharides affords one many opportunities to + +make very long linear aggregates end-to-end like this or even side + +branches. If you imagine that each one of these hydroxyls, + +in principle, represents a site for possible esterification, + +i.e., the formation of a bond to a neighboring side chain. + +Here we see these two linear chains and here we see the branch which is + +afforded, which is made possible by the availability of these unutilized + +hydroxyl side chains which are just waiting around to participate, + +if the opportunity allows them, in some kind of esterification + +reaction to form a covalent bond. Here is, by the way, glycogen, + +which is the way we store a lot of sugar in our liver. + +Here's a starch, which is what we get from many + +plants. And here's another very interesting polysaccharide. + +It's called cellulose. And we cannot digest cellulose, + +but termites can. And why they can is something we'll have to wait + +until next time to learn about. Have a great weekend. See you on + +Monday. \ No newline at end of file diff --git a/_HpMRwM6tAQ.txt b/_HpMRwM6tAQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..32154f2a2f8f165e80926839292b76e21ce32b42 --- /dev/null +++ b/_HpMRwM6tAQ.txt @@ -0,0 +1,2219 @@ +align:start position:0% + +first about issues of cost-benefit + + align:start position:0% +first about issues of cost-benefit + + + align:start position:0% +first about issues of cost-benefit +analysis if we're doing it and then come + + align:start position:0% +analysis if we're doing it and then come + + + align:start position:0% +analysis if we're doing it and then come +back to the issues that Lee outlined + + align:start position:0% +back to the issues that Lee outlined + + + align:start position:0% +back to the issues that Lee outlined +about what's wrong with cost-benefit + + align:start position:0% +about what's wrong with cost-benefit + + + align:start position:0% +about what's wrong with cost-benefit +analysis because it's whether or not you + + align:start position:0% +analysis because it's whether or not you + + + align:start position:0% +analysis because it's whether or not you +believe something that's wrong that many + + align:start position:0% +believe something that's wrong that many + + + align:start position:0% +believe something that's wrong that many +decisions are made with it so but first + + align:start position:0% +decisions are made with it so but first + + + align:start position:0% +decisions are made with it so but first +of all I'm impressed + + align:start position:0% +of all I'm impressed + + + align:start position:0% +of all I'm impressed +at what everyone has done here and + + align:start position:0% +at what everyone has done here and + + + align:start position:0% +at what everyone has done here and +particularly people doing this level of + + align:start position:0% +particularly people doing this level of + + + align:start position:0% +particularly people doing this level of +presentation Cole and level of + + align:start position:0% +presentation Cole and level of + + + align:start position:0% +presentation Cole and level of +impersonation of participants in the + + align:start position:0% +impersonation of participants in the + + + align:start position:0% +impersonation of participants in the +faith very impressive + + align:start position:0% + + + + align:start position:0% + +you seem to have grasped most of the + + align:start position:0% +you seem to have grasped most of the + + + align:start position:0% +you seem to have grasped most of the +things that I would end up talking about + + align:start position:0% +things that I would end up talking about + + + align:start position:0% +things that I would end up talking about +in cost-benefit analysis and it initial + + align:start position:0% +in cost-benefit analysis and it initial + + + align:start position:0% +in cost-benefit analysis and it initial +discussion let me try to move on to some + + align:start position:0% +discussion let me try to move on to some + + + align:start position:0% +discussion let me try to move on to some +of the more difficult or advanced issues + + align:start position:0% +of the more difficult or advanced issues + + + align:start position:0% +of the more difficult or advanced issues +that I think are touched on indirectly + + align:start position:0% +that I think are touched on indirectly + + + align:start position:0% +that I think are touched on indirectly +the first speaker mentioned their + + align:start position:0% +the first speaker mentioned their + + + align:start position:0% +the first speaker mentioned their +willingness to pay or willingness to + + align:start position:0% +willingness to pay or willingness to + + + align:start position:0% +willingness to pay or willingness to +accept this is a distinction that sounds + + align:start position:0% +accept this is a distinction that sounds + + + align:start position:0% +accept this is a distinction that sounds +almost the same they turn out to be + + align:start position:0% +almost the same they turn out to be + + + align:start position:0% +almost the same they turn out to be +extremely different in practice and + + align:start position:0% +extremely different in practice and + + + align:start position:0% +extremely different in practice and +economists who have written about + + align:start position:0% +economists who have written about + + + align:start position:0% +economists who have written about +methods have pretty much come to a + + align:start position:0% +methods have pretty much come to a + + + align:start position:0% +methods have pretty much come to a +consensus on willingness to pay I'm not + + align:start position:0% +consensus on willingness to pay I'm not + + + align:start position:0% +consensus on willingness to pay I'm not +sure that it's necessarily for that + + align:start position:0% +sure that it's necessarily for that + + + align:start position:0% +sure that it's necessarily for that +great reasons and one of the things I've + + align:start position:0% +great reasons and one of the things I've + + + align:start position:0% +great reasons and one of the things I've +said is that people feel strongly about + + align:start position:0% +said is that people feel strongly about + + + align:start position:0% +said is that people feel strongly about +the environment they might have + + align:start position:0% +the environment they might have + + + align:start position:0% +the environment they might have +ridiculously high willingness to accept + + align:start position:0% +ridiculously high willingness to accept + + + align:start position:0% +ridiculously high willingness to accept +values that they were the new self + + align:start position:0% +values that they were the new self + + + align:start position:0% +values that they were the new self +damaged unless you offered them an + + align:start position:0% +damaged unless you offered them an + + + align:start position:0% +damaged unless you offered them an +absurdly large amount of money but I + + align:start position:0% +absurdly large amount of money but I + + + align:start position:0% +absurdly large amount of money but I +mean that that might be data rather than + + align:start position:0% +mean that that might be data rather than + + + align:start position:0% +mean that that might be data rather than +a problem and Elvises nonetheless the + + align:start position:0% +a problem and Elvises nonetheless the + + + align:start position:0% +a problem and Elvises nonetheless the +the practice has settled on willingness + + align:start position:0% +the practice has settled on willingness + + + align:start position:0% +the practice has settled on willingness +to pay I think there's a question about + + align:start position:0% +to pay I think there's a question about + + + align:start position:0% +to pay I think there's a question about +what do the numbers mean if the costs + + align:start position:0% +what do the numbers mean if the costs + + + align:start position:0% +what do the numbers mean if the costs +and benefits are not comparably + + align:start position:0% +and benefits are not comparably + + + align:start position:0% +and benefits are not comparably +monetized and I think lurking behind the + + align:start position:0% +monetized and I think lurking behind the + + + align:start position:0% +monetized and I think lurking behind the +whole discussion is the assumption that + + align:start position:0% +whole discussion is the assumption that + + + align:start position:0% +whole discussion is the assumption that +the cost-benefit results are meaningful + + align:start position:0% +the cost-benefit results are meaningful + + + align:start position:0% +the cost-benefit results are meaningful +because they are comparably complete and + + align:start position:0% +because they are comparably complete and + + + align:start position:0% +because they are comparably complete and +that if they are not comparably + + align:start position:0% +that if they are not comparably + + + align:start position:0% +that if they are not comparably +completed for instance the accounting of + + align:start position:0% +completed for instance the accounting of + + + align:start position:0% +completed for instance the accounting of +costs is much more complete than the + + align:start position:0% +costs is much more complete than the + + + align:start position:0% +costs is much more complete than the +accounting of benefits then you have at + + align:start position:0% +accounting of benefits then you have at + + + align:start position:0% +accounting of benefits then you have at +best a lower bound rather than a point + + align:start position:0% +best a lower bound rather than a point + + + align:start position:0% +best a lower bound rather than a point +estimate of the exact right estimate so + + align:start position:0% +estimate of the exact right estimate so + + + align:start position:0% +estimate of the exact right estimate so +you know that's also essentially never + + align:start position:0% +you know that's also essentially never + + + align:start position:0% +you know that's also essentially never +recognized sometimes there's a throwaway + + align:start position:0% +recognized sometimes there's a throwaway + + + align:start position:0% +recognized sometimes there's a throwaway +qualification the question about how the + + align:start position:0% +qualification the question about how the + + + align:start position:0% +qualification the question about how the +economic benefits of job creation are + + align:start position:0% +economic benefits of job creation are + + + align:start position:0% +economic benefits of job creation are +handled is a separate puzzle this + + align:start position:0% +handled is a separate puzzle this + + + align:start position:0% +handled is a separate puzzle this +depends on the macroeconomic theories + + align:start position:0% +depends on the macroeconomic theories + + + align:start position:0% +depends on the macroeconomic theories +that one subscribes to cost-benefit + + align:start position:0% +that one subscribes to cost-benefit + + + align:start position:0% +that one subscribes to cost-benefit +analysis is sometimes but not + + align:start position:0% +analysis is sometimes but not + + + align:start position:0% +analysis is sometimes but not +necessarily embedded in a theory that + + align:start position:0% +necessarily embedded in a theory that + + + align:start position:0% +necessarily embedded in a theory that +assumes free markets reach at a state of + + align:start position:0% +assumes free markets reach at a state of + + + align:start position:0% +assumes free markets reach at a state of +full employment more or less all the + + align:start position:0% +full employment more or less all the + + + align:start position:0% +full employment more or less all the +time + + align:start position:0% +time + + + align:start position:0% +time +computable general equilibrium models + + align:start position:0% +computable general equilibrium models + + + align:start position:0% +computable general equilibrium models +which essentially conceal this + + align:start position:0% +which essentially conceal this + + + align:start position:0% +which essentially conceal this +assumption behind waves of mathematics + + align:start position:0% +assumption behind waves of mathematics + + + align:start position:0% +assumption behind waves of mathematics +but assume that labor markets clear well + + align:start position:0% +but assume that labor markets clear well + + + align:start position:0% +but assume that labor markets clear well +guess what if labor markets clear you + + align:start position:0% +guess what if labor markets clear you + + + align:start position:0% +guess what if labor markets clear you +don't create net jobs by putting people + + align:start position:0% +don't create net jobs by putting people + + + align:start position:0% +don't create net jobs by putting people +to work there are essentially no + + align:start position:0% +to work there are essentially no + + + align:start position:0% +to work there are essentially no +policymakers in the country who actually + + align:start position:0% +policymakers in the country who actually + + + align:start position:0% +policymakers in the country who actually +act as if they believe this right are we + + align:start position:0% +act as if they believe this right are we + + + align:start position:0% +act as if they believe this right are we +creating local jobs is a central + + align:start position:0% +creating local jobs is a central + + + align:start position:0% +creating local jobs is a central +question for for every policymaker so in + + align:start position:0% +question for for every policymaker so in + + + align:start position:0% +question for for every policymaker so in +that sense the calculation is correct + + align:start position:0% +that sense the calculation is correct + + + align:start position:0% +that sense the calculation is correct +relative to what people assume but not + + align:start position:0% +relative to what people assume but not + + + align:start position:0% +relative to what people assume but not +necessarily to correct relative to the + + align:start position:0% +necessarily to correct relative to the + + + align:start position:0% +necessarily to correct relative to the +theories the who should the question of + + align:start position:0% +theories the who should the question of + + + align:start position:0% +theories the who should the question of +is it worth doing this you know does the + + align:start position:0% +is it worth doing this you know does the + + + align:start position:0% +is it worth doing this you know does the +cost-benefit analysis on its own terms + + align:start position:0% +cost-benefit analysis on its own terms + + + align:start position:0% +cost-benefit analysis on its own terms +show that it's work remediating versus + + align:start position:0% +show that it's work remediating versus + + + align:start position:0% +show that it's work remediating versus +what does it show about development you + + align:start position:0% +what does it show about development you + + + align:start position:0% +what does it show about development you +know how I think people noted two + + align:start position:0% +know how I think people noted two + + + align:start position:0% +know how I think people noted two +separate questions and what it showed + + align:start position:0% +separate questions and what it showed + + + align:start position:0% +separate questions and what it showed +what you know is it worth remediating is + + align:start position:0% +what you know is it worth remediating is + + + align:start position:0% +what you know is it worth remediating is +a question that takes cost-benefit + + align:start position:0% +a question that takes cost-benefit + + + align:start position:0% +a question that takes cost-benefit +analysis what should be developed here + + align:start position:0% +analysis what should be developed here + + + align:start position:0% +analysis what should be developed here +strikes me as probably a more + + align:start position:0% +strikes me as probably a more + + + align:start position:0% +strikes me as probably a more +straightforward financial calculation + + align:start position:0% +straightforward financial calculation + + + align:start position:0% +straightforward financial calculation +about development unless it has + + align:start position:0% +about development unless it has + + + align:start position:0% +about development unless it has +environmental impacts we haven't talked + + align:start position:0% +environmental impacts we haven't talked + + + align:start position:0% +environmental impacts we haven't talked +about also the question of who should + + align:start position:0% + + + + align:start position:0% + +who should pay versus who benefits are + + align:start position:0% +who should pay versus who benefits are + + + align:start position:0% +who should pay versus who benefits are +again separate questions cost-benefit + + align:start position:0% +again separate questions cost-benefit + + + align:start position:0% +again separate questions cost-benefit +analysis identifies again in its own + + align:start position:0% +analysis identifies again in its own + + + align:start position:0% +analysis identifies again in its own +terms is it worth it for society to do + + align:start position:0% +terms is it worth it for society to do + + + align:start position:0% +terms is it worth it for society to do +it not who should pay should that people + + align:start position:0% +it not who should pay should that people + + + align:start position:0% +it not who should pay should that people +who benefit the most from development + + align:start position:0% +who benefit the most from development + + + align:start position:0% +who benefit the most from development +pay for it is a policy question about + + align:start position:0% +pay for it is a policy question about + + + align:start position:0% +pay for it is a policy question about +distribution of benefits if you were + + align:start position:0% +distribution of benefits if you were + + + align:start position:0% +distribution of benefits if you were +building low-income housing you would + + align:start position:0% +building low-income housing you would + + + align:start position:0% +building low-income housing you would +never suggest that the people who + + align:start position:0% +never suggest that the people who + + + align:start position:0% +never suggest that the people who +benefit is most from low-income housing + + align:start position:0% +benefit is most from low-income housing + + + align:start position:0% +benefit is most from low-income housing +should pay the cost that's not the point + + align:start position:0% +should pay the cost that's not the point + + + align:start position:0% +should pay the cost that's not the point +low-income housing the the discounting + + align:start position:0% +low-income housing the the discounting + + + align:start position:0% +low-income housing the the discounting +question I think applies in particular + + align:start position:0% +question I think applies in particular + + + align:start position:0% +question I think applies in particular +to health costs one of the other debates + + align:start position:0% +to health costs one of the other debates + + + align:start position:0% +to health costs one of the other debates +which my co-author at least I don't like + + align:start position:0% +which my co-author at least I don't like + + + align:start position:0% +which my co-author at least I don't like +particularly as highlighted is that if + + align:start position:0% +particularly as highlighted is that if + + + align:start position:0% +particularly as highlighted is that if +you have diseases that have a long + + align:start position:0% +you have diseases that have a long + + + align:start position:0% +you have diseases that have a long +latency period as you might well a + + align:start position:0% +latency period as you might well a + + + align:start position:0% +latency period as you might well a +Superfund pollution things that will + + align:start position:0% +Superfund pollution things that will + + + align:start position:0% +Superfund pollution things that will +show up 20 30 40 years after exposure do + + align:start position:0% +show up 20 30 40 years after exposure do + + + align:start position:0% +show up 20 30 40 years after exposure do +you discount them from the time when the + + align:start position:0% +you discount them from the time when the + + + align:start position:0% +you discount them from the time when the +disease appears work from the time when + + align:start position:0% +disease appears work from the time when + + + align:start position:0% +disease appears work from the time when +the risk and the exposure occurs and a + + align:start position:0% +the risk and the exposure occurs and a + + + align:start position:0% +the risk and the exposure occurs and a +high discount rate this can make a very + + align:start position:0% +high discount rate this can make a very + + + align:start position:0% +high discount rate this can make a very +large difference the government practice + + align:start position:0% +large difference the government practice + + + align:start position:0% +large difference the government practice +has drifted toward the more conservative + + align:start position:0% +has drifted toward the more conservative + + + align:start position:0% +has drifted toward the more conservative +approach of discounting from when the + + align:start position:0% +approach of discounting from when the + + + align:start position:0% +approach of discounting from when the +disease appears but they the discourse + + align:start position:0% +disease appears but they the discourse + + + align:start position:0% +disease appears but they the discourse +of risk which is involved seems to point + + align:start position:0% +of risk which is involved seems to point + + + align:start position:0% +of risk which is involved seems to point +to discounting from the time when the + + align:start position:0% +to discounting from the time when the + + + align:start position:0% +to discounting from the time when the +exposure happened which makes them look + + align:start position:0% +exposure happened which makes them look + + + align:start position:0% +exposure happened which makes them look +much larger and just expand the net + + align:start position:0% +much larger and just expand the net + + + align:start position:0% +much larger and just expand the net +but see about discounting on the first + + align:start position:0% +but see about discounting on the first + + + align:start position:0% +but see about discounting on the first +place you slice if you want one of those + + align:start position:0% +place you slice if you want one of those + + + align:start position:0% +place you slice if you want one of those +particulars well let me try just saying + + align:start position:0% +particulars well let me try just saying + + + align:start position:0% +particulars well let me try just saying +it once so I discounting applies to + + align:start position:0% +it once so I discounting applies to + + + align:start position:0% +it once so I discounting applies to +cases where in the costs and benefits + + align:start position:0% +cases where in the costs and benefits + + + align:start position:0% +cases where in the costs and benefits +happen at different years no one is + + align:start position:0% +happen at different years no one is + + + align:start position:0% +happen at different years no one is +indifferent between whether costs or + + align:start position:0% +indifferent between whether costs or + + + align:start position:0% +indifferent between whether costs or +benefits happen now or ten years from + + align:start position:0% +benefits happen now or ten years from + + + align:start position:0% +benefits happen now or ten years from +now and so trying to express everything + + align:start position:0% +now and so trying to express everything + + + align:start position:0% +now and so trying to express everything +as an equivalent present value the + + align:start position:0% +as an equivalent present value the + + + align:start position:0% +as an equivalent present value the +farther in the future it is generally + + align:start position:0% +farther in the future it is generally + + + align:start position:0% +farther in the future it is generally +the less it seems like it's worth today + + align:start position:0% +the less it seems like it's worth today + + + align:start position:0% +the less it seems like it's worth today +so if costs and benefits happen at very + + align:start position:0% +so if costs and benefits happen at very + + + align:start position:0% +so if costs and benefits happen at very +different times as they do in many + + align:start position:0% +different times as they do in many + + + align:start position:0% +different times as they do in many +environmental problems the rate at which + + align:start position:0% +environmental problems the rate at which + + + align:start position:0% +environmental problems the rate at which +we discount the future right we can all + + align:start position:0% +we discount the future right we can all + + + align:start position:0% +we discount the future right we can all +agree that getting getting paid for in + + align:start position:0% +agree that getting getting paid for in + + + align:start position:0% +agree that getting getting paid for in +the future is worth less than getting + + align:start position:0% +the future is worth less than getting + + + align:start position:0% +the future is worth less than getting +paid the same amount today but how much + + align:start position:0% +paid the same amount today but how much + + + align:start position:0% +paid the same amount today but how much +less is it worth what's the discount + + align:start position:0% +less is it worth what's the discount + + + align:start position:0% +less is it worth what's the discount +rate brings up that will affect + + align:start position:0% +rate brings up that will affect + + + align:start position:0% +rate brings up that will affect +essentially the trade-off between the + + align:start position:0% +essentially the trade-off between the + + + align:start position:0% +essentially the trade-off between the +price ratio between the future and the + + align:start position:0% +price ratio between the future and the + + + align:start position:0% +price ratio between the future and the +present and so the more the higher the + + align:start position:0% +present and so the more the higher the + + + align:start position:0% +present and so the more the higher the +discount rate the more unfavorable that + + align:start position:0% +discount rate the more unfavorable that + + + align:start position:0% +discount rate the more unfavorable that +is so one of the issues with the kind of + + align:start position:0% +is so one of the issues with the kind of + + + align:start position:0% +is so one of the issues with the kind of +toxic health hazards that arise in this + + align:start position:0% +toxic health hazards that arise in this + + + align:start position:0% +toxic health hazards that arise in this +scenario in particular is that you can + + align:start position:0% +scenario in particular is that you can + + + align:start position:0% +scenario in particular is that you can +be exposed to them today and you know + + align:start position:0% +be exposed to them today and you know + + + align:start position:0% +be exposed to them today and you know +cancer is famous for many cancers have + + align:start position:0% +cancer is famous for many cancers have + + + align:start position:0% +cancer is famous for many cancers have +very long latency period before there's + + align:start position:0% +very long latency period before there's + + + align:start position:0% +very long latency period before there's +any detectable disease but they come + + align:start position:0% +any detectable disease but they come + + + align:start position:0% +any detectable disease but they come +from exposures childhood exposures + + align:start position:0% +from exposures childhood exposures + + + align:start position:0% +from exposures childhood exposures +exposure as decades earlier people have + + align:start position:0% +exposure as decades earlier people have + + + align:start position:0% +exposure as decades earlier people have +the people who immigrated + + align:start position:0% +the people who immigrated + + + align:start position:0% +the people who immigrated +internationally have the cancer patterns + + align:start position:0% +internationally have the cancer patterns + + + align:start position:0% +internationally have the cancer patterns +of the country they lived in before they + + align:start position:0% +of the country they lived in before they + + + align:start position:0% +of the country they lived in before they +were twenty generally so that you need + + align:start position:0% +were twenty generally so that you need + + + align:start position:0% +were twenty generally so that you need +answers occur late in life so in that + + align:start position:0% +answers occur late in life so in that + + + align:start position:0% +answers occur late in life so in that +case if you're discounting the future at + + align:start position:0% +case if you're discounting the future at + + + align:start position:0% +case if you're discounting the future at +a big value you're exposed today you + + align:start position:0% +a big value you're exposed today you + + + align:start position:0% +a big value you're exposed today you +show signs of cancer thirty years from + + align:start position:0% +show signs of cancer thirty years from + + + align:start position:0% +show signs of cancer thirty years from +now how should we treat that as a harm + + align:start position:0% +now how should we treat that as a harm + + + align:start position:0% +now how should we treat that as a harm +that was done to you today when you were + + align:start position:0% +that was done to you today when you were + + + align:start position:0% +that was done to you today when you were +exposed or a harm that was done to you + + align:start position:0% +exposed or a harm that was done to you + + + align:start position:0% +exposed or a harm that was done to you +thirty years from now when you had + + align:start position:0% +thirty years from now when you had + + + align:start position:0% +thirty years from now when you had +cancer and I high enough discount rate + + align:start position:0% +cancer and I high enough discount rate + + + align:start position:0% +cancer and I high enough discount rate +those will be very different + + align:start position:0% + + + + align:start position:0% + +No then you really have discounting me + + align:start position:0% +No then you really have discounting me + + + align:start position:0% +No then you really have discounting me +because there's no way for future people + + align:start position:0% +because there's no way for future people + + + align:start position:0% +because there's no way for future people +to be at the table and make decisions so + + align:start position:0% +to be at the table and make decisions so + + + align:start position:0% +to be at the table and make decisions so +I mean the decisions are being made by + + align:start position:0% +I mean the decisions are being made by + + + align:start position:0% +I mean the decisions are being made by +today's people on you know you don't + + align:start position:0% +today's people on you know you don't + + + align:start position:0% +today's people on you know you don't +know what the future wants you don't + + align:start position:0% +know what the future wants you don't + + + align:start position:0% +know what the future wants you don't +know what the futures will anticipate + + align:start position:0% +know what the futures will anticipate + + + align:start position:0% +know what the futures will anticipate +will be so we're making decisions about + + align:start position:0% +will be so we're making decisions about + + + align:start position:0% +will be so we're making decisions about +what we think those things are worth and + + align:start position:0% +what we think those things are worth and + + + align:start position:0% +what we think those things are worth and +the farther in the future they are the + + align:start position:0% +the farther in the future they are the + + + align:start position:0% +the farther in the future they are the +more the more we discount them at a + + align:start position:0% +more the more we discount them at a + + + align:start position:0% +more the more we discount them at a +positive rate + + align:start position:0% + + + + align:start position:0% + +I'm just wondering like I and we can + + align:start position:0% +I'm just wondering like I and we can + + + align:start position:0% +I'm just wondering like I and we can +make a reasonable assumption that like + + align:start position:0% +make a reasonable assumption that like + + + align:start position:0% +make a reasonable assumption that like +for air pollution how much it might + + align:start position:0% +for air pollution how much it might + + + align:start position:0% +for air pollution how much it might +assess the people in the future also + + align:start position:0% +assess the people in the future also + + + align:start position:0% +assess the people in the future also +don't want information well I mean + + align:start position:0% +don't want information well I mean + + + align:start position:0% +don't want information well I mean +people who have thought a lot about this + + align:start position:0% +people who have thought a lot about this + + + align:start position:0% +people who have thought a lot about this +and again mark Sega often they mention + + align:start position:0% +and again mark Sega often they mention + + + align:start position:0% +and again mark Sega often they mention +is a philosopher who's looked at some of + + align:start position:0% +is a philosopher who's looked at some of + + + align:start position:0% +is a philosopher who's looked at some of +this + + align:start position:0% +this + + + align:start position:0% +this +it essentially conclude that we're gonna + + align:start position:0% +it essentially conclude that we're gonna + + + align:start position:0% +it essentially conclude that we're gonna +create the future and I if we preserve + + align:start position:0% +create the future and I if we preserve + + + align:start position:0% +create the future and I if we preserve +wild nature and act like we value it + + align:start position:0% +wild nature and act like we value it + + + align:start position:0% +wild nature and act like we value it +will probably have descendants who value + + align:start position:0% +will probably have descendants who value + + + align:start position:0% +will probably have descendants who value +that if we create the world + + align:start position:0% +that if we create the world + + + align:start position:0% +that if we create the world +that's all paved and has script models + + align:start position:0% +that's all paved and has script models + + + align:start position:0% +that's all paved and has script models +and excellent video games will probably + + align:start position:0% +and excellent video games will probably + + + align:start position:0% +and excellent video games will probably +create descendants who value that so + + align:start position:0% +create descendants who value that so + + + align:start position:0% +create descendants who value that so +it's like if there's a circularity and + + align:start position:0% +it's like if there's a circularity and + + + align:start position:0% +it's like if there's a circularity and +that what we do today will actually + + align:start position:0% +that what we do today will actually + + + align:start position:0% +that what we do today will actually +create the futures preferences so there + + align:start position:0% +create the futures preferences so there + + + align:start position:0% +create the futures preferences so there +is no way actually to do something from + + align:start position:0% +is no way actually to do something from + + + align:start position:0% +is no way actually to do something from +a hypothesis about what the future + + align:start position:0% +a hypothesis about what the future + + + align:start position:0% +a hypothesis about what the future +prefers because not only do they not + + align:start position:0% +prefers because not only do they not + + + align:start position:0% +prefers because not only do they not +exist yet but we will create them okay + + align:start position:0% +exist yet but we will create them okay + + + align:start position:0% +exist yet but we will create them okay +so so what do you do with this refusal + + align:start position:0% +so so what do you do with this refusal + + + align:start position:0% +so so what do you do with this refusal +of cost-benefit analysis for such + + align:start position:0% +of cost-benefit analysis for such + + + align:start position:0% +of cost-benefit analysis for such +excellent reasons as League outline you + + align:start position:0% +excellent reasons as League outline you + + + align:start position:0% +excellent reasons as League outline you +know I think again separating in this + + align:start position:0% +know I think again separating in this + + + align:start position:0% +know I think again separating in this +story separating the cleanup from the + + align:start position:0% +story separating the cleanup from the + + + align:start position:0% +story separating the cleanup from the +development there might be a stronger + + align:start position:0% +development there might be a stronger + + + align:start position:0% +development there might be a stronger +case for or the cleanup in a weaker one + + align:start position:0% +case for or the cleanup in a weaker one + + + align:start position:0% +case for or the cleanup in a weaker one +for development the more you're thinking + + align:start position:0% +for development the more you're thinking + + + align:start position:0% +for development the more you're thinking +about these non-monetized values I think + + align:start position:0% +about these non-monetized values I think + + + align:start position:0% +about these non-monetized values I think +that I've come to the conclusion that + + align:start position:0% +that I've come to the conclusion that + + + align:start position:0% +that I've come to the conclusion that +despite the validity of all those + + align:start position:0% +despite the validity of all those + + + align:start position:0% +despite the validity of all those +critiques and the importance of saying + + align:start position:0% +critiques and the importance of saying + + + align:start position:0% +critiques and the importance of saying +them every time you get a chance that + + align:start position:0% +them every time you get a chance that + + + align:start position:0% +them every time you get a chance that +you know if you have more than six + + align:start position:0% +you know if you have more than six + + + align:start position:0% +you know if you have more than six +minutes to talk about one of these + + align:start position:0% +minutes to talk about one of these + + + align:start position:0% +minutes to talk about one of these +things that you have to then go on and + + align:start position:0% +things that you have to then go on and + + + align:start position:0% +things that you have to then go on and +say using the prevailing values what + + align:start position:0% +say using the prevailing values what + + + align:start position:0% +say using the prevailing values what +would you get try to avoid endorsing + + align:start position:0% +would you get try to avoid endorsing + + + align:start position:0% +would you get try to avoid endorsing +them as a sign of you know yes we think + + align:start position:0% +them as a sign of you know yes we think + + + align:start position:0% +them as a sign of you know yes we think +this is the greatest idea ever but + + align:start position:0% +this is the greatest idea ever but + + + align:start position:0% +this is the greatest idea ever but +saying you you I've ended up saying + + align:start position:0% +saying you you I've ended up saying + + + align:start position:0% +saying you you I've ended up saying +using values that have become convention + + align:start position:0% +using values that have become convention + + + align:start position:0% +using values that have become convention +here's what you concluded so in this + + align:start position:0% +here's what you concluded so in this + + + align:start position:0% +here's what you concluded so in this +case you know thirty five million + + align:start position:0% +case you know thirty five million + + + align:start position:0% +case you know thirty five million +dollars damage is not very large if you + + align:start position:0% +dollars damage is not very large if you + + + align:start position:0% +dollars damage is not very large if you +think it's going to kill a few people + + align:start position:0% +think it's going to kill a few people + + + align:start position:0% +think it's going to kill a few people +because values of life and the six to + + align:start position:0% +because values of life and the six to + + + align:start position:0% +because values of life and the six to +eight million dollar range have become + + align:start position:0% +eight million dollar range have become + + + align:start position:0% +eight million dollar range have become +conventional we had more time I could + + align:start position:0% +conventional we had more time I could + + + align:start position:0% +conventional we had more time I could +tell you how absurd the basis for the + + align:start position:0% +tell you how absurd the basis for the + + + align:start position:0% +tell you how absurd the basis for the +sixteen million dollars for life is and + + align:start position:0% +sixteen million dollars for life is and + + + align:start position:0% +sixteen million dollars for life is and +the paradoxes that come from that but a + + align:start position:0% +the paradoxes that come from that but a + + + align:start position:0% +the paradoxes that come from that but a +given that that has become semi standard + + align:start position:0% +given that that has become semi standard + + + align:start position:0% +given that that has become semi standard +in the policy discourse a policy that + + align:start position:0% +in the policy discourse a policy that + + + align:start position:0% +in the policy discourse a policy that +saves a few lives predictably is clearly + + align:start position:0% +saves a few lives predictably is clearly + + + align:start position:0% +saves a few lives predictably is clearly +worth thirty five million dollars to + + align:start position:0% +worth thirty five million dollars to + + + align:start position:0% +worth thirty five million dollars to +society and conventional cost-benefit + + align:start position:0% +society and conventional cost-benefit + + + align:start position:0% +society and conventional cost-benefit +terms so that there's a kind of folk you + + align:start position:0% +terms so that there's a kind of folk you + + + align:start position:0% +terms so that there's a kind of folk you +know hold your nose and go with the + + align:start position:0% +know hold your nose and go with the + + + align:start position:0% +know hold your nose and go with the +lesser evil which American politics is + + align:start position:0% +lesser evil which American politics is + + + align:start position:0% +lesser evil which American politics is +so full of the fun occurs here too with + + align:start position:0% +so full of the fun occurs here too with + + + align:start position:0% +so full of the fun occurs here too with +that last sentence in a sense be + + align:start position:0% +that last sentence in a sense be + + + align:start position:0% +that last sentence in a sense be +adequate to just say to the governor I + + align:start position:0% +adequate to just say to the governor I + + + align:start position:0% +adequate to just say to the governor I +think you don't need to spend money on + + align:start position:0% +think you don't need to spend money on + + + align:start position:0% +think you don't need to spend money on +an elaborate analysis even using the + + align:start position:0% +an elaborate analysis even using the + + + align:start position:0% +an elaborate analysis even using the +prevailing values of sixty seven million + + align:start position:0% +prevailing values of sixty seven million + + + align:start position:0% +prevailing values of sixty seven million +dollars per person we undoubtedly would + + align:start position:0% +dollars per person we undoubtedly would + + + align:start position:0% +dollars per person we undoubtedly would +save six or seven - maybe 60 or 70 maybe + + align:start position:0% +save six or seven - maybe 60 or 70 maybe + + + align:start position:0% +save six or seven - maybe 60 or 70 maybe +six or seven hundred in the course of + + align:start position:0% +six or seven hundred in the course of + + + align:start position:0% +six or seven hundred in the course of +this so we don't even need to do when + + align:start position:0% +this so we don't even need to do when + + + align:start position:0% +this so we don't even need to do when +you further analysis I think that's + + align:start position:0% +you further analysis I think that's + + + align:start position:0% +you further analysis I think that's +right if it's clear that it saves a lot + + align:start position:0% +right if it's clear that it saves a lot + + + align:start position:0% +right if it's clear that it saves a lot +of lives and air pollution often kills + + align:start position:0% +of lives and air pollution often kills + + + align:start position:0% +of lives and air pollution often kills +people so that things of reduce air + + align:start position:0% +people so that things of reduce air + + + align:start position:0% +people so that things of reduce air +pollution are particularly successful in + + align:start position:0% +pollution are particularly successful in + + + align:start position:0% +pollution are particularly successful in +this there are a handful of these values + + align:start position:0% +this there are a handful of these values + + + align:start position:0% +this there are a handful of these values +that have become standard there's been + + align:start position:0% +that have become standard there's been + + + align:start position:0% +that have become standard there's been +an argument that you shouldn't allow + + align:start position:0% +an argument that you shouldn't allow + + + align:start position:0% +an argument that you shouldn't allow +other values and there's been a very + + align:start position:0% +other values and there's been a very + + + align:start position:0% +other values and there's been a very +partisan discourse about which values + + align:start position:0% +partisan discourse about which values + + + align:start position:0% +partisan discourse about which values +are allowed but the handful of values + + align:start position:0% +are allowed but the handful of values + + + align:start position:0% +are allowed but the handful of values +which have been allowed create strong + + align:start position:0% +which have been allowed create strong + + + align:start position:0% +which have been allowed create strong +arguments for some policies superfund + + align:start position:0% +arguments for some policies superfund + + + align:start position:0% +arguments for some policies superfund +ones actually are trickier to + + align:start position:0% +ones actually are trickier to + + + align:start position:0% +ones actually are trickier to +demonstrate the number of deaths like + + align:start position:0% +demonstrate the number of deaths like + + + align:start position:0% +demonstrate the number of deaths like +air pollution + + align:start position:0% +air pollution + + + align:start position:0% +air pollution +pollution so clearly kills people that + + align:start position:0% +pollution so clearly kills people that + + + align:start position:0% +pollution so clearly kills people that +it just doesn't have a chance of us we + + align:start position:0% +it just doesn't have a chance of us we + + + align:start position:0% +it just doesn't have a chance of us we +will stop \ No newline at end of file diff --git a/_m4Gvu90Ydw.txt b/_m4Gvu90Ydw.txt new file mode 100644 index 0000000000000000000000000000000000000000..f60ef1c64dbb682c97f10b44673ff8296f211cfb --- /dev/null +++ b/_m4Gvu90Ydw.txt @@ -0,0 +1,1045 @@ +As I'm going to argue repeatedly today, biology has become a science + +over the last 50 years. And, as a consequence, we can talk + +about some basic principles. We can talk about some laws and + +then begin to apply them to very interesting biological problems. + +And so our general strategy this semester, as it has been in the past, + +is to spend roughly the first half of the semester talking about the + +basic laws and rules that govern all forms of biological life + +on this planet. And you can see some of the specific + +kinds of problems, including the problem of cancer, + +how cancer cells begin to grow abnormally, how viruses proliferate, + +how the immune system functions, how the nervous system functions, + +stem cells and how they work and their impact on modern biology, + +molecular medicine, and finally perhaps the future of biology and + +even certain aspects of evolution. The fact of the matter is that we + +now understand lots of these things in ways that were inconceivable 50 + +years ago. And now we could begin to talk about things that 50 years + +ago people could not have dreamt of. When I took this course, and I did + +take it in 1961, we didn't know about 80% of what we + +now know. You cannot say that about mechanics + +in physics, you cannot say that about circuit theory in electronics, + +and you cannot say that, obviously, about chemistry. + +And I'm mentioning that to you simply because this field has + +changed enormously over the ensuing four decades. I won't tell you what + +grade I got in 7. 1 because if I would, + +and you might pry it out of me later in the semester, + +you probably would never show up again in lecture. + +But in any case, please know that this has been an + +area of enormous ferment. And the reason it's been in such + +enormous ferment is of the discovery in 1953 by Watson and Crick of the + +structure of the DNA double helix. Last year I said that we were so + +close to this discovery that both Watson and Crick are alive and with + +us and metabolically active, and more than 50 years, well, + +exactly 50 years after the discovery. Sadly, several months ago one of the + +two characters, Francis Crick died well into his + +eighties, and so he is no longer with us. But I want to impress on + +you the notion that 200 years from now, we will talk about Watson and + +Crick the same way that people talk about Isaac Newton in terms of + +physics. And that will be so because we are only beginning to + +perceive the ramifications of this enormous revolution that was + +triggered by their discovery. That is the field of molecular + +biology and genetics and biochemistry which has totally + +changed our perceptions of how life on Earth is actually organized. + +Much of the biology to which you may have been exposed until now has + +been a highly descriptive science. That is you may have had courses in + +high school where you had to memorize the names of different + +organisms, where you had to understand how evolutionary + +phylogenies were organized, where you had to learn the names of + +different organelles, and that biology was, for you, + +a field of memorization. And one point we would like, + +hopefully successfully, to drive home this semester is the notion + +that biology has now achieved a logical and rational coherence that + +allows us to articulate a whole set of rules that explain how all life + +forms on this planet are organized. It's no longer just a collection of + +jumbled facts. Indeed, if one masters these + +molecular and genetic principles, one can understand in principle a + +large number of processes that exist in the biosphere and begin to apply + +one's molecular biology to solving new problems in this arena. + +One of the important ideas that we'll refer to repeatedly this + +semester is the fact that many of the biological attributes that we + +posses now were already developed a very long time ago early in the + +inception of life on this planet. So if we look at the history of + +Earth, here the history of Earth is given as 5 billion years, + +this is in thousands obviously. The Earth is probably not that old. + +It's probably 4.5 or 4 or 3 billion years but, anyhow, + +that's when the planet first aggregated, as far as we know. + +One believes that no life existed for perhaps the first half billion + +years, but after half a billion years, which is a lot of time to be + +sure, there already begins to be traces of life forms on the surface + +of this planet. And that, itself, + +is an extraordinary testimonial, a testimonial to how evolutionary + +processes occur. We don't know how many planets + +there are in the universe where similar things happened. + +And we don't know whether the solution that were arrived at by + +other life systems in other places in the universe, + +which we may or may not ever discover, were the similar solutions + +to the ones that have been arrived at here. + +It's clear, for example, that to the extent that Darwinian + +Evolution governs the development of life forms on this planet that is + +not an artifact of the Earth. Darwinian Evolution is a logic + +which is applicable to all life forms and all biosystems that may + +exist in the universe, even the ones we have not discovered. + +However, there are specific solutions that were arrived at + +during the development of life on Earth which may be peculiar to Earth. + +The structure of the DNA double helix. + +The use of ribose in deoxyribose. The choice of amino acids to make + +proteins. And those specific solutions may not be universal. + +Whether they're universal in the sense of existing in all life forms + +across the planet, the fact is that many of the + +biochemical and molecular solutions that are represented in our own + +cells today, these solutions, these problems were solved already 2 + +and 3 billion years ago. And once they were solved they were + +kept and conserved almost unchanged for the intervening 2 or 3 billion + +years. And that strong degree of conservation means that we can begin + +to figure out what these principles were early on in evolution of life + +on this planet and begin to apply them to all modern life forms. + +From the point of view of evolution, almost all animals are identical in + +terms of their biochemistry and in terms of their physiology. + +The molecular biology of all eukaryotic cells, + +that is all cells that have nuclei in them, is almost the same. + +And, therefore, we're not going to focus much in this course this + +semester on specific species but rather focus on general principles + +that would allow us to understand the cells and the tissues and the + +physiological processes that are applicable to all species on the + +surface of the planet. Let's just look here and get us + +some perspective on this because, the fact of the matter is, is that + +multicellular life forms, like ourselves, we have, the average + +human being has roughly three or four or five times ten to the + +thirteenth cells in the body. That's an interesting figure. + +The average human being goes through roughly ten to the sixteenth + +cell divisions in a lifetime, i.e. ten to the sixteenth times in + +your body there will be cells that divide, grow and divide. + +Every day in your body there are roughly ten to the eleventh cells + +that grow and divide. Think of that, ten to the eleventh. + +And you can divide that by the number of minutes in a day and come + +up with an astounding degree of cellular replication going on. + +All of these processes can be traceable back to solutions that + +were arrived at very early in the evolution of life on this planet, + +perhaps 550, 600 million years ago when the first multicellular life + +forms began to evolve. Before that time, that is to say + +before 500 to 600 million years ago, there were single-cell organisms. + +For example, many of them survive to this day. There were yeast-like + +organisms. And there were bacteria. And we make one large and major + +distinction between the two major life forms on the planet in terms of + +cells. One are the prokaryotic cells. And these are the cells of + +bacteria, I'll show you an image of them shortly, which lack nuclei. + +And the eukaryotic cells which poses nuclei and indeed have a highly + +complex cytoplasm and overall cellular architecture. + +We think that the prokaryotic life forms on this planet evolved first + +probably on the order of 3 billion years ago, maybe 3. + +billion years ago, and that about 1. billion years ago cells evolved + +that contained nuclei. Again, I'll show them to you + +shortly. And these nucleated cells, + +the eukaryotes then existed in single-cell form for perhaps the + +next 700 or 800 million years until multi-cellular aggregates of + +eukaryotic cells first assembled to become the ancestors of the + +multi-cellular plants and the multi-cellular animals that exist on + +the surface of the Earth today. To put that in perspective, our + +species has only been on the planet for about 150, + +00 years. So we've all been here for that period of time. + +And a 150,000 sounds like a long time, in one sense, + +but it's just “a blink in the eye of the Lord” as one says in terms of + +the history of life on this planet, and obviously the history of the + +universe which is somewhere between 13 and 15 billion years old. + +You can begin to see that the appearance of humans represents a + +very small segment of the entire history of life on this planet. + +And here you can roughly see the way that life has developed during this + +period of time from the fossil record. You see that many plants + +actually go back a reasonable length of time, but not more than maybe 300 + +or 400 million years. Here are the Metazoa. + +And this represents -- + +Well, can you hear me? Wow, 614 came in handy. + +OK. So if we talk about another major division, + +we talk about protozoa and metazoa. The suffix zoa refers to animals, + +as in a zoo. And the protozoa represents single-cell organisms. + +The metazoa represent multi-cellular organisms. And we're going to be + +focusing largely on the biology of metazoan cells this semester, + +and we're going to be spending almost no time on plants. + +It's not that plants aren't important. It's just that we don't + +have time to cover everything. And, indeed, the molecular biology + +that you learn this semester will ultimately enable you to understand + +much about the physiology of multi-cellular plants which happen + +to be called metaphyta, a term you may never hear again in + +your entire life after today. That reminds me, + +by the way, that both Dr. Lander and I sometimes use big words. + +And people come up to me afterwards each semester each year and say + +Professor Weinberg, why don't you talk simple, + +why don't you talk the way we heard things in high school? + +And please understand that if I use big words sometimes it's to broaden + +your vocabulary so you can learn big words. + +One of the things you should be able, one of the big take-home lessons of + +this course should be that your vocabulary is expanded. + +Not just your scientific vocabulary but your general working English + +vocabulary. Perhaps the biggest goal of this course, + +by the way, is not that you learn the names of all the organelles and + +cells but that you learn how to think in a scientific and rational + +way. Not just because of this course but that this course + +helps you to do so. And as such, we don't place that + +much emphasis on memorization but to be able to think logically about + +scientific problems. Here we can begin to see the + +different kinds of metazoa, the animals. Here are the metaphyta + +and here are the protozoa, different words for all of these. + +And here we see our own phylum, the chordates. And, + +again, keep in mind that this line right down here is about 550 to 600 + +million years ago, just to give you a time scale for + +what's been going on, on this planet. + +One point we'll return to repeatedly throughout the semester is that all + +life forms on this planet are related to one another. + +It's not as if life was invented multiple times on this planet and + +that there are multiple independent inventions to the extent that life + +arose more than once on this planet, and it may have. The other + +alternative or competing life forms were soon wiped out by our ancestors, + +our single-cellular ancestors 3 billion years ago. + +And, therefore, everything that exists today on this + +planet represents the descendents of that successful group of cells that + +existed a very long time ago. Here we have all this family tree + +of the different metazoan forms that have been created by the florid hand + +of evolution. And we're not going to study those phylogenies simply + +because we want to understand principles that explain all of them. + +Not just how this or that particular organism is able to digest its food + +or is able to reproduce. Here's another thing we're not + +going to talk about. We're not going to talk about + +complicated life forms. We're not going to talk very much, + +in fact hardly at all, about ecology. This is just one such thing, + +the way that a parasite is able to, a tapeworm is able to infect people. + +This is, again, I'm showing you this not to say this is what we're + +going to talk about, we're not going to talk about that. + +We're not going to talk about that. There's a wealth of detail that's + +known about the way life exists in the biosphere that we're simply + +going to turn our backs on by focusing on some basic principles. + +We're also not going to talk about anatomy. Here in quick order are + +some of the anatomies you may have learned about in high school, + +and I'm giving them to you each with a three-second minute, + +a three-second showing to say we're not going to do all this. + +And rather just to reinforce our focus, we're going to limit + +ourselves to a very finite part of the biosphere. + +And here is one way of depicting the biosphere. It's obviously an + +arbitrary way of doing so but it's quite illustrative. + +Here we start from molecules. And, in fact, we will occasionally + +go down to submolecular atoms. And here's the next dimension of + +complexity, organelles. That is these specialized little + +organs within cells. We're going to focus on them as + +well. We're going to focus on cells. And when we start getting to + +tissues, we're going to start not talking so much about them. + +And we're not going to talk about organisms and organs or entire + +organisms or higher complex ecological communities. + +And the reason we're doing that is that for 40 years in this department, + +and increasingly in the rest of the world there is the acceptance of the + +notion that if we understand what goes on down here in these first + +three steps, we can understand almost everything else in principle. + +Of course, in practice we may not be able to apply those principles to + +how an organism works or to how the human brain works yet. + +Maybe we never will. But, in general, if one begins to + +understand these principles down here, one can understand much about + +how organismic embryologic develop occurs, one can understand a lot + +about a whole variety of disease processes, one can understand how + +one inherits disease susceptibilities, + +and one can understand why many organisms look the way they do, + +i.e. the process of developmental biology. + +And so, keep in mind that if you came to hear about all of these + +things, we're going to let you down. That's not what this is going to be + +about. This also dictates the dimensions of the universe that + +we're going to talk about because we're going to limit ourselves to + +the very, very small and not to the macroscopic. On some occasions + +we'll limit ourselves to items that are so small you cannot see them in + +the light microscope. On other occasions we may widen our + +gaze to look at things that are as large as a millimeter, + +but basically we're staying very, very small. Again, because we view, + +correctly or not, the fact that the big processes can be understood by + +delving into the molecular details of what happens invisibly and cannot + +be seen by most ways of visualizing things, including the light and + +often even the electron microscope. Keep in mind that 50 years ago we + +didn't know any of this, for all practical purposes, + +or very little of this. And keep in mind that we're so close to this + +revolution that we don't really understand its ramifications. + +I imagine it will be another 50 years before we really begin to + +appreciate the fallout, the long-term consequences of this + +revolution in biology which began 51 years ago. And so you're part of + +that and you're going to experience it much more than my generation did. + +And indeed one of the reasons why MIT decided about 10 or 12 years ago + +that every MIT undergraduate needed to have at least one semester of + +biology is that biology, in the same way as physics and + +chemistry and math, has become an integral part of every + +educated person's knowledge-base in terms of their ability to deal with + +the world in a rational way. In terms of public policy, + +in terms of all kinds of ethical issues, they need to understand + +what's really going on. Many of the issues that one talks + +about today about bioethics are articulated by people who haven't + +the vaguest idea about what we're talking about this semester. + +You will know much more than they will, and hopefully some time down + +the road, when you become more and more influential voices in society, + +you'll be able to contribute what you understood here, + +what you learned here to that discussion. + +Right now much of bioethical discussion is fueled by people who + +haven't the vaguest idea what a ribosome or mitochondrion or even a + +gene is, and therefore is often a discussion of mutually shared + +ignorance which you can diffuse by learning some basics, + +by learning some of the essentials. Here is the complexity of the cell + +we're going to focus on largely this semester, which is to say the + +eukaryotic rather than the prokaryotic cell. + +And this is just to give you a feeling for the overall dimensions + +of the cell and refer to many of the landmarks that will repeatedly be + +brought up during the course of this semester. + +Here is the nucleus. The term karion comes from the + +Greek meaning a seed or a kernel. And the nucleus is what gives the + +eukaryotic cell its name. Within the nucleus, although not + +shown here, are the chromosomes which carry DNA. + +You may have learned that a long time ago. Outside of the nucleus is + +this entire vast array of organelles that goes from the nuclear membrane, + +and I'm point to it right here, all the way out to the outside + +of the cell. The outside limiting membrane, + +the outer membrane of the cell is called the plasma membrane. + +And between the nucleus and the plasma membrane there is an enormous + +amount of biological and biochemical activity taking place. + +Here are, for example, the mitochondria. And the + +mitochondria, as one has learned, are the sources of energy production + +in the cell. And, therefore, we'll touch on them very + +briefly. This is an artist's conception of + +what a mitochondrion looks like. Almost always artists' conceptions + +of these things have only vague resemblance to the reality. + +But, in any case, you can begin to get a feeling for what one thinks + +about their appearance. Here are mitochondria sliced open + +by the hand of the artist. And, interestingly, mitochondria + +have their own DNA in them. One now accepts the fact that + +mitochondria are the descendents of bacteria which insinuated themselves + +into the cytoplasms of larger cells, roughly 1.5 billion years ago, and + +began to do a specialized job which increasingly became the job of + +energy production within cells. To this day, mitochondria retain + +some vestigial attributes of the bacterial ancestors which initially + +colonized or parasitized the cytoplasm of the cell. + +When I say parasitized, you might imagine that the + +mitochondria are taking advantage of the cell. + +But, in fact, the mitochondria represent the essential sources of + +energy production in the cell. Without our mitochondria, as you + +might learn by taking cyanide, for example, you don't live for very + +many minutes. And the vestiges of bacterial origins of mitochondria + +are still apparent in the fact that mitochondria still have their own + +DNA molecule, their own chromosome. They still have their own ribosomes + +and protein synthetic apparatus, even though the vast majority of the + +proteins inside mitochondria are imported from the cytoplasm, + +i.e., these vestigial bacteria now rely on proteins made by the cell at + +large that are imported into the mitochondrion to supplement the + +small number of vestigial bacterial proteins which are still made here + +inside the mitochondrion and used for essential function + +in energy production. Here is the Golgi apparatus. + +And the Golgi apparatus up here is used for the production of membranes. + +As one will learn throughout the semester, the membranes of a cell + +are in constant flux and are being pulled in and remodeled and + +regenerated. The Golgi apparatus is very important for that. + +Here's the rough endoplasmic reticulum. That's important for the + +synthesis of proteins which are going to be displayed on the surface + +of cells, you don't see them depicted here, + +or are going to be secreted into the extracellular space. + +Here are the ribosomes, which I might have mentioned briefly + +before. And these ribosomes are the factories where proteins are made. + +Again, we're going to talk a lot about them. And, + +finally, several other aspects, the cytoskeleton. The physical + +integrity, the architecture of the cell is maintained by a complex + +network of proteins which together are considered to be the + +cytoskeleton. And they enable the cell to have some rigidity, + +to resist tensile forces, and actually to move. + +Cells can actually move from one place to the other. + +They have motile properties. They're able to move from one + +location to another. The process of cell motility, + +if that's a word you'd like to learn. + +Here is what a prokaryotic cell looks like by contrast. + +And I just want to give you a feeling. First of all, + +it looks roughly like a mitochondrion that I + +discussed before. But you see that there is the + +absence of a nuclear membrane. There's the absence of the highly + +complex cytoarchitecture. Cyto always refers to cells. + +There's the absence of the complex cytoarchitecture that one associates + +with eukaryotic cells. In fact, all that a bacterium has + +is this area in the middle. It's called the nucleoid, a term + +which you also will probably never hear in your lifetime. + +And it represents simply an aggregate of the DNA of the + +chromosomes of the bacterium. And, in most bacteria, the DNA + +consists of only a single molecule of DNA which is responsible for + +carrying the genetic information of the bacteria. There's no membrane + +around this nucleoid. And outside of this area where the + +DNA is kept are largely ribosomes which are important for protein + +synthesis. There's a membrane on the outside of this called the + +plasma membrane, very similar to the plasma membrane + +of eukaryotic cells. And outside of that is a meshwork + +that's called the outer membrane, it's sometimes called the cell wall + +of the bacterium, which is simply there to impart + +structural rigidity to the bacterium making sure that it doesn't explode + +and holding it together. And then there are other versions + +of eukaryotic cells. Here's what a plant cell looks like. + +And it's almost identical to the cells in our body, except + +for two major features. For one thing, + +it has chloroplasts in it which are also, one believes now, + +the vestiges of parasitic bacteria that invade into the cytoplasm of + +eukaryotic cells. So, in addition to mitochondria + +which are responsible for energy production in all eukaryotic cells, + +we have here the chloroplasts which are responsible for harvesting light + +and converting it into energy in plant cells. The rest of the + +cytoplasm of a plant cell looks pretty much the same. + +One feature that I didn't really mention when I talked about an + +animal cell is in the middle of the nucleus, here you can see, + +is a structure called a nucleolus. And a nucleolus, or the nucleolus + +in the eukaryotic cell is responsible for making the large + +number of ribosomes which are exported from the nucleus into the + +cytoplasm. And, as I mentioned just before, + +the ribosomes are responsible for protein synthesis. + +It turns out this is a major synthetic effort on the part of most + +cells. Cells, like our own, have between 5 and 10 + +million ribosomes in the cytoplasm. So it's an enormous amount of + +biomass in the cytoplasm whose sole function is to synthesize proteins. + +As we will learn also, proteins that are synthesized by the + +ribosomes don't sit around forever. Some proteins have long lives. + +Some proteins have lifetimes of 15 minutes before they're degraded, + +before they're turned over. One other distinction between our + +cells, that is the cells of metazoa and metaphyta, + +are the cell walls, analogous to the cell walls of + +bacteria, this green thing on the outside. As I said before, + +we do not have cell walls around our cells. And we will, + +as the semester goes on, go into more and more details about + +different aspects of this cytoarchitecture during the first + +half of the semester. Here, for example, + +is an artist's depiction of the endoplasmic reticulum. + +Why it has such a complex name, I cannot tell you, but it does. + +It's called the ER in the patois of the street. The ER. + +And the endoplasmic reticulum is a series of membranes. + +Keep in mind, not the only membrane in the cell is the plasma membrane. + +Within the cytoplasm there are literally hundreds of membranes + +which are folded up in different ways. + +Here you see them depicted. And one set of these membranes, + +often they're organized much like tubes, represents the membranes of + +the endoplasmic reticulum which either lacks ribosomes attached to + +it or has these ribosomes attached to it which cause this to be called + +the rough endoplasmic reticulum to refer to its rough structure which + +is created by the studding of ribosomes on the surface. + +As we will learn, just trying to give you a feeling + +for the geography of what we're going to talk about this semester, + +these ribosomes on the surface of the endoplasmic reticulum are + +dedicated to the task of making highly specialized proteins which + +are either going to be dispatched to the surface of the cell where they + +will be displayed on the cell's surface or actually secreted into + +the extracellular space. Many of the proteins that are + +destined for our body are not kept within cells but are released into + +the extracellular space where they serve important functions, + +and so we're going to focus very much on them. + +Here's actually what some of these things look like in the electron + +microscope to see whether we can either believe or fully discredit + +the imaginations of the artists. Here's the rough endoplasmic + +reticulum I showed you in schematic form before. And you can see why + +it's called rough. All these black dots are ribosomes + +attached on the outside. Here's the Golgi apparatus. + +You see these vesicles indicated here. And a vesicle, + +just to use a new word, is simply a membranous bag. + +And keep in mind, by the way, that we're not going to + +spend the semester with these highly descriptive discussions. + +Our intent today is to get a lot of these descriptive discussions out of + +the way so that we can begin to talk in a common parlance about many of + +the parts, the molecular parts of cells and organisms. + +Here is the mitochondrion which we saw depicted before. + +It looks similar to, but not identical to the artist's + +description of that. And keep in mind that the + +mitochondrion in our cells, as I said before, are the + +descendents of parasitic bacteria. Here's the endoplasmic reticulum, + +and the way it would look, as it does in certain parts of the + +cell when it doesn't have all of these ribosomes studded on the + +surface. The endoplasmic reticulum here is involved in making membranes. + +The endoplasmic reticulum here is involved in the synthesis and export + +of proteins to the cell's surface and for secretion, as + +I mentioned before. Much of what we're going to talk + +about over the next days is going to be focused on the nucleus of the + +cell, that is on the chromosomes on the cell and on the material which + +is called chromatin which carries the genetic material. + +So the term chromatin is used in biology to refer simply to the + +mixture of DNA and proteins, which together constitutes the + +chromosomes. So chromatin has within it DNA, + +it has protein, and it has a little bit of RNA in it. + +And we're going to focus mostly on the DNA in the chromatin, + +because if we can begin to understand the way the DNA works and + +functions many other aspects will flow from that. + +I mentioned the cell's surface, and I just want to impress on you + +the fact that the plasma membrane of a cell is much more complicated than + +was depicted in these drawings that I showed you just before. + +If we had a way of visualizing the plasma membrane of a cell, + +we would discover that it's formed from lipids. We see such lipids + +there, phospholipids, many of them. We'll talk about them + +shortly. That the outside of the cell, there are many proteins, + +you see them here, which thread their way through the plasma + +membrane, have an extracellular and intracellular part. + +And these transmembrane proteins, which reach from outside to inside, + +represent a very important way by which the cell senses + +its environment. This plasma membrane, + +as we'll return to, represents a very effective barrier to segregate + +what's inside the cell from what's outside of the cell to increase + +concentrations of certain biochemical entities. + +But at the same time it creates a barrier to communication. + +And one of the things that cells have had to solve over the last 700 + +to 800 million years is ways by which the exterior of the cell is + +able to send certain signals and transmit that information to the + +interior of the cell. At the same time, + +cells have had to use a number of different, invent a number of + +different proteins, some of them indicated here, + +which are able to transport materials from the outside of the + +cell into the cell, or visa versa. So the existence of + +the plasma membrane represents a boon to the cell in the sense that + +it's able to segregate what's on the inside from what's on the outside. + +But it represents an impediment to communication which had to be solved, + +as well as an impediment to transport. And many of these + +transmembrane proteins are dedicated to solving those particular problems. + +Here you see, once again an artist's depiction + +form, aspects of the cytoskeleton of the cell. And when we talk about + +the cytoskeleton we talk about this network of proteins which, + +as I said before, gives the cell rigidity. + +Keep in mind that the prefix cyto or the suffix cyt refers always to + +cells. Allows the cell to have shape. And here you can see this + +network as depicted in one way, but here it's depicted actually much + +more dramatically. And here you begin to see the + +complexity of what exists inside the cell. Here are these proteins. + +These are polymers of proteins called vimentin which are present in + +very many mesenchymal cells. Here are microtubules made from + +another kind of protein. Here are microfilaments, + +in this case made of the molecule actin. And if we looked at + +individual molecules of actin they would be invisible. + +This is end-to-end polymerization of many actin molecules. + +And we're looking here under the microscope from one end of the cell + +to the other end of the cell. And you can see how these molecules, + +they create stiffness, and they also enable the cell to + +contract and to move. Some people might think that the + +interior of the cell is just water with some molecules floating around + +them. But if you actually look at what's present in the cell, + +more than 50% of the volume is taken up by proteins. + +It's not simply an aqueous solvent where everything moves around freely. + +It's a very viscous slush, a mush. And it's quite difficult + +there for many cells to move around from one part of the + +cell to the other. Here you begin to get a feeling now + +for how the connection, which we'll reinforce shortly in + +great detail, between individual molecules and the cytoskeleton. + +And here you see these actin fibers. I showed them to you just moments + +ago stretching from one end of the cell to the other. + +And each of these little globules is a single actin monomer which + +polymerize end-to-end and then form multi-strand aggregates to create + +the actin cytoskeleton. Here's an intermediate filament and + +here's the microtubules that are formed, once again giving us this + +impression that the cell is actually highly organized and that that high + +degree of organization is able to give it some physical structure and + +shape and form. I think we're going to end today + +two minutes early. You probably won't object. \ No newline at end of file diff --git a/_vyke3vF4Nk.txt b/_vyke3vF4Nk.txt new file mode 100644 index 0000000000000000000000000000000000000000..0321b49f2d5e7c7ee2fb2219461569bc11a0f600 --- /dev/null +++ b/_vyke3vF4Nk.txt @@ -0,0 +1,2015 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +[MUSIC PLAYING] + +PROFESSOR: In the last lecture, +we discussed a number + +of general properties for +systems, which, as you recall, + +applied both to continuous-time +and to + +discrete-time systems. + +These properties were the +properties associated with a + +system having memory. + +The issue of whether a system +is or isn't invertible, we + +talked about causality and +stability, and finally we + +talked about when linearity +and time invariance. + +In today's lecture, what +I'd like to do is focus + +specifically on linearity and +time invariance, and show how + +for systems that have those +properties, we can exploit + +them to generate a general +representation. + +Let me begin by just +reviewing the two + +properties again quickly. + +Time invariance, as you recall, +is a property that + +applied both to continuous-time +and + +discrete-time systems, and in +essence stated that for any + +given input and output +relationship if we simply + +shift the input, +then the output + +shifts by the same amount. + +And of course, exactly the same +kind of statement applied + +in discrete time. + +So time invariance was a +property that said that the + +system didn't care about +what the time origin + +of the signal is. + +Linearity was a property related +to the fact that if we + +have a set of outputs +associated with a + +given set of inputs-- + +as I've indicated here with the +inputs as phi_k and the + +outputs psi_k, then the property +of linearity states + +that if we have an input which +is a linear combination of + +those inputs, then the output is +a linear combination of the + +associated outputs. + +So that linear combination of +inputs generates, for a linear + +system, an output which is a +linear combination of the + +associated outputs. + +Now the question is, how can we +exploit the properties of + +linearity and time invariance? + +There's a basic strategy which +will flow more or less through + +most of this course. + +The strategy is to attempt to +decompose a signal, either + +continuous-time or +discrete-time, into a set of + +basic signals. + +I've indicated that here. + +And the question then is, what +basic signal should we pick? + +Well, the answer, kind of, is we +should pick a set of basic + +signals that provide a certain +degree of analytical + +convenience. + +So we choose a set of inputs +for the decomposition that + +provide outputs that we +can easily generate. + +Now, as we'll see, when we do +this, there are two classes of + +inputs that are particularly +suited to that strategy. + +One class is the set of delayed +impulses, namely + +decomposing a signal into a +linear combination of these. + +And as we'll see, that leads to +a representation for linear + +time-invariant systems, which is +referred to as convolution. + +The second is a decomposition +of inputs into complex + +exponentials-- + +a linear combination of +complex exponentials-- + +and that leads to a +representation of signals and + +systems through what we'll refer +to as Fourier analysis. + +Now, Fourier analysis will +be a topic for a + +set of later lectures. + +What I'd like to begin with is +the representation in terms of + +impulses and the associated +description of linear + +time-invariant systems +using convolution. + +So let's begin with a discussion +of discrete-time + +signals, and in particular the +issue of how discrete-time + +signals can be decomposed +as a linear + +combination of delayed impulses. + +Well, in fact, it's relatively +straightforward. + +What I've shown here is a +general sequence with values + +which I've indicated +at the top. + +And more or less as we did +when we talked about + +representing a unit step in +terms of impulses, we can + +think of this general sequence +as a sequence of impulses-- + +delayed, namely, occurring at +the appropriate time instant, + +and with the appropriate +amplitude. + +So we can think of this general +sequence and an + +impulse occurring at n = 0 and +with a height of x[0], plus an + +impulse of height x[1] + +occurring at time n = 1, +and so that's x[1] + +delta[n-1], an impulse +at -1 with an + +amplitude of x[-1], etc. + +So if we continued to generate +a set of weighted, delayed + +unit samples like that, and if +we added all these together, + +then that will generate +the total sequence. + +Algebraically, then, what that +corresponds to is representing + +the sequence as a sum of +individual terms as I've + +indicated here or in terms of a +general sum, the sum of x[k] + +delta[n-k]. + +So that's our strategy-- + +the strategy is to decompose an +arbitrary sequence into a + +linear combination of weighted, +delayed impulses. + +And here again is the +representation, which we just + +finished generating. + +Now, why is this representation +useful? + +It's useful because we now have +a decomposition of the + +sequence as a linear combination +of basic + +sequences, namely the +delayed impulses. + +And if we are talking about a +linear system, the response to + +that linear combination +is a linear + +combination of the responses. + +So if we denote the response +to a delayed impulse as + +h_k[n], then the response to +this general input is what + +I've indicated here, where y[n], +of course, is the output + +due to the general input x[n]. + +h_k[n] + +in is the output due to the +delayed impulse, and these are + +simply the coefficients +in the weighting. + +So for a linear system, we +have this representation. + +And if now, in addition, the +system is time-invariant, we + +can, in fact, relate the +outputs due to these + +individual delayed impulses. + +Specifically, if the system is +time-invariant, then the + +response to an impulse at time +k is exactly the same as the + +response to an impulse at time +0, shifted over to time k. + +Said another way, h_k[n] + +is simply h_0[n-k], where h_0 is +the response of the system + +to an impulse at n = 0. + +And it's generally useful to, +rather than carrying around + +h_0[n], just simply +define h_0[n] + +as h[n], which is the unit +sample or unit impulse + +response of the system. + +And so the consequence, then, is +for a linear time-invariant + +system, the output can +be expressed as + +this sum where h[n-k] + +is the response to an impulse +occurring at time n = k. + +And this is referred to as +the convolution sum. + +Now, we can-- + +just to emphasize how we've gone +about this, let me show + +it from another perspective. + +We of course have taken the +sequence x[n], we have + +decomposed it as a linear +combination of these weighted, + +delayed impulses. + +When these are added together, +those correspond to the + +original sequence x[n]. + +If this impulse, for example, +generates a + +response which is x[0] + +h[n], where h[n] + +is the response to a unit +impulse at n = 0, and the + +second one generates a delayed +weighted response, and the + +third one similarly, and we +generate these individual + +responses, these are all added +together, and it's that linear + +combination that forms +the final output. + +So that's really kind of the way +we're thinking about it. + +We have a general sequence, +we're thinking of each + +individual sample individually, +each one of + +those pops the system, and +because of linearity, the + +response is the sum of those +individual responses. + +That's what happens in discrete +time, and pretty much + +the same strategy works +in continuous time. + +In particular, we can begin in +continuous time with the + +notion of decomposing a +continuous-time signal into a + +succession of arbitrarily +narrow rectangles. + +And as the width of the +rectangles goes to 0, the + +approximation gets better. + +Essentially what's going to +happen is that each of those + +individual rectangles, as they +get narrower and narrower, + +correspond more and more +to an impulse. + +Let me show you what I mean. + +Here we have a continuous-time +signal, and I've approximated + +it by a staircase. + +So in essence I can think of +this as individual rectangles + +of heights associated with the +height of the continuous + +curve, and so I've indicated +that down below. + +Here, for example, is the +impulse corresponding to the + +rectangle between t = -2 +Delta and t = -Delta. + +Here's the one from -Delta to 0, +and as we continue on down, + +we get impulses, or rather +rectangles, from successive + +parts of the wave form. + +Now let's look specifically at +the rectangle, for example, + +starting at 0 and ending at +Delta, and the amplitude of it + +is x(Delta). + +So what we have-- + +actually, this should be x(0), +and so let me just + +correct that here. + +That's x(0). + +And so we have a rectangle +height x(0), and recall the + +function that I defined last +time as delta_Delta(t), which + +had height 1 / delta +and width delta. + +So multiplying finally by this +last little Delta, then, this + +is a representation +for the rectangle + +that I've shown there. + +Now there's a little bit of +algebra there to kind of track + +through, but what we're really +doing is just simply + +representing this in terms +of rectangles. + +What I want to do is describe +each rectangle as in terms of + +that function delta_Delta(t), +which in the limit, then, + +becomes an impulse. + +So let's track that through +a little further. + +When we have that linear +combination, then, we're + +saying that x(t) can be +represented by a sum as I + +indicate here, which I can then +write more generally in + +this form, just indicating that +this is an infinite sum. + +We now want to take the limit +as Delta goes to 0, and as + +Delta goes to 0, notice +that this term + +becomes arbitrarily narrow. + +This goes to our impulse +function, and this, of course, + +goes to x of tau. + +And in fact, in the limit, a +sum of this form is exactly + +the way an integral +is defined. + +So we have an expression +for y(t) in terms + +of an impulse function. + +There, I have to admit, is a +little bit of detail to kind + +of focus on at your leisure, but +this is the general flow + +of the strategy. + +So what we have now is an +integral that tells us that + +tells us how x(t) can be +described as a sum or linear + +combination involving +impulses. + +This bottom equation, by the +way, is often referred to as + +the sifting integral. + +In essence, what it says is that +if I take a time function + +x(t) and put it through that +integral, the impulse as it + +zips by generates x(t) +all over again. + +Now, at first glance, what it +could look like is that we've + +taken a time function x(t) and +proceeded to represent it in a + +very complicated way, in terms +of itself, and one could ask, + +why bother doing that? + +And the reason, going back to +what our strategy was, is that + +what we want to do is exploit +the property of linearity. + +So by describing a time +function as a linear + +combination of weighted, delayed +impulses, as in effect + +we've done through this +summation that corresponds to + +a decomposition in terms of +impulses, we can now exploit + +linearity, specifically +recognizing that the output of + +a linear system is the sum +of the responses to these + +individual inputs. + +So with h_kDelta(t) +corresponding to the response + +to delta_Delta(t-kDelta) and +the rest of this stuff, the + +x(kDelta) and this +little Delta are + +basically scale factors-- + +for a linear system, then, if +the input is expressed in this + +form, the output is expressed in +this form, and again taking + +the limit as Delta goes to +0, by definition, this + +corresponds to an integral. + +It's the integral that I +indicate here with h_tau(t) + +corresponding to the impulse +response due to an impulse + +occurring at time tau. + +Now, again, we can do +the same thing. + +In particular, if the system +is time-invariant, then the + +response to each of these +delayed impulses is simply a + +delayed version of the impulse +response, and so we can relate + +these individual terms. + +And in particular, then, the +response to an impulse + +occurring at time t = tau is +simply the response to an + +impulse occurring at time 0 +shifted over to the time + +origin tau. + +Again, as we did before, we'll +drop this subscript h_0, so + +h_0(t) we'll simply +define as h(t). + +What we're left with when we do +that is the description of + +a linear time-invariant system +through this integral, which + +tells us how the output is +related to the input and to + +the impulse response. + +Again, let's just quickly look +at this from another + +perspective as we did +in discrete time. + +Recall that what we've done +is to take the continuous + +function, decompose it in terms +of rectangles, and then + +each of these rectangles +generates its individual + +response, and then +these individual + +responses are added together. + +And as we go through that +process, of course, there's a + +process whereby we let the +approximation go to the + +representation of +a smooth curve. + +Now, again, I stress if there is +certainly a fair amount to + +kind of examine carefully there, +but it's important to + +also reflect on what we've done, +which is really pretty + +significant. + +What we've managed to accomplish +is to exploit the + +properties of linearity and time +invariance, so that the + +system could be represented in +terms only of its response to + +an impulse at time 0. + +So for a linear time-invariant +system-- + +quite amazingly, actually-- + +if you know its response to an +impulse at t = 0 or n = 0, + +depending on discrete or +continuous time, then in fact, + +through the convolution sum +in discrete time or the + +convolution integral in +continuous time, you can + +generate the response to +an arbitrary input. + +Let me just introduce a small +amount of notation. + +Again, reminding you of the +convolution sum in the + +discrete-time case, which looks +as I've indicated here-- + +the sum of x[k] + +h[n-k] + +will have the requirement of +making such frequent reference + +to convolution that it's +convenient to notationally + +represent it as I have here +with an asterisk. + +So x[n] + +* h[n] + +means or denotes the +convolution of x[n] + +with h[n]. + +And correspondingly in the +continuous-time case, we have + +the convolution integral, which +here is the sifting + +integral + +as we talked about, representing +x(t) in terms of + +itself as a linear combination +of delayed impulses. + +Here we have the convolution +integral, and again we'll use + +the asterisk to denote +convolution. + +Now, there's a lot about +convolution that we'll want to + +talk about. + +There are properties of +convolution which tell us + +about properties of linear +time-invariant systems. + +Also, it's important to focus +on the mechanics of + +implementing a convolution-- + +in other words, understanding +and generating some fluency + +and insight into what these +particular sum and integral + +expressions mean. + +So let's first look at +discrete-time convolution and + +examine more specifically what +in essence the sum tells us to + +do in terms of manipulating +the sequences. + +So returning to the expression +for the convolution sum, as I + +show here, the sum of x[k] + +h[n-k]-- + +let's focus in on an example +where we choose x[n] + +as a unit step and h[n] + +as a real exponential times +the a unit step. + +So the sequence x[n] + +is as I indicate here, +and the sequence h[n] + +is an exponential for positive +time and 0 for negative time. + +So we have x[n] + +and h[n], but now let's look +back at the equation and let + +me stress that what we +want is not x[n] + +and h[n]-- + +we want x[k], because +we're going to sum + +over k, and not h[k] + +but h[n-k]. + +So we have then from x[n], +it's straightforward to + +generate x[k]. + +It's simply changing the +index of summation. + +And what's h[n-k]? + +Well what's h[-k]? + +h[-k] + +is h[k] + +flipped over. + +So if this is what h[k] + +looks like, then this +is what h[n-k] + +looks like. + +In essence, what the operation +of convolution or the + +mechanics of convolution tells +us to do is to take the + +sequence h[n-k], +which is h[-k] + +positioned with its origin at +k = n, and multiply this + +sequence by this sequence and +sum the product from k = + +-infinity to +infinity. + +So if we were to compute, for +example, the output at n = 0-- + +as I positioned this sequence +here, this is at n = 0-- + +I would take this and multiply +it by this and sum from + +-infinity to +infinity. + +Or, for n = 1, I would position +it here, for n = 2, I + +would position it here. + +Well, you can kind of see +what the idea is. + +Let's look at this a little more +dynamically and see, in + +fact, how one sequence slides +past the other, and how the + +output y[n] + +builds up to the +correct answer. + +So the input that we're +considering is a step input, + +which I show here, and the +impulse response that we will + +convolve this with is a +decaying exponential. + +Now, to form the convolution, we +want the product of x[k]-- + +not with h[k], but with h[n-k], +corresponding to + +taking h[k] + +and reflecting it about the +origin and then shifting it + +appropriately. + +So here we see h[n-k] + +for n = 0, namely h[-k], and now +h[1-k], which we'll show + +next, is this shifted to +the right by one point. + +Here we have h[1-k]-- + +shifting to the right by one +more point is h[2-k], and + +shifting again to the right +we'll have h[3-k]. + +Now let's shift back to the left +until n is negative, and + +then we'll begin the +convolution. + +So here's n = 0, n = -1, +n = -2, and n = -3. + +Now, to form the convolution, +we want the product of x[k] + +with h[n-k] + +summed from -infinity +to +infinity. + +For n negative, that product is +0, and therefore the result + +of the convolution is 0. + +As we shift to the right, +we'll build up the + +convolution, and the result of +the convolution will be shown + +on the bottom trace. + +So we begin the process +with n negative, and + +here we have n = -1. + +At n = 0, we get our first +non-zero contribution. + +Now as we shift further to the +right corresponding to + +increasing n, we will accumulate +more and more terms + +in the sum, and the convolution +will build up. + +In particular for this example, +the result of the + +convolution increases +monotonically, asymptotically + +approaching a constant, and +that constant, in fact, is + +just simply the accumulation +of the values under the + +exponential. + +Now let's carry out the +convolution this time with an + +input which is a rectangular +pulse instead of a step input. + +Again, the same impulse +response, namely a decaying + +exponential, and so we want +to begin with h[n-k] + +and again with n negative +shown here. + +Again, with n negative, there +are no non-zero terms in the + +product, and so the convolution +for n negative + +will be 0 as it was in +the previous case. + +Again, on the bottom trace we'll +show the result of the + +convolution as the impulse +response slides along. + +At n = 0, we get our first +non-zero term. + +As n increases past 0, we will +begin to generate an output, + +basically the same as the output +that we generated with + +a step input, until the impulse +response reaches a + +point where as we slide further, +we slide outside the + +interval where the rectangle +is non-zero. + +So when we slide one point +further from what's shown + +here, the output will now decay, +corresponding to the + +fact that the impulse response +is sliding outside the + +interval in which the +input is non-zero. + +So, on the bottom trace we +now see the result of the + +convolution. + +OK. + +So what you've seen, then, is +an example of discrete-time + +convolution. + +Let's now look at an example +of continuous-time + +convolution. + +As you might expect, +continuous-time convolution + +operates in exactly +the same way. + +Continuous-time convolution-- + +we have the expression again +y(t) is an integral with now + +x(tau) and h(t-tau). + +It has exactly the same kind of +form as we had previously + +for discrete-time +convolution-- + +and in fact, the mechanics +of the continuous-time + +convolution are identical. + +So here is our example with x(t) +equal to a unit step and + +h(t) now a real exponential +times a unit step. + +I show here x(t), which is +the unit step function. + +Here we have h(t), which is an +exponential for positive time + +and 0 for negative time. + +Again, looking back at the +expression for convolution, + +it's not x(t) that we want, +it x(tau) that we want. + +And it's not h(t) or h(tau) that +we want, it's h(t-tau). + +We plan to multiply these +together and integrate over + +the variable tau, and that gives +us the output at any + +given time. + +If we want it at another time, +we change the value of t as an + +argument inside this integral. + +So here we have x(t), and here +we have h(t), which isn't + +quite what we wanted. + +Here we have x(tau), and that's +fine-- it's just x(t) + +with t relabeled as tau. + +Now, what is h(t-tau)? + +Well, here's h(tau), and +if we simply turn that + +over, here is h(t-tau). + +And h(t-tau) is positioned, +then, at tau equal to t. + +As we change the value of t that +change the position of + +this signal, now we multiply +these two together and + +integrate from -infinity to ++infinity with h(t-tau) + +positioned at the appropriate +value of t. + +Again, it's best really to see +this example and get the + +notion of the signal being +flipped and the two signals + +sliding past each other, +multiplying and integrating by + +looking at it dynamically +and observing how the + +answer builds up. + +Again, the input that we +consider is a step input. + +And again, we use an impulse +response which is a decaying + +exponential. + +To form the convolution, we want +the product of x(tau)-- + +not with h(tau), but +with h(t-tau). + +So we want h(t) time-reversed, +and then shifted appropriately + +depending on the value of t. + +Let's first just look at +h(t-tau) for t positive + +corresponding to shifting +h(-tau) out to the right, and + +here we have t increasing. + +Here is t decreasing, and +we'll want to begin the + +convolution with t negative, +corresponding to shifting + +h(-tau) to the left. + +Now to form the convolution, +we want the + +product of these two. + +For t negative, there are no +non-zero contributions to the + +integral, and so the convolution +will be 0 for t + +less than 0. + +On the bottom trace, we show the +result of the convolution, + +here for t negative, and for t +less than 0, we will continue + +to have 0 in the convolution. + +Now as t increases past 0, we +begin to get some non-zero + +contribution in the product, +indicated by the fact that the + +convolution-- + +the result of the +convolution-- + +starts to build up. + +As t increases further, we +will get more and more + +non-zero contribution +in the integrand. + +So, the result of the +convolution will be a + +monotonically increasing +function for this particular + +example, which asymptotically +approaches a constant. + +That constant will be +proportional to the area under + +the impulse response, because +of the fact that we're + +convolving with a step input. + +Now let's carry out the +convolution with an input + +which is a rectangular pulse-- + +again, an impulse response +which is an exponential. + +So to form the convolution, we +want x(tau) with h(t-tau)-- + +h(t-tau) shown here +for t negative. + +To form the convolution, we +take the integral of the + +product of these two, which +again will be 0 + +for t less than 0. + +The bottom trace shows the +result of the convolution + +here, shown as 0, and it will +continue to be 0 until t + +becomes positive, at which +point we build up some + +non-zero term in +the integrand. + +Now as we slide further, until +the impulse response shifts + +outside the interval in which +the pulse is non-zero, the + +output will build up. + +But here we've now begun to +leave that interval, and so + +the output will start to +decay exponentially. + +As the impulse response slides +further and further + +corresponding to increasing t, +then the output will decay + +exponentially, representing the +fact that there is less + +and less area in the product +of x(tau) and h(t-tau). + +Asymptotically, this output +will then approach 0. + +OK. + +So you've seen convolution, +you've seen the derivation of + +convolution, and kind of the +graphical representation of + +convolution. + +Finally, let's work again with +these two examples, and let's + +go through those two examples +analytically so that we + +finally see how, analytically, +the result develops for those + +same examples. + +Well, we have first the +discrete-time case, and let's + +take our discrete-time +example. + +In general, the convolution sum +is as I've indicated here. + +This is just our expression +from before, which is the + +convolution sum. + +If we take our two examples-- + +the example of an input which is +a unit step, and an impulse + +response, which is a real +exponential multiplied by a + +unit step-- + +we have then replacing x[k] + +by what we know the input +to be, and h[n-k] + +by what we know the impulse +response to be, the output is + +the expression that +we have here. + +Now, in this expression-- + +and you'll see this very +generally and with some more + +complicated examples when +you look at the text-- + +as you go to evaluate these +expressions, generally what + +happens is that the signals +have different analytical + +forms in different regions. + +That's, in fact, what +we have here. + +In particular, let's look at the +sum, and what we observe + +first of all is that the limits +on this sum are going + +to be modified, depending +on where this unit + +step is 0 and non-zero. + +In particular, if we first +consider what will turn out to + +be the simple case-- + +namely, n less than 0-- + +for n less than 0, this +unit step is 0 for k + +greater than n. + +With n less than 0, that means +that this unit step never is + +non-zero for k positive. + +On the other hand, this unit +step is never non-zero or + +always 0 for k negative. + +Let me just stress that by +looking at the particular + +graphs, here is the +unit step u[k]. + +Here is the unit step u[n-k], +and for n less than 0, so that + +this point comes before this +point, the product of these + +two is equal to 0. + +That means there is no overlap +between these two terms, and + +so it says that y[n], +the output, is 0 + +for n less than 0. + +Well, that was an easy one. + +For n greater than 0, it's not +quite as straightforward as + +coming out with the answer 0. + +So now let's look at what +happens when the two unit + +steps overlap, and this would +correspond to what I've + +labeled here as interval 2, +namely for n greater than 0. + +If we just look back at the +summation that we had, the + +summation now corresponds to +this unit step and this unit + +step, having some overlap. + +So for interval 2, corresponding +to n greater + +than 0, we have u[k], +the unit step. + +We have u[n-k], which is a unit +step going backward in + +time, but which extends for +positive values of n. + +If we think about multiplying +these two together, we will + +get in the product unity +for what values of k? + +Well, for k starting at 0 +corresponding to one of the + +unit steps and ending at +n corresponding to + +the other unit step. + +So we have an overlap between +these for k equal to 0, et + +cetera, up through +the value n. + +Now, that means that in terms +of the original sum, we can + +get rid of the unit steps +involved by simply changing + +the limits on the sum. + +The limits now are from 0 to +n, of the term alpha^(n-k). + +We had before a u[k] + +and u[n-k], and that disappeared +because we dealt + +with that simply by modifying +the limits. + +We now pull out the term +alpha^n, because the summation + +is on k, not on n, so +we can simply pull + +that term of the sum. + +We now have alpha^(-k), which +we can rewrite as + +(alpha^(-1))^k. + +The upshot of all of +this is that y[n] + +now we can reexpress as alpha^n, +the sum from 0 to n + +of (alpha^(-1)^k. + +The question is, how do +we evaluate that? + +It essentially corresponds to a +finite number of terms in a + +geometric series. + +That, by the way, is a summation +that will recur over + +and over and over and over +again, and it's one that you + +should write down, write on your +back pocket, write on the + +palm of your hand, or whatever +it takes to remember it. + +What you'll see is it that +will recur more or less + +throughout the course, and so +it's one worth remembering. + +In particular, what the sum of a +geometric series is, is what + +I've indicated here. + +We have the sum from +0 to r, of beta^k. + +It's 1 - beta^(r+1)-- + +this is one more than the upper +limit on the summation-- + +and in the denominator +is 1 - beta. + +So, this equation +is important. + +There's no point in attempting +to derive it. + +However you get to it, it's +important to retain it. + +We can now use that summation +in the expression + +that we just developed. + +So let's proceed to evaluate +that sum in closed form. + +We now go back to the expression +that we just + +worked out-- y[n] + +is alpha^n, the sum from +0 to n, (alpha^(-1))^k. + +This plays the role of beta +in the term that I just-- + +in the expression then +I just presented. + +So, using that result, we can +rewrite this summation as I + +indicate here. + +The final result that we end up +with after a certain amount + +of algebra is y[n] + +equal to (1 - alpha^(n+1)) +/ (1 - alpha). + +Let me just kind of indicate +with a few dots here that + +there is a certain amount of +algebra required in going from + +this step to this step, and I'd +like to leave you with the + +fun and opportunity of doing +that at your leisure. + +The expression we have +now for y[n], is y[n] + += (1 - alpha^(n+1)) +/ (1 - alpha). + +That's for n greater than 0. + +We had found out previously +there it was 0 + +for n less than 0. + +Finally, if we were to plot +this, what we would get is the + +graph that I indicate here. + +The first non-zero value occurs +at n = 0, and it has a + +height of 1, and then the next +non-zero value at 1, and this + +has a height of 1 + alpha, and +this is 1 + alpha + alpha^2. + +The sequence continues on like +that and asymptotically + +approaches, as n goes to +infinity, asymptotically + +approaches 1 / (1 - alpha), +which is consistent with the + +algebraic expression that we +have, that we developed, and + +obviously of course is also +consistent with the movie. + +That's our discrete-time +example, which we kind of went + +through graphically with the +transparencies, and we went + +through graphically with the +movie, and now we've gone + +through analytically. + +Now let's look analytically at +the continuous-time example, + +which pretty much flows +in the same way as + +we've just gone through. + +Again, we have the convolution +integral, which is the + +integral indicated at the top. + +Our example, you recall, was +with x(t) as a unit step, and + +h(t) as an exponential +times a unit step. + +So when we substitute those in, +this then corresponds to + +x(t) and this corresponds +to h(t-tau). + +Again, we have the same issue +more or less, which is that + +inside that integral, there +are two steps, one of them + +going forward in time and one +of them going backward in + +time, and we need to examine +when they overlap and when + +they don't. + +When they don't overlap, the +product, of course, is 0, and + +there's no point doing any +integration because the + +integrand is 0. + +So if we track it through, we +have again Interval 1, which + +is t less than 0. + +For t less than 0, this unit +step, which only begins at tau + += 0, and this unit step which is +0, by the time tau gets up + +to t and beyond. + +For t less than 0, there's no +overlap between the unit step + +going forward in time +and the unit step + +going backward in time. + +Consequently, the integrand is +equal to 0, and consequently, + +the output is equal to 0. + +We can likewise look at the +interval where the two unit + +steps do overlap. + +In that case what happens again +is that the overlap, in + +essence of the unit step, tells +us, gives us a range on + +the integration-- + +in particular, the two steps +overlap when t is greater than + +0 from tau = 0 to tau = t. + +For Interval 2, for +t greater than 0-- + +again, of course, we have +this expression. + +This product of this unit step +and this unit step is equal to + +1 in this range, and so that +allows us, then, to change the + +limits on the integral-- + +instead of from -infinity to ++infinity, we know that the + +integrand is non-zero only +over this range. + +Looking at this integral, we +can now pull out the term + +which corresponds to e^-at, just +as we pulled out a term + +in the discrete-time case. + +We notice in the integral that +we have e^(-a*-tau), so that + +gives us the integral from +0 to t of e^(a*tau). + +If we perform that integration, +we end up with + +this expression. + +Finally, multiplying this by +e^-at, we have for y(t), for t + +greater than 0, the algebraic +expression that I've indicated + +on the bottom. + +So we had worked out t +less than 0, and we + +come out with 0. + +We work out t greater than 0, +and we come out with this + +algebraic expression. + +If we plot this algebraic +expression as a function of + +time, we find that what it +corresponds to is an + +exponential behavior starting +at zero and exponentially + +heading asymptotically toward +the value 1 / a. + +We've gone through these +examples several ways, and one + +is analytically. + +In order to develop a feel and +fluency for convolution, it's + +absolutely essential to work +through a variety of examples, + +both understanding them +graphically and understanding + +them as we did here +analytically. + +You'll have an opportunity to +do that through the problems + +that I've suggested in the +video course manual. + +In the next lecture, what we'll +turn to are some general + +properties of convolution, and +show how this rather amazing + +representation of linear +time-invariant systems in fact + +leads to a variety of +properties of linear + +time-invariant systems. + +We'll find that convolution is +fairly rich in its properties, + +and what this leads to are some +very nice and desirable + +and exploitable properties of +linear time-invariant systems. + +Thank you. \ No newline at end of file diff --git a/aNLEnFtWwhg.txt b/aNLEnFtWwhg.txt new file mode 100644 index 0000000000000000000000000000000000000000..f5da55a30bd4b6b5dbaf7ecab572d4ac5c8f35a5 --- /dev/null +++ b/aNLEnFtWwhg.txt @@ -0,0 +1,403 @@ +align:start position:0% + +in this lecture we start our systematic + + align:start position:0% +in this lecture we start our systematic + + + align:start position:0% +in this lecture we start our systematic +study of Bayesian inference we will + + align:start position:0% +study of Bayesian inference we will + + + align:start position:0% +study of Bayesian inference we will +first talk a little bit about the big + + align:start position:0% +first talk a little bit about the big + + + align:start position:0% +first talk a little bit about the big +picture about inference in general the + + align:start position:0% +picture about inference in general the + + + align:start position:0% +picture about inference in general the +huge range of possible applications and + + align:start position:0% +huge range of possible applications and + + + align:start position:0% +huge range of possible applications and +the different types of problems that one + + align:start position:0% +the different types of problems that one + + + align:start position:0% +the different types of problems that one +may encounter for example we have + + align:start position:0% +may encounter for example we have + + + align:start position:0% +may encounter for example we have +hypothesis testing problems in which we + + align:start position:0% +hypothesis testing problems in which we + + + align:start position:0% +hypothesis testing problems in which we +are trying to choose between a finite + + align:start position:0% +are trying to choose between a finite + + + align:start position:0% +are trying to choose between a finite +and usually small number of alternative + + align:start position:0% +and usually small number of alternative + + + align:start position:0% +and usually small number of alternative +hypothesis or estimation problems where + + align:start position:0% +hypothesis or estimation problems where + + + align:start position:0% +hypothesis or estimation problems where +we want to estimate as close as we can + + align:start position:0% +we want to estimate as close as we can + + + align:start position:0% +we want to estimate as close as we can +and unknown numerical quantity we then + + align:start position:0% +and unknown numerical quantity we then + + + align:start position:0% +and unknown numerical quantity we then +move into the specifics of Bayesian + + align:start position:0% +move into the specifics of Bayesian + + + align:start position:0% +move into the specifics of Bayesian +inference the central idea is that we + + align:start position:0% +inference the central idea is that we + + + align:start position:0% +inference the central idea is that we +always use the Bayes rule to find the + + align:start position:0% +always use the Bayes rule to find the + + + align:start position:0% +always use the Bayes rule to find the +posterior distribution of an unknown + + align:start position:0% +posterior distribution of an unknown + + + align:start position:0% +posterior distribution of an unknown +random variable based on observations of + + align:start position:0% +random variable based on observations of + + + align:start position:0% +random variable based on observations of +a related random variable depending on + + align:start position:0% +a related random variable depending on + + + align:start position:0% +a related random variable depending on +whether the random variables are + + align:start position:0% +whether the random variables are + + + align:start position:0% +whether the random variables are +discrete or continuous we must of course + + align:start position:0% +discrete or continuous we must of course + + + align:start position:0% +discrete or continuous we must of course +use the appropriate version of the Bayes + + align:start position:0% +use the appropriate version of the Bayes + + + align:start position:0% +use the appropriate version of the Bayes +rule if we want to summarize the + + align:start position:0% +rule if we want to summarize the + + + align:start position:0% +rule if we want to summarize the +posterior in a single number that is to + + align:start position:0% +posterior in a single number that is to + + + align:start position:0% +posterior in a single number that is to +come up with a numerical estimate of the + + align:start position:0% +come up with a numerical estimate of the + + + align:start position:0% +come up with a numerical estimate of the +unknown random variable we then have + + align:start position:0% +unknown random variable we then have + + + align:start position:0% +unknown random variable we then have +some options one is to report the value + + align:start position:0% +some options one is to report the value + + + align:start position:0% +some options one is to report the value +at which the posterior is largest + + align:start position:0% +at which the posterior is largest + + + align:start position:0% +at which the posterior is largest +another is to report the mean of the + + align:start position:0% +another is to report the mean of the + + + align:start position:0% +another is to report the mean of the +conditional distribution these go under + + align:start position:0% +conditional distribution these go under + + + align:start position:0% +conditional distribution these go under +the acronyms map and LMS we will see + + align:start position:0% +the acronyms map and LMS we will see + + + align:start position:0% +the acronyms map and LMS we will see +shortly what these acronyms stand for + + align:start position:0% +shortly what these acronyms stand for + + + align:start position:0% +shortly what these acronyms stand for +given any particular method for coming + + align:start position:0% +given any particular method for coming + + + align:start position:0% +given any particular method for coming +up with a point estimate there are + + align:start position:0% +up with a point estimate there are + + + align:start position:0% +up with a point estimate there are +certain performance metrics that tell us + + align:start position:0% +certain performance metrics that tell us + + + align:start position:0% +certain performance metrics that tell us +how good the estimate is for hypothesis + + align:start position:0% +how good the estimate is for hypothesis + + + align:start position:0% +how good the estimate is for hypothesis +testing problems the appropriate metric + + align:start position:0% +testing problems the appropriate metric + + + align:start position:0% +testing problems the appropriate metric +is the probability of error the + + align:start position:0% +is the probability of error the + + + align:start position:0% +is the probability of error the +probability of making a mistake for + + align:start position:0% +probability of making a mistake for + + + align:start position:0% +probability of making a mistake for +problems of estimating a numerical + + align:start position:0% +problems of estimating a numerical + + + align:start position:0% +problems of estimating a numerical +quantity an appropriate metric that we + + align:start position:0% +quantity an appropriate metric that we + + + align:start position:0% +quantity an appropriate metric that we +will be using a lot is the expected + + align:start position:0% +will be using a lot is the expected + + + align:start position:0% +will be using a lot is the expected +value of the squared error as you will + + align:start position:0% +value of the squared error as you will + + + align:start position:0% +value of the squared error as you will +see there will be no new mathematics in + + align:start position:0% +see there will be no new mathematics in + + + align:start position:0% +see there will be no new mathematics in +this lecture just a few definitions a + + align:start position:0% +this lecture just a few definitions a + + + align:start position:0% +this lecture just a few definitions a +few new terms and an application of the + + align:start position:0% +few new terms and an application of the + + + align:start position:0% +few new terms and an application of the +Bayes rule nevertheless it is important + + align:start position:0% +Bayes rule nevertheless it is important + + + align:start position:0% +Bayes rule nevertheless it is important +to be able to apply the Bayes rule + + align:start position:0% +to be able to apply the Bayes rule + + + align:start position:0% +to be able to apply the Bayes rule +systematically and with confidence for + + align:start position:0% +systematically and with confidence for + + + align:start position:0% +systematically and with confidence for +this reason we will be going over + + align:start position:0% +this reason we will be going over + + + align:start position:0% +this reason we will be going over +several example \ No newline at end of file diff --git a/apzEJCsycVM.txt b/apzEJCsycVM.txt new file mode 100644 index 0000000000000000000000000000000000000000..c53023dd3c5ffd4acd82b4b672bfe162e157be88 --- /dev/null +++ b/apzEJCsycVM.txt @@ -0,0 +1,2115 @@ +align:start position:0% + +welcome back to recitation uh in this in + + align:start position:0% +welcome back to recitation uh in this in + + + align:start position:0% +welcome back to recitation uh in this in +this video I'd like us to do the + + align:start position:0% +this video I'd like us to do the + + + align:start position:0% +this video I'd like us to do the +following problem I want us to show that + + align:start position:0% +following problem I want us to show that + + + align:start position:0% +following problem I want us to show that +the function if I integrate x the N eus + + align:start position:0% +the function if I integrate x the N eus + + + align:start position:0% +the function if I integrate x the N eus +X from 1 to Infinity that that actually + + align:start position:0% +X from 1 to Infinity that that actually + + + align:start position:0% +X from 1 to Infinity that that actually +converges for any value of N and I want + + align:start position:0% +converges for any value of N and I want + + + align:start position:0% +converges for any value of N and I want +us to show this without using using + + align:start position:0% +us to show this without using using + + + align:start position:0% +us to show this without using using +integration by parts end times so I'd + + align:start position:0% +integration by parts end times so I'd + + + align:start position:0% +integration by parts end times so I'd +like you to figure out a way to show + + align:start position:0% +like you to figure out a way to show + + + align:start position:0% +like you to figure out a way to show +that this this integral converges and + + align:start position:0% +that this this integral converges and + + + align:start position:0% +that this this integral converges and +again what we mean by converges is for a + + align:start position:0% +again what we mean by converges is for a + + + align:start position:0% +again what we mean by converges is for a +fixed value here say some some B if I + + align:start position:0% +fixed value here say some some B if I + + + align:start position:0% +fixed value here say some some B if I +let as the limit as B goes to Infinity + + align:start position:0% +let as the limit as B goes to Infinity + + + align:start position:0% +let as the limit as B goes to Infinity +that that that sequence of of values + + align:start position:0% +that that that sequence of of values + + + align:start position:0% +that that that sequence of of values +converges to a finite number that's what + + align:start position:0% +converges to a finite number that's what + + + align:start position:0% +converges to a finite number that's what +we mean again when we say an integral + + align:start position:0% +we mean again when we say an integral + + + align:start position:0% +we mean again when we say an integral +converges ultimately we want to show + + align:start position:0% +converges ultimately we want to show + + + align:start position:0% +converges ultimately we want to show +this as finite so show this as finite + + align:start position:0% +this as finite so show this as finite + + + align:start position:0% +this as finite so show this as finite +without using integration by parts and + + align:start position:0% +without using integration by parts and + + + align:start position:0% +without using integration by parts and +times so I'll give you a little while to + + align:start position:0% +times so I'll give you a little while to + + + align:start position:0% +times so I'll give you a little while to +to work on it and then I'll be back and + + align:start position:0% +to work on it and then I'll be back and + + + align:start position:0% +to work on it and then I'll be back and +I will show you how I did it + + align:start position:0% + + + + align:start position:0% + +okay welcome back well I I want to show + + align:start position:0% +okay welcome back well I I want to show + + + align:start position:0% +okay welcome back well I I want to show +you how we we can show that this + + align:start position:0% +you how we we can show that this + + + align:start position:0% +you how we we can show that this +integral actually converges for any n + + align:start position:0% +integral actually converges for any n + + + align:start position:0% +integral actually converges for any n +and I don't want to have to use + + align:start position:0% +and I don't want to have to use + + + align:start position:0% +and I don't want to have to use +integration by parts and and kill off + + align:start position:0% +integration by parts and and kill off + + + align:start position:0% +integration by parts and and kill off +Powers of X in order to do that um so + + align:start position:0% +Powers of X in order to do that um so + + + align:start position:0% +Powers of X in order to do that um so +again the integral is from one to + + align:start position:0% +again the integral is from one to + + + align:start position:0% +again the integral is from one to +Infinity of x to the n e to the minus X + + align:start position:0% +Infinity of x to the n e to the minus X + + + align:start position:0% +Infinity of x to the n e to the minus X +DX and if you recall Professor jarrison + + align:start position:0% +DX and if you recall Professor jarrison + + + align:start position:0% +DX and if you recall Professor jarrison +was showing in in the lecture video + + align:start position:0% +was showing in in the lecture video + + + align:start position:0% +was showing in in the lecture video +that if you can show even from not one + + align:start position:0% +that if you can show even from not one + + + align:start position:0% +that if you can show even from not one +to Infinity but from very far out to + + align:start position:0% +to Infinity but from very far out to + + + align:start position:0% +to Infinity but from very far out to +Infinity that that that integral + + align:start position:0% +Infinity that that that integral + + + align:start position:0% +Infinity that that that integral +converges from one to whatever the far + + align:start position:0% +converges from one to whatever the far + + + align:start position:0% +converges from one to whatever the far +out value is this integral is finite + + align:start position:0% +out value is this integral is finite + + + align:start position:0% +out value is this integral is finite +okay doesn't blow up it's going to be + + align:start position:0% +okay doesn't blow up it's going to be + + + align:start position:0% +okay doesn't blow up it's going to be +potentially a very big number but it is + + align:start position:0% +potentially a very big number but it is + + + align:start position:0% +potentially a very big number but it is +going to be a finite number there are no + + align:start position:0% +going to be a finite number there are no + + + align:start position:0% +going to be a finite number there are no +places where we run into trouble with + + align:start position:0% +places where we run into trouble with + + + align:start position:0% +places where we run into trouble with +this function it's a continuous function + + align:start position:0% +this function it's a continuous function + + + align:start position:0% +this function it's a continuous function +um from one to Infinity so we can we can + + align:start position:0% +um from one to Infinity so we can we can + + + align:start position:0% +um from one to Infinity so we can we can +go very far out and say okay from very + + align:start position:0% +go very far out and say okay from very + + + align:start position:0% +go very far out and say okay from very +far out to Infinity the integral + + align:start position:0% +far out to Infinity the integral + + + align:start position:0% +far out to Infinity the integral +converges and then that's going to be + + align:start position:0% +converges and then that's going to be + + + align:start position:0% +converges and then that's going to be +enough so we did we did see that kind of + + align:start position:0% +enough so we did we did see that kind of + + + align:start position:0% +enough so we did we did see that kind of +technique earlier but I just want to + + align:start position:0% +technique earlier but I just want to + + + align:start position:0% +technique earlier but I just want to +remind you that's that's what we're + + align:start position:0% +remind you that's that's what we're + + + align:start position:0% +remind you that's that's what we're +going to do now you might have thought + + align:start position:0% +going to do now you might have thought + + + align:start position:0% +going to do now you might have thought +about this problem and said well I know + + align:start position:0% +about this problem and said well I know + + + align:start position:0% +about this problem and said well I know +that x to the N is much smaller than e + + align:start position:0% +that x to the N is much smaller than e + + + align:start position:0% +that x to the N is much smaller than e +to the X for uh for values of X very + + align:start position:0% +to the X for uh for values of X very + + + align:start position:0% +to the X for uh for values of X very +large so you might have said I think you + + align:start position:0% +large so you might have said I think you + + + align:start position:0% +large so you might have said I think you +used this notation also in the lecture x + + align:start position:0% +used this notation also in the lecture x + + + align:start position:0% +used this notation also in the lecture x +to the N is much smaller than e to the X + + align:start position:0% +to the N is much smaller than e to the X + + + align:start position:0% +to the N is much smaller than e to the X +for large x + + align:start position:0% + + + + align:start position:0% + +so what if we tried to do comparison + + align:start position:0% +so what if we tried to do comparison + + + align:start position:0% +so what if we tried to do comparison +with with those two functions we're + + align:start position:0% +with with those two functions we're + + + align:start position:0% +with with those two functions we're +going to see that's not quite enough but + + align:start position:0% +going to see that's not quite enough but + + + align:start position:0% +going to see that's not quite enough but +but let's let's say x is very large and + + align:start position:0% +but let's let's say x is very large and + + + align:start position:0% +but let's let's say x is very large and +let's look at a comparison if I say the + + align:start position:0% +let's look at a comparison if I say the + + + align:start position:0% +let's look at a comparison if I say the +integral from say some very large R to + + align:start position:0% +integral from say some very large R to + + + align:start position:0% +integral from say some very large R to +Infinity of x to the n e to the- X DX is + + align:start position:0% +Infinity of x to the n e to the- X DX is + + + align:start position:0% +Infinity of x to the n e to the- X DX is +certainly going to be much smaller than + + align:start position:0% +certainly going to be much smaller than + + + align:start position:0% +certainly going to be much smaller than +the integral from Big R to Infinity of e + + align:start position:0% +the integral from Big R to Infinity of e + + + align:start position:0% +the integral from Big R to Infinity of e +x * e- X + + align:start position:0% +x * e- X + + + align:start position:0% +x * e- X +DX and you think well you know that's + + align:start position:0% +DX and you think well you know that's + + + align:start position:0% +DX and you think well you know that's +that's a pretty good first step I'm + + align:start position:0% +that's a pretty good first step I'm + + + align:start position:0% +that's a pretty good first step I'm +doing all right but what happens here + + align:start position:0% +doing all right but what happens here + + + align:start position:0% +doing all right but what happens here +what's e to the x * e to Theus X it's e + + align:start position:0% +what's e to the x * e to Theus X it's e + + + align:start position:0% +what's e to the x * e to Theus X it's e +to x + x so it's e to the zero so it's + + align:start position:0% +to x + x so it's e to the zero so it's + + + align:start position:0% +to x + x so it's e to the zero so it's +one so this is integrating the constant + + align:start position:0% +one so this is integrating the constant + + + align:start position:0% +one so this is integrating the constant +one well the constant one from R to + + align:start position:0% +one well the constant one from R to + + + align:start position:0% +one well the constant one from R to +Infinity think of that it's the line + + align:start position:0% +Infinity think of that it's the line + + + align:start position:0% +Infinity think of that it's the line +yals 1 from R to Infinity it's an + + align:start position:0% +yals 1 from R to Infinity it's an + + + align:start position:0% +yals 1 from R to Infinity it's an +arbitrarily long rectangle that's got a + + align:start position:0% +arbitrarily long rectangle that's got a + + + align:start position:0% +arbitrarily long rectangle that's got a +lot of area it's got infinite area so + + align:start position:0% +lot of area it's got infinite area so + + + align:start position:0% +lot of area it's got infinite area so +this integral + + align:start position:0% +this integral + + + align:start position:0% +this integral +diverges that doesn't mean this one + + align:start position:0% +diverges that doesn't mean this one + + + align:start position:0% +diverges that doesn't mean this one +diverges right because this one's + + align:start position:0% +diverges right because this one's + + + align:start position:0% +diverges right because this one's +smaller than that one so this this one + + align:start position:0% +smaller than that one so this this one + + + align:start position:0% +smaller than that one so this this one +here could still converge even though + + align:start position:0% +here could still converge even though + + + align:start position:0% +here could still converge even though +this integral diverged again let me + + align:start position:0% +this integral diverged again let me + + + align:start position:0% +this integral diverged again let me +remind you why does this integral + + align:start position:0% +remind you why does this integral + + + align:start position:0% +remind you why does this integral +diverge because this is actually equal + + align:start position:0% +diverge because this is actually equal + + + align:start position:0% +diverge because this is actually equal +to one if I integrate one from R to + + align:start position:0% +to one if I integrate one from R to + + + align:start position:0% +to one if I integrate one from R to +Infinity I get something infinite so you + + align:start position:0% +Infinity I get something infinite so you + + + align:start position:0% +Infinity I get something infinite so you +might have started with that but that's + + align:start position:0% +might have started with that but that's + + + align:start position:0% +might have started with that but that's +not quite good enough right what is + + align:start position:0% +not quite good enough right what is + + + align:start position:0% +not quite good enough right what is +going to be good enough is if I pick any + + align:start position:0% +going to be good enough is if I pick any + + + align:start position:0% +going to be good enough is if I pick any +constant in front of this N I can put + + align:start position:0% +constant in front of this N I can put + + + align:start position:0% +constant in front of this N I can put +any constant in front of this N I want + + align:start position:0% +any constant in front of this N I want + + + align:start position:0% +any constant in front of this N I want +bigger than one and that's going to help + + align:start position:0% +bigger than one and that's going to help + + + align:start position:0% +bigger than one and that's going to help +us out so I'm going to pick the constant + + align:start position:0% +us out so I'm going to pick the constant + + + align:start position:0% +us out so I'm going to pick the constant +two because it's going to be easy and + + align:start position:0% +two because it's going to be easy and + + + align:start position:0% +two because it's going to be easy and +it's a nice fixed number if I so this is + + align:start position:0% +it's a nice fixed number if I so this is + + + align:start position:0% +it's a nice fixed number if I so this is +this is how you do it correctly or one + + align:start position:0% +this is how you do it correctly or one + + + align:start position:0% +this is how you do it correctly or one +one strategy to do it correctly if I + + align:start position:0% +one strategy to do it correctly if I + + + align:start position:0% +one strategy to do it correctly if I +take x to the 2 N instead of just x to + + align:start position:0% +take x to the 2 N instead of just x to + + + align:start position:0% +take x to the 2 N instead of just x to +the N for any n there's some r r big + + align:start position:0% +the N for any n there's some r r big + + + align:start position:0% +the N for any n there's some r r big +enough so that X the 2 N is much less + + align:start position:0% +enough so that X the 2 N is much less + + + align:start position:0% +enough so that X the 2 N is much less +than e to the + + align:start position:0% +than e to the + + + align:start position:0% +than e to the +X for all X bigger than some bigger than + + align:start position:0% +X for all X bigger than some bigger than + + + align:start position:0% +X for all X bigger than some bigger than +or equal to some R so if I go far enough + + align:start position:0% +or equal to some R so if I go far enough + + + align:start position:0% +or equal to some R so if I go far enough +out in X values + + align:start position:0% +out in X values + + + align:start position:0% +out in X values +x 2 N is much smaller than e e to X so + + align:start position:0% +x 2 N is much smaller than e e to X so + + + align:start position:0% +x 2 N is much smaller than e e to X so +let's say that that that value is + + align:start position:0% +let's say that that that value is + + + align:start position:0% +let's say that that that value is +capital r and then we're we're much + + align:start position:0% +capital r and then we're we're much + + + align:start position:0% +capital r and then we're we're much +smaller this is not very formal but it's + + align:start position:0% +smaller this is not very formal but it's + + + align:start position:0% +smaller this is not very formal but it's +getting closer to a formal kind of thing + + align:start position:0% +getting closer to a formal kind of thing + + + align:start position:0% +getting closer to a formal kind of thing +then that means x to the N is much + + align:start position:0% +then that means x to the N is much + + + align:start position:0% +then that means x to the N is much +smaller than e to X over + + align:start position:0% +smaller than e to X over + + + align:start position:0% +smaller than e to X over +2 right and that's going to be the key + + align:start position:0% +2 right and that's going to be the key + + + align:start position:0% +2 right and that's going to be the key +let's anticipate why that is the problem + + align:start position:0% +let's anticipate why that is the problem + + + align:start position:0% +let's anticipate why that is the problem +with the substitution of e to the X was + + align:start position:0% +with the substitution of e to the X was + + + align:start position:0% +with the substitution of e to the X was +that e to x * eus X gave you 1 but if if + + align:start position:0% +that e to x * eus X gave you 1 but if if + + + align:start position:0% +that e to x * eus X gave you 1 but if if +I use e to the X over 2 I'm going to end + + align:start position:0% +I use e to the X over 2 I'm going to end + + + align:start position:0% +I use e to the X over 2 I'm going to end +up with some some function e to the + + align:start position:0% +up with some some function e to the + + + align:start position:0% +up with some some function e to the +minus something and that's going to be + + align:start position:0% +minus something and that's going to be + + + align:start position:0% +minus something and that's going to be +good because that's going to converge so + + align:start position:0% +good because that's going to converge so + + + align:start position:0% +good because that's going to converge so +if you tried e to the X first and you + + align:start position:0% +if you tried e to the X first and you + + + align:start position:0% +if you tried e to the X first and you +saw you didn't get a good function you + + align:start position:0% +saw you didn't get a good function you + + + align:start position:0% +saw you didn't get a good function you +didn't you didn't have to stop there you + + align:start position:0% +didn't you didn't have to stop there you + + + align:start position:0% +didn't you didn't have to stop there you +could say well I was close the problem + + align:start position:0% +could say well I was close the problem + + + align:start position:0% +could say well I was close the problem +is I I canceled off all the e to the + + align:start position:0% +is I I canceled off all the e to the + + + align:start position:0% +is I I canceled off all the e to the +minus power which is what I want to keep + + align:start position:0% +minus power which is what I want to keep + + + align:start position:0% +minus power which is what I want to keep +around if I want to keep some of that + + align:start position:0% +around if I want to keep some of that + + + align:start position:0% +around if I want to keep some of that +around then I have to have a little less + + align:start position:0% +around then I have to have a little less + + + align:start position:0% +around then I have to have a little less +power of e to the X there I have to have + + align:start position:0% +power of e to the X there I have to have + + + align:start position:0% +power of e to the X there I have to have +e to I can't just have e to the X I + + align:start position:0% +e to I can't just have e to the X I + + + align:start position:0% +e to I can't just have e to the X I +should have something like square root + + align:start position:0% +should have something like square root + + + align:start position:0% +should have something like square root +of e to the x so e to X over 2 that's + + align:start position:0% +of e to the x so e to X over 2 that's + + + align:start position:0% +of e to the x so e to X over 2 that's +going to help us out so this is this is + + align:start position:0% +going to help us out so this is this is + + + align:start position:0% +going to help us out so this is this is +kind of as you're working on this type + + align:start position:0% +kind of as you're working on this type + + + align:start position:0% +kind of as you're working on this type +of problem this is some of the the + + align:start position:0% +of problem this is some of the the + + + align:start position:0% +of problem this is some of the the +thought process you want to go through + + align:start position:0% +thought process you want to go through + + + align:start position:0% +thought process you want to go through +so what do we see here we have x to the + + align:start position:0% +so what do we see here we have x to the + + + align:start position:0% +so what do we see here we have x to the +N is much less than e to the X over + + align:start position:0% +N is much less than e to the X over + + + align:start position:0% +N is much less than e to the X over +2 for X bigger than or equal to R so now + + align:start position:0% +2 for X bigger than or equal to R so now + + + align:start position:0% +2 for X bigger than or equal to R so now +let's do a comparison with our new + + align:start position:0% +let's do a comparison with our new + + + align:start position:0% +let's do a comparison with our new +comparative function so I'm going to + + align:start position:0% +comparative function so I'm going to + + + align:start position:0% +comparative function so I'm going to +come over and this will be our last line + + align:start position:0% +come over and this will be our last line + + + align:start position:0% +come over and this will be our last line +to finish us off so now we're + + align:start position:0% +to finish us off so now we're + + + align:start position:0% +to finish us off so now we're +integrating from R to infinity x to the + + align:start position:0% +integrating from R to infinity x to the + + + align:start position:0% +integrating from R to infinity x to the +n e- x DX and we know that's going to be + + align:start position:0% +n e- x DX and we know that's going to be + + + align:start position:0% +n e- x DX and we know that's going to be +much less + + align:start position:0% +much less + + + align:start position:0% +much less +than integral from R to + + align:start position:0% +than integral from R to + + + align:start position:0% +than integral from R to +Infinity e to the X over + + align:start position:0% +Infinity e to the X over + + + align:start position:0% +Infinity e to the X over +2 e to the- X DX and now let's figure + + align:start position:0% +2 e to the- X DX and now let's figure + + + align:start position:0% +2 e to the- X DX and now let's figure +out what this is e- X Plus X over2 is e- + + align:start position:0% +out what this is e- X Plus X over2 is e- + + + align:start position:0% +out what this is e- X Plus X over2 is e- +X over + + align:start position:0% + + + + align:start position:0% + +2 and the good news is this is we know + + align:start position:0% +2 and the good news is this is we know + + + align:start position:0% +2 and the good news is this is we know +this converges I I'll check and I'll + + align:start position:0% +this converges I I'll check and I'll + + + align:start position:0% +this converges I I'll check and I'll +show you remind you that it converges + + align:start position:0% +show you remind you that it converges + + + align:start position:0% +show you remind you that it converges +but we know this converges and the + + align:start position:0% +but we know this converges and the + + + align:start position:0% +but we know this converges and the +reason is because e Theus X is a + + align:start position:0% +reason is because e Theus X is a + + + align:start position:0% +reason is because e Theus X is a +function that decay is so fast as it + + align:start position:0% +function that decay is so fast as it + + + align:start position:0% +function that decay is so fast as it +goes to zero that's really why you get + + align:start position:0% +goes to zero that's really why you get + + + align:start position:0% +goes to zero that's really why you get +the convergence actually you could even + + align:start position:0% +the convergence actually you could even + + + align:start position:0% +the convergence actually you could even +compare this to uh X to Theus two right + + align:start position:0% +compare this to uh X to Theus two right + + + align:start position:0% +compare this to uh X to Theus two right +away and you could get something like + + align:start position:0% +away and you could get something like + + + align:start position:0% +away and you could get something like +you know this this Decay is faster than + + align:start position:0% +you know this this Decay is faster than + + + align:start position:0% +you know this this Decay is faster than +x to the minus two and we know X Theus 2 + + align:start position:0% +x to the minus two and we know X Theus 2 + + + align:start position:0% +x to the minus two and we know X Theus 2 +converges so you could even compare it + + align:start position:0% +converges so you could even compare it + + + align:start position:0% +converges so you could even compare it +to that you could do a second comparison + + align:start position:0% +to that you could do a second comparison + + + align:start position:0% +to that you could do a second comparison +in here but I'll actually calculate this + + align:start position:0% +in here but I'll actually calculate this + + + align:start position:0% +in here but I'll actually calculate this +just to remind us how we do this so eus + + align:start position:0% +just to remind us how we do this so eus + + + align:start position:0% +just to remind us how we do this so eus +x/ 2 if I want to find an + + align:start position:0% +x/ 2 if I want to find an + + + align:start position:0% +x/ 2 if I want to find an +anti-derivative I'm going to guess and + + align:start position:0% +anti-derivative I'm going to guess and + + + align:start position:0% +anti-derivative I'm going to guess and +check I know I'm going to have an eus X + + align:start position:0% +check I know I'm going to have an eus X + + + align:start position:0% +check I know I'm going to have an eus X +over two again and then I need to be + + align:start position:0% +over two again and then I need to be + + + align:start position:0% +over two again and then I need to be +able to kill off a negative one2 so I + + align:start position:0% +able to kill off a negative one2 so I + + + align:start position:0% +able to kill off a negative one2 so I +should put a -2 in front let's double + + align:start position:0% +should put a -2 in front let's double + + + align:start position:0% +should put a -2 in front let's double +check this is basically a substitution + + align:start position:0% +check this is basically a substitution + + + align:start position:0% +check this is basically a substitution +problem an easy substitution so eus X + + align:start position:0% +problem an easy substitution so eus X + + + align:start position:0% +problem an easy substitution so eus X +over2 it's derivative is + + align:start position:0% +over2 it's derivative is + + + align:start position:0% +over2 it's derivative is +-2X and then itself again the -2 * -2 + + align:start position:0% +-2X and then itself again the -2 * -2 + + + align:start position:0% +-2X and then itself again the -2 * -2 +gives me a one so again I'm just it's an + + align:start position:0% +gives me a one so again I'm just it's an + + + align:start position:0% +gives me a one so again I'm just it's an +easy substitution problem but I always + + align:start position:0% +easy substitution problem but I always + + + align:start position:0% +easy substitution problem but I always +want to check so if I evaluate that from + + align:start position:0% +want to check so if I evaluate that from + + + align:start position:0% +want to check so if I evaluate that from +R to Infinity well the point is e to the + + align:start position:0% +R to Infinity well the point is e to the + + + align:start position:0% +R to Infinity well the point is e to the +minus + + align:start position:0% +minus + + + align:start position:0% +minus +infinity this is zero as as X goes to + + align:start position:0% +infinity this is zero as as X goes to + + + align:start position:0% +infinity this is zero as as X goes to +Infinity this quantity goes to zero so I + + align:start position:0% +Infinity this quantity goes to zero so I + + + align:start position:0% +Infinity this quantity goes to zero so I +get 0 minus a -2 so plus 2 eus + + align:start position:0% +get 0 minus a -2 so plus 2 eus + + + align:start position:0% +get 0 minus a -2 so plus 2 eus +r/2 for some fixed Big R well that's + + align:start position:0% +r/2 for some fixed Big R well that's + + + align:start position:0% +r/2 for some fixed Big R well that's +finite that's a finite number so we come + + align:start position:0% +finite that's a finite number so we come + + + align:start position:0% +finite that's a finite number so we come +back here integral converges that + + align:start position:0% +back here integral converges that + + + align:start position:0% +back here integral converges that +integral was this integral and this + + align:start position:0% +integral was this integral and this + + + align:start position:0% +integral was this integral and this +integral then is bigger than this one so + + align:start position:0% +integral then is bigger than this one so + + + align:start position:0% +integral then is bigger than this one so +this one + + align:start position:0% +this one + + + align:start position:0% +this one +converges now this had a lot of pieces + + align:start position:0% +converges now this had a lot of pieces + + + align:start position:0% +converges now this had a lot of pieces +to it so I'm going to remind us sort of + + align:start position:0% +to it so I'm going to remind us sort of + + + align:start position:0% +to it so I'm going to remind us sort of +what was happening so let's go back to + + align:start position:0% +what was happening so let's go back to + + + align:start position:0% +what was happening so let's go back to +the original function and I'll just take + + align:start position:0% +the original function and I'll just take + + + align:start position:0% +the original function and I'll just take +us back through one more time okay so + + align:start position:0% +us back through one more time okay so + + + align:start position:0% +us back through one more time okay so +the original problem was show that this + + align:start position:0% +the original problem was show that this + + + align:start position:0% +the original problem was show that this +integral from one to Infinity of X the n + + align:start position:0% +integral from one to Infinity of X the n + + + align:start position:0% +integral from one to Infinity of X the n +eus x DX converges and I reminded you + + align:start position:0% +eus x DX converges and I reminded you + + + align:start position:0% +eus x DX converges and I reminded you +that you knew from lecture that if I + + align:start position:0% +that you knew from lecture that if I + + + align:start position:0% +that you knew from lecture that if I +could show that it converged for some + + align:start position:0% +could show that it converged for some + + + align:start position:0% +could show that it converged for some +very large number down here to Infinity + + align:start position:0% +very large number down here to Infinity + + + align:start position:0% +very large number down here to Infinity +that was sufficient because this + + align:start position:0% +that was sufficient because this + + + align:start position:0% +that was sufficient because this +function is continuous from one to + + align:start position:0% +function is continuous from one to + + + align:start position:0% +function is continuous from one to +Infinity I don't have to worry about + + align:start position:0% +Infinity I don't have to worry about + + + align:start position:0% +Infinity I don't have to worry about +places where um I might get infinite + + align:start position:0% +places where um I might get infinite + + + align:start position:0% +places where um I might get infinite +area in a finite interval I'm always + + align:start position:0% +area in a finite interval I'm always + + + align:start position:0% +area in a finite interval I'm always +going to have finite area in a finite + + align:start position:0% +going to have finite area in a finite + + + align:start position:0% +going to have finite area in a finite +interval so if I start at some Big R to + + align:start position:0% +interval so if I start at some Big R to + + + align:start position:0% +interval so if I start at some Big R to +infinity and that converges then I'm + + align:start position:0% +infinity and that converges then I'm + + + align:start position:0% +infinity and that converges then I'm +good because from one to R that'll be + + align:start position:0% +good because from one to R that'll be + + + align:start position:0% +good because from one to R that'll be +finite so then the point is you want to + + align:start position:0% +finite so then the point is you want to + + + align:start position:0% +finite so then the point is you want to +compare and I mentioned a comparison + + align:start position:0% +compare and I mentioned a comparison + + + align:start position:0% +compare and I mentioned a comparison +that doesn't quite work but is a good + + align:start position:0% +that doesn't quite work but is a good + + + align:start position:0% +that doesn't quite work but is a good +first test because you know x to the N + + align:start position:0% +first test because you know x to the N + + + align:start position:0% +first test because you know x to the N +is much less than e to the X for + + align:start position:0% +is much less than e to the X for + + + align:start position:0% +is much less than e to the X for +sufficiently large x you might think to + + align:start position:0% +sufficiently large x you might think to + + + align:start position:0% +sufficiently large x you might think to +compare it to that but the problem again + + align:start position:0% +compare it to that but the problem again + + + align:start position:0% +compare it to that but the problem again +was when we do that substitution we + + align:start position:0% +was when we do that substitution we + + + align:start position:0% +was when we do that substitution we +actually get an integral that diverges + + align:start position:0% +actually get an integral that diverges + + + align:start position:0% +actually get an integral that diverges +but a Divergent integral bigger than + + align:start position:0% +but a Divergent integral bigger than + + + align:start position:0% +but a Divergent integral bigger than +something doesn't mean this one diverges + + align:start position:0% +something doesn't mean this one diverges + + + align:start position:0% +something doesn't mean this one diverges +if if the Divergence was on the + + align:start position:0% +if if the Divergence was on the + + + align:start position:0% +if if the Divergence was on the +inequality was the other way then you + + align:start position:0% +inequality was the other way then you + + + align:start position:0% +inequality was the other way then you +you could show this one diverged but we + + align:start position:0% +you could show this one diverged but we + + + align:start position:0% +you could show this one diverged but we +we actually show convergence this way or + + align:start position:0% +we actually show convergence this way or + + + align:start position:0% +we actually show convergence this way or +we're trying to show convergence in this + + align:start position:0% +we're trying to show convergence in this + + + align:start position:0% +we're trying to show convergence in this +direction so we need to we need to say + + align:start position:0% +direction so we need to we need to say + + + align:start position:0% +direction so we need to we need to say +if this one converges then that one + + align:start position:0% +if this one converges then that one + + + align:start position:0% +if this one converges then that one +converges this diverging doesn't tell us + + align:start position:0% +converges this diverging doesn't tell us + + + align:start position:0% +converges this diverging doesn't tell us +anything about this so then we say okay + + align:start position:0% +anything about this so then we say okay + + + align:start position:0% +anything about this so then we say okay +this one didn't work but it almost + + align:start position:0% +this one didn't work but it almost + + + align:start position:0% +this one didn't work but it almost +worked so what if I what if I figure out + + align:start position:0% +worked so what if I what if I figure out + + + align:start position:0% +worked so what if I what if I figure out +a way to compare x to the N to a + + align:start position:0% +a way to compare x to the N to a + + + align:start position:0% +a way to compare x to the N to a +slightly smaller thing than e to the X + + align:start position:0% +slightly smaller thing than e to the X + + + align:start position:0% +slightly smaller thing than e to the X +and that slightly smaller thing is e to + + align:start position:0% +and that slightly smaller thing is e to + + + align:start position:0% +and that slightly smaller thing is e to +the X over2 it's not really slightly + + align:start position:0% +the X over2 it's not really slightly + + + align:start position:0% +the X over2 it's not really slightly +smaller but the smaller function is e to + + align:start position:0% +smaller but the smaller function is e to + + + align:start position:0% +smaller but the smaller function is e to +the X over + + align:start position:0% +the X over + + + align:start position:0% +the X over +2 okay and and this is a way to think + + align:start position:0% +2 okay and and this is a way to think + + + align:start position:0% +2 okay and and this is a way to think +about how that works is that for any + + align:start position:0% +about how that works is that for any + + + align:start position:0% +about how that works is that for any +power of x to the 2 N I can still get it + + align:start position:0% +power of x to the 2 N I can still get it + + + align:start position:0% +power of x to the 2 N I can still get it +smaller than e to the X for some + + align:start position:0% +smaller than e to the X for some + + + align:start position:0% +smaller than e to the X for some +sufficiently larg + + align:start position:0% +sufficiently larg + + + align:start position:0% +sufficiently larg +number okay and you don't even have to + + align:start position:0% +number okay and you don't even have to + + + align:start position:0% +number okay and you don't even have to +think about these RS as being the same I + + align:start position:0% +think about these RS as being the same I + + + align:start position:0% +think about these RS as being the same I +can change them I can make this bigger + + align:start position:0% +can change them I can make this bigger + + + align:start position:0% +can change them I can make this bigger +the this doesn't compare to this problem + + align:start position:0% +the this doesn't compare to this problem + + + align:start position:0% +the this doesn't compare to this problem +also so don't be confused by those two + + align:start position:0% +also so don't be confused by those two + + + align:start position:0% +also so don't be confused by those two +RS okay so then we found something we + + align:start position:0% +RS okay so then we found something we + + + align:start position:0% +RS okay so then we found something we +wanted to compare x to the N with then + + align:start position:0% +wanted to compare x to the N with then + + + align:start position:0% +wanted to compare x to the N with then +we come back over here and we actually + + align:start position:0% +we come back over here and we actually + + + align:start position:0% +we come back over here and we actually +see that we get a good comparison + + align:start position:0% +see that we get a good comparison + + + align:start position:0% +see that we get a good comparison +because we're able to see that the + + align:start position:0% +because we're able to see that the + + + align:start position:0% +because we're able to see that the +integral on the right hand side + + align:start position:0% +integral on the right hand side + + + align:start position:0% +integral on the right hand side +converges this integral is bigger than + + align:start position:0% +converges this integral is bigger than + + + align:start position:0% +converges this integral is bigger than +this integral so this integral converges + + align:start position:0% +this integral so this integral converges + + + align:start position:0% +this integral so this integral converges +so we know this integral con converges + + align:start position:0% +so we know this integral con converges + + + align:start position:0% +so we know this integral con converges +and and then the integral from 1 to R of + + align:start position:0% +and and then the integral from 1 to R of + + + align:start position:0% +and and then the integral from 1 to R of +this is finite so the integral from 1 to + + align:start position:0% +this is finite so the integral from 1 to + + + align:start position:0% +this is finite so the integral from 1 to +Infinity of this converges and that's + + align:start position:0% +Infinity of this converges and that's + + + align:start position:0% +Infinity of this converges and that's +that's sort of the strategy for doing + + align:start position:0% +that's sort of the strategy for doing + + + align:start position:0% +that's sort of the strategy for doing +these types of problems okay that's + + align:start position:0% +these types of problems okay that's + + + align:start position:0% +these types of problems okay that's +where I'll stop \ No newline at end of file diff --git a/avJ65YYAfD4.txt b/avJ65YYAfD4.txt new file mode 100644 index 0000000000000000000000000000000000000000..8bd05797705c72fcf32ec56fb4ad80cbfe55892d --- /dev/null +++ b/avJ65YYAfD4.txt @@ -0,0 +1,299 @@ +align:start position:0% + +what language issues are particularly + + align:start position:0% +what language issues are particularly + + + align:start position:0% +what language issues are particularly +poignant in today's political climate + + align:start position:0% +poignant in today's political climate + + + align:start position:0% +poignant in today's political climate +that they might talk about today + + align:start position:0% +that they might talk about today + + + align:start position:0% +that they might talk about today +one issue that critical is the right of + + align:start position:0% +one issue that critical is the right of + + + align:start position:0% +one issue that critical is the right of +people to have their lives community + + align:start position:0% +people to have their lives community + + + align:start position:0% +people to have their lives community +affairs conducted in their own language + + align:start position:0% +affairs conducted in their own language + + + align:start position:0% +affairs conducted in their own language +so for example if somes a dictator were + + align:start position:0% +so for example if somes a dictator were + + + align:start position:0% +so for example if somes a dictator were +to take over the United States and + + align:start position:0% +to take over the United States and + + + align:start position:0% +to take over the United States and +produce an edict saying the official + + align:start position:0% +produce an edict saying the official + + + align:start position:0% +produce an edict saying the official +language of the country is Swahili and + + align:start position:0% +language of the country is Swahili and + + + align:start position:0% +language of the country is Swahili and +that we all have to talk Swahili from + + align:start position:0% +that we all have to talk Swahili from + + + align:start position:0% +that we all have to talk Swahili from +now on and all official documents are in + + align:start position:0% +now on and all official documents are in + + + align:start position:0% +now on and all official documents are in +Swahili and if you want to get a + + align:start position:0% +Swahili and if you want to get a + + + align:start position:0% +Swahili and if you want to get a +driver's license you have to ask where + + align:start position:0% +driver's license you have to ask where + + + align:start position:0% +driver's license you have to ask where +Swahili and so on I think we'd probably + + align:start position:0% +Swahili and so on I think we'd probably + + + align:start position:0% +Swahili and so on I think we'd probably +object but that's the actual situation + + align:start position:0% +object but that's the actual situation + + + align:start position:0% +object but that's the actual situation +for example in Haiti so it's not Swahili + + align:start position:0% +for example in Haiti so it's not Swahili + + + align:start position:0% +for example in Haiti so it's not Swahili +it's French and the language the people + + align:start position:0% +it's French and the language the people + + + align:start position:0% +it's French and the language the people +speak is a different language creo so + + align:start position:0% +speak is a different language creo so + + + align:start position:0% +speak is a different language creo so +that's a kind of a problem that arises + + align:start position:0% +that's a kind of a problem that arises + + + align:start position:0% +that's a kind of a problem that arises +they there similar problems arise here + + align:start position:0% +they there similar problems arise here + + + align:start position:0% +they there similar problems arise here +we have spanish-speaking communities do + + align:start position:0% +we have spanish-speaking communities do + + + align:start position:0% +we have spanish-speaking communities do +they have a right to conduct their lives + + align:start position:0% +they have a right to conduct their lives + + + align:start position:0% +they have a right to conduct their lives +to have elementary school teaching and + + align:start position:0% +to have elementary school teaching and + + + align:start position:0% +to have elementary school teaching and +the language that the children know and + + align:start position:0% +the language that the children know and + + + align:start position:0% +the language that the children know and +speak of course they have to be assembly + + align:start position:0% +speak of course they have to be assembly + + + align:start position:0% +speak of course they have to be assembly +the general society but these are not + + align:start position:0% +the general society but these are not + + + align:start position:0% +the general society but these are not +incompatible goals in fact we know very + + align:start position:0% +incompatible goals in fact we know very + + + align:start position:0% +incompatible goals in fact we know very +well that a multilingual environment is + + align:start position:0% +well that a multilingual environment is + + + align:start position:0% +well that a multilingual environment is +actually stimulating it doesn't impede + + align:start position:0% +actually stimulating it doesn't impede + + + align:start position:0% +actually stimulating it doesn't impede +improves performance and understanding + + align:start position:0% +improves performance and understanding + + + align:start position:0% +improves performance and understanding +and being able to live in your own + + align:start position:0% +and being able to live in your own + + + align:start position:0% +and being able to live in your own +language certainly has that effect too + + align:start position:0% +language certainly has that effect too + + + align:start position:0% +language certainly has that effect too +so when I grew up not me personally but + + align:start position:0% +so when I grew up not me personally but + + + align:start position:0% +so when I grew up not me personally but +communities that were I was part of the + + align:start position:0% +communities that were I was part of the + + + align:start position:0% +communities that were I was part of the +native language of is Yiddish and they + + align:start position:0% +native language of is Yiddish and they + + + align:start position:0% +native language of is Yiddish and they +spoke Yiddish + + align:start position:0% +spoke Yiddish + + + align:start position:0% +spoke Yiddish +fine the kids with the school \ No newline at end of file diff --git a/b1P0hurY6UE.txt b/b1P0hurY6UE.txt new file mode 100644 index 0000000000000000000000000000000000000000..b71f079a82ad3a5f2bef3c28b1a026b6019f0f5e --- /dev/null +++ b/b1P0hurY6UE.txt @@ -0,0 +1,3125 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high-quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: OK. + +Let's start. + +So last lecture, what we +talked about was limitations + +of classical +statistical mechanics, + +and what I will +contrast with what + +I will talk about today, +which is new version. + +The old version of +quantum mechanics, + +which was based on the +observation originally from + +Planck, and then +expanded by Einstein, + +that for a harmonic +oscillator, a frequency omega, + +the energies cannot +take all values. + +But values that are multiples of +the frequency of the oscillator + +and then some integer n. + +What we did with +this observation + +to extract thermal +properties was to simply say + +that we will +construct a partition + +function for the +harmonic oscillator + +by summing over all of the +states of e to the minus beta e + +n according to the +formula given above. + +Just thinking that +these are allowed states + +of this oscillator-- and +this you can very easily do. + +It starts with the +first term and then + +it's a algebraic series, which +will give you that formula. + +Now, if you are sitting +at some temperature t, + +you say that the +average energy that you + +have in your system, well, +the formula that you have is + +minus the log z by the beta, +which if I apply to the z + +that I have about, essentially +weighs each one of these + +by these Boltzmann weights +by the corresponding energy + +and sums them. + +What we do is we get, +essentially, the contribution + +of the ground state. + +Actually, for all intents and +purposes, we can ignore this, + +and, hence, this. + +But for completion, +let's have them around. + +And then from what is +in the denominator, + +if you take derivative +with respect to beta, + +you will get a factor +of h bar omega. + +And then this factor of 1 minus +e to the minus beta h bar. + +Actually, we then additional +e to the minus beta + +h bar omega in here. + +Now, the thing that +we really compare to + +was what happens if we were to +take one more derivative to see + +how much the heat +capacity is that we + +have in the harmonic oscillator. + +So basically taking an average +of the raw formula with respect + +to temperature, realizing +that these betas are + +inverse temperatures. + +So derivatives with +respect to t will + +be related to +derivative with respect + +to beta, except that I've will +get an additional factor of 1 + +over k bt squared. + +So the whole thing I +could write that as kb + +and then I had the h bar +omega over kt squared. + +And then from these factors, +I had something like e + +to the minus e to the +h bar omega over kt. + +E to the h bar omega +over kt minus 1 squared. + +So if we were to plug +this function, the heat + +capacity in its natural +unit that are this kb, then + +as a function of +temperature, we get behavior + +that we can actually +express correctly + +in terms of the combination. + +You can see always +we get temperature + +in units of kb over h bar omega. + +So I can really plug +this in the form of, say, + +kt over h bar omega, +which we call t + +to some characteristic +temperature. + +And the behavior that we have +is that close to 0 temperatures, + +you go to 0 +exponentially, because + +of essentially the ratio +of these exponentials. + +We leave one exponential +in the denominator. + +So the gaps that you have +between n equals to 0 + +and n equals to 1 +translates to behavior + +of that at low temperatures +is exponentially + +decaying to leading order. + +Then, eventually, at +high temperatures, + +you get the classical result +where you saturate to 1. + +And so you will +have a curve that + +has a shift from one +behavior to another behavior. + +And the place where +this transition occurs + +is when this combination +is of the order of 1. + +I'm not saying it's precisely +1, but it's of the order of 1. + +So, basically, you have +this kind of behavior. + +OK? + +So we use this curve +to explain the heat + +capacity of diatomic gas, +such as the gas in this room, + +and why at room temperature, we +see a heat capacity in which it + +appears that the vibrational +degrees of freedom are frozen, + +are not contributing anything. + +While at temperatures above +the characteristic vibrational + +frequency, which for a +gas is of the order of 10 + +to the 3 degrees +k, you really get + +energy in the +harmonic oscillator + +also in the vibrations. + +And the heat capacity +jumps, because you + +have another way +of storing energy. + +So the next thing that we asked +was whether this describes also + +heat capacity of a solid. + +So basically, for +the diatomic gas, + +you have two atoms that +are bonded together + +into a molecule. + +And you consider the +vibrations of that. + +You can regard the +solid as a huge molecule + +with lots of atoms +joined together. + +And they have vibrations. + +And if you think about all of +those vibrations giving you + +something that is +similar to this, + +you would conclude that the +heat capacity of a solid + +should also have this +kind of behavior. + +Whereas we noted +that in actuality, + +the heat capacity of a solid +vanishes much more slowly + +at low temperatures. + +And the dependence +at low temperatures + +is proportional to t cubed. + +So at the end of +last lecture, we + +gave an explanation for +this, which I will repeat. + +Again, the picture is that the +solid, like a huge molecule, + +has vibrational modes. + +But these vibrational +modes cover a whole range + +of different frequencies. + +And so if you ask, what +are the frequencies omega + +alpha of vibrations of a +solid, the most natural way + +to characterize +them is, in fact, + +in terms of a wave vector k +that indicates a direction + +for the oscillatory wave that +you set up in the material. + +And depending on k, you'll +have different frequencies. + +And I said that, essentially, +the longest wave length + +corresponding to k equals to +0 is taking the whole solid + +and translating it. + +Again, thinking back about the +oxygen molecule, the oxygen + +molecule, you have +two coordinates. + +It's the relative coordinate +that has the vibration. + +And you have a center of mass +coordinate that has no energy. + +If you make a molecule +more and more complicated, + +you will have more modes, +but you will always + +have the 0 mode that +corresponds to the translation. + +And that carries over +all the way to the solid. + +So there is a mode that +corresponds to translations-- + +and, in fact, rotations-- +that would carry + +no energy, and corresponds, +therefore, to 0 frequency. + +And then if you start to make +long wavelength oscillations, + +the frequency is +going to be small. + +And, indeed, what we know +is that we tap on the solid + +and you create +sound waves, which + +means that the low-frequency +long wavelength + +modes have a dispersion +relation in which omega + +is proportional to k. + +We can write that as +omega is v times k, where + +v is the velocity of +the sound in the solid. + +Now, of course, the shortest +wave length that you can have + +is related to the separation +between the atoms in the solid. + +And so, basically, +there's a limit + +to the range of k's that +you can put in your system. + +And this linear +behavior is going + +to get modified once you get +towards the age of the solid. + +And the reason I +have alpha here is + +because you can have +different polarizations. + +There are three different +possible polarizations. + +So in principle, +you will have three + +of these curves in +the system hard. + +And these curves could +be very complicated + +when you get to the +edge of [INAUDIBLE] zone + +and you have to solve +a big dynamical matrix + +in order to extract what +the frequencies are, + +if you want to have +the complete spectrum. + +So the solid is a collection of +these harmonic oscillators that + +are, in principle, +very complicated. + +But we have the following. + +So I say, OK, I +have all of these. + +And I want to calculate +at a given temperature + +how much energy I +have put in the solid. + +So this energy that I +have put in the vibrations + +at some temperature t, assuming +that these vibrations are + +really a collection +of these oscillators. + +Well, what I have to do is +to add up all of these terms. + +There's going to be adding up +all of the h bar omega over 2s + +for all of these. + +OK? + +That will give me something +that I will simply call e 0, + +because it doesn't +depend on temperature. + +Presumably will exist +at 0 temperature. + +And I can even fold +into that whatever + +the value of the potential +energy of the interactions + +between the particles +is at 0 temperature. + +What I'm interested in really +is the temperature dependence. + +So I basically take the +formula that I have over there, + +and sum over all of +these oscillators. + +These oscillators are +characterized by polarization + +and by the wave vector k. + +And then I have, essentially, +h bar omega alpha + +of k divided by e to the beta +h bar omega alpha of k minus 1. + +So I have to apply that formula +to this potentially very + +complicated set of frequencies. + +The thing is, that according +to the picture that I have over + +here, to a 0 order +approximation, + +you would say that +the heat capacity is 1 + +if you are on this side, +0 if you're on that side. + +What distinguishes +those two sides + +is whether the frequency in +combination with temperature + +is less than or larger than 1. + +Basically, low frequencies +would end up being here. + +High frequencies would +end up being here. + +And would not contribute. + +So for a given temperature, +there is some borderline. + +That borderline would +correspond to kt over h bar. + +So let me draw where +that borderline is. + +Kt over h bar. + +For a particular temperature, +all of these modes + +are not really contributing. + +All of these modes +are contributing. + +If my temperature +is high enough, + +everything is contributing. + +And the total number +of oscillators is 3 n. + +It's the number of atoms. + +So essentially, I +will get 3 n times + +whatever formula +I have over there. + +As a come further +and further down, + +there's some kind of +complicated behavior + +as I go through this +spaghetti of modes. + +But when I get to low +enough structures, + +then, again, things +become simple, + +because I will only be +sensitive to the modes that + +are described by this +a omega being vk. + +OK? + +So if I'm interested +in t going to 0, + +means less than some +characteristic temperature + +that we have to define shortly. + +So let's say, replace this +with t less than some theta + +d that I have to +get for you shortly, + +then I will replace this +with e 0 plus sum over alpha + +and k of h bar v alpha +k e to the beta h bar e + +alpha k minus 1. + +OK? + +Now, for simplicity, +essentially I + +have to do three different sums. + +All of them are the +same up to having + +to use different values of +v. Let's just for simplicity + +assume that all of the +v alphas are the same v, + +so that I really have +only one velocity. + +There's really no difficulty +in generalizing this. + +So let's do this for +simplicity of algebra. + +So if I do that, then +the sum over alpha + +will simply give +me a factor of 3. + +There are three possible +polarizations, so I put a 3 + +there. + +And then I have to do +the summation over k. + +Well, what does the +summation over k mean? + +When I have a small molecule +for the, let's say, three + +or four atoms, then +I can enumerate + +what the different +vibrational states are. + +As I go to a large +solid, I essentially + +have modes that are +at each value of k, + +but, in reality, +they are discrete. + +They are very, very, very, +very finely separated + +by a separation that +is of the order of 2 + +pi over the size of the system. + +So to ensure that eventually +when you count all of the modes + +that you have here, +you, again, end up + +to have of the +order of n states. + +So if that's the case, +this sum, really I + +can replace with an integral, +because going from one point + +to the next point does +not make much difference. + +So I will have an +integral over k. + +But I have to know how +densely these things are. + +And in one direction +it is 2 pi over l. + +So the density would +be l over 2 pi. + +If I look at all +three directions, + +I have to multiply all of them. + +So I will get v +divided by 2 pi cubed. + +So this is the usual +density of states. + +And you go to description +in terms of wave numbers, + +or, later on, in +terms of momentums. + +And what we have here is +this integral h bar v k e + +to the beta h bar v k minus 1. + +OK? + +So let's simplify this +a little bit further. + +I have e 0. + +I have 3v. + +The integrand only depends +on the magnitude of k, + +so I can take advantage +of that spherical symmetry + +and write this as 4 pi k squared +v k divided by this 8 pi cubed. + +What I can do is I +can also introduce + +a factor of beta here, +multiplied by k t. + +Beta k t is 1. + +And if I call this +combination to be x, then what + +I have is k b t x +e to the x minus 1. + +Of course, k is simply +related to x by k + +being x kt over h bar v. + +And so at the next +level of approximation, + +this k squared v k I will write +in terms of x squared v x. + +And so what do I have? + +I have e 0. + +I have 3v divided +by 2 pi squared. + +Because of this factor of +kt that I will take outside + +I have a kt. + +I have a k squared +vk that I want + +to replace with x squared v x. + +And that will give me +an additional factor + +of kv over h bar v cubed. + +And then I have an +integral 0 to e 0 v + +x x cubed e to the x minus 1. + +Now, in principle, when I +start with this integration, + +I have a finite range +for k, which presumably + +would translate into +a finite range for x. + +But in reality none of +these modes is contributing, + +so I could extend the +range of integration + +all the way to infinity, +and make very small error + +at low temperatures. + +And the advantage of +that is that then this + +becomes a definite integral. + +Something that you +can look up in tables. + +And its value is in fact +pi to the fourth over 15. + +So substituting that over +there, what do we have? + +We have that the energy is +e 0 plus 3 divided by 15, + +will give me 5, which +turns the 2 into a 10. + +I have pi to the fourth +divided by pi squared, + +so there's a pi squared +that will survive out here. + +I have a kt. + +I have kt over h bar v cubed. + +And then I have a +factor of volume. + +But volume is proportional +to the number of particles + +that I have in the system +times the size of my unit cell. + +Let's call that a cubed. + +So this I can write +this as l a cubed. + +Why do I do that is because +when I then take the derivative, + +I'd like to write the heat +capacity per particle. + +So, indeed, if I now take the +derivative, which is de by dt, + +the answer will be +proportional to n and kv. + +The number of particles +and this k v, which + +is the function, the +unit of heat capacities. + +The overall dependence +is t to the fourth. + +So when I take derivatives, +I will get 4t cubed. + +That 4 will change the 1 over +10 to 2 pi squared over 5. + +And then I have the +combination kvt h bar + +v, and that factor of a +raised to the third power. + +So the whole thing is +proportional to t cubed. + +And the coefficient I will +call theta d for [INAUDIBLE]. + +And theta d I have calculated +to be h bar v over a h + +bar v a over k t. + +No, h bar v over a k t. + +So the heat capacity +of the solid + +is going to be proportional, +of course, to n k b. + +But most importantly, is +proportional to t cubed. + +And t cubed just came +from this argument + +that I need low omegas. + +And how many things +I have at the omega. + +How many frequencies do I +have that are vibrating? + +The number of those +frequencies is essentially + +the size of a cube in k space. + +So it goes like this-- maximum +k cubed in three dimensions. + +In two dimensions, it will +be squared and all of that. + +So it's very easy to figure out +from this dispersion relation + +what the low temperature +behavior of the heat capacity + +has to be. + +And you will see that this +is, in fact, predictive, + +in that later on +in the course, we + +will come an example of where +the heat capacity of a liquid, + +which was helium, was observed +to have this t cubed behavior + +based on that Landau immediately +postulated that there should be + +a phonon-like dispersion +inside that superfluid. + +OK. + +So that's the story of the +heat capacity of the solid. + +So we started with a molecule. + +We went from a molecule +into an entire solid. + +The next step that what +I'm going to do is I'm + +going to remove the solid +and just keep the box. + +So essentially, they +calculation that I + +did, if you think +about it, corresponded + +to having some kind +of a box, and having + +vibrational modes +inside the box. + +But let's imagine that +it is an empty box. + +But we know that even in +empty space we have light. + +So within an empty +box, we can still + +have modes of the +electromagnetic field. + +Modes of electromagnetic +field, just like the modes + +of the solid, we +can characterize + +by the direction along +which oscillations travel. + +And whereas for the atoms in the +solid, they have displacement + +and the corresponding momentum +for the electromagnetic field, + +you have the electric field. + +And its conjugate is +the magnetic field. + +And these things +will be oscillating + +to create for you a wave. + +Except that, whereas for +the solid, for each atom + +we had three +possible directions, + +and therefore we had three +branches, for this, since e + +and b have to be +orthogonal to k, + +you really have only +two polarizations. + +But apart from that, +the frequency spectrum + +is exactly the same +as we would have + +for the solids at low +temperature replacing + +to v that we have with +the speed of light. + +And so you would say, OK. + +If I were to calculate +the energy content that + +is inside the box, +what I have to do + +is to sum over all of the +modes and polarizations. + +Regarding each one of these +as a harmonic oscillator, + +going through the system +of quantizing according + +to this old quantum mechanics, +the harmonic oscillators, + +I have to add up the energy +content of each oscillator. + +And so what I have is +this h bar omega of k. + +And then I have +1/2 plus 1 over e + +to the beta h bar +omega of k minus 1. + +And then I can do exactly +the kinds of things + +that I had before, +replacing the sum over k + +with a v times an integral. + +So the whole thing +would be, first of all, + +proportional to v, going +from the sum over k + +to the integration over k. + +I would have to add all of +these h bar omega over 2s. + +Has no temperature dependence, +so let me just, again, call it + +some e 0. + +Actually, let's +call it epsilon 0, + +because it's more like +an energy density. + +And then I have the sum +over all of the other modes. + +There's two polarisations. + +So as opposed to the three +that I had before, I have two. + +I have, again, the +integral over k of 4 pi k + +squared v k divided +by 8 pi cubed, which + +is part of this density +of state calculation. + +I have, again, a +factor of h bar omega. + +Now, I realize that +my omega is ck. + +So I simply write +it as h bar ck. + +And then I have e to the +beta h bar ck minus 1. + +So we will again allow this +to go from 0 to infinity. + +And what do we get? + +We will get v epsilon 0 plus, +well, the 8 and 8 cancel. + +I have pi over pi squared. + +So pi over pi cubed. + +So it will give me +1 over pi squared. + +I have one factor of kt. + +Again, when I +introduce here a beta + +and then multiply by kt, +so that this dimension, + +this combination appears. + +Then I have, if I were to +change variable and call + +this the new variable, +I have factor + +of k squared dk, which +gives me, just as + +before over there, a factor +of kt over h bar c cubed. + +And then I have +this integral left, + +which is the 0 to infinity v +x x cubed e to the x minus 1, + +which we stated is pi +to the fourth over 15. + +So the part that is dependent +on temperature, the energy + +content, just as in this case, +scales as t to the fourth. + +There is one part +that we have over here + +from all of the 0s, which +is, in fact, an infinity. + +And maybe there is some +degree of worry about that. + +We didn't have to worry about +that infinity in this case, + +because the number of modes that +we had was, in reality, finite. + +So once we were to add up +properly all of these 0 point + +energies for this, we would +have gotten a finite number. + +It would have been large, but +it would have been finite. + +Whereas here, the difference +is that there is really + +no upper cut-off. + +So this k here, for a solid, +you have a minimum wavelength. + +You can't do things shorter than +the separation of particles. + +But for light, you can have +arbitrarily short wavelength, + +and that gives you this +infinity over here. + +So typically, we ignore that. + +Maybe it is related to the +cosmological constant, et + +cetera. + +But for our purposes, we are not +going to focus on that at all. + +And the interesting +part is this part, + +that proportional +to t to the fourth. + +There are two SOP +calculations to this + +that I will just give +part of the answer, + +because another +part of the answer + +is something that you +do in problem sets. + +One of them is that what we +have here is an energy density. + +It's proportional to volume. + +And we have seen +that energy densities + +are related to pressures. + +So indeed, there is a +corresponding pressure. + +That is, if you're +at the temperature t, + +this collection of vibrating +electromagnetic fields + +exerts a pressure on the +walls of the container. + +This pressure is related +to energy density. + +The factor of 1/3 comes because +of the dispersion relation. + +And you can show that in +one of the problem sets. + +You know that already. + +So that would say +that you would have, + +essentially, something +like some kind of p 0. + +And then something that +is proportional to t + +to the fourth. + +So I guess the correspondent +coefficient here + +would be p squared divided by +45 kt kt over h bar c cubed. + +So there is radiation +pressure that + +is proportional to temperature. + +The hotter you make this box, +the more pressure it will get + +exerted from it. + +There is, of course, +again this infinity + +that you may worry about. + +But here the problem +is less serious, + +because you would +say that in reality, + +if I have the wall +of the box, it + +is going to get pressure +from both sides. + +And if there's an infinite +pressure from both sides, + +they will cancel. + +So you don't have +to worry about that. + +But it turns out +that, actually, you + +can measure the consequences +of this pressure. + +And that occurs when rather +than having one plate, + +you have two plates +that there are + +some small separation apart. + +Then the modes of +radiation that you + +can fit in here because of the +quantizations that you have, + +are different from the modes +that you can have out here. + +So that difference, even from +the 0 point fluctuations-- + +the h bar omega over +2s-- will give you + +a pressure that pushes +these plates together. + +That's called a Casimir +force, or Casimir pressure. + +And that was predicted +by Casimir in 1950s, + +and was measured experimentally +roughly 10 years ago + +to high precision, matching +the formula that we had. + +So sometimes, these +infinities have + +consequences that you +have to worry about. + +But that's also to +indicate that there's + +kind of modern physics to this. + +But really it was the +origin of quantum mechanics, + +because of the other aspect +of the physics, which + +is imagine that again +you have this box. + +I draw it now as +an irregular box. + +And I open a hole of +size a inside the box. + +And then the radiation that +was inside at temperatures t + +will start to go out. + +So you have a hot box. + +You open a hole in it. + +And then the radiation +starts to come out. + +And so what you will have +is a flux of radiation. + +Flux means that this it energy +that is escaping per unit area + +and per unit time. + +So there's a flux, which +is per area per time. + +It turns out that +that flux-- and this + +is another factor, +this factor of 1/3 + +that I mentioned-- +is related the energy + +density with a +factor of 1 c over 4. + +Essentially, clearly the +velocity with which energy + +escaping is proportional to c. + +So you will get more +radiation flux the larger c. + +The answer has to be +proportional to c. + +And it is what is +inside that is escaping, + +so it has to be proportional +to the energy density + +that you have inside, some +kind of energy per unit volume. + +And the factor of 1/4 is one +of these geometric factors. + +Essentially, there's two +factors of cosine of theta. + +And you have to do an average +of cosine squared theta. + +And that will give you +the additional 1/4. + +OK? + +But rather than +looking-- so this + +would tell you that there is an +energy that is streaming out. + +That is, the net value +is proportional to t + +to the fourth. + +But more interestingly, +we can ask + +what is the flux per wavelength? + +And so for that, I can +just go back to the formula + +before I integrated +over k, and ask + +what is the energy density +in each interval of k? + +And so what I have to do is to +just go and look at the formula + +that I have prior to doing +the integration over k. + +Multiply it by c over 4. + +What do I have? + +I have 8 pi divided +by 8 pi cubed. + +I have a factor of k squared +from the density of states. + +I have this factor of h bar c +k divided by e to the beta h + +bar c k minus 1. + +So there's no analogue of +this, because I am not doing + +the integration over k. + +So we can simplify some +of these factors up front. + +But really, the story is +how does this quantity + +look as the function +of wave number, which + +is the inverse of wave +length, if you like. + +And what we see is that when +k goes to 0, essentially, + +this factor into +the beta h bar ck + +I have to expand +to lowest order. + +I will get beta h bar c k, +because the 1 disappears. + +H bar ck is cancelled, so +the answer is going to be + +proportional to inverse beta. + +It's going to be proportional +to kt and k squared. + +So, essentially, the low +k behavior part of this + +is proportional to k squared +c, of course, and kt. + +However, when I go to +the high k numbers, + +the exponential will +kill things off. + +So the large k part +of this is going + +to be exponentially small. + +And, actually, the curve will +look something like this, + +therefore. + +It will have a maximum around +the k, which presumably + +is of the order of +kt over h bar c. + +So basically, the +hotter you have, + +this will move to the right. + +The wavelengths +will become shorter. + +And, essentially, that's the +origin of the fact that can you + +heat some kind of material, it +will start to emit radiation. + +And the radiation will be +peaked at some frequency that + +is related to its temperature. + +Now, if we didn't have +this quantization effect, + +if h bar went to 0, +then what would happen + +is that this k squared kt +would continue forever. + +OK? + +Essentially, you +would have in each one + +of these modes of +radiation, classically, + +you would put a kt of energy. + +And since you could have +arbitrarily short wavelengths, + +you would have infinite +energy at shorter and shorter + +wavelengths. + +And you would have this +ultraviolet catastrophe. + +Of course, the +shape of this curve + +was experimentally known towards +the end of the 19th century. + +And so that was the basis +of thinking about it, + +and fitting an +exponential to the end, + +and eventually deducing +that this quantization + +of the oscillators would +potentially give you + +the reason for this to happen. + +Now, the way that I +have described it, + +I focused on having a cavity +and opening the cavity, + +and having the energy go out. + +Of course, the +experiments for black body + +are not done on cavities. + +They're done on some piece +of metal or some other thing + +that you heat up. + +And then you can look at the +spectrum of the radiation. + +And so, again, there +is some universality + +in this, that it is not so +sensitive to the properties + +of the material, +although there are + +some emissivity and +other factors that + +multiply the final result. + +So the final result, +in fact, would + +say that if I were to +integrate over frequencies, + +the total radiation flux, +which would be c over 4 times + +the energy density +total, is going + +to be proportional +to temperature + +to the fourth power. + +And this constant in front +is the Stefan-Boltzmann, + +which has some particular +value that you can look up, + +units of watts per area +per degrees Kelvin. + +So this perspective +is rather macroscopic. + +The radiated energy is +proportional to the surface + +area. + +If you make things +that are small, + +and the wavelengths that you're +looking at over here become + +compatible to the +size of the object, + +these formulas break down. + +And again, go forward +about 150 years or so, + +there is ongoing research-- +I guess more 200 years-- + +ongoing research on-- +no, 100 and something-- + +ongoing research on how these +classical laws of radiation + +are modified when you're dealing +with objects that are small + +compared to the wavelengths +that are emitted, etc. + +Any questions? + +So the next part of the story +is why did you do all of this? + +It works, but what +is the justification? + +In that I said there was +the old quantum mechanics. + +But really, we want to have +statements about quantum + +systems that are not +harmonic oscillators. + +And we want to be able +to understand actually + +what the underlying +basis is in the same way + +that they understand +how we were doing things + +for classical +statistical mechanics. + +And so really, we +want to look at how + +to make the transition +from classical to quantum + +statistical mechanics. + +So for that, let's +go and remind us. + +Actually, so +basically the question + +is something like +this-- what does + +this partition function mean? + +I'm calculating +things as if I have + +these states that are +the energy levels. + +And the probabilities are e +to the minus beta epsilon n. + +What does that mean? + +Classically, we knew +the Boltzmann rates + +had something to do with +the probability of finding + +a particle with a particular +position and momentum. + +So what is the +analogous thing here? + +And you know that in +new quantum mechanics, + +the interpretation of many +things is probabilistic. + +And in statistical +mechanics, even classically + +we had a probabilistic +interpretation. + +So presumably, we want to +build a probabilistic theory + +on top of another +probabilistic theory. + +So how do we go +about understanding + +precisely what is +happening over here? + +So let's kind of +remind ourselves + +of what we were doing in the +original classical statistical + +mechanics, and try to +see how we can make + +the corresponding +calculations when + +things are quantum mechanical. + +So, essentially, the +probabilistic sense + +that we had in classical +statistical mechanics + +was to assign probabilities +for micro states, given + +that we had some knowledge +of the macro state. + +So the classical +microstate mu was a point + +which was a collection of +p's and q's in phase space. + +So what is a quantum microstate? + +OK. + +So here, I'm just going to jump +several decades ahead, and just + +write the answer. + +And I'm going to +do it in somewhat + +of a more axiomatic way, +because it's not up to me + +to introduce quantum mechanics. + +I assume that you +know it already. + +Just a perspective +that I'm going to take. + +So the quantum microstate +is a complex unit vector + +in Hilbert space. + +OK? + +So for any vector space, we can +choose a set of unit vectors + +that form an orthonormal basis. + +And I'm going to use +this bra-ket notation. + +And so our psi, which is +a vector in this space, + +can be written in +terms of its components + +by pointing to the different +directions in this space, + +and components that I will +indicate by this psi n. + +And these are complex. + +And I will use the +notation that psi n + +is the complex +conjugate of n psi. + +And the norm of this I'm going +to indicate by psi psi, which + +is obtained by summing over +all n psi psi n star, which + +is essentially the +magnitude of n psi squared. + +And these are unit vectors. + +So all of these states +are normalized such + +that psi psi is equal to 1. + +Yes. + +AUDIENCE: You're not +allowing particle numbers + +to vary, are you? + +PROFESSOR: At this stage, no. + +Later on, when we do +the grand canonical, + +we will change +our Hilbert space. + +OK? + +So that's one concept. + +The other concept, +classically, we measure things. + +So we have classical observable. + +And these are +functions all of which + +depend on this p and +q in phase space. + +So basically, there's +the phase space. + +We can have some +particular function, + +such as the kinetic energy-- +sum over i pi squared + +over 2 n-- that's an +example of an observable. + +Kinetic energy, potential +energy, anything that we like, + +you can classically +write a sum function + +that you want to +evaluate in phase space, + +given that you are at some +particular point in phase + +space, the state of your system, +you can evaluate what that is. + +Now in quantum +mechanics, observables + +are operators, or matrices, if +you like, in this vector space. + +OK? + +So among the +various observables, + +certainly, are things +like the position + +and the momentum +of the particle. + +So there are presumably +matrices that + +correspond to +position and momentum. + +And for that, we look +at some other properties + +that this classical +systems have. + +We had defined classically +a Poisson bracket, + +which was a sum over all +alphas d a by d q alpha + +d b by d p alpha minus the a +by the p alpha b d by the q f. + +OK? + +And this is an +operation that you + +would like to, and happens +to, carry over in some sense + +into quantum mechanics. + +But one of the +consequence of this + +is you can check if I pick +a particular momentum, key, + +and a particular coordinate, +q, and put it over here, most + +of the time I will get 0, +unless the alphas match + +exactly the p q's +that I have up there. + +And if you go through +this whole thing, + +I will get something like +that is like a delta i j. + +OK. + +So this structure somehow +continues in quantum mechanics, + +in this sense that the matrices +that correspond to p and q + +satisfy the condition +that p i and q j, + +thinking of two matrices, +and this is the commutator, + +so this is p i q j minus q j +p i is h bar over i delta h. + +So once you have the matrices +that correspond to p and q, + +you can take any function of p +and q that you had over here, + +and then replace the p's and +q's that appear in, let's say, + +a series expansion, or an +expansion of this o in powers + +of p and q, with corresponding +matrices p hat and q hat. + +And that way, you will construct +a corresponding operator. + +There is one subtlety that +you've probably encountered, + +in that there is +some symmetrization + +that you have to do before +you can make this replacement. + +OK. + +So what does it mean? + +In classical theory, if +something is observable + +the answer that you +get is a number. + +Right? + +You can calculate what +the kinetic energy is. + +In quantum mechanics, +what does it + +mean that observable +is a matrix? + +The statement is +that observables + +don't have definite values, +but the expectation value + +of a particular observable +o in some state pi + +is given by psi o psi. + +Essentially, you take the vector +that correspond to the state, + +multiply the matrix on +it, and then sandwich it + +with the conjugate +of the vector, + +and that will give +you your state. + +So in terms of elements +of some particular basis, + +you would write this +as a sum over n and m. + +Psi n n o m m psi. + +And in that particular +basis, your operator + +would have these +matrix elements. + +Now again, another +property, if you're + +measuring something +that is observable, + +is presumably you will +get a number that is real. + +That is, you expect this +to be the same thing + +as its complex conjugate. + +And if you follow +this condition, + +you will see that that reality +implies that n o m should + +m o n complex conjugate, +which is typically written + +as the matrix being its +Hermitian conjugate, + +or being Hermitian. + +So all observables +in quantum mechanics + +would correspond to Hermitian +operators or matrices. + +OK. + +There's one other +piece, and then we + +can forget about axioms. + +We have a classical +time evolution. + +We know that the particular +point in the classical phase + +space changes as a +function of time, such + +that q i dot is +plus d h by d p i. + +P i dot is minus d h by d q i. + +By the way, both of these +can be written as q i + +and h Poisson bracket and +p i and h Poisson bracket. + +But there is a particular +function observable, h, + +the Hamiltonian, that derives +the classical evolution. + +And when we go to +quantum evolution, + +this vector that we have in +Hilbert space evolves according + +to i h bar d by dt +of the vector psi + +is the matrix that we +have acting on psi. + +OK. + +Fine. + +So these are the +basics that we need. + +Now we can go and do +statistical descriptions. + +So the main element that we +had in constructing statistical + +descriptions was deal +with a macrostate. + +We said that if I'm +interested in thinking + +about the properties of +one cubic meter of gas + +at standard temperature +and pressure, + +I'm not thinking about a +particular point in phase + +space, because +different gases that + +have exactly the same +macroscopic properties would + +correspond to many, many +different possible points + +in this phase space that are +changing as a function of time. + +So rather than thinking +about a single microstate, + +we talked about an ensemble. + +And this ensemble had a whole +bunch of possible microstates. + +In the simplest +prescription, maybe we + +said they were all +equally likely. + +But, actually, we could even +assign some kind of probability + +to them. + +And we want to know what to do +with this, because then what + +happened was from +this description, + +we then constructed a +density which was, again, + +some kind of a probability +in phase space. + +And we looked at +its time evolution. + +We looked at the averages +and all kinds of things + +in terms of this density. + +So the question is, what +happens to all of this + +when we go to +quantum descriptions? + +OK. + +You can follow a lot of that. + +We can, again, take the example +of the one cubic meter of gas + +at standard temperature +and pressure. + +But the rather than describing +the state of the system + +classically, I can +try to describe it + +quantum mechanically. + +Presumably the quantum +mechanical description + +at some limit becomes equivalent +to the classical description. + +So I will have an +ensemble of states. + +I don't know which +one of them I am in. + +I have lots of boxes. + +They would correspond to +different microstates, + +presumably. + +And this has, +actually, a word that + +is used more in the +quantum context. + +I guess one could use it +in the classical context. + +It's called a mixed state. + +A pure state is one +you know exactly. + +Mixed state is, well, +like the gas I tell you. + +I tell you only the +macroscopic information, + +you don't know much about +microscopically what it is. + +If these are possibilities, +and not knowing + +those possibilities, +you can say that it's + +a mixture of all these states. + +OK. + +Now, what would I use, +classically, a density for? + +What I could do is +I could calculate + +the average of some observable, +classically, in this ensemble. + +And what I would do +is I would integrate + +over the entirety of the six +n-dimensional phase space + +the o at some particular +point in phase space + +and the density at that +point in phase space. + +And this average I +will indicate by a bar. + +So my bars stand for +ensemble average, + +to make them distinct from +these quantum averages + +that I will indicate +with the Bra-Kets. + +OK? + +So let's try to do the analogue +of that in quantum states. + +I would say that, OK, for a +particular one of the members + +of this ensemble, +I can calculate + +what the expectation value is. + +This is the +expectation value that + +corresponds to this observable +o, if I was in a pure state psi + +alpha. + +But I don't know +that I am there. + +I have a probability, +so I do a summation + +over all of these states. + +And I will call that expectation +value ensemble average. + +So that's how +things are defined. + +Let's look at this in +some particular basis. + +I would write this as a sum +over alpha m and n p alpha psi + +alpha m m o n n psi alpha. + +So, essentially, writing +all of these psis + +in terms of their components, +just as I had done above. + +OK. + +Now what I want to do +is to reorder this. + +Do the summation +over n and m first, + +the summation over alpha last. + +So what do I have? + +I have m o n. + +And then I have a sum over +alpha of p alpha n psi alpha + +psi alpha n. + +So what I will do, this quantity +that alpha is summed over-- + +so it depends on the +two indices n and m. + +I can give it a name. + +I can call it n rho m. + +If I do that, then this o +bar average becomes simply-- + +let's see. + +This summation over n gives +me the matrix product o rho. + +And then summation over m gives +me the trace of the product. + +So this is the trace of rho o. + +OK? + +So I constructed +something that is + +kind of analogous +to the classical use + +of the density in phase space. + +So you would multiply +the density and the thing + +that you wanted to +calculate the observable. + +And the ensemble +average is obtained + +as a kind of summing over +all possible what values + +of that product in phase space. + +So here, I'm doing +something similar. + +I'm multiplying this +o by some matrix row. + +So, again, this I can think +of as having introduced + +a new matrix for an operator. + +And this is the density matrix. + +And if I basically +ignore, or write it + +in basis-independent +form, it is obtained + +by summing over all +alphas the alphas, + +and, essentially, +cutting off the n and m. + +I have the matrix that I would +form out of state alpha by, + +essentially, taking the +vector and its conjugate + +and multiplying rows and columns +together to make a matrix. + +And then multiplying or +averaging that matrix + +over all possible +values of the ensemble-- + +elements of the ensemble-- +would give me this density. + +So in the same way +that any observable + +in classical mechanics goes +over to an operator in quantum + +mechanics, we find that +we have another function + +in phase space-- this density. + +This density goes over to the +matrix or an operator that + +is given by this formula here. + +It is useful to enumerate +some properties of the density + +matrix. + +First of all, the density +matrix is positive definite. + +What does that mean? + +It means that if you +take the density matrix, + +multiply it by any state +on the right and the left + +to construct a number, this +number will be positive, + +because if I apply it to the +formula that I have over there, + +this is simply sum +over alpha p alpha. + +Then I have phi psi +psi alpha, and them + +psi alpha psi, which is +its complex conjugate. + +So I get the norm of that +product, which is positive. + +All of the p alphas are +positive probabilities. + +So this is certainly +something that is positive. + +We said that anything that +makes sense in quantum mechanics + +should be Hermitian. + +And it is easy to check. + +That if I take this +operator rho and do + +the complex conjugate, +essentially what happens + +is that I have to +take sum over alpha. + +Complex conjugate of p +alpha is p alpha itself. + +Probabilities are real numbers. + +If I take psi alpha psi alpha +and conjugate it, essentially + +I take this and put it here. + +And I take that and +put it over there. + +And I get the same thing. + +So it's the same thing as rho. + +And, finally, there's +a normalization. + +If, for my o over here in +the last formula, I choose 1, + +then I get the +expectation value of 1 + +has to be the trace of rho. + +And we can check that +the trace of rho, + +essentially, is +obtained by summing over + +all alpha p alpha, and the dot +product of the two psi alphas. + +Since any state in +quantum mechanics + +corresponds to a unit +vector, this is 1. + +So I get a sum over +alpha of p alphas. + +And these are +probabilities assigned + +to the members of the ensemble. + +They have to add up to 1. + +And so this is like this. + +So the quantity that +we were looking at, + +and built, essentially, all of +our later classical statistical + +mechanics, on is this density. + +Density was a probability +in phase space. + +Now, when you go to +quantum mechanics, + +we don't have phase space. + +We have Hilbert space. + +We already have a +probabilistic theory. + +Turns out that this +function, which + +was the probability in +phase space classically, + +gets promoted to this matrix, +the density matrix, that has, + +once you take traces and +do all kinds of things, + +the kinds of properties that +you would expect the probability + +to have classically. + +But it's not really +probability in the usual sense. + +It's a matrix. + +OK. + +There is one other thing +element of this to go through, + +which is that +classically, we said + +that, OK, I pick +a set of states. + +They correspond to some density. + +But the microstates are +changing as a function of time. + +So the density was changing +as a function of time. + +And we had Liouville's +theorem, which + +stated that d rho by d t +was the Poisson bracket + +of the Hamiltonian with rho. + +So we can quantum +mechanically ask, + +what happens to +our density matrix? + +So we have a matrix rho. + +I can ask, what is the time +derivative of that matrix? + +And, actually, I will +insert the i h bar here, + +because I anticipate +that, essentially, + +rho having that form, what I +will have is sum over alpha. + +And then I have i h bar d by +dt acting on these p alpha psi + +alpha psi f. + +So there rho is sum over alpha +p alpha psi alpha psi alpha. + +Sum over alpha p alpha +I can take outside. + +I h bar d by dt acts +on these two psis + +that are appearing a +complex conjugates. + +So it can either, d by dt, +act on one or the other. + +So I can write this +as sum over alpha p + +alpha i h bar d by dt acting +on psi alpha psi alpha, or i, + +or psi alpha, and then i h bar d +by dt acting on this psi alpha. + +Now, i h bar d by +dt psi alpha, we + +said that, essentially, the +quantum rule for time evolution + +is i h bar d by dt +of the state will + +give you is governed by h +times acting on psi alpha. + +If I were to take the complex +conjugate of this expression, + +what I would get +is minus i h bar + +d by dt acting on +psi that is pointing + +the other way of our +complex conjugation + +is h acting on the psi +in the opposite way. + +So this thing is minus psi +alpha with h f acting on it. + +OK. + +So then I can write the whole +thing as h-- for the first term + +take the h out front. + +I have a sum over +alpha p alpha psi alpha + +psi alpha, minus, from this +complex conjugation-- here, h + +is completely to the right-- +I have a sum over alpha + +p alpha psi alpha psi alpha. + +And then we have h. + +Now, these are again +getting rho back. + +So what I have established +is that i h bar, the time + +derivative of this +density matrix, + +is simply the commutator +of the operators h and o. + +So what we had up here was the +classical Liouville theorem, + +relating the time derivative +of the density in phase space + +to the Poisson bracket with h. + +What we have here is the +quantum version, where + +the time derivative +of this density matrix + +is the commutator of rho with h. + +Now we are done, because what +did we use this Liouville for? + +We used it to deduce that if +I have things that are not + +changing as a function of time, +I have equilibrium systems, + +where the density is invariant. + +It's the same. + +Then rho of equilibrium not +changing as a function of time + +can be achieved by simply +making it a function of h. + +And, more precisely, h +and conserved quantities + +that have 0 Poisson +bracket with h. + +How can I make the +quantum density matrix + +to be invariant of time? + +All I need to do is to ensure +that the Poisson bracket + +of that density with +the Hamiltonian is 0. + +Not the Poisson +bracket, the commutator. + +Clearly, the commutator +of h with itself is 0. + +Hh minus hh is 0. + +So this I can make +a function of h, + +and any other kind +of quantity also + +that has 0 commutator with h. + +So, essentially, the quantum +version also applies. + +That is, the quantum +version of rho equilibrium, + +I can make it by +constructing something + +that depends on +the Hilbert space + +through the dependence +of the Hamiltonian + +and on the Hilbert space and any +other conserved quantities that + +have 0 commutator also +with the Hamiltonian. + +So now, what we +will do next time + +is we can pick and choose +whatever rho equilibrium + +we had before. + +Canonical e to the minus beta h. + +We make this matrix to +be e to the minus beta h. + +Uniform anything, we +can just carry over + +whatever functional dependence +we had here to here. + +And we are ensure +to have something + +that is quantum +mechanically invariant. + +And we will then interpret +what the various quantities + +calculated through that +density matrix and the formulas + +that we described actually. + +OK? \ No newline at end of file diff --git a/cUzZ-qu3xws.txt b/cUzZ-qu3xws.txt new file mode 100644 index 0000000000000000000000000000000000000000..37199f582ff1a1f61335826f1934ccd1e3babcd6 --- /dev/null +++ b/cUzZ-qu3xws.txt @@ -0,0 +1,2484 @@ +PROFESSOR: Everyone +seems to be here. + +At least all the seats +are filled up, so + +why don't we begin. + +One thing that I did finally, +to be specific, I told you + +that we would have three quizzes +and that they would be + +uniformly spaced one third, and +2/3 and 2.89 thirds of the + +way through the term. + +And I figured out where +those dates would be. + +So since I have them, let +me give you the date. + +So Quiz 1 is going to be +on Thursday, October 6. + +Quiz 2 will be on Tuesday, +November 8, and Quiz 3 will be + +on Thursday, December 8. + +And this, as advertised, is +exactly one third of the way + +through the lectures. + +This is exactly 2/3 of the way +through the lectures, and this + +is the next to the last meeting +that we'll have. + +This is the week before the +final week of the terms. so I + +deliberately kept it a little +bit away from the usual + +end-of-term crunch. + +Being person who is sensitive to +symmetry and order, I find + +it highly regrettable that +we cannot have the + +quiz on October 8. + +Then you would on the 8th of +October, November, December, + +you have a quiz. + +Unfortunately, October 8, much +as that would beautify the + +schedule, is on a Saturday, +so we can't do it so. + +I could do it, but I don't +think anybody would come. + +I've been, believe it or not, +going through these problem + +sets in great detail. + +I didn't want to hand them out +until I had the list-- + +and you may or may not know-- +that is made up for the + +registrants in each class, And +we get a nice array of + +photographs with names and +department numbers and years + +numbers under them. + +That something, by the way, that +only the instructor in a + +class requests, not even the +secretary can do it. + +So this is not widely +broadcast. + +I found to my dismay though +when I finally got it that + +about one third of the +pictures are missing. + +And I don't know whether you +folks have been photographed + +fairly late on the term, +but a third of the + +pictures are missing. + +I already been putting some +faces in my memory banks, but + +to match up names and faces +so that I can hand out the + +problem sets individually, +I need more photographs. + +So I'll do it one way or another +next time, and we'll + +see some photographs, additional +photographs, have + +appeared in the interim. + +I've given you three problem +sets so far, and they were + +really just for fun as well as +to get you thinking about the + +right sorts of things, but +there were little puzzle. + +I'm, unfortunately, going to +have to tell you from now on + +no more cutesy little puzzles. + +You're going to get +real problem sets, + +long, tedious, drudgery. + +They're optional though, so +that's the saving grace. + +So I'm going to pass it around +the problem set 4. + +And this asks you to demonstrate +some of the things + +that we talked about last time +and convince yourself that + +they really work and ask +you to make some simple + +applications of Miller-Bravais +indices to + +two-dimensional lattices. + +And then finally, the last +problem is to get you thinking + +about patterns. + +And I've asked you to identify +the lattice points and the + +symmetry elements +in two patterns. + +I'm almost willing to wager that +not one of you will get + +it completely right, that +there's going to be some + +little thing that you +missed or did wrong. + +At one time, I bet a bag of +potato chips for everybody in + +the class against the class +wagering against me one bag of + +potato chips. + +Well, I'm going to watch my +weight, and I've won that + +invariably, and I really can't +eat that greasy sort of stuff. + +In any case, you'll see that +in the case of symmetry and + +patterns it is immensely +simplified when you know + +exactly what to look for, when +you know the number of + +possibilities was finite,. + +And when we're through with +this, you can ask just one + +question about a pattern and +then know exactly what the + +symmetry of that pattern has +to be and exactly where to + +look for everything else. + +I can guarantee you that by the +time you finish this class + +you will never sit in a bathroom +and stare at the tile + +floor and see it in exactly +the same way again. + +I think that's a good +observation because I like to + +think that that's what education +is all about, not + +sitting in the bathroom, but +seeing things differently + +after you've had the experience + +than you did before. + +That's what education +is all about. + +So have fun with the patterns. + +And again, it will become-- + +one seat up here. + +Today then we're about ready +to embark on an adventure. + +As I said last time, we'll +develop two-dimensional + +symmetries first because there +are relatively few of them, + +and one could do +this rigorously + +and in great detail. + +We're going to have to touch on +things more lightly when we + +get to three-dimensional +symmetries so we can finish at + +a decent point in the term. + +Let me remind you that we have +so far identified two types of + +symmetry that can exist in a +lattice, onefold, twofold, + +threefold, or sixfold +rotation axes. + +Any number of different +rotational symmetries are + +possible, but if you're going to +want them to be compatible + +with a lattice, you must +restrict the rotation axis to + +one of these five, including +a onefold axis, which is no + +symmetry it all. + +And in two-dimensions, besides +translation, we saw the + +operation of reflection. + +And now we're going to begin +to put things together and + +make elaborate combinations. + +The first thing I will ask is +can we have more than one of + +these symmetry elements present +and operating about + +the same locus at +the same time. + +The answer to that would +be, why not. + +Because if we look at a sixfold +rotation axis, that's + +really what a twofold rotation +axis does combined with what a + +threefold rotation axis does. + +And we plot these on top of one +another, and what we end + +up with is the arrangement of +motifs that is generated by + +sixfold axis. + +So in a sense, a sixfold axis is +a twofold axis superimposed + +on a threefold axis. + +That kind of a naive way about +thinking of this though. + +What we're really saying is that +what a sixfold axis has + +is the set of operations 1 A +2 pi/ 6, A twice 2 pi /6 -- + +that would be 120 degree +rotation-- + +and A pi, A 5 pi/6. + +And there's 1, 2, 3, 4, 5. + +And we're missing one. + +60, 120, 240. + +So that would be A twice +2 pi/3, 4 pi/6 + +So what we're really saying is +a sixfold axis consists of + +these six elements, and these +elements constitute a group + +because I can combine any two +of these rotation operations + +and find something that's +already a member of the set. + +By saying that a sixfold axis +consists of a threefold axis + +sitting on top of a twofold +axis, what we're saying is + +that there's one collection +of elements here, namely + +identity, or same thing as A 2 +pi and A pi, that is a subset + +of these, or we could +say a subgroup. + +So what we're doing in saying +that these two sets of + +rotation operations exist +simultaneously, we're saying + +that the twofold axis is a +subgroup of the sixfold axis. + +And similarly, we can separate +out three other elements, a + +onefold axis, same as A 2 pi; +a 120-degree rotation, A 2 + +pi/3; and a 240-degree +rotation, A 4 pi/3. + +And these three operations, +a group of rank 2, is what + +constitutes another subgroup, a +subset of elements which by + +themselves satisfy all of the +requirements of a group. + +So this is one example of how +we can have more than one + +symmetry element, a set of +operations existing about the + +same locus and space. + +This is not how one would go +about the deriving these + +higher symmetry however. + +Because what we have to do is +to add something to the set, + +something that's called an +extender, and then show that + +all the requirements of a set +being a group is satisfied; + +namely, that a combination of +any two elements in the group + +is also a member the group, that +for every operation an + +inverse exists, and the identity +operation is a member + +of the group. + +So you can build up more +higher symmetries, more + +complex symmetries by adding +some operation called an + +extender and then taking all +of the products of these + +elements and see what new +operations arise. + +So we can have more than one +symmetry element operating + +about the same locus and the set +of individual operations + +that it embodies. + +And here sitting all by itself +is a mirror plane. + +Why don't we combine a mirror +plane with the rotation axis? + +And we've already seen +examples of that. + +For example, in the square +pattern that these tiles make + +up, there's a fourfold axis in +the middle of each of the + +squares that are also mirror +planes that pass + +through that location. + +So let me look at a combination +that is a little + +simpler to handle. + +And what I'm going to say is +here sits a mirror plane with + +a reflection operation that +I'll call sigma 1 for the + +individual operation. + +And let me say that I combine +now in that space a second + +reflection operation +about a line that + +intersects the first one. + +And the question I'm going to +ask now is happens when I take + +a first motif, number 1, +reflected in the locus of the + +first mirror plane to get number +2, and then reflect + +that a second time in the locus +of the second mirror + +plane to get one that +sits up here. + +So the question is now what is +the operation sigma 1 followed + +by the operation sigma +2 equals to? + +We can almost answer by the +process of elimination. + +If this one is left handed, +reflection changes the + +polarity, so number +2 is right hand. + +And if we reflect a second time, +the right-handed one + +goes to a left-handed one. + +So what we're asking is how do +I get from one left-handed + +motif to another left-handed +motif? + +Of the three operations that +exist in a two-dimensional + +space could be translation. + +But, clearly, I can't take the +first one and slide it + +parallel to itself and make it +coincide with the third. + +So translation would not change +chirality, but that + +won't work. + +What's left? + +Rotation. + +Yes. + +You want to clarify +something first? + +AUDIENCE: That third one, it +looks kind of left-handed. + +[INAUDIBLE]. + +PROFESSOR: Oops. + +It does. + +It does indeed. + +Sorry about that. + +When you've got your nose poked +right in these things, + +it's easy to overlook it. + +Yes. + +Absolutely right. + +That should be over canted over +a bit more like I had it + +the first way. + +Very good thank you. + +I don't want to proceed much. + +Yes? + +AUDIENCE: What did +you [INAUDIBLE] + +axis [INAUDIBLE]? + +PROFESSOR: We could do that. + +And let's do it, and we're +going to encounter + +this sooner or later. + +So we have a first mirror plane +reflect from a first + +one, which is right handed, to +second one that's left handed. + +And then define a second locus, +and that one would take + +the second one and move it +over to here, the same + +distance on the other side +of this mirror plane. + +And I'll let you answer the +question since you asked it. + +How is the first one related +to the third one? + +AUDIENCE: Translation. + +PROFESSOR: Translation. + +Yes. + +AUDIENCE: It's translated. + +PROFESSOR: Exactly So if this +distance is delta, the first + +and the third are related +be a translation + +which is twice delta. + +So that would be in addition +where we'll eventually want to + +consider when we have patterns +that are based on a lattice. + +But right now, I want to +consider symmetry operations + +that leave at least a point in +space and move perhaps a line + +in the case of the +mirror plane. + +But back to the original +question, what is this first + +reflection followed by +a second reflection? + +We've just thrown +out translation. + +That won't work unless the +mirror planes are parallel to + +one of those. + +The only thing left +is rotation. + +And in point of fact, even +looking at this diagram, you + +can get from the first one to +the third one by a rotation. + +So the answer to the question +is that a combination of two + +reflection operations is a +rotation operation about the + +point of intersection of +the mirror planes. + +But we can go further and say +exactly how large this + +rotation is. + +Let's draw an extra +line in here. + +And let's say that this +angle is alpha. + +And if I repeat this +by reflection, that + +angle is also alpha. + +Let's label this angle beta. + +Repeat that by reflection, and +that angle must also be beta. + +The angle between the two mirror +planes is the angle mu. + +And clearly mu is equal +to alpha plus beta. + +So the answer to the question +quite generally is have two + +mirror planes intersect at an +angle mu, and their successive + +operation is going to be +equivalent to the net result + +of rotating through +twice of the angle + +between them mirror line. + +So we don't have to think +about that anymore now. + +We know if we combine +to mirror planes + +we get a net rotation. + +So that is a basic result, and +that's a first example of + +something that I'm going to +call by my own pet term. + +I'm going to call them +combination theorem, the + +theorem that tells you what you +get when you combine two + +operations. + +And what this is going to give +us is a way of filling in one + +box in the group multiplication +table. + +So knowing what two mirror +planes combined at an angle + +should be, I can now combine +the mirror planes at angles + +which gives me a rotation +operation which is one of the + +ones that's allowed +for a lattice. + +In general, if I'm not yet +putting these symmetry + +elements in a lattice, I could +combine them in such a way + +such that I got a 17-fold +rotation as the angle. + +And then the angle between +the mirror planes would + +be half of 2 pi/17. + +Could be a lovely symmetry, nice +for a pendant or a ring, + +but not for a lattice and +not for a crystal. + +So I'm going to want to combine +mirror planes at + +angles that correspond to +rotations that are compatible + +with the lattice. + +So what I could do is take +a first reflection + +locus, sigma 1. + +And if I want the rotation angle +to be 180 degrees for a + +twofold axis, I would want the +second mirror plane with the + +operation sigma 2 to be +at one half of pi with + +respect to the first. + +And for this specific +combination then, reflection + +in the first mirror planes +followed by reflection in the + +second mirror planes to give me +a third one, is going to be + +equivalent to-- + +Oops. + +Back here-- + +it's going to be equivalent +to a twofold axis. + +So sigma 1 followed by sigma 2 +at an angle one half of pi is + +going to be equivalent to the +rotation operation A pi. + +This is not yet a complete +pattern because here's a + +mirror planes that wants to +reflect this motifs as well. + +So let's just reflect number 3 +across the mirror planes 1. + +And then we're going to +get a fourth object. + +Now let's show that this +constitutes a group. + +We've got the identity operation +doing nothing. + +We've got the operation +sigma 1. + +We've got the operation +sigma 2, and we've got + +the operation a pi. + +I'll put the same operations +again in the vertical column. + +Here's operation 1 doing +nothing, sigma 1, + +sigma 2, and A pi. + +So doing nothing and following +it by one of these four + +operations just gives you the +same thing back again. + +And doing these operations +followed by 1 will give me the + +same operation back again. + +If I reflect twice across sigma +1 from left to right and + +right to left, I'm back to +where I started from. + +So sigma 1 followed by sigma 1 +is the identity operation. + +Sigma 1 followed by sigma +2 is what we just did. + +That turns out to be +the operation A pi. + +And sigma 1 reflection and +following that by A pi is the + +way in which I get to +the fourth one. + +So that is going to be +equal to sigma 2. + +Well, let me rips through the +last ones fairly quickly. + +Sigma 2 followed by signal 1. + +Sigma 2 followed by sigma +1 is the same as A pi. + +Sigma 2 followed by sigma 2 +gets us back to where we + +started from. + +That's the identity operation. + +Sigma 2 followed by A pi reflect +from here to here and + +then rotate. + +That's the same as sigma 1. + +And the final sequence, +rotation followed by + +reflection would give +me sigma 2. + +Rotation followed by sigma +2 will give me sigma 1. + +And doing the rotation operation +twice is the same as + +the identity operation. + +So are the group postulates +satisfied? + +Yes. + +The combination of any +two elements is a + +member of the group. + +For every operation, +an inverse exists. + +And we can answer that question +very easily by merely + +looking at the column under +a particular element, and + +somewhere we find the +identity operation. + +So sigma 1 is its own inverse. + +So, yes, an inverse exists +for every operation. + +And then finally, identity +is a member of the group. + +So everything's lights up. + +Bells ring. + +This set of four elements +is entitled to + +call itself a group. + +And in particular, it is a group +of rank 4 because there + +are four elements +in the group. + +I show you a cool thing. + +I noticed that the number of +objects in the pattern, the + +number of motifs in the pattern, +is exactly the same + +as the order of the group. + +Why? + +Because these four operations +tell you how to get from any + +operation to the remaining three +and tell you how to get + +it into itself. + +So identity relates +it to itself. + +Sigma 1 reflects it to here. + +A pi rotates it down to here. + +Sigma 2 reflects it +down to here. + +So there's always a one-to-one +correspondence between the + +elements that are in the group +and the rank of a group and + +the number of objects that +are in the pattern. + +Yes, sir? + +AUDIENCE: How do you show if +the inverse exists again? + +PROFESSOR: The inverse exists +if I can find something that + +combined with an element in +my basic set gives me the + +identity operation. + +So it's the operation followed +by its inverse has to be the + +same as doing nothing. + +So if I look under each element +and find the identity + +operation, then sigma 2 +is its own inverse. + +If I look under A pi, A +pi is its own inverse. + +This is generally +not the case. + +This is a very simple +symmetry. + +So really we can work with +commas and little figures, and + +that's one way of getting +these symmetries. + +But group theory I think you can +see is a very nice, very + +elegant language for +describing some + +characteristics of +these patterns. + +Now little bit of jargon. + +As if this material were not +confusing enough, there are + +two different languages that +are used to denote these + +unique combinations. + +This notation where we simply +have a number for a rotation + +axis or an m for mirror plane +is something that was first + +proposed by two + +mathematicians, Hermann and Mauguin. + +And this was adopted as the +preferred notation in the + +international tables, that hefty +tome that I brought it + +on the first day of classes. + +So this is also referred +to synonymously as the + +international notation. + +Let me put these things +out horizontally. + +For rotation axes by themselves, +the symbol in + +Hermann notation is simply n. + +And for lattice, n-- + +as we've seen many times-- + +is restricted to what in +Hermann-Mauguin notation would + +be either 1, 2, 3, 4, and 6. + +There's another type of notation +that is use quite + +frequently by condensed matter +physicist, and this is called + +the Schoenflies notation after +one of the mathematicians who + +was the first to derive the +three-dimensional symmetries. + +This was a curious thing. + +There were three people in +different parts of the world + +about the turn of the century-- +and this was before + +email or even air mail-- + +who were trying to derive the +three-dimensional symmetries. + +Schoenflies was one of them. + +And all three of them got to +the same place at about the + +same time, and the results +were obtained. + +But each one used his +own method and had + +his different notation. + +Schoenflies was one of the +people who did this. + +Schoenflies was a mathematician +and based his + +notation on group theory. + +Something called a cyclic +group is what + +the C stands for. + +And a cyclic group is one in +which all elements are power, + +so to speak, of some +basic operation. + +For example, a fourfold axis +consists of the set of + +operations A pi/2; a 90 degree +rotation; A pi, which can be + +written as A pi over 2 squared; +A pi over 2 squared; + +[? then we need ?] + +A pi/2; and A pi/ 2 again; A 3 +pi/2, which can be viewed as + +doing A pi/2 three times; and +finally, the identity + +operation, which is the same as +A 2 pi, which is equivalent + +to doing the basic operation +A pi/2 four times. + +So the group of rank 4, there +are four elements in the + +group, each one is a power of +the basic operation A pi/2. + +So a rotation axis by itself +as a cyclic group. + +Schoenflies indicates these +generically by C subscript n, + +where n is the rank +of the axis. + +Hence, this is C1. + +This is C2. + +This is C3. + +This is C4. + +And this is C6. + +A mirror plane by itself +is indicated m in the + +international notation. + +A mirror plane is also +a cyclic group. + +There are two operations, +reflection and reflection back + +to where you came from. + +Doing the reflection operation +twice is the + +same as doing nothing. + +So Schoenflies also call this +one C. And the one thing that + +is without meaning in English +is his subscript S. And + +Schoenflies was German, and +the S stands for spiegel, + +which is the German +word for mirror. + +We have in many cities +a paper that's + +called the Daily Mirror. + +In Germany, there's a paper +called Der Spiegel. + +So they use it the same +way in everyday life + +as well as in notation. + +So C sub S in the Schoenflies +notation is a mirror plane. + +Cyclic group the S stand +for spiegel. + +For the combinations of which we +have seen only one, in the + +Schoenflies notation these are +all of the form Cnv, a + +rotation axis Cn with a vertical +mirror plane passing + +through it. + +So this one, for example-- +we've yet + +to look at the others-- + +would be C2v. + +So we'll have to draw the first, +and then I'll give you + +the complete set. + +So this is a rotation axis with +a mirror plane passing + +vertically through it. + +Let's do a few more. + +And I think having done a couple +in great detail, we'll + +see what the others will look +like quite readily. + +Let's take a fourfold axis and +add to the rotation operations + +A pi/2, a first mirror plane +that I'll label sigma 1. + +I can permute the order of +operations and say that sigma + +1 followed by the rotation +operation A pi/2 is going to + +be equal to a second reflection +operation that is + +equal to one half of pi/2 +away from the first. + +So I'm claiming that if I +reflect in the first mirror + +plane and then rotate by 90 +degrees that should be another + +mirror plane at 45 degrees +to the first. + +So let me do exactly +what I advertised. + +Here's the first, one +right handed. + +Reflect across to get a second +one, which is left handed. + +Reflect, then rotate, and that +would bring my left-handed one + +up to this location here. + +So here's 3, and it's +left handed. + +And lo and behold, just as +advertised, I get from the + +first one to the third one by +reflecting across a mirror + +plane, which is one +half of pi/2. + +If let these symmetry elements +operate on each other, what + +I'll end up with is a +set of mirror planes + +at 45 degree intervals. + +And what I'll have is a pair +of objects hung in the same + +fashion at every mirror plane. + +Is that too fast? + +You want to go through +that a little slower? + +Oh, go ahead say, go through +it more slowly. + +Everybody's afraid to say, yeah, +yeah, and been seem like + +a class dummy. + +Do you want me to do +it more slowly? + +I see people still writing, so I +think what you'd rather have + +is me be quiet for a bit while +you catch up to where I am. + +In the Schoenflies notation, +this lovely thing here is C4. + +It's a rotation axis of rank 4 +with a vertical mirror plane + +added to it. + +And the international +notation, now the + +Hermann-Mauguin notation, is +just a running list of the + +individual symmetry elements +that are present. + +And now I really are going +to have a mouthful. + +This is a fourfold axis, so +the symbol for that is 4. + +This is a mirror plane. + +This is a mirror plane. + +This is a mirror plane. + +This is a mirror plane. + +This is a mirror plane. + +This is a mirror plane. + +That's a mirror plane, and +that's a mirror plane. + +So it looks as though I should +call this 4mmmmmmmm, which + +comes 4mmmmmmmm. + +Well, that is a typical +reaction. + +It's a lovely symmetry. + +But that is a mouthful. + +So it isn't really necessary to +give all these m's So the + +international notation is +a running list of the + +independent symmetry elements, +and that's the new wrinkle + +that I'm introducing. + +It's a running list of the +independent symmetry elements. + +And all these mirror planes are +just different sigma that + +exist as operations +in the group. + +But how many different kinds +of mirror planes are they? + +Well, there are two different +kinds of mirror planes, both + +in terms of the way in which +they function in the pattern. + +The two motifs related by +reflection hang close to this + +mirror plane, but they're widely +separated for this + +mirror plane. + +So the motifs do different +things relative to those two + +kinds of mirror planes. + +Another way of asking what's +independent is if I start with + +this 1 mirror plane and repeat +it by 90-degree rotations, + +I'll get these 4 mirror planes +90 degrees away. + +So they are not independent in +that these mirror planes are + +all related by the rotational +symmetry that's present. + +You don't get this mirror plane +in any fashion other + +than saying, if I combine the +rotation operation with this + +reflection operation sigma, +the net result is this + +reflection plane. + +So there are two mirror planes +that are distinct in this + +arrangement of symmetry +elements, distinct in the + +sense that they function in +different ways in the pattern; + +distinct in the sense that no +other operation that is + +present will throw these two +operations into one another. + +Another example, and this is in +fact symmetry 4mm, is the + +square tile. + +If you look at the mirror planes +there, they are 45 + +degrees apart. + +But one of those mirror planes +comes out normal to the edge + +of the tile. + +The other mirror plane comes out +of the vertex of the tile. + +So they are different in the way +they function in the space + +which has this symmetry. + +So, mercifully, we don't have +to call this 4mmmmmmmm. + +We drop the last 6 m's, and this +one is called simply for + +4mm, 2 kinds of mirror planes +with a fourfold axis. + +If you're familiar with the +way in which these were + +derived, the symbol tells you +exactly what you've got. + +So it's a very useful notation +for these symmetries. + +Let me pause here, give you +a chance to catch up. + +Yes, sir? + +AUDIENCE: So wait, all you did +here is take two separate + +mirror planes at an angle of +45 degrees between, and you + +ended up with a fourfold +symmetry. + +PROFESSOR: Exactly. + +AUDIENCE: But you didn't put on +the fourfold symmetry, it + +was just what fell out of it? + +PROFESSOR: No. + +I Got this mirror plane to begin +with by combining this + +reflection operation sigma with +the operation A pi/2, and + +that's where this operation +came from. + +But a general theorem that +says if I have a rotation + +operation A alpha and combine it +with a reflection operation + +sigma, the combined effect is +a reflection operation sigma + +2, which is alpha/2 away +from the first. + +So, again, showing you for this +now rather messy diagram, + +if I start with the reflection +operation that takes 1 of them + +throws of the 2 and then rotates +2 up to location 3, + +the way I get from 1 to 3 in one +shot is to reflect in this + +locus sigma 2. + +Yes, sir? + +AUDIENCE: You could have started +with any one of those + +two and got the third. + +PROFESSOR: Absolutely. + +Absolutely. + +The operations that are +present operate + +everything in the space. + +So when I say that there's a +mirror plane here that relates + +this one to this one, it also +relates this one to this one, + +this one to this one, this one +to this one, that mirror + +planes operates on everything. + +You can't say that a symmetry +operation grab this little + +packet of space and moves +it to another packet + +removed from it. + +To say it's a symmetry of a +pattern or of a crystal, it + +has to leave everything +invariant. + +OK. + +But, again, in terms of the +language of groups theory, if + +you combine this pair of +operations, then when you + +combine everything that you get +pairwise, you will get in + +this case a total of, +how many operations? + +How many operations are +in this pattern? + +I said a moment ago the rank of +the group is the number of + +operations that are present. + +It's the number of objects that +are in the group because + +each operation in a group tells +you how to get from + +anyone to all of the other. + +So, 2, 4, 6, 8, this is a group +of rank 8, and there are + +8 operation that are present. + +And I can rattle them +off quickly. + +Four operations, identity, +90, 180, 270 for + +the fourfold axis. + +That's 4. + +This mirror plane. + +This mirror plane. + +The mirror plane. + +And this mirror plane. + +That's 8. + +Four for rotation. + +Four for reflection. + +Other questions? + +All right. + +Let me then wrap up this +quickly and get + +onto something new. + +Did I hear the hiccup +or a question? + +No. + +It was a hiccup. + +Not a yawn I hope. + +Let me do the highest symmetry +of all in two dimensions, and + +this is if I take a sixfold +axis and combine it with a + +mirror plane. + +So here's the first +operation sigma. + +This one is something +of a bear to draw. + +This is sigma 1. + +Sigma 1 followed by the +operation A 2 pi/6 should be + +equal to a reflection that is an +angle one half of 2 pi/6 30 + +degrees away from the first. + +So this will be sigma 2. + +So if I reflect from 1 to 2 and +then rotate by 60 degrees, + +I'm going to get one +that sets up here. + +And the way I get from number +1 to number 3 in one shot is + +by a reflection sigma 2. + +Now if I draw in all of those +are mirror planes when they + +are repeated by the sixfold +axis, I shouldn't have given + +this my 6mmmmmm treatment +because there + +are 12 mirror planes. + +Two objects hanging on this one +in one fashion spaced in a + +different way that are +belly to belly. + +They're back to back here, so it +does something different in + +the pattern. + +A pair hanging here. + +A pair hanging in here. + +A pair hanging and here. + +A pair hanging in here. + +And finally, a pair +hanging in here. + +So there are a total +2, 4, 6, 8, 10, 12 + +motifs in this pattern. + +Pairs hanging on mirror planes +that are 30 degrees apart and + +hanging disposed and pointing +in different ways on the + +adjacent mirror planes. + +So this is one that we would +call in international notation + +6mmm and in Schoenflies +notation C6v. + +So we're making extraordinary +progress here. + +The one that I did for you +initially was C2v, and that's + +2mn in international notation. + +The only one that I left out to +this point is a threefold + +axis compared with a vertical +mirror planes. + +And let's start with the +operation A 2 pi/3, combined + +with that a first reflection +operation sigma 1 that passes + +through it. + +And for reference, I'll drawn +in some lines that are + +separated by intervals +of 60 degrees. + +So this reflection from 1 to 2 +followed by a rotation 120 + +degrees should give me +this one as number 3. + +The first is right handed. + +The second is left handed, and +the third stays left handed. + +And lo and behold, the way I get +from 1 to 3 directly is by + +a reflection sigma 2 across +a mirror line that is-- + +I'm sorry. + +This is number 1 down here-- +across a mirror line that is + +30 degrees away from +the first. + +If I would complete the pattern, +reflect this one + +across to here, take this pair +and reflect it or rotate it up + +here, and I have six objects. + +So this is a group of rank 6. + +And it has characteristics that +are quite analogous to + +those we did for the other +rotation axes in all respect + +except one. + +The international symbol for +this combination is C3v. + +We've got a threefold axis. + +We've got the mirror plane +that we added. + +And then we've got a mirror +plane that is 30 degrees away + +from the first-- + +I'm sorry-- + +60 degrees away from the first, + +one half of 120 degrees. + +I claim that this is not the +proper symbol because the + +mirror planes that are +listed should be the + +symmetry-independent, distinct +sort of mirror planes. + +And is that the case +with this one? + +The answer is no. + +It isn't. + +Here is one mirror plane. + +It's got a pair of motifs +hanging on it. + +This mirror plane here is a +mirror plane that has a pair + +of motifs hanging it. + +Same is true of this +mirror plane. + +So all six of these mirror +planes are doing the same + +thing in the pattern. + +Each one has a pair of a motifs +on either side of it in + +the same fashion. + +And I can get one mirror plane +and the motifs hanging on it + +by a rotation of 120 degrees. + +So there's only one kind of +mirror planes, so we don't + +need that m. + +So all of the other rotational +symmetries, m, a onefold axis + +with a mirror plane; 2mm, +4mm, 6mm have two + +kinds of mirror planes. + +C3v has only one kind +of mirror planes. + +And another way of showing +that is if I look at a + +trigonal prism. + +It's got a mirror plane coming +out of a corner and out of the + +opposite face. + +Mirror plane coming out +of the corner and out + +the opposite face. + +Mirror plane coming out +of a corner and out + +the opposite face. + +And that's exactly the +rearrangement of symmetry + +elements here. + +So each mirror planes when +drawn in relative to a + +trigonal prism, which is a body +that has this symmetry, + +each mirror planes does exactly +the same thing, as + +opposed to the square tile or +square prism that has one kind + +of mirror plane that comes out +of faces and one kind of + +mirror plane that comes +out of corners. + +So there are two different +types of mirror planes. + +Let's add them all up, +summarize, and we've got the + +cast of characters that we +can be use in deriving + +two-dimensional symmetries. + +We've got C1, which is a onefold +axis; C2, twofold + +axis; C3, that's a threefold +axis; C4, and that's a + +fourfold axis; C6, that's +a sixfold axis. + +Then we've got the additions +that involve adding a mirror + +plane to a rotational axis. + +So this is simply m and CS +in Schoenflies notation. + +Then we added a mirror plane +to a twofold axis. + +We've got C2 with a vertical +mirror plane, 2mm; C3v; and + +not 3mm, but only 3m; C4v, and +that's 4mm; and C6v, and + +that's 6mm. + +Add them all up, and there are +10 unique possibilities, no + +more, no less. + +Yes, sir? + +AUDIENCE: I'm missing a point. + +Why is there the mirror plane +sigma 2 rather than rotating + +sigma 1 is not different? + +How do you? + +PROFESSOR: The same thing is +going on, on this mirror plane + +as on this mirror planes, +on this mirror plane. + +Or if you like to see it in +terms of a geometric solid, + +the mirror planes here in a +trigonal prism all of them do + +the same thing. + +They come out of one corner and +out of the opposite edge. + +Each of these has one pair +of objects hanging on it. + +And that is true of +all three of them. + +And if you like, this end of +the mirror plane here is + +nothing more than one that's +related to the first one by + +one of the rotations of the +threefold axis extended back + +in the opposite direction. + +So the mirror plane doesn't +just work up here. + +It works down here as well. + +It works all through +the space. + +So any way you want to look at +it and whatever terms work for + +you, each of these mirror planes +is the same, but they + +have a different type +of end to them. + +There's something different +hanging at one end than + +at the other end. + +Think of it in terms of actual +physical object. + +AUDIENCE: [? What about the ?] +case of the fourfold + +[? there? ?] + +PROFESSOR: In the fourfold, +one comes out of the face. + +One comes out at the edge. + +The motifs are oriented and +spaced at a different distance + +from each of those neighboring +mirror planes. + +So these two are different. + +The fourfold axis never +rotates this + +one into this one. + +These two are not different +because the threefold axis + +rotates, if you do it twice, +this end into this end of what + +is one in the same mirror plane +as what's down on here. + +So what's confusing you I +think is that there's a + +polarity to the mirror planes. + +Both ends of the mirror planes +do not have the same + +disposition of motifs on them, +but there's nothing that says + +that this has to be the case. + +The motifs could just +be at one end. + +And that, if you think about +it a little bit if it help, + +figure out-- + +not on company time though, but +on your own time-- what a + +fivefold axis does. + +And a fivefold axis is a non +crystallographic symmetry. + +But it turns out that C5v, which +is a 5 with an m, has + +only one kind of mirror plane in +it as well and for exactly + +the same reason. + +A regular figure that has the +symmetry is a pentagon. + +A mirror plane comes out +a corner and out of + +the opposite face. + +And that's true for all of the +mirror planes that are in + +there and separated by +one half of 2 pi/5. + +AUDIENCE: That's just whether or +not the [INAUDIBLE] axis is + +[INAUDIBLE]? + +PROFESSOR: Yeah. + +That's what I said. + +Yeah. + +So before I go through all +of the rotation axes with + +vertical mirror planes, the +international notation would + +be 2mm, 3m, 4mm, 5m, +and 6mm, 7m. + +For the odd symmetries, there's +only one kind of + +mirror plane in a pattern, +in the tile, or + +whatever you want to have. + +So there are 10 distinct +possibilities, and these are + +called the Point Groups. + +Why? + +Because they are clusters of +symmetry elements about at + +least one point that's +fixed and embedded + +immovably in space. + +They're called groups because, +as we've seen for one simple + +example, the collection of +operations follows the + +postulates for the set of +elements which we have defined + +as a group. + +More specifically, we could +call these the 10 + +two-dimensional crystallographic +graphic Point + +Groups, which is more +of a mouthful. + +But it emphasizes the fact +that there are lots of + +two-dimensional Point Groups, +but the two-dimensional + +crystallographic Point Groups +are those that involve + +rotational symmetry that are +compatible with a lattice. + +Hence, they are +crystallographic. + +But the number of Point Groups +is actually infinite if you + +include the ones that are not +compatible with translation. + +All right. + +I think that's probably +a good place to quit. + +And guess what? + +My internal clock has told +me that this is the + +time for our break. + +This is one crossroads +in our development. + +And what we'll do next for the +faint hearted who may not want + +to have more of this stuff for +one day than what we've just + +done, we're now going to do +the final penultimate + +combination, and say we have +also shown that there are 5 + +two-dimensional lattices. + +And the final step will be to +say if we have a pattern that + +has symmetry and is based on +translation, we can obtain + +these by taking each of the 10 +crystallographic Point Groups + +in turn and dropping them into +each of the five lattices that + +can accommodate them. + +We would not try, for example, +to take a Point Group like 4mm + +and try to drop it into +the hexagonal lattice. + +It's not going to fit. + +But there will be two, maybe +three ways in which we can add + +a given Point Group to one +of these lattice types. + +And what we've done when +we finished is we have + +exhaustively derived the +symmetries' translational + +lattices and symmetry operations +of reflection and + +rotation that are possible for +two-dimensional crystal. + +You might say, well +two-dimensional crystal, I've + +heard that people who do thin +film work to make monolayers + +and really make a +two-dimensional crystal. + +That's not something you could +say only a few years ago. + +But why do we worry about +two-dimensional symmetries if + +we're not to be wallpaper +designers? + +Well, actually, I'll give +you one example. + +One of the difficulties you had +in conveying the nature of + +a crystal structure is taking +something that's fairly + +complicated in three dimensions +and getting it onto + +a two-dimensional +sheet of paper. + +And what you invariably do is +you project the contents of + +the unit cell down along +one of the cell edges. + +And what you have then is a +two-dimensional crystal + +structure with a lattice +and symmetry. + +So you'll see two-dimensional +representations of + +translationally periodic +arrangements of atoms quite + +frequently when you look at +projections of actual crystal + +structures, which is the only +reasonable way to convey the + +information of any structure +once you get on beyond the + +baby stuff of sodium chlorides, +zinc, sulfide and + +body-centered iron. + +OK. + +I'm going to pause, +suck in air. + +I am happy to turn you loose for +10 minutes and will meet + +here again, let's say, +at 10 after 3:00. \ No newline at end of file diff --git a/cm0io4R0tOM.txt b/cm0io4R0tOM.txt new file mode 100644 index 0000000000000000000000000000000000000000..1164189feaaa7709ac1204df9d4a773609ee3552 --- /dev/null +++ b/cm0io4R0tOM.txt @@ -0,0 +1,1616 @@ +FEMALE VOICE: The following +content is provided under a + +Creative Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation, or to view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Hi. + +Our lecture today concerns +mathematical induction, which, + +roughly speaking, is a technique +that one uses to + +prove something when one already +has a pretty good + +suspicion as to what the +right answer is. + +Now, rather than to philosophize +about this too + +long, let's tear right into a +problem and see, in action, + +just what the concept means. + +Recall that, in an earlier +lecture, we have proven that + +the limit of a sum is equal +to the sum of the limits + +provided, of course, that +there are only two + +terms in the sum. + +That is, if we have two +functions, 'f 1' and 'f 2', + +the limit of 'f1 of x' plus 'f2 +of x' as 'x' approaches + +'a' is the limit of 'f1 of x' as +'x' approaches 'a' plus the + +limit of 'f2 of x' as +'x' approaches 'a'. + +The question, now, is how +about the limit of 'x' + +approaches 'a' of 'f1 +of x', plus 'f2 of + +x', plus 'f3 of x'? + +Now, to tackle a problem like +this, we do what is so often + +done in any mathematical +logical procedure. + +We try to reduce an unfamiliar +problem to a familiar problem + +which has already been solved. + +Let's see what I mean by that. + +If this had been only two +terms in here that we're + +adding, we would have known how +to handle this problem. + +So what we observe is that since +the sum of two functions + +is, again, a function, we can +assume that our expression is + +written this way. + +Now, you see, we've reduced our +problem to the sum of two + +functions, namely, 'f1 of x' +plus 'f2 of x' being one of + +our functions, 'f3 of x' being +another of our functions. + +We know, now, what? + +That the limit of a sum is +the sum of the limits. + +If we have two functions, +you see this is, what? + +The limit 'f1 of x' plus 'f2 of +x', you see, plus the limit + +as 'x' approaches +'a', 'f3 of x'. + +But now, look what's in this +expression over here. + +This is now, what? + +The limit of the sum +of two functions. + +And, you see, we know that the +limit of a sum is the sum of + +the limits is true if we have +only two functions, so, from + +here, we get to here. + +And, from here, we +can say, what? + +This is the limit 'x' approaches +'a', 'f1 of x', + +plus the limit as 'x' approaches +'a', 'f2 of x', + +plus the limit as 'x' approaches +'a', 'f3 of x'. + +In other words, what we have +shown is that the limit of a + +sum equals the sum of the limits +is true not just the + +sum of two functions, but for +the sum of 3 as well. + +And, more importantly, the truth +for 3 hinged directly on + +the truth for 2. + +In other words, it wasn't just +that we proved that the + +formula was true for the sum of +three functions, we proved + +it on the assumption that it was +already true for the sum + +of two functions. + +And, by the way, notice how we +may now begin to suspect that + +this idea generalizes. + +For example, let's take +a look over here. + +Suppose I now said how +about the limit as + +'x' approaches 'a'? + +And we'll now take the sum of +four functions: 'f1 of x', + +plus 'f2 of x', plus 'f3 +of x', plus 'f4 of x'. + +See, what about something +like that? + +And, again, we argue the same +way as we did before. + +We say, you know, if +we had only had two + +functions in here-- + +and this gives us the +hint to do this-- + +see, we do know that the limit +of the sum is the sum of the + +limits if we have only +two functions. + +You see, now, I could +write this as, what? + +It's the limit of the first one, +as 'x' approaches 'a', + +but what is the first one? + +The first one is the function +'f1 of x', plus 'f2 of x', + +plus 'f3 of x', plus the +limit of the second. + +The second now you see, is +'f sub four of x' as 'x' + +approaches 'a'. + +Now, you see our previous +case told us, what? + +That the limit of a sum is equal +to the sum of the limits + +if you have the sum of +three functions. + +That's exactly what we have over +here, and now you see we + +can say, what? + +Ah, this is the limit of the +first as 'x' approaches 'a', + +plus the limit of the second +as 'x' approaches 'a', plus + +the limit of the third as 'x' +approaches 'a', plus the limit + +the fourth as 'x' +approaches 'a'. + +In other words, what +have we done now? + +We've shown that knowing that +the limit of a sum is the sum + +of the limits was true for a +sum of two functions and of + +three functions. + +We've shown, inescapably, that +the same result holds for the + +sum of four functions. + +Let's take a little breather +here and make a few asides. + +I think, sometimes, when one +starts to work too much with + +mathematical symbolism, we lose +track of the fact that + +things are not quite as +difficult as they might + +otherwise have seemed. + +You see, for one thing, my claim +is that we have already + +tackled this problem as recently +as first grade + +arithmetic. + +Namely, we learned, what? + +We learned tables. + +Remember the addition tables? + +You learned how to +add two numbers. + +All of a sudden somebody +says what is the sum of + +1, 2, 3, and 4? + +What is this number? + +And what we said was, look +at, we'll just add + +these two at a time. + +1 plus 2 is a number, +which is 3. + +3 plus 3 is a number, +namely 6. + +And 6 plus 4 is a number: 10. + +In other words, we essentially +did, what? + +We added the first +to the second. + +Then we added the sum of the +first two to the third, the + +sum of the first three to +the fourth, and that + +was how we did this. + +Of course, what we assumed in +doing this was that the sum of + +two numbers was, again, +a number. + +Up above, we assumed +that the sum of two + +functions was a function. + +And this is not quite as trivial +as it might otherwise + +have seemed. + +Namely, look at, if you add two +odd numbers, do you get + +like things when you combine +like things? + +The sum of two odd numbers +is always even. + +You see, you can't say let's +replace the sum of two odd + +numbers by another odd number. + +You can say it, but +it would be wrong. + +On the other hand, +another example. + +How about subtraction? + +That's a nice operation. + +If you subtract a positive +number from a positive number, + +are you guaranteed that the +result will be positive? + +Well, for example, what +about 3 less 5? + +The answer would +be negative 2. + +Positive minus positive can very +well be negative, so we + +must be sure, what? + +That, when we combine like +objects, we get like objects. + +And another thing that we +assumed was that our answer + +did not depend upon +voice inflection. + +Now, what does that mean? + +Let me show you something +over here. + +Look at the expression 12 +divided by 6 divided by 2. + +If you read this as if it said +12 divided by 6 divided by 2, + +the answer is 1. + +On the other hand, if you read +the same thing as if it said + +12 divided by 6 divided by +2, the answer is, what? + +12 divided by 3, which is 4. + +In other words, division depends +on voice inflection, + +whereas, addition doesn't. + +And I simply point out these +asides to show you that, as we + +go through advanced mathematical +analysis, we are + +always making use of the same +assumptions that we were + +making when we dealt with +more simple things. + +And I think this is the +healthiest way of seeing how + +our subject develops. + +We will leap from things that +we already know into + +generalizations that are +less familiar to us. + +At any rate, let's now return +to our main theme of + +mathematical induction +and try to summarize + +what's happened so far. + +We are working with a certain +conjecture, let's call it. + +The conjecture is that the limit +of the sum is the sum of + +the limits. + +We know that the conjecture +was true for two terms. + +We proved that, once it was +true for two terms, it was + +true for three terms. + +We then prove that, if it was +true for three terms, it was + +true for four terms. + +And now, if we have any +imagination at all, we might + +become suspicious and say, you +know, I think, if it's true, + +in general, for 'n' terms, +it's going to be + +true for 'n + 1' terms. + +And that brings us to our next +stage in our mathematical + +induction, namely, suppose the +limit of the sum is equal to + +the sum of the limits in the +case that there are 'n' terms + +in our sum. + +What can we conclude about the +limit of a sum in the case of + +'n + 1' terms? + +And, without going through the +proof here, we'll do these + +things in our supplementary +notes in our learning + +exercises, but, here, I just +want to focus our attention on + +what the main theme is. + +What we say is, since we can +add without worrying about + +voice inflection, why don't we +throw in a pair of braces + +here, thus reducing our problem +to the limit of a sum + +when we're adding but +two functions, + +use the theorem there. + +And, now, given the limit of the +sum of 'n' functions, we + +know that that's the +limit of a sum. + +And now, it appears that the +truth for 'n' is going to + +imply the truth for 'n + 1'. + +Now, of course, there may be +other problems that work + +structurally this way other than +the limit of a sum equals + +the sum of the limits. + +So let's generalize +that result. + +And the generalization +is what is known as + +mathematical induction. + +What mathematical induction says +is this, let's suppose we + +have a conjecture. + +Now, how we get the conjecture +is something we'll talk about + +in a while, but let's suppose +we have the conjecture. + +Well, to try to show that the +conjecture is true all the + +time, we had better be sure it's +true at least sometimes. + +So we say, OK, let's show that +the conjecture is true + +for 'n' equals 1. + +That's just a simple +verification. + +We show that it's true +for 'n' equals 1. + +Then we say OK, next, prove that +the truth for 'n' equals + +'k' implies the truth for +'n' equals 'k + 1'. + +In other words, we're not saying +that it's true for 'k', + +all we're saying is that, if +it's true for 'k', if it's + +true for 'k', the truth for +'n' equals 'k' implies the + +truth for 'n' equals 'k + 1'. + +Then, if that's true, our +conjecture is true for all + +whole numbers. + +Why is that? + +Well, let's take a look, +informally, here. + +Let's suppose that both of these +conditions are obeyed. + +We know the conjecture is +true when 'n' equals 1. + +Now, take 'k' to be 1. + +Since it's true for 1, this part +tells us it's going to be + +true for one more than +1, which is 2. + +Now that the conjecture is true +for 2, this says, what? + +It's going to be true for 3. + +And knowing that it's true +for 3, this will say + +it's true for 4. + +And now I'll loosely use the +word et cetera, and come back + +and reinforce that +as we go along. + +I think now, perhaps, the best +thing to do is to look at a + +second example. + +You see, what we did first of +all was we used an example to + +lead in to what the definition +would be. + +Now that we have the definition, +let's proceed + +directly to use it. + +Let me give you a conjecture. + +The conjecture which I have in +mind is that the sum of the + +first n positive numbers-- + +and this is an interesting +formula-- + +it's the last number multiplied +by one more than + +the last number divided by 2. + +Well, let's just see if that's +true at all for a while. + +Look at, if 'n' is 1, the +left-hand side here is 1. + +And 1 times 2 divided +by 2 is also 1. + +If 'n' is 2, the sum +of the first two + +numbers here is, what? + +One plus 2 is three. + +On the other hand, 2 times +3 divided by 2 is also 3. + +So, at least, our conjecture is +true for 'n' equals 1 and + +'n' equals 2. + +What does mathematical +induction say? + +Let's take a look again, now. + +You see, we showed that the +conjecture was true + +for 'n' equals 1. + +And, for good measure, we also +showed that it was true for + +'n' equals 2. + +So, we can check this off. + +We've done that. + +Now, what do we do? + +We assume the conjecture is +true for 'n' equals 'k'. + +That means, what? + +Well, just replace 'n' by 'k'. + +We're assuming that +this is true. + +From the truth of this, +what must we do next? + +Well, what we must do next is +investigate what happens if + +you add, what? + +Not 'k' numbers, but 'k + 1'. + +So, in other words, what happens +when you replace 'n' + +by 'k + 1'? + +Now, watch how we do this. + +The same thing that we did in +theory before, we say, look + +at, we already know how +to handle this amount. + +We're told that that's going to +be ''k' times 'k + 1' over + +2', so let's rewrite +this in this way. + +Now, we can replace the +bracketed expression by ''k' + +times 'k + 1' over 2'. + +We add on, of course, 'k + 1' +because that's the last term + +that's over here. + +Now, we factor out 'k + 1' +from this factor here. + +That leaves us with, what? + +'k/2 + 1'. + +And this, in turn, says, what? + +That the sum of the first 'k + +1' numbers is ''k + 1' times + +'k + 2' over 2'. + +And notice that that's exactly +what the conjecture should say + +when 'n' equals 'k + +1', namely, what? + +The sum of the first 'n' +numbers, no matter how many + +you have, is, what? + +The last number times one +more than the last + +number divided by 2. + +The sum of the first 'k ++ 1' numbers is, what? + +It's 'k + 1', the last one, +times 'k + 2', which is one + +more than the last one, +divided by 2. + +And now, what we've done is we +have verified the second part + +of our mathematical induction +setup, namely, if we go back + +to our basic definition over +here, we have to show, what? + +Prove that the truth for 'n' +equals 'k' implies the truth + +for 'n' equals 'k + 1', which +is exactly what we did. + +And, while you're thinking about +that, let's take a break + +for a few more asides which, I +think, may cement down this + +idea a little bit +more strongly. + +I mentioned before that +induction is something that + +one uses when one already has +a suspicion as to what the + +right answer is. + +I don't know how this grabs +you, buy my own particular + +feeling is that you do not look +at the sum of the first + +'n' numbers and say aha, it's +the last one times one more + +than the last one +divided by 2. + +You see, that's the nice thing +about textbook problems. + +When they give you a problem +on induction and they say + +prove this conjecture, notice +that they've already given you + +a tremendous hint, namely, +they've told you what the + +conjecture is. + +You see, in the textbook of real +life, one usually has to + +find out what the conjecture +is for oneself. + +In fact, in the form of a rather +interesting aside, + +there is a very interesting +mathematical anecdote + +connected with this particular +problem. + +It's an anecdote attributed to +the mathematician, Gauss, who, + +when he was a young chap, was a + +discipline problem in school. + +And the story is that his +teacher, as a punishment, + +asked him to add the +first 100 numbers. + +And Gauss wrote down the answer +very, very rapidly. + +And what he did was, he didn't +add these all up. + +What he observed was, what? + +The first one plus the last +one added up to 101. + +The second plus the next +to the last added + +up to 101, you see? + +And each pair going in this +way added up to 101. + +And how many pairs were +there, all together? + +Well, there were 100 numbers, +so there were 50 pairs. + +In other words, there +were, what? + +100 divided by 2 pairs, each +pair adding up to 101. + +And now, notice the recipe: 100, +namely the last number, + +times one more than the last +number, 101, divided by 2. + +By the way, in the exercises +on this assignment we have + +another problem, and that is, +if you think this one was + +already cumbersome, try guessing +what the recipe for + +this one is: what is the sum +of the first n squares? + +In other words, not 1, plus 2, +plus 3, et cetera, but 1 + +squared, plus 2 squared, plus +3 squared, et cetera. + +I give you the answer, but try +to think for a while as to how + +likely it is that you would have +conjectured this in the + +first place. + +It turns out to be ''n' +times 'n + 1' times + +'2 n + 1' over 6'. + +You see, the reason I bring this +out is that I call this a + +contrived example. + +It is not the case where the +mathematician would most + +likely have invented +mathematical induction. + +The case where he would have +invented mathematical + +induction is the case that we +did earlier, for example, + +where we talk about the +limit of a sum being + +the sum of the limits. + +You can actually see what's +happening, how the truth that + +'k' implies the truth +for 'k + 1'. + +And by the way, let me make +one more aside here that I + +forgot to mention earlier. + +In our definition of +mathematical induction, we + +said show the conjecture is +true for 'n' equals 1. + +This was quite hypocritical +because the very first example + +that I picked didn't even +start until 'n' was 2. + +We talked about the limit of +a sum being the sum of the + +limits, and the smallest +sum we talked about was + +the sum of two terms. + +The point that I wanted to +mention is, for example, + +suppose that the first number +you can prove the conjecture + +for is, for example, +'n' equals 7. + +I don't know why I picked 7. + +I had to pick something. + +Let's just call it +'n' equals 7. + +Suppose I can also show that, if +the conjecture is true for + +'k', it's true for 'k + 1'. + +Then, you see, what I can +conclude is I can conclude + +that it's true for 'n' greater +than or equal to 7. + +Namely, if it's true for 7, this +says it will be true for + +one more than 7, which is 8. + +If it's true for 8, this says +it will be true for 9. + +If it's true for 9, this +says it will be + +true for 10, et cetera. + +And we go on this way. + +Now, again, this may be a very +naive way of looking at it, + +but I always look at +mathematical induction as a + +bunch of toy soldiers stacked +up in a line in such a way + +that, if any one of the toy +soldiers falls down, he knocks + +down the one that's immediately +behind him, OK? + +You see what I'm driving +at here? + +If the first falls-- and, by +the way, that's a big if-- + +if the first falls, he knocks +down the second. + +The second falling knocks +down the third. + +The third falling knocks +down the fourth. + +The fourth falling down knocks +down the fifth, et cetera. + +Notice that, if the first +one doesn't fall, + +none of them fall. + +Or, for that matter, going back +to my previous analogy, + +if the seventh one is the first +one that falls, all the + +ones behind him fall down. + +Now, be very careful. + +Mathematical induction doesn't +say the first 50 fall down, or + +the first 100 fall down, +it says they all + +have to fall down. + +For example, here's a case where +several fall down, but, + +all of a sudden, one isn't +knocked down by the one in + +front of him. + +In other words, what +mathematical induction really + +involves is the idea not just +that something is true, but + +that it's true because the +previous one was true. + +You see, for example, is it +possible that all of the + +soldiers fall down even though +the one in front didn't knock + +the other guy down? + +I mean, it's possible all of +these go down, but for + +different reasons. + +Mathematical induction says +much more than that. + +Mathematical induction says +yes, they all go down, but + +each goes down because +of the one before. + +And, by the way, one +more little aside. + +Notice that, in our analog, +we assumed that + +there was a next one. + +You say, well, what do +you mean you assume + +there was a next one? + +Obviously, there has +to be a next one. + +But, the concept of next depends +on whole numbers. + +For example, when you +deal with fractions, + +there is no next one. + +Let me show you what +I mean by that. + +Let's talk about the real +numbers in general. + +On the number line, here's 0. + +What is the first fraction, +the first real number? + +I don't care what you call it. + +What is the first number which +is greater than 0? + +What is the first number which +is greater than 0? + +And the answer is, there +is none because + +whichever one you pick-- + +call it 'r'. + +Let 'r' stand for the first +number which you think is + +bigger than 0, OK? + +How about 'r/2'? + +'r/2' is still bigger than 0, +but 'r/2' is less than 'r'. + +In other words, given any number +you pick that's bigger + +than 0, you can fit +in another one. + +So, there is no number which +is immediately next to 0. + +In other words, as a caution, +notice that mathematical + +induction is used when +we're dealing with a + +whole number of objects. + +Now, let's emphasize some of +these little asides from a + +more specific point of view. + +Let me, first of all, give you +an example in which something + +is true for a whole bunch of +numbers, but, all of a sudden, + +isn't true in general. + +Now, how anybody ever stumbled +across the example I'm going + +to give you next, I have no +idea, but I find it's a very + +interesting concept. + +Let's look at this. + +Let's write down the following +function: 'p' of 'n', where + +'n' is any positive whole +number, will be defined to be + +'n' squared, minus +'n', plus 41. + +For example, 'p' of 1 will be +1 squared, minus 1, plus 41, + +which happens to be 41. + +41 happens to be a prime number: +a number which has no + +factors other than +itself and 1. + +Let's try 2 in here. + +2 squared, minus 2, plus 41, +is 43: also a prime number. + +Let's try 3 in here. + +3 squared is 9, minus 3 +is 6, plus 41 is 47: + +also a prime number. + +The amazing thing is that, as +you go all the way through to + +40, you get nothing +but prime numbers. + +And you say, ah, it's right +so far, it must be + +right all the time. + +And this is wishful thinking. + +This is like the man who wants +to count the deck of cards to + +see if the cards are all there, +and he says one, two, + +three, four, five. + +Well, so far, so good. + +They must all be here. + +It's like falling off the Empire +State building, and + +halfway down, somebody says, +"How you doing?" You say, "So + +far, so good." No, we're in a +little bit of trouble here + +because, as soon as we pick +'n' to be 41, watch what + +happens here. + +This becomes 41 squared, +minus 41, plus 41. + +And this is 41 squared, which, +obviously, is not a prime. + +It's 41 times 41. + +And here is an interesting +example where a certain + +formula generates nothing but +primes for the first 40 + +integers, but fails on +the 41st integer. + +Why did this happen? + +Because, evidently, the fact +that this was a prime in no + +way depended structurally +on the fact that + +this one was a prime. + +There is our mathematical +induction again, that not only + +must the conjecture be true, but +it must follow inescapably + +from the case before. + +If you'd like a more +fascinating, realistic + +example, it's something that +we call the unique + +factorization theorem of +elementary number theory. + +This says that every positive +whole number greater than one + +can be factored uniquely into a +product of primes, unique up + +to the order in which +you write them. + +For example, 2 is already +a prime, it's 2. + +3 is already a prime: 3. + +4 can be factored +as 2 times 2. + +5 can be factored as-- + +well, it's already +a prime, it's 5. + +6 can be written as, what? + +2 times 3. + +7 can be written, +of course, as 7. + +It's already a prime. + +8 is 2 times 2 times 2. + +9 is 3 times 3. + +10 is 2 times 5, and 11 +is already a prime. + +Well, this doesn't +prove anything. + +I'm just trying to demonstrate +what the theorem says. + +The interesting thing is do you + +notice how 'n + 1' factors-- + +I don't know what phrase to use +here, but let's call it + +considerably different +than 'n'. + +In other words, look at what +happened to 10 when I + +added 1 onto it. + +It factored into 2 times 5. + +I add 1 onto it, and, all of +a sudden, the factorization + +properties change. + +Let me give you an example. + +Look at 59. + +59 happens to be a prime. + +Look at 61. + +61 also happens to be a prime. + +By the way, for those of you are +number theory buffs, these + +are called twin primes. + +Consecutive odd numbers, which +are both prime, are called + +twin primes. + +By the way, 2 is the only even +prime, of course, because, if + +a number is greater than +2, and it's even, it's + +divisible by 2. + +So, 2 is the only even prime. + +Twin primes are, what? + +Consecutive odd numbers both +of which are primes. + +So, 59 and 61 are a pair +of twin primes. + +One might intuitively suspect, +therefore, that the number + +between them must be sort +of a prime too, or + +whatever that means. + +Obviously, it can't be a prime +because in between them comes + +60, which is, in particular, +an even number. + +But look at all the nice +factors that sixty has. + +60 is, what? + +It's one more than 59, one less +than 61, but look at how + +different it factors. + +In fact, a pseudo induction-type +thing is look + +at the factors of 60: +1, 2, 3, 4, 5, 6. + +We say, what? + +7, experimental error? + +No, no. + +But, this is not induction, +by the way. + +The fact that 1, 2, 3, 4, 5, +and 6 are all factors of 60 + +does not mean that 7 is going +to be a factor of 60. + +We do not say just because it +works so far, it's going to + +keep working. + +And I'm not going to belabor +this point anymore. + +Suffice it to say that look at +how differently 60 factors + +compare to the number the came +just before it and the number + +that came just after it. + +In other words, assuming that +the unique factorization + +theorem is true, the truth for +'n + 1', somehow or other, has + +nothing to do with the +truth for 'n'. + +And you see this is, again, +another weakness of, what's + +called, induction. + +Well, so, that's a weakness +of induction. + +The point that I'm making is why +shouldn't induction have + +some weaknesses? + +After all, if it could solve +every problem, what we would + +do is have a calculus book that +was three pages long. + +It would be called, +The Principle of + +Mathematical Induction. + +When we solved that problem by +induction, everything else + +would be done. + +No, there are problems +that do not lend + +themselves to induction. + +In summary, induction is a +particularly effective + +technique which one uses to +prove that something is true + +for all whole numbers provided +that one has a suspicion that + +this thing is true in +the first place. + +And secondly that, even if the +suspicion is true, the truth + +for the 'n' plus first case +follows inescapably from the + +truth for the n-th case. + +At any rate, this completes +our lecture for today. + +And, until next time, +good bye. + +MALE VOICE: Funding for the +publication of this video was + +provided by the Gabriella and +Paul Rosenbaum Foundation. + +Help OCW continue to provide +free and open access to MIT + +courses by making a donation +at ocw.mit.edu/donate. \ No newline at end of file diff --git a/cnF_eoMHbmQ.txt b/cnF_eoMHbmQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..610a13184fab84a5a505fab8d897efa1828d632b --- /dev/null +++ b/cnF_eoMHbmQ.txt @@ -0,0 +1,1779 @@ +align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +this week we're going to take a look at + + align:start position:0% +this week we're going to take a look at + + + align:start position:0% +this week we're going to take a look at +exactly what you do with the photographs + + align:start position:0% +exactly what you do with the photographs + + + align:start position:0% +exactly what you do with the photographs +after you've made them and once again + + align:start position:0% +after you've made them and once again + + + align:start position:0% +after you've made them and once again +frankly we could devote a full six- week + + align:start position:0% +frankly we could devote a full six- week + + + align:start position:0% +frankly we could devote a full six- week +course to just this idea alone + + align:start position:0% +course to just this idea alone + + + align:start position:0% +course to just this idea alone +presenting your work but we'll try to + + align:start position:0% +presenting your work but we'll try to + + + align:start position:0% +presenting your work but we'll try to +cover this topic as best as we can in + + align:start position:0% +cover this topic as best as we can in + + + align:start position:0% +cover this topic as best as we can in +just a couple of tutorials for you this + + align:start position:0% +just a couple of tutorials for you this + + + align:start position:0% +just a couple of tutorials for you this +week so let's start with a few figures + + align:start position:0% +week so let's start with a few figures + + + align:start position:0% +week so let's start with a few figures +just to dissect them and get you to + + align:start position:0% +just to dissect them and get you to + + + align:start position:0% +just to dissect them and get you to +think more about how you create figures + + align:start position:0% +think more about how you create figures + + + align:start position:0% +think more about how you create figures +with your image + + align:start position:0% +with your image + + + align:start position:0% +with your image +let's first take a look at a figure that + + align:start position:0% +let's first take a look at a figure that + + + align:start position:0% +let's first take a look at a figure that +the researchers made for a grand + + align:start position:0% +the researchers made for a grand + + + align:start position:0% +the researchers made for a grand +submission and here we see a host of the + + align:start position:0% +submission and here we see a host of the + + + align:start position:0% +submission and here we see a host of the +pieces of devices and the full devices + + align:start position:0% +pieces of devices and the full devices + + + align:start position:0% +pieces of devices and the full devices +all labeled they wanted to show what + + align:start position:0% +all labeled they wanted to show what + + + align:start position:0% +all labeled they wanted to show what +they were capable of creating of course + + align:start position:0% +they were capable of creating of course + + + align:start position:0% +they were capable of creating of course +which is quite important but there's so + + align:start position:0% +which is quite important but there's so + + + align:start position:0% +which is quite important but there's so +much going on the question is whether we + + align:start position:0% +much going on the question is whether we + + + align:start position:0% +much going on the question is whether we +want to bother looking anywhere by the + + align:start position:0% +want to bother looking anywhere by the + + + align:start position:0% +want to bother looking anywhere by the +way just a note I didn't make any of + + align:start position:0% +way just a note I didn't make any of + + + align:start position:0% +way just a note I didn't make any of +these images of the research but I knew + + align:start position:0% +these images of the research but I knew + + + align:start position:0% +these images of the research but I knew +that a few of the original images were + + align:start position:0% +that a few of the original images were + + + align:start position:0% +that a few of the original images were +in color so first of all why not use the + + align:start position:0% +in color so first of all why not use the + + + align:start position:0% +in color so first of all why not use the +color additions if you have them now + + align:start position:0% +color additions if you have them now + + + align:start position:0% +color additions if you have them now +let's concentrate on the composition of + + align:start position:0% +let's concentrate on the composition of + + + align:start position:0% +let's concentrate on the composition of +the figure why not somehow find a way + + align:start position:0% +the figure why not somehow find a way + + + align:start position:0% +the figure why not somehow find a way +that makes some sort of compositional + + align:start position:0% +that makes some sort of compositional + + + align:start position:0% +that makes some sort of compositional +sense so here we reordered all of these + + align:start position:0% +sense so here we reordered all of these + + + align:start position:0% +sense so here we reordered all of these +devices according to scale so we're + + align:start position:0% +devices according to scale so we're + + + align:start position:0% +devices according to scale so we're +giving the readers some idea of how to + + align:start position:0% +giving the readers some idea of how to + + + align:start position:0% +giving the readers some idea of how to +look at this very busy figure in + + align:start position:0% +look at this very busy figure in + + + align:start position:0% +look at this very busy figure in +addition we removed most of the labeling + + align:start position:0% +addition we removed most of the labeling + + + align:start position:0% +addition we removed most of the labeling +and we created a key to the images and + + align:start position:0% +and we created a key to the images and + + + align:start position:0% +and we created a key to the images and +that key would be labeled with letters + + align:start position:0% +that key would be labeled with letters + + + align:start position:0% +that key would be labeled with letters +so that if you wanted more information + + align:start position:0% +so that if you wanted more information + + + align:start position:0% +so that if you wanted more information +about this particular image within the + + align:start position:0% +about this particular image within the + + + align:start position:0% +about this particular image within the +figure for example its scale like this + + align:start position:0% +figure for example its scale like this + + + align:start position:0% +figure for example its scale like this +one you would then find that letter in + + align:start position:0% +one you would then find that letter in + + + align:start position:0% +one you would then find that letter in +the caption and get more information so + + align:start position:0% +the caption and get more information so + + + align:start position:0% +the caption and get more information so +you might not agree I hope you do but if + + align:start position:0% +you might not agree I hope you do but if + + + align:start position:0% +you might not agree I hope you do but if +you look at them side by side I hope you + + align:start position:0% +you look at them side by side I hope you + + + align:start position:0% +you look at them side by side I hope you +see that once again by simplifying + + align:start position:0% +see that once again by simplifying + + + align:start position:0% +see that once again by simplifying +editing down your figures to the + + align:start position:0% +editing down your figures to the + + + align:start position:0% +editing down your figures to the +essential piece pieces and organize them + + align:start position:0% +essential piece pieces and organize them + + + align:start position:0% +essential piece pieces and organize them +to tell your story that the reader and + + align:start position:0% +to tell your story that the reader and + + + align:start position:0% +to tell your story that the reader and +in this case the grand reviewer enjoys + + align:start position:0% +in this case the grand reviewer enjoys + + + align:start position:0% +in this case the grand reviewer enjoys +looking at your figure and understands + + align:start position:0% +looking at your figure and understands + + + align:start position:0% +looking at your figure and understands +the contents of your figure if you're + + align:start position:0% +the contents of your figure if you're + + + align:start position:0% +the contents of your figure if you're +using up space in your article your + + align:start position:0% +using up space in your article your + + + align:start position:0% +using up space in your article your +presentation or your Grant submission + + align:start position:0% +presentation or your Grant submission + + + align:start position:0% +presentation or your Grant submission +why not use that space so that the + + align:start position:0% +why not use that space so that the + + + align:start position:0% +why not use that space so that the +viewers actually want to look in this + + align:start position:0% +viewers actually want to look in this + + + align:start position:0% +viewers actually want to look in this +example you are seeing two photographs + + align:start position:0% +example you are seeing two photographs + + + align:start position:0% +example you are seeing two photographs +that I made quite a while ago depicting + + align:start position:0% +that I made quite a while ago depicting + + + align:start position:0% +that I made quite a while ago depicting +two ends of a long device the device was + + align:start position:0% +two ends of a long device the device was + + + align:start position:0% +two ends of a long device the device was +too long to get into one frame so the + + align:start position:0% +too long to get into one frame so the + + + align:start position:0% +too long to get into one frame so the +researchers used these two photographs + + align:start position:0% +researchers used these two photographs + + + align:start position:0% +researchers used these two photographs +in one figure the left and the right + + align:start position:0% +in one figure the left and the right + + + align:start position:0% +in one figure the left and the right +side of the device are combined + + align:start position:0% +side of the device are combined + + + align:start position:0% +side of the device are combined +indicating that it's much longer as you + + align:start position:0% +indicating that it's much longer as you + + + align:start position:0% +indicating that it's much longer as you +can see with this notation and we see + + align:start position:0% +can see with this notation and we see + + + align:start position:0% +can see with this notation and we see +all sorts of labels and arrows and sem + + align:start position:0% +all sorts of labels and arrows and sem + + + align:start position:0% +all sorts of labels and arrows and sem +inserts what I suggested first from the + + align:start position:0% +inserts what I suggested first from the + + + align:start position:0% +inserts what I suggested first from the +very beginning is please give us a + + align:start position:0% +very beginning is please give us a + + + align:start position:0% +very beginning is please give us a +little more space to breathe so many + + align:start position:0% +little more space to breathe so many + + + align:start position:0% +little more space to breathe so many +figures are packed so tightly with stuff + + align:start position:0% +figures are packed so tightly with stuff + + + align:start position:0% +figures are packed so tightly with stuff +and we actually don't know how to even + + align:start position:0% +and we actually don't know how to even + + + align:start position:0% +and we actually don't know how to even +start looking at it so for example + + align:start position:0% +start looking at it so for example + + + align:start position:0% +start looking at it so for example +adding space around the perimeter is + + align:start position:0% +adding space around the perimeter is + + + align:start position:0% +adding space around the perimeter is +what I did here by inserting the whole + + align:start position:0% +what I did here by inserting the whole + + + align:start position:0% +what I did here by inserting the whole +figure into the area with a larger + + align:start position:0% +figure into the area with a larger + + + align:start position:0% +figure into the area with a larger +canvas size and then I questioned the + + align:start position:0% +canvas size and then I questioned the + + + align:start position:0% +canvas size and then I questioned the +labeling if you are labeling within an + + align:start position:0% +labeling if you are labeling within an + + + align:start position:0% +labeling if you are labeling within an +image it's imperative to simplifier + + align:start position:0% +image it's imperative to simplifier + + + align:start position:0% +image it's imperative to simplifier +labeling and clean it up and make it + + align:start position:0% +labeling and clean it up and make it + + + align:start position:0% +labeling and clean it up and make it +nice and neat and here's what I mean by + + align:start position:0% +nice and neat and here's what I mean by + + + align:start position:0% +nice and neat and here's what I mean by +that + + align:start position:0% +that + + + align:start position:0% +that +try to put all of your labels lined up + + align:start position:0% +try to put all of your labels lined up + + + align:start position:0% +try to put all of your labels lined up +as best as you can either vertically and + + align:start position:0% +as best as you can either vertically and + + + align:start position:0% +as best as you can either vertically and +or + + align:start position:0% +or + + + align:start position:0% +or +horizontally and next question whether + + align:start position:0% +horizontally and next question whether + + + align:start position:0% +horizontally and next question whether +you really have to use a combination of + + align:start position:0% +you really have to use a combination of + + + align:start position:0% +you really have to use a combination of +upper and lowercase letters why not make + + align:start position:0% +upper and lowercase letters why not make + + + align:start position:0% +upper and lowercase letters why not make +all of your labels + + align:start position:0% +all of your labels + + + align:start position:0% +all of your labels +lowercase get rid of your arrows arrows + + align:start position:0% +lowercase get rid of your arrows arrows + + + align:start position:0% +lowercase get rid of your arrows arrows +with arrow heads are completely + + align:start position:0% +with arrow heads are completely + + + align:start position:0% +with arrow heads are completely +unnecessary they are distractions as + + align:start position:0% +unnecessary they are distractions as + + + align:start position:0% +unnecessary they are distractions as +labels lines without the arrow heads are + + align:start position:0% +labels lines without the arrow heads are + + + align:start position:0% +labels lines without the arrow heads are +much better to use they're just more + + align:start position:0% +much better to use they're just more + + + align:start position:0% +much better to use they're just more +refined rethink your colors how about + + align:start position:0% +refined rethink your colors how about + + + align:start position:0% +refined rethink your colors how about +using blue instead of fuchsia + + align:start position:0% +using blue instead of fuchsia + + + align:start position:0% +using blue instead of fuchsia +please so I hope you agree that this is + + align:start position:0% +please so I hope you agree that this is + + + align:start position:0% +please so I hope you agree that this is +a cleaner way of labeling your figures + + align:start position:0% +a cleaner way of labeling your figures + + + align:start position:0% +a cleaner way of labeling your figures +and in the end I also questioned the + + align:start position:0% +and in the end I also questioned the + + + align:start position:0% +and in the end I also questioned the +need for the sem inserts I'm not sure we + + align:start position:0% +need for the sem inserts I'm not sure we + + + align:start position:0% +need for the sem inserts I'm not sure we +really see more information about the + + align:start position:0% +really see more information about the + + + align:start position:0% +really see more information about the +structure of the device with these + + align:start position:0% +structure of the device with these + + + align:start position:0% +structure of the device with these +additional sems the optical image says + + align:start position:0% +additional sems the optical image says + + + align:start position:0% +additional sems the optical image says +all that we want to say and so I would + + align:start position:0% +all that we want to say and so I would + + + align:start position:0% +all that we want to say and so I would +have deleted the sems but if you insist + + align:start position:0% +have deleted the sems but if you insist + + + align:start position:0% +have deleted the sems but if you insist +on including inserts maybe because you + + align:start position:0% +on including inserts maybe because you + + + align:start position:0% +on including inserts maybe because you +just wanted to show that you were + + align:start position:0% +just wanted to show that you were + + + align:start position:0% +just wanted to show that you were +capable of making them which is fine at + + align:start position:0% +capable of making them which is fine at + + + align:start position:0% +capable of making them which is fine at +the very least Orient the inserts in the + + align:start position:0% +the very least Orient the inserts in the + + + align:start position:0% +the very least Orient the inserts in the +way the rest of the optical image is + + align:start position:0% +way the rest of the optical image is + + + align:start position:0% +way the rest of the optical image is +oriented here we're rotating these sem + + align:start position:0% +oriented here we're rotating these sem + + + align:start position:0% +oriented here we're rotating these sem +inserts 90° to make them more relevant + + align:start position:0% +inserts 90° to make them more relevant + + + align:start position:0% +inserts 90° to make them more relevant +to the full image and now let's look at + + align:start position:0% +to the full image and now let's look at + + + align:start position:0% +to the full image and now let's look at +them sides side by side once again I + + align:start position:0% +them sides side by side once again I + + + align:start position:0% +them sides side by side once again I +hope that you agree that the redo is a + + align:start position:0% +hope that you agree that the redo is a + + + align:start position:0% +hope that you agree that the redo is a +much cleaner and simplified figure which + + align:start position:0% +much cleaner and simplified figure which + + + align:start position:0% +much cleaner and simplified figure which +makes it more + + align:start position:0% +makes it more + + + align:start position:0% +makes it more +accessible let's look at another figure + + align:start position:0% +accessible let's look at another figure + + + align:start position:0% +accessible let's look at another figure +this Photograph up here made by the + + align:start position:0% +this Photograph up here made by the + + + align:start position:0% +this Photograph up here made by the +researcher shows the device and here you + + align:start position:0% +researcher shows the device and here you + + + align:start position:0% +researcher shows the device and here you +see another point of view of that same + + align:start position:0% +see another point of view of that same + + + align:start position:0% +see another point of view of that same +device down here we have a cad drawing + + align:start position:0% +device down here we have a cad drawing + + + align:start position:0% +device down here we have a cad drawing +to represent an important part of the + + align:start position:0% +to represent an important part of the + + + align:start position:0% +to represent an important part of the +device where eoli are traveling from one + + align:start position:0% +device where eoli are traveling from one + + + align:start position:0% +device where eoli are traveling from one +chamber to another and this other final + + align:start position:0% +chamber to another and this other final + + + align:start position:0% +chamber to another and this other final +piece of the figure is a micrograph of + + align:start position:0% +piece of the figure is a micrograph of + + + align:start position:0% +piece of the figure is a micrograph of +that very same important connection + + align:start position:0% +that very same important connection + + + align:start position:0% +that very same important connection +between the two + + align:start position:0% +between the two + + + align:start position:0% +between the two +Chambers the question is number one are + + align:start position:0% +Chambers the question is number one are + + + align:start position:0% +Chambers the question is number one are +these photographs more than good enough + + align:start position:0% +these photographs more than good enough + + + align:start position:0% +these photographs more than good enough +I know that we talk about this a lot but + + align:start position:0% +I know that we talk about this a lot but + + + align:start position:0% +I know that we talk about this a lot but +it's really important to think about it + + align:start position:0% +it's really important to think about it + + + align:start position:0% +it's really important to think about it +it's pretty clear when you put a + + align:start position:0% +it's pretty clear when you put a + + + align:start position:0% +it's pretty clear when you put a +photograph in your figure it's important + + align:start position:0% +photograph in your figure it's important + + + align:start position:0% +photograph in your figure it's important +to have the best photograph you can make + + align:start position:0% +to have the best photograph you can make + + + align:start position:0% +to have the best photograph you can make +I wasn't convinced that these images + + align:start position:0% +I wasn't convinced that these images + + + align:start position:0% +I wasn't convinced that these images +were the best that could be and so I + + align:start position:0% +were the best that could be and so I + + + align:start position:0% +were the best that could be and so I +offered to make another representation + + align:start position:0% +offered to make another representation + + + align:start position:0% +offered to make another representation +of the device and so here this is the + + align:start position:0% +of the device and so here this is the + + + align:start position:0% +of the device and so here this is the +image that I made which I hope you agree + + align:start position:0% +image that I made which I hope you agree + + + align:start position:0% +image that I made which I hope you agree +looks better so we decided to replace + + align:start position:0% +looks better so we decided to replace + + + align:start position:0% +looks better so we decided to replace +the first picture in the graphic the + + align:start position:0% +the first picture in the graphic the + + + align:start position:0% +the first picture in the graphic the +next question is something I feel pretty + + align:start position:0% +next question is something I feel pretty + + + align:start position:0% +next question is something I feel pretty +important to consider in this next + + align:start position:0% +important to consider in this next + + + align:start position:0% +important to consider in this next +photograph ask ourselves are we really + + align:start position:0% +photograph ask ourselves are we really + + + align:start position:0% +photograph ask ourselves are we really +giving more information or frankly is it + + align:start position:0% +giving more information or frankly is it + + + align:start position:0% +giving more information or frankly is it +just redundant and so we collaboratively + + align:start position:0% +just redundant and so we collaboratively + + + align:start position:0% +just redundant and so we collaboratively +decided that it's not an important piece + + align:start position:0% +decided that it's not an important piece + + + align:start position:0% +decided that it's not an important piece +in the figure it's not saying anything + + align:start position:0% +in the figure it's not saying anything + + + align:start position:0% +in the figure it's not saying anything +that we are not already saying so we + + align:start position:0% +that we are not already saying so we + + + align:start position:0% +that we are not already saying so we +deleted it we're simplifying we're + + align:start position:0% +deleted it we're simplifying we're + + + align:start position:0% +deleted it we're simplifying we're +editing down the figure to the essential + + align:start position:0% +editing down the figure to the essential + + + align:start position:0% +editing down the figure to the essential +pieces after I looked at other images + + align:start position:0% +pieces after I looked at other images + + + align:start position:0% +pieces after I looked at other images +that they made in the lab I suggested + + align:start position:0% +that they made in the lab I suggested + + + align:start position:0% +that they made in the lab I suggested +that we include a fluorescing image from + + align:start position:0% +that we include a fluorescing image from + + + align:start position:0% +that we include a fluorescing image from +their files of eoli going from one + + align:start position:0% +their files of eoli going from one + + + align:start position:0% +their files of eoli going from one +chamber to the next to sort of match the + + align:start position:0% +chamber to the next to sort of match the + + + align:start position:0% +chamber to the next to sort of match the +lower right sem of the same area and + + align:start position:0% +lower right sem of the same area and + + + align:start position:0% +lower right sem of the same area and +then they agreed and what I also + + align:start position:0% +then they agreed and what I also + + + align:start position:0% +then they agreed and what I also +suggested was to invert the fluorescing + + align:start position:0% +suggested was to invert the fluorescing + + + align:start position:0% +suggested was to invert the fluorescing +image so that it would work well with + + align:start position:0% +image so that it would work well with + + + align:start position:0% +image so that it would work well with +the rest of the pieces after all + + align:start position:0% +the rest of the pieces after all + + + align:start position:0% +the rest of the pieces after all +remember fluorescence in this situation + + align:start position:0% +remember fluorescence in this situation + + + align:start position:0% +remember fluorescence in this situation +is basically a tagging technique telling + + align:start position:0% +is basically a tagging technique telling + + + align:start position:0% +is basically a tagging technique telling +us of evidence of the presence of a + + align:start position:0% +us of evidence of the presence of a + + + align:start position:0% +us of evidence of the presence of a +particular structure in this case eoli + + align:start position:0% +particular structure in this case eoli + + + align:start position:0% +particular structure in this case eoli +we're not measuring or quantifying + + align:start position:0% +we're not measuring or quantifying + + + align:start position:0% +we're not measuring or quantifying +fluorescence and we'll talk about that + + align:start position:0% +fluorescence and we'll talk about that + + + align:start position:0% +fluorescence and we'll talk about that +later when we discuss image manipulation + + align:start position:0% +later when we discuss image manipulation + + + align:start position:0% +later when we discuss image manipulation +so in this case it's perfectly fine to + + align:start position:0% +so in this case it's perfectly fine to + + + align:start position:0% +so in this case it's perfectly fine to +reverse the gray scale in the image + + align:start position:0% +reverse the gray scale in the image + + + align:start position:0% +reverse the gray scale in the image +making this piece easier to read so we + + align:start position:0% +making this piece easier to read so we + + + align:start position:0% +making this piece easier to read so we +replace the image we deleted with this + + align:start position:0% +replace the image we deleted with this + + + align:start position:0% +replace the image we deleted with this +fluorescing image the researchers and + + align:start position:0% +fluorescing image the researchers and + + + align:start position:0% +fluorescing image the researchers and +they decided they preferred another CAD + + align:start position:0% +they decided they preferred another CAD + + + align:start position:0% +they decided they preferred another CAD +drawing to replace the first one which + + align:start position:0% +drawing to replace the first one which + + + align:start position:0% +drawing to replace the first one which +is fine and finally we aligned and + + align:start position:0% +is fine and finally we aligned and + + + align:start position:0% +is fine and finally we aligned and +resized all the images to give us equal + + align:start position:0% +resized all the images to give us equal + + + align:start position:0% +resized all the images to give us equal +framing so we finally came up with what + + align:start position:0% +framing so we finally came up with what + + + align:start position:0% +framing so we finally came up with what +we believed was a clearer figure less + + align:start position:0% +we believed was a clearer figure less + + + align:start position:0% +we believed was a clearer figure less +redundant and and it work quite well as + + align:start position:0% +redundant and and it work quite well as + + + align:start position:0% +redundant and and it work quite well as +you could see in the published paper so + + align:start position:0% +you could see in the published paper so + + + align:start position:0% +you could see in the published paper so +we should compare them side by side and + + align:start position:0% +we should compare them side by side and + + + align:start position:0% +we should compare them side by side and +once again I hope you see that the + + align:start position:0% +once again I hope you see that the + + + align:start position:0% +once again I hope you see that the +second one is a market Improvement this + + align:start position:0% +second one is a market Improvement this + + + align:start position:0% +second one is a market Improvement this +is what we do on campus we work together + + align:start position:0% +is what we do on campus we work together + + + align:start position:0% +is what we do on campus we work together +in groups to dissect all sorts of draft + + align:start position:0% +in groups to dissect all sorts of draft + + + align:start position:0% +in groups to dissect all sorts of draft +submission it really works very well and + + align:start position:0% +submission it really works very well and + + + align:start position:0% +submission it really works very well and +I encourage you to do the same on your + + align:start position:0% +I encourage you to do the same on your + + + align:start position:0% +I encourage you to do the same on your +own + + align:start position:0% +own + + + align:start position:0% +own +campuses here's another figure that + + align:start position:0% +campuses here's another figure that + + + align:start position:0% +campuses here's another figure that +another group of researchers put + + align:start position:0% +another group of researchers put + + + align:start position:0% +another group of researchers put +together the tin sulfide powder which + + align:start position:0% +together the tin sulfide powder which + + + align:start position:0% +together the tin sulfide powder which +yields some information then becomes + + align:start position:0% +yields some information then becomes + + + align:start position:0% +yields some information then becomes +deposited and we see that somehow in an + + align:start position:0% +deposited and we see that somehow in an + + + align:start position:0% +deposited and we see that somehow in an +sem of that layer and ultimately the + + align:start position:0% +sem of that layer and ultimately the + + + align:start position:0% +sem of that layer and ultimately the +idea is to show how the researchers + + align:start position:0% +idea is to show how the researchers + + + align:start position:0% +idea is to show how the researchers +fabricated this solar cell it is about + + align:start position:0% +fabricated this solar cell it is about + + + align:start position:0% +fabricated this solar cell it is about +process so we went through a whole + + align:start position:0% +process so we went through a whole + + + align:start position:0% +process so we went through a whole +series of iterations and questions I've + + align:start position:0% +series of iterations and questions I've + + + align:start position:0% +series of iterations and questions I've +eded them down here so you could see a + + align:start position:0% +eded them down here so you could see a + + + align:start position:0% +eded them down here so you could see a +number of the attempts by the + + align:start position:0% +number of the attempts by the + + + align:start position:0% +number of the attempts by the +researchers so when I came into the + + align:start position:0% +researchers so when I came into the + + + align:start position:0% +researchers so when I came into the +picture I first questioned whether the + + align:start position:0% +picture I first questioned whether the + + + align:start position:0% +picture I first questioned whether the +graph really had to be included in the + + align:start position:0% +graph really had to be included in the + + + align:start position:0% +graph really had to be included in the +figure perhaps it could have been placed + + align:start position:0% +figure perhaps it could have been placed + + + align:start position:0% +figure perhaps it could have been placed +elsewhere in the article and then we + + align:start position:0% +elsewhere in the article and then we + + + align:start position:0% +elsewhere in the article and then we +discussed whether it was important to + + align:start position:0% +discussed whether it was important to + + + align:start position:0% +discussed whether it was important to +show the powder they asked that I come + + align:start position:0% +show the powder they asked that I come + + + align:start position:0% +show the powder they asked that I come +up with another way of portraying the + + align:start position:0% +up with another way of portraying the + + + align:start position:0% +up with another way of portraying the +tin suied powder I tried it in vials I + + align:start position:0% +tin suied powder I tried it in vials I + + + align:start position:0% +tin suied powder I tried it in vials I +then suggested putting the sem within an + + align:start position:0% +then suggested putting the sem within an + + + align:start position:0% +then suggested putting the sem within an +illustration showing the various layers + + align:start position:0% +illustration showing the various layers + + + align:start position:0% +illustration showing the various layers +and then I made another photograph of + + align:start position:0% +and then I made another photograph of + + + align:start position:0% +and then I made another photograph of +the solar cell which I think is better + + align:start position:0% +the solar cell which I think is better + + + align:start position:0% +the solar cell which I think is better +from their rendition I hope you agree + + align:start position:0% +from their rendition I hope you agree + + + align:start position:0% +from their rendition I hope you agree +and we eventually evolv this final + + align:start position:0% +and we eventually evolv this final + + + align:start position:0% +and we eventually evolv this final +figure into this we concentrated on the + + align:start position:0% +figure into this we concentrated on the + + + align:start position:0% +figure into this we concentrated on the +picture of this solar cell did not need + + align:start position:0% +picture of this solar cell did not need + + + align:start position:0% +picture of this solar cell did not need +the vials of powder just showing the + + align:start position:0% +the vials of powder just showing the + + + align:start position:0% +the vials of powder just showing the +layers of the + + align:start position:0% +layers of the + + + align:start position:0% +layers of the +material much easier for the reader to + + align:start position:0% +material much easier for the reader to + + + align:start position:0% +material much easier for the reader to +see and understand what is going on in + + align:start position:0% +see and understand what is going on in + + + align:start position:0% +see and understand what is going on in +this figure again editing and + + align:start position:0% + + + + align:start position:0% + +simplifying \ No newline at end of file diff --git a/ct0QGoi3n4Q.txt b/ct0QGoi3n4Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..d5d53ab082f37e29f975b17a3e67f85cc24fbbcc --- /dev/null +++ b/ct0QGoi3n4Q.txt @@ -0,0 +1,3678 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK, so let's +get started. + +We're going to essentially +finish up on + +Poisson processes today. + +And today, we have the part of +it that's really the fun part. + +What we had until now was the +dry stuff, defining everything + +and so forth. + +As I said before, Poisson +processes are these perfect + +processes where everything that +could be true is true. + +And you have so many different +ways of looking at problems + +that you can solve problems +in a wide variety of ways. + +What you want try to do in the +problem set this week is to + +get out of the mode of starting +to write equations + +before you think about it. + +I mean, write equations, yes, +but while you're doing it, + +think about what the right way +of approaching the problem is. + +As far as I know, every part of +every problem there can be + +solved in one or two lines. + +There's nothing long. + +There's nothing complicated. + +But you have to find exactly +the right way of doing it. + +And that's what you're supposed +to learn because you + +find all sorts of processes in +the world, which are poorly + +modelled as Poisson processes. + +You get a lot of insight about +the real process by looking at + +Poisson processes, but you don't +get the whole story. + +And if you don't understand how +these relationships are + +connected to each other then +you have no hope of getting + +some sense of when Poisson +process theory is telling you + +something and when it isn't. + +That's why engineers are +different than mathematicians. + +Mathematicians live in +this beautiful world. + +And I love it. + +I love to live there. + +Love to go there for vacations +and so on because everything + +is perfectly clean. + +Everything has a +right solution. + +And if it's not a +right solution, + +it's a wrong solution. + +In engineering, everything +is kind of hazy. + +And you get insights about +things when you put a lot of + +insights together. + +You finally make judgments +about things. + +You use all sorts of +models to do this. + +And what you use a course like +this for is to understand what + +all these models are saying. + +And then be able to use them. + +So, the stuff that we'll be +talking about today is stuff + +you will use all the +rest of the term. + +Because everything we do, +surprisingly enough, from now + +on, has some relationships +with Poisson processes. + +It doesn't sound like they do, +but, in fact, they do. + +And this has a lot of the things +that look like tricks, + +but which are more +than tricks. + +They're really what comes from +a basic understanding of + +Poisson processes. + +So first, I'm going to +review a little bit + +what we did last time. + +Poisson process is an +arrival process. + +Remember what an arrival +process is. + +It's just a bunch of arrival +epochs, which have some + +statistics associated +with them. + +And it has IID +exponentially-distributed + +interarrival times. + +So the time between successive +arrivals is independent from + +one arrival to the next. + +And it has this exponential +distribution, which is what + +gives the Poisson process it's +very special characteristic. + +It can be represented by +its arrival epochs. + +These are the things you see +here, S1, S2, S3, and so + +forth, are the arrival epochs. + +If you can specify what the +probability relationship is + +for this set of joint random +variables then you know + +everything there is to know +about a Poisson process. + +If you specify the joint +distribution of these + +interarrival times, and that's +trivial because they're IID + +exponentially-distributed random +variables, then you + +know everything there is to +know about the process. + +And if you can specify N of +t, which is the number of + +arrivals up until time t for +every t then that specifies + +the process completely also. + +So we take the viewpoint here, +I mean, usually we view a + +stochastic process as either a +sequence of random variables + +or a continuum of random +variables. + +Here, we're viewing as this +three ways of looking at the + +same thing. + +So a Poisson process is then +either the sequence of + +interarrival times, the sequence +of arrival epochs, + +or, what we call the counting +process, N of t at each t + +greater than zero. + +The arrival epochs in N of +t are related either + +this way or this way. + +And we talked about that. + +The interarrival times +are memoryless. + +In other words, they satisfy +this relationship here. + +The probability that an +interarrival time Xi is + +greater than t plus x, for any +t and any x, which are + +positive, given that it's +greater than t. + +In other words, given that +you've already wasted time t + +waiting, the probability that +the time from here until the + +actual occurrence occurs +is again exponential. + +This is stated in conditional +form. + +We stated it before in just +joint probability form. + +OK, which says, that if you wait +for a while and nothing + +has happened, you just +keep on waiting. + +You're right where +you started. + +You haven't lost anything. + +You haven't gained anything. + +And we said that other renewal +processes, which are IID + +interarrival random variables, +you can have these heavy + +tailed distributions where if +nothing happens after while + +then you start to really feel +badly because you know + +nothing's going to happen +for an awful lot longer. + +Heavy tailed distribution's best +example is when you're + +trying to catch an airplane and +they say, it's going to be + +10 minutes late. + +That's the worst heavy tailed +distribution there is. + +And it drives you crazy. + +Because I've never caught a +plane that was supposed to be + +10 minutes late that wasn't +at least an hour late. + +And often, it got canceled, +which makes it not a random + +variable at all. + +One of the things we're +interested in now, and we + +talked about it a lot last +time, is you pick some + +arbitrary time t, that can +be any time at all. + +And you ask, how long is it from +time t-- t might be when + +you arrive to wait for +a bus or something-- + +how long is it until +the next bus comes? + +So Z is the random variable +that goes. + +And you really should put +some indices on this. + +But what it is is the random +variable from t until this + +slow arrival here that's poking +along finally comes in. + +Now, what we found is that the +interval Z, which is the time + +from this arrival back +to t, is exponential. + +And the way we showed that is +to say, let's condition Z on + +anything we want to +condition it on. + +And the things that's important +too condition it on + +is the value of N of t here, +which is N. And once we + +condition it on the fact that N +of t is n, we then condition + +on S sub n, which is the time +that this last arrival came. + +So if we condition Z on N of t +at time t and the time that + +this last arrival came in, which +is S sub two, in this + +case, then Z turns out to be, +again, just the time left to + +wait after we've already +waited for this + +given amount of time. + +We then find out that Z, +conditional on these two + +things that we don't understand +at all, it's just + +exponential, no matter +what they are. + +And since it's exponential no +matter what they are, we don't + +go to the trouble of trying to +figure out what they are. + +We just say, whatever +distribution they have, Z + +itself, unconditionally, is +just the same exponential + +random variable. + +So that was one of the main +things we did last time. + +Next thing we did was we started +to look at any set of + +time, say t1, t2, up to t sub +k, and then we looked at the + +increments. + +How many arrivals occurred +between zero and t1? + +How many arrivals occurred +between t1 and t2? + +How many between t2 and t3? + +So we looked at these Poisson +process increments, a whole + +bunch of random variables, and +we said, these are stationary + +and independent Poisson counting +processes, over their + +given intervals. + +In other words, if you stop the +first process, you stop + +looking at this at time t1. + +Then you look at this +from time t1 to t2. + +You look at this one from +tk minus 1 to tk. + +And you look at the last one, +the next last one, all + +the way up to tk. + +And there should be one +where you look at it + +from tk on to t. + +No, you're only looking +at k of them. + +So these are the things that +you're looking at. + +The statement is that these are + +independent random variables. + +The other statement is they're +stationary, which means, if + +you look at the number of +arrivals in this interval, + +here, it's a function +of t2 minus t1. + +But it's not a function +of t1 alone. + +It's only a function of the +length of the interval. + +The number of arrivals in any +interval of length tk minus tk + +minus 1 is a function only of +the length of that interval + +and not of where the +interval is. + +That's a reasonable way to look +at stationarity, I think. + +How many arrivals come in in a +given area is independent of + +where the area is. + +It depends only on how +long the interval is. + +OK, then we found that the +probability mass function for + +N of t, and now we're just +looking from zero to t because + +we know we get the same thing +over any interval, this + +probability mass function is +this nice function, which + +depends only and the +product lambda t. + +It never depends on lambda +alone or t alone. + +Lambda t to n, e to the minus +lambda t over n factorial. + +What the n factorial +is doing there. + +Well, it came out in +the derivation. + +By the time we finish today you +should have more ideas of + +where that factorial +came from. + +And we'll try to understand +that. + +By the stationary and +independent increment + +property, we know that these two +things are independent, N + +of t1 and the number of +arrivals in t1 to t. + +This is a Poisson +random variable. + +This is a Poisson +random variable. + +We know that the number of +arrivals between zero and t is + +also a Poisson random +variable. + +And what does that tell you? + +It tells you, you don't have +to go through all of this + +discrete convolution stuff. + +You probably should go through +it once just for your own + +edification to see that +this all works. + +But for a very lazy person +like me, who likes using + +arguments like this, I say, +well, these two things are + +independent. + +They are Poisson random +variables. + +Their sum is Poisson. + +And therefore, whenever you have +two independent Poisson + +random variables and you add +them together, what you get is + +a Poisson random variable whose +mean is the sum of the + +means of the two individual +random variables. + +In general, sums of independent +Poisson random + +variables are Poisson with +the means adding. + +Them we went through a couple of +alternate definitions of a + +Poisson process. + +And at this point, just from +what I've said so far, and + +from reading the notes and +understanding what I've said + +so far, it ought to be almost +clear that these alternate + +definitions, which we +talked about last + +time have to be valid. + +If an arrival process has the +stationary and independent + +increment properties and if N +of t has the Poisson PMF for + +given lambda, and all t, then +the process is Poisson. + +Now what is that saying? + +I mean, we've said that if we +can specify all of the random + +variables N of t for +all t, then we've + +specified the process. + +What does it mean to +specify a whole + +bunch of random variables? + +It is not sufficient to find the +distribution function of + +all those random variables. + +And one of the problems in the +homeworks at this time is to + +explicitly show that for +a simpler process, + +the Bernoulli process. + +And to actually construct an +example of where N of t is + +specified everywhere. + +But you don't have the +independence between different + +intervals, and therefore, +you don't + +have a Bernoulli process. + +You just have this nice binomial +formula everywhere. + +But it doesn't really +tell you much. + +OK, so, but here we're adding +on the independent increment + +properties, which says over any +set of intervals the joint + +distribution of how many +arrivals there are here, how + +many here, how many here, how +many here, those joint random + +variables are independent of +each other, which is what the + +independent increment +property says. + +So in fact, this tells you +everything you want to know + +because you now know the +relationship between each one + +of these intervals. + +So we see why the process +is Poisson. + +This one's a little trickier. + +If an arrival process has the +stationary and independent + +increment properties and it +satisfies this incremental + +condition, then the +processes Poisson. + +And the incremental condition +says that if you're looking at + +the number of arrivals in some +interval of size delta, the + +probability that this is equal +to N has the form 1 minus + +lambda delta plus o of delta, +where n equals zero. + +Lambda delta plus o of delta, +for n equals 1. + +o of delta for n greater +than or equal to 2. + +This intuitively is only +supposed to talk about very, + +very small delta. + +So if you take the Poisson +distribution lambda t to the + +N, e to the minus lambda t over +n factorial, and you look + +at what happens when t is +very small, this is + +what it turns into. + +When t is very small the +probability that there are no + +arrivals in this interval of +size delta is very large. + +It's 1 minus lambda delta plus +this extra term that says-- + +first point of view whenever +you see an o of delta is to + +say, oh, that's not important. + +And for N equals 1, there's +going to be one arrival with + +some fudge factor, which +is not important. + +And there's going to be two or +more arrivals with some fudge + +factor, which is +not important. + +The next thing we talked about +is that o of delta really is + +defined as any function which +is a function of delta where + +the limit of o of +delta divided by + +delta is equal to 0. + +In other words, it's some +function that goes to zero + +faster than delta does. + +So it's something which +is insignificant with + +relationship to this as +delta gets very small. + +Now, how do you use this kind +of statement to make some + +statement about larger +intervals? + +Well, you're clearly +stuck looking at + +differential equations. + +And the text does that. + +I refuse to talk about +differential equations in + +lecture or anyplace else. + +When I retired I said, I will +no longer talk about + +differential equations +anymore. + +And you know, you don't need to +because you can see what's + +happening here. + +And what you see is happening +is, in fact, what's happening. + +OK, so, that's where we +finished up last time. + +And now, we come to the really +fun stuff where we want to + +combine independent +Poisson processes. + +And then, we want to split +Poisson processes. + +And we want to play all sorts of +games with multiple Poisson + +processes, which looks very +hard, and because of this, + +it's very easy. + +Yes? + +AUDIENCE: The previous +definitions, they are if and + +only statements, right? + +PROFESSOR: They are what? + +AUDIENCE: If and only, +all Poisson + +processes satisfy tho-- + +PROFESSOR: Yes. + +OK, in other words, what you're +saying is, if you can + +satisfy those properties, this +is a Poisson process. + +I mean, we've already shown +that a Poisson process + +satisfies those properties. + +As a matter of fact, the way I +put it in the notes is these + +are three alternate definitions +where you could + +start out with any one of them +and derive the whole thing. + +Many people like to start out +with this incremental + +definition because it's +very physical. + +But it makes all the mathematics +much, much harder. + +And so, it's just a question +of what you prefer. + +I like to start out with +something clean, then derive + +things, and then say, does +it make any sense for the + +physical situation? + +And that's what we usually do. + +We don't usually start out with +a physical situation and + +analyze the hell out of it and +say, aha, this is a Poisson + +process because it satisfies +all these properties. + +It never satisfies all +those properties. + +I mean, you say it's a Poisson +process because a Poisson + +process is simple and you can +get some insight from it, not + +because it really is +a Poisson process. + +Let's talk about taking two +independent Poisson processes. + +Just to be a little more +precise, two counting + +processes, N1 of t and N2 of t +are independent if for all t1 + +up to t sub n the random +variables N1 of t1 to N1 of tn + +are independent of N1 of +t1 up to N2 of tn. + +Why don't I just say that for +all t they're independent? + +Because I don't even know +what that means. + +I mean, we've never defined +independence for an infinite + +number of things. + +So all we can do is say, for all +finite sets, we have this + +independence. + +Now, give you a short +pop quiz. + +Suppose that instead of doing it +this way, I say, for all t1 + +to tn the random variables +N1 of t1 to N1 of tn are + +independent of for all tao1, +tao2, tao3, tao4, N2 of tao1 + +up to N2 of tao sub n? + +That sounds much more +general, doesn't it? + +Because it's saying that I can +count one process at one set + +of times and the other process +at another set of times. + +Now, why isn't it any more +general to do it that way? + +Well, it's an unfair pop quiz +because if you can answer that + +question in the short one +sentence answer that you'd be + +willing to give in a class like +this, I would just give + +you A plus and tell +you go away. + +And you already know all the +things you should know. + +The argument is the following, +if you order these different + +times, first tao1 of tao1 is +less than t1 then t1, if + +that's the next one, and you +order them all along. + +And then you apply this +definition to + +that ordered set. + +t1, tao1, t2, t3, t4, tao2, t5, +tao3, and so forth, and + +you apply this definition, and +then you get the other + +definition. + +So one is not more general +than the other. + +The theorem then, is that if +N1 of t and N2 of t are + +independent Poisson processes, +one of them has + +a rate lambda 1. + +One of them has a +rate lambda 2. + +And if N of t is equal to N1 of +t plus N2 of t, that just + +means for every t this random +variable N of t is the sum of + +the random variable N1 +of t plus the random + +variable N2 of 2. + +This is true for all. + +This is, definition, for all t +greater than 0, then the sum N + +of t is a Poisson process of +rate lambda equals lambda 1 + +plus lambda 2. + +Looks almost obvious, +doesn't it? + +I said that today there +was lots of fun stuff. + +There's also a little bit of +ugly stuff and this is one of + +those half obvious things +that's ugly. + +And I'm not going to waste +a lot of time on it. + +You can read all about the +details in the notes. + +But I will spend a little +bit of time on it + +because it's important. + +The idea is that if you look at +any small increment, t to t + +plus delta, the number of +arrivals in the interval t to + +t plus delta is equal to the +number of arrivals in the + +interval t to t plus delta from +the first process plus + +that in the second process. + +So the probability that there's +one arrival in this + +combined process is the +probability that there's one + +arrival in the first process and +no arrivals in the second + +process, or that there's no +arrivals in the first process + +and one arrival in the +second process. + +That's just a very simple +case of convolution. + +Those are the only ways +you can get one in + +the combined process. + +This term here is delta +times lambda 1-- + +too early in the morning. + +I'm confusing my deltas +and lambdas. + +There are too many +of each of them. + +--plus o of delta. + +And this term here, probability +that there's zero + +for the second process +is 1 minus delta + +lambda 2 plus o of delta. + +And then this term is just +the opposite term + +corresponding to this. + +Now I multiply these +terms out. + +And what do I get? + +Well, this 1 here combines +with a delta lambda 1. + +Then there's a delta lambda 2 +times delta lambda 1, which is + +delta squared. + +It's a delta squared term, +so that's really + +an o of delta term. + +It's negligible as delta +goes to zero. + +So we forget about that. + +There's an o of delta times 1, +that's still an o of delta. + +There's an o of delta times +a delta lambda. + +And that's sort of an o of delta +squared if you wish. + +But it's still an o of delta. + +It goes to zero as +delta gets large. + +And goes to zero faster +than delta. + +What we're trying to do is to +find the terms that are + +significant in terms of delta. + +Namely, when delta gets very +small, I want to find things + +that are at least proportional +to delta and not of lower + +order than delta. + +So when I get done with all of +that, this is delta times + +lambda 1 plus lambda +2 plus o of delta. + +That's the incremental property +that we want a + +Poisson process to have. + +So it has that incremental +property. + +And those are the same sort of +argument if you want to for + +the number of arrivals in +t, that t plus delta. + +Maybe a picture of +this would help. + +Pictures always help +in the morning. + +Here we have two processes. + +We're looking at some interval +of time, t to t plus delta. + +t to plus delta. + +And we might have +an arrival here. + +We might have an arrival +here, an arrival + +here, an arrival here. + +Well, the probability of an +arrival here and an arrival + +here is something of order +delta squared. + +So that's something we ignore. + +So it says, we might have +an arrival here + +and no arrival here. + +This is a lambda 1. + +This is lambda 2 here. + +We might have an arrival here +and none here, or we might + +have an arrival here +and none there. + +Two arrivals is just too +unlikely to worry about, so we + +forget about it at least +for the time being. + +Now, after going through this +incremental argument, if you + +go back and say, let's forget +about all these o of deltas + +because they're very confusing, +let's just do the + +convolution knowing +what N of t is in + +both of these intervals. + +If you do that, it's much easier +to find out that the + +number of arrivals in this +sum of intervals. + +Number arrivals here, plus the +number of arrivals here, this + +is Poisson. + +This is Poisson. + +You add two Poisson, +you get Poisson. + +The rate of the sum of the +two Poisson is Poisson. + +So it's Poisson with lambda +1 plus lambda 2. + +Now how many of you saw that +and says, why is this idiot + +going through this incremental +argument? + +Anyone? + +I won't be embarrassed. + +I knew it anyway. + +And I did it for a reason. + +But I must confess, when I wrote +the first edition of + +this book I didn't +recognize that. + +So I went through this terribly +tedious argument. + +Anyway, the more important issue +is if you have the sum + +of many, many small independent +arrival + +processes-- + +OK, in other words, you +have the internet. + +And a node in the internet is +getting jobs, or messages, + +from all sorts of people, and +all sorts of processes, and + +all sorts of nonsense going to +all sorts of people, all sorts + +of processes, and all sorts +of nonsense and those are + +independent of each +other, not really + +independent of each other. + +But relative to the data rate +that's travelling over this + +internet, each of +those processes + +are very, very small. + +And what happens is the sum of +many, many small independent + +arrival processes tend to be +Poisson even if the small + +processes are not. + +In a sense, the independence +between the processes + +overcomes the dependence between +successive arrivals in + +each process. + +Now, I look at that and I say, +well, it's sort of a + +plausibility argument. + +You look at the argument in +the text, and you say, ah, + +it's sort of a plausibility +argument. + +I mean, proving this statement, +you need to put a + +lot of conditions on it. + +And you need to really go +through an awful lot of work. + +It's like proving the central +limit theorem, but it's + +probably harder than that. + +So, if you read the text, +and say you don't really + +understand the argument there, +I don't understand it either + +because I don't think +it's exactly right. + +And I was just trying to say +something to give some idea of + +why this is plausible. + +It should probably be changed. + +Next we want to talk about +splitting a Poisson process. + +So we start out with a +Poisson process here + +and a t of rate lambda. + +And what happens? + +These arrivals come +to some point. + +And some character is +standing there. + +It's like when you're having +your passport checked when you + +come back to Boston +after being away. + +In some places you press a +button, and if the button come + +up one way, you're sent off to +one line to be interrogated + +and all sorts of junk. + +And it's supposed +to be random. + +I have no idea whether it's +random or not, but it's + +supposed to be random. + +And otherwise, you go +through and you get + +through very quickly. + +So it's the same sort +of thing here. + +You have a bunch of arrivals. + +And each arrival is effectively +randomly shoveled + +this way or shoveled this way. + +With probability p, it's +shoveled this way. + +With probability 1 minus p, +it's shoveled this way. + +So you can characterize this +switch as a Bernoulli process. + +It's a Bernoulli process +because it's random and + +independent from, not +time to time now, + +but arrival to arrival. + +When we first looked at a +Poisson process, we said it's + +a sequence of random +variables. + +Sometimes we look at +in terms of time. + +Time doesn't really make +any difference there. + +It's just a sequence of +IID random variables. + +So you have a sequence of IID +random variables doing this + +switching here. + +You have a Poisson process +coming in. + +And when you look at the +combination of the Poisson + +process and the Bernoulli +process, you get some kind of + +process of things +coming out here. + +And another kind of process +of things coming out here. + +And the theorem says, that when +you combine this Poisson + +process with this independent +Bernoulli process, what you + +get is a Poisson process here +and an independent Poisson + +process here. + +And, of course, you need to know +what the probability is + +of being switched this way and +being switched that way. + +Each new process clearly has a +stationary and independent + +increment property. + +Why is that? + +Well, you look at some increment +of time and this + +process here is independent +from one period of time to + +another period of time. + +The Bernoulli process is just +switching the terms within + +that interval of time, which +is independent of all other + +intervals of time. + +So that when you look at the +combination of the Bernoulli + +process and the Poisson +process, you have the + +stationary and independent +increment property. + +And each satisfies the small +increment property. + +If you look at very +small delta here, + +unless each is Poisson. + +There's a more careful argument +in the notes. + +What I'm trying to do in the +lecture is not to give you + +careful proofs of things, but to +give you some insight into + +why they're true. + +So that you can read +the proof. + +And instead of going through +each line and saying, yes, I + +agree with that, yes, I agree +with that and you finally come + +to the end of the proof +and you think what? + +Which I've done all the time +because I don't really know + +what's going on. + +And you don't learn anything +from that kind of proof. + +If you're surprised when it's +done it means you ought to go + +back and look at it more +carefully because there's + +something there that you didn't +understand while it was + +wandering past you. + +The small increment property +really doesn't make it clear + +that the split processes +are independent. + +And for independence both +processes must sometimes have + +arrivals in the same +small increment. + +And this independence +is hidden in + +those o of delta terms. + +And if you want to resolve that +for yourself, you really + +have to look at the text. + +And you have to do +some work too. + +The nice thing about combining +and splitting is that you + +typically do them together. + +Most of the places where you +use combining and splitting + +you use both of them +repeatedly. + +The typical thing you do is +first, you look at separate + +independent Poisson processes. + +And you take those separate +independent Poisson processes, + +and you say, I want to look at +those as a combined process. + +And after you look at them as +a combined process, you then + +split them again. + +And what you're doing, when you +then split them again, is + +you're saying these two +independent Poisson processes + +that I started with, I can +view them as one Poisson + +process plus a Bernoulli +process. + +And you'd be amazed at how many +problems you can solve by + +doing that. + +You will be amazed when you +do the homework this time. + +If you don't use that property +at least 10 times, you haven't + +really understood what's being +asked for in those problems. + +Let's look at a simple +example. + +Let's look at a last come, +first served queue. + +Last come, first served queues +are rather peculiar. + +They are queues where arrivals +come in, and for some reason + +or other, when a new arrival +comes in that arrival goes + +into the server immediately. + +And the queue gets backed up. + +Whatever was being served +gets backed up. + +And the new arrival gets served, +which is fine for the + +new arrival, unless another +arrival comes + +in before it finishes. + +And then it gets +backed up too. + +So things get backed +up in the queue. + +And those that are lucky +enough to get + +through, get through. + +And those that aren't, don't. + +Anybody have any +idea why that-- + +I mean, it sounds like a very +unfair thing to do. + +But, in fact, it's not unfair +because you're not singling + +out any particular group +or anything. + +You're just that's +the rule you use. + +And it applies to everyone +equally, so it's not unfair. + +But why might it make +sense sometimes? + +Yeah? + +AUDIENCE: If you're doing a +first come, first served + +you're going to have a +certain distribution + +for your serve time. + +Whereas, if you do last +come, first served-- + +I don't know. + +I'm just trying to think that +there might some situations + +where the distribution of +service times in that is + +favorable overall, even though +some people, every once in a + +while, are feeling screwed. + +PROFESSOR: It's a good try. + +But it's not quite right. + +And, in fact, it's not right for +a Poisson process because + +for a Poisson process the server +is just chunking things + +out at rate mu, no +matter what. + +So it doesn't really +help anyone. + +If you have a heavy tail +distribution, if somebody who + +comes in and requires an +enormous amount of service, + +then you get everybody else +done first because that + +customer with a huge service +requirement keeps getting + +pushed back every time the queue +is empty he gets some + +service again. + +And then other people come in. + +And people with small service + +requirements get served quickly. + +And what that means +is it's not quite + +as crazy as it sounds. + +But the reason we want to look +at it here is because it's a + +nice example of this +combining and + +splitting of Poisson processes. + +So how does that happen? + +Well, you view services +as a Poisson process. + +Namely, we have an exponential +server here, where the time + +for each service is +exponentially distributed. + +Now, if you're awake, you point +out, well, what happens + +when the server has +nothing to do? + +Well, just suppose that there's +some very low priority + +set of jobs that the server +is doing, which also are + +exponentially distributed that +the server goes to when it has + +nothing to do. + +So the server is still doing +things exponentially at rate + +lambda, but if there's nothing +real to do then + +the output is wasted. + +So that's a Poisson process. + +The income is Poisson also. + +So the arrival process, plus the +service process, they're + +independent. + +So they're Poisson. + +And the rate is lambda +plus mu. + +Now, interesting question, +what's the probability that an + +arrival completes service before +being interrupted? + +I'm lucky, I get into +the server. + +I start getting served. + +What's the probability that +I finish before I get + +interrupted? + +Well, I get into service +at a particular time t. + +I look at this combined Poisson +process of arrivals + +and services and if the first +arrival in this combined + +process gets switched to +service, I'm done. + +If gets switched to arrival, +I'm interrupted. + +So the question is, what's the +probability that I get + +switched to-- + +I want to find the probability +that I'm interrupted, so + +what's the probability that a +new arrival in the combined + +process gets switched to +arrivals because that's the + +case where I get interrupted. + +And it's just lambda. + +The probability that I get +interrupted is lambda divided + +by lambda plus mu. + +And the probability that I +complete my service is mu over + +lambda plus mu. + +When mu is very large, when the +server is going very, very + +fast, I have a good chance +of finishing before being + +interrupted. + +When it's the other +way, I have a much + +smaller chance of finishing. + +More interesting, and more +difficult case, given that + +you're interrupted, what is the +probability that you have + +no further interruptions? + +In other words, I'm being +served, I get interrupted, so + +now I'm sitting at the +front of the queue. + +Everybody else that came in +before me is in back of me. + +I'm sitting there at the +front of the queue. + +This interrupting customer +is being served. + +What's the probability that I'm +going to finish my service + +before any further interruption +occurs? + +Have to be careful about +how to state this. + +The probability that there is +no further interruption is + +that two services occur before +the next arrival. + +And the probability of that is +mu over lambda plus mu the + +quantity squared. + +Now, whether you agree with +that number or not is + +immaterial. + +The thing I want you to +understand is that this is a + +method which you can use +in quite complicated + +circumstances. + +And it's something that applies +in so many places that + +it's amazing. + +OK, let's talk a little +bit about + +non-homogeneous Poisson processes. + +Maybe the most important +application of this is optical + +transmission. + +There's an optical stream of +photons that's modulated by + +variable power. + +Photon stream is reasonably +modeled as a Poisson process, + +not perfectly modeled +that way. + +But again, what we're doing here +is saying, let's look at + +this model. + +And then, see whether the +consequences of the model + +apply to the physical +situation. + +The modulation converts the +steady photon rate into a + +variable rate. + +So the arrivals are being +served, namely, they're being + +transmitted at some +rate, lambda of + +t, where t is varying. + +I mean, the photons have +nothing to do the + +information at all. + +They're just random photons. + +And the information is +represented by lambda t. + +The question is can +you actually send + +anything this way? + +We model the number of photons +in any interval t and t plus + +delta as a Poisson random +variable whose rate parameter + +over t and t plus delta, or +very small delta, is the + +average photon rate over t and +t plus delta times delta. + +So we go through this small +increment model again. + +But in the small increment +model, we have a lambda t + +instead of a lambda and +everything else is the same. + +And when you carry this +out, what you find-- + +and I'm not going to show +this or anything. + +I'm just going to tell it to you +because it's in the notes + +if you want to read +more about it. + +The probability that you have a +given number of arrivals in + +some given interval is a Poisson +random variable again. + +Namely, whether the process +is homogeneous or not + +homogeneous, if the original +photons are Poisson then what + +you wind up with is +this parameter + +of the Poisson process. + +m hat to the N e the minus m +hat divided by n factorial. + +And this parameter +here is what? + +It's the overall arrival +rate in that interval. + +So it's exactly what you'd +expect it to be. + +So what this is saying is +combining and splitting + +non-homogeneous processes +still works like in the + +homogeneous case. + +The independent exponential +in arrivals don't work. + +OK, let me say that +another way. + +When you're looking at +non-homogeneous Poisson + +processes, looking at them in +terms of a Poisson counting + +process is really a +neat thing to do. + +Because all of the Poisson +counting process formulas + +still work. + +And all you have to do when +you want to look at the + +distribution of the number +arrivals in an interval is + +look at the average arrival +rate over that interval. + +And that tells you everything. + +When you look at the +interarrival times and things + +like that they aren't +exponential anymore. + +And none of that works. + +So you get half the pie, but +not the whole thing. + +Now, the other thing, which is +really fun, and which will + +take us a bit of time, is to +study, now it's not a small + +increment but a bigger +increment, of a Poisson + +process when you condition +on N of t. + +In other words, if somebody +tells you how many arrivals + +have occurred by time t, how do +you analyze where those are + +arrivals occur, where the +arrival epochs are, + +and things like that? + +Well, since we're conditioning +on N of t, let's start out + +with N of t equals 23 because +that's obviously the simplest + +number to start out with. + +Obviously not. + +We start out with N of t equals +1 because that clearly + +is a simpler thing +to start with. + +So here's the situation +we have. + +We're assuming that there's +a one arrival + +up until this time. + +That one arrival has to +occur somewhere in + +this interval here. + +We don't know where it is. + +So we say, well, let's suppose +that it's in the interval s1 + +to s1 plus delta and try to find +the probability that it + +actually is in that interval. + +So we start out with something +that looks ugly. + +But we'll see it isn't as +ugly as it looks like. + +We'll look at the conditional +density of s1 given that N of + +t is equal to 1. + +That's what this is. + +This is a conditional +density here. + +And we say, well, how do we find +the conditional density? + +This a one dimensional +density. + +So what we're going to do is +we're going to look at the + +probability that there's one +arrival in this tiny interval. + +And then we're going to divide +by delta and that gives us the + +density, if everything +is well defined. + +So the density is going to be +the limit as delta goes to + +zero, which is the way you +always define densities, of + +the probability that there +is no arrivals in here. + +That there's one arrival here. + +And that there's no +arrivals here. + +So probability zero +arrivals here. + +Probability of one +arrival here. + +And probability of zero +arrivals here. + +We want to find that +probability. + +We want to divide for the +conditioning by the + +probability that there was one +arrival in the whole interval. + +This delta here is because we +want to go to the limit and + +get a density. + +OK, when we look at this and +we calculate this, e to the + +minus lambda s1 is +what this is. + +Lambda delta times e to +the minus lambda delta + +is what this is. + +And e to the minus lambda +t minus s1 minus delta + +is what this is. + +Because this last interval is +t minus s1 minus delta. + +Now, the remarkable thing is +when I add, I multiply e to + +the minus lambda s1 times e to +the minus lambda delta times e + +to the minus lambda t minus +s1 minus delta. + +There's an s1 here. + +An s1 one here. + +There's a delta here. + +And a delta here. + +This whole thing is e to +the minus lambda delta. + +And it cancels out with this e +to the minus lambda delta. + +That's going to happen +no matter how many + +arrivals I put in here. + +So that's an interesting +thing to observe. + +So what I wind up with is lambda +delta up here, lambda + +delta t here, and +my probability + +density is 1 over t. + +And now we look at that and we +say, my God, how strange. + +And then we look at it +and we say, oh, of + +course, it's obvious. + +Yes? + +AUDIENCE: Why do you use N s1 +and then the N tilde for the + +other two in the first +part in the limit? + +PROFESSOR: Here? + +AUDIENCE: You have p and s1 and +it's e N tilde on the top. + +Why do you use the N +and the N tilde? + +PROFESSOR: N of t is not +shown in the figure. + +N of t just says there is one +arrival up until time t, which + +is what lets me draw +the figure. + +AUDIENCE: I meant in +the limit as delta + +approaches zero, Pn, Professor. + +You used Pn and then Pn tilde +for the other two. + +Does that signify anything? + +PROFESSOR: OK, this term is the +probability that we have + +no arrivals between +zero and s1. + +This N tilde means number of +arrivals in an interval, which + +starts at s1 and goes +to s1 plus delta. + +So this is the probability we +have one arrival somewhere in + +this interval. + +And this term here is the +probability that we have no + +arrivals in s1 plus +delta up until t. + +And when we write all of those +things out everything cancels + +out except the 1 over t. + +And then we look at that +and we say, of course. + +If you look at the small +increment definition of a + +Poisson process, it says that +arrivals are equally likely at + +any point along here. + +If I condition on the fact that +there's been one arrival + +in this whole interval, and +they're equally likely to + +occur anywhere along here, the +only sensible thing that can + +happen is that the probability +density for where that arrival + +happens is uniform over +this whole interval. + +Now, the important point +is that this + +doesn't depend on s1. + +And it doesn't depend +on lambda. + +That's a little surprising +also. + +I mean, we have this Poisson +process where arrivals are + +dependent on lambda, but you +see, as soon as you say N of t + +equals 1, you sort +of wash that out. + +Because you're already +conditioning on the fact that + +there was only one arrival +by this time. + +So you have this nice +result here. + +But a result which looks +a little suspicious. + +Well, we were successful +with that. + +Let's go on to N +of t equals 2. + +We'll get the general +picture with this. + +We want to look at the +probability density of + +arrivals at s1. + +This s1 and an arrival here, +given that there were only two + +arrivals overall. + +And again, we take the limit +as delta goes to zero. + +And we take a little delta +interval here, a little delta + +interval here. + +So we're finding the probability +that there are two + +arrivals, one between s1 and +s1 plus delta and the other + +one between s2 and +s2 plus delta. + +So that probability should be +proportional to delta squared. + +And we're dividing by delta +squared to find the joint + +probability density. + +You don't believe that, go back +and look at how joint + +probability densities +are the defined. + +I mean, you have to define +them somehow. + +So you have to look at the +probability in a small area. + +And then shrink the +area to zero. + +And the area of the area +is delta squared. + +And you have to divide +by delta squared as + +you go to the limit. + +OK, so, we do the same thing +that we did before. + +The probability of no arrivals +in here is e to the + +minus lambda s1. + +In other words, we are taking +the unconditional probability + +and then we're dividing by the +conditioning probability. + +So the probability that there's +nothing arriving in + +here is that. + +The probability there's one +arrival in here is that. + +Probability that there's +nothing in + +this interval is this. + +Probability there's one in this +interval is lambda delta + +times e to the minus +lambda delta. + +And finally, this last term +here, we have to divide by + +delta squared to go +to a density. + +We have to divide by the +probability that there were + +actually just two +arrivals here. + +Well, again, the same +thing happens. + +If we take all the exponentials, +lambda s1, + +lambda delta, lambda 2 +in here, this term + +cancels out this term. + +This term here cancels +out this term. + +And all we're left with is e to +the minus lambda t up here, + +e to the minus lambda +t down here. + +And because the PMF function for +N of t is e to the minus + +lambda t over n factorial, n +factorial for n equals 2 is 2. + +We wind up with 2 +over t squared. + +Now that's a little +bit surprising. + +I'm going to show you a picture +in just a little bit, + +which makes it clear what +that 2 is doing there. + +But let's not worry about it too +much for the time being. + +The important thing +here is, again, + +it's independent lambda. + +And it's a independent +of s1 and s2. + +Namely, given that there are two +arrivals in here doesn't + +make any difference +where they are. + +This is, in some sense, uniform +over s1 and s2. + +And I have to be more careful +about what uniform means here. + +But we'll do that in +just a little bit. + +Now we can do the same thing +for N of t equals N, for + +arbitrary N. And when I put +in an arbitrary number of + +arrivals here I still get this +property that when I take e to + +the minus lambda of this region, +e to the minus lambda + +times this region, this, this, +this, this, this, this and so + +forth, when I get all done, it's +e to the minus lambda t. + +And it cancels out with +this term down here. + +We've done that down here. + +And what you come up with is +this joint density is equal to + +N factorial over t to the N. So +again, it's the same story. + +It's uniform. + +It doesn't depend on where the +s's are, except for the fact + +that s1 is less than +s2 is less than s3. + +We have to sort that out. + +It has this peculiar N factorial +here that doesn't + +depend on lambda, as I said. + +It does depend N in this way. + +That's a uniform N dimensional +probability density over the + +volume t to the N over N +factorial corresponding to the + +constraint region zero less than +s1 less than blah, blah, + +blah, less than s +sub N. Now that + +region is a little peculiar. + +This N factorial is +a little peculiar. + +The t to the N is +pretty obvious. + +Because when you have a joint +density over t things, each + +bounded between zero and +t, you expect to see + +a t to the N there. + +So if you ask, what's +going on? + +In a very simple minded way, the +question is how did this + +derivation know that the volume +of s1 to sn over zero + +less than s1, less than sn, less +than s2, is N factorial + +over t to the N? + +I have a uniform probability +density over + +some strange volume. + +And it's a strange volume +which satisfies this + +constraint. + +How do I know that this +is N factorial here? + +Very confusing at first. + +We saw the same question when +we derived the airline + +density, remember? + +There was an N factorial +there. + +And that N factorial when +we derived the Poisson + +distribution led to an +N factorial there. + +And, in fact, the fact that +we were using the Poisson + +distribution there is why that +N factorial appears here. + +It was because we stuck that +in when we were doing the + +derivation of the Poisson PMF. + +But it still seems a +little mystifying. + +So I want to try to resolve +that mystery. + +And to resolve it +let's look at a + +supposedly unrelated problem. + +And the unrelated problem is the +following, suppose U1 up + +to U sub n are n IID random +variables, independent and + +identically distributed random +variables, each uniform + +over zero to t. + +Well, now, the probability +density for those n random + +variables is very, +very simple. + +Because each one of them is +uniform over one to t. + +The joint density is +1 over t to the n. + +OK, no problem there. + +They're each independent. + +So the probability densities +multiply. + +Each one has a probability +density 1 over t. + +No matter where it is because +it's uniform. + +So you multiply them together. + +And no matter where you are in +this n dimensional cube, the + +probability density is +1 over t to the n. + +The next thing I want +to do is define-- + +now these are supposedly not the +same random variables as + +these arrival epochs +we had before. + +These are just defined +in terms of these + +uniform random variables. + +You're seeing a good example +here of why in probability + +theory we start out with axioms, +we derive properties. + +and we don't lock ourselves in +completely to some physical + +problem that we're +trying to solve. + +Because if we had locked +ourselves completely into a + +Poisson process, we wouldn't +even be able to look at this. + +We'd say, ah, that's nothing +to do with our problem. + +But it does. + +So wait. + +We're going to define +s1 as the minimum of + +U1 up to U sub n. + +In other words, these are +the order statistics of + +U1 up to U sub n. + +I choose U1 to be anything +between zero and t, U2 to be + +anything between zero and t. + +And then I choose s1 to be the +smaller of those two and s2 to + +be the larger of those two. + +This is zero to t. + +And here is say, U1. + +And here is U2. + +And then I transfer and call +this s1 and this s2. + +And if I have a U3 out here then +this becomes s2 and this + +becomes s3. + +So the order statistics are +just, you take these + +arrivals and you-- + +well, they don't have +to be arrivals. + +They're whatever they are. + +They're just uniform +random variables. + +And I just order them. + +So now my question is, the +region of volume t to the n, + +name I have a volume t to the n, +for the possible values of + +U1 up to U sub n. + +That volume where the density of +Un is non-zero, I can think + +of it as being partitioned +into n factorial regions. + +First region is U1 less +than U2, and so + +forth up to U sub n. + +The second one is U2 is less +than U1, less than U3 + +and so forth up. + +And for every permutation of +U1 to U sub n, I get a + +different ordering here. + +I don't even care about +the ordering anymore. + +All I care about is that the +number of permutations of U1 + +to U sub n-- + +or the integers one +to n, really is + +what I'm talking about. + +Number of permutations of +1 to n is n factorial. + +And for each one of those +permutations, I can talk about + +the region in which the first +permutation is less than the + +second permutation less than +the third and so forth. + +Those are disjoint-- + +they have to be the same +volume by symmetry. + +Now how does that symmetry +argument work there? + +I have n integers. + +There's no way to tell the +difference between them, + +except by giving them names. + +And each of them corresponds +to a IID random variable. + +And now, what I'm saying is that +the region which U1 is + +less than U2 has the same area +as the region where U2 + +is less than U1. + +And the argument is whatever you +want to do with U1 and U2 + +to find the area of that, I +can take your argument and + +every time you've written a U1, +I'll substitute U2 for it. + +And every time you've +written a U2 I'll + +substitute U1 for it. + +And it's the same argument. + +So that if you find the area +using your permutation, I get + +the same area just using +your argument again. + +And I can do this for as many +terms as I want to. + +OK, so this says that from +symmetry each volume is the + +same and thus, each volume +is t to the N + +divided by N factorial. + +Now the region where s sub N is +non-zero, s sub N are these + +ordering statistics. + +These are the terms in which you +wanted less than U2 less + +than U sub n after +I reordered them. + +The volume of the region where +S1 is less than S2 less than + +Sn less than or equal to t, the +region of that volume is + +exactly t to the N divided +by N factorial. + +Because it's one over +N factorial + +of the entire region. + +Now, you just have to think +about that symmetry argument + +for a while. + +The other thing you can do is +just integrate, which is what + +we did when we were deriving +the airline distribution. + +I mean, you just integrate +the thing out. + +And you find out that +that N factorial + +magically appears there. + +I think you get a better idea +of what's going on here. + +Let me go on to this slide, +which will explain a little + +bit what's going on here. + +Suppose I'm looking +at S1 and S2. + +The area where S1 is less +than S2 is this cross + +hatched area here. + +All the points in here +are points where S2 + +is bigger than S1. + +As advertised, the region where +S2 is bigger than S1 has + +the same area as the region +where S2 is less than S1. + +And all I'm saying is this same +property happens for N + +equals 3, N equals +4, and so forth. + +And the argument there really +is a symmetry argument. + +OK, I don't want to worry +about what the + +x's are at this point. + +I'm just showing you that a +little tiny area volume there + +has to be part of +this triangle. + +And I get that factor +of 2 because as S2 + +is bigger than S1. + +Let me give you an example of +using the ordering statistics, + +which we just talked about. + +Namely, looking at N IID random +variables, and then + +choosing S1 to be the smallest, +S2 to be the next + +smallest and so forth. + +What we've seen is that this S1 +to S sub N is identically + +distributed to the problem of +the epochs of arrivals in a + +Poisson process conditional on +N arrivals up until time t. + +So we can use either the uniform +distribution and + +ordering or we can use +Poisson results. + +Either one can give us results +about either process. + +Here what I'm going to do is use +order statistics to find + +the distribution function of S1 +conditional on N arrivals + +until time N. Conditional in +the fact that I found 1,000 + +arrivals up until time 1,000. + +I want to find the distribution +function of when + +the first arrival occurs. + +Now, if I know that 1,000 +arrivals have occurred by time + +1,000, the first arrival is +probably going to be pretty + +close to a Poisson +random variable. + +But I'd like to see that. + +OK, so the probability that +the minimum of these U sub + +i's, these uniform random +variables, is bigger than S1 + +is the product of the +probabilities that each one is + +bigger than S1. + +The only way that the minimum +can be bigger than S1 is that + +each of them are +bigger than S1. + +So this is the product from +I equals 1 to N of 1 + +minus S1 over t. + +Then we take the product of +things that are all the same. + +It's 1 minus S1 over t to the +N. And then I go into the + +domain of these arrival +epochs. + +And the probability that the +first arrival epoch, the + +complimentary distribution +function of that, is then 1 + +minus S1 over t to the N. + +You can also find the expected +value of S1 just by + +integrating this. + +Namely, integrate the +complimentary distribution + +function to get the +expected value. + +And what do you get? + +You get t over N plus 1. + +A little surprising, but +not as surprising + +as you would think. + +We're looking at an interval +from zero to t. + +We have three arrivals there. + +And then we're asking where +does the first one occur? + +And the argument is this +interval, this interval, this + +interval, and this interval +ought to have the same + +distribution. + +I mean, we haven't talked about +this interval yet, but + +it's there. + +I mean, the last of these +arrivals is not a t, it's + +somewhere before t. + +So I have n plus 1 +intervals on the + +side of these n arrivals. + +And what this is saying is the +nice symmetric result at the + +expected place where S1 winds +up is at t over n plus one. + +These intervals are in some +sense, at least as far as + +expectation is concerned, +are uniform. + +And we wind up with t over N +plus 1 as the expected value + +of where the first one is. + +That's nice and clean. + +If you look at this problem +and you think in terms of + +little tiny arrivals coming in +any place, and, in fact, you + +look at this U1 up to U +sub N, one arrival. + +I can think of it +as one arrival + +from each of N processes. + +And these are all Poisson +processes. + +They all add up to give a +joint Poisson process, a + +combined Poisson process, +with N arrivals. + +And then, I order the arrivals +to correspond to the overall + +sum process. + +And this is the answer I get. + +So the uniform idea is related +to adding up lots of little + +tiny processes. + +OK, now the next thing I want +to do, and I can see I'm not + +really going to get time to do +it, but I'd like to give you + +the results of it. + +If I look at a box, a little +cube, of area delta squared in + +the S1, S2 space. + +And I look at what that maps +in to, in terms of the + +interarrivals x1 and x2, if you +just map these points into + +this, you see that this square +here is going into a + +parallelepiped. + +And if know a little bit +of linear algebra-- + +well, you don't even need to +know any linear algebra to see + +that no matter where you put +this little square anywhere + +around here it's always going to +map into the same kind of a + +parallelepiped. + +So if I take this whole area and +I break it up into a grid, + +this area is going to be broken +up into a grid where + +it's things are going +down this way. + +And this way, we're going to +have a lot of these little + +tiny parallelepipeds. + +If I have uniform probability +density there, I'll have + +uniform probability +density there. + +The place where you need some +linear algebra, if you're + +dealing with n dimensions +instead of 2, is to see that + +the volume of this delta cube +here, for this problem here, + +is going to be identical +to the volume of + +the delta cube here. + +OK, so when you get all done +that, the area in the x1, x2 + +space where zero is less than x1 +plus x2 is less than t is t + +squared over 2 again. + +And the probability density +of these two interarrival + +intervals is again +2 over t squared. + +It's the same as the arrivals. + +I'm going to skip this slide. + +I want to get the one other +thing I wanted to talk about a + +little bit. + +There's a paradox. + +And the main interarrival time +for Poisson process is one + +over lambda. + +If I come at time t and I start +waiting for the next + +arrival, the mean time I have +to wait is 1 over lambda. + +If I come in and I start looking +back, at the last + +arrival, well, this says it's 1 +over lambda times 1 minus e + +to the minus lambda t, +which is what it is. + +We haven't derived that. + +But we know it's something. + +So, what's going on here? + +I come in at time t, the +interval between the last + +arrival and the next arrival, +the mean interval there is + +bigger than the mean interval +between arrivals + +in a Poisson process. + +That is a real paradox. + +And how do I explain that? + +It means that if I'm waiting for +buses, I'm always unlucky. + +And you're unlucky too and +we're all unlucky. + +Because whenever you arrive, the +amount of time between the + +last bus and the next bus is +bigger than it ought to be. + +And how do we explain that? + +Well, this sort of gives +you a really half-assed + +explanation of it. + +It's not very good. + +When we study renewals, we'll +find a good explanation of it. + +First choose a sample path +of a Poisson process. + +I mean, start out with +a sample path. + +And that has arrivals +going along. + +And we want to get rid of zero +because funny things happen + +around zero. + +So we'll start at one eon +and stop at n eons. + +And we'll look over +that interval. + +And then we'll choose t to be +a random variable in this + +interval here. + +OK, so, we choose some +t after we've looked + +at the sample path. + +And then we say for this random +value of t, how big is + +the interval between the +most recent arrival + +and the next arrival. + +And what you see is that since +I have these arrivals of a + +Poisson process laid out here, +the large intervals take up + +proportionally more area than +the little intervals. + +If I have a bunch of little tiny +intervals and some big + +intervals and then I choose a +random t along here, I'm much + +more likely to choose a t in +here, proportionally, than I + +am to choose a t in here. + +This mean time between the +arrivals is the average of + +this, this, this, +this, and this. + +And what I'm looking at here +is I picked some arbitrary + +point in time. + +These arbitrary points in time +are likely to lie in very + +large intervals. + +Yes? + +AUDIENCE: Can you please explain +again what is exactly + +is the paradox? + +PROFESSOR: The paradox is that +the mean time between arrival + +is one over lambda. + +But if I arrive to look for a +bus and the buses are Poisson, + +I arrive in an interval whose +mean length is larger than 1 + +over lambda. + +And that seems strange to me. + +Well, I think I'll stop here. + +And maybe we will spend just +a little time sorting + +this out next time. \ No newline at end of file diff --git a/dCJEeSD7hKk.txt b/dCJEeSD7hKk.txt new file mode 100644 index 0000000000000000000000000000000000000000..a3875cbc2a916dd3b038bf6336c60aba952e93e7 --- /dev/null +++ b/dCJEeSD7hKk.txt @@ -0,0 +1,9323 @@ +align:start position:0% + +okay so let me let me continue with the + + align:start position:0% +okay so let me let me continue with the + + + align:start position:0% +okay so let me let me continue with the +the topic of the previous lecture which + + align:start position:0% +the topic of the previous lecture which + + + align:start position:0% +the topic of the previous lecture which +is asset pricing and we said the the + + align:start position:0% +is asset pricing and we said the the + + + align:start position:0% +is asset pricing and we said the the +tricky thing with asset pricing is that + + align:start position:0% +tricky thing with asset pricing is that + + + align:start position:0% +tricky thing with asset pricing is that +the payoff of having an asset comes in + + align:start position:0% +the payoff of having an asset comes in + + + align:start position:0% +the payoff of having an asset comes in +the future and that that that + + align:start position:0% +the future and that that that + + + align:start position:0% +the future and that that that +implies at least two things the first + + align:start position:0% +implies at least two things the first + + + align:start position:0% +implies at least two things the first +one is that we need to have a method to + + align:start position:0% +one is that we need to have a method to + + + align:start position:0% +one is that we need to have a method to +Value returns in the future as of today + + align:start position:0% +Value returns in the future as of today + + + align:start position:0% +Value returns in the future as of today +okay so what is equivalent to after all + + align:start position:0% +okay so what is equivalent to after all + + + align:start position:0% +okay so what is equivalent to after all +if you want to buy a financial asset you + + align:start position:0% +if you want to buy a financial asset you + + + align:start position:0% +if you want to buy a financial asset you +need to pay for it today with dollars of + + align:start position:0% +need to pay for it today with dollars of + + + align:start position:0% +need to pay for it today with dollars of +today and you are expected to receive + + align:start position:0% +today and you are expected to receive + + + align:start position:0% +today and you are expected to receive +some payoff in the future you need to be + + align:start position:0% +some payoff in the future you need to be + + + align:start position:0% +some payoff in the future you need to be +able to compare these two things and the + + align:start position:0% +able to compare these two things and the + + + align:start position:0% +able to compare these two things and the +second is that is related is that + + align:start position:0% +second is that is related is that + + + align:start position:0% +second is that is related is that +because this payoff is in the future you + + align:start position:0% +because this payoff is in the future you + + + align:start position:0% +because this payoff is in the future you +need to have expectations about it okay + + align:start position:0% +need to have expectations about it okay + + + align:start position:0% +need to have expectations about it okay +so those are the two concepts we play + + align:start position:0% +so those are the two concepts we play + + + align:start position:0% +so those are the two concepts we play +with um and and uh and and there's a + + align:start position:0% +with um and and uh and and there's a + + + align:start position:0% +with um and and uh and and there's a +third related concept which is because + + align:start position:0% +third related concept which is because + + + align:start position:0% +third related concept which is because +it comes in the future many things can + + align:start position:0% +it comes in the future many things can + + + align:start position:0% +it comes in the future many things can +happen in between and so there's also a + + align:start position:0% +happen in between and so there's also a + + + align:start position:0% +happen in between and so there's also a +concept of risk okay those are the three + + align:start position:0% +concept of risk okay those are the three + + + align:start position:0% +concept of risk okay those are the three +elements we discuss and uh remember what + + align:start position:0% +elements we discuss and uh remember what + + + align:start position:0% +elements we discuss and uh remember what +we did I'm going to go very quickly over + + align:start position:0% +we did I'm going to go very quickly over + + + align:start position:0% +we did I'm going to go very quickly over +what we did in the previous lecture + + align:start position:0% +what we did in the previous lecture + + + align:start position:0% +what we did in the previous lecture +because I could see some phes H so so + + align:start position:0% +because I could see some phes H so so + + + align:start position:0% +because I could see some phes H so so +let me go quickly over that and then + + align:start position:0% +let me go quickly over that and then + + + align:start position:0% +let me go quickly over that and then +then continue with equity which was the + + align:start position:0% +then continue with equity which was the + + + align:start position:0% +then continue with equity which was the +next step + + align:start position:0% +next step + + + align:start position:0% +next step +um so the first step was says okay + + align:start position:0% +um so the first step was says okay + + + align:start position:0% +um so the first step was says okay +ignore the expectations part for now and + + align:start position:0% +ignore the expectations part for now and + + + align:start position:0% +ignore the expectations part for now and +risk and so on assume that you know the + + align:start position:0% +risk and so on assume that you know the + + + align:start position:0% +risk and so on assume that you know the +future and we ask the question H well + + align:start position:0% +future and we ask the question H well + + + align:start position:0% +future and we ask the question H well +how do we value a dollar next year ER in + + align:start position:0% +how do we value a dollar next year ER in + + + align:start position:0% +how do we value a dollar next year ER in +particular do one the question is it + + align:start position:0% +particular do one the question is it + + + align:start position:0% +particular do one the question is it +equivalent to having a dollar today and + + align:start position:0% +equivalent to having a dollar today and + + + align:start position:0% +equivalent to having a dollar today and +the answer quickly became no because + + align:start position:0% +the answer quickly became no because + + + align:start position:0% +the answer quickly became no because +imagine that you had the dollar today + + align:start position:0% +imagine that you had the dollar today + + + align:start position:0% +imagine that you had the dollar today +then you can invest it for a year and + + align:start position:0% +then you can invest it for a year and + + + align:start position:0% +then you can invest it for a year and +you get the return of the the onee + + align:start position:0% +you get the return of the the onee + + + align:start position:0% +you get the return of the the onee +interest rate return so with $1 today + + align:start position:0% +interest rate return so with $1 today + + + align:start position:0% +interest rate return so with $1 today +you can do more than with $1 in the + + align:start position:0% +you can do more than with $1 in the + + + align:start position:0% +you can do more than with $1 in the +future in fact that + + align:start position:0% +future in fact that + + + align:start position:0% +future in fact that +calculation give us the exact recipe to + + align:start position:0% +calculation give us the exact recipe to + + + align:start position:0% +calculation give us the exact recipe to +valuing a a dollar in the future because + + align:start position:0% +valuing a a dollar in the future because + + + align:start position:0% +valuing a a dollar in the future because +in order to get a dollar in the future I + + align:start position:0% +in order to get a dollar in the future I + + + align:start position:0% +in order to get a dollar in the future I +don't need a dollar today I need one + + align:start position:0% +don't need a dollar today I need one + + + align:start position:0% +don't need a dollar today I need one +over one plus the interest rate H I + + align:start position:0% +over one plus the interest rate H I + + + align:start position:0% +over one plus the interest rate H I +invest this in in the onee bond H and + + align:start position:0% +invest this in in the onee bond H and + + + align:start position:0% +invest this in in the onee bond H and +and I get a return of that over that + + align:start position:0% +and I get a return of that over that + + + align:start position:0% +and I get a return of that over that +amount that gives me exactly a dollar in + + align:start position:0% +amount that gives me exactly a dollar in + + + align:start position:0% +amount that gives me exactly a dollar in +the future okay so that giv us a very + + align:start position:0% +the future okay so that giv us a very + + + align:start position:0% +the future okay so that giv us a very +natural way of valuing a dollar next + + align:start position:0% +natural way of valuing a dollar next + + + align:start position:0% +natural way of valuing a dollar next +year it's just one over one plus the + + align:start position:0% +year it's just one over one plus the + + + align:start position:0% +year it's just one over one plus the +interest rate and by the same logic if I + + align:start position:0% +interest rate and by the same logic if I + + + align:start position:0% +interest rate and by the same logic if I +have a dollar today and I want to invest + + align:start position:0% +have a dollar today and I want to invest + + + align:start position:0% +have a dollar today and I want to invest +it for two years well I'm going to earn + + align:start position:0% +it for two years well I'm going to earn + + + align:start position:0% +it for two years well I'm going to earn +that interest rate for the first year + + align:start position:0% +that interest rate for the first year + + + align:start position:0% +that interest rate for the first year +and then I'm going to learn that earn + + align:start position:0% +and then I'm going to learn that earn + + + align:start position:0% +and then I'm going to learn that earn +that interest rate on the full product + + align:start position:0% +that interest rate on the full product + + + align:start position:0% +that interest rate on the full product +not not on the original Dollar in the + + align:start position:0% +not not on the original Dollar in the + + + align:start position:0% +not not on the original Dollar in the +one on the one plus it dollar I'm going + + align:start position:0% +one on the one plus it dollar I'm going + + + align:start position:0% +one on the one plus it dollar I'm going +to earn one plus it+ one and and and so + + align:start position:0% +to earn one plus it+ one and and and so + + + align:start position:0% +to earn one plus it+ one and and and so +I can generate sort of a lot of you know + + align:start position:0% +I can generate sort of a lot of you know + + + align:start position:0% +I can generate sort of a lot of you know +the interest rate is 10% on average a + + align:start position:0% +the interest rate is 10% on average a + + + align:start position:0% +the interest rate is 10% on average a +dollar today generates + + align:start position:0% +dollar today generates + + + align:start position:0% +dollar today generates +1.21 dollar two years from now so that + + align:start position:0% +1.21 dollar two years from now so that + + + align:start position:0% +1.21 dollar two years from now so that +tells you by the same logic that one + + align:start position:0% +tells you by the same logic that one + + + align:start position:0% +tells you by the same logic that one +over + + align:start position:0% + + + + align:start position:0% + +$1.21 today is equivalent to $1 in the + + align:start position:0% +$1.21 today is equivalent to $1 in the + + + align:start position:0% +$1.21 today is equivalent to $1 in the +Future Okay so then we said let's pick a + + align:start position:0% +Future Okay so then we said let's pick a + + + align:start position:0% +Future Okay so then we said let's pick a +very general asset an asset that has you + + align:start position:0% +very general asset an asset that has you + + + align:start position:0% +very general asset an asset that has you +know that pays ZT + + align:start position:0% +know that pays ZT + + + align:start position:0% +know that pays ZT +doll this year then ZT plus $1 uh one + + align:start position:0% +doll this year then ZT plus $1 uh one + + + align:start position:0% +doll this year then ZT plus $1 uh one +year from now ZT plus $2 two years from + + align:start position:0% +year from now ZT plus $2 two years from + + + align:start position:0% +year from now ZT plus $2 two years from +now and so on so forth up to n years + + align:start position:0% +now and so on so forth up to n years + + + align:start position:0% +now and so on so forth up to n years +ahead uh well what is the value of that + + align:start position:0% +ahead uh well what is the value of that + + + align:start position:0% +ahead uh well what is the value of that +asset today well you apply exactly the + + align:start position:0% +asset today well you apply exactly the + + + align:start position:0% +asset today well you apply exactly the +same logic that we apply here for every + + align:start position:0% +same logic that we apply here for every + + + align:start position:0% +same logic that we apply here for every +single uh year in the future and you get + + align:start position:0% +single uh year in the future and you get + + + align:start position:0% +single uh year in the future and you get +that's that's the the and that's called + + align:start position:0% +that's that's the the and that's called + + + align:start position:0% +that's that's the the and that's called +the present present discounted value h + + align:start position:0% +the present present discounted value h + + + align:start position:0% +the present present discounted value h +of those cash flows that gives you the + + align:start position:0% +of those cash flows that gives you the + + + align:start position:0% +of those cash flows that gives you the +value today okay present discounted + + align:start position:0% +value today okay present discounted + + + align:start position:0% +value today okay present discounted +those are the discount factors one over + + align:start position:0% +those are the discount factors one over + + + align:start position:0% +those are the discount factors one over +and then that's the value that you get + + align:start position:0% +and then that's the value that you get + + + align:start position:0% +and then that's the value that you get +out of that so that asset has that + + align:start position:0% +out of that so that asset has that + + + align:start position:0% +out of that so that asset has that +present discounted value of H future + + align:start position:0% +present discounted value of H future + + + align:start position:0% +present discounted value of H future +cash flows and uh and uh that should be + + align:start position:0% +cash flows and uh and uh that should be + + + align:start position:0% +cash flows and uh and uh that should be +more or less the price that you are + + align:start position:0% +more or less the price that you are + + + align:start position:0% +more or less the price that you are +willing to pay for that asset okay + + align:start position:0% +willing to pay for that asset okay + + + align:start position:0% +willing to pay for that asset okay +ER and then we introduce expectations + + align:start position:0% +ER and then we introduce expectations + + + align:start position:0% +ER and then we introduce expectations +okay well but we're talking about cash + + align:start position:0% +okay well but we're talking about cash + + + align:start position:0% +okay well but we're talking about cash +flows in the future in many cases we + + align:start position:0% +flows in the future in many cases we + + + align:start position:0% +flows in the future in many cases we +don't know well we don't know two things + + align:start position:0% +don't know well we don't know two things + + + align:start position:0% +don't know well we don't know two things +first we don't know what the cash flows + + align:start position:0% +first we don't know what the cash flows + + + align:start position:0% +first we don't know what the cash flows +may be in a very safe Bond you do know + + align:start position:0% +may be in a very safe Bond you do know + + + align:start position:0% +may be in a very safe Bond you do know +the cash flow but but but almost any + + align:start position:0% +the cash flow but but but almost any + + + align:start position:0% +the cash flow but but but almost any +other asset you don't know exactly the + + align:start position:0% +other asset you don't know exactly the + + + align:start position:0% +other asset you don't know exactly the +cash flows you receive and you don't + + align:start position:0% +cash flows you receive and you don't + + + align:start position:0% +cash flows you receive and you don't +know what the future interest rate one + + align:start position:0% +know what the future interest rate one + + + align:start position:0% +know what the future interest rate one +year interest rate will be okay so that + + align:start position:0% +year interest rate will be okay so that + + + align:start position:0% +year interest rate will be okay so that +took us to the concept of expected + + align:start position:0% +took us to the concept of expected + + + align:start position:0% +took us to the concept of expected +present discounted value in which you + + align:start position:0% +present discounted value in which you + + + align:start position:0% +present discounted value in which you +just replace all the things we don't + + align:start position:0% +just replace all the things we don't + + + align:start position:0% +just replace all the things we don't +know today for the expectations of those + + align:start position:0% +know today for the expectations of those + + + align:start position:0% +know today for the expectations of those +things okay so we don't know the cash + + align:start position:0% +things okay so we don't know the cash + + + align:start position:0% +things okay so we don't know the cash +flows in the future that's a reason but + + align:start position:0% +flows in the future that's a reason but + + + align:start position:0% +flows in the future that's a reason but +we have an expectation that's that's + + align:start position:0% +we have an expectation that's that's + + + align:start position:0% +we have an expectation that's that's +what we put there and uh we don't know + + align:start position:0% +what we put there and uh we don't know + + + align:start position:0% +what we put there and uh we don't know +the future we know the current interest + + align:start position:0% +the future we know the current interest + + + align:start position:0% +the future we know the current interest +rate but we don't know the future one + + align:start position:0% +rate but we don't know the future one + + + align:start position:0% +rate but we don't know the future one +year interest rate two-year interest + + align:start position:0% +year interest rate two-year interest + + + align:start position:0% +year interest rate two-year interest +rate NY year interest rate and so on so + + align:start position:0% +rate NY year interest rate and so on so + + + align:start position:0% +rate NY year interest rate and so on so +we put an expectation there okay so + + align:start position:0% +we put an expectation there okay so + + + align:start position:0% +we put an expectation there okay so +that's that's + + align:start position:0% +that's that's + + + align:start position:0% +that's that's +that and then I gave you some special + + align:start position:0% +that and then I gave you some special + + + align:start position:0% +that and then I gave you some special +cases that's a case in which the the + + align:start position:0% +cases that's a case in which the the + + + align:start position:0% +cases that's a case in which the the +interest rate is constant that's a case + + align:start position:0% +interest rate is constant that's a case + + + align:start position:0% +interest rate is constant that's a case +in which the the payoff in the future + + align:start position:0% +in which the the payoff in the future + + + align:start position:0% +in which the the payoff in the future +the + + align:start position:0% +the + + + align:start position:0% +the +coupons the are + + align:start position:0% +coupons the are + + + align:start position:0% +coupons the are +constant um that's a case in which both + + align:start position:0% +constant um that's a case in which both + + + align:start position:0% +constant um that's a case in which both +are constant the interest rate and H the + + align:start position:0% +are constant the interest rate and H the + + + align:start position:0% +are constant the interest rate and H the +payoffs in the future and for a bond for + + align:start position:0% +payoffs in the future and for a bond for + + + align:start position:0% +payoffs in the future and for a bond for +a for an inst a financial asset that + + align:start position:0% +a for an inst a financial asset that + + + align:start position:0% +a for an inst a financial asset that +lasts for n years that matures in in in + + align:start position:0% +lasts for n years that matures in in in + + + align:start position:0% +lasts for n years that matures in in in +years that's a case in which an asset + + align:start position:0% +years that's a case in which an asset + + + align:start position:0% +years that's a case in which an asset +that does not mature that goes on + + align:start position:0% +that does not mature that goes on + + + align:start position:0% +that does not mature that goes on +forever under these conditions and then + + align:start position:0% +forever under these conditions and then + + + align:start position:0% +forever under these conditions and then +I said well suppose that we look at the + + align:start position:0% +I said well suppose that we look at the + + + align:start position:0% +I said well suppose that we look at the +X dividend price that means after this + + align:start position:0% +X dividend price that means after this + + + align:start position:0% +X dividend price that means after this +year's dividend to this year payment + + align:start position:0% +year's dividend to this year payment + + + align:start position:0% +year's dividend to this year payment +then that's the value and I made the + + align:start position:0% +then that's the value and I made the + + + align:start position:0% +then that's the value and I made the +point there that that shows immediately + + align:start position:0% +point there that that shows immediately + + + align:start position:0% +point there that that shows immediately +something that will be present in almost + + align:start position:0% +something that will be present in almost + + + align:start position:0% +something that will be present in almost +any asset price which is as interest + + align:start position:0% +any asset price which is as interest + + + align:start position:0% +any asset price which is as interest +rate go down asset values tend to go up + + align:start position:0% +rate go down asset values tend to go up + + + align:start position:0% +rate go down asset values tend to go up +okay and the reason for that is because + + align:start position:0% +okay and the reason for that is because + + + align:start position:0% +okay and the reason for that is because +assets pay something in the future and + + align:start position:0% +assets pay something in the future and + + + align:start position:0% +assets pay something in the future and +if the interest rate Falls then you + + align:start position:0% +if the interest rate Falls then you + + + align:start position:0% +if the interest rate Falls then you +discount less the future so whatever + + align:start position:0% +discount less the future so whatever + + + align:start position:0% +discount less the future so whatever +you're going to receive is valued more + + align:start position:0% +you're going to receive is valued more + + + align:start position:0% +you're going to receive is valued more +because you discount less the Future + + align:start position:0% +because you discount less the Future + + + align:start position:0% +because you discount less the Future +Okay so that's that's effect in fact in + + align:start position:0% +Okay so that's that's effect in fact in + + + align:start position:0% +Okay so that's that's effect in fact in +this particular case if the interest + + align:start position:0% +this particular case if the interest + + + align:start position:0% +this particular case if the interest +rate goes to zero the value of that goes + + align:start position:0% +rate goes to zero the value of that goes + + + align:start position:0% +rate goes to zero the value of that goes +to Infinity because you you don't + + align:start position:0% +to Infinity because you you don't + + + align:start position:0% +to Infinity because you you don't +discount the future and you're going to + + align:start position:0% +discount the future and you're going to + + + align:start position:0% +discount the future and you're going to +receive infinite payments in the future + + align:start position:0% + + + + align:start position:0% + +okay uh then we look at specific + + align:start position:0% +okay uh then we look at specific + + + align:start position:0% +okay uh then we look at specific +Financial assets and we first look at + + align:start position:0% +Financial assets and we first look at + + + align:start position:0% +Financial assets and we first look at +the bonds okay H and we said one + + align:start position:0% +the bonds okay H and we said one + + + align:start position:0% +the bonds okay H and we said one +important distinction uh something + + align:start position:0% +important distinction uh something + + + align:start position:0% +important distinction uh something +whenever you buy a bond one of the + + align:start position:0% +whenever you buy a bond one of the + + + align:start position:0% +whenever you buy a bond one of the +things you want to know is the maturity + + align:start position:0% +things you want to know is the maturity + + + align:start position:0% +things you want to know is the maturity +of that bone this is a one-year bone a + + align:start position:0% +of that bone this is a one-year bone a + + + align:start position:0% +of that bone this is a one-year bone a +two-year bone five 10 30 those are sort + + align:start position:0% +two-year bone five 10 30 those are sort + + + align:start position:0% +two-year bone five 10 30 those are sort +of the typical US Treasury bones at + + align:start position:0% +of the typical US Treasury bones at + + + align:start position:0% +of the typical US Treasury bones at +least you want to know the maturity of + + align:start position:0% +least you want to know the maturity of + + + align:start position:0% +least you want to know the maturity of +the bone um so then we went into pricing + + align:start position:0% +the bone um so then we went into pricing + + + align:start position:0% +the bone um so then we went into pricing +a a different bonds we say well a bond + + align:start position:0% +a a different bonds we say well a bond + + + align:start position:0% +a a different bonds we say well a bond +the simplest bond is a bond is a + + align:start position:0% +the simplest bond is a bond is a + + + align:start position:0% +the simplest bond is a bond is a +one-year Bond that's suppose we have a + + align:start position:0% +one-year Bond that's suppose we have a + + + align:start position:0% +one-year Bond that's suppose we have a +bond that pays $100 uh at the end of the + + align:start position:0% +bond that pays $100 uh at the end of the + + + align:start position:0% +bond that pays $100 uh at the end of the +year and then + + align:start position:0% +year and then + + + align:start position:0% +year and then +it matures H well the price of that Bond + + align:start position:0% +it matures H well the price of that Bond + + + align:start position:0% +it matures H well the price of that Bond +should be the present discounted value + + align:start position:0% +should be the present discounted value + + + align:start position:0% +should be the present discounted value +of the flows of that bond which is 100 + + align:start position:0% +of the flows of that bond which is 100 + + + align:start position:0% +of the flows of that bond which is 100 +divided by one plus the one year + + align:start position:0% +divided by one plus the one year + + + align:start position:0% +divided by one plus the one year +interest rate at time t + + align:start position:0% +interest rate at time t + + + align:start position:0% +interest rate at time t +Okay ER and and I I notice again here + + align:start position:0% +Okay ER and and I I notice again here + + + align:start position:0% +Okay ER and and I I notice again here +but the same logic of what I explained + + align:start position:0% +but the same logic of what I explained + + + align:start position:0% +but the same logic of what I explained +before is that if the interest rate go + + align:start position:0% +before is that if the interest rate go + + + align:start position:0% +before is that if the interest rate go +one year interest rate goes up the price + + align:start position:0% +one year interest rate goes up the price + + + align:start position:0% +one year interest rate goes up the price +of that Bond will decline okay because + + align:start position:0% +of that Bond will decline okay because + + + align:start position:0% +of that Bond will decline okay because +that Bond pays you one year from now and + + align:start position:0% +that Bond pays you one year from now and + + + align:start position:0% +that Bond pays you one year from now and +one year from now when the interest rate + + align:start position:0% +one year from now when the interest rate + + + align:start position:0% +one year from now when the interest rate +is higher it's worth a little less than + + align:start position:0% +is higher it's worth a little less than + + + align:start position:0% +is higher it's worth a little less than +it was when the interest rate was a + + align:start position:0% +it was when the interest rate was a + + + align:start position:0% +it was when the interest rate was a +little lower + + align:start position:0% +little lower + + + align:start position:0% +little lower +okay okay and then we look at a two-year + + align:start position:0% +okay okay and then we look at a two-year + + + align:start position:0% +okay okay and then we look at a two-year +bone a bone that pays nothing up to two + + align:start position:0% +bone a bone that pays nothing up to two + + + align:start position:0% +bone a bone that pays nothing up to two +years from now and we said well two + + align:start position:0% +years from now and we said well two + + + align:start position:0% +years from now and we said well two +years from now pays 100 and then matures + + align:start position:0% +years from now pays 100 and then matures + + + align:start position:0% +years from now pays 100 and then matures +well the price of that Bond will be you + + align:start position:0% +well the price of that Bond will be you + + + align:start position:0% +well the price of that Bond will be you +know this okay and notice that in this + + align:start position:0% +know this okay and notice that in this + + + align:start position:0% +know this okay and notice that in this +case the price of a two-year Bond at + + align:start position:0% +case the price of a two-year Bond at + + + align:start position:0% +case the price of a two-year Bond at +time T goes down if the either of the + + align:start position:0% +time T goes down if the either of the + + + align:start position:0% +time T goes down if the either of the +one year rates goes up okay it can be + + align:start position:0% +one year rates goes up okay it can be + + + align:start position:0% +one year rates goes up okay it can be +the first this year's onee rate or maybe + + align:start position:0% +the first this year's onee rate or maybe + + + align:start position:0% +the first this year's onee rate or maybe +the expectation that the onee + + align:start position:0% +the expectation that the onee + + + align:start position:0% +the expectation that the onee +rate next year will go up + + align:start position:0% +rate next year will go up + + + align:start position:0% +rate next year will go up +okay + + align:start position:0% +okay + + + align:start position:0% +okay +good then I introduce an important + + align:start position:0% +good then I introduce an important + + + align:start position:0% +good then I introduce an important +concept which is this concept of + + align:start position:0% +concept which is this concept of + + + align:start position:0% +concept which is this concept of +Arbitrage pricing okay which + + align:start position:0% +Arbitrage pricing okay which + + + align:start position:0% +Arbitrage pricing okay which +is two + + align:start position:0% +is two + + + align:start position:0% +is two +instruments er um should give you sort + + align:start position:0% +instruments er um should give you sort + + + align:start position:0% +instruments er um should give you sort +of the same interest rate we're leaving + + align:start position:0% +of the same interest rate we're leaving + + + align:start position:0% +of the same interest rate we're leaving +risk considerations aside should give + + align:start position:0% +risk considerations aside should give + + + align:start position:0% +risk considerations aside should give +you the same return + + align:start position:0% +you the same return + + + align:start position:0% +you the same return +when you compare them er + + align:start position:0% +when you compare them er + + + align:start position:0% +when you compare them er +um over the same maturity okay so in + + align:start position:0% +um over the same maturity okay so in + + + align:start position:0% +um over the same maturity okay so in +this particular example I said look a + + align:start position:0% +this particular example I said look a + + + align:start position:0% +this particular example I said look a +one-year Bond and a two-year bond that + + align:start position:0% +one-year Bond and a two-year bond that + + + align:start position:0% +one-year Bond and a two-year bond that +you invest you hold for only one year + + align:start position:0% +you invest you hold for only one year + + + align:start position:0% +you invest you hold for only one year +should give you more or less the same + + align:start position:0% +should give you more or less the same + + + align:start position:0% +should give you more or less the same +return okay so so so that + + align:start position:0% +return okay so so so that + + + align:start position:0% +return okay so so so that +means that this is the return you get + + align:start position:0% +means that this is the return you get + + + align:start position:0% +means that this is the return you get +from a dollar in invested in a one-year + + align:start position:0% +from a dollar in invested in a one-year + + + align:start position:0% +from a dollar in invested in a one-year +Bond okay should be equal to the return + + align:start position:0% +Bond okay should be equal to the return + + + align:start position:0% +Bond okay should be equal to the return +you get by investing in a in a 2-year + + align:start position:0% +you get by investing in a in a 2-year + + + align:start position:0% +you get by investing in a in a 2-year +Bond and selling that Bond after one + + align:start position:0% +Bond and selling that Bond after one + + + align:start position:0% +Bond and selling that Bond after one +year and that's expression we had here + + align:start position:0% +year and that's expression we had here + + + align:start position:0% +year and that's expression we had here +okay if you this is what you pay for a + + align:start position:0% +okay if you this is what you pay for a + + + align:start position:0% +okay if you this is what you pay for a +for a for a two-year Bond and this is + + align:start position:0% +for a for a two-year Bond and this is + + + align:start position:0% +for a for a two-year Bond and this is +what you expect a ER to to be paid for + + align:start position:0% +what you expect a ER to to be paid for + + + align:start position:0% +what you expect a ER to to be paid for +that Bond when you sell it one year from + + align:start position:0% +that Bond when you sell it one year from + + + align:start position:0% +that Bond when you sell it one year from +now notice that one year from now the + + align:start position:0% +now notice that one year from now the + + + align:start position:0% +now notice that one year from now the +2-year Bond B will be a one-year Bond + + align:start position:0% +2-year Bond B will be a one-year Bond + + + align:start position:0% +2-year Bond B will be a one-year Bond +because one year will have expired and + + align:start position:0% +because one year will have expired and + + + align:start position:0% +because one year will have expired and +at that point it will be a oneyear bond + + align:start position:0% +at that point it will be a oneyear bond + + + align:start position:0% +at that point it will be a oneyear bond +that's the reason we have a sub subscrip + + align:start position:0% +that's the reason we have a sub subscrip + + + align:start position:0% +that's the reason we have a sub subscrip +p1t here so that means that we can solve + + align:start position:0% +p1t here so that means that we can solve + + + align:start position:0% +p1t here so that means that we can solve +from here that p2t is simply that but + + align:start position:0% +from here that p2t is simply that but + + + align:start position:0% +from here that p2t is simply that but +there's an expression like the one we + + align:start position:0% +there's an expression like the one we + + + align:start position:0% +there's an expression like the one we +had for the onee bond at time T there is + + align:start position:0% +had for the onee bond at time T there is + + + align:start position:0% +had for the onee bond at time T there is +one for t+ one we put expectations + + align:start position:0% +one for t+ one we put expectations + + + align:start position:0% +one for t+ one we put expectations +because we don't know the actual + + align:start position:0% +because we don't know the actual + + + align:start position:0% +because we don't know the actual +interest rate in the + + align:start position:0% +interest rate in the + + + align:start position:0% +interest rate in the +future and then I stuck this into there + + align:start position:0% +future and then I stuck this into there + + + align:start position:0% +future and then I stuck this into there +and we got exactly the same price that + + align:start position:0% +and we got exactly the same price that + + + align:start position:0% +and we got exactly the same price that +we got with the net percent expected + + align:start position:0% +we got with the net percent expected + + + align:start position:0% +we got with the net percent expected +percent discounted value approach okay + + align:start position:0% +percent discounted value approach okay + + + align:start position:0% +percent discounted value approach okay +and so this as a pricing this Arbitrage + + align:start position:0% +and so this as a pricing this Arbitrage + + + align:start position:0% +and so this as a pricing this Arbitrage +way of pricing things is an incredibly + + align:start position:0% +way of pricing things is an incredibly + + + align:start position:0% +way of pricing things is an incredibly +powerful tool that is used very + + align:start position:0% +powerful tool that is used very + + + align:start position:0% +powerful tool that is used very +extensively in finance this these are + + align:start position:0% +extensively in finance this these are + + + align:start position:0% +extensively in finance this these are +simple calculation but when net gets to + + align:start position:0% +simple calculation but when net gets to + + + align:start position:0% +simple calculation but when net gets to +be tricky much more complicated H this + + align:start position:0% +be tricky much more complicated H this + + + align:start position:0% +be tricky much more complicated H this +is is very + + align:start position:0% +is is very + + + align:start position:0% +is is very +useful then we talk about bond yields + + align:start position:0% +useful then we talk about bond yields + + + align:start position:0% +useful then we talk about bond yields +and bond yields are defined + + align:start position:0% +and bond yields are defined + + + align:start position:0% +and bond yields are defined +as the constant interest + + align:start position:0% +as the constant interest + + + align:start position:0% +as the constant interest +rate that ER that is consistent with the + + align:start position:0% +rate that ER that is consistent with the + + + align:start position:0% +rate that ER that is consistent with the +current price of that particular Bond + + align:start position:0% +current price of that particular Bond + + + align:start position:0% +current price of that particular Bond +okay so in the case of the two-year Bond + + align:start position:0% +okay so in the case of the two-year Bond + + + align:start position:0% +okay so in the case of the two-year Bond +we call the two-year rate that interest + + align:start position:0% +we call the two-year rate that interest + + + align:start position:0% +we call the two-year rate that interest +rate that is constant over the two + + align:start position:0% +rate that is constant over the two + + + align:start position:0% +rate that is constant over the two +periods that's okay that's the reason I + + align:start position:0% +periods that's okay that's the reason I + + + align:start position:0% +periods that's okay that's the reason I +Square it it's not i1 t * 1 i1 t + 1 I + + align:start position:0% +Square it it's not i1 t * 1 i1 t + 1 I + + + align:start position:0% +Square it it's not i1 t * 1 i1 t + 1 I +Square it it's not constant over time + + align:start position:0% +Square it it's not constant over time + + + align:start position:0% +Square it it's not constant over time +this the twoyear interest rate may be + + align:start position:0% +this the twoyear interest rate may be + + + align:start position:0% +this the twoyear interest rate may be +moving a lot I mean the the FED just + + align:start position:0% +moving a lot I mean the the FED just + + + align:start position:0% +moving a lot I mean the the FED just +hiked by 25 basis points I'm sure all + + align:start position:0% +hiked by 25 basis points I'm sure all + + + align:start position:0% +hiked by 25 basis points I'm sure all +rates are moving at this moment so the + + align:start position:0% +rates are moving at this moment so the + + + align:start position:0% +rates are moving at this moment so the +rates can be moving at all points in + + align:start position:0% +rates can be moving at all points in + + + align:start position:0% +rates can be moving at all points in +time but the what we Define as the yield + + align:start position:0% +time but the what we Define as the yield + + + align:start position:0% +time but the what we Define as the yield +is at one point in time you tell me the + + align:start position:0% +is at one point in time you tell me the + + + align:start position:0% +is at one point in time you tell me the +price of the bond you tell me the payoff + + align:start position:0% +price of the bond you tell me the payoff + + + align:start position:0% +price of the bond you tell me the payoff +of the bond then what is the the the + + align:start position:0% +of the bond then what is the the the + + + align:start position:0% +of the bond then what is the the the +constant interest rate that makes this + + align:start position:0% +constant interest rate that makes this + + + align:start position:0% +constant interest rate that makes this +price this expression equal to the + + align:start position:0% +price this expression equal to the + + + align:start position:0% +price this expression equal to the +actual price that's the way we Define + + align:start position:0% +actual price that's the way we Define + + + align:start position:0% +actual price that's the way we Define +the twoe rate that's the twoe rate and + + align:start position:0% +the twoe rate that's the twoe rate and + + + align:start position:0% +the twoe rate that's the twoe rate and +if you had a bond that pays 100 n years + + align:start position:0% +if you had a bond that pays 100 n years + + + align:start position:0% +if you had a bond that pays 100 n years +from now then there would be a constant + + align:start position:0% +from now then there would be a constant + + + align:start position:0% +from now then there would be a constant +interest rate i n no that that gives you + + align:start position:0% +interest rate i n no that that gives you + + + align:start position:0% +interest rate i n no that that gives you +100 divided by 1 plus I + + align:start position:0% +100 divided by 1 plus I + + + align:start position:0% +100 divided by 1 plus I +NT uh to the N to the end power that + + align:start position:0% +NT uh to the N to the end power that + + + align:start position:0% +NT uh to the N to the end power that +will give you a a that when you said + + align:start position:0% +will give you a a that when you said + + + align:start position:0% +will give you a a that when you said +that equal to the price the actual price + + align:start position:0% +that equal to the price the actual price + + + align:start position:0% +that equal to the price the actual price +of the bone the one you get out of + + align:start position:0% +of the bone the one you get out of + + + align:start position:0% +of the bone the one you get out of +expected present discounted value or out + + align:start position:0% +expected present discounted value or out + + + align:start position:0% +expected present discounted value or out +of Arbitrage then you have found the + + align:start position:0% +of Arbitrage then you have found the + + + align:start position:0% +of Arbitrage then you have found the +yield or the yield to + + align:start position:0% +yield or the yield to + + + align:start position:0% +yield or the yield to +maturity you know we know what the we + + align:start position:0% +maturity you know we know what the we + + + align:start position:0% +maturity you know we know what the we +already got the price from the previous + + align:start position:0% +already got the price from the previous + + + align:start position:0% +already got the price from the previous +slide we know that the price of this + + align:start position:0% +slide we know that the price of this + + + align:start position:0% +slide we know that the price of this +bond is going to be 100 that's a + + align:start position:0% +bond is going to be 100 that's a + + + align:start position:0% +bond is going to be 100 that's a +two-year Bond divided by this product of + + align:start position:0% +two-year Bond divided by this product of + + + align:start position:0% +two-year Bond divided by this product of +one plus interest rate one year interest + + align:start position:0% +one plus interest rate one year interest + + + align:start position:0% +one plus interest rate one year interest +rate so this has to be equal to that + + align:start position:0% +rate so this has to be equal to that + + + align:start position:0% +rate so this has to be equal to that +that's the way actually you calculate + + align:start position:0% +that's the way actually you calculate + + + align:start position:0% +that's the way actually you calculate +the two-year yield H and numerators are + + align:start position:0% +the two-year yield H and numerators are + + + align:start position:0% +the two-year yield H and numerators are +the same that means the denominators + + align:start position:0% +the same that means the denominators + + + align:start position:0% +the same that means the denominators +have to be the same and this implies + + align:start position:0% +have to be the same and this implies + + + align:start position:0% +have to be the same and this implies +approximately that that the 2-year rate + + align:start position:0% +approximately that that the 2-year rate + + + align:start position:0% +approximately that that the 2-year rate +is a sort of average of the expected + + align:start position:0% +is a sort of average of the expected + + + align:start position:0% +is a sort of average of the expected +one-year rates okay so in this case the + + align:start position:0% +one-year rates okay so in this case the + + + align:start position:0% +one-year rates okay so in this case the +two-year rate is a sort of average of + + align:start position:0% +two-year rate is a sort of average of + + + align:start position:0% +two-year rate is a sort of average of +the one-ear rate that means that when + + align:start position:0% +the one-ear rate that means that when + + + align:start position:0% +the one-ear rate that means that when +the when you expect the interest rate to + + align:start position:0% +the when you expect the interest rate to + + + align:start position:0% +the when you expect the interest rate to +be the onee rate to be rising over time + + align:start position:0% +be the onee rate to be rising over time + + + align:start position:0% +be the onee rate to be rising over time +then the 2-year rate will be above the + + align:start position:0% +then the 2-year rate will be above the + + + align:start position:0% +then the 2-year rate will be above the +oneyear rate + + align:start position:0% +oneyear rate + + + align:start position:0% +oneyear rate +today that's when the curve is we say + + align:start position:0% +today that's when the curve is we say + + + align:start position:0% +today that's when the curve is we say +the curve the Y curve is steep remember + + align:start position:0% +the curve the Y curve is steep remember + + + align:start position:0% +the curve the Y curve is steep remember +I show you in + + align:start position:0% + + + + align:start position:0% + +there when the curve looks like that so + + align:start position:0% +there when the curve looks like that so + + + align:start position:0% +there when the curve looks like that so +steep means that the the the later the + + align:start position:0% +steep means that the the the later the + + + align:start position:0% +steep means that the the the later the +the two-year rate the threee well here + + align:start position:0% +the two-year rate the threee well here + + + align:start position:0% +the two-year rate the threee well here +in particular the threeyear rate is the + + align:start position:0% +in particular the threeyear rate is the + + + align:start position:0% +in particular the threeyear rate is the +two-year rate is higher than the one-ear + + align:start position:0% +two-year rate is higher than the one-ear + + + align:start position:0% +two-year rate is higher than the one-ear +rate the threeyear rate is higher than + + align:start position:0% +rate the threeyear rate is higher than + + + align:start position:0% +rate the threeyear rate is higher than +the twoyear rate and so on so forth that + + align:start position:0% +the twoyear rate and so on so forth that + + + align:start position:0% +the twoyear rate and so on so forth that +happens when when you expect the market + + align:start position:0% +happens when when you expect the market + + + align:start position:0% +happens when when you expect the market +expects the interest rate to be rising + + align:start position:0% +expects the interest rate to be rising + + + align:start position:0% +expects the interest rate to be rising +over time the onee rate to be rising + + align:start position:0% +over time the onee rate to be rising + + + align:start position:0% +over time the onee rate to be rising +okay because + + align:start position:0% +okay because + + + align:start position:0% +okay because +remember the 2-year rate is the average + + align:start position:0% +remember the 2-year rate is the average + + + align:start position:0% +remember the 2-year rate is the average +of the exist the current oneyear rate + + align:start position:0% +of the exist the current oneyear rate + + + align:start position:0% +of the exist the current oneyear rate +plus the expected one-ear rate one year + + align:start position:0% +plus the expected one-ear rate one year + + + align:start position:0% +plus the expected one-ear rate one year +from now for that average to be higher + + align:start position:0% +from now for that average to be higher + + + align:start position:0% +from now for that average to be higher +than the onee rate now it has to be the + + align:start position:0% +than the onee rate now it has to be the + + + align:start position:0% +than the onee rate now it has to be the +case that the one expected one year rate + + align:start position:0% +case that the one expected one year rate + + + align:start position:0% +case that the one expected one year rate +one year from now has to be higher than + + align:start position:0% +one year from now has to be higher than + + + align:start position:0% +one year from now has to be higher than +the current onee rate okay so that's + + align:start position:0% +the current onee rate okay so that's + + + align:start position:0% +the current onee rate okay so that's +what you tend to get er that's when you + + align:start position:0% +what you tend to get er that's when you + + + align:start position:0% +what you tend to get er that's when you +get an upward slope in termal structure + + align:start position:0% +get an upward slope in termal structure + + + align:start position:0% +get an upward slope in termal structure +and when you get a downward slope in + + align:start position:0% +and when you get a downward slope in + + + align:start position:0% +and when you get a downward slope in +termal structure which is the way it + + align:start position:0% +termal structure which is the way it + + + align:start position:0% +termal structure which is the way it +looks right now actually right now looks + + align:start position:0% +looks right now actually right now looks + + + align:start position:0% +looks right now actually right now looks +very downward sloping there you are you + + align:start position:0% +very downward sloping there you are you + + + align:start position:0% +very downward sloping there you are you +know it looks very downward sloping is + + align:start position:0% +know it looks very downward sloping is + + + align:start position:0% +know it looks very downward sloping is +people expect that we're getting to the + + align:start position:0% +people expect that we're getting to the + + + align:start position:0% +people expect that we're getting to the +peak of current policy rate of shortterm + + align:start position:0% +peak of current policy rate of shortterm + + + align:start position:0% +peak of current policy rate of shortterm +interest rate and so people expect now + + align:start position:0% +interest rate and so people expect now + + + align:start position:0% +interest rate and so people expect now +for the interest rate to decline going + + align:start position:0% +for the interest rate to decline going + + + align:start position:0% +for the interest rate to decline going +forward and that's the reason the the + + align:start position:0% +forward and that's the reason the the + + + align:start position:0% +forward and that's the reason the the +the two-year rate now is lower than the + + align:start position:0% +the two-year rate now is lower than the + + + align:start position:0% +the two-year rate now is lower than the +onee + + align:start position:0% +onee + + + align:start position:0% +onee +rate and the fiveyear rate is lower than + + align:start position:0% +rate and the fiveyear rate is lower than + + + align:start position:0% +rate and the fiveyear rate is lower than +the two-year rate and so on + + align:start position:0% + + + + align:start position:0% + +as you can see here it's very + + align:start position:0% +as you can see here it's very + + + align:start position:0% +as you can see here it's very +steep okay then we said well let's add + + align:start position:0% +steep okay then we said well let's add + + + align:start position:0% +steep okay then we said well let's add +risk because yeah sure here we assume + + align:start position:0% +risk because yeah sure here we assume + + + align:start position:0% +risk because yeah sure here we assume +that you were in different between + + align:start position:0% +that you were in different between + + + align:start position:0% +that you were in different between +investing in a completely safe one-year + + align:start position:0% +investing in a completely safe one-year + + + align:start position:0% +investing in a completely safe one-year +Bond and a and a two-year bond in which + + align:start position:0% +Bond and a and a two-year bond in which + + + align:start position:0% +Bond and a and a two-year bond in which +you had to make an expectation about the + + align:start position:0% +you had to make an expectation about the + + + align:start position:0% +you had to make an expectation about the +price but that price could move around + + align:start position:0% +price but that price could move around + + + align:start position:0% +price but that price could move around +so there's risk on that price or the on + + align:start position:0% +so there's risk on that price or the on + + + align:start position:0% +so there's risk on that price or the on +the price of one + + align:start position:0% +the price of one + + + align:start position:0% +the price of one +year the one year born uh as of + + align:start position:0% +year the one year born uh as of + + + align:start position:0% +year the one year born uh as of +today and um and + + align:start position:0% +today and um and + + + align:start position:0% +today and um and +so so we added a risk and there are two + + align:start position:0% +so so we added a risk and there are two + + + align:start position:0% +so so we added a risk and there are two +type of risk in bonds one is default + + align:start position:0% +type of risk in bonds one is default + + + align:start position:0% +type of risk in bonds one is default +risk that you know that that they had + + align:start position:0% +risk that you know that that they had + + + align:start position:0% +risk that you know that that they had +promised that they would pay you a 100 + + align:start position:0% +promised that they would pay you a 100 + + + align:start position:0% +promised that they would pay you a 100 +but it may they it may happen that they + + align:start position:0% +but it may they it may happen that they + + + align:start position:0% +but it may they it may happen that they +cannot pay you the 100 the corporation + + align:start position:0% +cannot pay you the 100 the corporation + + + align:start position:0% +cannot pay you the 100 the corporation +or the government or so on Argentina + + align:start position:0% +or the government or so on Argentina + + + align:start position:0% +or the government or so on Argentina +defaults in his bonds regularly okay for + + align:start position:0% +defaults in his bonds regularly okay for + + + align:start position:0% +defaults in his bonds regularly okay for +example ER many of the of the of the + + align:start position:0% +example ER many of the of the of the + + + align:start position:0% +example ER many of the of the of the +regional banks that have gone under will + + align:start position:0% +regional banks that have gone under will + + + align:start position:0% +regional banks that have gone under will +default on their bonds as well okay so + + align:start position:0% +default on their bonds as well okay so + + + align:start position:0% +default on their bonds as well okay so +that kind of risk but we remove that + + align:start position:0% +that kind of risk but we remove that + + + align:start position:0% +that kind of risk but we remove that +risk and we focus for now on the I'm + + align:start position:0% +risk and we focus for now on the I'm + + + align:start position:0% +risk and we focus for now on the I'm +going to focus mostly on the price risk + + align:start position:0% +going to focus mostly on the price risk + + + align:start position:0% +going to focus mostly on the price risk +because I'm going to be talking mostly + + align:start position:0% +because I'm going to be talking mostly + + + align:start position:0% +because I'm going to be talking mostly +about US Treasury bonds US Treasury + + align:start position:0% +about US Treasury bonds US Treasury + + + align:start position:0% +about US Treasury bonds US Treasury +bonds have no default risk we think I me + + align:start position:0% +bonds have no default risk we think I me + + + align:start position:0% +bonds have no default risk we think I me +there could be an event in a few weeks + + align:start position:0% +there could be an event in a few weeks + + + align:start position:0% +there could be an event in a few weeks +from now but no one expects that to be a + + align:start position:0% +from now but no one expects that to be a + + + align:start position:0% +from now but no one expects that to be a +lasting event I mean if it is it's a + + align:start position:0% +lasting event I mean if it is it's a + + + align:start position:0% +lasting event I mean if it is it's a +real mess but but inent but there is + + align:start position:0% +real mess but but inent but there is + + + align:start position:0% +real mess but but inent but there is +also price risk because you have to hold + + align:start position:0% +also price risk because you have to hold + + + align:start position:0% +also price risk because you have to hold +this and then sell it at one year and + + align:start position:0% +this and then sell it at one year and + + + align:start position:0% +this and then sell it at one year and +you don't know exactly the price what + + align:start position:0% +you don't know exactly the price what + + + align:start position:0% +you don't know exactly the price what +the price will be okay there's a risk + + align:start position:0% +the price will be okay there's a risk + + + align:start position:0% +the price will be okay there's a risk +associated to that + + align:start position:0% +associated to that + + + align:start position:0% +associated to that +so so that means that really you + + align:start position:0% +so so that means that really you + + + align:start position:0% +so so that means that really you +shouldn't equalize the return on the + + align:start position:0% +shouldn't equalize the return on the + + + align:start position:0% +shouldn't equalize the return on the +oneyear bond to the return you expect to + + align:start position:0% +oneyear bond to the return you expect to + + + align:start position:0% +oneyear bond to the return you expect to +get in in the two-year bone you should + + align:start position:0% +get in in the two-year bone you should + + + align:start position:0% +get in in the two-year bone you should +add a little compensation for holding + + align:start position:0% +add a little compensation for holding + + + align:start position:0% +add a little compensation for holding +the two-year bone for going the two-year + + align:start position:0% +the two-year bone for going the two-year + + + align:start position:0% +the two-year bone for going the two-year +bone route okay and so rather than + + align:start position:0% +bone route okay and so rather than + + + align:start position:0% +bone route okay and so rather than +expect to make 1 plus + + align:start position:0% +expect to make 1 plus + + + align:start position:0% +expect to make 1 plus +i1t with with the two-year Bond after + + align:start position:0% +i1t with with the two-year Bond after + + + align:start position:0% +i1t with with the two-year Bond after +one year you should expect to earn a + + align:start position:0% +one year you should expect to earn a + + + align:start position:0% +one year you should expect to earn a +little more okay and that's what this xB + + align:start position:0% +little more okay and that's what this xB + + + align:start position:0% +little more okay and that's what this xB +being positive reflects and so in that + + align:start position:0% +being positive reflects and so in that + + + align:start position:0% +being positive reflects and so in that +case the price the price of the two-year + + align:start position:0% +case the price the price of the two-year + + + align:start position:0% +case the price the price of the two-year +bond is a little different from what we + + align:start position:0% +bond is a little different from what we + + + align:start position:0% +bond is a little different from what we +had in fact it's a little lower than + + align:start position:0% +had in fact it's a little lower than + + + align:start position:0% +had in fact it's a little lower than +what we have because that's a way you + + align:start position:0% +what we have because that's a way you + + + align:start position:0% +what we have because that's a way you +compensate for risk I sell you an + + align:start position:0% +compensate for risk I sell you an + + + align:start position:0% +compensate for risk I sell you an +instrument a little cheaper than it + + align:start position:0% +instrument a little cheaper than it + + + align:start position:0% +instrument a little cheaper than it +would have been in the absence of risk + + align:start position:0% +would have been in the absence of risk + + + align:start position:0% +would have been in the absence of risk +so you you expect to get a little a + + align:start position:0% +so you you expect to get a little a + + + align:start position:0% +so you you expect to get a little a +slightly higher return out of that okay + + align:start position:0% +slightly higher return out of that okay + + + align:start position:0% +slightly higher return out of that okay +so this price is lower than the price + + align:start position:0% +so this price is lower than the price + + + align:start position:0% +so this price is lower than the price +without the risk premium here no that + + align:start position:0% +without the risk premium here no that + + + align:start position:0% +without the risk premium here no that +means but the still is pro you + + align:start position:0% +means but the still is pro you + + + align:start position:0% +means but the still is pro you +so that's exactly how you get more + + align:start position:0% +so that's exactly how you get more + + + align:start position:0% +so that's exactly how you get more +return out of it because you were buying + + align:start position:0% +return out of it because you were buying + + + align:start position:0% +return out of it because you were buying +something at a lower price + + align:start position:0% + + + + align:start position:0% + +okay so I can do the same logic now and + + align:start position:0% +okay so I can do the same logic now and + + + align:start position:0% +okay so I can do the same logic now and +see what the two-year rate is but now + + align:start position:0% +see what the two-year rate is but now + + + align:start position:0% +see what the two-year rate is but now +that I have this take into account this + + align:start position:0% +that I have this take into account this + + + align:start position:0% +that I have this take into account this +risk and you have that the 2-year rate + + align:start position:0% +risk and you have that the 2-year rate + + + align:start position:0% +risk and you have that the 2-year rate +now is the average not only of the + + align:start position:0% +now is the average not only of the + + + align:start position:0% +now is the average not only of the +expected one-ear rate but also includes + + align:start position:0% +expected one-ear rate but also includes + + + align:start position:0% +expected one-ear rate but also includes +a risk premium okay and so and that + + align:start position:0% +a risk premium okay and so and that + + + align:start position:0% +a risk premium okay and so and that +tends to be the case that the the + + align:start position:0% +tends to be the case that the the + + + align:start position:0% +tends to be the case that the the +further out in the curve you are the + + align:start position:0% +further out in the curve you are the + + + align:start position:0% +further out in the curve you are the +larger is that risk premium it's called + + align:start position:0% +larger is that risk premium it's called + + + align:start position:0% +larger is that risk premium it's called +term premium because term is the same as + + align:start position:0% +term premium because term is the same as + + + align:start position:0% +term premium because term is the same as +maturity + + align:start position:0% +maturity + + + align:start position:0% +maturity +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +actually sometimes that that is + + align:start position:0% +actually sometimes that that is + + + align:start position:0% +actually sometimes that that is +negative and recently up to very + + align:start position:0% +negative and recently up to very + + + align:start position:0% +negative and recently up to very +recently now it's positive but until + + align:start position:0% +recently now it's positive but until + + + align:start position:0% +recently now it's positive but until +very recently that XB was negative and + + align:start position:0% +very recently that XB was negative and + + + align:start position:0% +very recently that XB was negative and +the reason for that you don't need to + + align:start position:0% +the reason for that you don't need to + + + align:start position:0% +the reason for that you don't need to +understand that now is because long-term + + align:start position:0% +understand that now is because long-term + + + align:start position:0% +understand that now is because long-term +Bonds were great + + align:start position:0% +Bonds were great + + + align:start position:0% +Bonds were great +Hedges H meaning meaning you know if + + align:start position:0% +Hedges H meaning meaning you know if + + + align:start position:0% +Hedges H meaning meaning you know if +there is a for any ma major event for a + + align:start position:0% +there is a for any ma major event for a + + + align:start position:0% +there is a for any ma major event for a +financial crisis or something like that + + align:start position:0% +financial crisis or something like that + + + align:start position:0% +financial crisis or something like that +because in a financial crisis or a major + + align:start position:0% +because in a financial crisis or a major + + + align:start position:0% +because in a financial crisis or a major +disaster interest rates tend to + + align:start position:0% +disaster interest rates tend to + + + align:start position:0% +disaster interest rates tend to +fall and when interest rates fall the + + align:start position:0% +fall and when interest rates fall the + + + align:start position:0% +fall and when interest rates fall the +price of bonds go up okay and and so so + + align:start position:0% +price of bonds go up okay and and so so + + + align:start position:0% +price of bonds go up okay and and so so +that was a good hedge if you wanted to + + align:start position:0% +that was a good hedge if you wanted to + + + align:start position:0% +that was a good hedge if you wanted to +to protect your your portfolio of + + align:start position:0% +to protect your your portfolio of + + + align:start position:0% +to protect your your portfolio of +equities and so on against a major + + align:start position:0% +equities and so on against a major + + + align:start position:0% +equities and so on against a major +catastrophic major event like a + + align:start position:0% +catastrophic major event like a + + + align:start position:0% +catastrophic major event like a +financial crisis or you know a war or + + align:start position:0% +financial crisis or you know a war or + + + align:start position:0% +financial crisis or you know a war or +something like that it was not a bad + + align:start position:0% +something like that it was not a bad + + + align:start position:0% +something like that it was not a bad +idea to have some long-term US Treasury + + align:start position:0% +idea to have some long-term US Treasury + + + align:start position:0% +idea to have some long-term US Treasury +Bonds in your portfolio because they + + align:start position:0% +Bonds in your portfolio because they + + + align:start position:0% +Bonds in your portfolio because they +would tend to go up precisely when + + align:start position:0% +would tend to go up precisely when + + + align:start position:0% +would tend to go up precisely when +everything else was going to be losing + + align:start position:0% +everything else was going to be losing + + + align:start position:0% +everything else was going to be losing +money okay and such reason tended to be + + align:start position:0% +money okay and such reason tended to be + + + align:start position:0% +money okay and such reason tended to be +negative now that's not the case because + + align:start position:0% +negative now that's not the case because + + + align:start position:0% +negative now that's not the case because +now one of the biggest risk is inflation + + align:start position:0% +now one of the biggest risk is inflation + + + align:start position:0% +now one of the biggest risk is inflation +and so so if there is an inflationary + + align:start position:0% +and so so if there is an inflationary + + + align:start position:0% +and so so if there is an inflationary +Spike then interest rate will go go down + + align:start position:0% +Spike then interest rate will go go down + + + align:start position:0% +Spike then interest rate will go go down +up not down and that means that price of + + align:start position:0% +up not down and that means that price of + + + align:start position:0% +up not down and that means that price of +bonds will decline so they will decline + + align:start position:0% +bonds will decline so they will decline + + + align:start position:0% +bonds will decline so they will decline +at the wrong time okay so the price of + + align:start position:0% +at the wrong time okay so the price of + + + align:start position:0% +at the wrong time okay so the price of +bonds of longterm bonds now will tend to + + align:start position:0% +bonds of longterm bonds now will tend to + + + align:start position:0% +bonds of longterm bonds now will tend to +decline when everything else is also + + align:start position:0% +decline when everything else is also + + + align:start position:0% +decline when everything else is also +plummeting I mean if we get a NE if we + + align:start position:0% +plummeting I mean if we get a NE if we + + + align:start position:0% +plummeting I mean if we get a NE if we +get an inflation surprise that inflation + + align:start position:0% +get an inflation surprise that inflation + + + align:start position:0% +get an inflation surprise that inflation +is a lot higher than people expected + + align:start position:0% +is a lot higher than people expected + + + align:start position:0% +is a lot higher than people expected +asset prices are going to decline all of + + align:start position:0% +asset prices are going to decline all of + + + align:start position:0% +asset prices are going to decline all of +them including long-term bonds and + + align:start position:0% +them including long-term bonds and + + + align:start position:0% +them including long-term bonds and +that's the reason now this XB is + + align:start position:0% + + + + align:start position:0% + +positive okay so that's I think that's + + align:start position:0% +positive okay so that's I think that's + + + align:start position:0% +positive okay so that's I think that's +what we we're at in the previous + + align:start position:0% +what we we're at in the previous + + + align:start position:0% +what we we're at in the previous +lecture any questions about that then + + align:start position:0% +lecture any questions about that then + + + align:start position:0% +lecture any questions about that then +I'm going to next step is to talk about + + align:start position:0% +I'm going to next step is to talk about + + + align:start position:0% +I'm going to next step is to talk about +Equity no yeah why don't we add the the + + align:start position:0% +Equity no yeah why don't we add the the + + + align:start position:0% +Equity no yeah why don't we add the the +risk to the interest rate one year + + align:start position:0% + + + + align:start position:0% + +now well because next year that one for + + align:start position:0% +now well because next year that one for + + + align:start position:0% +now well because next year that one for +this particular bond that that Bond will + + align:start position:0% +this particular bond that that Bond will + + + align:start position:0% +this particular bond that that Bond will +have no risk because it will be one year + + align:start position:0% +have no risk because it will be one year + + + align:start position:0% +have no risk because it will be one year +to go and at the end of that year you're + + align:start position:0% +to go and at the end of that year you're + + + align:start position:0% +to go and at the end of that year you're +going to get the 100 + + align:start position:0% +going to get the 100 + + + align:start position:0% +going to get the 100 +so there's no risk that hander if it was + + align:start position:0% +so there's no risk that hander if it was + + + align:start position:0% +so there's no risk that hander if it was +a three-year Bond then you would have in + + align:start position:0% +a three-year Bond then you would have in + + + align:start position:0% +a three-year Bond then you would have in +two of those you would have risk premium + + align:start position:0% +two of those you would have risk premium + + + align:start position:0% +two of those you would have risk premium +and but you wouldn't have it in the last + + align:start position:0% +and but you wouldn't have it in the last + + + align:start position:0% +and but you wouldn't have it in the last +one because in the last one you don't + + align:start position:0% +one because in the last one you don't + + + align:start position:0% +one because in the last one you don't +have the you're going to receive the + + align:start position:0% +have the you're going to receive the + + + align:start position:0% +have the you're going to receive the +100 if the bond could could could + + align:start position:0% +100 if the bond could could could + + + align:start position:0% +100 if the bond could could could +default so because I'm only looking at + + align:start position:0% +default so because I'm only looking at + + + align:start position:0% +default so because I'm only looking at +Price risk in the bond ER if the bond + + align:start position:0% +Price risk in the bond ER if the bond + + + align:start position:0% +Price risk in the bond ER if the bond +could could default then I would add an + + align:start position:0% +could could default then I would add an + + + align:start position:0% +could could default then I would add an +extra term there because it's Thea RIS + + align:start position:0% +extra term there because it's Thea RIS + + + align:start position:0% +extra term there because it's Thea RIS +but but here I'm just looking at price + + align:start position:0% +but but here I'm just looking at price + + + align:start position:0% +but but here I'm just looking at price +risk and I'm assuming the the unit of + + align:start position:0% +risk and I'm assuming the the unit of + + + align:start position:0% +risk and I'm assuming the the unit of +time is one year so just one year before + + align:start position:0% +time is one year so just one year before + + + align:start position:0% +time is one year so just one year before +it expires there's no more risk because + + align:start position:0% +it expires there's no more risk because + + + align:start position:0% +it expires there's no more risk because +there's no price in between and uh and + + align:start position:0% +there's no price in between and uh and + + + align:start position:0% +there's no price in between and uh and +you're going to receive + + align:start position:0% +you're going to receive + + + align:start position:0% +you're going to receive +100 at the end of a year in + + align:start position:0% +100 at the end of a year in + + + align:start position:0% +100 at the end of a year in +reality time is continuous so so every + + align:start position:0% +reality time is continuous so so every + + + align:start position:0% +reality time is continuous so so every +second there's a little bit of a risk so + + align:start position:0% +second there's a little bit of a risk so + + + align:start position:0% +second there's a little bit of a risk so +you have a little bit of that risk all + + align:start position:0% +you have a little bit of that risk all + + + align:start position:0% +you have a little bit of that risk all +the time except for the last second H + + align:start position:0% +the time except for the last second H + + + align:start position:0% +the time except for the last second H +but but I'm looking at a simple example + + align:start position:0% +but but I'm looking at a simple example + + + align:start position:0% +but but I'm looking at a simple example +where you know things happen every one + + align:start position:0% +where you know things happen every one + + + align:start position:0% +where you know things happen every one +year only + + align:start position:0% + + + + align:start position:0% + +in the book I think they mess up + + align:start position:0% +in the book I think they mess up + + + align:start position:0% +in the book I think they mess up +actually they put the r premium in the + + align:start position:0% +actually they put the r premium in the + + + align:start position:0% +actually they put the r premium in the +wrong place + + align:start position:0% +wrong place + + + align:start position:0% +wrong place +but there was another + + align:start position:0% +but there was another + + + align:start position:0% +but there was another +question + + align:start position:0% +question + + + align:start position:0% +question +no + + align:start position:0% +no + + + align:start position:0% +no +okay so let's look at the stock prices + + align:start position:0% +okay so let's look at the stock prices + + + align:start position:0% +okay so let's look at the stock prices +now ER so a stock price have two key + + align:start position:0% +now ER so a stock price have two key + + + align:start position:0% +now ER so a stock price have two key +differences with respect to + + align:start position:0% +differences with respect to + + + align:start position:0% +differences with respect to +um well several different but two that I + + align:start position:0% +um well several different but two that I + + + align:start position:0% +um well several different but two that I +want to highlight + + align:start position:0% +want to highlight + + + align:start position:0% +want to highlight +the first is that they don't pay coupons + + align:start position:0% +the first is that they don't pay coupons + + + align:start position:0% +the first is that they don't pay coupons +fixed amount they don't promise you to + + align:start position:0% +fixed amount they don't promise you to + + + align:start position:0% +fixed amount they don't promise you to +pay you know $100 two years from now + + align:start position:0% +pay you know $100 two years from now + + + align:start position:0% +pay you know $100 two years from now +anything like that they pay + + align:start position:0% +anything like that they pay + + + align:start position:0% +anything like that they pay +dividends okay they tell you we have a + + align:start position:0% +dividends okay they tell you we have a + + + align:start position:0% +dividends okay they tell you we have a +policy of paying dividends and even + + align:start position:0% +policy of paying dividends and even + + + align:start position:0% +policy of paying dividends and even +different companies differentiate + + align:start position:0% +different companies differentiate + + + align:start position:0% +different companies differentiate +themselves by how much they promise to + + align:start position:0% +themselves by how much they promise to + + + align:start position:0% +themselves by how much they promise to +give you on average in dividends but + + align:start position:0% +give you on average in dividends but + + + align:start position:0% +give you on average in dividends but +it's a promise that if everything goes + + align:start position:0% +it's a promise that if everything goes + + + align:start position:0% +it's a promise that if everything goes +as planned they'll pay you those + + align:start position:0% +as planned they'll pay you those + + + align:start position:0% +as planned they'll pay you those +dividends it's not a commitment to pay + + align:start position:0% +dividends it's not a commitment to pay + + + align:start position:0% +dividends it's not a commitment to pay +you a dividend when it's very different + + align:start position:0% +you a dividend when it's very different + + + align:start position:0% +you a dividend when it's very different +from a bond a bond says I'll pay you a + + align:start position:0% +from a bond a bond says I'll pay you a + + + align:start position:0% +from a bond a bond says I'll pay you a +coupon of this amount every six month + + align:start position:0% +coupon of this amount every six month + + + align:start position:0% +coupon of this amount every six month +and if you don't pay that coupon that's + + align:start position:0% +and if you don't pay that coupon that's + + + align:start position:0% +and if you don't pay that coupon that's +a + + align:start position:0% +a + + + align:start position:0% +a +default there's nothing like that in + + align:start position:0% +default there's nothing like that in + + + align:start position:0% +default there's nothing like that in +equity Equity you buy shares of apple + + align:start position:0% +equity Equity you buy shares of apple + + + align:start position:0% +equity Equity you buy shares of apple +and you sort of look at the history of + + align:start position:0% +and you sort of look at the history of + + + align:start position:0% +and you sort of look at the history of +dividend what what the CEO tell dur the + + align:start position:0% +dividend what what the CEO tell dur the + + + align:start position:0% +dividend what what the CEO tell dur the +last time in the last + + align:start position:0% +last time in the last + + + align:start position:0% +last time in the last +release and and and you know you you + + align:start position:0% +release and and and you know you you + + + align:start position:0% +release and and and you know you you +think okay these are more or less going + + align:start position:0% +think okay these are more or less going + + + align:start position:0% +think okay these are more or less going +to be my D but there's no + + align:start position:0% +to be my D but there's no + + + align:start position:0% +to be my D but there's no +commitment they will always tell you + + align:start position:0% +commitment they will always tell you + + + align:start position:0% +commitment they will always tell you +what's their plan but it's a plan it's + + align:start position:0% +what's their plan but it's a plan it's + + + align:start position:0% +what's their plan but it's a plan it's +not a commitment so that's the first + + align:start position:0% +not a commitment so that's the first + + + align:start position:0% +not a commitment so that's the first +thing it doesn't have fixed coupons or + + align:start position:0% +thing it doesn't have fixed coupons or + + + align:start position:0% +thing it doesn't have fixed coupons or +anything like that there's no commitment + + align:start position:0% +anything like that there's no commitment + + + align:start position:0% +anything like that there's no commitment +and in that sense there's no sense of + + align:start position:0% +and in that sense there's no sense of + + + align:start position:0% +and in that sense there's no sense of +default because there was no commitment + + align:start position:0% +default because there was no commitment + + + align:start position:0% +default because there was no commitment +so it's no default of if if a company + + align:start position:0% +so it's no default of if if a company + + + align:start position:0% +so it's no default of if if a company +has to cut dividends to zero that's not + + align:start position:0% +has to cut dividends to zero that's not + + + align:start position:0% +has to cut dividends to zero that's not +a default that's conditions changeed + + align:start position:0% +a default that's conditions changeed + + + align:start position:0% +a default that's conditions changeed +that's it there was no commitment to + + align:start position:0% +that's it there was no commitment to + + + align:start position:0% +that's it there was no commitment to +that the second feature is that they + + align:start position:0% +that the second feature is that they + + + align:start position:0% +that the second feature is that they +don't have a fixed terminal date + + align:start position:0% +don't have a fixed terminal date + + + align:start position:0% +don't have a fixed terminal date +99.9999999% of the B do have a terminal + + align:start position:0% +99.9999999% of the B do have a terminal + + + align:start position:0% +99.9999999% of the B do have a terminal +day they have a maturity I mean there's + + align:start position:0% +day they have a maturity I mean there's + + + align:start position:0% +day they have a maturity I mean there's +a few exceptions which are called + + align:start position:0% +a few exceptions which are called + + + align:start position:0% +a few exceptions which are called +perpetuities that I think the US has + + align:start position:0% +perpetuities that I think the US has + + + align:start position:0% +perpetuities that I think the US has +known for example but but but but most + + align:start position:0% +known for example but but but but most + + + align:start position:0% +known for example but but but but most +bonds have a a a a a maturity okay + + align:start position:0% +bonds have a a a a a maturity okay + + + align:start position:0% +bonds have a a a a a maturity okay +Equity doesn't come that way nobody + + align:start position:0% +Equity doesn't come that way nobody + + + align:start position:0% +Equity doesn't come that way nobody +tells you buy a share of Apple you don't + + align:start position:0% +tells you buy a share of Apple you don't + + + align:start position:0% +tells you buy a share of Apple you don't +buy shares of Apple that they will that + + align:start position:0% +buy shares of Apple that they will that + + + align:start position:0% +buy shares of Apple that they will that +will be retired 30 years from now okay + + align:start position:0% +will be retired 30 years from now okay + + + align:start position:0% +will be retired 30 years from now okay +they will be there as long as apples + + align:start position:0% +they will be there as long as apples + + + align:start position:0% +they will be there as long as apples +exist okay + + align:start position:0% +exist okay + + + align:start position:0% +exist okay +ER of course you know if you had shares + + align:start position:0% +ER of course you know if you had shares + + + align:start position:0% +ER of course you know if you had shares +of First Republic Bank you have nothing + + align:start position:0% +of First Republic Bank you have nothing + + + align:start position:0% +of First Republic Bank you have nothing +now because if that but but that was not + + align:start position:0% +now because if that but but that was not + + + align:start position:0% +now because if that but but that was not +the original plan if First Republic Bank + + align:start position:0% +the original plan if First Republic Bank + + + align:start position:0% +the original plan if First Republic Bank +had been more successful you would have + + align:start position:0% +had been more successful you would have + + + align:start position:0% +had been more successful you would have +the shares would have survived for a + + align:start position:0% +the shares would have survived for a + + + align:start position:0% +the shares would have survived for a +very long period of time okay so so + + align:start position:0% +very long period of time okay so so + + + align:start position:0% +very long period of time okay so so +there's no sense of maturity in + + align:start position:0% +there's no sense of maturity in + + + align:start position:0% +there's no sense of maturity in +principle Equity can last + + align:start position:0% +principle Equity can last + + + align:start position:0% +principle Equity can last +forever + + align:start position:0% + + + + align:start position:0% + +okay so I'm going use Arbitrage to to to + + align:start position:0% +okay so I'm going use Arbitrage to to to + + + align:start position:0% +okay so I'm going use Arbitrage to to to +price + + align:start position:0% +price + + + align:start position:0% +price +Equity so uh let me so let's we have the + + align:start position:0% +Equity so uh let me so let's we have the + + + align:start position:0% +Equity so uh let me so let's we have the +following H portfolio of options here ER + + align:start position:0% +following H portfolio of options here ER + + + align:start position:0% +following H portfolio of options here ER +one is our old oneyear Bond okay so you + + align:start position:0% +one is our old oneyear Bond okay so you + + + align:start position:0% +one is our old oneyear Bond okay so you +can invest your dollar today in a + + align:start position:0% +can invest your dollar today in a + + + align:start position:0% +can invest your dollar today in a +one-year Bond the alternative I'm going + + align:start position:0% +one-year Bond the alternative I'm going + + + align:start position:0% +one-year Bond the alternative I'm going +to say there's some Equity out there and + + align:start position:0% +to say there's some Equity out there and + + + align:start position:0% +to say there's some Equity out there and +I'm going to call the price of that + + align:start position:0% +I'm going to call the price of that + + + align:start position:0% +I'm going to call the price of that +Equity q and the dividend of + + align:start position:0% +Equity q and the dividend of + + + align:start position:0% +Equity q and the dividend of +that equity D + + align:start position:0% +that equity D + + + align:start position:0% +that equity D +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so let's price the stock by by aror + + align:start position:0% +so so let's price the stock by by aror + + + align:start position:0% +so so let's price the stock by by aror +so Equity is risky I mean that it's much + + align:start position:0% +so Equity is risky I mean that it's much + + + align:start position:0% +so Equity is risky I mean that it's much +riskier than than than than bonds unless + + align:start position:0% +riskier than than than than bonds unless + + + align:start position:0% +riskier than than than than bonds unless +you are into Argentinian bonds or things + + align:start position:0% +you are into Argentinian bonds or things + + + align:start position:0% +you are into Argentinian bonds or things +like that but I mean it's much riskier + + align:start position:0% +like that but I mean it's much riskier + + + align:start position:0% +like that but I mean it's much riskier +than bonds so there's always a risk + + align:start position:0% +than bonds so there's always a risk + + + align:start position:0% +than bonds so there's always a risk +premium and actually that's in itself is + + align:start position:0% +premium and actually that's in itself is + + + align:start position:0% +premium and actually that's in itself is +a trade you trade the RIS premium of + + align:start position:0% +a trade you trade the RIS premium of + + + align:start position:0% +a trade you trade the RIS premium of +equity market so I'm going to put an XS + + align:start position:0% +equity market so I'm going to put an XS + + + align:start position:0% +equity market so I'm going to put an XS +here so what what what do you expect to + + align:start position:0% +here so what what what do you expect to + + + align:start position:0% +here so what what what do you expect to +get from from holding remember Arbitrage + + align:start position:0% +get from from holding remember Arbitrage + + + align:start position:0% +get from from holding remember Arbitrage +means the same holding period so I'm + + align:start position:0% +means the same holding period so I'm + + + align:start position:0% +means the same holding period so I'm +going to compare investing in a oneyear + + align:start position:0% +going to compare investing in a oneyear + + + align:start position:0% +going to compare investing in a oneyear +safe + + align:start position:0% +safe + + + align:start position:0% +safe +Bond versus buying Equity today buying a + + align:start position:0% +Bond versus buying Equity today buying a + + + align:start position:0% +Bond versus buying Equity today buying a +stock holding it for a year and then + + align:start position:0% +stock holding it for a year and then + + + align:start position:0% +stock holding it for a year and then +selling it there okay that because + + align:start position:0% +selling it there okay that because + + + align:start position:0% +selling it there okay that because +that's same that's I cannot do Arbitrage + + align:start position:0% +that's same that's I cannot do Arbitrage + + + align:start position:0% +that's same that's I cannot do Arbitrage +comparing different holding periods + + align:start position:0% +comparing different holding periods + + + align:start position:0% +comparing different holding periods +that's a oneyear holding period so I'm + + align:start position:0% +that's a oneyear holding period so I'm + + + align:start position:0% +that's a oneyear holding period so I'm +saying this is what I'm going to get + + align:start position:0% +saying this is what I'm going to get + + + align:start position:0% +saying this is what I'm going to get +from the bond I'm going to require some + + align:start position:0% +from the bond I'm going to require some + + + align:start position:0% +from the bond I'm going to require some +risk compensation for that because risk + + align:start position:0% +risk compensation for that because risk + + + align:start position:0% +risk compensation for that because risk +Equity is risky so I'm going to want + + align:start position:0% +Equity is risky so I'm going to want + + + align:start position:0% +Equity is risky so I'm going to want +that and this is what I'm going to get + + align:start position:0% +that and this is what I'm going to get + + + align:start position:0% +that and this is what I'm going to get +that's my return on Equity I get this is + + align:start position:0% +that's my return on Equity I get this is + + + align:start position:0% +that's my return on Equity I get this is +what I'm going to pay today for the + + align:start position:0% +what I'm going to pay today for the + + + align:start position:0% +what I'm going to pay today for the +stock say for a share of Apple I'm going + + align:start position:0% +stock say for a share of Apple I'm going + + + align:start position:0% +stock say for a share of Apple I'm going +to get this this is the dividend I + + align:start position:0% +to get this this is the dividend I + + + align:start position:0% +to get this this is the dividend I +expect to get at the end of the year and + + align:start position:0% +expect to get at the end of the year and + + + align:start position:0% +expect to get at the end of the year and +then I this is the price at which I + + align:start position:0% +then I this is the price at which I + + + align:start position:0% +then I this is the price at which I +expect to + + align:start position:0% +expect to + + + align:start position:0% +expect to +sell that share one year from now okay + + align:start position:0% +sell that share one year from now okay + + + align:start position:0% +sell that share one year from now okay +so that's the return I'm expecting to + + align:start position:0% +so that's the return I'm expecting to + + + align:start position:0% +so that's the return I'm expecting to +get from holding the share of Apple for + + align:start position:0% +get from holding the share of Apple for + + + align:start position:0% +get from holding the share of Apple for +one period okay and that's what I need + + align:start position:0% +one period okay and that's what I need + + + align:start position:0% +one period okay and that's what I need +to compare with holding for one year one + + align:start position:0% +to compare with holding for one year one + + + align:start position:0% +to compare with holding for one year one +year bond but I want also to be + + align:start position:0% +year bond but I want also to be + + + align:start position:0% +year bond but I want also to be +compensated H for H risk + + align:start position:0% +compensated H for H risk + + + align:start position:0% +compensated H for H risk +okay + + align:start position:0% +okay + + + align:start position:0% +okay +good is this + + align:start position:0% + + + + align:start position:0% + +clear + + align:start position:0% +clear + + + align:start position:0% +clear +okay I don't know whether silence means + + align:start position:0% +okay I don't know whether silence means + + + align:start position:0% +okay I don't know whether silence means +yes or no but this is we did something + + align:start position:0% +yes or no but this is we did something + + + align:start position:0% +yes or no but this is we did something +like this with the 2ear Bond except that + + align:start position:0% +like this with the 2ear Bond except that + + + align:start position:0% +like this with the 2ear Bond except that +we didn't have a a dividend there you + + align:start position:0% +we didn't have a a dividend there you + + + align:start position:0% +we didn't have a a dividend there you +know because there was no coupon at date + + align:start position:0% +know because there was no coupon at date + + + align:start position:0% +know because there was no coupon at date +one we only had a final payment of 100 + + align:start position:0% +one we only had a final payment of 100 + + + align:start position:0% +one we only had a final payment of 100 +but we did this already when we compare + + align:start position:0% +but we did this already when we compare + + + align:start position:0% +but we did this already when we compare +the one-year bond with holding the + + align:start position:0% +the one-year bond with holding the + + + align:start position:0% +the one-year bond with holding the +two-year bond for one period we had + + align:start position:0% +two-year bond for one period we had + + + align:start position:0% +two-year bond for one period we had +exactly that except that there was the + + align:start position:0% +exactly that except that there was the + + + align:start position:0% +exactly that except that there was the +expected dividend there was Zero because + + align:start position:0% +expected dividend there was Zero because + + + align:start position:0% +expected dividend there was Zero because +there was no payment at the intermediate + + align:start position:0% +there was no payment at the intermediate + + + align:start position:0% +there was no payment at the intermediate +date okay good so we we know this + + align:start position:0% +date okay good so we we know this + + + align:start position:0% +date okay good so we we know this +concept already the only difference here + + align:start position:0% +concept already the only difference here + + + align:start position:0% +concept already the only difference here +is again that there is expected dividend + + align:start position:0% +is again that there is expected dividend + + + align:start position:0% +is again that there is expected dividend +and and second that we have a risk + + align:start position:0% +and and second that we have a risk + + + align:start position:0% +and and second that we have a risk +premium here which we had it for bonds + + align:start position:0% +premium here which we had it for bonds + + + align:start position:0% +premium here which we had it for bonds +but for Equity as I said it's typically + + align:start position:0% +but for Equity as I said it's typically + + + align:start position:0% +but for Equity as I said it's typically +much larger than for bonds especially if + + align:start position:0% +much larger than for bonds especially if + + + align:start position:0% +much larger than for bonds especially if +you're talking about treasury + + align:start position:0% + + + + align:start position:0% + +bonds so I'm going to reorganize this to + + align:start position:0% +bonds so I'm going to reorganize this to + + + align:start position:0% +bonds so I'm going to reorganize this to +solve out for the price this QT here + + align:start position:0% +solve out for the price this QT here + + + align:start position:0% +solve out for the price this QT here +that's what I want to figure out what is + + align:start position:0% +that's what I want to figure out what is + + + align:start position:0% +that's what I want to figure out what is +the price of the share of Apple okay + + align:start position:0% +the price of the share of Apple okay + + + align:start position:0% +the price of the share of Apple okay +well I can reorganize this which means + + align:start position:0% +well I can reorganize this which means + + + align:start position:0% +well I can reorganize this which means +you know move dollar QT to the left + + align:start position:0% +you know move dollar QT to the left + + + align:start position:0% +you know move dollar QT to the left +divide these two guys here by 1+ i1 t + + align:start position:0% +divide these two guys here by 1+ i1 t + + + align:start position:0% +divide these two guys here by 1+ i1 t +plus Xs and I get this okay so the price + + align:start position:0% +plus Xs and I get this okay so the price + + + align:start position:0% +plus Xs and I get this okay so the price +is equal to the + + align:start position:0% +is equal to the + + + align:start position:0% +is equal to the +discounted expected dividend I have to + + align:start position:0% +discounted expected dividend I have to + + + align:start position:0% +discounted expected dividend I have to +discount it because I expect to receive + + align:start position:0% +discount it because I expect to receive + + + align:start position:0% +discount it because I expect to receive +it one year from now and I want also + + align:start position:0% +it one year from now and I want also + + + align:start position:0% +it one year from now and I want also +compensation for risk plus the + + align:start position:0% +compensation for risk plus the + + + align:start position:0% +compensation for risk plus the +discounted value of the money I'm going + + align:start position:0% +discounted value of the money I'm going + + + align:start position:0% +discounted value of the money I'm going +to get from selling the share of Apple + + align:start position:0% +to get from selling the share of Apple + + + align:start position:0% +to get from selling the share of Apple +one year from now okay which I also + + align:start position:0% +one year from now okay which I also + + + align:start position:0% +one year from now okay which I also +discount by the interest rate but also + + align:start position:0% +discount by the interest rate but also + + + align:start position:0% +discount by the interest rate but also +with a risk premium because because it's + + align:start position:0% +with a risk premium because because it's + + + align:start position:0% +with a risk premium because because it's +a risky investment + + align:start position:0% +a risky investment + + + align:start position:0% +a risky investment +okay so that's what we + + align:start position:0% +okay so that's what we + + + align:start position:0% +okay so that's what we +have + + align:start position:0% +have + + + align:start position:0% +have +now notice + + align:start position:0% +now notice + + + align:start position:0% +now notice +that at t+ + + align:start position:0% +that at t+ + + + align:start position:0% +that at t+ +one I will have an expression like that + + align:start position:0% +one I will have an expression like that + + + align:start position:0% +one I will have an expression like that +as + + align:start position:0% +as + + + align:start position:0% +as +well okay again when we did the two-year + + align:start position:0% +well okay again when we did the two-year + + + align:start position:0% +well okay again when we did the two-year +Bond we didn't have an expression like + + align:start position:0% +Bond we didn't have an expression like + + + align:start position:0% +Bond we didn't have an expression like +that because after after one year the + + align:start position:0% +that because after after one year the + + + align:start position:0% +that because after after one year the +two-year bone was going to be a one-year + + align:start position:0% +two-year bone was going to be a one-year + + + align:start position:0% +two-year bone was going to be a one-year +bone and so we didn't need to think put + + align:start position:0% +bone and so we didn't need to think put + + + align:start position:0% +bone and so we didn't need to think put +a price there we just put the 100 okay + + align:start position:0% +a price there we just put the 100 okay + + + align:start position:0% +a price there we just put the 100 okay +here is different because we said this + + align:start position:0% +here is different because we said this + + + align:start position:0% +here is different because we said this +Equity never expires unless a company + + align:start position:0% +Equity never expires unless a company + + + align:start position:0% +Equity never expires unless a company +goes bankrupt it's + + align:start position:0% +goes bankrupt it's + + + align:start position:0% +goes bankrupt it's +there so in the next date I'm going to + + align:start position:0% +there so in the next date I'm going to + + + align:start position:0% +there so in the next date I'm going to +have an expression exactly like that I'm + + align:start position:0% +have an expression exactly like that I'm + + + align:start position:0% +have an expression exactly like that I'm +just going to have an expected t plus + + align:start position:0% +just going to have an expected t plus + + + align:start position:0% +just going to have an expected t plus +devent at T plus2 and expected price at + + align:start position:0% +devent at T plus2 and expected price at + + + align:start position:0% +devent at T plus2 and expected price at +T plus2 okay and so on so forth that + + align:start position:0% +T plus2 okay and so on so forth that + + + align:start position:0% +T plus2 okay and so on so forth that +means I can replace this expression here + + align:start position:0% +means I can replace this expression here + + + align:start position:0% +means I can replace this expression here +by an expression like this shifted all + + align:start position:0% +by an expression like this shifted all + + + align:start position:0% +by an expression like this shifted all +by one + + align:start position:0% + + + + align:start position:0% + +year okay and I keep can keep doing that + + align:start position:0% +year okay and I keep can keep doing that + + + align:start position:0% +year okay and I keep can keep doing that +then if I do that I'm going to get then + + align:start position:0% +then if I do that I'm going to get then + + + align:start position:0% +then if I do that I'm going to get then +two expected dividend here and then I'm + + align:start position:0% +two expected dividend here and then I'm + + + align:start position:0% +two expected dividend here and then I'm +going to get a h so I'm going to get + + align:start position:0% +going to get a h so I'm going to get + + + align:start position:0% +going to get a h so I'm going to get +something like this but shifted by one + + align:start position:0% +something like this but shifted by one + + + align:start position:0% +something like this but shifted by one +year and discounted by two terms in the + + align:start position:0% +year and discounted by two terms in the + + + align:start position:0% +year and discounted by two terms in the +denominator and then I want to get a + + align:start position:0% +denominator and then I want to get a + + + align:start position:0% +denominator and then I want to get a +expected Q QT + two around here okay + + align:start position:0% +expected Q QT + two around here okay + + + align:start position:0% +expected Q QT + two around here okay +well I can do a substitution of that as + + align:start position:0% +well I can do a substitution of that as + + + align:start position:0% +well I can do a substitution of that as +well + + align:start position:0% +well + + + align:start position:0% +well +again okay by everything shifted by two + + align:start position:0% +again okay by everything shifted by two + + + align:start position:0% +again okay by everything shifted by two +years and so on so I can keep going and + + align:start position:0% +years and so on so I can keep going and + + + align:start position:0% +years and so on so I can keep going and +I can keep going and going and going and + + align:start position:0% +I can keep going and going and going and + + + align:start position:0% +I can keep going and going and going and +going on forever okay so if you keep + + align:start position:0% +going on forever okay so if you keep + + + align:start position:0% +going on forever okay so if you keep +doing it you're going to end up with an + + align:start position:0% +doing it you're going to end up with an + + + align:start position:0% +doing it you're going to end up with an +expression that gives you the price of + + align:start position:0% +expression that gives you the price of + + + align:start position:0% +expression that gives you the price of +the asset as the expected present + + align:start position:0% +the asset as the expected present + + + align:start position:0% +the asset as the expected present +discounted value of all the future + + align:start position:0% +discounted value of all the future + + + align:start position:0% +discounted value of all the future +deviant you + + align:start position:0% +deviant you + + + align:start position:0% +deviant you +expect okay you see I'm summing DT plus2 + + align:start position:0% +expect okay you see I'm summing DT plus2 + + + align:start position:0% +expect okay you see I'm summing DT plus2 +three four five n doesn't stop here I + + align:start position:0% +three four five n doesn't stop here I + + + align:start position:0% +three four five n doesn't stop here I +stop here I'm going to have here A A you + + align:start position:0% +stop here I'm going to have here A A you + + + align:start position:0% +stop here I'm going to have here A A you +know a q e t+ n + one well I can replace + + align:start position:0% +know a q e t+ n + one well I can replace + + + align:start position:0% +know a q e t+ n + one well I can replace +that thing again and I can keep going + + align:start position:0% +that thing again and I can keep going + + + align:start position:0% +that thing again and I can keep going +keep going forever okay so you're going + + align:start position:0% +keep going forever okay so you're going + + + align:start position:0% +keep going forever okay so you're going +to integrate the expected dividend + + align:start position:0% +to integrate the expected dividend + + + align:start position:0% +to integrate the expected dividend +discounted expected dividend to + + align:start position:0% +discounted expected dividend to + + + align:start position:0% +discounted expected dividend to +Infinity now each future divent is is + + align:start position:0% +Infinity now each future divent is is + + + align:start position:0% +Infinity now each future divent is is +counting more and more heavily because + + align:start position:0% +counting more and more heavily because + + + align:start position:0% +counting more and more heavily because +the denominator is growing and growing + + align:start position:0% +the denominator is growing and growing + + + align:start position:0% +the denominator is growing and growing +and growing because it's out in the + + align:start position:0% +and growing because it's out in the + + + align:start position:0% +and growing because it's out in the +future is worth less and less okay but + + align:start position:0% +future is worth less and less okay but + + + align:start position:0% +future is worth less and less okay but +still it can go on forever and in fact + + align:start position:0% +still it can go on forever and in fact + + + align:start position:0% +still it can go on forever and in fact +even if you you substitute this stuff a + + align:start position:0% +even if you you substitute this stuff a + + + align:start position:0% +even if you you substitute this stuff a +million times there is going to still be + + align:start position:0% +million times there is going to still be + + + align:start position:0% +million times there is going to still be +a little price at the very end floating + + align:start position:0% +a little price at the very end floating + + + align:start position:0% +a little price at the very end floating +around okay discounted but it will never + + align:start position:0% +around okay discounted but it will never + + + align:start position:0% +around okay discounted but it will never +go + + align:start position:0% +go + + + align:start position:0% +go +away okay so it never ends there's no + + align:start position:0% +away okay so it never ends there's no + + + align:start position:0% +away okay so it never ends there's no +maturity they keep going + + align:start position:0% +maturity they keep going + + + align:start position:0% +maturity they keep going +okay now I did everything up to now for + + align:start position:0% +okay now I did everything up to now for + + + align:start position:0% +okay now I did everything up to now for +nominal in nominal terms you can do and + + align:start position:0% +nominal in nominal terms you can do and + + + align:start position:0% +nominal in nominal terms you can do and +that's the reason I I didn't want to + + align:start position:0% +that's the reason I I didn't want to + + + align:start position:0% +that's the reason I I didn't want to +spend much time with this you can do + + align:start position:0% +spend much time with this you can do + + + align:start position:0% +spend much time with this you can do +everything in real terms as well H and + + align:start position:0% +everything in real terms as well H and + + + align:start position:0% +everything in real terms as well H and +and and all all that happens there is + + align:start position:0% +and and all all that happens there is + + + align:start position:0% +and and all all that happens there is +just remove the dollars and just be + + align:start position:0% +just remove the dollars and just be + + + align:start position:0% +just remove the dollars and just be +careful to replace H H the nominal + + align:start position:0% +careful to replace H H the nominal + + + align:start position:0% +careful to replace H H the nominal +interest rate by the real interest rate + + align:start position:0% +interest rate by the real interest rate + + + align:start position:0% +interest rate by the real interest rate +but nothing deep there I can you can go + + align:start position:0% +but nothing deep there I can you can go + + + align:start position:0% +but nothing deep there I can you can go +to real pricing nominal pricing and so + + align:start position:0% +to real pricing nominal pricing and so + + + align:start position:0% +to real pricing nominal pricing and so +this okay but the the important concept + + align:start position:0% +this okay but the the important concept + + + align:start position:0% +this okay but the the important concept +is not that is is the fact that this + + align:start position:0% +is not that is is the fact that this + + + align:start position:0% +is not that is is the fact that this +that the the in principle we call that + + align:start position:0% +that the the in principle we call that + + + align:start position:0% +that the the in principle we call that +by the way the fundamental value of a of + + align:start position:0% +by the way the fundamental value of a of + + + align:start position:0% +by the way the fundamental value of a of +a of a of equity or of a stock it's the + + align:start position:0% +a of a of equity or of a stock it's the + + + align:start position:0% +a of a of equity or of a stock it's the +expected present discounted value of all + + align:start position:0% +expected present discounted value of all + + + align:start position:0% +expected present discounted value of all +the dividends and you have to discount + + align:start position:0% +the dividends and you have to discount + + + align:start position:0% +the dividends and you have to discount +it by the appropriate discounting factor + + align:start position:0% +it by the appropriate discounting factor + + + align:start position:0% +it by the appropriate discounting factor +which includes interest rates and risk + + align:start position:0% +which includes interest rates and risk + + + align:start position:0% +which includes interest rates and risk +premium but that's what we call + + align:start position:0% +premium but that's what we call + + + align:start position:0% +premium but that's what we call +typically fundamentals and we + + align:start position:0% +typically fundamentals and we + + + align:start position:0% +typically fundamentals and we +differentiate that from what we call + + align:start position:0% +differentiate that from what we call + + + align:start position:0% +differentiate that from what we call +sometimes I'm going to show you an + + align:start position:0% +sometimes I'm going to show you an + + + align:start position:0% +sometimes I'm going to show you an +example later on bubbles when when the + + align:start position:0% +example later on bubbles when when the + + + align:start position:0% +example later on bubbles when when the +price seems to exceed any reasonable + + align:start position:0% +price seems to exceed any reasonable + + + align:start position:0% +price seems to exceed any reasonable +sense of + + align:start position:0% +sense of + + + align:start position:0% +sense of +fundamentals okay + + align:start position:0% + + + + align:start position:0% + +okay good okay let me sort of start + + align:start position:0% +okay good okay let me sort of start + + + align:start position:0% +okay good okay let me sort of start +going back to to things that that um we + + align:start position:0% +going back to to things that that um we + + + align:start position:0% +going back to to things that that um we +worry about in this course and in fact + + align:start position:0% +worry about in this course and in fact + + + align:start position:0% +worry about in this course and in fact +it's a big issue I don't know what is + + align:start position:0% +it's a big issue I don't know what is + + + align:start position:0% +it's a big issue I don't know what is +happening to markets now what the FED + + align:start position:0% +happening to markets now what the FED + + + align:start position:0% +happening to markets now what the FED +did was very anticipated but but + + align:start position:0% +did was very anticipated but but + + + align:start position:0% +did was very anticipated but but +um but markets of often find a way to + + align:start position:0% +um but markets of often find a way to + + + align:start position:0% +um but markets of often find a way to +react to things even if things were + + align:start position:0% +react to things even if things were + + + align:start position:0% +react to things even if things were +anticipated + + align:start position:0% +anticipated + + + align:start position:0% +anticipated +but what happens so let me ask you a + + align:start position:0% +but what happens so let me ask you a + + + align:start position:0% +but what happens so let me ask you a +following + + align:start position:0% +following + + + align:start position:0% +following +question what is the effect what do you + + align:start position:0% +question what is the effect what do you + + + align:start position:0% +question what is the effect what do you +think is the effect of an expansionary + + align:start position:0% +think is the effect of an expansionary + + + align:start position:0% +think is the effect of an expansionary +monetary + + align:start position:0% +monetary + + + align:start position:0% +monetary +policy on the asset prices we have + + align:start position:0% +policy on the asset prices we have + + + align:start position:0% +policy on the asset prices we have +discussed so bonds and + + align:start position:0% +discussed so bonds and + + + align:start position:0% +discussed so bonds and +Equity let's start with bonds + + align:start position:0% +Equity let's start with bonds + + + align:start position:0% +Equity let's start with bonds +first what do you think is the effect of + + align:start position:0% +first what do you think is the effect of + + + align:start position:0% +first what do you think is the effect of +an expansion and monetary policy that + + align:start position:0% +an expansion and monetary policy that + + + align:start position:0% +an expansion and monetary policy that +means a reduction in the interest rate + + align:start position:0% +means a reduction in the interest rate + + + align:start position:0% +means a reduction in the interest rate +on the price of your onee bone twoyear + + align:start position:0% +on the price of your onee bone twoyear + + + align:start position:0% +on the price of your onee bone twoyear +bone any any year you pick + + align:start position:0% + + + + align:start position:0% + +we already talked about that + + align:start position:0% + + + + align:start position:0% + +earlier goes up the price of a bone is + + align:start position:0% +earlier goes up the price of a bone is + + + align:start position:0% +earlier goes up the price of a bone is +inversely related to the interest rate + + align:start position:0% +inversely related to the interest rate + + + align:start position:0% +inversely related to the interest rate +because if I cut an interest rate means + + align:start position:0% +because if I cut an interest rate means + + + align:start position:0% +because if I cut an interest rate means +a bon is something that pays the pay off + + align:start position:0% +a bon is something that pays the pay off + + + align:start position:0% +a bon is something that pays the pay off +is in the future that thing in the + + align:start position:0% +is in the future that thing in the + + + align:start position:0% +is in the future that thing in the +future is worth more if the interest + + align:start position:0% +future is worth more if the interest + + + align:start position:0% +future is worth more if the interest +rate goes down there's less discounting + + align:start position:0% +rate goes down there's less discounting + + + align:start position:0% +rate goes down there's less discounting +of it so the price of the bone any B + + align:start position:0% +of it so the price of the bone any B + + + align:start position:0% +of it so the price of the bone any B +here will go up the one year two year + + align:start position:0% +here will go up the one year two year + + + align:start position:0% +here will go up the one year two year +three year five year all of them will go + + align:start position:0% +three year five year all of them will go + + + align:start position:0% +three year five year all of them will go +up + + align:start position:0% +up + + + align:start position:0% +up +okay assuming that nothing changes as a + + align:start position:0% +okay assuming that nothing changes as a + + + align:start position:0% +okay assuming that nothing changes as a +result of the monetary policy look what + + align:start position:0% +result of the monetary policy look what + + + align:start position:0% +result of the monetary policy look what +happens is sometimes you know markets + + align:start position:0% +happens is sometimes you know markets + + + align:start position:0% +happens is sometimes you know markets +think oops the FED mess up and that + + align:start position:0% +think oops the FED mess up and that + + + align:start position:0% +think oops the FED mess up and that +leads to lots of changes in all the ter + + align:start position:0% +leads to lots of changes in all the ter + + + align:start position:0% +leads to lots of changes in all the ter +structure and things like that because + + align:start position:0% +structure and things like that because + + + align:start position:0% +structure and things like that because +they expect the market to react in a + + align:start position:0% +they expect the market to react in a + + + align:start position:0% +they expect the market to react in a +strange ways to to this mistake made by + + align:start position:0% +strange ways to to this mistake made by + + + align:start position:0% +strange ways to to this mistake made by +the FED but here I'm saying suppose that + + align:start position:0% +the FED but here I'm saying suppose that + + + align:start position:0% +the FED but here I'm saying suppose that +the FED just cuts the interest rate once + + align:start position:0% +the FED just cuts the interest rate once + + + align:start position:0% +the FED just cuts the interest rate once +and everyone believes that the FED would + + align:start position:0% +and everyone believes that the FED would + + + align:start position:0% +and everyone believes that the FED would +continue to do so and so on well then + + align:start position:0% +continue to do so and so on well then + + + align:start position:0% +continue to do so and so on well then +you're going to get a that that the + + align:start position:0% +you're going to get a that that the + + + align:start position:0% +you're going to get a that that the +price of bonds will go up what will + + align:start position:0% +price of bonds will go up what will + + + align:start position:0% +price of bonds will go up what will +happen to the price of + + align:start position:0% +happen to the price of + + + align:start position:0% +happen to the price of +stocks you want to + + align:start position:0% +stocks you want to + + + align:start position:0% +stocks you want to +answer + + align:start position:0% +answer + + + align:start position:0% +answer +up but + + align:start position:0% +up but + + + align:start position:0% +up but +it's well but it's important to see that + + align:start position:0% +it's well but it's important to see that + + + align:start position:0% +it's well but it's important to see that +it will go up probably for two reasons + + align:start position:0% +it will go up probably for two reasons + + + align:start position:0% +it will go up probably for two reasons +the first one is that that + + align:start position:0% +the first one is that that + + + align:start position:0% +the first one is that that +um is that it's also the case that the a + + align:start position:0% +um is that it's also the case that the a + + + align:start position:0% +um is that it's also the case that the a +lot of the price of an equity actually + + align:start position:0% +lot of the price of an equity actually + + + align:start position:0% +lot of the price of an equity actually +even more so than a bond has to do with + + align:start position:0% +even more so than a bond has to do with + + + align:start position:0% +even more so than a bond has to do with +expected payoffs in the future so if I + + align:start position:0% +expected payoffs in the future so if I + + + align:start position:0% +expected payoffs in the future so if I +lower interest rate just the effect of + + align:start position:0% +lower interest rate just the effect of + + + align:start position:0% +lower interest rate just the effect of +discounting will tend to raise the price + + align:start position:0% +discounting will tend to raise the price + + + align:start position:0% +discounting will tend to raise the price +of so even if I don't change the + + align:start position:0% +of so even if I don't change the + + + align:start position:0% +of so even if I don't change the +expected dividends at all the fact that + + align:start position:0% +expected dividends at all the fact that + + + align:start position:0% +expected dividends at all the fact that +interest rate goes down for the same + + align:start position:0% +interest rate goes down for the same + + + align:start position:0% +interest rate goes down for the same +reason that the price of a bond went up + + align:start position:0% +reason that the price of a bond went up + + + align:start position:0% +reason that the price of a bond went up +the price of equity will tend to go up + + align:start position:0% +the price of equity will tend to go up + + + align:start position:0% +the price of equity will tend to go up +okay so that's exactly is the same logic + + align:start position:0% +okay so that's exactly is the same logic + + + align:start position:0% +okay so that's exactly is the same logic +but there's an extra kick here for + + align:start position:0% +but there's an extra kick here for + + + align:start position:0% +but there's an extra kick here for +equity which is what that bonds did not + + align:start position:0% +equity which is what that bonds did not + + + align:start position:0% +equity which is what that bonds did not +have but Equity + + align:start position:0% +have but Equity + + + align:start position:0% +have but Equity +does at least if it is an equity that is + + align:start position:0% +does at least if it is an equity that is + + + align:start position:0% +does at least if it is an equity that is +positively related to aggregate activity + + align:start position:0% +positively related to aggregate activity + + + align:start position:0% +positively related to aggregate activity +but that's what I'm assuming + + align:start position:0% + + + + align:start position:0% + +here pay you a fixed amount for U uh + + align:start position:0% +here pay you a fixed amount for U uh + + + align:start position:0% +here pay you a fixed amount for U uh +stocks and you can't guarantee that + + align:start position:0% +stocks and you can't guarantee that + + + align:start position:0% +stocks and you can't guarantee that +P well yeah that's the logic no here the + + align:start position:0% +P well yeah that's the logic no here the + + + align:start position:0% +P well yeah that's the logic no here the +expansion monetary policy is cutting + + align:start position:0% +expansion monetary policy is cutting + + + align:start position:0% +expansion monetary policy is cutting +interest rate but as a result of that + + align:start position:0% +interest rate but as a result of that + + + align:start position:0% +interest rate but as a result of that +output is going up when output is going + + align:start position:0% +output is going up when output is going + + + align:start position:0% +output is going up when output is going +up sales will go up revenues will up + + align:start position:0% +up sales will go up revenues will up + + + align:start position:0% +up sales will go up revenues will up +dividends will probably go up as well so + + align:start position:0% +dividends will probably go up as well so + + + align:start position:0% +dividends will probably go up as well so +monetary policy can have very large + + align:start position:0% +monetary policy can have very large + + + align:start position:0% +monetary policy can have very large +effect I mean people in financial + + align:start position:0% +effect I mean people in financial + + + align:start position:0% +effect I mean people in financial +markets are looking at the FED all the + + align:start position:0% +markets are looking at the FED all the + + + align:start position:0% +markets are looking at the FED all the +time know because it can have a big + + align:start position:0% +time know because it can have a big + + + align:start position:0% +time know because it can have a big +impact on the price of those assets and + + align:start position:0% +impact on the price of those assets and + + + align:start position:0% +impact on the price of those assets and +an equity in particular can can be very + + align:start position:0% +an equity in particular can can be very + + + align:start position:0% +an equity in particular can can be very +strong and in fact that's one of the + + align:start position:0% +strong and in fact that's one of the + + + align:start position:0% +strong and in fact that's one of the +ways monetary policy + + align:start position:0% +ways monetary policy + + + align:start position:0% +ways monetary policy +works you know when when when the FED + + align:start position:0% +works you know when when when the FED + + + align:start position:0% +works you know when when when the FED +Cuts interest rates inflate it inflates + + align:start position:0% +Cuts interest rates inflate it inflates + + + align:start position:0% +Cuts interest rates inflate it inflates +the value of asset prices and that + + align:start position:0% +the value of asset prices and that + + + align:start position:0% +the value of asset prices and that +creates more wealth people feel richer + + align:start position:0% +creates more wealth people feel richer + + + align:start position:0% +creates more wealth people feel richer +consume more blah blah blah blah firms + + align:start position:0% +consume more blah blah blah blah firms + + + align:start position:0% +consume more blah blah blah blah firms +feel also richer they invest more and so + + align:start position:0% +feel also richer they invest more and so + + + align:start position:0% +feel also richer they invest more and so +on that's that's it that's that's + + align:start position:0% +on that's that's it that's that's + + + align:start position:0% +on that's that's it that's that's +deliberate in a sense okay that's one of + + align:start position:0% +deliberate in a sense okay that's one of + + + align:start position:0% +deliberate in a sense okay that's one of +the main mechanisms through which + + align:start position:0% +the main mechanisms through which + + + align:start position:0% +the main mechanisms through which +monetary policy affects aggregate demand + + align:start position:0% +monetary policy affects aggregate demand + + + align:start position:0% +monetary policy affects aggregate demand +just creates wealth and when there's too + + align:start position:0% +just creates wealth and when there's too + + + align:start position:0% +just creates wealth and when there's too +much demand too much agre demand like + + align:start position:0% +much demand too much agre demand like + + + align:start position:0% +much demand too much agre demand like +last like it's going on now that's the + + align:start position:0% +last like it's going on now that's the + + + align:start position:0% +last like it's going on now that's the +reason inflation and so on you know in + + align:start position:0% +reason inflation and so on you know in + + + align:start position:0% +reason inflation and so on you know in +2022 the FED went out and deliberately + + align:start position:0% +2022 the FED went out and deliberately + + + align:start position:0% +2022 the FED went out and deliberately +destroy wealth because that's what + + align:start position:0% +destroy wealth because that's what + + + align:start position:0% +destroy wealth because that's what +that's what near too raised interest + + align:start position:0% +that's what near too raised interest + + + align:start position:0% +that's what near too raised interest +rate a lot the price of equity came down + + align:start position:0% +rate a lot the price of equity came down + + + align:start position:0% +rate a lot the price of equity came down +even houses began to wobble okay the + + align:start position:0% +even houses began to wobble okay the + + + align:start position:0% +even houses began to wobble okay the +price of of of Treasury bonds s collapse + + align:start position:0% +price of of of Treasury bonds s collapse + + + align:start position:0% +price of of of Treasury bonds s collapse +and so on so forth + + align:start position:0% +and so on so forth + + + align:start position:0% +and so on so forth +okay + + align:start position:0% +okay + + + align:start position:0% +okay +good another experiment that we did sort + + align:start position:0% +good another experiment that we did sort + + + align:start position:0% +good another experiment that we did sort +of early on lecture three four but + + align:start position:0% +of early on lecture three four but + + + align:start position:0% +of early on lecture three four but +around there is what happens what do you + + align:start position:0% +around there is what happens what do you + + + align:start position:0% +around there is what happens what do you +think happens when there's an increase + + align:start position:0% +think happens when there's an increase + + + align:start position:0% +think happens when there's an increase +in consumer spending so suppose that now + + align:start position:0% +in consumer spending so suppose that now + + + align:start position:0% +in consumer spending so suppose that now +remember we had a a czo floating around + + align:start position:0% +remember we had a a czo floating around + + + align:start position:0% +remember we had a a czo floating around +an autonomous consumption + + align:start position:0% +an autonomous consumption + + + align:start position:0% +an autonomous consumption +component and so suppose that that goes + + align:start position:0% + + + + align:start position:0% + +up what do you think happens to asset + + align:start position:0% +up what do you think happens to asset + + + align:start position:0% +up what do you think happens to asset +prices and this is a big issue these + + align:start position:0% +prices and this is a big issue these + + + align:start position:0% +prices and this is a big issue these +days actually that depends on how the + + align:start position:0% +days actually that depends on how the + + + align:start position:0% +days actually that depends on how the +Federal + + align:start position:0% +Federal + + + align:start position:0% +Federal +Reserve exactly that's right that's + + align:start position:0% +Reserve exactly that's right that's + + + align:start position:0% +Reserve exactly that's right that's +that's that's very good it depends a lot + + align:start position:0% +that's that's very good it depends a lot + + + align:start position:0% +that's that's very good it depends a lot +I mean when financial markets receive + + align:start position:0% +I mean when financial markets receive + + + align:start position:0% +I mean when financial markets receive +news every day there are releases of + + align:start position:0% +news every day there are releases of + + + align:start position:0% +news every day there are releases of +news of of all sort of things okay and + + align:start position:0% +news of of all sort of things okay and + + + align:start position:0% +news of of all sort of things okay and +and in financial markets they people + + align:start position:0% +and in financial markets they people + + + align:start position:0% +and in financial markets they people +always think okay this is the news the + + align:start position:0% +always think okay this is the news the + + + align:start position:0% +always think okay this is the news the +obvious thing for this is you know good + + align:start position:0% +obvious thing for this is you know good + + + align:start position:0% +obvious thing for this is you know good +news because this will tend to increase + + align:start position:0% +news because this will tend to increase + + + align:start position:0% +news because this will tend to increase +output output will increase dividend + + align:start position:0% +output output will increase dividend + + + align:start position:0% +output output will increase dividend +that's a good good thing for for stocks + + align:start position:0% +that's a good good thing for for stocks + + + align:start position:0% +that's a good good thing for for stocks +uh but the immediate reaction is whoa + + align:start position:0% +uh but the immediate reaction is whoa + + + align:start position:0% +uh but the immediate reaction is whoa +but what will the FED do about this does + + align:start position:0% +but what will the FED do about this does + + + align:start position:0% +but what will the FED do about this does +the FED like + + align:start position:0% +the FED like + + + align:start position:0% +the FED like +that we have more great demand or not + + align:start position:0% +that we have more great demand or not + + + align:start position:0% +that we have more great demand or not +okay and so so so that's that's key here + + align:start position:0% +okay and so so so that's that's key here + + + align:start position:0% +okay and so so so that's that's key here +and and uh so suppose that in this case + + align:start position:0% +and and uh so suppose that in this case + + + align:start position:0% +and and uh so suppose that in this case +the FED did not like the FED like today + + align:start position:0% +the FED did not like the FED like today + + + align:start position:0% +the FED did not like the FED like today +the FED doesn't want more agregate + + align:start position:0% +the FED doesn't want more agregate + + + align:start position:0% +the FED doesn't want more agregate +demand today there no Central Bank + + align:start position:0% +demand today there no Central Bank + + + align:start position:0% +demand today there no Central Bank +around the world maybe in China but but + + align:start position:0% +around the world maybe in China but but + + + align:start position:0% +around the world maybe in China but but +there's no other Central Bank around the + + align:start position:0% +there's no other Central Bank around the + + + align:start position:0% +there's no other Central Bank around the +world that wants more Agate + + align:start position:0% +world that wants more Agate + + + align:start position:0% +world that wants more Agate +demand okay so so if it's if if you the + + align:start position:0% +demand okay so so if it's if if you the + + + align:start position:0% +demand okay so so if it's if if you the +the release is + + align:start position:0% +the release is + + + align:start position:0% +the release is +consumer are very bullish + + align:start position:0% +consumer are very bullish + + + align:start position:0% +consumer are very bullish +now that's not good news I mean + + align:start position:0% +now that's not good news I mean + + + align:start position:0% +now that's not good news I mean +Financial Market inm uh oh we have a Fed + + align:start position:0% +Financial Market inm uh oh we have a Fed + + + align:start position:0% +Financial Market inm uh oh we have a Fed +that is watching for inflation this + + align:start position:0% +that is watching for inflation this + + + align:start position:0% +that is watching for inflation this +means they're going to hike interest + + align:start position:0% +means they're going to hike interest + + + align:start position:0% +means they're going to hike interest +rates okay so what happens to the price + + align:start position:0% +rates okay so what happens to the price + + + align:start position:0% +rates okay so what happens to the price +of bonds then in this environment when C + + align:start position:0% +of bonds then in this environment when C + + + align:start position:0% +of bonds then in this environment when C +goes up and the FED doesn't like it and + + align:start position:0% +goes up and the FED doesn't like it and + + + align:start position:0% +goes up and the FED doesn't like it and +and markets know that the FED doesn't + + align:start position:0% +and markets know that the FED doesn't + + + align:start position:0% +and markets know that the FED doesn't +like it the FED may take a month to + + align:start position:0% +like it the FED may take a month to + + + align:start position:0% +like it the FED may take a month to +react to it but markets react + + align:start position:0% +react to it but markets react + + + align:start position:0% +react to it but markets react +immediately so oh this is what the FED + + align:start position:0% +immediately so oh this is what the FED + + + align:start position:0% +immediately so oh this is what the FED +will do one month from now okay so what + + align:start position:0% +will do one month from now okay so what + + + align:start position:0% +will do one month from now okay so what +do you think happens to the price of + + align:start position:0% +do you think happens to the price of + + + align:start position:0% +do you think happens to the price of +bonds if we get news that you know + + align:start position:0% +bonds if we get news that you know + + + align:start position:0% +bonds if we get news that you know +consumers + + align:start position:0% +consumers + + + align:start position:0% +consumers +are very bullish and and and and it + + align:start position:0% +are very bullish and and and and it + + + align:start position:0% +are very bullish and and and and it +turns out that we also have inflation of + + align:start position:0% +turns out that we also have inflation of + + + align:start position:0% +turns out that we also have inflation of +you know 4% or so so we know that the + + align:start position:0% +you know 4% or so so we know that the + + + align:start position:0% +you know 4% or so so we know that the +FED doesn't like more aggregate + + align:start position:0% +FED doesn't like more aggregate + + + align:start position:0% +FED doesn't like more aggregate +demand what do you think will happen to + + align:start position:0% +demand what do you think will happen to + + + align:start position:0% +demand what do you think will happen to +the price of + + align:start position:0% + + + + align:start position:0% + +bonds well + + align:start position:0% +bonds well + + + align:start position:0% +bonds well +again the news happened + + align:start position:0% +again the news happened + + + align:start position:0% +again the news happened +say er a week ago and the FED moves one + + align:start position:0% +say er a week ago and the FED moves one + + + align:start position:0% +say er a week ago and the FED moves one +week later so so markets are going to + + align:start position:0% +week later so so markets are going to + + + align:start position:0% +week later so so markets are going to +anticipate that in this case the FED + + align:start position:0% +anticipate that in this case the FED + + + align:start position:0% +anticipate that in this case the FED +will hike interest + + align:start position:0% +will hike interest + + + align:start position:0% +will hike interest +rates If the Fed if the markets + + align:start position:0% +rates If the Fed if the markets + + + align:start position:0% +rates If the Fed if the markets +anticipate that the FED will hike + + align:start position:0% +anticipate that the FED will hike + + + align:start position:0% +anticipate that the FED will hike +interest rate interest rate will go up + + align:start position:0% +interest rate interest rate will go up + + + align:start position:0% +interest rate interest rate will go up +immediately not the not the rate that + + align:start position:0% +immediately not the not the rate that + + + align:start position:0% +immediately not the not the rate that +the FED controls but the onee rate the + + align:start position:0% +the FED controls but the onee rate the + + + align:start position:0% +the FED controls but the onee rate the +twoyear rate the three month rate all + + align:start position:0% +twoyear rate the three month rate all + + + align:start position:0% +twoyear rate the three month rate all +those rates are going to go up + + align:start position:0% +those rates are going to go up + + + align:start position:0% +those rates are going to go up +immediately as a result of that okay and + + align:start position:0% +immediately as a result of that okay and + + + align:start position:0% +immediately as a result of that okay and +that we know reduces the price of bonds + + align:start position:0% +that we know reduces the price of bonds + + + align:start position:0% +that we know reduces the price of bonds +bonds and interest rate are the price of + + align:start position:0% +bonds and interest rate are the price of + + + align:start position:0% +bonds and interest rate are the price of +a bond and the interest R are inversely + + align:start position:0% +a bond and the interest R are inversely + + + align:start position:0% +a bond and the interest R are inversely +related so the anticipation that the FED + + align:start position:0% +related so the anticipation that the FED + + + align:start position:0% +related so the anticipation that the FED +will hyate will lead to higher interest + + align:start position:0% +will hyate will lead to higher interest + + + align:start position:0% +will hyate will lead to higher interest +rates at all Horizons and and and that + + align:start position:0% +rates at all Horizons and and and that + + + align:start position:0% +rates at all Horizons and and and that +will reduce the price of bonds okay so + + align:start position:0% +will reduce the price of bonds okay so + + + align:start position:0% +will reduce the price of bonds okay so +this thing that and for Equity well look + + align:start position:0% +this thing that and for Equity well look + + + align:start position:0% +this thing that and for Equity well look +what happened for Equity here well for + + align:start position:0% +what happened for Equity here well for + + + align:start position:0% +what happened for Equity here well for +Equity you say okay well I get the same + + align:start position:0% +Equity you say okay well I get the same + + + align:start position:0% +Equity you say okay well I get the same +discounting effect of the bond which is + + align:start position:0% +discounting effect of the bond which is + + + align:start position:0% +discounting effect of the bond which is +bad news goes down and uh and what ah + + align:start position:0% +bad news goes down and uh and what ah + + + align:start position:0% +bad news goes down and uh and what ah +but the good news is the dividend no + + align:start position:0% +but the good news is the dividend no + + + align:start position:0% +but the good news is the dividend no +because now I have more consumers well + + align:start position:0% +because now I have more consumers well + + + align:start position:0% +because now I have more consumers well +that depends on how much the FED + + align:start position:0% +that depends on how much the FED + + + align:start position:0% +that depends on how much the FED +dislikes this stuff because if the FED + + align:start position:0% +dislikes this stuff because if the FED + + + align:start position:0% +dislikes this stuff because if the FED +does this that mean it upsets it fully + + align:start position:0% +does this that mean it upsets it fully + + + align:start position:0% +does this that mean it upsets it fully +offsets the the effect on agre demand + + align:start position:0% +offsets the the effect on agre demand + + + align:start position:0% +offsets the the effect on agre demand +increasing the zero shift to the right + + align:start position:0% +increasing the zero shift to the right + + + align:start position:0% +increasing the zero shift to the right +that would have increased output to here + + align:start position:0% +that would have increased output to here + + + align:start position:0% +that would have increased output to here +the F doesn't want more output so we + + align:start position:0% +the F doesn't want more output so we + + + align:start position:0% +the F doesn't want more output so we +will hike interest rate up to the point + + align:start position:0% +will hike interest rate up to the point + + + align:start position:0% +will hike interest rate up to the point +which output doesn't go up that means + + align:start position:0% +which output doesn't go up that means + + + align:start position:0% +which output doesn't go up that means +divid are not going to go up + + align:start position:0% +divid are not going to go up + + + align:start position:0% +divid are not going to go up +either so we get just a negative effect + + align:start position:0% +either so we get just a negative effect + + + align:start position:0% +either so we get just a negative effect +of the discounting and we don't get the + + align:start position:0% +of the discounting and we don't get the + + + align:start position:0% +of the discounting and we don't get the +benefit of the extra activity that would + + align:start position:0% +benefit of the extra activity that would + + + align:start position:0% +benefit of the extra activity that would +have come from having consumers that are + + align:start position:0% +have come from having consumers that are + + + align:start position:0% +have come from having consumers that are +more optimistic and so on + + align:start position:0% +more optimistic and so on + + + align:start position:0% +more optimistic and so on +okay so this is actually this has + + align:start position:0% +okay so this is actually this has + + + align:start position:0% +okay so this is actually this has +happened a + + align:start position:0% +happened a + + + align:start position:0% +happened a +lot over the last few months this is an + + align:start position:0% +lot over the last few months this is an + + + align:start position:0% +lot over the last few months this is an +environment people call it's an + + align:start position:0% +environment people call it's an + + + align:start position:0% +environment people call it's an +environment where good news is bad news + + align:start position:0% +environment where good news is bad news + + + align:start position:0% +environment where good news is bad news +okay good news about aggregate demand + + align:start position:0% +okay good news about aggregate demand + + + align:start position:0% +okay good news about aggregate demand +consumers are happy blah blah blah is + + align:start position:0% +consumers are happy blah blah blah is + + + align:start position:0% +consumers are happy blah blah blah is +bad news or labor markets are very tight + + align:start position:0% +bad news or labor markets are very tight + + + align:start position:0% +bad news or labor markets are very tight +wages are going up all things that sound + + align:start position:0% +wages are going up all things that sound + + + align:start position:0% +wages are going up all things that sound +wonderful in other environments sound + + align:start position:0% +wonderful in other environments sound + + + align:start position:0% +wonderful in other environments sound +terrible news for the financial Market + + align:start position:0% +terrible news for the financial Market + + + align:start position:0% +terrible news for the financial Market +okay for most I mean there's difference + + align:start position:0% +okay for most I mean there's difference + + + align:start position:0% +okay for most I mean there's difference +in different sectors and so on but but + + align:start position:0% +in different sectors and so on but but + + + align:start position:0% +in different sectors and so on but but +for the aggregate for the average it's + + align:start position:0% +for the aggregate for the average it's + + + align:start position:0% +for the aggregate for the average it's +bad news so this is an environment where + + align:start position:0% +bad news so this is an environment where + + + align:start position:0% +bad news so this is an environment where +good news is bad news good news about + + align:start position:0% +good news is bad news good news about + + + align:start position:0% +good news is bad news good news about +aggregate demand you have to be specific + + align:start position:0% +aggregate demand you have to be specific + + + align:start position:0% +aggregate demand you have to be specific +about what good news about aggregate + + align:start position:0% +about what good news about aggregate + + + align:start position:0% +about what good news about aggregate +demand is bad news for asset markets + + align:start position:0% +demand is bad news for asset markets + + + align:start position:0% +demand is bad news for asset markets +it's not always like that if you're in a + + align:start position:0% +it's not always like that if you're in a + + + align:start position:0% +it's not always like that if you're in a +recession + + align:start position:0% +recession + + + align:start position:0% +recession +the FED doesn't want to fight that it + + align:start position:0% +the FED doesn't want to fight that it + + + align:start position:0% +the FED doesn't want to fight that it +wants to have more aggregate demand so + + align:start position:0% +wants to have more aggregate demand so + + + align:start position:0% +wants to have more aggregate demand so +if you get good news about aggregate + + align:start position:0% +if you get good news about aggregate + + + align:start position:0% +if you get good news about aggregate +demand that's very good news for asset + + align:start position:0% +demand that's very good news for asset + + + align:start position:0% +demand that's very good news for asset +prices because the FED will not offset + + align:start position:0% +prices because the FED will not offset + + + align:start position:0% +prices because the FED will not offset +that and you get the positive effect of + + align:start position:0% +that and you get the positive effect of + + + align:start position:0% +that and you get the positive effect of +extra dividends and things of that kind + + align:start position:0% +extra dividends and things of that kind + + + align:start position:0% +extra dividends and things of that kind +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +okay another component that is that + + align:start position:0% +okay another component that is that + + + align:start position:0% +okay another component that is that +moves asset prices a lot so monetary + + align:start position:0% +moves asset prices a lot so monetary + + + align:start position:0% +moves asset prices a lot so monetary +policy moves asset prices a lot okay and + + align:start position:0% +policy moves asset prices a lot okay and + + + align:start position:0% +policy moves asset prices a lot okay and +and mon monetary policy doesn't happen + + align:start position:0% +and mon monetary policy doesn't happen + + + align:start position:0% +and mon monetary policy doesn't happen +in some separate isolated space it it it + + align:start position:0% +in some separate isolated space it it it + + + align:start position:0% +in some separate isolated space it it it +reacts to news about the economy about + + align:start position:0% +reacts to news about the economy about + + + align:start position:0% +reacts to news about the economy about +consumers about firms about Regional + + align:start position:0% +consumers about firms about Regional + + + align:start position:0% +consumers about firms about Regional +Banks all sort of things + + align:start position:0% +Banks all sort of things + + + align:start position:0% +Banks all sort of things +okay a another Big Driver of asset + + align:start position:0% +okay a another Big Driver of asset + + + align:start position:0% +okay a another Big Driver of asset +prices is this guy here of of equity in + + align:start position:0% +prices is this guy here of of equity in + + + align:start position:0% +prices is this guy here of of equity in +particular is this risk premium okay so + + align:start position:0% +particular is this risk premium okay so + + + align:start position:0% +particular is this risk premium okay so +that risk premium can move a + + align:start position:0% +that risk premium can move a + + + align:start position:0% +that risk premium can move a +lot and and it's an important driver of + + align:start position:0% +lot and and it's an important driver of + + + align:start position:0% +lot and and it's an important driver of +asset + + align:start position:0% +asset + + + align:start position:0% +asset +prices this Index this is the it's + + align:start position:0% +prices this Index this is the it's + + + align:start position:0% +prices this Index this is the it's +called vix vix is I'm not going to + + align:start position:0% +called vix vix is I'm not going to + + + align:start position:0% +called vix vix is I'm not going to +explain what it is but people call it so + + align:start position:0% +explain what it is but people call it so + + + align:start position:0% +explain what it is but people call it so +you get the picture an index of fear in + + align:start position:0% +you get the picture an index of fear in + + + align:start position:0% +you get the picture an index of fear in +in the equity Market is it's done well + + align:start position:0% +in the equity Market is it's done well + + + align:start position:0% +in the equity Market is it's done well +I'm not going to tell you what it is + + align:start position:0% +I'm not going to tell you what it is + + + align:start position:0% +I'm not going to tell you what it is +it's based on option prices and + + align:start position:0% +it's based on option prices and + + + align:start position:0% +it's based on option prices and +so er so this is this is you know when + + align:start position:0% +so er so this is this is you know when + + + align:start position:0% +so er so this is this is you know when +people realize that covid was coming and + + align:start position:0% +people realize that covid was coming and + + + align:start position:0% +people realize that covid was coming and +so what you see is that this thing + + align:start position:0% +so what you see is that this thing + + + align:start position:0% +so what you see is that this thing +exploded up big big risk off that's a + + align:start position:0% +exploded up big big risk off that's a + + + align:start position:0% +exploded up big big risk off that's a +massive spike in the little + + align:start position:0% +massive spike in the little + + + align:start position:0% +massive spike in the little +excess well not surprisingly look what + + align:start position:0% +excess well not surprisingly look what + + + align:start position:0% +excess well not surprisingly look what +happened to equity you know collaps by + + align:start position:0% +happened to equity you know collaps by + + + align:start position:0% +happened to equity you know collaps by +35% or so part of that was expected + + align:start position:0% +35% or so part of that was expected + + + align:start position:0% +35% or so part of that was expected +deviant blah blah blah but a lot of it + + align:start position:0% +deviant blah blah blah but a lot of it + + + align:start position:0% +deviant blah blah blah but a lot of it +was the risk of and it's called risk off + + align:start position:0% +was the risk of and it's called risk off + + + align:start position:0% +was the risk of and it's called risk off +when markets are very fearful they don't + + align:start position:0% +when markets are very fearful they don't + + + align:start position:0% +when markets are very fearful they don't +want to take risk risk off okay ER the + + align:start position:0% +want to take risk risk off okay ER the + + + align:start position:0% +want to take risk risk off okay ER the +recovery actually also had a lot to do + + align:start position:0% +recovery actually also had a lot to do + + + align:start position:0% +recovery actually also had a lot to do +with the recovery on the risk + + align:start position:0% +with the recovery on the risk + + + align:start position:0% +with the recovery on the risk +environment people sort of got used to + + align:start position:0% +environment people sort of got used to + + + align:start position:0% +environment people sort of got used to +the thing but that recovery also was a + + align:start position:0% +the thing but that recovery also was a + + + align:start position:0% +the thing but that recovery also was a +result of very aggressive monetary + + align:start position:0% +result of very aggressive monetary + + + align:start position:0% +result of very aggressive monetary +policy the FED tried to offset this by + + align:start position:0% +policy the FED tried to offset this by + + + align:start position:0% +policy the FED tried to offset this by +cutting interest ratees very + + align:start position:0% +cutting interest ratees very + + + align:start position:0% +cutting interest ratees very +aggressively and that also give a boost + + align:start position:0% +aggressively and that also give a boost + + + align:start position:0% +aggressively and that also give a boost +to asset prices in fact they did so much + + align:start position:0% +to asset prices in fact they did so much + + + align:start position:0% +to asset prices in fact they did so much +that we end up with a big lots of + + align:start position:0% +that we end up with a big lots of + + + align:start position:0% +that we end up with a big lots of +overvaluation in asset prices and then + + align:start position:0% +overvaluation in asset prices and then + + + align:start position:0% +overvaluation in asset prices and then +that's reason when they hi rate so we + + align:start position:0% +that's reason when they hi rate so we + + + align:start position:0% +that's reason when they hi rate so we +have big a big decline in asset prices + + align:start position:0% +have big a big decline in asset prices + + + align:start position:0% +have big a big decline in asset prices +as a result + + align:start position:0% +as a result + + + align:start position:0% +as a result +okay what is this ah look this is a you + + align:start position:0% +okay what is this ah look this is a you + + + align:start position:0% +okay what is this ah look this is a you +know over the + + align:start position:0% +know over the + + + align:start position:0% +know over the +weekend over the + + align:start position:0% +weekend over the + + + align:start position:0% +weekend over the +weekend I I we talked about this in the + + align:start position:0% +weekend I I we talked about this in the + + + align:start position:0% +weekend I I we talked about this in the +previous lecture um essentially the + + align:start position:0% +previous lecture um essentially the + + + align:start position:0% +previous lecture um essentially the +First Republic Bank went + + align:start position:0% +First Republic Bank went + + + align:start position:0% +First Republic Bank went +under ER and JP Morgan absorb it ER so + + align:start position:0% +under ER and JP Morgan absorb it ER so + + + align:start position:0% +under ER and JP Morgan absorb it ER so +people thought that um that and Monday + + align:start position:0% +people thought that um that and Monday + + + align:start position:0% +people thought that um that and Monday +was was good because you know people + + align:start position:0% +was was good because you know people + + + align:start position:0% +was was good because you know people +thought that this mini crisis was + + align:start position:0% +thought that this mini crisis was + + + align:start position:0% +thought that this mini crisis was +over well + + align:start position:0% +over well + + + align:start position:0% +over well +yesterday ER it turns out that that two + + align:start position:0% +yesterday ER it turns out that that two + + + align:start position:0% +yesterday ER it turns out that that two +other Regional Banks the shares began to + + align:start position:0% +other Regional Banks the shares began to + + + align:start position:0% +other Regional Banks the shares began to +collapse in the same way as the First + + align:start position:0% +collapse in the same way as the First + + + align:start position:0% +collapse in the same way as the First +Republic Bank shares collapsed the week + + align:start position:0% +Republic Bank shares collapsed the week + + + align:start position:0% +Republic Bank shares collapsed the week +before okay so Panic immediately set in + + align:start position:0% +before okay so Panic immediately set in + + + align:start position:0% +before okay so Panic immediately set in +so the vix the fear + + align:start position:0% +so the vix the fear + + + align:start position:0% +so the vix the fear +Index this intraday so markets open here + + align:start position:0% +Index this intraday so markets open here + + + align:start position:0% +Index this intraday so markets open here +and and the shares of this this these + + align:start position:0% +and and the shares of this this these + + + align:start position:0% +and and the shares of this this these +two Banks began to decline very rapidly + + align:start position:0% +two Banks began to decline very rapidly + + + align:start position:0% +two Banks began to decline very rapidly +and so H vix went up a lot and what you + + align:start position:0% +and so H vix went up a lot and what you + + + align:start position:0% +and so H vix went up a lot and what you +look this is sp this is the main this is + + align:start position:0% +look this is sp this is the main this is + + + align:start position:0% +look this is sp this is the main this is +the SPX the the main SP S&P 500 is the + + align:start position:0% +the SPX the the main SP S&P 500 is the + + + align:start position:0% +the SPX the the main SP S&P 500 is the +main price index Equity price index in + + align:start position:0% +main price index Equity price index in + + + align:start position:0% +main price index Equity price index in +the US immediately decline okay so + + align:start position:0% +the US immediately decline okay so + + + align:start position:0% +the US immediately decline okay so +that's a XS moving here XS move up + + align:start position:0% +that's a XS moving here XS move up + + + align:start position:0% +that's a XS moving here XS move up +little X and then it began to come down + + align:start position:0% +little X and then it began to come down + + + align:start position:0% +little X and then it began to come down +and the markets began to recover so this + + align:start position:0% +and the markets began to recover so this + + + align:start position:0% +and the markets began to recover so this +risk on and off is a is a very big + + align:start position:0% +risk on and off is a is a very big + + + align:start position:0% +risk on and off is a is a very big +driver of Equity + + align:start position:0% + + + + align:start position:0% + +prices this is one of the banks actually + + align:start position:0% +prices this is one of the banks actually + + + align:start position:0% +prices this is one of the banks actually +that was in + + align:start position:0% +that was in + + + align:start position:0% +that was in +trouble ER you you see + + align:start position:0% +trouble ER you you see + + + align:start position:0% +trouble ER you you see +that by the end of the day this this + + align:start position:0% +that by the end of the day this this + + + align:start position:0% +that by the end of the day this this +this this is um P West P West had + + align:start position:0% +this this is um P West P West had + + + align:start position:0% +this this is um P West P West had +declined by 28% by the end of the day + + align:start position:0% +declined by 28% by the end of the day + + + align:start position:0% +declined by 28% by the end of the day +but you see things look very weird here + + align:start position:0% +but you see things look very weird here + + + align:start position:0% +but you see things look very weird here +they don't look like normal + + align:start position:0% +they don't look like normal + + + align:start position:0% +they don't look like normal +prices okay here they look like normal + + align:start position:0% +prices okay here they look like normal + + + align:start position:0% +prices okay here they look like normal +prices they're moving all the time + + align:start position:0% +prices they're moving all the time + + + align:start position:0% +prices they're moving all the time +here they don't what happens is that + + align:start position:0% +here they don't what happens is that + + + align:start position:0% +here they don't what happens is that +these prices decline so rapidly that + + align:start position:0% +these prices decline so rapidly that + + + align:start position:0% +these prices decline so rapidly that +they trigger what is called circuit + + align:start position:0% +they trigger what is called circuit + + + align:start position:0% +they trigger what is called circuit +breakers so the you cannot trade those + + align:start position:0% +breakers so the you cannot trade those + + + align:start position:0% +breakers so the you cannot trade those +those shares when they decline too + + align:start position:0% +those shares when they decline too + + + align:start position:0% +those shares when they decline too +rapidly and that's done deliberately so + + align:start position:0% +rapidly and that's done deliberately so + + + align:start position:0% +rapidly and that's done deliberately so +this little X doesn't get completely out + + align:start position:0% +this little X doesn't get completely out + + + align:start position:0% +this little X doesn't get completely out +of control people to come down okay and + + align:start position:0% +of control people to come down okay and + + + align:start position:0% +of control people to come down okay and +and so he trigger it several times just + + align:start position:0% +and so he trigger it several times just + + + align:start position:0% +and so he trigger it several times just +as the whole idea is that people come + + align:start position:0% +as the whole idea is that people come + + + align:start position:0% +as the whole idea is that people come +down you know they don't it's a request + + align:start position:0% +down you know they don't it's a request + + + align:start position:0% +down you know they don't it's a request +yeah just on the last Slide the previous + + align:start position:0% +yeah just on the last Slide the previous + + + align:start position:0% +yeah just on the last Slide the previous +or this one + + align:start position:0% + + + + align:start position:0% + +yeah either them dependent on the other + + align:start position:0% +yeah either them dependent on the other + + + align:start position:0% +yeah either them dependent on the other +or they more just showing the same sort + + align:start position:0% +or they more just showing the same sort + + + align:start position:0% +or they more just showing the same sort +of trend no no okay that's a a good + + align:start position:0% +of trend no no okay that's a a good + + + align:start position:0% +of trend no no okay that's a a good +question this is the risk component only + + align:start position:0% +question this is the risk component only + + + align:start position:0% +question this is the risk component only +so this is more independent what I'm + + align:start position:0% +so this is more independent what I'm + + + align:start position:0% +so this is more independent what I'm +saying when this guy goes up if nothing + + align:start position:0% +saying when this guy goes up if nothing + + + align:start position:0% +saying when this guy goes up if nothing +else happens H this will decline because + + align:start position:0% +else happens H this will decline because + + + align:start position:0% +else happens H this will decline because +you're discounting things more heavily + + align:start position:0% +you're discounting things more heavily + + + align:start position:0% +you're discounting things more heavily +but it is true that were some common + + align:start position:0% +but it is true that were some common + + + align:start position:0% +but it is true that were some common +elements they're also common elements + + align:start position:0% +elements they're also common elements + + + align:start position:0% +elements they're also common elements +which is people got very worried about + + align:start position:0% +which is people got very worried about + + + align:start position:0% +which is people got very worried about +having another Regional Bank collapsing + + align:start position:0% +having another Regional Bank collapsing + + + align:start position:0% +having another Regional Bank collapsing +and so on and so that that also created + + align:start position:0% +and so on and so that that also created + + + align:start position:0% +and so on and so that that also created +fear about the economy which is an + + align:start position:0% +fear about the economy which is an + + + align:start position:0% +fear about the economy which is an +independent reason for this to decline + + align:start position:0% +independent reason for this to decline + + + align:start position:0% +independent reason for this to decline +and normally in recessions as well this + + align:start position:0% +and normally in recessions as well this + + + align:start position:0% +and normally in recessions as well this +risk in appetite is is is is lower so so + + align:start position:0% +risk in appetite is is is is lower so so + + + align:start position:0% +risk in appetite is is is is lower so so +you're right that is a common component + + align:start position:0% +you're right that is a common component + + + align:start position:0% +you're right that is a common component +but the point I was highlighting is that + + align:start position:0% +but the point I was highlighting is that + + + align:start position:0% +but the point I was highlighting is that +is that this vix sort of is a Big Driver + + align:start position:0% +is that this vix sort of is a Big Driver + + + align:start position:0% +is that this vix sort of is a Big Driver +it has a big impact on Asser prices + + align:start position:0% +it has a big impact on Asser prices + + + align:start position:0% +it has a big impact on Asser prices +but it's not the cause it was an event + + align:start position:0% +but it's not the cause it was an event + + + align:start position:0% +but it's not the cause it was an event +that cost both but the fact that this + + align:start position:0% +that cost both but the fact that this + + + align:start position:0% +that cost both but the fact that this +event came with this biggest spike in in + + align:start position:0% +event came with this biggest spike in in + + + align:start position:0% +event came with this biggest spike in in +the vix meant that that the impact on + + align:start position:0% +the vix meant that that the impact on + + + align:start position:0% +the vix meant that that the impact on +the equity index was was larger than if + + align:start position:0% +the equity index was was larger than if + + + align:start position:0% +the equity index was was larger than if +it had been only news about the economy + + align:start position:0% +it had been only news about the economy + + + align:start position:0% +it had been only news about the economy +meaning that there was a recession ahead + + align:start position:0% +meaning that there was a recession ahead + + + align:start position:0% +meaning that there was a recession ahead +or something like that and let me just + + align:start position:0% +or something like that and let me just + + + align:start position:0% +or something like that and let me just +finish with a with with the opposite + + align:start position:0% +finish with a with with the opposite + + + align:start position:0% +finish with a with with the opposite +phenomenon you know I I wasbe in + + align:start position:0% +phenomenon you know I I wasbe in + + + align:start position:0% +phenomenon you know I I wasbe in +episodes of fear but sometimes markets + + align:start position:0% +episodes of fear but sometimes markets + + + align:start position:0% +episodes of fear but sometimes markets +get very carried away the opposite + + align:start position:0% +get very carried away the opposite + + + align:start position:0% +get very carried away the opposite +direction okay and here I'm showing you + + align:start position:0% +direction okay and here I'm showing you + + + align:start position:0% +direction okay and here I'm showing you +you know examples I put together this + + align:start position:0% +you know examples I put together this + + + align:start position:0% +you know examples I put together this +picture many years back and now deutche + + align:start position:0% +picture many years back and now deutche + + + align:start position:0% +picture many years back and now deutche +Bank keeps updating it which is it show + + align:start position:0% +Bank keeps updating it which is it show + + + align:start position:0% +Bank keeps updating it which is it show +you s some it seems that the world needs + + align:start position:0% +you s some it seems that the world needs + + + align:start position:0% +you s some it seems that the world needs +a bubble somewhere and here it show you + + align:start position:0% +a bubble somewhere and here it show you + + + align:start position:0% +a bubble somewhere and here it show you +several sort of big asset valuations you + + align:start position:0% +several sort of big asset valuations you + + + align:start position:0% +several sort of big asset valuations you +know look + + align:start position:0% +know look + + + align:start position:0% +know look +500% the here is the Nik I mean it was + + align:start position:0% +500% the here is the Nik I mean it was + + + align:start position:0% +500% the here is the Nik I mean it was +enormous appreciation of the Nik here + + align:start position:0% +enormous appreciation of the Nik here + + + align:start position:0% +enormous appreciation of the Nik here +was Bitcoin then it collapsed okay they + + align:start position:0% +was Bitcoin then it collapsed okay they + + + align:start position:0% +was Bitcoin then it collapsed okay they +always end up back but you never you see + + align:start position:0% +always end up back but you never you see + + + align:start position:0% +always end up back but you never you see +see this big sort of spiking up they + + align:start position:0% +see this big sort of spiking up they + + + align:start position:0% +see this big sort of spiking up they +almost always end up quite poorly now + + align:start position:0% +almost always end up quite poorly now + + + align:start position:0% +almost always end up quite poorly now +this is is much more likely that it + + align:start position:0% +this is is much more likely that it + + + align:start position:0% +this is is much more likely that it +happens in equity than in Bonds in bonds + + align:start position:0% +happens in equity than in Bonds in bonds + + + align:start position:0% +happens in equity than in Bonds in bonds +it cannot happen because there is a + + align:start position:0% +it cannot happen because there is a + + + align:start position:0% +it cannot happen because there is a +terminal date a terminal value so so + + align:start position:0% +terminal date a terminal value so so + + + align:start position:0% +terminal date a terminal value so so +what happens with these kind of things + + align:start position:0% +what happens with these kind of things + + + align:start position:0% +what happens with these kind of things +people dream that the value go will go + + align:start position:0% +people dream that the value go will go + + + align:start position:0% +people dream that the value go will go +to Infinity know and it could because + + align:start position:0% +to Infinity know and it could because + + + align:start position:0% +to Infinity know and it could because +the thing will last to infinity and and + + align:start position:0% +the thing will last to infinity and and + + + align:start position:0% +the thing will last to infinity and and +you know the price could go to Infinity + + align:start position:0% +you know the price could go to Infinity + + + align:start position:0% +you know the price could go to Infinity +for a bond that cannot happen because it + + align:start position:0% +for a bond that cannot happen because it + + + align:start position:0% +for a bond that cannot happen because it +is a terminal date and that date they're + + align:start position:0% +is a terminal date and that date they're + + + align:start position:0% +is a terminal date and that date they're +going to pay you 100 so it can't happen + + align:start position:0% +going to pay you 100 so it can't happen + + + align:start position:0% +going to pay you 100 so it can't happen +but for Equity people's imagination can + + align:start position:0% +but for Equity people's imagination can + + + align:start position:0% +but for Equity people's imagination can +run very wild in fact there is a famous + + align:start position:0% +run very wild in fact there is a famous + + + align:start position:0% +run very wild in fact there is a famous +bubble the south sea bubble is a company + + align:start position:0% +bubble the south sea bubble is a company + + + align:start position:0% +bubble the south sea bubble is a company +in the UK is famous for many reasons but + + align:start position:0% +in the UK is famous for many reasons but + + + align:start position:0% +in the UK is famous for many reasons but +but one of them is that Isaac Newton got + + align:start position:0% +but one of them is that Isaac Newton got + + + align:start position:0% +but one of them is that Isaac Newton got +involved in in this one and and you know + + align:start position:0% +involved in in this one and and you know + + + align:start position:0% +involved in in this one and and you know +he got carried away he he sold he made a + + align:start position:0% +he got carried away he he sold he made a + + + align:start position:0% +he got carried away he he sold he made a +profit you know he sold the shares at + + align:start position:0% +profit you know he sold the shares at + + + align:start position:0% +profit you know he sold the shares at +7,000 he profited 3500 pounds which must + + align:start position:0% +7,000 he profited 3500 pounds which must + + + align:start position:0% +7,000 he profited 3500 pounds which must +have been an enormous amount of money at + + align:start position:0% +have been an enormous amount of money at + + + align:start position:0% +have been an enormous amount of money at +the time prices kept going up couldn't + + align:start position:0% +the time prices kept going up couldn't + + + align:start position:0% +the time prices kept going up couldn't +resist went back in end up losing + + align:start position:0% +resist went back in end up losing + + + align:start position:0% +resist went back in end up losing +20,000 which was a lot of money so he + + align:start position:0% +20,000 which was a lot of money so he + + + align:start position:0% +20,000 which was a lot of money so he +famously say I can calculate theem + + align:start position:0% +famously say I can calculate theem + + + align:start position:0% +famously say I can calculate theem +motions of the heavenly bodies but not + + align:start position:0% +motions of the heavenly bodies but not + + + align:start position:0% +motions of the heavenly bodies but not +the madness of people this all about + + align:start position:0% +the madness of people this all about + + + align:start position:0% +the madness of people this all about +expectations okay let me stop here \ No newline at end of file diff --git a/ee6E6aUGpm0.txt b/ee6E6aUGpm0.txt new file mode 100644 index 0000000000000000000000000000000000000000..9b7982b0adacd749c4bbbfb1b962b986d5540cf4 --- /dev/null +++ b/ee6E6aUGpm0.txt @@ -0,0 +1,859 @@ +align:start position:0% + +as we discussed in the previous video + + align:start position:0% +as we discussed in the previous video + + + align:start position:0% +as we discussed in the previous video +Netflix was willing to pay over 1 + + align:start position:0% +Netflix was willing to pay over 1 + + + align:start position:0% +Netflix was willing to pay over 1 +million dollars for the best user rating + + align:start position:0% +million dollars for the best user rating + + + align:start position:0% +million dollars for the best user rating +algorithm which shows how critical the + + align:start position:0% +algorithm which shows how critical the + + + align:start position:0% +algorithm which shows how critical the +recommendation system is to their + + align:start position:0% +recommendation system is to their + + + align:start position:0% +recommendation system is to their +business in this video we'll discuss how + + align:start position:0% +business in this video we'll discuss how + + + align:start position:0% +business in this video we'll discuss how +recommendation systems work let's start + + align:start position:0% +recommendation systems work let's start + + + align:start position:0% +recommendation systems work let's start +by thinking about the data when + + align:start position:0% +by thinking about the data when + + + align:start position:0% +by thinking about the data when +predicting user ratings what data could + + align:start position:0% +predicting user ratings what data could + + + align:start position:0% +predicting user ratings what data could +be useful there are two main types of + + align:start position:0% +be useful there are two main types of + + + align:start position:0% +be useful there are two main types of +data that we could use the first is that + + align:start position:0% +data that we could use the first is that + + + align:start position:0% +data that we could use the first is that +for every movie in Netflix's database we + + align:start position:0% +for every movie in Netflix's database we + + + align:start position:0% +for every movie in Netflix's database we +have a ranking from all users who have + + align:start position:0% +have a ranking from all users who have + + + align:start position:0% +have a ranking from all users who have +ranked that movie the second is that we + + align:start position:0% +ranked that movie the second is that we + + + align:start position:0% +ranked that movie the second is that we +know facts about the movie itself the + + align:start position:0% +know facts about the movie itself the + + + align:start position:0% +know facts about the movie itself the +actors in the movie the director the + + align:start position:0% +actors in the movie the director the + + + align:start position:0% +actors in the movie the director the +genre classifications of the movie the + + align:start position:0% +genre classifications of the movie the + + + align:start position:0% +genre classifications of the movie the +year it was released etc as an example + + align:start position:0% +year it was released etc as an example + + + align:start position:0% +year it was released etc as an example +suppose we have the following user + + align:start position:0% +suppose we have the following user + + + align:start position:0% +suppose we have the following user +ratings for for users and for movies our + + align:start position:0% +ratings for for users and for movies our + + + align:start position:0% +ratings for for users and for movies our +users are Amy Bob Carl and Dan and our + + align:start position:0% +users are Amy Bob Carl and Dan and our + + + align:start position:0% +users are Amy Bob Carl and Dan and our +movies are men in black Apollo 13 + + align:start position:0% +movies are men in black Apollo 13 + + + align:start position:0% +movies are men in black Apollo 13 +Top Gun and Terminator the ratings are + + align:start position:0% +Top Gun and Terminator the ratings are + + + align:start position:0% +Top Gun and Terminator the ratings are +on a one to five scale where one is the + + align:start position:0% +on a one to five scale where one is the + + + align:start position:0% +on a one to five scale where one is the +lowest rating and five is the highest + + align:start position:0% +lowest rating and five is the highest + + + align:start position:0% +lowest rating and five is the highest +rating the blank entries mean that the + + align:start position:0% +rating the blank entries mean that the + + + align:start position:0% +rating the blank entries mean that the +user has not rated the movie we could + + align:start position:0% +user has not rated the movie we could + + + align:start position:0% +user has not rated the movie we could +suggest to Carl + + align:start position:0% +suggest to Carl + + + align:start position:0% +suggest to Carl +Betty Watchmen and black since Amy rated + + align:start position:0% +Betty Watchmen and black since Amy rated + + + align:start position:0% +Betty Watchmen and black since Amy rated +at highly she gave it a rating of five + + align:start position:0% +at highly she gave it a rating of five + + + align:start position:0% +at highly she gave it a rating of five +and Amy and Carl seemed to have similar + + align:start position:0% +and Amy and Carl seemed to have similar + + + align:start position:0% +and Amy and Carl seemed to have similar +ratings for the other movies this + + align:start position:0% +ratings for the other movies this + + + align:start position:0% +ratings for the other movies this +technique of using other users ratings + + align:start position:0% +technique of using other users ratings + + + align:start position:0% +technique of using other users ratings +to make predictions is called + + align:start position:0% +to make predictions is called + + + align:start position:0% +to make predictions is called +collaborative filtering note that we're + + align:start position:0% +collaborative filtering note that we're + + + align:start position:0% +collaborative filtering note that we're +not using any information about the + + align:start position:0% +not using any information about the + + + align:start position:0% +not using any information about the +movie itself here just the similarity + + align:start position:0% +movie itself here just the similarity + + + align:start position:0% +movie itself here just the similarity +between users instead we could use movie + + align:start position:0% +between users instead we could use movie + + + align:start position:0% +between users instead we could use movie +information to predict user ratings we + + align:start position:0% +information to predict user ratings we + + + align:start position:0% +information to predict user ratings we +saw on the table that Amy liked men and + + align:start position:0% +saw on the table that Amy liked men and + + + align:start position:0% +saw on the table that Amy liked men and +black she gave it a rating of five we + + align:start position:0% +black she gave it a rating of five we + + + align:start position:0% +black she gave it a rating of five we +know that this movie was directed by + + align:start position:0% +know that this movie was directed by + + + align:start position:0% +know that this movie was directed by +Barry Sonnenfeld + + align:start position:0% +Barry Sonnenfeld + + + align:start position:0% +Barry Sonnenfeld +is classified in the genres of action + + align:start position:0% +is classified in the genres of action + + + align:start position:0% +is classified in the genres of action +adventure sci-fi and comedy and it stars + + align:start position:0% +adventure sci-fi and comedy and it stars + + + align:start position:0% +adventure sci-fi and comedy and it stars +actor Will Smith based on this + + align:start position:0% +actor Will Smith based on this + + + align:start position:0% +actor Will Smith based on this +information we could make + + align:start position:0% +information we could make + + + align:start position:0% +information we could make +recommendations to + + align:start position:0% +recommendations to + + + align:start position:0% +recommendations to +Amy we could recommend to Amy another + + align:start position:0% +Amy we could recommend to Amy another + + + align:start position:0% +Amy we could recommend to Amy another +movie by the same director barry + + align:start position:0% +movie by the same director barry + + + align:start position:0% +movie by the same director barry +sonnenfeld movie get shorty we could + + align:start position:0% +sonnenfeld movie get shorty we could + + + align:start position:0% +sonnenfeld movie get shorty we could +instead recommend the movie Jurassic + + align:start position:0% +instead recommend the movie Jurassic + + + align:start position:0% +instead recommend the movie Jurassic +Park which is also classified in the + + align:start position:0% +Park which is also classified in the + + + align:start position:0% +Park which is also classified in the +genres of action-adventure and sci-fi or + + align:start position:0% +genres of action-adventure and sci-fi or + + + align:start position:0% +genres of action-adventure and sci-fi or +we could recommend to Amy another movie + + align:start position:0% +we could recommend to Amy another movie + + + align:start position:0% +we could recommend to Amy another movie +starring Will Smith hitch note that + + align:start position:0% +starring Will Smith hitch note that + + + align:start position:0% +starring Will Smith hitch note that +we're not using the ratings of other + + align:start position:0% +we're not using the ratings of other + + + align:start position:0% +we're not using the ratings of other +users at all here just information about + + align:start position:0% +users at all here just information about + + + align:start position:0% +users at all here just information about +the movie this technique is called + + align:start position:0% +the movie this technique is called + + + align:start position:0% +the movie this technique is called +content filtering there are strengths + + align:start position:0% +content filtering there are strengths + + + align:start position:0% +content filtering there are strengths +and weaknesses to both types of + + align:start position:0% +and weaknesses to both types of + + + align:start position:0% +and weaknesses to both types of +recommendation systems collaborative + + align:start position:0% +recommendation systems collaborative + + + align:start position:0% +recommendation systems collaborative +filtering can accurately suggest complex + + align:start position:0% +filtering can accurately suggest complex + + + align:start position:0% +filtering can accurately suggest complex +items without understanding the nature + + align:start position:0% +items without understanding the nature + + + align:start position:0% +items without understanding the nature +of the items + + align:start position:0% +of the items + + + align:start position:0% +of the items +it didn't matter at all that our items + + align:start position:0% +it didn't matter at all that our items + + + align:start position:0% +it didn't matter at all that our items +were movies in the collaborative + + align:start position:0% +were movies in the collaborative + + + align:start position:0% +were movies in the collaborative +filtering example we were just comparing + + align:start position:0% +filtering example we were just comparing + + + align:start position:0% +filtering example we were just comparing +user ratings however this requires a lot + + align:start position:0% +user ratings however this requires a lot + + + align:start position:0% +user ratings however this requires a lot +of data about the user to make accurate + + align:start position:0% +of data about the user to make accurate + + + align:start position:0% +of data about the user to make accurate +recommendations also when there are + + align:start position:0% +recommendations also when there are + + + align:start position:0% +recommendations also when there are +millions of items it needs a lot of + + align:start position:0% +millions of items it needs a lot of + + + align:start position:0% +millions of items it needs a lot of +computing power to compute the user + + align:start position:0% +computing power to compute the user + + + align:start position:0% +computing power to compute the user +similarities on the other hand content + + align:start position:0% +similarities on the other hand content + + + align:start position:0% +similarities on the other hand content +filtering requires very little data to + + align:start position:0% +filtering requires very little data to + + + align:start position:0% +filtering requires very little data to +get started but the major weakness of + + align:start position:0% +get started but the major weakness of + + + align:start position:0% +get started but the major weakness of +content filtering is that it can be + + align:start position:0% +content filtering is that it can be + + + align:start position:0% +content filtering is that it can be +limited in scope you're only + + align:start position:0% +limited in scope you're only + + + align:start position:0% +limited in scope you're only +recommending similar things to what the + + align:start position:0% +recommending similar things to what the + + + align:start position:0% +recommending similar things to what the +user has already liked so the + + align:start position:0% +user has already liked so the + + + align:start position:0% +user has already liked so the +recommendations are often not surprising + + align:start position:0% +recommendations are often not surprising + + + align:start position:0% +recommendations are often not surprising +or particularly insightful Netflix + + align:start position:0% +or particularly insightful Netflix + + + align:start position:0% +or particularly insightful Netflix +actually uses what's called a hybrid + + align:start position:0% +actually uses what's called a hybrid + + + align:start position:0% +actually uses what's called a hybrid +recommendation system they use both + + align:start position:0% +recommendation system they use both + + + align:start position:0% +recommendation system they use both +collaborative and content filtering as + + align:start position:0% +collaborative and content filtering as + + + align:start position:0% +collaborative and content filtering as +an example consider a collaborative + + align:start position:0% +an example consider a collaborative + + + align:start position:0% +an example consider a collaborative +filtering approach where we determined + + align:start position:0% +filtering approach where we determined + + + align:start position:0% +filtering approach where we determined +that Amy and Karl have similar + + align:start position:0% +that Amy and Karl have similar + + + align:start position:0% +that Amy and Karl have similar +preferences we could then do content + + align:start position:0% +preferences we could then do content + + + align:start position:0% +preferences we could then do content +filtering as well where we could find + + align:start position:0% +filtering as well where we could find + + + align:start position:0% +filtering as well where we could find +that the movie Terminator which they + + align:start position:0% +that the movie Terminator which they + + + align:start position:0% +that the movie Terminator which they +both liked is classified in almost the + + align:start position:0% +both liked is classified in almost the + + + align:start position:0% +both liked is classified in almost the +same set of genres as Starship Troopers + + align:start position:0% +same set of genres as Starship Troopers + + + align:start position:0% +same set of genres as Starship Troopers +so then we could recommend Starship + + align:start position:0% +so then we could recommend Starship + + + align:start position:0% +so then we could recommend Starship +Troopers to both Amy and Karl even + + align:start position:0% +Troopers to both Amy and Karl even + + + align:start position:0% +Troopers to both Amy and Karl even +though neither of them have seen it + + align:start position:0% +though neither of them have seen it + + + align:start position:0% +though neither of them have seen it +before + + align:start position:0% +before + + + align:start position:0% +before +if we were only doing collaborative + + align:start position:0% +if we were only doing collaborative + + + align:start position:0% +if we were only doing collaborative +filtering one of them would have had to + + align:start position:0% +filtering one of them would have had to + + + align:start position:0% +filtering one of them would have had to +have seen it before and if we were only + + align:start position:0% +have seen it before and if we were only + + + align:start position:0% +have seen it before and if we were only +doing content Phil + + align:start position:0% +doing content Phil + + + align:start position:0% +doing content Phil +terrene we would only be recommending to + + align:start position:0% +terrene we would only be recommending to + + + align:start position:0% +terrene we would only be recommending to +one user at a time so by combining the + + align:start position:0% +one user at a time so by combining the + + + align:start position:0% +one user at a time so by combining the +two methods the algorithm can be much + + align:start position:0% +two methods the algorithm can be much + + + align:start position:0% +two methods the algorithm can be much +more efficient and accurate in the next + + align:start position:0% +more efficient and accurate in the next + + + align:start position:0% +more efficient and accurate in the next +video we'll see how we can do content + + align:start position:0% +video we'll see how we can do content + + + align:start position:0% +video we'll see how we can do content +filtering by using a method called + + align:start position:0% +filtering by using a method called + + + align:start position:0% +filtering by using a method called +clustering \ No newline at end of file diff --git a/efpiHD_2O8E.txt b/efpiHD_2O8E.txt new file mode 100644 index 0000000000000000000000000000000000000000..5c8b45477253aa4dc4f64eccfc93d80d4159b893 --- /dev/null +++ b/efpiHD_2O8E.txt @@ -0,0 +1,331 @@ +align:start position:0% + +let's talk about kinetic energy we're + + align:start position:0% +let's talk about kinetic energy we're + + + align:start position:0% +let's talk about kinetic energy we're +calling kinetic energy K and it's given + + align:start position:0% +calling kinetic energy K and it's given + + + align:start position:0% +calling kinetic energy K and it's given +by 12 m v^ 2 and this is a scalar + + align:start position:0% +by 12 m v^ 2 and this is a scalar + + + align:start position:0% +by 12 m v^ 2 and this is a scalar +quantity um so it's going to be either + + align:start position:0% +quantity um so it's going to be either + + + align:start position:0% +quantity um so it's going to be either +zero or positive it's never going to be + + align:start position:0% +zero or positive it's never going to be + + + align:start position:0% +zero or positive it's never going to be +negative yeah the SI unit for kinetic + + align:start position:0% +negative yeah the SI unit for kinetic + + + align:start position:0% +negative yeah the SI unit for kinetic +energy is Jewel so we have one Jewel + + align:start position:0% +energy is Jewel so we have one Jewel + + + align:start position:0% +energy is Jewel so we have one Jewel +here for kinetic energy and the units + + align:start position:0% +here for kinetic energy and the units + + + align:start position:0% +here for kinetic energy and the units +come from this so we have + + align:start position:0% +come from this so we have + + + align:start position:0% +come from this so we have +kilogram and then meter per second + + align:start position:0% +kilogram and then meter per second + + + align:start position:0% +kilogram and then meter per second +squared um now let's assume we have an + + align:start position:0% +squared um now let's assume we have an + + + align:start position:0% +squared um now let's assume we have an +object that is first at rest and then it + + align:start position:0% +object that is first at rest and then it + + + align:start position:0% +object that is first at rest and then it +uh speeds up with a certain velocity + + align:start position:0% +uh speeds up with a certain velocity + + + align:start position:0% +uh speeds up with a certain velocity +yeah which means the object is going to + + align:start position:0% +yeah which means the object is going to + + + align:start position:0% +yeah which means the object is going to +experience a change in kinetic energy + + align:start position:0% +experience a change in kinetic energy + + + align:start position:0% +experience a change in kinetic energy +and so we'll Express this as 12 m v + + align:start position:0% +and so we'll Express this as 12 m v + + + align:start position:0% +and so we'll Express this as 12 m v +final squared minus 12 m v initial + + align:start position:0% +final squared minus 12 m v initial + + + align:start position:0% +final squared minus 12 m v initial +squared and uh if we have um a motion so + + align:start position:0% +squared and uh if we have um a motion so + + + align:start position:0% +squared and uh if we have um a motion so +velocity in uh in um let's say a 2d or a + + align:start position:0% +velocity in uh in um let's say a 2d or a + + + align:start position:0% +velocity in uh in um let's say a 2d or a +3D space then we can um then we have to + + align:start position:0% +3D space then we can um then we have to + + + align:start position:0% +3D space then we can um then we have to +consider all these components here and + + align:start position:0% +consider all these components here and + + + align:start position:0% +consider all these components here and +we can also pull out the 1 12 M and then + + align:start position:0% +we can also pull out the 1 12 M and then + + + align:start position:0% +we can also pull out the 1 12 M and then +we have v x X final squar + + + align:start position:0% +we have v x X final squar + + + + align:start position:0% +we have v x X final squar + +v y final squar + V Z final squar and + + align:start position:0% +v y final squar + V Z final squar and + + + align:start position:0% +v y final squar + V Z final squar and +then minus all the initial values X + + align:start position:0% +then minus all the initial values X + + + align:start position:0% +then minus all the initial values X +initial y + + align:start position:0% +initial y + + + align:start position:0% +initial y +initial and Z + + align:start position:0% +initial and Z + + + align:start position:0% +initial and Z +initial now um when we consider just a + + align:start position:0% +initial now um when we consider just a + + + align:start position:0% +initial now um when we consider just a +point + + align:start position:0% +point + + + align:start position:0% +point +particle then uh we can also ask what is + + align:start position:0% +particle then uh we can also ask what is + + + align:start position:0% +particle then uh we can also ask what is +the momentum how can we pair up momentum + + align:start position:0% +the momentum how can we pair up momentum + + + align:start position:0% +the momentum how can we pair up momentum +and kinetic energy so I'm writing it + + align:start position:0% +and kinetic energy so I'm writing it + + + align:start position:0% +and kinetic energy so I'm writing it +again here K = 12 m v^ + + align:start position:0% +again here K = 12 m v^ + + + align:start position:0% +again here K = 12 m v^ +2 if we multiply this by m upstairs and + + align:start position:0% +2 if we multiply this by m upstairs and + + + align:start position:0% +2 if we multiply this by m upstairs and +downstairs we're going to have M m^2 + + align:start position:0% +downstairs we're going to have M m^2 + + + align:start position:0% +downstairs we're going to have M m^2 +over v^ 2 and that's actually p^ squ + + align:start position:0% +over v^ 2 and that's actually p^ squ + + + align:start position:0% +over v^ 2 and that's actually p^ squ +remember P equals + + align:start position:0% +remember P equals + + + align:start position:0% +remember P equals +MV and so we're going to get that this + + align:start position:0% +MV and so we're going to get that this + + + align:start position:0% +MV and so we're going to get that this +actually can be expressed as p^2 over 2 + + align:start position:0% +actually can be expressed as p^2 over 2 + + + align:start position:0% +actually can be expressed as p^2 over 2 +m and so that is uh the itic energy um + + align:start position:0% +m and so that is uh the itic energy um + + + align:start position:0% +m and so that is uh the itic energy um +expressed in terms of the momentum of a + + align:start position:0% +expressed in terms of the momentum of a + + + align:start position:0% +expressed in terms of the momentum of a +particle \ No newline at end of file diff --git a/fSxEbNrIj2M.txt b/fSxEbNrIj2M.txt new file mode 100644 index 0000000000000000000000000000000000000000..2dd3020f7eb58c0ffca25bb3d33e9c249de8beaa --- /dev/null +++ b/fSxEbNrIj2M.txt @@ -0,0 +1,267 @@ +align:start position:0% + +so I think it's somewhat of a + + align:start position:0% +so I think it's somewhat of a + + + align:start position:0% +so I think it's somewhat of a +misconception that communication can be + + align:start position:0% +misconception that communication can be + + + align:start position:0% +misconception that communication can be +separated from the work that scientists + + align:start position:0% +separated from the work that scientists + + + align:start position:0% +separated from the work that scientists +do because so much of what scientists do + + align:start position:0% +do because so much of what scientists do + + + align:start position:0% +do because so much of what scientists do +in their you know daily lives is + + align:start position:0% +in their you know daily lives is + + + align:start position:0% +in their you know daily lives is +communication you know if you are a + + align:start position:0% +communication you know if you are a + + + align:start position:0% +communication you know if you are a +scientist and you are doing really + + align:start position:0% +scientist and you are doing really + + + align:start position:0% +scientist and you are doing really +really exciting work + + align:start position:0% +really exciting work + + + align:start position:0% +really exciting work +that work is not going to have any kind + + align:start position:0% +that work is not going to have any kind + + + align:start position:0% +that work is not going to have any kind +of impact if you can't tell people about + + align:start position:0% +of impact if you can't tell people about + + + align:start position:0% +of impact if you can't tell people about +it and a lot of you know the actual work + + align:start position:0% +it and a lot of you know the actual work + + + align:start position:0% +it and a lot of you know the actual work +that scientists do is writing up their + + align:start position:0% +that scientists do is writing up their + + + align:start position:0% +that scientists do is writing up their +results is talking about their results + + align:start position:0% +results is talking about their results + + + align:start position:0% +results is talking about their results +in all kinds of settings and to all + + align:start position:0% +in all kinds of settings and to all + + + align:start position:0% +in all kinds of settings and to all +kinds of people um and MIT students + + align:start position:0% +kinds of people um and MIT students + + + align:start position:0% +kinds of people um and MIT students +they're very proud of their work and + + align:start position:0% +they're very proud of their work and + + + align:start position:0% +they're very proud of their work and +they want their work to have impact and + + align:start position:0% +they want their work to have impact and + + + align:start position:0% +they want their work to have impact and +I think there is an understanding that + + align:start position:0% +I think there is an understanding that + + + align:start position:0% +I think there is an understanding that +um the way to have impact is to make + + align:start position:0% +um the way to have impact is to make + + + align:start position:0% +um the way to have impact is to make +sure that other people understand it and + + align:start position:0% +sure that other people understand it and + + + align:start position:0% +sure that other people understand it and +if other people don't then the work + + align:start position:0% +if other people don't then the work + + + align:start position:0% +if other people don't then the work +languishes and um you know there are all + + align:start position:0% +languishes and um you know there are all + + + align:start position:0% +languishes and um you know there are all +sorts of reasons why people want to + + align:start position:0% +sorts of reasons why people want to + + + align:start position:0% +sorts of reasons why people want to +communicate their work you know they may + + align:start position:0% +communicate their work you know they may + + + align:start position:0% +communicate their work you know they may +want to communicate their work you know + + align:start position:0% +want to communicate their work you know + + + align:start position:0% +want to communicate their work you know +in classes sure to get a good grade but + + align:start position:0% +in classes sure to get a good grade but + + + align:start position:0% +in classes sure to get a good grade but +they also you know eventually will be + + align:start position:0% +they also you know eventually will be + + + align:start position:0% +they also you know eventually will be +asking for funding um they will be + + align:start position:0% +asking for funding um they will be + + + align:start position:0% +asking for funding um they will be +communicating their work to um to change + + align:start position:0% +communicating their work to um to change + + + align:start position:0% +communicating their work to um to change +the the direction of research in their + + align:start position:0% +the the direction of research in their + + + align:start position:0% +the the direction of research in their +field you know they want to change the + + align:start position:0% +field you know they want to change the + + + align:start position:0% +field you know they want to change the +world um that's going to happen if and + + align:start position:0% +world um that's going to happen if and + + + align:start position:0% +world um that's going to happen if and +only if they can talk about it and write + + align:start position:0% +only if they can talk about it and write + + + align:start position:0% +only if they can talk about it and write +about it effectively \ No newline at end of file diff --git a/goPg4-iVa1s.txt b/goPg4-iVa1s.txt new file mode 100644 index 0000000000000000000000000000000000000000..9608fb5963f3ef22c7f5020fc2af41ef4ebf9de6 --- /dev/null +++ b/goPg4-iVa1s.txt @@ -0,0 +1,539 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop coreware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu now we're going to see what + + align:start position:0% +ocw.mit.edu now we're going to see what + + + align:start position:0% +ocw.mit.edu now we're going to see what +happens when the beam going into the + + align:start position:0% +happens when the beam going into the + + + align:start position:0% +happens when the beam going into the +cavity is an expanding + + align:start position:0% +cavity is an expanding + + + align:start position:0% +cavity is an expanding +beam what we've done done we've added + + align:start position:0% +beam what we've done done we've added + + + align:start position:0% +beam what we've done done we've added +this lens to the setup so that the beam + + align:start position:0% +this lens to the setup so that the beam + + + align:start position:0% +this lens to the setup so that the beam +leaving the + + align:start position:0% +leaving the + + + align:start position:0% +leaving the +lens is an expanding beam and I don't + + align:start position:0% +lens is an expanding beam and I don't + + + align:start position:0% +lens is an expanding beam and I don't +know whether you can see it that well uh + + align:start position:0% +know whether you can see it that well uh + + + align:start position:0% +know whether you can see it that well uh +on the card but the beam is an expanding + + align:start position:0% +on the card but the beam is an expanding + + + align:start position:0% +on the card but the beam is an expanding +beam it goes into the cavity and the + + align:start position:0% +beam it goes into the cavity and the + + + align:start position:0% +beam it goes into the cavity and the +transmitted beam is then goes to the to + + align:start position:0% +transmitted beam is then goes to the to + + + align:start position:0% +transmitted beam is then goes to the to +the screen over + + align:start position:0% +the screen over + + + align:start position:0% +the screen over +there and if we can see it in + + align:start position:0% + + + + align:start position:0% + +closeup we can see see that we we have + + align:start position:0% +closeup we can see see that we we have + + + align:start position:0% +closeup we can see see that we we have +rings instead of the spot that we had + + align:start position:0% +rings instead of the spot that we had + + + align:start position:0% +rings instead of the spot that we had +before and as the cavity length + + align:start position:0% +before and as the cavity length + + + align:start position:0% +before and as the cavity length +changes the diameter of the Rings uh + + align:start position:0% +changes the diameter of the Rings uh + + + align:start position:0% +changes the diameter of the Rings uh +change as uh as you can see in the in + + align:start position:0% +change as uh as you can see in the in + + + align:start position:0% +change as uh as you can see in the in +the + + align:start position:0% +the + + + align:start position:0% +the +insert just as a special treat for you + + align:start position:0% +insert just as a special treat for you + + + align:start position:0% +insert just as a special treat for you +we're also going to look at the + + align:start position:0% +we're also going to look at the + + + align:start position:0% +we're also going to look at the +reflected light from the cavity again + + align:start position:0% +reflected light from the cavity again + + + align:start position:0% +reflected light from the cavity again +we've added this Bean spitter here so we + + align:start position:0% +we've added this Bean spitter here so we + + + align:start position:0% +we've added this Bean spitter here so we +can sample the light and then will go + + align:start position:0% +can sample the light and then will go + + + align:start position:0% +can sample the light and then will go +from the beam splitter onto the smor + + align:start position:0% +from the beam splitter onto the smor + + + align:start position:0% +from the beam splitter onto the smor +onto onto the screen now the spot on the + + align:start position:0% +onto onto the screen now the spot on the + + + align:start position:0% +onto onto the screen now the spot on the +left is the associated with the + + align:start position:0% +left is the associated with the + + + align:start position:0% +left is the associated with the +reflected beam and the spot on the right + + align:start position:0% +reflected beam and the spot on the right + + + align:start position:0% +reflected beam and the spot on the right +is that associated with the transmitted + + align:start position:0% +is that associated with the transmitted + + + align:start position:0% +is that associated with the transmitted +beam now you can see that their Rings + + align:start position:0% +beam now you can see that their Rings + + + align:start position:0% +beam now you can see that their Rings +both of them are rings in the in the + + align:start position:0% +both of them are rings in the in the + + + align:start position:0% +both of them are rings in the in the +transmitted beam the Rings are bright in + + align:start position:0% +transmitted beam the Rings are bright in + + + align:start position:0% +transmitted beam the Rings are bright in +the reflected beam the Rings are dark + + align:start position:0% +the reflected beam the Rings are dark + + + align:start position:0% +the reflected beam the Rings are dark +now what I'm going to do + + align:start position:0% +now what I'm going to do + + + align:start position:0% +now what I'm going to do +is take off the + + align:start position:0% + + + + align:start position:0% + +scan and do the scanning by hand now + + align:start position:0% +scan and do the scanning by hand now + + + align:start position:0% +scan and do the scanning by hand now +let's go back and look at the at the two + + align:start position:0% +let's go back and look at the at the two + + + align:start position:0% +let's go back and look at the at the two +sets of rings you can see as + + align:start position:0% +sets of rings you can see as + + + align:start position:0% +sets of rings you can see as +I push a little bit you can see that the + + align:start position:0% +I push a little bit you can see that the + + + align:start position:0% +I push a little bit you can see that the +one on the right let's say when it goes + + align:start position:0% +one on the right let's say when it goes + + + align:start position:0% +one on the right let's say when it goes +bright the one on the left is dark I can + + align:start position:0% +bright the one on the left is dark I can + + + align:start position:0% +bright the one on the left is dark I can +also do it by applying a voltage to the + + align:start position:0% +also do it by applying a voltage to the + + + align:start position:0% +also do it by applying a voltage to the +p Electric Crystal Again by hand and + + align:start position:0% +p Electric Crystal Again by hand and + + + align:start position:0% +p Electric Crystal Again by hand and +variate by hand and you can see here + + align:start position:0% +variate by hand and you can see here + + + align:start position:0% +variate by hand and you can see here +that again the one on the right I can + + align:start position:0% +that again the one on the right I can + + + align:start position:0% +that again the one on the right I can +make the central spot bright you can see + + align:start position:0% +make the central spot bright you can see + + + align:start position:0% +make the central spot bright you can see +the one on the left or the reflected + + align:start position:0% +the one on the left or the reflected + + + align:start position:0% +the one on the left or the reflected +beam is dark and + + align:start position:0% +beam is dark and + + + align:start position:0% +beam is dark and +when the transmitted beam is dark in the + + align:start position:0% +when the transmitted beam is dark in the + + + align:start position:0% +when the transmitted beam is dark in the +center the reflected beam is bright so + + align:start position:0% +center the reflected beam is bright so + + + align:start position:0% +center the reflected beam is bright so +indeed they're opposite one + + align:start position:0% +indeed they're opposite one + + + align:start position:0% +indeed they're opposite one +another now the interesting thing is + + align:start position:0% +another now the interesting thing is + + + align:start position:0% +another now the interesting thing is +first of all is why do we have + + align:start position:0% +first of all is why do we have + + + align:start position:0% +first of all is why do we have +rings and also why the uh behavior is is + + align:start position:0% +rings and also why the uh behavior is is + + + align:start position:0% +rings and also why the uh behavior is is +as shown and again this is left to you + + align:start position:0% +as shown and again this is left to you + + + align:start position:0% +as shown and again this is left to you +to think about in the next + + align:start position:0% +to think about in the next + + + align:start position:0% +to think about in the next +demonstration instead of using a plain + + align:start position:0% +demonstration instead of using a plain + + + align:start position:0% +demonstration instead of using a plain +parallel cavity as we've used so far + + align:start position:0% +parallel cavity as we've used so far + + + align:start position:0% +parallel cavity as we've used so far +we're going to use a cavity with curved + + align:start position:0% +we're going to use a cavity with curved + + + align:start position:0% +we're going to use a cavity with curved +mirrors and I assure you it has lots of + + align:start position:0% +mirrors and I assure you it has lots of + + + align:start position:0% +mirrors and I assure you it has lots of +interesting things for us to learn from \ No newline at end of file diff --git a/hM2EAvMkhtk.txt b/hM2EAvMkhtk.txt new file mode 100644 index 0000000000000000000000000000000000000000..1846c9f7d8e46e69c316ca0cd3eeba0b5c3ba982 --- /dev/null +++ b/hM2EAvMkhtk.txt @@ -0,0 +1,9764 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu today we're going to be + + align:start position:0% +ocw.mit.edu today we're going to be + + + align:start position:0% +ocw.mit.edu today we're going to be +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +games and I know you guys as well as I + + align:start position:0% +games and I know you guys as well as I + + + align:start position:0% +games and I know you guys as well as I +hope I do the main thing that you guys + + align:start position:0% +hope I do the main thing that you guys + + + align:start position:0% +hope I do the main thing that you guys +want to talk about with games is how to + + align:start position:0% +want to talk about with games is how to + + + align:start position:0% +want to talk about with games is how to +do that Alpha Beta thing because it's + + align:start position:0% +do that Alpha Beta thing because it's + + + align:start position:0% +do that Alpha Beta thing because it's +pretty confusing and it's easy to get + + align:start position:0% +pretty confusing and it's easy to get + + + align:start position:0% +pretty confusing and it's easy to get +lost in a corner or something whereas + + align:start position:0% +lost in a corner or something whereas + + + align:start position:0% +lost in a corner or something whereas +doing the regular Minx in my experience + + align:start position:0% +doing the regular Minx in my experience + + + align:start position:0% +doing the regular Minx in my experience +most 6 or 34 students can do that and + + align:start position:0% +most 6 or 34 students can do that and + + + align:start position:0% +most 6 or 34 students can do that and +they do it right pretty much all the + + align:start position:0% +they do it right pretty much all the + + + align:start position:0% +they do it right pretty much all the +time however we're going to focus on all + + align:start position:0% +time however we're going to focus on all + + + align:start position:0% +time however we're going to focus on all +the different components of games and I + + align:start position:0% +the different components of games and I + + + align:start position:0% +the different components of games and I +put up two provocative Silver Star ideas + + align:start position:0% +put up two provocative Silver Star ideas + + + align:start position:0% +put up two provocative Silver Star ideas +up on the board which um will come into + + align:start position:0% +up on the board which um will come into + + + align:start position:0% +up on the board which um will come into +play here the snow white principal is a + + align:start position:0% +play here the snow white principal is a + + + align:start position:0% +play here the snow white principal is a +new name and has never been revealed + + align:start position:0% +new name and has never been revealed + + + align:start position:0% +new name and has never been revealed +until today because I made up the name + + align:start position:0% +until today because I made up the name + + + align:start position:0% +until today because I made up the name +recently so you will be the first people + + align:start position:0% +recently so you will be the first people + + + align:start position:0% +recently so you will be the first people +to hear it and decide if it works better + + align:start position:0% +to hear it and decide if it works better + + + align:start position:0% +to hear it and decide if it works better +than the the term grandfather clause for + + align:start position:0% +than the the term grandfather clause for + + + align:start position:0% +than the the term grandfather clause for +the thing that I'm trying to describe + + align:start position:0% +the thing that I'm trying to describe + + + align:start position:0% +the thing that I'm trying to describe +because most grandfathers don't eat + + align:start position:0% +because most grandfathers don't eat + + + align:start position:0% +because most grandfathers don't eat +their children + + align:start position:0% +their children + + + align:start position:0% +their children +so um here we've got a beautiful game + + align:start position:0% +so um here we've got a beautiful game + + + align:start position:0% +so um here we've got a beautiful game +tree it has notes from a through + + align:start position:0% +tree it has notes from a through + + + align:start position:0% +tree it has notes from a through +R this is this is our standard game tree + + align:start position:0% +R this is this is our standard game tree + + + align:start position:0% +R this is this is our standard game tree +from + + align:start position:0% +from + + + align:start position:0% +from +6034 we've got a maximizer up at the top + + align:start position:0% +6034 we've got a maximizer up at the top + + + align:start position:0% +6034 we've got a maximizer up at the top +who's trying to get the highest score + + align:start position:0% +who's trying to get the highest score + + + align:start position:0% +who's trying to get the highest score +possible the minimizer is her opponent + + align:start position:0% +possible the minimizer is her opponent + + + align:start position:0% +possible the minimizer is her opponent +and the minimizer is trying to get it to + + align:start position:0% +and the minimizer is trying to get it to + + + align:start position:0% +and the minimizer is trying to get it to +the lowest score possible and it's + + align:start position:0% +the lowest score possible and it's + + + align:start position:0% +the lowest score possible and it's +really unclear who wins or loses at each + + align:start position:0% +really unclear who wins or loses at each + + + align:start position:0% +really unclear who wins or loses at each +point they're just trying to get it to + + align:start position:0% +point they're just trying to get it to + + + align:start position:0% +point they're just trying to get it to +the highest or the lowest + + align:start position:0% +the highest or the lowest + + + align:start position:0% +the highest or the lowest +score all right so let's do a refresher + + align:start position:0% +score all right so let's do a refresher + + + align:start position:0% +score all right so let's do a refresher +hopefully like the quiz didn't put + + align:start position:0% +hopefully like the quiz didn't put + + + align:start position:0% +hopefully like the quiz didn't put +people into such Panic modes that they + + align:start position:0% +people into such Panic modes that they + + + align:start position:0% +people into such Panic modes that they +forgot Monday's lecture so let's make + + align:start position:0% +forgot Monday's lecture so let's make + + + align:start position:0% +forgot Monday's lecture so let's make +sure that we can do regular Minx + + align:start position:0% +sure that we can do regular Minx + + + align:start position:0% +sure that we can do regular Minx +algorithm on this tree and figure out + + align:start position:0% +algorithm on this tree and figure out + + + align:start position:0% +algorithm on this tree and figure out +the Mini max value at a so let's see how + + align:start position:0% +the Mini max value at a so let's see how + + + align:start position:0% +the Mini max value at a so let's see how +that works all right so if as you guys + + align:start position:0% +that works all right so if as you guys + + + align:start position:0% +that works all right so if as you guys +remember the game search when you're + + align:start position:0% +remember the game search when you're + + + align:start position:0% +remember the game search when you're +using regular minia Max is essentially a + + align:start position:0% +using regular minia Max is essentially a + + + align:start position:0% +using regular minia Max is essentially a +depth first search and at each level it + + align:start position:0% +depth first search and at each level it + + + align:start position:0% +depth first search and at each level it +it chooses between all of the children + + align:start position:0% +it chooses between all of the children + + + align:start position:0% +it chooses between all of the children +which whichever value that the parent + + align:start position:0% +which whichever value that the parent + + + align:start position:0% +which whichever value that the parent +wants so here at F it would choose the + + align:start position:0% +wants so here at F it would choose the + + + align:start position:0% +wants so here at F it would choose the +maximum of K and L for instance but + + align:start position:0% +maximum of K and L for instance but + + + align:start position:0% +maximum of K and L for instance but +that's getting ahead of ourselves + + align:start position:0% +that's getting ahead of ourselves + + + align:start position:0% +that's getting ahead of ourselves +because it's a depth first search so we + + align:start position:0% +because it's a depth first search so we + + + align:start position:0% +because it's a depth first search so we +best start at the top I'll help you guys + + align:start position:0% +best start at the top I'll help you guys + + + align:start position:0% +best start at the top I'll help you guys +out for a while so we're doing a we need + + align:start position:0% +out for a while so we're doing a we need + + + align:start position:0% +out for a while so we're doing a we need +the maximum BCD depth first search we go + + align:start position:0% +the maximum BCD depth first search we go + + + align:start position:0% +the maximum BCD depth first search we go +to B we're looking for the minimum into + + align:start position:0% +to B we're looking for the minimum into + + + align:start position:0% +to B we're looking for the minimum into +of E and F so having looked at + + align:start position:0% +of E and F so having looked at + + + align:start position:0% +of E and F so having looked at +e our current + + align:start position:0% +e our current + + + align:start position:0% +e our current +minimum of E and F is just + + align:start position:0% +minimum of E and F is just + + + align:start position:0% +minimum of E and F is just +two for the moment so this is going to + + align:start position:0% +two for the moment so this is going to + + + align:start position:0% +two for the moment so this is going to +be less than or equal to + + align:start position:0% +be less than or equal to + + + align:start position:0% +be less than or equal to +two all right then we go down to F which + + align:start position:0% +two all right then we go down to F which + + + align:start position:0% +two all right then we go down to F which +is a maximizer and it's children are K + + align:start position:0% +is a maximizer and it's children are K + + + align:start position:0% +is a maximizer and it's children are K +and L so now I'm going to start making + + align:start position:0% +and L so now I'm going to start making + + + align:start position:0% +and L so now I'm going to start making +you guys do stuff so what do you think + + align:start position:0% +you guys do stuff so what do you think + + + align:start position:0% +you guys do stuff so what do you think +what is the going to be the value Mini + + align:start position:0% +what is the going to be the value Mini + + + align:start position:0% +what is the going to be the value Mini +max value at + + align:start position:0% +max value at + + + align:start position:0% +max value at +F the mini value mini value at F what + + align:start position:0% +F the mini value mini value at F what + + + align:start position:0% +F the mini value mini value at F what +will that be would be the minimum of K + + align:start position:0% +will that be would be the minimum of K + + + align:start position:0% +will that be would be the minimum of K +and so that level is um a maximizer + + align:start position:0% +and so that level is um a maximizer + + + align:start position:0% +and so that level is um a maximizer +Maxim Max f is a Max + + align:start position:0% +Maxim Max f is a Max + + + align:start position:0% +Maxim Max f is a Max +K and L themselves are minimizers but + + align:start position:0% +K and L themselves are minimizers but + + + align:start position:0% +K and L themselves are minimizers but +they're pretty impotent minimizers + + align:start position:0% +they're pretty impotent minimizers + + + align:start position:0% +they're pretty impotent minimizers +because they don't get to choose they + + align:start position:0% +because they don't get to choose they + + + align:start position:0% +because they don't get to choose they +just have to do k l so the value is the + + align:start position:0% +just have to do k l so the value is the + + + align:start position:0% +just have to do k l so the value is the +Minimax value is three and yeah the path + + align:start position:0% +Minimax value is three and yeah the path + + + align:start position:0% +Minimax value is three and yeah the path +it would like to go is K so we'll say + + align:start position:0% +it would like to go is K so we'll say + + + align:start position:0% +it would like to go is K so we'll say +the Minimax value here is three it's in + + align:start position:0% +the Minimax value here is three it's in + + + align:start position:0% +the Minimax value here is three it's in +fact exactly equal to three all right so + + align:start position:0% +fact exactly equal to three all right so + + + align:start position:0% +fact exactly equal to three all right so +if this is three and this is two then + + align:start position:0% +if this is three and this is two then + + + align:start position:0% +if this is three and this is two then +everyone we know that the value of B + + align:start position:0% + + + + align:start position:0% + +is I hear three and two which one is it + + align:start position:0% +is I hear three and two which one is it + + + align:start position:0% +is I hear three and two which one is it +two that's + + align:start position:0% +two that's + + + align:start position:0% +two that's +right so the value here is two great + + align:start position:0% +right so the value here is two great + + + align:start position:0% +right so the value here is two great +let's go down into this Branch so C is + + align:start position:0% +let's go down into this Branch so C is + + + align:start position:0% +let's go down into this Branch so C is +going to be the minimum of G and six but + + align:start position:0% +going to be the minimum of G and six but + + + align:start position:0% +going to be the minimum of G and six but +we don't see that yet cuz we're doing a + + align:start position:0% +we don't see that yet cuz we're doing a + + + align:start position:0% +we don't see that yet cuz we're doing a +depth research it's going to be the + + align:start position:0% +depth research it's going to be the + + + align:start position:0% +depth research it's going to be the +minimum of G now we need the maximum of + + align:start position:0% +minimum of G now we need the maximum of + + + align:start position:0% +minimum of G now we need the maximum of +M and N we're going to need the minimum + + align:start position:0% +M and N we're going to need the minimum + + + align:start position:0% +M and N we're going to need the minimum +m is the minimum of Q and R so let's + + align:start position:0% +m is the minimum of Q and R so let's + + + align:start position:0% +m is the minimum of Q and R so let's +switch sides the minimum of Q and R + + align:start position:0% +switch sides the minimum of Q and R + + + align:start position:0% +switch sides the minimum of Q and R +is one let's see that's right it's one + + align:start position:0% +is one let's see that's right it's one + + + align:start position:0% +is one let's see that's right it's one +so M has a value of one but I'm going to + + align:start position:0% +so M has a value of one but I'm going to + + + align:start position:0% +so M has a value of one but I'm going to +stay over here because M has a value of + + align:start position:0% +stay over here because M has a value of + + + align:start position:0% +stay over here because M has a value of +one knowing that then we know that g has + + align:start position:0% +one knowing that then we know that g has + + + align:start position:0% +one knowing that then we know that g has +a value of seven that's right seven is + + align:start position:0% +a value of seven that's right seven is + + + align:start position:0% +a value of seven that's right seven is +higher than one and since G is a seven + + align:start position:0% +higher than one and since G is a seven + + + align:start position:0% +higher than one and since G is a seven +we now know going up to C that c has a + + align:start position:0% +we now know going up to C that c has a + + + align:start position:0% +we now know going up to C that c has a +value of six yes C has a value of six + + align:start position:0% +value of six yes C has a value of six + + + align:start position:0% +value of six yes C has a value of six +that's the minimum of six and seven so + + align:start position:0% +that's the minimum of six and seven so + + + align:start position:0% +that's the minimum of six and seven so +now I'm going to go back down because + + align:start position:0% +now I'm going to go back down because + + + align:start position:0% +now I'm going to go back down because +we've done one of the other sub trees + + align:start position:0% +we've done one of the other sub trees + + + align:start position:0% +we've done one of the other sub trees +this is a six all right great now we're + + align:start position:0% +this is a six all right great now we're + + + align:start position:0% +this is a six all right great now we're +going to go down to D hopefully it won't + + align:start position:0% +going to go down to D hopefully it won't + + + align:start position:0% +going to go down to D hopefully it won't +be too bad these things usually aren't + + align:start position:0% +be too bad these things usually aren't + + + align:start position:0% +be too bad these things usually aren't +terrible because they're made to be + + align:start position:0% +terrible because they're made to be + + + align:start position:0% +terrible because they're made to be +pruned a lot in Alpha Beta so let's see + + align:start position:0% +pruned a lot in Alpha Beta so let's see + + + align:start position:0% +pruned a lot in Alpha Beta so let's see +in D we go down to I and that's just a + + align:start position:0% +in D we go down to I and that's just a + + + align:start position:0% +in D we go down to I and that's just a +one we go down to J and let's see what's + + align:start position:0% +one we go down to J and let's see what's + + + align:start position:0% +one we go down to J and let's see what's +the Minimax value of + + align:start position:0% +the Minimax value of + + + align:start position:0% +the Minimax value of +J that's right 20 is the maximum of + + align:start position:0% +J that's right 20 is the maximum of + + + align:start position:0% +J that's right 20 is the maximum of +202 great so what's the minax value of + + align:start position:0% +202 great so what's the minax value of + + + align:start position:0% +202 great so what's the minax value of +D everyone said it one all right so + + align:start position:0% +D everyone said it one all right so + + + align:start position:0% +D everyone said it one all right so +what's the minax value at a + + align:start position:0% +what's the minax value at a + + + align:start position:0% +what's the minax value at a +six is Right six is higher than two it's + + align:start position:0% +six is Right six is higher than two it's + + + align:start position:0% +six is Right six is higher than two it's +higher than one our value is six and our + + align:start position:0% +higher than one our value is six and our + + + align:start position:0% +higher than one our value is six and our +path is everyone a c h that's + + align:start position:0% +path is everyone a c h that's + + + align:start position:0% +path is everyone a c h that's +it + + align:start position:0% +it + + + align:start position:0% +it +great is everyone good with Mini Max I + + align:start position:0% +great is everyone good with Mini Max I + + + align:start position:0% +great is everyone good with Mini Max I +know that usually a lot of people are + + align:start position:0% +know that usually a lot of people are + + + align:start position:0% +know that usually a lot of people are +there's usually a few people who aren't + + align:start position:0% +there's usually a few people who aren't + + + align:start position:0% +there's usually a few people who aren't +so if you're one of the people who would + + align:start position:0% +so if you're one of the people who would + + + align:start position:0% +so if you're one of the people who would +like some clarifications on Minx raise + + align:start position:0% +like some clarifications on Minx raise + + + align:start position:0% +like some clarifications on Minx raise +your hands there's probably a few other + + align:start position:0% +your hands there's probably a few other + + + align:start position:0% +your hands there's probably a few other +people who would like some + + align:start position:0% +people who would like some + + + align:start position:0% +people who would like some +to okay uh when you're doing this Max + + align:start position:0% +to okay uh when you're doing this Max + + + align:start position:0% +to okay uh when you're doing this Max +you're whenever vales are not sh you + + align:start position:0% +you're whenever vales are not sh you + + + align:start position:0% +you're whenever vales are not sh you +keep uh going down the tree and then + + align:start position:0% +keep uh going down the tree and then + + + align:start position:0% +keep uh going down the tree and then +just look at what they're trying to find + + align:start position:0% +just look at what they're trying to find + + + align:start position:0% +just look at what they're trying to find +the min max and just whatever values you + + align:start position:0% +the min max and just whatever values you + + + align:start position:0% +the min max and just whatever values you +get you go back up back TR yes our our + + align:start position:0% +get you go back up back TR yes our our + + + align:start position:0% +get you go back up back TR yes our our +our general uh the question was when you + + align:start position:0% +our general uh the question was when you + + + align:start position:0% +our general uh the question was when you +go um to do the minia Max and let's say + + align:start position:0% +go um to do the minia Max and let's say + + + align:start position:0% +go um to do the minia Max and let's say +you got e was two and you know that b is + + align:start position:0% +you got e was two and you know that b is + + + align:start position:0% +you got e was two and you know that b is +going to be less than or equal to two + + align:start position:0% +going to be less than or equal to two + + + align:start position:0% +going to be less than or equal to two +but you don't know F yet the question is + + align:start position:0% +but you don't know F yet the question is + + + align:start position:0% +but you don't know F yet the question is +do you go down the tree find the value + + align:start position:0% +do you go down the tree find the value + + + align:start position:0% +do you go down the tree find the value +at F and then go back up the answer is + + align:start position:0% +at F and then go back up the answer is + + + align:start position:0% +at F and then go back up the answer is +yes by default we use a depth first + + align:start position:0% +yes by default we use a depth first + + + align:start position:0% +yes by default we use a depth first +search however in non-alpha beta version + + align:start position:0% +search however in non-alpha beta version + + + align:start position:0% +search however in non-alpha beta version +just regular Minimax turns out it + + align:start position:0% +just regular Minimax turns out it + + + align:start position:0% +just regular Minimax turns out it +probably doesn't matter what you do I + + align:start position:0% +probably doesn't matter what you do I + + + align:start position:0% +probably doesn't matter what you do I +suggest doing a depth first search to + + align:start position:0% +suggest doing a depth first search to + + + align:start position:0% +suggest doing a depth first search to +get yourself in the mindset of Alpha + + align:start position:0% +get yourself in the mindset of Alpha + + + align:start position:0% +get yourself in the mindset of Alpha +Beta because order is very very + + align:start position:0% +Beta because order is very very + + + align:start position:0% +Beta because order is very very +important in Alpha Beta so um but here + + align:start position:0% +important in Alpha Beta so um but here + + + align:start position:0% +important in Alpha Beta so um but here +like I don't know you could do some + + align:start position:0% +like I don't know you could do some + + + align:start position:0% +like I don't know you could do some +weird bottom up search or whatever + + align:start position:0% +weird bottom up search or whatever + + + align:start position:0% +weird bottom up search or whatever +whatever you want it's going to give you + + align:start position:0% +whatever you want it's going to give you + + + align:start position:0% +whatever you want it's going to give you +the right answer unless it asks what + + align:start position:0% +the right answer unless it asks what + + + align:start position:0% +the right answer unless it asks what +order they evaluated but here's a hint + + align:start position:0% +order they evaluated but here's a hint + + + align:start position:0% +order they evaluated but here's a hint +the order they evaluated in um in uh is + + align:start position:0% +the order they evaluated in um in uh is + + + align:start position:0% +the order they evaluated in um in uh is +depth for search ORD so without even + + align:start position:0% +depth for search ORD so without even + + + align:start position:0% +depth for search ORD so without even +doing anything EK l q r n h i o p are + + align:start position:0% +doing anything EK l q r n h i o p are + + + align:start position:0% +doing anything EK l q r n h i o p are +the order of static evaluation in um in + + align:start position:0% +the order of static evaluation in um in + + + align:start position:0% +the order of static evaluation in um in +this tree + + align:start position:0% +this tree + + + align:start position:0% +this tree +so we don't have + + align:start position:0% +so we don't have + + + align:start position:0% +so we don't have +to which minimum Max so the question is + + align:start position:0% +to which minimum Max so the question is + + + align:start position:0% +to which minimum Max so the question is +we nodes like M and G we don't have to + + align:start position:0% +we nodes like M and G we don't have to + + + align:start position:0% +we nodes like M and G we don't have to +put values next to technically if we + + align:start position:0% +put values next to technically if we + + + align:start position:0% +put values next to technically if we +were doing this very formally and we + + align:start position:0% +were doing this very formally and we + + + align:start position:0% +were doing this very formally and we +couldn't remember and I wasn't up there + + align:start position:0% +couldn't remember and I wasn't up there + + + align:start position:0% +couldn't remember and I wasn't up there +among the people we could we would put + + align:start position:0% +among the people we could we would put + + + align:start position:0% +among the people we could we would put +one there so at M we would put a one but + + align:start position:0% +one there so at M we would put a one but + + + align:start position:0% +one there so at M we would put a one but +people remembered that so we didn't do + + align:start position:0% +people remembered that so we didn't do + + + align:start position:0% +people remembered that so we didn't do +it but then a g we would put a seven so + + align:start position:0% +it but then a g we would put a seven so + + + align:start position:0% +it but then a g we would put a seven so +if we were writing it out very formally + + align:start position:0% +if we were writing it out very formally + + + align:start position:0% +if we were writing it out very formally +we would have a one and a seven and at + + align:start position:0% +we would have a one and a seven and at + + + align:start position:0% +we would have a one and a seven and at +this D we would have a one and then at + + align:start position:0% +this D we would have a one and then at + + + align:start position:0% +this D we would have a one and then at +the a we would put a six and then that's + + align:start position:0% +the a we would put a six and then that's + + + align:start position:0% +the a we would put a six and then that's +that's the answer also we'd even put + + align:start position:0% +that's the answer also we'd even put + + + align:start position:0% +that's the answer also we'd even put +things like less than or greater than + + align:start position:0% +things like less than or greater than + + + align:start position:0% +things like less than or greater than +part way along the way however I believe + + align:start position:0% +part way along the way however I believe + + + align:start position:0% +part way along the way however I believe +that our Alpha Beta search is going to + + align:start position:0% +that our Alpha Beta search is going to + + + align:start position:0% +that our Alpha Beta search is going to +definitely fulfill everyone's quota of + + align:start position:0% +definitely fulfill everyone's quota of + + + align:start position:0% +definitely fulfill everyone's quota of +pedantically putting lots of numbers + + align:start position:0% +pedantically putting lots of numbers + + + align:start position:0% +pedantically putting lots of numbers +next to nodes on on a game tree and so + + align:start position:0% +next to nodes on on a game tree and so + + + align:start position:0% +next to nodes on on a game tree and so +um once you've done Alpha Beta if you + + align:start position:0% +um once you've done Alpha Beta if you + + + align:start position:0% +um once you've done Alpha Beta if you +can do it correctly you'll think ah Mini + + align:start position:0% +can do it correctly you'll think ah Mini + + + align:start position:0% +can do it correctly you'll think ah Mini +Max oh those were the days it's going to + + align:start position:0% +Max oh those were the days it's going to + + + align:start position:0% +Max oh those were the days it's going to +be easy because Alpha Beta is a little + + align:start position:0% +be easy because Alpha Beta is a little + + + align:start position:0% +be easy because Alpha Beta is a little +bit more + + align:start position:0% +bit more + + + align:start position:0% +bit more +complicated there's a lot of things that + + align:start position:0% +complicated there's a lot of things that + + + align:start position:0% +complicated there's a lot of things that +trick people up here for Alpha Beta + + align:start position:0% +trick people up here for Alpha Beta + + + align:start position:0% +trick people up here for Alpha Beta +however I will erase some of these + + align:start position:0% +however I will erase some of these + + + align:start position:0% +however I will erase some of these +numbers for the moment they're still + + align:start position:0% +numbers for the moment they're still + + + align:start position:0% +numbers for the moment they're still +right but we do it a little differently + + align:start position:0% +right but we do it a little differently + + + align:start position:0% +right but we do it a little differently +so what do alpha beta and beta add to + + align:start position:0% +so what do alpha beta and beta add to + + + align:start position:0% +so what do alpha beta and beta add to +this formula well this is a sort of a + + align:start position:0% +this formula well this is a sort of a + + + align:start position:0% +this formula well this is a sort of a +winning formula except for it's not + + align:start position:0% +winning formula except for it's not + + + align:start position:0% +winning formula except for it's not +because it takes too long but it's a + + align:start position:0% +because it takes too long but it's a + + + align:start position:0% +because it takes too long but it's a +very nice formula you as the maximizer + + align:start position:0% +very nice formula you as the maximizer + + + align:start position:0% +very nice formula you as the maximizer +say I try to think if I do this what's + + align:start position:0% +say I try to think if I do this what's + + + align:start position:0% +say I try to think if I do this what's +he going to do and then if he does that + + align:start position:0% +he going to do and then if he does that + + + align:start position:0% +he going to do and then if he does that +what's I'm going to do and then what I + + align:start position:0% +what's I'm going to do and then what I + + + align:start position:0% +what's I'm going to do and then what I +what is he going to do if I do that etc + + align:start position:0% +what is he going to do if I do that etc + + + align:start position:0% +what is he going to do if I do that etc +etc all the way to the bottom with Alpha + + align:start position:0% +etc all the way to the bottom with Alpha + + + align:start position:0% +etc all the way to the bottom with Alpha +and beta we add in what I like to call + + align:start position:0% +and beta we add in what I like to call + + + align:start position:0% +and beta we add in what I like to call +nuclear + + align:start position:0% +nuclear + + + align:start position:0% +nuclear +options I i' like in this game of + + align:start position:0% +options I i' like in this game of + + + align:start position:0% +options I i' like in this game of +maximizer minimizer you can think of it + + align:start position:0% +maximizer minimizer you can think of it + + + align:start position:0% +maximizer minimizer you can think of it +as like the cold war or the pelian war + + align:start position:0% +as like the cold war or the pelian war + + + align:start position:0% +as like the cold war or the pelian war +except the palanan war didn't have nukes + + align:start position:0% +except the palanan war didn't have nukes + + + align:start position:0% +except the palanan war didn't have nukes +so probably the Cold War um and you know + + align:start position:0% +so probably the Cold War um and you know + + + align:start position:0% +so probably the Cold War um and you know +in the Cold + + align:start position:0% +in the Cold + + + align:start position:0% +in the Cold +War um or any situation where you're up + + align:start position:0% +War um or any situation where you're up + + + align:start position:0% +War um or any situation where you're up +against an adversary who actually the + + align:start position:0% +against an adversary who actually the + + + align:start position:0% +against an adversary who actually the +this doesn't really work as well for the + + align:start position:0% +this doesn't really work as well for the + + + align:start position:0% +this doesn't really work as well for the +Cold War but in any situation where up + + align:start position:0% +Cold War but in any situation where up + + + align:start position:0% +Cold War but in any situation where up +you're against an adversary who's only + + align:start position:0% +you're against an adversary who's only + + + align:start position:0% +you're against an adversary who's only +goal in life is to destroy you you + + align:start position:0% +goal in life is to destroy you you + + + align:start position:0% +goal in life is to destroy you you +always want to find out what the best + + align:start position:0% +always want to find out what the best + + + align:start position:0% +always want to find out what the best +thing you can possibly do is you know if + + align:start position:0% +thing you can possibly do is you know if + + + align:start position:0% +thing you can possibly do is you know if +they hit that button and send nukes in + + align:start position:0% +they hit that button and send nukes in + + + align:start position:0% +they hit that button and send nukes in +from Cuba or if they send fighter pilots + + align:start position:0% +from Cuba or if they send fighter pilots + + + align:start position:0% +from Cuba or if they send fighter pilots +or whatever is going on so the idea of + + align:start position:0% +or whatever is going on so the idea of + + + align:start position:0% +or whatever is going on so the idea of +Alpha and beta is that they are numbers + + align:start position:0% +Alpha and beta is that they are numbers + + + align:start position:0% +Alpha and beta is that they are numbers +that + + align:start position:0% +that + + + align:start position:0% +that +represent the fail safe the worst case + + align:start position:0% +represent the fail safe the worst case + + + align:start position:0% +represent the fail safe the worst case +because obviously in you know in the + + align:start position:0% +because obviously in you know in the + + + align:start position:0% +because obviously in you know in the +Cold War sending nukes was not a good + + align:start position:0% +Cold War sending nukes was not a good + + + align:start position:0% +Cold War sending nukes was not a good +plan but uh um presumably us sending + + align:start position:0% +plan but uh um presumably us sending + + + align:start position:0% +plan but uh um presumably us sending +nukes would be better than just being + + align:start position:0% +nukes would be better than just being + + + align:start position:0% +nukes would be better than just being +attacked and killed so the alpha and + + align:start position:0% +attacked and killed so the alpha and + + + align:start position:0% +attacked and killed so the alpha and +beta represent the wor um the worst + + align:start position:0% +beta represent the wor um the worst + + + align:start position:0% +beta represent the wor um the worst +possible outcome you would be willing to + + align:start position:0% +possible outcome you would be willing to + + + align:start position:0% +possible outcome you would be willing to +accept for your side because right now + + align:start position:0% +accept for your side because right now + + + align:start position:0% +accept for your side because right now +you know you're guaranteed to be able to + + align:start position:0% +you know you're guaranteed to be able to + + + align:start position:0% +you know you're guaranteed to be able to +you're guaranteed to be able to force + + align:start position:0% +you're guaranteed to be able to force + + + align:start position:0% +you're guaranteed to be able to force +the conflict to that point or better so + + align:start position:0% +the conflict to that point or better so + + + align:start position:0% +the conflict to that point or better so +the alpha is the nuclear option the fail + + align:start position:0% +the alpha is the nuclear option the fail + + + align:start position:0% +the alpha is the nuclear option the fail +safe of the maximizer all right nuclear + + align:start position:0% +safe of the maximizer all right nuclear + + + align:start position:0% +safe of the maximizer all right nuclear +options + + align:start position:0% +options + + + align:start position:0% +options +Alpha is maximizer nuclear option + + align:start position:0% + + + + align:start position:0% + +and um beta is the minimizer nuclear + + align:start position:0% + + + + align:start position:0% + +option so we ask ourselves and people + + align:start position:0% +option so we ask ourselves and people + + + align:start position:0% +option so we ask ourselves and people +who were paying attention to it lecture + + align:start position:0% +who were paying attention to it lecture + + + align:start position:0% +who were paying attention to it lecture +or wrote stuff down know the answer + + align:start position:0% +or wrote stuff down know the answer + + + align:start position:0% +or wrote stuff down know the answer +already what could we possibly set to + + align:start position:0% +already what could we possibly set to + + + align:start position:0% +already what could we possibly set to +start off before we explore the tree and + + align:start position:0% +start off before we explore the tree and + + + align:start position:0% +start off before we explore the tree and +find anything what will we set as our + + align:start position:0% +find anything what will we set as our + + + align:start position:0% +find anything what will we set as our +nuclear option as our sort of fail safe + + align:start position:0% +nuclear option as our sort of fail safe + + + align:start position:0% +nuclear option as our sort of fail safe +we can always fall back on this + + align:start position:0% +we can always fall back on this + + + align:start position:0% +we can always fall back on this +number so I mean you could set zero you + + align:start position:0% +number so I mean you could set zero you + + + align:start position:0% +number so I mean you could set zero you +could try to set you know some low + + align:start position:0% +could try to set you know some low + + + align:start position:0% +could try to set you know some low +number for the maximizer CU if you set a + + align:start position:0% +number for the maximizer CU if you set a + + + align:start position:0% +number for the maximizer CU if you set a +high number for the maximizer as it's + + align:start position:0% +high number for the maximizer as it's + + + align:start position:0% +high number for the maximizer as it's +fail safe it's going to be really snoody + + align:start position:0% +fail safe it's going to be really snoody + + + align:start position:0% +fail safe it's going to be really snoody +and just say oh I won't take this path I + + align:start position:0% +and just say oh I won't take this path I + + + align:start position:0% +and just say oh I won't take this path I +already have a fail safe that's better + + align:start position:0% +already have a fail safe that's better + + + align:start position:0% +already have a fail safe that's better +than all these paths if you set like 100 + + align:start position:0% +than all these paths if you set like 100 + + + align:start position:0% +than all these paths if you set like 100 +you have no treat our default usually in + + align:start position:0% +you have no treat our default usually in + + + align:start position:0% +you have no treat our default usually in +6034 is to set negative Infinity for + + align:start position:0% +6034 is to set negative Infinity for + + + align:start position:0% +6034 is to set negative Infinity for +Alpha or negative some very large number + + align:start position:0% +Alpha or negative some very large number + + + align:start position:0% +Alpha or negative some very large number +if you're doing it in your + + align:start position:0% +if you're doing it in your + + + align:start position:0% +if you're doing it in your +lab uh so if we set negative + + align:start position:0% +lab uh so if we set negative + + + align:start position:0% +lab uh so if we set negative +Infinity as the default for Alpha that + + align:start position:0% +Infinity as the default for Alpha that + + + align:start position:0% +Infinity as the default for Alpha that +negative Infinity is basically maximizer + + align:start position:0% +negative Infinity is basically maximizer + + + align:start position:0% +negative Infinity is basically maximizer +loses so the maximizer goes in thinking + + align:start position:0% +loses so the maximizer goes in thinking + + + align:start position:0% +loses so the maximizer goes in thinking +oh my God if I don't look at this game + + align:start position:0% +oh my God if I don't look at this game + + + align:start position:0% +oh my God if I don't look at this game +tree I automatically lose he's willing + + align:start position:0% +tree I automatically lose he's willing + + + align:start position:0% +tree I automatically lose he's willing +to take the first path possibly + + align:start position:0% +to take the first path possibly + + + align:start position:0% +to take the first path possibly +presented and um that's why that + + align:start position:0% +presented and um that's why that + + + align:start position:0% +presented and um that's why that +negative Infinity is a good default for + + align:start position:0% +negative Infinity is a good default for + + + align:start position:0% +negative Infinity is a good default for +Alpha anyone have a good idea what a + + align:start position:0% +Alpha anyone have a good idea what a + + + align:start position:0% +Alpha anyone have a good idea what a +good default for beta is or just + + align:start position:0% +good default for beta is or just + + + align:start position:0% +good default for beta is or just +remember positive Infinity that's right + + align:start position:0% +remember positive Infinity that's right + + + align:start position:0% +remember positive Infinity that's right +because the minimizer comes in and she's + + align:start position:0% +because the minimizer comes in and she's + + + align:start position:0% +because the minimizer comes in and she's +like oh crap the maximizer automatically + + align:start position:0% +like oh crap the maximizer automatically + + + align:start position:0% +like oh crap the maximizer automatically +wins if I don't look at this uh I don't + + align:start position:0% +wins if I don't look at this uh I don't + + + align:start position:0% +wins if I don't look at this uh I don't +look at this node here that makes sure + + align:start position:0% +look at this node here that makes sure + + + align:start position:0% +look at this node here that makes sure +the maximizer and the minimizer both are + + align:start position:0% +the maximizer and the minimizer both are + + + align:start position:0% +the maximizer and the minimizer both are +willing to look at the first path they + + align:start position:0% +willing to look at the first path they + + + align:start position:0% +willing to look at the first path they +see every time because like look on this + + align:start position:0% +see every time because like look on this + + + align:start position:0% +see every time because like look on this +tree if 10 was Alpha the maximizer would + + align:start position:0% +tree if 10 was Alpha the maximizer would + + + align:start position:0% +tree if 10 was Alpha the maximizer would +just reject out of hand everything + + align:start position:0% +just reject out of hand everything + + + align:start position:0% +just reject out of hand everything +except for p and then we wouldn't have a + + align:start position:0% +except for p and then we wouldn't have a + + + align:start position:0% +except for p and then we wouldn't have a +tree the maximizer would lose because he + + align:start position:0% +tree the maximizer would lose because he + + + align:start position:0% +tree the maximizer would lose because he +would be + + align:start position:0% +would be + + + align:start position:0% +would be +like this chest game is very interesting + + align:start position:0% +like this chest game is very interesting + + + align:start position:0% +like this chest game is very interesting +however I have another option and to + + align:start position:0% +however I have another option and to + + + align:start position:0% +however I have another option and to +throw over the table that's 10 for me + + align:start position:0% +throw over the table that's 10 for me + + + align:start position:0% +throw over the table that's 10 for me +because you have to pick up the pieces I + + align:start position:0% +because you have to pick up the pieces I + + + align:start position:0% +because you have to pick up the pieces I +don't own this set I don't know so that + + align:start position:0% +don't own this set I don't know so that + + + align:start position:0% +don't own this set I don't know so that +is why we set negative infinity and + + align:start position:0% +is why we set negative infinity and + + + align:start position:0% +is why we set negative infinity and +positive Infinity as the default for + + align:start position:0% +positive Infinity as the default for + + + align:start position:0% +positive Infinity as the default for +Alpha and beta so how do alpha and beta + + align:start position:0% +Alpha and beta so how do alpha and beta + + + align:start position:0% +Alpha and beta so how do alpha and beta +propagate and what do they do the main + + align:start position:0% +propagate and what do they do the main + + + align:start position:0% +propagate and what do they do the main +purpose of Alpha and beta is that as we + + align:start position:0% +purpose of Alpha and beta is that as we + + + align:start position:0% +purpose of Alpha and beta is that as we +said Alpha let's say we have some chart + + align:start position:0% +said Alpha let's say we have some chart + + + align:start position:0% +said Alpha let's say we have some chart +of values Alpha which starts at negative + + align:start position:0% +of values Alpha which starts at negative + + + align:start position:0% +of values Alpha which starts at negative +Infinity is the worst that the maximizer + + align:start position:0% +Infinity is the worst that the maximizer + + + align:start position:0% +Infinity is the worst that the maximizer +is ready willing to accept because they + + align:start position:0% +is ready willing to accept because they + + + align:start position:0% +is ready willing to accept because they +know they can get that much or better it + + align:start position:0% +know they can get that much or better it + + + align:start position:0% +know they can get that much or better it +starts out that's the worst thing you + + align:start position:0% +starts out that's the worst thing you + + + align:start position:0% +starts out that's the worst thing you +can have so it's not a problem Infinity + + align:start position:0% +can have so it's not a problem Infinity + + + align:start position:0% +can have so it's not a problem Infinity +is the highest that the minimizer is + + align:start position:0% +is the highest that the minimizer is + + + align:start position:0% +is the highest that the minimizer is +willing to accept that's beta as you go + + align:start position:0% +willing to accept that's beta as you go + + + align:start position:0% +willing to accept that's beta as you go +along that the minimizer sees oh look at + + align:start position:0% +along that the minimizer sees oh look at + + + align:start position:0% +along that the minimizer sees oh look at +that I can guarantee that at best the + + align:start position:0% +that I can guarantee that at best the + + + align:start position:0% +that I can guarantee that at best the +maximizer gets you know 100 haha beta is + + align:start position:0% +maximizer gets you know 100 haha beta is + + + align:start position:0% +maximizer gets you know 100 haha beta is +now 100 maximizer sees oh yeah well I + + align:start position:0% +now 100 maximizer sees oh yeah well I + + + align:start position:0% +now 100 maximizer sees oh yeah well I +can guarantee you can get at the lowest + + align:start position:0% +can guarantee you can get at the lowest + + + align:start position:0% +can guarantee you can get at the lowest +you can get me to go to is zero so it's + + align:start position:0% +you can get me to go to is zero so it's + + + align:start position:0% +you can get me to go to is zero so it's +going to be zero and this keeps going on + + align:start position:0% +going to be zero and this keeps going on + + + align:start position:0% +going to be zero and this keeps going on +until maybe at + + align:start position:0% +until maybe at + + + align:start position:0% +until maybe at +6 Noe not drawn to scale uh maybe at six + + align:start position:0% +6 Noe not drawn to scale uh maybe at six + + + align:start position:0% +6 Noe not drawn to scale uh maybe at six +the maximizer says haha you can't make + + align:start position:0% +the maximizer says haha you can't make + + + align:start position:0% +the maximizer says haha you can't make +me go lower than six and the minimizer + + align:start position:0% +me go lower than six and the minimizer + + + align:start position:0% +me go lower than six and the minimizer +says aha you can't make me go higher + + align:start position:0% +says aha you can't make me go higher + + + align:start position:0% +says aha you can't make me go higher +than six and then six is the answer if + + align:start position:0% +than six and then six is the answer if + + + align:start position:0% +than six and then six is the answer if +you ever get to a point where if you + + align:start position:0% +you ever get to a point where if you + + + align:start position:0% +you ever get to a point where if you +ever get to a point where beta gets + + align:start position:0% +ever get to a point where beta gets + + + align:start position:0% +ever get to a point where beta gets +lower than alpha or Alpha gets lower + + align:start position:0% +lower than alpha or Alpha gets lower + + + align:start position:0% +lower than alpha or Alpha gets lower +than beta + + align:start position:0% +than beta + + + align:start position:0% +than beta +then you just say screw this I'm not + + align:start position:0% +then you just say screw this I'm not + + + align:start position:0% +then you just say screw this I'm not +even going to look at the I'm not even + + align:start position:0% +even going to look at the I'm not even + + + align:start position:0% +even going to look at the I'm not even +going to look at the remaining stuff I'm + + align:start position:0% +going to look at the remaining stuff I'm + + + align:start position:0% +going to look at the remaining stuff I'm +going to just prune now and go somewhere + + align:start position:0% +going to just prune now and go somewhere + + + align:start position:0% +going to just prune now and go somewhere +else that's less pointless than this + + align:start position:0% +else that's less pointless than this + + + align:start position:0% +else that's less pointless than this +because if the alpha gets higher than + + align:start position:0% +because if the alpha gets higher than + + + align:start position:0% +because if the alpha gets higher than +the beta what that's saying is the + + align:start position:0% +the beta what that's saying is the + + + align:start position:0% +the beta what that's saying is the +maximizer says oh man look at this + + align:start position:0% +maximizer says oh man look at this + + + align:start position:0% +maximizer says oh man look at this +minimizer the lowest you can make me go + + align:start position:0% +minimizer the lowest you can make me go + + + align:start position:0% +minimizer the lowest you can make me go +is one is say 50 and the minimizer says + + align:start position:0% +is one is say 50 and the minimizer says + + + align:start position:0% +is one is say 50 and the minimizer says +that's strange because the highest that + + align:start position:0% +that's strange because the highest that + + + align:start position:0% +that's strange because the highest that +you can make me go is 40 so something's + + align:start position:0% +you can make me go is 40 so something's + + + align:start position:0% +you can make me go is 40 so something's +generally um something's generally a + + align:start position:0% +generally um something's generally a + + + align:start position:0% +generally um something's generally a +Miss there it usually means that one of + + align:start position:0% +Miss there it usually means that one of + + + align:start position:0% +Miss there it usually means that one of +the two of them doesn't even want to be + + align:start position:0% +the two of them doesn't even want to be + + + align:start position:0% +the two of them doesn't even want to be +exploring that Branch at all so you you + + align:start position:0% +exploring that Branch at all so you you + + + align:start position:0% +exploring that Branch at all so you you +prune at that point all right so given + + align:start position:0% +prune at that point all right so given + + + align:start position:0% +prune at that point all right so given +that that's what we're looking for how + + align:start position:0% +that that's what we're looking for how + + + align:start position:0% +that that's what we're looking for how +do we move the alphas and betas + + align:start position:0% +do we move the alphas and betas + + + align:start position:0% +do we move the alphas and betas +throughout the tree there's a few + + align:start position:0% +throughout the tree there's a few + + + align:start position:0% +throughout the tree there's a few +different ways to draw them and some of + + align:start position:0% +different ways to draw them and some of + + + align:start position:0% +different ways to draw them and some of +them I consider to be very busy um + + align:start position:0% +them I consider to be very busy um + + + align:start position:0% +them I consider to be very busy um +probably in recitation and tutorial you + + align:start position:0% +probably in recitation and tutorial you + + + align:start position:0% +probably in recitation and tutorial you +will see a way that's busier and has + + align:start position:0% +will see a way that's busier and has + + + align:start position:0% +will see a way that's busier and has +more numbers technically every node has + + align:start position:0% +more numbers technically every node has + + + align:start position:0% +more numbers technically every node has +both an alpha and a beta however the one + + align:start position:0% +both an alpha and a beta however the one + + + align:start position:0% +both an alpha and a beta however the one +that that node is paying attention to is + + align:start position:0% +that that node is paying attention to is + + + align:start position:0% +that that node is paying attention to is +the alpha if it's a maximizer and the + + align:start position:0% +the alpha if it's a maximizer and the + + + align:start position:0% +the alpha if it's a maximizer and the +beta if it's a minimizer so I generally + + align:start position:0% +beta if it's a minimizer so I generally + + + align:start position:0% +beta if it's a minimizer so I generally +for my purposes only draw the alpha out + + align:start position:0% +for my purposes only draw the alpha out + + + align:start position:0% +for my purposes only draw the alpha out +for the maximizer and only draw the beta + + align:start position:0% +for the maximizer and only draw the beta + + + align:start position:0% +for the maximizer and only draw the beta +out for the minimizer very rarely but it + + align:start position:0% +out for the minimizer very rarely but it + + + align:start position:0% +out for the minimizer very rarely but it +happens they'll sometimes ask you well + + align:start position:0% +happens they'll sometimes ask you well + + + align:start position:0% +happens they'll sometimes ask you well +what's the beta of this node which is a + + align:start position:0% +what's the beta of this node which is a + + + align:start position:0% +what's the beta of this node which is a +maximizer node so it's good to know how + + align:start position:0% +maximizer node so it's good to know how + + + align:start position:0% +maximizer node so it's good to know how +it's derived but I think that it wastes + + align:start position:0% +it's derived but I think that it wastes + + + align:start position:0% +it's derived but I think that it wastes +your time to write it out that's my + + align:start position:0% +your time to write it out that's my + + + align:start position:0% +your time to write it out that's my +opinion we'll see how goes so the way + + align:start position:0% +opinion we'll see how goes so the way + + + align:start position:0% +opinion we'll see how goes so the way +that it works is the the way that Alpha + + align:start position:0% +that it works is the the way that Alpha + + + align:start position:0% +that it works is the the way that Alpha +and beta works is the Snow White + + align:start position:0% +and beta works is the Snow White + + + align:start position:0% +and beta works is the Snow White +principle so does everyone know the + + align:start position:0% +principle so does everyone know the + + + align:start position:0% +principle so does everyone know the +story of Snow + + align:start position:0% +story of Snow + + + align:start position:0% +story of Snow +White so you know there's a beautiful + + align:start position:0% +White so you know there's a beautiful + + + align:start position:0% +White so you know there's a beautiful +princess there's an evil queen + + align:start position:0% +princess there's an evil queen + + + align:start position:0% +princess there's an evil queen +stepmother miramir on the wall who's the + + align:start position:0% +stepmother miramir on the wall who's the + + + align:start position:0% +stepmother miramir on the wall who's the +first of them all finds out that uh that + + align:start position:0% +first of them all finds out that uh that + + + align:start position:0% +first of them all finds out that uh that +it's the the stepdaughter so much like + + align:start position:0% +it's the the stepdaughter so much like + + + align:start position:0% +it's the the stepdaughter so much like +in the real world in Snow White the + + align:start position:0% +in the real world in Snow White the + + + align:start position:0% +in the real world in Snow White the +stepdaughter the Snow White had the + + align:start position:0% +stepdaughter the Snow White had the + + + align:start position:0% +stepdaughter the Snow White had the +beauty of her parents she inherited + + align:start position:0% +beauty of her parents she inherited + + + align:start position:0% +beauty of her parents she inherited +those however much like in the real + + align:start position:0% +those however much like in the real + + + align:start position:0% +those however much like in the real +world maybe or perhaps not um the + + align:start position:0% +world maybe or perhaps not um the + + + align:start position:0% +world maybe or perhaps not um the +stepmother had an even better plan she + + align:start position:0% +stepmother had an even better plan she + + + align:start position:0% +stepmother had an even better plan she +hired a hunter to uh to sort of hunt + + align:start position:0% +hired a hunter to uh to sort of hunt + + + align:start position:0% +hired a hunter to uh to sort of hunt +Snow White pull out Snow White's heart + + align:start position:0% +Snow White pull out Snow White's heart + + + align:start position:0% +Snow White pull out Snow White's heart +and feed it to her so that she could + + align:start position:0% +and feed it to her so that she could + + + align:start position:0% +and feed it to her so that she could +gain Snow White's Beauty for herself how + + align:start position:0% +gain Snow White's Beauty for herself how + + + align:start position:0% +gain Snow White's Beauty for herself how +many people knew that version of the + + align:start position:0% +many people knew that version of the + + + align:start position:0% +many people knew that version of the +story a few people that's the original + + align:start position:0% +story a few people that's the original + + + align:start position:0% +story a few people that's the original +version of the story Disney didn't put + + align:start position:0% +version of the story Disney didn't put + + + align:start position:0% +version of the story Disney didn't put +that in the hunter then brought the + + align:start position:0% +that in the hunter then brought the + + + align:start position:0% +that in the hunter then brought the +heart of a deer which I think in Disney + + align:start position:0% +heart of a deer which I think in Disney + + + align:start position:0% +heart of a deer which I think in Disney +the hunter did kill a deer arbitrarily + + align:start position:0% +the hunter did kill a deer arbitrarily + + + align:start position:0% +the hunter did kill a deer arbitrarily +but it was not explained that that's why + + align:start position:0% +but it was not explained that that's why + + + align:start position:0% +but it was not explained that that's why +he was doing it so in Alpha Beta it's + + align:start position:0% +he was doing it so in Alpha Beta it's + + + align:start position:0% +he was doing it so in Alpha Beta it's +just like that + + align:start position:0% +just like that + + + align:start position:0% +just like that +by which I mean you start by inheriting + + align:start position:0% +by which I mean you start by inheriting + + + align:start position:0% +by which I mean you start by inheriting +the alpha and beta of your parents but + + align:start position:0% +the alpha and beta of your parents but + + + align:start position:0% +the alpha and beta of your parents but +if you see something that you like + + align:start position:0% +if you see something that you like + + + align:start position:0% +if you see something that you like +amongst your children you take it for + + align:start position:0% +amongst your children you take it for + + + align:start position:0% +amongst your children you take it for +yourself the Snow White principle so + + align:start position:0% +yourself the Snow White principle so + + + align:start position:0% +yourself the Snow White principle so +let's see how that goes well I told you + + align:start position:0% +let's see how that goes well I told you + + + align:start position:0% +let's see how that goes well I told you +guys that the default Alpha + + align:start position:0% +guys that the default Alpha + + + align:start position:0% +guys that the default Alpha +was negative Infinity so here Alpha is + + align:start position:0% +was negative Infinity so here Alpha is + + + align:start position:0% +was negative Infinity so here Alpha is +negative + + align:start position:0% +negative + + + align:start position:0% +negative +infinity and I told you that the default + + align:start position:0% +infinity and I told you that the default + + + align:start position:0% +infinity and I told you that the default +beta was positive Infinity we're doing a + + align:start position:0% +beta was positive Infinity we're doing a + + + align:start position:0% +beta was positive Infinity we're doing a +depth first search here all right beta + + align:start position:0% +depth first search here all right beta + + + align:start position:0% +depth first search here all right beta +is infinity all right + + align:start position:0% +is infinity all right + + + align:start position:0% +is infinity all right +so we come here to e now we could put an + + align:start position:0% +so we come here to e now we could put an + + + align:start position:0% +so we come here to e now we could put an +alpha but I never put some I never put + + align:start position:0% +alpha but I never put some I never put + + + align:start position:0% +alpha but I never put some I never put +an alpha or a beta for one of the + + align:start position:0% +an alpha or a beta for one of the + + + align:start position:0% +an alpha or a beta for one of the +terminal nodes because it can't really + + align:start position:0% +terminal nodes because it can't really + + + align:start position:0% +terminal nodes because it can't really +do anything it just you know it's just + + align:start position:0% +do anything it just you know it's just + + + align:start position:0% +do anything it just you know it's just +two so as we go down we take the alpha + + align:start position:0% +two so as we go down we take the alpha + + + align:start position:0% +two so as we go down we take the alpha +and beta from our parents but as we go + + align:start position:0% +and beta from our parents but as we go + + + align:start position:0% +and beta from our parents but as we go +up to a parent if the parent likes what + + align:start position:0% +up to a parent if the parent likes what + + + align:start position:0% +up to a parent if the parent likes what +it sees in the child it takes it instead + + align:start position:0% +it sees in the child it takes it instead + + + align:start position:0% +it sees in the child it takes it instead +so I ask you all the question would the + + align:start position:0% +so I ask you all the question would the + + + align:start position:0% +so I ask you all the question would the +minimizer prefer this two that it sees + + align:start position:0% +minimizer prefer this two that it sees + + + align:start position:0% +minimizer prefer this two that it sees +from its child or its own Infinity for a + + align:start position:0% +from its child or its own Infinity for a + + + align:start position:0% +from its child or its own Infinity for a +beta it likes the two that's absolutely + + align:start position:0% +beta it likes the two that's absolutely + + + align:start position:0% +beta it likes the two that's absolutely +right + + align:start position:0% +right + + + align:start position:0% +right +so + + align:start position:0% +so + + + align:start position:0% +so +two all right great so now we go down to + + align:start position:0% +two all right great so now we go down to + + + align:start position:0% +two all right great so now we go down to +F what is F's + + align:start position:0% + + + + align:start position:0% + +Alpha who says who says negative + + align:start position:0% +Alpha who says who says negative + + + align:start position:0% +Alpha who says who says negative +Infinity who says + + align:start position:0% +Infinity who says + + + align:start position:0% +Infinity who says +two no one oh you guys are you guys are + + align:start position:0% +two no one oh you guys are you guys are + + + align:start position:0% +two no one oh you guys are you guys are +you guys are good it's negative Infinity + + align:start position:0% +you guys are good it's negative Infinity + + + align:start position:0% +you guys are good it's negative Infinity +technically it also will have a beta of + + align:start position:0% +technically it also will have a beta of + + + align:start position:0% +technically it also will have a beta of +two but we're ignoring the beta and the + + align:start position:0% +two but we're ignoring the beta and the + + + align:start position:0% +two but we're ignoring the beta and the +alphas that have been progressing + + align:start position:0% +alphas that have been progressing + + + align:start position:0% +alphas that have been progressing +downward from parents negative Infinity + + align:start position:0% +downward from parents negative Infinity + + + align:start position:0% +downward from parents negative Infinity +that's why I called it the grandfather + + align:start position:0% +that's why I called it the grandfather + + + align:start position:0% +that's why I called it the grandfather +clause before because you would often + + align:start position:0% +clause before because you would often + + + align:start position:0% +clause before because you would often +look up to your grandparent to um to see + + align:start position:0% +look up to your grandparent to um to see + + + align:start position:0% +look up to your grandparent to um to see +what your default number is so we got an + + align:start position:0% +what your default number is so we got an + + + align:start position:0% +what your default number is so we got an +alpha of negative Infinity we then go + + align:start position:0% +alpha of negative Infinity we then go + + + align:start position:0% +alpha of negative Infinity we then go +down to the K it's a static evaluation + + align:start position:0% +down to the K it's a static evaluation + + + align:start position:0% +down to the K it's a static evaluation +and now I'm going to start calling on + + align:start position:0% +and now I'm going to start calling on + + + align:start position:0% +and now I'm going to start calling on +people individually so hopefully people + + align:start position:0% +people individually so hopefully people + + + align:start position:0% +people individually so hopefully people +paid attention to the Mob who were + + align:start position:0% +paid attention to the Mob who were + + + align:start position:0% +paid attention to the Mob who were +always correct um all right so we go + + align:start position:0% +always correct um all right so we go + + + align:start position:0% +always correct um all right so we go +down to K and we see a three f is a + + align:start position:0% +down to K and we see a three f is a + + + align:start position:0% +down to K and we see a three f is a +maximizer node so what does f do + + align:start position:0% +maximizer node so what does f do + + + align:start position:0% +maximizer node so what does f do +now outut yes switches its Alpha to + + align:start position:0% +now outut yes switches its Alpha to + + + align:start position:0% +now outut yes switches its Alpha to +three + + align:start position:0% + + + + align:start position:0% + +great all right so that's already that's + + align:start position:0% +great all right so that's already that's + + + align:start position:0% +great all right so that's already that's +already quite good it switches Alpha to + + align:start position:0% +already quite good it switches Alpha to + + + align:start position:0% +already quite good it switches Alpha to +three it's very happy it's got a three + + align:start position:0% +three it's very happy it's got a three + + + align:start position:0% +three it's very happy it's got a three +here that's a nice that's a nice value + + align:start position:0% +here that's a nice that's a nice value + + + align:start position:0% +here that's a nice that's a nice value +so what does it + + align:start position:0% +so what does it + + + align:start position:0% +so what does it +do let's see what does it do at + + align:start position:0% +do let's see what does it do at + + + align:start position:0% +do let's see what does it do at +L at L the next one it's gone to K went + + align:start position:0% +L at L the next one it's gone to K went + + + align:start position:0% +L at L the next one it's gone to K went +back up to F dep for search the next one + + align:start position:0% +back up to F dep for search the next one + + + align:start position:0% +back up to F dep for search the next one +would be L + + align:start position:0% + + + + align:start position:0% + +right inh from anywhere + + align:start position:0% +right inh from anywhere + + + align:start position:0% +right inh from anywhere +right well technically F could take L um + + align:start position:0% +right well technically F could take L um + + + align:start position:0% +right well technically F could take L um +could take L's value of zero if it liked + + align:start position:0% +could take L's value of zero if it liked + + + align:start position:0% +could take L's value of zero if it liked +it better than three but it's a + + align:start position:0% +it better than three but it's a + + + align:start position:0% +it better than three but it's a +maximizer so what doesn't want to take + + align:start position:0% +maximizer so what doesn't want to take + + + align:start position:0% +maximizer so what doesn't want to take +that okay that technically would be + + align:start position:0% +that okay that technically would be + + + align:start position:0% +that okay that technically would be +correct but I'm sorry I burden you with + + align:start position:0% +correct but I'm sorry I burden you with + + + align:start position:0% +correct but I'm sorry I burden you with +a trick question um in + + align:start position:0% +a trick question um in + + + align:start position:0% +a trick question um in +fact we don't look at L at + + align:start position:0% + + + + align:start position:0% + +all does everyone see that I'll explain + + align:start position:0% +all does everyone see that I'll explain + + + align:start position:0% +all does everyone see that I'll explain +the alpha at F has reached three but the + + align:start position:0% +the alpha at F has reached three but the + + + align:start position:0% +the alpha at F has reached three but the +beta at B is two so B looks down and + + align:start position:0% +beta at B is two so B looks down and + + + align:start position:0% +beta at B is two so B looks down and +says wait a minute if I go down to F my + + align:start position:0% +says wait a minute if I go down to F my + + + align:start position:0% +says wait a minute if I go down to F my +enemy's nuclear option my enem is the + + align:start position:0% +enemy's nuclear option my enem is the + + + align:start position:0% +enemy's nuclear option my enem is the +worst it can be for you know the best it + + align:start position:0% +worst it can be for you know the best it + + + align:start position:0% +worst it can be for you know the best it +can be for me is three f f is trumpeting + + align:start position:0% +can be for me is three f f is trumpeting + + + align:start position:0% +can be for me is three f f is trumpeting +around I was thinking of you know eating + + align:start position:0% +around I was thinking of you know eating + + + align:start position:0% +around I was thinking of you know eating +his hard or whatever but I didn't want + + align:start position:0% +his hard or whatever but I didn't want + + + align:start position:0% +his hard or whatever but I didn't want +to but it's going to be three it's going + + align:start position:0% +to but it's going to be three it's going + + + align:start position:0% +to but it's going to be three it's going +to be three or higher down um down there + + align:start position:0% +to be three or higher down um down there + + + align:start position:0% +to be three or higher down um down there +at F there's no way I want that I + + align:start position:0% +at F there's no way I want that I + + + align:start position:0% +at F there's no way I want that I +already have my own I already have my + + align:start position:0% +already have my own I already have my + + + align:start position:0% +already have my own I already have my +own default Escape + + align:start position:0% +own default Escape + + + align:start position:0% +own default Escape +and that's two that's going to be better + + align:start position:0% +and that's two that's going to be better + + + align:start position:0% +and that's two that's going to be better +than whatever comes out of that horrible + + align:start position:0% +than whatever comes out of that horrible + + + align:start position:0% +than whatever comes out of that horrible +F so screw + + align:start position:0% +F so screw + + + align:start position:0% +F so screw +it and we never look it + + align:start position:0% +it and we never look it + + + align:start position:0% +it and we never look it +out does everyone get that that is the + + align:start position:0% +out does everyone get that that is the + + + align:start position:0% +out does everyone get that that is the +main principle of Alpha Beta pruning you + + align:start position:0% +main principle of Alpha Beta pruning you + + + align:start position:0% +main principle of Alpha Beta pruning you +if you see an alpha it's higher than the + + align:start position:0% +if you see an alpha it's higher than the + + + align:start position:0% +if you see an alpha it's higher than the +beta above it as I said you know if + + align:start position:0% +beta above it as I said you know if + + + align:start position:0% +beta above it as I said you know if +Alpha goes up above the beta or if you + + align:start position:0% +Alpha goes up above the beta or if you + + + align:start position:0% +Alpha goes up above the beta or if you +see a beta and there's a like if there's + + align:start position:0% +see a beta and there's a like if there's + + + align:start position:0% +see a beta and there's a like if there's +a beta + + align:start position:0% +a beta + + + align:start position:0% +a beta +down here and it's lower than the alpha + + align:start position:0% +down here and it's lower than the alpha + + + align:start position:0% +down here and it's lower than the alpha +above it prune stop doing + + align:start position:0% +above it prune stop doing + + + align:start position:0% +above it prune stop doing +that the and the question is who prunes + + align:start position:0% +that the and the question is who prunes + + + align:start position:0% +that the and the question is who prunes +who decides that you don't look at L the + + align:start position:0% +who decides that you don't look at L the + + + align:start position:0% +who decides that you don't look at L the +the person who is thinking not to look + + align:start position:0% +the person who is thinking not to look + + + align:start position:0% +the person who is thinking not to look +at L is always up higher by at least two + + align:start position:0% +at L is always up higher by at least two + + + align:start position:0% +at L is always up higher by at least two +levels so up here B is saying H I don't + + align:start position:0% +levels so up here B is saying H I don't + + + align:start position:0% +levels so up here B is saying H I don't +want to look at L because f is already + + align:start position:0% +want to look at L because f is already + + + align:start position:0% +want to look at L because f is already +so terrible for me that it's just beyond + + align:start position:0% +so terrible for me that it's just beyond + + + align:start position:0% +so terrible for me that it's just beyond +belief it's going to be if if this is + + align:start position:0% +belief it's going to be if if this is + + + align:start position:0% +belief it's going to be if if this is +100 it might be 100 if this is if it's + + align:start position:0% +100 it might be 100 if this is if it's + + + align:start position:0% +100 it might be 100 if this is if it's +even if it's lower I'm still going to + + align:start position:0% +even if it's lower I'm still going to + + + align:start position:0% +even if it's lower I'm still going to +get a three + + align:start position:0% +get a three + + + align:start position:0% +get a three +there's a sanity check that I've written + + align:start position:0% +there's a sanity check that I've written + + + align:start position:0% +there's a sanity check that I've written +uh or that I that I sort of came up with + + align:start position:0% +uh or that I that I sort of came up with + + + align:start position:0% +uh or that I that I sort of came up with +just in case you're not sure that you + + align:start position:0% +just in case you're not sure that you + + + align:start position:0% +just in case you're not sure that you +can skip it because on a lot of these + + align:start position:0% +can skip it because on a lot of these + + + align:start position:0% +can skip it because on a lot of these +tests we ask you which ones do you + + align:start position:0% +tests we ask you which ones do you + + + align:start position:0% +tests we ask you which ones do you +evaluate which ones do you skip right so + + align:start position:0% +evaluate which ones do you skip right so + + + align:start position:0% +evaluate which ones do you skip right so +or we just say which ones do you + + align:start position:0% +or we just say which ones do you + + + align:start position:0% +or we just say which ones do you +evaluate and you don't write the ones + + align:start position:0% +evaluate and you don't write the ones + + + align:start position:0% +evaluate and you don't write the ones +that you skip here's my sanity test to + + align:start position:0% +that you skip here's my sanity test to + + + align:start position:0% +that you skip here's my sanity test to +see if you can skip it ask yourself if + + align:start position:0% +see if you can skip it ask yourself if + + + align:start position:0% +see if you can skip it ask yourself if +that node contain that I'm about to skip + + align:start position:0% +that node contain that I'm about to skip + + + align:start position:0% +that node contain that I'm about to skip +contained a negative infinity or some + + align:start position:0% +contained a negative infinity or some + + + align:start position:0% +contained a negative infinity or some +arbitrarily small number negative + + align:start position:0% +arbitrarily small number negative + + + align:start position:0% +arbitrarily small number negative +Infinity being the minimizer wins would + + align:start position:0% +Infinity being the minimizer wins would + + + align:start position:0% +Infinity being the minimizer wins would +it change + + align:start position:0% +it change + + + align:start position:0% +it change +anything now that I've answered that if + + align:start position:0% +anything now that I've answered that if + + + align:start position:0% +anything now that I've answered that if +it CH contained a positive Infinity + + align:start position:0% +it CH contained a positive Infinity + + + align:start position:0% +it CH contained a positive Infinity +would it change anything if the answer + + align:start position:0% +would it change anything if the answer + + + align:start position:0% +would it change anything if the answer +is no both + + align:start position:0% +is no both + + + align:start position:0% +is no both +times then you definitely correct in + + align:start position:0% +times then you definitely correct in + + + align:start position:0% +times then you definitely correct in +pruning it so look at that zero if it + + align:start position:0% +pruning it so look at that zero if it + + + align:start position:0% +pruning it so look at that zero if it +was a negative Infinity minimizer wins + + align:start position:0% +was a negative Infinity minimizer wins + + + align:start position:0% +was a negative Infinity minimizer wins +what would happen maximizer would say + + align:start position:0% +what would happen maximizer would say + + + align:start position:0% +what would happen maximizer would say +I'm not touching that with a 10-ft pole + + align:start position:0% +I'm not touching that with a 10-ft pole + + + align:start position:0% +I'm not touching that with a 10-ft pole +choosing three the minimizer would say + + align:start position:0% +choosing three the minimizer would say + + + align:start position:0% +choosing three the minimizer would say +oh screw that I'll take + + align:start position:0% +oh screw that I'll take + + + align:start position:0% +oh screw that I'll take +e let's say it was a positive Infinity + + align:start position:0% +e let's say it was a positive Infinity + + + align:start position:0% +e let's say it was a positive Infinity +the maxim would say Eureka Holy Grail I + + align:start position:0% +the maxim would say Eureka Holy Grail I + + + align:start position:0% +the maxim would say Eureka Holy Grail I +win minimizer would say yeah if I'm a + + align:start position:0% +win minimizer would say yeah if I'm a + + + align:start position:0% +win minimizer would say yeah if I'm a + and go down to F and then we go to + + align:start position:0% + and go down to F and then we go to + + + align:start position:0% + and go down to F and then we go to +E and take two so no matter what was + + align:start position:0% +E and take two so no matter what was + + + align:start position:0% +E and take two so no matter what was +there minimizer would go to E and you + + align:start position:0% +there minimizer would go to E and you + + + align:start position:0% +there minimizer would go to E and you +could say well what if it was exactly + + align:start position:0% +could say well what if it was exactly + + + align:start position:0% +could say well what if it was exactly +two but he still the maximizer would + + align:start position:0% +two but he still the maximizer would + + + align:start position:0% +two but he still the maximizer would +choose K and the minimizer would go to E + + align:start position:0% +choose K and the minimizer would go to E + + + align:start position:0% +choose K and the minimizer would go to E +so there's no reason to go down there we + + align:start position:0% +so there's no reason to go down there we + + + align:start position:0% +so there's no reason to go down there we +can just prune it off right now does + + align:start position:0% +can just prune it off right now does + + + align:start position:0% +can just prune it off right now does +everyone agree everyone see what I'm + + align:start position:0% +everyone agree everyone see what I'm + + + align:start position:0% +everyone agree everyone see what I'm +talking about here great so we're now + + align:start position:0% +talking about here great so we're now + + + align:start position:0% +talking about here great so we're now +done because with this Branch because + + align:start position:0% +done because with this Branch because + + + align:start position:0% +done because with this Branch because +beta is two so now we're up at Old Grand + + align:start position:0% +beta is two so now we're up at Old Grand + + + align:start position:0% +beta is two so now we're up at Old Grand +papy a and he has an alpha of negative + + align:start position:0% +papy a and he has an alpha of negative + + + align:start position:0% +papy a and he has an alpha of negative +Infinity everyone what what will he + + align:start position:0% +Infinity everyone what what will he + + + align:start position:0% +Infinity everyone what what will he +do two he'll take the two it's better + + align:start position:0% +do two he'll take the two it's better + + + align:start position:0% +do two he'll take the two it's better +than negative Infinity for him it's not + + align:start position:0% +than negative Infinity for him it's not + + + align:start position:0% +than negative Infinity for him it's not +wonderful but surely anything is better + + align:start position:0% +wonderful but surely anything is better + + + align:start position:0% +wonderful but surely anything is better +than an automatic + + align:start position:0% +than an automatic + + + align:start position:0% +than an automatic +loss all right now our highest know is a + + align:start position:0% +loss all right now our highest know is a + + + align:start position:0% +loss all right now our highest know is a +two so let's keep that in mind for our + + align:start position:0% +two so let's keep that in mind for our + + + align:start position:0% +two so let's keep that in mind for our +Alpha okay so let's let's go over here + + align:start position:0% +Alpha okay so let's let's go over here + + + align:start position:0% +Alpha okay so let's let's go over here +let's see so what will be the value at C + + align:start position:0% +let's see so what will be the value at C + + + align:start position:0% +let's see so what will be the value at C +what will be the beta + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +value go back to which one to G uh I'm + + align:start position:0% +value go back to which one to G uh I'm + + + align:start position:0% +value go back to which one to G uh I'm +not at G yet I'm actually um just + + align:start position:0% +not at G yet I'm actually um just + + + align:start position:0% +not at G yet I'm actually um just +starting the middle Branch so I'm going + + align:start position:0% +starting the middle Branch so I'm going + + + align:start position:0% +starting the middle Branch so I'm going +to C and what's going to be it starting + + align:start position:0% +to C and what's going to be it starting + + + align:start position:0% +to C and what's going to be it starting +Data before I U before I go + + align:start position:0% +Data before I U before I go + + + align:start position:0% +Data before I U before I go +down Infinity that's right default value + + align:start position:0% +down Infinity that's right default value + + + align:start position:0% +down Infinity that's right default value +is easier than it seemed all right so + + align:start position:0% +is easier than it seemed all right so + + + align:start position:0% +is easier than it seemed all right so +yes beta is equal to + + align:start position:0% +yes beta is equal to + + + align:start position:0% +yes beta is equal to +Infinity this should be better erased I + + align:start position:0% +Infinity this should be better erased I + + + align:start position:0% +Infinity this should be better erased I +think it's confusing people great okay + + align:start position:0% +think it's confusing people great okay + + + align:start position:0% +think it's confusing people great okay +so beta is equal to Infinity at C what + + align:start position:0% +so beta is equal to Infinity at C what + + + align:start position:0% +so beta is equal to Infinity at C what +is going to now we go down depth first + + align:start position:0% +is going to now we go down depth first + + + align:start position:0% +is going to now we go down depth first +sech to G what's going to be our Alpha + + align:start position:0% +sech to G what's going to be our Alpha + + + align:start position:0% +sech to G what's going to be our Alpha +at + + align:start position:0% +at + + + align:start position:0% +at +Gus ah it would seem so however take a + + align:start position:0% +Gus ah it would seem so however take a + + + align:start position:0% +Gus ah it would seem so however take a +look up at our at the you know great + + align:start position:0% +look up at our at the you know great + + + align:start position:0% +look up at our at the you know great +grand papy a it seems to have changed to + + align:start position:0% +grand papy a it seems to have changed to + + + align:start position:0% +grand papy a it seems to have changed to +two so this time it's two why is it two + + align:start position:0% +two so this time it's two why is it two + + + align:start position:0% +two so this time it's two why is it two +instead of negative Infinity why can we + + align:start position:0% +instead of negative Infinity why can we + + + align:start position:0% +instead of negative Infinity why can we +let a be so obnoxious and not start with + + align:start position:0% +let a be so obnoxious and not start with + + + align:start position:0% +let a be so obnoxious and not start with +saying oh I automatically lose well a + + align:start position:0% +saying oh I automatically lose well a + + + align:start position:0% +saying oh I automatically lose well a +knows that no matter how awful things + + align:start position:0% +knows that no matter how awful things + + + align:start position:0% +knows that no matter how awful things +get in that middle + + align:start position:0% +get in that middle + + + align:start position:0% +get in that middle +Branch he could just say screw the whole + + align:start position:0% +Branch he could just say screw the whole + + + align:start position:0% +Branch he could just say screw the whole +middle Branch I'm going to be that's + + align:start position:0% +middle Branch I'm going to be that's + + + align:start position:0% +middle Branch I'm going to be that's +something that that the minimizer can't + + align:start position:0% +something that that the minimizer can't + + + align:start position:0% +something that that the minimizer can't +do and we have to start at Infinity for + + align:start position:0% +do and we have to start at Infinity for + + + align:start position:0% +do and we have to start at Infinity for +the minimizer but the maximizer can + + align:start position:0% +the minimizer but the maximizer can + + + align:start position:0% +the minimizer but the maximizer can +because he has the choice at the top + + align:start position:0% +because he has the choice at the top + + + align:start position:0% +because he has the choice at the top +does everyone see that he can just say + + align:start position:0% +does everyone see that he can just say + + + align:start position:0% +does everyone see that he can just say +oh I'm not even going to C yes shows you + + align:start position:0% +oh I'm not even going to C yes shows you + + + align:start position:0% +oh I'm not even going to C yes shows you +I'm going to a taking the two so + + align:start position:0% +I'm going to a taking the two so + + + align:start position:0% +I'm going to a taking the two so +therefore Alpha is actually two at G all + + align:start position:0% +therefore Alpha is actually two at G all + + + align:start position:0% +therefore Alpha is actually two at G all +right great so we've got an alpha that's + + align:start position:0% +right great so we've got an alpha that's + + + align:start position:0% +right great so we've got an alpha that's +two at G we're going to go down to M + + align:start position:0% +two at G we're going to go down to M + + + align:start position:0% +two at G we're going to go down to M +it's a minimizer all right what's going + + align:start position:0% +it's a minimizer all right what's going + + + align:start position:0% +it's a minimizer all right what's going +to be our beta value at + + align:start position:0% + + + + align:start position:0% + +M or which is the beta default minus or + + align:start position:0% +M or which is the beta default minus or + + + align:start position:0% +M or which is the beta default minus or +positive Infinity where the + + align:start position:0% +positive Infinity where the + + + align:start position:0% +positive Infinity where the +minimizer positive Infinity that's right + + align:start position:0% +minimizer positive Infinity that's right + + + align:start position:0% +minimizer positive Infinity that's right +m is going to be a positive Infinity for + + align:start position:0% +m is going to be a positive Infinity for + + + align:start position:0% +m is going to be a positive Infinity for +beta again it picks it up from + + align:start position:0% + + + + align:start position:0% + +C great now we get to some actual values + + align:start position:0% +C great now we get to some actual values + + + align:start position:0% +C great now we get to some actual values +okay so we're at some actual values we + + align:start position:0% +okay so we're at some actual values we + + + align:start position:0% +okay so we're at some actual values we +are at Q so what's going to what's going + + align:start position:0% +are at Q so what's going to what's going + + + align:start position:0% +are at Q so what's going to what's going +to happen at M when M sees that Q is + + align:start position:0% +to happen at M when M sees that Q is + + + align:start position:0% +to happen at M when M sees that Q is +one + + align:start position:0% + + + + align:start position:0% + +um wait what do beta say what is beta it + + align:start position:0% +um wait what do beta say what is beta it + + + align:start position:0% +um wait what do beta say what is beta it +says Infinity I'm sorry it's hard to + + align:start position:0% +says Infinity I'm sorry it's hard to + + + align:start position:0% +says Infinity I'm sorry it's hard to +read beta is Infinity ADM + + align:start position:0% + + + + align:start position:0% + +so um that's right so beta is going to + + align:start position:0% +so um that's right so beta is going to + + + align:start position:0% +so um that's right so beta is going to +be they're going to put beta to one + + align:start position:0% +be they're going to put beta to one + + + align:start position:0% +be they're going to put beta to one +because it sees Q + + align:start position:0% +because it sees Q + + + align:start position:0% +because it sees Q +great all right so my next question is + + align:start position:0% +great all right so my next question is + + + align:start position:0% +great all right so my next question is +let's see uh my next question is what's + + align:start position:0% +let's see uh my next question is what's + + + align:start position:0% +let's see uh my next question is what's +going to happen at + + align:start position:0% + + + + align:start position:0% + +R there + + align:start position:0% +R there + + + align:start position:0% +R there +you have youve you've detected my trap + + align:start position:0% +you have youve you've detected my trap + + + align:start position:0% +you have youve you've detected my trap +the question is does it look at R the + + align:start position:0% +the question is does it look at R the + + + align:start position:0% +the question is does it look at R the +answer is no it doesn't look at R why + + align:start position:0% +answer is no it doesn't look at R why + + + align:start position:0% +answer is no it doesn't look at R why +doesn't look at R does everyone + + align:start position:0% +doesn't look at R does everyone + + + align:start position:0% +doesn't look at R does everyone +see yeah Alpha is now greater than the + + align:start position:0% +see yeah Alpha is now greater than the + + + align:start position:0% +see yeah Alpha is now greater than the +beta below it beta has gotten lower than + + align:start position:0% +beta below it beta has gotten lower than + + + align:start position:0% +beta below it beta has gotten lower than +Alpha this is the same thing I was + + align:start position:0% +Alpha this is the same thing I was + + + align:start position:0% +Alpha this is the same thing I was +talking about before when we figured out + + align:start position:0% +talking about before when we figured out + + + align:start position:0% +talking about before when we figured out +that the alpha here was two the + + align:start position:0% +that the alpha here was two the + + + align:start position:0% +that the alpha here was two the +maximizer says wait a minute if I if ma + + align:start position:0% +maximizer says wait a minute if I if ma + + + align:start position:0% +maximizer says wait a minute if I if ma +where G says if I go to m the best I'm + + align:start position:0% +where G says if I go to m the best I'm + + + align:start position:0% +where G says if I go to m the best I'm +getting out of this at one cuz if this + + align:start position:0% +getting out of this at one cuz if this + + + align:start position:0% +getting out of this at one cuz if this +is negative Infinity he'll minimizer + + align:start position:0% +is negative Infinity he'll minimizer + + + align:start position:0% +is negative Infinity he'll minimizer +will choose if this is positive Infinity + + align:start position:0% +will choose if this is positive Infinity + + + align:start position:0% +will choose if this is positive Infinity +he'll choose one best I'm going to get + + align:start position:0% +he'll choose one best I'm going to get + + + align:start position:0% +he'll choose one best I'm going to get +out of here is one if that's the case I + + align:start position:0% +out of here is one if that's the case I + + + align:start position:0% +out of here is one if that's the case I +might as well just gone to B and not + + align:start position:0% +might as well just gone to B and not + + + align:start position:0% +might as well just gone to B and not +even gone to C so I'm not going to go to + + align:start position:0% +even gone to C so I'm not going to go to + + + align:start position:0% +even gone to C so I'm not going to go to +m I'll go to n maybe maybe n's + + align:start position:0% +m I'll go to n maybe maybe n's + + + align:start position:0% +m I'll go to n maybe maybe n's +better does everyone see that great so + + align:start position:0% +better does everyone see that great so + + + align:start position:0% +better does everyone see that great so +let's say that the maximizer does go to + + align:start position:0% +let's say that the maximizer does go to + + + align:start position:0% +let's say that the maximizer does go to +end so what's going to happen with his + + align:start position:0% +end so what's going to happen with his + + + align:start position:0% +end so what's going to happen with his +Alpha it's to be seven that's right + + align:start position:0% +Alpha it's to be seven that's right + + + align:start position:0% +Alpha it's to be seven that's right +going to be seven seven is better than + + align:start position:0% +going to be seven seven is better than + + + align:start position:0% +going to be seven seven is better than +two and maximizer has control to get to + + align:start position:0% +two and maximizer has control to get to + + + align:start position:0% +two and maximizer has control to get to +that seven at least if it gets to + + align:start position:0% +that seven at least if it gets to + + + align:start position:0% +that seven at least if it gets to +G all right now the minimizer at C we'll + + align:start position:0% +G all right now the minimizer at C we'll + + + align:start position:0% +G all right now the minimizer at C we'll +do everyone this time the minimizer at C + + align:start position:0% +do everyone this time the minimizer at C + + + align:start position:0% +do everyone this time the minimizer at C +seeing that seven what does the + + align:start position:0% +seeing that seven what does the + + + align:start position:0% +seeing that seven what does the +minimizer + + align:start position:0% + + + + align:start position:0% + +do + + align:start position:0% + + + + align:start position:0% + +anyone so it sees the seven what does it + + align:start position:0% +anyone so it sees the seven what does it + + + align:start position:0% +anyone so it sees the seven what does it +do to its beta it takes the seven better + + align:start position:0% +do to its beta it takes the seven better + + + align:start position:0% +do to its beta it takes the seven better +than infinity anyway and yeah then it + + align:start position:0% +than infinity anyway and yeah then it + + + align:start position:0% +than infinity anyway and yeah then it +checks H and everyone again what happens + + align:start position:0% +checks H and everyone again what happens + + + align:start position:0% +checks H and everyone again what happens +at + + align:start position:0% +at + + + align:start position:0% +at +H takes the six it's lower than + + align:start position:0% + + + + align:start position:0% + +seven all right now we'll go back to + + align:start position:0% +seven all right now we'll go back to + + + align:start position:0% +seven all right now we'll go back to +having people do it on their own well + + align:start position:0% +having people do it on their own well + + + align:start position:0% +having people do it on their own well +all the way back to the top what does a + + align:start position:0% +all the way back to the top what does a + + + align:start position:0% +all the way back to the top what does a +do when it sees the Six coming out of + + align:start position:0% +do when it sees the Six coming out of + + + align:start position:0% +do when it sees the Six coming out of +C changes to six changes to six that's + + align:start position:0% +C changes to six changes to six that's + + + align:start position:0% +C changes to six changes to six that's +right Alpha equals six + + align:start position:0% +right Alpha equals six + + + align:start position:0% +right Alpha equals six +great home stretch people home stretch + + align:start position:0% +great home stretch people home stretch + + + align:start position:0% +great home stretch people home stretch +so the minimizer everyone has has a beta + + align:start position:0% +so the minimizer everyone has has a beta + + + align:start position:0% +so the minimizer everyone has has a beta +of infinity and if I wasn't a static + + align:start position:0% +of infinity and if I wasn't a static + + + align:start position:0% +of infinity and if I wasn't a static +node it would have an alpha of six but + + align:start position:0% +node it would have an alpha of six but + + + align:start position:0% +node it would have an alpha of six but +it is a static node so it just has a + + align:start position:0% +it is a static node so it just has a + + + align:start position:0% +it is a static node so it just has a +value of one so since it has a value of + + align:start position:0% +value of one so since it has a value of + + + align:start position:0% +value of one so since it has a value of +one everyone the beta + + align:start position:0% +one everyone the beta + + + align:start position:0% +one everyone the beta +becomes one and what next + + align:start position:0% +becomes one and what next + + + align:start position:0% +becomes one and what next +everyone prune that's + + align:start position:0% +everyone prune that's + + + align:start position:0% +everyone prune that's +right why prune well this time it's a + + align:start position:0% +right why prune well this time it's a + + + align:start position:0% +right why prune well this time it's a +himself who can prune a says well darn + + align:start position:0% +himself who can prune a says well darn + + + align:start position:0% +himself who can prune a says well darn +if I go to D I'm going to get one or + + align:start position:0% +if I go to D I'm going to get one or + + + align:start position:0% +if I go to D I'm going to get one or +something even worse than one might as + + align:start position:0% +something even worse than one might as + + + align:start position:0% +something even worse than one might as +well take my six while I have it prune + + align:start position:0% +well take my six while I have it prune + + + align:start position:0% +well take my six while I have it prune +all the rest all the way + + align:start position:0% + + + + align:start position:0% + +down everyone see that everyone cool + + align:start position:0% +down everyone see that everyone cool + + + align:start position:0% +down everyone see that everyone cool +with that it's not too bad if you take + + align:start position:0% +with that it's not too bad if you take + + + align:start position:0% +with that it's not too bad if you take +it one step at a time we did it our + + align:start position:0% +it one step at a time we did it our + + + align:start position:0% +it one step at a time we did it our +answer uh our question is which noes are + + align:start position:0% +answer uh our question is which noes are + + + align:start position:0% +answer uh our question is which noes are +evaluated in order our answer is + + align:start position:0% +evaluated in order our answer is + + + align:start position:0% +evaluated in order our answer is +everyone + + align:start position:0% +everyone + + + align:start position:0% +everyone +e + + align:start position:0% +e + + + align:start position:0% +e +k q + + align:start position:0% + + + + align:start position:0% + +uh n h + + align:start position:0% +uh n h + + + align:start position:0% +uh n h +i okay not so obvious I guess few people + + align:start position:0% +i okay not so obvious I guess few people + + + align:start position:0% +i okay not so obvious I guess few people +followed me but it is a e k q NH it's + + align:start position:0% +followed me but it is a e k q NH it's + + + align:start position:0% +followed me but it is a e k q NH it's +just step first order and we pruned some + + align:start position:0% +just step first order and we pruned some + + + align:start position:0% +just step first order and we pruned some +of them + + align:start position:0% +of them + + + align:start position:0% +of them +away great so that is Alpha Beta any + + align:start position:0% +away great so that is Alpha Beta any + + + align:start position:0% +away great so that is Alpha Beta any +questions about that before I give some + + align:start position:0% +questions about that before I give some + + + align:start position:0% +questions about that before I give some +questions about Progressive + + align:start position:0% +questions about Progressive + + + align:start position:0% +questions about Progressive +deepening all right we've got a bunch so + + align:start position:0% +deepening all right we've got a bunch so + + + align:start position:0% +deepening all right we've got a bunch so +first question you in order which evated + + align:start position:0% +first question you in order which evated + + + align:start position:0% +first question you in order which evated +are we excluding notes like uh FB C and + + align:start position:0% +are we excluding notes like uh FB C and + + + align:start position:0% +are we excluding notes like uh FB C and +D the question is when asked for the + + align:start position:0% +D the question is when asked for the + + + align:start position:0% +D the question is when asked for the +order of evaluation are we includ + + align:start position:0% +order of evaluation are we includ + + + align:start position:0% +order of evaluation are we includ +excluding FB C and D the answer is we're + + align:start position:0% +excluding FB C and D the answer is we're + + + align:start position:0% +excluding FB C and D the answer is we're +talking about here static evaluation the + + align:start position:0% +talking about here static evaluation the + + + align:start position:0% +talking about here static evaluation the +static evaluator is a very important and + + align:start position:0% +static evaluator is a very important and + + + align:start position:0% +static evaluator is a very important and +interesting function and I'll get back + + align:start position:0% +interesting function and I'll get back + + + align:start position:0% +interesting function and I'll get back +to something a few students have asked + + align:start position:0% +to something a few students have asked + + + align:start position:0% +to something a few students have asked +me about the static evaluator later and + + align:start position:0% +me about the static evaluator later and + + + align:start position:0% +me about the static evaluator later and +try to explain what it is it's basically + + align:start position:0% +try to explain what it is it's basically + + + align:start position:0% +try to explain what it is it's basically +the thing that pops out those numbers at + + align:start position:0% +the thing that pops out those numbers at + + + align:start position:0% +the thing that pops out those numbers at +the bottom of the leaves so when we ask + + align:start position:0% +the bottom of the leaves so when we ask + + + align:start position:0% +the bottom of the leaves so when we ask +what is the order of nodes that were + + align:start position:0% +what is the order of nodes that were + + + align:start position:0% +what is the order of nodes that were +statically evaluated we mean leaves + + align:start position:0% +statically evaluated we mean leaves + + + align:start position:0% +statically evaluated we mean leaves +only that's a good question any other + + align:start position:0% +only that's a good question any other + + + align:start position:0% +only that's a good question any other +questions let's see there was one up + + align:start position:0% +questions let's see there was one up + + + align:start position:0% +questions let's see there was one up +here before but it's gone might been the + + align:start position:0% +here before but it's gone might been the + + + align:start position:0% +here before but it's gone might been the +same one question so a similar question + + align:start position:0% +same one question so a similar question + + + align:start position:0% +same one question so a similar question +when you say static notes that just + + align:start position:0% +when you say static notes that just + + + align:start position:0% +when you say static notes that just +means the leaf notes means the leaf + + align:start position:0% +means the leaf notes means the leaf + + + align:start position:0% +means the leaf notes means the leaf +notes that's right the question is does + + align:start position:0% +notes that's right the question is does + + + align:start position:0% +notes that's right the question is does +static nodes being the leaf nodes the + + align:start position:0% +static nodes being the leaf nodes the + + + align:start position:0% +static nodes being the leaf nodes the +answer is yes static evaluation is when + + align:start position:0% +answer is yes static evaluation is when + + + align:start position:0% +answer is yes static evaluation is when +you compare the value of static to + + align:start position:0% +you compare the value of static to + + + align:start position:0% +you compare the value of static to +something static evaluation is when you + + align:start position:0% +something static evaluation is when you + + + align:start position:0% +something static evaluation is when you +get that number the static node let me + + align:start position:0% +get that number the static node let me + + + align:start position:0% +get that number the static node let me +explain um unless someone else has a + + align:start position:0% +explain um unless someone else has a + + + align:start position:0% +explain um unless someone else has a +another question about Alpha Beta let me + + align:start position:0% +another question about Alpha Beta let me + + + align:start position:0% +another question about Alpha Beta let me +explain static values because I was + + align:start position:0% +explain static values because I was + + + align:start position:0% +explain static values because I was +about to do that there is a question + + align:start position:0% +about to do that there is a question + + + align:start position:0% +about to do that there is a question +about Alpha Beta I'll come back to both + + align:start position:0% +about Alpha Beta I'll come back to both + + + align:start position:0% +about Alpha Beta I'll come back to both +of yours after I answer this you know + + align:start position:0% +of yours after I answer this you know + + + align:start position:0% +of yours after I answer this you know +you were mentioning a snow principle + + align:start position:0% +you were mentioning a snow principle + + + align:start position:0% +you were mentioning a snow principle +earlier and I'm a little bit confused + + align:start position:0% +earlier and I'm a little bit confused + + + align:start position:0% +earlier and I'm a little bit confused +when you say if we looking at one uh + + align:start position:0% +when you say if we looking at one uh + + + align:start position:0% +when you say if we looking at one uh +node sure and you're saying like either + + align:start position:0% +node sure and you're saying like either + + + align:start position:0% +node sure and you're saying like either +grab the value from the grandparent or + + align:start position:0% +grab the value from the grandparent or + + + align:start position:0% +grab the value from the grandparent or +grab it from the children so it always + + align:start position:0% +grab it from the children so it always + + + align:start position:0% +grab it from the children so it always +starts uh the question is what is the + + align:start position:0% +starts uh the question is what is the + + + align:start position:0% +starts uh the question is what is the +Snow White principle how does it work + + align:start position:0% +Snow White principle how does it work + + + align:start position:0% +Snow White principle how does it work +every node always starts off with taking + + align:start position:0% +every node always starts off with taking + + + align:start position:0% +every node always starts off with taking +the value of the same type alpha or beta + + align:start position:0% +the value of the same type alpha or beta + + + align:start position:0% +the value of the same type alpha or beta +from its grandparent it always starts + + align:start position:0% +from its grandparent it always starts + + + align:start position:0% +from its grandparent it always starts +that way now you say why the grandparent + + align:start position:0% +that way now you say why the grandparent + + + align:start position:0% +that way now you say why the grandparent +wouldn't take it from the parent it + + align:start position:0% +wouldn't take it from the parent it + + + align:start position:0% +wouldn't take it from the parent it +actually does but I'm not drawing out + + align:start position:0% +actually does but I'm not drawing out + + + align:start position:0% +actually does but I'm not drawing out +the alphas at all the minimizer levels + + align:start position:0% +the alphas at all the minimizer levels + + + align:start position:0% +the alphas at all the minimizer levels +because they don't do anything they just + + align:start position:0% +because they don't do anything they just + + + align:start position:0% +because they don't do anything they just +they're only even there to pass them + + align:start position:0% +they're only even there to pass them + + + align:start position:0% +they're only even there to pass them +down so all the values pass down down + + align:start position:0% +down so all the values pass down down + + + align:start position:0% +down so all the values pass down down +down down down to begin every value in + + align:start position:0% +down down down to begin every value in + + + align:start position:0% +down down down to begin every value in +every node in fact starts starts off + + align:start position:0% +every node in fact starts starts off + + + align:start position:0% +every node in fact starts starts off +with its with its grandparents with its + + align:start position:0% +with its with its grandparents with its + + + align:start position:0% +with its with its grandparents with its +parents values okay but then when the + + align:start position:0% +parents values okay but then when the + + + align:start position:0% +parents values okay but then when the +node sees a child that's completely done + + align:start position:0% +node sees a child that's completely done + + + align:start position:0% +node sees a child that's completely done +evaluating it's finished like let's say + + align:start position:0% +evaluating it's finished like let's say + + + align:start position:0% +evaluating it's finished like let's say +you can't it can't be in the process + + align:start position:0% +you can't it can't be in the process + + + align:start position:0% +you can't it can't be in the process +when when let's say C when C is complete + + align:start position:0% +when when let's say C when C is complete + + + align:start position:0% +when when let's say C when C is complete +it sees that g is completely done with + + align:start position:0% +it sees that g is completely done with + + + align:start position:0% +it sees that g is completely done with +all of its sub branches and is ready to + + align:start position:0% +all of its sub branches and is ready to + + + align:start position:0% +all of its sub branches and is ready to +return a value as if it was or if it's + + align:start position:0% +return a value as if it was or if it's + + + align:start position:0% +return a value as if it was or if it's +just a static evaluation then it's + + align:start position:0% +just a static evaluation then it's + + + align:start position:0% +just a static evaluation then it's +automatically completely done right + + align:start position:0% +automatically completely done right + + + align:start position:0% +automatically completely done right +because it has no + + align:start position:0% +because it has no + + + align:start position:0% +because it has no +children right a static value like K of + + align:start position:0% +children right a static value like K of + + + align:start position:0% +children right a static value like K of +three is automatically completely done + + align:start position:0% +three is automatically completely done + + + align:start position:0% +three is automatically completely done +it's got a three similarly when we came + + align:start position:0% +it's got a three similarly when we came + + + align:start position:0% +it's got a three similarly when we came +back to G after going to n and we knew + + align:start position:0% +back to G after going to n and we knew + + + align:start position:0% +back to G after going to n and we knew +that the value was seven that was + + align:start position:0% +that the value was seven that was + + + align:start position:0% +that the value was seven that was +completely done the value was definitely + + align:start position:0% +completely done the value was definitely + + + align:start position:0% +completely done the value was definitely +seven there was no other possibilities + + align:start position:0% +seven there was no other possibilities + + + align:start position:0% +seven there was no other possibilities +right that's after looking at the + + align:start position:0% +right that's after looking at the + + + align:start position:0% +right that's after looking at the +children yes so once you're done with + + align:start position:0% +children yes so once you're done with + + + align:start position:0% +children yes so once you're done with +all the children of G then g g comes up + + align:start position:0% +all the children of G then g g comes up + + + align:start position:0% +all the children of G then g g comes up +and says guess what guess what guys all + + align:start position:0% +and says guess what guess what guys all + + + align:start position:0% +and says guess what guess what guys all +right so technically before that you + + align:start position:0% +right so technically before that you + + + align:start position:0% +right so technically before that you +would have said that like G's Alpha is + + align:start position:0% +would have said that like G's Alpha is + + + align:start position:0% +would have said that like G's Alpha is +greater than or equal to one and then + + align:start position:0% +greater than or equal to one and then + + + align:start position:0% +greater than or equal to one and then +when we said when we looked at Q and + + align:start position:0% +when we said when we looked at Q and + + + align:start position:0% +when we said when we looked at Q and +then we looked at M we say it's equal + + align:start position:0% +then we looked at M we say it's equal + + + align:start position:0% +then we looked at M we say it's equal +exactly to seven we're done here and + + align:start position:0% +exactly to seven we're done here and + + + align:start position:0% +exactly to seven we're done here and +then at that point you know when it's + + align:start position:0% +then at that point you know when it's + + + align:start position:0% +then at that point you know when it's +fresh and ripe and has all of its + + align:start position:0% +fresh and ripe and has all of its + + + align:start position:0% +fresh and ripe and has all of its +highest value or its best value that's + + align:start position:0% +highest value or its best value that's + + + align:start position:0% +highest value or its best value that's +when the parent can you know eat its + + align:start position:0% +when the parent can you know eat its + + + align:start position:0% +when the parent can you know eat its +heart and gain that value itself so + + align:start position:0% +heart and gain that value itself so + + + align:start position:0% +heart and gain that value itself so +that's when C says for instance C says + + align:start position:0% +that's when C says for instance C says + + + align:start position:0% +that's when C says for instance C says +oh man I have an I have an Infinity + + align:start position:0% +oh man I have an I have an Infinity + + + align:start position:0% +oh man I have an I have an Infinity +that's that I really like that seven + + align:start position:0% +that's that I really like that seven + + + align:start position:0% +that's that I really like that seven +better and it take the seven but then it + + align:start position:0% +better and it take the seven but then it + + + align:start position:0% +better and it take the seven but then it +saw H and it said oh man that's a six + + align:start position:0% +saw H and it said oh man that's a six + + + align:start position:0% +saw H and it said oh man that's a six +that's even better than seven so it took + + align:start position:0% +that's even better than seven so it took + + + align:start position:0% +that's even better than seven so it took +the six Al + + align:start position:0% +the six Al + + + align:start position:0% +the six Al +seven so Alpha takes six because C is a + + align:start position:0% +seven so Alpha takes six because C is a + + + align:start position:0% +seven so Alpha takes six because C is a +minimizer C took the seven from G but + + align:start position:0% +minimizer C took the seven from G but + + + align:start position:0% +minimizer C took the seven from G but +then right after that c saw H and took + + align:start position:0% +then right after that c saw H and took + + + align:start position:0% +then right after that c saw H and took +the six cuz six is even lower uh than + + align:start position:0% +the six cuz six is even lower uh than + + + align:start position:0% +the six cuz six is even lower uh than +seven and then Alpha took the six + + align:start position:0% +seven and then Alpha took the six + + + align:start position:0% +seven and then Alpha took the six +because six was higher than two so it's + + align:start position:0% +because six was higher than two so it's + + + align:start position:0% +because six was higher than two so it's +not going to look like below the yeah + + align:start position:0% +not going to look like below the yeah + + + align:start position:0% +not going to look like below the yeah +the problem is that the maximizer + + align:start position:0% +the problem is that the maximizer + + + align:start position:0% +the problem is that the maximizer +doesn't have control there the + + align:start position:0% +doesn't have control there the + + + align:start position:0% +doesn't have control there the +minimizer's got control at C and the + + align:start position:0% +minimizer's got control at C and the + + + align:start position:0% +minimizer's got control at C and the +minimizer is going to make sure it's as + + align:start position:0% +minimizer is going to make sure it's as + + + align:start position:0% +minimizer is going to make sure it's as +low as possible the maximizer at a his + + align:start position:0% +low as possible the maximizer at a his + + + align:start position:0% +low as possible the maximizer at a his +only control is or her only control is + + align:start position:0% +only control is or her only control is + + + align:start position:0% +only control is or her only control is +the ability to send our A to B or C or D + + align:start position:0% +the ability to send our A to B or C or D + + + align:start position:0% +the ability to send our A to B or C or D +or at least and then at that point at C + + align:start position:0% +or at least and then at that point at C + + + align:start position:0% +or at least and then at that point at C +the minimizer gets to choose if we go to + + align:start position:0% +the minimizer gets to choose if we go to + + + align:start position:0% +the minimizer gets to choose if we go to +G or H and it's never going to choose G + + align:start position:0% +G or H and it's never going to choose G + + + align:start position:0% +G or H and it's never going to choose G +because G is higher than H all right + + align:start position:0% +because G is higher than H all right + + + align:start position:0% +because G is higher than H all right +awesome uh is there another question all + + align:start position:0% +awesome uh is there another question all + + + align:start position:0% +awesome uh is there another question all +right let's go back to static + + align:start position:0% +right let's go back to static + + + align:start position:0% +right let's go back to static +evaluations when I first took this class + + align:start position:0% +evaluations when I first took this class + + + align:start position:0% +evaluations when I first took this class +I had some weird thoughts about static + + align:start position:0% +I had some weird thoughts about static + + + align:start position:0% +I had some weird thoughts about static +evaluations I heard some students ask me + + align:start position:0% +evaluations I heard some students ask me + + + align:start position:0% +evaluations I heard some students ask me +this I almost got a question about it + + align:start position:0% +this I almost got a question about it + + + align:start position:0% +this I almost got a question about it +onto one of the tests but it was edited + + align:start position:0% +onto one of the tests but it was edited + + + align:start position:0% +onto one of the tests but it was edited +to some other weird question that was m + + align:start position:0% +to some other weird question that was m + + + align:start position:0% +to some other weird question that was m +to the B to the D minus one or something + + align:start position:0% +to the B to the D minus one or something + + + align:start position:0% +to the B to the D minus one or something +like that the last minute so I'm going + + align:start position:0% +like that the last minute so I'm going + + + align:start position:0% +like that the last minute so I'm going +to pose you guys the actual question + + align:start position:0% +to pose you guys the actual question + + + align:start position:0% +to pose you guys the actual question +that would have been on one of the older + + align:start position:0% +that would have been on one of the older + + + align:start position:0% +that would have been on one of the older +tests which is the following I had a + + align:start position:0% +tests which is the following I had a + + + align:start position:0% +tests which is the following I had a +student who came to be and said you know + + align:start position:0% +student who came to be and said you know + + + align:start position:0% +student who came to be and said you know +Mark when we do this alpab Beta pruning + + align:start position:0% +Mark when we do this alpab Beta pruning + + + align:start position:0% +Mark when we do this alpab Beta pruning +and all this other stuff we're trying to + + align:start position:0% +and all this other stuff we're trying to + + + align:start position:0% +and all this other stuff we're trying to +assume that we're really saving that + + align:start position:0% +assume that we're really saving that + + + align:start position:0% +assume that we're really saving that +much time by you know getting rid of a + + align:start position:0% +much time by you know getting rid of a + + + align:start position:0% +much time by you know getting rid of a +few static evaluations we in fact when + + align:start position:0% +few static evaluations we in fact when + + + align:start position:0% +few static evaluations we in fact when +we do Progressive deepening we're always + + align:start position:0% +we do Progressive deepening we're always + + + align:start position:0% +we do Progressive deepening we're always +just counting how many static + + align:start position:0% +just counting how many static + + + align:start position:0% +just counting how many static +evaluations do we have to do and he said + + align:start position:0% +evaluations do we have to do and he said + + + align:start position:0% +evaluations do we have to do and he said +I look at these static evaluations and + + align:start position:0% +I look at these static evaluations and + + + align:start position:0% +I look at these static evaluations and +there's just a three there it takes no + + align:start position:0% +there's just a three there it takes no + + + align:start position:0% +there's just a three there it takes no +time to do the static evaluation it's on + + align:start position:0% +time to do the static evaluation it's on + + + align:start position:0% +time to do the static evaluation it's on +the it's on the board it takes much + + align:start position:0% +the it's on the board it takes much + + + align:start position:0% +the it's on the board it takes much +longer to do the alpha beta it's faster + + align:start position:0% +longer to do the alpha beta it's faster + + + align:start position:0% +longer to do the alpha beta it's faster +by far to not do alpha beta so I had + + align:start position:0% +by far to not do alpha beta so I had + + + align:start position:0% +by far to not do alpha beta so I had +then tried to explain to that student I + + align:start position:0% +then tried to explain to that student I + + + align:start position:0% +then tried to explain to that student I +said okay we need to be clear about what + + align:start position:0% +said okay we need to be clear about what + + + align:start position:0% +said okay we need to be clear about what +static evaluations are you guys get it + + align:start position:0% +static evaluations are you guys get it + + + align:start position:0% +static evaluations are you guys get it +easy we put these numbers on the board a + + align:start position:0% +easy we put these numbers on the board a + + + align:start position:0% +easy we put these numbers on the board a +static evaluation let's say you're + + align:start position:0% +static evaluation let's say you're + + + align:start position:0% +static evaluation let's say you're +playing a game like + + align:start position:0% +playing a game like + + + align:start position:0% +playing a game like +chess the static evaluation takes a long + + align:start position:0% +chess the static evaluation takes a long + + + align:start position:0% +chess the static evaluation takes a long +time when I was in 6170 Java death lab + + align:start position:0% +time when I was in 6170 Java death lab + + + align:start position:0% +time when I was in 6170 Java death lab +used the class that used to exist we had + + align:start position:0% +used the class that used to exist we had + + + align:start position:0% +used the class that used to exist we had +a program called anti chest where I use + + align:start position:0% +a program called anti chest where I use + + + align:start position:0% +a program called anti chest where I use +my 6034 skills to write the AI + + align:start position:0% +my 6034 skills to write the AI + + + align:start position:0% +my 6034 skills to write the AI +and the static evaluator took a long + + align:start position:0% +and the static evaluator took a long + + + align:start position:0% +and the static evaluator took a long +time and we were timed so getting the + + align:start position:0% +time and we were timed so getting the + + + align:start position:0% +time and we were timed so getting the +static evaluator faster that was the + + align:start position:0% +static evaluator faster that was the + + + align:start position:0% +static evaluator faster that was the +most important thing why does it take a + + align:start position:0% +most important thing why does it take a + + + align:start position:0% +most important thing why does it take a +long time well the static evaluator is + + align:start position:0% +long time well the static evaluator is + + + align:start position:0% +long time well the static evaluator is +an evaluation of the board position the + + align:start position:0% +an evaluation of the board position the + + + align:start position:0% +an evaluation of the board position the +state of the game at a snapshot of time + + align:start position:0% +state of the game at a snapshot of time + + + align:start position:0% +state of the game at a snapshot of time +and that's not as easy as just saying oh + + align:start position:0% +and that's not as easy as just saying oh + + + align:start position:0% +and that's not as easy as just saying oh +here's the answer because in chess first + + align:start position:0% +here's the answer because in chess first + + + align:start position:0% +here's the answer because in chess first +of all not only did I have to look at + + align:start position:0% +of all not only did I have to look at + + + align:start position:0% +of all not only did I have to look at +how many pieces I had what areas that + + align:start position:0% +how many pieces I had what areas that + + + align:start position:0% +how many pieces I had what areas that +you know that I controlled also what was + + align:start position:0% +you know that I controlled also what was + + + align:start position:0% +you know that I controlled also what was +anti- chest but that's notwithstanding + + align:start position:0% +anti- chest but that's notwithstanding + + + align:start position:0% +anti- chest but that's notwithstanding +let's pretend it's regular chess I also + + align:start position:0% +let's pretend it's regular chess I also + + + align:start position:0% +let's pretend it's regular chess I also +had to look if it was in regular chess + + align:start position:0% +had to look if it was in regular chess + + + align:start position:0% +had to look if it was in regular chess +and I still had to do this in anti chest + + align:start position:0% +and I still had to do this in anti chest + + + align:start position:0% +and I still had to do this in anti chest +if my king was in check and what that + + align:start position:0% +if my king was in check and what that + + + align:start position:0% +if my king was in check and what that +meant is I had to look at all of my + + align:start position:0% +meant is I had to look at all of my + + + align:start position:0% +meant is I had to look at all of my +opponent's moves possible moves to see + + align:start position:0% +opponent's moves possible moves to see + + + align:start position:0% +opponent's moves possible moves to see +if any of them could take my king + + align:start position:0% +if any of them could take my king + + + align:start position:0% +if any of them could take my king +because for you know in regular chest + + align:start position:0% +because for you know in regular chest + + + align:start position:0% +because for you know in regular chest +it's illegal to put your king into check + + align:start position:0% +it's illegal to put your king into check + + + align:start position:0% +it's illegal to put your king into check +so you better not even allow that move + + align:start position:0% +so you better not even allow that move + + + align:start position:0% +so you better not even allow that move +and regardless getting into Checkmate is + + align:start position:0% +and regardless getting into Checkmate is + + + align:start position:0% +and regardless getting into Checkmate is +negative Infinity for you so it takes a + + align:start position:0% +negative Infinity for you so it takes a + + + align:start position:0% +negative Infinity for you so it takes a +really long time to do static + + align:start position:0% +really long time to do static + + + align:start position:0% +really long time to do static +evaluations at least good ones usually + + align:start position:0% +evaluations at least good ones usually + + + align:start position:0% +evaluations at least good ones usually +you want to avoid them because they're + + align:start position:0% +you want to avoid them because they're + + + align:start position:0% +you want to avoid them because they're +not just some number on the page they + + align:start position:0% +not just some number on the page they + + + align:start position:0% +not just some number on the page they +are some function you wrote that does a + + align:start position:0% +are some function you wrote that does a + + + align:start position:0% +are some function you wrote that does a +very careful analysis of the state of + + align:start position:0% +very careful analysis of the state of + + + align:start position:0% +very careful analysis of the state of +the game and says I'm going to heris + + align:start position:0% +the game and says I'm going to heris + + + align:start position:0% +the game and says I'm going to heris +guess that my value is pi and then or + + align:start position:0% +guess that my value is pi and then or + + + align:start position:0% +guess that my value is pi and then or +some other number and then rates that + + align:start position:0% +some other number and then rates that + + + align:start position:0% +some other number and then rates that +compared to other states does that make + + align:start position:0% +compared to other states does that make + + + align:start position:0% +compared to other states does that make +sense to everyone so the answer to the + + align:start position:0% +sense to everyone so the answer to the + + + align:start position:0% +sense to everyone so the answer to the +qu the hypothetical question that might + + align:start position:0% +qu the hypothetical question that might + + + align:start position:0% +qu the hypothetical question that might +have been on the old test what to when + + align:start position:0% +have been on the old test what to when + + + align:start position:0% +have been on the old test what to when +the person said I've got this great idea + + align:start position:0% +the person said I've got this great idea + + + align:start position:0% +the person said I've got this great idea +where we do tons of static evaluations + + align:start position:0% +where we do tons of static evaluations + + + align:start position:0% +where we do tons of static evaluations +you don't have to do this long Alpha + + align:start position:0% +you don't have to do this long Alpha + + + align:start position:0% +you don't have to do this long Alpha +Beta is don't do that the static + + align:start position:0% +Beta is don't do that the static + + + align:start position:0% +Beta is don't do that the static +evaluations actually take a long + + align:start position:0% +evaluations actually take a long + + + align:start position:0% +evaluations actually take a long +time does that clear it up for people + + align:start position:0% +time does that clear it up for people + + + align:start position:0% +time does that clear it up for people +who asked me before about static what is + + align:start position:0% +who asked me before about static what is + + + align:start position:0% +who asked me before about static what is +a static + + align:start position:0% +a static + + + align:start position:0% +a static +evaluation um why are the leaf nodes + + align:start position:0% +evaluation um why are the leaf nodes + + + align:start position:0% +evaluation um why are the leaf nodes +called + + align:start position:0% +called + + + align:start position:0% +called +Static + + align:start position:0% +Static + + + align:start position:0% +Static +basically and you might ask why are some + + align:start position:0% +basically and you might ask why are some + + + align:start position:0% +basically and you might ask why are some +of these static just + + align:start position:0% +of these static just + + + align:start position:0% +of these static just +arbitrarily the answer is when you're + + align:start position:0% +arbitrarily the answer is when you're + + + align:start position:0% +arbitrarily the answer is when you're +running out of time to expand deeper and + + align:start position:0% +running out of time to expand deeper and + + + align:start position:0% +running out of time to expand deeper and +you just need to stop that stage of the + + align:start position:0% +you just need to stop that stage of the + + + align:start position:0% +you just need to stop that stage of the +game maybe it's just getting too hairy + + align:start position:0% +game maybe it's just getting too hairy + + + align:start position:0% +game maybe it's just getting too hairy +maybe it's spreading out too much you + + align:start position:0% +maybe it's spreading out too much you + + + align:start position:0% +maybe it's spreading out too much you +have some heuristic that says this is + + align:start position:0% +have some heuristic that says this is + + + align:start position:0% +have some heuristic that says this is +where I stop for now it's a heuristic + + align:start position:0% +where I stop for now it's a heuristic + + + align:start position:0% +where I stop for now it's a heuristic +guess of the value it's kind of like + + align:start position:0% +guess of the value it's kind of like + + + align:start position:0% +guess of the value it's kind of like +those fistic values in the search tree + + align:start position:0% +those fistic values in the search tree + + + align:start position:0% +those fistic values in the search tree +that's a guess of how much work you have + + align:start position:0% +that's a guess of how much work you have + + + align:start position:0% +that's a guess of how much work you have +left to get to the goal here you say + + align:start position:0% +left to get to the goal here you say + + + align:start position:0% +left to get to the goal here you say +well I wish I could go deeper but I just + + align:start position:0% +well I wish I could go deeper but I just + + + align:start position:0% +well I wish I could go deeper but I just +don't have the time so here's what I + + align:start position:0% +don't have the time so here's what I + + + align:start position:0% +don't have the time so here's what I +think how I think I'm doing at this + + align:start position:0% +think how I think I'm doing at this + + + align:start position:0% +think how I think I'm doing at this +level it's not always right and that's + + align:start position:0% +level it's not always right and that's + + + align:start position:0% +level it's not always right and that's +going to lead us into the answer to one + + align:start position:0% +going to lead us into the answer to one + + + align:start position:0% +going to lead us into the answer to one +of the questions about Progressive + + align:start position:0% +of the questions about Progressive + + + align:start position:0% +of the questions about Progressive +deepening so I'll put up the progressive + + align:start position:0% +deepening so I'll put up the progressive + + + align:start position:0% +deepening so I'll put up the progressive +deepening question really quickly so the + + align:start position:0% +deepening question really quickly so the + + + align:start position:0% +deepening question really quickly so the +question is this suppose that let me see + + align:start position:0% +question is this suppose that let me see + + + align:start position:0% +question is this suppose that let me see +this is a maximizer yes suppose that + + align:start position:0% +this is a maximizer yes suppose that + + + align:start position:0% +this is a maximizer yes suppose that +um we do Progressive deepening on the + + align:start position:0% +um we do Progressive deepening on the + + + align:start position:0% +um we do Progressive deepening on the +the tree that is only two levels deep + + align:start position:0% +the tree that is only two levels deep + + + align:start position:0% +the tree that is only two levels deep +what is Progressive deepening in a + + align:start position:0% +what is Progressive deepening in a + + + align:start position:0% +what is Progressive deepening in a +nutshell if you don't remember from the + + align:start position:0% +nutshell if you don't remember from the + + + align:start position:0% +nutshell if you don't remember from the +lecture the idea is this it it doesn't + + align:start position:0% +lecture the idea is this it it doesn't + + + align:start position:0% +lecture the idea is this it it doesn't +take in this tree it it doesn't work but + + align:start position:0% +take in this tree it it doesn't work but + + + align:start position:0% +take in this tree it it doesn't work but +in trees that actually Branch like two + + align:start position:0% +in trees that actually Branch like two + + + align:start position:0% +in trees that actually Branch like two +to the end it doesn't take that much + + align:start position:0% +to the end it doesn't take that much + + + align:start position:0% +to the end it doesn't take that much +time to do like some of the top levels + + align:start position:0% +time to do like some of the top levels + + + align:start position:0% +time to do like some of the top levels +first and then move on to the bottom + + align:start position:0% +first and then move on to the bottom + + + align:start position:0% +first and then move on to the bottom +levels just do them one at a time so + + align:start position:0% +levels just do them one at a time so + + + align:start position:0% +levels just do them one at a time so +let's say we only did it up through J we + + align:start position:0% +let's say we only did it up through J we + + + align:start position:0% +let's say we only did it up through J we +only did the top two levels of the tree + + align:start position:0% +only did the top two levels of the tree + + + align:start position:0% +only did the top two levels of the tree +we'd like to reorder the tree so that + + align:start position:0% +we'd like to reorder the tree so that + + + align:start position:0% +we'd like to reorder the tree so that +Alpha Beta can prune as much as it + + align:start position:0% +Alpha Beta can prune as much as it + + + align:start position:0% +Alpha Beta can prune as much as it +possibly can at least we hope all right + + align:start position:0% +possibly can at least we hope all right + + + align:start position:0% +possibly can at least we hope all right +so let's pretend that we had a psychic + + align:start position:0% +so let's pretend that we had a psychic + + + align:start position:0% +so let's pretend that we had a psychic +awesome um genius friend who told us + + align:start position:0% +awesome um genius friend who told us + + + align:start position:0% +awesome um genius friend who told us +that the static values when we went up + + align:start position:0% +that the static values when we went up + + + align:start position:0% +that the static values when we went up +to two levels remember when we go to two + + align:start position:0% +to two levels remember when we go to two + + + align:start position:0% +to two levels remember when we go to two +levels FG and J have to get a static + + align:start position:0% +levels FG and J have to get a static + + + align:start position:0% +levels FG and J have to get a static +value right because we're not going down + + align:start position:0% +value right because we're not going down + + + align:start position:0% +value right because we're not going down +we do a static evaluation they get the + + align:start position:0% +we do a static evaluation they get the + + + align:start position:0% +we do a static evaluation they get the +exact correct numbers 3 7 and 20 genius + + align:start position:0% +exact correct numbers 3 7 and 20 genius + + + align:start position:0% +exact correct numbers 3 7 and 20 genius +brilliant all right so if that happens + + align:start position:0% +brilliant all right so if that happens + + + align:start position:0% +brilliant all right so if that happens +how is the be what is the best way that + + align:start position:0% +how is the be what is the best way that + + + align:start position:0% +how is the be what is the best way that +we could reorder that tree oh yeah uh + + align:start position:0% +we could reorder that tree oh yeah uh + + + align:start position:0% +we could reorder that tree oh yeah uh +yeah yeah so it's ABC D with values of 2 + + align:start position:0% +yeah yeah so it's ABC D with values of 2 + + + align:start position:0% +yeah yeah so it's ABC D with values of 2 +3 7 6 1 + + align:start position:0% +3 7 6 1 + + + align:start position:0% +3 7 6 1 +20 I'll draw + + align:start position:0% +20 I'll draw + + + align:start position:0% +20 I'll draw +that this is the non- reordered tree + + align:start position:0% + + + + align:start position:0% + +let's see so it's 2 + + align:start position:0% +let's see so it's 2 + + + align:start position:0% +let's see so it's 2 + + align:start position:0% + + + align:start position:0% + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +1 20 so what's the best way to reorder + + align:start position:0% +1 20 so what's the best way to reorder + + + align:start position:0% +1 20 so what's the best way to reorder +well first of all does anyone remember + + align:start position:0% +well first of all does anyone remember + + + align:start position:0% +well first of all does anyone remember +what Patrick said when he talked about + + align:start position:0% +what Patrick said when he talked about + + + align:start position:0% +what Patrick said when he talked about +Progressive + + align:start position:0% +Progressive + + + align:start position:0% +Progressive +deepening usually no one does so don't + + align:start position:0% +deepening usually no one does so don't + + + align:start position:0% +deepening usually no one does so don't +worry about it the best way to uh + + align:start position:0% +worry about it the best way to uh + + + align:start position:0% +worry about it the best way to uh +because at that time you guys didn't + + align:start position:0% +because at that time you guys didn't + + + align:start position:0% +because at that time you guys didn't +think oh I have to do this for the quiz + + align:start position:0% +think oh I have to do this for the quiz + + + align:start position:0% +think oh I have to do this for the quiz +you were just thinking oh man we've + + align:start position:0% +you were just thinking oh man we've + + + align:start position:0% +you were just thinking oh man we've +already heard alphab beta and all this + + align:start position:0% +already heard alphab beta and all this + + + align:start position:0% +already heard alphab beta and all this +other stuff and this is just a small + + align:start position:0% +other stuff and this is just a small + + + align:start position:0% +other stuff and this is just a small +fact but it's a very important fact and + + align:start position:0% +fact but it's a very important fact and + + + align:start position:0% +fact but it's a very important fact and +now you know you have to do it for the + + align:start position:0% +now you know you have to do it for the + + + align:start position:0% +now you know you have to do it for the +quiz so you're probably going to + + align:start position:0% +quiz so you're probably going to + + + align:start position:0% +quiz so you're probably going to +remember it the way you do it is you try + + align:start position:0% +remember it the way you do it is you try + + + align:start position:0% +remember it the way you do it is you try +to guess and you say which one of these + + align:start position:0% +to guess and you say which one of these + + + align:start position:0% +to guess and you say which one of these +is going to be a winner whichever one I + + align:start position:0% +is going to be a winner whichever one I + + + align:start position:0% +is going to be a winner whichever one I +think is going to be a winner at that + + align:start position:0% +think is going to be a winner at that + + + align:start position:0% +think is going to be a winner at that +level I put first why is that the case + + align:start position:0% +level I put first why is that the case + + + align:start position:0% +level I put first why is that the case +well something interesting you may have + + align:start position:0% +well something interesting you may have + + + align:start position:0% +well something interesting you may have +noticed here whenever you have a + + align:start position:0% +noticed here whenever you have a + + + align:start position:0% +noticed here whenever you have a +winner like the middle node or whenever + + align:start position:0% +winner like the middle node or whenever + + + align:start position:0% +winner like the middle node or whenever +you have whatever is the current best + + align:start position:0% +you have whatever is the current best + + + align:start position:0% +you have whatever is the current best +for your Alpha you sort of have to + + align:start position:0% +for your Alpha you sort of have to + + + align:start position:0% +for your Alpha you sort of have to +explore out a lot of that + + align:start position:0% +explore out a lot of that + + + align:start position:0% +explore out a lot of that +area like for instance the left node was + + align:start position:0% +area like for instance the left node was + + + align:start position:0% +area like for instance the left node was +our current best at two the middle + + align:start position:0% +our current best at two the middle + + + align:start position:0% +our current best at two the middle +Branch was our current best at that time + + align:start position:0% +Branch was our current best at that time + + + align:start position:0% +Branch was our current best at that time +was six it was the total best we had to + + align:start position:0% +was six it was the total best we had to + + + align:start position:0% +was six it was the total best we had to +explore a good number of nodes but on + + align:start position:0% +explore a good number of nodes but on + + + align:start position:0% +explore a good number of nodes but on +the right we just saw oh there's one + + align:start position:0% +the right we just saw oh there's one + + + align:start position:0% +the right we just saw oh there's one +we're done we cut everything off in + + align:start position:0% +we're done we cut everything off in + + + align:start position:0% +we're done we cut everything off in +other words the branch that turns out to + + align:start position:0% +other words the branch that turns out to + + + align:start position:0% +other words the branch that turns out to +be the one that you take you have to do + + align:start position:0% +be the one that you take you have to do + + + align:start position:0% +be the one that you take you have to do +pretty good amount of exploration to + + align:start position:0% +pretty good amount of exploration to + + + align:start position:0% +pretty good amount of exploration to +prove that it's the right one whereas if + + align:start position:0% +prove that it's the right one whereas if + + + align:start position:0% +prove that it's the right one whereas if +it's the wrong one you can sometimes + + align:start position:0% +it's the wrong one you can sometimes + + + align:start position:0% +it's the wrong one you can sometimes +with just one note say this is wrong + + align:start position:0% +with just one note say this is wrong + + + align:start position:0% +with just one note say this is wrong +done so therefore if the one that turns + + align:start position:0% +done so therefore if the one that turns + + + align:start position:0% +done so therefore if the one that turns +out to be the eventual winner is first + + align:start position:0% +out to be the eventual winner is first + + + align:start position:0% +out to be the eventual winner is first +of all then it's really easy to reject + + align:start position:0% +of all then it's really easy to reject + + + align:start position:0% +of all then it's really easy to reject +all the other branches do people see + + align:start position:0% +all the other branches do people see + + + align:start position:0% +all the other branches do people see +that sort of conceptually a little bit + + align:start position:0% +that sort of conceptually a little bit + + + align:start position:0% +that sort of conceptually a little bit +that if you get the best node right away + + align:start position:0% +that if you get the best node right away + + + align:start position:0% +that if you get the best node right away +you can just reject all the wrong ones + + align:start position:0% +you can just reject all the wrong ones + + + align:start position:0% +you can just reject all the wrong ones +pretty quickly that's our goal so how + + align:start position:0% +pretty quickly that's our goal so how + + + align:start position:0% +pretty quickly that's our goal so how +can we quote get the right one the best + + align:start position:0% +can we quote get the right one the best + + + align:start position:0% +can we quote get the right one the best +one right away well here's how we do + + align:start position:0% +one right away well here's how we do + + + align:start position:0% +one right away well here's how we do +it let's say we're at B which one is the + + align:start position:0% +it let's say we're at B which one is the + + + align:start position:0% +it let's say we're at B which one is the +minimizer likely to pick assuming that + + align:start position:0% +minimizer likely to pick assuming that + + + align:start position:0% +minimizer likely to pick assuming that +our heris is good and that um these + + align:start position:0% +our heris is good and that um these + + + align:start position:0% +our heris is good and that um these +guesses are pretty much close to the + + align:start position:0% +guesses are pretty much close to the + + + align:start position:0% +guesses are pretty much close to the +truth and turns out they're perfect so + + align:start position:0% +truth and turns out they're perfect so + + + align:start position:0% +truth and turns out they're perfect so +this is going to work so which one will + + align:start position:0% +this is going to work so which one will + + + align:start position:0% +this is going to work so which one will +the minimizer pick if it has to choose + + align:start position:0% +the minimizer pick if it has to choose + + + align:start position:0% +the minimizer pick if it has to choose +between E and F do we think e perfect + + align:start position:0% +between E and F do we think e perfect + + + align:start position:0% +between E and F do we think e perfect +which one will pick between G and + + align:start position:0% +which one will pick between G and + + + align:start position:0% +which one will pick between G and +H H which one will pick between I and + + align:start position:0% +H H which one will pick between I and + + + align:start position:0% +H H which one will pick between I and +J okay so what we're saying is we think + + align:start position:0% +J okay so what we're saying is we think + + + align:start position:0% +J okay so what we're saying is we think +it's going to pick e we think it's going + + align:start position:0% +it's going to pick e we think it's going + + + align:start position:0% +it's going to pick e we think it's going +to to pick H we think it's going to pick + + align:start position:0% +to to pick H we think it's going to pick + + + align:start position:0% +to to pick H we think it's going to pick +I so first of all we should put E before + + align:start position:0% +I so first of all we should put E before + + + align:start position:0% +I so first of all we should put E before +f h before G and I before J because we + + align:start position:0% +f h before G and I before J because we + + + align:start position:0% +f h before G and I before J because we +think it's going to pick those first + + align:start position:0% +think it's going to pick those first + + + align:start position:0% +think it's going to pick those first +those are POS our best ones to + + align:start position:0% +those are POS our best ones to + + + align:start position:0% +those are POS our best ones to +invalidate a poor Branch so now between + + align:start position:0% +invalidate a poor Branch so now between + + + align:start position:0% +invalidate a poor Branch so now between +2 six and one which is what we think + + align:start position:0% +2 six and one which is what we think + + + align:start position:0% +2 six and one which is what we think +we're going to get which one do we think + + align:start position:0% +we're going to get which one do we think + + + align:start position:0% +we're going to get which one do we think +the maximizer is going to take six then + + align:start position:0% +the maximizer is going to take six then + + + align:start position:0% +the maximizer is going to take six then +if it couldn't take six what would be + + align:start position:0% +if it couldn't take six what would be + + + align:start position:0% +if it couldn't take six what would be +its next best choice two then one that's + + align:start position:0% +its next best choice two then one that's + + + align:start position:0% +its next best choice two then one that's +just our order simple as that + + align:start position:0% +just our order simple as that + + + align:start position:0% +just our order simple as that +couldn't be anything easier that + + align:start position:0% +couldn't be anything easier that + + + align:start position:0% +couldn't be anything easier that +involves really complex trees a huge + + align:start position:0% +involves really complex trees a huge + + + align:start position:0% +involves really complex trees a huge +number of numbers and reordering those + + align:start position:0% +number of numbers and reordering those + + + align:start position:0% +number of numbers and reordering those +trees + + align:start position:0% +trees + + + align:start position:0% +trees +so C you guys Told Me CB oh sorry + + align:start position:0% +so C you guys Told Me CB oh sorry + + + align:start position:0% +so C you guys Told Me CB oh sorry +D you told me CB D I think yeah those + + align:start position:0% +D you told me CB D I think yeah those + + + align:start position:0% +D you told me CB D I think yeah those +the ones the maximizer likes and then + + align:start position:0% +the ones the maximizer likes and then + + + align:start position:0% +the ones the maximizer likes and then +the ones the minimizer likes you told me + + align:start position:0% +the ones the minimizer likes you told me + + + align:start position:0% +the ones the minimizer likes you told me +was + + align:start position:0% +was + + + align:start position:0% +was +H and before G because H is smaller than + + align:start position:0% +H and before G because H is smaller than + + + align:start position:0% +H and before G because H is smaller than +G you guys told me E before + + align:start position:0% +G you guys told me E before + + + align:start position:0% +G you guys told me E before +F and and you guys told me I before + + align:start position:0% + + + + align:start position:0% + +J and you guys would be correct in all + + align:start position:0% +J and you guys would be correct in all + + + align:start position:0% +J and you guys would be correct in all +regards we have 67 2 3 + + align:start position:0% +regards we have 67 2 3 + + + align:start position:0% +regards we have 67 2 3 +120 all the minimizers choose from + + align:start position:0% +120 all the minimizers choose from + + + align:start position:0% +120 all the minimizers choose from +smallest to highest the maximizer + + align:start position:0% +smallest to highest the maximizer + + + align:start position:0% +smallest to highest the maximizer +chooses from highest to lowest of the + + align:start position:0% +chooses from highest to lowest of the + + + align:start position:0% +chooses from highest to lowest of the +one that minimizers will take and if we + + align:start position:0% +one that minimizers will take and if we + + + align:start position:0% +one that minimizers will take and if we +did that you can see we would probably + + align:start position:0% +did that you can see we would probably + + + align:start position:0% +did that you can see we would probably +save some time let's see how much time + + align:start position:0% +save some time let's see how much time + + + align:start position:0% +save some time let's see how much time +let's say we looked at H first right + + align:start position:0% +let's say we looked at H first right + + + align:start position:0% +let's say we looked at H first right +what we looked at if we looked at H + + align:start position:0% +what we looked at if we looked at H + + + align:start position:0% +what we looked at if we looked at H +first we would still have actually had + + align:start position:0% +first we would still have actually had + + + align:start position:0% +first we would still have actually had +to look at Q and N however we would not + + align:start position:0% +to look at Q and N however we would not + + + align:start position:0% +to look at Q and N however we would not +have had to look at K do people see why + + align:start position:0% +have had to look at K do people see why + + + align:start position:0% +have had to look at K do people see why +if we already knew this brench was six + + align:start position:0% +if we already knew this brench was six + + + align:start position:0% +if we already knew this brench was six +as soon as we saw two for the beta here + + align:start position:0% +as soon as we saw two for the beta here + + + align:start position:0% +as soon as we saw two for the beta here +two is less than six we could have + + align:start position:0% +two is less than six we could have + + + align:start position:0% +two is less than six we could have +pruned we still would have had to look + + align:start position:0% +pruned we still would have had to look + + + align:start position:0% +pruned we still would have had to look +at I over here because you have to look + + align:start position:0% +at I over here because you have to look + + + align:start position:0% +at I over here because you have to look +at at least one thing in the new sub + + align:start position:0% +at at least one thing in the new sub + + + align:start position:0% +at at least one thing in the new sub +rench and it actually would have saved + + align:start position:0% +rench and it actually would have saved + + + align:start position:0% +rench and it actually would have saved +us one node oops so it winds up that in + + align:start position:0% +us one node oops so it winds up that in + + + align:start position:0% +us one node oops so it winds up that in +total how many nodes would we have + + align:start position:0% +total how many nodes would we have + + + align:start position:0% +total how many nodes would we have +evaluated if we did um if we did that + + align:start position:0% +evaluated if we did um if we did that + + + align:start position:0% +evaluated if we did um if we did that +little scheme of reordering well we + + align:start position:0% +little scheme of reordering well we + + + align:start position:0% +little scheme of reordering well we +normally had to do six right EK qh uh + + align:start position:0% +normally had to do six right EK qh uh + + + align:start position:0% +normally had to do six right EK qh uh +qnh hii how many do we evaluate if we do + + align:start position:0% +qnh hii how many do we evaluate if we do + + + align:start position:0% +qnh hii how many do we evaluate if we do +this um this Progressive deepening + + align:start position:0% +this um this Progressive deepening + + + align:start position:0% +this um this Progressive deepening +scheme how many times we run the static + + align:start position:0% +scheme how many times we run the static + + + align:start position:0% +scheme how many times we run the static +evaluator which of course you know the + + align:start position:0% +evaluator which of course you know the + + + align:start position:0% +evaluator which of course you know the +static evaluator takes a long time + + align:start position:0% +static evaluator takes a long time + + + align:start position:0% +static evaluator takes a long time +anyone have a + + align:start position:0% +anyone have a + + + align:start position:0% +anyone have a +guess I told you the only one we don't + + align:start position:0% +guess I told you the only one we don't + + + align:start position:0% +guess I told you the only one we don't +evaluate is + + align:start position:0% + + + + align:start position:0% + +K you raise your hand I won't I won't + + align:start position:0% +K you raise your hand I won't I won't + + + align:start position:0% +K you raise your hand I won't I won't +make anyone do uh give this + + align:start position:0% +make anyone do uh give this + + + align:start position:0% +make anyone do uh give this +one so I yeah I said the only one we + + align:start position:0% +one so I yeah I said the only one we + + + align:start position:0% +one so I yeah I said the only one we +save on is K so we still do EQ H and H + + align:start position:0% +save on is K so we still do EQ H and H + + + align:start position:0% +save on is K so we still do EQ H and H +and I over + + align:start position:0% +and I over + + + align:start position:0% +and I over +here there's two possible answers that I + + align:start position:0% +here there's two possible answers that I + + + align:start position:0% +here there's two possible answers that I +will accept so you have a higher chance + + align:start position:0% +will accept so you have a higher chance + + + align:start position:0% +will accept so you have a higher chance +of guessing it + + align:start position:0% + + + + align:start position:0% + +anyone does everyone agree that we did + + align:start position:0% +anyone does everyone agree that we did + + + align:start position:0% +anyone does everyone agree that we did +six before if we didn't do any + + align:start position:0% +six before if we didn't do any + + + align:start position:0% +six before if we didn't do any +Progressive deepening we just you know + + align:start position:0% +Progressive deepening we just you know + + + align:start position:0% +Progressive deepening we just you know +did e k q NH hi + + align:start position:0% +did e k q NH hi + + + align:start position:0% +did e k q NH hi +I and now we're not doing + + align:start position:0% +I and now we're not doing + + + align:start position:0% +I and now we're not doing +K okay people are saying five all right + + align:start position:0% +K okay people are saying five all right + + + align:start position:0% +K okay people are saying five all right +good that's not the right answer but at + + align:start position:0% +good that's not the right answer but at + + + align:start position:0% +good that's not the right answer but at +least shows that you can do taking away + + align:start position:0% +least shows that you can do taking away + + + align:start position:0% +least shows that you can do taking away +the one we did at least five over here + + align:start position:0% +the one we did at least five over here + + + align:start position:0% +the one we did at least five over here +there's two possible answers though + + align:start position:0% +there's two possible answers though + + + align:start position:0% +there's two possible answers though +because look over there in order to do + + align:start position:0% +because look over there in order to do + + + align:start position:0% +because look over there in order to do +the progressive deepening we had to do + + align:start position:0% +the progressive deepening we had to do + + + align:start position:0% +the progressive deepening we had to do +those static + + align:start position:0% +those static + + + align:start position:0% +those static +evaluations right + + align:start position:0% +evaluations right + + + align:start position:0% +evaluations right +so we either did we either did all those + + align:start position:0% +so we either did we either did all those + + + align:start position:0% +so we either did we either did all those +static evaluations and these five stat a + + align:start position:0% +static evaluations and these five stat a + + + align:start position:0% +static evaluations and these five stat a +k q n hi I these five static evaluations + + align:start position:0% +k q n hi I these five static evaluations + + + align:start position:0% +k q n hi I these five static evaluations +so we didn't do the + + align:start position:0% +so we didn't do the + + + align:start position:0% +so we didn't do the +K or or we might have saved ourselves + + align:start position:0% +K or or we might have saved ourselves + + + align:start position:0% +K or or we might have saved ourselves +because maybe we were smart and decided + + align:start position:0% +because maybe we were smart and decided + + + align:start position:0% +because maybe we were smart and decided +to cach the static values when we were + + align:start position:0% +to cach the static values when we were + + + align:start position:0% +to cach the static values when we were +going down the tree it's an + + align:start position:0% +going down the tree it's an + + + align:start position:0% +going down the tree it's an +implementation detail that on this test + + align:start position:0% +implementation detail that on this test + + + align:start position:0% +implementation detail that on this test +when we asked that question we didn't + + align:start position:0% +when we asked that question we didn't + + + align:start position:0% +when we asked that question we didn't +say but I mean by C is when we did it + + align:start position:0% +say but I mean by C is when we did it + + + align:start position:0% +say but I mean by C is when we did it +here and saw that um e was a two and + + align:start position:0% +here and saw that um e was a two and + + + align:start position:0% +here and saw that um e was a two and +then here oh we have to do the static + + align:start position:0% +then here oh we have to do the static + + + align:start position:0% +then here oh we have to do the static +value at e if we were smart we might + + align:start position:0% +value at e if we were smart we might + + + align:start position:0% +value at e if we were smart we might +have made a little hash table or + + align:start position:0% +have made a little hash table or + + + align:start position:0% +have made a little hash table or +something and put down two so we didn't + + align:start position:0% +something and put down two so we didn't + + + align:start position:0% +something and put down two so we didn't +have to do a static evaluation at e and + + align:start position:0% +have to do a static evaluation at e and + + + align:start position:0% +have to do a static evaluation at e and +if that happened well we save eh and I + + align:start position:0% +if that happened well we save eh and I + + + align:start position:0% +if that happened well we save eh and I +and we do three + + align:start position:0% +and we do three + + + align:start position:0% +and we do three +fewer does everyone see that however + + align:start position:0% +fewer does everyone see that however + + + align:start position:0% +fewer does everyone see that however +that's still more than six so it didn't + + align:start position:0% +that's still more than six so it didn't + + + align:start position:0% +that's still more than six so it didn't +save us time so you might say oh + + align:start position:0% +save us time so you might say oh + + + align:start position:0% +save us time so you might say oh +Progressive TP is a waste of time but + + align:start position:0% +Progressive TP is a waste of time but + + + align:start position:0% +Progressive TP is a waste of time but +it's not because this is a very very + + align:start position:0% +it's not because this is a very very + + + align:start position:0% +it's not because this is a very very +small not very branchy tree that was + + align:start position:0% +small not very branchy tree that was + + + align:start position:0% +small not very branchy tree that was +made so that you guys could easily do + + align:start position:0% +made so that you guys could easily do + + + align:start position:0% +made so that you guys could easily do +alpha beta and take the quiz and it + + align:start position:0% +alpha beta and take the quiz and it + + + align:start position:0% +alpha beta and take the quiz and it +wouldn't be bad if this tree was + + align:start position:0% +wouldn't be bad if this tree was + + + align:start position:0% +wouldn't be bad if this tree was +actually branching to um double even + + align:start position:0% +actually branching to um double even + + + align:start position:0% +actually branching to um double even +double at each level it would have what + + align:start position:0% +double at each level it would have what + + + align:start position:0% +double at each level it would have what +like 16 nodes down here at the bottom + + align:start position:0% +like 16 nodes down here at the bottom + + + align:start position:0% +like 16 nodes down here at the bottom +then you would want to be doing that + + align:start position:0% +then you would want to be doing that + + + align:start position:0% +then you would want to be doing that +Progressive deepening so now I ask you a + + align:start position:0% +Progressive deepening so now I ask you a + + + align:start position:0% +Progressive deepening so now I ask you a +conceptual Riddle question it's not + + align:start position:0% +conceptual Riddle question it's not + + + align:start position:0% +conceptual Riddle question it's not +really that much of a riddle but we'll + + align:start position:0% +really that much of a riddle but we'll + + + align:start position:0% +really that much of a riddle but we'll +see if anyone wants to answer again I + + align:start position:0% +see if anyone wants to answer again I + + + align:start position:0% +see if anyone wants to answer again I +won't call on you for this it's um + + align:start position:0% +won't call on you for this it's um + + + align:start position:0% +won't call on you for this it's um +according to this test um a student + + align:start position:0% +according to this test um a student + + + align:start position:0% +according to this test um a student +named Steve says okay I know I have to + + align:start position:0% +named Steve says okay I know I have to + + + align:start position:0% +named Steve says okay I know I have to +pay to do the progressive deepening here + + align:start position:0% +pay to do the progressive deepening here + + + align:start position:0% +pay to do the progressive deepening here +but let's ignore that because it's small + + align:start position:0% +but let's ignore that because it's small + + + align:start position:0% +but let's ignore that because it's small +in a large tree right it's not going to + + align:start position:0% +in a large tree right it's not going to + + + align:start position:0% +in a large tree right it's not going to +take that much Let's ignore the cost of + + align:start position:0% +take that much Let's ignore the cost of + + + align:start position:0% +take that much Let's ignore the cost of +the progressive deepening and only look + + align:start position:0% +the progressive deepening and only look + + + align:start position:0% +the progressive deepening and only look +at how much we do here he says when it + + align:start position:0% +at how much we do here he says when it + + + align:start position:0% +at how much we do here he says when it +comes to performing the alpha beta on + + align:start position:0% +comes to performing the alpha beta on + + + align:start position:0% +comes to performing the alpha beta on +the final level I'm guaranteed to always + + align:start position:0% +the final level I'm guaranteed to always + + + align:start position:0% +the final level I'm guaranteed to always +prune at least as well or better if I + + align:start position:0% +prune at least as well or better if I + + + align:start position:0% +prune at least as well or better if I +rearrange the nodes based on the best + + align:start position:0% +rearrange the nodes based on the best + + + align:start position:0% +rearrange the nodes based on the best +result from Progressive deepening + + align:start position:0% +result from Progressive deepening + + + align:start position:0% +result from Progressive deepening +do you + + align:start position:0% + + + + align:start position:0% + +agree can I repeat it okay the question + + align:start position:0% +agree can I repeat it okay the question + + + align:start position:0% +agree can I repeat it okay the question +is ignoring the cost that we pay + + align:start position:0% +is ignoring the cost that we pay + + + align:start position:0% +is ignoring the cost that we pay +progressively deepening here just forget + + align:start position:0% +progressively deepening here just forget + + + align:start position:0% +progressively deepening here just forget +about it at the final step at the final + + align:start position:0% +about it at the final step at the final + + + align:start position:0% +about it at the final step at the final +iteration question is am I guaranteed to + + align:start position:0% +iteration question is am I guaranteed to + + + align:start position:0% +iteration question is am I guaranteed to +do at least as well or better in my + + align:start position:0% +do at least as well or better in my + + + align:start position:0% +do at least as well or better in my +Alpha Beta pruning when I reorder based + + align:start position:0% +Alpha Beta pruning when I reorder based + + + align:start position:0% +Alpha Beta pruning when I reorder based +on the best level of um based on the + + align:start position:0% +on the best level of um based on the + + + align:start position:0% +on the best level of um based on the +best order for Progressive deing here + + align:start position:0% +best order for Progressive deing here + + + align:start position:0% +best order for Progressive deing here +certainly we did but the question is is + + align:start position:0% +certainly we did but the question is is + + + align:start position:0% +certainly we did but the question is is +Steve guaranteed + + align:start position:0% + + + + align:start position:0% + +answer what did you + + align:start position:0% +answer what did you + + + align:start position:0% +answer what did you +say that's the answer and the why which + + align:start position:0% +say that's the answer and the why which + + + align:start position:0% +say that's the answer and the why which +we asked to explain the the answer we + + align:start position:0% +we asked to explain the the answer we + + + align:start position:0% +we asked to explain the the answer we +got is that doesn't that depend on + + align:start position:0% +got is that doesn't that depend on + + + align:start position:0% +got is that doesn't that depend on +theistic perfectly correct the answer is + + align:start position:0% +theistic perfectly correct the answer is + + + align:start position:0% +theistic perfectly correct the answer is +no we're not guaranteed and it depends + + align:start position:0% +no we're not guaranteed and it depends + + + align:start position:0% +no we're not guaranteed and it depends +on theistic so if we were guaranteed + + align:start position:0% +on theistic so if we were guaranteed + + + align:start position:0% +on theistic so if we were guaranteed +that would mean our heris stick was + + align:start position:0% +that would mean our heris stick was + + + align:start position:0% +that would mean our heris stick was +Godlike like this heris stick if our + + align:start position:0% +Godlike like this heris stick if our + + + align:start position:0% +Godlike like this heris stick if our +heris stick already tells you the + + align:start position:0% +heris stick already tells you the + + + align:start position:0% +heris stick already tells you the +correct answer no matter what don't do + + align:start position:0% +correct answer no matter what don't do + + + align:start position:0% +correct answer no matter what don't do +game search just go to the the empty CH + + align:start position:0% +game search just go to the the empty CH + + + align:start position:0% +game search just go to the the empty CH +the chess board put all the pieces in + + align:start position:0% +the chess board put all the pieces in + + + align:start position:0% +the chess board put all the pieces in +the front rows and run the static + + align:start position:0% +the front rows and run the static + + + align:start position:0% +the front rows and run the static +evaluator on that and it'll say oh it + + align:start position:0% +evaluator on that and it'll say oh it + + + align:start position:0% +evaluator on that and it'll say oh it +looks like with this game not started + + align:start position:0% +looks like with this game not started + + + align:start position:0% +looks like with this game not started +that white is stupid so black will win + + align:start position:0% +that white is stupid so black will win + + + align:start position:0% +that white is stupid so black will win +in 15 turns and then you're done and you + + align:start position:0% +in 15 turns and then you're done and you + + + align:start position:0% +in 15 turns and then you're done and you +don't do a search we know that our heris + + align:start position:0% +don't do a search we know that our heris + + + align:start position:0% +don't do a search we know that our heris +is flawed in some way it could be very + + align:start position:0% +is flawed in some way it could be very + + + align:start position:0% +is flawed in some way it could be very +flawed if it's flawed so badly that it + + align:start position:0% +flawed if it's flawed so badly that it + + + align:start position:0% +flawed if it's flawed so badly that it +tells us a very bad result of what's + + align:start position:0% +tells us a very bad result of what's + + + align:start position:0% +tells us a very bad result of what's +actually going to happen even though we + + align:start position:0% +actually going to happen even though we + + + align:start position:0% +actually going to happen even though we +think the minimizer is going to go to H + + align:start position:0% +think the minimizer is going to go to H + + + align:start position:0% +think the minimizer is going to go to H +maybe it's wrong by a lot and it goes to + + align:start position:0% +maybe it's wrong by a lot and it goes to + + + align:start position:0% +maybe it's wrong by a lot and it goes to +G it could take us a even worse path and + + align:start position:0% +G it could take us a even worse path and + + + align:start position:0% +G it could take us a even worse path and +make us take longer question if it's + + align:start position:0% +make us take longer question if it's + + + align:start position:0% +make us take longer question if it's +atic How Could You C the values so you + + align:start position:0% +atic How Could You C the values so you + + + align:start position:0% +atic How Could You C the values so you +have to recate later the question is how + + align:start position:0% +have to recate later the question is how + + + align:start position:0% +have to recate later the question is how +can you cach the values if it's a + + align:start position:0% +can you cach the values if it's a + + + align:start position:0% +can you cach the values if it's a +heuristic so you don't have to + + align:start position:0% +heuristic so you don't have to + + + align:start position:0% +heuristic so you don't have to +recalculate them later the answer is it + + align:start position:0% +recalculate them later the answer is it + + + align:start position:0% +recalculate them later the answer is it +wouldn't help if there weren't these + + align:start position:0% +wouldn't help if there weren't these + + + align:start position:0% +wouldn't help if there weren't these +weird multi-level things where we stop + + align:start position:0% +weird multi-level things where we stop + + + align:start position:0% +weird multi-level things where we stop +at e some for some reason even though it + + align:start position:0% +at e some for some reason even though it + + + align:start position:0% +at e some for some reason even though it +goes down to five levels the way you + + align:start position:0% +goes down to five levels the way you + + + align:start position:0% +goes down to five levels the way you +could cach it is it is a heris but it's + + align:start position:0% +could cach it is it is a heris but it's + + + align:start position:0% +could cach it is it is a heris but it's +consistent and I don't mean consistent + + align:start position:0% +consistent and I don't mean consistent + + + align:start position:0% +consistent and I don't mean consistent +from search I mean it's a consistent + + align:start position:0% +from search I mean it's a consistent + + + align:start position:0% +from search I mean it's a consistent +heris in in the State game State e is + + align:start position:0% +heris in in the State game State e is + + + align:start position:0% +heris in in the State game State e is +let's say say that's the state where I + + align:start position:0% +let's say say that's the state where I + + + align:start position:0% +let's say say that's the state where I +moved out my night as the maximizer + + align:start position:0% +moved out my night as the maximizer + + + align:start position:0% +moved out my night as the maximizer +minimizer said you're doing the Night + + align:start position:0% +minimizer said you're doing the Night + + + align:start position:0% +minimizer said you're doing the Night +opening really and then did a + + align:start position:0% +opening really and then did a + + + align:start position:0% +opening really and then did a +Counterattack no matter how we get to e + + align:start position:0% +Counterattack no matter how we get to e + + + align:start position:0% +Counterattack no matter how we get to e +or where we go to get to e that's always + + align:start position:0% +or where we go to get to e that's always + + + align:start position:0% +or where we go to get to e that's always +going to be State e it's always going to + + align:start position:0% +going to be State e it's always going to + + + align:start position:0% +going to be State e it's always going to +have the same turistic value it's not + + align:start position:0% +have the same turistic value it's not + + + align:start position:0% +have the same turistic value it's not +like some guy who like goes around and + + align:start position:0% +like some guy who like goes around and + + + align:start position:0% +like some guy who like goes around and +just randomly pulls a number out of a + + align:start position:0% +just randomly pulls a number out of a + + + align:start position:0% +just randomly pulls a number out of a +hat for some we're going to have some + + align:start position:0% +hat for some we're going to have some + + + align:start position:0% +hat for some we're going to have some +value where that gives us points based + + align:start position:0% +value where that gives us points based + + + align:start position:0% +value where that gives us points based +on state e and it's going to be the same + + align:start position:0% +on state e and it's going to be the same + + + align:start position:0% +on state e and it's going to be the same +anytime we go to state e does that make + + align:start position:0% +anytime we go to state e does that make + + + align:start position:0% +anytime we go to state e does that make +sense it is a heuristic but it's always + + align:start position:0% +sense it is a heuristic but it's always + + + align:start position:0% +sense it is a heuristic but it's always +going to give the same value at e no + + align:start position:0% +going to give the same value at e no + + + align:start position:0% +going to give the same value at e no +matter how you got to + + align:start position:0% +matter how you got to + + + align:start position:0% +matter how you got to +e but it could be really bad in fact you + + align:start position:0% +e but it could be really bad in fact you + + + align:start position:0% +e but it could be really bad in fact you +might consider a heris that's the + + align:start position:0% +might consider a heris that's the + + + align:start position:0% +might consider a heris that's the +opposite of correct and always tells us + + align:start position:0% +opposite of correct and always tells us + + + align:start position:0% +opposite of correct and always tells us +the worst move and claims it's the best + + align:start position:0% +the worst move and claims it's the best + + + align:start position:0% +the worst move and claims it's the best +that's the heris that the minimizer are + + align:start position:0% +that's the heris that the minimizer are + + + align:start position:0% +that's the heris that the minimizer are +programmed into our computer perhaps in + + align:start position:0% +programmed into our computer perhaps in + + + align:start position:0% +programmed into our computer perhaps in +that case when we do Progressive + + align:start position:0% +that case when we do Progressive + + + align:start position:0% +that case when we do Progressive +deepening and we reorder we'll probably + + align:start position:0% +deepening and we reorder we'll probably + + + align:start position:0% +deepening and we reorder we'll probably +get the worst pruning possible so um we + + align:start position:0% +get the worst pruning possible so um we + + + align:start position:0% +get the worst pruning possible so um we +may not but we may so in that case + + align:start position:0% +may not but we may so in that case + + + align:start position:0% +may not but we may so in that case +you're not guaranteed hope that given a + + align:start position:0% +you're not guaranteed hope that given a + + + align:start position:0% +you're not guaranteed hope that given a +little a few clues in tutorial you guys + + align:start position:0% +little a few clues in tutorial you guys + + + align:start position:0% +little a few clues in tutorial you guys +are going to see some more interesting + + align:start position:0% +are going to see some more interesting + + + align:start position:0% +are going to see some more interesting +problems that go into a few other + + align:start position:0% +problems that go into a few other + + + align:start position:0% +problems that go into a few other +details I at least plan on doing yuan's + + align:start position:0% +details I at least plan on doing yuan's + + + align:start position:0% +details I at least plan on doing yuan's +interesting game problem from last year + + align:start position:0% +interesting game problem from last year + + + align:start position:0% +interesting game problem from last year +which asked a bunch of um asked a bunch + + align:start position:0% +which asked a bunch of um asked a bunch + + + align:start position:0% +which asked a bunch of um asked a bunch +of um varied things that are a little + + align:start position:0% +of um varied things that are a little + + + align:start position:0% +of um varied things that are a little +bit different from these so it should be + + align:start position:0% +bit different from these so it should be + + + align:start position:0% +bit different from these so it should be +it should be a lot of fun hopefully or + + align:start position:0% +it should be a lot of fun hopefully or + + + align:start position:0% +it should be a lot of fun hopefully or +at least useful to um do the next Quiz + + align:start position:0% +at least useful to um do the next Quiz + + + align:start position:0% +at least useful to um do the next Quiz +so have a great weekend don't stress out + + align:start position:0% +so have a great weekend don't stress out + + + align:start position:0% +so have a great weekend don't stress out +too much about the quiz \ No newline at end of file diff --git a/hWabPMYZzmo.txt b/hWabPMYZzmo.txt new file mode 100644 index 0000000000000000000000000000000000000000..c3be7db951a7a85c8596dd81b2997cd83fb18775 --- /dev/null +++ b/hWabPMYZzmo.txt @@ -0,0 +1,7395 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +the most there's a whole bunch of + + align:start position:0% +the most there's a whole bunch of + + + align:start position:0% +the most there's a whole bunch of +limitations of Haxby style correlations + + align:start position:0% +limitations of Haxby style correlations + + + align:start position:0% +limitations of Haxby style correlations +and one of them is that all the tests + + align:start position:0% +and one of them is that all the tests + + + align:start position:0% +and one of them is that all the tests +are binary the answer you get for + + align:start position:0% +are binary the answer you get for + + + align:start position:0% +are binary the answer you get for +anything you test is that there is or is + + align:start position:0% +anything you test is that there is or is + + + align:start position:0% +anything you test is that there is or is +not information about that distinction + + align:start position:0% +not information about that distinction + + + align:start position:0% +not information about that distinction +and see there's no continuous measure + + align:start position:0% +and see there's no continuous measure + + + align:start position:0% +and see there's no continuous measure +here + + align:start position:0% +here + + + align:start position:0% +here +it's just that two things are more they + + align:start position:0% +it's just that two things are more they + + + align:start position:0% +it's just that two things are more they +are different from one another or they + + align:start position:0% +are different from one another or they + + + align:start position:0% +are different from one another or they +are not different from one another and + + align:start position:0% +are not different from one another and + + + align:start position:0% +are not different from one another and +so once people started thinking about + + align:start position:0% +so once people started thinking about + + + align:start position:0% +so once people started thinking about +this method it became clear that this is + + align:start position:0% +this method it became clear that this is + + + align:start position:0% +this method it became clear that this is +actually just a special case of a much + + align:start position:0% +actually just a special case of a much + + + align:start position:0% +actually just a special case of a much +more general way of thinking about a + + align:start position:0% +more general way of thinking about a + + + align:start position:0% +more general way of thinking about a +former idea so the this particular + + align:start position:0% +former idea so the this particular + + + align:start position:0% +former idea so the this particular +method using special correlations is + + align:start position:0% +method using special correlations is + + + align:start position:0% +method using special correlations is +very stable and robust and but it's a + + align:start position:0% +very stable and robust and but it's a + + + align:start position:0% +very stable and robust and but it's a +but it's a special case of a much more + + align:start position:0% +but it's a special case of a much more + + + align:start position:0% +but it's a special case of a much more +general set and here's the more general + + align:start position:0% +general set and here's the more general + + + align:start position:0% +general set and here's the more general +idea the more general idea is that we + + align:start position:0% +idea the more general idea is that we + + + align:start position:0% +idea the more general idea is that we +can think of the response pattern to a + + align:start position:0% +can think of the response pattern to a + + + align:start position:0% +can think of the response pattern to a +stimulus in a set of voxels for example + + align:start position:0% +stimulus in a set of voxels for example + + + align:start position:0% +stimulus in a set of voxels for example +the voxels in a region we can think of + + align:start position:0% +the voxels in a region we can think of + + + align:start position:0% +the voxels in a region we can think of +that response pattern as a vector in + + align:start position:0% +that response pattern as a vector in + + + align:start position:0% +that response pattern as a vector in +this in voxel space so every time you + + align:start position:0% +this in voxel space so every time you + + + align:start position:0% +this in voxel space so every time you +present a stimulus you hit the response + + align:start position:0% +present a stimulus you hit the response + + + align:start position:0% +present a stimulus you hit the response +of all the voxels now instead of + + align:start position:0% +of all the voxels now instead of + + + align:start position:0% +of all the voxels now instead of +thinking of that as a spatial pattern + + align:start position:0% +thinking of that as a spatial pattern + + + align:start position:0% +thinking of that as a spatial pattern +think of that as a vector in voxel space + + align:start position:0% +think of that as a vector in voxel space + + + align:start position:0% +think of that as a vector in voxel space +every voxel defines a dimension and the + + align:start position:0% +every voxel defines a dimension and the + + + align:start position:0% +every voxel defines a dimension and the +position in voxel space is how much + + align:start position:0% +position in voxel space is how much + + + align:start position:0% +position in voxel space is how much +activity in each of those voxels there + + align:start position:0% +activity in each of those voxels there + + + align:start position:0% +activity in each of those voxels there +was can everybody do that mental + + align:start position:0% +was can everybody do that mental + + + align:start position:0% +was can everybody do that mental +transformation this is like the key + + align:start position:0% +transformation this is like the key + + + align:start position:0% +transformation this is like the key +insight that people had about MVPA is we + + align:start position:0% +insight that people had about MVPA is we + + + align:start position:0% +insight that people had about MVPA is we +had been thinking about everything in + + align:start position:0% +had been thinking about everything in + + + align:start position:0% +had been thinking about everything in +the spit in this in space in the space + + align:start position:0% +the spit in this in space in the space + + + align:start position:0% +the spit in this in space in the space +of cortex but instead of thinking of a + + align:start position:0% +of cortex but instead of thinking of a + + + align:start position:0% +of cortex but instead of thinking of a +spatial pattern on cortex treat each + + align:start position:0% +spatial pattern on cortex treat each + + + align:start position:0% +spatial pattern on cortex treat each +voxel as a dimension of a very + + align:start position:0% +voxel as a dimension of a very + + + align:start position:0% +voxel as a dimension of a very +multi-dimensional space now the response + + align:start position:0% +multi-dimensional space now the response + + + align:start position:0% +multi-dimensional space now the response +to every stimulus is one point in the in + + align:start position:0% +to every stimulus is one point in the in + + + align:start position:0% +to every stimulus is one point in the in +voxel space ok as soon as you think of + + align:start position:0% +voxel space ok as soon as you think of + + + align:start position:0% +voxel space ok as soon as you think of +it that way + + align:start position:0% +it that way + + + align:start position:0% +it that way +and then your mental representation of + + align:start position:0% +and then your mental representation of + + + align:start position:0% +and then your mental representation of +fMRI data looks like that + + align:start position:0% +fMRI data looks like that + + + align:start position:0% +fMRI data looks like that +right so your mental representation of + + align:start position:0% +right so your mental representation of + + + align:start position:0% +right so your mental representation of +MIT and it used to be a bold response + + align:start position:0% +MIT and it used to be a bold response + + + align:start position:0% +MIT and it used to be a bold response +and then it was a spatial pattern over + + align:start position:0% +and then it was a spatial pattern over + + + align:start position:0% +and then it was a spatial pattern over +cortex and now it's a point in voxel + + align:start position:0% +cortex and now it's a point in voxel + + + align:start position:0% +cortex and now it's a point in voxel +space and if you can follow those three + + align:start position:0% +space and if you can follow those three + + + align:start position:0% +space and if you can follow those three +transformations then you realize that a + + align:start position:0% +transformations then you realize that a + + + align:start position:0% +transformations then you realize that a +set of points in a multi-dimensional + + align:start position:0% +set of points in a multi-dimensional + + + align:start position:0% +set of points in a multi-dimensional +space is the kind of problem that all of + + align:start position:0% +space is the kind of problem that all of + + + align:start position:0% +space is the kind of problem that all of +machine learning for the last twenty + + align:start position:0% +machine learning for the last twenty + + + align:start position:0% +machine learning for the last twenty +years has been working on right and so + + align:start position:0% +years has been working on right and so + + + align:start position:0% +years has been working on right and so +everything that has ever happened in + + align:start position:0% +everything that has ever happened in + + + align:start position:0% +everything that has ever happened in +machine learning could now be used in + + align:start position:0% +machine learning could now be used in + + + align:start position:0% +machine learning could now be used in +fMRI because because machine learning + + align:start position:0% +fMRI because because machine learning + + + align:start position:0% +fMRI because because machine learning +has just absolutely proliferated in both + + align:start position:0% +has just absolutely proliferated in both + + + align:start position:0% +has just absolutely proliferated in both +techniques and problems and solutions to + + align:start position:0% +techniques and problems and solutions to + + + align:start position:0% +techniques and problems and solutions to +those problems for handling datasets + + align:start position:0% +those problems for handling datasets + + + align:start position:0% +those problems for handling datasets +where you have no idea where the data + + align:start position:0% +where you have no idea where the data + + + align:start position:0% +where you have no idea where the data +set came from but it's now represented + + align:start position:0% +set came from but it's now represented + + + align:start position:0% +set came from but it's now represented +as a point in a multi-dimensional points + + align:start position:0% +as a point in a multi-dimensional points + + + align:start position:0% +as a point in a multi-dimensional points +in the multi-dimensional space and so + + align:start position:0% +in the multi-dimensional space and so + + + align:start position:0% +in the multi-dimensional space and so +that's what happened about five years + + align:start position:0% +that's what happened about five years + + + align:start position:0% +that's what happened about five years +ago is that people realize that we could + + align:start position:0% +ago is that people realize that we could + + + align:start position:0% +ago is that people realize that we could +think of fMRI as the response to every + + align:start position:0% +think of fMRI as the response to every + + + align:start position:0% +think of fMRI as the response to every +stimulus as a point in voxel space the + + align:start position:0% +stimulus as a point in voxel space the + + + align:start position:0% +stimulus as a point in voxel space the +set of a set of data is a set of points + + align:start position:0% +set of a set of data is a set of points + + + align:start position:0% +set of a set of data is a set of points +in voxel space now do anything you want + + align:start position:0% +in voxel space now do anything you want + + + align:start position:0% +in voxel space now do anything you want +with that and the first most obvious + + align:start position:0% +with that and the first most obvious + + + align:start position:0% +with that and the first most obvious +thing to do is to think of this as a + + align:start position:0% +thing to do is to think of this as a + + + align:start position:0% +thing to do is to think of this as a +classification problem okay so we + + align:start position:0% +classification problem okay so we + + + align:start position:0% +classification problem okay so we +created conditions and our stimuli or + + align:start position:0% +created conditions and our stimuli or + + + align:start position:0% +created conditions and our stimuli or +dimensions and our stimuli so now we can + + align:start position:0% +dimensions and our stimuli so now we can + + + align:start position:0% +dimensions and our stimuli so now we can +ask can we decode those conditions can + + align:start position:0% +ask can we decode those conditions can + + + align:start position:0% +ask can we decode those conditions can +we find clusters can we find dimensions + + align:start position:0% +we find clusters can we find dimensions + + + align:start position:0% +we find clusters can we find dimensions +right all the standard things that + + align:start position:0% +right all the standard things that + + + align:start position:0% +right all the standard things that +people have done when you had points in + + align:start position:0% +people have done when you had points in + + + align:start position:0% +people have done when you had points in +multi-dimensional spaces and and so + + align:start position:0% +multi-dimensional spaces and and so + + + align:start position:0% +multi-dimensional spaces and and so +again the most common thing people now + + align:start position:0% +again the most common thing people now + + + align:start position:0% +again the most common thing people now +do is now that you think of fMRI data + + align:start position:0% +do is now that you think of fMRI data + + + align:start position:0% +do is now that you think of fMRI data +that way try linear classification of + + align:start position:0% +that way try linear classification of + + + align:start position:0% +that way try linear classification of +the categories or dimensions that you're + + align:start position:0% +the categories or dimensions that you're + + + align:start position:0% +the categories or dimensions that you're +interested in and typically you know + + align:start position:0% +interested in and typically you know + + + align:start position:0% +interested in and typically you know +using standard machine learning + + align:start position:0% +using standard machine learning + + + align:start position:0% +using standard machine learning +techniques so think of training a + + align:start position:0% +techniques so think of training a + + + align:start position:0% +techniques so think of training a +classifier on some of your data and + + align:start position:0% +classifier on some of your data and + + + align:start position:0% +classifier on some of your data and +testing it on independent data and + + align:start position:0% +testing it on independent data and + + + align:start position:0% +testing it on independent data and +trying to find the right classification + + align:start position:0% +trying to find the right classification + + + align:start position:0% +trying to find the right classification +techniques that can identify whatever + + align:start position:0% +techniques that can identify whatever + + + align:start position:0% +techniques that can identify whatever +distinction you're interested in in the + + align:start position:0% +distinction you're interested in in the + + + align:start position:0% +distinction you're interested in in the +data set that you built and so the way + + align:start position:0% +data set that you built and so the way + + + align:start position:0% +data set that you built and so the way +that this will look is that you take + + align:start position:0% +that this will look is that you take + + + align:start position:0% +that this will look is that you take +some now voxels are on the y axis of + + align:start position:0% +some now voxels are on the y axis of + + + align:start position:0% +some now voxels are on the y axis of +this heat map so we have whatever that + + align:start position:0% +this heat map so we have whatever that + + + align:start position:0% +this heat map so we have whatever that +is + + align:start position:0% +is + + + align:start position:0% +is +80-100 voxels in a region maybe more and + + align:start position:0% +80-100 voxels in a region maybe more and + + + align:start position:0% +80-100 voxels in a region maybe more and +for every + + align:start position:0% +for every + + + align:start position:0% +for every +ulis you have the response in every + + align:start position:0% +ulis you have the response in every + + + align:start position:0% +ulis you have the response in every +voxel to that stimulus right so that + + align:start position:0% +voxel to that stimulus right so that + + + align:start position:0% +voxel to that stimulus right so that +each of those columns now is a + + align:start position:0% +each of those columns now is a + + + align:start position:0% +each of those columns now is a +representation of where that stimulus + + align:start position:0% +representation of where that stimulus + + + align:start position:0% +representation of where that stimulus +landed in voxel space and you have a + + align:start position:0% +landed in voxel space and you have a + + + align:start position:0% +landed in voxel space and you have a +whole bunch of instances and so now what + + align:start position:0% +whole bunch of instances and so now what + + + align:start position:0% +whole bunch of instances and so now what +you're gonna do is use the training to + + align:start position:0% +you're gonna do is use the training to + + + align:start position:0% +you're gonna do is use the training to +learn a potential linear classifier that + + align:start position:0% +learn a potential linear classifier that + + + align:start position:0% +learn a potential linear classifier that +tells you what was the best way to + + align:start position:0% +tells you what was the best way to + + + align:start position:0% +tells you what was the best way to +separate the stimuli they came from one + + align:start position:0% +separate the stimuli they came from one + + + align:start position:0% +separate the stimuli they came from one +labelled set versus the stimuli that + + align:start position:0% +labelled set versus the stimuli that + + + align:start position:0% +labelled set versus the stimuli that +came from some other labelled set and + + align:start position:0% +came from some other labelled set and + + + align:start position:0% +came from some other labelled set and +the test of that is going to be taken + + align:start position:0% +the test of that is going to be taken + + + align:start position:0% +the test of that is going to be taken +new set take a new stimulus or a new + + align:start position:0% +new set take a new stimulus or a new + + + align:start position:0% +new set take a new stimulus or a new +response and use the classification you + + align:start position:0% +response and use the classification you + + + align:start position:0% +response and use the classification you +learned to try to decode which stimulus + + align:start position:0% +learned to try to decode which stimulus + + + align:start position:0% +learned to try to decode which stimulus +set that came from and measure your + + align:start position:0% +set that came from and measure your + + + align:start position:0% +set that came from and measure your +accuracy and so the new measure of that + + align:start position:0% +accuracy and so the new measure of that + + + align:start position:0% +accuracy and so the new measure of that +from of the information in fMRI is going + + align:start position:0% +from of the information in fMRI is going + + + align:start position:0% +from of the information in fMRI is going +to be classification accuracy that make + + align:start position:0% +to be classification accuracy that make + + + align:start position:0% +to be classification accuracy that make +sense for people with me um okay because + + align:start position:0% +sense for people with me um okay because + + + align:start position:0% +sense for people with me um okay because +that's that's where a lot of fMRI is + + align:start position:0% +that's that's where a lot of fMRI is + + + align:start position:0% +that's that's where a lot of fMRI is +right now is now thinking about + + align:start position:0% +right now is now thinking about + + + align:start position:0% +right now is now thinking about +responses to stimuli as points in voxel + + align:start position:0% +responses to stimuli as points in voxel + + + align:start position:0% +responses to stimuli as points in voxel +space and the problem as one of + + align:start position:0% +space and the problem as one of + + + align:start position:0% +space and the problem as one of +classification accuracy and independent + + align:start position:0% +classification accuracy and independent + + + align:start position:0% +classification accuracy and independent +data um okay here's one experiment that + + align:start position:0% +data um okay here's one experiment that + + + align:start position:0% +data um okay here's one experiment that +we did where we use classification so + + align:start position:0% +we did where we use classification so + + + align:start position:0% +we did where we use classification so +now another thing just to note is that + + align:start position:0% +now another thing just to note is that + + + align:start position:0% +now another thing just to note is that +in this context you're often trying to + + align:start position:0% +in this context you're often trying to + + + align:start position:0% +in this context you're often trying to +classify a single trial right so in our + + align:start position:0% +classify a single trial right so in our + + + align:start position:0% +classify a single trial right so in our +case we're always trying to classify a + + align:start position:0% +case we're always trying to classify a + + + align:start position:0% +case we're always trying to classify a +single child so we've gone from + + align:start position:0% +single child so we've gone from + + + align:start position:0% +single child so we've gone from +partitioning the data to two halves and + + align:start position:0% +partitioning the data to two halves and + + + align:start position:0% +partitioning the data to two halves and +asking about similarity to training on + + align:start position:0% +asking about similarity to training on + + + align:start position:0% +asking about similarity to training on +some of the data and now classifying + + align:start position:0% +some of the data and now classifying + + + align:start position:0% +some of the data and now classifying +single independent trials okay and so + + align:start position:0% +single independent trials okay and so + + + align:start position:0% +single independent trials okay and so +here's a case where we tried to do that + + align:start position:0% +here's a case where we tried to do that + + + align:start position:0% +here's a case where we tried to do that +and it was an extension of the stuff + + align:start position:0% +and it was an extension of the stuff + + + align:start position:0% +and it was an extension of the stuff +that I just showed you that you could + + align:start position:0% +that I just showed you that you could + + + align:start position:0% +that I just showed you that you could +classify seeing versus hearing and so we + + align:start position:0% +classify seeing versus hearing and so we + + + align:start position:0% +classify seeing versus hearing and so we +tried to replicate and extend that so we + + align:start position:0% +tried to replicate and extend that so we + + + align:start position:0% +tried to replicate and extend that so we +told people's stories like this there's + + align:start position:0% +told people's stories like this there's + + + align:start position:0% +told people's stories like this there's +a background so bellas pouring sleeping + + align:start position:0% +a background so bellas pouring sleeping + + + align:start position:0% +a background so bellas pouring sleeping +potion into Ardoin soup and when her + + align:start position:0% +potion into Ardoin soup and when her + + + align:start position:0% +potion into Ardoin soup and when her +sister Jen is waiting they're holding + + align:start position:0% +sister Jen is waiting they're holding + + + align:start position:0% +sister Jen is waiting they're holding +their breath while he starts to eat the + + align:start position:0% +their breath while he starts to eat the + + + align:start position:0% +their breath while he starts to eat the +conclusion of the story's always going + + align:start position:0% +conclusion of the story's always going + + + align:start position:0% +conclusion of the story's always going +to be the same the Bella concludes that + + align:start position:0% +to be the same the Bella concludes that + + + align:start position:0% +to be the same the Bella concludes that +the potion worked and then we tell you + + align:start position:0% +the potion worked and then we tell you + + + align:start position:0% +the potion worked and then we tell you +based on what evidence she made that + + align:start position:0% +based on what evidence she made that + + + align:start position:0% +based on what evidence she made that +conclusion + + align:start position:0% +conclusion + + + align:start position:0% +conclusion +so here the another case here is going + + align:start position:0% +so here the another case here is going + + + align:start position:0% +so here the another case here is going +to be well I stared through the secret + + align:start position:0% +to be well I stared through the secret + + + align:start position:0% +to be well I stared through the secret +people and waited in the bright light + + align:start position:0% +people and waited in the bright light + + + align:start position:0% +people and waited in the bright light +she saw his eyes closed and his head + + align:start position:0% +she saw his eyes closed and his head + + + align:start position:0% +she saw his eyes closed and his head +droop okay so that's her evidence for + + align:start position:0% +droop okay so that's her evidence for + + + align:start position:0% +droop okay so that's her evidence for +the conclusion that the potion has + + align:start position:0% +the conclusion that the potion has + + + align:start position:0% +the conclusion that the potion has +worked that's ok evidence + + align:start position:0% +worked that's ok evidence + + + align:start position:0% +worked that's ok evidence +and we can vary that in a bunch of ways + + align:start position:0% +and we can vary that in a bunch of ways + + + align:start position:0% +and we can vary that in a bunch of ways +so one is we can change the modality for + + align:start position:0% +so one is we can change the modality for + + + align:start position:0% +so one is we can change the modality for +evidence so instead of seeing something + + align:start position:0% +evidence so instead of seeing something + + + align:start position:0% +evidence so instead of seeing something +she can hear something and so for + + align:start position:0% +she can hear something and so for + + + align:start position:0% +she can hear something and so for +example she pressed her ear against the + + align:start position:0% +example she pressed her ear against the + + + align:start position:0% +example she pressed her ear against the +door and waited in the quiet she heard + + align:start position:0% +door and waited in the quiet she heard + + + align:start position:0% +door and waited in the quiet she heard +the spoon drop and a soft snore he said + + align:start position:0% +the spoon drop and a soft snore he said + + + align:start position:0% +the spoon drop and a soft snore he said +that's similar content of information + + align:start position:0% +that's similar content of information + + + align:start position:0% +that's similar content of information +but arrived at through a different + + align:start position:0% +but arrived at through a different + + + align:start position:0% +but arrived at through a different +modality um or we can change how good + + align:start position:0% +modality um or we can change how good + + + align:start position:0% +modality um or we can change how good +her evidence is and so in this case we + + align:start position:0% +her evidence is and so in this case we + + + align:start position:0% +her evidence is and so in this case we +did it by saying she tried to peer + + align:start position:0% +did it by saying she tried to peer + + + align:start position:0% +did it by saying she tried to peer +through a crack in the door in the dim + + align:start position:0% +through a crack in the door in the dim + + + align:start position:0% +through a crack in the door in the dim +light she squinted to see his eyes + + align:start position:0% +light she squinted to see his eyes + + + align:start position:0% +light she squinted to see his eyes +closed ok so that's less strong + + align:start position:0% +closed ok so that's less strong + + + align:start position:0% +closed ok so that's less strong +perceptual evidence for the conclusion + + align:start position:0% +perceptual evidence for the conclusion + + + align:start position:0% +perceptual evidence for the conclusion +that the potion has worked ok and so now + + align:start position:0% +that the potion has worked ok and so now + + + align:start position:0% +that the potion has worked ok and so now +what we're gonna ask is if we train on + + align:start position:0% +what we're gonna ask is if we train on + + + align:start position:0% +what we're gonna ask is if we train on +one set of stories on the pattern of + + align:start position:0% +one set of stories on the pattern of + + + align:start position:0% +one set of stories on the pattern of +activity in a brain region for stories + + align:start position:0% +activity in a brain region for stories + + + align:start position:0% +activity in a brain region for stories +that vary on either of these dimensions + + align:start position:0% +that vary on either of these dimensions + + + align:start position:0% +that vary on either of these dimensions +one at a time either very unmowed + + align:start position:0% +one at a time either very unmowed + + + align:start position:0% +one at a time either very unmowed +allottee or very unqualified + + align:start position:0% +allottee or very unqualified + + + align:start position:0% +allottee or very unqualified +this measure isn't binary anymore so + + align:start position:0% +this measure isn't binary anymore so + + + align:start position:0% +this measure isn't binary anymore so +since we're doing for every stimulus or + + align:start position:0% +since we're doing for every stimulus or + + + align:start position:0% +since we're doing for every stimulus or +class that we're asking whether whether + + align:start position:0% +class that we're asking whether whether + + + align:start position:0% +class that we're asking whether whether +we can classify that stimulus or not and + + align:start position:0% +we can classify that stimulus or not and + + + align:start position:0% +we can classify that stimulus or not and +we can get for every subject so we can + + align:start position:0% +we can get for every subject so we can + + + align:start position:0% +we can get for every subject so we can +get for each item the probability right + + align:start position:0% +get for each item the probability right + + + align:start position:0% +get for each item the probability right +for each subject for each item we get a + + align:start position:0% +for each subject for each item we get a + + + align:start position:0% +for each subject for each item we get a +measure of whether it was classified + + align:start position:0% +measure of whether it was classified + + + align:start position:0% +measure of whether it was classified +correctly or not + + align:start position:0% +correctly or not + + + align:start position:0% +correctly or not +so across subjects across items we know + + align:start position:0% +so across subjects across items we know + + + align:start position:0% +so across subjects across items we know +for every item the probability of it + + align:start position:0% +for every item the probability of it + + + align:start position:0% +for every item the probability of it +being correctly classified or not and + + align:start position:0% +being correctly classified or not and + + + align:start position:0% +being correctly classified or not and +then we can ask is that related to other + + align:start position:0% +then we can ask is that related to other + + + align:start position:0% +then we can ask is that related to other +continuous features of that item so and + + align:start position:0% +continuous features of that item so and + + + align:start position:0% +continuous features of that item so and +so in this case what we can say for + + align:start position:0% +so in this case what we can say for + + + align:start position:0% +so in this case what we can say for +example is the quality dimension have + + align:start position:0% +example is the quality dimension have + + + align:start position:0% +example is the quality dimension have +just how good your evidence is for the + + align:start position:0% +just how good your evidence is for the + + + align:start position:0% +just how good your evidence is for the +belief that you conclude that's a + + align:start position:0% +belief that you conclude that's a + + + align:start position:0% +belief that you conclude that's a +continuous metric so it's a continuous + + align:start position:0% +continuous metric so it's a continuous + + + align:start position:0% +continuous metric so it's a continuous +feature and it can be judged + + align:start position:0% +feature and it can be judged + + + align:start position:0% +feature and it can be judged +continuously by human observers so for + + align:start position:0% +continuously by human observers so for + + + align:start position:0% +continuously by human observers so for +each item we can ask how good is the + + align:start position:0% +each item we can ask how good is the + + + align:start position:0% +each item we can ask how good is the +evidence for the conclusion for this + + align:start position:0% +evidence for the conclusion for this + + + align:start position:0% +evidence for the conclusion for this +specific story and that problem that + + align:start position:0% +specific story and that problem that + + + align:start position:0% +specific story and that problem that +judgment by human observers of how good + + align:start position:0% +judgment by human observers of how good + + + align:start position:0% +judgment by human observers of how good +the evidence is continuously predicts + + align:start position:0% +the evidence is continuously predicts + + + align:start position:0% +the evidence is continuously predicts +and the probability of that item being + + align:start position:0% +and the probability of that item being + + + align:start position:0% +and the probability of that item being +classified as being good evidence or bad + + align:start position:0% +classified as being good evidence or bad + + + align:start position:0% +classified as being good evidence or bad +evidence even over above the label that + + align:start position:0% +evidence even over above the label that + + + align:start position:0% +evidence even over above the label that +we gave it so if you regress out the + + align:start position:0% +we gave it so if you regress out the + + + align:start position:0% +we gave it so if you regress out the +labels there's a continuous predictor + + align:start position:0% +labels there's a continuous predictor + + + align:start position:0% +labels there's a continuous predictor +so something like imagine under a + + align:start position:0% +so something like imagine under a + + + align:start position:0% +so something like imagine under a +population that responds a subpopulation + + align:start position:0% +population that responds a subpopulation + + + align:start position:0% +population that responds a subpopulation +of ourselves more the better the + + align:start position:0% +of ourselves more the better the + + + align:start position:0% +of ourselves more the better the +evidence continuously so that + + align:start position:0% +evidence continuously so that + + + align:start position:0% +evidence continuously so that +classification gets better at that + + align:start position:0% +classification gets better at that + + + align:start position:0% +classification gets better at that +dimension as you get further out on that + + align:start position:0% +dimension as you get further out on that + + + align:start position:0% +dimension as you get further out on that +dimension and it's also not redundant + + align:start position:0% +dimension and it's also not redundant + + + align:start position:0% +dimension and it's also not redundant +across brain regions so there's + + align:start position:0% +across brain regions so there's + + + align:start position:0% +across brain regions so there's +different information in different brain + + align:start position:0% +different information in different brain + + + align:start position:0% +different information in different brain +regions and this is just to show you + + align:start position:0% +regions and this is just to show you + + + align:start position:0% +regions and this is just to show you +that in two other brain regions so in + + align:start position:0% +that in two other brain regions so in + + + align:start position:0% +that in two other brain regions so in +the right STS we can decode quality but + + align:start position:0% +the right STS we can decode quality but + + + align:start position:0% +the right STS we can decode quality but +not modality and in the left TPJ we can + + align:start position:0% +not modality and in the left TPJ we can + + + align:start position:0% +not modality and in the left TPJ we can +decode modality but not quality and the + + align:start position:0% +decode modality but not quality and the + + + align:start position:0% +decode modality but not quality and the +left tbj we've replicated a bunch of + + align:start position:0% +left tbj we've replicated a bunch of + + + align:start position:0% +left tbj we've replicated a bunch of +times in the DM PFC we can't decode + + align:start position:0% +times in the DM PFC we can't decode + + + align:start position:0% +times in the DM PFC we can't decode +modality or quality and but we can + + align:start position:0% +modality or quality and but we can + + + align:start position:0% +modality or quality and but we can +decode valence which is the thing I told + + align:start position:0% +decode valence which is the thing I told + + + align:start position:0% +decode valence which is the thing I told +you the right TPJ doesn't decode and + + align:start position:0% +you the right TPJ doesn't decode and + + + align:start position:0% +you the right TPJ doesn't decode and +then if we go back and look at valence + + align:start position:0% +then if we go back and look at valence + + + align:start position:0% +then if we go back and look at valence +in this data set and we can only decode + + align:start position:0% +in this data set and we can only decode + + + align:start position:0% +in this data set and we can only decode +valence in the DM PFC so this is to me + + align:start position:0% +valence in the DM PFC so this is to me + + + align:start position:0% +valence in the DM PFC so this is to me +this is starting to get cool right three + + align:start position:0% +this is starting to get cool right three + + + align:start position:0% +this is starting to get cool right three +features of other people's mental states + + align:start position:0% +features of other people's mental states + + + align:start position:0% +features of other people's mental states +represented differentially in different + + align:start position:0% +represented differentially in different + + + align:start position:0% +represented differentially in different +brain regions this distinction between + + align:start position:0% +brain regions this distinction between + + + align:start position:0% +brain regions this distinction between +the more epistemic staff like modality + + align:start position:0% +the more epistemic staff like modality + + + align:start position:0% +the more epistemic staff like modality +and quality which is represented in the + + align:start position:0% +and quality which is represented in the + + + align:start position:0% +and quality which is represented in the +TPJ and valence which is represented in + + align:start position:0% +TPJ and valence which is represented in + + + align:start position:0% +TPJ and valence which is represented in +the DM PFC I think is real and deep and + + align:start position:0% +the DM PFC I think is real and deep and + + + align:start position:0% +the DM PFC I think is real and deep and +hints at one of the really most + + align:start position:0% +hints at one of the really most + + + align:start position:0% +hints at one of the really most +important distinctions within Arthur is + + align:start position:0% +important distinctions within Arthur is + + + align:start position:0% +important distinctions within Arthur is +mind that I mentioned at the very + + align:start position:0% +mind that I mentioned at the very + + + align:start position:0% +mind that I mentioned at the very +beginning between epistemic States and + + align:start position:0% +beginning between epistemic States and + + + align:start position:0% +beginning between epistemic States and +affective or motivational States so + + align:start position:0% +affective or motivational States so + + + align:start position:0% +affective or motivational States so +what's cool about classification + + align:start position:0% +what's cool about classification + + + align:start position:0% +what's cool about classification +analyses they have all the same + + align:start position:0% +analyses they have all the same + + + align:start position:0% +analyses they have all the same +properties as the Haxby style analyses + + align:start position:0% +properties as the Haxby style analyses + + + align:start position:0% +properties as the Haxby style analyses +in principle and because they're + + align:start position:0% +in principle and because they're + + + align:start position:0% +in principle and because they're +actually just a generalization of the + + align:start position:0% +actually just a generalization of the + + + align:start position:0% +actually just a generalization of the +hex B analysis and except that there are + + align:start position:0% +hex B analysis and except that there are + + + align:start position:0% +hex B analysis and except that there are +a lot less robust and because what + + align:start position:0% +a lot less robust and because what + + + align:start position:0% +a lot less robust and because what +you're trying to classify is single + + align:start position:0% +you're trying to classify is single + + + align:start position:0% +you're trying to classify is single +trials or single items and so noisy data + + align:start position:0% +trials or single items and so noisy data + + + align:start position:0% +trials or single items and so noisy data +collapses faster in these classification + + align:start position:0% +collapses faster in these classification + + + align:start position:0% +collapses faster in these classification +strategies than in Haxby style analysis + + align:start position:0% +strategies than in Haxby style analysis + + + align:start position:0% +strategies than in Haxby style analysis +for your averaging but otherwise those + + align:start position:0% +for your averaging but otherwise those + + + align:start position:0% +for your averaging but otherwise those +are the same two techniques what's nice + + align:start position:0% +are the same two techniques what's nice + + + align:start position:0% +are the same two techniques what's nice +about the classification analysis is you + + align:start position:0% +about the classification analysis is you + + + align:start position:0% +about the classification analysis is you +can get items specific outcomes right so + + align:start position:0% +can get items specific outcomes right so + + + align:start position:0% +can get items specific outcomes right so +you can say for a specific item I have + + align:start position:0% +you can say for a specific item I have + + + align:start position:0% +you can say for a specific item I have +how likely it is to be classified as one + + align:start position:0% +how likely it is to be classified as one + + + align:start position:0% +how likely it is to be classified as one +thing or another and this is where I + + align:start position:0% +thing or another and this is where I + + + align:start position:0% +thing or another and this is where I +started the talk before which is that in + + align:start position:0% +started the talk before which is that in + + + align:start position:0% +started the talk before which is that in +both of these cases we think of a + + align:start position:0% +both of these cases we think of a + + + align:start position:0% +both of these cases we think of a +hypothesis and test it sequentially and + + align:start position:0% +hypothesis and test it sequentially and + + + align:start position:0% +hypothesis and test it sequentially and +so the the representational similarity + + align:start position:0% +so the the representational similarity + + + align:start position:0% +so the the representational similarity +matrix has those tests whole hypothesis + + align:start position:0% +matrix has those tests whole hypothesis + + + align:start position:0% +matrix has those tests whole hypothesis +spaces instead of single features + + align:start position:0% +spaces instead of single features + + + align:start position:0% +spaces instead of single features +classification and Haxby + + align:start position:0% +classification and Haxby + + + align:start position:0% +classification and Haxby +style staff are ways to think of a + + align:start position:0% +style staff are ways to think of a + + + align:start position:0% +style staff are ways to think of a +feature or dimension that might be + + align:start position:0% +feature or dimension that might be + + + align:start position:0% +feature or dimension that might be +represented in a brain region you care + + align:start position:0% +represented in a brain region you care + + + align:start position:0% +represented in a brain region you care +about and test whether or not it's + + align:start position:0% +about and test whether or not it's + + + align:start position:0% +about and test whether or not it's +represented so there are way of thinking + + align:start position:0% +represented so there are way of thinking + + + align:start position:0% +represented so there are way of thinking +of a hypothesis and testing it and + + align:start position:0% +of a hypothesis and testing it and + + + align:start position:0% +of a hypothesis and testing it and +thinking of a hypothesis and testing it + + align:start position:0% +thinking of a hypothesis and testing it + + + align:start position:0% +thinking of a hypothesis and testing it +and that's what I mean by sequentially + + align:start position:0% +and that's what I mean by sequentially + + + align:start position:0% +and that's what I mean by sequentially +so you can think of it does the right + + align:start position:0% +so you can think of it does the right + + + align:start position:0% +so you can think of it does the right +TPJ represent the difference for example + + align:start position:0% +TPJ represent the difference for example + + + align:start position:0% +TPJ represent the difference for example +between Grace poisoning the person + + align:start position:0% +between Grace poisoning the person + + + align:start position:0% +between Grace poisoning the person +knowingly and poisoning the person + + align:start position:0% +knowingly and poisoning the person + + + align:start position:0% +knowingly and poisoning the person +unknowingly the answer to that is yes it + + align:start position:0% +unknowingly the answer to that is yes it + + + align:start position:0% +unknowingly the answer to that is yes it +does and but that's one hypothesis and + + align:start position:0% +does and but that's one hypothesis and + + + align:start position:0% +does and but that's one hypothesis and +then we could come up with another + + align:start position:0% +then we could come up with another + + + align:start position:0% +then we could come up with another +hypothesis and then another hypothesis + + align:start position:0% +hypothesis and then another hypothesis + + + align:start position:0% +hypothesis and then another hypothesis +and what's interesting about + + align:start position:0% +and what's interesting about + + + align:start position:0% +and what's interesting about +representational dissimilarity matrices + + align:start position:0% +representational dissimilarity matrices + + + align:start position:0% +representational dissimilarity matrices +one of the versions of MVP people use + + align:start position:0% +one of the versions of MVP people use + + + align:start position:0% +one of the versions of MVP people use +these days is that it takes a different + + align:start position:0% +these days is that it takes a different + + + align:start position:0% +these days is that it takes a different +approach so instead of trying to think + + align:start position:0% +approach so instead of trying to think + + + align:start position:0% +approach so instead of trying to think +of one hypothesis and test it it + + align:start position:0% +of one hypothesis and test it it + + + align:start position:0% +of one hypothesis and test it it +proposes a hypothesis space and test the + + align:start position:0% +proposes a hypothesis space and test the + + + align:start position:0% +proposes a hypothesis space and test the +space as a whole and that gives you both + + align:start position:0% +space as a whole and that gives you both + + + align:start position:0% +space as a whole and that gives you both +different sensitivity and strengths and + + align:start position:0% +different sensitivity and strengths and + + + align:start position:0% +different sensitivity and strengths and +different weaknesses and so I'll work + + align:start position:0% +different weaknesses and so I'll work + + + align:start position:0% +different weaknesses and so I'll work +through an example in which we did this + + align:start position:0% +through an example in which we did this + + + align:start position:0% +through an example in which we did this +and so here's I told you that I would + + align:start position:0% +and so here's I told you that I would + + + align:start position:0% +and so here's I told you that I would +come back to thinking about other + + align:start position:0% +come back to thinking about other + + + align:start position:0% +come back to thinking about other +people's feelings and in this experiment + + align:start position:0% +people's feelings and in this experiment + + + align:start position:0% +people's feelings and in this experiment +we took different kinds of things that + + align:start position:0% +we took different kinds of things that + + + align:start position:0% +we took different kinds of things that +people could feel as one subspace of + + align:start position:0% +people could feel as one subspace of + + + align:start position:0% +people could feel as one subspace of +theory of mind + + align:start position:0% +theory of mind + + + align:start position:0% +theory of mind +so our stimuli in this case are 200 + + align:start position:0% +so our stimuli in this case are 200 + + + align:start position:0% +so our stimuli in this case are 200 +stories about people having an emotional + + align:start position:0% +stories about people having an emotional + + + align:start position:0% +stories about people having an emotional +experience and we're gonna look at what + + align:start position:0% +experience and we're gonna look at what + + + align:start position:0% +experience and we're gonna look at what +can we understand about how your brain + + align:start position:0% +can we understand about how your brain + + + align:start position:0% +can we understand about how your brain +represents those different your + + align:start position:0% +represents those different your + + + align:start position:0% +represents those different your +knowledge that lets you sort out and + + align:start position:0% +knowledge that lets you sort out and + + + align:start position:0% +knowledge that lets you sort out and +people's experiences in those cases okay + + align:start position:0% +people's experiences in those cases okay + + + align:start position:0% +people's experiences in those cases okay +this is hard in the abstract let's do it + + align:start position:0% +this is hard in the abstract let's do it + + + align:start position:0% +this is hard in the abstract let's do it +in the concrete so I'm in the behavioral + + align:start position:0% +in the concrete so I'm in the behavioral + + + align:start position:0% +in the concrete so I'm in the behavioral +version of this task I give you a list + + align:start position:0% +version of this task I give you a list + + + align:start position:0% +version of this task I give you a list +of 20 different emotions jealous + + align:start position:0% +of 20 different emotions jealous + + + align:start position:0% +of 20 different emotions jealous +disappointed devastated embarrassed + + align:start position:0% +disappointed devastated embarrassed + + + align:start position:0% +disappointed devastated embarrassed +disgusted guilty impressed proud excited + + align:start position:0% +disgusted guilty impressed proud excited + + + align:start position:0% +disgusted guilty impressed proud excited +hopeful joyful accept Rach + + align:start position:0% +hopeful joyful accept Rach + + + align:start position:0% +hopeful joyful accept Rach +okay so you have 20 different choices + + align:start position:0% +okay so you have 20 different choices + + + align:start position:0% +okay so you have 20 different choices +and I'm gonna tell you a single story + + align:start position:0% +and I'm gonna tell you a single story + + + align:start position:0% +and I'm gonna tell you a single story +about a character you don't know and + + align:start position:0% +about a character you don't know and + + + align:start position:0% +about a character you don't know and +something they experienced very briefly + + align:start position:0% +something they experienced very briefly + + + align:start position:0% +something they experienced very briefly +and what I want you to think to yourself + + align:start position:0% +and what I want you to think to yourself + + + align:start position:0% +and what I want you to think to yourself +is which emotion did they experience in + + align:start position:0% +is which emotion did they experience in + + + align:start position:0% +is which emotion did they experience in +that case okay so here's one after an 18 + + align:start position:0% +that case okay so here's one after an 18 + + + align:start position:0% +that case okay so here's one after an 18 +hour flight + + align:start position:0% +hour flight + + + align:start position:0% +hour flight +Alice arrived in her vacation + + align:start position:0% +Alice arrived in her vacation + + + align:start position:0% +Alice arrived in her vacation +destination to learn that her baggage + + align:start position:0% +destination to learn that her baggage + + + align:start position:0% +destination to learn that her baggage +including camping gear for her trip + + align:start position:0% +including camping gear for her trip + + + align:start position:0% +including camping gear for her trip +hadn't made the flight after waiting at + + align:start position:0% +hadn't made the flight after waiting at + + + align:start position:0% +hadn't made the flight after waiting at +the airport for two nights she was + + align:start position:0% +the airport for two nights she was + + + align:start position:0% +the airport for two nights she was +informed that the airline had lost her + + align:start position:0% +informed that the airline had lost her + + + align:start position:0% +informed that the airline had lost her +luggage and wouldn't provide any + + align:start position:0% +luggage and wouldn't provide any + + + align:start position:0% +luggage and wouldn't provide any +compensation how many people think she + + align:start position:0% +compensation how many people think she + + + align:start position:0% +compensation how many people think she +felt joyful how many people think that + + align:start position:0% +felt joyful how many people think that + + + align:start position:0% +felt joyful how many people think that +she felt + + align:start position:0% +she felt + + + align:start position:0% +she felt +annoyed + + align:start position:0% + + + + align:start position:0% + +how about furious okay + + align:start position:0% +how about furious okay + + + align:start position:0% +how about furious okay +so furious is the modal answer and + + align:start position:0% +so furious is the modal answer and + + + align:start position:0% +so furious is the modal answer and +annoyed is the most likely second choice + + align:start position:0% +annoyed is the most likely second choice + + + align:start position:0% +annoyed is the most likely second choice +answer to that case and here's a + + align:start position:0% +answer to that case and here's a + + + align:start position:0% +answer to that case and here's a +different one Sara swore to her roommate + + align:start position:0% +different one Sara swore to her roommate + + + align:start position:0% +different one Sara swore to her roommate +that she would keep her new diet later + + align:start position:0% +that she would keep her new diet later + + + align:start position:0% +that she would keep her new diet later +she was in the kitchen she took a bite + + align:start position:0% +she was in the kitchen she took a bite + + + align:start position:0% +she was in the kitchen she took a bite +of a cake she bought for the dinner + + align:start position:0% +of a cake she bought for the dinner + + + align:start position:0% +of a cake she bought for the dinner +party when her roommates arrived home to + + align:start position:0% +party when her roommates arrived home to + + + align:start position:0% +party when her roommates arrived home to +find that she'd eaten half the cake and + + align:start position:0% +find that she'd eaten half the cake and + + + align:start position:0% +find that she'd eaten half the cake and +broken her diet how many people think + + align:start position:0% +broken her diet how many people think + + + align:start position:0% +broken her diet how many people think +that she would feel disgusted terrified + + align:start position:0% +that she would feel disgusted terrified + + + align:start position:0% +that she would feel disgusted terrified +embarrassed okay and just to give you a + + align:start position:0% +embarrassed okay and just to give you a + + + align:start position:0% +embarrassed okay and just to give you a +sense of how fine-grained your knowledge + + align:start position:0% +sense of how fine-grained your knowledge + + + align:start position:0% +sense of how fine-grained your knowledge +is in this case think about this + + align:start position:0% +is in this case think about this + + + align:start position:0% +is in this case think about this +difference in this case she swore she + + align:start position:0% +difference in this case she swore she + + + align:start position:0% +difference in this case she swore she +would keep her diet and then broke it + + align:start position:0% +would keep her diet and then broke it + + + align:start position:0% +would keep her diet and then broke it +right what about the difference between + + align:start position:0% +right what about the difference between + + + align:start position:0% +right what about the difference between +she first ate a cake and then swore she + + align:start position:0% +she first ate a cake and then swore she + + + align:start position:0% +she first ate a cake and then swore she +would keep her diet right that's a + + align:start position:0% +would keep her diet right that's a + + + align:start position:0% +would keep her diet right that's a +totally different texture to the story + + align:start position:0% +totally different texture to the story + + + align:start position:0% +totally different texture to the story +okay so we have incredibly fine-grained + + align:start position:0% +okay so we have incredibly fine-grained + + + align:start position:0% +okay so we have incredibly fine-grained +knowledge of how a description of a + + align:start position:0% +knowledge of how a description of a + + + align:start position:0% +knowledge of how a description of a +situation and predict an overall emotion + + align:start position:0% +situation and predict an overall emotion + + + align:start position:0% +situation and predict an overall emotion +um you can see that in a behavioral + + align:start position:0% +um you can see that in a behavioral + + + align:start position:0% +um you can see that in a behavioral +experiment so what I'm showing you here + + align:start position:0% +experiment so what I'm showing you here + + + align:start position:0% +experiment so what I'm showing you here +is on the y-axis the emotion that we + + align:start position:0% +is on the y-axis the emotion that we + + + align:start position:0% +is on the y-axis the emotion that we +intended when we wrote the story so 10 + + align:start position:0% +intended when we wrote the story so 10 + + + align:start position:0% +intended when we wrote the story so 10 +stories for each category for 200 + + align:start position:0% +stories for each category for 200 + + + align:start position:0% +stories for each category for 200 +stories on the x-axis is the percent of + + align:start position:0% +stories on the x-axis is the percent of + + + align:start position:0% +stories on the x-axis is the percent of +participants picking that label and so + + align:start position:0% +participants picking that label and so + + + align:start position:0% +participants picking that label and so +the first thing is that 65% of the time + + align:start position:0% +the first thing is that 65% of the time + + + align:start position:0% +the first thing is that 65% of the time +people pick the label we intend if + + align:start position:0% +people pick the label we intend if + + + align:start position:0% +people pick the label we intend if +instead you ask take half the subjects + + align:start position:0% +instead you ask take half the subjects + + + align:start position:0% +instead you ask take half the subjects +to determine a modal answer and the + + align:start position:0% +to determine a modal answer and the + + + align:start position:0% +to determine a modal answer and the +other half the subjects as the test set + + align:start position:0% +other half the subjects as the test set + + + align:start position:0% +other half the subjects as the test set +you get the same answer there's a spot + + align:start position:0% +you get the same answer there's a spot + + + align:start position:0% +you get the same answer there's a spot +65% agreement on the right single label + + align:start position:0% +65% agreement on the right single label + + + align:start position:0% +65% agreement on the right single label +out of 20 that's of course way above + + align:start position:0% +out of 20 that's of course way above + + + align:start position:0% +out of 20 that's of course way above +chance which is 5% so people are quite + + align:start position:0% +chance which is 5% so people are quite + + + align:start position:0% +chance which is 5% so people are quite +good at this and the off-diagonal is + + align:start position:0% +good at this and the off-diagonal is + + + align:start position:0% +good at this and the off-diagonal is +also meaningful so that also contains + + align:start position:0% +also meaningful so that also contains + + + align:start position:0% +also meaningful so that also contains +information the second best answer right + + align:start position:0% +information the second best answer right + + + align:start position:0% +information the second best answer right +so annoyed as opposed to furious for + + align:start position:0% +so annoyed as opposed to furious for + + + align:start position:0% +so annoyed as opposed to furious for +example okay so that's a huge amount of + + align:start position:0% +example okay so that's a huge amount of + + + align:start position:0% +example okay so that's a huge amount of +rich knowledge other people's + + align:start position:0% +rich knowledge other people's + + + align:start position:0% +rich knowledge other people's +experiences from these very brief + + align:start position:0% +experiences from these very brief + + + align:start position:0% +experiences from these very brief +descriptions of events to a very + + align:start position:0% +descriptions of events to a very + + + align:start position:0% +descriptions of events to a very +fine-grained classification of which + + align:start position:0% +fine-grained classification of which + + + align:start position:0% +fine-grained classification of which +emotion they're experiencing and one way + + align:start position:0% +emotion they're experiencing and one way + + + align:start position:0% +emotion they're experiencing and one way +to look at these data is to ask okay + + align:start position:0% +to look at these data is to ask okay + + + align:start position:0% +to look at these data is to ask okay +well that's knowledge that we have and + + align:start position:0% +well that's knowledge that we have and + + + align:start position:0% +well that's knowledge that we have and +where is that knowledge in the brain + + align:start position:0% +where is that knowledge in the brain + + + align:start position:0% +where is that knowledge in the brain +right that's sort of a first question + + align:start position:0% +right that's sort of a first question + + + align:start position:0% +right that's sort of a first question +you could ask and you could ask it by + + align:start position:0% +you could ask and you could ask it by + + + align:start position:0% +you could ask and you could ask it by +just saying and if we try to use so in + + align:start position:0% +just saying and if we try to use so in + + + align:start position:0% +just saying and if we try to use so in +this case we're gonna do trained and + + align:start position:0% +this case we're gonna do trained and + + + align:start position:0% +this case we're gonna do trained and +tacit so we train a classifier on a + + align:start position:0% +tacit so we train a classifier on a + + + align:start position:0% +tacit so we train a classifier on a +patch of cortex based on five examples + + align:start position:0% +patch of cortex based on five examples + + + align:start position:0% +patch of cortex based on five examples +from each condition and then we test on + + align:start position:0% +from each condition and then we test on + + + align:start position:0% +from each condition and then we test on +the remaining half of the data and we + + align:start position:0% +the remaining half of the data and we + + + align:start position:0% +the remaining half of the data and we +just ask based on the pattern of + + align:start position:0% +just ask based on the pattern of + + + align:start position:0% +just ask based on the pattern of +activity in a patch can you get above + + align:start position:0% +activity in a patch can you get above + + + align:start position:0% +activity in a patch can you get above +chance classification in the independent + + align:start position:0% +chance classification in the independent + + + align:start position:0% +chance classification in the independent +data and for every voxel where for every + + align:start position:0% +data and for every voxel where for every + + + align:start position:0% +data and for every voxel where for every +patch where that's true we put a sort of + + align:start position:0% +patch where that's true we put a sort of + + + align:start position:0% +patch where that's true we put a sort of +bright mark and then a square in the + + align:start position:0% +bright mark and then a square in the + + + align:start position:0% +bright mark and then a square in the +brain is they're relevant decoding that + + align:start position:0% +brain is they're relevant decoding that + + + align:start position:0% +brain is they're relevant decoding that +would let you be above chance on this + + align:start position:0% +would let you be above chance on this + + + align:start position:0% +would let you be above chance on this +distinction and the answer is in exactly + + align:start position:0% +distinction and the answer is in exactly + + + align:start position:0% +distinction and the answer is in exactly +the same brain regions that I have been + + align:start position:0% +the same brain regions that I have been + + + align:start position:0% +the same brain regions that I have been +talking about and showed you because + + align:start position:0% +talking about and showed you because + + + align:start position:0% +talking about and showed you because +where there's above chance of + + align:start position:0% +where there's above chance of + + + align:start position:0% +where there's above chance of +classification and then overlaid on the + + align:start position:0% +classification and then overlaid on the + + + align:start position:0% +classification and then overlaid on the +standard belief versus photo + + align:start position:0% +standard belief versus photo + + + align:start position:0% +standard belief versus photo +task in green so within the brain + + align:start position:0% +task in green so within the brain + + + align:start position:0% +task in green so within the brain +regions involved in theory of mind or + + align:start position:0% +regions involved in theory of mind or + + + align:start position:0% +regions involved in theory of mind or +social cognition are the brain regions + + align:start position:0% +social cognition are the brain regions + + + align:start position:0% +social cognition are the brain regions +that can above chance classify in this + + align:start position:0% +that can above chance classify in this + + + align:start position:0% +that can above chance classify in this +twenty way distinction and then this is + + align:start position:0% +twenty way distinction and then this is + + + align:start position:0% +twenty way distinction and then this is +just looking inside each one of those + + align:start position:0% +just looking inside each one of those + + + align:start position:0% +just looking inside each one of those +inside each of the regions that's four + + align:start position:0% +inside each of the regions that's four + + + align:start position:0% +inside each of the regions that's four +of the regions in that group that I + + align:start position:0% +of the regions in that group that I + + + align:start position:0% +of the regions in that group that I +showed you before there you can do above + + align:start position:0% +showed you before there you can do above + + + align:start position:0% +showed you before there you can do above +with using just the pattern of activity + + align:start position:0% +with using just the pattern of activity + + + align:start position:0% +with using just the pattern of activity +in that brain region you can do above + + align:start position:0% +in that brain region you can do above + + + align:start position:0% +in that brain region you can do above +chance classification on this twenty way + + align:start position:0% +chance classification on this twenty way + + + align:start position:0% +chance classification on this twenty way +distinction and there's a hint that that + + align:start position:0% +distinction and there's a hint that that + + + align:start position:0% +distinction and there's a hint that that +information is somewhat non redundant + + align:start position:0% +information is somewhat non redundant + + + align:start position:0% +information is somewhat non redundant +because if you combine information + + align:start position:0% +because if you combine information + + + align:start position:0% +because if you combine information +across all of them you do slightly then + + align:start position:0% +across all of them you do slightly then + + + align:start position:0% +across all of them you do slightly then +if you use any one of them alone okay so + + align:start position:0% +if you use any one of them alone okay so + + + align:start position:0% +if you use any one of them alone okay so +now the question is how can we study + + align:start position:0% +now the question is how can we study + + + align:start position:0% +now the question is how can we study +what knowledge is represented in each of + + align:start position:0% +what knowledge is represented in each of + + + align:start position:0% +what knowledge is represented in each of +these brain regions right so we know + + align:start position:0% +these brain regions right so we know + + + align:start position:0% +these brain regions right so we know +that there's some information about that + + align:start position:0% +that there's some information about that + + + align:start position:0% +that there's some information about that +2008 classification but can we learn + + align:start position:0% +2008 classification but can we learn + + + align:start position:0% +2008 classification but can we learn +anything about the representation of + + align:start position:0% +anything about the representation of + + + align:start position:0% +anything about the representation of +emotions in those brain regions using + + align:start position:0% +emotions in those brain regions using + + + align:start position:0% +emotions in those brain regions using +fMRI and that's a representation to + + align:start position:0% +fMRI and that's a representation to + + + align:start position:0% +fMRI and that's a representation to +similarity matrices come in as a + + align:start position:0% +similarity matrices come in as a + + + align:start position:0% +similarity matrices come in as a +strategy okay so the question is how + + align:start position:0% +strategy okay so the question is how + + + align:start position:0% +strategy okay so the question is how +might you represent the knowledge that + + align:start position:0% +might you represent the knowledge that + + + align:start position:0% +might you represent the knowledge that +you have of what Alice is experiencing + + align:start position:0% +you have of what Alice is experiencing + + + align:start position:0% +you have of what Alice is experiencing +for example in this story what's a + + align:start position:0% +for example in this story what's a + + + align:start position:0% +for example in this story what's a +possible hypothesis and and the way + + align:start position:0% +possible hypothesis and and the way + + + align:start position:0% +possible hypothesis and and the way +representational dissimilarity matrices + + align:start position:0% +representational dissimilarity matrices + + + align:start position:0% +representational dissimilarity matrices +work as a strategy for my analysis is + + align:start position:0% +work as a strategy for my analysis is + + + align:start position:0% +work as a strategy for my analysis is +that what you should do is think of + + align:start position:0% +that what you should do is think of + + + align:start position:0% +that what you should do is think of +multiple different hypotheses about how + + align:start position:0% +multiple different hypotheses about how + + + align:start position:0% +multiple different hypotheses about how +that knowledge could be represented and + + align:start position:0% +that knowledge could be represented and + + + align:start position:0% +that knowledge could be represented and +so a first hypothesis and which is deep + + align:start position:0% +so a first hypothesis and which is deep + + + align:start position:0% +so a first hypothesis and which is deep +in the literature on emotions is that we + + align:start position:0% +in the literature on emotions is that we + + + align:start position:0% +in the literature on emotions is that we +represent it we represent other people + + align:start position:0% +represent it we represent other people + + + align:start position:0% +represent it we represent other people +France + + align:start position:0% +France + + + align:start position:0% +France +in terms of two fundamental dimensions + + align:start position:0% +in terms of two fundamental dimensions + + + align:start position:0% +in terms of two fundamental dimensions +of emotional experience valence and + + align:start position:0% +of emotional experience valence and + + + align:start position:0% +of emotional experience valence and +arousal have you guys heard of valence + + align:start position:0% +arousal have you guys heard of valence + + + align:start position:0% +arousal have you guys heard of valence +and arousal as the two fundamental okay + + align:start position:0% +and arousal as the two fundamental okay + + + align:start position:0% +and arousal as the two fundamental okay +so there this hypothesis says when we + + align:start position:0% +so there this hypothesis says when we + + + align:start position:0% +so there this hypothesis says when we +think about emotions our own or other + + align:start position:0% +think about emotions our own or other + + + align:start position:0% +think about emotions our own or other +people we put emotions in a two + + align:start position:0% +people we put emotions in a two + + + align:start position:0% +people we put emotions in a two +dimensional space which is how good or + + align:start position:0% +dimensional space which is how good or + + + align:start position:0% +dimensional space which is how good or +bad did it make you feel how intense was + + align:start position:0% +bad did it make you feel how intense was + + + align:start position:0% +bad did it make you feel how intense was +it okay so terrified is negative and + + align:start position:0% +it okay so terrified is negative and + + + align:start position:0% +it okay so terrified is negative and +very intense lonely is negative but not + + align:start position:0% +very intense lonely is negative but not + + + align:start position:0% +very intense lonely is negative but not +that intense right that's the idea and + + align:start position:0% +that intense right that's the idea and + + + align:start position:0% +that intense right that's the idea and +happy is positive and somewhat intense + + align:start position:0% +happy is positive and somewhat intense + + + align:start position:0% +happy is positive and somewhat intense +thrilled is happy and more intense okay + + align:start position:0% +thrilled is happy and more intense okay + + + align:start position:0% +thrilled is happy and more intense okay +so that the idea is that there's these + + align:start position:0% +so that the idea is that there's these + + + align:start position:0% +so that the idea is that there's these +two basic dimensions of emotional + + align:start position:0% +two basic dimensions of emotional + + + align:start position:0% +two basic dimensions of emotional +experience and so one thing we can do is + + align:start position:0% +experience and so one thing we can do is + + + align:start position:0% +experience and so one thing we can do is +have each of our stories like this one + + align:start position:0% +have each of our stories like this one + + + align:start position:0% +have each of our stories like this one +we can have people tell us in that story + + align:start position:0% +we can have people tell us in that story + + + align:start position:0% +we can have people tell us in that story +was she feeling positive or negative how + + align:start position:0% +was she feeling positive or negative how + + + align:start position:0% +was she feeling positive or negative how +positive or negative and how intensely + + align:start position:0% +positive or negative and how intensely + + + align:start position:0% +positive or negative and how intensely +and so for each individual story we can + + align:start position:0% +and so for each individual story we can + + + align:start position:0% +and so for each individual story we can +have a representation of it as a point + + align:start position:0% +have a representation of it as a point + + + align:start position:0% +have a representation of it as a point +in that space and if you use just that + + align:start position:0% +in that space and if you use just that + + + align:start position:0% +in that space and if you use just that +you can classify our 200 stories + + align:start position:0% +you can classify our 200 stories + + + align:start position:0% +you can classify our 200 stories +reasonably well not as well as people + + align:start position:0% +reasonably well not as well as people + + + align:start position:0% +reasonably well not as well as people +can but still reasonably well okay so + + align:start position:0% +can but still reasonably well okay so + + + align:start position:0% +can but still reasonably well okay so +the 200 stories do clump into lumps in + + align:start position:0% +the 200 stories do clump into lumps in + + + align:start position:0% +the 200 stories do clump into lumps in +that two-dimensional space but another + + align:start position:0% +that two-dimensional space but another + + + align:start position:0% +that two-dimensional space but another +idea is that an valence and arousal seem + + align:start position:0% +idea is that an valence and arousal seem + + + align:start position:0% +idea is that an valence and arousal seem +not to capture the full texture of the + + align:start position:0% +not to capture the full texture of the + + + align:start position:0% +not to capture the full texture of the +20 dimensional the twenty categories + + align:start position:0% +20 dimensional the twenty categories + + + align:start position:0% +20 dimensional the twenty categories +that we urgently have it's not panted + + align:start position:0% +that we urgently have it's not panted + + + align:start position:0% +that we urgently have it's not panted +bed twenty categories and two dimensions + + align:start position:0% +bed twenty categories and two dimensions + + + align:start position:0% +bed twenty categories and two dimensions +you obviously can have twenty clusters + + align:start position:0% +you obviously can have twenty clusters + + + align:start position:0% +you obviously can have twenty clusters +in a two-dimensional space + + align:start position:0% +in a two-dimensional space + + + align:start position:0% +in a two-dimensional space +and but we have been tuition that it's + + align:start position:0% +and but we have been tuition that it's + + + align:start position:0% +and but we have been tuition that it's +not a two dimensional space that those + + align:start position:0% +not a two dimensional space that those + + + align:start position:0% +not a two dimensional space that those +two dimensions don't capture all the + + align:start position:0% +two dimensions don't capture all the + + + align:start position:0% +two dimensions don't capture all the +features that people have and know about + + align:start position:0% +features that people have and know about + + + align:start position:0% +features that people have and know about +when they use these stimuli and so based + + align:start position:0% +when they use these stimuli and so based + + + align:start position:0% +when they use these stimuli and so based +on another literature called appraisal + + align:start position:0% +on another literature called appraisal + + + align:start position:0% +on another literature called appraisal +theory what we try to do is is capture + + align:start position:0% +theory what we try to do is is capture + + + align:start position:0% +theory what we try to do is is capture +some of the abstract knowledge that + + align:start position:0% +some of the abstract knowledge that + + + align:start position:0% +some of the abstract knowledge that +people have about these situations that + + align:start position:0% +people have about these situations that + + + align:start position:0% +people have about these situations that +lets them identify which emotion it is + + align:start position:0% +lets them identify which emotion it is + + + align:start position:0% +lets them identify which emotion it is +okay and we did that by having them rate + + align:start position:0% +okay and we did that by having them rate + + + align:start position:0% +okay and we did that by having them rate +each of these stories on a bunch of + + align:start position:0% +each of these stories on a bunch of + + + align:start position:0% +each of these stories on a bunch of +abstract event features so those event + + align:start position:0% +abstract event features so those event + + + align:start position:0% +abstract event features so those event +features are things like was this + + align:start position:0% +features are things like was this + + + align:start position:0% +features are things like was this +situation caused by a person or some + + align:start position:0% +situation caused by a person or some + + + align:start position:0% +situation caused by a person or some +other so I hope you guys have the sense + + align:start position:0% +other so I hope you guys have the sense + + + align:start position:0% +other so I hope you guys have the sense +that if your luggage gets lost on your + + align:start position:0% +that if your luggage gets lost on your + + + align:start position:0% +that if your luggage gets lost on your +way to the trip it's different if that + + align:start position:0% +way to the trip it's different if that + + + align:start position:0% +way to the trip it's different if that +was airline incompetence versus a + + align:start position:0% +was airline incompetence versus a + + + align:start position:0% +was airline incompetence versus a +tornado right does everybody have that + + align:start position:0% +tornado right does everybody have that + + + align:start position:0% +tornado right does everybody have that +intuition the emotion is different okay + + align:start position:0% +intuition the emotion is different okay + + + align:start position:0% +intuition the emotion is different okay +so that's an important abstract feature + + align:start position:0% +so that's an important abstract feature + + + align:start position:0% +so that's an important abstract feature +of our knowledge of other people was it + + align:start position:0% +of our knowledge of other people was it + + + align:start position:0% +of our knowledge of other people was it +caused by you your + + align:start position:0% +caused by you your + + + align:start position:0% +caused by you your +Souths if you left your luggage at home + + align:start position:0% +Souths if you left your luggage at home + + + align:start position:0% +Souths if you left your luggage at home +that's different from if airline + + align:start position:0% +that's different from if airline + + + align:start position:0% +that's different from if airline +incompetence caused you not to have her + + align:start position:0% +incompetence caused you not to have her + + + align:start position:0% +incompetence caused you not to have her +luggage and does it refer to something + + align:start position:0% +luggage and does it refer to something + + + align:start position:0% +luggage and does it refer to something +in their past is she interacting with + + align:start position:0% +in their past is she interacting with + + + align:start position:0% +in their past is she interacting with +other people that makes a really big + + align:start position:0% +other people that makes a really big + + + align:start position:0% +other people that makes a really big +difference for example in Pride and + + align:start position:0% +difference for example in Pride and + + + align:start position:0% +difference for example in Pride and +embarrassment whether other people are + + align:start position:0% +embarrassment whether other people are + + + align:start position:0% +embarrassment whether other people are +around and how will it affect her future + + align:start position:0% +around and how will it affect her future + + + align:start position:0% +around and how will it affect her future +relationships so things that potentially + + align:start position:0% +relationships so things that potentially + + + align:start position:0% +relationships so things that potentially +cause harm to future relationships feel + + align:start position:0% +cause harm to future relationships feel + + + align:start position:0% +cause harm to future relationships feel +very different from things that are just + + align:start position:0% +very different from things that are just + + + align:start position:0% +very different from things that are just +annoying right now but will end okay so + + align:start position:0% +annoying right now but will end okay so + + + align:start position:0% +annoying right now but will end okay so +these are abstract features and they + + align:start position:0% +these are abstract features and they + + + align:start position:0% +these are abstract features and they +encapsulate things we know about emotion + + align:start position:0% +encapsulate things we know about emotion + + + align:start position:0% +encapsulate things we know about emotion +relevant features of the situations + + align:start position:0% +relevant features of the situations + + + align:start position:0% +relevant features of the situations +people find themselves in so we came up + + align:start position:0% +people find themselves in so we came up + + + align:start position:0% +people find themselves in so we came up +with 42 of these and we had every story + + align:start position:0% +with 42 of these and we had every story + + + align:start position:0% +with 42 of these and we had every story +rated on all of those dimensions and of + + align:start position:0% +rated on all of those dimensions and of + + + align:start position:0% +rated on all of those dimensions and of +course we can again classify the stories + + align:start position:0% +course we can again classify the stories + + + align:start position:0% +course we can again classify the stories +as 20 clusters in a 42 dimensional space + + align:start position:0% +as 20 clusters in a 42 dimensional space + + + align:start position:0% +as 20 clusters in a 42 dimensional space +right again of course we can and but the + + align:start position:0% +right again of course we can and but the + + + align:start position:0% +right again of course we can and but the +question is this is those data this is + + align:start position:0% +question is this is those data this is + + + align:start position:0% +question is this is those data this is +just every set of 10 stories and their + + align:start position:0% +just every set of 10 stories and their + + + align:start position:0% +just every set of 10 stories and their +average rating on our 38 on our 38 + + align:start position:0% +average rating on our 38 on our 38 + + + align:start position:0% +average rating on our 38 on our 38 +appraisal features so that creates a 38 + + align:start position:0% +appraisal features so that creates a 38 + + + align:start position:0% +appraisal features so that creates a 38 +dimensional space here the idea is for + + align:start position:0% +dimensional space here the idea is for + + + align:start position:0% +dimensional space here the idea is for +each category right like for all the + + align:start position:0% +each category right like for all the + + + align:start position:0% +each category right like for all the +stories about being jealous you can get + + align:start position:0% +stories about being jealous you can get + + + align:start position:0% +stories about being jealous you can get +for let's say for the two dimensions of + + align:start position:0% +for let's say for the two dimensions of + + + align:start position:0% +for let's say for the two dimensions of +valence and arousal the average value of + + align:start position:0% +valence and arousal the average value of + + + align:start position:0% +valence and arousal the average value of +valence in the average value of arousal + + align:start position:0% +valence in the average value of arousal + + + align:start position:0% +valence in the average value of arousal +right so that's a point in a two + + align:start position:0% +right so that's a point in a two + + + align:start position:0% +right so that's a point in a two +dimensional space the stories about + + align:start position:0% +dimensional space the stories about + + + align:start position:0% +dimensional space the stories about +being jealous okay then you take the + + align:start position:0% +being jealous okay then you take the + + + align:start position:0% +being jealous okay then you take the +stories about being terrified what's + + align:start position:0% +stories about being terrified what's + + + align:start position:0% +stories about being terrified what's +their valence and arousal okay so that's + + align:start position:0% +their valence and arousal okay so that's + + + align:start position:0% +their valence and arousal okay so that's +another point in a two dimensional space + + align:start position:0% +another point in a two dimensional space + + + align:start position:0% +another point in a two dimensional space +and then you take the distance between + + align:start position:0% +and then you take the distance between + + + align:start position:0% +and then you take the distance between +them and that number goes in a + + align:start position:0% +them and that number goes in a + + + align:start position:0% +them and that number goes in a +representational dissimilarity matrix so + + align:start position:0% +representational dissimilarity matrix so + + + align:start position:0% +representational dissimilarity matrix so +the further away you are in a two + + align:start position:0% +the further away you are in a two + + + align:start position:0% +the further away you are in a two +dimensional space the more dissimilar + + align:start position:0% +dimensional space the more dissimilar + + + align:start position:0% +dimensional space the more dissimilar +and you could do the same thing in a + + align:start position:0% +and you could do the same thing in a + + + align:start position:0% +and you could do the same thing in a +forty two dimensional space that's 38 + + align:start position:0% +forty two dimensional space that's 38 + + + align:start position:0% +forty two dimensional space that's 38 +dimensional say Sandy's a dimensional + + align:start position:0% +dimensional say Sandy's a dimensional + + + align:start position:0% +dimensional say Sandy's a dimensional +space you want what you need to know is + + align:start position:0% +space you want what you need to know is + + + align:start position:0% +space you want what you need to know is +just how far away you are and so what a + + align:start position:0% +just how far away you are and so what a + + + align:start position:0% +just how far away you are and so what a +representational dissimilarity matrix + + align:start position:0% +representational dissimilarity matrix + + + align:start position:0% +representational dissimilarity matrix +has in it is for every pair so the + + align:start position:0% +has in it is for every pair so the + + + align:start position:0% +has in it is for every pair so the +jealous stories versus the grateful + + align:start position:0% +jealous stories versus the grateful + + + align:start position:0% +jealous stories versus the grateful +stories the number in that cell is the + + align:start position:0% +stories the number in that cell is the + + + align:start position:0% +stories the number in that cell is the +distance from the mean position in your + + align:start position:0% +distance from the mean position in your + + + align:start position:0% +distance from the mean position in your +space of all the jealous stories to the + + align:start position:0% +space of all the jealous stories to the + + + align:start position:0% +space of all the jealous stories to the +mean position in your space of all the + + align:start position:0% +mean position in your space of all the + + + align:start position:0% +mean position in your space of all the +grateful stories that make sense and + + align:start position:0% +grateful stories that make sense and + + + align:start position:0% +grateful stories that make sense and +that could be true of any dimensionality + + align:start position:0% +that could be true of any dimensionality + + + align:start position:0% +that could be true of any dimensionality +when you know these 38 features so this + + align:start position:0% +when you know these 38 features so this + + + align:start position:0% +when you know these 38 features so this +is behavioral data when you know the 38 + + align:start position:0% +is behavioral data when you know the 38 + + + align:start position:0% +is behavioral data when you know the 38 +features of these emotions the green bar + + align:start position:0% +features of these emotions the green bar + + + align:start position:0% +features of these emotions the green bar +is how well you can classify new items + + align:start position:0% +is how well you can classify new items + + + align:start position:0% +is how well you can classify new items +behaviorally so if I give you a new item + + align:start position:0% +behaviorally so if I give you a new item + + + align:start position:0% +behaviorally so if I give you a new item +and all I tell you is its value in these + + align:start position:0% +and all I tell you is its value in these + + + align:start position:0% +and all I tell you is its value in these +38 dimensions how well can you tell me + + align:start position:0% +38 dimensions how well can you tell me + + + align:start position:0% +38 dimensions how well can you tell me +back which emotion category comes from + + align:start position:0% +back which emotion category comes from + + + align:start position:0% +back which emotion category comes from +the best you could possibly do is 65% + + align:start position:0% +the best you could possibly do is 65% + + + align:start position:0% +the best you could possibly do is 65% +because that's what human observers do + + align:start position:0% +because that's what human observers do + + + align:start position:0% +because that's what human observers do +in all of our so the reality is the + + align:start position:0% +in all of our so the reality is the + + + align:start position:0% +in all of our so the reality is the +human observers the features come from + + align:start position:0% +human observers the features come from + + + align:start position:0% +human observers the features come from +human observers so our ceiling is going + + align:start position:0% +human observers so our ceiling is going + + + align:start position:0% +human observers so our ceiling is going +to be 65% and the answer is about 55% + + align:start position:0% +to be 65% and the answer is about 55% + + + align:start position:0% +to be 65% and the answer is about 55% +okay and you can take that in two + + align:start position:0% +okay and you can take that in two + + + align:start position:0% +okay and you can take that in two +different ways one tendency is to say + + align:start position:0% +different ways one tendency is to say + + + align:start position:0% +different ways one tendency is to say +wow we know a lot of the key features + + align:start position:0% +wow we know a lot of the key features + + + align:start position:0% +wow we know a lot of the key features +that go into emotion attribution I think + + align:start position:0% +that go into emotion attribution I think + + + align:start position:0% +that go into emotion attribution I think +Amy who I did this work with had a + + align:start position:0% +Amy who I did this work with had a + + + align:start position:0% +Amy who I did this work with had a +tendency to feel that way and I think + + align:start position:0% +tendency to feel that way and I think + + + align:start position:0% +tendency to feel that way and I think +wow we thought of 38 things and we still + + align:start position:0% +wow we thought of 38 things and we still + + + align:start position:0% +wow we thought of 38 things and we still +didn't think of all the important things + + align:start position:0% +didn't think of all the important things + + + align:start position:0% +didn't think of all the important things +like what are those other things that we + + align:start position:0% +like what are those other things that we + + + align:start position:0% +like what are those other things that we +didn't think of that explained the rest + + align:start position:0% +didn't think of that explained the rest + + + align:start position:0% +didn't think of that explained the rest +of the variation so you can feel either + + align:start position:0% +of the variation so you can feel either + + + align:start position:0% +of the variation so you can feel either +way about this but in any case once you + + align:start position:0% +way about this but in any case once you + + + align:start position:0% +way about this but in any case once you +know the position of one of these + + align:start position:0% +know the position of one of these + + + align:start position:0% +know the position of one of these +stories in the 38 dimensional space of + + align:start position:0% +stories in the 38 dimensional space of + + + align:start position:0% +stories in the 38 dimensional space of +these features you know a lot about + + align:start position:0% +these features you know a lot about + + + align:start position:0% +these features you know a lot about +which emotion category it came from and + + align:start position:0% +which emotion category it came from and + + + align:start position:0% +which emotion category it came from and +and then this is the correlation to the + + align:start position:0% +and then this is the correlation to the + + + align:start position:0% +and then this is the correlation to the +neural RDM data that I showed you and so + + align:start position:0% +neural RDM data that I showed you and so + + + align:start position:0% +neural RDM data that I showed you and so +again what I should do so observers + + align:start position:0% +again what I should do so observers + + + align:start position:0% +again what I should do so observers +knowledge that's everything that we know + + align:start position:0% +knowledge that's everything that we know + + + align:start position:0% +knowledge that's everything that we know +that lets us classify a story valence + + align:start position:0% +that lets us classify a story valence + + + align:start position:0% +that lets us classify a story valence +and arousal is the yellow bar that's + + align:start position:0% +and arousal is the yellow bar that's + + + align:start position:0% +and arousal is the yellow bar that's +just these two features of the story and + + align:start position:0% +just these two features of the story and + + + align:start position:0% +just these two features of the story and +they're both less good than this + + align:start position:0% +they're both less good than this + + + align:start position:0% +they're both less good than this +intermediate thing which is the 38 + + align:start position:0% +intermediate thing which is the 38 + + + align:start position:0% +intermediate thing which is the 38 +dimensional space and one question is + + align:start position:0% +dimensional space and one question is + + + align:start position:0% +dimensional space and one question is +like do I really think it's 38 + + align:start position:0% +like do I really think it's 38 + + + align:start position:0% +like do I really think it's 38 +dimensions no definitely not that was + + align:start position:0% +dimensions no definitely not that was + + + align:start position:0% +dimensions no definitely not that was +just the set of all the things that we + + align:start position:0% +just the set of all the things that we + + + align:start position:0% +just the set of all the things that we +could think of how many dimensions is + + align:start position:0% +could think of how many dimensions is + + + align:start position:0% +could think of how many dimensions is +that really again I don't I don't know + + align:start position:0% +that really again I don't I don't know + + + align:start position:0% +that really again I don't I don't know +really but I can tell you that the best + + align:start position:0% +really but I can tell you that the best + + + align:start position:0% +really but I can tell you that the best +10 dimensions capture most of the + + align:start position:0% +10 dimensions capture most of the + + + align:start position:0% +10 dimensions capture most of the +information from the 38 dimensions so + + align:start position:0% +information from the 38 dimensions so + + + align:start position:0% +information from the 38 dimensions so +what we've discovered so far is 10 + + align:start position:0% +what we've discovered so far is 10 + + + align:start position:0% +what we've discovered so far is 10 +really important dimensions of your + + align:start position:0% +really important dimensions of your + + + align:start position:0% +really important dimensions of your +knowledge of emotion + + align:start position:0% +knowledge of emotion + + + align:start position:0% +knowledge of emotion +I don't again think that means that our + + align:start position:0% +I don't again think that means that our + + + align:start position:0% +I don't again think that means that our +knowledge of emotion is 10 dimensional + + align:start position:0% +knowledge of emotion is 10 dimensional + + + align:start position:0% +knowledge of emotion is 10 dimensional +lots of this is limited by this set of + + align:start position:0% +lots of this is limited by this set of + + + align:start position:0% +lots of this is limited by this set of +stimuli that we chose the resolution of + + align:start position:0% +stimuli that we chose the resolution of + + + align:start position:0% +stimuli that we chose the resolution of +the data that we have and so forth and + + align:start position:0% +the data that we have and so forth and + + + align:start position:0% +the data that we have and so forth and +so on and but in these data you need + + align:start position:0% +so on and but in these data you need + + + align:start position:0% +so on and but in these data you need +something on the order of 10 dimensions + + align:start position:0% +something on the order of 10 dimensions + + + align:start position:0% +something on the order of 10 dimensions +to get close to human performance or + + align:start position:0% +to get close to human performance or + + + align:start position:0% +to get close to human performance or +close to and the nor that the genuinely + + align:start position:0% +close to and the nor that the genuinely + + + align:start position:0% +close to and the nor that the genuinely +differential signal in the neural data + + align:start position:0% +differential signal in the neural data + + + align:start position:0% +differential signal in the neural data +if you take one thing away from this + + align:start position:0% +if you take one thing away from this + + + align:start position:0% +if you take one thing away from this +talk about the methods used in + + align:start position:0% +talk about the methods used in + + + align:start position:0% +talk about the methods used in +representational dissimilarity matrix + + align:start position:0% +representational dissimilarity matrix + + + align:start position:0% +representational dissimilarity matrix +really only one thing there's the one + + align:start position:0% +really only one thing there's the one + + + align:start position:0% +really only one thing there's the one +thing I want you to know the + + align:start position:0% +thing I want you to know the + + + align:start position:0% +thing I want you to know the +dimensionality of the C + + align:start position:0% +dimensionality of the C + + + align:start position:0% +dimensionality of the C +that generated your representational + + align:start position:0% +that generated your representational + + + align:start position:0% +that generated your representational +dissimilarity matrix does nothing for + + align:start position:0% +dissimilarity matrix does nothing for + + + align:start position:0% +dissimilarity matrix does nothing for +you in the fit to your data nothing at + + align:start position:0% +you in the fit to your data nothing at + + + align:start position:0% +you in the fit to your data nothing at +all it's a parameter free fit okay so + + align:start position:0% +all it's a parameter free fit okay so + + + align:start position:0% +all it's a parameter free fit okay so +anybody who has two Mo's words mean + + align:start position:0% +anybody who has two Mo's words mean + + + align:start position:0% +anybody who has two Mo's words mean +anything this will be important so I + + align:start position:0% +anything this will be important so I + + + align:start position:0% +anything this will be important so I +want you to actually know this + + align:start position:0% +want you to actually know this + + + align:start position:0% +want you to actually know this +representational dissimilarity matrices + + align:start position:0% +representational dissimilarity matrices + + + align:start position:0% +representational dissimilarity matrices +provide a parameter free fit to the data + + align:start position:0% +provide a parameter free fit to the data + + + align:start position:0% +provide a parameter free fit to the data +and therefore the dimensionality of the + + align:start position:0% +and therefore the dimensionality of the + + + align:start position:0% +and therefore the dimensionality of the +theory that generated the + + align:start position:0% +theory that generated the + + + align:start position:0% +theory that generated the +representational similarity matrix has + + align:start position:0% +representational similarity matrix has + + + align:start position:0% +representational similarity matrix has +nothing to do with the fit of the data + + align:start position:0% +nothing to do with the fit of the data + + + align:start position:0% +nothing to do with the fit of the data +that you can probably notice I should + + align:start position:0% +that you can probably notice I should + + + align:start position:0% +that you can probably notice I should +have ordered this better valence has two + + align:start position:0% +have ordered this better valence has two + + + align:start position:0% +have ordered this better valence has two +dimensions the observer's has a lot of + + align:start position:0% +dimensions the observer's has a lot of + + + align:start position:0% +dimensions the observer's has a lot of +dimensions I don't know how many but a + + align:start position:0% +dimensions I don't know how many but a + + + align:start position:0% +dimensions I don't know how many but a +lot more than 38 we know that because 38 + + align:start position:0% +lot more than 38 we know that because 38 + + + align:start position:0% +lot more than 38 we know that because 38 +doesn't explain all their data okay so + + align:start position:0% +doesn't explain all their data okay so + + + align:start position:0% +doesn't explain all their data okay so +as you go up in and in principle having + + align:start position:0% +as you go up in and in principle having + + + align:start position:0% +as you go up in and in principle having +more dimensions doesn't help in the set + + align:start position:0% +more dimensions doesn't help in the set + + + align:start position:0% +more dimensions doesn't help in the set +you can correctly see that they over fit + + align:start position:0% +you can correctly see that they over fit + + + align:start position:0% +you can correctly see that they over fit +rather than fitting the data okay and + + align:start position:0% +rather than fitting the data okay and + + + align:start position:0% +rather than fitting the data okay and +here's why because the way you build a + + align:start position:0% +here's why because the way you build a + + + align:start position:0% +here's why because the way you build a +representational similarity matrix is + + align:start position:0% +representational similarity matrix is + + + align:start position:0% +representational similarity matrix is +out of no matter how many dimensions you + + align:start position:0% +out of no matter how many dimensions you + + + align:start position:0% +out of no matter how many dimensions you +have in your data set for every pair of + + align:start position:0% +have in your data set for every pair of + + + align:start position:0% +have in your data set for every pair of +stimuli you take one number and then a + + align:start position:0% +stimuli you take one number and then a + + + align:start position:0% +stimuli you take one number and then a +representational to similarity matrix + + align:start position:0% +representational to similarity matrix + + + align:start position:0% +representational to similarity matrix +encodes the relationships among those + + align:start position:0% +encodes the relationships among those + + + align:start position:0% +encodes the relationships among those +numbers okay so so jealousy is more + + align:start position:0% +numbers okay so so jealousy is more + + + align:start position:0% +numbers okay so so jealousy is more +similar to irritation than it is to + + align:start position:0% +similar to irritation than it is to + + + align:start position:0% +similar to irritation than it is to +pride by how much okay and there's + + align:start position:0% +pride by how much okay and there's + + + align:start position:0% +pride by how much okay and there's +relative differences is all you have you + + align:start position:0% +relative differences is all you have you + + + align:start position:0% +relative differences is all you have you +have nothing else and so there's no + + align:start position:0% +have nothing else and so there's no + + + align:start position:0% +have nothing else and so there's no +parameters right you have the same + + align:start position:0% +parameters right you have the same + + + align:start position:0% +parameters right you have the same +amount of information in a + + align:start position:0% +amount of information in a + + + align:start position:0% +amount of information in a +representational dissimilarity matrix + + align:start position:0% +representational dissimilarity matrix + + + align:start position:0% +representational dissimilarity matrix +that you generated from a one + + align:start position:0% +that you generated from a one + + + align:start position:0% +that you generated from a one +dimensional theory a two dimensional + + align:start position:0% +dimensional theory a two dimensional + + + align:start position:0% +dimensional theory a two dimensional +theory of 38 dimensional theory and an + + align:start position:0% +theory of 38 dimensional theory and an + + + align:start position:0% +theory of 38 dimensional theory and an +infinite dimensional theory the size of + + align:start position:0% +infinite dimensional theory the size of + + + align:start position:0% +infinite dimensional theory the size of +the theory doesn't make any difference + + align:start position:0% +the theory doesn't make any difference + + + align:start position:0% +the theory doesn't make any difference +because what you get in the end is + + align:start position:0% +because what you get in the end is + + + align:start position:0% +because what you get in the end is +exactly the same thing the relative + + align:start position:0% +exactly the same thing the relative + + + align:start position:0% +exactly the same thing the relative +different distance between every two + + align:start position:0% +different distance between every two + + + align:start position:0% +different distance between every two +points in the set there's a few things + + align:start position:0% +points in the set there's a few things + + + align:start position:0% +points in the set there's a few things +to say about right so one thing to say + + align:start position:0% +to say about right so one thing to say + + + align:start position:0% +to say about right so one thing to say +about the representational dissimilarity + + align:start position:0% +about the representational dissimilarity + + + align:start position:0% +about the representational dissimilarity +analysis that I just showed you is that + + align:start position:0% +analysis that I just showed you is that + + + align:start position:0% +analysis that I just showed you is that +it tells you that the 38 dimensional + + align:start position:0% +it tells you that the 38 dimensional + + + align:start position:0% +it tells you that the 38 dimensional +theory is better than the valence theory + + align:start position:0% +theory is better than the valence theory + + + align:start position:0% +theory is better than the valence theory +eight the event feature series better + + align:start position:0% +eight the event feature series better + + + align:start position:0% +eight the event feature series better +than the valence theory but it doesn't + + align:start position:0% +than the valence theory but it doesn't + + + align:start position:0% +than the valence theory but it doesn't +tell you why right there doesn't tell + + align:start position:0% +tell you why right there doesn't tell + + + align:start position:0% +tell you why right there doesn't tell +you whether any specific one of those + + align:start position:0% +you whether any specific one of those + + + align:start position:0% +you whether any specific one of those +features is capturing variance in any + + align:start position:0% +features is capturing variance in any + + + align:start position:0% +features is capturing variance in any +specific one of those regions it tells + + align:start position:0% +specific one of those regions it tells + + + align:start position:0% +specific one of those regions it tells +you that that whole set + + align:start position:0% +you that that whole set + + + align:start position:0% +you that that whole set +was better than this other whole set and + + align:start position:0% +was better than this other whole set and + + + align:start position:0% +was better than this other whole set and +maybe this is where you're getting it + + align:start position:0% +maybe this is where you're getting it + + + align:start position:0% +maybe this is where you're getting it +it's much less good for trying post hoc + + align:start position:0% +it's much less good for trying post hoc + + + align:start position:0% +it's much less good for trying post hoc +things for saying but well but why which + + align:start position:0% +things for saying but well but why which + + + align:start position:0% +things for saying but well but why which +aspect of that theory was better than + + align:start position:0% +aspect of that theory was better than + + + align:start position:0% +aspect of that theory was better than +the valence and arousal it gives you an + + align:start position:0% +the valence and arousal it gives you an + + + align:start position:0% +the valence and arousal it gives you an +all things considered answer not a + + align:start position:0% +all things considered answer not a + + + align:start position:0% +all things considered answer not a +dimension specific answer that's that's + + align:start position:0% +dimension specific answer that's that's + + + align:start position:0% +dimension specific answer that's that's +one thing that is a limit in the way you + + align:start position:0% +one thing that is a limit in the way you + + + align:start position:0% +one thing that is a limit in the way you +should use representational the + + align:start position:0% +should use representational the + + + align:start position:0% +should use representational the +similarity analyses um there's there's + + align:start position:0% +similarity analyses um there's there's + + + align:start position:0% +similarity analyses um there's there's +two key problems that I think they're + + align:start position:0% +two key problems that I think they're + + + align:start position:0% +two key problems that I think they're +reflecting on about MVPA and one of them + + align:start position:0% +reflecting on about MVPA and one of them + + + align:start position:0% +reflecting on about MVPA and one of them +is a catastrophe and the other one is an + + align:start position:0% +is a catastrophe and the other one is an + + + align:start position:0% +is a catastrophe and the other one is an +incredibly deep puzzle and I think I + + align:start position:0% +incredibly deep puzzle and I think I + + + align:start position:0% +incredibly deep puzzle and I think I +should just save them right away before + + align:start position:0% +should just save them right away before + + + align:start position:0% +should just save them right away before +you get too excited because all of this + + align:start position:0% +you get too excited because all of this + + + align:start position:0% +you get too excited because all of this +stuff was really exciting and now I'm + + align:start position:0% +stuff was really exciting and now I'm + + + align:start position:0% +stuff was really exciting and now I'm +gonna tell you a catastrophe in a puzzle + + align:start position:0% +gonna tell you a catastrophe in a puzzle + + + align:start position:0% +gonna tell you a catastrophe in a puzzle +here's the catastrophe the catastrophe + + align:start position:0% +here's the catastrophe the catastrophe + + + align:start position:0% +here's the catastrophe the catastrophe +is that you can't make anything of null + + align:start position:0% +is that you can't make anything of null + + + align:start position:0% +is that you can't make anything of null +results okay now here's why because when + + align:start position:0% +results okay now here's why because when + + + align:start position:0% +results okay now here's why because when +I say that you can decode something from + + align:start position:0% +I say that you can decode something from + + + align:start position:0% +I say that you can decode something from +an MVPA analysis what I mean is that at + + align:start position:0% +an MVPA analysis what I mean is that at + + + align:start position:0% +an MVPA analysis what I mean is that at +the scale of voxels there's some signal + + align:start position:0% +the scale of voxels there's some signal + + + align:start position:0% +the scale of voxels there's some signal +in terms of which voxel is relatively + + align:start position:0% +in terms of which voxel is relatively + + + align:start position:0% +in terms of which voxel is relatively +higher or relatively lower in response + + align:start position:0% +higher or relatively lower in response + + + align:start position:0% +higher or relatively lower in response +to these stimuli right so in box'll + + align:start position:0% +to these stimuli right so in box'll + + + align:start position:0% +to these stimuli right so in box'll +space or in spatial space whichever one + + align:start position:0% +space or in spatial space whichever one + + + align:start position:0% +space or in spatial space whichever one +of those you find helpful it's that at + + align:start position:0% +of those you find helpful it's that at + + + align:start position:0% +of those you find helpful it's that at +the level of voxels we could cluster + + align:start position:0% +the level of voxels we could cluster + + + align:start position:0% +the level of voxels we could cluster +these stimuli and what that says is that + + align:start position:0% +these stimuli and what that says is that + + + align:start position:0% +these stimuli and what that says is that +there's something like distinct + + align:start position:0% +there's something like distinct + + + align:start position:0% +there's something like distinct +populations in this region responding + + align:start position:0% +populations in this region responding + + + align:start position:0% +populations in this region responding +across that feature dimension and + + align:start position:0% +across that feature dimension and + + + align:start position:0% +across that feature dimension and +they're spatially segregated enough that + + align:start position:0% +they're spatially segregated enough that + + + align:start position:0% +they're spatially segregated enough that +we could pick up on them with fMRI but + + align:start position:0% +we could pick up on them with fMRI but + + + align:start position:0% +we could pick up on them with fMRI but +who cares if they're spatially + + align:start position:0% +who cares if they're spatially + + + align:start position:0% +who cares if they're spatially +segregated enough that we can pick up + + align:start position:0% +segregated enough that we can pick up + + + align:start position:0% +segregated enough that we can pick up +with them with fMRI right + + align:start position:0% +with them with fMRI right + + + align:start position:0% +with them with fMRI right +efrem i is the scale of a millimeter and + + align:start position:0% +efrem i is the scale of a millimeter and + + + align:start position:0% +efrem i is the scale of a millimeter and +there could be many many many things + + align:start position:0% +there could be many many many things + + + align:start position:0% +there could be many many many things +that are represented by populations of + + align:start position:0% +that are represented by populations of + + + align:start position:0% +that are represented by populations of +neurons within a region that are not + + align:start position:0% +neurons within a region that are not + + + align:start position:0% +neurons within a region that are not +spatially organized at the scale of a + + align:start position:0% +spatially organized at the scale of a + + + align:start position:0% +spatially organized at the scale of a +millimeter not only could there be there + + align:start position:0% +millimeter not only could there be there + + + align:start position:0% +millimeter not only could there be there +absolutely definitely are there's a + + align:start position:0% +absolutely definitely are there's a + + + align:start position:0% +absolutely definitely are there's a +whole bunch of things that we already + + align:start position:0% +whole bunch of things that we already + + + align:start position:0% +whole bunch of things that we already +know are really important properties of + + align:start position:0% +know are really important properties of + + + align:start position:0% +know are really important properties of +neural representations of things we care + + align:start position:0% +neural representations of things we care + + + align:start position:0% +neural representations of things we care +about and we know that their spatial + + align:start position:0% +about and we know that their spatial + + + align:start position:0% +about and we know that their spatial +scale is not high enough that they could + + align:start position:0% +scale is not high enough that they could + + + align:start position:0% +scale is not high enough that they could +be picked up on with fMRI so two cases + + align:start position:0% +be picked up on with fMRI so two cases + + + align:start position:0% +be picked up on with fMRI so two cases +that I'll tell you about because you + + align:start position:0% +that I'll tell you about because you + + + align:start position:0% +that I'll tell you about because you +should care about them one is face + + align:start position:0% +should care about them one is face + + + align:start position:0% +should care about them one is face +responses in the middle temporal region + + align:start position:0% +responses in the middle temporal region + + + align:start position:0% +responses in the middle temporal region +that Doris and viñarock study for face + + align:start position:0% +that Doris and viñarock study for face + + + align:start position:0% +that Doris and viñarock study for face +representations in monkeys so in + + align:start position:0% +representations in monkeys so in + + + align:start position:0% +representations in monkeys so in +it's one of the middle ones in that one + + align:start position:0% +it's one of the middle ones in that one + + + align:start position:0% +it's one of the middle ones in that one +there's face features you can tell you + + align:start position:0% +there's face features you can tell you + + + align:start position:0% +there's face features you can tell you +how far apart the pupils are how high + + align:start position:0% +how far apart the pupils are how high + + + align:start position:0% +how far apart the pupils are how high +the eyebrows are did viñarock show you + + align:start position:0% +the eyebrows are did viñarock show you + + + align:start position:0% +the eyebrows are did viñarock show you +this amazing data totally amazing + + align:start position:0% +this amazing data totally amazing + + + align:start position:0% +this amazing data totally amazing +beautiful feature space at face identity + + align:start position:0% +beautiful feature space at face identity + + + align:start position:0% +beautiful feature space at face identity +representation one of the most + + align:start position:0% +representation one of the most + + + align:start position:0% +representation one of the most +strikingly beautiful things I've ever + + align:start position:0% +strikingly beautiful things I've ever + + + align:start position:0% +strikingly beautiful things I've ever +seen and he already knows me endorsed + + align:start position:0% +seen and he already knows me endorsed + + + align:start position:0% +seen and he already knows me endorsed +already know that there's no spatial + + align:start position:0% +already know that there's no spatial + + + align:start position:0% +already know that there's no spatial +relationship at all between the property + + align:start position:0% +relationship at all between the property + + + align:start position:0% +relationship at all between the property +that one neuron signals and its distance + + align:start position:0% +that one neuron signals and its distance + + + align:start position:0% +that one neuron signals and its distance +from other neurons that signal other + + align:start position:0% +from other neurons that signal other + + + align:start position:0% +from other neurons that signal other +properties there's no spatial + + align:start position:0% +properties there's no spatial + + + align:start position:0% +properties there's no spatial +organization at all so if you know that + + align:start position:0% +organization at all so if you know that + + + align:start position:0% +organization at all so if you know that +right here is a neuron the response to + + align:start position:0% +right here is a neuron the response to + + + align:start position:0% +right here is a neuron the response to +eye width + + align:start position:0% +eye width + + + align:start position:0% +eye width +you know nothing more about the neuron + + align:start position:0% +you know nothing more about the neuron + + + align:start position:0% +you know nothing more about the neuron +next to its preferred property than a + + align:start position:0% +next to its preferred property than a + + + align:start position:0% +next to its preferred property than a +neuron a centimeter away there's no + + align:start position:0% +neuron a centimeter away there's no + + + align:start position:0% +neuron a centimeter away there's no +spatial structure to which feature a + + align:start position:0% +spatial structure to which feature a + + + align:start position:0% +spatial structure to which feature a +given neuron responds to which means + + align:start position:0% +given neuron responds to which means + + + align:start position:0% +given neuron responds to which means +that you absolutely could not and cannot + + align:start position:0% +that you absolutely could not and cannot + + + align:start position:0% +that you absolutely could not and cannot +pick up on that in fMRI which doris has + + align:start position:0% +pick up on that in fMRI which doris has + + + align:start position:0% +pick up on that in fMRI which doris has +shown so this feature structure + + align:start position:0% +shown so this feature structure + + + align:start position:0% +shown so this feature structure +information cannot be picked up on with + + align:start position:0% +information cannot be picked up on with + + + align:start position:0% +information cannot be picked up on with +ephraim right even though it is there + + align:start position:0% +ephraim right even though it is there + + + align:start position:0% +ephraim right even though it is there +and really important another example is + + align:start position:0% +and really important another example is + + + align:start position:0% +and really important another example is +valence encoding in the amygdala image + + align:start position:0% +valence encoding in the amygdala image + + + align:start position:0% +valence encoding in the amygdala image +that contains some neurons that respond + + align:start position:0% +that contains some neurons that respond + + + align:start position:0% +that contains some neurons that respond +to positively valence events and other + + align:start position:0% +to positively valence events and other + + + align:start position:0% +to positively valence events and other +neurons that respond to negatively + + align:start position:0% +neurons that respond to negatively + + + align:start position:0% +neurons that respond to negatively +valence events and they are as spatially + + align:start position:0% +valence events and they are as spatially + + + align:start position:0% +valence events and they are as spatially +interleaved as physically possible + + align:start position:0% +interleaved as physically possible + + + align:start position:0% +interleaved as physically possible +that's what kate eyes data shows you + + align:start position:0% +that's what kate eyes data shows you + + + align:start position:0% +that's what kate eyes data shows you +couldn't get them more spatially into + + align:start position:0% +couldn't get them more spatially into + + + align:start position:0% +couldn't get them more spatially into +leave than they are they are close + + align:start position:0% +leave than they are they are close + + + align:start position:0% +leave than they are they are close +together as the size of the neurons + + align:start position:0% +together as the size of the neurons + + + align:start position:0% +together as the size of the neurons +allow so you absolutely will never be + + align:start position:0% +allow so you absolutely will never be + + + align:start position:0% +allow so you absolutely will never be +able to decode with that from our eye in + + align:start position:0% +able to decode with that from our eye in + + + align:start position:0% +able to decode with that from our eye in +those population amygdala that there are + + align:start position:0% +those population amygdala that there are + + + align:start position:0% +those population amygdala that there are +different populations for positive and + + align:start position:0% +different populations for positive and + + + align:start position:0% +different populations for positive and +negatively balanced events but there are + + align:start position:0% +negatively balanced events but there are + + + align:start position:0% +negatively balanced events but there are +okay so that means that when you see + + align:start position:0% +okay so that means that when you see + + + align:start position:0% +okay so that means that when you see +something in fMRI it's probably there + + align:start position:0% +something in fMRI it's probably there + + + align:start position:0% +something in fMRI it's probably there +but when you don't see it an fMRI you + + align:start position:0% +but when you don't see it an fMRI you + + + align:start position:0% +but when you don't see it an fMRI you +don't know that it's not there and the + + align:start position:0% +don't know that it's not there and the + + + align:start position:0% +don't know that it's not there and the +reason why that's a total catastrophe is + + align:start position:0% +reason why that's a total catastrophe is + + + align:start position:0% +reason why that's a total catastrophe is +if it means that when i tell you that a + + align:start position:0% +if it means that when i tell you that a + + + align:start position:0% +if it means that when i tell you that a +region kids a and not be i don't know + + align:start position:0% +region kids a and not be i don't know + + + align:start position:0% +region kids a and not be i don't know +that it doesn't could be and when I tell + + align:start position:0% +that it doesn't could be and when I tell + + + align:start position:0% +that it doesn't could be and when I tell +you that region that this thing is coded + + align:start position:0% +you that region that this thing is coded + + + align:start position:0% +you that region that this thing is coded +in region a and it's not coded in region + + align:start position:0% +in region a and it's not coded in region + + + align:start position:0% +in region a and it's not coded in region +B I don't know that it's not coded in + + align:start position:0% +B I don't know that it's not coded in + + + align:start position:0% +B I don't know that it's not coded in +region B so I can never show you a + + align:start position:0% +region B so I can never show you a + + + align:start position:0% +region B so I can never show you a +double dissociation I can never show you + + align:start position:0% +double dissociation I can never show you + + + align:start position:0% +double dissociation I can never show you +a single dissociation I can never show + + align:start position:0% +a single dissociation I can never show + + + align:start position:0% +a single dissociation I can never show +you a dissociation at all all I can say + + align:start position:0% +you a dissociation at all all I can say + + + align:start position:0% +you a dissociation at all all I can say +for sure is that the spatial scale of + + align:start position:0% +for sure is that the spatial scale of + + + align:start position:0% +for sure is that the spatial scale of +the information is different between one + + align:start position:0% +the information is different between one + + + align:start position:0% +the information is different between one +region and another or between one piece + + align:start position:0% +region and another or between one piece + + + align:start position:0% +region and another or between one piece +of information and another and we have + + align:start position:0% +of information and another and we have + + + align:start position:0% +of information and another and we have +no reason to believe that that matters + + align:start position:0% +no reason to believe that that matters + + + align:start position:0% +no reason to believe that that matters +at all + + align:start position:0% +at all + + + align:start position:0% +at all +but really important things are encoded + + align:start position:0% +but really important things are encoded + + + align:start position:0% +but really important things are encoded +at very fine spatial scales and so + + align:start position:0% +at very fine spatial scales and so + + + align:start position:0% +at very fine spatial scales and so +anytime I tell you which I told you + + align:start position:0% +anytime I tell you which I told you + + + align:start position:0% +anytime I tell you which I told you +hundred times because I think it's + + align:start position:0% +hundred times because I think it's + + + align:start position:0% +hundred times because I think it's +really cool that there's + + align:start position:0% +really cool that there's + + + align:start position:0% +really cool that there's +difference in what feature is encoded + + align:start position:0% +difference in what feature is encoded + + + align:start position:0% +difference in what feature is encoded +where you have no reason to believe me + + align:start position:0% +where you have no reason to believe me + + + align:start position:0% +where you have no reason to believe me +and that's the catastrophe it's a total + + align:start position:0% +and that's the catastrophe it's a total + + + align:start position:0% +and that's the catastrophe it's a total +catastrophe if you can't make + + align:start position:0% +catastrophe if you can't make + + + align:start position:0% +catastrophe if you can't make +distinctions you can't make any + + align:start position:0% +distinctions you can't make any + + + align:start position:0% +distinctions you can't make any +conclusions at all I'll just briefly say + + align:start position:0% +conclusions at all I'll just briefly say + + + align:start position:0% +conclusions at all I'll just briefly say +that the the the other thing that's a + + align:start position:0% +that the the the other thing that's a + + + align:start position:0% +that the the the other thing that's a +problem with this which is that this + + align:start position:0% +problem with this which is that this + + + align:start position:0% +problem with this which is that this +idea of similarity space the idea that + + align:start position:0% +idea of similarity space the idea that + + + align:start position:0% +idea of similarity space the idea that +you should think of a concept like + + align:start position:0% +you should think of a concept like + + + align:start position:0% +you should think of a concept like +jealous as a point in a + + align:start position:0% +jealous as a point in a + + + align:start position:0% +jealous as a point in a +multi-dimensional space and what it + + align:start position:0% +multi-dimensional space and what it + + + align:start position:0% +multi-dimensional space and what it +means to think of somebody is jealous is + + align:start position:0% +means to think of somebody is jealous is + + + align:start position:0% +means to think of somebody is jealous is +to think of them as a certain distance + + align:start position:0% +to think of them as a certain distance + + + align:start position:0% +to think of them as a certain distance +from irritated and angry and proud and + + align:start position:0% +from irritated and angry and proud and + + + align:start position:0% +from irritated and angry and proud and +impressed that idea has been thoroughly + + align:start position:0% +impressed that idea has been thoroughly + + + align:start position:0% +impressed that idea has been thoroughly +undermined in psychology and + + align:start position:0% +undermined in psychology and + + + align:start position:0% +undermined in psychology and +psychophysics and all and computational + + align:start position:0% +psychophysics and all and computational + + + align:start position:0% +psychophysics and all and computational +cognition that's it's really a bad + + align:start position:0% +cognition that's it's really a bad + + + align:start position:0% +cognition that's it's really a bad +theory of concepts that can't do any of + + align:start position:0% +theory of concepts that can't do any of + + + align:start position:0% +theory of concepts that can't do any of +the work that concepts are supposed to + + align:start position:0% +the work that concepts are supposed to + + + align:start position:0% +the work that concepts are supposed to +do one of the most important things they + + align:start position:0% +do one of the most important things they + + + align:start position:0% +do one of the most important things they +can't do is compositionality it can't + + align:start position:0% +can't do is compositionality it can't + + + align:start position:0% +can't do is compositionality it can't +explain the way concepts compose which + + align:start position:0% +explain the way concepts compose which + + + align:start position:0% +explain the way concepts compose which +is absolutely critical to the way that + + align:start position:0% +is absolutely critical to the way that + + + align:start position:0% +is absolutely critical to the way that +we think and even more critical to the + + align:start position:0% +we think and even more critical to the + + + align:start position:0% +we think and even more critical to the +way that we think about other people's + + align:start position:0% +way that we think about other people's + + + align:start position:0% +way that we think about other people's +minds because every thought you have + + align:start position:0% +minds because every thought you have + + + align:start position:0% +minds because every thought you have +about somebody else's mental state is a + + align:start position:0% +about somebody else's mental state is a + + + align:start position:0% +about somebody else's mental state is a +composition of an agent a mental state + + align:start position:0% +composition of an agent a mental state + + + align:start position:0% +composition of an agent a mental state +and a Content and so this whole way of + + align:start position:0% +and a Content and so this whole way of + + + align:start position:0% +and a Content and so this whole way of +thinking about concepts as points in + + align:start position:0% +thinking about concepts as points in + + + align:start position:0% +thinking about concepts as points in +multi-dimensional spaces works but + + align:start position:0% +multi-dimensional spaces works but + + + align:start position:0% +multi-dimensional spaces works but +shouldn't work and that's the other + + align:start position:0% +shouldn't work and that's the other + + + align:start position:0% +shouldn't work and that's the other +problem with this whole endeavor ok and + + align:start position:0% +problem with this whole endeavor ok and + + + align:start position:0% +problem with this whole endeavor ok and +there's a bunch of things that we're + + align:start position:0% +there's a bunch of things that we're + + + align:start position:0% +there's a bunch of things that we're +doing with this that I will just briefly + + align:start position:0% +doing with this that I will just briefly + + + align:start position:0% +doing with this that I will just briefly +mention in case people want to think + + align:start position:0% +mention in case people want to think + + + align:start position:0% +mention in case people want to think +about it or know about it the two things + + align:start position:0% +about it or know about it the two things + + + align:start position:0% +about it or know about it the two things +I'm really excited about one is adding + + align:start position:0% +I'm really excited about one is adding + + + align:start position:0% +I'm really excited about one is adding +temporal information so looking at the + + align:start position:0% +temporal information so looking at the + + + align:start position:0% +temporal information so looking at the +change in information in brain regions + + align:start position:0% +change in information in brain regions + + + align:start position:0% +change in information in brain regions +over time and how they influence one + + align:start position:0% +over time and how they influence one + + + align:start position:0% +over time and how they influence one +another and that's my postdoc stefano + + align:start position:0% +another and that's my postdoc stefano + + + align:start position:0% +another and that's my postdoc stefano +Ancelotti's project and another thing + + align:start position:0% +Ancelotti's project and another thing + + + align:start position:0% +Ancelotti's project and another thing +that I'm excited about is that to the + + align:start position:0% +that I'm excited about is that to the + + + align:start position:0% +that I'm excited about is that to the +degree that you take these positive + + align:start position:0% +degree that you take these positive + + + align:start position:0% +degree that you take these positive +claims of something interesting which I + + align:start position:0% +claims of something interesting which I + + + align:start position:0% +claims of something interesting which I +actually still do in spite of my end of + + align:start position:0% +actually still do in spite of my end of + + + align:start position:0% +actually still do in spite of my end of +the world talk and one thing that I + + align:start position:0% +the world talk and one thing that I + + + align:start position:0% +the world talk and one thing that I +think is really neat is the idea of + + align:start position:0% +think is really neat is the idea of + + + align:start position:0% +think is really neat is the idea of +increasingly differentiated bull + + align:start position:0% +increasingly differentiated bull + + + align:start position:0% +increasingly differentiated bull +representational spaces so it's taking + + align:start position:0% +representational spaces so it's taking + + + align:start position:0% +representational spaces so it's taking +two things so two sets of stimuli that + + align:start position:0% +two things so two sets of stimuli that + + + align:start position:0% +two things so two sets of stimuli that +produce clusters that are not separable + + align:start position:0% +produce clusters that are not separable + + + align:start position:0% +produce clusters that are not separable +for example in voxel or neural space and + + align:start position:0% +for example in voxel or neural space and + + + align:start position:0% +for example in voxel or neural space and +making them increasingly distinct so Jim + + align:start position:0% +making them increasingly distinct so Jim + + + align:start position:0% +making them increasingly distinct so Jim +de kado calls this unfolding a manifold + + align:start position:0% +de kado calls this unfolding a manifold + + + align:start position:0% +de kado calls this unfolding a manifold +right that idea which is Jim DeCarlo's + + align:start position:0% +right that idea which is Jim DeCarlo's + + + align:start position:0% +right that idea which is Jim DeCarlo's +model of the success of processing and + + align:start position:0% +model of the success of processing and + + + align:start position:0% +model of the success of processing and +stages from v1 to v2 - I - v4 - I T I + + align:start position:0% +stages from v1 to v2 - I - v4 - I T I + + + align:start position:0% +stages from v1 to v2 - I - v4 - I T I +think that's a really cool model of + + align:start position:0% +think that's a really cool model of + + + align:start position:0% +think that's a really cool model of +conceptual development than what you + + align:start position:0% +conceptual development than what you + + + align:start position:0% +conceptual development than what you +might have is + + align:start position:0% +might have is + + + align:start position:0% +might have is +neural responses that can't separate + + align:start position:0% +neural responses that can't separate + + + align:start position:0% +neural responses that can't separate +stimuli along some interesting dimension + + align:start position:0% +stimuli along some interesting dimension + + + align:start position:0% +stimuli along some interesting dimension +that unfold that representational space + + align:start position:0% +that unfold that representational space + + + align:start position:0% +that unfold that representational space +to make them were dissimilar as you get + + align:start position:0% +to make them were dissimilar as you get + + + align:start position:0% +to make them were dissimilar as you get +that concept more that dimension or + + align:start position:0% +that concept more that dimension or + + + align:start position:0% +that concept more that dimension or +feature of the stimuli more + + align:start position:0% +feature of the stimuli more + + + align:start position:0% +feature of the stimuli more +distinctively represented and so we've + + align:start position:0% +distinctively represented and so we've + + + align:start position:0% +distinctively represented and so we've +tried a first version of this with just + + align:start position:0% +tried a first version of this with just + + + align:start position:0% +tried a first version of this with just +offical so kids between age 7 and 12 get + + align:start position:0% +offical so kids between age 7 and 12 get + + + align:start position:0% +offical so kids between age 7 and 12 get +better and better at distinguishing + + align:start position:0% +better and better at distinguishing + + + align:start position:0% +better and better at distinguishing +people's beliefs that have good and bad + + align:start position:0% +people's beliefs that have good and bad + + + align:start position:0% +people's beliefs that have good and bad +evidence and we've shown that that's + + align:start position:0% +evidence and we've shown that that's + + + align:start position:0% +evidence and we've shown that that's +correlated with them with the neural + + align:start position:0% +correlated with them with the neural + + + align:start position:0% +correlated with them with the neural +signature in the right TPJ getting more + + align:start position:0% +signature in the right TPJ getting more + + + align:start position:0% +signature in the right TPJ getting more +and more distinct over that same time in + + align:start position:0% +and more distinct over that same time in + + + align:start position:0% +and more distinct over that same time in +those same kids and so I think thinking + + align:start position:0% +those same kids and so I think thinking + + + align:start position:0% +those same kids and so I think thinking +of representational dissimilarity as a + + align:start position:0% +of representational dissimilarity as a + + + align:start position:0% +of representational dissimilarity as a +model of conceptual change and while + + align:start position:0% +model of conceptual change and while + + + align:start position:0% +model of conceptual change and while +certainly wrong is probably really + + align:start position:0% +certainly wrong is probably really + + + align:start position:0% +certainly wrong is probably really +powerful and I'm very excited about it + + align:start position:0% +powerful and I'm very excited about it + + + align:start position:0% +powerful and I'm very excited about it +and the last thing I will do is thank + + align:start position:0% +and the last thing I will do is thank + + + align:start position:0% +and the last thing I will do is thank +the people who did the work especially + + align:start position:0% +the people who did the work especially + + + align:start position:0% +the people who did the work especially +everybody in my lab and two PhD students + + align:start position:0% +everybody in my lab and two PhD students + + + align:start position:0% +everybody in my lab and two PhD students +joy Koster Hale and Amy scary and you + + align:start position:0% +joy Koster Hale and Amy scary and you + + + align:start position:0% +joy Koster Hale and Amy scary and you +guys thank you + + align:start position:0% +guys thank you + + + align:start position:0% +guys thank you +[Applause] + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/iDfyX8WRIyM.txt b/iDfyX8WRIyM.txt new file mode 100644 index 0000000000000000000000000000000000000000..fef55b3c9be687f36b19791a53f78e3d97425ae9 --- /dev/null +++ b/iDfyX8WRIyM.txt @@ -0,0 +1,550 @@ +PROFESSOR: There are +two generalizations + +of the bijection rule +and the product rule that + +come up all the time and +play an essential role + +in the repertoire +of any counter. + +So let's look at those. + +The first of these +is a generalization + +of the product rule. + +And let's see an instance +where it comes up. + +Suppose I wanted to count +the number of lineups + +of five students in the class. + +So if I let S be the number +of students, and let's say, + +for the afternoon +session S is 91, then + +the number of lineups of +five students-- if I use + +the ordinary product +rule, I would + +get-- I'm talking about +S to the fifth, that is, + +sequences of length +five of elements of S. + +And so the product +rule would say, + +take 91 to the +fifth as the number + +of lineups of five students. + +And that would be correct if the +same student could appear twice + +in line, but that, +of course, isn't + +possible with real students. + +So the lineups have no repeats. + +And what we're really +counting is the number + +of those sequences of +length five of students + +with no repeats. + +And the generalized +product rule tells + +you quite straightforwardly +how to count those. + +Namely, there are 91 ways +to choose the first student + +among the 91. + +And whichever first +student you've chosen, + +that leaves 90 other students +you could choose to be second. + +And once you've chosen +the first two, that + +leaves 89 students you +could choose for the third, + +and 88 for the fourth, +and 87 for the fifth. + +And the formula then is 91 +times 90 times 89, 88, 87, + +for the number of sequences +of distinct students + +of length five. + +Now, one nice way to +express the 91 down + +to 87, in terms of factorials, +is its 91 factorial, + +which is the product +from 1 to 91, + +and divided by the +product from 1 to 86, + +which cancels out the first +86 terms in 91 factorial, + +leaving me with exactly +87 through 91 product. + +So the second rule is a sort +of obvious generalization + +of the bijectional, but I'm +getting ahead of myself. + +Let's state the generalized +product rule in general. + +So if we let Q be a set +of length-k sequences + +with the following +property, there + +are n1 possible first elements +among these length-k sequences. + +And for every one of the +first possible elements, + +if you look at the +number of tuples + +with what the second possible +coordinates for a given + +first coordinate, +it's always n2. + +And likewise, if you +look at the number + +of possible third coordinates +given the first two, it's n3 + +and it's uniform no matter +what the first two are. + +Then if you have this +kind of a set up, + +which is exactly what happens +when you're picking one student + +after another and +they can't compete, + +you discover that the +length-k sequences with n1 , + +first possible choices, n2, +second possible choices, + +down through nk, k-th possible +choices is n1 through nk. + +So that's the statement +of the generalized product + +rule in the magenta box. + +Now, we come to the generalized +bijection rule, which + +is called the division rule. + +And a simple, memorable +way to illustrate + +is if you wanted to count the +number of students in class + +6.042, you could count the +number of students fingers + +and divide by 10. + +Now, it's probably harder to +count fingers than students, + +so this is not meant +as a practical method. + +But it illustrates a basic +and straightforward idea. + +Of course, it's +implicitly assuming + +that we don't have any +instances of amputations + +or polydactylism, and that, +in fact, every student + +has exactly 10 fingers. + +OK, so in general, +the division rule + +can be stated this +way, if I have + +a total function from a set A to +a set B, domain A, co-domain B, + +and this mapping is k-to-1, +then the cardinality of A + +is simply k times the +cardinality of B. So k-to-1 + +means that exactly k A +elements hit each B element. + +Another way to say it is that +there are exactly k arrows + +into every element of B. So +then the number of arrows + +is simply k times B. And if +you have a total function on A, + +the number of arrows is +equal to the size of A, + +and that's where +we get the formula. + +OK. + +And that's the generalized +bijection rule. + +Let's apply it in +a crucial example + +that is absolutely basic and +we'll be using repeatedly. + +Suppose that I want to know how +many possible subsets of size + +four are there from the +numbers 1 through 13? + +So I have 13 possible +numbers that I can choose. + +I want to pick out +any four of them + +and I want to know how many +ways are there to do that. + +And we'll do that by finding +a mapping from things + +we know how to count to +these particular subsets. + +So what we know how +to count is if I + +let A be the set of all +permutations of 1 through 13, + +then I know that the size of A +is 13 factorial because there's + +13 choices for the first +element of the permutation, 12 + +for the second, down +to one for the 13th. + +And let's let B be this +object that I want to count, + +namely, the set of size four +subsets of 1 through 13. + +And I want to find +a mapping from A + +that I know how to count +to B that I don't yet + +know how to count, +but in a way where + +I can figure out that +it's k-to-1 for a k + +that I can also count. + +How do I do that? + +Well, let's take an +arbitrary permutation of A, + +that is to say, a +sequence of the elements + +of A in some order-- call +them a1, a2, through a13. + +So these numbers a1 through a13 +are those numbers 1 through 13 + +in some unknown order. + +And I'm going to map +a permutation of A, + +like this, to its +first four elements. + +Just take the first four +elements of the permutation + +and map them to +the set consisting + +of those four elements. + +Now, since this +is a permutation, + +these elements +are all different, + +so I really do get a set of +four different things here, + +a1, a2, and a3. + +And a4 is supposed +to be different. + +This gives me a very +well-defined total function + +from a permutation of 13 +numbers to set of its first four + +elements. + +And now what we want to know is +what kind of a mapping is this? + +And I'm going to argue that +it's k-to-1 for a k that's + +not very hard to count. + +So when I look at +what other things map + +to the set a1, a2, a3, a4, +we mapped a permutation + +to its first four elements. + +And if we've got a1 through a4 +as the set, what other things + +map to that set a1, a2, a3, a4? + +Well, the answer +is any permutation + +with the same first four +elements, but possibly + +in a different order, +because we're just + +going to take the +first four in sequence + +and map them to the set +of those first four. + +The order in which the +first four doesn't matter. + +OK? + +And likewise, the order of +the remaining nine elements, + +5 through 13, also +doesn't matter. + +Whatever they are, if I have +a given set of four elements + +to start, no matter what +the remaining 9 are, + +they're going to map to the +same subset of four elements. + +So there are 4 +factorial possible ways + +that the first four +elements can be permuted. + +And there are 9 factorial +ways that the last nine + +elements can be permuted. + +And every one of these goes to +the same set of four elements, + +a1 through a4. + +And those are the only +ones that go there. + +And so what we've figured +out is that the mapping + +of these kind of sequences with +the given four elements first + +in some order and +the remaining nine + +elements in some other +order is 4 factorial times 9 + +factorial-to-1. + +There are 4 factorial times +9 factorial permutations + +that map to any given +set of four elements. + +And that means that by +applying the division rule, + +I've discovered that the +size of A, which I know + +is 13 factorial, +is equal to that k + +of the k-to-1 of 4 factorial +times 9 factorial times + +the size of B. + +B is the subsets of size four +that I'm trying to count. + +And so what I get is +that the size of B + +is simply 13 factorial +divided by that k, 4 + +factorial 9 factorial, 13 +factorial over 4 factorial + +9 factorial. + +And this number +comes up so often + +that it has this +special notation called + +binomial coefficient notation, +which we read as 13 choose 4. + +In general, if I +have an n element set + +and I'm going to choose a subset +of m of them-- generalizing + +this argument because +the 4 and the 9 + +and the 13 were +completely arbitrary + +and the argument +works in general-- + +is that the number of ways +to choose a set of m elements + +among n is n choose m. + +And the definition +of n choose m is + +n factorial over +the m factorial ways + +to permute the first m elements +and the n minus m factorial + +ways to permute the +remaining n minus m elements. + +And again, that notation, +the binomial coefficient, + +is called n over +m is n choose m. + +This is an absolutely +fundamental formula + +that you need to remember +because we will be using it + +constantly and repeatedly. \ No newline at end of file diff --git a/jPTyYCm4U6Q.txt b/jPTyYCm4U6Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..6d39a162161743fd09c15895ba1d498dc9875aa5 --- /dev/null +++ b/jPTyYCm4U6Q.txt @@ -0,0 +1,1307 @@ +align:start position:0% + +edgerton's Boomer illustrates the + + align:start position:0% +edgerton's Boomer illustrates the + + + align:start position:0% +edgerton's Boomer illustrates the +induction of a current in a conductor + + align:start position:0% +induction of a current in a conductor + + + align:start position:0% +induction of a current in a conductor +subjected to a Time varying magnetic + + align:start position:0% +subjected to a Time varying magnetic + + + align:start position:0% +subjected to a Time varying magnetic +field and the associated magnetic + + align:start position:0% +field and the associated magnetic + + + align:start position:0% +field and the associated magnetic +forces it illustrates the interplay + + align:start position:0% +forces it illustrates the interplay + + + align:start position:0% +forces it illustrates the interplay +between the laws of Faraday ampere and + + align:start position:0% +between the laws of Faraday ampere and + + + align:start position:0% +between the laws of Faraday ampere and +ohm that determines the distribution + + align:start position:0% +ohm that determines the distribution + + + align:start position:0% +ohm that determines the distribution +duration and magnitude of currents in + + align:start position:0% +duration and magnitude of currents in + + + align:start position:0% +duration and magnitude of currents in +conductors under Magneto quasistatic + + align:start position:0% + + + + align:start position:0% + +conditions this is the coil + + align:start position:0% +conditions this is the coil + + + align:start position:0% +conditions this is the coil +the winding wire circulates like + + align:start position:0% +the winding wire circulates like + + + align:start position:0% +the winding wire circulates like +so and is connected to the capacitors in + + align:start position:0% +so and is connected to the capacitors in + + + align:start position:0% +so and is connected to the capacitors in +this cabinet by these + + align:start position:0% + + + + align:start position:0% + +leads when the high voltage power supply + + align:start position:0% +leads when the high voltage power supply + + + align:start position:0% +leads when the high voltage power supply +in the cabinet is turned + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +on the capacitor is charged to 4 + + align:start position:0% + + + + align:start position:0% + +K the switch then connects the capacitor + + align:start position:0% +K the switch then connects the capacitor + + + align:start position:0% +K the switch then connects the capacitor +to the coil it's closed when this button + + align:start position:0% +to the coil it's closed when this button + + + align:start position:0% +to the coil it's closed when this button +is + + align:start position:0% +is + + + align:start position:0% +is +[Music] + + align:start position:0% + + + + align:start position:0% + +pushed the switch consists of a spark + + align:start position:0% +pushed the switch consists of a spark + + + align:start position:0% +pushed the switch consists of a spark +gap which we just heard we can see it if + + align:start position:0% +gap which we just heard we can see it if + + + align:start position:0% +gap which we just heard we can see it if +we open this panel + + align:start position:0% + + + + align:start position:0% + +the switch is closed by a spark across + + align:start position:0% +the switch is closed by a spark across + + + align:start position:0% +the switch is closed by a spark across +this + + align:start position:0% +this + + + align:start position:0% +this +Gap that spark is activated by applying + + align:start position:0% +Gap that spark is activated by applying + + + align:start position:0% +Gap that spark is activated by applying +a voltage to this electrode to make a + + align:start position:0% +a voltage to this electrode to make a + + + align:start position:0% +a voltage to this electrode to make a +smaller electrical breakdown in the + + align:start position:0% + + + + align:start position:0% + +Gap just once we'll bypass the safety + + align:start position:0% +Gap just once we'll bypass the safety + + + align:start position:0% +Gap just once we'll bypass the safety +interlock that ordinarily disconnects + + align:start position:0% +interlock that ordinarily disconnects + + + align:start position:0% +interlock that ordinarily disconnects +the circuit when the panel is + + align:start position:0% + + + + align:start position:0% + +opened then when we push the button we + + align:start position:0% +opened then when we push the button we + + + align:start position:0% +opened then when we push the button we +can not only hear the spark discharge + + align:start position:0% +can not only hear the spark discharge + + + align:start position:0% +can not only hear the spark discharge +that closes the switch but see the + + align:start position:0% +that closes the switch but see the + + + align:start position:0% +that closes the switch but see the +associated flash as + + align:start position:0% + + + + align:start position:0% + +well maybe we can do it once + + align:start position:0% + + + + align:start position:0% + +more given the initial capacitor voltage + + align:start position:0% +more given the initial capacitor voltage + + + align:start position:0% +more given the initial capacitor voltage +of 4 Kilts and that the coil has has 50 + + align:start position:0% +of 4 Kilts and that the coil has has 50 + + + align:start position:0% +of 4 Kilts and that the coil has has 50 +turns we can use basic principles to + + align:start position:0% +turns we can use basic principles to + + + align:start position:0% +turns we can use basic principles to +estimate the winding current and hence + + align:start position:0% +estimate the winding current and hence + + + align:start position:0% +estimate the winding current and hence +the magnetic field intensity produced by + + align:start position:0% +the magnetic field intensity produced by + + + align:start position:0% +the magnetic field intensity produced by +the + + align:start position:0% +the + + + align:start position:0% +the +coil first we use ampere's integral law + + align:start position:0% +coil first we use ampere's integral law + + + align:start position:0% +coil first we use ampere's integral law +to relate the current to the + + align:start position:0% +to relate the current to the + + + align:start position:0% +to relate the current to the +field the line Contour encloses the + + align:start position:0% +field the line Contour encloses the + + + align:start position:0% +field the line Contour encloses the +current in the + + align:start position:0% + + + + align:start position:0% + +coil before we go on let's see how well + + align:start position:0% +coil before we go on let's see how well + + + align:start position:0% +coil before we go on let's see how well +we've approximated the current + + align:start position:0% +we've approximated the current + + + align:start position:0% +we've approximated the current +field this current probe will link one + + align:start position:0% +field this current probe will link one + + + align:start position:0% +field this current probe will link one +of the wires connected to the + + align:start position:0% + + + + align:start position:0% + +coil we display the coil current on the + + align:start position:0% +coil we display the coil current on the + + + align:start position:0% +coil we display the coil current on the +lower scope + + align:start position:0% +lower scope + + + align:start position:0% +lower scope +trace the voltage induced at the + + align:start position:0% +trace the voltage induced at the + + + align:start position:0% +trace the voltage induced at the +terminals of this + + align:start position:0% +terminals of this + + + align:start position:0% +terminals of this +coil by the time varying magnetic flux + + align:start position:0% +coil by the time varying magnetic flux + + + align:start position:0% +coil by the time varying magnetic flux +density will be used to deduce + + align:start position:0% +density will be used to deduce + + + align:start position:0% +density will be used to deduce +B this voltage will be displayed as the + + align:start position:0% +B this voltage will be displayed as the + + + align:start position:0% +B this voltage will be displayed as the +upper scope Trace + + align:start position:0% + + + + align:start position:0% + +here are the responses to the discharge + + align:start position:0% +here are the responses to the discharge + + + align:start position:0% +here are the responses to the discharge +of the + + align:start position:0% + + + + align:start position:0% + +capacitor the time axis is 2/10 of a + + align:start position:0% +capacitor the time axis is 2/10 of a + + + align:start position:0% +capacitor the time axis is 2/10 of a +millisecond per + + align:start position:0% +millisecond per + + + align:start position:0% +millisecond per +division so the period of the + + align:start position:0% +division so the period of the + + + align:start position:0% +division so the period of the +oscillation is about 1/3 of a + + align:start position:0% +oscillation is about 1/3 of a + + + align:start position:0% +oscillation is about 1/3 of a +millisecond the oscillation frequency is + + align:start position:0% +millisecond the oscillation frequency is + + + align:start position:0% +millisecond the oscillation frequency is +roughly the predicted 4 + + align:start position:0% +roughly the predicted 4 + + + align:start position:0% +roughly the predicted 4 +khz the duration of the lower Trace + + align:start position:0% +khz the duration of the lower Trace + + + align:start position:0% +khz the duration of the lower Trace +current and hence of the field is on the + + align:start position:0% +current and hence of the field is on the + + + align:start position:0% +current and hence of the field is on the +order of 1 + + align:start position:0% + + + + align:start position:0% + +millisecond the peak in the current on + + align:start position:0% +millisecond the peak in the current on + + + align:start position:0% +millisecond the peak in the current on +the lower Trace is about one + + align:start position:0% +the lower Trace is about one + + + align:start position:0% +the lower Trace is about one +division there are 1,000 amps per + + align:start position:0% +division there are 1,000 amps per + + + align:start position:0% +division there are 1,000 amps per +division so the peak current is about + + align:start position:0% +division so the peak current is about + + + align:start position:0% +division so the peak current is about +1,000 + + align:start position:0% +1,000 + + + align:start position:0% +1,000 +amps this is in the range of the + + align:start position:0% +amps this is in the range of the + + + align:start position:0% +amps this is in the range of the +estimated value of 1,600 amps remember + + align:start position:0% +estimated value of 1,600 amps remember + + + align:start position:0% +estimated value of 1,600 amps remember +we've not accounted for losses in the + + align:start position:0% +we've not accounted for losses in the + + + align:start position:0% +we've not accounted for losses in the +spark gap in the coil + + align:start position:0% + + + + align:start position:0% + +the dis could represent a + + align:start position:0% +the dis could represent a + + + align:start position:0% +the dis could represent a +hand in that case the experiment can + + align:start position:0% +hand in that case the experiment can + + + align:start position:0% +hand in that case the experiment can +literally give a feel for the + + align:start position:0% +literally give a feel for the + + + align:start position:0% +literally give a feel for the +consequence of subjecting a conductor to + + align:start position:0% +consequence of subjecting a conductor to + + + align:start position:0% +consequence of subjecting a conductor to +a Time varying magnetic + + align:start position:0% +a Time varying magnetic + + + align:start position:0% +a Time varying magnetic +field if the disc represents a hand what + + align:start position:0% +field if the disc represents a hand what + + + align:start position:0% +field if the disc represents a hand what +current density would be + + align:start position:0% + + + + align:start position:0% + +felt magnetic field created by the coil + + align:start position:0% +felt magnetic field created by the coil + + + align:start position:0% +felt magnetic field created by the coil +is non-uniform + + align:start position:0% +is non-uniform + + + align:start position:0% +is non-uniform +far away that of a + + align:start position:0% +far away that of a + + + align:start position:0% +far away that of a +dipole so we can discern what we're + + align:start position:0% +dipole so we can discern what we're + + + align:start position:0% +dipole so we can discern what we're +getting into by feeling the induced + + align:start position:0% +getting into by feeling the induced + + + align:start position:0% +getting into by feeling the induced +current in + + align:start position:0% +current in + + + align:start position:0% +current in +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +stages the sensation is of a short + + align:start position:0% +stages the sensation is of a short + + + align:start position:0% +stages the sensation is of a short +duration + + align:start position:0% +duration + + + align:start position:0% +duration +twinge much as would be expected for a + + align:start position:0% +twinge much as would be expected for a + + + align:start position:0% +twinge much as would be expected for a +pulse that lasts 1 millisecond + + align:start position:0% + + + + align:start position:0% + +uh I've been given to understand that + + align:start position:0% +uh I've been given to understand that + + + align:start position:0% +uh I've been given to understand that +Professor Zan is not going to try it + + align:start position:0% +Professor Zan is not going to try it + + + align:start position:0% +Professor Zan is not going to try it +with his hand lower than + + align:start position:0% + + + + align:start position:0% + +this so that you can see evidence of the + + align:start position:0% +this so that you can see evidence of the + + + align:start position:0% +this so that you can see evidence of the +field that you can't feel + + align:start position:0% +field that you can't feel + + + align:start position:0% +field that you can't feel +firsthand let's replace his hand by this + + align:start position:0% +firsthand let's replace his hand by this + + + align:start position:0% +firsthand let's replace his hand by this +wire + + align:start position:0% + + + + align:start position:0% + +Loop the wire is open at this + + align:start position:0% +Loop the wire is open at this + + + align:start position:0% +Loop the wire is open at this +point with the ends barely + + align:start position:0% + + + + align:start position:0% + +touching so the field induced around the + + align:start position:0% + + + + align:start position:0% + +Contour is concentrated at the + + align:start position:0% +Contour is concentrated at the + + + align:start position:0% +Contour is concentrated at the +Gap we go to a higher f- stop to protect + + align:start position:0% +Gap we go to a higher f- stop to protect + + + align:start position:0% +Gap we go to a higher f- stop to protect +the + + align:start position:0% + + + + align:start position:0% + +camera the integral of the electric + + align:start position:0% +camera the integral of the electric + + + align:start position:0% +camera the integral of the electric +field intensity is concentrated in a gap + + align:start position:0% +field intensity is concentrated in a gap + + + align:start position:0% +field intensity is concentrated in a gap +region that is initially relatively + + align:start position:0% +region that is initially relatively + + + align:start position:0% +region that is initially relatively +insulating so the electric field + + align:start position:0% +insulating so the electric field + + + align:start position:0% +insulating so the electric field +intensity between the almost touching + + align:start position:0% +intensity between the almost touching + + + align:start position:0% +intensity between the almost touching +wires is enough to produce a + + align:start position:0% + + + + align:start position:0% + +spark the conductivity of this aluminum + + align:start position:0% +spark the conductivity of this aluminum + + + align:start position:0% +spark the conductivity of this aluminum +disc is more than 10 million times + + align:start position:0% +disc is more than 10 million times + + + align:start position:0% +disc is more than 10 million times +larger than for human flesh and there's + + align:start position:0% +larger than for human flesh and there's + + + align:start position:0% +larger than for human flesh and there's +no Gap to limit the induced current + + align:start position:0% + + + + align:start position:0% + +the force can be used to shape + + align:start position:0% + + + + align:start position:0% + +Metals here the upward force is evident + + align:start position:0% +Metals here the upward force is evident + + + align:start position:0% +Metals here the upward force is evident +in the shaping of the outer edge of a + + align:start position:0% +in the shaping of the outer edge of a + + + align:start position:0% +in the shaping of the outer edge of a +foil disc + + align:start position:0% + + + + align:start position:0% + +for this experiment we use three times + + align:start position:0% +for this experiment we use three times + + + align:start position:0% +for this experiment we use three times +as much + + align:start position:0% + + + + align:start position:0% + +capacitance if the force can be used to + + align:start position:0% +capacitance if the force can be used to + + + align:start position:0% +capacitance if the force can be used to +shape the metal it can also be used to + + align:start position:0% +shape the metal it can also be used to + + + align:start position:0% +shape the metal it can also be used to +launch the disc + + align:start position:0% + + + + align:start position:0% + +I'm melter and as you know that's Zan we + + align:start position:0% +I'm melter and as you know that's Zan we + + + align:start position:0% +I'm melter and as you know that's Zan we +brought along an illuminary here to push + + align:start position:0% +brought along an illuminary here to push + + + align:start position:0% +brought along an illuminary here to push +that button finally this is Professor + + align:start position:0% +that button finally this is Professor + + + align:start position:0% +that button finally this is Professor +Doc ederton and uh it's his + + align:start position:0% +Doc ederton and uh it's his + + + align:start position:0% +Doc ederton and uh it's his +machine what we've done of course is to + + align:start position:0% +machine what we've done of course is to + + + align:start position:0% +machine what we've done of course is to +show you this disc and now if uh doc you + + align:start position:0% +show you this disc and now if uh doc you + + + align:start position:0% +show you this disc and now if uh doc you +turn on your machine ready here we go + + align:start position:0% +turn on your machine ready here we go + + + align:start position:0% +turn on your machine ready here we go +I'm going to step out of this I'll turn + + align:start position:0% +I'm going to step out of this I'll turn + + + align:start position:0% +I'm going to step out of this I'll turn +on the main power let it come up to + + align:start position:0% + + + + align:start position:0% + +charge want do it again do you have a + + align:start position:0% +charge want do it again do you have a + + + align:start position:0% +charge want do it again do you have a +favorite one there well the everyone's a + + align:start position:0% +favorite one there well the everyone's a + + + align:start position:0% +favorite one there well the everyone's a +little different let's try this one what + + align:start position:0% +little different let's try this one what + + + align:start position:0% +little different let's try this one what +do you + + align:start position:0% +do you + + + align:start position:0% +do you +say + + align:start position:0% + + + + align:start position:0% + +power little different ring to it little + + align:start position:0% +power little different ring to it little + + + align:start position:0% +power little different ring to it little +different ring now as I understand it + + align:start position:0% +different ring now as I understand it + + + align:start position:0% +different ring now as I understand it +this thing's got uh more capacitors in + + align:start position:0% +this thing's got uh more capacitors in + + + align:start position:0% +this thing's got uh more capacitors in +it maybe we get zom to uh put a little + + align:start position:0% +it maybe we get zom to uh put a little + + + align:start position:0% +it maybe we get zom to uh put a little +more in there you + + align:start position:0% +more in there you + + + align:start position:0% +more in there you +like one of the reasons I brought this + + align:start position:0% +like one of the reasons I brought this + + + align:start position:0% +like one of the reasons I brought this +man along is that uh in fact he mainly + + align:start position:0% +man along is that uh in fact he mainly + + + align:start position:0% +man along is that uh in fact he mainly +paid for this building so you see we + + align:start position:0% +paid for this building so you see we + + + align:start position:0% +paid for this building so you see we +don't care too much if we hurt that + + align:start position:0% + + + + align:start position:0% + +ceiling it' be nice to have an imprint + + align:start position:0% +ceiling it' be nice to have an imprint + + + align:start position:0% +ceiling it' be nice to have an imprint +up there wouldn't it right with you here + + align:start position:0% +up there wouldn't it right with you here + + + align:start position:0% +up there wouldn't it right with you here +I can say that okay let's see what + + align:start position:0% +I can say that okay let's see what + + + align:start position:0% +I can say that okay let's see what +happen this time well you got three + + align:start position:0% +happen this time well you got three + + + align:start position:0% +happen this time well you got three +capacitors on instead of one it should + + align:start position:0% +capacitors on instead of one it should + + + align:start position:0% +capacitors on instead of one it should +go a little + + align:start position:0% +go a little + + + align:start position:0% +go a little +higher one two 3 + + align:start position:0% +higher one two 3 + + + align:start position:0% +higher one two 3 +go missed me want to try our favorite + + align:start position:0% +go missed me want to try our favorite + + + align:start position:0% +go missed me want to try our favorite +yeah let's try that one + + align:start position:0% + + + + align:start position:0% + +hey knocked a hole in the ceiling I can + + align:start position:0% +hey knocked a hole in the ceiling I can + + + align:start position:0% +hey knocked a hole in the ceiling I can +see you enjoy that huh all right thank + + align:start position:0% +see you enjoy that huh all right thank + + + align:start position:0% +see you enjoy that huh all right thank +you very much sir \ No newline at end of file diff --git a/jTS5ZmrrzMs.txt b/jTS5ZmrrzMs.txt new file mode 100644 index 0000000000000000000000000000000000000000..77c6905f2fd7eb362d62c0b892c2d9d60f715785 --- /dev/null +++ b/jTS5ZmrrzMs.txt @@ -0,0 +1,907 @@ +align:start position:0% + +this is Dr Matlab lecture one using + + align:start position:0% +this is Dr Matlab lecture one using + + + align:start position:0% +this is Dr Matlab lecture one using +madlab for the first + + align:start position:0% +madlab for the first + + + align:start position:0% +madlab for the first +time when you turn mat laab on for the + + align:start position:0% +time when you turn mat laab on for the + + + align:start position:0% +time when you turn mat laab on for the +first time you'll be greeted with a + + align:start position:0% +first time you'll be greeted with a + + + align:start position:0% +first time you'll be greeted with a +window that looks like + + align:start position:0% +window that looks like + + + align:start position:0% +window that looks like +this the first thing we do is close all + + align:start position:0% +this the first thing we do is close all + + + align:start position:0% +this the first thing we do is close all +the windows that we don't need + + align:start position:0% +the windows that we don't need + + + align:start position:0% +the windows that we don't need +initially current directory the + + align:start position:0% +initially current directory the + + + align:start position:0% +initially current directory the +workspace the command history we're left + + align:start position:0% +workspace the command history we're left + + + align:start position:0% +workspace the command history we're left +with a command window + + align:start position:0% +with a command window + + + align:start position:0% +with a command window +this is the command prompt and this is + + align:start position:0% +this is the command prompt and this is + + + align:start position:0% +this is the command prompt and this is +the flashing cursor where our input will + + align:start position:0% +the flashing cursor where our input will + + + align:start position:0% +the flashing cursor where our input will +be + + align:start position:0% +be + + + align:start position:0% +be +placed the first thing we want to do is + + align:start position:0% +placed the first thing we want to do is + + + align:start position:0% +placed the first thing we want to do is +try using matlb as a giant calculator so + + align:start position:0% +try using matlb as a giant calculator so + + + align:start position:0% +try using matlb as a giant calculator so +for example we can ask matlb to + + align:start position:0% +for example we can ask matlb to + + + align:start position:0% +for example we can ask matlb to +calculate 1+ one the answer is two so we + + align:start position:0% +calculate 1+ one the answer is two so we + + + align:start position:0% +calculate 1+ one the answer is two so we +type what we want 3 + 4 hit + + align:start position:0% +type what we want 3 + 4 hit + + + align:start position:0% +type what we want 3 + 4 hit +enter and we get the answer 3 * 4 1 + 2 + + align:start position:0% +enter and we get the answer 3 * 4 1 + 2 + + + align:start position:0% +enter and we get the answer 3 * 4 1 + 2 +* + + align:start position:0% +* + + + align:start position:0% +* +3 2 to the power 4 5 to the power 3 + + align:start position:0% +3 2 to the power 4 5 to the power 3 + + + align:start position:0% +3 2 to the power 4 5 to the power 3 +Etc we can also ask whether two numbers + + align:start position:0% +Etc we can also ask whether two numbers + + + align:start position:0% +Etc we can also ask whether two numbers +are the same or whether one is greater + + align:start position:0% +are the same or whether one is greater + + + align:start position:0% +are the same or whether one is greater +than the other so to see if four is + + align:start position:0% +than the other so to see if four is + + + align:start position:0% +than the other so to see if four is +greater than five we type this this will + + align:start position:0% +greater than five we type this this will + + + align:start position:0% +greater than five we type this this will +tell us that the answer is no four is + + align:start position:0% +tell us that the answer is no four is + + + align:start position:0% +tell us that the answer is no four is +not greater than + + align:start position:0% +not greater than + + + align:start position:0% +not greater than +five we can ask is four less than five + + align:start position:0% +five we can ask is four less than five + + + align:start position:0% +five we can ask is four less than five +the answer is yes four is less than five + + align:start position:0% + + + + align:start position:0% + +sometimes we need a function in an + + align:start position:0% +sometimes we need a function in an + + + align:start position:0% +sometimes we need a function in an +expression not just an operator so for + + align:start position:0% +expression not just an operator so for + + + align:start position:0% +expression not just an operator so for +example to find the remainder we need to + + align:start position:0% +example to find the remainder we need to + + + align:start position:0% +example to find the remainder we need to +use the function REM here's the + + align:start position:0% +use the function REM here's the + + + align:start position:0% +use the function REM here's the +remainder of 15 when divided by four REM + + align:start position:0% +remainder of 15 when divided by four REM + + + align:start position:0% +remainder of 15 when divided by four REM +154 the answer is + + align:start position:0% +154 the answer is + + + align:start position:0% +154 the answer is +three to find out more about a function + + align:start position:0% +three to find out more about a function + + + align:start position:0% +three to find out more about a function +we use the help command help REM will + + align:start position:0% +we use the help command help REM will + + + align:start position:0% +we use the help command help REM will +tell us everything we need to know about + + align:start position:0% +tell us everything we need to know about + + + align:start position:0% +tell us everything we need to know about +Rim remainder after division there's a + + align:start position:0% +Rim remainder after division there's a + + + align:start position:0% +Rim remainder after division there's a +bit of an exp + + align:start position:0% +bit of an exp + + + align:start position:0% +bit of an exp +explation some conventions and the SE + + align:start position:0% +explation some conventions and the SE + + + align:start position:0% +explation some conventions and the SE +alsoo this is perhaps one of the most + + align:start position:0% +alsoo this is perhaps one of the most + + + align:start position:0% +alsoo this is perhaps one of the most +important parts of the help file is to + + align:start position:0% +important parts of the help file is to + + + align:start position:0% +important parts of the help file is to +help you find other commands that are + + align:start position:0% +help you find other commands that are + + + align:start position:0% +help you find other commands that are +useful and related to this command I + + align:start position:0% +useful and related to this command I + + + align:start position:0% +useful and related to this command I +encourage you to try to find the + + align:start position:0% +encourage you to try to find the + + + align:start position:0% +encourage you to try to find the +difference between mod and + + align:start position:0% + + + + align:start position:0% + +rim other than calculating Expressions + + align:start position:0% +rim other than calculating Expressions + + + align:start position:0% +rim other than calculating Expressions +we can also assign their value into + + align:start position:0% +we can also assign their value into + + + align:start position:0% +we can also assign their value into +variables so for example if I want to + + align:start position:0% +variables so for example if I want to + + + align:start position:0% +variables so for example if I want to +create a variable named X I type x + + align:start position:0% +create a variable named X I type x + + + align:start position:0% +create a variable named X I type x +equals and then the value that I want so + + align:start position:0% +equals and then the value that I want so + + + align:start position:0% +equals and then the value that I want so +for example x = 1 will create a variable + + align:start position:0% +for example x = 1 will create a variable + + + align:start position:0% +for example x = 1 will create a variable +called X and put one as the value into + + align:start position:0% +called X and put one as the value into + + + align:start position:0% +called X and put one as the value into +it I can also put the result of an + + align:start position:0% +it I can also put the result of an + + + align:start position:0% +it I can also put the result of an +expression into a variable here's Y = 2 + + align:start position:0% +expression into a variable here's Y = 2 + + + align:start position:0% +expression into a variable here's Y = 2 +* 3 of course that's six so it + + align:start position:0% +* 3 of course that's six so it + + + align:start position:0% +* 3 of course that's six so it +calculates the 6 and puts 2 * 3 into it + + align:start position:0% +calculates the 6 and puts 2 * 3 into it + + + align:start position:0% +calculates the 6 and puts 2 * 3 into it +so now Y is 6 and X is 1 and I can use x + + align:start position:0% +so now Y is 6 and X is 1 and I can use x + + + align:start position:0% +so now Y is 6 and X is 1 and I can use x +and y's if they are numbers x + y the + + align:start position:0% +and y's if they are numbers x + y the + + + align:start position:0% +and y's if they are numbers x + y the +answer is seven if I try to use a + + align:start position:0% +answer is seven if I try to use a + + + align:start position:0% +answer is seven if I try to use a +variable that doesn't yet exist for + + align:start position:0% +variable that doesn't yet exist for + + + align:start position:0% +variable that doesn't yet exist for +example Z Plus plus y I get an error + + align:start position:0% +example Z Plus plus y I get an error + + + align:start position:0% +example Z Plus plus y I get an error +undefined function of variable + + align:start position:0% +undefined function of variable + + + align:start position:0% +undefined function of variable +Z sometimes you're looking for command + + align:start position:0% +Z sometimes you're looking for command + + + align:start position:0% +Z sometimes you're looking for command +but you don't know the command you know + + align:start position:0% +but you don't know the command you know + + + align:start position:0% +but you don't know the command you know +that you're looking for something you + + align:start position:0% +that you're looking for something you + + + align:start position:0% +that you're looking for something you +just don't know what it's called in + + align:start position:0% +just don't know what it's called in + + + align:start position:0% +just don't know what it's called in +matlb in that case you should be using + + align:start position:0% +matlb in that case you should be using + + + align:start position:0% +matlb in that case you should be using +look for to find the command you're + + align:start position:0% +look for to find the command you're + + + align:start position:0% +look for to find the command you're +looking for so for example look for + + align:start position:0% +looking for so for example look for + + + align:start position:0% +looking for so for example look for +square will give you all the commands + + align:start position:0% +square will give you all the commands + + + align:start position:0% +square will give you all the commands +that have the word square in their help + + align:start position:0% +that have the word square in their help + + + align:start position:0% +that have the word square in their help +file of course I was looking for in this + + align:start position:0% +file of course I was looking for in this + + + align:start position:0% +file of course I was looking for in this +case square root and here it is I can + + align:start position:0% +case square root and here it is I can + + + align:start position:0% +case square root and here it is I can +either click on this and that will give + + align:start position:0% +either click on this and that will give + + + align:start position:0% +either click on this and that will give +me the help file of the square root or I + + align:start position:0% +me the help file of the square root or I + + + align:start position:0% +me the help file of the square root or I +can just type help square + + align:start position:0% +can just type help square + + + align:start position:0% +can just type help square +root and that will give me the + + align:start position:0% +root and that will give me the + + + align:start position:0% +root and that will give me the +same square root finds the square of the + + align:start position:0% +same square root finds the square of the + + + align:start position:0% +same square root finds the square of the +elements so if I do Square OT of four I + + align:start position:0% +elements so if I do Square OT of four I + + + align:start position:0% +elements so if I do Square OT of four I +get two notice that I get complex + + align:start position:0% +get two notice that I get complex + + + align:start position:0% +get two notice that I get complex +results if I get a + + align:start position:0% +results if I get a + + + align:start position:0% +results if I get a +non-positive input so Square < TK of + + align:start position:0% +non-positive input so Square < TK of + + + align:start position:0% +non-positive input so Square < TK of +minus 3 + + align:start position:0% +minus 3 + + + align:start position:0% +minus 3 +is the 3 * + + align:start position:0% +is the 3 * + + + align:start position:0% +is the 3 * +I which is of course very nice to know + + align:start position:0% +I which is of course very nice to know + + + align:start position:0% +I which is of course very nice to know +so 2 + + align:start position:0% +so 2 + + + align:start position:0% +so 2 +I squared should give me Min -4 and + + align:start position:0% +I squared should give me Min -4 and + + + align:start position:0% +I squared should give me Min -4 and +indeed 2 i^ s gives me Min -4 on the + + align:start position:0% +indeed 2 i^ s gives me Min -4 on the + + + align:start position:0% +indeed 2 i^ s gives me Min -4 on the +command line there's a useful trick + + align:start position:0% +command line there's a useful trick + + + align:start position:0% +command line there's a useful trick +involving the up button sometimes you're + + align:start position:0% +involving the up button sometimes you're + + + align:start position:0% +involving the up button sometimes you're +looking for something or you're typing + + align:start position:0% +looking for something or you're typing + + + align:start position:0% +looking for something or you're typing +something and you make a + + align:start position:0% +something and you make a + + + align:start position:0% +something and you make a +typo like + + align:start position:0% +typo like + + + align:start position:0% +typo like +this I've swapped the L and the E now I + + align:start position:0% +this I've swapped the L and the E now I + + + align:start position:0% +this I've swapped the L and the E now I +could retype Tye everything from scratch + + align:start position:0% +could retype Tye everything from scratch + + + align:start position:0% +could retype Tye everything from scratch +or I can press the up key up + + align:start position:0% + + + + align:start position:0% + +arrow and then the left Arrow until I + + align:start position:0% +arrow and then the left Arrow until I + + + align:start position:0% +arrow and then the left Arrow until I +can delete the E and put it in the right + + align:start position:0% +can delete the E and put it in the right + + + align:start position:0% +can delete the E and put it in the right +place now I hit enter and I get the help + + align:start position:0% +place now I hit enter and I get the help + + + align:start position:0% +place now I hit enter and I get the help +f with the up arrows and with the up + + align:start position:0% +f with the up arrows and with the up + + + align:start position:0% +f with the up arrows and with the up +arrow and the down arrows I can browse + + align:start position:0% +arrow and the down arrows I can browse + + + align:start position:0% +arrow and the down arrows I can browse +through the history of all the commands + + align:start position:0% +through the history of all the commands + + + align:start position:0% +through the history of all the commands +that I + + align:start position:0% + + + + align:start position:0% + +did if I have a longish expression on + + align:start position:0% +did if I have a longish expression on + + + align:start position:0% +did if I have a longish expression on +the command line and I want to erase the + + align:start position:0% +the command line and I want to erase the + + + align:start position:0% +the command line and I want to erase the +whole thing I could start erasing it or + + align:start position:0% +whole thing I could start erasing it or + + + align:start position:0% +whole thing I could start erasing it or +I could press contrl + + + align:start position:0% + + + + align:start position:0% + +C okay that's probably enough for today + + align:start position:0% +C okay that's probably enough for today + + + align:start position:0% +C okay that's probably enough for today +to exit mat lab I either look for the + + align:start position:0% +to exit mat lab I either look for the + + + align:start position:0% +to exit mat lab I either look for the +quit mat lab + + align:start position:0% +quit mat lab + + + align:start position:0% +quit mat lab +here or I can press Apple Q or from the + + align:start position:0% +here or I can press Apple Q or from the + + + align:start position:0% +here or I can press Apple Q or from the +command line I can type exit \ No newline at end of file diff --git a/jXU0OeAaHn8.txt b/jXU0OeAaHn8.txt new file mode 100644 index 0000000000000000000000000000000000000000..6c1f25369baffe7d8ba6735172e76cc5033bd824 --- /dev/null +++ b/jXU0OeAaHn8.txt @@ -0,0 +1,11112 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so this is a really really + + align:start position:0% +ocw.mit.edu so this is a really really + + + align:start position:0% +ocw.mit.edu so this is a really really +really really stunning fact in a sense + + align:start position:0% +really really stunning fact in a sense + + + align:start position:0% +really really stunning fact in a sense +about we talk about lots of forms of + + align:start position:0% +about we talk about lots of forms of + + + align:start position:0% +about we talk about lots of forms of +um inequality and unfairness in the + + align:start position:0% +um inequality and unfairness in the + + + align:start position:0% +um inequality and unfairness in the +world but here's a fact that's really um + + align:start position:0% +world but here's a fact that's really um + + + align:start position:0% +world but here's a fact that's really um +quite quite quite striking so here the + + align:start position:0% +quite quite quite striking so here the + + + align:start position:0% +quite quite quite striking so here the +fact you start from the basic just the + + align:start position:0% +fact you start from the basic just the + + + align:start position:0% +fact you start from the basic just the +fact it's um it's the fact that if you + + align:start position:0% +fact it's um it's the fact that if you + + + align:start position:0% +fact it's um it's the fact that if you +look at the ratio of men and women in + + align:start position:0% +look at the ratio of men and women in + + + align:start position:0% +look at the ratio of men and women in +the population + + align:start position:0% +the population + + + align:start position:0% +the population +most countries in the + + align:start position:0% +most countries in the + + + align:start position:0% +most countries in the +world have many more women than men uh + + align:start position:0% +world have many more women than men uh + + + align:start position:0% +world have many more women than men uh +this is mostly + + align:start position:0% +this is mostly + + + align:start position:0% +this is mostly +because women are just better designed + + align:start position:0% +because women are just better designed + + + align:start position:0% +because women are just better designed +um it turns out um when men get to the + + align:start position:0% +um it turns out um when men get to the + + + align:start position:0% +um it turns out um when men get to the +age of about uh 60 various things H bad + + align:start position:0% +age of about uh 60 various things H bad + + + align:start position:0% +age of about uh 60 various things H bad +things happen to them in particular + + align:start position:0% +things happen to them in particular + + + align:start position:0% +things happen to them in particular +their arteries seem to harden and they + + align:start position:0% +their arteries seem to harden and they + + + align:start position:0% +their arteries seem to harden and they +they get lots of them die from various + + align:start position:0% +they get lots of them die from various + + + align:start position:0% +they get lots of them die from various +cardiovascular + + align:start position:0% +cardiovascular + + + align:start position:0% +cardiovascular +diseases so uh as a result most + + align:start position:0% +diseases so uh as a result most + + + align:start position:0% +diseases so uh as a result most +countries have many more women than men + + align:start position:0% +countries have many more women than men + + + align:start position:0% +countries have many more women than men +I mean so the ratios are up there uh + + align:start position:0% +I mean so the ratios are up there uh + + + align:start position:0% +I mean so the ratios are up there uh +Europe has + + align:start position:0% +Europe has + + + align:start position:0% +Europe has +1.05 uh Subs Africa is + + align:start position:0% +1.05 uh Subs Africa is + + + align:start position:0% +1.05 uh Subs Africa is +1.02 + + align:start position:0% +1.02 + + + align:start position:0% +1.02 +um most of like most of Latin America is + + align:start position:0% +um most of like most of Latin America is + + + align:start position:0% +um most of like most of Latin America is +also above all of Latin America is above + + align:start position:0% +also above all of Latin America is above + + + align:start position:0% +also above all of Latin America is above +one the US is above one and while it + + align:start position:0% +one the US is above one and while it + + + align:start position:0% +one the US is above one and while it +doesn't look like a lot you know 4% + + align:start position:0% +doesn't look like a lot you know 4% + + + align:start position:0% +doesn't look like a lot you know 4% +we're talking about 4% of you know + + align:start position:0% +we're talking about 4% of you know + + + align:start position:0% +we're talking about 4% of you know +uh three billion so that's a fair number + + align:start position:0% +uh three billion so that's a fair number + + + align:start position:0% +uh three billion so that's a fair number +of extra women uh we're talking about + + align:start position:0% +of extra women uh we're talking about + + + align:start position:0% +of extra women uh we're talking about +the world has many more women than men + + align:start position:0% +the world has many more women than men + + + align:start position:0% +the world has many more women than men +overall but the one place where that's + + align:start position:0% +overall but the one place where that's + + + align:start position:0% +overall but the one place where that's +not true is in this belt which goes from + + align:start position:0% +not true is in this belt which goes from + + + align:start position:0% +not true is in this belt which goes from +basically North Africa to Korea that's + + align:start position:0% +basically North Africa to Korea that's + + + align:start position:0% +basically North Africa to Korea that's +that one belt in the world pretty much + + align:start position:0% +that one belt in the world pretty much + + + align:start position:0% +that one belt in the world pretty much +all the way you can draw a a belt um + + align:start position:0% +all the way you can draw a a belt um + + + align:start position:0% +all the way you can draw a a belt um +starting somewhere in in Morocco and + + align:start position:0% +starting somewhere in in Morocco and + + + align:start position:0% +starting somewhere in in Morocco and +keep going east about at that latitude + + align:start position:0% +keep going east about at that latitude + + + align:start position:0% +keep going east about at that latitude +and that belt and then go a bit north + + align:start position:0% +and that belt and then go a bit north + + + align:start position:0% +and that belt and then go a bit north +into China you'll find that that's where + + align:start position:0% +into China you'll find that that's where + + + align:start position:0% +into China you'll find that that's where +there are about 4% or less women than + + align:start position:0% +there are about 4% or less women than + + + align:start position:0% +there are about 4% or less women than +men so uh less and that's I think that + + align:start position:0% +men so uh less and that's I think that + + + align:start position:0% +men so uh less and that's I think that +the numbers um these numbers you are um + + align:start position:0% +the numbers um these numbers you are um + + + align:start position:0% +the numbers um these numbers you are um +sort of uh I think uh actually you know + + align:start position:0% +sort of uh I think uh actually you know + + + align:start position:0% +sort of uh I think uh actually you know +I'll show you these numbers are not + + align:start position:0% +I'll show you these numbers are not + + + align:start position:0% +I'll show you these numbers are not +necessar the worst numbers you're going + + align:start position:0% +necessar the worst numbers you're going + + + align:start position:0% +necessar the worst numbers you're going +to see so I'll show you some more + + align:start position:0% +to see so I'll show you some more + + + align:start position:0% +to see so I'll show you some more +striking numbers in a minute but I mean + + align:start position:0% +striking numbers in a minute but I mean + + + align:start position:0% +striking numbers in a minute but I mean +just the fact that there's 6% less women + + align:start position:0% +just the fact that there's 6% less women + + + align:start position:0% +just the fact that there's 6% less women +than men uh is striking given that um + + align:start position:0% +than men uh is striking given that um + + + align:start position:0% +than men uh is striking given that um +that's not the + + align:start position:0% +that's not the + + + align:start position:0% +that's not the +biological uh that doesn't look like the + + align:start position:0% +biological uh that doesn't look like the + + + align:start position:0% +biological uh that doesn't look like the +biological model and uh + + align:start position:0% +biological model and uh + + + align:start position:0% +biological model and uh +the way so amen who was a a Nobel Prize + + align:start position:0% +the way so amen who was a a Nobel Prize + + + align:start position:0% +the way so amen who was a a Nobel Prize +winner at Harvard uh did this + + align:start position:0% +winner at Harvard uh did this + + + align:start position:0% +winner at Harvard uh did this +calculation basically very simple + + align:start position:0% +calculation basically very simple + + + align:start position:0% +calculation basically very simple +calculation he he said look you know + + align:start position:0% +calculation he he said look you know + + + align:start position:0% +calculation he he said look you know +Subs Africa is the poorest part of the + + align:start position:0% +Subs Africa is the poorest part of the + + + align:start position:0% +Subs Africa is the poorest part of the +world + + align:start position:0% +world + + + align:start position:0% +world +uh that's so if there is some you know + + align:start position:0% +uh that's so if there is some you know + + + align:start position:0% +uh that's so if there is some you know +maybe institutional reason why women die + + align:start position:0% +maybe institutional reason why women die + + + align:start position:0% +maybe institutional reason why women die +so there might be reasons why women die + + align:start position:0% +so there might be reasons why women die + + + align:start position:0% +so there might be reasons why women die +which have to do with poverty what's an + + align:start position:0% +which have to do with poverty what's an + + + align:start position:0% +which have to do with poverty what's an +example of a reason which which would + + align:start position:0% +example of a reason which which would + + + align:start position:0% +example of a reason which which would +hurt women more than men why reason why + + align:start position:0% +hurt women more than men why reason why + + + align:start position:0% +hurt women more than men why reason why +poverty would hurt women more than men + + align:start position:0% +poverty would hurt women more than men + + + align:start position:0% +poverty would hurt women more than men +during child birth child birth the + + align:start position:0% +during child birth child birth the + + + align:start position:0% +during child birth child birth the +obvious one is child birth yeah and then + + align:start position:0% +obvious one is child birth yeah and then + + + align:start position:0% +obvious one is child birth yeah and then +like compounding upon that like if women + + align:start position:0% +like compounding upon that like if women + + + align:start position:0% +like compounding upon that like if women +in po situations have less access to + + align:start position:0% +in po situations have less access to + + + align:start position:0% +in po situations have less access to +contracept they going have more children + + align:start position:0% +contracept they going have more children + + + align:start position:0% +contracept they going have more children +which increases the likelihood that + + align:start position:0% +which increases the likelihood that + + + align:start position:0% +which increases the likelihood that +there will be + + align:start position:0% +there will be + + + align:start position:0% +there will be +complication so everything to do with + + align:start position:0% +complication so everything to do with + + + align:start position:0% +complication so everything to do with +child birth is a reason why you might + + align:start position:0% +child birth is a reason why you might + + + align:start position:0% +child birth is a reason why you might +think that in poor countries women will + + align:start position:0% +think that in poor countries women will + + + align:start position:0% +think that in poor countries women will +uh women will um have a disadvantage now + + align:start position:0% +uh women will um have a disadvantage now + + + align:start position:0% +uh women will um have a disadvantage now +you take that disadvantage you do see + + align:start position:0% +you take that disadvantage you do see + + + align:start position:0% +you take that disadvantage you do see +evidence of the disadvantage sub Africa + + align:start position:0% +evidence of the disadvantage sub Africa + + + align:start position:0% +evidence of the disadvantage sub Africa +has less women than Europe so you do see + + align:start position:0% +has less women than Europe so you do see + + + align:start position:0% +has less women than Europe so you do see +a example of a disad that disadvantage + + align:start position:0% +a example of a disad that disadvantage + + + align:start position:0% +a example of a disad that disadvantage +it's about uh 2 percentage points or 3 + + align:start position:0% +it's about uh 2 percentage points or 3 + + + align:start position:0% +it's about uh 2 percentage points or 3 +percentage points less women than than + + align:start position:0% +percentage points less women than than + + + align:start position:0% +percentage points less women than than +um than Europe but that's if you think + + align:start position:0% +um than Europe but that's if you think + + + align:start position:0% +um than Europe but that's if you think +of Subs Africa as the part of the world + + align:start position:0% +of Subs Africa as the part of the world + + + align:start position:0% +of Subs Africa as the part of the world +which is the highest uh maternal Mor + + align:start position:0% +which is the highest uh maternal Mor + + + align:start position:0% +which is the highest uh maternal Mor +mortality rates is the part of the world + + align:start position:0% +mortality rates is the part of the world + + + align:start position:0% +mortality rates is the part of the world +which has the highest fertility rates + + align:start position:0% +which has the highest fertility rates + + + align:start position:0% +which has the highest fertility rates +both to your point and your point it has + + align:start position:0% +both to your point and your point it has + + + align:start position:0% +both to your point and your point it has +the if you take the part of the world + + align:start position:0% +the if you take the part of the world + + + align:start position:0% +the if you take the part of the world +where women are most likely to die in + + align:start position:0% +where women are most likely to die in + + + align:start position:0% +where women are most likely to die in +childbirth and place where women have + + align:start position:0% +childbirth and place where women have + + + align:start position:0% +childbirth and place where women have +most + + align:start position:0% + + + + align:start position:0% + +children both of those are highest in + + align:start position:0% +children both of those are highest in + + + align:start position:0% +children both of those are highest in +Subs Africa so you could think of this + + align:start position:0% +Subs Africa so you could think of this + + + align:start position:0% +Subs Africa so you could think of this +as being a reasonable approximation of + + align:start position:0% +as being a reasonable approximation of + + + align:start position:0% +as being a reasonable approximation of +the worst case scenario so take the + + align:start position:0% +the worst case scenario so take the + + + align:start position:0% +the worst case scenario so take the +worst case scenario and then go to China + + align:start position:0% +worst case scenario and then go to China + + + align:start position:0% +worst case scenario and then go to China +so that's the excise let's take the + + align:start position:0% +so that's the excise let's take the + + + align:start position:0% +so that's the excise let's take the +worst case scenario um now go to China + + align:start position:0% +worst case scenario um now go to China + + + align:start position:0% +worst case scenario um now go to China +and ask um if we applied the CH the subs + + align:start position:0% +and ask um if we applied the CH the subs + + + align:start position:0% +and ask um if we applied the CH the subs +African ratio to the Chinese population + + align:start position:0% +African ratio to the Chinese population + + + align:start position:0% +African ratio to the Chinese population +how many more women would it have had + + align:start position:0% +how many more women would it have had + + + align:start position:0% +how many more women would it have had +the answer is they would have had 44 + + align:start position:0% +the answer is they would have had 44 + + + align:start position:0% +the answer is they would have had 44 +million more women so 44 million more + + align:start position:0% +million more women so 44 million more + + + align:start position:0% +million more women so 44 million more +women are missing and that then you keep + + align:start position:0% +women are missing and that then you keep + + + align:start position:0% +women are missing and that then you keep +doing that and same order of magnitude + + align:start position:0% +doing that and same order of magnitude + + + align:start position:0% +doing that and same order of magnitude +in India and then smaller countries so + + align:start position:0% +in India and then smaller countries so + + + align:start position:0% +in India and then smaller countries so +smaller numbers but it all adds up to + + align:start position:0% +smaller numbers but it all adds up to + + + align:start position:0% +smaller numbers but it all adds up to +about 100 million so you get about 100 + + align:start position:0% +about 100 million so you get about 100 + + + align:start position:0% +about 100 million so you get about 100 +million missing women in the world uh by + + align:start position:0% +million missing women in the world uh by + + + align:start position:0% +million missing women in the world uh by +doing this simple exercise and that's + + align:start position:0% +doing this simple exercise and that's + + + align:start position:0% +doing this simple exercise and that's +sort + + align:start position:0% + + + + align:start position:0% + +of Prima evidence as we'll see you have + + align:start position:0% +of Prima evidence as we'll see you have + + + align:start position:0% +of Prima evidence as we'll see you have +to think harder about exactly what this + + align:start position:0% +to think harder about exactly what this + + + align:start position:0% +to think harder about exactly what this +evidence means but it's Prim ay evidence + + align:start position:0% +evidence means but it's Prim ay evidence + + + align:start position:0% +evidence means but it's Prim ay evidence +of something very bizarre happening you + + align:start position:0% +of something very bizarre happening you + + + align:start position:0% +of something very bizarre happening you +know whether this is + + align:start position:0% +know whether this is + + + align:start position:0% +know whether this is +exactly what we'll see what's going on + + align:start position:0% +exactly what we'll see what's going on + + + align:start position:0% +exactly what we'll see what's going on +here but there's something very + + align:start position:0% +here but there's something very + + + align:start position:0% +here but there's something very +troubling about this fact because it + + align:start position:0% +troubling about this fact because it + + + align:start position:0% +troubling about this fact because it +seems like somehow populations are + + align:start position:0% +seems like somehow populations are + + + align:start position:0% +seems like somehow populations are +managing to get rid of Women quote + + align:start position:0% +managing to get rid of Women quote + + + align:start position:0% +managing to get rid of Women quote +unquote losing women um through through + + align:start position:0% +unquote losing women um through through + + + align:start position:0% +unquote losing women um through through +mechanisms which are not the normal + + align:start position:0% +mechanisms which are not the normal + + + align:start position:0% +mechanisms which are not the normal +biological + + align:start position:0% + + + + align:start position:0% + +mechanisms so that's the that's the + + align:start position:0% +mechanisms so that's the that's the + + + align:start position:0% +mechanisms so that's the that's the +missing women yeah so + + align:start position:0% +missing women yeah so + + + align:start position:0% +missing women yeah so +this in China are they like missing in + + align:start position:0% +this in China are they like missing in + + + align:start position:0% +this in China are they like missing in +like rural China or is it just like all + + align:start position:0% +like rural China or is it just like all + + + align:start position:0% +like rural China or is it just like all +around China show you in a minute show + + align:start position:0% +around China show you in a minute show + + + align:start position:0% +around China show you in a minute show +you all kinds of facts about China in + + align:start position:0% + + + + align:start position:0% + +fact + + align:start position:0% +fact + + + align:start position:0% +fact +so before I come to that there just some + + align:start position:0% +so before I come to that there just some + + + align:start position:0% +so before I come to that there just some +questions you might hypothesis you might + + align:start position:0% +questions you might hypothesis you might + + + align:start position:0% +questions you might hypothesis you might +have one + + align:start position:0% +have one + + + align:start position:0% +have one +is is is uh like development the answer + + align:start position:0% +is is is uh like development the answer + + + align:start position:0% +is is is uh like development the answer +maybe it's just that you know people are + + align:start position:0% +maybe it's just that you know people are + + + align:start position:0% +maybe it's just that you know people are +somehow too there's some some reason why + + align:start position:0% +somehow too there's some some reason why + + + align:start position:0% +somehow too there's some some reason why +just being + + align:start position:0% +just being + + + align:start position:0% +just being +underdeveloped for reasons we don't + + align:start position:0% +underdeveloped for reasons we don't + + + align:start position:0% +underdeveloped for reasons we don't +understand translates into less women we + + align:start position:0% +understand translates into less women we + + + align:start position:0% +understand translates into less women we +maybe we have a theory um + + align:start position:0% +maybe we have a theory um + + + align:start position:0% +maybe we have a theory um +that maybe it's the case that people are + + align:start position:0% +that maybe it's the case that people are + + + align:start position:0% +that maybe it's the case that people are +more traditional some something now what + + align:start position:0% +more traditional some something now what + + + align:start position:0% +more traditional some something now what +makes this fact much more worrying is + + align:start position:0% +makes this fact much more worrying is + + + align:start position:0% +makes this fact much more worrying is +that development is not making this fact + + align:start position:0% +that development is not making this fact + + + align:start position:0% +that development is not making this fact +go away that's sort of a at least + + align:start position:0% +go away that's sort of a at least + + + align:start position:0% +go away that's sort of a at least +within within modern history we don't + + align:start position:0% +within within modern history we don't + + + align:start position:0% +within within modern history we don't +know what what what happened 100 years + + align:start position:0% +know what what what happened 100 years + + + align:start position:0% +know what what what happened 100 years +ago but right now development is not + + align:start position:0% +ago but right now development is not + + + align:start position:0% +ago but right now development is not +making this fact go away um if you look + + align:start position:0% +making this fact go away um if you look + + + align:start position:0% +making this fact go away um if you look +at the sex ratio in India it's not + + align:start position:0% +at the sex ratio in India it's not + + + align:start position:0% +at the sex ratio in India it's not +changing it's in + + align:start position:0% +changing it's in + + + align:start position:0% +changing it's in +fact pretty much steady I'll show you + + align:start position:0% +fact pretty much steady I'll show you + + + align:start position:0% +fact pretty much steady I'll show you +numbers in a bit if you look at the sex + + align:start position:0% +numbers in a bit if you look at the sex + + + align:start position:0% +numbers in a bit if you look at the sex +in China it's + + align:start position:0% +in China it's + + + align:start position:0% +in China it's +falling it's less and less women every + + align:start position:0% +falling it's less and less women every + + + align:start position:0% +falling it's less and less women every +year in China and if you look at the uh + + align:start position:0% +year in China and if you look at the uh + + + align:start position:0% +year in China and if you look at the uh +richest parts of China versus the poest + + align:start position:0% +richest parts of China versus the poest + + + align:start position:0% +richest parts of China versus the poest +part to your question you see a negative + + align:start position:0% +part to your question you see a negative + + + align:start position:0% +part to your question you see a negative +correlation the richest parts of China + + align:start position:0% +correlation the richest parts of China + + + align:start position:0% +correlation the richest parts of China +are the ones which have the least women + + align:start position:0% +are the ones which have the least women + + + align:start position:0% +are the ones which have the least women +yeah do we know anything about missing + + align:start position:0% +yeah do we know anything about missing + + + align:start position:0% +yeah do we know anything about missing +men like maybe there's some component + + align:start position:0% +men like maybe there's some component + + + align:start position:0% +men like maybe there's some component +where uh there's just a general for + + align:start position:0% +where uh there's just a general for + + + align:start position:0% +where uh there's just a general for +children in some parts of the world and + + align:start position:0% +children in some parts of the world and + + + align:start position:0% +children in some parts of the world and +children total are missing not just the + + align:start position:0% +children total are missing not just the + + + align:start position:0% +children total are missing not just the +girls perfectly it's a good question I + + align:start position:0% +girls perfectly it's a good question I + + + align:start position:0% +girls perfectly it's a good question I +mean I think that's what people do when + + align:start position:0% +mean I think that's what people do when + + + align:start position:0% +mean I think that's what people do when +they say the infer mortality rate is too + + align:start position:0% +they say the infer mortality rate is too + + + align:start position:0% +they say the infer mortality rate is too +high or something + + align:start position:0% +high or something + + + align:start position:0% +high or something +and I think that that's a I mean that's + + align:start position:0% +and I think that that's a I mean that's + + + align:start position:0% +and I think that that's a I mean that's +that's also a concern it's not that + + align:start position:0% +that's also a concern it's not that + + + align:start position:0% +that's also a concern it's not that +there aren't other concerns because of + + align:start position:0% +there aren't other concerns because of + + + align:start position:0% +there aren't other concerns because of +this that's sort of what lot of lot of + + align:start position:0% +this that's sort of what lot of lot of + + + align:start position:0% +this that's sort of what lot of lot of +um like a lot of people who say that you + + align:start position:0% +um like a lot of people who say that you + + + align:start position:0% +um like a lot of people who say that you +know you shouldn't just look at GDP to + + align:start position:0% +know you shouldn't just look at GDP to + + + align:start position:0% +know you shouldn't just look at GDP to +measure welfare emphasize infant + + align:start position:0% +measure welfare emphasize infant + + + align:start position:0% +measure welfare emphasize infant +mortality rates infant mortality rates + + align:start position:0% +mortality rates infant mortality rates + + + align:start position:0% +mortality rates infant mortality rates +is exactly the question you're asking + + align:start position:0% +is exactly the question you're asking + + + align:start position:0% +is exactly the question you're asking +kind of missing boys and girls and you + + align:start position:0% +kind of missing boys and girls and you + + + align:start position:0% +kind of missing boys and girls and you +do see that that number is very high in + + align:start position:0% +do see that that number is very high in + + + align:start position:0% +do see that that number is very high in +Subs Africa Subs Africa has the highest + + align:start position:0% +Subs Africa Subs Africa has the highest + + + align:start position:0% +Subs Africa Subs Africa has the highest +INF mortality rate in the world by far + + align:start position:0% +INF mortality rate in the world by far + + + align:start position:0% +INF mortality rate in the world by far +China has now INF mortality rates which + + align:start position:0% +China has now INF mortality rates which + + + align:start position:0% +China has now INF mortality rates which +are approaching that in the US so it's + + align:start position:0% +are approaching that in the US so it's + + + align:start position:0% +are approaching that in the US so it's +not so INF mortality rates by itself is + + align:start position:0% +not so INF mortality rates by itself is + + + align:start position:0% +not so INF mortality rates by itself is +not the right by now it's not a huge + + align:start position:0% +not the right by now it's not a huge + + + align:start position:0% +not the right by now it's not a huge +problem in China China is down to the + + align:start position:0% +problem in China China is down to the + + + align:start position:0% +problem in China China is down to the +range where you know it's very very + + align:start position:0% +range where you know it's very very + + + align:start position:0% +range where you know it's very very +close to the US I think he has INF R of + + align:start position:0% +close to the US I think he has INF R of + + + align:start position:0% +close to the US I think he has INF R of +like 25 out of a thousand thousand life + + align:start position:0% +like 25 out of a thousand thousand life + + + align:start position:0% +like 25 out of a thousand thousand life +births us has 18 or I know 14 or + + align:start position:0% +births us has 18 or I know 14 or + + + align:start position:0% +births us has 18 or I know 14 or +something it's it's really in the range + + align:start position:0% +something it's it's really in the range + + + align:start position:0% +something it's it's really in the range +where where Subs Africa um SI Leon has + + align:start position:0% +where where Subs Africa um SI Leon has + + + align:start position:0% +where where Subs Africa um SI Leon has +140 so you if you just take the so if + + align:start position:0% +140 so you if you just take the so if + + + align:start position:0% +140 so you if you just take the so if +you want to see where INF mortality is a + + align:start position:0% +you want to see where INF mortality is a + + + align:start position:0% +you want to see where INF mortality is a +problem that's not where missing women + + align:start position:0% +problem that's not where missing women + + + align:start position:0% +problem that's not where missing women +is a problem these are different + + align:start position:0% +is a problem these are different + + + align:start position:0% +is a problem these are different +problems it's not to say you are not + + align:start position:0% +problems it's not to say you are not + + + align:start position:0% +problems it's not to say you are not +right that's another problem but it's + + align:start position:0% +right that's another problem but it's + + + align:start position:0% +right that's another problem but it's +it's a different one um + + align:start position:0% + + + + align:start position:0% + +so this is sort of uh just just to uh + + align:start position:0% +so this is sort of uh just just to uh + + + align:start position:0% +so this is sort of uh just just to uh +show you that fact if you look at which + + align:start position:0% +show you that fact if you look at which + + + align:start position:0% +show you that fact if you look at which +are the countries which have um this is + + align:start position:0% +are the countries which have um this is + + + align:start position:0% +are the countries which have um this is +the trend in the in so what I showed you + + align:start position:0% +the trend in the in so what I showed you + + + align:start position:0% +the trend in the in so what I showed you +so far was the levels how many women per + + align:start position:0% +so far was the levels how many women per + + + align:start position:0% +so far was the levels how many women per +men this is in + + align:start position:0% +men this is in + + + align:start position:0% +men this is in +2005 What's happen what's the future + + align:start position:0% +2005 What's happen what's the future + + + align:start position:0% +2005 What's happen what's the future +future is much more scary uh than the + + align:start position:0% +future is much more scary uh than the + + + align:start position:0% +future is much more scary uh than the +present the present is what and so if + + align:start position:0% +present the present is what and so if + + + align:start position:0% +present the present is what and so if +you like um 100 there was like 95 girls + + align:start position:0% +you like um 100 there was like 95 girls + + + align:start position:0% +you like um 100 there was like 95 girls +per 100 boys so that's about 105 boys + + align:start position:0% +per 100 boys so that's about 105 boys + + + align:start position:0% +per 100 boys so that's about 105 boys +per 100 + + align:start position:0% +per 100 + + + align:start position:0% +per 100 +girls right that's the current the + + align:start position:0% +girls right that's the current the + + + align:start position:0% +girls right that's the current the +future look at look at the number for + + align:start position:0% +future look at look at the number for + + + align:start position:0% +future look at look at the number for +Eastern + + align:start position:0% +Eastern + + + align:start position:0% +Eastern +Asia that numbers + + align:start position:0% +Asia that numbers + + + align:start position:0% +Asia that numbers +120 boys + + align:start position:0% +120 boys + + + align:start position:0% +120 boys +for uh 100 girls so that's like it's a + + align:start position:0% +for uh 100 girls so that's like it's a + + + align:start position:0% +for uh 100 girls so that's like it's a +completely different order of magnitude + + align:start position:0% +completely different order of magnitude + + + align:start position:0% +completely different order of magnitude +right it's like you know think of the + + align:start position:0% +right it's like you know think of the + + + align:start position:0% +right it's like you know think of the +Future these are the kids who are being + + align:start position:0% +Future these are the kids who are being + + + align:start position:0% +Future these are the kids who are being +born under five so at some point if this + + align:start position:0% +born under five so at some point if this + + + align:start position:0% +born under five so at some point if this +is what stays steady we're going to see + + align:start position:0% +is what stays steady we're going to see + + + align:start position:0% +is what stays steady we're going to see +numbers like more like + + align:start position:0% +numbers like more like + + + align:start position:0% +numbers like more like +120 than 105 right now the there are + + align:start position:0% +120 than 105 right now the there are + + + align:start position:0% +120 than 105 right now the there are +about 105 boys to 100 girls in China and + + align:start position:0% +about 105 boys to 100 girls in China and + + + align:start position:0% +about 105 boys to 100 girls in China and +that number is going to go up to closer + + align:start position:0% +that number is going to go up to closer + + + align:start position:0% +that number is going to go up to closer +to 100 20 if this coh as this cohort + + align:start position:0% +to 100 20 if this coh as this cohort + + + align:start position:0% +to 100 20 if this coh as this cohort +ages so that's so that's not that's just + + align:start position:0% +ages so that's so that's not that's just + + + align:start position:0% +ages so that's so that's not that's just +backing up the first claim I made which + + align:start position:0% +backing up the first claim I made which + + + align:start position:0% +backing up the first claim I made which +is not it's not getting better if you + + align:start position:0% +is not it's not getting better if you + + + align:start position:0% +is not it's not getting better if you +look at the number for India it's 108 + + align:start position:0% +look at the number for India it's 108 + + + align:start position:0% +look at the number for India it's 108 +108 is bigger than the current ratio for + + align:start position:0% +108 is bigger than the current ratio for + + + align:start position:0% +108 is bigger than the current ratio for +of of women to men to women in India so + + align:start position:0% +of of women to men to women in India so + + + align:start position:0% +of of women to men to women in India so +current ratio is about 106 and that's + + align:start position:0% +current ratio is about 106 and that's + + + align:start position:0% +current ratio is about 106 and that's +108 so all of these countries which are + + align:start position:0% +108 so all of these countries which are + + + align:start position:0% +108 so all of these countries which are +getting richer their ratio is getting + + align:start position:0% +getting richer their ratio is getting + + + align:start position:0% +getting richer their ratio is getting +worse do you see what this is how this + + align:start position:0% +worse do you see what this is how this + + + align:start position:0% +worse do you see what this is how this +is different from the one I showed you + + align:start position:0% +is different from the one I showed you + + + align:start position:0% +is different from the one I showed you +before this is the ratio among under + + align:start position:0% +before this is the ratio among under + + + align:start position:0% +before this is the ratio among under +fives so these are the future of that + + align:start position:0% +fives so these are the future of that + + + align:start position:0% +fives so these are the future of that +population whereas I showed you the + + align:start position:0% +population whereas I showed you the + + + align:start position:0% +population whereas I showed you the +present of the population future is + + align:start position:0% +present of the population future is + + + align:start position:0% +present of the population future is +worse not + + align:start position:0% + + + + align:start position:0% + +better + + align:start position:0% +better + + + align:start position:0% +better +um I mean Korea has the same kind of + + align:start position:0% +um I mean Korea has the same kind of + + + align:start position:0% +um I mean Korea has the same kind of +numbers which are worse + + align:start position:0% + + + + align:start position:0% + +um interestingly um Afghanistan and + + align:start position:0% +um interestingly um Afghanistan and + + + align:start position:0% +um interestingly um Afghanistan and +Nepal which are relatively poor + + align:start position:0% +Nepal which are relatively poor + + + align:start position:0% +Nepal which are relatively poor +countries which are not getting rich + + align:start position:0% +countries which are not getting rich + + + align:start position:0% +countries which are not getting rich +rich very fast actually you don't see + + align:start position:0% +rich very fast actually you don't see + + + align:start position:0% +rich very fast actually you don't see +much of a change they're about where + + align:start position:0% +much of a change they're about where + + + align:start position:0% +much of a change they're about where +they were so they their ratio is about + + align:start position:0% +they were so they their ratio is about + + + align:start position:0% +they were so they their ratio is about +in the under five is about what they are + + align:start position:0% +in the under five is about what they are + + + align:start position:0% +in the under five is about what they are +in the adult population so that suggest + + align:start position:0% +in the adult population so that suggest + + + align:start position:0% +in the adult population so that suggest +that they're not getting worse is a + + align:start position:0% +that they're not getting worse is a + + + align:start position:0% +that they're not getting worse is a +riching countries that are getting + + align:start position:0% +riching countries that are getting + + + align:start position:0% +riching countries that are getting +richer are getting worse yeah but when + + align:start position:0% +richer are getting worse yeah but when + + + align:start position:0% +richer are getting worse yeah but when +do you expect this number to be higher + + align:start position:0% +do you expect this number to be higher + + + align:start position:0% +do you expect this number to be higher +than the overall population because + + align:start position:0% +than the overall population because + + + align:start position:0% +than the overall population because +women are more likely to live longer and + + align:start position:0% +women are more likely to live longer and + + + align:start position:0% +women are more likely to live longer and +like more that's that's absolutely true + + align:start position:0% +like more that's that's absolutely true + + + align:start position:0% +like more that's that's absolutely true +so uh 120 won't go to 120 120 is going + + align:start position:0% +so uh 120 won't go to 120 120 is going + + + align:start position:0% +so uh 120 won't go to 120 120 is going +to go 115 that's about the difference so + + align:start position:0% +to go 115 that's about the difference so + + + align:start position:0% +to go 115 that's about the difference so +120 is going to go 115 or 14 but 114 is + + align:start position:0% +120 is going to go 115 or 14 but 114 is + + + align:start position:0% +120 is going to go 115 or 14 but 114 is +a lot better than worse than 106 so this + + align:start position:0% +a lot better than worse than 106 so this + + + align:start position:0% +a lot better than worse than 106 so this +number is + + align:start position:0% +number is + + + align:start position:0% +number is +just all the trends are bad that's sort + + align:start position:0% +just all the trends are bad that's sort + + + align:start position:0% +just all the trends are bad that's sort +of just just just to understand this is + + align:start position:0% +of just just just to understand this is + + + align:start position:0% +of just just just to understand this is +a big problem it's not one that's + + align:start position:0% +a big problem it's not one that's + + + align:start position:0% +a big problem it's not one that's +getting solved but on its own as far as + + align:start position:0% +getting solved but on its own as far as + + + align:start position:0% +getting solved but on its own as far as +I can + + align:start position:0% +I can + + + align:start position:0% +I can +tell um so here's another way to look at + + align:start position:0% +tell um so here's another way to look at + + + align:start position:0% +tell um so here's another way to look at +it so this is India and and + + align:start position:0% +it so this is India and and + + + align:start position:0% +it so this is India and and +China + + align:start position:0% +China + + + align:start position:0% +China +uh give yourself a few minutes to look + + align:start position:0% +uh give yourself a few minutes to look + + + align:start position:0% +uh give yourself a few minutes to look +at this so the the darkest areas are the + + align:start position:0% +at this so the the darkest areas are the + + + align:start position:0% +at this so the the darkest areas are the +worst areas + + align:start position:0% + + + + align:start position:0% + +does anybody know which are the richest + + align:start position:0% +does anybody know which are the richest + + + align:start position:0% +does anybody know which are the richest +richer areas of + + align:start position:0% + + + + align:start position:0% + +China the yeah it's pretty much exactly + + align:start position:0% +China the yeah it's pretty much exactly + + + align:start position:0% +China the yeah it's pretty much exactly +the same you know I think Shanghai is + + align:start position:0% +the same you know I think Shanghai is + + + align:start position:0% +the same you know I think Shanghai is +that gray area right there which is + + align:start position:0% +that gray area right there which is + + + align:start position:0% +that gray area right there which is +actually doing some surprisingly well + + align:start position:0% +actually doing some surprisingly well + + + align:start position:0% +actually doing some surprisingly well +the rest of China which is the the + + align:start position:0% +the rest of China which is the the + + + align:start position:0% +the rest of China which is the the +really poor areas of China are those + + align:start position:0% +really poor areas of China are those + + + align:start position:0% +really poor areas of China are those +very light areas in the east in the west + + align:start position:0% +very light areas in the east in the west + + + align:start position:0% +very light areas in the east in the west +that's the GOI desert the taklamakan + + align:start position:0% +that's the GOI desert the taklamakan + + + align:start position:0% +that's the GOI desert the taklamakan +desert the uh shinyang all the areas + + align:start position:0% +desert the uh shinyang all the areas + + + align:start position:0% +desert the uh shinyang all the areas +where you know with large Muslim + + align:start position:0% +where you know with large Muslim + + + align:start position:0% +where you know with large Muslim +populations are in the East these are + + align:start position:0% +populations are in the East these are + + + align:start position:0% +populations are in the East these are +the poorest parts of China and they are + + align:start position:0% +the poorest parts of China and they are + + + align:start position:0% +the poorest parts of China and they are +the ones which are doing by far the best + + align:start position:0% +the ones which are doing by far the best + + + align:start position:0% +the ones which are doing by far the best +uh the areas that are doing really badly + + align:start position:0% +uh the areas that are doing really badly + + + align:start position:0% +uh the areas that are doing really badly +are the most prosperous you know the + + align:start position:0% +are the most prosperous you know the + + + align:start position:0% +are the most prosperous you know the +dark areas in the Southeast are that's + + align:start position:0% +dark areas in the Southeast are that's + + + align:start position:0% +dark areas in the Southeast are that's +that's like uh Guangdong and guango and + + align:start position:0% +that's like uh Guangdong and guango and + + + align:start position:0% +that's like uh Guangdong and guango and +all these really like fast growing + + align:start position:0% +all these really like fast growing + + + align:start position:0% +all these really like fast growing +wealthy provinces of China that's the + + align:start position:0% +wealthy provinces of China that's the + + + align:start position:0% +wealthy provinces of China that's the +southeast um so that's that's a map that + + align:start position:0% +southeast um so that's that's a map that + + + align:start position:0% +southeast um so that's that's a map that +suggests + + align:start position:0% +suggests + + + align:start position:0% +suggests +again + + align:start position:0% +again + + + align:start position:0% +again +yeah so I'm not really sure exactly um + + align:start position:0% +yeah so I'm not really sure exactly um + + + align:start position:0% +yeah so I'm not really sure exactly um +how portion would play about the fact + + align:start position:0% +how portion would play about the fact + + + align:start position:0% +how portion would play about the fact +that um there's control in the number of + + align:start position:0% +that um there's control in the number of + + + align:start position:0% +that um there's control in the number of +kids that couples can have you now + + align:start position:0% +kids that couples can have you now + + + align:start position:0% +kids that couples can have you now +people might be deciding uh on purpose + + align:start position:0% +people might be deciding uh on purpose + + + align:start position:0% +people might be deciding uh on purpose +to have voice because they want voice + + align:start position:0% +to have voice because they want voice + + + align:start position:0% +to have voice because they want voice +for whatever reason and maybe the people + + align:start position:0% +for whatever reason and maybe the people + + + align:start position:0% +for whatever reason and maybe the people +who can make those decisions are people + + align:start position:0% +who can make those decisions are people + + + align:start position:0% +who can make those decisions are people +who tend to have more money because you + + align:start position:0% +who tend to have more money because you + + + align:start position:0% +who tend to have more money because you +know to have voice is expensive so I + + align:start position:0% +know to have voice is expensive so I + + + align:start position:0% +know to have voice is expensive so I +think that's has a lot to do with it + + align:start position:0% +think that's has a lot to do with it + + + align:start position:0% +think that's has a lot to do with it +we'll come back to that but you're + + align:start position:0% +we'll come back to that but you're + + + align:start position:0% +we'll come back to that but you're +totally right that uh lot of this I + + align:start position:0% +totally right that uh lot of this I + + + align:start position:0% +totally right that uh lot of this I +think is has something to do with + + align:start position:0% +think is has something to do with + + + align:start position:0% +think is has something to do with +people's active choices of + + align:start position:0% +people's active choices of + + + align:start position:0% +people's active choices of +we come back to that um in a little bit + + align:start position:0% +we come back to that um in a little bit + + + align:start position:0% +we come back to that um in a little bit +but but you this pattern is you know you + + align:start position:0% +but but you this pattern is you know you + + + align:start position:0% +but but you this pattern is you know you +think of if as the China gets even + + align:start position:0% +think of if as the China gets even + + + align:start position:0% +think of if as the China gets even +richer if this is the trend then it's a + + align:start position:0% +richer if this is the trend then it's a + + + align:start position:0% +richer if this is the trend then it's a +worrying Trend let's say um now look at + + align:start position:0% +worrying Trend let's say um now look at + + + align:start position:0% +worrying Trend let's say um now look at +India again do you + + align:start position:0% +India again do you + + + align:start position:0% +India again do you +know what what those relatively pale + + align:start position:0% +know what what those relatively pale + + + align:start position:0% +know what what those relatively pale +areas + + align:start position:0% + + + + align:start position:0% + +are the South India which + + align:start position:0% +are the South India which + + + align:start position:0% +are the South India which +is relatively prosperous + + align:start position:0% +is relatively prosperous + + + align:start position:0% +is relatively prosperous +and well educated and East India which + + align:start position:0% +and well educated and East India which + + + align:start position:0% +and well educated and East India which +is the poorest and the most backward + + align:start position:0% +is the poorest and the most backward + + + align:start position:0% +is the poorest and the most backward +part of + + align:start position:0% +part of + + + align:start position:0% +part of +India so if you take if you as you go + + align:start position:0% +India so if you take if you as you go + + + align:start position:0% +India so if you take if you as you go +west and North you're going to some of + + align:start position:0% +west and North you're going to some of + + + align:start position:0% +west and North you're going to some of +the Richer richest richest parts of + + align:start position:0% +the Richer richest richest parts of + + + align:start position:0% +the Richer richest richest parts of +richest state in India large state in + + align:start position:0% +richest state in India large state in + + + align:start position:0% +richest state in India large state in +India is um Maharashtra which is the + + align:start position:0% +India is um Maharashtra which is the + + + align:start position:0% +India is um Maharashtra which is the +kind of the striped State uh uh let's + + align:start position:0% +kind of the striped State uh uh let's + + + align:start position:0% +kind of the striped State uh uh let's +see on the west coast the first state + + align:start position:0% +see on the west coast the first state + + + align:start position:0% +see on the west coast the first state +that's not if you go from the south on + + align:start position:0% +that's not if you go from the south on + + + align:start position:0% +that's not if you go from the south on +the west coast the one the first striped + + align:start position:0% +the west coast the one the first striped + + + align:start position:0% +the west coast the one the first striped +one that's Maharashtra that's that's the + + align:start position:0% +one that's Maharashtra that's that's the + + + align:start position:0% +one that's Maharashtra that's that's the +richest but the second richest large + + align:start position:0% +richest but the second richest large + + + align:start position:0% +richest but the second richest large +state is Delhi is Punjab and Punjab is + + align:start position:0% +state is Delhi is Punjab and Punjab is + + + align:start position:0% +state is Delhi is Punjab and Punjab is +that uh piece of black that's right in + + align:start position:0% +that uh piece of black that's right in + + + align:start position:0% +that uh piece of black that's right in +the north so that that's that's + + align:start position:0% +the north so that that's that's + + + align:start position:0% +the north so that that's that's +literally the second richest and still + + align:start position:0% +literally the second richest and still + + + align:start position:0% +literally the second richest and still +recently the richest state in India is + + align:start position:0% +recently the richest state in India is + + + align:start position:0% +recently the richest state in India is +that area in Black so again same pattern + + align:start position:0% +that area in Black so again same pattern + + + align:start position:0% +that area in Black so again same pattern +Rich states have worse outcomes not + + align:start position:0% +Rich states have worse outcomes not + + + align:start position:0% +Rich states have worse outcomes not +better outcomes um there's no evidence + + align:start position:0% +better outcomes um there's no evidence + + + align:start position:0% +better outcomes um there's no evidence +of of um of a positive correlation + + align:start position:0% +of of um of a positive correlation + + + align:start position:0% +of of um of a positive correlation +between income and and uh the gender + + align:start position:0% +between income and and uh the gender + + + align:start position:0% +between income and and uh the gender +ratio is PAB the only state in India + + align:start position:0% +ratio is PAB the only state in India + + + align:start position:0% +ratio is PAB the only state in India +that has a different religion than the + + align:start position:0% +that has a different religion than the + + + align:start position:0% +that has a different religion than the +rest of the + + align:start position:0% +rest of the + + + align:start position:0% +rest of the +others or would that be a reason maybe + + align:start position:0% +others or would that be a reason maybe + + + align:start position:0% +others or would that be a reason maybe +uh so Punjab has um but that that's + + align:start position:0% +uh so Punjab has um but that that's + + + align:start position:0% +uh so Punjab has um but that that's +actually what that is is there really + + align:start position:0% +actually what that is is there really + + + align:start position:0% +actually what that is is there really +two states there there's Punjab and + + align:start position:0% +two states there there's Punjab and + + + align:start position:0% +two states there there's Punjab and +harana they used to be both a part of + + align:start position:0% +harana they used to be both a part of + + + align:start position:0% +harana they used to be both a part of +Punjab now they've been split into two + + align:start position:0% +Punjab now they've been split into two + + + align:start position:0% +Punjab now they've been split into two +states for some years one of one of + + align:start position:0% +states for some years one of one of + + + align:start position:0% +states for some years one of one of +those States is sik majority sik is a + + align:start position:0% +those States is sik majority sik is a + + + align:start position:0% +those States is sik majority sik is a +particular other religion the other is + + align:start position:0% +particular other religion the other is + + + align:start position:0% +particular other religion the other is +Hindu majority there's no difference + + align:start position:0% +Hindu majority there's no difference + + + align:start position:0% +Hindu majority there's no difference +actually harana is slightly worse than + + align:start position:0% +actually harana is slightly worse than + + + align:start position:0% +actually harana is slightly worse than +Punjab Delhi city is one of the worst + + align:start position:0% +Punjab Delhi city is one of the worst + + + align:start position:0% +Punjab Delhi city is one of the worst +places actually in in India so and + + align:start position:0% +places actually in in India so and + + + align:start position:0% +places actually in in India so and +that's one of the absolutely richest + + align:start position:0% +that's one of the absolutely richest + + + align:start position:0% +that's one of the absolutely richest +places so basically no evidence of a + + align:start position:0% +places so basically no evidence of a + + + align:start position:0% +places so basically no evidence of a +positive correlation between income and + + align:start position:0% +positive correlation between income and + + + align:start position:0% +positive correlation between income and +the gender ratio gender ratio if + + align:start position:0% +the gender ratio gender ratio if + + + align:start position:0% +the gender ratio gender ratio if +anything gets worse as as you get richer + + align:start position:0% +anything gets worse as as you get richer + + + align:start position:0% +anything gets worse as as you get richer +for reasons that may very well be close + + align:start position:0% +for reasons that may very well be close + + + align:start position:0% +for reasons that may very well be close +to what you suggesting but it's clear + + align:start position:0% +to what you suggesting but it's clear + + + align:start position:0% +to what you suggesting but it's clear +that you get this um rather dismal + + align:start position:0% +that you get this um rather dismal + + + align:start position:0% +that you get this um rather dismal +pattern here's some something else + + align:start position:0% +pattern here's some something else + + + align:start position:0% +pattern here's some something else +another fact about sort of China and + + align:start position:0% +another fact about sort of China and + + + align:start position:0% +another fact about sort of China and +it's sort of a very longterm view of + + align:start position:0% +it's sort of a very longterm view of + + + align:start position:0% +it's sort of a very longterm view of +China + + align:start position:0% +China + + + align:start position:0% +China +so if you look + + align:start position:0% +so if you look + + + align:start position:0% +so if you look +at this this starts in + + align:start position:0% +at this this starts in + + + align:start position:0% +at this this starts in + + align:start position:0% + + + align:start position:0% +and you can see that + + align:start position:0% +and you can see that + + + align:start position:0% +and you can see that +basically from the + + align:start position:0% +basically from the + + + align:start position:0% +basically from the +1920s the uh excess SE uh sex ratio + + align:start position:0% +1920s the uh excess SE uh sex ratio + + + align:start position:0% +1920s the uh excess SE uh sex ratio +which is + + align:start position:0% +which is + + + align:start position:0% +which is +um in the fiveyear in the fiveyear Birth + + align:start position:0% +um in the fiveyear in the fiveyear Birth + + + align:start position:0% +um in the fiveyear in the fiveyear Birth +Cohort so people who are born in that + + align:start position:0% +Cohort so people who are born in that + + + align:start position:0% +Cohort so people who are born in that +year what's the what's the fraction of + + align:start position:0% +year what's the what's the fraction of + + + align:start position:0% +year what's the what's the fraction of +boys versus girls so uh it used to be + + align:start position:0% +boys versus girls so uh it used to be + + + align:start position:0% +boys versus girls so uh it used to be +about you know 7% more boys than girls + + align:start position:0% +about you know 7% more boys than girls + + + align:start position:0% +about you know 7% more boys than girls +then it went up to about 16% during + + align:start position:0% +then it went up to about 16% during + + + align:start position:0% +then it went up to about 16% during +their years when there was a lot of + + align:start position:0% +their years when there was a lot of + + + align:start position:0% +their years when there was a lot of +political instability so if you take of + + align:start position:0% +political instability so if you take of + + + align:start position:0% +political instability so if you take of +that those years the Japanese invasion + + align:start position:0% +that those years the Japanese invasion + + + align:start position:0% +that those years the Japanese invasion +before that and after that in a sense + + align:start position:0% +before that and after that in a sense + + + align:start position:0% +before that and after that in a sense +China is in Civil War there's a big you + + align:start position:0% +China is in Civil War there's a big you + + + align:start position:0% +China is in Civil War there's a big you +know what are called the Warlords are + + align:start position:0% +know what are called the Warlords are + + + align:start position:0% +know what are called the Warlords are +fighting each other through China so + + align:start position:0% +fighting each other through China so + + + align:start position:0% +fighting each other through China so +during Wars you see this ratio going way + + align:start position:0% +during Wars you see this ratio going way + + + align:start position:0% +during Wars you see this ratio going way +up then it comes down down down down + + align:start position:0% +up then it comes down down down down + + + align:start position:0% +up then it comes down down down down +down down till about + + align:start position:0% + + + + align:start position:0% + +1976 or something now uh right around + + align:start position:0% +1976 or something now uh right around + + + align:start position:0% +1976 or something now uh right around +1976 something else happens China + + align:start position:0% +1976 something else happens China + + + align:start position:0% +1976 something else happens China +institutes What's called the one child + + align:start position:0% +institutes What's called the one child + + + align:start position:0% +institutes What's called the one child +policy one child policy is one where at + + align:start position:0% +policy one child policy is one where at + + + align:start position:0% +policy one child policy is one where at +least in the Richer areas where it was + + align:start position:0% +least in the Richer areas where it was + + + align:start position:0% +least in the Richer areas where it was +is the only place was enforced families + + align:start position:0% +is the only place was enforced families + + + align:start position:0% +is the only place was enforced families +were allowed to have only one child at + + align:start position:0% + + + + align:start position:0% + +most then that policy gets implemented + + align:start position:0% +most then that policy gets implemented + + + align:start position:0% +most then that policy gets implemented +in the mid '70s and you see what + + align:start position:0% +in the mid '70s and you see what + + + align:start position:0% +in the mid '70s and you see what +happened since what's striking is that + + align:start position:0% +happened since what's striking is that + + + align:start position:0% +happened since what's striking is that +it doesn't just go up and stay up it + + align:start position:0% +it doesn't just go up and stay up it + + + align:start position:0% +it doesn't just go up and stay up it +keeps going + + align:start position:0% +keeps going + + + align:start position:0% +keeps going +up so there's something else going on on + + align:start position:0% +up so there's something else going on on + + + align:start position:0% +up so there's something else going on on +top of the fact that the one child + + align:start position:0% +top of the fact that the one child + + + align:start position:0% +top of the fact that the one child +policy gets instituted in fact the over + + align:start position:0% +policy gets instituted in fact the over + + + align:start position:0% +policy gets instituted in fact the over +time the one child policy has been + + align:start position:0% +time the one child policy has been + + + align:start position:0% +time the one child policy has been +relaxed families which have had you know + + align:start position:0% +relaxed families which have had you know + + + align:start position:0% +relaxed families which have had you know +and this reflects some of the tastes of + + align:start position:0% +and this reflects some of the tastes of + + + align:start position:0% +and this reflects some of the tastes of +the population clearly families which + + align:start position:0% +the population clearly families which + + + align:start position:0% +the population clearly families which +had one daughter where in some areas + + align:start position:0% +had one daughter where in some areas + + + align:start position:0% +had one daughter where in some areas +were allowed to have a son or have a + + align:start position:0% +were allowed to have a son or have a + + + align:start position:0% +were allowed to have a son or have a +second child uh more more recently so + + align:start position:0% +second child uh more more recently so + + + align:start position:0% +second child uh more more recently so +there's some attempt to relax the policy + + align:start position:0% +there's some attempt to relax the policy + + + align:start position:0% +there's some attempt to relax the policy +in exactly the direction that suggests + + align:start position:0% +in exactly the direction that suggests + + + align:start position:0% +in exactly the direction that suggests +that there is a preference for boys uh + + align:start position:0% +that there is a preference for boys uh + + + align:start position:0% +that there is a preference for boys uh +but with all that the trend has been up + + align:start position:0% +but with all that the trend has been up + + + align:start position:0% +but with all that the trend has been up +yeah time those polies + + align:start position:0% +yeah time those polies + + + align:start position:0% +yeah time those polies +the + + align:start position:0% +the + + + align:start position:0% +the +relaxation the relaxation + + align:start position:0% +relaxation the relaxation + + + align:start position:0% +relaxation the relaxation +actually bunch of the relaxations happen + + align:start position:0% +actually bunch of the relaxations happen + + + align:start position:0% +actually bunch of the relaxations happen +you see that flattening in about + + align:start position:0% +you see that flattening in about + + + align:start position:0% +you see that flattening in about +1982 that's the first + + align:start position:0% +1982 that's the first + + + align:start position:0% +1982 that's the first +relaxation so you do see a flattening + + align:start position:0% +relaxation so you do see a flattening + + + align:start position:0% +relaxation so you do see a flattening +but the trend is bad but yeah kids being + + align:start position:0% +but the trend is bad but yeah kids being + + + align:start position:0% +but the trend is bad but yeah kids being +relaxed just been relaxed the first kid + + align:start position:0% +relaxed just been relaxed the first kid + + + align:start position:0% +relaxed just been relaxed the first kid +that you have a a girl right and then in + + align:start position:0% +that you have a a girl right and then in + + + align:start position:0% +that you have a a girl right and then in +that case you might then try to have a + + align:start position:0% +that case you might then try to have a + + + align:start position:0% +that case you might then try to have a +boy but then if you have a boy right + + align:start position:0% +boy but then if you have a boy right + + + align:start position:0% +boy but then if you have a boy right +away away and maybe just stop having + + align:start position:0% +away away and maybe just stop having + + + align:start position:0% +away away and maybe just stop having +kids so still uh actually let's let's + + align:start position:0% +kids so still uh actually let's let's + + + align:start position:0% +kids so still uh actually let's let's +take that + + align:start position:0% +take that + + + align:start position:0% +take that +so could this be generated by a stopping + + align:start position:0% +so could this be generated by a stopping + + + align:start position:0% +so could this be generated by a stopping +rule this is um so imagine that families + + align:start position:0% +rule this is um so imagine that families + + + align:start position:0% +rule this is um so imagine that families +have a stopping rule which says we will + + align:start position:0% +have a stopping rule which says we will + + + align:start position:0% +have a stopping rule which says we will +stop when we + + align:start position:0% +stop when we + + + align:start position:0% +stop when we +have the + + align:start position:0% +have the + + + align:start position:0% +have the +first boy okay this is the stopping rule + + align:start position:0% +first boy okay this is the stopping rule + + + align:start position:0% +first boy okay this is the stopping rule +this is a plausible stopping rule my + + align:start position:0% +this is a plausible stopping rule my + + + align:start position:0% +this is a plausible stopping rule my +mother + + align:start position:0% + + + + align:start position:0% + +had has three brothers it's one brother + + align:start position:0% +had has three brothers it's one brother + + + align:start position:0% +had has three brothers it's one brother +and three sisters the brother is the + + align:start position:0% +and three sisters the brother is the + + + align:start position:0% +and three sisters the brother is the +youngest so that's that's not an + + align:start position:0% +youngest so that's that's not an + + + align:start position:0% +youngest so that's that's not an +implausible stopping my mother's only + + align:start position:0% +implausible stopping my mother's only + + + align:start position:0% +implausible stopping my mother's only +brother has three daughters and one son + + align:start position:0% +brother has three daughters and one son + + + align:start position:0% +brother has three daughters and one son +the son is the youngest so it's not it's + + align:start position:0% +the son is the youngest so it's not it's + + + align:start position:0% +the son is the youngest so it's not it's +not an implausible stopping rule however + + align:start position:0% +not an implausible stopping rule however + + + align:start position:0% +not an implausible stopping rule however +um imagine we had this stopping + + align:start position:0% +um imagine we had this stopping + + + align:start position:0% +um imagine we had this stopping +rule but in any bir Earth the + + align:start position:0% +rule but in any bir Earth the + + + align:start position:0% +rule but in any bir Earth the +probability of boy and girl were + + align:start position:0% +probability of boy and girl were + + + align:start position:0% +probability of boy and girl were +equal what would be the population sex + + align:start position:0% + + + + align:start position:0% + +ratio you have more wom no + + align:start position:0% +ratio you have more wom no + + + align:start position:0% +ratio you have more wom no +it's which one if you keep having + + align:start position:0% +it's which one if you keep having + + + align:start position:0% +it's which one if you keep having +children when you you have women then + + align:start position:0% +children when you you have women then + + + align:start position:0% +children when you you have women then +and you stop as soon as you have one boy + + align:start position:0% +and you stop as soon as you have one boy + + + align:start position:0% +and you stop as soon as you have one boy +you'd have more women you'd expect it + + align:start position:0% + + + + align:start position:0% + +stop immediately stop + + align:start position:0% + + + + align:start position:0% + +iMed + + align:start position:0% + + + + align:start position:0% + +might will more most families + + align:start position:0% + + + + align:start position:0% + +will so you think there'll be more the + + align:start position:0% +will so you think there'll be more the + + + align:start position:0% +will so you think there'll be more the +boys one that I mean I think it pretty + + align:start position:0% +boys one that I mean I think it pretty + + + align:start position:0% +boys one that I mean I think it pretty +much + + align:start position:0% +much + + + align:start position:0% +much +even I think there'll be more boys if + + align:start position:0% +even I think there'll be more boys if + + + align:start position:0% +even I think there'll be more boys if +you have a boy you just stop so then + + align:start position:0% +you have a boy you just stop so then + + + align:start position:0% +you have a boy you just stop so then +that family just has a boy and if you + + align:start position:0% +that family just has a boy and if you + + + align:start position:0% +that family just has a boy and if you +have a girl and then you try again then + + align:start position:0% +have a girl and then you try again then + + + align:start position:0% +have a girl and then you try again then +you if you have a boy then right now you + + align:start position:0% +you if you have a boy then right now you + + + align:start position:0% +you if you have a boy then right now you +have one family with one boy and another + + align:start position:0% +have one family with one boy and another + + + align:start position:0% +have one family with one boy and another +family with a girl and a boy but there's + + align:start position:0% +family with a girl and a boy but there's + + + align:start position:0% +family with a girl and a boy but there's +still more boys than girls so like + + align:start position:0% +still more boys than girls so like + + + align:start position:0% +still more boys than girls so like +whenever you get the boy you stock so + + align:start position:0% +whenever you get the boy you stock so + + + align:start position:0% +whenever you get the boy you stock so +you would have come back to that yeah so + + align:start position:0% +you would have come back to that yeah so + + + align:start position:0% +you would have come back to that yeah so +like if you just do like an expected Val + + align:start position:0% +like if you just do like an expected Val + + + align:start position:0% +like if you just do like an expected Val +is like you like half like half the + + align:start position:0% +is like you like half like half the + + + align:start position:0% +is like you like half like half the +cases you have one boy qu the cases you + + align:start position:0% +cases you have one boy qu the cases you + + + align:start position:0% +cases you have one boy qu the cases you +have girl boy you're exactly right the + + align:start position:0% +have girl boy you're exactly right the + + + align:start position:0% +have girl boy you're exactly right the +answer is it doesn't change anything and + + align:start position:0% +answer is it doesn't change anything and + + + align:start position:0% +answer is it doesn't change anything and +it's very simple to see the reason why + + align:start position:0% +it's very simple to see the reason why + + + align:start position:0% +it's very simple to see the reason why +it doesn't change anything is very + + align:start position:0% +it doesn't change anything is very + + + align:start position:0% +it doesn't change anything is very +simple which is that every Birth has a + + align:start position:0% +simple which is that every Birth has a + + + align:start position:0% +simple which is that every Birth has a +50% chance of having a boy so just take + + align:start position:0% +50% chance of having a boy so just take + + + align:start position:0% +50% chance of having a boy so just take +the number of births forget about + + align:start position:0% +the number of births forget about + + + align:start position:0% +the number of births forget about +families there's there's a certain + + align:start position:0% +families there's there's a certain + + + align:start position:0% +families there's there's a certain +number of births let's say 50 million + + align:start position:0% +number of births let's say 50 million + + + align:start position:0% +number of births let's say 50 million +births 25 million of those births will + + align:start position:0% +births 25 million of those births will + + + align:start position:0% +births 25 million of those births will +be bo boys and 25 million of those + + align:start position:0% +be bo boys and 25 million of those + + + align:start position:0% +be bo boys and 25 million of those +births will be girls doesn't matter + + align:start position:0% +births will be girls doesn't matter + + + align:start position:0% +births will be girls doesn't matter +which family it happens every birth is a + + align:start position:0% +which family it happens every birth is a + + + align:start position:0% +which family it happens every birth is a +separate independent event and has 50% + + align:start position:0% +separate independent event and has 50% + + + align:start position:0% +separate independent event and has 50% +chance of being a boy so it paradoxical + + align:start position:0% +chance of being a boy so it paradoxical + + + align:start position:0% +chance of being a boy so it paradoxical +as it sound stopping rules don't change + + align:start position:0% +as it sound stopping rules don't change + + + align:start position:0% +as it sound stopping rules don't change +the sex ratio they change the + + align:start position:0% +the sex ratio they change the + + + align:start position:0% +the sex ratio they change the +distribution now here's what might be + + align:start position:0% +distribution now here's what might be + + + align:start position:0% +distribution now here's what might be +going on which is more + + align:start position:0% +going on which is more + + + align:start position:0% +going on which is more +complicated yeah but again but the the + + align:start position:0% +complicated yeah but again but the the + + + align:start position:0% +complicated yeah but again but the the +relaxation is not that like it's + + align:start position:0% +relaxation is not that like it's + + + align:start position:0% +relaxation is not that like it's +completely relaxed so that you're going + + align:start position:0% +completely relaxed so that you're going + + + align:start position:0% +completely relaxed so that you're going +to have it so that would be true if you + + align:start position:0% +to have it so that would be true if you + + + align:start position:0% +to have it so that would be true if you +can have as many kids as possible but + + align:start position:0% +can have as many kids as possible but + + + align:start position:0% +can have as many kids as possible but +but like doesn't it make a difference + + align:start position:0% +but like doesn't it make a difference + + + align:start position:0% +but like doesn't it make a difference +though if you have to + + align:start position:0% +though if you have to + + + align:start position:0% +though if you have to +stop um as as long as you don't + + align:start position:0% +stop um as as long as you don't + + + align:start position:0% +stop um as as long as you don't +determine the sex of the + + align:start position:0% +determine the sex of the + + + align:start position:0% +determine the sex of the +child directly it doesn't doesn't matter + + align:start position:0% +child directly it doesn't doesn't matter + + + align:start position:0% +child directly it doesn't doesn't matter +you going to every every birth is an + + align:start position:0% +you going to every every birth is an + + + align:start position:0% +you going to every every birth is an +independent event with a 50% chance of + + align:start position:0% +independent event with a 50% chance of + + + align:start position:0% +independent event with a 50% chance of +being a boy so take the number of births + + align:start position:0% +being a boy so take the number of births + + + align:start position:0% +being a boy so take the number of births +multiply by 50% you're going to get + + align:start position:0% +multiply by 50% you're going to get + + + align:start position:0% +multiply by 50% you're going to get +number of so it makes no difference now + + align:start position:0% +number of so it makes no difference now + + + align:start position:0% +number of so it makes no difference now +let's think of one more step in that + + align:start position:0% +let's think of one more step in that + + + align:start position:0% +let's think of one more step in that +argument which families would a lot of + + align:start position:0% +argument which families would a lot of + + + align:start position:0% +argument which families would a lot of +girls going on grow up in how many how + + align:start position:0% +girls going on grow up in how many how + + + align:start position:0% +girls going on grow up in how many how +many children would would they have more + + align:start position:0% +many children would would they have more + + + align:start position:0% +many children would would they have more +children or less children would girls + + align:start position:0% +children or less children would girls + + + align:start position:0% +children or less children would girls +grow up on average in a family with more + + align:start position:0% +grow up on average in a family with more + + + align:start position:0% +grow up on average in a family with more +children or less children more children + + align:start position:0% +children or less children more children + + + align:start position:0% +children or less children more children +so if you think that families that are + + align:start position:0% +so if you think that families that are + + + align:start position:0% +so if you think that families that are +more children have less + + align:start position:0% +more children have less + + + align:start position:0% +more children have less +resources then you have a stopping rule + + align:start position:0% +resources then you have a stopping rule + + + align:start position:0% +resources then you have a stopping rule +then girls would be growing up in + + align:start position:0% +then girls would be growing up in + + + align:start position:0% +then girls would be growing up in +families with more children and + + align:start position:0% +families with more children and + + + align:start position:0% +families with more children and +therefore less + + align:start position:0% +therefore less + + + align:start position:0% +therefore less +resources and therefore girls will + + align:start position:0% +resources and therefore girls will + + + align:start position:0% +resources and therefore girls will +be a stopping rule can have an effect on + + align:start position:0% +be a stopping rule can have an effect on + + + align:start position:0% +be a stopping rule can have an effect on +on child outcomes because it goes it + + align:start position:0% +on child outcomes because it goes it + + + align:start position:0% +on child outcomes because it goes it +girls it leads to girls being all living + + align:start position:0% +girls it leads to girls being all living + + + align:start position:0% +girls it leads to girls being all living +in large families and boys all living in + + align:start position:0% +in large families and boys all living in + + + align:start position:0% +in large families and boys all living in +small families so boys get all the + + align:start position:0% +small families so boys get all the + + + align:start position:0% +small families so boys get all the +attention the parental resources girls + + align:start position:0% +attention the parental resources girls + + + align:start position:0% +attention the parental resources girls +you know the seven girls and one boy in + + align:start position:0% +you know the seven girls and one boy in + + + align:start position:0% +you know the seven girls and one boy in +the in the girl families and therefore + + align:start position:0% +the in the girl families and therefore + + + align:start position:0% +the in the girl families and therefore +the girls end up with getting less + + align:start position:0% +the girls end up with getting less + + + align:start position:0% +the girls end up with getting less +resources so that's one possible reason + + align:start position:0% +resources so that's one possible reason + + + align:start position:0% +resources so that's one possible reason +why you might get this outcome is that + + align:start position:0% +why you might get this outcome is that + + + align:start position:0% +why you might get this outcome is that +it has something to do with the stopping + + align:start position:0% +it has something to do with the stopping + + + align:start position:0% +it has something to do with the stopping +rule but not directly has to do with the + + align:start position:0% +rule but not directly has to do with the + + + align:start position:0% +rule but not directly has to do with the +stopping rule then generates an + + align:start position:0% +stopping rule then generates an + + + align:start position:0% +stopping rule then generates an +allocation of girls across families yeah + + align:start position:0% +allocation of girls across families yeah + + + align:start position:0% +allocation of girls across families yeah +but so that's also true if you like if + + align:start position:0% +but so that's also true if you like if + + + align:start position:0% +but so that's also true if you like if +you think about like even with the + + align:start position:0% +you think about like even with the + + + align:start position:0% +you think about like even with the +relaxation like imagine a family in a + + align:start position:0% +relaxation like imagine a family in a + + + align:start position:0% +relaxation like imagine a family in a +rich area where you know like like + + align:start position:0% +rich area where you know like like + + + align:start position:0% +rich area where you know like like +everything is more expensive let's say + + align:start position:0% +everything is more expensive let's say + + + align:start position:0% +everything is more expensive let's say +even if it was a little bit more relaxed + + align:start position:0% +even if it was a little bit more relaxed + + + align:start position:0% +even if it was a little bit more relaxed +they still limit themselves to say okay + + align:start position:0% +they still limit themselves to say okay + + + align:start position:0% +they still limit themselves to say okay +we're going to have a maximum of two + + align:start position:0% +we're going to have a maximum of two + + + align:start position:0% +we're going to have a maximum of two +kids so let's say yeah like maybe the + + align:start position:0% +kids so let's say yeah like maybe the + + + align:start position:0% +kids so let's say yeah like maybe the +first uh kid that they have is a it's a + + align:start position:0% +first uh kid that they have is a it's a + + + align:start position:0% +first uh kid that they have is a it's a +girl but then they say you know the + + align:start position:0% +girl but then they say you know the + + + align:start position:0% +girl but then they say you know the +probability of having a girlfriend the + + align:start position:0% +probability of having a girlfriend the + + + align:start position:0% +probability of having a girlfriend the +next one maybe it's not really 50% % + + align:start position:0% +next one maybe it's not really 50% % + + + align:start position:0% +next one maybe it's not really 50% % +because they say well unless we get + + align:start position:0% +because they say well unless we get + + + align:start position:0% +because they say well unless we get +we're only going to have this kid if it + + align:start position:0% +we're only going to have this kid if it + + + align:start position:0% +we're only going to have this kid if it +is a boy yeah so you what you're saying + + align:start position:0% +is a boy yeah so you what you're saying + + + align:start position:0% +is a boy yeah so you what you're saying +is completely right that the only way + + align:start position:0% +is completely right that the only way + + + align:start position:0% +is completely right that the only way +you get away from 50/50 is by + + align:start position:0% +you get away from 50/50 is by + + + align:start position:0% +you get away from 50/50 is by +deliberately or at least doing something + + align:start position:0% +deliberately or at least doing something + + + align:start position:0% +deliberately or at least doing something +to the girl that makes her not live + + align:start position:0% +to the girl that makes her not live + + + align:start position:0% +to the girl that makes her not live +that's the only way you get there if she + + align:start position:0% +that's the only way you get there if she + + + align:start position:0% +that's the only way you get there if she +if if you have if the girls who are born + + align:start position:0% +if if you have if the girls who are born + + + align:start position:0% +if if you have if the girls who are born +live then you you can't get away from + + align:start position:0% +live then you you can't get away from + + + align:start position:0% +live then you you can't get away from +this it's it doesn't matter what your + + align:start position:0% +this it's it doesn't matter what your + + + align:start position:0% +this it's it doesn't matter what your +stopping rule is even if the government + + align:start position:0% +stopping rule is even if the government + + + align:start position:0% +stopping rule is even if the government +makes complicated policies the policies + + align:start position:0% +makes complicated policies the policies + + + align:start position:0% +makes complicated policies the policies +don't change that you know every birth + + align:start position:0% +don't change that you know every birth + + + align:start position:0% +don't change that you know every birth +is either a boy or a + + align:start position:0% +is either a boy or a + + + align:start position:0% +is either a boy or a +girl + + align:start position:0% +girl + + + align:start position:0% +girl +okay so uh here's the uh last fact I + + align:start position:0% +okay so uh here's the uh last fact I + + + align:start position:0% +okay so uh here's the uh last fact I +wanted you to see which is that if you + + align:start position:0% +wanted you to see which is that if you + + + align:start position:0% +wanted you to see which is that if you +look at the sex raes in India they're + + align:start position:0% +look at the sex raes in India they're + + + align:start position:0% +look at the sex raes in India they're +getting worse they got worse for a while + + align:start position:0% +getting worse they got worse for a while + + + align:start position:0% +getting worse they got worse for a while +now they have St stabilized at a low + + align:start position:0% +now they have St stabilized at a low + + + align:start position:0% +now they have St stabilized at a low +number so in 1900 there were 972 girls + + align:start position:0% +number so in 1900 there were 972 girls + + + align:start position:0% +number so in 1900 there were 972 girls +for boys men for women women for men now + + align:start position:0% +for boys men for women women for men now + + + align:start position:0% +for boys men for women women for men now +they're 933 so that's just the trend is + + align:start position:0% +they're 933 so that's just the trend is + + + align:start position:0% +they're 933 so that's just the trend is +in India you don't see a trend after + + align:start position:0% +in India you don't see a trend after + + + align:start position:0% +in India you don't see a trend after +1971 or 1981 but it's uh it's it's the + + align:start position:0% +1971 or 1981 but it's uh it's it's the + + + align:start position:0% +1971 or 1981 but it's uh it's it's the +trend historical trend is is very + + align:start position:0% +trend historical trend is is very + + + align:start position:0% +trend historical trend is is very +negative so that that brings us to the + + align:start position:0% +negative so that that brings us to the + + + align:start position:0% +negative so that that brings us to the +sort of the question before we get to + + align:start position:0% +sort of the question before we get to + + + align:start position:0% +sort of the question before we get to +policy in a sense we need to know what's + + align:start position:0% +policy in a sense we need to know what's + + + align:start position:0% +policy in a sense we need to know what's +going on what's going on there two + + align:start position:0% +going on what's going on there two + + + align:start position:0% +going on what's going on there two +possible answers one is kind of + + align:start position:0% +possible answers one is kind of + + + align:start position:0% +possible answers one is kind of +tradition and the other is economics so + + align:start position:0% +tradition and the other is economics so + + + align:start position:0% +tradition and the other is economics so +so one is like people are actually + + align:start position:0% +so one is like people are actually + + + align:start position:0% +so one is like people are actually +there's a set of traditions which make + + align:start position:0% +there's a set of traditions which make + + + align:start position:0% +there's a set of traditions which make +bad things happen but people are not + + align:start position:0% +bad things happen but people are not + + + align:start position:0% +bad things happen but people are not +willing them to happen and the other is + + align:start position:0% +willing them to happen and the other is + + + align:start position:0% +willing them to happen and the other is +that people are actually making choices + + align:start position:0% +that people are actually making choices + + + align:start position:0% +that people are actually making choices +uh to make these things happen so when + + align:start position:0% +uh to make these things happen so when + + + align:start position:0% +uh to make these things happen so when +the when the + + align:start position:0% +the when the + + + align:start position:0% +the when the +Cho so what we're going to spend some + + align:start position:0% +Cho so what we're going to spend some + + + align:start position:0% +Cho so what we're going to spend some +time doing is trying to distinguish + + align:start position:0% +time doing is trying to distinguish + + + align:start position:0% +time doing is trying to distinguish +between these two view views is it + + align:start position:0% +between these two view views is it + + + align:start position:0% +between these two view views is it +tradition is it economics + + align:start position:0% + + + + align:start position:0% + +so you could imagine just + + align:start position:0% +so you could imagine just + + + align:start position:0% +so you could imagine just +traditionally there's some Theory which + + align:start position:0% +traditionally there's some Theory which + + + align:start position:0% +traditionally there's some Theory which +says that girls need less food that's + + align:start position:0% +says that girls need less food that's + + + align:start position:0% +says that girls need less food that's +false but you you believe it and you + + align:start position:0% +false but you you believe it and you + + + align:start position:0% +false but you you believe it and you +don't actually actively do anything to + + align:start position:0% +don't actually actively do anything to + + + align:start position:0% +don't actually actively do anything to +make them die you just believe you have + + align:start position:0% +make them die you just believe you have + + + align:start position:0% +make them die you just believe you have +wrong beliefs you think girls need less + + align:start position:0% +wrong beliefs you think girls need less + + + align:start position:0% +wrong beliefs you think girls need less +food because you know adult women are + + align:start position:0% +food because you know adult women are + + + align:start position:0% +food because you know adult women are +smaller than adult men and so you feed + + align:start position:0% +smaller than adult men and so you feed + + + align:start position:0% +smaller than adult men and so you feed +your girls less this is not an attempt + + align:start position:0% +your girls less this is not an attempt + + + align:start position:0% +your girls less this is not an attempt +to kill them it's just a tradition + + align:start position:0% +to kill them it's just a tradition + + + align:start position:0% +to kill them it's just a tradition +tradition but then that could feedback + + align:start position:0% +tradition but then that could feedback + + + align:start position:0% +tradition but then that could feedback +and have a consequence right and you + + align:start position:0% +and have a consequence right and you + + + align:start position:0% +and have a consequence right and you +could so + + align:start position:0% +could so + + + align:start position:0% +could so +um problem is how do you test + + align:start position:0% + + + + align:start position:0% + +this yeah if you actually look at um + + align:start position:0% +this yeah if you actually look at um + + + align:start position:0% +this yeah if you actually look at um +like fertility rates so if if the I + + align:start position:0% +like fertility rates so if if the I + + + align:start position:0% +like fertility rates so if if the I +don't know like if the number of people + + align:start position:0% +don't know like if the number of people + + + align:start position:0% +don't know like if the number of people +that are born it's actually about 50/50 + + align:start position:0% +that are born it's actually about 50/50 + + + align:start position:0% +that are born it's actually about 50/50 +but then the number like within 5 years + + align:start position:0% +but then the number like within 5 years + + + align:start position:0% +but then the number like within 5 years +you see a clear difference so maybe + + align:start position:0% +you see a clear difference so maybe + + + align:start position:0% +you see a clear difference so maybe +something like that is happening but + + align:start position:0% +something like that is happening but + + + align:start position:0% +something like that is happening but +even in terms of um birth rate if + + align:start position:0% +even in terms of um birth rate if + + + align:start position:0% +even in terms of um birth rate if +there's a difference then should so part + + align:start position:0% +there's a difference then should so part + + + align:start position:0% +there's a difference then should so part +of it is one answer to this question is + + align:start position:0% +of it is one answer to this question is + + + align:start position:0% +of it is one answer to this question is +if these guys are not getting born then + + align:start position:0% +if these guys are not getting born then + + + align:start position:0% +if these guys are not getting born then +then obviously something else is going + + align:start position:0% +then obviously something else is going + + + align:start position:0% +then obviously something else is going +on now + + align:start position:0% +on now + + + align:start position:0% +on now +mostly uh till about 5 years ago or not + + align:start position:0% +mostly uh till about 5 years ago or not + + + align:start position:0% +mostly uh till about 5 years ago or not +five 15 years ago you you don't see a + + align:start position:0% +five 15 years ago you you don't see a + + + align:start position:0% +five 15 years ago you you don't see a +big Trend in birth rates the trend now + + align:start position:0% +big Trend in birth rates the trend now + + + align:start position:0% +big Trend in birth rates the trend now +you actually see a trend in birth rates + + align:start position:0% +you actually see a trend in birth rates + + + align:start position:0% +you actually see a trend in birth rates +as well reported births are getting they + + align:start position:0% +as well reported births are getting they + + + align:start position:0% +as well reported births are getting they +more and more uh reported boys relative + + align:start position:0% +more and more uh reported boys relative + + + align:start position:0% +more and more uh reported boys relative +to girls but about 15 years ago you + + align:start position:0% +to girls but about 15 years ago you + + + align:start position:0% +to girls but about 15 years ago you +don't see that what you did see was more + + align:start position:0% +don't see that what you did see was more + + + align:start position:0% +don't see that what you did see was more +different mortality rates for boys and + + align:start position:0% +different mortality rates for boys and + + + align:start position:0% +different mortality rates for boys and +girls so imagine that you wanted to test + + align:start position:0% +girls so imagine that you wanted to test + + + align:start position:0% +girls so imagine that you wanted to test +this view well the problem is how do you + + align:start position:0% +this view well the problem is how do you + + + align:start position:0% +this view well the problem is how do you +test it uh you don't actually observe + + align:start position:0% +test it uh you don't actually observe + + + align:start position:0% +test it uh you don't actually observe +who eats what in a + + align:start position:0% +who eats what in a + + + align:start position:0% +who eats what in a +family so it's hard to imagine you going + + align:start position:0% +family so it's hard to imagine you going + + + align:start position:0% +family so it's hard to imagine you going +and figuring out oh they're not feeding + + align:start position:0% +and figuring out oh they're not feeding + + + align:start position:0% +and figuring out oh they're not feeding +their daughter they're feeding their son + + align:start position:0% +their daughter they're feeding their son + + + align:start position:0% +their daughter they're feeding their son +I that's just too difficult to do + + align:start position:0% +I that's just too difficult to do + + + align:start position:0% +I that's just too difficult to do +because you know everybody eats out of + + align:start position:0% +because you know everybody eats out of + + + align:start position:0% +because you know everybody eats out of +the same cooked food and so it's going + + align:start position:0% +the same cooked food and so it's going + + + align:start position:0% +the same cooked food and so it's going +to be very hard to find so somebody had + + align:start position:0% +to be very hard to find so somebody had + + + align:start position:0% +to be very hard to find so somebody had +a very good idea of how to how to do it + + align:start position:0% +a very good idea of how to how to do it + + + align:start position:0% +a very good idea of how to how to do it +which is to look at Specialized adult + + align:start position:0% +which is to look at Specialized adult + + + align:start position:0% +which is to look at Specialized adult +Goods like + + align:start position:0% +Goods like + + + align:start position:0% +Goods like +cigarettes you + + align:start position:0% +cigarettes you + + + align:start position:0% +cigarettes you +know your daughter 5-year-old daughter + + align:start position:0% +know your daughter 5-year-old daughter + + + align:start position:0% +know your daughter 5-year-old daughter +doesn't smoke a cigarette nor does your + + align:start position:0% +doesn't smoke a cigarette nor does your + + + align:start position:0% +doesn't smoke a cigarette nor does your +five 5-year-old son + + align:start position:0% +five 5-year-old son + + + align:start position:0% +five 5-year-old son +so when when a son is + + align:start position:0% +so when when a son is + + + align:start position:0% +so when when a son is +born if there's an effect on how much + + align:start position:0% +born if there's an effect on how much + + + align:start position:0% +born if there's an effect on how much +smoking you do it has nothing to do + + align:start position:0% +smoking you do it has nothing to do + + + align:start position:0% +smoking you do it has nothing to do +with nothing to do with um the + + align:start position:0% +with nothing to do with um the + + + align:start position:0% +with nothing to do with um the +children you know uh children smoking so + + align:start position:0% +children you know uh children smoking so + + + align:start position:0% +children you know uh children smoking so +children are are not going to be a + + align:start position:0% +children are are not going to be a + + + align:start position:0% +children are are not going to be a +direct source of demand so then you can + + align:start position:0% +direct source of demand so then you can + + + align:start position:0% +direct source of demand so then you can +why is that good because then you can + + align:start position:0% +why is that good because then you can + + + align:start position:0% +why is that good because then you can +look at what happens to smoking when uh + + align:start position:0% +look at what happens to smoking when uh + + + align:start position:0% +look at what happens to smoking when uh +the family gets a boy or a + + align:start position:0% +the family gets a boy or a + + + align:start position:0% +the family gets a boy or a +girl and which one you if girls are fed + + align:start position:0% +girl and which one you if girls are fed + + + align:start position:0% +girl and which one you if girls are fed +less what would you + + align:start position:0% + + + + align:start position:0% + +expect cett + + align:start position:0% + + + + align:start position:0% + +lar right or smoking smoking goes down + + align:start position:0% +lar right or smoking smoking goes down + + + align:start position:0% +lar right or smoking smoking goes down +by less so the basic observation you + + align:start position:0% +by less so the basic observation you + + + align:start position:0% +by less so the basic observation you +should see is when a child is born adult + + align:start position:0% +should see is when a child is born adult + + + align:start position:0% +should see is when a child is born adult +income goes down right because adults + + align:start position:0% +income goes down right because adults + + + align:start position:0% +income goes down right because adults +have less money money to spend on + + align:start position:0% +have less money money to spend on + + + align:start position:0% +have less money money to spend on +themselves because they will feed feed + + align:start position:0% +themselves because they will feed feed + + + align:start position:0% +themselves because they will feed feed +the child but if they feed the boy less + + align:start position:0% +the child but if they feed the boy less + + + align:start position:0% +the child but if they feed the boy less +than the girl girl less than the boy + + align:start position:0% +than the girl girl less than the boy + + + align:start position:0% +than the girl girl less than the boy +then you'd see that they will they will + + align:start position:0% +then you'd see that they will they will + + + align:start position:0% +then you'd see that they will they will +uh they will when a boy is born they're + + align:start position:0% +uh they will when a boy is born they're + + + align:start position:0% +uh they will when a boy is born they're +going to really cut back on cigarettes + + align:start position:0% +going to really cut back on cigarettes + + + align:start position:0% +going to really cut back on cigarettes +but when a girl is born they'll cut back + + align:start position:0% +but when a girl is born they'll cut back + + + align:start position:0% +but when a girl is born they'll cut back +less because they're feeding the girl + + align:start position:0% +less because they're feeding the girl + + + align:start position:0% +less because they're feeding the girl +less + + align:start position:0% +less + + + align:start position:0% +less +so we have pretty precise measurement of + + align:start position:0% +so we have pretty precise measurement of + + + align:start position:0% +so we have pretty precise measurement of +demand for adult Goods so we can use + + align:start position:0% +demand for adult Goods so we can use + + + align:start position:0% +demand for adult Goods so we can use +that we don't know who who smokes but we + + align:start position:0% +that we don't know who who smokes but we + + + align:start position:0% +that we don't know who who smokes but we +know that the kids are not doing the + + align:start position:0% +know that the kids are not doing the + + + align:start position:0% +know that the kids are not doing the +smoking so therefore we can by observing + + align:start position:0% +smoking so therefore we can by observing + + + align:start position:0% +smoking so therefore we can by observing +what happens to a family when the child + + align:start position:0% +what happens to a family when the child + + + align:start position:0% +what happens to a family when the child +is born we can back out whether or not + + align:start position:0% +is born we can back out whether or not + + + align:start position:0% +is born we can back out whether or not +there is a a difference in in the way + + align:start position:0% +there is a a difference in in the way + + + align:start position:0% +there is a a difference in in the way +you feed boys or + + align:start position:0% +you feed boys or + + + align:start position:0% +you feed boys or +girls is that clear why that's better + + align:start position:0% +girls is that clear why that's better + + + align:start position:0% +girls is that clear why that's better +than trying to measure it's very hard to + + align:start position:0% +than trying to measure it's very hard to + + + align:start position:0% +than trying to measure it's very hard to +measure who eats what but clearly the + + align:start position:0% +measure who eats what but clearly the + + + align:start position:0% +measure who eats what but clearly the +kids don't eat they don't drinks uh + + align:start position:0% +kids don't eat they don't drinks uh + + + align:start position:0% +kids don't eat they don't drinks uh +don't smoke smoke cigarettes and they + + align:start position:0% +don't smoke smoke cigarettes and they + + + align:start position:0% +don't smoke smoke cigarettes and they +don't drink alcohol so if we looked at + + align:start position:0% +don't drink alcohol so if we looked at + + + align:start position:0% +don't drink alcohol so if we looked at +alcohol and cigarettes and a few other + + align:start position:0% +alcohol and cigarettes and a few other + + + align:start position:0% +alcohol and cigarettes and a few other +things that are essentially adult Goods + + align:start position:0% +things that are essentially adult Goods + + + align:start position:0% +things that are essentially adult Goods +we we should be able to back out what's + + align:start position:0% +we we should be able to back out what's + + + align:start position:0% +we we should be able to back out what's +happening when the child is + + align:start position:0% + + + + align:start position:0% + +born okay is that is that clear what + + align:start position:0% + + + + align:start position:0% + +the so um somebody did that I'll show + + align:start position:0% +the so um somebody did that I'll show + + + align:start position:0% +the so um somebody did that I'll show +you the data for India it um + + align:start position:0% + + + + align:start position:0% + +uh so take beverages beverages is + + align:start position:0% +uh so take beverages beverages is + + + align:start position:0% +uh so take beverages beverages is +doesn't include milk so uh it's soda and + + align:start position:0% +doesn't include milk so uh it's soda and + + + align:start position:0% +doesn't include milk so uh it's soda and +tea and all those things + + align:start position:0% +tea and all those things + + + align:start position:0% +tea and all those things +and this is just basically this table is + + align:start position:0% +and this is just basically this table is + + + align:start position:0% +and this is just basically this table is +horrible but this paper was published uh + + align:start position:0% +horrible but this paper was published uh + + + align:start position:0% +horrible but this paper was published uh +in a obscure Journal uh many years ago + + align:start position:0% +in a obscure Journal uh many years ago + + + align:start position:0% +in a obscure Journal uh many years ago +and the only way I could do is just this + + align:start position:0% +and the only way I could do is just this + + + align:start position:0% +and the only way I could do is just this +is just a scan of that there's nothing + + align:start position:0% +is just a scan of that there's nothing + + + align:start position:0% +is just a scan of that there's nothing +else I could find there's no electronic + + align:start position:0% +else I could find there's no electronic + + + align:start position:0% +else I could find there's no electronic +version Etc so um but it's what you're + + align:start position:0% +version Etc so um but it's what you're + + + align:start position:0% +version Etc so um but it's what you're +looking for is the effect of a boy + + align:start position:0% +looking for is the effect of a boy + + + align:start position:0% +looking for is the effect of a boy +versus a girl so males number of males + + align:start position:0% +versus a girl so males number of males + + + align:start position:0% +versus a girl so males number of males +between zero and four versus number of + + align:start position:0% +between zero and four versus number of + + + align:start position:0% +between zero and four versus number of +females between 0 and four and the + + align:start position:0% +females between 0 and four and the + + + align:start position:0% +females between 0 and four and the +effect of that on the consumption of + + align:start position:0% +effect of that on the consumption of + + + align:start position:0% +effect of that on the consumption of +beverages the answer is it has no effect + + align:start position:0% +beverages the answer is it has no effect + + + align:start position:0% +beverages the answer is it has no effect +that what's in the bracket is the T + + align:start position:0% +that what's in the bracket is the T + + + align:start position:0% +that what's in the bracket is the T +statistic the T statistics is zero but + + align:start position:0% +statistic the T statistics is zero but + + + align:start position:0% +statistic the T statistics is zero but +if + + align:start position:0% +if + + + align:start position:0% +if +anything uh yeah yeah I mean there's + + align:start position:0% +anything uh yeah yeah I mean there's + + + align:start position:0% +anything uh yeah yeah I mean there's +just both both the numbers are zero and + + align:start position:0% +just both both the numbers are zero and + + + align:start position:0% +just both both the numbers are zero and +that's basically what you find you find + + align:start position:0% +that's basically what you find you find + + + align:start position:0% +that's basically what you find you find +no effect of + + align:start position:0% +no effect of + + + align:start position:0% +no effect of +uh yeah you see you see what you'd + + align:start position:0% +uh yeah you see you see what you'd + + + align:start position:0% +uh yeah you see you see what you'd +expect which is that for + + align:start position:0% +expect which is that for + + + align:start position:0% +expect which is that for +example when a child is born you're just + + align:start position:0% +example when a child is born you're just + + + align:start position:0% +example when a child is born you're just +poor so you buy less rice less wheat uh + + align:start position:0% +poor so you buy less rice less wheat uh + + + align:start position:0% +poor so you buy less rice less wheat uh +but there's no no no difference between + + align:start position:0% +but there's no no no difference between + + + align:start position:0% +but there's no no no difference between +girls and boys boys and girls have the + + align:start position:0% +girls and boys boys and girls have the + + + align:start position:0% +girls and boys boys and girls have the +same effect if anything on + + align:start position:0% +same effect if anything on + + + align:start position:0% +same effect if anything on +both so you just find there's no + + align:start position:0% +both so you just find there's no + + + align:start position:0% +both so you just find there's no +evidence that basically there's no + + align:start position:0% +evidence that basically there's no + + + align:start position:0% +evidence that basically there's no +evidence that when a child is born + + align:start position:0% +evidence that when a child is born + + + align:start position:0% +evidence that when a child is born +family is cut boy child is born family + + align:start position:0% +family is cut boy child is born family + + + align:start position:0% +family is cut boy child is born family +is cut back more than when a girl child + + align:start position:0% +is cut back more than when a girl child + + + align:start position:0% +is cut back more than when a girl child +is born there's just you don't we don't + + align:start position:0% +is born there's just you don't we don't + + + align:start position:0% +is born there's just you don't we don't +find any evidence and this has been + + align:start position:0% +find any evidence and this has been + + + align:start position:0% +find any evidence and this has been +looked in many countries so another + + align:start position:0% +looked in many countries so another + + + align:start position:0% +looked in many countries so another +tradition story is the + + align:start position:0% +tradition story is the + + + align:start position:0% +tradition story is the +following imagine that tradition is you + + align:start position:0% +following imagine that tradition is you + + + align:start position:0% +following imagine that tradition is you +know when the child gets sick do I take + + align:start position:0% +know when the child gets sick do I take + + + align:start position:0% +know when the child gets sick do I take +it to the hospital and with a boy the + + align:start position:0% +it to the hospital and with a boy the + + + align:start position:0% +it to the hospital and with a boy the +tradition is I always take you to the + + align:start position:0% +tradition is I always take you to the + + + align:start position:0% +tradition is I always take you to the +hospital with with a girl I just let her + + align:start position:0% +hospital with with a girl I just let her + + + align:start position:0% +hospital with with a girl I just let her +you know give us some water and you know + + align:start position:0% +you know give us some water and you know + + + align:start position:0% +you know give us some water and you know +generally you know make um you know sing + + align:start position:0% +generally you know make um you know sing + + + align:start position:0% +generally you know make um you know sing +songs to her but I don't take her to the + + align:start position:0% +songs to her but I don't take her to the + + + align:start position:0% +songs to her but I don't take her to the +hospital something like that you + + align:start position:0% +hospital something like that you + + + align:start position:0% +hospital something like that you +know do we see any evidence of this so + + align:start position:0% +know do we see any evidence of this so + + + align:start position:0% +know do we see any evidence of this so +this is hard to study because you know + + align:start position:0% +this is hard to study because you know + + + align:start position:0% +this is hard to study because you know +we don't actually observe that many + + align:start position:0% +we don't actually observe that many + + + align:start position:0% +we don't actually observe that many +episodes of of life-threatening + + align:start position:0% +episodes of of life-threatening + + + align:start position:0% +episodes of of life-threatening +diseases but there's a nice uh there's a + + align:start position:0% +diseases but there's a nice uh there's a + + + align:start position:0% +diseases but there's a nice uh there's a +nice fact that Elana Rose identified + + align:start position:0% +nice fact that Elana Rose identified + + + align:start position:0% +nice fact that Elana Rose identified +which is the following she looked + + align:start position:0% +which is the following she looked + + + align:start position:0% +which is the following she looked +at area so over time different different + + align:start position:0% +at area so over time different different + + + align:start position:0% +at area so over time different different +parts of India have droughts at + + align:start position:0% +parts of India have droughts at + + + align:start position:0% +parts of India have droughts at +different points of time so some some PE + + align:start position:0% +different points of time so some some PE + + + align:start position:0% +different points of time so some some PE +some areas have droughts in in 2006 some + + align:start position:0% +some areas have droughts in in 2006 some + + + align:start position:0% +some areas have droughts in in 2006 some +have droughts in 2004 some have droughts + + align:start position:0% +have droughts in 2004 some have droughts + + + align:start position:0% +have droughts in 2004 some have droughts +in 1996 + + align:start position:0% +in 1996 + + + align:start position:0% +in 1996 +so and a drought is a time of economic + + align:start position:0% + + + + align:start position:0% + +stress so drought is + + align:start position:0% +stress so drought is + + + align:start position:0% +stress so drought is +when what's a + + align:start position:0% +when what's a + + + align:start position:0% +when what's a +drought why is it economic + + align:start position:0% + + + + align:start position:0% + +stress yeah it's basically you can't + + align:start position:0% +stress yeah it's basically you can't + + + align:start position:0% +stress yeah it's basically you can't +grow anything it's too dry so uh so when + + align:start position:0% +grow anything it's too dry so uh so when + + + align:start position:0% +grow anything it's too dry so uh so when +the rains fail uh crops fail families + + align:start position:0% +the rains fail uh crops fail families + + + align:start position:0% +the rains fail uh crops fail families +have no money + + align:start position:0% + + + + align:start position:0% + +how are they dealing with this + + align:start position:0% +how are they dealing with this + + + align:start position:0% +how are they dealing with this +particular emergency and the and there + + align:start position:0% +particular emergency and the and there + + + align:start position:0% +particular emergency and the and there +she finds some evidence that relative to + + align:start position:0% +she finds some evidence that relative to + + + align:start position:0% +she finds some evidence that relative to +non- Drought years in drought years + + align:start position:0% +non- Drought years in drought years + + + align:start position:0% +non- Drought years in drought years +girls die + + align:start position:0% +girls die + + + align:start position:0% +girls die +more so that suggest that emergencies + + align:start position:0% +more so that suggest that emergencies + + + align:start position:0% +more so that suggest that emergencies +might be a part of the story that in + + align:start position:0% +might be a part of the story that in + + + align:start position:0% +might be a part of the story that in +emergencies girls are not treated as + + align:start position:0% +emergencies girls are not treated as + + + align:start position:0% +emergencies girls are not treated as +well so I given one example which is not + + align:start position:0% +well so I given one example which is not + + + align:start position:0% +well so I given one example which is not +taking her to the hospital the other one + + align:start position:0% +taking her to the hospital the other one + + + align:start position:0% +taking her to the hospital the other one +might be when I don't have money I don't + + align:start position:0% +might be when I don't have money I don't + + + align:start position:0% +might be when I don't have money I don't +buy food for + + align:start position:0% +buy food for + + + align:start position:0% +buy food for +her so some some tradition of that kind + + align:start position:0% +her so some some tradition of that kind + + + align:start position:0% +her so some some tradition of that kind +might explain it problem is that + + align:start position:0% +might explain it problem is that + + + align:start position:0% +might explain it problem is that +droughts are not frequent enough and if + + align:start position:0% +droughts are not frequent enough and if + + + align:start position:0% +droughts are not frequent enough and if +you remember the trends the trends are + + align:start position:0% +you remember the trends the trends are + + + align:start position:0% +you remember the trends the trends are +all bad right they're all getting + + align:start position:0% +all bad right they're all getting + + + align:start position:0% +all bad right they're all getting +worse the India and China are getting + + align:start position:0% +worse the India and China are getting + + + align:start position:0% +worse the India and China are getting +richer the dependence on agriculture and + + align:start position:0% +richer the dependence on agriculture and + + + align:start position:0% +richer the dependence on agriculture and +general these kinds of extreme events is + + align:start position:0% +general these kinds of extreme events is + + + align:start position:0% +general these kinds of extreme events is +just going down people are just you know + + align:start position:0% +just going down people are just you know + + + align:start position:0% +just going down people are just you know +droughts don't matter as much as in + + align:start position:0% +droughts don't matter as much as in + + + align:start position:0% +droughts don't matter as much as in +India now then + + align:start position:0% +India now then + + + align:start position:0% +India now then +when it 20 30 years ago agriculture was + + align:start position:0% +when it 20 30 years ago agriculture was + + + align:start position:0% +when it 20 30 years ago agriculture was +50% of GDP now it's 25% of GDP so + + align:start position:0% +50% of GDP now it's 25% of GDP so + + + align:start position:0% +50% of GDP now it's 25% of GDP so +basically droughts matter less to people + + align:start position:0% +basically droughts matter less to people + + + align:start position:0% +basically droughts matter less to people +and since droughts matter less to people + + align:start position:0% +and since droughts matter less to people + + + align:start position:0% +and since droughts matter less to people +you would imagine the trend being + + align:start position:0% +you would imagine the trend being + + + align:start position:0% +you would imagine the trend being +favorable rather than against think of + + align:start position:0% +favorable rather than against think of + + + align:start position:0% +favorable rather than against think of +China most people are now in + + align:start position:0% +China most people are now in + + + align:start position:0% +China most people are now in +Industry they're not they they're also + + align:start position:0% +Industry they're not they they're also + + + align:start position:0% +Industry they're not they they're also +richer and as you get richer you would + + align:start position:0% +richer and as you get richer you would + + + align:start position:0% +richer and as you get richer you would +imagine that emergencies are less + + align:start position:0% +imagine that emergencies are less + + + align:start position:0% +imagine that emergencies are less +serious because you know you always have + + align:start position:0% +serious because you know you always have + + + align:start position:0% +serious because you know you always have +some money you're no no longer at the + + align:start position:0% +some money you're no no longer at the + + + align:start position:0% +some money you're no no longer at the +margin of starvation so problem with the + + align:start position:0% +margin of starvation so problem with the + + + align:start position:0% +margin of starvation so problem with the +story is that it's just inconsistent + + align:start position:0% +story is that it's just inconsistent + + + align:start position:0% +story is that it's just inconsistent +with the fact that things are getting + + align:start position:0% +with the fact that things are getting + + + align:start position:0% +with the fact that things are getting +worse over time you would think that + + align:start position:0% +worse over time you would think that + + + align:start position:0% +worse over time you would think that +under this story things would be getting + + align:start position:0% +under this story things would be getting + + + align:start position:0% +under this story things would be getting +better because it's an emergency story + + align:start position:0% +better because it's an emergency story + + + align:start position:0% +better because it's an emergency story +and as countries get richer and less + + align:start position:0% +and as countries get richer and less + + + align:start position:0% +and as countries get richer and less +exposed to risk there would be you would + + align:start position:0% +exposed to risk there would be you would + + + align:start position:0% +exposed to risk there would be you would +see less and less of this rather than + + align:start position:0% +see less and less of this rather than + + + align:start position:0% +see less and less of this rather than +more and more of this so that's why this + + align:start position:0% +more and more of this so that's why this + + + align:start position:0% +more and more of this so that's why this +can't be the whole explanation it could + + align:start position:0% +can't be the whole explanation it could + + + align:start position:0% +can't be the whole explanation it could +be a piece of + + align:start position:0% +be a piece of + + + align:start position:0% +be a piece of +it so here's + + align:start position:0% +it so here's + + + align:start position:0% +it so here's +a so going back to our distinction + + align:start position:0% +a so going back to our distinction + + + align:start position:0% +a so going back to our distinction +between the kind of the tradition based + + align:start position:0% +between the kind of the tradition based + + + align:start position:0% +between the kind of the tradition based +stories and the + + align:start position:0% +stories and the + + + align:start position:0% +stories and the +more economic stories here's a here's an + + align:start position:0% +more economic stories here's a here's an + + + align:start position:0% +more economic stories here's a here's an +economic fact which is striking so if + + align:start position:0% +economic fact which is striking so if + + + align:start position:0% +economic fact which is striking so if +you like + + align:start position:0% + + + + align:start position:0% + +um this so in other words what I mean by + + align:start position:0% +um this so in other words what I mean by + + + align:start position:0% +um this so in other words what I mean by +an economic story is that tradition + + align:start position:0% +an economic story is that tradition + + + align:start position:0% +an economic story is that tradition +based stories say that you know there's + + align:start position:0% +based stories say that you know there's + + + align:start position:0% +based stories say that you know there's +some Rule people use fixed rule which + + align:start position:0% +some Rule people use fixed rule which + + + align:start position:0% +some Rule people use fixed rule which +there's not they have not decided on + + align:start position:0% +there's not they have not decided on + + + align:start position:0% +there's not they have not decided on +this rule this is given to them and that + + align:start position:0% +this rule this is given to them and that + + + align:start position:0% +this rule this is given to them and that +rule somehow under some circumstances + + align:start position:0% +rule somehow under some circumstances + + + align:start position:0% +rule somehow under some circumstances +has bad outcomes for girls so in a when + + align:start position:0% +has bad outcomes for girls so in a when + + + align:start position:0% +has bad outcomes for girls so in a when +the girl is sick you don't take her to + + align:start position:0% +the girl is sick you don't take her to + + + align:start position:0% +the girl is sick you don't take her to +the hospital that's a + + align:start position:0% +the hospital that's a + + + align:start position:0% +the hospital that's a +rule this is something we now asking a + + align:start position:0% +rule this is something we now asking a + + + align:start position:0% +rule this is something we now asking a +question when the economic incentives to + + align:start position:0% +question when the economic incentives to + + + align:start position:0% +question when the economic incentives to +treat girls better changes do you treat + + align:start position:0% +treat girls better changes do you treat + + + align:start position:0% +treat girls better changes do you treat +them better that suggests that you're + + align:start position:0% +them better that suggests that you're + + + align:start position:0% +them better that suggests that you're +not don't have a fixed rule you're + + align:start position:0% +not don't have a fixed rule you're + + + align:start position:0% +not don't have a fixed rule you're +you're actually behaving in a kind of + + align:start position:0% +you're actually behaving in a kind of + + + align:start position:0% +you're actually behaving in a kind of +rational way quote unquote rational way + + align:start position:0% +rational way quote unquote rational way + + + align:start position:0% +rational way quote unquote rational way +you are you're actually planning to have + + align:start position:0% +you are you're actually planning to have + + + align:start position:0% +you are you're actually planning to have +bad things happen to + + align:start position:0% +bad things happen to + + + align:start position:0% +bad things happen to +girls so do you see what the distinction + + align:start position:0% +girls so do you see what the distinction + + + align:start position:0% +girls so do you see what the distinction +is between traditional tradition based + + align:start position:0% +is between traditional tradition based + + + align:start position:0% +is between traditional tradition based +stories and economic stories economic + + align:start position:0% +stories and economic stories economic + + + align:start position:0% +stories and economic stories economic +stories are ones which essentially say + + align:start position:0% +stories are ones which essentially say + + + align:start position:0% +stories are ones which essentially say +that you know we are making active + + align:start position:0% +that you know we are making active + + + align:start position:0% +that you know we are making active +choices which have consequences for + + align:start position:0% +choices which have consequences for + + + align:start position:0% +choices which have consequences for +girls rather than this is a rule we use + + align:start position:0% +girls rather than this is a rule we use + + + align:start position:0% +girls rather than this is a rule we use +and sometimes bad things happen because + + align:start position:0% +and sometimes bad things happen because + + + align:start position:0% +and sometimes bad things happen because +we use a particular + + align:start position:0% +we use a particular + + + align:start position:0% +we use a particular +rule here's a here's a is a nice example + + align:start position:0% +rule here's a here's a is a nice example + + + align:start position:0% +rule here's a here's a is a nice example +so in China um after + + align:start position:0% +so in China um after + + + align:start position:0% +so in China um after +1979 uh agriculture is liberalized + + align:start position:0% +1979 uh agriculture is liberalized + + + align:start position:0% +1979 uh agriculture is liberalized +meaning people are allowed to keep the + + align:start position:0% +meaning people are allowed to keep the + + + align:start position:0% +meaning people are allowed to keep the +money from growing their crops this is + + align:start position:0% +money from growing their crops this is + + + align:start position:0% +money from growing their crops this is +the start of China's economic Miracle + + align:start position:0% +the start of China's economic Miracle + + + align:start position:0% +the start of China's economic Miracle +it's uh it's called the family + + align:start position:0% +it's uh it's called the family + + + align:start position:0% +it's uh it's called the family +responsibility system and it's sort of + + align:start position:0% +responsibility system and it's sort of + + + align:start position:0% +responsibility system and it's sort of +when everything in China + + align:start position:0% +when everything in China + + + align:start position:0% +when everything in China +starts uh T is one crop where women have + + align:start position:0% +starts uh T is one crop where women have + + + align:start position:0% +starts uh T is one crop where women have +a compar comparative advantage and even + + align:start position:0% +a compar comparative advantage and even + + + align:start position:0% +a compar comparative advantage and even +absolute advantage which tea is + + align:start position:0% +absolute advantage which tea is + + + align:start position:0% +absolute advantage which tea is +something that has to be picked very + + align:start position:0% +something that has to be picked very + + + align:start position:0% +something that has to be picked very +patiently small Leaf the most valuable + + align:start position:0% +patiently small Leaf the most valuable + + + align:start position:0% +patiently small Leaf the most valuable +leaves in tea are the smallest ones you + + align:start position:0% +leaves in tea are the smallest ones you + + + align:start position:0% +leaves in tea are the smallest ones you +know so you have to pick the small + + align:start position:0% +know so you have to pick the small + + + align:start position:0% +know so you have to pick the small +leaves you have to pick them without + + align:start position:0% +leaves you have to pick them without + + + align:start position:0% +leaves you have to pick them without +bruising them the leave is bruised the + + align:start position:0% +bruising them the leave is bruised the + + + align:start position:0% +bruising them the leave is bruised the +price goes down so you know the best Le + + align:start position:0% +price goes down so you know the best Le + + + align:start position:0% +price goes down so you know the best Le +teas um like Chinese tees sell for you + + align:start position:0% +teas um like Chinese tees sell for you + + + align:start position:0% +teas um like Chinese tees sell for you +know + + align:start position:0% +know + + + align:start position:0% +know +$600 a kilogram so something of the + + align:start position:0% +$600 a kilogram so something of the + + + align:start position:0% +$600 a kilogram so something of the +order of magnitude of you know it's + + align:start position:0% +order of magnitude of you know it's + + + align:start position:0% +order of magnitude of you know it's +pretty expensive so if you actually have + + align:start position:0% +pretty expensive so if you actually have + + + align:start position:0% +pretty expensive so if you actually have +the best tees uh and you bruise a leaf + + align:start position:0% +the best tees uh and you bruise a leaf + + + align:start position:0% +the best tees uh and you bruise a leaf +that costs money so you better have + + align:start position:0% +that costs money so you better have + + + align:start position:0% +that costs money so you better have +somebody who picks with very delicate + + align:start position:0% +somebody who picks with very delicate + + + align:start position:0% +somebody who picks with very delicate +fingers turns out at least whether it's + + align:start position:0% +fingers turns out at least whether it's + + + align:start position:0% +fingers turns out at least whether it's +true or not I don't know but it's + + align:start position:0% +true or not I don't know but it's + + + align:start position:0% +true or not I don't know but it's +believed in China that women are better + + align:start position:0% +believed in China that women are better + + + align:start position:0% +believed in China that women are better +for picking expensive tea leaves okay + + align:start position:0% +for picking expensive tea leaves okay + + + align:start position:0% +for picking expensive tea leaves okay +maybe they are maybe this is a story + + align:start position:0% +maybe they are maybe this is a story + + + align:start position:0% +maybe they are maybe this is a story +that men made up to make them do it but + + align:start position:0% +that men made up to make them do it but + + + align:start position:0% +that men made up to make them do it but +what whatever the explanation this is + + align:start position:0% +what whatever the explanation this is + + + align:start position:0% +what whatever the explanation this is +this is a this is the belief so given + + align:start position:0% +this is a this is the belief so given + + + align:start position:0% +this is a this is the belief so given +that belief what matters is what people + + align:start position:0% +that belief what matters is what people + + + align:start position:0% +that belief what matters is what people +believe here right because that's you + + align:start position:0% +believe here right because that's you + + + align:start position:0% +believe here right because that's you +would imagine that another crop which is + + align:start position:0% +would imagine that another crop which is + + + align:start position:0% +would imagine that another crop which is +the opposite is fruits fruits need + + align:start position:0% +the opposite is fruits fruits need + + + align:start position:0% +the opposite is fruits fruits need +somebody to climb a tree and pick them + + align:start position:0% +somebody to climb a tree and pick them + + + align:start position:0% +somebody to climb a tree and pick them +and again in China the belief is that + + align:start position:0% +and again in China the belief is that + + + align:start position:0% +and again in China the belief is that +men are better at climbing trees uh + + align:start position:0% +men are better at climbing trees uh + + + align:start position:0% +men are better at climbing trees uh +maybe again false but uh so men are + + align:start position:0% +maybe again false but uh so men are + + + align:start position:0% +maybe again false but uh so men are +better so men are B better picking + + align:start position:0% +better so men are B better picking + + + align:start position:0% +better so men are B better picking +fruits women are better picking tea + + align:start position:0% +fruits women are better picking tea + + + align:start position:0% +fruits women are better picking tea +let's start impact okay at least that's + + align:start position:0% +let's start impact okay at least that's + + + align:start position:0% +let's start impact okay at least that's +what people believe let's start from + + align:start position:0% +what people believe let's start from + + + align:start position:0% +what people believe let's start from +there now + + align:start position:0% +there now + + + align:start position:0% +there now +um suppose + + align:start position:0% +um suppose + + + align:start position:0% +um suppose +parents respond to economic incentives + + align:start position:0% +parents respond to economic incentives + + + align:start position:0% +parents respond to economic incentives +then what would you expect happens when + + align:start position:0% +then what would you expect happens when + + + align:start position:0% +then what would you expect happens when +the price of tea goes up what what do + + align:start position:0% +the price of tea goes up what what do + + + align:start position:0% +the price of tea goes up what what do +you think will happen to their daughter + + align:start position:0% +you think will happen to their daughter + + + align:start position:0% +you think will happen to their daughter +yeah treat they treat their daughter + + align:start position:0% +yeah treat they treat their daughter + + + align:start position:0% +yeah treat they treat their daughter +better they're going to feed her more + + align:start position:0% +better they're going to feed her more + + + align:start position:0% +better they're going to feed her more +they're going to you know uh take her to + + align:start position:0% +they're going to you know uh take her to + + + align:start position:0% +they're going to you know uh take her to +the hospital more will ly Etc so you'd + + align:start position:0% +the hospital more will ly Etc so you'd + + + align:start position:0% +the hospital more will ly Etc so you'd +expect that and likewise when the price + + align:start position:0% +expect that and likewise when the price + + + align:start position:0% +expect that and likewise when the price +of fruits goes + + align:start position:0% +of fruits goes + + + align:start position:0% +of fruits goes +up you'd expect men to be boys to be + + align:start position:0% +up you'd expect men to be boys to be + + + align:start position:0% +up you'd expect men to be boys to be +treated better now in fact both price of + + align:start position:0% +treated better now in fact both price of + + + align:start position:0% +treated better now in fact both price of +food fruit and trees go up and that's a + + align:start position:0% +food fruit and trees go up and that's a + + + align:start position:0% +food fruit and trees go up and that's a +that's a trend so it's hard to use the + + align:start position:0% +that's a trend so it's hard to use the + + + align:start position:0% +that's a trend so it's hard to use the +trend to study this because everything's + + align:start position:0% +trend to study this because everything's + + + align:start position:0% +trend to study this because everything's +going up all the both tea and fruits are + + align:start position:0% +going up all the both tea and fruits are + + + align:start position:0% +going up all the both tea and fruits are +going up so you can't distinguish + + align:start position:0% +going up so you can't distinguish + + + align:start position:0% +going up so you can't distinguish +between these two but one thing you can + + align:start position:0% +between these two but one thing you can + + + align:start position:0% +between these two but one thing you can +do is you can look at areas which are + + align:start position:0% +do is you can look at areas which are + + + align:start position:0% +do is you can look at areas which are +are suitable for + + align:start position:0% + + + + align:start position:0% + +tea areas which are suitable for fruits + + align:start position:0% +tea areas which are suitable for fruits + + + align:start position:0% +tea areas which are suitable for fruits +and areas are suitable for + + align:start position:0% +and areas are suitable for + + + align:start position:0% +and areas are suitable for +neither now you can say when T prices go + + align:start position:0% +neither now you can say when T prices go + + + align:start position:0% +neither now you can say when T prices go +up do we see a bigger change in the + + align:start position:0% +up do we see a bigger change in the + + + align:start position:0% +up do we see a bigger change in the +gender ratio in the T favor in the T + + align:start position:0% +gender ratio in the T favor in the T + + + align:start position:0% +gender ratio in the T favor in the T +suitable areas relative to the + + align:start position:0% +suitable areas relative to the + + + align:start position:0% +suitable areas relative to the +others or you can ask when the price of + + align:start position:0% +others or you can ask when the price of + + + align:start position:0% +others or you can ask when the price of +of uh tea go fruits go up do we see a + + align:start position:0% +of uh tea go fruits go up do we see a + + + align:start position:0% +of uh tea go fruits go up do we see a +bigger change in the gender ratio in the + + align:start position:0% +bigger change in the gender ratio in the + + + align:start position:0% +bigger change in the gender ratio in the +fruit favored areas than in the areas + + align:start position:0% +fruit favored areas than in the areas + + + align:start position:0% +fruit favored areas than in the areas +where neither is favored so we're always + + align:start position:0% +where neither is favored so we're always + + + align:start position:0% +where neither is favored so we're always +comparing areas where you know basically + + align:start position:0% +comparing areas where you know basically + + + align:start position:0% +comparing areas where you know basically +wheat or rice grows with tea areas and + + align:start position:0% +wheat or rice grows with tea areas and + + + align:start position:0% +wheat or rice grows with tea areas and +fruit areas is that clear what we're + + align:start position:0% +fruit areas is that clear what we're + + + align:start position:0% +fruit areas is that clear what we're +doing we're asking when the price of + + align:start position:0% +doing we're asking when the price of + + + align:start position:0% +doing we're asking when the price of +fruits goes up do we see a different + + align:start position:0% +fruits goes up do we see a different + + + align:start position:0% +fruits goes up do we see a different +Trend in Fruit growing areas relative to + + align:start position:0% +Trend in Fruit growing areas relative to + + + align:start position:0% +Trend in Fruit growing areas relative to +wheat growing areas + + align:start position:0% + + + + align:start position:0% + +is it clear why that's why that's a good + + align:start position:0% +is it clear why that's why that's a good + + + align:start position:0% +is it clear why that's why that's a good +way to look at this + + align:start position:0% +way to look at this + + + align:start position:0% +way to look at this +question what are we worried about wored + + align:start position:0% +question what are we worried about wored + + + align:start position:0% +question what are we worried about wored +about if we just said well the price of + + align:start position:0% +about if we just said well the price of + + + align:start position:0% +about if we just said well the price of +t is going up what's happening + + align:start position:0% +t is going up what's happening + + + align:start position:0% +t is going up what's happening +to to uh girls well the price is T is + + align:start position:0% +to to uh girls well the price is T is + + + align:start position:0% +to to uh girls well the price is T is +going up but that's going up over time + + align:start position:0% +going up but that's going up over time + + + align:start position:0% +going up but that's going up over time +if the girl if the fraction of girls is + + align:start position:0% +if the girl if the fraction of girls is + + + align:start position:0% +if the girl if the fraction of girls is +going down we'll get a negative + + align:start position:0% +going down we'll get a negative + + + align:start position:0% +going down we'll get a negative +association out of that because there + + align:start position:0% +association out of that because there + + + align:start position:0% +association out of that because there +two things happening one is that it's + + align:start position:0% +two things happening one is that it's + + + align:start position:0% +two things happening one is that it's +just going down for other re reasons the + + align:start position:0% +just going down for other re reasons the + + + align:start position:0% +just going down for other re reasons the +are prices of T is going up for for + + align:start position:0% +are prices of T is going up for for + + + align:start position:0% +are prices of T is going up for for +whatever economic reasons and I'm going + + align:start position:0% +whatever economic reasons and I'm going + + + align:start position:0% +whatever economic reasons and I'm going +to correlate them I'll find a negative + + align:start position:0% +to correlate them I'll find a negative + + + align:start position:0% +to correlate them I'll find a negative +correlation so that's not what we want + + align:start position:0% +correlation so that's not what we want + + + align:start position:0% +correlation so that's not what we want +to do we want to look at areas which are + + align:start position:0% +to do we want to look at areas which are + + + align:start position:0% +to do we want to look at areas which are +suitable for tea that's where the price + + align:start position:0% +suitable for tea that's where the price + + + align:start position:0% +suitable for tea that's where the price +of tea should have an effect should not + + align:start position:0% +of tea should have an effect should not + + + align:start position:0% +of tea should have an effect should not +have an effect where in areas which are + + align:start position:0% +have an effect where in areas which are + + + align:start position:0% +have an effect where in areas which are +not suitable for tea so we're going to + + align:start position:0% +not suitable for tea so we're going to + + + align:start position:0% +not suitable for tea so we're going to +compare the effect of an increase in + + align:start position:0% +compare the effect of an increase in + + + align:start position:0% +compare the effect of an increase in +price of tea in girl suitable areas in + + align:start position:0% +price of tea in girl suitable areas in + + + align:start position:0% +price of tea in girl suitable areas in +t- suitable areas versus nont suitable + + align:start position:0% +t- suitable areas versus nont suitable + + + align:start position:0% +t- suitable areas versus nont suitable +areas not compared trends + + align:start position:0% +areas not compared trends + + + align:start position:0% +areas not compared trends +this is basically what is called doing a + + align:start position:0% +this is basically what is called doing a + + + align:start position:0% +this is basically what is called doing a +difference in difference I'm going to + + align:start position:0% +difference in difference I'm going to + + + align:start position:0% +difference in difference I'm going to +take High T periods High T price periods + + align:start position:0% +take High T periods High T price periods + + + align:start position:0% +take High T periods High T price periods +Low T price periods and compare T + + align:start position:0% +Low T price periods and compare T + + + align:start position:0% +Low T price periods and compare T +suitable areas and nont suitable + + align:start position:0% + + + + align:start position:0% + +areas you look more lost than I would + + align:start position:0% +areas you look more lost than I would + + + align:start position:0% +areas you look more lost than I would +expect it's a very easy idea so somebody + + align:start position:0% +expect it's a very easy idea so somebody + + + align:start position:0% +expect it's a very easy idea so somebody +else want to say back what what I'm + + align:start position:0% +else want to say back what what I'm + + + align:start position:0% +else want to say back what what I'm +trying to say who's going to volunteer + + align:start position:0% +trying to say who's going to volunteer + + + align:start position:0% +trying to say who's going to volunteer +to improve on that exposition + + align:start position:0% +to improve on that exposition + + + align:start position:0% +to improve on that exposition +I'm going to + + align:start position:0% + + + + align:start position:0% + +call okay go ahead um basically you're + + align:start position:0% +call okay go ahead um basically you're + + + align:start position:0% +call okay go ahead um basically you're +trying to see that if this does actually + + align:start position:0% +trying to see that if this does actually + + + align:start position:0% +trying to see that if this does actually +have an effect on how parents treat + + align:start position:0% +have an effect on how parents treat + + + align:start position:0% +have an effect on how parents treat +children you'll see girls treated better + + align:start position:0% +children you'll see girls treated better + + + align:start position:0% +children you'll see girls treated better +in places where te is like the cash crop + + align:start position:0% +in places where te is like the cash crop + + + align:start position:0% +in places where te is like the cash crop +or something and the price increases + + align:start position:0% +or something and the price increases + + + align:start position:0% +or something and the price increases +versus areas where te is not the cash + + align:start position:0% +versus areas where te is not the cash + + + align:start position:0% +versus areas where te is not the cash +crop but the price increases there + + align:start position:0% +crop but the price increases there + + + align:start position:0% +crop but the price increases there +shouldn't be a change in how the girls + + align:start position:0% +shouldn't be a change in how the girls + + + align:start position:0% +shouldn't be a change in how the girls +are treated right so we're going to + + align:start position:0% +are treated right so we're going to + + + align:start position:0% +are treated right so we're going to +compare area years when tea prices went + + align:start position:0% +compare area years when tea prices went + + + align:start position:0% +compare area years when tea prices went +up with t years when tea prices didn't + + align:start position:0% +up with t years when tea prices didn't + + + align:start position:0% +up with t years when tea prices didn't +go up and compare them with in areas + + align:start position:0% +go up and compare them with in areas + + + align:start position:0% +go up and compare them with in areas +where T is a plausible crop and areas + + align:start position:0% +where T is a plausible crop and areas + + + align:start position:0% +where T is a plausible crop and areas +where te cannot be + + align:start position:0% +where te cannot be + + + align:start position:0% +where te cannot be +grown so the increase in Te prices + + align:start position:0% +grown so the increase in Te prices + + + align:start position:0% +grown so the increase in Te prices +should have no effect where te cannot be + + align:start position:0% +should have no effect where te cannot be + + + align:start position:0% +should have no effect where te cannot be +grown it have a spurious effect maybe + + align:start position:0% +grown it have a spurious effect maybe + + + align:start position:0% +grown it have a spurious effect maybe +but no real effect it should have an + + align:start position:0% +but no real effect it should have an + + + align:start position:0% +but no real effect it should have an +effect where T can be grown so we're + + align:start position:0% +effect where T can be grown so we're + + + align:start position:0% +effect where T can be grown so we're +going to compare t t t possible areas + + align:start position:0% +going to compare t t t possible areas + + + align:start position:0% +going to compare t t t possible areas +with other areas when T prices go up + + align:start position:0% +with other areas when T prices go up + + + align:start position:0% +with other areas when T prices go up +versus when it doesn't yeah how do you + + align:start position:0% +versus when it doesn't yeah how do you + + + align:start position:0% +versus when it doesn't yeah how do you +think about it just like you have your + + align:start position:0% +think about it just like you have your + + + align:start position:0% +think about it just like you have your +control population where the T price + + align:start position:0% +control population where the T price + + + align:start position:0% +control population where the T price +where like the T price going up + + align:start position:0% +where like the T price going up + + + align:start position:0% +where like the T price going up +shouldn't have an effect and then you + + align:start position:0% +shouldn't have an effect and then you + + + align:start position:0% +shouldn't have an effect and then you +have your non control and you just take + + align:start position:0% +have your non control and you just take + + + align:start position:0% +have your non control and you just take +your data and subtract your control from + + align:start position:0% +your data and subtract your control from + + + align:start position:0% +your data and subtract your control from +it to see your actual difference that's + + align:start position:0% +it to see your actual difference that's + + + align:start position:0% +it to see your actual difference that's +exactly right so that's another way to + + align:start position:0% +exactly right so that's another way to + + + align:start position:0% +exactly right so that's another way to +say the same thing anybody else wants to + + align:start position:0% +say the same thing anybody else wants to + + + align:start position:0% +say the same thing anybody else wants to +add add anything to that so let me show + + align:start position:0% +add add anything to that so let me show + + + align:start position:0% +add add anything to that so let me show +you some some trends + + align:start position:0% +you some some trends + + + align:start position:0% +you some some trends +first so that's that's the basic fact + + align:start position:0% +first so that's that's the basic fact + + + align:start position:0% +first so that's that's the basic fact +which we want to uh so that's uh T + + align:start position:0% +which we want to uh so that's uh T + + + align:start position:0% +which we want to uh so that's uh T +prices suddenly in 79 you see St T + + align:start position:0% +prices suddenly in 79 you see St T + + + align:start position:0% +prices suddenly in 79 you see St T +prices just skyrocketing that's first + + align:start position:0% +prices just skyrocketing that's first + + + align:start position:0% +prices just skyrocketing that's first +fact uh tea prices are going up tea + + align:start position:0% +fact uh tea prices are going up tea + + + align:start position:0% +fact uh tea prices are going up tea +production is going up second thing is + + align:start position:0% +production is going up second thing is + + + align:start position:0% +production is going up second thing is +that if you look at tea versus other + + align:start position:0% +that if you look at tea versus other + + + align:start position:0% +that if you look at tea versus other +crops tea prices are going up faster + + align:start position:0% +crops tea prices are going up faster + + + align:start position:0% +crops tea prices are going up faster +than other crops so other crops are like + + align:start position:0% +than other crops so other crops are like + + + align:start position:0% +than other crops so other crops are like +grain grain uh is going up but tea is + + align:start position:0% +grain grain uh is going up but tea is + + + align:start position:0% +grain grain uh is going up but tea is +going up faster oil is going up but tea + + align:start position:0% +going up faster oil is going up but tea + + + align:start position:0% +going up faster oil is going up but tea +is going up faster so te is the crop + + align:start position:0% +is going up faster so te is the crop + + + align:start position:0% +is going up faster so te is the crop +that's going up fastest among these + + align:start position:0% +that's going up fastest among these + + + align:start position:0% +that's going up fastest among these +these crops um look at this one here + + align:start position:0% +these crops um look at this one here + + + align:start position:0% +these crops um look at this one here +we're comparing fruits with tea and + + align:start position:0% +we're comparing fruits with tea and + + + align:start position:0% +we're comparing fruits with tea and +fruits are going up much faster than + + align:start position:0% +fruits are going up much faster than + + + align:start position:0% +fruits are going up much faster than +fruits with other crops like grain oil + + align:start position:0% +fruits with other crops like grain oil + + + align:start position:0% +fruits with other crops like grain oil +and and uh cotton and again fruits are + + align:start position:0% +and and uh cotton and again fruits are + + + align:start position:0% +and and uh cotton and again fruits are +going up much faster so basically what + + align:start position:0% +going up much faster so basically what + + + align:start position:0% +going up much faster so basically what +matters is not the absolute price right + + align:start position:0% +matters is not the absolute price right + + + align:start position:0% +matters is not the absolute price right +matters the relative price matters + + align:start position:0% +matters the relative price matters + + + align:start position:0% +matters the relative price matters +because it's it's some it's what makes + + align:start position:0% +because it's it's some it's what makes + + + align:start position:0% +because it's it's some it's what makes +you want to do more T So T areas are + + align:start position:0% +you want to do more T So T areas are + + + align:start position:0% +you want to do more T So T areas are +benefiting relative to those other + + align:start position:0% + + + + align:start position:0% + +areas so here's the basic uh so this is + + align:start position:0% +areas so here's the basic uh so this is + + + align:start position:0% +areas so here's the basic uh so this is +a complicated graph so let's do this + + align:start position:0% +a complicated graph so let's do this + + + align:start position:0% +a complicated graph so let's do this +slowly okay try to understand what + + align:start position:0% +slowly okay try to understand what + + + align:start position:0% +slowly okay try to understand what +what's in this graph so what in what's + + align:start position:0% +what's in this graph so what in what's + + + align:start position:0% +what's in this graph so what in what's +in this graph + + align:start position:0% + + + + align:start position:0% + +is areas where which grow a lot of + + align:start position:0% + + + + align:start position:0% + +T this is the effect + + align:start position:0% +T this is the effect + + + align:start position:0% +T this is the effect +of this is the coefficient or in a + + align:start position:0% +of this is the coefficient or in a + + + align:start position:0% +of this is the coefficient or in a +regression + + align:start position:0% +regression + + + align:start position:0% +regression +of so this is the effect + + align:start position:0% + + + + align:start position:0% + +of having more area devoted to T in a + + align:start position:0% +of having more area devoted to T in a + + + align:start position:0% +of having more area devoted to T in a +particular year + + align:start position:0% +particular year + + + align:start position:0% +particular year +so what this is saying is that + + align:start position:0% +so what this is saying is that + + + align:start position:0% +so what this is saying is that +if before + + align:start position:0% +if before + + + align:start position:0% +if before +1979 you see um tea prices are low in + + align:start position:0% +1979 you see um tea prices are low in + + + align:start position:0% +1979 you see um tea prices are low in +those years you see some uh if you look + + align:start position:0% +those years you see some uh if you look + + + align:start position:0% +those years you see some uh if you look +at the fraction of males the fraction of + + align:start position:0% +at the fraction of males the fraction of + + + align:start position:0% +at the fraction of males the fraction of +L's bounces around but + + align:start position:0% +L's bounces around but + + + align:start position:0% +L's bounces around but +it's the effect the the fact that t is + + align:start position:0% +it's the effect the the fact that t is + + + align:start position:0% +it's the effect the the fact that t is +swn has essentially very close to Zero + + align:start position:0% +swn has essentially very close to Zero + + + align:start position:0% +swn has essentially very close to Zero +Effect after 1979 the fact that t is swn + + align:start position:0% +Effect after 1979 the fact that t is swn + + + align:start position:0% +Effect after 1979 the fact that t is swn +has a much bigger effect so this is the + + align:start position:0% +has a much bigger effect so this is the + + + align:start position:0% +has a much bigger effect so this is the +effect of how much land you put into + + align:start position:0% +effect of how much land you put into + + + align:start position:0% +effect of how much land you put into +T in a particular year so year by year + + align:start position:0% +T in a particular year so year by year + + + align:start position:0% +T in a particular year so year by year +so in that year what's happening in in + + align:start position:0% + + + + align:start position:0% + +1983 how many boys versus girls were + + align:start position:0% + + + + align:start position:0% + +born in high tea areas relative to low + + align:start position:0% +born in high tea areas relative to low + + + align:start position:0% +born in high tea areas relative to low +tea areas that's always the exercise so + + align:start position:0% +tea areas that's always the exercise so + + + align:start position:0% +tea areas that's always the exercise so +think of one more one more percent of + + align:start position:0% +think of one more one more percent of + + + align:start position:0% +think of one more one more percent of +land devoted to tea what what is the + + align:start position:0% +land devoted to tea what what is the + + + align:start position:0% +land devoted to tea what what is the +effect of that on the fraction of of + + align:start position:0% +effect of that on the fraction of of + + + align:start position:0% +effect of that on the fraction of of +fraction of boys born in + + align:start position:0% +fraction of boys born in + + + align:start position:0% +fraction of boys born in +1983 that's what that + + align:start position:0% +1983 that's what that + + + align:start position:0% +1983 that's what that +says so the main point to take away is + + align:start position:0% +says so the main point to take away is + + + align:start position:0% +says so the main point to take away is +that in 19 you see a big + + align:start position:0% +that in 19 you see a big + + + align:start position:0% +that in 19 you see a big +drop after + + align:start position:0% +drop after + + + align:start position:0% +drop after +1979 so uh T areas the fraction of boys + + align:start position:0% +1979 so uh T areas the fraction of boys + + + align:start position:0% +1979 so uh T areas the fraction of boys +born goes down right when you think it + + align:start position:0% +born goes down right when you think it + + + align:start position:0% +born goes down right when you think it +should go down which is when the price + + align:start position:0% +should go down which is when the price + + + align:start position:0% +should go down which is when the price +starts going up + + align:start position:0% +starts going up + + + align:start position:0% +starts going up +okay so that that's what this is + + align:start position:0% +okay so that that's what this is + + + align:start position:0% +okay so that that's what this is +saying you before that the average is + + align:start position:0% +saying you before that the average is + + + align:start position:0% +saying you before that the average is +kind of at + + align:start position:0% +kind of at + + + align:start position:0% +kind of at +point5 the after that the average is + + align:start position:0% +point5 the after that the average is + + + align:start position:0% +point5 the after that the average is +about 35 or something so the fraction of + + align:start position:0% +about 35 or something so the fraction of + + + align:start position:0% +about 35 or something so the fraction of +boys goes down after the change um this + + align:start position:0% +boys goes down after the change um this + + + align:start position:0% +boys goes down after the change um this +is what happens to in the fruit + + align:start position:0% +is what happens to in the fruit + + + align:start position:0% +is what happens to in the fruit +areas the opposite + + align:start position:0% +areas the opposite + + + align:start position:0% +areas the opposite +right after 79 fruit prices go up also a + + align:start position:0% +right after 79 fruit prices go up also a + + + align:start position:0% +right after 79 fruit prices go up also a +lot and fruit favors boys + + align:start position:0% +lot and fruit favors boys + + + align:start position:0% +lot and fruit favors boys +so the fraction of boys goes the ratio + + align:start position:0% +so the fraction of boys goes the ratio + + + align:start position:0% +so the fraction of boys goes the ratio +used to be lower it goes up + + align:start position:0% +used to be lower it goes up + + + align:start position:0% +used to be lower it goes up +afterwards yeah are signicant result yes + + align:start position:0% +afterwards yeah are signicant result yes + + + align:start position:0% +afterwards yeah are signicant result yes +so the average is significantly + + align:start position:0% +so the average is significantly + + + align:start position:0% +so the average is significantly +different so it's not you're right that + + align:start position:0% +different so it's not you're right that + + + align:start position:0% +different so it's not you're right that +year by year it did not significant but + + align:start position:0% +year by year it did not significant but + + + align:start position:0% +year by year it did not significant but +that's because it's a small sample of + + align:start position:0% +that's because it's a small sample of + + + align:start position:0% +that's because it's a small sample of +people but if you take the average of + + align:start position:0% +people but if you take the average of + + + align:start position:0% +people but if you take the average of +these these these periods the averages + + align:start position:0% +these these these periods the averages + + + align:start position:0% +these these these periods the averages +are significantly different I'm just + + align:start position:0% +are significantly different I'm just + + + align:start position:0% +are significantly different I'm just +having in trouble understanding how so + + align:start position:0% +having in trouble understanding how so + + + align:start position:0% +having in trouble understanding how so +women + + align:start position:0% +women + + + align:start position:0% +women +are are better at picking the tea leaves + + align:start position:0% +are are better at picking the tea leaves + + + align:start position:0% +are are better at picking the tea leaves +um I don't know I mean e the economics + + align:start position:0% +um I don't know I mean e the economics + + + align:start position:0% +um I don't know I mean e the economics +makes sense but I I can't + + align:start position:0% +makes sense but I I can't + + + align:start position:0% +makes sense but I I can't +see families conciously choosing to have + + align:start position:0% +see families conciously choosing to have + + + align:start position:0% +see families conciously choosing to have +more girls for 11 like in in 12 years + + align:start position:0% +more girls for 11 like in in 12 years + + + align:start position:0% +more girls for 11 like in in 12 years +they'll be able to well yes and no + + align:start position:0% +they'll be able to well yes and no + + + align:start position:0% +they'll be able to well yes and no +you're right that that but on the other + + align:start position:0% +you're right that that but on the other + + + align:start position:0% +you're right that that but on the other +hand it also sends a signal which + + align:start position:0% +hand it also sends a signal which + + + align:start position:0% +hand it also sends a signal which +reminds them oh well you know um two + + align:start position:0% +reminds them oh well you know um two + + + align:start position:0% +reminds them oh well you know um two +things one you might imagine that the + + align:start position:0% +things one you might imagine that the + + + align:start position:0% +things one you might imagine that the +women might be more Pro + + align:start position:0% +women might be more Pro + + + align:start position:0% +women might be more Pro +girls plausibly no and if you think that + + align:start position:0% +girls plausibly no and if you think that + + + align:start position:0% +girls plausibly no and if you think that +women income share goes up in the family + + align:start position:0% +women income share goes up in the family + + + align:start position:0% +women income share goes up in the family +more they have more say so that's one + + align:start position:0% +more they have more say so that's one + + + align:start position:0% +more they have more say so that's one +possible mechanism the second mechanism + + align:start position:0% +possible mechanism the second mechanism + + + align:start position:0% +possible mechanism the second mechanism +is just that you know they maybe when + + align:start position:0% +is just that you know they maybe when + + + align:start position:0% +is just that you know they maybe when +the income goes up when boy girls + + align:start position:0% +the income goes up when boy girls + + + align:start position:0% +the income goes up when boy girls +incomes go up they just look at it and + + align:start position:0% +incomes go up they just look at it and + + + align:start position:0% +incomes go up they just look at it and +say well maybe my girl will actually be + + align:start position:0% +say well maybe my girl will actually be + + + align:start position:0% +say well maybe my girl will actually be +you know after all all the every all the + + align:start position:0% +you know after all all the every all the + + + align:start position:0% +you know after all all the every all the +women are working these days why not + + align:start position:0% +women are working these days why not + + + align:start position:0% +women are working these days why not +have another girl they'll be fine + + align:start position:0% +have another girl they'll be fine + + + align:start position:0% +have another girl they'll be fine +they'll get they'll they'll have find a + + align:start position:0% +they'll get they'll they'll have find a + + + align:start position:0% +they'll get they'll they'll have find a +job as well I mean I I can't tell what's + + align:start position:0% +job as well I mean I I can't tell what's + + + align:start position:0% +job as well I mean I I can't tell what's +going on at that level but it's clear + + align:start position:0% +going on at that level but it's clear + + + align:start position:0% +going on at that level but it's clear +that this result is significant it's + + align:start position:0% +that this result is significant it's + + + align:start position:0% +that this result is significant it's +actually + + align:start position:0% + + + + align:start position:0% + +substantial okay final uh set of + + align:start position:0% +substantial okay final uh set of + + + align:start position:0% +substantial okay final uh set of +thoughts + + align:start position:0% +thoughts + + + align:start position:0% +thoughts +um suppose this goes on so no we back up + + align:start position:0% +um suppose this goes on so no we back up + + + align:start position:0% +um suppose this goes on so no we back up +what's going on how how are they losing + + align:start position:0% +what's going on how how are they losing + + + align:start position:0% +what's going on how how are they losing +all these girls if it's an economic + + align:start position:0% +all these girls if it's an economic + + + align:start position:0% +all these girls if it's an economic +mechanism we need to that's that says + + align:start position:0% +mechanism we need to that's that says + + + align:start position:0% +mechanism we need to that's that says +that there is incentive to lose the + + align:start position:0% +that there is incentive to lose the + + + align:start position:0% +that there is incentive to lose the +girls how are they actually doing + + align:start position:0% +girls how are they actually doing + + + align:start position:0% +girls how are they actually doing +it what's going + + align:start position:0% + + + + align:start position:0% + +on unfortunately it's all not very nice + + align:start position:0% +on unfortunately it's all not very nice + + + align:start position:0% +on unfortunately it's all not very nice +uh what's going on so two things are + + align:start position:0% +uh what's going on so two things are + + + align:start position:0% +uh what's going on so two things are +happening one one is basically the + + align:start position:0% +happening one one is basically the + + + align:start position:0% +happening one one is basically the +technology for + + align:start position:0% +technology for + + + align:start position:0% +technology for +pre-birth detection of gender of the + + align:start position:0% +pre-birth detection of gender of the + + + align:start position:0% +pre-birth detection of gender of the +child has improved a + + align:start position:0% +child has improved a + + + align:start position:0% +child has improved a +lot if you do + + align:start position:0% +lot if you do + + + align:start position:0% +lot if you do +amniocentesis which is an expensive + + align:start position:0% +amniocentesis which is an expensive + + + align:start position:0% +amniocentesis which is an expensive +procedure you can basically very high + + align:start position:0% +procedure you can basically very high + + + align:start position:0% +procedure you can basically very high +probability predict the gender of the + + align:start position:0% +probability predict the gender of the + + + align:start position:0% +probability predict the gender of the +child the reason why rich areas are + + align:start position:0% +child the reason why rich areas are + + + align:start position:0% +child the reason why rich areas are +doing the worst is precisely because of + + align:start position:0% +doing the worst is precisely because of + + + align:start position:0% +doing the worst is precisely because of +that rich areas are using this + + align:start position:0% +that rich areas are using this + + + align:start position:0% +that rich areas are using this +technology to figure out who their it's + + align:start position:0% +technology to figure out who their it's + + + align:start position:0% +technology to figure out who their it's +say expensive technology so you have to + + align:start position:0% +say expensive technology so you have to + + + align:start position:0% +say expensive technology so you have to +use it um you spend money to use it rich + + align:start position:0% +use it um you spend money to use it rich + + + align:start position:0% +use it um you spend money to use it rich +areas you see in like the Richer parts + + align:start position:0% +areas you see in like the Richer parts + + + align:start position:0% +areas you see in like the Richer parts +of India um signs up which + + align:start position:0% +of India um signs up which + + + align:start position:0% +of India um signs up which +say uh you would you rather spend + + align:start position:0% +say uh you would you rather spend + + + align:start position:0% +say uh you would you rather spend +basically uh $100 now or 100 uh $10,000 + + align:start position:0% +basically uh $100 now or 100 uh $10,000 + + + align:start position:0% +basically uh $100 now or 100 uh $10,000 +later uh which is basically the idea is + + align:start position:0% +later uh which is basically the idea is + + + align:start position:0% +later uh which is basically the idea is +that you have to give dowy for your + + align:start position:0% +that you have to give dowy for your + + + align:start position:0% +that you have to give dowy for your +daughter to get her married and that's + + align:start position:0% +daughter to get her married and that's + + + align:start position:0% +daughter to get her married and that's +your cost and so you should get rid of + + align:start position:0% +your cost and so you should get rid of + + + align:start position:0% +your cost and so you should get rid of +spend you know whatever $100 now + + align:start position:0% +spend you know whatever $100 now + + + align:start position:0% +spend you know whatever $100 now +identify her and then have a sexy an + + align:start position:0% +identify her and then have a sexy an + + + align:start position:0% +identify her and then have a sexy an +abortion uh rather than spend you see + + align:start position:0% +abortion uh rather than spend you see + + + align:start position:0% +abortion uh rather than spend you see +this signs up you know they're all + + align:start position:0% +this signs up you know they're all + + + align:start position:0% +this signs up you know they're all +illegal amnos synthesis about about 8 + + align:start position:0% +illegal amnos synthesis about about 8 + + + align:start position:0% +illegal amnos synthesis about about 8 +years ago was made illegal in India uh + + align:start position:0% +years ago was made illegal in India uh + + + align:start position:0% +years ago was made illegal in India uh +it's still completely prevalent and + + align:start position:0% +it's still completely prevalent and + + + align:start position:0% +it's still completely prevalent and +people and since people are willing to + + align:start position:0% +people and since people are willing to + + + align:start position:0% +people and since people are willing to +try to have many babies they even + + align:start position:0% +try to have many babies they even + + + align:start position:0% +try to have many babies they even +willing to do it if by using um a much + + align:start position:0% +willing to do it if by using um a much + + + align:start position:0% +willing to do it if by using um a much +weaker technology which is sonography + + align:start position:0% +weaker technology which is sonography + + + align:start position:0% +weaker technology which is sonography +sonography which is a technology that is + + align:start position:0% +sonography which is a technology that is + + + align:start position:0% +sonography which is a technology that is +legal you can doesn't identify the + + align:start position:0% +legal you can doesn't identify the + + + align:start position:0% +legal you can doesn't identify the +gender of the child all the time but + + align:start position:0% +gender of the child all the time but + + + align:start position:0% +gender of the child all the time but +about 25% of the time it does and when + + align:start position:0% +about 25% of the time it does and when + + + align:start position:0% +about 25% of the time it does and when +it does then you can immediately abort + + align:start position:0% +it does then you can immediately abort + + + align:start position:0% +it does then you can immediately abort +the child so they're using Technologies + + align:start position:0% +the child so they're using Technologies + + + align:start position:0% +the child so they're using Technologies +to identify this is why this is + + align:start position:0% +to identify this is why this is + + + align:start position:0% +to identify this is why this is +happening more in richer areas because + + align:start position:0% +happening more in richer areas because + + + align:start position:0% +happening more in richer areas because +Technologies cost money and the poorest + + align:start position:0% +Technologies cost money and the poorest + + + align:start position:0% +Technologies cost money and the poorest +areas are ones where the technology is + + align:start position:0% +areas are ones where the technology is + + + align:start position:0% +areas are ones where the technology is +less least used because it's just + + align:start position:0% +less least used because it's just + + + align:start position:0% +less least used because it's just +expensive so you see basically a very + + align:start position:0% +expensive so you see basically a very + + + align:start position:0% +expensive so you see basically a very +very clear correlation between uh where + + align:start position:0% +very clear correlation between uh where + + + align:start position:0% +very clear correlation between uh where +the technology arrives and the fraction + + align:start position:0% +the technology arrives and the fraction + + + align:start position:0% +the technology arrives and the fraction +of children uh boys being born so that's + + align:start position:0% +of children uh boys being born so that's + + + align:start position:0% +of children uh boys being born so that's +one one thing that's going on second + + align:start position:0% +one one thing that's going on second + + + align:start position:0% +one one thing that's going on second +thing that's going on almost surely is a + + align:start position:0% +thing that's going on almost surely is a + + + align:start position:0% +thing that's going on almost surely is a +lot of postbirth uh I think murder is + + align:start position:0% +lot of postbirth uh I think murder is + + + align:start position:0% +lot of postbirth uh I think murder is +the only word you could use uh I think + + align:start position:0% +the only word you could use uh I think + + + align:start position:0% +the only word you could use uh I think +unfortunately there's a lot of I think + + align:start position:0% +unfortunately there's a lot of I think + + + align:start position:0% +unfortunately there's a lot of I think +children being disposed of uh + + align:start position:0% +children being disposed of uh + + + align:start position:0% +children being disposed of uh +there villages which are report to + + align:start position:0% +there villages which are report to + + + align:start position:0% +there villages which are report to +have proudly report there's a news + + align:start position:0% +have proudly report there's a news + + + align:start position:0% +have proudly report there's a news +report I think from like the Chinese + + align:start position:0% +report I think from like the Chinese + + + align:start position:0% +report I think from like the Chinese +news agency which says that we haven't + + align:start position:0% +news agency which says that we haven't + + + align:start position:0% +news agency which says that we haven't +had a boy born in our village for The + + align:start position:0% +had a boy born in our village for The + + + align:start position:0% +had a boy born in our village for The +Last 5 Years a girl born in my our + + align:start position:0% +Last 5 Years a girl born in my our + + + align:start position:0% +Last 5 Years a girl born in my our +village in The Last 5 Years there was a + + align:start position:0% +village in The Last 5 Years there was a + + + align:start position:0% +village in The Last 5 Years there was a +news news report of the village Chief + + align:start position:0% +news news report of the village Chief + + + align:start position:0% +news news report of the village Chief +proudly announcing that he had there was + + align:start position:0% +proudly announcing that he had there was + + + align:start position:0% +proudly announcing that he had there was +no girl born in in his village in The + + align:start position:0% +no girl born in in his village in The + + + align:start position:0% +no girl born in in his village in The +Last 5 Years so I think there is a lot + + align:start position:0% +Last 5 Years so I think there is a lot + + + align:start position:0% +Last 5 Years so I think there is a lot +of just direct deliberate action going + + align:start position:0% +of just direct deliberate action going + + + align:start position:0% +of just direct deliberate action going +on on there now one thing to think about + + align:start position:0% +on on there now one thing to think about + + + align:start position:0% +on on there now one thing to think about +is there are many things to think about + + align:start position:0% +is there are many things to think about + + + align:start position:0% +is there are many things to think about +here how do you stop it well the + + align:start position:0% +here how do you stop it well the + + + align:start position:0% +here how do you stop it well the +government has tried it tried to have + + align:start position:0% +government has tried it tried to have + + + align:start position:0% +government has tried it tried to have +Technologies there's there's a bunch of + + align:start position:0% +Technologies there's there's a bunch of + + + align:start position:0% +Technologies there's there's a bunch of +programs around now for example + + align:start position:0% +programs around now for example + + + align:start position:0% +programs around now for example +um India has a number of states where + + align:start position:0% +um India has a number of states where + + + align:start position:0% +um India has a number of states where +they have programs which + + align:start position:0% +they have programs which + + + align:start position:0% +they have programs which +basically promise parents a certain + + align:start position:0% +basically promise parents a certain + + + align:start position:0% +basically promise parents a certain +amount of money if her if your girl + + align:start position:0% +amount of money if her if your girl + + + align:start position:0% +amount of money if her if your girl +graduates from high school quite a lot + + align:start position:0% +graduates from high school quite a lot + + + align:start position:0% +graduates from high school quite a lot +of money so that's one way to go is give + + align:start position:0% +of money so that's one way to go is give + + + align:start position:0% +of money so that's one way to go is give +incentives based on girl's + + align:start position:0% +incentives based on girl's + + + align:start position:0% +incentives based on girl's +sural + + align:start position:0% +sural + + + align:start position:0% +sural +um various versions of that that + + align:start position:0% +um various versions of that that + + + align:start position:0% +um various versions of that that +programmer but it's not not clear how + + align:start position:0% +programmer but it's not not clear how + + + align:start position:0% +programmer but it's not not clear how +well that works because in some some + + align:start position:0% +well that works because in some some + + + align:start position:0% +well that works because in some some +ways that's a still it's something + + align:start position:0% +ways that's a still it's something + + + align:start position:0% +ways that's a still it's something +that's based on 20 years later and you + + align:start position:0% +that's based on 20 years later and you + + + align:start position:0% +that's based on 20 years later and you +don't necessarily want people think that + + align:start position:0% +don't necessarily want people think that + + + align:start position:0% +don't necessarily want people think that +people are that responsive to so that's + + align:start position:0% +people are that responsive to so that's + + + align:start position:0% +people are that responsive to so that's +the other thing you can think about is + + align:start position:0% +the other thing you can think about is + + + align:start position:0% +the other thing you can think about is +is there any economic force that this + + align:start position:0% +is there any economic force that this + + + align:start position:0% +is there any economic force that this +sets + + align:start position:0% +sets + + + align:start position:0% +sets +by itself it sets on which will sets off + + align:start position:0% +by itself it sets on which will sets off + + + align:start position:0% +by itself it sets on which will sets off +which will then make kind of + + align:start position:0% +which will then make kind of + + + align:start position:0% +which will then make kind of +re-equilibrium so one issue that arises + + align:start position:0% +re-equilibrium so one issue that arises + + + align:start position:0% +re-equilibrium so one issue that arises +is is what's happening to the marriage + + align:start position:0% +is is what's happening to the marriage + + + align:start position:0% +is is what's happening to the marriage +market so what do you think will happen + + align:start position:0% +market so what do you think will happen + + + align:start position:0% +market so what do you think will happen +to the marriage + + align:start position:0% +to the marriage + + + align:start position:0% +to the marriage +Market in + + align:start position:0% +Market in + + + align:start position:0% +Market in +China well if there are fewer women then + + align:start position:0% +China well if there are fewer women then + + + align:start position:0% +China well if there are fewer women then +each one is essentially worth more yeah + + align:start position:0% +each one is essentially worth more yeah + + + align:start position:0% +each one is essentially worth more yeah +so you would see the emergence dowy + + align:start position:0% +so you would see the emergence dowy + + + align:start position:0% +so you would see the emergence dowy +should go down and bright price should + + align:start position:0% +should go down and bright price should + + + align:start position:0% +should go down and bright price should +should go up now one reason this hasn't + + align:start position:0% +should go up now one reason this hasn't + + + align:start position:0% +should go up now one reason this hasn't +happened + + align:start position:0% +happened + + + align:start position:0% +happened +already is that men at least in why this + + align:start position:0% +already is that men at least in why this + + + align:start position:0% +already is that men at least in why this +is happened already in India especially + + align:start position:0% +is happened already in India especially + + + align:start position:0% +is happened already in India especially +is that men tend to marry women who are + + align:start position:0% +is that men tend to marry women who are + + + align:start position:0% +is that men tend to marry women who are +younger than + + align:start position:0% +younger than + + + align:start position:0% +younger than +them if the population is growing then + + align:start position:0% +them if the population is growing then + + + align:start position:0% +them if the population is growing then +there and people marry women who are + + align:start position:0% +there and people marry women who are + + + align:start position:0% +there and people marry women who are +younger than + + align:start position:0% + + + + align:start position:0% + +them + + align:start position:0% +them + + + align:start position:0% +them +then even if there are fewer girls + + align:start position:0% +then even if there are fewer girls + + + align:start position:0% +then even if there are fewer girls +born the girls are from a different + + align:start position:0% +born the girls are from a different + + + align:start position:0% +born the girls are from a different +cohort from a younger + + align:start position:0% +cohort from a younger + + + align:start position:0% +cohort from a younger +cohort so there the population is + + align:start position:0% +cohort so there the population is + + + align:start position:0% +cohort so there the population is +growing so there are more girls + + align:start position:0% + + + + align:start position:0% + +around right so that's one problem that + + align:start position:0% +around right so that's one problem that + + + align:start position:0% +around right so that's one problem that +this Force might operate but only if + + align:start position:0% +this Force might operate but only if + + + align:start position:0% +this Force might operate but only if +population growth stops so it's going to + + align:start position:0% +population growth stops so it's going to + + + align:start position:0% +population growth stops so it's going to +operate more in China where population + + align:start position:0% +operate more in China where population + + + align:start position:0% +operate more in China where population +growth has stopped than in India where + + align:start position:0% +growth has stopped than in India where + + + align:start position:0% +growth has stopped than in India where +the population growth is still going on + + align:start position:0% +the population growth is still going on + + + align:start position:0% +the population growth is still going on +as long as it's population growth you're + + align:start position:0% +as long as it's population growth you're + + + align:start position:0% +as long as it's population growth you're +going to see this possibility of just + + align:start position:0% +going to see this possibility of just + + + align:start position:0% +going to see this possibility of just +going down in the cohort + + align:start position:0% +going down in the cohort + + + align:start position:0% +going down in the cohort +chain rather than so you might imagine + + align:start position:0% +chain rather than so you might imagine + + + align:start position:0% +chain rather than so you might imagine +that the price of gold would go up but + + align:start position:0% +that the price of gold would go up but + + + align:start position:0% +that the price of gold would go up but +it won't go up if people marry much + + align:start position:0% +it won't go up if people marry much + + + align:start position:0% +it won't go up if people marry much +younger women that's one issue second + + align:start position:0% +younger women that's one issue second + + + align:start position:0% +younger women that's one issue second +um isue so in China you do start so in + + align:start position:0% +um isue so in China you do start so in + + + align:start position:0% +um isue so in China you do start so in +China one of the things that people are + + align:start position:0% +China one of the things that people are + + + align:start position:0% +China one of the things that people are +often puzzled about is what's going on + + align:start position:0% +often puzzled about is what's going on + + + align:start position:0% +often puzzled about is what's going on +with this savings + + align:start position:0% +with this savings + + + align:start position:0% +with this savings +rate um the savings rate in China is + + align:start position:0% +rate um the savings rate in China is + + + align:start position:0% +rate um the savings rate in China is +personal savings rate is historically + + align:start position:0% +personal savings rate is historically + + + align:start position:0% +personal savings rate is historically +unprecedented people spend save 30% of + + align:start position:0% +unprecedented people spend save 30% of + + + align:start position:0% +unprecedented people spend save 30% of +their incomes this is as against + + align:start position:0% +their incomes this is as against + + + align:start position:0% +their incomes this is as against +compared to us which used to SP save + + align:start position:0% +compared to us which used to SP save + + + align:start position:0% +compared to us which used to SP save +zero till recently and after the crisis + + align:start position:0% +zero till recently and after the crisis + + + align:start position:0% +zero till recently and after the crisis +has gone up to + + align:start position:0% +has gone up to + + + align:start position:0% +has gone up to +7% uh so personal savings rate in the in + + align:start position:0% +7% uh so personal savings rate in the in + + + align:start position:0% +7% uh so personal savings rate in the in +China are massive so one puzzle people + + align:start position:0% +China are massive so one puzzle people + + + align:start position:0% +China are massive so one puzzle people +have often worried think been thinking + + align:start position:0% +have often worried think been thinking + + + align:start position:0% +have often worried think been thinking +about is what's going on with that it's + + align:start position:0% +about is what's going on with that it's + + + align:start position:0% +about is what's going on with that it's +a very nice paper which does the + + align:start position:0% +a very nice paper which does the + + + align:start position:0% +a very nice paper which does the +following it asks + + align:start position:0% +following it asks + + + align:start position:0% +following it asks +if I look at areas which have high + + align:start position:0% +if I look at areas which have high + + + align:start position:0% +if I look at areas which have high +gender + + align:start position:0% + + + + align:start position:0% + +ratios where women are really + + align:start position:0% + + + + align:start position:0% + +scarce are people saving more in those + + align:start position:0% +scarce are people saving more in those + + + align:start position:0% +scarce are people saving more in those +areas why would they save + + align:start position:0% + + + + align:start position:0% + +more why would you save more if you're a + + align:start position:0% +more why would you save more if you're a + + + align:start position:0% +more why would you save more if you're a +parent of a + + align:start position:0% +parent of a + + + align:start position:0% +parent of a +boy so in particular they ask if you're + + align:start position:0% +boy so in particular they ask if you're + + + align:start position:0% +boy so in particular they ask if you're +a parent of a boy in China easy because + + align:start position:0% +a parent of a boy in China easy because + + + align:start position:0% +a parent of a boy in China easy because +people have one child so you have either + + align:start position:0% +people have one child so you have either + + + align:start position:0% +people have one child so you have either +a parent of a boy or a parent of a girl + + align:start position:0% +a parent of a boy or a parent of a girl + + + align:start position:0% +a parent of a boy or a parent of a girl +if you're parent of a boy in an area + + align:start position:0% +if you're parent of a boy in an area + + + align:start position:0% +if you're parent of a boy in an area +where the gender ratio is particularly + + align:start position:0% +where the gender ratio is particularly + + + align:start position:0% +where the gender ratio is particularly +bad so very few + + align:start position:0% +bad so very few + + + align:start position:0% +bad so very few +girls you turns out you save more why + + align:start position:0% +girls you turns out you save more why + + + align:start position:0% +girls you turns out you save more why +would that be the + + align:start position:0% +would that be the + + + align:start position:0% +would that be the +case well + + align:start position:0% +case well + + + align:start position:0% +case well +you the price of a bride yeah you you + + align:start position:0% +you the price of a bride yeah you you + + + align:start position:0% +you the price of a bride yeah you you +have to buy your son a bride so people + + align:start position:0% +have to buy your son a bride so people + + + align:start position:0% +have to buy your son a bride so people +are saving more so basically they + + align:start position:0% +are saving more so basically they + + + align:start position:0% +are saving more so basically they +suggest that people are now beginning to + + align:start position:0% +suggest that people are now beginning to + + + align:start position:0% +suggest that people are now beginning to +save more more in order to buy this + + align:start position:0% +save more more in order to buy this + + + align:start position:0% +save more more in order to buy this +child a bride uh and the way you buy it + + align:start position:0% +child a bride uh and the way you buy it + + + align:start position:0% +child a bride uh and the way you buy it +is you don't go and buy her in a market + + align:start position:0% +is you don't go and buy her in a market + + + align:start position:0% +is you don't go and buy her in a market +but basically women have become very + + align:start position:0% +but basically women have become very + + + align:start position:0% +but basically women have become very +picky about not marrying into families + + align:start position:0% +picky about not marrying into families + + + align:start position:0% +picky about not marrying into families +which can't afford to give their son a + + align:start position:0% +which can't afford to give their son a + + + align:start position:0% +which can't afford to give their son a +separate apartment to to move into when + + align:start position:0% +separate apartment to to move into when + + + align:start position:0% +separate apartment to to move into when +uh when they get married China has very + + align:start position:0% +uh when they get married China has very + + + align:start position:0% +uh when they get married China has very +poor morgage market so you can't really + + align:start position:0% +poor morgage market so you can't really + + + align:start position:0% +poor morgage market so you can't really +take out a mortgage to buy a house so + + align:start position:0% +take out a mortgage to buy a house so + + + align:start position:0% +take out a mortgage to buy a house so +what you basically the only way you buy + + align:start position:0% +what you basically the only way you buy + + + align:start position:0% +what you basically the only way you buy +a house is you borrow from your parents + + align:start position:0% +a house is you borrow from your parents + + + align:start position:0% +a house is you borrow from your parents +or your parents give you a gift so + + align:start position:0% +or your parents give you a gift so + + + align:start position:0% +or your parents give you a gift so +parents now it's become a status issue + + align:start position:0% +parents now it's become a status issue + + + align:start position:0% +parents now it's become a status issue +for parents to marry their son and the + + align:start position:0% +for parents to marry their son and the + + + align:start position:0% +for parents to marry their son and the +way you marry your son is by buying him + + align:start position:0% +way you marry your son is by buying him + + + align:start position:0% +way you marry your son is by buying him +an apartment when he gets married so if + + align:start position:0% +an apartment when he gets married so if + + + align:start position:0% +an apartment when he gets married so if +you not don't have enough wealth you + + align:start position:0% +you not don't have enough wealth you + + + align:start position:0% +you not don't have enough wealth you +can't buy an apartment and then your son + + align:start position:0% +can't buy an apartment and then your son + + + align:start position:0% +can't buy an apartment and then your son +can't get married so this seems to be uh + + align:start position:0% +can't get married so this seems to be uh + + + align:start position:0% +can't get married so this seems to be uh +sort of one of the factors that might + + align:start position:0% +sort of one of the factors that might + + + align:start position:0% +sort of one of the factors that might +actually ree equilibri at China because + + align:start position:0% +actually ree equilibri at China because + + + align:start position:0% +actually ree equilibri at China because +it seems like one thing that's going on + + align:start position:0% +it seems like one thing that's going on + + + align:start position:0% +it seems like one thing that's going on +in China right now is this + + align:start position:0% +in China right now is this + + + align:start position:0% +in China right now is this +massive increase in savings and I'm sure + + align:start position:0% +massive increase in savings and I'm sure + + + align:start position:0% +massive increase in savings and I'm sure +that this this is not problem with this + + align:start position:0% +that this this is not problem with this + + + align:start position:0% +that this this is not problem with this +massive increase in savings is it's a + + align:start position:0% +massive increase in savings is it's a + + + align:start position:0% +massive increase in savings is it's a +completely it's a zero SU game right + + align:start position:0% +completely it's a zero SU game right + + + align:start position:0% +completely it's a zero SU game right +there are only so many girls so the fact + + align:start position:0% +there are only so many girls so the fact + + + align:start position:0% +there are only so many girls so the fact +that I'm saving a lot for my son just + + align:start position:0% +that I'm saving a lot for my son just + + + align:start position:0% +that I'm saving a lot for my son just +means my son can have a bride but not + + align:start position:0% +means my son can have a bride but not + + + align:start position:0% +means my son can have a bride but not +anybody else this it's not that the + + align:start position:0% +anybody else this it's not that the + + + align:start position:0% +anybody else this it's not that the +number of women go up because I + + align:start position:0% +number of women go up because I + + + align:start position:0% +number of women go up because I +save so this is not really solving the + + align:start position:0% +save so this is not really solving the + + + align:start position:0% +save so this is not really solving the +problem it's squeezing parents because + + align:start position:0% +problem it's squeezing parents because + + + align:start position:0% +problem it's squeezing parents because +parents now have to so if I'm going to + + align:start position:0% +parents now have to so if I'm going to + + + align:start position:0% +parents now have to so if I'm going to +save $1 more in order to buy my son a + + align:start position:0% +save $1 more in order to buy my son a + + + align:start position:0% +save $1 more in order to buy my son a +house so he can get married then + + align:start position:0% +house so he can get married then + + + align:start position:0% +house so he can get married then +somebody else is going to do want to do + + align:start position:0% +somebody else is going to do want to do + + + align:start position:0% +somebody else is going to do want to do +the same thing he's going to try to save + + align:start position:0% +the same thing he's going to try to save + + + align:start position:0% +the same thing he's going to try to save +even more than me and buy a house for + + align:start position:0% +even more than me and buy a house for + + + align:start position:0% +even more than me and buy a house for +his son so that competition is going to + + align:start position:0% +his son so that competition is going to + + + align:start position:0% +his son so that competition is going to +is a very kind of a negative competition + + align:start position:0% +is a very kind of a negative competition + + + align:start position:0% +is a very kind of a negative competition +everybody's getting hurt by that + + align:start position:0% +everybody's getting hurt by that + + + align:start position:0% +everybody's getting hurt by that +competition so that should make parents + + align:start position:0% +competition so that should make parents + + + align:start position:0% +competition so that should make parents +really rethink this strategy so I mean + + align:start position:0% +really rethink this strategy so I mean + + + align:start position:0% +really rethink this strategy so I mean +that's the one one sign of hope I see is + + align:start position:0% +that's the one one sign of hope I see is + + + align:start position:0% +that's the one one sign of hope I see is +this one which is the we the market + + align:start position:0% +this one which is the we the market + + + align:start position:0% +this one which is the we the market +forces seem to be kind of operating to + + align:start position:0% +forces seem to be kind of operating to + + + align:start position:0% +forces seem to be kind of operating to +make this problem better that's true in + + align:start position:0% +make this problem better that's true in + + + align:start position:0% +make this problem better that's true in +China less much less to it India because + + align:start position:0% +China less much less to it India because + + + align:start position:0% +China less much less to it India because +India still population is growing so + + align:start position:0% +India still population is growing so + + + align:start position:0% +India still population is growing so +there's still this margin of + + align:start position:0% +there's still this margin of + + + align:start position:0% +there's still this margin of +adjustment okay + + align:start position:0% +adjustment okay + + + align:start position:0% +adjustment okay +so questions comments stop yeah in China + + align:start position:0% +so questions comments stop yeah in China + + + align:start position:0% +so questions comments stop yeah in China +would you see that now increas in grow + + align:start position:0% +would you see that now increas in grow + + + align:start position:0% +would you see that now increas in grow +and because parents see that they don't + + align:start position:0% +and because parents see that they don't + + + align:start position:0% +and because parents see that they don't +have to save money have yeah you so you + + align:start position:0% +have to save money have yeah you so you + + + align:start position:0% +have to save money have yeah you so you +might see that we you aren seeing it yet + + align:start position:0% +might see that we you aren seeing it yet + + + align:start position:0% +might see that we you aren seeing it yet +but maybe once it gets clear that you + + align:start position:0% +but maybe once it gets clear that you + + + align:start position:0% +but maybe once it gets clear that you +know your daughter gets to live in a + + align:start position:0% +know your daughter gets to live in a + + + align:start position:0% +know your daughter gets to live in a +wonderful apartment Etc and having a son + + align:start position:0% +wonderful apartment Etc and having a son + + + align:start position:0% +wonderful apartment Etc and having a son +is a huge pain because you have to Now + + align:start position:0% +is a huge pain because you have to Now + + + align:start position:0% +is a huge pain because you have to Now +find ways to pay for his you know + + align:start position:0% +find ways to pay for his you know + + + align:start position:0% +find ways to pay for his you know +apartment you might start preferring + + align:start position:0% +apartment you might start preferring + + + align:start position:0% +apartment you might start preferring +daughters so maybe we'll see + + align:start position:0% + + + + align:start position:0% + +that okay thank you \ No newline at end of file diff --git a/jdboljUNQdM.txt b/jdboljUNQdM.txt new file mode 100644 index 0000000000000000000000000000000000000000..efeec94845ba1148c11f67795bd106aa8cf39a51 --- /dev/null +++ b/jdboljUNQdM.txt @@ -0,0 +1,2963 @@ +align:start position:0% + +So today uh we we set aside that part + + align:start position:0% +So today uh we we set aside that part + + + align:start position:0% +So today uh we we set aside that part +and look at what is uh often the hardest + + align:start position:0% +and look at what is uh often the hardest + + + align:start position:0% +and look at what is uh often the hardest +thing to actually make it real uh to put + + align:start position:0% +thing to actually make it real uh to put + + + align:start position:0% +thing to actually make it real uh to put +in the around design, build, learn, + + align:start position:0% +in the around design, build, learn, + + + align:start position:0% +in the around design, build, learn, +research. So we get to work in a sense. + + align:start position:0% +research. So we get to work in a sense. + + + align:start position:0% +research. So we get to work in a sense. +Um and just like yesterday, uh there are + + align:start position:0% +Um and just like yesterday, uh there are + + + align:start position:0% +Um and just like yesterday, uh there are +many people, experts, ideas that we + + align:start position:0% +many people, experts, ideas that we + + + align:start position:0% +many people, experts, ideas that we +couldn't ram into this two-day session + + align:start position:0% +couldn't ram into this two-day session + + + align:start position:0% +couldn't ram into this two-day session +in 10-minute segments. And so we are so + + align:start position:0% +in 10-minute segments. And so we are so + + + align:start position:0% +in 10-minute segments. And so we are so +aware of that. There is still a + + align:start position:0% +aware of that. There is still a + + + align:start position:0% +aware of that. There is still a +whiteboard + + align:start position:0% +whiteboard + + + align:start position:0% +whiteboard +um with at the break you can add the + + align:start position:0% +um with at the break you can add the + + + align:start position:0% +um with at the break you can add the +names of people and experts and ideas + + align:start position:0% +names of people and experts and ideas + + + align:start position:0% +names of people and experts and ideas +that you really think need to be in + + align:start position:0% +that you really think need to be in + + + align:start position:0% +that you really think need to be in +here. We may have attempted to get them + + align:start position:0% +here. We may have attempted to get them + + + align:start position:0% +here. We may have attempted to get them +here. Um but we really want to hear that + + align:start position:0% +here. Um but we really want to hear that + + + align:start position:0% +here. Um but we really want to hear that +from you as well as feedback. Um we're + + align:start position:0% +from you as well as feedback. Um we're + + + align:start position:0% +from you as well as feedback. Um we're +trying to capture and share kind of a + + align:start position:0% +trying to capture and share kind of a + + + align:start position:0% +trying to capture and share kind of a +pulse of information, the state of + + align:start position:0% +pulse of information, the state of + + + align:start position:0% +pulse of information, the state of +knowledge. As you saw yesterday, there's + + align:start position:0% +knowledge. As you saw yesterday, there's + + + align:start position:0% +knowledge. As you saw yesterday, there's +all kinds of views, all kinds of + + align:start position:0% +all kinds of views, all kinds of + + + align:start position:0% +all kinds of views, all kinds of +perspectives, all kinds of voices and + + align:start position:0% +perspectives, all kinds of voices and + + + align:start position:0% +perspectives, all kinds of voices and +language. and we just welcome them all. + + align:start position:0% +language. and we just welcome them all. + + + align:start position:0% +language. and we just welcome them all. +We're not saying that we shouldn't have + + align:start position:0% +We're not saying that we shouldn't have + + + align:start position:0% +We're not saying that we shouldn't have +some healthy debates. Um, so I really + + align:start position:0% +some healthy debates. Um, so I really + + + align:start position:0% +some healthy debates. Um, so I really +hope it goes as well today. And I want + + align:start position:0% +hope it goes as well today. And I want + + + align:start position:0% +hope it goes as well today. And I want +to pass it over to uh Juliet who will be + + align:start position:0% +to pass it over to uh Juliet who will be + + + align:start position:0% +to pass it over to uh Juliet who will be +moderating our very first session. + + align:start position:0% +moderating our very first session. + + + align:start position:0% +moderating our very first session. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Hello everyone. Um we're excited to + + align:start position:0% +Hello everyone. Um we're excited to + + + align:start position:0% +Hello everyone. Um we're excited to +start our day off with some talks about + + align:start position:0% +start our day off with some talks about + + + align:start position:0% +start our day off with some talks about +design principles for geothermal energy + + align:start position:0% +design principles for geothermal energy + + + align:start position:0% +design principles for geothermal energy +networks. We have three great speakers. + + align:start position:0% +networks. We have three great speakers. + + + align:start position:0% +networks. We have three great speakers. +Um two of them in person and then one + + align:start position:0% +Um two of them in person and then one + + + align:start position:0% +Um two of them in person and then one +online. So we'll start our day with + + align:start position:0% +online. So we'll start our day with + + + align:start position:0% +online. So we'll start our day with +Connor Dwe uh who is a licensed engineer + + align:start position:0% +Connor Dwe uh who is a licensed engineer + + + align:start position:0% +Connor Dwe uh who is a licensed engineer +at Geoys and who teaches an IGBA um + + align:start position:0% +at Geoys and who teaches an IGBA um + + + align:start position:0% +at Geoys and who teaches an IGBA um +ground source heat pump course. Um, + + align:start position:0% +ground source heat pump course. Um, + + + align:start position:0% +ground source heat pump course. Um, +Connor, + + align:start position:0% + + + + align:start position:0% + +>> okay, good morning everyone. Um, + + align:start position:0% +>> okay, good morning everyone. Um, + + + align:start position:0% +>> okay, good morning everyone. Um, +so I I spoke with Zena before this this + + align:start position:0% +so I I spoke with Zena before this this + + + align:start position:0% +so I I spoke with Zena before this this +meeting. I I just wanted to, you know, + + align:start position:0% +meeting. I I just wanted to, you know, + + + align:start position:0% +meeting. I I just wanted to, you know, +thank all of HEAT for putting on the + + align:start position:0% +thank all of HEAT for putting on the + + + align:start position:0% +thank all of HEAT for putting on the +session. and I left yesterday quite + + align:start position:0% +session. and I left yesterday quite + + + align:start position:0% +session. and I left yesterday quite +optimistic on the geothermal district + + align:start position:0% +optimistic on the geothermal district + + + align:start position:0% +optimistic on the geothermal district +space in the United States which is you + + align:start position:0% +space in the United States which is you + + + align:start position:0% +space in the United States which is you +know it's it's very um relieving I'll + + align:start position:0% +know it's it's very um relieving I'll + + + align:start position:0% +know it's it's very um relieving I'll +say with the with the times. So thank + + align:start position:0% +say with the with the times. So thank + + + align:start position:0% +say with the with the times. So thank +you all for putting this on. So my my + + align:start position:0% +you all for putting this on. So my my + + + align:start position:0% +you all for putting this on. So my my +background is in engineering uh I have a + + align:start position:0% +background is in engineering uh I have a + + + align:start position:0% +background is in engineering uh I have a +doctor in what's called uh earth energy + + align:start position:0% +doctor in what's called uh earth energy + + + align:start position:0% +doctor in what's called uh earth energy +resource engineering. I'm a licensed + + align:start position:0% +resource engineering. I'm a licensed + + + align:start position:0% +resource engineering. I'm a licensed +engineer in the state of New York and + + align:start position:0% +engineer in the state of New York and + + + align:start position:0% +engineer in the state of New York and +also uh the province of Ontario and + + align:start position:0% +also uh the province of Ontario and + + + align:start position:0% +also uh the province of Ontario and +Canada. Um I also help teach the + + align:start position:0% +Canada. Um I also help teach the + + + align:start position:0% +Canada. Um I also help teach the +certified geo exchange designer course + + align:start position:0% +certified geo exchange designer course + + + align:start position:0% +certified geo exchange designer course +which is run by international ground + + align:start position:0% +which is run by international ground + + + align:start position:0% +which is run by international ground +source heat seat pump association and + + align:start position:0% +source heat seat pump association and + + + align:start position:0% +source heat seat pump association and +this specific slide deck today just goes + + align:start position:0% +this specific slide deck today just goes + + + align:start position:0% +this specific slide deck today just goes +through that introductory level uh CGD + + align:start position:0% +through that introductory level uh CGD + + + align:start position:0% +through that introductory level uh CGD +type type course. So we thought we'd + + align:start position:0% +type type course. So we thought we'd + + + align:start position:0% +type type course. So we thought we'd +start with the fundamentals of heat + + align:start position:0% +start with the fundamentals of heat + + + align:start position:0% +start with the fundamentals of heat +transfer uh to get into you know the + + align:start position:0% +transfer uh to get into you know the + + + align:start position:0% +transfer uh to get into you know the +ground source heat pumps and and how + + align:start position:0% +ground source heat pumps and and how + + + align:start position:0% +ground source heat pumps and and how +they work. So we have conduction, + + align:start position:0% +they work. So we have conduction, + + + align:start position:0% +they work. So we have conduction, +convection and radiation. By definition, + + align:start position:0% +convection and radiation. By definition, + + + align:start position:0% +convection and radiation. By definition, +conduction is when heat is directly + + align:start position:0% +conduction is when heat is directly + + + align:start position:0% +conduction is when heat is directly +transmitted through a substance when + + align:start position:0% +transmitted through a substance when + + + align:start position:0% +transmitted through a substance when +there is a difference in temperature. So + + align:start position:0% +there is a difference in temperature. So + + + align:start position:0% +there is a difference in temperature. So +if you're holding a metal rod and that + + align:start position:0% +if you're holding a metal rod and that + + + align:start position:0% +if you're holding a metal rod and that +metal rod heats up on one end, you feel + + align:start position:0% +metal rod heats up on one end, you feel + + + align:start position:0% +metal rod heats up on one end, you feel +that heat through your hand through + + align:start position:0% +that heat through your hand through + + + align:start position:0% +that heat through your hand through +conduction of that metal rod. We have + + align:start position:0% +conduction of that metal rod. We have + + + align:start position:0% +conduction of that metal rod. We have +convection, which is the rising motion + + align:start position:0% +convection, which is the rising motion + + + align:start position:0% +convection, which is the rising motion +of warmer areas of a liquid or gas and + + align:start position:0% +of warmer areas of a liquid or gas and + + + align:start position:0% +of warmer areas of a liquid or gas and +the sinking motion of cooler areas of + + align:start position:0% +the sinking motion of cooler areas of + + + align:start position:0% +the sinking motion of cooler areas of +liquid or gas. So if you're holding your + + align:start position:0% +liquid or gas. So if you're holding your + + + align:start position:0% +liquid or gas. So if you're holding your +hand over a fire, you know that heat. + + align:start position:0% +hand over a fire, you know that heat. + + + align:start position:0% +hand over a fire, you know that heat. +You're not physically touching anything, + + align:start position:0% +You're not physically touching anything, + + + align:start position:0% +You're not physically touching anything, +but you feel that heat and that's that's + + align:start position:0% +but you feel that heat and that's that's + + + align:start position:0% +but you feel that heat and that's that's +convection. + + align:start position:0% +convection. + + + align:start position:0% +convection. +Lastly, we have radiation. The process + + align:start position:0% +Lastly, we have radiation. The process + + + align:start position:0% +Lastly, we have radiation. The process +where heat energy is transferred from + + align:start position:0% +where heat energy is transferred from + + + align:start position:0% +where heat energy is transferred from +one object to another through the + + align:start position:0% +one object to another through the + + + align:start position:0% +one object to another through the +emission of electromagnetic waves. I + + align:start position:0% +emission of electromagnetic waves. I + + + align:start position:0% +emission of electromagnetic waves. I +promise the rest of the rest the rest of + + align:start position:0% +promise the rest of the rest the rest of + + + align:start position:0% +promise the rest of the rest the rest of +this presentation won't be this dry. Um + + align:start position:0% +this presentation won't be this dry. Um + + + align:start position:0% +this presentation won't be this dry. Um +just getting through the fundamentals, + + align:start position:0% +just getting through the fundamentals, + + + align:start position:0% +just getting through the fundamentals, +but when you're suntanning, you know, + + align:start position:0% +but when you're suntanning, you know, + + + align:start position:0% +but when you're suntanning, you know, +you feel that heat, that's radiation. + + align:start position:0% +you feel that heat, that's radiation. + + + align:start position:0% +you feel that heat, that's radiation. +Okay, so geothermal. What is geothermal? + + align:start position:0% +Okay, so geothermal. What is geothermal? + + + align:start position:0% +Okay, so geothermal. What is geothermal? +While geo means relating to the earth + + align:start position:0% +While geo means relating to the earth + + + align:start position:0% +While geo means relating to the earth +and thermal means relating to heat. So + + align:start position:0% +and thermal means relating to heat. So + + + align:start position:0% +and thermal means relating to heat. So +the earth temperature is relatively + + align:start position:0% +the earth temperature is relatively + + + align:start position:0% +the earth temperature is relatively +constant throughout the year, right? + + align:start position:0% +constant throughout the year, right? + + + align:start position:0% +constant throughout the year, right? +It's around 50 here. I think it's 55 + + align:start position:0% +It's around 50 here. I think it's 55 + + + align:start position:0% +It's around 50 here. I think it's 55 +degrees Fahrenheit. Whereas in the + + align:start position:0% +degrees Fahrenheit. Whereas in the + + + align:start position:0% +degrees Fahrenheit. Whereas in the +winter time it's 10° outside and then in + + align:start position:0% +winter time it's 10° outside and then in + + + align:start position:0% +winter time it's 10° outside and then in +the summertime around 90° outside, but + + align:start position:0% +the summertime around 90° outside, but + + + align:start position:0% +the summertime around 90° outside, but +the ground stays that same 50 55° F. And + + align:start position:0% +the ground stays that same 50 55° F. And + + + align:start position:0% +the ground stays that same 50 55° F. And +to harness that energy, you can install + + align:start position:0% +to harness that energy, you can install + + + align:start position:0% +to harness that energy, you can install +a ground heat exchanger, which is + + align:start position:0% +a ground heat exchanger, which is + + + align:start position:0% +a ground heat exchanger, which is +plastic pipe that's buried in the ground + + align:start position:0% +plastic pipe that's buried in the ground + + + align:start position:0% +plastic pipe that's buried in the ground +and it transfers heat to a volume of + + align:start position:0% +and it transfers heat to a volume of + + + align:start position:0% +and it transfers heat to a volume of +earth around that around that pipe um + + align:start position:0% +earth around that around that pipe um + + + align:start position:0% +earth around that around that pipe um +through various ways. You know, shallow + + align:start position:0% +through various ways. You know, shallow + + + align:start position:0% +through various ways. You know, shallow +ground heat exchangers take advantage of + + align:start position:0% +ground heat exchangers take advantage of + + + align:start position:0% +ground heat exchangers take advantage of +radiation, mainly conduction. Um but + + align:start position:0% +radiation, mainly conduction. Um but + + + align:start position:0% +radiation, mainly conduction. Um but +there's also conve convective heat + + align:start position:0% +there's also conve convective heat + + + align:start position:0% +there's also conve convective heat +transfer with that groundwater. You have + + align:start position:0% +transfer with that groundwater. You have + + + align:start position:0% +transfer with that groundwater. You have +heat exchange fluid that's pumped + + align:start position:0% +heat exchange fluid that's pumped + + + align:start position:0% +heat exchange fluid that's pumped +through the pipe. I'm getting used to + + align:start position:0% +through the pipe. I'm getting used to + + + align:start position:0% +through the pipe. I'm getting used to +this laser here. heat exchange fluid + + align:start position:0% +this laser here. heat exchange fluid + + + align:start position:0% +this laser here. heat exchange fluid +that's pumped through this pipe and then + + align:start position:0% +that's pumped through this pipe and then + + + align:start position:0% +that's pumped through this pipe and then +connected to that heat pump. And the + + align:start position:0% +connected to that heat pump. And the + + + align:start position:0% +connected to that heat pump. And the +reason why these systems are more + + align:start position:0% +reason why these systems are more + + + align:start position:0% +reason why these systems are more +efficient is because of this sign graph + + align:start position:0% +efficient is because of this sign graph + + + align:start position:0% +efficient is because of this sign graph +here. So the source temperatures going + + align:start position:0% +here. So the source temperatures going + + + align:start position:0% +here. So the source temperatures going +to that heat pump from the ground heat + + align:start position:0% +to that heat pump from the ground heat + + + align:start position:0% +to that heat pump from the ground heat +exchanger range between around 40 to 90 + + align:start position:0% +exchanger range between around 40 to 90 + + + align:start position:0% +exchanger range between around 40 to 90 +degrees Fahrenheit, sometimes as low as + + align:start position:0% +degrees Fahrenheit, sometimes as low as + + + align:start position:0% +degrees Fahrenheit, sometimes as low as +30. But this specific graph is collected + + align:start position:0% +30. But this specific graph is collected + + + align:start position:0% +30. But this specific graph is collected +from four years worth of data in a very + + align:start position:0% +from four years worth of data in a very + + + align:start position:0% +from four years worth of data in a very +cold climate in in Winnipeg, Manitoba. + + align:start position:0% +cold climate in in Winnipeg, Manitoba. + + + align:start position:0% +cold climate in in Winnipeg, Manitoba. +So during this same time period, the + + align:start position:0% +So during this same time period, the + + + align:start position:0% +So during this same time period, the +outdoor air temperature ranged from -20 + + align:start position:0% +outdoor air temperature ranged from -20 + + + align:start position:0% +outdoor air temperature ranged from -20 +to + 100° F. So you can imagine that + + align:start position:0% +to + 100° F. So you can imagine that + + + align:start position:0% +to + 100° F. So you can imagine that +getting your source temperatures from + + align:start position:0% +getting your source temperatures from + + + align:start position:0% +getting your source temperatures from +the that more extreme uh you know air + + align:start position:0% +the that more extreme uh you know air + + + align:start position:0% +the that more extreme uh you know air +compared to your ground heat exchanger + + align:start position:0% +compared to your ground heat exchanger + + + align:start position:0% +compared to your ground heat exchanger +temperatures makes the heat pump work + + align:start position:0% +temperatures makes the heat pump work + + + align:start position:0% +temperatures makes the heat pump work +harder. It has to work harder to deliver + + align:start position:0% +harder. It has to work harder to deliver + + + align:start position:0% +harder. It has to work harder to deliver +that same amount of heat. Um so heat + + align:start position:0% +that same amount of heat. Um so heat + + + align:start position:0% +that same amount of heat. Um so heat +pumps like to receive more moderate + + align:start position:0% +pumps like to receive more moderate + + + align:start position:0% +pumps like to receive more moderate +temperatures so they don't need to work + + align:start position:0% +temperatures so they don't need to work + + + align:start position:0% +temperatures so they don't need to work +as hard. And how a heat pump works is + + align:start position:0% +as hard. And how a heat pump works is + + + align:start position:0% +as hard. And how a heat pump works is +just like a fridge, right? It's it's the + + align:start position:0% +just like a fridge, right? It's it's the + + + align:start position:0% +just like a fridge, right? It's it's the +vapor compression cycle is what it's + + align:start position:0% +vapor compression cycle is what it's + + + align:start position:0% +vapor compression cycle is what it's +called. It's no different than a fridge + + align:start position:0% +called. It's no different than a fridge + + + align:start position:0% +called. It's no different than a fridge +other than a reversing valve. But the + + align:start position:0% +other than a reversing valve. But the + + + align:start position:0% +other than a reversing valve. But the +the process is you have an evaporator + + align:start position:0% +the process is you have an evaporator + + + align:start position:0% +the process is you have an evaporator +that transfers heat with your external + + align:start position:0% +that transfers heat with your external + + + align:start position:0% +that transfers heat with your external +environment, right? So your air, your + + align:start position:0% +environment, right? So your air, your + + + align:start position:0% +environment, right? So your air, your +ground or your water. You have a + + align:start position:0% +ground or your water. You have a + + + align:start position:0% +ground or your water. You have a +compressor which compresses the + + align:start position:0% +compressor which compresses the + + + align:start position:0% +compressor which compresses the +refrigerant and increasing the pressure + + align:start position:0% +refrigerant and increasing the pressure + + + align:start position:0% +refrigerant and increasing the pressure +and temperature. Chemistry 101. If you + + align:start position:0% +and temperature. Chemistry 101. If you + + + align:start position:0% +and temperature. Chemistry 101. If you +increase pressure, you increase the + + align:start position:0% +increase pressure, you increase the + + + align:start position:0% +increase pressure, you increase the +temperature. You have your condenser + + align:start position:0% +temperature. You have your condenser + + + align:start position:0% +temperature. You have your condenser +which condenses the refrigerant vapor + + align:start position:0% +which condenses the refrigerant vapor + + + align:start position:0% +which condenses the refrigerant vapor +into liquid and that phase change + + align:start position:0% +into liquid and that phase change + + + align:start position:0% +into liquid and that phase change +transfers large amount of heat and then + + align:start position:0% +transfers large amount of heat and then + + + align:start position:0% +transfers large amount of heat and then +your expansion valve to rinse and repeat + + align:start position:0% +your expansion valve to rinse and repeat + + + align:start position:0% +your expansion valve to rinse and repeat +reduce the pressure and temperature to + + align:start position:0% +reduce the pressure and temperature to + + + align:start position:0% +reduce the pressure and temperature to +prepare for the next cycle. So our our + + align:start position:0% +prepare for the next cycle. So our our + + + align:start position:0% +prepare for the next cycle. So our our +ground source heat pump in heating again + + align:start position:0% +ground source heat pump in heating again + + + align:start position:0% +ground source heat pump in heating again +we have this reversing valve which + + align:start position:0% +we have this reversing valve which + + + align:start position:0% +we have this reversing valve which +differentiates our fridge from our our + + align:start position:0% +differentiates our fridge from our our + + + align:start position:0% +differentiates our fridge from our our +heat pump. So we can also do heating be + + align:start position:0% +heat pump. So we can also do heating be + + + align:start position:0% +heat pump. So we can also do heating be +strange if a fridge did heating. Um but + + align:start position:0% +strange if a fridge did heating. Um but + + + align:start position:0% +strange if a fridge did heating. Um but +we extract heat from our ground loop + + align:start position:0% +we extract heat from our ground loop + + + align:start position:0% +we extract heat from our ground loop +where we have three units of heat coming + + align:start position:0% +where we have three units of heat coming + + + align:start position:0% +where we have three units of heat coming +from the ground. We have our compressor + + align:start position:0% +from the ground. We have our compressor + + + align:start position:0% +from the ground. We have our compressor +which uses electricity to compress and + + align:start position:0% +which uses electricity to compress and + + + align:start position:0% +which uses electricity to compress and +heat the refrigerant. That electrically + + align:start position:0% +heat the refrigerant. That electrically + + + align:start position:0% +heat the refrigerant. That electrically +powered equipment generates heat as + + align:start position:0% +powered equipment generates heat as + + + align:start position:0% +powered equipment generates heat as +well. Right? That's your power input. + + align:start position:0% +well. Right? That's your power input. + + + align:start position:0% +well. Right? That's your power input. +That that compressor. There's also the + + align:start position:0% +That that compressor. There's also the + + + align:start position:0% +That that compressor. There's also the +circulation pump and fans. And then you + + align:start position:0% +circulation pump and fans. And then you + + + align:start position:0% +circulation pump and fans. And then you +give those four units of heat to the + + align:start position:0% +give those four units of heat to the + + + align:start position:0% +give those four units of heat to the +building. Right? So that hot refrigerant + + align:start position:0% +building. Right? So that hot refrigerant + + + align:start position:0% +building. Right? So that hot refrigerant +is pushed through the condenser and then + + align:start position:0% +is pushed through the condenser and then + + + align:start position:0% +is pushed through the condenser and then +rejects that heat to the air in the + + align:start position:0% +rejects that heat to the air in the + + + align:start position:0% +rejects that heat to the air in the +building. And this is how you get your + + align:start position:0% +building. And this is how you get your + + + align:start position:0% +building. And this is how you get your +coefficient of performance. So you may + + align:start position:0% +coefficient of performance. So you may + + + align:start position:0% +coefficient of performance. So you may +have heard the word coop or or + + align:start position:0% +have heard the word coop or or + + + align:start position:0% +have heard the word coop or or +coefficient of performance. And this is + + align:start position:0% +coefficient of performance. And this is + + + align:start position:0% +coefficient of performance. And this is +how it works. You you transfer those + + align:start position:0% +how it works. You you transfer those + + + align:start position:0% +how it works. You you transfer those +four units of of energy which is + + align:start position:0% +four units of of energy which is + + + align:start position:0% +four units of of energy which is +combined thermal and electrical energy + + align:start position:0% +combined thermal and electrical energy + + + align:start position:0% +combined thermal and electrical energy +to the space by only using one by only + + align:start position:0% +to the space by only using one by only + + + align:start position:0% +to the space by only using one by only +paying for one unit of electrical energy + + align:start position:0% +paying for one unit of electrical energy + + + align:start position:0% +paying for one unit of electrical energy +to power that compressor circulation + + align:start position:0% +to power that compressor circulation + + + align:start position:0% +to power that compressor circulation +pump and fans. + + align:start position:0% +pump and fans. + + + align:start position:0% +pump and fans. +In cooling mode, we have our heat that's + + align:start position:0% +In cooling mode, we have our heat that's + + + align:start position:0% +In cooling mode, we have our heat that's +extracted from the air in the building + + align:start position:0% +extracted from the air in the building + + + align:start position:0% +extracted from the air in the building +vaporizing the refrigerant. So, those + + align:start position:0% +vaporizing the refrigerant. So, those + + + align:start position:0% +vaporizing the refrigerant. So, those +three units of heat from the building, + + align:start position:0% +three units of heat from the building, + + + align:start position:0% +three units of heat from the building, +we have our compressor again that + + align:start position:0% +we have our compressor again that + + + align:start position:0% +we have our compressor again that +compresses the heat uh compresses and + + align:start position:0% +compresses the heat uh compresses and + + + align:start position:0% +compresses the heat uh compresses and +heats the refrigerant. Our reversing + + align:start position:0% +heats the refrigerant. Our reversing + + + align:start position:0% +heats the refrigerant. Our reversing +valve is on, right? So, we flip that + + align:start position:0% +valve is on, right? So, we flip that + + + align:start position:0% +valve is on, right? So, we flip that +flow of refrigerant. So, it's going in + + align:start position:0% +flow of refrigerant. So, it's going in + + + align:start position:0% +flow of refrigerant. So, it's going in +reverse now. And then that hot + + align:start position:0% +reverse now. And then that hot + + + align:start position:0% +reverse now. And then that hot +refrigerant is pushed through the + + align:start position:0% +refrigerant is pushed through the + + + align:start position:0% +refrigerant is pushed through the +condenser and rejects heat to that + + align:start position:0% +condenser and rejects heat to that + + + align:start position:0% +condenser and rejects heat to that +ground heat exchanger. We need to get + + align:start position:0% +ground heat exchanger. We need to get + + + align:start position:0% +ground heat exchanger. We need to get +rid of that electrical energy. an + + align:start position:0% +rid of that electrical energy. an + + + align:start position:0% +rid of that electrical energy. an +electrical heat and the heat from the + + align:start position:0% +electrical heat and the heat from the + + + align:start position:0% +electrical heat and the heat from the +building and we put that in the ground + + align:start position:0% +building and we put that in the ground + + + align:start position:0% +building and we put that in the ground +loop. So what's the difference between + + align:start position:0% +loop. So what's the difference between + + + align:start position:0% +loop. So what's the difference between +earth energy resource engineering or or + + align:start position:0% +earth energy resource engineering or or + + + align:start position:0% +earth energy resource engineering or or +geothermal engineering and conventional + + align:start position:0% +geothermal engineering and conventional + + + align:start position:0% +geothermal engineering and conventional +HVAC systems? Well, the the main + + align:start position:0% +HVAC systems? Well, the the main + + + align:start position:0% +HVAC systems? Well, the the main +difference is that for ground source + + align:start position:0% +difference is that for ground source + + + align:start position:0% +difference is that for ground source +heat pump systems, you should be + + align:start position:0% +heat pump systems, you should be + + + align:start position:0% +heat pump systems, you should be +considering the total demand, right? the + + align:start position:0% +considering the total demand, right? the + + + align:start position:0% +considering the total demand, right? the +total demand of a building, not just a + + align:start position:0% +total demand of a building, not just a + + + align:start position:0% +total demand of a building, not just a +peak of the coldest day of the year or + + align:start position:0% +peak of the coldest day of the year or + + + align:start position:0% +peak of the coldest day of the year or +the warmest day of the year, but your + + align:start position:0% +the warmest day of the year, but your + + + align:start position:0% +the warmest day of the year, but your +total heating and cooling on an annual + + align:start position:0% +total heating and cooling on an annual + + + align:start position:0% +total heating and cooling on an annual +basis to determine your total supply + + align:start position:0% +basis to determine your total supply + + + align:start position:0% +basis to determine your total supply +because you're designing your source, + + align:start position:0% +because you're designing your source, + + + align:start position:0% +because you're designing your source, +right? And so in a conventional system, + + align:start position:0% +right? And so in a conventional system, + + + align:start position:0% +right? And so in a conventional system, +you have a pipeline that's large enough + + align:start position:0% +you have a pipeline that's large enough + + + align:start position:0% +you have a pipeline that's large enough +to meet the peak heating day, the + + align:start position:0% +to meet the peak heating day, the + + + align:start position:0% +to meet the peak heating day, the +coldest day of the year, right? You have + + align:start position:0% +coldest day of the year, right? You have + + + align:start position:0% +coldest day of the year, right? You have +your natural gas pipeline that's feeding + + align:start position:0% +your natural gas pipeline that's feeding + + + align:start position:0% +your natural gas pipeline that's feeding +that equipment. You have your water + + align:start position:0% +that equipment. You have your water + + + align:start position:0% +that equipment. You have your water +utility line that's feeding your cooling + + align:start position:0% +utility line that's feeding your cooling + + + align:start position:0% +utility line that's feeding your cooling +tower to dissipate heat on the warmest + + align:start position:0% +tower to dissipate heat on the warmest + + + align:start position:0% +tower to dissipate heat on the warmest +day of the year. And as long as you pay + + align:start position:0% +day of the year. And as long as you pay + + + align:start position:0% +day of the year. And as long as you pay +your energy bill, you should be okay. + + align:start position:0% +your energy bill, you should be okay. + + + align:start position:0% +your energy bill, you should be okay. +But for a ground source heat pumps + + align:start position:0% +But for a ground source heat pumps + + + align:start position:0% +But for a ground source heat pumps +scenario, we are also considered with + + align:start position:0% +scenario, we are also considered with + + + align:start position:0% +scenario, we are also considered with +our our total loads, right? Again, + + align:start position:0% +our our total loads, right? Again, + + + align:start position:0% +our our total loads, right? Again, +because we're designing our source. So + + align:start position:0% +because we're designing our source. So + + + align:start position:0% +because we're designing our source. So +this example illustrates this. So we + + align:start position:0% +this example illustrates this. So we + + + align:start position:0% +this example illustrates this. So we +have a church, a retail store, and an + + align:start position:0% +have a church, a retail store, and an + + + align:start position:0% +have a church, a retail store, and an +apartment building. They may have the + + align:start position:0% +apartment building. They may have the + + + align:start position:0% +apartment building. They may have the +exact same peak and and peak heating and + + align:start position:0% +exact same peak and and peak heating and + + + align:start position:0% +exact same peak and and peak heating and +cooling loads, 40 tons of cooling and + + align:start position:0% +cooling loads, 40 tons of cooling and + + + align:start position:0% +cooling loads, 40 tons of cooling and +385 MBH of heating, but due to the + + align:start position:0% +385 MBH of heating, but due to the + + + align:start position:0% +385 MBH of heating, but due to the +difference in occupancy of those three + + align:start position:0% +difference in occupancy of those three + + + align:start position:0% +difference in occupancy of those three +different buildings, the total heating + + align:start position:0% +different buildings, the total heating + + + align:start position:0% +different buildings, the total heating +and cooling loads are going to change + + align:start position:0% +and cooling loads are going to change + + + align:start position:0% +and cooling loads are going to change +quite dramatically, right? You think + + align:start position:0% +quite dramatically, right? You think + + + align:start position:0% +quite dramatically, right? You think +about that church probably highly + + align:start position:0% +about that church probably highly + + + align:start position:0% +about that church probably highly +occupied once or twice a week, right? + + align:start position:0% +occupied once or twice a week, right? + + + align:start position:0% +occupied once or twice a week, right? +You have a lot of people in the room + + align:start position:0% +You have a lot of people in the room + + + align:start position:0% +You have a lot of people in the room +like this space, you have a lot of + + align:start position:0% +like this space, you have a lot of + + + align:start position:0% +like this space, you have a lot of +lights on. those internal heat gains + + align:start position:0% +lights on. those internal heat gains + + + align:start position:0% +lights on. those internal heat gains +help uh heat the space and that's only + + align:start position:0% +help uh heat the space and that's only + + + align:start position:0% +help uh heat the space and that's only +available maybe once or twice a week. So + + align:start position:0% +available maybe once or twice a week. So + + + align:start position:0% +available maybe once or twice a week. So +your heating load over an annual um set + + align:start position:0% +your heating load over an annual um set + + + align:start position:0% +your heating load over an annual um set +of of data is probably going to be + + align:start position:0% +of of data is probably going to be + + + align:start position:0% +of of data is probably going to be +higher than than your cooling load. + + align:start position:0% +higher than than your cooling load. + + + align:start position:0% +higher than than your cooling load. +Whereas your retail store, you know, you + + align:start position:0% +Whereas your retail store, you know, you + + + align:start position:0% +Whereas your retail store, you know, you +could think of maybe an IKEA, you have a + + align:start position:0% +could think of maybe an IKEA, you have a + + + align:start position:0% +could think of maybe an IKEA, you have a +lot of internal heat gains, a lot of + + align:start position:0% +lot of internal heat gains, a lot of + + + align:start position:0% +lot of internal heat gains, a lot of +people, a lot of lights, a lot of um + + align:start position:0% +people, a lot of lights, a lot of um + + + align:start position:0% +people, a lot of lights, a lot of um +internal heat gains that you need to get + + align:start position:0% +internal heat gains that you need to get + + + align:start position:0% +internal heat gains that you need to get +rid of. So you put those in the ground, + + align:start position:0% +rid of. So you put those in the ground, + + + align:start position:0% +rid of. So you put those in the ground, +right? you need to reject that heat and + + align:start position:0% +right? you need to reject that heat and + + + align:start position:0% +right? you need to reject that heat and +the apartment building probably + + align:start position:0% +the apartment building probably + + + align:start position:0% +the apartment building probably +relatively balanced between heating and + + align:start position:0% +relatively balanced between heating and + + + align:start position:0% +relatively balanced between heating and +cooling. So the heating and cooling load + + align:start position:0% +cooling. So the heating and cooling load + + + align:start position:0% +cooling. So the heating and cooling load +ratio can change even if the peak + + align:start position:0% +ratio can change even if the peak + + + align:start position:0% +ratio can change even if the peak +heating and cooling loads are the exact + + align:start position:0% +heating and cooling loads are the exact + + + align:start position:0% +heating and cooling loads are the exact +same. And how this affects the ground + + align:start position:0% +same. And how this affects the ground + + + align:start position:0% +same. And how this affects the ground +loop and why it's important is because + + align:start position:0% +loop and why it's important is because + + + align:start position:0% +loop and why it's important is because +and this is especially true for a + + align:start position:0% +and this is especially true for a + + + align:start position:0% +and this is especially true for a +vertical ground heat exchanger scenario + + align:start position:0% +vertical ground heat exchanger scenario + + + align:start position:0% +vertical ground heat exchanger scenario +with a lot of conduction, right? you + + align:start position:0% +with a lot of conduction, right? you + + + align:start position:0% +with a lot of conduction, right? you +have a fixed volume of earth that you're + + align:start position:0% +have a fixed volume of earth that you're + + + align:start position:0% +have a fixed volume of earth that you're +exchanging heat with and so it it's more + + align:start position:0% +exchanging heat with and so it it's more + + + align:start position:0% +exchanging heat with and so it it's more +similar to a battery in in that case + + align:start position:0% +similar to a battery in in that case + + + align:start position:0% +similar to a battery in in that case +compared to a conventional system there + + align:start position:0% +compared to a conventional system there + + + align:start position:0% +compared to a conventional system there +there are nuances right and there are + + align:start position:0% +there are nuances right and there are + + + align:start position:0% +there are nuances right and there are +you know each project is unique um but + + align:start position:0% +you know each project is unique um but + + + align:start position:0% +you know each project is unique um but +even in openloop systems for example + + align:start position:0% +even in openloop systems for example + + + align:start position:0% +even in openloop systems for example +where you're tapping into an aquifer and + + align:start position:0% +where you're tapping into an aquifer and + + + align:start position:0% +where you're tapping into an aquifer and +pulling heat and rejecting heat to an + + align:start position:0% +pulling heat and rejecting heat to an + + + align:start position:0% +pulling heat and rejecting heat to an +aquifer we've seen we've been measuring + + align:start position:0% +aquifer we've seen we've been measuring + + + align:start position:0% +aquifer we've seen we've been measuring +a system in Winnipeg over the past uh 5 + + align:start position:0% +a system in Winnipeg over the past uh 5 + + + align:start position:0% +a system in Winnipeg over the past uh 5 +years or so and they've increased the + + align:start position:0% +years or so and they've increased the + + + align:start position:0% +years or so and they've increased the +temperature of that aquifer by 5 to 8° F + + align:start position:0% +temperature of that aquifer by 5 to 8° F + + + align:start position:0% +temperature of that aquifer by 5 to 8° F +um just because they're rejecting so + + align:start position:0% +um just because they're rejecting so + + + align:start position:0% +um just because they're rejecting so +much heat into that aquifer. So what can + + align:start position:0% +much heat into that aquifer. So what can + + + align:start position:0% +much heat into that aquifer. So what can +happen is this curve here, this + + align:start position:0% +happen is this curve here, this + + + align:start position:0% +happen is this curve here, this +temperature drift where you may fall + + align:start position:0% +temperature drift where you may fall + + + align:start position:0% +temperature drift where you may fall +outside of those efficient operating + + align:start position:0% +outside of those efficient operating + + + align:start position:0% +outside of those efficient operating +parameters. When we talked about that + + align:start position:0% +parameters. When we talked about that + + + align:start position:0% +parameters. When we talked about that +ground source heat pump, it likes to be + + align:start position:0% +ground source heat pump, it likes to be + + + align:start position:0% +ground source heat pump, it likes to be +fed 30 to 90° Fahrenheit water, right? + + align:start position:0% +fed 30 to 90° Fahrenheit water, right? + + + align:start position:0% +fed 30 to 90° Fahrenheit water, right? +But what can happen is you can fall + + align:start position:0% +But what can happen is you can fall + + + align:start position:0% +But what can happen is you can fall +outside of those efficient operating + + align:start position:0% +outside of those efficient operating + + + align:start position:0% +outside of those efficient operating +ranges if you're not considering your + + align:start position:0% +ranges if you're not considering your + + + align:start position:0% +ranges if you're not considering your +total loads. if you're only looking at + + align:start position:0% +total loads. if you're only looking at + + + align:start position:0% +total loads. if you're only looking at +your peak loads. So, it's important to + + align:start position:0% +your peak loads. So, it's important to + + + align:start position:0% +your peak loads. So, it's important to +not only design again off of your your + + align:start position:0% +not only design again off of your your + + + align:start position:0% +not only design again off of your your +peak loads, which are certainly + + align:start position:0% +peak loads, which are certainly + + + align:start position:0% +peak loads, which are certainly +important, but your total loads are are + + align:start position:0% +important, but your total loads are are + + + align:start position:0% +important, but your total loads are are +also important to determine your your + + align:start position:0% +also important to determine your your + + + align:start position:0% +also important to determine your your +total demand to design your supply. + + align:start position:0% +total demand to design your supply. + + + align:start position:0% +total demand to design your supply. +So, when you have a customer or anyone + + align:start position:0% +So, when you have a customer or anyone + + + align:start position:0% +So, when you have a customer or anyone +frankly who's interested in a geothermal + + align:start position:0% +frankly who's interested in a geothermal + + + align:start position:0% +frankly who's interested in a geothermal +system, where do you start? If they say, + + align:start position:0% +system, where do you start? If they say, + + + align:start position:0% +system, where do you start? If they say, +"Hey, you know, Connor, I want I've + + align:start position:0% +"Hey, you know, Connor, I want I've + + + align:start position:0% +"Hey, you know, Connor, I want I've +heard of this geothermal technology. + + align:start position:0% +heard of this geothermal technology. + + + align:start position:0% +heard of this geothermal technology. +I've heard is pretty cool. Um, what do I + + align:start position:0% +I've heard is pretty cool. Um, what do I + + + align:start position:0% +I've heard is pretty cool. Um, what do I +do? Well, you'd probably want to start + + align:start position:0% +do? Well, you'd probably want to start + + + align:start position:0% +do? Well, you'd probably want to start +with the building, right? Again, + + align:start position:0% +with the building, right? Again, + + + align:start position:0% +with the building, right? Again, +determine your total demand to determine + + align:start position:0% +determine your total demand to determine + + + align:start position:0% +determine your total demand to determine +your supply. And then you can start + + align:start position:0% +your supply. And then you can start + + + align:start position:0% +your supply. And then you can start +looking at your mechanical system, your + + align:start position:0% +looking at your mechanical system, your + + + align:start position:0% +looking at your mechanical system, your +geothermal mechanical system, and your + + align:start position:0% +geothermal mechanical system, and your + + + align:start position:0% +geothermal mechanical system, and your +site and geology. The site and geology + + align:start position:0% +site and geology. The site and geology + + + align:start position:0% +site and geology. The site and geology +is going to dictate what type of ground + + align:start position:0% +is going to dictate what type of ground + + + align:start position:0% +is going to dictate what type of ground +heat exchanger you go with. There's many + + align:start position:0% +heat exchanger you go with. There's many + + + align:start position:0% +heat exchanger you go with. There's many +different ways to exchange heat with + + align:start position:0% +different ways to exchange heat with + + + align:start position:0% +different ways to exchange heat with +your external environment. Again, all + + align:start position:0% +your external environment. Again, all + + + align:start position:0% +your external environment. Again, all +you're doing is obtaining moderate + + align:start position:0% +you're doing is obtaining moderate + + + align:start position:0% +you're doing is obtaining moderate +temperatures so that your heat pump + + align:start position:0% +temperatures so that your heat pump + + + align:start position:0% +temperatures so that your heat pump +doesn't need to work as hard. So that + + align:start position:0% +doesn't need to work as hard. So that + + + align:start position:0% +doesn't need to work as hard. So that +could come from the air. You know, in + + align:start position:0% +could come from the air. You know, in + + + align:start position:0% +could come from the air. You know, in +Seattle, it's pretty moderate there. So + + align:start position:0% +Seattle, it's pretty moderate there. So + + + align:start position:0% +Seattle, it's pretty moderate there. So +air source works fine. Um, but in + + align:start position:0% +air source works fine. Um, but in + + + align:start position:0% +air source works fine. Um, but in +Winnipeg, in a cold climate like that, + + align:start position:0% +Winnipeg, in a cold climate like that, + + + align:start position:0% +Winnipeg, in a cold climate like that, +not so much. So you could have a + + align:start position:0% +not so much. So you could have a + + + align:start position:0% +not so much. So you could have a +vertical ground heat exchanger, + + align:start position:0% +vertical ground heat exchanger, + + + align:start position:0% +vertical ground heat exchanger, +horizontal surface water, aquafer. I'm + + align:start position:0% +horizontal surface water, aquafer. I'm + + + align:start position:0% +horizontal surface water, aquafer. I'm +staying at Susan Murkott's house right + + align:start position:0% +staying at Susan Murkott's house right + + + align:start position:0% +staying at Susan Murkott's house right +now, and she's a professor here at MIT, + + align:start position:0% +now, and she's a professor here at MIT, + + + align:start position:0% +now, and she's a professor here at MIT, +and she is a standing column, and that + + align:start position:0% +and she is a standing column, and that + + + align:start position:0% +and she is a standing column, and that +was pretty interesting to see. So there + + align:start position:0% +was pretty interesting to see. So there + + + align:start position:0% +was pretty interesting to see. So there +there's many different ways to give your + + align:start position:0% +there's many different ways to give your + + + align:start position:0% +there's many different ways to give your +heat pump source temperatures that are + + align:start position:0% +heat pump source temperatures that are + + + align:start position:0% +heat pump source temperatures that are +moderate. Um, but at the end of the day, + + align:start position:0% +moderate. Um, but at the end of the day, + + + align:start position:0% +moderate. Um, but at the end of the day, +what matters? Well, what matters is + + align:start position:0% +what matters? Well, what matters is + + + align:start position:0% +what matters? Well, what matters is +we're trying to save on energy, right? + + align:start position:0% +we're trying to save on energy, right? + + + align:start position:0% +we're trying to save on energy, right? +That's why we install these systems. But + + align:start position:0% +That's why we install these systems. But + + + align:start position:0% +That's why we install these systems. But +if it's going to cost you an arm and a + + align:start position:0% +if it's going to cost you an arm and a + + + align:start position:0% +if it's going to cost you an arm and a +leg to do that, it's probably not going + + align:start position:0% +leg to do that, it's probably not going + + + align:start position:0% +leg to do that, it's probably not going +to make a whole lot of sense. So, to + + align:start position:0% +to make a whole lot of sense. So, to + + + align:start position:0% +to make a whole lot of sense. So, to +balance the energy cost with the + + align:start position:0% +balance the energy cost with the + + + align:start position:0% +balance the energy cost with the +construction cost is the most important + + align:start position:0% +construction cost is the most important + + + align:start position:0% +construction cost is the most important +thing to make sure that it's practical, + + align:start position:0% +thing to make sure that it's practical, + + + align:start position:0% +thing to make sure that it's practical, +right? Because if if it's too expensive, + + align:start position:0% +right? Because if if it's too expensive, + + + align:start position:0% +right? Because if if it's too expensive, +nobody's going to buy it um at the end + + align:start position:0% +nobody's going to buy it um at the end + + + align:start position:0% +nobody's going to buy it um at the end +of the day. Um, and there are + + align:start position:0% +of the day. Um, and there are + + + align:start position:0% +of the day. Um, and there are +intangibles. You know, a lot of people + + align:start position:0% +intangibles. You know, a lot of people + + + align:start position:0% +intangibles. You know, a lot of people +value carbon in different ways. In + + align:start position:0% +value carbon in different ways. In + + + align:start position:0% +value carbon in different ways. In +Canada, we have a carbon tax. Um, so + + align:start position:0% +Canada, we have a carbon tax. Um, so + + + align:start position:0% +Canada, we have a carbon tax. Um, so +that's that's quantified. Um, but the + + align:start position:0% +that's that's quantified. Um, but the + + + align:start position:0% +that's that's quantified. Um, but the +main thing to consider when you're when + + align:start position:0% +main thing to consider when you're when + + + align:start position:0% +main thing to consider when you're when +you're looking at a geothermal system, + + align:start position:0% +you're looking at a geothermal system, + + + align:start position:0% +you're looking at a geothermal system, +in my opinion, is to balance these two + + align:start position:0% +in my opinion, is to balance these two + + + align:start position:0% +in my opinion, is to balance these two +things, construction cost, and then the + + align:start position:0% +things, construction cost, and then the + + + align:start position:0% +things, construction cost, and then the +energy savings that you're getting from + + align:start position:0% +energy savings that you're getting from + + + align:start position:0% +energy savings that you're getting from +that investment because you're buying an + + align:start position:0% +that investment because you're buying an + + + align:start position:0% +that investment because you're buying an +asset, which is that that ground heat + + align:start position:0% +asset, which is that that ground heat + + + align:start position:0% +asset, which is that that ground heat +exchanger. + + align:start position:0% +exchanger. + + + align:start position:0% +exchanger. +So, before I pass it to my colleague + + align:start position:0% +So, before I pass it to my colleague + + + align:start position:0% +So, before I pass it to my colleague +Nick, I thought I'd throw in a little + + align:start position:0% +Nick, I thought I'd throw in a little + + + align:start position:0% +Nick, I thought I'd throw in a little +segue slide here. I believe one person + + align:start position:0% +segue slide here. I believe one person + + + align:start position:0% +segue slide here. I believe one person +had a similar slide yesterday where it + + align:start position:0% +had a similar slide yesterday where it + + + align:start position:0% +had a similar slide yesterday where it +looks at the temperature in the + + align:start position:0% +looks at the temperature in the + + + align:start position:0% +looks at the temperature in the +distribution piping of district systems + + align:start position:0% +distribution piping of district systems + + + align:start position:0% +distribution piping of district systems +and over time we used to use really high + + align:start position:0% +and over time we used to use really high + + + align:start position:0% +and over time we used to use really high +temperature right I mean we still do + + align:start position:0% +temperature right I mean we still do + + + align:start position:0% +temperature right I mean we still do +today pressurized steam but that leads + + align:start position:0% +today pressurized steam but that leads + + + align:start position:0% +today pressurized steam but that leads +to low efficiency and so over time we've + + align:start position:0% +to low efficiency and so over time we've + + + align:start position:0% +to low efficiency and so over time we've +been able to reduce our temperature in + + align:start position:0% +been able to reduce our temperature in + + + align:start position:0% +been able to reduce our temperature in +our distribution piping which has led to + + align:start position:0% +our distribution piping which has led to + + + align:start position:0% +our distribution piping which has led to +an increase in efficiency so now we're + + align:start position:0% +an increase in efficiency so now we're + + + align:start position:0% +an increase in efficiency so now we're +dealing with ambient temperatures which + + align:start position:0% +dealing with ambient temperatures which + + + align:start position:0% +dealing with ambient temperatures which +has increased our efficiency in these + + align:start position:0% +has increased our efficiency in these + + + align:start position:0% +has increased our efficiency in these +district energy systems quite + + align:start position:0% +district energy systems quite + + + align:start position:0% +district energy systems quite +dramatically. So, thank you folks for + + align:start position:0% +dramatically. So, thank you folks for + + + align:start position:0% +dramatically. So, thank you folks for +listening and I'll now pass it to Nick. \ No newline at end of file diff --git a/jtSfWlQbmNY.txt b/jtSfWlQbmNY.txt new file mode 100644 index 0000000000000000000000000000000000000000..af7ec9d41bfd7e42a7d967d68721c37df3c1bdd2 --- /dev/null +++ b/jtSfWlQbmNY.txt @@ -0,0 +1,1435 @@ +align:start position:0% + +welcome back to 8701 so we continue our + + align:start position:0% +welcome back to 8701 so we continue our + + + align:start position:0% +welcome back to 8701 so we continue our +discussion on the + + align:start position:0% +discussion on the + + + align:start position:0% +discussion on the +feynman calculus and continue now + + align:start position:0% +feynman calculus and continue now + + + align:start position:0% +feynman calculus and continue now +talking about fermi's golden rule + + align:start position:0% +talking about fermi's golden rule + + + align:start position:0% +talking about fermi's golden rule +the heart of calculating decay weight + + align:start position:0% +the heart of calculating decay weight + + + align:start position:0% +the heart of calculating decay weight +and cross-section + + align:start position:0% +and cross-section + + + align:start position:0% +and cross-section +is from his golden rule and it simply + + align:start position:0% +is from his golden rule and it simply + + + align:start position:0% +is from his golden rule and it simply +tells you how we can use the calculation + + align:start position:0% +tells you how we can use the calculation + + + align:start position:0% +tells you how we can use the calculation +of amplitudes and the available phase + + align:start position:0% +of amplitudes and the available phase + + + align:start position:0% +of amplitudes and the available phase +space + + align:start position:0% +space + + + align:start position:0% +space +to make um assessment of rates decay + + align:start position:0% +to make um assessment of rates decay + + + align:start position:0% +to make um assessment of rates decay +rates and cross sections + + align:start position:0% +rates and cross sections + + + align:start position:0% +rates and cross sections +so the amplitude m uh holds all the + + align:start position:0% +so the amplitude m uh holds all the + + + align:start position:0% +so the amplitude m uh holds all the +dynamic + + align:start position:0% +dynamic + + + align:start position:0% +dynamic +information and we can we'll see that we + + align:start position:0% +information and we can we'll see that we + + + align:start position:0% +information and we can we'll see that we +can calculate + + align:start position:0% +can calculate + + + align:start position:0% +can calculate +um the amplitude by evaluating final + + align:start position:0% +um the amplitude by evaluating final + + + align:start position:0% +um the amplitude by evaluating final +diagrams directly using + + align:start position:0% +diagrams directly using + + + align:start position:0% +diagrams directly using +5 min rules the available phase space + + align:start position:0% +5 min rules the available phase space + + + align:start position:0% +5 min rules the available phase space +holds is a kinematic factor and it + + align:start position:0% +holds is a kinematic factor and it + + + align:start position:0% +holds is a kinematic factor and it +depends on masses + + align:start position:0% +depends on masses + + + align:start position:0% +depends on masses +on the energies and the momentum of the + + align:start position:0% +on the energies and the momentum of the + + + align:start position:0% +on the energies and the momentum of the +particle involved and then again + + align:start position:0% +particle involved and then again + + + align:start position:0% +particle involved and then again +thermos golden rule simply says that the + + align:start position:0% +thermos golden rule simply says that the + + + align:start position:0% +thermos golden rule simply says that the +transition + + align:start position:0% +transition + + + align:start position:0% +transition +rates or decay weights and cross + + align:start position:0% +rates or decay weights and cross + + + align:start position:0% +rates or decay weights and cross +sections are given by the product of the + + align:start position:0% +sections are given by the product of the + + + align:start position:0% +sections are given by the product of the +phase space + + align:start position:0% +phase space + + + align:start position:0% +phase space +and the square of the amplitude now this + + align:start position:0% +and the square of the amplitude now this + + + align:start position:0% +and the square of the amplitude now this +how does this now look like if we look + + align:start position:0% +how does this now look like if we look + + + align:start position:0% +how does this now look like if we look +at the golden rule for the case + + align:start position:0% +at the golden rule for the case + + + align:start position:0% +at the golden rule for the case +here we suppose having one particle + + align:start position:0% +here we suppose having one particle + + + align:start position:0% +here we suppose having one particle +decaying into + + align:start position:0% +decaying into + + + align:start position:0% +decaying into +a second third fourth nth particle you + + align:start position:0% +a second third fourth nth particle you + + + align:start position:0% +a second third fourth nth particle you +see that the + + align:start position:0% +see that the + + + align:start position:0% +see that the +decay rate is given by + + align:start position:0% + + + + align:start position:0% + +the matrix element the amplitude squared + + align:start position:0% +the matrix element the amplitude squared + + + align:start position:0% +the matrix element the amplitude squared +and the term which is the um + + align:start position:0% +and the term which is the um + + + align:start position:0% +and the term which is the um +the phase base factor there's also a + + align:start position:0% +the phase base factor there's also a + + + align:start position:0% +the phase base factor there's also a +factor here in front + + align:start position:0% +factor here in front + + + align:start position:0% +factor here in front +this s has to account we have to account + + align:start position:0% +this s has to account we have to account + + + align:start position:0% +this s has to account we have to account +for the fact that we might have + + align:start position:0% +for the fact that we might have + + + align:start position:0% +for the fact that we might have +the same particle in the final state or + + align:start position:0% +the same particle in the final state or + + + align:start position:0% +the same particle in the final state or +multiple the same particle current + + align:start position:0% +multiple the same particle current + + + align:start position:0% +multiple the same particle current +multiple times + + align:start position:0% +multiple times + + + align:start position:0% +multiple times +and we have to make sure that we don't + + align:start position:0% +and we have to make sure that we don't + + + align:start position:0% +and we have to make sure that we don't +have double counting and this double + + align:start position:0% +have double counting and this double + + + align:start position:0% +have double counting and this double +counting has to be corrected + + align:start position:0% +counting has to be corrected + + + align:start position:0% +counting has to be corrected +if all particles are different this + + align:start position:0% +if all particles are different this + + + align:start position:0% +if all particles are different this +extra factor is + + align:start position:0% +extra factor is + + + align:start position:0% +extra factor is +is one we'll look at this some more + + align:start position:0% +is one we'll look at this some more + + + align:start position:0% +is one we'll look at this some more +later + + align:start position:0% +later + + + align:start position:0% +later +now at first glance this looks like + + align:start position:0% +now at first glance this looks like + + + align:start position:0% +now at first glance this looks like +rather complicated but if you try to + + align:start position:0% +rather complicated but if you try to + + + align:start position:0% +rather complicated but if you try to +assess now + + align:start position:0% +assess now + + + align:start position:0% +assess now +what those individual terms mean you'll + + align:start position:0% +what those individual terms mean you'll + + + align:start position:0% +what those individual terms mean you'll +see that it's very accessible so + + align:start position:0% +see that it's very accessible so + + + align:start position:0% +see that it's very accessible so +when we try to calculate or use + + align:start position:0% +when we try to calculate or use + + + align:start position:0% +when we try to calculate or use +from this golden rule for the case we + + align:start position:0% +from this golden rule for the case we + + + align:start position:0% +from this golden rule for the case we +have to + + align:start position:0% +have to + + + align:start position:0% +have to +integrate over all outgoing particle for + + align:start position:0% +integrate over all outgoing particle for + + + align:start position:0% +integrate over all outgoing particle for +momenta + + align:start position:0% +momenta + + + align:start position:0% +momenta +but we have three kinematical + + align:start position:0% +but we have three kinematical + + + align:start position:0% +but we have three kinematical +constraints + + align:start position:0% +constraints + + + align:start position:0% +constraints +the first one is that the outgoing + + align:start position:0% +the first one is that the outgoing + + + align:start position:0% +the first one is that the outgoing +particles + + align:start position:0% +particles + + + align:start position:0% +particles +have to be unmasked so they have to be + + align:start position:0% +have to be unmasked so they have to be + + + align:start position:0% +have to be unmasked so they have to be +on mars shell + + align:start position:0% +on mars shell + + + align:start position:0% +on mars shell +we talked about this this issue of + + align:start position:0% +we talked about this this issue of + + + align:start position:0% +we talked about this this issue of +virtual + + align:start position:0% +virtual + + + align:start position:0% +virtual +visual or particle and mass shell before + + align:start position:0% +visual or particle and mass shell before + + + align:start position:0% +visual or particle and mass shell before +but simply they have to + + align:start position:0% +but simply they have to + + + align:start position:0% +but simply they have to +the energy of the particle has to follow + + align:start position:0% +the energy of the particle has to follow + + + align:start position:0% +the energy of the particle has to follow +this condition + + align:start position:0% +this condition + + + align:start position:0% +this condition +this is a delta function which simply + + align:start position:0% +this is a delta function which simply + + + align:start position:0% +this is a delta function which simply +means that this + + align:start position:0% +means that this + + + align:start position:0% +means that this +you know this gives us if the argument + + align:start position:0% +you know this gives us if the argument + + + align:start position:0% +you know this gives us if the argument +is is zero + + align:start position:0% +is is zero + + + align:start position:0% +is is zero +the delta function returns one the + + align:start position:0% +the delta function returns one the + + + align:start position:0% +the delta function returns one the +argument is nonzero + + align:start position:0% +argument is nonzero + + + align:start position:0% +argument is nonzero +then the function returns zero so this + + align:start position:0% +then the function returns zero so this + + + align:start position:0% +then the function returns zero so this +rather simplifies + + align:start position:0% +rather simplifies + + + align:start position:0% +rather simplifies +uh this term here so this first part + + align:start position:0% +uh this term here so this first part + + + align:start position:0% +uh this term here so this first part +here + + align:start position:0% +here + + + align:start position:0% +here +um in in our in our premise golden rule + + align:start position:0% +um in in our in our premise golden rule + + + align:start position:0% +um in in our in our premise golden rule +simply accounts for the fact that + + align:start position:0% +simply accounts for the fact that + + + align:start position:0% +simply accounts for the fact that +outgoing particles have to be + + align:start position:0% +outgoing particles have to be + + + align:start position:0% +outgoing particles have to be +on mass shell um outgoing particles also + + align:start position:0% +on mass shell um outgoing particles also + + + align:start position:0% +on mass shell um outgoing particles also +have to have positive + + align:start position:0% +have to have positive + + + align:start position:0% +have to have positive +energies and this explains our second + + align:start position:0% +energies and this explains our second + + + align:start position:0% +energies and this explains our second +factor here this factor and so this + + align:start position:0% +factor here this factor and so this + + + align:start position:0% +factor here this factor and so this +vector + + align:start position:0% +vector + + + align:start position:0% +vector +um is the heavy side function and this + + align:start position:0% +um is the heavy side function and this + + + align:start position:0% +um is the heavy side function and this +is simply + + align:start position:0% +is simply + + + align:start position:0% +is simply +zero for negative values and one for + + align:start position:0% +zero for negative values and one for + + + align:start position:0% +zero for negative values and one for +positive values + + align:start position:0% +positive values + + + align:start position:0% +positive values +and the last one means that energy and + + align:start position:0% +and the last one means that energy and + + + align:start position:0% +and the last one means that energy and +momentum of the particle have to + + align:start position:0% +momentum of the particle have to + + + align:start position:0% +momentum of the particle have to +conserve so the first particle + + align:start position:0% +conserve so the first particle + + + align:start position:0% +conserve so the first particle +minus the second third and so on for + + align:start position:0% +minus the second third and so on for + + + align:start position:0% +minus the second third and so on for +each of the component + + align:start position:0% +each of the component + + + align:start position:0% +each of the component +for the for energy and for the three + + align:start position:0% +for the for energy and for the three + + + align:start position:0% +for the for energy and for the three +components of the + + align:start position:0% +components of the + + + align:start position:0% +components of the +of the momentum have to be um zero for + + align:start position:0% +of the momentum have to be um zero for + + + align:start position:0% +of the momentum have to be um zero for +this to return one + + align:start position:0% +this to return one + + + align:start position:0% +this to return one +so again another delta function there's + + align:start position:0% +so again another delta function there's + + + align:start position:0% +so again another delta function there's +also vectors of pi + + align:start position:0% +also vectors of pi + + + align:start position:0% +also vectors of pi +and the simple rule here is for each + + align:start position:0% +and the simple rule here is for each + + + align:start position:0% +and the simple rule here is for each +delta function you have to account for a + + align:start position:0% +delta function you have to account for a + + + align:start position:0% +delta function you have to account for a +vector of two pi + + align:start position:0% +vector of two pi + + + align:start position:0% +vector of two pi +in your function so this basically + + align:start position:0% +in your function so this basically + + + align:start position:0% +in your function so this basically +explains already + + align:start position:0% +explains already + + + align:start position:0% +explains already +everything we see here on the slide + + align:start position:0% +everything we see here on the slide + + + align:start position:0% +everything we see here on the slide +so now we can calculate and i recommend + + align:start position:0% +so now we can calculate and i recommend + + + align:start position:0% +so now we can calculate and i recommend +to have a look at griffith chapter 6 for + + align:start position:0% +to have a look at griffith chapter 6 for + + + align:start position:0% +to have a look at griffith chapter 6 for +this + + align:start position:0% +this + + + align:start position:0% +this +if you look at two particle decays so + + align:start position:0% +if you look at two particle decays so + + + align:start position:0% +if you look at two particle decays so +one particle + + align:start position:0% +one particle + + + align:start position:0% +one particle +into two particles this simplifies quite + + align:start position:0% +into two particles this simplifies quite + + + align:start position:0% +into two particles this simplifies quite +tremendously + + align:start position:0% +tremendously + + + align:start position:0% +tremendously +because of all the delta functions here + + align:start position:0% +because of all the delta functions here + + + align:start position:0% +because of all the delta functions here +and the heavy side functions this + + align:start position:0% +and the heavy side functions this + + + align:start position:0% +and the heavy side functions this +equation + + align:start position:0% +equation + + + align:start position:0% +equation +simplifies directly to a factor + + align:start position:0% +simplifies directly to a factor + + + align:start position:0% +simplifies directly to a factor +you have the momentum of the particle + + align:start position:0% +you have the momentum of the particle + + + align:start position:0% +you have the momentum of the particle +here and a matrix element + + align:start position:0% +here and a matrix element + + + align:start position:0% +here and a matrix element +again you have this statistical factor + + align:start position:0% +again you have this statistical factor + + + align:start position:0% +again you have this statistical factor +here to account for the fact that + + align:start position:0% +here to account for the fact that + + + align:start position:0% +here to account for the fact that +there might be duplicates and then you + + align:start position:0% +there might be duplicates and then you + + + align:start position:0% +there might be duplicates and then you +know you want to keep + + align:start position:0% +know you want to keep + + + align:start position:0% +know you want to keep +the track of the statistical factor + + align:start position:0% +the track of the statistical factor + + + align:start position:0% +the track of the statistical factor +um for scattering the equation looks + + align:start position:0% +um for scattering the equation looks + + + align:start position:0% +um for scattering the equation looks +almost the same so you have the same + + align:start position:0% +almost the same so you have the same + + + align:start position:0% +almost the same so you have the same +um the same phase base factor almost the + + align:start position:0% +um the same phase base factor almost the + + + align:start position:0% +um the same phase base factor almost the +same face back + + align:start position:0% +same face back + + + align:start position:0% +same face back +factor matrix element again this is the + + align:start position:0% +factor matrix element again this is the + + + align:start position:0% +factor matrix element again this is the +transition rate is given by + + align:start position:0% +transition rate is given by + + + align:start position:0% +transition rate is given by +as thermic golden rules tells us by the + + align:start position:0% +as thermic golden rules tells us by the + + + align:start position:0% +as thermic golden rules tells us by the +matrix element squared + + align:start position:0% + + + + align:start position:0% + +and the phase based vector this overall + + align:start position:0% +and the phase based vector this overall + + + align:start position:0% +and the phase based vector this overall +factors we'll look at later + + align:start position:0% +factors we'll look at later + + + align:start position:0% +factors we'll look at later +um they're slightly different um but + + align:start position:0% +um they're slightly different um but + + + align:start position:0% +um they're slightly different um but +here as a rule we just want to you know + + align:start position:0% +here as a rule we just want to you know + + + align:start position:0% +here as a rule we just want to you know +make sure that we + + align:start position:0% +make sure that we + + + align:start position:0% +make sure that we +we have a way to access ss cross + + align:start position:0% +we have a way to access ss cross + + + align:start position:0% +we have a way to access ss cross +sections that this makes sense + + align:start position:0% +sections that this makes sense + + + align:start position:0% +sections that this makes sense +we'll see later in more detail + + align:start position:0% + + + + align:start position:0% + +for two body decays in the center of + + align:start position:0% +for two body decays in the center of + + + align:start position:0% +for two body decays in the center of +mass frame + + align:start position:0% +mass frame + + + align:start position:0% +mass frame +you know that the initial momentum in + + align:start position:0% +you know that the initial momentum in + + + align:start position:0% +you know that the initial momentum in +the center of mass frames + + align:start position:0% +the center of mass frames + + + align:start position:0% +the center of mass frames +of particle one and particles to have to + + align:start position:0% +of particle one and particles to have to + + + align:start position:0% +of particle one and particles to have to +be the same + + align:start position:0% +be the same + + + align:start position:0% +be the same +the outgoing momenta also have to be the + + align:start position:0% +the outgoing momenta also have to be the + + + align:start position:0% +the outgoing momenta also have to be the +same they don't necessarily have to be + + align:start position:0% +same they don't necessarily have to be + + + align:start position:0% +same they don't necessarily have to be +the same as the in-game method + + align:start position:0% +the same as the in-game method + + + align:start position:0% +the same as the in-game method +but when you use this uh the + + align:start position:0% +but when you use this uh the + + + align:start position:0% +but when you use this uh the +differential cross-section then + + align:start position:0% +differential cross-section then + + + align:start position:0% +differential cross-section then +can be calculated um quite + + align:start position:0% +can be calculated um quite + + + align:start position:0% +can be calculated um quite +quite straightforwardly again with the + + align:start position:0% +quite straightforwardly again with the + + + align:start position:0% +quite straightforwardly again with the +matrix element squared + + align:start position:0% +matrix element squared + + + align:start position:0% +matrix element squared +we have the final state momentum the + + align:start position:0% +we have the final state momentum the + + + align:start position:0% +we have the final state momentum the +initial state momenta + + align:start position:0% +initial state momenta + + + align:start position:0% +initial state momenta +and divide this by the sum of the energy + + align:start position:0% +and divide this by the sum of the energy + + + align:start position:0% +and divide this by the sum of the energy +squared + + align:start position:0% +squared + + + align:start position:0% +squared +together with a as an extra factor here + + align:start position:0% +together with a as an extra factor here + + + align:start position:0% +together with a as an extra factor here +so what we have seen here is just we + + align:start position:0% +so what we have seen here is just we + + + align:start position:0% +so what we have seen here is just we +have looked at it i didn't explain + + align:start position:0% +have looked at it i didn't explain + + + align:start position:0% +have looked at it i didn't explain +how we got to this um but we have seen + + align:start position:0% +how we got to this um but we have seen + + + align:start position:0% +how we got to this um but we have seen +from this golden rule which helps us to + + align:start position:0% +from this golden rule which helps us to + + + align:start position:0% +from this golden rule which helps us to +assess + + align:start position:0% +assess + + + align:start position:0% +assess +and we have seen how we can actually + + align:start position:0% +and we have seen how we can actually + + + align:start position:0% +and we have seen how we can actually +calculate um the phase of this factor + + align:start position:0% +calculate um the phase of this factor + + + align:start position:0% +calculate um the phase of this factor +in the next lecture please now see how + + align:start position:0% +in the next lecture please now see how + + + align:start position:0% +in the next lecture please now see how +we can calculate + + align:start position:0% +we can calculate + + + align:start position:0% +we can calculate +the matrix element itself and we'll + + align:start position:0% +the matrix element itself and we'll + + + align:start position:0% +the matrix element itself and we'll +start doing this by using a toy + + align:start position:0% +start doing this by using a toy + + + align:start position:0% +start doing this by using a toy +experiment or a toy model such that the + + align:start position:0% +experiment or a toy model such that the + + + align:start position:0% +experiment or a toy model such that the +discussion simplifies + + align:start position:0% +discussion simplifies + + + align:start position:0% +discussion simplifies +algebra simplifies quite a bit \ No newline at end of file diff --git a/jzzpxqVohhI.txt b/jzzpxqVohhI.txt new file mode 100644 index 0000000000000000000000000000000000000000..139d92ed99706fd20050995e5a2d623421003a7f --- /dev/null +++ b/jzzpxqVohhI.txt @@ -0,0 +1,2195 @@ +align:start position:0% + +hi everyone welcome back so today we'd + + align:start position:0% +hi everyone welcome back so today we'd + + + align:start position:0% +hi everyone welcome back so today we'd +like to uh tackle a problem in 4A series + + align:start position:0% +like to uh tackle a problem in 4A series + + + align:start position:0% +like to uh tackle a problem in 4A series +and uh specifically we're just going to + + align:start position:0% +and uh specifically we're just going to + + + align:start position:0% +and uh specifically we're just going to +compute the 4A series for uh a simple + + align:start position:0% +compute the 4A series for uh a simple + + + align:start position:0% +compute the 4A series for uh a simple +function so the function we're + + align:start position:0% +function so the function we're + + + align:start position:0% +function so the function we're +interested in is f of t uh which we're + + align:start position:0% +interested in is f of t uh which we're + + + align:start position:0% +interested in is f of t uh which we're +told is periodic with Period 2 pi F of T + + align:start position:0% +told is periodic with Period 2 pi F of T + + + align:start position:0% +told is periodic with Period 2 pi F of T +is one from minus pi to 0er and then + + align:start position:0% +is one from minus pi to 0er and then + + + align:start position:0% +is one from minus pi to 0er and then +it's minus one from Z to + + align:start position:0% +it's minus one from Z to + + + align:start position:0% +it's minus one from Z to +Pi so first off we're interested in + + align:start position:0% +Pi so first off we're interested in + + + align:start position:0% +Pi so first off we're interested in +sketching F of + + align:start position:0% +sketching F of + + + align:start position:0% +sketching F of +T secondly uh we'd like to compute the + + align:start position:0% +T secondly uh we'd like to compute the + + + align:start position:0% +T secondly uh we'd like to compute the +4A series uh for f of T and then thirdly + + align:start position:0% +4A series uh for f of T and then thirdly + + + align:start position:0% +4A series uh for f of T and then thirdly +uh we'd like to sketch the first + + align:start position:0% +uh we'd like to sketch the first + + + align:start position:0% +uh we'd like to sketch the first +non-zero term of the 4A series and uh we + + align:start position:0% +non-zero term of the 4A series and uh we + + + align:start position:0% +non-zero term of the 4A series and uh we +can specifically uh sketch this uh + + align:start position:0% +can specifically uh sketch this uh + + + align:start position:0% +can specifically uh sketch this uh +single term on top of f of T so I'll let + + align:start position:0% +single term on top of f of T so I'll let + + + align:start position:0% +single term on top of f of T so I'll let +you think about this problem for now and + + align:start position:0% +you think about this problem for now and + + + align:start position:0% +you think about this problem for now and +I'll be back in a moment + + align:start position:0% + + + + align:start position:0% + +hi everyone welcome back okay so let's + + align:start position:0% +hi everyone welcome back okay so let's + + + align:start position:0% +hi everyone welcome back okay so let's +take a look at sketching F of + + align:start position:0% + + + + align:start position:0% + +t Okay so for part + + align:start position:0% +t Okay so for part + + + align:start position:0% +t Okay so for part +A we have our axis T and we're told F of + + align:start position:0% +A we have our axis T and we're told F of + + + align:start position:0% +A we have our axis T and we're told F of +t uh within some interval so we might as + + align:start position:0% +t uh within some interval so we might as + + + align:start position:0% +t uh within some interval so we might as +well plot F of t on that + + align:start position:0% +well plot F of t on that + + + align:start position:0% +well plot F of t on that +interval okay so minus + + align:start position:0% + + + + align:start position:0% + +Pi Pi and zero we know that F of T is + + align:start position:0% + + + + align:start position:0% + +one from minus pi to + + align:start position:0% +one from minus pi to + + + align:start position:0% +one from minus pi to +0 we're also told that it's minus + + align:start position:0% +0 we're also told that it's minus + + + align:start position:0% +0 we're also told that it's minus +one from 0 to + + align:start position:0% + + + + align:start position:0% + +Pi and now uh to fill in the blanks or + + align:start position:0% +Pi and now uh to fill in the blanks or + + + align:start position:0% +Pi and now uh to fill in the blanks or +to complete the picture of f we're told + + align:start position:0% +to complete the picture of f we're told + + + align:start position:0% +to complete the picture of f we're told +that it has a period of 2 pi so note + + align:start position:0% +that it has a period of 2 pi so note + + + align:start position:0% +that it has a period of 2 pi so note +that they've told us what F looks like + + align:start position:0% +that they've told us what F looks like + + + align:start position:0% +that they've told us what F looks like +over the range uh of minus pi to Pi + + align:start position:0% +over the range uh of minus pi to Pi + + + align:start position:0% +over the range uh of minus pi to Pi +which is a length of 2 pi so basically + + align:start position:0% +which is a length of 2 pi so basically + + + align:start position:0% +which is a length of 2 pi so basically +what we can do is we can use this as a + + align:start position:0% +what we can do is we can use this as a + + + align:start position:0% +what we can do is we can use this as a +stamp and just pick up this entire + + align:start position:0% +stamp and just pick up this entire + + + align:start position:0% +stamp and just pick up this entire +picture shift it over one period 2 pi + + align:start position:0% +picture shift it over one period 2 pi + + + align:start position:0% +picture shift it over one period 2 pi +and just think of thinking of this uh + + align:start position:0% +and just think of thinking of this uh + + + align:start position:0% +and just think of thinking of this uh +picture and stamping it in multiple + + align:start position:0% +picture and stamping it in multiple + + + align:start position:0% +picture and stamping it in multiple +places so just filling this in + + align:start position:0% + + + + align:start position:0% + +it's going to look like a square + + align:start position:0% + + + + align:start position:0% + +wave which jumps between minus one and + + align:start position:0% +wave which jumps between minus one and + + + align:start position:0% +wave which jumps between minus one and +one at every multiple of + + align:start position:0% +one at every multiple of + + + align:start position:0% +one at every multiple of +Pi okay so this concludes part a uh for + + align:start position:0% +Pi okay so this concludes part a uh for + + + align:start position:0% +Pi okay so this concludes part a uh for +Part B which is the real meat of the + + align:start position:0% +Part B which is the real meat of the + + + align:start position:0% +Part B which is the real meat of the +meat of the problem uh we're interested + + align:start position:0% +meat of the problem uh we're interested + + + align:start position:0% +meat of the problem uh we're interested +in Computing the fora series for f of t + + align:start position:0% +in Computing the fora series for f of t + + + align:start position:0% +in Computing the fora series for f of t +now we can always write down a 4A series + + align:start position:0% +now we can always write down a 4A series + + + align:start position:0% +now we can always write down a 4A series +for any periodic + + align:start position:0% +for any periodic + + + align:start position:0% +for any periodic +function and specifically in this case + + align:start position:0% +function and specifically in this case + + + align:start position:0% +function and specifically in this case +so for Part B the periodic function + + align:start position:0% +so for Part B the periodic function + + + align:start position:0% +so for Part B the periodic function +we're interested in has Period 2 pi so + + align:start position:0% +we're interested in has Period 2 pi so + + + align:start position:0% +we're interested in has Period 2 pi so +in the + + align:start position:0% + + + + align:start position:0% + +notes for the class notes we've + + align:start position:0% +notes for the class notes we've + + + align:start position:0% +notes for the class notes we've +identified L with half the period so in + + align:start position:0% +identified L with half the period so in + + + align:start position:0% +identified L with half the period so in +this case L is 2 Pi / + + align:start position:0% +this case L is 2 Pi / + + + align:start position:0% +this case L is 2 Pi / +2 which gives us pi + + align:start position:0% +2 which gives us pi + + + align:start position:0% +2 which gives us pi +and just to recall what a fora series is + + align:start position:0% +and just to recall what a fora series is + + + align:start position:0% +and just to recall what a fora series is +what we do is we try and take our + + align:start position:0% +what we do is we try and take our + + + align:start position:0% +what we do is we try and take our +function f of + + align:start position:0% +function f of + + + align:start position:0% +function f of +T and write it down as a summation of ss + + align:start position:0% +T and write it down as a summation of ss + + + align:start position:0% +T and write it down as a summation of ss +and + + align:start position:0% +and + + + align:start position:0% +and +cosiness so in this case for a function + + align:start position:0% +cosiness so in this case for a function + + + align:start position:0% +cosiness so in this case for a function +f of T which is 2 pi periodic it's going + + align:start position:0% +f of T which is 2 pi periodic it's going + + + align:start position:0% +f of T which is 2 pi periodic it's going +to look something like this it's going + + align:start position:0% +to look something like this it's going + + + align:start position:0% +to look something like this it's going +to be a of 0 + + align:start position:0% +to be a of 0 + + + align:start position:0% +to be a of 0 +plus sum from Nal 1 there's going to be + + align:start position:0% +plus sum from Nal 1 there's going to be + + + align:start position:0% +plus sum from Nal 1 there's going to be +infinitely many terms but in this case + + align:start position:0% +infinitely many terms but in this case + + + align:start position:0% +infinitely many terms but in this case +we have a of n time cosine of + + align:start position:0% +we have a of n time cosine of + + + align:start position:0% +we have a of n time cosine of +NT and it's NT here because we have + + align:start position:0% +NT and it's NT here because we have + + + align:start position:0% +NT and it's NT here because we have +Period 2 pi plus + + align:start position:0% +Period 2 pi plus + + + align:start position:0% +Period 2 pi plus +BN sin + + align:start position:0% +BN sin + + + align:start position:0% +BN sin +nt Okay so this is the general + + align:start position:0% +nt Okay so this is the general + + + align:start position:0% +nt Okay so this is the general +form and when asked to compute the 4A + + align:start position:0% +form and when asked to compute the 4A + + + align:start position:0% +form and when asked to compute the 4A +series of a of a function the main + + align:start position:0% +series of a of a function the main + + + align:start position:0% +series of a of a function the main +difficulty is to compute these + + align:start position:0% +difficulty is to compute these + + + align:start position:0% +difficulty is to compute these +coefficients a n and + + align:start position:0% +coefficients a n and + + + align:start position:0% +coefficients a n and +BN however that essentially boils down + + align:start position:0% +BN however that essentially boils down + + + align:start position:0% +BN however that essentially boils down +to working out some integrals + + align:start position:0% + + + + align:start position:0% + +okay so let's take a look at what a of + + align:start position:0% +okay so let's take a look at what a of + + + align:start position:0% +okay so let's take a look at what a of +Zer + + align:start position:0% + + + + align:start position:0% + +is so a0 the formula for a z is 1 over 2 + + align:start position:0% +is so a0 the formula for a z is 1 over 2 + + + align:start position:0% +is so a0 the formula for a z is 1 over 2 +L so in this case it's 1 over 2 + + align:start position:0% +L so in this case it's 1 over 2 + + + align:start position:0% +L so in this case it's 1 over 2 +pi times the integral over one period of + + align:start position:0% +pi times the integral over one period of + + + align:start position:0% +pi times the integral over one period of +the function from minus pi to Pi of just + + align:start position:0% +the function from minus pi to Pi of just + + + align:start position:0% +the function from minus pi to Pi of just +F of + + align:start position:0% +F of + + + align:start position:0% +F of +T So notice how a z is just the average + + align:start position:0% +T So notice how a z is just the average + + + align:start position:0% +T So notice how a z is just the average +of the function so if we take a look at + + align:start position:0% +of the function so if we take a look at + + + align:start position:0% +of the function so if we take a look at +the function f of t f of T spends + + align:start position:0% +the function f of t f of T spends + + + align:start position:0% +the function f of t f of T spends +exactly half of its time at one and half + + align:start position:0% +exactly half of its time at one and half + + + align:start position:0% +exactly half of its time at one and half +of its time at minus one so immediately + + align:start position:0% +of its time at minus one so immediately + + + align:start position:0% +of its time at minus one so immediately +we could guess that the average value of + + align:start position:0% +we could guess that the average value of + + + align:start position:0% +we could guess that the average value of +f of T is going to be + + align:start position:0% + + + + align:start position:0% + +zero if you if you wanted to work it out + + align:start position:0% + + + + align:start position:0% + +specifically we would have 1 over 2 + + align:start position:0% + + + + align:start position:0% + +pi minus pi to Zer F of T takes on the + + align:start position:0% +pi minus pi to Zer F of T takes on the + + + align:start position:0% +pi minus pi to Zer F of T takes on the +value of plus one + + align:start position:0% + + + + align:start position:0% + +and then from 0 to + + align:start position:0% +and then from 0 to + + + align:start position:0% +and then from 0 to +Pi F of T takes on the value of minus + + align:start position:0% +Pi F of T takes on the value of minus + + + align:start position:0% +Pi F of T takes on the value of minus +one so we would end up getting Pi minus + + align:start position:0% +one so we would end up getting Pi minus + + + align:start position:0% +one so we would end up getting Pi minus +Pi which is + + align:start position:0% +Pi which is + + + align:start position:0% +Pi which is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay for a + + align:start position:0% + + + + align:start position:0% + +n the formula is one over half the + + align:start position:0% +n the formula is one over half the + + + align:start position:0% +n the formula is one over half the +period so note how a of zero is just a + + align:start position:0% +period so note how a of zero is just a + + + align:start position:0% +period so note how a of zero is just a +special case + + align:start position:0% +special case + + + align:start position:0% +special case +we always have the full period in a zero + + align:start position:0% +we always have the full period in a zero + + + align:start position:0% +we always have the full period in a zero +but in a n and + + align:start position:0% +but in a n and + + + align:start position:0% +but in a n and +BN uh the factor that divides the + + align:start position:0% +BN uh the factor that divides the + + + align:start position:0% +BN uh the factor that divides the +integral is always going to be half the + + align:start position:0% +integral is always going to be half the + + + align:start position:0% +integral is always going to be half the +period time minus pi to + + align:start position:0% +period time minus pi to + + + align:start position:0% +period time minus pi to +Pi F of + + align:start position:0% +Pi F of + + + align:start position:0% +Pi F of +T cosine + + align:start position:0% +T cosine + + + align:start position:0% +T cosine +NT + + align:start position:0% +NT + + + align:start position:0% +NT +DT and I I should point out that in + + align:start position:0% +DT and I I should point out that in + + + align:start position:0% +DT and I I should point out that in +general we only need to integrate over + + align:start position:0% +general we only need to integrate over + + + align:start position:0% +general we only need to integrate over +one period of the function so in some + + align:start position:0% +one period of the function so in some + + + align:start position:0% +one period of the function so in some +sense there's nothing special about + + align:start position:0% +sense there's nothing special about + + + align:start position:0% +sense there's nothing special about +minus pi and Pi it's just uh very often + + align:start position:0% +minus pi and Pi it's just uh very often + + + align:start position:0% +minus pi and Pi it's just uh very often +these are the easiest in uh bounds of + + align:start position:0% +these are the easiest in uh bounds of + + + align:start position:0% +these are the easiest in uh bounds of +integration to uh to integrate + + align:start position:0% + + + + align:start position:0% + +over but in practice we could have used + + align:start position:0% +over but in practice we could have used + + + align:start position:0% +over but in practice we could have used +0 to 2 pi or any other uh interval as + + align:start position:0% +0 to 2 pi or any other uh interval as + + + align:start position:0% +0 to 2 pi or any other uh interval as +long as it's exactly one period of the + + align:start position:0% +long as it's exactly one period of the + + + align:start position:0% +long as it's exactly one period of the +function okay so uh in this case uh I + + align:start position:0% +function okay so uh in this case uh I + + + align:start position:0% +function okay so uh in this case uh I +just like to take a look at the symmetry + + align:start position:0% +just like to take a look at the symmetry + + + align:start position:0% +just like to take a look at the symmetry +of f of T and we note that the the + + align:start position:0% +of f of T and we note that the the + + + align:start position:0% +of f of T and we note that the the +function f of t is actually uh odd about + + align:start position:0% +function f of t is actually uh odd about + + + align:start position:0% +function f of t is actually uh odd about +the + + align:start position:0% +the + + + align:start position:0% +the +origin so if F of T is odd and cosine T + + align:start position:0% +origin so if F of T is odd and cosine T + + + align:start position:0% +origin so if F of T is odd and cosine T +is an even function then an odd times an + + align:start position:0% +is an even function then an odd times an + + + align:start position:0% +is an even function then an odd times an +even function is going to be an odd + + align:start position:0% +even function is going to be an odd + + + align:start position:0% +even function is going to be an odd +function and when you integrate an odd + + align:start position:0% +function and when you integrate an odd + + + align:start position:0% +function and when you integrate an odd +function from minus any value to the + + align:start position:0% +function from minus any value to the + + + align:start position:0% +function from minus any value to the +same positive value so in this case + + align:start position:0% +same positive value so in this case + + + align:start position:0% +same positive value so in this case +minus pi to Pi we always get + + align:start position:0% +minus pi to Pi we always get + + + align:start position:0% +minus pi to Pi we always get +zero so this is actually zero because + + align:start position:0% +zero so this is actually zero because + + + align:start position:0% +zero so this is actually zero because +we're integrating an odd function over + + align:start position:0% +we're integrating an odd function over + + + align:start position:0% +we're integrating an odd function over +for a symmetric + + align:start position:0% + + + + align:start position:0% + +interval okay so lastly we have the + + align:start position:0% +interval okay so lastly we have the + + + align:start position:0% +interval okay so lastly we have the +values of uh + + align:start position:0% +values of uh + + + align:start position:0% +values of uh +BN which are one over + + align:start position:0% +BN which are one over + + + align:start position:0% +BN which are one over +Pi minus pi to + + align:start position:0% +Pi minus pi to + + + align:start position:0% +Pi minus pi to +Pi F of T of sin n + + align:start position:0% + + + + align:start position:0% + +t uh + + align:start position:0% +t uh + + + align:start position:0% +t uh +DT and if we were to look at just the + + align:start position:0% +DT and if we were to look at just the + + + align:start position:0% +DT and if we were to look at just the +Symmetry argument again F of T is an odd + + align:start position:0% +Symmetry argument again F of T is an odd + + + align:start position:0% +Symmetry argument again F of T is an odd +function sin T is an odd function and + + align:start position:0% +function sin T is an odd function and + + + align:start position:0% +function sin T is an odd function and +odd times an odd function is an even + + align:start position:0% +odd times an odd function is an even + + + align:start position:0% +odd times an odd function is an even +function when you integrate an even + + align:start position:0% +function when you integrate an even + + + align:start position:0% +function when you integrate an even +function over a symmetric bound uh you + + align:start position:0% +function over a symmetric bound uh you + + + align:start position:0% +function over a symmetric bound uh you +will essentially get twice the value of + + align:start position:0% +will essentially get twice the value of + + + align:start position:0% +will essentially get twice the value of +the integral from zero to one of the + + align:start position:0% +the integral from zero to one of the + + + align:start position:0% +the integral from zero to one of the +bounds so B of n in this case doesn't + + align:start position:0% +bounds so B of n in this case doesn't + + + align:start position:0% +bounds so B of n in this case doesn't +vanish which means we actually have to + + align:start position:0% +vanish which means we actually have to + + + align:start position:0% +vanish which means we actually have to +do some + + align:start position:0% + + + + align:start position:0% + +work okay so what what do we do well we + + align:start position:0% +work okay so what what do we do well we + + + align:start position:0% +work okay so what what do we do well we +know the value of f of t on two + + align:start position:0% +know the value of f of t on two + + + align:start position:0% +know the value of f of t on two +intervals so we're just going to have to + + align:start position:0% +intervals so we're just going to have to + + + align:start position:0% +intervals so we're just going to have to +work out each + + align:start position:0% +work out each + + + align:start position:0% +work out each +interval minus pi to 0 it takes on the + + align:start position:0% +interval minus pi to 0 it takes on the + + + align:start position:0% +interval minus pi to 0 it takes on the +value of one so we have s n + + align:start position:0% + + + + align:start position:0% + +t and then from 0 to + + align:start position:0% +t and then from 0 to + + + align:start position:0% +t and then from 0 to +Pi F of T takes on the value of minus + + align:start position:0% +Pi F of T takes on the value of minus + + + align:start position:0% +Pi F of T takes on the value of minus +one sin + + align:start position:0% + + + + align:start position:0% + +NT + + align:start position:0% +NT + + + align:start position:0% +NT +DTS and you'll note that these these + + align:start position:0% +DTS and you'll note that these these + + + align:start position:0% +DTS and you'll note that these these +integrals are actually the + + align:start position:0% + + + + align:start position:0% + +same so this is -2 over + + align:start position:0% + + + + align:start position:0% + +Pi 0 to Pi sin + + align:start position:0% +Pi 0 to Pi sin + + + align:start position:0% +Pi 0 to Pi sin +NT + + align:start position:0% + + + + align:start position:0% + +DT which if we + + align:start position:0% +DT which if we + + + align:start position:0% +DT which if we +integrate is 1 over + + align:start position:0% +integrate is 1 over + + + align:start position:0% +integrate is 1 over +n cosine + + align:start position:0% + + + + align:start position:0% + +NT evaluated between Z and pi + + align:start position:0% + + + + align:start position:0% + +so if I work this out we get a minus and + + align:start position:0% +so if I work this out we get a minus and + + + align:start position:0% +so if I work this out we get a minus and +a minus + + align:start position:0% + + + + align:start position:0% + +well get minus 1/ + + align:start position:0% +well get minus 1/ + + + align:start position:0% +well get minus 1/ +n cine n + + align:start position:0% +n cine n + + + align:start position:0% +n cine n +pi plus 1/ + + align:start position:0% +pi plus 1/ + + + align:start position:0% +pi plus 1/ +n so note that cosine of Z is just + + align:start position:0% + + + + align:start position:0% + +one okay and now if we take a look at + + align:start position:0% +one okay and now if we take a look at + + + align:start position:0% +one okay and now if we take a look at +cosine n Pi we you see that cosine and + + align:start position:0% +cosine n Pi we you see that cosine and + + + align:start position:0% +cosine n Pi we you see that cosine and +Pi oscillates between min-1 and 1 so + + align:start position:0% +Pi oscillates between min-1 and 1 so + + + align:start position:0% +Pi oscillates between min-1 and 1 so +cosine of pi is 1 cosine of 2 pi is 1 + + align:start position:0% +cosine of pi is 1 cosine of 2 pi is 1 + + + align:start position:0% +cosine of pi is 1 cosine of 2 pi is 1 +cosine of 3 Pi is - 1 dot dot dot so + + align:start position:0% +cosine of 3 Pi is - 1 dot dot dot so + + + align:start position:0% +cosine of 3 Pi is - 1 dot dot dot so +this term right here is + + align:start position:0% +this term right here is + + + align:start position:0% +this term right here is +actually 1 to the + + align:start position:0% + + + + align:start position:0% + +N okay so we have 2 over n + + align:start position:0% + + + + align:start position:0% + +Pi + + align:start position:0% +Pi + + + align:start position:0% +Pi +1us -1 to the n + + align:start position:0% + + + + align:start position:0% + +okay and now if we just plug in some + + align:start position:0% +okay and now if we just plug in some + + + align:start position:0% +okay and now if we just plug in some +values of B of zero B or sorry B of one + + align:start position:0% +values of B of zero B or sorry B of one + + + align:start position:0% +values of B of zero B or sorry B of one +B of uh two B of three B of four we can + + align:start position:0% +B of uh two B of three B of four we can + + + align:start position:0% +B of uh two B of three B of four we can +see what pattern uh emerges in the + + align:start position:0% +see what pattern uh emerges in the + + + align:start position:0% +see what pattern uh emerges in the +B's okay so B of + + align:start position:0% +B's okay so B of + + + align:start position:0% +B's okay so B of +one if I plug in one I get 1us Nega 1 is + + align:start position:0% +one if I plug in one I get 1us Nega 1 is + + + align:start position:0% +one if I plug in one I get 1us Nega 1 is +going to be two so I get -4 over + + align:start position:0% +going to be two so I get -4 over + + + align:start position:0% +going to be two so I get -4 over +Pi uh B of two + + align:start position:0% + + + + align:start position:0% + +is going to be 1 + + align:start position:0% +is going to be 1 + + + align:start position:0% +is going to be 1 +minus - 1^ squ is just one so this + + align:start position:0% + + + + align:start position:0% + +vanishes B of 3 is going to be 1 minus + + align:start position:0% +vanishes B of 3 is going to be 1 minus + + + align:start position:0% +vanishes B of 3 is going to be 1 minus +-1 cubed is just negative 1 so again we + + align:start position:0% +-1 cubed is just negative 1 so again we + + + align:start position:0% +-1 cubed is just negative 1 so again we +get ne uh 4 over 3 + + align:start position:0% + + + + align:start position:0% + +pi b of 4 is going to be + + align:start position:0% +pi b of 4 is going to be + + + align:start position:0% +pi b of 4 is going to be +zero dot dot + + align:start position:0% +zero dot dot + + + align:start position:0% +zero dot dot +dot okay + + align:start position:0% +dot okay + + + align:start position:0% +dot okay +so uh it's sometimes useful to write out + + align:start position:0% +so uh it's sometimes useful to write out + + + align:start position:0% +so uh it's sometimes useful to write out +what the 4A series looks like so I'll + + align:start position:0% +what the 4A series looks like so I'll + + + align:start position:0% +what the 4A series looks like so I'll +just write it out right + + align:start position:0% +just write it out right + + + align:start position:0% +just write it out right +here so we have F of + + align:start position:0% +here so we have F of + + + align:start position:0% +here so we have F of +T is going to be + + align:start position:0% +T is going to be + + + align:start position:0% +T is going to be +-4 over + + align:start position:0% +-4 over + + + align:start position:0% +-4 over +Pi Time s of + + align:start position:0% +Pi Time s of + + + align:start position:0% +Pi Time s of +t plus + + align:start position:0% +t plus + + + align:start position:0% +t plus +1/3 s of + + align:start position:0% + + + + align:start position:0% + +3T + 1/5 sin + + align:start position:0% +3T + 1/5 sin + + + align:start position:0% +3T + 1/5 sin +5T plus dot dot + + align:start position:0% +5T plus dot dot + + + align:start position:0% +5T plus dot dot +dot okay so this concludes uh part + + align:start position:0% + + + + align:start position:0% + +C oh sorry Part B and now lastly for + + align:start position:0% +C oh sorry Part B and now lastly for + + + align:start position:0% +C oh sorry Part B and now lastly for +part C we're asked to comp uh to sketch + + align:start position:0% +part C we're asked to comp uh to sketch + + + align:start position:0% +part C we're asked to comp uh to sketch +what does the uh the first for term look + + align:start position:0% +what does the uh the first for term look + + + align:start position:0% +what does the uh the first for term look +like okay so in this case the first for + + align:start position:0% +like okay so in this case the first for + + + align:start position:0% +like okay so in this case the first for +your term is going to + + align:start position:0% +your term is going to + + + align:start position:0% +your term is going to +be4 over Pi * sin t + + align:start position:0% +be4 over Pi * sin t + + + align:start position:0% +be4 over Pi * sin t +okay so I'm going to go back to our + + align:start position:0% +okay so I'm going to go back to our + + + align:start position:0% +okay so I'm going to go back to our +diagram from part A okay so let's go + + align:start position:0% +diagram from part A okay so let's go + + + align:start position:0% +diagram from part A okay so let's go +back to our diagram from part + + align:start position:0% +back to our diagram from part + + + align:start position:0% +back to our diagram from part +A now what does -4 over Pi sin t look + + align:start position:0% +A now what does -4 over Pi sin t look + + + align:start position:0% +A now what does -4 over Pi sin t look +like well it's a sine wave that has + + align:start position:0% +like well it's a sine wave that has + + + align:start position:0% +like well it's a sine wave that has +exactly a period 2 pi and it's going to + + align:start position:0% +exactly a period 2 pi and it's going to + + + align:start position:0% +exactly a period 2 pi and it's going to +line up exactly with this Square wave uh + + align:start position:0% +line up exactly with this Square wave uh + + + align:start position:0% +line up exactly with this Square wave uh +in addition minus 4 over Pi is just + + align:start position:0% +in addition minus 4 over Pi is just + + + align:start position:0% +in addition minus 4 over Pi is just +slightly larger than + + align:start position:0% +slightly larger than + + + align:start position:0% +slightly larger than +one so we're going to end up with sign + + align:start position:0% +one so we're going to end up with sign + + + align:start position:0% +one so we're going to end up with sign +which Peaks + + align:start position:0% +which Peaks + + + align:start position:0% +which Peaks +uh just slightly above one and slightly + + align:start position:0% +uh just slightly above one and slightly + + + align:start position:0% +uh just slightly above one and slightly +below one it's going to go through zero + + align:start position:0% +below one it's going to go through zero + + + align:start position:0% +below one it's going to go through zero +and it's going to go through each each + + align:start position:0% +and it's going to go through each each + + + align:start position:0% +and it's going to go through each each +value uh or each multiple of + + align:start position:0% +value uh or each multiple of + + + align:start position:0% +value uh or each multiple of +Pi so it might look something like + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +okay so this is the + + align:start position:0% + + + + align:start position:0% + +first forier + + align:start position:0% +first forier + + + align:start position:0% +first forier +term in the + + align:start position:0% +term in the + + + align:start position:0% +term in the +series and notice how this first for you + + align:start position:0% +series and notice how this first for you + + + align:start position:0% +series and notice how this first for you +term uh is actually a pretty good + + align:start position:0% +term uh is actually a pretty good + + + align:start position:0% +term uh is actually a pretty good +approximation to the square wave + + align:start position:0% +approximation to the square wave + + + align:start position:0% +approximation to the square wave +considering it's just one term in a + + align:start position:0% +considering it's just one term in a + + + align:start position:0% +considering it's just one term in a +series as we add more terms in the + + align:start position:0% +series as we add more terms in the + + + align:start position:0% +series as we add more terms in the +series we're going to look at we're + + align:start position:0% +series we're going to look at we're + + + align:start position:0% +series we're going to look at we're +going to get something which looks + + align:start position:0% +going to get something which looks + + + align:start position:0% +going to get something which looks +closer and closer to a square wave + + align:start position:0% +closer and closer to a square wave + + + align:start position:0% +closer and closer to a square wave +function okay so I just like to quickly + + align:start position:0% +function okay so I just like to quickly + + + align:start position:0% +function okay so I just like to quickly +recap when Computing a uh the 4A series + + align:start position:0% +recap when Computing a uh the 4A series + + + align:start position:0% +recap when Computing a uh the 4A series +for a periodic function uh the first + + align:start position:0% +for a periodic function uh the first + + + align:start position:0% +for a periodic function uh the first +useful thing to do is just write down + + align:start position:0% +useful thing to do is just write down + + + align:start position:0% +useful thing to do is just write down +the formula for a 4 Series and then + + align:start position:0% +the formula for a 4 Series and then + + + align:start position:0% +the formula for a 4 Series and then +write down the formulas for the + + align:start position:0% +write down the formulas for the + + + align:start position:0% +write down the formulas for the +coefficients of the 4 Series so write + + align:start position:0% +coefficients of the 4 Series so write + + + align:start position:0% +coefficients of the 4 Series so write +down the formulas for a z a n + + align:start position:0% +down the formulas for a z a n + + + align:start position:0% +down the formulas for a z a n +BN when Computing a z you can often just + + align:start position:0% +BN when Computing a z you can often just + + + align:start position:0% +BN when Computing a z you can often just +look at the average of the + + align:start position:0% +look at the average of the + + + align:start position:0% +look at the average of the +function when Computing a an and BN it's + + align:start position:0% +function when Computing a an and BN it's + + + align:start position:0% +function when Computing a an and BN it's +also useful to look at the symmetry of + + align:start position:0% +also useful to look at the symmetry of + + + align:start position:0% +also useful to look at the symmetry of +your function and if it's either even or + + align:start position:0% +your function and if it's either even or + + + align:start position:0% +your function and if it's either even or +odd uh symmetric then typically either + + align:start position:0% +odd uh symmetric then typically either + + + align:start position:0% +odd uh symmetric then typically either +all the a ends or all the B ends will + + align:start position:0% +all the a ends or all the B ends will + + + align:start position:0% +all the a ends or all the B ends will +vanish and then when you work out the + + align:start position:0% +vanish and then when you work out the + + + align:start position:0% +vanish and then when you work out the +integrals you can then reconstruct the + + align:start position:0% +integrals you can then reconstruct the + + + align:start position:0% +integrals you can then reconstruct the +4A + + align:start position:0% +4A + + + align:start position:0% +4A +Series so I'd like to conclude here and + + align:start position:0% +Series so I'd like to conclude here and + + + align:start position:0% +Series so I'd like to conclude here and +I'll see you next time \ No newline at end of file diff --git a/kOe3fGU_l3k.txt b/kOe3fGU_l3k.txt new file mode 100644 index 0000000000000000000000000000000000000000..63a031d7977b4e9e26e56d846aa3b5f95858a04d --- /dev/null +++ b/kOe3fGU_l3k.txt @@ -0,0 +1,10531 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common license. Your support + + align:start position:0% +a Creative Common license. Your support + + + align:start position:0% +a Creative Common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% +Courseware at ocw.mmit.edu. + + + align:start position:0% +Courseware at ocw.mmit.edu. +>> Today is pretty much just set aside for + + align:start position:0% +>> Today is pretty much just set aside for + + + align:start position:0% +>> Today is pretty much just set aside for +brainstorming. So, we're probably going + + align:start position:0% +brainstorming. So, we're probably going + + + align:start position:0% +brainstorming. So, we're probably going +to do about an hour of that uh just to + + align:start position:0% +to do about an hour of that uh just to + + + align:start position:0% +to do about an hour of that uh just to +like throw the ideas that people already + + align:start position:0% +like throw the ideas that people already + + + align:start position:0% +like throw the ideas that people already +have in their heads about what could be + + align:start position:0% +have in their heads about what could be + + + align:start position:0% +have in their heads about what could be +with the problem space that we're + + align:start position:0% +with the problem space that we're + + + align:start position:0% +with the problem space that we're +working on. I mean, this this whole + + align:start position:0% +working on. I mean, this this whole + + + align:start position:0% +working on. I mean, this this whole +preparing people to deal with violence + + align:start position:0% +preparing people to deal with violence + + + align:start position:0% +preparing people to deal with violence +uh and uh uh with with folks suffering + + align:start position:0% +uh and uh uh with with folks suffering + + + align:start position:0% +uh and uh uh with with folks suffering +from mental uh illness and you know + + align:start position:0% +from mental uh illness and you know + + + align:start position:0% +from mental uh illness and you know +there's a whole bunch of different + + align:start position:0% +there's a whole bunch of different + + + align:start position:0% +there's a whole bunch of different +things that people might be interested + + align:start position:0% +things that people might be interested + + + align:start position:0% +things that people might be interested +in working on. And the idea is that we + + align:start position:0% +in working on. And the idea is that we + + + align:start position:0% +in working on. And the idea is that we +hope hopefully if we can get this all + + align:start position:0% +hope hopefully if we can get this all + + + align:start position:0% +hope hopefully if we can get this all +out then um that we can spend next half + + align:start position:0% +out then um that we can spend next half + + + align:start position:0% +out then um that we can spend next half +hour and frankly the rest of this week + + align:start position:0% +hour and frankly the rest of this week + + + align:start position:0% +hour and frankly the rest of this week +uh trying to figure out who's in which + + align:start position:0% +uh trying to figure out who's in which + + + align:start position:0% +uh trying to figure out who's in which +team uh you know who's who's + + align:start position:0% +team uh you know who's who's + + + align:start position:0% +team uh you know who's who's +collaborating on similar topics and + + align:start position:0% +collaborating on similar topics and + + + align:start position:0% +collaborating on similar topics and +who's interested in working. + + align:start position:0% +who's interested in working. + + + align:start position:0% +who's interested in working. +Um and did anyone actually manage to get + + align:start position:0% +Um and did anyone actually manage to get + + + align:start position:0% +Um and did anyone actually manage to get +through any of the readings that I had + + align:start position:0% +through any of the readings that I had + + + align:start position:0% +through any of the readings that I had +put up? Okay. Right. So so there's a few + + align:start position:0% +put up? Okay. Right. So so there's a few + + + align:start position:0% +put up? Okay. Right. So so there's a few +things in there. I realized there wasn't + + align:start position:0% +things in there. I realized there wasn't + + + align:start position:0% +things in there. I realized there wasn't +a whole lot of time to read uh to read + + align:start position:0% +a whole lot of time to read uh to read + + + align:start position:0% +a whole lot of time to read uh to read +and there's probably more stuff up there + + align:start position:0% +and there's probably more stuff up there + + + align:start position:0% +and there's probably more stuff up there +to read than it needs to be necessarily + + align:start position:0% +to read than it needs to be necessarily + + + align:start position:0% +to read than it needs to be necessarily +but it's all there as resources any any + + align:start position:0% +but it's all there as resources any any + + + align:start position:0% +but it's all there as resources any any +ideas that people thought might be + + align:start position:0% +ideas that people thought might be + + + align:start position:0% +ideas that people thought might be +interesting to work on uh going uh + + align:start position:0% +interesting to work on uh going uh + + + align:start position:0% +interesting to work on uh going uh +Andrew and then + + align:start position:0% +Andrew and then + + + align:start position:0% +Andrew and then +>> so one of the basic issues I heard from + + align:start position:0% +>> so one of the basic issues I heard from + + + align:start position:0% +>> so one of the basic issues I heard from +the presentation and papers was + + align:start position:0% +the presentation and papers was + + + align:start position:0% +the presentation and papers was +communication + + align:start position:0% +communication + + + align:start position:0% +communication +>> so I guess uh the brainstorm simulation + + align:start position:0% +>> so I guess uh the brainstorm simulation + + + align:start position:0% +>> so I guess uh the brainstorm simulation +but the real world system would be + + align:start position:0% +but the real world system would be + + + align:start position:0% +but the real world system would be +communication between the psychiatrist + + align:start position:0% +communication between the psychiatrist + + + align:start position:0% +communication between the psychiatrist +and the like the + + align:start position:0% +and the like the + + + align:start position:0% +and the like the +>> patient patient + + align:start position:0% +>> patient patient + + + align:start position:0% +>> patient patient +>> patient yes the patient along with the + + align:start position:0% +>> patient yes the patient along with the + + + align:start position:0% +>> patient yes the patient along with the +psychiatrist with the person uh above + + align:start position:0% +psychiatrist with the person uh above + + + align:start position:0% +psychiatrist with the person uh above +them + + align:start position:0% +them + + + align:start position:0% +them +>> psychiatrist patient communication + + align:start position:0% +>> psychiatrist patient communication + + + align:start position:0% +>> psychiatrist patient communication +>> yes + + align:start position:0% +>> yes + + + align:start position:0% +>> yes +>> what's I for what they call + + align:start position:0% +>> what's I for what they call + + + align:start position:0% +>> what's I for what they call +>> patient + + align:start position:0% +>> patient + + + align:start position:0% +>> patient +>> person not the patient but patient + + align:start position:0% +>> person not the patient but patient + + + align:start position:0% +>> person not the patient but patient +psychiatrist person + + align:start position:0% +psychiatrist person + + + align:start position:0% +psychiatrist person +>> orderly + + align:start position:0% +>> orderly + + + align:start position:0% +>> orderly +>> nurse + + align:start position:0% +>> nurse + + + align:start position:0% +>> nurse +>> what what function do they have + + align:start position:0% +>> what what function do they have + + + align:start position:0% +>> what what function do they have +>> give us more information our system is + + align:start position:0% +>> give us more information our system is + + + align:start position:0% +>> give us more information our system is +under constraint + + align:start position:0% +under constraint + + + align:start position:0% +under constraint +>> mind psychiatrist patient for Yeah. But + + align:start position:0% +>> mind psychiatrist patient for Yeah. But + + + align:start position:0% +>> mind psychiatrist patient for Yeah. But +>> but I mean you're not talking about + + align:start position:0% +>> but I mean you're not talking about + + + align:start position:0% +>> but I mean you're not talking about +psychiatrist nurse patient. + + align:start position:0% +psychiatrist nurse patient. + + + align:start position:0% +psychiatrist nurse patient. +>> No, it's like uh + + align:start position:0% +>> No, it's like uh + + + align:start position:0% +>> No, it's like uh +>> psychiatrist resident. + + align:start position:0% +>> psychiatrist resident. + + + align:start position:0% +>> psychiatrist resident. +>> Sorry. Maybe like nurse patient and then + + align:start position:0% +>> Sorry. Maybe like nurse patient and then + + + align:start position:0% +>> Sorry. Maybe like nurse patient and then +nurse reporting instant to + + align:start position:0% +nurse reporting instant to + + + align:start position:0% +nurse reporting instant to +>> supervisor. Three levels. So + + align:start position:0% +>> supervisor. Three levels. So + + + align:start position:0% +>> supervisor. Three levels. So +>> yes, that's the one. + + align:start position:0% +>> yes, that's the one. + + + align:start position:0% +>> yes, that's the one. +>> So like you have a supervisor, + + align:start position:0% +>> So like you have a supervisor, + + + align:start position:0% +>> So like you have a supervisor, +>> you have a nurse. + + align:start position:0% +>> you have a nurse. + + + align:start position:0% +>> you have a nurse. +>> Yeah. Sorry guys. + + align:start position:0% +>> Yeah. Sorry guys. + + + align:start position:0% +>> Yeah. Sorry guys. +>> And you have the patient. Like those + + align:start position:0% +>> And you have the patient. Like those + + + align:start position:0% +>> And you have the patient. Like those +kind of like reporting up, reporting + + align:start position:0% +kind of like reporting up, reporting + + + align:start position:0% +kind of like reporting up, reporting +down. Great. + + align:start position:0% +down. Great. + + + align:start position:0% +down. Great. +>> All right. Uh yeah. So I have a couple + + align:start position:0% +>> All right. Uh yeah. So I have a couple + + + align:start position:0% +>> All right. Uh yeah. So I have a couple +ideas. One of them was maybe an idea + + align:start position:0% +ideas. One of them was maybe an idea + + + align:start position:0% +ideas. One of them was maybe an idea +like uh you have there's a patient and + + align:start position:0% +like uh you have there's a patient and + + + align:start position:0% +like uh you have there's a patient and +there's two uh I guess doctors + + align:start position:0% +there's two uh I guess doctors + + + align:start position:0% +there's two uh I guess doctors +psychiatrists + + align:start position:0% +psychiatrists + + + align:start position:0% +psychiatrists +>> and so one one psychiatrist is one + + align:start position:0% +>> and so one one psychiatrist is one + + + align:start position:0% +>> and so one one psychiatrist is one +psychiatrist is trying to calm the + + align:start position:0% +psychiatrist is trying to calm the + + + align:start position:0% +psychiatrist is trying to calm the +patient while the other is doing the + + align:start position:0% +patient while the other is doing the + + + align:start position:0% +patient while the other is doing the +opposite and trying to make this patient + + align:start position:0% +opposite and trying to make this patient + + + align:start position:0% +opposite and trying to make this patient +as angry as possible. So the way I'm + + align:start position:0% +as angry as possible. So the way I'm + + + align:start position:0% +as angry as possible. So the way I'm +thinking is with the one that makes you + + align:start position:0% +thinking is with the one that makes you + + + align:start position:0% +thinking is with the one that makes you +the psychiatrist is trying to uh enrage + + align:start position:0% +the psychiatrist is trying to uh enrage + + + align:start position:0% +the psychiatrist is trying to uh enrage +the patient that's kind of training in + + align:start position:0% +the patient that's kind of training in + + + align:start position:0% +the patient that's kind of training in +what not to say + + align:start position:0% +what not to say + + + align:start position:0% +what not to say +>> while the patient or the doctor is + + align:start position:0% +>> while the patient or the doctor is + + + align:start position:0% +>> while the patient or the doctor is +trying to calm them down is + + align:start position:0% +trying to calm them down is + + + align:start position:0% +trying to calm them down is +>> so so by showing how you can how what + + align:start position:0% +>> so so by showing how you can how what + + + align:start position:0% +>> so so by showing how you can how what +was the worst possible way to get + + align:start position:0% +was the worst possible way to get + + + align:start position:0% +was the worst possible way to get +>> Okay. So I couldn't call that good bad + + align:start position:0% +>> Okay. So I couldn't call that good bad + + + align:start position:0% +>> Okay. So I couldn't call that good bad +cup. + + align:start position:0% +cup. + + + align:start position:0% +cup. +>> Yeah. And then another idea I I had + + align:start position:0% +>> Yeah. And then another idea I I had + + + align:start position:0% +>> Yeah. And then another idea I I had +which I thought with bashing yesterday + + align:start position:0% +which I thought with bashing yesterday + + + align:start position:0% +which I thought with bashing yesterday +was um maybe have like have a team of + + align:start position:0% +was um maybe have like have a team of + + + align:start position:0% +was um maybe have like have a team of +psychiatrist working with one patient. + + align:start position:0% +psychiatrist working with one patient. + + + align:start position:0% +psychiatrist working with one patient. +But in interace in one of the uh + + align:start position:0% +But in interace in one of the uh + + + align:start position:0% +But in interace in one of the uh +psychiatrist is like a saver trying to + + align:start position:0% +psychiatrist is like a saver trying to + + + align:start position:0% +psychiatrist is like a saver trying to +is trying to enrage the patient. + + align:start position:0% +is trying to enrage the patient. + + + align:start position:0% +is trying to enrage the patient. +Remember the target audience is going to + + align:start position:0% +Remember the target audience is going to + + + align:start position:0% +Remember the target audience is going to +be psych like actual residents in so so + + align:start position:0% +be psych like actual residents in so so + + + align:start position:0% +be psych like actual residents in so so +so but but I'm going to like I I I just + + align:start position:0% +so but but I'm going to like I I I just + + + align:start position:0% +so but but I'm going to like I I I just +going to say several and a group + + align:start position:0% +going to say several and a group + + + align:start position:0% +going to say several and a group +>> of psychiatrists + + align:start position:0% + + + + align:start position:0% + +maybe an idea of the dynamic that we can + + align:start position:0% +maybe an idea of the dynamic that we can + + + align:start position:0% +maybe an idea of the dynamic that we can +play with. Okay. Uh John + + align:start position:0% +play with. Okay. Uh John + + + align:start position:0% +play with. Okay. Uh John +>> uh so three quick things. One would be + + align:start position:0% +>> uh so three quick things. One would be + + + align:start position:0% +>> uh so three quick things. One would be +I'm not exactly sure how this fits into + + align:start position:0% +I'm not exactly sure how this fits into + + + align:start position:0% +I'm not exactly sure how this fits into +a game, but uh simulating people who are + + align:start position:0% +a game, but uh simulating people who are + + + align:start position:0% +a game, but uh simulating people who are +delusional schizophrenic by either + + align:start position:0% +delusional schizophrenic by either + + + align:start position:0% +delusional schizophrenic by either +having every player have a a separate + + align:start position:0% +having every player have a a separate + + + align:start position:0% +having every player have a a separate +like audio track playing in their ear as + + align:start position:0% +like audio track playing in their ear as + + + align:start position:0% +like audio track playing in their ear as +they play. So there's like voices + + align:start position:0% +they play. So there's like voices + + + align:start position:0% +they play. So there's like voices +speaking to them and they have different + + align:start position:0% +speaking to them and they have different + + + align:start position:0% +speaking to them and they have different +audio experiences or having just one + + align:start position:0% +audio experiences or having just one + + + align:start position:0% +audio experiences or having just one +speaker that everyone can hear that uh + + align:start position:0% +speaker that everyone can hear that uh + + + align:start position:0% +speaker that everyone can hear that uh +that is playing audio. just + + align:start position:0% +that is playing audio. just + + + align:start position:0% +that is playing audio. just +incorporating audio into the experience + + align:start position:0% +incorporating audio into the experience + + + align:start position:0% +incorporating audio into the experience +to simulate in some way the internal + + align:start position:0% +to simulate in some way the internal + + + align:start position:0% +to simulate in some way the internal +thought process and perhaps these + + align:start position:0% +thought process and perhaps these + + + align:start position:0% +thought process and perhaps these +delusional thoughts that sort of you + + align:start position:0% +delusional thoughts that sort of you + + + align:start position:0% +delusional thoughts that sort of you +know the voice that tells you to go kill + + align:start position:0% +know the voice that tells you to go kill + + + align:start position:0% +know the voice that tells you to go kill +your mother and whatnot which isn't you + + align:start position:0% +your mother and whatnot which isn't you + + + align:start position:0% +your mother and whatnot which isn't you +know documented issue + + align:start position:0% +know documented issue + + + align:start position:0% +know documented issue +>> now this particular game doesn't have to + + align:start position:0% +>> now this particular game doesn't have to + + + align:start position:0% +>> now this particular game doesn't have to +be a board game doesn't have to be a + + align:start position:0% +be a board game doesn't have to be a + + + align:start position:0% +be a board game doesn't have to be a +card game you have a lot more + + align:start position:0% +card game you have a lot more + + + align:start position:0% +card game you have a lot more +flexibility on how what what you want to + + align:start position:0% +flexibility on how what what you want to + + + align:start position:0% +flexibility on how what what you want to +do I would suggest steering away from + + align:start position:0% +do I would suggest steering away from + + + align:start position:0% +do I would suggest steering away from +doing anything that requires digital + + align:start position:0% +doing anything that requires digital + + + align:start position:0% +doing anything that requires digital +logic like uh you know but you know MP3 + + align:start position:0% +logic like uh you know but you know MP3 + + + align:start position:0% +logic like uh you know but you know MP3 +players will be + + align:start position:0% +players will be + + + align:start position:0% +players will be +>> right exactly so something like that um + + align:start position:0% +>> right exactly so something like that um + + + align:start position:0% +>> right exactly so something like that um +so that's the first idea second thing + + align:start position:0% +so that's the first idea second thing + + + align:start position:0% +so that's the first idea second thing +would be a board game where you're in + + align:start position:0% +would be a board game where you're in + + + align:start position:0% +would be a board game where you're in +charge of managing a ward it's just a + + align:start position:0% +charge of managing a ward it's just a + + + align:start position:0% +charge of managing a ward it's just a +logistical making sure that you don't + + align:start position:0% +logistical making sure that you don't + + + align:start position:0% +logistical making sure that you don't +leave anyone neglected or or forget. + + align:start position:0% +leave anyone neglected or or forget. + + + align:start position:0% +leave anyone neglected or or forget. +>> Oh, definitely. Okay. So, yeah, people + + align:start position:0% +>> Oh, definitely. Okay. So, yeah, people + + + align:start position:0% +>> Oh, definitely. Okay. So, yeah, people +will + + align:start position:0% +will + + + align:start position:0% +will +>> So, you know, patients have their + + align:start position:0% +>> So, you know, patients have their + + + align:start position:0% +>> So, you know, patients have their +favorite nurse, you know, and they have + + align:start position:0% +favorite nurse, you know, and they have + + + align:start position:0% +favorite nurse, you know, and they have +sort of hidden issues that you have to + + align:start position:0% +sort of hidden issues that you have to + + + align:start position:0% +sort of hidden issues that you have to +uncover and and deal with. And if you + + align:start position:0% +uncover and and deal with. And if you + + + align:start position:0% +uncover and and deal with. And if you +leave something unattended and someone, + + align:start position:0% +leave something unattended and someone, + + + align:start position:0% +leave something unattended and someone, +you know, goes over, then they become + + align:start position:0% +you know, goes over, then they become + + + align:start position:0% +you know, goes over, then they become +violent. And so, you're kind of trying + + align:start position:0% +violent. And so, you're kind of trying + + + align:start position:0% +violent. And so, you're kind of trying +to make sure. And the the third idea + + align:start position:0% +to make sure. And the the third idea + + + align:start position:0% +to make sure. And the the third idea +would be to have uh one player pay as + + align:start position:0% +would be to have uh one player pay as + + + align:start position:0% +would be to have uh one player pay as +the patient and to simulate the their + + align:start position:0% +the patient and to simulate the their + + + align:start position:0% +the patient and to simulate the their +inability to communicate properly for + + align:start position:0% +inability to communicate properly for + + + align:start position:0% +inability to communicate properly for +whatever reason. the information of + + align:start position:0% +whatever reason. the information of + + + align:start position:0% +whatever reason. the information of +their own condition is hidden hidden + + align:start position:0% +their own condition is hidden hidden + + + align:start position:0% +their own condition is hidden hidden +from the player. And so, um, try to + + align:start position:0% +from the player. And so, um, try to + + + align:start position:0% +from the player. And so, um, try to +create a game experience that is + + align:start position:0% +create a game experience that is + + + align:start position:0% +create a game experience that is +genuinely frustrating because the the + + align:start position:0% +genuinely frustrating because the the + + + align:start position:0% +genuinely frustrating because the the +the player doesn't quite know what's + + align:start position:0% +the player doesn't quite know what's + + + align:start position:0% +the player doesn't quite know what's +wrong with them and can't articulate it + + align:start position:0% +wrong with them and can't articulate it + + + align:start position:0% +wrong with them and can't articulate it +properly and the other players are in + + align:start position:0% +properly and the other players are in + + + align:start position:0% +properly and the other players are in +charge of of finding it out and creates + + align:start position:0% +charge of of finding it out and creates + + + align:start position:0% +charge of of finding it out and creates +some sort of time constraint thing. So, + + align:start position:0% +some sort of time constraint thing. So, + + + align:start position:0% +some sort of time constraint thing. So, +it gets heated and and like + + align:start position:0% +it gets heated and and like + + + align:start position:0% +it gets heated and and like +>> there are a bunch of improv games that + + align:start position:0% +>> there are a bunch of improv games that + + + align:start position:0% +>> there are a bunch of improv games that +are exactly that. It's like I have + + align:start position:0% +are exactly that. It's like I have + + + align:start position:0% +are exactly that. It's like I have +something about me, but I can't tell you + + align:start position:0% +something about me, but I can't tell you + + + align:start position:0% +something about me, but I can't tell you +what it is. + + align:start position:0% +what it is. + + + align:start position:0% +what it is. +>> But, but you know, if the player doesn't + + align:start position:0% +>> But, but you know, if the player doesn't + + + align:start position:0% +>> But, but you know, if the player doesn't +even know that, it can get really + + align:start position:0% +even know that, it can get really + + + align:start position:0% +even know that, it can get really +>> right. Yeah. That's like the game where + + align:start position:0% +>> right. Yeah. That's like the game where + + + align:start position:0% +>> right. Yeah. That's like the game where +you have I can't remember what it's + + align:start position:0% +you have I can't remember what it's + + + align:start position:0% +you have I can't remember what it's +called, but the one where you have you + + align:start position:0% +called, but the one where you have you + + + align:start position:0% +called, but the one where you have you +try to make the other person say a word, + + align:start position:0% +try to make the other person say a word, + + + align:start position:0% +try to make the other person say a word, +but you can't use a certain series of + + align:start position:0% +but you can't use a certain series of + + + align:start position:0% +but you can't use a certain series of +like + + align:start position:0% + + + + align:start position:0% + +>> I just wanted to say on the simulating + + align:start position:0% +>> I just wanted to say on the simulating + + + align:start position:0% +>> I just wanted to say on the simulating +schizophrenia with audio tape. + + align:start position:0% +schizophrenia with audio tape. + + + align:start position:0% +schizophrenia with audio tape. +>> Um I've been part of RPGs which have + + align:start position:0% +>> Um I've been part of RPGs which have + + + align:start position:0% +>> Um I've been part of RPGs which have +done that well. So like live action role + + align:start position:0% +done that well. So like live action role + + + align:start position:0% +done that well. So like live action role +playing stuff which did which did it + + align:start position:0% +playing stuff which did which did it + + + align:start position:0% +playing stuff which did which did it +really well. It actually works. So um I + + align:start position:0% +really well. It actually works. So um I + + + align:start position:0% +really well. It actually works. So um I +recommend that it's actually quite + + align:start position:0% +recommend that it's actually quite + + + align:start position:0% +recommend that it's actually quite +>> exploring that further. + + align:start position:0% +>> exploring that further. + + + align:start position:0% +>> exploring that further. +>> Yeah. I mean it's been tried in a + + align:start position:0% +>> Yeah. I mean it's been tried in a + + + align:start position:0% +>> Yeah. I mean it's been tried in a +setting which I've seen before and + + align:start position:0% +setting which I've seen before and + + + align:start position:0% +setting which I've seen before and +worked really well. So I think it could + + align:start position:0% +worked really well. So I think it could + + + align:start position:0% +worked really well. So I think it could +work out. + + align:start position:0% +work out. + + + align:start position:0% +work out. +>> Mhm. + + align:start position:0% +>> Mhm. + + + align:start position:0% +>> Mhm. +>> You can do a refinement on that idea. + + align:start position:0% +>> You can do a refinement on that idea. + + + align:start position:0% +>> You can do a refinement on that idea. +>> Uh + + align:start position:0% +>> Uh + + + align:start position:0% +>> Uh +>> um so I know one of the main things that + + align:start position:0% +>> um so I know one of the main things that + + + align:start position:0% +>> um so I know one of the main things that +he was talking about is like knowing + + align:start position:0% +he was talking about is like knowing + + + align:start position:0% +he was talking about is like knowing +what to do and like just having the like + + align:start position:0% +what to do and like just having the like + + + align:start position:0% +what to do and like just having the like +going through the process of like what + + align:start position:0% +going through the process of like what + + + align:start position:0% +going through the process of like what +happens when somebody does something. + + align:start position:0% +happens when somebody does something. + + + align:start position:0% +happens when somebody does something. +And so that brought to mind like D and D + + align:start position:0% +And so that brought to mind like D and D + + + align:start position:0% +And so that brought to mind like D and D +and how like you have to prepare before + + align:start position:0% +and how like you have to prepare before + + + align:start position:0% +and how like you have to prepare before +the encounter and then in the encounter + + align:start position:0% +the encounter and then in the encounter + + + align:start position:0% +the encounter and then in the encounter +like you have certain actions that you + + align:start position:0% +like you have certain actions that you + + + align:start position:0% +like you have certain actions that you +can do like calm through speech, calm + + align:start position:0% +can do like calm through speech, calm + + + align:start position:0% +can do like calm through speech, calm +through, you know, presenting some + + align:start position:0% +through, you know, presenting some + + + align:start position:0% +through, you know, presenting some +object or some idea or whatever. Uh + + align:start position:0% +object or some idea or whatever. Uh + + + align:start position:0% +object or some idea or whatever. Uh +which I think would map pretty easily to + + align:start position:0% +which I think would map pretty easily to + + + align:start position:0% +which I think would map pretty easily to +the D&D space. Um and then you could + + align:start position:0% +the D&D space. Um and then you could + + + align:start position:0% +the D&D space. Um and then you could +also like you know you have certain + + align:start position:0% +also like you know you have certain + + + align:start position:0% +also like you know you have certain +abilities that are natural to your + + align:start position:0% +abilities that are natural to your + + + align:start position:0% +abilities that are natural to your +character like you're very charismatic + + align:start position:0% +character like you're very charismatic + + + align:start position:0% +character like you're very charismatic +which makes some things easier and such. + + align:start position:0% +which makes some things easier and such. + + + align:start position:0% +which makes some things easier and such. +I think that + + align:start position:0% +I think that + + + align:start position:0% +I think that +>> so + + align:start position:0% +>> so + + + align:start position:0% +>> so +>> so simplified D and D to um to handle + + align:start position:0% +>> so simplified D and D to um to handle + + + align:start position:0% +>> so simplified D and D to um to handle +interactions with patients. + + align:start position:0% +interactions with patients. + + + align:start position:0% +interactions with patients. +>> So so tabletop RPG style, + + align:start position:0% +>> So so tabletop RPG style, + + + align:start position:0% +>> So so tabletop RPG style, +>> right? + + align:start position:0% +>> right? + + + align:start position:0% +>> right? +>> And the kinds of things that you wanted + + align:start position:0% +>> And the kinds of things that you wanted + + + align:start position:0% +>> And the kinds of things that you wanted +to emphasize were things like + + align:start position:0% +to emphasize were things like + + + align:start position:0% +to emphasize were things like +preparation uh and sort of playing out + + align:start position:0% +preparation uh and sort of playing out + + + align:start position:0% +preparation uh and sort of playing out +your actual skills, + + align:start position:0% +your actual skills, + + + align:start position:0% +your actual skills, +>> right? + + align:start position:0% +>> right? + + + align:start position:0% +>> right? +>> You know the things that you're good at, + + align:start position:0% +>> You know the things that you're good at, + + + align:start position:0% +>> You know the things that you're good at, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +>> So natural skills + + align:start position:0% +>> So natural skills + + + align:start position:0% +>> So natural skills +and uh preparation + + align:start position:0% + + + + align:start position:0% + +All right. So, I kind of had an idea for + + align:start position:0% +All right. So, I kind of had an idea for + + + align:start position:0% +All right. So, I kind of had an idea for +a game that could potentially be a card + + align:start position:0% +a game that could potentially be a card + + + align:start position:0% +a game that could potentially be a card +game where the player who's playing as + + align:start position:0% +game where the player who's playing as + + + align:start position:0% +game where the player who's playing as +the patient and the player who's playing + + align:start position:0% +the patient and the player who's playing + + + align:start position:0% +the patient and the player who's playing +as the doctor are operating under + + align:start position:0% +as the doctor are operating under + + + align:start position:0% +as the doctor are operating under +different rules. And one of the main + + align:start position:0% +different rules. And one of the main + + + align:start position:0% +different rules. And one of the main +points of the game is that they don't + + align:start position:0% +points of the game is that they don't + + + align:start position:0% +points of the game is that they don't +act they're not actually aware of the + + align:start position:0% +act they're not actually aware of the + + + align:start position:0% +act they're not actually aware of the +other player's rules. So, for instance, + + align:start position:0% +other player's rules. So, for instance, + + + align:start position:0% +other player's rules. So, for instance, +the patient could have certain goals + + align:start position:0% +the patient could have certain goals + + + align:start position:0% +the patient could have certain goals +which he's trying to achieve, + + align:start position:0% +which he's trying to achieve, + + + align:start position:0% +which he's trying to achieve, +>> but he is unaware which of these goals + + align:start position:0% +>> but he is unaware which of these goals + + + align:start position:0% +>> but he is unaware which of these goals +is like completely unreasonable to the + + align:start position:0% +is like completely unreasonable to the + + + align:start position:0% +is like completely unreasonable to the +doctor. And the game, the doctor has + + align:start position:0% +doctor. And the game, the doctor has + + + align:start position:0% +doctor. And the game, the doctor has +certain actions he can take and and is + + align:start position:0% +certain actions he can take and and is + + + align:start position:0% +certain actions he can take and and is +unaware which of these are going to be + + align:start position:0% +unaware which of these are going to be + + + align:start position:0% +unaware which of these are going to be +threatening to the patient. And so there + + align:start position:0% +threatening to the patient. And so there + + + align:start position:0% +threatening to the patient. And so there +there could be an instance where the + + align:start position:0% +there could be an instance where the + + + align:start position:0% +there could be an instance where the +patient actually believes the only way + + align:start position:0% +patient actually believes the only way + + + align:start position:0% +patient actually believes the only way +he is capable of winning the game is by + + align:start position:0% +he is capable of winning the game is by + + + align:start position:0% +he is capable of winning the game is by +using violence. And so that could be one + + align:start position:0% +using violence. And so that could be one + + + align:start position:0% +using violence. And so that could be one +of the end conditions, + + align:start position:0% +of the end conditions, + + + align:start position:0% +of the end conditions, +>> right? + + align:start position:0% +>> right? + + + align:start position:0% +>> right? +>> So So sure and then you you kind of have + + align:start position:0% +>> So So sure and then you you kind of have + + + align:start position:0% +>> So So sure and then you you kind of have +to did you + + align:start position:0% +to did you + + + align:start position:0% +to did you +again to + + align:start position:0% +again to + + + align:start position:0% +again to +>> uh I really like the idea that uh a + + align:start position:0% +>> uh I really like the idea that uh a + + + align:start position:0% +>> uh I really like the idea that uh a +psychiatrist has to really keep their + + align:start position:0% +psychiatrist has to really keep their + + + align:start position:0% +psychiatrist has to really keep their +composure when they're dealing with a + + align:start position:0% +composure when they're dealing with a + + + align:start position:0% +composure when they're dealing with a +violent person. they can't raise their + + align:start position:0% +violent person. they can't raise their + + + align:start position:0% +violent person. they can't raise their +voice, they have to keep them a certain + + align:start position:0% +voice, they have to keep them a certain + + + align:start position:0% +voice, they have to keep them a certain +distance and they can't uh you know seem + + align:start position:0% +distance and they can't uh you know seem + + + align:start position:0% +distance and they can't uh you know seem +upset for whatever reason. So a sort of + + align:start position:0% +upset for whatever reason. So a sort of + + + align:start position:0% +upset for whatever reason. So a sort of +a party game idea, you could have, you + + align:start position:0% +a party game idea, you could have, you + + + align:start position:0% +a party game idea, you could have, you +know, two people um basically one person + + align:start position:0% +know, two people um basically one person + + + align:start position:0% +know, two people um basically one person +would just have to be throwing insult at + + align:start position:0% +would just have to be throwing insult at + + + align:start position:0% +would just have to be throwing insult at +the other person and the person who's + + align:start position:0% +the other person and the person who's + + + align:start position:0% +the other person and the person who's +receiving the insults would just have to + + align:start position:0% +receiving the insults would just have to + + + align:start position:0% +receiving the insults would just have to +stay calm the whole time and continue + + align:start position:0% +stay calm the whole time and continue + + + align:start position:0% +stay calm the whole time and continue +talking, which is really hard to do even + + align:start position:0% +talking, which is really hard to do even + + + align:start position:0% +talking, which is really hard to do even +if you know it's coming at you. + + align:start position:0% +if you know it's coming at you. + + + align:start position:0% +if you know it's coming at you. +>> So like keep your cool. I mean that that + + align:start position:0% +>> So like keep your cool. I mean that that + + + align:start position:0% +>> So like keep your cool. I mean that that +that could be a game where you're like + + align:start position:0% +that could be a game where you're like + + + align:start position:0% +that could be a game where you're like +literally insulting someone or it could + + align:start position:0% +literally insulting someone or it could + + + align:start position:0% +literally insulting someone or it could +be a thing where you're playing a + + align:start position:0% +be a thing where you're playing a + + + align:start position:0% +be a thing where you're playing a +character with a certain amount of like + + align:start position:0% +character with a certain amount of like + + + align:start position:0% +character with a certain amount of like +composure points or something like that + + align:start position:0% +composure points or something like that + + + align:start position:0% +composure points or something like that +and you know you're sort of like + + align:start position:0% +and you know you're sort of like + + + align:start position:0% +and you know you're sort of like +planning actions to try to maintain + + align:start position:0% +planning actions to try to maintain + + + align:start position:0% +planning actions to try to maintain +those + + align:start position:0% +those + + + align:start position:0% +those +>> uh and different tactics to be able to + + align:start position:0% +>> uh and different tactics to be able to + + + align:start position:0% +>> uh and different tactics to be able to +increase those or decrease those + + align:start position:0% +increase those or decrease those + + + align:start position:0% +increase those or decrease those +>> back uh co-op type game where you are a + + align:start position:0% +>> back uh co-op type game where you are a + + + align:start position:0% +>> back uh co-op type game where you are a +bunch of nurses trying to basically take + + align:start position:0% +bunch of nurses trying to basically take + + + align:start position:0% +bunch of nurses trying to basically take +care of the ward. So, it's a lot like + + align:start position:0% +care of the ward. So, it's a lot like + + + align:start position:0% +care of the ward. So, it's a lot like +Jeremy's uh Diner Dash style game, + + align:start position:0% +Jeremy's uh Diner Dash style game, + + + align:start position:0% +Jeremy's uh Diner Dash style game, +>> except you have a limitation to how many + + align:start position:0% +>> except you have a limitation to how many + + + align:start position:0% +>> except you have a limitation to how many +you can actually do at once. So, you + + align:start position:0% +you can actually do at once. So, you + + + align:start position:0% +you can actually do at once. So, you +will be forced to neglect one every so + + align:start position:0% +will be forced to neglect one every so + + + align:start position:0% +will be forced to neglect one every so +often. + + align:start position:0% +often. + + + align:start position:0% +often. +>> Patient one neglect one patient, one + + align:start position:0% +>> Patient one neglect one patient, one + + + align:start position:0% +>> Patient one neglect one patient, one +patient, one + + align:start position:0% +patient, one + + + align:start position:0% +patient, one +>> some nurses will get sick and they'll + + align:start position:0% +>> some nurses will get sick and they'll + + + align:start position:0% +>> some nurses will get sick and they'll +have to leave. + + align:start position:0% + + + + align:start position:0% + +>> So, so or or rather you have limited + + align:start position:0% +>> So, so or or rather you have limited + + + align:start position:0% +>> So, so or or rather you have limited +resources uh not quite nearly enough to + + align:start position:0% +resources uh not quite nearly enough to + + + align:start position:0% +resources uh not quite nearly enough to +deal with every single crisis that's + + align:start position:0% +deal with every single crisis that's + + + align:start position:0% +deal with every single crisis that's +going to happen. + + align:start position:0% +going to happen. + + + align:start position:0% +going to happen. +>> Okay. Um, so I the one thing that I kind + + align:start position:0% +>> Okay. Um, so I the one thing that I kind + + + align:start position:0% +>> Okay. Um, so I the one thing that I kind +of found interesting in like reading the + + align:start position:0% +of found interesting in like reading the + + + align:start position:0% +of found interesting in like reading the +stuff is that statistically the amount + + align:start position:0% +stuff is that statistically the amount + + + align:start position:0% +stuff is that statistically the amount +of violence that happens like with + + align:start position:0% +of violence that happens like with + + + align:start position:0% +of violence that happens like with +mental patients is is not actually like + + align:start position:0% +mental patients is is not actually like + + + align:start position:0% +mental patients is is not actually like +that different from the amount of + + align:start position:0% +that different from the amount of + + + align:start position:0% +that different from the amount of +violence that happens in general + + align:start position:0% +violence that happens in general + + + align:start position:0% +violence that happens in general +population. + + align:start position:0% +population. + + + align:start position:0% +population. +>> Um, and you know they talked about how + + align:start position:0% +>> Um, and you know they talked about how + + + align:start position:0% +>> Um, and you know they talked about how +like people going through this and like + + align:start position:0% +like people going through this and like + + + align:start position:0% +like people going through this and like +deciding to go into the profession might + + align:start position:0% +deciding to go into the profession might + + + align:start position:0% +deciding to go into the profession might +actually second guess themselves because + + align:start position:0% +actually second guess themselves because + + + align:start position:0% +actually second guess themselves because +they have this perception that there's + + align:start position:0% +they have this perception that there's + + + align:start position:0% +they have this perception that there's +more violence. So I think like + + align:start position:0% +more violence. So I think like + + + align:start position:0% +more violence. So I think like +incorporating something where you have + + align:start position:0% +incorporating something where you have + + + align:start position:0% +incorporating something where you have +um life in the ward and life outside of + + align:start position:0% +um life in the ward and life outside of + + + align:start position:0% +um life in the ward and life outside of +it to just like so you you incorporate + + align:start position:0% +it to just like so you you incorporate + + + align:start position:0% +it to just like so you you incorporate +both the things where you're trying to + + align:start position:0% +both the things where you're trying to + + + align:start position:0% +both the things where you're trying to +deal with the patients but you're also + + align:start position:0% +deal with the patients but you're also + + + align:start position:0% +deal with the patients but you're also +reinforcing this idea that like it's not + + align:start position:0% +reinforcing this idea that like it's not + + + align:start position:0% +reinforcing this idea that like it's not +it's not like significantly more + + align:start position:0% +it's not like significantly more + + + align:start position:0% +it's not like significantly more +dangerous than real life is. + + align:start position:0% +dangerous than real life is. + + + align:start position:0% +dangerous than real life is. +>> None of your patients stab you then you + + align:start position:0% +>> None of your patients stab you then you + + + align:start position:0% +>> None of your patients stab you then you +get in your way home. + + align:start position:0% +get in your way home. + + + align:start position:0% +get in your way home. +>> Yeah. Like something like that like you + + align:start position:0% +>> Yeah. Like something like that like you + + + align:start position:0% +>> Yeah. Like something like that like you +know it's it's just life. I mean I mean + + align:start position:0% +know it's it's just life. I mean I mean + + + align:start position:0% +know it's it's just life. I mean I mean +one thing one thing that would give you + + align:start position:0% +one thing one thing that would give you + + + align:start position:0% +one thing one thing that would give you +the uh you may put it up one one thing + + align:start position:0% +the uh you may put it up one one thing + + + align:start position:0% +the uh you may put it up one one thing +that could be really attractive is that + + align:start position:0% +that could be really attractive is that + + + align:start position:0% +that could be really attractive is that +that now broadens your audience to + + align:start position:0% +that now broadens your audience to + + + align:start position:0% +that now broadens your audience to +people who aren't just + + align:start position:0% +people who aren't just + + + align:start position:0% +people who aren't just +psychiatric + + align:start position:0% +psychiatric + + + align:start position:0% +psychiatric +>> right + + align:start position:0% +>> right + + + align:start position:0% +>> right +>> so I like the idea of the patient and + + align:start position:0% +>> so I like the idea of the patient and + + + align:start position:0% +>> so I like the idea of the patient and +doctor having different rules goals + + align:start position:0% +doctor having different rules goals + + + align:start position:0% +doctor having different rules goals +triggers etc. Um, but I also like the + + align:start position:0% +triggers etc. Um, but I also like the + + + align:start position:0% +triggers etc. Um, but I also like the +idea of incorporating like an escalation + + align:start position:0% +idea of incorporating like an escalation + + + align:start position:0% +idea of incorporating like an escalation +and deescalation into the conflict + + align:start position:0% +and deescalation into the conflict + + + align:start position:0% +and deescalation into the conflict +between the two of them. + + align:start position:0% +between the two of them. + + + align:start position:0% +between the two of them. +>> So I feel like part of the thing which + + align:start position:0% +>> So I feel like part of the thing which + + + align:start position:0% +>> So I feel like part of the thing which +was really compelling about the role + + align:start position:0% +was really compelling about the role + + + align:start position:0% +was really compelling about the role +playing scenario that they showed was um + + align:start position:0% +playing scenario that they showed was um + + + align:start position:0% +playing scenario that they showed was um +there was there was the sense in which + + align:start position:0% +there was there was the sense in which + + + align:start position:0% +there was there was the sense in which +the doctor can say things which can + + align:start position:0% +the doctor can say things which can + + + align:start position:0% +the doctor can say things which can +escalate or deescalate this the + + align:start position:0% +escalate or deescalate this the + + + align:start position:0% +escalate or deescalate this the +situation, right? Make it more or less + + align:start position:0% +situation, right? Make it more or less + + + align:start position:0% +situation, right? Make it more or less +likely that things will go in a good or + + align:start position:0% +likely that things will go in a good or + + + align:start position:0% +likely that things will go in a good or +bad way. And like one way which we could + + align:start position:0% +bad way. And like one way which we could + + + align:start position:0% +bad way. And like one way which we could +do which that could be done in partially + + align:start position:0% +do which that could be done in partially + + + align:start position:0% +do which that could be done in partially +through roles would be to have like + + align:start position:0% +through roles would be to have like + + + align:start position:0% +through roles would be to have like +hidden keywords which the um which the + + align:start position:0% +hidden keywords which the um which the + + + align:start position:0% +hidden keywords which the um which the +patient responds to or what have you and + + align:start position:0% +patient responds to or what have you and + + + align:start position:0% +patient responds to or what have you and +that kind of moves them into a different + + align:start position:0% +that kind of moves them into a different + + + align:start position:0% +that kind of moves them into a different +state and then like transitioning + + align:start position:0% +state and then like transitioning + + + align:start position:0% +state and then like transitioning +between these two states um changes the + + align:start position:0% +between these two states um changes the + + + align:start position:0% +between these two states um changes the +goals which the the patient has. They + + align:start position:0% +goals which the the patient has. They + + + align:start position:0% +goals which the the patient has. They +may be intent upon trying to get nurse + + align:start position:0% +may be intent upon trying to get nurse + + + align:start position:0% +may be intent upon trying to get nurse +what was the name nurse's name Dave or + + align:start position:0% +what was the name nurse's name Dave or + + + align:start position:0% +what was the name nurse's name Dave or +>> nurse John but for that as they get + + align:start position:0% +>> nurse John but for that as they get + + + align:start position:0% +>> nurse John but for that as they get +deescalated then they just want to + + align:start position:0% +deescalated then they just want to + + + align:start position:0% +deescalated then they just want to +change their meds but then as they get + + align:start position:0% +change their meds but then as they get + + + align:start position:0% +change their meds but then as they get +dis + + align:start position:0% +dis + + + align:start position:0% +dis +um deescalated from that they may just + + align:start position:0% +um deescalated from that they may just + + + align:start position:0% +um deescalated from that they may just +want to go home or something like that + + align:start position:0% +want to go home or something like that + + + align:start position:0% +want to go home or something like that +>> just coming up with the rules that model + + align:start position:0% +>> just coming up with the rules that model + + + align:start position:0% +>> just coming up with the rules that model +what an unreasonable patient + + align:start position:0% +what an unreasonable patient + + + align:start position:0% +what an unreasonable patient +>> Yeah. Yeah. + + align:start position:0% +>> Yeah. Yeah. + + + align:start position:0% +>> Yeah. Yeah. +to give up or or what would be he + + align:start position:0% +to give up or or what would be he + + + align:start position:0% +to give up or or what would be he +willing to give up + + align:start position:0% +willing to give up + + + align:start position:0% +willing to give up +>> and and and actually putting somebody in + + align:start position:0% +>> and and and actually putting somebody in + + + align:start position:0% +>> and and and actually putting somebody in +the shoes of that is actually really + + align:start position:0% +the shoes of that is actually really + + + align:start position:0% +the shoes of that is actually really +useful to sort of think about what I can + + align:start position:0% +useful to sort of think about what I can + + + align:start position:0% +useful to sort of think about what I can +do as a doctor. + + align:start position:0% +do as a doctor. + + + align:start position:0% +do as a doctor. +>> Uh so there was this game I used to play + + align:start position:0% +>> Uh so there was this game I used to play + + + align:start position:0% +>> Uh so there was this game I used to play +in my family where like you're given a + + align:start position:0% +in my family where like you're given a + + + align:start position:0% +in my family where like you're given a +scenario and like a certain number of + + align:start position:0% +scenario and like a certain number of + + + align:start position:0% +scenario and like a certain number of +words that you can't use but like you + + align:start position:0% +words that you can't use but like you + + + align:start position:0% +words that you can't use but like you +want someone to like guess them. So + + align:start position:0% +want someone to like guess them. So + + + align:start position:0% +want someone to like guess them. So +essentially like it's like you choose + + align:start position:0% +essentially like it's like you choose + + + align:start position:0% +essentially like it's like you choose +random words and you have a scenario and + + align:start position:0% +random words and you have a scenario and + + + align:start position:0% +random words and you have a scenario and +like very similar to what you were + + align:start position:0% +like very similar to what you were + + + align:start position:0% +like very similar to what you were +saying where like certain keywords do + + align:start position:0% +saying where like certain keywords do + + + align:start position:0% +saying where like certain keywords do +certain things but like you have to you + + align:start position:0% +certain things but like you have to you + + + align:start position:0% +certain things but like you have to you +have to somehow create like the best + + align:start position:0% +have to somehow create like the best + + + align:start position:0% +have to somehow create like the best +story or the best like calm down like + + align:start position:0% +story or the best like calm down like + + + align:start position:0% +story or the best like calm down like +passage to read to the patient and then + + align:start position:0% +passage to read to the patient and then + + + align:start position:0% +passage to read to the patient and then +like there's some arbit like arbitrator + + align:start position:0% +like there's some arbit like arbitrator + + + align:start position:0% +like there's some arbit like arbitrator +like the GM of the game that like + + align:start position:0% +like the GM of the game that like + + + align:start position:0% +like the GM of the game that like +decides like which of the three people + + align:start position:0% +decides like which of the three people + + + align:start position:0% +decides like which of the three people +that were playing like which one had the + + align:start position:0% +that were playing like which one had the + + + align:start position:0% +that were playing like which one had the +best story out of those um to sort of + + align:start position:0% +best story out of those um to sort of + + + align:start position:0% +best story out of those um to sort of +get you to like have to come up with + + align:start position:0% +get you to like have to come up with + + + align:start position:0% +get you to like have to come up with +something to deal with like you know you + + align:start position:0% +something to deal with like you know you + + + align:start position:0% +something to deal with like you know you +need nurse John right away. Best way to + + align:start position:0% +need nurse John right away. Best way to + + + align:start position:0% +need nurse John right away. Best way to +deal with that for + + align:start position:0% +deal with that for + + + align:start position:0% +deal with that for +>> I mean you you you could do a thing + + align:start position:0% +>> I mean you you you could do a thing + + + align:start position:0% +>> I mean you you you could do a thing +where you had to create a story out of a + + align:start position:0% +where you had to create a story out of a + + + align:start position:0% +where you had to create a story out of a +randomized collection of elements maybe + + align:start position:0% +randomized collection of elements maybe + + + align:start position:0% +randomized collection of elements maybe +cards you know uh but then some number + + align:start position:0% +cards you know uh but then some number + + + align:start position:0% +cards you know uh but then some number +of those cards specifically the other + + align:start position:0% +of those cards specifically the other + + + align:start position:0% +of those cards specifically the other +player or maybe there's a game master + + align:start position:0% +player or maybe there's a game master + + + align:start position:0% +player or maybe there's a game master +player specifically just saying that + + align:start position:0% +player specifically just saying that + + + align:start position:0% +player specifically just saying that +knows internally that you're not + + align:start position:0% +knows internally that you're not + + + align:start position:0% +knows internally that you're not +supposed to be able to use those words + + align:start position:0% +supposed to be able to use those words + + + align:start position:0% +supposed to be able to use those words +and there some 20 questions type of way + + align:start position:0% +and there some 20 questions type of way + + + align:start position:0% +and there some 20 questions type of way +to be able to try to figure out what + + align:start position:0% +to be able to try to figure out what + + + align:start position:0% +to be able to try to figure out what +those currents are without the language. + + align:start position:0% +those currents are without the language. + + + align:start position:0% +those currents are without the language. +So that that that would be like a doctor + + align:start position:0% +So that that that would be like a doctor + + + align:start position:0% +So that that that would be like a doctor +trying to figure out what they're + + align:start position:0% +trying to figure out what they're + + + align:start position:0% +trying to figure out what they're +dealing with, you know, while that + + align:start position:0% + + + + align:start position:0% + +>> you could make that game like guess who + + align:start position:0% +>> you could make that game like guess who + + + align:start position:0% +>> you could make that game like guess who +where each person like draws a card and + + align:start position:0% +where each person like draws a card and + + + align:start position:0% +where each person like draws a card and +you're allowed to like give a statement + + align:start position:0% +you're allowed to like give a statement + + + align:start position:0% +you're allowed to like give a statement +to the other person or ask them + + align:start position:0% +to the other person or ask them + + + align:start position:0% +to the other person or ask them +something and then you see whether like + + align:start position:0% +something and then you see whether like + + + align:start position:0% +something and then you see whether like +escalate or deescalate and each + + align:start position:0% +escalate or deescalate and each + + + align:start position:0% +escalate or deescalate and each +individual card has like traits where + + align:start position:0% +individual card has like traits where + + + align:start position:0% +individual card has like traits where +you talk about this that's bad, you talk + + align:start position:0% +you talk about this that's bad, you talk + + + align:start position:0% +you talk about this that's bad, you talk +about this that's good. + + align:start position:0% +about this that's good. + + + align:start position:0% +about this that's good. +>> I I'm not familiar with guess. So, uh, + + align:start position:0% +>> I I'm not familiar with guess. So, uh, + + + align:start position:0% +>> I I'm not familiar with guess. So, uh, +okay. So, it's not really that much like + + align:start position:0% +okay. So, it's not really that much like + + + align:start position:0% +okay. So, it's not really that much like +Guess Who. + + align:start position:0% + + + + align:start position:0% + +>> 20 questions. Is that + + align:start position:0% +>> 20 questions. Is that + + + align:start position:0% +>> 20 questions. Is that +>> the idea thing of is everyone just you + + align:start position:0% +>> the idea thing of is everyone just you + + + align:start position:0% +>> the idea thing of is everyone just you +have a whole bunch of character cards + + align:start position:0% +have a whole bunch of character cards + + + align:start position:0% +have a whole bunch of character cards +and each of them have traits like watch + + align:start position:0% +and each of them have traits like watch + + + align:start position:0% +and each of them have traits like watch +this? If you say this, they'll get + + align:start position:0% +this? If you say this, they'll get + + + align:start position:0% +this? If you say this, they'll get +upset. If you say this, it's not very + + align:start position:0% +upset. If you say this, it's not very + + + align:start position:0% +upset. If you say this, it's not very +fully fleshed out, but everyone just + + align:start position:0% +fully fleshed out, but everyone just + + + align:start position:0% +fully fleshed out, but everyone just +like randomly draws traits and you take + + align:start position:0% +like randomly draws traits and you take + + + align:start position:0% +like randomly draws traits and you take +turns like speaking to each other and + + align:start position:0% +turns like speaking to each other and + + + align:start position:0% +turns like speaking to each other and +then the patients either get like will + + align:start position:0% +then the patients either get like will + + + align:start position:0% +then the patients either get like will +respond and then either get like more + + align:start position:0% +respond and then either get like more + + + align:start position:0% +respond and then either get like more +angry or sing. + + align:start position:0% +angry or sing. + + + align:start position:0% +angry or sing. +>> So, It's almost like your like your role + + align:start position:0% +>> So, It's almost like your like your role + + + align:start position:0% +>> So, It's almost like your like your role +is a collection of randomized traits or + + align:start position:0% +is a collection of randomized traits or + + + align:start position:0% +is a collection of randomized traits or +randomized behavioral + + align:start position:0% +randomized behavioral + + + align:start position:0% +randomized behavioral +uh rules. + + align:start position:0% +uh rules. + + + align:start position:0% +uh rules. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Okay. So, rules + + align:start position:0% +>> Okay. So, rules + + + align:start position:0% +>> Okay. So, rules +defined + + align:start position:0% +defined + + + align:start position:0% +defined +by randomized rules. + + align:start position:0% + + + + align:start position:0% + +All those people um in the assassin's + + align:start position:0% +All those people um in the assassin's + + + align:start position:0% +All those people um in the assassin's +guild uh or familiar with the assassin's + + align:start position:0% +guild uh or familiar with the assassin's + + + align:start position:0% +guild uh or familiar with the assassin's +guild, there's the concept of cycripts. + + align:start position:0% +guild, there's the concept of cycripts. + + + align:start position:0% +guild, there's the concept of cycripts. +Uh things that you're that you as an + + align:start position:0% +Uh things that you're that you as an + + + align:start position:0% +Uh things that you're that you as an +individual player uh are are are given + + align:start position:0% +individual player uh are are are given + + + align:start position:0% +individual player uh are are are given +at the beginning of the game as things + + align:start position:0% +at the beginning of the game as things + + + align:start position:0% +at the beginning of the game as things +that you can do or you have to do or if + + align:start position:0% +that you can do or you have to do or if + + + align:start position:0% +that you can do or you have to do or if +you do something you have to do it under + + align:start position:0% +you do something you have to do it under + + + align:start position:0% +you do something you have to do it under +specific conditions. The psych + + align:start position:0% +specific conditions. The psych + + + align:start position:0% +specific conditions. The psych +psychological limitations is what + + align:start position:0% +psychological limitations is what + + + align:start position:0% +psychological limitations is what +they're called. It could be something as + + align:start position:0% +they're called. It could be something as + + + align:start position:0% +they're called. It could be something as +simple as you have to speak an accent + + align:start position:0% +simple as you have to speak an accent + + + align:start position:0% +simple as you have to speak an accent +all the time or you have to live. It + + align:start position:0% +all the time or you have to live. It + + + align:start position:0% +all the time or you have to live. It +could be something more like every time + + align:start position:0% +could be something more like every time + + + align:start position:0% +could be something more like every time +you see blur, you have to run away + + align:start position:0% +you see blur, you have to run away + + + align:start position:0% +you see blur, you have to run away +because there's a phobia and something + + align:start position:0% +because there's a phobia and something + + + align:start position:0% +because there's a phobia and something +like that. Uh, and some it might be + + align:start position:0% +like that. Uh, and some it might be + + + align:start position:0% +like that. Uh, and some it might be +interesting to think of collection of + + align:start position:0% +interesting to think of collection of + + + align:start position:0% +interesting to think of collection of +those things and that crafts how we + + align:start position:0% +those things and that crafts how we + + + align:start position:0% +those things and that crafts how we +behave. Um, so this makes me think I + + align:start position:0% +behave. Um, so this makes me think I + + + align:start position:0% +behave. Um, so this makes me think I +should probably do the live action class + + align:start position:0% +should probably do the live action class + + + align:start position:0% +should probably do the live action class +at some point and talk about party games + + align:start position:0% +at some point and talk about party games + + + align:start position:0% +at some point and talk about party games +and and + + align:start position:0% +and and + + + align:start position:0% +and and +uh I think you have + + align:start position:0% +uh I think you have + + + align:start position:0% +uh I think you have +>> Oh, I hope my hands are up. + + align:start position:0% +>> Oh, I hope my hands are up. + + + align:start position:0% +>> Oh, I hope my hands are up. +>> Okay, your hands are just up. + + align:start position:0% +>> Okay, your hands are just up. + + + align:start position:0% +>> Okay, your hands are just up. +like + + align:start position:0% +like + + + align:start position:0% +like +>> um another thing that a psychiatrist has + + align:start position:0% +>> um another thing that a psychiatrist has + + + align:start position:0% +>> um another thing that a psychiatrist has +to do when they're talking to a patient + + align:start position:0% +to do when they're talking to a patient + + + align:start position:0% +to do when they're talking to a patient +is to try to get the story out of them + + align:start position:0% +is to try to get the story out of them + + + align:start position:0% +is to try to get the story out of them +like why why they're upset. So you could + + align:start position:0% +like why why they're upset. So you could + + + align:start position:0% +like why why they're upset. So you could +have um a game where the patient has you + + align:start position:0% +have um a game where the patient has you + + + align:start position:0% +have um a game where the patient has you +know some set of of cards that uh has + + align:start position:0% +know some set of of cards that uh has + + + align:start position:0% +know some set of of cards that uh has +some some sort of story with some + + align:start position:0% +some some sort of story with some + + + align:start position:0% +some some sort of story with some +keywords and the doctor has to try to + + align:start position:0% +keywords and the doctor has to try to + + + align:start position:0% +keywords and the doctor has to try to +you know get the get these words out of + + align:start position:0% +you know get the get these words out of + + + align:start position:0% +you know get the get these words out of +him but the patient himself can't the + + align:start position:0% +him but the patient himself can't the + + + align:start position:0% +him but the patient himself can't the +patient himself doesn't fully know his + + align:start position:0% +patient himself doesn't fully know his + + + align:start position:0% +patient himself doesn't fully know his +story. So like he keeps on changing. You + + align:start position:0% +story. So like he keeps on changing. You + + + align:start position:0% +story. So like he keeps on changing. You +would keep modifying your story as you + + align:start position:0% +would keep modifying your story as you + + + align:start position:0% +would keep modifying your story as you +go by drawing cards and throwing them + + align:start position:0% +go by drawing cards and throwing them + + + align:start position:0% +go by drawing cards and throwing them +away and you can only really get the + + align:start position:0% +away and you can only really get the + + + align:start position:0% +away and you can only really get the +full picture once you get all the cards + + align:start position:0% +full picture once you get all the cards + + + align:start position:0% +full picture once you get all the cards +that the patient has in his hand. So + + align:start position:0% +that the patient has in his hand. So + + + align:start position:0% +that the patient has in his hand. So +wait, so does the patient have all the + + align:start position:0% +wait, so does the patient have all the + + + align:start position:0% +wait, so does the patient have all the +cards? + + align:start position:0% +cards? + + + align:start position:0% +cards? +>> The p the patient has his full story, + + align:start position:0% +>> The p the patient has his full story, + + + align:start position:0% +>> The p the patient has his full story, +but it keeps changing. + + align:start position:0% +but it keeps changing. + + + align:start position:0% +but it keeps changing. +>> Okay. So Okay. So + + align:start position:0% +>> Okay. So Okay. So + + + align:start position:0% +>> Okay. So Okay. So +ever changing story + + align:start position:0% +ever changing story + + + align:start position:0% +ever changing story +>> and and you want to kind of stay on top + + align:start position:0% +>> and and you want to kind of stay on top + + + align:start position:0% +>> and and you want to kind of stay on top +of entropy. + + align:start position:0% +of entropy. + + + align:start position:0% +of entropy. +>> Yeah. Okay. + + align:start position:0% +>> Yeah. Okay. + + + align:start position:0% +>> Yeah. Okay. +>> Cool. + + align:start position:0% +>> Cool. + + + align:start position:0% +>> Cool. +Um, this isn't a fully fleshed out idea, + + align:start position:0% +Um, this isn't a fully fleshed out idea, + + + align:start position:0% +Um, this isn't a fully fleshed out idea, +but as a mechanic, um, say there's a + + align:start position:0% +but as a mechanic, um, say there's a + + + align:start position:0% +but as a mechanic, um, say there's a +doctor and a patient, and the do and the + + align:start position:0% +doctor and a patient, and the do and the + + + align:start position:0% +doctor and a patient, and the do and the +only the only communication is through + + align:start position:0% +only the only communication is through + + + align:start position:0% +only the only communication is through +cards. So, the doctor will like give the + + align:start position:0% +cards. So, the doctor will like give the + + + align:start position:0% +cards. So, the doctor will like give the +patient two cards, and then the third + + align:start position:0% +patient two cards, and then the third + + + align:start position:0% +patient two cards, and then the third +card is randomly, uh, inserted off of + + align:start position:0% +card is randomly, uh, inserted off of + + + align:start position:0% +card is randomly, uh, inserted off of +like a deck and shuffled in, and the + + align:start position:0% +like a deck and shuffled in, and the + + + align:start position:0% +like a deck and shuffled in, and the +patient receives all three. + + align:start position:0% +patient receives all three. + + + align:start position:0% +patient receives all three. +>> So, it's like the patient might be + + align:start position:0% +>> So, it's like the patient might be + + + align:start position:0% +>> So, it's like the patient might be +schizophrenic and imagining things and + + align:start position:0% +schizophrenic and imagining things and + + + align:start position:0% +schizophrenic and imagining things and +they like get whatever the doctor's + + align:start position:0% +they like get whatever the doctor's + + + align:start position:0% +they like get whatever the doctor's +saying, but they also get like other + + align:start position:0% +saying, but they also get like other + + + align:start position:0% +saying, but they also get like other +random things as noise. So, so as a + + align:start position:0% +random things as noise. So, so as a + + + align:start position:0% +random things as noise. So, so as a +mechanic that will be + + align:start position:0% +mechanic that will be + + + align:start position:0% +mechanic that will be +um man I that's hard to describe two the + + align:start position:0% +um man I that's hard to describe two the + + + align:start position:0% +um man I that's hard to describe two the +idea that you will be adding a + + align:start position:0% +idea that you will be adding a + + + align:start position:0% +idea that you will be adding a +randomized + + align:start position:0% +randomized + + + align:start position:0% +randomized +>> so you get information that is both what + + align:start position:0% +>> so you get information that is both what + + + align:start position:0% +>> so you get information that is both what +the other person played and something + + align:start position:0% +the other person played and something + + + align:start position:0% +the other person played and something +random and you can't distinguish which + + align:start position:0% +random and you can't distinguish which + + + align:start position:0% +random and you can't distinguish which +is which + + align:start position:0% +is which + + + align:start position:0% +is which +>> so you have a communication channel and + + align:start position:0% +>> so you have a communication channel and + + + align:start position:0% +>> so you have a communication channel and +you're handing random noise. + + align:start position:0% +you're handing random noise. + + + align:start position:0% +you're handing random noise. +>> Yeah. + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% + + + + align:start position:0% + +And what is not? Yeah, + + align:start position:0% + + + + align:start position:0% + +I am running out of space. So, it's + + align:start position:0% +I am running out of space. So, it's + + + align:start position:0% +I am running out of space. So, it's +okay. + + align:start position:0% + + + + align:start position:0% + +>> Any other + + align:start position:0% +>> Any other + + + align:start position:0% +>> Any other +That's creepy. + + align:start position:0% + + + + align:start position:0% + +>> Anyone else? + + align:start position:0% + + + + align:start position:0% + +One concept I thought was interesting + + align:start position:0% +One concept I thought was interesting + + + align:start position:0% +One concept I thought was interesting +that I'm not really sure how you turn + + align:start position:0% +that I'm not really sure how you turn + + + align:start position:0% +that I'm not really sure how you turn +into a game immediately is the idea of + + align:start position:0% +into a game immediately is the idea of + + + align:start position:0% +into a game immediately is the idea of +the + + align:start position:0% +the + + + align:start position:0% +the +patient and bically the doctor or the + + align:start position:0% +patient and bically the doctor or the + + + align:start position:0% +patient and bically the doctor or the +rest of the world having to at the + + align:start position:0% +rest of the world having to at the + + + align:start position:0% +rest of the world having to at the +moment irreconcilable irreconcilable + + align:start position:0% +moment irreconcilable irreconcilable + + + align:start position:0% +moment irreconcilable irreconcilable +narratives + + align:start position:0% +narratives + + + align:start position:0% +narratives +>> and the goal of bringing those into some + + align:start position:0% +>> and the goal of bringing those into some + + + align:start position:0% +>> and the goal of bringing those into some +type of medium in which the patient can + + align:start position:0% +type of medium in which the patient can + + + align:start position:0% +type of medium in which the patient can +you know comfortably exist with this + + align:start position:0% +you know comfortably exist with this + + + align:start position:0% +you know comfortably exist with this +narrative that's in with the rest of the + + align:start position:0% +narrative that's in with the rest of the + + + align:start position:0% +narrative that's in with the rest of the +world, + + align:start position:0% +world, + + + align:start position:0% +world, +>> right? + + align:start position:0% +>> right? + + + align:start position:0% +>> right? +>> So the the idea again of that narrative + + align:start position:0% +>> So the the idea again of that narrative + + + align:start position:0% +>> So the the idea again of that narrative +disruption is kind of why people get + + align:start position:0% +disruption is kind of why people get + + + align:start position:0% +disruption is kind of why people get +violent in the first place and so maybe + + align:start position:0% +violent in the first place and so maybe + + + align:start position:0% +violent in the first place and so maybe +even taking out the question entirely of + + align:start position:0% +even taking out the question entirely of + + + align:start position:0% +even taking out the question entirely of +what makes is this person going to act + + align:start position:0% +what makes is this person going to act + + + align:start position:0% +what makes is this person going to act +violently, but can you even work + + align:start position:0% +violently, but can you even work + + + align:start position:0% +violently, but can you even work +together with somebody to change how + + align:start position:0% +together with somebody to change how + + + align:start position:0% +together with somebody to change how +they see the world until it makes sense + + align:start position:0% +they see the world until it makes sense + + + align:start position:0% +they see the world until it makes sense +on both on both sides? Yeah. + + align:start position:0% +on both on both sides? Yeah. + + + align:start position:0% +on both on both sides? Yeah. +>> Yeah. So that would something I can't + + align:start position:0% +>> Yeah. So that would something I can't + + + align:start position:0% +>> Yeah. So that would something I can't +like actually that you would gain for + + align:start position:0% +like actually that you would gain for + + + align:start position:0% +like actually that you would gain for +now be something like okay so you have + + align:start position:0% +now be something like okay so you have + + + align:start position:0% +now be something like okay so you have +the patient's trying to tell this + + align:start position:0% +the patient's trying to tell this + + + align:start position:0% +the patient's trying to tell this +patient and do doctor patient and doctor + + align:start position:0% +patient and do doctor patient and doctor + + + align:start position:0% +patient and do doctor patient and doctor +and one person trying to portray a + + align:start position:0% +and one person trying to portray a + + + align:start position:0% +and one person trying to portray a +message that one person the other person + + align:start position:0% +message that one person the other person + + + align:start position:0% +message that one person the other person +trying to portray to the other but + + align:start position:0% +trying to portray to the other but + + + align:start position:0% +trying to portray to the other but +there's like some something in the + + align:start position:0% +there's like some something in the + + + align:start position:0% +there's like some something in the +middle that's changing everything + + align:start position:0% +middle that's changing everything + + + align:start position:0% +middle that's changing everything +>> and so it's just trying to reconcile + + align:start position:0% +>> and so it's just trying to reconcile + + + align:start position:0% +>> and so it's just trying to reconcile +that difference pretty much + + align:start position:0% +that difference pretty much + + + align:start position:0% +that difference pretty much +>> figure out the connection like the + + align:start position:0% +>> figure out the connection like the + + + align:start position:0% +>> figure out the connection like the +communication between each other + + align:start position:0% +communication between each other + + + align:start position:0% +communication between each other +>> so so you kind of have a situation where + + align:start position:0% +>> so so you kind of have a situation where + + + align:start position:0% +>> so so you kind of have a situation where +you actually have three people playing + + align:start position:0% +you actually have three people playing + + + align:start position:0% +you actually have three people playing +And it's just some one person who's + + align:start position:0% +And it's just some one person who's + + + align:start position:0% +And it's just some one person who's +changing information on + + align:start position:0% +changing information on + + + align:start position:0% +changing information on +>> either predict unpredictable + + align:start position:0% +>> either predict unpredictable + + + align:start position:0% +>> either predict unpredictable +unpredictable way + + align:start position:0% +unpredictable way + + + align:start position:0% +unpredictable way +>> like maybe they they have their own + + align:start position:0% +>> like maybe they they have their own + + + align:start position:0% +>> like maybe they they have their own +objective in mind. + + align:start position:0% +objective in mind. + + + align:start position:0% +objective in mind. +>> So what they're trying the two people in + + align:start position:0% +>> So what they're trying the two people in + + + align:start position:0% +>> So what they're trying the two people in +the end are trying to like figure out + + align:start position:0% +the end are trying to like figure out + + + align:start position:0% +the end are trying to like figure out +what the other one's saying and then one + + align:start position:0% +what the other one's saying and then one + + + align:start position:0% +what the other one's saying and then one +person in the middle is trying to has + + align:start position:0% +person in the middle is trying to has + + + align:start position:0% +person in the middle is trying to has +their has their own agenda. + + align:start position:0% +their has their own agenda. + + + align:start position:0% +their has their own agenda. +>> That's like representing schizophrenia. + + align:start position:0% +>> That's like representing schizophrenia. + + + align:start position:0% +>> That's like representing schizophrenia. +So, so, so that there's a noisy + + align:start position:0% +So, so, so that there's a noisy + + + align:start position:0% +So, so, so that there's a noisy +communications channel with an agenda. I + + align:start position:0% +communications channel with an agenda. I + + + align:start position:0% +communications channel with an agenda. I +like that. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. I mean, that that could be a + + align:start position:0% +>> Yeah. I mean, that that could be a + + + align:start position:0% +>> Yeah. I mean, that that could be a +algorithm that could be a person. Uh, it + + align:start position:0% +algorithm that could be a person. Uh, it + + + align:start position:0% +algorithm that could be a person. Uh, it +could be a person running an algorithm + + align:start position:0% +could be a person running an algorithm + + + align:start position:0% +could be a person running an algorithm +in their head. So, yeah. + + align:start position:0% +in their head. So, yeah. + + + align:start position:0% +in their head. So, yeah. +>> Yeah. I mean, the noisy communication + + align:start position:0% +>> Yeah. I mean, the noisy communication + + + align:start position:0% +>> Yeah. I mean, the noisy communication +channel could represent the actual state + + align:start position:0% +channel could represent the actual state + + + align:start position:0% +channel could represent the actual state +of mind of the the patient. That is the + + align:start position:0% +of mind of the the patient. That is the + + + align:start position:0% +of mind of the the patient. That is the +point, right? But I mean and then + + align:start position:0% +point, right? But I mean and then + + + align:start position:0% +point, right? But I mean and then +depending upon again they're like the + + align:start position:0% +depending upon again they're like the + + + align:start position:0% +depending upon again they're like the +level of arousal that could change like + + align:start position:0% +level of arousal that could change like + + + align:start position:0% +level of arousal that could change like +how everything gets streamed into being + + align:start position:0% +how everything gets streamed into being + + + align:start position:0% +how everything gets streamed into being +like very combative. And so like + + align:start position:0% +like very combative. And so like + + + align:start position:0% +like very combative. And so like +everything the doctor says is sort of + + align:start position:0% +everything the doctor says is sort of + + + align:start position:0% +everything the doctor says is sort of +taken as being + + align:start position:0% + + + + align:start position:0% + +somehow + + align:start position:0% +somehow + + + align:start position:0% +somehow +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Yeah. some sort of some sort of variable + + align:start position:0% +>> Yeah. some sort of some sort of variable + + + align:start position:0% +>> Yeah. some sort of some sort of variable +that's actually going to affect how + + align:start position:0% +that's actually going to affect how + + + align:start position:0% +that's actually going to affect how +they're going to + + align:start position:0% +they're going to + + + align:start position:0% +they're going to +>> Yeah. + + align:start position:0% + + + + align:start position:0% + +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +Um, this meant well, this would probably + + align:start position:0% +Um, this meant well, this would probably + + + align:start position:0% +Um, this meant well, this would probably +only work once the first time you play + + align:start position:0% +only work once the first time you play + + + align:start position:0% +only work once the first time you play +through, but again, what you've + + align:start position:0% +through, but again, what you've + + + align:start position:0% +through, but again, what you've +concealed from the players or certain + + align:start position:0% +concealed from the players or certain + + + align:start position:0% +concealed from the players or certain +players themselves that + + align:start position:0% +players themselves that + + + align:start position:0% +players themselves that +uh what their goals are or what they + + align:start position:0% +uh what their goals are or what they + + + align:start position:0% +uh what their goals are or what they +believe to be true about the game state + + align:start position:0% +believe to be true about the game state + + + align:start position:0% +believe to be true about the game state +is in fact a delusion or not true. So + + align:start position:0% +is in fact a delusion or not true. So + + + align:start position:0% +is in fact a delusion or not true. So +you might you might tell them that it's + + align:start position:0% +you might you might tell them that it's + + + align:start position:0% +you might you might tell them that it's +about this is a game set in 2100 when + + align:start position:0% +about this is a game set in 2100 when + + + align:start position:0% +about this is a game set in 2100 when +you've been wrongly imprisoned in a + + align:start position:0% +you've been wrongly imprisoned in a + + + align:start position:0% +you've been wrongly imprisoned in a +psychiatric ward and you must fight your + + align:start position:0% +psychiatric ward and you must fight your + + + align:start position:0% +psychiatric ward and you must fight your +way out or something like that and + + align:start position:0% +way out or something like that and + + + align:start position:0% +way out or something like that and +there's a you know voice will guide you + + align:start position:0% +there's a you know voice will guide you + + + align:start position:0% +there's a you know voice will guide you +you know whatever and then and then but + + align:start position:0% +you know whatever and then and then but + + + align:start position:0% +you know whatever and then and then but +you don't you don't tell you don't tell + + align:start position:0% +you don't you don't tell you don't tell + + + align:start position:0% +you don't you don't tell you don't tell +that player that they're in fact playing + + align:start position:0% +that player that they're in fact playing + + + align:start position:0% +that player that they're in fact playing +a player who believes you know these + + align:start position:0% +a player who believes you know these + + + align:start position:0% +a player who believes you know these +things and you and then maybe you do + + align:start position:0% +things and you and then maybe you do + + + align:start position:0% +things and you and then maybe you do +some sort of live action role playing or + + align:start position:0% +some sort of live action role playing or + + + align:start position:0% +some sort of live action role playing or +not I'm not exactly sure but a game + + align:start position:0% +not I'm not exactly sure but a game + + + align:start position:0% +not I'm not exactly sure but a game +which otherwise are forces with this + + align:start position:0% +which otherwise are forces with this + + + align:start position:0% +which otherwise are forces with this +other guy who's convinced that this is + + align:start position:0% +other guy who's convinced that this is + + + align:start position:0% +other guy who's convinced that this is +what the game is about. So it's like an + + align:start position:0% +what the game is about. So it's like an + + + align:start position:0% +what the game is about. So it's like an +unreliable Yeah, I'm going to write an + + align:start position:0% +unreliable Yeah, I'm going to write an + + + align:start position:0% +unreliable Yeah, I'm going to write an +unreliable scenario. Uh I know the + + align:start position:0% +unreliable scenario. Uh I know the + + + align:start position:0% +unreliable scenario. Uh I know the +players don't know that going in, but uh + + align:start position:0% +players don't know that going in, but uh + + + align:start position:0% +players don't know that going in, but uh +if folks have seen the film The Cabinet + + align:start position:0% +if folks have seen the film The Cabinet + + + align:start position:0% +if folks have seen the film The Cabinet +of of Dr. Kagari, it's an old Germanic + + align:start position:0% +of of Dr. Kagari, it's an old Germanic + + + align:start position:0% +of of Dr. Kagari, it's an old Germanic +specialist uh white film and I could + + align:start position:0% +specialist uh white film and I could + + + align:start position:0% +specialist uh white film and I could +spoil it. Does anyone care? It's the old + + align:start position:0% +spoil it. Does anyone care? It's the old + + + align:start position:0% +spoil it. Does anyone care? It's the old +1920s. + + align:start position:0% + + + + align:start position:0% + +>> Unspoilers. I think you're fine. Uh but + + align:start position:0% +>> Unspoilers. I think you're fine. Uh but + + + align:start position:0% +>> Unspoilers. I think you're fine. Uh but +but the basic idea comes down to the + + align:start position:0% +but the basic idea comes down to the + + + align:start position:0% +but the basic idea comes down to the +hero of this sort of horror story is + + align:start position:0% +hero of this sort of horror story is + + + align:start position:0% +hero of this sort of horror story is +actually just a patient in the in + + align:start position:0% +actually just a patient in the in + + + align:start position:0% +actually just a patient in the in +psychiatric war and everybody who he + + align:start position:0% +psychiatric war and everybody who he + + + align:start position:0% +psychiatric war and everybody who he +believes is part of this story that he's + + align:start position:0% +believes is part of this story that he's + + + align:start position:0% +believes is part of this story that he's +uh conquering is somebody else in + + align:start position:0% +uh conquering is somebody else in + + + align:start position:0% +uh conquering is somebody else in +psychiatric war. The big villain is + + align:start position:0% +psychiatric war. The big villain is + + + align:start position:0% +psychiatric war. The big villain is +actually the person running. + + align:start position:0% +actually the person running. + + + align:start position:0% +actually the person running. +>> Is that like Shutter? + + align:start position:0% +>> Is that like Shutter? + + + align:start position:0% +>> Is that like Shutter? +>> Yeah. Yeah. It's like Shutter. + + align:start position:0% +>> Yeah. Yeah. It's like Shutter. + + + align:start position:0% +>> Yeah. Yeah. It's like Shutter. +>> Yeah. Yeah. not not not not entirely + + align:start position:0% +>> Yeah. Yeah. not not not not entirely + + + align:start position:0% +>> Yeah. Yeah. not not not not entirely +unlike a lot of different stories. But + + align:start position:0% +unlike a lot of different stories. But + + + align:start position:0% +unlike a lot of different stories. But +similarity idea of the you know maybe + + align:start position:0% +similarity idea of the you know maybe + + + align:start position:0% +similarity idea of the you know maybe +maybe the information we've been given + + align:start position:0% +maybe the information we've been given + + + align:start position:0% +maybe the information we've been given +is not that they need to be trusting + + align:start position:0% +is not that they need to be trusting + + + align:start position:0% +is not that they need to be trusting +something that go like that would be I + + align:start position:0% +something that go like that would be I + + + align:start position:0% +something that go like that would be I +guess a game mechanic part of that would + + align:start position:0% +guess a game mechanic part of that would + + + align:start position:0% +guess a game mechanic part of that would +be everyone's assigned a different role + + align:start position:0% +be everyone's assigned a different role + + + align:start position:0% +be everyone's assigned a different role +and one of those roles is patient and so + + align:start position:0% +and one of those roles is patient and so + + + align:start position:0% +and one of those roles is patient and so +you don't know if you're the patient or + + align:start position:0% +you don't know if you're the patient or + + + align:start position:0% +you don't know if you're the patient or +not and so you're trying to do your + + align:start position:0% +not and so you're trying to do your + + + align:start position:0% +not and so you're trying to do your +objectives and then as you play along + + align:start position:0% +objectives and then as you play along + + + align:start position:0% +objectives and then as you play along +you realize you may or start to realize + + align:start position:0% +you realize you may or start to realize + + + align:start position:0% +you realize you may or start to realize +things aren't actually as what they + + align:start position:0% +things aren't actually as what they + + + align:start position:0% +things aren't actually as what they +seem. So eventually you may figure out + + align:start position:0% +seem. So eventually you may figure out + + + align:start position:0% +seem. So eventually you may figure out +I'm actually the patient here. + + align:start position:0% +I'm actually the patient here. + + + align:start position:0% +I'm actually the patient here. +>> Right. Right. Who's trying to train who? + + align:start position:0% +>> Right. Right. Who's trying to train who? + + + align:start position:0% +>> Right. Right. Who's trying to train who? +And they're almost like fighting for + + align:start position:0% +And they're almost like fighting for + + + align:start position:0% +And they're almost like fighting for +authority in that sense possibly. Okay. + + align:start position:0% +authority in that sense possibly. Okay. + + + align:start position:0% +authority in that sense possibly. Okay. +>> Going along with that. Uh I think an + + align:start position:0% +>> Going along with that. Uh I think an + + + align:start position:0% +>> Going along with that. Uh I think an +interesting mechanic would be like the + + align:start position:0% +interesting mechanic would be like the + + + align:start position:0% +interesting mechanic would be like the +battle star black sylons method where + + align:start position:0% +battle star black sylons method where + + + align:start position:0% +battle star black sylons method where +you the person knows that they're Sylon, + + align:start position:0% +you the person knows that they're Sylon, + + + align:start position:0% +you the person knows that they're Sylon, +but they can infiltrate by doing that + + align:start position:0% +but they can infiltrate by doing that + + + align:start position:0% +but they can infiltrate by doing that +voting system at the end. What is that? + + align:start position:0% +voting system at the end. What is that? + + + align:start position:0% +voting system at the end. What is that? +It's the with the destiny part. + + align:start position:0% +It's the with the destiny part. + + + align:start position:0% +It's the with the destiny part. +>> So you know that someone's trying to + + align:start position:0% +>> So you know that someone's trying to + + + align:start position:0% +>> So you know that someone's trying to +sabotage you but you don't know who, + + align:start position:0% +sabotage you but you don't know who, + + + align:start position:0% +sabotage you but you don't know who, +>> right? So gosh, how um + + align:start position:0% +>> right? So gosh, how um + + + align:start position:0% +>> right? So gosh, how um +patient. + + align:start position:0% +patient. + + + align:start position:0% +patient. +>> So that's kind of who's the patient from + + align:start position:0% +>> So that's kind of who's the patient from + + + align:start position:0% +>> So that's kind of who's the patient from +a different way, right? It's like one is + + align:start position:0% +a different way, right? It's like one is + + + align:start position:0% +a different way, right? It's like one is +you know player knows + + align:start position:0% +you know player knows + + + align:start position:0% +you know player knows +>> who you know at least at least one + + align:start position:0% +>> who you know at least at least one + + + align:start position:0% +>> who you know at least at least one +person knows + + align:start position:0% +person knows + + + align:start position:0% +person knows +>> and then the other one is uh player + + align:start position:0% +>> and then the other one is uh player + + + align:start position:0% +>> and then the other one is uh player +needs to figure out whether they are it. + + align:start position:0% + + + + align:start position:0% + +>> This is just an interesting mechanic + + align:start position:0% +>> This is just an interesting mechanic + + + align:start position:0% +>> This is just an interesting mechanic +thing. So there was this again RPG + + align:start position:0% +thing. So there was this again RPG + + + align:start position:0% +thing. So there was this again RPG +called Brea the Oblivion that had this + + align:start position:0% +called Brea the Oblivion that had this + + + align:start position:0% +called Brea the Oblivion that had this +really interesting mechanic for handling + + align:start position:0% +really interesting mechanic for handling + + + align:start position:0% +really interesting mechanic for handling +the dark side that each player had which + + align:start position:0% +the dark side that each player had which + + + align:start position:0% +the dark side that each player had which +might be kind of relevant in this + + align:start position:0% +might be kind of relevant in this + + + align:start position:0% +might be kind of relevant in this +situation. Essentially, you had a + + align:start position:0% +situation. Essentially, you had a + + + align:start position:0% +situation. Essentially, you had a +different person who was also playing + + align:start position:0% +different person who was also playing + + + align:start position:0% +different person who was also playing +another protagonist also play your + + align:start position:0% +another protagonist also play your + + + align:start position:0% +another protagonist also play your +antagonist. + + align:start position:0% +antagonist. + + + align:start position:0% +antagonist. +>> And so they would either talk to you and + + align:start position:0% +>> And so they would either talk to you and + + + align:start position:0% +>> And so they would either talk to you and +tell you things or they would just + + align:start position:0% +tell you things or they would just + + + align:start position:0% +tell you things or they would just +directly control your character like if + + align:start position:0% +directly control your character like if + + + align:start position:0% +directly control your character like if +you kind of fail the compos the + + align:start position:0% +you kind of fail the compos the + + + align:start position:0% +you kind of fail the compos the +composure role. And taking the + + align:start position:0% +composure role. And taking the + + + align:start position:0% +composure role. And taking the +adversarial side of your character away + + align:start position:0% +adversarial side of your character away + + + align:start position:0% +adversarial side of your character away +from your control kind of um it it means + + align:start position:0% +from your control kind of um it it means + + + align:start position:0% +from your control kind of um it it means +that you your character is more likely + + align:start position:0% +that you your character is more likely + + + align:start position:0% +that you your character is more likely +to behave in a really disruptive way + + align:start position:0% +to behave in a really disruptive way + + + align:start position:0% +to behave in a really disruptive way +rather than just a controllably + + align:start position:0% +rather than just a controllably + + + align:start position:0% +rather than just a controllably +disruptive way how it would be if you + + align:start position:0% +disruptive way how it would be if you + + + align:start position:0% +disruptive way how it would be if you +were had a best interest in your + + align:start position:0% +were had a best interest in your + + + align:start position:0% +were had a best interest in your +character. + + align:start position:0% +character. + + + align:start position:0% +character. +>> So open takes control of your character. + + align:start position:0% +>> So open takes control of your character. + + + align:start position:0% +>> So open takes control of your character. +>> Yeah. Uh and and that might work really + + align:start position:0% +>> Yeah. Uh and and that might work really + + + align:start position:0% +>> Yeah. Uh and and that might work really +well with some of the ideas of I did a + + align:start position:0% +well with some of the ideas of I did a + + + align:start position:0% +well with some of the ideas of I did a +good cop bad cop ide. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +>> So, um actually going off of the uh the + + align:start position:0% +>> So, um actually going off of the uh the + + + align:start position:0% +>> So, um actually going off of the uh the +like the audio idea of like someone is + + align:start position:0% +like the audio idea of like someone is + + + align:start position:0% +like the audio idea of like someone is +is actually hearing voices and this + + align:start position:0% +is actually hearing voices and this + + + align:start position:0% +is actually hearing voices and this +whole um who was the patient thing, you + + align:start position:0% +whole um who was the patient thing, you + + + align:start position:0% +whole um who was the patient thing, you +could actually have things where you + + align:start position:0% +could actually have things where you + + + align:start position:0% +could actually have things where you +have uh one player is actually playing a + + align:start position:0% +have uh one player is actually playing a + + + align:start position:0% +have uh one player is actually playing a +patient who is schizophrenic + + align:start position:0% +patient who is schizophrenic + + + align:start position:0% +patient who is schizophrenic +>> and another player is playing the voices + + align:start position:0% +>> and another player is playing the voices + + + align:start position:0% +>> and another player is playing the voices +in his head. + + align:start position:0% +in his head. + + + align:start position:0% +in his head. +So you you but like they don't really + + align:start position:0% +So you you but like they don't really + + + align:start position:0% +So you you but like they don't really +know that like they they're playing this + + align:start position:0% +know that like they they're playing this + + + align:start position:0% +know that like they they're playing this +scenario where you know they they have + + align:start position:0% +scenario where you know they they have + + + align:start position:0% +scenario where you know they they have +some delusion that they're crafted or + + align:start position:0% +some delusion that they're crafted or + + + align:start position:0% +some delusion that they're crafted or +whatever. Um + + align:start position:0% +whatever. Um + + + align:start position:0% +whatever. Um +>> Oh. + + align:start position:0% +>> Oh. + + + align:start position:0% +>> Oh. +>> So like like having having like just + + align:start position:0% +>> So like like having having like just + + + align:start position:0% +>> So like like having having like just +have a person actually being the like + + align:start position:0% +have a person actually being the like + + + align:start position:0% +have a person actually being the like +like as you were saying like have an + + align:start position:0% +like as you were saying like have an + + + align:start position:0% +like as you were saying like have an +actual person be the dark side of of the + + align:start position:0% +actual person be the dark side of of the + + + align:start position:0% +actual person be the dark side of of the +patient. + + align:start position:0% +patient. + + + align:start position:0% +patient. +>> Um + + align:start position:0% +>> Um + + + align:start position:0% +>> Um +so but neither of them know who's the + + align:start position:0% +so but neither of them know who's the + + + align:start position:0% +so but neither of them know who's the +dark side. Well, I mean the the patient + + align:start position:0% +dark side. Well, I mean the the patient + + + align:start position:0% +dark side. Well, I mean the the patient +Yeah. I mean you could have + + align:start position:0% +Yeah. I mean you could have + + + align:start position:0% +Yeah. I mean you could have +>> one way you could arbitrate this is you + + align:start position:0% +>> one way you could arbitrate this is you + + + align:start position:0% +>> one way you could arbitrate this is you +could say that the the patient player is + + align:start position:0% +could say that the the patient player is + + + align:start position:0% +could say that the the patient player is +able to just basically do as they please + + align:start position:0% +able to just basically do as they please + + + align:start position:0% +able to just basically do as they please +but + + align:start position:0% +but + + + align:start position:0% +but +>> with there are rules which govern + + align:start position:0% +>> with there are rules which govern + + + align:start position:0% +>> with there are rules which govern +whether the dark side character can take + + align:start position:0% +whether the dark side character can take + + + align:start position:0% +whether the dark side character can take +over. + + align:start position:0% +over. + + + align:start position:0% +over. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Yeah. Yeah. Something like that. Or + + align:start position:0% +>> Yeah. Yeah. Something like that. Or + + + align:start position:0% +>> Yeah. Yeah. Something like that. Or +>> so and that means that means that the + + align:start position:0% +>> so and that means that means that the + + + align:start position:0% +>> so and that means that means that the +patient is kind of genuinely driven to + + align:start position:0% +patient is kind of genuinely driven to + + + align:start position:0% +patient is kind of genuinely driven to +try and reach a compromise but they can + + align:start position:0% +try and reach a compromise but they can + + + align:start position:0% +try and reach a compromise but they can +just be overruled by dark side. Yeah. + + align:start position:0% +just be overruled by dark side. Yeah. + + + align:start position:0% +just be overruled by dark side. Yeah. +>> So, + + align:start position:0% +>> So, + + + align:start position:0% +>> So, +>> and there could also be things where + + align:start position:0% +>> and there could also be things where + + + align:start position:0% +>> and there could also be things where +like it's it could be like more of a + + align:start position:0% +like it's it could be like more of a + + + align:start position:0% +like it's it could be like more of a +strong role playinging thing where the + + align:start position:0% +strong role playinging thing where the + + + align:start position:0% +strong role playinging thing where the +voice is actually just trying to + + align:start position:0% +voice is actually just trying to + + + align:start position:0% +voice is actually just trying to +convince him that yes, this delusion is + + align:start position:0% +convince him that yes, this delusion is + + + align:start position:0% +convince him that yes, this delusion is +real. + + align:start position:0% +real. + + + align:start position:0% +real. +>> So, but you still think you have a + + align:start position:0% +>> So, but you still think you have a + + + align:start position:0% +>> So, but you still think you have a +recorded thing or actually two different + + align:start position:0% +recorded thing or actually two different + + + align:start position:0% +recorded thing or actually two different +>> You could actually have two people just + + align:start position:0% +>> You could actually have two people just + + + align:start position:0% +>> You could actually have two people just +actually standing there talking to each + + align:start position:0% +actually standing there talking to each + + + align:start position:0% +actually standing there talking to each +other. + + align:start position:0% +other. + + + align:start position:0% +other. +>> Okay. So, two uh people playing one + + align:start position:0% +>> Okay. So, two uh people playing one + + + align:start position:0% +>> Okay. So, two uh people playing one +character. + + align:start position:0% +character. + + + align:start position:0% +character. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> It it would potentially require a lot of + + align:start position:0% +>> It it would potentially require a lot of + + + align:start position:0% +>> It it would potentially require a lot of +suspension of disbelief on the part of + + align:start position:0% +suspension of disbelief on the part of + + + align:start position:0% +suspension of disbelief on the part of +the uh person playing the psychiatrist. + + align:start position:0% +the uh person playing the psychiatrist. + + + align:start position:0% +the uh person playing the psychiatrist. +It might be one of those things that's + + align:start position:0% +It might be one of those things that's + + + align:start position:0% +It might be one of those things that's +easier to um mediate by having people + + align:start position:0% +easier to um mediate by having people + + + align:start position:0% +easier to um mediate by having people +uh talk through a screen or something + + align:start position:0% +uh talk through a screen or something + + + align:start position:0% +uh talk through a screen or something +like that, you know, uh or even a + + align:start position:0% +like that, you know, uh or even a + + + align:start position:0% +like that, you know, uh or even a +microphone and a speaker kind of thing. + + align:start position:0% +microphone and a speaker kind of thing. + + + align:start position:0% +microphone and a speaker kind of thing. +Could be a game where you can play on a + + align:start position:0% +Could be a game where you can play on a + + + align:start position:0% +Could be a game where you can play on a +phone. + + align:start position:0% +phone. + + + align:start position:0% +phone. +>> Uh that would be + + align:start position:0% +>> Uh that would be + + + align:start position:0% +>> Uh that would be +>> I've not seen many games that are + + align:start position:0% +>> I've not seen many games that are + + + align:start position:0% +>> I've not seen many games that are +designed specifically to be played on + + align:start position:0% +designed specifically to be played on + + + align:start position:0% +designed specifically to be played on +phones, but function. + + align:start position:0% +phones, but function. + + + align:start position:0% +phones, but function. +I definitely like that idea and I think + + align:start position:0% +I definitely like that idea and I think + + + align:start position:0% +I definitely like that idea and I think +it could work well with a card game as + + align:start position:0% +it could work well with a card game as + + + align:start position:0% +it could work well with a card game as +well if you have two players sharing the + + align:start position:0% +well if you have two players sharing the + + + align:start position:0% +well if you have two players sharing the +same hand and the player who actually + + align:start position:0% +same hand and the player who actually + + + align:start position:0% +same hand and the player who actually +gets to play the cards from the hand is + + align:start position:0% +gets to play the cards from the hand is + + + align:start position:0% +gets to play the cards from the hand is +whoever is in control of the patient and + + align:start position:0% +whoever is in control of the patient and + + + align:start position:0% +whoever is in control of the patient and +so as things uh diff as the state + + align:start position:0% +so as things uh diff as the state + + + align:start position:0% +so as things uh diff as the state +basically changes depending on what the + + align:start position:0% +basically changes depending on what the + + + align:start position:0% +basically changes depending on what the +doctor does uh different players become + + align:start position:0% +doctor does uh different players become + + + align:start position:0% +doctor does uh different players become +in control of the patient's hand. + + align:start position:0% +in control of the patient's hand. + + + align:start position:0% +in control of the patient's hand. +>> So so it seems like we actually have a + + align:start position:0% +>> So so it seems like we actually have a + + + align:start position:0% +>> So so it seems like we actually have a +lot of different options on how we could + + align:start position:0% +lot of different options on how we could + + + align:start position:0% +lot of different options on how we could +mechanic uh somebody who's mentally + + align:start position:0% +mechanic uh somebody who's mentally + + + align:start position:0% +mechanic uh somebody who's mentally +unstable. uh and um and a bunch of also + + align:start position:0% +unstable. uh and um and a bunch of also + + + align:start position:0% +unstable. uh and um and a bunch of also +a bunch of ideas of how how that state + + align:start position:0% +a bunch of ideas of how how that state + + + align:start position:0% +a bunch of ideas of how how that state +switch could happen uh or what rules + + align:start position:0% +switch could happen uh or what rules + + + align:start position:0% +switch could happen uh or what rules +make up. Uh so that's pretty cool and + + align:start position:0% +make up. Uh so that's pretty cool and + + + align:start position:0% +make up. Uh so that's pretty cool and +that that's not + + align:start position:0% +that that's not + + + align:start position:0% +that that's not +uh and that's not mutually exclusive + + align:start position:0% +uh and that's not mutually exclusive + + + align:start position:0% +uh and that's not mutually exclusive +from any other ideas specifically about + + align:start position:0% +from any other ideas specifically about + + + align:start position:0% +from any other ideas specifically about +a patient and a doctor, right? So all + + align:start position:0% +a patient and a doctor, right? So all + + + align:start position:0% +a patient and a doctor, right? So all +we're talking about what happens to the + + align:start position:0% +we're talking about what happens to the + + + align:start position:0% +we're talking about what happens to the +patient. Uh these are the rules that a + + align:start position:0% +patient. Uh these are the rules that a + + + align:start position:0% +patient. Uh these are the rules that a +patient could be operating under. The + + align:start position:0% +patient could be operating under. The + + + align:start position:0% +patient could be operating under. The +doctor could have a different set of + + align:start position:0% +doctor could have a different set of + + + align:start position:0% +doctor could have a different set of +rules, all rules. + + align:start position:0% +rules, all rules. + + + align:start position:0% +rules, all rules. +>> I was reading about this and I think + + align:start position:0% +>> I was reading about this and I think + + + align:start position:0% +>> I was reading about this and I think +that it turns out most violence in + + align:start position:0% +that it turns out most violence in + + + align:start position:0% +that it turns out most violence in +psychiatric wards happens uh to the + + align:start position:0% +psychiatric wards happens uh to the + + + align:start position:0% +psychiatric wards happens uh to the +patients themselves or to other patients + + align:start position:0% +patients themselves or to other patients + + + align:start position:0% +patients themselves or to other patients +by patients much more than it actually + + align:start position:0% +by patients much more than it actually + + + align:start position:0% +by patients much more than it actually +happens to towards practitioners. + + align:start position:0% +happens to towards practitioners. + + + align:start position:0% +happens to towards practitioners. +>> And I'm just noticing that I don't think + + align:start position:0% +>> And I'm just noticing that I don't think + + + align:start position:0% +>> And I'm just noticing that I don't think +any of our ideas addressed any of those + + align:start position:0% +any of our ideas addressed any of those + + + align:start position:0% +any of our ideas addressed any of those +issues. board management maybe gets a + + align:start position:0% +issues. board management maybe gets a + + + align:start position:0% +issues. board management maybe gets a +little closer. + + align:start position:0% +little closer. + + + align:start position:0% +little closer. +>> Yeah, people start turning on + + align:start position:0% +>> Yeah, people start turning on + + + align:start position:0% +>> Yeah, people start turning on +themselves. + + align:start position:0% +themselves. + + + align:start position:0% +themselves. +>> So, I was I was just thinking so another + + align:start position:0% +>> So, I was I was just thinking so another + + + align:start position:0% +>> So, I was I was just thinking so another +possible way that you could apply all + + align:start position:0% +possible way that you could apply all + + + align:start position:0% +possible way that you could apply all +this a lot of these role playing + + align:start position:0% +this a lot of these role playing + + + align:start position:0% +this a lot of these role playing +multiple role or auditory mechanics is + + align:start position:0% +multiple role or auditory mechanics is + + + align:start position:0% +multiple role or auditory mechanics is +to a situation. we should we we should + + align:start position:0% +to a situation. we should we we should + + + align:start position:0% +to a situation. we should we we should +probably do research in what situations + + align:start position:0% +probably do research in what situations + + + align:start position:0% +probably do research in what situations +lead to patients coming in contact with + + align:start position:0% +lead to patients coming in contact with + + + align:start position:0% +lead to patients coming in contact with +each other and then the encounter + + align:start position:0% +each other and then the encounter + + + align:start position:0% +each other and then the encounter +turning violent. And then perhaps just + + align:start position:0% +turning violent. And then perhaps just + + + align:start position:0% +turning violent. And then perhaps just +having + + align:start position:0% +having + + + align:start position:0% +having +all players be patients that have + + align:start position:0% +all players be patients that have + + + align:start position:0% +all players be patients that have +various different mental disorders. And + + align:start position:0% +various different mental disorders. And + + + align:start position:0% +various different mental disorders. And +then and just to help you understand in + + align:start position:0% +then and just to help you understand in + + + align:start position:0% +then and just to help you understand in +the as a patient what what kinds of + + align:start position:0% +the as a patient what what kinds of + + + align:start position:0% +the as a patient what what kinds of +behaviors and situations would lead you + + align:start position:0% +behaviors and situations would lead you + + + align:start position:0% +behaviors and situations would lead you +to uh going violent on someone else. + + align:start position:0% +to uh going violent on someone else. + + + align:start position:0% +to uh going violent on someone else. +>> Just sort of one of those like be in + + align:start position:0% +>> Just sort of one of those like be in + + + align:start position:0% +>> Just sort of one of those like be in +someone else's shoes helps you + + align:start position:0% +someone else's shoes helps you + + + align:start position:0% +someone else's shoes helps you +understand the situation better, + + align:start position:0% +understand the situation better, + + + align:start position:0% +understand the situation better, +>> right? So just putting them in uh in a + + align:start position:0% +>> right? So just putting them in uh in a + + + align:start position:0% +>> right? So just putting them in uh in a +situ uh putting them in an environment + + align:start position:0% +situ uh putting them in an environment + + + align:start position:0% +situ uh putting them in an environment +where everything that is necessary for + + align:start position:0% +where everything that is necessary for + + + align:start position:0% +where everything that is necessary for +your charact for a certain character to + + align:start position:0% +your charact for a certain character to + + + align:start position:0% +your charact for a certain character to +become upset environment and then just + + align:start position:0% +become upset environment and then just + + + align:start position:0% +become upset environment and then just +seeing how that naturally occurs without + + align:start position:0% +seeing how that naturally occurs without + + + align:start position:0% +seeing how that naturally occurs without +necessarily saying and now you + + align:start position:0% +necessarily saying and now you + + + align:start position:0% +necessarily saying and now you +>> okay + + align:start position:0% +>> okay + + + align:start position:0% +>> okay +a game of persuasion that's a cross + + align:start position:0% +a game of persuasion that's a cross + + + align:start position:0% +a game of persuasion that's a cross +between like BS and Uno. So, you have + + align:start position:0% +between like BS and Uno. So, you have + + + align:start position:0% +between like BS and Uno. So, you have +two doctors who are trying to get rid of + + align:start position:0% +two doctors who are trying to get rid of + + + align:start position:0% +two doctors who are trying to get rid of +cards in their hand. Um, and then the + + align:start position:0% +cards in their hand. Um, and then the + + + align:start position:0% +cards in their hand. Um, and then the +patient wants a certain set of cards and + + align:start position:0% +patient wants a certain set of cards and + + + align:start position:0% +patient wants a certain set of cards and +he's saying, "I'm looking for John." And + + align:start position:0% +he's saying, "I'm looking for John." And + + + align:start position:0% +he's saying, "I'm looking for John." And +the two doctors pull out a card, they + + align:start position:0% +the two doctors pull out a card, they + + + align:start position:0% +the two doctors pull out a card, they +say, "Oh, this is John." Or they can be + + align:start position:0% +say, "Oh, this is John." Or they can be + + + align:start position:0% +say, "Oh, this is John." Or they can be +like, "This isn't John, but I can help + + align:start position:0% +like, "This isn't John, but I can help + + + align:start position:0% +like, "This isn't John, but I can help +you out later." + + align:start position:0% +you out later." + + + align:start position:0% +you out later." +>> Oh, so this is a this is that almost + + align:start position:0% +>> Oh, so this is a this is that almost + + + align:start position:0% +>> Oh, so this is a this is that almost +seems like an educate um intended to + + align:start position:0% +seems like an educate um intended to + + + align:start position:0% +seems like an educate um intended to +teach people not to. + + align:start position:0% +teach people not to. + + + align:start position:0% +teach people not to. +>> So, um so I'm going to say + + align:start position:0% +>> So, um so I'm going to say + + + align:start position:0% +>> So, um so I'm going to say +fish. + + align:start position:0% +fish. + + + align:start position:0% +fish. +>> Yeah. Honest honesty. + + align:start position:0% + + + + align:start position:0% + +So, we got a pretty good pile here. Um, + + align:start position:0% +So, we got a pretty good pile here. Um, + + + align:start position:0% +So, we got a pretty good pile here. Um, +a lot of these + + align:start position:0% +a lot of these + + + align:start position:0% +a lot of these +uh can obviously be combined and there's + + align:start position:0% +uh can obviously be combined and there's + + + align:start position:0% +uh can obviously be combined and there's +no reason why multiple groups couldn't + + align:start position:0% +no reason why multiple groups couldn't + + + align:start position:0% +no reason why multiple groups couldn't +attempt to do similar topics. Uh, in + + align:start position:0% +attempt to do similar topics. Uh, in + + + align:start position:0% +attempt to do similar topics. Uh, in +fact, you could take exactly the same + + align:start position:0% +fact, you could take exactly the same + + + align:start position:0% +fact, you could take exactly the same +set and I'm pretty sure two different + + align:start position:0% +set and I'm pretty sure two different + + + align:start position:0% +set and I'm pretty sure two different +groups are going to come in the same + + align:start position:0% +groups are going to come in the same + + + align:start position:0% +groups are going to come in the same +way. So, that's fine. Uh, again, a lot + + align:start position:0% +way. So, that's fine. Uh, again, a lot + + + align:start position:0% +way. So, that's fine. Uh, again, a lot +of live of things that could probably be + + align:start position:0% +of live of things that could probably be + + + align:start position:0% +of live of things that could probably be +easier done live action or at least + + align:start position:0% +easier done live action or at least + + + align:start position:0% +easier done live action or at least +easier to prototype live action. the um + + align:start position:0% +easier to prototype live action. the um + + + align:start position:0% +easier to prototype live action. the um +the the the folks who were here on + + align:start position:0% +the the the folks who were here on + + + align:start position:0% +the the the folks who were here on +Monday um they are actually + + align:start position:0% +Monday um they are actually + + + align:start position:0% +Monday um they are actually +uh focused mostly on trying to see what + + align:start position:0% +uh focused mostly on trying to see what + + + align:start position:0% +uh focused mostly on trying to see what +could be moved out to more people uh + + align:start position:0% +could be moved out to more people uh + + + align:start position:0% +could be moved out to more people uh +more resident trainee uh in uh in the + + align:start position:0% +more resident trainee uh in uh in the + + + align:start position:0% +more resident trainee uh in uh in the +future. Your games don't necessarily + + align:start position:0% +future. Your games don't necessarily + + + align:start position:0% +future. Your games don't necessarily +need to do that but uh but you might + + align:start position:0% +need to do that but uh but you might + + + align:start position:0% +need to do that but uh but you might +want want to keep that this this + + align:start position:0% +want want to keep that this this + + + align:start position:0% +want want to keep that this this +assignment is game for a client after + + align:start position:0% +assignment is game for a client after + + + align:start position:0% +assignment is game for a client after +all. And you know, if you manage to + + align:start position:0% +all. And you know, if you manage to + + + align:start position:0% +all. And you know, if you manage to +address that need of the, you know, + + align:start position:0% +address that need of the, you know, + + + align:start position:0% +address that need of the, you know, +here's something that doesn't require + + align:start position:0% +here's something that doesn't require + + + align:start position:0% +here's something that doesn't require +one person from the original GMT + + align:start position:0% +one person from the original GMT + + + align:start position:0% +one person from the original GMT +to do it. And you can imagine like you + + align:start position:0% +to do it. And you can imagine like you + + + align:start position:0% +to do it. And you can imagine like you +know the acting exercise that that that + + align:start position:0% +know the acting exercise that that that + + + align:start position:0% +know the acting exercise that that that +that they ran through you know Dion's + + align:start position:0% +that they ran through you know Dion's + + + align:start position:0% +that they ran through you know Dion's +particularly talented uh at improvising + + align:start position:0% +particularly talented uh at improvising + + + align:start position:0% +particularly talented uh at improvising +to speak but you know requires + + align:start position:0% +to speak but you know requires + + + align:start position:0% +to speak but you know requires +requires uh you know people requires + + align:start position:0% +requires uh you know people requires + + + align:start position:0% +requires uh you know people requires +resources that not necessarily um every + + align:start position:0% +resources that not necessarily um every + + + align:start position:0% +resources that not necessarily um every +every training environment is going to + + align:start position:0% +every training environment is going to + + + align:start position:0% +every training environment is going to +have something that can be turned into a + + align:start position:0% +have something that can be turned into a + + + align:start position:0% +have something that can be turned into a +fairly understandable set set of rules + + align:start position:0% +fairly understandable set set of rules + + + align:start position:0% +fairly understandable set set of rules +or use or using technologies that are + + align:start position:0% +or use or using technologies that are + + + align:start position:0% +or use or using technologies that are +fairly accessible. um you know, if + + align:start position:0% +fairly accessible. um you know, if + + + align:start position:0% +fairly accessible. um you know, if +you're going to play your voice in + + align:start position:0% +you're going to play your voice in + + + align:start position:0% +you're going to play your voice in +someone's ear, it's going to be a lot + + align:start position:0% +someone's ear, it's going to be a lot + + + align:start position:0% +someone's ear, it's going to be a lot +easier if that was using uh something + + align:start position:0% +easier if that was using uh something + + + align:start position:0% +easier if that was using uh something +recorded or something like a phone as + + align:start position:0% +recorded or something like a phone as + + + align:start position:0% +recorded or something like a phone as +opposed to + + align:start position:0% +opposed to + + + align:start position:0% +opposed to +that if it was if it was a phone + + align:start position:0% +that if it was if it was a phone + + + align:start position:0% +that if it was if it was a phone +conversation actually going like so it's + + align:start position:0% +conversation actually going like so it's + + + align:start position:0% +conversation actually going like so it's +live and people are in different rooms + + align:start position:0% +live and people are in different rooms + + + align:start position:0% +live and people are in different rooms +and actually talking to each other over + + align:start position:0% +and actually talking to each other over + + + align:start position:0% +and actually talking to each other over +the phone over Skype or something like + + align:start position:0% +the phone over Skype or something like + + + align:start position:0% +the phone over Skype or something like +that. But but you're talking to someone, + + align:start position:0% +that. But but you're talking to someone, + + + align:start position:0% +that. But but you're talking to someone, +you have a phone up so then the other + + align:start position:0% +you have a phone up so then the other + + + align:start position:0% +you have a phone up so then the other +person can hear what you're saying and + + align:start position:0% +person can hear what you're saying and + + + align:start position:0% +person can hear what you're saying and +be the evil voice + + align:start position:0% +be the evil voice + + + align:start position:0% +be the evil voice +>> like you know. + + align:start position:0% +>> like you know. + + + align:start position:0% +>> like you know. +>> Yeah. such a thing that you don't even + + align:start position:0% +>> Yeah. such a thing that you don't even + + + align:start position:0% +>> Yeah. such a thing that you don't even +need to do on Skype, right? You just get + + align:start position:0% +need to do on Skype, right? You just get + + + align:start position:0% +need to do on Skype, right? You just get +two cell phones to hit with with + + align:start position:0% +two cell phones to hit with with + + + align:start position:0% +two cell phones to hit with with +handsree sets and and now the technology + + align:start position:0% +handsree sets and and now the technology + + + align:start position:0% +handsree sets and and now the technology +just becomes that much easier for for + + align:start position:0% +just becomes that much easier for for + + + align:start position:0% +just becomes that much easier for for +users to + + align:start position:0% +users to + + + align:start position:0% +users to +two phones and two two headsets. It's + + align:start position:0% +two phones and two two headsets. It's + + + align:start position:0% +two phones and two two headsets. It's +almost + + align:start position:0% +almost + + + align:start position:0% +almost +>> I mean or you could make it that like + + align:start position:0% +>> I mean or you could make it that like + + + align:start position:0% +>> I mean or you could make it that like +for some game that two people are + + align:start position:0% +for some game that two people are + + + align:start position:0% +for some game that two people are +playing that like two groups are playing + + align:start position:0% +playing that like two groups are playing + + + align:start position:0% +playing that like two groups are playing +the same game but they both hear the + + align:start position:0% +the same game but they both hear the + + + align:start position:0% +the same game but they both hear the +other group like this group would hear + + align:start position:0% +other group like this group would hear + + + align:start position:0% +other group like this group would hear +the other groups playing the game. So, + + align:start position:0% +the other groups playing the game. So, + + + align:start position:0% +the other groups playing the game. So, +it's not even just like a random + + align:start position:0% +it's not even just like a random + + + align:start position:0% +it's not even just like a random +conversation. It's like they're playing + + align:start position:0% +conversation. It's like they're playing + + + align:start position:0% +conversation. It's like they're playing +the same game you're playing, but you're + + align:start position:0% +the same game you're playing, but you're + + + align:start position:0% +the same game you're playing, but you're +hearing the other group playing the + + align:start position:0% +hearing the other group playing the + + + align:start position:0% +hearing the other group playing the +game. So, you get to + + align:start position:0% +game. So, you get to + + + align:start position:0% +game. So, you get to +>> Wow. + + align:start position:0% +>> Wow. + + + align:start position:0% +>> Wow. +>> Wow. + + align:start position:0% +>> Wow. + + + align:start position:0% +>> Wow. +>> Uh deep. + + align:start position:0% +>> Uh deep. + + + align:start position:0% +>> Uh deep. +>> I would say two groups + + align:start position:0% +>> I would say two groups + + + align:start position:0% +>> I would say two groups +uh you drop in the same game. + + align:start position:0% + + + + align:start position:0% + +So, I just wanted to say + + align:start position:0% +So, I just wanted to say + + + align:start position:0% +So, I just wanted to say +that I think the thing which is really + + align:start position:0% +that I think the thing which is really + + + align:start position:0% +that I think the thing which is really +hard if you don't if you're working with + + align:start position:0% +hard if you don't if you're working with + + + align:start position:0% +hard if you don't if you're working with +people who like don't really want to do + + align:start position:0% +people who like don't really want to do + + + align:start position:0% +people who like don't really want to do +a role playing thing + + align:start position:0% +a role playing thing + + + align:start position:0% +a role playing thing +>> is like building a level of emotional + + align:start position:0% +>> is like building a level of emotional + + + align:start position:0% +>> is like building a level of emotional +intensity and the fear of violence. + + align:start position:0% +intensity and the fear of violence. + + + align:start position:0% +intensity and the fear of violence. +Um, which is kind of the point of the + + align:start position:0% +Um, which is kind of the point of the + + + align:start position:0% +Um, which is kind of the point of the +training like you want to be able to + + align:start position:0% +training like you want to be able to + + + align:start position:0% +training like you want to be able to +deal with that kind of emotional stress + + align:start position:0% +deal with that kind of emotional stress + + + align:start position:0% +deal with that kind of emotional stress +on your feet. + + align:start position:0% +on your feet. + + + align:start position:0% +on your feet. +>> Yeah. Um, so I was just wondering + + align:start position:0% +>> Yeah. Um, so I was just wondering + + + align:start position:0% +>> Yeah. Um, so I was just wondering +because I don't have any good ideas if + + align:start position:0% +because I don't have any good ideas if + + + align:start position:0% +because I don't have any good ideas if +anyone could think of something which + + align:start position:0% +anyone could think of something which + + + align:start position:0% +anyone could think of something which +which works out + + align:start position:0% +which works out + + + align:start position:0% +which works out +>> which can like genuinely create a + + align:start position:0% +>> which can like genuinely create a + + + align:start position:0% +>> which can like genuinely create a +situation where a monkey would be afraid + + align:start position:0% +situation where a monkey would be afraid + + + align:start position:0% +situation where a monkey would be afraid +of violence. + + align:start position:0% +of violence. + + + align:start position:0% +of violence. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Without actually without somebody having + + align:start position:0% +>> Without actually without somebody having + + + align:start position:0% +>> Without actually without somebody having +to threaten another person. + + align:start position:0% +to threaten another person. + + + align:start position:0% +to threaten another person. +I don't think he's going to be able to + + align:start position:0% +I don't think he's going to be able to + + + align:start position:0% +I don't think he's going to be able to +color on + + align:start position:0% +color on + + + align:start position:0% +color on +>> well well if one player's role is + + align:start position:0% +>> well well if one player's role is + + + align:start position:0% +>> well well if one player's role is +actually + + align:start position:0% +actually + + + align:start position:0% +actually +not to understand but to provide the + + align:start position:0% +not to understand but to provide the + + + align:start position:0% +not to understand but to provide the +experience for the other + + align:start position:0% +experience for the other + + + align:start position:0% +experience for the other +>> and they're hearing a recording that is + + align:start position:0% +>> and they're hearing a recording that is + + + align:start position:0% +>> and they're hearing a recording that is +giving them cues as to what to do and + + align:start position:0% +giving them cues as to what to do and + + + align:start position:0% +giving them cues as to what to do and +one of their cues is eventually like and + + align:start position:0% +one of their cues is eventually like and + + + align:start position:0% +one of their cues is eventually like and +no player is not brief this and one of + + align:start position:0% +no player is not brief this and one of + + + align:start position:0% +no player is not brief this and one of +their cues is like and now you know + + align:start position:0% +their cues is like and now you know + + + align:start position:0% +their cues is like and now you know +grabbing the player by the shoulders and + + align:start position:0% +grabbing the player by the shoulders and + + + align:start position:0% +grabbing the player by the shoulders and +like shake them violently and say you + + align:start position:0% +like shake them violently and say you + + + align:start position:0% +like shake them violently and say you +know say something you could you could + + align:start position:0% +know say something you could you could + + + align:start position:0% +know say something you could you could +possibly create a situ situation where + + align:start position:0% +possibly create a situ situation where + + + align:start position:0% +possibly create a situ situation where +you're like, whoa, you know, buddy, + + align:start position:0% +you're like, whoa, you know, buddy, + + + align:start position:0% +you're like, whoa, you know, buddy, +>> but the problem is you have to be able + + align:start position:0% +>> but the problem is you have to be able + + + align:start position:0% +>> but the problem is you have to be able +to get somebody who can do that without + + align:start position:0% +to get somebody who can do that without + + + align:start position:0% +to get somebody who can do that without +like cracking up in the middle of it + + align:start position:0% +like cracking up in the middle of it + + + align:start position:0% +like cracking up in the middle of it +because like people do that when they're + + align:start position:0% +because like people do that when they're + + + align:start position:0% +because like people do that when they're +nervous and uncomfortable. Like you so + + align:start position:0% +nervous and uncomfortable. Like you so + + + align:start position:0% +nervous and uncomfortable. Like you so +you pretty much be reduced to finding + + align:start position:0% +you pretty much be reduced to finding + + + align:start position:0% +you pretty much be reduced to finding +professional actors and that's a limited + + align:start position:0% +professional actors and that's a limited + + + align:start position:0% +professional actors and that's a limited +resource that like limit puts a + + align:start position:0% +resource that like limit puts a + + + align:start position:0% +resource that like limit puts a +limitation on on how widespread your + + align:start position:0% +limitation on on how widespread your + + + align:start position:0% +limitation on on how widespread your +game + + align:start position:0% +game + + + align:start position:0% +game +>> even people will take things seriously + + align:start position:0% +>> even people will take things seriously + + + align:start position:0% +>> even people will take things seriously +resource you have. + + align:start position:0% +resource you have. + + + align:start position:0% +resource you have. +>> I have a thought where you have like + + align:start position:0% +>> I have a thought where you have like + + + align:start position:0% +>> I have a thought where you have like +it's a patient patient interaction. So + + align:start position:0% +it's a patient patient interaction. So + + + align:start position:0% +it's a patient patient interaction. So +you have two people in different rooms + + align:start position:0% +you have two people in different rooms + + + align:start position:0% +you have two people in different rooms +on the phone with each other trying to + + align:start position:0% +on the phone with each other trying to + + + align:start position:0% +on the phone with each other trying to +negotiate something. I don't know what + + align:start position:0% +negotiate something. I don't know what + + + align:start position:0% +negotiate something. I don't know what +what it would be and have two other + + align:start position:0% +what it would be and have two other + + + align:start position:0% +what it would be and have two other +people in each of in each of their rooms + + align:start position:0% +people in each of in each of their rooms + + + align:start position:0% +people in each of in each of their rooms +that are like talking in their ear and + + align:start position:0% +that are like talking in their ear and + + + align:start position:0% +that are like talking in their ear and +trying to distract them from the + + align:start position:0% +trying to distract them from the + + + align:start position:0% +trying to distract them from the +conversation. + + align:start position:0% +conversation. + + + align:start position:0% +conversation. +>> Okay. So so patient talking to patient + + align:start position:0% +>> Okay. So so patient talking to patient + + + align:start position:0% +>> Okay. So so patient talking to patient +uh maybe can like + + align:start position:0% +uh maybe can like + + + align:start position:0% +uh maybe can like +medicine + + align:start position:0% +medicine + + + align:start position:0% +medicine +uh with uh voices in person. Yeah. + + align:start position:0% +uh with uh voices in person. Yeah. + + + align:start position:0% +uh with uh voices in person. Yeah. +>> Yeah. + + align:start position:0% + + + + align:start position:0% + +>> Uh there is a specifically an article on + + align:start position:0% +>> Uh there is a specifically an article on + + + align:start position:0% +>> Uh there is a specifically an article on +that I think. So actually + + align:start position:0% + + + + align:start position:0% + +Patrick. + + align:start position:0% +Patrick. + + + align:start position:0% +Patrick. +>> Um so I was thinking something along the + + align:start position:0% +>> Um so I was thinking something along the + + + align:start position:0% +>> Um so I was thinking something along the +lines of of like battleship if you have + + align:start position:0% +lines of of like battleship if you have + + + align:start position:0% +lines of of like battleship if you have +um like a doctor player and patient + + align:start position:0% +um like a doctor player and patient + + + align:start position:0% +um like a doctor player and patient +player and they're both looking at this + + align:start position:0% +player and they're both looking at this + + + align:start position:0% +player and they're both looking at this +um their own version of the same board + + align:start position:0% +um their own version of the same board + + + align:start position:0% +um their own version of the same board +>> and if the uh the patient wants to get + + align:start position:0% +>> and if the uh the patient wants to get + + + align:start position:0% +>> and if the uh the patient wants to get +from one end to the other um and the + + align:start position:0% +from one end to the other um and the + + + align:start position:0% +from one end to the other um and the +doctor has to allow whether or not they + + align:start position:0% +doctor has to allow whether or not they + + + align:start position:0% +doctor has to allow whether or not they +can make their move but on the doctor's + + align:start position:0% +can make their move but on the doctor's + + + align:start position:0% +can make their move but on the doctor's +board they have like different obstacles + + align:start position:0% +board they have like different obstacles + + + align:start position:0% +board they have like different obstacles +and so then um like the patient will say + + align:start position:0% +and so then um like the patient will say + + + align:start position:0% +and so then um like the patient will say +I want to move from here to here and the + + align:start position:0% +I want to move from here to here and the + + + align:start position:0% +I want to move from here to here and the +doctor says I can't let you do that I + + align:start position:0% +doctor says I can't let you do that I + + + align:start position:0% +doctor says I can't let you do that I +can let you go from here to here um it'd + + align:start position:0% +can let you go from here to here um it'd + + + align:start position:0% +can let you go from here to here um it'd +be a game about a compromise + + align:start position:0% +be a game about a compromise + + + align:start position:0% +be a game about a compromise +>> okay so sort of uh okay um doctor + + align:start position:0% +>> okay so sort of uh okay um doctor + + + align:start position:0% +>> okay so sort of uh okay um doctor +mediated movement okay + + align:start position:0% +mediated movement okay + + + align:start position:0% +mediated movement okay +forward movement + + align:start position:0% + + + + align:start position:0% + +>> and and the battleship analogy is good + + align:start position:0% +>> and and the battleship analogy is good + + + align:start position:0% +>> and and the battleship analogy is good +to help us remember. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. Uh to address something that Owen + + align:start position:0% +>> Yeah. Uh to address something that Owen + + + align:start position:0% +>> Yeah. Uh to address something that Owen +said about the trying to simulate u + + align:start position:0% +said about the trying to simulate u + + + align:start position:0% +said about the trying to simulate u +fear. Uh I mean if you can add time + + align:start position:0% +fear. Uh I mean if you can add time + + + align:start position:0% +fear. Uh I mean if you can add time +pressure to any game then I think that + + align:start position:0% +pressure to any game then I think that + + + align:start position:0% +pressure to any game then I think that +that strong of a stress situation it + + align:start position:0% +that strong of a stress situation it + + + align:start position:0% +that strong of a stress situation it +could kind of almost be fear. It could + + align:start position:0% +could kind of almost be fear. It could + + + align:start position:0% +could kind of almost be fear. It could +be a spider + + align:start position:0% +be a spider + + + align:start position:0% +be a spider +>> because what what you're really going + + align:start position:0% +>> because what what you're really going + + + align:start position:0% +>> because what what you're really going +for is stress + + align:start position:0% +for is stress + + + align:start position:0% +for is stress +you're going to make decision + + align:start position:0% +you're going to make decision + + + align:start position:0% +you're going to make decision +>> falling creating. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Anyways, + + align:start position:0% +>> Anyways, + + + align:start position:0% +>> Anyways, +>> uh + + align:start position:0% +>> uh + + + align:start position:0% +>> uh +>> um so kind of like an idea of how to + + align:start position:0% +>> um so kind of like an idea of how to + + + align:start position:0% +>> um so kind of like an idea of how to +take the the doctor mediated board and + + align:start position:0% +take the the doctor mediated board and + + + align:start position:0% +take the the doctor mediated board and +move it into the real world is that you + + align:start position:0% +move it into the real world is that you + + + align:start position:0% +move it into the real world is that you +could have we're talking about these + + align:start position:0% +could have we're talking about these + + + align:start position:0% +could have we're talking about these +like phoneto phone conversations. You + + align:start position:0% +like phoneto phone conversations. You + + + align:start position:0% +like phoneto phone conversations. You +could have the patient is like um in a + + align:start position:0% +could have the patient is like um in a + + + align:start position:0% +could have the patient is like um in a +room but he's blindfolded + + align:start position:0% +room but he's blindfolded + + + align:start position:0% +room but he's blindfolded +>> and like he's trying to like move + + align:start position:0% +>> and like he's trying to like move + + + align:start position:0% +>> and like he's trying to like move +through the room like towards an exit in + + align:start position:0% +through the room like towards an exit in + + + align:start position:0% +through the room like towards an exit in +the room or something and the doctor has + + align:start position:0% +the room or something and the doctor has + + + align:start position:0% +the room or something and the doctor has +like some limited information about the + + align:start position:0% +like some limited information about the + + + align:start position:0% +like some limited information about the +room and has to like help him like + + align:start position:0% +room and has to like help him like + + + align:start position:0% +room and has to like help him like +navigate through the room and he'll say + + align:start position:0% +navigate through the room and he'll say + + + align:start position:0% +navigate through the room and he'll say +like I want to move you know forward and + + align:start position:0% +like I want to move you know forward and + + + align:start position:0% +like I want to move you know forward and +he's like well you yeah you I can't + + align:start position:0% +he's like well you yeah you I can't + + + align:start position:0% +he's like well you yeah you I can't +really let you do that because there's a + + align:start position:0% +really let you do that because there's a + + + align:start position:0% +really let you do that because there's a +pit of spikes in front of you. So you + + align:start position:0% +pit of spikes in front of you. So you + + + align:start position:0% +pit of spikes in front of you. So you +wouldn't necessarily actually have a + + align:start position:0% +wouldn't necessarily actually have a + + + align:start position:0% +wouldn't necessarily actually have a +real pitull of spikes in front of them, + + align:start position:0% +real pitull of spikes in front of them, + + + align:start position:0% +real pitull of spikes in front of them, +but like that that kind of thing where + + align:start position:0% +but like that that kind of thing where + + + align:start position:0% +but like that that kind of thing where +you're trying to like gather information + + align:start position:0% +you're trying to like gather information + + + align:start position:0% +you're trying to like gather information +and and help them through this and it + + align:start position:0% +and and help them through this and it + + + align:start position:0% +and and help them through this and it +you can like even put time pressure on + + align:start position:0% +you can like even put time pressure on + + + align:start position:0% +you can like even put time pressure on +it and say like, well, you know, I have + + align:start position:0% +it and say like, well, you know, I have + + + align:start position:0% +it and say like, well, you know, I have +to make a decision now because he wants + + align:start position:0% +to make a decision now because he wants + + + align:start position:0% +to make a decision now because he wants +to move now, + + align:start position:0% +to move now, + + + align:start position:0% +to move now, +>> but I might like accidentally move him + + align:start position:0% +>> but I might like accidentally move him + + + align:start position:0% +>> but I might like accidentally move him +into an obstacle and like how to deal + + align:start position:0% +into an obstacle and like how to deal + + + align:start position:0% +into an obstacle and like how to deal +with that. that or you could have a + + align:start position:0% +with that. that or you could have a + + + align:start position:0% +with that. that or you could have a +thing where no or you can combine it + + align:start position:0% +thing where no or you can combine it + + + align:start position:0% +thing where no or you can combine it +with some things that there are things + + align:start position:0% +with some things that there are things + + + align:start position:0% +with some things that there are things +that the that the patient needs to do + + align:start position:0% +that the that the patient needs to do + + + align:start position:0% +that the that the patient needs to do +that the patient can talk about. + + align:start position:0% +that the patient can talk about. + + + align:start position:0% +that the patient can talk about. +>> Uh and you know it might be something + + align:start position:0% +>> Uh and you know it might be something + + + align:start position:0% +>> Uh and you know it might be something +like the patient has to move every 10 + + align:start position:0% +like the patient has to move every 10 + + + align:start position:0% +like the patient has to move every 10 +seconds and only the patient knows this. + + align:start position:0% +seconds and only the patient knows this. + + + align:start position:0% +seconds and only the patient knows this. +The doctor doesn't + + align:start position:0% +The doctor doesn't + + + align:start position:0% +The doctor doesn't +>> the patient has a fear of moving to the + + align:start position:0% +>> the patient has a fear of moving to the + + + align:start position:0% +>> the patient has a fear of moving to the +left + + align:start position:0% +left + + + align:start position:0% +left +>> or something like that. Things like that + + align:start position:0% +>> or something like that. Things like that + + + align:start position:0% +>> or something like that. Things like that +patient has moved left. And I think it + + align:start position:0% +patient has moved left. And I think it + + + align:start position:0% +patient has moved left. And I think it +it also emphasizes the thing that um + + align:start position:0% +it also emphasizes the thing that um + + + align:start position:0% +it also emphasizes the thing that um +they were talking about on Monday in + + align:start position:0% +they were talking about on Monday in + + + align:start position:0% +they were talking about on Monday in +that you are both trying to to not like + + align:start position:0% +that you are both trying to to not like + + + align:start position:0% +that you are both trying to to not like +if if a it gets to the escalates to the + + align:start position:0% +if if a it gets to the escalates to the + + + align:start position:0% +if if a it gets to the escalates to the +point where violence happens, + + align:start position:0% +point where violence happens, + + + align:start position:0% +point where violence happens, +>> you're both trying to not let yourself + + align:start position:0% +>> you're both trying to not let yourself + + + align:start position:0% +>> you're both trying to not let yourself +get hurt, but you're also trying to not + + align:start position:0% +get hurt, but you're also trying to not + + + align:start position:0% +get hurt, but you're also trying to not +hurt them as well. + + align:start position:0% +hurt them as well. + + + align:start position:0% +hurt them as well. +>> And I think incorporating that some way + + align:start position:0% +>> And I think incorporating that some way + + + align:start position:0% +>> And I think incorporating that some way +would be cool. + + align:start position:0% +would be cool. + + + align:start position:0% +would be cool. +>> Definitely a lot of these ideas and sort + + align:start position:0% +>> Definitely a lot of these ideas and sort + + + align:start position:0% +>> Definitely a lot of these ideas and sort +of like mechanicking the patients + + align:start position:0% +of like mechanicking the patients + + + align:start position:0% +of like mechanicking the patients +limitations are really really cool. uh + + align:start position:0% +limitations are really really cool. uh + + + align:start position:0% +limitations are really really cool. uh +but again remember the audience is the + + align:start position:0% +but again remember the audience is the + + + align:start position:0% +but again remember the audience is the +resident. So understanding what what + + align:start position:0% +resident. So understanding what what + + + align:start position:0% +resident. So understanding what what +what what patient going through is + + align:start position:0% +what what patient going through is + + + align:start position:0% +what what patient going through is +useful but also understanding thinking + + align:start position:0% +useful but also understanding thinking + + + align:start position:0% +useful but also understanding thinking +of rules that help uh resident + + align:start position:0% +of rules that help uh resident + + + align:start position:0% +of rules that help uh resident +understand what they can do uh is also + + align:start position:0% +understand what they can do uh is also + + + align:start position:0% +understand what they can do uh is also +really important. So don't don't don't + + align:start position:0% +really important. So don't don't don't + + + align:start position:0% +really important. So don't don't don't +just think about throwing tons of + + align:start position:0% +just think about throwing tons of + + + align:start position:0% +just think about throwing tons of +limitations on them without also giving + + align:start position:0% +limitations on them without also giving + + + align:start position:0% +limitations on them without also giving +them abilities uh you know things that + + align:start position:0% +them abilities uh you know things that + + + align:start position:0% +them abilities uh you know things that +they can actively do that you can + + align:start position:0% +they can actively do that you can + + + align:start position:0% +they can actively do that you can +actually carry out. So ripping off the + + align:start position:0% +actually carry out. So ripping off the + + + align:start position:0% +actually carry out. So ripping off the +time pressure thing, I think that it + + align:start position:0% +time pressure thing, I think that it + + + align:start position:0% +time pressure thing, I think that it +might make sense for these kinds of + + align:start position:0% +might make sense for these kinds of + + + align:start position:0% +might make sense for these kinds of +escalation negotiation type situations + + align:start position:0% +escalation negotiation type situations + + + align:start position:0% +escalation negotiation type situations +for the um for the person who is + + align:start position:0% +for the um for the person who is + + + align:start position:0% +for the um for the person who is +controlling the patient to kind of know + + align:start position:0% +controlling the patient to kind of know + + + align:start position:0% +controlling the patient to kind of know +what their triggers are and every time + + align:start position:0% +what their triggers are and every time + + + align:start position:0% +what their triggers are and every time +like a bad thing is said then the they + + align:start position:0% +like a bad thing is said then the they + + + align:start position:0% +like a bad thing is said then the they +just reduce the amount of time that the + + align:start position:0% +just reduce the amount of time that the + + + align:start position:0% +just reduce the amount of time that the +doctor has to deal with them + + align:start position:0% +doctor has to deal with them + + + align:start position:0% +doctor has to deal with them +>> and like and they say that okay they + + align:start position:0% +>> and like and they say that okay they + + + align:start position:0% +>> and like and they say that okay they +just say like minus 10 seconds and like + + align:start position:0% +just say like minus 10 seconds and like + + + align:start position:0% +just say like minus 10 seconds and like +and the they have a timer and ticks down + + align:start position:0% +and the they have a timer and ticks down + + + align:start position:0% +and the they have a timer and ticks down +to reach the conclusion, getting the the + + align:start position:0% +to reach the conclusion, getting the the + + + align:start position:0% +to reach the conclusion, getting the the +doctor, getting them to where they want + + align:start position:0% +doctor, getting them to where they want + + + align:start position:0% +doctor, getting them to where they want +to be. + + align:start position:0% +to be. + + + align:start position:0% +to be. +>> Um, and and so rather than like raising + + align:start position:0% +>> Um, and and so rather than like raising + + + align:start position:0% +>> Um, and and so rather than like raising +their voice or being physically in some + + align:start position:0% +their voice or being physically in some + + + align:start position:0% +their voice or being physically in some +way, they just like adjust a timer and + + align:start position:0% +way, they just like adjust a timer and + + + align:start position:0% +way, they just like adjust a timer and +when it gets down to zero. So, + + align:start position:0% +when it gets down to zero. So, + + + align:start position:0% +when it gets down to zero. So, +>> yeah, I can see that I wrote equals + + align:start position:0% +>> yeah, I can see that I wrote equals + + + align:start position:0% +>> yeah, I can see that I wrote equals +reduce time variable + + align:start position:0% +reduce time variable + + + align:start position:0% +reduce time variable +actually equals. + + align:start position:0% +actually equals. + + + align:start position:0% +actually equals. +>> Okay. Um, + + align:start position:0% +>> Okay. Um, + + + align:start position:0% +>> Okay. Um, +just to say that way you can make your + + align:start position:0% +just to say that way you can make your + + + align:start position:0% +just to say that way you can make your +players feel pressure is to give them a + + align:start position:0% +players feel pressure is to give them a + + + align:start position:0% +players feel pressure is to give them a +really flat goal hierarchy, right? So, a + + align:start position:0% +really flat goal hierarchy, right? So, a + + + align:start position:0% +really flat goal hierarchy, right? So, a +good example is missile command. Does + + align:start position:0% +good example is missile command. Does + + + align:start position:0% +good example is missile command. Does +everyone know that game? So, missile + + align:start position:0% +everyone know that game? So, missile + + + align:start position:0% +everyone know that game? So, missile +command is you have like six cities and + + align:start position:0% +command is you have like six cities and + + + align:start position:0% +command is you have like six cities and +there's missiles coming and you have to + + align:start position:0% +there's missiles coming and you have to + + + align:start position:0% +there's missiles coming and you have to +shoot them all down and each city is + + align:start position:0% +shoot them all down and each city is + + + align:start position:0% +shoot them all down and each city is +equally valuable. So, if you lose one, + + align:start position:0% +equally valuable. So, if you lose one, + + + align:start position:0% +equally valuable. So, if you lose one, +you're in drastically reduced position. + + align:start position:0% +you're in drastically reduced position. + + + align:start position:0% +you're in drastically reduced position. +Um whereas games that tend to have like + + align:start position:0% +Um whereas games that tend to have like + + + align:start position:0% +Um whereas games that tend to have like +a more structured goal hierarchy will + + align:start position:0% +a more structured goal hierarchy will + + + align:start position:0% +a more structured goal hierarchy will +have like basically means you can afford + + align:start position:0% +have like basically means you can afford + + + align:start position:0% +have like basically means you can afford +a loss, right? So like chess is a good + + align:start position:0% +a loss, right? So like chess is a good + + + align:start position:0% +a loss, right? So like chess is a good +example. You say, "Okay, I can afford to + + align:start position:0% +example. You say, "Okay, I can afford to + + + align:start position:0% +example. You say, "Okay, I can afford to +lose this." Whereas a missile command, + + align:start position:0% +lose this." Whereas a missile command, + + + align:start position:0% +lose this." Whereas a missile command, +you can't afford to lose anything. So by + + align:start position:0% +you can't afford to lose anything. So by + + + align:start position:0% +you can't afford to lose anything. So by +really capping, + + align:start position:0% +really capping, + + + align:start position:0% +really capping, +you know, what the player has and what + + align:start position:0% +you know, what the player has and what + + + align:start position:0% +you know, what the player has and what +they're what they can afford to lose. + + align:start position:0% +they're what they can afford to lose. + + + align:start position:0% +they're what they can afford to lose. +And then making sure that, you know, all + + align:start position:0% +And then making sure that, you know, all + + + align:start position:0% +And then making sure that, you know, all +of their goals are equal value, that + + align:start position:0% +of their goals are equal value, that + + + align:start position:0% +of their goals are equal value, that +means that every loss and every failure + + align:start position:0% +means that every loss and every failure + + + align:start position:0% +means that every loss and every failure +is felt much more strongly. And I I felt + + align:start position:0% +is felt much more strongly. And I I felt + + + align:start position:0% +is felt much more strongly. And I I felt +like at least Dion when you were doing + + align:start position:0% +like at least Dion when you were doing + + + align:start position:0% +like at least Dion when you were doing +your the role play um there was this + + align:start position:0% +your the role play um there was this + + + align:start position:0% +your the role play um there was this +sense especially coming from Caesar that + + align:start position:0% +sense especially coming from Caesar that + + + align:start position:0% +sense especially coming from Caesar that +you know any one thing that goes wrong + + align:start position:0% +you know any one thing that goes wrong + + + align:start position:0% +you know any one thing that goes wrong +is really bad. There's like a really + + align:start position:0% +is really bad. There's like a really + + + align:start position:0% +is really bad. There's like a really +thin line there. + + align:start position:0% +thin line there. + + + align:start position:0% +thin line there. +>> I mean that's especially applicable when + + align:start position:0% +>> I mean that's especially applicable when + + + align:start position:0% +>> I mean that's especially applicable when +you're talking about the doctor's goals, + + align:start position:0% +you're talking about the doctor's goals, + + + align:start position:0% +you're talking about the doctor's goals, +not necessarily the patient's goals. + + align:start position:0% +not necessarily the patient's goals. + + + align:start position:0% +not necessarily the patient's goals. +>> Yeah. Yeah. From I mean from the + + align:start position:0% +>> Yeah. Yeah. From I mean from the + + + align:start position:0% +>> Yeah. Yeah. From I mean from the +doctor's position, right? There's you + + align:start position:0% +doctor's position, right? There's you + + + align:start position:0% +doctor's position, right? There's you +can't really afford a lot of mistakes in + + align:start position:0% +can't really afford a lot of mistakes in + + + align:start position:0% +can't really afford a lot of mistakes in +these situations. + + align:start position:0% + + + + align:start position:0% + +Um, I'm kind of the guest, but I was + + align:start position:0% +Um, I'm kind of the guest, but I was + + + align:start position:0% +Um, I'm kind of the guest, but I was +listening to what you're saying and um, + + align:start position:0% +listening to what you're saying and um, + + + align:start position:0% +listening to what you're saying and um, +I've had a thought on how you could + + align:start position:0% +I've had a thought on how you could + + + align:start position:0% +I've had a thought on how you could +combine lots of these different ideas. + + align:start position:0% +combine lots of these different ideas. + + + align:start position:0% +combine lots of these different ideas. +Um, I'm envisioning a game where there + + align:start position:0% +Um, I'm envisioning a game where there + + + align:start position:0% +Um, I'm envisioning a game where there +would be two types of players like you + + align:start position:0% +would be two types of players like you + + + align:start position:0% +would be two types of players like you +were mentioning, um, doctors and + + align:start position:0% +were mentioning, um, doctors and + + + align:start position:0% +were mentioning, um, doctors and +patients. And there would be one doctor + + align:start position:0% +patients. And there would be one doctor + + + align:start position:0% +patients. And there would be one doctor +and multiple patients. It would be a + + align:start position:0% +and multiple patients. It would be a + + + align:start position:0% +and multiple patients. It would be a +turn-based game where you'd go around, + + align:start position:0% +turn-based game where you'd go around, + + + align:start position:0% +turn-based game where you'd go around, +give each person a turn. and the doctor + + align:start position:0% +give each person a turn. and the doctor + + + align:start position:0% +give each person a turn. and the doctor +would always be in a relationship with + + align:start position:0% +would always be in a relationship with + + + align:start position:0% +would always be in a relationship with +each individual one and um limited + + align:start position:0% +each individual one and um limited + + + align:start position:0% +each individual one and um limited +vocabulary I thought was important. Um + + align:start position:0% +vocabulary I thought was important. Um + + + align:start position:0% +vocabulary I thought was important. Um +taking that from a couple of the ideas, + + align:start position:0% +taking that from a couple of the ideas, + + + align:start position:0% +taking that from a couple of the ideas, +the patient and the doctor each have + + align:start position:0% +the patient and the doctor each have + + + align:start position:0% +the patient and the doctor each have +their own set of vocabularies and the + + align:start position:0% +their own set of vocabularies and the + + + align:start position:0% +their own set of vocabularies and the +clash of that would introduce some um a + + align:start position:0% +clash of that would introduce some um a + + + align:start position:0% +clash of that would introduce some um a +mechanic there where the patient has um + + align:start position:0% +mechanic there where the patient has um + + + align:start position:0% +mechanic there where the patient has um +their own vocabulary describing to the + + align:start position:0% +their own vocabulary describing to the + + + align:start position:0% +their own vocabulary describing to the +doctor what they like, what they don't + + align:start position:0% +doctor what they like, what they don't + + + align:start position:0% +doctor what they like, what they don't +like. Um they know what they like, they + + align:start position:0% +like. Um they know what they like, they + + + align:start position:0% +like. Um they know what they like, they +don't like. you you could abstract it to + + align:start position:0% +don't like. you you could abstract it to + + + align:start position:0% +don't like. you you could abstract it to +um describe uh maybe + + align:start position:0% +um describe uh maybe + + + align:start position:0% +um describe uh maybe +anything that the doctor would have in + + align:start position:0% +anything that the doctor would have in + + + align:start position:0% +anything that the doctor would have in +their vocabulary. So, uh as one example, + + align:start position:0% +their vocabulary. So, uh as one example, + + + align:start position:0% +their vocabulary. So, uh as one example, +the doctor could give the patient a card + + align:start position:0% +the doctor could give the patient a card + + + align:start position:0% +the doctor could give the patient a card +with a shape or um some item on it and + + align:start position:0% +with a shape or um some item on it and + + + align:start position:0% +with a shape or um some item on it and +the item has attributes like color, + + align:start position:0% +the item has attributes like color, + + + align:start position:0% +the item has attributes like color, +shape, something that um somebody could + + align:start position:0% +shape, something that um somebody could + + + align:start position:0% +shape, something that um somebody could +like or dislike in their list. um they + + align:start position:0% +like or dislike in their list. um they + + + align:start position:0% +like or dislike in their list. um they +would look at this and see um one of + + align:start position:0% +would look at this and see um one of + + + align:start position:0% +would look at this and see um one of +these things clashes with something in + + align:start position:0% +these things clashes with something in + + + align:start position:0% +these things clashes with something in +my list of dislikes. I don't like that + + align:start position:0% +my list of dislikes. I don't like that + + + align:start position:0% +my list of dislikes. I don't like that +card. I'm going to escalate my um my + + align:start position:0% +card. I'm going to escalate my um my + + + align:start position:0% +card. I'm going to escalate my um my +anger, my uh displeasure with the + + align:start position:0% +anger, my uh displeasure with the + + + align:start position:0% +anger, my uh displeasure with the +situation. And so the doctor has a + + align:start position:0% +situation. And so the doctor has a + + + align:start position:0% +situation. And so the doctor has a +limited amount of time to deal with each + + align:start position:0% +limited amount of time to deal with each + + + align:start position:0% +limited amount of time to deal with each +patient. Um as the patient's escalation + + align:start position:0% +patient. Um as the patient's escalation + + + align:start position:0% +patient. Um as the patient's escalation +increases, + + align:start position:0% +increases, + + + align:start position:0% +increases, +they have less and less time to be dealt + + align:start position:0% +they have less and less time to be dealt + + + align:start position:0% +they have less and less time to be dealt +with. After a certain point, the doctor + + align:start position:0% +with. After a certain point, the doctor + + + align:start position:0% +with. After a certain point, the doctor +loses that patient. So you have that + + align:start position:0% +loses that patient. So you have that + + + align:start position:0% +loses that patient. So you have that +loss brought in. Um and then after all + + align:start position:0% +loss brought in. Um and then after all + + + align:start position:0% +loss brought in. Um and then after all +the patients have been lost, the the + + align:start position:0% +the patients have been lost, the the + + + align:start position:0% +the patients have been lost, the the +game is over. The way that it would be + + align:start position:0% +game is over. The way that it would be + + + align:start position:0% +game is over. The way that it would be +won is that the doctor is discovering + + align:start position:0% +won is that the doctor is discovering + + + align:start position:0% +won is that the doctor is discovering +the profile of each patient because they + + align:start position:0% +the profile of each patient because they + + + align:start position:0% +the profile of each patient because they +are trying to um like in a normal + + align:start position:0% +are trying to um like in a normal + + + align:start position:0% +are trying to um like in a normal +setting in a in a real life setting, + + align:start position:0% +setting in a in a real life setting, + + + align:start position:0% +setting in a in a real life setting, +you're trying to discover the the + + align:start position:0% +you're trying to discover the the + + + align:start position:0% +you're trying to discover the the +profile that allows the doctor to um + + align:start position:0% +profile that allows the doctor to um + + + align:start position:0% +profile that allows the doctor to um +deal with the patient in the best + + align:start position:0% +deal with the patient in the best + + + align:start position:0% +deal with the patient in the best +possible way so that they aren't + + align:start position:0% +possible way so that they aren't + + + align:start position:0% +possible way so that they aren't +violent. Um and yeah, so so so that that + + align:start position:0% +violent. Um and yeah, so so so that that + + + align:start position:0% +violent. Um and yeah, so so so that that +seems to play off the um the patient and + + align:start position:0% +seems to play off the um the patient and + + + align:start position:0% +seems to play off the um the patient and +doctor have different ro rules and goals + + align:start position:0% +doctor have different ro rules and goals + + + align:start position:0% +doctor have different ro rules and goals +and triggers. You know, you've got a + + align:start position:0% +and triggers. You know, you've got a + + + align:start position:0% +and triggers. You know, you've got a +situation where in in uh in what he was + + align:start position:0% +situation where in in uh in what he was + + + align:start position:0% +situation where in in uh in what he was +suggesting, you have one doctor to + + align:start position:0% +suggesting, you have one doctor to + + + align:start position:0% +suggesting, you have one doctor to +multiple patients. Um which is which is + + align:start position:0% +multiple patients. Um which is which is + + + align:start position:0% +multiple patients. Um which is which is +accurate. I'm not quite sure that that + + align:start position:0% +accurate. I'm not quite sure that that + + + align:start position:0% +accurate. I'm not quite sure that that +they'd be dealing with them + + align:start position:0% +they'd be dealing with them + + + align:start position:0% +they'd be dealing with them +simultaneously, but that might not + + align:start position:0% +simultaneously, but that might not + + + align:start position:0% +simultaneously, but that might not +matter for the purposes of strategy. Uh + + align:start position:0% +matter for the purposes of strategy. Uh + + + align:start position:0% +matter for the purposes of strategy. Uh +and uh and + + align:start position:0% +and uh and + + + align:start position:0% +and uh and +and yeah, it might be it might be kind + + align:start position:0% +and yeah, it might be it might be kind + + + align:start position:0% +and yeah, it might be it might be kind +of like those like those improv things + + align:start position:0% +of like those like those improv things + + + align:start position:0% +of like those like those improv things +where if you manage to figure out uh if + + align:start position:0% +where if you manage to figure out uh if + + + align:start position:0% +where if you manage to figure out uh if +you manage to figure out before time + + align:start position:0% +you manage to figure out before time + + + align:start position:0% +you manage to figure out before time +runs out what a person's profile is, + + align:start position:0% +runs out what a person's profile is, + + + align:start position:0% +runs out what a person's profile is, +that could be the win condition. So it's + + align:start position:0% +that could be the win condition. So it's + + + align:start position:0% +that could be the win condition. So it's +equal win uh if you manage to succeed is + + align:start position:0% +equal win uh if you manage to succeed is + + + align:start position:0% +equal win uh if you manage to succeed is +an equal loss if you don't manage to get + + align:start position:0% +an equal loss if you don't manage to get + + + align:start position:0% +an equal loss if you don't manage to get +it by time. combine it with something + + align:start position:0% +it by time. combine it with something + + + align:start position:0% +it by time. combine it with something +like the uh give a trigger and reduce + + align:start position:0% +like the uh give a trigger and reduce + + + align:start position:0% +like the uh give a trigger and reduce +the amount of time that you have + + align:start position:0% +the amount of time that you have + + + align:start position:0% +the amount of time that you have +available. Number of turns available for + + align:start position:0% +available. Number of turns available for + + + align:start position:0% +available. Number of turns available for +doesn't have to be real time. Um so yeah + + align:start position:0% +doesn't have to be real time. Um so yeah + + + align:start position:0% +doesn't have to be real time. Um so yeah +so so that so you can present with + + align:start position:0% +so so that so you can present with + + + align:start position:0% +so so that so you can present with +multiple patients. + + align:start position:0% + + + + align:start position:0% + +>> So like that doesn't even necessarily + + align:start position:0% +>> So like that doesn't even necessarily + + + align:start position:0% +>> So like that doesn't even necessarily +have to deal with uh actual talking + + align:start position:0% +have to deal with uh actual talking + + + align:start position:0% +have to deal with uh actual talking +about actual psychiatric warrant + + align:start position:0% +about actual psychiatric warrant + + + align:start position:0% +about actual psychiatric warrant +situations. That could be something + + align:start position:0% +situations. That could be something + + + align:start position:0% +situations. That could be something +like, you know, objects and colors, + + align:start position:0% +like, you know, objects and colors, + + + align:start position:0% +like, you know, objects and colors, +right? You know, it's more of a guessing + + align:start position:0% +right? You know, it's more of a guessing + + + align:start position:0% +right? You know, it's more of a guessing +game, but uh that might be too abstract + + align:start position:0% +game, but uh that might be too abstract + + + align:start position:0% +game, but uh that might be too abstract +possibly because because in the end, you + + align:start position:0% +possibly because because in the end, you + + + align:start position:0% +possibly because because in the end, you +kind of still want people to be able to + + align:start position:0% +kind of still want people to be able to + + + align:start position:0% +kind of still want people to be able to +tie it back to the experience of uh like + + align:start position:0% +tie it back to the experience of uh like + + + align:start position:0% +tie it back to the experience of uh like +to be able to make make an easy + + align:start position:0% +to be able to make make an easy + + + align:start position:0% +to be able to make make an easy +connection with uh what it's like to be + + align:start position:0% +connection with uh what it's like to be + + + align:start position:0% +connection with uh what it's like to be +a resident or what's going to be like to + + align:start position:0% +a resident or what's going to be like to + + + align:start position:0% +a resident or what's going to be like to +be a resident. Um so, uh this is where + + align:start position:0% +be a resident. Um so, uh this is where + + + align:start position:0% +be a resident. Um so, uh this is where +the theme needs to be pretty clear. Um + + align:start position:0% +the theme needs to be pretty clear. Um + + + align:start position:0% +the theme needs to be pretty clear. Um +but then like Clara, you know, is not + + align:start position:0% +but then like Clara, you know, is not + + + align:start position:0% +but then like Clara, you know, is not +meeting. The meeting has also done tied + + align:start position:0% +meeting. The meeting has also done tied + + + align:start position:0% +meeting. The meeting has also done tied +pretty well with young mechanics. Um so + + align:start position:0% +pretty well with young mechanics. Um so + + + align:start position:0% +pretty well with young mechanics. Um so +uh that's just something to keep in + + align:start position:0% +uh that's just something to keep in + + + align:start position:0% +uh that's just something to keep in +mind. + + align:start position:0% +mind. + + + align:start position:0% +mind. +Um + + align:start position:0% + + + + align:start position:0% + +okay. Um so we've got about another half + + align:start position:0% +okay. Um so we've got about another half + + + align:start position:0% +okay. Um so we've got about another half +an hour plus. Uh + + align:start position:0% +an hour plus. Uh + + + align:start position:0% +an hour plus. Uh +I think the plan was just to let + + align:start position:0% +I think the plan was just to let + + + align:start position:0% +I think the plan was just to let +everyone kind of like figure out what + + align:start position:0% +everyone kind of like figure out what + + + align:start position:0% +everyone kind of like figure out what +teams you wanted to be in. you know, + + align:start position:0% +teams you wanted to be in. you know, + + + align:start position:0% +teams you wanted to be in. you know, +this is kind of pre-class time to talk + + align:start position:0% +this is kind of pre-class time to talk + + + align:start position:0% +this is kind of pre-class time to talk +uh to talk with each other and um see if + + align:start position:0% +uh to talk with each other and um see if + + + align:start position:0% +uh to talk with each other and um see if +there's stuff in here that people were + + align:start position:0% +there's stuff in here that people were + + + align:start position:0% +there's stuff in here that people were +really psyched about. Is there is there + + align:start position:0% +really psyched about. Is there is there + + + align:start position:0% +really psyched about. Is there is there +anyone in this class that's already + + align:start position:0% +anyone in this class that's already + + + align:start position:0% +anyone in this class that's already +like, you know, this is something I + + align:start position:0% +like, you know, this is something I + + + align:start position:0% +like, you know, this is something I +really want to do? Um + + align:start position:0% +really want to do? Um + + + align:start position:0% +really want to do? Um +>> well, my preference is towards the + + align:start position:0% +>> well, my preference is towards the + + + align:start position:0% +>> well, my preference is towards the +management. + + align:start position:0% +management. + + + align:start position:0% +management. +>> Okay. So, what award management. + + align:start position:0% +>> Okay. So, what award management. + + + align:start position:0% +>> Okay. So, what award management. +So yeah, just one. + + align:start position:0% + + + + align:start position:0% + +>> Yeah, I don't really have any plans for + + align:start position:0% +>> Yeah, I don't really have any plans for + + + align:start position:0% +>> Yeah, I don't really have any plans for +this. + + align:start position:0% +this. + + + align:start position:0% +this. +>> I'd be interested in in uh in voices and + + align:start position:0% +>> I'd be interested in in uh in voices and + + + align:start position:0% +>> I'd be interested in in uh in voices and +hidden information. So + + align:start position:0% +hidden information. So + + + align:start position:0% +hidden information. So +fooling players in in and that results + + align:start position:0% +fooling players in in and that results + + + align:start position:0% +fooling players in in and that results +in them behaving in erratic ways as from + + align:start position:0% +in them behaving in erratic ways as from + + + align:start position:0% +in them behaving in erratic ways as from +the point of view of other players and + + align:start position:0% +the point of view of other players and + + + align:start position:0% +the point of view of other players and +then from the point of view the player + + align:start position:0% +then from the point of view the player + + + align:start position:0% +then from the point of view the player +who's behaving radically other players + + align:start position:0% +who's behaving radically other players + + + align:start position:0% +who's behaving radically other players +behaving erratically because it's not + + align:start position:0% +behaving erratically because it's not + + + align:start position:0% +behaving erratically because it's not +fitting with what they think is actually + + align:start position:0% +fitting with what they think is actually + + + align:start position:0% +fitting with what they think is actually +going on + + align:start position:0% +going on + + + align:start position:0% +going on +>> or voices or both or something like + + align:start position:0% +>> or voices or both or something like + + + align:start position:0% +>> or voices or both or something like +that. + + align:start position:0% +that. + + + align:start position:0% +that. +>> So that's that's kind of the general + + align:start position:0% +>> So that's that's kind of the general + + + align:start position:0% +>> So that's that's kind of the general +territory that you're interested in + + align:start position:0% +territory that you're interested in + + + align:start position:0% +territory that you're interested in +anyone who wants to + + align:start position:0% +anyone who wants to + + + align:start position:0% +anyone who wants to +>> I'm very interested in the escalation + + align:start position:0% +>> I'm very interested in the escalation + + + align:start position:0% +>> I'm very interested in the escalation +deescalation by hidden keywords. + + align:start position:0% + + + + align:start position:0% + +I like uh I like basically hidden rules, + + align:start position:0% +I like uh I like basically hidden rules, + + + align:start position:0% +I like uh I like basically hidden rules, +goals, and keywords and two different + + align:start position:0% +goals, and keywords and two different + + + align:start position:0% +goals, and keywords and two different +players uh playing the same character. + + align:start position:0% +players uh playing the same character. + + + align:start position:0% +players uh playing the same character. +Two mechanics I really like. + + align:start position:0% + + + + align:start position:0% + +Okay, we we have a couple of seeds out + + align:start position:0% +Okay, we we have a couple of seeds out + + + align:start position:0% +Okay, we we have a couple of seeds out +there and uh you know the caffeine helps + + align:start position:0% +there and uh you know the caffeine helps + + + align:start position:0% +there and uh you know the caffeine helps +us a bunch in the + + align:start position:0% +us a bunch in the + + + align:start position:0% +us a bunch in the +um what do we have on Friday? + + align:start position:0% +um what do we have on Friday? + + + align:start position:0% +um what do we have on Friday? +>> Um Friday we mostly just have + + align:start position:0% +>> Um Friday we mostly just have + + + align:start position:0% +>> Um Friday we mostly just have +brainstorming and team building + + align:start position:0% +brainstorming and team building + + + align:start position:0% +brainstorming and team building +schedule. I mean I think that time is + + align:start position:0% +schedule. I mean I think that time is + + + align:start position:0% +schedule. I mean I think that time is +pretty flexible. + + align:start position:0% +pretty flexible. + + + align:start position:0% +pretty flexible. +>> So what I can do maybe if folks can plan + + align:start position:0% +>> So what I can do maybe if folks can plan + + + align:start position:0% +>> So what I can do maybe if folks can plan +to come into Wednesday with the team + + align:start position:0% +to come into Wednesday with the team + + + align:start position:0% +to come into Wednesday with the team +then what I might do is I might move my + + align:start position:0% +then what I might do is I might move my + + + align:start position:0% +then what I might do is I might move my +my + + align:start position:0% +my + + + align:start position:0% +my +>> Friday. Friday. + + align:start position:0% +>> Friday. Friday. + + + align:start position:0% +>> Friday. Friday. +Yeah. Then um then I will I'll move my + + align:start position:0% +Yeah. Then um then I will I'll move my + + + align:start position:0% +Yeah. Then um then I will I'll move my +live action talk up till Friday instead. + + align:start position:0% +live action talk up till Friday instead. + + + align:start position:0% +live action talk up till Friday instead. +>> So So Wednesday we can just follow. It + + align:start position:0% +>> So So Wednesday we can just follow. It + + + align:start position:0% +>> So So Wednesday we can just follow. It +seems like a lot of people are going in + + align:start position:0% +seems like a lot of people are going in + + + align:start position:0% +seems like a lot of people are going in +that direction. + + align:start position:0% +that direction. + + + align:start position:0% +that direction. +Yeah. Okay. You don't have to do a live + + align:start position:0% +Yeah. Okay. You don't have to do a live + + + align:start position:0% +Yeah. Okay. You don't have to do a live +action game, but it's one of my favorite + + align:start position:0% +action game, but it's one of my favorite + + + align:start position:0% +action game, but it's one of my favorite +games. So \ No newline at end of file diff --git a/kWNv0-0tlAw.txt b/kWNv0-0tlAw.txt new file mode 100644 index 0000000000000000000000000000000000000000..7d1e0ace694040d46309e5a98653426c0fa371fd --- /dev/null +++ b/kWNv0-0tlAw.txt @@ -0,0 +1,3240 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: OK. + +So what we are talking about +is actually matrix elements. + +If you want to do anything +interesting in atomic physics, + +you have to copy or induce +transitions from one state + +to another state. + +Well, maybe that should be Hab. + +For many phenomenon, +which we will + +cover throughout the +rest of this semester, + +spontaneous +emission, coherences, + +and three-level instances, and +super radiance, all we need + +is a matrix element. + +And this matrix +element will just + +run through all the +equations, and be + +responsible for a lot of +interesting phenomenon. + +And for most of the +description of those phenomena, + +we don't have to know where +this matrix element comes from. + +The only thing we +have to know, there + +is a non-seeable matrix element +which drives the process. + +And as you know, +the matrix element, + +with an external field, is +called the Rabi frequency. + +And a lot of physics just +depends on the Rabi frequency. + +But what is behind? + +The engine behind the Rabi +frequency is a matrix element. + +So in the unit I started to +teach the week before spring + +break, we talked +about matrix elements. + +And for H, for the Hamiltonian, +we used the coupling of an atom + +to the electromagnetic field. + +And then we calculated, +what is the matrix element + +induced by the electric field? + +We made the dipole +approximation. + +And that's your plain, vanilla, +generic dipole operator + +which can connect two states. + +But we also consider, +what happens + +when we go beyond the +dipole approximation, + +and we found extra ways +of copying two states? + +For instance, we can +copy two states which + +have the same parity with +a quadrupole transition, + +or we can couple them with a +magnetic dipole transition. + +So these are other ways to +get into matrix elements. + +For most of the +course, you don't + +have to understand what +is behind the matrix, + +and you just know, +there is a number + +which drives the process. + +So what I want to finish +today is to discuss-- + +and these are called selection +rules-- which tell us, + +when are those numbers, +when is this matrix element + +which couples two +states, when is it zero, + +or when is it non-vanishing. + +And what is helpful +here is, well, + +as always in physics, +use symmetry. + +And if you have an +operator, let me give you + +examples immediately. + +But just think for a moment +about the electric dipole. + +The electric dipole is +the position operator R. + +And you want to know, can the +position operator R induce + +a transition between two states. + +The way to analyse it is +now in terms of symmetry. + +And for symmetry, +which is always + +fulfilled for isolated +atoms, is angular momentum. + +Angular momentum is a +conserved quantum number, + +we have rotation symmetry. + +So therefore, we want to now +understand matrix elements + +in the language of +rotation symmetry. + +And therefore, we don't want to +use a precision operator x, y, + +or z. + +x, y, z do not have +the rotation symmetry. + +We want to use linear +superpositions of x, y, + +and z-- I'll give you an example +in a moment-- in such a way + +that the operator becomes +an element of aesthetic + +of a spherical tensor. + +And spherical tensor, I +gave you the definition + +in the last lecture, the +element of spherical tensor, Ln, + +is defined by-- well, I connect +it with something you know, + +that it transforms +on the rotation, + +like the spherical +harmonics, ylm. + +So it is pretty much for an +operator, what the ylm, what + +the spherical harmonics +are for wave functions. + +I think I can do it more formal. + +And Professor Schwann +knows much more about it. + +I think these are elements of +the rotational symmetry group, + +But I don't want to go there. + +So what I mean by that is the +following, that if you take + +the position vector r, you +can expand it into a basis, + +which is x and y. + +But if you use the spherical +basis, x plus/minus iy. + +Then what appears are +the spherical harmonics. + +So in that case, +it's rather simple. + +The position vector has +actually in this representation + +components which +you can even see + +are the spherical harmonics. + +And therefore, we transform +like the spherical harmonics. + +Or just to give you +another example, if you + +have the operator, which is +responsible for the quadrupole + +transition, well, +you get the gist, + +it's a product of +two coordinates. + +So therefore, it's a +spherical tensor of rank two. + +And it so happens, +but I'm not deriving + +that, it is a superposition of +two components with Lm quantum + +number, 2 plus 1, 2 minus 1. + +So that's how we +should think about it. + +So, we want to ask, we want +to extend the operator, + +into operators which +have rotational symmetry, + +and these are those, or +these are those three. + +So instead of using the +vector Cartesian coordinate, + +we use its spherical components. + +And with that, we can +take this expression + +from the last +lecture, and rewrite + +it using the Wigner-Eckart +theorem into a way which + +allows us to immediately +formulate selection rules. + +So [INAUDIBLE] and primer +are the quantum numbers + +of the state, except +for angular momentum, + +so matricing about principle +quantum number of the hydrogen + +atom. + +And we want to copy from +a total angular momentum J + +prime to total angular +momentum J. Actually, + +we want to copy from J prime, +M prime to a state, JM. + +And what the Wigner-Eckart +theorem tells us + +that we can factor +out the M dependence. + +The M dependence just comes +from orientation in space. + +So M is just how you orient +wave functions and vectors + +and space. + +And you can sort of write this +matrix element as a projection. + +And this is nothing else than +the familiar Clebsch-Gordan + +coefficient. + +And the Clebsch-Gordan +coefficient + +for coupling the initial +state, JM, or to-- let me + +put it this way-- to start with +the initial state J prime, M + +prime, we have the L and +the M of our operator. + +And that should result +in a total angular + +momentum of J and M. + +So we retrieve +again the formalism + +of the addition of +two angular momenta. + +Sometimes, you +have two particles + +you couple into angular +momentum and ask, + +what is the total +angular momentum + +of the composite particles? + +But what we do here for +this selection rule, + +we have the initial +state, we calculate + +with the angular +momentum of the operator. + +You can think the +operator is a field which + +can transfer angular momentum. + +And then, of course, +the final state + +has to fulfill angular +momentum conservation. + +But one source of the +momentum is now the operator, + +is the external +field, is the photon, + +or the microwave drive, +whatever you apply. + +And yes, this +Wigner-Eckart theorem + +allows us to write the matrix +element as a reduced matrix + +element. + +Which really decides +whether the transition + +is non-vanishing or not, +times a factor which is just + +the orientation of the wave +function and of the operator + +in space. + +So for the Clebsch-Gordan +coefficient, + +we have a simple selection rule. + +And this is that for +the [INAUDIBLE] number, + +the M of the final state has to +be the M of the initial state, + +plus a little M of the operator. + +And for both the Clebsch-Gordan +and the reduced matrix element, + +we have the triangle rule. + +Well, if you couple two +angular momentum vectors + +to a final angular +momentum, the three vectors + +have to form a triangle. + +And the triangle rule says that +some-- let me write it down, + +and then you recognize it-- that +the angular momentum construct + +by the field has to fulfill +the triangle rule that J prime + +and J can be connected. + +Yes? + +AUDIENCE: What is this symbolic +meaning of the double bars? + +PROFESSOR: It's just +how, in many textbooks, + +the reduced matrix +element is written. + +It's nothing else +in a matrix element. + +But, you know, plus +the y that I looked + +at in the quantum +mechanics book. + +But what happens is +these are not states. + +J and J prime are not states. + +They have an independence. + +So we've taken out +the independence. + +So this is sort of a matrix +element between a state which + +may have been stripped +of its independence. + +So maybe, I don't know +if that's 100% correct, + +but if you have the +YLM in certain states, + +you have an e to +the IM and M part. + +And this has probably +been factored out. + +So these are not really states, +and the double line just + +means it's a reduced matrix +element with the meaning I just + +mentioned. + +It's a standard way of +factorizing matrix elements. + +And yeah, that means +reduced matrix elements. + +So in other words, when we +talk about selection rules, + +we want to use +the representation + +of spherical tensors, because +the spherical tensor, the rank + +of the spherical +tensor, just tells us + +how much angular momentum +is involved in the photon, + +is involved in this transition. + +So maybe just to +give you a question, + +so if I were to do a +multipole expansion, + +and I have an octupole +transition, what is now + +the angular momentum +transferred by a photon? + +STUDENT: 3? + +PROFESSOR: What? + +STUDENT: 3? + +STUDENT: 3? + +PROFESSOR: 3, yeah. + +The dipole is L equals 1. + +Quadrupole is spherical +tense of rank 2. + +L equals 2, so it's L equals 3. + +Now, can a photon transfer +three units of angular momentum? + +Can an atom get rid of +three units of, let's say, + +orbital or spin +angular momentum. + +We start in a state which +is J prime equals 3. + +You need one photon, +and you go to a state + +which is J prime equals 0. + +Is that possible or not? + +We don't have +[INAUDIBLE], but do you + +want to volunteer an answer? + +What's the angular +momentum of the photon? + +STUDENT: [INAUDIBLE]? + +PROFESSOR: Well, be careful. + +The photon has an +intrinsic angular momentum, + +which is like the +spin of the photon. + +That's plus/minus 1. + +But just imagine that +you have an atom, + +and the photon is not +immediate at the origin. + +The photon is emitted a +little bit further out. + +Then, with reference +to the origin, + +the photon has orbital +angular momentum. + +And that's what +we're talking about. + +In the multipole expansion, +we fall in powers of x, and z, + +and y of the spatial +coordinate of the electron. + +And that actually means we're +going away from the origin. + +And if you emit something +which is away from the origin, + +you have orbital +angular momentum. + +So, yes. + +An octupole transition +is exactly what I said. + +It means a photon is emitted, +and it changes the angular + +momentum of the atom left +behind by three units. + +That's what we +really mean by that. + +And that's what we mean +by those electrodes. + +The question that +you should maybe + +discuss after class +is, what happens + +if you detect this photon? + +Is that now a +supercharged photon, + +which has three units +of angular momentum? + +Is there something strange +in its polarization? + +Think about it, and if +you don't find the answer, + +we can discuss it +in the next class. + +OK. + +So this is the classification. + +Let's just focus on +the simple examples. + +We have discussed electric +dipole and magnetic dipole + +radiation. + +These are induced by vectors. + +Remember, E1 is +the dipole vector. + +For M1, the matrix element was +by the angular momentum vector. + +So + +These are vectors. + +And that means +the representation + +of the spherical tensors, +or the quantum numbers + +of the spherical tensors, +are the same of the Y1n. + +And so for dipole +radiation, whether it's + +electric or magnetic, we have +now with the dipole selection + +rules, which pretty +much save you + +at one unit of angular +momentum to state + +B. Can you reach +state A with that? + +And these selection rules are +that you can change the angular + +momentum between initial +state by 0 and 1. + +This is the triangle rule. + +And delta m can be +0 and plus/minus 1, + +depending on polarization, which +we want to discuss in a moment. + +So in angular momentum, +electric and magnetic dipoles + +have the same +selection rule, where + +when it comes to the +question of parity, + +we've already discussed that. + +That an electric dipole connects +to a state of opposite parity, + +whereas, the magnetic +dipole connects + +two states of the same parity. + +And of course, this comes about +because L is an axial vector, + +and R is a polar vector, which +have different symmetry when + +you invert the +coordinate system. + +The one higher multipole port +transition, which we discussed, + +was the electric quadrupole, E2. + +And the spherical +tensor operators + +for the quadrupole +transition, I gave you + +already the example of, let's +say, xz, products of two + +coordinates, because we went one +order higher than the dipole. + +They transform as Y2m. + +And therefore, we +have selection rules + +for quadrupole transitions, +which tell us now + +that we can change the total +angular momentum up to 2. + +And also, delta m can +change up to two units. + +And again, just to +emphasize, because people get + +confused all the time. + +When we talk about a +quadrupole transition, + +we mean absolutely +positively a transition + +where one photon is emitted. + +If you fully quantize +the field, there + +is one creation +operator of the photon. + +It's one photon +which is created, + +and this photon carries +away the angular momentum + +we've just specified. + +Questions about that? + +Let me conclude our +discussion of matrix elements + +by talking about something +which is experimentally + +very relevant. + +And this is how +selection rules depend + +on the polarization of light. + +And I only want to discuss +it for electric dipole + +transitions. + +So when we wrote down +the coupling of the atom + +to electromagnetic radiation, +we had the dipole operator, + +but we also had, +of course, the mode + +of the electromagnetic +field, which + +was characterized by a +polarization epsilon. + +So until now, when I talked +about selection rules, + +we discussed this part. + +But now we want to see how +it effects polarization. + +Well, the epsilon, for instance, +for circular polarization-- + +we'll talk about linear +polarization in a moment-- + +has this representation. + +So this is the unit +vector of the polarization + +of the electric field when +it's circularly polarization. + +And now remember, we +take this vector r, + +and expand it in +the following way. + +So if you multiply now the +operator r, or the matrix + +elements created by +this vectorate operator, + +by the polarization, you see +that one circular polarization + +checks out this component. + +The other circular +polarization projects this out. + +And later, we'll talk about that +linear polarization projects + +that out. + +So when we said that +we have matrix elements + +for dipole transition, +which can change + +angular momentum, or the +incremental number, by minus 1, + +plus 1, and 0, +this is now related + +to the polarization +of the light, + +either the photon +which is emitted, + +or when we use circularly +polarized light, + +we can only drive this +transition, that or that, + +because the scale of +product of the polarization + +vector and the matrix +element project out + +only one component of +the spherical tensor. + +So if you look at +the expansion above, + +we realize that the left- and +right-handed circular light + +projects now out +the spherical tensor + +operator, T1 plus minus 1. + +And since it's circularly +polarized light, + +and therefore, we find +this election rule + +that delta m, the Z component, +the Z component of the angular + +momentum, changes +by plus/minus 1 + +when the circular polarized +light is sigma plus or sigma + +minus, right-handed +or left-handed. + +OK. + +So this is responsible +for circular polarization. + +These are selection rules for +circularly polarized light. + +Let me conclude by +discussing the case + +of linear polarization. + +Well, when we ask +linear polarization, + +if we ask for linear +polarization along x or y, + +well, it's linear polarization, +but we should regard it + +as the linear superposition +of sigma plus and sigma minus. + +So in other words, if you have +the quantization axis along z, + +and you use light which +is polarized along x or y, + +the way how the light +talks to the atom + +with symmetric operators +is that the light + +is a superposition of +sigma plus and sigma minus. + +So what we have so far is, +so we had here the light key, + +the propagation of the +light was along the z-axis. + +But now, we want to look at +the other possibility that z, + +or the quantization +axis, is parallel + +to the polarization +of the electric field, + +which would mean that the +quantization axis is usually + +defined by an external +magnetic field. + +If you're talking about the +situation that the electric + +field of the electromagnetic +wave is parallel + +to the magnetic field, then +with this polarization, + +we peak out this spherical +tensor component, which is z, + +which is r times Y1,0. + +And that means that this +polarization of the light + +induces a transition for +which delta m equals 0. + +And this is referred +to as pi light. + +So maybe if that got +confusing for you, + +let me just help +out with a drawing. + +We have our atom here, which is +quantized by a magnetic field + +B. And if you shine light on +it, we have the electric field + +perpendicular to +the magnetic field. + +So this would be x and y. + +And the natural way to describe +it is by using x plus/minus IY. + +And we have selection rules +where delta m is plus/minus 1. + +But alternatively, we +can also shine light + +along this direction. + +And for the electric field, +which was perpendicular to B, + +we retrieve the previous case. + +We have superpositions of the +sigma plus and sigma minus. + +But the new case now is that +the electric field is parallel + +to B. And then, we +drive transitions, + +which have delta M equals 0. + +So these are sigma plus and +sigma minus transitions. + +And this here is what is +called a pi transition. + +Anyway, it's a +little bit formal, + +but I just wanted to +present it in this context. + +Questions? + +STUDENT: I have one slightly, +maybe, basic question. + +When we talk about polarization +in all these matrix elements-- + +so for example, +photon [INAUDIBLE], + +right-- these are single +photons [INAUDIBLE] elements. + +And so when we talk +about shining a laser, + +it has a polarization. + +But we don't talk +about polarization + +for single photons. + +Or do we? + +PROFESSOR: Actually, we +talk about-- the question + +is, what is the polarization? + +Do we talk about polarization +of single photons, + +or polarization of laser beams? + +Well, let me back +up and say, we talk + +about polarization of a mode +of the electromagnetic field. + +We will always expand +the electromagnetic field + +into modes. + +And the mode is +the polarization. + +It may happen that +at some point, + +a photon is emitting a +superposition of modes. + +But in the most +straightforward description, + +we always do a mode analysis. + +And often, we simplify +the case by saying + +that the atom +interacts only with one + +mode of the +electromagnetic field. + +And maybe in the case +of spontaneous emission, + +we then sum over all modes. + +But for each mode, there's +a specific polarization. + +And it doesn't matter if this +mode is filled with one atom, + +or with a laser beam, with +a classical electromagnetic + +field, which corresponds +to zillions of photons. + +STUDENT: [INAUDIBLE] +does it always + +end up being +electrical polarization + +in this case, then? + +Like because if +it's many photons, + +then there's a lot of +[INAUDIBLE] for each of them, + +or each of them +individually-- I don't know. + +PROFESSOR: No, it depends. + +If you have an atom, and it has +one unit of angular momentum, + +and it spontaneously +emits a photon, + +if the photon is emitted +along the quantization axis, + +it can only be sigma plus. + +If it's emitted in +the other direction, + +it has to be sigma minus. + +Now if you go at strange +angles, then at this angle, + +you overlay it with +different modes. + +And you may now find +photons in a superposition + +of polarizations, because +we have several modes which + +are connected with this +direction of emission. + +I think if you write it +down, it's pretty clear. + +It's just sort of +projection operators. + +And for spontaneous emission, +we sum over all modes. + +But for me, I always think +about-- we can always + +think about what a single +photon does by saying, well, + +if I'm getting confused +about a single photon, + +let me figure out +what many, many, many + +identical photons would be. + +And that would mean, +instead of a single photon + +in a certain mode, I +release a beam in this mode. + +And then, suddenly, I +can think, classically, + +I know what the +electric field is such. + +And then you go +back to the, what + +is the electric field +of a single photon, + +and usually make the connection. + +So I think at least +for the discussion + +of matrix elements, +transitions, angular momentum, + +I don't think you ever have +to distinguish between what + +single photons do and +what laser beams do. + +But there are important +aspects of single photons, + +non-classical aspects, which +we'll discuss in a short while. + +Other questions? + +OK. + +That's all I want to say +about selection rules. + +So with that now, we can +simply take the matrix element + +and run with it. + +So in this lecture +and on [INAUDIBLE], + +I want to talk +about basic aspects + +of atom-light interaction. + +And what I want to +talk today about it + +is the two important cases +when an atom interacts + +with monochromatic +wave, or when it + +interacts with a broad spectrum. + +In one case, when I +say monochromatic case, + +you may just think of the +best laser money can buy. + +Very, very sharp. + +Very, very monochromatic. + +When I talk about +a broad spectrum, + +you may just think about +black-body radiation, + +which is an ultra +broad spectrum. + +And they're two very +different cases. + +And some of it is just +related to Nancy's question, + +that if you have +a broad spectrum, + +we're always talking +about many, many modes, + +and they will be +incoherent, and they + +will be irreversible physics. + +Whereas for monochromatic +light, everything + +is a pure, plain wave, and +everything is coherent. + +So we want to sort of +talk about that first. + +And then later this week, +I think on Wednesday, + +we will talk about +spontaneous emission. + +But right now, we focus +on the simpler case, + +where we drive the system with +electromagnetic radiation, + +which is either +narrow-band or broadband. + +But let's just start +with a cartoon. + +We have an atom. + +And for that discussion, +all we need is two levels. + +And all we need is +that the two levels + +are connected by +some matrix element. + +And the basic +phenomenological situation + +is that we have one atom, +which sits in a vacuum. + +So we have volume, V, of vacuum. + +And what is important +now is that the walls + +of the imaginary boundary +of what defines our vacuum + +is at low temperature. + +And low temperature means that +the atom will irreversibly + +decay into the ground +state with a lifetime tau. + +And that means that +in some picture, + +the excited state +is the broadening, + +which is broadened by +the natural lifetime. + +And in our discussion, +we assume-- + +and this is what I said with +the cold walls of the vacuum-- + +that the energy +difference is much, + +much larger than the +relevant temperature. + +And this is very well fulfilled +for our standard atomic system. + +The typical excitation +energy, even + +for atoms with loosely bound +electrons, as the alkalis, + +is two electron volt, +which corresponds + +to a temperature +of 20,000 Kelvin. + +And even at the rather hot +temperature, definitely + +hot temperatures, in The +Center for Ultracold Atoms, + +but the KT at room +temperature corresponds + +to 25 milli-electron volt. + +So therefore, when we +have an atom in isolation, + +this is what we find. + +We find an atom which +will irreversibly decay + +to the ground state. + +And the fact that +it irreversibly + +decays to the ground +state is really + +an inequality between energies. + +If you will talk about +a hyperfine transition + +or something, there +may be a possibility + +that we have an excited state, +which is thermally excited. + +But in the following discussion, +when we drive the atom, + +and when we look at +spontaneous decay, + +we always assume that the +thermal energies are so small, + +that we really assume an atom +sitting in a cold vacuum. + +Actually, it's your next +homework assignment, + +where you will +consider, what are + +the effects of +black-body radiation. + +And you will actually +find out in your homework + +that they are non-negligible. + +So yes, there are corrections. + +But you will also find out +that the corrections are rather + +small, or it takes a long time +before black-body radiation + +induces any +observable transition. + +OK. + +So I'll just try to be a +little bit formal here. + +Give you sort of a sketch +of an atom in a cold vacuum. + +Ground state is stable. + +Excited state, +irreversibly decays. + +And now, we want to bring +life into this situation. + +Now we add light. + +And the light-- and this +is now our discussion-- + +has a [INAUDIBLE]. + +And we want to +distinguish the cases + +of narrow-band and +broadband radiation. + +So it's clear that +if the bandwidth + +of the light, the +only scale-- well, + +we have the scale of omega. + +But that's a huge scale. + +The only smaller scale, +which is given by the atom, + +is the natural linewidth. + +And depending, in +which case we are, + +we talk about +narrow-band excitation + +and broadband radiation. + +And once the linewidth is +much narrower than gamma, + +we don't get any +new physics when + +we assume perfectly +monochromatic light. + +So once we are much +smaller, we're really + +discussing the case +of, well, we can + +neglect the spectrum +broadening of the light source. + +Or in the other case, when +we have broadband light, + +we can pretty much +make the assumption + +that the light is +infinitely broad, + +and what matters is only the +spectral density of the light. + +So in a pictorial +representation, + +if this is the +frequency omega, we + +have the atom with the +natural linewidth gamma. + +Narrow-band means we are +much sharper than that. + +And broadband means +really wide distribution. + +So if we have +broadband light, it + +doesn't really matter +what the total power is. + +If the light is +very broad, there + +can be infinite +power in the wings, + +but the atoms don't care. + +What matters when we +have broadband radiation + +is the quantity called +the spectral density. + +And that's what we +need in the following. + +Which is, let me just +give you the units. + +Which is energy per volume +and frequency interval. + +So we can talk about the +spectral density as of omega. + +Or alternatively, when we +have a propagating beam, + +we don't want to +talk about energy, + +we want to talk about intensity. + +So it is intensity per +unit frequency interval. + +Which would mean I of omega +is the energy density, + +multiplied with +the speed of light. + +And that becomes energy +per area and time. + +So that's the flow of energy. + +But because we are +talking about board light, + +it has to be normalized +by the frequency interval. + +In contrast, +monochromatic radiation, + +it's sort of one +monochromatic electric field. + +And we will specify it by +the single frequency, omega, + +and the electric +field amplitude. + +Which when multiplied +by a matrix element + +becomes the Rabi frequency. + +Or we can characterize the +light by the intensity I. + +But then it's an +intensity which has + +the units of energy +per area time. + +It's not normalized to +any frequency interval, + +because we have assumed that +the frequency interval is 0. + +So if you now have a description +how these two forms of light + +interact with the +atom, at this point, + +and we come to that +later this week, + +we have to make an +assumption that we + +are looking at +times which are much + +smaller than the time +for spontaneous emission. + +So if you now, in a +perturbative sense, + +expose the atom's monochromatic +or broadband radiation, + +unless we have included +in the description + +the many, many modes for +spontaneous emission, + +we are limiting ourselves +to a very short time. + +This is, you would say, +a severe description, + +because atoms emit photons +after a short time. + +But we already capture, +without considering + +spontaneous emission, a +lot of different physics. + +And we can nicely +distinguish between features + +of monochromatic and features +of broadband excitation. + +OK. + +So let's start out with the +case of-- give me a second. + +OK. + +So if you look at the two cases, +in the monochromatic case, + +we will discuss the +idealized situation + +of an atom interacting +only with a single mode. + +And what we will find out is, +we will find out that now, + +in the optical domain, +we will find actually + +equations for the +two-level system which + +are identical to what +we discussed earlier + +when we discussed +spin [INAUDIBLE] + +in a magnetic field. + +So in that sense, +a two level system, + +driven by a laser system, +will behave identically + +to a spin driven by +a magnetic field. + +Shouldn't come as a surprise, +but I will show that to you. + +But I can go over +that very quickly. + +The board-band +case will actually + +follow from the +single mode case, + +because what we +assume is broadband + +means many, many modes. + +And then we do an averaging +over many single modes + +by assuming random freeze. + +But I also want +to show it to you + +because I picked +my verbs carefully. + +You have many, many +more things, but we + +assume that there +is a random phase. + +When we talked about one +photon emitted into a angle-- + +it maybe responds to +a question earlier-- + +this photon may be in a +coherent superposition. + +This is not many modes +in a broadband wave. + +Many modes in +broadband wave means + +that there is no correlation +whatsoever between the modes, + +and all we will be +able to talk about is + +an IMS value of +an electric field. + +But anyway, the result +is sort of predictable, + +and I wanted to tell +you what I'm aiming for. + +But it's now really worthwhile +to go through those exercises + +and look at what +happens in perturbation + +theory for short times when we +have monochromatic radiation, + +and when we have +broadband radiation. + +So the first discussion +will show Rabi flopping. + +I don't know how +many times we have + +looked at Rabi oscillation. + +But these are now +Rabi oscillations + +between two electronic states +covered by a laser beam. + +And I want to show you +how this comes about. + +And when I said strong +driving, well, we + +have only a limited time window +before spontaneous emission + +happens. + +We have to discuss +the physics we + +want to discuss in +this shot time window. + +And if you want +to excite an atom, + +and see Rabi oscillation +in a short time, + +you better have a +strong laser beam. + +So this is why the monochromatic +excitation that we discussed + +will pretty much automatically +be in this strong coupling + +limit. + +OK. + +So what do we have? + +We have a ground,and we +have an excited state. + +We have a matrix element. + +We know now where it comes from. + +And we have a monochromatic +time dependence. + +In perturbation +theory, we build up + +time-dependent [INAUDIBLE] +amplitude in the excited + +state, because we +couple the ground + +state with the +off-diagonal matrix + +element to the excited state. + +And we have to integrate +from the initial time + +to the final time. + +We have the time dependence +of the electromagnetic field, + +and we also need +the time dependence + +of the excited state. + +So when I integrate +now over t prime, + +I take out the ground +state amplitude, + +because we're doing +perturbation theory, + +and we assume that for +short times, needing order, + +the ground state amplitude is +one, as prepared initially. + +So this in integral can +be solved analytically. + +Some of you may remember +that the minus 1 + +has something to do with the +lower bound of the integral. + +And when we discuss the easy +polarizability, we said, + +this is a transient, and we +neglected it for good reasons. + +But now, we're really +interested in the time evolution + +of the system, so now +we have to keep it. + +OK. + +We are interested in the +probability in the excited + +state. + +So we take the above +expression and square it. + +And we find the well-known +result, with sine squared, + +divided by omega minus omega eg. + +OK. + +So this is pretty much +just straightforward, + +writing down an +analytic expression. + +But now, let's discuss it. + +For very short times, and this +is an important limiting case, + +the probability in +the excited state + +is proportionate +to times squared. + +And this is important. + +We're not getting a rate +which is proportional to time. + +We're obtaining something +which is time square. + +And the proportionality +to t square + +means it's a fully +coherent process. + +So whenever somebody +asks you, you + +switch on a strong +coupling from a ground + +to the excited state, what is +the probability in the excited + +state? + +It starts out quadratically. + +The linear dependence-- famous +golden rule, [INAUDIBLE] + +or such-- only come later. + +This is a very +universal feature. + +And even if you use +broadened light, + +for a time window, +delta T, which + +is shorter than the inverse +bandwidth of the light, + +talking about +Fourier's theory, you + +don't have time +to even figure out + +that your light is broad +and not monochromatic. + +For very short times, +the Fourier limit + +does not allow +you to distinguish + +whether the light is +broad or monochromatic. + +So what I just derived for +you, an initial quadratic + +dependence, is the +universal behavior + +of a quantum system +at very short times. + +Because it simply says the +amplitude in the excited state + +goes linearly in time, and +the probability, quadratic. + +OK. + +So this is for a +very short times. + +But if you look at it +now for longer times, + +we have actually-- we'll +see the atomic behavior, + +and these are Rabi oscillations. + +But there is one caveat. + +So we have derived. + +However, we have derived them +only perturbatively by assuming + +that the ground state +has always a population + +close to 100%, which +means we have assumed + +that the probability +in the excited state + +is much smaller than 1. + +Otherwise, we wouldn't +keep the ground state. + +And this is only fulfilled +if you inspect the solution. + +The solution is +only self-consistent + +if you have an off-resonant +case, where the Rabi + +oscillation only comes from a +small fraction of the ground + +state population of +the excited state. + +Of course, you all know +that Rabi oscillations, + +this formula, is also +varied on-resonance. + +And you can have +full Rabi flopping. + +But I want to make a case +here, distinguish carefully + +between monochromatic radiation +and broadband radiation. + +For that, I need for +perturbation theory. + +And therefore, I'm telling you +what perturbation theory gives + +us at short times, and in +terms of Rabi oscillations. + +STUDENT: So you're +saying we assume + +strong coupling with respect +to the atomic linewidth, + +but weak coupling with respect +to the resonance, for instance, + +in [INAUDIBLE]? + +PROFESSOR: It's +simple, but subtle. + +Yes. + +So what we have is, +we assume we switch + +on a monochromatic laser. + +Since we do not include +spontaneous emission, which + +will actually damp out Rabi +oscillation-- we'll talk about + +that later-- we +are only limited, + +we are limited here +to short times, which + +are shorter than the +spontaneous decay. + +And now, I gave you +one universal thing. + +At very, very short times, +it's always quadratic. + +It's a coherent process. + +So that's one simple, +limiting, exact case + +you should keep in your mind. + +But now the question is, if +you let the time go longer, + +something will happen. + +And there are several options. + +One is, if times go longer, +spontaneous emission happens. + +OK. + +We are invalid. + +The other possibility is, +when time gets longer, + +and we are on-resonance, we +deplete the ground state, + +or [INAUDIBLE] perturbation +theory doesn't deal with that. + +But if we are off-resonance, +we can allow time + +to go over many Rabi periods +and observe perturbative Rabi + +oscillations. + +So this is how we +have formulated it. + +We do perturbation +theory of the system + +without spontaneous emission. + +And eventually, we +violate our assumptions, + +either because spontaneous +emission kicks in, + +or because we deplete +the ground state + +when we drive it too hard, or +if we go too close to resonance. + +But the later +assumption, of course, + +that we can't drive it hard, +as you know, is artificial. + +We can actually discuss +the monochromatic case. + +Not just in perturbation theory, +but we can do it exactly. + +STUDENT: I want to +go back again to-- + +PROFESSOR: And this is +what I want to do now. + +But first, we can go back. + +STUDENT: So when we are +talking about non-B resonance + +and B-resonance, so if +we decrease the detuning, + +then we are getting +close to resonance. + +So again, this gets invalid. + +But if we increase +the detuning, we + +could exceed the +spontaneous emission rate. + +So then, we won't see any +Rabi oscillations again, + +because, at those time +periods, this oscillation + +would [INAUDIBLE] detuning. + +So to observe Rabi +oscillations, we + +have to be at times +more than the detuning, + +or more than +[INAUDIBLE] detuning. + +PROFESSOR: Oh, yeah. + +Of course. + +STUDENT: So the detuning has +to be less than [INAUDIBLE], + +but more [INAUDIBLE] that we +are still [INAUDIBLE] resonant. + +PROFESSOR: No. + +The detuning has to be larger +than the natural linewidth, + +because then the Rabi +oscillations are fast, + +and we have Rabi +oscillations which + +are faster than any damping +due to spontaneous decay. + +That's an image we +are talking about. + +So in the limit of our detuning, +you can detune very, very far, + +and you never reach the limit +of our perturbative abode. + +STUDENT: Yes. + +OK. + +PROFESSOR: Anyway, I +want to do perturbation + +theory of the broadband case. + +And the broadband case +will be an incoherent sum + +over the single mode case. + +So this is why I had +to bore you with, + +what do we get out of +perturbation theory + +for the monochromatic case? + +Of course, you know already +that in a two-level system, + +we can do it exactly. + +And I just want to +outline it, mainly + +to introduce some notation. + +So our Hamiltonian +here, which couples + +the ground in the excited state +is given by the dipole matrix + +element, the electric +field vector, + +and we call this +the Rabi frequency. + +And then we have a sinusoidal +or co-sinusoidal frequency + +dependence. + +And all I want to +do is to show you + +that a two-level system driven +by an electromagnetic field + +is identical to spin 1/2, +which we discussed earlier, + +and then we are done. + +There is one technical or +little trick we have to do, + +which is trivial, but +I want to mention it. + +So if you want to compare +directly with spin 1/2, + +we are now shifting +the ground state + +to half the +excitation frequency. + +In other words, just to make +the key analogy with the spin, + +usually we say for an electronic +transition, we start at 0, + +and we go up. + +But now we shift things +that the zero of energy + +is in the middle between the +ground and the excited state. + +And then, it looks like the +excited state, we spin up, + +the ground state, we spin down. + +So with that, our Hamiltonian +is now excited, excited, + +minus-- so all I've done +is I've shifted the origin. + +And the coupling, using +our definition of the Rabi + +frequency is couples +ground and excited state. + +And excited ground state. + +These are the two +off-diagonal matrix element. + +And the time dependence +is cosine omega t. + +So we are now very close to +exploit the correspondence + +with spin 1/2. + +Because after shifting +the ground state energy, + +this is the z component +of the spin operator, + +the [INAUDIBLE] matrix. + +And this here is +the x component. + +So therefore, for driving +an electronic transition + +with a laser beam, +we have actually + +spin Hamiltonian, which +has the standard form. + +So let me just write +it down, because it's + +an important result. + +The Hamiltonian for driving +and dipole transition + +with a linearly +polarized laser beam + +corresponds, or is identical, +to the Hamiltonian for spin 1/2, + +in a static magnetic field +along the Z direction, + +which causes a splitting +between spin up and spin down. + +And the splitting +is now omega eg + +plus a linearly +polarized oscillating + +field along the x direction. + +And you probably remember that +when we discussed the spin + +problem, what we +liked actually most + +was that we had a rotating +magnetic field, because it + +made everything simpler. + +And we are doing that +now by formally writing + +the [INAUDIBLE] polarized +field as a superposition + +of left-handed and right-handed, +or counter-rotating + +and co-rotating magnetic field. + +So let me just do that. + +So we have the Z part. + +And now, instead of having +just sigma x, cosine omega t, + +I add sigma y, +sine omega t, and I + +subtract sigma y, sine omega t. + +So now we have shown +that there is something + +in addition to the spin problem. + +We discover when we had a +rotating magnetic field, + +that we have two components +here which rotate. + +And these are the co and +counter rotating magnetic fields + +in the spin problem. + +And the counter rotating, you +remember in the spin problem, + +we solved the problem +exactly by going + +into a frame which rotated at +the Larmor frequency, which + +becomes now omega eg. + +And the co-rotating term +became stationary on resonance + +in this rotating frame, whereas +the counter-rotating term + +rotates at a very high frequency +in this frame at the Larmor + +frequency. + +So if this frequency, if +you fulfill the inequalities + +that the co-rotating term +is close to resonance, + +or in other words, we +are close to resonance, + +and we are not using an infinite +intensity of the laser beam, + +that we broaden everything +in co and counter + +rotating terms of +boson resonance. + +So if you fulfill +those two conditions, + +then we can neglect +the last term. + +And this is the rotating +wave approximation. + +So in other words, +in the spin problem, + +we can always assume +we haven't circularly + +polarized the rotating +magnetic field, + +and we have an exact solution. + +I say a little bit +more about it later. + +But in many situations, when +you excite an atom with a laser + +beam, you get both terms. + +And usually, you proceed +by neglecting one term, + +and by making the rotating +wave approximation. + +will, in one or two +lectures, discuss + +whether there are situations +where the counter-rotating term + +is exactly 0 due to angular +momentum selection rules, + +but that's a +separate discussion. + +In many situations, it cannot be +avoided, and it's always there. + +It's actually always +there to the point + +that when I talk to +some colleagues and say, + +I can create a +situation, an atom, where + +the counter-rotating +term is exactly 0, + +some colleagues +reacted with disbelief, + +and then eventually +felt that the situation + +I created for angular +momentum conservation + +was somewhat artificial. + +But we'll get there. + +It's an interesting discussion. + +But anyway, just remember that +for magnetic drive, if you + +use a rotating +magnetic field, you + +don't need a rotating +wave approximation. + +Everything rotates +at one frequency. + +But usually, when you drive a +two-level system with lasers, + +we usually have an extra term +which needs to be neglected. + +OK. + +But if you do the rotating +wave vapor approximation, + +we have now exactly +the situation + +we discussed for spin 1/2 in +a rotating magnetic field. + +And then, the same equation +has the same results. + +And then, our results for +spin 1/2 are now as expected. + +Rabi oscillations without +making any assumptions + +about perturbation theory. + +So this is an exact result +for the initial conditions + +that we start in +the ground state, + +and the initial population +of the excited state is 0. + +And as usual, I have used here +the generalized Rabi frequency, + +which is the quadrature sum +of these matrix elements + +squared and the detuning. + +OK. + +A lot of it was to get ready +for the broadband case. + +So that's-- yes, we have a +little bit more than five + +minutes. + +So, so far, we have discussed +the monochromatic case. + +What I really needed +as a new result, + +because I carried over +for the board-band case, + +was a perturbative result. + +But I also wanted to show you +that the perturbative result is + +one limiting case of the +exact solution, which I just + +derived by analogy to spin 1/2. + +OK. + +So we just had the result +that in perturbation theory, + +for sufficiently short +times, we discussed all that, + +that the excited state amplitude +has the following dependence. + +So this is nothing +else than-- I want + +to make sure you +recognize it-- Rabi + +oscillations at the +generalized Rabi frequency. + +The generalized Rabi frequency +is simply the detuning, + +because it's a +perturbative result. + +In perturbation +theory, you don't + +get power broadening, because +you assume that your drive + +field is perturbatively weak. + +So therefore, the +Rabi oscillation, + +our now Rabi oscillation +where the Rabi frequency, + +the generalized Rabi frequency, +is delta the detuning. + +And this is just rewriting. + +Let me just scroll up. + +This is this result here. + +I wasn't commenting on it. + +But this is nothing +else than the detuning. + +Look. + +I'm just reminding you what you +get from perturbation theory. + +Power broadening is not +part of perturbation theory. + +OK. + +So this is our +perturbative result. + +And now, we want +to integrate over + +that because we have a broadband +distribution of the light. + +So what we have to use now is +the energy density, W of omega. + +The electric field is +related, the energy + +of the electromagnetic field, is +1/2 epsilon the energy density + +of the electromagnetic field, +is 1/2 epsilon naught times + +the electric field squared. + +Well, if you have many modes, +we add the different modes + +in quadrature. + +And we still have +the same reaction + +between the electric field +squared and the total energy. + +But the total energy is now +an integral over d omega. + +We integrate over frequency +over the spectral distribution + +of the light. + +So this is how we go from energy +density to electric feels. + +But now, we want to +evaluate this expression. + +And what appears +in this expression + +is the Rabi frequency. + +Well, what we have +to do now is we + +have to go back from +the Rabi frequency. + +We assume linearly polarized +light in the x direction + +to the electric field. + +And that means, now, +that when we-- OK. + +We want to now take +this expression, + +and sum it up over all modes, +which means we integrate over, + +we write the Rabi +frequency squared + +as an electric field squared. + +And the electric +field squared is + +obtained as an integral over +the spectral distribution + +of the light. + +So this means we will +replace the Rabi frequency + +in this formula by an +integral over the energy + +density of the radiation. + +We have the matrix element +squared as a prefactor. + +I just try to +re-derive it, but I + +think the prefactor is +2 over epsilon naught. + +So, yes. + +With that, in +perturbation theory, + +the probability to be +in the excited state + +is-- let's just take +all of the prefactors. + +Now, I change the integration +variable from omega + +to detuning, we just +go from resonance-- + +we integrate relative +to the resonance. + +So our energy density is now +at the resonance, omega naught + +plus the detuning. + +And we have this Rabi +oscillation term. + +OK. + +So this is nothing else than +taking our perturbative Rabi + +oscillation formula, +which is coherent physics, + +and indicate over many moles. . + +I'm one step away +from the final result. + +If the energy density is +flat, is broadband-- so + +for the extreme +broadband case, we + +can pull that out +of the integral. + +And then, we are left only +with this function, F of t. + +And you can discuss +this function, F of t, + +is a standard result. + +And we have seen +many discussions + +in perturbation theory. + +If I plot this +function, versus delta, + +we have something +which has wiggles. + +Then, there is a maximum, +and it has wiggles. + +The width here is +t to the minus 1. + +And the amplitude is t squared. + +And this is the excited +state amplitude squared. + +So if we integrate +that over delta, + +we get something +which is linear in t. + +Something which goes as +t-square, and has a width 1/t. + +Yes, time is over. + +So the function F of t, +which is under the integrand, + +starts out at short +times, proportion + +to t squared, as we discussed. + +Maybe my drawing +should reflect that. + +But then it becomes linear. + +So for long times, the function +F of t becomes linear in t + +and the delta function +in the detuning delta. + +This is what you +have seen many times + +in the derivation of +Fermi's golden rule. + +I'm running out of time now. + +I'll pick up the +ball on Wednesday, + +and we'll discuss that result +and put it into context. + +But the take-home +message-- and what I + +really wanted to show you is +that we do have coherent Rabi + +oscillations. + +And by just performing +the integral + +over this broad +spectrum of the light, + +we lose the Rabi +oscillations, and we + +find rate equations, +Fermi's golden rule, + +and excitation probability +proportional to t. + +And we have done the transition +from coherent physics + +to irreversible physics. + +This is all hidden +in this one formula, + +but I want to fully explain +it when we start on Wednesday. + +Any last second +question about that? + +Cody? + +STUDENT: It looks +like we're integrating + +right over the point to where +perturbation theory becomes + +an exact, because we're +integrating over delta + +equals 0. + +And that's the most +important part. + +PROFESSOR: We are +integrating over it, + +but we are integrating over +it with the [INAUDIBLE]. + +So therefore, since +we have-- perturbation + +theory remains valid, actually. + +Perturbation theory +remains valid, + +as long as the excitation +probability is less than one. + +So I have not put a +scale on it, but we + +can go from a +quadratic dependence + +to linear dependence. + +As long as the probability +of being in the excited state + +is smaller than 1, perturbation +theory is exactly valid. + +So I think what +confuses you here + +is, we can do +resonant excitation. + +The broadband includes +resonant excitation. + +But for sufficiently +short times, + +we reach the rate +equation before we run out + +of [INAUDIBLE] +perturbation theory. \ No newline at end of file diff --git a/kmUPK9AIE64.txt b/kmUPK9AIE64.txt new file mode 100644 index 0000000000000000000000000000000000000000..6338847a32c5f0cf3eef8a99125fe022dafeb5a6 --- /dev/null +++ b/kmUPK9AIE64.txt @@ -0,0 +1,7928 @@ +align:start position:0% + +I expect that there will be many fun + + align:start position:0% +I expect that there will be many fun + + + align:start position:0% +I expect that there will be many fun +lectures in the sense that we're going + + align:start position:0% +lectures in the sense that we're going + + + align:start position:0% +lectures in the sense that we're going +to have you know we're going to be + + align:start position:0% +to have you know we're going to be + + + align:start position:0% +to have you know we're going to be +discussing a little more exactly at the + + align:start position:0% +discussing a little more exactly at the + + + align:start position:0% +discussing a little more exactly at the +right time in which that issue is an is + + align:start position:0% +right time in which that issue is an is + + + align:start position:0% +right time in which that issue is an is +an important issue at least as D in the + + align:start position:0% +an important issue at least as D in the + + + align:start position:0% +an important issue at least as D in the +newspapers and you know we live in we + + align:start position:0% +newspapers and you know we live in we + + + align:start position:0% +newspapers and you know we live in we +are going through a very interesting + + align:start position:0% +are going through a very interesting + + + align:start position:0% +are going through a very interesting +time for microeconomist inflation is + + align:start position:0% +time for microeconomist inflation is + + + align:start position:0% +time for microeconomist inflation is +unusually high something needs to be + + align:start position:0% +unusually high something needs to be + + + align:start position:0% +unusually high something needs to be +done about that er um we still have + + align:start position:0% +done about that er um we still have + + + align:start position:0% +done about that er um we still have +problems on the supply side of the + + align:start position:0% +problems on the supply side of the + + + align:start position:0% +problems on the supply side of the +economy as a result of CO as a result of + + align:start position:0% +economy as a result of CO as a result of + + + align:start position:0% +economy as a result of CO as a result of +the slow reopening of + + align:start position:0% +the slow reopening of + + + align:start position:0% +the slow reopening of +China um we have a war going on which is + + align:start position:0% +China um we have a war going on which is + + + align:start position:0% +China um we have a war going on which is +affecting also the price of energy and + + align:start position:0% +affecting also the price of energy and + + + align:start position:0% +affecting also the price of energy and +it's particularly impacting Europe and + + align:start position:0% +it's particularly impacting Europe and + + + align:start position:0% +it's particularly impacting Europe and +all these things are the situation is + + align:start position:0% +all these things are the situation is + + + align:start position:0% +all these things are the situation is +very fluid all of them can change at at + + align:start position:0% +very fluid all of them can change at at + + + align:start position:0% +very fluid all of them can change at at +any moment and uh and policy makers are + + align:start position:0% +any moment and uh and policy makers are + + + align:start position:0% +any moment and uh and policy makers are +s therefore paying very close attention + + align:start position:0% +s therefore paying very close attention + + + align:start position:0% +s therefore paying very close attention +to all these things it's not a normal + + align:start position:0% +to all these things it's not a normal + + + align:start position:0% +to all these things it's not a normal +time if you're a policy maker + + align:start position:0% +time if you're a policy maker + + + align:start position:0% +time if you're a policy maker +macroeconomist microeconomist policy + + align:start position:0% +macroeconomist microeconomist policy + + + align:start position:0% +macroeconomist microeconomist policy +maker uh you you are not sleeping a lot + + align:start position:0% +maker uh you you are not sleeping a lot + + + align:start position:0% +maker uh you you are not sleeping a lot +on these days and so so I expect that we + + align:start position:0% +on these days and so so I expect that we + + + align:start position:0% +on these days and so so I expect that we +will have plenty of time to discuss + + align:start position:0% +will have plenty of time to discuss + + + align:start position:0% +will have plenty of time to discuss +interesting things and analyze them um + + align:start position:0% +interesting things and analyze them um + + + align:start position:0% +interesting things and analyze them um +at a slightly higher level than you can + + align:start position:0% +at a slightly higher level than you can + + + align:start position:0% +at a slightly higher level than you can +do at this moment now I also told you in + + align:start position:0% +do at this moment now I also told you in + + + align:start position:0% +do at this moment now I also told you in +the previous in the introduction that + + align:start position:0% +the previous in the introduction that + + + align:start position:0% +the previous in the introduction that +that this particular + + align:start position:0% +that this particular + + + align:start position:0% +that this particular +lecture is not going to be of that kind + + align:start position:0% +lecture is not going to be of that kind + + + align:start position:0% +lecture is not going to be of that kind +you know it's going to be very boring in + + align:start position:0% +you know it's going to be very boring in + + + align:start position:0% +you know it's going to be very boring in +the sense that you know we need to start + + align:start position:0% +the sense that you know we need to start + + + align:start position:0% +the sense that you know we need to start +with definitions and and and I don't + + align:start position:0% +with definitions and and and I don't + + + align:start position:0% +with definitions and and and I don't +know who likes definitions I don't it's + + align:start position:0% +know who likes definitions I don't it's + + + align:start position:0% +know who likes definitions I don't it's +very boring now there is an interesting + + align:start position:0% +very boring now there is an interesting + + + align:start position:0% +very boring now there is an interesting +or a curious side of the definitions + + align:start position:0% +or a curious side of the definitions + + + align:start position:0% +or a curious side of the definitions +we're going to discuss which which is + + align:start position:0% +we're going to discuss which which is + + + align:start position:0% +we're going to discuss which which is +that if you were taking 1401 + + align:start position:0% +that if you were taking 1401 + + + align:start position:0% +that if you were taking 1401 +microeconomics many of the concepts + + align:start position:0% +microeconomics many of the concepts + + + align:start position:0% +microeconomics many of the concepts +we're going to describe require no + + align:start position:0% +we're going to describe require no + + + align:start position:0% +we're going to describe require no +definition they're obvious I mean if you + + align:start position:0% +definition they're obvious I mean if you + + + align:start position:0% +definition they're obvious I mean if you +I ask you for output of a factory that + + align:start position:0% +I ask you for output of a factory that + + + align:start position:0% +I ask you for output of a factory that +produces cars it's pretty obvious that + + align:start position:0% +produces cars it's pretty obvious that + + + align:start position:0% +produces cars it's pretty obvious that +it's a number of cars if I ask you for + + align:start position:0% +it's a number of cars if I ask you for + + + align:start position:0% +it's a number of cars if I ask you for +the prices of those cars is pretty + + align:start position:0% +the prices of those cars is pretty + + + align:start position:0% +the prices of those cars is pretty +obvious what the price of a car is not + + align:start position:0% +obvious what the price of a car is not + + + align:start position:0% +obvious what the price of a car is not +so for macro because if I ask you what + + align:start position:0% +so for macro because if I ask you what + + + align:start position:0% +so for macro because if I ask you what +is the output of the US economy well + + align:start position:0% +is the output of the US economy well + + + align:start position:0% +is the output of the US economy well +there's millions of goods and services + + align:start position:0% +there's millions of goods and services + + + align:start position:0% +there's millions of goods and services +are produced at the same time so so what + + align:start position:0% +are produced at the same time so so what + + + align:start position:0% +are produced at the same time so so what +do we mean by output a single measure of + + align:start position:0% +do we mean by output a single measure of + + + align:start position:0% +do we mean by output a single measure of +output or if I ask you about the price + + align:start position:0% +output or if I ask you about the price + + + align:start position:0% +output or if I ask you about the price +level or the inflation the rate at which + + align:start position:0% +level or the inflation the rate at which + + + align:start position:0% +level or the inflation the rate at which +that price level is changing well what + + align:start position:0% +that price level is changing well what + + + align:start position:0% +that price level is changing well what +are we talking about it's very easy to + + align:start position:0% +are we talking about it's very easy to + + + align:start position:0% +are we talking about it's very easy to +see where the price of a car is going up + + align:start position:0% +see where the price of a car is going up + + + align:start position:0% +see where the price of a car is going up +but if we're mixing sort of millions of + + align:start position:0% +but if we're mixing sort of millions of + + + align:start position:0% +but if we're mixing sort of millions of +different goods and services then it's a + + align:start position:0% +different goods and services then it's a + + + align:start position:0% +different goods and services then it's a +little harder and that's the reason we + + align:start position:0% +little harder and that's the reason we + + + align:start position:0% +little harder and that's the reason we +need this lecture because it's it's a + + align:start position:0% +need this lecture because it's it's a + + + align:start position:0% +need this lecture because it's it's a +little harder than 1401 and we need to + + align:start position:0% +little harder than 1401 and we need to + + + align:start position:0% +little harder than 1401 and we need to +Define basic things but they have a + + align:start position:0% +Define basic things but they have a + + + align:start position:0% +Define basic things but they have a +trick because you're suming apples and + + align:start position:0% +trick because you're suming apples and + + + align:start position:0% +trick because you're suming apples and +oranges not only apples and oranges + + align:start position:0% +oranges not only apples and oranges + + + align:start position:0% +oranges not only apples and oranges +apples oranges health services financial + + align:start position:0% +apples oranges health services financial + + + align:start position:0% +apples oranges health services financial +services all of them in in one piece and + + align:start position:0% +services all of them in in one piece and + + + align:start position:0% +services all of them in in one piece and +so so it's a little trickier and that's + + align:start position:0% +so so it's a little trickier and that's + + + align:start position:0% +so so it's a little trickier and that's +the reason we need this boring lecture + + align:start position:0% +the reason we need this boring lecture + + + align:start position:0% +the reason we need this boring lecture +we need to go through + + align:start position:0% +we need to go through + + + align:start position:0% +we need to go through +that slightly trickier definition of + + align:start position:0% +that slightly trickier definition of + + + align:start position:0% +that slightly trickier definition of +output prices and so + + align:start position:0% + + + + align:start position:0% + +on + + align:start position:0% +on + + + align:start position:0% +on +ER okay so let me let me start with the + + align:start position:0% +ER okay so let me let me start with the + + + align:start position:0% +ER okay so let me let me start with the +most basic thing aggregate output at the + + align:start position:0% +most basic thing aggregate output at the + + + align:start position:0% +most basic thing aggregate output at the +end of the day when where the econom is + + align:start position:0% +end of the day when where the econom is + + + align:start position:0% +end of the day when where the econom is +in a recession or not and so we don't + + align:start position:0% +in a recession or not and so we don't + + + align:start position:0% +in a recession or not and so we don't +like it or we do like it depends on what + + align:start position:0% +like it or we do like it depends on what + + + align:start position:0% +like it or we do like it depends on what +is happening to Output is output growing + + align:start position:0% +is happening to Output is output growing + + + align:start position:0% +is happening to Output is output growing +at the pace it used to grow is it + + align:start position:0% +at the pace it used to grow is it + + + align:start position:0% +at the pace it used to grow is it +growing less or it's declining well + + align:start position:0% +growing less or it's declining well + + + align:start position:0% +growing less or it's declining well +that's very important for macro and to + + align:start position:0% +that's very important for macro and to + + + align:start position:0% +that's very important for macro and to +understand the health of an economy the + + align:start position:0% +understand the health of an economy the + + + align:start position:0% +understand the health of an economy the +microeconomic health of an economy but + + align:start position:0% +microeconomic health of an economy but + + + align:start position:0% +microeconomic health of an economy but +we need to start by defining what we + + align:start position:0% +we need to start by defining what we + + + align:start position:0% +we need to start by defining what we +mean by + + align:start position:0% +mean by + + + align:start position:0% +mean by +output and because it's a tricky thing + + align:start position:0% +output and because it's a tricky thing + + + align:start position:0% +output and because it's a tricky thing +to do when you're adding so many apples + + align:start position:0% +to do when you're adding so many apples + + + align:start position:0% +to do when you're adding so many apples +oranges Financial Services ER + + align:start position:0% +oranges Financial Services ER + + + align:start position:0% +oranges Financial Services ER +entertainment and lots of things that + + align:start position:0% +entertainment and lots of things that + + + align:start position:0% +entertainment and lots of things that +are very different H it wasn't there we + + align:start position:0% +are very different H it wasn't there we + + + align:start position:0% +are very different H it wasn't there we +didn't have a good way of doing that in + + align:start position:0% +didn't have a good way of doing that in + + + align:start position:0% +didn't have a good way of doing that in +fact the national accounts as we know + + align:start position:0% +fact the national accounts as we know + + + align:start position:0% +fact the national accounts as we know +them in the US is something that we have + + align:start position:0% +them in the US is something that we have + + + align:start position:0% +them in the US is something that we have +since the post-war period in in the late + + align:start position:0% +since the post-war period in in the late + + + align:start position:0% +since the post-war period in in the late +40s that we develop the technique the + + align:start position:0% +40s that we develop the technique the + + + align:start position:0% +40s that we develop the technique the +approach to come up with a measure of + + align:start position:0% +approach to come up with a measure of + + + align:start position:0% +approach to come up with a measure of +our output before that we had measures + + align:start position:0% +our output before that we had measures + + + align:start position:0% +our output before that we had measures +proxies you know industrial production + + align:start position:0% +proxies you know industrial production + + + align:start position:0% +proxies you know industrial production +is very high I meaning we're producing + + align:start position:0% +is very high I meaning we're producing + + + align:start position:0% +is very high I meaning we're producing +lots of cars stuff like that and + + align:start position:0% +lots of cars stuff like that and + + + align:start position:0% +lots of cars stuff like that and +somebody but something systematic like + + align:start position:0% +somebody but something systematic like + + + align:start position:0% +somebody but something systematic like +we have today is a pretty recent uh + + align:start position:0% +we have today is a pretty recent uh + + + align:start position:0% +we have today is a pretty recent uh +thing okay we call that NEPA the + + align:start position:0% +thing okay we call that NEPA the + + + align:start position:0% +thing okay we call that NEPA the +national income and product + + align:start position:0% +national income and product + + + align:start position:0% +national income and product +account income and product that's going + + align:start position:0% +account income and product that's going + + + align:start position:0% +account income and product that's going +to be very important for macro as you'll + + align:start position:0% +to be very important for macro as you'll + + + align:start position:0% +to be very important for macro as you'll +see in a minute um so the main measure + + align:start position:0% +see in a minute um so the main measure + + + align:start position:0% +see in a minute um so the main measure +of aggregate output is what we call + + align:start position:0% +of aggregate output is what we call + + + align:start position:0% +of aggregate output is what we call +gross domestic product or simply GDP you + + align:start position:0% +gross domestic product or simply GDP you + + + align:start position:0% +gross domestic product or simply GDP you +hear GDP that means output of an economy + + align:start position:0% +hear GDP that means output of an economy + + + align:start position:0% +hear GDP that means output of an economy +why is gross and not net you're not + + align:start position:0% +why is gross and not net you're not + + + align:start position:0% +why is gross and not net you're not +going to worry about that in this course + + align:start position:0% +going to worry about that in this course + + + align:start position:0% +going to worry about that in this course +okay but that's you hear + + align:start position:0% +okay but that's you hear + + + align:start position:0% +okay but that's you hear +GDP most microeconomist wouldn't say + + align:start position:0% +GDP most microeconomist wouldn't say + + + align:start position:0% +GDP most microeconomist wouldn't say +output they would say GDP it's very + + align:start position:0% +output they would say GDP it's very + + + align:start position:0% +output they would say GDP it's very +short it's efficient and so on well + + align:start position:0% +short it's efficient and so on well + + + align:start position:0% +short it's efficient and so on well +that's what it means it's the output of + + align:start position:0% +that's what it means it's the output of + + + align:start position:0% +that's what it means it's the output of +an economy but how do we Define it as I + + align:start position:0% +an economy but how do we Define it as I + + + align:start position:0% +an economy but how do we Define it as I +said before it's much harder than when + + align:start position:0% +said before it's much harder than when + + + align:start position:0% +said before it's much harder than when +you have an individual + + align:start position:0% +you have an individual + + + align:start position:0% +you have an individual +good by the way I will be most of the + + align:start position:0% +good by the way I will be most of the + + + align:start position:0% +good by the way I will be most of the +time I will say + + align:start position:0% +time I will say + + + align:start position:0% +time I will say +Goods but really is goods and services + + align:start position:0% +Goods but really is goods and services + + + align:start position:0% +Goods but really is goods and services +but it's very long to say goods and + + align:start position:0% +but it's very long to say goods and + + + align:start position:0% +but it's very long to say goods and +services no so whenever I say Goods I'm + + align:start position:0% +services no so whenever I say Goods I'm + + + align:start position:0% +services no so whenever I say Goods I'm +not trying to play any trick on you I + + align:start position:0% +not trying to play any trick on you I + + + align:start position:0% +not trying to play any trick on you I +really mean goods and services I just + + align:start position:0% +really mean goods and services I just + + + align:start position:0% +really mean goods and services I just +mean lazy okay and most people are lazy + + align:start position:0% +mean lazy okay and most people are lazy + + + align:start position:0% +mean lazy okay and most people are lazy +that way okay now what is the difference + + align:start position:0% +that way okay now what is the difference + + + align:start position:0% +that way okay now what is the difference +between goods and services you you're + + align:start position:0% +between goods and services you you're + + + align:start position:0% +between goods and services you you're +not going to worry a lot about that in + + align:start position:0% +not going to worry a lot about that in + + + align:start position:0% +not going to worry a lot about that in +this no you're not going to worry at all + + align:start position:0% +this no you're not going to worry at all + + + align:start position:0% +this no you're not going to worry at all +about that in this course but just to + + align:start position:0% +about that in this course but just to + + + align:start position:0% +about that in this course but just to +get a sense goods are things that you + + align:start position:0% +get a sense goods are things that you + + + align:start position:0% +get a sense goods are things that you +know that are tangible services are + + align:start position:0% +know that are tangible services are + + + align:start position:0% +know that are tangible services are +things that are not that tangible there + + align:start position:0% +things that are not that tangible there + + + align:start position:0% +things that are not that tangible there +are benefits that you receive from the + + align:start position:0% +are benefits that you receive from the + + + align:start position:0% +are benefits that you receive from the +task that someone else operates on you + + align:start position:0% +task that someone else operates on you + + + align:start position:0% +task that someone else operates on you +so you go to the to you know the medical + + align:start position:0% +so you go to the to you know the medical + + + align:start position:0% +so you go to the to you know the medical +center you don't come up with a piece of + + align:start position:0% +center you don't come up with a piece of + + + align:start position:0% +center you don't come up with a piece of +a machine to well they may lend you + + align:start position:0% +a machine to well they may lend you + + + align:start position:0% +a machine to well they may lend you +something but but you don't come out + + align:start position:0% +something but but you don't come out + + + align:start position:0% +something but but you don't come out +with an objective you come out with the + + align:start position:0% +with an objective you come out with the + + + align:start position:0% +with an objective you come out with the +service provided by a doctor to you okay + + align:start position:0% +service provided by a doctor to you okay + + + align:start position:0% +service provided by a doctor to you okay +and the same happens if you go to a bank + + align:start position:0% +and the same happens if you go to a bank + + + align:start position:0% +and the same happens if you go to a bank +you don't come with a ATM with you what + + align:start position:0% +you don't come with a ATM with you what + + + align:start position:0% +you don't come with a ATM with you what +you come up with is the service of + + align:start position:0% +you come up with is the service of + + + align:start position:0% +you come up with is the service of +having done a transaction or deposit or + + align:start position:0% +having done a transaction or deposit or + + + align:start position:0% +having done a transaction or deposit or +go on a mortgage or something like that + + align:start position:0% +go on a mortgage or something like that + + + align:start position:0% +go on a mortgage or something like that +it's a service if you go to a + + align:start position:0% +it's a service if you go to a + + + align:start position:0% +it's a service if you go to a +restaurant again you don't what you can + + align:start position:0% +restaurant again you don't what you can + + + align:start position:0% +restaurant again you don't what you can +what you have is an experience it's a + + align:start position:0% +what you have is an experience it's a + + + align:start position:0% +what you have is an experience it's a +people provided an experience to you + + align:start position:0% +people provided an experience to you + + + align:start position:0% +people provided an experience to you +things are a little tricky because if + + align:start position:0% +things are a little tricky because if + + + align:start position:0% +things are a little tricky because if +you do a take out well is that an + + align:start position:0% +you do a take out well is that an + + + align:start position:0% +you do a take out well is that an +experience or is really the goods so so + + align:start position:0% +experience or is really the goods so so + + + align:start position:0% +experience or is really the goods so so +if you get into those details which + + align:start position:0% +if you get into those details which + + + align:start position:0% +if you get into those details which +you're not going to get it gets to be + + align:start position:0% +you're not going to get it gets to be + + + align:start position:0% +you're not going to get it gets to be +tricky but but but just to get a + + align:start position:0% +tricky but but but just to get a + + + align:start position:0% +tricky but but but just to get a +sense on average a consumer in the US + + align:start position:0% +sense on average a consumer in the US + + + align:start position:0% +sense on average a consumer in the US +two third of the consumption is in + + align:start position:0% +two third of the consumption is in + + + align:start position:0% +two third of the consumption is in +services not in Goods it's not sort of + + align:start position:0% +services not in Goods it's not sort of + + + align:start position:0% +services not in Goods it's not sort of +the banana and so on that you buy it's a + + align:start position:0% +the banana and so on that you buy it's a + + + align:start position:0% +the banana and so on that you buy it's a +lot of the financial services health + + align:start position:0% +lot of the financial services health + + + align:start position:0% +lot of the financial services health +services and entertainment and things + + align:start position:0% +services and entertainment and things + + + align:start position:0% +services and entertainment and things +like that traveling that's what you + + align:start position:0% +like that traveling that's what you + + + align:start position:0% +like that traveling that's what you +spend most of your time having clarified + + align:start position:0% +spend most of your time having clarified + + + align:start position:0% +spend most of your time having clarified +that you can of forget that from now on + + align:start position:0% +that you can of forget that from now on + + + align:start position:0% +that you can of forget that from now on +I'm going to say Goods occasionally may + + align:start position:0% +I'm going to say Goods occasionally may + + + align:start position:0% +I'm going to say Goods occasionally may +say goods and services but I always mean + + align:start position:0% +say goods and services but I always mean + + + align:start position:0% +say goods and services but I always mean +the same okay good so um so how do we + + align:start position:0% +the same okay good so um so how do we + + + align:start position:0% +the same okay good so um so how do we +measure these things so well there there + + align:start position:0% +measure these things so well there there + + + align:start position:0% +measure these things so well there there +are different ways ER of of of doing + + align:start position:0% +are different ways ER of of of doing + + + align:start position:0% +are different ways ER of of of doing +this something happened to my slide + + align:start position:0% +this something happened to my slide + + + align:start position:0% +this something happened to my slide +there okay there we + + align:start position:0% +there okay there we + + + align:start position:0% +there okay there we +are um so suppose that you have a an + + align:start position:0% +are um so suppose that you have a an + + + align:start position:0% +are um so suppose that you have a an +economy that is very simple I don't need + + align:start position:0% +economy that is very simple I don't need + + + align:start position:0% +economy that is very simple I don't need +to tell you how simple this economy is + + align:start position:0% +to tell you how simple this economy is + + + align:start position:0% +to tell you how simple this economy is +it has just two + + align:start position:0% +it has just two + + + align:start position:0% +it has just two +firms okay suppose we have an economy + + align:start position:0% +firms okay suppose we have an economy + + + align:start position:0% +firms okay suppose we have an economy +that's very simple has two firms one + + align:start position:0% +that's very simple has two firms one + + + align:start position:0% +that's very simple has two firms one +firm produces a steel and the other one + + align:start position:0% +firm produces a steel and the other one + + + align:start position:0% +firm produces a steel and the other one +produces cars and the company that + + align:start position:0% +produces cars and the company that + + + align:start position:0% +produces cars and the company that +produces cars buys all the steel from + + align:start position:0% +produces cars buys all the steel from + + + align:start position:0% +produces cars buys all the steel from +the company no body you as a consumer + + align:start position:0% +the company no body you as a consumer + + + align:start position:0% +the company no body you as a consumer +don't buy you don't buy steel directly + + align:start position:0% +don't buy you don't buy steel directly + + + align:start position:0% +don't buy you don't buy steel directly +the car company buys a steel uses to + + align:start position:0% +the car company buys a steel uses to + + + align:start position:0% +the car company buys a steel uses to +produce a car and you buy the car okay + + align:start position:0% +produce a car and you buy the car okay + + + align:start position:0% +produce a car and you buy the car okay +so that's our simple economy and that's + + align:start position:0% +so that's our simple economy and that's + + + align:start position:0% +so that's our simple economy and that's +those are the the accounts of the of the + + align:start position:0% +those are the the accounts of the of the + + + align:start position:0% +those are the the accounts of the of the +simple economy so there you have company + + align:start position:0% +simple economy so there you have company + + + align:start position:0% +simple economy so there you have company +one has a revenue from sales it sells + + align:start position:0% +one has a revenue from sales it sells + + + align:start position:0% +one has a revenue from sales it sells +$100 okay so price of steel times steel + + align:start position:0% +$100 okay so price of steel times steel + + + align:start position:0% +$100 okay so price of steel times steel +is + + align:start position:0% +is + + + align:start position:0% +is +$100 the second company H uses B is Ste + + align:start position:0% +$100 the second company H uses B is Ste + + + align:start position:0% +$100 the second company H uses B is Ste +uses workers and sells + + align:start position:0% +uses workers and sells + + + align:start position:0% +uses workers and sells +$200 no so the question I ask you the + + align:start position:0% +$200 no so the question I ask you the + + + align:start position:0% +$200 no so the question I ask you the +first question I ask you here is well + + align:start position:0% +first question I ask you here is well + + + align:start position:0% +first question I ask you here is well +what is the GDP of this economy here you + + align:start position:0% +what is the GDP of this economy here you + + + align:start position:0% +what is the GDP of this economy here you +have an economy that has two goods + + align:start position:0% +have an economy that has two goods + + + align:start position:0% +have an economy that has two goods +needless to say a real economy is a lot + + align:start position:0% +needless to say a real economy is a lot + + + align:start position:0% +needless to say a real economy is a lot +more complicated than this but you have + + align:start position:0% +more complicated than this but you have + + + align:start position:0% +more complicated than this but you have +two companies and I ask you what is + + align:start position:0% +two companies and I ask you what is + + + align:start position:0% +two companies and I ask you what is +GDP so the obvious things that you could + + align:start position:0% +GDP so the obvious things that you could + + + align:start position:0% +GDP so the obvious things that you could +come up with is well I Su all the + + align:start position:0% +come up with is well I Su all the + + + align:start position:0% +come up with is well I Su all the +revenues okay so that's the obvious one + + align:start position:0% +revenues okay so that's the obvious one + + + align:start position:0% +revenues okay so that's the obvious one +the total GDP of these economies is 300 + + align:start position:0% +the total GDP of these economies is 300 + + + align:start position:0% +the total GDP of these economies is 300 +that's a sensible + + align:start position:0% +that's a sensible + + + align:start position:0% +that's a sensible +answer okay at least at this moment I + + align:start position:0% +answer okay at least at this moment I + + + align:start position:0% +answer okay at least at this moment I +would accept that as a sensible answer + + align:start position:0% +would accept that as a sensible answer + + + align:start position:0% +would accept that as a sensible answer +in the quiz I wouldn't but here it's a + + align:start position:0% +in the quiz I wouldn't but here it's a + + + align:start position:0% +in the quiz I wouldn't but here it's a +sensible answer I mean well you ask me + + align:start position:0% +sensible answer I mean well you ask me + + + align:start position:0% +sensible answer I mean well you ask me +for what is the total output of that + + align:start position:0% +for what is the total output of that + + + align:start position:0% +for what is the total output of that +economy I sum up all the revenues on + + align:start position:0% +economy I sum up all the revenues on + + + align:start position:0% +economy I sum up all the revenues on +sales and that's + + align:start position:0% + + + + align:start position:0% + +300 okay so so um is it + + align:start position:0% +300 okay so so um is it + + + align:start position:0% +300 okay so so um is it +300 well or is it 200 I mean that's + + align:start position:0% +300 well or is it 200 I mean that's + + + align:start position:0% +300 well or is it 200 I mean that's +another you says well look only the + + align:start position:0% +another you says well look only the + + + align:start position:0% +another you says well look only the +final goods perhaps should count because + + align:start position:0% +final goods perhaps should count because + + + align:start position:0% +final goods perhaps should count because +you know this is the only thing that you + + align:start position:0% +you know this is the only thing that you + + + align:start position:0% +you know this is the only thing that you +as a consumer will ever see this part + + align:start position:0% +as a consumer will ever see this part + + + align:start position:0% +as a consumer will ever see this part +not that those are two sensible answers + + align:start position:0% +not that those are two sensible answers + + + align:start position:0% +not that those are two sensible answers +and what I'll show you in three + + align:start position:0% +and what I'll show you in three + + + align:start position:0% +and what I'll show you in three +different ways is that the right answer + + align:start position:0% +different ways is that the right answer + + + align:start position:0% +different ways is that the right answer +is 200 for that economy okay not 300 the + + align:start position:0% +is 200 for that economy okay not 300 the + + + align:start position:0% +is 200 for that economy okay not 300 the +right answer is + + align:start position:0% +right answer is + + + align:start position:0% +right answer is +200 so method + + align:start position:0% +200 so method + + + align:start position:0% +200 so method +one H and all these methods are used and + + align:start position:0% +one H and all these methods are used and + + + align:start position:0% +one H and all these methods are used and +they use to check each other H to + + align:start position:0% +they use to check each other H to + + + align:start position:0% +they use to check each other H to +compute H + + align:start position:0% +compute H + + + align:start position:0% +compute H +GDP uh so method one is what I said here + + align:start position:0% +GDP uh so method one is what I said here + + + align:start position:0% +GDP uh so method one is what I said here +is final goods you said + + align:start position:0% +is final goods you said + + + align:start position:0% +is final goods you said +GDP is the value of the final goods and + + align:start position:0% +GDP is the value of the final goods and + + + align:start position:0% +GDP is the value of the final goods and +services producing the economy during a + + align:start position:0% +services producing the economy during a + + + align:start position:0% +services producing the economy during a +given period of time notice that GDP is + + align:start position:0% +given period of time notice that GDP is + + + align:start position:0% +given period of time notice that GDP is +a concept of a flow it's something you + + align:start position:0% +a concept of a flow it's something you + + + align:start position:0% +a concept of a flow it's something you +produce in a year okay that's the reason + + align:start position:0% +produce in a year okay that's the reason + + + align:start position:0% +produce in a year okay that's the reason +you say GDP of the US in 2022 was you + + align:start position:0% +you say GDP of the US in 2022 was you + + + align:start position:0% +you say GDP of the US in 2022 was you +know 23 23 trillion dollar is in a year + + align:start position:0% +know 23 23 trillion dollar is in a year + + + align:start position:0% +know 23 23 trillion dollar is in a year +okay it's a it's a period of time okay + + align:start position:0% +okay it's a it's a period of time okay + + + align:start position:0% +okay it's a it's a period of time okay +so so that's one definition and one way + + align:start position:0% +so so that's one definition and one way + + + align:start position:0% +so so that's one definition and one way +of of of er + + align:start position:0% +of of of er + + + align:start position:0% +of of of er +of making sense of this definition is + + align:start position:0% +of making sense of this definition is + + + align:start position:0% +of making sense of this definition is +imagine that I give you the same economy + + align:start position:0% +imagine that I give you the same economy + + + align:start position:0% +imagine that I give you the same economy +with the same two factories and now all + + align:start position:0% +with the same two factories and now all + + + align:start position:0% +with the same two factories and now all +of a sudden I tell you you know what I'm + + align:start position:0% +of a sudden I tell you you know what I'm + + + align:start position:0% +of a sudden I tell you you know what I'm +going to merge the two companies so + + align:start position:0% +going to merge the two companies so + + + align:start position:0% +going to merge the two companies so +company the car company will buy the + + align:start position:0% +company the car company will buy the + + + align:start position:0% +company the car company will buy the +steel meal or whatever + + align:start position:0% +steel meal or whatever + + + align:start position:0% +steel meal or whatever +well if I now put together those two + + align:start position:0% +well if I now put together those two + + + align:start position:0% +well if I now put together those two +accounts now I never see the steel + + align:start position:0% +accounts now I never see the steel + + + align:start position:0% +accounts now I never see the steel +because it that's all happening inside + + align:start position:0% +because it that's all happening inside + + + align:start position:0% +because it that's all happening inside +the the factory and it's still the case + + align:start position:0% +the the factory and it's still the case + + + align:start position:0% +the the factory and it's still the case +that the economy would be producing 200 + + align:start position:0% +that the economy would be producing 200 + + + align:start position:0% +that the economy would be producing 200 +Cars and all that you would see is 200 + + align:start position:0% +Cars and all that you would see is 200 + + + align:start position:0% +Cars and all that you would see is 200 +no because I would put this thing + + align:start position:0% +no because I would put this thing + + + align:start position:0% +no because I would put this thing +together there was a steel that this + + align:start position:0% +together there was a steel that this + + + align:start position:0% +together there was a steel that this +company had purchased from that but now + + align:start position:0% +company had purchased from that but now + + + align:start position:0% +company had purchased from that but now +it's all inside okay so so if I put them + + align:start position:0% +it's all inside okay so so if I put them + + + align:start position:0% +it's all inside okay so so if I put them +together then that steel there doesn't + + align:start position:0% +together then that steel there doesn't + + + align:start position:0% +together then that steel there doesn't +appear because it's all produced inhouse + + align:start position:0% +appear because it's all produced inhouse + + + align:start position:0% +appear because it's all produced inhouse +and now GDP would be 200 well it makes + + align:start position:0% +and now GDP would be 200 well it makes + + + align:start position:0% +and now GDP would be 200 well it makes +no sense + + align:start position:0% +no sense + + + align:start position:0% +no sense +that just because I change the ownership + + align:start position:0% +that just because I change the ownership + + + align:start position:0% +that just because I change the ownership +structure of the companies that your GDP + + align:start position:0% +structure of the companies that your GDP + + + align:start position:0% +structure of the companies that your GDP +changes collapses from 300 to 200 if I + + align:start position:0% +changes collapses from 300 to 200 if I + + + align:start position:0% +changes collapses from 300 to 200 if I +only measuring final goods though I + + align:start position:0% +only measuring final goods though I + + + align:start position:0% +only measuring final goods though I +don't have that problem it's still 200 + + align:start position:0% +don't have that problem it's still 200 + + + align:start position:0% +don't have that problem it's still 200 +doesn't matter that I have the merge + + align:start position:0% +doesn't matter that I have the merge + + + align:start position:0% +doesn't matter that I have the merge +slice and LIC in 20 or whatever so + + align:start position:0% +slice and LIC in 20 or whatever so + + + align:start position:0% +slice and LIC in 20 or whatever so +that's that tells you that that's we're + + align:start position:0% +that's that tells you that that's we're + + + align:start position:0% +that's that tells you that that's we're +going the right way here because you + + align:start position:0% +going the right way here because you + + + align:start position:0% +going the right way here because you +know it's it's a very robust answer that + + align:start position:0% +know it's it's a very robust answer that + + + align:start position:0% +know it's it's a very robust answer that +is you don't count intermediate output + + align:start position:0% +is you don't count intermediate output + + + align:start position:0% +is you don't count intermediate output +you only count the final goods which are + + align:start position:0% +you only count the final goods which are + + + align:start position:0% +you only count the final goods which are +the things that the consumer will buy + + align:start position:0% +the things that the consumer will buy + + + align:start position:0% +the things that the consumer will buy +buy the firms will buy for investment + + align:start position:0% +buy the firms will buy for investment + + + align:start position:0% +buy the firms will buy for investment +and things of that kind that foreigners + + align:start position:0% +and things of that kind that foreigners + + + align:start position:0% +and things of that kind that foreigners +will + + align:start position:0% +will + + + align:start position:0% +will +buy alternative method is GDP is the sum + + align:start position:0% +buy alternative method is GDP is the sum + + + align:start position:0% +buy alternative method is GDP is the sum +of value + + align:start position:0% +of value + + + align:start position:0% +of value +added in the economy during a given + + align:start position:0% +added in the economy during a given + + + align:start position:0% +added in the economy during a given +period of time what is value added the + + align:start position:0% +period of time what is value added the + + + align:start position:0% +period of time what is value added the +difference between final the final goods + + align:start position:0% +difference between final the final goods + + + align:start position:0% +difference between final the final goods +produced by a company and the + + align:start position:0% +produced by a company and the + + + align:start position:0% +produced by a company and the +intermediate inputs it purchased to + + align:start position:0% +intermediate inputs it purchased to + + + align:start position:0% +intermediate inputs it purchased to +produce those + + align:start position:0% +produce those + + + align:start position:0% +produce those +goods okay so what is the value added of + + align:start position:0% +goods okay so what is the value added of + + + align:start position:0% +goods okay so what is the value added of +the steel company here + + align:start position:0% +the steel company here + + + align:start position:0% +the steel company here +it's the answer is there but you know + + align:start position:0% +it's the answer is there but you know + + + align:start position:0% +it's the answer is there but you know +but what is the value added it's 100 how + + align:start position:0% +but what is the value added it's 100 how + + + align:start position:0% +but what is the value added it's 100 how +do I know it's 100 well because it's not + + align:start position:0% +do I know it's 100 well because it's not + + + align:start position:0% +do I know it's 100 well because it's not +buying any intermediate input and the + + align:start position:0% +buying any intermediate input and the + + + align:start position:0% +buying any intermediate input and the +revenue is + + align:start position:0% +revenue is + + + align:start position:0% +revenue is +100 okay so that's the reason I get 100 + + align:start position:0% +100 okay so that's the reason I get 100 + + + align:start position:0% +100 okay so that's the reason I get 100 +there okay 100 there's no intermediate + + align:start position:0% +there okay 100 there's no intermediate + + + align:start position:0% +there okay 100 there's no intermediate +input what is the value added of the car + + align:start position:0% +input what is the value added of the car + + + align:start position:0% +input what is the value added of the car +company well the revenue on sales is 200 + + align:start position:0% +company well the revenue on sales is 200 + + + align:start position:0% +company well the revenue on sales is 200 +but it purchase 100 in intermediate + + align:start position:0% +but it purchase 100 in intermediate + + + align:start position:0% +but it purchase 100 in intermediate +inputs so the value is 200 minus 100 the + + align:start position:0% +inputs so the value is 200 minus 100 the + + + align:start position:0% +inputs so the value is 200 minus 100 the +value out of this company is 100 100 + + align:start position:0% +value out of this company is 100 100 + + + align:start position:0% +value out of this company is 100 100 +plus 100 I get my 200 again + + align:start position:0% +plus 100 I get my 200 again + + + align:start position:0% +plus 100 I get my 200 again +yep + + align:start position:0% +yep + + + align:start position:0% +yep +consider wages to be in really good no + + align:start position:0% +consider wages to be in really good no + + + align:start position:0% +consider wages to be in really good no +that's those are not Goods those are + + align:start position:0% +that's those are not Goods those are + + + align:start position:0% +that's those are not Goods those are +factors of + + align:start position:0% +factors of + + + align:start position:0% +factors of +production okay so this and the same + + align:start position:0% +production okay so this and the same + + + align:start position:0% +production okay so this and the same +there are machines in that factory that + + align:start position:0% +there are machines in that factory that + + + align:start position:0% +there are machines in that factory that +are helping you produce things that's a + + align:start position:0% +are helping you produce things that's a + + + align:start position:0% +are helping you produce things that's a +service of the machine it's Capital + + align:start position:0% +service of the machine it's Capital + + + align:start position:0% +service of the machine it's Capital +that's not an intermediate input an + + align:start position:0% +that's not an intermediate input an + + + align:start position:0% +that's not an intermediate input an +intermediate input is another good or + + align:start position:0% +intermediate input is another good or + + + align:start position:0% +intermediate input is another good or +service that you buy for the the purpose + + align:start position:0% +service that you buy for the the purpose + + + align:start position:0% +service that you buy for the the purpose +of producing that that good + + align:start position:0% +of producing that that good + + + align:start position:0% +of producing that that good +okay so workers is not workers are + + align:start position:0% +okay so workers is not workers are + + + align:start position:0% +okay so workers is not workers are +working inside your company and so on if + + align:start position:0% +working inside your company and so on if + + + align:start position:0% +working inside your company and so on if +the work was if the work was produced + + align:start position:0% +the work was if the work was produced + + + align:start position:0% +the work was if the work was produced +was outsourced and you had another + + align:start position:0% +was outsourced and you had another + + + align:start position:0% +was outsourced and you had another +company that produces something that you + + align:start position:0% +company that produces something that you + + + align:start position:0% +company that produces something that you +use from those workers that would be an + + align:start position:0% +use from those workers that would be an + + + align:start position:0% +use from those workers that would be an +intermediate input but you would have to + + align:start position:0% +intermediate input but you would have to + + + align:start position:0% +intermediate input but you would have to +count the value out of the other of the + + align:start position:0% +count the value out of the other of the + + + align:start position:0% +count the value out of the other of the +companies you have outsourced too you + + align:start position:0% +companies you have outsourced too you + + + align:start position:0% +companies you have outsourced too you +see so that's method two two and you see + + align:start position:0% +see so that's method two two and you see + + + align:start position:0% +see so that's method two two and you see +we get exactly at 200 those two method + + align:start position:0% +we get exactly at 200 those two method + + + align:start position:0% +we get exactly at 200 those two method +methods are called production methods + + align:start position:0% +methods are called production methods + + + align:start position:0% +methods are called production methods +there are different ways of measuring + + align:start position:0% +there are different ways of measuring + + + align:start position:0% +there are different ways of measuring +the production of the economy the third + + align:start position:0% +the production of the economy the third + + + align:start position:0% +the production of the economy the third +method and the last one is an income + + align:start position:0% +method and the last one is an income + + + align:start position:0% +method and the last one is an income +method which means look all that is + + align:start position:0% +method which means look all that is + + + align:start position:0% +method which means look all that is +produced has to be earned by someone the + + align:start position:0% +produced has to be earned by someone the + + + align:start position:0% +produced has to be earned by someone the +workers the owners of capital somebody + + align:start position:0% +workers the owners of capital somebody + + + align:start position:0% +workers the owners of capital somebody +has to own that if the firms sell + + align:start position:0% +has to own that if the firms sell + + + align:start position:0% +has to own that if the firms sell +collectively $200 those $200 have to be + + align:start position:0% +collectively $200 those $200 have to be + + + align:start position:0% +collectively $200 those $200 have to be +allocated to someone someone means + + align:start position:0% +allocated to someone someone means + + + align:start position:0% +allocated to someone someone means +workers the owners of capital of the + + align:start position:0% +workers the owners of capital of the + + + align:start position:0% +workers the owners of capital of the +first Ms or in realistic economies the + + align:start position:0% +first Ms or in realistic economies the + + + align:start position:0% +first Ms or in realistic economies the +government you pay taxes and things of + + align:start position:0% +government you pay taxes and things of + + + align:start position:0% +government you pay taxes and things of +that kind okay we're not going to worry + + align:start position:0% +that kind okay we're not going to worry + + + align:start position:0% +that kind okay we're not going to worry +about the government for a + + align:start position:0% +about the government for a + + + align:start position:0% +about the government for a +while so that's an alternative method + + align:start position:0% +while so that's an alternative method + + + align:start position:0% +while so that's an alternative method +it's method three you just sum the + + align:start position:0% +it's method three you just sum the + + + align:start position:0% +it's method three you just sum the +incomes so who are the factors of + + align:start position:0% +incomes so who are the factors of + + + align:start position:0% +incomes so who are the factors of +productions here related to your + + align:start position:0% +productions here related to your + + + align:start position:0% +productions here related to your +question in this there is no government + + align:start position:0% +question in this there is no government + + + align:start position:0% +question in this there is no government +here no taxes so we have only workers + + align:start position:0% +here no taxes so we have only workers + + + align:start position:0% +here no taxes so we have only workers +and profits you the capital the owners + + align:start position:0% +and profits you the capital the owners + + + align:start position:0% +and profits you the capital the owners +of the Company wages is 80 + 70 is + + align:start position:0% +of the Company wages is 80 + 70 is + + + align:start position:0% +of the Company wages is 80 + 70 is +150 profits is 20 + 30 50 150 in wages + + align:start position:0% +150 profits is 20 + 30 50 150 in wages + + + align:start position:0% +150 profits is 20 + 30 50 150 in wages +plus 50 in profit gives you back your + + align:start position:0% +plus 50 in profit gives you back your + + + align:start position:0% +plus 50 in profit gives you back your +200 okay so those are the three ways we + + align:start position:0% +200 okay so those are the three ways we + + + align:start position:0% +200 okay so those are the three ways we +have of measuring these things and you + + align:start position:0% +have of measuring these things and you + + + align:start position:0% +have of measuring these things and you +see they give you exactly the same + + align:start position:0% +see they give you exactly the same + + + align:start position:0% +see they give you exactly the same +result now there is + + align:start position:0% +result now there is + + + align:start position:0% +result now there is +something as I as I from the + + align:start position:0% +something as I as I from the + + + align:start position:0% +something as I as I from the +construction of national account there + + align:start position:0% +construction of national account there + + + align:start position:0% +construction of national account there +is something interesting in what I just + + align:start position:0% +is something interesting in what I just + + + align:start position:0% +is something interesting in what I just +said which is look I can that production + + align:start position:0% +said which is look I can that production + + + align:start position:0% +said which is look I can that production +is the same as + + align:start position:0% +is the same as + + + align:start position:0% +is the same as +income that's going to be very important + + align:start position:0% +income that's going to be very important + + + align:start position:0% +income that's going to be very important +for macro very important for macro + + align:start position:0% +for macro very important for macro + + + align:start position:0% +for macro very important for macro +and it's totally unimportant for + + align:start position:0% +and it's totally unimportant for + + + align:start position:0% +and it's totally unimportant for +micro when you're looking at a company + + align:start position:0% +micro when you're looking at a company + + + align:start position:0% +micro when you're looking at a company +for example in micro and you're looking + + align:start position:0% +for example in micro and you're looking + + + align:start position:0% +for example in micro and you're looking +at a car company by + + align:start position:0% +at a car company by + + + align:start position:0% +at a car company by +itself it is true that you know the + + align:start position:0% +itself it is true that you know the + + + align:start position:0% +itself it is true that you know the +output of that company becomes income + + align:start position:0% +output of that company becomes income + + + align:start position:0% +output of that company becomes income +part for the owners of the company and + + align:start position:0% +part for the owners of the company and + + + align:start position:0% +part for the owners of the company and +part for the workers but that income + + align:start position:0% +part for the workers but that income + + + align:start position:0% +part for the workers but that income +needs not be spent in cars can spend in + + align:start position:0% +needs not be spent in cars can spend in + + + align:start position:0% +needs not be spent in cars can spend in +food entertainment and whatever not so + + align:start position:0% +food entertainment and whatever not so + + + align:start position:0% +food entertainment and whatever not so +in + + align:start position:0% +in + + + align:start position:0% +in +macro because what else you going to + + align:start position:0% +macro because what else you going to + + + align:start position:0% +macro because what else you going to +spend it to than in the same good that + + align:start position:0% +spend it to than in the same good that + + + align:start position:0% +spend it to than in the same good that +you're producing in the aggregate good + + align:start position:0% +you're producing in the aggregate good + + + align:start position:0% +you're producing in the aggregate good +so it's very interesting that's a very + + align:start position:0% +so it's very interesting that's a very + + + align:start position:0% +so it's very interesting that's a very +distinctive feature of micro that is not + + align:start position:0% +distinctive feature of micro that is not + + + align:start position:0% +distinctive feature of micro that is not +present in micro is that that income has + + align:start position:0% +present in micro is that that income has + + + align:start position:0% +present in micro is that that income has +to be spent in the same Goods if the + + align:start position:0% +to be spent in the same Goods if the + + + align:start position:0% +to be spent in the same Goods if the +econom is closed later on we're going to + + align:start position:0% +econom is closed later on we're going to + + + align:start position:0% +econom is closed later on we're going to +open the economy to the rest of the + + align:start position:0% +open the economy to the rest of the + + + align:start position:0% +open the economy to the rest of the +world and then you get you buy some + + align:start position:0% +world and then you get you buy some + + + align:start position:0% +world and then you get you buy some +Chinese goods and blah blah blah but if + + align:start position:0% +Chinese goods and blah blah blah but if + + + align:start position:0% +Chinese goods and blah blah blah but if +you keep it close hey you are not going + + align:start position:0% +you keep it close hey you are not going + + + align:start position:0% +you keep it close hey you are not going +to buy cars that's what you work on but + + align:start position:0% +to buy cars that's what you work on but + + + align:start position:0% +to buy cars that's what you work on but +you're going to have to buy it in the + + align:start position:0% +you're going to have to buy it in the + + + align:start position:0% +you're going to have to buy it in the +single good of the + + align:start position:0% +single good of the + + + align:start position:0% +single good of the +economy which is the sum of all the + + align:start position:0% +economy which is the sum of all the + + + align:start position:0% +economy which is the sum of all the +goods that we we consume an average + + align:start position:0% +goods that we we consume an average + + + align:start position:0% +goods that we we consume an average +that's going to be very + + align:start position:0% +that's going to be very + + + align:start position:0% +that's going to be very +important anyways this time is this + + align:start position:0% +important anyways this time is this + + + align:start position:0% +important anyways this time is this +stuff move in the right direction okay + + align:start position:0% +stuff move in the right direction okay + + + align:start position:0% +stuff move in the right direction okay +so that's that's that's that now you + + align:start position:0% +so that's that's that's that now you + + + align:start position:0% +so that's that's that's that now you +know what GDP is and the different ways + + align:start position:0% +know what GDP is and the different ways + + + align:start position:0% +know what GDP is and the different ways +of measuring you're going to have to + + align:start position:0% +of measuring you're going to have to + + + align:start position:0% +of measuring you're going to have to +remember that + + align:start position:0% +remember that + + + align:start position:0% +remember that +for for p set one and for quiz one and + + align:start position:0% +for for p set one and for quiz one and + + + align:start position:0% +for for p set one and for quiz one and +you might as well forget it for the + + align:start position:0% +you might as well forget it for the + + + align:start position:0% +you might as well forget it for the +future it's good that you understand the + + align:start position:0% +future it's good that you understand the + + + align:start position:0% +future it's good that you understand the +concept but it's different ways of + + align:start position:0% +concept but it's different ways of + + + align:start position:0% +concept but it's different ways of +constructing is not very + + align:start position:0% +constructing is not very + + + align:start position:0% +constructing is not very +important second thing we need to worry + + align:start position:0% +important second thing we need to worry + + + align:start position:0% +important second thing we need to worry +about + + align:start position:0% +about + + + align:start position:0% +about +is that whenever you're thinking about + + align:start position:0% +is that whenever you're thinking about + + + align:start position:0% +is that whenever you're thinking about +the output of an economy you're really + + align:start position:0% +the output of an economy you're really + + + align:start position:0% +the output of an economy you're really +trying to think about the real output + + align:start position:0% +trying to think about the real output + + + align:start position:0% +trying to think about the real output +meaning number of cars and number of + + align:start position:0% +meaning number of cars and number of + + + align:start position:0% +meaning number of cars and number of +machines and so on but you have + + align:start position:0% +machines and so on but you have + + + align:start position:0% +machines and so on but you have +inflation for example then prices of + + align:start position:0% +inflation for example then prices of + + + align:start position:0% +inflation for example then prices of +these things are growing and so the + + align:start position:0% +these things are growing and so the + + + align:start position:0% +these things are growing and so the +total revenue on sales is growing but + + align:start position:0% +total revenue on sales is growing but + + + align:start position:0% +total revenue on sales is growing but +they don't mean the same and we want to + + align:start position:0% +they don't mean the same and we want to + + + align:start position:0% +they don't mean the same and we want to +certainly separate these two things and + + align:start position:0% +certainly separate these two things and + + + align:start position:0% +certainly separate these two things and +for that reason we have a concept which + + align:start position:0% +for that reason we have a concept which + + + align:start position:0% +for that reason we have a concept which +is called nominal GDP and another one + + align:start position:0% +is called nominal GDP and another one + + + align:start position:0% +is called nominal GDP and another one +which is called real GDP nominal GDP is + + align:start position:0% +which is called real GDP nominal GDP is + + + align:start position:0% +which is called real GDP nominal GDP is +the simplest thing on Earth is + + align:start position:0% +the simplest thing on Earth is + + + align:start position:0% +the simplest thing on Earth is +essentially you know we had only one + + align:start position:0% +essentially you know we had only one + + + align:start position:0% +essentially you know we had only one +final goods company there which was cars + + align:start position:0% +final goods company there which was cars + + + align:start position:0% +final goods company there which was cars +but mind you have cars refrigerators + + align:start position:0% +but mind you have cars refrigerators + + + align:start position:0% +but mind you have cars refrigerators +many many things nominal GDP simply you + + align:start position:0% +many many things nominal GDP simply you + + + align:start position:0% +many many things nominal GDP simply you +sum all the final goods and you multiply + + align:start position:0% +sum all the final goods and you multiply + + + align:start position:0% +sum all the final goods and you multiply +them by the the current price and that + + align:start position:0% +them by the the current price and that + + + align:start position:0% +them by the the current price and that +gives you the dollar GDP that you have I + + align:start position:0% +gives you the dollar GDP that you have I + + + align:start position:0% +gives you the dollar GDP that you have I +don't know what it is in the US today + + align:start position:0% +don't know what it is in the US today + + + align:start position:0% +don't know what it is in the US today +you could check it but it's $24 + + align:start position:0% +you could check it but it's $24 + + + align:start position:0% +you could check it but it's $24 +trillion a so that's it P * Q you know + + align:start position:0% +trillion a so that's it P * Q you know + + + align:start position:0% +trillion a so that's it P * Q you know +prices times quantity and you sum across + + align:start position:0% +prices times quantity and you sum across + + + align:start position:0% +prices times quantity and you sum across +all the final goods + + align:start position:0% +all the final goods + + + align:start position:0% +all the final goods +that's we have to that's one way of + + align:start position:0% +that's we have to that's one way of + + + align:start position:0% +that's we have to that's one way of +calculating thing that's nominal GDP but + + align:start position:0% +calculating thing that's nominal GDP but + + + align:start position:0% +calculating thing that's nominal GDP but +again what we really care about is we're + + align:start position:0% +again what we really care about is we're + + + align:start position:0% +again what we really care about is we're +going to get a lot about later on is how + + align:start position:0% +going to get a lot about later on is how + + + align:start position:0% +going to get a lot about later on is how +that econom is doing over time is it + + align:start position:0% +that econom is doing over time is it + + + align:start position:0% +that econom is doing over time is it +growing is it not growing nominal GDP + + align:start position:0% +growing is it not growing nominal GDP + + + align:start position:0% +growing is it not growing nominal GDP +can grow for two different reasons can + + align:start position:0% +can grow for two different reasons can + + + align:start position:0% +can grow for two different reasons can +grow because the economy is really + + align:start position:0% +grow because the economy is really + + + align:start position:0% +grow because the economy is really +becoming more productive is producing + + align:start position:0% +becoming more productive is producing + + + align:start position:0% +becoming more productive is producing +more Goods or because prices are going + + align:start position:0% +more Goods or because prices are going + + + align:start position:0% +more Goods or because prices are going +up now at this moment real nominal GDP + + align:start position:0% +up now at this moment real nominal GDP + + + align:start position:0% +up now at this moment real nominal GDP +is growing very fast in the US despite + + align:start position:0% +is growing very fast in the US despite + + + align:start position:0% +is growing very fast in the US despite +the fact that we may have recession this + + align:start position:0% +the fact that we may have recession this + + + align:start position:0% +the fact that we may have recession this +year we don't know but nobody has any + + align:start position:0% +year we don't know but nobody has any + + + align:start position:0% +year we don't know but nobody has any +doubt that nominal GDP will grow because + + align:start position:0% +doubt that nominal GDP will grow because + + + align:start position:0% +doubt that nominal GDP will grow because +we have lots of inflation and so you + + align:start position:0% +we have lots of inflation and so you + + + align:start position:0% +we have lots of inflation and so you +want to separate these two things and + + align:start position:0% +want to separate these two things and + + + align:start position:0% +want to separate these two things and +the thing that removes the inflation + + align:start position:0% +the thing that removes the inflation + + + align:start position:0% +the thing that removes the inflation +component is what we call real + + align:start position:0% +component is what we call real + + + align:start position:0% +component is what we call real +GDP and real GDP if you hear the word + + align:start position:0% +GDP and real GDP if you hear the word + + + align:start position:0% +GDP and real GDP if you hear the word +only GDP and and that was produced by + + align:start position:0% +only GDP and and that was produced by + + + align:start position:0% +only GDP and and that was produced by +somebody understand what he's talking + + align:start position:0% +somebody understand what he's talking + + + align:start position:0% +somebody understand what he's talking +about GDP really means real GDP okay if + + align:start position:0% +about GDP really means real GDP okay if + + + align:start position:0% +about GDP really means real GDP okay if +you just hear GDP people are try is + + align:start position:0% +you just hear GDP people are try is + + + align:start position:0% +you just hear GDP people are try is +trying to say the output of the economy + + align:start position:0% +trying to say the output of the economy + + + align:start position:0% +trying to say the output of the economy +well that's real GDP and the real GDP is + + align:start position:0% +well that's real GDP and the real GDP is + + + align:start position:0% +well that's real GDP and the real GDP is +computed many tricks but but essentially + + align:start position:0% +computed many tricks but but essentially + + + align:start position:0% +computed many tricks but but essentially +what you do is you consume you you you + + align:start position:0% +what you do is you consume you you you + + + align:start position:0% +what you do is you consume you you you +you also sum across all the + + align:start position:0% +you also sum across all the + + + align:start position:0% +you also sum across all the +goods you also Su across the goods but + + align:start position:0% +goods you also Su across the goods but + + + align:start position:0% +goods you also Su across the goods but +you use constant prices not the prices + + align:start position:0% +you use constant prices not the prices + + + align:start position:0% +you use constant prices not the prices +of that point in time + + align:start position:0% +of that point in time + + + align:start position:0% +of that point in time +necessarily okay so I'm going to give + + align:start position:0% +necessarily okay so I'm going to give + + + align:start position:0% +necessarily okay so I'm going to give +you a very concrete example but before + + align:start position:0% +you a very concrete example but before + + + align:start position:0% +you a very concrete example but before +doing that for this course we're going + + align:start position:0% +doing that for this course we're going + + + align:start position:0% +doing that for this course we're going +to call nominal GDP and all nominal + + align:start position:0% +to call nominal GDP and all nominal + + + align:start position:0% +to call nominal GDP and all nominal +variables are going to have that's what + + align:start position:0% +variables are going to have that's what + + + align:start position:0% +variables are going to have that's what +the textbook does they're going to have + + align:start position:0% +the textbook does they're going to have + + + align:start position:0% +the textbook does they're going to have +a dollar sign in front so that's our + + align:start position:0% +a dollar sign in front so that's our + + + align:start position:0% +a dollar sign in front so that's our +measure that's nominal GDP GDP is going + + align:start position:0% +measure that's nominal GDP GDP is going + + + align:start position:0% +measure that's nominal GDP GDP is going +to be Y without the dollar that's real + + align:start position:0% +to be Y without the dollar that's real + + + align:start position:0% +to be Y without the dollar that's real +GDP okay for the first part of the + + align:start position:0% +GDP okay for the first part of the + + + align:start position:0% +GDP okay for the first part of the +course up to quiz one we're we're going + + align:start position:0% +course up to quiz one we're we're going + + + align:start position:0% +course up to quiz one we're we're going +very we're going to worry very little + + align:start position:0% +very we're going to worry very little + + + align:start position:0% +very we're going to worry very little +about nominal things because we want to + + align:start position:0% +about nominal things because we want to + + + align:start position:0% +about nominal things because we want to +have prices completely fixed but but you + + align:start position:0% +have prices completely fixed but but you + + + align:start position:0% +have prices completely fixed but but you +still need to know the concept and + + align:start position:0% +still need to know the concept and + + + align:start position:0% +still need to know the concept and +that's real GDP so now let me give you + + align:start position:0% + + + + align:start position:0% + +an example so suppose you have this this + + align:start position:0% +an example so suppose you have this this + + + align:start position:0% +an example so suppose you have this this +this the simple economy we had before + + align:start position:0% +this the simple economy we had before + + + align:start position:0% +this the simple economy we had before +we're just going to look at final goods + + align:start position:0% +we're just going to look at final goods + + + align:start position:0% +we're just going to look at final goods +because that's what we need to look + + align:start position:0% +because that's what we need to look + + + align:start position:0% +because that's what we need to look +at to con to construct GDP and so this + + align:start position:0% +at to con to construct GDP and so this + + + align:start position:0% +at to con to construct GDP and so this +economy produces cars and supposedly + + align:start position:0% +economy produces cars and supposedly + + + align:start position:0% +economy produces cars and supposedly +produces 10 cars in 2011 12 cars in + + align:start position:0% +produces 10 cars in 2011 12 cars in + + + align:start position:0% +produces 10 cars in 2011 12 cars in +2012 and 13 cars in in 2013 but suppos + + align:start position:0% +2012 and 13 cars in in 2013 but suppos + + + align:start position:0% +2012 and 13 cars in in 2013 but suppos +the price of a car is what you see there + + align:start position:0% +the price of a car is what you see there + + + align:start position:0% +the price of a car is what you see there +20,000 24,000 and + + align:start position:0% +20,000 24,000 and + + + align:start position:0% +20,000 24,000 and +26,000 nominal GDP is simply the + + align:start position:0% +26,000 nominal GDP is simply the + + + align:start position:0% +26,000 nominal GDP is simply the +product you know of this times that that + + align:start position:0% +product you know of this times that that + + + align:start position:0% +product you know of this times that that +gives you + + align:start position:0% +gives you + + + align:start position:0% +gives you +$200,000 12 cars times $25,000 gives you + + align:start position:0% +$200,000 12 cars times $25,000 gives you + + + align:start position:0% +$200,000 12 cars times $25,000 gives you +288 and so on that's nominal + + align:start position:0% +288 and so on that's nominal + + + align:start position:0% +288 and so on that's nominal +GDP real + + align:start position:0% +GDP real + + + align:start position:0% +GDP real +GDP you have to + + align:start position:0% +GDP you have to + + + align:start position:0% +GDP you have to +pick which price you want to use but + + align:start position:0% +pick which price you want to use but + + + align:start position:0% +pick which price you want to use but +only use one and don't vary it over time + + align:start position:0% +only use one and don't vary it over time + + + align:start position:0% +only use one and don't vary it over time +okay so in this particular case we pick + + align:start position:0% +okay so in this particular case we pick + + + align:start position:0% +okay so in this particular case we pick + + align:start position:0% + + + align:start position:0% +okay so that means when you say GD real + + align:start position:0% +okay so that means when you say GD real + + + align:start position:0% +okay so that means when you say GD real +GDP at 20 2012 2012 base 2012 or at 2012 + + align:start position:0% +GDP at 20 2012 2012 base 2012 or at 2012 + + + align:start position:0% +GDP at 20 2012 2012 base 2012 or at 2012 +prices means that you're using the + + align:start position:0% +prices means that you're using the + + + align:start position:0% +prices means that you're using the +prices of 2012 you don't bury that you + + align:start position:0% +prices of 2012 you don't bury that you + + + align:start position:0% +prices of 2012 you don't bury that you +let quantities change over time but the + + align:start position:0% +let quantities change over time but the + + + align:start position:0% +let quantities change over time but the +prices remain fixed so in this case real + + align:start position:0% +prices remain fixed so in this case real + + + align:start position:0% +prices remain fixed so in this case real +GDP at + + align:start position:0% +GDP at + + + align:start position:0% +GDP at +$22 is you know is 10 cars times 25,000 + + align:start position:0% +$22 is you know is 10 cars times 25,000 + + + align:start position:0% +$22 is you know is 10 cars times 25,000 +that give you 240,000 + + align:start position:0% +that give you 240,000 + + + align:start position:0% +that give you 240,000 +12 cars time 24,000 28 + + align:start position:0% +12 cars time 24,000 28 + + + align:start position:0% +12 cars time 24,000 28 +this is interesting for this year + + align:start position:0% +this is interesting for this year + + + align:start position:0% +this is interesting for this year +nominal GDP is the same as real GDP why + + align:start position:0% +nominal GDP is the same as real GDP why + + + align:start position:0% +nominal GDP is the same as real GDP why +is + + align:start position:0% +is + + + align:start position:0% +is +that it's an + + align:start position:0% + + + + align:start position:0% + +accident exactly we're using that's a + + align:start position:0% +accident exactly we're using that's a + + + align:start position:0% +accident exactly we're using that's a +base year so that's nominal GDP will + + align:start position:0% +base year so that's nominal GDP will + + + align:start position:0% +base year so that's nominal GDP will +always be equal to real GDP at the base + + align:start position:0% +always be equal to real GDP at the base + + + align:start position:0% +always be equal to real GDP at the base +year that's the Year we're picking as + + align:start position:0% +year that's the Year we're picking as + + + align:start position:0% +year that's the Year we're picking as +the base know because those are the + + align:start position:0% +the base know because those are the + + + align:start position:0% +the base know because those are the +prices we're + + align:start position:0% +prices we're + + + align:start position:0% +prices we're +using I what about 2013 well is is not + + align:start position:0% +using I what about 2013 well is is not + + + align:start position:0% +using I what about 2013 well is is not +26,000 * 13 is 24, 1013 so we get 312 + + align:start position:0% +26,000 * 13 is 24, 1013 so we get 312 + + + align:start position:0% +26,000 * 13 is 24, 1013 so we get 312 +and it's obvious here that real GDP is + + align:start position:0% +and it's obvious here that real GDP is + + + align:start position:0% +and it's obvious here that real GDP is +growing less than nominal GDP why is + + align:start position:0% +growing less than nominal GDP why is + + + align:start position:0% +growing less than nominal GDP why is +that well because this economy has + + align:start position:0% +that well because this economy has + + + align:start position:0% +that well because this economy has +inflation prices are rising over time + + align:start position:0% +inflation prices are rising over time + + + align:start position:0% +inflation prices are rising over time +and we want to remove that when we want + + align:start position:0% +and we want to remove that when we want + + + align:start position:0% +and we want to remove that when we want +to look at the real concept the real + + align:start position:0% +to look at the real concept the real + + + align:start position:0% +to look at the real concept the real +concept removes the price + + align:start position:0% + + + + align:start position:0% + +effect there are times in which you + + align:start position:0% +effect there are times in which you + + + align:start position:0% +effect there are times in which you +don't want to remove all that price + + align:start position:0% +don't want to remove all that price + + + align:start position:0% +don't want to remove all that price +effect and it happens a lot for example + + align:start position:0% +effect and it happens a lot for example + + + align:start position:0% +effect and it happens a lot for example +in computers because sometimes the + + align:start position:0% +in computers because sometimes the + + + align:start position:0% +in computers because sometimes the +increase in the price of the computer is + + align:start position:0% +increase in the price of the computer is + + + align:start position:0% +increase in the price of the computer is +simply because the computer is better + + align:start position:0% +simply because the computer is better + + + align:start position:0% +simply because the computer is better +and and you want to correct for quality + + align:start position:0% +and and you want to correct for quality + + + align:start position:0% +and and you want to correct for quality +and so on but again that's not something + + align:start position:0% +and so on but again that's not something + + + align:start position:0% +and so on but again that's not something +you need to worry about in this course + + align:start position:0% + + + + align:start position:0% + +okay maybe some of you deciding the pace + + align:start position:0% +okay maybe some of you deciding the pace + + + align:start position:0% +okay maybe some of you deciding the pace +which you want me to move I'm really + + align:start position:0% +which you want me to move I'm really + + + align:start position:0% +which you want me to move I'm really +puzzled by this stuff here this is this + + align:start position:0% +puzzled by this stuff here this is this + + + align:start position:0% +puzzled by this stuff here this is this +is from the book and you see what + + align:start position:0% +is from the book and you see what + + + align:start position:0% +is from the book and you see what +happened in in the US with nominal and + + align:start position:0% +happened in in the US with nominal and + + + align:start position:0% +happened in in the US with nominal and +real GDP with base year 2012 so as I + + align:start position:0% +real GDP with base year 2012 so as I + + + align:start position:0% +real GDP with base year 2012 so as I +said before these two curves one is + + align:start position:0% +said before these two curves one is + + + align:start position:0% +said before these two curves one is +nominal GDP the red line the blue line + + align:start position:0% +nominal GDP the red line the blue line + + + align:start position:0% +nominal GDP the red line the blue line +is real GDP we're using Bas year 2012 so + + align:start position:0% +is real GDP we're using Bas year 2012 so + + + align:start position:0% +is real GDP we're using Bas year 2012 so +at that point they have to be the same + + align:start position:0% +at that point they have to be the same + + + align:start position:0% +at that point they have to be the same +and what you see very very clearly there + + align:start position:0% +and what you see very very clearly there + + + align:start position:0% +and what you see very very clearly there +is that a the Blue Line real GDP is + + align:start position:0% +is that a the Blue Line real GDP is + + + align:start position:0% +is that a the Blue Line real GDP is +flatter than the red line why is + + align:start position:0% +flatter than the red line why is + + + align:start position:0% +flatter than the red line why is +that why is it + + align:start position:0% + + + + align:start position:0% + +yeah is inflation see yeah by the way I + + align:start position:0% +yeah is inflation see yeah by the way I + + + align:start position:0% +yeah is inflation see yeah by the way I +do have a reference for you so ask me + + align:start position:0% +do have a reference for you so ask me + + + align:start position:0% +do have a reference for you so ask me +after the okay + + align:start position:0% +after the okay + + + align:start position:0% +after the okay +good um anyway so yeah in the US between + + align:start position:0% +good um anyway so yeah in the US between + + + align:start position:0% +good um anyway so yeah in the US between +1916 and 2018 real nominal GDP increased + + align:start position:0% +1916 and 2018 real nominal GDP increased + + + align:start position:0% +1916 and 2018 real nominal GDP increased +by a factor of 38 while real GDP by a + + align:start position:0% +by a factor of 38 while real GDP by a + + + align:start position:0% +by a factor of 38 while real GDP by a +factor of 5.7 big difference so so you + + align:start position:0% +factor of 5.7 big difference so so you + + + align:start position:0% +factor of 5.7 big difference so so you +better be careful when when you look at + + align:start position:0% +better be careful when when you look at + + + align:start position:0% +better be careful when when you look at +GDP that you are removing inflation + + align:start position:0% +GDP that you are removing inflation + + + align:start position:0% +GDP that you are removing inflation +especially in I mean if you were to look + + align:start position:0% +especially in I mean if you were to look + + + align:start position:0% +especially in I mean if you were to look +in + + align:start position:0% +in + + + align:start position:0% +in +Argentina these guys have had a + + align:start position:0% +Argentina these guys have had a + + + align:start position:0% +Argentina these guys have had a +recession a chronic recession for a long + + align:start position:0% +recession a chronic recession for a long + + + align:start position:0% +recession a chronic recession for a long +time big recessions but nominal GDP is + + align:start position:0% +time big recessions but nominal GDP is + + + align:start position:0% +time big recessions but nominal GDP is +explo clothing because they have 10,000% + + align:start position:0% +explo clothing because they have 10,000% + + + align:start position:0% +explo clothing because they have 10,000% +inflation so so so it makes a big + + align:start position:0% + + + + align:start position:0% + +difference especially over + + align:start position:0% +difference especially over + + + align:start position:0% +difference especially over +time this is just so you get the picture + + align:start position:0% +time this is just so you get the picture + + + align:start position:0% +time this is just so you get the picture +the complete picture for the US this is + + align:start position:0% +the complete picture for the US this is + + + align:start position:0% +the complete picture for the US this is +a GDP growth in the US since we have + + align:start position:0% +a GDP growth in the US since we have + + + align:start position:0% +a GDP growth in the US since we have +national accounts okay and some + + align:start position:0% +national accounts okay and some + + + align:start position:0% +national accounts okay and some +noticeable things well again + + align:start position:0% +noticeable things well again + + + align:start position:0% +noticeable things well again +recessions this was a big recession + + align:start position:0% +recessions this was a big recession + + + align:start position:0% +recessions this was a big recession +remember we call this the Great + + align:start position:0% +remember we call this the Great + + + align:start position:0% +remember we call this the Great +Recession big recession and well this is + + align:start position:0% +Recession big recession and well this is + + + align:start position:0% +Recession big recession and well this is +covid and then this is 2020 and then + + align:start position:0% +covid and then this is 2020 and then + + + align:start position:0% +covid and then this is 2020 and then +they bounce back in 2021 when we reopen + + align:start position:0% +they bounce back in 2021 when we reopen + + + align:start position:0% +they bounce back in 2021 when we reopen +the economy big growth but that's very + + align:start position:0% +the economy big growth but that's very + + + align:start position:0% +the economy big growth but that's very +anomalous I mean that's a very weird + + align:start position:0% +anomalous I mean that's a very weird + + + align:start position:0% +anomalous I mean that's a very weird +shock okay but that's a you see these + + align:start position:0% +shock okay but that's a you see these + + + align:start position:0% +shock okay but that's a you see these +are all the shaded areas are + + align:start position:0% +are all the shaded areas are + + + align:start position:0% +are all the shaded areas are +recessions recessions are defined in a + + align:start position:0% +recessions recessions are defined in a + + + align:start position:0% +recessions recessions are defined in a +slightly more complicated way than that + + align:start position:0% +slightly more complicated way than that + + + align:start position:0% +slightly more complicated way than that +but one sort of er popular way of + + align:start position:0% +but one sort of er popular way of + + + align:start position:0% +but one sort of er popular way of +describing ression is as episode where + + align:start position:0% +describing ression is as episode where + + + align:start position:0% +describing ression is as episode where +you have two consecutive quarters of + + align:start position:0% +you have two consecutive quarters of + + + align:start position:0% +you have two consecutive quarters of +negative inflation that's not the formal + + align:start position:0% +negative inflation that's not the formal + + + align:start position:0% +negative inflation that's not the formal +definition of res but it's pretty close + + align:start position:0% +definition of res but it's pretty close + + + align:start position:0% +definition of res but it's pretty close +okay and so so that's that's what you + + align:start position:0% +okay and so so that's that's what you + + + align:start position:0% +okay and so so that's that's what you +have + + align:start position:0% +have + + + align:start position:0% +have +there another concept is an employment + + align:start position:0% +there another concept is an employment + + + align:start position:0% +there another concept is an employment +rate the unemployment rate so that's GDP + + align:start position:0% +rate the unemployment rate so that's GDP + + + align:start position:0% +rate the unemployment rate so that's GDP +and we're going to the in the first part + + align:start position:0% +and we're going to the in the first part + + + align:start position:0% +and we're going to the in the first part +of the course we want to worry a lot + + align:start position:0% +of the course we want to worry a lot + + + align:start position:0% +of the course we want to worry a lot +about that we're going to build a model + + align:start position:0% +about that we're going to build a model + + + align:start position:0% +about that we're going to build a model +on how to find equilibrium H GDP okay + + align:start position:0% +on how to find equilibrium H GDP okay + + + align:start position:0% +on how to find equilibrium H GDP okay +and we're going to see what happens with + + align:start position:0% +and we're going to see what happens with + + + align:start position:0% +and we're going to see what happens with +fiscal policy with monetary policy how + + align:start position:0% +fiscal policy with monetary policy how + + + align:start position:0% +fiscal policy with monetary policy how +how does equilibrium GDP macroeconomic + + align:start position:0% +how does equilibrium GDP macroeconomic + + + align:start position:0% +how does equilibrium GDP macroeconomic +EIC output changes with different forms + + align:start position:0% +EIC output changes with different forms + + + align:start position:0% +EIC output changes with different forms +of policies or when consumers get scared + + align:start position:0% +of policies or when consumers get scared + + + align:start position:0% +of policies or when consumers get scared +or stuff like that + + align:start position:0% + + + + align:start position:0% + +okay what about the unemployment rate + + align:start position:0% +okay what about the unemployment rate + + + align:start position:0% +okay what about the unemployment rate +the unemployment rate is not something + + align:start position:0% +the unemployment rate is not something + + + align:start position:0% +the unemployment rate is not something +we want to worry a lot about until the + + align:start position:0% +we want to worry a lot about until the + + + align:start position:0% +we want to worry a lot about until the +second part of the course after quiz one + + align:start position:0% +second part of the course after quiz one + + + align:start position:0% +second part of the course after quiz one +but I still I want to get over with + + align:start position:0% +but I still I want to get over with + + + align:start position:0% +but I still I want to get over with +these + + align:start position:0% +these + + + align:start position:0% +these +definitions so what is employment is a + + align:start position:0% +definitions so what is employment is a + + + align:start position:0% +definitions so what is employment is a +number of people who have a job that's + + align:start position:0% +number of people who have a job that's + + + align:start position:0% +number of people who have a job that's +easy unemployment is slightly less easy + + align:start position:0% +easy unemployment is slightly less easy + + + align:start position:0% +easy unemployment is slightly less easy +because it's first of all obviously to + + align:start position:0% +because it's first of all obviously to + + + align:start position:0% +because it's first of all obviously to +be an employee you don't have to have a + + align:start position:0% +be an employee you don't have to have a + + + align:start position:0% +be an employee you don't have to have a +you cannot have a job so but it's not + + align:start position:0% +you cannot have a job so but it's not + + + align:start position:0% +you cannot have a job so but it's not +enough that you don't have a + + align:start position:0% +enough that you don't have a + + + align:start position:0% +enough that you don't have a +job is an + + align:start position:0% +job is an + + + align:start position:0% +job is an +unemployed person is somebody that + + align:start position:0% +unemployed person is somebody that + + + align:start position:0% +unemployed person is somebody that +doesn't have a job and is looking for + + align:start position:0% +doesn't have a job and is looking for + + + align:start position:0% +doesn't have a job and is looking for +one + + align:start position:0% +one + + + align:start position:0% +one +okay not all unemployed people look for + + align:start position:0% +okay not all unemployed people look for + + + align:start position:0% +okay not all unemployed people look for +your job not all non-employed people are + + align:start position:0% +your job not all non-employed people are + + + align:start position:0% +your job not all non-employed people are +looking for + + align:start position:0% +looking for + + + align:start position:0% +looking for +jobs okay so un to be unemployed you + + align:start position:0% +jobs okay so un to be unemployed you + + + align:start position:0% +jobs okay so un to be unemployed you +need to not have a job and be looking + + align:start position:0% +need to not have a job and be looking + + + align:start position:0% +need to not have a job and be looking +for one the labor force what we call the + + align:start position:0% +for one the labor force what we call the + + + align:start position:0% +for one the labor force what we call the +labor force is the sum of those two + + align:start position:0% +labor force is the sum of those two + + + align:start position:0% +labor force is the sum of those two +groups the employed and the unemployed + + align:start position:0% +groups the employed and the unemployed + + + align:start position:0% +groups the employed and the unemployed +that would like to get a + + align:start position:0% +that would like to get a + + + align:start position:0% +that would like to get a +job + + align:start position:0% +job + + + align:start position:0% +job +okay the unemployment rate which is + + align:start position:0% +okay the unemployment rate which is + + + align:start position:0% +okay the unemployment rate which is +something I showed you in the previous + + align:start position:0% +something I showed you in the previous + + + align:start position:0% +something I showed you in the previous +lecture is just a ratio of these two + + align:start position:0% +lecture is just a ratio of these two + + + align:start position:0% +lecture is just a ratio of these two +concepts the unemployed over the labor + + align:start position:0% +concepts the unemployed over the labor + + + align:start position:0% +concepts the unemployed over the labor +force notice over the labor force not + + align:start position:0% +force notice over the labor force not + + + align:start position:0% +force notice over the labor force not +population the labor force which is a + + align:start position:0% +population the labor force which is a + + + align:start position:0% +population the labor force which is a +sum of the employed and those that are + + align:start position:0% +sum of the employed and those that are + + + align:start position:0% +sum of the employed and those that are +unemployed that do not have a job and + + align:start position:0% +unemployed that do not have a job and + + + align:start position:0% +unemployed that do not have a job and +are looking for a job + + align:start position:0% + + + + align:start position:0% + +okay how how is an employment measure in + + align:start position:0% +okay how how is an employment measure in + + + align:start position:0% +okay how how is an employment measure in +the US is mostly a survey and I have the + + align:start position:0% +the US is mostly a survey and I have the + + + align:start position:0% +the US is mostly a survey and I have the +the the info there it's called the CPS + + align:start position:0% +the the info there it's called the CPS + + + align:start position:0% +the the info there it's called the CPS +the current population survey that + + align:start position:0% +the current population survey that + + + align:start position:0% +the current population survey that +consults lots of households and they ask + + align:start position:0% +consults lots of households and they ask + + + align:start position:0% +consults lots of households and they ask +them about the employment status whether + + align:start position:0% +them about the employment status whether + + + align:start position:0% +them about the employment status whether +they have been looking for a job over + + align:start position:0% +they have been looking for a job over + + + align:start position:0% +they have been looking for a job over +the last two weeks or not and so on and + + align:start position:0% +the last two weeks or not and so on and + + + align:start position:0% +the last two weeks or not and so on and +that's the way we come up with with the + + align:start position:0% +that's the way we come up with with the + + + align:start position:0% +that's the way we come up with with the +number as as I said before H those that + + align:start position:0% +number as as I said before H those that + + + align:start position:0% +number as as I said before H those that +do not have a job but are not looking + + align:start position:0% +do not have a job but are not looking + + + align:start position:0% +do not have a job but are not looking +for a job they haven't been looking for + + align:start position:0% +for a job they haven't been looking for + + + align:start position:0% +for a job they haven't been looking for +a job in the last two weeks are called + + align:start position:0% +a job in the last two weeks are called + + + align:start position:0% +a job in the last two weeks are called +not in the labor force that's that's + + align:start position:0% +not in the labor force that's that's + + + align:start position:0% +not in the labor force that's that's +what we say now these concepts are + + align:start position:0% +what we say now these concepts are + + + align:start position:0% +what we say now these concepts are +between an employed and not in the labor + + align:start position:0% +between an employed and not in the labor + + + align:start position:0% +between an employed and not in the labor +force is it's not not that clear we we + + align:start position:0% +force is it's not not that clear we we + + + align:start position:0% +force is it's not not that clear we we +we look at the employment rate but we + + align:start position:0% +we look at the employment rate but we + + + align:start position:0% +we look at the employment rate but we +also tend to look at those people as + + align:start position:0% +also tend to look at those people as + + + align:start position:0% +also tend to look at those people as +well because many people are simply + + align:start position:0% +well because many people are simply + + + align:start position:0% +well because many people are simply +discouraged they would like to get a job + + align:start position:0% +discouraged they would like to get a job + + + align:start position:0% +discouraged they would like to get a job +but they have been looking for a while + + align:start position:0% +but they have been looking for a while + + + align:start position:0% +but they have been looking for a while +and they haven't found it and it it + + align:start position:0% +and they haven't found it and it it + + + align:start position:0% +and they haven't found it and it it +happens that there is a lot more + + align:start position:0% +happens that there is a lot more + + + align:start position:0% +happens that there is a lot more +discouraged workers during recessions + + align:start position:0% +discouraged workers during recessions + + + align:start position:0% +discouraged workers during recessions +and when you're having a big recession + + align:start position:0% +and when you're having a big recession + + + align:start position:0% +and when you're having a big recession +it's very difficult to find a job so + + align:start position:0% +it's very difficult to find a job so + + + align:start position:0% +it's very difficult to find a job so +it's very easy to get discourage and so + + align:start position:0% +it's very easy to get discourage and so + + + align:start position:0% +it's very easy to get discourage and so +that's the reason we look at broader + + align:start position:0% +that's the reason we look at broader + + + align:start position:0% +that's the reason we look at broader +measures of non-employment than the + + align:start position:0% +measures of non-employment than the + + + align:start position:0% +measures of non-employment than the +typical unemployment rate because a lot + + align:start position:0% +typical unemployment rate because a lot + + + align:start position:0% +typical unemployment rate because a lot +of + + align:start position:0% +of + + + align:start position:0% +of +those not in the labor force people that + + align:start position:0% +those not in the labor force people that + + + align:start position:0% +those not in the labor force people that +do not have a job and are not looking + + align:start position:0% +do not have a job and are not looking + + + align:start position:0% +do not have a job and are not looking +for a job are really discouraged they + + align:start position:0% +for a job are really discouraged they + + + align:start position:0% +for a job are really discouraged they +just give up after a while + + align:start position:0% +just give up after a while + + + align:start position:0% +just give up after a while +okay the participation rate and that's a + + align:start position:0% +okay the participation rate and that's a + + + align:start position:0% +okay the participation rate and that's a +very important concept something you + + align:start position:0% +very important concept something you + + + align:start position:0% +very important concept something you +would have ignored most of the time is + + align:start position:0% +would have ignored most of the time is + + + align:start position:0% +would have ignored most of the time is +very critical at this moment the + + align:start position:0% +very critical at this moment the + + + align:start position:0% +very critical at this moment the +participation rate is the ratio of the + + align:start position:0% +participation rate is the ratio of the + + + align:start position:0% +participation rate is the ratio of the +labor force to the total population of + + align:start position:0% +labor force to the total population of + + + align:start position:0% +labor force to the total population of +working age and you exclude people you + + align:start position:0% +working age and you exclude people you + + + align:start position:0% +working age and you exclude people you +know in prison and stuff like that but + + align:start position:0% +know in prison and stuff like that but + + + align:start position:0% +know in prison and stuff like that but +but a so it's label force is which is + + align:start position:0% +but a so it's label force is which is + + + align:start position:0% +but a so it's label force is which is +the sum of the employed and the + + align:start position:0% +the sum of the employed and the + + + align:start position:0% +the sum of the employed and the +unemployed divided by those that could + + align:start position:0% +unemployed divided by those that could + + + align:start position:0% +unemployed divided by those that could +work in + + align:start position:0% +work in + + + align:start position:0% +work in +principle okay and that we call that's + + align:start position:0% +principle okay and that we call that's + + + align:start position:0% +principle okay and that we call that's +what we call the participation rate + + align:start position:0% +what we call the participation rate + + + align:start position:0% +what we call the participation rate +how do these numbers look I showed you + + align:start position:0% +how do these numbers look I showed you + + + align:start position:0% +how do these numbers look I showed you +this picture in the previous uh lecture + + align:start position:0% +this picture in the previous uh lecture + + + align:start position:0% +this picture in the previous uh lecture +and that's the unemployment rate it + + align:start position:0% +and that's the unemployment rate it + + + align:start position:0% +and that's the unemployment rate it +skyrocketed during covid but it has + + align:start position:0% +skyrocketed during covid but it has + + + align:start position:0% +skyrocketed during covid but it has +declined enormously and as I said in the + + align:start position:0% +declined enormously and as I said in the + + + align:start position:0% +declined enormously and as I said in the +previous lecture a big issue is that the + + align:start position:0% +previous lecture a big issue is that the + + + align:start position:0% +previous lecture a big issue is that the +unemployment rate today is extremely low + + align:start position:0% +unemployment rate today is extremely low + + + align:start position:0% +unemployment rate today is extremely low +we haven't seen levels like this since + + align:start position:0% +we haven't seen levels like this since + + + align:start position:0% +we haven't seen levels like this since +the early + + align:start position:0% +the early + + + align:start position:0% +the early +60s okay the unemployment rate today is + + align:start position:0% +60s okay the unemployment rate today is + + + align:start position:0% +60s okay the unemployment rate today is +at record low levels and that's a + + align:start position:0% +at record low levels and that's a + + + align:start position:0% +at record low levels and that's a +problem some wonderful but it's also as + + align:start position:0% +problem some wonderful but it's also as + + + align:start position:0% +problem some wonderful but it's also as +a problem because we have an inflation + + align:start position:0% +a problem because we have an inflation + + + align:start position:0% +a problem because we have an inflation +problem and those two things are + + align:start position:0% +problem and those two things are + + + align:start position:0% +problem and those two things are +connected as you will learn later on in + + align:start position:0% +connected as you will learn later on in + + + align:start position:0% +connected as you will learn later on in +the course okay but that's what we have + + align:start position:0% +the course okay but that's what we have + + + align:start position:0% +the course okay but that's what we have +right now that's the unemployment rate + + align:start position:0% +right now that's the unemployment rate + + + align:start position:0% +right now that's the unemployment rate +now the reason the unemployment rate is + + align:start position:0% +now the reason the unemployment rate is + + + align:start position:0% +now the reason the unemployment rate is +so low there are two reasons really one + + align:start position:0% +so low there are two reasons really one + + + align:start position:0% +so low there are two reasons really one +is that there was lots of stimulus + + align:start position:0% +is that there was lots of stimulus + + + align:start position:0% +is that there was lots of stimulus +policy fiscal policy monetary policy so + + align:start position:0% +policy fiscal policy monetary policy so + + + align:start position:0% +policy fiscal policy monetary policy so +aggregate demand and consumers that were + + align:start position:0% +aggregate demand and consumers that were + + + align:start position:0% +aggregate demand and consumers that were +fed up of being locked out of + + align:start position:0% +fed up of being locked out of + + + align:start position:0% +fed up of being locked out of +restaurants and trips and so on for two + + align:start position:0% +restaurants and trips and so on for two + + + align:start position:0% +restaurants and trips and so on for two +years you know decided to travel and so + + align:start position:0% +years you know decided to travel and so + + + align:start position:0% +years you know decided to travel and so +on so so and they had lots of + + align:start position:0% +on so so and they had lots of + + + align:start position:0% +on so so and they had lots of +savings the the US consumer accumulated + + align:start position:0% +savings the the US consumer accumulated + + + align:start position:0% +savings the the US consumer accumulated +excess saving of $2.7 trillion and now + + align:start position:0% +excess saving of $2.7 trillion and now + + + align:start position:0% +excess saving of $2.7 trillion and now +they're spending this time China a big + + align:start position:0% +they're spending this time China a big + + + align:start position:0% +they're spending this time China a big +reason why people expect a big bounce + + align:start position:0% +reason why people expect a big bounce + + + align:start position:0% +reason why people expect a big bounce +back is because they also had a lot of + + align:start position:0% +back is because they also had a lot of + + + align:start position:0% +back is because they also had a lot of +savings because they were locked up for + + align:start position:0% +savings because they were locked up for + + + align:start position:0% +savings because they were locked up for +for quite some time so so as a result of + + align:start position:0% +for quite some time so so as a result of + + + align:start position:0% +for quite some time so so as a result of +that there's lots of demand for goods + + align:start position:0% +that there's lots of demand for goods + + + align:start position:0% +that there's lots of demand for goods +and as you're going to learn in the next + + align:start position:0% +and as you're going to learn in the next + + + align:start position:0% +and as you're going to learn in the next +lecture that means lots of output as + + align:start position:0% +lecture that means lots of output as + + + align:start position:0% +lecture that means lots of output as +well H but the second H reason + + align:start position:0% + + + + align:start position:0% + +is the + + align:start position:0% + + + + align:start position:0% + +following is the participation rate okay + + align:start position:0% +following is the participation rate okay + + + align:start position:0% +following is the participation rate okay +people haven't come back to work in the + + align:start position:0% +people haven't come back to work in the + + + align:start position:0% +people haven't come back to work in the +magnitudes that we expected so that's a + + align:start position:0% +magnitudes that we expected so that's a + + + align:start position:0% +magnitudes that we expected so that's a +participation rate in the US remember + + align:start position:0% +participation rate in the US remember + + + align:start position:0% +participation rate in the US remember +participation rate is labor force over + + align:start position:0% +participation rate is labor force over + + + align:start position:0% +participation rate is labor force over +all those that could work in principle + + align:start position:0% +all those that could work in principle + + + align:start position:0% +all those that could work in principle +okay ER what do you think is this look + + align:start position:0% +okay ER what do you think is this look + + + align:start position:0% +okay ER what do you think is this look +at the participation rate used to be in + + align:start position:0% +at the participation rate used to be in + + + align:start position:0% +at the participation rate used to be in +the 6 below 60s and then there was a big + + align:start position:0% +the 6 below 60s and then there was a big + + + align:start position:0% +the 6 below 60s and then there was a big +rise in the participation rate in the + + align:start position:0% +rise in the participation rate in the + + + align:start position:0% +rise in the participation rate in the +US what do you think is this due + + align:start position:0% +US what do you think is this due + + + align:start position:0% +US what do you think is this due +to women joining work women yeah joining + + align:start position:0% +to women joining work women yeah joining + + + align:start position:0% +to women joining work women yeah joining +the workforce that's what it + + align:start position:0% +the workforce that's what it + + + align:start position:0% +the workforce that's what it +did okay that's that since then since + + align:start position:0% +did okay that's that since then since + + + align:start position:0% +did okay that's that since then since +just women did all that they had to do + + align:start position:0% +just women did all that they had to do + + + align:start position:0% +just women did all that they had to do +sort of we have been declining and that + + align:start position:0% +sort of we have been declining and that + + + align:start position:0% +sort of we have been declining and that +that's that's an issue but ER but look + + align:start position:0% +that's that's an issue but ER but look + + + align:start position:0% +that's that's an issue but ER but look +at what happened here lots of people + + align:start position:0% +at what happened here lots of people + + + align:start position:0% +at what happened here lots of people +exit the labor force during covid I mean + + align:start position:0% +exit the labor force during covid I mean + + + align:start position:0% +exit the labor force during covid I mean +you know they had to take care of the + + align:start position:0% +you know they had to take care of the + + + align:start position:0% +you know they had to take care of the +kids and and and or or the elderly and + + align:start position:0% +kids and and and or or the elderly and + + + align:start position:0% +kids and and and or or the elderly and +so people withdrew from the labor force + + align:start position:0% +so people withdrew from the labor force + + + align:start position:0% +so people withdrew from the labor force +they didn't want a job it was also + + align:start position:0% +they didn't want a job it was also + + + align:start position:0% +they didn't want a job it was also +discouraging it was very difficult to + + align:start position:0% +discouraging it was very difficult to + + + align:start position:0% +discouraging it was very difficult to +get a job for iag you work in a + + align:start position:0% +get a job for iag you work in a + + + align:start position:0% +get a job for iag you work in a +restaurant it was impossible to get a + + align:start position:0% +restaurant it was impossible to get a + + + align:start position:0% +restaurant it was impossible to get a +job in a restaurant so but everyone + + align:start position:0% +job in a restaurant so but everyone + + + align:start position:0% +job in a restaurant so but everyone +expected this to recover to the previous + + align:start position:0% +expected this to recover to the previous + + + align:start position:0% +expected this to recover to the previous +level and it hasn't okay so you be you + + align:start position:0% +level and it hasn't okay so you be you + + + align:start position:0% +level and it hasn't okay so you be you +see that the participation rate has not + + align:start position:0% +see that the participation rate has not + + + align:start position:0% +see that the participation rate has not +come back to the levels preo is + + align:start position:0% +come back to the levels preo is + + + align:start position:0% +come back to the levels preo is +substantially below and that's one of + + align:start position:0% +substantially below and that's one of + + + align:start position:0% +substantially below and that's one of +the reasons you know that restaurants + + align:start position:0% +the reasons you know that restaurants + + + align:start position:0% +the reasons you know that restaurants +complain that they don't have workers + + align:start position:0% +complain that they don't have workers + + + align:start position:0% +complain that they don't have workers +and so on so forth is that many people + + align:start position:0% +and so on so forth is that many people + + + align:start position:0% +and so on so forth is that many people +haven't come back to a labor force we + + align:start position:0% +haven't come back to a labor force we + + + align:start position:0% +haven't come back to a labor force we +thought this was going to be temporary + + align:start position:0% +thought this was going to be temporary + + + align:start position:0% +thought this was going to be temporary +now there's a concern that a lot of that + + align:start position:0% +now there's a concern that a lot of that + + + align:start position:0% +now there's a concern that a lot of that +is really permanent people decided that + + align:start position:0% +is really permanent people decided that + + + align:start position:0% +is really permanent people decided that +you know life at home wasn't that bad + + align:start position:0% +you know life at home wasn't that bad + + + align:start position:0% +you know life at home wasn't that bad +after all less income but but they spend + + align:start position:0% +after all less income but but they spend + + + align:start position:0% +after all less income but but they spend +more time with the kids or whatever and + + align:start position:0% +more time with the kids or whatever and + + + align:start position:0% +more time with the kids or whatever and +so H ER and that's an issue and that + + align:start position:0% +so H ER and that's an issue and that + + + align:start position:0% +so H ER and that's an issue and that +that's a big reason behind + + align:start position:0% +that's a big reason behind + + + align:start position:0% +that's a big reason behind +the low unemployment rate and the fact + + align:start position:0% +the low unemployment rate and the fact + + + align:start position:0% +the low unemployment rate and the fact +that we have all this inflation has to + + align:start position:0% +that we have all this inflation has to + + + align:start position:0% +that we have all this inflation has to +do with everyone in particular the fed + + align:start position:0% +do with everyone in particular the fed + + + align:start position:0% +do with everyone in particular the fed +miscalculated the bounce back of of the + + align:start position:0% +miscalculated the bounce back of of the + + + align:start position:0% +miscalculated the bounce back of of the +participation + + align:start position:0% + + + + align:start position:0% + +rate + + align:start position:0% +rate + + + align:start position:0% +rate +good so as I said before we're not going + + align:start position:0% +good so as I said before we're not going + + + align:start position:0% +good so as I said before we're not going +to look at labor market issues until + + align:start position:0% +to look at labor market issues until + + + align:start position:0% +to look at labor market issues until +sort of the second part of the course + + align:start position:0% +sort of the second part of the course + + + align:start position:0% +sort of the second part of the course +after quiz one and the same is for + + align:start position:0% +after quiz one and the same is for + + + align:start position:0% +after quiz one and the same is for +inflation we're not going to look at + + align:start position:0% +inflation we're not going to look at + + + align:start position:0% +inflation we're not going to look at +inflation issues until the second part + + align:start position:0% +inflation issues until the second part + + + align:start position:0% +inflation issues until the second part +of of the course because to connect them + + align:start position:0% +of of the course because to connect them + + + align:start position:0% +of of the course because to connect them +I mean I they are connected and we're + + align:start position:0% +I mean I they are connected and we're + + + align:start position:0% +I mean I they are connected and we're +not going to look at Labor markets until + + align:start position:0% +not going to look at Labor markets until + + + align:start position:0% +not going to look at Labor markets until +sort of a lecture from now or so okay + + align:start position:0% +sort of a lecture from now or so okay + + + align:start position:0% +sort of a lecture from now or so okay +but let's look at but this is an + + align:start position:0% +but let's look at but this is an + + + align:start position:0% +but let's look at but this is an +important variable and certainly + + align:start position:0% +important variable and certainly + + + align:start position:0% +important variable and certainly +something you're facing every single day + + align:start position:0% +something you're facing every single day + + + align:start position:0% +something you're facing every single day +in the newspapers and so on the + + align:start position:0% +in the newspapers and so on the + + + align:start position:0% +in the newspapers and so on the +inflation rate so by inflation when you + + align:start position:0% +inflation rate so by inflation when you + + + align:start position:0% +inflation rate so by inflation when you +hear inflation that typically means the + + align:start position:0% +hear inflation that typically means the + + + align:start position:0% +hear inflation that typically means the +sustained rise in the general level of + + align:start position:0% +sustained rise in the general level of + + + align:start position:0% +sustained rise in the general level of +prices so it's not that the price of + + align:start position:0% +prices so it's not that the price of + + + align:start position:0% +prices so it's not that the price of +cars went up relative to the price of + + align:start position:0% +cars went up relative to the price of + + + align:start position:0% +cars went up relative to the price of +hotels or now down price hotel is that + + align:start position:0% +hotels or now down price hotel is that + + + align:start position:0% +hotels or now down price hotel is that +on average prices are rising that's what + + align:start position:0% +on average prices are rising that's what + + + align:start position:0% +on average prices are rising that's what +we call an inflation + + align:start position:0% +we call an inflation + + + align:start position:0% +we call an inflation +inflation um so we're going to call the + + align:start position:0% +inflation um so we're going to call the + + + align:start position:0% +inflation um so we're going to call the +price level PT and there are many + + align:start position:0% +price level PT and there are many + + + align:start position:0% +price level PT and there are many +different price levels all you see so + + align:start position:0% +different price levels all you see so + + + align:start position:0% +different price levels all you see so +the inflation rate when you hear the + + align:start position:0% +the inflation rate when you hear the + + + align:start position:0% +the inflation rate when you hear the +inflation rate is the rate of change of + + align:start position:0% +inflation rate is the rate of change of + + + align:start position:0% +inflation rate is the rate of change of +that price + + align:start position:0% +that price + + + align:start position:0% +that price +level an episode of + + align:start position:0% +level an episode of + + + align:start position:0% +level an episode of +deflation the opposite of what we're + + align:start position:0% +deflation the opposite of what we're + + + align:start position:0% +deflation the opposite of what we're +experiencing now where we're exper + + align:start position:0% +experiencing now where we're exper + + + align:start position:0% +experiencing now where we're exper +inflation is when that inflation rate is + + align:start position:0% +inflation is when that inflation rate is + + + align:start position:0% +inflation is when that inflation rate is +negative Japan most prominently has + + align:start position:0% +negative Japan most prominently has + + + align:start position:0% +negative Japan most prominently has +experienced something like that not now + + align:start position:0% +experienced something like that not now + + + align:start position:0% +experienced something like that not now +but experienced it for on and off for + + align:start position:0% +but experienced it for on and off for + + + align:start position:0% +but experienced it for on and off for +the last three decades or so um so what + + align:start position:0% +the last three decades or so um so what + + + align:start position:0% +the last three decades or so um so what +is the price level there are many ways + + align:start position:0% +is the price level there are many ways + + + align:start position:0% +is the price level there are many ways +of defining it and then there many + + align:start position:0% +of defining it and then there many + + + align:start position:0% +of defining it and then there many +different price levels a very popular + + align:start position:0% +different price levels a very popular + + + align:start position:0% +different price levels a very popular +one is what is called the GDP deflator + + align:start position:0% +one is what is called the GDP deflator + + + align:start position:0% +one is what is called the GDP deflator +and it's the one you see Le you is never + + align:start position:0% +and it's the one you see Le you is never + + + align:start position:0% +and it's the one you see Le you is never +mentioned in the newspapers okay but we + + align:start position:0% +mentioned in the newspapers okay but we + + + align:start position:0% +mentioned in the newspapers okay but we +economists tend to look at the deflator + + align:start position:0% +economists tend to look at the deflator + + + align:start position:0% +economists tend to look at the deflator +the deflator is nothing else than the + + align:start position:0% +the deflator is nothing else than the + + + align:start position:0% +the deflator is nothing else than the +ratio of nominal GDP to real GDP another + + align:start position:0% +ratio of nominal GDP to real GDP another + + + align:start position:0% +ratio of nominal GDP to real GDP another +one is far more popular and more + + align:start position:0% +one is far more popular and more + + + align:start position:0% +one is far more popular and more +relevant for you as consumers is what we + + align:start position:0% +relevant for you as consumers is what we + + + align:start position:0% +relevant for you as consumers is what we +call the Consumer Price Index that's the + + align:start position:0% +call the Consumer Price Index that's the + + + align:start position:0% +call the Consumer Price Index that's the +CPI you hear CPI that's what it is so + + align:start position:0% +CPI you hear CPI that's what it is so + + + align:start position:0% +CPI you hear CPI that's what it is so +it's it's it's it's you calculate the + + align:start position:0% +it's it's it's it's you calculate the + + + align:start position:0% +it's it's it's it's you calculate the +rate of inflation from the CPI you + + align:start position:0% +rate of inflation from the CPI you + + + align:start position:0% +rate of inflation from the CPI you +calculate the same way but you use a CPI + + align:start position:0% +calculate the same way but you use a CPI + + + align:start position:0% +calculate the same way but you use a CPI +there instead of the GDP deflator now it + + align:start position:0% +there instead of the GDP deflator now it + + + align:start position:0% +there instead of the GDP deflator now it +turns + + align:start position:0% +turns + + + align:start position:0% +turns +out H that obviously confused with it it + + align:start position:0% +out H that obviously confused with it it + + + align:start position:0% +out H that obviously confused with it it +turns out that these two measures are + + align:start position:0% +turns out that these two measures are + + + align:start position:0% +turns out that these two measures are +sort of pretty well aligned okay there + + align:start position:0% +sort of pretty well aligned okay there + + + align:start position:0% +sort of pretty well aligned okay there +are differences that may be interesting + + align:start position:0% +are differences that may be interesting + + + align:start position:0% +are differences that may be interesting +at some specific point in time but they + + align:start position:0% +at some specific point in time but they + + + align:start position:0% +at some specific point in time but they +tell you more or less the same picture + + align:start position:0% +tell you more or less the same picture + + + align:start position:0% +tell you more or less the same picture +in particular there is absolutely no + + align:start position:0% +in particular there is absolutely no + + + align:start position:0% +in particular there is absolutely no +doubt that we have an inflation problem + + align:start position:0% +doubt that we have an inflation problem + + + align:start position:0% +doubt that we have an inflation problem +these days you can be as selective as + + align:start position:0% +these days you can be as selective as + + + align:start position:0% +these days you can be as selective as +you want with the price index you want + + align:start position:0% +you want with the price index you want + + + align:start position:0% +you want with the price index you want +to use and people are getting very + + align:start position:0% +to use and people are getting very + + + align:start position:0% +to use and people are getting very +selective now we have CPI + + align:start position:0% +selective now we have CPI + + + align:start position:0% +selective now we have CPI +excluding + + align:start position:0% +excluding + + + align:start position:0% +excluding +ER well one thing that that makes a lot + + align:start position:0% +ER well one thing that that makes a lot + + + align:start position:0% +ER well one thing that that makes a lot +of sense is to exclude the most volatile + + align:start position:0% +of sense is to exclude the most volatile + + + align:start position:0% +of sense is to exclude the most volatile +Goods so typically the CPI we we use + + align:start position:0% +Goods so typically the CPI we we use + + + align:start position:0% +Goods so typically the CPI we we use +what called core CPI which removes + + align:start position:0% +what called core CPI which removes + + + align:start position:0% +what called core CPI which removes +energy and food which are very volatile + + align:start position:0% +energy and food which are very volatile + + + align:start position:0% +energy and food which are very volatile +prices you don't want the thing to be + + align:start position:0% +prices you don't want the thing to be + + + align:start position:0% +prices you don't want the thing to be +moving all over the place but now we're + + align:start position:0% +moving all over the place but now we're + + + align:start position:0% +moving all over the place but now we're +also beginning to remove shelter because + + align:start position:0% +also beginning to remove shelter because + + + align:start position:0% +also beginning to remove shelter because +shelter inflation is very high and + + align:start position:0% +shelter inflation is very high and + + + align:start position:0% +shelter inflation is very high and +sticky and so on so so people can get to + + align:start position:0% +sticky and so on so so people can get to + + + align:start position:0% +sticky and so on so so people can get to +be very selective but no matter how you + + align:start position:0% +be very selective but no matter how you + + + align:start position:0% +be very selective but no matter how you +look at the thing we have a problem okay + + align:start position:0% +look at the thing we have a problem okay + + + align:start position:0% +look at the thing we have a problem okay +that there's no way around that so + + align:start position:0% +that there's no way around that so + + + align:start position:0% +that there's no way around that so +that's the the way again we're not going + + align:start position:0% +that's the the way again we're not going + + + align:start position:0% +that's the the way again we're not going +to look we're going to talk a lot about + + align:start position:0% +to look we're going to talk a lot about + + + align:start position:0% +to look we're going to talk a lot about +this problem of course but we need to + + align:start position:0% +this problem of course but we need to + + + align:start position:0% +this problem of course but we need to +build tools and and we're going to get + + align:start position:0% +build tools and and we're going to get + + + align:start position:0% +build tools and and we're going to get +there in about nine lectures from now + + align:start position:0% +there in about nine lectures from now + + + align:start position:0% +there in about nine lectures from now +okay nine lectures from now we're going + + align:start position:0% +okay nine lectures from now we're going + + + align:start position:0% +okay nine lectures from now we're going +to be able to talk about what what is + + align:start position:0% +to be able to talk about what what is + + + align:start position:0% +to be able to talk about what what is +going on in with Ms I mean you can talk + + align:start position:0% +going on in with Ms I mean you can talk + + + align:start position:0% +going on in with Ms I mean you can talk +whenever you want but with + + align:start position:0% +whenever you want but with + + + align:start position:0% +whenever you want but with +Ms okay so that those are the concepts I + + align:start position:0% +Ms okay so that those are the concepts I + + + align:start position:0% +Ms okay so that those are the concepts I +wanted to discuss today those are the + + align:start position:0% +wanted to discuss today those are the + + + align:start position:0% +wanted to discuss today those are the +definitions and relief that we got over + + align:start position:0% +definitions and relief that we got over + + + align:start position:0% +definitions and relief that we got over +this stuff let me just show you we have + + align:start position:0% +this stuff let me just show you we have + + + align:start position:0% +this stuff let me just show you we have +five minutes or + + align:start position:0% +five minutes or + + + align:start position:0% +five minutes or +so + + align:start position:0% +so + + + align:start position:0% +so +er equivalent numbers for other places + + align:start position:0% +er equivalent numbers for other places + + + align:start position:0% +er equivalent numbers for other places +around the world that's + + align:start position:0% +around the world that's + + + align:start position:0% +around the world that's +China okay + + align:start position:0% +China okay + + + align:start position:0% +China okay +that's China That's GDP growth for China + + align:start position:0% +that's China That's GDP growth for China + + + align:start position:0% +that's China That's GDP growth for China +and there are several things you can see + + align:start position:0% +and there are several things you can see + + + align:start position:0% +and there are several things you can see +from for this GDP series the first is + + align:start position:0% +from for this GDP series the first is + + + align:start position:0% +from for this GDP series the first is +that it was very high this these numbers + + align:start position:0% +that it was very high this these numbers + + + align:start position:0% +that it was very high this these numbers +look a lot on average it's a lot higher + + align:start position:0% +look a lot on average it's a lot higher + + + align:start position:0% +look a lot on average it's a lot higher +than the US when I show you the US you + + align:start position:0% +than the US when I show you the US you + + + align:start position:0% +than the US when I show you the US you +know the rate of growth was moving + + align:start position:0% +know the rate of growth was moving + + + align:start position:0% +know the rate of growth was moving +around 2% one and a half perc blah blah + + align:start position:0% +around 2% one and a half perc blah blah + + + align:start position:0% +around 2% one and a half perc blah blah +blah occasionally recessions and so on + + align:start position:0% +blah occasionally recessions and so on + + + align:start position:0% +blah occasionally recessions and so on +this is China look you had you know + + align:start position:0% +this is China look you had you know + + + align:start position:0% +this is China look you had you know +numbers like 10% or so that's + + align:start position:0% +numbers like 10% or so that's + + + align:start position:0% +numbers like 10% or so that's +interesting we want to know why is that + + align:start position:0% +interesting we want to know why is that + + + align:start position:0% +interesting we want to know why is that +you can have so much difference in + + align:start position:0% +you can have so much difference in + + + align:start position:0% +you can have so much difference in +different countries okay and and that's + + align:start position:0% +different countries okay and and that's + + + align:start position:0% +different countries okay and and that's +what we're going to do in the third part + + align:start position:0% +what we're going to do in the third part + + + align:start position:0% +what we're going to do in the third part +of the course when we look at growth + + align:start position:0% +of the course when we look at growth + + + align:start position:0% +of the course when we look at growth +we're going to look at these kind of + + align:start position:0% +we're going to look at these kind of + + + align:start position:0% +we're going to look at these kind of +factors what can give you sustained rate + + align:start position:0% +factors what can give you sustained rate + + + align:start position:0% +factors what can give you sustained rate +of growth sustain I mean for a long + + align:start position:0% +of growth sustain I mean for a long + + + align:start position:0% +of growth sustain I mean for a long +period of time higher than in another + + align:start position:0% +period of time higher than in another + + + align:start position:0% +period of time higher than in another +country the the main factor just to + + align:start position:0% +country the the main factor just to + + + align:start position:0% +country the the main factor just to +preview what will happen is is + + align:start position:0% +preview what will happen is is + + + align:start position:0% +preview what will happen is is +H is simply that China was a lot poorer + + align:start position:0% +H is simply that China was a lot poorer + + + align:start position:0% +H is simply that China was a lot poorer +than the us at the beginning and when + + align:start position:0% +than the us at the beginning and when + + + align:start position:0% +than the us at the beginning and when +you're poorer and you put your act + + align:start position:0% +you're poorer and you put your act + + + align:start position:0% +you're poorer and you put your act +together you can grow a lot faster than + + align:start position:0% +together you can grow a lot faster than + + + align:start position:0% +together you can grow a lot faster than +the rest now China is slowing down aside + + align:start position:0% +the rest now China is slowing down aside + + + align:start position:0% +the rest now China is slowing down aside +from covid it's very clear for quite + + align:start position:0% +from covid it's very clear for quite + + + align:start position:0% +from covid it's very clear for quite +some time that they have been worried + + align:start position:0% +some time that they have been worried + + + align:start position:0% +some time that they have been worried +because clearly GDP growth is + + align:start position:0% +because clearly GDP growth is + + + align:start position:0% +because clearly GDP growth is +declining okay and and and they're + + align:start position:0% +declining okay and and and they're + + + align:start position:0% +declining okay and and and they're +terrified about that and and and many of + + align:start position:0% +terrified about that and and and many of + + + align:start position:0% +terrified about that and and and many of +the things that are happening with China + + align:start position:0% +the things that are happening with China + + + align:start position:0% +the things that are happening with China +have to do with the fear Associated to + + align:start position:0% +have to do with the fear Associated to + + + align:start position:0% +have to do with the fear Associated to +uh slow down in the rate of growth when + + align:start position:0% +uh slow down in the rate of growth when + + + align:start position:0% +uh slow down in the rate of growth when +they are still quite poor in per + + align:start position:0% +they are still quite poor in per + + + align:start position:0% +they are still quite poor in per +terms okay so that's a lot of what + + align:start position:0% +terms okay so that's a lot of what + + + align:start position:0% +terms okay so that's a lot of what +happens in China has to do with + + align:start position:0% + + + + align:start position:0% + +that if you look at Japan look at Japan + + align:start position:0% +that if you look at Japan look at Japan + + + align:start position:0% +that if you look at Japan look at Japan +Japan also grew very fast in the 60s + + align:start position:0% +Japan also grew very fast in the 60s + + + align:start position:0% +Japan also grew very fast in the 60s +okay you see this very fast rate of + + align:start position:0% +okay you see this very fast rate of + + + align:start position:0% +okay you see this very fast rate of +growth then it began to slow down and + + align:start position:0% +growth then it began to slow down and + + + align:start position:0% +growth then it began to slow down and +pom here collapse they have a massive + + align:start position:0% +pom here collapse they have a massive + + + align:start position:0% +pom here collapse they have a massive +crash in the in in in financial markets + + align:start position:0% +crash in the in in in financial markets + + + align:start position:0% +crash in the in in in financial markets +equities and land the price of land was + + align:start position:0% +equities and land the price of land was + + + align:start position:0% +equities and land the price of land was +enormous in Japan at this time it had a + + align:start position:0% +enormous in Japan at this time it had a + + + align:start position:0% +enormous in Japan at this time it had a +big Financial + + align:start position:0% +big Financial + + + align:start position:0% +big Financial +bubble you know for those of you that + + align:start position:0% +bubble you know for those of you that + + + align:start position:0% +bubble you know for those of you that +know Japan or if you don't know it + + align:start position:0% +know Japan or if you don't know it + + + align:start position:0% +know Japan or if you don't know it +doesn't matter there's a the Imperial + + align:start position:0% +doesn't matter there's a the Imperial + + + align:start position:0% +doesn't matter there's a the Imperial +Park in Tokyo which is a park that is + + align:start position:0% +Park in Tokyo which is a park that is + + + align:start position:0% +Park in Tokyo which is a park that is +much smaller than Central Park or + + align:start position:0% +much smaller than Central Park or + + + align:start position:0% +much smaller than Central Park or +whatever the value of that land at some + + align:start position:0% +whatever the value of that land at some + + + align:start position:0% +whatever the value of that land at some +point in time was the same as the value + + align:start position:0% +point in time was the same as the value + + + align:start position:0% +point in time was the same as the value +of the entire State of California okay + + align:start position:0% +of the entire State of California okay + + + align:start position:0% +of the entire State of California okay +that's the order of magnitude it was not + + align:start position:0% +that's the order of magnitude it was not + + + align:start position:0% +that's the order of magnitude it was not +for sale but you know in terms of + + align:start position:0% +for sale but you know in terms of + + + align:start position:0% +for sale but you know in terms of +location times price but that's that + + align:start position:0% +location times price but that's that + + + align:start position:0% +location times price but that's that +bubble crash and since then Japan has + + align:start position:0% +bubble crash and since then Japan has + + + align:start position:0% +bubble crash and since then Japan has +never been able to recover its modu okay + + align:start position:0% +never been able to recover its modu okay + + + align:start position:0% +never been able to recover its modu okay +it has been sort of growing at a very + + align:start position:0% +it has been sort of growing at a very + + + align:start position:0% +it has been sort of growing at a very +low rate for a very long period of time + + align:start position:0% +low rate for a very long period of time + + + align:start position:0% +low rate for a very long period of time +and one of the things that scares China + + align:start position:0% +and one of the things that scares China + + + align:start position:0% +and one of the things that scares China +is that this may happen to them because + + align:start position:0% +is that this may happen to them because + + + align:start position:0% +is that this may happen to them because +this happened to Japan when they were + + align:start position:0% +this happened to Japan when they were + + + align:start position:0% +this happened to Japan when they were +already quite Rich Japan was pretty poor + + align:start position:0% +already quite Rich Japan was pretty poor + + + align:start position:0% +already quite Rich Japan was pretty poor +after the war naturally and they grew + + align:start position:0% +after the war naturally and they grew + + + align:start position:0% +after the war naturally and they grew +very fast in the 60s but then they had + + align:start position:0% +very fast in the 60s but then they had + + + align:start position:0% +very fast in the 60s but then they had +this issue Financial bubble and so on + + align:start position:0% +this issue Financial bubble and so on + + + align:start position:0% +this issue Financial bubble and so on +they crashing had never been able to + + align:start position:0% +they crashing had never been able to + + + align:start position:0% +they crashing had never been able to +recover and China is worried that you + + align:start position:0% +recover and China is worried that you + + + align:start position:0% +recover and China is worried that you +know that this slowdown happens to them + + align:start position:0% +know that this slowdown happens to them + + + align:start position:0% +know that this slowdown happens to them +ER before they have acquire reached sort + + align:start position:0% +ER before they have acquire reached sort + + + align:start position:0% +ER before they have acquire reached sort +of the level of income per capita that + + align:start position:0% +of the level of income per capita that + + + align:start position:0% +of the level of income per capita that +Japan reach when that + + align:start position:0% +Japan reach when that + + + align:start position:0% +Japan reach when that +happened they common factors behind the + + align:start position:0% +happened they common factors behind the + + + align:start position:0% +happened they common factors behind the +two of them as well demographic factors + + align:start position:0% +two of them as well demographic factors + + + align:start position:0% +two of them as well demographic factors +demographics are very negative for both + + align:start position:0% +demographics are very negative for both + + + align:start position:0% +demographics are very negative for both +of them and which naturally will slow + + align:start position:0% +of them and which naturally will slow + + + align:start position:0% +of them and which naturally will slow +down the rate of growth we're going to + + align:start position:0% +down the rate of growth we're going to + + + align:start position:0% +down the rate of growth we're going to +look at that later this is inflation in + + align:start position:0% +look at that later this is inflation in + + + align:start position:0% +look at that later this is inflation in +Japan H you see sort of the most + + align:start position:0% +Japan H you see sort of the most + + + align:start position:0% +Japan H you see sort of the most +countries had high inflation around + + align:start position:0% +countries had high inflation around + + + align:start position:0% +countries had high inflation around +there because the the were the price of + + align:start position:0% +there because the the were the price of + + + align:start position:0% +there because the the were the price of +oil they with massive oil shocks and so + + align:start position:0% +oil they with massive oil shocks and so + + + align:start position:0% +oil they with massive oil shocks and so +on so inflation was pretty high but the + + align:start position:0% +on so inflation was pretty high but the + + + align:start position:0% +on so inflation was pretty high but the +problem of Japan has been the opposite + + align:start position:0% +problem of Japan has been the opposite + + + align:start position:0% +problem of Japan has been the opposite +since the bubble crash in the late 80s + + align:start position:0% +since the bubble crash in the late 80s + + + align:start position:0% +since the bubble crash in the late 80s +early 990s they have had very low + + align:start position:0% +early 990s they have had very low + + + align:start position:0% +early 990s they have had very low +inflation + + align:start position:0% +inflation + + + align:start position:0% +inflation +H even deflation and that's been a big + + align:start position:0% +H even deflation and that's been a big + + + align:start position:0% +H even deflation and that's been a big +problem part of the reason why they have + + align:start position:0% +problem part of the reason why they have + + + align:start position:0% +problem part of the reason why they have +had so low growth is because they have + + align:start position:0% +had so low growth is because they have + + + align:start position:0% +had so low growth is because they have +been in this deflationary trap and then + + align:start position:0% +been in this deflationary trap and then + + + align:start position:0% +been in this deflationary trap and then +you something you will will look at + + align:start position:0% +you something you will will look at + + + align:start position:0% +you something you will will look at +later on in the course when when you + + align:start position:0% +later on in the course when when you + + + align:start position:0% +later on in the course when when you +have deflation it's pretty it's very + + align:start position:0% +have deflation it's pretty it's very + + + align:start position:0% +have deflation it's pretty it's very +difficult to use monetary policy to get + + align:start position:0% +difficult to use monetary policy to get + + + align:start position:0% +difficult to use monetary policy to get +out of a recession and that's the reason + + align:start position:0% +out of a recession and that's the reason + + + align:start position:0% +out of a recession and that's the reason +they keep getting a stack + + align:start position:0% +they keep getting a stack + + + align:start position:0% +they keep getting a stack +there so that's all I wanted to say for + + align:start position:0% +there so that's all I wanted to say for + + + align:start position:0% +there so that's all I wanted to say for +today and I'm relief again that this + + align:start position:0% +today and I'm relief again that this + + + align:start position:0% +today and I'm relief again that this +lecture is behind us in the next lecture + + align:start position:0% +lecture is behind us in the next lecture + + + align:start position:0% +lecture is behind us in the next lecture +we're going to introduce the first model + + align:start position:0% +we're going to introduce the first model + + + align:start position:0% +we're going to introduce the first model +what we're going to look at is is H is + + align:start position:0% +what we're going to look at is is H is + + + align:start position:0% +what we're going to look at is is H is +how to determine equilibrium GDP and how + + align:start position:0% +how to determine equilibrium GDP and how + + + align:start position:0% +how to determine equilibrium GDP and how +that depends on on the a variety of + + align:start position:0% +that depends on on the a variety of + + + align:start position:0% +that depends on on the a variety of +things including fiscal policy not + + align:start position:0% +things including fiscal policy not + + + align:start position:0% +things including fiscal policy not +monetary policy that will happen later + + align:start position:0% +monetary policy that will happen later + + + align:start position:0% +monetary policy that will happen later +um but uh how scared you are consumers + + align:start position:0% +um but uh how scared you are consumers + + + align:start position:0% +um but uh how scared you are consumers +preferences and fears and so on so + + align:start position:0% +preferences and fears and so on so + + + align:start position:0% +preferences and fears and so on so +that's the plan so unless there are any + + align:start position:0% +that's the plan so unless there are any + + + align:start position:0% +that's the plan so unless there are any +questions about + + align:start position:0% +questions about + + + align:start position:0% +questions about +this + + align:start position:0% +this + + + align:start position:0% +this +no so see you next Monday \ No newline at end of file diff --git a/ktm3HYt2kVs.txt b/ktm3HYt2kVs.txt new file mode 100644 index 0000000000000000000000000000000000000000..fd56a67b81469d6f29819005209e7ea8b25f282a --- /dev/null +++ b/ktm3HYt2kVs.txt @@ -0,0 +1,31275 @@ +align:start position:0% + +with you all here tonight I'm Lyn bander + + align:start position:0% +with you all here tonight I'm Lyn bander + + + align:start position:0% +with you all here tonight I'm Lyn bander +with the Cooperative development + + align:start position:0% +with the Cooperative development + + + align:start position:0% +with the Cooperative development +Institute shaku aljani and I'm also with + + align:start position:0% +Institute shaku aljani and I'm also with + + + align:start position:0% +Institute shaku aljani and I'm also with +the Cooperative development Institute + + align:start position:0% +the Cooperative development Institute + + + align:start position:0% +the Cooperative development Institute +and uh we've been doing Cooperative + + align:start position:0% +and uh we've been doing Cooperative + + + align:start position:0% +and uh we've been doing Cooperative +development for about 10 years looking + + align:start position:0% +development for about 10 years looking + + + align:start position:0% +development for about 10 years looking +at how communities can build uh + + align:start position:0% +at how communities can build uh + + + align:start position:0% +at how communities can build uh +resources within within their + + align:start position:0% +resources within within their + + + align:start position:0% +resources within within their +communities that um add value that stay + + align:start position:0% +communities that um add value that stay + + + align:start position:0% +communities that um add value that stay +in the community that don't walk off + + align:start position:0% +in the community that don't walk off + + + align:start position:0% +in the community that don't walk off +when another good opportunity comes + + align:start position:0% +when another good opportunity comes + + + align:start position:0% +when another good opportunity comes +along and um we've had a great time + + align:start position:0% +along and um we've had a great time + + + align:start position:0% +along and um we've had a great time +preparing this um syllabus that from the + + align:start position:0% +preparing this um syllabus that from the + + + align:start position:0% +preparing this um syllabus that from the +conversation that we had on the phone + + align:start position:0% +conversation that we had on the phone + + + align:start position:0% +conversation that we had on the phone +about the things that you were most + + align:start position:0% +about the things that you were most + + + align:start position:0% +about the things that you were most +interested in learning about and + + align:start position:0% +interested in learning about and + + + align:start position:0% +interested in learning about and +tonight's um Workshop is going to be on + + align:start position:0% +tonight's um Workshop is going to be on + + + align:start position:0% +tonight's um Workshop is going to be on +um strategic planning really thinking + + align:start position:0% +um strategic planning really thinking + + + align:start position:0% +um strategic planning really thinking +through a business idea looking at what + + align:start position:0% +through a business idea looking at what + + + align:start position:0% +through a business idea looking at what +it is um before you and whether or not + + align:start position:0% +it is um before you and whether or not + + + align:start position:0% +it is um before you and whether or not +it might be feasible um looking at um + + align:start position:0% +it might be feasible um looking at um + + + align:start position:0% +it might be feasible um looking at um +what the what the opportunities are in a + + align:start position:0% +what the what the opportunities are in a + + + align:start position:0% +what the what the opportunities are in a +community so that you can assess them + + align:start position:0% +community so that you can assess them + + + align:start position:0% +community so that you can assess them +and figure out what things to go forward + + align:start position:0% +and figure out what things to go forward + + + align:start position:0% +and figure out what things to go forward +with and what things to walk away from + + align:start position:0% +with and what things to walk away from + + + align:start position:0% +with and what things to walk away from +um because it's not likely that's going + + align:start position:0% +um because it's not likely that's going + + + align:start position:0% +um because it's not likely that's going +to be worth your time or the community + + align:start position:0% +to be worth your time or the community + + + align:start position:0% +to be worth your time or the community +folks time to pursue them and you know + + align:start position:0% +folks time to pursue them and you know + + + align:start position:0% +folks time to pursue them and you know +particularly at this point U uh + + align:start position:0% +particularly at this point U uh + + + align:start position:0% +particularly at this point U uh +beginning to talk about alternatives to + + align:start position:0% +beginning to talk about alternatives to + + + align:start position:0% +beginning to talk about alternatives to +U big box development to the wall Mar + + align:start position:0% +U big box development to the wall Mar + + + align:start position:0% +U big box development to the wall Mar +anization of of of our economy I think + + align:start position:0% +anization of of of our economy I think + + + align:start position:0% +anization of of of our economy I think +it's an important question you know as + + align:start position:0% +it's an important question you know as + + + align:start position:0% +it's an important question you know as +one of the things we talk about in there + + align:start position:0% +one of the things we talk about in there + + + align:start position:0% +one of the things we talk about in there +that communities all over the country + + align:start position:0% +that communities all over the country + + + align:start position:0% +that communities all over the country +are are trying to fight back and and for + + align:start position:0% +are are trying to fight back and and for + + + align:start position:0% +are are trying to fight back and and for +a number of different reasons whether U + + align:start position:0% +a number of different reasons whether U + + + align:start position:0% +a number of different reasons whether U +around workers issues uh uh + + align:start position:0% +around workers issues uh uh + + + align:start position:0% +around workers issues uh uh +um urban planning issues or um small + + align:start position:0% +um urban planning issues or um small + + + align:start position:0% +um urban planning issues or um small +business support issues but the question + + align:start position:0% +business support issues but the question + + + align:start position:0% +business support issues but the question +of what is the alternative I mean I've + + align:start position:0% +of what is the alternative I mean I've + + + align:start position:0% +of what is the alternative I mean I've +been a community organizer for 30 30 + + align:start position:0% +been a community organizer for 30 30 + + + align:start position:0% +been a community organizer for 30 30 +something years you can win sometimes on + + align:start position:0% +something years you can win sometimes on + + + align:start position:0% +something years you can win sometimes on +a just say no kind of thing but you + + align:start position:0% +a just say no kind of thing but you + + + align:start position:0% +a just say no kind of thing but you +can't win continually on that you have + + align:start position:0% +can't win continually on that you have + + + align:start position:0% +can't win continually on that you have +to be able to talk about what are what + + align:start position:0% +to be able to talk about what are what + + + align:start position:0% +to be able to talk about what are what +are you for you know what is your + + align:start position:0% +are you for you know what is your + + + align:start position:0% +are you for you know what is your +alternative to to to this to this + + align:start position:0% +alternative to to to this to this + + + align:start position:0% +alternative to to to this to this +predatory um um beast that we face and + + align:start position:0% +predatory um um beast that we face and + + + align:start position:0% +predatory um um beast that we face and +so that that was U it thought that this + + align:start position:0% +so that that was U it thought that this + + + align:start position:0% +so that that was U it thought that this +was a good way to not only begin to to + + align:start position:0% +was a good way to not only begin to to + + + align:start position:0% +was a good way to not only begin to to +uh um uh talk about this problem that we + + align:start position:0% +uh um uh talk about this problem that we + + + align:start position:0% +uh um uh talk about this problem that we +face in terms of the globalization and + + align:start position:0% +face in terms of the globalization and + + + align:start position:0% +face in terms of the globalization and +and and and and and some of these + + align:start position:0% +and and and and and some of these + + + align:start position:0% +and and and and and some of these +corporate players but also begin to + + align:start position:0% +corporate players but also begin to + + + align:start position:0% +corporate players but also begin to +start talking about the the the strength + + align:start position:0% +start talking about the the the strength + + + align:start position:0% +start talking about the the the strength +and and and positive experience of + + align:start position:0% +and and and positive experience of + + + align:start position:0% +and and and positive experience of +group-based business uh development um + + align:start position:0% +group-based business uh development um + + + align:start position:0% +group-based business uh development um +of all types over the LA over quite a + + align:start position:0% +of all types over the LA over quite a + + + align:start position:0% +of all types over the LA over quite a +few years happening in this country and + + align:start position:0% +few years happening in this country and + + + align:start position:0% +few years happening in this country and +around the world and and beginning to + + align:start position:0% +around the world and and beginning to + + + align:start position:0% +around the world and and beginning to +you know talk more about how can we U + + align:start position:0% +you know talk more about how can we U + + + align:start position:0% +you know talk more about how can we U +learn from the experiences develop the + + align:start position:0% +learn from the experiences develop the + + + align:start position:0% +learn from the experiences develop the +kind of tools and skills we need so that + + align:start position:0% +kind of tools and skills we need so that + + + align:start position:0% +kind of tools and skills we need so that +we can begin to really add a whole new + + align:start position:0% +we can begin to really add a whole new + + + align:start position:0% +we can begin to really add a whole new +weapon in our you know to our our + + align:start position:0% +weapon in our you know to our our + + + align:start position:0% +weapon in our you know to our our +artillery a new tool in our toolbox that + + align:start position:0% +artillery a new tool in our toolbox that + + + align:start position:0% +artillery a new tool in our toolbox that +that can really begin to help uh build + + align:start position:0% +that can really begin to help uh build + + + align:start position:0% +that can really begin to help uh build +sustainable + + align:start position:0% + + + + align:start position:0% + +communities' um today's session is on + + align:start position:0% +communities' um today's session is on + + + align:start position:0% +communities' um today's session is on +this um overview and planning tomorrow + + align:start position:0% +this um overview and planning tomorrow + + + align:start position:0% +this um overview and planning tomorrow +we're going to be doing business + + align:start position:0% +we're going to be doing business + + + align:start position:0% +we're going to be doing business +planning and the legal and accounting + + align:start position:0% +planning and the legal and accounting + + + align:start position:0% +planning and the legal and accounting +structures that support groups group + + align:start position:0% +structures that support groups group + + + align:start position:0% +structures that support groups group +based businesses um following in two + + align:start position:0% +based businesses um following in two + + + align:start position:0% +based businesses um following in two +weeks from today we're going to look at + + align:start position:0% +weeks from today we're going to look at + + + align:start position:0% +weeks from today we're going to look at +um me membership issues and um how you + + align:start position:0% +um me membership issues and um how you + + + align:start position:0% +um me membership issues and um how you +support uh governance so that a group of + + align:start position:0% +support uh governance so that a group of + + + align:start position:0% +support uh governance so that a group of +people can retain ownership and control + + align:start position:0% +people can retain ownership and control + + + align:start position:0% +people can retain ownership and control +over their business and the following + + align:start position:0% +over their business and the following + + + align:start position:0% +over their business and the following +day on Tuesday we're going to look at + + align:start position:0% +day on Tuesday we're going to look at + + + align:start position:0% +day on Tuesday we're going to look at +how how do you sustain these businesses + + align:start position:0% +how how do you sustain these businesses + + + align:start position:0% +how how do you sustain these businesses +once you get them up and running if you + + align:start position:0% +once you get them up and running if you + + + align:start position:0% +once you get them up and running if you +don't have the infrastructure for + + align:start position:0% +don't have the infrastructure for + + + align:start position:0% +don't have the infrastructure for +keeping them focused on their mission + + align:start position:0% +keeping them focused on their mission + + + align:start position:0% +keeping them focused on their mission +and and successful all of the + + align:start position:0% +and and successful all of the + + + align:start position:0% +and and successful all of the +development effort really was for not so + + align:start position:0% +development effort really was for not so + + + align:start position:0% +development effort really was for not so +um how what how can we sustain these + + align:start position:0% +um how what how can we sustain these + + + align:start position:0% +um how what how can we sustain these +businesses is that last day + + align:start position:0% +businesses is that last day + + + align:start position:0% +businesses is that last day +and um before we get started on our + + align:start position:0% +and um before we get started on our + + + align:start position:0% +and um before we get started on our +presentation I'm just wondering if + + align:start position:0% +presentation I'm just wondering if + + + align:start position:0% +presentation I'm just wondering if +people would be willing to go around and + + align:start position:0% +people would be willing to go around and + + + align:start position:0% +people would be willing to go around and +um talk just for a minute about what it + + align:start position:0% +um talk just for a minute about what it + + + align:start position:0% +um talk just for a minute about what it +is that you've done in terms of + + align:start position:0% +is that you've done in terms of + + + align:start position:0% +is that you've done in terms of +group-based Business Development to + + align:start position:0% +group-based Business Development to + + + align:start position:0% +group-based Business Development to +secure assets and communities that + + align:start position:0% +secure assets and communities that + + + align:start position:0% +secure assets and communities that +you've worked + + align:start position:0% + + + + align:start position:0% + +in actually haven't done a lot I think I + + align:start position:0% +in actually haven't done a lot I think I + + + align:start position:0% +in actually haven't done a lot I think I +think it's it's a good question the way + + align:start position:0% +think it's it's a good question the way + + + align:start position:0% +think it's it's a good question the way +you framed it + + align:start position:0% +you framed it + + + align:start position:0% +you framed it +because I think I've done a lot of + + align:start position:0% +because I think I've done a lot of + + + align:start position:0% +because I think I've done a lot of +community based work I've worked for + + align:start position:0% +community based work I've worked for + + + align:start position:0% +community based work I've worked for +programs and cdc's and different + + align:start position:0% +programs and cdc's and different + + + align:start position:0% +programs and cdc's and different +partnership projects and organizing but + + align:start position:0% +partnership projects and organizing but + + + align:start position:0% +partnership projects and organizing but +I think that I feel like I haven't spent + + align:start position:0% +I think that I feel like I haven't spent + + + align:start position:0% +I think that I feel like I haven't spent +a lot of time looking at this issue + + align:start position:0% +a lot of time looking at this issue + + + align:start position:0% +a lot of time looking at this issue +specifically on how do you leverage + + align:start position:0% +specifically on how do you leverage + + + align:start position:0% +specifically on how do you leverage +assets keep them in the community run + + align:start position:0% +assets keep them in the community run + + + align:start position:0% +assets keep them in the community run +businesses um so I feel like I really + + align:start position:0% +businesses um so I feel like I really + + + align:start position:0% +businesses um so I feel like I really +haven't spent a lot of time on that but + + align:start position:0% +haven't spent a lot of time on that but + + + align:start position:0% +haven't spent a lot of time on that but +um I've done a lot of youth work um sort + + align:start position:0% +um I've done a lot of youth work um sort + + + align:start position:0% +um I've done a lot of youth work um sort +of participatory planning + + align:start position:0% +of participatory planning + + + align:start position:0% +of participatory planning +work um university Community Partnership + + align:start position:0% +work um university Community Partnership + + + align:start position:0% +work um university Community Partnership +work um and and some of that has led to + + align:start position:0% +work um and and some of that has led to + + + align:start position:0% +work um and and some of that has led to +conversations about how do we support + + align:start position:0% +conversations about how do we support + + + align:start position:0% +conversations about how do we support +microenterprise how do we you know + + align:start position:0% +microenterprise how do we you know + + + align:start position:0% +microenterprise how do we you know +create a fund that people can draw from + + align:start position:0% +create a fund that people can draw from + + + align:start position:0% +create a fund that people can draw from +whether it's a credit union or um you + + align:start position:0% +whether it's a credit union or um you + + + align:start position:0% +whether it's a credit union or um you +know how does the University set up a + + align:start position:0% +know how does the University set up a + + + align:start position:0% +know how does the University set up a +loan situation that communities can draw + + align:start position:0% +loan situation that communities can draw + + + align:start position:0% +loan situation that communities can draw +from to do Community Development to even + + align:start position:0% +from to do Community Development to even + + + align:start position:0% +from to do Community Development to even +do partnership projects um with + + align:start position:0% +do partnership projects um with + + + align:start position:0% +do partnership projects um with +universities so how do they how do they + + align:start position:0% +universities so how do they how do they + + + align:start position:0% +universities so how do they how do they +create pools of money that they can + + align:start position:0% +create pools of money that they can + + + align:start position:0% +create pools of money that they can +support the communities to work with the + + align:start position:0% +support the communities to work with the + + + align:start position:0% +support the communities to work with the +universities in that way and educate + + align:start position:0% +universities in that way and educate + + + align:start position:0% +universities in that way and educate +their students the way they're doing on + + align:start position:0% +their students the way they're doing on + + + align:start position:0% +their students the way they're doing on +a daily basis so um but I feel like they + + align:start position:0% +a daily basis so um but I feel like they + + + align:start position:0% +a daily basis so um but I feel like they +haven't LED very far those are all + + align:start position:0% +haven't LED very far those are all + + + align:start position:0% +haven't LED very far those are all +pretty directly related to the topic + + align:start position:0% +pretty directly related to the topic + + + align:start position:0% +pretty directly related to the topic +though so thinking about it but I'm + + align:start position:0% +though so thinking about it but I'm + + + align:start position:0% +though so thinking about it but I'm +excited about the workshop too to kind + + align:start position:0% +excited about the workshop too to kind + + + align:start position:0% +excited about the workshop too to kind +of get down in it and I'm hoping from + + align:start position:0% +of get down in it and I'm hoping from + + + align:start position:0% +of get down in it and I'm hoping from +this point forward that I have more + + align:start position:0% +this point forward that I have more + + + align:start position:0% +this point forward that I have more +specific tools to kind of pick up on + + align:start position:0% +specific tools to kind of pick up on + + + align:start position:0% +specific tools to kind of pick up on +those ideas and say okay yeah how do we + + align:start position:0% +those ideas and say okay yeah how do we + + + align:start position:0% +those ideas and say okay yeah how do we +how do we do this like I think that a + + align:start position:0% +how do we do this like I think that a + + + align:start position:0% +how do we do this like I think that a +lot of that knowledge is is not really + + align:start position:0% + + + + align:start position:0% + +there do you want to talk about one + + align:start position:0% +there do you want to talk about one + + + align:start position:0% +there do you want to talk about one +thing that you worked + + align:start position:0% +thing that you worked + + + align:start position:0% +thing that you worked +on you've done a lot of support for + + align:start position:0% +on you've done a lot of support for + + + align:start position:0% +on you've done a lot of support for +group based business what infrastructure + + align:start position:0% +group based business what infrastructure + + + align:start position:0% +group based business what infrastructure +support + + align:start position:0% +support + + + align:start position:0% +support +work I + + align:start position:0% +work I + + + align:start position:0% +work I +do just in terms of developing programs + + align:start position:0% +do just in terms of developing programs + + + align:start position:0% +do just in terms of developing programs +that that supported them and you know at + + align:start position:0% +that that supported them and you know at + + + align:start position:0% +that that supported them and you know at +the policy level you dead work that + + align:start position:0% +the policy level you dead work that + + + align:start position:0% +the policy level you dead work that +supported that all right I'm making it + + align:start position:0% +supported that all right I'm making it + + + align:start position:0% +supported that all right I'm making it +up I made it all up no + + align:start position:0% +up I made it all up no + + + align:start position:0% +up I made it all up no +that's um I guess in public housing when + + align:start position:0% +that's um I guess in public housing when + + + align:start position:0% +that's um I guess in public housing when +I worked in public hous in New York one + + align:start position:0% +I worked in public hous in New York one + + + align:start position:0% +I worked in public hous in New York one +of the things we did was we uh we had an + + align:start position:0% +of the things we did was we uh we had an + + + align:start position:0% +of the things we did was we uh we had an +amnesty period for all of the residents + + align:start position:0% +amnesty period for all of the residents + + + align:start position:0% +amnesty period for all of the residents +the public housing actually had + + align:start position:0% +the public housing actually had + + + align:start position:0% +the public housing actually had +businesses because it was illegal W + + align:start position:0% +businesses because it was illegal W + + + align:start position:0% +businesses because it was illegal W +supposed to and we had an amnesty and uh + + align:start position:0% +supposed to and we had an amnesty and uh + + + align:start position:0% +supposed to and we had an amnesty and uh +we found out that well at least more + + align:start position:0% +we found out that well at least more + + + align:start position:0% +we found out that well at least more +than + + align:start position:0% +than + + + align:start position:0% +than +250 businesses like um applied they we + + align:start position:0% +250 businesses like um applied they we + + + align:start position:0% +250 businesses like um applied they we +said if you apply you can become legal + + align:start position:0% +said if you apply you can become legal + + + align:start position:0% +said if you apply you can become legal +and we we discovered more than + + align:start position:0% +and we we discovered more than + + + align:start position:0% +and we we discovered more than +250 businesses um most you know most of + + align:start position:0% +250 businesses um most you know most of + + + align:start position:0% +250 businesses um most you know most of +them were group businesses in one form + + align:start position:0% +them were group businesses in one form + + + align:start position:0% +them were group businesses in one form +or another and then we offered um + + align:start position:0% +or another and then we offered um + + + align:start position:0% +or another and then we offered um +housing contracts uh contracts with the + + align:start position:0% +housing contracts uh contracts with the + + + align:start position:0% +housing contracts uh contracts with the +housing authority to those businesses + + align:start position:0% +housing authority to those businesses + + + align:start position:0% +housing authority to those businesses +guarantee if they completed a 10-week uh + + align:start position:0% +guarantee if they completed a 10-week uh + + + align:start position:0% +guarantee if they completed a 10-week uh +training program and um many did and + + align:start position:0% +training program and um many did and + + + align:start position:0% +training program and um many did and +they got contracts um so that was one + + align:start position:0% +they got contracts um so that was one + + + align:start position:0% +they got contracts um so that was one +but you know I'm of a Preacher of a + + align:start position:0% +but you know I'm of a Preacher of a + + + align:start position:0% +but you know I'm of a Preacher of a +pretty big church and I felt like that + + align:start position:0% +pretty big church and I felt like that + + + align:start position:0% +pretty big church and I felt like that +was like a business cuz you were + + align:start position:0% +was like a business cuz you were + + + align:start position:0% +was like a business cuz you were +definitely collecting money you def + + align:start position:0% +definitely collecting money you def + + + align:start position:0% +definitely collecting money you def +spending money you had to keep the book + + align:start position:0% +spending money you had to keep the book + + + align:start position:0% +spending money you had to keep the book +you got to keep the cash flowing you + + align:start position:0% +you got to keep the cash flowing you + + + align:start position:0% +you got to keep the cash flowing you +know it really was uh you know like I + + align:start position:0% +know it really was uh you know like I + + + align:start position:0% +know it really was uh you know like I +thought it was like a + + align:start position:0% + + + + align:start position:0% + +business my name is Mariana leev bronis + + align:start position:0% +business my name is Mariana leev bronis + + + align:start position:0% +business my name is Mariana leev bronis +and I work at Lawrence Community Works + + align:start position:0% +and I work at Lawrence Community Works + + + align:start position:0% +and I work at Lawrence Community Works +which is the CDC in Lawrence and um + + align:start position:0% +which is the CDC in Lawrence and um + + + align:start position:0% +which is the CDC in Lawrence and um +personally I've been in a co-op in + + align:start position:0% +personally I've been in a co-op in + + + align:start position:0% +personally I've been in a co-op in +college um but this is my first time + + align:start position:0% +college um but this is my first time + + + align:start position:0% +college um but this is my first time +trying to brainstorm how to put one + + align:start position:0% +trying to brainstorm how to put one + + + align:start position:0% +trying to brainstorm how to put one +together and so we have we have a + + align:start position:0% +together and so we have we have a + + + align:start position:0% +together and so we have we have a +membership of about people and we're + + align:start position:0% +membership of about people and we're + + + align:start position:0% +membership of about people and we're +trying to figure out how to Leverage The + + align:start position:0% +trying to figure out how to Leverage The + + + align:start position:0% +trying to figure out how to Leverage The +Power of that Network for some sort of + + align:start position:0% +Power of that Network for some sort of + + + align:start position:0% +Power of that Network for some sort of +collective economic benefit um we don't + + align:start position:0% +collective economic benefit um we don't + + + align:start position:0% +collective economic benefit um we don't +really know where to start so that's why + + align:start position:0% +really know where to start so that's why + + + align:start position:0% +really know where to start so that's why +I'm + + align:start position:0% + + + + align:start position:0% + +here and my name is Shah and I've worked + + align:start position:0% +here and my name is Shah and I've worked + + + align:start position:0% +here and my name is Shah and I've worked +with a couple grou businesses coops + + align:start position:0% +with a couple grou businesses coops + + + align:start position:0% +with a couple grou businesses coops +mostly some from way doing with + + align:start position:0% +mostly some from way doing with + + + align:start position:0% +mostly some from way doing with +agriculture there's one uh in New + + align:start position:0% +agriculture there's one uh in New + + + align:start position:0% +agriculture there's one uh in New +Orleans uh was an urban project some + + align:start position:0% +Orleans uh was an urban project some + + + align:start position:0% +Orleans uh was an urban project some +youth from a housing project who had a + + align:start position:0% +youth from a housing project who had a + + + align:start position:0% +youth from a housing project who had a +couple of Community Gardens and um you + + align:start position:0% +couple of Community Gardens and um you + + + align:start position:0% +couple of Community Gardens and um you +know they grew many things but their + + align:start position:0% +know they grew many things but their + + + align:start position:0% +know they grew many things but their +main uh crop was uh peppers they grew + + align:start position:0% +main uh crop was uh peppers they grew + + + align:start position:0% +main uh crop was uh peppers they grew +seven varieties of hot peppers and they + + align:start position:0% +seven varieties of hot peppers and they + + + align:start position:0% +seven varieties of hot peppers and they +actually created their own uh uh recipe + + align:start position:0% +actually created their own uh uh recipe + + + align:start position:0% +actually created their own uh uh recipe +for hot sauce and Louis and was famous + + align:start position:0% +for hot sauce and Louis and was famous + + + align:start position:0% +for hot sauce and Louis and was famous +for hot sauce so it was you know it was + + align:start position:0% +for hot sauce so it was you know it was + + + align:start position:0% +for hot sauce so it was you know it was +fitting and it called at the same time + + align:start position:0% +fitting and it called at the same time + + + align:start position:0% +fitting and it called at the same time +as hot sauce and designed their own + + align:start position:0% +as hot sauce and designed their own + + + align:start position:0% +as hot sauce and designed their own +little label and we're trying to get + + align:start position:0% +little label and we're trying to get + + + align:start position:0% +little label and we're trying to get +funding and invest was to actually be + + align:start position:0% +funding and invest was to actually be + + + align:start position:0% +funding and invest was to actually be +able to Market it uh when I left and um + + align:start position:0% +able to Market it uh when I left and um + + + align:start position:0% +able to Market it uh when I left and um +I worked in Alabama with + + align:start position:0% +I worked in Alabama with + + + align:start position:0% +I worked in Alabama with +cooperatives and worked with uh I was + + align:start position:0% +cooperatives and worked with uh I was + + + align:start position:0% +cooperatives and worked with uh I was +director of the youth program there and + + align:start position:0% +director of the youth program there and + + + align:start position:0% +director of the youth program there and +did some Cooperative work with the + + align:start position:0% +did some Cooperative work with the + + + align:start position:0% +did some Cooperative work with the +community based I mean Community Support + + align:start position:0% +community based I mean Community Support + + + align:start position:0% +community based I mean Community Support +of agriculture product projects + + align:start position:0% +of agriculture product projects + + + align:start position:0% +of agriculture product projects +great do you want to talk about one or + + align:start position:0% +great do you want to talk about one or + + + align:start position:0% +great do you want to talk about one or +two of the things you've been connected + + align:start position:0% +two of the things you've been connected + + + align:start position:0% +two of the things you've been connected +to well I've um been doing community + + align:start position:0% +to well I've um been doing community + + + align:start position:0% +to well I've um been doing community +organizing in um Buffalo um uh New York + + align:start position:0% +organizing in um Buffalo um uh New York + + + align:start position:0% +organizing in um Buffalo um uh New York +City and then uh Florida and other + + align:start position:0% +City and then uh Florida and other + + + align:start position:0% +City and then uh Florida and other +Chicago and other places I came out of + + align:start position:0% +Chicago and other places I came out of + + + align:start position:0% +Chicago and other places I came out of +the steel industry I was worked I was a + + align:start position:0% +the steel industry I was worked I was a + + + align:start position:0% +the steel industry I was worked I was a +steel worker for almost 10 years and + + align:start position:0% +steel worker for almost 10 years and + + + align:start position:0% +steel worker for almost 10 years and +very active working around minority and + + align:start position:0% +very active working around minority and + + + align:start position:0% +very active working around minority and +and steel worker issues Union issue so + + align:start position:0% +and steel worker issues Union issue so + + + align:start position:0% +and steel worker issues Union issue so +um in the process we always did U our + + align:start position:0% +um in the process we always did U our + + + align:start position:0% +um in the process we always did U our +community work our Approach at back + + align:start position:0% +community work our Approach at back + + + align:start position:0% +community work our Approach at back +those days we I was a remember of the + + align:start position:0% +those days we I was a remember of the + + + align:start position:0% +those days we I was a remember of the +league of revolutionary black workers we + + align:start position:0% +league of revolutionary black workers we + + + align:start position:0% +league of revolutionary black workers we +used to say from the plant to the + + align:start position:0% +used to say from the plant to the + + + align:start position:0% +used to say from the plant to the +community from the community to the + + align:start position:0% +community from the community to the + + + align:start position:0% +community from the community to the +plant it was there was no difference to + + align:start position:0% +plant it was there was no difference to + + + align:start position:0% +plant it was there was no difference to +us you know so it was a common thing and + + align:start position:0% +us you know so it was a common thing and + + + align:start position:0% +us you know so it was a common thing and +we one of the things that we did um was + + align:start position:0% +we one of the things that we did um was + + + align:start position:0% +we one of the things that we did um was +was um Cooperative projects so we had + + align:start position:0% +was um Cooperative projects so we had + + + align:start position:0% +was um Cooperative projects so we had +I've um done uh a food coops fuel co-ops + + align:start position:0% +I've um done uh a food coops fuel co-ops + + + align:start position:0% +I've um done uh a food coops fuel co-ops +um Credit Unions um um you know and now + + align:start position:0% +um Credit Unions um um you know and now + + + align:start position:0% +um Credit Unions um um you know and now +at this point I'm working with a um um + + align:start position:0% +at this point I'm working with a um um + + + align:start position:0% +at this point I'm working with a um um +with projects in particularly in Buffalo + + align:start position:0% +with projects in particularly in Buffalo + + + align:start position:0% +with projects in particularly in Buffalo +where we're one of them is a young + + align:start position:0% +where we're one of them is a young + + + align:start position:0% +where we're one of them is a young +people that're trying to do a hot + + align:start position:0% +people that're trying to do a hot + + + align:start position:0% +people that're trying to do a hot +sauce we have to talk about that but + + align:start position:0% +sauce we have to talk about that but + + + align:start position:0% +sauce we have to talk about that but +then also um um with Community Land + + align:start position:0% +then also um um with Community Land + + + align:start position:0% +then also um um with Community Land +Trust and uh other forms of urban AG + + align:start position:0% +Trust and uh other forms of urban AG + + + align:start position:0% +Trust and uh other forms of urban AG +culture and um and then as well as uh + + align:start position:0% +culture and um and then as well as uh + + + align:start position:0% +culture and um and then as well as uh +looking at we're we're also talking + + align:start position:0% +looking at we're we're also talking + + + align:start position:0% +looking at we're we're also talking +about an urban rural project which um uh + + align:start position:0% +about an urban rural project which um uh + + + align:start position:0% +about an urban rural project which um uh +where we're talking about trying to use + + align:start position:0% +where we're talking about trying to use + + + align:start position:0% +where we're talking about trying to use +the uh the mandron example um um and so + + align:start position:0% +the uh the mandron example um um and so + + + align:start position:0% +the uh the mandron example um um and so +instead of just doing ones and twos kind + + align:start position:0% +instead of just doing ones and twos kind + + + align:start position:0% +instead of just doing ones and twos kind +of of cooperatives bringing U setting up + + align:start position:0% +of of cooperatives bringing U setting up + + + align:start position:0% +of of cooperatives bringing U setting up +networks of cooperatives that that that + + align:start position:0% +networks of cooperatives that that that + + + align:start position:0% +networks of cooperatives that that that +that U work together um linking Urban + + align:start position:0% +that U work together um linking Urban + + + align:start position:0% +that U work together um linking Urban +and RAR areas uh together and so we're + + align:start position:0% +and RAR areas uh together and so we're + + + align:start position:0% +and RAR areas uh together and so we're +at this point we're in the in the um + + align:start position:0% +at this point we're in the in the um + + + align:start position:0% +at this point we're in the in the um +fundraising stage and and and and + + align:start position:0% +fundraising stage and and and and + + + align:start position:0% +fundraising stage and and and and +development stage of and but our hope is + + align:start position:0% +development stage of and but our hope is + + + align:start position:0% +development stage of and but our hope is +to begin in in Western New York and + + align:start position:0% +to begin in in Western New York and + + + align:start position:0% +to begin in in Western New York and +western Mass to to begin to develop some + + align:start position:0% +western Mass to to begin to develop some + + + align:start position:0% +western Mass to to begin to develop some +m style uh um cooperatives and uh step + + align:start position:0% +m style uh um cooperatives and uh step + + + align:start position:0% +m style uh um cooperatives and uh step +from linking their inner cities to the + + align:start position:0% +from linking their inner cities to the + + + align:start position:0% +from linking their inner cities to the +rural + + align:start position:0% + + + + align:start position:0% + +areas and um for the last 10 years I've + + align:start position:0% +areas and um for the last 10 years I've + + + align:start position:0% +areas and um for the last 10 years I've +been working on about 40 Projects a year + + align:start position:0% +been working on about 40 Projects a year + + + align:start position:0% +been working on about 40 Projects a year +with four of them being you know my + + align:start position:0% +with four of them being you know my + + + align:start position:0% +with four of them being you know my +primary responsibility each year year + + align:start position:0% +primary responsibility each year year + + + align:start position:0% +primary responsibility each year year +and mostly in sustainable agriculture + + align:start position:0% +and mostly in sustainable agriculture + + + align:start position:0% +and mostly in sustainable agriculture +and sustainable energy and um right now + + align:start position:0% +and sustainable energy and um right now + + + align:start position:0% +and sustainable energy and um right now +I'm working with the low-income housing + + align:start position:0% +I'm working with the low-income housing + + + align:start position:0% +I'm working with the low-income housing +Co-op um a biodiesel production facility + + align:start position:0% +Co-op um a biodiesel production facility + + + align:start position:0% +Co-op um a biodiesel production facility +um a an energy a consumer energy + + align:start position:0% +um a an energy a consumer energy + + + align:start position:0% +um a an energy a consumer energy +Cooperative that's looking to build + + align:start position:0% +Cooperative that's looking to build + + + align:start position:0% +Cooperative that's looking to build +renewable energy resources and + + align:start position:0% +renewable energy resources and + + + align:start position:0% +renewable energy resources and +conservation efficiency in both + + align:start position:0% +conservation efficiency in both + + + align:start position:0% +conservation efficiency in both +lowincome communities to reduce the + + align:start position:0% +lowincome communities to reduce the + + + align:start position:0% +lowincome communities to reduce the +energy that they're using and their + + align:start position:0% +energy that they're using and their + + + align:start position:0% +energy that they're using and their +energy bills and um and in uh + + align:start position:0% +energy bills and um and in uh + + + align:start position:0% +energy bills and um and in uh +surrounding communities that really are + + align:start position:0% +surrounding communities that really are + + + align:start position:0% +surrounding communities that really are +interested in building um renewable + + align:start position:0% +interested in building um renewable + + + align:start position:0% +interested in building um renewable +energy resources and also sharing that + + align:start position:0% +energy resources and also sharing that + + + align:start position:0% +energy resources and also sharing that +resource with the low-income communities + + align:start position:0% +resource with the low-income communities + + + align:start position:0% +resource with the low-income communities +nearby um and another one too but I it's + + align:start position:0% +nearby um and another one too but I it's + + + align:start position:0% +nearby um and another one too but I it's +escaped me oh an herb processing + + align:start position:0% +escaped me oh an herb processing + + + align:start position:0% +escaped me oh an herb processing +facility um with some Farmers um and if + + align:start position:0% +facility um with some Farmers um and if + + + align:start position:0% +facility um with some Farmers um and if +they see this I'm sorry I forgot for a + + align:start position:0% +they see this I'm sorry I forgot for a + + + align:start position:0% +they see this I'm sorry I forgot for a +minute but um uh and that's pretty fun + + align:start position:0% +minute but um uh and that's pretty fun + + + align:start position:0% +minute but um uh and that's pretty fun +so those are the things I my pled at the + + align:start position:0% +so those are the things I my pled at the + + + align:start position:0% +so those are the things I my pled at the +moment um and I try in my work to um to + + align:start position:0% +moment um and I try in my work to um to + + + align:start position:0% +moment um and I try in my work to um to +do both urban and rural together as + + align:start position:0% +do both urban and rural together as + + + align:start position:0% +do both urban and rural together as +Shakur was was saying because I I feel + + align:start position:0% +Shakur was was saying because I I feel + + + align:start position:0% +Shakur was was saying because I I feel +like there's so many resources that are + + align:start position:0% +like there's so many resources that are + + + align:start position:0% +like there's so many resources that are +um of mutual need the folks in the rural + + align:start position:0% +um of mutual need the folks in the rural + + + align:start position:0% +um of mutual need the folks in the rural +areas need things in U that people in + + align:start position:0% +areas need things in U that people in + + + align:start position:0% +areas need things in U that people in +the urban areas have and vice versa and + + align:start position:0% +the urban areas have and vice versa and + + + align:start position:0% +the urban areas have and vice versa and +so a lot of synergy and um not isolating + + align:start position:0% +so a lot of synergy and um not isolating + + + align:start position:0% +so a lot of synergy and um not isolating +groups and bringing people together so + + align:start position:0% +groups and bringing people together so + + + align:start position:0% +groups and bringing people together so +pretty fun and with that the drums will + + align:start position:0% +pretty fun and with that the drums will + + + align:start position:0% +pretty fun and with that the drums will +roll and we have our presentation which + + align:start position:0% +roll and we have our presentation which + + + align:start position:0% +roll and we have our presentation which +we've been working on for you which + + align:start position:0% +we've been working on for you which + + + align:start position:0% +we've been working on for you which +we're pretty excited about yeah as said + + align:start position:0% +we're pretty excited about yeah as said + + + align:start position:0% +we're pretty excited about yeah as said +um the um the need is great now I mean + + align:start position:0% +um the um the need is great now I mean + + + align:start position:0% +um the um the need is great now I mean +we we're talking um um urban and rural + + align:start position:0% +we we're talking um um urban and rural + + + align:start position:0% +we we're talking um um urban and rural +communities are going through incredible + + align:start position:0% +communities are going through incredible + + + align:start position:0% +communities are going through incredible +strains and stresses um um um from + + align:start position:0% +strains and stresses um um um from + + + align:start position:0% +strains and stresses um um um from +massive job loss like I said from places + + align:start position:0% +massive job loss like I said from places + + + align:start position:0% +massive job loss like I said from places +like Buffalo I mean where the you know + + align:start position:0% +like Buffalo I mean where the you know + + + align:start position:0% +like Buffalo I mean where the you know +the um the entire city is almost emptied + + align:start position:0% +the um the entire city is almost emptied + + + align:start position:0% +the um the entire city is almost emptied +out I mean from going from 600,000 and + + align:start position:0% +out I mean from going from 600,000 and + + + align:start position:0% +out I mean from going from 600,000 and +um at places like steel plant where I + + align:start position:0% +um at places like steel plant where I + + + align:start position:0% +um at places like steel plant where I +used to First work there was 21,000 + + align:start position:0% +used to First work there was 21,000 + + + align:start position:0% +used to First work there was 21,000 +people working there now it's uh maybe + + align:start position:0% +people working there now it's uh maybe + + + align:start position:0% +people working there now it's uh maybe +100 you know um you know and + + align:start position:0% +100 you know um you know and + + + align:start position:0% +100 you know um you know and +a city that went from 600,000 to about + + align:start position:0% +a city that went from 600,000 to about + + + align:start position:0% +a city that went from 600,000 to about +250 I mean so they and that's the kind + + align:start position:0% +250 I mean so they and that's the kind + + + align:start position:0% +250 I mean so they and that's the kind +of things that are happening all over + + align:start position:0% +of things that are happening all over + + + align:start position:0% +of things that are happening all over +you know in in uh and rust Bel kind of + + align:start position:0% +you know in in uh and rust Bel kind of + + + align:start position:0% +you know in in uh and rust Bel kind of +areas and um the disinvestment the lack + + align:start position:0% +areas and um the disinvestment the lack + + + align:start position:0% +areas and um the disinvestment the lack +of affordable housing you know the um + + align:start position:0% +of affordable housing you know the um + + + align:start position:0% +of affordable housing you know the um +and so the idea of how do we begin to to + + align:start position:0% +and so the idea of how do we begin to to + + + align:start position:0% +and so the idea of how do we begin to to +forge some new um new methods of of of + + align:start position:0% +forge some new um new methods of of of + + + align:start position:0% +forge some new um new methods of of of +attacking these problems how do we begin + + align:start position:0% +attacking these problems how do we begin + + + align:start position:0% +attacking these problems how do we begin +to to to bring people together there's + + align:start position:0% +to to to bring people together there's + + + align:start position:0% +to to to bring people together there's +kindes of organizing going on but but uh + + align:start position:0% +kindes of organizing going on but but uh + + + align:start position:0% +kindes of organizing going on but but uh +the the question of how we can begin to + + align:start position:0% +the the question of how we can begin to + + + align:start position:0% +the the question of how we can begin to +actually do uh job creation actually + + align:start position:0% +actually do uh job creation actually + + + align:start position:0% +actually do uh job creation actually +begin to to create um um new kinds of + + align:start position:0% +begin to to create um um new kinds of + + + align:start position:0% +begin to to create um um new kinds of +opportunities um that the the um + + align:start position:0% +opportunities um that the the um + + + align:start position:0% +opportunities um that the the um +mechanisms have not been there and the + + align:start position:0% +mechanisms have not been there and the + + + align:start position:0% +mechanisms have not been there and the +traditional approaches haven't been + + align:start position:0% +traditional approaches haven't been + + + align:start position:0% +traditional approaches haven't been +working um it's moving by itself do you + + align:start position:0% +working um it's moving by itself do you + + + align:start position:0% +working um it's moving by itself do you +know why uh nope let me let's try this + + align:start position:0% +know why uh nope let me let's try this + + + align:start position:0% +know why uh nope let me let's try this +one okay + + align:start position:0% +one okay + + + align:start position:0% +one okay +yeah so + + align:start position:0% +yeah so + + + align:start position:0% +yeah so +um timer it's it shouldn't be we didn't + + align:start position:0% +um timer it's it shouldn't be we didn't + + + align:start position:0% +um timer it's it shouldn't be we didn't +put it on a timer want you to push down + + align:start position:0% +put it on a timer want you to push down + + + align:start position:0% +put it on a timer want you to push down +push right oh no it's going by itself + + align:start position:0% +push right oh no it's going by itself + + + align:start position:0% +push right oh no it's going by itself +that's the problem yeah okay but so like + + align:start position:0% +that's the problem yeah okay but so like + + + align:start position:0% +that's the problem yeah okay but so like +I said uh the the urban rural areas that + + align:start position:0% +I said uh the the urban rural areas that + + + align:start position:0% +I said uh the the urban rural areas that +finding um um sources of investment + + align:start position:0% +finding um um sources of investment + + + align:start position:0% +finding um um sources of investment +extremely difficult whether you're in + + align:start position:0% +extremely difficult whether you're in + + + align:start position:0% +extremely difficult whether you're in +inner city or rural area trying to uh + + align:start position:0% +inner city or rural area trying to uh + + + align:start position:0% +inner city or rural area trying to uh +education and job training of the + + align:start position:0% +education and job training of the + + + align:start position:0% +education and job training of the +educational system in most of the cities + + align:start position:0% +educational system in most of the cities + + + align:start position:0% +educational system in most of the cities +around the country are have completely + + align:start position:0% +around the country are have completely + + + align:start position:0% +around the country are have completely +um imploded and then and the rural areas + + align:start position:0% +um imploded and then and the rural areas + + + align:start position:0% +um imploded and then and the rural areas +have have never really even stepped to + + align:start position:0% +have have never really even stepped to + + + align:start position:0% +have have never really even stepped to +seriously up to the plate dig digital + + align:start position:0% +seriously up to the plate dig digital + + + align:start position:0% +seriously up to the plate dig digital +divide again those are the areas that + + align:start position:0% +divide again those are the areas that + + + align:start position:0% +divide again those are the areas that +are most left out of the uh out of the + + align:start position:0% +are most left out of the uh out of the + + + align:start position:0% +are most left out of the uh out of the +information age of the rural and seniors + + align:start position:0% +information age of the rural and seniors + + + align:start position:0% +information age of the rural and seniors +and and and the folks of color you know + + align:start position:0% +and and and the folks of color you know + + + align:start position:0% +and and and the folks of color you know +in inner cities and and also just few + + align:start position:0% +in inner cities and and also just few + + + align:start position:0% +in inner cities and and also just few +opportunities to to Really participate + + align:start position:0% +opportunities to to Really participate + + + align:start position:0% +opportunities to to Really participate +and and be involved um and and uh uh and + + align:start position:0% +and and be involved um and and uh uh and + + + align:start position:0% +and and be involved um and and uh uh and +and and and and processes where they can + + align:start position:0% +and and and and processes where they can + + + align:start position:0% +and and and and processes where they can +make a a a decisive voice in what their + + align:start position:0% +make a a a decisive voice in what their + + + align:start position:0% +make a a a decisive voice in what their +Community looks like and and and what + + align:start position:0% +Community looks like and and and what + + + align:start position:0% +Community looks like and and and what +kind kind of services and and and um uh + + align:start position:0% +kind kind of services and and and um uh + + + align:start position:0% +kind kind of services and and and um uh +um in infrastructures are set up inside + + align:start position:0% +um in infrastructures are set up inside + + + align:start position:0% +um in infrastructures are set up inside +of their + + align:start position:0% + + + + align:start position:0% + +communities did it go more than + + align:start position:0% +communities did it go more than + + + align:start position:0% +communities did it go more than +one just a small here + + align:start position:0% +one just a small here + + + align:start position:0% +one just a small here +yeah okay yeah few + + align:start position:0% +yeah okay yeah few + + + align:start position:0% +yeah okay yeah few +development fig how to position here + + align:start position:0% +development fig how to position here + + + align:start position:0% +development fig how to position here +it's pretty big to read down there okay + + align:start position:0% +it's pretty big to read down there okay + + + align:start position:0% +it's pretty big to read down there okay +so um we have what we call we've named + + align:start position:0% +so um we have what we call we've named + + + align:start position:0% +so um we have what we call we've named +the box door bust which is step one Box + + align:start position:0% +the box door bust which is step one Box + + + align:start position:0% +the box door bust which is step one Box +Store says we promise that we're going + + align:start position:0% +Store says we promise that we're going + + + align:start position:0% +Store says we promise that we're going +to bring great local economic benefit to + + align:start position:0% +to bring great local economic benefit to + + + align:start position:0% +to bring great local economic benefit to +you step two is the box store opens and + + align:start position:0% +you step two is the box store opens and + + + align:start position:0% +you step two is the box store opens and +um the soaks up a whole lot of + + align:start position:0% +um the soaks up a whole lot of + + + align:start position:0% +um the soaks up a whole lot of +development funds and tax rebates and um + + align:start position:0% +development funds and tax rebates and um + + + align:start position:0% +development funds and tax rebates and um +charges low prices because well they're + + align:start position:0% +charges low prices because well they're + + + align:start position:0% +charges low prices because well they're +not paying their folks very much and + + align:start position:0% +not paying their folks very much and + + + align:start position:0% +not paying their folks very much and +they're not ping the employees of their + + align:start position:0% +they're not ping the employees of their + + + align:start position:0% +they're not ping the employees of their +suppliers very much so they can charge + + align:start position:0% +suppliers very much so they can charge + + + align:start position:0% +suppliers very much so they can charge +their low wages and consumers save money + + align:start position:0% +their low wages and consumers save money + + + align:start position:0% +their low wages and consumers save money +it's very exciting step three in the box + + align:start position:0% +it's very exciting step three in the box + + + align:start position:0% +it's very exciting step three in the box +door bust is local businesses shut down + + align:start position:0% +door bust is local businesses shut down + + + align:start position:0% +door bust is local businesses shut down +people are out of work consumers um with + + align:start position:0% +people are out of work consumers um with + + + align:start position:0% +people are out of work consumers um with +are um left without expert personal + + align:start position:0% +are um left without expert personal + + + align:start position:0% +are um left without expert personal +service that they've come to know and + + align:start position:0% +service that they've come to know and + + + align:start position:0% +service that they've come to know and +without products that are tailored to + + align:start position:0% +without products that are tailored to + + + align:start position:0% +without products that are tailored to +their needs that the local businesses + + align:start position:0% +their needs that the local businesses + + + align:start position:0% +their needs that the local businesses +used to carry for them step four is the + + align:start position:0% +used to carry for them step four is the + + + align:start position:0% +used to carry for them step four is the +box door closes down because they've got + + align:start position:0% +box door closes down because they've got + + + align:start position:0% +box door closes down because they've got +some more profits promised somewhere + + align:start position:0% +some more profits promised somewhere + + + align:start position:0% +some more profits promised somewhere +else and all the jobs are lost all the + + align:start position:0% +else and all the jobs are lost all the + + + align:start position:0% +else and all the jobs are lost all the +public investment is lost consumers have + + align:start position:0% +public investment is lost consumers have + + + align:start position:0% +public investment is lost consumers have +no access to those products or services + + align:start position:0% +no access to those products or services + + + align:start position:0% +no access to those products or services +and they get to save some more money + + align:start position:0% +and they get to save some more money + + + align:start position:0% +and they get to save some more money +because they're not buying no they + + align:start position:0% +because they're not buying no they + + + align:start position:0% +because they're not buying no they +actually in step five they get to pay + + align:start position:0% +actually in step five they get to pay + + + align:start position:0% +actually in step five they get to pay +more money because they've got to drive + + align:start position:0% +more money because they've got to drive + + + align:start position:0% +more money because they've got to drive +farther to get those things um the + + align:start position:0% +farther to get those things um the + + + align:start position:0% +farther to get those things um the +community pays for uninsured health + + align:start position:0% +community pays for uninsured health + + + align:start position:0% +community pays for uninsured health +benefits unemployment costs um and uh + + align:start position:0% +benefits unemployment costs um and uh + + + align:start position:0% +benefits unemployment costs um and uh +the local economy loses the multiplier + + align:start position:0% +the local economy loses the multiplier + + + align:start position:0% +the local economy loses the multiplier +effect of all of those resources and + + align:start position:0% +effect of all of those resources and + + + align:start position:0% +effect of all of those resources and +we've seen it pharmaceutical industry + + align:start position:0% +we've seen it pharmaceutical industry + + + align:start position:0% +we've seen it pharmaceutical industry +we've seen it in in hardware stores + + align:start position:0% +we've seen it in in hardware stores + + + align:start position:0% +we've seen it in in hardware stores +we've seen it in clothing stores and + + align:start position:0% +we've seen it in clothing stores and + + + align:start position:0% +we've seen it in clothing stores and +this for some reason it's still a + + align:start position:0% +this for some reason it's still a + + + align:start position:0% +this for some reason it's still a +preferred economic development model um + + align:start position:0% +preferred economic development model um + + + align:start position:0% +preferred economic development model um +in most municipalities across the + + align:start position:0% +in most municipalities across the + + + align:start position:0% +in most municipalities across the +country and we're left scratching our + + align:start position:0% +country and we're left scratching our + + + align:start position:0% +country and we're left scratching our +heads and saying well you know every + + align:start position:0% +heads and saying well you know every + + + align:start position:0% +heads and saying well you know every +time we get to talk with somebody from + + align:start position:0% +time we get to talk with somebody from + + + align:start position:0% +time we get to talk with somebody from +one of these municipalities about the + + align:start position:0% +one of these municipalities about the + + + align:start position:0% +one of these municipalities about the +Alternatives they say we didn't know + + align:start position:0% +Alternatives they say we didn't know + + + align:start position:0% +Alternatives they say we didn't know +there were any we would love to know so + + align:start position:0% +there were any we would love to know so + + + align:start position:0% +there were any we would love to know so +Shakur and I are very excited about many + + align:start position:0% +Shakur and I are very excited about many + + + align:start position:0% +Shakur and I are very excited about many +and many other people very excited about + + align:start position:0% +and many other people very excited about + + + align:start position:0% +and many other people very excited about +trying to figure out how to really show + + align:start position:0% +trying to figure out how to really show + + + align:start position:0% +trying to figure out how to really show +people that these other Alternatives + + align:start position:0% +people that these other Alternatives + + + align:start position:0% +people that these other Alternatives +exist and have existed for a long time + + align:start position:0% +exist and have existed for a long time + + + align:start position:0% +exist and have existed for a long time +here in this country and around the + + align:start position:0% +here in this country and around the + + + align:start position:0% +here in this country and around the +world this isn't new this is just going + + align:start position:0% +world this isn't new this is just going + + + align:start position:0% +world this isn't new this is just going +back to some of the things that um + + align:start position:0% +back to some of the things that um + + + align:start position:0% +back to some of the things that um +cultures have known for for centuries + + align:start position:0% +cultures have known for for centuries + + + align:start position:0% +cultures have known for for centuries +about how you build real economic wealth + + align:start position:0% +about how you build real economic wealth + + + align:start position:0% +about how you build real economic wealth +in your community and as we've said I + + align:start position:0% +in your community and as we've said I + + + align:start position:0% +in your community and as we've said I +mean the worst of um of all the these + + align:start position:0% +mean the worst of um of all the these + + + align:start position:0% +mean the worst of um of all the these +players has been Walmart that they've um + + align:start position:0% +players has been Walmart that they've um + + + align:start position:0% +players has been Walmart that they've um +set up you know that and not only + + align:start position:0% +set up you know that and not only + + + align:start position:0% +set up you know that and not only +screwing up um job and and pay standards + + align:start position:0% +screwing up um job and and pay standards + + + align:start position:0% +screwing up um job and and pay standards +in in in um in in this country is it's + + align:start position:0% +in in in um in in this country is it's + + + align:start position:0% +in in in um in in this country is it's +having an effect on the entire world um + + align:start position:0% +having an effect on the entire world um + + + align:start position:0% +having an effect on the entire world um +it's you know one of the largest + + align:start position:0% +it's you know one of the largest + + + align:start position:0% +it's you know one of the largest +corporation in the world 1.2 million + + align:start position:0% +corporation in the world 1.2 million + + + align:start position:0% +corporation in the world 1.2 million +workers and um few with most with low + + align:start position:0% +workers and um few with most with low + + + align:start position:0% +workers and um few with most with low +pay most with um no employment and + + align:start position:0% +pay most with um no employment and + + + align:start position:0% +pay most with um no employment and +employer health coverage in in spite of + + align:start position:0% +employer health coverage in in spite of + + + align:start position:0% +employer health coverage in in spite of +the U the many U commercials that you + + align:start position:0% +the U the many U commercials that you + + + align:start position:0% +the U the many U commercials that you +will see that will you know talk to the + + align:start position:0% +will see that will you know talk to the + + + align:start position:0% +will see that will you know talk to the +op uh to the contrary and it that it + + align:start position:0% +op uh to the contrary and it that it + + + align:start position:0% +op uh to the contrary and it that it +drives its U suppliers is uh to to + + align:start position:0% +drives its U suppliers is uh to to + + + align:start position:0% +drives its U suppliers is uh to to +search the world for cheaper labor I + + align:start position:0% +search the world for cheaper labor I + + + align:start position:0% +search the world for cheaper labor I +mean and so that not only does it have + + align:start position:0% +mean and so that not only does it have + + + align:start position:0% +mean and so that not only does it have +an impact on on the that immediate group + + align:start position:0% +an impact on on the that immediate group + + + align:start position:0% +an impact on on the that immediate group +of folks that it spans out and so + + align:start position:0% +of folks that it spans out and so + + + align:start position:0% +of folks that it spans out and so +whether you're a toy supplier or a food + + align:start position:0% +whether you're a toy supplier or a food + + + align:start position:0% +whether you're a toy supplier or a food +supplier or whatever I mean uh did you + + align:start position:0% +supplier or whatever I mean uh did you + + + align:start position:0% +supplier or whatever I mean uh did you +all for to to dance to to Walmart's beat + + align:start position:0% +all for to to dance to to Walmart's beat + + + align:start position:0% +all for to to dance to to Walmart's beat +and like I said if it was a country it' + + align:start position:0% +and like I said if it was a country it' + + + align:start position:0% +and like I said if it was a country it' +be the fifth largest importer and it's + + align:start position:0% +be the fifth largest importer and it's + + + align:start position:0% +be the fifth largest importer and it's +particularly um um the particular + + align:start position:0% +particularly um um the particular + + + align:start position:0% +particularly um um the particular +relations that set up with uh China in + + align:start position:0% +relations that set up with uh China in + + + align:start position:0% +relations that set up with uh China in +spite of all the conversation that + + align:start position:0% +spite of all the conversation that + + + align:start position:0% +spite of all the conversation that +talking about democracy and other things + + align:start position:0% +talking about democracy and other things + + + align:start position:0% +talking about democracy and other things +um that it's that they're being cited um + + align:start position:0% +um that it's that they're being cited um + + + align:start position:0% +um that it's that they're being cited um +by other folks uh by as The Cutting play + + align:start position:0% +by other folks uh by as The Cutting play + + + align:start position:0% +by other folks uh by as The Cutting play +Health Care the impact they had on the + + align:start position:0% +Health Care the impact they had on the + + + align:start position:0% +Health Care the impact they had on the +entire um uh California um Supermarket + + align:start position:0% +entire um uh California um Supermarket + + + align:start position:0% +entire um uh California um Supermarket +structure Safeway proger you know the + + align:start position:0% +structure Safeway proger you know the + + + align:start position:0% +structure Safeway proger you know the +the list goes on and on Kmart True Value + + align:start position:0% +the list goes on and on Kmart True Value + + + align:start position:0% +the list goes on and on Kmart True Value +I mean um store stores that are are + + align:start position:0% +I mean um store stores that are are + + + align:start position:0% +I mean um store stores that are are +either going out of business or are + + align:start position:0% +either going out of business or are + + + align:start position:0% +either going out of business or are +reeling from the competition um uh you + + align:start position:0% +reeling from the competition um uh you + + + align:start position:0% +reeling from the competition um uh you +know it's a very long list and and the + + align:start position:0% +know it's a very long list and and the + + + align:start position:0% +know it's a very long list and and the +question is what are we going to be left + + align:start position:0% +question is what are we going to be left + + + align:start position:0% +question is what are we going to be left +with one big huge um uh corporation that + + align:start position:0% +with one big huge um uh corporation that + + + align:start position:0% +with one big huge um uh corporation that +that that then can um you know set a a + + align:start position:0% +that that then can um you know set a a + + + align:start position:0% +that that then can um you know set a a +pattern that uh that will Dev you know + + align:start position:0% +pattern that uh that will Dev you know + + + align:start position:0% +pattern that uh that will Dev you know +that is devastating uh the the living + + align:start position:0% +that is devastating uh the the living + + + align:start position:0% +that is devastating uh the the living +standards of American workers um you + + align:start position:0% +standards of American workers um you + + + align:start position:0% +standards of American workers um you +know as I said it's leading the Global + + align:start position:0% +know as I said it's leading the Global + + + align:start position:0% +know as I said it's leading the Global +and domestic corporate uh race to the + + align:start position:0% +and domestic corporate uh race to the + + + align:start position:0% +and domestic corporate uh race to the +bottom poor W poverty wages poor + + align:start position:0% +bottom poor W poverty wages poor + + + align:start position:0% +bottom poor W poverty wages poor +benefits and harassment you know some of + + align:start position:0% +benefits and harassment you know some of + + + align:start position:0% +benefits and harassment you know some of +you might have heard U you know how they + + align:start position:0% +you might have heard U you know how they + + + align:start position:0% +you might have heard U you know how they +lock their workers in in overnight um in + + align:start position:0% +lock their workers in in overnight um in + + + align:start position:0% +lock their workers in in overnight um in +order to stop spoilage theft you know uh + + align:start position:0% +order to stop spoilage theft you know uh + + + align:start position:0% +order to stop spoilage theft you know uh +you know so then you know people were + + align:start position:0% +you know so then you know people were + + + align:start position:0% +you know so then you know people were +not able to get out for emergency + + align:start position:0% +not able to get out for emergency + + + align:start position:0% +not able to get out for emergency +reasons and other things I mean + + align:start position:0% +reasons and other things I mean + + + align:start position:0% +reasons and other things I mean +functioning like a concentration + + align:start position:0% +functioning like a concentration + + + align:start position:0% +functioning like a concentration +camp and it's a battle I mean that one + + align:start position:0% +camp and it's a battle I mean that one + + + align:start position:0% +camp and it's a battle I mean that one +of the things uh you know there's been + + align:start position:0% +of the things uh you know there's been + + + align:start position:0% +of the things uh you know there's been +some talk I mean there's been a couple + + align:start position:0% +some talk I mean there's been a couple + + + align:start position:0% +some talk I mean there's been a couple +of big uh + + align:start position:0% +of big uh + + + align:start position:0% +of big uh +um um U victories against + + align:start position:0% +um um U victories against + + + align:start position:0% +um um U victories against +Walmart the work of um um Lan um Los + + align:start position:0% +Walmart the work of um um Lan um Los + + + align:start position:0% +Walmart the work of um um Lan um Los +Angeles for for uh for a new economy Los + + align:start position:0% +Angeles for for uh for a new economy Los + + + align:start position:0% +Angeles for for uh for a new economy Los +Angeles for new economy Mel and jiso and + + align:start position:0% +Angeles for new economy Mel and jiso and + + + align:start position:0% +Angeles for new economy Mel and jiso and +those you know beating them back there + + align:start position:0% +those you know beating them back there + + + align:start position:0% +those you know beating them back there +the the defea in uh Chicago and just + + align:start position:0% +the the defea in uh Chicago and just + + + align:start position:0% +the the defea in uh Chicago and just +recently the defea in uh Queens um but + + align:start position:0% +recently the defea in uh Queens um but + + + align:start position:0% +recently the defea in uh Queens um but +there's even many more I mean this we + + align:start position:0% +there's even many more I mean this we + + + align:start position:0% +there's even many more I mean this we +just got this from from Al Norman I mean + + align:start position:0% +just got this from from Al Norman I mean + + + align:start position:0% +just got this from from Al Norman I mean +and this was just over the last uh two + + align:start position:0% +and this was just over the last uh two + + + align:start position:0% +and this was just over the last uh two +years that uh um just in New England and + + align:start position:0% +years that uh um just in New England and + + + align:start position:0% +years that uh um just in New England and +and when you look at around the country + + align:start position:0% +and when you look at around the country + + + align:start position:0% +and when you look at around the country +it's a much longer list but just uh + + align:start position:0% +it's a much longer list but just uh + + + align:start position:0% +it's a much longer list but just uh +communities all over the place that have + + align:start position:0% +communities all over the place that have + + + align:start position:0% +communities all over the place that have +been uh fighting them now quite often + + align:start position:0% +been uh fighting them now quite often + + + align:start position:0% +been uh fighting them now quite often +they come back again I mean sometime you + + align:start position:0% +they come back again I mean sometime you + + + align:start position:0% +they come back again I mean sometime you +many times a a community will beat them + + align:start position:0% +many times a a community will beat them + + + align:start position:0% +many times a a community will beat them +once and then but with the you know + + align:start position:0% +once and then but with the you know + + + align:start position:0% +once and then but with the you know +reservoirs of capital and political + + align:start position:0% +reservoirs of capital and political + + + align:start position:0% +reservoirs of capital and political +power they have then they come right + + align:start position:0% +power they have then they come right + + + align:start position:0% +power they have then they come right +back at you again and you know and then + + align:start position:0% +back at you again and you know and then + + + align:start position:0% +back at you again and you know and then +maybe he might not be that successful + + align:start position:0% +maybe he might not be that successful + + + align:start position:0% +maybe he might not be that successful +and so but but one of the things that we + + align:start position:0% +and so but but one of the things that we + + + align:start position:0% +and so but but one of the things that we +need to get a sense of is that there is + + align:start position:0% +need to get a sense of is that there is + + + align:start position:0% +need to get a sense of is that there is +a a movement that's developing that + + align:start position:0% +a a movement that's developing that + + + align:start position:0% +a a movement that's developing that +brings together all kinds of sectors + + align:start position:0% +brings together all kinds of sectors + + + align:start position:0% +brings together all kinds of sectors +Labor uh folks that are concerned about + + align:start position:0% +Labor uh folks that are concerned about + + + align:start position:0% +Labor uh folks that are concerned about +U just good uh uh public planning U you + + align:start position:0% +U just good uh uh public planning U you + + + align:start position:0% +U just good uh uh public planning U you +know folks that want to see more small + + align:start position:0% +know folks that want to see more small + + + align:start position:0% +know folks that want to see more small +businesses and other things uh um um uh + + align:start position:0% +businesses and other things uh um um uh + + + align:start position:0% +businesses and other things uh um um uh +uh women's uh uh groups um since the + + align:start position:0% +uh women's uh uh groups um since the + + + align:start position:0% +uh women's uh uh groups um since the +lawsuits that have been done is showing + + align:start position:0% +lawsuits that have been done is showing + + + align:start position:0% +lawsuits that have been done is showing +that that that Walmart discriminates + + align:start position:0% +that that that Walmart discriminates + + + align:start position:0% +that that that Walmart discriminates +against woman women that there's a glass + + align:start position:0% +against woman women that there's a glass + + + align:start position:0% +against woman women that there's a glass +ceiling that's very low that stops them + + align:start position:0% +ceiling that's very low that stops them + + + align:start position:0% +ceiling that's very low that stops them +from moving up and U uh um and uh you + + align:start position:0% +from moving up and U uh um and uh you + + + align:start position:0% +from moving up and U uh um and uh you +know into the corporate and corporate + + align:start position:0% +know into the corporate and corporate + + + align:start position:0% +know into the corporate and corporate +power the um the abuses against um + + align:start position:0% +power the um the abuses against um + + + align:start position:0% +power the um the abuses against um +minority workers particularly against + + align:start position:0% +minority workers particularly against + + + align:start position:0% +minority workers particularly against +immigrant workers so it's it's U many + + align:start position:0% +immigrant workers so it's it's U many + + + align:start position:0% +immigrant workers so it's it's U many +different folks and and this and it's + + align:start position:0% +different folks and and this and it's + + + align:start position:0% +different folks and and this and it's +going across the board not only just + + align:start position:0% +going across the board not only just + + + align:start position:0% +going across the board not only just +Walmart it's against people fighting + + align:start position:0% +Walmart it's against people fighting + + + align:start position:0% +Walmart it's against people fighting +against Home Depot against uh you know + + align:start position:0% +against Home Depot against uh you know + + + align:start position:0% +against Home Depot against uh you know +all the different uh um um big box uh + + align:start position:0% +all the different uh um um big box uh + + + align:start position:0% +all the different uh um um big box uh +stores that are coming in and rampaging + + align:start position:0% +stores that are coming in and rampaging + + + align:start position:0% +stores that are coming in and rampaging +their their + + align:start position:0% +their their + + + align:start position:0% +their their +communities I'm going to said I mean you + + align:start position:0% +communities I'm going to said I mean you + + + align:start position:0% +communities I'm going to said I mean you +know part of this also is the you know + + align:start position:0% +know part of this also is the you know + + + align:start position:0% +know part of this also is the you know +as Lynn was saying before is is a + + align:start position:0% +as Lynn was saying before is is a + + + align:start position:0% +as Lynn was saying before is is a +recognition that that the traditional + + align:start position:0% +recognition that that the traditional + + + align:start position:0% +recognition that that the traditional +economic approaches development + + align:start position:0% +economic approaches development + + + align:start position:0% +economic approaches development +approaches have have have not worked in + + align:start position:0% +approaches have have have not worked in + + + align:start position:0% +approaches have have have not worked in +our inner cities and rural areas that if + + align:start position:0% +our inner cities and rural areas that if + + + align:start position:0% +our inner cities and rural areas that if +if we go by the the proof is in the + + align:start position:0% +if we go by the the proof is in the + + + align:start position:0% +if we go by the the proof is in the +pudding uh you know that that um um + + align:start position:0% +pudding uh you know that that um um + + + align:start position:0% +pudding uh you know that that um um +large amounts of money is being brought + + align:start position:0% +large amounts of money is being brought + + + align:start position:0% +large amounts of money is being brought +forth you know in fact Greg Lory says + + align:start position:0% +forth you know in fact Greg Lory says + + + align:start position:0% +forth you know in fact Greg Lory says +that uh there something like $50 billion + + align:start position:0% +that uh there something like $50 billion + + + align:start position:0% +that uh there something like $50 billion +a year and and state and uh um and uh uh + + align:start position:0% +a year and and state and uh um and uh uh + + + align:start position:0% +a year and and state and uh um and uh uh +Municipal U monies that go toward uh um + + align:start position:0% +Municipal U monies that go toward uh um + + + align:start position:0% +Municipal U monies that go toward uh um +development and and often like I said + + align:start position:0% +development and and often like I said + + + align:start position:0% +development and and often like I said +it's U Justified with anti poverty + + align:start position:0% +it's U Justified with anti poverty + + + align:start position:0% +it's U Justified with anti poverty +record uh rhetoric is often u based on + + align:start position:0% +record uh rhetoric is often u based on + + + align:start position:0% +record uh rhetoric is often u based on +uh poverty stats uh but then the monies + + align:start position:0% +uh poverty stats uh but then the monies + + + align:start position:0% +uh poverty stats uh but then the monies +go elsewhere U you know and and the I + + align:start position:0% +go elsewhere U you know and and the I + + + align:start position:0% +go elsewhere U you know and and the I +and you know the in place like in + + align:start position:0% +and you know the in place like in + + + align:start position:0% +and you know the in place like in +Buffalo for example you know just one um + + align:start position:0% +Buffalo for example you know just one um + + + align:start position:0% +Buffalo for example you know just one um +urban planning Fiasco after after + + align:start position:0% +urban planning Fiasco after after + + + align:start position:0% +urban planning Fiasco after after +another one using um uh CBD money to to + + align:start position:0% +another one using um uh CBD money to to + + + align:start position:0% +another one using um uh CBD money to to +to u u buy off floors of of patronage + + align:start position:0% +to u u buy off floors of of patronage + + + align:start position:0% +to u u buy off floors of of patronage +workers that don't do urban planning to + + align:start position:0% +workers that don't do urban planning to + + + align:start position:0% +workers that don't do urban planning to +to uh to giving the money away to folks + + align:start position:0% +to uh to giving the money away to folks + + + align:start position:0% +to uh to giving the money away to folks +like uh the Adelphia thugs the rigus + + align:start position:0% +like uh the Adelphia thugs the rigus + + + align:start position:0% +like uh the Adelphia thugs the rigus +family who was supposed to redevelop the + + align:start position:0% +family who was supposed to redevelop the + + + align:start position:0% +family who was supposed to redevelop the +Waterfront or then to to stadiums to + + align:start position:0% +Waterfront or then to to stadiums to + + + align:start position:0% +Waterfront or then to to stadiums to +then the next one now is uh is is + + align:start position:0% +then the next one now is uh is is + + + align:start position:0% +then the next one now is uh is is +casinos and you know adding a a whole + + align:start position:0% +casinos and you know adding a a whole + + + align:start position:0% +casinos and you know adding a a whole +new problem that's not you know creating + + align:start position:0% +new problem that's not you know creating + + + align:start position:0% +new problem that's not you know creating +a handful of jobs and create and then + + align:start position:0% +a handful of jobs and create and then + + + align:start position:0% +a handful of jobs and create and then +creating gambling dependencies and + + align:start position:0% +creating gambling dependencies and + + + align:start position:0% +creating gambling dependencies and +there's and there's something odd about + + align:start position:0% +there's and there's something odd about + + + align:start position:0% +there's and there's something odd about +the ethic around these + + align:start position:0% +the ethic around these + + + align:start position:0% +the ethic around these +funds there's many programs that these + + align:start position:0% +funds there's many programs that these + + + align:start position:0% +funds there's many programs that these +funds are administered through where + + align:start position:0% +funds are administered through where + + + align:start position:0% +funds are administered through where +there isn't even preference given to + + align:start position:0% +there isn't even preference given to + + + align:start position:0% +there isn't even preference given to +ways of spending that money that retains + + align:start position:0% +ways of spending that money that retains + + + align:start position:0% +ways of spending that money that retains +ownership in the public Sphere not only + + align:start position:0% +ownership in the public Sphere not only + + + align:start position:0% +ownership in the public Sphere not only +there isn't a preference but lots of + + align:start position:0% +there isn't a preference but lots of + + + align:start position:0% +there isn't a preference but lots of +times those programs don't even even + + align:start position:0% +times those programs don't even even + + + align:start position:0% +times those programs don't even even +allow you have to be a private developer + + align:start position:0% +allow you have to be a private developer + + + align:start position:0% +allow you have to be a private developer +you know to access those funds so what + + align:start position:0% +you know to access those funds so what + + + align:start position:0% +you know to access those funds so what +what's what's missing about our ethic + + align:start position:0% +what's what's missing about our ethic + + + align:start position:0% +what's what's missing about our ethic +about how those funds are are invested + + align:start position:0% +about how those funds are are invested + + + align:start position:0% +about how those funds are are invested +in our communities and why isn't that + + align:start position:0% +in our communities and why isn't that + + + align:start position:0% +in our communities and why isn't that +their pre why isn't their preference + + align:start position:0% +their pre why isn't their preference + + + align:start position:0% +their pre why isn't their preference +given for the kinds of group-based + + align:start position:0% +given for the kinds of group-based + + + align:start position:0% +given for the kinds of group-based +locally owned initiatives that we're + + align:start position:0% +locally owned initiatives that we're + + + align:start position:0% +locally owned initiatives that we're +going to be talking about tonight in all + + align:start position:0% +going to be talking about tonight in all + + + align:start position:0% +going to be talking about tonight in all +of the programs throughout all all of + + align:start position:0% +of the programs throughout all all of + + + align:start position:0% +of the programs throughout all all of +the agencies of federal and state local + + align:start position:0% + + + + align:start position:0% + +government as um um the director general + + align:start position:0% +government as um um the director general + + + align:start position:0% +government as um um the director general +of the World Health Health Organization + + align:start position:0% +of the World Health Health Organization + + + align:start position:0% +of the World Health Health Organization +is saying that this is the the challenge + + align:start position:0% +is saying that this is the the challenge + + + align:start position:0% +is saying that this is the the challenge +of the 21st century can we build + + align:start position:0% +of the 21st century can we build + + + align:start position:0% +of the 21st century can we build +sustainable communities uh uh and and + + align:start position:0% +sustainable communities uh uh and and + + + align:start position:0% +sustainable communities uh uh and and +whether or not we can begin to bring + + align:start position:0% +whether or not we can begin to bring + + + align:start position:0% +whether or not we can begin to bring +together the uh um the the the mix of of + + align:start position:0% +together the uh um the the the mix of of + + + align:start position:0% +together the uh um the the the mix of of +forces from uh political to to Vision to + + align:start position:0% +forces from uh political to to Vision to + + + align:start position:0% +forces from uh political to to Vision to +to to to uh uh Financial to and other + + align:start position:0% +to to to uh uh Financial to and other + + + align:start position:0% +to to to uh uh Financial to and other +you know technical assistance and other + + align:start position:0% +you know technical assistance and other + + + align:start position:0% +you know technical assistance and other +to be able to make uh true sustainable + + align:start position:0% +to be able to make uh true sustainable + + + align:start position:0% +to be able to make uh true sustainable +communities happen is is is the question + + align:start position:0% +communities happen is is is the question + + + align:start position:0% +communities happen is is is the question +um you know for this um uh this Century + + align:start position:0% +um you know for this um uh this Century + + + align:start position:0% +um you know for this um uh this Century +you know so + + align:start position:0% +you know so + + + align:start position:0% +you know so +if if if not box is Big Box approach is + + align:start position:0% +if if if not box is Big Box approach is + + + align:start position:0% +if if if not box is Big Box approach is +not the right way then what are the + + align:start position:0% +not the right way then what are the + + + align:start position:0% +not the right way then what are the +kinds of Alternatives that we can begin + + align:start position:0% +kinds of Alternatives that we can begin + + + align:start position:0% +kinds of Alternatives that we can begin +to look at how how can we begin to to + + align:start position:0% +to look at how how can we begin to to + + + align:start position:0% +to look at how how can we begin to to +redevelop communities that are are + + align:start position:0% +redevelop communities that are are + + + align:start position:0% +redevelop communities that are are +struggling to survive um and and we like + + align:start position:0% +struggling to survive um and and we like + + + align:start position:0% +struggling to survive um and and we like +to throw that out and just have first + + align:start position:0% +to throw that out and just have first + + + align:start position:0% +to throw that out and just have first +have a little conversation on it what + + align:start position:0% +have a little conversation on it what + + + align:start position:0% +have a little conversation on it what +what things that either you've seen in + + align:start position:0% +what things that either you've seen in + + + align:start position:0% +what things that either you've seen in +your experience or that U you've thought + + align:start position:0% +your experience or that U you've thought + + + align:start position:0% +your experience or that U you've thought +about that might be ways of how to of + + align:start position:0% +about that might be ways of how to of + + + align:start position:0% +about that might be ways of how to of +attacking some of those uh need uh you + + align:start position:0% +attacking some of those uh need uh you + + + align:start position:0% +attacking some of those uh need uh you +know serious um um issues that that are + + align:start position:0% +know serious um um issues that that are + + + align:start position:0% +know serious um um issues that that are +are are happening in in in urban and + + align:start position:0% +are are happening in in in urban and + + + align:start position:0% +are are happening in in in urban and +rural areas uh um how do we begin to + + align:start position:0% +rural areas uh um how do we begin to + + + align:start position:0% +rural areas uh um how do we begin to +construct some new alternative uh + + align:start position:0% + + + + align:start position:0% + +approaches so if box stores are no + + align:start position:0% +approaches so if box stores are no + + + align:start position:0% +approaches so if box stores are no +what's yes + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +um yeah it's + + align:start position:0% + + + + align:start position:0% + +it's difficult um in the sense that you + + align:start position:0% +it's difficult um in the sense that you + + + align:start position:0% +it's difficult um in the sense that you +know there's so many different ways um + + align:start position:0% +know there's so many different ways um + + + align:start position:0% +know there's so many different ways um +to approach it + + align:start position:0% +to approach it + + + align:start position:0% +to approach it +um you know uh from a microeconomic + + align:start position:0% +um you know uh from a microeconomic + + + align:start position:0% +um you know uh from a microeconomic +macroeconomic perspective you know just + + align:start position:0% +macroeconomic perspective you know just + + + align:start position:0% +macroeconomic perspective you know just +depends on on how you want to approach + + align:start position:0% +depends on on how you want to approach + + + align:start position:0% +depends on on how you want to approach +it um you know obviously you know while + + align:start position:0% +it um you know obviously you know while + + + align:start position:0% +it um you know obviously you know while +we're here you know cooperatives uh um + + align:start position:0% +we're here you know cooperatives uh um + + + align:start position:0% +we're here you know cooperatives uh um +you know small scale Community Based + + align:start position:0% +you know small scale Community Based + + + align:start position:0% +you know small scale Community Based +Industries are an alternative but how do + + align:start position:0% +Industries are an alternative but how do + + + align:start position:0% +Industries are an alternative but how do +you do that you know with the the push + + align:start position:0% +you do that you know with the the push + + + align:start position:0% +you do that you know with the the push +and P factor of you know scale and + + align:start position:0% +and P factor of you know scale and + + + align:start position:0% +and P factor of you know scale and +trying and trying to get bigger um you + + align:start position:0% +trying and trying to get bigger um you + + + align:start position:0% +trying and trying to get bigger um you +know uh we just spent a week down to + + align:start position:0% +know uh we just spent a week down to + + + align:start position:0% +know uh we just spent a week down to +Mississippi just looking at just + + align:start position:0% +Mississippi just looking at just + + + align:start position:0% +Mississippi just looking at just +different development models and things + + align:start position:0% +different development models and things + + + align:start position:0% +different development models and things +that have going on there and um you know + + align:start position:0% +that have going on there and um you know + + + align:start position:0% +that have going on there and um you know +a big problem I think you know this with + + align:start position:0% +a big problem I think you know this with + + + align:start position:0% +a big problem I think you know this with +the situation of you know these huge box + + align:start position:0% +the situation of you know these huge box + + + align:start position:0% +the situation of you know these huge box +uh style of of Industries and + + align:start position:0% +uh style of of Industries and + + + align:start position:0% +uh style of of Industries and +corporations I think you know the + + align:start position:0% +corporations I think you know the + + + align:start position:0% +corporations I think you know the +plantation agriculture system is another + + align:start position:0% +plantation agriculture system is another + + + align:start position:0% +plantation agriculture system is another +box you know a box on land and I think + + align:start position:0% +box you know a box on land and I think + + + align:start position:0% +box you know a box on land and I think +you know it's it's the same issue you + + align:start position:0% +you know it's it's the same issue you + + + align:start position:0% +you know it's it's the same issue you +know there you see small farmers are + + align:start position:0% +know there you see small farmers are + + + align:start position:0% +know there you see small farmers are +just unable to compete unable to survive + + align:start position:0% +just unable to compete unable to survive + + + align:start position:0% +just unable to compete unable to survive +because it's just such just because you + + align:start position:0% +because it's just such just because you + + + align:start position:0% +because it's just such just because you +know the market is so skewed the prices + + align:start position:0% +know the market is so skewed the prices + + + align:start position:0% +know the market is so skewed the prices +are so skewed you know the scale you + + align:start position:0% +are so skewed you know the scale you + + + align:start position:0% +are so skewed you know the scale you +have to reach in order to survive and + + align:start position:0% +have to reach in order to survive and + + + align:start position:0% +have to reach in order to survive and +substit because of just the huge volume + + align:start position:0% +substit because of just the huge volume + + + align:start position:0% +substit because of just the huge volume +that these large Plantation Farms are + + align:start position:0% +that these large Plantation Farms are + + + align:start position:0% +that these large Plantation Farms are +able to are able to uh achieve and so + + align:start position:0% +able to are able to uh achieve and so + + + align:start position:0% +able to are able to uh achieve and so +you know in that sense you know how can + + align:start position:0% +you know in that sense you know how can + + + align:start position:0% +you know in that sense you know how can +you talk about an alternative without + + align:start position:0% +you talk about an alternative without + + + align:start position:0% +you talk about an alternative without +talking about uh Land Reform and placing + + align:start position:0% +talking about uh Land Reform and placing + + + align:start position:0% +talking about uh Land Reform and placing +a cap on the amount of land that can be + + align:start position:0% +a cap on the amount of land that can be + + + align:start position:0% +a cap on the amount of land that can be +formed and and uh acreage uh uh supports + + align:start position:0% +formed and and uh acreage uh uh supports + + + align:start position:0% +formed and and uh acreage uh uh supports +and these types of things so you know + + align:start position:0% +and these types of things so you know + + + align:start position:0% +and these types of things so you know +I'm talking about you know the + + align:start position:0% +I'm talking about you know the + + + align:start position:0% +I'm talking about you know the +Alternatives you know I think you know + + align:start position:0% +Alternatives you know I think you know + + + align:start position:0% +Alternatives you know I think you know +the first thing we have to do is is is + + align:start position:0% +the first thing we have to do is is is + + + align:start position:0% +the first thing we have to do is is is +is think about you know ways of of just + + align:start position:0% +is think about you know ways of of just + + + align:start position:0% +is think about you know ways of of just +Li the growth of these corporations um + + align:start position:0% +Li the growth of these corporations um + + + align:start position:0% +Li the growth of these corporations um +you know to allow alternatives to be + + align:start position:0% +you know to allow alternatives to be + + + align:start position:0% +you know to allow alternatives to be +able to survive it's one thing to be + + align:start position:0% +able to survive it's one thing to be + + + align:start position:0% +able to survive it's one thing to be +able to create a Cooperative to be able + + align:start position:0% +able to create a Cooperative to be able + + + align:start position:0% +able to create a Cooperative to be able +to make it sustainable um you know and + + align:start position:0% +to make it sustainable um you know and + + + align:start position:0% +to make it sustainable um you know and +and keep it going in the face of all the + + align:start position:0% +and keep it going in the face of all the + + + align:start position:0% +and keep it going in the face of all the +pressure from Walmart and Home Depot + + align:start position:0% +pressure from Walmart and Home Depot + + + align:start position:0% +pressure from Walmart and Home Depot +these other + + align:start position:0% +these other + + + align:start position:0% +these other +people and of course you work with + + align:start position:0% +people and of course you work with + + + align:start position:0% +people and of course you work with +um Southern cooperatives + + align:start position:0% +um Southern cooperatives + + + align:start position:0% +um Southern cooperatives +and um you see any possibilities of + + align:start position:0% +and um you see any possibilities of + + + align:start position:0% +and um you see any possibilities of +being able to um you know one of + + align:start position:0% +being able to um you know one of + + + align:start position:0% +being able to um you know one of +problems of you know in this country + + align:start position:0% +problems of you know in this country + + + align:start position:0% +problems of you know in this country +saying a limit on anything you know I + + align:start position:0% +saying a limit on anything you know I + + + align:start position:0% +saying a limit on anything you know I +mean it's a you know it's a tough sell + + align:start position:0% +mean it's a you know it's a tough sell + + + align:start position:0% +mean it's a you know it's a tough sell +but what about U um + + align:start position:0% +but what about U um + + + align:start position:0% +but what about U um +uh is um um have you seen uh some + + align:start position:0% +uh is um um have you seen uh some + + + align:start position:0% +uh is um um have you seen uh some +successes in being able to to get uh um + + align:start position:0% +successes in being able to to get uh um + + + align:start position:0% +successes in being able to to get uh um +consumers to support uh locally grown + + align:start position:0% +consumers to support uh locally grown + + + align:start position:0% +consumers to support uh locally grown +Cooper or you know uh uh uh produce um + + align:start position:0% +Cooper or you know uh uh uh produce um + + + align:start position:0% +Cooper or you know uh uh uh produce um +being able to support U activities that + + align:start position:0% +being able to support U activities that + + + align:start position:0% +being able to support U activities that +that that would support their neighbors + + align:start position:0% +that that would support their neighbors + + + align:start position:0% +that that would support their neighbors +um uh kinds of entrepreneur activity um + + align:start position:0% +um uh kinds of entrepreneur activity um + + + align:start position:0% +um uh kinds of entrepreneur activity um +yeah definitely um and uh you know we + + align:start position:0% +yeah definitely um and uh you know we + + + align:start position:0% +yeah definitely um and uh you know we +were working you know primarily in the + + align:start position:0% +were working you know primarily in the + + + align:start position:0% +were working you know primarily in the +something in Green County um in West + + align:start position:0% +something in Green County um in West + + + align:start position:0% +something in Green County um in West +Alabama and you know uh it took us it + + align:start position:0% +Alabama and you know uh it took us it + + + align:start position:0% +Alabama and you know uh it took us it +took us a long time and it was actually + + align:start position:0% +took us a long time and it was actually + + + align:start position:0% +took us a long time and it was actually +the first time these Farmers had ever + + align:start position:0% +the first time these Farmers had ever + + + align:start position:0% +the first time these Farmers had ever +come together and do it and did it but + + align:start position:0% +come together and do it and did it but + + + align:start position:0% +come together and do it and did it but +we put together a farmers market between + + align:start position:0% +we put together a farmers market between + + + align:start position:0% +we put together a farmers market between +something and green conter like right on + + align:start position:0% +something and green conter like right on + + + align:start position:0% +something and green conter like right on +the border between these two it's the + + align:start position:0% +the border between these two it's the + + + align:start position:0% +the border between these two it's the +first time they ever been able to get + + align:start position:0% +first time they ever been able to get + + + align:start position:0% +first time they ever been able to get +together and actually coordinate + + align:start position:0% +together and actually coordinate + + + align:start position:0% +together and actually coordinate +themselves and do a Fess market and you + + align:start position:0% +themselves and do a Fess market and you + + + align:start position:0% +themselves and do a Fess market and you +know the success of it was was largely + + align:start position:0% +know the success of it was was largely + + + align:start position:0% +know the success of it was was largely +due to the fact that the closest grocery + + align:start position:0% +due to the fact that the closest grocery + + + align:start position:0% +due to the fact that the closest grocery +store for many people you know coming + + align:start position:0% +store for many people you know coming + + + align:start position:0% +store for many people you know coming +out of these rural areas me very rural + + align:start position:0% +out of these rural areas me very rural + + + align:start position:0% +out of these rural areas me very rural +you know with this 35 40 minutes drive + + align:start position:0% +you know with this 35 40 minutes drive + + + align:start position:0% +you know with this 35 40 minutes drive +away to just just to get to the postest + + align:start position:0% +away to just just to get to the postest + + + align:start position:0% +away to just just to get to the postest +grocery store and um and the prices were + + align:start position:0% +grocery store and um and the prices were + + + align:start position:0% +grocery store and um and the prices were +very high many people would go down to + + align:start position:0% +very high many people would go down to + + + align:start position:0% +very high many people would go down to +Meridian and go to Walmart where the + + align:start position:0% +Meridian and go to Walmart where the + + + align:start position:0% +Meridian and go to Walmart where the +prices were a lot cheaper and so you + + align:start position:0% +prices were a lot cheaper and so you + + + align:start position:0% +prices were a lot cheaper and so you +know just to have this this this this + + align:start position:0% +know just to have this this this this + + + align:start position:0% +know just to have this this this this +Farm's Market set up for people you know + + align:start position:0% +Farm's Market set up for people you know + + + align:start position:0% +Farm's Market set up for people you know +and they were able to get produce from + + align:start position:0% +and they were able to get produce from + + + align:start position:0% +and they were able to get produce from +people who they knew um so you know I + + align:start position:0% +people who they knew um so you know I + + + align:start position:0% +people who they knew um so you know I +mean you know there's definitely you + + align:start position:0% +mean you know there's definitely you + + + align:start position:0% +mean you know there's definitely you +know those types of opportunities you + + align:start position:0% +know those types of opportunities you + + + align:start position:0% +know those types of opportunities you +know are there um and I think you know + + align:start position:0% +know are there um and I think you know + + + align:start position:0% +know are there um and I think you know +the one thing that saved them from + + align:start position:0% +the one thing that saved them from + + + align:start position:0% +the one thing that saved them from +Walmart is the fact they rule that it + + align:start position:0% +Walmart is the fact they rule that it + + + align:start position:0% +Walmart is the fact they rule that it +just wasn't a large enough market for a + + align:start position:0% +just wasn't a large enough market for a + + + align:start position:0% +just wasn't a large enough market for a +huge Walmart to be able to even consider + + align:start position:0% +huge Walmart to be able to even consider + + + align:start position:0% +huge Walmart to be able to even consider +coming in there or grocer stor to even + + align:start position:0% +coming in there or grocer stor to even + + + align:start position:0% +coming in there or grocer stor to even +consider coming in there because it was + + align:start position:0% +consider coming in there because it was + + + align:start position:0% +consider coming in there because it was +just so isolated and so little in that + + align:start position:0% +just so isolated and so little in that + + + align:start position:0% +just so isolated and so little in that +region so that type of thing you know we + + align:start position:0% +region so that type of thing you know we + + + align:start position:0% +region so that type of thing you know we +were able to set + + align:start position:0% + + + + align:start position:0% + +up have thoughts about how do you know + + align:start position:0% +up have thoughts about how do you know + + + align:start position:0% +up have thoughts about how do you know +when you got a yes you know what are the + + align:start position:0% +when you got a yes you know what are the + + + align:start position:0% +when you got a yes you know what are the +things that we could say yes to I just + + align:start position:0% +things that we could say yes to I just + + + align:start position:0% +things that we could say yes to I just +think about organizing the community is + + align:start position:0% +think about organizing the community is + + + align:start position:0% +think about organizing the community is +first thing I think about in terms of an + + align:start position:0% +first thing I think about in terms of an + + + align:start position:0% +first thing I think about in terms of an +alternative because at the end of the + + align:start position:0% +alternative because at the end of the + + + align:start position:0% +alternative because at the end of the +day the community is their money that + + align:start position:0% +day the community is their money that + + + align:start position:0% +day the community is their money that +they're spending in the store and at the + + align:start position:0% +they're spending in the store and at the + + + align:start position:0% +they're spending in the store and at the +end of the day it's their families that + + align:start position:0% +end of the day it's their families that + + + align:start position:0% +end of the day it's their families that +you know are losing their jobs + + align:start position:0% +you know are losing their jobs + + + align:start position:0% +you know are losing their jobs +and um not having a community need + + align:start position:0% +and um not having a community need + + + align:start position:0% +and um not having a community need +served by you know the big box so + + align:start position:0% +served by you know the big box so + + + align:start position:0% +served by you know the big box so +whatever the alternative is going to be + + align:start position:0% +whatever the alternative is going to be + + + align:start position:0% +whatever the alternative is going to be +it seems to me will be successful or not + + align:start position:0% +it seems to me will be successful or not + + + align:start position:0% +it seems to me will be successful or not +depending on what the community does + + align:start position:0% +depending on what the community does + + + align:start position:0% +depending on what the community does +but most + + align:start position:0% +but most + + + align:start position:0% +but most +communities of course and not don't + + align:start position:0% +communities of course and not don't + + + align:start position:0% +communities of course and not don't +aren't organized to think that way and + + align:start position:0% +aren't organized to think that way and + + + align:start position:0% +aren't organized to think that way and +even if they are organized they don't + + align:start position:0% +even if they are organized they don't + + + align:start position:0% +even if they are organized they don't +often think in terms of + + align:start position:0% +often think in terms of + + + align:start position:0% +often think in terms of +economics I think organizing combined + + align:start position:0% +economics I think organizing combined + + + align:start position:0% +economics I think organizing combined +with asset building with family based + + align:start position:0% +with asset building with family based + + + align:start position:0% +with asset building with family based +asset building so that people are + + align:start position:0% +asset building so that people are + + + align:start position:0% +asset building so that people are +generating the sort of capital they + + align:start position:0% +generating the sort of capital they + + + align:start position:0% +generating the sort of capital they +would need in order to start their small + + align:start position:0% +would need in order to start their small + + + align:start position:0% +would need in order to start their small +businesses including you know loc um + + align:start position:0% +businesses including you know loc um + + + align:start position:0% +businesses including you know loc um +alternatives + + align:start position:0% + + + + align:start position:0% + +can you hit the um the function again so + + align:start position:0% +can you hit the um the function again so + + + align:start position:0% +can you hit the um the function again so +that it comes up here so we can see + + align:start position:0% + + + + align:start position:0% + +it then we won't be straining our + + align:start position:0% + + + + align:start position:0% + +next + + align:start position:0% +next + + + align:start position:0% +next +that's so much so um sustain communities + + align:start position:0% +that's so much so um sustain communities + + + align:start position:0% +that's so much so um sustain communities +are sustainable when they meet the needs + + align:start position:0% +are sustainable when they meet the needs + + + align:start position:0% +are sustainable when they meet the needs +of the present generation without + + align:start position:0% +of the present generation without + + + align:start position:0% +of the present generation without +compromising the needs of the future one + + align:start position:0% +compromising the needs of the future one + + + align:start position:0% +compromising the needs of the future one +so that's one of the criteria that we're + + align:start position:0% +so that's one of the criteria that we're + + + align:start position:0% +so that's one of the criteria that we're +we're thinking about and um when their + + align:start position:0% +we're thinking about and um when their + + + align:start position:0% +we're thinking about and um when their +members maintain or increase the + + align:start position:0% +members maintain or increase the + + + align:start position:0% +members maintain or increase the +community's resources over time um right + + align:start position:0% +community's resources over time um right + + + align:start position:0% +community's resources over time um right +along with what you were saying and um + + align:start position:0% +along with what you were saying and um + + + align:start position:0% +along with what you were saying and um +the the we're looking at three different + + align:start position:0% +the the we're looking at three different + + + align:start position:0% +the the we're looking at three different +ways that these locally owned + + align:start position:0% +ways that these locally owned + + + align:start position:0% +ways that these locally owned +group-based businesses build sustainable + + align:start position:0% +group-based businesses build sustainable + + + align:start position:0% +group-based businesses build sustainable +communities one is economically with the + + align:start position:0% +communities one is economically with the + + + align:start position:0% +communities one is economically with the +local ownership and control um they they + + align:start position:0% +local ownership and control um they they + + + align:start position:0% +local ownership and control um they they +focus the businesses that they're in in + + align:start position:0% +focus the businesses that they're in in + + + align:start position:0% +focus the businesses that they're in in +on what the community + + align:start position:0% +on what the community + + + align:start position:0% +on what the community +needs they provide jobs and resources + + align:start position:0% +needs they provide jobs and resources + + + align:start position:0% +needs they provide jobs and resources +and profits that actually stay in the + + align:start position:0% +and profits that actually stay in the + + + align:start position:0% +and profits that actually stay in the +community because people in the + + align:start position:0% +community because people in the + + + align:start position:0% +community because people in the +community don't send their stuff away + + align:start position:0% +community don't send their stuff away + + + align:start position:0% +community don't send their stuff away +they don't say oh we don't want to work + + align:start position:0% +they don't say oh we don't want to work + + + align:start position:0% +they don't say oh we don't want to work +in our Factory anymore we want someone + + align:start position:0% +in our Factory anymore we want someone + + + align:start position:0% +in our Factory anymore we want someone +you know from another country to work in + + align:start position:0% +you know from another country to work in + + + align:start position:0% +you know from another country to work in +our Factory and let's give up our own + + align:start position:0% +our Factory and let's give up our own + + + align:start position:0% +our Factory and let's give up our own +jobs so um it's a way of rooting Assets + + align:start position:0% +jobs so um it's a way of rooting Assets + + + align:start position:0% +jobs so um it's a way of rooting Assets +in the community and it also increases + + align:start position:0% +in the community and it also increases + + + align:start position:0% +in the community and it also increases +economic self-sufficiency and security + + align:start position:0% +economic self-sufficiency and security + + + align:start position:0% +economic self-sufficiency and security +and your point earlier is that it builds + + align:start position:0% +and your point earlier is that it builds + + + align:start position:0% +and your point earlier is that it builds +the community's assets that we we're + + align:start position:0% +the community's assets that we we're + + + align:start position:0% +the community's assets that we we're +taking on things um that might have been + + align:start position:0% +taking on things um that might have been + + + align:start position:0% +taking on things um that might have been +a a problem turning a a a vacant lot and + + align:start position:0% +a a problem turning a a a vacant lot and + + + align:start position:0% +a a problem turning a a a vacant lot and +then turning it into a a positive asset + + align:start position:0% +then turning it into a a positive asset + + + align:start position:0% +then turning it into a a positive asset +that produces wealth and and and + + align:start position:0% +that produces wealth and and and + + + align:start position:0% +that produces wealth and and and +empowers the community so we we work + + align:start position:0% +empowers the community so we we work + + + align:start position:0% +empowers the community so we we work +with a lot of locally owned group-based + + align:start position:0% +with a lot of locally owned group-based + + + align:start position:0% +with a lot of locally owned group-based +businesses that also promote + + align:start position:0% +businesses that also promote + + + align:start position:0% +businesses that also promote +sustainability because you people don't + + align:start position:0% +sustainability because you people don't + + + align:start position:0% +sustainability because you people don't +foul their own nest quite as easily as + + align:start position:0% +foul their own nest quite as easily as + + + align:start position:0% +foul their own nest quite as easily as +they'll foul somebody else's so if + + align:start position:0% +they'll foul somebody else's so if + + + align:start position:0% +they'll foul somebody else's so if +you're in there you're less likely to + + align:start position:0% +you're in there you're less likely to + + + align:start position:0% +you're in there you're less likely to +pollute your water supply and your Air + + align:start position:0% +pollute your water supply and your Air + + + align:start position:0% +pollute your water supply and your Air +Supply cuz you know your kids and their + + align:start position:0% +Supply cuz you know your kids and their + + + align:start position:0% +Supply cuz you know your kids and their +kids are going to be needing that that + + align:start position:0% +kids are going to be needing that that + + + align:start position:0% +kids are going to be needing that that +um we work with um a lot of groups who + + align:start position:0% +um we work with um a lot of groups who + + + align:start position:0% +um we work with um a lot of groups who +have who work in uh sustainable food and + + align:start position:0% +have who work in uh sustainable food and + + + align:start position:0% +have who work in uh sustainable food and +sustainable agric um sustainable energy + + align:start position:0% +sustainable agric um sustainable energy + + + align:start position:0% +sustainable agric um sustainable energy +and uh the uh food cooperatives were the + + align:start position:0% +and uh the uh food cooperatives were the + + + align:start position:0% +and uh the uh food cooperatives were the +first that pioneered and opened up the + + align:start position:0% +first that pioneered and opened up the + + + align:start position:0% +first that pioneered and opened up the +organic food market uh the energy cops + + align:start position:0% +organic food market uh the energy cops + + + align:start position:0% +organic food market uh the energy cops +that were working with they really + + align:start position:0% +that were working with they really + + + align:start position:0% +that were working with they really +pioneering and open up opening up the + + align:start position:0% +pioneering and open up opening up the + + + align:start position:0% +pioneering and open up opening up the +market for sustainable energy products + + align:start position:0% +market for sustainable energy products + + + align:start position:0% +market for sustainable energy products +and services so um these kinds of + + align:start position:0% +and services so um these kinds of + + + align:start position:0% +and services so um these kinds of +group-based businesses are willing to go + + align:start position:0% +group-based businesses are willing to go + + + align:start position:0% +group-based businesses are willing to go +into places that you can't make a big + + align:start position:0% +into places that you can't make a big + + + align:start position:0% +into places that you can't make a big +profit on uh it least initially and to + + align:start position:0% +profit on uh it least initially and to + + + align:start position:0% +profit on uh it least initially and to +help consumers understand why it's in + + align:start position:0% +help consumers understand why it's in + + + align:start position:0% +help consumers understand why it's in +their best interest to care about these + + align:start position:0% +their best interest to care about these + + + align:start position:0% +their best interest to care about these +things and to change their consumption + + align:start position:0% +things and to change their consumption + + + align:start position:0% +things and to change their consumption +patterns in order to keep their + + align:start position:0% +patterns in order to keep their + + + align:start position:0% +patterns in order to keep their +environment um safer and wher and better + + align:start position:0% +environment um safer and wher and better + + + align:start position:0% +environment um safer and wher and better +for their + + align:start position:0% + + + + align:start position:0% + +children and then this also increases + + align:start position:0% +children and then this also increases + + + align:start position:0% +children and then this also increases +the social sustainability I mean that + + align:start position:0% +the social sustainability I mean that + + + align:start position:0% +the social sustainability I mean that +also that even important asset of of + + align:start position:0% +also that even important asset of of + + + align:start position:0% +also that even important asset of of +developing their leadership skills their + + align:start position:0% +developing their leadership skills their + + + align:start position:0% +developing their leadership skills their +ability to to uh decide what to Vision + + align:start position:0% +ability to to uh decide what to Vision + + + align:start position:0% +ability to to uh decide what to Vision +to to plan together to work out + + align:start position:0% +to to plan together to work out + + + align:start position:0% +to to plan together to work out +differences to to to be able to to uh uh + + align:start position:0% +differences to to to be able to to uh uh + + + align:start position:0% +differences to to to be able to to uh uh +um develop those skills sets to to um + + align:start position:0% +um develop those skills sets to to um + + + align:start position:0% +um develop those skills sets to to um +move us a a um a um a community forward + + align:start position:0% +move us a a um a um a community forward + + + align:start position:0% +move us a a um a um a community forward +to deal with all the different + + align:start position:0% +to deal with all the different + + + align:start position:0% +to deal with all the different +stakeholders that they need to deal with + + align:start position:0% +stakeholders that they need to deal with + + + align:start position:0% +stakeholders that they need to deal with +in order to bring them together and move + + align:start position:0% +in order to bring them together and move + + + align:start position:0% +in order to bring them together and move +them in in one common Direction and uh + + align:start position:0% +them in in one common Direction and uh + + + align:start position:0% +them in in one common Direction and uh +and to me some times that's some of the + + align:start position:0% +and to me some times that's some of the + + + align:start position:0% +and to me some times that's some of the +most exciting things that that happens + + align:start position:0% +most exciting things that that happens + + + align:start position:0% +most exciting things that that happens +in a Cooperative way you know whether + + align:start position:0% +in a Cooperative way you know whether + + + align:start position:0% +in a Cooperative way you know whether +it's a a Cooperative working with a food + + align:start position:0% +it's a a Cooperative working with a food + + + align:start position:0% +it's a a Cooperative working with a food +Cooperative in Brooklyn or or you know + + align:start position:0% +Cooperative in Brooklyn or or you know + + + align:start position:0% +Cooperative in Brooklyn or or you know +in Urban a and and and buffalo when you + + align:start position:0% +in Urban a and and and buffalo when you + + + align:start position:0% +in Urban a and and and buffalo when you +see ordinary folks many times that have + + align:start position:0% +see ordinary folks many times that have + + + align:start position:0% +see ordinary folks many times that have +just been left out of so many different + + align:start position:0% +just been left out of so many different + + + align:start position:0% +just been left out of so many different +things not having the educational + + align:start position:0% +things not having the educational + + + align:start position:0% +things not having the educational +training not having the uh uh sense that + + align:start position:0% +training not having the uh uh sense that + + + align:start position:0% +training not having the uh uh sense that +they can make a difference and and just + + align:start position:0% +they can make a difference and and just + + + align:start position:0% +they can make a difference and and just +seeing them just Blossom you know in a + + align:start position:0% +seeing them just Blossom you know in a + + + align:start position:0% +seeing them just Blossom you know in a +in a period of months when you when that + + align:start position:0% +in a period of months when you when that + + + align:start position:0% +in a period of months when you when that +person gets moved into leadership + + align:start position:0% +person gets moved into leadership + + + align:start position:0% +person gets moved into leadership +positions and you know they're learning + + align:start position:0% +positions and you know they're learning + + + align:start position:0% +positions and you know they're learning +how to you know to read spreadsheets and + + align:start position:0% +how to you know to read spreadsheets and + + + align:start position:0% +how to you know to read spreadsheets and +uh you know and and understand balance + + align:start position:0% +uh you know and and understand balance + + + align:start position:0% +uh you know and and understand balance +sheets and you know and and figuring out + + align:start position:0% +sheets and you know and and figuring out + + + align:start position:0% +sheets and you know and and figuring out +and planning U you know and doing + + align:start position:0% +and planning U you know and doing + + + align:start position:0% +and planning U you know and doing +strategic planning you know things that + + align:start position:0% +strategic planning you know things that + + + align:start position:0% +strategic planning you know things that +they thought you know was a whole + + align:start position:0% +they thought you know was a whole + + + align:start position:0% +they thought you know was a whole +another group of people you know was + + align:start position:0% +another group of people you know was + + + align:start position:0% +another group of people you know was +their Province you know but then saying + + align:start position:0% +their Province you know but then saying + + + align:start position:0% +their Province you know but then saying +that that there's no mystery to it that + + align:start position:0% +that that there's no mystery to it that + + + align:start position:0% +that that there's no mystery to it that +and that they they can learn those + + align:start position:0% +and that they they can learn those + + + align:start position:0% +and that they they can learn those +things too if they work at it and you + + align:start position:0% +things too if they work at it and you + + + align:start position:0% +things too if they work at it and you +know in particularly when they provided + + align:start position:0% +know in particularly when they provided + + + align:start position:0% +know in particularly when they provided +the the proper support so uh to me I + + align:start position:0% +the the proper support so uh to me I + + + align:start position:0% +the the proper support so uh to me I +think that's one of the the great things + + align:start position:0% +think that's one of the the great things + + + align:start position:0% +think that's one of the the great things +even when they um to me even when they + + align:start position:0% +even when they um to me even when they + + + align:start position:0% +even when they um to me even when they +when we're not able to keep it + + align:start position:0% +when we're not able to keep it + + + align:start position:0% +when we're not able to keep it +sustainable and when a a Cooperative is + + align:start position:0% +sustainable and when a a Cooperative is + + + align:start position:0% +sustainable and when a a Cooperative is +in their area and then and then dies the + + align:start position:0% +in their area and then and then dies the + + + align:start position:0% +in their area and then and then dies the +uh the results of it always remain I + + align:start position:0% +uh the results of it always remain I + + + align:start position:0% +uh the results of it always remain I +mean you know I've gone back into + + align:start position:0% +mean you know I've gone back into + + + align:start position:0% +mean you know I've gone back into +Brooklyn and you know and I used to do a + + align:start position:0% +Brooklyn and you know and I used to do a + + + align:start position:0% +Brooklyn and you know and I used to do a +lot of um U um uh co-op housing + + align:start position:0% +lot of um U um uh co-op housing + + + align:start position:0% +lot of um U um uh co-op housing +organizing and and Crown Heights you + + align:start position:0% +organizing and and Crown Heights you + + + align:start position:0% +organizing and and Crown Heights you +know and when you just run into folks + + align:start position:0% +know and when you just run into folks + + + align:start position:0% +know and when you just run into folks +even if the place is not even the same + + align:start position:0% +even if the place is not even the same + + + align:start position:0% +even if the place is not even the same +anymore I mean just that that person is + + align:start position:0% +anymore I mean just that that person is + + + align:start position:0% +anymore I mean just that that person is +you know has been changed they're a new + + align:start position:0% +you know has been changed they're a new + + + align:start position:0% +you know has been changed they're a new +person they they they understand their + + align:start position:0% +person they they they understand their + + + align:start position:0% +person they they they understand their +own power and and they cared into all + + align:start position:0% +own power and and they cared into all + + + align:start position:0% +own power and and they cared into all +aspects of their life they get active on + + align:start position:0% +aspects of their life they get active on + + + align:start position:0% +aspects of their life they get active on +the job they get active you know in + + align:start position:0% +the job they get active you know in + + + align:start position:0% +the job they get active you know in +their Church they get active in + + align:start position:0% +their Church they get active in + + + align:start position:0% +their Church they get active in +politically you know it it it it carries + + align:start position:0% +politically you know it it it it carries + + + align:start position:0% +politically you know it it it it carries +over and so so that's I think one of the + + align:start position:0% +over and so so that's I think one of the + + + align:start position:0% +over and so so that's I think one of the +great powers of of that that U that's + + align:start position:0% +great powers of of that that U that's + + + align:start position:0% +great powers of of that that U that's +setting up group-based businesses + + align:start position:0% +setting up group-based businesses + + + align:start position:0% +setting up group-based businesses +changes the the landscape by changing + + align:start position:0% +changes the the landscape by changing + + + align:start position:0% +changes the the landscape by changing +the people I told you earlier that a lot + + align:start position:0% +the people I told you earlier that a lot + + + align:start position:0% +the people I told you earlier that a lot +of conversations I have with Municipal + + align:start position:0% +of conversations I have with Municipal + + + align:start position:0% +of conversations I have with Municipal +leaders about cooperatives they say well + + align:start position:0% +leaders about cooperatives they say well + + + align:start position:0% +leaders about cooperatives they say well +the you know box door development is the + + align:start position:0% +the you know box door development is the + + + align:start position:0% +the you know box door development is the +only one they know of and then we talk + + align:start position:0% +only one they know of and then we talk + + + align:start position:0% +only one they know of and then we talk +about Co-op development or other + + align:start position:0% +about Co-op development or other + + + align:start position:0% +about Co-op development or other +group-based business development they + + align:start position:0% +group-based business development they + + + align:start position:0% +group-based business development they +they say well that's really great + + align:start position:0% +they say well that's really great + + + align:start position:0% +they say well that's really great +sometimes I have people say we tried it + + align:start position:0% +sometimes I have people say we tried it + + + align:start position:0% +sometimes I have people say we tried it +yeah for + + align:start position:0% +yeah for + + + align:start position:0% +yeah for +you you know it was a disaster all these + + align:start position:0% +you you know it was a disaster all these + + + align:start position:0% +you you know it was a disaster all these +people were fighting nobody could manage + + align:start position:0% +people were fighting nobody could manage + + + align:start position:0% +people were fighting nobody could manage +the meetings it was you know and we + + align:start position:0% +the meetings it was you know and we + + + align:start position:0% +the meetings it was you know and we +won't ever do it again and so I talk + + align:start position:0% +won't ever do it again and so I talk + + + align:start position:0% +won't ever do it again and so I talk +with you know people in cdc's and and + + align:start position:0% +with you know people in cdc's and and + + + align:start position:0% +with you know people in cdc's and and +and I understand that you know it's it's + + align:start position:0% +and I understand that you know it's it's + + + align:start position:0% +and I understand that you know it's it's +it's it's easier to say to you know you + + align:start position:0% +it's it's easier to say to you know you + + + align:start position:0% +it's it's easier to say to you know you +you got an idea for a restaurant great + + align:start position:0% +you got an idea for a restaurant great + + + align:start position:0% +you got an idea for a restaurant great +I'll help you write your business plan + + align:start position:0% +I'll help you write your business plan + + + align:start position:0% +I'll help you write your business plan +and get you the money and then you can + + align:start position:0% +and get you the money and then you can + + + align:start position:0% +and get you the money and then you can +go out and start your business it's it's + + align:start position:0% +go out and start your business it's it's + + + align:start position:0% +go out and start your business it's it's +a simpler um equation but it's um it's + + align:start position:0% +a simpler um equation but it's um it's + + + align:start position:0% +a simpler um equation but it's um it's +also very thin um it only that + + align:start position:0% +also very thin um it only that + + + align:start position:0% +also very thin um it only that +restaurant will only be there with you + + align:start position:0% +restaurant will only be there with you + + + align:start position:0% +restaurant will only be there with you +as the owner while you're there in the + + align:start position:0% +as the owner while you're there in the + + + align:start position:0% +as the owner while you're there in the +community and while you're healthy and + + align:start position:0% +community and while you're healthy and + + + align:start position:0% +community and while you're healthy and +you know it's it's uh when you have a + + align:start position:0% +you know it's it's uh when you have a + + + align:start position:0% +you know it's it's uh when you have a +group of people you can also have a lot + + align:start position:0% +group of people you can also have a lot + + + align:start position:0% +group of people you can also have a lot +of great ideas and a lot of support and + + align:start position:0% +of great ideas and a lot of support and + + + align:start position:0% +of great ideas and a lot of support and +so sometimes group-based businesses take + + align:start position:0% +so sometimes group-based businesses take + + + align:start position:0% +so sometimes group-based businesses take +a little longer um and if people are + + align:start position:0% +a little longer um and if people are + + + align:start position:0% +a little longer um and if people are +trying to help start group Bas based + + align:start position:0% +trying to help start group Bas based + + + align:start position:0% +trying to help start group Bas based +businesses without all the pieces to do + + align:start position:0% +businesses without all the pieces to do + + + align:start position:0% +businesses without all the pieces to do +it there's kind of a technology to it + + align:start position:0% +it there's kind of a technology to it + + + align:start position:0% +it there's kind of a technology to it +you know managing these groups and um + + align:start position:0% +you know managing these groups and um + + + align:start position:0% +you know managing these groups and um +you you can't just because you've helped + + align:start position:0% +you you can't just because you've helped + + + align:start position:0% +you you can't just because you've helped +start entrepreneurs single entrepreneurs + + align:start position:0% +start entrepreneurs single entrepreneurs + + + align:start position:0% +start entrepreneurs single entrepreneurs +start a restaurant that doesn't mean + + align:start position:0% +start a restaurant that doesn't mean + + + align:start position:0% +start a restaurant that doesn't mean +that you have all the skills it takes to + + align:start position:0% +that you have all the skills it takes to + + + align:start position:0% +that you have all the skills it takes to +help a group of people start a + + align:start position:0% +help a group of people start a + + + align:start position:0% +help a group of people start a +group-based business um there's there's + + align:start position:0% +group-based business um there's there's + + + align:start position:0% +group-based business um there's there's +this added dimension of the whole group + + align:start position:0% +this added dimension of the whole group + + + align:start position:0% +this added dimension of the whole group +process and all of these skills that you + + align:start position:0% +process and all of these skills that you + + + align:start position:0% +process and all of these skills that you +know that are listed here and um what + + align:start position:0% +know that are listed here and um what + + + align:start position:0% +know that are listed here and um what +you get is a different you get a + + align:start position:0% +you get is a different you get a + + + align:start position:0% +you get is a different you get a +different result it has a different + + align:start position:0% +different result it has a different + + + align:start position:0% +different result it has a different +value in the community it it I don't + + align:start position:0% +value in the community it it I don't + + + align:start position:0% +value in the community it it I don't +think it replace is single entrepreneurs + + align:start position:0% +think it replace is single entrepreneurs + + + align:start position:0% +think it replace is single entrepreneurs +at all you know I think it's a good + + align:start position:0% +at all you know I think it's a good + + + align:start position:0% +at all you know I think it's a good +compliment too but um for all the folks + + align:start position:0% +compliment too but um for all the folks + + + align:start position:0% +compliment too but um for all the folks +you know doing Economic Development who + + align:start position:0% +you know doing Economic Development who + + + align:start position:0% +you know doing Economic Development who +said I give up it's way too hard you + + align:start position:0% +said I give up it's way too hard you + + + align:start position:0% +said I give up it's way too hard you +know what they really need is another + + align:start position:0% +know what they really need is another + + + align:start position:0% +know what they really need is another +partner in there to help manage that + + align:start position:0% +partner in there to help manage that + + + align:start position:0% +partner in there to help manage that +group process and there's technology for + + align:start position:0% +group process and there's technology for + + + align:start position:0% +group process and there's technology for +doing that just like there's business + + align:start position:0% +doing that just like there's business + + + align:start position:0% +doing that just like there's business +plans and you know governance systems + + align:start position:0% +plans and you know governance systems + + + align:start position:0% +plans and you know governance systems +for Boards of directors you know it's + + align:start position:0% +for Boards of directors you know it's + + + align:start position:0% +for Boards of directors you know it's +like there's pieces that and you just + + align:start position:0% +like there's pieces that and you just + + + align:start position:0% +like there's pieces that and you just +need all the pieces + + align:start position:0% +need all the pieces + + + align:start position:0% +need all the pieces +um and uh speaking of of the pieces um + + align:start position:0% +um and uh speaking of of the pieces um + + + align:start position:0% +um and uh speaking of of the pieces um +in order to start a group-based business + + align:start position:0% +in order to start a group-based business + + + align:start position:0% +in order to start a group-based business +you need these five things you need to + + align:start position:0% +you need these five things you need to + + + align:start position:0% +you need these five things you need to +have a community organizing effort so + + align:start position:0% +have a community organizing effort so + + + align:start position:0% +have a community organizing effort so +that people in the community understand + + align:start position:0% +that people in the community understand + + + align:start position:0% +that people in the community understand +why they want this locally rooted + + align:start position:0% +why they want this locally rooted + + + align:start position:0% +why they want this locally rooted +group-based business in their Community + + align:start position:0% +group-based business in their Community + + + align:start position:0% +group-based business in their Community +um and um and and a preferably a + + align:start position:0% +um and um and and a preferably a + + + align:start position:0% +um and um and and a preferably a +planning process a participatory + + align:start position:0% +planning process a participatory + + + align:start position:0% +planning process a participatory +planning process where people have + + align:start position:0% +planning process where people have + + + align:start position:0% +planning process where people have +identified the businesses that they need + + align:start position:0% +identified the businesses that they need + + + align:start position:0% +identified the businesses that they need +and which ones of them are best to have + + align:start position:0% +and which ones of them are best to have + + + align:start position:0% +and which ones of them are best to have +as group-based businesses and where + + align:start position:0% +as group-based businesses and where + + + align:start position:0% +as group-based businesses and where +where where you want to invest Community + + align:start position:0% +where where you want to invest Community + + + align:start position:0% +where where you want to invest Community +Resources into that development process + + align:start position:0% +Resources into that development process + + + align:start position:0% +Resources into that development process +the second is replicable business + + align:start position:0% +the second is replicable business + + + align:start position:0% +the second is replicable business +models it's really good to have + + align:start position:0% +models it's really good to have + + + align:start position:0% +models it's really good to have +something you know works and there are a + + align:start position:0% +something you know works and there are a + + + align:start position:0% +something you know works and there are a +lot of things that work lots and lots + + align:start position:0% +lot of things that work lots and lots + + + align:start position:0% +lot of things that work lots and lots +and lots of things that work um another + + align:start position:0% +and lots of things that work um another + + + align:start position:0% +and lots of things that work um another +the next thing is technical assistance + + align:start position:0% +the next thing is technical assistance + + + align:start position:0% +the next thing is technical assistance +um someone who knows how to go through + + align:start position:0% +um someone who knows how to go through + + + align:start position:0% +um someone who knows how to go through +this process and the technical + + align:start position:0% +this process and the technical + + + align:start position:0% +this process and the technical +assistance includes all of that group + + align:start position:0% +assistance includes all of that group + + + align:start position:0% +assistance includes all of that group +facilitation we were just talking about + + align:start position:0% +facilitation we were just talking about + + + align:start position:0% +facilitation we were just talking about +a second ago as well as the business + + align:start position:0% +a second ago as well as the business + + + align:start position:0% +a second ago as well as the business +planning as well as the financial + + align:start position:0% +planning as well as the financial + + + align:start position:0% +planning as well as the financial +analysis skills um you know the whole + + align:start position:0% +analysis skills um you know the whole + + + align:start position:0% +analysis skills um you know the whole +range of what it's Personnel development + + align:start position:0% +range of what it's Personnel development + + + align:start position:0% +range of what it's Personnel development +everything you need to start a business + + align:start position:0% +everything you need to start a business + + + align:start position:0% +everything you need to start a business +it's really important to have technical + + align:start position:0% +it's really important to have technical + + + align:start position:0% +it's really important to have technical +assistance from people who've been + + align:start position:0% +assistance from people who've been + + + align:start position:0% +assistance from people who've been +engaged in startup businesses before um + + align:start position:0% +engaged in startup businesses before um + + + align:start position:0% +engaged in startup businesses before um +to just kind of go out there and expect + + align:start position:0% +to just kind of go out there and expect + + + align:start position:0% +to just kind of go out there and expect +yourself to be able to recreate all of + + align:start position:0% +yourself to be able to recreate all of + + + align:start position:0% +yourself to be able to recreate all of +those Wheels I think is is + + align:start position:0% +those Wheels I think is is + + + align:start position:0% +those Wheels I think is is +um it's any one of these pieces you + + align:start position:0% +um it's any one of these pieces you + + + align:start position:0% +um it's any one of these pieces you +don't have every one of these pieces it + + align:start position:0% +don't have every one of these pieces it + + + align:start position:0% +don't have every one of these pieces it +probably won't work it's like a Five + + align:start position:0% +probably won't work it's like a Five + + + align:start position:0% +probably won't work it's like a Five +Legged + + align:start position:0% + + + + align:start position:0% + +stool and depending on one of the things + + align:start position:0% +stool and depending on one of the things + + + align:start position:0% +stool and depending on one of the things +we want to you know depending on what + + align:start position:0% +we want to you know depending on what + + + align:start position:0% +we want to you know depending on what +the actual project that you're doing uh + + align:start position:0% +the actual project that you're doing uh + + + align:start position:0% +the actual project that you're doing uh +where you're doing and who you're + + align:start position:0% +where you're doing and who you're + + + align:start position:0% +where you're doing and who you're +dealing with there you know they may + + align:start position:0% +dealing with there you know they may + + + align:start position:0% +dealing with there you know they may +grow in terms of you know uh certain + + align:start position:0% +grow in terms of you know uh certain + + + align:start position:0% +grow in terms of you know uh certain +projects demand a lot more Community + + align:start position:0% +projects demand a lot more Community + + + align:start position:0% +projects demand a lot more Community +organizing to make it happen as opposed + + align:start position:0% +organizing to make it happen as opposed + + + align:start position:0% +organizing to make it happen as opposed +to another one uh other ones some demand + + align:start position:0% +to another one uh other ones some demand + + + align:start position:0% +to another one uh other ones some demand +a heck of a lot more capital I mean ex + + align:start position:0% +a heck of a lot more capital I mean ex + + + align:start position:0% +a heck of a lot more capital I mean ex +you know so so being able to uh figure + + align:start position:0% +you know so so being able to uh figure + + + align:start position:0% +you know so so being able to uh figure +out U you know it has a very specific + + align:start position:0% +out U you know it has a very specific + + + align:start position:0% +out U you know it has a very specific +dimension in in um terms of the + + align:start position:0% +dimension in in um terms of the + + + align:start position:0% +dimension in in um terms of the +particular project where you're doing at + + align:start position:0% +particular project where you're doing at + + + align:start position:0% +particular project where you're doing at +what's the history all those things + + align:start position:0% +what's the history all those things + + + align:start position:0% +what's the history all those things +um and then money from Members I don't I + + align:start position:0% +um and then money from Members I don't I + + + align:start position:0% +um and then money from Members I don't I +don't work on a project unless members + + align:start position:0% +don't work on a project unless members + + + align:start position:0% +don't work on a project unless members +upfront say to me I'm willing to put in + + align:start position:0% +upfront say to me I'm willing to put in + + + align:start position:0% +upfront say to me I'm willing to put in +money and not + + align:start position:0% +money and not + + + align:start position:0% +money and not +$10 you know but I'm really willing to + + align:start position:0% +$10 you know but I'm really willing to + + + align:start position:0% +$10 you know but I'm really willing to +put in money and that depends how much + + align:start position:0% +put in money and that depends how much + + + align:start position:0% +put in money and that depends how much +depends on the people and what their + + align:start position:0% +depends on the people and what their + + + align:start position:0% +depends on the people and what their +resources are and what the needs of the + + align:start position:0% +resources are and what the needs of the + + + align:start position:0% +resources are and what the needs of the +business are + + align:start position:0% +business are + + + align:start position:0% +business are +but you know if if people want to start + + align:start position:0% +but you know if if people want to start + + + align:start position:0% +but you know if if people want to start +if Farmers want to start a processing + + align:start position:0% +if Farmers want to start a processing + + + align:start position:0% +if Farmers want to start a processing +facility I'd like for them to all be + + align:start position:0% +facility I'd like for them to all be + + + align:start position:0% +facility I'd like for them to all be +willing to put in at least five grand + + align:start position:0% +willing to put in at least five grand + + + align:start position:0% +willing to put in at least five grand +you know if they're on the low income + + align:start position:0% +you know if they're on the low income + + + align:start position:0% +you know if they're on the low income +side or price of a pickup truck if + + align:start position:0% +side or price of a pickup truck if + + + align:start position:0% +side or price of a pickup truck if +they're you know driving around it just + + align:start position:0% +they're you know driving around it just + + + align:start position:0% +they're you know driving around it just +it doesn't make sense to if people don't + + align:start position:0% +it doesn't make sense to if people don't + + + align:start position:0% +it doesn't make sense to if people don't +value it enough to put their own + + align:start position:0% +value it enough to put their own + + + align:start position:0% +value it enough to put their own +resources in don't put yours and a lot + + align:start position:0% +resources in don't put yours and a lot + + + align:start position:0% +resources in don't put yours and a lot +of times when you're dealing with + + align:start position:0% +of times when you're dealing with + + + align:start position:0% +of times when you're dealing with +low-income folk you know we get this + + align:start position:0% +low-income folk you know we get this + + + align:start position:0% +low-income folk you know we get this +attitude like oh well they can't afford + + align:start position:0% +attitude like oh well they can't afford + + + align:start position:0% +attitude like oh well they can't afford +to to uh do it I think it just caused + + align:start position:0% +to to uh do it I think it just caused + + + align:start position:0% +to to uh do it I think it just caused +maybe a greater amount of creativity I + + align:start position:0% +maybe a greater amount of creativity I + + + align:start position:0% +maybe a greater amount of creativity I +mean for example like the U uh the home + + align:start position:0% +mean for example like the U uh the home + + + align:start position:0% +mean for example like the U uh the home +care workers in in the Bronx uh you know + + align:start position:0% +care workers in in the Bronx uh you know + + + align:start position:0% +care workers in in the Bronx uh you know +now it's not you know you making 8 n 101 + + align:start position:0% +now it's not you know you making 8 n 101 + + + align:start position:0% +now it's not you know you making 8 n 101 +an hour it's not a tremendous amount of + + align:start position:0% +an hour it's not a tremendous amount of + + + align:start position:0% +an hour it's not a tremendous amount of +um um U you know income available to + + align:start position:0% +um um U you know income available to + + + align:start position:0% +um um U you know income available to +them but they they still set up a + + align:start position:0% +them but they they still set up a + + + align:start position:0% +them but they they still set up a +process where each um person they had to + + align:start position:0% +process where each um person they had to + + + align:start position:0% +process where each um person they had to +buy in with with $1,000 uh in order to + + align:start position:0% +buy in with with $1,000 uh in order to + + + align:start position:0% +buy in with with $1,000 uh in order to +buy in but then they worked it out where + + align:start position:0% +buy in but then they worked it out where + + + align:start position:0% +buy in but then they worked it out where +it U it was something like5 $6 a week um + + align:start position:0% +it U it was something like5 $6 a week um + + + align:start position:0% +it U it was something like5 $6 a week um +um went toward it and and you didn't + + align:start position:0% +um went toward it and and you didn't + + + align:start position:0% +um went toward it and and you didn't +have to wait till you know I think it + + align:start position:0% +have to wait till you know I think it + + + align:start position:0% +have to wait till you know I think it +was after the first $100 you you you had + + align:start position:0% +was after the first $100 you you you had + + + align:start position:0% +was after the first $100 you you you had +voting rights so it you know so you + + align:start position:0% +voting rights so it you know so you + + + align:start position:0% +voting rights so it you know so you +still you was able to become a u be a + + align:start position:0% +still you was able to become a u be a + + + align:start position:0% +still you was able to become a u be a +part a democratic part of that that that + + align:start position:0% +part a democratic part of that that that + + + align:start position:0% +part a democratic part of that that that +process but you had had to have that + + align:start position:0% +process but you had had to have that + + + align:start position:0% +process but you had had to have that +personal responsibility in that buying + + align:start position:0% +personal responsibility in that buying + + + align:start position:0% +personal responsibility in that buying +and in my attitude I you know I've I've + + align:start position:0% +and in my attitude I you know I've I've + + + align:start position:0% +and in my attitude I you know I've I've +done I've organized the you know + + align:start position:0% +done I've organized the you know + + + align:start position:0% +done I've organized the you know +networks of 600 block clubs in Buffalo + + align:start position:0% +networks of 600 block clubs in Buffalo + + + align:start position:0% +networks of 600 block clubs in Buffalo +bringing them together and some of the + + align:start position:0% +bringing them together and some of the + + + align:start position:0% +bringing them together and some of the +poorest communities and you know if + + align:start position:0% +poorest communities and you know if + + + align:start position:0% +poorest communities and you know if +everybody can come up with something I + + align:start position:0% +everybody can come up with something I + + + align:start position:0% +everybody can come up with something I +mean we would you know in order for them + + align:start position:0% +mean we would you know in order for them + + + align:start position:0% +mean we would you know in order for them +to be a part of even if it was even if + + align:start position:0% +to be a part of even if it was even if + + + align:start position:0% +to be a part of even if it was even if +it was five bucks you know just that + + align:start position:0% +it was five bucks you know just that + + + align:start position:0% +it was five bucks you know just that +that that buying then then they were + + align:start position:0% +that that buying then then they were + + + align:start position:0% +that that buying then then they were +more you you had them more seriously a + + align:start position:0% +more you you had them more seriously a + + + align:start position:0% +more you you had them more seriously a +part of their body was more in it you + + align:start position:0% +part of their body was more in it you + + + align:start position:0% +part of their body was more in it you +know it's uh you know that in terms of + + align:start position:0% +know it's uh you know that in terms of + + + align:start position:0% +know it's uh you know that in terms of +that commitment and you know so I think + + align:start position:0% +that commitment and you know so I think + + + align:start position:0% +that commitment and you know so I think +it it's it's um it's essential you know + + align:start position:0% +it it's it's um it's essential you know + + + align:start position:0% +it it's it's um it's essential you know +in terms of um you know I think that's + + align:start position:0% +in terms of um you know I think that's + + + align:start position:0% +in terms of um you know I think that's +one of the the strengths and power of + + align:start position:0% +one of the the strengths and power of + + + align:start position:0% +one of the the strengths and power of +the of the uh of the of the group + + align:start position:0% +the of the uh of the of the group + + + align:start position:0% +the of the uh of the of the group +building uh uh process + + align:start position:0% +building uh uh process + + + align:start position:0% +building uh uh process +uh business process is you know is is is + + align:start position:0% +uh business process is you know is is is + + + align:start position:0% +uh business process is you know is is is +is making sure that everyone um um you + + align:start position:0% +is making sure that everyone um um you + + + align:start position:0% +is making sure that everyone um um you +know that self-reliance um you know um + + align:start position:0% +know that self-reliance um you know um + + + align:start position:0% +know that self-reliance um you know um +that's that's involved when everyone + + align:start position:0% +that's that's involved when everyone + + + align:start position:0% +that's that's involved when everyone +puts up something toward it and and you + + align:start position:0% +puts up something toward it and and you + + + align:start position:0% +puts up something toward it and and you +know then we can still figure out other + + align:start position:0% +know then we can still figure out other + + + align:start position:0% +know then we can still figure out other +ways you know certain of T you know we + + align:start position:0% +ways you know certain of T you know we + + + align:start position:0% +ways you know certain of T you know we +might do more grants uhu or you know + + align:start position:0% +might do more grants uhu or you know + + + align:start position:0% +might do more grants uhu or you know +something uh um um from a foundation you + + align:start position:0% +something uh um um from a foundation you + + + align:start position:0% +something uh um um from a foundation you +know to assist getting a a low income uh + + align:start position:0% +know to assist getting a a low income uh + + + align:start position:0% +know to assist getting a a low income uh +Cooperative off the ground but there + + align:start position:0% +Cooperative off the ground but there + + + align:start position:0% +Cooperative off the ground but there +still has to be that money from the m + + align:start position:0% +still has to be that money from the m + + + align:start position:0% +still has to be that money from the m +MERS at the beginning and and I think + + align:start position:0% +MERS at the beginning and and I think + + + align:start position:0% +MERS at the beginning and and I think +that's every time I've seen where U + + align:start position:0% +that's every time I've seen where U + + + align:start position:0% +that's every time I've seen where U +folks have tried to go around that the + + align:start position:0% +folks have tried to go around that the + + + align:start position:0% +folks have tried to go around that the +results were disastrous and and and it + + align:start position:0% +results were disastrous and and and it + + + align:start position:0% +results were disastrous and and and it +and it CAU and there were problems in + + align:start position:0% +and it CAU and there were problems in + + + align:start position:0% +and it CAU and there were problems in +terms of people being serious you know + + align:start position:0% +terms of people being serious you know + + + align:start position:0% +terms of people being serious you know +in terms of their not only just on the + + align:start position:0% +in terms of their not only just on the + + + align:start position:0% +in terms of their not only just on the +money side but um in terms of their + + align:start position:0% +money side but um in terms of their + + + align:start position:0% +money side but um in terms of their +activity their commitment to it will + + align:start position:0% +activity their commitment to it will + + + align:start position:0% +activity their commitment to it will +responsib sustain you know willingness + + align:start position:0% +responsib sustain you know willingness + + + align:start position:0% +responsib sustain you know willingness +to sustain it takes a lot of work to + + align:start position:0% +to sustain it takes a lot of work to + + + align:start position:0% +to sustain it takes a lot of work to +sustain these group based businesses and + + align:start position:0% +sustain these group based businesses and + + + align:start position:0% +sustain these group based businesses and +if you don't have any sweat in the game + + align:start position:0% +if you don't have any sweat in the game + + + align:start position:0% +if you don't have any sweat in the game +you know it's easy you walk away + + align:start position:0% +you know it's easy you walk away + + + align:start position:0% +you know it's easy you walk away +you know and you might take a few things + + align:start position:0% +you know and you might take a few things + + + align:start position:0% +you know and you might take a few things +with you it's just you know people need + + align:start position:0% +with you it's just you know people need + + + align:start position:0% +with you it's just you know people need +to buy in both you know with their time + + align:start position:0% +to buy in both you know with their time + + + align:start position:0% +to buy in both you know with their time +and their and their cash um and then you + + align:start position:0% +and their and their cash um and then you + + + align:start position:0% +and their and their cash um and then you +need money from other sources so if + + align:start position:0% +need money from other sources so if + + + align:start position:0% +need money from other sources so if +people want to start um a print shop you + + align:start position:0% +people want to start um a print shop you + + + align:start position:0% +people want to start um a print shop you +know and they they okay I want to I want + + align:start position:0% +know and they they okay I want to I want + + + align:start position:0% +know and they they okay I want to I want +to we've got these five people together + + align:start position:0% +to we've got these five people together + + + align:start position:0% +to we've got these five people together +we think we'd like to start a print shop + + align:start position:0% +we think we'd like to start a print shop + + + align:start position:0% +we think we'd like to start a print shop +there isn't one nearby people are always + + align:start position:0% +there isn't one nearby people are always + + + align:start position:0% +there isn't one nearby people are always +looking for a place to get things copied + + align:start position:0% +looking for a place to get things copied + + + align:start position:0% +looking for a place to get things copied +we got to buy The + + align:start position:0% +we got to buy The + + + align:start position:0% +we got to buy The +copier you know like well we can each + + align:start position:0% +copier you know like well we can each + + + align:start position:0% +copier you know like well we can each +put in + + align:start position:0% +put in + + + align:start position:0% +put in +$500 well we've been saving up for a + + align:start position:0% +$500 well we've been saving up for a + + + align:start position:0% +$500 well we've been saving up for a +year you know we each got $500 together + + align:start position:0% +year you know we each got $500 together + + + align:start position:0% +year you know we each got $500 together +and that's a quarter of what's needed + + align:start position:0% +and that's a quarter of what's needed + + + align:start position:0% +and that's a quarter of what's needed +you know you have to have an idea where + + align:start position:0% +you know you have to have an idea where + + + align:start position:0% +you know you have to have an idea where +you're going to get the rest of it from + + align:start position:0% +you're going to get the rest of it from + + + align:start position:0% +you're going to get the rest of it from +you know you're going to be comfortable + + align:start position:0% +you know you're going to be comfortable + + + align:start position:0% +you know you're going to be comfortable +talking to the local bank you're going + + align:start position:0% +talking to the local bank you're going + + + align:start position:0% +talking to the local bank you're going +to be comfortable putting together + + align:start position:0% +to be comfortable putting together + + + align:start position:0% +to be comfortable putting together +what's needed to go talk to the local + + align:start position:0% +what's needed to go talk to the local + + + align:start position:0% +what's needed to go talk to the local +bank um but just thinking through is + + align:start position:0% +bank um but just thinking through is + + + align:start position:0% +bank um but just thinking through is +there a place that might be willing to + + align:start position:0% +there a place that might be willing to + + + align:start position:0% +there a place that might be willing to +help either bring in equity or bring in + + align:start position:0% +help either bring in equity or bring in + + + align:start position:0% +help either bring in equity or bring in +other debt to make this business happen + + align:start position:0% +other debt to make this business happen + + + align:start position:0% +other debt to make this business happen +um so what I'd like like to do with this + + align:start position:0% +um so what I'd like like to do with this + + + align:start position:0% +um so what I'd like like to do with this +these are these are to me so important + + align:start position:0% +these are these are to me so important + + + align:start position:0% +these are these are to me so important +that um if you're talking or thinking + + align:start position:0% +that um if you're talking or thinking + + + align:start position:0% +that um if you're talking or thinking +about doing any Project without all five + + align:start position:0% +about doing any Project without all five + + + align:start position:0% +about doing any Project without all five +of those things I really want to counsel + + align:start position:0% +of those things I really want to counsel + + + align:start position:0% +of those things I really want to counsel +you to reconsider or to see if you can + + align:start position:0% +you to reconsider or to see if you can + + + align:start position:0% +you to reconsider or to see if you can +find the one or two or three that are + + align:start position:0% +find the one or two or three that are + + + align:start position:0% +find the one or two or three that are +missing there's a lot of groups that say + + align:start position:0% +missing there's a lot of groups that say + + + align:start position:0% +missing there's a lot of groups that say +h Community Development Credit Union + + align:start position:0% +h Community Development Credit Union + + + align:start position:0% +h Community Development Credit Union +they're all over it works and we're + + align:start position:0% +they're all over it works and we're + + + align:start position:0% +they're all over it works and we're +great organizers let's start one come on + + align:start position:0% +great organizers let's start one come on + + + align:start position:0% +great organizers let's start one come on +let can you come to the meeting okay + + align:start position:0% +let can you come to the meeting okay + + + align:start position:0% +let can you come to the meeting okay +let's meet tomorrow night and we're + + align:start position:0% +let's meet tomorrow night and we're + + + align:start position:0% +let's meet tomorrow night and we're +going to get started and you meet and + + align:start position:0% +going to get started and you meet and + + + align:start position:0% +going to get started and you meet and +you meet and you meet and you meet and + + align:start position:0% +you meet and you meet and you meet and + + + align:start position:0% +you meet and you meet and you meet and +it's like what's happening what's not + + align:start position:0% +it's like what's happening what's not + + + align:start position:0% +it's like what's happening what's not +happening well why isn't it happening + + align:start position:0% +happening well why isn't it happening + + + align:start position:0% +happening well why isn't it happening +it's because you don't have the right + + align:start position:0% +it's because you don't have the right + + + align:start position:0% +it's because you don't have the right +you don't have all the ingredients you + + align:start position:0% +you don't have all the ingredients you + + + align:start position:0% +you don't have all the ingredients you +know you're making a cake without any + + align:start position:0% +know you're making a cake without any + + + align:start position:0% +know you're making a cake without any +eggs or liquid ingredients it's like not + + align:start position:0% +eggs or liquid ingredients it's like not + + + align:start position:0% +eggs or liquid ingredients it's like not +working so um yeah so I'd like what I'd + + align:start position:0% +working so um yeah so I'd like what I'd + + + align:start position:0% +working so um yeah so I'd like what I'd +like to do is take these five and um + + align:start position:0% +like to do is take these five and um + + + align:start position:0% +like to do is take these five and um +think through a rating scale it's like + + align:start position:0% +think through a rating scale it's like + + + align:start position:0% +think through a rating scale it's like +if you if you had a rating scale from 0 + + align:start position:0% +if you if you had a rating scale from 0 + + + align:start position:0% +if you if you had a rating scale from 0 +to 5 for Community + + align:start position:0% +to 5 for Community + + + align:start position:0% +to 5 for Community +organizing what would a zero be no + + align:start position:0% +organizing what would a zero be no + + + align:start position:0% +organizing what would a zero be no +Community organizing skills what would a + + align:start position:0% +Community organizing skills what would a + + + align:start position:0% +Community organizing skills what would a +zero look + + align:start position:0% +zero look + + + align:start position:0% +zero look +like and what I'd like to do is I'd like + + align:start position:0% +like and what I'd like to do is I'd like + + + align:start position:0% +like and what I'd like to do is I'd like +to type this up and have it for us when + + align:start position:0% +to type this up and have it for us when + + + align:start position:0% +to type this up and have it for us when +we're talking about case studies so you + + align:start position:0% +we're talking about case studies so you + + + align:start position:0% +we're talking about case studies so you +can look at things that you know of that + + align:start position:0% +can look at things that you know of that + + + align:start position:0% +can look at things that you know of that +have worked and not worked and I just + + align:start position:0% +have worked and not worked and I just + + + align:start position:0% +have worked and not worked and I just +want to kind of like go down and just be + + align:start position:0% +want to kind of like go down and just be + + + align:start position:0% +want to kind of like go down and just be +able to rate them let's do zero to three + + align:start position:0% +able to rate them let's do zero to three + + + align:start position:0% +able to rate them let's do zero to three +just so it's really fast but just so we + + align:start position:0% +just so it's really fast but just so we + + + align:start position:0% +just so it's really fast but just so we +can kind of take a look at well probably + + align:start position:0% +can kind of take a look at well probably + + + align:start position:0% +can kind of take a look at well probably +why didn't that work oh there was uh no + + align:start position:0% +why didn't that work oh there was uh no + + + align:start position:0% +why didn't that work oh there was uh no +money from members but I I guarantee for + + align:start position:0% +money from members but I I guarantee for + + + align:start position:0% +money from members but I I guarantee for +all the things all the projects you know + + align:start position:0% +all the things all the projects you know + + + align:start position:0% +all the things all the projects you know +that didn't work they didn't have one + + align:start position:0% +that didn't work they didn't have one + + + align:start position:0% +that didn't work they didn't have one +and all the projects you know that + + align:start position:0% +and all the projects you know that + + + align:start position:0% +and all the projects you know that +worked they had all of them I don't + + align:start position:0% +worked they had all of them I don't + + + align:start position:0% +worked they had all of them I don't +think there's exceptions how's that try + + align:start position:0% +think there's exceptions how's that try + + + align:start position:0% +think there's exceptions how's that try +to prove me wrong I'd love it um so what + + align:start position:0% +to prove me wrong I'd love it um so what + + + align:start position:0% +to prove me wrong I'd love it um so what +would a zero be for Community + + align:start position:0% + + + + align:start position:0% + +organizing it's no inut some top level + + align:start position:0% +organizing it's no inut some top level + + + align:start position:0% +organizing it's no inut some top level +official or Ed or someone who says let's + + align:start position:0% +official or Ed or someone who says let's + + + align:start position:0% +official or Ed or someone who says let's +do this and it has no connection and + + align:start position:0% +do this and it has no connection and + + + align:start position:0% +do this and it has no connection and +know and it doesn't make sense in terms + + align:start position:0% +know and it doesn't make sense in terms + + + align:start position:0% +know and it doesn't make sense in terms +of the local landscape well it might or + + align:start position:0% +of the local landscape well it might or + + + align:start position:0% +of the local landscape well it might or +might not make sense but who would know + + align:start position:0% +might not make sense but who would know + + + align:start position:0% +might not make sense but who would know +there's nobody's talking to anybody + + align:start position:0% +there's nobody's talking to anybody + + + align:start position:0% +there's nobody's talking to anybody +right so there's no + + align:start position:0% +right so there's no + + + align:start position:0% +right so there's no +conversation no common planning process + + align:start position:0% +conversation no common planning process + + + align:start position:0% +conversation no common planning process +I + + align:start position:0% +I + + + align:start position:0% +I +me and you see that a lot like said we + + align:start position:0% +me and you see that a lot like said we + + + align:start position:0% +me and you see that a lot like said we +like said ad will say Hey you know this + + align:start position:0% +like said ad will say Hey you know this + + + align:start position:0% +like said ad will say Hey you know this +would be a great idea let's former a + + align:start position:0% +would be a great idea let's former a + + + align:start position:0% +would be a great idea let's former a +youth worker Co-op they went to a you + + align:start position:0% +youth worker Co-op they went to a you + + + align:start position:0% +youth worker Co-op they went to a you +know they read a book or they went to + + align:start position:0% +know they read a book or they went to + + + align:start position:0% +know they read a book or they went to +what's name you know and then but then + + align:start position:0% +what's name you know and then but then + + + align:start position:0% +what's name you know and then but then +they have they talked to a group of + + align:start position:0% +they have they talked to a group of + + + align:start position:0% +they have they talked to a group of +young people first I mean and and just + + align:start position:0% +young people first I mean and and just + + + align:start position:0% +young people first I mean and and just +and and kind of began to tease it out + + align:start position:0% +and and kind of began to tease it out + + + align:start position:0% +and and kind of began to tease it out +what are your issues what are your + + align:start position:0% +what are your issues what are your + + + align:start position:0% +what are your issues what are your +concerns would you like what what his an + + align:start position:0% +concerns would you like what what his an + + + align:start position:0% +concerns would you like what what his an +approach what do you think about that or + + align:start position:0% +approach what do you think about that or + + + align:start position:0% +approach what do you think about that or +did you just design that idea you know + + align:start position:0% +did you just design that idea you know + + + align:start position:0% +did you just design that idea you know +from the top of your head and then said + + align:start position:0% +from the top of your head and then said + + + align:start position:0% +from the top of your head and then said +assigned some people and said get busy + + align:start position:0% +assigned some people and said get busy + + + align:start position:0% +assigned some people and said get busy +on it so what would a one look like so + + align:start position:0% +on it so what would a one look like so + + + align:start position:0% +on it so what would a one look like so +this is in the middle the one I know + + align:start position:0% +this is in the middle the one I know + + + align:start position:0% +this is in the middle the one I know +good too it's it's the you have people + + align:start position:0% +good too it's it's the you have people + + + align:start position:0% +good too it's it's the you have people +on The Advisory you know you have + + align:start position:0% +on The Advisory you know you have + + + align:start position:0% +on The Advisory you know you have +tokenized people in different positions + + align:start position:0% +tokenized people in different positions + + + align:start position:0% +tokenized people in different positions +where they're in an advisory role or + + align:start position:0% +where they're in an advisory role or + + + align:start position:0% +where they're in an advisory role or +something or they're Our Community + + align:start position:0% +something or they're Our Community + + + align:start position:0% +something or they're Our Community +member on our board or something + + align:start position:0% +member on our board or something + + + align:start position:0% +member on our board or something +um right like a CDC that has a resident + + align:start position:0% +um right like a CDC that has a resident + + + align:start position:0% +um right like a CDC that has a resident +on the board you know two residents on + + align:start position:0% +on the board you know two residents on + + + align:start position:0% +on the board you know two residents on +the + + align:start position:0% +the + + + align:start position:0% +the +board + + align:start position:0% +board + + + align:start position:0% +board +yeah and H and how about a two a oh + + align:start position:0% +yeah and H and how about a two a oh + + + align:start position:0% +yeah and H and how about a two a oh +geeez we're just gonna go on a zero to + + align:start position:0% +geeez we're just gonna go on a zero to + + + align:start position:0% +geeez we're just gonna go on a zero to +two um sorry about that I was about to + + align:start position:0% +two um sorry about that I was about to + + + align:start position:0% +two um sorry about that I was about to +say a two would be um if you're G to go + + align:start position:0% +say a two would be um if you're G to go + + + align:start position:0% +say a two would be um if you're G to go +to three no let's let's oh okay go ahead + + align:start position:0% +to three no let's let's oh okay go ahead + + + align:start position:0% +to three no let's let's oh okay go ahead +a two would be um like I've been you + + align:start position:0% +a two would be um like I've been you + + + align:start position:0% +a two would be um like I've been you +know at like in my community meetings + + align:start position:0% +know at like in my community meetings + + + align:start position:0% +know at like in my community meetings +and you know like like a Housing + + align:start position:0% +and you know like like a Housing + + + align:start position:0% +and you know like like a Housing +Development and then talking about stuff + + align:start position:0% +Development and then talking about stuff + + + align:start position:0% +Development and then talking about stuff +but no one's taking notes and you know + + align:start position:0% +but no one's taking notes and you know + + + align:start position:0% +but no one's taking notes and you know +the residents come and complain and talk + + align:start position:0% +the residents come and complain and talk + + + align:start position:0% +the residents come and complain and talk +about stuff and May so just venting + + align:start position:0% +about stuff and May so just venting + + + align:start position:0% +about stuff and May so just venting +instead of really uh Consulting + + align:start position:0% +instead of really uh Consulting + + + align:start position:0% +instead of really uh Consulting +or I think we should go even in or they + + align:start position:0% +or I think we should go even in or they + + + align:start position:0% +or I think we should go even in or they +have a really good public process but + + align:start position:0% +have a really good public process but + + + align:start position:0% +have a really good public process but +then it has no connection to so even + + align:start position:0% +then it has no connection to so even + + + align:start position:0% +then it has no connection to so even +though like maybe someone is taking + + align:start position:0% +though like maybe someone is taking + + + align:start position:0% +though like maybe someone is taking +notes or that meeting is run really well + + align:start position:0% +notes or that meeting is run really well + + + align:start position:0% +notes or that meeting is run really well +you know and there's good information + + align:start position:0% +you know and there's good information + + + align:start position:0% +you know and there's good information +there but then the final outcome comes + + align:start position:0% +there but then the final outcome comes + + + align:start position:0% +there but then the final outcome comes +out and there's a total disconnect or + + align:start position:0% +out and there's a total disconnect or + + + align:start position:0% +out and there's a total disconnect or +something's implemented or something's + + align:start position:0% +something's implemented or something's + + + align:start position:0% +something's implemented or something's +not implemented but there's but that + + align:start position:0% +not implemented but there's but that + + + align:start position:0% +not implemented but there's but that +doesn't connect the good public + + align:start position:0% +doesn't connect the good public + + + align:start position:0% +doesn't connect the good public +participatory process doesn't + + align:start position:0% +participatory process doesn't + + + align:start position:0% +participatory process doesn't +connect right I like um City Planning + + align:start position:0% +connect right I like um City Planning + + + align:start position:0% +connect right I like um City Planning +meetings invite residents to come + + align:start position:0% + + + + align:start position:0% + +speak then meanwhile they already have + + align:start position:0% +speak then meanwhile they already have + + + align:start position:0% +speak then meanwhile they already have +the plan you in their back + + align:start position:0% +the plan you in their back + + + align:start position:0% +the plan you in their back +pocket so let's see how many times you + + align:start position:0% +pocket so let's see how many times you + + + align:start position:0% +pocket so let's see how many times you +agree with me + + align:start position:0% +agree with me + + + align:start position:0% +agree with me +right Oran where there's no + + align:start position:0% +right Oran where there's no + + + align:start position:0% +right Oran where there's no +understanding of what's winnable at the + + align:start position:0% +understanding of what's winnable at the + + + align:start position:0% +understanding of what's winnable at the +end and so it can you you will allow + + align:start position:0% +end and so it can you you will allow + + + align:start position:0% +end and so it can you you will allow +people to go beyond what's actually + + align:start position:0% +people to go beyond what's actually + + + align:start position:0% +people to go beyond what's actually +realistic or what the group is capable + + align:start position:0% +realistic or what the group is capable + + + align:start position:0% +realistic or what the group is capable +of accomplishing so it can be a + + align:start position:0% +of accomplishing so it can be a + + + align:start position:0% +of accomplishing so it can be a +wonderfully participatory process that + + align:start position:0% +wonderfully participatory process that + + + align:start position:0% +wonderfully participatory process that +crashes because it lack understanding of + + align:start position:0% +crashes because it lack understanding of + + + align:start position:0% +crashes because it lack understanding of +you know their vision isn't really + + align:start position:0% + + + + align:start position:0% + +coherent or it could be everyone + + align:start position:0% +coherent or it could be everyone + + + align:start position:0% +coherent or it could be everyone +speaking English but most of the + + align:start position:0% +speaking English but most of the + + + align:start position:0% +speaking English but most of the +community folks speak another and + + align:start position:0% +community folks speak another and + + + align:start position:0% +community folks speak another and +there's there's no + + align:start position:0% + + + + align:start position:0% + +translation let see + + align:start position:0% +translation let see + + + align:start position:0% +translation let see +that or it can + + align:start position:0% +that or it can + + + align:start position:0% +that or it can +be go + + align:start position:0% +be go + + + align:start position:0% +be go +on the head the head of the Housing + + align:start position:0% +on the head the head of the Housing + + + align:start position:0% +on the head the head of the Housing +Authority tell residents the reason why + + align:start position:0% +Authority tell residents the reason why + + + align:start position:0% +Authority tell residents the reason why +no one is hiring them is because they + + align:start position:0% +no one is hiring them is because they + + + align:start position:0% +no one is hiring them is because they +dress bad and people are afraid of the + + align:start position:0% +dress bad and people are afraid of the + + + align:start position:0% +dress bad and people are afraid of the +gold teeth and the way that they comb + + align:start position:0% +gold teeth and the way that they comb + + + align:start position:0% +gold teeth and the way that they comb +their + + align:start position:0% + + + + align:start position:0% + +hair okay what do three look + + align:start position:0% + + + + align:start position:0% + +like good + + align:start position:0% + + + + align:start position:0% + +facilitation an understanding of what's + + align:start position:0% +facilitation an understanding of what's + + + align:start position:0% +facilitation an understanding of what's +winable + + align:start position:0% +winable + + + align:start position:0% +winable +um I think + + align:start position:0% +um I think + + + align:start position:0% +um I think +translation the final thing isn't + + align:start position:0% +translation the final thing isn't + + + align:start position:0% +translation the final thing isn't +totally defined until you know it's not + + align:start position:0% +totally defined until you know it's not + + + align:start position:0% +totally defined until you know it's not +not here we're coming together to plan + + align:start position:0% +not here we're coming together to plan + + + align:start position:0% +not here we're coming together to plan +this and then so that the final outcome + + align:start position:0% +this and then so that the final outcome + + + align:start position:0% +this and then so that the final outcome +is defined by the process by the group + + align:start position:0% +is defined by the process by the group + + + align:start position:0% +is defined by the process by the group +which is hard + + align:start position:0% + + + + align:start position:0% + +sometimes and going a commitment by the + + align:start position:0% +sometimes and going a commitment by the + + + align:start position:0% +sometimes and going a commitment by the +group to follow the function that they + + align:start position:0% +group to follow the function that they + + + align:start position:0% +group to follow the function that they +decide to pursue rather than desire to + + align:start position:0% +decide to pursue rather than desire to + + + align:start position:0% +decide to pursue rather than desire to +create a body that is then static and + + align:start position:0% +create a body that is then static and + + + align:start position:0% +create a body that is then static and +not able to adapt to wherever they + + align:start position:0% +not able to adapt to wherever they + + + align:start position:0% +not able to adapt to wherever they +decide to go because I think a lot of + + align:start position:0% +decide to go because I think a lot of + + + align:start position:0% +decide to go because I think a lot of +times the + + align:start position:0% +times the + + + align:start position:0% +times the +organizing suddenly becomes leads to the + + align:start position:0% +organizing suddenly becomes leads to the + + + align:start position:0% +organizing suddenly becomes leads to the +formation of a group that then is not + + align:start position:0% +formation of a group that then is not + + + align:start position:0% +formation of a group that then is not +capable of adapting to whatever they've + + align:start position:0% +capable of adapting to whatever they've + + + align:start position:0% +capable of adapting to whatever they've +decided to pursue so kind of having that + + align:start position:0% +decided to pursue so kind of having that + + + align:start position:0% +decided to pursue so kind of having that +informed process so + + align:start position:0% +informed process so + + + align:start position:0% +informed process so +along well along those lines that the + + align:start position:0% +along well along those lines that the + + + align:start position:0% +along well along those lines that the +process of leading up to it that the + + align:start position:0% +process of leading up to it that the + + + align:start position:0% +process of leading up to it that the +organizing process reflects what the + + align:start position:0% +organizing process reflects what the + + + align:start position:0% +organizing process reflects what the +thing will actually be and that the and + + align:start position:0% +thing will actually be and that the and + + + align:start position:0% +thing will actually be and that the and +that the group that comes together do + + align:start position:0% +that the group that comes together do + + + align:start position:0% +that the group that comes together do +that work stays together and continues + + align:start position:0% +that work stays together and continues + + + align:start position:0% +that work stays together and continues +forward something in that process hooked + + align:start position:0% +forward something in that process hooked + + + align:start position:0% +forward something in that process hooked +people engaged people changed people + + align:start position:0% +people engaged people changed people + + + align:start position:0% +people engaged people changed people +like you were talking about and and kept + + align:start position:0% +like you were talking about and and kept + + + align:start position:0% +like you were talking about and and kept +them at the table so they got something + + align:start position:0% +them at the table so they got something + + + align:start position:0% +them at the table so they got something +out of it as well I was just going to + + align:start position:0% +out of it as well I was just going to + + + align:start position:0% +out of it as well I was just going to +say something similar to that for just a + + align:start position:0% +say something similar to that for just a + + + align:start position:0% +say something similar to that for just a +local leadership + + align:start position:0% +local leadership + + + align:start position:0% +local leadership +capacity whether they're not dependent + + align:start position:0% +capacity whether they're not dependent + + + align:start position:0% +capacity whether they're not dependent +on the uh on the you know Community + + align:start position:0% +on the uh on the you know Community + + + align:start position:0% +on the uh on the you know Community +developers to to always provide this + + align:start position:0% +developers to to always provide this + + + align:start position:0% +developers to to always provide this +technical + + align:start position:0% +technical + + + align:start position:0% +technical +assistance to me the signing a a great + + align:start position:0% +assistance to me the signing a a great + + + align:start position:0% +assistance to me the signing a a great +meeting and a great process is one where + + align:start position:0% +meeting and a great process is one where + + + align:start position:0% +meeting and a great process is one where +everyone ends up in a different place + + align:start position:0% +everyone ends up in a different place + + + align:start position:0% +everyone ends up in a different place +yeah where it's not like someone came in + + align:start position:0% +yeah where it's not like someone came in + + + align:start position:0% +yeah where it's not like someone came in +with a plan or an agenda and then it + + align:start position:0% +with a plan or an agenda and then it + + + align:start position:0% +with a plan or an agenda and then it +went through the agenda but there's it's + + align:start position:0% +went through the agenda but there's it's + + + align:start position:0% +went through the agenda but there's it's +so + + align:start position:0% +so + + + align:start position:0% +so +vigorous there's so much exchange and + + align:start position:0% +vigorous there's so much exchange and + + + align:start position:0% +vigorous there's so much exchange and +listening going on that everyone sort of + + align:start position:0% +listening going on that everyone sort of + + + align:start position:0% +listening going on that everyone sort of +comes out different than how they + + align:start position:0% +comes out different than how they + + + align:start position:0% +comes out different than how they +came when you see somebody move from the + + align:start position:0% +came when you see somebody move from the + + + align:start position:0% +came when you see somebody move from the +back of the room to the front of the + + align:start position:0% +back of the room to the front of the + + + align:start position:0% +back of the room to the front of the +room at the next meeting + + align:start position:0% +room at the next meeting + + + align:start position:0% +room at the next meeting +you know something good is happening + + align:start position:0% +you know something good is happening + + + align:start position:0% +you know something good is happening +like yeah depending who that + + align:start position:0% +like yeah depending who that + + + align:start position:0% +like yeah depending who that +was what what they have in their pocket + + align:start position:0% +was what what they have in their pocket + + + align:start position:0% +was what what they have in their pocket +um the uh the way I talk about that is + + align:start position:0% +um the uh the way I talk about that is + + + align:start position:0% +um the uh the way I talk about that is +creating shared Vision you know that + + align:start position:0% +creating shared Vision you know that + + + align:start position:0% +creating shared Vision you know that +people kind of all walk in as + + align:start position:0% +people kind of all walk in as + + + align:start position:0% +people kind of all walk in as +individuals but the the process of of + + align:start position:0% +individuals but the the process of of + + + align:start position:0% +individuals but the the process of of +speaking and listening just kind of + + align:start position:0% +speaking and listening just kind of + + + align:start position:0% +speaking and listening just kind of +moves people to that other place where + + align:start position:0% +moves people to that other place where + + + align:start position:0% +moves people to that other place where +they go oh yeah we can see this and we + + align:start position:0% +they go oh yeah we can see this and we + + + align:start position:0% +they go oh yeah we can see this and we +we do + + align:start position:0% +we do + + + align:start position:0% +we do +we we want that oh I guess maybe it's + + align:start position:0% +we we want that oh I guess maybe it's + + + align:start position:0% +we we want that oh I guess maybe it's +not that it's this right here you know + + align:start position:0% +not that it's this right here you know + + + align:start position:0% +not that it's this right here you know +and everybody comes out and the more + + align:start position:0% +and everybody comes out and the more + + + align:start position:0% +and everybody comes out and the more +conversation the clearer that vision + + align:start position:0% +conversation the clearer that vision + + + align:start position:0% +conversation the clearer that vision +gets and the more buyin everybody has + + align:start position:0% +gets and the more buyin everybody has + + + align:start position:0% +gets and the more buyin everybody has +how about the next one zero on + + align:start position:0% +how about the next one zero on + + + align:start position:0% +how about the next one zero on +replicable business models you ever been + + align:start position:0% +replicable business models you ever been + + + align:start position:0% +replicable business models you ever been +to a meeting like + + align:start position:0% +to a meeting like + + + align:start position:0% +to a meeting like +that or with a group like that it's like + + align:start position:0% +that or with a group like that it's like + + + align:start position:0% +that or with a group like that it's like +a department meeting + + align:start position:0% +a department meeting + + + align:start position:0% +a department meeting +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +no models for + + align:start position:0% +no models for + + + align:start position:0% +no models for +that I guess I kind of like need to know + + align:start position:0% +that I guess I kind of like need to know + + + align:start position:0% +that I guess I kind of like need to know +more about this one because um I don't + + align:start position:0% +more about this one because um I don't + + + align:start position:0% +more about this one because um I don't +know business models as much but as in + + align:start position:0% +know business models as much but as in + + + align:start position:0% +know business models as much but as in +terms of organizing models or Community + + align:start position:0% +terms of organizing models or Community + + + align:start position:0% +terms of organizing models or Community +Development or planning models everyone + + align:start position:0% +Development or planning models everyone + + + align:start position:0% +Development or planning models everyone +always wants that replicable model and + + align:start position:0% +always wants that replicable model and + + + align:start position:0% +always wants that replicable model and +so I've kind of like like I'm kind of + + align:start position:0% +so I've kind of like like I'm kind of + + + align:start position:0% +so I've kind of like like I'm kind of +like oh God what's replicable + + align:start position:0% +like oh God what's replicable + + + align:start position:0% +like oh God what's replicable +because my experience has been like + + align:start position:0% +because my experience has been like + + + align:start position:0% +because my experience has been like +things don't always they're not things + + align:start position:0% +things don't always they're not things + + + align:start position:0% +things don't always they're not things +that work aren't always replicable and + + align:start position:0% +that work aren't always replicable and + + + align:start position:0% +that work aren't always replicable and +and I'm not talking about a process I'm + + align:start position:0% +and I'm not talking about a process I'm + + + align:start position:0% +and I'm not talking about a process I'm +talking about Community Development + + align:start position:0% +talking about Community Development + + + align:start position:0% +talking about Community Development +Credit Unions Community Land trusts for + + align:start position:0% +Credit Unions Community Land trusts for + + + align:start position:0% +Credit Unions Community Land trusts for +housing preserving affordable there's + + align:start position:0% +housing preserving affordable there's + + + align:start position:0% +housing preserving affordable there's +things we know that really work and they + + align:start position:0% +things we know that really work and they + + + align:start position:0% +things we know that really work and they +work really well you know there's just + + align:start position:0% +work really well you know there's just + + + align:start position:0% +work really well you know there's just +there's a long list of them um so + + align:start position:0% +there's a long list of them um so + + + align:start position:0% +there's a long list of them um so +instead of + + align:start position:0% +instead of + + + align:start position:0% +instead of +saying I'd like to start a rock climbing + + align:start position:0% +saying I'd like to start a rock climbing + + + align:start position:0% +saying I'd like to start a rock climbing +Co-op okay well maybe that's okay but + + align:start position:0% +Co-op okay well maybe that's okay but + + + align:start position:0% +Co-op okay well maybe that's okay but +you might get a zero on this scale and + + align:start position:0% +you might get a zero on this scale and + + + align:start position:0% +you might get a zero on this scale and +it might not work because we don't + + align:start position:0% +it might not work because we don't + + + align:start position:0% +it might not work because we don't +really know how to build rock climbing + + align:start position:0% +really know how to build rock climbing + + + align:start position:0% +really know how to build rock climbing +cops I mean maybe maybe that was a bad + + align:start position:0% +cops I mean maybe maybe that was a bad + + + align:start position:0% +cops I mean maybe maybe that was a bad +idea it might be + + align:start position:0% +idea it might be + + + align:start position:0% +idea it might be +fun land trust you know you know they + + align:start position:0% +fun land trust you know you know they + + + align:start position:0% +fun land trust you know you know they +work you've seen them + + align:start position:0% + + + + align:start position:0% + +work are there times when you know when + + align:start position:0% +work are there times when you know when + + + align:start position:0% +work are there times when you know when +they right thing and so is that part of + + align:start position:0% +they right thing and so is that part of + + + align:start position:0% +they right thing and so is that part of +this bullet as well and having yeah + + align:start position:0% +this bullet as well and having yeah + + + align:start position:0% +this bullet as well and having yeah +having enough information about what the + + align:start position:0% +having enough information about what the + + + align:start position:0% +having enough information about what the +various models exist I mean like the + + align:start position:0% +various models exist I mean like the + + + align:start position:0% +various models exist I mean like the +example of you know folks + + align:start position:0% +example of you know folks + + + align:start position:0% +example of you know folks +saying let's have a credit union or + + align:start position:0% +saying let's have a credit union or + + + align:start position:0% +saying let's have a credit union or +let's have a work at Co-op but but then + + align:start position:0% +let's have a work at Co-op but but then + + + align:start position:0% +let's have a work at Co-op but but then +they haven't uh you know taken the uh + + align:start position:0% +they haven't uh you know taken the uh + + + align:start position:0% +they haven't uh you know taken the uh +the extra step to say okay well what are + + align:start position:0% +the extra step to say okay well what are + + + align:start position:0% +the extra step to say okay well what are +some successful credit unions in in work + + align:start position:0% +some successful credit unions in in work + + + align:start position:0% +some successful credit unions in in work +at co-ops and what do they look like and + + align:start position:0% +at co-ops and what do they look like and + + + align:start position:0% +at co-ops and what do they look like and +what are some of the common traits and + + align:start position:0% +what are some of the common traits and + + + align:start position:0% +what are some of the common traits and +uh uh um you know and and uh you know + + align:start position:0% +uh uh um you know and and uh you know + + + align:start position:0% +uh uh um you know and and uh you know +what are some interesting different U + + align:start position:0% +what are some interesting different U + + + align:start position:0% +what are some interesting different U +activities that different ones did that + + align:start position:0% +activities that different ones did that + + + align:start position:0% +activities that different ones did that +might have some U um um bearing on on + + align:start position:0% +might have some U um um bearing on on + + + align:start position:0% +might have some U um um bearing on on +our situation you know so I think you + + align:start position:0% +our situation you know so I think you + + + align:start position:0% +our situation you know so I think you +know particular just getting people to + + align:start position:0% +know particular just getting people to + + + align:start position:0% +know particular just getting people to +see that there that uh their approaches + + align:start position:0% +see that there that uh their approaches + + + align:start position:0% +see that there that uh their approaches +of uh different ways of looking at + + align:start position:0% +of uh different ways of looking at + + + align:start position:0% +of uh different ways of looking at +things you know not only in this country + + align:start position:0% +things you know not only in this country + + + align:start position:0% +things you know not only in this country +but around the world even um um yeah I + + align:start position:0% +but around the world even um um yeah I + + + align:start position:0% +but around the world even um um yeah I +think that um like you know while you + + align:start position:0% +think that um like you know while you + + + align:start position:0% +think that um like you know while you +know businesses or organizations will + + align:start position:0% +know businesses or organizations will + + + align:start position:0% +know businesses or organizations will +have you know their own nuances that + + align:start position:0% +have you know their own nuances that + + + align:start position:0% +have you know their own nuances that +make them unique but I think you know + + align:start position:0% +make them unique but I think you know + + + align:start position:0% +make them unique but I think you know +that there are just some rules like you + + align:start position:0% +that there are just some rules like you + + + align:start position:0% +that there are just some rules like you +know to a Cooperative like um with the + + align:start position:0% +know to a Cooperative like um with the + + + align:start position:0% +know to a Cooperative like um with the +Federation work with the catering Co-op + + align:start position:0% +Federation work with the catering Co-op + + + align:start position:0% +Federation work with the catering Co-op +and um you know we we you know we um + + align:start position:0% +and um you know we we you know we um + + + align:start position:0% +and um you know we we you know we um +basically subsidized it for I think it's + + align:start position:0% +basically subsidized it for I think it's + + + align:start position:0% +basically subsidized it for I think it's +like the first nine months just to get + + align:start position:0% +like the first nine months just to get + + + align:start position:0% +like the first nine months just to get +them get them going and um you know but + + align:start position:0% +them get them going and um you know but + + + align:start position:0% +them get them going and um you know but +they just kept breaking the rules and + + align:start position:0% +they just kept breaking the rules and + + + align:start position:0% +they just kept breaking the rules and +you know instead of you know taking you + + align:start position:0% +you know instead of you know taking you + + + align:start position:0% +you know instead of you know taking you +know um you know paying themselves you + + align:start position:0% +know um you know paying themselves you + + + align:start position:0% +know um you know paying themselves you +know you know some salary I forgot + + align:start position:0% +know you know some salary I forgot + + + align:start position:0% +know you know some salary I forgot +exactly how much that they had initially + + align:start position:0% +exactly how much that they had initially + + + align:start position:0% +exactly how much that they had initially +agreed to pay themselves and then taking + + align:start position:0% +agreed to pay themselves and then taking + + + align:start position:0% +agreed to pay themselves and then taking +the profit in reinvesting it you know to + + align:start position:0% +the profit in reinvesting it you know to + + + align:start position:0% +the profit in reinvesting it you know to +keep the coop strong they took + + align:start position:0% +keep the coop strong they took + + + align:start position:0% +keep the coop strong they took +everything so there's nothing left to + + align:start position:0% +everything so there's nothing left to + + + align:start position:0% +everything so there's nothing left to +reinvest they made some good food though + + align:start position:0% +reinvest they made some good food though + + + align:start position:0% +reinvest they made some good food though +good food I was + + align:start position:0% +good food I was + + + align:start position:0% +good food I was +so I + + align:start position:0% +so I + + + align:start position:0% +so I +did but you know so you know so those + + align:start position:0% +did but you know so you know so those + + + align:start position:0% +did but you know so you know so those +types of rules about how to do a + + align:start position:0% +types of rules about how to do a + + + align:start position:0% +types of rules about how to do a +Cooperative you know you know are + + align:start position:0% +Cooperative you know you know are + + + align:start position:0% +Cooperative you know you know are +important I think those kind of + + align:start position:0% +important I think those kind of + + + align:start position:0% +important I think those kind of +replicable replicable business models + + align:start position:0% +replicable replicable business models + + + align:start position:0% +replicable replicable business models +are important because otherwise you get + + align:start position:0% +are important because otherwise you get + + + align:start position:0% +are important because otherwise you get +a case like that you know they're just + + align:start position:0% +a case like that you know they're just + + + align:start position:0% +a case like that you know they're just +taking all the profit and not + + align:start position:0% +taking all the profit and not + + + align:start position:0% +taking all the profit and not +reinvesting in they just fall apart and + + align:start position:0% +reinvesting in they just fall apart and + + + align:start position:0% +reinvesting in they just fall apart and +wonder + + align:start position:0% + + + + align:start position:0% + +why and you know I think maybe we should + + align:start position:0% +why and you know I think maybe we should + + + align:start position:0% +why and you know I think maybe we should +edit this because it's not so much + + align:start position:0% +edit this because it's not so much + + + align:start position:0% +edit this because it's not so much +replicable as feasible yeah Fe you know + + align:start position:0% +replicable as feasible yeah Fe you know + + + align:start position:0% +replicable as feasible yeah Fe you know +I think I think that's what I was going + + align:start position:0% +I think I think that's what I was going + + + align:start position:0% +I think I think that's what I was going +for and and it would be + + align:start position:0% +for and and it would be + + + align:start position:0% +for and and it would be +re it's Fe + + align:start position:0% +re it's Fe + + + align:start position:0% +re it's Fe +yeah it doesn't have to always it + + align:start position:0% +yeah it doesn't have to always it + + + align:start position:0% +yeah it doesn't have to always it +doesn't have to have been done a million + + align:start position:0% +doesn't have to have been done a million + + + align:start position:0% +doesn't have to have been done a million +times already although that's a little + + align:start position:0% +times already although that's a little + + + align:start position:0% +times already although that's a little +safer um but the rock climbing clup you + + align:start position:0% +safer um but the rock climbing clup you + + + align:start position:0% +safer um but the rock climbing clup you +know if you put a good business plan + + align:start position:0% +know if you put a good business plan + + + align:start position:0% +know if you put a good business plan +together and you got the right people in + + align:start position:0% +together and you got the right people in + + + align:start position:0% +together and you got the right people in +your right place you + + align:start position:0% +your right place you + + + align:start position:0% +your right place you +know planners love these + + align:start position:0% +know planners love these + + + align:start position:0% +know planners love these +abilities like it's like when you go to + + align:start position:0% +abilities like it's like when you go to + + + align:start position:0% +abilities like it's like when you go to +a meeting and at the end they're like + + align:start position:0% +a meeting and at the end they're like + + + align:start position:0% +a meeting and at the end they're like +let's start a list serve and you're like + + align:start position:0% +let's start a list serve and you're like + + + align:start position:0% +let's start a list serve and you're like +is that when we came they also them + + align:start position:0% +is that when we came they also them + + + align:start position:0% +is that when we came they also them +usually + + align:start position:0% +usually + + + align:start position:0% +usually +Z there we go plan language yes so so I + + align:start position:0% +Z there we go plan language yes so so I + + + align:start position:0% +Z there we go plan language yes so so I +I so let's talk about feasible business + + align:start position:0% +I so let's talk about feasible business + + + align:start position:0% +I so let's talk about feasible business +models I I sit with a lot of groups that + + align:start position:0% +models I I sit with a lot of groups that + + + align:start position:0% +models I I sit with a lot of groups that +say we've been meeting for six months we + + align:start position:0% +say we've been meeting for six months we + + + align:start position:0% +say we've been meeting for six months we +know exactly what we want to do we want + + align:start position:0% +know exactly what we want to do we want + + + align:start position:0% +know exactly what we want to do we want +to do this and this and this so we're + + align:start position:0% +to do this and this and this so we're + + + align:start position:0% +to do this and this and this so we're +going to make these products for these + + align:start position:0% +going to make these products for these + + + align:start position:0% +going to make these products for these +consumers and then we're going to sell + + align:start position:0% +consumers and then we're going to sell + + + align:start position:0% +consumers and then we're going to sell +it to these people and then we're going + + align:start position:0% +it to these people and then we're going + + + align:start position:0% +it to these people and then we're going +to make these things and we're going to + + align:start position:0% +to make these things and we're going to + + + align:start position:0% +to make these things and we're going to +do this and it's like I'm just exhausted + + align:start position:0% +do this and it's like I'm just exhausted + + + align:start position:0% +do this and it's like I'm just exhausted +by the time I they finish telling me + + align:start position:0% +by the time I they finish telling me + + + align:start position:0% +by the time I they finish telling me +and none of them have ever done it + + align:start position:0% +and none of them have ever done it + + + align:start position:0% +and none of them have ever done it +before and you know this it's just oh + + align:start position:0% +before and you know this it's just oh + + + align:start position:0% +before and you know this it's just oh +goodness so anyway so so how would you + + align:start position:0% +goodness so anyway so so how would you + + + align:start position:0% +goodness so anyway so so how would you +how would you rank a zero um for a + + align:start position:0% +how would you rank a zero um for a + + + align:start position:0% +how would you rank a zero um for a +feasibility feasible business + + align:start position:0% +feasibility feasible business + + + align:start position:0% +feasibility feasible business +model what do they look like no plan no + + align:start position:0% +model what do they look like no plan no + + + align:start position:0% +model what do they look like no plan no +plan no no connection no learning from + + align:start position:0% +plan no no connection no learning from + + + align:start position:0% +plan no no connection no learning from +anyone is done it + + align:start position:0% +anyone is done it + + + align:start position:0% +anyone is done it +before can I say no Focus + + align:start position:0% +before can I say no Focus + + + align:start position:0% +before can I say no Focus +that's no strategy no + + align:start position:0% + + + + align:start position:0% + +Focus probably good enough how about a + + align:start position:0% +Focus probably good enough how about a + + + align:start position:0% +Focus probably good enough how about a +one or a two or a three what do you + + align:start position:0% +one or a two or a three what do you + + + align:start position:0% +one or a two or a three what do you +think what is the scale now we're going + + align:start position:0% +think what is the scale now we're going + + + align:start position:0% +think what is the scale now we're going +from zero to three oh yeah okay we're + + align:start position:0% +from zero to three oh yeah okay we're + + + align:start position:0% +from zero to three oh yeah okay we're +making enough as we go + + align:start position:0% + + + + align:start position:0% + +along I know when we did the empowerment + + align:start position:0% +along I know when we did the empowerment + + + align:start position:0% +along I know when we did the empowerment +zone in New York we had hundreds of + + align:start position:0% +zone in New York we had hundreds of + + + align:start position:0% +zone in New York we had hundreds of +propos + + align:start position:0% +propos + + + align:start position:0% +propos +for businesses you know F folks wanting + + align:start position:0% +for businesses you know F folks wanting + + + align:start position:0% +for businesses you know F folks wanting +money you know to support + + align:start position:0% +money you know to support + + + align:start position:0% +money you know to support +and you + + align:start position:0% +and you + + + align:start position:0% +and you +know the many of them were just add- on + + align:start position:0% +know the many of them were just add- on + + + align:start position:0% +know the many of them were just add- on +to something that someone was struggling + + align:start position:0% +to something that someone was struggling + + + align:start position:0% +to something that someone was struggling +with already but it wasn't really clear + + align:start position:0% +with already but it wasn't really clear + + + align:start position:0% +with already but it wasn't really clear +that they were + + align:start position:0% +that they were + + + align:start position:0% +that they were +serving a need in the + + align:start position:0% +serving a need in the + + + align:start position:0% +serving a need in the +community um that it had growth + + align:start position:0% +community um that it had growth + + + align:start position:0% +community um that it had growth +potential uh you know basically + + align:start position:0% +potential uh you know basically + + + align:start position:0% +potential uh you know basically +um there was there was no reason to + + align:start position:0% +um there was there was no reason to + + + align:start position:0% +um there was there was no reason to +support it in particular one over + + align:start position:0% +support it in particular one over + + + align:start position:0% +support it in particular one over +another you couldn't even evaluate one + + align:start position:0% +another you couldn't even evaluate one + + + align:start position:0% +another you couldn't even evaluate one +over another and I most of the proposals + + align:start position:0% +over another and I most of the proposals + + + align:start position:0% +over another and I most of the proposals +I saw were just like that um and most of + + align:start position:0% +I saw were just like that um and most of + + + align:start position:0% +I saw were just like that um and most of +the + + align:start position:0% +the + + + align:start position:0% +the +entrepreneurs um were not organized + + align:start position:0% +entrepreneurs um were not organized + + + align:start position:0% +entrepreneurs um were not organized +together either they didn't support each + + align:start position:0% +together either they didn't support each + + + align:start position:0% +together either they didn't support each +other whatsoever so they weren't + + align:start position:0% +other whatsoever so they weren't + + + align:start position:0% +other whatsoever so they weren't +realizing any efficiencies in the + + align:start position:0% +realizing any efficiencies in the + + + align:start position:0% +realizing any efficiencies in the +housing area they weren't buying + + align:start position:0% +housing area they weren't buying + + + align:start position:0% +housing area they weren't buying +Insurance together they weren't buying + + align:start position:0% +Insurance together they weren't buying + + + align:start position:0% +Insurance together they weren't buying +fuel together nothing + + align:start position:0% +fuel together nothing + + + align:start position:0% +fuel together nothing +you know um so I I would give that a war + + align:start position:0% +you know um so I I would give that a war + + + align:start position:0% +you know um so I I would give that a war +so if we said the the one is which sorry + + align:start position:0% +so if we said the the one is which sorry + + + align:start position:0% +so if we said the the one is which sorry +I was on zero for that then you said one + + align:start position:0% +I was on zero for that then you said one + + + align:start position:0% +I was on zero for that then you said one +yeah I say one someone has a business + + align:start position:0% +yeah I say one someone has a business + + + align:start position:0% +yeah I say one someone has a business +but its growth potential is unclear its + + align:start position:0% +but its growth potential is unclear its + + + align:start position:0% +but its growth potential is unclear its +Market is + + align:start position:0% +Market is + + + align:start position:0% +Market is +unclear it doesn't cooperate or work + + align:start position:0% +unclear it doesn't cooperate or work + + + align:start position:0% +unclear it doesn't cooperate or work +with other businesses to realize + + align:start position:0% +with other businesses to realize + + + align:start position:0% +with other businesses to realize +efficiencies on things like buying + + align:start position:0% +efficiencies on things like buying + + + align:start position:0% +efficiencies on things like buying +products or you + + align:start position:0% +products or you + + + align:start position:0% +products or you +know there's there's no real Vision + + align:start position:0% +know there's there's no real Vision + + + align:start position:0% +know there's there's no real Vision +about how to + + align:start position:0% + + + + align:start position:0% + +grow great and two is somewhere in in + + align:start position:0% +grow great and two is somewhere in in + + + align:start position:0% +grow great and two is somewhere in in +the middle is that all right we'll just + + align:start position:0% +the middle is that all right we'll just + + + align:start position:0% +the middle is that all right we'll just +keep moving and technical + + align:start position:0% + + + + align:start position:0% + +assistance what's a zero for a group + + align:start position:0% +assistance what's a zero for a group + + + align:start position:0% +assistance what's a zero for a group +with that has access to zero technical + + align:start position:0% +with that has access to zero technical + + + align:start position:0% +with that has access to zero technical +assistance nobody's at the table with + + align:start position:0% +assistance nobody's at the table with + + + align:start position:0% +assistance nobody's at the table with +any experience yeah you know nobody's + + align:start position:0% +any experience yeah you know nobody's + + + align:start position:0% +any experience yeah you know nobody's +done any of it + + align:start position:0% +done any of it + + + align:start position:0% +done any of it +before and also can't even identify what + + align:start position:0% +before and also can't even identify what + + + align:start position:0% +before and also can't even identify what +the thing is that they need sometimes if + + align:start position:0% +the thing is that they need sometimes if + + + align:start position:0% +the thing is that they need sometimes if +you don't if no one's at the table who + + align:start position:0% +you don't if no one's at the table who + + + align:start position:0% +you don't if no one's at the table who +knows you you don't even know what you + + align:start position:0% +knows you you don't even know what you + + + align:start position:0% +knows you you don't even know what you +don't + + align:start position:0% +don't + + + align:start position:0% +don't +know oh that's sound like + + align:start position:0% +know oh that's sound like + + + align:start position:0% +know oh that's sound like +rum the + + align:start position:0% + + + + align:start position:0% + +unbl and then um and let's just say a + + align:start position:0% +unbl and then um and let's just say a + + + align:start position:0% +unbl and then um and let's just say a +three I'm going to kind of move us + + align:start position:0% +three I'm going to kind of move us + + + align:start position:0% +three I'm going to kind of move us +forward a three is a group has + + align:start position:0% +forward a three is a group has + + + align:start position:0% +forward a three is a group has +the technical expertise in each of the + + align:start position:0% +the technical expertise in each of the + + + align:start position:0% +the technical expertise in each of the +areas that they come across they're + + align:start position:0% +areas that they come across they're + + + align:start position:0% +areas that they come across they're +they're able to access someone who's + + align:start position:0% +they're able to access someone who's + + + align:start position:0% +they're able to access someone who's +done it before and not only done it + + align:start position:0% +done it before and not only done it + + + align:start position:0% +done it before and not only done it +before but done it well and been + + align:start position:0% +before but done it well and been + + + align:start position:0% +before but done it well and been +successful at it so they know that + + align:start position:0% +successful at it so they know that + + + align:start position:0% +successful at it so they know that +they're getting really good business + + align:start position:0% +they're getting really good business + + + align:start position:0% +they're getting really good business +planning financial analysis you know the + + align:start position:0% +planning financial analysis you know the + + + align:start position:0% +planning financial analysis you know the +whole all those steps along the way and + + align:start position:0% +whole all those steps along the way and + + + align:start position:0% +whole all those steps along the way and +I feel like and I don't know what I'm + + align:start position:0% +I feel like and I don't know what I'm + + + align:start position:0% +I feel like and I don't know what I'm +talking about but people that have those + + align:start position:0% +talking about but people that have those + + + align:start position:0% +talking about but people that have those +skills and also understand what you're + + align:start position:0% +skills and also understand what you're + + + align:start position:0% +skills and also understand what you're +trying to do because I'm working right + + align:start position:0% +trying to do because I'm working right + + + align:start position:0% +trying to do because I'm working right +now with like Harvard Business School + + align:start position:0% +now with like Harvard Business School + + + align:start position:0% +now with like Harvard Business School +and they have those skill let me just + + align:start position:0% +and they have those skill let me just + + + align:start position:0% +and they have those skill let me just +say you know what I mean but if they + + align:start position:0% +say you know what I mean but if they + + + align:start position:0% +say you know what I mean but if they +don't understand the community + + align:start position:0% +don't understand the community + + + align:start position:0% +don't understand the community +organizing aspects or the other stuff + + align:start position:0% +organizing aspects or the other stuff + + + align:start position:0% +organizing aspects or the other stuff +that you're trying to do I feel like + + align:start position:0% +that you're trying to do I feel like + + + align:start position:0% +that you're trying to do I feel like +their skills are not as useful as they + + align:start position:0% +their skills are not as useful as they + + + align:start position:0% +their skills are not as useful as they +should be I think that's one of the + + align:start position:0% +should be I think that's one of the + + + align:start position:0% +should be I think that's one of the +things that we um trying to get across + + align:start position:0% +things that we um trying to get across + + + align:start position:0% +things that we um trying to get across +in this it's it's um knowing you know + + align:start position:0% +in this it's it's um knowing you know + + + align:start position:0% +in this it's it's um knowing you know +being like a a good coach I mean of a of + + align:start position:0% +being like a a good coach I mean of a of + + + align:start position:0% +being like a a good coach I mean of a of +a of a of a a team you know knowing + + align:start position:0% +a of a of a a team you know knowing + + + align:start position:0% +a of a of a a team you know knowing +which what's the proper player for the + + align:start position:0% +which what's the proper player for the + + + align:start position:0% +which what's the proper player for the +for the for the proper you know bringing + + align:start position:0% +for the for the proper you know bringing + + + align:start position:0% +for the for the proper you know bringing +the the right set of skills I uh you + + align:start position:0% +the the right set of skills I uh you + + + align:start position:0% +the the right set of skills I uh you +know so know somebody that would be + + align:start position:0% +know so know somebody that would be + + + align:start position:0% +know so know somebody that would be +great in terms of do doing your + + align:start position:0% +great in terms of do doing your + + + align:start position:0% +great in terms of do doing your +financials but should never even uh walk + + align:start position:0% +financials but should never even uh walk + + + align:start position:0% +financials but should never even uh walk +in the room with with it with the + + align:start position:0% +in the room with with it with the + + + align:start position:0% +in the room with with it with the +community folk you know I mean or vice + + align:start position:0% +community folk you know I mean or vice + + + align:start position:0% +community folk you know I mean or vice +versa or something but to get the + + align:start position:0% +versa or something but to get the + + + align:start position:0% +versa or something but to get the +financials done you know I I'm working + + align:start position:0% +financials done you know I I'm working + + + align:start position:0% +financials done you know I I'm working +on this biodiesel production facility + + align:start position:0% +on this biodiesel production facility + + + align:start position:0% +on this biodiesel production facility +and it's $3.7 million that we're raising + + align:start position:0% +and it's $3.7 million that we're raising + + + align:start position:0% +and it's $3.7 million that we're raising +we're talking with outside Equity + + align:start position:0% +we're talking with outside Equity + + + align:start position:0% +we're talking with outside Equity +investors and you know if I didn't have + + align:start position:0% +investors and you know if I didn't have + + + align:start position:0% +investors and you know if I didn't have +somebody with an MBA in finance who + + align:start position:0% +somebody with an MBA in finance who + + + align:start position:0% +somebody with an MBA in finance who +understood this Co-op project and could + + align:start position:0% +understood this Co-op project and could + + + align:start position:0% +understood this Co-op project and could +transl PL and sit at the table with me + + align:start position:0% +transl PL and sit at the table with me + + + align:start position:0% +transl PL and sit at the table with me +with the venture capitalist and say you + + align:start position:0% +with the venture capitalist and say you + + + align:start position:0% +with the venture capitalist and say you +know they say well what's the IR and I + + align:start position:0% +know they say well what's the IR and I + + + align:start position:0% +know they say well what's the IR and I +go to Larry and say I think that's + + align:start position:0% +go to Larry and say I think that's + + + align:start position:0% +go to Larry and say I think that's +internal rate of return but do you know + + align:start position:0% +internal rate of return but do you know + + + align:start position:0% +internal rate of return but do you know +what it is you know he calculates it and + + align:start position:0% +what it is you know he calculates it and + + + align:start position:0% +what it is you know he calculates it and +tells it you know but I I don't have + + align:start position:0% +tells it you know but I I don't have + + + align:start position:0% +tells it you know but I I don't have +those skills um he has those skills and + + align:start position:0% +those skills um he has those skills and + + + align:start position:0% +those skills um he has those skills and +if if he didn't understand the co-op he + + align:start position:0% +if if he didn't understand the co-op he + + + align:start position:0% +if if he didn't understand the co-op he +could do that stuff for me but there's a + + align:start position:0% +could do that stuff for me but there's a + + + align:start position:0% +could do that stuff for me but there's a +whole lot about this project that needs + + align:start position:0% +whole lot about this project that needs + + + align:start position:0% +whole lot about this project that needs +to be integrated into the financials + + align:start position:0% +to be integrated into the financials + + + align:start position:0% +to be integrated into the financials +that you know if he did already really + + align:start position:0% +that you know if he did already really + + + align:start position:0% +that you know if he did already really +get what we were doing and why I I would + + align:start position:0% +get what we were doing and why I I would + + + align:start position:0% +get what we were doing and why I I would +have a really hard time so a and access + + align:start position:0% +have a really hard time so a and access + + + align:start position:0% +have a really hard time so a and access +to lawyers you got a great lawyer who's + + align:start position:0% +to lawyers you got a great lawyer who's + + + align:start position:0% +to lawyers you got a great lawyer who's +never ever dealt with any Co-op law + + align:start position:0% +never ever dealt with any Co-op law + + + align:start position:0% +never ever dealt with any Co-op law +legal statute any worker owned legal + + align:start position:0% +legal statute any worker owned legal + + + align:start position:0% +legal statute any worker owned legal +statute it's like they're going to want + + align:start position:0% +statute it's like they're going to want + + + align:start position:0% +statute it's like they're going to want +you're going to need them to do a lot of + + align:start position:0% +you're going to need them to do a lot of + + + align:start position:0% +you're going to need them to do a lot of +studying read the whole statute look at + + align:start position:0% +studying read the whole statute look at + + + align:start position:0% +studying read the whole statute look at +other sample you + + align:start position:0% +other sample you + + + align:start position:0% +other sample you +know incorporation documents whatever + + align:start position:0% +know incorporation documents whatever + + + align:start position:0% +know incorporation documents whatever +they got to do a lot of work to get up + + align:start position:0% +they got to do a lot of work to get up + + + align:start position:0% +they got to do a lot of work to get up +to speed so just because you got + + align:start position:0% +to speed so just because you got + + + align:start position:0% +to speed so just because you got +Financial skill skills or legal skills + + align:start position:0% +Financial skill skills or legal skills + + + align:start position:0% +Financial skill skills or legal skills +doesn't mean you're good for these + + align:start position:0% +doesn't mean you're good for these + + + align:start position:0% +doesn't mean you're good for these +projects and it's hard to get lawyers + + align:start position:0% +projects and it's hard to get lawyers + + + align:start position:0% +projects and it's hard to get lawyers +and accountants who have the background + + align:start position:0% +and accountants who have the background + + + align:start position:0% +and accountants who have the background +you need and part of our excitement and + + align:start position:0% +you need and part of our excitement and + + + align:start position:0% +you need and part of our excitement and +talking to folk like you I mean and I + + align:start position:0% +talking to folk like you I mean and I + + + align:start position:0% +talking to folk like you I mean and I +mean is is that we're not going to be + + align:start position:0% +mean is is that we're not going to be + + + align:start position:0% +mean is is that we're not going to be +successful unless we begin to populate + + align:start position:0% +successful unless we begin to populate + + + align:start position:0% +successful unless we begin to populate +um U we need to be able to create more + + align:start position:0% +um U we need to be able to create more + + + align:start position:0% +um U we need to be able to create more +experts that that are not only are + + align:start position:0% +experts that that are not only are + + + align:start position:0% +experts that that are not only are +skilled you know in in in in certain + + align:start position:0% +skilled you know in in in in certain + + + align:start position:0% +skilled you know in in in in certain +business kind of Savvy kind of uh uh + + align:start position:0% +business kind of Savvy kind of uh uh + + + align:start position:0% +business kind of Savvy kind of uh uh +skills that they need whether it's + + align:start position:0% +skills that they need whether it's + + + align:start position:0% +skills that they need whether it's +financials and other things but also + + align:start position:0% +financials and other things but also + + + align:start position:0% +financials and other things but also +have an appreciation + + align:start position:0% +have an appreciation + + + align:start position:0% +have an appreciation +the community organizing part you know + + align:start position:0% +the community organizing part you know + + + align:start position:0% +the community organizing part you know +that that you know expect that you know + + align:start position:0% +that that you know expect that you know + + + align:start position:0% +that that you know expect that you know +the the things we need to do to raise + + align:start position:0% +the the things we need to do to raise + + + align:start position:0% +the the things we need to do to raise +the capital things we need to do to you + + align:start position:0% +the capital things we need to do to you + + + align:start position:0% +the capital things we need to do to you +know the the the the train folks so that + + align:start position:0% +know the the the the train folks so that + + + align:start position:0% +know the the the the train folks so that +they develop their capacity we got to + + align:start position:0% +they develop their capacity we got to + + + align:start position:0% +they develop their capacity we got to +begin to start creating that corpse of + + align:start position:0% +begin to start creating that corpse of + + + align:start position:0% +begin to start creating that corpse of +folk that that that can you know walk + + align:start position:0% +folk that that that can you know walk + + + align:start position:0% +folk that that that can you know walk +kind of uh smoothly into all these + + align:start position:0% +kind of uh smoothly into all these + + + align:start position:0% +kind of uh smoothly into all these +different worlds and um you know and and + + align:start position:0% +different worlds and um you know and and + + + align:start position:0% +different worlds and um you know and and +that like I said that there there are + + align:start position:0% +that like I said that there there are + + + align:start position:0% +that like I said that there there are +folks out there and but it does take + + align:start position:0% +folks out there and but it does take + + + align:start position:0% +folks out there and but it does take +some real I think one of the points + + align:start position:0% +some real I think one of the points + + + align:start position:0% +some real I think one of the points +there is that it it requires you just + + align:start position:0% +there is that it it requires you just + + + align:start position:0% +there is that it it requires you just +can't say uh let me call the first + + align:start position:0% +can't say uh let me call the first + + + align:start position:0% +can't say uh let me call the first +lawyer or the or the first accountant + + align:start position:0% +lawyer or the or the first accountant + + + align:start position:0% +lawyer or the or the first accountant +that you really need to talk to like I + + align:start position:0% +that you really need to talk to like I + + + align:start position:0% +that you really need to talk to like I +said if they haven't had that experience + + align:start position:0% +said if they haven't had that experience + + + align:start position:0% +said if they haven't had that experience +then but how are they open are they + + align:start position:0% +then but how are they open are they + + + align:start position:0% +then but how are they open are they +willing to to to to learn you know to do + + align:start position:0% +willing to to to to learn you know to do + + + align:start position:0% +willing to to to to learn you know to do +some study to do some uh you know uh to + + align:start position:0% +some study to do some uh you know uh to + + + align:start position:0% +some study to do some uh you know uh to +talk to you know can you connect them up + + align:start position:0% +talk to you know can you connect them up + + + align:start position:0% +talk to you know can you connect them up +with you know and would they would be + + align:start position:0% +with you know and would they would be + + + align:start position:0% +with you know and would they would be +willing to connect up talk with some + + align:start position:0% +willing to connect up talk with some + + + align:start position:0% +willing to connect up talk with some +other folk from another region that that + + align:start position:0% +other folk from another region that that + + + align:start position:0% +other folk from another region that that +have more of those experiences and I + + align:start position:0% +have more of those experiences and I + + + align:start position:0% +have more of those experiences and I +said it's it's U it's complicated and + + align:start position:0% +said it's it's U it's complicated and + + + align:start position:0% +said it's it's U it's complicated and +and a lot a lot of times U some serious + + align:start position:0% +and a lot a lot of times U some serious + + + align:start position:0% +and a lot a lot of times U some serious +mistakes are made when folks don't + + align:start position:0% +mistakes are made when folks don't + + + align:start position:0% +mistakes are made when folks don't +appreciate that U you know that U uh you + + align:start position:0% +appreciate that U you know that U uh you + + + align:start position:0% +appreciate that U you know that U uh you +know that and and when you find places + + align:start position:0% +know that and and when you find places + + + align:start position:0% +know that and and when you find places +like CDI around the country where + + align:start position:0% +like CDI around the country where + + + align:start position:0% +like CDI around the country where +they've tried to bring together that + + align:start position:0% +they've tried to bring together that + + + align:start position:0% +they've tried to bring together that +focused uh skill set you know they play + + align:start position:0% +focused uh skill set you know they play + + + align:start position:0% +focused uh skill set you know they play +a very special role and we need we need + + align:start position:0% +a very special role and we need we need + + + align:start position:0% +a very special role and we need we need +we need you know 50 100 times more of + + align:start position:0% +we need you know 50 100 times more of + + + align:start position:0% +we need you know 50 100 times more of +them than than than we have right now + + align:start position:0% +them than than than we have right now + + + align:start position:0% +them than than than we have right now +and lots of times we'll go in and work + + align:start position:0% +and lots of times we'll go in and work + + + align:start position:0% +and lots of times we'll go in and work +with a CDC or another group to who's got + + align:start position:0% +with a CDC or another group to who's got + + + align:start position:0% +with a CDC or another group to who's got +a project that they haven't ever done + + align:start position:0% +a project that they haven't ever done + + + align:start position:0% +a project that they haven't ever done +this kind of before and so we'll help + + align:start position:0% +this kind of before and so we'll help + + + align:start position:0% +this kind of before and so we'll help +them you know hook up with the lawyers + + align:start position:0% +them you know hook up with the lawyers + + + align:start position:0% +them you know hook up with the lawyers +in their area or the accountants or the + + align:start position:0% +in their area or the accountants or the + + + align:start position:0% +in their area or the accountants or the +facilitators who know who understand + + align:start position:0% +facilitators who know who understand + + + align:start position:0% +facilitators who know who understand +enough about business development to be + + align:start position:0% +enough about business development to be + + + align:start position:0% +enough about business development to be +able to run those meetings and whatever + + align:start position:0% +able to run those meetings and whatever + + + align:start position:0% +able to run those meetings and whatever +so fun stuff so we're + + align:start position:0% +so fun stuff so we're + + + align:start position:0% +so fun stuff so we're +oners money from + + align:start position:0% +oners money from + + + align:start position:0% +oners money from +Members + + align:start position:0% + + + + align:start position:0% + +yes you don't have money for members you + + align:start position:0% +yes you don't have money for members you + + + align:start position:0% +yes you don't have money for members you +haven't you haven't done any organizing + + align:start position:0% +haven't you haven't done any organizing + + + align:start position:0% +haven't you haven't done any organizing +so a zero + + align:start position:0% +so a zero + + + align:start position:0% +so a zero +is there's just been no organizing + + align:start position:0% +is there's just been no organizing + + + align:start position:0% +is there's just been no organizing +that's happened at + + align:start position:0% +that's happened at + + + align:start position:0% +that's happened at +all I've also I've also had people you + + align:start position:0% +all I've also I've also had people you + + + align:start position:0% +all I've also I've also had people you +know somebody some Champion for the + + align:start position:0% +know somebody some Champion for the + + + align:start position:0% +know somebody some Champion for the +project goes out and + + align:start position:0% +project goes out and + + + align:start position:0% +project goes out and +say housing just come and join you'll we + + align:start position:0% +say housing just come and join you'll we + + + align:start position:0% +say housing just come and join you'll we +will never charge market rate you know + + align:start position:0% +will never charge market rate you know + + + align:start position:0% +will never charge market rate you know +this is going to be this is low income + + align:start position:0% +this is going to be this is low income + + + align:start position:0% +this is going to be this is low income +housing and it's going to be for you and + + align:start position:0% +housing and it's going to be for you and + + + align:start position:0% +housing and it's going to be for you and +you're not going to have to pay anything + + align:start position:0% +you're not going to have to pay anything + + + align:start position:0% +you're not going to have to pay anything +you + + align:start position:0% +you + + + align:start position:0% +you +know so I mean so there's sometimes + + align:start position:0% +know so I mean so there's sometimes + + + align:start position:0% +know so I mean so there's sometimes +there's organizing done but it's done + + align:start position:0% +there's organizing done but it's done + + + align:start position:0% +there's organizing done but it's done +with you know the wrong message going + + align:start position:0% +with you know the wrong message going + + + align:start position:0% +with you know the wrong message going +out you don't have to put anything in + + align:start position:0% +out you don't have to put anything in + + + align:start position:0% +out you don't have to put anything in +here this is just a gift to + + align:start position:0% +here this is just a gift to + + + align:start position:0% +here this is just a gift to +you so so zero is no money down one is + + align:start position:0% +you so so zero is no money down one is + + + align:start position:0% +you so so zero is no money down one is +$1 in two is $2 no um but so three is um + + align:start position:0% +$1 in two is $2 no um but so three is um + + + align:start position:0% +$1 in two is $2 no um but so three is um +I think three is I you know I watch my + + align:start position:0% +I think three is I you know I watch my + + + align:start position:0% +I think three is I you know I watch my +mother organize church people to go on + + align:start position:0% +mother organize church people to go on + + + align:start position:0% +mother organize church people to go on +these cruises people have very no money + + align:start position:0% +these cruises people have very no money + + + align:start position:0% +these cruises people have very no money +very little money and she spends the + + align:start position:0% +very little money and she spends the + + + align:start position:0% +very little money and she spends the +first couple of months + + align:start position:0% +first couple of months + + + align:start position:0% +first couple of months +after people after payday comes you know + + align:start position:0% +after people after payday comes you know + + + align:start position:0% +after people after payday comes you know +Mom's right there before they can hit + + align:start position:0% +Mom's right there before they can hit + + + align:start position:0% +Mom's right there before they can hit +the beer garden you know there's mom you + + align:start position:0% +the beer garden you know there's mom you + + + align:start position:0% +the beer garden you know there's mom you +know and and she collects you know $25 + + align:start position:0% +know and and she collects you know $25 + + + align:start position:0% +know and and she collects you know $25 +you know weekly but she's really on it + + align:start position:0% +you know weekly but she's really on it + + + align:start position:0% +you know weekly but she's really on it +these first two months but the thing is + + align:start position:0% +these first two months but the thing is + + + align:start position:0% +these first two months but the thing is +once you put your money in you don't get + + align:start position:0% +once you put your money in you don't get + + + align:start position:0% +once you put your money in you don't get +it back regardless you know folks sign + + align:start position:0% +it back regardless you know folks sign + + + align:start position:0% +it back regardless you know folks sign +up they want to go they put their first + + align:start position:0% +up they want to go they put their first + + + align:start position:0% +up they want to go they put their first +25 the second what happens is after they + + align:start position:0% +25 the second what happens is after they + + + align:start position:0% +25 the second what happens is after they +have $200 in she doesn't call anybody + + align:start position:0% +have $200 in she doesn't call anybody + + + align:start position:0% +have $200 in she doesn't call anybody +because their money's in it then they + + align:start position:0% +because their money's in it then they + + + align:start position:0% +because their money's in it then they +already know you know they're not + + align:start position:0% +already know you know they're not + + + align:start position:0% +already know you know they're not +getting + + align:start position:0% +getting + + + align:start position:0% +getting +back they want to make sure you know + + align:start position:0% +back they want to make sure you know + + + align:start position:0% +back they want to make sure you know +they don't fall behind somebody's going + + align:start position:0% +they don't fall behind somebody's going + + + align:start position:0% +they don't fall behind somebody's going +on it's interesting because the whole + + align:start position:0% +on it's interesting because the whole + + + align:start position:0% +on it's interesting because the whole +dynamic + + align:start position:0% +dynamic + + + align:start position:0% +dynamic +changes very interesting very + + align:start position:0% +changes very interesting very + + + align:start position:0% +changes very interesting very +interesting Str I got to try that + + align:start position:0% +interesting Str I got to try that + + + align:start position:0% +interesting Str I got to try that +one yeah I was going to say um added to + + align:start position:0% +one yeah I was going to say um added to + + + align:start position:0% +one yeah I was going to say um added to +that not not uh for number for number + + align:start position:0% +that not not uh for number for number + + + align:start position:0% +that not not uh for number for number +three not just that you know you get you + + align:start position:0% +three not just that you know you get you + + + align:start position:0% +three not just that you know you get you +know your members to pay but I think uh + + align:start position:0% +know your members to pay but I think uh + + + align:start position:0% +know your members to pay but I think uh +what's important in getting them to pay + + align:start position:0% +what's important in getting them to pay + + + align:start position:0% +what's important in getting them to pay +cuz a lot of organizations that I've + + align:start position:0% +cuz a lot of organizations that I've + + + align:start position:0% +cuz a lot of organizations that I've +been a part of we Tred to collect dues + + align:start position:0% +been a part of we Tred to collect dues + + + align:start position:0% +been a part of we Tred to collect dues +and these types of things there was + + align:start position:0% +and these types of things there was + + + align:start position:0% +and these types of things there was +never any uh sort of like uh a + + align:start position:0% +never any uh sort of like uh a + + + align:start position:0% +never any uh sort of like uh a +specific uh Target or say you know well + + align:start position:0% +specific uh Target or say you know well + + + align:start position:0% +specific uh Target or say you know well +you know we need this amount of money + + align:start position:0% +you know we need this amount of money + + + align:start position:0% +you know we need this amount of money +for this you know it was just it was + + align:start position:0% +for this you know it was just it was + + + align:start position:0% +for this you know it was just it was +just too open-ended and people like well + + align:start position:0% +just too open-ended and people like well + + + align:start position:0% +just too open-ended and people like well +what I'm giving money like what do we + + align:start position:0% +what I'm giving money like what do we + + + align:start position:0% +what I'm giving money like what do we +need it for you know we have you know + + align:start position:0% +need it for you know we have you know + + + align:start position:0% +need it for you know we have you know +why do we need to pay these this month + + align:start position:0% +why do we need to pay these this month + + + align:start position:0% +why do we need to pay these this month +you know to you know to do what you know + + align:start position:0% +you know to you know to do what you know + + + align:start position:0% +you know to you know to do what you know +to print out some more paper we could do + + align:start position:0% +to print out some more paper we could do + + + align:start position:0% +to print out some more paper we could do +that for fre from do it some place else + + align:start position:0% +that for fre from do it some place else + + + align:start position:0% +that for fre from do it some place else +but if there was like some targe that + + align:start position:0% +but if there was like some targe that + + + align:start position:0% +but if there was like some targe that +people were shooting for and there was + + align:start position:0% +people were shooting for and there was + + + align:start position:0% +people were shooting for and there was +some way to conceptualize that this this + + align:start position:0% +some way to conceptualize that this this + + + align:start position:0% +some way to conceptualize that this this +is what you might was going to and + + align:start position:0% +is what you might was going to and + + + align:start position:0% +is what you might was going to and +didn't be able to see the return at the + + align:start position:0% +didn't be able to see the return at the + + + align:start position:0% +didn't be able to see the return at the +end of it I think that would be you know + + align:start position:0% +end of it I think that would be you know + + + align:start position:0% +end of it I think that would be you know +a way that's very + + align:start position:0% +a way that's very + + + align:start position:0% +a way that's very +important and and for me a three is you + + align:start position:0% +important and and for me a three is you + + + align:start position:0% +important and and for me a three is you +finished your business plan you know + + align:start position:0% +finished your business plan you know + + + align:start position:0% +finished your business plan you know +what capital the business is going to + + align:start position:0% +what capital the business is going to + + + align:start position:0% +what capital the business is going to +need to start is it going to need $10 + + align:start position:0% +need to start is it going to need $10 + + + align:start position:0% +need to start is it going to need $10 +$100,00 000 3.7 million you know how + + align:start position:0% +$100,00 000 3.7 million you know how + + + align:start position:0% +$100,00 000 3.7 million you know how +much you need and you've got a strategy + + align:start position:0% +much you need and you've got a strategy + + + align:start position:0% +much you need and you've got a strategy +for getting it in and the members are + + align:start position:0% +for getting it in and the members are + + + align:start position:0% +for getting it in and the members are +are purchasing a significant portion of + + align:start position:0% +are purchasing a significant portion of + + + align:start position:0% +are purchasing a significant portion of +the business they're not purchasing 1% + + align:start position:0% +the business they're not purchasing 1% + + + align:start position:0% +the business they're not purchasing 1% +of the business with their member Equity + + align:start position:0% +of the business with their member Equity + + + align:start position:0% +of the business with their member Equity +they're purchasing 30% of the business + + align:start position:0% +they're purchasing 30% of the business + + + align:start position:0% +they're purchasing 30% of the business +maybe you know but a significant portion + + align:start position:0% +maybe you know but a significant portion + + + align:start position:0% +maybe you know but a significant portion +is coming from Members so they actually + + align:start position:0% +is coming from Members so they actually + + + align:start position:0% +is coming from Members so they actually +do own it it's not just the banks or + + align:start position:0% +do own it it's not just the banks or + + + align:start position:0% +do own it it's not just the banks or +some Grant that's owning this business + + align:start position:0% +some Grant that's owning this business + + + align:start position:0% +some Grant that's owning this business +it's really them um um and then money + + align:start position:0% +it's really them um um and then money + + + align:start position:0% +it's really them um um and then money +from other + + align:start position:0% + + + + align:start position:0% + +sources what's a zero no idea where to + + align:start position:0% +sources what's a zero no idea where to + + + align:start position:0% +sources what's a zero no idea where to +get + + align:start position:0% +get + + + align:start position:0% +get +it it's going to fall from Heaven when + + align:start position:0% +it it's going to fall from Heaven when + + + align:start position:0% +it it's going to fall from Heaven when +we need + + align:start position:0% +we need + + + align:start position:0% +we need +it number two is vure Capal same thing + + align:start position:0% +it number two is vure Capal same thing + + + align:start position:0% +it number two is vure Capal same thing +right + + align:start position:0% + + + + align:start position:0% + +there most of them want you and you know + + align:start position:0% +there most of them want you and you know + + + align:start position:0% +there most of them want you and you know +your kids and everything else you know + + align:start position:0% +your kids and everything else you know + + + align:start position:0% +your kids and everything else you know +at the end of the + + align:start position:0% + + + + align:start position:0% + +day great and three is you you know you + + align:start position:0% +day great and three is you you know you + + + align:start position:0% +day great and three is you you know you +got a really solid plan and you you you + + align:start position:0% +got a really solid plan and you you you + + + align:start position:0% +got a really solid plan and you you you +got you got three people for every one + + align:start position:0% +got you got three people for every one + + + align:start position:0% +got you got three people for every one +that you need to bring in you + + align:start position:0% +that you need to bring in you + + + align:start position:0% +that you need to bring in you +know + + align:start position:0% + + + + align:start position:0% + +um and the last ingredient is you have + + align:start position:0% +um and the last ingredient is you have + + + align:start position:0% +um and the last ingredient is you have +to have these things in place to sustain + + align:start position:0% +to have these things in place to sustain + + + align:start position:0% +to have these things in place to sustain +that business once you get it going so + + align:start position:0% +that business once you get it going so + + + align:start position:0% +that business once you get it going so +there's got to be ongoing Education and + + align:start position:0% +there's got to be ongoing Education and + + + align:start position:0% +there's got to be ongoing Education and +Training resources public policy + + align:start position:0% +Training resources public policy + + + align:start position:0% +Training resources public policy +advocacy industry information and + + align:start position:0% +advocacy industry information and + + + align:start position:0% +advocacy industry information and +technical assistance because guaranteed + + align:start position:0% +technical assistance because guaranteed + + + align:start position:0% +technical assistance because guaranteed +there are bumps in the road either + + align:start position:0% +there are bumps in the road either + + + align:start position:0% +there are bumps in the road either +something Big's going to change in the + + align:start position:0% +something Big's going to change in the + + + align:start position:0% +something Big's going to change in the +environment you know in your industry or + + align:start position:0% +environment you know in your industry or + + + align:start position:0% +environment you know in your industry or +there's going to be a new law that comes + + align:start position:0% +there's going to be a new law that comes + + + align:start position:0% +there's going to be a new law that comes +in and either messes with your business + + align:start position:0% +in and either messes with your business + + + align:start position:0% +in and either messes with your business +or makes your business work um there's + + align:start position:0% +or makes your business work um there's + + + align:start position:0% +or makes your business work um there's +there's there's your board is going to + + align:start position:0% +there's there's your board is going to + + + align:start position:0% +there's there's your board is going to +need to get trained you're going to get + + align:start position:0% +need to get trained you're going to get + + + align:start position:0% +need to get trained you're going to get +a whole new board within a few month + + align:start position:0% +a whole new board within a few month + + + align:start position:0% +a whole new board within a few month +month you know after the next annual + + align:start position:0% +month you know after the next annual + + + align:start position:0% +month you know after the next annual +election they'll be you know a third of + + align:start position:0% +election they'll be you know a third of + + + align:start position:0% +election they'll be you know a third of +the new board members and they need + + align:start position:0% +the new board members and they need + + + align:start position:0% +the new board members and they need +training how to do what they're doing + + align:start position:0% +training how to do what they're doing + + + align:start position:0% +training how to do what they're doing +yeah I think that's and that I think has + + align:start position:0% +yeah I think that's and that I think has + + + align:start position:0% +yeah I think that's and that I think has +a a lot to do with why so many of of + + align:start position:0% +a a lot to do with why so many of of + + + align:start position:0% +a a lot to do with why so many of of +these efforts don't sustain and and and + + align:start position:0% +these efforts don't sustain and and and + + + align:start position:0% +these efforts don't sustain and and and +continue that we're not paying attent + + align:start position:0% +continue that we're not paying attent + + + align:start position:0% +continue that we're not paying attent +you know we go through this effort you + + align:start position:0% +you know we go through this effort you + + + align:start position:0% +you know we go through this effort you +know to set them up and then you know + + align:start position:0% +know to set them up and then you know + + + align:start position:0% +know to set them up and then you know +not understanding that you know even + + align:start position:0% +not understanding that you know even + + + align:start position:0% +not understanding that you know even +sometimes even it might be just the + + align:start position:0% +sometimes even it might be just the + + + align:start position:0% +sometimes even it might be just the +challenges from success + + align:start position:0% +challenges from success + + + align:start position:0% +challenges from success +all of a sudden you know you've done so + + align:start position:0% +all of a sudden you know you've done so + + + align:start position:0% +all of a sudden you know you've done so +well and all of a sudden now other + + align:start position:0% +well and all of a sudden now other + + + align:start position:0% +well and all of a sudden now other +people are like whoa you know I want + + align:start position:0% +people are like whoa you know I want + + + align:start position:0% +people are like whoa you know I want +some of that you know and then you got + + align:start position:0% +some of that you know and then you got + + + align:start position:0% +some of that you know and then you got +all of a sudden you got predators and + + align:start position:0% +all of a sudden you got predators and + + + align:start position:0% +all of a sudden you got predators and +competitors and everything El that that + + align:start position:0% +competitors and everything El that that + + + align:start position:0% +competitors and everything El that that +that uh that when you were small fry do + + align:start position:0% +that uh that when you were small fry do + + + align:start position:0% +that uh that when you were small fry do +dealing with a need that you know the + + align:start position:0% +dealing with a need that you know the + + + align:start position:0% +dealing with a need that you know the +big uh Community you know thought was + + align:start position:0% +big uh Community you know thought was + + + align:start position:0% +big uh Community you know thought was +totally unimportant you know or or + + align:start position:0% +totally unimportant you know or or + + + align:start position:0% +totally unimportant you know or or +totally um um imp impossible to to + + align:start position:0% +totally um um imp impossible to to + + + align:start position:0% +totally um um imp impossible to to +really do something about once you prove + + align:start position:0% +really do something about once you prove + + + align:start position:0% +really do something about once you prove +that that something can be done you know + + align:start position:0% +that that something can be done you know + + + align:start position:0% +that that something can be done you know +uh uh that that success brings you a + + align:start position:0% +uh uh that that success brings you a + + + align:start position:0% +uh uh that that success brings you a +whole new set of problems how do we deal + + align:start position:0% +whole new set of problems how do we deal + + + align:start position:0% +whole new set of problems how do we deal +with it like I said I mean um the uh the + + align:start position:0% +with it like I said I mean um the uh the + + + align:start position:0% +with it like I said I mean um the uh the +the kinds of leadership issues uh that + + align:start position:0% +the kinds of leadership issues uh that + + + align:start position:0% +the kinds of leadership issues uh that +that that people uh go through you know + + align:start position:0% +that that people uh go through you know + + + align:start position:0% +that that people uh go through you know +once you think something that's been + + align:start position:0% +once you think something that's been + + + align:start position:0% +once you think something that's been +around 3 years 5 years 7 years 10 years + + align:start position:0% +around 3 years 5 years 7 years 10 years + + + align:start position:0% +around 3 years 5 years 7 years 10 years +you know um each each one of them I + + align:start position:0% +you know um each each one of them I + + + align:start position:0% +you know um each each one of them I +think that we need to be doing a better + + align:start position:0% +think that we need to be doing a better + + + align:start position:0% +think that we need to be doing a better +job at expect at preparing for and um + + align:start position:0% +job at expect at preparing for and um + + + align:start position:0% +job at expect at preparing for and um +and and you know I think like I said + + align:start position:0% +and and you know I think like I said + + + align:start position:0% +and and you know I think like I said +that this has I think been one of the + + align:start position:0% +that this has I think been one of the + + + align:start position:0% +that this has I think been one of the +the greatest weaknesses that that that + + align:start position:0% +the greatest weaknesses that that that + + + align:start position:0% +the greatest weaknesses that that that +that we face that we don't + + align:start position:0% +that we face that we don't + + + align:start position:0% +that we face that we don't +you know we don't think about the + + align:start position:0% +you know we don't think about the + + + align:start position:0% +you know we don't think about the +longterm sustainability and we don't + + align:start position:0% +longterm sustainability and we don't + + + align:start position:0% +longterm sustainability and we don't +make sure that all of these pieces are + + align:start position:0% +make sure that all of these pieces are + + + align:start position:0% +make sure that all of these pieces are +in place I would + + align:start position:0% +in place I would + + + align:start position:0% +in place I would +ask somewhere because almost every + + align:start position:0% +ask somewhere because almost every + + + align:start position:0% +ask somewhere because almost every +effort I've been associated with as as + + align:start position:0% +effort I've been associated with as as + + + align:start position:0% +effort I've been associated with as as +soon as it it's like up and operational + + align:start position:0% +soon as it it's like up and operational + + + align:start position:0% +soon as it it's like up and operational +it gets sedimented yeah very quickly you + + align:start position:0% +it gets sedimented yeah very quickly you + + + align:start position:0% +it gets sedimented yeah very quickly you +know got a great plan you put that put + + align:start position:0% +know got a great plan you put that put + + + align:start position:0% +know got a great plan you put that put +it on the Shelf you okay you're not + + align:start position:0% +it on the Shelf you okay you're not + + + align:start position:0% +it on the Shelf you okay you're not +looking at it every few months and you + + align:start position:0% +looking at it every few months and you + + + align:start position:0% +looking at it every few months and you +know anything changed you + + align:start position:0% +know anything changed you + + + align:start position:0% +know anything changed you +know very good point + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +yeah um and then we just wanted to run + + align:start position:0% +yeah um and then we just wanted to run + + + align:start position:0% +yeah um and then we just wanted to run +through just a little bit about what is + + align:start position:0% +through just a little bit about what is + + + align:start position:0% +through just a little bit about what is +out there right now um and in the + + align:start position:0% +out there right now um and in the + + + align:start position:0% +out there right now um and in the +Northeast there's uh 162 agricultural + + align:start position:0% +Northeast there's uh 162 agricultural + + + align:start position:0% +Northeast there's uh 162 agricultural +cooperatives with 82,000 members and 5 + + align:start position:0% +cooperatives with 82,000 members and 5 + + + align:start position:0% +cooperatives with 82,000 members and 5 +billion in sales you can see 1,400 + + align:start position:0% +billion in sales you can see 1,400 + + + align:start position:0% +billion in sales you can see 1,400 +Credit Unions you can see 60 retail food + + align:start position:0% +Credit Unions you can see 60 retail food + + + align:start position:0% +Credit Unions you can see 60 retail food +co-ops and, 1500 pre-order buying clubs + + align:start position:0% +co-ops and, 1500 pre-order buying clubs + + + align:start position:0% +co-ops and, 1500 pre-order buying clubs +there's um uh 55 firms with 4,300 member + + align:start position:0% +there's um uh 55 firms with 4,300 member + + + align:start position:0% +there's um uh 55 firms with 4,300 member +workers who are either in a worker Co-op + + align:start position:0% +workers who are either in a worker Co-op + + + align:start position:0% +workers who are either in a worker Co-op +or an ESOP there's 600,000 units of uh + + align:start position:0% +or an ESOP there's 600,000 units of uh + + + align:start position:0% +or an ESOP there's 600,000 units of uh +Cooperative housing there are um + + align:start position:0% +Cooperative housing there are um + + + align:start position:0% +Cooperative housing there are um +retailer owned wholesale cooperatives + + align:start position:0% +retailer owned wholesale cooperatives + + + align:start position:0% +retailer owned wholesale cooperatives +shoppr right Ace True Value Best Western + + align:start position:0% +shoppr right Ace True Value Best Western + + + align:start position:0% +shoppr right Ace True Value Best Western +Duncan Donuts KFC um there are day + + align:start position:0% +Duncan Donuts KFC um there are day + + + align:start position:0% +Duncan Donuts KFC um there are day +school and preschool cooperatives + + align:start position:0% +school and preschool cooperatives + + + align:start position:0% +school and preschool cooperatives +Regional educational cooperatives + + align:start position:0% +Regional educational cooperatives + + + align:start position:0% +Regional educational cooperatives +healthc care co-ops U Municipal + + align:start position:0% +healthc care co-ops U Municipal + + + align:start position:0% +healthc care co-ops U Municipal +co-ops just a a wide variety of lots of + + align:start position:0% +co-ops just a a wide variety of lots of + + + align:start position:0% +co-ops just a a wide variety of lots of +other kinds of Cooper so just to give + + align:start position:0% +other kinds of Cooper so just to give + + + align:start position:0% +other kinds of Cooper so just to give +you a sense here in the Northeast + + align:start position:0% +you a sense here in the Northeast + + + align:start position:0% +you a sense here in the Northeast +there's 10,000 + + align:start position:0% +there's 10,000 + + + align:start position:0% +there's 10,000 +cooperatives with a with um 10 million + + align:start position:0% +cooperatives with a with um 10 million + + + align:start position:0% +cooperatives with a with um 10 million +members it's not insignificant and there + + align:start position:0% +members it's not insignificant and there + + + align:start position:0% +members it's not insignificant and there +are lots of other group- based + + align:start position:0% +are lots of other group- based + + + align:start position:0% +are lots of other group- based +businesses these are the ones I have + + align:start position:0% +businesses these are the ones I have + + + align:start position:0% +businesses these are the ones I have +stats on um do you want to + + align:start position:0% +stats on um do you want to + + + align:start position:0% +stats on um do you want to +yeah as it say one of the points is that + + align:start position:0% +yeah as it say one of the points is that + + + align:start position:0% +yeah as it say one of the points is that +we haven't you know part of it is as our + + align:start position:0% +we haven't you know part of it is as our + + + align:start position:0% +we haven't you know part of it is as our +mistake as part of the Cooperative + + align:start position:0% +mistake as part of the Cooperative + + + align:start position:0% +mistake as part of the Cooperative +movement that we haven't done a good + + align:start position:0% +movement that we haven't done a good + + + align:start position:0% +movement that we haven't done a good +enough job of marketing that you know we + + align:start position:0% +enough job of marketing that you know we + + + align:start position:0% +enough job of marketing that you know we +have a thing called mocha marketing our + + align:start position:0% +have a thing called mocha marketing our + + + align:start position:0% +have a thing called mocha marketing our +Cooperative advantage and letting folks + + align:start position:0% +Cooperative advantage and letting folks + + + align:start position:0% +Cooperative advantage and letting folks +know that that you know that that there + + align:start position:0% +know that that you know that that there + + + align:start position:0% +know that that you know that that there +are um that most folks are touched by + + align:start position:0% +are um that most folks are touched by + + + align:start position:0% +are um that most folks are touched by +cooperatives in some way that every day + + align:start position:0% +cooperatives in some way that every day + + + align:start position:0% +cooperatives in some way that every day +in the US U 100 million um men women and + + align:start position:0% +in the US U 100 million um men women and + + + align:start position:0% +in the US U 100 million um men women and +children are affected by cooperatives + + align:start position:0% +children are affected by cooperatives + + + align:start position:0% +children are affected by cooperatives +and other group-based businesses uh you + + align:start position:0% +and other group-based businesses uh you + + + align:start position:0% +and other group-based businesses uh you +know uh 13.3 million checks and one .3 + + align:start position:0% +know uh 13.3 million checks and one .3 + + + align:start position:0% +know uh 13.3 million checks and one .3 +billion by uh by credit unions um 3 + + align:start position:0% +billion by uh by credit unions um 3 + + + align:start position:0% +billion by uh by credit unions um 3 +million people and going to Cooperative + + align:start position:0% +million people and going to Cooperative + + + align:start position:0% +million people and going to Cooperative +housing + + align:start position:0% +housing + + + align:start position:0% +housing +units no just this example Amalgamated + + align:start position:0% +units no just this example Amalgamated + + + align:start position:0% +units no just this example Amalgamated +housing was one of the first uh um um + + align:start position:0% +housing was one of the first uh um um + + + align:start position:0% +housing was one of the first uh um um +housing cooperatives back in 1920s uh uh + + align:start position:0% +housing cooperatives back in 1920s uh uh + + + align:start position:0% +housing cooperatives back in 1920s uh uh +and the nickel city housing Coop was + + align:start position:0% +and the nickel city housing Coop was + + + align:start position:0% +and the nickel city housing Coop was +just formed last year so it's it's a + + align:start position:0% +just formed last year so it's it's a + + + align:start position:0% +just formed last year so it's it's a +it's a Continuum that is that continues + + align:start position:0% +it's a Continuum that is that continues + + + align:start position:0% +it's a Continuum that is that continues +to to grow as and particularly needs to + + align:start position:0% +to to grow as and particularly needs to + + + align:start position:0% +to to grow as and particularly needs to +grow even more as as our housing prices + + align:start position:0% +grow even more as as our housing prices + + + align:start position:0% +grow even more as as our housing prices +become uh less and less affordable for + + align:start position:0% +become uh less and less affordable for + + + align:start position:0% +become uh less and less affordable for +many more and more people and amalgam + + align:start position:0% +many more and more people and amalgam + + + align:start position:0% +many more and more people and amalgam +housing was developed with a labor union + + align:start position:0% +housing was developed with a labor union + + + align:start position:0% +housing was developed with a labor union +consumer Alliance to build housing for + + align:start position:0% +consumer Alliance to build housing for + + + align:start position:0% +consumer Alliance to build housing for +people in communities and it's the + + align:start position:0% +people in communities and it's the + + + align:start position:0% +people in communities and it's the +reason um New York City is Affordable to + + align:start position:0% +reason um New York City is Affordable to + + + align:start position:0% +reason um New York City is Affordable to +workingclass people is because the + + align:start position:0% +workingclass people is because the + + + align:start position:0% +workingclass people is because the +unions and the cooperatives and the + + align:start position:0% +unions and the cooperatives and the + + + align:start position:0% +unions and the cooperatives and the +consumer co-ops work together to create + + align:start position:0% +consumer co-ops work together to create + + + align:start position:0% +consumer co-ops work together to create +housing and food resources and energy + + align:start position:0% +housing and food resources and energy + + + align:start position:0% +housing and food resources and energy +resources that are still um sustaining + + align:start position:0% +resources that are still um sustaining + + + align:start position:0% +resources that are still um sustaining +workingclass folks in New York today + + align:start position:0% +workingclass folks in New York today + + + align:start position:0% +workingclass folks in New York today +love to get back back to that yeah and + + align:start position:0% +love to get back back to that yeah and + + + align:start position:0% +love to get back back to that yeah and +you know then like I said 11 million + + align:start position:0% +you know then like I said 11 million + + + align:start position:0% +you know then like I said 11 million +people going to to work at a at at a + + align:start position:0% +people going to to work at a at at a + + + align:start position:0% +people going to to work at a at at a +worker corops and esops and that's a + + align:start position:0% +worker corops and esops and that's a + + + align:start position:0% +worker corops and esops and that's a +growing thing as particularly more and + + align:start position:0% +growing thing as particularly more and + + + align:start position:0% +growing thing as particularly more and +more uh folks are aging out and uh um + + align:start position:0% +more uh folks are aging out and uh um + + + align:start position:0% +more uh folks are aging out and uh um +and and you know how can you keep that + + align:start position:0% +and and you know how can you keep that + + + align:start position:0% +and and you know how can you keep that +business that was been functioning and + + align:start position:0% +business that was been functioning and + + + align:start position:0% +business that was been functioning and +but the the the kids not you know don't + + align:start position:0% +but the the the kids not you know don't + + + align:start position:0% +but the the the kids not you know don't +care for that family business anymore a + + align:start position:0% +care for that family business anymore a + + + align:start position:0% +care for that family business anymore a +lot of folks are turning to work at + + align:start position:0% +lot of folks are turning to work at + + + align:start position:0% +lot of folks are turning to work at +coops East opson um uh uh uh uh + + align:start position:0% +coops East opson um uh uh uh uh + + + align:start position:0% +coops East opson um uh uh uh uh +Cooperative health approaches 60,000 + + align:start position:0% +Cooperative health approaches 60,000 + + + align:start position:0% +Cooperative health approaches 60,000 +people and and and that number is going + + align:start position:0% +people and and and that number is going + + + align:start position:0% +people and and and that number is going +to grow a lot I mean that that there's a + + align:start position:0% +to grow a lot I mean that that there's a + + + align:start position:0% +to grow a lot I mean that that there's a +lot of attention and how how can we come + + align:start position:0% +lot of attention and how how can we come + + + align:start position:0% +lot of attention and how how can we come +up with some Cooperative uh group based + + align:start position:0% +up with some Cooperative uh group based + + + align:start position:0% +up with some Cooperative uh group based +approaches to uh to a healthc care + + align:start position:0% +approaches to uh to a healthc care + + + align:start position:0% +approaches to uh to a healthc care +problems so um you know every day uh 1.2 + + align:start position:0% +problems so um you know every day uh 1.2 + + + align:start position:0% +problems so um you know every day uh 1.2 +million in U and uh and Goods at natural + + align:start position:0% +million in U and uh and Goods at natural + + + align:start position:0% +million in U and uh and Goods at natural +food cooperatives and buying clubs I + + align:start position:0% +food cooperatives and buying clubs I + + + align:start position:0% +food cooperatives and buying clubs I +mean this whole organic food industry + + align:start position:0% +mean this whole organic food industry + + + align:start position:0% +mean this whole organic food industry +you know it's really you know as we T + + align:start position:0% +you know it's really you know as we T + + + align:start position:0% +you know it's really you know as we T +said before came from the um um we were + + align:start position:0% +said before came from the um um we were + + + align:start position:0% +said before came from the um um we were +the ones that help help to to set the uh + + align:start position:0% +the ones that help help to to set the uh + + + align:start position:0% +the ones that help help to to set the uh +the possibilities for it um you know + + align:start position:0% +the possibilities for it um you know + + + align:start position:0% +the possibilities for it um you know +then the the the uh uh hardware store + + align:start position:0% +then the the the uh uh hardware store + + + align:start position:0% +then the the the uh uh hardware store +cooperatives Ace True Values Etc I mean + + align:start position:0% +cooperatives Ace True Values Etc I mean + + + align:start position:0% +cooperatives Ace True Values Etc I mean +that that's one way that that they've + + align:start position:0% +that that's one way that that they've + + + align:start position:0% +that that's one way that that they've +been able to survive somewhat against + + align:start position:0% +been able to survive somewhat against + + + align:start position:0% +been able to survive somewhat against +the big boxes is is through uh + + align:start position:0% +the big boxes is is through uh + + + align:start position:0% +the big boxes is is through uh +purchasing co-ops uh where they uh + + align:start position:0% +purchasing co-ops uh where they uh + + + align:start position:0% +purchasing co-ops uh where they uh +brought together these uh um um you know + + align:start position:0% +brought together these uh um um you know + + + align:start position:0% +brought together these uh um um you know +just thousands of uh individual uh uh + + align:start position:0% +just thousands of uh individual uh uh + + + align:start position:0% +just thousands of uh individual uh uh +franchises and and and and buying + + align:start position:0% +franchises and and and and buying + + + align:start position:0% +franchises and and and and buying +together that's if you know important + + align:start position:0% +together that's if you know important + + + align:start position:0% +together that's if you know important +way to be able to to to fight Behemoth + + align:start position:0% +way to be able to to to fight Behemoth + + + align:start position:0% +way to be able to to to fight Behemoth +like um um like um um U Walmart and Home + + align:start position:0% +like um um like um um U Walmart and Home + + + align:start position:0% +like um um like um um U Walmart and Home +Depot and Etc every industry every small + + align:start position:0% +Depot and Etc every industry every small + + + align:start position:0% +Depot and Etc every industry every small +business industry is being taken over by + + align:start position:0% +business industry is being taken over by + + + align:start position:0% +business industry is being taken over by +consolidation and so the only way that + + align:start position:0% +consolidation and so the only way that + + + align:start position:0% +consolidation and so the only way that +they're staying in business so I is by + + align:start position:0% +they're staying in business so I is by + + + align:start position:0% +they're staying in business so I is by +forming purchasing cooperatives so + + align:start position:0% +forming purchasing cooperatives so + + + align:start position:0% +forming purchasing cooperatives so +there's funeral home cooperatives that + + align:start position:0% +there's funeral home cooperatives that + + + align:start position:0% +there's funeral home cooperatives that +are the only thing that are keeping + + align:start position:0% +are the only thing that are keeping + + + align:start position:0% +are the only thing that are keeping +locally owned funeral homes in our + + align:start position:0% +locally owned funeral homes in our + + + align:start position:0% +locally owned funeral homes in our +country there's um uh I worked with a + + align:start position:0% +country there's um uh I worked with a + + + align:start position:0% +country there's um uh I worked with a +fire a group of Fire proofing installers + + align:start position:0% +fire a group of Fire proofing installers + + + align:start position:0% +fire a group of Fire proofing installers +nationally who are trying to do that + + align:start position:0% +nationally who are trying to do that + + + align:start position:0% +nationally who are trying to do that +it's it's it's uh the largest growing + + align:start position:0% +it's it's it's uh the largest growing + + + align:start position:0% +it's it's it's uh the largest growing +sector of Cooperative businesses are + + align:start position:0% +sector of Cooperative businesses are + + + align:start position:0% +sector of Cooperative businesses are +these purchasing cooperatives to sustain + + align:start position:0% +these purchasing cooperatives to sustain + + + align:start position:0% +these purchasing cooperatives to sustain +small + + align:start position:0% +small + + + align:start position:0% +small +businesses there's welcome welcome how + + align:start position:0% +businesses there's welcome welcome how + + + align:start position:0% +businesses there's welcome welcome how +you + + align:start position:0% +you + + + align:start position:0% +you +doing and if I'll just make the + + align:start position:0% +doing and if I'll just make the + + + align:start position:0% +doing and if I'll just make the +announcement again if anybody doesn't + + align:start position:0% +announcement again if anybody doesn't + + + align:start position:0% +announcement again if anybody doesn't +want to be on our lovely videotape you + + align:start position:0% +want to be on our lovely videotape you + + + align:start position:0% +want to be on our lovely videotape you +need to sit in this section of the + + align:start position:0% +need to sit in this section of the + + + align:start position:0% +need to sit in this section of the +room welcome + + align:start position:0% +room welcome + + + align:start position:0% +room welcome +welcome so there's um 25 million people + + align:start position:0% +welcome so there's um 25 million people + + + align:start position:0% +welcome so there's um 25 million people +who get their electricity from consumer + + align:start position:0% +who get their electricity from consumer + + + align:start position:0% +who get their electricity from consumer +cooperatives um they own all the poles + + align:start position:0% +cooperatives um they own all the poles + + + align:start position:0% +cooperatives um they own all the poles +and wires and 75% of the United States + + align:start position:0% +and wires and 75% of the United States + + + align:start position:0% +and wires and 75% of the United States +all the rural + + align:start position:0% +all the rural + + + align:start position:0% +all the rural +areas and uh The Cooperative daycare + + align:start position:0% +areas and uh The Cooperative daycare + + + align:start position:0% +areas and uh The Cooperative daycare +centers is a you know a new approach I + + align:start position:0% +centers is a you know a new approach I + + + align:start position:0% +centers is a you know a new approach I +mean particularly as more and more + + align:start position:0% +mean particularly as more and more + + + align:start position:0% +mean particularly as more and more +attention to the importance of daycare + + align:start position:0% +attention to the importance of daycare + + + align:start position:0% +attention to the importance of daycare +as a way to get folks into the workforce + + align:start position:0% +as a way to get folks into the workforce + + + align:start position:0% +as a way to get folks into the workforce +um um a Cooperative approach as a as a + + align:start position:0% +um um a Cooperative approach as a as a + + + align:start position:0% +um um a Cooperative approach as a as a +way to come up with quality daycare that + + align:start position:0% +way to come up with quality daycare that + + + align:start position:0% +way to come up with quality daycare that +that that that more people can afford um + + align:start position:0% +that that that more people can afford um + + + align:start position:0% +that that that more people can afford um +is is an important uh option um and um + + align:start position:0% +is is an important uh option um and um + + + align:start position:0% +is is an important uh option um and um +that that all over the world 600 million + + align:start position:0% +that that all over the world 600 million + + + align:start position:0% +that that all over the world 600 million +people all over the world are + + align:start position:0% +people all over the world are + + + align:start position:0% +people all over the world are +participating in cooperatives and and + + align:start position:0% +participating in cooperatives and and + + + align:start position:0% +participating in cooperatives and and +and a lot of the um some of the most + + align:start position:0% +and a lot of the um some of the most + + + align:start position:0% +and a lot of the um some of the most +imaginative and creative and Innovative + + align:start position:0% +imaginative and creative and Innovative + + + align:start position:0% +imaginative and creative and Innovative +approaches are happening in different + + align:start position:0% +approaches are happening in different + + + align:start position:0% +approaches are happening in different +parts of world whether talk about mangr + + align:start position:0% +parts of world whether talk about mangr + + + align:start position:0% +parts of world whether talk about mangr +uh Cooperative uh Federation in in Spain + + align:start position:0% +uh Cooperative uh Federation in in Spain + + + align:start position:0% +uh Cooperative uh Federation in in Spain +where they you know handful of students + + align:start position:0% +where they you know handful of students + + + align:start position:0% +where they you know handful of students +um you know uh uh connecting up with uh + + align:start position:0% +um you know uh uh connecting up with uh + + + align:start position:0% +um you know uh uh connecting up with uh +father uh + + align:start position:0% +father uh + + + align:start position:0% +father uh +reso Mento you know back in the 40s and + + align:start position:0% +reso Mento you know back in the 40s and + + + align:start position:0% +reso Mento you know back in the 40s and +um and from that now you know we have um + + align:start position:0% +um and from that now you know we have um + + + align:start position:0% +um and from that now you know we have um +you know five billion dollar um worth in + + align:start position:0% +you know five billion dollar um worth in + + + align:start position:0% +you know five billion dollar um worth in +in in total sales manufacturing uh + + align:start position:0% +in in total sales manufacturing uh + + + align:start position:0% +in in total sales manufacturing uh +financials uh um you know and all all + + align:start position:0% +financials uh um you know and all all + + + align:start position:0% +financials uh um you know and all all +just all retail construction and U you + + align:start position:0% +just all retail construction and U you + + + align:start position:0% +just all retail construction and U you +know and and we think that has great + + align:start position:0% +know and and we think that has great + + + align:start position:0% +know and and we think that has great +bearing I mean he was created in this U + + align:start position:0% +bearing I mean he was created in this U + + + align:start position:0% +bearing I mean he was created in this U +appressed minority area of the + + align:start position:0% +appressed minority area of the + + + align:start position:0% +appressed minority area of the +bass region of Spain and and using that + + align:start position:0% +bass region of Spain and and using that + + + align:start position:0% +bass region of Spain and and using that +as a way to begin to to focus their + + align:start position:0% +as a way to begin to to focus their + + + align:start position:0% +as a way to begin to to focus their +attention you know a market that nobody + + align:start position:0% +attention you know a market that nobody + + + align:start position:0% +attention you know a market that nobody +else cared about or wanted and now that + + align:start position:0% +else cared about or wanted and now that + + + align:start position:0% +else cared about or wanted and now that +they're a global player you we think + + align:start position:0% +they're a global player you we think + + + align:start position:0% +they're a global player you we think +that has a lot of U that we can learn + + align:start position:0% +that has a lot of U that we can learn + + + align:start position:0% +that has a lot of U that we can learn +particularly for um for folks of racial + + align:start position:0% +particularly for um for folks of racial + + + align:start position:0% +particularly for um for folks of racial +minorities and others you know in our + + align:start position:0% +minorities and others you know in our + + + align:start position:0% +minorities and others you know in our +country um the many things that we can + + align:start position:0% +country um the many things that we can + + + align:start position:0% +country um the many things that we can +learn from uh the mugan movement seatu + + align:start position:0% +learn from uh the mugan movement seatu + + + align:start position:0% +learn from uh the mugan movement seatu +movement I think one of some of the most + + align:start position:0% +movement I think one of some of the most + + + align:start position:0% +movement I think one of some of the most +exciting things Happ you know 60s 300 U + + align:start position:0% +exciting things Happ you know 60s 300 U + + + align:start position:0% +exciting things Happ you know 60s 300 U +families coming together to uh uh mostly + + align:start position:0% +families coming together to uh uh mostly + + + align:start position:0% +families coming together to uh uh mostly +uh um women um to uh uh fight for uh + + align:start position:0% +uh um women um to uh uh fight for uh + + + align:start position:0% +uh um women um to uh uh fight for uh +lower milk prices and and and milk that + + align:start position:0% +lower milk prices and and and milk that + + + align:start position:0% +lower milk prices and and and milk that +wasn't adult U you know u u uh the milk + + align:start position:0% +wasn't adult U you know u u uh the milk + + + align:start position:0% +wasn't adult U you know u u uh the milk +products but but but genuine milk and + + align:start position:0% +products but but but genuine milk and + + + align:start position:0% +products but but but genuine milk and +from that they've built a a uh a + + align:start position:0% +from that they've built a a uh a + + + align:start position:0% +from that they've built a a uh a +movement where almost a quarter of the + + align:start position:0% +movement where almost a quarter of the + + + align:start position:0% +movement where almost a quarter of the +of the people in in in in Japan are + + align:start position:0% +of the people in in in in Japan are + + + align:start position:0% +of the people in in in in Japan are +organized in in what they call a Han + + align:start position:0% +organized in in what they call a Han + + + align:start position:0% +organized in in what they call a Han +structure u u almost block by block + + align:start position:0% +structure u u almost block by block + + + align:start position:0% +structure u u almost block by block +organizing where folks are are are you + + align:start position:0% +organizing where folks are are are you + + + align:start position:0% +organizing where folks are are are you +know and they're not just a consumer uh + + align:start position:0% +know and they're not just a consumer uh + + + align:start position:0% +know and they're not just a consumer uh +Cooperative where they're saying uh we + + align:start position:0% +Cooperative where they're saying uh we + + + align:start position:0% +Cooperative where they're saying uh we +want low prices they're demanding uh and + + align:start position:0% +want low prices they're demanding uh and + + + align:start position:0% +want low prices they're demanding uh and +and cutting deals with consumers with + + align:start position:0% +and cutting deals with consumers with + + + align:start position:0% +and cutting deals with consumers with +the producers themselves saying okay + + align:start position:0% +the producers themselves saying okay + + + align:start position:0% +the producers themselves saying okay +look we can guarantee you uh you're a um + + align:start position:0% +look we can guarantee you uh you're a um + + + align:start position:0% +look we can guarantee you uh you're a um +a dairy and we can guarantee you um this + + align:start position:0% +a dairy and we can guarantee you um this + + + align:start position:0% +a dairy and we can guarantee you um this +much uh uh um uh uh uh + + align:start position:0% +much uh uh um uh uh uh + + + align:start position:0% +much uh uh um uh uh uh +business what's the not only the cost + + align:start position:0% +business what's the not only the cost + + + align:start position:0% +business what's the not only the cost +are you going to get to us but also what + + align:start position:0% +are you going to get to us but also what + + + align:start position:0% +are you going to get to us but also what +is the quality you know so they you know + + align:start position:0% +is the quality you know so they you know + + + align:start position:0% +is the quality you know so they you know +so they've have been able to you know to + + align:start position:0% +so they've have been able to you know to + + + align:start position:0% +so they've have been able to you know to +talk you know combine low cost and and + + align:start position:0% +talk you know combine low cost and and + + + align:start position:0% +talk you know combine low cost and and +high quality which we haven't been able + + align:start position:0% +high quality which we haven't been able + + + align:start position:0% +high quality which we haven't been able +to do in this country + + align:start position:0% +to do in this country + + + align:start position:0% +to do in this country +and and they've turned it into a + + align:start position:0% +and and they've turned it into a + + + align:start position:0% +and and they've turned it into a +political movement where now it's 're + + align:start position:0% +political movement where now it's 're + + + align:start position:0% +political movement where now it's 're +they're um they have a strong + + align:start position:0% +they're um they have a strong + + + align:start position:0% +they're um they have a strong +environmental Focus they're running + + align:start position:0% +environmental Focus they're running + + + align:start position:0% +environmental Focus they're running +candidates based on that they've been + + align:start position:0% +candidates based on that they've been + + + align:start position:0% +candidates based on that they've been +able to raise enough monies from the the + + align:start position:0% +able to raise enough monies from the the + + + align:start position:0% +able to raise enough monies from the the +group-based businesses that they've uh + + align:start position:0% +group-based businesses that they've uh + + + align:start position:0% +group-based businesses that they've uh +um that they've U invested in to be able + + align:start position:0% +um that they've U invested in to be able + + + align:start position:0% +um that they've U invested in to be able +to support political change and and and + + align:start position:0% +to support political change and and and + + + align:start position:0% +to support political change and and and +uh in Japan and now I mean from that you + + align:start position:0% +uh in Japan and now I mean from that you + + + align:start position:0% +uh in Japan and now I mean from that you +know a large number I mean like I said + + align:start position:0% +know a large number I mean like I said + + + align:start position:0% +know a large number I mean like I said +still a very a woman-led movement in in + + align:start position:0% +still a very a woman-led movement in in + + + align:start position:0% +still a very a woman-led movement in in +a in a patriarchal country and and and + + align:start position:0% +a in a patriarchal country and and and + + + align:start position:0% +a in a patriarchal country and and and +out and they're beginning to make a + + align:start position:0% +out and they're beginning to make a + + + align:start position:0% +out and they're beginning to make a +difference uh U you know so I think it + + align:start position:0% +difference uh U you know so I think it + + + align:start position:0% +difference uh U you know so I think it +has tremendous things that we can learn + + align:start position:0% +has tremendous things that we can learn + + + align:start position:0% +has tremendous things that we can learn +think talking about this neighborhood + + align:start position:0% +think talking about this neighborhood + + + align:start position:0% +think talking about this neighborhood +organizing which I've done quite a bit + + align:start position:0% +organizing which I've done quite a bit + + + align:start position:0% +organizing which I've done quite a bit +of the idea of being able to organize + + align:start position:0% +of the idea of being able to organize + + + align:start position:0% +of the idea of being able to organize +door by door talking about you know as + + align:start position:0% +door by door talking about you know as + + + align:start position:0% +door by door talking about you know as +they call it seatu a shab I mean which + + align:start position:0% +they call it seatu a shab I mean which + + + align:start position:0% +they call it seatu a shab I mean which +mean a Cooperative style Cooperative way + + align:start position:0% +mean a Cooperative style Cooperative way + + + align:start position:0% +mean a Cooperative style Cooperative way +of living you know where they begin to + + align:start position:0% +of living you know where they begin to + + + align:start position:0% +of living you know where they begin to +say not only do we are we going to just + + align:start position:0% +say not only do we are we going to just + + + align:start position:0% +say not only do we are we going to just +get together to buy milk and dairy and + + align:start position:0% +get together to buy milk and dairy and + + + align:start position:0% +get together to buy milk and dairy and +and meats and other things but how can + + align:start position:0% +and meats and other things but how can + + + align:start position:0% +and meats and other things but how can +we St think cooperatively act + + align:start position:0% +we St think cooperatively act + + + align:start position:0% +we St think cooperatively act +cooperative and our daily living and + + align:start position:0% +cooperative and our daily living and + + + align:start position:0% +cooperative and our daily living and +they and they and they've organized so + + align:start position:0% +they and they and they've organized so + + + align:start position:0% +they and they and they've organized so +that every 8 to 10 houses are are + + align:start position:0% +that every 8 to 10 houses are are + + + align:start position:0% +that every 8 to 10 houses are are +meeting together in in Hans and you know + + align:start position:0% +meeting together in in Hans and you know + + + align:start position:0% +meeting together in in Hans and you know +and then there's a structure that takes + + align:start position:0% +and then there's a structure that takes + + + align:start position:0% +and then there's a structure that takes +it up to a democratic governance of this + + align:start position:0% +it up to a democratic governance of this + + + align:start position:0% +it up to a democratic governance of this +National structure you know so I think + + align:start position:0% +National structure you know so I think + + + align:start position:0% +National structure you know so I think +it's you know tremendous possibilities + + align:start position:0% +it's you know tremendous possibilities + + + align:start position:0% +it's you know tremendous possibilities +of how we can take you know Community + + align:start position:0% +of how we can take you know Community + + + align:start position:0% +of how we can take you know Community +organizing and and a Cooperative process + + align:start position:0% +organizing and and a Cooperative process + + + align:start position:0% +organizing and and a Cooperative process +and and and really try to develop power + + align:start position:0% +and and and really try to develop power + + + align:start position:0% +and and and really try to develop power +over how the uh uh U the pro uh The + + align:start position:0% +over how the uh uh U the pro uh The + + + align:start position:0% +over how the uh uh U the pro uh The +Producers um impact you know so we can + + align:start position:0% +Producers um impact you know so we can + + + align:start position:0% +Producers um impact you know so we can +begin to make demands to the Walmarts of + + align:start position:0% +begin to make demands to the Walmarts of + + + align:start position:0% +begin to make demands to the Walmarts of +of the world um and then um you know uh + + align:start position:0% +of the world um and then um you know uh + + + align:start position:0% +of the world um and then um you know uh +Sako the uh South South African Credit + + align:start position:0% +Sako the uh South South African Credit + + + align:start position:0% +Sako the uh South South African Credit +Union where they you know again where + + align:start position:0% +Union where they you know again where + + + align:start position:0% +Union where they you know again where +they're organizing using U uh all kinds + + align:start position:0% +they're organizing using U uh all kinds + + + align:start position:0% +they're organizing using U uh all kinds +of creative ways of uh of using uh their + + align:start position:0% +of creative ways of uh of using uh their + + + align:start position:0% +of creative ways of uh of using uh their +culture and other ways you know to talk + + align:start position:0% +culture and other ways you know to talk + + + align:start position:0% +culture and other ways you know to talk +about financial literacy to to to to + + align:start position:0% +about financial literacy to to to to + + + align:start position:0% +about financial literacy to to to to +engage folks in in their own and and uh + + align:start position:0% +engage folks in in their own and and uh + + + align:start position:0% +engage folks in in their own and and uh +uh taking power their Financial + + align:start position:0% +uh taking power their Financial + + + align:start position:0% +uh taking power their Financial +Empowerment of you know and they're you + + align:start position:0% +Empowerment of you know and they're you + + + align:start position:0% +Empowerment of you know and they're you +know going from the from Individual + + align:start position:0% +know going from the from Individual + + + align:start position:0% +know going from the from Individual +tribes to to to to organizing in the uh + + align:start position:0% +tribes to to to to organizing in the uh + + + align:start position:0% +tribes to to to to organizing in the uh +um in the uh cities and and it's again + + align:start position:0% +um in the uh cities and and it's again + + + align:start position:0% +um in the uh cities and and it's again +you know being able to show that uh um + + align:start position:0% +you know being able to show that uh um + + + align:start position:0% +you know being able to show that uh um +um you know that that and they've done a + + align:start position:0% +um you know that that and they've done a + + + align:start position:0% +um you know that that and they've done a +lot of things with uh linkoln culture I + + align:start position:0% +lot of things with uh linkoln culture I + + + align:start position:0% +lot of things with uh linkoln culture I +mean with a credit union that has some + + align:start position:0% +mean with a credit union that has some + + + align:start position:0% +mean with a credit union that has some +of the the you know produces some + + align:start position:0% +of the the you know produces some + + + align:start position:0% +of the the you know produces some +incredible music and dances and + + align:start position:0% +incredible music and dances and + + + align:start position:0% +incredible music and dances and +everything I mean where the everything + + align:start position:0% +everything I mean where the everything + + + align:start position:0% +everything I mean where the everything +is all combined and you know and and the + + align:start position:0% +is all combined and you know and and the + + + align:start position:0% +is all combined and you know and and the +to build the power of this uh uh uh + + align:start position:0% +to build the power of this uh uh uh + + + align:start position:0% +to build the power of this uh uh uh +movement using the culture and using the + + align:start position:0% +movement using the culture and using the + + + align:start position:0% +movement using the culture and using the +uh dance and using song as a way of of + + align:start position:0% +uh dance and using song as a way of of + + + align:start position:0% +uh dance and using song as a way of of +of of talking about educating in a in a + + align:start position:0% +of of talking about educating in a in a + + + align:start position:0% +of of talking about educating in a in a +broad way about how people can take + + align:start position:0% +broad way about how people can take + + + align:start position:0% +broad way about how people can take +power over their financial lives so + + align:start position:0% +power over their financial lives so + + + align:start position:0% +power over their financial lives so +again I mean it goes back to the point + + align:start position:0% +again I mean it goes back to the point + + + align:start position:0% +again I mean it goes back to the point +we was talking about again about U + + align:start position:0% +we was talking about again about U + + + align:start position:0% +we was talking about again about U +feasible uh business models that one of + + align:start position:0% +feasible uh business models that one of + + + align:start position:0% +feasible uh business models that one of +the things that we got to do out in this + + align:start position:0% +the things that we got to do out in this + + + align:start position:0% +the things that we got to do out in this +country is break this uh you know this + + align:start position:0% +country is break this uh you know this + + + align:start position:0% +country is break this uh you know this +um mindset that only things that are + + align:start position:0% +um mindset that only things that are + + + align:start position:0% +um mindset that only things that are +important are things that happen in this + + align:start position:0% +important are things that happen in this + + + align:start position:0% +important are things that happen in this +country and not and and begin to look at + + align:start position:0% +country and not and and begin to look at + + + align:start position:0% +country and not and and begin to look at +the incredible things that they're doing + + align:start position:0% +the incredible things that they're doing + + + align:start position:0% +the incredible things that they're doing +going in Canada and Europe and Asia and + + align:start position:0% +going in Canada and Europe and Asia and + + + align:start position:0% +going in Canada and Europe and Asia and +Africa and Latin America you know around + + align:start position:0% +Africa and Latin America you know around + + + align:start position:0% +Africa and Latin America you know around +the + + align:start position:0% +the + + + align:start position:0% +the +cooperatives so in our culture where we + + align:start position:0% +cooperatives so in our culture where we + + + align:start position:0% +cooperatives so in our culture where we +only cooperate when we have + + align:start position:0% +only cooperate when we have + + + align:start position:0% +only cooperate when we have +to um it's hard for us to understand + + align:start position:0% +to um it's hard for us to understand + + + align:start position:0% +to um it's hard for us to understand +that there are other ways of being in + + align:start position:0% +that there are other ways of being in + + + align:start position:0% +that there are other ways of being in +the world and that there are other + + align:start position:0% +the world and that there are other + + + align:start position:0% +the world and that there are other +things that work besides the things that + + align:start position:0% +things that work besides the things that + + + align:start position:0% +things that work besides the things that +we've seen and we've done and you can't + + align:start position:0% +we've seen and we've done and you can't + + + align:start position:0% +we've seen and we've done and you can't +grow up in a farm community in the + + align:start position:0% +grow up in a farm community in the + + + align:start position:0% +grow up in a farm community in the +midwest without having cooperatives be + + align:start position:0% +midwest without having cooperatives be + + + align:start position:0% +midwest without having cooperatives be +most of your life could is they have Fe + + align:start position:0% +most of your life could is they have Fe + + + align:start position:0% +most of your life could is they have Fe +food feed co-ops and marketing co-ops + + align:start position:0% +food feed co-ops and marketing co-ops + + + align:start position:0% +food feed co-ops and marketing co-ops +and you know Co-op stores because + + align:start position:0% +and you know Co-op stores because + + + align:start position:0% +and you know Co-op stores because +there's so much disinvestment in those + + align:start position:0% +there's so much disinvestment in those + + + align:start position:0% +there's so much disinvestment in those +rural areas you and there's places that + + align:start position:0% +rural areas you and there's places that + + + align:start position:0% +rural areas you and there's places that +I visited in Atlantic Canada where you + + align:start position:0% +I visited in Atlantic Canada where you + + + align:start position:0% +I visited in Atlantic Canada where you +can be born in a Cooperative hospital + + align:start position:0% +can be born in a Cooperative hospital + + + align:start position:0% +can be born in a Cooperative hospital +and die in a Cooperative funeral home + + align:start position:0% +and die in a Cooperative funeral home + + + align:start position:0% +and die in a Cooperative funeral home +and do all of your economic activity in + + align:start position:0% +and do all of your economic activity in + + + align:start position:0% +and do all of your economic activity in +between with cooperatives because + + align:start position:0% +between with cooperatives because + + + align:start position:0% +between with cooperatives because +everybody else left town and they either + + align:start position:0% +everybody else left town and they either + + + align:start position:0% +everybody else left town and they either +had to move or create their own + + align:start position:0% +had to move or create their own + + + align:start position:0% +had to move or create their own +infrastructure and they stayed with the + + align:start position:0% +infrastructure and they stayed with the + + + align:start position:0% +infrastructure and they stayed with the +help of the Catholic church and rebuilt + + align:start position:0% +help of the Catholic church and rebuilt + + + align:start position:0% +help of the Catholic church and rebuilt +their whole infrastructure so um if + + align:start position:0% +their whole infrastructure so um if + + + align:start position:0% +their whole infrastructure so um if +anybody I'm hoping that you all will + + align:start position:0% +anybody I'm hoping that you all will + + + align:start position:0% +anybody I'm hoping that you all will +leave today if you didn't know much + + align:start position:0% +leave today if you didn't know much + + + align:start position:0% +leave today if you didn't know much +about co-ops before you came in knowing + + align:start position:0% +about co-ops before you came in knowing + + + align:start position:0% +about co-ops before you came in knowing +that if somebody says oh yeah we tried + + align:start position:0% +that if somebody says oh yeah we tried + + + align:start position:0% +that if somebody says oh yeah we tried +to do that once and it didn't work + + align:start position:0% +to do that once and it didn't work + + + align:start position:0% +to do that once and it didn't work +knowing that there's another answer and + + align:start position:0% +knowing that there's another answer and + + + align:start position:0% +knowing that there's another answer and +there's some other options and there's + + align:start position:0% +there's some other options and there's + + + align:start position:0% +there's some other options and there's +some other people who actually have + + align:start position:0% +some other people who actually have + + + align:start position:0% +some other people who actually have +figured this out and um once you know + + align:start position:0% +figured this out and um once you know + + + align:start position:0% +figured this out and um once you know +how to do something it's really easy to + + align:start position:0% +how to do something it's really easy to + + + align:start position:0% +how to do something it's really easy to +do again but the first time sometimes + + align:start position:0% +do again but the first time sometimes + + + align:start position:0% +do again but the first time sometimes +can be a little + + align:start position:0% +can be a little + + + align:start position:0% +can be a little +challenging um I think I want to let's + + align:start position:0% +challenging um I think I want to let's + + + align:start position:0% +challenging um I think I want to let's +go into the role play + + align:start position:0% + + + + align:start position:0% + +um what I actually what I'd like to do + + align:start position:0% +um what I actually what I'd like to do + + + align:start position:0% +um what I actually what I'd like to do +I'm just going to abandon this for a + + align:start position:0% +I'm just going to abandon this for a + + + align:start position:0% +I'm just going to abandon this for a +moment all right what I'd like to do is + + align:start position:0% +moment all right what I'd like to do is + + + align:start position:0% +moment all right what I'd like to do is +take you into the handout that says + + align:start position:0% +take you into the handout that says + + + align:start position:0% +take you into the handout that says +first things + + align:start position:0% +first things + + + align:start position:0% +first things +first and um what Shakur and I did was + + align:start position:0% +first and um what Shakur and I did was + + + align:start position:0% +first and um what Shakur and I did was +we pulled together our favorite things + + align:start position:0% +we pulled together our favorite things + + + align:start position:0% +we pulled together our favorite things +that we've been using over the last 10 + + align:start position:0% +that we've been using over the last 10 + + + align:start position:0% +that we've been using over the last 10 +years when we sat down to work with a + + align:start position:0% +years when we sat down to work with a + + + align:start position:0% +years when we sat down to work with a +group of people and we edited them so + + align:start position:0% +group of people and we edited them so + + + align:start position:0% +group of people and we edited them so +they're even better than anything we've + + align:start position:0% +they're even better than anything we've + + + align:start position:0% +they're even better than anything we've +ever used with people before and it was + + align:start position:0% +ever used with people before and it was + + + align:start position:0% +ever used with people before and it was +really fun to take the time to go + + align:start position:0% +really fun to take the time to go + + + align:start position:0% +really fun to take the time to go +through and do that so I'm hoping you'll + + align:start position:0% +through and do that so I'm hoping you'll + + + align:start position:0% +through and do that so I'm hoping you'll +find these this is our little you know + + align:start position:0% +find these this is our little you know + + + align:start position:0% +find these this is our little you know +our little bible for you know when + + align:start position:0% +our little bible for you know when + + + align:start position:0% +our little bible for you know when +you're first getting started with a + + align:start position:0% +you're first getting started with a + + + align:start position:0% +you're first getting started with a +group um so the first things are + + align:start position:0% +group um so the first things are + + + align:start position:0% +group um so the first things are +strategic + + align:start position:0% +strategic + + + align:start position:0% +strategic +planning you know that's the first thing + + align:start position:0% +planning you know that's the first thing + + + align:start position:0% +planning you know that's the first thing +you do we we we continue with it later + + align:start position:0% +you do we we we continue with it later + + + align:start position:0% +you do we we we continue with it later +on and we start with it at the beginning + + align:start position:0% +on and we start with it at the beginning + + + align:start position:0% +on and we start with it at the beginning +um and really creating the share a + + align:start position:0% +um and really creating the share a + + + align:start position:0% +um and really creating the share a +shared business a shared vision for the + + align:start position:0% +shared business a shared vision for the + + + align:start position:0% +shared business a shared vision for the +business um some groups I've worked with + + align:start position:0% +business um some groups I've worked with + + + align:start position:0% +business um some groups I've worked with +it's + + align:start position:0% +it's + + + align:start position:0% +it's +been you know 9 months before we came + + align:start position:0% +been you know 9 months before we came + + + align:start position:0% +been you know 9 months before we came +out with a shared Vision there was one + + align:start position:0% +out with a shared Vision there was one + + + align:start position:0% +out with a shared Vision there was one +group um that I work with where um uh + + align:start position:0% +group um that I work with where um uh + + + align:start position:0% +group um that I work with where um uh +and other people in my office we we met + + align:start position:0% +and other people in my office we we met + + + align:start position:0% +and other people in my office we we met +with them for nine months and there were + + align:start position:0% +with them for nine months and there were + + + align:start position:0% +with them for nine months and there were +about 50 people in the room for the all + + align:start position:0% +about 50 people in the room for the all + + + align:start position:0% +about 50 people in the room for the all +the first meetings and they wanted to + + align:start position:0% +the first meetings and they wanted to + + + align:start position:0% +the first meetings and they wanted to +start A photoal tes manufacturing + + align:start position:0% +start A photoal tes manufacturing + + + align:start position:0% +start A photoal tes manufacturing +company and but they weren't really sure + + align:start position:0% +company and but they weren't really sure + + + align:start position:0% +company and but they weren't really sure +and but they wanted to be worker owned + + align:start position:0% +and but they wanted to be worker owned + + + align:start position:0% +and but they wanted to be worker owned +but they were weren't really sure who + + align:start position:0% +but they were weren't really sure who + + + align:start position:0% +but they were weren't really sure who +was going to work in it whether any of + + align:start position:0% +was going to work in it whether any of + + + align:start position:0% +was going to work in it whether any of +them were or whether they all wanted to + + align:start position:0% +them were or whether they all wanted to + + + align:start position:0% +them were or whether they all wanted to +or whether that would work so it was it + + align:start position:0% +or whether that would work so it was it + + + align:start position:0% +or whether that would work so it was it +was we kind of we kind of muddled and + + align:start position:0% +was we kind of we kind of muddled and + + + align:start position:0% +was we kind of we kind of muddled and +there really wasn't money at the table + + align:start position:0% +there really wasn't money at the table + + + align:start position:0% +there really wasn't money at the table +they but they were meeting and they were + + align:start position:0% +they but they were meeting and they were + + + align:start position:0% +they but they were meeting and they were +really enthusiastic about creating a + + align:start position:0% +really enthusiastic about creating a + + + align:start position:0% +really enthusiastic about creating a +manufacturing company and um as we went + + align:start position:0% +manufacturing company and um as we went + + + align:start position:0% +manufacturing company and um as we went +along the vision became kind of more + + align:start position:0% +along the vision became kind of more + + + align:start position:0% +along the vision became kind of more +realistic and more realistic and they + + align:start position:0% +realistic and more realistic and they + + + align:start position:0% +realistic and more realistic and they +ended up starting a photov voltaics + + align:start position:0% +ended up starting a photov voltaics + + + align:start position:0% +ended up starting a photov voltaics +installation company that's that's going + + align:start position:0% +installation company that's that's going + + + align:start position:0% +installation company that's that's going +now but it we did probably nine months + + align:start position:0% +now but it we did probably nine months + + + align:start position:0% +now but it we did probably nine months +of this strategic planning work and what + + align:start position:0% +of this strategic planning work and what + + + align:start position:0% +of this strategic planning work and what +I'm proud of is that we didn't move + + align:start position:0% +I'm proud of is that we didn't move + + + align:start position:0% +I'm proud of is that we didn't move +forward with that development process + + align:start position:0% +forward with that development process + + + align:start position:0% +forward with that development process +until the group had a shared vision for + + align:start position:0% +until the group had a shared vision for + + + align:start position:0% +until the group had a shared vision for +what it was they wanted to do and it's + + align:start position:0% +what it was they wanted to do and it's + + + align:start position:0% +what it was they wanted to do and it's +hard because you know as soon as they + + align:start position:0% +hard because you know as soon as they + + + align:start position:0% +hard because you know as soon as they +get one idea there's a group of them + + align:start position:0% +get one idea there's a group of them + + + align:start position:0% +get one idea there's a group of them +that wants to go off and start well + + align:start position:0% +that wants to go off and start well + + + align:start position:0% +that wants to go off and start well +we're going to start the business + + align:start position:0% +we're going to start the business + + + align:start position:0% +we're going to start the business +planning process you know let's get the + + align:start position:0% +planning process you know let's get the + + + align:start position:0% +planning process you know let's get the +feasibility market research and anyway + + align:start position:0% +feasibility market research and anyway + + + align:start position:0% +feasibility market research and anyway +so it was nice oh actually what what + + align:start position:0% +so it was nice oh actually what what + + + align:start position:0% +so it was nice oh actually what what +what some groups do is they want to + + align:start position:0% +what some groups do is they want to + + + align:start position:0% +what some groups do is they want to +start the publicity let's call a press + + align:start position:0% +start the publicity let's call a press + + + align:start position:0% +start the publicity let's call a press +conference because this is what we're + + align:start position:0% +conference because this is what we're + + + align:start position:0% +conference because this is what we're +going to do so and there was a lot you + + align:start position:0% +going to do so and there was a lot you + + + align:start position:0% +going to do so and there was a lot you +know there's a lot of that that happened + + align:start position:0% +know there's a lot of that that happened + + + align:start position:0% +know there's a lot of that that happened +with this particular group and there was + + align:start position:0% +with this particular group and there was + + + align:start position:0% +with this particular group and there was +consensus among everyone that start the + + align:start position:0% +consensus among everyone that start the + + + align:start position:0% +consensus among everyone that start the +publicity that that's what or that that + + align:start position:0% +publicity that that's what or that that + + + align:start position:0% +publicity that that's what or that that +the manufacturing was what they wanted + + align:start position:0% +the manufacturing was what they wanted + + + align:start position:0% +the manufacturing was what they wanted +to or the installation well they didn't + + align:start position:0% +to or the installation well they didn't + + + align:start position:0% +to or the installation well they didn't +really know maybe it was going to be um + + align:start position:0% +really know maybe it was going to be um + + + align:start position:0% +really know maybe it was going to be um +you know wind turbine Parts maybe it was + + align:start position:0% +you know wind turbine Parts maybe it was + + + align:start position:0% +you know wind turbine Parts maybe it was +going to be solar um panel Parts maybe + + align:start position:0% +going to be solar um panel Parts maybe + + + align:start position:0% +going to be solar um panel Parts maybe +you know there was a lot lot of none of + + align:start position:0% +you know there was a lot lot of none of + + + align:start position:0% +you know there was a lot lot of none of +them had any experience in any + + align:start position:0% +them had any experience in any + + + align:start position:0% +them had any experience in any +manufacturing so it you know it just + + align:start position:0% +manufacturing so it you know it just + + + align:start position:0% +manufacturing so it you know it just +took a while to get to something where + + align:start position:0% +took a while to get to something where + + + align:start position:0% +took a while to get to something where +we could hit bottom where they could get + + align:start position:0% +we could hit bottom where they could get + + + align:start position:0% +we could hit bottom where they could get +a whole get access to some of the other + + align:start position:0% +a whole get access to some of the other + + + align:start position:0% +a whole get access to some of the other +um elements of that puzzle you know um + + align:start position:0% +um elements of that puzzle you know um + + + align:start position:0% +um elements of that puzzle you know um +and and get enough information so they + + align:start position:0% +and and get enough information so they + + + align:start position:0% +and and get enough information so they +could actually come to clarity about + + align:start position:0% +could actually come to clarity about + + + align:start position:0% +could actually come to clarity about +what they were going to do I guess my + + align:start position:0% +what they were going to do I guess my + + + align:start position:0% +what they were going to do I guess my +question is is it was it sort of like a + + align:start position:0% +question is is it was it sort of like a + + + align:start position:0% +question is is it was it sort of like a +majority rule kind of thing I mean at + + align:start position:0% +majority rule kind of thing I mean at + + + align:start position:0% +majority rule kind of thing I mean at +the end of the day it's like all right + + align:start position:0% +the end of the day it's like all right + + + align:start position:0% +the end of the day it's like all right +we got to do do something and and does + + align:start position:0% +we got to do do something and and does + + + align:start position:0% +we got to do do something and and does +everybody have to be on board or um it's + + align:start position:0% +everybody have to be on board or um it's + + + align:start position:0% +everybody have to be on board or um it's +so tricky how do you answer that + + align:start position:0% +so tricky how do you answer that + + + align:start position:0% +so tricky how do you answer that +question yeah you you got to there's no + + align:start position:0% +question yeah you you got to there's no + + + align:start position:0% +question yeah you you got to there's no +stock answer I think feeling that that + + align:start position:0% +stock answer I think feeling that that + + + align:start position:0% +stock answer I think feeling that that +at least a there's a strong consensus I + + align:start position:0% +at least a there's a strong consensus I + + + align:start position:0% +at least a there's a strong consensus I +mean you you know um you never usually + + align:start position:0% +mean you you know um you never usually + + + align:start position:0% +mean you you know um you never usually +get 100% but at least uh trying to get a + + align:start position:0% +get 100% but at least uh trying to get a + + + align:start position:0% +get 100% but at least uh trying to get a +sense that a number of the key players + + align:start position:0% +sense that a number of the key players + + + align:start position:0% +sense that a number of the key players +the the um the uh very vocal ones and + + align:start position:0% +the the um the uh very vocal ones and + + + align:start position:0% +the the um the uh very vocal ones and +the even not so vocal ones that that + + align:start position:0% +the even not so vocal ones that that + + + align:start position:0% +the even not so vocal ones that that +that there that they actually share the + + align:start position:0% +that there that they actually share the + + + align:start position:0% +that there that they actually share the +vision and ready move forward you know + + align:start position:0% +vision and ready move forward you know + + + align:start position:0% +vision and ready move forward you know +but like you know and it's a it's a + + align:start position:0% +but like you know and it's a it's a + + + align:start position:0% +but like you know and it's a it's a +juggling act because you know also the + + align:start position:0% +juggling act because you know also the + + + align:start position:0% +juggling act because you know also the +other issue is that you you don't want + + align:start position:0% +other issue is that you you don't want + + + align:start position:0% +other issue is that you you don't want +to stay too long in a process of just uh + + align:start position:0% +to stay too long in a process of just uh + + + align:start position:0% +to stay too long in a process of just uh +visioning and not and not getting out + + align:start position:0% +visioning and not and not getting out + + + align:start position:0% +visioning and not and not getting out +and doing things and so you got you know + + align:start position:0% +and doing things and so you got you know + + + align:start position:0% +and doing things and so you got you know +so you you you got to balance that need + + align:start position:0% +so you you you got to balance that need + + + align:start position:0% +so you you you got to balance that need +to get out and get something done so + + align:start position:0% +to get out and get something done so + + + align:start position:0% +to get out and get something done so +people can feel like there's a reason to + + align:start position:0% +people can feel like there's a reason to + + + align:start position:0% +people can feel like there's a reason to +it but also making sure that that + + align:start position:0% +it but also making sure that that + + + align:start position:0% +it but also making sure that that +there's a that that you got a a solid a + + align:start position:0% +there's a that that you got a a solid a + + + align:start position:0% +there's a that that you got a a solid a +feasible plan that that has the + + align:start position:0% +feasible plan that that has the + + + align:start position:0% +feasible plan that that has the +possibility of some success and so so + + align:start position:0% +possibility of some success and so so + + + align:start position:0% +possibility of some success and so so +it's some some groups I've worked with + + align:start position:0% +it's some some groups I've worked with + + + align:start position:0% +it's some some groups I've worked with +they've actually split up and gone in + + align:start position:0% +they've actually split up and gone in + + + align:start position:0% +they've actually split up and gone in +different directions you know half of + + align:start position:0% +different directions you know half of + + + align:start position:0% +different directions you know half of +them decided oh we really want to do + + align:start position:0% +them decided oh we really want to do + + + align:start position:0% +them decided oh we really want to do +this and the other half said oh no we + + align:start position:0% +this and the other half said oh no we + + + align:start position:0% +this and the other half said oh no we +really want to do this some groups never + + align:start position:0% +really want to do this some groups never + + + align:start position:0% +really want to do this some groups never +come to agreement and I'm not in charge + + align:start position:0% +come to agreement and I'm not in charge + + + align:start position:0% +come to agreement and I'm not in charge +you know as the co-op development + + align:start position:0% +you know as the co-op development + + + align:start position:0% +you know as the co-op development +support person I'm just not you know I + + align:start position:0% +support person I'm just not you know I + + + align:start position:0% +support person I'm just not you know I +just feed back to them and say I'm + + align:start position:0% +just feed back to them and say I'm + + + align:start position:0% +just feed back to them and say I'm +noticing that you know eight of you look + + align:start position:0% +noticing that you know eight of you look + + + align:start position:0% +noticing that you know eight of you look +like you're ready to move and three of + + align:start position:0% +like you're ready to move and three of + + + align:start position:0% +like you're ready to move and three of +you um you know want to + + align:start position:0% +you um you know want to + + + align:start position:0% +you um you know want to +stay in the room and keep talking so + + align:start position:0% +stay in the room and keep talking so + + + align:start position:0% +stay in the room and keep talking so +what would you like to do and just you + + align:start position:0% +what would you like to do and just you + + + align:start position:0% +what would you like to do and just you +know ask the group what is your + + align:start position:0% +know ask the group what is your + + + align:start position:0% +know ask the group what is your +decision- making process who are the + + align:start position:0% +decision- making process who are the + + + align:start position:0% +decision- making process who are the +decision makers here is everyone in the + + align:start position:0% +decision makers here is everyone in the + + + align:start position:0% +decision makers here is everyone in the +room participating in the decision oh no + + align:start position:0% +room participating in the decision oh no + + + align:start position:0% +room participating in the decision oh no +no not Sally and Joe this is the first + + align:start position:0% +no not Sally and Joe this is the first + + + align:start position:0% +no not Sally and Joe this is the first +time they came to a meeting you know so + + align:start position:0% +time they came to a meeting you know so + + + align:start position:0% +time they came to a meeting you know so +they don't get to vote we're going to + + align:start position:0% +they don't get to vote we're going to + + + align:start position:0% +they don't get to vote we're going to +the rest of us are voting you know and + + align:start position:0% +the rest of us are voting you know and + + + align:start position:0% +the rest of us are voting you know and +so the it's the group's decision about + + align:start position:0% +so the it's the group's decision about + + + align:start position:0% +so the it's the group's decision about +who decides and when and so it's my job + + align:start position:0% +who decides and when and so it's my job + + + align:start position:0% +who decides and when and so it's my job +to just keep helping them to be clear + + align:start position:0% +to just keep helping them to be clear + + + align:start position:0% +to just keep helping them to be clear +about what their decision- making + + align:start position:0% +about what their decision- making + + + align:start position:0% +about what their decision- making +process is and who's included in + + align:start position:0% +process is and who's included in + + + align:start position:0% +process is and who's included in +it um I said we'll talk a little more + + align:start position:0% +it um I said we'll talk a little more + + + align:start position:0% +it um I said we'll talk a little more +about that that role I me because it can + + align:start position:0% +about that that role I me because it can + + + align:start position:0% +about that that role I me because it can +get um little dicey at different points + + align:start position:0% +get um little dicey at different points + + + align:start position:0% +get um little dicey at different points +I like say when when you know at Point + + align:start position:0% +I like say when when you know at Point + + + align:start position:0% +I like say when when you know at Point +at certain points saying this is not + + align:start position:0% +at certain points saying this is not + + + align:start position:0% +at certain points saying this is not +making sense I wish you the best but uh + + align:start position:0% +making sense I wish you the best but uh + + + align:start position:0% +making sense I wish you the best but uh +I got to go elsewhere cuz cuz I only + + align:start position:0% +I got to go elsewhere cuz cuz I only + + + align:start position:0% +I got to go elsewhere cuz cuz I only +have so much time and only so much + + align:start position:0% +have so much time and only so much + + + align:start position:0% +have so much time and only so much +things I can do I mean like I'm working + + align:start position:0% +things I can do I mean like I'm working + + + align:start position:0% +things I can do I mean like I'm working +with a a group in Buffalo I mean that it + + align:start position:0% +with a a group in Buffalo I mean that it + + + align:start position:0% +with a a group in Buffalo I mean that it +was there was uh 12 people in the room + + align:start position:0% +was there was uh 12 people in the room + + + align:start position:0% +was there was uh 12 people in the room +and there was um and there was six + + align:start position:0% +and there was um and there was six + + + align:start position:0% +and there was um and there was six +different ideas from wind energy to to a + + align:start position:0% +different ideas from wind energy to to a + + + align:start position:0% +different ideas from wind energy to to a +a bottle water company to a cowash and + + align:start position:0% +a bottle water company to a cowash and + + + align:start position:0% +a bottle water company to a cowash and +you know work at Co carow wash and uh + + align:start position:0% +you know work at Co carow wash and uh + + + align:start position:0% +you know work at Co carow wash and uh +you know and I say I mean you know so I + + align:start position:0% +you know and I say I mean you know so I + + + align:start position:0% +you know and I say I mean you know so I +had to tell them I mean uh we can't this + + align:start position:0% +had to tell them I mean uh we can't this + + + align:start position:0% +had to tell them I mean uh we can't this +we can't go for it with this + + align:start position:0% +we can't go for it with this + + + align:start position:0% +we can't go for it with this +I you're going to have to talk some more + + align:start position:0% +I you're going to have to talk some more + + + align:start position:0% +I you're going to have to talk some more +and um here's some ideas on how to help + + align:start position:0% +and um here's some ideas on how to help + + + align:start position:0% +and um here's some ideas on how to help +you do it I mean uh you know should we + + align:start position:0% +you do it I mean uh you know should we + + + align:start position:0% +you do it I mean uh you know should we +you know give gave him some local + + align:start position:0% +you know give gave him some local + + + align:start position:0% +you know give gave him some local +facilitators that help them in the + + align:start position:0% +facilitators that help them in the + + + align:start position:0% +facilitators that help them in the +process and say I'll be back at such and + + align:start position:0% +process and say I'll be back at such and + + + align:start position:0% +process and say I'll be back at such and +such point and I hope we've uh whed it + + align:start position:0% +such point and I hope we've uh whed it + + + align:start position:0% +such point and I hope we've uh whed it +down to maybe one maybe or at least two + + align:start position:0% +down to maybe one maybe or at least two + + + align:start position:0% +down to maybe one maybe or at least two +you then we can then we can start + + align:start position:0% +you then we can then we can start + + + align:start position:0% +you then we can then we can start +working further but lots of times I'll + + align:start position:0% +working further but lots of times I'll + + + align:start position:0% +working further but lots of times I'll +be once or twice with a group and then + + align:start position:0% +be once or twice with a group and then + + + align:start position:0% +be once or twice with a group and then +I'll give them this page and say when + + align:start position:0% +I'll give them this page and say when + + + align:start position:0% +I'll give them this page and say when +you have the answers to this question + + align:start position:0% +you have the answers to this question + + + align:start position:0% +you have the answers to this question +you know to or at least the first two + + align:start position:0% +you know to or at least the first two + + + align:start position:0% +you know to or at least the first two +sections of this question you know this + + align:start position:0% +sections of this question you know this + + + align:start position:0% +sections of this question you know this +page call me back I'd love to come and + + align:start position:0% +page call me back I'd love to come and + + + align:start position:0% +page call me back I'd love to come and +talk with you about it but it's hard for + + align:start position:0% +talk with you about it but it's hard for + + + align:start position:0% +talk with you about it but it's hard for +people to get clear cuz in order to + + align:start position:0% +people to get clear cuz in order to + + + align:start position:0% +people to get clear cuz in order to +choose this you have to not choose all + + align:start position:0% +choose this you have to not choose all + + + align:start position:0% +choose this you have to not choose all +these other things and nobody knows + + align:start position:0% +these other things and nobody knows + + + align:start position:0% +these other things and nobody knows +what's really going to work and so it's + + align:start position:0% +what's really going to work and so it's + + + align:start position:0% +what's really going to work and so it's +hard but if they don't get focused they + + align:start position:0% +hard but if they don't get focused they + + + align:start position:0% +hard but if they don't get focused they +will not be successful you know you can + + align:start position:0% +will not be successful you know you can + + + align:start position:0% +will not be successful you know you can +only do one thing well when you get + + align:start position:0% +only do one thing well when you get + + + align:start position:0% +only do one thing well when you get +started so how how to how to you know + + align:start position:0% +started so how how to how to you know + + + align:start position:0% +started so how how to how to you know +let go of all those other things and um + + align:start position:0% +let go of all those other things and um + + + align:start position:0% +let go of all those other things and um +the kinectic energy C when they started + + align:start position:0% +the kinectic energy C when they started + + + align:start position:0% +the kinectic energy C when they started +there were 16 members of the board of + + align:start position:0% +there were 16 members of the board of + + + align:start position:0% +there were 16 members of the board of +directors they wanted green electricity + + align:start position:0% +directors they wanted green electricity + + + align:start position:0% +directors they wanted green electricity +conservation Efficiency Services both + + align:start position:0% +conservation Efficiency Services both + + + align:start position:0% +conservation Efficiency Services both +for for residential and Commercial um + + align:start position:0% +for for residential and Commercial um + + + align:start position:0% +for for residential and Commercial um +photov voltaics installation a heating + + align:start position:0% +photov voltaics installation a heating + + + align:start position:0% +photov voltaics installation a heating +oil Cooperative uh purchase and + + align:start position:0% +oil Cooperative uh purchase and + + + align:start position:0% +oil Cooperative uh purchase and +cooperative and there was there were + + align:start position:0% +cooperative and there was there were + + + align:start position:0% +cooperative and there was there were +five I can't remember what the fifth one + + align:start position:0% +five I can't remember what the fifth one + + + align:start position:0% +five I can't remember what the fifth one +was and that board of directors insisted + + align:start position:0% +was and that board of directors insisted + + + align:start position:0% +was and that board of directors insisted +that they needed all of those products + + align:start position:0% +that they needed all of those products + + + align:start position:0% +that they needed all of those products +and services because you had to have a + + align:start position:0% +and services because you had to have a + + + align:start position:0% +and services because you had to have a +package of products and services in + + align:start position:0% +package of products and services in + + + align:start position:0% +package of products and services in +order to attract members and they signed + + align:start position:0% +order to attract members and they signed + + + align:start position:0% +order to attract members and they signed +on 13,000 people I mean it households + + align:start position:0% +on 13,000 people I mean it households + + + align:start position:0% +on 13,000 people I mean it households +was a magnificent feat but it was too + + align:start position:0% +was a magnificent feat but it was too + + + align:start position:0% +was a magnificent feat but it was too +hard you know to do all of those + + align:start position:0% +hard you know to do all of those + + + align:start position:0% +hard you know to do all of those +products and services and negotiate all + + align:start position:0% +products and services and negotiate all + + + align:start position:0% +products and services and negotiate all +those contracts and blah blah blah and + + align:start position:0% +those contracts and blah blah blah and + + + align:start position:0% +those contracts and blah blah blah and +they would have they would have had an + + align:start position:0% +they would have they would have had an + + + align:start position:0% +they would have they would have had an +easier time had they picked one and done + + align:start position:0% +easier time had they picked one and done + + + align:start position:0% +easier time had they picked one and done +that really well and taken the 6,000 + + align:start position:0% +that really well and taken the 6,000 + + + align:start position:0% +that really well and taken the 6,000 +people who wanted that one and then + + align:start position:0% +people who wanted that one and then + + + align:start position:0% +people who wanted that one and then +added on as they kind of stabilized and + + align:start position:0% +added on as they kind of stabilized and + + + align:start position:0% +added on as they kind of stabilized and +and they're not in business anymore + + align:start position:0% +and they're not in business anymore + + + align:start position:0% +and they're not in business anymore +that's only one of the reasons why + + align:start position:0% +that's only one of the reasons why + + + align:start position:0% +that's only one of the reasons why +they're not in business but + + align:start position:0% +they're not in business but + + + align:start position:0% +they're not in business but +um yes so first things first so the + + align:start position:0% +um yes so first things first so the + + + align:start position:0% +um yes so first things first so the +Strategic planning process is where you + + align:start position:0% +Strategic planning process is where you + + + align:start position:0% +Strategic planning process is where you +create a shared business a shared vision + + align:start position:0% +create a shared business a shared vision + + + align:start position:0% +create a shared business a shared vision +for the business where you craft a + + align:start position:0% +for the business where you craft a + + + align:start position:0% +for the business where you craft a +viable business strategy so you say this + + align:start position:0% +viable business strategy so you say this + + + align:start position:0% +viable business strategy so you say this +is how we want the world to be different + + align:start position:0% +is how we want the world to be different + + + align:start position:0% +is how we want the world to be different +because this business exists and this is + + align:start position:0% +because this business exists and this is + + + align:start position:0% +because this business exists and this is +how we're going to go about making that + + align:start position:0% +how we're going to go about making that + + + align:start position:0% +how we're going to go about making that +happen and you understand the best + + align:start position:0% +happen and you understand the best + + + align:start position:0% +happen and you understand the best +practices in group-based business + + align:start position:0% +practices in group-based business + + + align:start position:0% +practices in group-based business +development and build a development plan + + align:start position:0% +development and build a development plan + + + align:start position:0% +development and build a development plan +for your business so on the next couple + + align:start position:0% +for your business so on the next couple + + + align:start position:0% +for your business so on the next couple +of pages we gave you uh keys to + + align:start position:0% +of pages we gave you uh keys to + + + align:start position:0% +of pages we gave you uh keys to +successful Co-op development + + align:start position:0% +successful Co-op development + + + align:start position:0% +successful Co-op development +project starts with and these are + + align:start position:0% +project starts with and these are + + + align:start position:0% +project starts with and these are +handouts that I give to groups who are + + align:start position:0% +handouts that I give to groups who are + + + align:start position:0% +handouts that I give to groups who are +thinking about it project starts with a + + align:start position:0% +thinking about it project starts with a + + + align:start position:0% +thinking about it project starts with a +compelling need a strong Champion a + + align:start position:0% +compelling need a strong Champion a + + + align:start position:0% +compelling need a strong Champion a +Clear Vision people find these you know + + align:start position:0% +Clear Vision people find these you know + + + align:start position:0% +Clear Vision people find these you know +these are kind of common sense but they + + align:start position:0% +these are kind of common sense but they + + + align:start position:0% +these are kind of common sense but they +find them very grounding when they're + + align:start position:0% +find them very grounding when they're + + + align:start position:0% +find them very grounding when they're +getting started and it's a good + + align:start position:0% +getting started and it's a good + + + align:start position:0% +getting started and it's a good +checklist to go back to a couple times + + align:start position:0% +checklist to go back to a couple times + + + align:start position:0% +checklist to go back to a couple times +and say you know how are we doing do we + + align:start position:0% +and say you know how are we doing do we + + + align:start position:0% +and say you know how are we doing do we +have have three or four greatly I mean + + align:start position:0% +have have three or four greatly I mean + + + align:start position:0% +have have three or four greatly I mean +you got a champion you got the + + align:start position:0% +you got a champion you got the + + + align:start position:0% +you got a champion you got the +compelling vision and then but then you + + align:start position:0% +compelling vision and then but then you + + + align:start position:0% +compelling vision and then but then you +know a couple other I mean really key + + align:start position:0% +know a couple other I mean really key + + + align:start position:0% +know a couple other I mean really key +things are just not there I mean so at + + align:start position:0% +things are just not there I mean so at + + + align:start position:0% +things are just not there I mean so at +least giving them that checklist then + + align:start position:0% +least giving them that checklist then + + + align:start position:0% +least giving them that checklist then +they can begin to it helps in that + + align:start position:0% +they can begin to it helps in that + + + align:start position:0% +they can begin to it helps in that +conversation of U of of of are we really + + align:start position:0% +conversation of U of of of are we really + + + align:start position:0% +conversation of U of of of are we really +ready to launch yet or you know do we + + align:start position:0% +ready to launch yet or you know do we + + + align:start position:0% +ready to launch yet or you know do we +need more time Division and discuss and + + align:start position:0% +need more time Division and discuss and + + + align:start position:0% +need more time Division and discuss and +plan the the backside of that first page + + align:start position:0% +plan the the backside of that first page + + + align:start position:0% +plan the the backside of that first page +the second page is um the different + + align:start position:0% +the second page is um the different + + + align:start position:0% +the second page is um the different +roles in the development process and + + align:start position:0% +roles in the development process and + + + align:start position:0% +roles in the development process and +these are the roles as we see them in + + align:start position:0% +these are the roles as we see them in + + + align:start position:0% +these are the roles as we see them in +the way we do co-op development at The + + align:start position:0% +the way we do co-op development at The + + + align:start position:0% +the way we do co-op development at The +Cooperative development Institute there + + align:start position:0% +Cooperative development Institute there + + + align:start position:0% +Cooperative development Institute there +are other ways to parse this out but + + align:start position:0% +are other ways to parse this out but + + + align:start position:0% +are other ways to parse this out but +these we just find it helpful to and I + + align:start position:0% +these we just find it helpful to and I + + + align:start position:0% +these we just find it helpful to and I +would say none of our projects do this + + align:start position:0% +would say none of our projects do this + + + align:start position:0% +would say none of our projects do this +exactly you know it's always a + + align:start position:0% +exactly you know it's always a + + + align:start position:0% +exactly you know it's always a +conversation like how about we do this + + align:start position:0% +conversation like how about we do this + + + align:start position:0% +conversation like how about we do this +and you do that oh you want to do that + + align:start position:0% +and you do that oh you want to do that + + + align:start position:0% +and you do that oh you want to do that +too that's great okay then we'll do this + + align:start position:0% +too that's great okay then we'll do this + + + align:start position:0% +too that's great okay then we'll do this +but coming to um a clear understanding + + align:start position:0% +but coming to um a clear understanding + + + align:start position:0% +but coming to um a clear understanding +of who's doing what helps uh it took us + + align:start position:0% +of who's doing what helps uh it took us + + + align:start position:0% +of who's doing what helps uh it took us +a while to figure out all the things we + + align:start position:0% +a while to figure out all the things we + + + align:start position:0% +a while to figure out all the things we +needed to clarify but um so if we start + + align:start position:0% +needed to clarify but um so if we start + + + align:start position:0% +needed to clarify but um so if we start +with this and then edit it with each of + + align:start position:0% +with this and then edit it with each of + + + align:start position:0% +with this and then edit it with each of +the groups that we're working with we + + align:start position:0% +the groups that we're working with we + + + align:start position:0% +the groups that we're working with we +find that pretty helpful and + + align:start position:0% +find that pretty helpful and + + + align:start position:0% +find that pretty helpful and +particularly really um like said as + + align:start position:0% +particularly really um like said as + + + align:start position:0% +particularly really um like said as +seeing yourself for example like you + + align:start position:0% +seeing yourself for example like you + + + align:start position:0% +seeing yourself for example like you +know if you know let's say a group of uh + + align:start position:0% +know if you know let's say a group of uh + + + align:start position:0% +know if you know let's say a group of uh +grad students going to work with a + + align:start position:0% +grad students going to work with a + + + align:start position:0% +grad students going to work with a +community + + align:start position:0% +community + + + align:start position:0% +community +organization you know having clear sense + + align:start position:0% +organization you know having clear sense + + + align:start position:0% +organization you know having clear sense +of what is your role in that I mean and + + align:start position:0% +of what is your role in that I mean and + + + align:start position:0% +of what is your role in that I mean and +and what are the responsibilities you're + + align:start position:0% +and what are the responsibilities you're + + + align:start position:0% +and what are the responsibilities you're +going to take on and what are you not + + align:start position:0% +going to take on and what are you not + + + align:start position:0% +going to take on and what are you not +going to take on you know and and and + + align:start position:0% +going to take on you know and and and + + + align:start position:0% +going to take on you know and and and +and uh with the uh sitting down with the + + align:start position:0% +and uh with the uh sitting down with the + + + align:start position:0% +and uh with the uh sitting down with the +champion you know that maybe that one or + + align:start position:0% +champion you know that maybe that one or + + + align:start position:0% +champion you know that maybe that one or +two or three people that really excited + + align:start position:0% +two or three people that really excited + + + align:start position:0% +two or three people that really excited +about this and really want to make this + + align:start position:0% +about this and really want to make this + + + align:start position:0% +about this and really want to make this +happen you know and and coming together + + align:start position:0% +happen you know and and coming together + + + align:start position:0% +happen you know and and coming together +with some kind of clear sense Within on + + align:start position:0% +with some kind of clear sense Within on + + + align:start position:0% +with some kind of clear sense Within on +what on what those expectations are it + + align:start position:0% +what on what those expectations are it + + + align:start position:0% +what on what those expectations are it +can save you a lot of problems in in the + + align:start position:0% +can save you a lot of problems in in the + + + align:start position:0% +can save you a lot of problems in in the +you know as as you as you move along I + + align:start position:0% +you know as as you as you move along I + + + align:start position:0% +you know as as you as you move along I +mean if um I've I've seen some just um + + align:start position:0% +mean if um I've I've seen some just um + + + align:start position:0% +mean if um I've I've seen some just um +ugly scenes kind of develop uh you know + + align:start position:0% +ugly scenes kind of develop uh you know + + + align:start position:0% +ugly scenes kind of develop uh you know +that that started out well but then + + align:start position:0% +that that started out well but then + + + align:start position:0% +that that started out well but then +there was you know they had uh just a + + align:start position:0% +there was you know they had uh just a + + + align:start position:0% +there was you know they had uh just a +lot of just unreasonable expectations uh + + align:start position:0% +lot of just unreasonable expectations uh + + + align:start position:0% +lot of just unreasonable expectations uh +um um on either side and so I having + + align:start position:0% +um um on either side and so I having + + + align:start position:0% +um um on either side and so I having +that conversation you know like I said + + align:start position:0% +that conversation you know like I said + + + align:start position:0% +that conversation you know like I said +having something like this that also has + + align:start position:0% +having something like this that also has + + + align:start position:0% +having something like this that also has +the credibility of you know that it's + + align:start position:0% +the credibility of you know that it's + + + align:start position:0% +the credibility of you know that it's +been Ed and worked in in a number of + + align:start position:0% +been Ed and worked in in a number of + + + align:start position:0% +been Ed and worked in in a number of +different situation also helps in terms + + align:start position:0% +different situation also helps in terms + + + align:start position:0% +different situation also helps in terms +of uh having that um um you know + + align:start position:0% +of uh having that um um you know + + + align:start position:0% +of uh having that um um you know +beginning to negotiate out uh U those + + align:start position:0% +beginning to negotiate out uh U those + + + align:start position:0% +beginning to negotiate out uh U those +understandings of + + align:start position:0% +understandings of + + + align:start position:0% +understandings of +roles used to do like a formal + + align:start position:0% +roles used to do like a formal + + + align:start position:0% +roles used to do like a formal +agreement yes we often put this in anou + + align:start position:0% +agreement yes we often put this in anou + + + align:start position:0% +agreement yes we often put this in anou +yeah that's yeah usually and then this + + align:start position:0% +yeah that's yeah usually and then this + + + align:start position:0% +yeah that's yeah usually and then this +this next set of pages this chart is my + + align:start position:0% +this next set of pages this chart is my + + + align:start position:0% +this next set of pages this chart is my +favorite if I could only have one I'd + + align:start position:0% +favorite if I could only have one I'd + + + align:start position:0% +favorite if I could only have one I'd +keep this one + + align:start position:0% +keep this one + + + align:start position:0% +keep this one +but it it um it's just a really great + + align:start position:0% +but it it um it's just a really great + + + align:start position:0% +but it it um it's just a really great +worksheet by the time I work through + + align:start position:0% +worksheet by the time I work through + + + align:start position:0% +worksheet by the time I work through +this with people they have an idea of + + align:start position:0% +this with people they have an idea of + + + align:start position:0% +this with people they have an idea of +what it's going to take to get their + + align:start position:0% +what it's going to take to get their + + + align:start position:0% +what it's going to take to get their +business started and we keep checking in + + align:start position:0% +business started and we keep checking in + + + align:start position:0% +business started and we keep checking in +on it okay um how much did that actually + + align:start position:0% +on it okay um how much did that actually + + + align:start position:0% +on it okay um how much did that actually +cost us you know who was going to do + + align:start position:0% +cost us you know who was going to do + + + align:start position:0% +cost us you know who was going to do +that did they follow through um are we + + align:start position:0% +that did they follow through um are we + + + align:start position:0% +that did they follow through um are we +getting it done by the time we said we + + align:start position:0% +getting it done by the time we said we + + + align:start position:0% +getting it done by the time we said we +were going to um you know we we haven't + + align:start position:0% +were going to um you know we we haven't + + + align:start position:0% +were going to um you know we we haven't +done member development and it's six + + align:start position:0% +done member development and it's six + + + align:start position:0% +done member development and it's six +months later you know the what we said + + align:start position:0% +months later you know the what we said + + + align:start position:0% +months later you know the what we said +we were going to do in stage one what + + align:start position:0% +we were going to do in stage one what + + + align:start position:0% +we were going to do in stage one what +does that mean about our organizing work + + align:start position:0% +does that mean about our organizing work + + + align:start position:0% +does that mean about our organizing work +and who's doing it and do we need to get + + align:start position:0% +and who's doing it and do we need to get + + + align:start position:0% +and who's doing it and do we need to get +some more people on there and what's up + + align:start position:0% +some more people on there and what's up + + + align:start position:0% +some more people on there and what's up +with that but this um this is kind of + + align:start position:0% +with that but this um this is kind of + + + align:start position:0% +with that but this um this is kind of +the the the the blueprint for how the + + align:start position:0% +the the the the blueprint for how the + + + align:start position:0% +the the the the blueprint for how the +process moves forward and just again + + align:start position:0% +process moves forward and just again + + + align:start position:0% +process moves forward and just again +just filling it out um I usually do this + + align:start position:0% +just filling it out um I usually do this + + + align:start position:0% +just filling it out um I usually do this +the second or third time I meet with + + align:start position:0% +the second or third time I meet with + + + align:start position:0% +the second or third time I meet with +people when we have kind of an idea of + + align:start position:0% +people when we have kind of an idea of + + + align:start position:0% +people when we have kind of an idea of +what it is they're going to do and + + align:start position:0% +what it is they're going to do and + + + align:start position:0% +what it is they're going to do and +people leave so excited because it's + + align:start position:0% +people leave so excited because it's + + + align:start position:0% +people leave so excited because it's +tangible what the end result's going to + + align:start position:0% +tangible what the end result's going to + + + align:start position:0% +tangible what the end result's going to +look like but it's also sobering also + + align:start position:0% +look like but it's also sobering also + + + align:start position:0% +look like but it's also sobering also +cuz I mean that that + + align:start position:0% +cuz I mean that that + + + align:start position:0% +cuz I mean that that +you can you know and particularly when + + align:start position:0% +you can you know and particularly when + + + align:start position:0% +you can you know and particularly when +you're dealing with folks that may have + + align:start position:0% +you're dealing with folks that may have + + + align:start position:0% +you're dealing with folks that may have +had no business experience at all you + + align:start position:0% +had no business experience at all you + + + align:start position:0% +had no business experience at all you +know the thought that you know oh we can + + align:start position:0% +know the thought that you know oh we can + + + align:start position:0% +know the thought that you know oh we can +three months we'll knock this out you + + align:start position:0% +three months we'll knock this out you + + + align:start position:0% +three months we'll knock this out you +know we'll visioned we would have done + + align:start position:0% +know we'll visioned we would have done + + + align:start position:0% +know we'll visioned we would have done +the business plan feasibility studies uh + + align:start position:0% +the business plan feasibility studies uh + + + align:start position:0% +the business plan feasibility studies uh +you know structured the board and you + + align:start position:0% +you know structured the board and you + + + align:start position:0% +you know structured the board and you +know and we got a product and we're hid + + align:start position:0% +know and we got a product and we're hid + + + align:start position:0% +know and we got a product and we're hid +in the streets you know no I meanless + + align:start position:0% +in the streets you know no I meanless + + + align:start position:0% +in the streets you know no I meanless +you know and getting folks to see that + + align:start position:0% +you know and getting folks to see that + + + align:start position:0% +you know and getting folks to see that +it's a much more a larger commitment of + + align:start position:0% +it's a much more a larger commitment of + + + align:start position:0% +it's a much more a larger commitment of +time and effort U you know so that U you + + align:start position:0% +time and effort U you know so that U you + + + align:start position:0% +time and effort U you know so that U you +know that there may be a lot you know + + align:start position:0% +know that there may be a lot you know + + + align:start position:0% +know that there may be a lot you know +know a lot of shortcuts that may happen + + align:start position:0% +know a lot of shortcuts that may happen + + + align:start position:0% +know a lot of shortcuts that may happen +depending on what what uh assets people + + align:start position:0% +depending on what what uh assets people + + + align:start position:0% +depending on what what uh assets people +already have in place but at least + + align:start position:0% +already have in place but at least + + + align:start position:0% +already have in place but at least +giving them a sense of this is what + + align:start position:0% +giving them a sense of this is what + + + align:start position:0% +giving them a sense of this is what +generally how long it takes so you know + + align:start position:0% +generally how long it takes so you know + + + align:start position:0% +generally how long it takes so you know +it sobers them give them sense that + + align:start position:0% +it sobers them give them sense that + + + align:start position:0% +it sobers them give them sense that +we're not this is not going to be done + + align:start position:0% +we're not this is not going to be done + + + align:start position:0% +we're not this is not going to be done +you know in a in a half a year that that + + align:start position:0% +you know in a in a half a year that that + + + align:start position:0% +you know in a in a half a year that that +we're really talking about one two three + + align:start position:0% +we're really talking about one two three + + + align:start position:0% +we're really talking about one two three +years of uh work to really get this U + + align:start position:0% +years of uh work to really get this U + + + align:start position:0% +years of uh work to really get this U +business up and running + + align:start position:0% + + + + align:start position:0% + +um yep then we've got the group based + + align:start position:0% +um yep then we've got the group based + + + align:start position:0% +um yep then we've got the group based +planning overview so + + align:start position:0% +planning overview so + + + align:start position:0% +planning overview so +when it's business planning overview so + + align:start position:0% +when it's business planning overview so + + + align:start position:0% +when it's business planning overview so +when it's time to actually they've got a + + align:start position:0% +when it's time to actually they've got a + + + align:start position:0% +when it's time to actually they've got a +shared Vision they've got a development + + align:start position:0% +shared Vision they've got a development + + + align:start position:0% +shared Vision they've got a development +plan we've got the money raised to pay + + align:start position:0% +plan we've got the money raised to pay + + + align:start position:0% +plan we've got the money raised to pay +for the development process this um + + align:start position:0% +for the development process this um + + + align:start position:0% +for the development process this um +gives a good overview of what happens in + + align:start position:0% +gives a good overview of what happens in + + + align:start position:0% +gives a good overview of what happens in +a business planning process um and again + + align:start position:0% +a business planning process um and again + + + align:start position:0% +a business planning process um and again +this is something that we can you can + + align:start position:0% +this is something that we can you can + + + align:start position:0% +this is something that we can you can +hand out to people and it's it's + + align:start position:0% +hand out to people and it's it's + + + align:start position:0% +hand out to people and it's it's +um it's + + align:start position:0% +um it's + + + align:start position:0% +um it's +accessible we should have put this up on + + align:start position:0% +accessible we should have put this up on + + + align:start position:0% +accessible we should have put this up on +the + + align:start position:0% +the + + + align:start position:0% +the +board that much video and then it yeah + + align:start position:0% +board that much video and then it yeah + + + align:start position:0% +board that much video and then it yeah +and the the the rest of this packet up + + align:start position:0% +and the the the rest of this packet up + + + align:start position:0% +and the the the rest of this packet up +until the end is um there's a workbook + + align:start position:0% +until the end is um there's a workbook + + + align:start position:0% +until the end is um there's a workbook +for um for doing market + + align:start position:0% +for um for doing market + + + align:start position:0% +for um for doing market +analysis who are the customers and how + + align:start position:0% +analysis who are the customers and how + + + align:start position:0% +analysis who are the customers and how +can we design what we're doing to fit + + align:start position:0% +can we design what we're doing to fit + + + align:start position:0% +can we design what we're doing to fit +who they are and it's a great workbook + + align:start position:0% +who they are and it's a great workbook + + + align:start position:0% +who they are and it's a great workbook +I've used it with a lot of groups and it + + align:start position:0% +I've used it with a lot of groups and it + + + align:start position:0% +I've used it with a lot of groups and it +it if you have any ideas for a business + + align:start position:0% +it if you have any ideas for a business + + + align:start position:0% +it if you have any ideas for a business +and you want to kind of get go from the + + align:start position:0% +and you want to kind of get go from the + + + align:start position:0% +and you want to kind of get go from the +very surface down a few inches to see + + align:start position:0% +very surface down a few inches to see + + + align:start position:0% +very surface down a few inches to see +whether it could work and what could + + align:start position:0% +whether it could work and what could + + + align:start position:0% +whether it could work and what could +really work and how you might really do + + align:start position:0% +really work and how you might really do + + + align:start position:0% +really work and how you might really do +it it's a great first step in the + + align:start position:0% +it it's a great first step in the + + + align:start position:0% +it it's a great first step in the +business planning process and then + + align:start position:0% +business planning process and then + + + align:start position:0% +business planning process and then +there's a fe there's some feasibility + + align:start position:0% +there's a fe there's some feasibility + + + align:start position:0% +there's a fe there's some feasibility +resources to see um once you know you've + + align:start position:0% +resources to see um once you know you've + + + align:start position:0% +resources to see um once you know you've +got a good idea and there's a market for + + align:start position:0% +got a good idea and there's a market for + + + align:start position:0% +got a good idea and there's a market for +it or you have a good idea that you have + + align:start position:0% +it or you have a good idea that you have + + + align:start position:0% +it or you have a good idea that you have +a market for it the next step is to + + align:start position:0% +a market for it the next step is to + + + align:start position:0% +a market for it the next step is to +check it out financially you know Is it + + align:start position:0% +check it out financially you know Is it + + + align:start position:0% +check it out financially you know Is it +feasible um and you do a little bit more + + align:start position:0% +feasible um and you do a little bit more + + + align:start position:0% +feasible um and you do a little bit more +research and you might have two or three + + align:start position:0% +research and you might have two or three + + + align:start position:0% +research and you might have two or three +business models that you're checking out + + align:start position:0% +business models that you're checking out + + + align:start position:0% +business models that you're checking out +would be better for us to do this or + + align:start position:0% +would be better for us to do this or + + + align:start position:0% +would be better for us to do this or +this or this and you want to compare + + align:start position:0% +this or this and you want to compare + + + align:start position:0% +this or this and you want to compare +those the best feasibility studies I've + + align:start position:0% +those the best feasibility studies I've + + + align:start position:0% +those the best feasibility studies I've +seen do that they don't just take one + + align:start position:0% +seen do that they don't just take one + + + align:start position:0% +seen do that they don't just take one +model and prove it they take one or two + + align:start position:0% +model and prove it they take one or two + + + align:start position:0% +model and prove it they take one or two +variations on that model and see which + + align:start position:0% +variations on that model and see which + + + align:start position:0% +variations on that model and see which +one would be the most effective way to + + align:start position:0% +one would be the most effective way to + + + align:start position:0% +one would be the most effective way to +implement that business um so the res + + align:start position:0% +implement that business um so the res + + + align:start position:0% +implement that business um so the res +the next set of resources are from + + align:start position:0% +the next set of resources are from + + + align:start position:0% +the next set of resources are from +colleagues of mine in in the midwest who + + align:start position:0% +colleagues of mine in in the midwest who + + + align:start position:0% +colleagues of mine in in the midwest who +um put together actually it's a the + + align:start position:0% +um put together actually it's a the + + + align:start position:0% +um put together actually it's a the +colleagues wrote it but it's a national + + align:start position:0% +colleagues wrote it but it's a national + + + align:start position:0% +colleagues wrote it but it's a national +Co-op resource on how to do feasibility + + align:start position:0% +Co-op resource on how to do feasibility + + + align:start position:0% +Co-op resource on how to do feasibility +studies um put out by The clusa + + align:start position:0% +studies um put out by The clusa + + + align:start position:0% +studies um put out by The clusa +Institute which actually works in + + align:start position:0% +Institute which actually works in + + + align:start position:0% +Institute which actually works in +internationally uh a lot in India and + + align:start position:0% +internationally uh a lot in India and + + + align:start position:0% +internationally uh a lot in India and +Africa um and then the last one is just + + align:start position:0% +Africa um and then the last one is just + + + align:start position:0% +Africa um and then the last one is just +an outline for a B for a business plan + + align:start position:0% +an outline for a B for a business plan + + + align:start position:0% +an outline for a B for a business plan +from SBA and I never use outlines for a + + align:start position:0% +from SBA and I never use outlines for a + + + align:start position:0% +from SBA and I never use outlines for a +business plan I always say what is it + + align:start position:0% +business plan I always say what is it + + + align:start position:0% +business plan I always say what is it +that this group needs to know in order + + align:start position:0% +that this group needs to know in order + + + align:start position:0% +that this group needs to know in order +to really successfully implement this + + align:start position:0% +to really successfully implement this + + + align:start position:0% +to really successfully implement this +business but it's nice to have those I + + align:start position:0% +business but it's nice to have those I + + + align:start position:0% +business but it's nice to have those I +those the outline there to kind of give + + align:start position:0% +those the outline there to kind of give + + + align:start position:0% +those the outline there to kind of give +a check you know kind of say well do I + + align:start position:0% +a check you know kind of say well do I + + + align:start position:0% +a check you know kind of say well do I +need to say anything more about business + + align:start position:0% +need to say anything more about business + + + align:start position:0% +need to say anything more about business +operations or or governance or whatever + + align:start position:0% +operations or or governance or whatever + + + align:start position:0% +operations or or governance or whatever +in case you neglected to put that down + + align:start position:0% +in case you neglected to put that down + + + align:start position:0% +in case you neglected to put that down +but it's um I find short business plans + + align:start position:0% +but it's um I find short business plans + + + align:start position:0% +but it's um I find short business plans +are the best and um the the + + align:start position:0% +are the best and um the the + + + align:start position:0% +are the best and um the the +reason well what this is a lot of + + align:start position:0% +reason well what this is a lot of + + + align:start position:0% +reason well what this is a lot of +planning planners love it a lot of + + align:start position:0% +planning planners love it a lot of + + + align:start position:0% +planning planners love it a lot of +community people want to start the + + align:start position:0% +community people want to start the + + + align:start position:0% +community people want to start the +business you you've all been out in the + + align:start position:0% +business you you've all been out in the + + + align:start position:0% +business you you've all been out in the +world long enough what happens when + + align:start position:0% +world long enough what happens when + + + align:start position:0% +world long enough what happens when +Community folks just start a + + align:start position:0% +Community folks just start a + + + align:start position:0% +Community folks just start a +business what's the result of skipping + + align:start position:0% +business what's the result of skipping + + + align:start position:0% +business what's the result of skipping +this planning part + + align:start position:0% + + + + align:start position:0% + +it doesn't it doesn't go very far people + + align:start position:0% +it doesn't it doesn't go very far people + + + align:start position:0% +it doesn't it doesn't go very far people +um you know may have um you know + + align:start position:0% +um you know may have um you know + + + align:start position:0% +um you know may have um you know +conflicting interests may not understand + + align:start position:0% +conflicting interests may not understand + + + align:start position:0% +conflicting interests may not understand +their functions and you know like like + + align:start position:0% +their functions and you know like like + + + align:start position:0% +their functions and you know like like +with the uher and Coop they took + + align:start position:0% +with the uher and Coop they took + + + align:start position:0% +with the uher and Coop they took +everything instead of you know recycling + + align:start position:0% +everything instead of you know recycling + + + align:start position:0% +everything instead of you know recycling +it back into the + + align:start position:0% +it back into the + + + align:start position:0% +it back into the +Cooper people may not really be cohesive + + align:start position:0% +Cooper people may not really be cohesive + + + align:start position:0% +Cooper people may not really be cohesive +in the community just for + + align:start position:0% +in the community just for + + + align:start position:0% +in the community just for +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah I I find that there's no way + + align:start position:0% +yeah I I find that there's no way + + + align:start position:0% +yeah I I find that there's no way +everybody has the same idea about how + + align:start position:0% +everybody has the same idea about how + + + align:start position:0% +everybody has the same idea about how +that business is going to get + + align:start position:0% +that business is going to get + + + align:start position:0% +that business is going to get +implemented not there's not even a + + align:start position:0% +implemented not there's not even a + + + align:start position:0% +implemented not there's not even a +chance there's not a prayer of a chance + + align:start position:0% +chance there's not a prayer of a chance + + + align:start position:0% +chance there's not a prayer of a chance +so if you've got three people in the + + align:start position:0% +so if you've got three people in the + + + align:start position:0% +so if you've got three people in the +room and they're going to start a + + align:start position:0% +room and they're going to start a + + + align:start position:0% +room and they're going to start a +business together and they haven't done + + align:start position:0% +business together and they haven't done + + + align:start position:0% +business together and they haven't done +any planning they're all going to go off + + align:start position:0% +any planning they're all going to go off + + + align:start position:0% +any planning they're all going to go off +in different directions and instead of + + align:start position:0% +in different directions and instead of + + + align:start position:0% +in different directions and instead of +working it out ahead of time you're + + align:start position:0% +working it out ahead of time you're + + + align:start position:0% +working it out ahead of time you're +going to be working it out while you're + + align:start position:0% +going to be working it out while you're + + + align:start position:0% +going to be working it out while you're +spending money and you know your cash is + + align:start position:0% +spending money and you know your cash is + + + align:start position:0% +spending money and you know your cash is +depleted and you haven't had time to + + align:start position:0% +depleted and you haven't had time to + + + align:start position:0% +depleted and you haven't had time to +solve the problem before for you you + + align:start position:0% +solve the problem before for you you + + + align:start position:0% +solve the problem before for you you +know you didn't even know you had a + + align:start position:0% +know you didn't even know you had a + + + align:start position:0% +know you didn't even know you had a +problem and it's already closed the + + align:start position:0% +problem and it's already closed the + + + align:start position:0% +problem and it's already closed the +business down because you haven't had a + + align:start position:0% +business down because you haven't had a + + + align:start position:0% +business down because you haven't had a +chance to work it through you you've + + align:start position:0% +chance to work it through you you've + + + align:start position:0% +chance to work it through you you've +targeted the wrong product to the wrong + + align:start position:0% +targeted the wrong product to the wrong + + + align:start position:0% +targeted the wrong product to the wrong +Market you're you know you're trying to + + align:start position:0% +Market you're you know you're trying to + + + align:start position:0% +Market you're you know you're trying to +deliver it in the wrong way there's if + + align:start position:0% +deliver it in the wrong way there's if + + + align:start position:0% +deliver it in the wrong way there's if +you go through the business planning + + align:start position:0% +you go through the business planning + + + align:start position:0% +you go through the business planning +process you can vet a whole lot of + + align:start position:0% +process you can vet a whole lot of + + + align:start position:0% +process you can vet a whole lot of +problems before they bite the business + + align:start position:0% +problems before they bite the business + + + align:start position:0% +problems before they bite the business +and so um it's it's just good sound um + + align:start position:0% +and so um it's it's just good sound um + + + align:start position:0% +and so um it's it's just good sound um +way to start any business but if you + + align:start position:0% +way to start any business but if you + + + align:start position:0% +way to start any business but if you +want to start a group-based business + + align:start position:0% +want to start a group-based business + + + align:start position:0% +want to start a group-based business +there are no shortcuts because you've + + align:start position:0% +there are no shortcuts because you've + + + align:start position:0% +there are no shortcuts because you've +got a group of people who want to share + + align:start position:0% +got a group of people who want to share + + + align:start position:0% +got a group of people who want to share +decision- making and the only way to + + align:start position:0% +decision- making and the only way to + + + align:start position:0% +decision- making and the only way to +share decision making is to + + align:start position:0% +share decision making is to + + + align:start position:0% +share decision making is to +plan like say once you this is your road + + align:start position:0% +plan like say once you this is your road + + + align:start position:0% +plan like say once you this is your road +map you know um it's not something to to + + align:start position:0% +map you know um it's not something to to + + + align:start position:0% +map you know um it's not something to to +produce and then put on the shelf that + + align:start position:0% +produce and then put on the shelf that + + + align:start position:0% +produce and then put on the shelf that +this is something that like in that + + align:start position:0% +this is something that like in that + + + align:start position:0% +this is something that like in that +catering mean they'd have a clear sense + + align:start position:0% +catering mean they'd have a clear sense + + + align:start position:0% +catering mean they'd have a clear sense +of what are the financial projections + + align:start position:0% +of what are the financial projections + + + align:start position:0% +of what are the financial projections +that they need you know on a + + align:start position:0% +that they need you know on a + + + align:start position:0% +that they need you know on a +month-by-month basis for the next three + + align:start position:0% +month-by-month basis for the next three + + + align:start position:0% +month-by-month basis for the next three +years or whatever and uh U you know so + + align:start position:0% +years or whatever and uh U you know so + + + align:start position:0% +years or whatever and uh U you know so +that would dictate you know that how + + align:start position:0% +that would dictate you know that how + + + align:start position:0% +that would dictate you know that how +they moved uh you know understand on + + align:start position:0% +they moved uh you know understand on + + + align:start position:0% +they moved uh you know understand on +what your your competitors are and all + + align:start position:0% +what your your competitors are and all + + + align:start position:0% +what your your competitors are and all +those other things I mean just that + + align:start position:0% +those other things I mean just that + + + align:start position:0% +those other things I mean just that +process of being able to talk it out and + + align:start position:0% +process of being able to talk it out and + + + align:start position:0% +process of being able to talk it out and +you know and then for me you like I've + + align:start position:0% +you know and then for me you like I've + + + align:start position:0% +you know and then for me you like I've +always we can you know periodically get + + align:start position:0% +always we can you know periodically get + + + align:start position:0% +always we can you know periodically get +back to it and look again and make sure + + align:start position:0% +back to it and look again and make sure + + + align:start position:0% +back to it and look again and make sure +that that it's it's still um uh valid + + align:start position:0% +that that it's it's still um uh valid + + + align:start position:0% +that that it's it's still um uh valid +and you know maybe that needs there's + + align:start position:0% +and you know maybe that needs there's + + + align:start position:0% +and you know maybe that needs there's +some new stuff that got thrown in the + + align:start position:0% +some new stuff that got thrown in the + + + align:start position:0% +some new stuff that got thrown in the +game there's a new competitor and you + + align:start position:0% +game there's a new competitor and you + + + align:start position:0% +game there's a new competitor and you +know the the markets changed in some + + align:start position:0% +know the the markets changed in some + + + align:start position:0% +know the the markets changed in some +significant way and you know gives you a + + align:start position:0% +significant way and you know gives you a + + + align:start position:0% +significant way and you know gives you a +a process to be able to look at it come + + align:start position:0% +a process to be able to look at it come + + + align:start position:0% +a process to be able to look at it come +and like I said and come to some unified + + align:start position:0% +and like I said and come to some unified + + + align:start position:0% +and like I said and come to some unified +uh decision making on on it and uh it's + + align:start position:0% +uh decision making on on it and uh it's + + + align:start position:0% +uh decision making on on it and uh it's +but it's I think it's it's it's just + + align:start position:0% +but it's I think it's it's it's just + + + align:start position:0% +but it's I think it's it's it's just +time really well spent um but I I agree + + align:start position:0% +time really well spent um but I I agree + + + align:start position:0% +time really well spent um but I I agree +with I mean if it doesn't have to be you + + align:start position:0% +with I mean if it doesn't have to be you + + + align:start position:0% +with I mean if it doesn't have to be you +know you know a lot of times you can get + + align:start position:0% +know you know a lot of times you can get + + + align:start position:0% +know you know a lot of times you can get +these telephone book size business plans + + align:start position:0% +these telephone book size business plans + + + align:start position:0% +these telephone book size business plans +I mean I think that you know it's it's + + align:start position:0% +I mean I think that you know it's it's + + + align:start position:0% +I mean I think that you know it's it's +not necessary to have that sience but um + + align:start position:0% +not necessary to have that sience but um + + + align:start position:0% +not necessary to have that sience but um +at least a lot of the key questions have + + align:start position:0% +at least a lot of the key questions have + + + align:start position:0% +at least a lot of the key questions have +to be dealt + + align:start position:0% + + + + align:start position:0% + +with so the the next thing we're going + + align:start position:0% +with so the the next thing we're going + + + align:start position:0% +with so the the next thing we're going +to do is um engage in this role play and + + align:start position:0% +to do is um engage in this role play and + + + align:start position:0% +to do is um engage in this role play and +I've given you each a different card + + align:start position:0% +I've given you each a different card + + + align:start position:0% +I've given you each a different card +except the two of you have the same + + align:start position:0% +except the two of you have the same + + + align:start position:0% +except the two of you have the same +card all right and um so if you could um + + align:start position:0% +card all right and um so if you could um + + + align:start position:0% +card all right and um so if you could um +take a minute to read your card and then + + align:start position:0% +take a minute to read your card and then + + + align:start position:0% +take a minute to read your card and then +when you're ready introduce yourself to + + align:start position:0% +when you're ready introduce yourself to + + + align:start position:0% +when you're ready introduce yourself to +the group so people know all you have to + + align:start position:0% +the group so people know all you have to + + + align:start position:0% +the group so people know all you have to +just say is which role you're + + align:start position:0% +just say is which role you're + + + align:start position:0% +just say is which role you're +playing and it would be good not to um + + align:start position:0% +playing and it would be good not to um + + + align:start position:0% +playing and it would be good not to um +actually tell anybody else what's on + + align:start position:0% +actually tell anybody else what's on + + + align:start position:0% +actually tell anybody else what's on +your card just act it through + + align:start position:0% + + + + align:start position:0% + +so if the grad students could convene + + align:start position:0% +so if the grad students could convene + + + align:start position:0% +so if the grad students could convene +that would be good + + align:start position:0% + + + + align:start position:0% + +say that again so if if the grad + + align:start position:0% +say that again so if if the grad + + + align:start position:0% +say that again so if if the grad +students could serve as the facilitators + + align:start position:0% +students could serve as the facilitators + + + align:start position:0% +students could serve as the facilitators +for this role play that would be good + + align:start position:0% +for this role play that would be good + + + align:start position:0% +for this role play that would be good +yes well that was a good thing to start + + align:start position:0% + + + + align:start position:0% + +with well thanks for coming everybody to + + align:start position:0% +with well thanks for coming everybody to + + + align:start position:0% +with well thanks for coming everybody to +the meeting um can everybody go around + + align:start position:0% +the meeting um can everybody go around + + + align:start position:0% +the meeting um can everybody go around +and introduce themselves + + align:start position:0% +and introduce themselves + + + align:start position:0% +and introduce themselves +yes do you want to go first oh I'm sorry + + align:start position:0% +yes do you want to go first oh I'm sorry + + + align:start position:0% +yes do you want to go first oh I'm sorry +yes I am a No Name graduate student + + align:start position:0% + + + + align:start position:0% + +University and uh we are here to uh talk + + align:start position:0% +University and uh we are here to uh talk + + + align:start position:0% +University and uh we are here to uh talk +about this groc + + align:start position:0% +about this groc + + + align:start position:0% +about this groc +store + + align:start position:0% +store + + + align:start position:0% +store +working okay and actually before you + + align:start position:0% +working okay and actually before you + + + align:start position:0% +working okay and actually before you +start I'm going to ask you to the two of + + align:start position:0% +start I'm going to ask you to the two of + + + align:start position:0% +start I'm going to ask you to the two of +you to take this those two seats over + + align:start position:0% +you to take this those two seats over + + + align:start position:0% +you to take this those two seats over +there it'll just be more fun for the + + align:start position:0% + + + + align:start position:0% + +videotape and if the if you guys could + + align:start position:0% +videotape and if the if you guys could + + + align:start position:0% +videotape and if the if you guys could +just all move down just a little + + align:start position:0% +just all move down just a little + + + align:start position:0% +just all move down just a little +bit K you can say yeah that's great + + align:start position:0% + + + + align:start position:0% + +and the microphone's here in the middle + + align:start position:0% +and the microphone's here in the middle + + + align:start position:0% +and the microphone's here in the middle +of the table if you could speak to + + align:start position:0% + + + + align:start position:0% + +that still + + align:start position:0% +that still + + + align:start position:0% +that still +okay no um hi I'm salana I'm + + align:start position:0% +okay no um hi I'm salana I'm + + + align:start position:0% +okay no um hi I'm salana I'm +representing Community a I'm interested + + align:start position:0% +representing Community a I'm interested + + + align:start position:0% +representing Community a I'm interested +in making this grocery store + + align:start position:0% +in making this grocery store + + + align:start position:0% +in making this grocery store +happen I think it'll bring a lot of good + + align:start position:0% +happen I think it'll bring a lot of good + + + align:start position:0% +happen I think it'll bring a lot of good +things to the neighbor + + align:start position:0% + + + + align:start position:0% + +representing Community a yes well you're + + align:start position:0% +representing Community a yes well you're + + + align:start position:0% +representing Community a yes well you're +a Community member I'm + + align:start position:0% + + + + align:start position:0% + +aair um you're the chair of this + + align:start position:0% +aair um you're the chair of this + + + align:start position:0% +aair um you're the chair of this +community group I'm the chair of this + + align:start position:0% +community group I'm the chair of this + + + align:start position:0% +community group I'm the chair of this +community group and um I run a catering + + align:start position:0% +community group and um I run a catering + + + align:start position:0% +community group and um I run a catering +business um here in the community and um + + align:start position:0% +business um here in the community and um + + + align:start position:0% +business um here in the community and um +I'm just here to support the effort of + + align:start position:0% +I'm just here to support the effort of + + + align:start position:0% +I'm just here to support the effort of +getting this grocery + + align:start position:0% +getting this grocery + + + align:start position:0% +getting this grocery +store I'm uh Community B + + align:start position:0% +store I'm uh Community B + + + align:start position:0% +store I'm uh Community B +and I think there ought to be a grocery + + align:start position:0% +and I think there ought to be a grocery + + + align:start position:0% +and I think there ought to be a grocery +store but one that really works and one + + align:start position:0% +store but one that really works and one + + + align:start position:0% +store but one that really works and one +that really + + align:start position:0% +that really + + + align:start position:0% +that really +happens + + align:start position:0% +happens + + + align:start position:0% +happens +and I don't think this is a safe + + align:start position:0% +and I don't think this is a safe + + + align:start position:0% +and I don't think this is a safe +neighborhood I think that's one of the + + align:start position:0% +neighborhood I think that's one of the + + + align:start position:0% +neighborhood I think that's one of the +first issues that has to be addressed to + + align:start position:0% +first issues that has to be addressed to + + + align:start position:0% +first issues that has to be addressed to +I think who I think we need to have + + align:start position:0% +I think who I think we need to have + + + align:start position:0% +I think who I think we need to have +experienced business people running this + + align:start position:0% +experienced business people running this + + + align:start position:0% +experienced business people running this +St see + + align:start position:0% + + + + align:start position:0% + +so I'm Shing the meeting um okay well I + + align:start position:0% +so I'm Shing the meeting um okay well I + + + align:start position:0% +so I'm Shing the meeting um okay well I +guess well I think that the graduate + + align:start position:0% +guess well I think that the graduate + + + align:start position:0% +guess well I think that the graduate +students The Graduate students they're + + align:start position:0% +students The Graduate students they're + + + align:start position:0% +students The Graduate students they're +here to facilitate this I was going to + + align:start position:0% +here to facilitate this I was going to + + + align:start position:0% +here to facilitate this I was going to +say perap we could hear from our young + + align:start position:0% +say perap we could hear from our young + + + align:start position:0% +say perap we could hear from our young +graduate + + align:start position:0% +graduate + + + align:start position:0% +graduate +students oh I know + + align:start position:0% +students oh I know + + + align:start position:0% +students oh I know +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +away well um we've uh uh done um a + + align:start position:0% +away well um we've uh uh done um a + + + align:start position:0% +away well um we've uh uh done um a +little bit of research and and which is + + align:start position:0% +little bit of research and and which is + + + align:start position:0% +little bit of research and and which is +welome you while we are here and uh you + + align:start position:0% +welome you while we are here and uh you + + + align:start position:0% +welome you while we are here and uh you +know we just talk about the issues of uh + + align:start position:0% +know we just talk about the issues of uh + + + align:start position:0% +know we just talk about the issues of uh +basically access in this community and + + align:start position:0% +basically access in this community and + + + align:start position:0% +basically access in this community and +the fact that there isn't a a viable + + align:start position:0% +the fact that there isn't a a viable + + + align:start position:0% +the fact that there isn't a a viable +grocery store you know in this community + + align:start position:0% +grocery store you know in this community + + + align:start position:0% +grocery store you know in this community +and people have to drive out of the + + align:start position:0% +and people have to drive out of the + + + align:start position:0% +and people have to drive out of the +community uh just in order to access + + align:start position:0% +community uh just in order to access + + + align:start position:0% +community uh just in order to access +food and uh so many people in this area + + align:start position:0% +food and uh so many people in this area + + + align:start position:0% +food and uh so many people in this area +just don't don't even own cars their own + + align:start position:0% +just don't don't even own cars their own + + + align:start position:0% +just don't don't even own cars their own +personal Transportation be able to + + align:start position:0% +personal Transportation be able to + + + align:start position:0% +personal Transportation be able to +access food so we're trying to look at + + align:start position:0% +access food so we're trying to look at + + + align:start position:0% +access food so we're trying to look at +um possible um alternative um ideas uh + + align:start position:0% +um possible um alternative um ideas uh + + + align:start position:0% +um possible um alternative um ideas uh +one of you know one was uh + + align:start position:0% +one of you know one was uh + + + align:start position:0% +one of you know one was uh +Transportation cooperatives but I think + + align:start position:0% +Transportation cooperatives but I think + + + align:start position:0% +Transportation cooperatives but I think +this idea of the brers to actually + + align:start position:0% +this idea of the brers to actually + + + align:start position:0% +this idea of the brers to actually +within this community you know would + + align:start position:0% +within this community you know would + + + align:start position:0% +within this community you know would +allow you know just local local assets + + align:start position:0% +allow you know just local local assets + + + align:start position:0% +allow you know just local local assets +and allow these resources maintained + + align:start position:0% +and allow these resources maintained + + + align:start position:0% +and allow these resources maintained +here to be maintained here in this + + align:start position:0% +here to be maintained here in this + + + align:start position:0% +here to be maintained here in this +community to allow some building to go + + align:start position:0% +community to allow some building to go + + + align:start position:0% +community to allow some building to go +on here and um yeah and so you know + + align:start position:0% +on here and um yeah and so you know + + + align:start position:0% +on here and um yeah and so you know +we're just trying to you know just to + + align:start position:0% +we're just trying to you know just to + + + align:start position:0% +we're just trying to you know just to +get together with local Global Community + + align:start position:0% +get together with local Global Community + + + align:start position:0% +get together with local Global Community +people to see you know how we can U + + align:start position:0% +people to see you know how we can U + + + align:start position:0% +people to see you know how we can U +begin to initiate this process and just + + align:start position:0% +begin to initiate this process and just + + + align:start position:0% +begin to initiate this process and just +to start the + + align:start position:0% +to start the + + + align:start position:0% +to start the +dialogue this + + align:start position:0% +dialogue this + + + align:start position:0% +dialogue this +Ro yes um Young no name um when you + + align:start position:0% +Ro yes um Young no name um when you + + + align:start position:0% +Ro yes um Young no name um when you +first came to me a few weeks ago with + + align:start position:0% +first came to me a few weeks ago with + + + align:start position:0% +first came to me a few weeks ago with +this idea for your class Pro project um + + align:start position:0% +this idea for your class Pro project um + + + align:start position:0% +this idea for your class Pro project um +you you talked about this idea of a + + align:start position:0% +you you talked about this idea of a + + + align:start position:0% +you you talked about this idea of a +cooperatively owned supermarket and I + + align:start position:0% +cooperatively owned supermarket and I + + + align:start position:0% +cooperatively owned supermarket and I +I'm just not really sure what you mean + + align:start position:0% +I'm just not really sure what you mean + + + align:start position:0% +I'm just not really sure what you mean +by that and I'm not sure if that is + + align:start position:0% +by that and I'm not sure if that is + + + align:start position:0% +by that and I'm not sure if that is +going to happen I guess is my + + align:start position:0% +going to happen I guess is my + + + align:start position:0% +going to happen I guess is my +concern so I I'd like to see the story + + align:start position:0% +concern so I I'd like to see the story + + + align:start position:0% +concern so I I'd like to see the story +here I'd like to support your ideas I + + align:start position:0% +here I'd like to support your ideas I + + + align:start position:0% +here I'd like to support your ideas I +think it's interesting um we do want to + + align:start position:0% +think it's interesting um we do want to + + + align:start position:0% +think it's interesting um we do want to +keep Assets in our community um so I'm + + align:start position:0% +keep Assets in our community um so I'm + + + align:start position:0% +keep Assets in our community um so I'm +just you know I'm just wondering how you + + align:start position:0% +just you know I'm just wondering how you + + + align:start position:0% +just you know I'm just wondering how you +see this this planning process playing + + align:start position:0% +see this this planning process playing + + + align:start position:0% +see this this planning process playing +out well no offense to Mr M name + + align:start position:0% +out well no offense to Mr M name + + + align:start position:0% +out well no offense to Mr M name +but we we live here in this + + align:start position:0% +but we we live here in this + + + align:start position:0% +but we we live here in this +neighborhood uh Mr noname and his fellow + + align:start position:0% +neighborhood uh Mr noname and his fellow + + + align:start position:0% +neighborhood uh Mr noname and his fellow +students don't live here they're just + + align:start position:0% +students don't live here they're just + + + align:start position:0% +students don't live here they're just +here for some course assignment to get a + + align:start position:0% +here for some course assignment to get a + + + align:start position:0% +here for some course assignment to get a +grade and at the end of the day we're + + align:start position:0% +grade and at the end of the day we're + + + align:start position:0% +grade and at the end of the day we're +going to be stuck with whatever gets put + + align:start position:0% +going to be stuck with whatever gets put + + + align:start position:0% +going to be stuck with whatever gets put +up here and Mr no name said that his + + align:start position:0% +up here and Mr no name said that his + + + align:start position:0% +up here and Mr no name said that his +group did a little bit of research and + + align:start position:0% +group did a little bit of research and + + + align:start position:0% +group did a little bit of research and +that's my problem you know we need more + + align:start position:0% +that's my problem you know we need more + + + align:start position:0% +that's my problem you know we need more +than a little bit of research and we + + align:start position:0% +than a little bit of research and we + + + align:start position:0% +than a little bit of research and we +don't this isn't a research project this + + align:start position:0% +don't this isn't a research project this + + + align:start position:0% +don't this isn't a research project this +is a grocery + + align:start position:0% +is a grocery + + + align:start position:0% +is a grocery +store and we want quality groceries in + + align:start position:0% +store and we want quality groceries in + + + align:start position:0% +store and we want quality groceries in +here and that takes one a little bit of + + align:start position:0% +here and that takes one a little bit of + + + align:start position:0% +here and that takes one a little bit of +research to figure out cuz we haven't + + align:start position:0% +research to figure out cuz we haven't + + + align:start position:0% +research to figure out cuz we haven't +had it here in 20 + + align:start position:0% +had it here in 20 + + + align:start position:0% +had it here in 20 +years so but it seems to me that there's + + align:start position:0% +years so but it seems to me that there's + + + align:start position:0% +years so but it seems to me that there's +a lot of effort and energy going towards + + align:start position:0% +a lot of effort and energy going towards + + + align:start position:0% +a lot of effort and energy going towards +this I mean I think that the research + + align:start position:0% +this I mean I think that the research + + + align:start position:0% +this I mean I think that the research +will help and I'm sure that the graduate + + align:start position:0% +will help and I'm sure that the graduate + + + align:start position:0% +will help and I'm sure that the graduate +students will do more as they get more + + align:start position:0% +students will do more as they get more + + + align:start position:0% +students will do more as they get more +invested in the place but I think there + + align:start position:0% +invested in the place but I think there + + + align:start position:0% +invested in the place but I think there +are also people here in the community + + align:start position:0% +are also people here in the community + + + align:start position:0% +are also people here in the community +that are willing to put forth the energy + + align:start position:0% +that are willing to put forth the energy + + + align:start position:0% +that are willing to put forth the energy +and um the effort to push it through to + + align:start position:0% +and um the effort to push it through to + + + align:start position:0% +and um the effort to push it through to +fruition there's a lot of energy in the + + align:start position:0% +fruition there's a lot of energy in the + + + align:start position:0% +fruition there's a lot of energy in the +riots in the 60s probably don't remember + + align:start position:0% +riots in the 60s probably don't remember + + + align:start position:0% +riots in the 60s probably don't remember +that but it didn't mean this anything + + align:start position:0% +that but it didn't mean this anything + + + align:start position:0% +that but it didn't mean this anything +got built so I mean I I welcome your + + align:start position:0% +got built so I mean I I welcome your + + + align:start position:0% +got built so I mean I I welcome your +energy but you know I think we need to + + align:start position:0% +energy but you know I think we need to + + + align:start position:0% +energy but you know I think we need to +have something serious that's going to + + align:start position:0% +have something serious that's going to + + + align:start position:0% +have something serious that's going to +work here next + + align:start position:0% +work here next + + + align:start position:0% +work here next +not something you can do for your course + + align:start position:0% +not something you can do for your course + + + align:start position:0% +not something you can do for your course +in you know in a few months time and + + align:start position:0% +in you know in a few months time and + + + align:start position:0% +in you know in a few months time and +leave and it's not something that you + + align:start position:0% +leave and it's not something that you + + + align:start position:0% +leave and it's not something that you +can ask people in this neighborhood to + + align:start position:0% +can ask people in this neighborhood to + + + align:start position:0% +can ask people in this neighborhood to +put their money up for when they don't + + align:start position:0% +put their money up for when they don't + + + align:start position:0% +put their money up for when they don't +know it's going to work cuz they can't + + align:start position:0% +know it's going to work cuz they can't + + + align:start position:0% +know it's going to work cuz they can't +afford for it to + + align:start position:0% + + + + align:start position:0% + +fail well um in terms of the uh amount + + align:start position:0% +fail well um in terms of the uh amount + + + align:start position:0% +fail well um in terms of the uh amount +of research um you know we just tried to + + align:start position:0% +of research um you know we just tried to + + + align:start position:0% +of research um you know we just tried to +do uh you know just um a very small + + align:start position:0% +do uh you know just um a very small + + + align:start position:0% +do uh you know just um a very small +study just start off wasn't much of a + + align:start position:0% +study just start off wasn't much of a + + + align:start position:0% +study just start off wasn't much of a +study um but we did put put a lot of + + align:start position:0% +study um but we did put put a lot of + + + align:start position:0% +study um but we did put put a lot of +work and effort uh we actually went door + + align:start position:0% +work and effort uh we actually went door + + + align:start position:0% +work and effort uh we actually went door +too uh with the survey and talked to + + align:start position:0% +too uh with the survey and talked to + + + align:start position:0% +too uh with the survey and talked to +people about you know their issues of + + align:start position:0% +people about you know their issues of + + + align:start position:0% +people about you know their issues of +accessing accessing food and how far + + align:start position:0% +accessing accessing food and how far + + + align:start position:0% +accessing accessing food and how far +they had to drive to get to the grocery + + align:start position:0% +they had to drive to get to the grocery + + + align:start position:0% +they had to drive to get to the grocery +store how long it took them and um and + + align:start position:0% +store how long it took them and um and + + + align:start position:0% +store how long it took them and um and +just to talk with them about um the + + align:start position:0% +just to talk with them about um the + + + align:start position:0% +just to talk with them about um the +different options that they you know + + align:start position:0% +different options that they you know + + + align:start position:0% +different options that they you know +would consider uh to be viable options + + align:start position:0% +would consider uh to be viable options + + + align:start position:0% +would consider uh to be viable options +and and the majority of the residents in + + align:start position:0% +and and the majority of the residents in + + + align:start position:0% +and and the majority of the residents in +the community who we talk to um you know + + align:start position:0% +the community who we talk to um you know + + + align:start position:0% +the community who we talk to um you know +were open to and and were pretty excited + + align:start position:0% +were open to and and were pretty excited + + + align:start position:0% +were open to and and were pretty excited +about the idea of actually owning their + + align:start position:0% +about the idea of actually owning their + + + align:start position:0% +about the idea of actually owning their +own store and um you're exactly right + + align:start position:0% +own store and um you're exactly right + + + align:start position:0% +own store and um you're exactly right +that you know I don't live in this + + align:start position:0% +that you know I don't live in this + + + align:start position:0% +that you know I don't live in this +community um and this is uh you know a + + align:start position:0% +community um and this is uh you know a + + + align:start position:0% +community um and this is uh you know a +project that we're doing through school + + align:start position:0% +project that we're doing through school + + + align:start position:0% +project that we're doing through school +but I see it I see it as as an + + align:start position:0% +but I see it I see it as as an + + + align:start position:0% +but I see it I see it as as an +opportunity and and it's a great course + + align:start position:0% +opportunity and and it's a great course + + + align:start position:0% +opportunity and and it's a great course +um you know that is allowing me you know + + align:start position:0% +um you know that is allowing me you know + + + align:start position:0% +um you know that is allowing me you know +to venture out into a community and + + align:start position:0% +to venture out into a community and + + + align:start position:0% +to venture out into a community and +actually work with communities and do + + align:start position:0% +actually work with communities and do + + + align:start position:0% +actually work with communities and do +this type of work you know through + + align:start position:0% +this type of work you know through + + + align:start position:0% +this type of work you know through +course through class which is why I'm + + align:start position:0% +course through class which is why I'm + + + align:start position:0% +course through class which is why I'm +studying in first place uh CU I would + + align:start position:0% +studying in first place uh CU I would + + + align:start position:0% +studying in first place uh CU I would +like just continue with this type of + + align:start position:0% +like just continue with this type of + + + align:start position:0% +like just continue with this type of +work throughout my career um but you + + align:start position:0% +work throughout my career um but you + + + align:start position:0% +work throughout my career um but you +know so acknowledging that you know we + + align:start position:0% +know so acknowledging that you know we + + + align:start position:0% +know so acknowledging that you know we +won't be here very long uh which is why + + align:start position:0% +won't be here very long uh which is why + + + align:start position:0% +won't be here very long uh which is why +we think the Cooperative model is such + + align:start position:0% +we think the Cooperative model is such + + + align:start position:0% +we think the Cooperative model is such +an advantageous model for the community + + align:start position:0% +an advantageous model for the community + + + align:start position:0% +an advantageous model for the community +because it's one that the community will + + align:start position:0% +because it's one that the community will + + + align:start position:0% +because it's one that the community will +own and the community will control now + + align:start position:0% +own and the community will control now + + + align:start position:0% +own and the community will control now +um you know different models of + + align:start position:0% +um you know different models of + + + align:start position:0% +um you know different models of +development would try to you know get + + align:start position:0% +development would try to you know get + + + align:start position:0% +development would try to you know get +you know an Albertson's or k or some + + align:start position:0% +you know an Albertson's or k or some + + + align:start position:0% +you know an Albertson's or k or some +someone else to come into your community + + align:start position:0% +someone else to come into your community + + + align:start position:0% +someone else to come into your community +which is not a grer store that you own + + align:start position:0% +which is not a grer store that you own + + + align:start position:0% +which is not a grer store that you own +but it's privately owned and so once + + align:start position:0% +but it's privately owned and so once + + + align:start position:0% +but it's privately owned and so once +they come into the community you're + + align:start position:0% +they come into the community you're + + + align:start position:0% +they come into the community you're +stuck with them and you don't own them + + align:start position:0% +stuck with them and you don't own them + + + align:start position:0% +stuck with them and you don't own them +you know they pretty much you know bring + + align:start position:0% +you know they pretty much you know bring + + + align:start position:0% +you know they pretty much you know bring +whatever food that they get to come into + + align:start position:0% +whatever food that they get to come into + + + align:start position:0% +whatever food that they get to come into +this neighborhood and as you said you + + align:start position:0% +this neighborhood and as you said you + + + align:start position:0% +this neighborhood and as you said you +know the perceptions outside of this + + align:start position:0% +know the perceptions outside of this + + + align:start position:0% +know the perceptions outside of this +neighborhood is that it's unsafe it's + + align:start position:0% +neighborhood is that it's unsafe it's + + + align:start position:0% +neighborhood is that it's unsafe it's +violent it's drug infested so you know + + align:start position:0% +violent it's drug infested so you know + + + align:start position:0% +violent it's drug infested so you know +people you know honestly are less + + align:start position:0% +people you know honestly are less + + + align:start position:0% +people you know honestly are less +concerned about the types of food and + + align:start position:0% +concerned about the types of food and + + + align:start position:0% +concerned about the types of food and +the quality of food that you get but in + + align:start position:0% +the quality of food that you get but in + + + align:start position:0% +the quality of food that you get but in +a grer in a grocery store that you own + + align:start position:0% +a grer in a grocery store that you own + + + align:start position:0% +a grer in a grocery store that you own +and that you control as residents and as + + align:start position:0% +and that you control as residents and as + + + align:start position:0% +and that you control as residents and as +members of this Cooperative you can + + align:start position:0% +members of this Cooperative you can + + + align:start position:0% +members of this Cooperative you can +contract with you know Farmers that you + + align:start position:0% +contract with you know Farmers that you + + + align:start position:0% +contract with you know Farmers that you +know you know people you know to + + align:start position:0% +know you know people you know to + + + align:start position:0% +know you know people you know to +bringing the food that you like so you + + align:start position:0% +bringing the food that you like so you + + + align:start position:0% +bringing the food that you like so you +know I think this this could be a very + + align:start position:0% +know I think this this could be a very + + + align:start position:0% +know I think this this could be a very +good idea so you know I understand your + + align:start position:0% +good idea so you know I understand your + + + align:start position:0% +good idea so you know I understand your +concerns and I think it's very much + + align:start position:0% +concerns and I think it's very much + + + align:start position:0% +concerns and I think it's very much +needed you know to have you know a very + + align:start position:0% +needed you know to have you know a very + + + align:start position:0% +needed you know to have you know a very +critical View and for us to kind of step + + align:start position:0% +critical View and for us to kind of step + + + align:start position:0% +critical View and for us to kind of step +slowly in this process um but you know + + align:start position:0% +slowly in this process um but you know + + + align:start position:0% +slowly in this process um but you know +we just give it a chance we're also + + align:start position:0% +we just give it a chance we're also + + + align:start position:0% +we just give it a chance we're also +interested in leveraging resources to + + align:start position:0% +interested in leveraging resources to + + + align:start position:0% +interested in leveraging resources to +continue the process so that whether or + + align:start position:0% +continue the process so that whether or + + + align:start position:0% +continue the process so that whether or +not he and I are still players in it + + align:start position:0% +not he and I are still players in it + + + align:start position:0% +not he and I are still players in it +that you're still connected with + + align:start position:0% +that you're still connected with + + + align:start position:0% +that you're still connected with +resources that enable the process to + + align:start position:0% +resources that enable the process to + + + align:start position:0% +resources that enable the process to +move forward with you know with more + + align:start position:0% +move forward with you know with more + + + align:start position:0% +move forward with you know with more +technical assistance and other key + + align:start position:0% +technical assistance and other key + + + align:start position:0% +technical assistance and other key +Community Players so it's not we're not + + align:start position:0% +Community Players so it's not we're not + + + align:start position:0% +Community Players so it's not we're not +here just to pitch it and leave we are + + align:start position:0% +here just to pitch it and leave we are + + + align:start position:0% +here just to pitch it and leave we are +interested in enabling proc to move + + align:start position:0% +interested in enabling proc to move + + + align:start position:0% +interested in enabling proc to move +forward look the fact of the matter is + + align:start position:0% +forward look the fact of the matter is + + + align:start position:0% +forward look the fact of the matter is +you're right about there's energy behind + + align:start position:0% +you're right about there's energy behind + + + align:start position:0% +you're right about there's energy behind +it now the the city's put up a million + + align:start position:0% +it now the the city's put up a million + + + align:start position:0% +it now the the city's put up a million +dollar loan we we we we just want to + + align:start position:0% +dollar loan we we we we just want to + + + align:start position:0% +dollar loan we we we we just want to +know when we're going to look out our + + align:start position:0% +know when we're going to look out our + + + align:start position:0% +know when we're going to look out our +window and see a supermarket there I + + align:start position:0% +window and see a supermarket there I + + + align:start position:0% +window and see a supermarket there I +mean the the money is there but I don't + + align:start position:0% +mean the the money is there but I don't + + + align:start position:0% +mean the the money is there but I don't +know like what is what does it cost and + + align:start position:0% +know like what is what does it cost and + + + align:start position:0% +know like what is what does it cost and +and I don't I don't know about this + + align:start position:0% +and I don't I don't know about this + + + align:start position:0% +and I don't I don't know about this +cooperative thing like I just want to I + + align:start position:0% +cooperative thing like I just want to I + + + align:start position:0% +cooperative thing like I just want to I +just want to be able to supply my + + align:start position:0% +just want to be able to supply my + + + align:start position:0% +just want to be able to supply my +catering business and walk to the store + + align:start position:0% +catering business and walk to the store + + + align:start position:0% +catering business and walk to the store +and you know I got my own problems so I + + align:start position:0% +and you know I got my own problems so I + + + align:start position:0% +and you know I got my own problems so I +just I just you know the city's put up a + + align:start position:0% +just I just you know the city's put up a + + + align:start position:0% +just I just you know the city's put up a +million dollars when is there going to + + align:start position:0% +million dollars when is there going to + + + align:start position:0% +million dollars when is there going to +be a supermarket on the corner you know + + align:start position:0% +be a supermarket on the corner you know + + + align:start position:0% +be a supermarket on the corner you know +maybe I'm the oldest person here but I + + align:start position:0% +maybe I'm the oldest person here but I + + + align:start position:0% +maybe I'm the oldest person here but I +remember the federal government put up + + align:start position:0% +remember the federal government put up + + + align:start position:0% +remember the federal government put up +all millions of dollars for small black + + align:start position:0% +all millions of dollars for small black + + + align:start position:0% +all millions of dollars for small black +businesses and that money just nobody + + align:start position:0% +businesses and that money just nobody + + + align:start position:0% +businesses and that money just nobody +exactly knows where the money went but + + align:start position:0% +exactly knows where the money went but + + + align:start position:0% +exactly knows where the money went but +the business is aren here anymore and I + + align:start position:0% +the business is aren here anymore and I + + + align:start position:0% +the business is aren here anymore and I +just have two questions what's what's + + align:start position:0% +just have two questions what's what's + + + align:start position:0% +just have two questions what's what's +going to stop folks from robbing your + + align:start position:0% +going to stop folks from robbing your + + + align:start position:0% +going to stop folks from robbing your +store blind how you going to prevent + + align:start position:0% +store blind how you going to prevent + + + align:start position:0% +store blind how you going to prevent +that I don't see how you're not going to + + align:start position:0% +that I don't see how you're not going to + + + align:start position:0% +that I don't see how you're not going to +have the same + + align:start position:0% +have the same + + + align:start position:0% +have the same +problem the other supermarkets going to + + align:start position:0% +problem the other supermarkets going to + + + align:start position:0% +problem the other supermarkets going to +have unless we have a new police station + + align:start position:0% +have unless we have a new police station + + + align:start position:0% +have unless we have a new police station +down here what's your plan on that + + align:start position:0% +down here what's your plan on that + + + align:start position:0% +down here what's your plan on that +number two how are you going to get if + + align:start position:0% +number two how are you going to get if + + + align:start position:0% +number two how are you going to get if +people in this neighborhood are going to + + align:start position:0% +people in this neighborhood are going to + + + align:start position:0% +people in this neighborhood are going to +put their own money into it I don't care + + align:start position:0% +put their own money into it I don't care + + + align:start position:0% +put their own money into it I don't care +about what the city's going to put into + + align:start position:0% +about what the city's going to put into + + + align:start position:0% +about what the city's going to put into +it what are people in this neighborhood + + align:start position:0% +it what are people in this neighborhood + + + align:start position:0% +it what are people in this neighborhood +going to put into it see these people + + align:start position:0% +going to put into it see these people + + + align:start position:0% +going to put into it see these people +here will tell you they fly to the moon + + align:start position:0% +here will tell you they fly to the moon + + + align:start position:0% +here will tell you they fly to the moon +you you send them out a survey they say + + align:start position:0% +you you send them out a survey they say + + + align:start position:0% +you you send them out a survey they say +yeah we'll go to the moon now you ask + + align:start position:0% +yeah we'll go to the moon now you ask + + + align:start position:0% +yeah we'll go to the moon now you ask +them to put $200 for their ticket to go + + align:start position:0% +them to put $200 for their ticket to go + + + align:start position:0% +them to put $200 for their ticket to go +to the Moon then they're not going to + + align:start position:0% +to the Moon then they're not going to + + + align:start position:0% +to the Moon then they're not going to +the Moon anymore they're going to stay + + align:start position:0% +the Moon anymore they're going to stay + + + align:start position:0% +the Moon anymore they're going to stay +right where they are so my question for + + align:start position:0% +right where they are so my question for + + + align:start position:0% +right where they are so my question for +you is how are you going to get them to + + align:start position:0% +you is how are you going to get them to + + + align:start position:0% +you is how are you going to get them to +put their money where their mouth is cuz + + align:start position:0% +put their money where their mouth is cuz + + + align:start position:0% +put their money where their mouth is cuz +I know these people + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% +here + + + align:start position:0% +here +well the question on how to get uh the + + align:start position:0% +well the question on how to get uh the + + + align:start position:0% +well the question on how to get uh the +community and the people involved I + + align:start position:0% +community and the people involved I + + + align:start position:0% +community and the people involved I +think + + align:start position:0% +think + + + align:start position:0% +think +uh I mean first of all we as being + + align:start position:0% +uh I mean first of all we as being + + + align:start position:0% +uh I mean first of all we as being +Outsiders in this community would have + + align:start position:0% +Outsiders in this community would have + + + align:start position:0% +Outsiders in this community would have +to rely more on you and because you are + + align:start position:0% +to rely more on you and because you are + + + align:start position:0% +to rely more on you and because you are +the leadership in this community and uh + + align:start position:0% +the leadership in this community and uh + + + align:start position:0% +the leadership in this community and uh +you know so we would actually have to uh + + align:start position:0% +you know so we would actually have to uh + + + align:start position:0% +you know so we would actually have to uh +um you know U refer or defer that charge + + align:start position:0% +um you know U refer or defer that charge + + + align:start position:0% +um you know U refer or defer that charge +to you uh you know as far as you know + + align:start position:0% +to you uh you know as far as you know + + + align:start position:0% +to you uh you know as far as you know +attempting to organize this community + + align:start position:0% +attempting to organize this community + + + align:start position:0% +attempting to organize this community +but you know in terms + + align:start position:0% +but you know in terms + + + align:start position:0% +but you know in terms +of the + + align:start position:0% +of the + + + align:start position:0% +of the +viability in terms of in terms of in + + align:start position:0% +viability in terms of in terms of in + + + align:start position:0% +viability in terms of in terms of in +terms of the viability uh we are uh + + align:start position:0% +terms of the viability uh we are uh + + + align:start position:0% +terms of the viability uh we are uh +prepared and we are um you know uh uh + + align:start position:0% +prepared and we are um you know uh uh + + + align:start position:0% +prepared and we are um you know uh uh +how do you say uh organizing ourselves + + align:start position:0% +how do you say uh organizing ourselves + + + align:start position:0% +how do you say uh organizing ourselves +and and we're you know getting ourselves + + align:start position:0% +and and we're you know getting ourselves + + + align:start position:0% +and and we're you know getting ourselves +uh ready to to assist you in doing you + + align:start position:0% +uh ready to to assist you in doing you + + + align:start position:0% +uh ready to to assist you in doing you +know business strategy modeling uh + + align:start position:0% +know business strategy modeling uh + + + align:start position:0% +know business strategy modeling uh +feasibility assessments uh + + align:start position:0% +feasibility assessments uh + + + align:start position:0% +feasibility assessments uh +capitalization assessments to really do + + align:start position:0% +capitalization assessments to really do + + + align:start position:0% +capitalization assessments to really do +more of the type of studies that that + + align:start position:0% +more of the type of studies that that + + + align:start position:0% +more of the type of studies that that +that you feel that we need in order to + + align:start position:0% +that you feel that we need in order to + + + align:start position:0% +that you feel that we need in order to +assess you know the viability and + + align:start position:0% +assess you know the viability and + + + align:start position:0% +assess you know the viability and +sustainability of its store now in terms + + align:start position:0% +sustainability of its store now in terms + + + align:start position:0% +sustainability of its store now in terms +of you know the safety um you know I + + align:start position:0% +of you know the safety um you know I + + + align:start position:0% +of you know the safety um you know I +think that there are multiple ways to + + align:start position:0% +think that there are multiple ways to + + + align:start position:0% +think that there are multiple ways to +deal with that I think there are + + align:start position:0% +deal with that I think there are + + + align:start position:0% +deal with that I think there are +positive ways and there uh punitive and + + align:start position:0% +positive ways and there uh punitive and + + + align:start position:0% +positive ways and there uh punitive and +negative ways I think more police or + + align:start position:0% +negative ways I think more police or + + + align:start position:0% +negative ways I think more police or +getting a new police station is an + + align:start position:0% +getting a new police station is an + + + align:start position:0% +getting a new police station is an +actually punitive or negative you know + + align:start position:0% +actually punitive or negative you know + + + align:start position:0% +actually punitive or negative you know +reinforcement to trying to deal with + + align:start position:0% +reinforcement to trying to deal with + + + align:start position:0% +reinforcement to trying to deal with +that type of situation and I would + + align:start position:0% +that type of situation and I would + + + align:start position:0% +that type of situation and I would +personally but this is not my community + + align:start position:0% +personally but this is not my community + + + align:start position:0% +personally but this is not my community +it's up to you but my personal you know + + align:start position:0% +it's up to you but my personal you know + + + align:start position:0% +it's up to you but my personal you know +uh um choice or my personal um ideas + + align:start position:0% +uh um choice or my personal um ideas + + + align:start position:0% +uh um choice or my personal um ideas +would be to look for more positive uh + + align:start position:0% +would be to look for more positive uh + + + align:start position:0% +would be to look for more positive uh +methods of dealing with violence of of + + align:start position:0% +methods of dealing with violence of of + + + align:start position:0% +methods of dealing with violence of of +of of dealing with you know some of the + + align:start position:0% +of of dealing with you know some of the + + + align:start position:0% +of of dealing with you know some of the +root causes to you know these types of + + align:start position:0% +root causes to you know these types of + + + align:start position:0% +root causes to you know these types of +crimes in any Community you know and so + + align:start position:0% +crimes in any Community you know and so + + + align:start position:0% +crimes in any Community you know and so +you know just adding more police to our + + align:start position:0% +you know just adding more police to our + + + align:start position:0% +you know just adding more police to our +neighborhood you know um you know the + + align:start position:0% +neighborhood you know um you know the + + + align:start position:0% +neighborhood you know um you know the +city where I'm from we have more police + + align:start position:0% +city where I'm from we have more police + + + align:start position:0% +city where I'm from we have more police +per capita than any other city in the + + align:start position:0% +per capita than any other city in the + + + align:start position:0% +per capita than any other city in the +country but crime is on the rise murder + + align:start position:0% +country but crime is on the rise murder + + + align:start position:0% +country but crime is on the rise murder +raid is on the rise so you know it just + + align:start position:0% +raid is on the rise so you know it just + + + align:start position:0% +raid is on the rise so you know it just +doesn't really you know what I'm saying + + align:start position:0% +doesn't really you know what I'm saying + + + align:start position:0% +doesn't really you know what I'm saying +so I think that there are much deeper + + align:start position:0% +so I think that there are much deeper + + + align:start position:0% +so I think that there are much deeper +issues that need to be involved and I + + align:start position:0% +issues that need to be involved and I + + + align:start position:0% +issues that need to be involved and I +think you know organizing a community + + align:start position:0% +think you know organizing a community + + + align:start position:0% +think you know organizing a community +around this Cooperative idea but getting + + align:start position:0% +around this Cooperative idea but getting + + + align:start position:0% +around this Cooperative idea but getting +a community organized and mobilized can + + align:start position:0% +a community organized and mobilized can + + + align:start position:0% +a community organized and mobilized can +can then lead to that possibility of + + align:start position:0% +can then lead to that possibility of + + + align:start position:0% +can then lead to that possibility of +addressing these various other issues + + align:start position:0% +addressing these various other issues + + + align:start position:0% +addressing these various other issues +that that are involved because it's + + align:start position:0% +that that are involved because it's + + + align:start position:0% +that that are involved because it's +because the power is is within this + + align:start position:0% +because the power is is within this + + + align:start position:0% +because the power is is within this +community to address its own + + align:start position:0% + + + + align:start position:0% + +needs well I would posee there are there + + align:start position:0% +needs well I would posee there are there + + + align:start position:0% +needs well I would posee there are there +different ways of thinking about this I + + align:start position:0% +different ways of thinking about this I + + + align:start position:0% +different ways of thinking about this I +mean why wouldn't we just say + + align:start position:0% +mean why wouldn't we just say + + + align:start position:0% +mean why wouldn't we just say +Albertson's come in and Albert has got + + align:start position:0% +Albertson's come in and Albert has got + + + align:start position:0% +Albertson's come in and Albert has got +everything I need to run my catering + + align:start position:0% +everything I need to run my catering + + + align:start position:0% +everything I need to run my catering +company I'll tell you that right now my + + align:start position:0% +company I'll tell you that right now my + + + align:start position:0% +company I'll tell you that right now my +sister-in-law down in next County over + + align:start position:0% +sister-in-law down in next County over + + + align:start position:0% +sister-in-law down in next County over +she sh there sometimes when I go pick up + + align:start position:0% +she sh there sometimes when I go pick up + + + align:start position:0% +she sh there sometimes when I go pick up +the kids I just go there and go shopping + + align:start position:0% +the kids I just go there and go shopping + + + align:start position:0% +the kids I just go there and go shopping +because I I need everything I need and I + + align:start position:0% +because I I need everything I need and I + + + align:start position:0% +because I I need everything I need and I +need it in bulk and I need it all at + + align:start position:0% +need it in bulk and I need it all at + + + align:start position:0% +need it in bulk and I need it all at +once so I don't know what this + + align:start position:0% +once so I don't know what this + + + align:start position:0% +once so I don't know what this +Cooperative Supermarket they going to + + align:start position:0% +Cooperative Supermarket they going to + + + align:start position:0% +Cooperative Supermarket they going to +have everything I need and then when is + + align:start position:0% +have everything I need and then when is + + + align:start position:0% +have everything I need and then when is +it and how long is it going to + + align:start position:0% +it and how long is it going to + + + align:start position:0% +it and how long is it going to +take + + align:start position:0% +take + + + align:start position:0% +take +um it may it may take it may take a + + align:start position:0% +um it may it may take it may take a + + + align:start position:0% +um it may it may take it may take a +little while to together but I think one + + align:start position:0% +little while to together but I think one + + + align:start position:0% +little while to together but I think one +of the benefits of it is that there will + + align:start position:0% +of the benefits of it is that there will + + + align:start position:0% +of the benefits of it is that there will +because it will be owned by people here + + align:start position:0% +because it will be owned by people here + + + align:start position:0% +because it will be owned by people here +like you can guarantee a certain + + align:start position:0% +like you can guarantee a certain + + + align:start position:0% +like you can guarantee a certain +permanence to it whereas Albertson's May + + align:start position:0% +permanence to it whereas Albertson's May + + + align:start position:0% +permanence to it whereas Albertson's May +pick up and go um and move somewhere + + align:start position:0% +pick up and go um and move somewhere + + + align:start position:0% +pick up and go um and move somewhere +further and although you might have a + + align:start position:0% +further and although you might have a + + + align:start position:0% +further and although you might have a +car and be able to get there there are a + + align:start position:0% +car and be able to get there there are a + + + align:start position:0% +car and be able to get there there are a +lot of people who don't have access to + + align:start position:0% +lot of people who don't have access to + + + align:start position:0% +lot of people who don't have access to +it here and so there is a pretty + + align:start position:0% +it here and so there is a pretty + + + align:start position:0% +it here and so there is a pretty +significant Community need and so there + + align:start position:0% +significant Community need and so there + + + align:start position:0% +significant Community need and so there +would it would be theoretically more + + align:start position:0% +would it would be theoretically more + + + align:start position:0% +would it would be theoretically more +sustainable here which would benefit you + + align:start position:0% +sustainable here which would benefit you + + + align:start position:0% +sustainable here which would benefit you +in the long term right and also um just + + align:start position:0% +in the long term right and also um just + + + align:start position:0% +in the long term right and also um just +through just if you um just assess the + + align:start position:0% +through just if you um just assess the + + + align:start position:0% +through just if you um just assess the +uh shipping methods and the U + + align:start position:0% +uh shipping methods and the U + + + align:start position:0% +uh shipping methods and the U +procurement methods of of a large store + + align:start position:0% +procurement methods of of a large store + + + align:start position:0% +procurement methods of of a large store +large store like alant you know they + + align:start position:0% +large store like alant you know they + + + align:start position:0% +large store like alant you know they +pull Gres from God knows where you know + + align:start position:0% +pull Gres from God knows where you know + + + align:start position:0% +pull Gres from God knows where you know +they ship it it's full of all types of + + align:start position:0% +they ship it it's full of all types of + + + align:start position:0% +they ship it it's full of all types of +chemicals and pesticides and preserv to + + align:start position:0% +chemicals and pesticides and preserv to + + + align:start position:0% +chemicals and pesticides and preserv to +keep it fresh because they're shipping + + align:start position:0% +keep it fresh because they're shipping + + + align:start position:0% +keep it fresh because they're shipping +it from God knows where I think you know + + align:start position:0% +it from God knows where I think you know + + + align:start position:0% +it from God knows where I think you know +um in our idea of this Cooperative you + + align:start position:0% +um in our idea of this Cooperative you + + + align:start position:0% +um in our idea of this Cooperative you +know there are there are tons literally + + align:start position:0% +know there are there are tons literally + + + align:start position:0% +know there are there are tons literally +tons many u local small farmers + + align:start position:0% +tons many u local small farmers + + + align:start position:0% +tons many u local small farmers +mediumsized Farmers you know right + + align:start position:0% +mediumsized Farmers you know right + + + align:start position:0% +mediumsized Farmers you know right +outside of this community you know in in + + align:start position:0% +outside of this community you know in in + + + align:start position:0% +outside of this community you know in in +in in these rural areas we could be + + align:start position:0% +in in these rural areas we could be + + + align:start position:0% +in in these rural areas we could be +accessing and getting um locally grown + + align:start position:0% +accessing and getting um locally grown + + + align:start position:0% +accessing and getting um locally grown +fresh produce delivered to the store + + align:start position:0% +fresh produce delivered to the store + + + align:start position:0% +fresh produce delivered to the store +daily you know and you know always doing + + align:start position:0% +daily you know and you know always doing + + + align:start position:0% +daily you know and you know always doing +it in both you know you you you you may + + align:start position:0% +it in both you know you you you you may + + + align:start position:0% +it in both you know you you you you may +reduce prices on one end and both + + align:start position:0% +reduce prices on one end and both + + + align:start position:0% +reduce prices on one end and both +but you also you know create the risk of + + align:start position:0% +but you also you know create the risk of + + + align:start position:0% +but you also you know create the risk of +reducing quality when you're doing it + + align:start position:0% +reducing quality when you're doing it + + + align:start position:0% +reducing quality when you're doing it +that way and I think you know just just + + align:start position:0% +that way and I think you know just just + + + align:start position:0% +that way and I think you know just just +a system of you know us building this + + align:start position:0% +a system of you know us building this + + + align:start position:0% +a system of you know us building this +model here but supporting you know rural + + align:start position:0% +model here but supporting you know rural + + + align:start position:0% +model here but supporting you know rural +farmers who you know are right next to + + align:start position:0% +farmers who you know are right next to + + + align:start position:0% +farmers who you know are right next to +us who aren't getting the you know the + + align:start position:0% +us who aren't getting the you know the + + + align:start position:0% +us who aren't getting the you know the +support that they need you I think it + + align:start position:0% +support that they need you I think it + + + align:start position:0% +support that they need you I think it +just builds just U just a deeper system + + align:start position:0% +just builds just U just a deeper system + + + align:start position:0% +just builds just U just a deeper system +of solidarity and I think you know also + + align:start position:0% +of solidarity and I think you know also + + + align:start position:0% +of solidarity and I think you know also +I think you know the value that that + + align:start position:0% +I think you know the value that that + + + align:start position:0% +I think you know the value that that +your catering business will will get + + align:start position:0% +your catering business will will get + + + align:start position:0% +your catering business will will get +from supporting a local industry from + + align:start position:0% +from supporting a local industry from + + + align:start position:0% +from supporting a local industry from +from from from going into a store of + + align:start position:0% +from from from going into a store of + + + align:start position:0% +from from from going into a store of +residents of of people within your + + align:start position:0% +residents of of people within your + + + align:start position:0% +residents of of people within your +community I think you know the value + + align:start position:0% +community I think you know the value + + + align:start position:0% +community I think you know the value +that that you get as a catering business + + align:start position:0% +that that you get as a catering business + + + align:start position:0% +that that you get as a catering business +you know seeing seeing that process + + align:start position:0% +you know seeing seeing that process + + + align:start position:0% +you know seeing seeing that process +going on I think you know people you + + align:start position:0% +going on I think you know people you + + + align:start position:0% +going on I think you know people you +know may come may come to recognize your + + align:start position:0% +know may come may come to recognize your + + + align:start position:0% +know may come may come to recognize your +business more you know and you make it + + align:start position:0% +business more you know and you make it + + + align:start position:0% +business more you know and you make it +more activity because so I'm going to do + + align:start position:0% +more activity because so I'm going to do + + + align:start position:0% +more activity because so I'm going to do +a time for just a minute just to + + align:start position:0% +a time for just a minute just to + + + align:start position:0% +a time for just a minute just to +redirect I'm going to redirect for just + + align:start position:0% +redirect I'm going to redirect for just + + + align:start position:0% +redirect I'm going to redirect for just +a second um it's been great + + align:start position:0% +a second um it's been great + + + align:start position:0% +a second um it's been great +great I mean how many people have been + + align:start position:0% +great I mean how many people have been + + + align:start position:0% +great I mean how many people have been +in community where you have these kinds + + align:start position:0% +in community where you have these kinds + + + align:start position:0% +in community where you have these kinds +of conversations I me this is like + + align:start position:0% +of conversations I me this is like + + + align:start position:0% +of conversations I me this is like +regular typical why starting group- + + align:start position:0% +regular typical why starting group- + + + align:start position:0% +regular typical why starting group- +based businesses is so hard um but I'd + + align:start position:0% +based businesses is so hard um but I'd + + + align:start position:0% +based businesses is so hard um but I'd +like to ask the two of you to do is to + + align:start position:0% +like to ask the two of you to do is to + + + align:start position:0% +like to ask the two of you to do is to +um say that come from the position where + + align:start position:0% +um say that come from the position where + + + align:start position:0% +um say that come from the position where +you don't know what the end result is + + align:start position:0% +you don't know what the end result is + + + align:start position:0% +you don't know what the end result is +going to be but what you're interested + + align:start position:0% +going to be but what you're interested + + + align:start position:0% +going to be but what you're interested +in doing is helping them decide what + + align:start position:0% +in doing is helping them decide what + + + align:start position:0% +in doing is helping them decide what +they want to do so rather than defending + + align:start position:0% +they want to do so rather than defending + + + align:start position:0% +they want to do so rather than defending +that + + align:start position:0% +that + + + align:start position:0% +that +position tell them well you know we're + + align:start position:0% +position tell them well you know we're + + + align:start position:0% +position tell them well you know we're +here just to give you information what + + align:start position:0% +here just to give you information what + + + align:start position:0% +here just to give you information what +other information do you need and here's + + align:start position:0% +other information do you need and here's + + + align:start position:0% +other information do you need and here's +our strategic planning you know list of + + align:start position:0% +our strategic planning you know list of + + + align:start position:0% +our strategic planning you know list of +questions and let's let's try to get + + align:start position:0% +questions and let's let's try to get + + + align:start position:0% +questions and let's let's try to get +onto that so try that for a minute and + + align:start position:0% +onto that so try that for a minute and + + + align:start position:0% +onto that so try that for a minute and +see how that Albertson let's look at + + align:start position:0% + + + + align:start position:0% + +Albertson you know so just see if you + + align:start position:0% +Albertson you know so just see if you + + + align:start position:0% +Albertson you know so just see if you +can see if you can + + align:start position:0% +can see if you can + + + align:start position:0% +can see if you can +do see if you can do something to build + + align:start position:0% +do see if you can do something to build + + + align:start position:0% +do see if you can do something to build +um an agreement about what the next you + + align:start position:0% +um an agreement about what the next you + + + align:start position:0% +um an agreement about what the next you +know how to get started on the next step + + align:start position:0% +know how to get started on the next step + + + align:start position:0% +know how to get started on the next step +so that they can have the information + + align:start position:0% +so that they can have the information + + + align:start position:0% +so that they can have the information +they need to decide what's best for them + + align:start position:0% + + + + align:start position:0% + +um I'm not actually + + align:start position:0% + + + + align:start position:0% + +Tex and then you got very strong + + align:start position:0% +Tex and then you got very strong + + + align:start position:0% +Tex and then you got very strong +opposition here I mean Phil is like he + + align:start position:0% +opposition here I mean Phil is like he + + + align:start position:0% +opposition here I mean Phil is like he +summed up all the uh the conservative + + align:start position:0% +summed up all the uh the conservative + + + align:start position:0% +summed up all the uh the conservative +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +opposition but uh so my first question + + align:start position:0% +opposition but uh so my first question + + + align:start position:0% +opposition but uh so my first question +to the uh three of you would be you know + + align:start position:0% +to the uh three of you would be you know + + + align:start position:0% +to the uh three of you would be you know +what would be your vision of how not + + align:start position:0% +what would be your vision of how not + + + align:start position:0% +what would be your vision of how not +only you know this this Co-op but just + + align:start position:0% +only you know this this Co-op but just + + + align:start position:0% +only you know this this Co-op but just +this issue of of of getting you know + + align:start position:0% +this issue of of of getting you know + + + align:start position:0% +this issue of of of getting you know +great greater access to food uh in this + + align:start position:0% +great greater access to food uh in this + + + align:start position:0% +great greater access to food uh in this +community how can how do you think that + + align:start position:0% +community how can how do you think that + + + align:start position:0% +community how can how do you think that +could best be solved what does that look + + align:start position:0% +could best be solved what does that look + + + align:start position:0% +could best be solved what does that look +like you know whether it be a + + align:start position:0% +like you know whether it be a + + + align:start position:0% +like you know whether it be a +Cooperative store whether it be in + + align:start position:0% +Cooperative store whether it be in + + + align:start position:0% +Cooperative store whether it be in +Albertson whether it be um you know um + + align:start position:0% +Albertson whether it be um you know um + + + align:start position:0% +Albertson whether it be um you know um +delivery cooperatives to get people you + + align:start position:0% +delivery cooperatives to get people you + + + align:start position:0% +delivery cooperatives to get people you +know food or to get people transport + + align:start position:0% +know food or to get people transport + + + align:start position:0% +know food or to get people transport +outside you know we' considered many + + align:start position:0% +outside you know we' considered many + + + align:start position:0% +outside you know we' considered many +different options but what for you is + + align:start position:0% +different options but what for you is + + + align:start position:0% +different options but what for you is +would be the best option + + align:start position:0% +would be the best option + + + align:start position:0% +would be the best option +I would just like there to be food that + + align:start position:0% +I would just like there to be food that + + + align:start position:0% +I would just like there to be food that +I + + align:start position:0% +I + + + align:start position:0% +I +want + + align:start position:0% +want + + + align:start position:0% +want +um not crazy stuff but like meat and + + align:start position:0% +um not crazy stuff but like meat and + + + align:start position:0% +um not crazy stuff but like meat and +potatoes simple but also having a place + + align:start position:0% +potatoes simple but also having a place + + + align:start position:0% +potatoes simple but also having a place +where kids can get jobs and there just + + align:start position:0% +where kids can get jobs and there just + + + align:start position:0% +where kids can get jobs and there just +isn't a lot of opportunity for that here + + align:start position:0% +isn't a lot of opportunity for that here + + + align:start position:0% +isn't a lot of opportunity for that here +um so I don't know if the community + + align:start position:0% +um so I don't know if the community + + + align:start position:0% +um so I don't know if the community +owned route is the best way to get to + + align:start position:0% +owned route is the best way to get to + + + align:start position:0% +owned route is the best way to get to +that um will that mean more jobs Less + + align:start position:0% + + + + align:start position:0% + +jobs I don't need an option the city's + + align:start position:0% +jobs I don't need an option the city's + + + align:start position:0% +jobs I don't need an option the city's +going to build a police station police + + align:start position:0% +going to build a police station police + + + align:start position:0% +going to build a police station police +station gets built alerson is going to + + align:start position:0% +station gets built alerson is going to + + + align:start position:0% +station gets built alerson is going to +come here going to have a grocery store + + align:start position:0% +come here going to have a grocery store + + + align:start position:0% +come here going to have a grocery store +that's right here and now that's on the + + align:start position:0% +that's right here and now that's on the + + + align:start position:0% +that's right here and now that's on the +table I don't + + align:start position:0% +table I don't + + + align:start position:0% +table I don't +know what you're talking about options + + align:start position:0% +know what you're talking about options + + + align:start position:0% +know what you're talking about options +because this community is not organized + + align:start position:0% +because this community is not organized + + + align:start position:0% +because this community is not organized +right now well for some option by the + + align:start position:0% +right now well for some option by the + + + align:start position:0% +right now well for some option by the +time we're done talking you know I don't + + align:start position:0% +time we're done talking you know I don't + + + align:start position:0% +time we're done talking you know I don't +have too many much more years left here + + align:start position:0% +have too many much more years left here + + + align:start position:0% +have too many much more years left here +you know and I just want to buy + + align:start position:0% +you know and I just want to buy + + + align:start position:0% +you know and I just want to buy +something before I'm + + align:start position:0% +something before I'm + + + align:start position:0% +something before I'm +gone I don't know what you're saying the + + align:start position:0% +gone I don't know what you're saying the + + + align:start position:0% +gone I don't know what you're saying the +community is not organized we got over + + align:start position:0% +community is not organized we got over + + + align:start position:0% +community is not organized we got over +200 people coming out for these planning + + align:start position:0% +200 people coming out for these planning + + + align:start position:0% +200 people coming out for these planning +meetings I think we got the numbers we + + align:start position:0% +meetings I think we got the numbers we + + + align:start position:0% +meetings I think we got the numbers we +got the people we are organized contrary + + align:start position:0% +got the people we are organized contrary + + + align:start position:0% +got the people we are organized contrary +to Sir Thompson's beliefs + + align:start position:0% +to Sir Thompson's beliefs + + + align:start position:0% +to Sir Thompson's beliefs +but we we need to see something happen + + align:start position:0% +but we we need to see something happen + + + align:start position:0% +but we we need to see something happen +and I agree with you on that um so we + + align:start position:0% +and I agree with you on that um so we + + + align:start position:0% +and I agree with you on that um so we +got the numbers we got people they're + + align:start position:0% +got the numbers we got people they're + + + align:start position:0% +got the numbers we got people they're +here at the table but I think we don't + + align:start position:0% +here at the table but I think we don't + + + align:start position:0% +here at the table but I think we don't +know how to get from here to here we + + align:start position:0% +know how to get from here to here we + + + align:start position:0% +know how to get from here to here we +know the city's putting up money we know + + align:start position:0% +know the city's putting up money we know + + + align:start position:0% +know the city's putting up money we know +safety is an issue in our community but + + align:start position:0% +safety is an issue in our community but + + + align:start position:0% +safety is an issue in our community but +we we want to know when we're going to + + align:start position:0% +we we want to know when we're going to + + + align:start position:0% +we we want to know when we're going to +wake up and see a grocery store on the + + align:start position:0% + + + + align:start position:0% + +corner and whatever process you have + + align:start position:0% +corner and whatever process you have + + + align:start position:0% +corner and whatever process you have +that's going to lead us to that point + + align:start position:0% +that's going to lead us to that point + + + align:start position:0% +that's going to lead us to that point +you know + + align:start position:0% +you know + + + align:start position:0% +you know +quicker I'm I'm going to get behind that + + align:start position:0% +quicker I'm I'm going to get behind that + + + align:start position:0% +quicker I'm I'm going to get behind that +now we're going to jump forward 6 + + align:start position:0% +now we're going to jump forward 6 + + + align:start position:0% +now we're going to jump forward 6 +months would you like to have we'll keep + + align:start position:0% +months would you like to have we'll keep + + + align:start position:0% +months would you like to have we'll keep +you in your same Rong + + align:start position:0% +you in your same Rong + + + align:start position:0% +you in your same Rong +yeah okay + + align:start position:0% + + + + align:start position:0% + +wait sorry would you pass that to the + + align:start position:0% +wait sorry would you pass that to the + + + align:start position:0% +wait sorry would you pass that to the +grad Student + + align:start position:0% + + + + align:start position:0% + +please that student Community the you're + + align:start position:0% +please that student Community the you're + + + align:start position:0% +please that student Community the you're +doing such a great job we have to have + + align:start position:0% +doing such a great job we have to have + + + align:start position:0% +doing such a great job we have to have +you continue in that roll and the + + align:start position:0% +you continue in that roll and the + + + align:start position:0% +you continue in that roll and the +chair and Community a + + align:start position:0% + + + + align:start position:0% + +so it's 6 months + + align:start position:0% +so it's 6 months + + + align:start position:0% +so it's 6 months +later and not a lot more has + + align:start position:0% + + + + align:start position:0% + +happened still a got + + align:start position:0% +happened still a got + + + align:start position:0% +happened still a got +no I came + + align:start position:0% +no I came + + + align:start position:0% +no I came +[Laughter] + + align:start position:0% + + + + align:start position:0% + +yet okay + + align:start position:0% + + + + align:start position:0% + +sure + + align:start position:0% +sure + + + align:start position:0% +sure +um so having completed all the + + align:start position:0% +um so having completed all the + + + align:start position:0% +um so having completed all the +feasibility study in the market research + + align:start position:0% +feasibility study in the market research + + + align:start position:0% +feasibility study in the market research +we are actually able to get this um + + align:start position:0% +we are actually able to get this um + + + align:start position:0% +we are actually able to get this um +grocery store up and running um and we + + align:start position:0% +grocery store up and running um and we + + + align:start position:0% +grocery store up and running um and we +need to get what is it + + align:start position:0% +need to get what is it + + + align:start position:0% +need to get what is it +um sorry um so but in order to according + + align:start position:0% +um sorry um so but in order to according + + + align:start position:0% +um sorry um so but in order to according +to the business plan we're going to need + + align:start position:0% +to the business plan we're going to need + + + align:start position:0% +to the business plan we're going to need +to get 500 members um to join each for + + align:start position:0% +to get 500 members um to join each for + + + align:start position:0% +to get 500 members um to join each for +$25 and so we're here now to plan the + + align:start position:0% +$25 and so we're here now to plan the + + + align:start position:0% +$25 and so we're here now to plan the +membership Drive are we going to get 500 + + align:start position:0% +membership Drive are we going to get 500 + + + align:start position:0% +membership Drive are we going to get 500 +people um to sign on for this we've gone + + align:start position:0% +people um to sign on for this we've gone + + + align:start position:0% +people um to sign on for this we've gone +door too already we know the people are + + align:start position:0% +door too already we know the people are + + + align:start position:0% +door too already we know the people are +interested but we've got to get the Buy + + align:start position:0% +interested but we've got to get the Buy + + + align:start position:0% +interested but we've got to get the Buy +in now so um oh and the other the other + + align:start position:0% +in now so um oh and the other the other + + + align:start position:0% +in now so um oh and the other the other +thing that happened in the six months is + + align:start position:0% +thing that happened in the six months is + + + align:start position:0% +thing that happened in the six months is +the business planning happened and the + + align:start position:0% +the business planning happened and the + + + align:start position:0% +the business planning happened and the +group did vote to adopt the business + + align:start position:0% +group did vote to adopt the business + + + align:start position:0% +group did vote to adopt the business +plan and and build the store despite the + + align:start position:0% +plan and and build the store despite the + + + align:start position:0% +plan and and build the store despite the +Cooperative store despite some um + + align:start position:0% +Cooperative store despite some um + + + align:start position:0% +Cooperative store despite some um +minority uh opposition + + align:start position:0% + + + + align:start position:0% + +yes so what are you talking about now + + align:start position:0% +yes so what are you talking about now + + + align:start position:0% +yes so what are you talking about now +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +honey I read my + + align:start position:0% + + + + align:start position:0% + +card + + align:start position:0% +card + + + align:start position:0% +card +um well according to the to the market + + align:start position:0% +um well according to the to the market + + + align:start position:0% +um well according to the to the market +research and the feasibility study this + + align:start position:0% +research and the feasibility study this + + + align:start position:0% +research and the feasibility study this +this store can work the store can hold + + align:start position:0% +this store can work the store can hold + + + align:start position:0% +this store can work the store can hold +water in the city and it resonates with + + align:start position:0% +water in the city and it resonates with + + + align:start position:0% +water in the city and it resonates with +community members here um people are + + align:start position:0% +community members here um people are + + + align:start position:0% +community members here um people are +really interested in doing it in order + + align:start position:0% +really interested in doing it in order + + + align:start position:0% +really interested in doing it in order +to make it work that we're going to need + + align:start position:0% +to make it work that we're going to need + + + align:start position:0% +to make it work that we're going to need +500 people to buy in um 25 bucks a piece + + align:start position:0% +500 people to buy in um 25 bucks a piece + + + align:start position:0% +500 people to buy in um 25 bucks a piece +um um so what we need to do now is + + align:start position:0% +um um so what we need to do now is + + + align:start position:0% +um um so what we need to do now is +strategize the membership drive to get + + align:start position:0% +strategize the membership drive to get + + + align:start position:0% +strategize the membership drive to get +people to buy into it + + align:start position:0% + + + + align:start position:0% + +um yes um um yeah we've been uh again + + align:start position:0% +um yes um um yeah we've been uh again + + + align:start position:0% +um yes um um yeah we've been uh again +doing our door to door campaign to try + + align:start position:0% +doing our door to door campaign to try + + + align:start position:0% +doing our door to door campaign to try +to get members to sign up and um you + + align:start position:0% +to get members to sign up and um you + + + align:start position:0% +to get members to sign up and um you +know um when we uh first first begin to + + align:start position:0% +know um when we uh first first begin to + + + align:start position:0% +know um when we uh first first begin to +meet 6 months ago you mentioned that + + align:start position:0% +meet 6 months ago you mentioned that + + + align:start position:0% +meet 6 months ago you mentioned that +that you that that you had that we had + + align:start position:0% +that you that that you had that we had + + + align:start position:0% +that you that that you had that we had +about 200 250 people coming out to these + + align:start position:0% +about 200 250 people coming out to these + + + align:start position:0% +about 200 250 people coming out to these +meetings and that's about half of what + + align:start position:0% +meetings and that's about half of what + + + align:start position:0% +meetings and that's about half of what +we need um just to uh you know get get + + align:start position:0% +we need um just to uh you know get get + + + align:start position:0% +we need um just to uh you know get get +signed up we had 200 people coming to + + align:start position:0% +signed up we had 200 people coming to + + + align:start position:0% +signed up we had 200 people coming to +these meetings but people are sick and + + align:start position:0% +these meetings but people are sick and + + + align:start position:0% +these meetings but people are sick and +tired of come into these meetings and + + align:start position:0% +tired of come into these meetings and + + + align:start position:0% +tired of come into these meetings and +nothing gets done and we just argue + + align:start position:0% +nothing gets done and we just argue + + + align:start position:0% +nothing gets done and we just argue +about this and that and we don't you + + align:start position:0% +about this and that and we don't you + + + align:start position:0% +about this and that and we don't you +know we don't have we don't have two 200 + + align:start position:0% +know we don't have we don't have two 200 + + + align:start position:0% +know we don't have we don't have two 200 +we got 200 people that want to see a + + align:start position:0% +we got 200 people that want to see a + + + align:start position:0% +we got 200 people that want to see a +grocery store we don't have 200 people + + align:start position:0% +grocery store we don't have 200 people + + + align:start position:0% +grocery store we don't have 200 people +that want to come to meetings all the + + align:start position:0% +that want to come to meetings all the + + + align:start position:0% +that want to come to meetings all the +time + + align:start position:0% +time + + + align:start position:0% +time +well I hear you and um I think you know + + align:start position:0% +well I hear you and um I think you know + + + align:start position:0% +well I hear you and um I think you know +but right now you know we're we're at + + align:start position:0% +but right now you know we're we're at + + + align:start position:0% +but right now you know we're we're at +the point where you know once we get the + + align:start position:0% +the point where you know once we get the + + + align:start position:0% +the point where you know once we get the +um initial investment we can actually + + align:start position:0% +um initial investment we can actually + + + align:start position:0% +um initial investment we can actually +begin begin building I think you know I + + align:start position:0% +begin begin building I think you know I + + + align:start position:0% +begin begin building I think you know I +think that the community will begin to + + align:start position:0% +think that the community will begin to + + + align:start position:0% +think that the community will begin to +see results you know very very + + align:start position:0% +see results you know very very + + + align:start position:0% +see results you know very very +soon well you know I + + align:start position:0% +soon well you know I + + + align:start position:0% +soon well you know I +think school's almost over and it's time + + align:start position:0% +think school's almost over and it's time + + + align:start position:0% +think school's almost over and it's time +for you all to go home and get your a + + align:start position:0% +for you all to go home and get your a + + + align:start position:0% +for you all to go home and get your a +you got a A for talking but now it's + + align:start position:0% +you got a A for talking but now it's + + + align:start position:0% +you got a A for talking but now it's +money time talking about people's money + + align:start position:0% +money time talking about people's money + + + align:start position:0% +money time talking about people's money +putting on the table and the city has + + align:start position:0% +putting on the table and the city has + + + align:start position:0% +putting on the table and the city has +been here they're ready to build this + + align:start position:0% +been here they're ready to build this + + + align:start position:0% +been here they're ready to build this +police station they like they want to do + + align:start position:0% +police station they like they want to do + + + align:start position:0% +police station they like they want to do +it here we can have alberon come in here + + align:start position:0% +it here we can have alberon come in here + + + align:start position:0% +it here we can have alberon come in here +we've been sitting here for 6 months now + + align:start position:0% +we've been sitting here for 6 months now + + + align:start position:0% +we've been sitting here for 6 months now +and it's time for this foolishness to + + align:start position:0% +and it's time for this foolishness to + + + align:start position:0% +and it's time for this foolishness to +stop and we just need to move on let + + align:start position:0% +stop and we just need to move on let + + + align:start position:0% +stop and we just need to move on let +them build this here police station get + + align:start position:0% +them build this here police station get + + + align:start position:0% +them build this here police station get +some get some police here get some + + align:start position:0% +some get some police here get some + + + align:start position:0% +some get some police here get some +supermarkets so the old folks can shop + + align:start position:0% +supermarkets so the old folks can shop + + + align:start position:0% +supermarkets so the old folks can shop +and we can stop all this nonsense going + + align:start position:0% +and we can stop all this nonsense going + + + align:start position:0% +and we can stop all this nonsense going +on here and you don't have just cuz you + + align:start position:0% +on here and you don't have just cuz you + + + align:start position:0% +on here and you don't have just cuz you +had a few people few people from here + + align:start position:0% +had a few people few people from here + + + align:start position:0% +had a few people few people from here +voting on this thing the more people out + + align:start position:0% +voting on this thing the more people out + + + align:start position:0% +voting on this thing the more people out +in that Community they didn't vote on + + align:start position:0% +in that Community they didn't vote on + + + align:start position:0% +in that Community they didn't vote on +anything and these people voting here + + align:start position:0% +anything and these people voting here + + + align:start position:0% +anything and these people voting here +doesn't mean a thing cuz you haven't + + align:start position:0% +doesn't mean a thing cuz you haven't + + + align:start position:0% +doesn't mean a thing cuz you haven't +collected that money and you're not + + align:start position:0% +collected that money and you're not + + + align:start position:0% +collected that money and you're not +going to collect that + + align:start position:0% +going to collect that + + + align:start position:0% +going to collect that +money that's all I have to + + align:start position:0% + + + + align:start position:0% + +say just going + + align:start position:0% +say just going + + + align:start position:0% +say just going +nowhere fast I'm just hoping that we can + + align:start position:0% +nowhere fast I'm just hoping that we can + + + align:start position:0% +nowhere fast I'm just hoping that we can +come to some sort of organization + + align:start position:0% +come to some sort of organization + + + align:start position:0% +come to some sort of organization +understanding what these 200 people are + + align:start position:0% +understanding what these 200 people are + + + align:start position:0% +understanding what these 200 people are +still coming here for like of course we + + align:start position:0% +still coming here for like of course we + + + align:start position:0% +still coming here for like of course we +all want to see a grocery store but it + + align:start position:0% +all want to see a grocery store but it + + + align:start position:0% +all want to see a grocery store but it +might be really hard for them there's + + align:start position:0% +might be really hard for them there's + + + align:start position:0% +might be really hard for them there's +people coming here because TVs on + + align:start position:0% +people coming here because TVs on + + + align:start position:0% +people coming here because TVs on +runs that's why they come in here well I + + align:start position:0% +runs that's why they come in here well I + + + align:start position:0% +runs that's why they come in here well I +think I mean I think there should be + + align:start position:0% +think I mean I think there should be + + + align:start position:0% +think I mean I think there should be +some sort of collective voice I mean + + align:start position:0% +some sort of collective voice I mean + + + align:start position:0% +some sort of collective voice I mean +can't we can't we figure out a way to + + align:start position:0% +can't we can't we figure out a way to + + + align:start position:0% +can't we can't we figure out a way to +have a board or something like a board + + align:start position:0% +have a board or something like a board + + + align:start position:0% +have a board or something like a board +of directors to sort of look guide every + + align:start position:0% +of directors to sort of look guide every + + + align:start position:0% +of directors to sort of look guide every +CDC in this neighborhood has a board of + + align:start position:0% +CDC in this neighborhood has a board of + + + align:start position:0% +CDC in this neighborhood has a board of +directors they haven't gotten nothing + + align:start position:0% +directors they haven't gotten nothing + + + align:start position:0% +directors they haven't gotten nothing +done it all it does is waste people's + + align:start position:0% +done it all it does is waste people's + + + align:start position:0% +done it all it does is waste people's +time they spend all this time trying to + + align:start position:0% +time they spend all this time trying to + + + align:start position:0% +time they spend all this time trying to +deal with people's personalities and + + align:start position:0% +deal with people's personalities and + + + align:start position:0% +deal with people's personalities and +this person this person got they know + + align:start position:0% +this person this person got they know + + + align:start position:0% +this person this person got they know +this person they're they're on the board + + align:start position:0% +this person they're they're on the board + + + align:start position:0% +this person they're they're on the board +of directors I am not wasting my time + + align:start position:0% +of directors I am not wasting my time + + + align:start position:0% +of directors I am not wasting my time +with a sense of board of directors we + + align:start position:0% +with a sense of board of directors we + + + align:start position:0% +with a sense of board of directors we +just need to make a decision we just + + align:start position:0% +just need to make a decision we just + + + align:start position:0% +just need to make a decision we just +need to move forward I think people + + align:start position:0% +need to move forward I think people + + + align:start position:0% +need to move forward I think people +could come out and arguing at these + + align:start position:0% +could come out and arguing at these + + + align:start position:0% +could come out and arguing at these +meetings it's not getting nothing done + + align:start position:0% +meetings it's not getting nothing done + + + align:start position:0% +meetings it's not getting nothing done +right I um completely agree because we + + align:start position:0% +right I um completely agree because we + + + align:start position:0% +right I um completely agree because we +we came to agreement that we wanted to + + align:start position:0% +we came to agreement that we wanted to + + + align:start position:0% +we came to agreement that we wanted to +go ahead and try to get the store up and + + align:start position:0% +go ahead and try to get the store up and + + + align:start position:0% +go ahead and try to get the store up and +running you know we did the feasibility + + align:start position:0% +running you know we did the feasibility + + + align:start position:0% +running you know we did the feasibility +study came back very positive um you + + align:start position:0% +study came back very positive um you + + + align:start position:0% +study came back very positive um you +know we looked at the numbers of people + + align:start position:0% +know we looked at the numbers of people + + + align:start position:0% +know we looked at the numbers of people +who would be hired um and being that it + + align:start position:0% +who would be hired um and being that it + + + align:start position:0% +who would be hired um and being that it +it is a community owned store being that + + align:start position:0% +it is a community owned store being that + + + align:start position:0% +it is a community owned store being that +you know 80% of the profits are not + + align:start position:0% +you know 80% of the profits are not + + + align:start position:0% +you know 80% of the profits are not +going to go to alberon Central someplace + + align:start position:0% +going to go to alberon Central someplace + + + align:start position:0% +going to go to alberon Central someplace +wherever that is you know that but that + + align:start position:0% +wherever that is you know that but that + + + align:start position:0% +wherever that is you know that but that +all the profits all the revenue from the + + align:start position:0% +all the profits all the revenue from the + + + align:start position:0% +all the profits all the revenue from the +stay within this community you know we + + align:start position:0% +stay within this community you know we + + + align:start position:0% +stay within this community you know we +can you know we we also found that we + + align:start position:0% +can you know we we also found that we + + + align:start position:0% +can you know we we also found that we +can pay you know um a 15 20% higher uh + + align:start position:0% +can pay you know um a 15 20% higher uh + + + align:start position:0% +can pay you know um a 15 20% higher uh +average salary to the workers in the + + align:start position:0% +average salary to the workers in the + + + align:start position:0% +average salary to the workers in the +store that alberon would pay uh not to + + align:start position:0% +store that alberon would pay uh not to + + + align:start position:0% +store that alberon would pay uh not to +mention you know the turnover rate at + + align:start position:0% +mention you know the turnover rate at + + + align:start position:0% +mention you know the turnover rate at +these alberon supermarkets they bring + + align:start position:0% +these alberon supermarkets they bring + + + align:start position:0% +these alberon supermarkets they bring +these little high school kids in there + + align:start position:0% +these little high school kids in there + + + align:start position:0% +these little high school kids in there +working to death when they the front out + + align:start position:0% +working to death when they the front out + + + align:start position:0% +working to death when they the front out +of school and they fire them and they + + align:start position:0% +of school and they fire them and they + + + align:start position:0% +of school and they fire them and they +bring someone else in because they get a + + align:start position:0% +bring someone else in because they get a + + + align:start position:0% +bring someone else in because they get a +tax uh a tax write off to hire kids from + + align:start position:0% +tax uh a tax write off to hire kids from + + + align:start position:0% +tax uh a tax write off to hire kids from +these poor Disturbed communities you + + align:start position:0% +these poor Disturbed communities you + + + align:start position:0% +these poor Disturbed communities you +know so that that's how that's how that + + align:start position:0% +know so that that's how that's how that + + + align:start position:0% +know so that that's how that's how that +whole thing works so but you know we're + + align:start position:0% +whole thing works so but you know we're + + + align:start position:0% +whole thing works so but you know we're +but we're ready to go um you know um + + align:start position:0% +but we're ready to go um you know um + + + align:start position:0% +but we're ready to go um you know um +right now what we need is just this + + align:start position:0% +right now what we need is just this + + + align:start position:0% +right now what we need is just this +initial investment money to get the + + align:start position:0% +initial investment money to get the + + + align:start position:0% +initial investment money to get the +thing in the ground we have the + + align:start position:0% +thing in the ground we have the + + + align:start position:0% +thing in the ground we have the +developer he's ready you know they're + + align:start position:0% +developer he's ready you know they're + + + align:start position:0% +developer he's ready you know they're +ready to sign the contract it's a local + + align:start position:0% +ready to sign the contract it's a local + + + align:start position:0% +ready to sign the contract it's a local +business you know just ready to get the + + align:start position:0% +business you know just ready to get the + + + align:start position:0% +business you know just ready to get the +store buil to do the renovations you + + align:start position:0% +store buil to do the renovations you + + + align:start position:0% +store buil to do the renovations you +know the structure of the building is + + align:start position:0% +know the structure of the building is + + + align:start position:0% +know the structure of the building is +actually sound we just need to do the + + align:start position:0% +actually sound we just need to do the + + + align:start position:0% +actually sound we just need to do the +internal Renovations you know you know + + align:start position:0% +internal Renovations you know you know + + + align:start position:0% +internal Renovations you know you know +get you know business plan together the + + align:start position:0% +get you know business plan together the + + + align:start position:0% +get you know business plan together the +name of the store even you know and just + + align:start position:0% +name of the store even you know and just + + + align:start position:0% +name of the store even you know and just +get that together and we are ready to go + + align:start position:0% +get that together and we are ready to go + + + align:start position:0% +get that together and we are ready to go +uh you know we've talked to a number of + + align:start position:0% +uh you know we've talked to a number of + + + align:start position:0% +uh you know we've talked to a number of +farmers who are ready to contract with + + align:start position:0% +farmers who are ready to contract with + + + align:start position:0% +farmers who are ready to contract with +us to to supply the grocery store fresh + + align:start position:0% +us to to supply the grocery store fresh + + + align:start position:0% +us to to supply the grocery store fresh +produce you know we've talked to + + align:start position:0% +produce you know we've talked to + + + align:start position:0% +produce you know we've talked to +different you know you know we we've + + align:start position:0% +different you know you know we we've + + + align:start position:0% +different you know you know we we've +done Market Research in the community to + + align:start position:0% +done Market Research in the community to + + + align:start position:0% +done Market Research in the community to +find out what types of processed Goods + + align:start position:0% +find out what types of processed Goods + + + align:start position:0% +find out what types of processed Goods +people you know would like to have in + + align:start position:0% +people you know would like to have in + + + align:start position:0% +people you know would like to have in +the store you know from macaroni and + + align:start position:0% +the store you know from macaroni and + + + align:start position:0% +the store you know from macaroni and +cheese you know those types of things + + align:start position:0% +cheese you know those types of things + + + align:start position:0% +cheese you know those types of things +you know soft drinks you know qued water + + align:start position:0% +you know soft drinks you know qued water + + + align:start position:0% +you know soft drinks you know qued water +these types of things we're ready to go + + align:start position:0% +these types of things we're ready to go + + + align:start position:0% +these types of things we're ready to go +excuse me we who excuse me who's we um + + align:start position:0% +excuse me we who excuse me who's we um + + + align:start position:0% +excuse me we who excuse me who's we um +our who's we see see you're a student + + align:start position:0% +our who's we see see you're a student + + + align:start position:0% +our who's we see see you're a student +you're not you are going you ready to go + + align:start position:0% +you're not you are going you ready to go + + + align:start position:0% +you're not you are going you ready to go +cuz semester's over you going what now + + align:start position:0% +cuz semester's over you going what now + + + align:start position:0% +cuz semester's over you going what now +this this is this is what I'm saying + + align:start position:0% +this this is this is what I'm saying + + + align:start position:0% +this this is this is what I'm saying +right here you're ready to go you can go + + align:start position:0% +right here you're ready to go you can go + + + align:start position:0% +right here you're ready to go you can go +on you did we're we're not going + + align:start position:0% +on you did we're we're not going + + + align:start position:0% +on you did we're we're not going +anywhere and and if I had a dollar for + + align:start position:0% +anywhere and and if I had a dollar for + + + align:start position:0% +anywhere and and if I had a dollar for +all this foolish every hour this + + align:start position:0% +all this foolish every hour this + + + align:start position:0% +all this foolish every hour this +foolishness you've been talking in here + + align:start position:0% +foolishness you've been talking in here + + + align:start position:0% +foolishness you've been talking in here +I'd be able to build my own supermarket + + align:start position:0% +I'd be able to build my own supermarket + + + align:start position:0% +I'd be able to build my own supermarket +well I wonder when you're going to go + + align:start position:0% +well I wonder when you're going to go + + + align:start position:0% +well I wonder when you're going to go +ask that University for the investment + + align:start position:0% +ask that University for the investment + + + align:start position:0% +ask that University for the investment +money they always send in students down + + align:start position:0% +money they always send in students down + + + align:start position:0% +money they always send in students down +here to do feasibility studies and it's + + align:start position:0% +here to do feasibility studies and it's + + + align:start position:0% +here to do feasibility studies and it's +such a small amount of money why don't + + align:start position:0% +such a small amount of money why don't + + + align:start position:0% +such a small amount of money why don't +you go back to the university and see if + + align:start position:0% +you go back to the university and see if + + + align:start position:0% +you go back to the university and see if +they'll I'm + + align:start position:0% + + + + align:start position:0% + +not don't get smart with me I well you + + align:start position:0% +not don't get smart with me I well you + + + align:start position:0% +not don't get smart with me I well you +said something really interesting + + align:start position:0% +said something really interesting + + + align:start position:0% +said something really interesting +earlier about all the 200 people who + + align:start position:0% +earlier about all the 200 people who + + + align:start position:0% +earlier about all the 200 people who +didn't vote in this and those are the + + align:start position:0% +didn't vote in this and those are the + + + align:start position:0% +didn't vote in this and those are the +people who I think we need to go talk to + + align:start position:0% +people who I think we need to go talk to + + + align:start position:0% +people who I think we need to go talk to +about whether they'd be interested in + + align:start position:0% +about whether they'd be interested in + + + align:start position:0% +about whether they'd be interested in +getting involved in this and maybe + + align:start position:0% +getting involved in this and maybe + + + align:start position:0% +getting involved in this and maybe +buying in because I think there is a + + align:start position:0% +buying in because I think there is a + + + align:start position:0% +buying in because I think there is a +large there are a lot of people who are + + align:start position:0% +large there are a lot of people who are + + + align:start position:0% +large there are a lot of people who are +involved in this who aren't going + + align:start position:0% +involved in this who aren't going + + + align:start position:0% +involved in this who aren't going +anywhere but would maybe be interested + + align:start position:0% +anywhere but would maybe be interested + + + align:start position:0% +anywhere but would maybe be interested +in this and so we still need to go talk + + align:start position:0% +in this and so we still need to go talk + + + align:start position:0% +in this and so we still need to go talk +to them and so once you start talking to + + align:start position:0% +to them and so once you start talking to + + + align:start position:0% +to them and so once you start talking to +all those people we're never going to + + align:start position:0% +all those people we're never going to + + + align:start position:0% +all those people we're never going to +get anything done here you want to pull + + align:start position:0% +get anything done here you want to pull + + + align:start position:0% +get anything done here you want to pull +200 more people in who aren't even + + align:start position:0% +200 more people in who aren't even + + + align:start position:0% +200 more people in who aren't even +interested in this and we can't even get + + align:start position:0% +interested in this and we can't even get + + + align:start position:0% +interested in this and we can't even get +anything done with 20 people here but + + align:start position:0% +anything done with 20 people here but + + + align:start position:0% +anything done with 20 people here but +that's why if we + + align:start position:0% + + + + align:start position:0% + +had give yourself a round of applause + + align:start position:0% +had give yourself a round of applause + + + align:start position:0% +had give yourself a round of applause +that was magnificent + + align:start position:0% +that was magnificent + + + align:start position:0% +that was magnificent +um this store did not get built it had + + align:start position:0% +um this store did not get built it had + + + align:start position:0% +um this store did not get built it had +the money it had the business plan it + + align:start position:0% +the money it had the business plan it + + + align:start position:0% +the money it had the business plan it +had most the great majority of the + + align:start position:0% +had most the great majority of the + + + align:start position:0% +had most the great majority of the +people in the community that wanted to + + align:start position:0% +people in the community that wanted to + + + align:start position:0% +people in the community that wanted to +do it it didn't get + + align:start position:0% +do it it didn't get + + + align:start position:0% +do it it didn't get +built um but what was it like to be to + + align:start position:0% +built um but what was it like to be to + + + align:start position:0% +built um but what was it like to be to +be in this + + align:start position:0% + + + + align:start position:0% + +um very stressful very + + align:start position:0% +um very stressful very + + + align:start position:0% +um very stressful very +stressful + + align:start position:0% +stressful + + + align:start position:0% +stressful +like hold it down Bill's the only one + + align:start position:0% +like hold it down Bill's the only one + + + align:start position:0% +like hold it down Bill's the only one +who had a good time + + align:start position:0% + + + + align:start position:0% + +yeah I'm always in the other seat + + align:start position:0% + + + + align:start position:0% + +you yeah it's pretty relaxing just to + + align:start position:0% +you yeah it's pretty relaxing just to + + + align:start position:0% +you yeah it's pretty relaxing just to +come in and just get to say no every + + align:start position:0% +come in and just get to say no every + + + align:start position:0% +come in and just get to say no every +single time you know what's going to + + align:start position:0% +single time you know what's going to + + + align:start position:0% +single time you know what's going to +happen like I said as as of of this + + align:start position:0% +happen like I said as as of of this + + + align:start position:0% +happen like I said as as of of this +point of Wan you know of having clear + + align:start position:0% +point of Wan you know of having clear + + + align:start position:0% +point of Wan you know of having clear +roles and you know and and and U and + + align:start position:0% +roles and you know and and and U and + + + align:start position:0% +roles and you know and and and U and +being able to uh instead of uh cuz that + + align:start position:0% +being able to uh instead of uh cuz that + + + align:start position:0% +being able to uh instead of uh cuz that +was one of the things that happened + + align:start position:0% +was one of the things that happened + + + align:start position:0% +was one of the things that happened +where the the grad students became we + + align:start position:0% +where the the grad students became we + + + align:start position:0% +where the the grad students became we +were going to be the Defenders of the + + align:start position:0% +were going to be the Defenders of the + + + align:start position:0% +were going to be the Defenders of the +cooperatives with two or three other + + align:start position:0% +cooperatives with two or three other + + + align:start position:0% +cooperatives with two or three other +community people and then you had the + + align:start position:0% +community people and then you had the + + + align:start position:0% +community people and then you had the +folks that were opposed instead of like + + align:start position:0% +folks that were opposed instead of like + + + align:start position:0% +folks that were opposed instead of like +let's you know these are all questions + + align:start position:0% +let's you know these are all questions + + + align:start position:0% +let's you know these are all questions +that that should be U answered in the + + align:start position:0% +that that should be U answered in the + + + align:start position:0% +that that should be U answered in the +strategic planning you know we have some + + align:start position:0% +strategic planning you know we have some + + + align:start position:0% +strategic planning you know we have some +ideas toward it um you know but but uh + + align:start position:0% +ideas toward it um you know but but uh + + + align:start position:0% +ideas toward it um you know but but uh +uh as well as many other members in this + + align:start position:0% +uh as well as many other members in this + + + align:start position:0% +uh as well as many other members in this +room but we're going to all sit help you + + align:start position:0% +room but we're going to all sit help you + + + align:start position:0% +room but we're going to all sit help you +sit down together and uh and come up + + align:start position:0% +sit down together and uh and come up + + + align:start position:0% +sit down together and uh and come up +with a plan that you will implement that + + align:start position:0% +with a plan that you will implement that + + + align:start position:0% +with a plan that you will implement that +you will that will be your plan this is + + align:start position:0% +you will that will be your plan this is + + + align:start position:0% +you will that will be your plan this is +not our I mean our job is to you know + + align:start position:0% +not our I mean our job is to you know + + + align:start position:0% +not our I mean our job is to you know +we're we're just providing you Tech + + align:start position:0% +we're we're just providing you Tech + + + align:start position:0% +we're we're just providing you Tech +assist but you know being clear that + + align:start position:0% +assist but you know being clear that + + + align:start position:0% +assist but you know being clear that +that this is um the our Market is that + + align:start position:0% +that this is um the our Market is that + + + align:start position:0% +that this is um the our Market is that +our is yall you know and we're just + + align:start position:0% +our is yall you know and we're just + + + align:start position:0% +our is yall you know and we're just +assisting you that you know and getting + + align:start position:0% +assisting you that you know and getting + + + align:start position:0% +assisting you that you know and getting +that process and having a clear + + align:start position:0% +that process and having a clear + + + align:start position:0% +that process and having a clear +understanding on that you know and then + + align:start position:0% +understanding on that you know and then + + + align:start position:0% +understanding on that you know and then +using good negotiating skills so so that + + align:start position:0% +using good negotiating skills so so that + + + align:start position:0% +using good negotiating skills so so that +um um because on some of those uh things + + align:start position:0% +um um because on some of those uh things + + + align:start position:0% +um um because on some of those uh things +that um for example like the issues of + + align:start position:0% +that um for example like the issues of + + + align:start position:0% +that um for example like the issues of +security that + + align:start position:0% +security that + + + align:start position:0% +security that +uh you know that that uh you know there + + align:start position:0% +uh you know that that uh you know there + + + align:start position:0% +uh you know that that uh you know there +were important kernels of of uh of U of + + align:start position:0% +were important kernels of of uh of U of + + + align:start position:0% +were important kernels of of uh of U of +things that needed to be dealt with you + + align:start position:0% +things that needed to be dealt with you + + + align:start position:0% +things that needed to be dealt with you +know so you know are not dismissing them + + align:start position:0% +know so you know are not dismissing them + + + align:start position:0% +know so you know are not dismissing them +even though they may have been colored + + align:start position:0% +even though they may have been colored + + + align:start position:0% +even though they may have been colored +with a you know a more conservative + + align:start position:0% +with a you know a more conservative + + + align:start position:0% +with a you know a more conservative +approach than we may have wanted it say + + align:start position:0% +approach than we may have wanted it say + + + align:start position:0% +approach than we may have wanted it say +but figuring out okay how can we answer + + align:start position:0% +but figuring out okay how can we answer + + + align:start position:0% +but figuring out okay how can we answer +those questions in a in a strategic + + align:start position:0% +those questions in a in a strategic + + + align:start position:0% +those questions in a in a strategic +planning process that you will control + + align:start position:0% +planning process that you will control + + + align:start position:0% +planning process that you will control +and and and um and and you like I said + + align:start position:0% +and and and um and and you like I said + + + align:start position:0% +and and and um and and you like I said +and and doing that and then you know + + align:start position:0% +and and doing that and then you know + + + align:start position:0% +and and doing that and then you know +then bringing making sure that new + + align:start position:0% +then bringing making sure that new + + + align:start position:0% +then bringing making sure that new +people are being brought to the table + + align:start position:0% +people are being brought to the table + + + align:start position:0% +people are being brought to the table +that are um making sure that uh uh you + + align:start position:0% +that are um making sure that uh uh you + + + align:start position:0% +that are um making sure that uh uh you +know that you know that that this + + align:start position:0% +know that you know that that this + + + align:start position:0% +know that you know that that this +process of structure and other things + + align:start position:0% +process of structure and other things + + + align:start position:0% +process of structure and other things +are addressed you know not as a a battle + + align:start position:0% +are addressed you know not as a a battle + + + align:start position:0% +are addressed you know not as a a battle +between the grad students from out + + align:start position:0% +between the grad students from out + + + align:start position:0% +between the grad students from out +outside the community and and the + + align:start position:0% +outside the community and and the + + + align:start position:0% +outside the community and and the +community but but uh a discussion about + + align:start position:0% +community but but uh a discussion about + + + align:start position:0% +community but but uh a discussion about +what things work um U paying attention + + align:start position:0% +what things work um U paying attention + + + align:start position:0% +what things work um U paying attention +to uh replica model models um feasible + + align:start position:0% +to uh replica model models um feasible + + + align:start position:0% +to uh replica model models um feasible +models being able to say this is not + + align:start position:0% +models being able to say this is not + + + align:start position:0% +models being able to say this is not +something just read about it in the book + + align:start position:0% +something just read about it in the book + + + align:start position:0% +something just read about it in the book +but being able to you know you know uh + + align:start position:0% +but being able to you know you know uh + + + align:start position:0% +but being able to you know you know uh +may you know other folks have um like + + align:start position:0% +may you know other folks have um like + + + align:start position:0% +may you know other folks have um like +brought folks you know you know U uh you + + align:start position:0% +brought folks you know you know U uh you + + + align:start position:0% +brought folks you know you know U uh you +know Chicago and Southside they got a + + align:start position:0% +know Chicago and Southside they got a + + + align:start position:0% +know Chicago and Southside they got a +great Supermarket you know Cooperative + + align:start position:0% +great Supermarket you know Cooperative + + + align:start position:0% +great Supermarket you know Cooperative +Supermarket been around for a jillion + + align:start position:0% +Supermarket been around for a jillion + + + align:start position:0% +Supermarket been around for a jillion +years runs as good as any of the other + + align:start position:0% +years runs as good as any of the other + + + align:start position:0% +years runs as good as any of the other +chains you know so you know and in + + align:start position:0% +chains you know so you know and in + + + align:start position:0% +chains you know so you know and in +different situations we brought the + + align:start position:0% +different situations we brought the + + + align:start position:0% +different situations we brought the +those leaders in there and say look you + + align:start position:0% +those leaders in there and say look you + + + align:start position:0% +those leaders in there and say look you +know Community people and said look yeah + + align:start position:0% +know Community people and said look yeah + + + align:start position:0% +know Community people and said look yeah +we get better service than any of the + + align:start position:0% +we get better service than any of the + + + align:start position:0% +we get better service than any of the +chains and you know and it just CU it + + align:start position:0% +chains and you know and it just CU it + + + align:start position:0% +chains and you know and it just CU it +says co-op on it that doesn't mean it's + + align:start position:0% +says co-op on it that doesn't mean it's + + + align:start position:0% +says co-op on it that doesn't mean it's +you know it's some Little Hippie dippy + + align:start position:0% +you know it's some Little Hippie dippy + + + align:start position:0% +you know it's some Little Hippie dippy +in a in a in a in a in a in a dirty room + + align:start position:0% +in a in a in a in a in a in a dirty room + + + align:start position:0% +in a in a in a in a in a in a dirty room +somewhere you know so so so I mean so + + align:start position:0% +somewhere you know so so so I mean so + + + align:start position:0% +somewhere you know so so so I mean so +again I mean uh um + + align:start position:0% +again I mean uh um + + + align:start position:0% +again I mean uh um +um making sure you have some strong some + + align:start position:0% +um making sure you have some strong some + + + align:start position:0% +um making sure you have some strong some +serious Clarity on the row and um you + + align:start position:0% +serious Clarity on the row and um you + + + align:start position:0% +serious Clarity on the row and um you +know and making sure that we don't step + + align:start position:0% +know and making sure that we don't step + + + align:start position:0% +know and making sure that we don't step +beyond our our our role as as technical + + align:start position:0% +beyond our our our role as as technical + + + align:start position:0% +beyond our our our role as as technical +assistance providers and sist you know + + align:start position:0% +assistance providers and sist you know + + + align:start position:0% +assistance providers and sist you know +and that our our key job is to empower + + align:start position:0% +and that our our key job is to empower + + + align:start position:0% +and that our our key job is to empower +you to make the most the best most + + align:start position:0% +you to make the most the best most + + + align:start position:0% +you to make the most the best most +informed uh uh decision decision that + + align:start position:0% +informed uh uh decision decision that + + + align:start position:0% +informed uh uh decision decision that +you can about about your future and + + align:start position:0% +you can about about your future and + + + align:start position:0% +you can about about your future and +about your community but we set you guys + + align:start position:0% +about your community but we set you guys + + + align:start position:0% +about your community but we set you guys +up to be the advocates for the co-op so + + align:start position:0% +up to be the advocates for the co-op so + + + align:start position:0% +up to be the advocates for the co-op so +we we definitely you know we fed you + + align:start position:0% +we we definitely you know we fed you + + + align:start position:0% +we we definitely you know we fed you +that in the first card so um thoughts + + align:start position:0% +that in the first card so um thoughts + + + align:start position:0% +that in the first card so um thoughts +what was it like how did you like being + + align:start position:0% +what was it like how did you like being + + + align:start position:0% +what was it like how did you like being +in your + + align:start position:0% +in your + + + align:start position:0% +in your +role it was so uh + + align:start position:0% +role it was so uh + + + align:start position:0% +role it was so uh +familiar you know I I mean I I it's just + + align:start position:0% +familiar you know I I mean I I it's just + + + align:start position:0% +familiar you know I I mean I I it's just +so I've heard this arguments so many + + align:start position:0% +so I've heard this arguments so many + + + align:start position:0% +so I've heard this arguments so many +times you know I feel like uh + + align:start position:0% +times you know I feel like uh + + + align:start position:0% +times you know I feel like uh +I feel like + + align:start position:0% +I feel like + + + align:start position:0% +I feel like +it's a classic common thing that comes + + align:start position:0% +it's a classic common thing that comes + + + align:start position:0% +it's a classic common thing that comes +up all the time there's always somebody + + align:start position:0% +up all the time there's always somebody + + + align:start position:0% +up all the time there's always somebody +and who's going to raise all this stuff + + align:start position:0% +and who's going to raise all this stuff + + + align:start position:0% +and who's going to raise all this stuff +and you know always and how about the + + align:start position:0% +and you know always and how about the + + + align:start position:0% +and you know always and how about the +other community person how' you feel + + align:start position:0% + + + + align:start position:0% + +S I was I was kind of in between so I + + align:start position:0% +S I was I was kind of in between so I + + + align:start position:0% +S I was I was kind of in between so I +like understood where pH was coming from + + align:start position:0% +like understood where pH was coming from + + + align:start position:0% +like understood where pH was coming from +but I wanted to I was hopeful that we + + align:start position:0% +but I wanted to I was hopeful that we + + + align:start position:0% +but I wanted to I was hopeful that we +could figure out something else like an + + align:start position:0% +could figure out something else like an + + + align:start position:0% +could figure out something else like an +alternative but I I had no I had nothing + + align:start position:0% +alternative but I I had no I had nothing + + + align:start position:0% +alternative but I I had no I had nothing +else but the ability to come to + + align:start position:0% +else but the ability to come to + + + align:start position:0% +else but the ability to come to +meetings so um I couldn't say well there + + align:start position:0% +meetings so um I couldn't say well there + + + align:start position:0% +meetings so um I couldn't say well there +is this model in Chicago and and we can + + align:start position:0% +is this model in Chicago and and we can + + + align:start position:0% +is this model in Chicago and and we can +make demands on Albertson if that's + + align:start position:0% +make demands on Albertson if that's + + + align:start position:0% +make demands on Albertson if that's +really what we want or um no we do have + + align:start position:0% +really what we want or um no we do have + + + align:start position:0% +really what we want or um no we do have +the capacity to run a co-op because it + + align:start position:0% +the capacity to run a co-op because it + + + align:start position:0% +the capacity to run a co-op because it +was just so unfamiliar to me + + align:start position:0% +was just so unfamiliar to me + + + align:start position:0% +was just so unfamiliar to me +so Advocate one way or the other um + + align:start position:0% +so Advocate one way or the other um + + + align:start position:0% +so Advocate one way or the other um +besides well there's another way besides + + align:start position:0% +besides well there's another way besides + + + align:start position:0% +besides well there's another way besides +Albert s police + + align:start position:0% +Albert s police + + + align:start position:0% +Albert s police +station some more + + align:start position:0% +station some more + + + align:start position:0% +station some more +information would have been helpful to + + align:start position:0% +information would have been helpful to + + + align:start position:0% +information would have been helpful to +right and all too often that's a usually + + align:start position:0% +right and all too often that's a usually + + + align:start position:0% +right and all too often that's a usually +it's a sizable chunk of folk that's just + + align:start position:0% +it's a sizable chunk of folk that's just + + + align:start position:0% +it's a sizable chunk of folk that's just +caught in the middle want to see + + align:start position:0% +caught in the middle want to see + + + align:start position:0% +caught in the middle want to see +something positive you know don't want + + align:start position:0% +something positive you know don't want + + + align:start position:0% +something positive you know don't want +to be negative you know want you want to + + align:start position:0% +to be negative you know want you want to + + + align:start position:0% +to be negative you know want you want to +unify but but don't have all the + + align:start position:0% +unify but but don't have all the + + + align:start position:0% +unify but but don't have all the +information they need to be able to to + + align:start position:0% +information they need to be able to to + + + align:start position:0% +information they need to be able to to +be a stronger voice you know shut me up + + align:start position:0% +be a stronger voice you know shut me up + + + align:start position:0% +be a stronger voice you know shut me up +I mean if they were to put information + + align:start position:0% +I mean if they were to put information + + + align:start position:0% +I mean if they were to put information +on the table just + + align:start position:0% +on the table just + + + align:start position:0% +on the table just +shr so as Shakur was saying site visits + + align:start position:0% +shr so as Shakur was saying site visits + + + align:start position:0% +shr so as Shakur was saying site visits +to other places some reading uh guests + + align:start position:0% +to other places some reading uh guests + + + align:start position:0% +to other places some reading uh guests +coming in to say we've done it before + + align:start position:0% +coming in to say we've done it before + + + align:start position:0% +coming in to say we've done it before +this is how we did it all of those kinds + + align:start position:0% +this is how we did it all of those kinds + + + align:start position:0% +this is how we did it all of those kinds +of things really support those members + + align:start position:0% +of things really support those members + + + align:start position:0% +of things really support those members +who really want to see something happen + + align:start position:0% +who really want to see something happen + + + align:start position:0% +who really want to see something happen +but need education in order to be able + + align:start position:0% +but need education in order to be able + + + align:start position:0% +but need education in order to be able +to really participate in that planning + + align:start position:0% +to really participate in that planning + + + align:start position:0% +to really participate in that planning +process and how about Miss chair how was + + align:start position:0% +process and how about Miss chair how was + + + align:start position:0% +process and how about Miss chair how was +your role I never really took on the + + align:start position:0% +your role I never really took on the + + + align:start position:0% +your role I never really took on the +chair role but I mean I was sort of + + align:start position:0% +chair role but I mean I was sort of + + + align:start position:0% +chair role but I mean I was sort of +supposed to be chairing the meeting + + align:start position:0% +supposed to be chairing the meeting + + + align:start position:0% +supposed to be chairing the meeting +you know at first I was kind of like + + align:start position:0% +you know at first I was kind of like + + + align:start position:0% +you know at first I was kind of like +okay whatever but then I was sick of the + + align:start position:0% +okay whatever but then I was sick of the + + + align:start position:0% +okay whatever but then I was sick of the +students and then I just wanted actually + + align:start position:0% +students and then I just wanted actually + + + align:start position:0% +students and then I just wanted actually +the numbers had shrunk so much which was + + align:start position:0% +the numbers had shrunk so much which was + + + align:start position:0% +the numbers had shrunk so much which was +the last thing I said before you + + align:start position:0% +the last thing I said before you + + + align:start position:0% +the last thing I said before you +switched us was I was like we've got + + align:start position:0% +switched us was I was like we've got + + + align:start position:0% +switched us was I was like we've got +numbers you're wrong then we had no + + align:start position:0% +numbers you're wrong then we had no + + + align:start position:0% +numbers you're wrong then we had no +numbers and he was right and um and then + + align:start position:0% +numbers and he was right and um and then + + + align:start position:0% +numbers and he was right and um and then +I just wanted people to stop coming to + + align:start position:0% +I just wanted people to stop coming to + + + align:start position:0% +I just wanted people to stop coming to +the meetings because then I thought + + align:start position:0% +the meetings because then I thought + + + align:start position:0% +the meetings because then I thought +maybe something could get done which is + + align:start position:0% +maybe something could get done which is + + + align:start position:0% +maybe something could get done which is +just such a weird thing that also + + align:start position:0% +just such a weird thing that also + + + align:start position:0% +just such a weird thing that also +happened like in the community and then + + align:start position:0% +happened like in the community and then + + + align:start position:0% +happened like in the community and then +like the whole board of directors thing + + align:start position:0% +like the whole board of directors thing + + + align:start position:0% +like the whole board of directors thing +and the thing and the numbers and like + + align:start position:0% +and the thing and the numbers and like + + + align:start position:0% +and the thing and the numbers and like +so you don't really want want people to + + align:start position:0% +so you don't really want want people to + + + align:start position:0% +so you don't really want want people to +come to the meeting cuz you just want to + + align:start position:0% +come to the meeting cuz you just want to + + + align:start position:0% +come to the meeting cuz you just want to +get things done but appear like you have + + align:start position:0% +get things done but appear like you have + + + align:start position:0% +get things done but appear like you have +some kind of process of consensus so um + + align:start position:0% +some kind of process of consensus so um + + + align:start position:0% +some kind of process of consensus so um +but I didn't I just felt like I didn't + + align:start position:0% +but I didn't I just felt like I didn't + + + align:start position:0% +but I didn't I just felt like I didn't +really have anything to like I was just + + align:start position:0% +really have anything to like I was just + + + align:start position:0% +really have anything to like I was just +annoyed but I didn't have anything to + + align:start position:0% +annoyed but I didn't have anything to + + + align:start position:0% +annoyed but I didn't have anything to +push or ask I didn't even know what to + + align:start position:0% +push or ask I didn't even know what to + + + align:start position:0% +push or ask I didn't even know what to +ask for from them because I was just + + align:start position:0% +ask for from them because I was just + + + align:start position:0% +ask for from them because I was just +sick of them and when he was saying for + + align:start position:0% +sick of them and when he was saying for + + + align:start position:0% +sick of them and when he was saying for +them to go on like I was like fine go on + + align:start position:0% +them to go on like I was like fine go on + + + align:start position:0% +them to go on like I was like fine go on +but I was feeling like you never want to + + align:start position:0% +but I was feeling like you never want to + + + align:start position:0% +but I was feeling like you never want to +be in a position where like I don't know + + align:start position:0% +be in a position where like I don't know + + + align:start position:0% +be in a position where like I don't know +if that's like negotiating skills like + + align:start position:0% +if that's like negotiating skills like + + + align:start position:0% +if that's like negotiating skills like +if C could have been like we're only + + align:start position:0% +if C could have been like we're only + + + align:start position:0% +if C could have been like we're only +here as long as you want us to be here + + align:start position:0% +here as long as you want us to be here + + + align:start position:0% +here as long as you want us to be here +and then I mean he could have gotten in + + align:start position:0% +and then I mean he could have gotten in + + + align:start position:0% +and then I mean he could have gotten in +a position where you were like you're + + align:start position:0% +a position where you were like you're + + + align:start position:0% +a position where you were like you're +done go home but rather than like we're + + align:start position:0% +done go home but rather than like we're + + + align:start position:0% +done go home but rather than like we're +here to push this agenda but like we're + + align:start position:0% +here to push this agenda but like we're + + + align:start position:0% +here to push this agenda but like we're +only here I don't know but I just felt + + align:start position:0% +only here I don't know but I just felt + + + align:start position:0% +only here I don't know but I just felt +like I had nothing to like I had no I + + align:start position:0% +like I had nothing to like I had no I + + + align:start position:0% +like I had nothing to like I had no I +was sort of the chair but I had no I was + + align:start position:0% +was sort of the chair but I had no I was + + + align:start position:0% +was sort of the chair but I had no I was +not a chair in our role play at all and + + align:start position:0% +not a chair in our role play at all and + + + align:start position:0% +not a chair in our role play at all and +I had no like yeah ability a lot of + + align:start position:0% +I had no like yeah ability a lot of + + + align:start position:0% +I had no like yeah ability a lot of +chairs function in that capacity and so + + align:start position:0% +chairs function in that capacity and so + + + align:start position:0% +chairs function in that capacity and so +really good + + align:start position:0% +really good + + + align:start position:0% +really good +facilitation for the minority community + + align:start position:0% +facilitation for the minority community + + + align:start position:0% +facilitation for the minority community +person who was really against the + + align:start position:0% +person who was really against the + + + align:start position:0% +person who was really against the +project would have been very useful that + + align:start position:0% +project would have been very useful that + + + align:start position:0% +project would have been very useful that +most chairs don't have those skills yeah + + align:start position:0% +most chairs don't have those skills yeah + + + align:start position:0% +most chairs don't have those skills yeah +because there was nothing don't know how + + align:start position:0% +because there was nothing don't know how + + + align:start position:0% +because there was nothing don't know how +do it said that my role was a chair but + + align:start position:0% +do it said that my role was a chair but + + + align:start position:0% +do it said that my role was a chair but +there was nothing in my car that said + + align:start position:0% +there was nothing in my car that said + + + align:start position:0% +there was nothing in my car that said +that I was supposed to like convene or + + align:start position:0% +that I was supposed to like convene or + + + align:start position:0% +that I was supposed to like convene or +do run the meeting in any way so I + + align:start position:0% +do run the meeting in any way so I + + + align:start position:0% +do run the meeting in any way so I +didn't really feel like that was what I + + align:start position:0% +didn't really feel like that was what I + + + align:start position:0% +didn't really feel like that was what I +was supposed to do at all yeah like I + + align:start position:0% +was supposed to do at all yeah like I + + + align:start position:0% +was supposed to do at all yeah like I +and I kind of knew where he was coming + + align:start position:0% +and I kind of knew where he was coming + + + align:start position:0% +and I kind of knew where he was coming +from so I was like yeah whatever and + + align:start position:0% +from so I was like yeah whatever and + + + align:start position:0% +from so I was like yeah whatever and +again we we set you up for one of the + + align:start position:0% +again we we set you up for one of the + + + align:start position:0% +again we we set you up for one of the +classic roles in these Community groups + + align:start position:0% +classic roles in these Community groups + + + align:start position:0% +classic roles in these Community groups +where the chair doesn't have the skills + + align:start position:0% +where the chair doesn't have the skills + + + align:start position:0% +where the chair doesn't have the skills +doesn't have training is sometimes + + align:start position:0% +doesn't have training is sometimes + + + align:start position:0% +doesn't have training is sometimes +facilitating meetings with hundreds of + + align:start position:0% +facilitating meetings with hundreds of + + + align:start position:0% +facilitating meetings with hundreds of +people there and is you know never done + + align:start position:0% +people there and is you know never done + + + align:start position:0% +people there and is you know never done +it before and doesn't know how to make + + align:start position:0% +it before and doesn't know how to make + + + align:start position:0% +it before and doesn't know how to make +an agenda keep an agenda make sure that + + align:start position:0% +an agenda keep an agenda make sure that + + + align:start position:0% +an agenda keep an agenda make sure that +the group is moving forward on its + + align:start position:0% +the group is moving forward on its + + + align:start position:0% +the group is moving forward on its +agenda on what's most important to it + + align:start position:0% +agenda on what's most important to it + + + align:start position:0% +agenda on what's most important to it +and not allowing minority voices to + + align:start position:0% +and not allowing minority voices to + + + align:start position:0% +and not allowing minority voices to +actually take over and um sideswipe you + + align:start position:0% +actually take over and um sideswipe you + + + align:start position:0% +actually take over and um sideswipe you +know the intention of the whole group + + align:start position:0% +know the intention of the whole group + + + align:start position:0% +know the intention of the whole group +and with a good facilitator you can keep + + align:start position:0% +and with a good facilitator you can keep + + + align:start position:0% +and with a good facilitator you can keep +on the vision yes you know Mr Thomas we' + + align:start position:0% +on the vision yes you know Mr Thomas we' + + + align:start position:0% +on the vision yes you know Mr Thomas we' +we've heard you and um you know we're + + align:start position:0% +we've heard you and um you know we're + + + align:start position:0% +we've heard you and um you know we're +going to move forward you know um thank + + align:start position:0% +going to move forward you know um thank + + + align:start position:0% +going to move forward you know um thank +you very much for expressing your + + align:start position:0% +you very much for expressing your + + + align:start position:0% +you very much for expressing your +opinion and the decision of the group is + + align:start position:0% +opinion and the decision of the group is + + + align:start position:0% +opinion and the decision of the group is +to move in this direction and we're glad + + align:start position:0% +to move in this direction and we're glad + + + align:start position:0% +to move in this direction and we're glad +that you're still joining us but + + align:start position:0% +that you're still joining us but + + + align:start position:0% +that you're still joining us but +uh yeah but again more education is + + align:start position:0% +uh yeah but again more education is + + + align:start position:0% +uh yeah but again more education is +needed to really build the leadership + + align:start position:0% +needed to really build the leadership + + + align:start position:0% +needed to really build the leadership +capacity of that chair to you know be + + align:start position:0% +capacity of that chair to you know be + + + align:start position:0% +capacity of that chair to you know be +able to pull it off it's like I said + + align:start position:0% +able to pull it off it's like I said + + + align:start position:0% +able to pull it off it's like I said +tremendously difficult position and that + + align:start position:0% +tremendously difficult position and that + + + align:start position:0% +tremendously difficult position and that +that that person I mean it was wanted to + + align:start position:0% +that that person I mean it was wanted to + + + align:start position:0% +that that person I mean it was wanted to +make it work had you know but then + + align:start position:0% +make it work had you know but then + + + align:start position:0% +make it work had you know but then +didn't feel it was necessary and then a + + align:start position:0% +didn't feel it was necessary and then a + + + align:start position:0% +didn't feel it was necessary and then a +lot of times you get in the position + + align:start position:0% +lot of times you get in the position + + + align:start position:0% +lot of times you get in the position +where then they start to strike out you + + align:start position:0% +where then they start to strike out you + + + align:start position:0% +where then they start to strike out you +know I mean then they get defensive and + + align:start position:0% +know I mean then they get defensive and + + + align:start position:0% +know I mean then they get defensive and +then you know then they get you know and + + align:start position:0% +then you know then they get you know and + + + align:start position:0% +then you know then they get you know and +um you know and become combative you + + align:start position:0% +um you know and become combative you + + + align:start position:0% +um you know and become combative you +know cuz that's all they know how to do + + align:start position:0% +know cuz that's all they know how to do + + + align:start position:0% +know cuz that's all they know how to do +at that point you know so again I mean + + align:start position:0% +at that point you know so again I mean + + + align:start position:0% +at that point you know so again I mean +putting them in a situation where they + + align:start position:0% +putting them in a situation where they + + + align:start position:0% +putting them in a situation where they +can learn those skills uh um and and and + + align:start position:0% +can learn those skills uh um and and and + + + align:start position:0% +can learn those skills uh um and and and +and become stronger chairs U you know as + + align:start position:0% +and become stronger chairs U you know as + + + align:start position:0% +and become stronger chairs U you know as +well as looking for new new leaders like + + align:start position:0% +well as looking for new new leaders like + + + align:start position:0% +well as looking for new new leaders like +uh the community a mean you know and so + + align:start position:0% +uh the community a mean you know and so + + + align:start position:0% +uh the community a mean you know and so +that that um so that those you can for + + align:start position:0% +that that um so that those you can for + + + align:start position:0% +that that um so that those you can for +form a leadership core and not just you + + align:start position:0% +form a leadership core and not just you + + + align:start position:0% +form a leadership core and not just you +know one leader you know and begin to + + align:start position:0% +know one leader you know and begin to + + + align:start position:0% +know one leader you know and begin to +build you know a group of folk that that + + align:start position:0% +build you know a group of folk that that + + + align:start position:0% +build you know a group of folk that that +will stand up for democracy and and and + + align:start position:0% +will stand up for democracy and and and + + + align:start position:0% +will stand up for democracy and and and +and focusing the vision and moving it + + align:start position:0% +and focusing the vision and moving it + + + align:start position:0% +and focusing the vision and moving it +forward in and how about grad students + + align:start position:0% +forward in and how about grad students + + + align:start position:0% +forward in and how about grad students +we set you up in the hardest role yeah + + align:start position:0% +we set you up in the hardest role yeah + + + align:start position:0% +we set you up in the hardest role yeah +it didn't feel so good + + align:start position:0% +it didn't feel so good + + + align:start position:0% +it didn't feel so good +no well being I think trying to sort of + + align:start position:0% +no well being I think trying to sort of + + + align:start position:0% +no well being I think trying to sort of +thinking of I knew I knew we weren't the + + align:start position:0% +thinking of I knew I knew we weren't the + + + align:start position:0% +thinking of I knew I knew we weren't the +chairs but sort of trying to facilitate + + align:start position:0% +chairs but sort of trying to facilitate + + + align:start position:0% +chairs but sort of trying to facilitate +at the same time that we're pushing + + align:start position:0% +at the same time that we're pushing + + + align:start position:0% +at the same time that we're pushing +pushing we couldn't have actually been + + align:start position:0% +pushing we couldn't have actually been + + + align:start position:0% +pushing we couldn't have actually been +pushing as aggressively I think as we + + align:start position:0% +pushing as aggressively I think as we + + + align:start position:0% +pushing as aggressively I think as we +were but we we set you up for that too + + align:start position:0% +were but we we set you up for that too + + + align:start position:0% +were but we we set you up for that too +um so that was just really that was + + align:start position:0% +um so that was just really that was + + + align:start position:0% +um so that was just really that was +really awkward um and so I think that it + + align:start position:0% +really awkward um and so I think that it + + + align:start position:0% +really awkward um and so I think that it +just highlighted for me the need for a + + align:start position:0% +just highlighted for me the need for a + + + align:start position:0% +just highlighted for me the need for a +really quality facilitation in these + + align:start position:0% +really quality facilitation in these + + + align:start position:0% +really quality facilitation in these +meetings and and a clear sense of role + + align:start position:0% +meetings and and a clear sense of role + + + align:start position:0% +meetings and and a clear sense of role +and a clear sense of role yeah I yeah I + + align:start position:0% +and a clear sense of role yeah I yeah I + + + align:start position:0% +and a clear sense of role yeah I yeah I +thought that + + align:start position:0% +thought that + + + align:start position:0% +thought that +was right I'll say the same thing cuz + + align:start position:0% +was right I'll say the same thing cuz + + + align:start position:0% +was right I'll say the same thing cuz +like with us like I would never want to + + align:start position:0% +like with us like I would never want to + + + align:start position:0% +like with us like I would never want to +go into a chair at a meeting um you know + + align:start position:0% +go into a chair at a meeting um you know + + + align:start position:0% +go into a chair at a meeting um you know +that that just didn't feel right and + + align:start position:0% +that that just didn't feel right and + + + align:start position:0% +that that just didn't feel right and +then also um uh it just seemed like U + + align:start position:0% +then also um uh it just seemed like U + + + align:start position:0% +then also um uh it just seemed like U +you know they were you know skeptical + + align:start position:0% +you know they were you know skeptical + + + align:start position:0% +you know they were you know skeptical +you know about the whole thing and so I + + align:start position:0% +you know about the whole thing and so I + + + align:start position:0% +you know about the whole thing and so I +was like well you know why you + + align:start position:0% +was like well you know why you + + + align:start position:0% +was like well you know why you +here you know you know I I really wanted + + align:start position:0% +here you know you know I I really wanted + + + align:start position:0% +here you know you know I I really wanted +to say well look you know you know we'll + + align:start position:0% +to say well look you know you know we'll + + + align:start position:0% +to say well look you know you know we'll +come back and y'all figure it out you + + align:start position:0% +come back and y'all figure it out you + + + align:start position:0% +come back and y'all figure it out you +know I'm say cuz I don't know you know + + align:start position:0% +know I'm say cuz I don't know you know + + + align:start position:0% +know I'm say cuz I don't know you know +but felt like you know okay we're here + + align:start position:0% +but felt like you know okay we're here + + + align:start position:0% +but felt like you know okay we're here +and you know the C said we were supposed + + align:start position:0% +and you know the C said we were supposed + + + align:start position:0% +and you know the C said we were supposed +to do this just doing what the C told + + align:start position:0% +to do this just doing what the C told + + + align:start position:0% +to do this just doing what the C told +me but um you know so yeah you know it + + align:start position:0% +me but um you know so yeah you know it + + + align:start position:0% +me but um you know so yeah you know it +was just it just the whole thing I would + + align:start position:0% +was just it just the whole thing I would + + + align:start position:0% +was just it just the whole thing I would +have preferred to have you know to been + + align:start position:0% +have preferred to have you know to been + + + align:start position:0% +have preferred to have you know to been +a ro of facilitator or chair of the + + align:start position:0% +a ro of facilitator or chair of the + + + align:start position:0% +a ro of facilitator or chair of the +meeting cuz also I felt like as chair + + align:start position:0% +meeting cuz also I felt like as chair + + + align:start position:0% +meeting cuz also I felt like as chair +like you know we were supposed to be + + align:start position:0% +like you know we were supposed to be + + + align:start position:0% +like you know we were supposed to be +leading this the initiative and I was + + align:start position:0% +leading this the initiative and I was + + + align:start position:0% +leading this the initiative and I was +like well that's not who we supposed to + + align:start position:0% +like well that's not who we supposed to + + + align:start position:0% +like well that's not who we supposed to +be either so that's why got into this + + align:start position:0% +be either so that's why got into this + + + align:start position:0% +be either so that's why got into this +whole defensive thing about trying to + + align:start position:0% +whole defensive thing about trying to + + + align:start position:0% +whole defensive thing about trying to +get it forward but you know that's not + + align:start position:0% +get it forward but you know that's not + + + align:start position:0% +get it forward but you know that's not +where we supposed to be I think also a + + align:start position:0% +where we supposed to be I think also a + + + align:start position:0% +where we supposed to be I think also a +lot of the things that we said to the + + align:start position:0% +lot of the things that we said to the + + + align:start position:0% +lot of the things that we said to the +grad students like are things that + + align:start position:0% +grad students like are things that + + + align:start position:0% +grad students like are things that +people think but they don't say in a + + align:start position:0% +people think but they don't say in a + + + align:start position:0% +people think but they don't say in a +meeting CU they're respectful or + + align:start position:0% +meeting CU they're respectful or + + + align:start position:0% +meeting CU they're respectful or +whatever so a lot of times those things + + align:start position:0% +whatever so a lot of times those things + + + align:start position:0% +whatever so a lot of times those things +don't get said and that's what people + + align:start position:0% +don't get said and that's what people + + + align:start position:0% +don't get said and that's what people +are + + align:start position:0% + + + + align:start position:0% + +thinking when it gets to a certain + + align:start position:0% +thinking when it gets to a certain + + + align:start position:0% +thinking when it gets to a certain +temperature I've + + align:start position:0% +temperature I've + + + align:start position:0% +temperature I've +heard very bad things said in me it's + + align:start position:0% +heard very bad things said in me it's + + + align:start position:0% +heard very bad things said in me it's +true though I find it much harder to be + + align:start position:0% +true though I find it much harder to be + + + align:start position:0% +true though I find it much harder to be +in meetings where those things aren't + + align:start position:0% +in meetings where those things aren't + + + align:start position:0% +in meetings where those things aren't +being said you know I I find it much + + align:start position:0% +being said you know I I find it much + + + align:start position:0% +being said you know I I find it much +harder to deal with and and that happens + + align:start position:0% + + + + align:start position:0% + +long we only have a few minutes left you + + align:start position:0% +long we only have a few minutes left you + + + align:start position:0% +long we only have a few minutes left you +all have hung in there very well um I + + align:start position:0% +all have hung in there very well um I + + + align:start position:0% +all have hung in there very well um I +want to share with you a development + + align:start position:0% +want to share with you a development + + + align:start position:0% +want to share with you a development +plan which I have to collect back from + + align:start position:0% +plan which I have to collect back from + + + align:start position:0% +plan which I have to collect back from +you um this is from a project I'm + + align:start position:0% +you um this is from a project I'm + + + align:start position:0% +you um this is from a project I'm +working on right now and this is the + + align:start position:0% +working on right now and this is the + + + align:start position:0% +working on right now and this is the +opposite extreme of a highly functional + + align:start position:0% +opposite extreme of a highly functional + + + align:start position:0% +opposite extreme of a highly functional +um project where and this we're doing + + align:start position:0% +um project where and this we're doing + + + align:start position:0% +um project where and this we're doing +every two um and uh so if I I think it's + + align:start position:0% +every two um and uh so if I I think it's + + + align:start position:0% +every two um and uh so if I I think it's +and and um this is the biodiesel + + align:start position:0% +and and um this is the biodiesel + + + align:start position:0% +and and um this is the biodiesel +business that I'm putting together and + + align:start position:0% +business that I'm putting together and + + + align:start position:0% +business that I'm putting together and +we um this is not the beginning + + align:start position:0% +we um this is not the beginning + + + align:start position:0% +we um this is not the beginning +development plan this is our current + + align:start position:0% +development plan this is our current + + + align:start position:0% +development plan this is our current +development plan so we've already gone + + align:start position:0% +development plan so we've already gone + + + align:start position:0% +development plan so we've already gone +through the business planning process + + align:start position:0% +through the business planning process + + + align:start position:0% +through the business planning process +but we had something that kind of looked + + align:start position:0% +but we had something that kind of looked + + + align:start position:0% +but we had something that kind of looked +like this for all the beginning business + + align:start position:0% +like this for all the beginning business + + + align:start position:0% +like this for all the beginning business +planning stages but I this format I + + align:start position:0% +planning stages but I this format I + + + align:start position:0% +planning stages but I this format I +think is just very powerful again it's + + align:start position:0% +think is just very powerful again it's + + + align:start position:0% +think is just very powerful again it's +just really clear saying what is it that + + align:start position:0% +just really clear saying what is it that + + + align:start position:0% +just really clear saying what is it that +we have to do what are the activities + + align:start position:0% +we have to do what are the activities + + + align:start position:0% +we have to do what are the activities +who are the decision makers and so we've + + align:start position:0% +who are the decision makers and so we've + + + align:start position:0% +who are the decision makers and so we've +hired our manager so we've got the + + align:start position:0% +hired our manager so we've got the + + + align:start position:0% +hired our manager so we've got the +manager um in as the decision making + + align:start position:0% +manager um in as the decision making + + + align:start position:0% +manager um in as the decision making +maker for a bunch of key things what are + + align:start position:0% +maker for a bunch of key things what are + + + align:start position:0% +maker for a bunch of key things what are +the things the board's going to decide + + align:start position:0% +the things the board's going to decide + + + align:start position:0% +the things the board's going to decide +and you'll notice on the second page + + align:start position:0% +and you'll notice on the second page + + + align:start position:0% +and you'll notice on the second page +those are the equity decisions the + + align:start position:0% +those are the equity decisions the + + + align:start position:0% +those are the equity decisions the +decision to accept Equity decision to + + align:start position:0% +decision to accept Equity decision to + + + align:start position:0% +decision to accept Equity decision to +accept debt and um corporate identity + + align:start position:0% +accept debt and um corporate identity + + + align:start position:0% +accept debt and um corporate identity +issues those are the things the board + + align:start position:0% +issues those are the things the board + + + align:start position:0% +issues those are the things the board +said but the board said they were + + align:start position:0% +said but the board said they were + + + align:start position:0% +said but the board said they were +comfortable delegating the rest of the + + align:start position:0% +comfortable delegating the rest of the + + + align:start position:0% +comfortable delegating the rest of the +things to the C CEO within all of the + + align:start position:0% +things to the C CEO within all of the + + + align:start position:0% +things to the C CEO within all of the +established policies and they have a um + + align:start position:0% +established policies and they have a um + + + align:start position:0% +established policies and they have a um +you know a set of Poli 10 policies that + + align:start position:0% +you know a set of Poli 10 policies that + + + align:start position:0% +you know a set of Poli 10 policies that +the CEO has to make these decisions + + align:start position:0% +the CEO has to make these decisions + + + align:start position:0% +the CEO has to make these decisions +within in addition to the budget and um + + align:start position:0% +within in addition to the budget and um + + + align:start position:0% +within in addition to the budget and um +then there's measurement criteria about + + align:start position:0% +then there's measurement criteria about + + + align:start position:0% +then there's measurement criteria about +when each of these things has to be done + + align:start position:0% +when each of these things has to be done + + + align:start position:0% +when each of these things has to be done +and what success looks like and um then + + align:start position:0% +and what success looks like and um then + + + align:start position:0% +and what success looks like and um then +on a monthly basis the CEO has to check + + align:start position:0% +on a monthly basis the CEO has to check + + + align:start position:0% +on a monthly basis the CEO has to check +off in this last column you know whether + + align:start position:0% +off in this last column you know whether + + + align:start position:0% +off in this last column you know whether +this thing is on schedule whether it's + + align:start position:0% +this thing is on schedule whether it's + + + align:start position:0% +this thing is on schedule whether it's +delayed whether the criteria is met and + + align:start position:0% +delayed whether the criteria is met and + + + align:start position:0% +delayed whether the criteria is met and +the only thing that makes it to the + + align:start position:0% +the only thing that makes it to the + + + align:start position:0% +the only thing that makes it to the +board meeting is when it's delayed and + + align:start position:0% +board meeting is when it's delayed and + + + align:start position:0% +board meeting is when it's delayed and +then the board chooses whether or not to + + align:start position:0% +then the board chooses whether or not to + + + align:start position:0% +then the board chooses whether or not to +discuss it so the board's in charge of + + align:start position:0% +discuss it so the board's in charge of + + + align:start position:0% +discuss it so the board's in charge of +its agenda it sets the agenda based on + + align:start position:0% +its agenda it sets the agenda based on + + + align:start position:0% +its agenda it sets the agenda based on +its criteria um so it's very much about + + align:start position:0% +its criteria um so it's very much about + + + align:start position:0% +its criteria um so it's very much about +member ownership and control even those + + align:start position:0% +member ownership and control even those + + + align:start position:0% +member ownership and control even those +are tremendous amount is delegated to + + align:start position:0% +are tremendous amount is delegated to + + + align:start position:0% +are tremendous amount is delegated to +the CEO so um having this kind of a + + align:start position:0% +the CEO so um having this kind of a + + + align:start position:0% +the CEO so um having this kind of a +clear development plan is main is + + align:start position:0% +clear development plan is main is + + + align:start position:0% +clear development plan is main is +keeping the project on track making sure + + align:start position:0% +keeping the project on track making sure + + + align:start position:0% +keeping the project on track making sure +that the members what the memb want is + + align:start position:0% +that the members what the memb want is + + + align:start position:0% +that the members what the memb want is +getting + + align:start position:0% +getting + + + align:start position:0% +getting +done um as uh through their board um + + align:start position:0% +done um as uh through their board um + + + align:start position:0% +done um as uh through their board um +representatives and keeping the power + + align:start position:0% +representatives and keeping the power + + + align:start position:0% +representatives and keeping the power +relationship between the board of + + align:start position:0% +relationship between the board of + + + align:start position:0% +relationship between the board of +directors which is representatives of + + align:start position:0% +directors which is representatives of + + + align:start position:0% +directors which is representatives of +the members um keeping them in charge of + + align:start position:0% +the members um keeping them in charge of + + + align:start position:0% +the members um keeping them in charge of +the CEO rather than the other way around + + align:start position:0% +the CEO rather than the other way around + + + align:start position:0% +the CEO rather than the other way around +and this is a really high-powered + + align:start position:0% +and this is a really high-powered + + + align:start position:0% +and this is a really high-powered +incredibly talented guy you know and so + + align:start position:0% +incredibly talented guy you know and so + + + align:start position:0% +incredibly talented guy you know and so +we want to make sure that we we're in + + align:start position:0% +we want to make sure that we we're in + + + align:start position:0% +we want to make sure that we we're in +right relationship with him and um so + + align:start position:0% +right relationship with him and um so + + + align:start position:0% +right relationship with him and um so +this tool um and tools like this are I + + align:start position:0% +this tool um and tools like this are I + + + align:start position:0% +this tool um and tools like this are I +think tremendously useful and I think + + align:start position:0% +think tremendously useful and I think + + + align:start position:0% +think tremendously useful and I think +this just great work on that part of Lyn + + align:start position:0% +this just great work on that part of Lyn + + + align:start position:0% +this just great work on that part of Lyn +and the other folks that have done the + + align:start position:0% +and the other folks that have done the + + + align:start position:0% +and the other folks that have done the +biodiesel because this is a a very um + + align:start position:0% +biodiesel because this is a a very um + + + align:start position:0% +biodiesel because this is a a very um +diverse group you know low-income folk + + align:start position:0% +diverse group you know low-income folk + + + align:start position:0% +diverse group you know low-income folk +other folk I mean uh and uh and like I + + align:start position:0% +other folk I mean uh and uh and like I + + + align:start position:0% +other folk I mean uh and uh and like I +said and being able to you know in a in + + align:start position:0% +said and being able to you know in a in + + + align:start position:0% +said and being able to you know in a in +a fairly Technical and difficult uh U + + align:start position:0% +a fairly Technical and difficult uh U + + + align:start position:0% +a fairly Technical and difficult uh U +complex um industry U usually that those + + align:start position:0% +complex um industry U usually that those + + + align:start position:0% +complex um industry U usually that those +are all the um um uh you know uh uh + + align:start position:0% +are all the um um uh you know uh uh + + + align:start position:0% +are all the um um uh you know uh uh +factors that will lead the Seas and to + + align:start position:0% +factors that will lead the Seas and to + + + align:start position:0% +factors that will lead the Seas and to +be able to do pretty damn much what he + + align:start position:0% +be able to do pretty damn much what he + + + align:start position:0% +be able to do pretty damn much what he +wants to do you know or or she wants to + + align:start position:0% +wants to do you know or or she wants to + + + align:start position:0% +wants to do you know or or she wants to +do I mean so so to be able to to set up + + align:start position:0% +do I mean so so to be able to to set up + + + align:start position:0% +do I mean so so to be able to to set up +a process where you know where there's + + align:start position:0% +a process where you know where there's + + + align:start position:0% +a process where you know where there's +true member uh ownership and control of + + align:start position:0% +true member uh ownership and control of + + + align:start position:0% +true member uh ownership and control of +that uh and and being able to break down + + align:start position:0% +that uh and and being able to break down + + + align:start position:0% +that uh and and being able to break down +you know like say relatively complex um + + align:start position:0% +you know like say relatively complex um + + + align:start position:0% +you know like say relatively complex um +items and and and and into things that + + align:start position:0% +items and and and and into things that + + + align:start position:0% +items and and and and into things that +that that folks can handle and control I + + align:start position:0% +that that folks can handle and control I + + + align:start position:0% +that that folks can handle and control I +mean you know I think it shows the + + align:start position:0% +mean you know I think it shows the + + + align:start position:0% +mean you know I think it shows the +potential I mean so it's uh mean just + + align:start position:0% +potential I mean so it's uh mean just + + + align:start position:0% +potential I mean so it's uh mean just +really good work and but like I said and + + align:start position:0% +really good work and but like I said and + + + align:start position:0% +really good work and but like I said and +I think the kind of thing that we ought + + align:start position:0% +I think the kind of thing that we ought + + + align:start position:0% +I think the kind of thing that we ought +to that that we have to be about you + + align:start position:0% +to that that we have to be about you + + + align:start position:0% +to that that we have to be about you +know showing that that you know no + + align:start position:0% +know showing that that you know no + + + align:start position:0% +know showing that that you know no +matter what the community that that U + + align:start position:0% +matter what the community that that U + + + align:start position:0% +matter what the community that that U +that they can U that they can take on + + align:start position:0% +that they can U that they can take on + + + align:start position:0% +that they can U that they can take on +those tasks and and and be you know + + align:start position:0% +those tasks and and and be you know + + + align:start position:0% +those tasks and and and be you know +strong um um um knowledgeable uh uh u u + + align:start position:0% +strong um um um knowledgeable uh uh u u + + + align:start position:0% +strong um um um knowledgeable uh uh u u +board members that control all the key + + align:start position:0% +board members that control all the key + + + align:start position:0% +board members that control all the key +aspects of the of the process in my + + align:start position:0% +aspects of the of the process in my + + + align:start position:0% +aspects of the of the process in my +former role as a manager I mean um one + + align:start position:0% +former role as a manager I mean um one + + + align:start position:0% +former role as a manager I mean um one +of the things I really resented about + + align:start position:0% +of the things I really resented about + + + align:start position:0% +of the things I really resented about +certain advocacy groups was when they + + align:start position:0% +certain advocacy groups was when they + + + align:start position:0% +certain advocacy groups was when they +would confront me with + + align:start position:0% +would confront me with + + + align:start position:0% +would confront me with +we want X you here is your you either + + align:start position:0% +we want X you here is your you either + + + align:start position:0% +we want X you here is your you either +say yes or no and what I really wanted + + align:start position:0% +say yes or no and what I really wanted + + + align:start position:0% +say yes or no and what I really wanted +was to be able to have a conversation + + align:start position:0% +was to be able to have a conversation + + + align:start position:0% +was to be able to have a conversation +informed conversation with you know the + + align:start position:0% +informed conversation with you know the + + + align:start position:0% +informed conversation with you know the +the residents you know the clients right + + align:start position:0% +the residents you know the clients right + + + align:start position:0% +the residents you know the clients right +so we could you know make sense and and + + align:start position:0% +so we could you know make sense and and + + + align:start position:0% +so we could you know make sense and and +they could understand the complexity and + + align:start position:0% +they could understand the complexity and + + + align:start position:0% +they could understand the complexity and +this and that and you know I found that + + align:start position:0% +this and that and you know I found that + + + align:start position:0% +this and that and you know I found that +a lot of Advocates like didn't really do + + align:start position:0% +a lot of Advocates like didn't really do + + + align:start position:0% +a lot of Advocates like didn't really do +that kind of work with the residents + + align:start position:0% +that kind of work with the residents + + + align:start position:0% +that kind of work with the residents +they they they just sort of wanted to + + align:start position:0% +they they they just sort of wanted to + + + align:start position:0% +they they they just sort of wanted to +win a victory you know against + + align:start position:0% +win a victory you know against + + + align:start position:0% +win a victory you know against +management you know and anyhow this was + + align:start position:0% +management you know and anyhow this was + + + align:start position:0% +management you know and anyhow this was +when I was wearing a management hat I I + + align:start position:0% +when I was wearing a management hat I I + + + align:start position:0% +when I was wearing a management hat I I +think it's really possible to have good + + align:start position:0% +think it's really possible to have good + + + align:start position:0% +think it's really possible to have good +relationships with managers when you do + + align:start position:0% +relationships with managers when you do + + + align:start position:0% +relationships with managers when you do +have that component you were talking + + align:start position:0% +have that component you were talking + + + align:start position:0% +have that component you were talking +about when you you you know when the res + + align:start position:0% +about when you you you know when the res + + + align:start position:0% +about when you you you know when the res +when the clients really do learn the + + align:start position:0% +when the clients really do learn the + + + align:start position:0% +when the clients really do learn the +business so you're having a real + + align:start position:0% +business so you're having a real + + + align:start position:0% +business so you're having a real +conversation and yet expertise is + + align:start position:0% +conversation and yet expertise is + + + align:start position:0% +conversation and yet expertise is +respected and so this was a this was a + + align:start position:0% +respected and so this was a this was a + + + align:start position:0% +respected and so this was a this was a +conversation that lasted well this board + + align:start position:0% +conversation that lasted well this board + + + align:start position:0% +conversation that lasted well this board +is the most functional board I've ever + + align:start position:0% +is the most functional board I've ever + + + align:start position:0% +is the most functional board I've ever +worked with um it lasted for six weeks a + + align:start position:0% +worked with um it lasted for six weeks a + + + align:start position:0% +worked with um it lasted for six weeks a +lot of email back and forth and then two + + align:start position:0% +lot of email back and forth and then two + + + align:start position:0% +lot of email back and forth and then two +two different board meetings where we + + align:start position:0% +two different board meetings where we + + + align:start position:0% +two different board meetings where we +looked at it and then adopted it and + + align:start position:0% +looked at it and then adopted it and + + + align:start position:0% +looked at it and then adopted it and +um it it's it's it it leaves that they + + align:start position:0% +um it it's it's it it leaves that they + + + align:start position:0% +um it it's it's it it leaves that they +were willing to delegate the selection + + align:start position:0% +were willing to delegate the selection + + + align:start position:0% +were willing to delegate the selection +of the technology I was + + align:start position:0% +of the technology I was + + + align:start position:0% +of the technology I was +surprised because it's really a big deal + + align:start position:0% +surprised because it's really a big deal + + + align:start position:0% +surprised because it's really a big deal +for this business which technology + + align:start position:0% +for this business which technology + + + align:start position:0% +for this business which technology +provider they choose to provide the + + align:start position:0% +provider they choose to provide the + + + align:start position:0% +provider they choose to provide the +equipment for making the biodiesel but + + align:start position:0% +equipment for making the biodiesel but + + + align:start position:0% +equipment for making the biodiesel but +they said he has a lot more expertise he + + align:start position:0% +they said he has a lot more expertise he + + + align:start position:0% +they said he has a lot more expertise he +has a PHD in + + align:start position:0% +has a PHD in + + + align:start position:0% +has a PHD in +microbiology and he's already started up + + align:start position:0% +microbiology and he's already started up + + + align:start position:0% +microbiology and he's already started up +uh you know three other Tech businesses + + align:start position:0% +uh you know three other Tech businesses + + + align:start position:0% +uh you know three other Tech businesses +and he's ordered this kind of kind of + + align:start position:0% +and he's ordered this kind of kind of + + + align:start position:0% +and he's ordered this kind of kind of +equipment before we don't really know so + + align:start position:0% +equipment before we don't really know so + + + align:start position:0% +equipment before we don't really know so +as long as he stays within this output + + align:start position:0% +as long as he stays within this output + + + align:start position:0% +as long as he stays within this output +this budget you know this quality that + + align:start position:0% +this budget you know this quality that + + + align:start position:0% +this budget you know this quality that +we want our + + align:start position:0% +we want our + + + align:start position:0% +we want our +product he's going to make the decision + + align:start position:0% +product he's going to make the decision + + + align:start position:0% +product he's going to make the decision +so it's like the conversation all + + align:start position:0% +so it's like the conversation all + + + align:start position:0% +so it's like the conversation all +happened and now everybody knows what + + align:start position:0% +happened and now everybody knows what + + + align:start position:0% +happened and now everybody knows what +their job is and what they're going to + + align:start position:0% +their job is and what they're going to + + + align:start position:0% +their job is and what they're going to +be involved in and how it's going to + + align:start position:0% +be involved in and how it's going to + + + align:start position:0% +be involved in and how it's going to +work so this this Co-op this actually is + + align:start position:0% +work so this this Co-op this actually is + + + align:start position:0% +work so this this Co-op this actually is +an LLC the um Co-op power is the co-op + + align:start position:0% +an LLC the um Co-op power is the co-op + + + align:start position:0% +an LLC the um Co-op power is the co-op +that owns that has a 51% ownership stake + + align:start position:0% +that owns that has a 51% ownership stake + + + align:start position:0% +that owns that has a 51% ownership stake +in this LLC because it needed um outside + + align:start position:0% +in this LLC because it needed um outside + + + align:start position:0% +in this LLC because it needed um outside +Capital so it couldn't they couldn't + + align:start position:0% +Capital so it couldn't they couldn't + + + align:start position:0% +Capital so it couldn't they couldn't +just keep it within the co-op but that + + align:start position:0% +just keep it within the co-op but that + + + align:start position:0% +just keep it within the co-op but that +this Co-op business you know is able to + + align:start position:0% +this Co-op business you know is able to + + + align:start position:0% +this Co-op business you know is able to +own and + + align:start position:0% +own and + + + align:start position:0% +own and +control what it wants and it clear about + + align:start position:0% +control what it wants and it clear about + + + align:start position:0% +control what it wants and it clear about +what it wants and how it's going to + + align:start position:0% +what it wants and how it's going to + + + align:start position:0% +what it wants and how it's going to +measure that so how how did they come to + + align:start position:0% +measure that so how how did they come to + + + align:start position:0% +measure that so how how did they come to +the process of deciding that there were + + align:start position:0% +the process of deciding that there were + + + align:start position:0% +the process of deciding that there were +three steps under WBO contracts and + + align:start position:0% +three steps under WBO contracts and + + + align:start position:0% +three steps under WBO contracts and +three steps under biod dieso sales how + + align:start position:0% +three steps under biod dieso sales how + + + align:start position:0% +three steps under biod dieso sales how +are they able to evaluate it CU I I mean + + align:start position:0% +are they able to evaluate it CU I I mean + + + align:start position:0% +are they able to evaluate it CU I I mean +me looking at this knowing nothing about + + align:start position:0% +me looking at this knowing nothing about + + + align:start position:0% +me looking at this knowing nothing about +technology would say this looks great + + align:start position:0% +technology would say this looks great + + + align:start position:0% +technology would say this looks great +but I have no idea if there's a key + + align:start position:0% +but I have no idea if there's a key + + + align:start position:0% +but I have no idea if there's a key +piece missing or and and there's there + + align:start position:0% +piece missing or and and there's there + + + align:start position:0% +piece missing or and and there's there +were there's other expertise at the + + align:start position:0% +were there's other expertise at the + + + align:start position:0% +were there's other expertise at the +table in terms of the business planner + + align:start position:0% +table in terms of the business planner + + + align:start position:0% +table in terms of the business planner +the CEO myself as the I'm the interim + + align:start position:0% +the CEO myself as the I'm the interim + + + align:start position:0% +the CEO myself as the I'm the interim +manager until the transition to the new + + align:start position:0% +manager until the transition to the new + + + align:start position:0% +manager until the transition to the new +manager takes place so that you know + + align:start position:0% +manager takes place so that you know + + + align:start position:0% +manager takes place so that you know +there people at the table who've been + + align:start position:0% +there people at the table who've been + + + align:start position:0% +there people at the table who've been +doing a lot of that research and a lot + + align:start position:0% +doing a lot of that research and a lot + + + align:start position:0% +doing a lot of that research and a lot +of conversation and they the board added + + align:start position:0% +of conversation and they the board added + + + align:start position:0% +of conversation and they the board added +more things than we had thought of you + + align:start position:0% +more things than we had thought of you + + + align:start position:0% +more things than we had thought of you +know and changed some things around and + + align:start position:0% +know and changed some things around and + + + align:start position:0% +know and changed some things around and +said you know we're really not sure + + align:start position:0% +said you know we're really not sure + + + align:start position:0% +said you know we're really not sure +whether 85% is you know the right number + + align:start position:0% +whether 85% is you know the right number + + + align:start position:0% +whether 85% is you know the right number +you know so and then they got to hear + + align:start position:0% +you know so and then they got to hear + + + align:start position:0% +you know so and then they got to hear +the new the incoming CEO and me and the + + align:start position:0% +the new the incoming CEO and me and the + + + align:start position:0% +the new the incoming CEO and me and the +business planner talk about well this is + + align:start position:0% +business planner talk about well this is + + + align:start position:0% +business planner talk about well this is +why we picked the + + align:start position:0% +why we picked the + + + align:start position:0% +why we picked the +85% it you know one of us wanted this + + align:start position:0% +85% it you know one of us wanted this + + + align:start position:0% +85% it you know one of us wanted this +one and so they got to listen to the + + align:start position:0% +one and so they got to listen to the + + + align:start position:0% +one and so they got to listen to the +reasoning behind it and educate + + align:start position:0% +reasoning behind it and educate + + + align:start position:0% +reasoning behind it and educate +themselves about what you know what was + + align:start position:0% +themselves about what you know what was + + + align:start position:0% +themselves about what you know what was +our thinking about that and then make + + align:start position:0% +our thinking about that and then make + + + align:start position:0% +our thinking about that and then make +their own decisions so there's a lot of + + align:start position:0% +their own decisions so there's a lot of + + + align:start position:0% +their own decisions so there's a lot of +conversation about each of those pieces + + align:start position:0% +conversation about each of those pieces + + + align:start position:0% +conversation about each of those pieces +and I think everybody came away kind of + + align:start position:0% +and I think everybody came away kind of + + + align:start position:0% +and I think everybody came away kind of +understanding at a much deeper level + + align:start position:0% +understanding at a much deeper level + + + align:start position:0% +understanding at a much deeper level +anyway but understanding a lot of what + + align:start position:0% +anyway but understanding a lot of what + + + align:start position:0% +anyway but understanding a lot of what +it's going to take to actually put this + + align:start position:0% +it's going to take to actually put this + + + align:start position:0% +it's going to take to actually put this +business on the ground + + align:start position:0% + + + + align:start position:0% + +timing okay we have just three slides + + align:start position:0% +timing okay we have just three slides + + + align:start position:0% +timing okay we have just three slides +left the um the reason I want to talk to + + align:start position:0% +left the um the reason I want to talk to + + + align:start position:0% +left the um the reason I want to talk to +you about thank you for remembering that + + align:start position:0% +you about thank you for remembering that + + + align:start position:0% +you about thank you for remembering that +the reason I want to talk to you about + + align:start position:0% +the reason I want to talk to you about + + + align:start position:0% +the reason I want to talk to you about +Northeast biodiesel is because it's a + + align:start position:0% +Northeast biodiesel is because it's a + + + align:start position:0% +Northeast biodiesel is because it's a +mechanism for um for generating money + + align:start position:0% +mechanism for um for generating money + + + align:start position:0% +mechanism for um for generating money +for education and Community organizing + + align:start position:0% +for education and Community organizing + + + align:start position:0% +for education and Community organizing +and that's one of the things that Phil + + align:start position:0% +and that's one of the things that Phil + + + align:start position:0% +and that's one of the things that Phil +and I have been talking about for a long + + align:start position:0% +and I have been talking about for a long + + + align:start position:0% +and I have been talking about for a long +time it's like what kind of businesses + + align:start position:0% +time it's like what kind of businesses + + + align:start position:0% +time it's like what kind of businesses +will generate revenue for communities to + + align:start position:0% +will generate revenue for communities to + + + align:start position:0% +will generate revenue for communities to +organize themselves and educate + + align:start position:0% +organize themselves and educate + + + align:start position:0% +organize themselves and educate +themselves and um Northeast biodiesel is + + align:start position:0% +themselves and um Northeast biodiesel is + + + align:start position:0% +themselves and um Northeast biodiesel is +one example of a business where you have + + align:start position:0% +one example of a business where you have + + + align:start position:0% +one example of a business where you have +a profit making + + align:start position:0% +a profit making + + + align:start position:0% +a profit making +entity that's owned entirely or in part + + align:start position:0% +entity that's owned entirely or in part + + + align:start position:0% +entity that's owned entirely or in part +by members or other entities whose top + + align:start position:0% +by members or other entities whose top + + + align:start position:0% +by members or other entities whose top +priority is organizing and education + + align:start position:0% +priority is organizing and education + + + align:start position:0% +priority is organizing and education +that's what I've decided my formula is + + align:start position:0% +that's what I've decided my formula is + + + align:start position:0% +that's what I've decided my formula is +it's a new Theory um but um you want to + + align:start position:0% +it's a new Theory um but um you want to + + + align:start position:0% +it's a new Theory um but um you want to +go to the next one and so an example is + + align:start position:0% +go to the next one and so an example is + + + align:start position:0% +go to the next one and so an example is +a nonprofit that has a real estate + + align:start position:0% +a nonprofit that has a real estate + + + align:start position:0% +a nonprofit that has a real estate +development company that returns profit + + align:start position:0% +development company that returns profit + + + align:start position:0% +development company that returns profit +um back to the nonprofit organizing and + + align:start position:0% +um back to the nonprofit organizing and + + + align:start position:0% +um back to the nonprofit organizing and +education programs that's done a lot a + + align:start position:0% +education programs that's done a lot a + + + align:start position:0% +education programs that's done a lot a +labor union that provides Capital needed + + align:start position:0% +labor union that provides Capital needed + + + align:start position:0% +labor union that provides Capital needed +for a worker owned business that uses + + align:start position:0% +for a worker owned business that uses + + + align:start position:0% +for a worker owned business that uses +its share of the profits to support + + align:start position:0% +its share of the profits to support + + + align:start position:0% +its share of the profits to support +local organizing and education or a + + align:start position:0% +local organizing and education or a + + + align:start position:0% +local organizing and education or a +consumer Cooperative like this energy + + align:start position:0% +consumer Cooperative like this energy + + + align:start position:0% +consumer Cooperative like this energy +Cooperative that uses a portion of their + + align:start position:0% +Cooperative that uses a portion of their + + + align:start position:0% +Cooperative that uses a portion of their +profits for organizing and education + + align:start position:0% +profits for organizing and education + + + align:start position:0% +profits for organizing and education +programs actually this is a this is a a + + align:start position:0% +programs actually this is a this is a a + + + align:start position:0% +programs actually this is a this is a a +little bit different variation on that + + align:start position:0% +little bit different variation on that + + + align:start position:0% +little bit different variation on that +but yes please and this is our last + + align:start position:0% +but yes please and this is our last + + + align:start position:0% +but yes please and this is our last +slide + + align:start position:0% + + + + align:start position:0% + +yes a lot of little + + align:start position:0% + + + + align:start position:0% + +fish thank you yes this is really good + + align:start position:0% +fish thank you yes this is really good + + + align:start position:0% +fish thank you yes this is really good +how was it yeah \ No newline at end of file diff --git a/kz2tvO_ZAKI.txt b/kz2tvO_ZAKI.txt new file mode 100644 index 0000000000000000000000000000000000000000..e0c06fed66c23d050068db992916c6cb31df034b --- /dev/null +++ b/kz2tvO_ZAKI.txt @@ -0,0 +1,723 @@ +align:start position:0% + +we now come to the third and final kind + + align:start position:0% +we now come to the third and final kind + + + align:start position:0% +we now come to the third and final kind +of calculation out of the calculations + + align:start position:0% +of calculation out of the calculations + + + align:start position:0% +of calculation out of the calculations +that we carried out in our earlier + + align:start position:0% +that we carried out in our earlier + + + align:start position:0% +that we carried out in our earlier +example the setting is exactly the same + + align:start position:0% +example the setting is exactly the same + + + align:start position:0% +example the setting is exactly the same +as in our discussion of the total + + align:start position:0% +as in our discussion of the total + + + align:start position:0% +as in our discussion of the total +probability theorem we have a sample + + align:start position:0% +probability theorem we have a sample + + + align:start position:0% +probability theorem we have a sample +space which is partitioned into a number + + align:start position:0% +space which is partitioned into a number + + + align:start position:0% +space which is partitioned into a number +of disjoint subsets or events which we + + align:start position:0% +of disjoint subsets or events which we + + + align:start position:0% +of disjoint subsets or events which we +think of as scenarios we are given the + + align:start position:0% +think of as scenarios we are given the + + + align:start position:0% +think of as scenarios we are given the +probability of each scenario and we + + align:start position:0% +probability of each scenario and we + + + align:start position:0% +probability of each scenario and we +think of these probabilities as being + + align:start position:0% +think of these probabilities as being + + + align:start position:0% +think of these probabilities as being +some kind of initial beliefs they + + align:start position:0% +some kind of initial beliefs they + + + align:start position:0% +some kind of initial beliefs they +capture how likely we believe each + + align:start position:0% +capture how likely we believe each + + + align:start position:0% +capture how likely we believe each +scenario to be now under each scenario + + align:start position:0% +scenario to be now under each scenario + + + align:start position:0% +scenario to be now under each scenario +we also have the probability that an + + align:start position:0% +we also have the probability that an + + + align:start position:0% +we also have the probability that an +event of interest event B will occur + + align:start position:0% +event of interest event B will occur + + + align:start position:0% +event of interest event B will occur +then the probabilistic experiment is + + align:start position:0% +then the probabilistic experiment is + + + align:start position:0% +then the probabilistic experiment is +carried out and perhaps we observe that + + align:start position:0% +carried out and perhaps we observe that + + + align:start position:0% +carried out and perhaps we observe that +event B did indeed occur once that + + align:start position:0% +event B did indeed occur once that + + + align:start position:0% +event B did indeed occur once that +happens maybe this should cause us to + + align:start position:0% +happens maybe this should cause us to + + + align:start position:0% +happens maybe this should cause us to +revise our beliefs about the likelihood + + align:start position:0% +revise our beliefs about the likelihood + + + align:start position:0% +revise our beliefs about the likelihood +of the different scenarios having + + align:start position:0% +of the different scenarios having + + + align:start position:0% +of the different scenarios having +observed that B occurred perhaps certain + + align:start position:0% +observed that B occurred perhaps certain + + + align:start position:0% +observed that B occurred perhaps certain +scenarios are more likely than others + + align:start position:0% +scenarios are more likely than others + + + align:start position:0% +scenarios are more likely than others +how do we revise our beliefs by + + align:start position:0% +how do we revise our beliefs by + + + align:start position:0% +how do we revise our beliefs by +calculating conditional probabilities + + align:start position:0% +calculating conditional probabilities + + + align:start position:0% +calculating conditional probabilities +and how do we calculate conditional + + align:start position:0% +and how do we calculate conditional + + + align:start position:0% +and how do we calculate conditional +probabilities we start from the + + align:start position:0% +probabilities we start from the + + + align:start position:0% +probabilities we start from the +definition of conditional probabilities + + align:start position:0% +definition of conditional probabilities + + + align:start position:0% +definition of conditional probabilities +the probability of one event given + + align:start position:0% +the probability of one event given + + + align:start position:0% +the probability of one event given +another is the probability that both + + align:start position:0% +another is the probability that both + + + align:start position:0% +another is the probability that both +events occur divided by the probability + + align:start position:0% +events occur divided by the probability + + + align:start position:0% +events occur divided by the probability +of the conditioning event how do we + + align:start position:0% +of the conditioning event how do we + + + align:start position:0% +of the conditioning event how do we +continue well we simply realize that the + + align:start position:0% +continue well we simply realize that the + + + align:start position:0% +continue well we simply realize that the +numerator is what we can calculate using + + align:start position:0% +numerator is what we can calculate using + + + align:start position:0% +numerator is what we can calculate using +the multiplication rule and the + + align:start position:0% +the multiplication rule and the + + + align:start position:0% +the multiplication rule and the +denominator is exactly what we calculate + + align:start position:0% +denominator is exactly what we calculate + + + align:start position:0% +denominator is exactly what we calculate +using the total probability theorem so + + align:start position:0% +using the total probability theorem so + + + align:start position:0% +using the total probability theorem so +we have everything we need to calculate + + align:start position:0% +we have everything we need to calculate + + + align:start position:0% +we have everything we need to calculate +those revised beliefs or conditional + + align:start position:0% +those revised beliefs or conditional + + + align:start position:0% +those revised beliefs or conditional +probabilities and this is all the reason + + align:start position:0% +probabilities and this is all the reason + + + align:start position:0% +probabilities and this is all the reason +the Bayes rule it is actually a very + + align:start position:0% +the Bayes rule it is actually a very + + + align:start position:0% +the Bayes rule it is actually a very +simple calculation it's a very simple + + align:start position:0% +simple calculation it's a very simple + + + align:start position:0% +simple calculation it's a very simple +calculation however it is a quite + + align:start position:0% +calculation however it is a quite + + + align:start position:0% +calculation however it is a quite +important one + + align:start position:0% +important one + + + align:start position:0% +important one +it's history goes way back in the middle + + align:start position:0% +it's history goes way back in the middle + + + align:start position:0% +it's history goes way back in the middle +of the 18th century a Presbyterian + + align:start position:0% +of the 18th century a Presbyterian + + + align:start position:0% +of the 18th century a Presbyterian +minister Thomas Bayes worked it out it + + align:start position:0% +minister Thomas Bayes worked it out it + + + align:start position:0% +minister Thomas Bayes worked it out it +was published a few years after his + + align:start position:0% +was published a few years after his + + + align:start position:0% +was published a few years after his +death and it was quickly recognized for + + align:start position:0% +death and it was quickly recognized for + + + align:start position:0% +death and it was quickly recognized for +its significance it's a systematic way + + align:start position:0% +its significance it's a systematic way + + + align:start position:0% +its significance it's a systematic way +for incorporating new evidence it's a + + align:start position:0% +for incorporating new evidence it's a + + + align:start position:0% +for incorporating new evidence it's a +systematic way for learning from + + align:start position:0% +systematic way for learning from + + + align:start position:0% +systematic way for learning from +experience and it forms the foundation + + align:start position:0% +experience and it forms the foundation + + + align:start position:0% +experience and it forms the foundation +of a major branch of mathematics so + + align:start position:0% +of a major branch of mathematics so + + + align:start position:0% +of a major branch of mathematics so +called Bayesian inference which we will + + align:start position:0% +called Bayesian inference which we will + + + align:start position:0% +called Bayesian inference which we will +study in some detail later in this + + align:start position:0% +study in some detail later in this + + + align:start position:0% +study in some detail later in this +course the general idea is that we start + + align:start position:0% +course the general idea is that we start + + + align:start position:0% +course the general idea is that we start +with a probabilistic model which + + align:start position:0% +with a probabilistic model which + + + align:start position:0% +with a probabilistic model which +involves a number of possible scenarios + + align:start position:0% +involves a number of possible scenarios + + + align:start position:0% +involves a number of possible scenarios +and we have some initial beliefs on the + + align:start position:0% +and we have some initial beliefs on the + + + align:start position:0% +and we have some initial beliefs on the +likelihood of each possible scenario + + align:start position:0% +likelihood of each possible scenario + + + align:start position:0% +likelihood of each possible scenario +there's also some particular event that + + align:start position:0% +there's also some particular event that + + + align:start position:0% +there's also some particular event that +may occur under each scenario and we + + align:start position:0% +may occur under each scenario and we + + + align:start position:0% +may occur under each scenario and we +know how likely it is to occur under + + align:start position:0% +know how likely it is to occur under + + + align:start position:0% +know how likely it is to occur under +each scenario this is our model of the + + align:start position:0% +each scenario this is our model of the + + + align:start position:0% +each scenario this is our model of the +situation under each particular + + align:start position:0% +situation under each particular + + + align:start position:0% +situation under each particular +situation the model tells us how likely + + align:start position:0% +situation the model tells us how likely + + + align:start position:0% +situation the model tells us how likely +event B is to occur if we actually + + align:start position:0% +event B is to occur if we actually + + + align:start position:0% +event B is to occur if we actually +observe that B occurred then we use that + + align:start position:0% +observe that B occurred then we use that + + + align:start position:0% +observe that B occurred then we use that +information to draw conclusions about + + align:start position:0% +information to draw conclusions about + + + align:start position:0% +information to draw conclusions about +the possible causes of B or conclusions + + align:start position:0% +the possible causes of B or conclusions + + + align:start position:0% +the possible causes of B or conclusions +about the more likely or less likely + + align:start position:0% +about the more likely or less likely + + + align:start position:0% +about the more likely or less likely +scenarios that may have caused this + + align:start position:0% +scenarios that may have caused this + + + align:start position:0% +scenarios that may have caused this +event to occur and that's what inference + + align:start position:0% +event to occur and that's what inference + + + align:start position:0% +event to occur and that's what inference +is having observed B we make inferences + + align:start position:0% +is having observed B we make inferences + + + align:start position:0% +is having observed B we make inferences +as to how likely a particular scenario + + align:start position:0% +as to how likely a particular scenario + + + align:start position:0% +as to how likely a particular scenario +AI is going to be and that likelihood is + + align:start position:0% +AI is going to be and that likelihood is + + + align:start position:0% +AI is going to be and that likelihood is +captured by these conditional + + align:start position:0% +captured by these conditional + + + align:start position:0% +captured by these conditional +probabilities of AI given the event B so + + align:start position:0% +probabilities of AI given the event B so + + + align:start position:0% +probabilities of AI given the event B so +that's what the Bayes rule is doing + + align:start position:0% +that's what the Bayes rule is doing + + + align:start position:0% +that's what the Bayes rule is doing +starting from conditional probabilities + + align:start position:0% +starting from conditional probabilities + + + align:start position:0% +starting from conditional probabilities +going in one direction it allows us to + + align:start position:0% +going in one direction it allows us to + + + align:start position:0% +going in one direction it allows us to +calculate conditional probabilities + + align:start position:0% +calculate conditional probabilities + + + align:start position:0% +calculate conditional probabilities +going in the opposite direction it + + align:start position:0% +going in the opposite direction it + + + align:start position:0% +going in the opposite direction it +allows us to revise the probabilities of + + align:start position:0% +allows us to revise the probabilities of + + + align:start position:0% +allows us to revise the probabilities of +the different scenarios taking to + + align:start position:0% +the different scenarios taking to + + + align:start position:0% +the different scenarios taking to +account the new information and that's + + align:start position:0% +account the new information and that's + + + align:start position:0% +account the new information and that's +exactly what inference is all about as + + align:start position:0% +exactly what inference is all about as + + + align:start position:0% +exactly what inference is all about as +we're going to see later in this + + align:start position:0% +we're going to see later in this + + + align:start position:0% +we're going to see later in this +less \ No newline at end of file diff --git a/l-8-c7g-LY4.txt b/l-8-c7g-LY4.txt new file mode 100644 index 0000000000000000000000000000000000000000..63fb3391800f364204bb7d6d4c899c826eaab8e2 --- /dev/null +++ b/l-8-c7g-LY4.txt @@ -0,0 +1,2741 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation, or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So we will have +weekly quiz tomorrow. + +There's been a lot of coverage, +and so to focus you + +a bit, I'm going to confine the +weekly quiz to glasses and + +chemical kinetics. + +So you don't have to worry +about diffusion. + +We'll catch up on that, +but I know there's so + +much material there. + +Let's keep it confined to +glasses and chemical kinetics. + +And I'll be available +today 4:30 to 5:30. + +If you can't be at that time, +send me a note, and I'm sure + +we can figure out a time +to get together. + +So what I want to do today +is to start a new unit. + +We're going to start talking +today about solutions, and do + +some solution chemistry, OK? + +Today we talk about solutions. + +And you might initially +say, why are we + +talking about solutions? + +This is solid-state chemistry. + +I think up until now, you've +seen that it's pretty rare + +that we use solids in +their pure form. + +We usually have mixtures. + +So for example, when we studied +glasses, we modified + +the glasses with an alkaline +earth oxide. + +Well we, in fact, were +making a solution of + +more than one component. + +So it's to get certain +properties + +that we study solutions. + +Secondly, coming out of liquid +phase is a way to make solids. + +So in terms of processing, we +need to understand something + +about solutions. + +And then lastly, we're going +to be studying, towards the + +end of the semester, a big +unit on biochemistry. + +And biochemistry, why, you +say, biochemistry? + +Why is he doing biochemistry? + +I thought this was solid-state +chemistry. + +We are solid-state devices, but +we're made of soft matter. + +At least the exoskeleton +is soft matter. + +The endoskeleton is +ceramic, right? + +Our bone structure is ceramic. + +Hydroxyapatite, calcium +hydroxyapatite, and the + +outside is a polymer. + +So look at this. + +Confirmational changes +in polymer. + +But the chemistry, the +biochemistry, so much of it + +takes place in aqueous +solution. + +So hence, we better +know something + +about aqueous solution. + +So to this, we go almost right +back to the first day. + +You remember, was the second +lecture, and we showed this + +figure, and all the different +categories of matter. + +And we started over here with +elements, and we moved into + +some pure substance compounds, +et cetera, et cetera. + +Now we're going to move +over to here. + +So homogeneous mixture +containing uniform composition + +and properties, as opposed +to a heterogeneous mix. + +So we're now over here. + +We're working our way +through the diagram. + +All right. + +So let's get a couple of +basic definitions up. + +So the solution is really +a mix of at least two + +constituents. + +One, the majority constituent +is called the solvent, and + +then we can have one +or more solutes. + +So the solvent, this is the +majority constituent, and then + +the solutes are the minority +constituents. + +And in some instances, +it's pretty hard to + +tell which is which. + +And as far as types +of solutions, I + +want to broaden this. + +You know, when I say solution, +you're probably thinking about + +aqueous solution. + +But I want to take a minute and +work through this chart. + +And this is all posted, +so you don't have to + +write it all down. + +Just follow with me. + +So most of the general chemistry +subjects will just + +stop at the end of +the first line. + +They'll treat solutions +as aqueous solutions. + +But in material science, we +think of things broadly. + +So a good example of a simple +aqueous solution is sodium + +chloride and water. + +Sodium chloride is the solute +and water is the solvent. + +But you can have a +liquid solute. + +So wine-- + +in case you've ever encountered +this beverage, + +it's primarily water, but it +can contain up to about 14% + +ethyl alcohol, and there are +other constituents that give + +the color and the flavor +and so on. + +And you can have a gas in a +liquid, and that would be + +seltzer, where CO2 +is dissolved. + +It's actually dissolved. + +If you take a look at a bottle +of bubbly water on the shelf, + +you don't see the bubbles. + +The carbon dioxide is +actually dissolved. + +You can have a gas as a solvent, +and air would be an + +example of that, where the +solvent is nitrogen. + +And then we have as solutes +oxygen, argon, carbon dioxide, + +if you live next to a power +plant, it's sulfur dioxide, if + +you live next to an aluminum +smelter, it's + +tetrafluoromethane, and so on. + +So we have all kinds of +solutes in the air. + +And then we can have +solid solutions. + +And OK, as soon as you see the +word solid, you know, that + +means you're 3.091. + +So what do we see for solids? + +Metal alloys. + +We saw carbon dissolved +in iron. + +Well, that's a solution. + +It's homogeneous, single phase, +just as the definition + +on that chart 1.11 said. + +Semiconductor, boron doping into +silicon, the boron sits + +on a silicon lattice site. + +So this is a true solution. + +The boron is the solute, and +silicon is the solvent. + +We can have the ceramic. + +We talked about the +oxygen sensor. + +The oxygen sensor is zirconia, +which has been stabilized with + +the addition of calcium oxide. + +As one example. + +In contemporary work, they +might use another oxide. + +But what's the purpose +of the calcium oxide? + +Well, I told you that it's +to increase the vacancy + +population, give you +a rapid response + +on your oxygen sensor. + +And as we're going to learn +later, that's true, and + +there's a second value in +putting in the calcium oxide. + +And it stabilizes, that's why +they use the term stabilize, + +it stabilizes the cubic +form of zirconia. + +Zirconia has a different +crystallographic + +modifications. + +The cubic one is the one that +gives us the best ability to + +transfer oxygen, and the +addition of calcium oxide as a + +solute, the calcium ions +actually sit on the zirconium + +lattice, that's a true +solid solution. + +It also makes the cubic zirconia +stable, and with + +Christmas coming, you know, it's +the poor man's diamond, + +and that's the same +material there. + +And to modify a glass, as I +mentioned earlier, adding a + +alkaline earth oxide breaks +the silicate network. + +That's a solution. + +Now here's an inverse one, +where the solid is the + +solvent, and the liquid +is the solute. + +So this was dentist's office +practice going back to the + +time when I was your age. + +If you had a feeling, the +dentist had silver and mercury + +in the dentist's office, and +would add liquid mercury to + +silver and make up this amalgam, +and then jam that + +into the tooth. + +Actually, that was the B +part of the operation. + +There was this dentist here in +the United States, and if I + +could find him, I would like +to have a word with him. + +But he had this theory. + +You see, the amalgam is +a metallic alloy. + +And so obviously, it has +metallic bonding. + +And the tooth is-- + +it's a ceramic. + +So what kind of bonds are going +to form between a metal + +and a ceramic? + +They're not very good. + +So this dentist had the theory +that the way to increase the + +bonding capability of the +amalgam to the tooth was to + +maximize contact areas. + +So when you went in with a tiny, +tiny little cavity, the + +dentist would drill the tooth +out, removing about 75% of the + +volume of the tooth, and then +they would make this amalgam + +and shove that in. + +And you'd wear that for about +20 years, until one day you + +bite into a muffin that's got a +little piece of walnut shell + +in it, and the amalgam +flexes, and your + +thin-walled tooth goes bang! + +Like that. + +And now you get to go back to +the dentist's office for yet + +some more medieval treatment. + +Actually, things have +improved somewhat. + +Thanks to material science. + +But they're not using this +amalgam anymore. + +But there are a number of us who +are still walking around + +with silver and mercury +in our mouths, and-- + +yeah. + +Enough about my dental +problems. + +Now let's go on to +intercalation. + +You can put a gas +into a solid. + +And I told you about this one, +where if you want to store + +hydrogen, and this is a big +problem, if we're going to + +talk about hydrogen-powered +vehicles. + +A problem as big as, how to +get the fuel cell cheap + +enough, is where are you going +to store the hydrogen on the + +car, and one of the materials +that's been proposed is this + +alloy of lanthanum and nickel +that can intercalate huge + +amounts of hydrogen. + +So that forms a solid +solution. + +So those are examples of +solutions, and we're going to + +go back and make sure that we +cover the basic Gen Chem at + +the top here. + +But I want you know +that solution + +chemistry is very broad. + +Now when you dissolve something, +you actually have + +things down at the +atomic level. + +So for example, in brine, you +actually have below two + +nanometers as particle size. + +You actually have sodium ions +and chloride ions dissolved + +completely, which means that +the solution is clear, + +colorless, and transparent +to visible light. + +Water is clear, colorless, +transparent to visible light. + +If you had sodium chloride, it +remains clear, colorless, + +transparent to visible light. + +You can't filter, and you can't +wait for the sodium + +chloride to settle out, because +it's bonded within the + +structure of the liquid water. + +And this has implications. + +There's so much water on the +planet, but there's not so + +much fresh water +on the planet. + +And desalination can't be +accomplished by filtration. + +A filter that had a pore size +small enough to trap sodium + +ions, the pore size would be +so small, water molecules + +couldn't go through. + +So this is the concept. + +At the other end, you can get +something called a suspension, + +where the particle size is +greater than about 1,000 + +nanometers, and blood is a good +example of that, where + +it's opaque. + +Visible light doesn't go +through, but you can filter + +out some of the matter +in blood. + +And if you let it sit for a +while, it'll settle in it + +gravitational field. + +And in between, you have this +whole zone of colloids. + +And so between colloids and +suspensions, the only + +difference is particle size. + +And this whole thing we would +just call a dispersion of + +another phase, either another +solid phase, or + +another liquid phase. + +And it's kind of an interesting +physical chemistry + +about the dispersion, +what makes it work. + +For example, in milk, milk +is a good example of a + +dispersion. + +You have a fatty phase, and +you have an aqueous phase. + +The aqueous phase, where +all the minerals are. + +Why? + +Because the minerals are-- + +what kind of compound? + +They're not metallic, they're +not covalent. + +They're ionic. + +The ionic compounds dissolve in +the aqueous phase, and then + +in the fatty phase, that's +where you have the + +protein and so on. + +But the fatty phase is clear and +colorless, and the aqueous + +phase is clear and colorless. + +And yet milk is white. + +It's, as the term implies, +it's milky. + +Why? + +What's going on? + +You have a second phase here. + +This could be the fatty phase, +and this is the aqueous phase. + +They're both clear and +colorless, but they have + +different indices +of refraction. + +And since this has n fatty +phase, and this has n aqueous + +phase, this interface +scatters the light. + +So if you want to start a +business, if you want to try + +to tailor the index so that the +index of the aqueous phase + +matches the index of refraction +of the fatty phase, + +you'd have the two dissolve, +one and the other, and it + +would be transparent, +divisible light. + +So you would have milk +that isn't milky. + +I mean, the public would +be very confused. + +But anyways. + +So that's what you do. + +So why does this thing +not settle? + +Because they do have a density +difference, and again, going + +back to the days when I was not +a college student but a + +youngster, there was still +this form of milk called + +pasteurized milk. + +Well, all milk is pasteurized, +but this milk was not + +homogenized. + +And what would happen is, there +was this person that + +would deliver milk. + +This was a borosilicate +glass bottle. + +And here would be the cream. + +The cream would rise +to the top. + +We have all these expressions +in our language. + +And then this would be the milk +here, and you could skim + +this off for coffee or sugar, +and then this would be a + +low-fat milk. + +But people wanted this all +mixed, so then they went to + +homogenized milk. + +So what is homogenized milk? + +This is your red cap, now. + +All the milk is homogenized. + +This was a big thing. + +This was simply called +pasteurized. + +I'm going to get to the physical +chemistry here. + +It's very interesting. + +Because this is lower density, +and yet in homogenized milk it + +doesn't rise. + +So let's take a look at what +goes on in the physical + +chemistry of homogenized milk, +because it's all about these + +various systems. So I'm going +to take this particle here, + +and its sum insoluble cluster. + +And I'm not specifying +the cluster size. + +It's probably greater than +about two nanometers. + +So there are two forces +acting on this. + +There's a settling force and +there's a buoyancy force. + +Obviously, otherwise +it wouldn't float. + +So there's some kind of +a buoyancy force. + +Settling force and +a buoyancy force. + +Well, the settling force, this +is just the gravity. + +Right? + +This is the force of gravity. + +And we know the force +of gravity. + +That goes with the mass. + +Come on, get that cell +phone out of here. + +This force of gravity goes as +the mass, and the mass, we + +know, goes as the volume. + +And the volume goes as the +cube of the radius. + +I'm assuming this is a spherical +particle, all right? + +Now, the buoyancy force. + +The buoyancy force is +the interfacial + +force between the two. + +There's some binding +across here. + +Maybe weak van der Waals, or +if this fatty phase has + +molecules in it that are polar, +then there could be + +dipole-dipole interaction. + +But in any case, there's +some kind of an + +interfacial force here. + +And this is all chemical +bonding + +between solute and solvent. + +But you see, the force +is a weak force. + +If it were a really strong +force, it would + +dissolve this thing. + +It won't quite dissolve it, +but there is some kind of + +dipole-dipole weak force. + +And this one here is operating +across the surface area. + +That's the contact. + +So this force goes as the area, +and area goes as the + +square of the radius, +whereas mass goes as + +the cube of the radius. + +So you know, from your math, +that r cubed dominates r + +squared, but only at large r. + +It's not always the +case, is it? + +Maybe before you got here, +you thought that. + +But now that you've been at +MIT a few months, you know + +that r squared can dominate +r cubed at small r. + +Interfacial forces dominate. + +And that's exactly what happens +in these dispersions, + +and that's why they +don't settle out. + +Now, homogenized milk is simply +milk that has been + +agitated in such a way as to +reduce the fat globule size + +below a critical value so that +these interfacial forces hold + +the fat globules +in suspension. + +If you waited long enough, they +would agglomerate and + +settle, but that time is +probably longer than the shelf + +life of the milk. + +So the milk probably spoils +before stuff settles out. + +So this is all very important +to understand. + +The range that exists between +insolubility and this sort of + +clustering, and suspension, +and so on. + +By the way, a lot of +pharmaceuticals are like this. + +A lot of pharmaceuticals. + +So when it says, shake +well before + +using, they're not kidding. + +Because the active ingredient +will settle. + +And you're drinking just the +solvent, just the vehicle. + +And all of the potency is on +the bottom of the bottle. + +Shake that thing up! + +I can't say what it does +to the taste, but + +that's another problem. + +Actually, I threw in +this slide here. + +We're not going to spend any +time on it, but you can look + +at it at some point. + +This is a whole taxonomy +of colloids. + +Solid-liquid emulsions, +aerosols, they're all part of + +this magic zone between +solubility and + +just brick, all right? + +There's this whole fine, +pardon the pun, + +the whole fine structure. + +OK, So let's get to +the chemistry. + +Obviously there's something to +do with bonding here, right? + +So here's a simple experiment, +and this is taken right from + +the reading. + +So I've just taken this episode +that is written up in + +the reading. + +So we've got two beakers +here, and in each + +beaker, we have a bilayer. + +We've poured in some carbon +tetrachloride, liquid, and + +we've poured in some water. + +And these two are immiscible, +because carbon tetrachloride + +is obviously a non-polar liquid, +and water is a polar + +liquid with hydrogen +bonding capability. + +And in one beaker, we introduce +crystals of iodine. + +In the other beaker, we +introduce crystals of + +potassium permanganate. + +And then we shake them +up, and we wait. + +And eventually we see that on +the left, the iodine dissolves + +in the carbon tetrachloride. + +And we're using the purple +color as an indicator. + +And this is kind of cute, +because both potassium + +permanganate and iodine will +render things purple. + +So you're comparing +purple to purple. + +They could have chosen something +else, but this is + +kind of cute. + +All right. + +So here you end up with a +solution of iodine and carbon + +tetrachloride, whereas on the +right side, you end up with a + +solution of potassium +permanganate and water, and + +nothing in the carbon +tetrachloride. + +So what can we infer +from this? + +Well, let's take a look at the +possible interactions. + +So first of all let's +categorize H2O. + +This is polar, it's a polar +liquid, with hydrogen bonding + +capability. + +Carbon tetrachloride +is non-polar. + +It's very toxic. + +When I was a child, we had this +in the medicine cabinet. + +It's a non-polar solvent. + +It's fantastic for getting +grease stains off. + +Every man had this. + +With a little handkerchief, +you'd take a little grease + +stain off your tie. + +You can't buy this stuff. + +You can't even guy it for +research anymore. + +It's too bad. + +It's great stuff. + +Highly toxic, though. + +But you know, there's +a time and a place. + +All right. + +So then here's iodine. + +Iodine, we know, is non-polar. + +It's a homonuclear molecule, +it has to be non-polar. + +And so what holds iodine +together in the crystal? + +There's only one bond, and +that's van der Waals, right? + +It's a van der Waals solid, +whereas potassium permanganate + +is an ionic solid. + +Potassium permanganate is ionic, +and it consists of + +potassium cations and +permanganate anions. + +And what we find is that the +non-polar solute dissolves in + +the non-polar solvent, and the +ionic solute dissolves in the + +polar solvent with hydrogen +bonding capability. + +So from this, we can infer the +general rule, which is + +encapsulated in the language +used in chemistry textbooks. + +Like dissolves like. + +And what they're really saying +here, is that like solutes + +dissolve in like solvents. + +Solute-solvent is like +dissolves like. + +OK. + +It's a good place to +start, but it's + +an incomplete picture. + +So I want to show you +that there's some + +sophistication here. + +This is taken from one +of the other books. + +And it shows just the rules for +ionic compounds in water. + +And I just showed you, from this +example, that the ionic + +compound dissolved in water. + +And what you see here is that +some ionic compounds dissolve + +in water, but there's +a whole set or + +insoluble ionic compounds. + +So it's not straightforward. + +But we know from 3.091, we know +that we can make sense of + +this on the basis +of competition. + +Competition between what holds +the compound in the solid + +state versus what will pull +it into the liquid state. + +So for example, we can compare +sodium chloride, which we know + +dissolves in water. + +So sodium chloride, as a +crystalline solid, will + +dissolve to form sodium chloride +aqueous solution. + +Whereas if you look at magnesium +oxide, which is also + +an ionic crystal, it does not, +to any standard imaginable, + +dissolve to form an aqueous +solution of magnesium oxide. + +And what's the difference +here? + +The difference here is, compare +solvation energy, in + +other words, the energy that you +got by pulling this into + +solution, and forming bonds +between sodium and chlorine in + +water, with the crystallization +energy. + +And what's that all about? + +Well, that's the Madelung +constant, remember? + +Madelung constant. + +q1 q2 over 4 pi epsilon +0 r, where this + +is the cation anion. + +And you can see here that sodium +chloride has sodium + +cations and chloride anions, and +there's a certain binding + +energy in the crystal. + +Magnesium has 2 plus. + +Oxide is 2 minus. + +The binding energy between +magnesium and oxygen is so + +great that there's no driving +force to dissolve. + +Now, I don't expect you to be +able to look at this and tell + +me whether something's going +to dissolve or not. + +But if I were to say to you, +explain why sodium chloride + +forms solutions with water, and +magnesium oxide doesn't, + +that you could go through +this rationalization. + +And here's a cartoon from the +textbook that tries to + +illustrate this solvation. + +Here you can see a crystal of +sodium chloride, in the + +inimitable fashion, as drawn by +chemistry books, where the + +chloride ion is green, and +the sodium ion is blue. + +And that's OK. + +I can live with the +color-coding, as long as we + +agree amongst ourselves, these +ions are clear and colorless, + +because they have octet +stability in + +their electronic shell. + +And here's water, with the +hydrogen shown in white, and + +the oxygen shown in red. + +And you can see that the oxide +end, the oxygen end, the delta + +negative end of the water, is +trying to wrest sodium cation + +out of the lattice, +and ultimately + +surround it by a cage. + +And the same thing here. + +You see the hydrogen ends of +the water trying to pull + +chloride out, and ultimately +surround it with + +a water-like cage. + +So this is the competition +I was talking about. + +In the case of sodium chloride, +water wins. + +In the case of magnesium +oxide, water loses. + +The binding energy between +magnesium and oxygen and the + +crystal dominate. + +So you don't see +that solvation. + +OK. + +Let's talk about metrics now. + +Let's look at some metrics +of solubility. + +It's quantifiable. + +So we can express a measure of +solubility in terms of a + +quantity known as molarity. + +So we can express moles of +solute per liter of solvent. + +And this is called molarity, and +the symbol is capital M. + +So we can say, for example, a +1 molar solution of sodium + +chloride in water, we'll write +1 molar NaCl, and then we'll + +write subscript aq, +meaning aqueous. + +So it's an aqueous solution at +a concentration of 1 mole of + +NaCl per liter. + +And the liter is named after a +person, so that's capital L, + +per liter of solution. + +And remember, the solution +is the sum of + +the water plus solute. + +For dilute solutions, there's +very little difference between + +the total amount of water and +the total amount of solution. + +But in certain instances, the +presence of the solute + +actually has a volumetric +change on here. + +So strictly speaking, it's +per liter of solution + +And as I've shown you, there +are degrees of solubility. + +So people represent the +threshold of solubility as c + +of the solute. + +When c of the solute is less +than about a million molar, + +0.001 molar, we call +this insoluble. + +So something is vanishingly +soluble, we + +say that's the value. + +So we'll call this +the threshold. + +And then, something that's quite +soluble, we'd say that + +the concentration of the solute +starts to exceed at + +about 0.1 molar. + +And then we would say, that +qualifies as soluble. + +So now let's look at two +extremes in solubility, + +operating off of this. + +So in the one case, we can +have complete solubility. + +So examples of that, where +things are completely miscible + +in one another. + +Complete solubility. + +By the way, some people will +use the term miscibility. + +When something is miscible +it means it's soluble. + +Same idea. + +If something is insoluble, some +people might say it's + +immiscible. + +Same thing. + +OK? + +So complete solubility is +ethyl alcohol and water. + +You can mix them in +all proportions. + +Continuously variable. + +On the solid alloy is +silver and gold. + +Silver and gold, you can make +alloys of any composition + +between 100% gold +and 100% silver. + +Now, that's the exception. + +Most cases are situations +of limited solubility. + +So they go up to a maximum, +which we can denote C-star or + +C saturation. + +This is the maximum +solubility. + +So an example of something +that's sparingly soluble in + +water is silver chloride. + +Let's look at silver chloride. + +So silver chloride, I'm going to +start here, silver chloride + +as a crystal, and I'm going +to dissolve that in water. + +So that gives me AgCl aq. + +So that's just simply the +formation of an aqueous + +solution of silver chloride. + +And when the reaction moves from +left to right, we call + +that dissolution. + +The silver chloride is +dissolving, and when the + +system moves from right to +left, we call that-- + +now here I'm going to nitpick +with the book. + +The book calls the left reaction +crystallization. + +And that's correct. + +It is crystallization in this +case, because silver chloride + +is a crystal. + +But it is possible, in other +systems, to have the solute + +come out of solution, and +make a solid that is + +noncrystalline. + +And you know that all crystals +are solids, but not all solids + +are crystals. + +You can have an amorphous +solid. + +So what would happen if you were +to bring out of solution + +an amorphous solid? + +It would be silly to call +it crystallization. + +So I prefer to use the +term precipitation. + +And there's another term that +you can use, and I learned + +this one from reading the +literature of geochemistry. + +What the geochemists call the +reaction going from solution + +to make a solid, they say +the system exsolves. + +This is dissolve, +this is exsolve. + +So this is called exsolution. + +It's amazing what you can +do when you know a + +little bit of Latin. + +So this exsolves. + +So that's the exsolution, or the +crystallization reaction. + +Now I'm going to show you what +won Arrhenius his Nobel prize. + +Arrhenius did not get the Nobel +prize for his brilliant + +work on activation energy. + +He got his Nobel prize on the +theory of electrolytic + +dissociation, which was, people +knew that you could + +dissolve salts and water, but +they didn't know how. + +And it was Arrhenius who said +that the salts go into + +solution by dissociating +and forming ions. + +So goes in as Ag plus Ag plus +aq plus chloride ion-- + +thank you. + +And that, ladies and gentleman, +was a Nobel prize + +for Arrhenius. + +And you can see that there's +a relationship between the + +amount of silver chloride +and the amount of ions. + +So there's a mass balance there, +that the concentration + +of silver chloride dissolved, in +fact, equals, in this case, + +by stoichiometry, the +concentration of Ag plus, + +because of the nature of the +dissociation reaction on a + +mass balance basis. + +And that also equals the +concentration of the + +chloride ion, OK? + +So that's the way we can +look at the system. + +And how do we know that this +thing has limited solubility? + +Well, there's various ways of +measuring it, and one of them + +involves conductivity. + +Here's the conductivity +of pure water. + +And you know that water has +very, very poor conductivity, + +and in fact, what's happening +here, when we add silver + +chloride is, we're adding charge +carriers, because the + +audience are charged species. + +So they can carry charge. + +And you can see that this is a +measure of conductivity as a + +function of silver chloride +concentration. + +And as you add silver chloride +to higher and higher values, + +the conductivity goes up. + +And look at even the tiniest +amount of silver chloride has + +a conductivity that's about, +what, half an order of + +magnitude higher than +the conductivity + +of pure water itself. + +So I would say that this is +akin to doping, isn't it? + +So up here, when you've got 10 +to the minus 6 Siemens per + +centimeter conductivity, that +aqueous solution is + +demonstrating the extrinsic +behavior. + +This is very similar +to doping. + +And at some point, we get to +this value here, around 10 to + +the minus 5 moles of silver +chloride per liter, and then + +adding more silver chloride has +no impact on conductivity. + +Which tells you that you've +hit saturation. + +This is akin to adding more and +more sugar to the cup of + +tea, until finally the sugar +just falls to the bottom. + +You can stir all you want, but +you won't get it to dissolve, + +because you've hit saturation. + +So that indicates the presence +of a saturated solution. + +And so we can talk about that +value, and we can say that for + +silver chloride, the +concentration at saturation is + +equal to 1.3 times 10 to the +minus 5 moles per liter. + +Moles of silver chloride +per liter. + +And obviously, that's equal to, +according to that, it's + +equal to the silver +ion concentration. + +I'm going to use square brackets +to indicate moles of + +silver, ion per liter +of solution, which + +is also equal to-- + +pardon me-- it's also equal to +the chloride ion concentration + +at saturation. + +Now I'm going to ask you +a simple question. + +Suppose I've got a beaker here, +and I know the maximum I + +can get here, the maximum is 1.3 +times 10 to the minus 5. + +Now this is a really +simple question. + +Suppose I am about to add +silver chloride-- + +let's say this is +1 liter already. + +All right? + +I've got one liter. + +And you'd tell me, well, you can +put in 1.3 times 10 to the + +minus 5 moles to get +the saturation. + +Suppose instead of 1 liter of +pure water, I had 1 liter of + +water already containing, say, +1 times 10 to the minus 5 + +molar silver chloride. + +Well, that's kind of +obvious, isn't it? + +I'm only going to be able to put +0.3 moles in, because 0.3 + +times 10 to the minus 5, because +I've already got + +silver chloride in there. + +That's easy. + +Now let's make the question +a little more interesting. + +Suppose instead of a certain +amount of silver chloride in + +there, I have no silver +chloride in there. + +But I've got, say, 0.1 molar +sodium chloride. + +It's a salt. + +It's a difference salt. + +So the question is, does the +presence of a different salt + +have an impact on how much +silver chloride I can put into + +this solution? + +And the answer is, yes. + +The answer is yes. + +So what we find is that the +presence of the other salt, in + +this case, has an impact, +because sodium chloride goes + +in as sodium plus, and +chloride minus. + +So there's already a boatload of +chloride ion in there, and + +that has an impact on +this relationship. + +So how do we answer the +question, what is the + +solubility of silver chloride +in the presence of other + +chloride ions? + +And for that, we define +something called the + +solubility product. + +And you need it in order to +answer the question, how do + +you determine the solubility +of a solute when there are + +other solutes present already? + +And it's denoted capital K, +lowercase sp, subscript. + +Solubility product. + +And it's equal to simply +the ion products of the + +constituents. + +So the solubility product of +silver chloride is the product + +of the silver ion concentration, +and the + +chloride ion concentration. + +And you know that in a solution +of silver chloride + +alone, if nothing else, that +the concentration of silver + +ion equals the concentration +of chloride ion. + +That's the whole business +of dissolving by itself. + +And so I can then just +say that Ksp. + +will then equal the +concentration of silver ion + +squared, which we also know is +equal to the concentration of + +silver chloride aqueous. + +See, all of these +are the same. + +So this solubility +is the same. + +I can just put that in, which +is just concentration of + +silver chloride. + +Square that. + +So if I square 1.3 times 10 to +the minus 5, I end up with a + +solubility product of 1.8 times +10 to the minus 10. + +So now I can use this in order +to determine how much + +solubility I get in the presence +of another salt. + +So in this case, I'm going to +put 0.1 molar sodium chloride. + +And these are strong salts, so +we're going to get complete + +dissociation. + +Gives me 0.1 molar sodium ion, +and 0.1 molar chloride ion, + +when it dissociates. + +Now you see the difference. + +Because the silver chloride, by +itself, gives me 10 to the + +minus 5 molar chloride ions. + +When I add sodium chloride, +I get 4 as a + +magnitude more chloride. + +So let's go back to the Ksp. + +So Ksp, this is for +silver chloride. + +Ksp for silver chloride is +going to be equal to the + +silver concentration and the +chloride concentration. + +And in this case, the silver +concentration is just equal to + +whatever that solubility is. + +Because there's only source +of silver ion, + +and it's silver chloride. + +So I can write that as + +concentration of silver chloride. + +That's good. + +And now this one here is what? + +I've got two sources. + +I've got silver chloride, I +I've got sodium chloride. + +So it's going to equal +this thing here. + +0.1 plus whatever I get +from silver chloride. + +And it's vanishingly +small, isn't it? + +The concentration of silver +chloride, whatever it is. + +This is nothing, so I'm just +going to neglect it. + +It's dominated now. + +The chlorine is flooded by +the silver chloride. + +And this product +is a constant. + +That's still equal to +10 to the minus 10. + +So I can turn this around and +solve for the concentration of + +silver chloride, which +is equal to the + +concentration of silver io. + +And that's equal to, what is +it, 10 to of the minus 10 + +divided by 0.1, which +then gives me-- + +what's the number here? + +Plug that in. + +And I end up with 10 +to the 1.8 times 10 + +to the minus 9 molar. + +Right? + +So look. + +Look at what's happened by +having the chloride present + +from sodium chloride in +such a large amount. + +It's repressed. + +It has repressed the +dissolution. + +The presence of chloride then +has a negative impact on + +solubility, and instead of +having 10 to the minus 5 + +molar, it's down to 10 to +the the minus 9 molar. + +And this effect of repressing +solubility by adding a second + +solute is called the common +ion effect, OK? + +Solubility repression by second +solute is known as the + +common ion effect. + +And this is used +in processing. + +If I want to trigger +the precipitation-- + +see, if I started with a +solution containing 10 to the + +minus 5 molar of silver +chloride, and I throw in some + +sodium chloride, it'll start + +precipitating out silver chloride. + +So if I wanted to make a fine +precipitate of silver + +chloride, I make a pregnant +solution. + +And I could drop the +temperature, because you can + +imagine that solubility is a +function of temperature, or I + +could keep it isothermal, throw +in some sodium chloride, + +and out comes silver chloride. + +So since the common ion effect +on it and its value in + +processing. + +OK. + +Good. + +Well, I think I'm going +to hold it there. + +I"ll show you just +one more thing. + +If you've got stoichiometry +like this-- + +this is a difluoride +of magnesium. + +If it goes into solution, you +get magnesium cation plus 2 + +fluoride anions. + +And so if I wrote the Ksp for +this reaction, it would be the + +product of the magnesium +concentration and the fluoride + +ion concentration. + +Because there's the two +here, this is squared. + +So this, too, will transfer up +there, and then throw in some + +sodium fluoride, and cause the +other thing to exsolve, and + +away we go. + +All right. + +I've got a couple of +things to show you. + +We're talking a lot +about Arrhenius. + +This is a book I have. It's an +English translation of a book + +written by Arrhenius in the late +1800s, and it was printed + +in English around 1908. + +And Arrhenius was a genius. + +He wrote on all sorts +of topics here. + +Biology, physics, you name it. + +And one of the things and he +was interested in was the + +origins of the earth. + +So this chapter is called, +Celestial Bodies as Abodes of + +Organisms. Already speculating +on whether you could have life + +as we know it exist elsewhere +in the universe. + +And one of the things he talks +about is global warming. + +So this is Arrhenius +on global warming. + +I'll read you the last paragraph +of this chapter. + +There had been some major +volcanic eruptions that had + +caused cooling when Krakatoa +in 1883 and + +Martinique in 1902. + +Major plumes of soot that caused +dramatic decreases in + +temperature. + +So now here comes the +last paragraph. + +We often hear lamentations that +the coal stored up in the + +earth is wasted by the +present generation-- + +remember, this is written +100 years ago-- + +without any thought +of the future. + +And we are terrified by the +awful destruction of life and + +property which is followed the +volcanic eruptions of our day. + +We may find a kind of +consolation in the + +consideration that adheres +in every other case. + +There is good mixed +with the evil. + +By the influence of the +increasing percentage of + +carbonic acid in the +atmosphere-- that's CO2-- + +we may hope to enjoy ages with +more equitable and better + +climates.-- + +Remember, he's a Swede; +it's cold-- + +especially as regards the colder +regions of the earth, + +ages when the earth will bring +forth much more abundant crops + +than at present for +the benefit of + +rapidly propagating mankind. + +So it's interesting +to see the world-- + +it's a great book to read. + +And you can see people in the +1830s were already calculating + +heat transfer coefficients +to how much + +the earth was changing. + +We're going to post these +to the website. + +This was, last year, in +the New York Times. + +Every Tuesday they have +a science section. + +And this was about glass. + +And very, actually, with your +3.091 knowledge, you'll read + +this like a newspaper, and +it'll be very easy. + +And they go through +the structure. + +Here's the structure +of a window glass. + +You can see the network, +former network + +modifier, and so on. + +And they talk about how +difficult it is from a first + +principle's standpoint to model +the structure of glass. + +These oxide glasses are complex +and not easy to model. + +So when you're trying to +engineer the glasses, instead + +of trial and error, it's hard +to do so by theory. + +And it talks about some efforts +at theory, and so on. + +And the last thing I want +to talk about is + +bulk metallic glasses. + +You recall that I showed you +metallic glass that was made + +by melting gold silicon, +and dripping it onto a + +water-cooled copper wheel that +was zooming around to give us + +a cooling rate of about a +million degrees a second. + +And those strips had +to be very, very + +thin, the metal strips. + +Because you've got liquid +dripping down, and we're + +pulling the solid away, +and there's a + +finite thickness here. + +Let's use a Greek letter, xi. + +There's a finite thickness xi. + +Because what's happening is that +this is the water-cooled + +copper wheel, and you're +extracting heat here. + +But eventually, the thermal +conductivity of the metal is + +the limiter. + +In other words, I don't +care how cold. + +You can put this in liquid +helium if you want. + +You can't get the heat through +the metal fast enough. + +And what happens is, when you +look down here, the lower part + +is amorphous and the upper +part is crystalline. + +So you don't end up with +metallic glass. + +You end up with some metallic +glass, and the upper part is + +crystalline. + +So what happens when you end up +with the limitation being + +the thermal conductivity +of the metal? + +At that point, you're +finished. + +And this was typically on +the order of microns. + +And then they got up to, +sort of, submillimeter. + +And that was it. + +So the glass that I showed +you was foil. + +Now what happened was, +with more research-- + +so here we are. + +This is Pol Duwez at Caltech, +gold silicon. + +And this is the thickness +in centimeters. + +So you were down here at some +tens of microns, all right? + +Now, in the '60s, research at +Harvard uncovered a set of + +palladium alloys that had better +thermal conductivity + +and, remember the first day, +about the analogy to the + +musical chairs? + +These things have slightly +more complicated crystal + +structures. + +So for a given cooling rate, the +metal has more difficulty + +finding the proper +lattice site. + +And they were able to make +metallic glasses that were on + +the order of 0.1 centimeters. + +That's still fairly thin. + +And then back to Caltech in the +late '80s, early '90s, and + +a man by name of Bill Johnson +was able to develop a set of + +alloys that can be made +in bulk form. + +Totally amorphous metal. + +And these are known as bulk +metallic glasses. + +And look at the complexity +of the alloy designation. + +So now you see, well, why +are they doing this? + +Because look, this is strength +versus elastic limit. + +So you can either have things +like polymers, that you can + +stretch very, very far, but they +don't have much strength. + +Or you can have things like +certain steels, that are very, + +very strong, but you can't +bend them very far. + +And bulk metallic glass has +put you right up here. + +You have strong alloys +that have very, very + +high elastic limits. + +So they make great golf clubs +and tennis rackets and so on, + +because they can flex way back, +store enormous energy, + +and then spring. + +So here are some bulk metallic +glasses, and + +here's a classic one. + +This is zirconium, titanium, +copper, nickel, beryllium. + +All right, now how +do we get that? + +Well, zirconium and titanium are +body-centered cubic, we've + +got copper and nickel are +face-centered cubic, and + +beryllium is hexagonal +close-packed. + +So the idea here is the +principle of confusion. + +So the alloy is fighting +with itself. + +You know, am I face-centered +cubic, am I body-centered + +cubic, am I hexagonal? + +And this confusion about what +the crystal structure is to be + +leads to quenching and the +disorder of a liquid state, + +and preventing the formation +of grain boundaries, + +dislocations and so on. + +So I want to show you one +example besides golf clubs. + +Dave, could we cut to the +document camera here? + +Get this thing down. + +So this is a-- + +I'm not endorsing the product at +all, but you know, this is + +one of the companies +that makes, this + +is SanDisk, I think. + +And they make these +flash memories. + +This just looks like a another +piece of metal, and in fact, + +it's very disarming, +because they call + +this model the Titanium. + +Well, it has about +13% titanium. + +The interesting thing here, +what's so cool about this, + +this is bulk metallic glass. + +And what's attractive about +the fact that it's bulk + +metallic glass is, that it can +be shaped by casting, from the + +liquid state to very, +very fine precision. + +So you see all of these slots +and everything, and on the + +side, all of this kind of +stuff, and on the end. + +All of this is done by casting +from the liquid + +state, in one operation. + +And this is a clam shell. + +There's two pieces here. + +I don't know if you can see, +but there's two pieces that + +have been sandwiched together. + +You can see on the edge there. + +And the impact that has on +manufacturing costs is + +phenomenal, because normally +you make the basic shells, + +then you have to drill, +and you've got to + +auger out, and so on. + +This thing, one step operation, + +including the labeling. + +There's no subsequent +processing. + +And this is done by a company +out in Michigan + +called Liquid Metal. + +And they've licensed the +technology and so on. + +And again, I'm not trying to +make a commercial thing, but + +I'm just trying to show you that +these ideas of changing + +properties for engineered +materials, you know, are + +around us everywhere. + +And this is relatively recent. + +Bulk metallic glass. + +Fantastic example of structure +property relations. + +OK. \ No newline at end of file diff --git a/lVfm6C51t_Y.txt b/lVfm6C51t_Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..955dfad3fb5fd0834707a60cae7aeb10f8dd7e01 --- /dev/null +++ b/lVfm6C51t_Y.txt @@ -0,0 +1,16656 @@ +align:start position:0% + +what we're talking about today is + + align:start position:0% +what we're talking about today is + + + align:start position:0% +what we're talking about today is +another patent + + align:start position:0% +another patent + + + align:start position:0% +another patent +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +7016539 and of course it's there in + + align:start position:0% +7016539 and of course it's there in + + + align:start position:0% +7016539 and of course it's there in +materials + + align:start position:0% +materials + + + align:start position:0% +materials +on stella and this is going up one level + + align:start position:0% +on stella and this is going up one level + + + align:start position:0% +on stella and this is going up one level +so it builds on what we've done + + align:start position:0% +so it builds on what we've done + + + align:start position:0% +so it builds on what we've done +before and its purpose is to detect + + align:start position:0% +before and its purpose is to detect + + + align:start position:0% +before and its purpose is to detect +objects recognize objects + + align:start position:0% +objects recognize objects + + + align:start position:0% +objects recognize objects +determine their pose in space + + align:start position:0% +determine their pose in space + + + align:start position:0% +determine their pose in space +inspect objects and + + align:start position:0% +inspect objects and + + + align:start position:0% +inspect objects and +you know do do a few other things + + align:start position:0% +you know do do a few other things + + + align:start position:0% +you know do do a few other things +so what's the problem they're trying to + + align:start position:0% +so what's the problem they're trying to + + + align:start position:0% +so what's the problem they're trying to +solve + + align:start position:0% +solve + + + align:start position:0% +solve +uh well + + align:start position:0% +uh well + + + align:start position:0% +uh well +we're trying to manipulate perhaps using + + align:start position:0% +we're trying to manipulate perhaps using + + + align:start position:0% +we're trying to manipulate perhaps using +a robot arm or some other machinery + + align:start position:0% +a robot arm or some other machinery + + + align:start position:0% +a robot arm or some other machinery +objects out in the world and we want to + + align:start position:0% +objects out in the world and we want to + + + align:start position:0% +objects out in the world and we want to +know + + align:start position:0% +know + + + align:start position:0% +know +where they are and what they are + + align:start position:0% +where they are and what they are + + + align:start position:0% +where they are and what they are +and + + align:start position:0% +and + + + align:start position:0% +and +we are going to start off by + + align:start position:0% +we are going to start off by + + + align:start position:0% +we are going to start off by +assuming that we have very accurate + + align:start position:0% +assuming that we have very accurate + + + align:start position:0% +assuming that we have very accurate +edge information that that's + + align:start position:0% +edge information that that's + + + align:start position:0% +edge information that that's +we went through all of that and so + + align:start position:0% +we went through all of that and so + + + align:start position:0% +we went through all of that and so +what came before this so if you if when + + align:start position:0% +what came before this so if you if when + + + align:start position:0% +what came before this so if you if when +we look at the patent in a minute + + align:start position:0% +we look at the patent in a minute + + + align:start position:0% +we look at the patent in a minute +uh the prior art + + align:start position:0% +uh the prior art + + + align:start position:0% +uh the prior art +uh for doing this + + align:start position:0% +uh for doing this + + + align:start position:0% +uh for doing this +had + + align:start position:0% +had + + + align:start position:0% +had +four different + + align:start position:0% +four different + + + align:start position:0% +four different +components so one was + + align:start position:0% +components so one was + + + align:start position:0% +components so one was +blob analysis + + align:start position:0% + + + + align:start position:0% + +and more + + align:start position:0% +and more + + + align:start position:0% +and more +more properly + + align:start position:0% +more properly + + + align:start position:0% +more properly +this is + + align:start position:0% +this is + + + align:start position:0% +this is +binary image processing + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +if there's a way of + + align:start position:0% +if there's a way of + + + align:start position:0% +if there's a way of +distinguishing object from background + + align:start position:0% +distinguishing object from background + + + align:start position:0% +distinguishing object from background +we can create binary images + + align:start position:0% +we can create binary images + + + align:start position:0% +we can create binary images +and binary images have lots of + + align:start position:0% +and binary images have lots of + + + align:start position:0% +and binary images have lots of +advantages one of them is + + align:start position:0% +advantages one of them is + + + align:start position:0% +advantages one of them is +they're much smaller + + align:start position:0% +they're much smaller + + + align:start position:0% +they're much smaller +because you've got one bit instead of + + align:start position:0% +because you've got one bit instead of + + + align:start position:0% +because you've got one bit instead of +eight + + align:start position:0% +eight + + + align:start position:0% +eight +and they're much easier to process + + align:start position:0% +and they're much easier to process + + + align:start position:0% +and they're much easier to process +because they're only that many things + + align:start position:0% +because they're only that many things + + + align:start position:0% +because they're only that many things +you can do with one bit + + align:start position:0% +you can do with one bit + + + align:start position:0% +you can do with one bit +and so + + align:start position:0% +and so + + + align:start position:0% +and so +they require less computing power less + + align:start position:0% +they require less computing power less + + + align:start position:0% +they require less computing power less +memory and in the days when you know + + align:start position:0% +memory and in the days when you know + + + align:start position:0% +memory and in the days when you know +memory was not so easily available that + + align:start position:0% +memory was not so easily available that + + + align:start position:0% +memory was not so easily available that +was very attractive so what do you do + + align:start position:0% +was very attractive so what do you do + + + align:start position:0% +was very attractive so what do you do +with a binary image well + + align:start position:0% +with a binary image well + + + align:start position:0% +with a binary image well +we're not going to do a whole lot of + + align:start position:0% +we're not going to do a whole lot of + + + align:start position:0% +we're not going to do a whole lot of +that but obviously one thing you can do + + align:start position:0% +that but obviously one thing you can do + + + align:start position:0% +that but obviously one thing you can do +is + + align:start position:0% +is + + + align:start position:0% +is +find some kind of threshold + + align:start position:0% +find some kind of threshold + + + align:start position:0% +find some kind of threshold +and then + + align:start position:0% +and then + + + align:start position:0% +and then +you get hopefully connected areas + + align:start position:0% +you get hopefully connected areas + + + align:start position:0% +you get hopefully connected areas +and you can find properties of those + + align:start position:0% +and you can find properties of those + + + align:start position:0% +and you can find properties of those +connected areas + + align:start position:0% +connected areas + + + align:start position:0% +connected areas +such as area + + align:start position:0% +such as area + + + align:start position:0% +such as area +perimeter + + align:start position:0% +perimeter + + + align:start position:0% +perimeter +centroid + + align:start position:0% + + + + align:start position:0% + +so there are a few things that are + + align:start position:0% +so there are a few things that are + + + align:start position:0% +so there are a few things that are +fairly easy to compute + + align:start position:0% + + + + align:start position:0% + +area of perimeter and + + align:start position:0% +area of perimeter and + + + align:start position:0% +area of perimeter and +centroid being amongst them + + align:start position:0% +centroid being amongst them + + + align:start position:0% +centroid being amongst them +as is euler number + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +what's euler number well in this context + + align:start position:0% +what's euler number well in this context + + + align:start position:0% +what's euler number well in this context +the euler number is the number of blobs + + align:start position:0% +the euler number is the number of blobs + + + align:start position:0% +the euler number is the number of blobs +minus the number of holes + + align:start position:0% +minus the number of holes + + + align:start position:0% +minus the number of holes +so for example + + align:start position:0% + + + + align:start position:0% + +the euler number + + align:start position:0% +the euler number + + + align:start position:0% +the euler number +for that letter + + align:start position:0% +for that letter + + + align:start position:0% +for that letter +would be + + align:start position:0% +would be + + + align:start position:0% +would be +one + + align:start position:0% +one + + + align:start position:0% +one +minus two or minus one + + align:start position:0% +minus two or minus one + + + align:start position:0% +minus two or minus one +and it turns out that + + align:start position:0% +and it turns out that + + + align:start position:0% +and it turns out that +some of these can be computed + + align:start position:0% +some of these can be computed + + + align:start position:0% +some of these can be computed +in very efficient ways so first of all + + align:start position:0% +in very efficient ways so first of all + + + align:start position:0% +in very efficient ways so first of all +there's a green theorem + + align:start position:0% + + + + align:start position:0% + +that where we saw that there are certain + + align:start position:0% +that where we saw that there are certain + + + align:start position:0% +that where we saw that there are certain +computations on areas + + align:start position:0% +computations on areas + + + align:start position:0% +computations on areas +that can be uh changed into computations + + align:start position:0% +that can be uh changed into computations + + + align:start position:0% +that can be uh changed into computations +along boundaries and you know area + + align:start position:0% +along boundaries and you know area + + + align:start position:0% +along boundaries and you know area +perimeter + + align:start position:0% +perimeter + + + align:start position:0% +perimeter +centroid + + align:start position:0% +centroid + + + align:start position:0% +centroid +uh are all in that category and then + + align:start position:0% +uh are all in that category and then + + + align:start position:0% +uh are all in that category and then +there's some low-level binary image + + align:start position:0% +there's some low-level binary image + + + align:start position:0% +there's some low-level binary image +processing operations + + align:start position:0% +processing operations + + + align:start position:0% +processing operations +and it turns out that + + align:start position:0% +and it turns out that + + + align:start position:0% +and it turns out that +d3 can be implemented + + align:start position:0% +d3 can be implemented + + + align:start position:0% +d3 can be implemented +in a very efficient parallel way by + + align:start position:0% +in a very efficient parallel way by + + + align:start position:0% +in a very efficient parallel way by +performing local computations so for + + align:start position:0% +performing local computations so for + + + align:start position:0% +performing local computations so for +example you know with perimeter all you + + align:start position:0% +example you know with perimeter all you + + + align:start position:0% +example you know with perimeter all you +need to do is look for places where + + align:start position:0% +need to do is look for places where + + + align:start position:0% +need to do is look for places where +there's a one pixel next to a zero pixel + + align:start position:0% +there's a one pixel next to a zero pixel + + + align:start position:0% +there's a one pixel next to a zero pixel +and if you can identify all of those + + align:start position:0% +and if you can identify all of those + + + align:start position:0% +and if you can identify all of those +places and count them up you're done + + align:start position:0% +places and count them up you're done + + + align:start position:0% +places and count them up you're done +so the idea is that there's certain + + align:start position:0% +so the idea is that there's certain + + + align:start position:0% +so the idea is that there's certain +things that can be done by counting + + align:start position:0% +things that can be done by counting + + + align:start position:0% +things that can be done by counting +local properties because area is an + + align:start position:0% +local properties because area is an + + + align:start position:0% +local properties because area is an +obvious one is the pixel zero or one and + + align:start position:0% +obvious one is the pixel zero or one and + + + align:start position:0% +obvious one is the pixel zero or one and +if it's one you count it and otherwise + + align:start position:0% +if it's one you count it and otherwise + + + align:start position:0% +if it's one you count it and otherwise +not and and you can do it by going + + align:start position:0% +not and and you can do it by going + + + align:start position:0% +not and and you can do it by going +sequentially through the image but + + align:start position:0% +sequentially through the image but + + + align:start position:0% +sequentially through the image but +that's of course very expensive + + align:start position:0% +that's of course very expensive + + + align:start position:0% +that's of course very expensive +so you can imagine parallel methods + + align:start position:0% +so you can imagine parallel methods + + + align:start position:0% +so you can imagine parallel methods +including parallel hardware people build + + align:start position:0% +including parallel hardware people build + + + align:start position:0% +including parallel hardware people build +parallel hardware for this kind of thing + + align:start position:0% +parallel hardware for this kind of thing + + + align:start position:0% +parallel hardware for this kind of thing +which will compute area perimeter and + + align:start position:0% +which will compute area perimeter and + + + align:start position:0% +which will compute area perimeter and +very surprisingly also euler number + + align:start position:0% +very surprisingly also euler number + + + align:start position:0% +very surprisingly also euler number +so that was + + align:start position:0% +so that was + + + align:start position:0% +so that was +one approach + + align:start position:0% +one approach + + + align:start position:0% +one approach +and + + align:start position:0% +and + + + align:start position:0% +and +one problem with it is + + align:start position:0% +one problem with it is + + + align:start position:0% +one problem with it is +it involved the threshold + + align:start position:0% +it involved the threshold + + + align:start position:0% +it involved the threshold +right so if you're + + align:start position:0% +right so if you're + + + align:start position:0% +right so if you're +faced with a real world image you have + + align:start position:0% +faced with a real world image you have + + + align:start position:0% +faced with a real world image you have +to somehow distinguish background from + + align:start position:0% +to somehow distinguish background from + + + align:start position:0% +to somehow distinguish background from +foreground maybe they're a different + + align:start position:0% +foreground maybe they're a different + + + align:start position:0% +foreground maybe they're a different +color + + align:start position:0% +color + + + align:start position:0% +color +maybe they're different brightness maybe + + align:start position:0% +maybe they're different brightness maybe + + + align:start position:0% +maybe they're different brightness maybe +different texture so you have to find + + align:start position:0% +different texture so you have to find + + + align:start position:0% +different texture so you have to find +some way of separating + + align:start position:0% +some way of separating + + + align:start position:0% +some way of separating +and that means you have to make a + + align:start position:0% +and that means you have to make a + + + align:start position:0% +and that means you have to make a +decision early on + + align:start position:0% +decision early on + + + align:start position:0% +decision early on +and as we mentioned last time that's not + + align:start position:0% +and as we mentioned last time that's not + + + align:start position:0% +and as we mentioned last time that's not +always a good thing because your + + align:start position:0% +always a good thing because your + + + align:start position:0% +always a good thing because your +decision may be wrong and there's no way + + align:start position:0% +decision may be wrong and there's no way + + + align:start position:0% +decision may be wrong and there's no way +to undo that so + + align:start position:0% +to undo that so + + + align:start position:0% +to undo that so +now + + align:start position:0% +now + + + align:start position:0% +now +once we + + align:start position:0% +once we + + + align:start position:0% +once we +oh i said shape in uh quotation marks so + + align:start position:0% +oh i said shape in uh quotation marks so + + + align:start position:0% +oh i said shape in uh quotation marks so +um + + align:start position:0% +um + + + align:start position:0% +um +a lot of these are computed using + + align:start position:0% +a lot of these are computed using + + + align:start position:0% +a lot of these are computed using +moments so this is the based on the + + align:start position:0% +moments so this is the based on the + + + align:start position:0% +moments so this is the based on the +zeroth moment + + align:start position:0% +zeroth moment + + + align:start position:0% +zeroth moment +and this is based on the first moment + + align:start position:0% + + + + align:start position:0% + +and um + + align:start position:0% +and um + + + align:start position:0% +and um +what's a moment well just to refresh + + align:start position:0% +what's a moment well just to refresh + + + align:start position:0% +what's a moment well just to refresh +your memory + + align:start position:0% + + + + align:start position:0% + +so the zeroth moment is where you just + + align:start position:0% +so the zeroth moment is where you just + + + align:start position:0% +so the zeroth moment is where you just +take the integral of e of x y + + align:start position:0% +take the integral of e of x y + + + align:start position:0% +take the integral of e of x y +times one times one + + align:start position:0% +times one times one + + + align:start position:0% +times one times one +and if e of x y is a binary image that's + + align:start position:0% +and if e of x y is a binary image that's + + + align:start position:0% +and if e of x y is a binary image that's +just computing the area that is one so + + align:start position:0% +just computing the area that is one so + + + align:start position:0% +just computing the area that is one so +and these others are computed in a in a + + align:start position:0% +and these others are computed in a in a + + + align:start position:0% +and these others are computed in a in a +similar fashion + + align:start position:0% +similar fashion + + + align:start position:0% +similar fashion +so um those are particularly uh easy to + + align:start position:0% +so um those are particularly uh easy to + + + align:start position:0% +so um those are particularly uh easy to +compute + + align:start position:0% +compute + + + align:start position:0% +compute +and + + align:start position:0% + + + + align:start position:0% + +what's you know what's the problem with + + align:start position:0% +what's you know what's the problem with + + + align:start position:0% +what's you know what's the problem with +this method well in a lot of cases there + + align:start position:0% +this method well in a lot of cases there + + + align:start position:0% +this method well in a lot of cases there +is no thresholding method there's no + + align:start position:0% +is no thresholding method there's no + + + align:start position:0% +is no thresholding method there's no +magic trick that will distinguish + + align:start position:0% +magic trick that will distinguish + + + align:start position:0% +magic trick that will distinguish +foreground from background you know in + + align:start position:0% +foreground from background you know in + + + align:start position:0% +foreground from background you know in +the autonomous vehicle you're looking at + + align:start position:0% +the autonomous vehicle you're looking at + + + align:start position:0% +the autonomous vehicle you're looking at +cars ahead of you and some of them are + + align:start position:0% +cars ahead of you and some of them are + + + align:start position:0% +cars ahead of you and some of them are +brighter than the background and some + + align:start position:0% +brighter than the background and some + + + align:start position:0% +brighter than the background and some +are darker than the background + + align:start position:0% +are darker than the background + + + align:start position:0% +are darker than the background +so + + align:start position:0% +so + + + align:start position:0% +so +that method is limited to cases where + + align:start position:0% +that method is limited to cases where + + + align:start position:0% +that method is limited to cases where +we have a clear distinction it's very + + align:start position:0% +we have a clear distinction it's very + + + align:start position:0% +we have a clear distinction it's very +important though to realize that these + + align:start position:0% +important though to realize that these + + + align:start position:0% +important though to realize that these +methods are widely used but not on raw + + align:start position:0% +methods are widely used but not on raw + + + align:start position:0% +methods are widely used but not on raw +images they're used on the result of + + align:start position:0% +images they're used on the result of + + + align:start position:0% +images they're used on the result of +some computation where + + align:start position:0% +some computation where + + + align:start position:0% +some computation where +the computation + + align:start position:0% +the computation + + + align:start position:0% +the computation +combines brightness levels in some way + + align:start position:0% +combines brightness levels in some way + + + align:start position:0% +combines brightness levels in some way +to arrive at some conclusion + + align:start position:0% +to arrive at some conclusion + + + align:start position:0% +to arrive at some conclusion +and give you a binary result + + align:start position:0% +and give you a binary result + + + align:start position:0% +and give you a binary result +and and then + + align:start position:0% +and and then + + + align:start position:0% +and and then +you need to know these methods + + align:start position:0% +you need to know these methods + + + align:start position:0% +you need to know these methods +okay there's also something called + + align:start position:0% +okay there's also something called + + + align:start position:0% +okay there's also something called +binary template + + align:start position:0% + + + + align:start position:0% + +where + + align:start position:0% + + + + align:start position:0% + +you use a + + align:start position:0% +you use a + + + align:start position:0% +you use a +master image + + align:start position:0% +master image + + + align:start position:0% +master image +to + + align:start position:0% +to + + + align:start position:0% +to +define the object so + + align:start position:0% +define the object so + + + align:start position:0% +define the object so +this comes up a lot in these methods + + align:start position:0% +this comes up a lot in these methods + + + align:start position:0% +this comes up a lot in these methods +where you have a sample that you + + align:start position:0% +where you have a sample that you + + + align:start position:0% +where you have a sample that you +consider the standard often called a + + align:start position:0% +consider the standard often called a + + + align:start position:0% +consider the standard often called a +golden template + + align:start position:0% +golden template + + + align:start position:0% +golden template +and then and you try to make it so that + + align:start position:0% +and then and you try to make it so that + + + align:start position:0% +and then and you try to make it so that +its image is as clean as possible and it + + align:start position:0% +its image is as clean as possible and it + + + align:start position:0% +its image is as clean as possible and it +doesn't have any defects and so on and + + align:start position:0% +doesn't have any defects and so on and + + + align:start position:0% +doesn't have any defects and so on and +you then compute something for example a + + align:start position:0% +you then compute something for example a + + + align:start position:0% +you then compute something for example a +template by thresholding + + align:start position:0% +template by thresholding + + + align:start position:0% +template by thresholding +and that is then used as a method for + + align:start position:0% +and that is then used as a method for + + + align:start position:0% +and that is then used as a method for +recognizing and determining the pose so + + align:start position:0% +recognizing and determining the pose so + + + align:start position:0% +recognizing and determining the pose so +you you take that template and you move + + align:start position:0% +you you take that template and you move + + + align:start position:0% +you you take that template and you move +it around in the image until it uh + + align:start position:0% +it around in the image until it uh + + + align:start position:0% +it around in the image until it uh +matches uh what is there in the image + + align:start position:0% +matches uh what is there in the image + + + align:start position:0% +matches uh what is there in the image +and we won't say much more about that + + align:start position:0% +and we won't say much more about that + + + align:start position:0% +and we won't say much more about that +both + + align:start position:0% +both + + + align:start position:0% +both +so the binary template methods uh + + align:start position:0% +so the binary template methods uh + + + align:start position:0% +so the binary template methods uh +accuracy is + + align:start position:0% +accuracy is + + + align:start position:0% +accuracy is +limited + + align:start position:0% +limited + + + align:start position:0% +limited +to perhaps a pixel + + align:start position:0% +to perhaps a pixel + + + align:start position:0% +to perhaps a pixel +then uh we get to things that were more + + align:start position:0% +then uh we get to things that were more + + + align:start position:0% +then uh we get to things that were more +widely used so let's call that two + + align:start position:0% + + + + align:start position:0% + +we get to + + align:start position:0% +we get to + + + align:start position:0% +we get to +normalize correlation + + align:start position:0% + + + + align:start position:0% + +and in fact when cognac started + + align:start position:0% +and in fact when cognac started + + + align:start position:0% +and in fact when cognac started +that was their big claim to fame + + align:start position:0% +that was their big claim to fame + + + align:start position:0% +that was their big claim to fame +that they could do normalized + + align:start position:0% +that they could do normalized + + + align:start position:0% +that they could do normalized +correlation at high speeds and get + + align:start position:0% +correlation at high speeds and get + + + align:start position:0% +correlation at high speeds and get +reasonable accuracy like a quarter of a + + align:start position:0% +reasonable accuracy like a quarter of a + + + align:start position:0% +reasonable accuracy like a quarter of a +pixel + + align:start position:0% +pixel + + + align:start position:0% +pixel +position + + align:start position:0% +position + + + align:start position:0% +position +and so so what is that well + + align:start position:0% +and so so what is that well + + + align:start position:0% +and so so what is that well +the idea is kind of let's try all + + align:start position:0% +the idea is kind of let's try all + + + align:start position:0% +the idea is kind of let's try all +possible positions for the match and see + + align:start position:0% +possible positions for the match and see + + + align:start position:0% +possible positions for the match and see +which one which one is the best so if we + + align:start position:0% +which one which one is the best so if we + + + align:start position:0% +which one which one is the best so if we +have two images e1 and e2 where perhaps + + align:start position:0% +have two images e1 and e2 where perhaps + + + align:start position:0% +have two images e1 and e2 where perhaps +e1 is the golden master + + align:start position:0% +e1 is the golden master + + + align:start position:0% +e1 is the golden master +then what we're looking at is something + + align:start position:0% +then what we're looking at is something + + + align:start position:0% +then what we're looking at is something +like + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +we take the difference of the two images + + align:start position:0% +we take the difference of the two images + + + align:start position:0% +we take the difference of the two images +and + + align:start position:0% +and + + + align:start position:0% +and +we uh + + align:start position:0% +we uh + + + align:start position:0% +we uh +well let's square it + + align:start position:0% + + + + align:start position:0% + +so this is + + align:start position:0% +so this is + + + align:start position:0% +so this is +uh max sorry mine + + align:start position:0% + + + + align:start position:0% + +um so + + align:start position:0% +um so + + + align:start position:0% +um so +it's clear what we're doing here we're + + align:start position:0% +it's clear what we're doing here we're + + + align:start position:0% +it's clear what we're doing here we're +taking one of the two images and moving + + align:start position:0% +taking one of the two images and moving + + + align:start position:0% +taking one of the two images and moving +it around + + align:start position:0% +it around + + + align:start position:0% +it around +and trying to find the alignment where + + align:start position:0% +and trying to find the alignment where + + + align:start position:0% +and trying to find the alignment where +the difference between the shifted image + + align:start position:0% +the difference between the shifted image + + + align:start position:0% +the difference between the shifted image +and the other image is as small as + + align:start position:0% +and the other image is as small as + + + align:start position:0% +and the other image is as small as +possible + + align:start position:0% +possible + + + align:start position:0% +possible +and so + + align:start position:0% +and so + + + align:start position:0% +and so +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +there's a related method called + + align:start position:0% +there's a related method called + + + align:start position:0% +there's a related method called +correlation + + align:start position:0% + + + + align:start position:0% + +now notice that + + align:start position:0% +now notice that + + + align:start position:0% +now notice that +right now i'm only + + align:start position:0% + + + + align:start position:0% + +allowing for translation so we're just + + align:start position:0% +allowing for translation so we're just + + + align:start position:0% +allowing for translation so we're just +allowing for shift and and the reason + + align:start position:0% +allowing for shift and and the reason + + + align:start position:0% +allowing for shift and and the reason +for that is that + + align:start position:0% +for that is that + + + align:start position:0% +for that is that +of course we want to be able to deal + + align:start position:0% +of course we want to be able to deal + + + align:start position:0% +of course we want to be able to deal +with rotation scaling + + align:start position:0% +with rotation scaling + + + align:start position:0% +with rotation scaling +aspect ratio changes slant whatever + + align:start position:0% +aspect ratio changes slant whatever + + + align:start position:0% +aspect ratio changes slant whatever +but + + align:start position:0% +but + + + align:start position:0% +but +this method is so expensive + + align:start position:0% +this method is so expensive + + + align:start position:0% +this method is so expensive +computationally that you know + + align:start position:0% +computationally that you know + + + align:start position:0% +computationally that you know +translation is about all we can do + + align:start position:0% +translation is about all we can do + + + align:start position:0% +translation is about all we can do +right why is it computation expensive + + align:start position:0% +right why is it computation expensive + + + align:start position:0% +right why is it computation expensive +well because basically you have to + + align:start position:0% +well because basically you have to + + + align:start position:0% +well because basically you have to +look at every pixel + + align:start position:0% +look at every pixel + + + align:start position:0% +look at every pixel +for every possible position + + align:start position:0% +for every possible position + + + align:start position:0% +for every possible position +so if they're in pixels and you're going + + align:start position:0% +so if they're in pixels and you're going + + + align:start position:0% +so if they're in pixels and you're going +to try m different positions the you + + align:start position:0% +to try m different positions the you + + + align:start position:0% +to try m different positions the you +need n times m computations so + + align:start position:0% +need n times m computations so + + + align:start position:0% +need n times m computations so +uh with n being you know a million or + + align:start position:0% +uh with n being you know a million or + + + align:start position:0% +uh with n being you know a million or +something or more and the possible + + align:start position:0% +something or more and the possible + + + align:start position:0% +something or more and the possible +positions being also all of the shifts + + align:start position:0% +positions being also all of the shifts + + + align:start position:0% +positions being also all of the shifts +in the pic in the image + + align:start position:0% +in the pic in the image + + + align:start position:0% +in the pic in the image +maybe half a million you're talking you + + align:start position:0% +maybe half a million you're talking you + + + align:start position:0% +maybe half a million you're talking you +know a lot of operations + + align:start position:0% +know a lot of operations + + + align:start position:0% +know a lot of operations +these two are related + + align:start position:0% +these two are related + + + align:start position:0% +these two are related +in that if we expand this out + + align:start position:0% +in that if we expand this out + + + align:start position:0% +in that if we expand this out +you know if we expand out the integrand + + align:start position:0% +you know if we expand out the integrand + + + align:start position:0% +you know if we expand out the integrand +we get + + align:start position:0% +we get + + + align:start position:0% +we get +e1 + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +where we have the + + align:start position:0% +where we have the + + + align:start position:0% +where we have the +correlation + + align:start position:0% + + + + align:start position:0% + +appearing in the middle so + + align:start position:0% +appearing in the middle so + + + align:start position:0% +appearing in the middle so +maximizing + + align:start position:0% +maximizing + + + align:start position:0% +maximizing +this + + align:start position:0% +this + + + align:start position:0% +this +is + + align:start position:0% +is + + + align:start position:0% +is +minimizing that + + align:start position:0% +minimizing that + + + align:start position:0% +minimizing that +assuming that this is constant + + align:start position:0% + + + + align:start position:0% + +and um + + align:start position:0% + + + + align:start position:0% + +and it should be right because this is + + align:start position:0% +and it should be right because this is + + + align:start position:0% +and it should be right because this is +just you take the second image and you + + align:start position:0% +just you take the second image and you + + + align:start position:0% +just you take the second image and you +just square all of the gray levels and + + align:start position:0% +just square all of the gray levels and + + + align:start position:0% +just square all of the gray levels and +add them up and that doesn't change this + + align:start position:0% +add them up and that doesn't change this + + + align:start position:0% +add them up and that doesn't change this +one's a little bit more questionable + + align:start position:0% +one's a little bit more questionable + + + align:start position:0% +one's a little bit more questionable +because you take the first image and you + + align:start position:0% +because you take the first image and you + + + align:start position:0% +because you take the first image and you +shift it around and then add up the + + align:start position:0% +shift it around and then add up the + + + align:start position:0% +shift it around and then add up the +squares of the pixels so maybe some of + + align:start position:0% +squares of the pixels so maybe some of + + + align:start position:0% +squares of the pixels so maybe some of +the pixels go out of the frame and stuff + + align:start position:0% +the pixels go out of the frame and stuff + + + align:start position:0% +the pixels go out of the frame and stuff +like that but + + align:start position:0% +like that but + + + align:start position:0% +like that but +to a large degree + + align:start position:0% +to a large degree + + + align:start position:0% +to a large degree +those terms are constant so + + align:start position:0% +those terms are constant so + + + align:start position:0% +those terms are constant so +minimizing this thing basically means we + + align:start position:0% +minimizing this thing basically means we + + + align:start position:0% +minimizing this thing basically means we +have to maximize that so + + align:start position:0% +have to maximize that so + + + align:start position:0% +have to maximize that so +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well while we're there + + align:start position:0% + + + + align:start position:0% + +i want to relate this to our + + align:start position:0% +i want to relate this to our + + + align:start position:0% +i want to relate this to our +gradient-based methods + + align:start position:0% + + + + align:start position:0% + +right because you know we're talking + + align:start position:0% +right because you know we're talking + + + align:start position:0% +right because you know we're talking +about fixed optical flow optical mouse + + align:start position:0% +about fixed optical flow optical mouse + + + align:start position:0% +about fixed optical flow optical mouse +all of that stuff and there we were + + align:start position:0% +all of that stuff and there we were + + + align:start position:0% +all of that stuff and there we were +computing an offset + + align:start position:0% +computing an offset + + + align:start position:0% +computing an offset +typically a small offset like a + + align:start position:0% +typically a small offset like a + + + align:start position:0% +typically a small offset like a +fraction of a pixel or + + align:start position:0% +fraction of a pixel or + + + align:start position:0% +fraction of a pixel or +maybe a couple of pixels + + align:start position:0% +maybe a couple of pixels + + + align:start position:0% +maybe a couple of pixels +and + + align:start position:0% +and + + + align:start position:0% +and +so it looks like here's another way of + + align:start position:0% +so it looks like here's another way of + + + align:start position:0% +so it looks like here's another way of +doing it right we + + align:start position:0% +doing it right we + + + align:start position:0% +doing it right we +maximize the correlation + + align:start position:0% +maximize the correlation + + + align:start position:0% +maximize the correlation +so let's look at that so let's suppose + + align:start position:0% +so let's look at that so let's suppose + + + align:start position:0% +so let's look at that so let's suppose +that delta x and delta y are small + + align:start position:0% +that delta x and delta y are small + + + align:start position:0% +that delta x and delta y are small +then we can use taylor series expansion + + align:start position:0% +then we can use taylor series expansion + + + align:start position:0% +then we can use taylor series expansion +and we get + + align:start position:0% +and we get + + + align:start position:0% +and we get +e1 of xy + + align:start position:0% +e1 of xy + + + align:start position:0% +e1 of xy +minus + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +so then we have minus delta x e x minus + + align:start position:0% +so then we have minus delta x e x minus + + + align:start position:0% +so then we have minus delta x e x minus +delta y + + align:start position:0% +delta y + + + align:start position:0% +delta y +and then we have the difference of these + + align:start position:0% +and then we have the difference of these + + + align:start position:0% +and then we have the difference of these +two + + align:start position:0% +two + + + align:start position:0% +two +which we can take to be the + + align:start position:0% +which we can take to be the + + + align:start position:0% +which we can take to be the +change in time right because we can + + align:start position:0% +change in time right because we can + + + align:start position:0% +change in time right because we can +think of these two images as two images + + align:start position:0% +think of these two images as two images + + + align:start position:0% +think of these two images as two images +that uh correspond to two different + + align:start position:0% +that uh correspond to two different + + + align:start position:0% +that uh correspond to two different +times + + align:start position:0% + + + + align:start position:0% + +so we're going to + + align:start position:0% +so we're going to + + + align:start position:0% +so we're going to +let's see minimize this + + align:start position:0% + + + + align:start position:0% + +so if i divide through by delta t and + + align:start position:0% +so if i divide through by delta t and + + + align:start position:0% +so if i divide through by delta t and +take the limit as delta t goes to 0 + + align:start position:0% +take the limit as delta t goes to 0 + + + align:start position:0% +take the limit as delta t goes to 0 +i get that right because delta x over + + align:start position:0% +i get that right because delta x over + + + align:start position:0% +i get that right because delta x over +delta t + + align:start position:0% +delta t + + + align:start position:0% +delta t +goes to u and of course the minus signs + + align:start position:0% +goes to u and of course the minus signs + + + align:start position:0% +goes to u and of course the minus signs +don't matter because i'm squaring + + align:start position:0% +don't matter because i'm squaring + + + align:start position:0% +don't matter because i'm squaring +and delta y over delta t goes to v and + + align:start position:0% +and delta y over delta t goes to v and + + + align:start position:0% +and delta y over delta t goes to v and +so on so that's all very familiar + + align:start position:0% +so on so that's all very familiar + + + align:start position:0% +so on so that's all very familiar +yeah + + align:start position:0% + + + + align:start position:0% + +the goal is to + + align:start position:0% +the goal is to + + + align:start position:0% +the goal is to +find + + align:start position:0% +find + + + align:start position:0% +find +an object to recognize it and determine + + align:start position:0% +an object to recognize it and determine + + + align:start position:0% +an object to recognize it and determine +its pose so right now what we're talking + + align:start position:0% +its pose so right now what we're talking + + + align:start position:0% +its pose so right now what we're talking +about is focused on this part the + + align:start position:0% +about is focused on this part the + + + align:start position:0% +about is focused on this part the +determining the pose so + + align:start position:0% +determining the pose so + + + align:start position:0% +determining the pose so +so we have an image of + + align:start position:0% +so we have an image of + + + align:start position:0% +so we have an image of +what the integrated circuit is supposed + + align:start position:0% +what the integrated circuit is supposed + + + align:start position:0% +what the integrated circuit is supposed +to look like + + align:start position:0% +to look like + + + align:start position:0% +to look like +and then we have an image of a runtime + + align:start position:0% +and then we have an image of a runtime + + + align:start position:0% +and then we have an image of a runtime +image of a + + align:start position:0% +image of a + + + align:start position:0% +image of a +integrated circuit and we're trying to + + align:start position:0% +integrated circuit and we're trying to + + + align:start position:0% +integrated circuit and we're trying to +put it in the right place for the next + + align:start position:0% +put it in the right place for the next + + + align:start position:0% +put it in the right place for the next +step of the manufacturing process for + + align:start position:0% +step of the manufacturing process for + + + align:start position:0% +step of the manufacturing process for +example and so we need to find out + + align:start position:0% +example and so we need to find out + + + align:start position:0% +example and so we need to find out +you know how far is my runtime image + + align:start position:0% +you know how far is my runtime image + + + align:start position:0% +you know how far is my runtime image +shifted relative to the training image + + align:start position:0% +shifted relative to the training image + + + align:start position:0% +shifted relative to the training image +and then i can move the stage and do the + + align:start position:0% +and then i can move the stage and do the + + + align:start position:0% +and then i can move the stage and do the +next stage of car + + align:start position:0% +next stage of car + + + align:start position:0% +next stage of car +and so these are various methods + + align:start position:0% +and so these are various methods + + + align:start position:0% +and so these are various methods +of + + align:start position:0% +of + + + align:start position:0% +of +trying to get that alignment so for + + align:start position:0% +trying to get that alignment so for + + + align:start position:0% +trying to get that alignment so for +example the sum of square of differences + + align:start position:0% +example the sum of square of differences + + + align:start position:0% +example the sum of square of differences +is saying okay i'm going to shift one of + + align:start position:0% +is saying okay i'm going to shift one of + + + align:start position:0% +is saying okay i'm going to shift one of +the images until it matches the other + + align:start position:0% +the images until it matches the other + + + align:start position:0% +the images until it matches the other +image as close as possible + + align:start position:0% +image as close as possible + + + align:start position:0% +image as close as possible +and then interestingly enough that's + + align:start position:0% +and then interestingly enough that's + + + align:start position:0% +and then interestingly enough that's +actually equivalent to the correlation + + align:start position:0% +actually equivalent to the correlation + + + align:start position:0% +actually equivalent to the correlation +which isn't obvious you know why should + + align:start position:0% +which isn't obvious you know why should + + + align:start position:0% +which isn't obvious you know why should +the integral of the product of the two + + align:start position:0% +the integral of the product of the two + + + align:start position:0% +the integral of the product of the two +things be maximum + + align:start position:0% + + + + align:start position:0% + +and then in turn + + align:start position:0% +and then in turn + + + align:start position:0% +and then in turn +for small displacements that's actually + + align:start position:0% +for small displacements that's actually + + + align:start position:0% +for small displacements that's actually +very similar to our gradient-based + + align:start position:0% +very similar to our gradient-based + + + align:start position:0% +very similar to our gradient-based +methods right we had that optical mass + + align:start position:0% +methods right we had that optical mass + + + align:start position:0% +methods right we had that optical mass +we wanted to know how far it moved + + align:start position:0% +we wanted to know how far it moved + + + align:start position:0% +we wanted to know how far it moved +very similar problem + + align:start position:0% +very similar problem + + + align:start position:0% +very similar problem +and um + + align:start position:0% +and um + + + align:start position:0% +and um +interestingly enough if you read the + + align:start position:0% +interestingly enough if you read the + + + align:start position:0% +interestingly enough if you read the +the patterns on optical mice you + + align:start position:0% +the patterns on optical mice you + + + align:start position:0% +the patterns on optical mice you +probably didn't think there were but + + align:start position:0% +probably didn't think there were but + + + align:start position:0% +probably didn't think there were but +there are dozens of patterns on optical + + align:start position:0% +there are dozens of patterns on optical + + + align:start position:0% +there are dozens of patterns on optical +mice + + align:start position:0% +mice + + + align:start position:0% +mice +because individually a mouse doesn't + + align:start position:0% +because individually a mouse doesn't + + + align:start position:0% +because individually a mouse doesn't +cost hardly anything so you're not going + + align:start position:0% +cost hardly anything so you're not going + + + align:start position:0% +cost hardly anything so you're not going +to make much money but you can sell a + + align:start position:0% +to make much money but you can sell a + + + align:start position:0% +to make much money but you can sell a +billion of them so people have + + align:start position:0% +billion of them so people have + + + align:start position:0% +billion of them so people have +thought it worth patenting and almost + + align:start position:0% +thought it worth patenting and almost + + + align:start position:0% +thought it worth patenting and almost +all the patent recommend the gradient + + align:start position:0% +all the patent recommend the gradient + + + align:start position:0% +all the patent recommend the gradient +based methods + + align:start position:0% +based methods + + + align:start position:0% +based methods +and when you take them apart and you + + align:start position:0% +and when you take them apart and you + + + align:start position:0% +and when you take them apart and you +reverse engineer them + + align:start position:0% +reverse engineer them + + + align:start position:0% +reverse engineer them +a whole bunch of them don't a whole + + align:start position:0% +a whole bunch of them don't a whole + + + align:start position:0% +a whole bunch of them don't a whole +bunch of them use + + align:start position:0% +bunch of them use + + + align:start position:0% +bunch of them use +so + + align:start position:0% +so + + + align:start position:0% +so +the patents all say correlation sorry i + + align:start position:0% +the patents all say correlation sorry i + + + align:start position:0% +the patents all say correlation sorry i +think i said it the wrong way around the + + align:start position:0% +think i said it the wrong way around the + + + align:start position:0% +think i said it the wrong way around the +patents are all about correlation the + + align:start position:0% +patents are all about correlation the + + + align:start position:0% +patents are all about correlation the +you know + + align:start position:0% +you know + + + align:start position:0% +you know +hewlett-packard agilent all those people + + align:start position:0% +hewlett-packard agilent all those people + + + align:start position:0% +hewlett-packard agilent all those people +have patents on this but then + + align:start position:0% +have patents on this but then + + + align:start position:0% +have patents on this but then +when you take them apart and you reverse + + align:start position:0% +when you take them apart and you reverse + + + align:start position:0% +when you take them apart and you reverse +engineer them which you're not supposed + + align:start position:0% +engineer them which you're not supposed + + + align:start position:0% +engineer them which you're not supposed +to do you often find that they're + + align:start position:0% +to do you often find that they're + + + align:start position:0% +to do you often find that they're +actually using gradient based methods + + align:start position:0% +actually using gradient based methods + + + align:start position:0% +actually using gradient based methods +because they're cheaper + + align:start position:0% +because they're cheaper + + + align:start position:0% +because they're cheaper +more accurate whatever the limitation is + + align:start position:0% +more accurate whatever the limitation is + + + align:start position:0% +more accurate whatever the limitation is +the you know that the movement is not + + align:start position:0% +the you know that the movement is not + + + align:start position:0% +the you know that the movement is not +very large so often those mice run at a + + align:start position:0% +very large so often those mice run at a + + + align:start position:0% +very large so often those mice run at a +higher frame rate + + align:start position:0% +higher frame rate + + + align:start position:0% +higher frame rate +to compensate a lot of the gaming mice + + align:start position:0% +to compensate a lot of the gaming mice + + + align:start position:0% +to compensate a lot of the gaming mice +uh work that way they have a very high + + align:start position:0% +uh work that way they have a very high + + + align:start position:0% +uh work that way they have a very high +frame rate so the motion + + align:start position:0% +frame rate so the motion + + + align:start position:0% +frame rate so the motion +from frame to frame is very very small + + align:start position:0% +from frame to frame is very very small + + + align:start position:0% +from frame to frame is very very small +so anyway so these are all sort of + + align:start position:0% +so anyway so these are all sort of + + + align:start position:0% +so anyway so these are all sort of +connected so i just thought i'd throw + + align:start position:0% +connected so i just thought i'd throw + + + align:start position:0% +connected so i just thought i'd throw +this in + + align:start position:0% +this in + + + align:start position:0% +this in +because we're talking about determining + + align:start position:0% +because we're talking about determining + + + align:start position:0% +because we're talking about determining +the pose so in the simplest case pose + + align:start position:0% +the pose so in the simplest case pose + + + align:start position:0% +the pose so in the simplest case pose +means you know the shift + + align:start position:0% +means you know the shift + + + align:start position:0% +means you know the shift +of course we'll be more interested in + + align:start position:0% +of course we'll be more interested in + + + align:start position:0% +of course we'll be more interested in +cases where it also includes rotation + + align:start position:0% +cases where it also includes rotation + + + align:start position:0% +cases where it also includes rotation +and maybe scaling and and so on + + align:start position:0% +and maybe scaling and and so on + + + align:start position:0% +and maybe scaling and and so on +so okay so back to + + align:start position:0% +so okay so back to + + + align:start position:0% +so okay so back to +correlation so uh sum of squares of + + align:start position:0% +correlation so uh sum of squares of + + + align:start position:0% +correlation so uh sum of squares of +differences is used sometimes uh but it + + align:start position:0% +differences is used sometimes uh but it + + + align:start position:0% +differences is used sometimes uh but it +has some drawbacks so for example if one + + align:start position:0% +has some drawbacks so for example if one + + + align:start position:0% +has some drawbacks so for example if one +of the two images is is substantially + + align:start position:0% +of the two images is is substantially + + + align:start position:0% +of the two images is is substantially +brighter than the other then they won't + + align:start position:0% +brighter than the other then they won't + + + align:start position:0% +brighter than the other then they won't +match very well + + align:start position:0% +match very well + + + align:start position:0% +match very well +whereas the correlation will give you a + + align:start position:0% +whereas the correlation will give you a + + + align:start position:0% +whereas the correlation will give you a +high match + + align:start position:0% +high match + + + align:start position:0% +high match +anyway well + + align:start position:0% +anyway well + + + align:start position:0% +anyway well +i guess one problem with the correlation + + align:start position:0% +i guess one problem with the correlation + + + align:start position:0% +i guess one problem with the correlation +is you know how high is high where's the + + align:start position:0% +is you know how high is high where's the + + + align:start position:0% +is you know how high is high where's the +threshold + + align:start position:0% +threshold + + + align:start position:0% +threshold +i mean so when when we plot that versus + + align:start position:0% +i mean so when when we plot that versus + + + align:start position:0% +i mean so when when we plot that versus +delta x delta y we expect there to be a + + align:start position:0% +delta x delta y we expect there to be a + + + align:start position:0% +delta x delta y we expect there to be a +peak + + align:start position:0% +peak + + + align:start position:0% +peak +at the correct displacement + + align:start position:0% +at the correct displacement + + + align:start position:0% +at the correct displacement +and that + + align:start position:0% +and that + + + align:start position:0% +and that +will still occur even if + + align:start position:0% +will still occur even if + + + align:start position:0% +will still occur even if +you multi you know it's obvious if you + + align:start position:0% +you multi you know it's obvious if you + + + align:start position:0% +you multi you know it's obvious if you +take e2 and multiply it by k + + align:start position:0% +take e2 and multiply it by k + + + align:start position:0% +take e2 and multiply it by k +it's really going to disturb the sum of + + align:start position:0% +it's really going to disturb the sum of + + + align:start position:0% +it's really going to disturb the sum of +squares of differences + + align:start position:0% +squares of differences + + + align:start position:0% +squares of differences +but it's not going to remove the peak of + + align:start position:0% +but it's not going to remove the peak of + + + align:start position:0% +but it's not going to remove the peak of +the correlation the peak will just be k + + align:start position:0% +the correlation the peak will just be k + + + align:start position:0% +the correlation the peak will just be k +times higher so that's one reason people + + align:start position:0% +times higher so that's one reason people + + + align:start position:0% +times higher so that's one reason people +very often use correlation even though + + align:start position:0% +very often use correlation even though + + + align:start position:0% +very often use correlation even though +it's it has some other drawbacks + + align:start position:0% +it's it has some other drawbacks + + + align:start position:0% +it's it has some other drawbacks +computational + + align:start position:0% +computational + + + align:start position:0% +computational +okay so let's suppose we do that well + + align:start position:0% +okay so let's suppose we do that well + + + align:start position:0% +okay so let's suppose we do that well +now there are issues like + + align:start position:0% +now there are issues like + + + align:start position:0% +now there are issues like +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +you know if uh + + align:start position:0% +you know if uh + + + align:start position:0% +you know if uh +as i mentioned if the contrast + + align:start position:0% +as i mentioned if the contrast + + + align:start position:0% +as i mentioned if the contrast +is different you will get a different + + align:start position:0% +is different you will get a different + + + align:start position:0% +is different you will get a different +peak value it would be really nice if + + align:start position:0% +peak value it would be really nice if + + + align:start position:0% +peak value it would be really nice if +instead you had a number that sort of + + align:start position:0% +instead you had a number that sort of + + + align:start position:0% +instead you had a number that sort of +said zero is no match and one is match + + align:start position:0% +said zero is no match and one is match + + + align:start position:0% +said zero is no match and one is match +here we have something that can get big + + align:start position:0% +here we have something that can get big + + + align:start position:0% +here we have something that can get big +and you're looking for the biggest but + + align:start position:0% +and you're looking for the biggest but + + + align:start position:0% +and you're looking for the biggest but +you it you you know if it's not very big + + align:start position:0% +you it you you know if it's not very big + + + align:start position:0% +you it you you know if it's not very big +do you know it how good a match is it + + align:start position:0% +do you know it how good a match is it + + + align:start position:0% +do you know it how good a match is it +are you matching up a picture of a cat + + align:start position:0% +are you matching up a picture of a cat + + + align:start position:0% +are you matching up a picture of a cat +with a picture of a dog you don't know + + align:start position:0% +with a picture of a dog you don't know + + + align:start position:0% +with a picture of a dog you don't know +because you're just looking for the peak + + align:start position:0% +because you're just looking for the peak + + + align:start position:0% +because you're just looking for the peak +so um what to do about that + + align:start position:0% +so um what to do about that + + + align:start position:0% +so um what to do about that +well that's where normalized correlation + + align:start position:0% +well that's where normalized correlation + + + align:start position:0% +well that's where normalized correlation +comes into it + + align:start position:0% + + + + align:start position:0% + +so first um offset + + align:start position:0% +so first um offset + + + align:start position:0% +so first um offset +so + + align:start position:0% +so + + + align:start position:0% +so +if i add a constant to one of the images + + align:start position:0% +if i add a constant to one of the images + + + align:start position:0% +if i add a constant to one of the images +it shouldn't change the match but it is + + align:start position:0% +it shouldn't change the match but it is + + + align:start position:0% +it shouldn't change the match but it is +going to uh disturb this calculation + + align:start position:0% +going to uh disturb this calculation + + + align:start position:0% +going to uh disturb this calculation +and it's uh therefore advantageous to + + align:start position:0% +and it's uh therefore advantageous to + + + align:start position:0% +and it's uh therefore advantageous to +first subtract out + + align:start position:0% +first subtract out + + + align:start position:0% +first subtract out +the + + align:start position:0% +the + + + align:start position:0% +the +mean okay so we'd have a new + + align:start position:0% + + + + align:start position:0% + +so we compute the average of e1 and we + + align:start position:0% +so we compute the average of e1 and we + + + align:start position:0% +so we compute the average of e1 and we +subtract that from everything + + align:start position:0% +subtract that from everything + + + align:start position:0% +subtract that from everything +so that if the overall level goes up or + + align:start position:0% +so that if the overall level goes up or + + + align:start position:0% +so that if the overall level goes up or +down it has no effect right we've + + align:start position:0% +down it has no effect right we've + + + align:start position:0% +down it has no effect right we've +cancelled that out + + align:start position:0% + + + + align:start position:0% + +of course it does mean now that e1 prime + + align:start position:0% +of course it does mean now that e1 prime + + + align:start position:0% +of course it does mean now that e1 prime +can have both positive and negative + + align:start position:0% +can have both positive and negative + + + align:start position:0% +can have both positive and negative +values well in fact it will have both + + align:start position:0% +values well in fact it will have both + + + align:start position:0% +values well in fact it will have both +positive and negative l's and the same + + align:start position:0% +positive and negative l's and the same + + + align:start position:0% +positive and negative l's and the same +for e2 + + align:start position:0% + + + + align:start position:0% + +okay so what does this do this gets rid + + align:start position:0% +okay so what does this do this gets rid + + + align:start position:0% +okay so what does this do this gets rid +of any uh offset in the image brightness + + align:start position:0% +of any uh offset in the image brightness + + + align:start position:0% +of any uh offset in the image brightness +and so it makes the process uh less + + align:start position:0% +and so it makes the process uh less + + + align:start position:0% +and so it makes the process uh less +sensitive to changes in + + align:start position:0% +sensitive to changes in + + + align:start position:0% +sensitive to changes in +the optical setup + + align:start position:0% +the optical setup + + + align:start position:0% +the optical setup +but in addition + + align:start position:0% +but in addition + + + align:start position:0% +but in addition +what we'd like to do is make it + + align:start position:0% +what we'd like to do is make it + + + align:start position:0% +what we'd like to do is make it +independent of contrast so that + + align:start position:0% +independent of contrast so that + + + align:start position:0% +independent of contrast so that +in many circumstances + + align:start position:0% +in many circumstances + + + align:start position:0% +in many circumstances +if the contrast changes by a factor of + + align:start position:0% +if the contrast changes by a factor of + + + align:start position:0% +if the contrast changes by a factor of +two it shouldn't change your match + + align:start position:0% +two it shouldn't change your match + + + align:start position:0% +two it shouldn't change your match +because there are cases where you you + + align:start position:0% +because there are cases where you you + + + align:start position:0% +because there are cases where you you +want to know about that because it could + + align:start position:0% +want to know about that because it could + + + align:start position:0% +want to know about that because it could +be an indication of a defect but in this + + align:start position:0% +be an indication of a defect but in this + + + align:start position:0% +be an indication of a defect but in this +alignment problem uh we may not want to + + align:start position:0% +alignment problem uh we may not want to + + + align:start position:0% +alignment problem uh we may not want to +care about that and so in that case what + + align:start position:0% +care about that and so in that case what + + + align:start position:0% +care about that and so in that case what +we do is + + align:start position:0% + + + + align:start position:0% + +we compute the correlation again as + + align:start position:0% +we compute the correlation again as + + + align:start position:0% +we compute the correlation again as +before + + align:start position:0% +before + + + align:start position:0% +before +but now we normalize it + + align:start position:0% + + + + align:start position:0% + +or if you like you can turn it into two + + align:start position:0% +or if you like you can turn it into two + + + align:start position:0% +or if you like you can turn it into two +square roots + + align:start position:0% +square roots + + + align:start position:0% +square roots +whichever way you want to do it so um + + align:start position:0% +whichever way you want to do it so um + + + align:start position:0% +whichever way you want to do it so um +so we're sort of removing we're trying + + align:start position:0% +so we're sort of removing we're trying + + + align:start position:0% +so we're sort of removing we're trying +to remove as many things that could + + align:start position:0% +to remove as many things that could + + + align:start position:0% +to remove as many things that could +disturb the computation as possible one + + align:start position:0% +disturb the computation as possible one + + + align:start position:0% +disturb the computation as possible one +is a shift in mean and the other one is + + align:start position:0% +is a shift in mean and the other one is + + + align:start position:0% +is a shift in mean and the other one is +the shift in contrast + + align:start position:0% +the shift in contrast + + + align:start position:0% +the shift in contrast +brightness and contrast and so this one + + align:start position:0% +brightness and contrast and so this one + + + align:start position:0% +brightness and contrast and so this one +here has the great feature that + + align:start position:0% +here has the great feature that + + + align:start position:0% +here has the great feature that +um if we have a perfect match + + align:start position:0% +um if we have a perfect match + + + align:start position:0% +um if we have a perfect match +if e1 equals e2 uh what do we get + + align:start position:0% + + + + align:start position:0% + +e 1 equals e 2 means this one's the + + align:start position:0% +e 1 equals e 2 means this one's the + + + align:start position:0% +e 1 equals e 2 means this one's the +integral of e 1 e 2 squared + + align:start position:0% +integral of e 1 e 2 squared + + + align:start position:0% +integral of e 1 e 2 squared +e 1 e 2 + + align:start position:0% +e 1 e 2 + + + align:start position:0% +e 1 e 2 +e 1 squared and this one's integral e 1 + + align:start position:0% +e 1 squared and this one's integral e 1 + + + align:start position:0% +e 1 squared and this one's integral e 1 +squared this one's integral e 1 squared + + align:start position:0% +squared this one's integral e 1 squared + + + align:start position:0% +squared this one's integral e 1 squared +i multiply these take the square root so + + align:start position:0% +i multiply these take the square root so + + + align:start position:0% +i multiply these take the square root so +the whole thing + + align:start position:0% +the whole thing + + + align:start position:0% +the whole thing +you can see how it's cancelling out yeah + + align:start position:0% +you can see how it's cancelling out yeah + + + align:start position:0% +you can see how it's cancelling out yeah +so the oh yes thank you we went to all + + align:start position:0% +so the oh yes thank you we went to all + + + align:start position:0% +so the oh yes thank you we went to all +the trouble of subtracting out the mean + + align:start position:0% +the trouble of subtracting out the mean + + + align:start position:0% +the trouble of subtracting out the mean +and then + + align:start position:0% +and then + + + align:start position:0% +and then +we dropped it so okay + + align:start position:0% +we dropped it so okay + + + align:start position:0% +we dropped it so okay +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +the ideal value for this is one + + align:start position:0% +the ideal value for this is one + + + align:start position:0% +the ideal value for this is one +so if we have a perfect match uh that + + align:start position:0% +so if we have a perfect match uh that + + + align:start position:0% +so if we have a perfect match uh that +that is one + + align:start position:0% +that is one + + + align:start position:0% +that is one +and you can show that + + align:start position:0% +and you can show that + + + align:start position:0% +and you can show that +this is limited to the range minus one + + align:start position:0% +this is limited to the range minus one + + + align:start position:0% +this is limited to the range minus one +to plus one + + align:start position:0% + + + + align:start position:0% + +it has to lie in that range minus one is + + align:start position:0% +it has to lie in that range minus one is + + + align:start position:0% +it has to lie in that range minus one is +you in some sense have a perfect + + align:start position:0% +you in some sense have a perfect + + + align:start position:0% +you in some sense have a perfect +mismatch what that means is that one of + + align:start position:0% +mismatch what that means is that one of + + + align:start position:0% +mismatch what that means is that one of +the image is the negative of the other + + align:start position:0% +the image is the negative of the other + + + align:start position:0% +the image is the negative of the other +so not very likely in practice and 0 + + align:start position:0% +so not very likely in practice and 0 + + + align:start position:0% +so not very likely in practice and 0 +means well there's no real correlation + + align:start position:0% +means well there's no real correlation + + + align:start position:0% +means well there's no real correlation +of course if you take + + align:start position:0% +of course if you take + + + align:start position:0% +of course if you take +you know two arbitrary pictures you're + + align:start position:0% +you know two arbitrary pictures you're + + + align:start position:0% +you know two arbitrary pictures you're +going to get some number it's very + + align:start position:0% +going to get some number it's very + + + align:start position:0% +going to get some number it's very +unlikely you'll get zero but you won't + + align:start position:0% +unlikely you'll get zero but you won't + + + align:start position:0% +unlikely you'll get zero but you won't +get a number close to one unless there + + align:start position:0% +get a number close to one unless there + + + align:start position:0% +get a number close to one unless there +really is a reasonable match + + align:start position:0% +really is a reasonable match + + + align:start position:0% +really is a reasonable match +and so this is called + + align:start position:0% +and so this is called + + + align:start position:0% +and so this is called +pearson's correlation + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +so that means that + + align:start position:0% + + + + align:start position:0% + +the normalized correlation method for + + align:start position:0% +the normalized correlation method for + + + align:start position:0% +the normalized correlation method for +finding the pose uh has the property now + + align:start position:0% +finding the pose uh has the property now + + + align:start position:0% +finding the pose uh has the property now +that um not only can we find the peak + + align:start position:0% +that um not only can we find the peak + + + align:start position:0% +that um not only can we find the peak +but we can have some sort of uh measure + + align:start position:0% +but we can have some sort of uh measure + + + align:start position:0% +but we can have some sort of uh measure +of success like you know if the + + align:start position:0% +of success like you know if the + + + align:start position:0% +of success like you know if the +correlation is 0.6 that's that's not + + align:start position:0% +correlation is 0.6 that's that's not + + + align:start position:0% +correlation is 0.6 that's that's not +great uh if the correlation is 0.95 well + + align:start position:0% +great uh if the correlation is 0.95 well + + + align:start position:0% +great uh if the correlation is 0.95 well +that's probably a very good match so it + + align:start position:0% +that's probably a very good match so it + + + align:start position:0% +that's probably a very good match so it +probably is an acceptable uh match + + align:start position:0% +probably is an acceptable uh match + + + align:start position:0% +probably is an acceptable uh match +uh again as i mentioned it's expensive + + align:start position:0% +uh again as i mentioned it's expensive + + + align:start position:0% +uh again as i mentioned it's expensive +and one of cognex's early claim to fame + + align:start position:0% +and one of cognex's early claim to fame + + + align:start position:0% +and one of cognex's early claim to fame +was that they were able to speed it up + + align:start position:0% +was that they were able to speed it up + + + align:start position:0% +was that they were able to speed it up +tremendously by clever uh programming + + align:start position:0% +tremendously by clever uh programming + + + align:start position:0% +tremendously by clever uh programming +and making use of the + + align:start position:0% +and making use of the + + + align:start position:0% +and making use of the +multi-byte instructions that were + + align:start position:0% +multi-byte instructions that were + + + align:start position:0% +multi-byte instructions that were +available on intel platform + + align:start position:0% + + + + align:start position:0% + +so what's wrong with this + + align:start position:0% +so what's wrong with this + + + align:start position:0% +so what's wrong with this +well uh there are a number of things one + + align:start position:0% +well uh there are a number of things one + + + align:start position:0% +well uh there are a number of things one +of them is that if part of one of the + + align:start position:0% +of them is that if part of one of the + + + align:start position:0% +of them is that if part of one of the +objects is obscured so you've got your + + align:start position:0% +objects is obscured so you've got your + + + align:start position:0% +objects is obscured so you've got your +golden template where everything is + + align:start position:0% +golden template where everything is + + + align:start position:0% +golden template where everything is +perfect and then you have the real world + + align:start position:0% +perfect and then you have the real world + + + align:start position:0% +perfect and then you have the real world +thing where maybe there's a piece of + + align:start position:0% +thing where maybe there's a piece of + + + align:start position:0% +thing where maybe there's a piece of +paper lying over the corner of the + + align:start position:0% +paper lying over the corner of the + + + align:start position:0% +paper lying over the corner of the +object or a second object is sort of + + align:start position:0% +object or a second object is sort of + + + align:start position:0% +object or a second object is sort of +partially lying on top of it well that's + + align:start position:0% +partially lying on top of it well that's + + + align:start position:0% +partially lying on top of it well that's +going to mess this up because in that + + align:start position:0% +going to mess this up because in that + + + align:start position:0% +going to mess this up because in that +area the e1 and e2 won't be matching + + align:start position:0% +area the e1 and e2 won't be matching + + + align:start position:0% +area the e1 and e2 won't be matching +or if you have + + align:start position:0% +or if you have + + + align:start position:0% +or if you have +missing parts + + align:start position:0% +missing parts + + + align:start position:0% +missing parts +you've got a + + align:start position:0% +you've got a + + + align:start position:0% +you've got a +gear with various teeth and some of the + + align:start position:0% +gear with various teeth and some of the + + + align:start position:0% +gear with various teeth and some of the +teeth are not there + + align:start position:0% +teeth are not there + + + align:start position:0% +teeth are not there +then that's going to affect this + + align:start position:0% +then that's going to affect this + + + align:start position:0% +then that's going to affect this +match + + align:start position:0% +match + + + align:start position:0% +match +nevertheless it was uh + + align:start position:0% +nevertheless it was uh + + + align:start position:0% +nevertheless it was uh +you know used quite a bit uh + + align:start position:0% +you know used quite a bit uh + + + align:start position:0% +you know used quite a bit uh +for a while and + + align:start position:0% +for a while and + + + align:start position:0% +for a while and +now we're going to the patent which says + + align:start position:0% +now we're going to the patent which says + + + align:start position:0% +now we're going to the patent which says +we can do better so um + + align:start position:0% + + + + align:start position:0% + +see if i have a bit more luckier than i + + align:start position:0% +see if i have a bit more luckier than i + + + align:start position:0% +see if i have a bit more luckier than i +did earlier today + + align:start position:0% +did earlier today + + + align:start position:0% +did earlier today +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +patent number 7016 so we've come up a + + align:start position:0% +patent number 7016 so we've come up a + + + align:start position:0% +patent number 7016 so we've come up a +bit the last one was in the six million + + align:start position:0% +bit the last one was in the six million + + + align:start position:0% +bit the last one was in the six million +methods for fast robust + + align:start position:0% +methods for fast robust + + + align:start position:0% +methods for fast robust +multi-dimensional pattern recognition so + + align:start position:0% +multi-dimensional pattern recognition so + + + align:start position:0% +multi-dimensional pattern recognition so +it's a little confusing terminology + + align:start position:0% +it's a little confusing terminology + + + align:start position:0% +it's a little confusing terminology +multi-dimensional what it what is it + + align:start position:0% +multi-dimensional what it what is it + + + align:start position:0% +multi-dimensional what it what is it +talking about it's primarily aimed at 2d + + align:start position:0% +talking about it's primarily aimed at 2d + + + align:start position:0% +talking about it's primarily aimed at 2d +images and flat surfaces + + align:start position:0% +images and flat surfaces + + + align:start position:0% +images and flat surfaces +but multi-dimensional means they want to + + align:start position:0% +but multi-dimensional means they want to + + + align:start position:0% +but multi-dimensional means they want to +deal with not just translation but + + align:start position:0% +deal with not just translation but + + + align:start position:0% +deal with not just translation but +rotation + + align:start position:0% +rotation + + + align:start position:0% +rotation +scaling + + align:start position:0% +scaling + + + align:start position:0% +scaling +skew and whatever + + align:start position:0% +skew and whatever + + + align:start position:0% +skew and whatever +and they emphasize that because the + + align:start position:0% +and they emphasize that because the + + + align:start position:0% +and they emphasize that because the +previous method + + align:start position:0% +previous method + + + align:start position:0% +previous method +the best method was normalized + + align:start position:0% +the best method was normalized + + + align:start position:0% +the best method was normalized +correlation and it was so + + align:start position:0% +correlation and it was so + + + align:start position:0% +correlation and it was so +computationally expensive that you + + align:start position:0% +computationally expensive that you + + + align:start position:0% +computationally expensive that you +couldn't really do anything other than + + align:start position:0% +couldn't really do anything other than + + + align:start position:0% +couldn't really do anything other than +translation and so this one is called + + align:start position:0% +translation and so this one is called + + + align:start position:0% +translation and so this one is called +multi-dimensional and then the usual + + align:start position:0% +multi-dimensional and then the usual + + + align:start position:0% +multi-dimensional and then the usual +stuff the list of inventors they're + + align:start position:0% +stuff the list of inventors they're + + + align:start position:0% +stuff the list of inventors they're +signees again cognex + + align:start position:0% +signees again cognex + + + align:start position:0% +signees again cognex +and then the field which we said wasn't + + align:start position:0% +and then the field which we said wasn't + + + align:start position:0% +and then the field which we said wasn't +particularly important + + align:start position:0% +particularly important + + + align:start position:0% +particularly important +and then the references so + + align:start position:0% +and then the references so + + + align:start position:0% +and then the references so +the first bunch of references are their + + align:start position:0% +the first bunch of references are their + + + align:start position:0% +the first bunch of references are their +own citations + + align:start position:0% +own citations + + + align:start position:0% +own citations +and i guess up at the top on the right + + align:start position:0% +and i guess up at the top on the right + + + align:start position:0% +and i guess up at the top on the right +are some starred ones which the patent + + align:start position:0% +are some starred ones which the patent + + + align:start position:0% +are some starred ones which the patent +examiner uh threw in the pot + + align:start position:0% +examiner uh threw in the pot + + + align:start position:0% +examiner uh threw in the pot +along with the field from where they + + align:start position:0% +along with the field from where they + + + align:start position:0% +along with the field from where they +came + + align:start position:0% +came + + + align:start position:0% +came +and then there are + + align:start position:0% +and then there are + + + align:start position:0% +and then there are +several + + align:start position:0% +several + + + align:start position:0% +several +publications general public which isn't + + align:start position:0% +publications general public which isn't + + + align:start position:0% +publications general public which isn't +that common in patents + + align:start position:0% +that common in patents + + + align:start position:0% +that common in patents +okay so abstract so this + + align:start position:0% +okay so abstract so this + + + align:start position:0% +okay so abstract so this +they say it right up front discloses a + + align:start position:0% +they say it right up front discloses a + + + align:start position:0% +they say it right up front discloses a +method for determining the absence of + + align:start position:0% +method for determining the absence of + + + align:start position:0% +method for determining the absence of +presence of one or more instance of a + + align:start position:0% +presence of one or more instance of a + + + align:start position:0% +presence of one or more instance of a +predetermined pattern in an image and + + align:start position:0% +predetermined pattern in an image and + + + align:start position:0% +predetermined pattern in an image and +for determining the location of each + + align:start position:0% +for determining the location of each + + + align:start position:0% +for determining the location of each +found image within a multi-dimensional + + align:start position:0% +found image within a multi-dimensional + + + align:start position:0% +found image within a multi-dimensional +space + + align:start position:0% +space + + + align:start position:0% +space +a model + + align:start position:0% +a model + + + align:start position:0% +a model +representing the pattern to be found the + + align:start position:0% +representing the pattern to be found the + + + align:start position:0% +representing the pattern to be found the +model including a plurality of probes so + + align:start position:0% +model including a plurality of probes so + + + align:start position:0% +model including a plurality of probes so +talk about what probes are each probe + + align:start position:0% +talk about what probes are each probe + + + align:start position:0% +talk about what probes are each probe +represents a relative position at which + + align:start position:0% +represents a relative position at which + + + align:start position:0% +represents a relative position at which +a test is performed so this is very + + align:start position:0% +a test is performed so this is very + + + align:start position:0% +a test is performed so this is very +different in nature from all of the + + align:start position:0% +different in nature from all of the + + + align:start position:0% +different in nature from all of the +other stuff we talked about before in + + align:start position:0% +other stuff we talked about before in + + + align:start position:0% +other stuff we talked about before in +that it's creating this abstract + + align:start position:0% +that it's creating this abstract + + + align:start position:0% +that it's creating this abstract +representation and using that in the + + align:start position:0% +representation and using that in the + + + align:start position:0% +representation and using that in the +match + + align:start position:0% +match + + + align:start position:0% +match +the method further includes a comparison + + align:start position:0% +the method further includes a comparison + + + align:start position:0% +the method further includes a comparison +of the model with a runtime image at + + align:start position:0% +of the model with a runtime image at + + + align:start position:0% +of the model with a runtime image at +each of a plurality of poses so you try + + align:start position:0% +each of a plurality of poses so you try + + + align:start position:0% +each of a plurality of poses so you try +different positions rotations etc + + align:start position:0% +different positions rotations etc + + + align:start position:0% +different positions rotations etc +and a match score is computed and then + + align:start position:0% +and a match score is computed and then + + + align:start position:0% +and a match score is computed and then +you can define a match surface and + + align:start position:0% +you can define a match surface and + + + align:start position:0% +you can define a match surface and +you're looking for the peak of that + + align:start position:0% +you're looking for the peak of that + + + align:start position:0% +you're looking for the peak of that +surface but now remember it's in a + + align:start position:0% +surface but now remember it's in a + + + align:start position:0% +surface but now remember it's in a +multi-dimensional space so you could be + + align:start position:0% +multi-dimensional space so you could be + + + align:start position:0% +multi-dimensional space so you could be +in five-dimensional space looking for a + + align:start position:0% +in five-dimensional space looking for a + + + align:start position:0% +in five-dimensional space looking for a +peak and the match score is also + + align:start position:0% +peak and the match score is also + + + align:start position:0% +peak and the match score is also +compared with an accept threshold so we + + align:start position:0% +compared with an accept threshold so we + + + align:start position:0% +compared with an accept threshold so we +do have finally have thresholds but the + + align:start position:0% +do have finally have thresholds but the + + + align:start position:0% +do have finally have thresholds but the +attempt is to have + + align:start position:0% +attempt is to have + + + align:start position:0% +attempt is to have +delay any decision making have + + align:start position:0% +delay any decision making have + + + align:start position:0% +delay any decision making have +thresholds + + align:start position:0% +thresholds + + + align:start position:0% +thresholds +right at the end when you have a lot of + + align:start position:0% +right at the end when you have a lot of + + + align:start position:0% +right at the end when you have a lot of +information + + align:start position:0% +information + + + align:start position:0% +information +and used to provide a location of any + + align:start position:0% +and used to provide a location of any + + + align:start position:0% +and used to provide a location of any +instances of the pattern of the image so + + align:start position:0% +instances of the pattern of the image so + + + align:start position:0% +instances of the pattern of the image so +that may include the case where there's + + align:start position:0% +that may include the case where there's + + + align:start position:0% +that may include the case where there's +more than one instance of the pattern in + + align:start position:0% +more than one instance of the pattern in + + + align:start position:0% +more than one instance of the pattern in +the image + + align:start position:0% +the image + + + align:start position:0% +the image +or zero instances of the pattern in the + + align:start position:0% +or zero instances of the pattern in the + + + align:start position:0% +or zero instances of the pattern in the +image + + align:start position:0% + + + + align:start position:0% + +okay and then of course the examiner + + align:start position:0% +okay and then of course the examiner + + + align:start position:0% +okay and then of course the examiner +pulled out + + align:start position:0% +pulled out + + + align:start position:0% +pulled out +one of the figures which he thought was + + align:start position:0% +one of the figures which he thought was + + + align:start position:0% +one of the figures which he thought was +most relevant and actually let's just + + align:start position:0% +most relevant and actually let's just + + + align:start position:0% +most relevant and actually let's just +look at that so the idea is we have a + + align:start position:0% +look at that so the idea is we have a + + + align:start position:0% +look at that so the idea is we have a +training image + + align:start position:0% +training image + + + align:start position:0% +training image +the golden standard and this could be + + align:start position:0% +the golden standard and this could be + + + align:start position:0% +the golden standard and this could be +the top of a phillips head screwdriver + + align:start position:0% +the top of a phillips head screwdriver + + + align:start position:0% +the top of a phillips head screwdriver +it's true or something + + align:start position:0% +it's true or something + + + align:start position:0% +it's true or something +and then there's code training which + + align:start position:0% +and then there's code training which + + + align:start position:0% +and then there's code training which +produces a model + + align:start position:0% +produces a model + + + align:start position:0% +produces a model +and then there's a runtime image when + + align:start position:0% +and then there's a runtime image when + + + align:start position:0% +and then there's a runtime image when +you're actually running the system the + + align:start position:0% +you're actually running the system the + + + align:start position:0% +you're actually running the system the +robot's moving stuff around + + align:start position:0% +robot's moving stuff around + + + align:start position:0% +robot's moving stuff around +and you combine the model with a runtime + + align:start position:0% +and you combine the model with a runtime + + + align:start position:0% +and you combine the model with a runtime +image using a list of generalized + + align:start position:0% +image using a list of generalized + + + align:start position:0% +image using a list of generalized +degrees of freedom so + + align:start position:0% +degrees of freedom so + + + align:start position:0% +degrees of freedom so +generalized in the sense they don't need + + align:start position:0% +generalized in the sense they don't need + + + align:start position:0% +generalized in the sense they don't need +to be just the obvious things like + + align:start position:0% +to be just the obvious things like + + + align:start position:0% +to be just the obvious things like +translation and rotation + + align:start position:0% +translation and rotation + + + align:start position:0% +translation and rotation +and so at runtime + + align:start position:0% +and so at runtime + + + align:start position:0% +and so at runtime +you then do this comparison then you + + align:start position:0% +you then do this comparison then you + + + align:start position:0% +you then do this comparison then you +produce a list of results a list of + + align:start position:0% +produce a list of results a list of + + + align:start position:0% +produce a list of results a list of +potential matches along with scores of + + align:start position:0% +potential matches along with scores of + + + align:start position:0% +potential matches along with scores of +those matches so + + align:start position:0% +those matches so + + + align:start position:0% +those matches so +and you know they're more references + + align:start position:0% +and you know they're more references + + + align:start position:0% +and you know they're more references +that went over from + + align:start position:0% +that went over from + + + align:start position:0% +that went over from +the idea is to get all of that other + + align:start position:0% +the idea is to get all of that other + + + align:start position:0% +the idea is to get all of that other +stuff on the front page so if there's + + align:start position:0% +stuff on the front page so if there's + + + align:start position:0% +stuff on the front page so if there's +too much of anything like references + + align:start position:0% +too much of anything like references + + + align:start position:0% +too much of anything like references +that end up on the second page and you + + align:start position:0% +that end up on the second page and you + + + align:start position:0% +that end up on the second page and you +can see these last few were put in by + + align:start position:0% +can see these last few were put in by + + + align:start position:0% +can see these last few were put in by +the examiner + + align:start position:0% +the examiner + + + align:start position:0% +the examiner +and i guess uh you know bill silva + + align:start position:0% +and i guess uh you know bill silva + + + align:start position:0% +and i guess uh you know bill silva +coming from an academic world references + + align:start position:0% +coming from an academic world references + + + align:start position:0% +coming from an academic world references +you may recognize some of these names + + align:start position:0% +you may recognize some of these names + + + align:start position:0% +you may recognize some of these names +like + + align:start position:0% +like + + + align:start position:0% +like +eric crimson anyone know about eric + + align:start position:0% +eric crimson anyone know about eric + + + align:start position:0% +eric crimson anyone know about eric +crimson + + align:start position:0% +crimson + + + align:start position:0% +crimson +big shot here at mit so at that time he + + align:start position:0% +big shot here at mit so at that time he + + + align:start position:0% +big shot here at mit so at that time he +was doing vision + + align:start position:0% +was doing vision + + + align:start position:0% +was doing vision +see what can happen to you + + align:start position:0% +see what can happen to you + + + align:start position:0% +see what can happen to you +you can be working on vision next thing + + align:start position:0% +you can be working on vision next thing + + + align:start position:0% +you can be working on vision next thing +you know you're an important person so + + align:start position:0% +you know you're an important person so + + + align:start position:0% +you know you're an important person so +sorry shouldn't shouldn't make fun uh + + align:start position:0% +sorry shouldn't shouldn't make fun uh + + + align:start position:0% +sorry shouldn't shouldn't make fun uh +training image so there's figure one + + align:start position:0% +training image so there's figure one + + + align:start position:0% +training image so there's figure one +there we just saw that + + align:start position:0% +there we just saw that + + + align:start position:0% +there we just saw that +um + + align:start position:0% + + + + align:start position:0% + +and here is figure two and now + + align:start position:0% +and here is figure two and now + + + align:start position:0% +and here is figure two and now +this should look very familiar to you + + align:start position:0% +this should look very familiar to you + + + align:start position:0% +this should look very familiar to you +because most of this is what we talked + + align:start position:0% +because most of this is what we talked + + + align:start position:0% +because most of this is what we talked +about in the previous pattern right so + + align:start position:0% +about in the previous pattern right so + + + align:start position:0% +about in the previous pattern right so +um starting here we estimate the + + align:start position:0% +um starting here we estimate the + + + align:start position:0% +um starting here we estimate the +gradient the x and y components we do + + align:start position:0% +gradient the x and y components we do + + + align:start position:0% +gradient the x and y components we do +the cartesian to polar conversion which + + align:start position:0% +the cartesian to polar conversion which + + + align:start position:0% +the cartesian to polar conversion which +could be done using chordic or some + + align:start position:0% +could be done using chordic or some + + + align:start position:0% +could be done using chordic or some +other method and it produces the + + align:start position:0% +other method and it produces the + + + align:start position:0% +other method and it produces the +gradient magnitude and the gradient + + align:start position:0% +gradient magnitude and the gradient + + + align:start position:0% +gradient magnitude and the gradient +direction again at every pixel so we can + + align:start position:0% +direction again at every pixel so we can + + + align:start position:0% +direction again at every pixel so we can +think of it as an image + + align:start position:0% +think of it as an image + + + align:start position:0% +think of it as an image +we do a peak detection in the direction + + align:start position:0% +we do a peak detection in the direction + + + align:start position:0% +we do a peak detection in the direction +of the gradient you know quantized + + align:start position:0% +of the gradient you know quantized + + + align:start position:0% +of the gradient you know quantized +direction of the gradient and from that + + align:start position:0% +direction of the gradient and from that + + + align:start position:0% +direction of the gradient and from that +we get column row magnitude direction + + align:start position:0% +we get column row magnitude direction + + + align:start position:0% +we get column row magnitude direction +and then we do the sub pixel + + align:start position:0% +and then we do the sub pixel + + + align:start position:0% +and then we do the sub pixel +interpolation and all those clever + + align:start position:0% +interpolation and all those clever + + + align:start position:0% +interpolation and all those clever +things like the plane projection and the + + align:start position:0% +things like the plane projection and the + + + align:start position:0% +things like the plane projection and the +bias removal and what we end up with in + + align:start position:0% +bias removal and what we end up with in + + + align:start position:0% +bias removal and what we end up with in +the end is a + + align:start position:0% +the end is a + + + align:start position:0% +the end is a +list of boundary points so that's the + + align:start position:0% +list of boundary points so that's the + + + align:start position:0% +list of boundary points so that's the +output of that previous one there are a + + align:start position:0% +output of that previous one there are a + + + align:start position:0% +output of that previous one there are a +couple of the extra things here that + + align:start position:0% +couple of the extra things here that + + + align:start position:0% +couple of the extra things here that +weren't there + + align:start position:0% +weren't there + + + align:start position:0% +weren't there +the top row + + align:start position:0% +the top row + + + align:start position:0% +the top row +so in in the previous discussion they + + align:start position:0% +so in in the previous discussion they + + + align:start position:0% +so in in the previous discussion they +did mention multiscale but they didn't + + align:start position:0% +did mention multiscale but they didn't + + + align:start position:0% +did mention multiscale but they didn't +talk about it much in the pattern but + + align:start position:0% +talk about it much in the pattern but + + + align:start position:0% +talk about it much in the pattern but +here it's more important and so we are + + align:start position:0% +here it's more important and so we are + + + align:start position:0% +here it's more important and so we are +working + + align:start position:0% +working + + + align:start position:0% +working +at sub samples + + align:start position:0% +at sub samples + + + align:start position:0% +at sub samples +of the image + + align:start position:0% +of the image + + + align:start position:0% +of the image +possibly several different layers + + align:start position:0% +possibly several different layers + + + align:start position:0% +possibly several different layers +different resolutions + + align:start position:0% +different resolutions + + + align:start position:0% +different resolutions +and of course before we subsample by + + align:start position:0% +and of course before we subsample by + + + align:start position:0% +and of course before we subsample by +nyquist + + align:start position:0% +nyquist + + + align:start position:0% +nyquist +we have to + + align:start position:0% +we have to + + + align:start position:0% +we have to +try and remove high frequencies or we + + align:start position:0% +try and remove high frequencies or we + + + align:start position:0% +try and remove high frequencies or we +get aliasing so we have a low pass + + align:start position:0% +get aliasing so we have a low pass + + + align:start position:0% +get aliasing so we have a low pass +filter or approximation to a low-pass + + align:start position:0% +filter or approximation to a low-pass + + + align:start position:0% +filter or approximation to a low-pass +filter so we take the source image we + + align:start position:0% +filter so we take the source image we + + + align:start position:0% +filter so we take the source image we +low-pass filter we sub-sample and we may + + align:start position:0% +low-pass filter we sub-sample and we may + + + align:start position:0% +low-pass filter we sub-sample and we may +do this several times at different + + align:start position:0% +do this several times at different + + + align:start position:0% +do this several times at different +resolutions and then we do all of this + + align:start position:0% +resolutions and then we do all of this + + + align:start position:0% +resolutions and then we do all of this +edge detection stuff and we end up with + + align:start position:0% +edge detection stuff and we end up with + + + align:start position:0% +edge detection stuff and we end up with +a list of potential boundary points + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% + + + + align:start position:0% + +talking of multiple scales + + align:start position:0% + + + + align:start position:0% + +what would be nice to do is to use the + + align:start position:0% +what would be nice to do is to use the + + + align:start position:0% +what would be nice to do is to use the +coarsest scale that'll work because the + + align:start position:0% +coarsest scale that'll work because the + + + align:start position:0% +coarsest scale that'll work because the +computational load depends of course + + align:start position:0% +computational load depends of course + + + align:start position:0% +computational load depends of course +heavily on the scale if you're working + + align:start position:0% +heavily on the scale if you're working + + + align:start position:0% +heavily on the scale if you're working +at the full image resolution there's a + + align:start position:0% +at the full image resolution there's a + + + align:start position:0% +at the full image resolution there's a +lot of computing going on if you work at + + align:start position:0% +lot of computing going on if you work at + + + align:start position:0% +lot of computing going on if you work at +half a resolution you know it's a + + align:start position:0% +half a resolution you know it's a + + + align:start position:0% +half a resolution you know it's a +quarter the amount of work and so on so + + align:start position:0% +quarter the amount of work and so on so + + + align:start position:0% +quarter the amount of work and so on so +uh one of the aspects of this patent is + + align:start position:0% +uh one of the aspects of this patent is + + + align:start position:0% +uh one of the aspects of this patent is +how do i decide what is the courses + + align:start position:0% +how do i decide what is the courses + + + align:start position:0% +how do i decide what is the courses +level that i can use and + + align:start position:0% +level that i can use and + + + align:start position:0% +level that i can use and +they go through a whole story about that + + align:start position:0% +they go through a whole story about that + + + align:start position:0% +they go through a whole story about that +and for some reason it ends up being the + + align:start position:0% +and for some reason it ends up being the + + + align:start position:0% +and for some reason it ends up being the +first step up there and that's kind of + + align:start position:0% +first step up there and that's kind of + + + align:start position:0% +first step up there and that's kind of +there because + + align:start position:0% +there because + + + align:start position:0% +there because +you can't do any of the other stuff un + + align:start position:0% +you can't do any of the other stuff un + + + align:start position:0% +you can't do any of the other stuff un +unless you've picked a particular + + align:start position:0% +unless you've picked a particular + + + align:start position:0% +unless you've picked a particular +resolution but actually + + align:start position:0% +resolution but actually + + + align:start position:0% +resolution but actually +the way it really works is you run it at + + align:start position:0% +the way it really works is you run it at + + + align:start position:0% +the way it really works is you run it at +several different resolutions and you + + align:start position:0% +several different resolutions and you + + + align:start position:0% +several different resolutions and you +look at the results and decide which is + + align:start position:0% +look at the results and decide which is + + + align:start position:0% +look at the results and decide which is +the closest resolution that gives me + + align:start position:0% +the closest resolution that gives me + + + align:start position:0% +the closest resolution that gives me +reliable results + + align:start position:0% +reliable results + + + align:start position:0% +reliable results +okay then process the training image to + + align:start position:0% +okay then process the training image to + + + align:start position:0% +okay then process the training image to +obtain the boundary points that's that + + align:start position:0% +obtain the boundary points that's that + + + align:start position:0% +obtain the boundary points that's that +previous + + align:start position:0% +previous + + + align:start position:0% +previous +patent + + align:start position:0% +patent + + + align:start position:0% +patent +then we connect neighboring boundary + + align:start position:0% +then we connect neighboring boundary + + + align:start position:0% +then we connect neighboring boundary +points that have consistent directions + + align:start position:0% +points that have consistent directions + + + align:start position:0% +points that have consistent directions +uh so you you start to chain them + + align:start position:0% +uh so you you start to chain them + + + align:start position:0% +uh so you you start to chain them +together organize connected boundary + + align:start position:0% +together organize connected boundary + + + align:start position:0% +together organize connected boundary +points in the chain + + align:start position:0% +points in the chain + + + align:start position:0% +points in the chain +and we talked a little bit about how you + + align:start position:0% +and we talked a little bit about how you + + + align:start position:0% +and we talked a little bit about how you +break them where there's a sudden change + + align:start position:0% +break them where there's a sudden change + + + align:start position:0% +break them where there's a sudden change +in direction because that's probably a + + align:start position:0% +in direction because that's probably a + + + align:start position:0% +in direction because that's probably a +corner + + align:start position:0% +corner + + + align:start position:0% +corner +of some sort uh then you so here's the + + align:start position:0% +of some sort uh then you so here's the + + + align:start position:0% +of some sort uh then you so here's the +form of thresholding uh as we said that + + align:start position:0% +form of thresholding uh as we said that + + + align:start position:0% +form of thresholding uh as we said that +um + + align:start position:0% +um + + + align:start position:0% +um +you know it's going to find edges + + align:start position:0% +you know it's going to find edges + + + align:start position:0% +you know it's going to find edges +everywhere including + + align:start position:0% +everywhere including + + + align:start position:0% +everywhere including +background texture and some of those + + align:start position:0% +background texture and some of those + + + align:start position:0% +background texture and some of those +quote edges have the feature that they + + align:start position:0% +quote edges have the feature that they + + + align:start position:0% +quote edges have the feature that they +have very low contrast + + align:start position:0% +have very low contrast + + + align:start position:0% +have very low contrast +so we can + + align:start position:0% +so we can + + + align:start position:0% +so we can +we could have a threshold and say no we + + align:start position:0% +we could have a threshold and say no we + + + align:start position:0% +we could have a threshold and say no we +don't want those edges but that's + + align:start position:0% +don't want those edges but that's + + + align:start position:0% +don't want those edges but that's +again premature decision making + + align:start position:0% +again premature decision making + + + align:start position:0% +again premature decision making +what they do instead is chain them + + align:start position:0% +what they do instead is chain them + + + align:start position:0% +what they do instead is chain them +together and if they're sort of + + align:start position:0% +together and if they're sort of + + + align:start position:0% +together and if they're sort of +consistent even if they're weak it's + + align:start position:0% +consistent even if they're weak it's + + + align:start position:0% +consistent even if they're weak it's +still an acceptable edge + + align:start position:0% +still an acceptable edge + + + align:start position:0% +still an acceptable edge +if + + align:start position:0% +if + + + align:start position:0% +if +when you chain them together + + align:start position:0% +when you chain them together + + + align:start position:0% +when you chain them together +you can only get very short chains or + + align:start position:0% +you can only get very short chains or + + + align:start position:0% +you can only get very short chains or +their combined weight is very low then + + align:start position:0% +their combined weight is very low then + + + align:start position:0% +their combined weight is very low then +you know throw them out they're just due + + align:start position:0% +you know throw them out they're just due + + + align:start position:0% +you know throw them out they're just due +to noise so the thresholding has been + + align:start position:0% +to noise so the thresholding has been + + + align:start position:0% +to noise so the thresholding has been +postponed all the way down here + + align:start position:0% +postponed all the way down here + + + align:start position:0% +postponed all the way down here +divide change in the segments at low uh + + align:start position:0% +divide change in the segments at low uh + + + align:start position:0% +divide change in the segments at low uh +curvature separated by corners of high + + align:start position:0% +curvature separated by corners of high + + + align:start position:0% +curvature separated by corners of high +curvature + + align:start position:0% +curvature + + + align:start position:0% +curvature +okay and then right now we've got you + + align:start position:0% +okay and then right now we've got you + + + align:start position:0% +okay and then right now we've got you +know an edge + + align:start position:0% +know an edge + + + align:start position:0% +know an edge +uh + + align:start position:0% +uh + + + align:start position:0% +uh +this edge point at every pixel + + align:start position:0% +this edge point at every pixel + + + align:start position:0% +this edge point at every pixel +at whatever resolution we're working at + + align:start position:0% +at whatever resolution we're working at + + + align:start position:0% +at whatever resolution we're working at +and that may not always make sense there + + align:start position:0% +and that may not always make sense there + + + align:start position:0% +and that may not always make sense there +may be that may be highly redundant so + + align:start position:0% +may be that may be highly redundant so + + + align:start position:0% +may be that may be highly redundant so +instead we're going to replace them with + + align:start position:0% +instead we're going to replace them with + + + align:start position:0% +instead we're going to replace them with +a set of points that have desired + + align:start position:0% +a set of points that have desired + + + align:start position:0% +a set of points that have desired +spacing so you can control you know i i + + align:start position:0% +spacing so you can control you know i i + + + align:start position:0% +spacing so you can control you know i i +don't want more than a thousand edge + + align:start position:0% +don't want more than a thousand edge + + + align:start position:0% +don't want more than a thousand edge +points in my model or you can say i + + align:start position:0% +points in my model or you can say i + + + align:start position:0% +points in my model or you can say i +don't want edge points to be further + + align:start position:0% +don't want edge points to be further + + + align:start position:0% +don't want edge points to be further +away than three pixels + + align:start position:0% +away than three pixels + + + align:start position:0% +away than three pixels +but we do not use the edge points from + + align:start position:0% +but we do not use the edge points from + + + align:start position:0% +but we do not use the edge points from +the + + align:start position:0% +the + + + align:start position:0% +the +pre-processing edge pre-processing + + align:start position:0% +pre-processing edge pre-processing + + + align:start position:0% +pre-processing edge pre-processing +directly instead we we fit to the edges + + align:start position:0% +directly instead we we fit to the edges + + + align:start position:0% +directly instead we we fit to the edges +and we + + align:start position:0% +and we + + + align:start position:0% +and we +and you'll see that in in the pattern + + align:start position:0% +and you'll see that in in the pattern + + + align:start position:0% +and you'll see that in in the pattern +then we + + align:start position:0% +then we + + + align:start position:0% +then we +so that's what this is create probes + + align:start position:0% +so that's what this is create probes + + + align:start position:0% +so that's what this is create probes +evenly spaced along statement and store + + align:start position:0% +evenly spaced along statement and store + + + align:start position:0% +evenly spaced along statement and store +and model + + align:start position:0% + + + + align:start position:0% + +so that's creating the model and the + + align:start position:0% +so that's creating the model and the + + + align:start position:0% +so that's creating the model and the +model also has a granularity and it has + + align:start position:0% +model also has a granularity and it has + + + align:start position:0% +model also has a granularity and it has +a contrast and + + align:start position:0% +a contrast and + + + align:start position:0% +a contrast and +the contrast doesn't so much + + align:start position:0% +the contrast doesn't so much + + + align:start position:0% +the contrast doesn't so much +matter in terms of magnitude more a + + align:start position:0% +matter in terms of magnitude more a + + + align:start position:0% +matter in terms of magnitude more a +matter of sign + + align:start position:0% +matter of sign + + + align:start position:0% +matter of sign +so in integrated circuit processing + + align:start position:0% +so in integrated circuit processing + + + align:start position:0% +so in integrated circuit processing +often you'll see as contrast between + + align:start position:0% +often you'll see as contrast between + + + align:start position:0% +often you'll see as contrast between +different materials + + align:start position:0% +different materials + + + align:start position:0% +different materials +but depending on the lighting and + + align:start position:0% +but depending on the lighting and + + + align:start position:0% +but depending on the lighting and +depending on the process the contrast + + align:start position:0% +depending on the process the contrast + + + align:start position:0% +depending on the process the contrast +may actually be flipped so what in the + + align:start position:0% +may actually be flipped so what in the + + + align:start position:0% +may actually be flipped so what in the +master image looked like it was darker + + align:start position:0% +master image looked like it was darker + + + align:start position:0% +master image looked like it was darker +on one side and brighter on the other + + align:start position:0% +on one side and brighter on the other + + + align:start position:0% +on one side and brighter on the other +side may end up being reversed in the + + align:start position:0% +side may end up being reversed in the + + + align:start position:0% +side may end up being reversed in the +runtime image and so you want to be able + + align:start position:0% +runtime image and so you want to be able + + + align:start position:0% +runtime image and so you want to be able +to cope with that i mean the other + + align:start position:0% +to cope with that i mean the other + + + align:start position:0% +to cope with that i mean the other +situations where that doesn't make any + + align:start position:0% +situations where that doesn't make any + + + align:start position:0% +situations where that doesn't make any +sense where if the contrast is flipped + + align:start position:0% +sense where if the contrast is flipped + + + align:start position:0% +sense where if the contrast is flipped +there's something horribly wrong and you + + align:start position:0% +there's something horribly wrong and you + + + align:start position:0% +there's something horribly wrong and you +know you should just stop + + align:start position:0% +know you should just stop + + + align:start position:0% +know you should just stop +but in the case of integrated circuit + + align:start position:0% +but in the case of integrated circuit + + + align:start position:0% +but in the case of integrated circuit +the way light reflects off + + align:start position:0% +the way light reflects off + + + align:start position:0% +the way light reflects off +semiconductors is such that you may want + + align:start position:0% +semiconductors is such that you may want + + + align:start position:0% +semiconductors is such that you may want +to + + align:start position:0% +to + + + align:start position:0% +to +deal with a flip contrast and so part of + + align:start position:0% +deal with a flip contrast and so part of + + + align:start position:0% +deal with a flip contrast and so part of +the training + + align:start position:0% +the training + + + align:start position:0% +the training +is to determine + + align:start position:0% +is to determine + + + align:start position:0% +is to determine +what contrasts the origin the master + + align:start position:0% +what contrasts the origin the master + + + align:start position:0% +what contrasts the origin the master +copy has + + align:start position:0% +copy has + + + align:start position:0% +copy has +okay so this you know that's sort of + + align:start position:0% +okay so this you know that's sort of + + + align:start position:0% +okay so this you know that's sort of +what we've done so far we + + align:start position:0% +what we've done so far we + + + align:start position:0% +what we've done so far we +find these edge fragments and + + align:start position:0% +find these edge fragments and + + + align:start position:0% +find these edge fragments and +so here's a question for you + + align:start position:0% +so here's a question for you + + + align:start position:0% +so here's a question for you +where the pixels + + align:start position:0% +where the pixels + + + align:start position:0% +where the pixels +so are these squares the pixels + + align:start position:0% +so are these squares the pixels + + + align:start position:0% +so are these squares the pixels +or the centers of the pixels at the + + align:start position:0% +or the centers of the pixels at the + + + align:start position:0% +or the centers of the pixels at the +intersections of the + + align:start position:0% +intersections of the + + + align:start position:0% +intersections of the +lines + + align:start position:0% + + + + align:start position:0% + +well i'll let you ponder that okay so + + align:start position:0% +well i'll let you ponder that okay so + + + align:start position:0% +well i'll let you ponder that okay so +there uh + + align:start position:0% + + + + align:start position:0% + +and this is explaining various parts of + + align:start position:0% +and this is explaining various parts of + + + align:start position:0% +and this is explaining various parts of +the + + align:start position:0% +the + + + align:start position:0% +the +combining the edge frame it's connecting + + align:start position:0% +combining the edge frame it's connecting + + + align:start position:0% +combining the edge frame it's connecting +the edge fragments so how do you connect + + align:start position:0% +the edge fragments so how do you connect + + + align:start position:0% +the edge fragments so how do you connect +the edge fragments pairwise well you + + align:start position:0% +the edge fragments pairwise well you + + + align:start position:0% +the edge fragments pairwise well you +have to look at the neighbors and that + + align:start position:0% +have to look at the neighbors and that + + + align:start position:0% +have to look at the neighbors and that +means a number of things one of them is + + align:start position:0% +means a number of things one of them is + + + align:start position:0% +means a number of things one of them is +you have to decide what order to look at + + align:start position:0% +you have to decide what order to look at + + + align:start position:0% +you have to decide what order to look at +the neighbors in + + align:start position:0% +the neighbors in + + + align:start position:0% +the neighbors in +and you want you may run into trouble + + align:start position:0% +and you want you may run into trouble + + + align:start position:0% +and you want you may run into trouble +and you may need tie breaking + + align:start position:0% +and you may need tie breaking + + + align:start position:0% +and you may need tie breaking +very similar to the tie breaking we + + align:start position:0% +very similar to the tie breaking we + + + align:start position:0% +very similar to the tie breaking we +talked about before + + align:start position:0% +talked about before + + + align:start position:0% +talked about before +okay well this is about the sequence + + align:start position:0% +okay well this is about the sequence + + + align:start position:0% +okay well this is about the sequence +that you go around to look at the + + align:start position:0% +that you go around to look at the + + + align:start position:0% +that you go around to look at the +neighbors + + align:start position:0% +neighbors + + + align:start position:0% +neighbors +and then so now you've got them + + align:start position:0% +and then so now you've got them + + + align:start position:0% +and then so now you've got them +connected up pairwise so these are + + align:start position:0% +connected up pairwise so these are + + + align:start position:0% +connected up pairwise so these are +associated in the data structure + + align:start position:0% +associated in the data structure + + + align:start position:0% +associated in the data structure +and then you start worrying about uh + + align:start position:0% +and then you start worrying about uh + + + align:start position:0% +and then you start worrying about uh +where to break them based on curvature + + align:start position:0% +where to break them based on curvature + + + align:start position:0% +where to break them based on curvature +so + + align:start position:0% +so + + + align:start position:0% +so +relatively low curvature up here so + + align:start position:0% +relatively low curvature up here so + + + align:start position:0% +relatively low curvature up here so +those probably should stay together and + + align:start position:0% +those probably should stay together and + + + align:start position:0% +those probably should stay together and +then here there's a maximum of curvature + + align:start position:0% +then here there's a maximum of curvature + + + align:start position:0% +then here there's a maximum of curvature +and and you'd want to + + align:start position:0% +and and you'd want to + + + align:start position:0% +and and you'd want to +probably break up the + + align:start position:0% + + + + align:start position:0% + +and finally you do a probe selection so + + align:start position:0% +and finally you do a probe selection so + + + align:start position:0% +and finally you do a probe selection so +here's the top of the + + align:start position:0% +here's the top of the + + + align:start position:0% +here's the top of the +phillips screw + + align:start position:0% +phillips screw + + + align:start position:0% +phillips screw +and you know from a perfect golden + + align:start position:0% +and you know from a perfect golden + + + align:start position:0% +and you know from a perfect golden +master image and this is our model + + align:start position:0% +master image and this is our model + + + align:start position:0% +master image and this is our model +so we don't store the image uh we store + + align:start position:0% +so we don't store the image uh we store + + + align:start position:0% +so we don't store the image uh we store +these probes and again these these + + align:start position:0% +these probes and again these these + + + align:start position:0% +these probes and again these these +probes are derived from the edges but + + align:start position:0% +probes are derived from the edges but + + + align:start position:0% +probes are derived from the edges but +they're not the edge points they're + + align:start position:0% +they're not the edge points they're + + + align:start position:0% +they're not the edge points they're +interpolated + + align:start position:0% +interpolated + + + align:start position:0% +interpolated +based on you know how many you want + + align:start position:0% +based on you know how many you want + + + align:start position:0% +based on you know how many you want +and you can see that + + align:start position:0% +and you can see that + + + align:start position:0% +and you can see that +they're always pointing so they have a + + align:start position:0% +they're always pointing so they have a + + + align:start position:0% +they're always pointing so they have a +position + + align:start position:0% +position + + + align:start position:0% +position +and they have a direction right that's + + align:start position:0% +and they have a direction right that's + + + align:start position:0% +and they have a direction right that's +the direction of the gradient + + align:start position:0% +the direction of the gradient + + + align:start position:0% +the direction of the gradient +and um + + align:start position:0% +and um + + + align:start position:0% +and um +that's that so that's the model plus as + + align:start position:0% +that's that so that's the model plus as + + + align:start position:0% +that's that so that's the model plus as +i mentioned there's granularity and + + align:start position:0% +i mentioned there's granularity and + + + align:start position:0% +i mentioned there's granularity and +contrast but the the main this is the + + align:start position:0% +contrast but the the main this is the + + + align:start position:0% +contrast but the the main this is the +key thing to remember that this is the + + align:start position:0% +key thing to remember that this is the + + + align:start position:0% +key thing to remember that this is the +model and what are we going to do with + + align:start position:0% +model and what are we going to do with + + + align:start position:0% +model and what are we going to do with +that model well now we want to know + + align:start position:0% +that model well now we want to know + + + align:start position:0% +that model well now we want to know +whether there's a place in the image + + align:start position:0% +whether there's a place in the image + + + align:start position:0% +whether there's a place in the image +where + + align:start position:0% +where + + + align:start position:0% +where +the image matches this model and so we + + align:start position:0% +the image matches this model and so we + + + align:start position:0% +the image matches this model and so we +take the model and we map it onto the + + align:start position:0% +take the model and we map it onto the + + + align:start position:0% +take the model and we map it onto the +image + + align:start position:0% +image + + + align:start position:0% +image +and we we don't look everywhere we only + + align:start position:0% +and we we don't look everywhere we only + + + align:start position:0% +and we we don't look everywhere we only +look where the probes are so the probes + + align:start position:0% +look where the probes are so the probes + + + align:start position:0% +look where the probes are so the probes +are basically + + align:start position:0% +are basically + + + align:start position:0% +are basically +like things where you go to collect + + align:start position:0% +like things where you go to collect + + + align:start position:0% +like things where you go to collect +evidence so like in this case instead of + + align:start position:0% +evidence so like in this case instead of + + + align:start position:0% +evidence so like in this case instead of +having to deal with thousands of pixels + + align:start position:0% +having to deal with thousands of pixels + + + align:start position:0% +having to deal with thousands of pixels +you're dealing with i don't know 100 + + align:start position:0% +you're dealing with i don't know 100 + + + align:start position:0% +you're dealing with i don't know 100 +probes + + align:start position:0% +probes + + + align:start position:0% +probes +and you you map them onto the image you + + align:start position:0% +and you you map them onto the image you + + + align:start position:0% +and you you map them onto the image you +look at the gradient there and you say + + align:start position:0% +look at the gradient there and you say + + + align:start position:0% +look at the gradient there and you say +well if the gradient is + + align:start position:0% +well if the gradient is + + + align:start position:0% +well if the gradient is +you know like that and the novel says it + + align:start position:0% +you know like that and the novel says it + + + align:start position:0% +you know like that and the novel says it +should be that that's no good that's an + + align:start position:0% +should be that that's no good that's an + + + align:start position:0% +should be that that's no good that's an +error + + align:start position:0% +error + + + align:start position:0% +error +so you you + + align:start position:0% +so you you + + + align:start position:0% +so you you +compare the gradients + + align:start position:0% +compare the gradients + + + align:start position:0% +compare the gradients +with the gradients actually observed in + + align:start position:0% +with the gradients actually observed in + + + align:start position:0% +with the gradients actually observed in +the runtime image and you may + + align:start position:0% +the runtime image and you may + + + align:start position:0% +the runtime image and you may +take into account + + align:start position:0% +take into account + + + align:start position:0% +take into account +the direction of the gradient and the + + align:start position:0% +the direction of the gradient and the + + + align:start position:0% +the direction of the gradient and the +magnitude of the gradient + + align:start position:0% +magnitude of the gradient + + + align:start position:0% +magnitude of the gradient +now it turns out that in many cases the + + align:start position:0% +now it turns out that in many cases the + + + align:start position:0% +now it turns out that in many cases the +magnitude of gradient is not very + + align:start position:0% +magnitude of gradient is not very + + + align:start position:0% +magnitude of gradient is not very +reliable it depends on all kinds of + + align:start position:0% +reliable it depends on all kinds of + + + align:start position:0% +reliable it depends on all kinds of +factors you know materials lighting + + align:start position:0% +factors you know materials lighting + + + align:start position:0% +factors you know materials lighting +accidents of alignment and whereas the + + align:start position:0% +accidents of alignment and whereas the + + + align:start position:0% +accidents of alignment and whereas the +direction of the gradient is much more + + align:start position:0% +direction of the gradient is much more + + + align:start position:0% +direction of the gradient is much more +likely to be maintained even if there's + + align:start position:0% +likely to be maintained even if there's + + + align:start position:0% +likely to be maintained even if there's +a change in illumination change of + + align:start position:0% +a change in illumination change of + + + align:start position:0% +a change in illumination change of +material and so on so + + align:start position:0% +material and so on so + + + align:start position:0% +material and so on so +when you do the comparison you probably + + align:start position:0% +when you do the comparison you probably + + + align:start position:0% +when you do the comparison you probably +want to focus on the direction + + align:start position:0% + + + + align:start position:0% + +so so that's an example but you can you + + align:start position:0% +so so that's an example but you can you + + + align:start position:0% +so so that's an example but you can you +can do more and + + align:start position:0% +can do more and + + + align:start position:0% +can do more and +here's a different example + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +each of those + + align:start position:0% +each of those + + + align:start position:0% +each of those +probes + + align:start position:0% +probes + + + align:start position:0% +probes +has a position a direction it also has a + + align:start position:0% +has a position a direction it also has a + + + align:start position:0% +has a position a direction it also has a +weight and that's basically a way of + + align:start position:0% +weight and that's basically a way of + + + align:start position:0% +weight and that's basically a way of +saying you know how important is this + + align:start position:0% +saying you know how important is this + + + align:start position:0% +saying you know how important is this +one you might for example have some weak + + align:start position:0% +one you might for example have some weak + + + align:start position:0% +one you might for example have some weak +edges in the in the master image and say + + align:start position:0% +edges in the in the master image and say + + + align:start position:0% +edges in the in the master image and say +well + + align:start position:0% +well + + + align:start position:0% +well +it's probably not as important that + + align:start position:0% +it's probably not as important that + + + align:start position:0% +it's probably not as important that +these match very well so you can assign + + align:start position:0% +these match very well so you can assign + + + align:start position:0% +these match very well so you can assign +a weight based on whatever but that's + + align:start position:0% +a weight based on whatever but that's + + + align:start position:0% +a weight based on whatever but that's +one reason another way to assign a + + align:start position:0% +one reason another way to assign a + + + align:start position:0% +one reason another way to assign a +weight is to manually decide these are + + align:start position:0% +weight is to manually decide these are + + + align:start position:0% +weight is to manually decide these are +important edges and these aren't so in + + align:start position:0% +important edges and these aren't so in + + + align:start position:0% +important edges and these aren't so in +this case + + align:start position:0% +this case + + + align:start position:0% +this case +the master object is you know the + + align:start position:0% +the master object is you know the + + + align:start position:0% +the master object is you know the +prototypical + + align:start position:0% +prototypical + + + align:start position:0% +prototypical +design for cell phone shape as apple + + align:start position:0% +design for cell phone shape as apple + + + align:start position:0% +design for cell phone shape as apple +says rectangle was rounded corners we + + align:start position:0% +says rectangle was rounded corners we + + + align:start position:0% +says rectangle was rounded corners we +patented that and so that's that shape + + align:start position:0% +patented that and so that's that shape + + + align:start position:0% +patented that and so that's that shape +and so we have all of these gradient + + align:start position:0% +and so we have all of these gradient + + + align:start position:0% +and so we have all of these gradient +directions uh along there which is you + + align:start position:0% +directions uh along there which is you + + + align:start position:0% +directions uh along there which is you +know very familiar to from the previous + + align:start position:0% +know very familiar to from the previous + + + align:start position:0% +know very familiar to from the previous +exam but then we also have these guys so + + align:start position:0% +exam but then we also have these guys so + + + align:start position:0% +exam but then we also have these guys so +so what's that + + align:start position:0% +so what's that + + + align:start position:0% +so what's that +well these were introduced manually + + align:start position:0% +well these were introduced manually + + + align:start position:0% +well these were introduced manually +and they have negative weights + + align:start position:0% +and they have negative weights + + + align:start position:0% +and they have negative weights +so that if you're matching against this + + align:start position:0% +so that if you're matching against this + + + align:start position:0% +so that if you're matching against this +one that means there's something wrong + + align:start position:0% +one that means there's something wrong + + + align:start position:0% +one that means there's something wrong +because the object's supposed to stop + + align:start position:0% +because the object's supposed to stop + + + align:start position:0% +because the object's supposed to stop +over here + + align:start position:0% +over here + + + align:start position:0% +over here +and so this is to take care of the + + align:start position:0% +and so this is to take care of the + + + align:start position:0% +and so this is to take care of the +possibility that an object has certain + + align:start position:0% +possibility that an object has certain + + + align:start position:0% +possibility that an object has certain +symmetries + + align:start position:0% +symmetries + + + align:start position:0% +symmetries +like in this case we can slide it in + + align:start position:0% +like in this case we can slide it in + + + align:start position:0% +like in this case we can slide it in +this direction and we maintain all of + + align:start position:0% +this direction and we maintain all of + + + align:start position:0% +this direction and we maintain all of +these still match all along the bottom + + align:start position:0% +these still match all along the bottom + + + align:start position:0% +these still match all along the bottom +edge but then we wander outside the + + align:start position:0% +edge but then we wander outside the + + + align:start position:0% +edge but then we wander outside the +acceptable area over here and we get + + align:start position:0% +acceptable area over here and we get + + + align:start position:0% +acceptable area over here and we get +penalized because + + align:start position:0% +penalized because + + + align:start position:0% +penalized because +these probes have a negative weight + + align:start position:0% +these probes have a negative weight + + + align:start position:0% +these probes have a negative weight +and the same with the movement in the + + align:start position:0% +and the same with the movement in the + + + align:start position:0% +and the same with the movement in the +vertical direction which would maintain + + align:start position:0% +vertical direction which would maintain + + + align:start position:0% +vertical direction which would maintain +matches for all of these things on the + + align:start position:0% +matches for all of these things on the + + + align:start position:0% +matches for all of these things on the +side but when you get out here it'll say + + align:start position:0% +side but when you get out here it'll say + + + align:start position:0% +side but when you get out here it'll say +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +there's a negative contribution + + align:start position:0% +there's a negative contribution + + + align:start position:0% +there's a negative contribution +to the + + align:start position:0% +to the + + + align:start position:0% +to the +to the total now it's a nice idea + + align:start position:0% +to the total now it's a nice idea + + + align:start position:0% +to the total now it's a nice idea +it's not really used and the reason is + + align:start position:0% +it's not really used and the reason is + + + align:start position:0% +it's not really used and the reason is +that the others you can generate + + align:start position:0% +that the others you can generate + + + align:start position:0% +that the others you can generate +automatically + + align:start position:0% +automatically + + + align:start position:0% +automatically +these require some human intervention + + align:start position:0% +these require some human intervention + + + align:start position:0% +these require some human intervention +i don't think anyone's + + align:start position:0% +i don't think anyone's + + + align:start position:0% +i don't think anyone's +really used them + + align:start position:0% +really used them + + + align:start position:0% +really used them +in some automated way you know the + + align:start position:0% +in some automated way you know the + + + align:start position:0% +in some automated way you know the +others you can just + + align:start position:0% +others you can just + + + align:start position:0% +others you can just +run our edge process and + + align:start position:0% +run our edge process and + + + align:start position:0% +run our edge process and +the + + align:start position:0% +the + + + align:start position:0% +the +flow chart i just showed you and and + + align:start position:0% +flow chart i just showed you and and + + + align:start position:0% +flow chart i just showed you and and +you're done + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so here they're describing their + + align:start position:0% +so here they're describing their + + + align:start position:0% +so here they're describing their +notation and remember that this was you + + align:start position:0% +notation and remember that this was you + + + align:start position:0% +notation and remember that this was you +know in the heydays of uh oh we're doing + + align:start position:0% +know in the heydays of uh oh we're doing + + + align:start position:0% +know in the heydays of uh oh we're doing +object oriented programming everything + + align:start position:0% +object oriented programming everything + + + align:start position:0% +object oriented programming everything +has to be an object + + align:start position:0% +has to be an object + + + align:start position:0% +has to be an object +so all of these things now are objects + + align:start position:0% +so all of these things now are objects + + + align:start position:0% +so all of these things now are objects +so + + align:start position:0% +so + + + align:start position:0% +so +so what are these objects uh so the so + + align:start position:0% +so what are these objects uh so the so + + + align:start position:0% +so what are these objects uh so the so +the model is what you get from the + + align:start position:0% +the model is what you get from the + + + align:start position:0% +the model is what you get from the +master image + + align:start position:0% +master image + + + align:start position:0% +master image +and the what the model consists of it + + align:start position:0% +and the what the model consists of it + + + align:start position:0% +and the what the model consists of it +contains probes those are the things + + align:start position:0% +contains probes those are the things + + + align:start position:0% +contains probes those are the things +that have position direction and weight + + align:start position:0% +that have position direction and weight + + + align:start position:0% +that have position direction and weight +and + + align:start position:0% +and + + + align:start position:0% +and +probes created by training step + + align:start position:0% +probes created by training step + + + align:start position:0% +probes created by training step +and then they contain the granularity + + align:start position:0% +and then they contain the granularity + + + align:start position:0% +and then they contain the granularity +which was that one number that tells you + + align:start position:0% +which was that one number that tells you + + + align:start position:0% +which was that one number that tells you +what's the cause of scale it'll work at + + align:start position:0% +what's the cause of scale it'll work at + + + align:start position:0% +what's the cause of scale it'll work at +and contrast which + + align:start position:0% +and contrast which + + + align:start position:0% +and contrast which +we we discussed so so that's the whole + + align:start position:0% +we we discussed so so that's the whole + + + align:start position:0% +we we discussed so so that's the whole +um + + align:start position:0% +um + + + align:start position:0% +um +that's what a model is + + align:start position:0% +that's what a model is + + + align:start position:0% +that's what a model is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +okay um probe object okay so what's a + + align:start position:0% +okay um probe object okay so what's a + + + align:start position:0% +okay um probe object okay so what's a +probe + + align:start position:0% +probe + + + align:start position:0% +probe +did i miss something no okay so what's a + + align:start position:0% +did i miss something no okay so what's a + + + align:start position:0% +did i miss something no okay so what's a +probe well it has a position a direction + + align:start position:0% +probe well it has a position a direction + + + align:start position:0% +probe well it has a position a direction +and a weight and you can see what these + + align:start position:0% +and a weight and you can see what these + + + align:start position:0% +and a weight and you can see what these +are + + align:start position:0% +are + + + align:start position:0% +are +a two vector a binary angle and the + + align:start position:0% +a two vector a binary angle and the + + + align:start position:0% +a two vector a binary angle and the +weight is is a real number which may be + + align:start position:0% +weight is is a real number which may be + + + align:start position:0% +weight is is a real number which may be +positive or negative + + align:start position:0% +positive or negative + + + align:start position:0% +positive or negative +what's a compiled probe object so + + align:start position:0% +what's a compiled probe object so + + + align:start position:0% +what's a compiled probe object so +while this method is obviously much more + + align:start position:0% +while this method is obviously much more + + + align:start position:0% +while this method is obviously much more +computationally efficient + + align:start position:0% +computationally efficient + + + align:start position:0% +computationally efficient +than say + + align:start position:0% +than say + + + align:start position:0% +than say +normalized correlation because we're + + align:start position:0% +normalized correlation because we're + + + align:start position:0% +normalized correlation because we're +only looking at probe positions of which + + align:start position:0% +only looking at probe positions of which + + + align:start position:0% +only looking at probe positions of which +there might be dozens or hundreds + + align:start position:0% +there might be dozens or hundreds + + + align:start position:0% +there might be dozens or hundreds +instead of you know millions of pixels + + align:start position:0% +instead of you know millions of pixels + + + align:start position:0% +instead of you know millions of pixels +there still + + align:start position:0% +there still + + + align:start position:0% +there still +is a concern with speed and so + + align:start position:0% +is a concern with speed and so + + + align:start position:0% +is a concern with speed and so +translation is treated differently + + align:start position:0% +translation is treated differently + + + align:start position:0% +translation is treated differently +because translation is so easy to + + align:start position:0% +because translation is so easy to + + + align:start position:0% +because translation is so easy to +implement you know it's just like an + + align:start position:0% +implement you know it's just like an + + + align:start position:0% +implement you know it's just like an +offset in the i and j coefficient of a + + align:start position:0% +offset in the i and j coefficient of a + + + align:start position:0% +offset in the i and j coefficient of a +matrix axis and so all the other + + align:start position:0% +matrix axis and so all the other + + + align:start position:0% +matrix axis and so all the other +transformations rotation scaling + + align:start position:0% +transformations rotation scaling + + + align:start position:0% +transformations rotation scaling +asymmetric + + align:start position:0% +asymmetric + + + align:start position:0% +asymmetric +aspect ratio changes whatever um are + + align:start position:0% +aspect ratio changes whatever um are + + + align:start position:0% +aspect ratio changes whatever um are +done uh at the abstract level but right + + align:start position:0% +done uh at the abstract level but right + + + align:start position:0% +done uh at the abstract level but right +at the end uh the the translational part + + align:start position:0% +at the end uh the the translational part + + + align:start position:0% +at the end uh the the translational part +is dealt with in a very simple you know + + align:start position:0% +is dealt with in a very simple you know + + + align:start position:0% +is dealt with in a very simple you know +nested loop + + align:start position:0% +nested loop + + + align:start position:0% +nested loop +i and j loop that just shift things in + + align:start position:0% +i and j loop that just shift things in + + + align:start position:0% +i and j loop that just shift things in +in pixel increments + + align:start position:0% +in pixel increments + + + align:start position:0% +in pixel increments +in the x and y so that means that your + + align:start position:0% +in the x and y so that means that your + + + align:start position:0% +in the x and y so that means that your +model + + align:start position:0% +model + + + align:start position:0% +model +can be + + align:start position:0% +can be + + + align:start position:0% +can be +brought into that world by taking into + + align:start position:0% +brought into that world by taking into + + + align:start position:0% +brought into that world by taking into +account all the other transformations + + align:start position:0% +account all the other transformations + + + align:start position:0% +account all the other transformations +so the compiled probe object is the set + + align:start position:0% +so the compiled probe object is the set + + + align:start position:0% +so the compiled probe object is the set +of probes which are now specialized to + + align:start position:0% +of probes which are now specialized to + + + align:start position:0% +of probes which are now specialized to +image coordinates and you can just + + align:start position:0% +image coordinates and you can just + + + align:start position:0% +image coordinates and you can just +superimpose that on the image and move + + align:start position:0% +superimpose that on the image and move + + + align:start position:0% +superimpose that on the image and move +it around until it + + align:start position:0% +it around until it + + + align:start position:0% +it around until it +you know to compute the match uh but + + align:start position:0% +you know to compute the match uh but + + + align:start position:0% +you know to compute the match uh but +you're only dealing with translation at + + align:start position:0% +you're only dealing with translation at + + + align:start position:0% +you're only dealing with translation at +that level so it's kind of a detail but + + align:start position:0% +that level so it's kind of a detail but + + + align:start position:0% +that level so it's kind of a detail but +it's an important detail and so the + + align:start position:0% +it's an important detail and so the + + + align:start position:0% +it's an important detail and so the +compiled object is very similar to + + align:start position:0% +compiled object is very similar to + + + align:start position:0% +compiled object is very similar to +compile pro it's very similar to the + + align:start position:0% +compile pro it's very similar to the + + + align:start position:0% +compile pro it's very similar to the +probe it has a direction and a weight uh + + align:start position:0% +probe it has a direction and a weight uh + + + align:start position:0% +probe it has a direction and a weight uh +the big difference is that the offset is + + align:start position:0% +the big difference is that the offset is + + + align:start position:0% +the big difference is that the offset is +an integer in pixels as opposed to + + align:start position:0% +an integer in pixels as opposed to + + + align:start position:0% +an integer in pixels as opposed to +everything up to that point was you know + + align:start position:0% +everything up to that point was you know + + + align:start position:0% +everything up to that point was you know +a real variable it + + align:start position:0% +a real variable it + + + align:start position:0% +a real variable it +uh not wasn't quantized + + align:start position:0% + + + + align:start position:0% + +oh well + + align:start position:0% +oh well + + + align:start position:0% +oh well +let's see + + align:start position:0% +let's see + + + align:start position:0% +let's see +um + + align:start position:0% +um + + + align:start position:0% +um +compile probe so this is a function that + + align:start position:0% +compile probe so this is a function that + + + align:start position:0% +compile probe so this is a function that +compiles the probes + + align:start position:0% +compiles the probes + + + align:start position:0% +compiles the probes +i'm not going to go through all this + + align:start position:0% +i'm not going to go through all this + + + align:start position:0% +i'm not going to go through all this +you'll be happy to know so + + align:start position:0% + + + + align:start position:0% + +so the matrix c is the non-translation + + align:start position:0% +so the matrix c is the non-translation + + + align:start position:0% +so the matrix c is the non-translation +portion of the map + + align:start position:0% +portion of the map + + + align:start position:0% +portion of the map +um so as i explained that + + align:start position:0% +um so as i explained that + + + align:start position:0% +um so as i explained that +includes all of the transformations + + align:start position:0% +includes all of the transformations + + + align:start position:0% +includes all of the transformations +except translation + + align:start position:0% +except translation + + + align:start position:0% +except translation +then + + align:start position:0% +then + + + align:start position:0% +then +uh what is the map well the map is this + + align:start position:0% +uh what is the map well the map is this + + + align:start position:0% +uh what is the map well the map is this +uh transformation that has multiple + + align:start position:0% +uh transformation that has multiple + + + align:start position:0% +uh transformation that has multiple +degrees of freedom + + align:start position:0% +degrees of freedom + + + align:start position:0% +degrees of freedom +um that we're trying to find the uh the + + align:start position:0% +um that we're trying to find the uh the + + + align:start position:0% +um that we're trying to find the uh the +maximum of + + align:start position:0% +maximum of + + + align:start position:0% +maximum of +um + + align:start position:0% +um + + + align:start position:0% +um +vector of let's go past that + + align:start position:0% + + + + align:start position:0% + +okay so so far we've pretty much dealt + + align:start position:0% +okay so so far we've pretty much dealt + + + align:start position:0% +okay so so far we've pretty much dealt +with uh how to build the model how to + + align:start position:0% +with uh how to build the model how to + + + align:start position:0% +with uh how to build the model how to +take the the nice image of the object + + align:start position:0% +take the the nice image of the object + + + align:start position:0% +take the the nice image of the object +that's you know free of clutter and + + align:start position:0% +that's you know free of clutter and + + + align:start position:0% +that's you know free of clutter and +background smooth and so on and create + + align:start position:0% +background smooth and so on and create + + + align:start position:0% +background smooth and so on and create +the model and now we start to talk about + + align:start position:0% +the model and now we start to talk about + + + align:start position:0% +the model and now we start to talk about +how to use the model so as i mentioned + + align:start position:0% +how to use the model so as i mentioned + + + align:start position:0% +how to use the model so as i mentioned +we map + + align:start position:0% +we map + + + align:start position:0% +we map +the model onto the image it's very + + align:start position:0% +the model onto the image it's very + + + align:start position:0% +the model onto the image it's very +important to remember this because we're + + align:start position:0% +important to remember this because we're + + + align:start position:0% +important to remember this because we're +going to talk later about a different + + align:start position:0% +going to talk later about a different + + + align:start position:0% +going to talk later about a different +pattern where it's just the other way + + align:start position:0% +pattern where it's just the other way + + + align:start position:0% +pattern where it's just the other way +around where we map the runtime image on + + align:start position:0% +around where we map the runtime image on + + + align:start position:0% +around where we map the runtime image on +top of the model and it turns out why do + + align:start position:0% +top of the model and it turns out why do + + + align:start position:0% +top of the model and it turns out why do +we do it this way well you could + + align:start position:0% +we do it this way well you could + + + align:start position:0% +we do it this way well you could +certainly transform the image + + align:start position:0% +certainly transform the image + + + align:start position:0% +certainly transform the image +rather than the model but the model has + + align:start position:0% +rather than the model but the model has + + + align:start position:0% +rather than the model but the model has +a few dozen points in it's very cheap to + + align:start position:0% +a few dozen points in it's very cheap to + + + align:start position:0% +a few dozen points in it's very cheap to +transform whereas the image has you know + + align:start position:0% +transform whereas the image has you know + + + align:start position:0% +transform whereas the image has you know +lots of pixels so it's going to be + + align:start position:0% +lots of pixels so it's going to be + + + align:start position:0% +lots of pixels so it's going to be +expensive + + align:start position:0% +expensive + + + align:start position:0% +expensive +you can you know use photoshop to rotate + + align:start position:0% +you can you know use photoshop to rotate + + + align:start position:0% +you can you know use photoshop to rotate +translate your image certainly all of + + align:start position:0% +translate your image certainly all of + + + align:start position:0% +translate your image certainly all of +that's possible but we're trying to + + align:start position:0% +that's possible but we're trying to + + + align:start position:0% +that's possible but we're trying to +avoid that expense and so in this case + + align:start position:0% +avoid that expense and so in this case + + + align:start position:0% +avoid that expense and so in this case +it's important to remember the map is + + align:start position:0% +it's important to remember the map is + + + align:start position:0% +it's important to remember the map is +from the model and it plunks the model + + align:start position:0% +from the model and it plunks the model + + + align:start position:0% +from the model and it plunks the model +down on top of the runtime image okay + + align:start position:0% +down on top of the runtime image okay + + + align:start position:0% +down on top of the runtime image okay +now what do we do well at every probe + + align:start position:0% +now what do we do well at every probe + + + align:start position:0% +now what do we do well at every probe +position we ask the runtime image what's + + align:start position:0% +position we ask the runtime image what's + + + align:start position:0% +position we ask the runtime image what's +the gradient here + + align:start position:0% +the gradient here + + + align:start position:0% +the gradient here +well we actually pre-compute the + + align:start position:0% +well we actually pre-compute the + + + align:start position:0% +well we actually pre-compute the +gradient and we sample it but we and + + align:start position:0% +gradient and we sample it but we and + + + align:start position:0% +gradient and we sample it but we and +then we compare and as i mentioned we're + + align:start position:0% +then we compare and as i mentioned we're + + + align:start position:0% +then we compare and as i mentioned we're +more concerned about direction of + + align:start position:0% +more concerned about direction of + + + align:start position:0% +more concerned about direction of +gradient and magnitude + + align:start position:0% +gradient and magnitude + + + align:start position:0% +gradient and magnitude +and so how do we + + align:start position:0% +and so how do we + + + align:start position:0% +and so how do we +score this well if they're the same + + align:start position:0% +score this well if they're the same + + + align:start position:0% +score this well if they're the same +direction that's great if they're 90 + + align:start position:0% +direction that's great if they're 90 + + + align:start position:0% +direction that's great if they're 90 +degrees apart that's horrible and so + + align:start position:0% +degrees apart that's horrible and so + + + align:start position:0% +degrees apart that's horrible and so +here's a grading function + + align:start position:0% +here's a grading function + + + align:start position:0% +here's a grading function +which is in degrees between the two + + align:start position:0% +which is in degrees between the two + + + align:start position:0% +which is in degrees between the two +directions of the + + align:start position:0% +directions of the + + + align:start position:0% +directions of the +gradients and you can see that + + align:start position:0% +gradients and you can see that + + + align:start position:0% +gradients and you can see that +there's a bit of slop so if you're off + + align:start position:0% +there's a bit of slop so if you're off + + + align:start position:0% +there's a bit of slop so if you're off +by up to + + align:start position:0% +by up to + + + align:start position:0% +by up to +11.25 degrees that's as good as zero and + + align:start position:0% +11.25 degrees that's as good as zero and + + + align:start position:0% +11.25 degrees that's as good as zero and +that's because you know all these + + align:start position:0% +that's because you know all these + + + align:start position:0% +that's because you know all these +calculations have some limitations some + + align:start position:0% +calculations have some limitations some + + + align:start position:0% +calculations have some limitations some +noise and so on so you want to allow a + + align:start position:0% +noise and so on so you want to allow a + + + align:start position:0% +noise and so on so you want to allow a +little bit of slop in the direction of + + align:start position:0% +little bit of slop in the direction of + + + align:start position:0% +little bit of slop in the direction of +the gradient + + align:start position:0% +the gradient + + + align:start position:0% +the gradient +but then you don't want to fall off a + + align:start position:0% +but then you don't want to fall off a + + + align:start position:0% +but then you don't want to fall off a +cliff you don't want to say okay if it's + + align:start position:0% +cliff you don't want to say okay if it's + + + align:start position:0% +cliff you don't want to say okay if it's +11.3 + + align:start position:0% +11.3 + + + align:start position:0% +11.3 +degrees then you know it's no match so + + align:start position:0% +degrees then you know it's no match so + + + align:start position:0% +degrees then you know it's no match so +instead you grab you linearly decrease + + align:start position:0% +instead you grab you linearly decrease + + + align:start position:0% +instead you grab you linearly decrease +it until you get to 22.5 at which point + + align:start position:0% +it until you get to 22.5 at which point + + + align:start position:0% +it until you get to 22.5 at which point +you say okay well this isn't a match + + align:start position:0% +you say okay well this isn't a match + + + align:start position:0% +you say okay well this isn't a match +anymore that's that's too much of a + + align:start position:0% +anymore that's that's too much of a + + + align:start position:0% +anymore that's that's too much of a +difference half of 45 degrees + + align:start position:0% +difference half of 45 degrees + + + align:start position:0% +difference half of 45 degrees +and you know it's arbitrary how you pick + + align:start position:0% +and you know it's arbitrary how you pick + + + align:start position:0% +and you know it's arbitrary how you pick +these things uh but the + + align:start position:0% +these things uh but the + + + align:start position:0% +these things uh but the +picking of them has an effect later on + + align:start position:0% +picking of them has an effect later on + + + align:start position:0% +picking of them has an effect later on +the quality + + align:start position:0% +the quality + + + align:start position:0% +the quality +okay so this is a probe direction + + align:start position:0% +okay so this is a probe direction + + + align:start position:0% +okay so this is a probe direction +difference + + align:start position:0% +difference + + + align:start position:0% +difference +rating function + + align:start position:0% +rating function + + + align:start position:0% +rating function +which considers the polarity which + + align:start position:0% +which considers the polarity which + + + align:start position:0% +which considers the polarity which +considers the contrast the polarity of + + align:start position:0% +considers the contrast the polarity of + + + align:start position:0% +considers the contrast the polarity of +the contrast so so of course it wraps + + align:start position:0% +the contrast so so of course it wraps + + + align:start position:0% +the contrast so so of course it wraps +around because when you get close to 360 + + align:start position:0% +around because when you get close to 360 + + + align:start position:0% +around because when you get close to 360 +again you will allow a small you know i + + align:start position:0% +again you will allow a small you know i + + + align:start position:0% +again you will allow a small you know i +mean this is just minus 11.25 degrees + + align:start position:0% +mean this is just minus 11.25 degrees + + + align:start position:0% +mean this is just minus 11.25 degrees +and that's minus 22.5 degrees so that's + + align:start position:0% +and that's minus 22.5 degrees so that's + + + align:start position:0% +and that's minus 22.5 degrees so that's +the function that's used in rating + + align:start position:0% +the function that's used in rating + + + align:start position:0% +the function that's used in rating +how well a probe matches the + + align:start position:0% +how well a probe matches the + + + align:start position:0% +how well a probe matches the +corresponding point in the runtime image + + align:start position:0% +corresponding point in the runtime image + + + align:start position:0% +corresponding point in the runtime image +now if you say + + align:start position:0% +now if you say + + + align:start position:0% +now if you say +in my situation + + align:start position:0% +in my situation + + + align:start position:0% +in my situation +there may be a reversal of contrast then + + align:start position:0% +there may be a reversal of contrast then + + + align:start position:0% +there may be a reversal of contrast then +i shouldn't use this because then 180 + + align:start position:0% +i shouldn't use this because then 180 + + + align:start position:0% +i shouldn't use this because then 180 +degrees difference in direction + + align:start position:0% +degrees difference in direction + + + align:start position:0% +degrees difference in direction +should be accepted as well + + align:start position:0% +should be accepted as well + + + align:start position:0% +should be accepted as well +right and so that's what the next figure + + align:start position:0% +right and so that's what the next figure + + + align:start position:0% +right and so that's what the next figure +is + + align:start position:0% +is + + + align:start position:0% +is +so here we're allowing a small slop + + align:start position:0% +so here we're allowing a small slop + + + align:start position:0% +so here we're allowing a small slop +around zero and a little bit about 180 + + align:start position:0% +around zero and a little bit about 180 + + + align:start position:0% +around zero and a little bit about 180 +degrees and the other angles are not + + align:start position:0% +degrees and the other angles are not + + + align:start position:0% +degrees and the other angles are not +accepted + + align:start position:0% +accepted + + + align:start position:0% +accepted +and + + align:start position:0% +and + + + align:start position:0% +and +that's + + align:start position:0% +that's + + + align:start position:0% +that's +important for some integrated circuit + + align:start position:0% +important for some integrated circuit + + + align:start position:0% +important for some integrated circuit +situations as i mentioned + + align:start position:0% +situations as i mentioned + + + align:start position:0% +situations as i mentioned +there's a drawback of course which is + + align:start position:0% +there's a drawback of course which is + + + align:start position:0% +there's a drawback of course which is +you know + + align:start position:0% +you know + + + align:start position:0% +you know +inevitably we'll be looking at + + align:start position:0% +inevitably we'll be looking at + + + align:start position:0% +inevitably we'll be looking at +completely unrelated parts of the image + + align:start position:0% +completely unrelated parts of the image + + + align:start position:0% +completely unrelated parts of the image +and there's some small chance that they + + align:start position:0% +and there's some small chance that they + + + align:start position:0% +and there's some small chance that they +happen to have the right gradient + + align:start position:0% +happen to have the right gradient + + + align:start position:0% +happen to have the right gradient +so how often is that going to happen + + align:start position:0% +so how often is that going to happen + + + align:start position:0% +so how often is that going to happen +well up here + + align:start position:0% +well up here + + + align:start position:0% +well up here +it's fairly rare right because we can + + align:start position:0% +it's fairly rare right because we can + + + align:start position:0% +it's fairly rare right because we can +sort of roughly say this + + align:start position:0% +sort of roughly say this + + + align:start position:0% +sort of roughly say this +let's see um maybe a 20 degree band so + + align:start position:0% +let's see um maybe a 20 degree band so + + + align:start position:0% +let's see um maybe a 20 degree band so +that means 20 degrees out of 360 one in + + align:start position:0% +that means 20 degrees out of 360 one in + + + align:start position:0% +that means 20 degrees out of 360 one in +one in 18. so the the chance of random + + align:start position:0% +one in 18. so the the chance of random + + + align:start position:0% +one in 18. so the the chance of random +matches actually pretending to be good + + align:start position:0% +matches actually pretending to be good + + + align:start position:0% +matches actually pretending to be good +matches is one in 18. well here it's + + align:start position:0% +matches is one in 18. well here it's + + + align:start position:0% +matches is one in 18. well here it's +twice as much + + align:start position:0% +twice as much + + + align:start position:0% +twice as much +so so this is not as robust against + + align:start position:0% +so so this is not as robust against + + + align:start position:0% +so so this is not as robust against +noise as as that one so if you know that + + align:start position:0% +noise as as that one so if you know that + + + align:start position:0% +noise as as that one so if you know that +the contrast is not going to be reversed + + align:start position:0% +the contrast is not going to be reversed + + + align:start position:0% +the contrast is not going to be reversed +don't do yours don't use this you use + + align:start position:0% +don't do yours don't use this you use + + + align:start position:0% +don't do yours don't use this you use +that okay and so similarly you might say + + align:start position:0% +that okay and so similarly you might say + + + align:start position:0% +that okay and so similarly you might say +well i want a wider margin let's go out + + align:start position:0% +well i want a wider margin let's go out + + + align:start position:0% +well i want a wider margin let's go out +to 45 degrees well that's all very well + + align:start position:0% +to 45 degrees well that's all very well + + + align:start position:0% +to 45 degrees well that's all very well +except that means that you're going to + + align:start position:0% +except that means that you're going to + + + align:start position:0% +except that means that you're going to +be accepting more of these random + + align:start position:0% +be accepting more of these random + + + align:start position:0% +be accepting more of these random +alignments + + align:start position:0% + + + + align:start position:0% + +then i mentioned that we can also look + + align:start position:0% +then i mentioned that we can also look + + + align:start position:0% +then i mentioned that we can also look +at the gradient magnitude and in some + + align:start position:0% +at the gradient magnitude and in some + + + align:start position:0% +at the gradient magnitude and in some +cases you know you might want to just + + align:start position:0% +cases you know you might want to just + + + align:start position:0% +cases you know you might want to just +ignore it because it's not as reliable + + align:start position:0% +ignore it because it's not as reliable + + + align:start position:0% +ignore it because it's not as reliable +or you can + + align:start position:0% +or you can + + + align:start position:0% +or you can +use it directly as a weighting factor + + align:start position:0% +use it directly as a weighting factor + + + align:start position:0% +use it directly as a weighting factor +you know the bigger the gradient + + align:start position:0% +you know the bigger the gradient + + + align:start position:0% +you know the bigger the gradient +magnitude the more likely this is + + align:start position:0% +magnitude the more likely this is + + + align:start position:0% +magnitude the more likely this is +important + + align:start position:0% +important + + + align:start position:0% +important +or you can say well that's true up to a + + align:start position:0% +or you can say well that's true up to a + + + align:start position:0% +or you can say well that's true up to a +point so you set a target level which is + + align:start position:0% +point so you set a target level which is + + + align:start position:0% +point so you set a target level which is +perhaps the gradient magnitude the + + align:start position:0% +perhaps the gradient magnitude the + + + align:start position:0% +perhaps the gradient magnitude the +contrast on the master image the + + align:start position:0% +contrast on the master image the + + + align:start position:0% +contrast on the master image the +training image + + align:start position:0% +training image + + + align:start position:0% +training image +and then + + align:start position:0% +and then + + + align:start position:0% +and then +it saturates so + + align:start position:0% +it saturates so + + + align:start position:0% +it saturates so +it goes up the bigger the gradient + + align:start position:0% +it goes up the bigger the gradient + + + align:start position:0% +it goes up the bigger the gradient +magnitude the better + + align:start position:0% +magnitude the better + + + align:start position:0% +magnitude the better +but it it has a limit it doesn't just + + align:start position:0% +but it it has a limit it doesn't just + + + align:start position:0% +but it it has a limit it doesn't just +keep on growing so so there's a function + + align:start position:0% +keep on growing so so there's a function + + + align:start position:0% +keep on growing so so there's a function +for + + align:start position:0% +for + + + align:start position:0% +for +scoring how well the directions of the + + align:start position:0% +scoring how well the directions of the + + + align:start position:0% +scoring how well the directions of the +gradients match and this is + + align:start position:0% +gradients match and this is + + + align:start position:0% +gradients match and this is +for scoring how well the magnitudes + + align:start position:0% +for scoring how well the magnitudes + + + align:start position:0% +for scoring how well the magnitudes +match up and remember these are applied + + align:start position:0% +match up and remember these are applied + + + align:start position:0% +match up and remember these are applied +at at every probe position so you map + + align:start position:0% +at at every probe position so you map + + + align:start position:0% +at at every probe position so you map +the model onto the runtime image + + align:start position:0% +the model onto the runtime image + + + align:start position:0% +the model onto the runtime image +then at every pro position you check + + align:start position:0% +then at every pro position you check + + + align:start position:0% +then at every pro position you check +what the gradient is and you compare it + + align:start position:0% +what the gradient is and you compare it + + + align:start position:0% +what the gradient is and you compare it +with the gradient in so so that's uh + + align:start position:0% +with the gradient in so so that's uh + + + align:start position:0% +with the gradient in so so that's uh +sort of the key part of the method + + align:start position:0% +sort of the key part of the method + + + align:start position:0% +sort of the key part of the method +uh then we get to the degrees of freedom + + align:start position:0% +uh then we get to the degrees of freedom + + + align:start position:0% +uh then we get to the degrees of freedom +so obviously uh + + align:start position:0% +so obviously uh + + + align:start position:0% +so obviously uh +translation you know movement in x + + align:start position:0% +translation you know movement in x + + + align:start position:0% +translation you know movement in x +movement and y are degrees of freedom + + align:start position:0% +movement and y are degrees of freedom + + + align:start position:0% +movement and y are degrees of freedom +but we also want to deal with rotation + + align:start position:0% +but we also want to deal with rotation + + + align:start position:0% +but we also want to deal with rotation +and + + align:start position:0% + + + + align:start position:0% + +and scaling and okay let me go on to the + + align:start position:0% +and scaling and okay let me go on to the + + + align:start position:0% +and scaling and okay let me go on to the +next page so this is a description of + + align:start position:0% +next page so this is a description of + + + align:start position:0% +next page so this is a description of +what a generalized degree of freedom is + + align:start position:0% +what a generalized degree of freedom is + + + align:start position:0% +what a generalized degree of freedom is +in as far as they're concerned + + align:start position:0% +in as far as they're concerned + + + align:start position:0% +in as far as they're concerned +and then here's some here's some + + align:start position:0% +and then here's some here's some + + + align:start position:0% +and then here's some here's some +examples well actually this is probably + + align:start position:0% +examples well actually this is probably + + + align:start position:0% +examples well actually this is probably +all of the ones you might ever want + + align:start position:0% +all of the ones you might ever want + + + align:start position:0% +all of the ones you might ever want +so we have rotation and + + align:start position:0% +so we have rotation and + + + align:start position:0% +so we have rotation and +it has as parameters and angle in + + align:start position:0% +it has as parameters and angle in + + + align:start position:0% +it has as parameters and angle in +degrees and it does it does it wrap + + align:start position:0% +degrees and it does it does it wrap + + + align:start position:0% +degrees and it does it does it wrap +around it's important that the search + + align:start position:0% +around it's important that the search + + + align:start position:0% +around it's important that the search +method uh be informed about whether when + + align:start position:0% +method uh be informed about whether when + + + align:start position:0% +method uh be informed about whether when +you go off the max you come back at the + + align:start position:0% +you go off the max you come back at the + + + align:start position:0% +you go off the max you come back at the +min well yeah for for rotation that's + + align:start position:0% +min well yeah for for rotation that's + + + align:start position:0% +min well yeah for for rotation that's +certainly true and the cycle is 360 + + align:start position:0% +certainly true and the cycle is 360 + + + align:start position:0% +certainly true and the cycle is 360 +degrees so it turns after 360 degrees + + align:start position:0% +degrees so it turns after 360 degrees + + + align:start position:0% +degrees so it turns after 360 degrees +and how does it map the coordinates well + + align:start position:0% +and how does it map the coordinates well + + + align:start position:0% +and how does it map the coordinates well +the standard formula except maybe the + + align:start position:0% +the standard formula except maybe the + + + align:start position:0% +the standard formula except maybe the +minus sign is in a place that we + + align:start position:0% +minus sign is in a place that we + + + align:start position:0% +minus sign is in a place that we +wouldn't want it to be + + align:start position:0% +wouldn't want it to be + + + align:start position:0% +wouldn't want it to be +and then you need to figure out uh the + + align:start position:0% +and then you need to figure out uh the + + + align:start position:0% +and then you need to figure out uh the +steps you you're going to explore each + + align:start position:0% +steps you you're going to explore each + + + align:start position:0% +steps you you're going to explore each +of these degrees of freedom in steps now + + align:start position:0% +of these degrees of freedom in steps now + + + align:start position:0% +of these degrees of freedom in steps now +in translation you might just do you + + align:start position:0% +in translation you might just do you + + + align:start position:0% +in translation you might just do you +know pixel steps but what what should + + align:start position:0% +know pixel steps but what what should + + + align:start position:0% +know pixel steps but what what should +you use for + + align:start position:0% +you use for + + + align:start position:0% +you use for +rotations it's not obvious + + align:start position:0% +rotations it's not obvious + + + align:start position:0% +rotations it's not obvious +and then how does it change the scale of + + align:start position:0% +and then how does it change the scale of + + + align:start position:0% +and then how does it change the scale of +of the image + + align:start position:0% +of the image + + + align:start position:0% +of the image +well in this case it preserves the scale + + align:start position:0% +well in this case it preserves the scale + + + align:start position:0% +well in this case it preserves the scale +when you rotate something it stays the + + align:start position:0% +when you rotate something it stays the + + + align:start position:0% +when you rotate something it stays the +same size + + align:start position:0% +same size + + + align:start position:0% +same size +then you might have shear now that means + + align:start position:0% +then you might have shear now that means + + + align:start position:0% +then you might have shear now that means +that you're + + align:start position:0% +that you're + + + align:start position:0% +that you're +turning a right angle into a non-right + + align:start position:0% +turning a right angle into a non-right + + + align:start position:0% +turning a right angle into a non-right +angle + + align:start position:0% +angle + + + align:start position:0% +angle +and + + align:start position:0% +and + + + align:start position:0% +and +you know here's the matrix + + align:start position:0% +you know here's the matrix + + + align:start position:0% +you know here's the matrix +transformation for it + + align:start position:0% +transformation for it + + + align:start position:0% +transformation for it +and + + align:start position:0% + + + + align:start position:0% + +this used to be much more of an issue + + align:start position:0% +this used to be much more of an issue + + + align:start position:0% +this used to be much more of an issue +than it is now + + align:start position:0% +than it is now + + + align:start position:0% +than it is now +because today um + + align:start position:0% +because today um + + + align:start position:0% +because today um +image + + align:start position:0% + + + + align:start position:0% + +images typically don't have much of a + + align:start position:0% +images typically don't have much of a + + + align:start position:0% +images typically don't have much of a +shear in them so + + align:start position:0% +shear in them so + + + align:start position:0% +shear in them so +in the old days + + align:start position:0% +in the old days + + + align:start position:0% +in the old days +images were made by devices that had + + align:start position:0% +images were made by devices that had + + + align:start position:0% +images were made by devices that had +electromagnetic deflection and so + + align:start position:0% +electromagnetic deflection and so + + + align:start position:0% +electromagnetic deflection and so +the x-axis + + align:start position:0% +the x-axis + + + align:start position:0% +the x-axis +was only as perpendicular to the y-axis + + align:start position:0% +was only as perpendicular to the y-axis + + + align:start position:0% +was only as perpendicular to the y-axis +as somebody made it when they assembled + + align:start position:0% +as somebody made it when they assembled + + + align:start position:0% +as somebody made it when they assembled +it so it was quite + + align:start position:0% +it so it was quite + + + align:start position:0% +it so it was quite +common to have some kind of angle + + align:start position:0% +common to have some kind of angle + + + align:start position:0% +common to have some kind of angle +other than 90 degrees + + align:start position:0% +other than 90 degrees + + + align:start position:0% +other than 90 degrees +no huge not hugely different but you + + align:start position:0% +no huge not hugely different but you + + + align:start position:0% +no huge not hugely different but you +know one or two degrees it could be off + + align:start position:0% +know one or two degrees it could be off + + + align:start position:0% +know one or two degrees it could be off +and so you might want to do a search for + + align:start position:0% +and so you might want to do a search for + + + align:start position:0% +and so you might want to do a search for +that + + align:start position:0% +that + + + align:start position:0% +that +or + + align:start position:0% +or + + + align:start position:0% +or +suppose that + + align:start position:0% +suppose that + + + align:start position:0% +suppose that +you're working in a world where things + + align:start position:0% +you're working in a world where things + + + align:start position:0% +you're working in a world where things +aren't exactly two-dimensional you know + + align:start position:0% +aren't exactly two-dimensional you know + + + align:start position:0% +aren't exactly two-dimensional you know +something might be + + align:start position:0% +something might be + + + align:start position:0% +something might be +instead of lying on the conveyor belt + + align:start position:0% +instead of lying on the conveyor belt + + + align:start position:0% +instead of lying on the conveyor belt +it's tilted slightly well then if you + + align:start position:0% +it's tilted slightly well then if you + + + align:start position:0% +it's tilted slightly well then if you +look at the image of that it will not + + align:start position:0% +look at the image of that it will not + + + align:start position:0% +look at the image of that it will not +image as a rectangle it will image as a + + align:start position:0% +image as a rectangle it will image as a + + + align:start position:0% +image as a rectangle it will image as a +rhombus + + align:start position:0% +rhombus + + + align:start position:0% +rhombus +and so + + align:start position:0% +and so + + + align:start position:0% +and so +you might want to + + align:start position:0% +you might want to + + + align:start position:0% +you might want to +in that situation allow for this + + align:start position:0% +in that situation allow for this + + + align:start position:0% +in that situation allow for this +transformation of course if that doesn't + + align:start position:0% +transformation of course if that doesn't + + + align:start position:0% +transformation of course if that doesn't +happen to you leave it out because it's + + align:start position:0% +happen to you leave it out because it's + + + align:start position:0% +happen to you leave it out because it's +going to increase the cost of + + align:start position:0% +going to increase the cost of + + + align:start position:0% +going to increase the cost of +computation + + align:start position:0% +computation + + + align:start position:0% +computation +uh then we get to size + + align:start position:0% +uh then we get to size + + + align:start position:0% +uh then we get to size +now uh scaling now you might say well + + align:start position:0% +now uh scaling now you might say well + + + align:start position:0% +now uh scaling now you might say well +we'll just increase + + align:start position:0% +we'll just increase + + + align:start position:0% +we'll just increase +you know linearly the + + align:start position:0% +you know linearly the + + + align:start position:0% +you know linearly the +size the + + align:start position:0% +size the + + + align:start position:0% +size the +width and height of everything but + + align:start position:0% +width and height of everything but + + + align:start position:0% +width and height of everything but +that's not a good idea because what's a + + align:start position:0% +that's not a good idea because what's a + + + align:start position:0% +that's not a good idea because what's a +linear increase for a small object is + + align:start position:0% +linear increase for a small object is + + + align:start position:0% +linear increase for a small object is +relatively large + + align:start position:0% +relatively large + + + align:start position:0% +relatively large +uh compared to the same linear increase + + align:start position:0% +uh compared to the same linear increase + + + align:start position:0% +uh compared to the same linear increase +applied to a large object so it's more + + align:start position:0% +applied to a large object so it's more + + + align:start position:0% +applied to a large object so it's more +reasonable to + + align:start position:0% +reasonable to + + + align:start position:0% +reasonable to +work in a logarithmic scale so that + + align:start position:0% +work in a logarithmic scale so that + + + align:start position:0% +work in a logarithmic scale so that +means the increment in the size is not + + align:start position:0% +means the increment in the size is not + + + align:start position:0% +means the increment in the size is not +you know + + align:start position:0% +you know + + + align:start position:0% +you know +uh 0.01 but it's it's it's one percent + + align:start position:0% +uh 0.01 but it's it's it's one percent + + + align:start position:0% +uh 0.01 but it's it's it's one percent +or let's say 10 and then when you + + align:start position:0% +or let's say 10 and then when you + + + align:start position:0% +or let's say 10 and then when you +increase again it'll be not 20 but 21 + + align:start position:0% +increase again it'll be not 20 but 21 + + + align:start position:0% +increase again it'll be not 20 but 21 +percent and so on you get the idea so + + align:start position:0% +percent and so on you get the idea so + + + align:start position:0% +percent and so on you get the idea so +that's where this comes from so for the + + align:start position:0% +that's where this comes from so for the + + + align:start position:0% +that's where this comes from so for the +logarithmic uh size factor + + align:start position:0% +logarithmic uh size factor + + + align:start position:0% +logarithmic uh size factor +it does not cycle around + + align:start position:0% +it does not cycle around + + + align:start position:0% +it does not cycle around +and + + align:start position:0% +and + + + align:start position:0% +and +this is the mapping for it we have the + + align:start position:0% +this is the mapping for it we have the + + + align:start position:0% +this is the mapping for it we have the +exponential part in there and this is + + align:start position:0% +exponential part in there and this is + + + align:start position:0% +exponential part in there and this is +how the scale changes + + align:start position:0% +how the scale changes + + + align:start position:0% +how the scale changes +in that case + + align:start position:0% +in that case + + + align:start position:0% +in that case +and so + + align:start position:0% +and so + + + align:start position:0% +and so +here's one that only scales x and here's + + align:start position:0% +here's one that only scales x and here's + + + align:start position:0% +here's one that only scales x and here's +one that only scales y and of course + + align:start position:0% +one that only scales y and of course + + + align:start position:0% +one that only scales y and of course +these are sort of redundant because uh + + align:start position:0% +these are sort of redundant because uh + + + align:start position:0% +these are sort of redundant because uh +you know + + align:start position:0% +you know + + + align:start position:0% +you know +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +in the case that x and y scale the same + + align:start position:0% +in the case that x and y scale the same + + + align:start position:0% +in the case that x and y scale the same +we just use that rather than these two + + align:start position:0% +we just use that rather than these two + + + align:start position:0% +we just use that rather than these two +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +and then there's an aspect ratio one + + align:start position:0% +and then there's an aspect ratio one + + + align:start position:0% +and then there's an aspect ratio one +again this is this used to be more + + align:start position:0% +again this is this used to be more + + + align:start position:0% +again this is this used to be more +common than now because the sca + + align:start position:0% +common than now because the sca + + + align:start position:0% +common than now because the sca +scan in the y direction was very + + align:start position:0% +scan in the y direction was very + + + align:start position:0% +scan in the y direction was very +different from the scan in the x + + align:start position:0% +different from the scan in the x + + + align:start position:0% +different from the scan in the x +direction now you know people + + align:start position:0% +direction now you know people + + + align:start position:0% +direction now you know people +make incredible high resolution high + + align:start position:0% +make incredible high resolution high + + + align:start position:0% +make incredible high resolution high +accuracy + + align:start position:0% +accuracy + + + align:start position:0% +accuracy +image sensors where you know + + align:start position:0% +image sensors where you know + + + align:start position:0% +image sensors where you know +that the + + align:start position:0% +that the + + + align:start position:0% +that the +axes are as close to 90 degrees apart as + + align:start position:0% +axes are as close to 90 degrees apart as + + + align:start position:0% +axes are as close to 90 degrees apart as +they can be and then the + + align:start position:0% +they can be and then the + + + align:start position:0% +they can be and then the +pixel size + + align:start position:0% +pixel size + + + align:start position:0% +pixel size +is either perfectly square + + align:start position:0% +is either perfectly square + + + align:start position:0% +is either perfectly square +or at least you know what it is you've + + align:start position:0% +or at least you know what it is you've + + + align:start position:0% +or at least you know what it is you've +got to be careful about that because + + align:start position:0% +got to be careful about that because + + + align:start position:0% +got to be careful about that because +often it'll be something like 504 over + + align:start position:0% +often it'll be something like 504 over + + + align:start position:0% +often it'll be something like 504 over + + align:start position:0% + + + align:start position:0% +and when you look at the chip it looks + + align:start position:0% +and when you look at the chip it looks + + + align:start position:0% +and when you look at the chip it looks +like it's one to one but + + align:start position:0% +like it's one to one but + + + align:start position:0% +like it's one to one but +read the specs + + align:start position:0% +read the specs + + + align:start position:0% +read the specs +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you may need to have to take care of + + align:start position:0% +so you may need to have to take care of + + + align:start position:0% +so you may need to have to take care of +aspect ratio and so on now the the + + align:start position:0% +aspect ratio and so on now the the + + + align:start position:0% +aspect ratio and so on now the the +bottom ones are as i said this is + + align:start position:0% +bottom ones are as i said this is + + + align:start position:0% +bottom ones are as i said this is +somewhat redundant like these down here + + align:start position:0% +somewhat redundant like these down here + + + align:start position:0% +somewhat redundant like these down here +are linear scale factors and i already + + align:start position:0% +are linear scale factors and i already + + + align:start position:0% +are linear scale factors and i already +said those are probably not as + + align:start position:0% +said those are probably not as + + + align:start position:0% +said those are probably not as +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +and okay + + align:start position:0% +and okay + + + align:start position:0% +and okay +so those are called generalized degrees + + align:start position:0% +so those are called generalized degrees + + + align:start position:0% +so those are called generalized degrees +of freedom i mean in some sense all you + + align:start position:0% +of freedom i mean in some sense all you + + + align:start position:0% +of freedom i mean in some sense all you +really need for 2d work is translation + + align:start position:0% +really need for 2d work is translation + + + align:start position:0% +really need for 2d work is translation +rotation and maybe scaling + + align:start position:0% +rotation and maybe scaling + + + align:start position:0% +rotation and maybe scaling +but you know they allow for + + align:start position:0% +but you know they allow for + + + align:start position:0% +but you know they allow for +more than that + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +some weird terminology + + align:start position:0% +some weird terminology + + + align:start position:0% +some weird terminology +probe mer is the + + align:start position:0% +probe mer is the + + + align:start position:0% +probe mer is the +probe minimum enclosing rectangle so for + + align:start position:0% +probe minimum enclosing rectangle so for + + + align:start position:0% +probe minimum enclosing rectangle so for +some operations you can cut down the + + align:start position:0% +some operations you can cut down the + + + align:start position:0% +some operations you can cut down the +computation by checking only the minimum + + align:start position:0% +computation by checking only the minimum + + + align:start position:0% +computation by checking only the minimum +and closing rectangle and so they carry + + align:start position:0% +and closing rectangle and so they carry + + + align:start position:0% +and closing rectangle and so they carry +that around + + align:start position:0% +that around + + + align:start position:0% +that around +as well + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +so think of this multi-dimensional space + + align:start position:0% +so think of this multi-dimensional space + + + align:start position:0% +so think of this multi-dimensional space +now of + + align:start position:0% +now of + + + align:start position:0% +now of +pose so poses translation rotation etc + + align:start position:0% +pose so poses translation rotation etc + + + align:start position:0% +pose so poses translation rotation etc +and it can be multi-dimensional and one + + align:start position:0% +and it can be multi-dimensional and one + + + align:start position:0% +and it can be multi-dimensional and one +of the things that can happen is that + + align:start position:0% +of the things that can happen is that + + + align:start position:0% +of the things that can happen is that +when we do this search for the peak + + align:start position:0% +when we do this search for the peak + + + align:start position:0% +when we do this search for the peak +we end up in this space + + align:start position:0% +we end up in this space + + + align:start position:0% +we end up in this space +with + + align:start position:0% +with + + + align:start position:0% +with +values that are very close together + + align:start position:0% +values that are very close together + + + align:start position:0% +values that are very close together +and you'd + + align:start position:0% +and you'd + + + align:start position:0% +and you'd +you know because we got there + + align:start position:0% +you know because we got there + + + align:start position:0% +you know because we got there +in different ways using translation and + + align:start position:0% +in different ways using translation and + + + align:start position:0% +in different ways using translation and +rotation and scaling and we don't want + + align:start position:0% +rotation and scaling and we don't want + + + align:start position:0% +rotation and scaling and we don't want +to + + align:start position:0% +to + + + align:start position:0% +to +report both of those values and so we + + align:start position:0% +report both of those values and so we + + + align:start position:0% +report both of those values and so we +need to have a way of telling whether + + align:start position:0% +need to have a way of telling whether + + + align:start position:0% +need to have a way of telling whether +two poses are very close together in + + align:start position:0% +two poses are very close together in + + + align:start position:0% +two poses are very close together in +that space and that's what this is about + + align:start position:0% +that space and that's what this is about + + + align:start position:0% +that space and that's what this is about +we won't go into that in detail but it's + + align:start position:0% +we won't go into that in detail but it's + + + align:start position:0% +we won't go into that in detail but it's +to remove any overlap + + align:start position:0% + + + + align:start position:0% + +okay overlap examples + + align:start position:0% +okay overlap examples + + + align:start position:0% +okay overlap examples +you know + + align:start position:0% +you know + + + align:start position:0% +you know +flow charts flow charts used to be quite + + align:start position:0% +flow charts flow charts used to be quite + + + align:start position:0% +flow charts flow charts used to be quite +the thing + + align:start position:0% +the thing + + + align:start position:0% +the thing +and i guess + + align:start position:0% + + + + align:start position:0% + +let's + + align:start position:0% +let's + + + align:start position:0% +let's +let's get to the text + + align:start position:0% + + + + align:start position:0% + +lots of figures + + align:start position:0% +lots of figures + + + align:start position:0% +lots of figures +okay + + align:start position:0% +okay + + + align:start position:0% +okay +oh + + align:start position:0% +oh + + + align:start position:0% +oh +then the + + align:start position:0% +then the + + + align:start position:0% +then the +the bottom level the translational + + align:start position:0% +the bottom level the translational + + + align:start position:0% +the bottom level the translational +search + + align:start position:0% +search + + + align:start position:0% +search +should be done + + align:start position:0% +should be done + + + align:start position:0% +should be done +in an efficient way and also + + align:start position:0% +in an efficient way and also + + + align:start position:0% +in an efficient way and also +should allow for different uh resolution + + align:start position:0% +should allow for different uh resolution + + + align:start position:0% +should allow for different uh resolution +and so here uh our is our sequence of + + align:start position:0% +and so here uh our is our sequence of + + + align:start position:0% +and so here uh our is our sequence of +search patterns that can be used + + align:start position:0% +search patterns that can be used + + + align:start position:0% +search patterns that can be used +efficiently at the lowest level and + + align:start position:0% +efficiently at the lowest level and + + + align:start position:0% +efficiently at the lowest level and +you'll notice that they're basically + + align:start position:0% +you'll notice that they're basically + + + align:start position:0% +you'll notice that they're basically +organized around the hexagon and that's + + align:start position:0% +organized around the hexagon and that's + + + align:start position:0% +organized around the hexagon and that's +as i mentioned because you get a four + + align:start position:0% +as i mentioned because you get a four + + + align:start position:0% +as i mentioned because you get a four +over pi advantage in terms of work done + + align:start position:0% +over pi advantage in terms of work done + + + align:start position:0% +over pi advantage in terms of work done +versus resolution + + align:start position:0% +versus resolution + + + align:start position:0% +versus resolution +and so here's the you know lowest level + + align:start position:0% +and so here's the you know lowest level + + + align:start position:0% +and so here's the you know lowest level +that's just like a red black + + align:start position:0% +that's just like a red black + + + align:start position:0% +that's just like a red black +checkerboard + + align:start position:0% +checkerboard + + + align:start position:0% +checkerboard +and then there's the next highest scale + + align:start position:0% +and then there's the next highest scale + + + align:start position:0% +and then there's the next highest scale +and so on so + + align:start position:0% +and so on so + + + align:start position:0% +and so on so +they get a slight and this isn't huge + + align:start position:0% +they get a slight and this isn't huge + + + align:start position:0% +they get a slight and this isn't huge +some of the other things they do get the + + align:start position:0% +some of the other things they do get the + + + align:start position:0% +some of the other things they do get the +orders of magnitude improvement this + + align:start position:0% +orders of magnitude improvement this + + + align:start position:0% +orders of magnitude improvement this +gets you relatively small + + align:start position:0% +gets you relatively small + + + align:start position:0% +gets you relatively small +uh improvement but uh working on these + + align:start position:0% +uh improvement but uh working on these + + + align:start position:0% +uh improvement but uh working on these +patterns is uh + + align:start position:0% +patterns is uh + + + align:start position:0% +patterns is uh +uh helpful and um + + align:start position:0% +uh helpful and um + + + align:start position:0% +uh helpful and um +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +and um + + align:start position:0% +and um + + + align:start position:0% +and um +remember we talked about peak detection + + align:start position:0% +remember we talked about peak detection + + + align:start position:0% +remember we talked about peak detection +and how you had to deal with + + align:start position:0% +and how you had to deal with + + + align:start position:0% +and how you had to deal with +ties you had to have a tie breaker well + + align:start position:0% +ties you had to have a tie breaker well + + + align:start position:0% +ties you had to have a tie breaker well +it gets a little bit harder on a + + align:start position:0% +it gets a little bit harder on a + + + align:start position:0% +it gets a little bit harder on a +hexagonal grid but here's the here's one + + align:start position:0% +hexagonal grid but here's the here's one + + + align:start position:0% +hexagonal grid but here's the here's one +solution + + align:start position:0% +solution + + + align:start position:0% +solution +so you you check that the center point + + align:start position:0% +so you you check that the center point + + + align:start position:0% +so you you check that the center point +has a larger value than these three + + align:start position:0% +has a larger value than these three + + + align:start position:0% +has a larger value than these three +and it has a larger than or equal to + + align:start position:0% +and it has a larger than or equal to + + + align:start position:0% +and it has a larger than or equal to +value than those three and that ensures + + align:start position:0% +value than those three and that ensures + + + align:start position:0% +value than those three and that ensures +that you're not going to detect adjacent + + align:start position:0% +that you're not going to detect adjacent + + + align:start position:0% +that you're not going to detect adjacent +things that are + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +okay now let's see if i can find this + + align:start position:0% +okay now let's see if i can find this + + + align:start position:0% +okay now let's see if i can find this +place + + align:start position:0% +place + + + align:start position:0% +place +so one of the nice things they do is + + align:start position:0% +so one of the nice things they do is + + + align:start position:0% +so one of the nice things they do is +they + + align:start position:0% +they + + + align:start position:0% +they +explain the terminology + + align:start position:0% +explain the terminology + + + align:start position:0% +explain the terminology +oh here we go + + align:start position:0% + + + + align:start position:0% + +so there's a common term in patent law + + align:start position:0% +so there's a common term in patent law + + + align:start position:0% +so there's a common term in patent law +which is that a common expression which + + align:start position:0% +which is that a common expression which + + + align:start position:0% +which is that a common expression which +is that the inventor can be his own + + align:start position:0% +is that the inventor can be his own + + + align:start position:0% +is that the inventor can be his own +lexicographer which just means that + + align:start position:0% +lexicographer which just means that + + + align:start position:0% +lexicographer which just means that +if you define the term in some way in + + align:start position:0% +if you define the term in some way in + + + align:start position:0% +if you define the term in some way in +the patent + + align:start position:0% +the patent + + + align:start position:0% +the patent +then that's the way it reads for the + + align:start position:0% +then that's the way it reads for the + + + align:start position:0% +then that's the way it reads for the +pattern whether there's someone else + + align:start position:0% +pattern whether there's someone else + + + align:start position:0% +pattern whether there's someone else +that agrees whether that's the right + + align:start position:0% +that agrees whether that's the right + + + align:start position:0% +that agrees whether that's the right +usage for that word or not sort of like + + align:start position:0% +usage for that word or not sort of like + + + align:start position:0% +usage for that word or not sort of like +i was listening to a program + + align:start position:0% +i was listening to a program + + + align:start position:0% +i was listening to a program +uh on canadian broadcasting and he kept + + align:start position:0% +uh on canadian broadcasting and he kept + + + align:start position:0% +uh on canadian broadcasting and he kept +on talking about the neoliberal agenda + + align:start position:0% +on talking about the neoliberal agenda + + + align:start position:0% +on talking about the neoliberal agenda +and stuff like that and i'm like wait a + + align:start position:0% +and stuff like that and i'm like wait a + + + align:start position:0% +and stuff like that and i'm like wait a +minute everything he's talking about is + + align:start position:0% +minute everything he's talking about is + + + align:start position:0% +minute everything he's talking about is +right-wing how come he's calling a + + align:start position:0% +right-wing how come he's calling a + + + align:start position:0% +right-wing how come he's calling a +neoliberal well he wrote the book he + + align:start position:0% +neoliberal well he wrote the book he + + + align:start position:0% +neoliberal well he wrote the book he +called the book the neo-liberal blah + + align:start position:0% +called the book the neo-liberal blah + + + align:start position:0% +called the book the neo-liberal blah +blah blah so he gets to define the term + + align:start position:0% +blah blah so he gets to define the term + + + align:start position:0% +blah blah so he gets to define the term +and and it's my fault for + + align:start position:0% +and and it's my fault for + + + align:start position:0% +and and it's my fault for +using my interpretation of it so here + + align:start position:0% +using my interpretation of it so here + + + align:start position:0% +using my interpretation of it so here +they very explicitly do that they define + + align:start position:0% +they very explicitly do that they define + + + align:start position:0% +they very explicitly do that they define +all of the + + align:start position:0% +all of the + + + align:start position:0% +all of the +interest all of the important parts so + + align:start position:0% +interest all of the important parts so + + + align:start position:0% +interest all of the important parts so +object what is an object it's any + + align:start position:0% +object what is an object it's any + + + align:start position:0% +object what is an object it's any +physical or simulated object or portion + + align:start position:0% +physical or simulated object or portion + + + align:start position:0% +physical or simulated object or portion +thereof having characteristics that can + + align:start position:0% +thereof having characteristics that can + + + align:start position:0% +thereof having characteristics that can +be measured by an image forming device + + align:start position:0% +be measured by an image forming device + + + align:start position:0% +be measured by an image forming device +or simulated by a data processing device + + align:start position:0% +or simulated by a data processing device + + + align:start position:0% +or simulated by a data processing device +now this is classic uh generalization + + align:start position:0% +now this is classic uh generalization + + + align:start position:0% +now this is classic uh generalization +right we're just talking about images + + align:start position:0% +right we're just talking about images + + + align:start position:0% +right we're just talking about images +taken with a camera + + align:start position:0% +taken with a camera + + + align:start position:0% +taken with a camera +and the the the patent attorney says + + align:start position:0% +and the the the patent attorney says + + + align:start position:0% +and the the the patent attorney says +wait a minute this has much wider + + align:start position:0% +wait a minute this has much wider + + + align:start position:0% +wait a minute this has much wider +applications so they're talking about + + align:start position:0% +applications so they're talking about + + + align:start position:0% +applications so they're talking about +not just images that were made from real + + align:start position:0% +not just images that were made from real + + + align:start position:0% +not just images that were made from real +objects but graphics so this could be + + align:start position:0% +objects but graphics so this could be + + + align:start position:0% +objects but graphics so this could be +used on out you know data + + align:start position:0% +used on out you know data + + + align:start position:0% +used on out you know data +simulated by a data processing device + + align:start position:0% +simulated by a data processing device + + + align:start position:0% +simulated by a data processing device +and + + align:start position:0% +and + + + align:start position:0% +and +you can read into this x-ray images + + align:start position:0% +you can read into this x-ray images + + + align:start position:0% +you can read into this x-ray images +doesn't have to be visible light images + + align:start position:0% +doesn't have to be visible light images + + + align:start position:0% +doesn't have to be visible light images +so then what's an image a + + align:start position:0% +so then what's an image a + + + align:start position:0% +so then what's an image a +two-dimensional function + + align:start position:0% +two-dimensional function + + + align:start position:0% +two-dimensional function +whose values correspond to physical + + align:start position:0% +whose values correspond to physical + + + align:start position:0% +whose values correspond to physical +characteristics of an object + + align:start position:0% +characteristics of an object + + + align:start position:0% +characteristics of an object +and then i guess we have to go up there + + align:start position:0% + + + + align:start position:0% + +uh such as brightness radiant energy + + align:start position:0% +uh such as brightness radiant energy + + + align:start position:0% +uh such as brightness radiant energy +reflected or otherwise color temperature + + align:start position:0% +reflected or otherwise color temperature + + + align:start position:0% +reflected or otherwise color temperature +height you can see how much fun they had + + align:start position:0% +height you can see how much fun they had + + + align:start position:0% +height you can see how much fun they had +trying to generalize this as much as + + align:start position:0% +trying to generalize this as much as + + + align:start position:0% +trying to generalize this as much as +possible brightness the physical or + + align:start position:0% +possible brightness the physical or + + + align:start position:0% +possible brightness the physical or +simulated quantity represented by the + + align:start position:0% +simulated quantity represented by the + + + align:start position:0% +simulated quantity represented by the +values of an image regardless of source + + align:start position:0% +values of an image regardless of source + + + align:start position:0% +values of an image regardless of source +so that's to make sure that just because + + align:start position:0% +so that's to make sure that just because + + + align:start position:0% +so that's to make sure that just because +you said brightness it doesn't exclude + + align:start position:0% +you said brightness it doesn't exclude + + + align:start position:0% +you said brightness it doesn't exclude +anything else like temperature + + align:start position:0% +anything else like temperature + + + align:start position:0% +anything else like temperature +x-ray intensity + + align:start position:0% +x-ray intensity + + + align:start position:0% +x-ray intensity +i don't know + + align:start position:0% +i don't know + + + align:start position:0% +i don't know +okay uh granularity so that's where they + + align:start position:0% +okay uh granularity so that's where they + + + align:start position:0% +okay uh granularity so that's where they +talk about the + + align:start position:0% +talk about the + + + align:start position:0% +talk about the +size in units of distance below which + + align:start position:0% +size in units of distance below which + + + align:start position:0% +size in units of distance below which +spatial variations in image brightness + + align:start position:0% +spatial variations in image brightness + + + align:start position:0% +spatial variations in image brightness +are increasingly attenuated so when you + + align:start position:0% +are increasingly attenuated so when you + + + align:start position:0% +are increasingly attenuated so when you +blow an image up there comes a point + + align:start position:0% +blow an image up there comes a point + + + align:start position:0% +blow an image up there comes a point +where it starts to look blurry and + + align:start position:0% +where it starts to look blurry and + + + align:start position:0% +where it starts to look blurry and +you can relate the definition of + + align:start position:0% +you can relate the definition of + + + align:start position:0% +you can relate the definition of +granularity to to that point + + align:start position:0% + + + + align:start position:0% + +can be thought of as being related to + + align:start position:0% +can be thought of as being related to + + + align:start position:0% +can be thought of as being related to +resolution boundary what's a boundary an + + align:start position:0% +resolution boundary what's a boundary an + + + align:start position:0% +resolution boundary what's a boundary an +imaginary contour open ended or closed + + align:start position:0% +imaginary contour open ended or closed + + + align:start position:0% +imaginary contour open ended or closed +straight or curved smooth or sharp you + + align:start position:0% +straight or curved smooth or sharp you + + + align:start position:0% +straight or curved smooth or sharp you +know take your pick + + align:start position:0% +know take your pick + + + align:start position:0% +know take your pick +i love the thing where it says um for + + align:start position:0% +i love the thing where it says um for + + + align:start position:0% +i love the thing where it says um for +example it'll say something like the + + align:start position:0% +example it'll say something like the + + + align:start position:0% +example it'll say something like the +words and and or + + align:start position:0% +words and and or + + + align:start position:0% +words and and or +mean both and and or it's like what + + align:start position:0% +mean both and and or it's like what + + + align:start position:0% +mean both and and or it's like what +you know it's like + + align:start position:0% +you know it's like + + + align:start position:0% +you know it's like +that way they generalize everything and + + align:start position:0% +that way they generalize everything and + + + align:start position:0% +that way they generalize everything and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it gets worse i mean to to us + + align:start position:0% +it gets worse i mean to to us + + + align:start position:0% +it gets worse i mean to to us +thinking about logic you know and and or + + align:start position:0% +thinking about logic you know and and or + + + align:start position:0% +thinking about logic you know and and or +very different concepts + + align:start position:0% +very different concepts + + + align:start position:0% +very different concepts +but + + align:start position:0% +but + + + align:start position:0% +but +you can now go through the whole + + align:start position:0% +you can now go through the whole + + + align:start position:0% +you can now go through the whole +document replace all occurrences of and + + align:start position:0% +document replace all occurrences of and + + + align:start position:0% +document replace all occurrences of and +with or and try all possible + + align:start position:0% +with or and try all possible + + + align:start position:0% +with or and try all possible +combinations and it's still + + align:start position:0% +combinations and it's still + + + align:start position:0% +combinations and it's still +covered by that pattern + + align:start position:0% +covered by that pattern + + + align:start position:0% +covered by that pattern +uh gradient well we know what a gradient + + align:start position:0% +uh gradient well we know what a gradient + + + align:start position:0% +uh gradient well we know what a gradient +is vector at a given point in an image + + align:start position:0% +is vector at a given point in an image + + + align:start position:0% +is vector at a given point in an image +given the direction magnitude of + + align:start position:0% +given the direction magnitude of + + + align:start position:0% +given the direction magnitude of +greatest change in brightness at a + + align:start position:0% +greatest change in brightness at a + + + align:start position:0% +greatest change in brightness at a +specified granularity uh pattern a + + align:start position:0% +specified granularity uh pattern a + + + align:start position:0% +specified granularity uh pattern a +specifier specific geometric arrangement + + align:start position:0% +specifier specific geometric arrangement + + + align:start position:0% +specifier specific geometric arrangement +of quantum is lying in a bounded subset + + align:start position:0% +of quantum is lying in a bounded subset + + + align:start position:0% +of quantum is lying in a bounded subset +of the plane of quantus state context + + align:start position:0% +of the plane of quantus state context + + + align:start position:0% +of the plane of quantus state context +representing the boundary so could you + + align:start position:0% +representing the boundary so could you + + + align:start position:0% +representing the boundary so could you +have come up with that definition + + align:start position:0% +have come up with that definition + + + align:start position:0% +have come up with that definition +i mean this takes art you know do you + + align:start position:0% +i mean this takes art you know do you + + + align:start position:0% +i mean this takes art you know do you +get a degree in law before you can do + + align:start position:0% +get a degree in law before you can do + + + align:start position:0% +get a degree in law before you can do +this uh model a set of data encoding + + align:start position:0% +this uh model a set of data encoding + + + align:start position:0% +this uh model a set of data encoding +characteristics of a pattern to be found + + align:start position:0% +characteristics of a pattern to be found + + + align:start position:0% +characteristics of a pattern to be found +were used by a pattern finding method + + align:start position:0% +were used by a pattern finding method + + + align:start position:0% +were used by a pattern finding method +training an act of creating a model from + + align:start position:0% +training an act of creating a model from + + + align:start position:0% +training an act of creating a model from +an image of an example object or from a + + align:start position:0% +an image of an example object or from a + + + align:start position:0% +an image of an example object or from a +geometric description of it i haven't + + align:start position:0% +geometric description of it i haven't + + + align:start position:0% +geometric description of it i haven't +discussed that i've sort of assumed so + + align:start position:0% +discussed that i've sort of assumed so + + + align:start position:0% +discussed that i've sort of assumed so +far we're making the model from a real + + align:start position:0% +far we're making the model from a real + + + align:start position:0% +far we're making the model from a real +image but of course if you have the cad + + align:start position:0% +image but of course if you have the cad + + + align:start position:0% +image but of course if you have the cad +for the object you might very well say + + align:start position:0% +for the object you might very well say + + + align:start position:0% +for the object you might very well say +well that's even more of a golden + + align:start position:0% +well that's even more of a golden + + + align:start position:0% +well that's even more of a golden +standard that that's really the truth + + align:start position:0% +standard that that's really the truth + + + align:start position:0% +standard that that's really the truth +and so you could produce the model from + + align:start position:0% +and so you could produce the model from + + + align:start position:0% +and so you could produce the model from +the + + align:start position:0% +the + + + align:start position:0% +the +you know mechanical drawing or + + align:start position:0% +you know mechanical drawing or + + + align:start position:0% +you know mechanical drawing or +equivalent computer version + + align:start position:0% +equivalent computer version + + + align:start position:0% +equivalent computer version +downside is if there's some + + align:start position:0% +downside is if there's some + + + align:start position:0% +downside is if there's some +process in manufacturing that does not + + align:start position:0% +process in manufacturing that does not + + + align:start position:0% +process in manufacturing that does not +reproduce the cad exactly you you won't + + align:start position:0% +reproduce the cad exactly you you won't + + + align:start position:0% +reproduce the cad exactly you you won't +capture that because you're working and + + align:start position:0% +capture that because you're working and + + + align:start position:0% +capture that because you're working and +you know this is very common for example + + align:start position:0% +you know this is very common for example + + + align:start position:0% +you know this is very common for example +in printed circuits or integrated + + align:start position:0% +in printed circuits or integrated + + + align:start position:0% +in printed circuits or integrated +circuits you have a perfectly + + align:start position:0% +circuits you have a perfectly + + + align:start position:0% +circuits you have a perfectly +rectangular layout with sharp corners + + align:start position:0% +rectangular layout with sharp corners + + + align:start position:0% +rectangular layout with sharp corners +well when you go through and expose the + + align:start position:0% +well when you go through and expose the + + + align:start position:0% +well when you go through and expose the +material and put it in the chemical bath + + align:start position:0% +material and put it in the chemical bath + + + align:start position:0% +material and put it in the chemical bath +that corner is not going to be a sharp + + align:start position:0% +that corner is not going to be a sharp + + + align:start position:0% +that corner is not going to be a sharp +corner it's going to be rounded and so + + align:start position:0% +corner it's going to be rounded and so + + + align:start position:0% +corner it's going to be rounded and so +those are situations where working with + + align:start position:0% +those are situations where working with + + + align:start position:0% +those are situations where working with +the real object is better than working + + align:start position:0% +the real object is better than working + + + align:start position:0% +the real object is better than working +with with a cat + + align:start position:0% +with with a cat + + + align:start position:0% +with with a cat +okay pose a mapping from pattern to + + align:start position:0% +okay pose a mapping from pattern to + + + align:start position:0% +okay pose a mapping from pattern to +image coordinates we discussed that + + align:start position:0% +image coordinates we discussed that + + + align:start position:0% +image coordinates we discussed that +representing a specific transformation + + align:start position:0% +representing a specific transformation + + + align:start position:0% +representing a specific transformation +superposition of a pattern onto an image + + align:start position:0% +superposition of a pattern onto an image + + + align:start position:0% +superposition of a pattern onto an image +so as i mentioned this is unusual in + + align:start position:0% +so as i mentioned this is unusual in + + + align:start position:0% +so as i mentioned this is unusual in +that they've gone to the trouble of + + align:start position:0% +that they've gone to the trouble of + + + align:start position:0% +that they've gone to the trouble of +breaking out and listing + + align:start position:0% +breaking out and listing + + + align:start position:0% +breaking out and listing +the terms that they will use + + align:start position:0% + + + + align:start position:0% + +which is very good because then if + + align:start position:0% +which is very good because then if + + + align:start position:0% +which is very good because then if +there's any argument about what what the + + align:start position:0% +there's any argument about what what the + + + align:start position:0% +there's any argument about what what the +specification means or indeed what the + + align:start position:0% +specification means or indeed what the + + + align:start position:0% +specification means or indeed what the +claims mean then that's uh + + align:start position:0% +claims mean then that's uh + + + align:start position:0% +claims mean then that's uh +right defined there so let's jump ahead + + align:start position:0% +right defined there so let's jump ahead + + + align:start position:0% +right defined there so let's jump ahead +so the rest is you know the usual stuff + + align:start position:0% +so the rest is you know the usual stuff + + + align:start position:0% +so the rest is you know the usual stuff +the the the background of of why this is + + align:start position:0% +the the the background of of why this is + + + align:start position:0% +the the the background of of why this is +the best things in sliced cheese or + + align:start position:0% +the best things in sliced cheese or + + + align:start position:0% +the best things in sliced cheese or +sliced bread and then you know what is + + align:start position:0% +sliced bread and then you know what is + + + align:start position:0% +sliced bread and then you know what is +the prior art so they talk about all the + + align:start position:0% +the prior art so they talk about all the + + + align:start position:0% +the prior art so they talk about all the +things we talked about + + align:start position:0% +things we talked about + + + align:start position:0% +things we talked about +um you know binary templates + + align:start position:0% +um you know binary templates + + + align:start position:0% +um you know binary templates +blob analysis + + align:start position:0% +blob analysis + + + align:start position:0% +blob analysis +correlation + + align:start position:0% +correlation + + + align:start position:0% +correlation +and half transforms which we haven't + + align:start position:0% +and half transforms which we haven't + + + align:start position:0% +and half transforms which we haven't +talked about and then they get to the + + align:start position:0% +talked about and then they get to the + + + align:start position:0% +talked about and then they get to the +summary of the invention + + align:start position:0% +summary of the invention + + + align:start position:0% +summary of the invention +which pretty quickly goes into + + align:start position:0% +which pretty quickly goes into + + + align:start position:0% +which pretty quickly goes into +the discussion of the figures + + align:start position:0% +the discussion of the figures + + + align:start position:0% +the discussion of the figures +and details of the figures and then + + align:start position:0% +and details of the figures and then + + + align:start position:0% +and details of the figures and then +there's some + + align:start position:0% +there's some + + + align:start position:0% +there's some +equations uh to hear the explanation + + align:start position:0% +equations uh to hear the explanation + + + align:start position:0% +equations uh to hear the explanation +it's fairly long there's here the + + align:start position:0% +it's fairly long there's here the + + + align:start position:0% +it's fairly long there's here the +figures i'm trying to get to the claims + + align:start position:0% +figures i'm trying to get to the claims + + + align:start position:0% +figures i'm trying to get to the claims +uh wow there's even an integral sign + + align:start position:0% +uh wow there's even an integral sign + + + align:start position:0% +uh wow there's even an integral sign +that's neat + + align:start position:0% +that's neat + + + align:start position:0% +that's neat +yeah wow + + align:start position:0% +yeah wow + + + align:start position:0% +yeah wow +oh that's the noise calculation integral + + align:start position:0% +oh that's the noise calculation integral + + + align:start position:0% +oh that's the noise calculation integral +from 0 to 360. + + align:start position:0% +from 0 to 360. + + + align:start position:0% +from 0 to 360. +and + + align:start position:0% +and + + + align:start position:0% +and +you know it gets gets kind of uh + + align:start position:0% +you know it gets gets kind of uh + + + align:start position:0% +you know it gets gets kind of uh +interesting there's some some real math + + align:start position:0% +interesting there's some some real math + + + align:start position:0% +interesting there's some some real math +there + + align:start position:0% + + + + align:start position:0% + +okay we're come on oh here we go claims + + align:start position:0% + + + + align:start position:0% + +preferred + + align:start position:0% +preferred + + + align:start position:0% +preferred +um okay must be down the bottom here + + align:start position:0% +um okay must be down the bottom here + + + align:start position:0% +um okay must be down the bottom here +claim one okay what is claimed is + + align:start position:0% +claim one okay what is claimed is + + + align:start position:0% +claim one okay what is claimed is +a method for determining the presence or + + align:start position:0% +a method for determining the presence or + + + align:start position:0% +a method for determining the presence or +absence of at least one instance of a + + align:start position:0% +absence of at least one instance of a + + + align:start position:0% +absence of at least one instance of a +predetermined pattern in a runtime image + + align:start position:0% +predetermined pattern in a runtime image + + + align:start position:0% +predetermined pattern in a runtime image +and for determining the + + align:start position:0% +and for determining the + + + align:start position:0% +and for determining the +multi-dimensional location + + align:start position:0% +multi-dimensional location + + + align:start position:0% +multi-dimensional location +location in parentheses posed of each + + align:start position:0% +location in parentheses posed of each + + + align:start position:0% +location in parentheses posed of each +present instance the message comprising + + align:start position:0% +present instance the message comprising + + + align:start position:0% +present instance the message comprising +and so then they go on and describe the + + align:start position:0% +and so then they go on and describe the + + + align:start position:0% +and so then they go on and describe the +details and and we'll talk some about + + align:start position:0% +details and and we'll talk some about + + + align:start position:0% +details and and we'll talk some about +those details they also + + align:start position:0% + + + + align:start position:0% + +didn't say this up front but they + + align:start position:0% +didn't say this up front but they + + + align:start position:0% +didn't say this up front but they +incorporate inspect the possibility of + + align:start position:0% +incorporate inspect the possibility of + + + align:start position:0% +incorporate inspect the possibility of +inspection and the possibility of + + align:start position:0% +inspection and the possibility of + + + align:start position:0% +inspection and the possibility of +recognition so + + align:start position:0% +recognition so + + + align:start position:0% +recognition so +recognition is + + align:start position:0% +recognition is + + + align:start position:0% +recognition is +what's going to happen if you have a + + align:start position:0% +what's going to happen if you have a + + + align:start position:0% +what's going to happen if you have a +very good match + + align:start position:0% +very good match + + + align:start position:0% +very good match +and so + + align:start position:0% + + + + align:start position:0% + +if you have the possibility of seeing + + align:start position:0% +if you have the possibility of seeing + + + align:start position:0% +if you have the possibility of seeing +more than one object well you run this + + align:start position:0% +more than one object well you run this + + + align:start position:0% +more than one object well you run this +process for each of them and presumably + + align:start position:0% +process for each of them and presumably + + + align:start position:0% +process for each of them and presumably +most of them won't be a good match and + + align:start position:0% +most of them won't be a good match and + + + align:start position:0% +most of them won't be a good match and +one of them will and so that's that's + + align:start position:0% +one of them will and so that's that's + + + align:start position:0% +one of them will and so that's that's +your recognition + + align:start position:0% +your recognition + + + align:start position:0% +your recognition +the other thing inspection + + align:start position:0% +the other thing inspection + + + align:start position:0% +the other thing inspection +this method works even if parts of the + + align:start position:0% +this method works even if parts of the + + + align:start position:0% +this method works even if parts of the +object are obscured + + align:start position:0% +object are obscured + + + align:start position:0% +object are obscured +or parts of the object are missing + + align:start position:0% +or parts of the object are missing + + + align:start position:0% +or parts of the object are missing +but of course the the match is going to + + align:start position:0% +but of course the the match is going to + + + align:start position:0% +but of course the the match is going to +decrease in quality as you you know + + align:start position:0% +decrease in quality as you you know + + + align:start position:0% +decrease in quality as you you know +remove things + + align:start position:0% +remove things + + + align:start position:0% +remove things +so if your gear has lost one tooth + + align:start position:0% +so if your gear has lost one tooth + + + align:start position:0% +so if your gear has lost one tooth +you'll still get a pretty good match if + + align:start position:0% +you'll still get a pretty good match if + + + align:start position:0% +you'll still get a pretty good match if +it's losing two teeth not so good and so + + align:start position:0% +it's losing two teeth not so good and so + + + align:start position:0% +it's losing two teeth not so good and so +on so that obviously tells you you can + + align:start position:0% +on so that obviously tells you you can + + + align:start position:0% +on so that obviously tells you you can +use it for inspection so after you've + + align:start position:0% +use it for inspection so after you've + + + align:start position:0% +use it for inspection so after you've +found the object in pose + + align:start position:0% +found the object in pose + + + align:start position:0% +found the object in pose +and you've matched it you can then uh + + align:start position:0% +and you've matched it you can then uh + + + align:start position:0% +and you've matched it you can then uh +qualify just how good a match it is and + + align:start position:0% +qualify just how good a match it is and + + + align:start position:0% +qualify just how good a match it is and +that might be a way of doing um you know + + align:start position:0% +that might be a way of doing um you know + + + align:start position:0% +that might be a way of doing um you know +rejection of a part that's not + + align:start position:0% +rejection of a part that's not + + + align:start position:0% +rejection of a part that's not +satisfactory + + align:start position:0% +satisfactory + + + align:start position:0% +satisfactory +so this one is mostly method claims i'm + + align:start position:0% +so this one is mostly method claims i'm + + + align:start position:0% +so this one is mostly method claims i'm +trying to remember if this the method uh + + align:start position:0% +trying to remember if this the method uh + + + align:start position:0% +trying to remember if this the method uh +and then a lot of dependent claims the + + align:start position:0% +and then a lot of dependent claims the + + + align:start position:0% +and then a lot of dependent claims the +method of claim one plus this + + align:start position:0% +method of claim one plus this + + + align:start position:0% +method of claim one plus this +and i can't remember if this one + + align:start position:0% +and i can't remember if this one + + + align:start position:0% +and i can't remember if this one +uh still has apparatus claims the method + + align:start position:0% +uh still has apparatus claims the method + + + align:start position:0% +uh still has apparatus claims the method +of claim one these are all method claims + + align:start position:0% +of claim one these are all method claims + + + align:start position:0% +of claim one these are all method claims +no all method claims i think what + + align:start position:0% +no all method claims i think what + + + align:start position:0% +no all method claims i think what +happened is that the uh legal situation + + align:start position:0% +happened is that the uh legal situation + + + align:start position:0% +happened is that the uh legal situation +changed slightly and they didn't have to + + align:start position:0% +changed slightly and they didn't have to + + + align:start position:0% +changed slightly and they didn't have to +do that game anymore of having both + + align:start position:0% +do that game anymore of having both + + + align:start position:0% +do that game anymore of having both +apparatus and and methods + + align:start position:0% +apparatus and and methods + + + align:start position:0% +apparatus and and methods +okay where are we okay + + align:start position:0% +okay where are we okay + + + align:start position:0% +okay where are we okay +so um + + align:start position:0% +so um + + + align:start position:0% +so um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +i hope the idea of this of probes is uh + + align:start position:0% +i hope the idea of this of probes is uh + + + align:start position:0% +i hope the idea of this of probes is uh +quite clear + + align:start position:0% +quite clear + + + align:start position:0% +quite clear +and um + + align:start position:0% +and um + + + align:start position:0% +and um +and the model the models composed of + + align:start position:0% +and the model the models composed of + + + align:start position:0% +and the model the models composed of +these probes + + align:start position:0% + + + + align:start position:0% + +and and the huge advantage + + align:start position:0% +and and the huge advantage + + + align:start position:0% +and and the huge advantage +of using the probes compared to using + + align:start position:0% +of using the probes compared to using + + + align:start position:0% +of using the probes compared to using +say uh correlation + + align:start position:0% +say uh correlation + + + align:start position:0% +say uh correlation +because we're now only looking + + align:start position:0% +because we're now only looking + + + align:start position:0% +because we're now only looking +at a small number of points in the + + align:start position:0% +at a small number of points in the + + + align:start position:0% +at a small number of points in the +gradient image now the uh + + align:start position:0% +gradient image now the uh + + + align:start position:0% +gradient image now the uh +you know theoretically we could just + + align:start position:0% +you know theoretically we could just + + + align:start position:0% +you know theoretically we could just +compute the gradient when we need to + + align:start position:0% +compute the gradient when we need to + + + align:start position:0% +compute the gradient when we need to +match it + + align:start position:0% +match it + + + align:start position:0% +match it +but since we're going to do this + + align:start position:0% +but since we're going to do this + + + align:start position:0% +but since we're going to do this +matching many many times with different + + align:start position:0% +matching many many times with different + + + align:start position:0% +matching many many times with different +orientations and positions for the model + + align:start position:0% +orientations and positions for the model + + + align:start position:0% +orientations and positions for the model +um there's a definite advantage to + + align:start position:0% +um there's a definite advantage to + + + align:start position:0% +um there's a definite advantage to +pre-computing the + + align:start position:0% +pre-computing the + + + align:start position:0% +pre-computing the +pre-computing the + + align:start position:0% +pre-computing the + + + align:start position:0% +pre-computing the +gradient so + + align:start position:0% +gradient so + + + align:start position:0% +gradient so +we use that other pattern to finish that + + align:start position:0% +we use that other pattern to finish that + + + align:start position:0% +we use that other pattern to finish that +job and then we jump in and superimpose + + align:start position:0% +job and then we jump in and superimpose + + + align:start position:0% +job and then we jump in and superimpose +we map the + + align:start position:0% +we map the + + + align:start position:0% +we map the +model on top of the runtime image and + + align:start position:0% +model on top of the runtime image and + + + align:start position:0% +model on top of the runtime image and +there's just a few places and we're + + align:start position:0% +there's just a few places and we're + + + align:start position:0% +there's just a few places and we're +collecting evidence so at every one of + + align:start position:0% +collecting evidence so at every one of + + + align:start position:0% +collecting evidence so at every one of +those probe phrases we're asking the + + align:start position:0% +those probe phrases we're asking the + + + align:start position:0% +those probe phrases we're asking the +question you know is + + align:start position:0% +question you know is + + + align:start position:0% +question you know is +does this support a hypothesis that + + align:start position:0% +does this support a hypothesis that + + + align:start position:0% +does this support a hypothesis that +there's an object with this pose and + + align:start position:0% +there's an object with this pose and + + + align:start position:0% +there's an object with this pose and +then we add up all of the evidence and + + align:start position:0% +then we add up all of the evidence and + + + align:start position:0% +then we add up all of the evidence and +that gives us a score + + align:start position:0% +that gives us a score + + + align:start position:0% +that gives us a score +and then from that we can build a score + + align:start position:0% +and then from that we can build a score + + + align:start position:0% +and then from that we can build a score +surface in this multi-dimensional space + + align:start position:0% +surface in this multi-dimensional space + + + align:start position:0% +surface in this multi-dimensional space +now it's much easier to visualize if we + + align:start position:0% +now it's much easier to visualize if we + + + align:start position:0% +now it's much easier to visualize if we +only deal with translation then we have + + align:start position:0% +only deal with translation then we have + + + align:start position:0% +only deal with translation then we have +a function that you know varies with x + + align:start position:0% +a function that you know varies with x + + + align:start position:0% +a function that you know varies with x +and y and we're looking for the peak and + + align:start position:0% +and y and we're looking for the peak and + + + align:start position:0% +and y and we're looking for the peak and +that's our translation + + align:start position:0% +that's our translation + + + align:start position:0% +that's our translation +we're done but of course we're also + + align:start position:0% +we're done but of course we're also + + + align:start position:0% +we're done but of course we're also +interested in dealing with + + align:start position:0% +interested in dealing with + + + align:start position:0% +interested in dealing with +rotation scaling etc so it's a little + + align:start position:0% +rotation scaling etc so it's a little + + + align:start position:0% +rotation scaling etc so it's a little +more difficult but same idea + + align:start position:0% +more difficult but same idea + + + align:start position:0% +more difficult but same idea +let me just talk a little bit about this + + align:start position:0% +let me just talk a little bit about this + + + align:start position:0% +let me just talk a little bit about this +noise issue + + align:start position:0% +noise issue + + + align:start position:0% +noise issue +so + + align:start position:0% + + + + align:start position:0% + +it's called noise which is kind of a + + align:start position:0% +it's called noise which is kind of a + + + align:start position:0% +it's called noise which is kind of a +misnomer + + align:start position:0% +misnomer + + + align:start position:0% +misnomer +um in the patent + + align:start position:0% +um in the patent + + + align:start position:0% +um in the patent +remember we had this scoring function + + align:start position:0% +remember we had this scoring function + + + align:start position:0% +remember we had this scoring function +for um + + align:start position:0% +for um + + + align:start position:0% +for um +where this was the difference in + + align:start position:0% +where this was the difference in + + + align:start position:0% +where this was the difference in +degrees between the + + align:start position:0% +degrees between the + + + align:start position:0% +degrees between the +model + + align:start position:0% +model + + + align:start position:0% +model +probe direction and the gradient runtime + + align:start position:0% +probe direction and the gradient runtime + + + align:start position:0% +probe direction and the gradient runtime +gradient direction and i said that + + align:start position:0% +gradient direction and i said that + + + align:start position:0% +gradient direction and i said that +there's some probability that + + align:start position:0% +there's some probability that + + + align:start position:0% +there's some probability that +if you're just superimposing this in + + align:start position:0% +if you're just superimposing this in + + + align:start position:0% +if you're just superimposing this in +some random place in the runtime image + + align:start position:0% +some random place in the runtime image + + + align:start position:0% +some random place in the runtime image +that you're going to get a match and so + + align:start position:0% +that you're going to get a match and so + + + align:start position:0% +that you're going to get a match and so +how bad is that well obviously what you + + align:start position:0% +how bad is that well obviously what you + + + align:start position:0% +how bad is that well obviously what you +want to do is just integrate + + align:start position:0% + + + + align:start position:0% + +what shall we call this thing i don't + + align:start position:0% +what shall we call this thing i don't + + + align:start position:0% +what shall we call this thing i don't +know uh + + align:start position:0% +know uh + + + align:start position:0% +know uh +scoring function + + align:start position:0% + + + + align:start position:0% + +right so um + + align:start position:0% +right so um + + + align:start position:0% +right so um +if this was 22.5 + + align:start position:0% +if this was 22.5 + + + align:start position:0% +if this was 22.5 +and this was + + align:start position:0% +and this was + + + align:start position:0% +and this was +11.25 you know we we can calculate this + + align:start position:0% +11.25 you know we we can calculate this + + + align:start position:0% +11.25 you know we we can calculate this +this integral i forget what it comes out + + align:start position:0% +this integral i forget what it comes out + + + align:start position:0% +this integral i forget what it comes out +to and then also obviously if we + + align:start position:0% +to and then also obviously if we + + + align:start position:0% +to and then also obviously if we +use the + + align:start position:0% +use the + + + align:start position:0% +use the +method that is insensitive to the sign + + align:start position:0% +method that is insensitive to the sign + + + align:start position:0% +method that is insensitive to the sign +of contrast then we double + + align:start position:0% +of contrast then we double + + + align:start position:0% +of contrast then we double +we double the amount that we're going to + + align:start position:0% +we double the amount that we're going to + + + align:start position:0% +we double the amount that we're going to +get from random matches + + align:start position:0% +get from random matches + + + align:start position:0% +get from random matches +now the + + align:start position:0% +now the + + + align:start position:0% +now the +two aspects to that one of them is we + + align:start position:0% +two aspects to that one of them is we + + + align:start position:0% +two aspects to that one of them is we +can calculate how much this is going to + + align:start position:0% +can calculate how much this is going to + + + align:start position:0% +can calculate how much this is going to +offset the result and we can subtract so + + align:start position:0% +offset the result and we can subtract so + + + align:start position:0% +offset the result and we can subtract so +we can take out this error + + align:start position:0% +we can take out this error + + + align:start position:0% +we can take out this error +but the other one is of course that + + align:start position:0% +but the other one is of course that + + + align:start position:0% +but the other one is of course that +is going to contribute to the noise in + + align:start position:0% +is going to contribute to the noise in + + + align:start position:0% +is going to contribute to the noise in +the result that you know + + align:start position:0% +the result that you know + + + align:start position:0% +the result that you know +that it's not not as good so here's a + + align:start position:0% +that it's not not as good so here's a + + + align:start position:0% +that it's not not as good so here's a +here's an idea so this is kind of a + + align:start position:0% +here's an idea so this is kind of a + + + align:start position:0% +here's an idea so this is kind of a +nuisance to compute this to take the two + + align:start position:0% +nuisance to compute this to take the two + + + align:start position:0% +nuisance to compute this to take the two +directions + + align:start position:0% +directions + + + align:start position:0% +directions +take the difference in angle and then + + align:start position:0% +take the difference in angle and then + + + align:start position:0% +take the difference in angle and then +look it up in + + align:start position:0% +look it up in + + + align:start position:0% +look it up in +in this function or table + + align:start position:0% +in this function or table + + + align:start position:0% +in this function or table +um + + align:start position:0% +um + + + align:start position:0% +um +how about if we just take the dot + + align:start position:0% +how about if we just take the dot + + + align:start position:0% +how about if we just take the dot +products of these two vectors you know + + align:start position:0% +products of these two vectors you know + + + align:start position:0% +products of these two vectors you know +if you have two unit vectors we can just + + align:start position:0% +if you have two unit vectors we can just + + + align:start position:0% +if you have two unit vectors we can just +take the dot product + + align:start position:0% + + + + align:start position:0% + +and that's going to be the cosine of the + + align:start position:0% +and that's going to be the cosine of the + + + align:start position:0% +and that's going to be the cosine of the +angle + + align:start position:0% +angle + + + align:start position:0% +angle +between them right so that that would be + + align:start position:0% +between them right so that that would be + + + align:start position:0% +between them right so that that would be +very cheap to compute because then in + + align:start position:0% +very cheap to compute because then in + + + align:start position:0% +very cheap to compute because then in +the probe i just saw the v1 and in the + + align:start position:0% +the probe i just saw the v1 and in the + + + align:start position:0% +the probe i just saw the v1 and in the +runtime image i've got v2 computed by + + align:start position:0% +runtime image i've got v2 computed by + + + align:start position:0% +runtime image i've got v2 computed by +that uh previous pattern and then i just + + align:start position:0% +that uh previous pattern and then i just + + + align:start position:0% +that uh previous pattern and then i just +take the dot product which is going to + + align:start position:0% +take the dot product which is going to + + + align:start position:0% +take the dot product which is going to +be cheaper than using that method + + align:start position:0% +be cheaper than using that method + + + align:start position:0% +be cheaper than using that method +because in this method i have to use a + + align:start position:0% +because in this method i have to use a + + + align:start position:0% +because in this method i have to use a +tan to get the angle + + align:start position:0% +tan to get the angle + + + align:start position:0% +tan to get the angle +and i have to use it twice once in the + + align:start position:0% +and i have to use it twice once in the + + + align:start position:0% +and i have to use it twice once in the +well once in the training so who cares + + align:start position:0% +well once in the training so who cares + + + align:start position:0% +well once in the training so who cares +you only do that once but once in the + + align:start position:0% +you only do that once but once in the + + + align:start position:0% +you only do that once but once in the +runtime image + + align:start position:0% +runtime image + + + align:start position:0% +runtime image +so what's wrong with that well + + align:start position:0% +so what's wrong with that well + + + align:start position:0% +so what's wrong with that well +that means that my weighting function + + align:start position:0% +that means that my weighting function + + + align:start position:0% +that means that my weighting function +looks like this + + align:start position:0% + + + + align:start position:0% + +right because if they're lined up i get + + align:start position:0% +right because if they're lined up i get + + + align:start position:0% +right because if they're lined up i get +one + + align:start position:0% +one + + + align:start position:0% +one +uh if they're opposite each other i get + + align:start position:0% +uh if they're opposite each other i get + + + align:start position:0% +uh if they're opposite each other i get +minus one + + align:start position:0% + + + + align:start position:0% + +and um + + align:start position:0% +and um + + + align:start position:0% +and um +so that's a potential + + align:start position:0% +so that's a potential + + + align:start position:0% +so that's a potential +this isn't in the pattern + + align:start position:0% +this isn't in the pattern + + + align:start position:0% +this isn't in the pattern +this is an alternate + + align:start position:0% +this is an alternate + + + align:start position:0% +this is an alternate +not as good uh scoring for + + align:start position:0% +not as good uh scoring for + + + align:start position:0% +not as good uh scoring for +gradient direction function + + align:start position:0% +gradient direction function + + + align:start position:0% +gradient direction function +now + + align:start position:0% +now + + + align:start position:0% +now +this is the one that takes into account + + align:start position:0% +this is the one that takes into account + + + align:start position:0% +this is the one that takes into account +polarity but i can also think of the one + + align:start position:0% +polarity but i can also think of the one + + + align:start position:0% +polarity but i can also think of the one +that + + align:start position:0% +that + + + align:start position:0% +that +is insensitive to polarity + + align:start position:0% +is insensitive to polarity + + + align:start position:0% +is insensitive to polarity +which would be + + align:start position:0% + + + + align:start position:0% + +the absolute value of that + + align:start position:0% +the absolute value of that + + + align:start position:0% +the absolute value of that +and so + + align:start position:0% +and so + + + align:start position:0% +and so +i think you can see what the problem is + + align:start position:0% +i think you can see what the problem is + + + align:start position:0% +i think you can see what the problem is +which is this is going to be producing a + + align:start position:0% +which is this is going to be producing a + + + align:start position:0% +which is this is going to be producing a +fairly large result just from random + + align:start position:0% +fairly large result just from random + + + align:start position:0% +fairly large result just from random +matches right so we'd have to take the + + align:start position:0% +matches right so we'd have to take the + + + align:start position:0% +matches right so we'd have to take the +integral of cosine the absolute value of + + align:start position:0% +integral of cosine the absolute value of + + + align:start position:0% +integral of cosine the absolute value of +cosine from 0 to 360 degrees and i don't + + align:start position:0% +cosine from 0 to 360 degrees and i don't + + + align:start position:0% +cosine from 0 to 360 degrees and i don't +know i forget what it is + + align:start position:0% +know i forget what it is + + + align:start position:0% +know i forget what it is +pi over 4 or something + + align:start position:0% +pi over 4 or something + + + align:start position:0% +pi over 4 or something +but it's it's you know it's a large + + align:start position:0% +but it's it's you know it's a large + + + align:start position:0% +but it's it's you know it's a large +number whereas the number here is very + + align:start position:0% +number whereas the number here is very + + + align:start position:0% +number whereas the number here is very +small uh let's estimate this oh we we + + align:start position:0% +small uh let's estimate this oh we we + + + align:start position:0% +small uh let's estimate this oh we we +did we said 20 over it's like 1 in 18 + + align:start position:0% +did we said 20 over it's like 1 in 18 + + + align:start position:0% +did we said 20 over it's like 1 in 18 +i don't think that's right but it's + + align:start position:0% +i don't think that's right but it's + + + align:start position:0% +i don't think that's right but it's +approximately that this is going to be + + align:start position:0% +approximately that this is going to be + + + align:start position:0% +approximately that this is going to be +much larger like one and a half or + + align:start position:0% +much larger like one and a half or + + + align:start position:0% +much larger like one and a half or +something so yes that is much easier to + + align:start position:0% +something so yes that is much easier to + + + align:start position:0% +something so yes that is much easier to +compute but it's not nearly as good so + + align:start position:0% +compute but it's not nearly as good so + + + align:start position:0% +compute but it's not nearly as good so +they didn't use that + + align:start position:0% +they didn't use that + + + align:start position:0% +they didn't use that +so uh what's this what remains to say + + align:start position:0% +so uh what's this what remains to say + + + align:start position:0% +so uh what's this what remains to say +about this so this was very successful + + align:start position:0% +about this so this was very successful + + + align:start position:0% +about this so this was very successful +and um + + align:start position:0% +and um + + + align:start position:0% +and um +we do still need to talk about the + + align:start position:0% +we do still need to talk about the + + + align:start position:0% +we do still need to talk about the +scoring functions how are these + + align:start position:0% +scoring functions how are these + + + align:start position:0% +scoring functions how are these +measurements combined + + align:start position:0% +measurements combined + + + align:start position:0% +measurements combined +but then just + + align:start position:0% +but then just + + + align:start position:0% +but then just +stepping up a level + + align:start position:0% +stepping up a level + + + align:start position:0% +stepping up a level +um + + align:start position:0% +um + + + align:start position:0% +um +what's the disadvantage of this method + + align:start position:0% +what's the disadvantage of this method + + + align:start position:0% +what's the disadvantage of this method +it's quantized + + align:start position:0% +it's quantized + + + align:start position:0% +it's quantized +we're quantizing pose space + + align:start position:0% +we're quantizing pose space + + + align:start position:0% +we're quantizing pose space +so we're only looking + + align:start position:0% +so we're only looking + + + align:start position:0% +so we're only looking +at let's say + + align:start position:0% +at let's say + + + align:start position:0% +at let's say +uh rotations that are multiples of five + + align:start position:0% +uh rotations that are multiples of five + + + align:start position:0% +uh rotations that are multiples of five +degrees i mean we get to decide how to + + align:start position:0% +degrees i mean we get to decide how to + + + align:start position:0% +degrees i mean we get to decide how to +how much to quantize it + + align:start position:0% +how much to quantize it + + + align:start position:0% +how much to quantize it +um but it is quantized + + align:start position:0% +um but it is quantized + + + align:start position:0% +um but it is quantized +we also um + + align:start position:0% +we also um + + + align:start position:0% +we also um +you know how do we make that decision + + align:start position:0% +you know how do we make that decision + + + align:start position:0% +you know how do we make that decision +well we could make it very fine but then + + align:start position:0% +well we could make it very fine but then + + + align:start position:0% +well we could make it very fine but then +the computation is very slow so there's + + align:start position:0% +the computation is very slow so there's + + + align:start position:0% +the computation is very slow so there's +there's a trade-off there and so + + align:start position:0% +there's a trade-off there and so + + + align:start position:0% +there's a trade-off there and so +how can we improve on that well one way + + align:start position:0% +how can we improve on that well one way + + + align:start position:0% +how can we improve on that well one way +is to + + align:start position:0% + + + + align:start position:0% + +use the method with fairly coarse + + align:start position:0% +use the method with fairly coarse + + + align:start position:0% +use the method with fairly coarse +quantization + + align:start position:0% +quantization + + + align:start position:0% +quantization +and then + + align:start position:0% +and then + + + align:start position:0% +and then +but then we have to search the whole + + align:start position:0% +but then we have to search the whole + + + align:start position:0% +but then we have to search the whole +pose space right initially we don't know + + align:start position:0% +pose space right initially we don't know + + + align:start position:0% +pose space right initially we don't know +anything we could be rotated five + + align:start position:0% +anything we could be rotated five + + + align:start position:0% +anything we could be rotated five +degrees 143 degrees whatever so we're + + align:start position:0% +degrees 143 degrees whatever so we're + + + align:start position:0% +degrees 143 degrees whatever so we're +forced to search the whole post space + + align:start position:0% +forced to search the whole post space + + + align:start position:0% +forced to search the whole post space +but once you have a number of potential + + align:start position:0% +but once you have a number of potential + + + align:start position:0% +but once you have a number of potential +matches + + align:start position:0% +matches + + + align:start position:0% +matches +and typically there'll be you want to + + align:start position:0% +and typically there'll be you want to + + + align:start position:0% +and typically there'll be you want to +retain more than one + + align:start position:0% +retain more than one + + + align:start position:0% +retain more than one +then you can + + align:start position:0% +then you can + + + align:start position:0% +then you can +search with finer quantization near + + align:start position:0% +search with finer quantization near + + + align:start position:0% +search with finer quantization near +there and so + + align:start position:0% +there and so + + + align:start position:0% +there and so +that's another important aspect of this + + align:start position:0% +that's another important aspect of this + + + align:start position:0% +that's another important aspect of this +and we'll need to + + align:start position:0% +and we'll need to + + + align:start position:0% +and we'll need to +talk about that + + align:start position:0% + + + + align:start position:0% + +so the idea is that + + align:start position:0% +so the idea is that + + + align:start position:0% +so the idea is that +it's kind of like multi-scale + + align:start position:0% +it's kind of like multi-scale + + + align:start position:0% +it's kind of like multi-scale +that we + + align:start position:0% +that we + + + align:start position:0% +that we +we at a core scale we run through the + + align:start position:0% +we at a core scale we run through the + + + align:start position:0% +we at a core scale we run through the +whole course + + align:start position:0% +whole course + + + align:start position:0% +whole course +post space and then we use a block just + + align:start position:0% +post space and then we use a block just + + + align:start position:0% +post space and then we use a block just +around + + align:start position:0% +around + + + align:start position:0% +around +the areas that seem to produce a good + + align:start position:0% +the areas that seem to produce a good + + + align:start position:0% +the areas that seem to produce a good +result + + align:start position:0% +result + + + align:start position:0% +result +to get a + + align:start position:0% +to get a + + + align:start position:0% +to get a +more accurate result + + align:start position:0% +more accurate result + + + align:start position:0% +more accurate result +well + + align:start position:0% +well + + + align:start position:0% +well +so what i was + + align:start position:0% +so what i was + + + align:start position:0% +so what i was +again the patterns online you + + align:start position:0% +again the patterns online you + + + align:start position:0% +again the patterns online you +should probably look at it + + align:start position:0% +should probably look at it + + + align:start position:0% +should probably look at it +and + + align:start position:0% +and + + + align:start position:0% +and +what what i still have left to do + + align:start position:0% +what what i still have left to do + + + align:start position:0% +what what i still have left to do +is talk about the different + + align:start position:0% +is talk about the different + + + align:start position:0% +is talk about the different +scoring functions because + + align:start position:0% +scoring functions because + + + align:start position:0% +scoring functions because +in some cases + + align:start position:0% +in some cases + + + align:start position:0% +in some cases +we would like a score that we can + + align:start position:0% +we would like a score that we can + + + align:start position:0% +we would like a score that we can +compare to an absolute threshold and say + + align:start position:0% +compare to an absolute threshold and say + + + align:start position:0% +compare to an absolute threshold and say +okay if it's bigger than 0.95 then we + + align:start position:0% +okay if it's bigger than 0.95 then we + + + align:start position:0% +okay if it's bigger than 0.95 then we +definitely have a match you know that + + align:start position:0% +definitely have a match you know that + + + align:start position:0% +definitely have a match you know that +kind of thing we talked about with + + align:start position:0% +kind of thing we talked about with + + + align:start position:0% +kind of thing we talked about with +normalized correlation in other cases + + align:start position:0% +normalized correlation in other cases + + + align:start position:0% +normalized correlation in other cases +we just want to get a result as fast as + + align:start position:0% +we just want to get a result as fast as + + + align:start position:0% +we just want to get a result as fast as +possible + + align:start position:0% +possible + + + align:start position:0% +possible +and we find the peak and we don't really + + align:start position:0% +and we find the peak and we don't really + + + align:start position:0% +and we find the peak and we don't really +care how big the peak is so those are + + align:start position:0% +care how big the peak is so those are + + + align:start position:0% +care how big the peak is so those are +two different computations + + align:start position:0% +two different computations + + + align:start position:0% +two different computations +and + + align:start position:0% +and + + + align:start position:0% +and +depending on what we're doing one may be + + align:start position:0% +depending on what we're doing one may be + + + align:start position:0% +depending on what we're doing one may be +more efficient than the other + + align:start position:0% +more efficient than the other + + + align:start position:0% +more efficient than the other +then we might want to do things like + + align:start position:0% +then we might want to do things like + + + align:start position:0% +then we might want to do things like +remove this + + align:start position:0% +remove this + + + align:start position:0% +remove this +this term which i think this is actually + + align:start position:0% +this term which i think this is actually + + + align:start position:0% +this term which i think this is actually +3 over 32 but in any case it's not too + + align:start position:0% +3 over 32 but in any case it's not too + + + align:start position:0% +3 over 32 but in any case it's not too +hard to cover so uh + + align:start position:0% +hard to cover so uh + + + align:start position:0% +hard to cover so uh +let's call that n + + align:start position:0% +let's call that n + + + align:start position:0% +let's call that n +uh do we actually want to remove that + + align:start position:0% +uh do we actually want to remove that + + + align:start position:0% +uh do we actually want to remove that +well that's going to mean that there's + + align:start position:0% +well that's going to mean that there's + + + align:start position:0% +well that's going to mean that there's +more computation but it'll be more + + align:start position:0% +more computation but it'll be more + + + align:start position:0% +more computation but it'll be more +accurate so depending on where we are in + + align:start position:0% +accurate so depending on where we are in + + + align:start position:0% +accurate so depending on where we are in +the process + + align:start position:0% +the process + + + align:start position:0% +the process +uh like you know we're getting close to + + align:start position:0% +uh like you know we're getting close to + + + align:start position:0% +uh like you know we're getting close to +the answer we want to refine it to make + + align:start position:0% +the answer we want to refine it to make + + + align:start position:0% +the answer we want to refine it to make +it as accurate as possible then we'll + + align:start position:0% +it as accurate as possible then we'll + + + align:start position:0% +it as accurate as possible then we'll +throw that in + + align:start position:0% +throw that in + + + align:start position:0% +throw that in +and just bite the bullet on it taking + + align:start position:0% +and just bite the bullet on it taking + + + align:start position:0% +and just bite the bullet on it taking +more computation + + align:start position:0% + + + + align:start position:0% + +okay a couple of points that i've + + align:start position:0% +okay a couple of points that i've + + + align:start position:0% +okay a couple of points that i've +highlighted here + + align:start position:0% +highlighted here + + + align:start position:0% +highlighted here +one of them is that + + align:start position:0% +one of them is that + + + align:start position:0% +one of them is that +if we're making working multi-scale + + align:start position:0% +if we're making working multi-scale + + + align:start position:0% +if we're making working multi-scale +then we'll want to use different probes + + align:start position:0% +then we'll want to use different probes + + + align:start position:0% +then we'll want to use different probes +at different scales + + align:start position:0% +at different scales + + + align:start position:0% +at different scales +and this is kind of even more + + align:start position:0% +and this is kind of even more + + + align:start position:0% +and this is kind of even more +sophisticated way of proceeding where + + align:start position:0% +sophisticated way of proceeding where + + + align:start position:0% +sophisticated way of proceeding where +instead of just fixing the quantization + + align:start position:0% +instead of just fixing the quantization + + + align:start position:0% +instead of just fixing the quantization +fixing the + + align:start position:0% +fixing the + + + align:start position:0% +fixing the +granularity + + align:start position:0% +granularity + + + align:start position:0% +granularity +we try it at different granularities + + align:start position:0% +we try it at different granularities + + + align:start position:0% +we try it at different granularities +and + + align:start position:0% +and + + + align:start position:0% +and +if we do that we need different models + + align:start position:0% +if we do that we need different models + + + align:start position:0% +if we do that we need different models +for each of those granularities + + align:start position:0% +for each of those granularities + + + align:start position:0% +for each of those granularities +then there's a need for + + align:start position:0% +then there's a need for + + + align:start position:0% +then there's a need for +fast low-pass filtering because we're + + align:start position:0% +fast low-pass filtering because we're + + + align:start position:0% +fast low-pass filtering because we're +trying to build these multi-levels and + + align:start position:0% +trying to build these multi-levels and + + + align:start position:0% +trying to build these multi-levels and +we'll talk about that because another + + align:start position:0% +we'll talk about that because another + + + align:start position:0% +we'll talk about that because another +patent which is much easier than this + + align:start position:0% +patent which is much easier than this + + + align:start position:0% +patent which is much easier than this +one + + align:start position:0% +one + + + align:start position:0% +one +gives us methods for very rapidly + + align:start position:0% +gives us methods for very rapidly + + + align:start position:0% +gives us methods for very rapidly +performing uh convolutions and low-pass + + align:start position:0% +performing uh convolutions and low-pass + + + align:start position:0% +performing uh convolutions and low-pass +filtering + + align:start position:0% +filtering + + + align:start position:0% +filtering +gradient direction is more reliable than + + align:start position:0% +gradient direction is more reliable than + + + align:start position:0% +gradient direction is more reliable than +brightness + + align:start position:0% +brightness + + + align:start position:0% +brightness +contrast we talked about that + + align:start position:0% +contrast we talked about that + + + align:start position:0% +contrast we talked about that +each test provides direct evidence of + + align:start position:0% +each test provides direct evidence of + + + align:start position:0% +each test provides direct evidence of +pattern presence we talked about how the + + align:start position:0% +pattern presence we talked about how the + + + align:start position:0% +pattern presence we talked about how the +probes will contribute evidence + + align:start position:0% +probes will contribute evidence + + + align:start position:0% +probes will contribute evidence +probes are not restricted to the pixel + + align:start position:0% +probes are not restricted to the pixel + + + align:start position:0% +probes are not restricted to the pixel +grid oh that's an important one i mean + + align:start position:0% +grid oh that's an important one i mean + + + align:start position:0% +grid oh that's an important one i mean +they first of all they derive from edge + + align:start position:0% +they first of all they derive from edge + + + align:start position:0% +they first of all they derive from edge +points + + align:start position:0% +points + + + align:start position:0% +points +that we already interpolated so those + + align:start position:0% +that we already interpolated so those + + + align:start position:0% +that we already interpolated so those +were already on not on the pixel grid + + align:start position:0% +were already on not on the pixel grid + + + align:start position:0% +were already on not on the pixel grid +but then we in addition we throw those + + align:start position:0% +but then we in addition we throw those + + + align:start position:0% +but then we in addition we throw those +out and we put our own probes in uh + + align:start position:0% +out and we put our own probes in uh + + + align:start position:0% +out and we put our own probes in uh +separately + + align:start position:0% + + + + align:start position:0% + +accuracy limit oh accuracy limited by + + align:start position:0% +accuracy limit oh accuracy limited by + + + align:start position:0% +accuracy limit oh accuracy limited by +quantization of search space so that's + + align:start position:0% +quantization of search space so that's + + + align:start position:0% +quantization of search space so that's +um why am i emphasizing that well + + align:start position:0% +um why am i emphasizing that well + + + align:start position:0% +um why am i emphasizing that well +because that's going to take us to + + align:start position:0% +because that's going to take us to + + + align:start position:0% +because that's going to take us to +another pattern that does it a different + + align:start position:0% +another pattern that does it a different + + + align:start position:0% +another pattern that does it a different +way which is not limited in that respect + + align:start position:0% +way which is not limited in that respect + + + align:start position:0% +way which is not limited in that respect +so why are we talking about this one + + align:start position:0% +so why are we talking about this one + + + align:start position:0% +so why are we talking about this one +well because the other one needs a good + + align:start position:0% +well because the other one needs a good + + + align:start position:0% +well because the other one needs a good +first guess and so this is the way to + + align:start position:0% +first guess and so this is the way to + + + align:start position:0% +first guess and so this is the way to +get a very good first guess + + align:start position:0% +get a very good first guess + + + align:start position:0% +get a very good first guess +and then the other one can refine it and + + align:start position:0% +and then the other one can refine it and + + + align:start position:0% +and then the other one can refine it and +and not it's not limited to + + align:start position:0% +and not it's not limited to + + + align:start position:0% +and not it's not limited to +discrete steps in the in the pose space + + align:start position:0% +discrete steps in the in the pose space + + + align:start position:0% +discrete steps in the in the pose space +okay that's it for today \ No newline at end of file diff --git a/lsS2NysCVM4.txt b/lsS2NysCVM4.txt new file mode 100644 index 0000000000000000000000000000000000000000..32cd862b75697b5df990d475fdf850cf3b198ff5 --- /dev/null +++ b/lsS2NysCVM4.txt @@ -0,0 +1,2464 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Ladies and gentlemen, +welcome to this + +lecture on nonlinear finite +element analysis of solids and + +structures. + +In the previous lectures, we +considered the general + +continuum mechanics formulations +that we use for + +nonlinear finite element +analysis. + +And we also introduced briefly +the finite element matrices. + +In the coming lectures, I would +like now to discuss with + +you these finite element +matrices in more detail. + +Finite element matrices can +generally be categorized as + +continuum elements. + +We call them sometimes +also solid elements. + +The truss element, for +example, would + +be a continuum element. + +The 2D element, the +3D elements would + +be continuum elements. + +The 2D and 3D elements we may +also call solid elements. + +And as another category, we have +the structural elements. + +Structure elements are beam +elements, plate elements, + +shell elements. + +Of course, a distinguishing +feature between the structural + +elements and the continuum +elements is that continuum + +elements carry only nodal point +displacements as degrees + +of freedom, whereas the +structural elements have also + +rotational degrees of freedom +at their nodes. + +In this lecture, I like to talk +about the 2D continuum + +elements, the 2D plane stress, +plane strain, and + +axisymmetric elements. + +These elements are used very, +very widely in the engineering + +professions for all sorts +of analyses-- + +plane stress analyses of plates, +plane strain analysis + +all dams, axisymmetric analysis +of shells, and + +so on and so on. + +The elements are very general, +and can be used for geometric + +and material nonlinear +analyses. + +I also like to then, at the +end of the lecture, talk + +briefly about the 3D elements +that are also very widely + +used, and that are really +formulated in the same way as + +the 2D elements. + +Therefore, once you understand +to 2D elements very well, it + +is fairly easy to generalize +these concepts or use these + +concepts also to construct and +formulate 3D elements. + +Let me now go over to my view +graph and discuss it with you + +the information that I have +on these view graphs. + +Once again, I like to talk +about plane stress, plane + +strain elements, and +axisymmetric + +elements in this lecture. + +And these derivations that we +will be discussing, as I said + +already, are directly applicable +also, or can + +directly be extended to three +dimensional elements. + +Let's look at a typical +2D element, + +two dimensional element. + +This is a nine-node element in +the stationary coordinate + +frame, x1, x2. + +x times 0, we would see +this element here. + +Notice there are nine +nodes, 1 to 9. + +Notice that we will be +talking about the + +isoparametric elements. + +And these have the R and F +auxiliary coordinate system, + +the natural coordinate system, +just like in linear analysis. + +X times 0, to the +element is here. + +And at time t, the +element is here. + +Notice that the element has +undergone large displacements, + +large rotations. + +You don't see very large +rotations here, but the + +rotations could be very large. + +And certainly also +large strains. + +You can see directly that the +element here has grown from + +its size, so certainly +it must have been + +subjected to large strains. + +So we consider really a +very general motion. + +But remember, once again, that +the coordinate frame, x1, x2, + +the Cartesian coordinate frame, +remains stationary, as + +we have discussed in the +previous lectures. + +Because the elements are +isoparametric elements, we can + +directly write these +expressions. + +That 0x1's, the coordinates of +the material points in the + +elements at time 0, are given +via this interpolation. + +The hk are the interpolation +functions that we also use in + +linear analysis. + +The 0x1k are the nodal +point coordinates. + +k refers to the nodal point. + +1 refers to the coordinate +direction. + +0 refers to the fact that +they're looking at the + +configuration at time 0. + +This 0 is, of course, the +same 0 that we see here. + +This one is the same one +that we see there. + +We are summing, of course, +of all the nodes. + +And for the element that I just +had on the previous view + +graph, it would be nine nodes, +so n is equal to 9. + +We have a similar expression +for the + +x2 coordinate direction. + +In other words, 0x2 is +given like that. + +This is the x2 coordinate of a +material particle, and it's + +expressed in terms of the nodal +point coordinates of the + +elements expressed in terms of +the nodal point coordinates of + +the element. + +The same expression is also +applicable at time t. + +Notice all we have exchanged +is the 0 to a t, 0 to a t. + +And similarly here for +the x2 coordinate. + +0 to t, and similar +here, 0 to t. + +Let us look at an example. + +Here we have depicted +a four-node element. + +The original element +lies here. + +It's black. + +The R and F system, +of course, is the + +natural coordinate system. + +This is a configuration of +the element at time 0. + +It moves into that configuration +to time t, or it + +is at, in this configuration, +at time t. + +Notice that these are the +interpolations that I just + +introduced you to. + +The hk functions +are, of course, + +interpolation functions. + +Once again, these are here, the +nodal point coordinates. + +k is the nodal point, t is the +time that we're looking at, xi + +means the i's direction. + +i, of course, in this particular +case, 1 or 2. + +Similarly, for the original +geometry of the element. + +The hk's are listed out here +on the right-hand side. + +Notice these are the same +interpolation functions that + +we are using in linear +analysis. + +No difference there. + +For example, h1 is +given right here. + +And this is, of course, the +interpolation function + +corresponding to nodal point +1, as shown right there. + +You are probably very familiar +with these interpolation + +functions, and I don't need +to go into details there. + +But let us look now at the +following, namely what had + +happened in the motion +to a nodal point. + +A typical nodal point would be +the second nodal point here. + +The original coordinates +are as shown. + +And these original coordinates +have grown, or have become + +larger as shown here, because +this node here has moved to + +that new position. + +Notice this is now here, the +coordinate of node 2, of + +course, x1 coordinate. + +This superscript 2 means node +2, this 1 means 1 direction. + +t means time t. + +Here we have 1 and +2 and time 0. + +Notice here, 2, 2 times 0. + +This 2 here, the bottom 2, means +coordinate direction 2. + +This top 2 means +nodal point 2. + +This is a convention that +we want to use. + +It is a bit heavy, but we have +to somehow use a convention to + +label our coordinates, and this +is the one that I chose + +some time ago. + +Similar here for the +2 coordinate, x2 + +coordinate, at time t. + +tx2 at nodal point 2. + +That upper 2, once again, +be the nodal point 2. + +And of course, this would +also apply for all + +the other nodal points. + +If we look at the motion of a +material particle that is in + +the element, we would obtain +that motion from the motion of + +the nodal points. + +Here we have now, in a nine-node +element that is + +originality here, and moves +into this position. + +At time t it is in +this position. + +Let's look at one particular +particle within the element. + +Here we have one particle +right there. + +Notice that this particle +here is given via this + +relationship here. + +r and s are both 0.5-- + +you see r positive means this +direction, s positive means + +that direction, r and +s 0.5 is there. + +We would use r and s equal to +0.5, substitute into hk. + +And then, of course, we have 9 +such hk's, substitute r and s + +equal to 0.5 into each +of these hk's. + +And sum out, this right-hand +side, to get the coordinate, + +the coordinates-- + +there are two, of course-- + +of this point here, this +material particle, at time 0. + +That's how we would obtain +the coordinates of + +that material particle. + +Now, at time t, we proceed +much in the same way. + +Here we have the equation. + +We would, again, take hk at r +equal to 0.5, s equal to 0.5, + +for all case, and multiply +these hk values by these + +values here, which of course, +are given because we must know + +where these nodal points +have arrived at. + +So we can evaluate the +right-hand side to directly + +get these two values, there are +two such values, tx1 and + +tx2, which gives then the +position of this material + +particle at time t. + +Notice that the isoparametric +coordinates of a material + +particle never change. + +You put that here in red because +that is very important + +to keep in mind. + +Of course, the actual +coordinates of the particle + +change, because that particle +moves through space in a + +stationary coordinate +frame, x1 and x2. + +But we are in s coordinates. + +The natural coordinates +do not change. + +Well a major advantage of the +isoparametric finite element + +analysis is that we can directly +write, of course, at + +the displacements, are given +as shown here via the nodal + +point displacements. + +tU1 is the displacement of +the material particle + +into the one direction. + +The hk's are the isoparametric +interpolation functions. + +And these are the nodal +point displacements. + +k being the nodal point +displacements + +of nodal point k. + +Similarly, for the +2 direction. + +And this holds at time t, and +it also holds for the + +incremental displacements from +time t to time t plus delta t, + +as written right here. + +That this is, in fact, 2 can +easily be shown from the + +coordinate interpolations. + +You see we had already these two +interpolations, and all we + +need to do now is subtract on +the left-hand side, and on the + +right-hand side, to obtain +this equation here. + +And what are left with here, +of course, must be the + +displacement of the material +particle that + +we're looking at-- + +tUi. + +And here, we must have +the displacement + +of the nodal points. + +And these are denoted as tUik. + +And that is exactly the +relationships that we were + +just dealing with, tUi +is equal to hk tUik. + +There is one very important +point that I like to + +point out to you. + +Namely, that these equations +show directly that if we use a + +finite element mesh that is +originally compatible, in + +other words, compatible in a +linear analysis, than this + +finite element mesh will remain +compatible throughout + +the motion, throughout the +large deformation motion. + +And that is a very +important point. + +That we can say that the mesh +which originally is compatible + +will remain compatible +throughout the analysis. + +That follows directly from +these equations. + +The element matrices that we +need, of course, require + +derivatives, and these are +obtained much in the same way + +as in linear analysis. + +We need this derivative here, +partial tUi, with respect to + +the original coordinates. + +This is the actual derivative. + +This is the abbreviation +that we used + +in the earlier lectures. + +And we obtained this derivative +by taking the + +differentiation of the hk's with +respect to the original + +coordinates. + +Of course, these are numbers. + +These are the nodal point +displacements. + +So it's this one that we really +need to evaluate this + +derivative. + +Similarly, for the incremental +displacements. + +We want to take the +differentiation of the + +incremental displacement with +respect to the original + +coordinates. + +It's achieved this way. + +Once again, here we have an +expression that we need to + +evaluate, which also goes +in here, of course. + +And as we evaluate, as we will +just now see, much in the same + +way as in linear analysis. + +Notice, here we have written +down the partial of Ui with + +respect to the current +coordinates + +obtained as given here. + +Of course, these are the nodal +point displacement increments, + +and here we have the +differentiation of the hk's + +with respect to the current +coordinates now. + +So once we have these evaluated, +these expressions + +evaluated, we can obtain all +of the derivatives that go + +into the strain displacement +matrices that we want to have + +for the element. + +The derivatives are evaluated +using the chain rule, just as + +in linear analysis. + +We are using that partial hk +with respect to r, is given as + +partial hk with respect to x1 +times partial x1 with respect + +to r, et cetera. + +Of course, these are here +the derivatives + +that we want to calculate. + +Notice, this is what we +need to calculate in + +order to get these. + +And these here, just like in +linear analysis, go into the + +Jacobian matrix written +down here. + +Here we have the Jacobian +matrix. + +And this is what we want. + +Therefore, we need to invert +the Jacobian matrix, as in + +linear analysis. + +And we obtain via this +relationship here, the + +required derivatives. + +The entries in this +matrix involve + +derivatives of this form. + +Partial x1, 0x1 with +respect to r, with + +respect to s and so on. + +And those are obtained here as +shown on the right-hand side. + +Notice here, of course, we only +need differentiations + +with respect to r, with +respect to the natural + +coordinates. + +And since the functions hk are +a function of r and f, we can + +directly evaluate these kinds of +expressions that go in the + +Jacobian matrix, and the +inverse, of course. + +If we want to take derivatives +with respect to the current + +coordinates, we proceed +much in the same way. + +This is the relationship that +we arrive at by simply + +substituting instead of the +0xi, the txi in to the + +Jacobian matrix, and of course, +into the expressions + +that are in here. + +So here we have a Jacobian +matrix that is giving the + +derivatives of the current +coordinates at time t with + +respect to the natural +coordinates. + +Such an element is obtained +as shown here. + +It involves again only the +differentiation of the + +interpolation functions with +respect to the natural + +coordinates. + +Here, of course with respect +to s, because we want to + +differentiate with +respect to s. + +Of course, these are the nodal +point coordinate at time t, + +which are known. + +We invert this relationship +here to obtain the + +differentiation that +we need to have. + +We are now ready to compute the +required element matrices + +for the total Lagrangian +formulation. + +And the element matrices that we +want to compute, of course, + +our those established in +the early lectures. + +The matrices that go into +evaluating these matrices are + +listed here. + +Here, of course, the tangent +constitutive relationship, + +which we will talk +about much later. + +Not in this lecture. + +Here we have the linear strain +displacement matrix, the + +nonlinear strain displacement +matrix. + +Here again, the linear strain +displacement matrix, a stress + +vector, and a stress matrix. + +Let's see now how these matrices +look for the two + +dimensional case. + +The constitutive relation, +just very briefly-- + +again, much more detail will be +given in a later lecture-- + +would be relating the increment +in stress to the + +increments in strain. + +Notice there's a 2 here, and +this is the matrix which is + +established from this +relationship here. + +In the early lectures, +we used this + +relationship, the tensor notation. + +Well we have now a matrix +notation, and this is the + +relationship with that +matrix notation. + +C for a linear elastic material +would look as shown + +here, and you are familiar with +this relationship from + +linear analysis. + +It's the same matrix that we +encounter in linear analysis. + +Of course, e being Young's +modulus, nu + +being Poisson's ratio. + +We also derived in the early +lectures the expression for + +the incremental strain terms. + +And here they are listed out. + +We have derived these right-hand +side expressions. + +We notice that what is here +underscored by a blue line was + +the initial displacement +effect. + +And is this initial displacement +effect, of + +course, is a particular in +gradient off the total + +Lagrangian formulation, +as we discussed + +in the early lectures. + +The nonlinear strain terms that +we also derived in the + +earlier lectures, are +listed here for the + +two dimensional case. + +We have seen all these +expressions on the earlier + +view graph, except that we use +then additional notation, in + +other words, a notation that +involved k and j's and i's, + +and we have to sum over k. + +Well if you do so, you directly +arrive at these + +relationships here. + +It's an interesting point to +derive this expression and the + +linear strain part for the hoop +strain-- this is called + +the hoop strain-- + +in the axisymmetric case. + +And let us look at +that derivation + +a bit more in detail. + +Here we have an axisymmetric +element in its original + +configuration. + +At time 0 it has moved into this +configuration up to time + +t plus delta t. + +Since we want to get the +incremental strain from time t + +to time t plus delta t, we're +looking at the configuration + +of time t plus delta t +in this derivation. + +Notice that this here is the +axis of revolution, which we + +denote as x2, x1 is this axis. + +And if we look as a plan view +onto this element, we would + +see this x1, x2 coming out of +the view graph, and x3 going + +down like this. + +Notice this here we label as +0ds, the initial length of a + +hoop fiber, so to say. + +In fact, this hoop fiber starts +right there at 0x1, + +which is, and I have to go now +upwards to the upper graph + +again, which is nothing else +than the starting point of + +that fiber. + +In other words, this green dot, +this green dot is nothing + +else than the start +of this arrow. + +I could say let's line +them up like that. + +So this arrow here goes really +into the view graph up there. + +If you look further to the right +here we see that we have + +also a blue arrow, of +course, curved. + +We call it the hoop, it's a +circle really, the radius + +around this origin that we're +looking at, like that. + +And notice that the start of +this arrow here is this blue + +dot right there. + +A material fiber, a material +particle, let's put it this + +way, a material particle that +has moved from here to there + +causes, in axisymmetric +analysis, this fiber here to + +take on this length. + +And of course, the change +in this length + +gives us the hoop strain. + +Let us look at this relationship +here, because + +that gives us a relationship +between the change in the + +length of the fiber, green +fiber, blue fiber, so to say, + +in plan view. + +And that is nothing else than +0x1 dividing t plus delta x1. + +Why is that the case? + +Well you see it by geometry +from this picture. + +And we will use this expression +here now to + +evaluate the actual strain. + +We find that the +Green-Lagrangian strain can be + +written as in this form. + +We substitute the expression +that we just obtained for this + +relationship. + +We substitute the +displacements. + +Displacements to configuration +t, and incremental + +displacement from t to t plus +delta t divided by the 0x1, of + +course, still here. + +We then go through a number of +steps of arithmetic, I'm sure + +you can easily do those, and +you arrive at this result. + +If we look at this, we find that +this here expression only + +involves the displacements +to time t. + +And that must, therefore, +be the Green-Lagrangian + +strain at time t. + +Notice that this expression +here involves incremental + +displacements, linear +incremental displacement, no + +products of them, +and the initial + +displacement at time t. + +This is the initial displacement +effect, which we + +always have in the total +Lagrangian formulation. + +This is a linear strain term +involving only the incremental + +displacement. + +And this the total linear +strain increment. + +Notice this is a total nonlinear +strain incremental. + +It involves the incremental +displacement u1 squared, and + +that's why it is a nonlinear +strain increment. + +Of course, this total here is +the incremental strain. + +This total is the incremental +strain. + +It's a nice derivation that +gives some insight into how + +these expressions that I had +already on the earlier view + +graph are arrived at. + +Well we are now ready to +construct the B matrix. + +On the left-hand side, +we would have, + +of course, the strains. + +If you look at the linear strain +displacement matrix, we + +have the linear strains here. + +Notice there's a 2 here because +of the 0e12 being + +equal to 0e21. + +We simply put 2 times +0e12 in here. + +And this is a total linear +strain increment. + +Here we have a sum of two +matrices giving us a total + +linear strain displacement +matrix. + +This is the one that does +not include the initial + +displacement effect. + +That one includes initial +displacement effect. + +And here we have the nodal point +incremental displacement + +the way we defined them +in an earlier lecture. + +Well the entries in t0BL0 are +shown here, involving of + +course, four-nodal point +k derivatives of the + +interpolation functions +corresponding + +to nodal point k. + +Notice that this last row is +only included if we are + +dealing with an axisymmetric +analysis. + +And notice that these are then +exactly the terms that we also + +have in linear analysis. + +So no surprises here. + +No new entries, as a matter +of fact, when + +compared to linear analysis. + +Except that we see a 0 here, +meaning, of course, that we're + +taking a differentiation with +respect to the original + +coordinates. + +Generally, in linear analysis, +if you look at the book, of + +course, you would not see this +0 here because it's not + +necessary to have +that 0 there. + +We always take differentiations +with respect + +to the original geometry. + +Maybe a quick word also how +we want to read this here. + +Notice these two entries here, +of course, nothing else in + +these two blue entries. + +Because these two entries +multiply these two columns, + +for readability I put this entry +there, put this entry + +there, so that you directly +see this column here + +corresponds to u1k, and this +column corresponds to u2k. + +Of course, both columns +correspond to node k. + +If we look at the matrix t0BL1, +which includes now the + +initial displacement effect, +in fact, introduces the + +initial displacement effect to +the total strain displacement + +matrix, it looks this way. + +Once again, this is a +contribution coming + +corresponding to u1k This +is the contribution + +corresponding to u2k. + +And notice here you have the +initial displacement effect + +appearing right here. + +All initial displacement +effects. + +And similarly here, initial +displacement effect. + +Once again, if you don't have +an axisymmetric analysis, in + +other words, you have a plane +stress, plane strain case, you + +would drop this last row. + +We construct the t0BNL +and T0S matrix. + +Next for the geometric stiffness +matrix, and we + +talked about this expression in +the earlier lecture, notice + +that this here is giving up, of +course, the matrix, the k + +matrix, that we're looking +for, this part here. + +And the F matrix looks +as shown here. + +I pointed out very strongly in +the earlier lecture that we + +construct the S and the BNL such +that when this product is + +taken, we get directly +this one. + +Because this is basic. + +This is obtained from the +continuum mechanics + +formulation. + +And we want to evaluate this. + +Therefore, we construct the +BNL and S such that this + +product, indeed, gives +us this contribution. + +And as is constructed +as shown here. + +The BNL is constructed +as shown here. + +Notice the u2k contributions, +the u1k + +contribution for node k. + +Finally, we also need the +t0S vector, hat vector. + +I pointed out in the earlier +lecture that this vector and + +this matrix are constructed in +such a way that this product + +here gives us exactly this +expression here. + +This is basic coming from +continuum mechanics, and this + +is what we have to capture. + +The entries in F hat +are given here. + +And with this then, we would be +ready to actually calculate + +all the matrices and vectors +for the total Lagrangian + +formulation. + +Let us now look at an example to +reinforce our understanding + +of how all of these matrices +are constructed, + +how they are evaluated. + +Here we have the +following case. + +A four-node element +originally in the + +configuration shown in black. + +Four nodes, as you can see, +one, two, three, four. + +This element moves from time +0 to time t into this + +configuration. + +The RAD configuration. + +Node 0.1 move there, node +0.2 move there. + +Notice that the element has +stretched and sheared over, + +but it has only stretched into +the vertical direction, not + +into the horizontal direction. + +Let us identify the lengths, +values that we + +have to deal with. + +0.2 here, 0.2 there. + +Notice that the displacement +upward is 0.1. + +And the shearing over, +so to say, is 0.1. + +We want to consider plane +strain conditions. + +And the problem that we like to +pose is calculate these two + +matrices, the linear strain, +and the nonlinear strain + +displacement matrix for +this particular case. + +Let's first look now a bit at +what's happening here to the + +material fiber. + +If we look at the horizontal +material fiber, shown here in + +black in the original +configuration, we notice that + +these material fibers are simply +translated rigidly over + +horizontally. + +As shown here via +the red arrows. + +So these black material fibers +lying horizontally are simply + +sheared over rigidly, as shown +by the red arrows. + +2 time t, of course. + +Let's look now at the vertical +fibers in this problem. + +Let's see what has +happened to them. + +Here we have the vertical fiber +shown in black in the + +original configuration. + +Let's see how they end up in +their final configuration. + +We see that these fibers have +actually stretched, they've + +become longer, and they have +also rotated over. + +Well this is the kinematics +that we are looking at. + +And let us now attack the +problem of constructing, once + +again, the linear strain +displacement matrix, and the + +nonlinear strain displacement +matrix. + +We do so by first identifying +which is the isoparametric + +coordinate system that we use. + +That coordinate system is +shown here, r and s. + +Let us then now start +this problem. + +And we identify simply by +inspection really because it's + +a fairly simple geometry that +we're dealing with. + +That this differentiation is +nothing else than 0.1, this + +differentiation is 0, that one +is 0, and this one is 0.1. + +Of course, these are the +elements that go into the + +Jacobian matrix, as I +discussed earlier. + +We put these elements into this +2 by 2 matrix, calculate + +the determinant, interesting +to note what the value is. + +That one is needed, of course, +later on in the numerical + +integration of the matrices. + +And we also recognize that to +obtain this derivative of an + +interpolation function, +we need to + +invert this matrix here. + +This 0.1 inverted gives +us 10, and that is + +this 10 right there. + +Therefore, we have now partial +with respect to x1, 0x1 is 10 + +times partial with respect to +R. Of course, in the actual + +expression, we would put hk's +in here, and hk's in there. + +Similar we get the +differentiation + +with respect to x2. + +We will use this expression +here, putting the actual hk's + +in there and in there. + +Well this is some preparatory +work to actually complete the + +problem of constructing the +linear strain and nonlinear + +strain displacement matrix. + +And I think this is actually +a very good point where you + +might want to sit back and try +to complete the whole problem. + +Ladies and gentlemen, +welcome again. + +I hope you've had a close look +at the example, and surely I + +would be very interested +in knowing how it went. + +But let us now look +at the solution. + +We already discussed that for +this example, the Jacobian is + +given by this matrix here. + +And therefore, these are the +differentiations that we can + +directly use. + +Notice, of course, we need the +differentiation with respect + +to the x1 coordinate, and with +respect to the x2 coordinate + +of all the interpolation +functions. + +One way to proceed now is to +make a little table where we + +have here in this column the +nodes, we have in this column + +here the differentiations that +we need, partial hk with + +respect to 0x1. + +Further differentiations here, +partial hk with respect to x2. + +Notice that the Jacobian, the +inverse of the Jacobian matrix + +being 10, makes a 1/4 +equal to 2.-- + +1/4 times 10 being +equal to 2.5. + +So that's why you see +the 2.5 here. + +These are the nodal point +displacements, which, of + +course, are given for this +particular case. + +And with these nodal point +displacements given, and these + +differentiations calculated +as listed here, we can now + +evaluate these products here. + +And that is done as shown +in these columns. + +Notice the sum of these gives +us these differentiations + +here, which go into the initial +displacement effect of + +the strain displacement +matrix. + +Well like that, of course, you +can also calculate the + +differentiations of the +t0u21 and the t0u22. + +And both these terms are also +required in the initial + +displacement effect of the +strain displacement matrix. + +Another way to proceed, to get +this initial displacement + +effect, is to evaluate the +deformation gradient. + +In an earlier lecture, we talked +about the deformation + +gradient and it's listed +right here. + +It's a 2 by 2 matrix because +we're talking about a two + +dimensional motion. + +And here you have, for example, +partial tx2 with + +respect to 0x1. + +Here you have partial tx1 +with respect to 0x1. + +0x1, et cetera. + +And if we take this deformation +gradient or the + +elements of that information +gradient, we can directly + +obtain these differentiations +here. + +In other words, t0x11 +minus 1 must give us + +this expression here. + +t0x12, being that one here, +gives us tu1 with respect to + +0x2, in shorthand notation +written as + +shown here, et cetera. + +So we can obtain, in other +words, these elements also + +from the deformation gradient. + +Let us now look at how the +columns of the strain + +displacement matrices look. + +We simply substitute into the +general expressions that I + +gave you earlier, and here we +have the t0 be a 0 entry for + +node three. + +Of course there are eight +columns altogether because we + +have a four-node element. + +We just showed two such +columns here for-- + +namely, those corresponding +to node three. + +Similarly, for t0BL1, we +get these entries here. + +Once again, also for node +three, of course. + +Similarly, we can also construct +the corresponding + +columns in the t0BNL matrix. + +And these columns are +given right there. + +Once again, for node three. + +This is, of course, also a +matrix that have altogether + +eight columns, because there are +four nodes, eight degrees + +of freedom. + +Let us now, as a next step, +consider the updated + +Lagrangian formulation in the +general plane stress, plane + +strain, axisymmetric case. + +In the updated Lagrangian +formulation, we have + +identified earlier, in an +earlier lecture, that we need + +these matrices and +that vector. + +This is, of course, a linear +strain stiffness matrix, + +that's a nonlinear strain +stiffness matrix, and that is + +the force vector that +corresponds to the internet + +element stresses. + +The matrices that go into the +calculation of these matrices + +are listed here. + +The tangent material +relationship, the linear + +strain displacement +matrix go into the + +calculation of this k matrix. + +This stress matrix, and that +strain displacement matrix, + +the nonlinear strain +displacement matrix, these two + +quantities go into the +calculation of this k matrix. + +And this stress vector, +and that linear strain + +displacement matrix +goes into the + +calculation of that F vector. + +We already derived that all +earlier in an earlier lecture. + +The stress strain matrix +is listed here. + +Notice that we have the +incremental stresses. + +Of course, these are increments +in the second + +Piola-Kirchhoff stresses +from time t onwards. + +That's why you have +the t here. + +That's why this t corresponds, +of course, to the updated + +Lagrangian formulation. + +Here we have the material +tensor, here we have the + +strain terms. + +Once again, the 2 that I pointed +out early already for + +the total Lagrangian +case as well. + +Of course this matrix here, +contains the elements of the + +material tensor, tCijrs, which +we used earlier when we talked + +about the continuum mechanics +formations. + +Well for the linear elastic +case, we would simply use the + +very familiar stress strain law +that we are using also in + +linear analysis. + +Young's modulus, Poisson's +ratio. + +So this is one typical case +for this C matrix. + +Of course, we will discuss later +on in later lectures how + +we construct the C matrix for +all sorts of material + +conditions. + +We need for the B matrix, for +the linear strain displacement + +matrix, these entries here, +meaning we need these + +differentiations. + +Notice partial u1 with respect +to tx1 is in shorthand + +notation written +as shown here. + +te22 is equal to that element, +and similarly we go on. + +Notice this, of course, is +again, the hoop strain. + +For the nonlinear strain +displacement matrix, we need + +to look at the nonlinear +strain terms. + +And the nonlinear strain terms +are listed out here now. + +We identified these strain +terms earlier when we + +discussed the updated Lagrangian +formulation in an + +earlier lecture. + +Of course, at that time, the +strain terms were represented + +in terms of ijk indices. + +Now we have to simply put i and +j equal to 1, for example, + +and k equal to 1, and equal to +2, and you will directly + +obtain from the earlier +expression that I presented to + +you this term here. + +And similarly, you obtain all +the other terms as well. + +By the way, the hoop strain, +the linear, and here we see + +the nonlinear hoop strain, +expression would be derived in + +the same way as we have done +it in this lecture for the + +total Lagrangian formulation. + +It would actually be a good +exercise for you to do so one + +and see how that goes. + +We construct the ttBL matrix to +capture the total strain, + +total linear strain, listed in +this vector here as shown by + +this equation. + +Of course, here we have the +nodal point displacements. + +The nodal point displacements +are in this vector. + +Denote always that these are +the discrete nodal point + +displacements. + +This last term, of course, +we only introduced in + +axisymmetric analysis. + +The entries in this ttBL matrix +are shown here for a + +typical node k. + +We use the same kind of picture +as for the total + +Lagrangian formulation. + +Notice here are the actual +displacements, the way they + +would appear in a vector. + +But since this element here hits +this column so to say, we + +have written it here +once more in blue. + +This element here hits this +column, and we have therefore + +written it here once +more in blue. + +So this is really the column +corresponding to the case node + +and the u1, the 1 direction. + +This is the column corresponding +to the case node + +and the 2 direction. + +If you compare this matrix with +the matrix that we use in + +linear analysis, you would see +that the matrix looks very + +similar, except that in linear +analysis you would not have + +this t, or you don't put that t +there in general because the + +t would, of course, be actually +the 0 configuration + +because all the differentiations +are referred + +to 0 configuration anyway. + +And it is common to not have +an index down here. + +If you look at this textbook, +chapter five, you would, for + +example, see there expressions +such as this + +without this t there. + +So there's really not much +of a surprise right here. + +You will surely see that this +is the right relationship to + +use in the B matrix +based on your + +knowledge of linear analysis. + +The expression of the nonlinear +strain displacement + +matrix and the stress matrix are +these two expressions are + +constructed in such a way as to +have that this product on + +the left-hand side is equal +to that expression there. + +I pointed that out already +earlier, that on the + +right-hand side this is the +continuum mechanics variable, + +and this continuum mechanics +variable is, of course, the + +basic quantity, the basic +quantity that we actually want + +to capture. + +And we construct this matrix +and that matrix + +such as to do so. + +I should just point out there +should be no bar here. + +Of course, this is a tensor +quantity, it's not a matrix, + +and so there should +be no bar there. + +That was a little error +on my part. + +The entries in the t tau +are given right here. + +The last row and column are, +of course, only included if + +you deal with an axisymmetric +analysis. + +ttBNL is shown here. + +Notice again, differentiations +with respect to time t. + +And the last row is only +included if you have an + +axisymmetric analysis. + +Finally, we want to also +construct our stress vector + +such that when it is entered +here with the BL matrix that + +we already have defined, we +capture via this product here + +exactly that term. + +This is the term that is basic, +that we have derived + +from the continuum mechanics +formulation. + +This is what we want to capture, +and we do so by this + +expression. + +And t tau hat is given +right here. + +It lists all the stresses +really, including the hoop + +stress if you have an +axisymmetric analysis. + +This completes what I wanted +to say about the two + +dimensional elements. + +We talked about the total +Lagrangian formulation, and + +the updated Lagrangian +formulation of these elements. + +In other words, we really +presented the matrices + +corresponding to these +formulations + +in quite some detail. + +These details that we discussed +for the two + +dimensional elements are also +almost directly applicable for + +the three dimensional +elements. + +And here we have a typical +eight-node element in a + +stationary coordinate frame, +x1, x2, x3, in its original + +configuration. + +The nodal point coordinates +are listed here. + +Notice k, of course, stands +again for the node k. + +1, 2, 3 stands for the +directions 1, 2, 3. + +And the left superscript here +stands for the time 0, the + +configuration 0. + +The element moves from time +0 to time t up to this + +configuration here. + +And the nodal points +now are tx1k-- + +nodal point coordinate +I should have said. + +Now tx1k, tx2k, tx3k. + +The notation is much the same +as we have been using in two + +dimensional analysis. + +Of course, we now have a third +coordinate, the x3 coordinate + +also in the formulation. + +We now use interpolations much +the same way as for the two + +dimensional elements. + +For the original configuration, +we have these + +interpolations. + +Notice, the third direction +enters now. + +Once again, these are the +interpolation functions. + +These are the nodal point +coordinates corresponding to + +the 1 direction. + +These are the nodal point +coordinates corresponding to + +the 2 direction, and so on. + +Of course, we now also have to +introduce the nodal point + +coordinates corresponding +to the 3 direction. + +And if the number of nodes, +if you have an eight-node + +element, and of course is 8. + +These are the interpolations +used for the original geometry + +of the element, and for the +configuration at time t, we + +use these interpolations. + +Notice these are now the nodal +points coordinates + +corresponding to time t. + +We use still the same +interpolation + +functions, of course. + +And N is the same number as for +the 0 interpolation, or + +rather for the interpolation +of the original geometry. + +In other words, for the +eight-node element that we + +briefly considered, N is in +each case equal to 8. + +We use these expressions, we +subtract from tx1 the 0x1 from + +tx2, the 0x2 expression from +tx3, the 0x3 expression, and + +directly obtain the +interpolations for the + +displacement of the elements. + +And once we have the +displacement interpolation, + +we, of course, can directly find +the derivative of these + +displacement interpolations +to obtain the strain + +interpolations. + +And these expressions then, +the derivatives of the + +displacement interpolation, +enter into the construction of + +the strain displacement +matrices. + +So we see that basically, the +same procedure that we + +discussed with two dimensional +analysis is directly + +applicable to the three +dimensional analysis, the only + +difference being that the third +direction, x3, has to be + +interpolated, the displacements +have to be + +carried along corresponding +to the third + +direction, et cetera. + +This then brings me to the end +of what I wanted to say in + +this lecture. + +Thank you very much for +your attention. \ No newline at end of file diff --git a/m4ZuXay_qOo.txt b/m4ZuXay_qOo.txt new file mode 100644 index 0000000000000000000000000000000000000000..f6051cb831d86ba587f607f6d11339bdcc8e61b9 --- /dev/null +++ b/m4ZuXay_qOo.txt @@ -0,0 +1,10267 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right hello people + + align:start position:0% +ocw.mit.edu all right hello people + + + align:start position:0% +ocw.mit.edu all right hello people +welcome back to the second week of our + + align:start position:0% +welcome back to the second week of our + + + align:start position:0% +welcome back to the second week of our +course course uh I'm happy to I'm happy + + align:start position:0% +course course uh I'm happy to I'm happy + + + align:start position:0% +course course uh I'm happy to I'm happy +to have this wonderful live audience but + + align:start position:0% +to have this wonderful live audience but + + + align:start position:0% +to have this wonderful live audience but +I also would like very briefly to + + align:start position:0% +I also would like very briefly to + + + align:start position:0% +I also would like very briefly to +address our video audience who will no + + align:start position:0% +address our video audience who will no + + + align:start position:0% +address our video audience who will no +doubt be watching this long after I'm + + align:start position:0% +doubt be watching this long after I'm + + + align:start position:0% +doubt be watching this long after I'm +dead on mit's open + + align:start position:0% +dead on mit's open + + + align:start position:0% +dead on mit's open +courseware uh so think of this as a + + align:start position:0% +courseware uh so think of this as a + + + align:start position:0% +courseware uh so think of this as a +voice from the grave uh you will some + + align:start position:0% +voice from the grave uh you will some + + + align:start position:0% +voice from the grave uh you will some +you will sometimes notice you in the + + align:start position:0% +you will sometimes notice you in the + + + align:start position:0% +you will sometimes notice you in the +video audience will sometimes notice + + align:start position:0% +video audience will sometimes notice + + + align:start position:0% +video audience will sometimes notice +that as I'm lecturing to this Lively + + align:start position:0% +that as I'm lecturing to this Lively + + + align:start position:0% +that as I'm lecturing to this Lively +group I will turn this way and look up + + align:start position:0% +group I will turn this way and look up + + + align:start position:0% +group I will turn this way and look up +you should realize that what I'm turning + + align:start position:0% +you should realize that what I'm turning + + + align:start position:0% +you should realize that what I'm turning +at turning toward and looking up at is + + align:start position:0% +at turning toward and looking up at is + + + align:start position:0% +at turning toward and looking up at is +this project this projection screen + + align:start position:0% +this project this projection screen + + + align:start position:0% +this project this projection screen +which we will show you uh and it + + align:start position:0% +which we will show you uh and it + + + align:start position:0% +which we will show you uh and it +sometimes has this outline on it which + + align:start position:0% +sometimes has this outline on it which + + + align:start position:0% +sometimes has this outline on it which +guides us through the hopefully guides + + align:start position:0% +guides us through the hopefully guides + + + align:start position:0% +guides us through the hopefully guides +us through each lecture and sometimes + + align:start position:0% +us through each lecture and sometimes + + + align:start position:0% +us through each lecture and sometimes +has other information and M and material + + align:start position:0% +has other information and M and material + + + align:start position:0% +has other information and M and material +on it uh sometimes it isn't worth + + align:start position:0% +on it uh sometimes it isn't worth + + + align:start position:0% +on it uh sometimes it isn't worth +shifting over to show the video audience + + align:start position:0% +shifting over to show the video audience + + + align:start position:0% +shifting over to show the video audience +that image but that's what I'm looking + + align:start position:0% +that image but that's what I'm looking + + + align:start position:0% +that image but that's what I'm looking +at when I look so + + align:start position:0% + + + + align:start position:0% + +strange I'd like to begin today by + + align:start position:0% +strange I'd like to begin today by + + + align:start position:0% +strange I'd like to begin today by +taking a step back by uh reminding + + align:start position:0% +taking a step back by uh reminding + + + align:start position:0% +taking a step back by uh reminding +reming you that the order in which we're + + align:start position:0% +reming you that the order in which we're + + + align:start position:0% +reming you that the order in which we're +watching the movies in this course is a + + align:start position:0% +watching the movies in this course is a + + + align:start position:0% +watching the movies in this course is a +little bit arbitrary because I wanted to + + align:start position:0% +little bit arbitrary because I wanted to + + + align:start position:0% +little bit arbitrary because I wanted to +use the feature films as the defining uh + + align:start position:0% +use the feature films as the defining uh + + + align:start position:0% +use the feature films as the defining uh +as the defining date and that's the + + align:start position:0% +as the defining date and that's the + + + align:start position:0% +as the defining date and that's the +reason that we made Keaton come first + + align:start position:0% +reason that we made Keaton come first + + + align:start position:0% +reason that we made Keaton come first +because the general is an earlier film + + align:start position:0% +because the general is an earlier film + + + align:start position:0% +because the general is an earlier film +it it was uh almost a decade earlier + + align:start position:0% +it it was uh almost a decade earlier + + + align:start position:0% +it it was uh almost a decade earlier +than uh modern times but the truth is + + align:start position:0% +than uh modern times but the truth is + + + align:start position:0% +than uh modern times but the truth is +chaplain entered film before Keaton and + + align:start position:0% +chaplain entered film before Keaton and + + + align:start position:0% +chaplain entered film before Keaton and +uh Keaton had certain advantages when uh + + align:start position:0% +uh Keaton had certain advantages when uh + + + align:start position:0% +uh Keaton had certain advantages when uh +by the time he entered the movies in + + align:start position:0% +by the time he entered the movies in + + + align:start position:0% +by the time he entered the movies in +part because of chaplain's example + + align:start position:0% +part because of chaplain's example + + + align:start position:0% +part because of chaplain's example +although also because of the Fairly + + align:start position:0% +although also because of the Fairly + + + align:start position:0% +although also because of the Fairly +complicated way in which silent film had + + align:start position:0% +complicated way in which silent film had + + + align:start position:0% +complicated way in which silent film had +already elaborated itself after the + + align:start position:0% +already elaborated itself after the + + + align:start position:0% +already elaborated itself after the +first 10 years or so of the 20th century + + align:start position:0% +first 10 years or so of the 20th century + + + align:start position:0% +first 10 years or so of the 20th century +so I want to take a step back into that + + align:start position:0% +so I want to take a step back into that + + + align:start position:0% +so I want to take a step back into that +into that early phase just before + + align:start position:0% +into that early phase just before + + + align:start position:0% +into that early phase just before +Chaplan uh uh becomes a filmmaker at the + + align:start position:0% +Chaplan uh uh becomes a filmmaker at the + + + align:start position:0% +Chaplan uh uh becomes a filmmaker at the +uh at the really in 1911 I think is when + + align:start position:0% +uh at the really in 1911 I think is when + + + align:start position:0% +uh at the really in 1911 I think is when +he joins the Keystone the Keystone + + align:start position:0% +he joins the Keystone the Keystone + + + align:start position:0% +he joins the Keystone the Keystone +Studios uh just to remind you of a story + + align:start position:0% +Studios uh just to remind you of a story + + + align:start position:0% +Studios uh just to remind you of a story +that is systematically in David Cook's + + align:start position:0% +that is systematically in David Cook's + + + align:start position:0% +that is systematically in David Cook's +history of narrative film which you + + align:start position:0% +history of narrative film which you + + + align:start position:0% +history of narrative film which you +which is part of our required reading in + + align:start position:0% +which is part of our required reading in + + + align:start position:0% +which is part of our required reading in +the course uh and I hope you will attend + + align:start position:0% +the course uh and I hope you will attend + + + align:start position:0% +the course uh and I hope you will attend +especially to the details cook offers + + align:start position:0% +especially to the details cook offers + + + align:start position:0% +especially to the details cook offers +about those early years in Hollywood if + + align:start position:0% +about those early years in Hollywood if + + + align:start position:0% +about those early years in Hollywood if +you read those chapters from cook about + + align:start position:0% +you read those chapters from cook about + + + align:start position:0% +you read those chapters from cook about +the early uh years of Hollywood before + + align:start position:0% +the early uh years of Hollywood before + + + align:start position:0% +the early uh years of Hollywood before +chaplain the movies before chaplain + + align:start position:0% +chaplain the movies before chaplain + + + align:start position:0% +chaplain the movies before chaplain +you'll recall that one of the most + + align:start position:0% +you'll recall that one of the most + + + align:start position:0% +you'll recall that one of the most +fundamental things that happens before + + align:start position:0% +fundamental things that happens before + + + align:start position:0% +fundamental things that happens before +chaplain even appears is the + + align:start position:0% +chaplain even appears is the + + + align:start position:0% +chaplain even appears is the +establishment essentially of the + + align:start position:0% +establishment essentially of the + + + align:start position:0% +establishment essentially of the +industry I was describing last last time + + align:start position:0% +industry I was describing last last time + + + align:start position:0% +industry I was describing last last time +uh certain uh the migration to the West + + align:start position:0% +uh certain uh the migration to the West + + + align:start position:0% +uh certain uh the migration to the West +Coast is worth mentioning because movies + + align:start position:0% +Coast is worth mentioning because movies + + + align:start position:0% +Coast is worth mentioning because movies +of course begin their career in the + + align:start position:0% +of course begin their career in the + + + align:start position:0% +of course begin their career in the +United States on the East Coast Edison's + + align:start position:0% +United States on the East Coast Edison's + + + align:start position:0% +United States on the East Coast Edison's +first movie studio was in East Orange + + align:start position:0% +first movie studio was in East Orange + + + align:start position:0% +first movie studio was in East Orange +New Jersey much of the uh the Biograph + + align:start position:0% +New Jersey much of the uh the Biograph + + + align:start position:0% +New Jersey much of the uh the Biograph +company was originally located in on the + + align:start position:0% +company was originally located in on the + + + align:start position:0% +company was originally located in on the +east coast and mo a lot of almost all + + align:start position:0% +east coast and mo a lot of almost all + + + align:start position:0% +east coast and mo a lot of almost all +the original earliest films uh even the + + align:start position:0% +the original earliest films uh even the + + + align:start position:0% +the original earliest films uh even the +earliest films that were put into + + align:start position:0% +earliest films that were put into + + + align:start position:0% +earliest films that were put into +production and shown uh uh commercially + + align:start position:0% +production and shown uh uh commercially + + + align:start position:0% +production and shown uh uh commercially +were made in the were made were made on + + align:start position:0% +were made in the were made were made on + + + align:start position:0% +were made in the were made were made on +the East Coast uh + + align:start position:0% +the East Coast uh + + + align:start position:0% +the East Coast uh +what why did people move to the West + + align:start position:0% +what why did people move to the West + + + align:start position:0% +what why did people move to the West +Coast why did Hollywood become the sort + + align:start position:0% +Coast why did Hollywood become the sort + + + align:start position:0% +Coast why did Hollywood become the sort +of center of the movie industry what + + align:start position:0% +of center of the movie industry what + + + align:start position:0% +of center of the movie industry what +explains it it happens very early so + + align:start position:0% +explains it it happens very early so + + + align:start position:0% +explains it it happens very early so +it's a and it's a one might think of it + + align:start position:0% +it's a and it's a one might think of it + + + align:start position:0% +it's a and it's a one might think of it +as a very important moment in the + + align:start position:0% +as a very important moment in the + + + align:start position:0% +as a very important moment in the +history of culture of popular culture + + align:start position:0% +history of culture of popular culture + + + align:start position:0% +history of culture of popular culture +because Hollywood remains uh for all the + + align:start position:0% +because Hollywood remains uh for all the + + + align:start position:0% +because Hollywood remains uh for all the +changes that the movie industry has + + align:start position:0% +changes that the movie industry has + + + align:start position:0% +changes that the movie industry has +undergone Hollywood remains a kind of + + align:start position:0% +undergone Hollywood remains a kind of + + + align:start position:0% +undergone Hollywood remains a kind of +the the kind of center of what is now a + + align:start position:0% +the the kind of center of what is now a + + + align:start position:0% +the the kind of center of what is now a +kind of global Enterprise of movie + + align:start position:0% +kind of global Enterprise of movie + + + align:start position:0% +kind of global Enterprise of movie +making what helps to explain the move to + + align:start position:0% +making what helps to explain the move to + + + align:start position:0% +making what helps to explain the move to +the West Coast nothing fancy in the back + + align:start position:0% +the West Coast nothing fancy in the back + + + align:start position:0% +the West Coast nothing fancy in the back +yes film around they could film you + + align:start position:0% +yes film around they could film you + + + align:start position:0% +yes film around they could film you +around why is that + + align:start position:0% +around why is that + + + align:start position:0% +around why is that +important especially in the early days + + align:start position:0% +important especially in the early days + + + align:start position:0% +important especially in the early days +you can make movies whenever you don't + + align:start position:0% +you can make movies whenever you don't + + + align:start position:0% +you can make movies whenever you don't +have to produce them in the summer and + + align:start position:0% +have to produce them in the summer and + + + align:start position:0% +have to produce them in the summer and +then yes you don't you're not dependent + + align:start position:0% +then yes you don't you're not dependent + + + align:start position:0% +then yes you don't you're not dependent +on the weather you're not as de not as + + align:start position:0% +on the weather you're not as de not as + + + align:start position:0% +on the weather you're not as de not as +dependent on the weather the sun always + + align:start position:0% +dependent on the weather the sun always + + + align:start position:0% +dependent on the weather the sun always +shines in California you you if it's + + align:start position:0% +shines in California you you if it's + + + align:start position:0% +shines in California you you if it's +overcast you can still you can still + + align:start position:0% +overcast you can still you can still + + + align:start position:0% +overcast you can still you can still +film if it's there's no there's there's + + align:start position:0% +film if it's there's no there's there's + + + align:start position:0% +film if it's there's no there's there's +virtually there's no snow there's + + align:start position:0% +virtually there's no snow there's + + + align:start position:0% +virtually there's no snow there's +virtually no there's virtually no rain + + align:start position:0% +virtually no there's virtually no rain + + + align:start position:0% +virtually no there's virtually no rain +the the the weather is very cond the + + align:start position:0% +the the the weather is very cond the + + + align:start position:0% +the the the weather is very cond the +weather is very condu conducive to the + + align:start position:0% +weather is very condu conducive to the + + + align:start position:0% +weather is very condu conducive to the +making of film and especially in this + + align:start position:0% +making of film and especially in this + + + align:start position:0% +making of film and especially in this +early phase when film stock was was + + align:start position:0% +early phase when film stock was was + + + align:start position:0% +early phase when film stock was was +relatively primitive compared to the + + align:start position:0% +relatively primitive compared to the + + + align:start position:0% +relatively primitive compared to the +complexity of film stock we have today + + align:start position:0% +complexity of film stock we have today + + + align:start position:0% +complexity of film stock we have today +the film film stock is so subtle that it + + align:start position:0% +the film film stock is so subtle that it + + + align:start position:0% +the film film stock is so subtle that it +they can you can film in the dark you + + align:start position:0% +they can you can film in the dark you + + + align:start position:0% +they can you can film in the dark you +can film by Fire Light even amateur uh + + align:start position:0% +can film by Fire Light even amateur uh + + + align:start position:0% +can film by Fire Light even amateur uh +uh folks owning camcorders can film + + align:start position:0% +uh folks owning camcorders can film + + + align:start position:0% +uh folks owning camcorders can film +virtually in the dark they can film by + + align:start position:0% +virtually in the dark they can film by + + + align:start position:0% +virtually in the dark they can film by +they can film by by by Electric Light + + align:start position:0% +they can film by by by Electric Light + + + align:start position:0% +they can film by by by Electric Light +inside a room uh in the in or tape they + + align:start position:0% +inside a room uh in the in or tape they + + + align:start position:0% +inside a room uh in the in or tape they +can they can video tape in that way uh + + align:start position:0% +can they can video tape in that way uh + + + align:start position:0% +can they can video tape in that way uh +in the in the in the earliest days of + + align:start position:0% +in the in the in the earliest days of + + + align:start position:0% +in the in the in the earliest days of +film you needed a tremendous amount of + + align:start position:0% +film you needed a tremendous amount of + + + align:start position:0% +film you needed a tremendous amount of +light to expose the film and what what + + align:start position:0% +light to expose the film and what what + + + align:start position:0% +light to expose the film and what what +what it meant that you were dependent on + + align:start position:0% +what it meant that you were dependent on + + + align:start position:0% +what it meant that you were dependent on +on the weather uh so that was one major + + align:start position:0% +on the weather uh so that was one major + + + align:start position:0% +on the weather uh so that was one major +reason but there's another one that's + + align:start position:0% +reason but there's another one that's + + + align:start position:0% +reason but there's another one that's +even more important in some ways even + + align:start position:0% +even more important in some ways even + + + align:start position:0% +even more important in some ways even +though that would seem a sufficient + + align:start position:0% +though that would seem a sufficient + + + align:start position:0% +though that would seem a sufficient +reason for explaining why the migration + + align:start position:0% +reason for explaining why the migration + + + align:start position:0% +reason for explaining why the migration +to the West Coast occurred there's + + align:start position:0% +to the West Coast occurred there's + + + align:start position:0% +to the West Coast occurred there's +another even more powerful one it has to + + align:start position:0% +another even more powerful one it has to + + + align:start position:0% +another even more powerful one it has to +do with the idea of patent Warfare yes + + align:start position:0% +do with the idea of patent Warfare yes + + + align:start position:0% +do with the idea of patent Warfare yes +what's what what's your suggestion you + + align:start position:0% +what's what what's your suggestion you + + + align:start position:0% +what's what what's your suggestion you +don't have to give the right answer give + + align:start position:0% +don't have to give the right answer give + + + align:start position:0% +don't have to give the right answer give +them different types of terrains all in + + align:start position:0% +them different types of terrains all in + + + align:start position:0% +them different types of terrains all in +CL oh that's also true yes the + + align:start position:0% +CL oh that's also true yes the + + + align:start position:0% +CL oh that's also true yes the +environment of Southern California is + + align:start position:0% +environment of Southern California is + + + align:start position:0% +environment of Southern California is +particularly conducive to to a variety + + align:start position:0% +particularly conducive to to a variety + + + align:start position:0% +particularly conducive to to a variety +of of film projects there are mountains + + align:start position:0% +of of film projects there are mountains + + + align:start position:0% +of of film projects there are mountains +nearby there's ocean nearby uh there's + + align:start position:0% +nearby there's ocean nearby uh there's + + + align:start position:0% +nearby there's ocean nearby uh there's +desert nearby so and and of course + + align:start position:0% +desert nearby so and and of course + + + align:start position:0% +desert nearby so and and of course +that's also something that makes it a a + + align:start position:0% +that's also something that makes it a a + + + align:start position:0% +that's also something that makes it a a +uniquely valuable environment maybe not + + align:start position:0% +uniquely valuable environment maybe not + + + align:start position:0% +uniquely valuable environment maybe not +a unique environment but but a + + align:start position:0% +a unique environment but but a + + + align:start position:0% +a unique environment but but a +particularly valuable environment for + + align:start position:0% +particularly valuable environment for + + + align:start position:0% +particularly valuable environment for +the movie that's a good answer and + + align:start position:0% +the movie that's a good answer and + + + align:start position:0% +the movie that's a good answer and +you're right about that but there's + + align:start position:0% +you're right about that but there's + + + align:start position:0% +you're right about that but there's +something else that has to do with + + align:start position:0% +something else that has to do with + + + align:start position:0% +something else that has to do with +conditions in the East and Thomas + + align:start position:0% +conditions in the East and Thomas + + + align:start position:0% +conditions in the East and Thomas +Edison remember Edison you know uh you + + align:start position:0% +Edison remember Edison you know uh you + + + align:start position:0% +Edison remember Edison you know uh you +know in a certain way wanted to lay + + align:start position:0% +know in a certain way wanted to lay + + + align:start position:0% +know in a certain way wanted to lay +claim to virtually every invention in + + align:start position:0% +claim to virtually every invention in + + + align:start position:0% +claim to virtually every invention in +the early part of the 20th century and + + align:start position:0% +the early part of the 20th century and + + + align:start position:0% +the early part of the 20th century and +he was primed to do so he was already + + align:start position:0% +he was primed to do so he was already + + + align:start position:0% +he was primed to do so he was already +recognized as a great genius as as as + + align:start position:0% +recognized as a great genius as as as + + + align:start position:0% +recognized as a great genius as as as +the as the premier entrepreneurial + + align:start position:0% +the as the premier entrepreneurial + + + align:start position:0% +the as the premier entrepreneurial +inventor of his era uh and he + + align:start position:0% +inventor of his era uh and he + + + align:start position:0% +inventor of his era uh and he +immediately as he had done with as he + + align:start position:0% +immediately as he had done with as he + + + align:start position:0% +immediately as he had done with as he +had done with other projects of his + + align:start position:0% +had done with other projects of his + + + align:start position:0% +had done with other projects of his +began to take out patents to try to + + align:start position:0% +began to take out patents to try to + + + align:start position:0% +began to take out patents to try to +control uh the use of movie technology + + align:start position:0% +control uh the use of movie technology + + + align:start position:0% +control uh the use of movie technology +he wanted to become of the Edison + + align:start position:0% +he wanted to become of the Edison + + + align:start position:0% +he wanted to become of the Edison +Monopoly he wanted he was he was + + align:start position:0% +Monopoly he wanted he was he was + + + align:start position:0% +Monopoly he wanted he was he was +fantasizing that he would that that he + + align:start position:0% +fantasizing that he would that that he + + + align:start position:0% +fantasizing that he would that that he +would control the movie what whatever + + align:start position:0% +would control the movie what whatever + + + align:start position:0% +would control the movie what whatever +the movie industry would become Edison's + + align:start position:0% +the movie industry would become Edison's + + + align:start position:0% +the movie industry would become Edison's +company fantasized it was going to take + + align:start position:0% +company fantasized it was going to take + + + align:start position:0% +company fantasized it was going to take +control of that and in fact the Edison + + align:start position:0% +control of that and in fact the Edison + + + align:start position:0% +control of that and in fact the Edison +Company hired uh um law enforcement + + align:start position:0% +Company hired uh um law enforcement + + + align:start position:0% +Company hired uh um law enforcement +officers and according to some + + align:start position:0% +officers and according to some + + + align:start position:0% +officers and according to some +historians even in some places hired + + align:start position:0% +historians even in some places hired + + + align:start position:0% +historians even in some places hired +goons thugs to to go and break up the + + align:start position:0% +goons thugs to to go and break up the + + + align:start position:0% +goons thugs to to go and break up the +the uh the sets and the the the the the + + align:start position:0% +the uh the sets and the the the the the + + + align:start position:0% +the uh the sets and the the the the the +the shooting of uh rival producers who + + align:start position:0% +the shooting of uh rival producers who + + + align:start position:0% +the shooting of uh rival producers who +were according to Edison infringing on + + align:start position:0% +were according to Edison infringing on + + + align:start position:0% +were according to Edison infringing on +Edison copyrights so the other reason + + align:start position:0% +Edison copyrights so the other reason + + + align:start position:0% +Edison copyrights so the other reason +and another reason for the move to the + + align:start position:0% +and another reason for the move to the + + + align:start position:0% +and another reason for the move to the +West Coast was a lot of + + align:start position:0% +West Coast was a lot of + + + align:start position:0% +West Coast was a lot of +entrepreneurial uh uh uh Movie Makers + + align:start position:0% +entrepreneurial uh uh uh Movie Makers + + + align:start position:0% +entrepreneurial uh uh uh Movie Makers +wanted to get free of the patent police + + align:start position:0% +wanted to get free of the patent police + + + align:start position:0% +wanted to get free of the patent police +they wanted to get out from under the + + align:start position:0% +they wanted to get out from under the + + + align:start position:0% +they wanted to get out from under the +scrutiny of Edison and his police uh uh + + align:start position:0% +scrutiny of Edison and his police uh uh + + + align:start position:0% +scrutiny of Edison and his police uh uh +and and by running to the West Coast + + align:start position:0% +and and by running to the West Coast + + + align:start position:0% +and and by running to the West Coast +they were able to do so and and in fact + + align:start position:0% +they were able to do so and and in fact + + + align:start position:0% +they were able to do so and and in fact +Edison was unsuccessful in controlling + + align:start position:0% +Edison was unsuccessful in controlling + + + align:start position:0% +Edison was unsuccessful in controlling +the technology as as cook and other + + align:start position:0% +the technology as as cook and other + + + align:start position:0% +the technology as as cook and other +historians have made have made clear to + + align:start position:0% +historians have made have made clear to + + + align:start position:0% +historians have made have made clear to +us so the move to the West Coast is a + + align:start position:0% +us so the move to the West Coast is a + + + align:start position:0% +us so the move to the West Coast is a +very important one and I will return to + + align:start position:0% +very important one and I will return to + + + align:start position:0% +very important one and I will return to +the cultural the so the historic IAL and + + align:start position:0% +the cultural the so the historic IAL and + + + align:start position:0% +the cultural the so the historic IAL and +ideological or intellectual implications + + align:start position:0% +ideological or intellectual implications + + + align:start position:0% +ideological or intellectual implications +of his of that move to the West Coast in + + align:start position:0% +of his of that move to the West Coast in + + + align:start position:0% +of his of that move to the West Coast in +a in a in a few lectures uh maybe next + + align:start position:0% +a in a in a few lectures uh maybe next + + + align:start position:0% +a in a in a few lectures uh maybe next +week if I if I get the opportunity uh + + align:start position:0% +week if I if I get the opportunity uh + + + align:start position:0% +week if I if I get the opportunity uh +because I want to talk a little bit more + + align:start position:0% +because I want to talk a little bit more + + + align:start position:0% +because I want to talk a little bit more +about what what it meant for American + + align:start position:0% +about what what it meant for American + + + align:start position:0% +about what what it meant for American +movies that film was made on the + + align:start position:0% +movies that film was made on the + + + align:start position:0% +movies that film was made on the +farthest Western verge of the society + + align:start position:0% +farthest Western verge of the society + + + align:start position:0% +farthest Western verge of the society +away from cultural centers unlike the + + align:start position:0% +away from cultural centers unlike the + + + align:start position:0% +away from cultural centers unlike the +way in which movies developed in Europe + + align:start position:0% +way in which movies developed in Europe + + + align:start position:0% +way in which movies developed in Europe +and I'll talk about that implication a + + align:start position:0% +and I'll talk about that implication a + + + align:start position:0% +and I'll talk about that implication a +bit later uh probably next week when we + + align:start position:0% +bit later uh probably next week when we + + + align:start position:0% +bit later uh probably next week when we +talk about the the German the great + + align:start position:0% +talk about the the German the great + + + align:start position:0% +talk about the the German the great +German silent film that concludes our + + align:start position:0% +German silent film that concludes our + + + align:start position:0% +German silent film that concludes our +segment on silent films so even so so so + + align:start position:0% +segment on silent films so even so so so + + + align:start position:0% +segment on silent films so even so so so +before so even before chaplain enters + + align:start position:0% +before so even before chaplain enters + + + align:start position:0% +before so even before chaplain enters +the rudiments or the more than the + + align:start position:0% +the rudiments or the more than the + + + align:start position:0% +the rudiments or the more than the +rudiments the basic system of mass + + align:start position:0% +rudiments the basic system of mass + + + align:start position:0% +rudiments the basic system of mass +production of studi based production uh + + align:start position:0% +production of studi based production uh + + + align:start position:0% +production of studi based production uh +of distrib of manufacturer of the films + + align:start position:0% +of distrib of manufacturer of the films + + + align:start position:0% +of distrib of manufacturer of the films +in in in one place and then the + + align:start position:0% +in in in one place and then the + + + align:start position:0% +in in in one place and then the +distribution system that that developed + + align:start position:0% +distribution system that that developed + + + align:start position:0% +distribution system that that developed +in which theaters is eventually rented + + align:start position:0% +in which theaters is eventually rented + + + align:start position:0% +in which theaters is eventually rented +or purchased films from The Producers uh + + align:start position:0% +or purchased films from The Producers uh + + + align:start position:0% +or purchased films from The Producers uh +was already was already in place and of + + align:start position:0% +was already was already in place and of + + + align:start position:0% +was already was already in place and of +course the two great figures here is is + + align:start position:0% +course the two great figures here is is + + + align:start position:0% +course the two great figures here is is +Thomas in the great fig and and cook + + align:start position:0% +Thomas in the great fig and and cook + + + align:start position:0% +Thomas in the great fig and and cook +writes very well about in and his + + align:start position:0% +writes very well about in and his + + + align:start position:0% +writes very well about in and his +contribution to the movies probably the + + align:start position:0% +contribution to the movies probably the + + + align:start position:0% +contribution to the movies probably the +person we could to whom we could + + align:start position:0% +person we could to whom we could + + + align:start position:0% +person we could to whom we could +attribute the invention of the movie + + align:start position:0% +attribute the invention of the movie + + + align:start position:0% +attribute the invention of the movie +studio I suppose and Max senet who who + + align:start position:0% +studio I suppose and Max senet who who + + + align:start position:0% +studio I suppose and Max senet who who +developed the Keystone Studios out of + + align:start position:0% +developed the Keystone Studios out of + + + align:start position:0% +developed the Keystone Studios out of +which so many important uh early + + align:start position:0% +which so many important uh early + + + align:start position:0% +which so many important uh early +comedies emerged and the studio to which + + align:start position:0% +comedies emerged and the studio to which + + + align:start position:0% +comedies emerged and the studio to which +chapl to to which which chaplain joined + + align:start position:0% +chapl to to which which chaplain joined + + + align:start position:0% +chapl to to which which chaplain joined +when he came to the United States in 19 + + align:start position:0% +when he came to the United States in 19 + + + align:start position:0% +when he came to the United States in 19 +uh uh uh to to become a movie maker at + + align:start position:0% +uh uh uh to to become a movie maker at + + + align:start position:0% +uh uh uh to to become a movie maker at +the after the I think 1911 or or or 1912 + + align:start position:0% +the after the I think 1911 or or or 1912 + + + align:start position:0% +the after the I think 1911 or or or 1912 +so so uh in and Max Senate are important + + align:start position:0% +so so uh in and Max Senate are important + + + align:start position:0% +so so uh in and Max Senate are important +and one might say one further thing + + align:start position:0% +and one might say one further thing + + + align:start position:0% +and one might say one further thing +about about this moment um uh as you + + align:start position:0% +about about this moment um uh as you + + + align:start position:0% +about about this moment um uh as you +know if you've read cook Senate created + + align:start position:0% +know if you've read cook Senate created + + + align:start position:0% +know if you've read cook Senate created +what came to be called the Keystone + + align:start position:0% +what came to be called the Keystone + + + align:start position:0% +what came to be called the Keystone +Studios and they were named Keystone + + align:start position:0% +Studios and they were named Keystone + + + align:start position:0% +Studios and they were named Keystone +Studios were named I think or maybe it + + align:start position:0% +Studios were named I think or maybe it + + + align:start position:0% +Studios were named I think or maybe it +was the reverse I'm not sure uh was + + align:start position:0% +was the reverse I'm not sure uh was + + + align:start position:0% +was the reverse I'm not sure uh was +associated with their Prime product in + + align:start position:0% +associated with their Prime product in + + + align:start position:0% +associated with their Prime product in +the early days and they were called the + + align:start position:0% +the early days and they were called the + + + align:start position:0% +the early days and they were called the +Keystone Cops comedies we're going to + + align:start position:0% +Keystone Cops comedies we're going to + + + align:start position:0% +Keystone Cops comedies we're going to +show you a fragment of those in a in a + + align:start position:0% +show you a fragment of those in a in a + + + align:start position:0% +show you a fragment of those in a in a +moment they were frenzied action + + align:start position:0% +moment they were frenzied action + + + align:start position:0% +moment they were frenzied action +frenzied physical frenzied physical + + align:start position:0% +frenzied physical frenzied physical + + + align:start position:0% +frenzied physical frenzied physical +action uh so this is the ERA this is the + + align:start position:0% +action uh so this is the ERA this is the + + + align:start position:0% +action uh so this is the ERA this is the +moment the period the before in the fir + + align:start position:0% +moment the period the before in the fir + + + align:start position:0% +moment the period the before in the fir +the first 10 years of the movie industry + + align:start position:0% +the first 10 years of the movie industry + + + align:start position:0% +the first 10 years of the movie industry +in the United States when uh the basic + + align:start position:0% +in the United States when uh the basic + + + align:start position:0% +in the United States when uh the basic +system is being is being uh uh uh by + + align:start position:0% +system is being is being uh uh uh by + + + align:start position:0% +system is being is being uh uh uh by +trial and error uh worked out and by the + + align:start position:0% +trial and error uh worked out and by the + + + align:start position:0% +trial and error uh worked out and by the +time chaplain comes to join the system + + align:start position:0% +time chaplain comes to join the system + + + align:start position:0% +time chaplain comes to join the system +uh after the first decade or so of the + + align:start position:0% +uh after the first decade or so of the + + + align:start position:0% +uh after the first decade or so of the +20th century the system essentially is + + align:start position:0% +20th century the system essentially is + + + align:start position:0% +20th century the system essentially is +in place there are already a number of + + align:start position:0% +in place there are already a number of + + + align:start position:0% +in place there are already a number of +famous performers in both in comedy and + + align:start position:0% +famous performers in both in comedy and + + + align:start position:0% +famous performers in both in comedy and +in and in drama uh there are there are + + align:start position:0% +in and in drama uh there are there are + + + align:start position:0% +in and in drama uh there are there are +emerging certain particular Studios that + + align:start position:0% +emerging certain particular Studios that + + + align:start position:0% +emerging certain particular Studios that +uh that uh who who have refined a mass + + align:start position:0% +uh that uh who who have refined a mass + + + align:start position:0% +uh that uh who who have refined a mass +production technique to produce their + + align:start position:0% +production technique to produce their + + + align:start position:0% +production technique to produce their +movies on a on on a on a regular basis + + align:start position:0% +movies on a on on a on a regular basis + + + align:start position:0% +movies on a on on a on a regular basis +so an expanding an expanding market for + + align:start position:0% +so an expanding an expanding market for + + + align:start position:0% +so an expanding an expanding market for +the movies is being met by a systematic + + align:start position:0% +the movies is being met by a systematic + + + align:start position:0% +the movies is being met by a systematic +manufacturing process that in and Senate + + align:start position:0% +manufacturing process that in and Senate + + + align:start position:0% +manufacturing process that in and Senate +begin to work out in in in in in uh in + + align:start position:0% +begin to work out in in in in in uh in + + + align:start position:0% +begin to work out in in in in in uh in +systematic and and uh uh long lasting + + align:start position:0% +systematic and and uh uh long lasting + + + align:start position:0% +systematic and and uh uh long lasting +ways in ways that in a certain sense + + align:start position:0% +ways in ways that in a certain sense + + + align:start position:0% +ways in ways that in a certain sense +continue in residual form in vestigal + + align:start position:0% +continue in residual form in vestigal + + + align:start position:0% +continue in residual form in vestigal +form to dominate the production of + + align:start position:0% +form to dominate the production of + + + align:start position:0% +form to dominate the production of +movies even today when we were talking + + align:start position:0% +movies even today when we were talking + + + align:start position:0% +movies even today when we were talking +about the primitiveness and the + + align:start position:0% +about the primitiveness and the + + + align:start position:0% +about the primitiveness and the +Simplicity of early film there was one + + align:start position:0% +Simplicity of early film there was one + + + align:start position:0% +Simplicity of early film there was one +film I had on the stocks we didn't have + + align:start position:0% +film I had on the stocks we didn't have + + + align:start position:0% +film I had on the stocks we didn't have +time to show you last week and I thought + + align:start position:0% +time to show you last week and I thought + + + align:start position:0% +time to show you last week and I thought +I would show this to you as a way of + + align:start position:0% +I would show this to you as a way of + + + align:start position:0% +I would show this to you as a way of +illustrating again uh how relatively + + align:start position:0% +illustrating again uh how relatively + + + align:start position:0% +illustrating again uh how relatively +simple the early films are see how much + + align:start position:0% +simple the early films are see how much + + + align:start position:0% +simple the early films are see how much +how how influential that first sneeze + + align:start position:0% + + + + align:start position:0% + +was the name of this film is the whole + + align:start position:0% +was the name of this film is the whole + + + align:start position:0% +was the name of this film is the whole +damn family there's Mr Dam there's Mrs + + align:start position:0% +damn family there's Mr Dam there's Mrs + + + align:start position:0% +damn family there's Mr Dam there's Mrs +Helen + + align:start position:0% + + + + align:start position:0% + +Dam there's their son Jimmy Dam + + align:start position:0% + + + + align:start position:0% + +now you the Simplicity of these + + align:start position:0% +now you the Simplicity of these + + + align:start position:0% +now you the Simplicity of these +movements are part of what's interesting + + align:start position:0% +movements are part of what's interesting + + + align:start position:0% +movements are part of what's interesting +to us I mean this is still an era in + + align:start position:0% +to us I mean this is still an era in + + + align:start position:0% +to us I mean this is still an era in +which people are just fascinated by the + + align:start position:0% +which people are just fascinated by the + + + align:start position:0% +which people are just fascinated by the +idea that movies capture + + align:start position:0% +idea that movies capture + + + align:start position:0% +idea that movies capture +movies but what's the joke here and the + + align:start position:0% +movies but what's the joke here and the + + + align:start position:0% +movies but what's the joke here and the +joke is embedded I suppose in the title + + align:start position:0% +joke is embedded I suppose in the title + + + align:start position:0% +joke is embedded I suppose in the title +the whole damn + + align:start position:0% + + + + align:start position:0% + +family there's Miss IP + + align:start position:0% + + + + align:start position:0% + +Dam there's baby Dam + + align:start position:0% + + + + align:start position:0% + +what an + + align:start position:0% + + + + align:start position:0% + +actor see how it's framed as if it's a + + align:start position:0% +actor see how it's framed as if it's a + + + align:start position:0% +actor see how it's framed as if it's a +painting how stationary the camera is + + align:start position:0% +painting how stationary the camera is + + + align:start position:0% +painting how stationary the camera is +there's the damn cook what's the joke + + align:start position:0% +there's the damn cook what's the joke + + + align:start position:0% +there's the damn cook what's the joke +here finally we're going to come to the + + align:start position:0% +here finally we're going to come to the + + + align:start position:0% +here finally we're going to come to the +damn dog what's going on here there's a + + align:start position:0% +damn dog what's going on here there's a + + + align:start position:0% +damn dog what's going on here there's a +right there's a kind it's kind of risque + + align:start position:0% +right there's a kind it's kind of risque + + + align:start position:0% +right there's a kind it's kind of risque +in in remember we're talking about late + + align:start position:0% +in in remember we're talking about late + + + align:start position:0% +in in remember we're talking about late +Victorian post Victorian era what's the + + align:start position:0% +Victorian post Victorian era what's the + + + align:start position:0% +Victorian post Victorian era what's the +joke here it's the play on the word damn + + align:start position:0% +joke here it's the play on the word damn + + + align:start position:0% +joke here it's the play on the word damn +right it doesn't strike you as shocking + + align:start position:0% +right it doesn't strike you as shocking + + + align:start position:0% +right it doesn't strike you as shocking +but in fact you if you said damn you in + + align:start position:0% +but in fact you if you said damn you in + + + align:start position:0% +but in fact you if you said damn you in +1890 or in 1900 in certain quarters + + align:start position:0% +1890 or in 1900 in certain quarters + + + align:start position:0% +1890 or in 1900 in certain quarters +people step back and said oh my goodness + + align:start position:0% +people step back and said oh my goodness + + + align:start position:0% +people step back and said oh my goodness +there's a kind of semi vulgarity there + + align:start position:0% +there's a kind of semi vulgarity there + + + align:start position:0% +there's a kind of semi vulgarity there +in other words the fact that it's not an + + align:start position:0% +in other words the fact that it's not an + + + align:start position:0% +in other words the fact that it's not an +accident that that that this is not the + + align:start position:0% +accident that that that this is not the + + + align:start position:0% +accident that that that this is not the +thorburn family right uh or the Smith + + align:start position:0% +thorburn family right uh or the Smith + + + align:start position:0% +thorburn family right uh or the Smith +family it's significant that it's the + + align:start position:0% +family it's significant that it's the + + + align:start position:0% +family it's significant that it's the +damn family why because they want to + + align:start position:0% +damn family why because they want to + + + align:start position:0% +damn family why because they want to +make a joke what's wrong with the joke + + align:start position:0% +make a joke what's wrong with the joke + + + align:start position:0% +make a joke what's wrong with the joke +why is it a stupid joke for a movie + + align:start position:0% +why is it a stupid joke for a movie + + + align:start position:0% +why is it a stupid joke for a movie +because it's not a visual joke right + + align:start position:0% +because it's not a visual joke right + + + align:start position:0% +because it's not a visual joke right +what does it depend on it depends on + + align:start position:0% +what does it depend on it depends on + + + align:start position:0% +what does it depend on it depends on +language right it's almost as if the + + align:start position:0% +language right it's almost as if the + + + align:start position:0% +language right it's almost as if the +whole point of this film depends on a + + align:start position:0% +whole point of this film depends on a + + + align:start position:0% +whole point of this film depends on a +joke that depends not on anything that + + align:start position:0% +joke that depends not on anything that + + + align:start position:0% +joke that depends not on anything that +you could experience visually but that + + align:start position:0% +you could experience visually but that + + + align:start position:0% +you could experience visually but that +is resonant in in in in a verbal trick + + align:start position:0% +is resonant in in in in a verbal trick + + + align:start position:0% +is resonant in in in in a verbal trick +and it's a trivial joke it's not much of + + align:start position:0% +and it's a trivial joke it's not much of + + + align:start position:0% +and it's a trivial joke it's not much of +it's not much of a joke but the film + + align:start position:0% +it's not much of a joke but the film + + + align:start position:0% +it's not much of a joke but the film +depends upon it and it's it's evidence + + align:start position:0% +depends upon it and it's it's evidence + + + align:start position:0% +depends upon it and it's it's evidence +in a very modest and and but at the same + + align:start position:0% +in a very modest and and but at the same + + + align:start position:0% +in a very modest and and but at the same +time dramatic and obvious way of how + + align:start position:0% +time dramatic and obvious way of how + + + align:start position:0% +time dramatic and obvious way of how +long how of of this process whereby the + + align:start position:0% +long how of of this process whereby the + + + align:start position:0% +long how of of this process whereby the +new medium this new visual medium has to + + align:start position:0% +new medium this new visual medium has to + + + align:start position:0% +new medium this new visual medium has to +emerge out of uh media some of which are + + align:start position:0% +emerge out of uh media some of which are + + + align:start position:0% +emerge out of uh media some of which are +not visual at all but are verbal and the + + align:start position:0% +not visual at all but are verbal and the + + + align:start position:0% +not visual at all but are verbal and the +it's as if early filmmakers haven't yet + + align:start position:0% +it's as if early filmmakers haven't yet + + + align:start position:0% +it's as if early filmmakers haven't yet +learned fully how to exploit the + + align:start position:0% +learned fully how to exploit the + + + align:start position:0% +learned fully how to exploit the +qualities of the medium they're they're + + align:start position:0% +qualities of the medium they're they're + + + align:start position:0% +qualities of the medium they're they're +working in so it's a verbal joke rather + + align:start position:0% +working in so it's a verbal joke rather + + + align:start position:0% +working in so it's a verbal joke rather +than a visual joke + + align:start position:0% + + + + align:start position:0% + +um much more powerful and much more + + align:start position:0% +um much more powerful and much more + + + align:start position:0% +um much more powerful and much more +successful were the were the Keystone + + align:start position:0% +successful were the were the Keystone + + + align:start position:0% +successful were the were the Keystone +cop comedies themselves and I have we + + align:start position:0% +cop comedies themselves and I have we + + + align:start position:0% +cop comedies themselves and I have we +have one example of that to show you I'm + + align:start position:0% +have one example of that to show you I'm + + + align:start position:0% +have one example of that to show you I'm +not sure that this is a characteristic + + align:start position:0% +not sure that this is a characteristic + + + align:start position:0% +not sure that this is a characteristic +example but it's it uh it's close enough + + align:start position:0% +example but it's it uh it's close enough + + + align:start position:0% +example but it's it uh it's close enough +to give you a a sort of sense of what + + align:start position:0% +to give you a a sort of sense of what + + + align:start position:0% +to give you a a sort of sense of what +the Keystone comedies were like before + + align:start position:0% +the Keystone comedies were like before + + + align:start position:0% +the Keystone comedies were like before +chaplain entered the + + align:start position:0% + + + + align:start position:0% + +game the essential joke of the Keystone + + align:start position:0% +game the essential joke of the Keystone + + + align:start position:0% +game the essential joke of the Keystone +cops comedies there were I don't know + + align:start position:0% +cops comedies there were I don't know + + + align:start position:0% +cops comedies there were I don't know +even know how many there were perhaps + + align:start position:0% +even know how many there were perhaps + + + align:start position:0% +even know how many there were perhaps +hundreds there were certainly dozens and + + align:start position:0% +hundreds there were certainly dozens and + + + align:start position:0% +hundreds there were certainly dozens and +dozens they were immensely popular early + + align:start position:0% +dozens they were immensely popular early + + + align:start position:0% +dozens they were immensely popular early +short films uh some Scholars have film + + align:start position:0% +short films uh some Scholars have film + + + align:start position:0% +short films uh some Scholars have film +Scholars have speculated that one reason + + align:start position:0% +Scholars have speculated that one reason + + + align:start position:0% +Scholars have speculated that one reason +for their popularity was that they made + + align:start position:0% +for their popularity was that they made + + + align:start position:0% +for their popularity was that they made +fun of policeman that there was a an + + align:start position:0% +fun of policeman that there was a an + + + align:start position:0% +fun of policeman that there was a an +implicit sort of a mild Anar mildly + + align:start position:0% +implicit sort of a mild Anar mildly + + + align:start position:0% +implicit sort of a mild Anar mildly +anarchic impulse in these early comedies + + align:start position:0% +anarchic impulse in these early comedies + + + align:start position:0% +anarchic impulse in these early comedies +because authority figures people in + + align:start position:0% +because authority figures people in + + + align:start position:0% +because authority figures people in +uniform were being shown to be clownish + + align:start position:0% +uniform were being shown to be clownish + + + align:start position:0% +uniform were being shown to be clownish +in some way uh the primary element of + + align:start position:0% +in some way uh the primary element of + + + align:start position:0% +in some way uh the primary element of +course is to find ways to exploit the + + align:start position:0% +course is to find ways to exploit the + + + align:start position:0% +course is to find ways to exploit the +movie's capacity to show motion + + align:start position:0% + + + + align:start position:0% + +right and one reason I want you to see + + align:start position:0% +right and one reason I want you to see + + + align:start position:0% +right and one reason I want you to see +this relatively crude + + align:start position:0% +this relatively crude + + + align:start position:0% +this relatively crude +example is that there's a certain sense + + align:start position:0% +example is that there's a certain sense + + + align:start position:0% +example is that there's a certain sense +in which a short film you're going the + + align:start position:0% +in which a short film you're going the + + + align:start position:0% +in which a short film you're going the +short film that you saw last week from + + align:start position:0% +short film that you saw last week from + + + align:start position:0% +short film that you saw last week from +Katon the film cops is a sort of + + align:start position:0% +Katon the film cops is a sort of + + + align:start position:0% +Katon the film cops is a sort of +reprieve + + align:start position:0% +reprieve + + + align:start position:0% +reprieve +of this tradition of movie making + + align:start position:0% +of this tradition of movie making + + + align:start position:0% +of this tradition of movie making +although you can see how much more his + + align:start position:0% +although you can see how much more his + + + align:start position:0% +although you can see how much more his +short how much more coherent and + + align:start position:0% +short how much more coherent and + + + align:start position:0% +short how much more coherent and +character oriented chaplain Keaton's + + align:start position:0% +character oriented chaplain Keaton's + + + align:start position:0% +character oriented chaplain Keaton's +short film was but the way in which + + align:start position:0% +short film was but the way in which + + + align:start position:0% +short film was but the way in which +especially the cops are mocked and shown + + align:start position:0% +especially the cops are mocked and shown + + + align:start position:0% +especially the cops are mocked and shown +to be completely clownish figures almost + + align:start position:0% +to be completely clownish figures almost + + + align:start position:0% +to be completely clownish figures almost +all of the Keystone Cops comedies to my + + align:start position:0% +all of the Keystone Cops comedies to my + + + align:start position:0% +all of the Keystone Cops comedies to my +knowledge involved incompetent policemen + + align:start position:0% +knowledge involved incompetent policemen + + + align:start position:0% +knowledge involved incompetent policemen +who engaged in Mad active chases which + + align:start position:0% +who engaged in Mad active chases which + + + align:start position:0% +who engaged in Mad active chases which +often ended badly for the policemen + + align:start position:0% +often ended badly for the policemen + + + align:start position:0% +often ended badly for the policemen +sometimes they would end up all po + + align:start position:0% +sometimes they would end up all po + + + align:start position:0% +sometimes they would end up all po +flying into a river or an ocean or a or + + align:start position:0% +flying into a river or an ocean or a or + + + align:start position:0% +flying into a river or an ocean or a or +some other or some other natural uh + + align:start position:0% + + + + align:start position:0% + +disaster and I think you know you can + + align:start position:0% +disaster and I think you know you can + + + align:start position:0% +disaster and I think you know you can +also see I mean part I mean there are + + align:start position:0% +also see I mean part I mean there are + + + align:start position:0% +also see I mean part I mean there are +you know look at that that was actually + + align:start position:0% +you know look at that that was actually + + + align:start position:0% +you know look at that that was actually +very dramatic effect for an early film + + align:start position:0% +very dramatic effect for an early film + + + align:start position:0% +very dramatic effect for an early film +right uh so there's an awful there's an + + align:start position:0% +right uh so there's an awful there's an + + + align:start position:0% +right uh so there's an awful there's an +awful lot about this that would have + + align:start position:0% +awful lot about this that would have + + + align:start position:0% +awful lot about this that would have +interested early early seeing that car + + align:start position:0% +interested early early seeing that car + + + align:start position:0% +interested early early seeing that car +turn over some people in the audience + + align:start position:0% +turn over some people in the audience + + + align:start position:0% +turn over some people in the audience +might never have seen that in the in the + + align:start position:0% +might never have seen that in the in the + + + align:start position:0% +might never have seen that in the in the +movies + + align:start position:0% +movies + + + align:start position:0% +movies +before and one could say that these + + align:start position:0% +before and one could say that these + + + align:start position:0% +before and one could say that these +films in a certain way anticipate uh um + + align:start position:0% +films in a certain way anticipate uh um + + + align:start position:0% +films in a certain way anticipate uh um +a great deal of the ridiculous action + + align:start position:0% +a great deal of the ridiculous action + + + align:start position:0% +a great deal of the ridiculous action +adventure activity that we see in films + + align:start position:0% +adventure activity that we see in films + + + align:start position:0% +adventure activity that we see in films +even + + align:start position:0% +even + + + align:start position:0% +even +today + + align:start position:0% +today + + + align:start position:0% +today +uh but this is typical of those early + + align:start position:0% +uh but this is typical of those early + + + align:start position:0% +uh but this is typical of those early +films where they'll make where they'll + + align:start position:0% +films where they'll make where they'll + + + align:start position:0% +films where they'll make where they'll +make incredibly implausible jokes just + + align:start position:0% +make incredibly implausible jokes just + + + align:start position:0% +make incredibly implausible jokes just +for the sake of making the joke uh and + + align:start position:0% +for the sake of making the joke uh and + + + align:start position:0% +for the sake of making the joke uh and +I'm not sure I'm all right I'm maxent at + + align:start position:0% +I'm not sure I'm all right I'm maxent at + + + align:start position:0% +I'm not sure I'm all right I'm maxent at +comedy this is the kind of Comedy that + + align:start position:0% +comedy this is the kind of Comedy that + + + align:start position:0% +comedy this is the kind of Comedy that +was being made by the Senate studio uh + + align:start position:0% +was being made by the Senate studio uh + + + align:start position:0% +was being made by the Senate studio uh +before chaplain arrived there were also + + align:start position:0% +before chaplain arrived there were also + + + align:start position:0% +before chaplain arrived there were also +certain figures uh uh Fatty Arbuckle who + + align:start position:0% +certain figures uh uh Fatty Arbuckle who + + + align:start position:0% +certain figures uh uh Fatty Arbuckle who +went to who worked with the fat comedian + + align:start position:0% +went to who worked with the fat comedian + + + align:start position:0% +went to who worked with the fat comedian +who worked with Buster Keaton is an is + + align:start position:0% +who worked with Buster Keaton is an is + + + align:start position:0% +who worked with Buster Keaton is an is +an example who had already begun to + + align:start position:0% +an example who had already begun to + + + align:start position:0% +an example who had already begun to +establish comic personi something like + + align:start position:0% +establish comic personi something like + + + align:start position:0% +establish comic personi something like +the Persona that chaplain and Keaton + + align:start position:0% +the Persona that chaplain and Keaton + + + align:start position:0% +the Persona that chaplain and Keaton +created so they were not the first to do + + align:start position:0% +created so they were not the first to do + + + align:start position:0% +created so they were not the first to do +this and there was so there was a + + align:start position:0% +this and there was so there was a + + + align:start position:0% +this and there was so there was a +subtler and more already somewhat more + + align:start position:0% +subtler and more already somewhat more + + + align:start position:0% +subtler and more already somewhat more +character oriented comedy beginning to + + align:start position:0% +character oriented comedy beginning to + + + align:start position:0% +character oriented comedy beginning to +emerge before chaplain appears but + + align:start position:0% +emerge before chaplain appears but + + + align:start position:0% +emerge before chaplain appears but +chaplain's entry into American movies is + + align:start position:0% +chaplain's entry into American movies is + + + align:start position:0% +chaplain's entry into American movies is +also a turning point a fundamental + + align:start position:0% +also a turning point a fundamental + + + align:start position:0% +also a turning point a fundamental +Turning Point as many scholars have have + + align:start position:0% +Turning Point as many scholars have have + + + align:start position:0% +Turning Point as many scholars have have +recognized uh and and it's a turning + + align:start position:0% +recognized uh and and it's a turning + + + align:start position:0% +recognized uh and and it's a turning +point primarily because what chaplain + + align:start position:0% +point primarily because what chaplain + + + align:start position:0% +point primarily because what chaplain +introduces I mean introduces many many + + align:start position:0% +introduces I mean introduces many many + + + align:start position:0% +introduces I mean introduces many many +things to to Comedy but he introduces + + align:start position:0% +things to to Comedy but he introduces + + + align:start position:0% +things to to Comedy but he introduces +one thing + + align:start position:0% +one thing + + + align:start position:0% +one thing +especially or at least two things + + align:start position:0% +especially or at least two things + + + align:start position:0% +especially or at least two things +especially the first thing that he + + align:start position:0% +especially the first thing that he + + + align:start position:0% +especially the first thing that he +introduces is what we might call the + + align:start position:0% +introduces is what we might call the + + + align:start position:0% +introduces is what we might call the +principle of the Slowdown instead of + + align:start position:0% +principle of the Slowdown instead of + + + align:start position:0% +principle of the Slowdown instead of +frenzied motion all the time in chaplain + + align:start position:0% +frenzied motion all the time in chaplain + + + align:start position:0% +frenzied motion all the time in chaplain +comedies their moments of quiet and in + + align:start position:0% +comedies their moments of quiet and in + + + align:start position:0% +comedies their moments of quiet and in +these moments of quiet and this is why + + align:start position:0% +these moments of quiet and this is why + + + align:start position:0% +these moments of quiet and this is why +they're important what begins to happen + + align:start position:0% +they're important what begins to happen + + + align:start position:0% +they're important what begins to happen +is an attention is thrown away from + + align:start position:0% +is an attention is thrown away from + + + align:start position:0% +is an attention is thrown away from +violent frenzied physical action toward + + align:start position:0% +violent frenzied physical action toward + + + align:start position:0% +violent frenzied physical action toward +character what chaplain introduces into + + align:start position:0% +character what chaplain introduces into + + + align:start position:0% +character what chaplain introduces into +movies is an in is a is a a somewhat + + align:start position:0% +movies is an in is a is a a somewhat + + + align:start position:0% +movies is an in is a is a a somewhat +more systematic and serious interesting + + align:start position:0% +more systematic and serious interesting + + + align:start position:0% +more systematic and serious interesting +character than had ever occurred before + + align:start position:0% +character than had ever occurred before + + + align:start position:0% +character than had ever occurred before +and what follows from that introduction + + align:start position:0% +and what follows from that introduction + + + align:start position:0% +and what follows from that introduction +from slowing down the action creating + + align:start position:0% +from slowing down the action creating + + + align:start position:0% +from slowing down the action creating +moments of human interaction in which in + + align:start position:0% +moments of human interaction in which in + + + align:start position:0% +moments of human interaction in which in +which the interest is essentially + + align:start position:0% +which the interest is essentially + + + align:start position:0% +which the interest is essentially +psychological and individual rather than + + align:start position:0% +psychological and individual rather than + + + align:start position:0% +psychological and individual rather than +an interest simply in frenzied motion + + align:start position:0% +an interest simply in frenzied motion + + + align:start position:0% +an interest simply in frenzied motion +and jokes and or or frenzied motion and + + align:start position:0% +and jokes and or or frenzied motion and + + + align:start position:0% +and jokes and or or frenzied motion and +suspense which is what you would get + + align:start position:0% +suspense which is what you would get + + + align:start position:0% +suspense which is what you would get +from a Griffith melodrama what you're + + align:start position:0% +from a Griffith melodrama what you're + + + align:start position:0% +from a Griffith melodrama what you're +getting is a so this introduces several + + align:start position:0% +getting is a so this introduces several + + + align:start position:0% +getting is a so this introduces several +things first of all it introduces a + + align:start position:0% +things first of all it introduces a + + + align:start position:0% +things first of all it introduces a +tonal variation it means that in the + + align:start position:0% +tonal variation it means that in the + + + align:start position:0% +tonal variation it means that in the +middle of comedies there could be quiet + + align:start position:0% +middle of comedies there could be quiet + + + align:start position:0% +middle of comedies there could be quiet +serious moments and in fact it becomes + + align:start position:0% +serious moments and in fact it becomes + + + align:start position:0% +serious moments and in fact it becomes +the Hallmark of chaplain's Comedy that + + align:start position:0% +the Hallmark of chaplain's Comedy that + + + align:start position:0% +the Hallmark of chaplain's Comedy that +it really is often not funny or at least + + align:start position:0% +it really is often not funny or at least + + + align:start position:0% +it really is often not funny or at least +that it's based on unfunny materials and + + align:start position:0% +that it's based on unfunny materials and + + + align:start position:0% +that it's based on unfunny materials and +that there are poor poent and moving + + align:start position:0% +that there are poor poent and moving + + + align:start position:0% +that there are poor poent and moving +moments it's it's as if chaplain + + align:start position:0% +moments it's it's as if chaplain + + + align:start position:0% +moments it's it's as if chaplain +combines comic and melodramatic elements + + align:start position:0% +combines comic and melodramatic elements + + + align:start position:0% +combines comic and melodramatic elements +especially in his best in his best work + + align:start position:0% +especially in his best in his best work + + + align:start position:0% +especially in his best in his best work +I don't mean that when he came into the + + align:start position:0% +I don't mean that when he came into the + + + align:start position:0% +I don't mean that when he came into the +films he began to do this in fact he + + align:start position:0% +films he began to do this in fact he + + + align:start position:0% +films he began to do this in fact he +discovered how to do this in the course + + align:start position:0% +discovered how to do this in the course + + + align:start position:0% +discovered how to do this in the course +of his uh in the course of his career + + align:start position:0% +of his uh in the course of his career + + + align:start position:0% +of his uh in the course of his career +about which I will speak in a moment so + + align:start position:0% +about which I will speak in a moment so + + + align:start position:0% +about which I will speak in a moment so +chaplain brings an a new interest in in + + align:start position:0% +chaplain brings an a new interest in in + + + align:start position:0% +chaplain brings an a new interest in in +in uh character and in psychological + + align:start position:0% +in uh character and in psychological + + + align:start position:0% +in uh character and in psychological +nuance and because of that introduces + + align:start position:0% +nuance and because of that introduces + + + align:start position:0% +nuance and because of that introduces +tonal + + align:start position:0% +tonal + + + align:start position:0% +tonal +variation a complexity of tone we think + + align:start position:0% +variation a complexity of tone we think + + + align:start position:0% +variation a complexity of tone we think +of the figure as as indelible and + + align:start position:0% +of the figure as as indelible and + + + align:start position:0% +of the figure as as indelible and +uh uh unchanging in a certain way his + + align:start position:0% +uh uh unchanging in a certain way his + + + align:start position:0% +uh uh unchanging in a certain way his +costume always the same his face always + + align:start position:0% +costume always the same his face always + + + align:start position:0% +costume always the same his face always +the same the kinds of problems he gets + + align:start position:0% +the same the kinds of problems he gets + + + align:start position:0% +the same the kinds of problems he gets +into always similar and that's partly + + align:start position:0% +into always similar and that's partly + + + align:start position:0% +into always similar and that's partly +true but the was not born fully + + align:start position:0% +true but the was not born fully + + + align:start position:0% +true but the was not born fully +fully dressed in chaplain's brain uh he + + align:start position:0% +fully dressed in chaplain's brain uh he + + + align:start position:0% +fully dressed in chaplain's brain uh he +he he evolved the champ over a series of + + align:start position:0% +he he evolved the champ over a series of + + + align:start position:0% +he he evolved the champ over a series of +over a series of short films uh in the + + align:start position:0% +over a series of short films uh in the + + + align:start position:0% +over a series of short films uh in the +in the uh in the period from 1911 + + align:start position:0% +in the uh in the period from 1911 + + + align:start position:0% +in the uh in the period from 1911 +through about 194 13 or 14 and one way I + + align:start position:0% +through about 194 13 or 14 and one way I + + + align:start position:0% +through about 194 13 or 14 and one way I +can dramatize this for you was to show + + align:start position:0% +can dramatize this for you was to show + + + align:start position:0% +can dramatize this for you was to show +you how Charlie looked in the very first + + align:start position:0% +you how Charlie looked in the very first + + + align:start position:0% +you how Charlie looked in the very first +film he appeared in he was not an actor + + align:start position:0% +film he appeared in he was not an actor + + + align:start position:0% +film he appeared in he was not an actor +he was not a director in this film he + + align:start position:0% +he was not a director in this film he + + + align:start position:0% +he was not a director in this film he +was just an actor and he was a walk-on + + align:start position:0% +was just an actor and he was a walk-on + + + align:start position:0% +was just an actor and he was a walk-on +actor he was not the star the camera had + + align:start position:0% +actor he was not the star the camera had + + + align:start position:0% +actor he was not the star the camera had +an immediate affinity for him and after + + align:start position:0% +an immediate affinity for him and after + + + align:start position:0% +an immediate affinity for him and after +people saw this film the first film he + + align:start position:0% +people saw this film the first film he + + + align:start position:0% +people saw this film the first film he +appeared in this a still from a film + + align:start position:0% +appeared in this a still from a film + + + align:start position:0% +appeared in this a still from a film +called kid Auto races at Venice it's a + + align:start position:0% +called kid Auto races at Venice it's a + + + align:start position:0% +called kid Auto races at Venice it's a +kind of documentary about soapbox racing + + align:start position:0% +kind of documentary about soapbox racing + + + align:start position:0% +kind of documentary about soapbox racing +and chaplain the chaplain character had + + align:start position:0% +and chaplain the chaplain character had + + + align:start position:0% +and chaplain the chaplain character had +just been hired by Max senet uh to join + + align:start position:0% +just been hired by Max senet uh to join + + + align:start position:0% +just been hired by Max senet uh to join +this Keystone Studios and he made an + + align:start position:0% +this Keystone Studios and he made an + + + align:start position:0% +this Keystone Studios and he made an +appearance in the film he really didn't + + align:start position:0% +appearance in the film he really didn't + + + align:start position:0% +appearance in the film he really didn't +have anything to do but his appearance + + align:start position:0% +have anything to do but his appearance + + + align:start position:0% +have anything to do but his appearance +in the film caused all kinds of interest + + align:start position:0% +in the film caused all kinds of interest + + + align:start position:0% +in the film caused all kinds of interest +but uh in the a the audience wanted to + + align:start position:0% +but uh in the a the audience wanted to + + + align:start position:0% +but uh in the a the audience wanted to +know who that character was why he was + + align:start position:0% +know who that character was why he was + + + align:start position:0% +know who that character was why he was +so interesting and what was interesting + + align:start position:0% +so interesting and what was interesting + + + align:start position:0% +so interesting and what was interesting +about him you can see the the the + + align:start position:0% +about him you can see the the the + + + align:start position:0% +about him you can see the the the +beginnings of the U uh costume + + align:start position:0% +beginnings of the U uh costume + + + align:start position:0% +beginnings of the U uh costume +there but not not not the complete + + align:start position:0% +there but not not not the complete + + + align:start position:0% +there but not not not the complete +here's another early version of chaplain + + align:start position:0% +here's another early version of chaplain + + + align:start position:0% +here's another early version of chaplain +with his Co wearing a long coat and not + + align:start position:0% +with his Co wearing a long coat and not + + + align:start position:0% +with his Co wearing a long coat and not +looking not looking very nice uh this is + + align:start position:0% +looking not looking very nice uh this is + + + align:start position:0% +looking not looking very nice uh this is +um uh uh Charlie is supposed to be drunk + + align:start position:0% +um uh uh Charlie is supposed to be drunk + + + align:start position:0% +um uh uh Charlie is supposed to be drunk +in this picture that's one reason he + + align:start position:0% +in this picture that's one reason he + + + align:start position:0% +in this picture that's one reason he +looks nasty uh and he's it's in a film + + align:start position:0% +looks nasty uh and he's it's in a film + + + align:start position:0% +looks nasty uh and he's it's in a film +called Mabel's married life and uh uh uh + + align:start position:0% +called Mabel's married life and uh uh uh + + + align:start position:0% +called Mabel's married life and uh uh uh +he's he's um he's actually in + + align:start position:0% +he's he's um he's actually in + + + align:start position:0% +he's he's um he's actually in +conversation with a dummy in this in + + align:start position:0% +conversation with a dummy in this in + + + align:start position:0% +conversation with a dummy in this in +this sequence uh but you can see here + + align:start position:0% +this sequence uh but you can see here + + + align:start position:0% +this sequence uh but you can see here +that that the long Cod violates our idea + + align:start position:0% +that that the long Cod violates our idea + + + align:start position:0% +that that the long Cod violates our idea +of who the was and so it took a + + align:start position:0% +of who the was and so it took a + + + align:start position:0% +of who the was and so it took a +while before the + + align:start position:0% +while before the + + + align:start position:0% +while before the +chaplain Persona completely emerged and + + align:start position:0% +chaplain Persona completely emerged and + + + align:start position:0% +chaplain Persona completely emerged and +it was partly a a matter of trial and + + align:start position:0% +it was partly a a matter of trial and + + + align:start position:0% +it was partly a a matter of trial and +error although very quick trial and + + align:start position:0% +error although very quick trial and + + + align:start position:0% +error although very quick trial and +trial and error well I want to say a + + align:start position:0% +trial and error well I want to say a + + + align:start position:0% +trial and error well I want to say a +word about chaplain's career to give you + + align:start position:0% +word about chaplain's career to give you + + + align:start position:0% +word about chaplain's career to give you +a fuller sense of of how swiftly he + + align:start position:0% +a fuller sense of of how swiftly he + + + align:start position:0% +a fuller sense of of how swiftly he +became an icon and how significant his + + align:start position:0% +became an icon and how significant his + + + align:start position:0% +became an icon and how significant his +example is for our understanding of the + + align:start position:0% +example is for our understanding of the + + + align:start position:0% +example is for our understanding of the +power of movies chaplain's dates are + + align:start position:0% +power of movies chaplain's dates are + + + align:start position:0% +power of movies chaplain's dates are +1889 to + + align:start position:0% +1889 to + + + align:start position:0% +1889 to +1977 uh he and his early child he was + + align:start position:0% +1977 uh he and his early child he was + + + align:start position:0% +1977 uh he and his early child he was +born in England and and his his early + + align:start position:0% +born in England and and his his early + + + align:start position:0% +born in England and and his his early +childhood is actually the stuff of diin + + align:start position:0% +childhood is actually the stuff of diin + + + align:start position:0% +childhood is actually the stuff of diin +and melodrama uh both terms I + + align:start position:0% +and melodrama uh both terms I + + + align:start position:0% +and melodrama uh both terms I +chose with some intentionality because + + align:start position:0% +chose with some intentionality because + + + align:start position:0% +chose with some intentionality because +uh there are parallels between uh + + align:start position:0% +uh there are parallels between uh + + + align:start position:0% +uh there are parallels between uh +Charlie chaplain's early life and the + + align:start position:0% +Charlie chaplain's early life and the + + + align:start position:0% +Charlie chaplain's early life and the +victimization that that Dickens + + align:start position:0% +victimization that that Dickens + + + align:start position:0% +victimization that that Dickens +dramatizes so powerfully in many of his + + align:start position:0% +dramatizes so powerfully in many of his + + + align:start position:0% +dramatizes so powerfully in many of his +uh famous novels and there are parallels + + align:start position:0% +uh famous novels and there are parallels + + + align:start position:0% +uh famous novels and there are parallels +between dickens's own childhood and + + align:start position:0% +between dickens's own childhood and + + + align:start position:0% +between dickens's own childhood and +chaplain's childhood Dickens the great + + align:start position:0% +chaplain's childhood Dickens the great + + + align:start position:0% +chaplain's childhood Dickens the great +19th century novelist who like chaplain + + align:start position:0% +19th century novelist who like chaplain + + + align:start position:0% +19th century novelist who like chaplain +was interested in victims Lay Laid + + align:start position:0% +was interested in victims Lay Laid + + + align:start position:0% +was interested in victims Lay Laid +emphasis on the the problems of of of + + align:start position:0% +emphasis on the the problems of of of + + + align:start position:0% +emphasis on the the problems of of of +vulnerable people of women of children + + align:start position:0% +vulnerable people of women of children + + + align:start position:0% +vulnerable people of women of children +who wrote variations on what we might + + align:start position:0% +who wrote variations on what we might + + + align:start position:0% +who wrote variations on what we might +call the mortgage melodrama all his + + align:start position:0% +call the mortgage melodrama all his + + + align:start position:0% +call the mortgage melodrama all his +career his greatest works could be said + + align:start position:0% +career his greatest works could be said + + + align:start position:0% +career his greatest works could be said +to be forms of melodrama I'm talking + + align:start position:0% +to be forms of melodrama I'm talking + + + align:start position:0% +to be forms of melodrama I'm talking +about Charles Dickens the great 19th + + align:start position:0% +about Charles Dickens the great 19th + + + align:start position:0% +about Charles Dickens the great 19th +century English novelist and chaplain + + align:start position:0% +century English novelist and chaplain + + + align:start position:0% +century English novelist and chaplain +grew up in an environment that was + + align:start position:0% +grew up in an environment that was + + + align:start position:0% +grew up in an environment that was +steeped not only in Dickens but in the + + align:start position:0% +steeped not only in Dickens but in the + + + align:start position:0% +steeped not only in Dickens but in the +traditions of stage and novelistic + + align:start position:0% +traditions of stage and novelistic + + + align:start position:0% +traditions of stage and novelistic +melodrama that permeated European + + align:start position:0% +melodrama that permeated European + + + align:start position:0% +melodrama that permeated European +culture and especially English culture + + align:start position:0% +culture and especially English culture + + + align:start position:0% +culture and especially English culture +of this time uh but his but his wife was + + align:start position:0% +of this time uh but his but his wife was + + + align:start position:0% +of this time uh but his but his wife was +a very was a very difficult one in some + + align:start position:0% +a very was a very difficult one in some + + + align:start position:0% +a very was a very difficult one in some +ways as well uh his his father died when + + align:start position:0% +ways as well uh his his father died when + + + align:start position:0% +ways as well uh his his father died when +he was eight uh his mother was in and + + align:start position:0% +he was eight uh his mother was in and + + + align:start position:0% +he was eight uh his mother was in and +out of Institutions uh Mo all of her + + align:start position:0% +out of Institutions uh Mo all of her + + + align:start position:0% +out of Institutions uh Mo all of her +life there were periods in chaplain's + + align:start position:0% +life there were periods in chaplain's + + + align:start position:0% +life there were periods in chaplain's +life when he was just a little child + + align:start position:0% +life when he was just a little child + + + align:start position:0% +life when he was just a little child +when he was literally completely + + align:start position:0% +when he was literally completely + + + align:start position:0% +when he was literally completely +abandoned and he and his older brother + + align:start position:0% +abandoned and he and his older brother + + + align:start position:0% +abandoned and he and his older brother +spent time living in doorways in the + + align:start position:0% +spent time living in doorways in the + + + align:start position:0% +spent time living in doorways in the +Streets of London he was literally a + + align:start position:0% +Streets of London he was literally a + + + align:start position:0% +Streets of London he was literally a +homeless urchin as a child he he began + + align:start position:0% +homeless urchin as a child he he began + + + align:start position:0% +homeless urchin as a child he he began +to act on the stage from the age of + + align:start position:0% +to act on the stage from the age of + + + align:start position:0% +to act on the stage from the age of +seven uh and almost immediately was + + align:start position:0% +seven uh and almost immediately was + + + align:start position:0% +seven uh and almost immediately was +recognized as having uh astonishing + + align:start position:0% +recognized as having uh astonishing + + + align:start position:0% +recognized as having uh astonishing +astonishing gifts he worked from 1906 + + align:start position:0% +astonishing gifts he worked from 1906 + + + align:start position:0% +astonishing gifts he worked from 1906 +through 1913 for a theatrical company in + + align:start position:0% +through 1913 for a theatrical company in + + + align:start position:0% +through 1913 for a theatrical company in +England called the Carno company k a r n + + align:start position:0% +England called the Carno company k a r n + + + align:start position:0% +England called the Carno company k a r n +o and it was a company that put + + align:start position:0% +o and it was a company that put + + + align:start position:0% +o and it was a company that put +on a certain kind of the a certain kind + + align:start position:0% +on a certain kind of the a certain kind + + + align:start position:0% +on a certain kind of the a certain kind +of theatrical Anthology in which there + + align:start position:0% +of theatrical Anthology in which there + + + align:start position:0% +of theatrical Anthology in which there +would be skits comic skits and serious + + align:start position:0% +would be skits comic skits and serious + + + align:start position:0% +would be skits comic skits and serious +skits acted out sometimes uh uh uh when + + align:start position:0% +skits acted out sometimes uh uh uh when + + + align:start position:0% +skits acted out sometimes uh uh uh when +the skits were over people would come + + align:start position:0% +the skits were over people would come + + + align:start position:0% +the skits were over people would come +and do s there would be song and dance + + align:start position:0% +and do s there would be song and dance + + + align:start position:0% +and do s there would be song and dance +numbers uh + + align:start position:0% +numbers uh + + + align:start position:0% +numbers uh +uh sometimes just straight singing it + + align:start position:0% +uh sometimes just straight singing it + + + align:start position:0% +uh sometimes just straight singing it +was a kind a kind of British variety + + align:start position:0% +was a kind a kind of British variety + + + align:start position:0% +was a kind a kind of British variety +show influenced especially by the + + align:start position:0% +show influenced especially by the + + + align:start position:0% +show influenced especially by the +traditions of the British Music Hall and + + align:start position:0% +traditions of the British Music Hall and + + + align:start position:0% +traditions of the British Music Hall and +the Carno company was a traveling + + align:start position:0% +the Carno company was a traveling + + + align:start position:0% +the Carno company was a traveling +company first chaplain worked with the + + align:start position:0% +company first chaplain worked with the + + + align:start position:0% +company first chaplain worked with the +company all around the British aisles + + align:start position:0% +company all around the British aisles + + + align:start position:0% +company all around the British aisles +and then in I think 1909 or 1910 the + + align:start position:0% +and then in I think 1909 or 1910 the + + + align:start position:0% +and then in I think 1909 or 1910 the +Carno company made a triumphant tour of + + align:start position:0% +Carno company made a triumphant tour of + + + align:start position:0% +Carno company made a triumphant tour of +the United States by this time chaplain + + align:start position:0% +the United States by this time chaplain + + + align:start position:0% +the United States by this time chaplain +was one of the leading actors in the in + + align:start position:0% +was one of the leading actors in the in + + + align:start position:0% +was one of the leading actors in the in +the one of the great U uh uh features of + + align:start position:0% +the one of the great U uh uh features of + + + align:start position:0% +the one of the great U uh uh features of +the Carno company performances were + + align:start position:0% +the Carno company performances were + + + align:start position:0% +the Carno company performances were +pantomim performan and chaplain was a + + align:start position:0% +pantomim performan and chaplain was a + + + align:start position:0% +pantomim performan and chaplain was a +particularly brilliant pantomimist uh so + + align:start position:0% +particularly brilliant pantomimist uh so + + + align:start position:0% +particularly brilliant pantomimist uh so +that and so he had a very significant + + align:start position:0% +that and so he had a very significant + + + align:start position:0% +that and so he had a very significant +career he was already a successful + + align:start position:0% +career he was already a successful + + + align:start position:0% +career he was already a successful +performer on the stage in the Carno + + align:start position:0% +performer on the stage in the Carno + + + align:start position:0% +performer on the stage in the Carno +company and and and uh uh Drew on + + align:start position:0% +company and and and uh uh Drew on + + + align:start position:0% +company and and and uh uh Drew on +traditions of perform his father had + + align:start position:0% +traditions of perform his father had + + + align:start position:0% +traditions of perform his father had +been a chaplain's father was a popular + + align:start position:0% +been a chaplain's father was a popular + + + align:start position:0% +been a chaplain's father was a popular +singer who actually songs were published + + align:start position:0% +singer who actually songs were published + + + align:start position:0% +singer who actually songs were published +and he he sang in the musicals for for a + + align:start position:0% +and he he sang in the musicals for for a + + + align:start position:0% +and he he sang in the musicals for for a +certain period uh uh and chaplain's + + align:start position:0% +certain period uh uh and chaplain's + + + align:start position:0% +certain period uh uh and chaplain's +mother had Visions or fantasies of being + + align:start position:0% +mother had Visions or fantasies of being + + + align:start position:0% +mother had Visions or fantasies of being +a performer herself and used to perform + + align:start position:0% +a performer herself and used to perform + + + align:start position:0% +a performer herself and used to perform +in private lead to Charlie so Charlie + + align:start position:0% +in private lead to Charlie so Charlie + + + align:start position:0% +in private lead to Charlie so Charlie +come Charlie was steeped in performance + + align:start position:0% +come Charlie was steeped in performance + + + align:start position:0% +come Charlie was steeped in performance +steeped in theater and as a young boy + + align:start position:0% +steeped in theater and as a young boy + + + align:start position:0% +steeped in theater and as a young boy +from the age of seven on was already + + align:start position:0% +from the age of seven on was already + + + align:start position:0% +from the age of seven on was already +sort of acting on stage almost + + align:start position:0% +sort of acting on stage almost + + + align:start position:0% +sort of acting on stage almost +continuously after the age of eight or + + align:start position:0% +continuously after the age of eight or + + + align:start position:0% +continuously after the age of eight or +nine made his living as an made his + + align:start position:0% +nine made his living as an made his + + + align:start position:0% +nine made his living as an made his +living as an actor so as a relatively + + align:start position:0% +living as an actor so as a relatively + + + align:start position:0% +living as an actor so as a relatively +young man uh he he uh uh made a trip to + + align:start position:0% +young man uh he he uh uh made a trip to + + + align:start position:0% +young man uh he he uh uh made a trip to +the United States with the Caro company + + align:start position:0% +the United States with the Caro company + + + align:start position:0% +the United States with the Caro company +the Caro company toured various cities + + align:start position:0% +the Caro company toured various cities + + + align:start position:0% +the Caro company toured various cities +in the United States was a great success + + align:start position:0% +in the United States was a great success + + + align:start position:0% +in the United States was a great success +a second tour almost immediately + + align:start position:0% +a second tour almost immediately + + + align:start position:0% +a second tour almost immediately +followed I think you know within six + + align:start position:0% +followed I think you know within six + + + align:start position:0% +followed I think you know within six +months and on that second tour Max + + align:start position:0% +months and on that second tour Max + + + align:start position:0% +months and on that second tour Max +Senate saw Chaplan perform and went and + + align:start position:0% +Senate saw Chaplan perform and went and + + + align:start position:0% +Senate saw Chaplan perform and went and +hired him away from the Carno company we + + align:start position:0% +hired him away from the Carno company we + + + align:start position:0% +hired him away from the Carno company we +saw that Chaplan had certain gifts as a + + align:start position:0% +saw that Chaplan had certain gifts as a + + + align:start position:0% +saw that Chaplan had certain gifts as a +performer that would work in the infant + + align:start position:0% +performer that would work in the infant + + + align:start position:0% +performer that would work in the infant +medium of the movies and hired him away + + align:start position:0% +medium of the movies and hired him away + + + align:start position:0% +medium of the movies and hired him away +and it was an inspired decision uh when + + align:start position:0% +and it was an inspired decision uh when + + + align:start position:0% +and it was an inspired decision uh when +chaplain first joined the Keystone uh + + align:start position:0% +chaplain first joined the Keystone uh + + + align:start position:0% +chaplain first joined the Keystone uh +Studios uh in 19 I think it's 1911 the + + align:start position:0% +Studios uh in 19 I think it's 1911 the + + + align:start position:0% +Studios uh in 19 I think it's 1911 the +date is in cook so be careful of my my + + align:start position:0% +date is in cook so be careful of my my + + + align:start position:0% +date is in cook so be careful of my my +my date maybe a year or two off um but + + align:start position:0% +my date maybe a year or two off um but + + + align:start position:0% +my date maybe a year or two off um but +around 1911 he joins the Carno company + + align:start position:0% +around 1911 he joins the Carno company + + + align:start position:0% +around 1911 he joins the Carno company +his first few films his first three or + + align:start position:0% +his first few films his first three or + + + align:start position:0% +his first few films his first three or +four films he's just a performer in but + + align:start position:0% +four films he's just a performer in but + + + align:start position:0% +four films he's just a performer in but +he has an immediate affinity for the + + align:start position:0% +he has an immediate affinity for the + + + align:start position:0% +he has an immediate affinity for the +camera as well and within half a dozen + + align:start position:0% +camera as well and within half a dozen + + + align:start position:0% +camera as well and within half a dozen +films he's already beginning to direct + + align:start position:0% +films he's already beginning to direct + + + align:start position:0% +films he's already beginning to direct +as well as to act and within a + + align:start position:0% +as well as to act and within a + + + align:start position:0% +as well as to act and within a +relatively short time he's in control of + + align:start position:0% +relatively short time he's in control of + + + align:start position:0% +relatively short time he's in control of +every he's he become he gets to be in + + align:start position:0% +every he's he become he gets to be in + + + align:start position:0% +every he's he become he gets to be in +control of every every aspect of the + + align:start position:0% +control of every every aspect of the + + + align:start position:0% +control of every every aspect of the +making of film we can of the making of + + align:start position:0% +making of film we can of the making of + + + align:start position:0% +making of film we can of the making of +his films we can get some sense of how + + align:start position:0% +his films we can get some sense of how + + + align:start position:0% +his films we can get some sense of how +uh richly and symbiotically the audience + + align:start position:0% +uh richly and symbiotically the audience + + + align:start position:0% +uh richly and symbiotically the audience +reacted to the the the character of the + + align:start position:0% +reacted to the the the character of the + + + align:start position:0% +reacted to the the the character of the + that uh chaplain created by + + align:start position:0% + that uh chaplain created by + + + align:start position:0% + that uh chaplain created by +talking in monetary terms about and uh + + align:start position:0% +talking in monetary terms about and uh + + + align:start position:0% +talking in monetary terms about and uh +in monetary terms about the development + + align:start position:0% +in monetary terms about the development + + + align:start position:0% +in monetary terms about the development +of his career about the progress of his + + align:start position:0% +of his career about the progress of his + + + align:start position:0% +of his career about the progress of his +career he joined officially joined the + + align:start position:0% +career he joined officially joined the + + + align:start position:0% +career he joined officially joined the +Keystone company uh in 1914 uh he was + + align:start position:0% +Keystone company uh in 1914 uh he was + + + align:start position:0% +Keystone company uh in 1914 uh he was +hired in 1911 1912 came over to the + + align:start position:0% +hired in 1911 1912 came over to the + + + align:start position:0% +hired in 1911 1912 came over to the +United States and from 1914 and 1915 he + + align:start position:0% +United States and from 1914 and 1915 he + + + align:start position:0% +United States and from 1914 and 1915 he +just that one year he worked for the + + align:start position:0% +just that one year he worked for the + + + align:start position:0% +just that one year he worked for the +Keystone company and made 35 films uh in + + align:start position:0% +Keystone company and made 35 films uh in + + + align:start position:0% +Keystone company and made 35 films uh in +that oneyear period he received what was + + align:start position:0% +that oneyear period he received what was + + + align:start position:0% +that oneyear period he received what was +was then a princely salary of $150 a + + align:start position:0% +was then a princely salary of $150 a + + + align:start position:0% +was then a princely salary of $150 a +week the the final films of those 35 the + + align:start position:0% +week the the final films of those 35 the + + + align:start position:0% +week the the final films of those 35 the +last 15 or 20 or so of them featured the + + align:start position:0% +last 15 or 20 or so of them featured the + + + align:start position:0% +last 15 or 20 or so of them featured the +tram figure who had now been fully + + align:start position:0% +tram figure who had now been fully + + + align:start position:0% +tram figure who had now been fully +elaborated in various Adventures that + + align:start position:0% +elaborated in various Adventures that + + + align:start position:0% +elaborated in various Adventures that +became characteristic of chaplain's + + align:start position:0% +became characteristic of chaplain's + + + align:start position:0% +became characteristic of chaplain's +vision of the and they were + + align:start position:0% +vision of the and they were + + + align:start position:0% +vision of the and they were +unbelievably Popular by far the most + + align:start position:0% +unbelievably Popular by far the most + + + align:start position:0% +unbelievably Popular by far the most +popular shorts that had ever been sent + + align:start position:0% +popular shorts that had ever been sent + + + align:start position:0% +popular shorts that had ever been sent +out of any movie production company uh + + align:start position:0% +out of any movie production company uh + + + align:start position:0% +out of any movie production company uh +and they made chaplain a household name + + align:start position:0% +and they made chaplain a household name + + + align:start position:0% +and they made chaplain a household name +first in the United States and then + + align:start position:0% +first in the United States and then + + + align:start position:0% +first in the United States and then +fairly quickly all over the world so so + + align:start position:0% +fairly quickly all over the world so so + + + align:start position:0% +fairly quickly all over the world so so +successful were those early films that + + align:start position:0% +successful were those early films that + + + align:start position:0% +successful were those early films that +in 1915 he was hired Away by another + + align:start position:0% +in 1915 he was hired Away by another + + + align:start position:0% +in 1915 he was hired Away by another +company the sna company ESS n a y and + + align:start position:0% +company the sna company ESS n a y and + + + align:start position:0% +company the sna company ESS n a y and +for another year 1915 1916 he worked + + align:start position:0% +for another year 1915 1916 he worked + + + align:start position:0% +for another year 1915 1916 he worked +just for the sna company but his salary + + align:start position:0% +just for the sna company but his salary + + + align:start position:0% +just for the sna company but his salary +went up from $150 a week to + + align:start position:0% +went up from $150 a week to + + + align:start position:0% +went up from $150 a week to +$1,250 a week in one year and that's a + + align:start position:0% +$1,250 a week in one year and that's a + + + align:start position:0% +$1,250 a week in one year and that's a +gigant a thousand more than $1,000 a + + align:start position:0% +gigant a thousand more than $1,000 a + + + align:start position:0% +gigant a thousand more than $1,000 a +week in in uh 1915 is a is an + + align:start position:0% +week in in uh 1915 is a is an + + + align:start position:0% +week in in uh 1915 is a is an +unbelievable Fortune of course + + align:start position:0% +unbelievable Fortune of course + + + align:start position:0% +unbelievable Fortune of course +he makes only 14 films in that period so + + align:start position:0% +he makes only 14 films in that period so + + + align:start position:0% +he makes only 14 films in that period so +he goes from making 35 films in a year + + align:start position:0% +he goes from making 35 films in a year + + + align:start position:0% +he goes from making 35 films in a year +to making only 14 films and those 14 + + align:start position:0% +to making only 14 films and those 14 + + + align:start position:0% +to making only 14 films and those 14 +films are more highly finished he spends + + align:start position:0% +films are more highly finished he spends + + + align:start position:0% +films are more highly finished he spends +more time with them we can see in this + + align:start position:0% +more time with them we can see in this + + + align:start position:0% +more time with them we can see in this +period we can see chaplain learning we + + align:start position:0% +period we can see chaplain learning we + + + align:start position:0% +period we can see chaplain learning we +can see chaplain enacting in small the + + align:start position:0% +can see chaplain enacting in small the + + + align:start position:0% +can see chaplain enacting in small the +the fedot principle we can see Chaplan + + align:start position:0% +the fedot principle we can see Chaplan + + + align:start position:0% +the fedot principle we can see Chaplan +enacting in small the principle I talked + + align:start position:0% +enacting in small the principle I talked + + + align:start position:0% +enacting in small the principle I talked +about last week in which we see him + + align:start position:0% +about last week in which we see him + + + align:start position:0% +about last week in which we see him +learning uh to to develop performance + + align:start position:0% +learning uh to to develop performance + + + align:start position:0% +learning uh to to develop performance +styles that are appropriate to the + + align:start position:0% +styles that are appropriate to the + + + align:start position:0% +styles that are appropriate to the +camera appropriate to the to the to to + + align:start position:0% +camera appropriate to the to the to to + + + align:start position:0% +camera appropriate to the to the to to +to to cinematic experience uh developing + + align:start position:0% +to to cinematic experience uh developing + + + align:start position:0% +to to cinematic experience uh developing +de developing uh techniques as a + + align:start position:0% +de developing uh techniques as a + + + align:start position:0% +de developing uh techniques as a +director to emphasize certain aspects of + + align:start position:0% +director to emphasize certain aspects of + + + align:start position:0% +director to emphasize certain aspects of +the tra's character uh uh uh + + align:start position:0% +the tra's character uh uh uh + + + align:start position:0% +the tra's character uh uh uh +experimenting with with tonal variation + + align:start position:0% +experimenting with with tonal variation + + + align:start position:0% +experimenting with with tonal variation +in his films experimenting with w w with + + align:start position:0% +in his films experimenting with w w with + + + align:start position:0% +in his films experimenting with w w with +various kinds of of of of comic devices + + align:start position:0% +various kinds of of of of comic devices + + + align:start position:0% +various kinds of of of of comic devices +some of which some of which he imports + + align:start position:0% +some of which some of which he imports + + + align:start position:0% +some of which some of which he imports +from his performances with the Carno + + align:start position:0% +from his performances with the Carno + + + align:start position:0% +from his performances with the Carno +company and some of which he uh some of + + align:start position:0% +company and some of which he uh some of + + + align:start position:0% +company and some of which he uh some of +which he many of which he refines + + align:start position:0% +which he many of which he refines + + + align:start position:0% +which he many of which he refines +changes because he's working in the + + align:start position:0% +changes because he's working in the + + + align:start position:0% +changes because he's working in the +movies one famous example of this + + align:start position:0% +movies one famous example of this + + + align:start position:0% +movies one famous example of this +migration from stage to screen is is a + + align:start position:0% +migration from stage to screen is is a + + + align:start position:0% +migration from stage to screen is is a +bit that chaplain was especially famous + + align:start position:0% +bit that chaplain was especially famous + + + align:start position:0% +bit that chaplain was especially famous +for when he worked for the Carno company + + align:start position:0% +for when he worked for the Carno company + + + align:start position:0% +for when he worked for the Carno company +he did a bit for them a pantomim called + + align:start position:0% +he did a bit for them a pantomim called + + + align:start position:0% +he did a bit for them a pantomim called +the inebriate swell the inebriated the + + align:start position:0% + + + + align:start position:0% + +drunk uh Aristocrat that's what a swell + + align:start position:0% +drunk uh Aristocrat that's what a swell + + + align:start position:0% +drunk uh Aristocrat that's what a swell +is a rich Aristocrat who a man about + + align:start position:0% +is a rich Aristocrat who a man about + + + align:start position:0% +is a rich Aristocrat who a man about +town the inebriate the drunk the drunken + + align:start position:0% +town the inebriate the drunk the drunken + + + align:start position:0% +town the inebriate the drunk the drunken +Aristocrat right and and and it was one + + align:start position:0% +Aristocrat right and and and it was one + + + align:start position:0% +Aristocrat right and and and it was one +of the most popular pie that he that he + + align:start position:0% +of the most popular pie that he that he + + + align:start position:0% +of the most popular pie that he that he +performed on stage for the Caro company + + align:start position:0% +performed on stage for the Caro company + + + align:start position:0% +performed on stage for the Caro company +he remade a version of it a very famous + + align:start position:0% +he remade a version of it a very famous + + + align:start position:0% +he remade a version of it a very famous +film it's one of the very few short + + align:start position:0% +film it's one of the very few short + + + align:start position:0% +film it's one of the very few short +Chaplin where chaplain doesn't play the + + align:start position:0% +Chaplin where chaplain doesn't play the + + + align:start position:0% +Chaplin where chaplain doesn't play the + where he's dressed up in a tuxedo + + align:start position:0% + where he's dressed up in a tuxedo + + + align:start position:0% + where he's dressed up in a tuxedo +and he plays the inebriated swell uh and + + align:start position:0% +and he plays the inebriated swell uh and + + + align:start position:0% +and he plays the inebriated swell uh and +it's a film called 1 a and in the entire + + align:start position:0% +it's a film called 1 a and in the entire + + + align:start position:0% +it's a film called 1 a and in the entire +film chaplain plays a a man who is drunk + + align:start position:0% +film chaplain plays a a man who is drunk + + + align:start position:0% +film chaplain plays a a man who is drunk +and who keeps encountering objects that + + align:start position:0% +and who keeps encountering objects that + + + align:start position:0% +and who keeps encountering objects that +he misunderstands right so as an example + + align:start position:0% +he misunderstands right so as an example + + + align:start position:0% +he misunderstands right so as an example +he comes across a clothes Tree in his + + align:start position:0% +he comes across a clothes Tree in his + + + align:start position:0% +he comes across a clothes Tree in his +house and instead of hanging his clothes + + align:start position:0% +house and instead of hanging his clothes + + + align:start position:0% +house and instead of hanging his clothes +on it he Embraces it as if it's his wife + + align:start position:0% +on it he Embraces it as if it's his wife + + + align:start position:0% +on it he Embraces it as if it's his wife +right uh that sort of thing and uh one + + align:start position:0% +right uh that sort of thing and uh one + + + align:start position:0% +right uh that sort of thing and uh one +of the things that the the the almost + + align:start position:0% +of the things that the the the almost + + + align:start position:0% +of the things that the the the almost +the entire length of 1 a. has has only + + align:start position:0% +the entire length of 1 a. has has only + + + align:start position:0% +the entire length of 1 a. has has only +one performer in the chaplain himself uh + + align:start position:0% +one performer in the chaplain himself uh + + + align:start position:0% +one performer in the chaplain himself uh +and he kind of he kind of recreates and + + align:start position:0% +and he kind of he kind of recreates and + + + align:start position:0% +and he kind of he kind of recreates and +modifies what he had done on stage in + + align:start position:0% +modifies what he had done on stage in + + + align:start position:0% +modifies what he had done on stage in +that performance it is in many ways a + + align:start position:0% +that performance it is in many ways a + + + align:start position:0% +that performance it is in many ways a +very brilliant performance and shows how + + align:start position:0% +very brilliant performance and shows how + + + align:start position:0% +very brilliant performance and shows how +imaginatively chaplain the chaplain + + align:start position:0% +imaginatively chaplain the chaplain + + + align:start position:0% +imaginatively chaplain the chaplain +character can interact with objects a + + align:start position:0% +character can interact with objects a + + + align:start position:0% +character can interact with objects a +theme to which I'll return tonight when + + align:start position:0% +theme to which I'll return tonight when + + + align:start position:0% +theme to which I'll return tonight when +I talk more systematically about Modern + + align:start position:0% +I talk more systematically about Modern + + + align:start position:0% +I talk more systematically about Modern +Times And about certain of chaplain's + + align:start position:0% +Times And about certain of chaplain's + + + align:start position:0% +Times And about certain of chaplain's +favorite strategies for establishing + + align:start position:0% +favorite strategies for establishing + + + align:start position:0% +favorite strategies for establishing +character + + align:start position:0% +character + + + align:start position:0% +character +um so he works for the sna company makes + + align:start position:0% +um so he works for the sna company makes + + + align:start position:0% +um so he works for the sna company makes +14 films including uh in 1915 a film + + align:start position:0% +14 films including uh in 1915 a film + + + align:start position:0% +14 films including uh in 1915 a film +called the fragments of which I'm + + align:start position:0% +called the fragments of which I'm + + + align:start position:0% +called the fragments of which I'm +going to show you in a couple of SE in + + align:start position:0% +going to show you in a couple of SE in + + + align:start position:0% +going to show you in a couple of SE in +in in a few minutes uh then he's so + + align:start position:0% +in in a few minutes uh then he's so + + + align:start position:0% +in in a few minutes uh then he's so +successful again and the and the 14 + + align:start position:0% +successful again and the and the 14 + + + align:start position:0% +successful again and the and the 14 +films he makes starring the become + + align:start position:0% +films he makes starring the become + + + align:start position:0% +films he makes starring the become +International uh I don't know what to + + align:start position:0% +International uh I don't know what to + + + align:start position:0% +International uh I don't know what to +call them International phenomen best + + align:start position:0% +call them International phenomen best + + + align:start position:0% +call them International phenomen best +sellers they be they and the + + align:start position:0% +sellers they be they and the + + + align:start position:0% +sellers they be they and the +becomes uh the most sought-after and the + + align:start position:0% +becomes uh the most sought-after and the + + + align:start position:0% +becomes uh the most sought-after and the +most memorable character in in in the + + align:start position:0% +most memorable character in in in the + + + align:start position:0% +most memorable character in in in the +movies so he's hired away again by the + + align:start position:0% +movies so he's hired away again by the + + + align:start position:0% +movies so he's hired away again by the +mutual company one year later and from + + align:start position:0% +mutual company one year later and from + + + align:start position:0% +mutual company one year later and from +1916 to 1917 he works for the mutual + + align:start position:0% +1916 to 1917 he works for the mutual + + + align:start position:0% +1916 to 1917 he works for the mutual +company in which he + + align:start position:0% +company in which he + + + align:start position:0% +company in which he +makes this time $1 million for that year + + align:start position:0% +makes this time $1 million for that year + + + align:start position:0% +makes this time $1 million for that year +and he makes only eight films in that + + align:start position:0% +and he makes only eight films in that + + + align:start position:0% +and he makes only eight films in that +year so he goes from uh from $150 a week + + align:start position:0% +year so he goes from uh from $150 a week + + + align:start position:0% +year so he goes from uh from $150 a week +to $1,250 a week to a million dollars a + + align:start position:0% +to $1,250 a week to a million dollars a + + + align:start position:0% +to $1,250 a week to a million dollars a +year right uh uh within three years + + align:start position:0% +year right uh uh within three years + + + align:start position:0% +year right uh uh within three years +right uh and and each each move gives + + align:start position:0% +right uh and and each each move gives + + + align:start position:0% +right uh and and each each move gives +him greater creative freedom gives him + + align:start position:0% +him greater creative freedom gives him + + + align:start position:0% +him greater creative freedom gives him +more autonomy he begins to sort of + + align:start position:0% +more autonomy he begins to sort of + + + align:start position:0% +more autonomy he begins to sort of +really refine his art and we can see the + + align:start position:0% +really refine his art and we can see the + + + align:start position:0% +really refine his art and we can see the +process happening in these in these + + align:start position:0% +process happening in these in these + + + align:start position:0% +process happening in these in these +shorts uh in in the films you're going + + align:start position:0% +shorts uh in in the films you're going + + + align:start position:0% +shorts uh in in the films you're going +to see tonight two of the films uh uh + + align:start position:0% +to see tonight two of the films uh uh + + + align:start position:0% +to see tonight two of the films uh uh +two of the both of the short films Easy + + align:start position:0% +two of the both of the short films Easy + + + align:start position:0% +two of the both of the short films Easy +Street 1917 and the Immigrant also made + + align:start position:0% +Street 1917 and the Immigrant also made + + + align:start position:0% +Street 1917 and the Immigrant also made +in 1917 come from this Mutual period and + + align:start position:0% +in 1917 come from this Mutual period and + + + align:start position:0% +in 1917 come from this Mutual period and +I mention this to you because they're + + align:start position:0% +I mention this to you because they're + + + align:start position:0% +I mention this to you because they're +already in some sense sophisticated + + align:start position:0% +already in some sense sophisticated + + + align:start position:0% +already in some sense sophisticated +films even though they're not full + + align:start position:0% +films even though they're not full + + + align:start position:0% +films even though they're not full +featurelength films and you can see that + + align:start position:0% +featurelength films and you can see that + + + align:start position:0% +featurelength films and you can see that +chaplain is bringing all the resources + + align:start position:0% +chaplain is bringing all the resources + + + align:start position:0% +chaplain is bringing all the resources +of his narrative skills of his skills of + + align:start position:0% +of his narrative skills of his skills of + + + align:start position:0% +of his narrative skills of his skills of +in creating character uh to bear on + + align:start position:0% +in creating character uh to bear on + + + align:start position:0% +in creating character uh to bear on +those film they're already in some sense + + align:start position:0% +those film they're already in some sense + + + align:start position:0% +those film they're already in some sense +sophisticated uh works of narrative uh + + align:start position:0% +sophisticated uh works of narrative uh + + + align:start position:0% +sophisticated uh works of narrative uh +and and uh there is a there is an + + align:start position:0% +and and uh there is a there is an + + + align:start position:0% +and and uh there is a there is an +apprentice period that occurs earlier + + align:start position:0% +apprentice period that occurs earlier + + + align:start position:0% +apprentice period that occurs earlier +which I have just describe to you + + align:start position:0% +which I have just describe to you + + + align:start position:0% +which I have just describe to you +finally uh in his career he moves uh in + + align:start position:0% +finally uh in his career he moves uh in + + + align:start position:0% +finally uh in his career he moves uh in +1918 to a company called First National + + align:start position:0% +1918 to a company called First National + + + align:start position:0% +1918 to a company called First National +which he uh uh uh um for for for for + + align:start position:0% +which he uh uh uh um for for for for + + + align:start position:0% +which he uh uh uh um for for for for +which and that those are the people who + + align:start position:0% +which and that those are the people who + + + align:start position:0% +which and that those are the people who +pay him a million dollars I'm sorry I + + align:start position:0% +pay him a million dollars I'm sorry I + + + align:start position:0% +pay him a million dollars I'm sorry I +made a mistake his Mutual salary was a + + align:start position:0% +made a mistake his Mutual salary was a + + + align:start position:0% +made a mistake his Mutual salary was a +mere $670,000 and he gets a million when + + align:start position:0% +mere $670,000 and he gets a million when + + + align:start position:0% +mere $670,000 and he gets a million when +he goes to work for First National in + + align:start position:0% +he goes to work for First National in + + + align:start position:0% +he goes to work for First National in +1918 when he uh when he makes uh among + + align:start position:0% +1918 when he uh when he makes uh among + + + align:start position:0% +1918 when he uh when he makes uh among +other films one of my favorite chaplain + + align:start position:0% +other films one of my favorite chaplain + + + align:start position:0% +other films one of my favorite chaplain +shorts a film in which we see the + + align:start position:0% +shorts a film in which we see the + + + align:start position:0% +shorts a film in which we see the +character playing a GI in the first + + align:start position:0% +character playing a GI in the first + + + align:start position:0% +character playing a GI in the first +world war it's called shoulder arms and + + align:start position:0% +world war it's called shoulder arms and + + + align:start position:0% +world war it's called shoulder arms and +it's a characteristic chaplain short + + align:start position:0% +it's a characteristic chaplain short + + + align:start position:0% +it's a characteristic chaplain short +except that now what Charlie is doing is + + align:start position:0% +except that now what Charlie is doing is + + + align:start position:0% +except that now what Charlie is doing is +contending with the Kaiser's Army he's + + align:start position:0% +contending with the Kaiser's Army he's + + + align:start position:0% +contending with the Kaiser's Army he's +fighting the he's fighting World War I + + align:start position:0% +fighting the he's fighting World War I + + + align:start position:0% +fighting the he's fighting World War I +in earlier films we'd seen him fighting + + align:start position:0% +in earlier films we'd seen him fighting + + + align:start position:0% +in earlier films we'd seen him fighting +ice storms we'd seen him fighting + + align:start position:0% +ice storms we'd seen him fighting + + + align:start position:0% +ice storms we'd seen him fighting +against hunger we'd seen him fighting in + + align:start position:0% +against hunger we'd seen him fighting in + + + align:start position:0% +against hunger we'd seen him fighting in +the literally fighting in the boxing + + align:start position:0% +the literally fighting in the boxing + + + align:start position:0% +the literally fighting in the boxing +ring in a film called the champion we'd + + align:start position:0% +ring in a film called the champion we'd + + + align:start position:0% +ring in a film called the champion we'd +seen him working as an assistant to a + + align:start position:0% +seen him working as an assistant to a + + + align:start position:0% +seen him working as an assistant to a +pawn broker in a film called The Pawn + + align:start position:0% +pawn broker in a film called The Pawn + + + align:start position:0% +pawn broker in a film called The Pawn +Broker a whole series of jobs and T by + + align:start position:0% +Broker a whole series of jobs and T by + + + align:start position:0% +Broker a whole series of jobs and T by +the time uh we get to 1918 it's almost + + align:start position:0% +the time uh we get to 1918 it's almost + + + align:start position:0% +the time uh we get to 1918 it's almost +as if the has held a whole + + align:start position:0% +as if the has held a whole + + + align:start position:0% +as if the has held a whole +virtually every job you could imagine he + + align:start position:0% +virtually every job you could imagine he + + + align:start position:0% +virtually every job you could imagine he +does he can't hold the job for long + + align:start position:0% +does he can't hold the job for long + + + align:start position:0% +does he can't hold the job for long +because he's a bum he's a he's a + + align:start position:0% +because he's a bum he's a he's a + + + align:start position:0% +because he's a bum he's a he's a +he's he's Foot Loose U again a theme to + + align:start position:0% +he's he's Foot Loose U again a theme to + + + align:start position:0% +he's he's Foot Loose U again a theme to +which I'll return when we talk about + + align:start position:0% +which I'll return when we talk about + + + align:start position:0% +which I'll return when we talk about +modern times this evening um uh and then + + align:start position:0% +modern times this evening um uh and then + + + align:start position:0% +modern times this evening um uh and then +finally in 1919 he move chaplain has + + align:start position:0% +finally in 1919 he move chaplain has + + + align:start position:0% +finally in 1919 he move chaplain has +become such a gigantic figure such an + + align:start position:0% +become such a gigantic figure such an + + + align:start position:0% +become such a gigantic figure such an +international icon that he joins with + + align:start position:0% +international icon that he joins with + + + align:start position:0% +international icon that he joins with +certain other icons DW Griffith the the + + align:start position:0% +certain other icons DW Griffith the the + + + align:start position:0% +certain other icons DW Griffith the the +greatest most famous director of the + + align:start position:0% +greatest most famous director of the + + + align:start position:0% +greatest most famous director of the +silent era uh + + align:start position:0% +silent era uh + + + align:start position:0% +silent era uh +uh and two Mary pford and Douglas + + align:start position:0% +uh and two Mary pford and Douglas + + + align:start position:0% +uh and two Mary pford and Douglas +Fairbanks the two most famous actors + + align:start position:0% +Fairbanks the two most famous actors + + + align:start position:0% +Fairbanks the two most famous actors +after chaplain of the silent era the + + align:start position:0% +after chaplain of the silent era the + + + align:start position:0% +after chaplain of the silent era the +four of them get together and they form + + align:start position:0% +four of them get together and they form + + + align:start position:0% +four of them get together and they form +United Artists uh and they formed it in + + align:start position:0% +United Artists uh and they formed it in + + + align:start position:0% +United Artists uh and they formed it in +part to create their own company so that + + align:start position:0% +part to create their own company so that + + + align:start position:0% +part to create their own company so that +they would be able to control their + + align:start position:0% +they would be able to control their + + + align:start position:0% +they would be able to control their +artistic output and when chaplain + + align:start position:0% +artistic output and when chaplain + + + align:start position:0% +artistic output and when chaplain +working for United Artists beginning in + + align:start position:0% +working for United Artists beginning in + + + align:start position:0% +working for United Artists beginning in +1919 Chaplan goes to work on his feature + + align:start position:0% +1919 Chaplan goes to work on his feature + + + align:start position:0% +1919 Chaplan goes to work on his feature +films and he makes the great film The + + align:start position:0% +films and he makes the great film The + + + align:start position:0% +films and he makes the great film The +Great silent features that are at the + + align:start position:0% +Great silent features that are at the + + + align:start position:0% +Great silent features that are at the +heart of his achievement he makes the + + align:start position:0% +heart of his achievement he makes the + + + align:start position:0% +heart of his achievement he makes the +gold rush in + + align:start position:0% +gold rush in + + + align:start position:0% +gold rush in +1925 a film called the Circ Us in 1928 a + + align:start position:0% +1925 a film called the Circ Us in 1928 a + + + align:start position:0% +1925 a film called the Circ Us in 1928 a +more imperfect and broken back film in + + align:start position:0% +more imperfect and broken back film in + + + align:start position:0% +more imperfect and broken back film in +some way but full of his some of his + + align:start position:0% +some way but full of his some of his + + + align:start position:0% +some way but full of his some of his +most imaginative comic performances one + + align:start position:0% +most imaginative comic performances one + + + align:start position:0% +most imaginative comic performances one +of his great films in 1931 called city + + align:start position:0% +of his great films in 1931 called city + + + align:start position:0% +of his great films in 1931 called city +lights and then finally in 1936 the film + + align:start position:0% +lights and then finally in 1936 the film + + + align:start position:0% +lights and then finally in 1936 the film +you're going to see tonight already + + align:start position:0% +you're going to see tonight already + + + align:start position:0% +you're going to see tonight already +deeply into the sound era a film that + + align:start position:0% +deeply into the sound era a film that + + + align:start position:0% +deeply into the sound era a film that +remains in some fundamental way a silent + + align:start position:0% +remains in some fundamental way a silent + + + align:start position:0% +remains in some fundamental way a silent +film modern times Chaplin then goes on + + align:start position:0% +film modern times Chaplin then goes on + + + align:start position:0% +film modern times Chaplin then goes on +when after the sound era is over to make + + align:start position:0% +when after the sound era is over to make + + + align:start position:0% +when after the sound era is over to make +a series of movies in the in the sound + + align:start position:0% +a series of movies in the in the sound + + + align:start position:0% +a series of movies in the in the sound +era and they all have some modest + + align:start position:0% +era and they all have some modest + + + align:start position:0% +era and they all have some modest +interest for us because they're chaplain + + align:start position:0% +interest for us because they're chaplain + + + align:start position:0% +interest for us because they're chaplain +films some some images from them are + + align:start position:0% +films some some images from them are + + + align:start position:0% +films some some images from them are +that remain very famous to this day in + + align:start position:0% +that remain very famous to this day in + + + align:start position:0% +that remain very famous to this day in +fact one of them was in the New York + + align:start position:0% +fact one of them was in the New York + + + align:start position:0% +fact one of them was in the New York +Times today does any of you notice it + + align:start position:0% +Times today does any of you notice it + + + align:start position:0% +Times today does any of you notice it +there was an article about a a scholar + + align:start position:0% +there was an article about a a scholar + + + align:start position:0% +there was an article about a a scholar +of of globes who uh had found evidence + + align:start position:0% +of of globes who uh had found evidence + + + align:start position:0% +of of globes who uh had found evidence +for the idea that a particular globe in + + align:start position:0% +for the idea that a particular globe in + + + align:start position:0% +for the idea that a particular globe in +a German Museum which was said to have + + align:start position:0% +a German Museum which was said to have + + + align:start position:0% +a German Museum which was said to have +been Hitler's Globe was not Hitler's + + align:start position:0% +been Hitler's Globe was not Hitler's + + + align:start position:0% +been Hitler's Globe was not Hitler's +Globe okay it's a the guy but but in the + + align:start position:0% +Globe okay it's a the guy but but in the + + + align:start position:0% +Globe okay it's a the guy but but in the +middle of the story what they what and + + align:start position:0% +middle of the story what they what and + + + align:start position:0% +middle of the story what they what and +anytime you anytime a person of a + + align:start position:0% +anytime you anytime a person of a + + + align:start position:0% +anytime you anytime a person of a +certain age hears the word globe and + + align:start position:0% +certain age hears the word globe and + + + align:start position:0% +certain age hears the word globe and +Hitler they think of Charlie's film The + + align:start position:0% +Hitler they think of Charlie's film The + + + align:start position:0% +Hitler they think of Charlie's film The +Great Dictator you're smiling while you + + align:start position:0% +Great Dictator you're smiling while you + + + align:start position:0% +Great Dictator you're smiling while you +know the image that they have you seen + + align:start position:0% +know the image that they have you seen + + + align:start position:0% +know the image that they have you seen +The Great Dictator what what what is the + + align:start position:0% +The Great Dictator what what what is the + + + align:start position:0% +The Great Dictator what what what is the +image they're talking + + align:start position:0% +image they're talking + + + align:start position:0% +image they're talking +about yes there's a moment in the film + + align:start position:0% +about yes there's a moment in the film + + + align:start position:0% +about yes there's a moment in the film +it's a a moment of great it's it's not + + align:start position:0% +it's a a moment of great it's it's not + + + align:start position:0% +it's a a moment of great it's it's not +really a very good film I mean and + + align:start position:0% +really a very good film I mean and + + + align:start position:0% +really a very good film I mean and +chaplain silent chaplain sound films are + + align:start position:0% +chaplain silent chaplain sound films are + + + align:start position:0% +chaplain silent chaplain sound films are +mostly of historical interest despite + + align:start position:0% +mostly of historical interest despite + + + align:start position:0% +mostly of historical interest despite +what some chaplain Buffs would say his + + align:start position:0% +what some chaplain Buffs would say his + + + align:start position:0% +what some chaplain Buffs would say his +great work is he's a silent artist and + + align:start position:0% +great work is he's a silent artist and + + + align:start position:0% +great work is he's a silent artist and +this the the sound film caused problems + + align:start position:0% +this the the sound film caused problems + + + align:start position:0% +this the the sound film caused problems +for him that he couldn't fully adjust to + + align:start position:0% +for him that he couldn't fully adjust to + + + align:start position:0% +for him that he couldn't fully adjust to +but every one of his sound films has + + align:start position:0% +but every one of his sound films has + + + align:start position:0% +but every one of his sound films has +interest and uh has brilliant moments + + align:start position:0% +interest and uh has brilliant moments + + + align:start position:0% +interest and uh has brilliant moments +and the one you are remembering is one + + align:start position:0% +and the one you are remembering is one + + + align:start position:0% +and the one you are remembering is one +of the most remarkable and astonishing + + align:start position:0% +of the most remarkable and astonishing + + + align:start position:0% +of the most remarkable and astonishing +symbolic moments in chaplain's work it's + + align:start position:0% +symbolic moments in chaplain's work it's + + + align:start position:0% +symbolic moments in chaplain's work it's +the it's an incredibly ambitious film it + + align:start position:0% +the it's an incredibly ambitious film it + + + align:start position:0% +the it's an incredibly ambitious film it +tells us how ambitious a com a figure + + align:start position:0% +tells us how ambitious a com a figure + + + align:start position:0% +tells us how ambitious a com a figure +chaplain was because he makes a satire + + align:start position:0% +chaplain was because he makes a satire + + + align:start position:0% +chaplain was because he makes a satire +of Hitler and melini in an era when + + align:start position:0% +of Hitler and melini in an era when + + + align:start position:0% +of Hitler and melini in an era when +Hitler and melini are not yet recognized + + align:start position:0% +Hitler and melini are not yet recognized + + + align:start position:0% +Hitler and melini are not yet recognized +for the egregious monstrous evil figures + + align:start position:0% +for the egregious monstrous evil figures + + + align:start position:0% +for the egregious monstrous evil figures +that we know them to have been they were + + align:start position:0% +that we know them to have been they were + + + align:start position:0% +that we know them to have been they were +taken seriously they were they they had + + align:start position:0% +taken seriously they were they they had + + + align:start position:0% +taken seriously they were they they had +been voted into office th millions and + + align:start position:0% +been voted into office th millions and + + + align:start position:0% +been voted into office th millions and +millions of people thought they were + + align:start position:0% +millions of people thought they were + + + align:start position:0% +millions of people thought they were +admirable leaders so when chaplain made + + align:start position:0% +admirable leaders so when chaplain made + + + align:start position:0% +admirable leaders so when chaplain made +The Great Dictator in 19 what 40 or 41 + + align:start position:0% +The Great Dictator in 19 what 40 or 41 + + + align:start position:0% +The Great Dictator in 19 what 40 or 41 +uh he was doing something incredibly + + align:start position:0% +uh he was doing something incredibly + + + align:start position:0% +uh he was doing something incredibly +daring and he was actually showing that + + align:start position:0% +daring and he was actually showing that + + + align:start position:0% +daring and he was actually showing that +he thought the movies were a art for + + align:start position:0% +he thought the movies were a art for + + + align:start position:0% +he thought the movies were a art for +were an art form capable of taking on + + align:start position:0% +were an art form capable of taking on + + + align:start position:0% +were an art form capable of taking on +the largest political subjects so even + + align:start position:0% +the largest political subjects so even + + + align:start position:0% +the largest political subjects so even +though there are problems in the film + + align:start position:0% +though there are problems in the film + + + align:start position:0% +though there are problems in the film +and it's not an absolutely great film + + align:start position:0% +and it's not an absolutely great film + + + align:start position:0% +and it's not an absolutely great film +not memorable artistically in its own + + align:start position:0% +not memorable artistically in its own + + + align:start position:0% +not memorable artistically in its own +way there are moments in it that are + + align:start position:0% +way there are moments in it that are + + + align:start position:0% +way there are moments in it that are +remarkable and it's also a significant + + align:start position:0% +remarkable and it's also a significant + + + align:start position:0% +remarkable and it's also a significant +document because it reminds us of + + align:start position:0% +document because it reminds us of + + + align:start position:0% +document because it reminds us of +chaplain's Ambitions as an artist + + align:start position:0% +chaplain's Ambitions as an artist + + + align:start position:0% +chaplain's Ambitions as an artist +Chaplin was one of the very first + + align:start position:0% +Chaplin was one of the very first + + + align:start position:0% +Chaplin was one of the very first +filmmakers along with DW Griffith I + + align:start position:0% +filmmakers along with DW Griffith I + + + align:start position:0% +filmmakers along with DW Griffith I +suppose to realize that the movies had + + align:start position:0% +suppose to realize that the movies had + + + align:start position:0% +suppose to realize that the movies had +an aesthetic possibility an aesthetic uh + + align:start position:0% +an aesthetic possibility an aesthetic uh + + + align:start position:0% +an aesthetic possibility an aesthetic uh +aesthetic uh uh uh uh latent aesthetic + + align:start position:0% +aesthetic uh uh uh uh latent aesthetic + + + align:start position:0% +aesthetic uh uh uh uh latent aesthetic +energies and and and powers that needed + + align:start position:0% +energies and and and powers that needed + + + align:start position:0% +energies and and and powers that needed +to be that if they were tapped would + + align:start position:0% +to be that if they were tapped would + + + align:start position:0% +to be that if they were tapped would +make the movies the equivalent of + + align:start position:0% +make the movies the equivalent of + + + align:start position:0% +make the movies the equivalent of +traditional art forms like theater and + + align:start position:0% +traditional art forms like theater and + + + align:start position:0% +traditional art forms like theater and +the novel and of course he was right + + align:start position:0% +the novel and of course he was right + + + align:start position:0% +the novel and of course he was right +about that that and he even made some + + align:start position:0% +about that that and he even made some + + + align:start position:0% +about that that and he even made some +films that achiev that that level of + + align:start position:0% +films that achiev that that level of + + + align:start position:0% +films that achiev that that level of +seriousness and resonance the moment + + align:start position:0% +seriousness and resonance the moment + + + align:start position:0% +seriousness and resonance the moment +that you're remembering what what + + align:start position:0% +that you're remembering what what + + + align:start position:0% +that you're remembering what what +happens in + + align:start position:0% +happens in + + + align:start position:0% +happens in +it yes it's a moment of sort of uh manic + + align:start position:0% +it yes it's a moment of sort of uh manic + + + align:start position:0% +it yes it's a moment of sort of uh manic +Glee in which the Hitler character + + align:start position:0% +Glee in which the Hitler character + + + align:start position:0% +Glee in which the Hitler character +played by Charlie Chaplain takes a globe + + align:start position:0% +played by Charlie Chaplain takes a globe + + + align:start position:0% +played by Charlie Chaplain takes a globe +out and it's like a balloon and he pops + + align:start position:0% +out and it's like a balloon and he pops + + + align:start position:0% +out and it's like a balloon and he pops +it up and down and we see him we see him + + align:start position:0% +it up and down and we see him we see him + + + align:start position:0% +it up and down and we see him we see him +throwing it up and kicking it with his + + align:start position:0% +throwing it up and kicking it with his + + + align:start position:0% +throwing it up and kicking it with his +hand foot like that and and what it's + + align:start position:0% +hand foot like that and and what it's + + + align:start position:0% +hand foot like that and and what it's +it's a kind of fantasy of world + + align:start position:0% +it's a kind of fantasy of world + + + align:start position:0% +it's a kind of fantasy of world +domination it's supposed to it's and + + align:start position:0% +domination it's supposed to it's and + + + align:start position:0% +domination it's supposed to it's and +it's supposed to show what a ridiculous + + align:start position:0% +it's supposed to show what a ridiculous + + + align:start position:0% +it's supposed to show what a ridiculous +and infantile figure uh this mock Hitler + + align:start position:0% +and infantile figure uh this mock Hitler + + + align:start position:0% +and infantile figure uh this mock Hitler +is uh and and it is the most memorable + + align:start position:0% +is uh and and it is the most memorable + + + align:start position:0% +is uh and and it is the most memorable +image from that film so in this article + + align:start position:0% +image from that film so in this article + + + align:start position:0% +image from that film so in this article +that really had nothing to do with + + align:start position:0% +that really had nothing to do with + + + align:start position:0% +that really had nothing to do with +chaplain there was a picture of Charlie + + align:start position:0% +chaplain there was a picture of Charlie + + + align:start position:0% +chaplain there was a picture of Charlie +uh playing Hitler kicking the balloon up + + align:start position:0% +uh playing Hitler kicking the balloon up + + + align:start position:0% +uh playing Hitler kicking the balloon up +and down and one reason that I think + + align:start position:0% +and down and one reason that I think + + + align:start position:0% +and down and one reason that I think +it's significant is that that it's a + + align:start position:0% +it's significant is that that it's a + + + align:start position:0% +it's significant is that that it's a +mark of chaplain's greatness as an + + align:start position:0% +mark of chaplain's greatness as an + + + align:start position:0% +mark of chaplain's greatness as an +artist that even in his even in his + + align:start position:0% +artist that even in his even in his + + + align:start position:0% +artist that even in his even in his +imperfect texts even even in the films + + align:start position:0% +imperfect texts even even in the films + + + align:start position:0% +imperfect texts even even in the films +that really do not uh belong to the to + + align:start position:0% +that really do not uh belong to the to + + + align:start position:0% +that really do not uh belong to the to +the category to to to to the most + + align:start position:0% +the category to to to to the most + + + align:start position:0% +the category to to to to the most +important category of his of his most + + align:start position:0% +important category of his of his most + + + align:start position:0% +important category of his of his most +lasting and valuable art they still are + + align:start position:0% +lasting and valuable art they still are + + + align:start position:0% +lasting and valuable art they still are +part the images from those works are + + align:start position:0% +part the images from those works are + + + align:start position:0% +part the images from those works are +still part of our common cultural + + align:start position:0% +still part of our common cultural + + + align:start position:0% +still part of our common cultural +inheritance he's a very great artist the + + align:start position:0% +inheritance he's a very great artist the + + + align:start position:0% +inheritance he's a very great artist the +first great artist of the movies and and + + align:start position:0% +first great artist of the movies and and + + + align:start position:0% +first great artist of the movies and and +a figure who whose imaginative uh uh + + align:start position:0% +a figure who whose imaginative uh uh + + + align:start position:0% +a figure who whose imaginative uh uh +Creations remain uh uh uh vital and + + align:start position:0% +Creations remain uh uh uh vital and + + + align:start position:0% +Creations remain uh uh uh vital and +alive today in a way that very few + + align:start position:0% +alive today in a way that very few + + + align:start position:0% +alive today in a way that very few +artists from that era remain um um + + align:start position:0% +artists from that era remain um um + + + align:start position:0% +artists from that era remain um um +similarly uh accessible and important to + + align:start position:0% +similarly uh accessible and important to + + + align:start position:0% +similarly uh accessible and important to +people + + align:start position:0% +people + + + align:start position:0% +people +it's a and it's a mark of of the reach + + align:start position:0% +it's a and it's a mark of of the reach + + + align:start position:0% +it's a and it's a mark of of the reach +of chaplain's imagination that that this + + align:start position:0% +of chaplain's imagination that that this + + + align:start position:0% +of chaplain's imagination that that this +is so of his importance as a figure well + + align:start position:0% +is so of his importance as a figure well + + + align:start position:0% +is so of his importance as a figure well +uh there's there's much more one could + + align:start position:0% +uh there's there's much more one could + + + align:start position:0% +uh there's there's much more one could +say about the development of his career + + align:start position:0% +say about the development of his career + + + align:start position:0% +say about the development of his career +but I I want to I want to cut this short + + align:start position:0% +but I I want to I want to cut this short + + + align:start position:0% +but I I want to I want to cut this short +because I want to show you the moment I + + align:start position:0% +because I want to show you the moment I + + + align:start position:0% +because I want to show you the moment I +I mean I don't mean that there's only a + + align:start position:0% +I mean I don't mean that there's only a + + + align:start position:0% +I mean I don't mean that there's only a +single moment but I want to show you + + align:start position:0% +single moment but I want to show you + + + align:start position:0% +single moment but I want to show you +fragments from the film in which we can + + align:start position:0% +fragments from the film in which we can + + + align:start position:0% +fragments from the film in which we can +see chaplain really discovering + + align:start position:0% +see chaplain really discovering + + + align:start position:0% +see chaplain really discovering +certain aspects of what he wants to do + + align:start position:0% +certain aspects of what he wants to do + + + align:start position:0% +certain aspects of what he wants to do +and also where we can see chap screwing + + align:start position:0% +and also where we can see chap screwing + + + align:start position:0% +and also where we can see chap screwing +up we can see chaplain at a stage before + + align:start position:0% +up we can see chaplain at a stage before + + + align:start position:0% +up we can see chaplain at a stage before +he becomes the the the uh self-confident + + align:start position:0% +he becomes the the the uh self-confident + + + align:start position:0% +he becomes the the the uh self-confident +totally autonomous uh artist he he + + align:start position:0% +totally autonomous uh artist he he + + + align:start position:0% +totally autonomous uh artist he he +becomes relatively soon can we can we + + align:start position:0% +becomes relatively soon can we can we + + + align:start position:0% +becomes relatively soon can we can we +put up fragments from the champ from + + align:start position:0% +put up fragments from the champ from + + + align:start position:0% +put up fragments from the champ from +from the uh from the uh this is a + + align:start position:0% +from the uh from the uh this is a + + + align:start position:0% +from the uh from the uh this is a +film + + align:start position:0% +film + + + align:start position:0% +film +um appropriately called the in + + align:start position:0% +um appropriately called the in + + + align:start position:0% +um appropriately called the in +which uh and it's a fairly + + align:start position:0% +which uh and it's a fairly + + + align:start position:0% +which uh and it's a fairly +characteristic uh chaplain film but I + + align:start position:0% +characteristic uh chaplain film but I + + + align:start position:0% +characteristic uh chaplain film but I +think it's I think it's the film in + + align:start position:0% +think it's I think it's the film in + + + align:start position:0% +think it's I think it's the film in +which among other things chaplain + + align:start position:0% +which among other things chaplain + + + align:start position:0% +which among other things chaplain +discovers that he can Mel that he can + + align:start position:0% +discovers that he can Mel that he can + + + align:start position:0% +discovers that he can Mel that he can +marry melodrama and comedy it's the film + + align:start position:0% +marry melodrama and comedy it's the film + + + align:start position:0% +marry melodrama and comedy it's the film +in which he discovers that he can do + + align:start position:0% +in which he discovers that he can do + + + align:start position:0% +in which he discovers that he can do +effects that are pathetic and poignant + + align:start position:0% +effects that are pathetic and poignant + + + align:start position:0% +effects that are pathetic and poignant +and sentimental and mix them with comedy + + align:start position:0% +and sentimental and mix them with comedy + + + align:start position:0% +and sentimental and mix them with comedy +in ways that are interesting so here's a + + align:start position:0% +in ways that are interesting so here's a + + + align:start position:0% +in ways that are interesting so here's a +scene where Charlie is rescuing a damsel + + align:start position:0% +scene where Charlie is rescuing a damsel + + + align:start position:0% +scene where Charlie is rescuing a damsel +right he does it in a kind of comic way + + align:start position:0% +right he does it in a kind of comic way + + + align:start position:0% +right he does it in a kind of comic way +he's a kind of bum himself but he's + + align:start position:0% +he's a kind of bum himself but he's + + + align:start position:0% +he's a kind of bum himself but he's +always a kind of chalc + + align:start position:0% +always a kind of chalc + + + align:start position:0% +always a kind of chalc +figure can you jump ahead I want let's + + align:start position:0% +figure can you jump ahead I want let's + + + align:start position:0% +figure can you jump ahead I want let's +just show the next the next one Greg uh + + align:start position:0% +just show the next the next one Greg uh + + + align:start position:0% +just show the next the next one Greg uh +I'm just going to show you a bad moment + + align:start position:0% +I'm just going to show you a bad moment + + + align:start position:0% +I'm just going to show you a bad moment +here uh after he rescues this W girl she + + align:start position:0% +here uh after he rescues this W girl she + + + align:start position:0% +here uh after he rescues this W girl she +turns out to be the daughter of a farmer + + align:start position:0% +turns out to be the daughter of a farmer + + + align:start position:0% +turns out to be the daughter of a farmer +he's then uh he's then hired by the + + align:start position:0% +he's then uh he's then hired by the + + + align:start position:0% +he's then uh he's then hired by the +farmer by by by the by the farmer in in + + align:start position:0% +farmer by by by the by the farmer in in + + + align:start position:0% +farmer by by by the by the farmer in in +gratitude and then we get this bit and + + align:start position:0% +gratitude and then we get this bit and + + + align:start position:0% +gratitude and then we get this bit and +I'm showing you this bit partly because + + align:start position:0% +I'm showing you this bit partly because + + + align:start position:0% +I'm showing you this bit partly because +I want you to see that it isn't really + + align:start position:0% +I want you to see that it isn't really + + + align:start position:0% +I want you to see that it isn't really +all that funny or that it's just kind of + + align:start position:0% +all that funny or that it's just kind of + + + align:start position:0% +all that funny or that it's just kind of +easy slapstick + + align:start position:0% + + + + align:start position:0% + +I don't mean it's that it's with it's + + align:start position:0% +I don't mean it's that it's with it's + + + align:start position:0% +I don't mean it's that it's with it's +without interest it obviously has some + + align:start position:0% + + + + align:start position:0% + +interest but this incompetence is + + align:start position:0% +interest but this incompetence is + + + align:start position:0% +interest but this incompetence is +inconsistent in some respects with uh + + align:start position:0% +inconsistent in some respects with uh + + + align:start position:0% +inconsistent in some respects with uh +the coherent character that he's that + + align:start position:0% +the coherent character that he's that + + + align:start position:0% +the coherent character that he's that +that that he's going to begin to create + + align:start position:0% +that that he's going to begin to create + + + align:start position:0% +that that he's going to begin to create +I don't mean I I I shouldn't it's never + + align:start position:0% +I don't mean I I I shouldn't it's never + + + align:start position:0% +I don't mean I I I shouldn't it's never +that the becomes this fully + + align:start position:0% +that the becomes this fully + + + align:start position:0% +that the becomes this fully +competent charact but this kind of joke + + align:start position:0% +competent charact but this kind of joke + + + align:start position:0% +competent charact but this kind of joke +here look at this that's that's a + + align:start position:0% +here look at this that's that's a + + + align:start position:0% +here look at this that's that's a +foolish joke that makes him that + + align:start position:0% +foolish joke that makes him that + + + align:start position:0% +foolish joke that makes him that +trivializes him in a way can you think + + align:start position:0% +trivializes him in a way can you think + + + align:start position:0% +trivializes him in a way can you think +of examples of that in Katon you + + align:start position:0% +of examples of that in Katon you + + + align:start position:0% +of examples of that in Katon you +remember in cops where for example when + + align:start position:0% +remember in cops where for example when + + + align:start position:0% +remember in cops where for example when +he's riding along in his in his card and + + align:start position:0% +he's riding along in his in his card and + + + align:start position:0% +he's riding along in his in his card and +he he he devises that uh that that + + align:start position:0% +he he he devises that uh that that + + + align:start position:0% +he he he devises that uh that that +mechanism that ends up punching the cop + + align:start position:0% +mechanism that ends up punching the cop + + + align:start position:0% +mechanism that ends up punching the cop +that would be an example of a kind of + + align:start position:0% +that would be an example of a kind of + + + align:start position:0% +that would be an example of a kind of +it's a joke but it sort of violates the + + align:start position:0% +it's a joke but it sort of violates the + + + align:start position:0% +it's a joke but it sort of violates the +spirit of the movie it's it's as if it's + + align:start position:0% +spirit of the movie it's it's as if it's + + + align:start position:0% +spirit of the movie it's it's as if it's +seems it seems a piece of debris that is + + align:start position:0% +seems it seems a piece of debris that is + + + align:start position:0% +seems it seems a piece of debris that is +forced into the film that may may have a + + align:start position:0% +forced into the film that may may have a + + + align:start position:0% +forced into the film that may may have a +comic moment but makes the film less + + align:start position:0% +comic moment but makes the film less + + + align:start position:0% +comic moment but makes the film less +coherent that kind of thing is + + align:start position:0% +coherent that kind of thing is + + + align:start position:0% +coherent that kind of thing is +characteristic of the a bit later + + align:start position:0% +characteristic of the a bit later + + + align:start position:0% +characteristic of the a bit later +in the I don't have time to show + + align:start position:0% +in the I don't have time to show + + + align:start position:0% +in the I don't have time to show +you this this uh passage a bit later in + + align:start position:0% +you this this uh passage a bit later in + + + align:start position:0% +you this this uh passage a bit later in +the we see Charlie confronting the + + align:start position:0% +the we see Charlie confronting the + + + align:start position:0% +the we see Charlie confronting the +woman that he had rescued and + + align:start position:0% +woman that he had rescued and + + + align:start position:0% +woman that he had rescued and +discovering for the first time is it a + + align:start position:0% +discovering for the first time is it a + + + align:start position:0% +discovering for the first time is it a +long sequence + + align:start position:0% +long sequence + + + align:start position:0% +long sequence +Greg well put it up while I'm talking if + + align:start position:0% +Greg well put it up while I'm talking if + + + align:start position:0% +Greg well put it up while I'm talking if +you can find it uh you can see you can + + align:start position:0% +you can find it uh you can see you can + + + align:start position:0% +you can find it uh you can see you can +see in this sequence which I'll let run + + align:start position:0% +see in this sequence which I'll let run + + + align:start position:0% +see in this sequence which I'll let run +behind me while you pay attention to my + + align:start position:0% +behind me while you pay attention to my + + + align:start position:0% +behind me while you pay attention to my +words uh and while the camera looks at + + align:start position:0% +words uh and while the camera looks at + + + align:start position:0% +words uh and while the camera looks at +it and then comes back to me uh you what + + align:start position:0% +it and then comes back to me uh you what + + + align:start position:0% +it and then comes back to me uh you what +you can see happening in this in this + + align:start position:0% +you can see happening in this in this + + + align:start position:0% +you can see happening in this in this +sequence is chaplain discovering how he + + align:start position:0% +sequence is chaplain discovering how he + + + align:start position:0% +sequence is chaplain discovering how he +can be not just comical but but + + align:start position:0% +can be not just comical but but + + + align:start position:0% +can be not just comical but but +sentimental how he can elicit sympathy + + align:start position:0% +sentimental how he can elicit sympathy + + + align:start position:0% +sentimental how he can elicit sympathy +from his audience create sentimental + + align:start position:0% +from his audience create sentimental + + + align:start position:0% +from his audience create sentimental +effects in words what Charlie has just + + align:start position:0% +effects in words what Charlie has just + + + align:start position:0% +effects in words what Charlie has just +done here in this image is he's meeting + + align:start position:0% +done here in this image is he's meeting + + + align:start position:0% +done here in this image is he's meeting +the girl's boyfriend he didn't know the + + align:start position:0% +the girl's boyfriend he didn't know the + + + align:start position:0% +the girl's boyfriend he didn't know the +girl had a boyfriend he was falling in + + align:start position:0% +girl had a boyfriend he was falling in + + + align:start position:0% +girl had a boyfriend he was falling in +love with + + align:start position:0% +love with + + + align:start position:0% +love with +her watch his expression here + + align:start position:0% + + + + align:start position:0% + +see he's very upset by what he's learned + + align:start position:0% +see he's very upset by what he's learned + + + align:start position:0% +see he's very upset by what he's learned +and that in other words this is not a + + align:start position:0% +and that in other words this is not a + + + align:start position:0% +and that in other words this is not a +funny moment and and this is the moment + + align:start position:0% +funny moment and and this is the moment + + + align:start position:0% +funny moment and and this is the moment +I think in chaplain's career where he + + align:start position:0% +I think in chaplain's career where he + + + align:start position:0% +I think in chaplain's career where he +realizes the films he's going to make + + align:start position:0% +realizes the films he's going to make + + + align:start position:0% +realizes the films he's going to make +should not be thought of as simply + + align:start position:0% +should not be thought of as simply + + + align:start position:0% +should not be thought of as simply +comedies at all but as something more + + align:start position:0% +comedies at all but as something more + + + align:start position:0% +comedies at all but as something more +complicated than that as comedies with + + align:start position:0% +complicated than that as comedies with + + + align:start position:0% +complicated than that as comedies with +heart as comedies devoted to character + + align:start position:0% +heart as comedies devoted to character + + + align:start position:0% +heart as comedies devoted to character +as comedies that are interested in human + + align:start position:0% +as comedies that are interested in human + + + align:start position:0% +as comedies that are interested in human +interactions and that Discovery + + align:start position:0% +interactions and that Discovery + + + align:start position:0% +interactions and that Discovery +tremendously enlarged movie comedy + + align:start position:0% +tremendously enlarged movie comedy + + + align:start position:0% +tremendously enlarged movie comedy +tremendously enlarge the movies more + + align:start position:0% +tremendously enlarge the movies more + + + align:start position:0% +tremendously enlarge the movies more +generally right uh and then we can see + + align:start position:0% +generally right uh and then we can see + + + align:start position:0% +generally right uh and then we can see +Charlie saying uh um Charlie says + + align:start position:0% +Charlie saying uh um Charlie says + + + align:start position:0% +Charlie saying uh um Charlie says +goodbye and he writes this little sad + + align:start position:0% +goodbye and he writes this little sad + + + align:start position:0% +goodbye and he writes this little sad +message and he and he leaves her so it's + + align:start position:0% +message and he and he leaves her so it's + + + align:start position:0% +message and he and he leaves her so it's +the moment when posos sentiment enters + + align:start position:0% +the moment when posos sentiment enters + + + align:start position:0% +the moment when posos sentiment enters +chaplain's work and in the films you'll + + align:start position:0% +chaplain's work and in the films you'll + + + align:start position:0% +chaplain's work and in the films you'll +see tonight you'll understand why after + + align:start position:0% +see tonight you'll understand why after + + + align:start position:0% +see tonight you'll understand why after +he made this discovery he began to meld + + align:start position:0% +he made this discovery he began to meld + + + align:start position:0% +he made this discovery he began to meld +these two elements more and more fully + + align:start position:0% +these two elements more and more fully + + + align:start position:0% +these two elements more and more fully +together so what this is a way of + + align:start position:0% +together so what this is a way of + + + align:start position:0% +together so what this is a way of +reinforcing what I called last week the + + align:start position:0% +reinforcing what I called last week the + + + align:start position:0% +reinforcing what I called last week the +multiplicity principle what we can see + + align:start position:0% +multiplicity principle what we can see + + + align:start position:0% +multiplicity principle what we can see +is that in those jokes with the + + align:start position:0% +is that in those jokes with the + + + align:start position:0% +is that in those jokes with the +Pitchfork there was no multiplicity they + + align:start position:0% +Pitchfork there was no multiplicity they + + + align:start position:0% +Pitchfork there was no multiplicity they +were just funny because Charlie didn't + + align:start position:0% +were just funny because Charlie didn't + + + align:start position:0% +were just funny because Charlie didn't +know how to use the Pitchfork right but + + align:start position:0% +know how to use the Pitchfork right but + + + align:start position:0% +know how to use the Pitchfork right but +later moments in this film and in many + + align:start position:0% +later moments in this film and in many + + + align:start position:0% +later moments in this film and in many +later films we see chaplain beginning to + + align:start position:0% +later films we see chaplain beginning to + + + align:start position:0% +later films we see chaplain beginning to +create effects which have more than one + + align:start position:0% +create effects which have more than one + + + align:start position:0% +create effects which have more than one +consequence more than one significance + + align:start position:0% +consequence more than one significance + + + align:start position:0% +consequence more than one significance +for the audience one of the most + + align:start position:0% +for the audience one of the most + + + align:start position:0% +for the audience one of the most +remarkable things about the chase scenes + + align:start position:0% +remarkable things about the chase scenes + + + align:start position:0% +remarkable things about the chase scenes +that Charlie Chaplain develops and + + align:start position:0% +that Charlie Chaplain develops and + + + align:start position:0% +that Charlie Chaplain develops and +begins to perform in his films and + + align:start position:0% +begins to perform in his films and + + + align:start position:0% +begins to perform in his films and +you'll see wonderful examples of them + + align:start position:0% +you'll see wonderful examples of them + + + align:start position:0% +you'll see wonderful examples of them +tonight is that the chase scenes + + align:start position:0% +tonight is that the chase scenes + + + align:start position:0% +tonight is that the chase scenes +themselves are tremendously moving + + align:start position:0% +themselves are tremendously moving + + + align:start position:0% +themselves are tremendously moving +they're tremendously comical uh they + + align:start position:0% +they're tremendously comical uh they + + + align:start position:0% +they're tremendously comical uh they +they're full of they're they're full of + + align:start position:0% +they're full of they're they're full of + + + align:start position:0% +they're full of they're they're full of +they're full of comic bits that are just + + align:start position:0% +they're full of comic bits that are just + + + align:start position:0% +they're full of comic bits that are just +as imaginative as any comic sequence one + + align:start position:0% +as imaginative as any comic sequence one + + + align:start position:0% +as imaginative as any comic sequence one +could ask for but they do something else + + align:start position:0% +could ask for but they do something else + + + align:start position:0% +could ask for but they do something else +in addition to amuse us they declare for + + align:start position:0% +in addition to amuse us they declare for + + + align:start position:0% +in addition to amuse us they declare for +CH Charlie's character when Charlie runs + + align:start position:0% +CH Charlie's character when Charlie runs + + + align:start position:0% +CH Charlie's character when Charlie runs +away from someone what we can see him + + align:start position:0% +away from someone what we can see him + + + align:start position:0% +away from someone what we can see him +doing is using his intelligence using + + align:start position:0% +doing is using his intelligence using + + + align:start position:0% +doing is using his intelligence using +his + + align:start position:0% +his + + + align:start position:0% +his +improvisatory um uh uh capacity to + + align:start position:0% +improvisatory um uh uh capacity to + + + align:start position:0% +improvisatory um uh uh capacity to +figure out how to get away so that even + + align:start position:0% +figure out how to get away so that even + + + align:start position:0% +figure out how to get away so that even +when he's running he is also expressing + + align:start position:0% +when he's running he is also expressing + + + align:start position:0% +when he's running he is also expressing +his nature and when the audience sees + + align:start position:0% +his nature and when the audience sees + + + align:start position:0% +his nature and when the audience sees +the imaginative or clever or daring way + + align:start position:0% +the imaginative or clever or daring way + + + align:start position:0% +the imaginative or clever or daring way +in which he makes his Escape in a + + align:start position:0% +in which he makes his Escape in a + + + align:start position:0% +in which he makes his Escape in a +particular Chase sequence they're not + + align:start position:0% +particular Chase sequence they're not + + + align:start position:0% +particular Chase sequence they're not +just being amused by a joke they are + + align:start position:0% +just being amused by a joke they are + + + align:start position:0% +just being amused by a joke they are +also understanding his character in a + + align:start position:0% +also understanding his character in a + + + align:start position:0% +also understanding his character in a +deep way he's he he he's defining his + + align:start position:0% +deep way he's he he he's defining his + + + align:start position:0% +deep way he's he he he's defining his +character even as he's also amusing us + + align:start position:0% +character even as he's also amusing us + + + align:start position:0% +character even as he's also amusing us +so we can feel the multiplicity of that + + align:start position:0% +so we can feel the multiplicity of that + + + align:start position:0% +so we can feel the multiplicity of that +the density the texture of that always a + + align:start position:0% +the density the texture of that always a + + + align:start position:0% +the density the texture of that always a +mark of superior entertainment always a + + align:start position:0% +mark of superior entertainment always a + + + align:start position:0% +mark of superior entertainment always a +Mark I would say of art itself well uh + + align:start position:0% +Mark I would say of art itself well uh + + + align:start position:0% +Mark I would say of art itself well uh +one way to clarify some of this and + + align:start position:0% +one way to clarify some of this and + + + align:start position:0% +one way to clarify some of this and +especially to clarify chaplain's + + align:start position:0% +especially to clarify chaplain's + + + align:start position:0% +especially to clarify chaplain's +remarkable popularity is to talk about + + align:start position:0% +remarkable popularity is to talk about + + + align:start position:0% +remarkable popularity is to talk about +the as a myth uh as a Mythic + + align:start position:0% +the as a myth uh as a Mythic + + + align:start position:0% +the as a myth uh as a Mythic +figure and if you think about his + + align:start position:0% +figure and if you think about his + + + align:start position:0% +figure and if you think about his +costume you'll understand what what + + align:start position:0% +costume you'll understand what what + + + align:start position:0% +costume you'll understand what what +partly what I mean he wears a coat and + + align:start position:0% +partly what I mean he wears a coat and + + + align:start position:0% +partly what I mean he wears a coat and +vest that are too tight right and pants + + align:start position:0% +vest that are too tight right and pants + + + align:start position:0% +vest that are too tight right and pants +and shoes that are too big so the + + align:start position:0% +and shoes that are too big so the + + + align:start position:0% +and shoes that are too big so the +principle of mismatch or of ambiguity is + + align:start position:0% +principle of mismatch or of ambiguity is + + + align:start position:0% +principle of mismatch or of ambiguity is +built into his costume right uh and and + + align:start position:0% +built into his costume right uh and and + + + align:start position:0% +built into his costume right uh and and +then he carries this cane and this hat + + align:start position:0% +then he carries this cane and this hat + + + align:start position:0% +then he carries this cane and this hat +is now he shows a kind of Elegance but + + align:start position:0% +is now he shows a kind of Elegance but + + + align:start position:0% +is now he shows a kind of Elegance but +it's a kind of shabby down down Market + + align:start position:0% +it's a kind of shabby down down Market + + + align:start position:0% +it's a kind of shabby down down Market +El Elegance but the question is does + + align:start position:0% +El Elegance but the question is does + + + align:start position:0% +El Elegance but the question is does +Char is Charlie downwardly mobile is he + + align:start position:0% +Char is Charlie downwardly mobile is he + + + align:start position:0% +Char is Charlie downwardly mobile is he +an aristocrat who's fallen on hard times + + align:start position:0% +an aristocrat who's fallen on hard times + + + align:start position:0% +an aristocrat who's fallen on hard times +or is he a poor person who has put on HS + + align:start position:0% +or is he a poor person who has put on HS + + + align:start position:0% +or is he a poor person who has put on HS +and and aspires to the world of of + + align:start position:0% +and and aspires to the world of of + + + align:start position:0% +and and aspires to the world of of +tuxedos and fan and fancy clothes this + + align:start position:0% +tuxedos and fan and fancy clothes this + + + align:start position:0% +tuxedos and fan and fancy clothes this +question is never answered and that + + align:start position:0% +question is never answered and that + + + align:start position:0% +question is never answered and that +ambiguity in his character may be part + + align:start position:0% +ambiguity in his character may be part + + + align:start position:0% +ambiguity in his character may be part +of why the audience is able to identify + + align:start position:0% +of why the audience is able to identify + + + align:start position:0% +of why the audience is able to identify +with him there's a there's an + + align:start position:0% +with him there's a there's an + + + align:start position:0% +with him there's a there's an +uncertainty about where he belongs + + align:start position:0% +uncertainty about where he belongs + + + align:start position:0% +uncertainty about where he belongs +about a a kind of mismatch or an + + align:start position:0% +about a a kind of mismatch or an + + + align:start position:0% +about a a kind of mismatch or an +ambiguity inherent in his costume his + + align:start position:0% +ambiguity inherent in his costume his + + + align:start position:0% +ambiguity inherent in his costume his +body itself is a is a source of his myth + + align:start position:0% +body itself is a is a source of his myth + + + align:start position:0% +body itself is a is a source of his myth +as well of his myth mythological status + + align:start position:0% +as well of his myth mythological status + + + align:start position:0% +as well of his myth mythological status +it's small dextrous energetic incredibly + + align:start position:0% +it's small dextrous energetic incredibly + + + align:start position:0% +it's small dextrous energetic incredibly +graceful he's one of the great acrobats + + align:start position:0% +graceful he's one of the great acrobats + + + align:start position:0% +graceful he's one of the great acrobats +and physical dancers physical performers + + align:start position:0% +and physical dancers physical performers + + + align:start position:0% +and physical dancers physical performers +that we've ever you'll ever see and in + + align:start position:0% +that we've ever you'll ever see and in + + + align:start position:0% +that we've ever you'll ever see and in +the films you'll see tonight you'll see + + align:start position:0% +the films you'll see tonight you'll see + + + align:start position:0% +the films you'll see tonight you'll see +many examples of this including examples + + align:start position:0% +many examples of this including examples + + + align:start position:0% +many examples of this including examples +of CH chaplain on skates of chaplain of + + align:start position:0% +of CH chaplain on skates of chaplain of + + + align:start position:0% +of CH chaplain on skates of chaplain of +of of chaplain doing the equivalent of + + align:start position:0% +of of chaplain doing the equivalent of + + + align:start position:0% +of of chaplain doing the equivalent of +dances and and of chaplain of his of his + + align:start position:0% +dances and and of chaplain of his of his + + + align:start position:0% +dances and and of chaplain of his of his +dextrous in situations involving running + + align:start position:0% +dextrous in situations involving running + + + align:start position:0% +dextrous in situations involving running +or Escape as uh uh just as powerfully uh + + align:start position:0% +or Escape as uh uh just as powerfully uh + + + align:start position:0% +or Escape as uh uh just as powerfully uh +as as one as as anyone we'll see + + align:start position:0% +as as one as as anyone we'll see + + + align:start position:0% +as as one as as anyone we'll see +dramatizations of this just as powerful + + align:start position:0% +dramatizations of this just as powerful + + + align:start position:0% +dramatizations of this just as powerful +as anyone could ever imagine ever hope + + align:start position:0% +as anyone could ever imagine ever hope + + + align:start position:0% +as anyone could ever imagine ever hope +for uh and then his face so his costume + + align:start position:0% +for uh and then his face so his costume + + + align:start position:0% +for uh and then his face so his costume +his body and then his face are part of + + align:start position:0% +his body and then his face are part of + + + align:start position:0% +his body and then his face are part of +the myth as well his an unbelievably + + align:start position:0% +the myth as well his an unbelievably + + + align:start position:0% +the myth as well his an unbelievably +expressive face his face is a theater in + + align:start position:0% +expressive face his face is a theater in + + + align:start position:0% +expressive face his face is a theater in +itself and it was chaplain more than any + + align:start position:0% +itself and it was chaplain more than any + + + align:start position:0% +itself and it was chaplain more than any +other early director who explored the + + align:start position:0% +other early director who explored the + + + align:start position:0% +other early director who explored the +implications of the close-up uh and I'll + + align:start position:0% +implications of the close-up uh and I'll + + + align:start position:0% +implications of the close-up uh and I'll +show you some examples tonight of the + + align:start position:0% +show you some examples tonight of the + + + align:start position:0% +show you some examples tonight of the +power of of the way in which chaplain + + align:start position:0% +power of of the way in which chaplain + + + align:start position:0% +power of of the way in which chaplain +manages to uh use the close-up for in in + + align:start position:0% +manages to uh use the close-up for in in + + + align:start position:0% +manages to uh use the close-up for in in +in silent film for incredibly El but to + + align:start position:0% +in silent film for incredibly El but to + + + align:start position:0% +in silent film for incredibly El but to +do so to do so and to be at the same + + align:start position:0% +do so to do so and to be at the same + + + align:start position:0% +do so to do so and to be at the same +time what we might call deeply + + align:start position:0% +time what we might call deeply + + + align:start position:0% +time what we might call deeply +incredibly eloquent uh a silence that is + + align:start position:0% +incredibly eloquent uh a silence that is + + + align:start position:0% +incredibly eloquent uh a silence that is +eloquent because of the uh qualities in + + align:start position:0% +eloquent because of the uh qualities in + + + align:start position:0% +eloquent because of the uh qualities in +his face um and the moral qualities of + + align:start position:0% +his face um and the moral qualities of + + + align:start position:0% +his face um and the moral qualities of +the are also appropriately + + align:start position:0% +the are also appropriately + + + align:start position:0% +the are also appropriately +ambiguous uh he has chalc qualities he + + align:start position:0% +ambiguous uh he has chalc qualities he + + + align:start position:0% +ambiguous uh he has chalc qualities he +wants to defend children and and + + align:start position:0% +wants to defend children and and + + + align:start position:0% +wants to defend children and and +vulnerable women he's always a kind of + + align:start position:0% +vulnerable women he's always a kind of + + + align:start position:0% +vulnerable women he's always a kind of +uh defender of the weak but at the same + + align:start position:0% +uh defender of the weak but at the same + + + align:start position:0% +uh defender of the weak but at the same +time he's an opportunist and also a + + align:start position:0% +time he's an opportunist and also a + + + align:start position:0% +time he's an opportunist and also a +Survivor and these qualities don't fit + + align:start position:0% +Survivor and these qualities don't fit + + + align:start position:0% +Survivor and these qualities don't fit +perfectly together and we see both + + align:start position:0% +perfectly together and we see both + + + align:start position:0% +perfectly together and we see both +elements in the in the character + + align:start position:0% +elements in the in the character + + + align:start position:0% +elements in the in the character +again and again again tonight in in the + + align:start position:0% +again and again again tonight in in the + + + align:start position:0% +again and again again tonight in in the +Immigrant especially you'll see both + + align:start position:0% +Immigrant especially you'll see both + + + align:start position:0% +Immigrant especially you'll see both +sides of of of the chaplain character + + align:start position:0% +sides of of of the chaplain character + + + align:start position:0% +sides of of of the chaplain character +both his opportunistic side and also his + + align:start position:0% +both his opportunistic side and also his + + + align:start position:0% +both his opportunistic side and also his +chalri side so so so he was so so these + + align:start position:0% +chalri side so so so he was so so these + + + align:start position:0% +chalri side so so so he was so so these +these qualities created a kind of Mythic + + align:start position:0% +these qualities created a kind of Mythic + + + align:start position:0% +these qualities created a kind of Mythic +Aura a Mythic Authority for chaplain and + + align:start position:0% +Aura a Mythic Authority for chaplain and + + + align:start position:0% +Aura a Mythic Authority for chaplain and +there's one other thing that contributed + + align:start position:0% +there's one other thing that contributed + + + align:start position:0% +there's one other thing that contributed +to the myth it was that it was that + + align:start position:0% +to the myth it was that it was that + + + align:start position:0% +to the myth it was that it was that +there's a historical reality to the hobo + + align:start position:0% +there's a historical reality to the hobo + + + align:start position:0% +there's a historical reality to the hobo +figure long before Charlie Chaplan began + + align:start position:0% +figure long before Charlie Chaplan began + + + align:start position:0% +figure long before Charlie Chaplan began +to perform as a kind of tra figure + + align:start position:0% +to perform as a kind of tra figure + + + align:start position:0% +to perform as a kind of tra figure +in the movies there were real Tramps in + + align:start position:0% +in the movies there were real Tramps in + + + align:start position:0% +in the movies there were real Tramps in +the society and and that that the the + + align:start position:0% +the society and and that that the the + + + align:start position:0% +the society and and that that the the +the existence of a genuine popul a + + align:start position:0% +the existence of a genuine popul a + + + align:start position:0% +the existence of a genuine popul a +genuine population of homeless people + + align:start position:0% +genuine population of homeless people + + + align:start position:0% +genuine population of homeless people +who they often rode the rails they off + + align:start position:0% +who they often rode the rails they off + + + align:start position:0% +who they often rode the rails they off +uh and and and they were they were they + + align:start position:0% +uh and and and they were they were they + + + align:start position:0% +uh and and and they were they were they +were present actors in most most small + + align:start position:0% +were present actors in most most small + + + align:start position:0% +were present actors in most most small +large and small cities in the country + + align:start position:0% +large and small cities in the country + + + align:start position:0% +large and small cities in the country +the the fact was there was a population + + align:start position:0% +the the fact was there was a population + + + align:start position:0% +the the fact was there was a population +of homeless people and that that the + + align:start position:0% +of homeless people and that that the + + + align:start position:0% +of homeless people and that that the + figure alluded to and reminded the + + align:start position:0% + figure alluded to and reminded the + + + align:start position:0% + figure alluded to and reminded the +audience of and that also gave him + + align:start position:0% +audience of and that also gave him + + + align:start position:0% +audience of and that also gave him +helped to helped to strengthen his his + + align:start position:0% +helped to helped to strengthen his his + + + align:start position:0% +helped to helped to strengthen his his +Mythic power because it was as if the + + align:start position:0% +Mythic power because it was as if the + + + align:start position:0% +Mythic power because it was as if the +audience was recognizing that there were + + align:start position:0% +audience was recognizing that there were + + + align:start position:0% +audience was recognizing that there were +uh that that that in some sense Charlie + + align:start position:0% +uh that that that in some sense Charlie + + + align:start position:0% +uh that that that in some sense Charlie +was a kind of embodiment or a symbol of + + align:start position:0% +was a kind of embodiment or a symbol of + + + align:start position:0% +was a kind of embodiment or a symbol of +this of this social + + align:start position:0% +this of this social + + + align:start position:0% +this of this social +actuality so he was he had a kind of + + align:start position:0% +actuality so he was he had a kind of + + + align:start position:0% +actuality so he was he had a kind of +Mythic power that communicated itself to + + align:start position:0% +Mythic power that communicated itself to + + + align:start position:0% +Mythic power that communicated itself to +his to to his audience and it meant that + + align:start position:0% +his to to his audience and it meant that + + + align:start position:0% +his to to his audience and it meant that +every repetition of the of a film + + align:start position:0% +every repetition of the of a film + + + align:start position:0% +every repetition of the of a film +which might very well go through the + + align:start position:0% +which might very well go through the + + + align:start position:0% +which might very well go through the +same motions but put the in a + + align:start position:0% +same motions but put the in a + + + align:start position:0% +same motions but put the in a +slightly different environment or a + + align:start position:0% +slightly different environment or a + + + align:start position:0% +slightly different environment or a +slightly different job would be pleasing + + align:start position:0% +slightly different job would be pleasing + + + align:start position:0% +slightly different job would be pleasing +to the audience some principle of + + align:start position:0% +to the audience some principle of + + + align:start position:0% +to the audience some principle of +repetition and variation right well + + align:start position:0% +repetition and variation right well + + + align:start position:0% +repetition and variation right well +finally the Paradox of of chaplain's + + align:start position:0% +finally the Paradox of of chaplain's + + + align:start position:0% +finally the Paradox of of chaplain's +work and the Paradox I want you to think + + align:start position:0% +work and the Paradox I want you to think + + + align:start position:0% +work and the Paradox I want you to think +about tonight and will end with this + + align:start position:0% +about tonight and will end with this + + + align:start position:0% +about tonight and will end with this +point uh is that chaplain's world is + + align:start position:0% +point uh is that chaplain's world is + + + align:start position:0% +point uh is that chaplain's world is +full of Comedy it's a comic it's a + + align:start position:0% +full of Comedy it's a comic it's a + + + align:start position:0% +full of Comedy it's a comic it's a +comedian's world although it's more than + + align:start position:0% +comedian's world although it's more than + + + align:start position:0% +comedian's world although it's more than +just comic as I've suggested But the + + align:start position:0% +just comic as I've suggested But the + + + align:start position:0% +just comic as I've suggested But the +irony of chaplain's world is that the + + align:start position:0% +irony of chaplain's world is that the + + + align:start position:0% +irony of chaplain's world is that the +comedy is so fundamentally based on + + align:start position:0% +comedy is so fundamentally based on + + + align:start position:0% +comedy is so fundamentally based on +things that are so deeply unfunny + + align:start position:0% +things that are so deeply unfunny + + + align:start position:0% +things that are so deeply unfunny +chaplain's the most deeply social and in + + align:start position:0% +chaplain's the most deeply social and in + + + align:start position:0% +chaplain's the most deeply social and in +some ways even political of directors + + align:start position:0% +some ways even political of directors + + + align:start position:0% +some ways even political of directors +and I'll discuss this aspect of his work + + align:start position:0% +and I'll discuss this aspect of his work + + + align:start position:0% +and I'll discuss this aspect of his work +tonight when we talk about modern times + + align:start position:0% +tonight when we talk about modern times + + + align:start position:0% +tonight when we talk about modern times +and some of his other some of his other + + align:start position:0% +and some of his other some of his other + + + align:start position:0% +and some of his other some of his other +films but the crucial Point here is that + + align:start position:0% +films but the crucial Point here is that + + + align:start position:0% +films but the crucial Point here is that +chaplain's world is a world of Elemental + + align:start position:0% +chaplain's world is a world of Elemental + + + align:start position:0% +chaplain's world is a world of Elemental +themes virtually every single chaplain + + align:start position:0% +themes virtually every single chaplain + + + align:start position:0% +themes virtually every single chaplain +movie is about Hunger aggression + + align:start position:0% +movie is about Hunger aggression + + + align:start position:0% +movie is about Hunger aggression +victimization confinement I mean the + + align:start position:0% +victimization confinement I mean the + + + align:start position:0% +victimization confinement I mean the +subject matter of chaplain's Comedy is + + align:start position:0% +subject matter of chaplain's Comedy is + + + align:start position:0% +subject matter of chaplain's Comedy is +the LA is the is the furthest from + + align:start position:0% +the LA is the is the furthest from + + + align:start position:0% +the LA is the is the furthest from +Comedy and part of his genius part of + + align:start position:0% +Comedy and part of his genius part of + + + align:start position:0% +Comedy and part of his genius part of +what makes him such a remarkable and + + align:start position:0% +what makes him such a remarkable and + + + align:start position:0% +what makes him such a remarkable and +important artist is that this immensely + + align:start position:0% +important artist is that this immensely + + + align:start position:0% +important artist is that this immensely +unpromising material this disturbing and + + align:start position:0% +unpromising material this disturbing and + + + align:start position:0% +unpromising material this disturbing and +uh in in many ways frightening material + + align:start position:0% +uh in in many ways frightening material + + + align:start position:0% +uh in in many ways frightening material +dramatized sometimes with full + + align:start position:0% +dramatized sometimes with full + + + align:start position:0% +dramatized sometimes with full +frightening effect chaplain often + + align:start position:0% +frightening effect chaplain often + + + align:start position:0% +frightening effect chaplain often +because of his diminutiveness puts + + align:start position:0% +because of his diminutiveness puts + + + align:start position:0% +because of his diminutiveness puts +himself up against large figures giant + + align:start position:0% +himself up against large figures giant + + + align:start position:0% +himself up against large figures giant +figures to emphasize his vulnerability + + align:start position:0% +figures to emphasize his vulnerability + + + align:start position:0% +figures to emphasize his vulnerability +and smallness again and again the + + align:start position:0% +and smallness again and again the + + + align:start position:0% +and smallness again and again the +substance of chaplain's Comedy is the + + align:start position:0% +substance of chaplain's Comedy is the + + + align:start position:0% +substance of chaplain's Comedy is the +substance of victimization aggression + + align:start position:0% +substance of victimization aggression + + + align:start position:0% +substance of victimization aggression +misery uh uh inequality inequity in + + align:start position:0% +misery uh uh inequality inequity in + + + align:start position:0% +misery uh uh inequality inequity in +other words the subject matter of + + align:start position:0% +other words the subject matter of + + + align:start position:0% +other words the subject matter of +chaplain's work is the furthest from + + align:start position:0% +chaplain's work is the furthest from + + + align:start position:0% +chaplain's work is the furthest from +Comedy and yet he makes enduring comedy + + align:start position:0% +Comedy and yet he makes enduring comedy + + + align:start position:0% +Comedy and yet he makes enduring comedy +enduring melodrama out of those + + align:start position:0% +enduring melodrama out of those + + + align:start position:0% +enduring melodrama out of those +unpromising materials that Paradox is + + align:start position:0% +unpromising materials that Paradox is + + + align:start position:0% +unpromising materials that Paradox is +about chaplain's world is at the heart + + align:start position:0% +about chaplain's world is at the heart + + + align:start position:0% +about chaplain's world is at the heart +of his work and it's at the heart of why + + align:start position:0% +of his work and it's at the heart of why + + + align:start position:0% +of his work and it's at the heart of why +he why of all silent directors his very + + align:start position:0% +he why of all silent directors his very + + + align:start position:0% +he why of all silent directors his very +best films remain interesting today + + align:start position:0% +best films remain interesting today + + + align:start position:0% +best films remain interesting today +intrinsically not just because they're + + align:start position:0% +intrinsically not just because they're + + + align:start position:0% +intrinsically not just because they're +wonderfully interesting artifacts but + + align:start position:0% +wonderfully interesting artifacts but + + + align:start position:0% +wonderfully interesting artifacts but +intrinsically because they remain + + align:start position:0% +intrinsically because they remain + + + align:start position:0% +intrinsically because they remain +serious valuable films some of the films + + align:start position:0% +serious valuable films some of the films + + + align:start position:0% +serious valuable films some of the films +you'll all of the chaplain films you're + + align:start position:0% +you'll all of the chaplain films you're + + + align:start position:0% +you'll all of the chaplain films you're +going to see tonight the two shorts and + + align:start position:0% +going to see tonight the two shorts and + + + align:start position:0% +going to see tonight the two shorts and +modern times fit that description as I + + align:start position:0% +modern times fit that description as I + + + align:start position:0% +modern times fit that description as I +hope you will agree see you this + + align:start position:0% + + + + align:start position:0% + +evening for \ No newline at end of file diff --git a/mB_rrEN_Ltc.txt b/mB_rrEN_Ltc.txt new file mode 100644 index 0000000000000000000000000000000000000000..bf63bd1214494391d1e61f2a90ff5450843d0b24 --- /dev/null +++ b/mB_rrEN_Ltc.txt @@ -0,0 +1,8307 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay let's get on with today's lecture + + align:start position:0% +okay let's get on with today's lecture + + + align:start position:0% +okay let's get on with today's lecture +and I want to look at a variety of + + align:start position:0% +and I want to look at a variety of + + + align:start position:0% +and I want to look at a variety of +different problems different class + + align:start position:0% +different problems different class + + + align:start position:0% +different problems different class +different classes of problems we're + + align:start position:0% +different classes of problems we're + + + align:start position:0% +different classes of problems we're +going to look at four different classes + + align:start position:0% +going to look at four different classes + + + align:start position:0% +going to look at four different classes +of problems and talk about the way you + + align:start position:0% +of problems and talk about the way you + + + align:start position:0% +of problems and talk about the way you +to go about approaching them we need + + align:start position:0% +to go about approaching them we need + + + align:start position:0% +to go about approaching them we need +very few fundamental laws we're going to + + align:start position:0% +very few fundamental laws we're going to + + + align:start position:0% +very few fundamental laws we're going to +use we use the same fundamental laws + + align:start position:0% +use we use the same fundamental laws + + + align:start position:0% +use we use the same fundamental laws +again and again and the issue is really + + align:start position:0% +again and again and the issue is really + + + align:start position:0% +again and again and the issue is really +how do you go about applying them one is + + align:start position:0% +how do you go about applying them one is + + + align:start position:0% +how do you go about applying them one is +the some this fundamental laws for rigid + + align:start position:0% +the some this fundamental laws for rigid + + + align:start position:0% +the some this fundamental laws for rigid +bodies so the fundamental laws that are + + align:start position:0% +bodies so the fundamental laws that are + + + align:start position:0% +bodies so the fundamental laws that are +always true the sum of the external + + align:start position:0% +always true the sum of the external + + + align:start position:0% +always true the sum of the external +forces vectors time rate of change of + + align:start position:0% +forces vectors time rate of change of + + + align:start position:0% +forces vectors time rate of change of +the momentum of the system with respect + + align:start position:0% +the momentum of the system with respect + + + align:start position:0% +the momentum of the system with respect +to an inertial frame and we know that + + align:start position:0% +to an inertial frame and we know that + + + align:start position:0% +to an inertial frame and we know that +didn't we recognize as mass times + + align:start position:0% +didn't we recognize as mass times + + + align:start position:0% +didn't we recognize as mass times +acceleration Newton's second law the + + align:start position:0% +acceleration Newton's second law the + + + align:start position:0% +acceleration Newton's second law the +other one is the summation of external + + align:start position:0% +other one is the summation of external + + + align:start position:0% +other one is the summation of external +torques and that one is the time + + align:start position:0% +torques and that one is the time + + + align:start position:0% +torques and that one is the time +derivative of angular momentum with + + align:start position:0% +derivative of angular momentum with + + + align:start position:0% +derivative of angular momentum with +respect to a point which you choose this + + align:start position:0% +respect to a point which you choose this + + + align:start position:0% +respect to a point which you choose this +is an A + + align:start position:0% + + + + align:start position:0% + +plus the velocity of a with respect to + + align:start position:0% +plus the velocity of a with respect to + + + align:start position:0% +plus the velocity of a with respect to +the inertial frame cross with the + + align:start position:0% +the inertial frame cross with the + + + align:start position:0% +the inertial frame cross with the +momentum with respect to the inertial + + align:start position:0% +momentum with respect to the inertial + + + align:start position:0% +momentum with respect to the inertial +frame so that's the torque equation now + + align:start position:0% +frame so that's the torque equation now + + + align:start position:0% +frame so that's the torque equation now +we have two special cases of this where + + align:start position:0% +we have two special cases of this where + + + align:start position:0% +we have two special cases of this where +the second term goes away one is when + + align:start position:0% +the second term goes away one is when + + + align:start position:0% +the second term goes away one is when +you are at the center of gravity in + + align:start position:0% +you are at the center of gravity in + + + align:start position:0% +you are at the center of gravity in +which case by definition the velocity of + + align:start position:0% +which case by definition the velocity of + + + align:start position:0% +which case by definition the velocity of +that point and the momentum are in the + + align:start position:0% +that point and the momentum are in the + + + align:start position:0% +that point and the momentum are in the +same direction the cross product + + align:start position:0% +same direction the cross product + + + align:start position:0% +same direction the cross product +disappears so we there's two special + + align:start position:0% +disappears so we there's two special + + + align:start position:0% +disappears so we there's two special +cases we use all the time when it's + + align:start position:0% +cases we use all the time when it's + + + align:start position:0% +cases we use all the time when it's +simplifies to that one is when you're at + + align:start position:0% +simplifies to that one is when you're at + + + align:start position:0% +simplifies to that one is when you're at +the center of gravity the other is when + + align:start position:0% +the center of gravity the other is when + + + align:start position:0% +the center of gravity the other is when +for whatever reason this velocity is + + align:start position:0% +for whatever reason this velocity is + + + align:start position:0% +for whatever reason this velocity is +parallel to that and the cross product + + align:start position:0% +parallel to that and the cross product + + + align:start position:0% +parallel to that and the cross product +goes to zero and sometimes the velocity + + align:start position:0% +goes to zero and sometimes the velocity + + + align:start position:0% +goes to zero and sometimes the velocity +is just plain zero so lots of there are + + align:start position:0% +is just plain zero so lots of there are + + + align:start position:0% +is just plain zero so lots of there are +some certain cases that we use lots of + + align:start position:0% +some certain cases that we use lots of + + + align:start position:0% +some certain cases that we use lots of +times when that term goes away but + + align:start position:0% +times when that term goes away but + + + align:start position:0% +times when that term goes away but +sometimes it doesn't need to have to put + + align:start position:0% +sometimes it doesn't need to have to put + + + align:start position:0% +sometimes it doesn't need to have to put +up put up with it + + align:start position:0% + + + + align:start position:0% + +so those are our two fundamental laws + + align:start position:0% +so those are our two fundamental laws + + + align:start position:0% +so those are our two fundamental laws +and the question really is how to go + + align:start position:0% +and the question really is how to go + + + align:start position:0% +and the question really is how to go +about applying them so I'm going to look + + align:start position:0% +about applying them so I'm going to look + + + align:start position:0% +about applying them so I'm going to look +at four four classes of problems + + align:start position:0% + + + + align:start position:0% + +sort of name them right now pure I know + + align:start position:0% +sort of name them right now pure I know + + + align:start position:0% +sort of name them right now pure I know +the simplest of heart is pure rotation + + align:start position:0% + + + + align:start position:0% + +about a fixed axis through G through the + + align:start position:0% +about a fixed axis through G through the + + + align:start position:0% +about a fixed axis through G through the +center of mass pretty trivial we can all + + align:start position:0% +center of mass pretty trivial we can all + + + align:start position:0% +center of mass pretty trivial we can all +do those kind of problems a second-class + + align:start position:0% + + + + align:start position:0% + +pure rotation about fix axis at a which + + align:start position:0% +pure rotation about fix axis at a which + + + align:start position:0% +pure rotation about fix axis at a which +is not equal to G and not at the center + + align:start position:0% +is not equal to G and not at the center + + + align:start position:0% +is not equal to G and not at the center +of mass again pretty simple problems + + align:start position:0% + + + + align:start position:0% + +third class no external + + align:start position:0% + + + + align:start position:0% + +I'll call it no external constraints + + align:start position:0% + + + + align:start position:0% + +we'll have to look at you an example to + + align:start position:0% +we'll have to look at you an example to + + + align:start position:0% +we'll have to look at you an example to +see how to really mean I will give you + + align:start position:0% +see how to really mean I will give you + + + align:start position:0% +see how to really mean I will give you +an example right now which will do you + + align:start position:0% +an example right now which will do you + + + align:start position:0% +an example right now which will do you +have this hockey puck with a string + + align:start position:0% +have this hockey puck with a string + + + align:start position:0% +have this hockey puck with a string +attached to it force in this whole thing + + align:start position:0% +attached to it force in this whole thing + + + align:start position:0% +attached to it force in this whole thing +is on on a frictionless surface so it's + + align:start position:0% +is on on a frictionless surface so it's + + + align:start position:0% +is on on a frictionless surface so it's +constrained so it can't go through the + + align:start position:0% +constrained so it can't go through the + + + align:start position:0% +constrained so it can't go through the +surface but so no external constraints + + align:start position:0% +surface but so no external constraints + + + align:start position:0% +surface but so no external constraints +in the direction that the motion can + + align:start position:0% +in the direction that the motion can + + + align:start position:0% +in the direction that the motion can +happen so this is a 2d problem can move + + align:start position:0% +happen so this is a 2d problem can move + + + align:start position:0% +happen so this is a 2d problem can move +in the XY and rotation but it's not + + align:start position:0% +in the XY and rotation but it's not + + + align:start position:0% +in the XY and rotation but it's not +touching there's no contains + + align:start position:0% +touching there's no contains + + + align:start position:0% +touching there's no contains +constraining it in them in the + + align:start position:0% +constraining it in them in the + + + align:start position:0% +constraining it in them in the +directions of movement which are allowed + + align:start position:0% +directions of movement which are allowed + + + align:start position:0% +directions of movement which are allowed +in the problem that's just too much + + align:start position:0% +in the problem that's just too much + + + align:start position:0% +in the problem that's just too much +words to write up here so this kind of + + align:start position:0% +words to write up here so this kind of + + + align:start position:0% +words to write up here so this kind of +problem and the fourth are problems with + + align:start position:0% + + + + align:start position:0% + +moving points of constraint now though + + align:start position:0% +moving points of constraint now though + + + align:start position:0% +moving points of constraint now though +you won't see a textbook with sections + + align:start position:0% +you won't see a textbook with sections + + + align:start position:0% +you won't see a textbook with sections +broken out like this I'm using my own + + align:start position:0% +broken out like this I'm using my own + + + align:start position:0% +broken out like this I'm using my own +terminology I just made it up last night + + align:start position:0% +terminology I just made it up last night + + + align:start position:0% +terminology I just made it up last night +as I was finishing off the lecture but + + align:start position:0% +as I was finishing off the lecture but + + + align:start position:0% +as I was finishing off the lecture but +so you this is just give I'm trying to + + align:start position:0% +so you this is just give I'm trying to + + + align:start position:0% +so you this is just give I'm trying to +give you some insight and this is the + + align:start position:0% +give you some insight and this is the + + + align:start position:0% +give you some insight and this is the +way I think about these things so let's + + align:start position:0% +way I think about these things so let's + + + align:start position:0% +way I think about these things so let's +quickly go through examples from the + + align:start position:0% +quickly go through examples from the + + + align:start position:0% +quickly go through examples from the +first couple of types because they're + + align:start position:0% +first couple of types because they're + + + align:start position:0% +first couple of types because they're +especially easy so what are we saying + + align:start position:0% +especially easy so what are we saying + + + align:start position:0% +especially easy so what are we saying +they're pure rotation about a fixed axis + + align:start position:0% +they're pure rotation about a fixed axis + + + align:start position:0% +they're pure rotation about a fixed axis +through G okay center of mass is + + align:start position:0% +through G okay center of mass is + + + align:start position:0% +through G okay center of mass is +somewhere along this axle the axle is + + align:start position:0% +somewhere along this axle the axle is + + + align:start position:0% +somewhere along this axle the axle is +fixed so object can spin around it and + + align:start position:0% +fixed so object can spin around it and + + + align:start position:0% +fixed so object can spin around it and +these kind of problems are particularly + + align:start position:0% +these kind of problems are particularly + + + align:start position:0% +these kind of problems are particularly +simple so I'm not going to dwell on them + + align:start position:0% +simple so I'm not going to dwell on them + + + align:start position:0% +simple so I'm not going to dwell on them +but here's class 1 1+1 problems and it's + + align:start position:0% +but here's class 1 1+1 problems and it's + + + align:start position:0% +but here's class 1 1+1 problems and it's +basically the exact ly rotors of almost + + align:start position:0% +basically the exact ly rotors of almost + + + align:start position:0% +basically the exact ly rotors of almost +all kinds so for these problems you use + + align:start position:0% +all kinds so for these problems you use + + + align:start position:0% +all kinds so for these problems you use +momentum angular momentum with respect + + align:start position:0% +momentum angular momentum with respect + + + align:start position:0% +momentum angular momentum with respect +to the center of mass you can express it + + align:start position:0% +to the center of mass you can express it + + + align:start position:0% +to the center of mass you can express it +as IG times ikx Megha Y Omega Z all + + align:start position:0% +as IG times ikx Megha Y Omega Z all + + + align:start position:0% +as IG times ikx Megha Y Omega Z all +these problems can be expressed with a + + align:start position:0% +these problems can be expressed with a + + + align:start position:0% +these problems can be expressed with a +moment of inertia matrix times the + + align:start position:0% +moment of inertia matrix times the + + + align:start position:0% +moment of inertia matrix times the +rotation vector and it'll give you a + + align:start position:0% +rotation vector and it'll give you a + + + align:start position:0% +rotation vector and it'll give you a +checks hyh D and you can use that second + + align:start position:0% +checks hyh D and you can use that second + + + align:start position:0% +checks hyh D and you can use that second +formula up there the torques + + align:start position:0% +formula up there the torques + + + align:start position:0% +formula up there the torques +our dhdt so it's through dicks through G + + align:start position:0% +our dhdt so it's through dicks through G + + + align:start position:0% +our dhdt so it's through dicks through G +so the second term doesn't appear so to + + align:start position:0% +so the second term doesn't appear so to + + + align:start position:0% +so the second term doesn't appear so to +do these problems some of the C I'll + + align:start position:0% +do these problems some of the C I'll + + + align:start position:0% +do these problems some of the C I'll +just give an example here for 2d planar + + align:start position:0% +just give an example here for 2d planar + + + align:start position:0% +just give an example here for 2d planar +motion they get especially simple then + + align:start position:0% +motion they get especially simple then + + + align:start position:0% +motion they get especially simple then +for 2d planar motion that means Omega + + align:start position:0% +for 2d planar motion that means Omega + + + align:start position:0% +for 2d planar motion that means Omega +here is zero zero and we'll let Z be the + + align:start position:0% +here is zero zero and we'll let Z be the + + + align:start position:0% +here is zero zero and we'll let Z be the +rotation axis and this H then with + + align:start position:0% +rotation axis and this H then with + + + align:start position:0% +rotation axis and this H then with +respect to G just becomes i ZZ omega z + + align:start position:0% +respect to G just becomes i ZZ omega z + + + align:start position:0% +respect to G just becomes i ZZ omega z +those are the all those 2d planar motion + + align:start position:0% +those are the all those 2d planar motion + + + align:start position:0% +those are the all those 2d planar motion +problems boil down with this and d hg DT + + align:start position:0% +problems boil down with this and d hg DT + + + align:start position:0% +problems boil down with this and d hg DT +then is eyes easy with respect to G + + align:start position:0% +then is eyes easy with respect to G + + + align:start position:0% +then is eyes easy with respect to G +Omega Z dot or more familiar notation so + + align:start position:0% +Omega Z dot or more familiar notation so + + + align:start position:0% +Omega Z dot or more familiar notation so +all those planar motion problems passing + + align:start position:0% +all those planar motion problems passing + + + align:start position:0% +all those planar motion problems passing +through axis passing through G like this + + align:start position:0% +through axis passing through G like this + + + align:start position:0% +through axis passing through G like this +does for those problems does this matrix + + align:start position:0% +does for those problems does this matrix + + + align:start position:0% +does for those problems does this matrix +have to be with respect to principal + + align:start position:0% +have to be with respect to principal + + + align:start position:0% +have to be with respect to principal +axes you have your Xyz coordinate system + + align:start position:0% +axes you have your Xyz coordinate system + + + align:start position:0% +axes you have your Xyz coordinate system +to do these to do this style of problem + + align:start position:0% +to do these to do this style of problem + + + align:start position:0% +to do these to do this style of problem +does that actually have to be expressed + + align:start position:0% +does that actually have to be expressed + + + align:start position:0% +does that actually have to be expressed +in principal coordinates so that it's + + align:start position:0% +in principal coordinates so that it's + + + align:start position:0% +in principal coordinates so that it's +diagonal + + align:start position:0% + + + + align:start position:0% + +doesn't have to be this this you're + + align:start position:0% +doesn't have to be this this you're + + + align:start position:0% +doesn't have to be this this you're +worried about rotation about z you'll + + align:start position:0% +worried about rotation about z you'll + + + align:start position:0% +worried about rotation about z you'll +find that that statement still always + + align:start position:0% +find that that statement still always + + + align:start position:0% +find that that statement still always +true now there may be if the thing could + + align:start position:0% +true now there may be if the thing could + + + align:start position:0% +true now there may be if the thing could +definitely have imbalances and have + + align:start position:0% +definitely have imbalances and have + + + align:start position:0% +definitely have imbalances and have +unusual other torques that will fall out + + align:start position:0% +unusual other torques that will fall out + + + align:start position:0% +unusual other torques that will fall out +on the problem but the for the motion + + align:start position:0% +on the problem but the for the motion + + + align:start position:0% +on the problem but the for the motion +around the axis of spin this and wertham + + align:start position:0% + + + + align:start position:0% + +where you only have a one Omega Z + + align:start position:0% +where you only have a one Omega Z + + + align:start position:0% +where you only have a one Omega Z +component just the one component you + + align:start position:0% +component just the one component you + + + align:start position:0% +component just the one component you +will get it'll work out just fine yeah + + align:start position:0% +will get it'll work out just fine yeah + + + align:start position:0% +will get it'll work out just fine yeah +some kind of you'll end up with you will + + align:start position:0% +some kind of you'll end up with you will + + + align:start position:0% +some kind of you'll end up with you will +end up with is first of all if you have + + align:start position:0% +end up with is first of all if you have + + + align:start position:0% +end up with is first of all if you have +a day off diagonal Z terms XE Y Z terms + + align:start position:0% +a day off diagonal Z terms XE Y Z terms + + + align:start position:0% +a day off diagonal Z terms XE Y Z terms +when you multiply that out you will find + + align:start position:0% +when you multiply that out you will find + + + align:start position:0% +when you multiply that out you will find +components of H that are in directions + + align:start position:0% +components of H that are in directions + + + align:start position:0% +components of H that are in directions +in the Z direction as well as perhaps in + + align:start position:0% +in the Z direction as well as perhaps in + + + align:start position:0% +in the Z direction as well as perhaps in +the X&Y and those off those other two + + align:start position:0% +the X&Y and those off those other two + + + align:start position:0% +the X&Y and those off those other two +components tell you that H is not + + align:start position:0% +components tell you that H is not + + + align:start position:0% +components tell you that H is not +pointing in the same direction as Omega + + align:start position:0% +pointing in the same direction as Omega + + + align:start position:0% +pointing in the same direction as Omega +right and that it tells you instantly + + align:start position:0% +right and that it tells you instantly + + + align:start position:0% +right and that it tells you instantly +that the thing is dynamically unbalanced + + align:start position:0% +that the thing is dynamically unbalanced + + + align:start position:0% +that the thing is dynamically unbalanced +and we'll have other torques that are + + align:start position:0% +and we'll have other torques that are + + + align:start position:0% +and we'll have other torques that are +trying to bend that axle right so there + + align:start position:0% +trying to bend that axle right so there + + + align:start position:0% +trying to bend that axle right so there +will always appear all right let's move + + align:start position:0% +will always appear all right let's move + + + align:start position:0% +will always appear all right let's move +on I want to make sure we get through + + align:start position:0% +on I want to make sure we get through + + + align:start position:0% +on I want to make sure we get through +this today class two problems these are + + align:start position:0% +this today class two problems these are + + + align:start position:0% +this today class two problems these are +basically the pure rotation around some + + align:start position:0% +basically the pure rotation around some + + + align:start position:0% +basically the pure rotation around some +point that's not through G and for again + + align:start position:0% +point that's not through G and for again + + + align:start position:0% +point that's not through G and for again +though this is a fixed key here is fixed + + align:start position:0% +though this is a fixed key here is fixed + + + align:start position:0% +though this is a fixed key here is fixed +axis at a it's not moving this is what + + align:start position:0% +axis at a it's not moving this is what + + + align:start position:0% +axis at a it's not moving this is what +makes these problems simpler for these + + align:start position:0% +makes these problems simpler for these + + + align:start position:0% +makes these problems simpler for these +kinds of problems you do the sum of the + + align:start position:0% +kinds of problems you do the sum of the + + + align:start position:0% +kinds of problems you do the sum of the +torques with respect to a external + + align:start position:0% +torques with respect to a external + + + align:start position:0% +torques with respect to a external +torques + + align:start position:0% + + + + align:start position:0% + +and because that points fix the second + + align:start position:0% +and because that points fix the second + + + align:start position:0% +and because that points fix the second +terms don't appear the V cross P terms + + align:start position:0% +terms don't appear the V cross P terms + + + align:start position:0% +terms don't appear the V cross P terms +and you can write these as I a moment of + + align:start position:0% +and you can write these as I a moment of + + + align:start position:0% +and you can write these as I a moment of +inertia matrix times whatever the + + align:start position:0% +inertia matrix times whatever the + + + align:start position:0% +inertia matrix times whatever the +rotations are and you would in order to + + align:start position:0% +rotations are and you would in order to + + + align:start position:0% +rotations are and you would in order to +define the mass moment of inertia matrix + + align:start position:0% +define the mass moment of inertia matrix + + + align:start position:0% +define the mass moment of inertia matrix +you must have chosen a set of + + align:start position:0% +you must have chosen a set of + + + align:start position:0% +you must have chosen a set of +coordinates attached to the body right + + align:start position:0% +coordinates attached to the body right + + + align:start position:0% +coordinates attached to the body right +and then with those coordinates you have + + align:start position:0% +and then with those coordinates you have + + + align:start position:0% +and then with those coordinates you have +computed the moments of inertia for the + + align:start position:0% +computed the moments of inertia for the + + + align:start position:0% +computed the moments of inertia for the +body and if you chose wisely + + align:start position:0% +body and if you chose wisely + + + align:start position:0% +body and if you chose wisely +you get principal coordinates and you + + align:start position:0% +you get principal coordinates and you + + + align:start position:0% +you get principal coordinates and you +only get diagonal entries on the matrix + + align:start position:0% +only get diagonal entries on the matrix + + + align:start position:0% +only get diagonal entries on the matrix +to chose unwisely you will get other + + align:start position:0% +to chose unwisely you will get other + + + align:start position:0% +to chose unwisely you will get other +stuff but it's still a valid mass moment + + align:start position:0% +stuff but it's still a valid mass moment + + + align:start position:0% +stuff but it's still a valid mass moment +of inertia matrix it just gives rise you + + align:start position:0% +of inertia matrix it just gives rise you + + + align:start position:0% +of inertia matrix it just gives rise you +have to deal with a bunch of other terms + + align:start position:0% +have to deal with a bunch of other terms + + + align:start position:0% +have to deal with a bunch of other terms +so this will still yield the same answer + + align:start position:0% +so this will still yield the same answer + + + align:start position:0% +so this will still yield the same answer +how do you get i with respect to a this + + align:start position:0% +how do you get i with respect to a this + + + align:start position:0% +how do you get i with respect to a this +is a this is opportunities when you can + + align:start position:0% +is a this is opportunities when you can + + + align:start position:0% +is a this is opportunities when you can +use parallel axis yeah + + align:start position:0% + + + + align:start position:0% + +I forgive this excuse me we need to you + + align:start position:0% +I forgive this excuse me we need to you + + + align:start position:0% +I forgive this excuse me we need to you +need to have finished that out this is + + align:start position:0% +need to have finished that out this is + + + align:start position:0% +need to have finished that out this is +is H so the time derivative of H is the + + align:start position:0% +is H so the time derivative of H is the + + + align:start position:0% +is H so the time derivative of H is the +time derivative of this expression you + + align:start position:0% +time derivative of this expression you + + + align:start position:0% +time derivative of this expression you +have to figure out the moment of inertia + + align:start position:0% +have to figure out the moment of inertia + + + align:start position:0% +have to figure out the moment of inertia +and the rotation rates and you may get + + align:start position:0% +and the rotation rates and you may get + + + align:start position:0% +and the rotation rates and you may get +multiple terms only one of which let's + + align:start position:0% +multiple terms only one of which let's + + + align:start position:0% +multiple terms only one of which let's +say that this will work out you will get + + align:start position:0% +say that this will work out you will get + + + align:start position:0% +say that this will work out you will get +multiple terms you will get torques that + + align:start position:0% +multiple terms you will get torques that + + + align:start position:0% +multiple terms you will get torques that +are not in the direction of spin against + + align:start position:0% +are not in the direction of spin against + + + align:start position:0% +are not in the direction of spin against +these could be these might be unbalanced + + align:start position:0% +these could be these might be unbalanced + + + align:start position:0% +these could be these might be unbalanced +on the other hand it may be for 2d + + align:start position:0% +on the other hand it may be for 2d + + + align:start position:0% +on the other hand it may be for 2d +problems which is sort of common so for + + align:start position:0% +problems which is sort of common so for + + + align:start position:0% +problems which is sort of common so for +the 2d planar motion which most of the + + align:start position:0% +the 2d planar motion which most of the + + + align:start position:0% +the 2d planar motion which most of the +problems we do are then what your s'what + + align:start position:0% +problems we do are then what your s'what + + + align:start position:0% +problems we do are then what your s'what +you would do is you're saying Omega is + + align:start position:0% +you would do is you're saying Omega is + + + align:start position:0% +you would do is you're saying Omega is +say 0 0 Omega Z which simplifies that + + align:start position:0% +say 0 0 Omega Z which simplifies that + + + align:start position:0% +say 0 0 Omega Z which simplifies that +multiplying this thing out quite a lot + + align:start position:0% +multiplying this thing out quite a lot + + + align:start position:0% +multiplying this thing out quite a lot +and if i with respect to G is diagonal + + align:start position:0% +and if i with respect to G is diagonal + + + align:start position:0% +and if i with respect to G is diagonal +then that means you chose your G you + + align:start position:0% +then that means you chose your G you + + + align:start position:0% +then that means you chose your G you +chose principal axes right then but then + + align:start position:0% +chose principal axes right then but then + + + align:start position:0% +chose principal axes right then but then +how do you get to i with respect to a + + align:start position:0% +how do you get to i with respect to a + + + align:start position:0% +how do you get to i with respect to a +for 2d problems you know really simple + + align:start position:0% +for 2d problems you know really simple + + + align:start position:0% +for 2d problems you know really simple +ones how do you get to i with respect to + + align:start position:0% +ones how do you get to i with respect to + + + align:start position:0% +ones how do you get to i with respect to +a that's when you it's the classic case + + align:start position:0% +a that's when you it's the classic case + + + align:start position:0% +a that's when you it's the classic case +for using the parallel axis theorem + + align:start position:0% +for using the parallel axis theorem + + + align:start position:0% +for using the parallel axis theorem +so for these 2d planar motion problems + + align:start position:0% +so for these 2d planar motion problems + + + align:start position:0% +so for these 2d planar motion problems +and it planar motion problems then you + + align:start position:0% +and it planar motion problems then you + + + align:start position:0% +and it planar motion problems then you +can use + + align:start position:0% + + + + align:start position:0% + +parallel axis okay we're going to do + + align:start position:0% +parallel axis okay we're going to do + + + align:start position:0% +parallel axis okay we're going to do +I'll do an example so this is kind of a + + align:start position:0% +I'll do an example so this is kind of a + + + align:start position:0% +I'll do an example so this is kind of a +setup for this an example of this on the + + align:start position:0% +setup for this an example of this on the + + + align:start position:0% +setup for this an example of this on the +homework what problem on the homework is + + align:start position:0% +homework what problem on the homework is + + + align:start position:0% +homework what problem on the homework is +just perfect for this it's 2d planar + + align:start position:0% +just perfect for this it's 2d planar + + + align:start position:0% +just perfect for this it's 2d planar +motion about a fixed point yeah the + + align:start position:0% +motion about a fixed point yeah the + + + align:start position:0% +motion about a fixed point yeah the +cylinder is me and disc with the square + + align:start position:0% +cylinder is me and disc with the square + + + align:start position:0% +cylinder is me and disc with the square +cut out with a pin at the top turning it + + align:start position:0% +cut out with a pin at the top turning it + + + align:start position:0% +cut out with a pin at the top turning it +into a pendulum + + align:start position:0% +into a pendulum + + + align:start position:0% +into a pendulum +that's the fixed point you can figure + + align:start position:0% +that's the fixed point you can figure + + + align:start position:0% +that's the fixed point you can figure +this out you can use parallel axis and + + align:start position:0% +this out you can use parallel axis and + + + align:start position:0% +this out you can use parallel axis and +we're going to do an example right now + + align:start position:0% +we're going to do an example right now + + + align:start position:0% +we're going to do an example right now +that's almost identical to that problem + + align:start position:0% +that's almost identical to that problem + + + align:start position:0% +that's almost identical to that problem +and we started it last time so this the + + align:start position:0% +and we started it last time so this the + + + align:start position:0% +and we started it last time so this the +example I want to work is very similar + + align:start position:0% +example I want to work is very similar + + + align:start position:0% +example I want to work is very similar +it's basically this problem is that + + align:start position:0% +it's basically this problem is that + + + align:start position:0% +it's basically this problem is that +pendulum okay so let's just work it + + align:start position:0% +pendulum okay so let's just work it + + + align:start position:0% +pendulum okay so let's just work it +through quickly we had done the setup + + align:start position:0% +through quickly we had done the setup + + + align:start position:0% +through quickly we had done the setup +last last time + + align:start position:0% + + + + align:start position:0% + +so last time I basically had derived an + + align:start position:0% +so last time I basically had derived an + + + align:start position:0% +so last time I basically had derived an +example of the parallel axis theorem for + + align:start position:0% +example of the parallel axis theorem for + + + align:start position:0% +example of the parallel axis theorem for +my little stick here and I'll give you + + align:start position:0% +my little stick here and I'll give you + + + align:start position:0% +my little stick here and I'll give you +the some geometry some values so here's + + align:start position:0% +the some geometry some values so here's + + + align:start position:0% +the some geometry some values so here's +G there's the point I want it to rotate + + align:start position:0% +G there's the point I want it to rotate + + + align:start position:0% +G there's the point I want it to rotate +about a the distance between these two + + align:start position:0% +about a the distance between these two + + + align:start position:0% +about a the distance between these two +points is D it's going to pop up in my + + align:start position:0% +points is D it's going to pop up in my + + + align:start position:0% +points is D it's going to pop up in my +parallel axis theorem the got a set of + + align:start position:0% +parallel axis theorem the got a set of + + + align:start position:0% +parallel axis theorem the got a set of +coordinates here my G is course in the + + align:start position:0% +coordinates here my G is course in the + + + align:start position:0% +coordinates here my G is course in the +center of this thing the geometric + + align:start position:0% +center of this thing the geometric + + + align:start position:0% +center of this thing the geometric +Center so I have a and the body fixed + + align:start position:0% +Center so I have a and the body fixed + + + align:start position:0% +Center so I have a and the body fixed +set of axes which I'm going to call Z + + align:start position:0% +set of axes which I'm going to call Z + + + align:start position:0% +set of axes which I'm going to call Z +and my X is in this direction so that + + align:start position:0% +and my X is in this direction so that + + + align:start position:0% +and my X is in this direction so that +would make my Y going into the board so + + align:start position:0% +would make my Y going into the board so + + + align:start position:0% +would make my Y going into the board so +the Y is like kind of like that okay and + + align:start position:0% +the Y is like kind of like that okay and + + + align:start position:0% +the Y is like kind of like that okay and +this has some properties the dimension + + align:start position:0% +this has some properties the dimension + + + align:start position:0% +this has some properties the dimension +in this direction is a direction and + + align:start position:0% +in this direction is a direction and + + + align:start position:0% +in this direction is a direction and +this dimension is B so it's a got a with + + align:start position:0% +this dimension is B so it's a got a with + + + align:start position:0% +this dimension is B so it's a got a with +a thickness B and a length L + + align:start position:0% + + + + align:start position:0% + +so when you compute these our symmetry + + align:start position:0% +so when you compute these our symmetry + + + align:start position:0% +so when you compute these our symmetry +now so the axes that I've chosen for + + align:start position:0% +now so the axes that I've chosen for + + + align:start position:0% +now so the axes that I've chosen for +this problem are they principal axes all + + align:start position:0% +this problem are they principal axes all + + + align:start position:0% +this problem are they principal axes all +right perpend there's three three planes + + align:start position:0% +right perpend there's three three planes + + + align:start position:0% +right perpend there's three three planes +of symmetry in this problem and I've got + + align:start position:0% +of symmetry in this problem and I've got + + + align:start position:0% +of symmetry in this problem and I've got +one for one principal axis perpendicular + + align:start position:0% +one for one principal axis perpendicular + + + align:start position:0% +one for one principal axis perpendicular +every one of them and all three pass + + align:start position:0% +every one of them and all three pass + + + align:start position:0% +every one of them and all three pass +through the center of mass and they're + + align:start position:0% +through the center of mass and they're + + + align:start position:0% +through the center of mass and they're +orthogonal to one another so those are + + align:start position:0% +orthogonal to one another so those are + + + align:start position:0% +orthogonal to one another so those are +conditions are all satisfied for these + + align:start position:0% +conditions are all satisfied for these + + + align:start position:0% +conditions are all satisfied for these +to be principal axes for this + + align:start position:0% +to be principal axes for this + + + align:start position:0% +to be principal axes for this +rectangular body okay and it's uniform + + align:start position:0% +rectangular body okay and it's uniform + + + align:start position:0% +rectangular body okay and it's uniform +density so I'll give you the four bodies + + align:start position:0% +density so I'll give you the four bodies + + + align:start position:0% +density so I'll give you the four bodies +like this in your book or any book on + + align:start position:0% +like this in your book or any book on + + + align:start position:0% +like this in your book or any book on +dynamics you can look up then the + + align:start position:0% +dynamics you can look up then the + + + align:start position:0% +dynamics you can look up then the +properties the I Z Z and we're going to + + align:start position:0% +properties the I Z Z and we're going to + + + align:start position:0% +properties the I Z Z and we're going to +spin this thing this thing we're going + + align:start position:0% +spin this thing this thing we're going + + + align:start position:0% +spin this thing this thing we're going +to have it rotating about 20 years yeah + + align:start position:0% +to have it rotating about 20 years yeah + + + align:start position:0% +to have it rotating about 20 years yeah +around the z axis so I'll set it up so + + align:start position:0% +around the z axis so I'll set it up so + + + align:start position:0% +around the z axis so I'll set it up so +it's what that's the way I've drilled my + + align:start position:0% +it's what that's the way I've drilled my + + + align:start position:0% +it's what that's the way I've drilled my +holes so it's going back and forth so + + align:start position:0% +holes so it's going back and forth so + + + align:start position:0% +holes so it's going back and forth so +the wide part of its this way so i ZZ + + align:start position:0% +the wide part of its this way so i ZZ + + + align:start position:0% +the wide part of its this way so i ZZ +with respect to g m l squared plus a + + align:start position:0% +with respect to g m l squared plus a + + + align:start position:0% +with respect to g m l squared plus a +squared over 12 i YY + + align:start position:0% + + + + align:start position:0% + +okay now just to make a point the + + align:start position:0% +okay now just to make a point the + + + align:start position:0% +okay now just to make a point the +dimensions L thirty two point one + + align:start position:0% +dimensions L thirty two point one + + + align:start position:0% +dimensions L thirty two point one +centimeters a four point seventy one B + + align:start position:0% +centimeters a four point seventy one B + + + align:start position:0% +centimeters a four point seventy one B +one point two five and eventually my D + + align:start position:0% +one point two five and eventually my D + + + align:start position:0% +one point two five and eventually my D +this offset the for example where I've + + align:start position:0% +this offset the for example where I've + + + align:start position:0% +this offset the for example where I've +drilled that hole is at ten point two + + align:start position:0% +drilled that hole is at ten point two + + + align:start position:0% +drilled that hole is at ten point two +the point I want to make here lots of + + align:start position:0% +the point I want to make here lots of + + + align:start position:0% +the point I want to make here lots of +times we could be nice if I could just + + align:start position:0% +times we could be nice if I could just + + + align:start position:0% +times we could be nice if I could just +make the simplification to call this a + + align:start position:0% +make the simplification to call this a + + + align:start position:0% +make the simplification to call this a +slender rod be able to ignore these a + + align:start position:0% +slender rod be able to ignore these a + + + align:start position:0% +slender rod be able to ignore these a +and B dimensions in this just to get + + align:start position:0% +and B dimensions in this just to get + + + align:start position:0% +and B dimensions in this just to get +quick answers you think that's slender + + align:start position:0% +quick answers you think that's slender + + + align:start position:0% +quick answers you think that's slender +enough so it's about it's not even ten + + align:start position:0% +enough so it's about it's not even ten + + + align:start position:0% +enough so it's about it's not even ten +times the length the width here isn't + + align:start position:0% +times the length the width here isn't + + + align:start position:0% +times the length the width here isn't +even ten it's probably six or seven okay + + align:start position:0% +even ten it's probably six or seven okay + + + align:start position:0% +even ten it's probably six or seven okay +so the key issue then if you look at + + align:start position:0% +so the key issue then if you look at + + + align:start position:0% +so the key issue then if you look at +this is really what's the ratio of a + + align:start position:0% +this is really what's the ratio of a + + + align:start position:0% +this is really what's the ratio of a +squared to l squared that would tell you + + align:start position:0% +squared to l squared that would tell you + + + align:start position:0% +squared to l squared that would tell you +something about the relative relative + + align:start position:0% +something about the relative relative + + + align:start position:0% +something about the relative relative +importance of the a squared term to the + + align:start position:0% +importance of the a squared term to the + + + align:start position:0% +importance of the a squared term to the +l squared so let me tell you about that + + align:start position:0% +l squared so let me tell you about that + + + align:start position:0% +l squared so let me tell you about that +so a squared over l squared is 0.02 to + + align:start position:0% +so a squared over l squared is 0.02 to + + + align:start position:0% +so a squared over l squared is 0.02 to +be squared over l squared is 0.002 so + + align:start position:0% +be squared over l squared is 0.002 so + + + align:start position:0% +be squared over l squared is 0.002 so +even with this kind of fat stick the + + align:start position:0% +even with this kind of fat stick the + + + align:start position:0% +even with this kind of fat stick the +approximation of ml squared over 12 is + + align:start position:0% +approximation of ml squared over 12 is + + + align:start position:0% +approximation of ml squared over 12 is +pretty good it's only 2% off and this + + align:start position:0% +pretty good it's only 2% off and this + + + align:start position:0% +pretty good it's only 2% off and this +approximation l squared over 12 is less + + align:start position:0% +approximation l squared over 12 is less + + + align:start position:0% +approximation l squared over 12 is less +than two-tenths of a percent off so we + + align:start position:0% +than two-tenths of a percent off so we + + + align:start position:0% +than two-tenths of a percent off so we +often use roughly slender things we + + align:start position:0% +often use roughly slender things we + + + align:start position:0% +often use roughly slender things we +often times you say ml squared over 12 + + align:start position:0% +often times you say ml squared over 12 + + + align:start position:0% +often times you say ml squared over 12 +for spin about their center okay + + align:start position:0% +for spin about their center okay + + + align:start position:0% +for spin about their center okay +the we would now need to apply parallel + + align:start position:0% +the we would now need to apply parallel + + + align:start position:0% +the we would now need to apply parallel +axis I want to spin this around let this + + align:start position:0% +axis I want to spin this around let this + + + align:start position:0% +axis I want to spin this around let this +rotate around not + + align:start position:0% +rotate around not + + + align:start position:0% +rotate around not +gee but now around two-point off to the + + align:start position:0% +gee but now around two-point off to the + + + align:start position:0% +gee but now around two-point off to the +side so we worked out last time that I + + align:start position:0% +side so we worked out last time that I + + + align:start position:0% +side so we worked out last time that I +Zizi with respect to a is eyes easy G + + align:start position:0% +Zizi with respect to a is eyes easy G + + + align:start position:0% +Zizi with respect to a is eyes easy G +plus MD squared so in this so in this + + align:start position:0% +plus MD squared so in this so in this + + + align:start position:0% +plus MD squared so in this so in this +particular problem I have this eyes easy + + align:start position:0% +particular problem I have this eyes easy + + + align:start position:0% +particular problem I have this eyes easy +about gzip Rox Emmitt Li ml squared over + + align:start position:0% +about gzip Rox Emmitt Li ml squared over + + + align:start position:0% +about gzip Rox Emmitt Li ml squared over +12 so just by way of example to see what + + align:start position:0% +12 so just by way of example to see what + + + align:start position:0% +12 so just by way of example to see what +we might find out here is let's let D + + align:start position:0% +we might find out here is let's let D + + + align:start position:0% +we might find out here is let's let D +equal L over 2 that would be if I move + + align:start position:0% +equal L over 2 that would be if I move + + + align:start position:0% +equal L over 2 that would be if I move +this one to I put my hole right at the + + align:start position:0% +this one to I put my hole right at the + + + align:start position:0% +this one to I put my hole right at the +very top how would this thing behave I + + align:start position:0% +very top how would this thing behave I + + + align:start position:0% +very top how would this thing behave I +don't have a co hole right at the top + + align:start position:0% +don't have a co hole right at the top + + + align:start position:0% +don't have a co hole right at the top +but I have one close okay so let's just + + align:start position:0% +but I have one close okay so let's just + + + align:start position:0% +but I have one close okay so let's just +just because the numbers are easy to + + align:start position:0% +just because the numbers are easy to + + + align:start position:0% +just because the numbers are easy to +work what happens if you put in L over 2 + + align:start position:0% +work what happens if you put in L over 2 + + + align:start position:0% +work what happens if you put in L over 2 +into this formula well then I Zizi + + align:start position:0% +into this formula well then I Zizi + + + align:start position:0% +into this formula well then I Zizi +a is ml squared over 12 plus M L over 2 + + align:start position:0% +a is ml squared over 12 plus M L over 2 + + + align:start position:0% +a is ml squared over 12 plus M L over 2 +squared is l squared over 4 and that's M + + align:start position:0% +squared is l squared over 4 and that's M + + + align:start position:0% +squared is l squared over 4 and that's M +l squared over 3 which is a number + + align:start position:0% +l squared over 3 which is a number + + + align:start position:0% +l squared over 3 which is a number +you'll run into again and again and + + align:start position:0% +you'll run into again and again and + + + align:start position:0% +you'll run into again and again and +again in mechanical engineering because + + align:start position:0% +again in mechanical engineering because + + + align:start position:0% +again in mechanical engineering because +examples like this are used a lot the + + align:start position:0% +examples like this are used a lot the + + + align:start position:0% +examples like this are used a lot the +mass moment of inertia about a slender + + align:start position:0% +mass moment of inertia about a slender + + + align:start position:0% +mass moment of inertia about a slender +rod pinned at its end ml squared over 3 + + align:start position:0% + + + + align:start position:0% + +so let's take this problem - a little + + align:start position:0% +so let's take this problem - a little + + + align:start position:0% +so let's take this problem - a little +more towards completion that some of the + + align:start position:0% +more towards completion that some of the + + + align:start position:0% +more towards completion that some of the +external moments with respect to a D H + + align:start position:0% +external moments with respect to a D H + + + align:start position:0% +external moments with respect to a D H +ad T and that's going to be D by DT in + + align:start position:0% +ad T and that's going to be D by DT in + + + align:start position:0% +ad T and that's going to be D by DT in +this problem the only rotation is Omega + + align:start position:0% +this problem the only rotation is Omega + + + align:start position:0% +this problem the only rotation is Omega +Z so this is going to be I Z Z with + + align:start position:0% +Z so this is going to be I Z Z with + + + align:start position:0% +Z so this is going to be I Z Z with +respect to a Omega Z okay and that just + + align:start position:0% +respect to a Omega Z okay and that just + + + align:start position:0% +respect to a Omega Z okay and that just +gives us eyes easy a Omega Z dot or are + + align:start position:0% +gives us eyes easy a Omega Z dot or are + + + align:start position:0% +gives us eyes easy a Omega Z dot or are +familiar it's easy a theta double dot if + + align:start position:0% +familiar it's easy a theta double dot if + + + align:start position:0% +familiar it's easy a theta double dot if +you want and we'll make here's an hour + + align:start position:0% +you want and we'll make here's an hour + + + align:start position:0% +you want and we'll make here's an hour +here's our problem it simplifies to this + + align:start position:0% +here's our problem it simplifies to this + + + align:start position:0% +here's our problem it simplifies to this +slender rod and let me do the more + + align:start position:0% +slender rod and let me do the more + + + align:start position:0% +slender rod and let me do the more +general case here's my rod the pivot + + align:start position:0% +general case here's my rod the pivot + + + align:start position:0% +general case here's my rod the pivot +point that it's going around is here + + align:start position:0% +point that it's going around is here + + + align:start position:0% +point that it's going around is here +here's this is d still and this is G and + + align:start position:0% +here's this is d still and this is G and + + + align:start position:0% +here's this is d still and this is G and +it's swinging with respect to this point + + align:start position:0% +it's swinging with respect to this point + + + align:start position:0% +it's swinging with respect to this point +so here's the angle theta so it swings + + align:start position:0% +so here's the angle theta so it swings + + + align:start position:0% +so here's the angle theta so it swings +about this point that you've fixed and + + align:start position:0% +about this point that you've fixed and + + + align:start position:0% +about this point that you've fixed and +that point is D above the the center of + + align:start position:0% +that point is D above the the center of + + + align:start position:0% +that point is D above the the center of +gravity center of mass so what are the + + align:start position:0% +gravity center of mass so what are the + + + align:start position:0% +gravity center of mass so what are the +external moments about this point + + align:start position:0% +external moments about this point + + + align:start position:0% +external moments about this point +there's no torque right at the point but + + align:start position:0% +there's no torque right at the point but + + + align:start position:0% +there's no torque right at the point but +a Freebody diagram of this drawing this + + align:start position:0% +a Freebody diagram of this drawing this + + + align:start position:0% +a Freebody diagram of this drawing this +as a here's a point of rotation here it + + align:start position:0% +as a here's a point of rotation here it + + + align:start position:0% +as a here's a point of rotation here it +is displaced through an angle theta the + + align:start position:0% +is displaced through an angle theta the + + + align:start position:0% +is displaced through an angle theta the +weight of the object can all be + + align:start position:0% +weight of the object can all be + + + align:start position:0% +weight of the object can all be +concentrated thought of for the purposes + + align:start position:0% +concentrated thought of for the purposes + + + align:start position:0% +concentrated thought of for the purposes +of the Freebody diagram is acting + + align:start position:0% +of the Freebody diagram is acting + + + align:start position:0% +of the Freebody diagram is acting +through G + + align:start position:0% +through G + + + align:start position:0% +through G +here's the mass add G gravity acting + + align:start position:0% +here's the mass add G gravity acting + + + align:start position:0% +here's the mass add G gravity acting +down on it and the length of this arm + + align:start position:0% +down on it and the length of this arm + + + align:start position:0% +down on it and the length of this arm +here that is about which it's swinging + + align:start position:0% +here that is about which it's swinging + + + align:start position:0% +here that is about which it's swinging +is D so the torque about this is and is + + align:start position:0% +is D so the torque about this is and is + + + align:start position:0% +is D so the torque about this is and is +pulling it back - M G d sine-theta + + align:start position:0% + + + + align:start position:0% + +probably you've seen that many times + + align:start position:0% +probably you've seen that many times + + + align:start position:0% +probably you've seen that many times +before including the recent homework and + + align:start position:0% +before including the recent homework and + + + align:start position:0% +before including the recent homework and +that must be equal to AI z z about a + + align:start position:0% +that must be equal to AI z z about a + + + align:start position:0% +that must be equal to AI z z about a +theta double dot so we have a new we + + align:start position:0% +theta double dot so we have a new we + + + align:start position:0% +theta double dot so we have a new we +have an equation of motion just + + align:start position:0% +have an equation of motion just + + + align:start position:0% +have an equation of motion just +collecting the terms together so this is + + align:start position:0% +collecting the terms together so this is + + + align:start position:0% +collecting the terms together so this is +a oscillator that for this problem has + + align:start position:0% +a oscillator that for this problem has + + + align:start position:0% +a oscillator that for this problem has +no external excitation this is its + + align:start position:0% +no external excitation this is its + + + align:start position:0% +no external excitation this is its +equation of motion and I need a theta + + align:start position:0% +equation of motion and I need a theta + + + align:start position:0% +equation of motion and I need a theta +double dot okay but is it linear is it + + align:start position:0% +double dot okay but is it linear is it + + + align:start position:0% +double dot okay but is it linear is it +linear kunos not a linear equation of + + align:start position:0% +linear kunos not a linear equation of + + + align:start position:0% +linear kunos not a linear equation of +motion but for sure it is an oscillator + + align:start position:0% +motion but for sure it is an oscillator + + + align:start position:0% +motion but for sure it is an oscillator +right and for anything that vibrates you + + align:start position:0% +right and for anything that vibrates you + + + align:start position:0% +right and for anything that vibrates you +can lots of nonlinear problems that + + align:start position:0% +can lots of nonlinear problems that + + + align:start position:0% +can lots of nonlinear problems that +exhibit vibration they you can think of + + align:start position:0% +exhibit vibration they you can think of + + + align:start position:0% +exhibit vibration they you can think of +them you can pose problems where you say + + align:start position:0% +them you can pose problems where you say + + + align:start position:0% +them you can pose problems where you say +okay what's their static equilibrium + + align:start position:0% +okay what's their static equilibrium + + + align:start position:0% +okay what's their static equilibrium +position and think of a very small + + align:start position:0% +position and think of a very small + + + align:start position:0% +position and think of a very small +motion about that static equilibrium + + align:start position:0% +motion about that static equilibrium + + + align:start position:0% +motion about that static equilibrium +position + + align:start position:0% +position + + + align:start position:0% +position +you can always linearize about the + + align:start position:0% +you can always linearize about the + + + align:start position:0% +you can always linearize about the +static equilibrium position and be able + + align:start position:0% +static equilibrium position and be able + + + align:start position:0% +static equilibrium position and be able +to come up with linearize equation of + + align:start position:0% +to come up with linearize equation of + + + align:start position:0% +to come up with linearize equation of +motion that at least from that you can + + align:start position:0% +motion that at least from that you can + + + align:start position:0% +motion that at least from that you can +calculate the natural frequency of the + + align:start position:0% +calculate the natural frequency of the + + + align:start position:0% +calculate the natural frequency of the +system for small motions around its + + align:start position:0% +system for small motions around its + + + align:start position:0% +system for small motions around its +linear around its static equilibrium + + align:start position:0% +linear around its static equilibrium + + + align:start position:0% +linear around its static equilibrium +position so in this case that's pretty + + align:start position:0% +position so in this case that's pretty + + + align:start position:0% +position so in this case that's pretty +easy to do and you've seen it before for + + align:start position:0% + + + + align:start position:0% + +small theta sine theta is approximately + + align:start position:0% +small theta sine theta is approximately + + + align:start position:0% +small theta sine theta is approximately +equal to theta so we are going to + + align:start position:0% +equal to theta so we are going to + + + align:start position:0% +equal to theta so we are going to +linearize the equation this theta equals + + align:start position:0% +linearize the equation this theta equals + + + align:start position:0% +linearize the equation this theta equals +0 is the static equilibrium position so + + align:start position:0% +0 is the static equilibrium position so + + + align:start position:0% +0 is the static equilibrium position so +we're linearizing around zero and round + + align:start position:0% +we're linearizing around zero and round + + + align:start position:0% +we're linearizing around zero and round +zero that's the approximation so you + + align:start position:0% +zero that's the approximation so you + + + align:start position:0% +zero that's the approximation so you +just substitute that in ICCA + + align:start position:0% +just substitute that in ICCA + + + align:start position:0% +just substitute that in ICCA +theta double dot plus m g d theta equals + + align:start position:0% +theta double dot plus m g d theta equals + + + align:start position:0% +theta double dot plus m g d theta equals +zero + + align:start position:0% +zero + + + align:start position:0% +zero +there's your linearized equation of + + align:start position:0% +there's your linearized equation of + + + align:start position:0% +there's your linearized equation of +motion I want an estimate of the natural + + align:start position:0% +motion I want an estimate of the natural + + + align:start position:0% +motion I want an estimate of the natural +frequency so you know find Omega n so + + align:start position:0% +frequency so you know find Omega n so + + + align:start position:0% +frequency so you know find Omega n so +this is basically entering into solving + + align:start position:0% +this is basically entering into solving + + + align:start position:0% +this is basically entering into solving +differential equations but I let mother + + align:start position:0% +differential equations but I let mother + + + align:start position:0% +differential equations but I let mother +nature tell me what the answer is + + align:start position:0% +nature tell me what the answer is + + + align:start position:0% +nature tell me what the answer is +I do the example and I say it oscillates + + align:start position:0% +I do the example and I say it oscillates + + + align:start position:0% +I do the example and I say it oscillates +looks a lot like sine Omega T to me all + + align:start position:0% +looks a lot like sine Omega T to me all + + + align:start position:0% +looks a lot like sine Omega T to me all +right + + align:start position:0% +right + + + align:start position:0% +right +plug in china mega t let's find out some + + align:start position:0% + + + + align:start position:0% + +theta amplitude sine Omega T plug it in + + align:start position:0% +theta amplitude sine Omega T plug it in + + + align:start position:0% +theta amplitude sine Omega T plug it in +so you plug that in and you get minus + + align:start position:0% +so you plug that in and you get minus + + + align:start position:0% +so you plug that in and you get minus +Omega squared is easy a plus mg D and + + align:start position:0% +Omega squared is easy a plus mg D and + + + align:start position:0% +Omega squared is easy a plus mg D and +all of this you can factor out the theta + + align:start position:0% +all of this you can factor out the theta + + + align:start position:0% +all of this you can factor out the theta +zero sine Omega T equals zero so what + + align:start position:0% +zero sine Omega T equals zero so what + + + align:start position:0% +zero sine Omega T equals zero so what +you get and general theta that's not + + align:start position:0% +you get and general theta that's not + + + align:start position:0% +you get and general theta that's not +zero L so you have a trivial problem not + + align:start position:0% +zero L so you have a trivial problem not + + + align:start position:0% +zero L so you have a trivial problem not +moving at all but in order for this + + align:start position:0% +moving at all but in order for this + + + align:start position:0% +moving at all but in order for this +equation and this can be any anything + + align:start position:0% +equation and this can be any anything + + + align:start position:0% +equation and this can be any anything +between zero minus one and plus one + + align:start position:0% +between zero minus one and plus one + + + align:start position:0% +between zero minus one and plus one +depending on the time so in order to + + align:start position:0% +depending on the time so in order to + + + align:start position:0% +depending on the time so in order to +satisfy this equation this part inside + + align:start position:0% +satisfy this equation this part inside + + + align:start position:0% +satisfy this equation this part inside +of the parenthesis has to be zero and + + align:start position:0% +of the parenthesis has to be zero and + + + align:start position:0% +of the parenthesis has to be zero and +when you just solve that you find that + + align:start position:0% +when you just solve that you find that + + + align:start position:0% +when you just solve that you find that +Omega squared equals + + align:start position:0% + + + + align:start position:0% + +M G D over eyes easy a and the reason + + align:start position:0% +M G D over eyes easy a and the reason + + + align:start position:0% +M G D over eyes easy a and the reason +I've gone to the you know bother of + + align:start position:0% +I've gone to the you know bother of + + + align:start position:0% +I've gone to the you know bother of +working this out in detail right to the + + align:start position:0% +working this out in detail right to the + + + align:start position:0% +working this out in detail right to the +end is that every one degree of freedom + + align:start position:0% +end is that every one degree of freedom + + + align:start position:0% +end is that every one degree of freedom +rotational oscillator that you will ever + + align:start position:0% +rotational oscillator that you will ever + + + align:start position:0% +rotational oscillator that you will ever +encounter sticks wheels with static + + align:start position:0% +encounter sticks wheels with static + + + align:start position:0% +encounter sticks wheels with static +imbalances show you this one it's an + + align:start position:0% +imbalances show you this one it's an + + + align:start position:0% +imbalances show you this one it's an +oscillator to any one degree of freedom + + align:start position:0% +oscillator to any one degree of freedom + + + align:start position:0% +oscillator to any one degree of freedom +oscillator rotational oscillator + + align:start position:0% +oscillator rotational oscillator + + + align:start position:0% +oscillator rotational oscillator +pendulum basically all pendulum this is + + align:start position:0% +pendulum basically all pendulum this is + + + align:start position:0% +pendulum basically all pendulum this is +the formula for the natural frequency so + + align:start position:0% +the formula for the natural frequency so + + + align:start position:0% +the formula for the natural frequency so +it's going to be of that form for any + + align:start position:0% +it's going to be of that form for any + + + align:start position:0% +it's going to be of that form for any +pendulum so any one DOF pendulum this is + + align:start position:0% +pendulum so any one DOF pendulum this is + + + align:start position:0% +pendulum so any one DOF pendulum this is +the generic answer so that cut out + + align:start position:0% +the generic answer so that cut out + + + align:start position:0% +the generic answer so that cut out +problem for today has to come down to + + align:start position:0% +problem for today has to come down to + + + align:start position:0% +problem for today has to come down to +this where this is the distance between + + align:start position:0% +this where this is the distance between + + + align:start position:0% +this where this is the distance between +the mass Center and the point of + + align:start position:0% +the mass Center and the point of + + + align:start position:0% +the mass Center and the point of +rotation and that's your mass moment + + align:start position:0% +rotation and that's your mass moment + + + align:start position:0% +rotation and that's your mass moment +inertia about the point of rotation so + + align:start position:0% +inertia about the point of rotation so + + + align:start position:0% +inertia about the point of rotation so +it's worth kind of knowing that one okay + + align:start position:0% +it's worth kind of knowing that one okay + + + align:start position:0% +it's worth kind of knowing that one okay +keep moving + + align:start position:0% + + + + align:start position:0% + +now things begin to get interesting the + + align:start position:0% +now things begin to get interesting the + + + align:start position:0% +now things begin to get interesting the +these latter two classes are are harder + + align:start position:0% +these latter two classes are are harder + + + align:start position:0% +these latter two classes are are harder +conceptually but once you have a + + align:start position:0% +conceptually but once you have a + + + align:start position:0% +conceptually but once you have a +solution method for them they're not all + + align:start position:0% +solution method for them they're not all + + + align:start position:0% +solution method for them they're not all +that hard + + align:start position:0% +that hard + + + align:start position:0% +that hard +this one is one of the problem I + + align:start position:0% +this one is one of the problem I + + + align:start position:0% +this one is one of the problem I +described at the beginning we've got + + align:start position:0% +described at the beginning we've got + + + align:start position:0% +described at the beginning we've got +this hockey puck like thing and a string + + align:start position:0% +this hockey puck like thing and a string + + + align:start position:0% +this hockey puck like thing and a string +wrapped around it pulling on it with a + + align:start position:0% +wrapped around it pulling on it with a + + + align:start position:0% +wrapped around it pulling on it with a +known force in this problem they call it + + align:start position:0% +known force in this problem they call it + + + align:start position:0% +known force in this problem they call it +a hundred and fifty Newtons the mass of + + align:start position:0% +a hundred and fifty Newtons the mass of + + + align:start position:0% +a hundred and fifty Newtons the mass of +this thing is 75 kilograms the it's on a + + align:start position:0% +this thing is 75 kilograms the it's on a + + + align:start position:0% +this thing is 75 kilograms the it's on a +frictionless surface okay and we want to + + align:start position:0% +frictionless surface okay and we want to + + + align:start position:0% +frictionless surface okay and we want to +find its acceleration of the center of + + align:start position:0% +find its acceleration of the center of + + + align:start position:0% +find its acceleration of the center of +mass and the rotation of the center of + + align:start position:0% +mass and the rotation of the center of + + + align:start position:0% +mass and the rotation of the center of +the center of mass so find theta double + + align:start position:0% +the center of mass so find theta double + + + align:start position:0% +the center of mass so find theta double +dot and find the linear acceleration + + align:start position:0% +dot and find the linear acceleration + + + align:start position:0% +dot and find the linear acceleration +that's basically the name of the problem + + align:start position:0% +that's basically the name of the problem + + + align:start position:0% +that's basically the name of the problem +and they give you that it's 75 kilograms + + align:start position:0% +and they give you that it's 75 kilograms + + + align:start position:0% +and they give you that it's 75 kilograms +150 Newtons and + + align:start position:0% +150 Newtons and + + + align:start position:0% +150 Newtons and +Kappa the radius of gyration is 0.15 + + align:start position:0% +Kappa the radius of gyration is 0.15 + + + align:start position:0% +Kappa the radius of gyration is 0.15 +meters this is defined as the radius of + + align:start position:0% +meters this is defined as the radius of + + + align:start position:0% +meters this is defined as the radius of +gyration so what's what's that it's the + + align:start position:0% +gyration so what's what's that it's the + + + align:start position:0% +gyration so what's what's that it's the +radius of gyration is really appropriate + + align:start position:0% +radius of gyration is really appropriate + + + align:start position:0% +radius of gyration is really appropriate +really only useful about for mostly 2d + + align:start position:0% +really only useful about for mostly 2d + + + align:start position:0% +really only useful about for mostly 2d +rotational problems around 1x around an + + align:start position:0% +rotational problems around 1x around an + + + align:start position:0% +rotational problems around 1x around an +axis of rotation and what it means is + + align:start position:0% +axis of rotation and what it means is + + + align:start position:0% +axis of rotation and what it means is +this is the distance away from the + + align:start position:0% +this is the distance away from the + + + align:start position:0% +this is the distance away from the +center of rotation at which you could + + align:start position:0% +center of rotation at which you could + + + align:start position:0% +center of rotation at which you could +concentrate all of the math and have the + + align:start position:0% +concentrate all of the math and have the + + + align:start position:0% +concentrate all of the math and have the +same mass moment of inertia okay + + align:start position:0% +same mass moment of inertia okay + + + align:start position:0% +same mass moment of inertia okay +so this this has here's G here at the + + align:start position:0% +so this this has here's G here at the + + + align:start position:0% +so this this has here's G here at the +center uniform disc we know that there + + align:start position:0% +center uniform disc we know that there + + + align:start position:0% +center uniform disc we know that there +is an i ZZ about G for this problem and + + align:start position:0% +is an i ZZ about G for this problem and + + + align:start position:0% +is an i ZZ about G for this problem and +I need to pick a coordinate system so we + + align:start position:0% +I need to pick a coordinate system so we + + + align:start position:0% +I need to pick a coordinate system so we +talked about things here get em out of + + align:start position:0% +talked about things here get em out of + + + align:start position:0% +talked about things here get em out of +the center so I'm going to let Z be + + align:start position:0% +the center so I'm going to let Z be + + + align:start position:0% +the center so I'm going to let Z be +upwards and because I'm looking ahead + + align:start position:0% +upwards and because I'm looking ahead + + + align:start position:0% +upwards and because I'm looking ahead +and want to keep the equation simple I'm + + align:start position:0% +and want to keep the equation simple I'm + + + align:start position:0% +and want to keep the equation simple I'm +going to make my x-axis here parallel to + + align:start position:0% +going to make my x-axis here parallel to + + + align:start position:0% +going to make my x-axis here parallel to +F so I only have to deal with one vector + + align:start position:0% +F so I only have to deal with one vector + + + align:start position:0% +F so I only have to deal with one vector +vector component equation and then that + + align:start position:0% +vector component equation and then that + + + align:start position:0% +vector component equation and then that +makes the y-axis this way okay so I'm + + align:start position:0% +makes the y-axis this way okay so I'm + + + align:start position:0% +makes the y-axis this way okay so I'm +interested in eyes easy because I'm + + align:start position:0% +interested in eyes easy because I'm + + + align:start position:0% +interested in eyes easy because I'm +spinning around the z axis I know that + + align:start position:0% +spinning around the z axis I know that + + + align:start position:0% +spinning around the z axis I know that +for a uniform disk that's the principal + + align:start position:0% +for a uniform disk that's the principal + + + align:start position:0% +for a uniform disk that's the principal +axis is the vertical one and what I'm + + align:start position:0% +axis is the vertical one and what I'm + + + align:start position:0% +axis is the vertical one and what I'm +saying is that you can then set find + + align:start position:0% +saying is that you can then set find + + + align:start position:0% +saying is that you can then set find +there's an i ZZ of g that is can be + + align:start position:0% +there's an i ZZ of g that is can be + + + align:start position:0% +there's an i ZZ of g that is can be +expressed as M Kappa squared so Kappa in + + align:start position:0% +expressed as M Kappa squared so Kappa in + + + align:start position:0% +expressed as M Kappa squared so Kappa in +effect is just as easy G over m square + + align:start position:0% +effect is just as easy G over m square + + + align:start position:0% +effect is just as easy G over m square +root now why do we use that kind of + + align:start position:0% +root now why do we use that kind of + + + align:start position:0% +root now why do we use that kind of +thing + + align:start position:0% +thing + + + align:start position:0% +thing +well the the way this problem was set up + + align:start position:0% +well the the way this problem was set up + + + align:start position:0% +well the the way this problem was set up +I actually took it out of a book it with + + align:start position:0% +I actually took it out of a book it with + + + align:start position:0% +I actually took it out of a book it with +this it wasn't a uniform disk you'd say + + align:start position:0% +this it wasn't a uniform disk you'd say + + + align:start position:0% +this it wasn't a uniform disk you'd say +it's a pulley wheel or something and + + align:start position:0% +it's a pulley wheel or something and + + + align:start position:0% +it's a pulley wheel or something and +it's got spokes in here and a rim it's + + align:start position:0% +it's got spokes in here and a rim it's + + + align:start position:0% +it's got spokes in here and a rim it's +still axially simply it still has some + + align:start position:0% +still axially simply it still has some + + + align:start position:0% +still axially simply it still has some +axial symmetries but it's getting a + + align:start position:0% +axial symmetries but it's getting a + + + align:start position:0% +axial symmetries but it's getting a +little messy it's hard for you you can't + + align:start position:0% +little messy it's hard for you you can't + + + align:start position:0% +little messy it's hard for you you can't +just say that's mr squared over two it's + + align:start position:0% +just say that's mr squared over two it's + + + align:start position:0% +just say that's mr squared over two it's +got some other mass moment of inertia + + align:start position:0% +got some other mass moment of inertia + + + align:start position:0% +got some other mass moment of inertia +about the center but it's got holes and + + align:start position:0% +about the center but it's got holes and + + + align:start position:0% +about the center but it's got holes and +stuff in it because of the spokes so + + align:start position:0% +stuff in it because of the spokes so + + + align:start position:0% +stuff in it because of the spokes so +oftentimes you'll be given the mat the + + align:start position:0% +oftentimes you'll be given the mat the + + + align:start position:0% +oftentimes you'll be given the mat the +radius of gyration because it's a little + + align:start position:0% +radius of gyration because it's a little + + + align:start position:0% +radius of gyration because it's a little +difficult to give you a mathematical + + align:start position:0% +difficult to give you a mathematical + + + align:start position:0% +difficult to give you a mathematical +description of what the actual as easy + + align:start position:0% +description of what the actual as easy + + + align:start position:0% +description of what the actual as easy +is + + align:start position:0% +is + + + align:start position:0% +is +that's often why you do it and it's + + align:start position:0% +that's often why you do it and it's + + + align:start position:0% +that's often why you do it and it's +saying is you can measure rather than + + align:start position:0% +saying is you can measure rather than + + + align:start position:0% +saying is you can measure rather than +try to calculate you can actually just + + align:start position:0% +try to calculate you can actually just + + + align:start position:0% +try to calculate you can actually just +measure the mass moment of inertia of + + align:start position:0% +measure the mass moment of inertia of + + + align:start position:0% +measure the mass moment of inertia of +something so how would I measure my I + + align:start position:0% +something so how would I measure my I + + + align:start position:0% +something so how would I measure my I +say I didn't know any formulas but how + + align:start position:0% +say I didn't know any formulas but how + + + align:start position:0% +say I didn't know any formulas but how +would I measure the mass moment of + + align:start position:0% +would I measure the mass moment of + + + align:start position:0% +would I measure the mass moment of +inertia of this in the Z direction what + + align:start position:0% +inertia of this in the Z direction what + + + align:start position:0% +inertia of this in the Z direction what +experiment would you do she says apply + + align:start position:0% +experiment would you do she says apply + + + align:start position:0% +experiment would you do she says apply +torque measure the angular acceleration + + align:start position:0% +torque measure the angular acceleration + + + align:start position:0% +torque measure the angular acceleration +hang a weight off of it known weight + + align:start position:0% +hang a weight off of it known weight + + + align:start position:0% +hang a weight off of it known weight +wrap a string around it known mass known + + align:start position:0% +wrap a string around it known mass known + + + align:start position:0% +wrap a string around it known mass known +G known torque around the center measure + + align:start position:0% +G known torque around the center measure + + + align:start position:0% +G known torque around the center measure +the angular acceleration I fade a double + + align:start position:0% +the angular acceleration I fade a double + + + align:start position:0% +the angular acceleration I fade a double +dot equals the torque + + align:start position:0% +dot equals the torque + + + align:start position:0% +dot equals the torque +you know the torque you know the measure + + align:start position:0% +you know the torque you know the measure + + + align:start position:0% +you know the torque you know the measure +the theta double dot calculate I I + + align:start position:0% +the theta double dot calculate I I + + + align:start position:0% +the theta double dot calculate I I +equals I'm Kappa squared and you could + + align:start position:0% +equals I'm Kappa squared and you could + + + align:start position:0% +equals I'm Kappa squared and you could +just say well Kappa for this system is + + align:start position:0% +just say well Kappa for this system is + + + align:start position:0% +just say well Kappa for this system is +okay that's that's how you use it I'll + + align:start position:0% +okay that's that's how you use it I'll + + + align:start position:0% +okay that's that's how you use it I'll +give you an example really hard to + + align:start position:0% +give you an example really hard to + + + align:start position:0% +give you an example really hard to +calculate mass moment inertia a marine + + align:start position:0% +calculate mass moment inertia a marine + + + align:start position:0% +calculate mass moment inertia a marine +propeller you actually do want to know + + align:start position:0% +propeller you actually do want to know + + + align:start position:0% +propeller you actually do want to know +the mass moment nourish about its center + + align:start position:0% +the mass moment nourish about its center + + + align:start position:0% +the mass moment nourish about its center +for purposes of torsional oscillations + + align:start position:0% +for purposes of torsional oscillations + + + align:start position:0% +for purposes of torsional oscillations +on the shaft etc hard to calculate + + align:start position:0% +on the shaft etc hard to calculate + + + align:start position:0% +on the shaft etc hard to calculate +pretty easy to measure okay so how many + + align:start position:0% +pretty easy to measure okay so how many + + + align:start position:0% +pretty easy to measure okay so how many +degrees of freedom does this problem + + align:start position:0% +degrees of freedom does this problem + + + align:start position:0% +degrees of freedom does this problem +have well when we say it's 2d it's a + + align:start position:0% +have well when we say it's 2d it's a + + + align:start position:0% +have well when we say it's 2d it's a +rigid body but it's 2d which means it's + + align:start position:0% +rigid body but it's 2d which means it's + + + align:start position:0% +rigid body but it's 2d which means it's +lying on a plane it's a planar motion + + align:start position:0% +lying on a plane it's a planar motion + + + align:start position:0% +lying on a plane it's a planar motion +problem it only allowed to rotate in Z + + align:start position:0% +problem it only allowed to rotate in Z + + + align:start position:0% +problem it only allowed to rotate in Z +not allowed to rotate in around the x + + align:start position:0% +not allowed to rotate in around the x + + + align:start position:0% +not allowed to rotate in around the x +axis or the y axis so there's two rigid + + align:start position:0% +axis or the y axis so there's two rigid + + + align:start position:0% +axis or the y axis so there's two rigid +body six degrees of freedom possible + + align:start position:0% +body six degrees of freedom possible + + + align:start position:0% +body six degrees of freedom possible +there's two immediately that you said it + + align:start position:0% +there's two immediately that you said it + + + align:start position:0% +there's two immediately that you said it +can't rotate so we're down to four + + align:start position:0% +can't rotate so we're down to four + + + align:start position:0% +can't rotate so we're down to four +it cannot cannot translate in the Z + + align:start position:0% +it cannot cannot translate in the Z + + + align:start position:0% +it cannot cannot translate in the Z +direction right we're down to three okay + + align:start position:0% +direction right we're down to three okay + + + align:start position:0% +direction right we're down to three okay +so that believes us what so the degrees + + align:start position:0% +so that believes us what so the degrees + + + align:start position:0% +so that believes us what so the degrees +of freedom for this problem is six minus + + align:start position:0% +of freedom for this problem is six minus + + + align:start position:0% +of freedom for this problem is six minus +three constraints is three that means we + + align:start position:0% +three constraints is three that means we + + + align:start position:0% +three constraints is three that means we +have to have three equations of motion + + align:start position:0% +have to have three equations of motion + + + align:start position:0% +have to have three equations of motion +and they would account for what are the + + align:start position:0% +and they would account for what are the + + + align:start position:0% +and they would account for what are the +possible another way of saying this what + + align:start position:0% +possible another way of saying this what + + + align:start position:0% +possible another way of saying this what +are the possible + + align:start position:0% +are the possible + + + align:start position:0% +are the possible +motions now this problem XY and Z or + + align:start position:0% +motions now this problem XY and Z or + + + align:start position:0% +motions now this problem XY and Z or +rotation in Z okay + + align:start position:0% + + + + align:start position:0% + +so now we've set the problem up now to + + align:start position:0% +so now we've set the problem up now to + + + align:start position:0% +so now we've set the problem up now to +go about solving it we need let's do we + + align:start position:0% +go about solving it we need let's do we + + + align:start position:0% +go about solving it we need let's do we +need a Freebody diagram so here's my + + align:start position:0% +need a Freebody diagram so here's my + + + align:start position:0% +need a Freebody diagram so here's my +disk here's the force any other and + + align:start position:0% +disk here's the force any other and + + + align:start position:0% +disk here's the force any other and +there's certainly has weight in the z + + align:start position:0% +there's certainly has weight in the z + + + align:start position:0% +there's certainly has weight in the z +direction but we're not there's no z + + align:start position:0% +direction but we're not there's no z + + + align:start position:0% +direction but we're not there's no z +acceleration so in the plane of the + + align:start position:0% +acceleration so in the plane of the + + + align:start position:0% +acceleration so in the plane of the +board that's the only external force is + + align:start position:0% +board that's the only external force is + + + align:start position:0% +board that's the only external force is +acting on this right okay there's our G + + align:start position:0% + + + + align:start position:0% + +now this problem and I'll say generalize + + align:start position:0% +now this problem and I'll say generalize + + + align:start position:0% +now this problem and I'll say generalize +on this in a few minutes this problem + + align:start position:0% +on this in a few minutes this problem + + + align:start position:0% +on this in a few minutes this problem +can be always be restated as recast let + + align:start position:0% +can be always be restated as recast let + + + align:start position:0% +can be always be restated as recast let +me put it that way as here's your point + + align:start position:0% +me put it that way as here's your point + + + align:start position:0% +me put it that way as here's your point +G with a force acting on the center of + + align:start position:0% +G with a force acting on the center of + + + align:start position:0% +G with a force acting on the center of +mass see this force doesn't go through + + align:start position:0% +mass see this force doesn't go through + + + align:start position:0% +mass see this force doesn't go through +the center of mass this force goes + + align:start position:0% +the center of mass this force goes + + + align:start position:0% +the center of mass this force goes +through the center of mass I'm going to + + align:start position:0% +through the center of mass I'm going to + + + align:start position:0% +through the center of mass I'm going to +replace that problem with this problem + + align:start position:0% +replace that problem with this problem + + + align:start position:0% +replace that problem with this problem +pure moment acting about the center of + + align:start position:0% +pure moment acting about the center of + + + align:start position:0% +pure moment acting about the center of +mass problem so you can always make this + + align:start position:0% +mass problem so you can always make this + + + align:start position:0% +mass problem so you can always make this +transition and I'll do the general case + + align:start position:0% +transition and I'll do the general case + + + align:start position:0% +transition and I'll do the general case +for you in just a minute but you can + + align:start position:0% +for you in just a minute but you can + + + align:start position:0% +for you in just a minute but you can +always do this so that's kind of my + + align:start position:0% +always do this so that's kind of my + + + align:start position:0% +always do this so that's kind of my +second point here third point we need + + align:start position:0% +second point here third point we need + + + align:start position:0% +second point here third point we need +then this is our free body diagram we + + align:start position:0% +then this is our free body diagram we + + + align:start position:0% +then this is our free body diagram we +need our apply our laws of motion so + + align:start position:0% +need our apply our laws of motion so + + + align:start position:0% +need our apply our laws of motion so +some of the forces in the Y are now + + align:start position:0% +some of the forces in the Y are now + + + align:start position:0% +some of the forces in the Y are now +remember this is Z coming out of the + + align:start position:0% +remember this is Z coming out of the + + + align:start position:0% +remember this is Z coming out of the +board + + align:start position:0% +board + + + align:start position:0% +board +y this way X this way some of the forces + + align:start position:0% +y this way X this way some of the forces + + + align:start position:0% +y this way X this way some of the forces +in the Y 0m acceleration of G in the Y + + align:start position:0% +in the Y 0m acceleration of G in the Y + + + align:start position:0% +in the Y 0m acceleration of G in the Y +Direction zero so you know there's no + + align:start position:0% +Direction zero so you know there's no + + + align:start position:0% +Direction zero so you know there's no +acceleration in the Y so we saw it has + + align:start position:0% +acceleration in the Y so we saw it has + + + align:start position:0% +acceleration in the Y so we saw it has +three degrees of freedom + + align:start position:0% +three degrees of freedom + + + align:start position:0% +three degrees of freedom +that's the first equation of motion give + + align:start position:0% +that's the first equation of motion give + + + align:start position:0% +that's the first equation of motion give +you a trivial result so y double dot is + + align:start position:0% +you a trivial result so y double dot is + + + align:start position:0% +you a trivial result so y double dot is +there + + align:start position:0% +there + + + align:start position:0% +there +that's your first equation of motion + + align:start position:0% +that's your first equation of motion + + + align:start position:0% +that's your first equation of motion +then you have a second equation of + + align:start position:0% +then you have a second equation of + + + align:start position:0% +then you have a second equation of +motion sum of the forces in the + + align:start position:0% +motion sum of the forces in the + + + align:start position:0% +motion sum of the forces in the +x-direction equals just our F I hat it's + + align:start position:0% +x-direction equals just our F I hat it's + + + align:start position:0% +x-direction equals just our F I hat it's +positive x-direction because we were + + align:start position:0% +positive x-direction because we were + + + align:start position:0% +positive x-direction because we were +clever and how we set up the coordinate + + align:start position:0% +clever and how we set up the coordinate + + + align:start position:0% +clever and how we set up the coordinate +system and that's got to be M X double + + align:start position:0% +system and that's got to be M X double + + + align:start position:0% +system and that's got to be M X double +dot I hat direction so we know right + + align:start position:0% +dot I hat direction so we know right + + + align:start position:0% +dot I hat direction so we know right +away that X double dot is the force F + + align:start position:0% +away that X double dot is the force F + + + align:start position:0% +away that X double dot is the force F +divided by M and that's 150 Newton's + + align:start position:0% +divided by M and that's 150 Newton's + + + align:start position:0% +divided by M and that's 150 Newton's +over 75 kilograms or 2 meters per second + + align:start position:0% +over 75 kilograms or 2 meters per second + + + align:start position:0% +over 75 kilograms or 2 meters per second +squared all right the third one then is + + align:start position:0% +squared all right the third one then is + + + align:start position:0% +squared all right the third one then is +the moment of inertia with respect to G + + align:start position:0% +the moment of inertia with respect to G + + + align:start position:0% +the moment of inertia with respect to G +in this problem the m'excuse of the + + align:start position:0% +in this problem the m'excuse of the + + + align:start position:0% +in this problem the m'excuse of the +angular momentum is some i CZ g times + + align:start position:0% +angular momentum is some i CZ g times + + + align:start position:0% +angular momentum is some i CZ g times +omega z and that's what we're looking + + align:start position:0% +omega z and that's what we're looking + + + align:start position:0% +omega z and that's what we're looking +for so this is another way of izg G + + align:start position:0% +for so this is another way of izg G + + + align:start position:0% +for so this is another way of izg G +theta dot k hat direction and we're + + align:start position:0% +theta dot k hat direction and we're + + + align:start position:0% +theta dot k hat direction and we're +going to apply that the external torques + + align:start position:0% +going to apply that the external torques + + + align:start position:0% +going to apply that the external torques +sum of the torques is d H with respect + + align:start position:0% +sum of the torques is d H with respect + + + align:start position:0% +sum of the torques is d H with respect +to G DT and that's going to give us i ZZ + + align:start position:0% +to G DT and that's going to give us i ZZ + + + align:start position:0% +to G DT and that's going to give us i ZZ +g theta double dot + + align:start position:0% + + + + align:start position:0% + +so this third class of problems you are + + align:start position:0% +so this third class of problems you are + + + align:start position:0% +so this third class of problems you are +best just working with respect to the + + align:start position:0% +best just working with respect to the + + + align:start position:0% +best just working with respect to the +center of mass that's kind of the point + + align:start position:0% +center of mass that's kind of the point + + + align:start position:0% +center of mass that's kind of the point +here there's no there's notes not know + + align:start position:0% +here there's no there's notes not know + + + align:start position:0% +here there's no there's notes not know +contours of contact + + align:start position:0% +contours of contact + + + align:start position:0% +contours of contact +there's just known external forces you + + align:start position:0% +there's just known external forces you + + + align:start position:0% +there's just known external forces you +have to deal with them do your work with + + align:start position:0% +have to deal with them do your work with + + + align:start position:0% +have to deal with them do your work with +respect to the center of mass so we have + + align:start position:0% +respect to the center of mass so we have + + + align:start position:0% +respect to the center of mass so we have +force equations we have moment equations + + align:start position:0% +force equations we have moment equations + + + align:start position:0% +force equations we have moment equations +and basically you're you know you know I + + align:start position:0% +and basically you're you know you know I + + + align:start position:0% +and basically you're you know you know I +Zizi for this problem is Kappa squared m + + align:start position:0% +Zizi for this problem is Kappa squared m + + + align:start position:0% +Zizi for this problem is Kappa squared m +and you're given m and you're given + + align:start position:0% +and you're given m and you're given + + + align:start position:0% +and you're given m and you're given +Kappa so you can now and what we have to + + align:start position:0% +Kappa so you can now and what we have to + + + align:start position:0% +Kappa so you can now and what we have to +actually last thing left here is to + + align:start position:0% +actually last thing left here is to + + + align:start position:0% +actually last thing left here is to +figure out the torque what's the torque + + align:start position:0% +figure out the torque what's the torque + + + align:start position:0% +figure out the torque what's the torque +well it's our in this direction crossed + + align:start position:0% +well it's our in this direction crossed + + + align:start position:0% +well it's our in this direction crossed +with F in that direction so it's our J + + align:start position:0% +with F in that direction so it's our J + + + align:start position:0% +with F in that direction so it's our J +cross with F I J cross I - right RF - + + align:start position:0% +cross with F I J cross I - right RF - + + + align:start position:0% +cross with F I J cross I - right RF - +our F okay hat so you can now solve for + + align:start position:0% +our F okay hat so you can now solve for + + + align:start position:0% +our F okay hat so you can now solve for +theta double dot as RF over eyes easy or + + align:start position:0% +theta double dot as RF over eyes easy or + + + align:start position:0% +theta double dot as RF over eyes easy or +RF over M Kappa squared + + align:start position:0% + + + + align:start position:0% + +and that says - says it's rotating this + + align:start position:0% +and that says - says it's rotating this + + + align:start position:0% +and that says - says it's rotating this +way which is what you'd expect + + align:start position:0% +way which is what you'd expect + + + align:start position:0% +way which is what you'd expect +right now I've meant to ask you a + + align:start position:0% +right now I've meant to ask you a + + + align:start position:0% +right now I've meant to ask you a +question before we started but to think + + align:start position:0% +question before we started but to think + + + align:start position:0% +question before we started but to think +about this about it right at the + + align:start position:0% +about this about it right at the + + + align:start position:0% +about this about it right at the +beginning and said okay this is the + + align:start position:0% +beginning and said okay this is the + + + align:start position:0% +beginning and said okay this is the +problem if I grab this string and pull + + align:start position:0% +problem if I grab this string and pull + + + align:start position:0% +problem if I grab this string and pull +in this direction will there be any + + align:start position:0% +in this direction will there be any + + + align:start position:0% +in this direction will there be any +motion in the Y direction + + align:start position:0% +motion in the Y direction + + + align:start position:0% +motion in the Y direction +if I meant to start that way I'm really + + align:start position:0% +if I meant to start that way I'm really + + + align:start position:0% +if I meant to start that way I'm really +kicking myself for not doing that + + align:start position:0% +kicking myself for not doing that + + + align:start position:0% +kicking myself for not doing that +because a lot of people think that + + align:start position:0% +because a lot of people think that + + + align:start position:0% +because a lot of people think that +there's possible that it can move off in + + align:start position:0% +there's possible that it can move off in + + + align:start position:0% +there's possible that it can move off in +the Y direction because it's not being + + align:start position:0% +the Y direction because it's not being + + + align:start position:0% +the Y direction because it's not being +loaded symmetrically you're pulling on a + + align:start position:0% +loaded symmetrically you're pulling on a + + + align:start position:0% +loaded symmetrically you're pulling on a +side then people think it'll kind of try + + align:start position:0% +side then people think it'll kind of try + + + align:start position:0% +side then people think it'll kind of try +to move away like that it doesn't does + + align:start position:0% +to move away like that it doesn't does + + + align:start position:0% +to move away like that it doesn't does +it okay + + align:start position:0% + + + + align:start position:0% + +so an important generalization we've got + + align:start position:0% +so an important generalization we've got + + + align:start position:0% +so an important generalization we've got +a rigid body you have a force acting on + + align:start position:0% +a rigid body you have a force acting on + + + align:start position:0% +a rigid body you have a force acting on +it has a mass center here so + + align:start position:0% + + + + align:start position:0% + +perpendicular to that force is some + + align:start position:0% +perpendicular to that force is some + + + align:start position:0% +perpendicular to that force is some +distance okay + + align:start position:0% +distance okay + + + align:start position:0% +distance okay +we'll call it D you can always equate + + align:start position:0% +we'll call it D you can always equate + + + align:start position:0% +we'll call it D you can always equate +this problem to and set it up as force + + align:start position:0% +this problem to and set it up as force + + + align:start position:0% +this problem to and set it up as force +conceptually you can think of it as + + align:start position:0% +conceptually you can think of it as + + + align:start position:0% +conceptually you can think of it as +equal and opposite forces which cancel + + align:start position:0% +equal and opposite forces which cancel + + + align:start position:0% +equal and opposite forces which cancel +one another this is like I've done + + align:start position:0% +one another this is like I've done + + + align:start position:0% +one another this is like I've done +nothing to this problem and then a force + + align:start position:0% +nothing to this problem and then a force + + + align:start position:0% +nothing to this problem and then a force +acting at this distance F this is our + + align:start position:0% +acting at this distance F this is our + + + align:start position:0% +acting at this distance F this is our +distance D so this problem is identical + + align:start position:0% +distance D so this problem is identical + + + align:start position:0% +distance D so this problem is identical +for that problem I've just added and + + align:start position:0% +for that problem I've just added and + + + align:start position:0% +for that problem I've just added and +taken away two more forces right so the + + align:start position:0% +taken away two more forces right so the + + + align:start position:0% +taken away two more forces right so the +total forces on the system are still F + + align:start position:0% +total forces on the system are still F + + + align:start position:0% +total forces on the system are still F +and there's still an F operating in a at + + align:start position:0% +and there's still an F operating in a at + + + align:start position:0% +and there's still an F operating in a at +a lever arm D but now if I put these two + + align:start position:0% +a lever arm D but now if I put these two + + + align:start position:0% +a lever arm D but now if I put these two +together they are equal and opposite and + + align:start position:0% +together they are equal and opposite and + + + align:start position:0% +together they are equal and opposite and +they form a couple a moment acting like + + align:start position:0% +they form a couple a moment acting like + + + align:start position:0% +they form a couple a moment acting like +that so this is equivalent to here's G + + align:start position:0% +that so this is equivalent to here's G + + + align:start position:0% +that so this is equivalent to here's G +with an F on it and a moment M naught + + align:start position:0% +with an F on it and a moment M naught + + + align:start position:0% +with an F on it and a moment M naught +okay and this M naught is my D cross F + + align:start position:0% +okay and this M naught is my D cross F + + + align:start position:0% +okay and this M naught is my D cross F +so that's the generalization for what I + + align:start position:0% +so that's the generalization for what I + + + align:start position:0% +so that's the generalization for what I +did up here I mean I went from that to + + align:start position:0% +did up here I mean I went from that to + + + align:start position:0% +did up here I mean I went from that to +that and this is why you can do that + + align:start position:0% +that and this is why you can do that + + + align:start position:0% +that and this is why you can do that +okay and so there's a if there's a gent + + align:start position:0% +okay and so there's a if there's a gent + + + align:start position:0% +okay and so there's a if there's a gent +now if you have an object and lots of + + align:start position:0% +now if you have an object and lots of + + + align:start position:0% +now if you have an object and lots of +different forces acting on it this is fi + + align:start position:0% +different forces acting on it this is fi + + + align:start position:0% +different forces acting on it this is fi +down here + + align:start position:0% +down here + + + align:start position:0% +down here +and here's G you can draw a radius from + + align:start position:0% +and here's G you can draw a radius from + + + align:start position:0% +and here's G you can draw a radius from +G to this point so I'll call that R i + + align:start position:0% +G to this point so I'll call that R i + + + align:start position:0% +G to this point so I'll call that R i +with respect to G then two way to + + align:start position:0% +with respect to G then two way to + + + align:start position:0% +with respect to G then two way to +generalize this is that this is equal to + + align:start position:0% + + + + align:start position:0% + +some F total and a moment acting at G + + align:start position:0% + + + + align:start position:0% + +okay and all that you have to do there + + align:start position:0% +okay and all that you have to do there + + + align:start position:0% +okay and all that you have to do there +is F total is the summation of the F is + + align:start position:0% +is F total is the summation of the F is + + + align:start position:0% +is F total is the summation of the F is +vector sum and the mg the M with respect + + align:start position:0% +vector sum and the mg the M with respect + + + align:start position:0% +vector sum and the mg the M with respect +to G here is the summation of the r i + + align:start position:0% +to G here is the summation of the r i + + + align:start position:0% +to G here is the summation of the r i +with respect to G cross Fi so that's the + + align:start position:0% +with respect to G cross Fi so that's the + + + align:start position:0% +with respect to G cross Fi so that's the +Jets the generalization for multiple + + align:start position:0% +Jets the generalization for multiple + + + align:start position:0% +Jets the generalization for multiple +forces on a body so you are making an + + align:start position:0% +forces on a body so you are making an + + + align:start position:0% +forces on a body so you are making an +equivalent force acting at G and a + + align:start position:0% +equivalent force acting at G and a + + + align:start position:0% +equivalent force acting at G and a +moment acting at G and I shouldn't call + + align:start position:0% +moment acting at G and I shouldn't call + + + align:start position:0% +moment acting at G and I shouldn't call +this little G that's really confusing so + + align:start position:0% +this little G that's really confusing so + + + align:start position:0% +this little G that's really confusing so +that's the generalization when you need + + align:start position:0% +that's the generalization when you need + + + align:start position:0% +that's the generalization when you need +to do problems like this okay + + align:start position:0% + + + + align:start position:0% + +catch your breath while I scrub a board + + align:start position:0% +catch your breath while I scrub a board + + + align:start position:0% +catch your breath while I scrub a board +here now we got to move on to these + + align:start position:0% +here now we got to move on to these + + + align:start position:0% +here now we got to move on to these +class Philip its class four problems + + align:start position:0% + + + + align:start position:0% + +moving points an example is that truck + + align:start position:0% +moving points an example is that truck + + + align:start position:0% +moving points an example is that truck +problem that you had known acceleration + + align:start position:0% + + + + align:start position:0% + +so there's two common ways of doing this + + align:start position:0% +so there's two common ways of doing this + + + align:start position:0% +so there's two common ways of doing this +problem you can do this problem by + + align:start position:0% +problem you can do this problem by + + + align:start position:0% +problem you can do this problem by +summing forces at the center of mass of + + align:start position:0% +summing forces at the center of mass of + + + align:start position:0% +summing forces at the center of mass of +that pipe and summing moments around it + + align:start position:0% +that pipe and summing moments around it + + + align:start position:0% +that pipe and summing moments around it +but the moment around this comes from a + + align:start position:0% +but the moment around this comes from a + + + align:start position:0% +but the moment around this comes from a +friction force here what you don't know + + align:start position:0% +friction force here what you don't know + + + align:start position:0% +friction force here what you don't know +so that introduces an unknown that you + + align:start position:0% +so that introduces an unknown that you + + + align:start position:0% +so that introduces an unknown that you +have to then solve for so if you work + + align:start position:0% +have to then solve for so if you work + + + align:start position:0% +have to then solve for so if you work +around G for this pipe you can do it you + + align:start position:0% +around G for this pipe you can do it you + + + align:start position:0% +around G for this pipe you can do it you +can work around G you could say some of + + align:start position:0% +can work around G you could say some of + + + align:start position:0% +can work around G you could say some of +the moments around G sum of the forces + + align:start position:0% +the moments around G sum of the forces + + + align:start position:0% +the moments around G sum of the forces +spec to G but you have to deal with + + align:start position:0% +spec to G but you have to deal with + + + align:start position:0% +spec to G but you have to deal with +unknown forces so you're working with + + align:start position:0% +unknown forces so you're working with + + + align:start position:0% +unknown forces so you're working with +respect to G implies unknown forces e + + align:start position:0% +respect to G implies unknown forces e + + + align:start position:0% +respect to G implies unknown forces e +eat for example friction so you'd really + + align:start position:0% +eat for example friction so you'd really + + + align:start position:0% +eat for example friction so you'd really +maybe rather work around the point of + + align:start position:0% +maybe rather work around the point of + + + align:start position:0% +maybe rather work around the point of +contact a because if you some of your + + align:start position:0% +contact a because if you some of your + + + align:start position:0% +contact a because if you some of your +moments about a the friction force has + + align:start position:0% +moments about a the friction force has + + + align:start position:0% +moments about a the friction force has +no moment arm and you know it doesn't + + align:start position:0% +no moment arm and you know it doesn't + + + align:start position:0% +no moment arm and you know it doesn't +appear in the answer all right + + align:start position:0% +appear in the answer all right + + + align:start position:0% +appear in the answer all right +so but this gets trickier this is more + + align:start position:0% +so but this gets trickier this is more + + + align:start position:0% +so but this gets trickier this is more +this is a little more + + align:start position:0% + + + + align:start position:0% + +sophisticated I'll just call it step and + + align:start position:0% +sophisticated I'll just call it step and + + + align:start position:0% +sophisticated I'll just call it step and +you need to do this you need a little + + align:start position:0% +you need to do this you need a little + + + align:start position:0% +you need to do this you need a little +theorem so to work with respect to a you + + align:start position:0% +theorem so to work with respect to a you + + + align:start position:0% +theorem so to work with respect to a you +need to be able to say that the angular + + align:start position:0% +need to be able to say that the angular + + + align:start position:0% +need to be able to say that the angular +momentum with respect to a it's you now + + align:start position:0% +momentum with respect to a it's you now + + + align:start position:0% +momentum with respect to a it's you now +are working around a moving point maybe + + align:start position:0% +are working around a moving point maybe + + + align:start position:0% +are working around a moving point maybe +accelerating it's very handy to be able + + align:start position:0% +accelerating it's very handy to be able + + + align:start position:0% +accelerating it's very handy to be able +to say it's the angular momentum around + + align:start position:0% +to say it's the angular momentum around + + + align:start position:0% +to say it's the angular momentum around +G which is easier to calculate plus our + + align:start position:0% +G which is easier to calculate plus our + + + align:start position:0% +G which is easier to calculate plus our +G a the distance from the center of mass + + align:start position:0% +G a the distance from the center of mass + + + align:start position:0% +G a the distance from the center of mass +to the point you're working on cross the + + align:start position:0% +to the point you're working on cross the + + + align:start position:0% +to the point you're working on cross the +linear momentum of the system with + + align:start position:0% +linear momentum of the system with + + + align:start position:0% +linear momentum of the system with +respect to the inertial frame we need + + align:start position:0% +respect to the inertial frame we need + + + align:start position:0% +respect to the inertial frame we need +this so this is a formula we need and + + align:start position:0% + + + + align:start position:0% + +let's see why this is true I think this + + align:start position:0% +let's see why this is true I think this + + + align:start position:0% +let's see why this is true I think this +is sort of thing you know that's is the + + align:start position:0% +is sort of thing you know that's is the + + + align:start position:0% +is sort of thing you know that's is the +formula to come out of the blue here and + + align:start position:0% +formula to come out of the blue here and + + + align:start position:0% +formula to come out of the blue here and +why is it true so I don't use you like + + align:start position:0% +why is it true so I don't use you like + + + align:start position:0% +why is it true so I don't use you like +to do proofs but the proofs of this in + + align:start position:0% +to do proofs but the proofs of this in + + + align:start position:0% +to do proofs but the proofs of this in +on the board but the proof of this is + + align:start position:0% +on the board but the proof of this is + + + align:start position:0% +on the board but the proof of this is +really quite simple + + align:start position:0% + + + + align:start position:0% + +here's a little mass point MI and this + + align:start position:0% +here's a little mass point MI and this + + + align:start position:0% +here's a little mass point MI and this +radius is R of i with respect to a this + + align:start position:0% +radius is R of i with respect to a this + + + align:start position:0% +radius is R of i with respect to a this +is R of G with respect to a and + + align:start position:0% +is R of G with respect to a and + + + align:start position:0% +is R of G with respect to a and +therefore this is our of i with respect + + align:start position:0% +therefore this is our of i with respect + + + align:start position:0% +therefore this is our of i with respect +to G is this one and we know that this + + align:start position:0% +to G is this one and we know that this + + + align:start position:0% +to G is this one and we know that this +Plus this gives us that so we can say R + + align:start position:0% +Plus this gives us that so we can say R + + + align:start position:0% +Plus this gives us that so we can say R +I particle i with respect to a is our G + + align:start position:0% +I particle i with respect to a is our G + + + align:start position:0% +I particle i with respect to a is our G +with respect to a plus r i with respect + + align:start position:0% +with respect to a plus r i with respect + + + align:start position:0% +with respect to a plus r i with respect +to G all vectors + + align:start position:0% + + + + align:start position:0% + +so the angular momentum of that body + + align:start position:0% +so the angular momentum of that body + + + align:start position:0% +so the angular momentum of that body +which is from the basic definition of + + align:start position:0% +which is from the basic definition of + + + align:start position:0% +which is from the basic definition of +angular momentum is the summation of all + + align:start position:0% +angular momentum is the summation of all + + + align:start position:0% +angular momentum is the summation of all +little mass bits of the RI with respect + + align:start position:0% +little mass bits of the RI with respect + + + align:start position:0% +little mass bits of the RI with respect +to a across the linear momentum of each + + align:start position:0% +to a across the linear momentum of each + + + align:start position:0% +to a across the linear momentum of each +little mass bit but we can expand that + + align:start position:0% +little mass bit but we can expand that + + + align:start position:0% +little mass bit but we can expand that +with that sum so this is the summation + + align:start position:0% +with that sum so this is the summation + + + align:start position:0% +with that sum so this is the summation +of my our G with respect to a plus our i + + align:start position:0% +of my our G with respect to a plus our i + + + align:start position:0% +of my our G with respect to a plus our i +with respect to G cross P I owe + + align:start position:0% +with respect to G cross P I owe + + + align:start position:0% +with respect to G cross P I owe +summation over all the mass bits I'm + + align:start position:0% +summation over all the mass bits I'm + + + align:start position:0% +summation over all the mass bits I'm +going to expand this and I can expand + + align:start position:0% +going to expand this and I can expand + + + align:start position:0% +going to expand this and I can expand +this into this times that summations of + + align:start position:0% +this into this times that summations of + + + align:start position:0% +this into this times that summations of +this times that and this times that so + + align:start position:0% +this times that and this times that so + + + align:start position:0% +this times that and this times that so +that becomes a our G a cross summation + + align:start position:0% +that becomes a our G a cross summation + + + align:start position:0% +that becomes a our G a cross summation +of a puts Pio this is a little M is V I + + align:start position:0% +of a puts Pio this is a little M is V I + + + align:start position:0% +of a puts Pio this is a little M is V I +with respect to O each one has velocity + + align:start position:0% +with respect to O each one has velocity + + + align:start position:0% +with respect to O each one has velocity +each one has a mass so this is mi V I + + align:start position:0% +each one has a mass so this is mi V I + + + align:start position:0% +each one has a mass so this is mi V I +with respect to O plus the summation R + + align:start position:0% +with respect to O plus the summation R + + + align:start position:0% +with respect to O plus the summation R +IG s + + align:start position:0% +IG s + + + align:start position:0% +IG s +cross mi v io s now notice I pulled this + + align:start position:0% +cross mi v io s now notice I pulled this + + + align:start position:0% +cross mi v io s now notice I pulled this +one outside of the summation that's + + align:start position:0% +one outside of the summation that's + + + align:start position:0% +one outside of the summation that's +because this is a single this is a fixed + + align:start position:0% +because this is a single this is a fixed + + + align:start position:0% +because this is a single this is a fixed +number it doesn't change in the + + align:start position:0% +number it doesn't change in the + + + align:start position:0% +number it doesn't change in the +summation it's just the distance from my + + align:start position:0% +summation it's just the distance from my + + + align:start position:0% +summation it's just the distance from my +starting point to G so I can pull it out + + align:start position:0% +starting point to G so I can pull it out + + + align:start position:0% +starting point to G so I can pull it out +and do the summation and then do the + + align:start position:0% +and do the summation and then do the + + + align:start position:0% +and do the summation and then do the +cross product what is the summation of + + align:start position:0% +cross product what is the summation of + + + align:start position:0% +cross product what is the summation of +all the m/v is for the body + + align:start position:0% + + + + align:start position:0% + +that's the momentum of each little + + align:start position:0% +that's the momentum of each little + + + align:start position:0% +that's the momentum of each little +particle add them all up what do you get + + align:start position:0% +particle add them all up what do you get + + + align:start position:0% +particle add them all up what do you get +this is our G a cross P with respect to + + align:start position:0% +this is our G a cross P with respect to + + + align:start position:0% +this is our G a cross P with respect to +O that's this term and this is all the + + align:start position:0% +O that's this term and this is all the + + + align:start position:0% +O that's this term and this is all the +little distances from the center of mass + + align:start position:0% + + + + align:start position:0% + +to the cross with the momentum of each + + align:start position:0% +to the cross with the momentum of each + + + align:start position:0% +to the cross with the momentum of each +little one what's that + + align:start position:0% +little one what's that + + + align:start position:0% +little one what's that +well this is it this looks like a + + align:start position:0% +well this is it this looks like a + + + align:start position:0% +well this is it this looks like a +definition of angular momentum this is + + align:start position:0% +definition of angular momentum this is + + + align:start position:0% +definition of angular momentum this is +the angular momentum of every little + + align:start position:0% +the angular momentum of every little + + + align:start position:0% +the angular momentum of every little +mass particle with respect to G add it + + align:start position:0% +mass particle with respect to G add it + + + align:start position:0% +mass particle with respect to G add it +up this is H with respect to G which is + + align:start position:0% +up this is H with respect to G which is + + + align:start position:0% +up this is H with respect to G which is +what we set out to prove so the H with + + align:start position:0% +what we set out to prove so the H with + + + align:start position:0% +what we set out to prove so the H with +respect to a is H with respect to G Plus + + align:start position:0% +respect to a is H with respect to G Plus + + + align:start position:0% +respect to a is H with respect to G Plus +RG a cross the linear momentum of the + + align:start position:0% +RG a cross the linear momentum of the + + + align:start position:0% +RG a cross the linear momentum of the +body yep he I respect I mean the + + align:start position:0% +body yep he I respect I mean the + + + align:start position:0% +body yep he I respect I mean the +velocity + + align:start position:0% + + + + align:start position:0% + +you got to get in there + + align:start position:0% +you got to get in there + + + align:start position:0% +you got to get in there +but instead of writing out our as a son + + align:start position:0% +but instead of writing out our as a son + + + align:start position:0% +but instead of writing out our as a son +can write out the velocity as the sum of + + align:start position:0% +can write out the velocity as the sum of + + + align:start position:0% +can write out the velocity as the sum of +the respect to the origin are you know I + + align:start position:0% +the respect to the origin are you know I + + + align:start position:0% +the respect to the origin are you know I +H the definition of angular momentum + + align:start position:0% +H the definition of angular momentum + + + align:start position:0% +H the definition of angular momentum +yeah + + align:start position:0% + + + + align:start position:0% + +the velocity and you can figure out if + + align:start position:0% +the velocity and you can figure out if + + + align:start position:0% +the velocity and you can figure out if +you had a momentum visual piece and + + align:start position:0% +you had a momentum visual piece and + + + align:start position:0% +you had a momentum visual piece and +multiplied by RI a that's that is the + + align:start position:0% +multiplied by RI a that's that is the + + + align:start position:0% +multiplied by RI a that's that is the +angular momentum with respect to a but I + + align:start position:0% +angular momentum with respect to a but I + + + align:start position:0% +angular momentum with respect to a but I +broke it apart so that I could show you + + align:start position:0% +broke it apart so that I could show you + + + align:start position:0% +broke it apart so that I could show you +that this formula I want to use has two + + align:start position:0% +that this formula I want to use has two + + + align:start position:0% +that this formula I want to use has two +pieces why I use that okay so then if I + + align:start position:0% +pieces why I use that okay so then if I + + + align:start position:0% +pieces why I use that okay so then if I +can use that it's easy to get HS respect + + align:start position:0% +can use that it's easy to get HS respect + + + align:start position:0% +can use that it's easy to get HS respect +to G sometimes it's really hard to know + + align:start position:0% +to G sometimes it's really hard to know + + + align:start position:0% +to G sometimes it's really hard to know +what to do around it with things that + + align:start position:0% +what to do around it with things that + + + align:start position:0% +what to do around it with things that +happen around this point a so now let's + + align:start position:0% +happen around this point a so now let's + + + align:start position:0% +happen around this point a so now let's +go back I think to understand this we + + align:start position:0% +go back I think to understand this we + + + align:start position:0% +go back I think to understand this we +need to go back to our truck problem we + + align:start position:0% +need to go back to our truck problem we + + + align:start position:0% +need to go back to our truck problem we +now have a formula that you know where + + align:start position:0% +now have a formula that you know where + + + align:start position:0% +now have a formula that you know where +it comes from we have our truck that is + + align:start position:0% +it comes from we have our truck that is + + + align:start position:0% +it comes from we have our truck that is +accelerating at x1 double dot and we + + align:start position:0% +accelerating at x1 double dot and we + + + align:start position:0% +accelerating at x1 double dot and we +want to find out what the what's theta + + align:start position:0% +want to find out what the what's theta + + + align:start position:0% +want to find out what the what's theta +double dot for that pipe what's it doing + + align:start position:0% +double dot for that pipe what's it doing + + + align:start position:0% +double dot for that pipe what's it doing +so first we needed some kinematics and + + align:start position:0% + + + + align:start position:0% + +in particular what is the x2 I don't + + align:start position:0% +in particular what is the x2 I don't + + + align:start position:0% +in particular what is the x2 I don't +know label this very well it didn't so + + align:start position:0% +know label this very well it didn't so + + + align:start position:0% +know label this very well it didn't so +here's my pipe here's my truck bed that + + align:start position:0% +here's my pipe here's my truck bed that + + + align:start position:0% +here's my pipe here's my truck bed that +it's in contact with trucks moving at x1 + + align:start position:0% +it's in contact with trucks moving at x1 + + + align:start position:0% +it's in contact with trucks moving at x1 +double dot we know the in an inertial + + align:start position:0% +double dot we know the in an inertial + + + align:start position:0% +double dot we know the in an inertial +frame the movement of the center of mass + + align:start position:0% +frame the movement of the center of mass + + + align:start position:0% +frame the movement of the center of mass +of my pipe is x2 and it has some angular + + align:start position:0% +of my pipe is x2 and it has some angular + + + align:start position:0% +of my pipe is x2 and it has some angular +rotation rate I'll call or angular + + align:start position:0% +rotation rate I'll call or angular + + + align:start position:0% +rotation rate I'll call or angular +rotation I'll call theta so the movement + + align:start position:0% +rotation I'll call theta so the movement + + + align:start position:0% +rotation I'll call theta so the movement +of this guy I need to be able to express + + align:start position:0% +of this guy I need to be able to express + + + align:start position:0% +of this guy I need to be able to express +in terms of x1 and theta + + align:start position:0% +in terms of x1 and theta + + + align:start position:0% +in terms of x1 and theta +well if this is fixed to the truck and + + align:start position:0% +well if this is fixed to the truck and + + + align:start position:0% +well if this is fixed to the truck and +you just the truck move forward then X 2 + + align:start position:0% +you just the truck move forward then X 2 + + + align:start position:0% +you just the truck move forward then X 2 +would be equal to x1 but in fact it + + align:start position:0% +would be equal to x1 but in fact it + + + align:start position:0% +would be equal to x1 but in fact it +rolls back a little bit and the distance + + align:start position:0% +rolls back a little bit and the distance + + + align:start position:0% +rolls back a little bit and the distance +this point moves if it rolls through an + + align:start position:0% +this point moves if it rolls through an + + + align:start position:0% +this point moves if it rolls through an +angle theta is it rolls backwards and + + align:start position:0% +angle theta is it rolls backwards and + + + align:start position:0% +angle theta is it rolls backwards and +amount are theta + + align:start position:0% + + + + align:start position:0% + +and we're going to need to take two + + align:start position:0% +and we're going to need to take two + + + align:start position:0% +and we're going to need to take two +derivatives of that x2 double dot equals + + align:start position:0% +derivatives of that x2 double dot equals + + + align:start position:0% +derivatives of that x2 double dot equals +x1 double dot minus R theta double dot + + align:start position:0% +x1 double dot minus R theta double dot + + + align:start position:0% +x1 double dot minus R theta double dot +so that's the little kinematic + + align:start position:0% +so that's the little kinematic + + + align:start position:0% +so that's the little kinematic +relationship we need to do this problem + + align:start position:0% + + + + align:start position:0% + +next we apply I need to apply a physical + + align:start position:0% +next we apply I need to apply a physical + + + align:start position:0% +next we apply I need to apply a physical +law which is the one I've derived so + + align:start position:0% +law which is the one I've derived so + + + align:start position:0% +law which is the one I've derived so +this is our physics here now our + + align:start position:0% +this is our physics here now our + + + align:start position:0% +this is our physics here now our +physical law and that's that the + + align:start position:0% +physical law and that's that the + + + align:start position:0% +physical law and that's that the +external torques D H respect to a DT + + align:start position:0% +external torques D H respect to a DT + + + align:start position:0% +external torques D H respect to a DT +plus V AO cross P oh and in this case is + + align:start position:0% +plus V AO cross P oh and in this case is + + + align:start position:0% +plus V AO cross P oh and in this case is +there is this na is VA o zero now in + + align:start position:0% +there is this na is VA o zero now in + + + align:start position:0% +there is this na is VA o zero now in +fact it's x1 dot right it's in the i + + align:start position:0% +fact it's x1 dot right it's in the i + + + align:start position:0% +fact it's x1 dot right it's in the i +direction + + align:start position:0% +direction + + + align:start position:0% +direction +how about what direction is P the + + align:start position:0% +how about what direction is P the + + + align:start position:0% +how about what direction is P the +momentum of the pipe + + align:start position:0% + + + + align:start position:0% + +we move in the Y direction up down it + + align:start position:0% +we move in the Y direction up down it + + + align:start position:0% +we move in the Y direction up down it +only moves in the X so this velocity is + + align:start position:0% +only moves in the X so this velocity is + + + align:start position:0% +only moves in the X so this velocity is +only in the X this is in the X where I + + align:start position:0% +only in the X this is in the X where I + + + align:start position:0% +only in the X this is in the X where I +had direction this cross product is zero + + align:start position:0% +had direction this cross product is zero + + + align:start position:0% +had direction this cross product is zero +so it just happens that they're parallel + + align:start position:0% +so it just happens that they're parallel + + + align:start position:0% +so it just happens that they're parallel +so this thing goes to zero you don't + + align:start position:0% +so this thing goes to zero you don't + + + align:start position:0% +so this thing goes to zero you don't +have to deal with it that's because + + align:start position:0% +have to deal with it that's because + + + align:start position:0% +have to deal with it that's because +these guys are parallel parallel motion + + align:start position:0% +these guys are parallel parallel motion + + + align:start position:0% +these guys are parallel parallel motion +but you did have to consider it you did + + align:start position:0% +but you did have to consider it you did + + + align:start position:0% +but you did have to consider it you did +if the think about it it's not just + + align:start position:0% +if the think about it it's not just + + + align:start position:0% +if the think about it it's not just +trivially zero okay so that means that + + align:start position:0% +trivially zero okay so that means that + + + align:start position:0% +trivially zero okay so that means that +the torques about a is just DHA DT and h + + align:start position:0% +the torques about a is just DHA DT and h + + + align:start position:0% +the torques about a is just DHA DT and h +a for this problem is I well it's H G + + align:start position:0% +a for this problem is I well it's H G + + + align:start position:0% +a for this problem is I well it's H G +which is eyes easy G theta double dot + + align:start position:0% +which is eyes easy G theta double dot + + + align:start position:0% +which is eyes easy G theta double dot +but I have to put in this set theta dot + + align:start position:0% +but I have to put in this set theta dot + + + align:start position:0% +but I have to put in this set theta dot +excuse me this is just the H I have to + + align:start position:0% +excuse me this is just the H I have to + + + align:start position:0% +excuse me this is just the H I have to +put in the second term R G with respect + + align:start position:0% +put in the second term R G with respect + + + align:start position:0% +put in the second term R G with respect +to a cross P with respect to O so here's + + align:start position:0% +to a cross P with respect to O so here's + + + align:start position:0% +to a cross P with respect to O so here's +my H a now to write it again up here + + align:start position:0% +my H a now to write it again up here + + + align:start position:0% +my H a now to write it again up here +this is as easy G theta double dot theta + + align:start position:0% +this is as easy G theta double dot theta + + + align:start position:0% +this is as easy G theta double dot theta +dot in the K and now this second term R + + align:start position:0% +dot in the K and now this second term R + + + align:start position:0% +dot in the K and now this second term R +is RJ my y-axis is up the radius of this + + align:start position:0% +is RJ my y-axis is up the radius of this + + + align:start position:0% +is RJ my y-axis is up the radius of this +thing is R is the radius so the moment + + align:start position:0% +thing is R is the radius so the moment + + + align:start position:0% +thing is R is the radius so the moment +arm is RJ crossed with the linear + + align:start position:0% +arm is RJ crossed with the linear + + + align:start position:0% +arm is RJ crossed with the linear +momentum of that piece of pipe which is + + align:start position:0% +momentum of that piece of pipe which is + + + align:start position:0% +momentum of that piece of pipe which is +the mass of the pipe times X 2 dot in + + align:start position:0% +the mass of the pipe times X 2 dot in + + + align:start position:0% +the mass of the pipe times X 2 dot in +the I Direction J cross I is minus K so + + align:start position:0% +the I Direction J cross I is minus K so + + + align:start position:0% +the I Direction J cross I is minus K so +I Zizi + + align:start position:0% +I Zizi + + + align:start position:0% +I Zizi +expected G theta double dot theta dot I + + align:start position:0% +expected G theta double dot theta dot I + + + align:start position:0% +expected G theta double dot theta dot I +keep taking the derivative a little too + + align:start position:0% +keep taking the derivative a little too + + + align:start position:0% +keep taking the derivative a little too +soon okay + + align:start position:0% +soon okay + + + align:start position:0% +soon okay +- our mx2 dot K and now some of the + + align:start position:0% +- our mx2 dot K and now some of the + + + align:start position:0% +- our mx2 dot K and now some of the +torques D by DT of H with respect to a + + align:start position:0% +torques D by DT of H with respect to a + + + align:start position:0% +torques D by DT of H with respect to a +take the derivatives eyes easy G theta + + align:start position:0% +take the derivatives eyes easy G theta + + + align:start position:0% +take the derivatives eyes easy G theta +double dot K minus R M x2 double dot K + + align:start position:0% +double dot K minus R M x2 double dot K + + + align:start position:0% +double dot K minus R M x2 double dot K +unfortunately none of these unit vectors + + align:start position:0% +unfortunately none of these unit vectors + + + align:start position:0% +unfortunately none of these unit vectors +are rotating so we don't have to deal + + align:start position:0% +are rotating so we don't have to deal + + + align:start position:0% +are rotating so we don't have to deal +with any of that and I'm almost to the + + align:start position:0% +with any of that and I'm almost to the + + + align:start position:0% +with any of that and I'm almost to the +end but now I have to go back to that + + align:start position:0% +end but now I have to go back to that + + + align:start position:0% +end but now I have to go back to that +original kinematic relationship which + + align:start position:0% +original kinematic relationship which + + + align:start position:0% +original kinematic relationship which +set allows me to express x2 in terms of + + align:start position:0% +set allows me to express x2 in terms of + + + align:start position:0% +set allows me to express x2 in terms of +x1 + R theta and if I substitute that in + + align:start position:0% +x1 + R theta and if I substitute that in + + + align:start position:0% +x1 + R theta and if I substitute that in +here and solve for it I get theta double + + align:start position:0% +here and solve for it I get theta double + + + align:start position:0% +here and solve for it I get theta double +dot equals M R over Y Z Z G Plus M R + + align:start position:0% +dot equals M R over Y Z Z G Plus M R + + + align:start position:0% +dot equals M R over Y Z Z G Plus M R +squared X double dot whole thing x1 + + align:start position:0% +squared X double dot whole thing x1 + + + align:start position:0% +squared X double dot whole thing x1 +double dot + + align:start position:0% +double dot + + + align:start position:0% +double dot +so you've accelerated x1 double dot the + + align:start position:0% +so you've accelerated x1 double dot the + + + align:start position:0% +so you've accelerated x1 double dot the +thing starts rolling in and actually + + align:start position:0% +thing starts rolling in and actually + + + align:start position:0% +thing starts rolling in and actually +throwing backwards which is the plus + + align:start position:0% +throwing backwards which is the plus + + + align:start position:0% +throwing backwards which is the plus +theta direction at this rate we did this + + align:start position:0% +theta direction at this rate we did this + + + align:start position:0% +theta direction at this rate we did this +using this formula for H a now the + + align:start position:0% +using this formula for H a now the + + + align:start position:0% +using this formula for H a now the +beauty of this formula is that it works + + align:start position:0% +beauty of this formula is that it works + + + align:start position:0% +beauty of this formula is that it works +for moving points a points that are + + align:start position:0% +for moving points a points that are + + + align:start position:0% +for moving points a points that are +moving he even can be accelerating all + + align:start position:0% +moving he even can be accelerating all + + + align:start position:0% +moving he even can be accelerating all +sorts of nasty conditions true it's + + align:start position:0% +sorts of nasty conditions true it's + + + align:start position:0% +sorts of nasty conditions true it's +based on the fundamental definition of + + align:start position:0% +based on the fundamental definition of + + + align:start position:0% +based on the fundamental definition of +angular momentum so the book yeah make + + align:start position:0% +angular momentum so the book yeah make + + + align:start position:0% +angular momentum so the book yeah make +sure + + align:start position:0% +sure + + + align:start position:0% +sure +in this first line here on a fiscal wall + + align:start position:0% +in this first line here on a fiscal wall + + + align:start position:0% +in this first line here on a fiscal wall +that that stroke doesn't mean that V sub + + align:start position:0% +that that stroke doesn't mean that V sub + + + align:start position:0% +that that stroke doesn't mean that V sub +a was zero event that that term this + + align:start position:0% +a was zero event that that term this + + + align:start position:0% +a was zero event that that term this +term zero because these happen to be + + align:start position:0% +term zero because these happen to be + + + align:start position:0% +term zero because these happen to be +parallel cross product is zero in this + + align:start position:0% +parallel cross product is zero in this + + + align:start position:0% +parallel cross product is zero in this +case if it had not turned out to be + + align:start position:0% +case if it had not turned out to be + + + align:start position:0% +case if it had not turned out to be +they were different directions got to be + + align:start position:0% +they were different directions got to be + + + align:start position:0% +they were different directions got to be +a nonzero term and you would have to + + align:start position:0% +a nonzero term and you would have to + + + align:start position:0% +a nonzero term and you would have to +bring it along and take its derivative + + align:start position:0% +bring it along and take its derivative + + + align:start position:0% +bring it along and take its derivative +along with the other stuff okay but this + + align:start position:0% +along with the other stuff okay but this + + + align:start position:0% +along with the other stuff okay but this +is a really powerful method now the book + + align:start position:0% +is a really powerful method now the book + + + align:start position:0% +is a really powerful method now the book +is reasonably good in lots of points but + + align:start position:0% +is reasonably good in lots of points but + + + align:start position:0% +is reasonably good in lots of points but +in Chapter 17 when it does problems that + + align:start position:0% +in Chapter 17 when it does problems that + + + align:start position:0% +in Chapter 17 when it does problems that +are kind of like this it introduces + + align:start position:0% +are kind of like this it introduces + + + align:start position:0% +are kind of like this it introduces +something I find it hard to digest what + + align:start position:0% +something I find it hard to digest what + + + align:start position:0% +something I find it hard to digest what +they're doing as particularly where's + + align:start position:0% +they're doing as particularly where's + + + align:start position:0% +they're doing as particularly where's +Matt there's equation 1715 when you get + + align:start position:0% +Matt there's equation 1715 when you get + + + align:start position:0% +Matt there's equation 1715 when you get +to that bit of the book just ignore it + + align:start position:0% +to that bit of the book just ignore it + + + align:start position:0% +to that bit of the book just ignore it +use this method okay the author tries to + + align:start position:0% +use this method okay the author tries to + + + align:start position:0% +use this method okay the author tries to +give you kind of a little trick that you + + align:start position:0% +give you kind of a little trick that you + + + align:start position:0% +give you kind of a little trick that you +can use but the probability ryx is you + + align:start position:0% +can use but the probability ryx is you + + + align:start position:0% +can use but the probability ryx is you +have to memorize them so what I've shown + + align:start position:0% +have to memorize them so what I've shown + + + align:start position:0% +have to memorize them so what I've shown +you today is on this a based on basic + + align:start position:0% +you today is on this a based on basic + + + align:start position:0% +you today is on this a based on basic +definition of angular momentum that + + align:start position:0% +definition of angular momentum that + + + align:start position:0% +definition of angular momentum that +expression to the top is always usable + + align:start position:0% +expression to the top is always usable + + + align:start position:0% +expression to the top is always usable +not just special little conditions which + + align:start position:0% +not just special little conditions which + + + align:start position:0% +not just special little conditions which +is what is the formula in the book is + + align:start position:0% +is what is the formula in the book is + + + align:start position:0% +is what is the formula in the book is +generated for we've got a couple of + + align:start position:0% +generated for we've got a couple of + + + align:start position:0% +generated for we've got a couple of +minutes let let you ask questions and + + align:start position:0% +minutes let let you ask questions and + + + align:start position:0% +minutes let let you ask questions and +then I'll just pose a conceptual problem + + align:start position:0% +then I'll just pose a conceptual problem + + + align:start position:0% +then I'll just pose a conceptual problem +or two and ask you what method you'd use + + align:start position:0% +or two and ask you what method you'd use + + + align:start position:0% +or two and ask you what method you'd use +yeah + + align:start position:0% + + + + align:start position:0% + +oh you know boy + + align:start position:0% +oh you know boy + + + align:start position:0% +oh you know boy +I'm planting contact in order to be able + + align:start position:0% +I'm planting contact in order to be able + + + align:start position:0% +I'm planting contact in order to be able +to do this good enough if we're going to + + align:start position:0% +to do this good enough if we're going to + + + align:start position:0% +to do this good enough if we're going to +know something here right important + + align:start position:0% +know something here right important + + + align:start position:0% +know something here right important +catch thank you why is this true + + align:start position:0% + + + + align:start position:0% + +so we chose it why we chose to work + + align:start position:0% +so we chose it why we chose to work + + + align:start position:0% +so we chose it why we chose to work +around point a with respect to that + + align:start position:0% +around point a with respect to that + + + align:start position:0% +around point a with respect to that +point there are no external forces that + + align:start position:0% +point there are no external forces that + + + align:start position:0% +point there are no external forces that +create moments on that pipe with respect + + align:start position:0% +create moments on that pipe with respect + + + align:start position:0% +create moments on that pipe with respect +to that point and that's why you can say + + align:start position:0% +to that point and that's why you can say + + + align:start position:0% +to that point and that's why you can say +that the time derivative of this angular + + align:start position:0% +that the time derivative of this angular + + + align:start position:0% +that the time derivative of this angular +momentum is equal to zero because there + + align:start position:0% +momentum is equal to zero because there + + + align:start position:0% +momentum is equal to zero because there +are no external torques if you had + + align:start position:0% +are no external torques if you had + + + align:start position:0% +are no external torques if you had +picked any if you pick G to do this + + align:start position:0% +picked any if you pick G to do this + + + align:start position:0% +picked any if you pick G to do this +problem with the sum of the torques + + align:start position:0% +problem with the sum of the torques + + + align:start position:0% +problem with the sum of the torques +about G be zero no you'd have to put + + align:start position:0% +about G be zero no you'd have to put + + + align:start position:0% +about G be zero no you'd have to put +that friction force in there and have RF + + align:start position:0% +that friction force in there and have RF + + + align:start position:0% +that friction force in there and have RF +and figure out F is we completely + + align:start position:0% +and figure out F is we completely + + + align:start position:0% +and figure out F is we completely +avoided having to calculate the friction + + align:start position:0% +avoided having to calculate the friction + + + align:start position:0% +avoided having to calculate the friction +force that's the point of being able to + + align:start position:0% +force that's the point of being able to + + + align:start position:0% +force that's the point of being able to +use techniques like this and can make + + align:start position:0% +use techniques like this and can make + + + align:start position:0% +use techniques like this and can make +your computations around points of + + align:start position:0% +your computations around points of + + + align:start position:0% +your computations around points of +contact okay + + align:start position:0% + + + + align:start position:0% + +the so what so that your textbooks have + + align:start position:0% +the so what so that your textbooks have + + + align:start position:0% +the so what so that your textbooks have +lots of problems like this you've got a + + align:start position:0% +lots of problems like this you've got a + + + align:start position:0% +lots of problems like this you've got a +box on a cart you're kids pushing it and + + align:start position:0% +box on a cart you're kids pushing it and + + + align:start position:0% +box on a cart you're kids pushing it and +it gets a little exuberant and pushes a + + align:start position:0% +it gets a little exuberant and pushes a + + + align:start position:0% +it gets a little exuberant and pushes a +little too hard accelerates the cart a + + align:start position:0% +little too hard accelerates the cart a + + + align:start position:0% +little too hard accelerates the cart a +little too fast and the Box falls over + + align:start position:0% +little too fast and the Box falls over + + + align:start position:0% +little too fast and the Box falls over +and breaks the lamp or whatever's in it + + align:start position:0% +and breaks the lamp or whatever's in it + + + align:start position:0% +and breaks the lamp or whatever's in it +all right and if you if it's this way + + align:start position:0% +all right and if you if it's this way + + + align:start position:0% +all right and if you if it's this way +and I accelerate it it's much more + + align:start position:0% +and I accelerate it it's much more + + + align:start position:0% +and I accelerate it it's much more +tolerant falls over easier this way but + + align:start position:0% +tolerant falls over easier this way but + + + align:start position:0% +tolerant falls over easier this way but +if I asked you gave you a problem and + + align:start position:0% +if I asked you gave you a problem and + + + align:start position:0% +if I asked you gave you a problem and +said calculate the maximum acceleration + + align:start position:0% +said calculate the maximum acceleration + + + align:start position:0% +said calculate the maximum acceleration +that I can put on this object such that + + align:start position:0% +that I can put on this object such that + + + align:start position:0% +that I can put on this object such that +it just barely want to just right at the + + align:start position:0% +it just barely want to just right at the + + + align:start position:0% +it just barely want to just right at the +edge of tipping over but doesn't tipping + + align:start position:0% +edge of tipping over but doesn't tipping + + + align:start position:0% +edge of tipping over but doesn't tipping +over what's that maximum acceleration + + align:start position:0% +over what's that maximum acceleration + + + align:start position:0% +over what's that maximum acceleration +that you don't tip + + align:start position:0% +that you don't tip + + + align:start position:0% +that you don't tip +what method would you use one I do the + + align:start position:0% +what method would you use one I do the + + + align:start position:0% +what method would you use one I do the +three three kind of four classes of + + align:start position:0% +three three kind of four classes of + + + align:start position:0% +three three kind of four classes of +approaches to problems + + align:start position:0% + + + + align:start position:0% + +she I here for anybody else want to bid + + align:start position:0% +she I here for anybody else want to bid + + + align:start position:0% +she I here for anybody else want to bid +here's more for with three work why he + + align:start position:0% +here's more for with three work why he + + + align:start position:0% +here's more for with three work why he +says three would be complicated three + + align:start position:0% +says three would be complicated three + + + align:start position:0% +says three would be complicated three +means taking moments and forces with + + align:start position:0% +means taking moments and forces with + + + align:start position:0% +means taking moments and forces with +respect to the center of madness if you + + align:start position:0% +respect to the center of madness if you + + + align:start position:0% +respect to the center of madness if you +do that what do you have to deal with in + + align:start position:0% +do that what do you have to deal with in + + + align:start position:0% +do that what do you have to deal with in +this product you have to have to then + + align:start position:0% +this product you have to have to then + + + align:start position:0% +this product you have to have to then +around the center of mass there's a + + align:start position:0% +around the center of mass there's a + + + align:start position:0% +around the center of mass there's a +friction force there's a normal force + + align:start position:0% +friction force there's a normal force + + + align:start position:0% +friction force there's a normal force +pushing up here and the way you do this + + align:start position:0% +pushing up here and the way you do this + + + align:start position:0% +pushing up here and the way you do this +problem is you just where it's just + + align:start position:0% +problem is you just where it's just + + + align:start position:0% +problem is you just where it's just +barely about to go all of the forces + + align:start position:0% +barely about to go all of the forces + + + align:start position:0% +barely about to go all of the forces +pushing on this corner burial think of + + align:start position:0% +pushing on this corner burial think of + + + align:start position:0% +pushing on this corner burial think of +it it just it lifting up a fraction you + + align:start position:0% +it it just it lifting up a fraction you + + + align:start position:0% +it it just it lifting up a fraction you +know all of that contact point moves to + + align:start position:0% +know all of that contact point moves to + + + align:start position:0% +know all of that contact point moves to +right here you have an upward force and + + align:start position:0% +right here you have an upward force and + + + align:start position:0% +right here you have an upward force and +a friction force and then they create a + + align:start position:0% +a friction force and then they create a + + + align:start position:0% +a friction force and then they create a +moment about G but if you do the forces + + align:start position:0% +moment about G but if you do the forces + + + align:start position:0% +moment about G but if you do the forces +around G you have to solve for those two + + align:start position:0% +around G you have to solve for those two + + + align:start position:0% +around G you have to solve for those two +you do the forces around a the trick + + align:start position:0% +you do the forces around a the trick + + + align:start position:0% +you do the forces around a the trick +here is figuring out where is a but if + + align:start position:0% +here is figuring out where is a but if + + + align:start position:0% +here is figuring out where is a but if +you realize a is right here and you do + + align:start position:0% +you realize a is right here and you do + + + align:start position:0% +you realize a is right here and you do +what we just did this problem just piece + + align:start position:0% +what we just did this problem just piece + + + align:start position:0% +what we just did this problem just piece +of cake \ No newline at end of file diff --git a/mq3nFovdG3o.txt b/mq3nFovdG3o.txt new file mode 100644 index 0000000000000000000000000000000000000000..c68867e42c8f8c70552ef9eb20fbf7e72e606901 --- /dev/null +++ b/mq3nFovdG3o.txt @@ -0,0 +1,3600 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: I guess +we should start. + +This is the last of +these lectures. + +The final will be on next +Wednesday, as I hope you all + +know by this time, in the ice +rink, whatever that means. + +And there was some question +about how many sheets of paper + +you could bring in +as crib sheets. + +And it seems like the reasonable +thing is four + +sheets, which means you can +bring in the two sheets you + +made up for the quiz +plus two more. + +Or you can make up four new +ones if you want or do + +whatever you want. + +I don't think it's very +important how many sheets you + +bring in, because I've never +seen anybody referring to + +their sheets. + +I mean, it's a good way of +organizing what you know to + +try to put it on four +sheets of paper. + +I want to mostly review what +we've done throughout the + +term, with a few more general +comments thrown in. + +I thought I'd start with +martingales, because we then + +completely finish what +we wanted to + +talk about last time. + +And the Strong Law of +Large Numbers was + +left slightly hanging. + +And I want to show you +how to do that in a + +little better way. + +And also show you that it's a +more general theorem than it + +appears to be at first sight. + +So let's go with martingales. + +The basic definition is a +sequence of random variables + +is a martingale, if, for all +elements of the sequence, the + +expected value of Zn, given all +of the previous values, is + +equal to the random variable, +Z n minus 1. + +Remember, and we've talked about +this a number of times, + +when you're talking about the +expected value of one random + +variable, given a bunch of other +random variables, you're + +only taking the expectation +over the first part. + +You're only taking the +expectation over Z sub n. + +And the other quantities are +still random variables. + +Namely, you have an expected +value Z sub n, for each sample + +value of Z n minus 1, all +the way down to Z 1. + +And what the definition says is +it's a martingale only if, + +for all sample values of those +earlier values, the expected + +value is equal to the sample +value of the most recent one. + +Namely, the memory is all +contained right in this last + +term, effectively. + +At least as far as expectation +is concerned. + +Memory might be far broader than +that for everything else. + +And the first thing we did with +martingales is we said + +the expected value was again, +if you're only given part of + +the history, if you're only +given the history from i back + +to 1, where i is strictly less +than n minus 1, that expected + +value is equal to Zi. + +So no matter where you start +going back, the expected value + +of Z sub n is the most recent +value that is given. + +So if the most recent value +given is Z 1, then the + +expected value of Zn, +given Z1, is Z1. + +And also along with that, you +have the relationship, the + +expected value of Zn is equal +to the expected value of Zi, + +just by taking the expected +value over Z sub i. + +So all of that's sort +of straightforward. + +We talked a good deal about +the increments of a + +martingale. + +The increments, X sub n equals +Z sub n minus Zn minus 1, are + +very much like the increments +that we have when a renewal + +process, when a Poisson +process, all of these + +processes we talked about we +can define in various ways. + +And here we can define a +martingale in two ways also. + +One is by the actual martingale +itself, which are, + +in a sense, the sums +of the increments. + +And the other ways in terms +of the increments. + +And the increments satisfy the +property that the expected + +value of Xn, given all the +earlier values, is equal to 0. + +Namely, no matter what are all +the earlier values are, X sub + +n has mean 0 in order +to be a martingale. + +A good special case of this is +where X sub n is equal to U + +sub n times Y sub n, where the +U sub n are IID, equiprobable + +1 and minus 1. + +And the Y sub i's are anything +you want them to be. + +It's just that the U sub i's +have to be independent + +of the Y sub i. + +So I think this shows that in +fact martingales are really a + +pretty broad class of things. + +And they were invented to talk +about fair gambling games, + +where they wanted to give the +gambler the opportunity to do + +whatever he wanted to do. + +But the game itself was defined +in such a way that, no + +matter what you do, +the game is fair. + +You establish bets in one +whatever things you want to. + +And when you wind up with it, +the expected value of X sub n, + +given the past, is always 0. + +And that's equivalent to saying +the expected value of Z + +sub n, given the past, +is equal to Z sub i. + +Examples we talked about are 0 +mean random walks and products + +of unit-mean IID random +variables. + +So they're both these product +martingales, and there are + +these sum martingales. + +And those are just two simple +examples, which + +come up all the time. + +Then we talked about +submartingales. + +A submartingale is like +a martingale, except + +it grows with time. + +And we're not going to talk +about supermartingales, + +because a supermartingale is +just a negative submartingale. + +So we don't have to +talk about that. + +A martingale is a +submartingale. + +So anything you know about +submartingales applies to + +martingales also. + +So you can state theorems for +submartingales and they apply + +to martingales just as well. + +You can say stronger things very +often about martingales. + +And then we have the same +theorem for submartingales. + +Now that should say, and it did +say, until my evil twin + +got a hold of it, if Zn is a +submartingales, then for n + +greater than i, greater than +0, this expected value is + +greater than or equal to Zi. + +And the expected value Zn is +greater than equal to the + +expected value of Zi. + +In other words, this theorem, +for submartingales, is the + +same as the corresponding +theorem for martingales, + +except now you have inequalities +there, just like + +you have inequalities in +the definition of the + +submartingales. + +So there's nothing +strange there. + +Then we found out that, if you +have a convex function, from + +the reals into the reals, then +Jensen's inequality says that + +the expected value of h of X is +greater than or equal to h + +of the expected value of x. + +We showed a picture for +that you remember. + +There's a convex curve. + +There's some straight line. + +And what Jensen's inequality +says is you take an average + +over the expected value +of X, and you're + +somewhere above the line. + +And you take the average +first, and you're + +sitting on the line. + +So if h of X is convex, that's +what Jensen's inequality is. + +And it follows from that that, +if Zn is a submartingale-- + +and that includes +martingales-- + +and h is convex and the expected +value of h of X is + +finite, then h of Zn is +a martingale also. + +In other words, if you have +a martingale Z sub n, the + +expected value of Z sub +n is a submartingale. + +The expected value of E to +R Zn is a martingale. + +Use whatever convex function you +want to, and you wind up, + +martingales go into +submartingales. + +You can't get out of the range +of submartingales that easily. + +We then talked about stopped +martingales and stopped + +submartingales. + +We said a stopped process, +for a possibly + +defective stopping time-- + +now you remember what +a stopping time is? + +A stopping time is a random +variable, which is a function + +of everything that takes place +up until the time of stopping. + +And you have to look at the +definition carefully, because + +stopping time comes in too many +places to just say it and + +understand what it means. + +But it's clear what it means, +if you view yourself as an + +observer watching a sequence of +random variables, of sample + +values of random variables, +one after another. + +And after you see a certain +number of random variables, + +your rule says, stop. + +And then you don't +observe anymore. + +So you just observe this +finite number. + +And then you stop +at that point. + +And then you're all done. + +If it's a possibly defective +stopping rule, then you might + +keep on going forever, +or you might stop. + +You don't know what you're +going to do. + +The stopped process Z sub n +star is a little different + +from what we were +doing before. + +Before what we were doing +is we were sitting there + +observing this process. + +At a certain point, the stopping +rule said stop. + +And before, we were +very obedient. + +And when the stopping rule told +us to stop, we stopped. + +Now, since we know a little +more, we question authority a + +little more. + +And when the stopping rule says +stop, we break things + +into two processes. + +There's the original process, +which keeps on going. + +And there this stopped process, +which just stops. + +And it's convenient to have a +stopped process instead of + +just a stopping rule. + +Because with a stopped process, +you can look at any + +time into the future, and if +it's already stopped, you know + +what the stopped value is. + +You know what it was +when it stopped. + +You don't necessarily know when +it stopped, by looking at + +in the future. + +But you know that it did stop. + +So the stopped process, well, +it says here what it is. + +It satisfies the stopped value +at time n as equal to Z sub n, + +if n is less than or equal to +the stopping time J, and Z sub + +n star is equal to Z sub J, +if n is greater than J. + +So you get up to the stopping +timing, and you stop. + +And then it just stays +fixed forever after. + +And the nice theorem there is +that the stopped process for a + +submartingale, with a possibly +defective stopping rule, is a + +submartingale again. + +What that means is it's just a +concise way of writing, the + +stopped process for a martingale +is a martingale in + +its own right. + +And the stopped process for +a submartingale is a + +submartingale in +its own right. + +So the convenient thing is, you +can take a martingale, you + +can stop it, you still +have a martingale. + +And everything you know about +martingales applies to this + +stopping process. + +So we're getting to the point +where, starting out with a + +martingale, we can do lots +of things with it. + +And that's the whole +mathematical game. + +With a mathematical +game, you build up + +theorems from nothing. + +As an experimentalist or an +engineer, you sort of try to + +figure out those things from +the reality around you. + +Here, we're just +building it up. + +And the other part of that +theorem says that the expected + +value of Z1 is less than or +equal to the expected value of + +Zn star, is less than or equal +to the expected value of Zn + +for a submartingale. + +And they're all equal +to a martingale. + +In other words, the marginal +expectations for a martingale, + +they start out a Z1. + +They stay at Z1. + +And for the stopped process, +they stay at that same value. + +And that's not too surprising. + +Because if you have a +martingale, if you go until + +you reach the stopping point, +from that stopping point on, + +the martingale has mean +0, from that point on. + +Not the martingale itself, +but the increments of the + +martingale have mean 0, +from that point on. + +And the stopped process +has mean 0. + +In other words, the stopped +process, the increments are + +actually 0. + +Whereas for the original +process, the + +increments wobble around. + +But they still have mean 0. + +So this is a very nice and +useful thing to know. + +If you look at this product +martingale, Z sub n is E to + +the rsn minus n gamma or r . + +Why is that a martingale? + +How do you know it's +a martingale? + +Well, you look at the expected +value of this. + +And it's expected +value of this. + +The expected value of E to rsn +is the moment generating + +function of Z sub +n, of s sub n. + +It's moment generating +function of E to rsn. + +And the moment generating +function of E to rsn is just E + +to the n gamma of r. + +So this is clearly something +which should be a martingale, + +because it just keeps at +that level all along. + +If you have a stopping rule, +such as a threshold crossing, + +then you've got a stopped +martingale. + +And subject to some little +mathematical nitpicks, which + +the text talks about, this leads +you to the much more + +general version of Wald's +identity, which says that the + +expected value of Z, at the time +of stopping, is equal to + +the expected value of +E to the rsJ minus J + +gamma of r equals 1. + +This you remember is what Wald's +identity was when we + +were just talking about +random walks. + +And this was a more general +version, because it's talking + +about general stopping rules, +instead of just to thresholds. + +But it does have these little +mathematical nitpicks in it, + +which I'm not going to +talk about here. + +Then we have Kolmogorov's +submartingale inequality. + +We talked about all of these +things last time. + +So we're going pretty quickly +through them. + +The submartingale inequality +is really the Markov + +inequality souped up. + +And what it says is, if you +have a non-negative + +submartingale, that can +include a non-negative + +martingale, for any positive +integer m, the probability + +that the maximum is a Z sub i, +from 1 to m, is greater than + +or equal to a, is less than or +equal to the expected value of + +Z sub m over a. + +You see all that the Markov +inequality says is the + +probability that Z sub m is +greater than or equal to a, is + +less than or equal to this. + +This puts a lot more teeth into +it, because it lets you + +talk about all of these random +variables, up until time m. + +And it says the maximum +of them satisfies this + +inequality. + +I mean, we always knew that +the Markov inequality was + +very, very weak. + +And this is also pretty weak. + +But it's not quite as +weak, because it + +covers a lot more things. + +If you have a non-negative +martingale-- + +this is submartingales, +this is martingales. + +You see here, with +submartingales, the expected + +value of Z sub m keeps +increasing with m. + +So there's a trade-off between +making m large and + +not making m large. + +If you're dealing with a +martingale, then expected + +value Z sub m is constant +over all time. + +It doesn't change. + +And therefore, you can take +this inequality here. + +You can go to the limit, +as m goes to infinity. + +And you wind up with a +probability, the sup of Zm, + +greater than or equal to a, is +less than or equal to the + +expected value of the first of +those random variables, the + +expected value of +Z1 divided by a. + +So this looks like a very +powerful inequality. + +It turns out that I don't know +many applications of that. + +And I don't know why. + +It seems like it ought +to be very useful. + +But I know one reason, which is +what I'm going to show you + +next, which is how you can +really use the submartingale + +inequality to make it do an +awful lot of things that you + +wouldn't imagine that it +could do otherwise. + +First, you go to the Kolmogorov +version of the + +Chebyshev inequality. + +This has the same relationship +to the Kolmogorov + +submartingale inequality as +Chebyshev has to Markov. + +Namely, what you do is, instead +of looking at the + +random variables Z sub n, you +look at the random variable Z + +sub n squared. + +And what do we know now? + +If Z sub n is a martingale or +a submartingale, Z sub n + +squared is a martingale +or submartingale also. + +Namely, well, the only thing +we can be sure of is that Z + +sub n squared is a +submartingale. + +But if it's a submartingale, +then we can apply this + +inequality again. + +And what it tells us, in this +case, is the probability at + +the maximum of the magnitudes +of these random variables. + +Probably the maximum is greater +than or equal to b, is + +less than or equal to the +expected value of Z sub m + +squared over b squared. + +So before, just like the Markov +inequality, the Markov + +inequality only works for +non-negative random variables. + +You go to the Chebyshev +inequality, because that works + +for negative or positive +random variables. + +So that makes it kind of neat. + +And then what you have is this +thing, which goes down as 1 + +over b squared, which looks +a little stronger. + +But that's not the real reason +that you want to use it. + +Now, this inequality here only +works for the first m values + +of this random variable. + +What we're usually interested +in here is what happens as m + +gets very large. + +As m gets very large, this +thing, very often, blows up. + +So this [INAUDIBLE] + +does not really do what +you would like an + +inequality to do. + +So what we're going to do is, +first, we're going to say, if + +you had this inequality here, +then you can lower bound this + +by taking just a maximum, not +over 1 up to m, but only over + +m over 2 up to m. + +Now why do we want to do that? + +Well, hold on and you'll see. + +But anyway this is bigger +than, greater than + +or equal to, this. + +So what we're going to do now +is we're going to take this + +inequality. + +We're going to use it for m +equals 2 to the m, for m + +equals 2 to the k plus 1, m +equals 2 to the k plus 2, all + +the way up to infinity. + +And so we're going to find the +probability of the union over + +j greater than or equal to k of +this quantity here, but now + +just maximized over 2 to the j +minus 1, less than n, less + +than or equal 2 to the j. + +And then the maximum of Z sub +n, greater than or equal to. + +And now, for each one of these +j's here, we'll put in + +whatever b sub j we want. + +So the general form of this +inequality then becomes. + +We have this term on the left. + +We use the union bound. + +And we get this term +on the right. + +So at this point, we have an +inequality, which works for + +all n, instead of just +for values smaller + +than some given amount. + +So this is sort of a general +technique for taking an + +inequality, which only works +up to a certain value, and + +extending it so it works +over all values. + +You have to be pretty careful +about how you choose b sub j. + +Now what we're going +to do is say, OK. + +And remember, what is happening +here is we started + +out with a submartingale +or a martingale. + +When we take Z n squared, we +still have a submartingale. + +So we can use a submartingale +inequality, which is what + +we're doing here. + +We're using the submartingale +inequality on Zm squared + +rather than on Zm. + +And Zm squared is non-negative, + +so that works there. + +Then we go down to this point. + +We take a union over +all of these terms. + +And note what happens. + +Every n is included in one +of these terms, every n + +beyond 2 the k. + +So if we want to prove something +about the limiting + +values of Z sub n, we have +everything included there, + +everything beyond 2 to the k. + +But as far as the limit is +concerned, you don't care + +about any initial finite set. + +You care what happens after +that initial finite set. + +So what we have then +[INAUDIBLE] + +of these terms, less than +or equal to this term. + +When I apply this to a random +walk S sub n, S sub n is a + +submartingale, at this point. + +The expected value +of x squared will + +assume a sigma squared. + +The expected value now S sub +n, or Z sub n is we'll call + +it, is the sum of these n +IID random variables. + +So the expected value-- + +AUDIENCE: 10 o'clock. + +PROFESSOR: The expected value +of Z to the 2J is just 2 to + +the J times the expected value +of x squared, in other words, + +sigma squared. + +[INAUDIBLE] just doing this +for a 0 mean [INAUDIBLE] + +variable, because [INAUDIBLE] + +given an arbitrary +non-0 [INAUDIBLE] + +random variable. + +You can look at it as to +mean plus a random + +variable, which is 0 mean. + +So that's the same ideas +we're using here. + +So we take this inequality now, +and I'm going to use for + +b sub J, 3/2 to the +J. Why 3/2 to J? + +Well you'll see in +just a second. + +But when I use 3/2 to the J here +I get the maximum over S + +sub n, greater than or equal +to 3/2 to the J. + +And over here I get b sub J +squared is 9/4 to the J. And + +here I have 2 the J also. + +So when I sum this, it winds up +with 8/9 to the k times 9 + +sigma squared. + +So what I have now is something +where, when k gets + +larger, this term +is going to 0. + +And I have something over here, +well that doesn't look + +quite so attractive, but +just wait a minute. + +What I'm really interested +in is not S sub n. + +But I'm interested in +S sub n over n. + +For the strong law of large +numbers, I'd like to show that + +S sub n over n approaches +a limit. + +And n in this case runs between +2 to the J minus 1 and + +2 to the J. + +So when I put that in here-- + +we'll see what that amounts +to in the next slide. + +For the strong law of large +numbers, what our theorem says + +is that the probability of the +set of sample points, for + +which S sub n over n equals 0, +that set of sample points has + +probability y. + +So the proof of that, if I pick +up this equation from the + +previous slide, and when I lower +bound the left side of + +this, what I'm going to get, I'm +going to divide by n here. + +And I'm going to divide by +something a little bit + +smaller, which is 2 to +the J minus 1 here. + +So I get the maximum of S sub +n over n, greater than or + +equal to 2 times 3/4 to the J. + +Now you see why I picked-- + +I think you see at this +point why I picked the + +sub j the way I did. + +I wanted to pick it t to be +smaller than 2 to the J. And I + +wanted to pick it to be big +enough that it drove the right + +hand term to 0. + +So now we're done really. + +Because, if I look at this +expression here, a sample + +sequence S sub n of omega, +that's not contained in this + +union, has to approach 0. + +Because these terms from 2 to +the J minus 1 to 2 to the J, + +in order to be in this set, they +have to be greater than + +or equal to 2 times +3/4 to the J. + +As j gets larger and larger, +this term goes to 0. + +So the only terms that exceed +that are terms that are + +arbitrarily small. + +So the complement of this set is +the set of terms for which + +S sub n over n does +not approach 0. + +But the probability of that is +8/9 to the k times time some + +garbage over here. + +So now it's true for all k. + +The terms which approach 0, +namely the sampled values for + +which S sub n over n approaches +0 are all + +complimentary to this set. + +So the probability that S sub n +over omega over n approaches + +0 is greater than 1 minus +this quantity here. + +That's true for all k. + +And since it's true for all +k, this term goes to 0. + +And the theorem is proven. + +Now why did I want to +go through this. + +There are perhaps easier ways +to prove the strong law of + +large numbers, just assuming +that the variance is finite. + +Why this particular y? + +Well, if you look at this, it +applies to much more than just + +sums of IID random variables. + +It applies to arbitrary +martingales, so long as these + +conditions are satisfied. + +It applies to these cases, like +where you have a random + +variable, which is plus or minus +1 times some arbitrary + +random variable. + +So this gives you sort of a +general way of proving strong + +laws of large numbers +for strange + +sequences of random variables. + +So that's the reason for +going through this. + +We now have a way of proving +strong laws of large numbers + +for lots of different kinds of +martingales, rather than just + +for this set of things here. + +So let's move on back to Markov +chains, countable or + +finite state. + +I'm moving back to chapter three +and five in the text, + +mostly chapter five, and trying +to finish some sort of + +review of what we've done. + +When I look back at what we've +done, it seems like we've + +proven an awful lot theorems. + +So all I can do is talk +about the theorems. + +I should say something, again, +this last day, on this last + +lecture, about why we spend so +much time proving theorems. + +In other words, we've just +proven a theorem here. + +I promised you I would prove a +theorem every lecture, along + +with talking about why they're +important and so on. + +And most of you are engineers +or you're scientists in + +various fields. + +You're not mathematicians. + +Why should you be interested +in all these theorems. + +Why should you take abstract +courses, which + +look like math courses? + +And the reason is this kind of +stuff is more important for + +you than it is for +mathematicians. + +And it's more important for +you, because when you're + +dealing with a real engineering +or real scientific + +problem, how do you +deal with it? + +I mean, you have a real +mess facing you. + +You spend a lot of time trying +to understand what that mess + +is all about. + +And you don't form a model of +it, and then apply theorems. + +What you do is to try +to understand it. + +You look at multiple models. + +When we were looking at +hypothesis testing, we said + +we're going to assume a +priori probabilities. + +I lied about that +a little bit. + +We we're not assuming a +priori probabilities. + +We we're assuming a class of +probability models, each of + +which had a priori probabilities +in them. + +And then we said something +about that class of + +probability models. + +And saying something about +that class of probability + +models, we were able to say a +great deal more than you can + +say if you refuse to even think +about a model, which + +doesn't have a priori +probabilities in it. + +So by looking at lots of +different models, you can + +understand an enormous number +of things without really + +having any one model which +describes the whole + +situation for you. + +And that's why we try to prove +theorems for models, because + +then, when you understand lots +of simple models, you have + +these complicated physical +situations, and + +you play with them. + +You play with them by applying +various simple models that you + +understand to them. + +And as you do this, you +gradually understand the + +physical process better. + +And that's the way we +discover things. + +OK, end of lecture. + +Not end of lecture, but end of +partial lecture about why you + +want to learn some +mathematics. + +The first passage time from +state i to j, remember, is the + +smallest n, when you start off +in state i, at which you get + +to state j. + +You start off in state i. + +You jump from one lily +pad to another. + +You eventually wind up +at lily pad number j. + +And we want to know how long +it takes you to get to j. + +That's a random variable, +obviously. + +And this Tij, as possibly the +effective random variable, + +that has the probability +mass function. + +It's the definition of +what this probability + +mass function is. + +And it has a distribution +function. + +And the probability +mass function-- + +you probably remember +how we derived this. + +We derived it by sort of +crawling up on it, by looking + +at it, first, for n equals 1, +in which case it's just a + +transition probability +of n equals 2. + +In which case, it's the +probability that you first go + +to k, and then in n minus +1 steps, you go to j. + +But you have to leave j out, +because if you go to j in the + +first step, you've already +had your first passage. + +so + +We define a state to be +recurrent, if T sub jj is + +non-defective. + +And we define it to be +transient otherwise. + +In other words, if it's not +certain that you ever get to + +state j, then you define it +to be transient, if it's + +recurrent and it's positive +recurrent, if the expected + +value of T sub jj is +less than infinity. + +And it's null recurrent +otherwise. + +How do we know how +to analyze this? + +Well we study renewal +processes. + +And if you look at the renewal +process where you've got a + +renewal every time you hit +state j, you start + +out on stage j. + +The first time you hit state +j, that's a renewal. + +The next time you hit state +j, that's another renewal. + +You have a renewal process where +the interrenewal time is + +a random variable, which has +the PMF F sub ij event. + +Excuse me, if you have a renewal +process, if you start + +in state j, where T sub jj is +the amount of time before + +renewal occurs, from that time +on, you get another renewal + +with another random variable +with the same + +distribution as Tjj. + +And F sub ij is the PMF +of that renewal time. + +And F sub ij is the distribution +function of it. + +So then when we define the state +j as being recurrent, + +what we're really doing is going +back to what we know + +about renewal processes and +saying a Markov chain is + +recurrent if the renewal process +that we define for + +that countable state Markov +chain has these various + +properties for this renewal +random variable. + +For each recurrent j, there's +an integer renewal counting + +process N sub jj of t. + +You start in state j at time t, +which is after t steps of + +the Markov process. + +What you're interested is how +many times have you hit state + +j, up until time t. + +That's the counting process we +talk about in renewal theory. + +So N sub jj of t is the number +of visits to j starting in j. + +And it has the interrenewal +distribution F sub jj, which + +is that quantity up there. + +We have a delayed renewal +counting process N sub ij of + +t, if we count visits +to j, starting in i. + +We didn't talk much about +delayed renewal processes, + +except for pointing out that +when you have a delayed + +renewal process, it +really is the same + +as a renewal processes. + +It just has some arbitrary +amount of time that's required + +to get to state j for the +first time and the keep + +recurrent on. + +Even if the expected time to +get to j for first time is + +infinite, and the expected time +for renewals from j to j + +is finite, you still have this +same renewal processes. + +You can even lose an infinite +amount of time at the + +beginning, and you amortize +it over time. + +Don't ask me why you can +amortize an infinite amount of + +time over time. + +But you can. + +And actually if you read about +delayed renewal processes, you + +see why you actually get that. + +So all states in a class are +positive recurrent, or all are + +null recurrent, or all +are transient. + +We've proved that theorem. + +It wasn't really a very +hard theorem to prove. + +And you can sort of see +that it ought to be. + +Then we define the chain as +being irreducible, if all + +state pairs communicate. + +In other words, if for every +pair of states, there's a path + +that goes from one state +to the other state. + +This is intuitively a simple +idea, if you have a finite + +state and Markov chain. + +If you have a countably infinite +state Markov chain, + +it seems to be a little +more peculiar. + +But it really isn't. + +For a countably infinite state +an Markov chain every state + +has a finite number. + +And you can take every +pair of states. + +You can identify them. + +And you can see whether there's +a path going from one + +to the other. + +For all of these birth-death +processes we've talked about, + +I mean, it's obvious whether +the states all + +communicate or not. + +You just see if there's +any break in the + +chain at any point. + +And it really looks +like a chain. + +It's a node, two transitions, +another node, two transitions, + +another node. + +And that's just the way chains +are supposed to work. + +An irreducible class might +be positive recurrent. + +It might be null recurrent. + +Or it might be transient. + +And we already have seen what +makes a state null recurrent + +or transient. + +And it's the same thing +for the class. + +We started out by saying +a state is either null + +recurrent, positive recurrent, +or transient depending on this + +renewal process associated +with it. + +And now there's this theorem, +which says that if one node in + +a class of states is positive +recurrent, they all are. + +And you ought to be able +to sort of see + +the reason for that. + +If I have one state which is +positive recurrent, it means + +that the expected time to +go from this state to + +this state is finite. + +Now if I had some other +state, I have to go + +from here to there. + +I can go through here and +then off to there. + +So the amount of time it takes +to get to there, and then from + +there to there, is also finite, +expected amount, and + +the same backwards. + +So that was the way +we proved this. + +If we have an irreducible +Markov chain-- + +now this is the theorem you +really use all the time. + +This is sort of says how you +operate with these things. + +It says the steady +state equations-- + +they're the equations you've +used in half the problems + +you've done with +Markov chains-- + +if these equations have a +solution for the pi sub j's, + +remember the Markov chain is +defined in terms of the + +transition probabilities +P sub ij. + +We solve these equations to find +out what the steady state + +probabilities pi sub j are. + +And the theorem says, if you can +find the solution to those + +equations-- + +pi sub j's have to +add up to 1-- + +then the solution is unique. + +The pi sub j's are equal to 1 +over the mean time to go from + +that state back to +that state again. + +And what does that mean? + +What that really gives you is +not a way to find pi sub j. + +It gives you a way to +find a T sub jj. + +Because these equations are more +often the way that you + +solve for the steady state +probabilities. + +And then that gives you a way +to find the mean recurrence + +time between visits to +this given state. + +And what else does +this theorem say? + +It says if the states are +positive recurrent, then the + +steady state equations +have a solution. + +So this is an if and only +if kind of statement. + +It relates these equations, +these steady state equations, + +to solutions and says, if +these equations have a + +solution, then in fact +you have the + +steady state equations. + +They satisfy all these +relationships about mean + +recurrence time. + +And if the states are positive +recurrent, then those + +equations have a solution. + +And in the solutions, the pi +sub j's are all possible. + +So it's an infinite set of +equations, so you can't + +necessarily solve it. + +But you sort of know everything +there is to know + +about it, at this point. + +Well, there's one other thing, +when you have a birth-death + +chain, these equations simplify +a great deal. + +The counting processes under +positive recurrence have to + +satisfy this equation. + +And my evil twin brother got a +hold of this and left out the + +n in the copy that you have. + +And I spotted it when I looked +at it just a little bit. + +He was still sleeping, so +I've managed to find it. + +So it's corrected here. + +And what does that say? + +It says, when you have positive +recurrence, if you + +look from 0 out to t, and you +count the number of times that + +you hit state j, that's +a random variable. + +If you take that and divide by +n, you look from time 0 out to + +time N, N sub ij of N, it's +the number of times + +you visit state j. + +You divide that by N, and +you go to the limit. + +And there's a strong law of +large numbers there, which was + +a strong law of large numbers +for renewal processes, which + +says that it has a limit +with probability 1. + +And this says that limit +is pi sub j. + +And that's sort of +obvious, again. + +I mean, visualize +what happens. + +You start out in state j. + +For one unit of time, +you're in state j. + +Then you go away from state j, +and for a long time you're out + +in the wilderness. + +And then you finally get +back to state j again. + +Think of a renewal reward +process, where you get 1 unit + +of reward every time you're in +state j and 0 reward every + +time you're not in state j. + +That means every interrenewal +period, you pick + +up one unit of reward. + +Well, this is what that says. + +It says that the fraction of +those visits to state j-- + +that out of the total visits in +the Markov chain, the ones + +that go to state j have +probability pi sub j. + +So again this is another +relationship with these steady + +state probabilities. + +The steady state probabilities +tell you what these mean + +recurrence times are. + +And that tells you +what this is. + +This, in a sense, is +the same as this. + +Those are just sort of +the same results. + +So there's nothing +special about it. + +We talked a little bit about +the Markov model of age of + +renewal process for any +integer valued renewal + +process, you can find a Markov +chain which gives you the age + +of that process. + +You visualize being +in state j. + +And you visualize being in state +0, of this Markov model, + +at the point where you +have a renewal. + +One step later, if you have +another renewal, that happens + +with probability P sub 00, you +go back to state 0 again. + +If you don't have a renewal +in the next time, + +you go to state 1. + +From state 1, you might +go to state 2. + +When you're in state 2, it means +you're two time units + +away from state 0. + +If you go back to state 0, it +means you have a renewal in + +three time units. + +Otherwise you go to state 3. + +Then you might have a renewal +and so forth. + +So for this very simple kind +of Markov chain, this tells + +you everything there is to +know, in the sense, about + +integer value renewal +processes. + +So there's this nice connection +between the two. + +And it lets you see pretty +easily about when you have no + +recurrence. + +Now we spend a lot of time +talking about these + +birth-death Markov chains. + +And the easy way to solve for +birth-death Markov of chains + +is to say intuitively that +between any two adjacent + +states, the number of times +you go up has to equal the + +number of times you go down, +plus or minus 1. + +If you start out here and you +end up here, you're going this + +way one more time than you've +gone that way and vice versa. + +And combining that with the +steady state equations that we + +now have been talking about, +it must be that the steady + +state probability +of pi sub i-- + +pi sub i times P sub i is the +probability of going from + +state 2 to state 3. + +It's the probability of being +in state 2 and making a + +transition to state 3. + +This probability here is the +probability of being in state + +3 and going to state 2. + +And we're saying that +asymptotically, as you look + +over an infinite number of +transitions, those two have to + +be the same. + +The other way to do it, if you +like algebra, is to start out + +with a steady state equation. + +And you can derive +this right away. + +I think it's nicer to +see intuitively + +why it has be true. + +And what that says is if rho sub +i is equal to P sub i over + +Q sub i plus 1, P sub i is the +up transition probability. + +Q sub i is the down transition +probability. + +Rho sub i is the ratio of the +two state probabilities. + +And that's equal to this +equation here. + +That's just how to calculate +these things. + +And you've done that. + +Let's go on to Markov +processes. + +I have no idea where I'm +going to finish up. + +I had a lot to do. + +I better not waste +too much time. + +Remember what a Markov +process is now. + +At least the way we started +out thinking about, it's a + +Markov chain along with +a holding time. + +And each state is +a Markov chain. + +And the holding times are +exponential, to be a countable + +state Markov process. + +So we can visualize it +as a sequence of + +states, X0, X1, X2, X3. + +And a sequence of holding +times, U1, U2, U3, U4. + +these are all random +variables. + +And this kind of dependence +diagram says what random + +variables depend on what +random variables. + +U1, given X0, is independent +of the rest of the world. + +U2, given X1, is independent +of the rest of the + +world, and so forth. + +And if you look at this graph +here and you visualize the + +fact that because of Bayes' +rule, you could go + +both ways on this. + +In other words, if this, given +this, is independent of + +everything else, we +can go through the + +same kind of argument. + +And we can make these arrows +go the opposite way. + +And we can say, if we just +consider these states here, we + +can say that, given X3, U4 is +independent of X2 and also + +independent of U3 and X1 +and U2 and so forth. + +So if you look at the dependence +graph of a Markov + +chain, which is which states +depend on which other states, + +those arrows there that we have, +which make it easier to + +see what's going on, you +can take them off. + +You can redraw them in any way +you want to and look at the + +dependencies in the +opposite way. + +Now to understand what the +state is at any time t, + +there's an equation +to do that. + +It's an equation that +isn't much help. + +I think it's more help to look +at this and to see from this + +what's going on. + +You start in some +state that's 0. + +And starting in state 0, there's +a holding time in U0. + +The holding time is U1. + +And you stay in. + +And the time in U1 is an +exponential random variable + +with rate U sub i. + +That's what this says. + +So at the end of that holding +time, you go from state i to + +some other state. + +This is the state you go to. + +The state you go to is according +to the mark Markov + +chain probabilities. + +And it's state j in this case. + +You stay in state j until the +holding time U2, which is a + +function of j, finishes you up +at this time and so forth. + +So if you want to look at what +state you're in at a given + +time, namely pick a time here +and say what's the state at + +this time, as a random +variable. + +So what you have to do then is +you have to climb your way up + +from here to there. + +And you have to talk about the +value of S1, S2, and S3. + +And those are exponential +random variables. + +But they're exponential random +variables that depend on the + +state that you're in. + +So as you're climbing your way +up and looking at this sample + +function of the process, you +have to look at U1 an X0. + +X0 defines what U1 is, +as a random variable. + +It says that U1 is an +exponential random variable, + +with rate U sub i. + +So you get to here, then you +have some holding time here, + +which is a function of j and +so forth, the whole way up. + +Which is why I said that an +equation for X of t, in terms + +of these S's is not going to +help you a great deal. + +Understanding how the process +is working I think + +helps you a lot more. + +We said that there were three +ways to represent a Markov + +process, which I'm giving +here in terms + +just of Markov chains. + +The first one-- + +and the fact that these are all +for M/M/1 doesn't make any + +difference. + +It's just these three +general [INAUDIBLE]. + +One of them is, you look at it +in terms of the embedded + +Markov chain. + +For this embedded Markov +chain, the transition + +probabilities, when you're in +state 0 in an M/M/1 queue, + +what's the next state +you go to? + +Well the only state you +can go to is state 1. + +Because we don't have any +self transitions. + +So you go up to state +1 eventually. + +From state 1, you can go that +way, with probability mu over + +lambda plus mu. + +Or you can go this way, with +probability lambda over lambda + +plus mu, and so forth +the whole way out. + +The next way of describing it, +which is almost the same, is + +instead of using the transition +probabilities and + +the embedded chain, you look +directly at the transition + +rates for the Poisson process. + +Meaning the transition rates are +the new sub i's associated + +with the different states. + +When you get in state i, the +amount of time you spend is + +state i is an exponential +random variable. + +And when you make a transition, +you're either + +going to go to one state or +another state, in this case. + +In general, you might go to any +one of a number of states. + +Now if I tell that we start out +in state one and the next + +state we go is state 2, now I +ask you what's the expected + +amount of time that that +transition took? + +What's the answer? + +Is it queue 1, 2, or +is it mu sub 1? + +Anybody awake out there? + +AUDIENCE: Sir, could you +repeat the question? + +PROFESSOR: Yes. + +The question is, we started +out in state 1. + +Given that we started out in +state 1 and given that the + +next state is state 2, what's +the amount of time that it + +takes to go from 1 to 2? + +It's an exponential +random variable. + +What's the rate of that +random variable? + +AUDIENCE: Lambda plus U. + +PROFESSOR: What? + +AUDIENCE: Lambda plus U. + +PROFESSOR: Lambda plus mu? + +Yes. + +Lambda plus mu in the +case of M/M/1 queue. + +If you have an arbitrary change, +why the amount of time + +that it takes is mu sub I. This +is just back to this old + +thing about splitting and + +combining of Poisson processes. + +When you have a combined Poisson +process, which is what + +you have here, when you're in +state i, there's a combined + +Poisson process, which is +running, which says you go + +right with probability. + +Lambda, you go left with +probability mu + +for an M/M/1 queue. + +And you can look at it in terms +of, first, you see what + +the next state is. + +And then you ask how long did +it take to get there? + +Or you look at in terms of how +long does it take to make a + +transition and then which +state did you go to? + +And with these combined Poisson +processes, those two + +questions are independent +of each other. + +And if there's one thing you +remember from all of this, + +please remember that. + +Because it's something that +you use in almost every + +problem that you do with Markov + +chains and Markov processes. + +It just comes up all the time. + +This final version here is +looking at the same Markov + +process, but looking at it in +sample time instead of looking + +at the embedded queue. + +Now the important thing here +is, when you look at it in + +sample time, you might not +be able to do this. + +Because with this entire +cannibal state Markov chain, + +you might not be able to +define these self-loop + +transition probabilities. + +Because these numbers +might get too large. + +But for the M/M/1 queue, +you can do it. + +The important thing is that the +steady state probabilities + +you find for these states are +not the same as the steady + +state probabilities you find for +the embedded Markov chain. + +They are in fact the same as the +steady state probabilities + +for the Markov process itself. + +That's these steady state +probabilities are the fraction + +of time that you spend +in state j. + +And this is a sample time +Markov process. + +It is the same fraction of time +you spend in state j. + +Here you have this +embedded chain. + +And for example, in the embedded +chain, the only place + +you go from state +0 is state 1. + +Here from state 0, you +can stay in state + +0 for a long time. + +Because here the increments +of time are constant. + +We can look at delayed renewal +reward theorems for the + +renewal process to see what's +going on here, for the + +fraction of time we +spend in state j. + +We look at that picture +up there. + +We start out in state +j, for example. + +Same as the renewal reward +process that we had for a + +Markov chain. + +We got a reward of 1 for the +amount of time that we + +stay in state j. + +After that, we're wandering +around in the wilderness. + +We finally come back +to state j again. + +We get 1 unit of reward +times the amount of + +time we spend here. + +In other words, we're +accumulating reward at a rate + +of 1 unit per unit time, +up to there. + +So the average reward we get per +unit time is the expected + +value of U of j divided by the +expected interrenewal time, + +which is 1 over mu j times the +expected time, from one + +renewal to the next. + +Which tells us that the fraction +of time we spend in + +state j is equal to the fraction +of transitions that + +go to state j, divided by the +rate at which we leave state + +j, times the expected +number of overall + +transitions per unit time. + +This is an important result. + +Because depending on what M sub +i is, depending on what + +the number of transitions per +unit time is, it really tells + +you what's going on. + +Because all of these bizarre +Markov processes that we've + +looked at are bizarre because of +the way that this behaves. + +This can infinite or can be 0. + +At this point, we've been +talking about the expected + +number of transitions per unit +time as a random variable, as + +a limit in probability +1, given that we + +start in state i. + +And suddenly, we see that it +doesn't depend on i at all. + +So there is some number, M bar, +which is the expected + +number of transitions per unit +time, which is independent of + +what state we started in. + +We call that M M bar instead +M sub I. And that's this + +quantity here. + +And what we get from that it +is the fraction of time we + +spend in state j is +proportional to pi + +j over mu sub j. + +But since it has to add up to +1, we have to divide it by + +this quantity here. + +And this quantity here +is one over-- + +this is the expected number of +transitions per unit time. + +And if we try to get the pi sub +j's from P sub j's, the + +corresponding thing, as we find +out, the expected number + +transitions per unit time as +a sum over i, P sub i, + +times mu sub i. + +You can play all sorts of games +with these equations. + +And when you do so, all of those +things become evident. + +I would advise you to just +cross this equation out. + +I don't know what +it came from. + +But it doesn't mean anything. + +We spent a lot of time talking +about what happens when the + +expected number of transitions +per unit time + +is either 0 or infinity. + +We had this case we looked at of +an M/M/1 type queue, where + +the server got rattled +as time went on. + +And the server got rattled +with more and + +more customers waiting. + +The customer's got discouraged +and didn't come in. + +So we had a process where the +longer the queue got, the + +longer time it took for +anything to happen. + +So that as far as the embedded +Markov chain went, + +everything was fine. + +But then we looked at the +process itself, the time that + +it took in each of these higher +order states was so + +large, that, as a process, +it didn't make any sense. + +So the P sub i's were all 0. + +The pi sub i's all +looked fine. + +And the other kind of cases, +where the expected number of + +transitions per unit time +becomes infinite. + +And that's just the opposite +kind of case, where, when you + +get to the higher ordered +states, things start happening + +very, very fast. + +The higher ordered state you +go to, the faster the + +transitions occur. + +It's like a small child. + +I mean, the more excited the +small child gets, the faster + +things happen. + +And the faster things +happen, the more + +excited the child gets. + +So pretty soon things are +happening so fast, the child + +just collapses. + +And if you're lucky, +the child sleeps. + +So you can think +of it that way. + +We talked about reversibility. + +And reversibility for Markov +processes I think is somewhat + +easier to see then + +reversibility for Markov chains. + +If you're dealing with a Markov +process, we're sitting + +in state i for a while. + +At some time we make +a transition. + +We go to state j. + +We sit there for a long time. + +Then we go to state +k and so forth. + +If we try to look at this +process coming back the other + +way, we see that we're +in state k. + +At a certain point, we +had a transition. + +We had a transition +into state j. + +And how long does it +take before that + +transition is over? + +We're in state j, so the amount +of time that it takes + +is an exponentially distributed +random variable. + +And it's exponentially +distributed with the same + +amount of time, whether we're +coming in this way or whether + +we're coming in this way. + +And that's the notion +of reversibility. + +It doesn't make any difference +whether you look at it from + +right to left or from +left to right. + +And in this kind of situation, +if you find the steady state + +probabilities for these +transitions or you find the + +steady state fraction of time +you spend in each state. + +I mean, we just showed that if +you look at this process going + +backwards, if you define all +the probabilities coming + +backwards, the expected amount +of time that you spend in + +state i or the rate for leaving +state i is independent + +of right to left. + +And a slightly more complicated +argument says the + +P sub i's are the same +going right to left. + +And the fraction of time you +spend in each state is + +obviously the same going +from right to left as + +these limits occur. + +So that gives you all these +bizarre conditions for + +queuing, which are +very useful. + +I'm not going to say any +more about that except + +the guessing theorem. + +The guessing theorem says +suppose a Markov process is + +irreducible. + +You can check pretty +easily whether it's + +irreducible or not. + +You can't necessarily +check very easily + +whether it's recurrent. + +And suppose P sub i is a set +of probabilities that + +satisfies P sub i times +Q sub ij equals P sub + +j times Q sub ji. + +In other words, this is the +probability of being in state + +i, and the next transition +is to state j. + +This is the probability of being +in state j, and the next + +transition to state i. + +This says that if you can find +a set of probabilities which + +satisfy these equations, and +if they also satisfy this + +condition, P sub i, mu sub i, +less than infinity, then P sub + +i is greater than 0 for all i. + +P sub i is a steady state time +averaged probability state i. + +The processes is reversible. + +And the embedded chain is +positive recurring. + +So all you have to do is +solve those equations. + +And if you can solve those +equations, you're done. + +Everything is fine. + +You don't have to know anything +about reversibility + +or renewal theory or +anything else. + +If you have that theorem, +you just + +solve for those equations. + +Solve these equations by +guessing what the solution is, + +and then you in fact have +a reversible process. + +So the useful application of +this is that all birth-death + +processes are reversible if this +equation is satisfied. + +And you can immediately +find the steady state + +probabilities of them. + +I'm not going to have much +time for random walks. + +But random walks are +what we've been + +talking about all term. + +We just didn't call them random +walks until we got to + +the seventh chapter. + +But a random walk is a sequence +of random variables, + +where each Sn in the sequence +is a sum of some number of + +underlying IID random variables, +X1 up to X sub n. + +Well we're interested in +exponential bounds on S sub n + +for large n. + +These are known as +Chernoff bounds. + +We talked about them back +in chapter one. + +I'm not going to mention +them again now. + +We're interested in threshold +crossings. + +If you have two thresholds, one +positive threshold, one + +negative threshold, you would +like to know what's the + +stopping time when S sub +n first crosses alpha? + +Or what's the stopping time when +it first crosses beta? + +What's the probability of +crossing alpha before you + +cross beta or vice versa? + +And what's the distribution of +the overshoot, when you pass + +one of them? + +So there all those questions. + +We pretty much talked +about the first two. + +The question of overshoot, +I think I mentioned this. + +The text doesn't say +much about it. + +Overshoot is just a nasty, +nasty problem. + +If you ever have to find the +overshoot of something, go + +look for a computer program to +simulate it or something. + +You're not going to solve +the problem very easily. + +Fowler is the only book I know +which does a reasonable job of + +trying to solve this. + +And you have to be +extraordinarily patient. + +I mean Fowler does everything +in the nicest possible way. + +Or at least he always seem to +do everything in the nicest + +possible way. + +Most textbooks you look at, +after you understand the + +subject, you look at and you +say, oh, he should have done + +it this way. + +I've never had that experience +with Fowler at all. + +Always, I look at it. + +I say, oh, there's an +easier way to do it. + +I try to do it the easier way. + +And then I find something's +wrong with it. + +And then I go back and say, +ah, I got to do it the way + +Fowler did it. + +So if you're serious about this +field and you don't have + +a copy of this very +old book, get it, + +because it's solid gold. + +Suppose a random variable has a +moment generating function, + +expected value of E to +the zr over some + +positive region of r. + +And suppose it has a mean +which is negative. + +The Chernoff bound says that for +any alpha greater than 0 + +and any r in 0 to r plus, the +probability that Z is greater + +than or equal to alpha is +less than or equal to + +this quantity here. + +You remember, we derived this. + +The derivation is very simple. + +It's a an obvious result. + +It's a little strange. + +Because this says that for +this random variable it's + +complimentary distribution +function has to go down as e + +to the minus r alpha. + +Now all random variables can't +go down exponentially as e to + +the minus r alpha. + +The reason for this is that +these moment generating + +functions down exist +for all alpha. + +So what it's really saying is +where it exists, it goes down + +with alpha as e to the +minus r alpha. + +We then define the +semi-invariant moment + +generating function. + +And then a more convenient way +of stating the Chernoff bound + +was in this way. + +You look here. + +And you say, for a fixed value +of n here, this probability of + +S sub n is greater than or equal +to n a, is something + +which is going down +exponentially with n. + +And if you optimize over +r, this bound is + +exponentially tight. + +In other words, if you try to +replace this with anything + +smaller, namely which goes down +faster, than for large + +enough n, the bound +will be false. + +So this is the tightest bound +you can get when you + +optimize it over r. + +So its exponential in n. + +Mostly we wanted to use it +for threshold crossings. + +And for threshold crossings, we +would like to look at it in + +another way. + +And we dealt with this +graphically. + +Probability of Sn greater +than or equal to alpha. + +Now what we want to do is +hold alpha constant. + +Alpha is some threshold +up there. + +We want to ask, what's the +probability that after n + +trials, we're sitting +above alpha? + +And we'd like to try +to solve that for + +different values of n. + +The Chernoff bound, in this +case, this quantity here is + +this intercept here. + +You take the semi-invariant +moment + +generating function as convex. + +You draw this curve. + +You take a tangent of +slope alpha over n. + +And you see where +it hits here. + +And this is the exponent +that you have. + +This is a negative exponent. + +As you very n, this tilts +around on this curve. + +And it comes in to this point. + +It goes back out again. + +That's what happens to it. + +And that smallest exponent, as +you vary n, is the most likely + +time at which you're going +to cross that threshold. + +And what we found, +from looking at + +Wald's equality is that-- + +let me go on, because we're +running out of time. + +Wald's identity for two +thresholds says this. + +And the corollary says, if the +underlying random variable is + +less than 0, and if the +r at which the-- + +the second solution of +gamma of r equals 0. + +You have this convex curve. + +Gamma is always equal to 0. + +There's some other value of r, +for which gamma is equal to 0. + +And that's r star. + +And this says that the +probability that we have + +crossed alpha at time j, where +j is the time of first + +crossing, is less than +or equal e to the + +minus alpha r star. + +This bound is tight also. + +And that's a very nice result. + +Because that just says that all +you got do is find r star. + +And that tells you what the +probability of crossing a + +threshold is. + +And it's a very tight bound +if alpha is very large. + +It doesn't make any difference +what the negative threshold + +is, or whether it's +there or not. + +This tells you the thing +you want to know. + +I think I'm going to stop at +that point, because I have + +been sort of rushing to +get to this point. + +And it doesn't do any good +to keep rushing. + +So thank you all for being +around all term. + +I appreciate it. + +Thank you. \ No newline at end of file diff --git a/oDOs8Yxydo0.txt b/oDOs8Yxydo0.txt new file mode 100644 index 0000000000000000000000000000000000000000..30f66722a96ae1bceeb72caa05b84f4fa82ed291 --- /dev/null +++ b/oDOs8Yxydo0.txt @@ -0,0 +1,3062 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK. + +OK, settle down. + +Settle down. + +Let's get started. + +So last day we started talking +about diffusion. + +Diffusion is a solid-state +mass transport by random + +atomic motion. + +I made the first point last day +and today I'll make the + +second point. + +We'll see why it's random +atomic motion. + +We reasoned that we +could describe + +the ingress of material. + +Here I'm showing a concentration +profile. + +A profile is nothing more than +a plot of something as a + +function of position. + +So, this is looking +at, for example, + +the doping of a wafer. + +This is the free surface +at x equals 0. + +As we go to the right, +it represents depth. + +And we fix the concentration +at the surface and the + +material tails off to zero +deep inside the specimen. + +Fick in 1855 annunciated the law +of diffusion, shown here, + +that says that the rate of +ingress expressed by the flux + +is proportional to the instant +gradient in concentration. + +And the constant proportionality +is the + +diffusion coefficient. + +This is where all the material +science lies. + +It's inside the D. + +That's what we're going to +talk about more today. + +And so we see things tail off +and what we want to do is + +figure out what the mathematics +are that'll allow + +us to render this thing into a +functional representation. + +Because all we know right now +is that we've got something + +tailing off. + +Ok? + +And so this is the gradient +multiplied by the diffusion + +coefficient and you can +see that the red line + +represents the flux. + +The gradient is maximum at the +surface, so the flux is + +maximum at the surface. + +And as we move farther and +farther into the piece, the + +gradient in concentration +becomes less steep, which + +means the absolute magnitude +of the flux becomes less + +steep, and we go deep inside +where there is no doping yet. + +The variation of concentration +is constantly 0, so the slope + +is zero, which means +the flux is zero. + +So the two sort of track, +one and the other. + +And we recognize these are +negative slopes since the + +minus sign is here. + +Even though we have a +negative slope, we + +have a positive ingress. + +And then the other thing that +we realized was that the + +diffusion coefficient has a +temperature dependence. + +And the temperature dependence +looks like this. + +It's an exponential of some +kind of a characteristic + +energy divided by the product +of -- this is the gas + +constant, this is not the +Rydberg constant. + +The gas constant is simply the +Boltzmann constant per mole. + +So if you take the Boltzmann +constant, multiply it by the + +Avogadro number, you get this. + +But if you see something times +T, you know it's got to be + +either gas constant or +Boltzmann constant. + +This two-letter character string +has to have something + +akin to a Boltzmann constant, +otherwise you don't end up + +with an energy term. + +And this in the top is +a barrier energy. + +It's a barrier energy to +diffusion and out here we have + +the pre-exponential. + +Unfortunately we didn't give +it the letter F in honor of + +Fick, it's just D naught. + +And so there it is. + +So if we take this equation and +we plot it, natural log of + +d versus 1 over T, that'll +linearize the equation, and we + +end up with something that +gives us a straight line. + +And the slope is minus Q over +R, where this Q is some kind + +of a barrier energy. + +And the R is the gas constant +or the Boltzmann constant. + +So this is the gas constant. + +It's on your table +of constants. + +It's got a value in SI units +of 8.314 joules per mole + +Kelvin, OK? + +Just the Boltzmann times +Avogadro number. + +So now I want to invite you +to join me in some pattern + +recognition. + +If I give you the temperature +dependence of a quantity that + +looks like this , in other +words, the logarithm of that + +physical parameter versus +1 over T, gives + +you a straight line. + +You know from the work that we +did on chemical kinetics, this + +is the representation +of something that is + +an activated process. + +Remember the box that would fall +on its side, and it had + +to go up on its corner? + +So we had some physical sense +of what activation is. + +Now this has a log, something +versus 1 over T dependence. + +This represents some kind +of an activation energy. + +An activation energy. + +But what's the activated process +that's going on here? + +So that's where I want to take +you into the atomistics. + +So here's a cartoon taken from +one of the readings. + +And it shows a set of atoms here +and the atom next to the + +vacancy wants to move +into the vacancy. + +And you can see the artist's +rendition is showing that in + +order to get from the current +position into the vacant + +position, it's got to squeeze +through this narrow channel. + +And it takes energy to move +through that channel. + +And there's an activation +barrier + +associated with that motion. + +Can you see when the atom +is sitting right + +at the saddle point? + +The system is highly activated +because it's pushing out + +against those atoms. And then +finally it falls into the new + +slot and the energy drops. + +So the activation energy is +associated with moving through + +this saddle point. + +So what really happens here, +I'll tell you right now. + +First of all, we have to +recognize that the system is + +depicted there, because it's a +freeze frame, but we know that + +above 0 Kelvin, everything +is in motion. + +So the only way we can +rationalize what's going on is + +to, first of all, recognize +that we + +have a pulsating lattice. + +We have a pulsating lattice. + +Everything's vibrating. + +And what's the heartbeat? + +What's the idle speed? + +I've told you this before. + +Everything that's going on in +this room has an idle speed, a + +heartbeat, of 10 trillion +times a second. + +That's the Debye +frequency, OK? + +The idle speed or +the heartbeat. + +The heartbeat is called +the Debye frequency. + +Here's frequency, lowercase nu, +in honor of Peter Debye. + +And it's on the order +of about 10 to the + +thirteenth per second. + +10 to the thirteenth Hertz. + +That's 10 trillion. + +So 10 trillion times a second +atoms are going like this. + +Pulsating. + +All right? + +So what has to happen for +that operation to occur? + +Well, I've got an atom here, +vacancy next door, but because + +it's close packed the atoms +on either side close in. + +There's no way this can +squeeze through. + +But, imagine, 10 trillion +times a second. + +If I'm lucky enough to see the +moment when the atom above + +pulsates up, the atom below +pulsates down, a channel can + +open up and then this thing +can squirt through. + +Now, that doesn't happen +every time. + +If it did, history +would have ended. + +At 10 trillion times a second, +it's all over for everybody. + +Right? + +So what happens? + +What's the frequency at which +we will get this unique + +combination? + +It turns out that frequency, +noted gamma, is called the + +jump frequency. + +That's the jump frequency. + +And the jump frequency is on the +order of about 10 to the + +eighth Hertz. + +10 to the eighth Hertz, which +is about 100 million. + +So if you take the ratio of +the Debye frequency to the + +jump frequency, you see you get +a value of about one try + +in about 10 to the fifth +is successful. + +One try in about 10 to the +fifth is successful. + +And that explains what's +going on here. + +So, what now does that +mean in terms of Q? + +What's the breakdown of Q? + +Well, clearly, Q, the activation +energy for + +diffusion, must involve +both the energy to + +form the vacancy -- + +I'm going to call it delta Hv, +and that's the energy for + +vacancy formation -- + +if you don't have vacancies, +you cannot have motion -- + +plus the delta H sub +m which is the + +energy for atom migration. + +So you have to form the +vacancies and then you've got + +to squeeze through those +saddle points. + +So that's how we get +a sense of it. + +And I think I've got +another slide. + +OK, so they're I've simply put +the markings on for you so you + +can see the atoms above +and below jumping + +in the right direction. + +That allows the atom on the left +to squirt to the right. + +Now, this is also related +to energetics. + +It's related to energetics +because the energy to form a + +vacancy and the energy to +squeeze through those saddle + +points must be related to +the binding energy. + +And what else is related +to binding energy? + +Melting point. + +So, this is an elegant plot +that simply shows that the + +energy -- these are all FCC +metals: lead, aluminum, + +silver, gold, copper, +and iron. + +They're all FCC on +this chart here. + +Iron has both BCC and +FCC, but this is + +comparing apples to apples. + +And you can see that there's +lead melts at 327, aluminum at + +660, silver 980, +all the way up. + +Iron 1535. + +And you can see that the +activation energy for -- + +that's this Q-value -- + +the activation energy +for diffusion scales + +with melting point. + +Again, an indication that this +analysis makes sense. + +And then, here's the other +one, the interstitial. + +If you have interstitial +diffusion you've got plenty of + +interstitials, so you don't +have to pay the penalty to + +create the interstitial, but +it's much, much more difficult + +to squeeze through +the saddle point. + +So, it turns out that activation +energy for + +diffusion by interstitial +means is still + +fairly highly activated. + +So this is in the case +of substitutional + +systems, all right? + +This is for substitutional. + +Substitutional atoms. What +do I mean by that? + +An atom that sits on +a lattice site. + +If an atom sits on a lattice +site, it has to jump to + +another lattice site, which +means there needs to be a + +vacant lattice site. + +On the other hand, if we're +talking about interstitial + +special atoms -- + +not substitutional atoms, +interstitial atoms -- + +the assumption is that there's +plenty of interstitial sites. + +There are very few systems that +I can think of where the + +interstitial sites are so +heavily occupied that this + +assumption is invalid. + +So in that case, you +don't have to + +pay for vacancy formation. + +It's simply equal to the +enthalpy, which we know is + +analogous to the energy +for a condensed + +system of atom migration. + +Atom migration gives you the +whole story and it goes back + +to the same picture, +and so on. + +Now, I said it's random walks, +so let's look at another one. + +So, this is an interesting +example. + +This is self-diffusion +in cobalt. + +Cobalt has a number +of isotopes. + +One of them is 59 and +one of them is 60. + +60 is a radioisotope. + +Cobalt 60 is a radioisotope and +it's used in a variety of + +technical endeavors. + +And so what we've got here is +a sandwich of cobalt 59 -- + +cobalt 60 and cobalt 59. + +So even though cobalt 60 has +radioactivity and it's got a + +different number of neutrons in +the nucleus, chemically it + +is identical to cobalt 59, +just as carbon 14 is + +chemically identical +to carbon 12. + +So there's no concentration +gradient. + +Fick's Law says it's +supposed to go by + +concentration gradient. + +The concentration gradient is +zero across that piece. + +And yet if you wait for +long enough, you will + +start to see -- + +the dark atoms here are meant to +represent cobalt 60 in the + +sandwich -- + +after some period of time, the +cobalt 60's will move outward. + +And if you wait long enough, +the cobalt 60 concentration + +will be uniform throughout +the specimen. + +So what's going on? + +There's no chemical +concentration gradient, and + +yet over time, the cobalt +60 spreads out. + +And the answer is this is +happening by random walk. + +We've got the pulsating +lattice. + +Pulsating lattice. + +10 trillion times a second those +atoms are vibrating and + +there's going to be +some vacancy. + +All of a sudden an atom +falls into a vacancy. + +And the mathematics of this -- +look at this, this is no + +accident -- this curve here +represents something that + +looks like a Gaussian +distribution. + +At any given time, the amount +of cobalt 60 that's veered + +from the center band can be +portrayed by the Gaussian + +distribution, the bell curve. + +And what's the physical model +for the bell curve? + +It's the drunken sailor. + +Or I guess I have to be PC. + +I'm not going to just +pick on sailors. + +Maybe it's the drunken cougar, +the soccer mom + +that went out drinking. + +OK, so what happens with the +drunken cougar, she comes to + +the door, and she starts +to walk, all right? + +And then she walks one way or +the other way, until she + +finally falls. + +And if you go through the number +of steps that it'll + +take before the drunken sailor +falls, you get this + +distribution. + +It's an old physics problem. + +The drunken sailor problem. + +And it's a normal +distribution. + +And that normal distribution +tells you that everything's + +going about by random jumping. + +Random jumping, according +to this, all right? + +So that's why we say +that diffusion is + +a random walk problem. + +Before I turn this off, I want +you to take a look carefully. + +What's wrong with this +textbook cartoon? + +Any ideas? + +It's a substitutional +system, right? + +It's cobalt and cobalt. + +This is absolutely impossible. + +What's wrong with it? + +There are no vacancies. + +There are no vacancies. + +It's impossible. + +There's no vacancies +to jump into. + +This thing is jam-packed, so +it's physically unrealistic + +from a thermodynamic +standpoint. + +There has to be some finite +population of vacancies. + +Given this system, there's no +way that the black atom could + +jump into the neighboring site, +because you'd have to + +have the entire system open up, +and the chances of that + +happening are vanishingly +small. + +So it just shows you, just +because something costs 150 + +bucks and is pressed between two +hard covers doesn't mean + +it's full of truth, OK? + +Be careful here when +you look at this. + +So, again, the artist +needed to be guided. + +We need to put a few of these +things out, just to give + +symbolic recognition to +the fact that we need + +to have some vacancies. + +OK. + +All right, let's keep going. + +Let's keep going. + +Here is some data. + +Here is some data. + +Various data. + +This is diffusion. + +This is the logarithm of the +diffusion coefficient + +versus 1 over T. + +So let's look at the top. + +This is hydrogen in iron. + +So temperature increases +from right to left. + +So, go up, up, up, up, up. + +And roughly 900 degrees +Centigrade, iron changes from + +BCC to FCC. + +And you know from our previous +unit, the number of nearest + +neighbors in FCC is greater, +so there's less + +void fraction, right? + +So that means that it's much +more difficult to move. + +And you can see, first of all, +the order of magnitude drop in + +the diffusion coefficient, and +also, it's subtle, but the + +slope is steeper, because the +activation energy for + +diffusion is steeper in a +closer-packed system. + +This is carbon in iron. + +Same thing. + +Relatively gentle slope at the +same temperature, there's a + +phase change to FCC and it takes +much, much more energy + +per unit increase in temperature +to get the + +comparable increase in the +value of diffusion + +coefficient. + +This is iron, self-diffusion +in iron. + +So this would be radio +tracer iron in iron. + +Very much lower. + +You see these values are up +around 10 to the minus 5, 10 + +to the minus 6. + +This is down to 10 to the minus +11, 10 to the minus 12 + +centimeters squared +per second. + +Iron diffusion changes at the +transition temperature. + +Now iron going through +FCC iron. + +Here's the last one. + +Look at this one. + +This is carbon in graphite. + +So how does carbon -- +suppose I had some + +carbon 14 in graphite. + +What's the bonding +in graphite? + +Silence. + +It's covalent. + +It's sp2 hybridized. + +It's really strong bonds. + +The activation energy -- + +you know, forget just jumping +through that saddle point -- + +you've got to break those +covalent bonds. + +It's very, very high energy +to get carbon to + +move through graphite. + +And so you see very, very low +values and very, very steep + +temperature dependence. + +Now, there's another way +to think about this. + +Again, this is now looking +at the atomistics. + +So this is the same material +trying to indicate that if you + +use Fick's Law, moving in from +the surface into the bulk, we + +have a certain front. + +So this is some isoconcentration +line. + +So we could take this value off +of the graph arbitrarily. + +So they're saying c +greater than c i. + +Because it trails off +to zero, right? + +It's asymptotic. + +There's no sharp cut-off here. + +It trails off. + +So what they're doing in that +graph is arbitrarily saying, + +let's call this ci. + +And where's the front at +concentration ci, given a + +constant value of cs +at the surface? + +And you can see that there's a +near-constant rate of advance + +through the bulk. + +But along the grain boundary you +go much, much farther in + +the same amount of time. + +Why? + +Because the atoms in the grain +boundary are not bounded the + +same way as the atoms +in the bulk. + +There's this gap, this +misalignment. + +And so, it's easier to make that +jump, and you can see you + +get much, much more advancement + +along the grain boundary. + +And this is a crack. + +And this material covers +the surface. + +You get surface diffusion. + +Surface diffusion is very +important in many processes, + +and it's very fast, because on a +surface, you've got no atoms + +on the top. + +It's almost liquid-like, +isn't it? + +You've got atoms to the bottom, +but you've got no + +atoms to the top, so you +can move unconstrained. + +Go back to this one. + +Imagine here. + +Imagine if you didn't have any +atoms on the top, how easy it + +would be to make that jump. + +All right, let's go and +see what the data are. + +Nothing like data. + +And I got data for you. + +Let's look. + +Click, click, click. + +All right. + +Here's the data. + +This is all for the diffusion +of silver. + +So I'm going to use this value, +this schematic, and I'm + +going to give you the value for +silver diffusion in the + +bulk, silver diffusion in the +grain boundary, and silver + +diffusion along the surface. + +So these are the data. + +So this is log diffusion +coefficient versus 1 over T. + +Only, I hate this +graph, because + +somebody got really wimpy. + +You know, it bothers them. + +You see, when you plot something +like this, you end + +up with, if 1 over T increases +from left to right, this + +really means that +high temperature + +is over here, right? + +1 over T increases this way, +which means temperature is + +increasing this way. + +So somebody, some weenie, got +all nervous here and put the + +numbers backwards, you see? + +That way, the high temperature +is over here, but it looks + +stupid, because when I see an +activation plot, I want a + +negative slope. + +It's non-physical to have +a positive slope. + +So I condemned this and +I turned it around. + +So now let's look at +it the right way. + +So this is log d versus 1 over +T, and this is the bulk, + +lattice or bulk. + +This is grain boundary and this +is surface diffusion, all + +in solid silver. + +OK, look at this. + +First of all -- + +I'm going to jump from here +-- one, two, three, four. + +Four orders of magnitude faster +diffusion along a grain + +boundary, which makes sense, +because it's less constrained. + +And now let's go from grain +boundary at constant + +temperature up to surface. + +One, two, three. + +Three orders of magnitude +along the surface. + +So you can see the effects. + +And there's the melting point +of silver, right here. + +So at the melting point of +silver, the diffusion + +coefficient is about 10 to the +minus 8 centimeters squared + +per second, which is the +diffusion coefficient of + +virtually every metal at +its melting point. + +So I happen to know +that number. + +10 to the minus 8 centimeters +squared per second. + +Not that I know it as a function +of temperature, but I + +know it can't be any +faster than that. + +So I said, this is near +liquid-like behavior, what's + +the next thing to look for? + +Let's get some data from real +liquids and see if this hunch + +is correct. + +What's the number here? + +10 to the minus 5 to 10 to the +minus 4 centimeters squared + +per second. + +This is diffusion in molten +ferrous alloys. + +This is manganese +in molten iron. + +10 to the minus 5, 10 +to the minus 4. + +Bingo. + +It really does behave like a +liquid, in terms of diffusion. + +Surface diffusion is very fast, +very fast. And it's all + +explained by this simple +model of atom jumping. + +And I continued it. + +Here's data from glasses. + +We studied glasses. + +So here's a suite of +different glasses. + +Log k. + +This is permeability, which +is related to diffusion + +coefficient. + +There's a gas constant in there, +but forget about it. + +So this is essentially log of +the diffusion coefficient + +versus 1 over T. + +We've got a family of lines. + +And what's the difference +here? + +This is pure fused +silica up here. + +SiO2. + +There's borosilicate, there's +soda lime, and + +there's lead borate. + +So what's happening? + +We're adding more and +more modifier as we + +go from top to bottom. + +And as we add modifier, we +break the length of the + +silicate network, which means it +packs tighter and tighter, + +and as you get tighter and +tighter packing, the diffusion + +coefficient gets lower +and lower. + +So train your eye. + +Let's pick 200 degrees +Centigrade, right here. + +So at constant temperature, the +more modifier you put in, + +the lower the diffusion +coefficient because things are + +more tightly packed. + +It's like walking down the +infinite corridor in the + +middle of the hour, versus +walking down on the hour. + +On the hour, there's +too many people. + +It's tighter packing. + +And if you're the least bit +civilized, you're going to + +have to move a little bit +slower, whereas, if you walk + +down the infinite at around +now, no problem. + +It's liquid-like behavior. + +And now this is the isotherm +at 300 hundred degrees C. + +This is from some old +Corning literature. + +Corning used to make +glass, at one time. + +And this is the logarithm +of diffusivity. + +And this is now the set of +silica B203 and P205, and + +these are all network +formers, right? + +They all form covalent bonds. + +So the more silicate, borate, +phosphate you put in, the more + +stretched out becomes +the network. + +And sure enough, look up here. + +See they didn't have names for +their glasses like the Malibu + +or the Corvette or something. + +They called their glasses +by four-digit numbers. + +So someone would say, oh, this +customer needs, oh, I'd sell + +them a 7040. + +All right? + +Because it has a certain +mix of properties. + +So forget about what those +numbers are, just know that + +this axis indicates that as you +move up, up, up, up, up, + +the higher diffusivity is +associated with a much more + +open structure. + +So, again, a link between +atomistic behavior and + +atomistic structure. + +It's all there. + +OK. + +So let's leave that up +there while we go + +a little bit forward. + +OK, so now, so we've been down +buried at the atomistic level. + +Now let's jump up to the +continuum level. + +We'll go back to Fick's +first law. + +And I want to do something a +little more quantitative. + +So I want to look at diffusion +across a permeable membrane. + +So this is gas through +a membrane. + +Gas through a membrane. + +And the membrane +is shown here. + +This is the walls +of the membrane. + +Membrane has thickness L. + +Membrane of thickness L. + +In fact, we'll give it a name. + +Let's call it membrane. + +All right, so here's the +membrane of thickness L, and + +I'm going to put gas on the +left at P1, and it's a + +constant P1. + +So we keep -- + +we've got a ballast here, so +even though something starts + +diffusing, the amount that we +lose doesn't affect the + +constant pressure over here. + +And on the right side, I'm +going to put a second + +pressure, P2. + +And just for argument's sake, +I'm going to say that P2 is + +less than P1. + +So that means we're going to +end up with mass transport + +from left to right. + +And so, I want to ask, what's +this going to look like if we + +use Fick's Law? + +And so beneath I'll make a plot, +a concentration profile, + +from x equals 0 to x equals L. + +And I can morph this +into concentration. + +We know the gas law +is PV equals nRT. + +This is the gas law. + +P is pressure. + +P is pressure. + +V you know is volume. + +But I'm going to write all these +out, because some of + +these letters are used so many +times that we don't know, is + +this the Rydberg constant? + +No, it's the gas constant +that you've seen + +on the first board. + +It's the Boltzmann constant +times the Avogadro number. + +T is absolute temperature, +temperature in Kelvins. + +And n is not the quantum number, +it's mole number. + +Mole number. + +PV equals nRT. + +And we know that concentration +of i is mole + +number of i over V. + +Both of those appear in here. + +So if you take what's underneath +there, and I'll + +expose it in a second, you'll +convince yourself that Ci + +equals Pi divided by RT. + +And that's how you get that +permeability thing to turn + +around as well. + +OK, so, I started with gas +pressure, but I'm now going to + +write this in terms +of concentration. + +So I'm going to morph P1 into C1 +and over here, P2 into C2. + +And I want to plot +the profile. + +So what's the profile +look like? + +I'm going to plot the profile +at steady state. + +At steady state. + +At steady state, after I've +waited a while, I have a + +straight-line profile across +here, at steady state. + +It's pinned at the two ends. + +It's pinned at the two +ends and varies + +continuously across here. + +And you can see from Fick's +Law, that if you have a + +situation in which the gradient +is invariant across + +the piece, the gradient is -- + +dc by dx is the same here, as it +is here, as it is here, as + +it is here. dc by dx is +invariant, right? + +It doesn't change. + +This is a straight line. + +Well, if dc by dx is invariant, +and d is a + +constant, then J is invariant, +which just means + +no sources are sinks. + +All of the material that +goes in, must come out. + +This means that J is not +a function of time. + +J is invariant. + +J is not a function of time. + +I come back here ten +minutes later, I + +have the same profile. + +That's what steady +state means. + +That's what study state means. + +OK, and then, of course, if I +wanted to be a little bit + +pedantic, I could say, in +certain systems, the diffusion + +coefficient is a function +of concentration. + +So, when the diffusion +coefficient is a function of + +concentration, then even at +steady state, you might have + +some bowing of the profile, +but that's a + +little bit more advanced. + +OK. + +So, I can describe everything +that's going on here. + +If I wanted to know how much +material leaves from inside + +over a certain period of time, +then I can simply say that + +total material lost is given by +Fick's first law when you + +have steady state. + +It's simply going to equal the +product of the flux, which is + +mass per unit area per +unit time times the + +area times the time. + +And that's sort of analogous +to Faraday's Law, right? + +If I wanted to look at how much +electrical charge I get + +for a certain period of time +with current passing, I could + +say that the total charge is +the product of the current + +times the time. + +You know this relationship. + +Well, can you see that J times A +is analogous to the current? + +It's the mass current. + +It's mass flow rate. + +Mass flow rate per unit area +times area gives me something + +that's analogous to the current, +and the time is the + +time, this is the total material +lost, this is the + +total electrical charge. + +These two are the comparable +equations. + +OK. + +Now, I want to go to the more +sophisticated question, and + +that is, what happens +before steady state? + +Before steady state +is achieved? + +Suppose at time zero, the +membrane has no gas in it. + +And at time zero, I inflate +the left side. + +And just to keep things +simple, I'm going to + +set c2 equals 0. + +It's a linear equation. + +You can always add it, but I +just want to keep it simpler + +for the analysis. + +So, suppose at t equals 0, we +inflate to c1 on the left side + +of the empty membrane. + +There's nothing in +the membrane. + +So, let's see what happens. + +First, I'm going to solve +the problem graphically. + +Because we know what's +going to happen. + +I'm going to have to +do the mathematics. + +So, here's what we expect. + +This is going from 0 to L. + +And we've got nothing in the +membrane on both sides, so + +that's good. + +And then, at time zero, +I inflate to c1. + +There's nothing in here. + +So, what do I have? + +Well, I know if I wait long +enough, it's eventually going + +to look like this. + +Because that's the steady +state solution. + +I've put here c2 equals +0, for simplicity, but + +we can change it. + +It's a linear equation. + +We can just add. + +So, what happens +at time 0 plus? + +I start getting diffusion in +from left to right, following + +Fick's Law. + +So it's going to look +like this, isn't it? + +This is the approach +to steady state. + +Some books will call it +nonsteady state or unsteady. + +Unsteady to me means unsteady, +so I refuse to use those + +terms. I call this +the transient. + +That's the literary term. + +The transient. + +We're talking about the approach +to steady state. + +And in some systems, you never +get to steady state. + +But that's OK. + +So here's what it's going to +look like at some very, very + +short time afterwards. + +It's going to look like that, +only somewhat modified for + +this geometry. + +So it's going to look +like this, isn't it? + +It's pinned at c1, and it's +pinned at 0, and it varies + +continuously. + +So this is at time t 1. + +What happens at time t 2? + +At time t 2, it advances +a little bit farther. + +But in all instances, the slope +and the shape is given + +by this, Fick's first law. + +So this is at time t 2. + +And let's do one more. + +Three's a charm. + +So, let's take a green one. + +All right, so here's at t 3, +still pinned at c 1 and still + +pinned at 0. + +So this is at t3. + +And then finally, this +is steady state. + +So if we park at any place -- + +let's park at x1. + +Watch here. + +Can you see that the slope +at t1 is gentle? + +The slope at t2 is +steeper than t1. + +The slope at t3 is steeper +than t2, and this is the + +highest. So, we go from nothing, +to gradual, gradual, + +gradual, until we finally +reach steady + +state, and we stop. + +And then at that point, we just +continue to have to mass + +flowing through. + +And look, the concentration is +zero, but the flux is not + +zero, because the flux isn't +related to the concentration. + +It's related to the +concentration gradient. + +Zero concentration, +but non-zero + +concentration gradient. + +In fact, just for grins and +chuckles, I could plot the + +ascent of this. + +I could plot time +at x equals x1. + +I could plot J. + +And what's J? + +At time zero, it's zero. + +Then it's small, then it's +larger, larger, larger + +asymptotically. + +And this is J of steady state. + +And this is t1, t2, t3. + +That's the approach +to steady state. + +And you might say, well, +this is kind of + +a professor's pedantry. + +It's not! + +This is doping of +semiconductors. + +You don't run processes +at equilibrium. + +You run them far from +equilibrium. + +So in the transient mode, +doping, outgassing, drying, + +what have you. + +So, now I want to give +you the shape of the + +concentration profile. + +So how do I do that? + +OK, so the shape of the +transient profile is not given + +by Fick's Law. + +The Fick's Law just gives +me the gradient. + +In other words, here's +what I want. + +I want C as a function of +x at any given time. + +That's what I want. + +I want to be able to +plot the profile. + +So, profile is C of x, but +C of x varies with time. + +So, I need C of x at +different times. + +What gives me that? + +What gives me that is +Fick's second law. + +Go to FSL, Fick's second law. + +Now, Fick's second law, I'm just +going to put it up here. + +I'm going to show you +the solution. + +I don't expect you +to solve it. + +I would, you were all required +to have differential equations + +as a pre-req, but you don't. + +So, I'm just going to put it +up here so that you see it. + +It's a partial differential +equation, and + +it looks like this. + +And it's really beautiful. + +It's got a beautiful symmetry +and the fonts look great, so + +that's why we put it up here. + +So, this is the partial in +time goes as the double + +derivative in space, because +we need a two-variable + +function, right? + +We want x and t. + +And this assumes that the +diffusion coefficient is not a + +function of concentration. + +If it is, the equation +is messier. + +This assumes a constant +diffusion coefficient. + +So, this, as you can see, is a +partial differential equation, + +which is a bummer, because it's +hard to solve, all right? + +But, it's linear. + +It's a linear partial +differential equation, which + +means the solutions +are additive. + +We know this already +from LCAOMO. + +So, I can handle, because I can +solve it once and then I + +can give you ways to patch +it, to make it useful. + +So, the solution. + +First of all, how do I +specify this fully? + +Every time you differentiate +-- + +I'm going to give you some +math here, real math + +that you can use. + +When you differentiate, you +throw away information, right? + +The derivative of a +constant is zero. + +So, what was the value +of the constant? + +It's gone. + +You lost it. + +So you have to bring it back. + +So when I double derivative +this, I need two pieces of + +spacial information. + +And when I take a derivative +with respect to time, I need + +one piece of temporal +information. + +That's math. + +All the other lemmas and +postulates, forget them. + +This is how you use +it, all right? + +So, I need two pieces of spatial +information and one + +piece of temporal information. + +So these specify our boundary +conditions, right? + +So, what are our boundary +conditions. + +So, I will need the +concentration of + +all x at time 0. + +That's this. + +The answer to this question. + +And what we're going to do is +say that it's a constant. + +I don't know what the constant +is, it could be zero, it could + +be any arbitrary number, but +I'm going to give you the + +solution for the situation +in which the initial + +concentration is a constant. + +So, you could look at this and +say, well, what happens if + +it's a non-zero constant? + +You ready for linearity? + +Watch this. + +This is how cool linearity is. + +You see this set of solutions? + +This is the set of solutions +for C equals 0. + +What if C equals some +non-zero value? + +I just shift the origin down to +here to the non-zero value + +and everything sits there. + +That's what superposition +gives you. + +That whole set of solutions +just gets jacked up by the + +value of C naught. + +If C naught is 0, this slams +down onto the x-axis. + +That's real math. + +You're the master. + +The math is the slave. Never +let math enslave you. + +I won't. + +I refuse. + +So that's how you make C +equals C naught work. + +And then you have to peg the +concentration at the surface. + +I can give you examples where +that's not the situation, + +where you have a variable +concentration at the surface. + +The solution I'm going to give +you won't work for those. + +So, x equals 0 is the surface. + +So, at x equals 0 at all time, I +have some fixed value, which + +I'm going to just +call C surface. + +And I need a third boundary +condition. + +And the third boundary +condition is a + +mathematical trick. + +We're going to say that this +only works at short times. + +It's called the short time. + +And at short times, I'm +going to say that -- + +from the perspective of the +diffusion experiment -- + +at very, very short times, +this sample appears to be + +infinitely long. + +Because the amount of material +that goes in doesn't hit the + +other side. + +So, at very, very short times, +we can pretend that it's + +semi-infinite. + +And so then we can write that +the concentration -- + +this is the short time, which +means infinite size, and + +you'll see that the +two are related -- + +that the concentration at +infinity, then, doesn't change + +from the initial value. + +The concentration at infinity +for all time must equal the + +initial value C naught. + +And so if you put these three +boundary conditions into that + +equation, you end +up with this. + +This is the thing. + +You get C minus Cs over +C naught minus Cs. + +This is surface concentration. + +This is initial concentration. + +This is C. + +It varies by this amount. + +Error function of x over 2 times +the square root of Dt. + +So, you tell me the time and I +can tell you the relationship + +between concentration +and position. + +Now I've got to tell you what +the error function is. + +Here's the error function. + +This is this problem before. + +This is the solution I'm +going to show you. + +Here's Cs. + +Here's C naught. + +The most general case. + +C naught could be zero. + +And this curve here is given +by this equation, OK? + +And this is an example +of doping, isn't it? + +This is how doping would work. + +And this is the case where C +s is greater than C naught. + +If we turn it around and we make +the surface concentration + +less than the initial +concentration, we'll get the + +complementary situation. + +The complementary situation +looks like this. + +So in this case, C naught is up +here, Cs is down here, and + +we end up with this. + +So now matter is going +out, because Cs + +is less than C naught. + +So this is -- + +what do you want to call it -- +this is effusion, this is some + +kind of a drying process, +outgassing. + +And this is doping. + +And what's the shape +of this curve? + +The shape of this curve. + +ERF. + +That's what math is. + +You find a mathematical +function that + +templates for the curve. + +And ERF, I'm going to show you, +is related to random walk + +statistics. + +So, it's physically validated. + +It's the best fit. + +I mean, heck, if you find +anything that is pinned at two + +ends and has curvature, you'll +get a reasonable fit, but + +what's the right fit? + +The right fit is this. + +The error function +looks like this. + +Here's the error function. + +Error function. + +I'm going to plot ERF of +z as a function of z. + +And it goes from 0 to 1. + +It looks like this. + +All right? + +And here's an error +function table. + +Those are exact values. + +And it turns out that ERF +is pretty much linear up + +to about point 6. + +Up to about point 6. + +ERF of point 6 not to less +than about 1% is point 6. + +And then as you go farther and +farther out, and eventually, + +ERF of infinity equals 1. + +But you don't even need tables +for 0 up to point 6. + +And you can push it, go to +point 6, 5, if you want. + +Yeah, let's do it. + +Let's push harder. + +6, 5. + +It's linear. + +You don't need tables. + +Right? + +And so ERF of 0 equals 0. + +Oh, let me give you +the function. + +You know how you can +define sine? + +Sine is that integral of +something over 1 minus blah, + +blah, blah? + +We've got a definition +for this one, too. + +It's cool. + +It's cool. + +Here's what the error +function looks like. + +ERF of z equals the integral +from 0 to z of e to the minus + +u squared du. + +You might say, why is he +showing us all of this? + +Because he wants to torment +you, that's why. + +No, it's because I'm trying +to teach you something. + +What's e to the minus +u squared? + +Actually, I think I can squeeze +it in right there. + +What's e to the minus +u squared du? + +This function here, that's the +bell curve, isn't it? e to the + +minus u squared. + +That's this thing. + +It's symmetric, right? + +It's a minus u squared, so +it doesn't matter if u is + +positive or negative. + +And e to the 0 was 1, and +then back and forth. + +And so what this is doing, is +it's integrating from zero out + +to some value. + +That's all. + +That's the random walk. + +This is the drunken sailor. + +How far does the drunken +sailor go? + +That's the shape of this +curve, the integral. + +And we'd like it to be so that +if you integrate from zero to + +infinity, the area +will be one. + +It turns out that this area +here is root pi over 2. + +So, therefore, to normalize, +we put 2 over root pi. + +That's how you get the +error function. + +All right? + +So, the integral from zero to +zero is zero, and the integral + +from 0 to 1 is going to be, +whatever it is, point 8, 4, et + +cetera, et cetera. + +So, that's it. + +That's it. + +Now we have the functional +relationship to describe any + +of these curves. + +And you'll get some practice +in doing that. + +And it's a lot of fun. + +Because now you can talk about +how long it's going to take to + +dope something, and so on. + +Outgassing. + +And now I'm going to show you +something really cool, and I'm + +not kidding you. + +This has served me well. + +I've been here 30 some odd +years, and I've been in + +consulting situations where I +can, in my head, figure out + +order of magnitude of what it's +going to take to run a + +diffusion problem. + +Because you've got, up here, C +minus Cs over C naught minus + +Cs equals ERF error function +of x over 2 roots of Dt. + +So, this runs from 0 to 1. + +The right side. + +When I went to school, the left +side of the equation had + +to do the same thing as the +right side of the equation. + +So if the right side of the +equation runs from 0 to 1, the + +left side of the equation +runs from 0 to 1. + +So, let's pick a -- are +you ready -- average + +value from 0 to 1. + +What would you pick? + +I'd pick point 5. + +Now, I don't have to go to the +error function tables because + +point 5 is less than point 6. + +So ERF of x over 2 root Dt is +essentially equal to x over 2 + +roots of Dt. + +So, now I've got one half equals +one half x over root + +Dt, from which I can say that +x is approximately equal to + +the square root of Dt. + +And I can be sitting in a +meeting and someone says, gee, + +I don't know how long +it's going to take. + +This thing's going to go +down about 100 microns. + +And how long is it +going to take? + +So, I pick a number, like, OK, +if this is 100 microns, and + +this thing here is 10 to the +minus 8, now you just take the + +square root of that, and tell +them, oh, it's going to take + +so many minutes, and +they go, huh? + +How did you get that? + +It's right there. + +And I'm not trying to tell +them a number for three + +significant figures. + +They just want to know is it +going to take a minute, an + +hour, a day, or are we +out of business? + +And you can make that +calculation with this. + +This is so powerful. + +And everything I told you about +diffusion applies to + +conductive heat transport. + +You can do the same thing for +heat transfer, figure out how + +long it's going to take +for a wave to go in. + +This is really powerful stuff. + +Anyway. + +Let's move on. + +Well, there's our pal. + +OK, so I was going to give you +the last element today. + +The last element. + +Remember, we talked +about clean air. + +So, I'm showing you the +catalytic converter. + +That's this thing here, +coated with platinum, + +rhodium, and so on. + +And I'm showing you the +electronic control module. + +That's the CPU. + +It's a little bit toned down +from a Pentium, but it + +certainly started from +one of these units. + +So, we've studied all of this. + +Right? + +OK. + +And, so now, I want to talk +about this piece here, the + +oxygen sensor. why do we +need an oxygen sensor? + +Remember, the last day I told +you that to get rid of NO, the + +NOx, you have to reduce, And to +get rid of CO and unburned + +hydrocarbons, you +have to oxidize. + +Well, you have to pick. + +You can't have two different +atmospheres in the same place + +at the same time. + +Turns out there's a +lucky sweet spot. + +Can you see that the conversion +efficiency is high + +for both reduction and oxidation +reactions if you peg + +the air-to-fuel ratio at 14.6. + +So you can't just set the +carburetor or the fuel + +injectors at some arbitrary +ratio, because as you change + +humidity, as you change +temperature -- what happens + +when the temperature +goes down? + +How much oxygen is +there in the air? + +It's still 20%, but +PV equals nRT. + +You ever try barbecuing +when it's -- + +I mean, I don't know, maybe +you're not from the Northeast. + +But if you want to barbecue +when it's 0 Fahrenheit? + +Do you think you get a hotter +fire or a colder fire? + +How much oxygen is there +per unit volume in cold + +air versus warm air? + +Think about it. + +It'll be on the next exam. + +I'm just kidding. + +OK. + +So, anyway, here's the sweet +spot that gives you both + +oxidation and reduction. + +And so we need a +feedback loop. + +That feedback loop is provided +by the oxygen sensor. + +Dave, would you mind cutting +to the document camera? + +So this is an oxygen sensor +that's used on automobiles. + +Here's the plug. + +This goes into the pin set. + +And the oxygen sensor is +inside this housing. + +This housing, you can see -- + +OK, what I'm going to +show you is what's + +going on inside here. + +This has got all kinds of +protective stuff on it so that + +it doesn't get dented during +installation and so on. + +But it sits inside the +exhaust train. + +It sits inside the +exhaust train. + +Now, may we go back to +the slides, please? + +Every car that's running a +catalytic converter has to + +have one of those in order to +control, right here, to make + +sure the air-to-fuel +ratio is optimum. + +Otherwise, the catalytic +converter is either not doing + +a good job on NOx, or it's +not doing a good job on + +hydrocarbons and whatever +the other thing is. + +Anyway, so here's what +it looks like. + +So, this is what's inside. + +It's a closed, one-end tube +made of zirconia. + +Zirconium oxide. + +And zirconium oxide conducts +oxide ions. + +And there are platinum +electrodes on the + +front and the back. + +And what I showed you +was from this side. + +And this is the exhaust gas +going along here, and this is + +the edge of your +exhaust train. + +And two wires coming off of +that sensor go to the CPU. + +The CPU measures voltage and +then from there, it regulates + +the air-to-fuel mix to the +engine, to the exhaust gas, + +and around and around and around +we go, so that when + +exhaust gas gets to the +catalytic convert, it is + +optimally being converted. + +So, we want to get +fast response. + +We don't want slow response. + +And it's a solid-state sensor +and solid-state diffusion is + +slow, but that's we +have to rely upon. + +So we add a dopant. + +We add a dopant to zirconia +to stabilize its crystal + +structure and create more oxygen +vacancies to get faster + +diffusion and a shorter +response time. + +So what we add is calcia, one +of the candidates, and it + +creates oxygen vacancies, and +these oxygen vacancies allow + +us to get more rapid +response time. + +So, these oxygen vacancies +compensate for the charge + +imbalance, thanks to the +addition of calcia. + +So, it's an engineered +material. + +Without this it doesn't +work, all right? + +And so, now what I've shown you +is that on the basis of + +this oxygen sensor, we can +monitor the exhaust gas flow + +so as to optimize the conversion +here in the + +catalytic converter and do so by +sending information to the + +CPU on the car. + +And the number one consumer +of CPU's is the automobile + +industry, because every car +has at least one, if not + +multiple, CPU's. + +So this is a good example of how +understanding the lessons + +of solid state chemistry can +allow us to build fuel + +efficient automobiles that have +minimum toxic emissions + +to the environment. + +All right, we'll see +you on Monday. \ No newline at end of file diff --git a/oG6FyY2r9G0.txt b/oG6FyY2r9G0.txt new file mode 100644 index 0000000000000000000000000000000000000000..209575df3a6b4b3de49dbead1ccdc2f436639f06 --- /dev/null +++ b/oG6FyY2r9G0.txt @@ -0,0 +1,16749 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu what do you think AI people + + align:start position:0% +ocw.mit.edu what do you think AI people + + + align:start position:0% +ocw.mit.edu what do you think AI people +should work on next + + align:start position:0% + + + + align:start position:0% + +you know what question I was going to + + align:start position:0% +you know what question I was going to + + + align:start position:0% +you know what question I was going to +ask you before you very before you said + + align:start position:0% +ask you before you very before you said + + + align:start position:0% +ask you before you very before you said +your question oh okay I was going to ask + + align:start position:0% +your question oh okay I was going to ask + + + align:start position:0% +your question oh okay I was going to ask +you um what kind of questions do you + + align:start position:0% +you um what kind of questions do you + + + align:start position:0% +you um what kind of questions do you +think that AI people should be asking + + align:start position:0% +think that AI people should be asking + + + align:start position:0% +think that AI people should be asking +right + + align:start position:0% + + + + align:start position:0% + +now that's right anybody have a meta + + align:start position:0% +now that's right anybody have a meta + + + align:start position:0% +now that's right anybody have a meta +question + + align:start position:0% + + + + align:start position:0% + +one good question + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +oops I could focus it better but + + align:start position:0% + + + + align:start position:0% + +or make it + + align:start position:0% + + + + align:start position:0% + +bigger is that enough + + align:start position:0% + + + + align:start position:0% + +layers it's possible that I got the idea + + align:start position:0% +layers it's possible that I got the idea + + + align:start position:0% +layers it's possible that I got the idea +from from Sigman Freud + + align:start position:0% +from from Sigman Freud + + + align:start position:0% +from from Sigman Freud +that who uh + + align:start position:0% + + + + align:start position:0% + +who knows what Sigman Freud's three + + align:start position:0% +who knows what Sigman Freud's three + + + align:start position:0% +who knows what Sigman Freud's three +layers + + align:start position:0% +layers + + + align:start position:0% +layers +were + + align:start position:0% + + + + align:start position:0% + +sure can't here ego super + + align:start position:0% + + + + align:start position:0% + +ego Freud wrote about 30 books I know + + align:start position:0% +ego Freud wrote about 30 books I know + + + align:start position:0% +ego Freud wrote about 30 books I know +because I had a graduate student once + + align:start position:0% +because I had a graduate student once + + + align:start position:0% +because I had a graduate student once +who decided to quit computer science and + + align:start position:0% +who decided to quit computer science and + + + align:start position:0% +who decided to quit computer science and +go into emergency + + align:start position:0% +go into emergency + + + align:start position:0% +go into emergency +medicine he had an MD which he wasn't + + align:start position:0% +medicine he had an MD which he wasn't + + + align:start position:0% +medicine he had an MD which he wasn't +using and he suddenly + + align:start position:0% +using and he suddenly + + + align:start position:0% +using and he suddenly +got fed up with computer + + align:start position:0% +got fed up with computer + + + align:start position:0% +got fed up with computer +science so he sold me his set of Frey + + align:start position:0% +science so he sold me his set of Frey + + + align:start position:0% +science so he sold me his set of Frey +books which is + + align:start position:0% + + + + align:start position:0% + +but in Freud's + + align:start position:0% +but in Freud's + + + align:start position:0% +but in Freud's +Vision these don't seem to be a stack + + align:start position:0% +Vision these don't seem to be a stack + + + align:start position:0% +Vision these don't seem to be a stack +but + + align:start position:0% +but + + + align:start position:0% +but +there's this thing which is basic + + align:start position:0% + + + + align:start position:0% + +instincts I shouldn't say + + align:start position:0% +instincts I shouldn't say + + + align:start position:0% +instincts I shouldn't say +basic + + align:start position:0% + + + + align:start position:0% + +maybe to a large extent built + + align:start position:0% + + + + align:start position:0% + +in and this is learned socially + + align:start position:0% + + + + align:start position:0% + +and I think the nice thing about Freud's + + align:start position:0% +and I think the nice thing about Freud's + + + align:start position:0% +and I think the nice thing about Freud's +concept which as far as I know doesn't + + align:start position:0% +concept which as far as I know doesn't + + + align:start position:0% +concept which as far as I know doesn't +appear much in earlier + + align:start position:0% +appear much in earlier + + + align:start position:0% +appear much in earlier +psychology is that these these + + align:start position:0% +psychology is that these these + + + align:start position:0% +psychology is that these these +conflict + + align:start position:0% +conflict + + + align:start position:0% +conflict +and um when a child grows up uh a lot + + align:start position:0% +and um when a child grows up uh a lot + + + align:start position:0% +and um when a child grows up uh a lot +of what we call civilization or + + align:start position:0% +of what we call civilization or + + + align:start position:0% +of what we call civilization or +socialization or whatever comes from + + align:start position:0% +socialization or whatever comes from + + + align:start position:0% +socialization or whatever comes from +taking the built-in instincts which is + + align:start position:0% +taking the built-in instincts which is + + + align:start position:0% +taking the built-in instincts which is +if you see something you like take it + + align:start position:0% +if you see something you like take it + + + align:start position:0% +if you see something you like take it +and uh the social constraints that say + + align:start position:0% + + + + align:start position:0% + +uh uh you should negotiate and if you + + align:start position:0% +uh uh you should negotiate and if you + + + align:start position:0% +uh uh you should negotiate and if you +want something someone else has you + + align:start position:0% +want something someone else has you + + + align:start position:0% +want something someone else has you +should fool them into warning to give it + + align:start position:0% +should fool them into warning to give it + + + align:start position:0% +should fool them into warning to give it +to + + align:start position:0% +to + + + align:start position:0% +to +you or whatever + + align:start position:0% + + + + align:start position:0% + +so so in + + align:start position:0% +so so in + + + align:start position:0% +so so in +fact when I make this big stack of + + align:start position:0% +fact when I make this big stack of + + + align:start position:0% +fact when I make this big stack of +mechanisms that + + align:start position:0% + + + + align:start position:0% + +really well that is that's + + align:start position:0% + + + + align:start position:0% + +actually not the organization + + align:start position:0% + + + + align:start position:0% + +that the book starts to develop chapter + + align:start position:0% +that the book starts to develop chapter + + + align:start position:0% +that the book starts to develop chapter +by chapter which was + + align:start position:0% + + + + align:start position:0% + +instincts + + align:start position:0% +instincts + + + align:start position:0% +instincts +learned learned + + align:start position:0% +learned learned + + + align:start position:0% +learned learned +reactions and so forth up + + align:start position:0% +reactions and so forth up + + + align:start position:0% +reactions and so forth up +to + + align:start position:0% +to + + + align:start position:0% +to +uh self-conscious + + align:start position:0% + + + + align:start position:0% + +what's the next to top + + align:start position:0% +what's the next to top + + + align:start position:0% +what's the next to top +layer what I + + align:start position:0% +layer what I + + + align:start position:0% +layer what I +forgotten I yeah I guess so it's hard to + + align:start position:0% +forgotten I yeah I guess so it's hard to + + + align:start position:0% +forgotten I yeah I guess so it's hard to +tell the reason I had six layers is that + + align:start position:0% +tell the reason I had six layers is that + + + align:start position:0% +tell the reason I had six layers is that +um + + align:start position:0% +um + + + align:start position:0% +um +unlike what people do when making + + align:start position:0% +unlike what people do when making + + + align:start position:0% +unlike what people do when making +theories in science is + + align:start position:0% +theories in science is + + + align:start position:0% +theories in science is +I assume that uh what whatever ideas I + + align:start position:0% +I assume that uh what whatever ideas I + + + align:start position:0% +I assume that uh what whatever ideas I +have they're not enough that is instead + + align:start position:0% +have they're not enough that is instead + + + align:start position:0% +have they're not enough that is instead +of trying to reduce the mind to as few + + align:start position:0% +of trying to reduce the mind to as few + + + align:start position:0% +of trying to reduce the mind to as few +reactions as few mechanisms as + + align:start position:0% +reactions as few mechanisms as + + + align:start position:0% +reactions as few mechanisms as +possible I think you want to leave room + + align:start position:0% +possible I think you want to leave room + + + align:start position:0% +possible I think you want to leave room +uh if your theory is to live for a few + + align:start position:0% +uh if your theory is to live for a few + + + align:start position:0% +uh if your theory is to live for a few +years you want to leave room for new + + align:start position:0% +years you want to leave room for new + + + align:start position:0% +years you want to leave room for new +ideas so the last three layers uh + + align:start position:0% +ideas so the last three layers uh + + + align:start position:0% +ideas so the last three layers uh +beginning with reflective thought and + + align:start position:0% +beginning with reflective thought and + + + align:start position:0% +beginning with reflective thought and +self-reflective and + + align:start position:0% +self-reflective and + + + align:start position:0% +self-reflective and +and the ideals uh it's hard to imagine + + align:start position:0% +and the ideals uh it's hard to imagine + + + align:start position:0% +and the ideals uh it's hard to imagine +any clear boundaries and at some point + + align:start position:0% +any clear boundaries and at some point + + + align:start position:0% +any clear boundaries and at some point +uh when you make your own Theory uh + + align:start position:0% +uh when you make your own Theory uh + + + align:start position:0% +uh when you make your own Theory uh +maybe you can squeeze it into these + + align:start position:0% +maybe you can squeeze it into these + + + align:start position:0% +maybe you can squeeze it into these +extra boxes that that I have uh sort of + + align:start position:0% +extra boxes that that I have uh sort of + + + align:start position:0% +extra boxes that that I have uh sort of +a little later in the + + align:start position:0% + + + + align:start position:0% + +book uh another hierarchy appears + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +that's this is I'm imagining as a + + align:start position:0% +that's this is I'm imagining as a + + + align:start position:0% +that's this is I'm imagining as a +functional + + align:start position:0% + + + + align:start position:0% + +diagram to show + + align:start position:0% +diagram to show + + + align:start position:0% +diagram to show +how knowledge or skills or abilities or + + align:start position:0% +how knowledge or skills or abilities or + + + align:start position:0% +how knowledge or skills or abilities or +uh whatever you want to call them the + + align:start position:0% +uh whatever you want to call them the + + + align:start position:0% +uh whatever you want to call them the +things that people + + align:start position:0% +things that people + + + align:start position:0% +things that people +do uh might be + + align:start position:0% +do uh might be + + + align:start position:0% +do uh might be +arranged and as far as I know + + align:start position:0% +arranged and as far as I know + + + align:start position:0% +arranged and as far as I know +uh + + align:start position:0% +uh + + + align:start position:0% +uh +because virtually every psychologist in + + align:start position:0% +because virtually every psychologist in + + + align:start position:0% +because virtually every psychologist in +the last 100 years has suffered from + + align:start position:0% +the last 100 years has suffered from + + + align:start position:0% +the last 100 years has suffered from +physics + + align:start position:0% +physics + + + align:start position:0% +physics +envy that you know they want to make + + align:start position:0% +envy that you know they want to make + + + align:start position:0% +envy that you know they want to make +something like Newton's + + align:start position:0% +something like Newton's + + + align:start position:0% +something like Newton's +Laws + + align:start position:0% +Laws + + + align:start position:0% +Laws +uh the result has been that except for + + align:start position:0% +uh the result has been that except for + + + align:start position:0% +uh the result has been that except for +the work of people like Newell and Simon + + align:start position:0% +the work of people like Newell and Simon + + + align:start position:0% +the work of people like Newell and Simon +and uh other Pioneers who uh started + + align:start position:0% +and uh other Pioneers who uh started + + + align:start position:0% +and uh other Pioneers who uh started +research in artificial intelligence + + align:start position:0% +research in artificial intelligence + + + align:start position:0% +research in artificial intelligence +the uh you've heard me complain about + + align:start position:0% +the uh you've heard me complain about + + + align:start position:0% +the uh you've heard me complain about +neuroscientists but there's pretty much + + align:start position:0% +neuroscientists but there's pretty much + + + align:start position:0% +neuroscientists but there's pretty much +the same complaint to be leveled against + + align:start position:0% +the same complaint to be leveled against + + + align:start position:0% +the same complaint to be leveled against +most cognitive scientists who for + + align:start position:0% +most cognitive scientists who for + + + align:start position:0% +most cognitive scientists who for +example try to say uh maybe the entire + + align:start position:0% +example try to say uh maybe the entire + + + align:start position:0% +example try to say uh maybe the entire +human mind is a collection of rules and + + align:start position:0% +human mind is a collection of rules and + + + align:start position:0% +human mind is a collection of rules and +uh if then rules well in some sense you + + align:start position:0% +uh if then rules well in some sense you + + + align:start position:0% +uh if then rules well in some sense you +could make anything out of if then rules + + align:start position:0% +could make anything out of if then rules + + + align:start position:0% +could make anything out of if then rules +but uh the chance are if you try to make + + align:start position:0% +but uh the chance are if you try to make + + + align:start position:0% +but uh the chance are if you try to make +a learning machine that just tried to + + align:start position:0% +a learning machine that just tried to + + + align:start position:0% +a learning machine that just tried to +add rules uh in some beautifully General + + align:start position:0% +add rules uh in some beautifully General + + + align:start position:0% +add rules uh in some beautifully General +fashion uh I suspect the chances are it + + align:start position:0% +fashion uh I suspect the chances are it + + + align:start position:0% +fashion uh I suspect the chances are it +would learn for a while and then get + + align:start position:0% +would learn for a while and then get + + + align:start position:0% +would learn for a while and then get +stuck and indeed that's what happened uh + + align:start position:0% +stuck and indeed that's what happened uh + + + align:start position:0% +stuck and indeed that's what happened uh +maybe five or six times in the history + + align:start position:0% +maybe five or six times in the history + + + align:start position:0% +maybe five or six times in the history +of artificial + + align:start position:0% +of artificial + + + align:start position:0% +of artificial +intelligence uh Doug lett's system + + align:start position:0% +intelligence uh Doug lett's system + + + align:start position:0% +intelligence uh Doug lett's system +called am automated mathematician + + align:start position:0% +called am automated mathematician + + + align:start position:0% +called am automated mathematician +uh was a wonderful PhD thesis and it it + + align:start position:0% +uh was a wonderful PhD thesis and it it + + + align:start position:0% +uh was a wonderful PhD thesis and it it +learned + + align:start position:0% +learned + + + align:start position:0% +learned +arithmetic + + align:start position:0% +arithmetic + + + align:start position:0% +arithmetic +by completely by itself he just uh set + + align:start position:0% +by completely by itself he just uh set + + + align:start position:0% +by completely by itself he just uh set +up the thing biased so that it would uh + + align:start position:0% +up the thing biased so that it would uh + + + align:start position:0% +up the thing biased so that it would uh +have some concept of numbers like six is + + align:start position:0% +have some concept of numbers like six is + + + align:start position:0% +have some concept of numbers like six is +the successor of five and stuff like + + align:start position:0% +the successor of five and stuff like + + + align:start position:0% +the successor of five and stuff like +that and it it Fooled Around and + + align:start position:0% +that and it it Fooled Around and + + + align:start position:0% +that and it it Fooled Around and +uh discovered various regularities I + + align:start position:0% +uh discovered various regularities I + + + align:start position:0% +uh discovered various regularities I +think I mentioned it the other day uh it + + align:start position:0% +think I mentioned it the other day uh it + + + align:start position:0% +think I mentioned it the other day uh it +first developed a concept of number + + align:start position:0% +first developed a concept of number + + + align:start position:0% +first developed a concept of number +which wasn't very + + align:start position:0% +which wasn't very + + + align:start position:0% +which wasn't very +hard because he wrote + + align:start position:0% +hard because he wrote + + + align:start position:0% +hard because he wrote +the whole thing in the uh AI language + + align:start position:0% +the whole thing in the uh AI language + + + align:start position:0% +the whole thing in the uh AI language +called lisp how many of you know + + align:start position:0% +called lisp how many of you know + + + align:start position:0% +called lisp how many of you know +lisp that's a lot uh in looking at + + align:start position:0% +lisp that's a lot uh in looking at + + + align:start position:0% +lisp that's a lot uh in looking at +the biographies of the late John + + align:start position:0% +the biographies of the late John + + + align:start position:0% +the biographies of the late John +McCarthy all week + + align:start position:0% +McCarthy all week + + + align:start position:0% +McCarthy all week +uh there were lots of attempts by the + + align:start position:0% +uh there were lots of attempts by the + + + align:start position:0% +uh there were lots of attempts by the +writers to say what lisp + + align:start position:0% + + + + align:start position:0% + +was the tragedy is you probably could + + align:start position:0% +was the tragedy is you probably could + + + align:start position:0% +was the tragedy is you probably could +have described it exactly in a paragraph + + align:start position:0% +have described it exactly in a paragraph + + + align:start position:0% +have described it exactly in a paragraph +It's + + align:start position:0% +It's + + + align:start position:0% +It's +because it's saying + + align:start position:0% + + + + align:start position:0% + +that each structure has two parts and + + align:start position:0% +that each structure has two parts and + + + align:start position:0% +that each structure has two parts and +each of those has two parts and I don't + + align:start position:0% +each of those has two parts and I don't + + + align:start position:0% +each of those has two parts and I don't +remember seeing any + + align:start position:0% +remember seeing any + + + align:start position:0% +remember seeing any +uh attempt to say something about this + + align:start position:0% +uh attempt to say something about this + + + align:start position:0% +uh attempt to say something about this +programming language in yes how do you + + align:start position:0% +programming language in yes how do you + + + align:start position:0% +programming language in yes how do you +um imagine layers interact with each + + align:start position:0% +um imagine layers interact with each + + + align:start position:0% +um imagine layers interact with each +other those uh yeah those and those the + + align:start position:0% +other those uh yeah those and those the + + + align:start position:0% +other those uh yeah those and those the +six + + align:start position:0% +six + + + align:start position:0% +six +layers I think they're they're layers of + + align:start position:0% +layers I think they're they're layers of + + + align:start position:0% +layers I think they're they're layers of +organization + + align:start position:0% + + + + align:start position:0% + +but yes because the trans frames a + + align:start position:0% +but yes because the trans frames a + + + align:start position:0% +but yes because the trans frames a +transframe is made of two + + align:start position:0% +transframe is made of two + + + align:start position:0% +transframe is made of two +frames and but + + align:start position:0% +frames and but + + + align:start position:0% +frames and but +then + + align:start position:0% +then + + + align:start position:0% +then +uh if there were a neuroscientist who + + align:start position:0% +uh if there were a neuroscientist who + + + align:start position:0% +uh if there were a neuroscientist who +said oh maybe when you see an apple and + + align:start position:0% +said oh maybe when you see an apple and + + + align:start position:0% +said oh maybe when you see an apple and +you're hungry you reach out and eat + + align:start position:0% +you're hungry you reach out and eat + + + align:start position:0% +you're hungry you reach out and eat +it uh so that's a + + align:start position:0% +it uh so that's a + + + align:start position:0% +it uh so that's a +you could think of that as a simple + + align:start position:0% +you could think of that as a simple + + + align:start position:0% +you could think of that as a simple +reflex if this then that or you could + + align:start position:0% +reflex if this then that or you could + + + align:start position:0% +reflex if this then that or you could +say if I'm hungry now and I want to be + + align:start position:0% +say if I'm hungry now and I want to be + + + align:start position:0% +say if I'm hungry now and I want to be +not hungry what's a possible action + + align:start position:0% +not hungry what's a possible action + + + align:start position:0% +not hungry what's a possible action +could I do and that action might be look + + align:start position:0% +could I do and that action might be look + + + align:start position:0% +could I do and that action might be look +for an apple + + align:start position:0% +for an apple + + + align:start position:0% +for an apple +or yes so I was teaching my class on the + + align:start position:0% +or yes so I was teaching my class on the + + + align:start position:0% +or yes so I was teaching my class on the +day that the carpi passed away and then + + align:start position:0% +day that the carpi passed away and then + + + align:start position:0% +day that the carpi passed away and then +I was explaining and I have had some + + align:start position:0% +I was explaining and I have had some + + + align:start position:0% +I was explaining and I have had some +students in the class computer scientist + + align:start position:0% +students in the class computer scientist + + + align:start position:0% +students in the class computer scientist +and so I was thinking about that same + + align:start position:0% +and so I was thinking about that same + + + align:start position:0% +and so I was thinking about that same +problem which is how do I explain what + + align:start position:0% +problem which is how do I explain what + + + align:start position:0% +problem which is how do I explain what +lisp was and I remember and so I said um + + align:start position:0% +lisp was and I remember and so I said um + + + align:start position:0% +lisp was and I remember and so I said um +well before that there were languages + + align:start position:0% +well before that there were languages + + + align:start position:0% +well before that there were languages +like forr that manipulated numbers lisp + + align:start position:0% +like forr that manipulated numbers lisp + + + align:start position:0% +like forr that manipulated numbers lisp +was the fourth first language to + + align:start position:0% +was the fourth first language to + + + align:start position:0% +was the fourth first language to +manipulate ideas + + align:start position:0% +manipulate ideas + + + align:start position:0% +manipulate ideas +MH yes it can manipulate representations + + align:start position:0% +MH yes it can manipulate representations + + + align:start position:0% +MH yes it can manipulate representations +of yes it's manipulating the ideas that + + align:start position:0% +of yes it's manipulating the ideas that + + + align:start position:0% +of yes it's manipulating the ideas that +the are represented by these expressions + + align:start position:0% +the are represented by these expressions + + + align:start position:0% +the are represented by these expressions +and uh one thing that interests me is uh + + align:start position:0% +and uh one thing that interests me is uh + + + align:start position:0% +and uh one thing that interests me is uh +another analog between psychology + + align:start position:0% +another analog between psychology + + + align:start position:0% +another analog between psychology +and modern cognitive psychology and and + + align:start position:0% +and modern cognitive psychology and and + + + align:start position:0% +and modern cognitive psychology and and +computer science or artificial + + align:start position:0% +computer science or artificial + + + align:start position:0% +computer science or artificial +intelligence is the idea of a + + align:start position:0% +intelligence is the idea of a + + + align:start position:0% +intelligence is the idea of a +goal + + align:start position:0% +goal + + + align:start position:0% +goal +where uh what does it mean to have a + + align:start position:0% +where uh what does it mean to have a + + + align:start position:0% +where uh what does it mean to have a +goal and you could say it's a piece of + + align:start position:0% +goal and you could say it's a piece of + + + align:start position:0% +goal and you could say it's a piece of +Machinery which says that if there's a + + align:start position:0% + + + + align:start position:0% + +situation what you have + + align:start position:0% +situation what you have + + + align:start position:0% +situation what you have +now and if you have a + + align:start position:0% +now and if you have a + + + align:start position:0% +now and if you have a +representation of some future + + align:start position:0% +representation of some future + + + align:start position:0% +representation of some future +thing what you + + align:start position:0% + + + + align:start position:0% + +want so of course at any time you're in + + align:start position:0% +want so of course at any time you're in + + + align:start position:0% +want so of course at any time you're in +a situation that uh your brain is + + align:start position:0% +a situation that uh your brain is + + + align:start position:0% +a situation that uh your brain is +somehow representing maybe five or 10 + + align:start position:0% +somehow representing maybe five or 10 + + + align:start position:0% +somehow representing maybe five or 10 +ways not just one but uh what does it + + align:start position:0% +ways not just one but uh what does it + + + align:start position:0% +ways not just one but uh what does it +mean to have a goal and what it means is + + align:start position:0% +mean to have a goal and what it means is + + + align:start position:0% +mean to have a goal and what it means is +to have two representations one one is a + + align:start position:0% +to have two representations one one is a + + + align:start position:0% +to have two representations one one is a +representation you've made of some + + align:start position:0% +representation you've made of some + + + align:start position:0% +representation you've made of some +structure which says uh what things are + + align:start position:0% +structure which says uh what things are + + + align:start position:0% +structure which says uh what things are +like now and the other is some + + align:start position:0% +like now and the other is some + + + align:start position:0% +like now and the other is some +representation of what you want + + align:start position:0% + + + + align:start position:0% + +and don't think I need + + align:start position:0% +and don't think I need + + + align:start position:0% +and don't think I need +that and the important thing thing is + + align:start position:0% +that and the important thing thing is + + + align:start position:0% +that and the important thing thing is +what are the + + align:start position:0% + + + + align:start position:0% + +differences and instead of saying what's + + align:start position:0% +differences and instead of saying what's + + + align:start position:0% +differences and instead of saying what's +the difference maybe it's good to + + align:start position:0% +the difference maybe it's good to + + + align:start position:0% +the difference maybe it's good to +say what are the + + align:start position:0% +say what are the + + + align:start position:0% +say what are the +differences so what does it mean to have + + align:start position:0% +differences so what does it mean to have + + + align:start position:0% +differences so what does it mean to have +a goal it means + + align:start position:0% +a goal it means + + + align:start position:0% +a goal it means +to have some piece of Machinery turned + + align:start position:0% +to have some piece of Machinery turned + + + align:start position:0% +to have some piece of Machinery turned +on you can imagine a goal that you don't + + align:start position:0% +on you can imagine a goal that you don't + + + align:start position:0% +on you can imagine a goal that you don't +have right like I can I could say what's + + align:start position:0% +have right like I can I could say what's + + + align:start position:0% +have right like I can I could say what's +David's goal it's to get people to + + align:start position:0% +David's goal it's to get people to + + + align:start position:0% +David's goal it's to get people to +uh go to that + + align:start position:0% +uh go to that + + + align:start position:0% +uh go to that +meeting + + align:start position:0% + + + + align:start position:0% + +uh so the different what you want is to + + align:start position:0% +uh so the different what you want is to + + + align:start position:0% +uh so the different what you want is to +minimize the differences between what + + align:start position:0% +minimize the differences between what + + + align:start position:0% +minimize the differences between what +you have and what you want and so there + + align:start position:0% +you have and what you want and so there + + + align:start position:0% +you have and what you want and so there +has to be a Machinery which does + + align:start position:0% +has to be a Machinery which does + + + align:start position:0% +has to be a Machinery which does +what + + align:start position:0% +what + + + align:start position:0% +what +uh it picks out one of these differences + + align:start position:0% +uh it picks out one of these differences + + + align:start position:0% +uh it picks out one of these differences +and tries to get rid of it and how can + + align:start position:0% +and tries to get rid of it and how can + + + align:start position:0% +and tries to get rid of it and how can +you get rid of it uh there's two + + align:start position:0% +you get rid of it uh there's two + + + align:start position:0% +you get rid of it uh there's two +ways + + align:start position:0% +ways + + + align:start position:0% +ways +uh the good way is to change the + + align:start position:0% +uh the good way is to change the + + + align:start position:0% +uh the good way is to change the +situation so that difference + + align:start position:0% +situation so that difference + + + align:start position:0% +situation so that difference +disappears the other way is to say oh + + align:start position:0% +disappears the other way is to say oh + + + align:start position:0% +disappears the other way is to say oh +that would take a year uh I should give + + align:start position:0% +that would take a year uh I should give + + + align:start position:0% +that would take a year uh I should give +up that goal and + + align:start position:0% +up that goal and + + + align:start position:0% +up that goal and +uh that's I'm + + align:start position:0% +uh that's I'm + + + align:start position:0% +uh that's I'm +digressing so you want something that + + align:start position:0% + + + + align:start position:0% + +removes the feedback has to go this way + + align:start position:0% +removes the feedback has to go this way + + + align:start position:0% +removes the feedback has to go this way +let's change the + + align:start position:0% + + + + align:start position:0% + +world and get rid of that difference + + align:start position:0% +world and get rid of that difference + + + align:start position:0% +world and get rid of that difference +so + + align:start position:0% +so + + + align:start position:0% +so +uh well how do you get rid of a + + align:start position:0% +uh well how do you get rid of a + + + align:start position:0% +uh well how do you get rid of a +difference that depends on maybe you + + align:start position:0% +difference that depends on maybe you + + + align:start position:0% +difference that depends on maybe you +have a uh built-in + + align:start position:0% +have a uh built-in + + + align:start position:0% +have a uh built-in +reflex + + align:start position:0% + + + + align:start position:0% + +like like if you have too much CO2 in + + align:start position:0% +like like if you have too much CO2 in + + + align:start position:0% +like like if you have too much CO2 in +your blood something senses it and uh + + align:start position:0% +your blood something senses it and uh + + + align:start position:0% +your blood something senses it and uh +tells you to breathe so you've got + + align:start position:0% +tells you to breathe so you've got + + + align:start position:0% +tells you to breathe so you've got +builtin + + align:start position:0% + + + + align:start position:0% + +things and the question is how do you + + align:start position:0% +things and the question is how do you + + + align:start position:0% +things and the question is how do you +represent these sorts of things and in + + align:start position:0% +represent these sorts of things and in + + + align:start position:0% +represent these sorts of things and in +fact I think I got a lot of this idea + + align:start position:0% +fact I think I got a lot of this idea + + + align:start position:0% +fact I think I got a lot of this idea +from the PHD thesis of Patrick Winston + + align:start position:0% +from the PHD thesis of Patrick Winston + + + align:start position:0% +from the PHD thesis of Patrick Winston +who was was here a minute + + align:start position:0% + + + + align:start position:0% + +ago um + + align:start position:0% + + + + align:start position:0% + +but the question is how do you + + align:start position:0% +but the question is how do you + + + align:start position:0% +but the question is how do you +represent what you want and how do you + + align:start position:0% +represent what you want and how do you + + + align:start position:0% +represent what you want and how do you +represent what you have and I think the + + align:start position:0% +represent what you have and I think the + + + align:start position:0% +represent what you have and I think the +big difference + + align:start position:0% +big difference + + + align:start position:0% +big difference +between uh people and other primates and + + align:start position:0% +between uh people and other primates and + + + align:start position:0% +between uh people and other primates and +reptils and amphibians reptiles fish and + + align:start position:0% +reptils and amphibians reptiles fish and + + + align:start position:0% +reptils and amphibians reptiles fish and +going back to plants and so forth is + + align:start position:0% +going back to plants and so forth is + + + align:start position:0% +going back to plants and so forth is +that + + align:start position:0% + + + + align:start position:0% + +we have these very high level powerful + + align:start position:0% +we have these very high level powerful + + + align:start position:0% +we have these very high level powerful +ways of representing differences between + + align:start position:0% +ways of representing differences between + + + align:start position:0% +ways of representing differences between +things and uh this enables us to + + align:start position:0% +things and uh this enables us to + + + align:start position:0% +things and uh this enables us to +develop reflexes for getting rid of the + + align:start position:0% +develop reflexes for getting rid of the + + + align:start position:0% +develop reflexes for getting rid of the +differences so this is a what I think is + + align:start position:0% +differences so this is a what I think is + + + align:start position:0% +differences so this is a what I think is +might be a picture of how the brain is + + align:start position:0% +might be a picture of how the brain is + + + align:start position:0% +might be a picture of how the brain is +organized and at every level these + + align:start position:0% +organized and at every level these + + + align:start position:0% +organized and at every level these +things are made of neurons but you + + align:start position:0% +things are made of neurons but you + + + align:start position:0% +things are made of neurons but you +shouldn't be looking at the neurons + + align:start position:0% +shouldn't be looking at the neurons + + + align:start position:0% +shouldn't be looking at the neurons +individually + + align:start position:0% +individually + + + align:start position:0% +individually +uh to see how the brain works it's it's + + align:start position:0% +uh to see how the brain works it's it's + + + align:start position:0% +uh to see how the brain works it's it's +like looking at a computer and saying oh + + align:start position:0% +like looking at a computer and saying oh + + + align:start position:0% +like looking at a computer and saying oh +I understand that all I have to do is + + align:start position:0% +I understand that all I have to do is + + + align:start position:0% +I understand that all I have to do is +know a great deal about how each + + align:start position:0% +know a great deal about how each + + + align:start position:0% +know a great deal about how each +transistor works the great thing about a + + align:start position:0% +transistor works the great thing about a + + + align:start position:0% +transistor works the great thing about a +computer is that it doesn't matter how + + align:start position:0% +computer is that it doesn't matter how + + + align:start position:0% +computer is that it doesn't matter how +the transistor works the important thing + + align:start position:0% +the transistor works the important thing + + + align:start position:0% +the transistor works the important thing +is to recognize oh look they usually + + align:start position:0% +is to recognize oh look they usually + + + align:start position:0% +is to recognize oh look they usually +come in pairs or really four or 10 or + + align:start position:0% +come in pairs or really four or 10 or + + + align:start position:0% +come in pairs or really four or 10 or +whatever called a flipflop + + align:start position:0% +whatever called a flipflop + + + align:start position:0% +whatever called a flipflop +up + + align:start position:0% +up + + + align:start position:0% +up +and + + align:start position:0% + + + + align:start position:0% + +uh do you ever do you ever see a + + align:start position:0% +uh do you ever do you ever see a + + + align:start position:0% +uh do you ever do you ever see a +neuroscientist saying where are the + + align:start position:0% +neuroscientist saying where are the + + + align:start position:0% +neuroscientist saying where are the +flip-flops in this or that it's very + + align:start position:0% +flip-flops in this or that it's very + + + align:start position:0% +flip-flops in this or that it's very +strange they're it's as though they're + + align:start position:0% +strange they're it's as though they're + + + align:start position:0% +strange they're it's as though they're +trying to develop a very powerful + + align:start position:0% +trying to develop a very powerful + + + align:start position:0% +trying to develop a very powerful +computer without using any concepts from + + align:start position:0% +computer without using any concepts from + + + align:start position:0% +computer without using any concepts from +computer + + align:start position:0% +computer + + + align:start position:0% +computer +science it's a marvelous phenomenon and + + align:start position:0% +science it's a marvelous phenomenon and + + + align:start position:0% +science it's a marvelous phenomenon and +you have to + + align:start position:0% +you have to + + + align:start position:0% +you have to +wonder where did they grow up and how + + align:start position:0% +wonder where did they grow up and how + + + align:start position:0% +wonder where did they grow up and how +did they stay + + align:start position:0% +did they stay + + + align:start position:0% +did they stay +isolated biology departments I + + align:start position:0% +isolated biology departments I + + + align:start position:0% +isolated biology departments I +think biology departments what + + align:start position:0% +think biology departments what + + + align:start position:0% +think biology departments what +psychology departments well I started + + align:start position:0% +psychology departments well I started + + + align:start position:0% +psychology departments well I started +out in biology pretty much and then I + + align:start position:0% +out in biology pretty much and then I + + + align:start position:0% +out in biology pretty much and then I +ran + + align:start position:0% + + + + align:start position:0% + +across these early papers one of which + + align:start position:0% +across these early papers one of which + + + align:start position:0% +across these early papers one of which +was by + + align:start position:0% +was by + + + align:start position:0% +was by +lein and uh mullik and Pitts and people + + align:start position:0% +lein and uh mullik and Pitts and people + + + align:start position:0% +lein and uh mullik and Pitts and people +like that in the late in the early + + align:start position:0% +like that in the late in the early + + + align:start position:0% +like that in the late in the early +1940s the idea of symbolic neurons + + align:start position:0% +1940s the idea of symbolic neurons + + + align:start position:0% +1940s the idea of symbolic neurons +appeared uh it had first appeared in + + align:start position:0% +appeared uh it had first appeared in + + + align:start position:0% +appeared uh it had first appeared in +1895 or so with the uh paper that uh + + align:start position:0% +1895 or so with the uh paper that uh + + + align:start position:0% +1895 or so with the uh paper that uh +Sigman Freud wrote but couldn't get + + align:start position:0% +Sigman Freud wrote but couldn't get + + + align:start position:0% +Sigman Freud wrote but couldn't get +published I think I mentioned that + + align:start position:0% +published I think I mentioned that + + + align:start position:0% +published I think I mentioned that +called project for a scientific + + align:start position:0% +called project for a scientific + + + align:start position:0% +called project for a scientific +psychology and it had the idea of + + align:start position:0% +psychology and it had the idea of + + + align:start position:0% +psychology and it had the idea of +neurons with uh various levels of + + align:start position:0% +neurons with uh various levels of + + + align:start position:0% +neurons with uh various levels of +activation and and sometimes you would + + align:start position:0% +activation and and sometimes you would + + + align:start position:0% +activation and and sometimes you would +have a pair of them and one would be + + align:start position:0% +have a pair of them and one would be + + + align:start position:0% +have a pair of them and one would be +inhibiting the other uh and so that + + align:start position:0% +inhibiting the other uh and so that + + + align:start position:0% +inhibiting the other uh and so that +could store some information and he's + + align:start position:0% +could store some information and he's + + + align:start position:0% +could store some information and he's +not very explicit about how these things + + align:start position:0% +not very explicit about how these things + + + align:start position:0% +not very explicit about how these things +might work but as far as I know it's + + align:start position:0% +might work but as far as I know it's + + + align:start position:0% +might work but as far as I know it's +about the + + align:start position:0% +about the + + + align:start position:0% +about the +first uh attempt to have a biological + + align:start position:0% +first uh attempt to have a biological + + + align:start position:0% +first uh attempt to have a biological +theory of information processing at all + + align:start position:0% +theory of information processing at all + + + align:start position:0% +theory of information processing at all +and + + align:start position:0% +and + + + align:start position:0% +and +um he was unable to get it + + align:start position:0% + + + + align:start position:0% + +published yeah but since Mardy did this + + align:start position:0% +published yeah but since Mardy did this + + + align:start position:0% +published yeah but since Mardy did this +just die do you have any summary + + align:start position:0% +just die do you have any summary + + + align:start position:0% +just die do you have any summary +Reflections on the stuff that he did or + + align:start position:0% +Reflections on the stuff that he did or + + + align:start position:0% +Reflections on the stuff that he did or +his contributions there are a lot of + + align:start position:0% +his contributions there are a lot of + + + align:start position:0% +his contributions there are a lot of +things that he did and + + align:start position:0% + + + + align:start position:0% + +uh I noticed that none of the + + align:start position:0% +uh I noticed that none of the + + + align:start position:0% +uh I noticed that none of the +obituaries actually had any + + align:start position:0% +obituaries actually had any + + + align:start position:0% +obituaries actually had any +background uh what had happened is that + + align:start position:0% +background uh what had happened is that + + + align:start position:0% +background uh what had happened is that +uh new and Simon had started to + + align:start position:0% +uh new and Simon had started to + + + align:start position:0% +uh new and Simon had started to +make uh + + align:start position:0% +make uh + + + align:start position:0% +make uh +they had struggled to make programs that + + align:start position:0% +they had struggled to make programs that + + + align:start position:0% +they had struggled to make programs that +could do symbolic + + align:start position:0% +could do symbolic + + + align:start position:0% +could do symbolic +logic and they made a language + + align:start position:0% + + + + align:start position:0% + +called + + align:start position:0% + + + + align:start position:0% + +IPL and IPL was a language of very + + align:start position:0% +IPL and IPL was a language of very + + + align:start position:0% +IPL and IPL was a language of very +microscopic + + align:start position:0% +microscopic + + + align:start position:0% +microscopic +operations like you have several + + align:start position:0% +operations like you have several + + + align:start position:0% +operations like you have several +registers put a symbol in a reg register + + align:start position:0% + + + + align:start position:0% + +uh perhaps do a piece of arithmetic on + + align:start position:0% +uh perhaps do a piece of arithmetic on + + + align:start position:0% +uh perhaps do a piece of arithmetic on +two symbols if they're numbers if not + + align:start position:0% +two symbols if they're numbers if not + + + align:start position:0% +two symbols if they're numbers if not +uh link + + align:start position:0% +uh link + + + align:start position:0% +uh link +up you could sort of make + + align:start position:0% +up you could sort of make + + + align:start position:0% +up you could sort of make +registers + + align:start position:0% +registers + + + align:start position:0% +registers +artificially uh in the memory of the + + align:start position:0% +artificially uh in the memory of the + + + align:start position:0% +artificially uh in the memory of the +computer and you could take two or three + + align:start position:0% +computer and you could take two or three + + + align:start position:0% +computer and you could take two or three +registers and you + + align:start position:0% +registers and you + + + align:start position:0% +registers and you +could it had instructions for making + + align:start position:0% +could it had instructions for making + + + align:start position:0% +could it had instructions for making +lists or trees so you could arrange + + align:start position:0% +lists or trees so you could arrange + + + align:start position:0% +lists or trees so you could arrange +these in a way + + align:start position:0% + + + + align:start position:0% + +that so here are the three things and + + align:start position:0% +that so here are the three things and + + + align:start position:0% +that so here are the three things and +this is just a simple list but I've + + align:start position:0% +this is just a simple list but I've + + + align:start position:0% +this is just a simple list but I've +drawn it as though these two were + + align:start position:0% +drawn it as though these two were + + + align:start position:0% +drawn it as though these two were +subsidiary to that of course that + + align:start position:0% +subsidiary to that of course that + + + align:start position:0% +subsidiary to that of course that +depends on what program is going to look + + align:start position:0% +depends on what program is going to look + + + align:start position:0% +depends on what program is going to look +at this and you could have a program + + align:start position:0% +at this and you could have a program + + + align:start position:0% +at this and you could have a program +which can say here are two arguments for + + align:start position:0% +which can say here are two arguments for + + + align:start position:0% +which can say here are two arguments for +a function and it doesn't matter what + + align:start position:0% +a function and it doesn't matter what + + + align:start position:0% +a function and it doesn't matter what +order they're in just depends how you + + align:start position:0% +order they're in just depends how you + + + align:start position:0% +order they're in just depends how you +wrote the function so new and Simon had + + align:start position:0% +wrote the function so new and Simon had + + + align:start position:0% +wrote the function so new and Simon had +written a programming language which + + align:start position:0% +written a programming language which + + + align:start position:0% +written a programming language which +said put something in a register link it + + align:start position:0% +said put something in a register link it + + + align:start position:0% +said put something in a register link it +to another register and + + align:start position:0% +to another register and + + + align:start position:0% +to another register and +uh then perform the usual arithmetic + + align:start position:0% +uh then perform the usual arithmetic + + + align:start position:0% +uh then perform the usual arithmetic +operations in fact what they were doing + + align:start position:0% +operations in fact what they were doing + + + align:start position:0% +operations in fact what they were doing +is mostly performing logical operations + + align:start position:0% +is mostly performing logical operations + + + align:start position:0% +is mostly performing logical operations +because even the early computers had ANS + + align:start position:0% +because even the early computers had ANS + + + align:start position:0% +because even the early computers had ANS +and ores and exors and things like that + + align:start position:0% +and ores and exors and things like that + + + align:start position:0% +and ores and exors and things like that +um so + + align:start position:0% + + + + align:start position:0% + +uh try to remember what they were using + + align:start position:0% +uh try to remember what they were using + + + align:start position:0% +uh try to remember what they were using +for oh uh so new and Simon had written a + + align:start position:0% +for oh uh so new and Simon had written a + + + align:start position:0% +for oh uh so new and Simon had written a +program that uh could deal with Boolean + + align:start position:0% +program that uh could deal with Boolean + + + align:start position:0% +program that uh could deal with Boolean +functions and prove little theorems + + align:start position:0% +functions and prove little theorems + + + align:start position:0% +functions and prove little theorems +about you know uh Not A or B is not is + + align:start position:0% +about you know uh Not A or B is not is + + + align:start position:0% +about you know uh Not A or B is not is +not a or not B is that + + align:start position:0% + + + + align:start position:0% + +wrong I forget should have more + + align:start position:0% +wrong I forget should have more + + + align:start position:0% +wrong I forget should have more +knots anyway they they wrote this + + align:start position:0% +knots anyway they they wrote this + + + align:start position:0% +knots anyway they they wrote this +beautiful but clumsy thing made of very + + align:start position:0% +beautiful but clumsy thing made of very + + + align:start position:0% +beautiful but clumsy thing made of very +simple logical Primitives McCarthy at + + align:start position:0% +simple logical Primitives McCarthy at + + + align:start position:0% +simple logical Primitives McCarthy at +the same time IBM had spent 400 man + + align:start position:0% +the same time IBM had spent 400 man + + + align:start position:0% +the same time IBM had spent 400 man +years + + align:start position:0% +years + + + align:start position:0% +years +writing a program called Fortran one or + + align:start position:0% +writing a program called Fortran one or + + + align:start position:0% +writing a program called Fortran one or +Fortran I'm not sure that people had + + align:start position:0% +Fortran I'm not sure that people had + + + align:start position:0% +Fortran I'm not sure that people had +serial number numbers on programming + + align:start position:0% +serial number numbers on programming + + + align:start position:0% +serial number numbers on programming +languages yet because we're talking + + align:start position:0% +languages yet because we're talking + + + align:start position:0% +languages yet because we're talking +about the middle + + align:start position:0% +about the middle + + + align:start position:0% +about the middle +1950s uh and McCarthy had been thinking + + align:start position:0% +1950s uh and McCarthy had been thinking + + + align:start position:0% +1950s uh and McCarthy had been thinking +about how would you make AI programs + + align:start position:0% +about how would you make AI programs + + + align:start position:0% +about how would you make AI programs +that could do symbolic + + align:start position:0% +that could do symbolic + + + align:start position:0% +that could do symbolic +reasoning and he was indeed particularly + + align:start position:0% +reasoning and he was indeed particularly + + + align:start position:0% +reasoning and he was indeed particularly +interested in + + align:start position:0% + + + + align:start position:0% + +logic backtrack in fact new and Simon + + align:start position:0% +logic backtrack in fact new and Simon + + + align:start position:0% +logic backtrack in fact new and Simon +had + + align:start position:0% +had + + + align:start position:0% +had +uh got their program to find proofs of + + align:start position:0% +uh got their program to find proofs of + + + align:start position:0% +uh got their program to find proofs of +most of the theorems in the first volume + + align:start position:0% +most of the theorems in the first volume + + + align:start position:0% +most of the theorems in the first volume +of Russell and Whitehead's prinkipia + + align:start position:0% +of Russell and Whitehead's prinkipia + + + align:start position:0% +of Russell and Whitehead's prinkipia +Mathematica which is a huge TW volume + + align:start position:0% +Mathematica which is a huge TW volume + + + align:start position:0% +Mathematica which is a huge TW volume +book uh from about 1905 I think uh which + + align:start position:0% +book uh from about 1905 I think uh which + + + align:start position:0% +book uh from about 1905 I think uh which +was the first attempt to successful + + align:start position:0% +was the first attempt to successful + + + align:start position:0% +was the first attempt to successful +attempt to reduce mathematics to logic + + align:start position:0% +attempt to reduce mathematics to logic + + + align:start position:0% +attempt to reduce mathematics to logic +and they managed to get up to calculus + + align:start position:0% +and they managed to get up to calculus + + + align:start position:0% +and they managed to get up to calculus +and show that differentiation and + + align:start position:0% +and show that differentiation and + + + align:start position:0% +and show that differentiation and +integration can be expressed as logical + + align:start position:0% +integration can be expressed as logical + + + align:start position:0% +integration can be expressed as logical +functions of variables it's a great tour + + align:start position:0% +functions of variables it's a great tour + + + align:start position:0% +functions of variables it's a great tour +to force because you had + + align:start position:0% + + + + align:start position:0% + +to because logic itself barely existed + + align:start position:0% +to because logic itself barely existed + + + align:start position:0% +to because logic itself barely existed +bull and a few others had uh including + + align:start position:0% +bull and a few others had uh including + + + align:start position:0% +bull and a few others had uh including +lenets had invented uh Boolean algebra + + align:start position:0% +lenets had invented uh Boolean algebra + + + align:start position:0% +lenets had invented uh Boolean algebra +like things and + + align:start position:0% +like things and + + + align:start position:0% +like things and +around uh Fraga and uh others had got + + align:start position:0% +around uh Fraga and uh others had got + + + align:start position:0% +around uh Fraga and uh others had got +predicate calculus with their exists and + + align:start position:0% +predicate calculus with their exists and + + + align:start position:0% +predicate calculus with their exists and +for all and that stuff was just + + align:start position:0% +for all and that stuff was just + + + align:start position:0% +for all and that stuff was just +appearing and Russell and Whitehead + + align:start position:0% +appearing and Russell and Whitehead + + + align:start position:0% +appearing and Russell and Whitehead +wrote this huge book which got all the + + align:start position:0% +wrote this huge book which got all the + + + align:start position:0% +wrote this huge book which got all the +way up to uh describing continuous and + + align:start position:0% +way up to uh describing continuous and + + + align:start position:0% +way up to uh describing continuous and +differentiable functions and so forth + + align:start position:0% +differentiable functions and so forth + + + align:start position:0% +differentiable functions and so forth +the first volume was huge and just did + + align:start position:0% +the first volume was huge and just did + + + align:start position:0% +the first volume was huge and just did +propositional + + align:start position:0% +propositional + + + align:start position:0% +propositional +calculus which Aristotle had done some + + align:start position:0% +calculus which Aristotle had done some + + + align:start position:0% +calculus which Aristotle had done some +of + + align:start position:0% +of + + + align:start position:0% +of +also and um anyway McCarthy looked at + + align:start position:0% +also and um anyway McCarthy looked at + + + align:start position:0% +also and um anyway McCarthy looked at +that and said uh why can't there be a + + align:start position:0% +that and said uh why can't there be a + + + align:start position:0% +that and said uh why can't there be a +functional language like Fortran that + + align:start position:0% +functional language like Fortran that + + + align:start position:0% +functional language like Fortran that +can do symbolic reasoning and uh pretty + + align:start position:0% +can do symbolic reasoning and uh pretty + + + align:start position:0% +can do symbolic reasoning and uh pretty +much all by himself he uh got the basic + + align:start position:0% +much all by himself he uh got the basic + + + align:start position:0% +much all by himself he uh got the basic +ideas from lisp they're built on the new + + align:start position:0% +ideas from lisp they're built on the new + + + align:start position:0% +ideas from lisp they're built on the new +and Simon + + align:start position:0% +and Simon + + + align:start position:0% +and Simon +experiment and + + align:start position:0% +experiment and + + + align:start position:0% +experiment and +uh um but he + + align:start position:0% +uh um but he + + + align:start position:0% +uh um but he +basically converted + + align:start position:0% +basically converted + + + align:start position:0% +basically converted +the symbolic system into something like + + align:start position:0% +the symbolic system into something like + + + align:start position:0% +the symbolic system into something like +Fortran which was only able to + + align:start position:0% +Fortran which was only able to + + + align:start position:0% +Fortran which was only able to +manipulate numbers into list which was + + align:start position:0% +manipulate numbers into list which was + + + align:start position:0% +manipulate numbers into list which was +able to uh manipulate arbitrary symbols + + align:start position:0% +able to uh manipulate arbitrary symbols + + + align:start position:0% +able to uh manipulate arbitrary symbols +in various ways and + + align:start position:0% +in various ways and + + + align:start position:0% +in various ways and +uh if you want to know more about that + + align:start position:0% +uh if you want to know more about that + + + align:start position:0% +uh if you want to know more about that +there's a + + align:start position:0% +there's a + + + align:start position:0% +there's a +great you can find McCarthy's homepage + + align:start position:0% +great you can find McCarthy's homepage + + + align:start position:0% +great you can find McCarthy's homepage +at Stanford just by uh I think if + + align:start position:0% +at Stanford just by uh I think if + + + align:start position:0% +at Stanford just by uh I think if +you Google search for McCarthy + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +sale sale is Stanford artificial + + align:start position:0% +sale sale is Stanford artificial + + + align:start position:0% +sale sale is Stanford artificial +intelligence + + align:start position:0% +intelligence + + + align:start position:0% +intelligence +laboratory and uh you'll get his + + align:start position:0% +laboratory and uh you'll get his + + + align:start position:0% +laboratory and uh you'll get his +homepage and there's a 1994 article + + align:start position:0% +homepage and there's a 1994 article + + + align:start position:0% +homepage and there's a 1994 article +about how he invented lisp + + align:start position:0% +about how he invented lisp + + + align:start position:0% +about how he invented lisp +yes right after you started talking + + align:start position:0% +yes right after you started talking + + + align:start position:0% +yes right after you started talking +about lisp you jumped over and you said + + align:start position:0% +about lisp you jumped over and you said + + + align:start position:0% +about lisp you jumped over and you said +here's here's a the now and the want + + align:start position:0% +here's here's a the now and the want + + + align:start position:0% +here's here's a the now and the want +which is the current state and the + + align:start position:0% +which is the current state and the + + + align:start position:0% +which is the current state and the +desired State and I I think you're going + + align:start position:0% +desired State and I I think you're going + + + align:start position:0% +desired State and I I think you're going +for some kind of uh analogy between the + + align:start position:0% +for some kind of uh analogy between the + + + align:start position:0% +for some kind of uh analogy between the +symbolic evaluation available in this + + align:start position:0% +symbolic evaluation available in this + + + align:start position:0% +symbolic evaluation available in this +and what conscious entities do however + + align:start position:0% +and what conscious entities do however + + + align:start position:0% +and what conscious entities do however +one of the most beautiful things about + + align:start position:0% +one of the most beautiful things about + + + align:start position:0% +one of the most beautiful things about +this is the homo ionicity the fact that + + align:start position:0% +this is the homo ionicity the fact that + + + align:start position:0% +this is the homo ionicity the fact that +you have things such as macros what is + + align:start position:0% +you have things such as macros what is + + + align:start position:0% +you have things such as macros what is +there in in the conscious entity that is + + align:start position:0% +there in in the conscious entity that is + + + align:start position:0% +there in in the conscious entity that is +equivalent to the macro macros yes um + + align:start position:0% +equivalent to the macro macros yes um + + + align:start position:0% +equivalent to the macro macros yes um +well each of these levels is + + align:start position:0% + + + + align:start position:0% + +each of these levels are ways of + + align:start position:0% +each of these levels are ways of + + + align:start position:0% +each of these levels are ways of +combining things at the previous level + + align:start position:0% +combining things at the previous level + + + align:start position:0% +combining things at the previous level +so + + align:start position:0% +so + + + align:start position:0% +so +that the way I drew it at the top there + + align:start position:0% +that the way I drew it at the top there + + + align:start position:0% +that the way I drew it at the top there +are stories where + + align:start position:0% +are stories where + + + align:start position:0% +are stories where +you what's a story you mention + + align:start position:0% +you what's a story you mention + + + align:start position:0% +you what's a story you mention +some characters and you in a typical + + align:start position:0% +some characters and you in a typical + + + align:start position:0% +some characters and you in a typical +story then you say and here's a problem + + align:start position:0% +story then you say and here's a problem + + + align:start position:0% +story then you say and here's a problem +these characters + + align:start position:0% +these characters + + + align:start position:0% +these characters +encountered and here's what uh Joe did + + align:start position:0% +encountered and here's what uh Joe did + + + align:start position:0% +encountered and here's what uh Joe did +to solve the problem but it didn't work + + align:start position:0% +to solve the problem but it didn't work + + + align:start position:0% +to solve the problem but it didn't work +and here are the bugs + + align:start position:0% +and here are the bugs + + + align:start position:0% +and here are the bugs +and + + align:start position:0% +and + + + align:start position:0% +and +uh the reason that didn't work is that + + align:start position:0% +uh the reason that didn't work is that + + + align:start position:0% +uh the reason that didn't work is that +Mary was in the way so he killed her and + + align:start position:0% +Mary was in the way so he killed her and + + + align:start position:0% +Mary was in the way so he killed her and +then blah blah blah and so that's what + + align:start position:0% +then blah blah blah and so that's what + + + align:start position:0% +then blah blah blah and so that's what +stories + + align:start position:0% +stories + + + align:start position:0% +stories +are if you just write a series of + + align:start position:0% +are if you just write a series of + + + align:start position:0% +are if you just write a series of +sentences it's not a story um even + + align:start position:0% +sentences it's not a story um even + + + align:start position:0% +sentences it's not a story um even +though the New Yorker managed to make + + align:start position:0% +though the New Yorker managed to make + + + align:start position:0% +though the New Yorker managed to make +those into stories for about period of + + align:start position:0% +those into stories for about period of + + + align:start position:0% +those into stories for about period of +20 years uh but a typical story + + align:start position:0% +20 years uh but a typical story + + + align:start position:0% +20 years uh but a typical story +introduces a scene and it introduces a + + align:start position:0% +introduces a scene and it introduces a + + + align:start position:0% +introduces a scene and it introduces a +problem and then it produces a solution + + align:start position:0% +problem and then it produces a solution + + + align:start position:0% +problem and then it produces a solution +but the solution has a bug and then the + + align:start position:0% +but the solution has a bug and then the + + + align:start position:0% +but the solution has a bug and then the +rest of it is how you get around that + + align:start position:0% +rest of it is how you get around that + + + align:start position:0% +rest of it is how you get around that +bug and how you maybe change the goals + + align:start position:0% +bug and how you maybe change the goals + + + align:start position:0% +bug and how you maybe change the goals +in the worst case but um so a story is a + + align:start position:0% +in the worst case but um so a story is a + + + align:start position:0% +in the worst case but um so a story is a +series of + + align:start position:0% +series of + + + align:start position:0% +series of +incidents I wonder if I brought my death + + align:start position:0% +incidents I wonder if I brought my death + + + align:start position:0% +incidents I wonder if I brought my death +ray + + align:start position:0% + + + + align:start position:0% + +looks like I + + align:start position:0% + + + + align:start position:0% + +didn't + + align:start position:0% +didn't + + + align:start position:0% +didn't +oh but you don't need it with + + align:start position:0% + + + + align:start position:0% + +this you have to be here + + align:start position:0% + + + + align:start position:0% + +anyway uh but what's a story made of + + align:start position:0% +anyway uh but what's a story made of + + + align:start position:0% +anyway uh but what's a story made of +well there + + align:start position:0% +well there + + + align:start position:0% +well there +situations and you do something and you + + align:start position:0% +situations and you do something and you + + + align:start position:0% +situations and you do something and you +get a new + + align:start position:0% +get a new + + + align:start position:0% +get a new +situation so what's that that's + + align:start position:0% +situation so what's that that's + + + align:start position:0% +situation so what's that that's +what this thing I called a transframe + + align:start position:0% +what this thing I called a transframe + + + align:start position:0% +what this thing I called a transframe +which is a pair of + + align:start position:0% +which is a pair of + + + align:start position:0% +which is a pair of +situations and okay so what's an + + align:start position:0% +situations and okay so what's an + + + align:start position:0% +situations and okay so what's an +individual situation well it's a big + + align:start position:0% +individual situation well it's a big + + + align:start position:0% +individual situation well it's a big +network of nodes and + + align:start position:0% + + + + align:start position:0% + +relationships and + + align:start position:0% +relationships and + + + align:start position:0% +relationships and +uh I'm not sure why I have semantic + + align:start position:0% +uh I'm not sure why I have semantic + + + align:start position:0% +uh I'm not sure why I have semantic +networks down here rather than here + + align:start position:0% + + + + align:start position:0% + +but oh well a + + align:start position:0% +but oh well a + + + align:start position:0% +but oh well a +frame is + + align:start position:0% +frame is + + + align:start position:0% +frame is +a collection of + + align:start position:0% +a collection of + + + align:start position:0% +a collection of +representations that's sort of uh + + align:start position:0% +representations that's sort of uh + + + align:start position:0% +representations that's sort of uh +stereotyped or a canned uh that is might + + align:start position:0% +stereotyped or a canned uh that is might + + + align:start position:0% +stereotyped or a canned uh that is might +have a single word like + + align:start position:0% +have a single word like + + + align:start position:0% +have a single word like +uh + + align:start position:0% + + + + align:start position:0% + +oh just about any word uh breaking + + align:start position:0% +oh just about any word uh breaking + + + align:start position:0% +oh just about any word uh breaking +something if I say John broke the + + align:start position:0% +something if I say John broke the + + + align:start position:0% +something if I say John broke the +X you immediately say + + align:start position:0% +X you immediately say + + + align:start position:0% +X you immediately say +oh that's a transframe here's an object + + align:start position:0% +oh that's a transframe here's an object + + + align:start position:0% +oh that's a transframe here's an object +that had certain + + align:start position:0% +that had certain + + + align:start position:0% +that had certain +properties uh parts and relationships + + align:start position:0% +properties uh parts and relationships + + + align:start position:0% +properties uh parts and relationships +and it's been replaced by this thing + + align:start position:0% +and it's been replaced by this thing + + + align:start position:0% +and it's been replaced by this thing +which has uh most of the same objects + + align:start position:0% +which has uh most of the same objects + + + align:start position:0% +which has uh most of the same objects +except but different relationships or + + align:start position:0% +except but different relationships or + + + align:start position:0% +except but different relationships or +one of the objects is missing and has + + align:start position:0% +one of the objects is missing and has + + + align:start position:0% +one of the objects is missing and has +been replaced by another frame and so + + align:start position:0% + + + + align:start position:0% + +forth so one question is what's the + + align:start position:0% +forth so one question is what's the + + + align:start position:0% +forth so one question is what's the +relation so this this is a picture of uh + + align:start position:0% +relation so this this is a picture of uh + + + align:start position:0% +relation so this this is a picture of uh +cognitive + + align:start position:0% +cognitive + + + align:start position:0% +cognitive +representations everything is made of + + align:start position:0% +representations everything is made of + + + align:start position:0% +representations everything is made of +little parts and in + + align:start position:0% +little parts and in + + + align:start position:0% +little parts and in +the Society of mind I described the idea + + align:start position:0% +the Society of mind I described the idea + + + align:start position:0% +the Society of mind I described the idea +of Kines which is what's a + + align:start position:0% +of Kines which is what's a + + + align:start position:0% +of Kines which is what's a +Kine it's an imaginary structure in the + + align:start position:0% +Kine it's an imaginary structure in the + + + align:start position:0% +Kine it's an imaginary structure in the +nervous + + align:start position:0% +nervous + + + align:start position:0% +nervous +system which + + align:start position:0% +system which + + + align:start position:0% +system which +is there's really two kinds there's + + align:start position:0% +is there's really two kinds there's + + + align:start position:0% +is there's really two kinds there's +a there's a sort of perceptual Kline + + align:start position:0% +a there's a sort of perceptual Kline + + + align:start position:0% +a there's a sort of perceptual Kline +which is something that + + align:start position:0% +which is something that + + + align:start position:0% +which is something that +recognizes that say 10 features of a + + align:start position:0% +recognizes that say 10 features of a + + + align:start position:0% +recognizes that say 10 features of a +situation are present and + + align:start position:0% +situation are present and + + + align:start position:0% +situation are present and +if if these are all present then a + + align:start position:0% +if if these are all present then a + + + align:start position:0% +if if these are all present then a +certain uh bunch of neurons or neural + + align:start position:0% +certain uh bunch of neurons or neural + + + align:start position:0% +certain uh bunch of neurons or neural +activity goes on and on the other hand + + align:start position:0% +activity goes on and on the other hand + + + align:start position:0% +activity goes on and on the other hand +uh when you think of something like a + + align:start position:0% +uh when you think of something like a + + + align:start position:0% +uh when you think of something like a +word uh + + align:start position:0% +word uh + + + align:start position:0% +word uh +suppose suppose I say + + align:start position:0% +suppose suppose I say + + + align:start position:0% +suppose suppose I say +microphone then you're likely to think + + align:start position:0% +microphone then you're likely to think + + + align:start position:0% +microphone then you're likely to think +of + + align:start position:0% +of + + + align:start position:0% +of +something that has a business end which + + align:start position:0% +something that has a business end which + + + align:start position:0% +something that has a business end which +collects sounds and it uh has a stand or + + align:start position:0% +collects sounds and it uh has a stand or + + + align:start position:0% +collects sounds and it uh has a stand or +maybe it has a handle and if you're an + + align:start position:0% +maybe it has a handle and if you're an + + + align:start position:0% +maybe it has a handle and if you're an +engineer you know that probably it has a + + align:start position:0% +engineer you know that probably it has a + + + align:start position:0% +engineer you know that probably it has a +battery or transmitter or a + + align:start position:0% + + + + align:start position:0% + +wire so those are the things that I call + + align:start position:0% +wire so those are the things that I call + + + align:start position:0% +wire so those are the things that I call +frames or k lines really and uh anyway + + align:start position:0% +frames or k lines really and uh anyway + + + align:start position:0% +frames or k lines really and uh anyway +uh + + align:start position:0% +uh + + + align:start position:0% +uh +this chapter eight of the + + align:start position:0% + + + + align:start position:0% + +uh emotion machine talks about that and + + align:start position:0% +uh emotion machine talks about that and + + + align:start position:0% +uh emotion machine talks about that and +there's a lot of detail in the old book + + align:start position:0% +there's a lot of detail in the old book + + + align:start position:0% +there's a lot of detail in the old book +The Society of Mind about what K lines + + align:start position:0% +The Society of Mind about what K lines + + + align:start position:0% +The Society of Mind about what K lines +and things like that could be made + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% + + + + align:start position:0% + +now whatever those are and as far as I + + align:start position:0% +now whatever those are and as far as I + + + align:start position:0% +now whatever those are and as far as I +know + + align:start position:0% +know + + + align:start position:0% +know +uh no matter how hard you look you won't + + align:start position:0% +uh no matter how hard you look you won't + + + align:start position:0% +uh no matter how hard you look you won't +find any published theories of what in + + align:start position:0% +find any published theories of what in + + + align:start position:0% +find any published theories of what in +the nerve + + align:start position:0% +the nerve + + + align:start position:0% +the nerve +system is used to represent the things + + align:start position:0% +system is used to represent the things + + + align:start position:0% +system is used to represent the things +above the that sort of midline there + + align:start position:0% + + + + align:start position:0% + +of cortical columns I suspect that + + align:start position:0% +of cortical columns I suspect that + + + align:start position:0% +of cortical columns I suspect that +almost everything that the brain does + + align:start position:0% +almost everything that the brain does + + + align:start position:0% +almost everything that the brain does +that the human brain does that fish and + + align:start position:0% +that the human brain does that fish and + + + align:start position:0% +that the human brain does that fish and +uh and those lower animals or earlier + + align:start position:0% +uh and those lower animals or earlier + + + align:start position:0% +uh and those lower animals or earlier +animals I should say I'm not sure that + + align:start position:0% +animals I should say I'm not sure that + + + align:start position:0% +animals I should say I'm not sure that +higher and lower or makes any sense U + + align:start position:0% +higher and lower or makes any sense U + + + align:start position:0% +higher and lower or makes any sense U +are + + align:start position:0% +are + + + align:start position:0% +are +probably uh symbolic processes where it + + align:start position:0% +probably uh symbolic processes where it + + + align:start position:0% +probably uh symbolic processes where it +probably does more harm than good to + + align:start position:0% +probably does more harm than good to + + + align:start position:0% +probably does more harm than good to +have elaborate theories of what's the + + align:start position:0% +have elaborate theories of what's the + + + align:start position:0% +have elaborate theories of what's the +physiological chemistry of neurons but + + align:start position:0% +physiological chemistry of neurons but + + + align:start position:0% +physiological chemistry of neurons but +at some point we want to know uh what in + + align:start position:0% +at some point we want to know uh what in + + + align:start position:0% +at some point we want to know uh what in +fact uh the brain is made of a cortical + + align:start position:0% +fact uh the brain is made of a cortical + + + align:start position:0% +fact uh the brain is made of a cortical +column has uh a few 200 brain cells + + align:start position:0% +column has uh a few 200 brain cells + + + align:start position:0% +column has uh a few 200 brain cells +arranged and + + align:start position:0% +arranged and + + + align:start position:0% +arranged and +uh there are several projects around the + + align:start position:0% +uh there are several projects around the + + + align:start position:0% +uh there are several projects around the +world uh trying to take electron + + align:start position:0% +world uh trying to take electron + + + align:start position:0% +world uh trying to take electron +microscopes and pieces of mouse brain or + + align:start position:0% +microscopes and pieces of mouse brain or + + + align:start position:0% +microscopes and pieces of mouse brain or +cat + + align:start position:0% +cat + + + align:start position:0% +cat +brain and uh make a huge connection + + align:start position:0% +brain and uh make a huge connection + + + align:start position:0% +brain and uh make a huge connection +Matrix uh the problem is that the uh + + align:start position:0% +Matrix uh the problem is that the uh + + + align:start position:0% +Matrix uh the problem is that the uh +electron + + align:start position:0% +electron + + + align:start position:0% +electron +microscope even the electron microscope + + align:start position:0% +microscope even the electron microscope + + + align:start position:0% +microscope even the electron microscope +pictures still aren't good enough to + + align:start position:0% +pictures still aren't good enough to + + + align:start position:0% +pictures still aren't good enough to +show you at each syap perap what is + + align:start position:0% +show you at each syap perap what is + + + align:start position:0% +show you at each syap perap what is +probably going on eventually people will + + align:start position:0% +probably going on eventually people will + + + align:start position:0% +probably going on eventually people will +get theories of that and get slightly + + align:start position:0% +get theories of that and get slightly + + + align:start position:0% +get theories of that and get slightly +better instruments and I'm not sure that + + align:start position:0% +better instruments and I'm not sure that + + + align:start position:0% +better instruments and I'm not sure that +the present diagrams that they're + + align:start position:0% +the present diagrams that they're + + + align:start position:0% +the present diagrams that they're +producing are going to be much used to + + align:start position:0% +producing are going to be much used to + + + align:start position:0% +producing are going to be much used to +anyone yes it's a nice question this + + align:start position:0% +anyone yes it's a nice question this + + + align:start position:0% +anyone yes it's a nice question this +question might be a little bit difficult + + align:start position:0% +question might be a little bit difficult + + + align:start position:0% +question might be a little bit difficult +but um so I'm going to start from uh the + + align:start position:0% +but um so I'm going to start from uh the + + + align:start position:0% +but um so I'm going to start from uh the +goal being a difference between now is + + align:start position:0% +goal being a difference between now is + + + align:start position:0% +goal being a difference between now is +the now State and the desired State how + + align:start position:0% +the now State and the desired State how + + + align:start position:0% +the now State and the desired State how +do we reduce the difference yeah and + + align:start position:0% +do we reduce the difference yeah and + + + align:start position:0% +do we reduce the difference yeah and +yeah how do we get the difference and uh + + align:start position:0% +yeah how do we get the difference and uh + + + align:start position:0% +yeah how do we get the difference and uh +so uh and now I'm going to + + align:start position:0% +so uh and now I'm going to + + + align:start position:0% +so uh and now I'm going to +also uh take the fact of this the + + align:start position:0% +also uh take the fact of this the + + + align:start position:0% +also uh take the fact of this the +animals being different and I i' say + + align:start position:0% +animals being different and I i' say + + + align:start position:0% +animals being different and I i' say +that one of the biggest big + + align:start position:0% +that one of the biggest big + + + align:start position:0% +that one of the biggest big +differences is that we as people we can + + align:start position:0% +differences is that we as people we can + + + align:start position:0% +differences is that we as people we can +describe this + + align:start position:0% + + + + align:start position:0% + +differenes oh I use this it's not it + + align:start position:0% +differenes oh I use this it's not it + + + align:start position:0% +differenes oh I use this it's not it +actually is only good for the recording + + align:start position:0% +actually is only good for the recording + + + align:start position:0% +actually is only good for the recording +okay so we can describe these + + align:start position:0% +okay so we can describe these + + + align:start position:0% +okay so we can describe these +differences and talk with them talk + + align:start position:0% +differences and talk with them talk + + + align:start position:0% +differences and talk with them talk +about them with other people uh without + + align:start position:0% +about them with other people uh without + + + align:start position:0% +about them with other people uh without +having to act on those goals or + + align:start position:0% +having to act on those goals or + + + align:start position:0% +having to act on those goals or +hypothetical goals so if everything that + + align:start position:0% +hypothetical goals so if everything that + + + align:start position:0% +hypothetical goals so if everything that +has to do with goals is + + align:start position:0% +has to do with goals is + + + align:start position:0% +has to do with goals is +represented uh with a complex structure + + align:start position:0% +represented uh with a complex structure + + + align:start position:0% +represented uh with a complex structure +like this one and um and I want to + + align:start position:0% +like this one and um and I want to + + + align:start position:0% +like this one and um and I want to +implement it in a + + align:start position:0% +implement it in a + + + align:start position:0% +implement it in a +computer well I can just uh for every + + align:start position:0% +computer well I can just uh for every + + + align:start position:0% +computer well I can just uh for every +every hypothetical case that has to do + + align:start position:0% +every hypothetical case that has to do + + + align:start position:0% +every hypothetical case that has to do +with the solving a certain problem I can + + align:start position:0% +with the solving a certain problem I can + + + align:start position:0% +with the solving a certain problem I can +just make more copies in the + + align:start position:0% +just make more copies in the + + + align:start position:0% +just make more copies in the +memory but if I have a human brain then + + align:start position:0% +memory but if I have a human brain then + + + align:start position:0% +memory but if I have a human brain then +uh I don't know + + align:start position:0% +uh I don't know + + + align:start position:0% +uh I don't know +how convenient it it's to postulate that + + align:start position:0% +how convenient it it's to postulate that + + + align:start position:0% +how convenient it it's to postulate that +there is like a huge memory data Bank + + align:start position:0% +there is like a huge memory data Bank + + + align:start position:0% +there is like a huge memory data Bank +where you can make copies of uh + + align:start position:0% +where you can make copies of uh + + + align:start position:0% +where you can make copies of uh +everything that's going on or if you + + align:start position:0% +everything that's going on or if you + + + align:start position:0% +everything that's going on or if you +have have to assume some kind of um uh a + + align:start position:0% +have have to assume some kind of um uh a + + + align:start position:0% +have have to assume some kind of um uh a +huge collection of pointers and acting + + align:start position:0% +huge collection of pointers and acting + + + align:start position:0% +huge collection of pointers and acting +on those pointers so uh I just this is + + align:start position:0% +on those pointers so uh I just this is + + + align:start position:0% +on those pointers so uh I just this is +just a random point and I'd like to hear + + align:start position:0% +just a random point and I'd like to hear + + + align:start position:0% +just a random point and I'd like to hear +if you have any ideas on + + align:start position:0% +if you have any ideas on + + + align:start position:0% +if you have any ideas on +this that's a important question that + + align:start position:0% + + + + align:start position:0% + +uh we know quite a bit + + align:start position:0% + + + + align:start position:0% + +about the functions of some parts of the + + align:start position:0% +about the functions of some parts of the + + + align:start position:0% +about the functions of some parts of the +brain and so if you I don't think I've + + align:start position:0% +brain and so if you I don't think I've + + + align:start position:0% +brain and so if you I don't think I've +ever tried to draw a brain but + + align:start position:0% + + + + align:start position:0% + +uh there's a structure called the + + align:start position:0% +uh there's a structure called the + + + align:start position:0% +uh there's a structure called the +amydala + + align:start position:0% +amydala + + + align:start position:0% +amydala +how do you spell + + align:start position:0% + + + + align:start position:0% + +it I believe that means almond shaped is + + align:start position:0% +it I believe that means almond shaped is + + + align:start position:0% +it I believe that means almond shaped is +that right anybody have a Google + + align:start position:0% +that right anybody have a Google + + + align:start position:0% +that right anybody have a Google +handy + + align:start position:0% +handy + + + align:start position:0% +handy +and that's down here + + align:start position:0% +and that's down here + + + align:start position:0% +and that's down here +somewhere and it has the + + align:start position:0% +somewhere and it has the + + + align:start position:0% +somewhere and it has the +property that it uh contains the + + align:start position:0% +property that it uh contains the + + + align:start position:0% +property that it uh contains the +short-term memories so anything that's + + align:start position:0% +short-term memories so anything that's + + + align:start position:0% +short-term memories so anything that's +happened in the last couple of + + align:start position:0% +happened in the last couple of + + + align:start position:0% +happened in the last couple of +seconds is somehow represented here in a + + align:start position:0% +seconds is somehow represented here in a + + + align:start position:0% +seconds is somehow represented here in a +in + + align:start position:0% +in + + + align:start position:0% +in +a Trent + + align:start position:0% +a Trent + + + align:start position:0% +a Trent +way and uh everything that's happened in + + align:start position:0% +way and uh everything that's happened in + + + align:start position:0% +way and uh everything that's happened in +the last 20 minutes or so uh leaves + + align:start position:0% +the last 20 minutes or so uh leaves + + + align:start position:0% +the last 20 minutes or so uh leaves +traces in the amydala + + align:start position:0% +traces in the amydala + + + align:start position:0% +traces in the amydala +U so that if somebody's in an automobile + + align:start position:0% +U so that if somebody's in an automobile + + + align:start position:0% +U so that if somebody's in an automobile +accident or + + align:start position:0% +accident or + + + align:start position:0% +accident or +uh or is knocked out by a real powerful + + align:start position:0% +uh or is knocked out by a real powerful + + + align:start position:0% +uh or is knocked out by a real powerful +boxing + + align:start position:0% +boxing + + + align:start position:0% +boxing +punch then uh when you wake up later you + + align:start position:0% +punch then uh when you wake up later you + + + align:start position:0% +punch then uh when you wake up later you +can't remember anything that + + align:start position:0% +can't remember anything that + + + align:start position:0% +can't remember anything that +happened in about a 20 minutes or a half + + align:start position:0% +happened in about a 20 minutes or a half + + + align:start position:0% +happened in about a 20 minutes or a half +hour before the trauma so that's a very + + align:start position:0% +hour before the trauma so that's a very + + + align:start position:0% +hour before the trauma so that's a very +good experiment to try and uh there's a + + align:start position:0% +good experiment to try and uh there's a + + + align:start position:0% +good experiment to try and uh there's a +lot of + + align:start position:0% +lot of + + + align:start position:0% +lot of +evidence that this happens + + align:start position:0% +evidence that this happens + + + align:start position:0% +evidence that this happens +because uh the memories of the last half + + align:start position:0% +because uh the memories of the last half + + + align:start position:0% +because uh the memories of the last half +hour or so are stored in the conjecture + + align:start position:0% +hour or so are stored in the conjecture + + + align:start position:0% +hour or so are stored in the conjecture +is in a dynamic form maybe they huge + + align:start position:0% +is in a dynamic form maybe they huge + + + align:start position:0% +is in a dynamic form maybe they huge +numbers of Loops of neurons connected in + + align:start position:0% + + + + align:start position:0% + +circles or Circle + + align:start position:0% +circles or Circle + + + align:start position:0% +circles or Circle +anyway nobody really knows but uh if you + + align:start position:0% +anyway nobody really knows but uh if you + + + align:start position:0% +anyway nobody really knows but uh if you +have a bunch of neurons connected in a + + align:start position:0% +have a bunch of neurons connected in a + + + align:start position:0% +have a bunch of neurons connected in a +big circle maybe 20 or 30 of them then + + align:start position:0% +big circle maybe 20 or 30 of them then + + + align:start position:0% +big circle maybe 20 or 30 of them then +you can probably put uh 10 or 20 bits of + + align:start position:0% +you can probably put uh 10 or 20 bits of + + + align:start position:0% +you can probably put uh 10 or 20 bits of +information in form of different spaced + + align:start position:0% +information in form of different spaced + + + align:start position:0% +information in form of different spaced +pulses and a great mystery would be uh + + align:start position:0% +pulses and a great mystery would be uh + + + align:start position:0% +pulses and a great mystery would be uh +how does the brain manage to maintain + + align:start position:0% +how does the brain manage to maintain + + + align:start position:0% +how does the brain manage to maintain +that particular pattern of pulses for 10 + + align:start position:0% +that particular pattern of pulses for 10 + + + align:start position:0% +that particular pattern of pulses for 10 +or 20 minutes uh + + align:start position:0% +or 20 minutes uh + + + align:start position:0% +or 20 minutes uh +then um no one knows where it goes after + + align:start position:0% +then um no one knows where it goes after + + + align:start position:0% +then um no one knows where it goes after +the 20 minutes but uh if a person gets + + align:start position:0% +the 20 minutes but uh if a person gets + + + align:start position:0% +the 20 minutes but uh if a person gets +enough sleep that + + align:start position:0% +enough sleep that + + + align:start position:0% +enough sleep that +night uh then uh it turns out that it's + + align:start position:0% +night uh then uh it turns out that it's + + + align:start position:0% +night uh then uh it turns out that it's +no longer in the amydala and it's + + align:start position:0% +no longer in the amydala and it's + + + align:start position:0% +no longer in the amydala and it's +somewhere else in the brain and so one + + align:start position:0% +somewhere else in the brain and so one + + + align:start position:0% +somewhere else in the brain and so one +question + + align:start position:0% + + + + align:start position:0% + +is if there's all the stuff stored here + + align:start position:0% +is if there's all the stuff stored here + + + align:start position:0% +is if there's all the stuff stored here +and you might think of it as uh what's + + align:start position:0% +and you might think of it as uh what's + + + align:start position:0% +and you might think of it as uh what's +happened in the primary memory you know + + align:start position:0% +happened in the primary memory you know + + + align:start position:0% +happened in the primary memory you know +every computer uh starts out with uh + + align:start position:0% +every computer uh starts out with uh + + + align:start position:0% +every computer uh starts out with uh +maybe just uh the first computers had + + align:start position:0% +maybe just uh the first computers had + + + align:start position:0% +maybe just uh the first computers had +just two or three registers uh then they + + align:start position:0% +just two or three registers uh then they + + + align:start position:0% +just two or three registers uh then they +got 16 and 32 and I imagine how many + + align:start position:0% +got 16 and 32 and I imagine how many + + + align:start position:0% +got 16 and 32 and I imagine how many +fast registers are there in a modern + + align:start position:0% +fast registers are there in a modern + + + align:start position:0% +fast registers are there in a modern +computer I haven't been paying attention + + align:start position:0% +computer I haven't been paying attention + + + align:start position:0% +computer I haven't been paying attention +maybe 64 May whatever + + align:start position:0% +maybe 64 May whatever + + + align:start position:0% +maybe 64 May whatever +uh anyway they're gone but the next day + + align:start position:0% +uh anyway they're gone but the next day + + + align:start position:0% +uh anyway they're gone but the next day +if you've gotten some sleep you can + + align:start position:0% +if you've gotten some sleep you can + + + align:start position:0% +if you've gotten some sleep you can +retrieve them somehow they they're + + align:start position:0% +retrieve them somehow they they're + + + align:start position:0% +retrieve them somehow they they're +copied somewhere else as far as I know + + align:start position:0% +copied somewhere else as far as I know + + + align:start position:0% +copied somewhere else as far as I know +there is no theory of how the brain + + align:start position:0% +there is no theory of how the brain + + + align:start position:0% +there is no theory of how the brain +decides where to put them and how it + + align:start position:0% +decides where to put them and how it + + + align:start position:0% +decides where to put them and how it +records it and so forth something very + + align:start position:0% +records it and so forth something very + + + align:start position:0% +records it and so forth something very +strange about this big science lacking + + align:start position:0% +strange about this big science lacking + + + align:start position:0% +strange about this big science lacking +theories isn't + + align:start position:0% +theories isn't + + + align:start position:0% +theories isn't +there what would you do if you you were + + align:start position:0% +there what would you do if you you were + + + align:start position:0% +there what would you do if you you were +in a profession where they're talking + + align:start position:0% +in a profession where they're talking + + + align:start position:0% +in a profession where they're talking +about dozens and dozens of in mechanisms + + align:start position:0% +about dozens and dozens of in mechanisms + + + align:start position:0% +about dozens and dozens of in mechanisms +which clearly exist and you say how do + + align:start position:0% +which clearly exist and you say how do + + + align:start position:0% +which clearly exist and you say how do +you think that works and they say well I + + align:start position:0% +you think that works and they say well I + + + align:start position:0% +you think that works and they say well I +don't + + align:start position:0% +don't + + + align:start position:0% +don't +know none of my friends know either so I + + align:start position:0% +know none of my friends know either so I + + + align:start position:0% +know none of my friends know either so I +guess it's + + align:start position:0% + + + + align:start position:0% + +okay uh so we don't know how it picks a + + align:start position:0% +okay uh so we don't know how it picks a + + + align:start position:0% +okay uh so we don't know how it picks a +place to put them and we don't know how + + align:start position:0% +place to put them and we don't know how + + + align:start position:0% +place to put them and we don't know how +when you ask a question it gets back + + align:start position:0% +when you ask a question it gets back + + + align:start position:0% +when you ask a question it gets back +there so that you can repr proces it and + + align:start position:0% +there so that you can repr proces it and + + + align:start position:0% +there so that you can repr proces it and +talk about it but + + align:start position:0% +talk about it but + + + align:start position:0% +talk about it but +anyway uh so I made up these theories + + align:start position:0% +anyway uh so I made up these theories + + + align:start position:0% +anyway uh so I made up these theories +that things are stored in the form of K + + align:start position:0% +that things are stored in the form of K + + + align:start position:0% +that things are stored in the form of K +lines and uh uh there's a lot of + + align:start position:0% +lines and uh uh there's a lot of + + + align:start position:0% +lines and uh uh there's a lot of +discussion in the Society of + + align:start position:0% +discussion in the Society of + + + align:start position:0% +discussion in the Society of +mind about how klines probably have to + + align:start position:0% +mind about how klines probably have to + + + align:start position:0% +mind about how klines probably have to +work and so forth and if you look at the + + align:start position:0% +work and so forth and if you look at the + + + align:start position:0% +work and so forth and if you look at the +Society of + + align:start position:0% +Society of + + + align:start position:0% +Society of +Mind you'll in Amazon you'll find this + + align:start position:0% +Mind you'll in Amazon you'll find this + + + align:start position:0% +Mind you'll in Amazon you'll find this +enraging review by a neurologist named + + align:start position:0% +enraging review by a neurologist named + + + align:start position:0% +enraging review by a neurologist named +Robert restac who says he introduces + + align:start position:0% +Robert restac who says he introduces + + + align:start position:0% +Robert restac who says he introduces +these undefined terms called Kines and + + align:start position:0% +these undefined terms called Kines and + + + align:start position:0% +these undefined terms called Kines and +paranome and things like that of which + + align:start position:0% +paranome and things like that of which + + + align:start position:0% +paranome and things like that of which +there's whole chapters in the + + align:start position:0% +there's whole chapters in the + + + align:start position:0% +there's whole chapters in the +book so + + align:start position:0% +book so + + + align:start position:0% +book so +that's that's my my favorite review of + + align:start position:0% +that's that's my my favorite review of + + + align:start position:0% +that's that's my my favorite review of +the explaining the problem of getting + + align:start position:0% +the explaining the problem of getting + + + align:start position:0% +the explaining the problem of getting +Neuroscience to grow up yes who had a + + align:start position:0% +Neuroscience to grow up yes who had a + + + align:start position:0% +Neuroscience to grow up yes who had a +question yes um so um like one thing + + align:start position:0% +question yes um so um like one thing + + + align:start position:0% +question yes um so um like one thing +that like troubles me is um how do you + + align:start position:0% +that like troubles me is um how do you + + + align:start position:0% +that like troubles me is um how do you +think brain decides to do things like + + align:start position:0% +think brain decides to do things like + + + align:start position:0% +think brain decides to do things like +how do they decide what to do did you + + align:start position:0% +how do they decide what to do did you + + + align:start position:0% +how do they decide what to do did you +say well say you want to like relate a + + align:start position:0% +say well say you want to like relate a + + + align:start position:0% +say well say you want to like relate a +story so how but like hundreds of things + + align:start position:0% +story so how but like hundreds of things + + + align:start position:0% +story so how but like hundreds of things +happen like how do you select cuz how do + + align:start position:0% +happen like how do you select cuz how do + + + align:start position:0% +happen like how do you select cuz how do +you select what you tell and one not to + + align:start position:0% +you select what you tell and one not to + + + align:start position:0% +you select what you tell and one not to +it seems like you need some sort of like + + align:start position:0% +it seems like you need some sort of like + + + align:start position:0% +it seems like you need some sort of like +intentionality behind it but like how do + + align:start position:0% +intentionality behind it but like how do + + + align:start position:0% +intentionality behind it but like how do +we learn to do that in the first place + + align:start position:0% +we learn to do that in the first place + + + align:start position:0% +we learn to do that in the first place +almost like when you describe a goal you + + align:start position:0% +almost like when you describe a goal you + + + align:start position:0% +almost like when you describe a goal you +describe what's going on now and what + + align:start position:0% +describe what's going on now and what + + + align:start position:0% +describe what's going on now and what +the thing you want but then how do you + + align:start position:0% +the thing you want but then how do you + + + align:start position:0% +the thing you want but then how do you +you know how do you + + align:start position:0% +you know how do you + + + align:start position:0% +you know how do you +decide which few things to be considered + + align:start position:0% +decide which few things to be considered + + + align:start position:0% +decide which few things to be considered +oh you're asking a wonderful question + + align:start position:0% +oh you're asking a wonderful question + + + align:start position:0% +oh you're asking a wonderful question +which is uh after all if I were to talk + + align:start position:0% +which is uh after all if I were to talk + + + align:start position:0% +which is uh after all if I were to talk +to you for an + + align:start position:0% +to you for an + + + align:start position:0% +to you for an +hour uh about your goals you could tell + + align:start position:0% +hour uh about your goals you could tell + + + align:start position:0% +hour uh about your goals you could tell +me hundreds of goals that you have so + + align:start position:0% +me hundreds of goals that you have so + + + align:start position:0% +me hundreds of goals that you have so +the question is how how do you pick the + + align:start position:0% +the question is how how do you pick the + + + align:start position:0% +the question is how how do you pick the +one that you're thinking about now yeah + + align:start position:0% +one that you're thinking about now yeah + + + align:start position:0% +one that you're thinking about now yeah +like how do you represent also how do + + align:start position:0% +like how do you represent also how do + + + align:start position:0% +like how do you represent also how do +you represent like the priority of + + align:start position:0% +you represent like the priority of + + + align:start position:0% +you represent like the priority of +goals cuz you they almost they're almost + + align:start position:0% +goals cuz you they almost they're almost + + + align:start position:0% +goals cuz you they almost they're almost +described as like the friend machines + + align:start position:0% +described as like the friend machines + + + align:start position:0% +described as like the friend machines +has turned on all the time but you know + + align:start position:0% +has turned on all the time but you know + + + align:start position:0% +has turned on all the time but you know +how do you resolve conflicts how do you + + align:start position:0% +how do you resolve conflicts how do you + + + align:start position:0% +how do you resolve conflicts how do you +like decide which one to go first and + + align:start position:0% +like decide which one to go first and + + + align:start position:0% +like decide which one to go first and +which one's get first okay how do you + + align:start position:0% +which one's get first okay how do you + + + align:start position:0% +which one's get first okay how do you +represent the relations of your + + align:start position:0% +represent the relations of your + + + align:start position:0% +represent the relations of your +goals the standard theory for which + + align:start position:0% +goals the standard theory for which + + + align:start position:0% +goals the standard theory for which +there's no + + align:start position:0% +there's no + + + align:start position:0% +there's no +evidence is + + align:start position:0% +evidence is + + + align:start position:0% +evidence is +that in fact you use the word + + align:start position:0% +that in fact you use the word + + + align:start position:0% +that in fact you use the word +hierarchy + + align:start position:0% +hierarchy + + + align:start position:0% +hierarchy +so if you ask a naive person they'll + + align:start position:0% +so if you ask a naive person they'll + + + align:start position:0% +so if you ask a naive person they'll +give you a pretty good theory um uh + + align:start position:0% +give you a pretty good theory um uh + + + align:start position:0% +give you a pretty good theory um uh +completely wrong but good + + align:start position:0% +completely wrong but good + + + align:start position:0% +completely wrong but good +and the standard Theory says well + + align:start position:0% +and the standard Theory says well + + + align:start position:0% +and the standard Theory says well +there's one big + + align:start position:0% +there's one big + + + align:start position:0% +there's one big +goal at the + + align:start position:0% +goal at the + + + align:start position:0% +goal at the +top and you say what is it and uh some + + align:start position:0% +top and you say what is it and uh some + + + align:start position:0% +top and you say what is it and uh some +people would say well maybe it's to + + align:start position:0% + + + + align:start position:0% + +reproduce uh Darwin could but didn't + + align:start position:0% +reproduce uh Darwin could but didn't + + + align:start position:0% +reproduce uh Darwin could but didn't +argue that or + + align:start position:0% + + + + align:start position:0% + +or to + + align:start position:0% + + + + align:start position:0% + +survive or something like + + align:start position:0% +survive or something like + + + align:start position:0% +survive or something like +that okay so if you take that + + align:start position:0% +that okay so if you take that + + + align:start position:0% +that okay so if you take that +one then it's obvious what this what the + + align:start position:0% +one then it's obvious what this what the + + + align:start position:0% +one then it's obvious what this what the +next calls in the hierarchy would be I'm + + align:start position:0% +next calls in the hierarchy would be I'm + + + align:start position:0% +next calls in the hierarchy would be I'm +not saying this is how things work I + + align:start position:0% +not saying this is how things work I + + + align:start position:0% +not saying this is how things work I +don't think it does but so there's + + align:start position:0% +don't think it does but so there's + + + align:start position:0% +don't think it does but so there's +food and there's air + + align:start position:0% + + + + align:start position:0% + +air gets very high + + align:start position:0% +air gets very high + + + align:start position:0% +air gets very high +priority if you put a pillow over + + align:start position:0% +priority if you put a pillow over + + + align:start position:0% +priority if you put a pillow over +somebody their first priority is to + + align:start position:0% +somebody their first priority is to + + + align:start position:0% +somebody their first priority is to +breathe and they don't even think about + + align:start position:0% +breathe and they don't even think about + + + align:start position:0% +breathe and they don't even think about +eating for a long time so that's very + + align:start position:0% + + + + align:start position:0% + +nice I don't know what comes after + + align:start position:0% +nice I don't know what comes after + + + align:start position:0% +nice I don't know what comes after +that if you're out in the cold freezing + + align:start position:0% +that if you're out in the cold freezing + + + align:start position:0% +that if you're out in the cold freezing +then uh + + align:start position:0% +then uh + + + align:start position:0% +then uh +there's + + align:start position:0% +there's + + + align:start position:0% +there's +temp the nice thing about Brea air and + + align:start position:0% +temp the nice thing about Brea air and + + + align:start position:0% +temp the nice thing about Brea air and +temp is that if you have those goals you + + align:start position:0% +temp is that if you have those goals you + + + align:start position:0% +temp is that if you have those goals you +can satisfy them in parallel because in + + align:start position:0% +can satisfy them in parallel because in + + + align:start position:0% +can satisfy them in parallel because in +fact you don't need much of a hierarchy + + align:start position:0% +fact you don't need much of a hierarchy + + + align:start position:0% +fact you don't need much of a hierarchy +the breathing thing has this Servo + + align:start position:0% +the breathing thing has this Servo + + + align:start position:0% +the breathing thing has this Servo +mechanism where um if there's a higher + + align:start position:0% +mechanism where um if there's a higher + + + align:start position:0% +mechanism where um if there's a higher +level of CO2 than normal in your blood + + align:start position:0% +level of CO2 than normal in your blood + + + align:start position:0% +level of CO2 than normal in your blood +then the what is it the Vegas nerve or I + + align:start position:0% +then the what is it the Vegas nerve or I + + + align:start position:0% +then the what is it the Vegas nerve or I +don't + + align:start position:0% +don't + + + align:start position:0% +don't +know they know a lot about which part of + + align:start position:0% +know they know a lot about which part of + + + align:start position:0% +know they know a lot about which part of +the brain gets excited and raises your + + align:start position:0% +the brain gets excited and raises your + + + align:start position:0% +the brain gets excited and raises your +breathing rate or your heartbeat rate or + + align:start position:0% +breathing rate or your heartbeat rate or + + + align:start position:0% +breathing rate or your heartbeat rate or +uh my favorite animal is the sword + + align:start position:0% +uh my favorite animal is the sword + + + align:start position:0% +uh my favorite animal is the sword +fish + + align:start position:0% +fish + + + align:start position:0% +fish +because how many of you know about Brown + + align:start position:0% + + + + align:start position:0% + +fat Brown fat is a particular particular + + align:start position:0% +fat Brown fat is a particular particular + + + align:start position:0% +fat Brown fat is a particular particular +thing found in + + align:start position:0% +thing found in + + + align:start position:0% +thing found in +invertebrates and it's fat and it's + + align:start position:0% +invertebrates and it's fat and it's + + + align:start position:0% +invertebrates and it's fat and it's +brown I + + align:start position:0% +brown I + + + align:start position:0% +brown I +guess and it has the property that uh + + align:start position:0% +guess and it has the property that uh + + + align:start position:0% +guess and it has the property that uh +it's can be innervated by nerve fibers + + align:start position:0% +it's can be innervated by nerve fibers + + + align:start position:0% +it's can be innervated by nerve fibers +and they cause it to start burning + + align:start position:0% +and they cause it to start burning + + + align:start position:0% +and they cause it to start burning +calories and the swordfish is normally + + align:start position:0% +calories and the swordfish is normally + + + align:start position:0% +calories and the swordfish is normally +cold + + align:start position:0% +cold + + + align:start position:0% +cold +blooded but it its cored arteries have a + + align:start position:0% +blooded but it its cored arteries have a + + + align:start position:0% +blooded but it its cored arteries have a +big organ of brown fat around them just + + align:start position:0% +big organ of brown fat around them just + + + align:start position:0% +big organ of brown fat around them just +as the blood comes into the brain and if + + align:start position:0% +as the blood comes into the brain and if + + + align:start position:0% +as the blood comes into the brain and if +you turn on the brown fat it warms the + + align:start position:0% +you turn on the brown fat it warms the + + + align:start position:0% +you turn on the brown fat it warms the +brain and the IQ of the swordfish goes + + align:start position:0% +brain and the IQ of the swordfish goes + + + align:start position:0% +brain and the IQ of the swordfish goes +way up and it swims faster and uh uses + + align:start position:0% +way up and it swims faster and uh uses + + + align:start position:0% +way up and it swims faster and uh uses +better evasive tactics and + + align:start position:0% +better evasive tactics and + + + align:start position:0% +better evasive tactics and +uh I'm trying to remember there are a + + align:start position:0% +uh I'm trying to remember there are a + + + align:start position:0% +uh I'm trying to remember there are a +couple of other animals that are known + + align:start position:0% +couple of other animals that are known + + + align:start position:0% +couple of other animals that are known +to coldblooded animals that are known to + + align:start position:0% +to coldblooded animals that are known to + + + align:start position:0% +to coldblooded animals that are known to +have a warm-blooded brain that they can + + align:start position:0% +have a warm-blooded brain that they can + + + align:start position:0% +have a warm-blooded brain that they can +is that a great feature I + + align:start position:0% + + + + align:start position:0% + +wonder does our brain do a little bit of + + align:start position:0% +wonder does our brain do a little bit of + + + align:start position:0% +wonder does our brain do a little bit of +that + + align:start position:0% +that + + + align:start position:0% +that +uh I got lost telling funny + + align:start position:0% + + + + align:start position:0% + +stories so + + align:start position:0% +stories so + + + align:start position:0% +stories so +anyway uh this Kine idea is very simple + + align:start position:0% +anyway uh this Kine idea is very simple + + + align:start position:0% +anyway uh this Kine idea is very simple +it says that + + align:start position:0% +it says that + + + align:start position:0% +it says that +uh perhaps the way human memory works is + + align:start position:0% +uh perhaps the way human memory works is + + + align:start position:0% +uh perhaps the way human memory works is +that that uh here and there you + + align:start position:0% +that that uh here and there you + + + align:start position:0% +that that uh here and there you +have big collections of nerve fibers + + align:start position:0% +have big collections of nerve fibers + + + align:start position:0% +have big collections of nerve fibers +that go somewhere and go to lots of + + align:start position:0% +that go somewhere and go to lots of + + + align:start position:0% +that go somewhere and go to lots of +cells let's say thousands of these cells + + align:start position:0% +cells let's say thousands of these cells + + + align:start position:0% +cells let's say thousands of these cells +and each one is connected to some in + + align:start position:0% +and each one is connected to some in + + + align:start position:0% +and each one is connected to some in +some particular combination imagine + + align:start position:0% +some particular combination imagine + + + align:start position:0% +some particular combination imagine +there's a 100 wires + + align:start position:0% +there's a 100 wires + + + align:start position:0% +there's a 100 wires +here + + align:start position:0% +here + + + align:start position:0% +here +and each of these cells is connected to + + align:start position:0% +and each of these cells is connected to + + + align:start position:0% +and each of these cells is connected to +say 10 of those + + align:start position:0% +say 10 of those + + + align:start position:0% +say 10 of those +wires then how many + + align:start position:0% +wires then how many + + + align:start position:0% +wires then how many +different cells could you have for + + align:start position:0% +different cells could you have for + + + align:start position:0% +different cells could you have for +remembering different features of what's + + align:start position:0% +remembering different features of what's + + + align:start position:0% +remembering different features of what's +on this big bus bar well how many ways + + align:start position:0% +on this big bus bar well how many ways + + + align:start position:0% +on this big bus bar well how many ways +are there picking 10 things out of a 100 + + align:start position:0% +are there picking 10 things out of a 100 + + + align:start position:0% +are there picking 10 things out of a 100 +it's about 100 to the 10th + + align:start position:0% +it's about 100 to the 10th + + + align:start position:0% +it's about 100 to the 10th +power so here's a simple kind of memory + + align:start position:0% +power so here's a simple kind of memory + + + align:start position:0% +power so here's a simple kind of memory +where you + + align:start position:0% +where you + + + align:start position:0% +where you +have of course it'd be useless unless + + align:start position:0% +have of course it'd be useless unless + + + align:start position:0% +have of course it'd be useless unless +these bits by themselves have a little + + align:start position:0% +these bits by themselves have a little + + + align:start position:0% +these bits by themselves have a little +have some correlation with some useful + + align:start position:0% +have some correlation with some useful + + + align:start position:0% +have some correlation with some useful +concept and then at any particular time + + align:start position:0% +concept and then at any particular time + + + align:start position:0% +concept and then at any particular time +on this particular U bunch of fibers in + + align:start position:0% +on this particular U bunch of fibers in + + + align:start position:0% +on this particular U bunch of fibers in +the brain uh maybe 20 of these are + + align:start position:0% +the brain uh maybe 20 of these are + + + align:start position:0% +the brain uh maybe 20 of these are +turned + + align:start position:0% +turned + + + align:start position:0% +turned +on and if something very important has + + align:start position:0% +on and if something very important has + + + align:start position:0% +on and if something very important has +happened you send a signal to all these + + align:start position:0% +happened you send a signal to all these + + + align:start position:0% +happened you send a signal to all these +cells and say any of you cells who are + + align:start position:0% +cells and say any of you cells who are + + + align:start position:0% +cells and say any of you cells who are +seeing more than uh 10 or 15 of these 20 + + align:start position:0% +seeing more than uh 10 or 15 of these 20 + + + align:start position:0% +seeing more than uh 10 or 15 of these 20 +fibers at this moment uh should remember + + align:start position:0% +fibers at this moment uh should remember + + + align:start position:0% +fibers at this moment uh should remember +that and set themselves to do something + + align:start position:0% +that and set themselves to do something + + + align:start position:0% +that and set themselves to do something +next time you see that pattern something + + align:start position:0% +next time you see that pattern something + + + align:start position:0% +next time you see that pattern something +like that something has to decide which + + align:start position:0% +like that something has to decide which + + + align:start position:0% +like that something has to decide which +of these cells is going to copy at this + + align:start position:0% +of these cells is going to copy at this + + + align:start position:0% +of these cells is going to copy at this +time and so forth but so there's a + + align:start position:0% +time and so forth but so there's a + + + align:start position:0% +time and so forth but so there's a +theory of how + + align:start position:0% +theory of how + + + align:start position:0% +theory of how +memory kind of symbolic memory might + + align:start position:0% +memory kind of symbolic memory might + + + align:start position:0% +memory kind of symbolic memory might +work in the brain and I got this idea + + align:start position:0% +work in the brain and I got this idea + + + align:start position:0% +work in the brain and I got this idea +from a paper I don't remember what their + + align:start position:0% +from a paper I don't remember what their + + + align:start position:0% +from a paper I don't remember what their +their idea was but by uh David Waltz who + + align:start position:0% +their idea was but by uh David Waltz who + + + align:start position:0% +their idea was but by uh David Waltz who +uh and Jordan Pollock poock is + + align:start position:0% +uh and Jordan Pollock poock is + + + align:start position:0% +uh and Jordan Pollock poock is +a AI theorist at brandise I guess who in + + align:start position:0% +a AI theorist at brandise I guess who in + + + align:start position:0% +a AI theorist at brandise I guess who in +recent years has turned into some kind + + align:start position:0% +recent years has turned into some kind + + + align:start position:0% +recent years has turned into some kind +of artist and makes all sorts of + + align:start position:0% +of artist and makes all sorts of + + + align:start position:0% +of artist and makes all sorts of +beautiful things and simple robots that + + align:start position:0% +beautiful things and simple robots that + + + align:start position:0% +beautiful things and simple robots that +do this and that David Waltz + + align:start position:0% +do this and that David Waltz + + + align:start position:0% +do this and that David Waltz +uh uh search his web page sometime + + align:start position:0% +uh uh search his web page sometime + + + align:start position:0% +uh uh search his web page sometime +because he was here for many years as a + + align:start position:0% +because he was here for many years as a + + + align:start position:0% +because he was here for many years as a +graduate student and then developed + + align:start position:0% +graduate student and then developed + + + align:start position:0% +graduate student and then developed +beautiful theories of + + align:start position:0% +beautiful theories of + + + align:start position:0% +beautiful theories of +vision when did Dave move do you + + align:start position:0% +vision when did Dave move do you + + + align:start position:0% +vision when did Dave move do you +remember + + align:start position:0% +remember + + + align:start position:0% +remember +Pat + + align:start position:0% +Pat + + + align:start position:0% +Pat +anyway something like + + align:start position:0% +anyway something like + + + align:start position:0% +anyway something like +that + + align:start position:0% +that + + + align:start position:0% +that +uh but as far as I know I + + align:start position:0% +uh but as far as I know I + + + align:start position:0% +uh but as far as I know I +uh so I made up this Theory which is + + align:start position:0% +uh so I made up this Theory which is + + + align:start position:0% +uh so I made up this Theory which is +really uh copied from wals and pollic + + align:start position:0% +really uh copied from wals and pollic + + + align:start position:0% +really uh copied from wals and pollic +but simplified + + align:start position:0% +but simplified + + + align:start position:0% +but simplified +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +neatened up and that + + align:start position:0% +neatened up and that + + + align:start position:0% +neatened up and that +became uh then I went on and made other + + align:start position:0% +became uh then I went on and made other + + + align:start position:0% +became uh then I went on and made other +theories based on that but uh without + + align:start position:0% +theories based on that but uh without + + + align:start position:0% +theories based on that but uh without +them I would have been stuck in some + + align:start position:0% +them I would have been stuck in some + + + align:start position:0% +them I would have been stuck in some +condition reflex theory for a long time + + align:start position:0% +condition reflex theory for a long time + + + align:start position:0% +condition reflex theory for a long time +I suspect a minute yeah so you mentioned + + align:start position:0% +I suspect a minute yeah so you mentioned + + + align:start position:0% +I suspect a minute yeah so you mentioned +the role that the amigdala plays in + + align:start position:0% +the role that the amigdala plays in + + + align:start position:0% +the role that the amigdala plays in +storing like short-term memory um and + + align:start position:0% +storing like short-term memory um and + + + align:start position:0% +storing like short-term memory um and +you mentioned that you know like the + + align:start position:0% +you mentioned that you know like the + + + align:start position:0% +you mentioned that you know like the +members that are stor there are wiped + + align:start position:0% +members that are stor there are wiped + + + align:start position:0% +members that are stor there are wiped +out well that's a question no presumably + + align:start position:0% +out well that's a question no presumably + + + align:start position:0% +out well that's a question no presumably +uh as you grow up your aula gets better + + align:start position:0% +uh as you grow up your aula gets better + + + align:start position:0% +uh as you grow up your aula gets better +at uh learning what to recognize but + + align:start position:0% +at uh learning what to recognize but + + + align:start position:0% +at uh learning what to recognize but +I've never seen any discussion or theory + + align:start position:0% +I've never seen any discussion or theory + + + align:start position:0% +I've never seen any discussion or theory +of how much of your short-term memory is + + align:start position:0% +of how much of your short-term memory is + + + align:start position:0% +of how much of your short-term memory is +how do you learn and develop and and get + + align:start position:0% +how do you learn and develop and and get + + + align:start position:0% +how do you learn and develop and and get +better at remembering things that are + + align:start position:0% +better at remembering things that are + + + align:start position:0% +better at remembering things that are +worth + + align:start position:0% +worth + + + align:start position:0% +worth +remembering sorry go ahead my question + + align:start position:0% +remembering sorry go ahead my question + + + align:start position:0% +remembering sorry go ahead my question +is saying that so the what whatever + + align:start position:0% +is saying that so the what whatever + + + align:start position:0% +is saying that so the what whatever +memories are stored in the migdala + + align:start position:0% +memories are stored in the migdala + + + align:start position:0% +memories are stored in the migdala +during um whatever stor in the mdala is + + align:start position:0% +during um whatever stor in the mdala is + + + align:start position:0% +during um whatever stor in the mdala is +wiped out um after you sleep right what + + align:start position:0% +wiped out um after you sleep right what + + + align:start position:0% +wiped out um after you sleep right what +sort of implications does this have + + align:start position:0% +sort of implications does this have + + + align:start position:0% +sort of implications does this have +about uh remembering dreams because my + + align:start position:0% +about uh remembering dreams because my + + + align:start position:0% +about uh remembering dreams because my +understanding is that um you know after + + align:start position:0% +understanding is that um you know after + + + align:start position:0% +understanding is that um you know after +you have like a locid + + align:start position:0% +you have like a locid + + + align:start position:0% +you have like a locid +dream uh like you tend to forget like + + align:start position:0% +dream uh like you tend to forget like + + + align:start position:0% +dream uh like you tend to forget like +the memories of the dream are wiped out + + align:start position:0% +the memories of the dream are wiped out + + + align:start position:0% +the memories of the dream are wiped out +after a certain point later on in the + + align:start position:0% +after a certain point later on in the + + + align:start position:0% +after a certain point later on in the +day + + align:start position:0% +day + + + align:start position:0% +day +so what sort of implications does it + + align:start position:0% +so what sort of implications does it + + + align:start position:0% +so what sort of implications does it +have on the ability of people to + + align:start position:0% +have on the ability of people to + + + align:start position:0% +have on the ability of people to +remember that good question + + align:start position:0% + + + + align:start position:0% + +uh there have been some theories but the + + align:start position:0% +uh there have been some theories but the + + + align:start position:0% +uh there have been some theories but the +I think I mentioned Freud's theory which + + align:start position:0% +I think I mentioned Freud's theory which + + + align:start position:0% +I think I mentioned Freud's theory which +is that you're not remembering anything + + align:start position:0% +is that you're not remembering anything + + + align:start position:0% +is that you're not remembering anything +when you wake up you make up the + + align:start position:0% + + + + align:start position:0% + +dream and uh I think that's uh surely + + align:start position:0% +dream and uh I think that's uh surely + + + align:start position:0% +dream and uh I think that's uh surely +completely wrong uh but Freud made it up + + align:start position:0% +completely wrong uh but Freud made it up + + + align:start position:0% +completely wrong uh but Freud made it up +because he was mad at + + align:start position:0% + + + + align:start position:0% + +Yung Yung had some Yung had a theory + + align:start position:0% +Yung Yung had some Yung had a theory + + + align:start position:0% +Yung Yung had some Yung had a theory +that people have telepathic connections + + align:start position:0% +that people have telepathic connections + + + align:start position:0% +that people have telepathic connections +with other people and so uh uh he had + + align:start position:0% +with other people and so uh uh he had + + + align:start position:0% +with other people and so uh uh he had +been Freud student or uh disciple for + + align:start position:0% +been Freud student or uh disciple for + + + align:start position:0% +been Freud student or uh disciple for +some years and then he went + + align:start position:0% +some years and then he went + + + align:start position:0% +some years and then he went +uh mystical and Freud went up the wall + + align:start position:0% +uh mystical and Freud went up the wall + + + align:start position:0% +uh mystical and Freud went up the wall +because uh young was obviously very + + align:start position:0% +because uh young was obviously very + + + align:start position:0% +because uh young was obviously very +smart + + align:start position:0% + + + + align:start position:0% + +imaginative I'm trying to think if I've + + align:start position:0% +imaginative I'm trying to think if I've + + + align:start position:0% +imaginative I'm trying to think if I've +had a very good student who turned + + align:start position:0% +had a very good student who turned + + + align:start position:0% +had a very good student who turned +mystical + + align:start position:0% +mystical + + + align:start position:0% +mystical +but one or two but not not like + + align:start position:0% +but one or two but not not like + + + align:start position:0% +but one or two but not not like +that anyway uh that's a great question + + align:start position:0% +that anyway uh that's a great question + + + align:start position:0% +that anyway uh that's a great question +and when I said things hang around in + + align:start position:0% +and when I said things hang around in + + + align:start position:0% +and when I said things hang around in +the amigdala for 20 minutes U that's + + align:start position:0% +the amigdala for 20 minutes U that's + + + align:start position:0% +the amigdala for 20 minutes U that's +that's just some things and uh + + align:start position:0% +that's just some things and uh + + + align:start position:0% +that's just some things and uh +clearly they have to + + align:start position:0% +clearly they have to + + + align:start position:0% +clearly they have to +hang if it takes sleep the next night + + align:start position:0% +hang if it takes sleep the next night + + + align:start position:0% +hang if it takes sleep the next night +which is8 hours or 16 hours later to uh + + align:start position:0% +which is8 hours or 16 hours later to uh + + + align:start position:0% +which is8 hours or 16 hours later to uh +solidify it or to copy it in some way + + align:start position:0% +solidify it or to copy it in some way + + + align:start position:0% +solidify it or to copy it in some way +into the other parts of the brain it + + align:start position:0% +into the other parts of the brain it + + + align:start position:0% +into the other parts of the brain it +must still be in the amydala or + + align:start position:0% +must still be in the amydala or + + + align:start position:0% +must still be in the amydala or +somewhere so in fact + + align:start position:0% +somewhere so in fact + + + align:start position:0% +somewhere so in fact +maybe maybe there's the amydala and some + + align:start position:0% +maybe maybe there's the amydala and some + + + align:start position:0% +maybe maybe there's the amydala and some +other other parts of the brain that have + + align:start position:0% +other other parts of the brain that have + + + align:start position:0% +other other parts of the brain that have +haven't been identified that contain + + align:start position:0% +haven't been identified that contain + + + align:start position:0% +haven't been identified that contain +uh slightly different copies of the + + align:start position:0% +uh slightly different copies of the + + + align:start position:0% +uh slightly different copies of the +memories for a longer time and so forth + + align:start position:0% +memories for a longer time and so forth + + + align:start position:0% +memories for a longer time and so forth +so uh who knows where and how they work + + align:start position:0% +so uh who knows where and how they work + + + align:start position:0% +so uh who knows where and how they work +U maybe the language centers remember uh + + align:start position:0% +U maybe the language centers remember uh + + + align:start position:0% +U maybe the language centers remember uh +paragraphs of things that you've heard + + align:start position:0% +paragraphs of things that you've heard + + + align:start position:0% +paragraphs of things that you've heard +or said uh for some time and so forth I + + align:start position:0% +or said uh for some time and so forth I + + + align:start position:0% +or said uh for some time and so forth I +don't think anybody really knows much + + align:start position:0% +don't think anybody really knows much + + + align:start position:0% +don't think anybody really knows much +about uh they're very sure about the + + align:start position:0% +about uh they're very sure about the + + + align:start position:0% +about uh they're very sure about the +amydala + + align:start position:0% +amydala + + + align:start position:0% +amydala +because uh injuring the amydala + + align:start position:0% +because uh injuring the amydala + + + align:start position:0% +because uh injuring the amydala +or uh or injecting novacaine into a + + align:start position:0% +or uh or injecting novacaine into a + + + align:start position:0% +or uh or injecting novacaine into a +blood vessel that goes there has such a + + align:start position:0% +blood vessel that goes there has such a + + + align:start position:0% +blood vessel that goes there has such a +dramatic effect on you just can't + + align:start position:0% +dramatic effect on you just can't + + + align:start position:0% +dramatic effect on you just can't +remember anything for that short period + + align:start position:0% +remember anything for that short period + + + align:start position:0% +remember anything for that short period +of half hour or so but there must be + + align:start position:0% +of half hour or so but there must be + + + align:start position:0% +of half hour or so but there must be +lots of + + align:start position:0% +lots of + + + align:start position:0% +lots of +other maybe memories are stored in 10 + + align:start position:0% +other maybe memories are stored in 10 + + + align:start position:0% +other maybe memories are stored in 10 +different ways in 10 different parts of + + align:start position:0% +different ways in 10 different parts of + + + align:start position:0% +different ways in 10 different parts of +the brain brain who knows one problem + + align:start position:0% +the brain brain who knows one problem + + + align:start position:0% +the brain brain who knows one problem +that I think I mentioned is that uh + + align:start position:0% +that I think I mentioned is that uh + + + align:start position:0% +that I think I mentioned is that uh +although a great deal has been learned + + align:start position:0% +although a great deal has been learned + + + align:start position:0% +although a great deal has been learned +about the brain from uh modern scanning + + align:start position:0% +about the brain from uh modern scanning + + + align:start position:0% +about the brain from uh modern scanning +techniques uh almost every result that + + align:start position:0% +techniques uh almost every result that + + + align:start position:0% +techniques uh almost every result that +people talk about is are is obtained by + + align:start position:0% +people talk about is are is obtained by + + + align:start position:0% +people talk about is are is obtained by +turning up the contrast so that most of + + align:start position:0% +turning up the contrast so that most of + + + align:start position:0% +turning up the contrast so that most of +the brain is dark and nerve centers that + + align:start position:0% +the brain is dark and nerve centers that + + + align:start position:0% +the brain is dark and nerve centers that +are uh highly active show up in your you + + align:start position:0% +are uh highly active show up in your you + + + align:start position:0% +are uh highly active show up in your you +know you've Al all seen these pictures + + align:start position:0% +know you've Al all seen these pictures + + + align:start position:0% +know you've Al all seen these pictures +which show three or four places in the + + align:start position:0% +which show three or four places in the + + + align:start position:0% +which show three or four places in the +brain lighting + + align:start position:0% +brain lighting + + + align:start position:0% +brain lighting +up uh well there's a good chance that + + align:start position:0% +up uh well there's a good chance that + + + align:start position:0% +up uh well there's a good chance that +for any particular event there might be + + align:start position:0% +for any particular event there might be + + + align:start position:0% +for any particular event there might be +10 or 20 places that have just increased + + align:start position:0% +10 or 20 places that have just increased + + + align:start position:0% +10 or 20 places that have just increased +a little bit and uh when they turn up + + align:start position:0% +a little bit and uh when they turn up + + + align:start position:0% +a little bit and uh when they turn up +the contrast all that evidence is lost + + align:start position:0% +the contrast all that evidence is lost + + + align:start position:0% +the contrast all that evidence is lost +because uh those regions all become + + align:start position:0% +because uh those regions all become + + + align:start position:0% +because uh those regions all become +black or whatever anyway yeah exper of + + align:start position:0% +black or whatever anyway yeah exper of + + + align:start position:0% +black or whatever anyway yeah exper of +that I would go as far as to say that + + align:start position:0% +that I would go as far as to say that + + + align:start position:0% +that I would go as far as to say that +probably if they have a finding that + + align:start position:0% +probably if they have a finding that + + + align:start position:0% +probably if they have a finding that +where there are no specific + + align:start position:0% +where there are no specific + + + align:start position:0% +where there are no specific +areas so you have a pretty uniform + + align:start position:0% +areas so you have a pretty uniform + + + align:start position:0% +areas so you have a pretty uniform +picture of what of the changes in + + align:start position:0% +picture of what of the changes in + + + align:start position:0% +picture of what of the changes in +metabolism then you don't uh make + + align:start position:0% +metabolism then you don't uh make + + + align:start position:0% +metabolism then you don't uh make +theories or you don't publish that + + align:start position:0% +theories or you don't publish that + + + align:start position:0% +theories or you don't publish that +result because you don't have any clear + + align:start position:0% +result because you don't have any clear + + + align:start position:0% +result because you don't have any clear +areas where to point that and then + + align:start position:0% +areas where to point that and then + + + align:start position:0% +areas where to point that and then +nobody knows that okay that particular + + align:start position:0% +nobody knows that okay that particular + + + align:start position:0% +nobody knows that okay that particular +thing was actually exciting to hold all + + align:start position:0% +thing was actually exciting to hold all + + + align:start position:0% +thing was actually exciting to hold all +of all of brain that's just a casess + + align:start position:0% +of all of brain that's just a casess + + + align:start position:0% +of all of brain that's just a casess +yeah could be some things involve very + + align:start position:0% +yeah could be some things involve very + + + align:start position:0% +yeah could be some things involve very +large amounts of brain but I'm inclined + + align:start position:0% +large amounts of brain but I'm inclined + + + align:start position:0% +large amounts of brain but I'm inclined +to doubt it probably probably you want + + align:start position:0% +to doubt it probably probably you want + + + align:start position:0% +to doubt it probably probably you want +to turn a lot of things off most of the + + align:start position:0% +to turn a lot of things off most of the + + + align:start position:0% +to turn a lot of things off most of the +time so they don't fill up with random + + align:start position:0% +time so they don't fill up with random + + + align:start position:0% +time so they don't fill up with random +garbage who knows yes just want to + + align:start position:0% +garbage who knows yes just want to + + + align:start position:0% +garbage who knows yes just want to +follow up on that why do you think that + + align:start position:0% +follow up on that why do you think that + + + align:start position:0% +follow up on that why do you think that +hierarchy of goals is naive and like + + align:start position:0% +hierarchy of goals is naive and like + + + align:start position:0% +hierarchy of goals is naive and like +more specific features of goals do you + + align:start position:0% +more specific features of goals do you + + + align:start position:0% +more specific features of goals do you +think that structure doesn't achieve oh + + align:start position:0% +think that structure doesn't achieve oh + + + align:start position:0% +think that structure doesn't achieve oh +I didn't finish that did I + + align:start position:0% + + + + align:start position:0% + +um she's + + align:start position:0% +um she's + + + align:start position:0% +um she's +asking I started to say what's the + + align:start position:0% +asking I started to say what's the + + + align:start position:0% +asking I started to say what's the +hierarchy of goals but it looks like I + + align:start position:0% +hierarchy of goals but it looks like I + + + align:start position:0% +hierarchy of goals but it looks like I +got stuck on the well-defined + + align:start position:0% +got stuck on the well-defined + + + align:start position:0% +got stuck on the well-defined +instinctive goals that you need to stay + + align:start position:0% +instinctive goals that you need to stay + + + align:start position:0% +instinctive goals that you need to stay +alive and uh I guess + + align:start position:0% +alive and uh I guess + + + align:start position:0% +alive and uh I guess +my answer is I don't have any good + + align:start position:0% +my answer is I don't have any good + + + align:start position:0% +my answer is I don't have any good +theories of + + align:start position:0% +theories of + + + align:start position:0% +theories of +how how you do that at any time uh when + + align:start position:0% +how how you do that at any time uh when + + + align:start position:0% +how how you do that at any time uh when +you're talking to somebody you usually + + align:start position:0% +you're talking to somebody you usually + + + align:start position:0% +you're talking to somebody you usually +have a couple of very clear goals + + align:start position:0% +have a couple of very clear goals + + + align:start position:0% +have a couple of very clear goals +like I want to explain this uh I want + + align:start position:0% +like I want to explain this uh I want + + + align:start position:0% +like I want to explain this uh I want +this other person to understand this for + + align:start position:0% +this other person to understand this for + + + align:start position:0% +this other person to understand this for +this reason + + align:start position:0% +this reason + + + align:start position:0% +this reason +uh I'm having trouble maybe I have to + + align:start position:0% +uh I'm having trouble maybe I have to + + + align:start position:0% +uh I'm having trouble maybe I have to +get his or her attention by and then you + + align:start position:0% +get his or her attention by and then you + + + align:start position:0% +get his or her attention by and then you +get a subgoal of uh doing some social + + align:start position:0% +get a subgoal of uh doing some social + + + align:start position:0% +get a subgoal of uh doing some social +thing to convince them to listen to you + + align:start position:0% +thing to convince them to listen to you + + + align:start position:0% +thing to convince them to listen to you +and all sorts of things but + + align:start position:0% + + + + align:start position:0% + +uh I just don't have a a nice picture + + align:start position:0% +uh I just don't have a a nice picture + + + align:start position:0% +uh I just don't have a a nice picture +when you're writing a AI program you + + align:start position:0% +when you're writing a AI program you + + + align:start position:0% +when you're writing a AI program you +usually have goals and subg goals in a + + align:start position:0% +usually have goals and subg goals in a + + + align:start position:0% +usually have goals and subg goals in a +very clear Arrangement like the uh + + align:start position:0% +very clear Arrangement like the uh + + + align:start position:0% +very clear Arrangement like the uh +theorum improving programs are wonderful + + align:start position:0% +theorum improving programs are wonderful + + + align:start position:0% +theorum improving programs are wonderful +because you've you've proved some kind + + align:start position:0% +because you've you've proved some kind + + + align:start position:0% +because you've you've proved some kind +of expression but the particular theorem + + align:start position:0% +of expression but the particular theorem + + + align:start position:0% +of expression but the particular theorem +you are trying to prove has another + + align:start position:0% +you are trying to prove has another + + + align:start position:0% +you are trying to prove has another +condition which is different from this + + align:start position:0% +condition which is different from this + + + align:start position:0% +condition which is different from this +condition and + + align:start position:0% +condition and + + + align:start position:0% +condition and +uh people have gone quite far in making + + align:start position:0% +uh people have gone quite far in making + + + align:start position:0% +uh people have gone quite far in making +models + + align:start position:0% +models + + + align:start position:0% +models +of + + align:start position:0% +of + + + align:start position:0% +of +um something like theorem proving where + + align:start position:0% +um something like theorem proving where + + + align:start position:0% +um something like theorem proving where +the world is very simple if you're + + align:start position:0% +the world is very simple if you're + + + align:start position:0% +the world is very simple if you're +proving something in Geometry or group + + align:start position:0% +proving something in Geometry or group + + + align:start position:0% +proving something in Geometry or group +Theory or or a little fragment of + + align:start position:0% +Theory or or a little fragment of + + + align:start position:0% +Theory or or a little fragment of +mathematics then there're only five or + + align:start position:0% +mathematics then there're only five or + + + align:start position:0% +mathematics then there're only five or + + align:start position:0% + + + align:start position:0% +assumptions hanging around and so you + + align:start position:0% +assumptions hanging around and so you + + + align:start position:0% +assumptions hanging around and so you +could actually plan a little bit of + + align:start position:0% +could actually plan a little bit of + + + align:start position:0% +could actually plan a little bit of +exhaustive search to go three or four + + align:start position:0% +exhaustive search to go three or four + + + align:start position:0% +exhaustive search to go three or four +levels and then you would do something + + align:start position:0% +levels and then you would do something + + + align:start position:0% +levels and then you would do something +like in a chest program of over time + + align:start position:0% +like in a chest program of over time + + + align:start position:0% +like in a chest program of over time +discovering it never pays to uh explore + + align:start position:0% +discovering it never pays to uh explore + + + align:start position:0% +discovering it never pays to uh explore +a tree that has this feature because of + + align:start position:0% +a tree that has this feature because of + + + align:start position:0% +a tree that has this feature because of +whatever yes are goals relevant + + align:start position:0% +whatever yes are goals relevant + + + align:start position:0% +whatever yes are goals relevant +like we always have goals or it's just + + align:start position:0% +like we always have goals or it's just + + + align:start position:0% +like we always have goals or it's just +like something right like when I play + + align:start position:0% +like something right like when I play + + + align:start position:0% +like something right like when I play +chance maybe I have a goal but why + + align:start position:0% +chance maybe I have a goal but why + + + align:start position:0% +chance maybe I have a goal but why +should I have a goal life why isn't that + + align:start position:0% +should I have a goal life why isn't that + + + align:start position:0% +should I have a goal life why isn't that +like maybe I don't know that goal of + + align:start position:0% +like maybe I don't know that goal of + + + align:start position:0% +like maybe I don't know that goal of +reproduce is + + align:start position:0% +reproduce is + + + align:start position:0% +reproduce is +created at some points of my life or + + align:start position:0% +created at some points of my life or + + + align:start position:0% +created at some points of my life or +like I don't know why why are gos + + align:start position:0% +like I don't know why why are gos + + + align:start position:0% +like I don't know why why are gos +important + + align:start position:0% +important + + + align:start position:0% +important +well the survival goals are important + + align:start position:0% +well the survival goals are important + + + align:start position:0% +well the survival goals are important +because if you cross the street without + + align:start position:0% +because if you cross the street without + + + align:start position:0% +because if you cross the street without +looking + + align:start position:0% +looking + + + align:start position:0% +looking +you you could do that about 20 times + + align:start position:0% +you you could do that about 20 times + + + align:start position:0% +you you could do that about 20 times +before you're + + align:start position:0% + + + + align:start position:0% + +dead so why are + + align:start position:0% +dead so why are + + + align:start position:0% +dead so why are +there + + align:start position:0% +there + + + align:start position:0% +there +uh the survival Go I mean well if you + + align:start position:0% +uh the survival Go I mean well if you + + + align:start position:0% +uh the survival Go I mean well if you +don't make a living you'll starve so now + + align:start position:0% +don't make a living you'll starve so now + + + align:start position:0% +don't make a living you'll starve so now +you have to if you've if you've + + align:start position:0% +you have to if you've if you've + + + align:start position:0% +you have to if you've if you've +committed yourself to being a + + align:start position:0% +committed yourself to being a + + + align:start position:0% +committed yourself to being a +mathematician now you have to be a good + + align:start position:0% +mathematician now you have to be a good + + + align:start position:0% +mathematician now you have to be a good +mathematician or else you'll starve and + + align:start position:0% +mathematician or else you'll starve and + + + align:start position:0% +mathematician or else you'll starve and +so + + align:start position:0% +so + + + align:start position:0% +so +forth I was a pretty good mathematician + + align:start position:0% +forth I was a pretty good mathematician + + + align:start position:0% +forth I was a pretty good mathematician +only my goal is I had to be the best + + align:start position:0% +only my goal is I had to be the best + + + align:start position:0% +only my goal is I had to be the best +mathematician so I + + align:start position:0% + + + + align:start position:0% + +quit you don't want to have a goal you + + align:start position:0% +quit you don't want to have a goal you + + + align:start position:0% +quit you don't want to have a goal you +can't + + align:start position:0% +can't + + + align:start position:0% +can't +achieve yeah but is that part of inell + + align:start position:0% +achieve yeah but is that part of inell + + + align:start position:0% +achieve yeah but is that part of inell +like well a lot of people do have one so + + align:start position:0% +like well a lot of people do have one so + + + align:start position:0% +like well a lot of people do have one so +it eats up a lot of their time and + + align:start position:0% +it eats up a lot of their time and + + + align:start position:0% +it eats up a lot of their time and +they're wasting + + align:start position:0% +they're wasting + + + align:start position:0% +they're wasting +it I'm not sure what the question is how + + align:start position:0% +it I'm not sure what the question is how + + + align:start position:0% +it I'm not sure what the question is how +do you make + + align:start position:0% +do you make + + + align:start position:0% +do you make +a I think the feature of humans is that + + align:start position:0% +a I think the feature of humans is that + + + align:start position:0% +a I think the feature of humans is that +they're they sort of general purpose so + + align:start position:0% +they're they sort of general purpose so + + + align:start position:0% +they're they sort of general purpose so +there are a lot of things people do uh + + align:start position:0% +there are a lot of things people do uh + + + align:start position:0% +there are a lot of things people do uh +which which are bad things to + + align:start position:0% +which which are bad things to + + + align:start position:0% +which which are bad things to +do you can't justify them uh you could + + align:start position:0% +do you can't justify them uh you could + + + align:start position:0% +do you can't justify them uh you could +think of people as part of a huge search + + align:start position:0% +think of people as part of a huge search + + + align:start position:0% +think of people as part of a huge search +Project process and as a + + align:start position:0% +Project process and as a + + + align:start position:0% +Project process and as a +species or a genetic system it pays to + + align:start position:0% +species or a genetic system it pays to + + + align:start position:0% +species or a genetic system it pays to +have a few crazy ones every now and then + + align:start position:0% +have a few crazy ones every now and then + + + align:start position:0% +have a few crazy ones every now and then +because if the environment suddenly + + align:start position:0% +because if the environment suddenly + + + align:start position:0% +because if the environment suddenly +changes maybe they'll be the only ones + + align:start position:0% +changes maybe they'll be the only ones + + + align:start position:0% +changes maybe they'll be the only ones +who + + align:start position:0% +who + + + align:start position:0% +who +survive that's William Calvin's question + + align:start position:0% +survive that's William Calvin's question + + + align:start position:0% +survive that's William Calvin's question +how come people evolved intelligence so + + align:start position:0% +how come people evolved intelligence so + + + align:start position:0% +how come people evolved intelligence so +rapidly in five million + + align:start position:0% +rapidly in five million + + + align:start position:0% +rapidly in five million +years and + + align:start position:0% +years and + + + align:start position:0% +years and +uh he attributes it partly + + align:start position:0% +uh he attributes it partly + + + align:start position:0% +uh he attributes it partly +to 10 five or how many periods of global + + align:start position:0% +to 10 five or how many periods of global + + + align:start position:0% +to 10 five or how many periods of global +cooling were there it's about six or + + align:start position:0% +cooling were there it's about six or + + + align:start position:0% +cooling were there it's about six or +seven ice ages in the + + align:start position:0% +seven ice ages in the + + + align:start position:0% +seven ice ages in the +last anybody know the history of the + + align:start position:0% + + + + align:start position:0% + +earth anyway some evidence used at least + + align:start position:0% +earth anyway some evidence used at least + + + align:start position:0% +earth anyway some evidence used at least +used to be I haven't paid any attention + + align:start position:0% +used to be I haven't paid any attention + + + align:start position:0% +used to be I haven't paid any attention +is that human populations got down to + + align:start position:0% +is that human populations got down to + + + align:start position:0% +is that human populations got down to +maybe just tens of thousands several + + align:start position:0% +maybe just tens of thousands several + + + align:start position:0% +maybe just tens of thousands several +times in the the last million years and + + align:start position:0% +times in the the last million years and + + + align:start position:0% +times in the the last million years and +so only the really different ones + + align:start position:0% +so only the really different ones + + + align:start position:0% +so only the really different ones +managed to pull + + align:start position:0% +managed to pull + + + align:start position:0% +managed to pull +through might be the ones who had all + + align:start position:0% +through might be the ones who had all + + + align:start position:0% +through might be the ones who had all +sorts of useless + + align:start position:0% +sorts of useless + + + align:start position:0% +sorts of useless +abilities yes so you talking about the + + align:start position:0% +abilities yes so you talking about the + + + align:start position:0% +abilities yes so you talking about the +ones who ate the + + align:start position:0% +ones who ate the + + + align:start position:0% +ones who ate the +others which would have been punished + + align:start position:0% +others which would have been punished + + + align:start position:0% +others which would have been punished +before that go ahead you were talking + + align:start position:0% +before that go ahead you were talking + + + align:start position:0% +before that go ahead you were talking +about representing like the K lines and + + align:start position:0% +about representing like the K lines and + + + align:start position:0% +about representing like the K lines and +everything like having some lines and + + align:start position:0% +everything like having some lines and + + + align:start position:0% +everything like having some lines and +then activating some of these feature so + + align:start position:0% +then activating some of these feature so + + + align:start position:0% +then activating some of these feature so +like in the case of learning good I like + + align:start position:0% +like in the case of learning good I like + + + align:start position:0% +like in the case of learning good I like +change some of these connections and if + + align:start position:0% +change some of these connections and if + + + align:start position:0% +change some of these connections and if +this is the case how will this affect + + align:start position:0% +this is the case how will this affect + + + align:start position:0% +this is the case how will this affect +like the higher uh order like higher + + align:start position:0% +like the higher uh order like higher + + + align:start position:0% +like the higher uh order like higher +objects like frames and everything like + + align:start position:0% +objects like frames and everything like + + + align:start position:0% +objects like frames and everything like +if you change something that's like + + align:start position:0% +if you change something that's like + + + align:start position:0% +if you change something that's like +really in the low level representation + + align:start position:0% +really in the low level representation + + + align:start position:0% +really in the low level representation +will this affect a lot wouldn't like the + + align:start position:0% +will this affect a lot wouldn't like the + + + align:start position:0% +will this affect a lot wouldn't like the +whole system break because some sub + + align:start position:0% +whole system break because some sub + + + align:start position:0% +whole system break because some sub +procedure wouldn't be able to return + + align:start position:0% +procedure wouldn't be able to return + + + align:start position:0% +procedure wouldn't be able to return +prop that's great that's another + + align:start position:0% +prop that's great that's another + + + align:start position:0% +prop that's great that's another +question I can't begin to answer uh + + align:start position:0% +question I can't begin to answer uh + + + align:start position:0% +question I can't begin to answer uh +namely when you learn learn + + align:start position:0% +namely when you learn learn + + + align:start position:0% +namely when you learn learn +something do you let's take the extreme + + align:start position:0% +something do you let's take the extreme + + + align:start position:0% +something do you let's take the extreme +form do you start a new representation + + align:start position:0% +form do you start a new representation + + + align:start position:0% +form do you start a new representation +or you modify an old one okay that's a + + align:start position:0% +or you modify an old one okay that's a + + + align:start position:0% +or you modify an old one okay that's a +choice if you modify an old one can you + + align:start position:0% +choice if you modify an old one can you + + + align:start position:0% +choice if you modify an old one can you +do that without losing the previous + + align:start position:0% +do that without losing the previous + + + align:start position:0% +do that without losing the previous +version so for example if I uh grow up + + align:start position:0% +version so for example if I uh grow up + + + align:start position:0% +version so for example if I uh grow up +monolingually which I did so I learned + + align:start position:0% +monolingually which I did so I learned + + + align:start position:0% +monolingually which I did so I learned +English and then + + align:start position:0% +English and then + + + align:start position:0% +English and then +I can't remember why + + align:start position:0% +I can't remember why + + + align:start position:0% +I can't remember why +but for some reason around fourth grade + + align:start position:0% +but for some reason around fourth grade + + + align:start position:0% +but for some reason around fourth grade +uh somebody tried to teach some teacher + + align:start position:0% +uh somebody tried to teach some teacher + + + align:start position:0% +uh somebody tried to teach some teacher +tried to teach us + + align:start position:0% +tried to teach us + + + align:start position:0% +tried to teach us +German and so uh for each German word uh + + align:start position:0% +German and so uh for each German word uh + + + align:start position:0% +German and so uh for each German word uh +I tried very hard to find the equivalent + + align:start position:0% +I tried very hard to find the equivalent + + + align:start position:0% +I tried very hard to find the equivalent +English word and figure out how to move + + align:start position:0% +English word and figure out how to move + + + align:start position:0% +English word and figure out how to move +your mouth so that it comes out German + + align:start position:0% +your mouth so that it comes out German + + + align:start position:0% +your mouth so that it comes out German +which is which actually for many words + + align:start position:0% +which is which actually for many words + + + align:start position:0% +which is which actually for many words +works fine because English is a mixture + + align:start position:0% +works fine because English is a mixture + + + align:start position:0% +works fine because English is a mixture +of German and other things and for many + + align:start position:0% +of German and other things and for many + + + align:start position:0% +of German and other things and for many +words it doesn't so that was a bad idea + + align:start position:0% +words it doesn't so that was a bad idea + + + align:start position:0% +words it doesn't so that was a bad idea +and if I had gotten very good at it I + + align:start position:0% +and if I had gotten very good at it I + + + align:start position:0% +and if I had gotten very good at it I +could have lost some + + align:start position:0% +could have lost some + + + align:start position:0% +could have lost some +English anyway + + align:start position:0% +English anyway + + + align:start position:0% +English anyway +uh that's a great set of questions do + + align:start position:0% +uh that's a great set of questions do + + + align:start position:0% +uh that's a great set of questions do +you make when do you make new memories + + align:start position:0% +you make when do you make new memories + + + align:start position:0% +you make when do you make new memories +when do you modify old ones and uh the + + align:start position:0% +when do you modify old ones and uh the + + + align:start position:0% +when do you modify old ones and uh the +hard one is uh if you can't modify an + + align:start position:0% +hard one is uh if you can't modify an + + + align:start position:0% +hard one is uh if you can't modify an +old one how do you make a + + align:start position:0% +old one how do you make a + + + align:start position:0% +old one how do you make a +copy uh that's different and there's a + + align:start position:0% +copy uh that's different and there's a + + + align:start position:0% +copy uh that's different and there's a +section called in society of mind about + + align:start position:0% +section called in society of mind about + + + align:start position:0% +section called in society of mind about +uh how we do that in Language by + + align:start position:0% +uh how we do that in Language by + + + align:start position:0% +uh how we do that in Language by +paraphrasing what someone said or uh you + + align:start position:0% +paraphrasing what someone said or uh you + + + align:start position:0% +paraphrasing what someone said or uh you +say something in your own head and you + + align:start position:0% +say something in your own head and you + + + align:start position:0% +say something in your own head and you +misunderstand it I'm doing that all the + + align:start position:0% +misunderstand it I'm doing that all the + + + align:start position:0% +misunderstand it I'm doing that all the +time I say such and such is a this or + + align:start position:0% +time I say such and such is a this or + + + align:start position:0% +time I say such and such is a this or +that and then it's as though somebody + + align:start position:0% +that and then it's as though somebody + + + align:start position:0% +that and then it's as though somebody +else had said that and I have something + + align:start position:0% +else had said that and I have something + + + align:start position:0% +else had said that and I have something +no that's wrong he meant + + align:start position:0% +no that's wrong he meant + + + align:start position:0% +no that's wrong he meant +this so uh when you're talking to + + align:start position:0% +this so uh when you're talking to + + + align:start position:0% +this so uh when you're talking to +yourself you're actually converting some + + align:start position:0% +yourself you're actually converting some + + + align:start position:0% +yourself you're actually converting some +mysterious um inarticulate + + align:start position:0% +mysterious um inarticulate + + + align:start position:0% +mysterious um inarticulate +representation to speech and then you're + + align:start position:0% +representation to speech and then you're + + + align:start position:0% +representation to speech and then you're +running it through your brain and + + align:start position:0% +running it through your brain and + + + align:start position:0% +running it through your brain and +listening to it and converting the + + align:start position:0% +listening to it and converting the + + + align:start position:0% +listening to it and converting the +speech back to a new representation so I + + align:start position:0% +speech back to a new representation so I + + + align:start position:0% +speech back to a new representation so I +think the wonderful thing about language + + align:start position:0% +think the wonderful thing about language + + + align:start position:0% +think the wonderful thing about language +is it's not just for + + align:start position:0% +is it's not just for + + + align:start position:0% +is it's not just for +expressing uh it may + + align:start position:0% +expressing uh it may + + + align:start position:0% +expressing uh it may +be + + align:start position:0% +be + + + align:start position:0% +be +uh how come the only animal that thinks + + align:start position:0% +uh how come the only animal that thinks + + + align:start position:0% +uh how come the only animal that thinks +the way we do is the only animal that + + align:start position:0% +the way we do is the only animal that + + + align:start position:0% +the way we do is the only animal that +talks the way we + + align:start position:0% +talks the way we + + + align:start position:0% +talks the way we +do who knows maybe + + align:start position:0% +do who knows maybe + + + align:start position:0% +do who knows maybe +Wills but nobody has decoded them do + + align:start position:0% +Wills but nobody has decoded them do + + + align:start position:0% +Wills but nobody has decoded them do +something like + + align:start position:0% +something like + + + align:start position:0% +something like +that but that's a question how how do + + align:start position:0% +that but that's a question how how do + + + align:start position:0% +that but that's a question how how do +you copy a memory to make a new version + + align:start position:0% +you copy a memory to make a new version + + + align:start position:0% +you copy a memory to make a new version +and the answer is uh you can ask anyone + + align:start position:0% +and the answer is uh you can ask anyone + + + align:start position:0% +and the answer is uh you can ask anyone +and they'll say I don't + + align:start position:0% +and they'll say I don't + + + align:start position:0% +and they'll say I don't +know why aren't there five theories of + + align:start position:0% +know why aren't there five theories of + + + align:start position:0% +know why aren't there five theories of +that + + align:start position:0% +that + + + align:start position:0% +that +yeah uh why I I don't know if that's + + align:start position:0% +yeah uh why I I don't know if that's + + + align:start position:0% +yeah uh why I I don't know if that's +true but I believe there is kind of sort + + align:start position:0% +true but I believe there is kind of sort + + + align:start position:0% +true but I believe there is kind of sort +of objective map between words in + + align:start position:0% +of objective map between words in + + + align:start position:0% +of objective map between words in +language like for example no no so for + + align:start position:0% +language like for example no no so for + + + align:start position:0% +language like for example no no so for +example if I have a a table I say like + + align:start position:0% +example if I have a a table I say like + + + align:start position:0% +example if I have a a table I say like +Mesa in Portuguese and like I can + + align:start position:0% +Mesa in Portuguese and like I can + + + align:start position:0% +Mesa in Portuguese and like I can +there's sort of objective map even for + + align:start position:0% +there's sort of objective map even for + + + align:start position:0% +there's sort of objective map even for +like colors which is sort of weird cuz + + align:start position:0% +like colors which is sort of weird cuz + + + align:start position:0% +like colors which is sort of weird cuz +you're like kind of + + align:start position:0% +you're like kind of + + + align:start position:0% +you're like kind of +dividing like + + align:start position:0% +dividing like + + + align:start position:0% +dividing like +the all the colors into junks of colors + + align:start position:0% +the all the colors into junks of colors + + + align:start position:0% +the all the colors into junks of colors +and like even I believe for like Words + + align:start position:0% +and like even I believe for like Words + + + align:start position:0% +and like even I believe for like Words +uh language that were not formed + + align:start position:0% +uh language that were not formed + + + align:start position:0% +uh language that were not formed +like the same ancestry I don't know + + align:start position:0% +like the same ancestry I don't know + + + align:start position:0% +like the same ancestry I don't know +there's for me it seems that there's + + align:start position:0% +there's for me it seems that there's + + + align:start position:0% +there's for me it seems that there's +some sort of Jac M between + + align:start position:0% +some sort of Jac M between + + + align:start position:0% +some sort of Jac M between +words well there are certain things that + + align:start position:0% +words well there are certain things that + + + align:start position:0% +words well there are certain things that +are just sort of like naturally more + + align:start position:0% +are just sort of like naturally more + + + align:start position:0% +are just sort of like naturally more +useful to talk about and so a lot of + + align:start position:0% +useful to talk about and so a lot of + + + align:start position:0% +useful to talk about and so a lot of +languages tend to have words for the + + align:start position:0% +languages tend to have words for the + + + align:start position:0% +languages tend to have words for the +same thing like like we have a word that + + align:start position:0% +same thing like like we have a word that + + + align:start position:0% +same thing like like we have a word that +means table um but if like there some + + align:start position:0% +means table um but if like there some + + + align:start position:0% +means table um but if like there some +that doesn't have table they probably + + align:start position:0% +that doesn't have table they probably + + + align:start position:0% +that doesn't have table they probably +wouldn't have a single word for table + + align:start position:0% +wouldn't have a single word for table + + + align:start position:0% +wouldn't have a single word for table +and regarding the colors thing there + + align:start position:0% +and regarding the colors thing there + + + align:start position:0% +and regarding the colors thing there +have actually been some interesting + + align:start position:0% +have actually been some interesting + + + align:start position:0% +have actually been some interesting +studies done on that like they've done + + align:start position:0% +studies done on that like they've done + + + align:start position:0% +studies done on that like they've done +color survey color naming surveys with + + align:start position:0% +color survey color naming surveys with + + + align:start position:0% +color survey color naming surveys with +lots of languages in the world and it + + align:start position:0% +lots of languages in the world and it + + + align:start position:0% +lots of languages in the world and it +turns out that like different languages + + align:start position:0% +turns out that like different languages + + + align:start position:0% +turns out that like different languages +like partition the color space + + align:start position:0% +like partition the color space + + + align:start position:0% +like partition the color space +differently I was just to + + align:start position:0% +differently I was just to + + + align:start position:0% +differently I was just to +ask they tend to do it similarly is the + + align:start position:0% +ask they tend to do it similarly is the + + + align:start position:0% +ask they tend to do it similarly is the +way that people perceive colors the way + + align:start position:0% +way that people perceive colors the way + + + align:start position:0% +way that people perceive colors the way +they divide up the space based on the + + align:start position:0% +they divide up the space based on the + + + align:start position:0% +they divide up the space based on the +number of wordss that they have is + + align:start position:0% +number of wordss that they have is + + + align:start position:0% +number of wordss that they have is +actually like maximizing the similarity + + align:start position:0% +actually like maximizing the similarity + + + align:start position:0% +actually like maximizing the similarity +of things with the same name and + + align:start position:0% +of things with the same name and + + + align:start position:0% +of things with the same name and +difference + + align:start position:0% +difference + + + align:start position:0% +difference +between + + align:start position:0% +between + + + align:start position:0% +between +yesi did some interesting studies on + + align:start position:0% +yesi did some interesting studies on + + + align:start position:0% +yesi did some interesting studies on +that right I'm trying to remember when + + align:start position:0% +that right I'm trying to remember when + + + align:start position:0% +that right I'm trying to remember when +children use colors + + align:start position:0% + + + + align:start position:0% + +let's see I had a daughter who have + + align:start position:0% +let's see I had a daughter who have + + + align:start position:0% +let's see I had a daughter who have +still must say and she uh suddenly + + align:start position:0% +still must say and she uh suddenly + + + align:start position:0% +still must say and she uh suddenly +started color + + align:start position:0% +started color + + + align:start position:0% +started color +words and had six or seven of them in + + align:start position:0% +words and had six or seven of them in + + + align:start position:0% +words and had six or seven of them in +just a couple of days and she sort of + + align:start position:0% +just a couple of days and she sort of + + + align:start position:0% +just a couple of days and she sort of +got interested in that and so suddenly I + + align:start position:0% +got interested in that and so suddenly I + + + align:start position:0% +got interested in that and so suddenly I +said oh my gosh this is this is what + + align:start position:0% +said oh my gosh this is this is what + + + align:start position:0% +said oh my gosh this is this is what +Maria montesorri calls + + align:start position:0% +Maria montesorri calls + + + align:start position:0% +Maria montesorri calls +a I forget what she called it what's the + + align:start position:0% +a I forget what she called it what's the + + + align:start position:0% +a I forget what she called it what's the +this moment when you the child is open + + align:start position:0% +this moment when you the child is open + + + align:start position:0% +this moment when you the child is open +to being taught so I said this is her + + align:start position:0% +to being taught so I said this is her + + + align:start position:0% +to being taught so I said this is her +chance to learn a lot of new color names + + align:start position:0% +chance to learn a lot of new color names + + + align:start position:0% +chance to learn a lot of new color names +so I said and what about this I said + + align:start position:0% +so I said and what about this I said + + + align:start position:0% +so I said and what about this I said +that's + + align:start position:0% +that's + + + align:start position:0% +that's +aqua and she said that's blue + + align:start position:0% + + + + align:start position:0% + +green and I said no that's this is + + align:start position:0% +green and I said no that's this is + + + align:start position:0% +green and I said no that's this is +aqua and uh she + + align:start position:0% + + + + align:start position:0% + +refused so + + align:start position:0% +refused so + + + align:start position:0% +refused so +that was that so some months later she + + align:start position:0% +that was that so some months later she + + + align:start position:0% +that was that so some months later she +learned some more color names but it + + align:start position:0% +learned some more color names but it + + + align:start position:0% +learned some more color names but it +wasn't the + + align:start position:0% +wasn't the + + + align:start position:0% +wasn't the +same when she was saying blue green was + + align:start position:0% +same when she was saying blue green was + + + align:start position:0% +same when she was saying blue green was +that because somebody had taught her + + align:start position:0% +that because somebody had taught her + + + align:start position:0% +that because somebody had taught her +blue green or it was because she was + + align:start position:0% +blue green or it was because she was + + + align:start position:0% +blue green or it was because she was +combining those two colors I think she + + align:start position:0% +combining those two colors I think she + + + align:start position:0% +combining those two colors I think she +was combining it do you remember I think + + align:start position:0% +was combining it do you remember I think + + + align:start position:0% +was combining it do you remember I think +you combining it cuz it looked a little + + align:start position:0% +you combining it cuz it looked a little + + + align:start position:0% +you combining it cuz it looked a little +blue and a little + + align:start position:0% +blue and a little + + + align:start position:0% +blue and a little +green so she so she had a concept that + + align:start position:0% +green so she so she had a concept that + + + align:start position:0% +green so she so she had a concept that +there were like certain building blocks + + align:start position:0% +there were like certain building blocks + + + align:start position:0% +there were like certain building blocks +in colors it looked like she wouldn't + + align:start position:0% +in colors it looked like she wouldn't + + + align:start position:0% +in colors it looked like she wouldn't +accept a new + + align:start position:0% +accept a new + + + align:start position:0% +accept a new +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +one and I always wondered if I was 15 + + align:start position:0% +one and I always wondered if I was 15 + + + align:start position:0% +one and I always wondered if I was 15 +minutes too + + align:start position:0% +minutes too + + + align:start position:0% +minutes too +late when does the montauri door + + align:start position:0% + + + + align:start position:0% + +shut sort of similarly there's studies + + align:start position:0% +shut sort of similarly there's studies + + + align:start position:0% +shut sort of similarly there's studies +done on different languages with how + + align:start position:0% +done on different languages with how + + + align:start position:0% +done on different languages with how +well people distinguish different colors + + align:start position:0% +well people distinguish different colors + + + align:start position:0% +well people distinguish different colors +so like in Russian uh there's a + + align:start position:0% +so like in Russian uh there's a + + + align:start position:0% +so like in Russian uh there's a +different word that means light blue and + + align:start position:0% +different word that means light blue and + + + align:start position:0% +different word that means light blue and +dark blue so Russians are better at + + align:start position:0% +dark blue so Russians are better at + + + align:start position:0% +dark blue so Russians are better at +distinguishing different shades of blue + + align:start position:0% +distinguishing different shades of blue + + + align:start position:0% +distinguishing different shades of blue +than say American and there's also a lot + + align:start position:0% +than say American and there's also a lot + + + align:start position:0% +than say American and there's also a lot +of languages that have that don't have + + align:start position:0% +of languages that have that don't have + + + align:start position:0% +of languages that have that don't have +distinct words for blue and green and + + align:start position:0% +distinct words for blue and green and + + + align:start position:0% +distinct words for blue and green and +people who native speakers of those + + align:start position:0% +people who native speakers of those + + + align:start position:0% +people who native speakers of those +languages have trouble distinguishing + + align:start position:0% +languages have trouble distinguishing + + + align:start position:0% +languages have trouble distinguishing +mus well that gives me a great idea uh + + align:start position:0% +mus well that gives me a great idea uh + + + align:start position:0% +mus well that gives me a great idea uh +if I had some un if I could have found + + align:start position:0% +if I had some un if I could have found + + + align:start position:0% +if I had some un if I could have found +some unfamiliar objects and colored them + + align:start position:0% +some unfamiliar objects and colored them + + + align:start position:0% +some unfamiliar objects and colored them +Aqua that might have fooled + + align:start position:0% + + + + align:start position:0% + +her there must + + align:start position:0% + + + + align:start position:0% + +be is there a branch of psychology that + + align:start position:0% +be is there a branch of psychology that + + + align:start position:0% +be is there a branch of psychology that +worries about + + align:start position:0% + + + + align:start position:0% + +because there must be names for sounds + + align:start position:0% +because there must be names for sounds + + + align:start position:0% +because there must be names for sounds +too and certainly A lot's known about + + align:start position:0% +too and certainly A lot's known about + + + align:start position:0% +too and certainly A lot's known about +ages at which children can't get new + + align:start position:0% +ages at which children can't get new + + + align:start position:0% +ages at which children can't get new +phon + + align:start position:0% +phon + + + align:start position:0% +phon +names + + align:start position:0% +names + + + align:start position:0% +names +yes story uh memory and language so I'm + + align:start position:0% +yes story uh memory and language so I'm + + + align:start position:0% +yes story uh memory and language so I'm +bilingual maybe other bilingual people + + align:start position:0% +bilingual maybe other bilingual people + + + align:start position:0% +bilingual maybe other bilingual people +in the audience could confirm this I + + align:start position:0% +in the audience could confirm this I + + + align:start position:0% +in the audience could confirm this I +didn't know that what's your other + + align:start position:0% +didn't know that what's your other + + + align:start position:0% +didn't know that what's your other +language French For Heaven's + + align:start position:0% +language French For Heaven's + + + align:start position:0% +language French For Heaven's +Sake I've known Henry for 20 odd years + + align:start position:0% +Sake I've known Henry for 20 odd years + + + align:start position:0% +Sake I've known Henry for 20 odd years +um uh so one thing that can happen is + + align:start position:0% +um uh so one thing that can happen is + + + align:start position:0% +um uh so one thing that can happen is +you can be talking with another + + align:start position:0% +you can be talking with another + + + align:start position:0% +you can be talking with another +bilingual person and um so I can be + + align:start position:0% +bilingual person and um so I can be + + + align:start position:0% +bilingual person and um so I can be +talking with someone who also both + + align:start position:0% +talking with someone who also both + + + align:start position:0% +talking with someone who also both +speaks French and English and then like + + align:start position:0% +speaks French and English and then like + + + align:start position:0% +speaks French and English and then like +a week later I'll remember every detail + + align:start position:0% +a week later I'll remember every detail + + + align:start position:0% +a week later I'll remember every detail +about a complicated conversation you + + align:start position:0% +about a complicated conversation you + + + align:start position:0% +about a complicated conversation you +know we were working on this project we + + align:start position:0% +know we were working on this project we + + + align:start position:0% +know we were working on this project we +were going to need it this and all this + + align:start position:0% +were going to need it this and all this + + + align:start position:0% +were going to need it this and all this +stuff I remember every detail except + + align:start position:0% +stuff I remember every detail except + + + align:start position:0% +stuff I remember every detail except +which language we have the + + align:start position:0% +which language we have the + + + align:start position:0% +which language we have the +conversation yeah my entire family is by + + align:start position:0% +conversation yeah my entire family is by + + + align:start position:0% +conversation yeah my entire family is by +Lord we serve gener speak a mix of + + align:start position:0% +Lord we serve gener speak a mix of + + + align:start position:0% +Lord we serve gener speak a mix of +Russian and English all the time so I + + align:start position:0% +Russian and English all the time so I + + + align:start position:0% +Russian and English all the time so I +can never remember you know even what + + align:start position:0% +can never remember you know even what + + + align:start position:0% +can never remember you know even what +language I'm speaking at the + + align:start position:0% +language I'm speaking at the + + + align:start position:0% +language I'm speaking at the +time yeah that mystifies me because if + + align:start position:0% +time yeah that mystifies me because if + + + align:start position:0% +time yeah that mystifies me because if +we're storing it in language how could I + + align:start position:0% +we're storing it in language how could I + + + align:start position:0% +we're storing it in language how could I +forget what + + align:start position:0% +forget what + + + align:start position:0% +forget what +language well I think there is a very + + align:start position:0% +language well I think there is a very + + + align:start position:0% +language well I think there is a very +simple answer to that one you have a a + + align:start position:0% +simple answer to that one you have a a + + + align:start position:0% +simple answer to that one you have a a +language that's neither English or + + align:start position:0% +language that's neither English or + + + align:start position:0% +language that's neither English or +French and you just have a a very simple + + align:start position:0% +French and you just have a a very simple + + + align:start position:0% +French and you just have a a very simple +like tag going there and then you just + + align:start position:0% +like tag going there and then you just + + + align:start position:0% +like tag going there and then you just +uh whenever you want to express + + align:start position:0% +uh whenever you want to express + + + align:start position:0% +uh whenever you want to express +something in English or French you just + + align:start position:0% +something in English or French you just + + + align:start position:0% +something in English or French you just +incode U the code incode whatever is the + + align:start position:0% +incode U the code incode whatever is the + + + align:start position:0% +incode U the code incode whatever is the +word those thoughts that you were having + + align:start position:0% +word those thoughts that you were having + + + align:start position:0% +word those thoughts that you were having +well that's a question what is that + + align:start position:0% +well that's a question what is that + + + align:start position:0% +well that's a question what is that +language do you have any thoughts on + + align:start position:0% +language do you have any thoughts on + + + align:start position:0% +language do you have any thoughts on +there you remind me I think I mentioned + + align:start position:0% +there you remind me I think I mentioned + + + align:start position:0% +there you remind me I think I mentioned +this but I was once at a meeting in + + align:start position:0% +this but I was once at a meeting in + + + align:start position:0% +this but I was once at a meeting in +yavan + + align:start position:0% +yavan + + + align:start position:0% +yavan +Armenia um + + align:start position:0% +Armenia um + + + align:start position:0% +Armenia um +and there was a translator who was + + align:start position:0% +and there was a translator who was + + + align:start position:0% +and there was a translator who was +practically real + + align:start position:0% +practically real + + + align:start position:0% +practically real +time and at Francis Crick was talking + + align:start position:0% +time and at Francis Crick was talking + + + align:start position:0% +time and at Francis Crick was talking +and at some point the + + align:start position:0% +and at some point the + + + align:start position:0% +and at some point the +translator switched and he started + + align:start position:0% +translator switched and he started + + + align:start position:0% +translator switched and he started +translating from English to English so + + align:start position:0% +translating from English to English so + + + align:start position:0% +translating from English to English so +so quick would quick would say something + + align:start position:0% +so quick would quick would say something + + + align:start position:0% +so quick would quick would say something +and the translator would translate it + + align:start position:0% +and the translator would translate it + + + align:start position:0% +and the translator would translate it +into English very well I + + align:start position:0% +into English very well I + + + align:start position:0% +into English very well I +thought wasn't quite the same + + align:start position:0% +thought wasn't quite the same + + + align:start position:0% +thought wasn't quite the same +words and uh after a while somebody + + align:start position:0% +words and uh after a while somebody + + + align:start position:0% +words and uh after a while somebody +asked him why he was doing that + + align:start position:0% +asked him why he was doing that + + + align:start position:0% +asked him why he was doing that +and he said he didn't realize he had + + align:start position:0% +and he said he didn't realize he had + + + align:start position:0% +and he said he didn't realize he had +switched do you think that could happen + + align:start position:0% +switched do you think that could happen + + + align:start position:0% +switched do you think that could happen +to you I + + align:start position:0% + + + + align:start position:0% + +suppose yeah I think that there are + + align:start position:0% +suppose yeah I think that there are + + + align:start position:0% +suppose yeah I think that there are +other ways of like transmitting ideas + + align:start position:0% +other ways of like transmitting ideas + + + align:start position:0% +other ways of like transmitting ideas +and learning I don't know maybe like + + align:start position:0% +and learning I don't know maybe like + + + align:start position:0% +and learning I don't know maybe like +arts or music besid language that can be + + align:start position:0% +arts or music besid language that can be + + + align:start position:0% +arts or music besid language that can be +really + + align:start position:0% + + + + align:start position:0% + +helpful uh I don't think there's + + align:start position:0% +helpful uh I don't think there's + + + align:start position:0% +helpful uh I don't think there's +anything nearly like language but art is + + align:start position:0% +anything nearly like language but art is + + + align:start position:0% +anything nearly like language but art is +pretty good but but it's so + + align:start position:0% + + + + align:start position:0% + +ambiguous cartoons they're awfully good + + align:start position:0% +ambiguous cartoons they're awfully good + + + align:start position:0% +ambiguous cartoons they're awfully good +uh how + + align:start position:0% +uh how + + + align:start position:0% +uh how +about + + align:start position:0% +about + + + align:start position:0% +about +what how about L list yeah that all + + align:start position:0% +what how about L list yeah that all + + + align:start position:0% +what how about L list yeah that all +right programming + + align:start position:0% + + + + align:start position:0% + +languages yes why is mathematics so hard + + align:start position:0% +languages yes why is mathematics so hard + + + align:start position:0% +languages yes why is mathematics so hard +I wonder + + align:start position:0% +I wonder + + + align:start position:0% +I wonder +if the habit of using a single letter + + align:start position:0% +if the habit of using a single letter + + + align:start position:0% +if the habit of using a single letter +for every + + align:start position:0% +for every + + + align:start position:0% +for every +variable might + + align:start position:0% +variable might + + + align:start position:0% +variable might +be might make it easy and hard it's hard + + align:start position:0% +be might make it easy and hard it's hard + + + align:start position:0% +be might make it easy and hard it's hard +who knows + + align:start position:0% + + + + align:start position:0% + +but yes you have great questions like + + align:start position:0% +but yes you have great questions like + + + align:start position:0% +but yes you have great questions like +last year you mention mathematics is + + align:start position:0% +last year you mention mathematics is + + + align:start position:0% +last year you mention mathematics is +hard I about it say it again last year + + align:start position:0% +hard I about it say it again last year + + + align:start position:0% +hard I about it say it again last year +you mentioned that mathematics is hard + + align:start position:0% +you mentioned that mathematics is hard + + + align:start position:0% +you mentioned that mathematics is hard +and I do I like go about it and I do + + align:start position:0% +and I do I like go about it and I do + + + align:start position:0% +and I do I like go about it and I do +feel like there's a like extreme lack of + + align:start position:0% +feel like there's a like extreme lack of + + + align:start position:0% +feel like there's a like extreme lack of +representations of ideas like solving a + + align:start position:0% +representations of ideas like solving a + + + align:start position:0% +representations of ideas like solving a +problem like you need to identify so + + align:start position:0% +problem like you need to identify so + + + align:start position:0% +problem like you need to identify so +many things and there's so many um like + + align:start position:0% +many things and there's so many um like + + + align:start position:0% +many things and there's so many um like +processes you know that you apply to + + align:start position:0% +processes you know that you apply to + + + align:start position:0% +processes you know that you apply to +them without having a + + align:start position:0% +them without having a + + + align:start position:0% +them without having a +name any of them for like classification + + align:start position:0% +name any of them for like classification + + + align:start position:0% +name any of them for like classification +well you have induction and deduction + + align:start position:0% +well you have induction and deduction + + + align:start position:0% +well you have induction and deduction +that's about it and contradiction like + + align:start position:0% +that's about it and contradiction like + + + align:start position:0% +that's about it and contradiction like +yes and you have + + align:start position:0% + + + + align:start position:0% + +this one feature of mathematics is + + align:start position:0% +this one feature of mathematics is + + + align:start position:0% +this one feature of mathematics is +completely un rund + + align:start position:0% +completely un rund + + + align:start position:0% +completely un rund +representations I wonder if there's some + + align:start position:0% +representations I wonder if there's some + + + align:start position:0% +representations I wonder if there's some +way to fix that or change it it's isn't + + align:start position:0% +way to fix that or change it it's isn't + + + align:start position:0% +way to fix that or change it it's isn't +that what + + align:start position:0% +that what + + + align:start position:0% +that what +other activity do we have where there's + + align:start position:0% +other activity do we have where there's + + + align:start position:0% +other activity do we have where there's +absolutely no redundancy at all in a + + align:start position:0% +absolutely no redundancy at all in a + + + align:start position:0% +absolutely no redundancy at all in a +mathematical experence it's just so so + + align:start position:0% +mathematical experence it's just so so + + + align:start position:0% +mathematical experence it's just so so +for some people people it's delightful + + align:start position:0% +for some people people it's delightful + + + align:start position:0% +for some people people it's delightful +and other + + align:start position:0% +and other + + + align:start position:0% +and other +people it's very + + align:start position:0% +people it's very + + + align:start position:0% +people it's very +hard I mentioned lick lier who uh in + + align:start position:0% +hard I mentioned lick lier who uh in + + + align:start position:0% +hard I mentioned lick lier who uh in +programming he he + + align:start position:0% +programming he he + + + align:start position:0% +programming he he +would he would have very long variable + + align:start position:0% +would he would have very long variable + + + align:start position:0% +would he would have very long variable +names sometimes they'd even be sentences + + align:start position:0% +names sometimes they'd even be sentences + + + align:start position:0% +names sometimes they'd even be sentences +like the register in which I put the + + align:start position:0% +like the register in which I put the + + + align:start position:0% +like the register in which I put the +result of and uh the great thing was you + + align:start position:0% +result of and uh the great thing was you + + + align:start position:0% +result of and uh the great thing was you +could read those programs they looked + + align:start position:0% +could read those programs they looked + + + align:start position:0% +could read those programs they looked +sort of stupid but but uh + + align:start position:0% +sort of stupid but but uh + + + align:start position:0% +sort of stupid but but uh +he didn't have to make he didn't have to + + align:start position:0% +he didn't have to make he didn't have to + + + align:start position:0% +he didn't have to make he didn't have to +what do you call notes he didn't have to + + align:start position:0% +what do you call notes he didn't have to + + + align:start position:0% +what do you call notes he didn't have to +have exclamation point this means + + align:start position:0% +have exclamation point this means + + + align:start position:0% +have exclamation point this means +that comments + + align:start position:0% + + + + align:start position:0% + +comments like when I when I like sit in + + align:start position:0% +comments like when I when I like sit in + + + align:start position:0% +comments like when I when I like sit in +like a algebraic theology class I can't + + align:start position:0% +like a algebraic theology class I can't + + + align:start position:0% +like a algebraic theology class I can't +like I just can't make myself accept the + + align:start position:0% +like I just can't make myself accept the + + + align:start position:0% +like I just can't make myself accept the +concepts unless I can understand it + + align:start position:0% +concepts unless I can understand it + + + align:start position:0% +concepts unless I can understand it +algebra and in like a + + align:start position:0% +algebra and in like a + + + align:start position:0% +algebra and in like a +geometric uhhuh what kind of math do you + + align:start position:0% +geometric uhhuh what kind of math do you + + + align:start position:0% +geometric uhhuh what kind of math do you +like do + + align:start position:0% +like do + + + align:start position:0% +like do +topology iology I likey I love topology + + align:start position:0% +topology iology I likey I love topology + + + align:start position:0% +topology iology I likey I love topology +that + + align:start position:0% +that + + + align:start position:0% +that +was I once was tutoring a high school + + align:start position:0% +was I once was tutoring a high school + + + align:start position:0% +was I once was tutoring a high school +student who couldn't do + + align:start position:0% +student who couldn't do + + + align:start position:0% +student who couldn't do +Algebra I'm I don't know if I mentioned + + align:start position:0% +Algebra I'm I don't know if I mentioned + + + align:start position:0% +Algebra I'm I don't know if I mentioned +this and it turned out he didn't know + + align:start position:0% +this and it turned out he didn't know + + + align:start position:0% +this and it turned out he didn't know +how to use + + align:start position:0% + + + + align:start position:0% + +parentheses so you know he would have an + + align:start position:0% +parentheses so you know he would have an + + + align:start position:0% +parentheses so you know he would have an +expression + + align:start position:0% + + + + align:start position:0% + +stuff like that + + align:start position:0% + + + + align:start position:0% + +and but if there was something in + + align:start position:0% + + + + align:start position:0% + +there he didn't know what that meant + + align:start position:0% +there he didn't know what that meant + + + align:start position:0% +there he didn't know what that meant +because he knew sometimes he would he + + align:start position:0% +because he knew sometimes he would he + + + align:start position:0% +because he knew sometimes he would he +didn't know how to match + + align:start position:0% +didn't know how to match + + + align:start position:0% +didn't know how to match +them + + align:start position:0% +them + + + align:start position:0% +them +so I couldn't figure out why and I asked + + align:start position:0% +so I couldn't figure out why and I asked + + + align:start position:0% +so I couldn't figure out why and I asked +how come and he said maybe I was sick + + align:start position:0% +how come and he said maybe I was sick + + + align:start position:0% +how come and he said maybe I was sick +the day they explained + + align:start position:0% +the day they explained + + + align:start position:0% +the day they explained +parenthesis + + align:start position:0% +parenthesis + + + align:start position:0% +parenthesis +and so I gave him little exercises like + + align:start position:0% +and so I gave him little exercises like + + + align:start position:0% +and so I gave him little exercises like +make them into eggs you see if you make + + align:start position:0% +make them into eggs you see if you make + + + align:start position:0% +make them into eggs you see if you make +this into an egg then this egg won't + + align:start position:0% + + + + align:start position:0% + +work + + align:start position:0% +work + + + align:start position:0% +work +and the funny thing was he got that in + + align:start position:0% +and the funny thing was he got that in + + + align:start position:0% +and the funny thing was he got that in +five minutes and then he didn't have any + + align:start position:0% +five minutes and then he didn't have any + + + align:start position:0% +five minutes and then he didn't have any +trouble with algebra the + + align:start position:0% +trouble with algebra the + + + align:start position:0% +trouble with algebra the +rest can you imagine I wonder I've never + + align:start position:0% +rest can you imagine I wonder I've never + + + align:start position:0% +rest can you imagine I wonder I've never +done much tutoring but if you can find + + align:start position:0% +done much tutoring but if you can find + + + align:start position:0% +done much tutoring but if you can find +the bug like that it must be great + + align:start position:0% +the bug like that it must be great + + + align:start position:0% +the bug like that it must be great +fun but I I bet it doesn't happen very + + align:start position:0% +fun but I I bet it doesn't happen very + + + align:start position:0% +fun but I I bet it doesn't happen very +often that was so funny I couldn't + + align:start position:0% +often that was so funny I couldn't + + + align:start position:0% +often that was so funny I couldn't +imagine not you know + + align:start position:0% + + + + align:start position:0% + +so if you don't have + + align:start position:0% +so if you don't have + + + align:start position:0% +so if you don't have +language there must + + align:start position:0% + + + + align:start position:0% + +be well what is it why are some people + + align:start position:0% +be well what is it why are some people + + + align:start position:0% +be well what is it why are some people +so much better at math than others is it + + align:start position:0% +so much better at math than others is it + + + align:start position:0% +so much better at math than others is it +just that they've not understood about + + align:start position:0% +just that they've not understood about + + + align:start position:0% +just that they've not understood about +five + + align:start position:0% +five + + + align:start position:0% +five +things I feel like I feel like they have + + align:start position:0% +things I feel like I feel like they have + + + align:start position:0% +things I feel like I feel like they have +like a set of things they know um to go + + align:start position:0% +like a set of things they know um to go + + + align:start position:0% +like a set of things they know um to go +to when they face a problem so well + + align:start position:0% +to when they face a problem so well + + + align:start position:0% +to when they face a problem so well +that's kind of simar to your + + align:start position:0% +that's kind of simar to your + + + align:start position:0% +that's kind of simar to your +fam story but like I feel like they know + + align:start position:0% +fam story but like I feel like they know + + + align:start position:0% +fam story but like I feel like they know +exactly um they have names for concepts + + align:start position:0% +exactly um they have names for concepts + + + align:start position:0% +exactly um they have names for concepts +of like ways of solving problems mhm so + + align:start position:0% +of like ways of solving problems mhm so + + + align:start position:0% +of like ways of solving problems mhm so +they look at a problem they're like I'm + + align:start position:0% +they look at a problem they're like I'm + + + align:start position:0% +they look at a problem they're like I'm +going to try this approach and then if + + align:start position:0% +going to try this approach and then if + + + align:start position:0% +going to try this approach and then if +it doesn't work I I no this other + + align:start position:0% +it doesn't work I I no this other + + + align:start position:0% +it doesn't work I I no this other +approach I just try it instead of like + + align:start position:0% +approach I just try it instead of like + + + align:start position:0% +approach I just try it instead of like +looking at the problem and and you think + + align:start position:0% +looking at the problem and and you think + + + align:start position:0% +looking at the problem and and you think +okay so what possible like thing what + + align:start position:0% +okay so what possible like thing what + + + align:start position:0% +okay so what possible like thing what +possible method can oh names for + + align:start position:0% +possible method can oh names for + + + align:start position:0% +possible method can oh names for +methods so do you have public names or + + align:start position:0% +methods so do you have public names or + + + align:start position:0% +methods so do you have public names or +are they secret names like I feel like + + align:start position:0% +are they secret names like I feel like + + + align:start position:0% +are they secret names like I feel like +they're secret names they're just like + + align:start position:0% +they're secret names they're just like + + + align:start position:0% +they're secret names they're just like +stor CU they can't explain it to other + + align:start position:0% +stor CU they can't explain it to other + + + align:start position:0% +stor CU they can't explain it to other +people they can't be like this problem + + align:start position:0% +people they can't be like this problem + + + align:start position:0% +people they can't be like this problem +like very few of this problem and that + + align:start position:0% +like very few of this problem and that + + + align:start position:0% +like very few of this problem and that +problem they generally they have the + + align:start position:0% +problem they generally they have the + + + align:start position:0% +problem they generally they have the +general same method although they're + + align:start position:0% +general same method although they're + + + align:start position:0% +general same method although they're +very + + align:start position:0% +very + + + align:start position:0% +very +defective I had a friend who was a + + align:start position:0% +defective I had a friend who was a + + + align:start position:0% +defective I had a friend who was a +composer and she had all sorts of sounds + + align:start position:0% +composer and she had all sorts of sounds + + + align:start position:0% +composer and she had all sorts of sounds +and they were filed away on tapes and + + align:start position:0% +and they were filed away on tapes and + + + align:start position:0% +and they were filed away on tapes and +the tapes had little symbols on them and + + align:start position:0% +the tapes had little symbols on them and + + + align:start position:0% +the tapes had little symbols on them and +if she needed a + + align:start position:0% +if she needed a + + + align:start position:0% +if she needed a +sound she would go to the closet and + + align:start position:0% +sound she would go to the closet and + + + align:start position:0% +sound she would go to the closet and +pull out the right tape and it had more + + align:start position:0% +pull out the right tape and it had more + + + align:start position:0% +pull out the right tape and it had more +symbols written on the Reel and she'd + + align:start position:0% +symbols written on the Reel and she'd + + + align:start position:0% +symbols written on the Reel and she'd +get this thing which might be a + + align:start position:0% +get this thing which might be a + + + align:start position:0% +get this thing which might be a +thunderstorm or or a bird or + + align:start position:0% +thunderstorm or or a bird or + + + align:start position:0% +thunderstorm or or a bird or +something so I asked her what was her + + align:start position:0% +something so I asked her what was her + + + align:start position:0% +something so I asked her what was her +notation for these sounds + + align:start position:0% +notation for these sounds + + + align:start position:0% +notation for these sounds +and she giggled and said I can't tell + + align:start position:0% +and she giggled and said I can't tell + + + align:start position:0% +and she giggled and said I can't tell +you it's it's too + + align:start position:0% +you it's it's too + + + align:start position:0% +you it's it's too +embarrassing I never found + + align:start position:0% +embarrassing I never found + + + align:start position:0% +embarrassing I never found +out but she had developed some code for + + align:start position:0% +out but she had developed some code for + + + align:start position:0% +out but she had developed some code for +sounds yeah so I would say that they + + align:start position:0% +sounds yeah so I would say that they + + + align:start position:0% +sounds yeah so I would say that they +have somewh more + + align:start position:0% +have somewh more + + + align:start position:0% +have somewh more +representation + + align:start position:0% +representation + + + align:start position:0% +representation +of uh like things that M requires and + + align:start position:0% +of uh like things that M requires and + + + align:start position:0% +of uh like things that M requires and +symbols or like patterns of + + align:start position:0% +symbols or like patterns of + + + align:start position:0% +symbols or like patterns of +solutions and like + + align:start position:0% +solutions and like + + + align:start position:0% +solutions and like +ation is optimal and if you're good at + + align:start position:0% +ation is optimal and if you're good at + + + align:start position:0% +ation is optimal and if you're good at +map doesn't mean that you're good at + + align:start position:0% +map doesn't mean that you're good at + + + align:start position:0% +map doesn't mean that you're good at +playing music because when you play + + align:start position:0% +playing music because when you play + + + align:start position:0% +playing music because when you play +music well you have maybe a good + + align:start position:0% +music well you have maybe a good + + + align:start position:0% +music well you have maybe a good +representation of the sounds and + + align:start position:0% +representation of the sounds and + + + align:start position:0% +representation of the sounds and +so it's just being + + align:start position:0% + + + + align:start position:0% + +upes and so you cannot access like oh so + + align:start position:0% +upes and so you cannot access like oh so + + + align:start position:0% +upes and so you cannot access like oh so +I have these Solutions these patterns of + + align:start position:0% +I have these Solutions these patterns of + + + align:start position:0% +I have these Solutions these patterns of +solutions that + + align:start position:0% +solutions that + + + align:start position:0% +solutions that +I need to I don't know I need to solve + + align:start position:0% +I need to I don't know I need to solve + + + align:start position:0% +I need to I don't know I need to solve +this B problem uh I have I don't know by + + align:start position:0% +this B problem uh I have I don't know by + + + align:start position:0% +this B problem uh I have I don't know by +induction or by contradiction and in in + + align:start position:0% +induction or by contradiction and in in + + + align:start position:0% +induction or by contradiction and in in +his brain or somebody that knows a lot + + align:start position:0% +his brain or somebody that knows a lot + + + align:start position:0% +his brain or somebody that knows a lot +like the person can access very fast or + + align:start position:0% +like the person can access very fast or + + + align:start position:0% +like the person can access very fast or +the representation itself is very well + + align:start position:0% +the representation itself is very well + + + align:start position:0% +the representation itself is very well +defined so you oh you + + align:start position:0% +defined so you oh you + + + align:start position:0% +defined so you oh you +can that's an interesting whole + + align:start position:0% + + + + align:start position:0% + +I remember let me interrupt uh I was + + align:start position:0% +I remember let me interrupt uh I was + + + align:start position:0% +I remember let me interrupt uh I was +once in some + + align:start position:0% +once in some + + + align:start position:0% +once in some +class and math + + align:start position:0% +class and math + + + align:start position:0% +class and math +class and it was about n dimensional + + align:start position:0% +class and it was about n dimensional + + + align:start position:0% +class and it was about n dimensional +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +spaces + + align:start position:0% +spaces + + + align:start position:0% +spaces +and some student + + align:start position:0% + + + + align:start position:0% + +asked + + align:start position:0% +asked + + + align:start position:0% +asked +well how do you imagine an n-dimensional + + align:start position:0% +well how do you imagine an n-dimensional + + + align:start position:0% +well how do you imagine an n-dimensional +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +space and there's two stories so and the + + align:start position:0% +space and there's two stories so and the + + + align:start position:0% +space and there's two stories so and the +instructor who I forget who fought for a + + align:start position:0% +instructor who I forget who fought for a + + + align:start position:0% +instructor who I forget who fought for a +while then he said oh it's very simple + + align:start position:0% +while then he said oh it's very simple + + + align:start position:0% +while then he said oh it's very simple +just pick a particular + + align:start position:0% +just pick a particular + + + align:start position:0% +just pick a particular +n so that was completely + + align:start position:0% + + + + align:start position:0% + +useless so + + align:start position:0% +useless so + + + align:start position:0% +useless so +then next time and I was a disciple of a + + align:start position:0% +then next time and I was a disciple of a + + + align:start position:0% +then next time and I was a disciple of a +mathematician at Harvard named Andrew + + align:start position:0% +mathematician at Harvard named Andrew + + + align:start position:0% +mathematician at Harvard named Andrew +Gleason + + align:start position:0% +Gleason + + + align:start position:0% +Gleason +who was a wonderful man uh only a couple + + align:start position:0% +who was a wonderful man uh only a couple + + + align:start position:0% +who was a wonderful man uh only a couple +of years older than me but uh he had won + + align:start position:0% +of years older than me but uh he had won + + + align:start position:0% +of years older than me but uh he had won +the putam three times first + + align:start position:0% +the putam three times first + + + align:start position:0% +the putam three times first +prize and I said what would you tell a + + align:start position:0% +prize and I said what would you tell a + + + align:start position:0% +prize and I said what would you tell a +student who wanted to understand an + + align:start position:0% +student who wanted to understand an + + + align:start position:0% +student who wanted to understand an +n-dimensional Vector space what it + + align:start position:0% +n-dimensional Vector space what it + + + align:start position:0% +n-dimensional Vector space what it +means and he said + + align:start position:0% +means and he said + + + align:start position:0% +means and he said +well you should give him five or six + + align:start position:0% +well you should give him five or six + + + align:start position:0% +well you should give him five or six +ways + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +like I don't + + align:start position:0% +like I don't + + + align:start position:0% +like I don't +know like imagine a bunch of + + align:start position:0% + + + + align:start position:0% + +arrows and remember that each of them is + + align:start position:0% +arrows and remember that each of them is + + + align:start position:0% +arrows and remember that each of them is +at right angles to all the + + align:start position:0% +at right angles to all the + + + align:start position:0% +at right angles to all the +others just like + + align:start position:0% +others just like + + + align:start position:0% +others just like +that and then he added and you should + + align:start position:0% +that and then he added and you should + + + align:start position:0% +that and then he added and you should +make the sum and if there's an infinite + + align:start position:0% +make the sum and if there's an infinite + + + align:start position:0% +make the sum and if there's an infinite +number you should have the sum of the + + align:start position:0% +number you should have the sum of the + + + align:start position:0% +number you should have the sum of the +squares of their lengths converge to a + + align:start position:0% +squares of their lengths converge to a + + + align:start position:0% +squares of their lengths converge to a +finite value and then he said or you + + align:start position:0% +finite value and then he said or you + + + align:start position:0% +finite value and then he said or you +should think of it as a furry a series + + align:start position:0% +should think of it as a furry a series + + + align:start position:0% +should think of it as a furry a series +with things of different + + align:start position:0% +with things of different + + + align:start position:0% +with things of different +frequencies + + align:start position:0% +frequencies + + + align:start position:0% +frequencies +and then he said or you should think + + align:start position:0% +and then he said or you should think + + + align:start position:0% +and then he said or you should think +of an object in a topological space face + + align:start position:0% +of an object in a topological space face + + + align:start position:0% +of an object in a topological space face +and each Dimension is finding the + + align:start position:0% +and each Dimension is finding the + + + align:start position:0% +and each Dimension is finding the +boundary of the last one and he went on + + align:start position:0% +boundary of the last one and he went on + + + align:start position:0% +boundary of the last one and he went on +for about six or seven and that was a + + align:start position:0% +for about six or seven and that was a + + + align:start position:0% +for about six or seven and that was a +great idea that + + align:start position:0% +great idea that + + + align:start position:0% +great idea that +is well have seven completely different + + align:start position:0% +is well have seven completely different + + + align:start position:0% +is well have seven completely different +ways and I + + align:start position:0% +ways and I + + + align:start position:0% +ways and I +remember I once had the same + + align:start position:0% +remember I once had the same + + + align:start position:0% +remember I once had the same +conversation with Richard + + align:start position:0% +conversation with Richard + + + align:start position:0% +conversation with Richard +fean I said well how did you do that and + + align:start position:0% +fean I said well how did you do that and + + + align:start position:0% +fean I said well how did you do that and +he said well uh when I grew up I always + + align:start position:0% +he said well uh when I grew up I always + + + align:start position:0% +he said well uh when I grew up I always +whatever was I always thought of three + + align:start position:0% +whatever was I always thought of three + + + align:start position:0% +whatever was I always thought of three +or four representations so if one of + + align:start position:0% +or four representations so if one of + + + align:start position:0% +or four representations so if one of +them didn't work another one would what + + align:start position:0% +them didn't work another one would what + + + align:start position:0% +them didn't work another one would what +yeah so my idea for somebody who wanted + + align:start position:0% +yeah so my idea for somebody who wanted + + + align:start position:0% +yeah so my idea for somebody who wanted +if you asked them about how to + + align:start position:0% +if you asked them about how to + + + align:start position:0% +if you asked them about how to +understand U multiple Dimension spaces + + align:start position:0% +understand U multiple Dimension spaces + + + align:start position:0% +understand U multiple Dimension spaces +would say read flatl read + + align:start position:0% +would say read flatl read + + + align:start position:0% +would say read flatl read +flat cuz that would give you the analogy + + align:start position:0% +flat cuz that would give you the analogy + + + align:start position:0% +flat cuz that would give you the analogy +right once you have that analogy then + + align:start position:0% +right once you have that analogy then + + + align:start position:0% +right once you have that analogy then +you could it would be easy to extend + + align:start position:0% +you could it would be easy to extend + + + align:start position:0% +you could it would be easy to extend +into other dimensions oh good has + + align:start position:0% +into other dimensions oh good has + + + align:start position:0% +into other dimensions oh good has +anybody written a 4D flat land where you + + align:start position:0% +anybody written a 4D flat land where you + + + align:start position:0% +anybody written a 4D flat land where you +make fun of the 3D people + + align:start position:0% +make fun of the 3D people + + + align:start position:0% +make fun of the 3D people +who is they can't get out of a paper + + align:start position:0% +who is they can't get out of a paper + + + align:start position:0% +who is they can't get out of a paper +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +bag and so like there will be some + + align:start position:0% +bag and so like there will be some + + + align:start position:0% +bag and so like there will be some +events that maybe will prove that so for + + align:start position:0% +events that maybe will prove that so for + + + align:start position:0% +events that maybe will prove that so for +example in my case when I do a lot of + + align:start position:0% +example in my case when I do a lot of + + + align:start position:0% +example in my case when I do a lot of +math I when I try to talk to people it's + + align:start position:0% +math I when I try to talk to people it's + + + align:start position:0% +math I when I try to talk to people it's +very hard and like maybe I'm in my + + align:start position:0% +very hard and like maybe I'm in my + + + align:start position:0% +very hard and like maybe I'm in my +representation of like solving problems + + align:start position:0% +representation of like solving problems + + + align:start position:0% +representation of like solving problems +in math + + align:start position:0% +in math + + + align:start position:0% +in math +and uh people tend to get better in MAF + + align:start position:0% +and uh people tend to get better in MAF + + + align:start position:0% +and uh people tend to get better in MAF +they practice a lot because they are + + align:start position:0% +they practice a lot because they are + + + align:start position:0% +they practice a lot because they are +optimizing the representation Ma + + align:start position:0% +optimizing the representation Ma + + + align:start position:0% +optimizing the representation Ma +and that would be + + align:start position:0% +and that would be + + + align:start position:0% +and that would be +Cas I I think I understand the problem + + align:start position:0% +Cas I I think I understand the problem + + + align:start position:0% +Cas I I think I understand the problem +but I don't think I have any friends + + align:start position:0% +but I don't think I have any friends + + + align:start position:0% +but I don't think I have any friends +left who are not mathematicians + + align:start position:0% + + + + align:start position:0% + +that's what happens if you live + + align:start position:0% +that's what happens if you live + + + align:start position:0% +that's what happens if you live +in this place long + + align:start position:0% + + + + align:start position:0% + +enough yeah I feel like so that's one + + align:start position:0% +enough yeah I feel like so that's one + + + align:start position:0% +enough yeah I feel like so that's one +way they're doing better I feel like the + + align:start position:0% +way they're doing better I feel like the + + + align:start position:0% +way they're doing better I feel like the +other way they're do better is they you + + align:start position:0% +other way they're do better is they you + + + align:start position:0% +other way they're do better is they you +know they like objectify things that we + + align:start position:0% +know they like objectify things that we + + + align:start position:0% +know they like objectify things that we +don't objectify like it's it's it's like + + align:start position:0% +don't objectify like it's it's it's like + + + align:start position:0% +don't objectify like it's it's it's like +the you know learning how to learn + + align:start position:0% +the you know learning how to learn + + + align:start position:0% +the you know learning how to learn +better idea learning how to learn better + + align:start position:0% +better idea learning how to learn better + + + align:start position:0% +better idea learning how to learn better +to learn better + + align:start position:0% +to learn better + + + align:start position:0% +to learn better +like so it's one thing to like know what + + align:start position:0% +like so it's one thing to like know what + + + align:start position:0% +like so it's one thing to like know what +the what the right representation is for + + align:start position:0% +the what the right representation is for + + + align:start position:0% +the what the right representation is for +particular power with like the right + + align:start position:0% +particular power with like the right + + + align:start position:0% +particular power with like the right +method is is another thing to like + + align:start position:0% +method is is another thing to like + + + align:start position:0% +method is is another thing to like +optimize that process so like what + + align:start position:0% +optimize that process so like what + + + align:start position:0% +optimize that process so like what +process did I use like in finding the + + align:start position:0% +process did I use like in finding the + + + align:start position:0% +process did I use like in finding the +representation and then they make that + + align:start position:0% +representation and then they make that + + + align:start position:0% +representation and then they make that +into a concept and then they have a lot + + align:start position:0% +into a concept and then they have a lot + + + align:start position:0% +into a concept and then they have a lot +of this kind of + + align:start position:0% +of this kind of + + + align:start position:0% +of this kind of +Concepts have you ever helped somebody + + align:start position:0% +Concepts have you ever helped somebody + + + align:start position:0% +Concepts have you ever helped somebody +to learn better + + align:start position:0% + + + + align:start position:0% + +so yeah when I what did you tell them so + + align:start position:0% +so yeah when I what did you tell them so + + + align:start position:0% +so yeah when I what did you tell them so +she she had trouble with um basically + + align:start position:0% +she she had trouble with um basically + + + align:start position:0% +she she had trouble with um basically +like two truth tables something like + + align:start position:0% +like two truth tables something like + + + align:start position:0% +like two truth tables something like +that like and or and stuff like + + align:start position:0% +that like and or and stuff like + + + align:start position:0% +that like and or and stuff like +that um so she like her repres her way + + align:start position:0% +that um so she like her repres her way + + + align:start position:0% +that um so she like her repres her way +of seeing the problem is to make a + + align:start position:0% +of seeing the problem is to make a + + + align:start position:0% +of seeing the problem is to make a +chart and I forgot what I told her I + + align:start position:0% +chart and I forgot what I told her I + + + align:start position:0% +chart and I forgot what I told her I +told her to kind of like math simple + + align:start position:0% +told her to kind of like math simple + + + align:start position:0% +told her to kind of like math simple +problems you + + align:start position:0% +problems you + + + align:start position:0% +problems you +know maybe most people don't + + align:start position:0% +know maybe most people don't + + + align:start position:0% +know maybe most people don't +have don't have the word representation + + align:start position:0% +have don't have the word representation + + + align:start position:0% +have don't have the word representation +in + + align:start position:0% +in + + + align:start position:0% +in +their in their + + align:start position:0% +their in their + + + align:start position:0% +their in their +language is there any place in grade + + align:start position:0% +language is there any place in grade + + + align:start position:0% +language is there any place in grade +school where + + align:start position:0% +school where + + + align:start position:0% +school where +you ex where you actually talk about + + align:start position:0% +you ex where you actually talk about + + + align:start position:0% +you ex where you actually talk about +what's your representation of + + align:start position:0% +what's your representation of + + + align:start position:0% +what's your representation of +acceleration + + align:start position:0% +acceleration + + + align:start position:0% +acceleration +is do we teach that word as part of any + + align:start position:0% +is do we teach that word as part of any + + + align:start position:0% +is do we teach that word as part of any +subjects you're you're uh drawing some + + align:start position:0% +subjects you're you're uh drawing some + + + align:start position:0% +subjects you're you're uh drawing some +uhuh vase or something like that we'll + + align:start position:0% +uhuh vase or something like that we'll + + + align:start position:0% +uhuh vase or something like that we'll +ask you to represent + + align:start position:0% +ask you to represent + + + align:start position:0% +ask you to represent +it + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +it's but it's hard to get out of yeah + + align:start position:0% +it's but it's hard to get out of yeah + + + align:start position:0% +it's but it's hard to get out of yeah +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +they're radically different + + align:start position:0% +they're radically different + + + align:start position:0% +they're radically different +representation + + align:start position:0% + + + + align:start position:0% + +I yes I don't + + align:start position:0% + + + + align:start position:0% + +know something limited + + align:start position:0% + + + + align:start position:0% + +toct take your + + align:start position:0% +toct take your + + + align:start position:0% +toct take your +toys take your toys what that yes that's + + align:start position:0% +toys take your toys what that yes that's + + + align:start position:0% +toys take your toys what that yes that's +a to represent physical structures as + + align:start position:0% +a to represent physical structures as + + + align:start position:0% +a to represent physical structures as +Tinker + + align:start position:0% + + + + align:start position:0% + +chys yeah I wrote a little article + + align:start position:0% +chys yeah I wrote a little article + + + align:start position:0% +chys yeah I wrote a little article +complaining about + + align:start position:0% + + + + align:start position:0% + +the popularity of Lego as opposed to + + align:start position:0% +the popularity of Lego as opposed to + + + align:start position:0% +the popularity of Lego as opposed to +Tinker toy + + align:start position:0% +Tinker toy + + + align:start position:0% +Tinker toy +because the children who grow up with + + align:start position:0% +because the children who grow up with + + + align:start position:0% +because the children who grow up with +Lego can't understand how to make + + align:start position:0% +Lego can't understand how to make + + + align:start position:0% +Lego can't understand how to make +something Strong by making a + + align:start position:0% +something Strong by making a + + + align:start position:0% +something Strong by making a +triangle + + align:start position:0% +triangle + + + align:start position:0% +triangle +and so I sort of had the conjecture + + align:start position:0% +and so I sort of had the conjecture + + + align:start position:0% +and so I sort of had the conjecture +that that uh although those people could + + align:start position:0% +that that uh although those people could + + + align:start position:0% +that that uh although those people could +build all sorts of wonderful houses and + + align:start position:0% +build all sorts of wonderful houses and + + + align:start position:0% +build all sorts of wonderful houses and +things they they ended up uh deficient + + align:start position:0% +things they they ended up uh deficient + + + align:start position:0% +things they they ended up uh deficient +in having the the most important of all + + align:start position:0% +in having the the most important of all + + + align:start position:0% +in having the the most important of all +architectural + + align:start position:0% +architectural + + + align:start position:0% +architectural +Concepts a triangle is infinitely + + align:start position:0% +Concepts a triangle is infinitely + + + align:start position:0% +Concepts a triangle is infinitely +strong + + align:start position:0% +strong + + + align:start position:0% +strong +because I mean you can't you can't alter + + align:start position:0% +because I mean you can't you can't alter + + + align:start position:0% +because I mean you can't you can't alter +a triangle without breaking it + + align:start position:0% +a triangle without breaking it + + + align:start position:0% +a triangle without breaking it +whereas + + align:start position:0% + + + + align:start position:0% + +uh whereas I don't know what that's a + + align:start position:0% +uh whereas I don't know what that's a + + + align:start position:0% +uh whereas I don't know what that's a +runon sentence I can't finish + + align:start position:0% + + + + align:start position:0% + +this explains the deterioration of + + align:start position:0% +this explains the deterioration of + + + align:start position:0% +this explains the deterioration of +society Marvin we don't have + + align:start position:0% +society Marvin we don't have + + + align:start position:0% +society Marvin we don't have +uh we don't have Tinker Toys and we + + align:start position:0% +uh we don't have Tinker Toys and we + + + align:start position:0% +uh we don't have Tinker Toys and we +don't have chemistry set with chemicals + + align:start position:0% +don't have chemistry set with chemicals + + + align:start position:0% +don't have chemistry set with chemicals +that make + + align:start position:0% + + + + align:start position:0% + +explosives you have to go to terrorist + + align:start position:0% +explosives you have to go to terrorist + + + align:start position:0% +explosives you have to go to terrorist +school to get a good Ed + + align:start position:0% + + + + align:start position:0% + +education so actually um in this + + align:start position:0% +education so actually um in this + + + align:start position:0% +education so actually um in this +conversation about being good at things + + align:start position:0% +conversation about being good at things + + + align:start position:0% +conversation about being good at things +and learning how to learn better um I + + align:start position:0% +and learning how to learn better um I + + + align:start position:0% +and learning how to learn better um I +think that um a point that sort of + + align:start position:0% +think that um a point that sort of + + + align:start position:0% +think that um a point that sort of +relates to this idea of Tinker sets and + + align:start position:0% +relates to this idea of Tinker sets and + + + align:start position:0% +relates to this idea of Tinker sets and +um playing around with things I think + + align:start position:0% +um playing around with things I think + + + align:start position:0% +um playing around with things I think +that it's not enough to Simply come up + + align:start position:0% +that it's not enough to Simply come up + + + align:start position:0% +that it's not enough to Simply come up +with um the best representations of a + + align:start position:0% +with um the best representations of a + + + align:start position:0% +with um the best representations of a +concept um in order to actually be good + + align:start position:0% +concept um in order to actually be good + + + align:start position:0% +concept um in order to actually be good +at something whether it's music or + + align:start position:0% +at something whether it's music or + + + align:start position:0% +at something whether it's music or +speaking a new language you have to not + + align:start position:0% +speaking a new language you have to not + + + align:start position:0% +speaking a new language you have to not +only understand it conceptually but you + + align:start position:0% +only understand it conceptually but you + + + align:start position:0% +only understand it conceptually but you +actually have to like gain a certain + + align:start position:0% +actually have to like gain a certain + + + align:start position:0% +actually have to like gain a certain +amount of fluency and to gain fluency + + align:start position:0% +amount of fluency and to gain fluency + + + align:start position:0% +amount of fluency and to gain fluency +you do have to like play around with the + + align:start position:0% +you do have to like play around with the + + + align:start position:0% +you do have to like play around with the +thing a lot whether it's like turning it + + align:start position:0% +thing a lot whether it's like turning it + + + align:start position:0% +thing a lot whether it's like turning it +around in your mind or practicing it + + align:start position:0% +around in your mind or practicing it + + + align:start position:0% +around in your mind or practicing it +physically so in the case of math it's + + align:start position:0% +physically so in the case of math it's + + + align:start position:0% +physically so in the case of math it's +like yeah you can come up with like all + + align:start position:0% +like yeah you can come up with like all + + + align:start position:0% +like yeah you can come up with like all +these different representations of it + + align:start position:0% +these different representations of it + + + align:start position:0% +these different representations of it +and like that's the first step + + align:start position:0% +and like that's the first step + + + align:start position:0% +and like that's the first step +understanding in it it's great once you + + align:start position:0% +understanding in it it's great once you + + + align:start position:0% +understanding in it it's great once you +understand it but just because you + + align:start position:0% +understand it but just because you + + + align:start position:0% +understand it but just because you +understand the concept like on a + + align:start position:0% +understand the concept like on a + + + align:start position:0% +understand the concept like on a +conceptual level doesn't mean that you + + align:start position:0% +conceptual level doesn't mean that you + + + align:start position:0% +conceptual level doesn't mean that you +can actually + + align:start position:0% +can actually + + + align:start position:0% +can actually +like know when to use it or like know + + align:start position:0% +like know when to use it or like know + + + align:start position:0% +like know when to use it or like know +how to use it when you're solving a + + align:start position:0% +how to use it when you're solving a + + + align:start position:0% +how to use it when you're solving a +problem and similarly for music um like + + align:start position:0% +problem and similarly for music um like + + + align:start position:0% +problem and similarly for music um like +say I guess I'm mostly talking in the + + align:start position:0% +say I guess I'm mostly talking in the + + + align:start position:0% +say I guess I'm mostly talking in the +case of improvisational music when I'm + + align:start position:0% +case of improvisational music when I'm + + + align:start position:0% +case of improvisational music when I'm +trying to speak speak something with the + + align:start position:0% +trying to speak speak something with the + + + align:start position:0% +trying to speak speak something with the +music so I have something that I want to + + align:start position:0% +music so I have something that I want to + + + align:start position:0% +music so I have something that I want to +say and maybe it's something that's sort + + align:start position:0% +say and maybe it's something that's sort + + + align:start position:0% +say and maybe it's something that's sort +of lowlevel I'm trying to resolve one + + align:start position:0% +of lowlevel I'm trying to resolve one + + + align:start position:0% +of lowlevel I'm trying to resolve one +chord to get to some sort of cadence now + + align:start position:0% +chord to get to some sort of cadence now + + + align:start position:0% +chord to get to some sort of cadence now +um I can have multiple ways of resolving + + align:start position:0% +um I can have multiple ways of resolving + + + align:start position:0% +um I can have multiple ways of resolving +the cord and in order to do this I have + + align:start position:0% +the cord and in order to do this I have + + + align:start position:0% +the cord and in order to do this I have +a vocabulary of the different ways and + + align:start position:0% +a vocabulary of the different ways and + + + align:start position:0% +a vocabulary of the different ways and +if one way doesn't occur to me when I'm + + align:start position:0% +if one way doesn't occur to me when I'm + + + align:start position:0% +if one way doesn't occur to me when I'm +playing the piece I can try another way + + align:start position:0% +playing the piece I can try another way + + + align:start position:0% +playing the piece I can try another way +but the important thing is that I have + + align:start position:0% +but the important thing is that I have + + + align:start position:0% +but the important thing is that I have +some way that I can resolve it in real + + align:start position:0% +some way that I can resolve it in real + + + align:start position:0% +some way that I can resolve it in real +time or else my piece is never going to + + align:start position:0% +time or else my piece is never going to + + + align:start position:0% +time or else my piece is never going to +come out um and then the same thing + + align:start position:0% +come out um and then the same thing + + + align:start position:0% +come out um and then the same thing +about learning different languages or + + align:start position:0% +about learning different languages or + + + align:start position:0% +about learning different languages or +speaking different languages in order to + + align:start position:0% +speaking different languages in order to + + + align:start position:0% +speaking different languages in order to +be able to speak or to express ourselves + + align:start position:0% +be able to speak or to express ourselves + + + align:start position:0% +be able to speak or to express ourselves +like we we have to have not only + + align:start position:0% +like we we have to have not only + + + align:start position:0% +like we we have to have not only +understanding of the language of the + + align:start position:0% +understanding of the language of the + + + align:start position:0% +understanding of the language of the +structure but being mediacy of being + + align:start position:0% +structure but being mediacy of being + + + align:start position:0% +structure but being mediacy of being +able to access it and that comes with + + align:start position:0% +able to access it and that comes with + + + align:start position:0% +able to access it and that comes with +practice with + + align:start position:0% +practice with + + + align:start position:0% +practice with +thinkering what have + + align:start position:0% +thinkering what have + + + align:start position:0% +thinkering what have +you well + + align:start position:0% +you well + + + align:start position:0% +you well +maybe that's goes in several + + align:start position:0% +maybe that's goes in several + + + align:start position:0% +maybe that's goes in several +directions one thing + + align:start position:0% +directions one thing + + + align:start position:0% +directions one thing +about where in our education system do + + align:start position:0% +about where in our education system do + + + align:start position:0% +about where in our education system do +we + + align:start position:0% +we + + + align:start position:0% +we +uh in grade school is there a place + + align:start position:0% +uh in grade school is there a place + + + align:start position:0% +uh in grade school is there a place +where you emphasize having several + + align:start position:0% +where you emphasize having several + + + align:start position:0% +where you emphasize having several +representations because so I can't think + + align:start position:0% +representations because so I can't think + + + align:start position:0% +representations because so I can't think +clearly right now but seems to me they + + align:start position:0% +clearly right now but seems to me they + + + align:start position:0% +clearly right now but seems to me they +usually trying to tell them the one best + + align:start position:0% +usually trying to tell them the one best + + + align:start position:0% +usually trying to tell them the one best +way + + align:start position:0% + + + + align:start position:0% + +and's the idea of the one best way and B + + align:start position:0% +and's the idea of the one best way and B + + + align:start position:0% +and's the idea of the one best way and B +there's the idea of like reinforcing + + align:start position:0% +there's the idea of like reinforcing + + + align:start position:0% +there's the idea of like reinforcing +similar the same process over and over + + align:start position:0% +similar the same process over and over + + + align:start position:0% +similar the same process over and over +again so when you learn math it's like + + align:start position:0% +again so when you learn math it's like + + + align:start position:0% +again so when you learn math it's like +you learned this technique and you + + align:start position:0% +you learned this technique and you + + + align:start position:0% +you learned this technique and you +reinforce the technique by doing a bunch + + align:start position:0% +reinforce the technique by doing a bunch + + + align:start position:0% +reinforce the technique by doing a bunch +of homework problems that are + + align:start position:0% +of homework problems that are + + + align:start position:0% +of homework problems that are +essentially like repetitions of the same + + align:start position:0% +essentially like repetitions of the same + + + align:start position:0% +essentially like repetitions of the same +thing whereas I think a better way of + + align:start position:0% +thing whereas I think a better way of + + + align:start position:0% +thing whereas I think a better way of +doing it well two better ways a you have + + align:start position:0% +doing it well two better ways a you have + + + align:start position:0% +doing it well two better ways a you have +multiple representations and two you + + align:start position:0% +multiple representations and two you + + + align:start position:0% +multiple representations and two you +create problems where you make people + + align:start position:0% +create problems where you make people + + + align:start position:0% +create problems where you make people +like Traverse paths differently and + + align:start position:0% +like Traverse paths differently and + + + align:start position:0% +like Traverse paths differently and +different people may have different + + align:start position:0% +different people may have different + + + align:start position:0% +different people may have different +solutions and each time you solve the + + align:start position:0% +solutions and each time you solve the + + + align:start position:0% +solutions and each time you solve the +problem you may have a different + + align:start position:0% +problem you may have a different + + + align:start position:0% +problem you may have a different +solution but the idea is you lay out + + align:start position:0% +solution but the idea is you lay out + + + align:start position:0% +solution but the idea is you lay out +like a whole network of paths in your + + align:start position:0% +like a whole network of paths in your + + + align:start position:0% +like a whole network of paths in your +head to solve any given type of problem + + align:start position:0% +head to solve any given type of problem + + + align:start position:0% +head to solve any given type of problem +so where in grade school do you ask + + align:start position:0% +so where in grade school do you ask + + + align:start position:0% +so where in grade school do you ask +children to solve the same problem three + + align:start position:0% +children to solve the same problem three + + + align:start position:0% +children to solve the same problem three +ways can anybody think + + align:start position:0% +ways can anybody think + + + align:start position:0% +ways can anybody think +of is that part of + + align:start position:0% +of is that part of + + + align:start position:0% +of is that part of +Education what closest thing I with + + align:start position:0% +Education what closest thing I with + + + align:start position:0% +Education what closest thing I with +fractions what about literature class + + align:start position:0% +fractions what about literature class + + + align:start position:0% +fractions what about literature class +they ask you for interpretations of + + align:start position:0% +they ask you for interpretations of + + + align:start position:0% +they ask you for interpretations of +novels yes I bet there are things that + + align:start position:0% +novels yes I bet there are things that + + + align:start position:0% +novels yes I bet there are things that +happen in literature that don't happen + + align:start position:0% +happen in literature that don't happen + + + align:start position:0% +happen in literature that don't happen +anywhere else in the curriculum but they + + align:start position:0% +anywhere else in the curriculum but they + + + align:start position:0% +anywhere else in the curriculum but they +probably don't have most most children + + align:start position:0% +probably don't have most most children + + + align:start position:0% +probably don't have most most children +don't transfer + + align:start position:0% +don't transfer + + + align:start position:0% +don't transfer +it when I was in China and like learning + + align:start position:0% +it when I was in China and like learning + + + align:start position:0% +it when I was in China and like learning +math when we like try to find areas of + + align:start position:0% +math when we like try to find areas of + + + align:start position:0% +math when we like try to find areas of +like certain geometric shapes we always + + align:start position:0% + + + + align:start position:0% + +do in topology whatever it is you just + + align:start position:0% +do in topology whatever it is you just + + + align:start position:0% +do in topology whatever it is you just +make it into triangles or simplexes so + + align:start position:0% +make it into triangles or simplexes so + + + align:start position:0% +make it into triangles or simplexes so +that's very strange subject + + align:start position:0% +that's very strange subject + + + align:start position:0% +that's very strange subject +maybe one reason why is so nice is + + align:start position:0% +maybe one reason why is so nice is + + + align:start position:0% +maybe one reason why is so nice is +because you can like think about it as + + align:start position:0% +because you can like think about it as + + + align:start position:0% +because you can like think about it as +like logical concept like you know sets + + align:start position:0% +like logical concept like you know sets + + + align:start position:0% +like logical concept like you know sets +you know you contain with the liit + + align:start position:0% +you know you contain with the liit + + + align:start position:0% +you know you contain with the liit +points stuff like that um and then you + + align:start position:0% +points stuff like that um and then you + + + align:start position:0% +points stuff like that um and then you +can imagine it as like + + align:start position:0% +can imagine it as like + + + align:start position:0% +can imagine it as like +picture Co + + align:start position:0% +picture Co + + + align:start position:0% +picture Co +sense where in real life do you have + + align:start position:0% +sense where in real life do you have + + + align:start position:0% +sense where in real life do you have +Duality that's a nice feature of a lot + + align:start position:0% +Duality that's a nice feature of a lot + + + align:start position:0% +Duality that's a nice feature of a lot +of mathematics there's whatever you're + + align:start position:0% +of mathematics there's whatever you're + + + align:start position:0% +of mathematics there's whatever you're +doing in some Fields there's a dual way + + align:start position:0% +doing in some Fields there's a dual way + + + align:start position:0% +doing in some Fields there's a dual way +where you you look at the space of the + + align:start position:0% +where you you look at the space of the + + + align:start position:0% +where you you look at the space of the +functions on on the objects rather than + + align:start position:0% +functions on on the objects rather than + + + align:start position:0% +functions on on the objects rather than +the objects I can't think of + + align:start position:0% +the objects I can't think of + + + align:start position:0% +the objects I can't think of +any where is that in + + align:start position:0% +any where is that in + + + align:start position:0% +any where is that in +Lop is there anything like that in real + + align:start position:0% + + + + align:start position:0% + +life because in mathematics a lot of + + align:start position:0% +life because in mathematics a lot of + + + align:start position:0% +life because in mathematics a lot of +problems suddenly become much easier in + + align:start position:0% +problems suddenly become much easier in + + + align:start position:0% +problems suddenly become much easier in +their dual + + align:start position:0% +their dual + + + align:start position:0% +their dual +form you just change everything + + align:start position:0% + + + + align:start position:0% + +I've been facing one + + align:start position:0% +I've been facing one + + + align:start position:0% +I've been facing one +way I was just I guess a couple of + + align:start position:0% +way I was just I guess a couple of + + + align:start position:0% +way I was just I guess a couple of +points I you said why is it difficult um + + align:start position:0% +points I you said why is it difficult um + + + align:start position:0% +points I you said why is it difficult um +whenever I've struggled I think it's + + align:start position:0% +whenever I've struggled I think it's + + + align:start position:0% +whenever I've struggled I think it's +because it's constructive so and you + + align:start position:0% +because it's constructive so and you + + + align:start position:0% +because it's constructive so and you +have to hold a lot in your head you know + + align:start position:0% +have to hold a lot in your head you know + + + align:start position:0% +have to hold a lot in your head you know +the entire structure of uh almost a + + align:start position:0% +the entire structure of uh almost a + + + align:start position:0% +the entire structure of uh almost a +field right because if you're learning + + align:start position:0% +field right because if you're learning + + + align:start position:0% +field right because if you're learning +algeb topology you're holding all of + + align:start position:0% +algeb topology you're holding all of + + + align:start position:0% +algeb topology you're holding all of +algebra and all of that whole structure + + align:start position:0% +algebra and all of that whole structure + + + align:start position:0% +algebra and all of that whole structure +in your head so sometimes it becomes + + align:start position:0% +in your head so sometimes it becomes + + + align:start position:0% +in your head so sometimes it becomes +difficult if you haven't abstracted at + + align:start position:0% +difficult if you haven't abstracted at + + + align:start position:0% +difficult if you haven't abstracted at +the right level and what I found I think + + align:start position:0% +the right level and what I found I think + + + align:start position:0% +the right level and what I found I think +my advisor which is really good many + + align:start position:0% +my advisor which is really good many + + + align:start position:0% +my advisor which is really good many +times and they he said two things this + + align:start position:0% +times and they he said two things this + + + align:start position:0% +times and they he said two things this +is really good mathematicians are really + + align:start position:0% +is really good mathematicians are really + + + align:start position:0% +is really good mathematicians are really +good at making analogies in mathematics + + align:start position:0% +good at making analogies in mathematics + + + align:start position:0% +good at making analogies in mathematics +and I was studying algebraic geometry + + align:start position:0% +and I was studying algebraic geometry + + + align:start position:0% +and I was studying algebraic geometry +and he says a really good algebraic + + align:start position:0% +and he says a really good algebraic + + + align:start position:0% +and he says a really good algebraic +geometers can boil everything down to + + align:start position:0% +geometers can boil everything down to + + + align:start position:0% +geometers can boil everything down to +linear algebra so and he say and you can + + align:start position:0% +linear algebra so and he say and you can + + + align:start position:0% +linear algebra so and he say and you can +only do that if you at the right level + + align:start position:0% +only do that if you at the right level + + + align:start position:0% +only do that if you at the right level +um and in techniques of doing that but + + align:start position:0% +um and in techniques of doing that but + + + align:start position:0% +um and in techniques of doing that but +uh I think the difficulty is in + + align:start position:0% +uh I think the difficulty is in + + + align:start position:0% +uh I think the difficulty is in +that I mean an analogy is a relationship + + align:start position:0% +that I mean an analogy is a relationship + + + align:start position:0% +that I mean an analogy is a relationship +between two objects and if you're good + + align:start position:0% +between two objects and if you're good + + + align:start position:0% +between two objects and if you're good +at making anies you're you're you're a a + + align:start position:0% +at making anies you're you're you're a a + + + align:start position:0% +at making anies you're you're you're a a +level Beyond a level above you know just + + align:start position:0% +level Beyond a level above you know just + + + align:start position:0% +level Beyond a level above you know just +looking at the objects you're looking at + + align:start position:0% +looking at the objects you're looking at + + + align:start position:0% +looking at the objects you're looking at +relationships of object and like + + align:start position:0% +relationships of object and like + + + align:start position:0% +relationships of object and like +regarding like the practicing thing I + + align:start position:0% +regarding like the practicing thing I + + + align:start position:0% +regarding like the practicing thing I +mean it's still related representations + + align:start position:0% +mean it's still related representations + + + align:start position:0% +mean it's still related representations +because at each practice you're learning + + align:start position:0% +because at each practice you're learning + + + align:start position:0% +because at each practice you're learning +something new about like this type of + + align:start position:0% +something new about like this type of + + + align:start position:0% +something new about like this type of +problems that make make you make make + + align:start position:0% +problems that make make you make make + + + align:start position:0% +problems that make make you make make +you better at identifying them in the + + align:start position:0% +you better at identifying them in the + + + align:start position:0% +you better at identifying them in the +future so and it's not like numerous + + align:start position:0% +future so and it's not like numerous + + + align:start position:0% +future so and it's not like numerous +practices like the number of practices + + align:start position:0% +practices like the number of practices + + + align:start position:0% +practices like the number of practices +doesn't matter to your ability of + + align:start position:0% +doesn't matter to your ability of + + + align:start position:0% +doesn't matter to your ability of +solving problems it's like what you + + align:start position:0% +solving problems it's like what you + + + align:start position:0% +solving problems it's like what you +learn from each practice if you can like + + align:start position:0% +learn from each practice if you can like + + + align:start position:0% +learn from each practice if you can like +do do do one do a thing once have a + + align:start position:0% +do do do one do a thing once have a + + + align:start position:0% +do do do one do a thing once have a +friend who tells me who basically told + + align:start position:0% +friend who tells me who basically told + + + align:start position:0% +friend who tells me who basically told +me how to math like it's like you look + + align:start position:0% +me how to math like it's like you look + + + align:start position:0% +me how to math like it's like you look +at the problem you solve it once you go + + align:start position:0% +at the problem you solve it once you go + + + align:start position:0% +at the problem you solve it once you go +back and you think about how you solved + + align:start position:0% +back and you think about how you solved + + + align:start position:0% +back and you think about how you solved +it like what's the process to solve it + + align:start position:0% +it like what's the process to solve it + + + align:start position:0% +it like what's the process to solve it +so a good problem is make up another + + align:start position:0% +so a good problem is make up another + + + align:start position:0% +so a good problem is make up another +problem like + + align:start position:0% +problem like + + + align:start position:0% +problem like +this that's essentially what you were + + align:start position:0% +this that's essentially what you were + + + align:start position:0% +this that's essentially what you were +learning it's probably too hard to + + align:start position:0% +learning it's probably too hard to + + + align:start position:0% +learning it's probably too hard to +grade you can't teach things you can't + + align:start position:0% +grade you can't teach things you can't + + + align:start position:0% +grade you can't teach things you can't +grade in the modern yes so I believe + + align:start position:0% +grade in the modern yes so I believe + + + align:start position:0% +grade in the modern yes so I believe +that Ma is too abstract and so it's + + align:start position:0% +that Ma is too abstract and so it's + + + align:start position:0% +that Ma is too abstract and so it's +difficult to go from one representation + + align:start position:0% +difficult to go from one representation + + + align:start position:0% +difficult to go from one representation +to another and that would be the whole + + align:start position:0% +to another and that would be the whole + + + align:start position:0% +to another and that would be the whole +problem I can't learn A New Concept + + align:start position:0% +problem I can't learn A New Concept + + + align:start position:0% +problem I can't learn A New Concept +without having a concept that's very + + align:start position:0% +without having a concept that's very + + + align:start position:0% +without having a concept that's very +near that concept that's very similar so + + align:start position:0% +near that concept that's very similar so + + + align:start position:0% +near that concept that's very similar so +it's just that if I don't have good + + align:start position:0% +it's just that if I don't have good + + + align:start position:0% +it's just that if I don't have good +representations of a lot of things it's + + align:start position:0% +representations of a lot of things it's + + + align:start position:0% +representations of a lot of things it's +difficult to put to representation so + + align:start position:0% +difficult to put to representation so + + + align:start position:0% +difficult to put to representation so +when I learn I don't know topology I + + align:start position:0% +when I learn I don't know topology I + + + align:start position:0% +when I learn I don't know topology I +should know I don't know analysis and + + align:start position:0% +should know I don't know analysis and + + + align:start position:0% +should know I don't know analysis and +then I can go from there to there + + align:start position:0% +then I can go from there to there + + + align:start position:0% +then I can go from there to there +because the representation is very close + + align:start position:0% +because the representation is very close + + + align:start position:0% +because the representation is very close +and so people + + align:start position:0% +and so people + + + align:start position:0% +and so people +that are good at M maybe they have a lot + + align:start position:0% +that are good at M maybe they have a lot + + + align:start position:0% +that are good at M maybe they have a lot +of representation so it's easier to add + + align:start position:0% +of representation so it's easier to add + + + align:start position:0% +of representation so it's easier to add +a new representation of a thing because + + align:start position:0% +a new representation of a thing because + + + align:start position:0% +a new representation of a thing because +it's + + align:start position:0% + + + + align:start position:0% + +like certainly would be nice to + + align:start position:0% +like certainly would be nice to + + + align:start position:0% +like certainly would be nice to +know like in the same of vectors I + + align:start position:0% +know like in the same of vectors I + + + align:start position:0% +know like in the same of vectors I +already have the concept of like I don't + + align:start position:0% +already have the concept of like I don't + + + align:start position:0% +already have the concept of like I don't +know the the perpendicular lines and so + + align:start position:0% +know the the perpendicular lines and so + + + align:start position:0% +know the the perpendicular lines and so +just adding more lines it's easy but + + align:start position:0% +just adding more lines it's easy but + + + align:start position:0% +just adding more lines it's easy but +like just I don't know great uh I don't + + align:start position:0% +like just I don't know great uh I don't + + + align:start position:0% +like just I don't know great uh I don't +know n dimensional thing it's very + + align:start position:0% +know n dimensional thing it's very + + + align:start position:0% +know n dimensional thing it's very +abstract I don't have any other + + align:start position:0% +abstract I don't have any other + + + align:start position:0% +abstract I don't have any other +representation that's closed by that + + align:start position:0% +representation that's closed by that + + + align:start position:0% +representation that's closed by that +concept M it's just that I need a lot of + + align:start position:0% +concept M it's just that I need a lot of + + + align:start position:0% +concept M it's just that I need a lot of +Concepts and representations and then I + + align:start position:0% +Concepts and representations and then I + + + align:start position:0% +Concepts and representations and then I +need like one that's close by yes + + align:start position:0% +need like one that's close by yes + + + align:start position:0% +need like one that's close by yes +between the vectors and the + + align:start position:0% +between the vectors and the + + + align:start position:0% +between the vectors and the +furer they're so different + + align:start position:0% + + + + align:start position:0% + +what would be in between those + + align:start position:0% + + + + align:start position:0% + +two the is built by other kind of + + align:start position:0% +two the is built by other kind of + + + align:start position:0% +two the is built by other kind of +Concepts I don't I don't think actually + + align:start position:0% +Concepts I don't I don't think actually + + + align:start position:0% +Concepts I don't I don't think actually +square + + align:start position:0% +square + + + align:start position:0% +square +waves probably square waves are easier + + align:start position:0% +waves probably square waves are easier + + + align:start position:0% +waves probably square waves are easier +to understand than SS and + + align:start position:0% + + + + align:start position:0% + +cosiness but they're not continuous + + align:start position:0% +cosiness but they're not continuous + + + align:start position:0% +cosiness but they're not continuous +I mean that not + + align:start position:0% + + + + align:start position:0% + +differentiable who has a problem to + + align:start position:0% +differentiable who has a problem to + + + align:start position:0% +differentiable who has a problem to +solve I comment on the I think sh sh's + + align:start position:0% +solve I comment on the I think sh sh's + + + align:start position:0% +solve I comment on the I think sh sh's +comment on U on uh having lots of + + align:start position:0% +comment on U on uh having lots of + + + align:start position:0% +comment on U on uh having lots of +practice and uh I don't think that + + align:start position:0% +practice and uh I don't think that + + + align:start position:0% +practice and uh I don't think that +actually so much out RS like the repr + + align:start position:0% +actually so much out RS like the repr + + + align:start position:0% +actually so much out RS like the repr +representational view or well I don't + + align:start position:0% +representational view or well I don't + + + align:start position:0% +representational view or well I don't +know what's going on neurologically but + + align:start position:0% +know what's going on neurologically but + + + align:start position:0% +know what's going on neurologically but +if you have new + + align:start position:0% +if you have new + + + align:start position:0% +if you have new +representations if you assume that they + + align:start position:0% +representations if you assume that they + + + align:start position:0% +representations if you assume that they +are symbolic representations in this + + align:start position:0% +are symbolic representations in this + + + align:start position:0% +are symbolic representations in this +sense they are kind of a generative + + align:start position:0% +sense they are kind of a generative + + + align:start position:0% +sense they are kind of a generative +things you can combine them and you can + + align:start position:0% +things you can combine them and you can + + + align:start position:0% +things you can combine them and you can +make a lot of stuff but uh usually when + + align:start position:0% +make a lot of stuff but uh usually when + + + align:start position:0% +make a lot of stuff but uh usually when +you learn something + + align:start position:0% +you learn something + + + align:start position:0% +you learn something +new like if you learn the rule there's + + align:start position:0% +new like if you learn the rule there's + + + align:start position:0% +new like if you learn the rule there's +going to be exceptions so uh when you + + align:start position:0% +going to be exceptions so uh when you + + + align:start position:0% +going to be exceptions so uh when you +repeat things + + align:start position:0% +repeat things + + + align:start position:0% +repeat things +one of the reasons for that might be to + + align:start position:0% +one of the reasons for that might be to + + + align:start position:0% +one of the reasons for that might be to +find out + + align:start position:0% +find out + + + align:start position:0% +find out +box you might have have well now when + + align:start position:0% +box you might have have well now when + + + align:start position:0% +box you might have have well now when +you practice a little piece of music by + + align:start position:0% +you practice a little piece of music by + + + align:start position:0% +you practice a little piece of music by +repeating do you change your + + align:start position:0% +repeating do you change your + + + align:start position:0% +repeating do you change your +representation or do just repeat and + + align:start position:0% +representation or do just repeat and + + + align:start position:0% +representation or do just repeat and +hope it gets + + align:start position:0% +hope it gets + + + align:start position:0% +hope it gets +better so I think there's a difference + + align:start position:0% +better so I think there's a difference + + + align:start position:0% +better so I think there's a difference +between um okay so there's practice in + + align:start position:0% +between um okay so there's practice in + + + align:start position:0% +between um okay so there's practice in +this sense of traditional classical + + align:start position:0% +this sense of traditional classical + + + align:start position:0% +this sense of traditional classical +music practice and then there's the idea + + align:start position:0% +music practice and then there's the idea + + + align:start position:0% +music practice and then there's the idea +of like T practice if you will so um I + + align:start position:0% +of like T practice if you will so um I + + + align:start position:0% +of like T practice if you will so um I +think that the type of practice that I'm + + align:start position:0% +think that the type of practice that I'm + + + align:start position:0% +think that the type of practice that I'm +advocating is the type of practice where + + align:start position:0% +advocating is the type of practice where + + + align:start position:0% +advocating is the type of practice where +like you're actually sort of turning + + align:start position:0% +like you're actually sort of turning + + + align:start position:0% +like you're actually sort of turning +around the concept or the thing the the + + align:start position:0% +around the concept or the thing the the + + + align:start position:0% +around the concept or the thing the the +object in your head so that you're + + align:start position:0% +object in your head so that you're + + + align:start position:0% +object in your head so that you're +looking at it from many different + + align:start position:0% +looking at it from many different + + + align:start position:0% +looking at it from many different +perspectives and connecting it to many + + align:start position:0% +perspectives and connecting it to many + + + align:start position:0% +perspectives and connecting it to many +different things which is um very which + + align:start position:0% +different things which is um very which + + + align:start position:0% +different things which is um very which +is actually conducive to expanding your + + align:start position:0% +is actually conducive to expanding your + + + align:start position:0% +is actually conducive to expanding your +representation connecting it to + + align:start position:0% +representation connecting it to + + + align:start position:0% +representation connecting it to +different concepts like all the good + + align:start position:0% +different concepts like all the good + + + align:start position:0% +different concepts like all the good +things that help us remember it and + + align:start position:0% +things that help us remember it and + + + align:start position:0% +things that help us remember it and +better use it this is very different + + align:start position:0% +better use it this is very different + + + align:start position:0% +better use it this is very different +from like the CL classical music + + align:start position:0% +from like the CL classical music + + + align:start position:0% +from like the CL classical music +practice which like having been a + + align:start position:0% +practice which like having been a + + + align:start position:0% +practice which like having been a +classical pianist for 18 years like it's + + align:start position:0% +classical pianist for 18 years like it's + + + align:start position:0% +classical pianist for 18 years like it's +not a really good way of doing things + + align:start position:0% +not a really good way of doing things + + + align:start position:0% +not a really good way of doing things +well I was wondering is there has there + + align:start position:0% +well I was wondering is there has there + + + align:start position:0% +well I was wondering is there has there +been any studies on children or have + + align:start position:0% +been any studies on children or have + + + align:start position:0% +been any studies on children or have +have there been any children who have + + align:start position:0% +have there been any children who have + + + align:start position:0% +have there been any children who have +just played piano or some keyboard + + align:start position:0% +just played piano or some keyboard + + + align:start position:0% +just played piano or some keyboard +instrument that need to all their lives + + align:start position:0% +instrument that need to all their lives + + + align:start position:0% +instrument that need to all their lives +and then they suddenly have something + + align:start position:0% +and then they suddenly have something + + + align:start position:0% +and then they suddenly have something +where uh when you press it uh where + + align:start position:0% +where uh when you press it uh where + + + align:start position:0% +where uh when you press it uh where +where you can control the volume a + + align:start position:0% +where you can control the volume a + + + align:start position:0% +where you can control the volume a +theramin yeah yeah yeah yeah but if if a + + align:start position:0% +theramin yeah yeah yeah yeah but if if a + + + align:start position:0% +theramin yeah yeah yeah yeah but if if a +child were very suddenly to learn a + + align:start position:0% +child were very suddenly to learn a + + + align:start position:0% +child were very suddenly to learn a +completely new dimension that's the + + align:start position:0% +completely new dimension that's the + + + align:start position:0% +completely new dimension that's the +Dynamics and uh how will it react to + + align:start position:0% +Dynamics and uh how will it react to + + + align:start position:0% +Dynamics and uh how will it react to +that so I don't know if there are any + + align:start position:0% +that so I don't know if there are any + + + align:start position:0% +that so I don't know if there are any +such cases but I would suspect that you + + align:start position:0% +such cases but I would suspect that you + + + align:start position:0% +such cases but I would suspect that you +could go to a suitably backwards + + align:start position:0% +could go to a suitably backwards + + + align:start position:0% +could go to a suitably backwards +backward place even nowadays and find + + align:start position:0% +backward place even nowadays and find + + + align:start position:0% +backward place even nowadays and find +some children who not that there was a + + align:start position:0% +some children who not that there was a + + + align:start position:0% +some children who not that there was a +nice period in the media lab + + align:start position:0% +nice period in the media lab + + + align:start position:0% +nice period in the media lab +when we were + + align:start position:0% + + + + align:start position:0% + +building three-dimensional theramin for + + align:start position:0% +building three-dimensional theramin for + + + align:start position:0% +building three-dimensional theramin for +pen of pen and Teller because he's quite + + align:start position:0% +pen of pen and Teller because he's quite + + + align:start position:0% +pen of pen and Teller because he's quite +a good + + align:start position:0% +a good + + + align:start position:0% +a good +musician we're making gadgets so he + + align:start position:0% +musician we're making gadgets so he + + + align:start position:0% +musician we're making gadgets so he +could wave his + + align:start position:0% +could wave his + + + align:start position:0% +could wave his +hands but I wonder In classical is + + align:start position:0% +hands but I wonder In classical is + + + align:start position:0% +hands but I wonder In classical is +it there ought to be some very short + + align:start position:0% +it there ought to be some very short + + + align:start position:0% +it there ought to be some very short +pieces that come in 10 + + align:start position:0% + + + + align:start position:0% + +variations because we make children + + align:start position:0% +variations because we make children + + + align:start position:0% +variations because we make children +learn + + align:start position:0% + + + + align:start position:0% + +fairly long pieces where it's just + + align:start position:0% +fairly long pieces where it's just + + + align:start position:0% +fairly long pieces where it's just +repeating belly variations which is like + + align:start position:0% +repeating belly variations which is like + + + align:start position:0% +repeating belly variations which is like +32 or 33 like really short pieces um + + align:start position:0% +32 or 33 like really short pieces um + + + align:start position:0% +32 or 33 like really short pieces um +well but only eight people in the world + + align:start position:0% +well but only eight people in the world + + + align:start position:0% +well but only eight people in the world +can play + + align:start position:0% +can play + + + align:start position:0% +can play +it that's but I guess the the thing with + + align:start position:0% +it that's but I guess the the thing with + + + align:start position:0% +it that's but I guess the the thing with +classical music is that it's it kind of + + align:start position:0% +classical music is that it's it kind of + + + align:start position:0% +classical music is that it's it kind of +just makes you learn this one thing and + + align:start position:0% +just makes you learn this one thing and + + + align:start position:0% +just makes you learn this one thing and +you learn it by repeating it over and + + align:start position:0% +you learn it by repeating it over and + + + align:start position:0% +you learn it by repeating it over and +over again whereas like in something + + align:start position:0% +over again whereas like in something + + + align:start position:0% +over again whereas like in something +like jazz that's more improvisational + + align:start position:0% +like jazz that's more improvisational + + + align:start position:0% +like jazz that's more improvisational +it's like you have a template and each + + align:start position:0% +it's like you have a template and each + + + align:start position:0% +it's like you have a template and each +time you go through it you can Traverse + + align:start position:0% +time you go through it you can Traverse + + + align:start position:0% +time you go through it you can Traverse +a different path through it but even for + + align:start position:0% +a different path through it but even for + + + align:start position:0% +a different path through it but even for +like classical classical music where + + align:start position:0% +like classical classical music where + + + align:start position:0% +like classical classical music where +you're playing the same thing each time + + align:start position:0% +you're playing the same thing each time + + + align:start position:0% +you're playing the same thing each time +I think that there's still like a good + + align:start position:0% +I think that there's still like a good + + + align:start position:0% +I think that there's still like a good +way of doing it and a not so good way + + align:start position:0% +way of doing it and a not so good way + + + align:start position:0% +way of doing it and a not so good way +the good way being like each time you + + align:start position:0% +the good way being like each time you + + + align:start position:0% +the good way being like each time you +practice it you subtly vary it somehow + + align:start position:0% +practice it you subtly vary it somehow + + + align:start position:0% +practice it you subtly vary it somehow +like you change the expression a bit you + + align:start position:0% +like you change the expression a bit you + + + align:start position:0% +like you change the expression a bit you +play it faster slower things like that + + align:start position:0% +play it faster slower things like that + + + align:start position:0% +play it faster slower things like that +um and I I guess this goes back to the + + align:start position:0% +um and I I guess this goes back to the + + + align:start position:0% +um and I I guess this goes back to the +whole like it's like each time you + + align:start position:0% +whole like it's like each time you + + + align:start position:0% +whole like it's like each time you +reinforce an idea like simply repeating + + align:start position:0% +reinforce an idea like simply repeating + + + align:start position:0% +reinforce an idea like simply repeating +it well like in the beginning like it + + align:start position:0% +it well like in the beginning like it + + + align:start position:0% +it well like in the beginning like it +might help you familiarize yourself with + + align:start position:0% +might help you familiarize yourself with + + + align:start position:0% +might help you familiarize yourself with +the idea but if you repeat it and Vary + + align:start position:0% +the idea but if you repeat it and Vary + + + align:start position:0% +the idea but if you repeat it and Vary +it slightly each time to like look at + + align:start position:0% +it slightly each time to like look at + + + align:start position:0% +it slightly each time to like look at +different dimensions of it then you + + align:start position:0% +different dimensions of it then you + + + align:start position:0% +different dimensions of it then you +learn it better how many of you know + + align:start position:0% +learn it better how many of you know + + + align:start position:0% +learn it better how many of you know +that + + align:start position:0% + + + + align:start position:0% + +piece Pig 's Dell well you should Google + + align:start position:0% +piece Pig 's Dell well you should Google + + + align:start position:0% +piece Pig 's Dell well you should Google +it up and listen to it it has 32 is it + + align:start position:0% +it up and listen to it it has 32 is it + + + align:start position:0% +it up and listen to it it has 32 is it + + align:start position:0% + + + align:start position:0% +I think it's 32 and then there's the + + align:start position:0% +I think it's 32 and then there's the + + + align:start position:0% +I think it's 32 and then there's the +original theme so it's like 33 total + + align:start position:0% +original theme so it's like 33 total + + + align:start position:0% +original theme so it's like 33 total +maybe the one I like is the next to last + + align:start position:0% +maybe the one I like is the next to last + + + align:start position:0% +maybe the one I like is the next to last +which + + align:start position:0% + + + + align:start position:0% + +is the + + align:start position:0% + + + + align:start position:0% + +Fugue so that'll give you another view + + align:start position:0% +Fugue so that'll give you another view + + + align:start position:0% +Fugue so that'll give you another view +of classical music because the pieces + + align:start position:0% +of classical music because the pieces + + + align:start position:0% +of classical music because the pieces +are fairly + + align:start position:0% +are fairly + + + align:start position:0% +are fairly +short and they all have some ideas in + + align:start position:0% +short and they all have some ideas in + + + align:start position:0% +short and they all have some ideas in +common and it's sort of like poetry what + + align:start position:0% +common and it's sort of like poetry what + + + align:start position:0% +common and it's sort of like poetry what +do you + + align:start position:0% +do you + + + align:start position:0% +do you +make what do you call those + + align:start position:0% +make what do you call those + + + align:start position:0% +make what do you call those +poems where there're many verses and + + align:start position:0% +poems where there're many verses and + + + align:start position:0% +poems where there're many verses and +each verse ends with the same line but + + align:start position:0% +each verse ends with the same line but + + + align:start position:0% +each verse ends with the same line but +it means something different each + + align:start position:0% +it means something different each + + + align:start position:0% +it means something different each +time it's it's a + + align:start position:0% +time it's it's a + + + align:start position:0% +time it's it's a +very + + align:start position:0% +very + + + align:start position:0% +very +what what's an example of it can you + + align:start position:0% +what what's an example of it can you + + + align:start position:0% +what what's an example of it can you +think of the I I couldn't hear you well + + align:start position:0% +think of the I I couldn't hear you well + + + align:start position:0% +think of the I I couldn't hear you well +there's like it's like a Rondo except + + align:start position:0% +there's like it's like a Rondo except + + + align:start position:0% +there's like it's like a Rondo except +that the it changes its meaning each + + align:start position:0% +that the it changes its meaning each + + + align:start position:0% +that the it changes its meaning each +time and it's the same words it's + + align:start position:0% +time and it's the same words it's + + + align:start position:0% +time and it's the same words it's +they're pretty hard to make I + + align:start position:0% +they're pretty hard to make I + + + align:start position:0% +they're pretty hard to make I +guess of that that does that um there's + + align:start position:0% +guess of that that does that um there's + + + align:start position:0% +guess of that that does that um there's +the famous one that's what like Do Not + + align:start position:0% +the famous one that's what like Do Not + + + align:start position:0% +the famous one that's what like Do Not +Go Gentle into the night or something + + align:start position:0% +Go Gentle into the night or something + + + align:start position:0% +Go Gentle into the night or something +huh rage rage against the coming of + + align:start position:0% +huh rage rage against the coming of + + + align:start position:0% +huh rage rage against the coming of +something anyway I'll I'll email you the + + align:start position:0% +something anyway I'll I'll email you the + + + align:start position:0% +something anyway I'll I'll email you the +diabelli + + align:start position:0% +diabelli + + + align:start position:0% +diabelli +or I had a friend madfred kleines who + + align:start position:0% +or I had a friend madfred kleines who + + + align:start position:0% +or I had a friend madfred kleines who +wrote this book called santic + + align:start position:0% + + + + align:start position:0% + +who used to play that particular + + align:start position:0% +who used to play that particular + + + align:start position:0% +who used to play that particular +bethoven + + align:start position:0% +bethoven + + + align:start position:0% +bethoven +thing + + align:start position:0% + + + + align:start position:0% + +well last important + + align:start position:0% + + + + align:start position:0% + +question thanks for coming \ No newline at end of file diff --git a/oKwGNgCTd-Q.txt b/oKwGNgCTd-Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..08eb2cbd515d6efa731f7711399b72fe9ac18b9f --- /dev/null +++ b/oKwGNgCTd-Q.txt @@ -0,0 +1,2047 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So we're going to +start directly today and look + +at chain reactions. + +And explosions. + +So chain reactions, how +many people have + +heard of chain reactions? + +Lot of people have heard +of chain reactions. + +Have seen chain reactions +done, in kinetics. + +No. + +Alright, well, then I'll +do chain reactions. + +Chain reactions. + +Chain reactions are reactions +that feed on themselves. + +And there are three parts +to a chain reaction. + +There's an initiation step, +which is where your reactant + +makes an intermediate. + +And that's usually +a slow step. + +There's a propagation step, +where the intermediate reacts + +with your reactant, becomes +a feedstock. + +And then there's some +intermediate plus maybe a + +first product. + +Then there's that second +intermediate, can further + +react to re-form the initial +intermediate. + +And that's the loop. + +That's the loop of the +chain reaction. + +Plus maybe a second product. + +And then there's a +termination step. + +Which is where when your +intermediate, I1, becomes a + +stable product. + +Or I2 becomes a stable +product. + +Basically, where the +intermediates + +come out of the loop. + +So if you look at this loop +here, you have your reactant + +that comes into the loop. + +And then go around the loop. + +You create I1, and maybe +a product comes out. + +Maybe I1 gets terminated, but +most likely it keeps going + +around the loop. + +Creating I2, which reacts with, +the reactant at some + +point gets included +in the circle. + +And I1 comes again, and I2, +and I1 comes, and I2. + +And every time you form +I1 or I2, you may + +form some of the product. + +So this is the initial feed. + +Then you go in circles. + +Eating up R, spitting +out products. + +Keep going in circles. + +And at some point the +termination's going to win, + +and the circle stops, and +the chain has stopped. + +And there are two kinds +of chain reactions. + +There's a stable chain and an +unstable chain, where you get + +your explosion. + +Stable chain, or also called +stationary, chain reaction, is + +where the amount of these +intermediates, I1 and I2, are + +constant in time. + +So you don't build up +any intermediate. + +So I1 constant in time, which is +why it's called stationary. + +Then you have the unstable, +or non-stationary chain. + +Where in that case +your intermediate + +increases in time. + +So in the example I gave here, +you destroy I1 in the first + +step, you create it in +the second step. + +Comes back, you destroy it, you +create it, you destroy it + +you create it. + +For every I1 that you +start out with, you + +end up with an I1. + +There's no change in the +concentration of I1. + +But if instead I put a two here, +than my reactant creates + +an intermediate I1. + +I destroy it. + +Create a new I2, the I2 +decomposes, creates two I1's. + +So after the first cycle, +let's look at the + +concentration of P2 here, after +the first cycle here I + +have one I1, and make one P2. + +But I make two I2's. + +So now I have two I1's +coming in here. + +So I have twice this reaction. + +I make two I2's. + +These two I2's form +two products. + +And now four I1's, +two times two. + +These four I1's go through +the process. + +I get four P2's. + +So third cycle, I +get four P2's. + +And I get two times +four, eight I1's. + +These eight I1's go through, +and I get eight here. + +For cycle, et cetera. + +So I end up with something that +goes like, so this is two + +to the zero power. + +This is two to the first, two +to the second, two to the + +third, et cetera. + +Eventually you get two +to the 25 or whatever + +after so many cycles. + +And if these are gas phase +products, so if there's an + +exothermic process where heat +gets created at any of these + +steps here, then you end +up with a problem. + +The thing goes out of control. + +Sometimes that's a good thing. + +If that's what you want to do. + +And sometimes it's +a bad thing. + +Depends on what you +want to do. + +OK, so we're going to +show two examples + +of these chain reactions. + +One is stable chain and the +other one is unstable chain. + +And go through the process of +how you solve for them. + +So the first example +is taking, so + +let's do a stable chain. + +Take acetaldehyde, CH3CHO, +that decomposers to form + +methane and carbon monoxide. + +That's the reaction. + +And here are the observations. + +There are two observations. + +The first one is that methane +and carbon dioxide are not the + +only products that are formed. + +In fact, there's a trace amount +of ethane and hydrogen, + +dihydrogen are also formed. + +That's a clue to something +funny is going on here. + +That there's a mechanism that's +more complicated than + +just this decomposing in +a first order process. + +And the other thing is that +the rate, if you do an + +experiment and you measure, +somehow you do a half time + +experiment, or an initial rate +experiment, or one of the ways + +that we talked about early on, +you measure the rate of the + +reaction and you find that it's +proportional to something + +to the 3/2 power. + +That's pretty weird. + +It's not a simple mechanism. + +It's pretty weird. + +And so those two observations +are clues, usually, that + +you've got a chain reaction. + +The fact that you have a trace +amount of extra things, that's + +usually due to a termination +reaction. + +It's not a major product, it's +a minor product that's the + +termination of the chain. + +And then this funny power +here, in the kinetics. + +Of the rate of reaction, +that's also + +usually a chain reaction. + +So now we have to figure out +if there's a mechanism that + +supports those observations. + +And I'm going to tell you +possible mechanism that + +supports those observations. + +And you can do experiments to +show that you can fish out + +certain intermediates. + +It's not proved that that's the +ultimate mechanism, but + +it's at least consistent with +these observations. + +More hidden chemistry. + +OK, so this is the mechanism +that's proposed. + +And then we'll figure out +whether this proposed + +mechanism fits the data. + +So, the proposed mechanism is +that the initiation step + +consists of the acetaldehyde, +CH3CHO, + +decomposing into a radical. + +Chain reactions often have +radical processes also. + +Because the radicals love +to make chains. + +To the methyl radical, and +then the CHO radical. + +So this is the first step. + +It's the decomposition +step, it's very slow. + +That molecule doesn't really +want to fall apart. + +Then there's a propagation +step. + +And that's the methyl radical +plus the acetaldehyde, your + +reactant, forming with +the system rate k2. + +Forming CH3CO radical, +plus methane. + +So that is their product right +here, coming out of the first + +step of the propagation. + +And then this new intermediate +here, so there's this one here + +would be I1. + +The methyl radical. + +And the CH3CO radical +here, this is I2. + +And you have to use that +up in the second step. + +CH3CO. + +That decomposes on its own. + +Rate k3, to form the first +intermediate back, the methyl + +radical, plus the second +product, CO. + +And then this intermediate +then feeds + +the first step back. + +And you've got your cycle. + +And every point you spit +out your two products. + +And this could go on forever. + +But it doesn't, because at some +point those two methyl + +radicals, two of those +methyl radicals can + +get along, can collide. + +And in a very easy way. + +So we've got a few termination +steps. + +You can form two times CH3 +radical ethane, C2H6. + +Rate k4, let's call this k4. + +And then there are other side +reactions that can happen. + +For instance, this radical +here, which we + +haven't used up. + +That can also react. + +It's just sitting around, slowly +building up as this + +thing, very slowly building +up, because the first step + +here is very slow. + +You don't need very much +of this methyl radical + +to start the chain. + +Then you start chewing +up the reactant. + +But you're still building up a +little bit of this guy here. + +This is a side reaction. + +It's not a termination reaction, +because that + +radical's not involved in the +chain propagation step. + +But that radical can react with +some other species, M, + +and it could be any of +the other species. + +Because it's just a chaperone. + +It's just a, to help this +thing to decompose. + +CO plus H radical plus +the chaperone back. + +And then that hydrogen radical +here can itself react with + +your reactant. + +CH3 acetaldehyde, CH3CHO, +with a rate k6. + +To form hydrogen gas plus your +intermediate, CH3CO. + +And this intermediate can feed +the step right here. + +OK, so in terms of the +observations, then, we got the + +right products. + +Methane, and carbon monoxide. + +We've got the right amount of +trace stuff, the ethane coming + +out from the termination step. + +And hydrogen gas coming out +from the side reaction. + +And I should probably have +written CO also forming from + +the side reaction - well, CO +is a real product, so it's + +happening both from the side +reactions as well as from the + +main reaction. + +So we've got all the species +taken into account. + +And now we've got to show that +this mechanism here, in fact, + +gives rise to this 3/2 power. + +And I know I won't be able +to do it on one board. + +I want to keep all up, +so let me use up. + +So the first thing, as we've +been doing in kinetics this + +whole time is, you've got to +write down all your rates. + +Once you've got that down, and +you haven't made a mistake, + +then you basically have +the problem solved. + +So you write down all +your rate laws. + +Eventually, what we're +interested in showing is the + +rate of the reaction, +is that power. + +So that's write down what the +rate of the reaction is. + +The rate of reaction is the rate +of formation of one of + +the products. + +Let's say the methane. + +So we write down that rate. + +How was it formed? + +It's formed through +the k2 step. + +It's formed through this +step right here. + +Which is a second order in +CH3 radical times CH3CHO. + +acetaldehyde. + +We're going to keep that in +the back of our mind. + +Because we're going to +need this again. + +Because we want to show, at the +end, that in fact this is, + +this rate is proportional +to this funny power. + +There's the intermediate +sitting here. + +So what's the rate for this +intermediate here is CH3, dt. + +There are many places that +it's coming from. + +It's being created in the first +step, and so the hard + +part here is bean-counting. + +Making sure that you've found +all the places where the + +species is being created. k1 +times acetaldehyde, CH3CHO, + +and then it's destroyed through +the second step, minus + +k2 CH3, better get your +signs right also. + +So there's the destruction, +there's the formation. + +Times acetaldehyde, CH3CHO. + +Then it gets created again, +through the second step of the + +propagation, rate k3. + +Radical CH3CO. + +And then it finally +gets destroyed in + +the termination step. + +We've got to put that in, even +though it may be a very small + +amount compared to these +other amounts there. + +So the termination step is k4. + +And it's a second order +process, CH3 squared. + +We've got another +intermediate. + +We want to write down all +our intermediates here. + +Because they're all +related, it's the + +intermediates sitting here. + +So there are going +to be a couple of + +differential equations. + +So we've got to write +down the equation + +for that CH3CO radical. + +And again, you look +at your mechanism. + +And you find out where +it's coming from. + +It's being created +in this step. + +Destroyed in this step. + +It's also being created +in this step. + +But we're going to ignore that +side reaction for now. + +Just to make our lives a little +bit easier. k2 CH3. + +You've got to put the +termination step in, but the + +side reactions are +not so important. + +CH3. + +Because if you don't put the +termination step in, then your + +reaction's just going +to go on forever. + +That's just not physical. + +Minus k3 CH3CO. + +Creation and destruction. + +OK, so now what do we do? + +Well, we know it's +a chain reaction. + +A stable chain reaction. + +Because we don't create more +intermediates than + +we started out with. + +The first step is always +very slow. + +Initiation at this +step is slow. + +So we're not making very much +of this methyl radical. + +We're not making very +much of it. + +And we're not making any +more of it here. + +So during this whole time that +the chain reaction is + +happening, this methyl radical +here is in small quantities. + +Small quantities and it's +not going to change + +very much at all. + +It's pretty much stationary. + +Magic word is stationary. + +Stationary means it's +not changing. + +Not changing, so which +approximation + +does that belong to? + +That's a steady state +approximation. + +We've got a steady state here. + +Chain, which is going blah, +blah, blah, blah, stationary. + +Steady state. + +All sounds the same. + +So that's the clue here. + +This is going to be a steady +state approximation problem. + +So we're going to put +a steady state here. + +We're going to put a +steady state here. + +We're going to set this +equal to zero. + +We're going to put a steady +state right here. + +We're going to put a +steady state here. + +We're going to set this +equal to zero. + +And suddenly the problem +becomes a + +tractable algebraic problem. + +Now we have, to solve this, +let's do it in one more place. + +Let's put it right here. + +So now we have two equations, +two algebraic equations. + +Two unknowns. + +These two intermediates. + +The concentration of these two + +intermediates are the two unknowns. + +Two equations, two unknowns, +we can solve it. + +It can be messy. + +But not necessarily tricky. + +Just turn the crank. + +And computers could do this. + +So, let me just write +the answer. + +Because I don't want to go +through the algebra. + +After you turn the crank, what +you want is to get this out. + +You've got your two equations, +two unknowns. + +You turn the crank. + +And you get that form for the +concentration of the methyl + +radical two k4. + +CH3CHO turns out to be +to the 1/2 power. + +When you do that. + +There's the funny +power coming up. + +That's going to be here. + +And then this is what you +want to put into here. + +So, and there's the +acetaldehyde, + +sitting right here. + +There's one acetaldehyde +to the 1/2 power, times + +acetaldehyde to the one power, +that's the whole + +thing to a 3/2 power. + +So in fact, the rate is +proportion to the 3/2, + +according to our mechanism. + +And all these rate constants +go into it as well. + +And what we find is that the +rate of reaction is equal to + +k2 times square root +of k1 over two k4. + +CH2CHO to the 3/2 power. + +Basically, k prime to an +effective rate times that. + +It's a typical problem. + +Any questions on this +one right here? + +Yes. + +STUDENT:: [INAUDIBLE] + +PROFESSOR: Here? + +Right here. + +STUDENT:: [INAUDIBLE] + +PROFESSOR: You know, according +to my notes I don't have it, + +yes, you're absolutely right. + +There's a two here. + +Thank you very much. + +It's arbitrary. + +Where the two comes from, I +didn't want to get into this. + +Sometimes it's a matter +of convention. + +When you have a second order +reaction, A plus B going to C, + +you write your rate of the +reaction, as let's write it + +here, k times A times B. +Sometimes we have 2A goes to + +C. You have a rate k2, and the +rate of the reaction is, you + +can write it as dC/dt, which is +minus k2 times A squared. + +But if you write dA/dt, because +of the stoichiometry. + +dA/dt concentration for, so you +have that C is equal to A0 + +minus A, twice. + +So dC/dt is equal to +minus two dA/dt. + +So minus 1/2 dC/dt is +equal to dA/dt. + +So dA/dt is equal to minus +1/2 k2 A squared. + +And instead of having the 1/2 +here, what we do is we + +redefine our rate constant. + +So that's k2 prime is +equal to twice k2. + +You put a two here, +a prime here. + +Get rid of this here. + +And there's the two sitting +right here. + +Purely convention. + +Not something to really +worry about. + +You've just got to have it right +at the beginning, and + +keep that two in, if you're +going to put it in there. + +Does that make sense? + +It's the stoichiometry, it's +because of this two sitting + +right here. + +Then you have a choice. + +You can either say the rate of +the reaction is the rate of + +formation of this thing. + +Or you can say the rate of +reaction is the rate of + +destruction of A. And then if +you say that this is the rate, + +and you don't want to have any +factors in here, then the two + +shows up here. + +If you want to say this is the +rate, you don't want any + +factors in here, then you're +going to have a + +different rate constant. + +Purely arbitrary choice. + +Good question, though. + +Any other questions? + +OK. + +So, there's another thing about +the chain reactions, a + +bit of nomenclature that's +interesting to talk about. + +It's the chain length. + +And that nomenclature is due to +the fact that many of these + +chain reactions are used +for polymer reactions. + +Where you use radical +polymerization and then you + +have, basically, in a polymer +reaction you'll have an + +initiator and then you'll +add a monomer + +through a radical process. + +And another monomer will add +through a radical process. + +Another monomer will add, +another monomer will add, + +another monomer will +add, and then + +you're going to terminate. + +And then you end up +with a chain. + +A polymer chain. + +So your product, instead of +being molecular products, the + +product is adding a monomer +to the chain + +of the growing polymer. + +And then it's meaningful to +talk about chain length. + +So that's where the nomenclature +comes from. + +It's a number of cycles of the +reaction before you get a + +termination step. + +So we can define the chain +length as the number of + +propagation steps per +initiation step. + +That gives you the chain. + +Each one of these is +a propagation step. + +And there's the initiation +step here. + +And this could also be +termination step. + +In in a stable chain, +or termination step. + +There's a termination +step here. + +For every initiation step in a +stable chain, you've got a + +termination step. + +Because you're not building +up intermediates. + +So you create it. + +At the end of the chain +you terminate it. + +You have as many initiation +as termination steps. + +So you have a choice here, +in the algebra. + +You can use either one. + +So another way, instead +of doing numbers here, + +you can also rate. + +This is also the rate of +propagation divided by the + +rate of initiation. + +You just take the derivative of +this with respect to time + +of the top and bottom. + +Same thing. + +So we can also define it as rate +of propagation divided by + +rate of, let's say, +termination. + +Or initiation, whichever is your +favorite one to use to + +make it simple. + +So, for instance, in our example +here, the rate of + +propagation is the rate, also +the rate of product formation. + +Since we have a product +formation. + +Rate of propagation is +the rate of forming + +this methane here. + +So in our example here, the rate +of forming the methane is + +the rate reaction here. + +This is this right here. + +So you can plug this +here on top. + +I may not write it down because +I don't want to spend + +time writing too much down. + +So this guy goes +right in there. + +And then the rate of termination +is going to be, + +the rate of termination is, +well, let's not use + +termination because that has +intermediates in it it. + +Let's use initiation. + +Since we have a choice. + +Rate of initiation. + +Either one works fine. + +Initiation is k1 times the +acetaldehyde. k1 times CH3CHO. + +So there's the 3/2 power, +which, where is it? + +There's 1/2 plus, so 1/2 plus +one is the 3/2 power here. + +So there's CH3CHO to +the 3/2 power. + +CH3CHO to the 3/2 power, then +some effective rate k prime. + +And you end up with chain length +going to the 1/2 power. + +So there's some k double prime, +so effective rate times + +CH3CHO to the 1/2 power. + +That's the length of chain. + +It depends on the concentration +of the reactant. + +And the typical chain's on the +order of a couple hundred or + +something like this, usually. + +You always have a termination +step at at some point. + +Maybe a few thousand if you're +doing polymer chemistry and + +sometimes millions, if +you're very good at + +doing polymer chemistry. + +OK, any questions on +the stable chain? + +OK, let's do the +explosion now. + +And so this is the +typical example. + +Of an unstable chain. + +It's the formation of water +from hydrogen and oxygen. + +2 H2O. + +That's the reaction. + +Gas phase reaction. + +And the observation is that +that, well, you know the + +observation. + +You put a spark in a balloon +that contains hydrogen and + +oxygen and get an explosion. + +So we're going to have +to account for that. + +Sometimes you don't +get an explosion. + +Sometimes it kind +of peters out. + +You have a drop of +water coming out. + +Not bad. + +And there's a temperature +dependence to it also. + +So, whatever mechanism we put in +there needs to account for + +all the pressure dependence, the +stoichiometry dependence, + +and the temperature +dependence. + +So this is the mechanism +that's proposed. + +Initiation. + +You have your hydrogen +molecule. + +Spark, or something slow +that decomposes it to + +two hydrogen radicals. + +This could be a spark plug, +and every time you make a + +little bit of the radical. + +Then you have a branching +step. + +Where your radical reacts with +the oxygen molecule to form a + +hydroxyl radical. + +Plus an oxygen. + +Oxygen atom plus your hydrogen +gas, your reactant, reacts to + +form more hydroxyl radical plus +the initial intermediate. + +And then the hydroxyl radical, +I don't know why I have + +parentheses here, hydroxyl +radical reacts with the + +reactant again, the hydrogen +gas, k3, to form more of the + +initial intermediate plus +water, your product. + +So there are three steps +to the branching here. + +You get one intermediate, one +of the initial intermediates + +here coming in. + +Forms a second intermediate. + +OH radical. + +Two OH radicals. + +And the OH radicals +form the hydrogen. + +There's also radical hydrogen +that's formed right here. + +So you have this formation. + +So because you're forming two +hydroxyl radicals here, in + +this step here you're actually +forming the equivalent of two + +hydrogen radicals. + +So, one hydrogen atom here. + +After going through the +branching, you end up with + +three hydrogen radicals. + +So you go from one to +three in one cycle. + +And the second time around, +you go from three to nine. + +The next time, you go +from nine to 27. + +Pretty soon you've +got a couple of + +billion hydrogen radicals. + +And that's the problem +right there. + +Or the opportunity. + +The opportunity to +get something + +that goes out of control. + +And there are termination +steps. + +That we need to take +into account. + +The hydrogen radical +can hit the wall. + +Before it finds something +to react with. + +And gets stuck. + +So if the pressure is +low enough, you know + +that's going to happen. + +You're going to make +a hydrogen radical. + +Hardly any gas molecules +around. + +It's going to find a wall, +it's going to get stuck. + +It's very reactive. + +So that's going to terminate +the process. + +Hydrogen radical could re-find +an oxygen and another + +chaperone, that's a termolecular +process. + +That's an unlikely process. + +But nevertheless, +it could happen. + +With another termination step, +to form the HO2 radical plus + +M. And then that HO2 too radical +can react in a side + +reaction to form some +products, but not + +be part of the chain. + +Yes. + +STUDENT:: [INAUDIBLE] + +PROFESSOR: How do we get +three hydrogens? + +Because there are two hydroxyl +radicals here. + +And so in this step here, you +actually have two hydroxyl + +radicals to form two, so I could +multiply this by two. + +But you usually don't do that. + +So this already tells you what +conditions you're going to + +get, with something where the +termination is fast, compared + +to the propagation. + +Because you have low pressure. + +If you can't get that hydrogen +radical to react with + +something before hitting the +wall, you're going to be OK. + +You're not getting +an explosion. + +This tells you that a very +high pressure, where the + +probability of having a +three-body collision becomes + +high enough, then you're +going to terminate + +the chain as well. + +Those hydrogen radicals are +going to find oxygen molecules + +and some other molecule and form +this radical before you + +propagate the chain. + +At least some reasonably +high pressure. + +So that's the clue here. + +What's the strategy? + +The strategy is to assume that +everything's going to be fine. + +That is, stable. + +That's going to be +the strategy. + +And then we're going +to do a proof by + +contradiction, basically. + +We can assume that the +chain is stable. + +That we can use the steady +state approximation. + +We're going to apply the steady +state approximation. + +We're going to find where +that breaks down. + +And where it breaks down means +that it wasn't right. + +That the intermediate +concentration was too high. + +And that means that we're going +to get an explosion. + +That's the logic. + +So strategy is a proof by +contradiction, basically. + +Proof by contradiction. + +So we're going to assume that +the propagation, or the + +intermediates, are in +small quantities. + +We're going to assume that we +can use the steady state + +approximation, the d[O]/dt +steady state is equal to zero. + +That the hydroxyl radical, +d[OH]/dt, steady state is + +equal to zero. + +And that d[H]/dt steady state +is equal to zero. + +These are going to be +our assumptions. + +That all the intermediates +are in small quantities. + +And they don't change +very much. + +And now we're going to write +down, you write down the rates + +that correspond to these guys. + +And then you solve. + +So I'm only going to do +this first one here. + +So you write dO/dt, you see +where it gets formed. + +It gets formed in the +first step here. + +So it's going to be k1 times H +radical times O2, and it gets + +destroyed in the second +step here, minus k2 + +times O times H2. + +You set the steady state +approximation, you get a + +steady state. + +Steady state here, you set +that equal to zero. + +You solve for O, radical +O, steady state. + +And you find that it's k1 times +H times O2 times k2 H2. + +Then you do the same thing +for the other radicals. + +You solve for OH steady state. + +And you get some expression +which is in the notes. + +I'm not going to write +it down, it's + +going to get too messy. + +But the expression that I will +write down is the final + +expression, which we're going +to be taking into account. + +So, this expression here, +for the oxygen atom. + +It has the radical in there. + +So it's not, we'd like something +that's just in terms + +of the rates and either +products or reactants. + +And this hydroxyl radical, the +concentration turns out, it + +will also be a function of +the concentration of + +the hydrogen radical. + +So what we really want, I don't +want to cover this up, + +let me go on this board here. + +So when you solve for this, the +hydrogen atom is where you + +get something that's free +of intermediates. + +And has just rates in it. + +There's a termination rate here +going in the denominator. + +Another termination rate +in the denominator. + +Times O2 times M, where M could +be anything, really. + +Minus, and there's the creation +rate of the first + +propagation step. + +O2 here. + +So now we have to see +whether or not our + +approximation was valid. + +We made an approximation. + +We said the steady state +approximation was valid. + +If it is valid, then this +concentration, this pressure + +here, needs to be small. + +Needs to be small +at all times. + +If it's not small, then steady +state is not valid, we have a + +branching non-stable chain and +we've got an explosion. + +So let's look at the different +possibilities here. + +What are the possibilities? + +Well, the first possibility is +that as we saw intuitively, + +when we wrote down this equation +here, the first + +possibility is that we're +at low pressure. + +Where at low pressure, then, k1 +times oxygen is very small. + +Because the concentration of +oxygen is small, the pressure + +is small. k5 times the pressure +of oxygen times the + +pressure of M is small also. + +So k5 T O M, O2 times +M is small. + +And they're both, then, much +smaller than k4 times the + +time. k4 termination. + +The hydrogen radical hits +the wall before + +finding anything else. + +End of chain. + +So in the equation here, +these two guys are + +small compared to here. + +RI, the initiation rate, +is very small. + +You control that +by your spark. + +Once a second, once a minute. + +Could be really, slow. + +Steady state is good. + +We don't have an +unstable chain. + +No explosion here. + +Medium pressure. + +You've got a medium pressure +where two k1 times oxygen + +concentration is +approximately. + +You're building up your +concentration. + +This is getting bigger here. + +This is a constant. + +This is getting bigger. + +This is also getting bigger, but +you've got this rate here + +and this rate here. + +At some point, at some point, +this rate here, two k1 times + +oxygen concentration, is going +to be on the order of k4 T + +plus k5 T times oxygen times M. +At some point it's going to + +be like that. + +And then you're in +big trouble. + +You're in big trouble, because +you've got a denominator here + +that's really tiny. + +Could be even, if you hit it +right on the nail, you get + +zero in the denominator and then +you're in real trouble + +from the math perspective. + +But from the physical science +perspective, it's + +not being in trouble. + +Is just that your approximation +is wrong. + +The approximation that +you were in a + +stationary state was wrong. + +And so that means that in this +case here, if you want to have + +an explosion, you've got it. + +So you adjust everything until +you're in a situation. + +And then finally, you keep +increasing the pressure. + +And then if you increase it +high enough, then this guy + +here, which goes as the square +of the pressures, is going to + +overwhelm this. + +Which goes linearly +with pressure. + +And k5, the termination step, +O2 times M, is going to be + +bigger than two k1 times +the pressure of O2. + +And then you've got something +small again. + +This is where that's hydrogen +radical here is able to + +undergo a termolecular process +before finding a reactant. + +Then steady state is valid. + +OK. + +At very high pressures, you get +in trouble again, because + +this hydroxyl radical, this HO2 +radical, so at very high + +pressure. then what happens +is that you have this side + +reaction, HO2 radical plus +hydrogen goes to H2O plus + +hydroxyl radical. + +So there's a probability that +this radical here finds a + +hydrogen molecule. + +And then feeds into the +propagation through this + +hydroxyl radical that's +the result. + +And then that keeps the +chain propagating. + +So at very high pressure, +you're in trouble again. + +And you get an explosion +again. + +So you can plot this as a +function of the pressure. + +And we're going to put +pressure, actually, + +on the y axis here. + +Let's put pressure here. + +Put temperature here. + +And so for a given temperature, +let's call it + +temperature T prime, at low +pressure there's no explosion. + +Then there's a range +of pressures. + +Where there's an explosion. + +Medium pressures. + +And then a high pressure +termination wins again. + +And then if it's really high +you get explosion again. + +You do this for, as a function +of temperature. + +And what you find that is a +diagram, looks like a phase + +diagram, that looks something +like this. + +Where at high temperature, you +get an explosion at low + +temperatures, and this steady +state is valid. + +OK, any questions on this? + +Don't try this in +your kitchen. + +Go to the desert if you +want to do this. + +Or don't do it either. + +OK. \ No newline at end of file diff --git a/o_qO7RYBF10.txt b/o_qO7RYBF10.txt new file mode 100644 index 0000000000000000000000000000000000000000..5b052db7821775b3ac65e4216b449256662d2103 --- /dev/null +++ b/o_qO7RYBF10.txt @@ -0,0 +1,1539 @@ +align:start position:0% + +let us now study a very important + + align:start position:0% +let us now study a very important + + + align:start position:0% +let us now study a very important +counting problem the problem of counting + + align:start position:0% +counting problem the problem of counting + + + align:start position:0% +counting problem the problem of counting +combinations what is a combination we + + align:start position:0% +combinations what is a combination we + + + align:start position:0% +combinations what is a combination we +start with a set of n elements and we're + + align:start position:0% +start with a set of n elements and we're + + + align:start position:0% +start with a set of n elements and we're +also given a non negative integer K and + + align:start position:0% +also given a non negative integer K and + + + align:start position:0% +also given a non negative integer K and +we want to construct or to choose a + + align:start position:0% +we want to construct or to choose a + + + align:start position:0% +we want to construct or to choose a +subset of the original set that has + + align:start position:0% +subset of the original set that has + + + align:start position:0% +subset of the original set that has +exactly K elements in different language + + align:start position:0% +exactly K elements in different language + + + align:start position:0% +exactly K elements in different language +we want to pick a combination of K + + align:start position:0% +we want to pick a combination of K + + + align:start position:0% +we want to pick a combination of K +elements of the original set in how many + + align:start position:0% +elements of the original set in how many + + + align:start position:0% +elements of the original set in how many +ways can this be done + + align:start position:0% +ways can this be done + + + align:start position:0% +ways can this be done +let us introduce some notation we use + + align:start position:0% +let us introduce some notation we use + + + align:start position:0% +let us introduce some notation we use +this notation here which we read as n + + align:start position:0% +this notation here which we read as n + + + align:start position:0% +this notation here which we read as n +choose K to denote exactly the quantity + + align:start position:0% +choose K to denote exactly the quantity + + + align:start position:0% +choose K to denote exactly the quantity +that we want to calculate namely the + + align:start position:0% +that we want to calculate namely the + + + align:start position:0% +that we want to calculate namely the +number of subsets of a given an element + + align:start position:0% +number of subsets of a given an element + + + align:start position:0% +number of subsets of a given an element +set where we only count those subsets + + align:start position:0% +set where we only count those subsets + + + align:start position:0% +set where we only count those subsets +that have exactly K elements how are we + + align:start position:0% +that have exactly K elements how are we + + + align:start position:0% +that have exactly K elements how are we +going to calculate this quantity instead + + align:start position:0% +going to calculate this quantity instead + + + align:start position:0% +going to calculate this quantity instead +of proceeding directly we're going to + + align:start position:0% +of proceeding directly we're going to + + + align:start position:0% +of proceeding directly we're going to +consider a somewhat different counting + + align:start position:0% +consider a somewhat different counting + + + align:start position:0% +consider a somewhat different counting +problem which we're going to approach in + + align:start position:0% +problem which we're going to approach in + + + align:start position:0% +problem which we're going to approach in +two different ways + + align:start position:0% +two different ways + + + align:start position:0% +two different ways +get two different answers compare those + + align:start position:0% +get two different answers compare those + + + align:start position:0% +get two different answers compare those +answers and by comparing them we are + + align:start position:0% +answers and by comparing them we are + + + align:start position:0% +answers and by comparing them we are +going to get an equation which is going + + align:start position:0% +going to get an equation which is going + + + align:start position:0% +going to get an equation which is going +to give us in the end the desired number + + align:start position:0% +to give us in the end the desired number + + + align:start position:0% +to give us in the end the desired number +the alternative problem that we're going + + align:start position:0% +the alternative problem that we're going + + + align:start position:0% +the alternative problem that we're going +to use is the following we start as + + align:start position:0% +to use is the following we start as + + + align:start position:0% +to use is the following we start as +before with our given set that consists + + align:start position:0% +before with our given set that consists + + + align:start position:0% +before with our given set that consists +of n elements but instead of picking a + + align:start position:0% +of n elements but instead of picking a + + + align:start position:0% +of n elements but instead of picking a +subset work what we want to do is to + + align:start position:0% +subset work what we want to do is to + + + align:start position:0% +subset work what we want to do is to +construct a list an ordered sequence + + align:start position:0% +construct a list an ordered sequence + + + align:start position:0% +construct a list an ordered sequence +that consists of K distinct elements + + align:start position:0% +that consists of K distinct elements + + + align:start position:0% +that consists of K distinct elements +taken out of the original set so we + + align:start position:0% +taken out of the original set so we + + + align:start position:0% +taken out of the original set so we +think of having K different slots and we + + align:start position:0% +think of having K different slots and we + + + align:start position:0% +think of having K different slots and we +want to fill each one of those slots + + align:start position:0% +want to fill each one of those slots + + + align:start position:0% +want to fill each one of those slots +with one of the elements of the original + + align:start position:0% +with one of the elements of the original + + + align:start position:0% +with one of the elements of the original +set in how many ways can this be done + + align:start position:0% +set in how many ways can this be done + + + align:start position:0% +set in how many ways can this be done +well we want to use the counting + + align:start position:0% +well we want to use the counting + + + align:start position:0% +well we want to use the counting +principle so we want to decompose this + + align:start position:0% +principle so we want to decompose this + + + align:start position:0% +principle so we want to decompose this +problem into a in two stages so what we + + align:start position:0% +problem into a in two stages so what we + + + align:start position:0% +problem into a in two stages so what we +can do is to choose each one of the K + + align:start position:0% +can do is to choose each one of the K + + + align:start position:0% +can do is to choose each one of the K +items that go into this list one at a + + align:start position:0% +items that go into this list one at a + + + align:start position:0% +items that go into this list one at a +time + + align:start position:0% +time + + + align:start position:0% +time +we first choose an item that goes to the + + align:start position:0% +we first choose an item that goes to the + + + align:start position:0% +we first choose an item that goes to the +first position to the first slot having + + align:start position:0% +first position to the first slot having + + + align:start position:0% +first position to the first slot having +used one of the items in that set we're + + align:start position:0% +used one of the items in that set we're + + + align:start position:0% +used one of the items in that set we're +left with n minus 1 choices for the item + + align:start position:0% +left with n minus 1 choices for the item + + + align:start position:0% +left with n minus 1 choices for the item +that can go into the second slot and we + + align:start position:0% +that can go into the second slot and we + + + align:start position:0% +that can go into the second slot and we +continue similarly when we're ready to + + align:start position:0% +continue similarly when we're ready to + + + align:start position:0% +continue similarly when we're ready to +fill the last slot we have already used + + align:start position:0% +fill the last slot we have already used + + + align:start position:0% +fill the last slot we have already used +K minus 1 of the items which means that + + align:start position:0% +K minus 1 of the items which means that + + + align:start position:0% +K minus 1 of the items which means that +the number of choices that we're going + + align:start position:0% +the number of choices that we're going + + + align:start position:0% +the number of choices that we're going +to have at that stage is n minus K plus + + align:start position:0% +to have at that stage is n minus K plus + + + align:start position:0% +to have at that stage is n minus K plus +1 at this point it's also useful to + + align:start position:0% +1 at this point it's also useful to + + + align:start position:0% +1 at this point it's also useful to +simplify that expression a bit we + + align:start position:0% +simplify that expression a bit we + + + align:start position:0% +simplify that expression a bit we +observe that this is the same as n + + align:start position:0% +observe that this is the same as n + + + align:start position:0% +observe that this is the same as n +factorial divided by n minus K factorial + + align:start position:0% +factorial divided by n minus K factorial + + + align:start position:0% +factorial divided by n minus K factorial +why is this the case you can verify that + + align:start position:0% +why is this the case you can verify that + + + align:start position:0% +why is this the case you can verify that +this is correct by moving the + + align:start position:0% +this is correct by moving the + + + align:start position:0% +this is correct by moving the +denominator to the other side and when + + align:start position:0% +denominator to the other side and when + + + align:start position:0% +denominator to the other side and when +you do that you realize that you have + + align:start position:0% +you do that you realize that you have + + + align:start position:0% +you do that you realize that you have +the product of all terms from n down to + + align:start position:0% +the product of all terms from n down to + + + align:start position:0% +the product of all terms from n down to +n minus k plus 1 and then you have the + + align:start position:0% +n minus k plus 1 and then you have the + + + align:start position:0% +n minus k plus 1 and then you have the +product of n minus K going all the way + + align:start position:0% +product of n minus K going all the way + + + align:start position:0% +product of n minus K going all the way +down to 1 + + align:start position:0% +down to 1 + + + align:start position:0% +down to 1 +then that's exactly the product which is + + align:start position:0% +then that's exactly the product which is + + + align:start position:0% +then that's exactly the product which is +the same as n factorial it's the product + + align:start position:0% +the same as n factorial it's the product + + + align:start position:0% +the same as n factorial it's the product +of all integers from n all the way down + + align:start position:0% +of all integers from n all the way down + + + align:start position:0% +of all integers from n all the way down +to 1 so this was the first method of + + align:start position:0% +to 1 so this was the first method of + + + align:start position:0% +to 1 so this was the first method of +constructing the list that we wanted how + + align:start position:0% +constructing the list that we wanted how + + + align:start position:0% +constructing the list that we wanted how +about the second method what we can do + + align:start position:0% +about the second method what we can do + + + align:start position:0% +about the second method what we can do +is to first choose K items out of the + + align:start position:0% +is to first choose K items out of the + + + align:start position:0% +is to first choose K items out of the +original set and then take those K items + + align:start position:0% +original set and then take those K items + + + align:start position:0% +original set and then take those K items +and order them in a sequence to obtain + + align:start position:0% +and order them in a sequence to obtain + + + align:start position:0% +and order them in a sequence to obtain +an ordered list so we construct our + + align:start position:0% +an ordered list so we construct our + + + align:start position:0% +an ordered list so we construct our +ordered list in two stages in the first + + align:start position:0% +ordered list in two stages in the first + + + align:start position:0% +ordered list in two stages in the first +stage how many choices we have that's + + align:start position:0% +stage how many choices we have that's + + + align:start position:0% +stage how many choices we have that's +the number of subsets with K elements + + align:start position:0% +the number of subsets with K elements + + + align:start position:0% +the number of subsets with K elements +out of the original set this number we + + align:start position:0% +out of the original set this number we + + + align:start position:0% +out of the original set this number we +don't know what it is that's what we're + + align:start position:0% +don't know what it is that's what we're + + + align:start position:0% +don't know what it is that's what we're +trying to calculate but we have a symbol + + align:start position:0% +trying to calculate but we have a symbol + + + align:start position:0% +trying to calculate but we have a symbol +for it it's n choose K how about the + + align:start position:0% +for it it's n choose K how about the + + + align:start position:0% +for it it's n choose K how about the +second stage we have K elements and we + + align:start position:0% +second stage we have K elements and we + + + align:start position:0% +second stage we have K elements and we +want to arrange them in a sequence + + align:start position:0% +want to arrange them in a sequence + + + align:start position:0% +want to arrange them in a sequence +that is we want to form a permutation of + + align:start position:0% +that is we want to form a permutation of + + + align:start position:0% +that is we want to form a permutation of +those K elements this is a problem that + + align:start position:0% +those K elements this is a problem that + + + align:start position:0% +those K elements this is a problem that +we have already studied and we know that + + align:start position:0% +we have already studied and we know that + + + align:start position:0% +we have already studied and we know that +the answer is K factorial according to + + align:start position:0% +the answer is K factorial according to + + + align:start position:0% +the answer is K factorial according to +the counting principle the number of + + align:start position:0% +the counting principle the number of + + + align:start position:0% +the counting principle the number of +ways that this two-stage construction + + align:start position:0% +ways that this two-stage construction + + + align:start position:0% +ways that this two-stage construction +can be made is equal to the product of + + align:start position:0% +can be made is equal to the product of + + + align:start position:0% +can be made is equal to the product of +the number of ways number of options + + align:start position:0% +the number of ways number of options + + + align:start position:0% +the number of ways number of options +that we have at the first stage times + + align:start position:0% +that we have at the first stage times + + + align:start position:0% +that we have at the first stage times +the number of options that we have at + + align:start position:0% +the number of options that we have at + + + align:start position:0% +the number of options that we have at +the second stage so this is one answer + + align:start position:0% +the second stage so this is one answer + + + align:start position:0% +the second stage so this is one answer +for the number of possible ordered + + align:start position:0% +for the number of possible ordered + + + align:start position:0% +for the number of possible ordered +sequences this is another answer of + + align:start position:0% +sequences this is another answer of + + + align:start position:0% +sequences this is another answer of +course both of them are correct and + + align:start position:0% +course both of them are correct and + + + align:start position:0% +course both of them are correct and +therefore they have to be equal and by + + align:start position:0% +therefore they have to be equal and by + + + align:start position:0% +therefore they have to be equal and by +using that equality we can now find a + + align:start position:0% +using that equality we can now find a + + + align:start position:0% +using that equality we can now find a +formula for this coefficient and choose + + align:start position:0% +formula for this coefficient and choose + + + align:start position:0% +formula for this coefficient and choose +K simply by taking this K factorial + + align:start position:0% +K simply by taking this K factorial + + + align:start position:0% +K simply by taking this K factorial +factor and sending it to the denominator + + align:start position:0% +factor and sending it to the denominator + + + align:start position:0% +factor and sending it to the denominator +of that expression so by equating this + + align:start position:0% +of that expression so by equating this + + + align:start position:0% +of that expression so by equating this +expression with that expression here we + + align:start position:0% +expression with that expression here we + + + align:start position:0% +expression with that expression here we +find the final answer which is that the + + align:start position:0% +find the final answer which is that the + + + align:start position:0% +find the final answer which is that the +number of choices and choose K is equal + + align:start position:0% +number of choices and choose K is equal + + + align:start position:0% +number of choices and choose K is equal +to this expression here now this + + align:start position:0% +to this expression here now this + + + align:start position:0% +to this expression here now this +expression is valid only for numbers + + align:start position:0% +expression is valid only for numbers + + + align:start position:0% +expression is valid only for numbers +that make sense + + align:start position:0% +that make sense + + + align:start position:0% +that make sense +so n can be any integer any non-negative + + align:start position:0% +so n can be any integer any non-negative + + + align:start position:0% +so n can be any integer any non-negative +integer and K the only case that makes + + align:start position:0% +integer and K the only case that makes + + + align:start position:0% +integer and K the only case that makes +sense would be case from 0 1 up to n you + + align:start position:0% +sense would be case from 0 1 up to n you + + + align:start position:0% +sense would be case from 0 1 up to n you +may be wondering about some of the + + align:start position:0% +may be wondering about some of the + + + align:start position:0% +may be wondering about some of the +extreme cases of that formula what does + + align:start position:0% +extreme cases of that formula what does + + + align:start position:0% +extreme cases of that formula what does +it mean for and to be 0 or for k equal + + align:start position:0% +it mean for and to be 0 or for k equal + + + align:start position:0% +it mean for and to be 0 or for k equal +to 0 so let us consider now some extent + + align:start position:0% +to 0 so let us consider now some extent + + + align:start position:0% +to 0 so let us consider now some extent +of these extreme cases and make a sanity + + align:start position:0% +of these extreme cases and make a sanity + + + align:start position:0% +of these extreme cases and make a sanity +check about this formula so this is the + + align:start position:0% +check about this formula so this is the + + + align:start position:0% +check about this formula so this is the +formula that we have and that we want to + + align:start position:0% +formula that we have and that we want to + + + align:start position:0% +formula that we have and that we want to +check the first case to consider is the + + align:start position:0% +check the first case to consider is the + + + align:start position:0% +check the first case to consider is the +extreme case of n choose n what does + + align:start position:0% +extreme case of n choose n what does + + + align:start position:0% +extreme case of n choose n what does +that correspond to out of a set with n + + align:start position:0% +that correspond to out of a set with n + + + align:start position:0% +that correspond to out of a set with n +elements we want to choose a subset that + + align:start position:0% +elements we want to choose a subset that + + + align:start position:0% +elements we want to choose a subset that +has n elements + + align:start position:0% +has n elements + + + align:start position:0% +has n elements +there's not much of a choice here you + + align:start position:0% +there's not much of a choice here you + + + align:start position:0% +there's not much of a choice here you +just have to take all of the elements of + + align:start position:0% +just have to take all of the elements of + + + align:start position:0% +just have to take all of the elements of +the original set and put them in the + + align:start position:0% +the original set and put them in the + + + align:start position:0% +the original set and put them in the +subset so the subset is the same as the + + align:start position:0% +subset so the subset is the same as the + + + align:start position:0% +subset so the subset is the same as the +set itself so we only have one choice + + align:start position:0% +set itself so we only have one choice + + + align:start position:0% +set itself so we only have one choice +here that should be the answer let's + + align:start position:0% +here that should be the answer let's + + + align:start position:0% +here that should be the answer let's +check it with the formula the formula + + align:start position:0% +check it with the formula the formula + + + align:start position:0% +check it with the formula the formula +gives us n factorial divided by n + + align:start position:0% +gives us n factorial divided by n + + + align:start position:0% +gives us n factorial divided by n +factorial and then since K is equal to n + + align:start position:0% +factorial and then since K is equal to n + + + align:start position:0% +factorial and then since K is equal to n +here we get 0 factorial is this correct + + align:start position:0% +here we get 0 factorial is this correct + + + align:start position:0% +here we get 0 factorial is this correct +well it becomes correct as long as we + + align:start position:0% +well it becomes correct as long as we + + + align:start position:0% +well it becomes correct as long as we +adopt the convention that 0 factorial is + + align:start position:0% +adopt the convention that 0 factorial is + + + align:start position:0% +adopt the convention that 0 factorial is +equal to 1 we're going to adopt this + + align:start position:0% +equal to 1 we're going to adopt this + + + align:start position:0% +equal to 1 we're going to adopt this +convention and keep it throughout this + + align:start position:0% +convention and keep it throughout this + + + align:start position:0% +convention and keep it throughout this +course let us look at another extreme + + align:start position:0% +course let us look at another extreme + + + align:start position:0% +course let us look at another extreme +case now the coefficient and choose 0 + + align:start position:0% +case now the coefficient and choose 0 + + + align:start position:0% +case now the coefficient and choose 0 +this time let us start from the formula + + align:start position:0% +this time let us start from the formula + + + align:start position:0% +this time let us start from the formula +the formula tells us that this should be + + align:start position:0% +the formula tells us that this should be + + + align:start position:0% +the formula tells us that this should be +n factorial divided by 0 factorial and + + align:start position:0% +n factorial divided by 0 factorial and + + + align:start position:0% +n factorial divided by 0 factorial and +divided by n factorial + + align:start position:0% +divided by n factorial + + + align:start position:0% +divided by n factorial +since the number K is equal to 0 using + + align:start position:0% +since the number K is equal to 0 using + + + align:start position:0% +since the number K is equal to 0 using +the convention that we have this is + + align:start position:0% +the convention that we have this is + + + align:start position:0% +the convention that we have this is +equal to 1 so this is again equal to 1 + + align:start position:0% +equal to 1 so this is again equal to 1 + + + align:start position:0% +equal to 1 so this is again equal to 1 +is it the correct answer how many + + align:start position:0% +is it the correct answer how many + + + align:start position:0% +is it the correct answer how many +subsets of a given set are there that + + align:start position:0% +subsets of a given set are there that + + + align:start position:0% +subsets of a given set are there that +have exactly zero elements well there's + + align:start position:0% +have exactly zero elements well there's + + + align:start position:0% +have exactly zero elements well there's +only one subset that has exactly 0 + + align:start position:0% +only one subset that has exactly 0 + + + align:start position:0% +only one subset that has exactly 0 +elements and this is the empty set so + + align:start position:0% +elements and this is the empty set so + + + align:start position:0% +elements and this is the empty set so +this explains this particular answer and + + align:start position:0% +this explains this particular answer and + + + align:start position:0% +this explains this particular answer and +shows that it is meaningful and that it + + align:start position:0% +shows that it is meaningful and that it + + + align:start position:0% +shows that it is meaningful and that it +makes sense now let us use our + + align:start position:0% +makes sense now let us use our + + + align:start position:0% +makes sense now let us use our +understanding of those coefficients to + + align:start position:0% +understanding of those coefficients to + + + align:start position:0% +understanding of those coefficients to +solve the somewhat harder problem + + align:start position:0% +solve the somewhat harder problem + + + align:start position:0% +solve the somewhat harder problem +suppose that for some reason you want to + + align:start position:0% +suppose that for some reason you want to + + + align:start position:0% +suppose that for some reason you want to +calculate this sum what is it going to + + align:start position:0% +calculate this sum what is it going to + + + align:start position:0% +calculate this sum what is it going to +be one way of approaching this problem + + align:start position:0% +be one way of approaching this problem + + + align:start position:0% +be one way of approaching this problem +is to use the formula for these + + align:start position:0% +is to use the formula for these + + + align:start position:0% +is to use the formula for these +coefficients do a lot of algebra and if + + align:start position:0% +coefficients do a lot of algebra and if + + + align:start position:0% +coefficients do a lot of algebra and if +you are really patient and careful + + align:start position:0% +you are really patient and careful + + + align:start position:0% +you are really patient and careful +eventually you should be able to get the + + align:start position:0% +eventually you should be able to get the + + + align:start position:0% +eventually you should be able to get the +right answer but this is very painful + + align:start position:0% +right answer but this is very painful + + + align:start position:0% +right answer but this is very painful +let us think whether there's a clever + + align:start position:0% +let us think whether there's a clever + + + align:start position:0% +let us think whether there's a clever +way a shortcut of + + align:start position:0% +way a shortcut of + + + align:start position:0% +way a shortcut of +deigning this answer let us try to think + + align:start position:0% +deigning this answer let us try to think + + + align:start position:0% +deigning this answer let us try to think +what this sum is all about this sum + + align:start position:0% +what this sum is all about this sum + + + align:start position:0% +what this sum is all about this sum +includes this term which is the number + + align:start position:0% +includes this term which is the number + + + align:start position:0% +includes this term which is the number +of zero element subsets this number + + align:start position:0% +of zero element subsets this number + + + align:start position:0% +of zero element subsets this number +which is the number of subsets that have + + align:start position:0% +which is the number of subsets that have + + + align:start position:0% +which is the number of subsets that have +one element and we keep going all the + + align:start position:0% +one element and we keep going all the + + + align:start position:0% +one element and we keep going all the +way to the number of subsets that have + + align:start position:0% +way to the number of subsets that have + + + align:start position:0% +way to the number of subsets that have +exactly n elements so we're counting + + align:start position:0% +exactly n elements so we're counting + + + align:start position:0% +exactly n elements so we're counting +zero element subsets one element subsets + + align:start position:0% +zero element subsets one element subsets + + + align:start position:0% +zero element subsets one element subsets +all the way up to n so what we're + + align:start position:0% +all the way up to n so what we're + + + align:start position:0% +all the way up to n so what we're +counting really is the number of all + + align:start position:0% +counting really is the number of all + + + align:start position:0% +counting really is the number of all +subsets of our given set but this is a + + align:start position:0% +subsets of our given set but this is a + + + align:start position:0% +subsets of our given set but this is a +number that we know what it is the + + align:start position:0% +number that we know what it is the + + + align:start position:0% +number that we know what it is the +number of subsets of a given set with n + + align:start position:0% +number of subsets of a given set with n + + + align:start position:0% +number of subsets of a given set with n +elements is two to the N so by thinking + + align:start position:0% +elements is two to the N so by thinking + + + align:start position:0% +elements is two to the N so by thinking +carefully and interpreting the terms in + + align:start position:0% +carefully and interpreting the terms in + + + align:start position:0% +carefully and interpreting the terms in +this sum we were able to solve this + + align:start position:0% +this sum we were able to solve this + + + align:start position:0% +this sum we were able to solve this +problem very fast something that would + + align:start position:0% +problem very fast something that would + + + align:start position:0% +problem very fast something that would +be extremely tedious if we had tried to + + align:start position:0% +be extremely tedious if we had tried to + + + align:start position:0% +be extremely tedious if we had tried to +do it algebraically for some practice + + align:start position:0% +do it algebraically for some practice + + + align:start position:0% +do it algebraically for some practice +with this idea why don't you pause at + + align:start position:0% +with this idea why don't you pause at + + + align:start position:0% +with this idea why don't you pause at +this point and try to solve the problem + + align:start position:0% +this point and try to solve the problem + + + align:start position:0% +this point and try to solve the problem +of a similar nature \ No newline at end of file diff --git a/ogrcXqbvbL4.txt b/ogrcXqbvbL4.txt new file mode 100644 index 0000000000000000000000000000000000000000..614cebcf07f9943dab3c2570674540a617a6b80a --- /dev/null +++ b/ogrcXqbvbL4.txt @@ -0,0 +1,12355 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu question we know how to do + + align:start position:0% +ocw.mit.edu question we know how to do + + + align:start position:0% +ocw.mit.edu question we know how to do +matching and running we've seen an + + align:start position:0% +matching and running we've seen an + + + align:start position:0% +matching and running we've seen an +example of that in this Theory there's + + align:start position:0% +example of that in this Theory there's + + + align:start position:0% +example of that in this Theory there's +this label V on the fields and we want + + align:start position:0% +this label V on the fields and we want + + + align:start position:0% +this label V on the fields and we want +to figure out how that affects doing + + align:start position:0% +to figure out how that affects doing + + + align:start position:0% +to figure out how that affects doing +matching and running so we started out + + align:start position:0% +matching and running so we started out + + + align:start position:0% +matching and running so we started out +talking about the wave function + + align:start position:0% +talking about the wave function + + + align:start position:0% +talking about the wave function +normalization + + align:start position:0% +normalization + + + align:start position:0% +normalization +calculation so we have these fields + + align:start position:0% +calculation so we have these fields + + + align:start position:0% +calculation so we have these fields +which we can have a bare version of and + + align:start position:0% +which we can have a bare version of and + + + align:start position:0% +which we can have a bare version of and +a re normalized version of in the usual + + align:start position:0% +a re normalized version of in the usual + + + align:start position:0% +a re normalized version of in the usual +way so this is renormalized and this is + + align:start position:0% +way so this is renormalized and this is + + + align:start position:0% +way so this is renormalized and this is +bare some Z factor between them but I'll + + align:start position:0% +bare some Z factor between them but I'll + + + align:start position:0% +bare some Z factor between them but I'll +call Z for + + align:start position:0% +call Z for + + + align:start position:0% +call Z for +zhey and so we have to calculate at + + align:start position:0% +zhey and so we have to calculate at + + + align:start position:0% +zhey and so we have to calculate at +lowest order this + + align:start position:0% + + + + align:start position:0% + +diagram send in a momentum + + align:start position:0% +diagram send in a momentum + + + align:start position:0% +diagram send in a momentum +P this is Q + + + align:start position:0% +P this is Q + + + + align:start position:0% +P this is Q + +P use the fan + + align:start position:0% + + + + align:start position:0% + +rules use dimensional regularization + + align:start position:0% + + + + align:start position:0% + +use dimensional regularization with + + align:start position:0% +use dimensional regularization with + + + align:start position:0% +use dimensional regularization with +msar so there's + + align:start position:0% +msar so there's + + + align:start position:0% +msar so there's +some extra + + align:start position:0% + + + + align:start position:0% + +factors and use F and gauge which is + + align:start position:0% +factors and use F and gauge which is + + + align:start position:0% +factors and use F and gauge which is +usually the simplest gauge choice so + + align:start position:0% +usually the simplest gauge choice so + + + align:start position:0% +usually the simplest gauge choice so +each of these vertices here gives a + + align:start position:0% +each of these vertices here gives a + + + align:start position:0% +each of these vertices here gives a +v there's a v mu from this + + align:start position:0% +v there's a v mu from this + + + align:start position:0% +v there's a v mu from this +vertex a v mu from that + + align:start position:0% +vertex a v mu from that + + + align:start position:0% +vertex a v mu from that +vertex and that's where this v^ s comes + + align:start position:0% +vertex and that's where this v^ s comes + + + align:start position:0% +vertex and that's where this v^ s comes +from and then there's a + + align:start position:0% +from and then there's a + + + align:start position:0% +from and then there's a +one propagator here it's very + + align:start position:0% +one propagator here it's very + + + align:start position:0% +one propagator here it's very +traditional to denote a heavy Quark by + + align:start position:0% +traditional to denote a heavy Quark by + + + align:start position:0% +traditional to denote a heavy Quark by +two lines rather than one line so you + + align:start position:0% +two lines rather than one line so you + + + align:start position:0% +two lines rather than one line so you +know which lines are heavy and which + + align:start position:0% +know which lines are heavy and which + + + align:start position:0% +know which lines are heavy and which +lines are light so these two lines is a + + align:start position:0% +lines are light so these two lines is a + + + align:start position:0% +lines are light so these two lines is a +heavy quark and that gives this + + align:start position:0% +heavy quark and that gives this + + + align:start position:0% +heavy quark and that gives this +propagator here this v.q plus p and then + + align:start position:0% +propagator here this v.q plus p and then + + + align:start position:0% +propagator here this v.q plus p and then +there's a relativistic propagator for + + align:start position:0% +there's a relativistic propagator for + + + align:start position:0% +there's a relativistic propagator for +the gluon that's the q^ squ I've taken + + align:start position:0% +the gluon that's the q^ squ I've taken + + + align:start position:0% +the gluon that's the q^ squ I've taken +into account all the eyes when I put + + align:start position:0% +into account all the eyes when I put + + + align:start position:0% +into account all the eyes when I put +this minus sign and this is just the + + align:start position:0% +this minus sign and this is just the + + + align:start position:0% +this minus sign and this is just the +fundamental Casmir from dotting two Tas + + align:start position:0% +fundamental Casmir from dotting two Tas + + + align:start position:0% +fundamental Casmir from dotting two Tas +together + + align:start position:0% + + + + align:start position:0% + +okay so when you have an integral like + + align:start position:0% +okay so when you have an integral like + + + align:start position:0% +okay so when you have an integral like +this uh so v^2 is one that's one + + align:start position:0% +this uh so v^2 is one that's one + + + align:start position:0% +this uh so v^2 is one that's one +simplification uh when you have an + + align:start position:0% +simplification uh when you have an + + + align:start position:0% +simplification uh when you have an +integral like that where you have a + + align:start position:0% +integral like that where you have a + + + align:start position:0% +integral like that where you have a +linear momentum in one propagator in a + + align:start position:0% +linear momentum in one propagator in a + + + align:start position:0% +linear momentum in one propagator in a +quadratic momentum in the other + + align:start position:0% +quadratic momentum in the other + + + align:start position:0% +quadratic momentum in the other +propagator you don't want to use the + + align:start position:0% +propagator you don't want to use the + + + align:start position:0% +propagator you don't want to use the +standard fan + + align:start position:0% + + + + align:start position:0% + +trick I call this trick the georgei + + align:start position:0% + + + + align:start position:0% + +trick so it's very similar to The Fan + + align:start position:0% +trick so it's very similar to The Fan + + + align:start position:0% +trick so it's very similar to The Fan +trick but slightly + + align:start position:0% + + + + align:start position:0% + +different so you use an integral that + + align:start position:0% +different so you use an integral that + + + align:start position:0% +different so you use an integral that +goes from zero to + + align:start position:0% + + + + align:start position:0% + +infinity and you can convince + + align:start position:0% +infinity and you can convince + + + align:start position:0% +infinity and you can convince +yourself that this is + + align:start position:0% +yourself that this is + + + align:start position:0% +yourself that this is +true and so then set a equal to Q ^2 and + + align:start position:0% +true and so then set a equal to Q ^2 and + + + align:start position:0% +true and so then set a equal to Q ^2 and +b equal to V do Q + + + align:start position:0% + + + + align:start position:0% + +p and the reason that you want to use + + align:start position:0% +p and the reason that you want to use + + + align:start position:0% +p and the reason that you want to use +this trick rather than the usual one is + + align:start position:0% +this trick rather than the usual one is + + + align:start position:0% +this trick rather than the usual one is +that if if you use the usual one you'd + + align:start position:0% +that if if you use the usual one you'd + + + align:start position:0% +that if if you use the usual one you'd +get an X multiplying this and a 1 - x + + align:start position:0% +get an X multiplying this and a 1 - x + + + align:start position:0% +get an X multiplying this and a 1 - x +multiplying that but then you would have + + align:start position:0% +multiplying that but then you would have + + + align:start position:0% +multiplying that but then you would have +an X multiplying the q^2 so when you + + align:start position:0% +an X multiplying the q^2 so when you + + + align:start position:0% +an X multiplying the q^2 so when you +complete this you it it would be when + + align:start position:0% +complete this you it it would be when + + + align:start position:0% +complete this you it it would be when +you want to complete the square you'd + + align:start position:0% +you want to complete the square you'd + + + align:start position:0% +you want to complete the square you'd +like nothing to multiply the Q squ you'd + + align:start position:0% +like nothing to multiply the Q squ you'd + + + align:start position:0% +like nothing to multiply the Q squ you'd +like the Q squ just to be bare by itself + + align:start position:0% +like the Q squ just to be bare by itself + + + align:start position:0% +like the Q squ just to be bare by itself +with no F and parameter multiplying it + + align:start position:0% +with no F and parameter multiplying it + + + align:start position:0% +with no F and parameter multiplying it +and this trick does that because a has + + align:start position:0% +and this trick does that because a has + + + align:start position:0% +and this trick does that because a has +no fan parameter multi multiplying it or + + align:start position:0% +no fan parameter multi multiplying it or + + + align:start position:0% +no fan parameter multi multiplying it or +georgei parameter in this + + align:start position:0% +georgei parameter in this + + + align:start position:0% +georgei parameter in this +case okay so we combine denominators + + align:start position:0% + + + + align:start position:0% + +and usual + + align:start position:0% +and usual + + + align:start position:0% +and usual +way and the denominator would + + align:start position:0% +way and the denominator would + + + align:start position:0% +way and the denominator would +become this and if I kept the I + + align:start position:0% + + + + align:start position:0% + +Epsilon it would be that if we combine + + align:start position:0% +Epsilon it would be that if we combine + + + align:start position:0% +Epsilon it would be that if we combine +these two denominators here so this + + align:start position:0% +these two denominators here so this + + + align:start position:0% +these two denominators here so this +Factor would be + + align:start position:0% + + + + align:start position:0% + +that and we can then complete the square + + align:start position:0% +that and we can then complete the square + + + align:start position:0% +that and we can then complete the square +and write this as some momentum squared + + align:start position:0% +and write this as some momentum squared + + + align:start position:0% +and write this as some momentum squared +minus whatever is left over + + align:start position:0% + + + + align:start position:0% + +where T is Q + Lambda + + align:start position:0% +where T is Q + Lambda + + + align:start position:0% +where T is Q + Lambda +V and then + + align:start position:0% + + + + align:start position:0% + +a the rest of the stuff which is + + align:start position:0% + + + + align:start position:0% + +this okay so + + align:start position:0% +this okay so + + + align:start position:0% +this okay so +then this + + align:start position:0% + + + + align:start position:0% + +Sky now we just have our + + align:start position:0% +Sky now we just have our + + + align:start position:0% +Sky now we just have our +usual quadratic integral that we can use + + align:start position:0% +usual quadratic integral that we can use + + + align:start position:0% +usual quadratic integral that we can use +the + + align:start position:0% +the + + + align:start position:0% +the +standard rules to + + align:start position:0% + + + + align:start position:0% + +do and then instead of an integral over + + align:start position:0% +do and then instead of an integral over + + + align:start position:0% +do and then instead of an integral over +X we have this integral over Lambda + + align:start position:0% + + + + align:start position:0% + +there's some factors that I'm + + align:start position:0% + + + + align:start position:0% + +dropping so there's that e the oiler + + align:start position:0% +dropping so there's that e the oiler + + + align:start position:0% +dropping so there's that e the oiler +gamma time Epsilon and the 4 Pius + + align:start position:0% +gamma time Epsilon and the 4 Pius + + + align:start position:0% +gamma time Epsilon and the 4 Pius +Epsilon so write in everything with d + + align:start position:0% +Epsilon so write in everything with d + + + align:start position:0% +Epsilon so write in everything with d +equals 4 - 2 + + align:start position:0% + + + + align:start position:0% + +Epsilon do that integral which is + + align:start position:0% +Epsilon do that integral which is + + + align:start position:0% +Epsilon do that integral which is +just giving giving some gamma + + align:start position:0% + + + + align:start position:0% + +functions and if you think about the + + align:start position:0% +functions and if you think about the + + + align:start position:0% +functions and if you think about the +dimensions here so we end up with + + align:start position:0% +dimensions here so we end up with + + + align:start position:0% +dimensions here so we end up with +something that D minus 3 if you think if + + align:start position:0% +something that D minus 3 if you think if + + + align:start position:0% +something that D minus 3 if you think if +you want to look at the dimensions D + + align:start position:0% +you want to look at the dimensions D + + + align:start position:0% +you want to look at the dimensions D +over2 minus 2 is + + align:start position:0% +over2 minus 2 is + + + align:start position:0% +over2 minus 2 is +dimensionless okay the Lambda had + + align:start position:0% +dimensionless okay the Lambda had + + + align:start position:0% +dimensionless okay the Lambda had +Dimensions if we go back here that's + + align:start position:0% +Dimensions if we go back here that's + + + align:start position:0% +Dimensions if we go back here that's +obvious Q is dimension full V is + + align:start position:0% +obvious Q is dimension full V is + + + align:start position:0% +obvious Q is dimension full V is +dimension less so Lambda has Dimension + + align:start position:0% +dimension less so Lambda has Dimension + + + align:start position:0% +dimension less so Lambda has Dimension +one so the dimensions of + + align:start position:0% +one so the dimensions of + + + align:start position:0% +one so the dimensions of +the the dimensions of the me to the 2 + + align:start position:0% +the the dimensions of the me to the 2 + + + align:start position:0% +the the dimensions of the me to the 2 +Epsilon are compensating the dimensions + + align:start position:0% +Epsilon are compensating the dimensions + + + align:start position:0% +Epsilon are compensating the dimensions +here and then there's one power of + + align:start position:0% +here and then there's one power of + + + align:start position:0% +here and then there's one power of +Dimension left and that's why if I take + + align:start position:0% +Dimension left and that's why if I take + + + align:start position:0% +Dimension left and that's why if I take +D equals 4 I'm getting one power of + + align:start position:0% +D equals 4 I'm getting one power of + + + align:start position:0% +D equals 4 I'm getting one power of +momentum upstairs which is what we'd + + align:start position:0% +momentum upstairs which is what we'd + + + align:start position:0% +momentum upstairs which is what we'd +expect for an inverse propagator for a + + align:start position:0% +expect for an inverse propagator for a + + + align:start position:0% +expect for an inverse propagator for a +heavy Quark is one factor of V.P + + align:start position:0% +heavy Quark is one factor of V.P + + + align:start position:0% +heavy Quark is one factor of V.P +so expand + + align:start position:0% + + + + align:start position:0% + +this we + + align:start position:0% +this we + + + align:start position:0% +this we +go + + align:start position:0% +go + + + align:start position:0% +go +Divergence so add a counter + + align:start position:0% +Divergence so add a counter + + + align:start position:0% +Divergence so add a counter +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +term for wave function normalization + + align:start position:0% + + + + align:start position:0% + +so if we did that in msar then the Z + + align:start position:0% +so if we did that in msar then the Z + + + align:start position:0% +so if we did that in msar then the Z +would be just + + align:start position:0% +would be just + + + align:start position:0% +would be just +this and that would be the appropriate + + align:start position:0% +this and that would be the appropriate + + + align:start position:0% +this and that would be the appropriate +counterterm to kill off the one over + + align:start position:0% +counterterm to kill off the one over + + + align:start position:0% +counterterm to kill off the one over +Epsilon + + align:start position:0% +Epsilon + + + align:start position:0% +Epsilon +Divergence I'm going to carry out the + + align:start position:0% +Divergence I'm going to carry out the + + + align:start position:0% +Divergence I'm going to carry out the +calculation today or this discussion of + + align:start position:0% +calculation today or this discussion of + + + align:start position:0% +calculation today or this discussion of +matching in msar for everything and I'll + + align:start position:0% +matching in msar for everything and I'll + + + align:start position:0% +matching in msar for everything and I'll +show you that some there's a slight + + align:start position:0% +show you that some there's a slight + + + align:start position:0% +show you that some there's a slight +complication that shows up in that case + + align:start position:0% +complication that shows up in that case + + + align:start position:0% +complication that shows up in that case +but we said that we could do + + align:start position:0% +but we said that we could do + + + align:start position:0% +but we said that we could do +matching + + align:start position:0% +matching + + + align:start position:0% +matching +um basically you could have two choices + + align:start position:0% +um basically you could have two choices + + + align:start position:0% +um basically you could have two choices +here you could either use on shell re + + align:start position:0% +here you could either use on shell re + + + align:start position:0% +here you could either use on shell re +normalization or you could use msar + + align:start position:0% +normalization or you could use msar + + + align:start position:0% +normalization or you could use msar +what's the difference in in msar you + + align:start position:0% +what's the difference in in msar you + + + align:start position:0% +what's the difference in in msar you +just keep the Divergence in the Z in on + + align:start position:0% +just keep the Divergence in the Z in on + + + align:start position:0% +just keep the Divergence in the Z in on +Shel normalization you keep some extra + + align:start position:0% +Shel normalization you keep some extra + + + align:start position:0% +Shel normalization you keep some extra +terms here all right and either way that + + align:start position:0% +terms here all right and either way that + + + align:start position:0% +terms here all right and either way that +we choose to do things we should + + align:start position:0% +we choose to do things we should + + + align:start position:0% +we choose to do things we should +actually end up with the same matching + + align:start position:0% +actually end up with the same matching + + + align:start position:0% +actually end up with the same matching +and I want to show you why that's true + + align:start position:0% +and I want to show you why that's true + + + align:start position:0% +and I want to show you why that's true +so we let in order to show you why + + align:start position:0% +so we let in order to show you why + + + align:start position:0% +so we let in order to show you why +that's true I'll pick to use msar at + + align:start position:0% +that's true I'll pick to use msar at + + + align:start position:0% +that's true I'll pick to use msar at +this point and we'll see what + + align:start position:0% +this point and we'll see what + + + align:start position:0% +this point and we'll see what +complication that leads to later + + align:start position:0% +complication that leads to later + + + align:start position:0% +complication that leads to later +on okay so that's one thing that needs + + align:start position:0% +on okay so that's one thing that needs + + + align:start position:0% +on okay so that's one thing that needs +to be re normalized and if we look at + + align:start position:0% +to be re normalized and if we look at + + + align:start position:0% +to be re normalized and if we look at +this guy and we compare it to + + align:start position:0% +this guy and we compare it to + + + align:start position:0% +this guy and we compare it to +zi this is not the same as zi in + + align:start position:0% +zi this is not the same as zi in + + + align:start position:0% +zi this is not the same as zi in +qcd so this is something different and + + align:start position:0% +qcd so this is something different and + + + align:start position:0% +qcd so this is something different and +the reason it's different is because we + + align:start position:0% +the reason it's different is because we + + + align:start position:0% +the reason it's different is because we +did a different Loop intergral had this + + align:start position:0% +did a different Loop intergral had this + + + align:start position:0% +did a different Loop intergral had this +heavy Quark propagator not the light + + align:start position:0% +heavy Quark propagator not the light + + + align:start position:0% +heavy Quark propagator not the light +Quark propagator + + align:start position:0% + + + + align:start position:0% + +so we have to renormalize also local + + align:start position:0% +so we have to renormalize also local + + + align:start position:0% +so we have to renormalize also local +operators and so let's think about + + align:start position:0% +operators and so let's think about + + + align:start position:0% +operators and so let's think about +something that would make a heavy to + + align:start position:0% +something that would make a heavy to + + + align:start position:0% +something that would make a heavy to +light transition so for example if you + + align:start position:0% +light transition so for example if you + + + align:start position:0% +light transition so for example if you +looked at B goes to + + align:start position:0% +looked at B goes to + + + align:start position:0% +looked at B goes to +U + + align:start position:0% +U + + + align:start position:0% +U +electron + + align:start position:0% + + + + align:start position:0% + +nutrino then that would be a heavy to + + align:start position:0% +nutrino then that would be a heavy to + + + align:start position:0% +nutrino then that would be a heavy to +light transition the B cork is heavy the + + align:start position:0% +light transition the B cork is heavy the + + + align:start position:0% +light transition the B cork is heavy the +uork is light so to describe that you + + align:start position:0% +uork is light so to describe that you + + + align:start position:0% +uork is light so to describe that you +would use some operator that has one + + align:start position:0% +would use some operator that has one + + + align:start position:0% +would use some operator that has one +heavy quk and one light cork so let me + + align:start position:0% +heavy quk and one light cork so let me + + + align:start position:0% +heavy quk and one light cork so let me +call the light Quark small + + align:start position:0% +call the light Quark small + + + align:start position:0% +call the light Quark small +q and the heavy Quark big + + align:start position:0% +q and the heavy Quark big + + + align:start position:0% +q and the heavy Quark big +q and so you'd have some operator that + + align:start position:0% +q and so you'd have some operator that + + + align:start position:0% +q and so you'd have some operator that +looks like that and we could write down + + align:start position:0% +looks like that and we could write down + + + align:start position:0% +looks like that and we could write down +a renormalized + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +operator we normalized fields and then + + align:start position:0% +operator we normalized fields and then + + + align:start position:0% +operator we normalized fields and then +group all the Z factors into a counter + + align:start position:0% +group all the Z factors into a counter + + + align:start position:0% +group all the Z factors into a counter +term + + align:start position:0% + + + + align:start position:0% + +so let's think about doing the peration + + align:start position:0% +so let's think about doing the peration + + + align:start position:0% +so let's think about doing the peration +theory that way so this is the + + align:start position:0% +theory that way so this is the + + + align:start position:0% +theory that way so this is the +normalized operator this is the counter + + align:start position:0% + + + + align:start position:0% + +term so there's a way function factor zq + + align:start position:0% +term so there's a way function factor zq + + + align:start position:0% +term so there's a way function factor zq +for the light Quirk a z for the heavy + + align:start position:0% +for the light Quirk a z for the heavy + + + align:start position:0% +for the light Quirk a z for the heavy +Quirk and then there's some zo for the + + align:start position:0% +Quirk and then there's some zo for the + + + align:start position:0% +Quirk and then there's some zo for the +operator re normalization + + align:start position:0% + + + + align:start position:0% + +okay so to normalize this operator at + + align:start position:0% +okay so to normalize this operator at + + + align:start position:0% +okay so to normalize this operator at +one + + align:start position:0% +one + + + align:start position:0% +one +Loop we insert + + align:start position:0% +Loop we insert + + + align:start position:0% +Loop we insert +it and we do a one Loop + + align:start position:0% + + + + align:start position:0% + +diagram I'm just going to tell you the + + align:start position:0% +diagram I'm just going to tell you the + + + align:start position:0% +diagram I'm just going to tell you the +answers let's draw the diagram so here's + + align:start position:0% +answers let's draw the diagram so here's + + + align:start position:0% +answers let's draw the diagram so here's +the operator inserted here's your heavy + + align:start position:0% +the operator inserted here's your heavy + + + align:start position:0% +the operator inserted here's your heavy +Quark here's your light + + align:start position:0% +Quark here's your light + + + align:start position:0% +Quark here's your light +Quark you have a diagram like that + + align:start position:0% + + + + align:start position:0% + +and then you combine this + + align:start position:0% +and then you combine this + + + align:start position:0% +and then you combine this +calculation with + + align:start position:0% +calculation with + + + align:start position:0% +calculation with +the wave function re + + align:start position:0% + + + + align:start position:0% + +normalization Z zq zq is the same as + + align:start position:0% +normalization Z zq zq is the same as + + + align:start position:0% +normalization Z zq zq is the same as +Z should have called this Z zq for a + + align:start position:0% +Z should have called this Z zq for a + + + align:start position:0% +Z should have called this Z zq for a +light + + align:start position:0% +light + + + align:start position:0% +light +Quark combine these things together and + + align:start position:0% +Quark combine these things together and + + + align:start position:0% +Quark combine these things together and +then because that graph is telling you + + align:start position:0% +then because that graph is telling you + + + align:start position:0% +then because that graph is telling you +the this counter you need + + align:start position:0% +the this counter you need + + + align:start position:0% +the this counter you need +zo + + align:start position:0% +zo + + + align:start position:0% +zo +and that + + align:start position:0% +and that + + + align:start position:0% +and that +calculation which you can look at in + + align:start position:0% +calculation which you can look at in + + + align:start position:0% +calculation which you can look at in +your reading if you want to look at more + + align:start position:0% +your reading if you want to look at more + + + align:start position:0% +your reading if you want to look at more +details just gives you kind of something + + align:start position:0% +details just gives you kind of something + + + align:start position:0% +details just gives you kind of something +about what you'd expect gives you a one + + align:start position:0% +about what you'd expect gives you a one + + + align:start position:0% +about what you'd expect gives you a one +over Epsilon Divergence factor of G + + align:start position:0% +over Epsilon Divergence factor of G + + + align:start position:0% +over Epsilon Divergence factor of G +^2 so the operator here has a + + align:start position:0% + + + + align:start position:0% + +normalization it's + + align:start position:0% + + + + align:start position:0% + +just minus alpha s over pi that's the + + align:start position:0% +just minus alpha s over pi that's the + + + align:start position:0% +just minus alpha s over pi that's the +anomalous + + align:start position:0% + + + + align:start position:0% + +Dimension so what is this anomalous + + align:start position:0% +Dimension so what is this anomalous + + + align:start position:0% +Dimension so what is this anomalous +Dimension + + align:start position:0% +Dimension + + + align:start position:0% +Dimension +doing it's if you were to consider this + + align:start position:0% +doing it's if you were to consider this + + + align:start position:0% +doing it's if you were to consider this +this kind of process in full + + align:start position:0% +this kind of process in full + + + align:start position:0% +this kind of process in full +qcd then you'd have here gamma mu 1 + + align:start position:0% +qcd then you'd have here gamma mu 1 + + + align:start position:0% +qcd then you'd have here gamma mu 1 +minus gamma 5 and that's a partially + + align:start position:0% +minus gamma 5 and that's a partially + + + align:start position:0% +minus gamma 5 and that's a partially +conserved current so there would be + + align:start position:0% +conserved current so there would be + + + align:start position:0% +conserved current so there would be +actually no anomalous Dimension to this + + align:start position:0% +actually no anomalous Dimension to this + + + align:start position:0% +actually no anomalous Dimension to this +operator the vertex graph that we just + + align:start position:0% +operator the vertex graph that we just + + + align:start position:0% +operator the vertex graph that we just +drew over there would cancel the wave + + align:start position:0% +drew over there would cancel the wave + + + align:start position:0% +drew over there would cancel the wave +function graphs exactly there' be no + + align:start position:0% +function graphs exactly there' be no + + + align:start position:0% +function graphs exactly there' be no +anomalous Dimension but here we have one + + align:start position:0% +anomalous Dimension but here we have one + + + align:start position:0% +anomalous Dimension but here we have one +and that's because these guys are not + + align:start position:0% +and that's because these guys are not + + + align:start position:0% +and that's because these guys are not +equivalent anymore you saw that the Z + + align:start position:0% +equivalent anymore you saw that the Z + + + align:start position:0% +equivalent anymore you saw that the Z +for the heavy cor changed and the vertex + + align:start position:0% +for the heavy cor changed and the vertex + + + align:start position:0% +for the heavy cor changed and the vertex +graph also changes and we're left with + + align:start position:0% +graph also changes and we're left with + + + align:start position:0% +graph also changes and we're left with +something and this remainder has to do + + align:start position:0% +something and this remainder has to do + + + align:start position:0% +something and this remainder has to do +with re normalization group Evolution + + align:start position:0% +with re normalization group Evolution + + + align:start position:0% +with re normalization group Evolution +below the mass of the heavy Quark above + + align:start position:0% +below the mass of the heavy Quark above + + + align:start position:0% +below the mass of the heavy Quark above +the mass of the heavy Quark there's no + + align:start position:0% +the mass of the heavy Quark there's no + + + align:start position:0% +the mass of the heavy Quark there's no +renormalization group evolution of this + + align:start position:0% +renormalization group evolution of this + + + align:start position:0% +renormalization group evolution of this +current below the mass of the heavy + + align:start position:0% +current below the mass of the heavy + + + align:start position:0% +current below the mass of the heavy +Quirk there is + + align:start position:0% + + + + align:start position:0% + +so there's additional logs and that's + + align:start position:0% +so there's additional logs and that's + + + align:start position:0% +so there's additional logs and that's +because mq is now being treated as + + align:start position:0% +because mq is now being treated as + + + align:start position:0% +because mq is now being treated as +infinite so things that from the point + + align:start position:0% +infinite so things that from the point + + + align:start position:0% +infinite so things that from the point +of view of qcd where logs of mq have now + + align:start position:0% +of view of qcd where logs of mq have now + + + align:start position:0% +of view of qcd where logs of mq have now +become UV divergences and that gives an + + align:start position:0% +become UV divergences and that gives an + + + align:start position:0% +become UV divergences and that gives an +extra anomal + + align:start position:0% + + + + align:start position:0% + +Dimension one thing you can note about + + align:start position:0% +Dimension one thing you can note about + + + align:start position:0% +Dimension one thing you can note about +this anomalous Dimension is that I + + align:start position:0% +this anomalous Dimension is that I + + + align:start position:0% +this anomalous Dimension is that I +didn't really specifi for you what the + + align:start position:0% +didn't really specifi for you what the + + + align:start position:0% +didn't really specifi for you what the +gamma was though I told you for this + + align:start position:0% +gamma was though I told you for this + + + align:start position:0% +gamma was though I told you for this +process it would be gamma mu1 minus + + align:start position:0% +process it would be gamma mu1 minus + + + align:start position:0% +process it would be gamma mu1 minus +gamma 5 and the result here + + align:start position:0% + + + + align:start position:0% + +actually if you carry out this + + align:start position:0% +actually if you carry out this + + + align:start position:0% +actually if you carry out this +calculation with arbitrary gamma you + + align:start position:0% +calculation with arbitrary gamma you + + + align:start position:0% +calculation with arbitrary gamma you +find that it's + + align:start position:0% +find that it's + + + align:start position:0% +find that it's +independent of + + align:start position:0% +independent of + + + align:start position:0% +independent of +gamma so you get the same Universal an + + align:start position:0% +gamma so you get the same Universal an + + + align:start position:0% +gamma so you get the same Universal an +almost dimension for any spin + + align:start position:0% +almost dimension for any spin + + + align:start position:0% +almost dimension for any spin +structure and that's partly related to + + align:start position:0% +structure and that's partly related to + + + align:start position:0% +structure and that's partly related to +the things that we talked about last + + align:start position:0% +the things that we talked about last + + + align:start position:0% +the things that we talked about last +time with the spin symmetry of + + align:start position:0% +time with the spin symmetry of + + + align:start position:0% +time with the spin symmetry of +hqet which is uh telling you that + + align:start position:0% +hqet which is uh telling you that + + + align:start position:0% +hqet which is uh telling you that +certain couplings are not sensitive to + + align:start position:0% +certain couplings are not sensitive to + + + align:start position:0% +certain couplings are not sensitive to +the spin and effectively in this + + align:start position:0% +the spin and effectively in this + + + align:start position:0% +the spin and effectively in this +diagram you're getting a v slash here + + align:start position:0% +diagram you're getting a v slash here + + + align:start position:0% +diagram you're getting a v slash here +well let me try to go through it but + + align:start position:0% +well let me try to go through it but + + + align:start position:0% +well let me try to go through it but +leave it for looking at your reading but + + align:start position:0% +leave it for looking at your reading but + + + align:start position:0% +leave it for looking at your reading but +we'll talk a little bit more about this + + align:start position:0% +we'll talk a little bit more about this + + + align:start position:0% +we'll talk a little bit more about this +in a + + align:start position:0% + + + + align:start position:0% + +minute I won't try to explain where that + + align:start position:0% +minute I won't try to explain where that + + + align:start position:0% +minute I won't try to explain where that +comes from from the + + align:start position:0% +comes from from the + + + align:start position:0% +comes from from the +diagram so let's look at another + + align:start position:0% +diagram so let's look at another + + + align:start position:0% +diagram so let's look at another +case the only real interesting thing + + align:start position:0% +case the only real interesting thing + + + align:start position:0% +case the only real interesting thing +that happened here was that we got well + + align:start position:0% +that happened here was that we got well + + + align:start position:0% +that happened here was that we got well +the fact that the answer was non zero + + align:start position:0% +the fact that the answer was non zero + + + align:start position:0% +the fact that the answer was non zero +was interesting and the fact that it was + + align:start position:0% +was interesting and the fact that it was + + + align:start position:0% +was interesting and the fact that it was +independent of gamma but something but + + align:start position:0% +independent of gamma but something but + + + align:start position:0% +independent of gamma but something but +the V didn't show up and the reason that + + align:start position:0% +the V didn't show up and the reason that + + + align:start position:0% +the V didn't show up and the reason that +the V didn't show up in this calculation + + align:start position:0% +the V didn't show up in this calculation + + + align:start position:0% +the V didn't show up in this calculation +here is because there was only one V and + + align:start position:0% +here is because there was only one V and + + + align:start position:0% +here is because there was only one V and +v^2 was equal to one so V couldn't + + align:start position:0% +v^2 was equal to one so V couldn't + + + align:start position:0% +v^2 was equal to one so V couldn't +really show up because we had to get a + + align:start position:0% +really show up because we had to get a + + + align:start position:0% +really show up because we had to get a +scalar answer and since v^ s is equal to + + align:start position:0% +scalar answer and since v^ s is equal to + + + align:start position:0% +scalar answer and since v^ s is equal to +one just it's not showing up so + + align:start position:0% +one just it's not showing up so + + + align:start position:0% +one just it's not showing up so +something more interesting is to look at + + align:start position:0% +something more interesting is to look at + + + align:start position:0% +something more interesting is to look at +instead of a heavy to light transition + + align:start position:0% +instead of a heavy to light transition + + + align:start position:0% +instead of a heavy to light transition +like that a heavy to heavy + + align:start position:0% + + + + align:start position:0% + +transition spend a little bit more time + + align:start position:0% +transition spend a little bit more time + + + align:start position:0% +transition spend a little bit more time +on this + + align:start position:0% +on this + + + align:start position:0% +on this +one so let's have two heavy + + align:start position:0% +one so let's have two heavy + + + align:start position:0% +one so let's have two heavy +fields and I'm going to take them in a + + align:start position:0% +fields and I'm going to take them in a + + + align:start position:0% +fields and I'm going to take them in a +current where they have different + + align:start position:0% +current where they have different + + + align:start position:0% +current where they have different +velocities V and V + + align:start position:0% +velocities V and V + + + align:start position:0% +velocities V and V +Prime so let me imagine I went through + + align:start position:0% +Prime so let me imagine I went through + + + align:start position:0% +Prime so let me imagine I went through +this procedure of separating out counter + + align:start position:0% +this procedure of separating out counter + + + align:start position:0% +this procedure of separating out counter +term + + align:start position:0% +term + + + align:start position:0% +term +and and Co and and normalized + + align:start position:0% +and and Co and and normalized + + + align:start position:0% +and and Co and and normalized +Operator just like I did over there + + align:start position:0% + + + + align:start position:0% + +so I have these two terms two types of + + align:start position:0% +so I have these two terms two types of + + + align:start position:0% +so I have these two terms two types of +structures now I don't have a zq but I + + align:start position:0% +structures now I don't have a zq but I + + + align:start position:0% +structures now I don't have a zq but I +have two heavy quarks so I have Z root Z + + align:start position:0% +have two heavy quarks so I have Z root Z + + + align:start position:0% +have two heavy quarks so I have Z root Z +root Z which is just + + align:start position:0% +root Z which is just + + + align:start position:0% +root Z which is just +Z so an example of this would be + + align:start position:0% +Z so an example of this would be + + + align:start position:0% +Z so an example of this would be +something like a bon changing to say a d + + align:start position:0% +something like a bon changing to say a d + + + align:start position:0% +something like a bon changing to say a d +star + + align:start position:0% +star + + + align:start position:0% +star +meeson an electron and a neutrino so + + align:start position:0% +meeson an electron and a neutrino so + + + align:start position:0% +meeson an electron and a neutrino so +having a charm Quark replace our up + + align:start position:0% + + + + align:start position:0% + +Quark okay okay so now the charm Cork + + align:start position:0% +Quark okay okay so now the charm Cork + + + align:start position:0% +Quark okay okay so now the charm Cork +and the B quk could both be thought of + + align:start position:0% +and the B quk could both be thought of + + + align:start position:0% +and the B quk could both be thought of +as heavy they have different masses but + + align:start position:0% +as heavy they have different masses but + + + align:start position:0% +as heavy they have different masses but +we take the both of those masses to + + align:start position:0% +we take the both of those masses to + + + align:start position:0% +we take the both of those masses to +Infinity so we can use hqt for both of + + align:start position:0% + + + + align:start position:0% + +them so MB and MC are going to + + align:start position:0% +them so MB and MC are going to + + + align:start position:0% +them so MB and MC are going to +infinity + + align:start position:0% +infinity + + + align:start position:0% +infinity +and there's no reason why in this + + align:start position:0% +and there's no reason why in this + + + align:start position:0% +and there's no reason why in this +process that the B Quirk and the charm + + align:start position:0% +process that the B Quirk and the charm + + + align:start position:0% +process that the B Quirk and the charm +Quirk should have the same velocity and + + align:start position:0% +Quirk should have the same velocity and + + + align:start position:0% +Quirk should have the same velocity and +so we'll give them different velocities + + align:start position:0% +so we'll give them different velocities + + + align:start position:0% +so we'll give them different velocities +V and V Prime + + align:start position:0% + + + + align:start position:0% + +okay so we can go through the same thing + + align:start position:0% +okay so we can go through the same thing + + + align:start position:0% +okay so we can go through the same thing +we already calculated zh so we just have + + align:start position:0% +we already calculated zh so we just have + + + align:start position:0% +we already calculated zh so we just have +to + + align:start position:0% + + + + align:start position:0% + +calculate a graph like + + align:start position:0% +calculate a graph like + + + align:start position:0% +calculate a graph like +this where two we have two heavy + + align:start position:0% +this where two we have two heavy + + + align:start position:0% +this where two we have two heavy +quirks but the heavy quirks have + + align:start position:0% +quirks but the heavy quirks have + + + align:start position:0% +quirks but the heavy quirks have +different + + align:start position:0% + + + + align:start position:0% + +velocities so what would that + + align:start position:0% +velocities so what would that + + + align:start position:0% +velocities so what would that +calculation look + + align:start position:0% + + + + align:start position:0% + +like again in F engage + + align:start position:0% + + + + align:start position:0% + +and let me just take the external quirks + + align:start position:0% +and let me just take the external quirks + + + align:start position:0% +and let me just take the external quirks +to have zero momentum for + + align:start position:0% +to have zero momentum for + + + align:start position:0% +to have zero momentum for +Simplicity zero residual momentum so + + align:start position:0% +Simplicity zero residual momentum so + + + align:start position:0% +Simplicity zero residual momentum so +this guy has like k equal z k equal + + align:start position:0% +this guy has like k equal z k equal + + + align:start position:0% +this guy has like k equal z k equal +zero so the hqt fan rule for this guy + + align:start position:0% +zero so the hqt fan rule for this guy + + + align:start position:0% +zero so the hqt fan rule for this guy +has a v.q if Q is the loop + + align:start position:0% +has a v.q if Q is the loop + + + align:start position:0% +has a v.q if Q is the loop +momenta and this guy has a V prime. + + align:start position:0% +momenta and this guy has a V prime. + + + align:start position:0% +momenta and this guy has a V prime. +Q okay so the integral that I have to do + + align:start position:0% +Q okay so the integral that I have to do + + + align:start position:0% +Q okay so the integral that I have to do +is that + + align:start position:0% +is that + + + align:start position:0% +is that +integral and you can do this again with + + align:start position:0% +integral and you can do this again with + + + align:start position:0% +integral and you can do this again with +one of these tricks with like where you + + align:start position:0% +one of these tricks with like where you + + + align:start position:0% +one of these tricks with like where you +use Lambda + + align:start position:0% +use Lambda + + + align:start position:0% +use Lambda +parameters and then one of the handouts + + align:start position:0% +parameters and then one of the handouts + + + align:start position:0% +parameters and then one of the handouts +on the web page i' given you the + + align:start position:0% +on the web page i' given you the + + + align:start position:0% +on the web page i' given you the +appropriate trick with two Lambda + + align:start position:0% +appropriate trick with two Lambda + + + align:start position:0% +appropriate trick with two Lambda +parameters for this + + align:start position:0% + + + + align:start position:0% + +integral this integral actually has both + + align:start position:0% +integral this integral actually has both + + + align:start position:0% +integral this integral actually has both +ultraviolet + + align:start position:0% +ultraviolet + + + align:start position:0% +ultraviolet +and infrared + + align:start position:0% +and infrared + + + align:start position:0% +and infrared +divergences we're here in our discussion + + align:start position:0% +divergences we're here in our discussion + + + align:start position:0% +divergences we're here in our discussion +only interested in the ultraviolet + + align:start position:0% +only interested in the ultraviolet + + + align:start position:0% +only interested in the ultraviolet +ones because we're worrying about the + + align:start position:0% +ones because we're worrying about the + + + align:start position:0% +ones because we're worrying about the +anomal dimension right + + align:start position:0% + + + + align:start position:0% + +now and again I'm not going to drag you + + align:start position:0% +now and again I'm not going to drag you + + + align:start position:0% +now and again I'm not going to drag you +through the details of this + + align:start position:0% + + + + align:start position:0% + +calculation it's it's essentially just + + align:start position:0% +calculation it's it's essentially just + + + align:start position:0% +calculation it's it's essentially just +do the findan parameter combine + + align:start position:0% +do the findan parameter combine + + + align:start position:0% +do the findan parameter combine +denominators with two fan parameters + + align:start position:0% +denominators with two fan parameters + + + align:start position:0% +denominators with two fan parameters +complete the square do the loop integral + + align:start position:0% +complete the square do the loop integral + + + align:start position:0% +complete the square do the loop integral +do the F and parameter integrals get get + + align:start position:0% +do the F and parameter integrals get get + + + align:start position:0% +do the F and parameter integrals get get +an answer + + align:start position:0% +an answer + + + align:start position:0% +an answer +combine it together with the the counter + + align:start position:0% +combine it together with the the counter + + + align:start position:0% +combine it together with the the counter +terms for the wave function + + align:start position:0% +terms for the wave function + + + align:start position:0% +terms for the wave function +normalization and see what type of + + align:start position:0% +normalization and see what type of + + + align:start position:0% +normalization and see what type of +counterterm you get left + + align:start position:0% +counterterm you get left + + + align:start position:0% +counterterm you get left +over and it's more interesting + + align:start position:0% +over and it's more interesting + + + align:start position:0% +over and it's more interesting +than the heavy toight + + align:start position:0% +than the heavy toight + + + align:start position:0% +than the heavy toight +case so here's what it looks + + align:start position:0% + + + + align:start position:0% + +like where W is v. V Prime + + align:start position:0% +like where W is v. V Prime + + + align:start position:0% +like where W is v. V Prime +and this function R of + + align:start position:0% +and this function R of + + + align:start position:0% +and this function R of +w is the following it's + + align:start position:0% +w is the following it's + + + align:start position:0% +w is the following it's +log W +un w^2 + + align:start position:0% + + + + align:start position:0% + +-1 over theare Ro of w^2 minus + + align:start position:0% + + + + align:start position:0% + +one okay so it's kind of a non-trivial + + align:start position:0% + + + + align:start position:0% + +structure so that counter term lead to a + + align:start position:0% +structure so that counter term lead to a + + + align:start position:0% +structure so that counter term lead to a +normal Dimension which depends on this R + + align:start position:0% +normal Dimension which depends on this R + + + align:start position:0% +normal Dimension which depends on this R +of + + align:start position:0% + + + + align:start position:0% + +w so the reason that that that can + + align:start position:0% +w so the reason that that that can + + + align:start position:0% +w so the reason that that that can +happen is because V squar is One V Prime + + align:start position:0% +happen is because V squar is One V Prime + + + align:start position:0% +happen is because V squar is One V Prime +squ is one but v. V Prime need not be + + align:start position:0% + + + + align:start position:0% + +one so B ^2 was one B Prime squ was one + + align:start position:0% +one so B ^2 was one B Prime squ was one + + + align:start position:0% +one so B ^2 was one B Prime squ was one +but v.v + + align:start position:0% +but v.v + + + align:start position:0% +but v.v +Prime is not + + align:start position:0% + + + + align:start position:0% + +fixed well it's not fixed simply + + align:start position:0% +fixed well it's not fixed simply + + + align:start position:0% +fixed well it's not fixed simply +by that's poor choice of + + align:start position:0% + + + + align:start position:0% + +words this is a parameter that can + + align:start position:0% + + + + align:start position:0% + +vary so it will be fixed by kinematics + + align:start position:0% +vary so it will be fixed by kinematics + + + align:start position:0% +vary so it will be fixed by kinematics +but it can depend on the kinematics + + align:start position:0% +but it can depend on the kinematics + + + align:start position:0% +but it can depend on the kinematics +so let me go through this and organize + + align:start position:0% +so let me go through this and organize + + + align:start position:0% +so let me go through this and organize +it as a bunch of notes + + align:start position:0% +it as a bunch of notes + + + align:start position:0% +it as a bunch of notes +comments + + align:start position:0% + + + + align:start position:0% + +so this is what I just said that it + + align:start position:0% +so this is what I just said that it + + + align:start position:0% +so this is what I just said that it +depends on the answer depends on v.v + + align:start position:0% +depends on the answer depends on v.v + + + align:start position:0% +depends on the answer depends on v.v +Prime and the way that you should think + + align:start position:0% +Prime and the way that you should think + + + align:start position:0% +Prime and the way that you should think +about this is that you have a + + align:start position:0% +about this is that you have a + + + align:start position:0% +about this is that you have a +current in the effective Theory so this + + align:start position:0% +current in the effective Theory so this + + + align:start position:0% +current in the effective Theory so this +is in the + + align:start position:0% +is in the + + + align:start position:0% +is in the +HQ current + + align:start position:0% + + + + align:start position:0% + +and just like we label it by its lorence + + align:start position:0% +and just like we label it by its lorence + + + align:start position:0% +and just like we label it by its lorence +index mu we should label it also by the + + align:start position:0% +index mu we should label it also by the + + + align:start position:0% +index mu we should label it also by the +V and the V Prime because the fields + + align:start position:0% +V and the V Prime because the fields + + + align:start position:0% +V and the V Prime because the fields +involve V and V Prime + + align:start position:0% +involve V and V Prime + + + align:start position:0% +involve V and V Prime +so we thought of this as some Vector + + align:start position:0% +so we thought of this as some Vector + + + align:start position:0% +so we thought of this as some Vector +current or axial Vector + + align:start position:0% +current or axial Vector + + + align:start position:0% +current or axial Vector +current labeled by mu we would also + + align:start position:0% +current labeled by mu we would also + + + align:start position:0% +current labeled by mu we would also +label the current by V and V + + align:start position:0% + + + + align:start position:0% + +Prime so these are indices that are just + + align:start position:0% +Prime so these are indices that are just + + + align:start position:0% +Prime so these are indices that are just +indices on the current and when you + + align:start position:0% +indices on the current and when you + + + align:start position:0% +indices on the current and when you +think about the Wilson coefficient or + + align:start position:0% +think about the Wilson coefficient or + + + align:start position:0% +think about the Wilson coefficient or +the anomalous Dimension it can depend on + + align:start position:0% +the anomalous Dimension it can depend on + + + align:start position:0% +the anomalous Dimension it can depend on +the + + align:start position:0% + + + + align:start position:0% + +indices now because the Wilson + + align:start position:0% +indices now because the Wilson + + + align:start position:0% +indices now because the Wilson +coefficient is a + + align:start position:0% + + + + align:start position:0% + +scalar it really only depends on + + align:start position:0% +scalar it really only depends on + + + align:start position:0% +scalar it really only depends on +W so if you think about Wilson + + align:start position:0% +W so if you think about Wilson + + + align:start position:0% +W so if you think about Wilson +coefficients they depend on alpha s they + + align:start position:0% +coefficients they depend on alpha s they + + + align:start position:0% +coefficients they depend on alpha s they +depend on scale mu they depend on the + + align:start position:0% +depend on scale mu they depend on the + + + align:start position:0% +depend on scale mu they depend on the +hard scales in your + + align:start position:0% +hard scales in your + + + align:start position:0% +hard scales in your +problem and the hard scales in the + + align:start position:0% +problem and the hard scales in the + + + align:start position:0% +problem and the hard scales in the +problem here for us + + align:start position:0% +problem here for us + + + align:start position:0% +problem here for us +are MB * V and MC * V Prime because + + align:start position:0% +are MB * V and MC * V Prime because + + + align:start position:0% +are MB * V and MC * V Prime because +those are the heavy scales of the he of + + align:start position:0% +those are the heavy scales of the he of + + + align:start position:0% +those are the heavy scales of the he of +the heavy charm Cork and the heavy B quk + + align:start position:0% +the heavy charm Cork and the heavy B quk + + + align:start position:0% +the heavy charm Cork and the heavy B quk +that we're + + align:start position:0% +that we're + + + align:start position:0% +that we're +removing but since we know that this + + align:start position:0% +removing but since we know that this + + + align:start position:0% +removing but since we know that this +thing is a scalar we can just Square + + align:start position:0% +thing is a scalar we can just Square + + + align:start position:0% +thing is a scalar we can just Square +these dot them into each other so it's + + align:start position:0% +these dot them into each other so it's + + + align:start position:0% +these dot them into each other so it's +really a function of + + align:start position:0% +really a function of + + + align:start position:0% +really a function of +mu of alpha s + + align:start position:0% +mu of alpha s + + + align:start position:0% +mu of alpha s +mu MB ^ 2 from squaring the MB term and + + align:start position:0% +mu MB ^ 2 from squaring the MB term and + + + align:start position:0% +mu MB ^ 2 from squaring the MB term and +charm squar and then this W Factor + + align:start position:0% + + + + align:start position:0% + +those are the scalar quantities you can + + align:start position:0% +those are the scalar quantities you can + + + align:start position:0% +those are the scalar quantities you can +depend + + align:start position:0% + + + + align:start position:0% + +on so what should I take for the + + align:start position:0% +on so what should I take for the + + + align:start position:0% +on so what should I take for the +W well we can work that out for an + + align:start position:0% +W well we can work that out for an + + + align:start position:0% +W well we can work that out for an +example like the one I was saying that + + align:start position:0% +example like the one I was saying that + + + align:start position:0% +example like the one I was saying that +we're doing like B to D star L new so + + align:start position:0% +we're doing like B to D star L new so + + + align:start position:0% +we're doing like B to D star L new so +let me show you how that works + + align:start position:0% + + + + align:start position:0% + +so for the B + + align:start position:0% +so for the B + + + align:start position:0% +so for the B +mezon for momentum we can take it to be + + align:start position:0% +mezon for momentum we can take it to be + + + align:start position:0% +mezon for momentum we can take it to be +m capital B mezon time V + + align:start position:0% +m capital B mezon time V + + + align:start position:0% +m capital B mezon time V +mu and by momentum conservation that's + + align:start position:0% +mu and by momentum conservation that's + + + align:start position:0% +mu and by momentum conservation that's +going to be the dstar momentum which we + + align:start position:0% +going to be the dstar momentum which we + + + align:start position:0% +going to be the dstar momentum which we +can take to be MD star time V Prime U + + align:start position:0% +can take to be MD star time V Prime U + + + align:start position:0% +can take to be MD star time V Prime U +and then a momentum transfer which I + + align:start position:0% +and then a momentum transfer which I + + + align:start position:0% +and then a momentum transfer which I +call Q this is a different Q than my + + align:start position:0% +call Q this is a different Q than my + + + align:start position:0% +call Q this is a different Q than my +Loop momentum Q sorry about + + align:start position:0% + + + + align:start position:0% + +that so then we can just take this + + align:start position:0% +that so then we can just take this + + + align:start position:0% +that so then we can just take this +relation and we can square it and we can + + align:start position:0% +relation and we can square it and we can + + + align:start position:0% +relation and we can square it and we can +get v. V Prime so if you look at Q ^2 + + align:start position:0% + + + + align:start position:0% + +you can solve this for V do V Prime and + + align:start position:0% +you can solve this for V do V Prime and + + + align:start position:0% +you can solve this for V do V Prime and +it's just fixed you see that v. V Prime + + align:start position:0% +it's just fixed you see that v. V Prime + + + align:start position:0% +it's just fixed you see that v. V Prime +is fixed in terms of the Meson masses + + align:start position:0% +is fixed in terms of the Meson masses + + + align:start position:0% +is fixed in terms of the Meson masses +and the momentum transfer and that's the + + align:start position:0% +and the momentum transfer and that's the + + + align:start position:0% +and the momentum transfer and that's the +momentum transfer to the leptons here + + align:start position:0% +momentum transfer to the leptons here + + + align:start position:0% +momentum transfer to the leptons here +how much momentum do they carry away so + + align:start position:0% +how much momentum do they carry away so + + + align:start position:0% +how much momentum do they carry away so +you can think of all those things as + + align:start position:0% +you can think of all those things as + + + align:start position:0% +you can think of all those things as +external you fix how much momentum the + + align:start position:0% +external you fix how much momentum the + + + align:start position:0% +external you fix how much momentum the +leptons carry away these are fixed + + align:start position:0% +leptons carry away these are fixed + + + align:start position:0% +leptons carry away these are fixed +numbers you look them up in the PDG and + + align:start position:0% +numbers you look them up in the PDG and + + + align:start position:0% +numbers you look them up in the PDG and +then you know what value of v.v Prime to + + align:start position:0% +then you know what value of v.v Prime to + + + align:start position:0% +then you know what value of v.v Prime to +plug in here now it's a function of q^ s + + align:start position:0% +plug in here now it's a function of q^ s + + + align:start position:0% +plug in here now it's a function of q^ s +q^ s can vary in the + + align:start position:0% +q^ s can vary in the + + + align:start position:0% +q^ s can vary in the +process so in that sense it's a + + align:start position:0% +process so in that sense it's a + + + align:start position:0% +process so in that sense it's a +non-trivial function not just a fixed + + align:start position:0% +non-trivial function not just a fixed + + + align:start position:0% +non-trivial function not just a fixed +number but for any fixed kinematic + + align:start position:0% +number but for any fixed kinematic + + + align:start position:0% +number but for any fixed kinematic +configuration any fixed Q then it would + + align:start position:0% +configuration any fixed Q then it would + + + align:start position:0% +configuration any fixed Q then it would +just be a + + align:start position:0% +just be a + + + align:start position:0% +just be a +number so if you look at this in + + align:start position:0% +number so if you look at this in + + + align:start position:0% +number so if you look at this in +practice you find that this guy for this + + align:start position:0% +practice you find that this guy for this + + + align:start position:0% +practice you find that this guy for this +particular case goes from 1 to 1.5 so + + align:start position:0% +particular case goes from 1 to 1.5 so + + + align:start position:0% +particular case goes from 1 to 1.5 so +that's the kinematic range that's + + align:start position:0% +that's the kinematic range that's + + + align:start position:0% +that's the kinematic range that's +allowed + + align:start position:0% + + + + align:start position:0% + +so it is + + align:start position:0% +so it is + + + align:start position:0% +so it is +fixed by external kinematics kinematics + + align:start position:0% +fixed by external kinematics kinematics + + + align:start position:0% +fixed by external kinematics kinematics +that is external to the Dynamics inside + + align:start position:0% +that is external to the Dynamics inside + + + align:start position:0% +that is external to the Dynamics inside +the loop + + align:start position:0% + + + + align:start position:0% + +and in that way the Wilson coefficient + + align:start position:0% +and in that way the Wilson coefficient + + + align:start position:0% +and in that way the Wilson coefficient +here is more non-trivial than the ones + + align:start position:0% +here is more non-trivial than the ones + + + align:start position:0% +here is more non-trivial than the ones +we saw earlier which just depended on + + align:start position:0% +we saw earlier which just depended on + + + align:start position:0% +we saw earlier which just depended on +masses now it's depending on masses as + + align:start position:0% +masses now it's depending on masses as + + + align:start position:0% +masses now it's depending on masses as +well as this function of v.v + + align:start position:0% +well as this function of v.v + + + align:start position:0% +well as this function of v.v +prime + + align:start position:0% + + + + align:start position:0% + +okay again one finds that this gamma + + align:start position:0% +okay again one finds that this gamma + + + align:start position:0% +okay again one finds that this gamma +t comes out to be exactly the same + + align:start position:0% +t comes out to be exactly the same + + + align:start position:0% +t comes out to be exactly the same +independent of the choice + + align:start position:0% +independent of the choice + + + align:start position:0% +independent of the choice +of the spin structure so we could do + + align:start position:0% +of the spin structure so we could do + + + align:start position:0% +of the spin structure so we could do +this calculation with any spin structure + + align:start position:0% +this calculation with any spin structure + + + align:start position:0% +this calculation with any spin structure +we like and heavy Quirk symmetry in this + + align:start position:0% +we like and heavy Quirk symmetry in this + + + align:start position:0% +we like and heavy Quirk symmetry in this +case + + align:start position:0% +case + + + align:start position:0% +case +is all you take all it takes to show + + align:start position:0% +is all you take all it takes to show + + + align:start position:0% +is all you take all it takes to show +that this gamma T is independent of the + + align:start position:0% +that this gamma T is independent of the + + + align:start position:0% +that this gamma T is independent of the +spin + + align:start position:0% +spin + + + align:start position:0% +spin +structure so if you think about that + + align:start position:0% +structure so if you think about that + + + align:start position:0% +structure so if you think about that +from the loop graph actually in this + + align:start position:0% +from the loop graph actually in this + + + align:start position:0% +from the loop graph actually in this +case it's it's pretty easy to see + + align:start position:0% +case it's it's pretty easy to see + + + align:start position:0% +case it's it's pretty easy to see +because remember that this vertex didn't + + align:start position:0% +because remember that this vertex didn't + + + align:start position:0% +because remember that this vertex didn't +have any spin structure the propagator + + align:start position:0% +have any spin structure the propagator + + + align:start position:0% +have any spin structure the propagator +had no spin structure so nothing in the + + align:start position:0% +had no spin structure so nothing in the + + + align:start position:0% +had no spin structure so nothing in the +calculation had spin structure so the + + align:start position:0% +calculation had spin structure so the + + + align:start position:0% +calculation had spin structure so the +only thing that had spin structure is + + align:start position:0% +only thing that had spin structure is + + + align:start position:0% +only thing that had spin structure is +the gamma you stuck in there so it's + + align:start position:0% +the gamma you stuck in there so it's + + + align:start position:0% +the gamma you stuck in there so it's +just a scaler times gamma so doesn't + + align:start position:0% +just a scaler times gamma so doesn't + + + align:start position:0% +just a scaler times gamma so doesn't +care about the gamma whatever the tree + + align:start position:0% +care about the gamma whatever the tree + + + align:start position:0% +care about the gamma whatever the tree +level gamma is it just goes through it's + + align:start position:0% +level gamma is it just goes through it's + + + align:start position:0% +level gamma is it just goes through it's +not touched by heavy Quark by the hqt + + align:start position:0% + + + + align:start position:0% + +lran so what is physically going on here + + align:start position:0% +lran so what is physically going on here + + + align:start position:0% +lran so what is physically going on here +and what is the HQ doing for you is that + + align:start position:0% +and what is the HQ doing for you is that + + + align:start position:0% +and what is the HQ doing for you is that +there's logs like this mq over Lambda + + align:start position:0% +there's logs like this mq over Lambda + + + align:start position:0% +there's logs like this mq over Lambda +qcd in qcd and by going over to HQ + + align:start position:0% +qcd in qcd and by going over to HQ + + + align:start position:0% +qcd in qcd and by going over to HQ +this + + align:start position:0% +this + + + align:start position:0% +this +becomes a log of mu over Lambda + + align:start position:0% +becomes a log of mu over Lambda + + + align:start position:0% +becomes a log of mu over Lambda +qcd which is encoded in HQ operators + + align:start position:0% +qcd which is encoded in HQ operators + + + align:start position:0% +qcd which is encoded in HQ operators +like this + + align:start position:0% + + + + align:start position:0% + +current as well + + align:start position:0% +current as well + + + align:start position:0% +current as well +as a log of mu over mq or mq over + + align:start position:0% +as a log of mu over mq or mq over + + + align:start position:0% +as a log of mu over mq or mq over +mu which is in the hqt coefficient + + align:start position:0% +mu which is in the hqt coefficient + + + align:start position:0% +mu which is in the hqt coefficient +functions hqt Wilson coefficients so + + align:start position:0% +functions hqt Wilson coefficients so + + + align:start position:0% +functions hqt Wilson coefficients so +just how we much exactly the same as how + + align:start position:0% +just how we much exactly the same as how + + + align:start position:0% +just how we much exactly the same as how +we talked about it for integrating out a + + align:start position:0% +we talked about it for integrating out a + + + align:start position:0% +we talked about it for integrating out a +heavy particle the logs get split up + + align:start position:0% +heavy particle the logs get split up + + + align:start position:0% +heavy particle the logs get split up +into pieces in the Wilson coefficient + + align:start position:0% +into pieces in the Wilson coefficient + + + align:start position:0% +into pieces in the Wilson coefficient +pieces in The Matrix elements + + align:start position:0% +pieces in The Matrix elements + + + align:start position:0% +pieces in The Matrix elements +operators here we're separating mq heavy + + align:start position:0% +operators here we're separating mq heavy + + + align:start position:0% +operators here we're separating mq heavy +cork mass and it's both the charm and + + align:start position:0% +cork mass and it's both the charm and + + + align:start position:0% +cork mass and it's both the charm and +the bottom in the case of that we're + + align:start position:0% +the bottom in the case of that we're + + + align:start position:0% +the bottom in the case of that we're +talking + + align:start position:0% +talking + + + align:start position:0% +talking +about and the enal dimension that we + + align:start position:0% +about and the enal dimension that we + + + align:start position:0% +about and the enal dimension that we +calculated sums up those logs and + + align:start position:0% +calculated sums up those logs and + + + align:start position:0% +calculated sums up those logs and +summing up those logs + + align:start position:0% +summing up those logs + + + align:start position:0% +summing up those logs +involves a non-trivial function of this + + align:start position:0% + + + + align:start position:0% + +W but we actually know exactly the + + align:start position:0% +W but we actually know exactly the + + + align:start position:0% +W but we actually know exactly the +non-trivial function because we can + + align:start position:0% +non-trivial function because we can + + + align:start position:0% +non-trivial function because we can +calculate + + align:start position:0% +calculate + + + align:start position:0% +calculate +it and it's + + align:start position:0% +it and it's + + + align:start position:0% +it and it's +just this guy here + + align:start position:0% + + + + align:start position:0% + +okay so the new wrinkle that can come in + + align:start position:0% +okay so the new wrinkle that can come in + + + align:start position:0% +okay so the new wrinkle that can come in +in hqt is that the anomalous Dimension + + align:start position:0% +in hqt is that the anomalous Dimension + + + align:start position:0% +in hqt is that the anomalous Dimension +become can become a more non-trivial + + align:start position:0% + + + + align:start position:0% + +thing so if you look at it at leading + + align:start position:0% +thing so if you look at it at leading + + + align:start position:0% +thing so if you look at it at leading +log + + align:start position:0% +log + + + align:start position:0% +log +order the rest is kind of pretty + + align:start position:0% +order the rest is kind of pretty + + + align:start position:0% +order the rest is kind of pretty +straightforward + + align:start position:0% +straightforward + + + align:start position:0% +straightforward +so if you go through the leading log + + align:start position:0% +so if you go through the leading log + + + align:start position:0% +so if you go through the leading log +result you would do the same type of + + align:start position:0% +result you would do the same type of + + + align:start position:0% +result you would do the same type of +thing that we did before you would match + + align:start position:0% +thing that we did before you would match + + + align:start position:0% +thing that we did before you would match +it some scale + + align:start position:0% + + + + align:start position:0% + +and at that scale you can normalize + + align:start position:0% +and at that scale you can normalize + + + align:start position:0% +and at that scale you can normalize +things so that the Wilson coefficient at + + align:start position:0% +things so that the Wilson coefficient at + + + align:start position:0% +things so that the Wilson coefficient at +mual + + align:start position:0% +mual + + + align:start position:0% +mual +mq is just one at tree + + align:start position:0% +mq is just one at tree + + + align:start position:0% +mq is just one at tree +level and then the leading log + + align:start position:0% +level and then the leading log + + + align:start position:0% +level and then the leading log +result is a function these various + + align:start position:0% +result is a function these various + + + align:start position:0% +result is a function these various +things which in general is C of mq times + + align:start position:0% +things which in general is C of mq times + + + align:start position:0% +things which in general is C of mq times +some + + align:start position:0% +some + + + align:start position:0% +some +Evolution from mq to Mu suppressing some + + align:start position:0% +Evolution from mq to Mu suppressing some + + + align:start position:0% +Evolution from mq to Mu suppressing some +of the + + align:start position:0% +of the + + + align:start position:0% +of the +dependencies Del leeting log result is + + align:start position:0% +dependencies Del leeting log result is + + + align:start position:0% +dependencies Del leeting log result is +one for this + + align:start position:0% +one for this + + + align:start position:0% +one for this +and then this guy at lowest order is + + align:start position:0% +and then this guy at lowest order is + + + align:start position:0% +and then this guy at lowest order is +just a ratio of Alphas + + align:start position:0% + + + + align:start position:0% + +again and then there's + + align:start position:0% +again and then there's + + + align:start position:0% +again and then there's +a the gamma for the purpose of solving + + align:start position:0% +a the gamma for the purpose of solving + + + align:start position:0% +a the gamma for the purpose of solving +the RG is just the only thing that + + align:start position:0% +the RG is just the only thing that + + + align:start position:0% +the RG is just the only thing that +matters is it's + + align:start position:0% + + + + align:start position:0% + +Alpha so gamma is a constant for heavy + + align:start position:0% +Alpha so gamma is a constant for heavy + + + align:start position:0% +Alpha so gamma is a constant for heavy +to + + align:start position:0% +to + + + align:start position:0% +to +light just a number + + align:start position:0% + + + + align:start position:0% + +for that current was a + + align:start position:0% +for that current was a + + + align:start position:0% +for that current was a +constant this solution is actually valid + + align:start position:0% +constant this solution is actually valid + + + align:start position:0% +constant this solution is actually valid +for both of them and then it's a + + align:start position:0% + + + + align:start position:0% + +function of this + + align:start position:0% +function of this + + + align:start position:0% +function of this +W for the + + align:start position:0% + + + + align:start position:0% + +current where we have two heavy quirks + + align:start position:0% +current where we have two heavy quirks + + + align:start position:0% +current where we have two heavy quirks +so the W dependence just goes along for + + align:start position:0% +so the W dependence just goes along for + + + align:start position:0% +so the W dependence just goes along for +the ride and you're solving the + + align:start position:0% +the ride and you're solving the + + + align:start position:0% +the ride and you're solving the +anomalous Dimension + + align:start position:0% +anomalous Dimension + + + align:start position:0% +anomalous Dimension +equation okay so that's what that's what + + align:start position:0% +equation okay so that's what that's what + + + align:start position:0% +equation okay so that's what that's what +resumming the logs would look like + + align:start position:0% +resumming the logs would look like + + + align:start position:0% +resumming the logs would look like +essentially all each log is getting + + align:start position:0% +essentially all each log is getting + + + align:start position:0% +essentially all each log is getting +extra of powers of this factor of + + align:start position:0% + + + + align:start position:0% + +gamma so that was number + + align:start position:0% +gamma so that was number + + + align:start position:0% +gamma so that was number +four so any questions about + + align:start position:0% + + + + align:start position:0% + +that okay pretty + + align:start position:0% + + + + align:start position:0% + +straightforward so much of this + + align:start position:0% +straightforward so much of this + + + align:start position:0% +straightforward so much of this +essentially all of the story except for + + align:start position:0% +essentially all of the story except for + + + align:start position:0% +essentially all of the story except for +this little wrinkle is very similar to + + align:start position:0% +this little wrinkle is very similar to + + + align:start position:0% +this little wrinkle is very similar to +integrating out a massive particle + + align:start position:0% +integrating out a massive particle + + + align:start position:0% +integrating out a massive particle +and the other part of the story that's + + align:start position:0% +and the other part of the story that's + + + align:start position:0% +and the other part of the story that's +similar is that the HQ Matrix elements + + align:start position:0% +similar is that the HQ Matrix elements + + + align:start position:0% +similar is that the HQ Matrix elements +depend on mu as + + align:start position:0% + + + + align:start position:0% + +well and so in our example that we + + align:start position:0% +well and so in our example that we + + + align:start position:0% +well and so in our example that we +talked about last time we had a matrix + + align:start position:0% +talked about last time we had a matrix + + + align:start position:0% +talked about last time we had a matrix +element so let me give + + align:start position:0% +element so let me give + + + align:start position:0% +element so let me give +it to you in the context of that + + align:start position:0% +it to you in the context of that + + + align:start position:0% +it to you in the context of that +example so last time we were talking + + align:start position:0% +example so last time we were talking + + + align:start position:0% +example so last time we were talking +about something with is a Decay + + align:start position:0% + + + + align:start position:0% + +constant and that's one example of this + + align:start position:0% +constant and that's one example of this + + + align:start position:0% +constant and that's one example of this +heavy Delight + + align:start position:0% + + + + align:start position:0% + +current so we had a current which had + + align:start position:0% +current so we had a current which had + + + align:start position:0% +current so we had a current which had +one heavy Quark one light quark and then + + align:start position:0% +one heavy Quark one light quark and then + + + align:start position:0% +one heavy Quark one light quark and then +a heavy Meson and we figured out that + + align:start position:0% +a heavy Meson and we figured out that + + + align:start position:0% +a heavy Meson and we figured out that +this was giving some a * V mu and now + + align:start position:0% +this was giving some a * V mu and now + + + align:start position:0% +this was giving some a * V mu and now +I'm telling you that you should think of + + align:start position:0% +I'm telling you that you should think of + + + align:start position:0% +I'm telling you that you should think of +the a as a function of mu The Matrix + + align:start position:0% +the a as a function of mu The Matrix + + + align:start position:0% +the a as a function of mu The Matrix +element here is a function of mu + + align:start position:0% + + + + align:start position:0% + +okay so that's just a slight + + align:start position:0% +okay so that's just a slight + + + align:start position:0% +okay so that's just a slight +modification to what we talked about + + align:start position:0% +modification to what we talked about + + + align:start position:0% +modification to what we talked about +last + + align:start position:0% +last + + + align:start position:0% +last +time and + + align:start position:0% +time and + + + align:start position:0% +time and +again if you + + align:start position:0% +again if you + + + align:start position:0% +again if you +want for this Matrix element you want mu + + align:start position:0% +want for this Matrix element you want mu + + + align:start position:0% +want for this Matrix element you want mu +to be say a + + align:start position:0% +to be say a + + + align:start position:0% +to be say a +GV for some scale that's greater than + + align:start position:0% +GV for some scale that's greater than + + + align:start position:0% +GV for some scale that's greater than +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +qcd and so what you would do is You' + + align:start position:0% +qcd and so what you would do is You' + + + align:start position:0% +qcd and so what you would do is You' +evaluate Matrix elements and Define that + + align:start position:0% +evaluate Matrix elements and Define that + + + align:start position:0% +evaluate Matrix elements and Define that +parameter at some scale like a g and do + + align:start position:0% +parameter at some scale like a g and do + + + align:start position:0% +parameter at some scale like a g and do +re normalization group Evolution from + + align:start position:0% +re normalization group Evolution from + + + align:start position:0% +re normalization group Evolution from +the heavy cork Mass down to a + + align:start position:0% +the heavy cork Mass down to a + + + align:start position:0% +the heavy cork Mass down to a +GV okay so that's how + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +normalization group Evolution story + + align:start position:0% +normalization group Evolution story + + + align:start position:0% +normalization group Evolution story +would + + align:start position:0% + + + + align:start position:0% + +be you don't want to run all the way + + align:start position:0% +be you don't want to run all the way + + + align:start position:0% +be you don't want to run all the way +down to Lambda qcd because the anomalous + + align:start position:0% +down to Lambda qcd because the anomalous + + + align:start position:0% +down to Lambda qcd because the anomalous +Dimension has to remain perturbative so + + align:start position:0% +Dimension has to remain perturbative so + + + align:start position:0% +Dimension has to remain perturbative so +you decide where your what Your cut off + + align:start position:0% +you decide where your what Your cut off + + + align:start position:0% +you decide where your what Your cut off +is for where you think peration theory + + align:start position:0% +is for where you think peration theory + + + align:start position:0% +is for where you think peration theory +is still valid often people pick + + align:start position:0% +is still valid often people pick + + + align:start position:0% +is still valid often people pick +something like one GV or one and a half + + align:start position:0% +something like one GV or one and a half + + + align:start position:0% +something like one GV or one and a half +GV these types of + + align:start position:0% +GV these types of + + + align:start position:0% +GV these types of +[Applause] + + align:start position:0% + + + + align:start position:0% + +problems and again this is just + + align:start position:0% +problems and again this is just + + + align:start position:0% +problems and again this is just +separating out all the mqs making sure + + align:start position:0% +separating out all the mqs making sure + + + align:start position:0% +separating out all the mqs making sure +that your Matrix element here has no mqs + + align:start position:0% +that your Matrix element here has no mqs + + + align:start position:0% +that your Matrix element here has no mqs +it does have an extra cut off + + align:start position:0% +it does have an extra cut off + + + align:start position:0% +it does have an extra cut off +me okay so that's the RG story + + align:start position:0% +me okay so that's the RG story + + + align:start position:0% +me okay so that's the RG story +let's also talk a little bit about the + + align:start position:0% +let's also talk a little bit about the + + + align:start position:0% +let's also talk a little bit about the +matching + + align:start position:0% + + + + align:start position:0% + +story so these are the perative + + align:start position:0% + + + + align:start position:0% + +corrections at the scale + + align:start position:0% +corrections at the scale + + + align:start position:0% +corrections at the scale +mq so alpha s at + + align:start position:0% +mq so alpha s at + + + align:start position:0% +mq so alpha s at +mq we had perturbative Corrections at + + align:start position:0% +mq we had perturbative Corrections at + + + align:start position:0% +mq we had perturbative Corrections at +the W scale when we integrated out the w + + align:start position:0% +the W scale when we integrated out the w + + + align:start position:0% +the W scale when we integrated out the w +b on now we have another set of + + align:start position:0% +b on now we have another set of + + + align:start position:0% +b on now we have another set of +perturbative Corrections at the heavy + + align:start position:0% +perturbative Corrections at the heavy + + + align:start position:0% +perturbative Corrections at the heavy +quk Mass scale when we ever integrate + + align:start position:0% +quk Mass scale when we ever integrate + + + align:start position:0% +quk Mass scale when we ever integrate +out the heavy Quark Mass it's different + + align:start position:0% +out the heavy Quark Mass it's different + + + align:start position:0% +out the heavy Quark Mass it's different +because we're now passing from something + + align:start position:0% +because we're now passing from something + + + align:start position:0% +because we're now passing from something +that looked like a full qcd Theory with + + align:start position:0% +that looked like a full qcd Theory with + + + align:start position:0% +that looked like a full qcd Theory with +some external operators we're now + + align:start position:0% +some external operators we're now + + + align:start position:0% +some external operators we're now +passing to this hqet theory for the + + align:start position:0% +passing to this hqet theory for the + + + align:start position:0% +passing to this hqet theory for the +heavy + + align:start position:0% + + + + align:start position:0% + +Quark so if you + + align:start position:0% +Quark so if you + + + align:start position:0% +Quark so if you +like we previously had MW we knew how to + + align:start position:0% +like we previously had MW we knew how to + + + align:start position:0% +like we previously had MW we knew how to +do a normalization group Evolution there + + align:start position:0% +do a normalization group Evolution there + + + align:start position:0% +do a normalization group Evolution there +and we had a sort of HW Theory here now + + align:start position:0% +and we had a sort of HW Theory here now + + + align:start position:0% +and we had a sort of HW Theory here now +we integrate out the heavy Quark mass + + align:start position:0% +we integrate out the heavy Quark mass + + + align:start position:0% +we integrate out the heavy Quark mass +and we passed to an HQ Theory below that + + align:start position:0% +and we passed to an HQ Theory below that + + + align:start position:0% +and we passed to an HQ Theory below that +scale + + align:start position:0% + + + + align:start position:0% + +so if you go if you go back to the kind + + align:start position:0% +so if you go if you go back to the kind + + + align:start position:0% +so if you go if you go back to the kind +of HW + + align:start position:0% +of HW + + + align:start position:0% +of HW +Theory let me call it that and we want + + align:start position:0% +Theory let me call it that and we want + + + align:start position:0% +Theory let me call it that and we want +to match that onto + + align:start position:0% +to match that onto + + + align:start position:0% +to match that onto +HQ and we do it with calculation like + + align:start position:0% +HQ and we do it with calculation like + + + align:start position:0% +HQ and we do it with calculation like +this and I'll just use this heavy light + + align:start position:0% +this and I'll just use this heavy light + + + align:start position:0% +this and I'll just use this heavy light +example + + align:start position:0% + + + + align:start position:0% + +still so here's a matrix element that + + align:start position:0% +still so here's a matrix element that + + + align:start position:0% +still so here's a matrix element that +you could consider for the + + align:start position:0% +you could consider for the + + + align:start position:0% +you could consider for the +matching and let me write it with a + + align:start position:0% +matching and let me write it with a + + + align:start position:0% +matching and let me write it with a +bunch of schematic objects and then + + align:start position:0% +bunch of schematic objects and then + + + align:start position:0% +bunch of schematic objects and then +explain what they + + align:start position:0% + + + + align:start position:0% + +are so the user Spinners and I'm taking + + align:start position:0% +are so the user Spinners and I'm taking + + + align:start position:0% +are so the user Spinners and I'm taking +zero zero momentum here just for + + align:start position:0% + + + + align:start position:0% + +Simplicity these RS are residue factors + + align:start position:0% +Simplicity these RS are residue factors + + + align:start position:0% +Simplicity these RS are residue factors +that come in so so far in in this when + + align:start position:0% +that come in so so far in in this when + + + align:start position:0% +that come in so so far in in this when +we calculated the wave function rization + + align:start position:0% +we calculated the wave function rization + + + align:start position:0% +we calculated the wave function rization +graphs we just took the Divergent piece + + align:start position:0% +graphs we just took the Divergent piece + + + align:start position:0% +graphs we just took the Divergent piece +and if you do that when you do the + + align:start position:0% +and if you do that when you do the + + + align:start position:0% +and if you do that when you do the +matching computation you have to use lsz + + align:start position:0% +matching computation you have to use lsz + + + align:start position:0% +matching computation you have to use lsz +and so the finite Pieces come back in + + align:start position:0% +and so the finite Pieces come back in + + + align:start position:0% +and so the finite Pieces come back in +and you call them residues so these are + + align:start position:0% +and you call them residues so these are + + + align:start position:0% +and you call them residues so these are +finite + + align:start position:0% + + + + align:start position:0% + +residues that you have to take account + + align:start position:0% +residues that you have to take account + + + align:start position:0% +residues that you have to take account +of finite in a UV + + align:start position:0% +of finite in a UV + + + align:start position:0% +of finite in a UV +sense so UV finite + + align:start position:0% +sense so UV finite + + + align:start position:0% +sense so UV finite +residues you have to take into account + + align:start position:0% +residues you have to take into account + + + align:start position:0% +residues you have to take into account +if you're just using msar and this here + + align:start position:0% +if you're just using msar and this here + + + align:start position:0% +if you're just using msar and this here +would be the vertex re normalization + + align:start position:0% + + + + align:start position:0% + +graph okay both diagrams look like this + + align:start position:0% +graph okay both diagrams look like this + + + align:start position:0% +graph okay both diagrams look like this +in qcd they're + + align:start position:0% + + + + align:start position:0% + +both same type of structure and then in + + align:start position:0% +both same type of structure and then in + + + align:start position:0% +both same type of structure and then in +hqt it's a similar thing we can write + + align:start position:0% +hqt it's a similar thing we can write + + + align:start position:0% +hqt it's a similar thing we can write +down a formula for the S Matrix + + align:start position:0% +down a formula for the S Matrix + + + align:start position:0% +down a formula for the S Matrix +element the same + + align:start position:0% +element the same + + + align:start position:0% +element the same +States now with our effective Theory + + align:start position:0% + + + + align:start position:0% + +current + + align:start position:0% +current + + + align:start position:0% +current +and we know how to transition from + + align:start position:0% +and we know how to transition from + + + align:start position:0% +and we know how to transition from +effective Theory and full theory + + align:start position:0% +effective Theory and full theory + + + align:start position:0% +effective Theory and full theory +states talked about that last time + + align:start position:0% +states talked about that last time + + + align:start position:0% +states talked about that last time +and so there again would be some residue + + align:start position:0% +and so there again would be some residue + + + align:start position:0% +and so there again would be some residue +factors and if the residue factors are + + align:start position:0% +factors and if the residue factors are + + + align:start position:0% +factors and if the residue factors are +not the same in the two theories you + + align:start position:0% +not the same in the two theories you + + + align:start position:0% +not the same in the two theories you +have to account for that and they won't + + align:start position:0% +have to account for that and they won't + + + align:start position:0% +have to account for that and they won't +be because one of the the heavy Quark + + align:start position:0% +be because one of the the heavy Quark + + + align:start position:0% +be because one of the the heavy Quark +residue will be different than the heavy + + align:start position:0% +residue will be different than the heavy + + + align:start position:0% +residue will be different than the heavy +Quark residue here + + align:start position:0% + + + + align:start position:0% + +so this guy + + align:start position:0% +so this guy + + + align:start position:0% +so this guy +here this finite piece of this graph + + align:start position:0% +here this finite piece of this graph + + + align:start position:0% +here this finite piece of this graph +this guy here will be the same as above + + align:start position:0% +this guy here will be the same as above + + + align:start position:0% +this guy here will be the same as above +and this guy here + + align:start position:0% + + + + align:start position:0% + +is this guy here is the heavy + + align:start position:0% +is this guy here is the heavy + + + align:start position:0% +is this guy here is the heavy +cork vertex graph which is independent + + align:start position:0% +cork vertex graph which is independent + + + align:start position:0% +cork vertex graph which is independent +of the spin structure it's not not not + + align:start position:0% +of the spin structure it's not not not + + + align:start position:0% +of the spin structure it's not not not +independent of the spin structure up + + align:start position:0% +independent of the spin structure up + + + align:start position:0% +independent of the spin structure up +there + + align:start position:0% + + + + align:start position:0% + +so we could carry out the calculations + + align:start position:0% +so we could carry out the calculations + + + align:start position:0% +so we could carry out the calculations +of those Loop + + align:start position:0% +of those Loop + + + align:start position:0% +of those Loop +diagrams and then we can subtract and we + + align:start position:0% +diagrams and then we can subtract and we + + + align:start position:0% +diagrams and then we can subtract and we +can see what's left over and whatever is + + align:start position:0% +can see what's left over and whatever is + + + align:start position:0% +can see what's left over and whatever is +left over is the Wilson + + align:start position:0% +left over is the Wilson + + + align:start position:0% +left over is the Wilson +coefficient okay so very similar to what + + align:start position:0% +coefficient okay so very similar to what + + + align:start position:0% +coefficient okay so very similar to what +we did + + align:start position:0% + + + + align:start position:0% + +before + + align:start position:0% +before + + + align:start position:0% +before +calculate subtract + + align:start position:0% + + + + align:start position:0% + +what you find when you do that is that + + align:start position:0% +what you find when you do that is that + + + align:start position:0% +what you find when you do that is that +there's actually two currents if you + + align:start position:0% +there's actually two currents if you + + + align:start position:0% +there's actually two currents if you +consider a vector + + align:start position:0% +consider a vector + + + align:start position:0% +consider a vector +current where gamma is gamma + + align:start position:0% + + + + align:start position:0% + +mu then the effective field Theory which + + align:start position:0% +mu then the effective field Theory which + + + align:start position:0% +mu then the effective field Theory which +is + + align:start position:0% +is + + + align:start position:0% +is +hqt has two effective Theory + + align:start position:0% + + + + align:start position:0% + +currents that are + + align:start position:0% + + + + align:start position:0% + +vector so you have C1 and C2 + + align:start position:0% + + + + align:start position:0% + +the reason that there's two is because + + align:start position:0% +the reason that there's two is because + + + align:start position:0% +the reason that there's two is because +we have another Vector to play with + + align:start position:0% +we have another Vector to play with + + + align:start position:0% +we have another Vector to play with +which is V + + align:start position:0% +which is V + + + align:start position:0% +which is V +mu so I can have + + align:start position:0% +mu so I can have + + + align:start position:0% +mu so I can have +qar V + + align:start position:0% +qar V + + + align:start position:0% +qar V +mu replacing the gamma + + align:start position:0% + + + + align:start position:0% + +mu so VM wasn't an external thing in qcd + + align:start position:0% +mu so VM wasn't an external thing in qcd + + + align:start position:0% +mu so VM wasn't an external thing in qcd +it was part of the Dynamics here it's an + + align:start position:0% +it was part of the Dynamics here it's an + + + align:start position:0% +it was part of the Dynamics here it's an +external thing so it's allowed to + + align:start position:0% +external thing so it's allowed to + + + align:start position:0% +external thing so it's allowed to +replace gamma mu as one of the + + align:start position:0% +replace gamma mu as one of the + + + align:start position:0% +replace gamma mu as one of the +structures + + align:start position:0% + + + + align:start position:0% + +and if you go through the calculation + + align:start position:0% +and if you go through the calculation + + + align:start position:0% +and if you go through the calculation +this is the just to show you what the + + align:start position:0% +this is the just to show you what the + + + align:start position:0% +this is the just to show you what the +result looks + + align:start position:0% + + + + align:start position:0% + +like remember the heavy to light case is + + align:start position:0% +like remember the heavy to light case is + + + align:start position:0% +like remember the heavy to light case is +the case where you're not getting a + + align:start position:0% +the case where you're not getting a + + + align:start position:0% +the case where you're not getting a +non-trivial function on the right hand + + align:start position:0% + + + + align:start position:0% + +side you get a non-zero resulted order + + align:start position:0% +side you get a non-zero resulted order + + + align:start position:0% +side you get a non-zero resulted order +Alpha ask for both of those those + + align:start position:0% + + + + align:start position:0% + +coefficients okay so the reading also + + align:start position:0% +coefficients okay so the reading also + + + align:start position:0% +coefficients okay so the reading also +goes through this whole thing for the + + align:start position:0% +goes through this whole thing for the + + + align:start position:0% +goes through this whole thing for the +heavy heavy to heavy case which is more + + align:start position:0% +heavy heavy to heavy case which is more + + + align:start position:0% +heavy heavy to heavy case which is more +interesting but it's not really more + + align:start position:0% +interesting but it's not really more + + + align:start position:0% +interesting but it's not really more +non-trivial than what we've talked about + + align:start position:0% +non-trivial than what we've talked about + + + align:start position:0% +non-trivial than what we've talked about +so far already with the anomalous + + align:start position:0% +so far already with the anomalous + + + align:start position:0% +so far already with the anomalous +Dimension you get results that are + + align:start position:0% +Dimension you get results that are + + + align:start position:0% +Dimension you get results that are +functions of w the bson coefficient + + align:start position:0% +functions of w the bson coefficient + + + align:start position:0% +functions of w the bson coefficient +would have functions of w showing up + + align:start position:0% +would have functions of w showing up + + + align:start position:0% +would have functions of w showing up +here okay so I won't go through + + align:start position:0% +here okay so I won't go through + + + align:start position:0% +here okay so I won't go through +that now if you wanted to carry out this + + align:start position:0% +that now if you wanted to carry out this + + + align:start position:0% +that now if you wanted to carry out this +calcul a it looks like it's kind of + + align:start position:0% +calcul a it looks like it's kind of + + + align:start position:0% +calcul a it looks like it's kind of +involved this graph this graph this + + align:start position:0% +involved this graph this graph this + + + align:start position:0% +involved this graph this graph this +graph all these diagrams to + + align:start position:0% +graph all these diagrams to + + + align:start position:0% +graph all these diagrams to +consider you'd like to make your life as + + align:start position:0% +consider you'd like to make your life as + + + align:start position:0% +consider you'd like to make your life as +easy as possible and there's actually a + + align:start position:0% +easy as possible and there's actually a + + + align:start position:0% +easy as possible and there's actually a +very nice trick here for doing that that + + align:start position:0% +very nice trick here for doing that that + + + align:start position:0% +very nice trick here for doing that that +I have to mention to you it's kind of + + align:start position:0% +I have to mention to you it's kind of + + + align:start position:0% +I have to mention to you it's kind of +magical so what is the fastest way that + + align:start position:0% +magical so what is the fastest way that + + + align:start position:0% +magical so what is the fastest way that +I could get this result + + align:start position:0% + + + + align:start position:0% + +so this is a nice trick to remember if + + align:start position:0% +so this is a nice trick to remember if + + + align:start position:0% +so this is a nice trick to remember if +you ever have to do a calculation like + + align:start position:0% +you ever have to do a calculation like + + + align:start position:0% +you ever have to do a calculation like +that because it's not specific to + + align:start position:0% + + + + align:start position:0% + +HQ so let's pick our infrared regulator + + align:start position:0% +HQ so let's pick our infrared regulator + + + align:start position:0% +HQ so let's pick our infrared regulator +to make the effective Theory as simple + + align:start position:0% +to make the effective Theory as simple + + + align:start position:0% +to make the effective Theory as simple +as possible we have some choice in how + + align:start position:0% +as possible we have some choice in how + + + align:start position:0% +as possible we have some choice in how +to pick the infared regulator the result + + align:start position:0% +to pick the infared regulator the result + + + align:start position:0% +to pick the infared regulator the result +for Wilson coefficients and an almost + + align:start position:0% +for Wilson coefficients and an almost + + + align:start position:0% +for Wilson coefficients and an almost +Dimensions will not depend on that + + align:start position:0% +Dimensions will not depend on that + + + align:start position:0% +Dimensions will not depend on that +choice so let's use that freedom and + + align:start position:0% +choice so let's use that freedom and + + + align:start position:0% +choice so let's use that freedom and +make things as simple as we + + align:start position:0% + + + + align:start position:0% + +can and the choice that does that here + + align:start position:0% +can and the choice that does that here + + + align:start position:0% +can and the choice that does that here +is to use dimensional + + align:start position:0% +is to use dimensional + + + align:start position:0% +is to use dimensional +regularization + + align:start position:0% +regularization + + + align:start position:0% +regularization +for the + + align:start position:0% +for the + + + align:start position:0% +for the +UV as we've been discussing but also for + + align:start position:0% +UV as we've been discussing but also for + + + align:start position:0% +UV as we've been discussing but also for +the + + align:start position:0% +the + + + align:start position:0% +the +infrared so let's use dimensional + + align:start position:0% +infrared so let's use dimensional + + + align:start position:0% +infrared so let's use dimensional +regularization for + + align:start position:0% +regularization for + + + align:start position:0% +regularization for +both if you do + + align:start position:0% +both if you do + + + align:start position:0% +both if you do +that you can convince yourself + + align:start position:0% +that you can convince yourself + + + align:start position:0% +that you can convince yourself +that all Heavy cork effective Theory + + align:start position:0% +that all Heavy cork effective Theory + + + align:start position:0% +that all Heavy cork effective Theory +graphs with on shell external momentum + + align:start position:0% +graphs with on shell external momentum + + + align:start position:0% +graphs with on shell external momentum +so I can take the external momentum on + + align:start position:0% +so I can take the external momentum on + + + align:start position:0% +so I can take the external momentum on +shell I don't need it to regulate + + align:start position:0% +shell I don't need it to regulate + + + align:start position:0% +shell I don't need it to regulate +divergences because I'm going to use m a + + align:start position:0% +divergences because I'm going to use m a + + + align:start position:0% +divergences because I'm going to use m a +SP I'm going to use di dim R to do + + align:start position:0% +SP I'm going to use di dim R to do + + + align:start position:0% +SP I'm going to use di dim R to do +that + + align:start position:0% + + + + align:start position:0% + +so all the gra all the integrals are + + align:start position:0% +so all the gra all the integrals are + + + align:start position:0% +so all the gra all the integrals are +scalas + + align:start position:0% + + + + align:start position:0% + +and that means that they come out to be + + align:start position:0% +and that means that they come out to be + + + align:start position:0% +and that means that they come out to be +something that if you think about it is + + align:start position:0% +something that if you think about it is + + + align:start position:0% +something that if you think about it is +either zero or zero in a way where you + + align:start position:0% +either zero or zero in a way where you + + + align:start position:0% +either zero or zero in a way where you +have an UltraViolet Divergence + + align:start position:0% +have an UltraViolet Divergence + + + align:start position:0% +have an UltraViolet Divergence +counseling an infrared Divergence which + + align:start position:0% +counseling an infrared Divergence which + + + align:start position:0% +counseling an infrared Divergence which +is still + + align:start position:0% +is still + + + align:start position:0% +is still +zero now you have to think about the + + align:start position:0% +zero now you have to think about the + + + align:start position:0% +zero now you have to think about the +fact that there's both of these going on + + align:start position:0% +fact that there's both of these going on + + + align:start position:0% +fact that there's both of these going on +because you still have to think about + + align:start position:0% +because you still have to think about + + + align:start position:0% +because you still have to think about +adding counter terms to hqt to cancel + + align:start position:0% +adding counter terms to hqt to cancel + + + align:start position:0% +adding counter terms to hqt to cancel +the UV divergences + + align:start position:0% + + + + align:start position:0% + +but the answers are very simple because + + align:start position:0% +but the answers are very simple because + + + align:start position:0% +but the answers are very simple because +you can throw away all the finite pieces + + align:start position:0% +you can throw away all the finite pieces + + + align:start position:0% +you can throw away all the finite pieces +if you have 1 over Epsilon minus 1 + + align:start position:0% +if you have 1 over Epsilon minus 1 + + + align:start position:0% +if you have 1 over Epsilon minus 1 +Epsilon if you multiply that by Epsilon + + align:start position:0% +Epsilon if you multiply that by Epsilon + + + align:start position:0% +Epsilon if you multiply that by Epsilon +that term's not + + align:start position:0% +that term's not + + + align:start position:0% +that term's not +there + + align:start position:0% +there + + + align:start position:0% +there +so one over Epsilon gets removed by + + align:start position:0% +so one over Epsilon gets removed by + + + align:start position:0% +so one over Epsilon gets removed by +counter + + align:start position:0% +counter + + + align:start position:0% +counter +terms and there's no finite pieces left + + align:start position:0% +terms and there's no finite pieces left + + + align:start position:0% +terms and there's no finite pieces left +over so just + + align:start position:0% +over so just + + + align:start position:0% +over so just +use msar so you just strip off that + + align:start position:0% +use msar so you just strip off that + + + align:start position:0% +use msar so you just strip off that +exactly and you're left with 1 over + + align:start position:0% +exactly and you're left with 1 over + + + align:start position:0% +exactly and you're left with 1 over +Epsilon + + align:start position:0% + + + + align:start position:0% + +I now if you + + align:start position:0% +I now if you + + + align:start position:0% +I now if you +so so the effective Theory diagrams are + + align:start position:0% +so so the effective Theory diagrams are + + + align:start position:0% +so so the effective Theory diagrams are +just simply all 1 / Epsilon + + align:start position:0% +just simply all 1 / Epsilon + + + align:start position:0% +just simply all 1 / Epsilon +I now the reason that this is making + + align:start position:0% +I now the reason that this is making + + + align:start position:0% +I now the reason that this is making +things simple is because you also know a + + align:start position:0% +things simple is because you also know a + + + align:start position:0% +things simple is because you also know a +fact which is that the IR divergences in + + align:start position:0% +fact which is that the IR divergences in + + + align:start position:0% +fact which is that the IR divergences in +the full Theory and the effective Theory + + align:start position:0% +the full Theory and the effective Theory + + + align:start position:0% +the full Theory and the effective Theory +have to match up so these Epsilon one + + align:start position:0% +have to match up so these Epsilon one + + + align:start position:0% +have to match up so these Epsilon one +over Epsilon RS have to match up with + + align:start position:0% +over Epsilon RS have to match up with + + + align:start position:0% +over Epsilon RS have to match up with +your full Theory + + align:start position:0% + + + + align:start position:0% + +calculation so if you renormalize the + + align:start position:0% +calculation so if you renormalize the + + + align:start position:0% +calculation so if you renormalize the +qcd calculation which you can't really + + align:start position:0% +qcd calculation which you can't really + + + align:start position:0% +qcd calculation which you can't really +get around doing you have to do that + + align:start position:0% +get around doing you have to do that + + + align:start position:0% +get around doing you have to do that +calculation so you do that calculation + + align:start position:0% +calculation so you do that calculation + + + align:start position:0% +calculation so you do that calculation +in P dim + + align:start position:0% + + + + align:start position:0% + +rag same IR + + align:start position:0% +rag same IR + + + align:start position:0% +rag same IR +regulator which is a nice regulator to + + align:start position:0% +regulator which is a nice regulator to + + + align:start position:0% +regulator which is a nice regulator to +use for qcd you do the UV + + align:start position:0% +use for qcd you do the UV + + + align:start position:0% +use for qcd you do the UV +renormalization using the standard + + align:start position:0% +renormalization using the standard + + + align:start position:0% +renormalization using the standard +counter + + align:start position:0% +counter + + + align:start position:0% +counter +terms and what will you get + + align:start position:0% +terms and what will you get + + + align:start position:0% +terms and what will you get +get you would get something that looks + + align:start position:0% +get you would get something that looks + + + align:start position:0% +get you would get something that looks +like a number over Epsilon + + align:start position:0% +like a number over Epsilon + + + align:start position:0% +like a number over Epsilon +I and then you'll + + align:start position:0% +I and then you'll + + + align:start position:0% +I and then you'll +get numbers times + + align:start position:0% +get numbers times + + + align:start position:0% +get numbers times +logs U over + + align:start position:0% +logs U over + + + align:start position:0% +logs U over +mq plus other things this thing here is + + align:start position:0% +mq plus other things this thing here is + + + align:start position:0% +mq plus other things this thing here is +just cancels with the If I subtract HQ + + align:start position:0% +just cancels with the If I subtract HQ + + + align:start position:0% +just cancels with the If I subtract HQ +this is just canceling + + align:start position:0% +this is just canceling + + + align:start position:0% +this is just canceling +this so + + align:start position:0% +this so + + + align:start position:0% +this so +this guy + + align:start position:0% +this guy + + + align:start position:0% +this guy +here can + + align:start position:0% +here can + + + align:start position:0% +here can +cancels when we subtract + + align:start position:0% + + + + align:start position:0% + +HQ and so the matching is then just + + align:start position:0% + + + + align:start position:0% + +this so I don't actually even have to + + align:start position:0% +this so I don't actually even have to + + + align:start position:0% +this so I don't actually even have to +consider calculating the heavy if I use + + align:start position:0% +consider calculating the heavy if I use + + + align:start position:0% +consider calculating the heavy if I use +all these facts that I know if I trust + + align:start position:0% +all these facts that I know if I trust + + + align:start position:0% +all these facts that I know if I trust +them then I don't even have to calculate + + align:start position:0% +them then I don't even have to calculate + + + align:start position:0% +them then I don't even have to calculate +the hqt graphs I just say let me imagine + + align:start position:0% +the hqt graphs I just say let me imagine + + + align:start position:0% +the hqt graphs I just say let me imagine +that I calculate them they're all scal + + align:start position:0% +that I calculate them they're all scal + + + align:start position:0% +that I calculate them they're all scal +they look like that let me imagine that + + align:start position:0% +they look like that let me imagine that + + + align:start position:0% +they look like that let me imagine that +I renormalize them all the one over + + align:start position:0% +I renormalize them all the one over + + + align:start position:0% +I renormalize them all the one over +Epsilon UVS are gone I'm left with one + + align:start position:0% +Epsilon UVS are gone I'm left with one + + + align:start position:0% +Epsilon UVS are gone I'm left with one +over Epsilon IRS I do this calculation I + + align:start position:0% +over Epsilon IRS I do this calculation I + + + align:start position:0% +over Epsilon IRS I do this calculation I +say let me imagine that these cancel + + align:start position:0% +say let me imagine that these cancel + + + align:start position:0% +say let me imagine that these cancel +each other and then I have the + + align:start position:0% +each other and then I have the + + + align:start position:0% +each other and then I have the +matching so that's exploiting all the + + align:start position:0% +matching so that's exploiting all the + + + align:start position:0% +matching so that's exploiting all the +facts that we know about effective + + align:start position:0% +facts that we know about effective + + + align:start position:0% +facts that we know about effective +theories and full theories to get the + + align:start position:0% +theories and full theories to get the + + + align:start position:0% +theories and full theories to get the +matching as quickly as possible by just + + align:start position:0% +matching as quickly as possible by just + + + align:start position:0% +matching as quickly as possible by just +doing the full Theory calculation with a + + align:start position:0% +doing the full Theory calculation with a + + + align:start position:0% +doing the full Theory calculation with a +particular + + align:start position:0% +particular + + + align:start position:0% +particular +regulator it's not checking anything + + align:start position:0% +regulator it's not checking anything + + + align:start position:0% +regulator it's not checking anything +it's not checking that the full Theory + + align:start position:0% +it's not checking that the full Theory + + + align:start position:0% +it's not checking that the full Theory +and the effective Theory have the IR + + align:start position:0% +and the effective Theory have the IR + + + align:start position:0% +and the effective Theory have the IR +divergences matching up etc etc + + align:start position:0% +divergences matching up etc etc + + + align:start position:0% +divergences matching up etc etc +but if you just if you know that that's + + align:start position:0% +but if you just if you know that that's + + + align:start position:0% +but if you just if you know that that's +true if you trust that it's true then + + align:start position:0% +true if you trust that it's true then + + + align:start position:0% +true if you trust that it's true then +this is the fastest way to get the match + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +up seems like magic + + align:start position:0% + + + + align:start position:0% + +right okay so sometimes you can exploit + + align:start position:0% +right okay so sometimes you can exploit + + + align:start position:0% +right okay so sometimes you can exploit +what you know about the effective + + align:start position:0% +what you know about the effective + + + align:start position:0% +what you know about the effective +Theory to get things more + + align:start position:0% +Theory to get things more + + + align:start position:0% +Theory to get things more +quickly so questions about that + + align:start position:0% + + + + align:start position:0% + +um yeah so so if you think about the + + align:start position:0% +um yeah so so if you think about the + + + align:start position:0% +um yeah so so if you think about the +loop + + align:start position:0% + + + + align:start position:0% + +integral then the D here right being 4 - + + align:start position:0% +integral then the D here right being 4 - + + + align:start position:0% +integral then the D here right being 4 - +2 Epsilon having Epsilon greater than + + align:start position:0% +2 Epsilon having Epsilon greater than + + + align:start position:0% +2 Epsilon having Epsilon greater than +zero decreasing the powers of Q in the + + align:start position:0% +zero decreasing the powers of Q in the + + + align:start position:0% +zero decreasing the powers of Q in the +numerator is making it more UV + + align:start position:0% +numerator is making it more UV + + + align:start position:0% +numerator is making it more UV +convergent so to regulate the IR you + + align:start position:0% +convergent so to regulate the IR you + + + align:start position:0% +convergent so to regulate the IR you +want to have Epsilon on the other + + align:start position:0% +want to have Epsilon on the other + + + align:start position:0% +want to have Epsilon on the other +side so this is what you need for the + + align:start position:0% +side so this is what you need for the + + + align:start position:0% +side so this is what you need for the +regulating ir and this is what you need + + align:start position:0% +regulating ir and this is what you need + + + align:start position:0% +regulating ir and this is what you need +for regulating UV so it may seem + + align:start position:0% +for regulating UV so it may seem + + + align:start position:0% +for regulating UV so it may seem +contradictory that you could even do + + align:start position:0% +contradictory that you could even do + + + align:start position:0% +contradictory that you could even do +both of these things at the same time + + align:start position:0% +both of these things at the same time + + + align:start position:0% +both of these things at the same time +because greater than zero and less than + + align:start position:0% +because greater than zero and less than + + + align:start position:0% +because greater than zero and less than +zero but you could always think of + + align:start position:0% +zero but you could always think of + + + align:start position:0% +zero but you could always think of +splitting up this integral with a hard + + align:start position:0% +splitting up this integral with a hard + + + align:start position:0% +splitting up this integral with a hard +cut off somewhere in between and then + + align:start position:0% +cut off somewhere in between and then + + + align:start position:0% +cut off somewhere in between and then +just using this above and this below + + align:start position:0% +just using this above and this below + + + align:start position:0% +just using this above and this below +that cut off and the cut off dependence + + align:start position:0% +that cut off and the cut off dependence + + + align:start position:0% +that cut off and the cut off dependence +will cancel when you put the pieces back + + align:start position:0% +will cancel when you put the pieces back + + + align:start position:0% +will cancel when you put the pieces back +together so it's actually valid to just + + align:start position:0% +together so it's actually valid to just + + + align:start position:0% +together so it's actually valid to just +do calculations and for the most part + + align:start position:0% +do calculations and for the most part + + + align:start position:0% +do calculations and for the most part +you can just close your eyes and you'll + + align:start position:0% +you can just close your eyes and you'll + + + align:start position:0% +you can just close your eyes and you'll +get some gamma of epsilons and some + + align:start position:0% +get some gamma of epsilons and some + + + align:start position:0% +get some gamma of epsilons and some +gamma of minus epsilons and those will + + align:start position:0% +gamma of minus epsilons and those will + + + align:start position:0% +gamma of minus epsilons and those will +be separately regulating the + + align:start position:0% +be separately regulating the + + + align:start position:0% +be separately regulating the +divergences and if you ever worry about + + align:start position:0% +divergences and if you ever worry about + + + align:start position:0% +divergences and if you ever worry about +it you can do what I said you can put a + + align:start position:0% +it you can do what I said you can put a + + + align:start position:0% +it you can do what I said you can put a +cut off in and check that you're not + + align:start position:0% +cut off in and check that you're not + + + align:start position:0% +cut off in and check that you're not +making + + align:start position:0% +making + + + align:start position:0% +making +mistakes but for the most part it just + + align:start position:0% +mistakes but for the most part it just + + + align:start position:0% +mistakes but for the most part it just +works + + align:start position:0% + + + + align:start position:0% + +automatically any + + align:start position:0% + + + + align:start position:0% + +other + + align:start position:0% + + + + align:start position:0% + +yeah can + + align:start position:0% +yeah can + + + align:start position:0% +yeah can +that's right yeah so formally this is + + align:start position:0% +that's right yeah so formally this is + + + align:start position:0% +that's right yeah so formally this is +zero um and the reason that you have to + + align:start position:0% +zero um and the reason that you have to + + + align:start position:0% +zero um and the reason that you have to +worry about zero is because you have to + + align:start position:0% +worry about zero is because you have to + + + align:start position:0% +worry about zero is because you have to +C add a counter term to cancel this your + + align:start position:0% +C add a counter term to cancel this your + + + align:start position:0% +C add a counter term to cancel this your +UV counter term you have to still add it + + align:start position:0% +UV counter term you have to still add it + + + align:start position:0% +UV counter term you have to still add it +and then it cancels this and then you + + align:start position:0% +and then it cancels this and then you + + + align:start position:0% +and then it cancels this and then you +get something non zero so the the bare + + align:start position:0% +get something non zero so the the bare + + + align:start position:0% +get something non zero so the the bare +graph is zero the counter terms non zero + + align:start position:0% +graph is zero the counter terms non zero + + + align:start position:0% +graph is zero the counter terms non zero +and the normalized graph is non + + align:start position:0% +and the normalized graph is non + + + align:start position:0% +and the normalized graph is non +zero this is + + align:start position:0% +zero this is + + + align:start position:0% +zero this is +a subtlety that's worth remembering + + align:start position:0% +a subtlety that's worth remembering + + + align:start position:0% +a subtlety that's worth remembering +if you ever want to do calculations this + + align:start position:0% + + + + align:start position:0% + +way okay so that's some of the + + align:start position:0% +way okay so that's some of the + + + align:start position:0% +way okay so that's some of the +complications and fascinating facts + + align:start position:0% +complications and fascinating facts + + + align:start position:0% +complications and fascinating facts +about HQ in the perturbative + + align:start position:0% + + + + align:start position:0% + +sector let's come back and talk + + align:start position:0% +sector let's come back and talk + + + align:start position:0% +sector let's come back and talk +about power Corrections + + align:start position:0% + + + + align:start position:0% + +which are I'll go under the title of + + align:start position:0% +which are I'll go under the title of + + + align:start position:0% +which are I'll go under the title of +well maybe I should just call them power + + align:start position:0% +well maybe I should just call them power + + + align:start position:0% +well maybe I should just call them power +Corrections better + + align:start position:0% + + + + align:start position:0% + +title + + align:start position:0% +title + + + align:start position:0% +title +so we have an effective Theory we've so + + align:start position:0% +so we have an effective Theory we've so + + + align:start position:0% +so we have an effective Theory we've so +far talked about it at lowest order we + + align:start position:0% +far talked about it at lowest order we + + + align:start position:0% +far talked about it at lowest order we +stopped at lowest order we had this hqt + + align:start position:0% +stopped at lowest order we had this hqt + + + align:start position:0% +stopped at lowest order we had this hqt +lran and we talked about using that lran + + align:start position:0% +lran and we talked about using that lran + + + align:start position:0% +lran and we talked about using that lran +to carry out some perative calculations + + align:start position:0% +to carry out some perative calculations + + + align:start position:0% +to carry out some perative calculations +what if we went to higher order in the + + align:start position:0% +what if we went to higher order in the + + + align:start position:0% +what if we went to higher order in the +power counting expansion which is 1 over + + align:start position:0% +power counting expansion which is 1 over + + + align:start position:0% +power counting expansion which is 1 over +mq okay so power Corrections here mean + + align:start position:0% +mq okay so power Corrections here mean + + + align:start position:0% +mq okay so power Corrections here mean +means higher order in 1 over + + align:start position:0% + + + + align:start position:0% + +mq so let me show you how you + + align:start position:0% +mq so let me show you how you + + + align:start position:0% +mq so let me show you how you +can construct those + + align:start position:0% +can construct those + + + align:start position:0% +can construct those +terms so let me go back to a + + align:start position:0% +terms so let me go back to a + + + align:start position:0% +terms so let me go back to a +representation of the full qcd + + align:start position:0% +representation of the full qcd + + + align:start position:0% +representation of the full qcd +lran which we had in terms of this B + + align:start position:0% +lran which we had in terms of this B + + + align:start position:0% +lran which we had in terms of this B +field and the Q + + align:start position:0% + + + + align:start position:0% + +field and when we first talked about + + align:start position:0% +field and when we first talked about + + + align:start position:0% +field and when we first talked about +this we just dropped all the terms with + + align:start position:0% +this we just dropped all the terms with + + + align:start position:0% +this we just dropped all the terms with +a + + align:start position:0% +a + + + align:start position:0% +a +B but now I'm going to do something a + + align:start position:0% +B but now I'm going to do something a + + + align:start position:0% +B but now I'm going to do something a +little more sophisticated with + + align:start position:0% + + + + align:start position:0% + +them and really just integrate them + + align:start position:0% + + + + align:start position:0% + +out so we had this and this was really + + align:start position:0% +out so we had this and this was really + + + align:start position:0% +out so we had this and this was really +just us writing qcd in a fancy way it + + align:start position:0% +just us writing qcd in a fancy way it + + + align:start position:0% +just us writing qcd in a fancy way it +was convenient for this + + align:start position:0% + + + + align:start position:0% + +discussion so this is really just qcd + + align:start position:0% +discussion so this is really just qcd + + + align:start position:0% +discussion so this is really just qcd +written in a fancy way + + align:start position:0% + + + + align:start position:0% + +so if we want to take this lran at tree + + align:start position:0% +so if we want to take this lran at tree + + + align:start position:0% +so if we want to take this lran at tree +level we can just integrate out + + align:start position:0% +level we can just integrate out + + + align:start position:0% +level we can just integrate out +BV this is a lran that has quadratic + + align:start position:0% +BV this is a lran that has quadratic + + + align:start position:0% +BV this is a lran that has quadratic +dependence on + + align:start position:0% +dependence on + + + align:start position:0% +dependence on +BV so you can think that the path + + align:start position:0% +BV so you can think that the path + + + align:start position:0% +BV so you can think that the path +integral in this formula here would be + + align:start position:0% +integral in this formula here would be + + + align:start position:0% +integral in this formula here would be +quadratic path integral and those we can + + align:start position:0% +quadratic path integral and those we can + + + align:start position:0% +quadratic path integral and those we can +always just + + align:start position:0% + + + + align:start position:0% + +solve + + align:start position:0% +solve + + + align:start position:0% +solve +and what effectively integrating out BV + + align:start position:0% +and what effectively integrating out BV + + + align:start position:0% +and what effectively integrating out BV +amounts to is solving for the equations + + align:start position:0% +amounts to is solving for the equations + + + align:start position:0% +amounts to is solving for the equations +of motion of BV + + align:start position:0% +of motion of BV + + + align:start position:0% +of motion of BV +and plugging that back in + + align:start position:0% + + + + align:start position:0% + +so the type of diagrams I was drawing + + align:start position:0% +so the type of diagrams I was drawing + + + align:start position:0% +so the type of diagrams I was drawing +before where we had this wiggly line it + + align:start position:0% +before where we had this wiggly line it + + + align:start position:0% +before where we had this wiggly line it +was a BV propagator we can integrate out + + align:start position:0% +was a BV propagator we can integrate out + + + align:start position:0% +was a BV propagator we can integrate out +that by solving for the equation of + + align:start position:0% +that by solving for the equation of + + + align:start position:0% +that by solving for the equation of +motion so we look for + + align:start position:0% +motion so we look for + + + align:start position:0% +motion so we look for +variation with respect to BV bar and set + + align:start position:0% +variation with respect to BV bar and set + + + align:start position:0% +variation with respect to BV bar and set +it to + + align:start position:0% +it to + + + align:start position:0% +it to +zero that + + align:start position:0% + + + + align:start position:0% + +gives this + + align:start position:0% +gives this + + + align:start position:0% +gives this +equation and we solve this formally for + + align:start position:0% +equation and we solve this formally for + + + align:start position:0% +equation and we solve this formally for +BV by just adverting this + + align:start position:0% + + + + align:start position:0% + +operator to get that + + align:start position:0% +operator to get that + + + align:start position:0% +operator to get that +equation and then we can plug that + + align:start position:0% +equation and then we can plug that + + + align:start position:0% +equation and then we can plug that +equation back into this equation + + align:start position:0% + + + + align:start position:0% + +which is still a qcd lran actually but + + align:start position:0% +which is still a qcd lran actually but + + + align:start position:0% +which is still a qcd lran actually but +then we expand and once we expand we + + align:start position:0% +then we expand and once we expand we + + + align:start position:0% +then we expand and once we expand we +match on to the hqt LR in order by order + + align:start position:0% +match on to the hqt LR in order by order + + + align:start position:0% +match on to the hqt LR in order by order +tree + + align:start position:0% +tree + + + align:start position:0% +tree +level so the first term is the term + + align:start position:0% +level so the first term is the term + + + align:start position:0% +level so the first term is the term +we've been + + align:start position:0% +we've been + + + align:start position:0% +we've been +discussing the next term we drop the v.d + + align:start position:0% +discussing the next term we drop the v.d + + + align:start position:0% +discussing the next term we drop the v.d +here because that's + + align:start position:0% +here because that's + + + align:start position:0% +here because that's +small we just have 1 over two m + + align:start position:0% +small we just have 1 over two m + + + align:start position:0% +small we just have 1 over two m +q there's two D + + align:start position:0% + + + + align:start position:0% + +transverses I know would be higher order + + align:start position:0% +transverses I know would be higher order + + + align:start position:0% +transverses I know would be higher order +terms as well but we'll stop at that + + align:start position:0% +terms as well but we'll stop at that + + + align:start position:0% +terms as well but we'll stop at that +order so this is + + align:start position:0% +order so this is + + + align:start position:0% +order so this is +l0 first order term and this would be L1 + + align:start position:0% +l0 first order term and this would be L1 + + + align:start position:0% +l0 first order term and this would be L1 +high order + + align:start position:0% + + + + align:start position:0% + +terms so what is this guy it's useful to + + align:start position:0% +terms so what is this guy it's useful to + + + align:start position:0% +terms so what is this guy it's useful to +write that guy actually in terms of two + + align:start position:0% +write that guy actually in terms of two + + + align:start position:0% +write that guy actually in terms of two +different things and you'll see why + + align:start position:0% +different things and you'll see why + + + align:start position:0% +different things and you'll see why +momentarily so it's got two coant + + align:start position:0% +momentarily so it's got two coant + + + align:start position:0% +momentarily so it's got two coant +derivatives and both of them are dotted + + align:start position:0% +derivatives and both of them are dotted + + + align:start position:0% +derivatives and both of them are dotted +into gamma matrices it involves this + + align:start position:0% +into gamma matrices it involves this + + + align:start position:0% +into gamma matrices it involves this +thing D + + align:start position:0% +thing D + + + align:start position:0% +thing D +transverse which remember is the full D + + align:start position:0% +transverse which remember is the full D + + + align:start position:0% +transverse which remember is the full D +minus a projection onto V so it's + + align:start position:0% +minus a projection onto V so it's + + + align:start position:0% +minus a projection onto V so it's +something that's transverse to + + align:start position:0% +something that's transverse to + + + align:start position:0% +something that's transverse to +V so what I want to do to simplify this + + align:start position:0% +V so what I want to do to simplify this + + + align:start position:0% +V so what I want to do to simplify this +guy here is I want to do the following + + align:start position:0% +guy here is I want to do the following + + + align:start position:0% +guy here is I want to do the following +I'm going to use the fact I'm going to + + align:start position:0% +I'm going to use the fact I'm going to + + + align:start position:0% +I'm going to use the fact I'm going to +write it in terms of a field strength by + + align:start position:0% +write it in terms of a field strength by + + + align:start position:0% +write it in terms of a field strength by +using the fact that the commutator of + + align:start position:0% +using the fact that the commutator of + + + align:start position:0% +using the fact that the commutator of +two + + align:start position:0% +two + + + align:start position:0% +two +D's gives me a + + align:start position:0% +D's gives me a + + + align:start position:0% +D's gives me a +G and the commutator of two + + align:start position:0% +G and the commutator of two + + + align:start position:0% +G and the commutator of two +sigmas I'll write sorry the commutator + + align:start position:0% +sigmas I'll write sorry the commutator + + + align:start position:0% +sigmas I'll write sorry the commutator +of two gamas gives me something I can + + align:start position:0% +of two gamas gives me something I can + + + align:start position:0% +of two gamas gives me something I can +call + + align:start position:0% + + + + align:start position:0% + +Sigma so let me write this as the + + align:start position:0% +Sigma so let me write this as the + + + align:start position:0% +Sigma so let me write this as the +symmetric piece and then the anti- + + align:start position:0% +symmetric piece and then the anti- + + + align:start position:0% +symmetric piece and then the anti- +symmetric + + align:start position:0% + + + + align:start position:0% + +piece and I do a symmetrization + + align:start position:0% +piece and I do a symmetrization + + + align:start position:0% +piece and I do a symmetrization +in both the fields and the direct + + align:start position:0% + + + + align:start position:0% + +structures then dtt dtdt + + align:start position:0% + + + + align:start position:0% + +slash anticommutator + + align:start position:0% + + + + align:start position:0% + +so then this is anti- symmetric it + + align:start position:0% +so then this is anti- symmetric it + + + align:start position:0% +so then this is anti- symmetric it +automatically forces that anti- + + align:start position:0% +automatically forces that anti- + + + align:start position:0% +automatically forces that anti- +symmetric this guy is a gme new so for + + align:start position:0% +symmetric this guy is a gme new so for + + + align:start position:0% +symmetric this guy is a gme new so for +this piece we just get DT + + align:start position:0% +this piece we just get DT + + + align:start position:0% +this piece we just get DT +squared and this piece once we track all + + align:start position:0% +squared and this piece once we track all + + + align:start position:0% +squared and this piece once we track all +the + + align:start position:0% + + + + align:start position:0% + +twos and the eyes + + align:start position:0% +twos and the eyes + + + align:start position:0% +twos and the eyes +gives sigma. + + align:start position:0% + + + + align:start position:0% + +G and so the usual way of writing + + align:start position:0% +G and so the usual way of writing + + + align:start position:0% +G and so the usual way of writing +L1 is as follows you say L1 using this + + align:start position:0% +L1 is as follows you say L1 using this + + + align:start position:0% +L1 is as follows you say L1 using this +formula plugging it in is has two + + align:start position:0% + + + + align:start position:0% + +terms and you'll see + + align:start position:0% +terms and you'll see + + + align:start position:0% +terms and you'll see +why when I write them down that we + + align:start position:0% +why when I write them down that we + + + align:start position:0% +why when I write them down that we +wanted to do this + + align:start position:0% + + + + align:start position:0% + +okay so that's what L1 is after plugging + + align:start position:0% +okay so that's what L1 is after plugging + + + align:start position:0% +okay so that's what L1 is after plugging +that in now the reason that to do this + + align:start position:0% +that in now the reason that to do this + + + align:start position:0% +that in now the reason that to do this +is that if we ask about symmetry + + align:start position:0% +is that if we ask about symmetry + + + align:start position:0% +is that if we ask about symmetry +breaking that's something that can + + align:start position:0% +breaking that's something that can + + + align:start position:0% +breaking that's something that can +happen from subleading terms at lowest + + align:start position:0% +happen from subleading terms at lowest + + + align:start position:0% +happen from subleading terms at lowest +order we had a symmetry heavy cork + + align:start position:0% +order we had a symmetry heavy cork + + + align:start position:0% +order we had a symmetry heavy cork +Symmetry and that is broken by these + + align:start position:0% +Symmetry and that is broken by these + + + align:start position:0% +Symmetry and that is broken by these +interactions but it's actually broken in + + align:start position:0% +interactions but it's actually broken in + + + align:start position:0% +interactions but it's actually broken in +different ways by these two + + align:start position:0% +different ways by these two + + + align:start position:0% +different ways by these two +terms this term here doesn't have any + + align:start position:0% +terms this term here doesn't have any + + + align:start position:0% +terms this term here doesn't have any +spin structure so it doesn't break the + + align:start position:0% +spin structure so it doesn't break the + + + align:start position:0% +spin structure so it doesn't break the +spin symmetry + + align:start position:0% +spin symmetry + + + align:start position:0% +spin symmetry +it does have flavor structure because of + + align:start position:0% +it does have flavor structure because of + + + align:start position:0% +it does have flavor structure because of +the mq so it breaks the flavor + + align:start position:0% +the mq so it breaks the flavor + + + align:start position:0% +the mq so it breaks the flavor +symmetry so this is a kinetic + + align:start position:0% +symmetry so this is a kinetic + + + align:start position:0% +symmetry so this is a kinetic +energy type + + align:start position:0% +energy type + + + align:start position:0% +energy type +correction and it breaks flavor symmetry + + align:start position:0% +correction and it breaks flavor symmetry + + + align:start position:0% +correction and it breaks flavor symmetry +because of the dependence on Q in the + + align:start position:0% + + + + align:start position:0% + +mq and this guy breaks both because it + + align:start position:0% +mq and this guy breaks both because it + + + align:start position:0% +mq and this guy breaks both because it +has a spin structure now and it's a + + align:start position:0% +has a spin structure now and it's a + + + align:start position:0% +has a spin structure now and it's a +Magnetic Moment type term + + align:start position:0% + + + + align:start position:0% + +all right so it's kind sigma. B field + + align:start position:0% +all right so it's kind sigma. B field + + + align:start position:0% +all right so it's kind sigma. B field +type + + align:start position:0% + + + + align:start position:0% + +interaction that's what I mean by + + align:start position:0% +interaction that's what I mean by + + + align:start position:0% +interaction that's what I mean by +Magnetic Moment type + + align:start position:0% + + + + align:start position:0% + +term okay so that's what the subleading + + align:start position:0% +term okay so that's what the subleading + + + align:start position:0% +term okay so that's what the subleading +power Corrections look like and if we + + align:start position:0% +power Corrections look like and if we + + + align:start position:0% +power Corrections look like and if we +want to use the effective Theory to talk + + align:start position:0% +want to use the effective Theory to talk + + + align:start position:0% +want to use the effective Theory to talk +about power Corrections we could do that + + align:start position:0% +about power Corrections we could do that + + + align:start position:0% +about power Corrections we could do that +we're constructing them here by knowing + + align:start position:0% +we're constructing them here by knowing + + + align:start position:0% +we're constructing them here by knowing +the full Theory just integrating out + + align:start position:0% +the full Theory just integrating out + + + align:start position:0% +the full Theory just integrating out +explicitly the + + align:start position:0% + + + + align:start position:0% + +fields okay which is very nice thing if + + align:start position:0% +fields okay which is very nice thing if + + + align:start position:0% +fields okay which is very nice thing if +you could do + + align:start position:0% + + + + align:start position:0% + +it now you could do it the other way + + align:start position:0% +it now you could do it the other way + + + align:start position:0% +it now you could do it the other way +which would be to think + + align:start position:0% +which would be to think + + + align:start position:0% +which would be to think +about just writing them from the bottom + + align:start position:0% +about just writing them from the bottom + + + align:start position:0% +about just writing them from the bottom +up and there is one way in which that's + + align:start position:0% +up and there is one way in which that's + + + align:start position:0% +up and there is one way in which that's +more General than what we've talked + + align:start position:0% +more General than what we've talked + + + align:start position:0% +more General than what we've talked +about + + align:start position:0% +about + + + align:start position:0% +about +and that's because what we talked about + + align:start position:0% +and that's because what we talked about + + + align:start position:0% +and that's because what we talked about +was tree + + align:start position:0% + + + + align:start position:0% + +level and if you wanted to include Loop + + align:start position:0% +level and if you wanted to include Loop + + + align:start position:0% +level and if you wanted to include Loop +Corrections how do we know that there's + + align:start position:0% +Corrections how do we know that there's + + + align:start position:0% +Corrections how do we know that there's +not some other operator here that we + + align:start position:0% +not some other operator here that we + + + align:start position:0% +not some other operator here that we +missed because it just vanished at tree + + align:start position:0% +missed because it just vanished at tree + + + align:start position:0% +missed because it just vanished at tree +level for + + align:start position:0% +level for + + + align:start position:0% +level for +example we've seen examples where that + + align:start position:0% +example we've seen examples where that + + + align:start position:0% +example we've seen examples where that +happens there's an operator that only + + align:start position:0% +happens there's an operator that only + + + align:start position:0% +happens there's an operator that only +shows up at Loop + + align:start position:0% + + + + align:start position:0% + +level so we could think about it from + + align:start position:0% +level so we could think about it from + + + align:start position:0% +level so we could think about it from +the bottom up even though this is a top + + align:start position:0% +the bottom up even though this is a top + + + align:start position:0% +the bottom up even though this is a top +down effective theory in order to make + + align:start position:0% +down effective theory in order to make + + + align:start position:0% +down effective theory in order to make +sure we're not missing anything and if + + align:start position:0% +sure we're not missing anything and if + + + align:start position:0% +sure we're not missing anything and if +we wanted to do that we should enumerate + + align:start position:0% +we wanted to do that we should enumerate + + + align:start position:0% +we wanted to do that we should enumerate +all the possible things the symmetries + + align:start position:0% +all the possible things the symmetries + + + align:start position:0% +all the possible things the symmetries +and all that we can use to constrain the + + align:start position:0% +and all that we can use to constrain the + + + align:start position:0% +and all that we can use to constrain the +form of The + + align:start position:0% +form of The + + + align:start position:0% +form of The +Operators so let's + + align:start position:0% +Operators so let's + + + align:start position:0% +Operators so let's +enumerate so there's the power counting + + align:start position:0% +enumerate so there's the power counting + + + align:start position:0% +enumerate so there's the power counting +of + + align:start position:0% + + + + align:start position:0% + +course that's pretty simple here all the + + align:start position:0% +course that's pretty simple here all the + + + align:start position:0% +course that's pretty simple here all the +powers of 1/ mq are being made + + align:start position:0% +powers of 1/ mq are being made + + + align:start position:0% +powers of 1/ mq are being made +explicit and they just tell us what + + align:start position:0% +explicit and they just tell us what + + + align:start position:0% +explicit and they just tell us what +dimension of operator to look for + + align:start position:0% + + + + align:start position:0% + +just as in our integrating out heavy + + align:start position:0% +just as in our integrating out heavy + + + align:start position:0% +just as in our integrating out heavy +particles so we just know the dimension + + align:start position:0% +particles so we just know the dimension + + + align:start position:0% +particles so we just know the dimension +of the fields that we have to put in the + + align:start position:0% +of the fields that we have to put in the + + + align:start position:0% +of the fields that we have to put in the +numerator from how many mqs we're + + align:start position:0% +numerator from how many mqs we're + + + align:start position:0% +numerator from how many mqs we're +talking + + align:start position:0% + + + + align:start position:0% + +about there's gauge symmetry of course + + align:start position:0% +about there's gauge symmetry of course + + + align:start position:0% +about there's gauge symmetry of course +so use covariant + + align:start position:0% + + + + align:start position:0% + +derivatives very easy to take into + + align:start position:0% +derivatives very easy to take into + + + align:start position:0% +derivatives very easy to take into +account + + align:start position:0% + + + + align:start position:0% + +there's discret symmetries like charge + + align:start position:0% +there's discret symmetries like charge + + + align:start position:0% +there's discret symmetries like charge +conjugation parity and time reversal + + align:start position:0% +conjugation parity and time reversal + + + align:start position:0% +conjugation parity and time reversal +which are symmetries of qcd if we drop + + align:start position:0% +which are symmetries of qcd if we drop + + + align:start position:0% +which are symmetries of qcd if we drop +the Theta term and we can impose them as + + align:start position:0% +the Theta term and we can impose them as + + + align:start position:0% +the Theta term and we can impose them as +well and again + + align:start position:0% + + + + align:start position:0% + +that's + + align:start position:0% + + + + align:start position:0% + +easy I wouldn't be making a list if + + align:start position:0% +easy I wouldn't be making a list if + + + align:start position:0% +easy I wouldn't be making a list if +there wasn't at least one thing that was + + align:start position:0% + + + + align:start position:0% + +hard and + + align:start position:0% +hard and + + + align:start position:0% +hard and +non-trivial but discret Sy are + + align:start position:0% +non-trivial but discret Sy are + + + align:start position:0% +non-trivial but discret Sy are +[Applause] + + align:start position:0% + + + + align:start position:0% + +easy the thing that actually is the hard + + align:start position:0% +easy the thing that actually is the hard + + + align:start position:0% +easy the thing that actually is the hard +hardest is Laurent + + align:start position:0% + + + + align:start position:0% + +symmetry well you say just dot Loren and + + align:start position:0% +symmetry well you say just dot Loren and + + + align:start position:0% +symmetry well you say just dot Loren and +disase into luren and + + align:start position:0% + + + + align:start position:0% + +disease but you have to ask the question + + align:start position:0% +disease but you have to ask the question + + + align:start position:0% +disease but you have to ask the question +whether we even have Loren variance in + + align:start position:0% +whether we even have Loren variance in + + + align:start position:0% +whether we even have Loren variance in +this + + align:start position:0% +this + + + align:start position:0% +this +Theory and it turns out that part of the + + align:start position:0% +Theory and it turns out that part of the + + + align:start position:0% +Theory and it turns out that part of the +laurance group is actually broken by + + align:start position:0% +laurance group is actually broken by + + + align:start position:0% +laurance group is actually broken by +having this heavy Quirk and doing this + + align:start position:0% +having this heavy Quirk and doing this + + + align:start position:0% +having this heavy Quirk and doing this +type of expansion that we've been + + align:start position:0% +type of expansion that we've been + + + align:start position:0% +type of expansion that we've been +talking + + align:start position:0% +talking + + + align:start position:0% +talking +about so if you think about the six + + align:start position:0% +about so if you think about the six + + + align:start position:0% +about so if you think about the six +generators of the Laurence group the + + align:start position:0% +generators of the Laurence group the + + + align:start position:0% +generators of the Laurence group the +Boost and the rotations there's a part + + align:start position:0% +Boost and the rotations there's a part + + + align:start position:0% +Boost and the rotations there's a part +that I could call the transverse part + + align:start position:0% +that I could call the transverse part + + + align:start position:0% +that I could call the transverse part +which is transverse of the Velocity so + + align:start position:0% +which is transverse of the Velocity so + + + align:start position:0% +which is transverse of the Velocity so +in the rest frame that would be M12 + + align:start position:0% +in the rest frame that would be M12 + + + align:start position:0% +in the rest frame that would be M12 +M23 and + + align:start position:0% + + + + align:start position:0% + +M13 and those are the + + align:start position:0% +M13 and those are the + + + align:start position:0% +M13 and those are the +rotations so this is + + align:start position:0% +rotations so this is + + + align:start position:0% +rotations so this is +V is like this so no matter what V you + + align:start position:0% +V is like this so no matter what V you + + + align:start position:0% +V is like this so no matter what V you +pick there's always three generators + + align:start position:0% +pick there's always three generators + + + align:start position:0% +pick there's always three generators +that are + + align:start position:0% +that are + + + align:start position:0% +that are +rotations and then there's the + + align:start position:0% +rotations and then there's the + + + align:start position:0% +rotations and then there's the +boosts and you should think of the + + align:start position:0% +boosts and you should think of the + + + align:start position:0% +boosts and you should think of the +boosts as taking V mu and then M dotted + + align:start position:0% +boosts as taking V mu and then M dotted + + + align:start position:0% +boosts as taking V mu and then M dotted +into the V and then making the other guy + + align:start position:0% +into the V and then making the other guy + + + align:start position:0% +into the V and then making the other guy +transverse we need to note it like that + + align:start position:0% +transverse we need to note it like that + + + align:start position:0% +transverse we need to note it like that +so the new IND index is transverse and + + align:start position:0% +so the new IND index is transverse and + + + align:start position:0% +so the new IND index is transverse and +the rest frame that's + + align:start position:0% +the rest frame that's + + + align:start position:0% +the rest frame that's +m01 m02 and m03 + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +and so introducing VM actually breaks + + align:start position:0% +and so introducing VM actually breaks + + + align:start position:0% +and so introducing VM actually breaks +the + + align:start position:0% + + + + align:start position:0% + +boosts symmetry + + align:start position:0% + + + + align:start position:0% + +and if you like you could think that the + + align:start position:0% +and if you like you could think that the + + + align:start position:0% +and if you like you could think that the +reason it it breaks the Symmetry is + + align:start position:0% +reason it it breaks the Symmetry is + + + align:start position:0% +reason it it breaks the Symmetry is +because it gives a preferred frame which + + align:start position:0% +because it gives a preferred frame which + + + align:start position:0% +because it gives a preferred frame which +is the rest frame of the heavy Quark if + + align:start position:0% +is the rest frame of the heavy Quark if + + + align:start position:0% +is the rest frame of the heavy Quark if +you have a preferred frame then you've + + align:start position:0% +you have a preferred frame then you've + + + align:start position:0% +you have a preferred frame then you've +broken Loren and + + align:start position:0% + + + + align:start position:0% + +variance so that's + + align:start position:0% +variance so that's + + + align:start position:0% +variance so that's +bad and it turns out there's actually a + + align:start position:0% +bad and it turns out there's actually a + + + align:start position:0% +bad and it turns out there's actually a +hidden symmetry of this effective theory + + align:start position:0% +hidden symmetry of this effective theory + + + align:start position:0% +hidden symmetry of this effective theory +that partially restores this + + align:start position:0% + + + + align:start position:0% + +breaking and it restores it in exactly + + align:start position:0% +breaking and it restores it in exactly + + + align:start position:0% +breaking and it restores it in exactly +the amount that it needs to restore it + + align:start position:0% + + + + align:start position:0% + +that is it restores it in at low + + align:start position:0% + + + + align:start position:0% + +energies and it's called + + align:start position:0% +energies and it's called + + + align:start position:0% +energies and it's called +reparameterization + + align:start position:0% +reparameterization + + + align:start position:0% +reparameterization +invariance which I'll write once and + + align:start position:0% +invariance which I'll write once and + + + align:start position:0% +invariance which I'll write once and +then forever more talk about his RPI + + align:start position:0% +then forever more talk about his RPI + + + align:start position:0% +then forever more talk about his RPI +reparameterization in + + align:start position:0% +reparameterization in + + + align:start position:0% +reparameterization in +variance and it's an additional symmetry + + align:start position:0% +variance and it's an additional symmetry + + + align:start position:0% +variance and it's an additional symmetry +that we have on VM + + align:start position:0% + + + + align:start position:0% + +itself so let's go back and think about + + align:start position:0% +itself so let's go back and think about + + + align:start position:0% +itself so let's go back and think about +how we introduced VM in the first place + + align:start position:0% +how we introduced VM in the first place + + + align:start position:0% +how we introduced VM in the first place +so we're saying that V mu breaks part of + + align:start position:0% +so we're saying that V mu breaks part of + + + align:start position:0% +so we're saying that V mu breaks part of +the Symmetry but how did we how did we + + align:start position:0% +the Symmetry but how did we how did we + + + align:start position:0% +the Symmetry but how did we how did we +decide on what VM + + align:start position:0% +decide on what VM + + + align:start position:0% +decide on what VM +was how much Freedom was there when we + + align:start position:0% +was how much Freedom was there when we + + + align:start position:0% +was how much Freedom was there when we +defined VM at the beginning + + align:start position:0% + + + + align:start position:0% + +if we're saying that it breaks it we + + align:start position:0% +if we're saying that it breaks it we + + + align:start position:0% +if we're saying that it breaks it we +should + + align:start position:0% +should + + + align:start position:0% +should +know how much Freedom there was because + + align:start position:0% +know how much Freedom there was because + + + align:start position:0% +know how much Freedom there was because +a freedom to Define different V's could + + align:start position:0% +a freedom to Define different V's could + + + align:start position:0% +a freedom to Define different V's could +restore symmetry just realized in a + + align:start position:0% +restore symmetry just realized in a + + + align:start position:0% +restore symmetry just realized in a +different way and that's what + + align:start position:0% + + + + align:start position:0% + +happens so where did it come from we had + + align:start position:0% +happens so where did it come from we had + + + align:start position:0% +happens so where did it come from we had +P of a heavy Clark and we split that + + align:start position:0% +P of a heavy Clark and we split that + + + align:start position:0% +P of a heavy Clark and we split that +into two pieces + + align:start position:0% +into two pieces + + + align:start position:0% +into two pieces +mqv plus + + align:start position:0% +mqv plus + + + align:start position:0% +mqv plus +K but this split into two pieces is + + align:start position:0% +K but this split into two pieces is + + + align:start position:0% +K but this split into two pieces is +arbitrary by some amount we could move + + align:start position:0% +arbitrary by some amount we could move + + + align:start position:0% +arbitrary by some amount we could move +pieces back and forth between here and + + align:start position:0% +pieces back and forth between here and + + + align:start position:0% +pieces back and forth between here and +here and we would still have the same + + align:start position:0% + + + + align:start position:0% + +Theory we have to be careful that we're + + align:start position:0% +Theory we have to be careful that we're + + + align:start position:0% +Theory we have to be careful that we're +moving back pieces that don't violate + + align:start position:0% +moving back pieces that don't violate + + + align:start position:0% +moving back pieces that don't violate +the power counting and that's what I + + align:start position:0% +the power counting and that's what I + + + align:start position:0% +the power counting and that's what I +mean by somewhat arbitrary here not + + align:start position:0% +mean by somewhat arbitrary here not + + + align:start position:0% +mean by somewhat arbitrary here not +completely arbitrary there was a point + + align:start position:0% +completely arbitrary there was a point + + + align:start position:0% +completely arbitrary there was a point +to doing this because we wanted to + + align:start position:0% +to doing this because we wanted to + + + align:start position:0% +to doing this because we wanted to +separate out the big piece and the small + + align:start position:0% +separate out the big piece and the small + + + align:start position:0% +separate out the big piece and the small +piece but we could always move a small + + align:start position:0% +piece but we could always move a small + + + align:start position:0% +piece but we could always move a small +piece back over here and that wouldn't + + align:start position:0% +piece back over here and that wouldn't + + + align:start position:0% +piece back over here and that wouldn't +change this this + + align:start position:0% +change this this + + + align:start position:0% +change this this +decomposition so the invariance that you + + align:start position:0% +decomposition so the invariance that you + + + align:start position:0% +decomposition so the invariance that you +have is the + + align:start position:0% +have is the + + + align:start position:0% +have is the +following you can take V mu and send it + + align:start position:0% +following you can take V mu and send it + + + align:start position:0% +following you can take V mu and send it +to V + + align:start position:0% +to V + + + align:start position:0% +to V +mu plus some Epsilon mu over + + align:start position:0% +mu plus some Epsilon mu over + + + align:start position:0% +mu plus some Epsilon mu over +mq and K + + align:start position:0% +mq and K + + + align:start position:0% +mq and K +mu goes to K + + align:start position:0% +mu goes to K + + + align:start position:0% +mu goes to K +mu minus Epsilon + + align:start position:0% +mu minus Epsilon + + + align:start position:0% +mu minus Epsilon +mu that moves a piece back and forth + + align:start position:0% +mu that moves a piece back and forth + + + align:start position:0% +mu that moves a piece back and forth +between them and as long as I think that + + align:start position:0% + + + + align:start position:0% + +mu is some parameter that's doesn't have + + align:start position:0% +mu is some parameter that's doesn't have + + + align:start position:0% +mu is some parameter that's doesn't have +a par counting in IE it's order doesn't + + align:start position:0% +a par counting in IE it's order doesn't + + + align:start position:0% +a par counting in IE it's order doesn't +have any mqs in it it's just something + + align:start position:0% +have any mqs in it it's just something + + + align:start position:0% +have any mqs in it it's just something +of order Lambda + + align:start position:0% +of order Lambda + + + align:start position:0% +of order Lambda +qcd + + align:start position:0% + + + + align:start position:0% + +say then that makes the power counting + + align:start position:0% +say then that makes the power counting + + + align:start position:0% +say then that makes the power counting +still true that's was the point of this + + align:start position:0% +still true that's was the point of this + + + align:start position:0% +still true that's was the point of this +decomposition and it allows us to move a + + align:start position:0% +decomposition and it allows us to move a + + + align:start position:0% +decomposition and it allows us to move a +small piece back and forth the small + + align:start position:0% +small piece back and forth the small + + + align:start position:0% +small piece back and forth the small +piece this + + align:start position:0% +piece this + + + align:start position:0% +piece this +Epsilon so that's a symmetry that's + + align:start position:0% +Epsilon so that's a symmetry that's + + + align:start position:0% +Epsilon so that's a symmetry that's +called reparameterization variance + + align:start position:0% +called reparameterization variance + + + align:start position:0% +called reparameterization variance +so we have to make sure that when we + + align:start position:0% +so we have to make sure that when we + + + align:start position:0% +so we have to make sure that when we +construct our effective theory that it + + align:start position:0% +construct our effective theory that it + + + align:start position:0% +construct our effective theory that it +satisfies the Symmetry if we want it to + + align:start position:0% +satisfies the Symmetry if we want it to + + + align:start position:0% +satisfies the Symmetry if we want it to +be a Boos in variant if we want to + + align:start position:0% +be a Boos in variant if we want to + + + align:start position:0% +be a Boos in variant if we want to +restore boost invariance to the + + align:start position:0% +restore boost invariance to the + + + align:start position:0% +restore boost invariance to the +theory so this parameter Epsilon you can + + align:start position:0% +theory so this parameter Epsilon you can + + + align:start position:0% +theory so this parameter Epsilon you can +think of as you could consider it to be + + align:start position:0% +think of as you could consider it to be + + + align:start position:0% +think of as you could consider it to be +a finite reparameterization symmetry but + + align:start position:0% +a finite reparameterization symmetry but + + + align:start position:0% +a finite reparameterization symmetry but +you don't really have to worry about + + align:start position:0% +you don't really have to worry about + + + align:start position:0% +you don't really have to worry about +finite Transformations you can just do + + align:start position:0% +finite Transformations you can just do + + + align:start position:0% +finite Transformations you can just do +the + + align:start position:0% +the + + + align:start position:0% +the +infimal so we'll think about Epsilon mu + + align:start position:0% +infimal so we'll think about Epsilon mu + + + align:start position:0% +infimal so we'll think about Epsilon mu +as infant tesmo + + align:start position:0% + + + + align:start position:0% + +and it has that counting that I put over + + align:start position:0% +and it has that counting that I put over + + + align:start position:0% +and it has that counting that I put over +there now V ^2 was equal to one and + + align:start position:0% +there now V ^2 was equal to one and + + + align:start position:0% +there now V ^2 was equal to one and +that's also something we don't want to + + align:start position:0% +that's also something we don't want to + + + align:start position:0% +that's also something we don't want to +spoil but that's easy we just say that + + align:start position:0% +spoil but that's easy we just say that + + + align:start position:0% +spoil but that's easy we just say that +Epsilon dob is equal to zero that + + align:start position:0% +Epsilon dob is equal to zero that + + + align:start position:0% +Epsilon dob is equal to zero that +maintains this condition so that means + + align:start position:0% +maintains this condition so that means + + + align:start position:0% +maintains this condition so that means +that there's three different components + + align:start position:0% +that there's three different components + + + align:start position:0% +that there's three different components +of + + align:start position:0% + + + + align:start position:0% + +Epsilon non-trivial components to + + align:start position:0% +Epsilon non-trivial components to + + + align:start position:0% +Epsilon non-trivial components to +Epsilon + + align:start position:0% +Epsilon + + + align:start position:0% +Epsilon +and those three components of Epsilon + + align:start position:0% +and those three components of Epsilon + + + align:start position:0% +and those three components of Epsilon +are exactly related to the three booths + + align:start position:0% + + + + align:start position:0% + +here okay we have a three family three + + align:start position:0% +here okay we have a three family three + + + align:start position:0% +here okay we have a three family three +parameter family of + + align:start position:0% + + + + align:start position:0% + +Transformations which are the three + + align:start position:0% +Transformations which are the three + + + align:start position:0% +Transformations which are the three +components of the Epsilon which in the + + align:start position:0% +components of the Epsilon which in the + + + align:start position:0% +components of the Epsilon which in the +rest frame would just be the one two and + + align:start position:0% +rest frame would just be the one two and + + + align:start position:0% +rest frame would just be the one two and +three what do we do what about the + + align:start position:0% +three what do we do what about the + + + align:start position:0% +three what do we do what about the +fields how does the the field the QV + + align:start position:0% +fields how does the the field the QV + + + align:start position:0% +fields how does the the field the QV +change under this type of + + align:start position:0% + + + + align:start position:0% + +transformation let me take the field at + + align:start position:0% +transformation let me take the field at + + + align:start position:0% +transformation let me take the field at +x equals z for + + align:start position:0% + + + + align:start position:0% + +now so V slash on QV it was equal to + + align:start position:0% +now so V slash on QV it was equal to + + + align:start position:0% +now so V slash on QV it was equal to +zero and if I do the transformation then + + align:start position:0% +zero and if I do the transformation then + + + align:start position:0% +zero and if I do the transformation then +this V SL + + align:start position:0% +this V SL + + + align:start position:0% +this V SL +changes becomes V slash plus Epsilon SL + + align:start position:0% +changes becomes V slash plus Epsilon SL + + + align:start position:0% +changes becomes V slash plus Epsilon SL +over + + align:start position:0% +over + + + align:start position:0% +over +mq let me imagine QV changes + + align:start position:0% + + + + align:start position:0% + +goes to QV plus Delta + + align:start position:0% +goes to QV plus Delta + + + align:start position:0% +goes to QV plus Delta +QV and I have to do that on both + + align:start position:0% + + + + align:start position:0% + +sides then I can take this so this thing + + align:start position:0% +sides then I can take this so this thing + + + align:start position:0% +sides then I can take this so this thing +here is some order Epsilon + + align:start position:0% +here is some order Epsilon + + + align:start position:0% +here is some order Epsilon +change and I can take this equation and + + align:start position:0% +change and I can take this equation and + + + align:start position:0% +change and I can take this equation and +I can just solve so the piece that's + + align:start position:0% +I can just solve so the piece that's + + + align:start position:0% +I can just solve so the piece that's +order Epsilon to the 0o just satisfied + + align:start position:0% +order Epsilon to the 0o just satisfied + + + align:start position:0% +order Epsilon to the 0o just satisfied +solve for the piece that's order Epsilon + + align:start position:0% +solve for the piece that's order Epsilon + + + align:start position:0% +solve for the piece that's order Epsilon +and that gives me an equation for Delta + + align:start position:0% +and that gives me an equation for Delta + + + align:start position:0% +and that gives me an equation for Delta +QV so + + align:start position:0% +QV so + + + align:start position:0% +QV so +rearranging this equation I find that 1 + + align:start position:0% +rearranging this equation I find that 1 + + + align:start position:0% +rearranging this equation I find that 1 +minus V Delta + + align:start position:0% +minus V Delta + + + align:start position:0% +minus V Delta +QV is Epsilon + + align:start position:0% + + + + align:start position:0% + +slash over mq * + + align:start position:0% +slash over mq * + + + align:start position:0% +slash over mq * +QV and this + + align:start position:0% +QV and this + + + align:start position:0% +QV and this +equation has the + + align:start position:0% + + + + align:start position:0% + +solution that Delta + + align:start position:0% +solution that Delta + + + align:start position:0% +solution that Delta +QV is Epsilon slash over 2 mq remember + + align:start position:0% +QV is Epsilon slash over 2 mq remember + + + align:start position:0% +QV is Epsilon slash over 2 mq remember +that Epsilon is + + align:start position:0% +that Epsilon is + + + align:start position:0% +that Epsilon is +transverse to V so if I push a v slash + + align:start position:0% +transverse to V so if I push a v slash + + + align:start position:0% +transverse to V so if I push a v slash +so if I plug that solution in here and I + + align:start position:0% +so if I plug that solution in here and I + + + align:start position:0% +so if I plug that solution in here and I +push the V + + align:start position:0% +push the V + + + align:start position:0% +push the V +slash and I push a v slash through the + + align:start position:0% +slash and I push a v slash through the + + + align:start position:0% +slash and I push a v slash through the +Epsilon well then I can push the V slash + + align:start position:0% +Epsilon well then I can push the V slash + + + align:start position:0% +Epsilon well then I can push the V slash +through the Epsilon let it hit the QV + + align:start position:0% +through the Epsilon let it hit the QV + + + align:start position:0% +through the Epsilon let it hit the QV +that's giving a factor of two because it + + align:start position:0% +that's giving a factor of two because it + + + align:start position:0% +that's giving a factor of two because it +anti- commutes that's this two here and + + align:start position:0% +anti- commutes that's this two here and + + + align:start position:0% +anti- commutes that's this two here and +then I would get what I wrote on the + + align:start position:0% +then I would get what I wrote on the + + + align:start position:0% +then I would get what I wrote on the +right hand + + align:start position:0% +right hand + + + align:start position:0% +right hand +side so if it's not obvious check for + + align:start position:0% +side so if it's not obvious check for + + + align:start position:0% +side so if it's not obvious check for +yourself that that's a solution + + align:start position:0% +yourself that that's a solution + + + align:start position:0% +yourself that that's a solution +so that's how you derive the change to + + align:start position:0% +so that's how you derive the change to + + + align:start position:0% +so that's how you derive the change to +the field under this + + align:start position:0% + + + + align:start position:0% + +reparameterization and so when we talk + + align:start position:0% +reparameterization and so when we talk + + + align:start position:0% +reparameterization and so when we talk +about operators in the effective Theory + + align:start position:0% +about operators in the effective Theory + + + align:start position:0% +about operators in the effective Theory +we have to worry how does the Symmetry + + align:start position:0% +we have to worry how does the Symmetry + + + align:start position:0% +we have to worry how does the Symmetry +act on + + align:start position:0% + + + + align:start position:0% + +them and it's kind of a non-trivial + + align:start position:0% +them and it's kind of a non-trivial + + + align:start position:0% +them and it's kind of a non-trivial +symmetry was not apparent to us when we + + align:start position:0% +symmetry was not apparent to us when we + + + align:start position:0% +symmetry was not apparent to us when we +started right + + align:start position:0% + + + + align:start position:0% + +okay so the full + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +reparametrization is V mu goes to + + align:start position:0% +reparametrization is V mu goes to + + + align:start position:0% +reparametrization is V mu goes to +V plus Epsilon over + + align:start position:0% +V plus Epsilon over + + + align:start position:0% +V plus Epsilon over +mq and then if I take QV of + + align:start position:0% +mq and then if I take QV of + + + align:start position:0% +mq and then if I take QV of +X then + + align:start position:0% +X then + + + align:start position:0% +X then +that is what I + + align:start position:0% +that is what I + + + align:start position:0% +that is what I +said there's this Epsilon SL over 2 mq + + align:start position:0% +said there's this Epsilon SL over 2 mq + + + align:start position:0% +said there's this Epsilon SL over 2 mq +piece this is the transformation so it + + align:start position:0% +piece this is the transformation so it + + + align:start position:0% +piece this is the transformation so it +goes to itself plus this extra piece and + + align:start position:0% +goes to itself plus this extra piece and + + + align:start position:0% +goes to itself plus this extra piece and +the fact that I take it at X adds one + + align:start position:0% +the fact that I take it at X adds one + + + align:start position:0% +the fact that I take it at X adds one +little slight wrinkle and it just gives + + align:start position:0% +little slight wrinkle and it just gives + + + align:start position:0% +little slight wrinkle and it just gives +us extra phase factor and that extra + + align:start position:0% +us extra phase factor and that extra + + + align:start position:0% +us extra phase factor and that extra +phase factor is exactly what encodes the + + align:start position:0% +phase factor is exactly what encodes the + + + align:start position:0% +phase factor is exactly what encodes the +change of K so this if you like encodes + + align:start position:0% +change of K so this if you like encodes + + + align:start position:0% +change of K so this if you like encodes +the + + align:start position:0% +the + + + align:start position:0% +the +derivatives should go to derivatives + + align:start position:0% +derivatives should go to derivatives + + + align:start position:0% +derivatives should go to derivatives +minus Epsilon or in momentum space that + + align:start position:0% +minus Epsilon or in momentum space that + + + align:start position:0% +minus Epsilon or in momentum space that +K should go to k minus + + align:start position:0% +K should go to k minus + + + align:start position:0% +K should go to k minus +Epsilon okay so previously we had a rule + + align:start position:0% +Epsilon okay so previously we had a rule + + + align:start position:0% +Epsilon okay so previously we had a rule +for K but now I've encoded that in this + + align:start position:0% + + + + align:start position:0% + +space okay so that's the that's the + + align:start position:0% +space okay so that's the that's the + + + align:start position:0% +space okay so that's the that's the +Symmetry that we should look + + align:start position:0% + + + + align:start position:0% + +into so what does it + + align:start position:0% +into so what does it + + + align:start position:0% +into so what does it +do so what this does is it restores + + align:start position:0% +do so what this does is it restores + + + align:start position:0% +do so what this does is it restores +invariance under boosts but only small + + align:start position:0% +invariance under boosts but only small + + + align:start position:0% +invariance under boosts but only small +boosts + + align:start position:0% + + + + align:start position:0% + +the reason that I call them small boost + + align:start position:0% +the reason that I call them small boost + + + align:start position:0% +the reason that I call them small boost +is because Epsilon here had to be a + + align:start position:0% +is because Epsilon here had to be a + + + align:start position:0% +is because Epsilon here had to be a +water Lambda qcd it couldn't have been a + + align:start position:0% +water Lambda qcd it couldn't have been a + + + align:start position:0% +water Lambda qcd it couldn't have been a +water + + align:start position:0% + + + + align:start position:0% + +mq that's what I mean by small and from + + align:start position:0% +mq that's what I mean by small and from + + + align:start position:0% +mq that's what I mean by small and from +the point of view of this Theory this is + + align:start position:0% +the point of view of this Theory this is + + + align:start position:0% +the point of view of this Theory this is +all we care about + + align:start position:0% + + + + align:start position:0% + +because we want to remain in within the + + align:start position:0% +because we want to remain in within the + + + align:start position:0% +because we want to remain in within the +region where the effective theory was + + align:start position:0% +region where the effective theory was + + + align:start position:0% +region where the effective theory was +valid the whole setup of the effective + + align:start position:0% +valid the whole setup of the effective + + + align:start position:0% +valid the whole setup of the effective +Theory involved dividing out a large + + align:start position:0% +Theory involved dividing out a large + + + align:start position:0% +Theory involved dividing out a large +piece in a small piece if we allow back + + align:start position:0% +piece in a small piece if we allow back + + + align:start position:0% +piece in a small piece if we allow back +large pieces then then the game is over + + align:start position:0% +large pieces then then the game is over + + + align:start position:0% +large pieces then then the game is over +and the you wouldn't be formulating + + align:start position:0% +and the you wouldn't be formulating + + + align:start position:0% +and the you wouldn't be formulating +correctly the effective Theory because + + align:start position:0% +correctly the effective Theory because + + + align:start position:0% +correctly the effective Theory because +you'd spoil the power + + align:start position:0% +you'd spoil the power + + + align:start position:0% +you'd spoil the power +counting okay so this is what we this is + + align:start position:0% +counting okay so this is what we this is + + + align:start position:0% +counting okay so this is what we this is +this hidden symmetry we called + + align:start position:0% +this hidden symmetry we called + + + align:start position:0% +this hidden symmetry we called +reparameterization inv variance and it's + + align:start position:0% +reparameterization inv variance and it's + + + align:start position:0% +reparameterization inv variance and it's +not special to hqt anytime you have + + align:start position:0% +not special to hqt anytime you have + + + align:start position:0% +not special to hqt anytime you have +fields that are labeled by something you + + align:start position:0% +fields that are labeled by something you + + + align:start position:0% +fields that are labeled by something you +should think about whether there's a + + align:start position:0% +should think about whether there's a + + + align:start position:0% +should think about whether there's a +symmetry like + + align:start position:0% +symmetry like + + + align:start position:0% +symmetry like +this okay so that's the entire list of + + align:start position:0% +this okay so that's the entire list of + + + align:start position:0% +this okay so that's the entire list of +the symmetries that you should consider + + align:start position:0% +the symmetries that you should consider + + + align:start position:0% +the symmetries that you should consider +uh in order to think about doing a + + align:start position:0% +uh in order to think about doing a + + + align:start position:0% +uh in order to think about doing a +bottomup approach to hqb simple ones and + + align:start position:0% +bottomup approach to hqb simple ones and + + + align:start position:0% +bottomup approach to hqb simple ones and +then there's this one that's a little + + align:start position:0% +then there's this one that's a little + + + align:start position:0% +then there's this one that's a little +more + + align:start position:0% + + + + align:start position:0% + +complicated so let's go back and now + + align:start position:0% +complicated so let's go back and now + + + align:start position:0% +complicated so let's go back and now +consider the one over mq operators + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% + + + + align:start position:0% + +general and it turns out that there's + + align:start position:0% +general and it turns out that there's + + + align:start position:0% +general and it turns out that there's +not any missing operators that the two + + align:start position:0% +not any missing operators that the two + + + align:start position:0% +not any missing operators that the two +operators we have are actually the + + align:start position:0% +operators we have are actually the + + + align:start position:0% +operators we have are actually the +complete set that you can write + + align:start position:0% +complete set that you can write + + + align:start position:0% +complete set that you can write +down at this + + align:start position:0% +down at this + + + align:start position:0% +down at this +Dimension using all the properties of + + align:start position:0% +Dimension using all the properties of + + + align:start position:0% +Dimension using all the properties of +the + + align:start position:0% +the + + + align:start position:0% +the +field so we didn't miss anything from + + align:start position:0% +field so we didn't miss anything from + + + align:start position:0% +field so we didn't miss anything from +that point of view + + align:start position:0% + + + + align:start position:0% + +so let me write them down again and let + + align:start position:0% +so let me write them down again and let + + + align:start position:0% +so let me write them down again and let +me write them down in a way where I + + align:start position:0% +me write them down in a way where I + + + align:start position:0% +me write them down in a way where I +imagine that radiative Corrections have + + align:start position:0% +imagine that radiative Corrections have + + + align:start position:0% +imagine that radiative Corrections have +come in as well and I'll give them some + + align:start position:0% +come in as well and I'll give them some + + + align:start position:0% +come in as well and I'll give them some +Wilson coefficients which are + + align:start position:0% +Wilson coefficients which are + + + align:start position:0% +Wilson coefficients which are +generically called CK and CF that's the + + align:start position:0% +generically called CK and CF that's the + + + align:start position:0% +generically called CK and CF that's the +standard + + align:start position:0% +standard + + + align:start position:0% +standard +notation so this is a Wilson + + align:start position:0% + + + + align:start position:0% + +coefficient that's a Wilson coefficient + + align:start position:0% +coefficient that's a Wilson coefficient + + + align:start position:0% +coefficient that's a Wilson coefficient +so this is not 43s it's Wilson + + align:start position:0% +so this is not 43s it's Wilson + + + align:start position:0% +so this is not 43s it's Wilson +coefficient the name is the same as the + + align:start position:0% +coefficient the name is the same as the + + + align:start position:0% +coefficient the name is the same as the +CF that is for third but this is a + + align:start position:0% +CF that is for third but this is a + + + align:start position:0% +CF that is for third but this is a +little CF not a big + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +CF so if we want to so it's gauge + + align:start position:0% +CF so if we want to so it's gauge + + + align:start position:0% +CF so if we want to so it's gauge +invariant has the right par etc etc we + + align:start position:0% +invariant has the right par etc etc we + + + align:start position:0% +invariant has the right par etc etc we +should worry about the + + align:start position:0% +should worry about the + + + align:start position:0% +should worry about the +reparameterization in + + align:start position:0% + + + + align:start position:0% + +variance so let's do that so at lowest + + align:start position:0% +variance so let's do that so at lowest + + + align:start position:0% +variance so let's do that so at lowest +order it's a the the phase is + + align:start position:0% +order it's a the the phase is + + + align:start position:0% +order it's a the the phase is +what + + align:start position:0% +what + + + align:start position:0% +what +changes and the leading order lran is + + align:start position:0% +changes and the leading order lran is + + + align:start position:0% +changes and the leading order lran is +invariant because v. Epsilon is + + align:start position:0% + + + + align:start position:0% + +zero so i' order mq to the + + align:start position:0% +zero so i' order mq to the + + + align:start position:0% +zero so i' order mq to the +zero since V do Epsilon is zero you + + align:start position:0% +zero since V do Epsilon is zero you + + + align:start position:0% +zero since V do Epsilon is zero you +don't get an leading order change so our + + align:start position:0% +don't get an leading order change so our + + + align:start position:0% +don't get an leading order change so our +lran was invariant this invariance this + + align:start position:0% +lran was invariant this invariance this + + + align:start position:0% +lran was invariant this invariance this +reparameterization in variance mixes + + align:start position:0% +reparameterization in variance mixes + + + align:start position:0% +reparameterization in variance mixes +orders it connects orders in the + + align:start position:0% +orders it connects orders in the + + + align:start position:0% +orders it connects orders in the +expansion there was a term that was + + align:start position:0% +expansion there was a term that was + + + align:start position:0% +expansion there was a term that was +order one which is this piece and + + align:start position:0% +order one which is this piece and + + + align:start position:0% +order one which is this piece and +there's a term that's order one over mq + + align:start position:0% +there's a term that's order one over mq + + + align:start position:0% +there's a term that's order one over mq +so the Symmetry is actually making a + + align:start position:0% +so the Symmetry is actually making a + + + align:start position:0% +so the Symmetry is actually making a +connection between leading order and + + align:start position:0% +connection between leading order and + + + align:start position:0% +connection between leading order and +subing Order + + align:start position:0% + + + + align:start position:0% + +operators so we could ask about this + + align:start position:0% +operators so we could ask about this + + + align:start position:0% +operators so we could ask about this +Delta l0 and there will be a piece at + + align:start position:0% +Delta l0 and there will be a piece at + + + align:start position:0% +Delta l0 and there will be a piece at +order 1 over + + align:start position:0% +order 1 over + + + align:start position:0% +order 1 over +mq so let's just write out all these + + align:start position:0% + + + + align:start position:0% + +things transforming + + align:start position:0% + + + + align:start position:0% + +everything this is our leading order + + align:start position:0% + + + + align:start position:0% + +lran after imposing the field change as + + align:start position:0% +lran after imposing the field change as + + + align:start position:0% +lran after imposing the field change as +well as the V change the v.d becomes + + align:start position:0% +well as the V change the v.d becomes + + + align:start position:0% +well as the V change the v.d becomes +this and the field becomes + + align:start position:0% + + + + align:start position:0% + +that so there's three things here are + + align:start position:0% +that so there's three things here are + + + align:start position:0% +that so there's three things here are +being + + align:start position:0% +being + + + align:start position:0% +being +changed expand this + + align:start position:0% +changed expand this + + + align:start position:0% +changed expand this +out use things like 1+ V SL over + + align:start position:0% +out use things like 1+ V SL over + + + align:start position:0% +out use things like 1+ V SL over +2 Epsilon + + align:start position:0% +2 Epsilon + + + align:start position:0% +2 Epsilon +slash 1+ V SL over + + align:start position:0% +slash 1+ V SL over + + + align:start position:0% +slash 1+ V SL over +2 equal to Epsilon Dov is equal to zero + + align:start position:0% +2 equal to Epsilon Dov is equal to zero + + + align:start position:0% +2 equal to Epsilon Dov is equal to zero +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +simplify do some direct algebra and you + + align:start position:0% +simplify do some direct algebra and you + + + align:start position:0% +simplify do some direct algebra and you +can boil this down to something simple + + align:start position:0% +can boil this down to something simple + + + align:start position:0% +can boil this down to something simple +which is that the entire + + align:start position:0% +which is that the entire + + + align:start position:0% +which is that the entire +change is just an Epsilon D over + + align:start position:0% +change is just an Epsilon D over + + + align:start position:0% +change is just an Epsilon D over +mq * + + align:start position:0% + + + + align:start position:0% + +QV and if you look at this it has to + + align:start position:0% +QV and if you look at this it has to + + + align:start position:0% +QV and if you look at this it has to +cancel against something that's order m + + align:start position:0% +cancel against something that's order m + + + align:start position:0% +cancel against something that's order m +1 over + + align:start position:0% +1 over + + + align:start position:0% +1 over +mq and if you look at the terms that we + + align:start position:0% +mq and if you look at the terms that we + + + align:start position:0% +mq and if you look at the terms that we +had at order one which are 1 over mq + + align:start position:0% +had at order one which are 1 over mq + + + align:start position:0% +had at order one which are 1 over mq +there was a kinetic piece we called it + + align:start position:0% +there was a kinetic piece we called it + + + align:start position:0% +there was a kinetic piece we called it +kinetic energy piece + + align:start position:0% +kinetic energy piece + + + align:start position:0% +kinetic energy piece +and if we do the change there there is a + + align:start position:0% +and if we do the change there there is a + + + align:start position:0% +and if we do the change there there is a +contribution from the phase in this case + + align:start position:0% +contribution from the phase in this case + + + align:start position:0% +contribution from the phase in this case +because we had transverse + + align:start position:0% + + + + align:start position:0% + +derivatives so we can have Epsilon DOD + + align:start position:0% +derivatives so we can have Epsilon DOD + + + align:start position:0% +derivatives so we can have Epsilon DOD +transverse that's + + align:start position:0% + + + + align:start position:0% + +nonzero and if you go through the + + align:start position:0% +nonzero and if you go through the + + + align:start position:0% +nonzero and if you go through the +leading order change to this guy as well + + align:start position:0% +leading order change to this guy as well + + + align:start position:0% +leading order change to this guy as well +as the guy that's the magnetic + + align:start position:0% +as the guy that's the magnetic + + + align:start position:0% +as the guy that's the magnetic +guy you find that the magnetic guy is + + align:start position:0% +guy you find that the magnetic guy is + + + align:start position:0% +guy you find that the magnetic guy is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +at this + + align:start position:0% +at this + + + align:start position:0% +at this +order it's non zero at higher orders but + + align:start position:0% +order it's non zero at higher orders but + + + align:start position:0% +order it's non zero at higher orders but +at this order it's zero and the kinetic + + align:start position:0% +at this order it's zero and the kinetic + + + align:start position:0% +at this order it's zero and the kinetic +guy does have a transformation it has + + align:start position:0% +guy does have a transformation it has + + + align:start position:0% +guy does have a transformation it has +exactly the same form as this guy here + + align:start position:0% +exactly the same form as this guy here + + + align:start position:0% +exactly the same form as this guy here +if epsilon's dotted into the D then it's + + align:start position:0% +if epsilon's dotted into the D then it's + + + align:start position:0% +if epsilon's dotted into the D then it's +a d + + align:start position:0% +a d + + + align:start position:0% +a d +transverse but this guy has a Wilson + + align:start position:0% +transverse but this guy has a Wilson + + + align:start position:0% +transverse but this guy has a Wilson +coefficient this guy doesn't so in order + + align:start position:0% +coefficient this guy doesn't so in order + + + align:start position:0% +coefficient this guy doesn't so in order +for these to cancel you actually learn + + align:start position:0% +for these to cancel you actually learn + + + align:start position:0% +for these to cancel you actually learn +something + + align:start position:0% +something + + + align:start position:0% +something +non-trivial the Symmetry teaches you + + align:start position:0% +non-trivial the Symmetry teaches you + + + align:start position:0% +non-trivial the Symmetry teaches you +something non-trivial about the + + align:start position:0% +something non-trivial about the + + + align:start position:0% +something non-trivial about the +subleading lran that Wilson coefficient + + align:start position:0% +subleading lran that Wilson coefficient + + + align:start position:0% +subleading lran that Wilson coefficient +has to be + + align:start position:0% +has to be + + + align:start position:0% +has to be +one to all R in pration + + align:start position:0% +one to all R in pration + + + align:start position:0% +one to all R in pration +theory in order for the Symmetry not to + + align:start position:0% +theory in order for the Symmetry not to + + + align:start position:0% +theory in order for the Symmetry not to +be + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +violated + + align:start position:0% +violated + + + align:start position:0% +violated +imposing yeah so the Symmetry is Boost + + align:start position:0% +imposing yeah so the Symmetry is Boost + + + align:start position:0% +imposing yeah so the Symmetry is Boost +in variance and it seems like a + + align:start position:0% +in variance and it seems like a + + + align:start position:0% +in variance and it seems like a +reasonable symmetry to impose yeah + + align:start position:0% + + + + align:start position:0% + +me small + + align:start position:0% + + + + align:start position:0% + +boosts so as long as your scheme and + + align:start position:0% +boosts so as long as your scheme and + + + align:start position:0% +boosts so as long as your scheme and +your regulator don't break the symmetry + + align:start position:0% +your regulator don't break the symmetry + + + align:start position:0% +your regulator don't break the symmetry +which is always + + align:start position:0% +which is always + + + align:start position:0% +which is always +something that you have to worry about + + align:start position:0% +something that you have to worry about + + + align:start position:0% +something that you have to worry about +if in general + + align:start position:0% + + + + align:start position:0% + +then this guy is one to all + + align:start position:0% +then this guy is one to all + + + align:start position:0% +then this guy is one to all +orders okay so if you did something like + + align:start position:0% +orders okay so if you did something like + + + align:start position:0% +orders okay so if you did something like +dimensional regularization and you + + align:start position:0% +dimensional regularization and you + + + align:start position:0% +dimensional regularization and you +thought you should calculate this guy + + align:start position:0% +thought you should calculate this guy + + + align:start position:0% +thought you should calculate this guy +you just find that it would be one and + + align:start position:0% +you just find that it would be one and + + + align:start position:0% +you just find that it would be one and +you'd Wonder was that there a symmetry + + align:start position:0% +you'd Wonder was that there a symmetry + + + align:start position:0% +you'd Wonder was that there a symmetry +that tells you it's + + align:start position:0% +that tells you it's + + + align:start position:0% +that tells you it's +one okay so you don't have to figure out + + align:start position:0% +one okay so you don't have to figure out + + + align:start position:0% +one okay so you don't have to figure out +that guy the other guy which we've + + align:start position:0% +that guy the other guy which we've + + + align:start position:0% +that guy the other guy which we've +called CF you do have to figure out + + align:start position:0% +called CF you do have to figure out + + + align:start position:0% +called CF you do have to figure out +because it wasn't + + align:start position:0% +because it wasn't + + + align:start position:0% +because it wasn't +constrained and at lowest order + + align:start position:0% + + + + align:start position:0% + +the other coefficient is not constrained + + align:start position:0% +the other coefficient is not constrained + + + align:start position:0% +the other coefficient is not constrained +in this + + align:start position:0% +in this + + + align:start position:0% +in this +way and so it does get in an almost + + align:start position:0% +way and so it does get in an almost + + + align:start position:0% +way and so it does get in an almost +Dimension and so we could calculate + + align:start position:0% +Dimension and so we could calculate + + + align:start position:0% +Dimension and so we could calculate +it it's a good homework problem you may + + align:start position:0% +it it's a good homework problem you may + + + align:start position:0% +it it's a good homework problem you may +see it on a future homework + + align:start position:0% + + + + align:start position:0% + +set and there is an anomalous Dimension + + align:start position:0% +set and there is an anomalous Dimension + + + align:start position:0% +set and there is an anomalous Dimension +and when you solve that anomalous + + align:start position:0% +and when you solve that anomalous + + + align:start position:0% +and when you solve that anomalous +Dimension you're again getting something + + align:start position:0% +Dimension you're again getting something + + + align:start position:0% +Dimension you're again getting something +that's a ratio of alpha to some power in + + align:start position:0% +that's a ratio of alpha to some power in + + + align:start position:0% +that's a ratio of alpha to some power in +this case it's a nonabelian power the + + align:start position:0% +this case it's a nonabelian power the + + + align:start position:0% +this case it's a nonabelian power the +adjoint + + align:start position:0% + + + + align:start position:0% + +Casmir okay so that guy does have an + + align:start position:0% +Casmir okay so that guy does have an + + + align:start position:0% +Casmir okay so that guy does have an +anomal + + align:start position:0% +anomal + + + align:start position:0% +anomal +Dimension I think we'll stop there today + + align:start position:0% +Dimension I think we'll stop there today + + + align:start position:0% +Dimension I think we'll stop there today +and we'll talk more about power + + align:start position:0% +and we'll talk more about power + + + align:start position:0% +and we'll talk more about power +Corrections and sort of phenomenology of + + align:start position:0% +Corrections and sort of phenomenology of + + + align:start position:0% +Corrections and sort of phenomenology of +them and how they how we can make + + align:start position:0% +them and how they how we can make + + + align:start position:0% +them and how they how we can make +non-trivial predictions of from them uh + + align:start position:0% +non-trivial predictions of from them uh + + + align:start position:0% +non-trivial predictions of from them uh +next time \ No newline at end of file diff --git a/on1rmY3Tw5U.txt b/on1rmY3Tw5U.txt new file mode 100644 index 0000000000000000000000000000000000000000..fae55ffc9939d9e465004fd5664d0aad08c9809b --- /dev/null +++ b/on1rmY3Tw5U.txt @@ -0,0 +1,4947 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +Rachid why don't you give us that point + + align:start position:0% +Rachid why don't you give us that point + + + align:start position:0% +Rachid why don't you give us that point +that you were making to me about yes so + + align:start position:0% +that you were making to me about yes so + + + align:start position:0% +that you were making to me about yes so +DARPA relies very heavily on this + + align:start position:0% +DARPA relies very heavily on this + + + align:start position:0% +DARPA relies very heavily on this +program manager structure so they give + + align:start position:0% +program manager structure so they give + + + align:start position:0% +program manager structure so they give +these program in it there's a lot of + + align:start position:0% +these program in it there's a lot of + + + align:start position:0% +these program in it there's a lot of +power and a lot of leeway to do whatever + + align:start position:0% +power and a lot of leeway to do whatever + + + align:start position:0% +power and a lot of leeway to do whatever +they want but they have they have to + + align:start position:0% +they want but they have they have to + + + align:start position:0% +they want but they have they have to +have a very distinct vision from the + + align:start position:0% +have a very distinct vision from the + + + align:start position:0% +have a very distinct vision from the +outset like a really when they start to + + align:start position:0% +outset like a really when they start to + + + align:start position:0% +outset like a really when they start to +be able to do things and so I was + + align:start position:0% +be able to do things and so I was + + + align:start position:0% +be able to do things and so I was +concerned that these program managers + + align:start position:0% +concerned that these program managers + + + align:start position:0% +concerned that these program managers +we're gonna basically be coming from the + + align:start position:0% +we're gonna basically be coming from the + + + align:start position:0% +we're gonna basically be coming from the +same places over and over again and so + + align:start position:0% +same places over and over again and so + + + align:start position:0% +same places over and over again and so +have very similar visions and you're + + align:start position:0% +have very similar visions and you're + + + align:start position:0% +have very similar visions and you're +gonna be able to miss out on a lot of + + align:start position:0% +gonna be able to miss out on a lot of + + + align:start position:0% +gonna be able to miss out on a lot of +different talent that exists outside or + + align:start position:0% +different talent that exists outside or + + + align:start position:0% +different talent that exists outside or +a lot of different new projects or new + + align:start position:0% +a lot of different new projects or new + + + align:start position:0% +a lot of different new projects or new +fields maybe look just like we were + + align:start position:0% +fields maybe look just like we were + + + align:start position:0% +fields maybe look just like we were +taught me that new collaborations + + align:start position:0% +taught me that new collaborations + + + align:start position:0% +taught me that new collaborations +between biology and kind of humans in + + align:start position:0% +between biology and kind of humans in + + + align:start position:0% +between biology and kind of humans in +computer science things like that but + + align:start position:0% +computer science things like that but + + + align:start position:0% +computer science things like that but +that was really my main program managers + + align:start position:0% +that was really my main program managers + + + align:start position:0% +that was really my main program managers +weren't being chosen as I grew believes + + align:start position:0% +weren't being chosen as I grew believes + + + align:start position:0% +weren't being chosen as I grew believes +in the word but that the selection + + align:start position:0% +in the word but that the selection + + + align:start position:0% +in the word but that the selection +process of these program managers was + + align:start position:0% +process of these program managers was + + + align:start position:0% +process of these program managers was +actually might it might be too narrow + + align:start position:0% +actually might it might be too narrow + + + align:start position:0% +actually might it might be too narrow +but they do get visionaries + + align:start position:0% + + + + align:start position:0% + +yeah I wasn't man + + align:start position:0% +yeah I wasn't man + + + align:start position:0% +yeah I wasn't man +okay so I'm gonna move us to Timmy + + align:start position:0% +okay so I'm gonna move us to Timmy + + + align:start position:0% +okay so I'm gonna move us to Timmy +Carlton and Tammy's big perception about + + align:start position:0% +Carlton and Tammy's big perception about + + + align:start position:0% +Carlton and Tammy's big perception about +DARPA is this vision perception that + + align:start position:0% +DARPA is this vision perception that + + + align:start position:0% +DARPA is this vision perception that +that's what a critical factor that makes + + align:start position:0% +that's what a critical factor that makes + + + align:start position:0% +that's what a critical factor that makes +DARPA different and there is a process + + align:start position:0% +DARPA different and there is a process + + + align:start position:0% +DARPA different and there is a process +that DARPA has developed for this + + align:start position:0% +that DARPA has developed for this + + + align:start position:0% +that DARPA has developed for this +radical technological visioning and + + align:start position:0% +radical technological visioning and + + + align:start position:0% +radical technological visioning and +essentially she argues that there's six + + align:start position:0% +essentially she argues that there's six + + + align:start position:0% +essentially she argues that there's six +stages that they use to kind of get + + align:start position:0% +stages that they use to kind of get + + + align:start position:0% +stages that they use to kind of get +their first recruitment of great talent + + align:start position:0% +their first recruitment of great talent + + + align:start position:0% +their first recruitment of great talent +and the talent they hear about talent + + align:start position:0% +and the talent they hear about talent + + + align:start position:0% +and the talent they hear about talent +from this DARPA network which is now + + align:start position:0% +from this DARPA network which is now + + + align:start position:0% +from this DARPA network which is now +quite huge because all of the people + + align:start position:0% +quite huge because all of the people + + + align:start position:0% +quite huge because all of the people +that get DARPA contracts and awards they + + align:start position:0% +that get DARPA contracts and awards they + + + align:start position:0% +that get DARPA contracts and awards they +stay in this kind of DARPA family and + + align:start position:0% +stay in this kind of DARPA family and + + + align:start position:0% +stay in this kind of DARPA family and +typically researchers love to work for + + align:start position:0% +typically researchers love to work for + + + align:start position:0% +typically researchers love to work for +DARPA because you know working on DARPA + + align:start position:0% +DARPA because you know working on DARPA + + + align:start position:0% +DARPA because you know working on DARPA +hard problems is really intriguing so + + align:start position:0% +hard problems is really intriguing so + + + align:start position:0% +hard problems is really intriguing so +that's a community that that tends to + + align:start position:0% +that's a community that that tends to + + + align:start position:0% +that's a community that that tends to +know each other and be in communication + + align:start position:0% +know each other and be in communication + + + align:start position:0% +know each other and be in communication +as well as the community of former DARPA + + align:start position:0% +as well as the community of former DARPA + + + align:start position:0% +as well as the community of former DARPA +program managers and efficient and + + align:start position:0% +program managers and efficient and + + + align:start position:0% +program managers and efficient and +officials so a lot of the talent comes + + align:start position:0% +officials so a lot of the talent comes + + + align:start position:0% +officials so a lot of the talent comes +through that Network which kind of knows + + align:start position:0% +through that Network which kind of knows + + + align:start position:0% +through that Network which kind of knows +what what's going to work so the + + align:start position:0% +what what's going to work so the + + + align:start position:0% +what what's going to work so the +recruitment and the vision get United in + + align:start position:0% +recruitment and the vision get United in + + + align:start position:0% +recruitment and the vision get United in +a way in that recruitment process then + + align:start position:0% +a way in that recruitment process then + + + align:start position:0% +a way in that recruitment process then +comes the stage of the vision + + align:start position:0% +comes the stage of the vision + + + align:start position:0% +comes the stage of the vision +formulation right the program manager + + align:start position:0% +formulation right the program manager + + + align:start position:0% +formulation right the program manager +has got to figure out what they're going + + align:start position:0% +has got to figure out what they're going + + + align:start position:0% +has got to figure out what they're going +to do with their four or five years and + + align:start position:0% +to do with their four or five years and + + + align:start position:0% +to do with their four or five years and +they have got to formulate a radical + + align:start position:0% +they have got to formulate a radical + + + align:start position:0% +they have got to formulate a radical +vision a right-left vision what's going + + align:start position:0% +vision a right-left vision what's going + + + align:start position:0% +vision a right-left vision what's going +to come out of that pipeline and what's + + align:start position:0% +to come out of that pipeline and what's + + + align:start position:0% +to come out of that pipeline and what's +the fundamental research that gonna get + + align:start position:0% +the fundamental research that gonna get + + + align:start position:0% +the fundamental research that gonna get +me there + + align:start position:0% +me there + + + align:start position:0% +me there +and it's driving for that breakthrough + + align:start position:0% +and it's driving for that breakthrough + + + align:start position:0% +and it's driving for that breakthrough +that's the organizing proposition then + + align:start position:0% +that's the organizing proposition then + + + align:start position:0% +that's the organizing proposition then +they've got to go through defining a + + align:start position:0% +they've got to go through defining a + + + align:start position:0% +they've got to go through defining a +program and it's launched often they + + align:start position:0% +program and it's launched often they + + + align:start position:0% +program and it's launched often they +will have a workshop an invitation-only + + align:start position:0% +will have a workshop an invitation-only + + + align:start position:0% +will have a workshop an invitation-only +workshop where they'll assemble twenty + + align:start position:0% +workshop where they'll assemble twenty + + + align:start position:0% +workshop where they'll assemble twenty +five thirty forty the kind of best + + align:start position:0% +five thirty forty the kind of best + + + align:start position:0% +five thirty forty the kind of best +thinkers on a pro in a project area and + + align:start position:0% +thinkers on a pro in a project area and + + + align:start position:0% +thinkers on a pro in a project area and +meet for a day or two days I've watched + + align:start position:0% +meet for a day or two days I've watched + + + align:start position:0% +meet for a day or two days I've watched +one of those which got held up at held + + align:start position:0% +one of those which got held up at held + + + align:start position:0% +one of those which got held up at held +up at MIT as part of the the beginnings + + align:start position:0% +up at MIT as part of the the beginnings + + + align:start position:0% +up at MIT as part of the the beginnings +of creating this biological technologies + + align:start position:0% +of creating this biological technologies + + + align:start position:0% +of creating this biological technologies +office and they brought in just an + + align:start position:0% +office and they brought in just an + + + align:start position:0% +office and they brought in just an +amazing collection + + align:start position:0% +amazing collection + + + align:start position:0% +amazing collection +from MIT and from elsewhere of thinkers + + align:start position:0% +from MIT and from elsewhere of thinkers + + + align:start position:0% +from MIT and from elsewhere of thinkers +about what some of the early projects + + align:start position:0% +about what some of the early projects + + + align:start position:0% +about what some of the early projects +might be to achieve some of these + + align:start position:0% +might be to achieve some of these + + + align:start position:0% +might be to achieve some of these +capabilities so the deputy director of + + align:start position:0% +capabilities so the deputy director of + + + align:start position:0% +capabilities so the deputy director of +DARPA came up and kind of helped run + + align:start position:0% +DARPA came up and kind of helped run + + + align:start position:0% +DARPA came up and kind of helped run +this workshop and things is through the + + align:start position:0% +this workshop and things is through the + + + align:start position:0% +this workshop and things is through the +office wasn't set up for a while until + + align:start position:0% +office wasn't set up for a while until + + + align:start position:0% +office wasn't set up for a while until +the next DARPA director but it really + + align:start position:0% +the next DARPA director but it really + + + align:start position:0% +the next DARPA director but it really +helped contribute to that portfolio and + + align:start position:0% +helped contribute to that portfolio and + + + align:start position:0% +helped contribute to that portfolio and +it was a really serious effort so the + + align:start position:0% +it was a really serious effort so the + + + align:start position:0% +it was a really serious effort so the +program manager develops a portfolio + + align:start position:0% +program manager develops a portfolio + + + align:start position:0% +program manager develops a portfolio +approach of standing up a series of + + align:start position:0% +approach of standing up a series of + + + align:start position:0% +approach of standing up a series of +groups are going to be working on this + + align:start position:0% +groups are going to be working on this + + + align:start position:0% +groups are going to be working on this +and in or relating them and the program + + align:start position:0% +and in or relating them and the program + + + align:start position:0% +and in or relating them and the program +manager is also kind of responsible for + + align:start position:0% +manager is also kind of responsible for + + + align:start position:0% +manager is also kind of responsible for +making this technology transfer in other + + align:start position:0% +making this technology transfer in other + + + align:start position:0% +making this technology transfer in other +words it's not enough just to do + + align:start position:0% +words it's not enough just to do + + + align:start position:0% +words it's not enough just to do +something cool you've got to move it + + align:start position:0% +something cool you've got to move it + + + align:start position:0% +something cool you've got to move it +into the implementation stage and how is + + align:start position:0% +into the implementation stage and how is + + + align:start position:0% +into the implementation stage and how is +that gonna happen + + align:start position:0% +that gonna happen + + + align:start position:0% +that gonna happen +so the purga managers got to undertake + + align:start position:0% +so the purga managers got to undertake + + + align:start position:0% +so the purga managers got to undertake +all of these you know various steps so + + align:start position:0% +all of these you know various steps so + + + align:start position:0% +all of these you know various steps so +the criteria for being DARPA hard is + + align:start position:0% +the criteria for being DARPA hard is + + + align:start position:0% +the criteria for being DARPA hard is +that the project has to be technology + + align:start position:0% +that the project has to be technology + + + align:start position:0% +that the project has to be technology +technologically very challenging it's + + align:start position:0% +technologically very challenging it's + + + align:start position:0% +technologically very challenging it's +got to extend beyond the current limits + + align:start position:0% +got to extend beyond the current limits + + + align:start position:0% +got to extend beyond the current limits +of technology and knowledge otherwise + + align:start position:0% +of technology and knowledge otherwise + + + align:start position:0% +of technology and knowledge otherwise +they don't really want to do it it's got + + align:start position:0% +they don't really want to do it it's got + + + align:start position:0% +they don't really want to do it it's got +to be actionable which means it can be + + align:start position:0% +to be actionable which means it can be + + + align:start position:0% +to be actionable which means it can be +made it can be built it can be produced + + align:start position:0% +made it can be built it can be produced + + + align:start position:0% +made it can be built it can be produced +so if it can't be why do it right you've + + align:start position:0% +so if it can't be why do it right you've + + + align:start position:0% +so if it can't be why do it right you've +got to be able to demonstrate that it's + + align:start position:0% +got to be able to demonstrate that it's + + + align:start position:0% +got to be able to demonstrate that it's +actionable typically multidisciplinary + + align:start position:0% +actionable typically multidisciplinary + + + align:start position:0% +actionable typically multidisciplinary +that it's going to draw on a variety of + + align:start position:0% +that it's going to draw on a variety of + + + align:start position:0% +that it's going to draw on a variety of +areas of expertise it's got to be + + align:start position:0% +areas of expertise it's got to be + + + align:start position:0% +areas of expertise it's got to be +far-reaching it's got to change things + + align:start position:0% +far-reaching it's got to change things + + + align:start position:0% +far-reaching it's got to change things +it's got to be very ambitious at a big + + align:start position:0% +it's got to be very ambitious at a big + + + align:start position:0% +it's got to be very ambitious at a big +scale don't do little things it's kind + + align:start position:0% +scale don't do little things it's kind + + + align:start position:0% +scale don't do little things it's kind +of a DARPA sub rule and various + + align:start position:0% +of a DARPA sub rule and various + + + align:start position:0% +of a DARPA sub rule and various +techniques to flesh out division include + + align:start position:0% +techniques to flesh out division include + + + align:start position:0% +techniques to flesh out division include +those expert only workshops and a + + align:start position:0% +those expert only workshops and a + + + align:start position:0% +those expert only workshops and a +proof-of-concept effort sometimes if + + align:start position:0% +proof-of-concept effort sometimes if + + + align:start position:0% +proof-of-concept effort sometimes if +it's some idea looks promising that + + align:start position:0% +it's some idea looks promising that + + + align:start position:0% +it's some idea looks promising that +they'll do what DARPA calls a seedling + + align:start position:0% +they'll do what DARPA calls a seedling + + + align:start position:0% +they'll do what DARPA calls a seedling +just put a little money on it and let + + align:start position:0% +just put a little money on it and let + + + align:start position:0% +just put a little money on it and let +somebody play with it a real thinker + + align:start position:0% +somebody play with it a real thinker + + + align:start position:0% +somebody play with it a real thinker +play with it and see what it might + + align:start position:0% +play with it and see what it might + + + align:start position:0% +play with it and see what it might +materialize into so they've got that + + align:start position:0% +materialize into so they've got that + + + align:start position:0% +materialize into so they've got that +seedling capability there is no training + + align:start position:0% +seedling capability there is no training + + + align:start position:0% +seedling capability there is no training +system for program managers they don't + + align:start position:0% +system for program managers they don't + + + align:start position:0% +system for program managers they don't +go through any kind of training they + + align:start position:0% +go through any kind of training they + + + align:start position:0% +go through any kind of training they +just arrive and they kind of learn from + + align:start position:0% +just arrive and they kind of learn from + + + align:start position:0% +just arrive and they kind of learn from +other program managers what + + align:start position:0% +other program managers what + + + align:start position:0% +other program managers what +they're supposed to do so there's a very + + align:start position:0% +they're supposed to do so there's a very + + + align:start position:0% +they're supposed to do so there's a very +strong kind of DARPA culture about how + + align:start position:0% +strong kind of DARPA culture about how + + + align:start position:0% +strong kind of DARPA culture about how +it operates that gets communicated by + + align:start position:0% +it operates that gets communicated by + + + align:start position:0% +it operates that gets communicated by +word of mouth and kind of learning by + + align:start position:0% +word of mouth and kind of learning by + + + align:start position:0% +word of mouth and kind of learning by +doing and it's it's informal exchange + + align:start position:0% +doing and it's it's informal exchange + + + align:start position:0% +doing and it's it's informal exchange +right but there are there is a very + + align:start position:0% +right but there are there is a very + + + align:start position:0% +right but there are there is a very +strong kind of operating rule set DARPA + + align:start position:0% +strong kind of operating rule set DARPA + + + align:start position:0% +strong kind of operating rule set DARPA +program managers really have to be quite + + align:start position:0% +program managers really have to be quite + + + align:start position:0% +program managers really have to be quite +entrepreneurial and Martine you are + + align:start position:0% +entrepreneurial and Martine you are + + + align:start position:0% +entrepreneurial and Martine you are +raising this earlier they've got to + + align:start position:0% +raising this earlier they've got to + + + align:start position:0% +raising this earlier they've got to +stand up a whole new territory and to do + + align:start position:0% +stand up a whole new territory and to do + + + align:start position:0% +stand up a whole new territory and to do +that they've got to be highly + + align:start position:0% +that they've got to be highly + + + align:start position:0% +that they've got to be highly +entrepreneurial about how to bring that + + align:start position:0% +entrepreneurial about how to bring that + + + align:start position:0% +entrepreneurial about how to bring that +about and the decision to stand up a + + align:start position:0% +about and the decision to stand up a + + + align:start position:0% +about and the decision to stand up a +vision program this is not set up + + align:start position:0% +vision program this is not set up + + + align:start position:0% +vision program this is not set up +through peer review there isn't + + align:start position:0% +through peer review there isn't + + + align:start position:0% +through peer review there isn't +consensus decision-making at DARPA the + + align:start position:0% +consensus decision-making at DARPA the + + + align:start position:0% +consensus decision-making at DARPA the +program manager has got to have a really + + align:start position:0% +program manager has got to have a really + + + align:start position:0% +program manager has got to have a really +strong vision and it's got to get really + + align:start position:0% +strong vision and it's got to get really + + + align:start position:0% +strong vision and it's got to get really +organized and then it's got to withstand + + align:start position:0% +organized and then it's got to withstand + + + align:start position:0% +organized and then it's got to withstand +the office director and then the DARPA + + align:start position:0% +the office director and then the DARPA + + + align:start position:0% +the office director and then the DARPA +direct you're really tearing through it + + align:start position:0% +direct you're really tearing through it + + + align:start position:0% +direct you're really tearing through it +and really analyzing so once you get + + align:start position:0% +and really analyzing so once you get + + + align:start position:0% +and really analyzing so once you get +that though the approvals can be very + + align:start position:0% +that though the approvals can be very + + + align:start position:0% +that though the approvals can be very +fast once the decision is made to stand + + align:start position:0% +fast once the decision is made to stand + + + align:start position:0% +fast once the decision is made to stand +something up and the program manager + + align:start position:0% +something up and the program manager + + + align:start position:0% +something up and the program manager +really is to go back to that term that + + align:start position:0% +really is to go back to that term that + + + align:start position:0% +really is to go back to that term that +you like Steph a vision champion they've + + align:start position:0% +you like Steph a vision champion they've + + + align:start position:0% +you like Steph a vision champion they've +got a champion this vision and make it + + align:start position:0% +got a champion this vision and make it + + + align:start position:0% +got a champion this vision and make it +happen that's what the program managers + + align:start position:0% +happen that's what the program managers + + + align:start position:0% +happen that's what the program managers +got to do so DARPA starts with the + + align:start position:0% +got to do so DARPA starts with the + + + align:start position:0% +got to do so DARPA starts with the +vision that is not how industry operates + + align:start position:0% +vision that is not how industry operates + + + align:start position:0% +vision that is not how industry operates +right that's now how other government + + align:start position:0% +right that's now how other government + + + align:start position:0% +right that's now how other government +agencies operate it's industry works + + align:start position:0% +agencies operate it's industry works + + + align:start position:0% +agencies operate it's industry works +largely on what's called a stage gate + + align:start position:0% +largely on what's called a stage gate + + + align:start position:0% +largely on what's called a stage gate +system so industry is going to want to + + align:start position:0% +system so industry is going to want to + + + align:start position:0% +system so industry is going to want to +do typically more incremental kind of + + align:start position:0% +do typically more incremental kind of + + + align:start position:0% +do typically more incremental kind of +advances because the advances can snap + + align:start position:0% +advances because the advances can snap + + + align:start position:0% +advances because the advances can snap +on to markets that it's already got and + + align:start position:0% +on to markets that it's already got and + + + align:start position:0% +on to markets that it's already got and +economic opportunities that are RACs and + + align:start position:0% +economic opportunities that are RACs and + + + align:start position:0% +economic opportunities that are RACs and +technologies that it's already starting + + align:start position:0% +technologies that it's already starting + + + align:start position:0% +technologies that it's already starting +to explore so it's typically you know + + align:start position:0% +to explore so it's typically you know + + + align:start position:0% +to explore so it's typically you know +want to do more incremental advances and + + align:start position:0% +want to do more incremental advances and + + + align:start position:0% +want to do more incremental advances and +it's only going to do those incremental + + align:start position:0% +it's only going to do those incremental + + + align:start position:0% +it's only going to do those incremental +advances if + + align:start position:0% +advances if + + + align:start position:0% +advances if +they can you know optimize them + + align:start position:0% +they can you know optimize them + + + align:start position:0% +they can you know optimize them +economically so an industry R&D project + + align:start position:0% +economically so an industry R&D project + + + align:start position:0% +economically so an industry R&D project +has got to go through a series of stage + + align:start position:0% +has got to go through a series of stage + + + align:start position:0% +has got to go through a series of stage +gates which essentially is a way of + + align:start position:0% +gates which essentially is a way of + + + align:start position:0% +gates which essentially is a way of +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +tearing down a large menu of stuff and + + align:start position:0% +tearing down a large menu of stuff and + + + align:start position:0% +tearing down a large menu of stuff and +getting to the most economically optimal + + align:start position:0% +getting to the most economically optimal + + + align:start position:0% +getting to the most economically optimal +industries stage-gate process is not a + + align:start position:0% +industries stage-gate process is not a + + + align:start position:0% +industries stage-gate process is not a +technology visioning system right it's + + align:start position:0% +technology visioning system right it's + + + align:start position:0% +technology visioning system right it's +not deciding on a vision and doing what + + align:start position:0% +not deciding on a vision and doing what + + + align:start position:0% +not deciding on a vision and doing what +everything that's already get there + + align:start position:0% +everything that's already get there + + + align:start position:0% +everything that's already get there +which the way diaper operates it's a + + align:start position:0% +which the way diaper operates it's a + + + align:start position:0% +which the way diaper operates it's a +much more limited set of procedural + + align:start position:0% +much more limited set of procedural + + + align:start position:0% +much more limited set of procedural +stage gates that technology ideas got to + + align:start position:0% +stage gates that technology ideas got to + + + align:start position:0% +stage gates that technology ideas got to +go through so DARPA is just working on a + + align:start position:0% +go through so DARPA is just working on a + + + align:start position:0% +go through so DARPA is just working on a +very different kind of organizational + + align:start position:0% +very different kind of organizational + + + align:start position:0% +very different kind of organizational +model from the way in which things are + + align:start position:0% +model from the way in which things are + + + align:start position:0% +model from the way in which things are +done either at other agencies or at or + + align:start position:0% +done either at other agencies or at or + + + align:start position:0% +done either at other agencies or at or +within industry and starting with this + + align:start position:0% +within industry and starting with this + + + align:start position:0% +within industry and starting with this +vision upfront is a really interesting + + align:start position:0% +vision upfront is a really interesting + + + align:start position:0% +vision upfront is a really interesting +organizational idea that you all should + + align:start position:0% +organizational idea that you all should + + + align:start position:0% +organizational idea that you all should +kind of keep in mind when you're + + align:start position:0% +kind of keep in mind when you're + + + align:start position:0% +kind of keep in mind when you're +operating out there and sin ape your own + + align:start position:0% +operating out there and sin ape your own + + + align:start position:0% +operating out there and sin ape your own +companies and doing your own startups so + + align:start position:0% +companies and doing your own startups so + + + align:start position:0% +companies and doing your own startups so +max you've got Tammy Carlton's piece the + + align:start position:0% +max you've got Tammy Carlton's piece the + + + align:start position:0% +max you've got Tammy Carlton's piece the +key step within Carlton's five steps + + align:start position:0% +key step within Carlton's five steps + + + align:start position:0% +key step within Carlton's five steps +that I thought was most interesting was + + align:start position:0% +that I thought was most interesting was + + + align:start position:0% +that I thought was most interesting was +the fifth one technology transfer which + + align:start position:0% +the fifth one technology transfer which + + + align:start position:0% +the fifth one technology transfer which +is supposed to bridge that the Rd the + + align:start position:0% +is supposed to bridge that the Rd the + + + align:start position:0% +is supposed to bridge that the Rd the +valley of death as it were that enables + + align:start position:0% +valley of death as it were that enables + + + align:start position:0% +valley of death as it were that enables +a different scientific idea to be + + align:start position:0% +a different scientific idea to be + + + align:start position:0% +a different scientific idea to be +commercialized and to actually affect + + align:start position:0% +commercialized and to actually affect + + + align:start position:0% +commercialized and to actually affect +people all over the world and eventually + + align:start position:0% +people all over the world and eventually + + + align:start position:0% +people all over the world and eventually +while reading I kind of realized that + + align:start position:0% +while reading I kind of realized that + + + align:start position:0% +while reading I kind of realized that +hey DARPA seems like they have a pretty + + align:start position:0% +hey DARPA seems like they have a pretty + + + align:start position:0% +hey DARPA seems like they have a pretty +decent organization they get things done + + align:start position:0% +decent organization they get things done + + + align:start position:0% +decent organization they get things done +relatively efficiently they have a lot + + align:start position:0% +relatively efficiently they have a lot + + + align:start position:0% +relatively efficiently they have a lot +of money why is it they have and I + + align:start position:0% +of money why is it they have and I + + + align:start position:0% +of money why is it they have and I +actually I just decided to start + + align:start position:0% +actually I just decided to start + + + align:start position:0% +actually I just decided to start +googling just to try to figure out if + + align:start position:0% +googling just to try to figure out if + + + align:start position:0% +googling just to try to figure out if +DARPA had done anything related to + + align:start position:0% +DARPA had done anything related to + + + align:start position:0% +DARPA had done anything related to +Fusion and I couldn't find anything so + + align:start position:0% +Fusion and I couldn't find anything so + + + align:start position:0% +Fusion and I couldn't find anything so +I'm curious why not I can actually door + + align:start position:0% +I'm curious why not I can actually door + + + align:start position:0% +I'm curious why not I can actually door +deferred on energy technologies to RPE + + align:start position:0% +deferred on energy technologies to RPE + + + align:start position:0% +deferred on energy technologies to RPE +okay when RP got stood up + + align:start position:0% +okay when RP got stood up + + + align:start position:0% +okay when RP got stood up +because DARPA views RP is + + align:start position:0% +because DARPA views RP is + + + align:start position:0% +because DARPA views RP is +a compatriot and rpe you know + + align:start position:0% +a compatriot and rpe you know + + + align:start position:0% +a compatriot and rpe you know +interesting he has done some extremely + + align:start position:0% +interesting he has done some extremely + + + align:start position:0% +interesting he has done some extremely +interesting work one on fusion right + + align:start position:0% +interesting work one on fusion right + + + align:start position:0% +interesting work one on fusion right +yeah but Lockheed Martin's whoa well + + align:start position:0% +yeah but Lockheed Martin's whoa well + + + align:start position:0% +yeah but Lockheed Martin's whoa well +they have the scar works when you do and + + align:start position:0% +they have the scar works when you do and + + + align:start position:0% +they have the scar works when you do and +darkus done an enormous amount of work + + align:start position:0% +darkus done an enormous amount of work + + + align:start position:0% +darkus done an enormous amount of work +with the skunk works overtime including + + align:start position:0% +with the skunk works overtime including + + + align:start position:0% +with the skunk works overtime including +still well I granted yes they definitely + + align:start position:0% +still well I granted yes they definitely + + + align:start position:0% +still well I granted yes they definitely +have the facilities they definitely have + + align:start position:0% +have the facilities they definitely have + + + align:start position:0% +have the facilities they definitely have +the project managers I just feel that + + align:start position:0% +the project managers I just feel that + + + align:start position:0% +the project managers I just feel that +it's a it's a bit of an area outside + + align:start position:0% +it's a it's a bit of an area outside + + + align:start position:0% +it's a it's a bit of an area outside +their expertise they're gonna + + align:start position:0% +their expertise they're gonna + + + align:start position:0% +their expertise they're gonna +accidentally make it fly right and look + + align:start position:0% +accidentally make it fly right and look + + + align:start position:0% +accidentally make it fly right and look +another issue for DARPA is remember + + align:start position:0% +another issue for DARPA is remember + + + align:start position:0% +another issue for DARPA is remember +these technologies have got to get stood + + align:start position:0% +these technologies have got to get stood + + + align:start position:0% +these technologies have got to get stood +up in the lifetime of the yeah project + + align:start position:0% +up in the lifetime of the yeah project + + + align:start position:0% +up in the lifetime of the yeah project +five seems like a five-year project so + + align:start position:0% +five seems like a five-year project so + + + align:start position:0% +five seems like a five-year project so +if you can't do it within five years + + align:start position:0% +if you can't do it within five years + + + align:start position:0% +if you can't do it within five years +it's very hard to put it on the DARPA + + align:start position:0% +it's very hard to put it on the DARPA + + + align:start position:0% +it's very hard to put it on the DARPA +agenda well you mentioned that some of + + align:start position:0% +agenda well you mentioned that some of + + + align:start position:0% +agenda well you mentioned that some of +the projects would get handed off to + + align:start position:0% +the projects would get handed off to + + + align:start position:0% +the projects would get handed off to +other project managers yeah that's how + + align:start position:0% +other project managers yeah that's how + + + align:start position:0% +other project managers yeah that's how +long a manager last right yes but it's + + align:start position:0% +long a manager last right yes but it's + + + align:start position:0% +long a manager last right yes but it's +not always how long a project was yes + + align:start position:0% +not always how long a project was yes + + + align:start position:0% +not always how long a project was yes +sometimes there can be intergenerational + + align:start position:0% +sometimes there can be intergenerational + + + align:start position:0% +sometimes there can be intergenerational +transfers and then look Lickliter + + align:start position:0% +transfers and then look Lickliter + + + align:start position:0% +transfers and then look Lickliter +develop different kind of system he + + align:start position:0% +develop different kind of system he + + + align:start position:0% +develop different kind of system he +created a community that kept continuing + + align:start position:0% +created a community that kept continuing + + + align:start position:0% +created a community that kept continuing +with the same kind of ethos working on + + align:start position:0% +with the same kind of ethos working on + + + align:start position:0% +with the same kind of ethos working on +that same set of agenda items working + + align:start position:0% +that same set of agenda items working + + + align:start position:0% +that same set of agenda items working +them down one after another and making + + align:start position:0% +them down one after another and making + + + align:start position:0% +them down one after another and making +progress year after year on each of them + + align:start position:0% +progress year after year on each of them + + + align:start position:0% +progress year after year on each of them +so that's a different kind of way that + + align:start position:0% +so that's a different kind of way that + + + align:start position:0% +so that's a different kind of way that +DARPA is gonna be organized but + + align:start position:0% +DARPA is gonna be organized but + + + align:start position:0% +DARPA is gonna be organized but +typically once the program manager leads + + align:start position:0% +typically once the program manager leads + + + align:start position:0% +typically once the program manager leads +who had the vision their job is to get + + align:start position:0% +who had the vision their job is to get + + + align:start position:0% +who had the vision their job is to get +that implemented in their in their in + + align:start position:0% +that implemented in their in their in + + + align:start position:0% +that implemented in their in their in +effect DARPA lifetime and if they + + align:start position:0% +effect DARPA lifetime and if they + + + align:start position:0% +effect DARPA lifetime and if they +haven't then it's hard for DARPA to + + align:start position:0% +haven't then it's hard for DARPA to + + + align:start position:0% +haven't then it's hard for DARPA to +continue that which you know we could + + align:start position:0% +continue that which you know we could + + + align:start position:0% +continue that which you know we could +view as a weakness of the program on the + + align:start position:0% +view as a weakness of the program on the + + + align:start position:0% +view as a weakness of the program on the +other hand you could view it as a + + align:start position:0% +other hand you could view it as a + + + align:start position:0% +other hand you could view it as a +strength yeah because then they make + + align:start position:0% +strength yeah because then they make + + + align:start position:0% +strength yeah because then they make +sure the things that if they are working + + align:start position:0% +sure the things that if they are working + + + align:start position:0% +sure the things that if they are working +then they keep they may proceed with it + + align:start position:0% +then they keep they may proceed with it + + + align:start position:0% +then they keep they may proceed with it +or they talk to someone else right yeah + + align:start position:0% + + + + align:start position:0% + +so speaking of Licklider actually while + + align:start position:0% +so speaking of Licklider actually while + + + align:start position:0% +so speaking of Licklider actually while +I was reading I noticed that look + + align:start position:0% +I was reading I noticed that look + + + align:start position:0% +I was reading I noticed that look +lighter had mentioned that he that he + + align:start position:0% +lighter had mentioned that he that he + + + align:start position:0% +lighter had mentioned that he that he +heavily relied on standardized tests + + align:start position:0% +heavily relied on standardized tests + + + align:start position:0% +heavily relied on standardized tests +when picking candidates so like that + + align:start position:0% +when picking candidates so like that + + + align:start position:0% +when picking candidates so like that +recruitment of great talent given that + + align:start position:0% +recruitment of great talent given that + + + align:start position:0% +recruitment of great talent given that +literally everyone in this room has + + align:start position:0% +literally everyone in this room has + + + align:start position:0% +literally everyone in this room has +experience with standardized testing and + + align:start position:0% +experience with standardized testing and + + + align:start position:0% +experience with standardized testing and +at least I can't speak for everyone but + + align:start position:0% +at least I can't speak for everyone but + + + align:start position:0% +at least I can't speak for everyone but +I don't like it very much + + align:start position:0% +I don't like it very much + + + align:start position:0% +I don't like it very much +I wonder if this which remember he was a + + align:start position:0% +I wonder if this which remember he was a + + + align:start position:0% +I wonder if this which remember he was a +psychologist coming out of the testing + + align:start position:0% +psychologist coming out of the testing + + + align:start position:0% +psychologist coming out of the testing +world right so that's probably part of + + align:start position:0% +world right so that's probably part of + + + align:start position:0% +world right so that's probably part of +the reason there's only so much + + align:start position:0% +the reason there's only so much + + + align:start position:0% +the reason there's only so much +sanitized test can tell you like they + + align:start position:0% +sanitized test can tell you like they + + + align:start position:0% +sanitized test can tell you like they +won't really tell you how you work with + + align:start position:0% +won't really tell you how you work with + + + align:start position:0% +won't really tell you how you work with +people they won't tell you anything + + align:start position:0% +people they won't tell you anything + + + align:start position:0% +people they won't tell you anything +about how you work on anything that's + + align:start position:0% +about how you work on anything that's + + + align:start position:0% +about how you work on anything that's +not related to I don't know math or + + align:start position:0% +not related to I don't know math or + + + align:start position:0% +not related to I don't know math or +literature he did come up with a pretty + + align:start position:0% +literature he did come up with a pretty + + + align:start position:0% +literature he did come up with a pretty +talented team though yeah especially + + align:start position:0% +talented team though yeah especially + + + align:start position:0% +talented team though yeah especially +when it comes to leadership because you + + align:start position:0% +when it comes to leadership because you + + + align:start position:0% +when it comes to leadership because you +have to figure it out really really good + + align:start position:0% +have to figure it out really really good + + + align:start position:0% +have to figure it out really really good +visionary leaders will go figure out is + + align:start position:0% +visionary leaders will go figure out is + + + align:start position:0% +visionary leaders will go figure out is +like okay they have ice they they're + + align:start position:0% +like okay they have ice they they're + + + align:start position:0% +like okay they have ice they they're +intellectuals introverts extroverts and + + align:start position:0% +intellectuals introverts extroverts and + + + align:start position:0% +intellectuals introverts extroverts and +they have a supporting type to their + + align:start position:0% +they have a supporting type to their + + + align:start position:0% +they have a supporting type to their +psyche psyche and then palate the Avatar + + align:start position:0% +psyche psyche and then palate the Avatar + + + align:start position:0% +psyche psyche and then palate the Avatar +have like team groups so like it's + + align:start position:0% +have like team groups so like it's + + + align:start position:0% +have like team groups so like it's +pretty good it's like + + align:start position:0% +pretty good it's like + + + align:start position:0% +pretty good it's like +leaders and I know it's been pretty + + align:start position:0% +leaders and I know it's been pretty + + + align:start position:0% +leaders and I know it's been pretty +effective in Madrid TV but you say to us + + align:start position:0% +effective in Madrid TV but you say to us + + + align:start position:0% +effective in Madrid TV but you say to us +it's also really good for the figure + + align:start position:0% +it's also really good for the figure + + + align:start position:0% +it's also really good for the figure +happens in be a really good a scientist + + align:start position:0% +happens in be a really good a scientist + + + align:start position:0% +happens in be a really good a scientist +because it's usually highly introverted + + align:start position:0% +because it's usually highly introverted + + + align:start position:0% +because it's usually highly introverted +new insights that doesn't follow up the + + align:start position:0% +new insights that doesn't follow up the + + + align:start position:0% +new insights that doesn't follow up the +crowd so I can see why that's important + + align:start position:0% +crowd so I can see why that's important + + + align:start position:0% +crowd so I can see why that's important +like the GRE might be but also liking + + align:start position:0% +like the GRE might be but also liking + + + align:start position:0% +like the GRE might be but also liking +that's your scores low but if you've + + align:start position:0% +that's your scores low but if you've + + + align:start position:0% +that's your scores low but if you've +come out with a good body of work then + + align:start position:0% +come out with a good body of work then + + + align:start position:0% +come out with a good body of work then +they can probably assume that you are + + align:start position:0% +they can probably assume that you are + + + align:start position:0% +they can probably assume that you are +pretty smart even if you didn't do long + + align:start position:0% +pretty smart even if you didn't do long + + + align:start position:0% +pretty smart even if you didn't do long +sentences + + align:start position:0% + + + + align:start position:0% + +because I'm Luton and it says that she + + align:start position:0% +because I'm Luton and it says that she + + + align:start position:0% +because I'm Luton and it says that she +has a her background is in communication + + align:start position:0% +has a her background is in communication + + + align:start position:0% +has a her background is in communication +and then she got a master's in public + + align:start position:0% +and then she got a master's in public + + + align:start position:0% +and then she got a master's in public +relations and then she did a PhD in + + align:start position:0% +relations and then she did a PhD in + + + align:start position:0% +relations and then she did a PhD in +mechanical engineering design but that + + align:start position:0% +mechanical engineering design but that + + + align:start position:0% +mechanical engineering design but that +must have been back in the day when the + + align:start position:0% +must have been back in the day when the + + + align:start position:0% +must have been back in the day when the +d.school at Stanford accepted + + align:start position:0% +d.school at Stanford accepted + + + align:start position:0% +d.school at Stanford accepted +non-engineers + + align:start position:0% +non-engineers + + + align:start position:0% +non-engineers +and non-scientists because now they + + align:start position:0% +and non-scientists because now they + + + align:start position:0% +and non-scientists because now they +don't so it would be curious to think + + align:start position:0% +don't so it would be curious to think + + + align:start position:0% +don't so it would be curious to think +about you know the ways in which her + + align:start position:0% +about you know the ways in which her + + + align:start position:0% +about you know the ways in which her +background in particular might give her + + align:start position:0% +background in particular might give her + + + align:start position:0% +background in particular might give her +that insight that might that an engineer + + align:start position:0% +that insight that might that an engineer + + + align:start position:0% +that insight that might that an engineer +might not have about this particular + + align:start position:0% +might not have about this particular + + + align:start position:0% +might not have about this particular +field right going back to the question + + align:start position:0% +field right going back to the question + + + align:start position:0% +field right going back to the question +of multi-disciplinary great groups but I + + align:start position:0% +of multi-disciplinary great groups but I + + + align:start position:0% +of multi-disciplinary great groups but I +don't know to what extent for example + + align:start position:0% +don't know to what extent for example + + + align:start position:0% +don't know to what extent for example +someone like me might be accepted and + + align:start position:0% +someone like me might be accepted and + + + align:start position:0% +someone like me might be accepted and +maybe like lily's them I know the most + + align:start position:0% +maybe like lily's them I know the most + + + align:start position:0% +maybe like lily's them I know the most +famous women in my field has an + + align:start position:0% +famous women in my field has an + + + align:start position:0% +famous women in my field has an +undergraduate degree in German + + align:start position:0% + + + + align:start position:0% + +is his agrees in history and he almost + + align:start position:0% +is his agrees in history and he almost + + + align:start position:0% +is his agrees in history and he almost +barely didn't pass he said like he's + + align:start position:0% +barely didn't pass he said like he's + + + align:start position:0% +barely didn't pass he said like he's +limits nightmares because he didn't + + align:start position:0% +limits nightmares because he didn't + + + align:start position:0% +limits nightmares because he didn't +Jesus + + align:start position:0% + + + + align:start position:0% + +all right so we're gonna move out of the + + align:start position:0% +all right so we're gonna move out of the + + + align:start position:0% +all right so we're gonna move out of the +testing world back to the DARPA world + + align:start position:0% +testing world back to the DARPA world + + + align:start position:0% +testing world back to the DARPA world +sure so one of the things that constant + + align:start position:0% +sure so one of the things that constant + + + align:start position:0% +sure so one of the things that constant +pointed out was that as DARPA has aged + + align:start position:0% +pointed out was that as DARPA has aged + + + align:start position:0% +pointed out was that as DARPA has aged +so to have its project managers like + + align:start position:0% +so to have its project managers like + + + align:start position:0% +so to have its project managers like +even though they cycle between new + + align:start position:0% +even though they cycle between new + + + align:start position:0% +even though they cycle between new +managers every like four or five years + + align:start position:0% +managers every like four or five years + + + align:start position:0% +managers every like four or five years +the age the average age of the managers + + align:start position:0% +the age the average age of the managers + + + align:start position:0% +the age the average age of the managers +that they would pick was going up + + align:start position:0% +that they would pick was going up + + + align:start position:0% +that they would pick was going up +steadily so I'm curious if anyone has + + align:start position:0% +steadily so I'm curious if anyone has + + + align:start position:0% +steadily so I'm curious if anyone has +thoughts on what the effect that would + + align:start position:0% +thoughts on what the effect that would + + + align:start position:0% +thoughts on what the effect that would +be on their managerial ability or on on + + align:start position:0% +be on their managerial ability or on on + + + align:start position:0% +be on their managerial ability or on on +DARPA steer direction of the whole yeah + + align:start position:0% +DARPA steer direction of the whole yeah + + + align:start position:0% +DARPA steer direction of the whole yeah +so the average age of the project + + align:start position:0% +so the average age of the project + + + align:start position:0% +so the average age of the project +managers has been increasing as DARPA + + align:start position:0% +managers has been increasing as DARPA + + + align:start position:0% +managers has been increasing as DARPA +has I don't remember the numbers yeah + + align:start position:0% +has I don't remember the numbers yeah + + + align:start position:0% +has I don't remember the numbers yeah +one of the reasons max you know maybe + + align:start position:0% +one of the reasons max you know maybe + + + align:start position:0% +one of the reasons max you know maybe +that it's I mean watching MIT it's very + + align:start position:0% +that it's I mean watching MIT it's very + + + align:start position:0% +that it's I mean watching MIT it's very +hard for younger faculty to walk out of + + align:start position:0% +hard for younger faculty to walk out of + + + align:start position:0% +hard for younger faculty to walk out of +the place right before they get tenure + + align:start position:0% +the place right before they get tenure + + + align:start position:0% +the place right before they get tenure +it's hard enough to walk out once you + + align:start position:0% +it's hard enough to walk out once you + + + align:start position:0% +it's hard enough to walk out once you +get tenure but it's impossible to walk + + align:start position:0% +get tenure but it's impossible to walk + + + align:start position:0% +get tenure but it's impossible to walk +out before you get tenure and because + + align:start position:0% +out before you get tenure and because + + + align:start position:0% +out before you get tenure and because +you're establishing a whole you know + + align:start position:0% +you're establishing a whole you know + + + align:start position:0% +you're establishing a whole you know +your research portfolio and your whole + + align:start position:0% +your research portfolio and your whole + + + align:start position:0% +your research portfolio and your whole +researching system and it's very hard to + + align:start position:0% +researching system and it's very hard to + + + align:start position:0% +researching system and it's very hard to +walk out of that in addition when you go + + align:start position:0% +walk out of that in addition when you go + + + align:start position:0% +walk out of that in addition when you go +to DARPA you've got a conflict once + + align:start position:0% +to DARPA you've got a conflict once + + + align:start position:0% +to DARPA you've got a conflict once +you've worked there you have a conflict + + align:start position:0% +you've worked there you have a conflict + + + align:start position:0% +you've worked there you have a conflict +of interest with DARPA Yukie you're not + + align:start position:0% +of interest with DARPA Yukie you're not + + + align:start position:0% +of interest with DARPA Yukie you're not +gonna be able to deal with the agency + + align:start position:0% +gonna be able to deal with the agency + + + align:start position:0% +gonna be able to deal with the agency +for a certain period of time so if they + + align:start position:0% +for a certain period of time so if they + + + align:start position:0% +for a certain period of time so if they +happen to be funding your research + + align:start position:0% +happen to be funding your research + + + align:start position:0% +happen to be funding your research +before they're not kind of able to + + align:start position:0% +before they're not kind of able to + + + align:start position:0% +before they're not kind of able to +continue funding your research once + + align:start position:0% +continue funding your research once + + + align:start position:0% +continue funding your research once +you've worked there so it's gotten more + + align:start position:0% +you've worked there so it's gotten more + + + align:start position:0% +you've worked there so it's gotten more +complicated for DARPA to recruit at the + + align:start position:0% +complicated for DARPA to recruit at the + + + align:start position:0% +complicated for DARPA to recruit at the +university level it's gotten a lot more + + align:start position:0% +university level it's gotten a lot more + + + align:start position:0% +university level it's gotten a lot more +difficult so the route between MIT and + + align:start position:0% +difficult so the route between MIT and + + + align:start position:0% +difficult so the route between MIT and +DARPA frankly used to be a lot easier to + + align:start position:0% +DARPA frankly used to be a lot easier to + + + align:start position:0% +DARPA frankly used to be a lot easier to +manage and when I look at MIT colleagues + + align:start position:0% +manage and when I look at MIT colleagues + + + align:start position:0% +manage and when I look at MIT colleagues +here who have gone to DARPA they're they + + align:start position:0% +here who have gone to DARPA they're they + + + align:start position:0% +here who have gone to DARPA they're they +they are more typically fairly far along + + align:start position:0% +they are more typically fairly far along + + + align:start position:0% +they are more typically fairly far along +and very assured about their career and + + align:start position:0% +and very assured about their career and + + + align:start position:0% +and very assured about their career and +their research foundation and the + + align:start position:0% +their research foundation and the + + + align:start position:0% +their research foundation and the +writing they've done that stuff and they + + align:start position:0% +writing they've done that stuff and they + + + align:start position:0% +writing they've done that stuff and they +can take a three or five year break and + + align:start position:0% +can take a three or five year break and + + + align:start position:0% +can take a three or five year break and +get that really big visionary thing that + + align:start position:0% +get that really big visionary thing that + + + align:start position:0% +get that really big visionary thing that +they've wanted to work on forever done + + align:start position:0% +they've wanted to work on forever done + + + align:start position:0% +they've wanted to work on forever done +when they go to DARPA but it's + + align:start position:0% +when they go to DARPA but it's + + + align:start position:0% +when they go to DARPA but it's +harder when you're trying to administer + + align:start position:0% +harder when you're trying to administer + + + align:start position:0% +harder when you're trying to administer +a whole research portfolio again with + + align:start position:0% +a whole research portfolio again with + + + align:start position:0% +a whole research portfolio again with +the IPA Authority you've got a certain + + align:start position:0% +the IPA Authority you've got a certain + + + align:start position:0% +the IPA Authority you've got a certain +freedom to come back to your + + align:start position:0% +freedom to come back to your + + + align:start position:0% +freedom to come back to your +organization and keep the day-to-day + + align:start position:0% +organization and keep the day-to-day + + + align:start position:0% +organization and keep the day-to-day +stuff going but it's still not simple so + + align:start position:0% +stuff going but it's still not simple so + + + align:start position:0% +stuff going but it's still not simple so +that may be one part of the reason that + + align:start position:0% +that may be one part of the reason that + + + align:start position:0% +that may be one part of the reason that +you tend to get somewhat older faculty + + align:start position:0% +you tend to get somewhat older faculty + + + align:start position:0% +you tend to get somewhat older faculty +than they probably used to at the + + align:start position:0% +than they probably used to at the + + + align:start position:0% +than they probably used to at the +beginning I think having to kind of + + align:start position:0% +beginning I think having to kind of + + + align:start position:0% +beginning I think having to kind of +establish yourself and figure out what + + align:start position:0% +establish yourself and figure out what + + + align:start position:0% +establish yourself and figure out what +your vision is you have more time you're + + align:start position:0% +your vision is you have more time you're + + + align:start position:0% +your vision is you have more time you're +older to like happy business yeah and + + align:start position:0% +older to like happy business yeah and + + + align:start position:0% +older to like happy business yeah and +perspective as well just thinking about + + align:start position:0% +perspective as well just thinking about + + + align:start position:0% +perspective as well just thinking about +advisers I've had over the years and + + align:start position:0% +advisers I've had over the years and + + + align:start position:0% +advisers I've had over the years and +younger or newer advisers versus more + + align:start position:0% +younger or newer advisers versus more + + + align:start position:0% +younger or newer advisers versus more +established advisers they definitely + + align:start position:0% +established advisers they definitely + + + align:start position:0% +established advisers they definitely +have a different perspective + + align:start position:0% +have a different perspective + + + align:start position:0% +have a different perspective +and yeah NASA is actually having the + + align:start position:0% +and yeah NASA is actually having the + + + align:start position:0% +and yeah NASA is actually having the +same phenomenon of having directors who + + align:start position:0% +same phenomenon of having directors who + + + align:start position:0% +same phenomenon of having directors who +are progressively older and older for + + align:start position:0% +are progressively older and older for + + + align:start position:0% +are progressively older and older for +that very same thing + + align:start position:0% +that very same thing + + + align:start position:0% +that very same thing +can it it's very difficult to draw + + align:start position:0% +can it it's very difficult to draw + + + align:start position:0% +can it it's very difficult to draw +someone away from a mid-range career at + + align:start position:0% +someone away from a mid-range career at + + + align:start position:0% +someone away from a mid-range career at +they're being very successful at having + + align:start position:0% +they're being very successful at having + + + align:start position:0% +they're being very successful at having +success getting grants and it's hard to + + align:start position:0% +success getting grants and it's hard to + + + align:start position:0% +success getting grants and it's hard to +get them into administration or director + + align:start position:0% +get them into administration or director + + + align:start position:0% +get them into administration or director +chefs are management what even the + + align:start position:0% +chefs are management what even the + + + align:start position:0% +chefs are management what even the +difference between young + + align:start position:0% + + + + align:start position:0% + +in general the actually the more + + align:start position:0% +in general the actually the more + + + align:start position:0% +in general the actually the more +established and older advisors that I've + + align:start position:0% +established and older advisors that I've + + + align:start position:0% +established and older advisors that I've +had have had a lot more perspicacity + + align:start position:0% +had have had a lot more perspicacity + + + align:start position:0% +had have had a lot more perspicacity +with respect to what projects are + + align:start position:0% +with respect to what projects are + + + align:start position:0% +with respect to what projects are +worthwhile actually or through its long + + align:start position:0% +worthwhile actually or through its long + + + align:start position:0% +worthwhile actually or through its long +experience you're suggesting because + + align:start position:0% +experience you're suggesting because + + + align:start position:0% +experience you're suggesting because +they've seen a lot yeah next up in + + align:start position:0% +they've seen a lot yeah next up in + + + align:start position:0% +they've seen a lot yeah next up in +another question I'm sure + + align:start position:0% + + + + align:start position:0% + +um so carlton mentioned that DARPA in + + align:start position:0% +um so carlton mentioned that DARPA in + + + align:start position:0% +um so carlton mentioned that DARPA in +order to save time when they are trying + + align:start position:0% +order to save time when they are trying + + + align:start position:0% +order to save time when they are trying +to develop these projects they tried to + + align:start position:0% +to develop these projects they tried to + + + align:start position:0% +to develop these projects they tried to +discourage consensus but I didn't really + + align:start position:0% +discourage consensus but I didn't really + + + align:start position:0% +discourage consensus but I didn't really +see as a I think was the second the next + + align:start position:0% +see as a I think was the second the next + + + align:start position:0% +see as a I think was the second the next +slide you have yeah so like I I + + align:start position:0% +slide you have yeah so like I I + + + align:start position:0% +slide you have yeah so like I I +understand why because then it ensures + + align:start position:0% +understand why because then it ensures + + + align:start position:0% +understand why because then it ensures +that whatever you're trying to develop + + align:start position:0% +that whatever you're trying to develop + + + align:start position:0% +that whatever you're trying to develop +it gets done quickly but just because if + + align:start position:0% +it gets done quickly but just because if + + + align:start position:0% +it gets done quickly but just because if +it gets done quickly doesn't really mean + + align:start position:0% +it gets done quickly doesn't really mean + + + align:start position:0% +it gets done quickly doesn't really mean +that it gets done right so I I guess I + + align:start position:0% +that it gets done right so I I guess I + + + align:start position:0% +that it gets done right so I I guess I +was curious what people thought on the + + align:start position:0% +was curious what people thought on the + + + align:start position:0% +was curious what people thought on the +that specifically that decision yeah + + align:start position:0% +that specifically that decision yeah + + + align:start position:0% +that specifically that decision yeah +it's a very interesting point max and + + align:start position:0% +it's a very interesting point max and + + + align:start position:0% +it's a very interesting point max and +actually RPE and we'll talk about it + + align:start position:0% +actually RPE and we'll talk about it + + + align:start position:0% +actually RPE and we'll talk about it +when we get the RPE but and and the + + align:start position:0% +when we get the RPE but and and the + + + align:start position:0% +when we get the RPE but and and the +energy class but RP does have a process + + align:start position:0% +energy class but RP does have a process + + + align:start position:0% +energy class but RP does have a process +it's much smaller agency so it's 300 + + align:start position:0% +it's much smaller agency so it's 300 + + + align:start position:0% +it's much smaller agency so it's 300 +million not three billion like DARPA so + + align:start position:0% +million not three billion like DARPA so + + + align:start position:0% +million not three billion like DARPA so +it's like a big DARPA office you know + + align:start position:0% +it's like a big DARPA office you know + + + align:start position:0% +it's like a big DARPA office you know +sizable Dipel office when one of its + + align:start position:0% +sizable Dipel office when one of its + + + align:start position:0% +sizable Dipel office when one of its +five or six offices so RP does have a + + align:start position:0% +five or six offices so RP does have a + + + align:start position:0% +five or six offices so RP does have a +consensus process they bring in they + + align:start position:0% +consensus process they bring in they + + + align:start position:0% +consensus process they bring in they +call them project directors but their + + align:start position:0% +call them project directors but their + + + align:start position:0% +call them project directors but their +program managers and that community + + align:start position:0% +program managers and that community + + + align:start position:0% +program managers and that community +really you have to present your vision + + align:start position:0% +really you have to present your vision + + + align:start position:0% +really you have to present your vision +to that community and that's a very + + align:start position:0% +to that community and that's a very + + + align:start position:0% +to that community and that's a very +tough-minded group and a very + + align:start position:0% +tough-minded group and a very + + + align:start position:0% +tough-minded group and a very +sophisticated group and and the director + + align:start position:0% +sophisticated group and and the director + + + align:start position:0% +sophisticated group and and the director +is quite sophisticated at DARPA so RB is + + align:start position:0% +is quite sophisticated at DARPA so RB is + + + align:start position:0% +is quite sophisticated at DARPA so RB is +historically as well so they did a + + align:start position:0% +historically as well so they did a + + + align:start position:0% +historically as well so they did a +variation on this at DARPA it's much + + align:start position:0% +variation on this at DARPA it's much + + + align:start position:0% +variation on this at DARPA it's much +more convinced your office director and + + align:start position:0% +more convinced your office director and + + + align:start position:0% +more convinced your office director and +then the office director will work with + + align:start position:0% +then the office director will work with + + + align:start position:0% +then the office director will work with +you on convincing that director of DARPA + + align:start position:0% +you on convincing that director of DARPA + + + align:start position:0% +you on convincing that director of DARPA +it's a simpler more straightforward + + align:start position:0% +it's a simpler more straightforward + + + align:start position:0% +it's a simpler more straightforward +process you do get support from other + + align:start position:0% +process you do get support from other + + + align:start position:0% +process you do get support from other +program managers who will have a lot of + + align:start position:0% +program managers who will have a lot of + + + align:start position:0% +program managers who will have a lot of +advice and ideas for you so it's a + + align:start position:0% +advice and ideas for you so it's a + + + align:start position:0% +advice and ideas for you so it's a +pretty supportive operation nobody's in + + align:start position:0% +pretty supportive operation nobody's in + + + align:start position:0% +pretty supportive operation nobody's in +competition with each other they're + + align:start position:0% +competition with each other they're + + + align:start position:0% +competition with each other they're +there to help each other so that's a + + align:start position:0% +there to help each other so that's a + + + align:start position:0% +there to help each other so that's a +positive although again they're + + align:start position:0% +positive although again they're + + + align:start position:0% +positive although again they're +competing to achieve their vision and + + align:start position:0% +competing to achieve their vision and + + + align:start position:0% +competing to achieve their vision and +everybody kind of knows who's getting + + align:start position:0% +everybody kind of knows who's getting + + + align:start position:0% +everybody kind of knows who's getting +their vision done and kind of who is in + + align:start position:0% +their vision done and kind of who is in + + + align:start position:0% +their vision done and kind of who is in +trouble with their visions so that's + + align:start position:0% +trouble with their visions so that's + + + align:start position:0% +trouble with their visions so that's +kind of known understood as a certain + + align:start position:0% +kind of known understood as a certain + + + align:start position:0% +kind of known understood as a certain +kind of competition in that way but it's + + align:start position:0% +kind of competition in that way but it's + + + align:start position:0% +kind of competition in that way but it's +not a direct one-on-one competition with + + align:start position:0% +not a direct one-on-one competition with + + + align:start position:0% +not a direct one-on-one competition with +each other but at Rp there is more + + align:start position:0% +each other but at Rp there is more + + + align:start position:0% +each other but at Rp there is more +consensus decision-making and you know + + align:start position:0% +consensus decision-making and you know + + + align:start position:0% +consensus decision-making and you know +Lou yo and she was telling us about + + align:start position:0% +Lou yo and she was telling us about + + + align:start position:0% +Lou yo and she was telling us about +Xerox PARC remember your whole + + align:start position:0% +Xerox PARC remember your whole + + + align:start position:0% +Xerox PARC remember your whole +discussion about the dealer process and + + align:start position:0% +discussion about the dealer process and + + + align:start position:0% +discussion about the dealer process and +having to bring your idea to the whole + + align:start position:0% +having to bring your idea to the whole + + + align:start position:0% +having to bring your idea to the whole +team sitting around on beanbags who + + align:start position:0% +team sitting around on beanbags who + + + align:start position:0% +team sitting around on beanbags who +would tear it apart that's that's kind + + align:start position:0% +would tear it apart that's that's kind + + + align:start position:0% +would tear it apart that's that's kind +of a consensus process it's it's a + + align:start position:0% +of a consensus process it's it's a + + + align:start position:0% +of a consensus process it's it's a +definite tough-minded review process + + align:start position:0% +definite tough-minded review process + + + align:start position:0% +definite tough-minded review process +that DARPA doesn't really quite have so + + align:start position:0% +that DARPA doesn't really quite have so + + + align:start position:0% +that DARPA doesn't really quite have so +there may be strengths and weaknesses in + + align:start position:0% +there may be strengths and weaknesses in + + + align:start position:0% +there may be strengths and weaknesses in +both models max what do you think on + + align:start position:0% +both models max what do you think on + + + align:start position:0% +both models max what do you think on +that + + align:start position:0% + + + + align:start position:0% + +yeah I could see that the strengths and + + align:start position:0% +yeah I could see that the strengths and + + + align:start position:0% +yeah I could see that the strengths and +weaknesses of both works it just feels + + align:start position:0% +weaknesses of both works it just feels + + + align:start position:0% +weaknesses of both works it just feels +if you have less consensus than you have + + align:start position:0% +if you have less consensus than you have + + + align:start position:0% +if you have less consensus than you have +and less if you have fewer people that + + align:start position:0% +and less if you have fewer people that + + + align:start position:0% +and less if you have fewer people that +are trying to discuss these ideas then + + align:start position:0% +are trying to discuss these ideas then + + + align:start position:0% +are trying to discuss these ideas then +there might be some critical flaw that + + align:start position:0% +there might be some critical flaw that + + + align:start position:0% +there might be some critical flaw that +you might not that you might dismiss + + align:start position:0% +you might not that you might dismiss + + + align:start position:0% +you might not that you might dismiss +just because there are fewer people with + + align:start position:0% +just because there are fewer people with + + + align:start position:0% +just because there are fewer people with +more diverse experiences of course if + + align:start position:0% +more diverse experiences of course if + + + align:start position:0% +more diverse experiences of course if +you have a decent idea of the science + + align:start position:0% +you have a decent idea of the science + + + align:start position:0% +you have a decent idea of the science +behind it and you it's not something as + + align:start position:0% +behind it and you it's not something as + + + align:start position:0% +behind it and you it's not something as +untested as fusion for example then I + + align:start position:0% +untested as fusion for example then I + + + align:start position:0% +untested as fusion for example then I +then I can see it working pretty well if + + align:start position:0% +then I can see it working pretty well if + + + align:start position:0% +then I can see it working pretty well if +I mean if you had to do that first + + align:start position:0% +I mean if you had to do that first + + + align:start position:0% +I mean if you had to do that first +I could see it having problems with + + align:start position:0% +I could see it having problems with + + + align:start position:0% +I could see it having problems with +something untested like stealth but + + align:start position:0% +something untested like stealth but + + + align:start position:0% +something untested like stealth but +apparently they made it work so maybe + + align:start position:0% +apparently they made it work so maybe + + + align:start position:0% +apparently they made it work so maybe +there go there passing my expectations + + align:start position:0% +there go there passing my expectations + + + align:start position:0% +there go there passing my expectations +it's looking at a perspective like it's + + align:start position:0% +it's looking at a perspective like it's + + + align:start position:0% +it's looking at a perspective like it's +pretty common mantra to say like you + + align:start position:0% +pretty common mantra to say like you + + + align:start position:0% +pretty common mantra to say like you +want to have an idea that people kind of + + align:start position:0% +want to have an idea that people kind of + + + align:start position:0% +want to have an idea that people kind of +say it's not a good idea because like + + align:start position:0% +say it's not a good idea because like + + + align:start position:0% +say it's not a good idea because like +the idea is if you come up with + + align:start position:0% +the idea is if you come up with + + + align:start position:0% +the idea is if you come up with +something that's pretty innovative most + + align:start position:0% +something that's pretty innovative most + + + align:start position:0% +something that's pretty innovative most +likely people won't agree with it or it + + align:start position:0% +likely people won't agree with it or it + + + align:start position:0% +likely people won't agree with it or it +doesn't make sense or you have an + + align:start position:0% +doesn't make sense or you have an + + + align:start position:0% +doesn't make sense or you have an +insight that other people don't get also + + align:start position:0% +insight that other people don't get also + + + align:start position:0% +insight that other people don't get also +if you're an expert you probably know + + align:start position:0% +if you're an expert you probably know + + + align:start position:0% +if you're an expert you probably know +some things that other people don't know + + align:start position:0% +some things that other people don't know + + + align:start position:0% +some things that other people don't know +that you have to bring them up to speed + + align:start position:0% +that you have to bring them up to speed + + + align:start position:0% +that you have to bring them up to speed +on especially if it's a totally new area + + align:start position:0% +on especially if it's a totally new area + + + align:start position:0% +on especially if it's a totally new area +and so the history has been out there + + align:start position:0% +and so the history has been out there + + + align:start position:0% +and so the history has been out there +just saying that for new fields who was + + align:start position:0% +just saying that for new fields who was + + + align:start position:0% +just saying that for new fields who was +the expert right it wouldn't be a PhD + + align:start position:0% +the expert right it wouldn't be a PhD + + + align:start position:0% +the expert right it wouldn't be a PhD +because if you love + + align:start position:0% +because if you love + + + align:start position:0% +because if you love +it's it's this person who just started + + align:start position:0% +it's it's this person who just started + + + align:start position:0% +it's it's this person who just started +working on it so Bill Gates was an + + align:start position:0% +working on it so Bill Gates was an + + + align:start position:0% +working on it so Bill Gates was an +expert on uh first on software for + + align:start position:0% +expert on uh first on software for + + + align:start position:0% +expert on uh first on software for +personal computers before that even + + align:start position:0% +personal computers before that even + + + align:start position:0% +personal computers before that even +became a thing so it's very common to + + align:start position:0% +became a thing so it's very common to + + + align:start position:0% +became a thing so it's very common to +contends is actually really bad because + + align:start position:0% +contends is actually really bad because + + + align:start position:0% +contends is actually really bad because +you put down these ideas based on new + + align:start position:0% +you put down these ideas based on new + + + align:start position:0% +you put down these ideas based on new +insights yeah and another because you + + align:start position:0% +insights yeah and another because you + + + align:start position:0% +insights yeah and another because you +have to you have to assume memories I + + align:start position:0% +have to you have to assume memories I + + + align:start position:0% +have to you have to assume memories I +could have a group in which all members + + align:start position:0% +could have a group in which all members + + + align:start position:0% +could have a group in which all members +have a personality type that they will + + align:start position:0% +have a personality type that they will + + + align:start position:0% +have a personality type that they will +concede to someone else's idea or get + + align:start position:0% +concede to someone else's idea or get + + + align:start position:0% +concede to someone else's idea or get +consensus even if it's not their pet + + align:start position:0% +consensus even if it's not their pet + + + align:start position:0% +consensus even if it's not their pet +project or their favorite you know + + align:start position:0% +project or their favorite you know + + + align:start position:0% +project or their favorite you know +anything and some people aren't supposed + + align:start position:0% +anything and some people aren't supposed + + + align:start position:0% +anything and some people aren't supposed +to do that no matter what + + align:start position:0% + + + + align:start position:0% + +how about a closing thought on this + + align:start position:0% +how about a closing thought on this + + + align:start position:0% +how about a closing thought on this +Thanks sure so overall I feel that DARPA + + align:start position:0% +Thanks sure so overall I feel that DARPA + + + align:start position:0% +Thanks sure so overall I feel that DARPA +seems to have been a pretty great + + align:start position:0% +seems to have been a pretty great + + + align:start position:0% +seems to have been a pretty great +success they've made lots of really cool + + align:start position:0% +success they've made lots of really cool + + + align:start position:0% +success they've made lots of really cool +projects they do it very quickly + + align:start position:0% +projects they do it very quickly + + + align:start position:0% +projects they do it very quickly +not sure how cheaply they do it but they + + align:start position:0% +not sure how cheaply they do it but they + + + align:start position:0% +not sure how cheaply they do it but they +get it done and because of that + + align:start position:0% +get it done and because of that + + + align:start position:0% +get it done and because of that +continued success I feel that they that + + align:start position:0% +continued success I feel that they that + + + align:start position:0% +continued success I feel that they that +that's probably why they continue to get + + align:start position:0% +that's probably why they continue to get + + + align:start position:0% +that's probably why they continue to get +so much funding I really try to + + align:start position:0% +so much funding I really try to + + + align:start position:0% +so much funding I really try to +emphasize that technology transfer + + align:start position:0% +emphasize that technology transfer + + + align:start position:0% +emphasize that technology transfer +aspect because it ensures that the + + align:start position:0% +aspect because it ensures that the + + + align:start position:0% +aspect because it ensures that the +technology that they develop isn't just + + align:start position:0% +technology that they develop isn't just + + + align:start position:0% +technology that they develop isn't just +oh it's a nice new toy for the military + + align:start position:0% +oh it's a nice new toy for the military + + + align:start position:0% +oh it's a nice new toy for the military +to have it ensures that whatever they + + align:start position:0% +to have it ensures that whatever they + + + align:start position:0% +to have it ensures that whatever they +make from the internet GPS etc that + + align:start position:0% +make from the internet GPS etc that + + + align:start position:0% +make from the internet GPS etc that +everyone can use it + + align:start position:0% +everyone can use it + + + align:start position:0% +everyone can use it +and that it makes our entire society + + align:start position:0% +and that it makes our entire society + + + align:start position:0% +and that it makes our entire society +better so yeah I guess that's pretty + + align:start position:0% +better so yeah I guess that's pretty + + + align:start position:0% +better so yeah I guess that's pretty +much just why I like DARPA there's a lot + + align:start position:0% +much just why I like DARPA there's a lot + + + align:start position:0% +much just why I like DARPA there's a lot +of my Tivo cool all right let me do a + + align:start position:0% +of my Tivo cool all right let me do a + + + align:start position:0% +of my Tivo cool all right let me do a +quick wrap-up of of today's class so we + + align:start position:0% +quick wrap-up of of today's class so we + + + align:start position:0% +quick wrap-up of of today's class so we +did Mitch Walters book and it's really I + + align:start position:0% +did Mitch Walters book and it's really I + + + align:start position:0% +did Mitch Walters book and it's really I +really wanted to kind of portray the + + align:start position:0% +really wanted to kind of portray the + + + align:start position:0% +really wanted to kind of portray the +governmental role in supporting me + + align:start position:0% +governmental role in supporting me + + + align:start position:0% +governmental role in supporting me +you know the earlier stage of the + + align:start position:0% +you know the earlier stage of the + + + align:start position:0% +you know the earlier stage of the +evolution of computing it was a proving + + align:start position:0% +evolution of computing it was a proving + + + align:start position:0% +evolution of computing it was a proving +ground for new concepts and designs and + + align:start position:0% +ground for new concepts and designs and + + + align:start position:0% +ground for new concepts and designs and +architectures it created the Defense + + align:start position:0% +architectures it created the Defense + + + align:start position:0% +architectures it created the Defense +Department created an initial market for + + align:start position:0% +Department created an initial market for + + + align:start position:0% +Department created an initial market for +a lot of new products and services and + + align:start position:0% +a lot of new products and services and + + + align:start position:0% +a lot of new products and services and +in fact whole industries this greatly + + align:start position:0% +in fact whole industries this greatly + + + align:start position:0% +in fact whole industries this greatly +expanded university research + + align:start position:0% +expanded university research + + + align:start position:0% +expanded university research +capabilities the computing revolution + + align:start position:0% +capabilities the computing revolution + + + align:start position:0% +capabilities the computing revolution +and you know it was done to further + + align:start position:0% +and you know it was done to further + + + align:start position:0% +and you know it was done to further +governmental missions but it had + + align:start position:0% +governmental missions but it had + + + align:start position:0% +governmental missions but it had +obviously a dramatic societal effects so + + align:start position:0% +obviously a dramatic societal effects so + + + align:start position:0% +obviously a dramatic societal effects so +it featured governmental agencies + + align:start position:0% +it featured governmental agencies + + + align:start position:0% +it featured governmental agencies +playing a pretty central role DARPA as + + align:start position:0% +playing a pretty central role DARPA as + + + align:start position:0% +playing a pretty central role DARPA as +we discussed was critical but some of + + align:start position:0% +we discussed was critical but some of + + + align:start position:0% +we discussed was critical but some of +the others were were necessary and + + align:start position:0% +the others were were necessary and + + + align:start position:0% +the others were were necessary and +needed and the governmental agencies + + align:start position:0% +needed and the governmental agencies + + + align:start position:0% +needed and the governmental agencies +sponsored these industry University + + align:start position:0% +sponsored these industry University + + + align:start position:0% +sponsored these industry University +collaborations that led to great + + align:start position:0% +collaborations that led to great + + + align:start position:0% +collaborations that led to great +strength in the university side and + + align:start position:0% +strength in the university side and + + + align:start position:0% +strength in the university side and +focus areas around them so in the in the + + align:start position:0% +focus areas around them so in the in the + + + align:start position:0% +focus areas around them so in the in the +reading that we did from the textbook + + align:start position:0% +reading that we did from the textbook + + + align:start position:0% +reading that we did from the textbook +the essential point here was that DARPA + + align:start position:0% +the essential point here was that DARPA + + + align:start position:0% +the essential point here was that DARPA +was uniquely able to combine an + + align:start position:0% +was uniquely able to combine an + + + align:start position:0% +was uniquely able to combine an +innovation institutional role as well as + + align:start position:0% +innovation institutional role as well as + + + align:start position:0% +innovation institutional role as well as +a great group's innovation at the + + align:start position:0% +a great group's innovation at the + + + align:start position:0% +a great group's innovation at the +face-to-face level kind of role you know + + align:start position:0% +face-to-face level kind of role you know + + + align:start position:0% +face-to-face level kind of role you know +that's a remarkable accomplishment and + + align:start position:0% +that's a remarkable accomplishment and + + + align:start position:0% +that's a remarkable accomplishment and +then DARP his ability as we talked about + + align:start position:0% +then DARP his ability as we talked about + + + align:start position:0% +then DARP his ability as we talked about +and Tim in in that reading as well to + + align:start position:0% +and Tim in in that reading as well to + + + align:start position:0% +and Tim in in that reading as well to +innovate in a legacy sector to do a + + align:start position:0% +innovate in a legacy sector to do a + + + align:start position:0% +innovate in a legacy sector to do a +frontier sector like IT but also + + align:start position:0% +frontier sector like IT but also + + + align:start position:0% +frontier sector like IT but also +innovate within a legacy sector and do + + align:start position:0% +innovate within a legacy sector and do + + + align:start position:0% +innovate within a legacy sector and do +things like stealth and UAVs that's a + + align:start position:0% +things like stealth and UAVs that's a + + + align:start position:0% +things like stealth and UAVs that's a +pretty fascinating organization that's + + align:start position:0% +pretty fascinating organization that's + + + align:start position:0% +pretty fascinating organization that's +flexible and interesting and and able to + + align:start position:0% +flexible and interesting and and able to + + + align:start position:0% +flexible and interesting and and able to +do great stuff Glenn Fong's piece was + + align:start position:0% +do great stuff Glenn Fong's piece was + + + align:start position:0% +do great stuff Glenn Fong's piece was +really about DARPA playing the central + + align:start position:0% +really about DARPA playing the central + + + align:start position:0% +really about DARPA playing the central +institutional mobilization role for the + + align:start position:0% +institutional mobilization role for the + + + align:start position:0% +institutional mobilization role for the +IT revolution and Tammy Carlton's piece + + align:start position:0% +IT revolution and Tammy Carlton's piece + + + align:start position:0% +IT revolution and Tammy Carlton's piece +really told us about this kind of + + align:start position:0% +really told us about this kind of + + + align:start position:0% +really told us about this kind of +central importance of technology + + align:start position:0% +central importance of technology + + + align:start position:0% +central importance of technology +visioning as a key modus operandi that + + align:start position:0% +visioning as a key modus operandi that + + + align:start position:0% +visioning as a key modus operandi that +that DARPA has been able to operate in + + align:start position:0% +that DARPA has been able to operate in + + + align:start position:0% +that DARPA has been able to operate in +any closing questions good luck with + + align:start position:0% +any closing questions good luck with + + + align:start position:0% +any closing questions good luck with +your paper outlines let me know if you + + align:start position:0% +your paper outlines let me know if you + + + align:start position:0% +your paper outlines let me know if you +have questions and I look forward to + + align:start position:0% +have questions and I look forward to + + + align:start position:0% +have questions and I look forward to +seeing you on Tuesday \ No newline at end of file diff --git a/opL7d8vY0KA.txt b/opL7d8vY0KA.txt new file mode 100644 index 0000000000000000000000000000000000000000..89604f7ae137dd4f42e3a33b59a52d9e9ff72ef9 --- /dev/null +++ b/opL7d8vY0KA.txt @@ -0,0 +1,3043 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation, or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So we are going +to switch directions. + +Rather than thinking +about binary variables, + +these Ising variables, +that were discrete, + +think again about a lattice. + +But now at each site we put a +spin that has unit magnitude, + +but m component. + +That is, Si has +components 1, 2, to n. + +And the constraint that this +sum over alpha Si alpha squared + +is unit. + +So clearly, if I-- let's +put it here explicitly. + +Alpha of 1 to n, so that's +when I look at the case of n + +equals to 1, essentially +I have one component. + +2 squared has to be 1, so +it's either plus or minus. + +We recover the Ising variable. + +For n equals to 2, +it's essentially + +a unit vector who's +angle theta, for example, + +can change in three dimensions +if we were exploring + +the surface of the cube. + +And we always +assume that we have + +a weight that tends to make +our spins to be parallel. + +So we use, essentially, the +same form as the Ising model. + +We sum over near neighbors. + +And the interaction, +rather than sigma I sigma + +j, we put it as this +Si dot Sj, where + +these are the dot +products of two vectors. + +Let's call the dimensionless +interaction in front K0. + +So when we want to calculate +the partition function, + +we need to integrate +over all configurations + +of these spins of this weight. + +Now for each case, we +have to do n components. + +But there is a constraint, +which is this one. + +Now I'm going to be focused +on the ground state. + +So when t equals to 0, we +expect that spontaneously + +the particular configuration +will be chosen. + +Everybody will be aligned +to that configuration. + +Without loss of generality, +let's choose aligned state + +to point along the +last component. + +That is, all of the +Si at t equal to 0 + +will be of the form 0,0, except +that the last component is + +pointing along some +particular direction. + +So if it was two components, the +y component would always be 1. + +It would be aligned +along the y direction. + +Yes, question? + +AUDIENCE: What dimensionality +is the lattice? + +PROFESSOR: It can be anything. + +So basically we have two +parameters, as usual. + +n is the dimensionality +of spin, and d + +would be the dimensionality +of our lattice. + +In practice for what +the calculations + +that we are going +to be doing, we + +will be focusing in +d that is close to 2. + +Now if the odd fluctuations +at finite t, what happens + +is that the state of the +vector is going to change. + +So this Si at finite +temperature would no longer + +be pointing along +the last component. + +It will start to +have fluctuations. + +Those fluctuations will change +the 0 from the ground state + +to some value I'll call +pi 1, the next one pi 2, + +all of the big pi n minus 1. + +And since the whole entire +thing is a unit vector, + +the last component has to +shrink to adjust for that. + +So we would indicate the +last component by sigma. + +So essentially this subspace of +fluctuations around the ground + +state is captured +through this vector + +pi that is n minus +1 dimensional. + +And this corresponds +to the transverse modes + +that we're looking +at when we were doing + +the expansion of the +Landau-Ginzburg model + +around its symmetry +broken state. + +In this case, the +longitudinal mode, + +essentially, is +infinitely stiff. + +You don't have the +ability to stretch along + +the longitudinal mode +because of the constraint + +that we have put over here. + +So if you think back, +we had this wine bottle, + +or Mexican hat potential. + +And the Goldstone +modes corresponded + +to going along the +bottom, and how easy + +it was to climb +this Mexican hat was + +determined by the +longitudinal mode. + +In this case, the Mexican hat +has become very, very stiff + +to climb on the sides. + +So you don't have the +longitudinal mode. + +You just have these +Goldstone modes. + +The cost to pay +for that is that I + +have to be very careful in +calculating the partition + +function. + +If I'm integrating +over the n components + +of some particular spin, +I have to make sure + +that I remember that this sum +of all of these components is 1. + +So I have to integrate +subject to that constraint. + +And the way that I have +broken things down now, + +I'm integrating over the n minus +1 component of this vector pi. + +And this additional +direction, d Sigma, + +but I can't do both +of them independently. + +Because there's a +delta function that + +enforces that sigma squared +plus pi squared equals to 1. + +The pi squared corresponds +to the magnitude + +of this n minus 1 +component vector. + +And essentially, I can solve +for this delta function, + +and really replace +this sigma over here + +with square root of +1 minus pi squared. + +But I have to be a little bit +careful in my integrations. + +Because this delta +function I can + +write as a delta +function of sigma + +plus or minus square root +of 1 minus pi squared. + +And there is a rule that if +I use this delta function + +to set sigma to be equal to +square root of 1 minus pi + +squared, like I +have done over here, + +I have to be careful that the +delta function of a times x + +is actually a delta function +of x divided by modulus of a. + +So essentially, I have to +substitute something here. + +So this is, in fact, equal +to the integration in the pi + +directions because of the +use of this delta function + +to set the value +of sigma, I have + +to divide by the square +root of 1 minus pi squared. + +Which actually +shortly we will write + +this in the following way. + +I guess there's an +overall factor of 1/2 + +but it doesn't really matter. + +So yes? + +AUDIENCE: So what do +you do with the fact + +that there are two places where +the delta function is done? + +PROFESSOR: I'm +continuously connecting + +to the solution that +starts at 0 temperature + +with a particular state. + +So I have removed that +ambiguity by the starting + +points of my cube. + +But if I was integrating +over all possibilities, + +then I should really +add that on too. + +And really just make +the partition function + +with the sum of two +equivalent terms-- + +one around this ground state, +one around another state. + +AUDIENCE: The product is +supposed to be for a lattice + +site-- for the integration +variable, not for the-- + +PROFESSOR: Right. + +So I did something bad here. + +So here I should have written-- +so this is an n component + +integration that I have +to do on each side. + +Now let's pick one of the sides. + +So let's say we +pick the side pi. + +For that, I have a small +n integration to do. + +What does it say? + +It basically says +that if, for example, + +I am looking at the +case of n equals to 2, + +then I have started +with a state that + +points along this direction. + +But now I'm allowing +fluctuations pi + +in this direction. + +And I can't simply say that the +amount of these fluctuations, + +pi, is going let's say from +minus infinity to infinity. + +Because how much +pi I have changes + +actually whether it is +small or whether it is large + +when I'm down here. + +And so there's constraints +let's say on how big pi can be. + +Pi cannot be larger than 1. + +And essentially, a +particular magnitude + +of pi-- how much weight does +it has, it is captured by this. + +So that's one thing +to remember when + +we are dealing with +integration over unit spins, + +and we want to look +at the fluctuations. + +The other choice of notation +that I would like to do + +is the following. + +I said that my +starting [INAUDIBLE] + +is a 0 sum over all nearest +neighbors Si dot Sj. + +Now in the state +where all of the spins + +are pointing in one direction, +this factor is unity. + +So the 0 temperature state gets +a factor of 1 here on each one. + +Let's say we are in a +hyper cubic lattice. + +There are d bonds per site. + +So at 0 temperature, I +would have NdK0, basically-- + +the value of this ground state. + +And then if I have +fluctuations from that state, + +I can capture that as +follows, as minus K0 over 2. + +It's a reduction in this energy, +as sum over ij Si minus Sj + +squared. + +And you can check that. + +If I square these +terms, I'm going + +to get 1, 1, 1/2, which +basically reproduces + +this, which actually +goes over her. + +And the dot product, minus 2 Si +dot Sj, cancels this minus 1/2, + +basically gives +you this exactly. + +So the reason I write +it in this fashion + +is because very shortly, I want +to switch from going and doing + +things on a lattice to +going to a continuum. + +And you can see that +this form, summing over + +the difference between +near neighbors, + +I very nicely can go +to a gradient squared. + +So essentially that's +what I want to do. + +Whenever I have a +sum over a site, + +I want to replace it with +an integral over a space. + +And I guess to keep +things dimensionless, + +I have to divide by a to get d. + +So I can call that the density +that I have to include, + +which is also the same thing +as the number of lattice + +points in the body of the box. + +So my minus beta +H in the continuum + +goes over to whatever +the contribution + +of the completely +aligned state is. + +And then whatever the +difference of the spins + +is, because of the +small fluctuations, + +I will capture through an +integration of gradient of S + +squared. + +And I call the original +coupling that we're basically + +the strength of the +interaction divide by KdK0. + +Clearly in order +to get the coupling + +that I have in the +continuum, I have + +to have this fact of a to the d. + +But then in the gradient, I +also have to divide by distance. + +So there's something here, a +factor of a to the 2 minus d + +that relates these two factors. + +It should be the +other way around. + +It doesn't matter. + +AUDIENCE: Question. + +PROFESSOR: Yes. + +AUDIENCE: This step is +only valid for a cubicle-- + +PROFESSOR: Yes. + +So if it was something +like a triangular lattice, + +or something, there would be +some miracle factors here. + +AUDIENCE: But I +mean like writing + +the difference of +the spin squared + +as the gradient squared. + +Like if it were a +triangular lattice? + +PROFESSOR: Yeah, +so the statement + +is that whatever +lattice you have, + +what am I doing at the +level of the lattice, + +I'm trying to keep +things that are + +close to each other aligned. + +So when I go to the continuum, +how is this captured, + +it's a term like a +gradient squared. + +Now on the hyper cubic +lattices, the relationship + +between what you +put on the bonds + +of the hyper cubic lattice and +what we've got in the continuum + +is immediately apparent. + +If you try to do it on +the triangular lattice, + +you still can. + +And you'll find that +at the end of the day, + +you will get the factor +of square root of 3, + +or something like that. + +So there's some miracle +factor that comes into play. + +And then at the end +of the day, I also + +want to replace these +gradient of a squared + +naturally in terms of +essentially S has n components. + +N minus one of them are pi, +and one of them is sigma. + +So this would be minus +K/2 integral d dx. + +I have gradient of +the pi component, + +and a gradient of the +sigma component squared. + +So after integrating sigma +using the delta functions, + +I'm going to the +continuum limit. + +The partition function +that we have to evaluate up + +to various non-singular +factors, such as this constant + +over here, is obtained +by integrating over + +all configurations +of our pi field, + +now regarded as a +continuously varying object + +under the dimensional lattice. + +And the weight, +which is as follows, + +there is a gradient of +pi squared, essentially + +this term over here. + +There is the gradient +the other term. + +The other term, however, +if I use the delta function + +in square root of 1 +minus pi squared squared. + +And then there's this +factor from the integration + +that I have to be careful +of, which I can also + +take to the exponent, and write +as, again, this density times + +log of 1 minus pi squared. + +There's, I think, a +factor of [INAUDIBLE]. + +So the weight that I +had started with, with S + +dot S was kind of +very simple-looking. + +But because of the +constraints, was + +hiding a number of conditions. + +And if we explicitly +look at those conditions + +and ask what is the +weight of the fluctuations + +that I have to put +around the ground + +state, these +Goldstone modes, that + +is captured with +this Hamiltonian. + +Part of it is this +old contribution + +from Goldstone +modes, the transfer + +modes that we had seen. + +But now being more careful, we +see that these Goldstone modes, + +I have to be careful about +integrating over them + +because of the additional terms +that capture, essentially, + +the original full symmetry, +full rotational symmetry, + +that was present in +integration over S. Yes? + +AUDIENCE: The integration-- +the functional integration, + +pi should be linked +up to a sphere of 1. + +PROFESSOR: This will keep. + +So I put that +constraint over here. + +And it's not just that it +is limited to something, + +but for a particular +value of pi, + +it gets this additional weight. + +So if you like, once I +try to take my integrals + +outside that region, that +factor says the weight as usual. + +So this entity is called +the non-linear sigma model. + +And I never understood why they +don't call it a non-linear pi + +model. + +Because we integrate +immediately with sigma. + +That's how it is. + +So what you're going to do +if we had, essentially, stuff + +that the first term not included +any of the other things, + +we will have had the +analysis of Goldstone modes + +that we had done previously. + +The effect of these +things, you can + +see if I start making +expansion in powers of pi, + +is to generate +interactions that will + +be non-linear terms +among the parts. + +So these Goldstone modes +that we were previously + +dealing with as independent +modes of the system, + +are actually +non-linearly coupled. + +And we want to know +what the effect of that + +is on the behavior +of the entire system. + +So whenever we're faced +with a non-linear theory, + +we have to do some kind of +a preservative analysis. + +And the first thing that +you may be tempted to do + +is to expand the +powers of pi, and then + +look at the Gaussian part, +and then the higher order + +parts, etc. + +That's a way of doing it. + +But there's actually another +way that is more consistent, + +which is to organize +the terms in this weight + +according to powers +of temperature. + +Because after all, I started +with a zero temperature + +configuration. + +And I'm hoping +that I'm expanding + +for small fluctuation. + +So my idea is to-- I +know the ground state. + +I want to see what happens +if I go slightly beyond that. + +And the reason for +fluctuations is temperature, + +so organize terms in this +effective Hamiltonian + +for the pis in powers +of temperature. + +And temperature, by this I mean +the inverse of this coupling + +constant, K, +because even, again, + +if I go through +my old derivation, + +you can see that +I go minus beta H, + +so K0 should be inversely +proportional to temperature. + +K is proportion to K0. + +It should be inversely +proportional to temperature. + +So to some overall +coefficient, let's just + +define temperature [INAUDIBLE]. + +Now we see that at the +level that we were looking + +at things before, +from this term it's + +kind of like a +Gaussian form, where + +I have something like K, which +is the inverse temperature + +pi squared. + +So just on dimensional grounds, +up to functional forms, etc. + +we expect pi squared to be +proportional to temperature + +at the 0 order, if you like. + +Because, again, if +temperature goes to 0, + +there's not going +to no fluctuations. + +As I go away from 0 temperature, +the average fluctuations + +will be 0. + +Average squared will be +proportional to temperature. + +It all makes sense. + +So then if I look +at this term, I + +see that dimensionally, +it is inverse temperature + +pi squared is of the +order of temperature. + +So this is dimensionally +t to the 0. + +Whereas if I start +to expand this, + +this log I can start to +expand as minus pi squared + +plus pi to the 4th over 2 pi to +the 6th over 3, and so forth. + +You can see that subsequent +terms in this series + +are higher and higher +order in this temperature. + +This will be the order of +temperature-- temperature + +squared, temperature cubed. + +And already we can see +that this term is small + +compared to this term. + +So although this +is a Gaussian term, + +and I would've +maybe been tempted + +to put it in the 0 +order Hamiltonian, + +If I'm organizing +things according + +to orders of temperature, my +0-th order will remain this. + +This will be the +contribution to first order, + +2nd order, 3rd order. + +And similarly, I can +start expanding this. + +Square root is 1 minus +pi squared over 2. + +So then I take the gradient +of minus pi squared over 2. + +I will get pi gradient of pi. + +You can see that the lowest +order term in this expansion + +will be pi gradient of +pi squared, and then + +higher order terms. + +And this is something that +is order of pi to the 4th, + +so it gives the order of +temperature squared multiplied + +by inverse temperatures. + +So this is a term that is +contributing to order of T + +to 0, T to the 1. + +So basically, at order of T +to 0, I have as my beta H0 + +just the integral d dx K/2 +gradient of pi squared. + +While at order of +T the 1st power, + +I will have a correction +which has two types of terms. + +One term is this K/2 integral +d dx pi gradient of pi squared, + +coming from what was the +gradient of sigma squared. + +And then from here, I +will get a minus rho + +over 2 integral d dx pi squared. + +And then there will be other +terms like order of T squared, + +U2, and so forth. + +So I just re-organized terms +in this interacting Hamiltonian + +in what I expected to be +powers of this temperature. + +Now here we-- one of the +first things that we will do + +is to look at this and +realize that we can decompose + +into modes by going +to previous space, + +I do a Fourier transform. + +This thing becomes K/2 integral +dd q divided by 2 pi to the d q + +squared pi theta of q squared. + +So let's write it as +pi theta [INAUDIBLE]. + +And again, as usual, +we will end up + +needing to calculate averages +with this Gaussian rate. + +And what we have here is that +pi alpha of q1 pi beta of q2, + +we get this 0-th ordered rate. + +The components have +to be the same. + +The sum of the two +momenta has to be 0. + +And if so, I just +get K q squared. + +Now I can similarly +Fourier transform the terms + +that I have over here. + +So the interactions +to one-- first one + +becomes rather complicated. + +We saw that when we +have something that's is + +four powers of a field. + +And when we go to +Fourier space, rather + +than having one +integral over x, we + +ended up with +multiple integrals. + +So I will have, essentially, +Fourier transform + +of four factors of pi. + +For each one of them I +will have an integration. + +So I will have dd +q1, dd q2, dd q3. + +And the reason I +don't have the 4th one + +is because of the integration +over x, forcing the four q's + +to be added up to 0. + +So I will have pi alpha +of q1, pi alpha of q2, + +Now note that this +high gradient of pi + +came from a gradient +of pi squared, + +which means that the two +pis that go with this, + +carry the same index. + +Whereas for the next +factor, pi gradient of pi, + +they came from different ones. + +So I have pi q3 I beta +minus q1 minus q2 minus q3. + +Now if I just written +this, this would've + +been the Fourier transform of +my usual 4th order interaction. + +But that's not what +I have because I + +have two additional gradients. + +And so for two of +these factors actually + +I had to take the +gradient first. + +And every time I take a +gradient in Fourier space, + +I will bring a factor of I q. + +So I will have here I q1 +dotted with Iq let's say 3. + +So the Fourier transform of +the leading quartic interaction + +that I have, is actually the +form that I have over here. + +There is a trivial +term that comes + +from Fourier transforming. + +It's pi squared because +then I Fourier transform + +that, I get simply pi +alpha of q squared. + +Yes? + +AUDIENCE: Does it +matter which q's + +you're pulling out +as the gradient? + +PROFESSOR: You can see that +these four pis over here + +in Fourier space appear +completely interchangeably. + +So it really doesn't matter, no. + +Because by permutation and +re-ordering these integration, + +you can move it +into something else. + +No, there is-- I shouldn't-- +I'll draw a diagram that + +corresponds to that that will +make one constraint apparent. + +So when I was drawing +interaction terms for m + +to the 4th tier for +Landau-Ginzburg, + +and I have something +that has 4 interactions, + +I would draw something +that has 2 lines. + +But the 2 lines had 2 branches. + +And the branching was supposed +to indicate that 2 of them + +were carrier 1 +index, and 2 of them + +were carrying the same index. + +Now I have to make +sure that I indicate + +that the branches +of these things + +additionally have +these gradients + +for the Iq's +associated with them. + +And I make a +convention the branch, + +or the q, that has the gradient +on it, I will put a line. + +Now you can see +that if I go back + +and look at the origin of +this, that one of the gradients + +acts on one pair of +pis, and the other acts + +of the other pairs of pis. + +So the other dashed line I +cannot put on the same branch, + +but I have to put over here. + +So the one constraint that +I have to be careful of + +is that these Iq' should +pick one from alpha and one + +from beta. + +This is the diagrammatic +presentation. + +So what I can do is to now +start doing perturbation + +in these interaction. + +You want to do the +lowest order to see + +what the first correction +because of fluctuations + +and interaction of +these Goldstone modes. + +But rather than do +things in two steps, + +first doing perturbation, +encountering difficulty, + +and then converting things +to a normalization group, + +which we've already seen that +happen, that story, in dealing + +with the Landau-Ginzburg +model, Let's immediately + +do the perturbative +renormalization group + +of this model. + +So what I'm supposed +to do things + +is to note that all +of these theories + +came from some +underlying lattice model. + +I was carefully drawing +for you the first lattice + +model originally. + +Which means that there +is some cut off here, + +some lattice cut off. + +Which means that when +I go to Fourier space, + +there is always some kind of a +range of wave numbers or wave + +vectors that I have +to integrate with. + +So essentially, my +pi's are limited + +after I do a little +bit of averaging, + +if you like that there is +some shortest wavelength, + +and the corresponding +largest wave number, lambda, + +in [INAUDIBLE]. + +And the procedure for +RG, the first one, + +was to think about +all of these pi modes, + +and brake them into two pieces. + +One's that we're responding +to the short wavelength + +fluctuations that we +want to get rid of, + +and the ones that correspond +to long wavelength fluctuations + +that we would like to keep. + +So my task is as follows, that +I have to really calculate + +the partition function over +here, which in it's Fourier + +representation indicates +averaging over all modes + +that's are in this orange. + +But those modes I'm +going to represent + +as D pi lesser, as +well as D pi greater. + +Each one of these +pi's is, of course, + +an n minus on component vector. + +And I have a rate +that i obtained + +by substituting pi lesser and +pi greater in the expressions + +that I have up there. + +And we can see already that +the 0-th order terms, as usual, + +nicely separates out +into a contribution + +that we have for pi lesser, +a contribution that we have + +for pi greater, and that the +interaction terms will then + +involve both of these modes. + +And in principle, I +could proceed and include + +higher and higher orders. + +Now I want to get rid of all +of the modes that are here. + +So that I have an effective +theory governing the modes + +that are the longer wavelengths, +once I have gotten rid + +of the short wavelength +fluctuations. + +So formally, once I have +integrated over pi greater + +in this double +integral, I will be + +left with the integration +over the pi lesser field. + +And the exponential gets +modified as follows. + +First of all, if I were +to ignore the interactions + +at the lowest order, +the effect of doing + +the integration of the Gaussian +modes that are out here, + +will, as usual, +be a contribution + +to the free energy of the +system coming from the modes + +that I integrated out. + +And clearly it also +depends, I forgot to say, + +that the range of integration +is now between lambda over b + +lambda, where b is my +renormalization factor. + +Yes? + +AUDIENCE: Because you're +coming from a lattice, does + +the particular shape of +the Brillouin zone matter + +more now, or still not really? + +PROFESSOR: It is in no +way different from what + +we were doing before in +the Landau-Ginzburg model. + +In the Landau-Ginzburg model, +I could have also started + +by putting spins, +or whatever degrees + +of freedom on a lattice. + +And let's say if I was +in hyper cubic lattice, + +I would've had Brillouin +zones, such as this. + +And the first thing +that we always said + +was that integrating +all of these things + +gives you an additional +totally harmless component + +to the energy that has +no similar part in it. + +So we're always searching +for the singularities that + +arise at the core +of this integration. + +Whatever you do +with the boundaries, + +no matter how complicated shapes +they have, they don't matter. + +So going back to here. + +If we had ignored +the interactions, + +integrating over +pi greater would've + +giving me this contribution +to the free energy. + +And, of course, beta H0 of +pi lesser would've remained. + +But now the effect of having +the interactions, as usual, + +it is like integrating +into the minus + +u with the rate over here. + +So I would have an +average such as this. + +And we do the cumulant +expansion, as usual. + +And the first term I +would get is the average + +of this quantity with +respect to the Gaussian rate, + +integrating out the high +component modes, high frequency + +modes, and high +order corrections. + +Yes? + +AUDIENCE: So right here you're +doing two expansions kind + +of simultaneously. + +One is you have non-linear +model that you're + +expanding different +powers and temperature. + +And then you +further on expand it + +to cumulants to be able +to account for that. + +PROFESSOR: No, because I +can organize this expansion + +in cumulants in +powers of temperature. + +So this u has an expansion +that is u1, u2, etc. + +organized in powers +of temperature. + +AUDIENCE: OK. + +PROFESSOR: And then when +I take the first cumulant, + +you can see that the average, +the lowest order term, + +will be-- + +AUDIENCE: The first cumulant +is linear in temperature, + +and that's what you want? + +PROFESSOR: Right. + +So I'm being consistent +also with the perturbation + +that I had originally stated. + +Actually, since I drew a +diagram for the first term, + +I should state that this term, +since we are now also thinking + +of it as a correction +in u1, I have + +to regard it as 2 factors of pi. + +So I could potentially represent +it by a diagram such as this. + +So diagrammatically, my u1 +that I have to take the average + +is composed of +these two entities. + +So what I need to do is to take +the average of that expression. + +So I can either do +that average over here. + +Take the average +of this expression, + +or do it diagrammatically. + +Let us go by the +diagrammatic route. + +So essentially, +what I'm doing is + +that every line that I see over +there that corresponds to pi, + +I am really decomposing +into two parts. + +One of them I will draw as a +straight line that corresponds + +to the pi lesser +that I am keeping. + +Or I replace it +with a wavy line, + +which is the pi greater that +I would be averaging over. + +So the first diagram I +had essentially something + +like this-- actually, +the second diagram. + +The one that comes +from rho pi squared. + +It's actually trivial, so let's +go through the possibilities. + +I can either have both of +these to be pi lessers-- sorry, + +pi greaters. + +So this is pi +greater, pi greater. + +And when I have +to do an average, + +then I can use +the formula that I + +have in red about the +average of 2 pi greaters. + +And that would +essentially amount + +to closing this thing down. + +And numerically, it would gives +me a factor of minus rho over 2 + +integral d dK over 2 pi to the +d in the interval between lambda + +over b, lambda . + +And I have the +average of pi alpha pi + +alpha using a factor +of delta alpha alpha. + +Summing over alpha will give +me a factor of n minus 1. + +And the average would be +something like K k squared. + +So I would have to evaluate +something like this. + +But at the end of the day, +I don't care about it. + +Why don't I care about it? + +Because clearly the result of +doing this is another constant. + +It doesn't depend on pi lesser. + +So this is an addition +to the free energy + +once I integrate modes between +lambda over b to lambda, + +there is a contribution +to the free energy that + +comes from this term. + +It doesn't change +the rate that I + +have to assign to configurations +of the pi lesser field. + +That's another possibility. + +Another possibility is I +have one of them being a pi + +greater, one of them +being a pi lesser. + +Clearly, when I try to get +an average of this form, + +I have an average +of one factor of pi + +with a Gaussian +field that is even. + +So this is 0. + +We don't have to worry about it. + +And finally, I will get a +term, which is like this. + +Which doesn't involve +any integrations, + +and really amounts to +taking that term that I + +have over there, and just +making both of those pi + +to be pi lessers. + +So it's essentially the same +form that will reappear, + +now the integration being +from 0 to lambda over 2. + +So we know exactly what happens +with the term on the right. + +Nothing useful, or important +information emerges from it. + +If I go and look at +this one however, + +depending on where +I choose to put + +the solid lines +or the wavy lines, + +I will have a number +of possibilities. + +One thing that is +clearly going to be there + +is essentially I put pi lesser +for each one of the branches. + +Essentially, when i write +it here like this one, + +it is reproducing +the integration + +that I have over there, +except that, again, it + +only goes between 0 and lambda. + +And now I can start +adding wavy lines. + +Any diagram that has one wavy, +and I can put the wavy line + +either on that type +of branch, or I + +can put it on this +type of branch. + +It has only one factor of pi. + +By symmetry, it will +go to 0, like this. + +There will be things +that will have + +three factors of pi lesser. + +And all of these-- +again because I'm + +dealing with an odd +number of factors of pi + +greater that I'm +averaging will give me 0. + +There's one other thing +that is kind of interesting. + +I can have all four +of these lines wavy. + +And if I calculate +that average, there's + +a number of ways of +contracting these four + +pi's that will give +me nontrivial factors. + +But these are also contributions +to the free energy. + +They don't depend on the +pi's that I'm leaving out. + +So they don't have to worry +about any of these diagrams + +so far. + +Now I dealt with the 0, +1, 3, and 4 wavy lines. + +So I'm left with 2 wavy +lines and 2 straight lines. + +So let's go through those. + +I could have one +branch be wavy lines + +and one branch be +straight lines. + +And then I take the +average of this object. + +I have a pi greater-- +a pi greater here, + +and therefore I can +do an average of two + +of those pi greaters. + +That average will give me a +factor of 1 over K k squared. + +I have to integrate over that. + +But one of these branches had +this additional dash thing + +that corresponds to +having a factor of k. + +So the integral +that I have to do + +involves something like this. + +And then I integrate over the +entirety of the k integration. + +This is an odd power, and so +that will give me a 0 also. + +So this is also 0. + +And there's another +one that's is + +like this where I go like this. + +And although I do the +same thing now with two + +different branches, the k +integration is the same. + +And that vanishes too. + +So you say, is there +anything that is left? + +The answer is yes. + +So the things that are +left are the following. + +I can do something like this. + +Or I can do something like this. + +So these are the two things that +survive and will be nontrivial. + +You can see that +this one will be + +proportional to +pi lesser squared, + +while this one is going to +be proportional to gradient + +of pi lesser squared. + +So this one will renormalize, +if you like, this coefficient. + +Whereas this one, we've modified +and renormalize our coupling + +straight. + +So it turns out +that that is really + +the more important point. + +But let's calculate +the other one too. + +Yes? + +AUDIENCE: Why do we connect the +ones down here with the loops, + +but left all the ends +free in the ones. + +Was that just a matter of the +case of how to write diagram, + +or does that signify something? + +PROFESSOR: Could +you repeat that? + +I'm not sure I understand. + +AUDIENCE: So when we had two +wavy line, both coming out + +one of the diagram, this +line, they just stop. + +We connected them +together when we + +were writing the ones +on the bottom line. + +PROFESSOR: So basically, I +start with an entity that + +has two solid lines +and two wavy lines. + +And what I'm supposed to do +is to do an integration-- + +an average of this +over these pi greaters. + +Now the process of +averaging essentially joins + +the two branches. + +If I had the momentum here, +q1, and a momentum here, + +q2, if I had an +index here, alpha, + +and an index here, beta, +that process of averaging + +is equivalent to saying the +same momentum has to go through, + +the same index +has to go through. + +There is no averaging that is +being done on the solid lines, + +so there is-- meaningless +to do anything. + +So this entity +means the following. + +I have K/ 2 let's call +it legs 1, 2, 3, and 4. + +Integral q1 and q2, but q1 +and q2 you can see explicitly + +are solid. + +So these are the integration +from 0 to lambda over b. + +I have an integration over +q3, which is over a wavy line. + +So it's between lambda +over b and lambda. + +If I call this branch alpha +and this branch beta, from here + +I have actually pi lesser alpha +of q1 pi lesser beta of q2. + +I should have put them +outside the integration, + +but it doesn't matter. + +And then here I had pi +alpha of q3, pi beta of q4. + +But these also had these +lines associated with them. + +So I have here actually +an i q3, an i q4. + +Again, q4 has to stand for minus +q1 minus q2 minus q3 from this. + +And then I had the pi +pi here, which give me, + +because of the averaging, +delta alpha beta. + +And then I will +have an integration + +that forces q2 plus q4 to be 0. + +And then I have K q3 squared. + +Now q3 plus q4 is the same thing +as minus q1 minus q3, if you + +like, because of +that constraint. + +So I can take that +outside the integration. + +There's no problem. + +I have one integration left, +which is 1 over K q3 squared, + +but these two then +become the same. + +These pi's I will take outside. + +I note that because of this +constraint, q1 and q2 being + +the same, these two really +become one integration that + +goes between 0 +and lambda over b. + +And these indices have +been made to be the same. + +So I have pi alpha of +q, this q, squared. + +Then I have the integration +from lambda over b to lambda. + +D d q3 2 pi to the d. + +Here I have i q3 i q4. + +But q4 was said to be minus q3. + +So the two i's and the +minus cancel each other. + +And I will get a +factor of q3 squared. + +And then here I have a +factor of K q3 squared. + +So the overall thing +is just that we + +can see that the K's cancel. + +I have one factor integral +dd q 2 pi to the d. + +I have pi alpha of q squared. + +And these are q lessers. + +I integrated out this quantity. + +The q3's vanish, so I really +have the integral of q3 + +over 2 pi to the d. + +Now if I had done the +integral of q3 2 pi + +to the d, all the way from 0 to +lambda, what would I have done? + +If I multiply this +volume here, that + +would be the number of modes. + +So this is, in fact, N/V, +which is the quantity + +that I have called the density. + +But what I'm doing +is, in fact, doing + +just a fraction of this integral +from 0 to lambda over b. + +So if I do the fraction +from 0 to lambda over b, + +then I will get 1 +minus b to the minus d. + +Sorry, from lambda +over b to lambda. + +Then if I had done all of +the way from 0 to lambda, + +I will have had one, +but I'm subtracting + +this fraction of it. + +So the answer is rho 1 +minus b to the minus d. + +The overall thing here gets +multiplied by rho 1 minus + +b to the minus d. + +It just would correct that +factor of density that we have. + +We'll see shortly it's not +something to worry about. + +The next one is really the +more interesting thing. + +So here we have this diagram, +which is K/2 integral from 0 + +to lambda over b. + +Essentially, I will +get the same structure. + +This time let me write +the pi alpha lesser + +of q1 pi beta lesser of q2 +outside the last configuration. + +I have the integral from lambda +over b to lambda dd of q3 2 + +pi to the 3d. + +And I will have the same +delta function structure, + +except that now these factors +of i q become i q1 times i q2. + +So I can put them +outside already. + +And then I have here +the delta function. + +So the only difference is +that previously the q squared + +was inside the integration. + +Now the q squared is +outside the integration. + +So the final answer will +be K/2 integral 0 to lambda + +over d d d q 2 pi to the d. + +I have a q squared. + +pi of q lesser squared. + +And the coefficient +of that would + +look like what I had before, +except without this factor. + +So it's the integral +from lambda over b + +to lambda dd of q3 divided by 2 +pi to the d 1 over Kq3 squared. + +So once I do explicitly +this calculation, + +the answer is going to be +a weight that only depends + +on this pi lesser +that I'm keeping + +and I would indicate that +by beta H tilde, as usual. + +That depends of this pi lesser. + +And we now have all +of the terms that + +contribute to this beta H tilde. + +So let's write them down. + +There's a number of +terms that correspond + +to changes in the free energy. + +So we have a V delta f p at +the 0-th order contribution + +of delta f p at the first +order that are essentially + +a bunch of diagrams, both from +here as well as from here. + +But we don't really +care about them. + +Then we have types of +terms that look like this. + +I can write them already +after Fourier transformation + +in real space. + +So let me do that. + +I have integral dd +x in real space, + +realizing that my cut +off has been changed + +to ba-- things that are +proportional to gradient + +of pi lesser squared. + +Now gradient of +pi lesser squared + +is the things I in +Fourier space becomes + +q squared pi lesser squared. + +And what is the coefficient? + +I had K/2, which +comes from here. + +If I don't do anything, I +just have the 0-th order modes + +acting on these. + +But I just calculated +a correction + +to that that is +something like this. + +So in addition to +what I had before, + +I have this correction, +K/2 times this integral. + +And I'm going to call the +result of this integral + +to be I sub d-- see +that this integral is + +proportional to 1/K. + +And when the integration-- +let's call the result + +of the integral +Id of b because it + +depends on both +dimension of integration, + +as well as the factor +V through here. + +So I have 1/K Id of b. + +So that's one type of +that I have generated. + +I started from this +0-th order form. + +And I saw that once I make the +expansion of this to the lowest + +order, I will get a +correction to that. + +And actually, just to +sort of think about it + +in terms of formulae, +you see what + +happened was that the first +term that I had over here + +was pi gradient of +pi repeated twice. + +And what I did was +I essentially did + +an average of these two pi's and +got the correction to gradient + +of pi squared, which is what was +computed here and [INAUDIBLE]. + +The next term that I have +is this term by itself, + +not calculated with the pi +lessers only-- so this object. + +So I will write it as K/2 +I gradient of pi squared. + +There's no correction. + +The final term that +I have is this term. + +So I have minus rho over +2 pi lesser squared. + +And then the correction that I +have was exactly the same form. + +It was 1 minus 1 minus +b to the minus b. + +The rho over 2 is going to +be hung onto both of them. + +You can see that there's +a rho and there's a 2. + +And so basically I have +two add this to that. + +And to first order, this is +the entire thing of the thing + +that I will get. + +So this however is +just a course gradient. + +It's the first step of the RG. + +And it has to be followed by +the next two steps of the RG. + +Where here, you +look at you field + +and you can see that the +field is much coarser + +because the short distance +cut off rather than being a, + +has been switched to ba. + +So you define your x prime +to x/b, so that you shrink. + +You get the same course pixel +size that you had before. + +And you also have to +do a change in pi. + +So you replace pi lesser +with some factor zeta pi + +prime, so that the +contrast will look fine. + +So once I do that, you +can see that this effect + +of this transformation +is that this coupling + +K will change to K prime. + +Because of the change +of x with b x prime, + +from the integration, +I will get b to the d. + +From the two derivatives, I +will get V to the minus 2. + +From the fact that I have +replace two pi lessers with pi + +primes, I will get a +factor of zeta squared. + +And then I will have this +factor K 1 plus 1/K Id of b. + +So this is the recursion formula +that we will be dealing with. + +Now there is some +subtleties that + +go with this formula that +are worth thinking about. + +Our original system had really +one coupling parameter K + +that because of the constraints +of the full symmetry + +of this field, S, part of it +became the quadratic part that + +was the free field theory. + +But part of it made +the interactions. + +But because of this +vertical symmetry, + +to form of that +interaction was fixed + +and had to be +proportional to K. Now + +if we do our normalization group +correctly, to full symmetry + +that we had has to be +maintained at all levels. + +Which means that the functional +form that I should end up with + +should have the same property +in that the higher order + +coefficient should be +related to the lower order + +coefficient, exactly the same +way as we had over there. + +And at least at this stage, it +looks like that did not happen. + +That is, we got the +correction to this term, + +but we didn't get the +correction to this term. + +We shouldn't be worried +about that right + +here because we calculated +things consistently corrections + +to order of T. And +this was already + +a term that was order +of T. So the real check + +is if you go and calculate +the next order correction, + +you better get a correction +to this term at next order + +that matches exactly this. + +People have done that, +and have checked that. + +And that indeed is the case. + +So one is consistent with this. + +There are other kinds +of consistency checks + +that have happened +all over the place, + +like the fact that this +came back 1 minus 1 + +came out to be b to the minus +d, so that the density is + +the same as before, +consistent with the fact + +that you shrunk the +lattice after RG so + +that the pixel size was +the same as before is + +a consequence of that. + +You may worry that that's +not entirely the case + +because when I do +this, I will have also + +a factor of zeta squared. + +But it turns out that zeta is +1 plus order of temperature, + +as we will shortly see. + +So I gain consistent-- +everything's + +consistent at this level +that we've calculated things. + +And the only change +is this factor. + +Now the one thing that +we haven't calculated + +is what this zeta is. + +So to calculate zeta, +I note the following + +that I start with +a unit vector that + +is pointing at 0 temperature +along this direction. + +Now because of +fluctuations, this + +is going to be kind of +rotating around this. + +So there is this vector +that is rotating. + +If you average it over some +time, what you will see + +is that the average in all +of these direction is 0. + +The variance is not 0, +but the average is 0. + +But because of +those fluctuations, + +the effective length that +you see in this direction + +has shrunk. + +How much has it shrunk by +is related to this rescaling + +factor that I should chose. + +And so it's essentially +average of something + +like 1 minus pi squared. + +But really it is the +pi lesser squares + +that I'm averaging over. + +Which the lowest order is 1 +minus 1/2 the average of pi + +lesser squared, which +is 1 minus 1/2 . + +Now this is an N minus +1 component vector. + +So each one of the components +will give you one contribution. + +The contribution that +you get for one of these + +is simply the average +of pi squared, which + +is 1 over K k squared, which +I have to integrate over K's + +that lie between lambda +over b and lambda. + +And you can see that this is +1 minus 1/2 N and minus 1. + +It is inversely +proportional to K. + +And then the integration +that I have to do + +is precisely the same +integration as here. + +So it is, again, this Id of b. + +So let me write the answer, +say a couple of words about it, + +and then we will deal +with it next time. + +So K prime is going +to be b to the d + +minus 2-- a new +interaction parameters. + +It is one factor of +1 plus 1/K Id of b. + +And then there's one factor +of this square of zeta. + +So that gives you N minus +1 over K Id of b times K. + +So we'll analyze this +more next time around. + +But I thought I would give you +the physical reason for how + +this interaction +parameter changes. + +Let's say we are +in two dimensions. + +So let's forget +about this factor. + +In two dimensions, we can see +that there is one factor that + +says at finite temperature, +we are going to get weaker. + +The interaction is +going to get weaker. + +And the reason for +that is precisely what + +I was explaining over here. + +That is, you have some +kind of a unit vector, + +but because of its +fluctuations, you + +will see that it +will loop shorter. + +And it is less +likely to be ordered. + +The more components +it has to fluctuate, + +the shorter it will look like. + +So there is that term. + +So if this was the +only effect, then K + +will become weaker and weaker. + +And it will have disorder. + +But this effect says +that it actually + +gets stronger because +of the interactions + +that you have among the modes. + +And to show you this to you, +we can experiment with it + +yourself. + +So this is a sheet of paper. + +This bend is an example +of a Goldstone mode + +because I could have +rotated this sheet + +without any cost of energy. + +So this bend is a Goldstone mode +that costs very little energy. + +Now this paper has the +kinds of constraints + +that we have over here. + +And because of +those constraints, + +if I make a mode +in this direction, + +I'm not going to be able to +bend it in the other directions. + +So clearly the mode that +you have this direction, + +and this direction, are coupled. + +That's kind of an example +of something like this. + +Now while it is easy to do this +bend because of this coupling, + +if thermal fluctuations +have created modes + +that are shorter wavelength, +and I have already + +created those modes +over here, then you + +can experiment yourself. + +You'll see that this is harder +to bend compared to this. + +You can see this already. + +So that's the effect +that you have over here. + +So it's the competition +between these two. + +And depending on which +one wins, and you + +can see that that +depends on whether n + +is larger than 2 or less than 2. + +So essentially for n +that is larger than 2, + +you'll find that this term wins. + +And you get disorder +in two dimension. + +And is less than 2, +you will get order + +like we know the Ising +model can be order. + +But there's other +things that can + +be captured by this expression, +that we will look at next time. \ No newline at end of file diff --git a/os0qdddXrMs.txt b/os0qdddXrMs.txt new file mode 100644 index 0000000000000000000000000000000000000000..c5fe849a665dae376ea9ea9dda65ecbda7168530 --- /dev/null +++ b/os0qdddXrMs.txt @@ -0,0 +1,1307 @@ +Recall, please, that we were discussing last time + +the fact that the immune system makes a wide diversity of antibody + +molecules. And, by the way, a synonym for an + +antibody molecule is an immunoglobulin. + +Recall that we used that word very briefly. Another word we use, + +by the way, was the word antigen. And, an antigen is a functional term. + +That was pretty funny. An antigen is a functional term. + +An antigen is an agent that provokes an immune response. + +And, the term antigen doesn't really refer to any specific + +chemical structure. It doesn't even have to be a + +protein. Antigen simply refers to some chemical entity that creates + +some response from the immune system. We also use the word in + +passing, epitope. And, an epitope refers to a small + +region, for example, a protein against which an antibody + +has developed reactivity. And if you recall our discussion + +last time, a protein obviously of some size has multiple distinct + +epitopes, each of which can be recognized by a distinct antibody + +molecule. And, for us, could we, + +I'm sorry if I got all this political discussion + +started, thank you. Thank you. An epitope, + +from the point of view of a protein is an oligo peptide. + +So, a stretch of amino acids of maybe ten, or 12, + +or 15 amino acids forms an epitope. And therefore, you can imagine + +there are multiple epitopes on the surface of a protein. + +In fact, antibodies can sometimes recognize the internal parts of the + +protein because protein can sometimes become denatured + +or degraded. Indeed, as we will discuss shortly, + +proteins also become cleaved into oligo peptides. + +These oligo peptides can come from any part of the protein, + +to state the obvious, and therefore there might be internal epitopes + +that exist in a protein that are not normally exposed by the native + +protein. Recall that we were dealing with the issue of how the + +immune system is able to create a wide diversity of antibodies, + +immunoglobulins would share in common a constant domain. + +And the constant domain is formed by these invariant regions of the light + +and the heavy chains. We call this the heterotetramer in + +contrast to the variable domain up here which recognizes the antigen + +that initially provoked the production of this antibody molecule. + +And, the immune system may at any one point in time be making hundreds + +of thousands, maybe even millions or tens of millions of distinct + +antibody species that differ one from the other by the antigen + +recognition site here at this part of the antibody molecule. + +And recall as well that since these are proteins, the + +antigen-recognizing pocket is itself an oligopeptide, + +which combined in some complementary fashion to whatever antigen + +initially provoked the synthesis of this antibody molecule. + +At the end of last time, we discussed the fact that + +antibodies are made by B cells, and the fact that in the disease of + +multiple myeloma, one ends up with a monoclonal + +disease, that is to say, one of a vastly heterogeneous + +population of B cells begins to proliferate uncontrollably. + +And now, all of its descendants make a single antibody species. + +And that single antibody species consists once again of a heavy and a + +light chain, whose identity is created by the antigen-recognizing + +pocket that it happens to carry. And this begins to suggest a notion + +of clonal expansion. By that, I mean the following. + +Let's imagine a scenario where we start out with a naīve immune system + +where we have a whole series of different B cells. + +And this series goes here from 1-15, but in fact this could go from one + +up to a million. And each of these antibody + +producing B cells, or each of these B cells, + +has in principle the ability to respond to a different antigen. + +Let's just imagine that. And now, what we can imagine is + +that an antigen such as, for example, poliovirus comes into + +the body, and it is recognized by two different clones of these B + +cells. And that recognition, we can imagine, acts as a mytogenic + +signal, a growth stimulatory signal for these two particular clones and + +B cells. It almost acts as if it were a growth factor. + +But of course, we're not talking about growth factors here. + +We're talking about antigens, including antigens brought into the + +tissue by a foreign infectious agent. And therefore, + +the recognition of the antigen by these two B cells may thereafter + +provoke their clonal expansion. By that I mean to say that they + +will preferentially begin to proliferate whereas all the other B + +cells, which are not in any way responsive to that antigen will just + +sit there like bumps on a log. And, if there is, + +therefore, clonal expansion, now there will be a much larger + +number of cells in the immune system that are capable of producing the + +antibody that recognizes its provoking antigen. + +Again, recall that this number may go up to a million. + +This is just a great simplification. Now here, we use the word plasma + +cells. And in fact, if one wants to get the nomenclature + +very proper, the plasma cells are the products of B cells which mature + +into the antibody producing plasma cells. + +They are very close on the same lineage of cells, + +and what that means in the end for us is if once there's an active + +immune response, there's been the preferential + +expansion of certain sub-populations of B cells and plasma cells, + +and other ones of them which don't recognize these antigens just sit + +there are underrepresented in the total population of cells. + +Still, the fundamental question that we posed last time + +was the following. If it's the case, + +and it happens to be that each of these B cells makes an antibody + +having a distinct reactivity, a distinct ability to react to one + +or another antigen how do they make so many different kinds of antibody + +molecules. How do they know how to do that. We argued that it's + +implausible that the amino acid sequences of each antibody molecule + +are encoded in the germ line. Why? Well, if there are indeed a + +million or even 100 million distinct antibodies can be made by the immune + +system, clearly there can't be 100 million genes, + +each of which is dedicated to the production of a distinct + +antibody molecule. And the solution to this puzzle was + +first worked out by Susumu Tonegawa already more than 20 years ago who + +happens to be in our biology department. And what he discovered + +was the following, that the way that the antibody + +producing genes are organized is really quite extraordinary + +and unusual. Here's the heavy chain of the gene, + +and keep in mind that there's a heavy and a light chain gene. + +The heavy and the light chain genes are in different chromosomes. + +And therefore, the genes that are responsible for encoding these two + +proteins, the heavy and the light chain, they're on different + +chromosomes, and encode by different genes. OK, so what Tonegawa + +discovered was the following, that the variable region of an + +antibody molecule which is at its end terminus is encoded by small + +segments of DNA that are carried in one very large genetic locus, + +an immunoglobulin locus. And what happens in humans is the + +following. There are in humans rather than mice, + +this number should be 100 in humans, there are 100 distinct V segments + +that are encoded in this antibody locus. Each one is roughly the same + +size, and they're located in a large tandem array. + +Similarly, there are in humans 30 of these desegments. + +The numbers change here if one goes from mouse to human, + +but that's irrelevant. And, there are six of the J + +segments. And, much of the antigen-recognizing + +capacity, much of the variable region is encoded in the green and + +the blue region of the gene, and the encoding happens as follows. + + There is a combinatorial fashion the + +random fusion of V, D, and J segments. There are + +specific, highly specialized enzyme that will choose one specific V + +segment, one specific D segment, and one specific J segment, + +ostensibly on a stochastic basis, a totally random basis, and fuse + +them together. And if that happens, + +and the intervening DNA sequences are discarded, + +then right away we can see that through the combinatorial + +mathematics that results from this, there is the possibility for having + +100 times 30, which is 3, 00, times six, which is already 180, + +00 distinct combinations encoding the reading frame of this particular + +antibody molecule. Here, I've just said V23, + +I guess, D7, J2. But again, let's imagine, which is + +approximately the case, that each of these combinations can + +be fused with roughly equal probability. + +What happens subsequently, then, is that this variable region + +sequence, which has been formed by fusion, is then the transcript that + +comes from that is spliced to the constant region which is towards the + +C terminus. So here, when we talk about the V, + +D, and J segments, we're talking about the segments that are encoding + +this portion. Here's this portion of the antibody molecule. + +Keep in mind, from here on down, we're talking about constant region + +segments which are not affected by these combinatorial fusions. + +And, in the overhead I just showed you, I was just talking about how + +the heavy chain gene is rearranged. And what that results as a + +consequence is the following. This is just another version of + +what I just showed you before, where the V, D, and J segments + +become fused randomly to one another creating a V, D, + +J fusion thing, which then by splicing is fused to the constant + +region which here is called C sub-mu. + +For reasons of why it's called sub-mu I'll mention in a moment. + +And this is the actual messenger RNA which then goes into the + +cytoplasm. And what we can now imagine is the following, + +that when the immune system first begins, it randomly fuses whole + +series of V, D, and J segments together, + +and all kinds of combinations. The same happens in both the heavy + +chain and the light chain, although the light chain is slightly + +simpler. But that's irrelevant for us + +conceptually. And then, we end up having hundreds of + +millions of distinct V cells, each of which has a different + +combination of heavy and light chains because keep in mind the + +light chain genes are also being rearranged combinatorially. + +They're also being fused. And therefore, we can have 180, + +00 distinct heavy chains, and I forget the exact number for the + +number of light chains. It's a bit less, + +but we can multiply those two combinations by one another because + +keep in mind that the gene encoding the heavy chain here in its variable + +region, and the gene encoding the light chain in its variable region + +are organized on separate chromosomes. And, + +they're fused together. These segments are fused together + +randomly. So, the total number of antibody + +molecules we can make is 180, 00 distinct kinds of these. + +And, I've just slipped up in knowing the total number of these that can + +be made, although we could figure it out shortly if it were really + +important. But once again, the number is in the many thousands. + +And therefore, overall, the total number of distinct antibody + +molecules one can make on the basis of this is this. + +Did I get the math right, 60 by 30, 18,000. It's 18, + +00. So, there's 18,000 distinct of these that can be made, + +and the number of these, I think, is closer to 10,000. + +I forget, but multiplied, let's call it 10,000 for a moment. + +That's not the right number. There's 10,000 different ones of + +these, and 18, 00 of these that can be made. + +Multiply them together, and you get the total number of combinations of + +antibody molecules it could make because it is the case that the + +antigen recognition site here is created cooperatively, + +collaboratively, by the heavy and light chain. You had a question? + +So, the gene is rearranged, and when the rearrangement occurs, + +on V segment is fused to one D segment, is fused to one J segment. + +And all of the extraneous segments that are between them have been + +deleted from the chromosome. So, this leads me to a second point + +I wanted to make, and that is that here we are dealing + +with a process of somatic mutation. + +We talked about last time or the time before last the fact that + +somatic mutation is generally a process that can lead to cancer, + +i.e. the mutation of germ line genes that are in one way or another + +corrupted by random mutational processes. But here, + +I'm talking about a somatic mutational process, + +which is highly directed and highly organized, and focused on creating a + +series of rearranged genes that can then serve as the template for the + +production of an antibody molecule. So here, let's just look at this + +again. Here, I'll tell you, there are many V genes. There are + +many D genes, and there are many J genes. And, this is the embryonic + +DNA. After large segments of the immunoglobulin locus are deleted, + +and then the surviving V, D, and J segments become fused in the DNA + +directly to one another. And when that happens, + +the resulting B cell DNA can be transcribed, and via splicing create + +an mRNA where the region in between the J's chain and the constant + +region chain called, here C, is further deleted. + +So, each messenger RNA has one V, one D, and one J segment together + +with a constant region segment. There are yet other processes that + +further diversify how many different variable regions can be encoded. + +One of them is the following. It turns out that the process by + +which the V and D, and the D and J genes are fused + +together, those segments are fused together, is a bit sloppy. + +And therefore, sometimes the fusion will occur creating a sequence of + +nucleotides that has a nonsense codon in. Sometimes it will create + +a coherent reading frame that creates yet another kind of amino + +acid sequence there. And therefore, this is not a highly + +ordered process in the sense that these micro-architecture of the + +points with the V and the D, and the D and the J are fused is a + +little bit chaotic. So that creates even further + +randomization of the nucleotide sequence. And then, + +finally, once this gene has been created, there is a process which is + +called hypermutation, where through mechanisms which are + +not well understood, the nucleotide sequence of this + +region is actually further changed. + +It's mutated by certain enzymes. For example, there's an enzyme + +called cytidine deaminase, which takes off the amine group off + +of the cytidines in that region, and thereby effectively converts the + +C's in that coding region more into having a T coding capacity. + +This happens somatically, and here once again I'm talking + +about a further dimension of diversification. + +One of the dimensions diversification, + +first of all, the V and the J chains rearrange independently, + +randomly, and stochastically. Secondly, the joining of the + +segments is a bit sloppy. And thirdly, there is somatic + +hypermutation. There's an enzyme like this which + +is actually an actively mutagenic enzyme which fiddles around with + +some of the C's in this portion of the gene, thereby further + +diversifying the coding ability of the immunoglobulin gene that's + +encoded by the cell. And what this means is the following, + +that if we imagine this scheme here where each of these B cells + +recognize it's a different antigen, initially there may be 100 million + +distinct B cell clones that are created, each the consequence of a + +different random mutation. That happens early in the + +development of the immune system. Thereafter, there are certain + +selective processes there at play. One important selective process is + +the elimination of B cells that have failed to make nicely rearranged + +antibody molecules. What do I mean by that? + +I told you how sloppy the V, D, J joining is. And therefore, + +many of these joinings could create reading frames that are incoherent + +with stop codons in the middle. And therefore, + +those cells which happen to have created antibody molecules which are + +highly mutant and clearly structurally defective are + +eliminated. So, one prerequisite for the survival of + +these B cells early in the development of the immune system is + +that they've learned how to make functional heavy and light chains. + +If they don't, they're right away wiped out. They're eliminated. + +Here's another very important prerequisite for survival, + +that these B cells don't make antibodies that react with antigens + +that are native to the body's own tissues. What do I mean by that? + +Well, one of the wonders of the immune system is the following, + +that it can recognize foreign antigens that are brought into the + +body from the outside including, for example, the epitopes on the + +surface of polio virus particle. It can recognize many different + +viruses, surface antigens present on the surface of bacteria, + +and fungi, and all kinds of other infectious agents. + +But importantly, the immune system also sees hundreds + +of millions of different epitopes of the proteins that are present + +endogenously, native proteins in our tissues. A priori, + +the native proteins, what's called our own self-proteins, + +are perfectly qualified to function as antigens. + +And yet, the immune system rarely develops strong reactivity against + +them. Thus, the immune system has the ability to recognize self versus + +non-self. What do I mean by self versus non-self? + +Self are the body's own native proteins, which are in principal + +conceivably antigenic. Non-cell are foreign invaders that + +bring strange epitopes into the cell. + +And what happens is that B cells, which make antibodies, that + +recognize native proteins in our tissues are, if things are working + +well, rapidly eliminated early in the development of the immune system. + +What happens if that elimination fails to occur properly? + +If it fails to occur, one has the process of autoimmune disease. + +And, there are multiple autoimmune diseases. + +Type one diabetes, early onset diabetes happens when + +the immune system recognizes antigens that are present in the + +islet cells in the pancreas that make insulin. Rheumatoid arthritis, + +which inflicts a large portion of the elderly, happens when the immune + +system recognizes antigens that are present normally in the cartilage in + +our joints. Lupus happens when, it's an autoimmune called lupus + +which is often fatal, happens when the immune system + +recognizes proteins in many different tissues. + +And once again, in all of these cases, + +there is a breakdown of the mechanisms governing immune + +tolerance. And what do I mean by tolerance? I mean the mechanisms + +whereby the immune system tolerates native antigens, + +but is conversely intolerant of foreign antigens. + +The word intolerant is not used in immunology, but I'm just using it + +for the sake of explanation here. So, immune tolerance is a very + +important area of current immunological research. + +We don't really understand why we don't have much more autoimmune + +disease than we do. And by the way, only listed two or + +three of the most common kinds of autoimmune diseases that happen with + +the mechanisms that normally guarantee immune tolerance failed. + +And therefore, these B cells survive are ones that make + +functional antibodies and those whose antibodies do not recognize + +self-antigens. They are permitted to survive, + +and once again, we imagine that those that happened to make + +antibodies that recognize particular foreign antigens undergo or enjoy + +clonal expansion. During the development of the + +immune response, there is a further diversification + +of the antigen-recognizing domain of the protein by hypermutation. + +And therefore, descendants of these initially + +developed cells, which have begun to expand because + +they make an antibody, may develop antibody molecules that + +are even more able to bind avidly to the antigen. It could be that + +initially, these antibody-producing cells make antibody molecules that + +bind nicely to the antigen but not really avidly. Avidly means + +really tightly. And, that's enough to get their + +clonal expansion going, but during the process of clonal + +expansion, this hypermutation creates further variants of these + +cells, further mutates their antibody producing genes so that + +some of the descendants of these cells will produce antibody + +molecules that bind even more tightly and specifically to the + +provoking antigen. And when that happens, + +the quality of the antibodies is improved progressively. + +Now clearly, the somatic hypermutation once again, + +it's a random hypermutation. And those clones of cells in which + +the hypermutation created less effective antibodies will not have + +their proliferation stimulated. Those clones of cells whose + +antibodies make more and more tightly binding antibodies will + +preferentially have their proliferation stimulated. + +And as a consequence, they will now be the ones that are + +favored to yield the plasma cells that produce large amounts of + +antibody molecules. So, we have now this very unusual + +and very interesting way by which B cells and plasma cells are able to + +create a wide diversity of antibody molecules. Now, + +one of the interesting things, actually, is the fact that this + +constant region contains one of a variety of distinct + +constant regions. Initially, when one produces the + +first immune response, the first immune response as we said + +before produces a constant region which is called CM, + +and I had the right overhead this morning. Ah, here it is. + +Here's the way the genes are actually rearranged. + +Here's the rearranged V, D, and J, and here's the splice to + +the constant region. And downstream are a whole series of + +constant region segments. What's the first one: CM. + +I told you about that before. Thereafter, C sub delta, C sub + +gamma-3, gamma-1, gamma-2, gamma-8, and so forth. + +And therefore, the initial event can create an ig-mu, an IgM + +antibody molecule. The mu region creates an IgM. + +Later, as the immune response develops further, + +this mu segment may become deleted. And now, the splice may occur to a + +delta or a gamma change. And therefore, if the intervening + +constant region is changed, you might get what's called an IgG. + +An IgG is an immunoglobulin which is produced when this + +antigen-recognizing region becomes spliced down to here or here by + +virtue of the deletion of these intervening constant + +region segments. What's the purpose of what's called + +class switching? Because these are different classes + +of antibodies, because they have different + +functions. Note importantly that when this class switching occurs, + +it has no effect on the antigen-recognizing site of the + +antibody molecule. Rather, it affects the constant + +region of the antibody molecule. Well, how does that work? The + +initially made antibody molecule, I told you, is IgM. And in fact, if + +you look at the structure of IgM, it looks like this. Here's, let's + +say, a B cell, and the IgM molecule is actually not + +secreted into the extra cellular space like a soluble + +antibody molecule. Here's what IgM looks like from very + +schematically IgM has our standard antigen-recognizing site, + +but IgM is embedded in the plasma membrane of the B cell exactly the + +way that a growth factor receptor is embedded in the plasma membrane of a + +B cell. But keep in mind that I just said that this IgM molecule has + +an antigen-recognizing domain up here, which is exactly the way we + +described it before. So, the antigen recognition is not + +affected by whether we have an IgM molecule here. + +Only the location of the antibody molecule, and as I'll show shortly, + +the function of this antibody molecule is affected by this IgM. + +Later on, descendants of this B cell will mature into those that + +secrete IgG molecules into the plasma. + +So, here's a maturation that's going on. But look here. + +Once again, the antigen-recognizing domains of this IgG are unaffected + +by this conversion. Here, the constant region is + +tethering the antibody molecule to the plasma membrane. + +Here's the antigen-recognizing sites. + +After this maturation occurs, the secreted IgG molecules, which go + +into the solution, have identical antigen-recognizing + +sites, but now they're soluble proteins. Well, + +you'll say, why does the immune system do that? + +And, it goes back to an overhead I showed you just moments ago in which + +there was a puzzle implicitly created by the image on the overhead. + +And here it is. Let's look at this for a moment. + +What detail is now explained in this scheme? What detail is now + +explained? I told you that B cells can be stimulated by certain + +antigens. Let's imagine that each of these B cells made only secreted + +antibody, OK, instead of making cell surface antibody because the cell + +surface antibody, which is being made in this scheme, + +is actually the IgM molecules. Let's say this B cell over here is + +making an antigen. I'll just draw it as, + +there's the antigen, is making an antibody against this antigen, + +and it's secreting antibody against this. And I'd just argue that the B + +cell that makes good antibody is favored. It has its proliferation + +stimulated, right? That's what we talked about. + +But if this B cell sends all of its antibody into the plasma, + +how is it going to know that it's making a good antibody? + +It can't because all of the antigen recognition is happening by the + +secreted antibody. So, what happens with the IgM + +molecules. The first antibody molecule this produced is IgM. + +And, it stays tethered to the plasma membrane of the B cell. + +It's a transmembrane protein, and it functions much like a + +growth factor receptor. That is to say, + +when the antigen binds out here, there are signals that are radiated + +into the cell that induce the proliferation of this cell. + +And now, these cells that produce the antigen-recognizing IgM + +molecules on their surface can now have their proliferation stimulated. + +That solves the puzzle here which is created by this scheme. + +If all these B cells just made secreted antibody like this, + +then there would be no way to encourage their proliferation + +because there would be no way of telling this B cell you're + +doing a good thing. Keep making more of these antibody + +molecules. Here, the antigen-recognizing capability + +is embedded in the plasma membrane. And when an antigen binds this, the + +IgM molecule's organized so that now growth stimulatory signals are sent + +into the cell which cause this cell to begin to proliferate, + +producing more IgM containing cells which are further stimulated + +to proliferate. And ultimately after this has gone + +on for a while, there is a class switching which + +deletes the IgM region of the gene chain region, and causes a + +conversion to IgG. Again, the conversion from here to + +here doesn't change the antigen-recognizing capability of + +these two antibodies. It just makes a cell surface + +transmembrane protein or a secreted protein. (pause) + + No, the VDJ choice happens in the + +nucleus. It's a fusion of different DNA segments, and when it's + +transcribed, that fused VDJ is now spliced to a constant region segment. + +The choice of VDJ is a fusion of DNA segments. It happens in + +chromosomal DNA. It results in the deletion of all + +the segments that aren't used. So, all that's left in the + +immunoglobulin locus of a B cell is a DNA segment encoding V fused to a + +DNA segment encoding D, fused to a DNA segment encoding J. + +So now, you have a new somatically mutated immunoglobulin gene, + +lest there be any residual confusion about that. So, + +you see the elegance of this class-switching thing. + +Now there's yet other constant region segments that are used for + +other purposes. For example, when you have + +allergies, there's an activation of the igE antibodies. + +When you have secreted antibody production in the colon, + +igA is used more for that. So, different ones of these + +constant regions are used for different immunological applications. + +The IgM molecule, as I've said, is used here just as a + +way of telling the B cell that it's done well by making the right kind + +of antigen-recognizing site. The real business of creating + +antibodies is the soluble antibody production, the immunoglobulins, + +or the gammaglobulins because the vast majority of antibodies floating + +around the blood plasma are in fact IgGs. The IgMs are, + +as implied by this, actually just largely tethered to the surface of + +cells. So, this really is an extraordinary, + +elegant way of creating essentially hundreds of millions of different + +antigen-recognizing domains each created collaboratively between a + +heavy and a light chain. And once these antigen-recognizing + +domains are created through changes in DNA structure, + +then they can be used for different immunological applications, + +driving B cell proliferation, secreting soluble antibodies that + +are used to neutralize virus particles in the blood, + +or if they're hyperactive to create allergic reactions or to create + +immunity in certain regions of the gut and so forth. + +So, this class switching doesn't change the antigen-recognizing + +capability. It just changes the utilization of how already-developed + +VDJ segments and their antigen-recognizing capability are + +exploited by cells of the immune system. + +Now, one thing that's not really clear by all this is how all this + +develops at the cellular level because what I've talked about until + +now is called humeral immunity. Well, we talk about somebody having + +a good sense of humor. But the actual original meaning of + +the word humor in Latin was fluids that were fluxing through your body, + +and were responsible for your different mood states. + +So, if you were depressed or there just was a national election, + +there would be black fluids, black humors coursing through + +your blood. And if you were in a good mood, + +there were other humors coursing through your blood. + +And that leads through this etymology to the term of humeral + +immunity, which is to say the soluble immunity, + +i.e. the production of soluble antibody molecules. + +But I will tell you that there's a second arm of the immune system + +which is equally important, and that's called cellular immunity. + +And, to make a long story short, and we'll elaborate it on Monday + +briefly. Cellular immunity is largely created when you have a kind + +of immune cell that's called a cell rather than the B cells we've been + +talking about until now, which is able, and this cellular + +immunity is among other things, cytotoxic. + +And, it can recognize a second cell over here. Here's a second cell. + +This is its target cell because the second target cell is displaying on + +its surface certain antigens. So, antigens are being displayed on + +the surface of the target cell. I've indicated them here as just + +little, blue strokes. And the T cell is able to recognize + +these antigens on the surface of this cell here, + +and is able to kill this cell through a series of interesting + +mechanisms. This doesn't involve the intervention of soluble antibody + +molecules. Here, we're talking about one cell + +recognizing another, and it turns out to be very + +important for antiviral defenses. I've told you one way by which + +antiviral defenses are achieved. Soluble antibody molecules are + +secreted into the blood plasma like IgGs. They recognize an epitope on + +the surface of a virus particle. They glom onto that epitope on the + +surface of the virus particle, and they neutralize the virus + +particle. And, that's very important. + +We started out in our discussion of poliovirus talking about that. + +But this also turns out to be very important. Why is it important? + +For the following reason: when this cell, let's say this cell is + +infected by poliovirus on the inside. + +It turns out, interestingly enough, that the cell has a way which we'll + +discuss of processing poliovirus polypeptides, viral polypeptides, + +and displaying them on the cell surface. In other words, + +the cell can chew up some poliovirus proteins, put them to the outside, + +and tell the outside world, these are the kinds of the proteins that + +are being made right now inside of me. + +You the immune system can't really look through the plasma membrane so + +I'm going to tell you this is what's going on inside of me. + +There are poliovirus proteins being made as we speak. + +On the outside of the cell, these are displayed even though + +poliovirus replication is recurring exclusively inside the cell. + +A cytotoxic T cell here may recognize these antigens on the + +surface of the poliovirus infected cell, and proceed to kill the cell. + +Why is that interesting or important? Because the cytotoxic cell will + +kill the virus-infected cell while the virus infection is still in full + +swing. And therefore, by killing the virus-infected cell, + +it will abort the entire bioreplication cycle because the + +virus won't have enough time to replicate or proliferate inside the + +infected cell before it happens. It's preemptively killed by the + +cytotoxic T cell. And in fact, this way of eliminating + +viral infections from our body is as important and often more important + +than the neutralization of soluble virus particles in our plasma. + +And all that gets now to have us focus increasingly on the mechanisms + +by which antigens are recognized and processed so that the immune system + +can begin to respond to them. So, I want to get into that now, + +into the aspects in which we look at the cellular arms of + +the immune system. The most important thing initially + +in the immune response is that let's say poliovirus particle is + +recognized and digested by certain phagocytic cells of the immune + +system. What's a phagocytic cell: a cell that is able to gobble + +up other things. So, a well-known phagocytic cell is + +a macrophage. And there you can see the term phagocyte, + +macrophage. Phagos means to chew up or to swallow, + +so macrophage might see a particle like this surround that particle, + +and then internalize that particle and digest it, + +let's say a poliovirus particle. Macrophage could envelop a + +poliovirus particle and internalize it. + +It could do the same thing with a bacteria. Here, + +we'll use as an abbreviation for macrophage this. + +So, that's macrophage. There are yet other even more + +important phagocytic cells of the immune system that are called + +dendritic cells. Now, these cells gobble up whatever + +happens to be around them. They don't care. + +They are promiscuous sewer, gutter trollers. Whatever happens + +to be around, they will gobble up whatever happens to be around. + +They'll put it inside of them, and now they do something really + +interesting. The dendritic cells, the macrophages, the phagocytic + +cells, they don't digest the internalized particles down to amino + +acids. They digest the virus particle down to oligopeptides. + +Usually if 10, 12, 14 amino acids long: very important. + +So they don't make amino acids. They make oligopeptides. Why are + +they doing this digestion? Because these cells are + +exhibitionists and they want to show the rest of the world what they've + +just swallowed up. It's really important to them. + +Go figure. So, what do they do? + +They take these oligopeptides that they've just internalized and they + +put them on the cell surface via molecules which are called MHC class + +2. MHC class 2 is the name of these molecules, and these are cell + +surface receptors. And, these MHT C class 2 molecules + +have included in them an oligopeptide that has just been + +produced by the proteolytic cleavage of an internalized infectious agent, + +let's say. And so, the macrophage has many of these MHC class 2 + +molecules on its surface, and it displays to the outside world + +what it has just captured in terms of these oligopeptides. + +And these oligopeptides are, by the way, roughly the size of an + +epitope. Therefore, this macrophage is just so excited. + +It's like a little kid who has just found something, + +so excited to show the world what it's just found and gobbled up and + +processed. And over here is a class of cells which are called T helper + +cells. And the T helper cells are interesting in their + +own right, right? The T helper cells have evolved + +through a mechanism that is similar to and parallel to the evolution of + +the B cells. As a consequence, there are many different kinds of T + +helper cells. Each one, so TH-1, TH-2, TH-3, each of which + +displays on its surface a T cell receptor. + +What kind of T cell receptor does it display? A T cell receptor that has + +gone through exactly the same kind of hoops that the antibody genes + +have gone through. That is, each T cell expresses on + +its surface an antigen-recognizing receptor just like the IgM molecule + +except it's made by T cells and it's created by these stochastic + +processes of fusing DNA segments. So, each of these T cells, + +and again, there are millions of them, has a different T cell + +receptor with a different antigen-recognizing capability. + +And here's what happens in the immune system. + +Let's imagine, as I say every year, + +that we're in a Middle Eastern bazaar, and that Middle Eastern + +bazaar, here are all the shops on the sides on the sides of this long + +bazaar. It's sometimes called a shuk or a suk. + +And here we're going to have a macrophage or a dendritic cell + +moving through the bazaar. Hanging out in front of the stores + +are a whole bunch of T helper cells. + + Business is slow, + +so all these T helper cells are just hanging out in front, + +and as is not the custom in this region, let's pretend all the T + +helper cells are girls just for the heck of it. It doesn't make any + +difference. And each of these T helper cells is displaying its own T + +cell receptor which has arisen through stochastic mechanisms and + +which recognizes a different oligopeptide. + +And here we have now the macrophage coming through like a vendor, + +a street vendor, saying, look girls, look at the epitope I just gobbled + +up and produced. Isn't it great? And, + +it's using its MHC class 2 molecules to present, it's like hands, + +presenting the epitopes. It's flogging them like a street vendor, + +and it walks down through this bazaar, and each of the T helper + +cells, they're congregating along the sides of the road, + +and most of them say look at this drip. + +Look at the garbage he's selling us today. I am totally uninterested. + +He was here last week with some other chump too. + +Let's hope he disappears quickly. And meanwhile the macrophage or the + +dendritic cell is very anxiously trying to find someone who has even + +the slightest bit of affection or respect for him. + +And this goes on for a long time. + +And finally, the macrophage finds a T helper cell over here. + +So, here's the T helper cell, and it turns out that by coincidence + +the T helper cell has on here surface a T cell receptor that + +recognizes the epitope that the macrophage is peddling. + +So, here's the macrophage. Macrophage has on its surface this + +oligopeptide held by the MHC class 2 hands. So, here's the peptide. + +And this T cell receptor which I'll abbreviate TCR recognizes, + +binds strongly to the epitope that's being flogged by the macrophage. + +And this is, I will tell you honestly, love at first sight. + +She says, oh, I can't believe it. You're selling an epitope that I + +just happen to love. This is very exciting. + +And all the other T helper cells say, oh my God, + +what does she see in him? And she gets all excited because + +there's a direct complementarity. In fact, to tell the truth, the T + +cell receptor recognizes not only the epitope but also the surrounding + +amino acids in the fingers of the MHC class 2 molecule. + +It's this constellation of things that's recognized by the T cell + +receptor and gets this T cell receptor really excited. + +And what does she do? Well, we can't talk about everything + +because this is polite company. But most important for what she + +does is she begins to proliferate like mad. Well, + +you know, cells have a limited repertoire of behavioral routines. + +Next time we're going to figure out how this leads to an immune response. + +So, we're going to be on [intention? all weekend. \ No newline at end of file diff --git a/os_XGBNPllM.txt b/os_XGBNPllM.txt new file mode 100644 index 0000000000000000000000000000000000000000..adec618a78231dc6ec4ac4e717a365667db31f2e --- /dev/null +++ b/os_XGBNPllM.txt @@ -0,0 +1,12927 @@ +align:start position:0% + +so i'm going to prove a few theorems + + align:start position:0% +so i'm going to prove a few theorems + + + align:start position:0% +so i'm going to prove a few theorems +about limits which will allow us to + + align:start position:0% +about limits which will allow us to + + + align:start position:0% +about limits which will allow us to +compute limits um + + align:start position:0% +compute limits um + + + align:start position:0% +compute limits um +or at least + + align:start position:0% + + + + align:start position:0% + +you know we can use to prove that + + align:start position:0% +you know we can use to prove that + + + align:start position:0% +you know we can use to prove that +other non-trivial limits exist using + + align:start position:0% +other non-trivial limits exist using + + + align:start position:0% +other non-trivial limits exist using +these theorems + + align:start position:0% +these theorems + + + align:start position:0% +these theorems +rather than using the definition + + align:start position:0% +rather than using the definition + + + align:start position:0% +rather than using the definition +directly + + align:start position:0% +directly + + + align:start position:0% +directly +so + + align:start position:0% + + + + align:start position:0% + +this first + + align:start position:0% +this first + + + align:start position:0% +this first +theorem + + align:start position:0% +theorem + + + align:start position:0% +theorem +is + + align:start position:0% +is + + + align:start position:0% +is +kind of the easiest theorem in the world + + align:start position:0% +kind of the easiest theorem in the world + + + align:start position:0% +kind of the easiest theorem in the world +because + + align:start position:0% +because + + + align:start position:0% +because +it's simply kind of just restating the + + align:start position:0% +it's simply kind of just restating the + + + align:start position:0% +it's simply kind of just restating the +definition of convergence of + + align:start position:0% +definition of convergence of + + + align:start position:0% +definition of convergence of +a sequence so + + align:start position:0% +a sequence so + + + align:start position:0% +a sequence so +i'm going to state it + + align:start position:0% + + + + align:start position:0% + +as follows so pretty short + + align:start position:0% +as follows so pretty short + + + align:start position:0% +as follows so pretty short +that if i have + + align:start position:0% +that if i have + + + align:start position:0% +that if i have +a sequence + + align:start position:0% +a sequence + + + align:start position:0% +a sequence +x sub n + + align:start position:0% +x sub n + + + align:start position:0% +x sub n +then it converges to x + + align:start position:0% + + + + align:start position:0% + +if and only if + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +sequence obtained by taking the absolute + + align:start position:0% +sequence obtained by taking the absolute + + + align:start position:0% +sequence obtained by taking the absolute +value of x of n minus x + + align:start position:0% +value of x of n minus x + + + align:start position:0% +value of x of n minus x +equals zero + + align:start position:0% +equals zero + + + align:start position:0% +equals zero +okay or the limit of that sequence is + + align:start position:0% +okay or the limit of that sequence is + + + align:start position:0% +okay or the limit of that sequence is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +so what is the proof + + align:start position:0% +so what is the proof + + + align:start position:0% +so what is the proof +it follows just immediately from the + + align:start position:0% +it follows just immediately from the + + + align:start position:0% +it follows just immediately from the +definition + + align:start position:0% +definition + + + align:start position:0% +definition +so i'm not even going to write anything + + align:start position:0% +so i'm not even going to write anything + + + align:start position:0% +so i'm not even going to write anything +i'll leave it to you + + align:start position:0% + + + + align:start position:0% + +but the proof follows from + + align:start position:0% +but the proof follows from + + + align:start position:0% +but the proof follows from +the definition + + align:start position:0% +the definition + + + align:start position:0% +the definition +and the simple fact that + + align:start position:0% +and the simple fact that + + + align:start position:0% +and the simple fact that +x sub n minus x an absolute value + + align:start position:0% +x sub n minus x an absolute value + + + align:start position:0% +x sub n minus x an absolute value +is equal to + + align:start position:0% + + + + align:start position:0% + +the absolute value of the absolute value + + align:start position:0% +the absolute value of the absolute value + + + align:start position:0% +the absolute value of the absolute value +of x of n minus x minus 0. okay + + align:start position:0% +of x of n minus x minus 0. okay + + + align:start position:0% +of x of n minus x minus 0. okay +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +you know the definition says for all + + align:start position:0% +you know the definition says for all + + + align:start position:0% +you know the definition says for all +epsilon positive you have to find an m + + align:start position:0% +epsilon positive you have to find an m + + + align:start position:0% +epsilon positive you have to find an m +so that this is less than epsilon for + + align:start position:0% +so that this is less than epsilon for + + + align:start position:0% +so that this is less than epsilon for +all n bigger than or equal to capital m + + align:start position:0% +all n bigger than or equal to capital m + + + align:start position:0% +all n bigger than or equal to capital m +but if you found such a capital m for + + align:start position:0% +but if you found such a capital m for + + + align:start position:0% +but if you found such a capital m for +this to be less than epsilon then this + + align:start position:0% +this to be less than epsilon then this + + + align:start position:0% +this to be less than epsilon then this +will be less than epsilon which is + + align:start position:0% +will be less than epsilon which is + + + align:start position:0% +will be less than epsilon which is +saying that this limit equals zero + + align:start position:0% +saying that this limit equals zero + + + align:start position:0% +saying that this limit equals zero +and then going the other direction is + + align:start position:0% +and then going the other direction is + + + align:start position:0% +and then going the other direction is +the same thing so this is just following + + align:start position:0% +the same thing so this is just following + + + align:start position:0% +the same thing so this is just following +directly from the definition + + align:start position:0% +directly from the definition + + + align:start position:0% +directly from the definition +um + + align:start position:0% +um + + + align:start position:0% +um +and this simple fact + + align:start position:0% +and this simple fact + + + align:start position:0% +and this simple fact +okay that was a very silly + + align:start position:0% +okay that was a very silly + + + align:start position:0% +okay that was a very silly +fact about limits but a very useful one + + align:start position:0% +fact about limits but a very useful one + + + align:start position:0% +fact about limits but a very useful one +in conjunction with + + align:start position:0% +in conjunction with + + + align:start position:0% +in conjunction with +the next serum which is + + align:start position:0% +the next serum which is + + + align:start position:0% +the next serum which is +not so trivial + + align:start position:0% +not so trivial + + + align:start position:0% +not so trivial +which is the squeeze theorem + + align:start position:0% + + + + align:start position:0% + +and it says the following so + + align:start position:0% + + + + align:start position:0% + +let a n + + align:start position:0% + + + + align:start position:0% + +b in + + align:start position:0% + + + + align:start position:0% + +an xn + + align:start position:0% +an xn + + + align:start position:0% +an xn +be + + align:start position:0% + + + + align:start position:0% + +sequences + + align:start position:0% +sequences + + + align:start position:0% +sequences +such that the following holds + + align:start position:0% + + + + align:start position:0% + +for all n natural numbers + + align:start position:0% +for all n natural numbers + + + align:start position:0% +for all n natural numbers +a sub n is less than or equal to x of n + + align:start position:0% +a sub n is less than or equal to x of n + + + align:start position:0% +a sub n is less than or equal to x of n +is less than or equal to b sub n + + align:start position:0% +is less than or equal to b sub n + + + align:start position:0% +is less than or equal to b sub n +and + + align:start position:0% + + + + align:start position:0% + +a sub n and b sub n are convergent + + align:start position:0% +a sub n and b sub n are convergent + + + align:start position:0% +a sub n and b sub n are convergent +sequences + + align:start position:0% +sequences + + + align:start position:0% +sequences +so + + align:start position:0% +so + + + align:start position:0% +so +and their limits + + align:start position:0% + + + + align:start position:0% + +equal each other + + align:start position:0% + + + + align:start position:0% + +and are given by some number call it x + + align:start position:0% + + + + align:start position:0% + +then the conclusion + + align:start position:0% + + + + align:start position:0% + +is that + + align:start position:0% + + + + align:start position:0% + +the limit as n goes to infinity of x of + + align:start position:0% +the limit as n goes to infinity of x of + + + align:start position:0% +the limit as n goes to infinity of x of +n equals x so when i write something + + align:start position:0% +n equals x so when i write something + + + align:start position:0% +n equals x so when i write something +like this you should also kind of + + align:start position:0% +like this you should also kind of + + + align:start position:0% +like this you should also kind of +there's kind of + + align:start position:0% +there's kind of + + + align:start position:0% +there's kind of +half a sentence before that + + align:start position:0% +half a sentence before that + + + align:start position:0% +half a sentence before that +that goes with this saying you know x + + align:start position:0% +that goes with this saying you know x + + + align:start position:0% +that goes with this saying you know x +sub n is a convergent sequence and its + + align:start position:0% +sub n is a convergent sequence and its + + + align:start position:0% +sub n is a convergent sequence and its +limit is equal to x all right so it's + + align:start position:0% +limit is equal to x all right so it's + + + align:start position:0% +limit is equal to x all right so it's +kind of two statements in one + + align:start position:0% +kind of two statements in one + + + align:start position:0% +kind of two statements in one +when i write that + + align:start position:0% + + + + align:start position:0% + +um so + + align:start position:0% +um so + + + align:start position:0% +um so +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +if you just + + align:start position:0% + + + + align:start position:0% + +draw a picture the squeeze theorem + + align:start position:0% +draw a picture the squeeze theorem + + + align:start position:0% +draw a picture the squeeze theorem +shouldn't be too surprising + + align:start position:0% + + + + align:start position:0% + +so this is a little discussion + + align:start position:0% + + + + align:start position:0% + +so here's x the common limit + + align:start position:0% +so here's x the common limit + + + align:start position:0% +so here's x the common limit +of + + align:start position:0% +of + + + align:start position:0% +of +a sub n and b sub n + + align:start position:0% +a sub n and b sub n + + + align:start position:0% +a sub n and b sub n +and + + align:start position:0% +and + + + align:start position:0% +and +so we can imagine that uh we're trying + + align:start position:0% +so we can imagine that uh we're trying + + + align:start position:0% +so we can imagine that uh we're trying +to show the limit as n goes to infinity + + align:start position:0% +to show the limit as n goes to infinity + + + align:start position:0% +to show the limit as n goes to infinity +of x of n equals x so that means we have + + align:start position:0% +of x of n equals x so that means we have + + + align:start position:0% +of x of n equals x so that means we have +to find for every epsilon + + align:start position:0% +to find for every epsilon + + + align:start position:0% +to find for every epsilon +capital m so that x sub n is between + + align:start position:0% +capital m so that x sub n is between + + + align:start position:0% +capital m so that x sub n is between +x plus epsilon and x minus epsilon + + align:start position:0% +x plus epsilon and x minus epsilon + + + align:start position:0% +x plus epsilon and x minus epsilon +so + + align:start position:0% +so + + + align:start position:0% +so +if i go out a little bit + + align:start position:0% +if i go out a little bit + + + align:start position:0% +if i go out a little bit +i would hope i can find a natural number + + align:start position:0% +i would hope i can find a natural number + + + align:start position:0% +i would hope i can find a natural number +capital m so that + + align:start position:0% + + + + align:start position:0% + +x of n minus x is or x sub n is in this + + align:start position:0% +x of n minus x is or x sub n is in this + + + align:start position:0% +x of n minus x is or x sub n is in this +little interval + + align:start position:0% +little interval + + + align:start position:0% +little interval +now if i'm assuming that a sub n and x + + align:start position:0% +now if i'm assuming that a sub n and x + + + align:start position:0% +now if i'm assuming that a sub n and x +of n + + align:start position:0% +of n + + + align:start position:0% +of n +if a sub n and b sub n are squeezing x + + align:start position:0% +if a sub n and b sub n are squeezing x + + + align:start position:0% +if a sub n and b sub n are squeezing x +of n in other words x of n is between + + align:start position:0% +of n in other words x of n is between + + + align:start position:0% +of n in other words x of n is between +the two + + align:start position:0% +the two + + + align:start position:0% +the two +then and b sub n is converging to x then + + align:start position:0% +then and b sub n is converging to x then + + + align:start position:0% +then and b sub n is converging to x then +um + + align:start position:0% +um + + + align:start position:0% +um +for n + + align:start position:0% +for n + + + align:start position:0% +for n +bigger than or equal to some integer m + + align:start position:0% +bigger than or equal to some integer m + + + align:start position:0% +bigger than or equal to some integer m +zero + + align:start position:0% +zero + + + align:start position:0% +zero +um + + align:start position:0% +um + + + align:start position:0% +um +all of the + + align:start position:0% +all of the + + + align:start position:0% +all of the +b sub n's are in this interval okay + + align:start position:0% +b sub n's are in this interval okay + + + align:start position:0% +b sub n's are in this interval okay +maybe they're not there maybe they could + + align:start position:0% +maybe they're not there maybe they could + + + align:start position:0% +maybe they're not there maybe they could +be over here + + align:start position:0% +be over here + + + align:start position:0% +be over here +but the way i drew it is just to the + + align:start position:0% +but the way i drew it is just to the + + + align:start position:0% +but the way i drew it is just to the +right of x okay + + align:start position:0% +right of x okay + + + align:start position:0% +right of x okay +and likewise since a sub n is converging + + align:start position:0% +and likewise since a sub n is converging + + + align:start position:0% +and likewise since a sub n is converging +to x there exists + + align:start position:0% + + + + align:start position:0% + +some other integer m sub 1 so that if i + + align:start position:0% +some other integer m sub 1 so that if i + + + align:start position:0% +some other integer m sub 1 so that if i +look at a sub n + + align:start position:0% +look at a sub n + + + align:start position:0% +look at a sub n +it's also in this interval maybe it's + + align:start position:0% +it's also in this interval maybe it's + + + align:start position:0% +it's also in this interval maybe it's +over here maybe it's + + align:start position:0% +over here maybe it's + + + align:start position:0% +over here maybe it's +well it can't be to the right of b sub n + + align:start position:0% +well it can't be to the right of b sub n + + + align:start position:0% +well it can't be to the right of b sub n +uh because that inequality up there um + + align:start position:0% +uh because that inequality up there um + + + align:start position:0% +uh because that inequality up there um +strictly implies that a sub n is less + + align:start position:0% +strictly implies that a sub n is less + + + align:start position:0% +strictly implies that a sub n is less +than or equal to b sub n + + align:start position:0% +than or equal to b sub n + + + align:start position:0% +than or equal to b sub n +um + + align:start position:0% +um + + + align:start position:0% +um +but it's in this interval + + align:start position:0% +but it's in this interval + + + align:start position:0% +but it's in this interval +right + + align:start position:0% +right + + + align:start position:0% +right +so then what would that have what would + + align:start position:0% +so then what would that have what would + + + align:start position:0% +so then what would that have what would +that say + + align:start position:0% +that say + + + align:start position:0% +that say +if i look at n bigger than or equal to m + + align:start position:0% +if i look at n bigger than or equal to m + + + align:start position:0% +if i look at n bigger than or equal to m +plus + + align:start position:0% +plus + + + align:start position:0% +plus +m 1 m 0 plus m 1 + + align:start position:0% +m 1 m 0 plus m 1 + + + align:start position:0% +m 1 m 0 plus m 1 +then n is bigger than both m 0 + + align:start position:0% +then n is bigger than both m 0 + + + align:start position:0% +then n is bigger than both m 0 +this guy and n is bigger than both m one + + align:start position:0% +this guy and n is bigger than both m one + + + align:start position:0% +this guy and n is bigger than both m one +this guy and therefore if i look at x + + align:start position:0% +this guy and therefore if i look at x + + + align:start position:0% +this guy and therefore if i look at x +sub n it's going to be between these two + + align:start position:0% +sub n it's going to be between these two + + + align:start position:0% +sub n it's going to be between these two +and in particular it's going to be in + + align:start position:0% +and in particular it's going to be in + + + align:start position:0% +and in particular it's going to be in +this interval + + align:start position:0% +this interval + + + align:start position:0% +this interval +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's uh the proof in a picture and + + align:start position:0% +so that's uh the proof in a picture and + + + align:start position:0% +so that's uh the proof in a picture and +now our goal is just to + + align:start position:0% +now our goal is just to + + + align:start position:0% +now our goal is just to +to write it down + + align:start position:0% +to write it down + + + align:start position:0% +to write it down +okay so that's that's the picture of of + + align:start position:0% +okay so that's that's the picture of of + + + align:start position:0% +okay so that's that's the picture of of +the proof but you know if you're + + align:start position:0% +the proof but you know if you're + + + align:start position:0% +the proof but you know if you're +actually trying to guess that why this + + align:start position:0% +actually trying to guess that why this + + + align:start position:0% +actually trying to guess that why this +would be true i mean the b sub bins you + + align:start position:0% +would be true i mean the b sub bins you + + + align:start position:0% +would be true i mean the b sub bins you +can imagine are are getting very close + + align:start position:0% +can imagine are are getting very close + + + align:start position:0% +can imagine are are getting very close +to x + + align:start position:0% +to x + + + align:start position:0% +to x +the a sub n's are also getting very + + align:start position:0% +the a sub n's are also getting very + + + align:start position:0% +the a sub n's are also getting very +close to x + + align:start position:0% +close to x + + + align:start position:0% +close to x +x sub n is in between the two so it's + + align:start position:0% +x sub n is in between the two so it's + + + align:start position:0% +x sub n is in between the two so it's +getting squeezed to x and that's the + + align:start position:0% +getting squeezed to x and that's the + + + align:start position:0% +getting squeezed to x and that's the +that's the name + + align:start position:0% +that's the name + + + align:start position:0% +that's the name +all right + + align:start position:0% + + + + align:start position:0% + +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so now we just need to turn this into + + align:start position:0% +so now we just need to turn this into + + + align:start position:0% +so now we just need to turn this into +written word so we need to show we're + + align:start position:0% +written word so we need to show we're + + + align:start position:0% +written word so we need to show we're +going to show that x sub n converges to + + align:start position:0% +going to show that x sub n converges to + + + align:start position:0% +going to show that x sub n converges to +x + + align:start position:0% +x + + + align:start position:0% +x +um so we're all we have is an epsilon + + align:start position:0% +um so we're all we have is an epsilon + + + align:start position:0% +um so we're all we have is an epsilon +delta proof + + align:start position:0% +delta proof + + + align:start position:0% +delta proof +um or we could use uh that theorem but + + align:start position:0% +um or we could use uh that theorem but + + + align:start position:0% +um or we could use uh that theorem but +let's go with an epsilon delta proof + + align:start position:0% +let's go with an epsilon delta proof + + + align:start position:0% +let's go with an epsilon delta proof +i mean not epsilon delta epsilon epsilon + + align:start position:0% +i mean not epsilon delta epsilon epsilon + + + align:start position:0% +i mean not epsilon delta epsilon epsilon +m + + align:start position:0% +m + + + align:start position:0% +m +epsilon delta proofs will come later + + align:start position:0% +epsilon delta proofs will come later + + + align:start position:0% +epsilon delta proofs will come later +so let epsilon be positive + + align:start position:0% +so let epsilon be positive + + + align:start position:0% +so let epsilon be positive +and + + align:start position:0% +and + + + align:start position:0% +and +since b sub n converges to x + + align:start position:0% +since b sub n converges to x + + + align:start position:0% +since b sub n converges to x +there exists a m sub zero in natural + + align:start position:0% +there exists a m sub zero in natural + + + align:start position:0% +there exists a m sub zero in natural +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +such that for all n bigger than or equal + + align:start position:0% +such that for all n bigger than or equal + + + align:start position:0% +such that for all n bigger than or equal +to m sub zero + + align:start position:0% +to m sub zero + + + align:start position:0% +to m sub zero +um + + align:start position:0% + + + + align:start position:0% + +b sub n + + align:start position:0% +b sub n + + + align:start position:0% +b sub n +minus x is less than epsilon + + align:start position:0% +minus x is less than epsilon + + + align:start position:0% +minus x is less than epsilon +an absolute value which + + align:start position:0% + + + + align:start position:0% + +is the same as + + align:start position:0% + + + + align:start position:0% + +saying well i mean it's not the same but + + align:start position:0% +saying well i mean it's not the same but + + + align:start position:0% +saying well i mean it's not the same but +it implies that b sub n is less than + + align:start position:0% +it implies that b sub n is less than + + + align:start position:0% +it implies that b sub n is less than +x plus epsilon + + align:start position:0% + + + + align:start position:0% + +since a sub n is converged to x as well + + align:start position:0% +since a sub n is converged to x as well + + + align:start position:0% +since a sub n is converged to x as well +there exists an m sub 1 + + align:start position:0% +there exists an m sub 1 + + + align:start position:0% +there exists an m sub 1 +natural number + + align:start position:0% +natural number + + + align:start position:0% +natural number +such that + + align:start position:0% +such that + + + align:start position:0% +such that +for all n bigger than or equal to m1 + + align:start position:0% + + + + align:start position:0% + +a sub n minus x and absolute value is + + align:start position:0% +a sub n minus x and absolute value is + + + align:start position:0% +a sub n minus x and absolute value is +less than epsilon + + align:start position:0% +less than epsilon + + + align:start position:0% +less than epsilon +which implies + + align:start position:0% +which implies + + + align:start position:0% +which implies +a sub n is between x minus epsilon and x + + align:start position:0% +a sub n is between x minus epsilon and x + + + align:start position:0% +a sub n is between x minus epsilon and x +plus epsilon but i'm only going to use + + align:start position:0% +plus epsilon but i'm only going to use + + + align:start position:0% +plus epsilon but i'm only going to use +one of those inequalities so + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +now i'm going to choose the capital m + + align:start position:0% +now i'm going to choose the capital m + + + align:start position:0% +now i'm going to choose the capital m +for my sequence x sub n that i'm trying + + align:start position:0% +for my sequence x sub n that i'm trying + + + align:start position:0% +for my sequence x sub n that i'm trying +to show converges to x + + align:start position:0% +to show converges to x + + + align:start position:0% +to show converges to x +so choose m to be + + align:start position:0% +so choose m to be + + + align:start position:0% +so choose m to be +m sub 0 plus m sub 1. i mean you could + + align:start position:0% +m sub 0 plus m sub 1. i mean you could + + + align:start position:0% +m sub 0 plus m sub 1. i mean you could +have chosen it to be the maximum of the + + align:start position:0% +have chosen it to be the maximum of the + + + align:start position:0% +have chosen it to be the maximum of the +two + + align:start position:0% +two + + + align:start position:0% +two +but this works just fine as well + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +if n is bigger than or equal to m + + align:start position:0% +if n is bigger than or equal to m + + + align:start position:0% +if n is bigger than or equal to m +this implies n is bigger than or equal + + align:start position:0% +this implies n is bigger than or equal + + + align:start position:0% +this implies n is bigger than or equal +to m0 + + align:start position:0% +to m0 + + + align:start position:0% +to m0 +and n is bigger than or equal to m1 + + align:start position:0% +and n is bigger than or equal to m1 + + + align:start position:0% +and n is bigger than or equal to m1 +which implies that both of these + + align:start position:0% +which implies that both of these + + + align:start position:0% +which implies that both of these +inequalities here are valid + + align:start position:0% +inequalities here are valid + + + align:start position:0% +inequalities here are valid +for this n + + align:start position:0% +for this n + + + align:start position:0% +for this n +so then + + align:start position:0% +so then + + + align:start position:0% +so then +x minus epsilon is less than a sub n + + align:start position:0% +x minus epsilon is less than a sub n + + + align:start position:0% +x minus epsilon is less than a sub n +which by assumption is less than or + + align:start position:0% +which by assumption is less than or + + + align:start position:0% +which by assumption is less than or +equal to + + align:start position:0% + + + + align:start position:0% + +x sub n + + align:start position:0% + + + + align:start position:0% + +which is less than or equal to b sub n + + align:start position:0% +which is less than or equal to b sub n + + + align:start position:0% +which is less than or equal to b sub n +which is less than + + align:start position:0% +which is less than + + + align:start position:0% +which is less than +x plus epsilon + + align:start position:0% +x plus epsilon + + + align:start position:0% +x plus epsilon +now these string of inequalities + + align:start position:0% +now these string of inequalities + + + align:start position:0% +now these string of inequalities +therefore tell us that x minus epsilon + + align:start position:0% +therefore tell us that x minus epsilon + + + align:start position:0% +therefore tell us that x minus epsilon +is less than x of n is less than + + align:start position:0% +is less than x of n is less than + + + align:start position:0% +is less than x of n is less than +x plus epsilon + + align:start position:0% + + + + align:start position:0% + +which is + + align:start position:0% +which is + + + align:start position:0% +which is +equivalent to saying the absolute value + + align:start position:0% +equivalent to saying the absolute value + + + align:start position:0% +equivalent to saying the absolute value +of x + + align:start position:0% +of x + + + align:start position:0% +of x +sub n minus x + + align:start position:0% +sub n minus x + + + align:start position:0% +sub n minus x +is less than epsilon and therefore + + align:start position:0% + + + + align:start position:0% + +x sub n converges to x + + align:start position:0% + + + + align:start position:0% + +so these two + + align:start position:0% +so these two + + + align:start position:0% +so these two +facts together + + align:start position:0% + + + + align:start position:0% + +kind of give us a very robust and short + + align:start position:0% +kind of give us a very robust and short + + + align:start position:0% +kind of give us a very robust and short +way to prove + + align:start position:0% +way to prove + + + align:start position:0% +way to prove +limits of sequences + + align:start position:0% + + + + align:start position:0% + +so for example let me give you a + + align:start position:0% + + + + align:start position:0% + +simple one + + align:start position:0% + + + + align:start position:0% + +let's show the limit as n goes to + + align:start position:0% +let's show the limit as n goes to + + + align:start position:0% +let's show the limit as n goes to +infinity of n squared over n squared + + align:start position:0% +infinity of n squared over n squared + + + align:start position:0% +infinity of n squared over n squared +plus n + + align:start position:0% +plus n + + + align:start position:0% +plus n +plus 1 + + align:start position:0% +plus 1 + + + align:start position:0% +plus 1 +equals 1. + + align:start position:0% +equals 1. + + + align:start position:0% +equals 1. +so + + align:start position:0% +so + + + align:start position:0% +so +i mean this + + align:start position:0% +i mean this + + + align:start position:0% +i mean this +is a very simple limit to use these + + align:start position:0% +is a very simple limit to use these + + + align:start position:0% +is a very simple limit to use these +theorems on but in practice um you know + + align:start position:0% +theorems on but in practice um you know + + + align:start position:0% +theorems on but in practice um you know +you don't always have just a simple + + align:start position:0% +you don't always have just a simple + + + align:start position:0% +you don't always have just a simple +expression like this + + align:start position:0% +expression like this + + + align:start position:0% +expression like this +um + + align:start position:0% +um + + + align:start position:0% +um +okay so + + align:start position:0% + + + + align:start position:0% + +and we'll use these two theorems in + + align:start position:0% +and we'll use these two theorems in + + + align:start position:0% +and we'll use these two theorems in +conjunction to prove some other theorems + + align:start position:0% +conjunction to prove some other theorems + + + align:start position:0% +conjunction to prove some other theorems +here in a minute but let's just see it + + align:start position:0% +here in a minute but let's just see it + + + align:start position:0% +here in a minute but let's just see it +in action once + + align:start position:0% +in action once + + + align:start position:0% +in action once +um + + align:start position:0% +um + + + align:start position:0% +um +let me look at + + align:start position:0% +let me look at + + + align:start position:0% +let me look at +so + + align:start position:0% +so + + + align:start position:0% +so +this + + align:start position:0% +this + + + align:start position:0% +this +sequence converges to one if and only if + + align:start position:0% +sequence converges to one if and only if + + + align:start position:0% +sequence converges to one if and only if +the absolute value of the difference + + align:start position:0% +the absolute value of the difference + + + align:start position:0% +the absolute value of the difference +converges to zero so let's look at the + + align:start position:0% +converges to zero so let's look at the + + + align:start position:0% +converges to zero so let's look at the +absolute value of the difference + + align:start position:0% + + + + align:start position:0% + +this is equal to now just doing the + + align:start position:0% +this is equal to now just doing the + + + align:start position:0% +this is equal to now just doing the +algebra this is equal to + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +taking absolute values gives me + + align:start position:0% + + + + align:start position:0% + +n plus one over n squared + + align:start position:0% +n plus one over n squared + + + align:start position:0% +n plus one over n squared +plus n plus one + + align:start position:0% + + + + align:start position:0% + +and this is less than or equal to this + + align:start position:0% +and this is less than or equal to this + + + align:start position:0% +and this is less than or equal to this +one is making things bigger so i can + + align:start position:0% +one is making things bigger so i can + + + align:start position:0% +one is making things bigger so i can +drop it and this is less than or equal + + align:start position:0% +drop it and this is less than or equal + + + align:start position:0% +drop it and this is less than or equal +to n + + align:start position:0% +to n + + + align:start position:0% +to n +plus one over + + align:start position:0% +plus one over + + + align:start position:0% +plus one over +n squared plus n now n squared plus n i + + align:start position:0% +n squared plus n now n squared plus n i + + + align:start position:0% +n squared plus n now n squared plus n i +can factor into n times n plus one so + + align:start position:0% +can factor into n times n plus one so + + + align:start position:0% +can factor into n times n plus one so +then that cancels with this n plus one + + align:start position:0% +then that cancels with this n plus one + + + align:start position:0% +then that cancels with this n plus one +on top + + align:start position:0% +on top + + + align:start position:0% +on top +and i just get one over n + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +zero is less than or equal to + + align:start position:0% +zero is less than or equal to + + + align:start position:0% +zero is less than or equal to +n squared over n squared plus n plus 1 + + align:start position:0% +n squared over n squared plus n plus 1 + + + align:start position:0% +n squared over n squared plus n plus 1 +minus 1 + + align:start position:0% +minus 1 + + + align:start position:0% +minus 1 +which is less than or equal to + + align:start position:0% +which is less than or equal to + + + align:start position:0% +which is less than or equal to +1 over n + + align:start position:0% +1 over n + + + align:start position:0% +1 over n +now 1 over n we've shown + + align:start position:0% +now 1 over n we've shown + + + align:start position:0% +now 1 over n we've shown +using epsilon delta proof i mean epsilon + + align:start position:0% +using epsilon delta proof i mean epsilon + + + align:start position:0% +using epsilon delta proof i mean epsilon +m proof we've shown 1 over n converges + + align:start position:0% +m proof we've shown 1 over n converges + + + align:start position:0% +m proof we've shown 1 over n converges +to 0. + + align:start position:0% +to 0. + + + align:start position:0% +to 0. +so since + + align:start position:0% + + + + align:start position:0% + +zero converges to zero the left side + + align:start position:0% +zero converges to zero the left side + + + align:start position:0% +zero converges to zero the left side +and one over n converges to zero the + + align:start position:0% +and one over n converges to zero the + + + align:start position:0% +and one over n converges to zero the +right side + + align:start position:0% +right side + + + align:start position:0% +right side +that implies by the squeeze theorem + + align:start position:0% + + + + align:start position:0% + +n squared over n squared plus n plus one + + align:start position:0% +n squared over n squared plus n plus one + + + align:start position:0% +n squared over n squared plus n plus one +minus one converges to zero + + align:start position:0% + + + + align:start position:0% + +by the squeeze theorem + + align:start position:0% +by the squeeze theorem + + + align:start position:0% +by the squeeze theorem +which implies that + + align:start position:0% + + + + align:start position:0% + +n squared over n squared plus n plus 1 + + align:start position:0% +n squared over n squared plus n plus 1 + + + align:start position:0% +n squared over n squared plus n plus 1 +converges to 1 + + align:start position:0% +converges to 1 + + + align:start position:0% +converges to 1 +by that first theorem + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now you can imagine that instead of + + align:start position:0% +now you can imagine that instead of + + + align:start position:0% +now you can imagine that instead of +having this at your disposal + + align:start position:0% + + + + align:start position:0% + +i asked you to do + + align:start position:0% +i asked you to do + + + align:start position:0% +i asked you to do +an epsilon proof epsilon m proof of this + + align:start position:0% +an epsilon proof epsilon m proof of this + + + align:start position:0% +an epsilon proof epsilon m proof of this +statement + + align:start position:0% + + + + align:start position:0% + +then you would have taken this and + + align:start position:0% +then you would have taken this and + + + align:start position:0% +then you would have taken this and +played with it just like we did here + + align:start position:0% +played with it just like we did here + + + align:start position:0% +played with it just like we did here +and gotten to one over n + + align:start position:0% +and gotten to one over n + + + align:start position:0% +and gotten to one over n +and therefore if this is less than + + align:start position:0% +and therefore if this is less than + + + align:start position:0% +and therefore if this is less than +epsilon that would imply this is less + + align:start position:0% +epsilon that would imply this is less + + + align:start position:0% +epsilon that would imply this is less +than epsilon + + align:start position:0% + + + + align:start position:0% + +so you would choose capital m to be + + align:start position:0% +so you would choose capital m to be + + + align:start position:0% +so you would choose capital m to be +so that one over capital m is less than + + align:start position:0% +so that one over capital m is less than + + + align:start position:0% +so that one over capital m is less than +epsilon but + + align:start position:0% +epsilon but + + + align:start position:0% +epsilon but +using these two theorems kind of saves + + align:start position:0% +using these two theorems kind of saves + + + align:start position:0% +using these two theorems kind of saves +us some + + align:start position:0% +us some + + + align:start position:0% +us some +a little work and a little time + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% + + + + align:start position:0% + +so at the end of the lecture last time + + align:start position:0% +so at the end of the lecture last time + + + align:start position:0% +so at the end of the lecture last time +we discussed the notion of subsequences + + align:start position:0% +we discussed the notion of subsequences + + + align:start position:0% +we discussed the notion of subsequences +and we showed that + + align:start position:0% +and we showed that + + + align:start position:0% +and we showed that +limiting limits and subsequences + + align:start position:0% +limiting limits and subsequences + + + align:start position:0% +limiting limits and subsequences +interact + + align:start position:0% +interact + + + align:start position:0% +interact +nicely meaning + + align:start position:0% +nicely meaning + + + align:start position:0% +nicely meaning +if i have a convergent sequence then + + align:start position:0% +if i have a convergent sequence then + + + align:start position:0% +if i have a convergent sequence then +every subsequence converges to the same + + align:start position:0% +every subsequence converges to the same + + + align:start position:0% +every subsequence converges to the same +thing + + align:start position:0% +thing + + + align:start position:0% +thing +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +now a natural question is how do limits + + align:start position:0% +now a natural question is how do limits + + + align:start position:0% +now a natural question is how do limits +interact with the order of the real + + align:start position:0% +interact with the order of the real + + + align:start position:0% +interact with the order of the real +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +okay um + + align:start position:0% + + + + align:start position:0% + +right r has this uh these two + + align:start position:0% +right r has this uh these two + + + align:start position:0% +right r has this uh these two +fundamental properties about it that um + + align:start position:0% +fundamental properties about it that um + + + align:start position:0% +fundamental properties about it that um +it's + + align:start position:0% +it's + + + align:start position:0% +it's +so first off that it has the least upper + + align:start position:0% +so first off that it has the least upper + + + align:start position:0% +so first off that it has the least upper +bound property and also that it's a uh + + align:start position:0% +bound property and also that it's a uh + + + align:start position:0% +bound property and also that it's a uh +an ordered field + + align:start position:0% +an ordered field + + + align:start position:0% +an ordered field +so first natural question is how does + + align:start position:0% +so first natural question is how does + + + align:start position:0% +so first natural question is how does +this definition of limit convergence um + + align:start position:0% +this definition of limit convergence um + + + align:start position:0% +this definition of limit convergence um +interact with the order + + align:start position:0% +interact with the order + + + align:start position:0% +interact with the order +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so this first theorem states + + align:start position:0% + + + + align:start position:0% + +or this theorem that kind of answers + + align:start position:0% +or this theorem that kind of answers + + + align:start position:0% +or this theorem that kind of answers +this question is the following is that + + align:start position:0% +this question is the following is that + + + align:start position:0% +this question is the following is that +limit limits respect order + + align:start position:0% +limit limits respect order + + + align:start position:0% +limit limits respect order +basically + + align:start position:0% +basically + + + align:start position:0% +basically +so if + + align:start position:0% + + + + align:start position:0% + +xn + + align:start position:0% + + + + align:start position:0% + +yn + + align:start position:0% + + + + align:start position:0% + +are + + align:start position:0% + + + + align:start position:0% + +convergent sequences + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +for all n + + align:start position:0% + + + + align:start position:0% + +x n is less than or equal to y n + + align:start position:0% +x n is less than or equal to y n + + + align:start position:0% +x n is less than or equal to y n +then what should be the conclusion the + + align:start position:0% +then what should be the conclusion the + + + align:start position:0% +then what should be the conclusion the +limit as n goes to infinity so what i + + align:start position:0% +limit as n goes to infinity so what i + + + align:start position:0% +limit as n goes to infinity so what i +said a minute ago as limits respect + + align:start position:0% +said a minute ago as limits respect + + + align:start position:0% +said a minute ago as limits respect +inequality then i should be able to take + + align:start position:0% +inequality then i should be able to take + + + align:start position:0% +inequality then i should be able to take +the limits of both sides and still have + + align:start position:0% +the limits of both sides and still have + + + align:start position:0% +the limits of both sides and still have +this inequality + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +limit as n goes to infinity is less than + + align:start position:0% +limit as n goes to infinity is less than + + + align:start position:0% +limit as n goes to infinity is less than +or equal to the limit + + align:start position:0% + + + + align:start position:0% + +as n goes to infinity of y sub n + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +the simple corollary that follows from + + align:start position:0% +the simple corollary that follows from + + + align:start position:0% +the simple corollary that follows from +this + + align:start position:0% +this + + + align:start position:0% +this +is that + + align:start position:0% + + + + align:start position:0% + +if x event is a + + align:start position:0% + + + + align:start position:0% + +convergence sequence + + align:start position:0% + + + + align:start position:0% + +and for all in a natural number + + align:start position:0% + + + + align:start position:0% + +you have two numbers + + align:start position:0% +you have two numbers + + + align:start position:0% +you have two numbers +uh + + align:start position:0% +uh + + + align:start position:0% +uh +a and b such that a sub n is less than + + align:start position:0% +a and b such that a sub n is less than + + + align:start position:0% +a and b such that a sub n is less than +or equal to + + align:start position:0% +or equal to + + + align:start position:0% +or equal to +or a is less than or equal to x of n is + + align:start position:0% +or a is less than or equal to x of n is + + + align:start position:0% +or a is less than or equal to x of n is +less than or equal to b + + align:start position:0% +less than or equal to b + + + align:start position:0% +less than or equal to b +then + + align:start position:0% +then + + + align:start position:0% +then +this implies that + + align:start position:0% + + + + align:start position:0% + +the limit of x sub n is also between + + align:start position:0% +the limit of x sub n is also between + + + align:start position:0% +the limit of x sub n is also between +a and b + + align:start position:0% +a and b + + + align:start position:0% +a and b +okay + + align:start position:0% +okay + + + align:start position:0% +okay +let me say + + align:start position:0% +let me say + + + align:start position:0% +let me say +something very brief about + + align:start position:0% + + + + align:start position:0% + +what this says and doesn't say + + align:start position:0% +what this says and doesn't say + + + align:start position:0% +what this says and doesn't say +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +so what does this not say + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +you may lose a strict inequality meaning + + align:start position:0% +you may lose a strict inequality meaning + + + align:start position:0% +you may lose a strict inequality meaning +what + + align:start position:0% + + + + align:start position:0% + +it can be the case that x sub n is less + + align:start position:0% +it can be the case that x sub n is less + + + align:start position:0% +it can be the case that x sub n is less +than y sub n for all n but the limit of + + align:start position:0% +than y sub n for all n but the limit of + + + align:start position:0% +than y sub n for all n but the limit of +x of n equals the limit of y sub n + + align:start position:0% +x of n equals the limit of y sub n + + + align:start position:0% +x of n equals the limit of y sub n +okay so simply having less than x sub n + + align:start position:0% +okay so simply having less than x sub n + + + align:start position:0% +okay so simply having less than x sub n +less than y sub n does not imply the + + align:start position:0% +less than y sub n does not imply the + + + align:start position:0% +less than y sub n does not imply the +limit of x sub n is less than the limit + + align:start position:0% +limit of x sub n is less than the limit + + + align:start position:0% +limit of x sub n is less than the limit +of y sub n + + align:start position:0% +of y sub n + + + align:start position:0% +of y sub n +all right so what do i mean by this + + align:start position:0% + + + + align:start position:0% + +this does not imply that + + align:start position:0% +this does not imply that + + + align:start position:0% +this does not imply that +the limit + + align:start position:0% + + + + align:start position:0% + +is less than y sub n + + align:start position:0% +is less than y sub n + + + align:start position:0% +is less than y sub n +now at this point in class i would ask + + align:start position:0% +now at this point in class i would ask + + + align:start position:0% +now at this point in class i would ask +somebody to give me a counter example + + align:start position:0% + + + + align:start position:0% + +so at this point i'm going to take + + align:start position:0% +so at this point i'm going to take + + + align:start position:0% +so at this point i'm going to take +a bite of my cookie + + align:start position:0% +a bite of my cookie + + + align:start position:0% +a bite of my cookie +and let you think about that + + align:start position:0% + + + + align:start position:0% + +i didn't have to take a bite in my + + align:start position:0% +i didn't have to take a bite in my + + + align:start position:0% +i didn't have to take a bite in my +cookie you could have just paused the + + align:start position:0% +cookie you could have just paused the + + + align:start position:0% +cookie you could have just paused the +video and thought about it + + align:start position:0% + + + + align:start position:0% + +but then i wouldn't get a bite of my + + align:start position:0% +but then i wouldn't get a bite of my + + + align:start position:0% +but then i wouldn't get a bite of my +cookie + + align:start position:0% +cookie + + + align:start position:0% +cookie +okay + + align:start position:0% + + + + align:start position:0% + +so what's an example of two sequences + + align:start position:0% +so what's an example of two sequences + + + align:start position:0% +so what's an example of two sequences +that satisfy this + + align:start position:0% +that satisfy this + + + align:start position:0% +that satisfy this +but don't satisfy this + + align:start position:0% + + + + align:start position:0% + +if x of n equals 0 for all n + + align:start position:0% + + + + align:start position:0% + +and y sub n equals 1 over n + + align:start position:0% +and y sub n equals 1 over n + + + align:start position:0% +and y sub n equals 1 over n +right + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +x sub n is less than y sub n for all n + + align:start position:0% + + + + align:start position:0% + +and what's the limit + + align:start position:0% + + + + align:start position:0% + +x have been well that's just zero + + align:start position:0% + + + + align:start position:0% + +and we've + + align:start position:0% + + + + align:start position:0% + +and before the limit of y sub n that's + + align:start position:0% +and before the limit of y sub n that's + + + align:start position:0% +and before the limit of y sub n that's +just zero and these two things equal + + align:start position:0% +just zero and these two things equal + + + align:start position:0% +just zero and these two things equal +each other this is not less than that + + align:start position:0% +each other this is not less than that + + + align:start position:0% +each other this is not less than that +okay so i just want to make that that + + align:start position:0% +okay so i just want to make that that + + + align:start position:0% +okay so i just want to make that that +small point + + align:start position:0% + + + + align:start position:0% + +it could pop up as a small question on + + align:start position:0% +it could pop up as a small question on + + + align:start position:0% +it could pop up as a small question on +one of the midterms + + align:start position:0% +one of the midterms + + + align:start position:0% +one of the midterms +i should say the midterm and + + align:start position:0% +i should say the midterm and + + + align:start position:0% +i should say the midterm and +possibly the final + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so let's prove uh + + align:start position:0% + + + + align:start position:0% + +let's prove one two follows immediately + + align:start position:0% +let's prove one two follows immediately + + + align:start position:0% +let's prove one two follows immediately +from one right um + + align:start position:0% +from one right um + + + align:start position:0% +from one right um +for two we simply take + + align:start position:0% +for two we simply take + + + align:start position:0% +for two we simply take +you know for example the upper + + align:start position:0% +you know for example the upper + + + align:start position:0% +you know for example the upper +inequality x of n is less than or equal + + align:start position:0% +inequality x of n is less than or equal + + + align:start position:0% +inequality x of n is less than or equal +to b we take y sub n to be the constant + + align:start position:0% +to b we take y sub n to be the constant + + + align:start position:0% +to b we take y sub n to be the constant +sequence b + + align:start position:0% +sequence b + + + align:start position:0% +sequence b +and + + align:start position:0% +and + + + align:start position:0% +and +um for the other one we would take + + align:start position:0% +um for the other one we would take + + + align:start position:0% +um for the other one we would take +the bigger sequence to be x sub n and + + align:start position:0% +the bigger sequence to be x sub n and + + + align:start position:0% +the bigger sequence to be x sub n and +the smaller sequence to be the constant + + align:start position:0% +the smaller sequence to be the constant + + + align:start position:0% +the smaller sequence to be the constant +sequence a so two follows immediately + + align:start position:0% +sequence a so two follows immediately + + + align:start position:0% +sequence a so two follows immediately +from one so we're just going to do one + + align:start position:0% +from one so we're just going to do one + + + align:start position:0% +from one so we're just going to do one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and we haven't done a proof by + + align:start position:0% +and we haven't done a proof by + + + align:start position:0% +and we haven't done a proof by +contradiction in a while so why not do + + align:start position:0% +contradiction in a while so why not do + + + align:start position:0% +contradiction in a while so why not do +it by contradiction + + align:start position:0% +it by contradiction + + + align:start position:0% +it by contradiction +um okay so the proof uh + + align:start position:0% + + + + align:start position:0% + +let's label these sequences so i don't + + align:start position:0% +let's label these sequences so i don't + + + align:start position:0% +let's label these sequences so i don't +have to write + + align:start position:0% +have to write + + + align:start position:0% +have to write +um + + align:start position:0% +um + + + align:start position:0% +um +limit as n goes to infinity and limit of + + align:start position:0% +limit as n goes to infinity and limit of + + + align:start position:0% +limit as n goes to infinity and limit of +x of n and limit as n goes to infinity + + align:start position:0% +x of n and limit as n goes to infinity + + + align:start position:0% +x of n and limit as n goes to infinity +of y sub n so much + + align:start position:0% +of y sub n so much + + + align:start position:0% +of y sub n so much +so let's call their limits x and y + + align:start position:0% + + + + align:start position:0% + +and what we want to show + + align:start position:0% + + + + align:start position:0% + +x is less than or equal to y + + align:start position:0% +x is less than or equal to y + + + align:start position:0% +x is less than or equal to y +right that's our goal and we're going to + + align:start position:0% +right that's our goal and we're going to + + + align:start position:0% +right that's our goal and we're going to +prove this by contradiction + + align:start position:0% + + + + align:start position:0% + +that is let's assume y is less than x + + align:start position:0% +that is let's assume y is less than x + + + align:start position:0% +that is let's assume y is less than x +and arrive at a false statement + + align:start position:0% +and arrive at a false statement + + + align:start position:0% +and arrive at a false statement +which contradicts our + + align:start position:0% +which contradicts our + + + align:start position:0% +which contradicts our +setting or assumptions that we have + + align:start position:0% +setting or assumptions that we have + + + align:start position:0% +setting or assumptions that we have +assume y + + align:start position:0% +assume y + + + align:start position:0% +assume y +is less than x + + align:start position:0% +is less than x + + + align:start position:0% +is less than x +now + + align:start position:0% +now + + + align:start position:0% +now +um + + align:start position:0% +um + + + align:start position:0% +um +let me draw a picture here to go along + + align:start position:0% +let me draw a picture here to go along + + + align:start position:0% +let me draw a picture here to go along +with what's + + align:start position:0% +with what's + + + align:start position:0% +with what's +going to happen + + align:start position:0% + + + + align:start position:0% + +so if y + + align:start position:0% +so if y + + + align:start position:0% +so if y +is less than x + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +all of the y sub n's have to be near y + + align:start position:0% +all of the y sub n's have to be near y + + + align:start position:0% +all of the y sub n's have to be near y +as a if i go far enough out and all the + + align:start position:0% +as a if i go far enough out and all the + + + align:start position:0% +as a if i go far enough out and all the +exit bins have to be near x as long as i + + align:start position:0% +exit bins have to be near x as long as i + + + align:start position:0% +exit bins have to be near x as long as i +go far enough out + + align:start position:0% +go far enough out + + + align:start position:0% +go far enough out +right so that would contradict + + align:start position:0% +right so that would contradict + + + align:start position:0% +right so that would contradict +eventually the fact that the x sub n's + + align:start position:0% +eventually the fact that the x sub n's + + + align:start position:0% +eventually the fact that the x sub n's +are supposed to be less than or equal to + + align:start position:0% +are supposed to be less than or equal to + + + align:start position:0% +are supposed to be less than or equal to +the y sub n's right if y is less than x + + align:start position:0% +the y sub n's right if y is less than x + + + align:start position:0% +the y sub n's right if y is less than x +and let's say i go out + + align:start position:0% + + + + align:start position:0% + +let's say half the distance between y + + align:start position:0% +let's say half the distance between y + + + align:start position:0% +let's say half the distance between y +and x + + align:start position:0% +and x + + + align:start position:0% +and x +so this is + + align:start position:0% + + + + align:start position:0% + +if you like the + + align:start position:0% +if you like the + + + align:start position:0% +if you like the +midpoint and all the y sub n's are here + + align:start position:0% + + + + align:start position:0% + +and all the x bins + + align:start position:0% +and all the x bins + + + align:start position:0% +and all the x bins +are here and the y sub n's + + align:start position:0% + + + + align:start position:0% + +are here then i cannot have x sub n less + + align:start position:0% +are here then i cannot have x sub n less + + + align:start position:0% +are here then i cannot have x sub n less +than or equal to y sub n which is my + + align:start position:0% +than or equal to y sub n which is my + + + align:start position:0% +than or equal to y sub n which is my +assumption right + + align:start position:0% + + + + align:start position:0% + +which is the assumption in my in my + + align:start position:0% +which is the assumption in my in my + + + align:start position:0% +which is the assumption in my in my +theorem + + align:start position:0% +theorem + + + align:start position:0% +theorem +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now i i + + align:start position:0% +now i i + + + align:start position:0% +now i i +maybe i should have written this here + + align:start position:0% + + + + align:start position:0% + +sometimes it's good to to reiterate what + + align:start position:0% +sometimes it's good to to reiterate what + + + align:start position:0% +sometimes it's good to to reiterate what +your assumptions are suppose we're all + + align:start position:0% +your assumptions are suppose we're all + + + align:start position:0% +your assumptions are suppose we're all +in x is less than or y sub n + + align:start position:0% +in x is less than or y sub n + + + align:start position:0% +in x is less than or y sub n +and + + align:start position:0% + + + + align:start position:0% + +like that and so the thing we're trying + + align:start position:0% +like that and so the thing we're trying + + + align:start position:0% +like that and so the thing we're trying +to show is is this okay so we assume + + align:start position:0% +to show is is this okay so we assume + + + align:start position:0% +to show is is this okay so we assume +the negation of this and arrive at a + + align:start position:0% +the negation of this and arrive at a + + + align:start position:0% +the negation of this and arrive at a +contradiction + + align:start position:0% +contradiction + + + align:start position:0% +contradiction +uh + + align:start position:0% +uh + + + align:start position:0% +uh +to the things we're assuming or just a + + align:start position:0% +to the things we're assuming or just a + + + align:start position:0% +to the things we're assuming or just a +general + + align:start position:0% +general + + + align:start position:0% +general +um true facts + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +yeah i had to had to add the word true + + align:start position:0% +yeah i had to had to add the word true + + + align:start position:0% +yeah i had to had to add the word true +on the facts because there like i said + + align:start position:0% +on the facts because there like i said + + + align:start position:0% +on the facts because there like i said +at some point there's alternative facts + + align:start position:0% +at some point there's alternative facts + + + align:start position:0% +at some point there's alternative facts +flying around out there + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this picture we're going to turn this + + align:start position:0% +so this picture we're going to turn this + + + align:start position:0% +so this picture we're going to turn this +into a proof + + align:start position:0% +into a proof + + + align:start position:0% +into a proof +so + + align:start position:0% + + + + align:start position:0% + +since y n converges to y + + align:start position:0% +since y n converges to y + + + align:start position:0% +since y n converges to y +exists a natural number m sub + + align:start position:0% +exists a natural number m sub + + + align:start position:0% +exists a natural number m sub +sub zero such that + + align:start position:0% + + + + align:start position:0% + +for all n + + align:start position:0% + + + + align:start position:0% + +bigger than or equal to m sub zero + + align:start position:0% + + + + align:start position:0% + +y sub n minus y + + align:start position:0% +y sub n minus y + + + align:start position:0% +y sub n minus y +is less than + + align:start position:0% + + + + align:start position:0% + +x minus y over 2. now that's a positive + + align:start position:0% +x minus y over 2. now that's a positive + + + align:start position:0% +x minus y over 2. now that's a positive +number because we're assuming + + align:start position:0% +number because we're assuming + + + align:start position:0% +number because we're assuming +x is bigger than y + + align:start position:0% +x is bigger than y + + + align:start position:0% +x is bigger than y +all right + + align:start position:0% +all right + + + align:start position:0% +all right +and by the definition of limit + + align:start position:0% +and by the definition of limit + + + align:start position:0% +and by the definition of limit +given any positive number i can find an + + align:start position:0% +given any positive number i can find an + + + align:start position:0% +given any positive number i can find an +integer so that for all n bigger than or + + align:start position:0% +integer so that for all n bigger than or + + + align:start position:0% +integer so that for all n bigger than or +equal to that integer this thing is less + + align:start position:0% +equal to that integer this thing is less + + + align:start position:0% +equal to that integer this thing is less +than that small number and i'm just + + align:start position:0% +than that small number and i'm just + + + align:start position:0% +than that small number and i'm just +choosing that small number to be this + + align:start position:0% +choosing that small number to be this + + + align:start position:0% +choosing that small number to be this +very special small number because + + align:start position:0% +very special small number because + + + align:start position:0% +very special small number because +that's going to + + align:start position:0% +that's going to + + + align:start position:0% +that's going to +help me arrive at a contradiction + + align:start position:0% + + + + align:start position:0% + +since xn converges to x there exists a + + align:start position:0% +since xn converges to x there exists a + + + align:start position:0% +since xn converges to x there exists a +m1 natural number + + align:start position:0% +m1 natural number + + + align:start position:0% +m1 natural number +such that for all n + + align:start position:0% +such that for all n + + + align:start position:0% +such that for all n +bigger than or equal to m1 + + align:start position:0% + + + + align:start position:0% + +x sub n minus x is less than + + align:start position:0% +x sub n minus x is less than + + + align:start position:0% +x sub n minus x is less than +the same thing + + align:start position:0% +the same thing + + + align:start position:0% +the same thing +okay so this is + + align:start position:0% +okay so this is + + + align:start position:0% +okay so this is +um + + align:start position:0% +um + + + align:start position:0% +um +putting into a precise form what i was + + align:start position:0% +putting into a precise form what i was + + + align:start position:0% +putting into a precise form what i was +saying that all the x bins need to be + + align:start position:0% +saying that all the x bins need to be + + + align:start position:0% +saying that all the x bins need to be +close to x eventually and all the y sub + + align:start position:0% +close to x eventually and all the y sub + + + align:start position:0% +close to x eventually and all the y sub +n's need to be close to y eventually and + + align:start position:0% +n's need to be close to y eventually and + + + align:start position:0% +n's need to be close to y eventually and +how eventually well eventually enough so + + align:start position:0% +how eventually well eventually enough so + + + align:start position:0% +how eventually well eventually enough so +that + + align:start position:0% +that + + + align:start position:0% +that +i'm in these two + + align:start position:0% +i'm in these two + + + align:start position:0% +i'm in these two +disjoint intervals + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +let n be + + align:start position:0% + + + + align:start position:0% + +m sub 0 plus m sub 1 + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +n is bigger than or equal to m sub 0 and + + align:start position:0% +n is bigger than or equal to m sub 0 and + + + align:start position:0% +n is bigger than or equal to m sub 0 and +n is bigger than or equal to m sub 1. so + + align:start position:0% +n is bigger than or equal to m sub 1. so + + + align:start position:0% +n is bigger than or equal to m sub 1. so +both of these inequalities are valid + + align:start position:0% +both of these inequalities are valid + + + align:start position:0% +both of these inequalities are valid +for this n + + align:start position:0% +for this n + + + align:start position:0% +for this n +and what does this mean + + align:start position:0% +and what does this mean + + + align:start position:0% +and what does this mean +well then that implies that y sub n + + align:start position:0% +well then that implies that y sub n + + + align:start position:0% +well then that implies that y sub n +so let me um + + align:start position:0% + + + + align:start position:0% + +tack on one more inequality just by + + align:start position:0% +tack on one more inequality just by + + + align:start position:0% +tack on one more inequality just by +removing the absolute values + + align:start position:0% +removing the absolute values + + + align:start position:0% +removing the absolute values +this uh + + align:start position:0% +this uh + + + align:start position:0% +this uh +and adding y this tells me y sub n is + + align:start position:0% +and adding y this tells me y sub n is + + + align:start position:0% +and adding y this tells me y sub n is +less than + + align:start position:0% + + + + align:start position:0% + +x plus y over two + + align:start position:0% +x plus y over two + + + align:start position:0% +x plus y over two +and this tells me + + align:start position:0% +and this tells me + + + align:start position:0% +and this tells me +x of n is less than + + align:start position:0% + + + + align:start position:0% + +or the other way sorry + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% + + + + align:start position:0% + +we'll just write this down here so then + + align:start position:0% +we'll just write this down here so then + + + align:start position:0% +we'll just write this down here so then +y sub n + + align:start position:0% + + + + align:start position:0% + +is less than + + align:start position:0% + + + + align:start position:0% + +y plus x minus y over 2 which equals + + align:start position:0% +y plus x minus y over 2 which equals + + + align:start position:0% +y plus x minus y over 2 which equals +x plus y over 2 + + align:start position:0% +x plus y over 2 + + + align:start position:0% +x plus y over 2 +which equals x minus + + align:start position:0% +which equals x minus + + + align:start position:0% +which equals x minus +x minus y over 2 + + align:start position:0% +x minus y over 2 + + + align:start position:0% +x minus y over 2 +and this is less than + + align:start position:0% +and this is less than + + + align:start position:0% +and this is less than +x sub n + + align:start position:0% +x sub n + + + align:start position:0% +x sub n +right by the second inequality so this + + align:start position:0% +right by the second inequality so this + + + align:start position:0% +right by the second inequality so this +follows + + align:start position:0% +follows + + + align:start position:0% +follows +from the first inequality + + align:start position:0% +from the first inequality + + + align:start position:0% +from the first inequality +this follows from the second inequality + + align:start position:0% +this follows from the second inequality + + + align:start position:0% +this follows from the second inequality +right + + align:start position:0% +right + + + align:start position:0% +right +which implies for this specific n y sub + + align:start position:0% +which implies for this specific n y sub + + + align:start position:0% +which implies for this specific n y sub +n is less than + + align:start position:0% +n is less than + + + align:start position:0% +n is less than +x sub n and this is a contradiction to + + align:start position:0% +x sub n and this is a contradiction to + + + align:start position:0% +x sub n and this is a contradiction to +our assumption + + align:start position:0% +our assumption + + + align:start position:0% +our assumption +that y sub n is bigger than or equal to + + align:start position:0% +that y sub n is bigger than or equal to + + + align:start position:0% +that y sub n is bigger than or equal to +x sub n for all n + + align:start position:0% +x sub n for all n + + + align:start position:0% +x sub n for all n +okay so we had just found based on this + + align:start position:0% +okay so we had just found based on this + + + align:start position:0% +okay so we had just found based on this +this assumption here that + + align:start position:0% +this assumption here that + + + align:start position:0% +this assumption here that +uh we arrive at a contradiction to our + + align:start position:0% +uh we arrive at a contradiction to our + + + align:start position:0% +uh we arrive at a contradiction to our +other assumptions and therefore + + align:start position:0% +other assumptions and therefore + + + align:start position:0% +other assumptions and therefore +this must be false + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +that's how limits interact with + + align:start position:0% +that's how limits interact with + + + align:start position:0% +that's how limits interact with +inequalities + + align:start position:0% +inequalities + + + align:start position:0% +inequalities +so if i have two sequences one bigger + + align:start position:0% +so if i have two sequences one bigger + + + align:start position:0% +so if i have two sequences one bigger +than the other then the limits respect + + align:start position:0% +than the other then the limits respect + + + align:start position:0% +than the other then the limits respect +that inequality um + + align:start position:0% +that inequality um + + + align:start position:0% +that inequality um +that has to deal with the order part of + + align:start position:0% +that has to deal with the order part of + + + align:start position:0% +that has to deal with the order part of +r being an ordered field so what about + + align:start position:0% +r being an ordered field so what about + + + align:start position:0% +r being an ordered field so what about +the field part of r being an ordered + + align:start position:0% +the field part of r being an ordered + + + align:start position:0% +the field part of r being an ordered +field so how + + align:start position:0% + + + + align:start position:0% + +does uh + + align:start position:0% +does uh + + + align:start position:0% +does uh +limits + + align:start position:0% + + + + align:start position:0% + +interact with algebraic + + align:start position:0% + + + + align:start position:0% + +operations + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +uh quite well it turns out so what's the + + align:start position:0% +uh quite well it turns out so what's the + + + align:start position:0% +uh quite well it turns out so what's the +theorem + + align:start position:0% + + + + align:start position:0% + +so suppose i have two convergent + + align:start position:0% +so suppose i have two convergent + + + align:start position:0% +so suppose i have two convergent +sequences + + align:start position:0% + + + + align:start position:0% + +limit as n goes to infinity of x of n + + align:start position:0% +limit as n goes to infinity of x of n + + + align:start position:0% +limit as n goes to infinity of x of n +equals x + + align:start position:0% +equals x + + + align:start position:0% +equals x +and + + align:start position:0% + + + + align:start position:0% + +limit as n goes to infinity of y sub n + + align:start position:0% +limit as n goes to infinity of y sub n + + + align:start position:0% +limit as n goes to infinity of y sub n +equals y + + align:start position:0% +equals y + + + align:start position:0% +equals y +then + + align:start position:0% + + + + align:start position:0% + +several things hold + + align:start position:0% + + + + align:start position:0% + +the first is that + + align:start position:0% +the first is that + + + align:start position:0% +the first is that +again you should kind of read this as + + align:start position:0% +again you should kind of read this as + + + align:start position:0% +again you should kind of read this as +two statements written in one the limit + + align:start position:0% +two statements written in one the limit + + + align:start position:0% +two statements written in one the limit +as n goes to infinity of x of n plus y + + align:start position:0% +as n goes to infinity of x of n plus y + + + align:start position:0% +as n goes to infinity of x of n plus y +sub n + + align:start position:0% +sub n + + + align:start position:0% +sub n +so this is a new sequence that i form by + + align:start position:0% +so this is a new sequence that i form by + + + align:start position:0% +so this is a new sequence that i form by +just taking the term by term sum of + + align:start position:0% +just taking the term by term sum of + + + align:start position:0% +just taking the term by term sum of +these two things + + align:start position:0% +these two things + + + align:start position:0% +these two things +um + + align:start position:0% +um + + + align:start position:0% +um +this sequence this new sequence is + + align:start position:0% +this sequence this new sequence is + + + align:start position:0% +this sequence this new sequence is +convergent and the limit equals the sum + + align:start position:0% +convergent and the limit equals the sum + + + align:start position:0% +convergent and the limit equals the sum +of the limits + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +the second is + + align:start position:0% + + + + align:start position:0% + +all seeing r + + align:start position:0% + + + + align:start position:0% + +the limit as n goes to infinity of the + + align:start position:0% +the limit as n goes to infinity of the + + + align:start position:0% +the limit as n goes to infinity of the +new sequence obtained by taking every + + align:start position:0% +new sequence obtained by taking every + + + align:start position:0% +new sequence obtained by taking every +entry of the sequence x sub n and + + align:start position:0% +entry of the sequence x sub n and + + + align:start position:0% +entry of the sequence x sub n and +multiplying it by this fixed number c + + align:start position:0% + + + + align:start position:0% + +the limit of that product is the product + + align:start position:0% +the limit of that product is the product + + + align:start position:0% +the limit of that product is the product +of + + align:start position:0% +of + + + align:start position:0% +of +c and x + + align:start position:0% +c and x + + + align:start position:0% +c and x +so limits respect what one would call + + align:start position:0% +so limits respect what one would call + + + align:start position:0% +so limits respect what one would call +scalar multiplication + + align:start position:0% + + + + align:start position:0% + +but we could be more general than that + + align:start position:0% +but we could be more general than that + + + align:start position:0% +but we could be more general than that +c you can think of as just + + align:start position:0% +c you can think of as just + + + align:start position:0% +c you can think of as just +one example of a convergent sequence + + align:start position:0% +one example of a convergent sequence + + + align:start position:0% +one example of a convergent sequence +just a constant sequence but in general + + align:start position:0% +just a constant sequence but in general + + + align:start position:0% +just a constant sequence but in general +we have that + + align:start position:0% +we have that + + + align:start position:0% +we have that +the product of two convergent sequences + + align:start position:0% +the product of two convergent sequences + + + align:start position:0% +the product of two convergent sequences +is convergent + + align:start position:0% +is convergent + + + align:start position:0% +is convergent +and + + align:start position:0% +and + + + align:start position:0% +and +the limit of the product is the product + + align:start position:0% +the limit of the product is the product + + + align:start position:0% +the limit of the product is the product +of the limit + + align:start position:0% + + + + align:start position:0% + +and finally if we have something for + + align:start position:0% +and finally if we have something for + + + align:start position:0% +and finally if we have something for +write it over here + + align:start position:0% +write it over here + + + align:start position:0% +write it over here +if we have something for + + align:start position:0% +if we have something for + + + align:start position:0% +if we have something for +a + + align:start position:0% +a + + + align:start position:0% +a +product then perhaps we have something + + align:start position:0% +product then perhaps we have something + + + align:start position:0% +product then perhaps we have something +by a quotient and that's as long as we + + align:start position:0% +by a quotient and that's as long as we + + + align:start position:0% +by a quotient and that's as long as we +can divide things so + + align:start position:0% + + + + align:start position:0% + +if for all n + + align:start position:0% + + + + align:start position:0% + +y sub n does not equal 0 + + align:start position:0% +y sub n does not equal 0 + + + align:start position:0% +y sub n does not equal 0 +and the limit + + align:start position:0% +and the limit + + + align:start position:0% +and the limit +y does not equal 0 + + align:start position:0% +y does not equal 0 + + + align:start position:0% +y does not equal 0 +then + + align:start position:0% + + + + align:start position:0% + +limit of the quotient x sub n over y sub + + align:start position:0% +limit of the quotient x sub n over y sub + + + align:start position:0% +limit of the quotient x sub n over y sub +n + + align:start position:0% +n + + + align:start position:0% +n +is the quotient of the limits + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +we're gonna prove uh + + align:start position:0% + + + + align:start position:0% + +we're gonna prove this first one using + + align:start position:0% +we're gonna prove this first one using + + + align:start position:0% +we're gonna prove this first one using +this this + + align:start position:0% +this this + + + align:start position:0% +this this +scheme of using both this + + align:start position:0% +scheme of using both this + + + align:start position:0% +scheme of using both this +simple theorem about limits and the + + align:start position:0% +simple theorem about limits and the + + + align:start position:0% +simple theorem about limits and the +squeeze theorem + + align:start position:0% + + + + align:start position:0% + +and it's quite simple so + + align:start position:0% + + + + align:start position:0% + +we just use the triangle inequality + + align:start position:0% + + + + align:start position:0% + +by the triangle inequality 0 is less + + align:start position:0% +by the triangle inequality 0 is less + + + align:start position:0% +by the triangle inequality 0 is less +than or equal to + + align:start position:0% +than or equal to + + + align:start position:0% +than or equal to +x sub n plus y sub n + + align:start position:0% +x sub n plus y sub n + + + align:start position:0% +x sub n plus y sub n +x plus y + + align:start position:0% +x plus y + + + align:start position:0% +x plus y +and x sub n minus x y sub n minus y and + + align:start position:0% +and x sub n minus x y sub n minus y and + + + align:start position:0% +and x sub n minus x y sub n minus y and +then i use the triangle inequality i get + + align:start position:0% +then i use the triangle inequality i get + + + align:start position:0% +then i use the triangle inequality i get +x of n minus x plus + + align:start position:0% +x of n minus x plus + + + align:start position:0% +x of n minus x plus +y sub n + + align:start position:0% +y sub n + + + align:start position:0% +y sub n +o + + align:start position:0% +o + + + align:start position:0% +o +you know it scratched that + + align:start position:0% +you know it scratched that + + + align:start position:0% +you know it scratched that +because in fact + + align:start position:0% +because in fact + + + align:start position:0% +because in fact +i was trying to be too clever + + align:start position:0% +i was trying to be too clever + + + align:start position:0% +i was trying to be too clever +and would have ended up using the + + align:start position:0% +and would have ended up using the + + + align:start position:0% +and would have ended up using the +theorem to prove the theorem so let's + + align:start position:0% +theorem to prove the theorem so let's + + + align:start position:0% +theorem to prove the theorem so let's +not do that it's never good to use the + + align:start position:0% +not do that it's never good to use the + + + align:start position:0% +not do that it's never good to use the +theorem you're trying to prove to prove + + align:start position:0% +theorem you're trying to prove to prove + + + align:start position:0% +theorem you're trying to prove to prove +the theorem that you're trying to prove + + align:start position:0% +the theorem that you're trying to prove + + + align:start position:0% +the theorem that you're trying to prove +so let's go back to basics and + + align:start position:0% +so let's go back to basics and + + + align:start position:0% +so let's go back to basics and +use the definition + + align:start position:0% + + + + align:start position:0% + +let epsilon be positive + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +since x sub n converges to x + + align:start position:0% + + + + align:start position:0% + +there exists a natural number m + + align:start position:0% + + + + align:start position:0% + +such + + align:start position:0% +such + + + align:start position:0% +such +that we're all n bigger than or equal to + + align:start position:0% +that we're all n bigger than or equal to + + + align:start position:0% +that we're all n bigger than or equal to +m naught + + align:start position:0% +m naught + + + align:start position:0% +m naught +x of n minus x + + align:start position:0% +x of n minus x + + + align:start position:0% +x of n minus x +it's supposed to be m but it looks like + + align:start position:0% +it's supposed to be m but it looks like + + + align:start position:0% +it's supposed to be m but it looks like +a k + + align:start position:0% +a k + + + align:start position:0% +a k +less than epsilon over two y the two + + align:start position:0% +less than epsilon over two y the two + + + align:start position:0% +less than epsilon over two y the two +well you see in a minute um + + align:start position:0% + + + + align:start position:0% + +and similarly for the sequence y there + + align:start position:0% +and similarly for the sequence y there + + + align:start position:0% +and similarly for the sequence y there +exists + + align:start position:0% +exists + + + align:start position:0% +exists +in one natural number + + align:start position:0% +in one natural number + + + align:start position:0% +in one natural number +such that + + align:start position:0% + + + + align:start position:0% + +for all n bigger than or equal to m one + + align:start position:0% +for all n bigger than or equal to m one + + + align:start position:0% +for all n bigger than or equal to m one +y sub n minus y is less than epsilon + + align:start position:0% +y sub n minus y is less than epsilon + + + align:start position:0% +y sub n minus y is less than epsilon +over two + + align:start position:0% +over two + + + align:start position:0% +over two +so i have these two integers + + align:start position:0% +so i have these two integers + + + align:start position:0% +so i have these two integers +which are given to me by the fact that x + + align:start position:0% +which are given to me by the fact that x + + + align:start position:0% +which are given to me by the fact that x +of n converges to x + + align:start position:0% +of n converges to x + + + align:start position:0% +of n converges to x +y sub n converges to y + + align:start position:0% +y sub n converges to y + + + align:start position:0% +y sub n converges to y +um + + align:start position:0% +um + + + align:start position:0% +um +and the definition of convergence + + align:start position:0% +and the definition of convergence + + + align:start position:0% +and the definition of convergence +i can always find these two integers for + + align:start position:0% +i can always find these two integers for + + + align:start position:0% +i can always find these two integers for +any small tolerance and i'm choosing the + + align:start position:0% +any small tolerance and i'm choosing the + + + align:start position:0% +any small tolerance and i'm choosing the +tolerance to be epsilon over 2 for some + + align:start position:0% +tolerance to be epsilon over 2 for some + + + align:start position:0% +tolerance to be epsilon over 2 for some +reason which you'll see in a minute + + align:start position:0% +reason which you'll see in a minute + + + align:start position:0% +reason which you'll see in a minute +and so what is the integer + + align:start position:0% +and so what is the integer + + + align:start position:0% +and so what is the integer +capital m that i choose for this epsilon + + align:start position:0% +capital m that i choose for this epsilon + + + align:start position:0% +capital m that i choose for this epsilon +for the sequence x sub n plus y sub n + + align:start position:0% + + + + align:start position:0% + +i'm going to choose m to be + + align:start position:0% + + + + align:start position:0% + +m not plus m1 + + align:start position:0% +m not plus m1 + + + align:start position:0% +m not plus m1 +and now i need to show that this choice + + align:start position:0% +and now i need to show that this choice + + + align:start position:0% +and now i need to show that this choice +of m works + + align:start position:0% +of m works + + + align:start position:0% +of m works +and if n is bigger than or equal to m + + align:start position:0% +and if n is bigger than or equal to m + + + align:start position:0% +and if n is bigger than or equal to m +this implies that n is + + align:start position:0% + + + + align:start position:0% + +bigger than or equal to m0 and + + align:start position:0% +bigger than or equal to m0 and + + + align:start position:0% +bigger than or equal to m0 and +m is bigger than or equal to m1 so both + + align:start position:0% +m is bigger than or equal to m1 so both + + + align:start position:0% +m is bigger than or equal to m1 so both +of these inequalities are valid for this + + align:start position:0% +of these inequalities are valid for this + + + align:start position:0% +of these inequalities are valid for this +n + + align:start position:0% +n + + + align:start position:0% +n +and therefore i get + + align:start position:0% +and therefore i get + + + align:start position:0% +and therefore i get +x of n plus y sub n + + align:start position:0% +x of n plus y sub n + + + align:start position:0% +x of n plus y sub n +minus + + align:start position:0% +minus + + + align:start position:0% +minus +x plus y + + align:start position:0% +x plus y + + + align:start position:0% +x plus y +and now i do what i was going to do a + + align:start position:0% +and now i do what i was going to do a + + + align:start position:0% +and now i do what i was going to do a +minute ago when i was going to use the + + align:start position:0% +minute ago when i was going to use the + + + align:start position:0% +minute ago when i was going to use the +theorem to prove the theorem x sub n + + align:start position:0% +theorem to prove the theorem x sub n + + + align:start position:0% +theorem to prove the theorem x sub n +minus x y sub n minus y i group those + + align:start position:0% +minus x y sub n minus y i group those + + + align:start position:0% +minus x y sub n minus y i group those +together and then i use the triangle + + align:start position:0% +together and then i use the triangle + + + align:start position:0% +together and then i use the triangle +inequality this is less than or equal to + + align:start position:0% +inequality this is less than or equal to + + + align:start position:0% +inequality this is less than or equal to +x of n minus x + + align:start position:0% +x of n minus x + + + align:start position:0% +x of n minus x +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +plus y sub n minus y + + align:start position:0% +plus y sub n minus y + + + align:start position:0% +plus y sub n minus y +and now this is less than epsilon over + + align:start position:0% +and now this is less than epsilon over + + + align:start position:0% +and now this is less than epsilon over +two this is less than epsilon over two + + align:start position:0% +two this is less than epsilon over two + + + align:start position:0% +two this is less than epsilon over two +so + + align:start position:0% + + + + align:start position:0% + +equals epsilon and now you can see why i + + align:start position:0% +equals epsilon and now you can see why i + + + align:start position:0% +equals epsilon and now you can see why i +chose the two because i wanted to show + + align:start position:0% +chose the two because i wanted to show + + + align:start position:0% +chose the two because i wanted to show +this was less than epsilon and i had + + align:start position:0% +this was less than epsilon and i had + + + align:start position:0% +this was less than epsilon and i had +control over these two things + + align:start position:0% +control over these two things + + + align:start position:0% +control over these two things +and the sum of controls + + align:start position:0% +and the sum of controls + + + align:start position:0% +and the sum of controls +gives me epsilon so i choose the control + + align:start position:0% +gives me epsilon so i choose the control + + + align:start position:0% +gives me epsilon so i choose the control +to be epsilon over two if i had three + + align:start position:0% +to be epsilon over two if i had three + + + align:start position:0% +to be epsilon over two if i had three +sequences + + align:start position:0% +sequences + + + align:start position:0% +sequences +then you could probably guess i would + + align:start position:0% +then you could probably guess i would + + + align:start position:0% +then you could probably guess i would +choose epsilon over three meaning if i + + align:start position:0% +choose epsilon over three meaning if i + + + align:start position:0% +choose epsilon over three meaning if i +had a + + align:start position:0% +had a + + + align:start position:0% +had a +xc sequences xn y sub n and z sub n and + + align:start position:0% +xc sequences xn y sub n and z sub n and + + + align:start position:0% +xc sequences xn y sub n and z sub n and +i looked at the sum x sub n plus y sub n + + align:start position:0% +i looked at the sum x sub n plus y sub n + + + align:start position:0% +i looked at the sum x sub n plus y sub n +plus z sub n + + align:start position:0% +plus z sub n + + + align:start position:0% +plus z sub n +i could show that converges to the sum + + align:start position:0% +i could show that converges to the sum + + + align:start position:0% +i could show that converges to the sum +of the limits and i would choose + + align:start position:0% +of the limits and i would choose + + + align:start position:0% +of the limits and i would choose +these integers m sub 0 m sub 1 m sub 2 + + align:start position:0% +these integers m sub 0 m sub 1 m sub 2 + + + align:start position:0% +these integers m sub 0 m sub 1 m sub 2 +so that i have epsilon over 3 here so + + align:start position:0% +so that i have epsilon over 3 here so + + + align:start position:0% +so that i have epsilon over 3 here so +that they sum up to epsilon + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +now we prove too + + align:start position:0% +now we prove too + + + align:start position:0% +now we prove too +that uh for this + + align:start position:0% +that uh for this + + + align:start position:0% +that uh for this +single scalar multiplication if you like + + align:start position:0% +single scalar multiplication if you like + + + align:start position:0% +single scalar multiplication if you like +where you just multiply each term by a + + align:start position:0% +where you just multiply each term by a + + + align:start position:0% +where you just multiply each term by a +single number + + align:start position:0% +single number + + + align:start position:0% +single number +the limit respects that multiplication + + align:start position:0% +the limit respects that multiplication + + + align:start position:0% +the limit respects that multiplication +do + + align:start position:0% +do + + + align:start position:0% +do +an epsilon proof again + + align:start position:0% + + + + align:start position:0% + +since x sub n converges to x so now + + align:start position:0% +since x sub n converges to x so now + + + align:start position:0% +since x sub n converges to x so now +we're trying to show that second limit + + align:start position:0% +we're trying to show that second limit + + + align:start position:0% +we're trying to show that second limit +there exists + + align:start position:0% + + + + align:start position:0% + +m sub 0 a natural number + + align:start position:0% +m sub 0 a natural number + + + align:start position:0% +m sub 0 a natural number +such that + + align:start position:0% + + + + align:start position:0% + +for all n bigger than or equal to m sub + + align:start position:0% +for all n bigger than or equal to m sub + + + align:start position:0% +for all n bigger than or equal to m sub + + align:start position:0% + + + + align:start position:0% + +x of n + + align:start position:0% +x of n + + + align:start position:0% +x of n +minus x is less than + + align:start position:0% + + + + align:start position:0% + +epsilon over the absolute value of c + + align:start position:0% +epsilon over the absolute value of c + + + align:start position:0% +epsilon over the absolute value of c +plus one + + align:start position:0% +plus one + + + align:start position:0% +plus one +okay + + align:start position:0% + + + + align:start position:0% + +and now you have to trust me + + align:start position:0% +and now you have to trust me + + + align:start position:0% +and now you have to trust me +why that thing well you'll see it'll + + align:start position:0% +why that thing well you'll see it'll + + + align:start position:0% +why that thing well you'll see it'll +come out just like this did + + align:start position:0% +come out just like this did + + + align:start position:0% +come out just like this did +so for the sequence uh + + align:start position:0% +so for the sequence uh + + + align:start position:0% +so for the sequence uh +c times x sub n we'll choose m to be + + align:start position:0% +c times x sub n we'll choose m to be + + + align:start position:0% +c times x sub n we'll choose m to be +just this m sub zero + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +if n is bigger than or equal to m so m + + align:start position:0% +if n is bigger than or equal to m so m + + + align:start position:0% +if n is bigger than or equal to m so m +which is equal to m sub zero + + align:start position:0% +which is equal to m sub zero + + + align:start position:0% +which is equal to m sub zero +this implies this inequality holds + + align:start position:0% +this implies this inequality holds + + + align:start position:0% +this implies this inequality holds +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +c times x of n minus x c times x + + align:start position:0% +c times x of n minus x c times x + + + align:start position:0% +c times x of n minus x c times x +this c pops out of the absolute value + + align:start position:0% +this c pops out of the absolute value + + + align:start position:0% +this c pops out of the absolute value +and becomes the absolute value of c + + align:start position:0% +and becomes the absolute value of c + + + align:start position:0% +and becomes the absolute value of c +times the absolute value of x of n minus + + align:start position:0% +times the absolute value of x of n minus + + + align:start position:0% +times the absolute value of x of n minus +x + + align:start position:0% + + + + align:start position:0% + +and which is less than so i'm writing + + align:start position:0% +and which is less than so i'm writing + + + align:start position:0% +and which is less than so i'm writing +less than here but this thing is less + + align:start position:0% +less than here but this thing is less + + + align:start position:0% +less than here but this thing is less +than that i'm not + + align:start position:0% +than that i'm not + + + align:start position:0% +than that i'm not +is less than + + align:start position:0% +is less than + + + align:start position:0% +is less than +c + + align:start position:0% +c + + + align:start position:0% +c +over + + align:start position:0% +over + + + align:start position:0% +over +c plus one + + align:start position:0% +c plus one + + + align:start position:0% +c plus one +epsilon + + align:start position:0% +epsilon + + + align:start position:0% +epsilon +okay now this uh + + align:start position:0% +okay now this uh + + + align:start position:0% +okay now this uh +quotient here + + align:start position:0% +quotient here + + + align:start position:0% +quotient here +this number over + + align:start position:0% +this number over + + + align:start position:0% +this number over +this + + align:start position:0% +this + + + align:start position:0% +this +uh number plus one is always less than + + align:start position:0% +uh number plus one is always less than + + + align:start position:0% +uh number plus one is always less than +one + + align:start position:0% + + + + align:start position:0% + +so this positive number which is less + + align:start position:0% +so this positive number which is less + + + align:start position:0% +so this positive number which is less +than one or non-negative number which is + + align:start position:0% +than one or non-negative number which is + + + align:start position:0% +than one or non-negative number which is +less than one + + align:start position:0% +less than one + + + align:start position:0% +less than one +is going to be less than 1 times epsilon + + align:start position:0% +is going to be less than 1 times epsilon + + + align:start position:0% +is going to be less than 1 times epsilon +which gives me epsilon + + align:start position:0% + + + + align:start position:0% + +and maybe you're wondering + + align:start position:0% +and maybe you're wondering + + + align:start position:0% +and maybe you're wondering +why didn't i choose + + align:start position:0% +why didn't i choose + + + align:start position:0% +why didn't i choose +so this is just + + align:start position:0% +so this is just + + + align:start position:0% +so this is just +a little + + align:start position:0% +a little + + + align:start position:0% +a little +smidgen of sophistication not much just + + align:start position:0% +smidgen of sophistication not much just + + + align:start position:0% +smidgen of sophistication not much just +a little okay + + align:start position:0% +a little okay + + + align:start position:0% +a little okay +why didn't i choose this so that epsilon + + align:start position:0% +why didn't i choose this so that epsilon + + + align:start position:0% +why didn't i choose this so that epsilon +it's epsilon over the absolute value of + + align:start position:0% +it's epsilon over the absolute value of + + + align:start position:0% +it's epsilon over the absolute value of +c so that when i stick in + + align:start position:0% +c so that when i stick in + + + align:start position:0% +c so that when i stick in +uh my any quality for this guy i just + + align:start position:0% +uh my any quality for this guy i just + + + align:start position:0% +uh my any quality for this guy i just +get epsilon + + align:start position:0% +get epsilon + + + align:start position:0% +get epsilon +well what if c equals zero so then i'm + + align:start position:0% +well what if c equals zero so then i'm + + + align:start position:0% +well what if c equals zero so then i'm +telling you to choose + + align:start position:0% +telling you to choose + + + align:start position:0% +telling you to choose +capital m sub zero so that the absolute + + align:start position:0% +capital m sub zero so that the absolute + + + align:start position:0% +capital m sub zero so that the absolute +value of x of n minus x is less than + + align:start position:0% +value of x of n minus x is less than + + + align:start position:0% +value of x of n minus x is less than +epsilon over zero division by zero is a + + align:start position:0% +epsilon over zero division by zero is a + + + align:start position:0% +epsilon over zero division by zero is a +no-no okay + + align:start position:0% +no-no okay + + + align:start position:0% +no-no okay +but if we fudge it a little by adding + + align:start position:0% +but if we fudge it a little by adding + + + align:start position:0% +but if we fudge it a little by adding +one + + align:start position:0% +one + + + align:start position:0% +one +we get something that's uh still does + + align:start position:0% +we get something that's uh still does + + + align:start position:0% +we get something that's uh still does +the job it still gives me + + align:start position:0% +the job it still gives me + + + align:start position:0% +the job it still gives me +some number which is + + align:start position:0% +some number which is + + + align:start position:0% +some number which is +non-negative and less than one + + align:start position:0% +non-negative and less than one + + + align:start position:0% +non-negative and less than one +um which is enough + + align:start position:0% +um which is enough + + + align:start position:0% +um which is enough +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +let's prove that the limit of the + + align:start position:0% +let's prove that the limit of the + + + align:start position:0% +let's prove that the limit of the +product is the product of the limits + + align:start position:0% + + + + align:start position:0% + +since the sequence y sub n converges to + + align:start position:0% +since the sequence y sub n converges to + + + align:start position:0% +since the sequence y sub n converges to +y it's a convergent sequence and + + align:start position:0% +y it's a convergent sequence and + + + align:start position:0% +y it's a convergent sequence and +therefore it's bounded + + align:start position:0% + + + + align:start position:0% + +that means that there exists + + align:start position:0% + + + + align:start position:0% + +some non-negative + + align:start position:0% +some non-negative + + + align:start position:0% +some non-negative +real number b + + align:start position:0% + + + + align:start position:0% + +such that for all + + align:start position:0% +such that for all + + + align:start position:0% +such that for all +natural numbers in + + align:start position:0% + + + + align:start position:0% + +y sub n is less than or equal to b an + + align:start position:0% +y sub n is less than or equal to b an + + + align:start position:0% +y sub n is less than or equal to b an +absolute value + + align:start position:0% +absolute value + + + align:start position:0% +absolute value +okay + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +if i look at x sub n times y sub n minus + + align:start position:0% +if i look at x sub n times y sub n minus + + + align:start position:0% +if i look at x sub n times y sub n minus +x times y + + align:start position:0% +x times y + + + align:start position:0% +x times y +and i add and subtract um + + align:start position:0% +and i add and subtract um + + + align:start position:0% +and i add and subtract um +x + + align:start position:0% +x + + + align:start position:0% +x +times y sub n + + align:start position:0% +times y sub n + + + align:start position:0% +times y sub n +i can write this as + + align:start position:0% + + + + align:start position:0% + +plus um + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +and now i use the triangle inequality + + align:start position:0% +and now i use the triangle inequality + + + align:start position:0% +and now i use the triangle inequality +that this is less than or equal to + + align:start position:0% +that this is less than or equal to + + + align:start position:0% +that this is less than or equal to +x sub n minus x times y sub n + + align:start position:0% +x sub n minus x times y sub n + + + align:start position:0% +x sub n minus x times y sub n +plus + + align:start position:0% +plus + + + align:start position:0% +plus +y sub n minus + + align:start position:0% +y sub n minus + + + align:start position:0% +y sub n minus +y times absolute value of x + + align:start position:0% +y times absolute value of x + + + align:start position:0% +y times absolute value of x +and y sub n is bounded by b for all n so + + align:start position:0% +and y sub n is bounded by b for all n so + + + align:start position:0% +and y sub n is bounded by b for all n so +this is less than or equal to + + align:start position:0% + + + + align:start position:0% + +plus + + align:start position:0% + + + + align:start position:0% + +y sub n minus y times the absolute value + + align:start position:0% +y sub n minus y times the absolute value + + + align:start position:0% +y sub n minus y times the absolute value +of x + + align:start position:0% +of x + + + align:start position:0% +of x +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% + + + + align:start position:0% + +let me just state the obvious that we + + align:start position:0% +let me just state the obvious that we + + + align:start position:0% +let me just state the obvious that we +get 0 is less than or equal to + + align:start position:0% +get 0 is less than or equal to + + + align:start position:0% +get 0 is less than or equal to +x of n times y sub n minus x times y + + align:start position:0% +x of n times y sub n minus x times y + + + align:start position:0% +x of n times y sub n minus x times y +and this is less than or equal to + + align:start position:0% +and this is less than or equal to + + + align:start position:0% +and this is less than or equal to +as we've shown here + + align:start position:0% + + + + align:start position:0% + +plus + + align:start position:0% +plus + + + align:start position:0% +plus +x times + + align:start position:0% +x times + + + align:start position:0% +x times +y sub n minus y + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +now the right hand side so the left side + + align:start position:0% +now the right hand side so the left side + + + align:start position:0% +now the right hand side so the left side +of this inequality converges to zero + + align:start position:0% +of this inequality converges to zero + + + align:start position:0% +of this inequality converges to zero +the right side also converges to zero + + align:start position:0% +the right side also converges to zero + + + align:start position:0% +the right side also converges to zero +because we've just shown by one and two + + align:start position:0% +because we've just shown by one and two + + + align:start position:0% +because we've just shown by one and two +by two this converges to zero + + align:start position:0% + + + + align:start position:0% + +and by that theorem since x n converges + + align:start position:0% +and by that theorem since x n converges + + + align:start position:0% +and by that theorem since x n converges +to x + + align:start position:0% +to x + + + align:start position:0% +to x +this product here converges to zero b is + + align:start position:0% +this product here converges to zero b is + + + align:start position:0% +this product here converges to zero b is +a fixed number + + align:start position:0% +a fixed number + + + align:start position:0% +a fixed number +and the same thing for this + + align:start position:0% +and the same thing for this + + + align:start position:0% +and the same thing for this +that converges to zero + + align:start position:0% +that converges to zero + + + align:start position:0% +that converges to zero +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +by two + + align:start position:0% +by two + + + align:start position:0% +by two +this + + align:start position:0% +this + + + align:start position:0% +this +sum converges to zero + + align:start position:0% +sum converges to zero + + + align:start position:0% +sum converges to zero +okay so these two arrows are by + + align:start position:0% +okay so these two arrows are by + + + align:start position:0% +okay so these two arrows are by +two + + align:start position:0% +two + + + align:start position:0% +two +and this is by one + + align:start position:0% + + + + align:start position:0% + +so me just summarize by one + + align:start position:0% +so me just summarize by one + + + align:start position:0% +so me just summarize by one +and two + + align:start position:0% +and two + + + align:start position:0% +and two +the right-hand side + + align:start position:0% +the right-hand side + + + align:start position:0% +the right-hand side +of this inequality + + align:start position:0% +of this inequality + + + align:start position:0% +of this inequality +b times x of n minus x + + align:start position:0% +b times x of n minus x + + + align:start position:0% +b times x of n minus x +plus + + align:start position:0% +plus + + + align:start position:0% +plus +an absolute value of x times + + align:start position:0% +an absolute value of x times + + + align:start position:0% +an absolute value of x times +y sub n minus y + + align:start position:0% +y sub n minus y + + + align:start position:0% +y sub n minus y +this converges to zero + + align:start position:0% +this converges to zero + + + align:start position:0% +this converges to zero +which + + align:start position:0% +which + + + align:start position:0% +which +by the squeeze theorem + + align:start position:0% +by the squeeze theorem + + + align:start position:0% +by the squeeze theorem +implies that + + align:start position:0% + + + + align:start position:0% + +this is by + + align:start position:0% + + + + align:start position:0% + +squeeze theorem + + align:start position:0% + + + + align:start position:0% + +which implies that x sub n times y sub n + + align:start position:0% +which implies that x sub n times y sub n + + + align:start position:0% +which implies that x sub n times y sub n +converges to x times y + + align:start position:0% +converges to x times y + + + align:start position:0% +converges to x times y +by that first theorem okay so i'm not + + align:start position:0% +by that first theorem okay so i'm not + + + align:start position:0% +by that first theorem okay so i'm not +going to keep referring to that first + + align:start position:0% +going to keep referring to that first + + + align:start position:0% +going to keep referring to that first +theorem because i'm just going to it's + + align:start position:0% +theorem because i'm just going to it's + + + align:start position:0% +theorem because i'm just going to it's +such a simple fact i'm just going to + + align:start position:0% +such a simple fact i'm just going to + + + align:start position:0% +such a simple fact i'm just going to +keep + + align:start position:0% +keep + + + align:start position:0% +keep +using it without referencing it namely + + align:start position:0% +using it without referencing it namely + + + align:start position:0% +using it without referencing it namely +that the sequence an x a sequence + + align:start position:0% +that the sequence an x a sequence + + + align:start position:0% +that the sequence an x a sequence +converges to x if and only if the + + align:start position:0% +converges to x if and only if the + + + align:start position:0% +converges to x if and only if the +absolute value of this thing + + align:start position:0% +absolute value of this thing + + + align:start position:0% +absolute value of this thing +uh this difference converges to zero + + align:start position:0% +uh this difference converges to zero + + + align:start position:0% +uh this difference converges to zero +okay + + align:start position:0% + + + + align:start position:0% + +all right so that proves the + + align:start position:0% + + + + align:start position:0% + +limit of the product is the product of + + align:start position:0% +limit of the product is the product of + + + align:start position:0% +limit of the product is the product of +the limits + + align:start position:0% +the limits + + + align:start position:0% +the limits +now for the quotient + + align:start position:0% +now for the quotient + + + align:start position:0% +now for the quotient +we can use + + align:start position:0% +we can use + + + align:start position:0% +we can use +three + + align:start position:0% +three + + + align:start position:0% +three +once we've proven it for just one over y + + align:start position:0% +once we've proven it for just one over y + + + align:start position:0% +once we've proven it for just one over y +sub n right + + align:start position:0% +sub n right + + + align:start position:0% +sub n right +so + + align:start position:0% + + + + align:start position:0% + +what do i mean + + align:start position:0% + + + + align:start position:0% + +so now we're assuming + + align:start position:0% + + + + align:start position:0% + +that y sub n is not equal to 0 + + align:start position:0% +that y sub n is not equal to 0 + + + align:start position:0% +that y sub n is not equal to 0 +for all n and y does not equal 0. okay + + align:start position:0% + + + + align:start position:0% + +so if we prove + + align:start position:0% +so if we prove + + + align:start position:0% +so if we prove +this statement that the limit as n goes + + align:start position:0% +this statement that the limit as n goes + + + align:start position:0% +this statement that the limit as n goes +to infinity of y one over y sub n equals + + align:start position:0% +to infinity of y one over y sub n equals + + + align:start position:0% +to infinity of y one over y sub n equals +one over y + + align:start position:0% +one over y + + + align:start position:0% +one over y +then + + align:start position:0% +then + + + align:start position:0% +then +by three + + align:start position:0% + + + + align:start position:0% + +implies + + align:start position:0% + + + + align:start position:0% + +at the limit as n goes to infinity of + + align:start position:0% +at the limit as n goes to infinity of + + + align:start position:0% +at the limit as n goes to infinity of +x sub n over y sub n equals + + align:start position:0% +x sub n over y sub n equals + + + align:start position:0% +x sub n over y sub n equals +x over y because x sub n over y sub n is + + align:start position:0% +x over y because x sub n over y sub n is + + + align:start position:0% +x over y because x sub n over y sub n is +just the product of x sub n and one over + + align:start position:0% +just the product of x sub n and one over + + + align:start position:0% +just the product of x sub n and one over +y sub n + + align:start position:0% +y sub n + + + align:start position:0% +y sub n +okay so we just need to prove + + align:start position:0% + + + + align:start position:0% + +this special case if you like + + align:start position:0% + + + + align:start position:0% + +and we're going to do it kind of the + + align:start position:0% +and we're going to do it kind of the + + + align:start position:0% +and we're going to do it kind of the +same way now because we're dividing by + + align:start position:0% +same way now because we're dividing by + + + align:start position:0% +same way now because we're dividing by +y + + align:start position:0% +y + + + align:start position:0% +y +sub n + + align:start position:0% +sub n + + + align:start position:0% +sub n +so here we use that we had an upper + + align:start position:0% +so here we use that we had an upper + + + align:start position:0% +so here we use that we had an upper +bound for the product here + + align:start position:0% +bound for the product here + + + align:start position:0% +bound for the product here +but when we take one over y sub n to get + + align:start position:0% +but when we take one over y sub n to get + + + align:start position:0% +but when we take one over y sub n to get +an upper bound of that + + align:start position:0% +an upper bound of that + + + align:start position:0% +an upper bound of that +means we need + + align:start position:0% +means we need + + + align:start position:0% +means we need +sort of a low we need a lower bound on y + + align:start position:0% +sort of a low we need a lower bound on y + + + align:start position:0% +sort of a low we need a lower bound on y +sub n on the absolute values of y sub n + + align:start position:0% +sub n on the absolute values of y sub n + + + align:start position:0% +sub n on the absolute values of y sub n +and we get that by our assumption that + + align:start position:0% +and we get that by our assumption that + + + align:start position:0% +and we get that by our assumption that +uh the limit is non-zero for all n and + + align:start position:0% +uh the limit is non-zero for all n and + + + align:start position:0% +uh the limit is non-zero for all n and +so is the y sub + + align:start position:0% +so is the y sub + + + align:start position:0% +so is the y sub +n's so + + align:start position:0% + + + + align:start position:0% + +first thing we prove or or let me write + + align:start position:0% +first thing we prove or or let me write + + + align:start position:0% +first thing we prove or or let me write +this as a claim + + align:start position:0% + + + + align:start position:0% + +there exists a positive number b little + + align:start position:0% +there exists a positive number b little + + + align:start position:0% +there exists a positive number b little +b + + align:start position:0% +b + + + align:start position:0% +b +that + + align:start position:0% +that + + + align:start position:0% +that +for all natural numbers in + + align:start position:0% + + + + align:start position:0% + +y sub n is bigger than or equal to b + + align:start position:0% +y sub n is bigger than or equal to b + + + align:start position:0% +y sub n is bigger than or equal to b +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and we know that a sequence is bounded + + align:start position:0% +and we know that a sequence is bounded + + + align:start position:0% +and we know that a sequence is bounded +so we know that there's always a capital + + align:start position:0% +so we know that there's always a capital + + + align:start position:0% +so we know that there's always a capital +b so that absolute value of y sub n is + + align:start position:0% +b so that absolute value of y sub n is + + + align:start position:0% +b so that absolute value of y sub n is +bigger than or is less than or equal to + + align:start position:0% +bigger than or is less than or equal to + + + align:start position:0% +bigger than or is less than or equal to +b but for sequences that are + + align:start position:0% +b but for sequences that are + + + align:start position:0% +b but for sequences that are +uh + + align:start position:0% +uh + + + align:start position:0% +uh +non-zero and converging to a non-zero + + align:start position:0% +non-zero and converging to a non-zero + + + align:start position:0% +non-zero and converging to a non-zero +limit then + + align:start position:0% +limit then + + + align:start position:0% +limit then +you can bound them um + + align:start position:0% +you can bound them um + + + align:start position:0% +you can bound them um +away from + + align:start position:0% +away from + + + align:start position:0% +away from +from zero + + align:start position:0% +from zero + + + align:start position:0% +from zero +um and it's kind of the same proof that + + align:start position:0% +um and it's kind of the same proof that + + + align:start position:0% +um and it's kind of the same proof that +we + + align:start position:0% +we + + + align:start position:0% +we +gave for showing that a convergent + + align:start position:0% +gave for showing that a convergent + + + align:start position:0% +gave for showing that a convergent +sequence is + + align:start position:0% +sequence is + + + align:start position:0% +sequence is +bounded uh above + + align:start position:0% +bounded uh above + + + align:start position:0% +bounded uh above +so + + align:start position:0% + + + + align:start position:0% + +let me draw a quick picture + + align:start position:0% +let me draw a quick picture + + + align:start position:0% +let me draw a quick picture +and let's assume that the limit is + + align:start position:0% +and let's assume that the limit is + + + align:start position:0% +and let's assume that the limit is +positive just for the sake of the + + align:start position:0% +positive just for the sake of the + + + align:start position:0% +positive just for the sake of the +picture + + align:start position:0% + + + + align:start position:0% + +so this is a little discussion on why + + align:start position:0% +so this is a little discussion on why + + + align:start position:0% +so this is a little discussion on why +this is true and this picture is going + + align:start position:0% +this is true and this picture is going + + + align:start position:0% +this is true and this picture is going +to look + + align:start position:0% + + + + align:start position:0% + +at least the explanation is going to be + + align:start position:0% +at least the explanation is going to be + + + align:start position:0% +at least the explanation is going to be +kind of similar to + + align:start position:0% +kind of similar to + + + align:start position:0% +kind of similar to +um + + align:start position:0% +um + + + align:start position:0% +um +why a sequence is bounded and this one + + align:start position:0% +why a sequence is bounded and this one + + + align:start position:0% +why a sequence is bounded and this one +is why it's + + align:start position:0% +is why it's + + + align:start position:0% +is why it's +kind of bounded below + + align:start position:0% +kind of bounded below + + + align:start position:0% +kind of bounded below +uh so let's assume that the limit y is + + align:start position:0% +uh so let's assume that the limit y is + + + align:start position:0% +uh so let's assume that the limit y is +positive + + align:start position:0% +positive + + + align:start position:0% +positive +and let's say i go out + + align:start position:0% +and let's say i go out + + + align:start position:0% +and let's say i go out +uh + + align:start position:0% +uh + + + align:start position:0% +uh +within distance + + align:start position:0% +within distance + + + align:start position:0% +within distance +let's say y over 2 so that i'm still + + align:start position:0% +let's say y over 2 so that i'm still + + + align:start position:0% +let's say y over 2 so that i'm still +positive so this is + + align:start position:0% +positive so this is + + + align:start position:0% +positive so this is +y minus + + align:start position:0% +y minus + + + align:start position:0% +y minus +y over 2 absolute value so in this + + align:start position:0% +y over 2 absolute value so in this + + + align:start position:0% +y over 2 absolute value so in this +picture y is positive so that's just + + align:start position:0% +picture y is positive so that's just + + + align:start position:0% +picture y is positive so that's just +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +y over 2. + + align:start position:0% +y over 2. + + + align:start position:0% +y over 2. +then what uh what can i say that + + align:start position:0% +then what uh what can i say that + + + align:start position:0% +then what uh what can i say that +eventually + + align:start position:0% +eventually + + + align:start position:0% +eventually +all of the y sub n's + + align:start position:0% + + + + align:start position:0% + +are here + + align:start position:0% +are here + + + align:start position:0% +are here +in this interval away from zero and in + + align:start position:0% +in this interval away from zero and in + + + align:start position:0% +in this interval away from zero and in +fact their absolute value + + align:start position:0% +fact their absolute value + + + align:start position:0% +fact their absolute value +is bounded by + + align:start position:0% + + + + align:start position:0% + +y over 2. so let me just write it that + + align:start position:0% +y over 2. so let me just write it that + + + align:start position:0% +y over 2. so let me just write it that +way + + align:start position:0% + + + + align:start position:0% + +so all the y sub n's for n bigger than + + align:start position:0% +so all the y sub n's for n bigger than + + + align:start position:0% +so all the y sub n's for n bigger than +or equal to some m all have to lie in + + align:start position:0% +or equal to some m all have to lie in + + + align:start position:0% +or equal to some m all have to lie in +this interval because they're converging + + align:start position:0% +this interval because they're converging + + + align:start position:0% +this interval because they're converging +to y and y is + + align:start position:0% +to y and y is + + + align:start position:0% +to y and y is +positive and therefore an absolute value + + align:start position:0% +positive and therefore an absolute value + + + align:start position:0% +positive and therefore an absolute value +they're all bounded above below i mean + + align:start position:0% +they're all bounded above below i mean + + + align:start position:0% +they're all bounded above below i mean +by y over two they're all uh at least + + align:start position:0% +by y over two they're all uh at least + + + align:start position:0% +by y over two they're all uh at least +distance y over two to zero + + align:start position:0% +distance y over two to zero + + + align:start position:0% +distance y over two to zero +okay and then all that's left to handle + + align:start position:0% +okay and then all that's left to handle + + + align:start position:0% +okay and then all that's left to handle +are + + align:start position:0% +are + + + align:start position:0% +are +maybe some definitely many um that are + + align:start position:0% +maybe some definitely many um that are + + + align:start position:0% +maybe some definitely many um that are +left + + align:start position:0% +left + + + align:start position:0% +left +um + + align:start position:0% +um + + + align:start position:0% +um +y sub one y sub two + + align:start position:0% +y sub one y sub two + + + align:start position:0% +y sub one y sub two +y sub m minus one + + align:start position:0% +y sub m minus one + + + align:start position:0% +y sub m minus one +that are scattered + + align:start position:0% +that are scattered + + + align:start position:0% +that are scattered +uh on the real line + + align:start position:0% +uh on the real line + + + align:start position:0% +uh on the real line +but are nonzero okay so we're just going + + align:start position:0% +but are nonzero okay so we're just going + + + align:start position:0% +but are nonzero okay so we're just going +to end up taking the minimum of this + + align:start position:0% +to end up taking the minimum of this + + + align:start position:0% +to end up taking the minimum of this +number + + align:start position:0% +number + + + align:start position:0% +number +and the absolute value of these numbers + + align:start position:0% +and the absolute value of these numbers + + + align:start position:0% +and the absolute value of these numbers +okay + + align:start position:0% + + + + align:start position:0% + +okay um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +since the y sub n is converged to y + + align:start position:0% +since the y sub n is converged to y + + + align:start position:0% +since the y sub n is converged to y +and y + + align:start position:0% +and y + + + align:start position:0% +and y +does not equal zero + + align:start position:0% + + + + align:start position:0% + +there exists + + align:start position:0% +there exists + + + align:start position:0% +there exists +an integer + + align:start position:0% +an integer + + + align:start position:0% +an integer +m + + align:start position:0% +m + + + align:start position:0% +m +such that + + align:start position:0% +such that + + + align:start position:0% +such that +all n bigger than or equal to capital m + + align:start position:0% +all n bigger than or equal to capital m + + + align:start position:0% +all n bigger than or equal to capital m +so this picture was uh why this claim is + + align:start position:0% +so this picture was uh why this claim is + + + align:start position:0% +so this picture was uh why this claim is +true it was not the proof of why this + + align:start position:0% +true it was not the proof of why this + + + align:start position:0% +true it was not the proof of why this +claim is true what i'm writing now is + + align:start position:0% +claim is true what i'm writing now is + + + align:start position:0% +claim is true what i'm writing now is +the actual proof of why this claim is + + align:start position:0% +the actual proof of why this claim is + + + align:start position:0% +the actual proof of why this claim is +true um + + align:start position:0% +true um + + + align:start position:0% +true um +such that for all n bigger than or equal + + align:start position:0% +such that for all n bigger than or equal + + + align:start position:0% +such that for all n bigger than or equal +to capital m + + align:start position:0% +to capital m + + + align:start position:0% +to capital m +y sub n minus y + + align:start position:0% +y sub n minus y + + + align:start position:0% +y sub n minus y +and absolute value is less than + + align:start position:0% +and absolute value is less than + + + align:start position:0% +and absolute value is less than +y over two okay so for this picture i + + align:start position:0% +y over two okay so for this picture i + + + align:start position:0% +y over two okay so for this picture i +drew where y is positive that would have + + align:start position:0% +drew where y is positive that would have + + + align:start position:0% +drew where y is positive that would have +just been y over 2 + + align:start position:0% +just been y over 2 + + + align:start position:0% +just been y over 2 +but you have to use a absolute value for + + align:start position:0% +but you have to use a absolute value for + + + align:start position:0% +but you have to use a absolute value for +the other case that y is is negative + + align:start position:0% +the other case that y is is negative + + + align:start position:0% +the other case that y is is negative +because this has to be a positive number + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +for all n bigger than or equal to m + + align:start position:0% +for all n bigger than or equal to m + + + align:start position:0% +for all n bigger than or equal to m +this + + align:start position:0% +this + + + align:start position:0% +this +inequality and the triangle inequality + + align:start position:0% +inequality and the triangle inequality + + + align:start position:0% +inequality and the triangle inequality +gives me so if i look at + + align:start position:0% +gives me so if i look at + + + align:start position:0% +gives me so if i look at +the absolute value of y this is equal to + + align:start position:0% + + + + align:start position:0% + +absolute value of y minus y sub n plus y + + align:start position:0% +absolute value of y minus y sub n plus y + + + align:start position:0% +absolute value of y minus y sub n plus y +sub n and now i use a triangle + + align:start position:0% +sub n and now i use a triangle + + + align:start position:0% +sub n and now i use a triangle +inequality + + align:start position:0% + + + + align:start position:0% + +which is less than this is less than + + align:start position:0% +which is less than this is less than + + + align:start position:0% +which is less than this is less than +y over 2 + + align:start position:0% +y over 2 + + + align:start position:0% +y over 2 +plus + + align:start position:0% +plus + + + align:start position:0% +plus +y sub n + + align:start position:0% +y sub n + + + align:start position:0% +y sub n +and i started off with the absolute + + align:start position:0% +and i started off with the absolute + + + align:start position:0% +and i started off with the absolute +value of y + + align:start position:0% +value of y + + + align:start position:0% +value of y +so when i subtract that over + + align:start position:0% + + + + align:start position:0% + +that tells me that + + align:start position:0% +that tells me that + + + align:start position:0% +that tells me that +the absolute value of y over 2 + + align:start position:0% +the absolute value of y over 2 + + + align:start position:0% +the absolute value of y over 2 +is less than + + align:start position:0% +is less than + + + align:start position:0% +is less than +absolute value + + align:start position:0% +absolute value + + + align:start position:0% +absolute value +of y sub n for all n bigger than or + + align:start position:0% +of y sub n for all n bigger than or + + + align:start position:0% +of y sub n for all n bigger than or +equal to capital m + + align:start position:0% +equal to capital m + + + align:start position:0% +equal to capital m +okay + + align:start position:0% + + + + align:start position:0% + +so then i let b + + align:start position:0% +so then i let b + + + align:start position:0% +so then i let b +to be + + align:start position:0% +to be + + + align:start position:0% +to be +the minimum of + + align:start position:0% +the minimum of + + + align:start position:0% +the minimum of +several numbers + + align:start position:0% +several numbers + + + align:start position:0% +several numbers +you know i'm writing min but i should + + align:start position:0% +you know i'm writing min but i should + + + align:start position:0% +you know i'm writing min but i should +write inf but + + align:start position:0% + + + + align:start position:0% + +so if you like + + align:start position:0% +so if you like + + + align:start position:0% +so if you like +let me write + + align:start position:0% + + + + align:start position:0% + +inf + + align:start position:0% +inf + + + align:start position:0% +inf +of + + align:start position:0% +of + + + align:start position:0% +of +y1 + + align:start position:0% +y1 + + + align:start position:0% +y1 +y + + align:start position:0% +y + + + align:start position:0% +y +m minus 1 + + align:start position:0% +m minus 1 + + + align:start position:0% +m minus 1 +and + + align:start position:0% + + + + align:start position:0% + +y over 2. + + align:start position:0% +y over 2. + + + align:start position:0% +y over 2. +and by what you are doing on the + + align:start position:0% +and by what you are doing on the + + + align:start position:0% +and by what you are doing on the +assignment i think it was assignment two + + align:start position:0% +assignment i think it was assignment two + + + align:start position:0% +assignment i think it was assignment two +this imp always exists in a finite set + + align:start position:0% +this imp always exists in a finite set + + + align:start position:0% +this imp always exists in a finite set +right this is a finite set of uh + + align:start position:0% +right this is a finite set of uh + + + align:start position:0% +right this is a finite set of uh +positive numbers + + align:start position:0% +positive numbers + + + align:start position:0% +positive numbers +and therefore it's emphem exists as one + + align:start position:0% +and therefore it's emphem exists as one + + + align:start position:0% +and therefore it's emphem exists as one +of these elements one of these + + align:start position:0% +of these elements one of these + + + align:start position:0% +of these elements one of these +m numbers is the infimum + + align:start position:0% +m numbers is the infimum + + + align:start position:0% +m numbers is the infimum +and they're all positive so this is a + + align:start position:0% +and they're all positive so this is a + + + align:start position:0% +and they're all positive so this is a +positive number + + align:start position:0% + + + + align:start position:0% + +and so then + + align:start position:0% +and so then + + + align:start position:0% +and so then +simply how this number is defined it + + align:start position:0% +simply how this number is defined it + + + align:start position:0% +simply how this number is defined it +follows + + align:start position:0% +follows + + + align:start position:0% +follows +that + + align:start position:0% +that + + + align:start position:0% +that +we're all in + + align:start position:0% + + + + align:start position:0% + +y sub n is bigger than or equal to cap + + align:start position:0% +y sub n is bigger than or equal to cap + + + align:start position:0% +y sub n is bigger than or equal to cap +is bigger than or equal to b + + align:start position:0% +is bigger than or equal to b + + + align:start position:0% +is bigger than or equal to b +okay + + align:start position:0% + + + + align:start position:0% + +right because + + align:start position:0% +right because + + + align:start position:0% +right because +again if n is between little n is + + align:start position:0% +again if n is between little n is + + + align:start position:0% +again if n is between little n is +between one and capital m minus one then + + align:start position:0% +between one and capital m minus one then + + + align:start position:0% +between one and capital m minus one then +certainly that any that the absolute + + align:start position:0% +certainly that any that the absolute + + + align:start position:0% +certainly that any that the absolute +value of that thing is bigger than or + + align:start position:0% +value of that thing is bigger than or + + + align:start position:0% +value of that thing is bigger than or +equal to the smaller of all of these + + align:start position:0% +equal to the smaller of all of these + + + align:start position:0% +equal to the smaller of all of these +right + + align:start position:0% +right + + + align:start position:0% +right +which is bigger than or equal to b + + align:start position:0% +which is bigger than or equal to b + + + align:start position:0% +which is bigger than or equal to b +and if n is bigger than or equal to + + align:start position:0% +and if n is bigger than or equal to + + + align:start position:0% +and if n is bigger than or equal to +capital m then we proved over here that + + align:start position:0% +capital m then we proved over here that + + + align:start position:0% +capital m then we proved over here that +y sub n is bigger than + + align:start position:0% +y sub n is bigger than + + + align:start position:0% +y sub n is bigger than +the absolute value of y over two + + align:start position:0% +the absolute value of y over two + + + align:start position:0% +the absolute value of y over two +which is bigger than or equal to the + + align:start position:0% +which is bigger than or equal to the + + + align:start position:0% +which is bigger than or equal to the +minimum of these numbers and y over two + + align:start position:0% +minimum of these numbers and y over two + + + align:start position:0% +minimum of these numbers and y over two +which equals b so + + align:start position:0% +which equals b so + + + align:start position:0% +which equals b so +all right so that proves the claim + + align:start position:0% + + + + align:start position:0% + +that proves the claim but we haven't + + align:start position:0% +that proves the claim but we haven't + + + align:start position:0% +that proves the claim but we haven't +proved what we wanted to yet that the + + align:start position:0% +proved what we wanted to yet that the + + + align:start position:0% +proved what we wanted to yet that the +limit as n goes to infinity of one over + + align:start position:0% +limit as n goes to infinity of one over + + + align:start position:0% +limit as n goes to infinity of one over +y sub n equals one over y + + align:start position:0% +y sub n equals one over y + + + align:start position:0% +y sub n equals one over y +um but this follows + + align:start position:0% + + + + align:start position:0% + +almost immediately from + + align:start position:0% +almost immediately from + + + align:start position:0% +almost immediately from +what we've done so far + + align:start position:0% +what we've done so far + + + align:start position:0% +what we've done so far +so + + align:start position:0% +so + + + align:start position:0% +so +now we're going to use the claim to + + align:start position:0% +now we're going to use the claim to + + + align:start position:0% +now we're going to use the claim to +prove it so we look at + + align:start position:0% + + + + align:start position:0% + +compute that + + align:start position:0% +compute that + + + align:start position:0% +compute that +0 is less than or equal to + + align:start position:0% +0 is less than or equal to + + + align:start position:0% +0 is less than or equal to +1 over y sub n minus 1 over y + + align:start position:0% +1 over y sub n minus 1 over y + + + align:start position:0% +1 over y sub n minus 1 over y +we're going to show that this goes to 0 + + align:start position:0% +we're going to show that this goes to 0 + + + align:start position:0% +we're going to show that this goes to 0 +using those two theorems + + align:start position:0% +using those two theorems + + + align:start position:0% +using those two theorems +and so by algebra that's equal to + + align:start position:0% + + + + align:start position:0% + +and using the absolute value this is 1 + + align:start position:0% +and using the absolute value this is 1 + + + align:start position:0% +and using the absolute value this is 1 +over y sub n minus y + + align:start position:0% +over y sub n minus y + + + align:start position:0% +over y sub n minus y +i mean the absolute value of y sub n + + align:start position:0% +i mean the absolute value of y sub n + + + align:start position:0% +i mean the absolute value of y sub n +minus y over + + align:start position:0% +minus y over + + + align:start position:0% +minus y over +absolute value of y sub n + + align:start position:0% +absolute value of y sub n + + + align:start position:0% +absolute value of y sub n +absolute value of y + + align:start position:0% + + + + align:start position:0% + +now y sub n is bigger than or equal to b + + align:start position:0% +now y sub n is bigger than or equal to b + + + align:start position:0% +now y sub n is bigger than or equal to b +so this is less than or equal to + + align:start position:0% +so this is less than or equal to + + + align:start position:0% +so this is less than or equal to +1 over + + align:start position:0% +1 over + + + align:start position:0% +1 over +b + + align:start position:0% +b + + + align:start position:0% +b +times y + + align:start position:0% + + + + align:start position:0% + +times + + align:start position:0% +times + + + align:start position:0% +times +y sub n minus y + + align:start position:0% +y sub n minus y + + + align:start position:0% +y sub n minus y +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so just to summarize we've shown that 0 + + align:start position:0% +so just to summarize we've shown that 0 + + + align:start position:0% +so just to summarize we've shown that 0 +is less than + + align:start position:0% +is less than + + + align:start position:0% +is less than +1 over y sub n minus 1 over y + + align:start position:0% +1 over y sub n minus 1 over y + + + align:start position:0% +1 over y sub n minus 1 over y +is less than 1 over + + align:start position:0% + + + + align:start position:0% + +b times 1 over or b times the absolute + + align:start position:0% +b times 1 over or b times the absolute + + + align:start position:0% +b times 1 over or b times the absolute +value of y times + + align:start position:0% + + + + align:start position:0% + +y sub n minus y + + align:start position:0% +y sub n minus y + + + align:start position:0% +y sub n minus y +now + + align:start position:0% +now + + + align:start position:0% +now +this goes to 0 + + align:start position:0% + + + + align:start position:0% + +because it's just a constant sequence + + align:start position:0% +because it's just a constant sequence + + + align:start position:0% +because it's just a constant sequence +this + + align:start position:0% +this + + + align:start position:0% +this +converges to zero because + + align:start position:0% +converges to zero because + + + align:start position:0% +converges to zero because +y sub n minus y and absolute value goes + + align:start position:0% +y sub n minus y and absolute value goes + + + align:start position:0% +y sub n minus y and absolute value goes +to zero this is just a fixed number + + align:start position:0% +to zero this is just a fixed number + + + align:start position:0% +to zero this is just a fixed number +times that and by what we've proven for + + align:start position:0% +times that and by what we've proven for + + + align:start position:0% +times that and by what we've proven for +um + + align:start position:0% +um + + + align:start position:0% +um +two this product converges to zero + + align:start position:0% +two this product converges to zero + + + align:start position:0% +two this product converges to zero +so + + align:start position:0% + + + + align:start position:0% + +by the squeeze theorem we get that + + align:start position:0% +by the squeeze theorem we get that + + + align:start position:0% +by the squeeze theorem we get that +one over y sub n + + align:start position:0% + + + + align:start position:0% + +this converges to zero + + align:start position:0% +this converges to zero + + + align:start position:0% +this converges to zero +which implies + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so another big property about the real + + align:start position:0% +so another big property about the real + + + align:start position:0% +so another big property about the real +numbers that we proved after we stated + + align:start position:0% +numbers that we proved after we stated + + + align:start position:0% +numbers that we proved after we stated +the existence of the real numbers + + align:start position:0% +the existence of the real numbers + + + align:start position:0% +the existence of the real numbers +which + + align:start position:0% +which + + + align:start position:0% +which +remember was this is defined as this + + align:start position:0% +remember was this is defined as this + + + align:start position:0% +remember was this is defined as this +ordered field with the least upper bound + + align:start position:0% +ordered field with the least upper bound + + + align:start position:0% +ordered field with the least upper bound +property + + align:start position:0% + + + + align:start position:0% + +we proved that the square root of 2 + + align:start position:0% +we proved that the square root of 2 + + + align:start position:0% +we proved that the square root of 2 +exists + + align:start position:0% +exists + + + align:start position:0% +exists +as a real number + + align:start position:0% + + + + align:start position:0% + +there was really nothing special about 2 + + align:start position:0% +there was really nothing special about 2 + + + align:start position:0% +there was really nothing special about 2 +in fact you could prove that the square + + align:start position:0% +in fact you could prove that the square + + + align:start position:0% +in fact you could prove that the square +root of + + align:start position:0% +root of + + + align:start position:0% +root of +x exists as a real number for any x + + align:start position:0% +x exists as a real number for any x + + + align:start position:0% +x exists as a real number for any x +that's a + + align:start position:0% +that's a + + + align:start position:0% +that's a +positive or non-negative number + + align:start position:0% + + + + align:start position:0% + +so the square root of a real number is + + align:start position:0% +so the square root of a real number is + + + align:start position:0% +so the square root of a real number is +well defined see + + align:start position:0% +well defined see + + + align:start position:0% +well defined see +it's + + align:start position:0% +it's + + + align:start position:0% +it's +um + + align:start position:0% +um + + + align:start position:0% +um +or the square root of a non-negative + + align:start position:0% +or the square root of a non-negative + + + align:start position:0% +or the square root of a non-negative +number is well-defined + + align:start position:0% +number is well-defined + + + align:start position:0% +number is well-defined +and always exists as a real number + + align:start position:0% +and always exists as a real number + + + align:start position:0% +and always exists as a real number +so you can + + align:start position:0% +so you can + + + align:start position:0% +so you can +ask + + align:start position:0% + + + + align:start position:0% + +how does + + align:start position:0% +how does + + + align:start position:0% +how does +uh + + align:start position:0% +uh + + + align:start position:0% +uh +limits interact with square roots + + align:start position:0% + + + + align:start position:0% + +and they interact just as you think they + + align:start position:0% +and they interact just as you think they + + + align:start position:0% +and they interact just as you think they +should + + align:start position:0% + + + + align:start position:0% + +if i have a sequence so that for all n x + + align:start position:0% +if i have a sequence so that for all n x + + + align:start position:0% +if i have a sequence so that for all n x +of n is bigger than or equal to zero + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +it's a convergent sequence converging to + + align:start position:0% +it's a convergent sequence converging to + + + align:start position:0% +it's a convergent sequence converging to +some number x then + + align:start position:0% + + + + align:start position:0% + +the limit of the square roots of these + + align:start position:0% +the limit of the square roots of these + + + align:start position:0% +the limit of the square roots of these +guys equals + + align:start position:0% +guys equals + + + align:start position:0% +guys equals +the square root of the limit + + align:start position:0% +the square root of the limit + + + align:start position:0% +the square root of the limit +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now i want you to + + align:start position:0% +now i want you to + + + align:start position:0% +now i want you to +just take a second here and and + + align:start position:0% +just take a second here and and + + + align:start position:0% +just take a second here and and +understand that this this is a + + align:start position:0% +understand that this this is a + + + align:start position:0% +understand that this this is a +meaningful statement because + + align:start position:0% +meaningful statement because + + + align:start position:0% +meaningful statement because +since the x sub bends are all + + align:start position:0% +since the x sub bends are all + + + align:start position:0% +since the x sub bends are all +non-negative by + + align:start position:0% +non-negative by + + + align:start position:0% +non-negative by +a theorem that let's see did i erase it + + align:start position:0% +a theorem that let's see did i erase it + + + align:start position:0% +a theorem that let's see did i erase it +already + + align:start position:0% +already + + + align:start position:0% +already +the one that had to deal with limits and + + align:start position:0% + + + + align:start position:0% + +limits and the order so since the x sub + + align:start position:0% +limits and the order so since the x sub + + + align:start position:0% +limits and the order so since the x sub +n's are all non-negative that implies + + align:start position:0% +n's are all non-negative that implies + + + align:start position:0% +n's are all non-negative that implies +that x is non-negative so that this + + align:start position:0% +that x is non-negative so that this + + + align:start position:0% +that x is non-negative so that this +square root is meaningful okay + + align:start position:0% +square root is meaningful okay + + + align:start position:0% +square root is meaningful okay +so first check whenever somebody says + + align:start position:0% +so first check whenever somebody says + + + align:start position:0% +so first check whenever somebody says +here's this theorem + + align:start position:0% +here's this theorem + + + align:start position:0% +here's this theorem +or + + align:start position:0% +or + + + align:start position:0% +or +this theorem is uh + + align:start position:0% +this theorem is uh + + + align:start position:0% +this theorem is uh +i think the serum is true + + align:start position:0% +i think the serum is true + + + align:start position:0% +i think the serum is true +is um + + align:start position:0% +is um + + + align:start position:0% +is um +to check to make sure that this uh that + + align:start position:0% +to check to make sure that this uh that + + + align:start position:0% +to check to make sure that this uh that +a theorem is meaningful + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +let's prove this so there's two cases to + + align:start position:0% +let's prove this so there's two cases to + + + align:start position:0% +let's prove this so there's two cases to +consider + + align:start position:0% +consider + + + align:start position:0% +consider +x is equal to zero or x is non-zero so + + align:start position:0% +x is equal to zero or x is non-zero so + + + align:start position:0% +x is equal to zero or x is non-zero so +let's do the first case + + align:start position:0% + + + + align:start position:0% + +so the limit is zero so we'll do this + + align:start position:0% +so the limit is zero so we'll do this + + + align:start position:0% +so the limit is zero so we'll do this +proof uh + + align:start position:0% +proof uh + + + align:start position:0% +proof uh +using the definition of limits + + align:start position:0% +using the definition of limits + + + align:start position:0% +using the definition of limits +meaning the epsilon m + + align:start position:0% +meaning the epsilon m + + + align:start position:0% +meaning the epsilon m +definition + + align:start position:0% +definition + + + align:start position:0% +definition +so we want to show that the limit of the + + align:start position:0% +so we want to show that the limit of the + + + align:start position:0% +so we want to show that the limit of the +square root of x sub n equals 0. + + align:start position:0% +square root of x sub n equals 0. + + + align:start position:0% +square root of x sub n equals 0. +so let epsilon be positive + + align:start position:0% + + + + align:start position:0% + +and since + + align:start position:0% + + + + align:start position:0% + +x sub n converges to + + align:start position:0% +x sub n converges to + + + align:start position:0% +x sub n converges to + + align:start position:0% + + + align:start position:0% +exists + + align:start position:0% +exists + + + align:start position:0% +exists +natural number m sub 0 + + align:start position:0% +natural number m sub 0 + + + align:start position:0% +natural number m sub 0 +such that + + align:start position:0% + + + + align:start position:0% + +if n is bigger than or equal to m 0 then + + align:start position:0% + + + + align:start position:0% + +x sub n minus the limit which is just + + align:start position:0% +x sub n minus the limit which is just + + + align:start position:0% +x sub n minus the limit which is just +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know + + align:start position:0% +you know + + + align:start position:0% +you know +0 and taking the absolute value which is + + align:start position:0% +0 and taking the absolute value which is + + + align:start position:0% +0 and taking the absolute value which is +just x of n + + align:start position:0% + + + + align:start position:0% + +which is equal to x of n because x of n + + align:start position:0% +which is equal to x of n because x of n + + + align:start position:0% +which is equal to x of n because x of n +is not negative + + align:start position:0% +is not negative + + + align:start position:0% +is not negative +is less than + + align:start position:0% + + + + align:start position:0% + +epsilon squared + + align:start position:0% +epsilon squared + + + align:start position:0% +epsilon squared +okay remember i can always find no + + align:start position:0% +okay remember i can always find no + + + align:start position:0% +okay remember i can always find no +matter what + + align:start position:0% +matter what + + + align:start position:0% +matter what +is underneath my hand since x sub n + + align:start position:0% +is underneath my hand since x sub n + + + align:start position:0% +is underneath my hand since x sub n +converges to zero i can find a natural + + align:start position:0% +converges to zero i can find a natural + + + align:start position:0% +converges to zero i can find a natural +number so that that thing is less than + + align:start position:0% +number so that that thing is less than + + + align:start position:0% +number so that that thing is less than +what's underneath my hand and the thing + + align:start position:0% +what's underneath my hand and the thing + + + align:start position:0% +what's underneath my hand and the thing +that i'm going to have underneath my + + align:start position:0% +that i'm going to have underneath my + + + align:start position:0% +that i'm going to have underneath my +hand that's going to make things work + + align:start position:0% +hand that's going to make things work + + + align:start position:0% +hand that's going to make things work +out for the square root is epsilon + + align:start position:0% +out for the square root is epsilon + + + align:start position:0% +out for the square root is epsilon +squared + + align:start position:0% +squared + + + align:start position:0% +squared +okay + + align:start position:0% + + + + align:start position:0% + +choose m to be m sub 0. + + align:start position:0% +choose m to be m sub 0. + + + align:start position:0% +choose m to be m sub 0. +so i'm going to show this m works for + + align:start position:0% +so i'm going to show this m works for + + + align:start position:0% +so i'm going to show this m works for +the sequence square root of x of n + + align:start position:0% +the sequence square root of x of n + + + align:start position:0% +the sequence square root of x of n +and if n is bigger than or equal to m + + align:start position:0% +and if n is bigger than or equal to m + + + align:start position:0% +and if n is bigger than or equal to m +the square root of x sub n + + align:start position:0% +the square root of x sub n + + + align:start position:0% +the square root of x sub n +minus 0 which is just + + align:start position:0% + + + + align:start position:0% + +x sub n + + align:start position:0% + + + + align:start position:0% + +now it's also so we didn't strictly + + align:start position:0% +now it's also so we didn't strictly + + + align:start position:0% +now it's also so we didn't strictly +speaking prove this but it's not um + + align:start position:0% + + + + align:start position:0% + +you know too hard to show that square + + align:start position:0% +you know too hard to show that square + + + align:start position:0% +you know too hard to show that square +roots respect + + align:start position:0% + + + + align:start position:0% + +inequalities so x sub n is less than + + align:start position:0% +inequalities so x sub n is less than + + + align:start position:0% +inequalities so x sub n is less than +epsilon squared so the square root is + + align:start position:0% +epsilon squared so the square root is + + + align:start position:0% +epsilon squared so the square root is +less than epsilon squared + + align:start position:0% +less than epsilon squared + + + align:start position:0% +less than epsilon squared +which equals epsilon + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so the second case + + align:start position:0% +so the second case + + + align:start position:0% +so the second case +is + + align:start position:0% + + + + align:start position:0% + +x not equal to 0 + + align:start position:0% + + + + align:start position:0% + +and to do this case we'll use those two + + align:start position:0% +and to do this case we'll use those two + + + align:start position:0% +and to do this case we'll use those two +theorems + + align:start position:0% +theorems + + + align:start position:0% +theorems +again + + align:start position:0% +again + + + align:start position:0% +again +so + + align:start position:0% +so + + + align:start position:0% +so +and let's look at + + align:start position:0% +and let's look at + + + align:start position:0% +and let's look at +square root of x sub n minus square root + + align:start position:0% +square root of x sub n minus square root + + + align:start position:0% +square root of x sub n minus square root +of x + + align:start position:0% +of x + + + align:start position:0% +of x +now if i + + align:start position:0% +now if i + + + align:start position:0% +now if i +uh + + align:start position:0% + + + + align:start position:0% + +write this as + + align:start position:0% + + + + align:start position:0% + +i multiply top and bottom + + align:start position:0% +i multiply top and bottom + + + align:start position:0% +i multiply top and bottom +by x of n plus absolute or square root + + align:start position:0% +by x of n plus absolute or square root + + + align:start position:0% +by x of n plus absolute or square root +of x + + align:start position:0% +of x + + + align:start position:0% +of x +square root of x sub n plus square root + + align:start position:0% +square root of x sub n plus square root + + + align:start position:0% +square root of x sub n plus square root +of x which is a positive number it's + + align:start position:0% +of x which is a positive number it's + + + align:start position:0% +of x which is a positive number it's +fine to divide by it as well + + align:start position:0% +fine to divide by it as well + + + align:start position:0% +fine to divide by it as well +because x is non-zero + + align:start position:0% +because x is non-zero + + + align:start position:0% +because x is non-zero +so here not just non-zero it's positive + + align:start position:0% +so here not just non-zero it's positive + + + align:start position:0% +so here not just non-zero it's positive +because x has to be non-negative + + align:start position:0% +because x has to be non-negative + + + align:start position:0% +because x has to be non-negative +now this is the product of something + + align:start position:0% +now this is the product of something + + + align:start position:0% +now this is the product of something +minus something else + + align:start position:0% +minus something else + + + align:start position:0% +minus something else +with something plus something else so + + align:start position:0% +with something plus something else so + + + align:start position:0% +with something plus something else so +then that's going to be the difference + + align:start position:0% +then that's going to be the difference + + + align:start position:0% +then that's going to be the difference +of the squares so that's equal to + + align:start position:0% + + + + align:start position:0% + +over and + + align:start position:0% +over and + + + align:start position:0% +over and +again these are positive numbers so that + + align:start position:0% +again these are positive numbers so that + + + align:start position:0% +again these are positive numbers so that +they come out of the absolute value + + align:start position:0% +they come out of the absolute value + + + align:start position:0% +they come out of the absolute value +and + + align:start position:0% +and + + + align:start position:0% +and +this is non-negative so in fact it's + + align:start position:0% +this is non-negative so in fact it's + + + align:start position:0% +this is non-negative so in fact it's +only making things bigger on the bottom + + align:start position:0% +only making things bigger on the bottom + + + align:start position:0% +only making things bigger on the bottom +and therefore things smaller overall so + + align:start position:0% +and therefore things smaller overall so + + + align:start position:0% +and therefore things smaller overall so +this is less than or equal to + + align:start position:0% +this is less than or equal to + + + align:start position:0% +this is less than or equal to +just if i replace this by square root of + + align:start position:0% +just if i replace this by square root of + + + align:start position:0% +just if i replace this by square root of +x + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so what did i prove + + align:start position:0% + + + + align:start position:0% + +1 over square root of x + + align:start position:0% + + + + align:start position:0% + +all right and + + align:start position:0% +all right and + + + align:start position:0% +all right and +so by assumption x of n converges to x + + align:start position:0% +so by assumption x of n converges to x + + + align:start position:0% +so by assumption x of n converges to x +so this goes to zero this is a fixed + + align:start position:0% +so this goes to zero this is a fixed + + + align:start position:0% +so this goes to zero this is a fixed +number multiplied by this thing going to + + align:start position:0% +number multiplied by this thing going to + + + align:start position:0% +number multiplied by this thing going to +zero so by + + align:start position:0% +zero so by + + + align:start position:0% +zero so by +um number two and the theorem we proved + + align:start position:0% +um number two and the theorem we proved + + + align:start position:0% +um number two and the theorem we proved +before this whole product converges to + + align:start position:0% +before this whole product converges to + + + align:start position:0% +before this whole product converges to +zero okay so and of course this + + align:start position:0% +zero okay so and of course this + + + align:start position:0% +zero okay so and of course this +converges to zero so this thing in the + + align:start position:0% +converges to zero so this thing in the + + + align:start position:0% +converges to zero so this thing in the +middle must converge to zero by the + + align:start position:0% +middle must converge to zero by the + + + align:start position:0% +middle must converge to zero by the +squeeze theorem + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +that's the square root + + align:start position:0% +that's the square root + + + align:start position:0% +that's the square root +and + + align:start position:0% + + + + align:start position:0% + +let me just remark + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +so this + + align:start position:0% +so this + + + align:start position:0% +so this +number three up here that the limit of + + align:start position:0% +number three up here that the limit of + + + align:start position:0% +number three up here that the limit of +the product is a product of the limits + + align:start position:0% +the product is a product of the limits + + + align:start position:0% +the product is a product of the limits +this thus implies that the limit of xn + + align:start position:0% +this thus implies that the limit of xn + + + align:start position:0% +this thus implies that the limit of xn +squared converges to x squared so the + + align:start position:0% +squared converges to x squared so the + + + align:start position:0% +squared converges to x squared so the +square + + align:start position:0% +square + + + align:start position:0% +square +of x sub n converges to the square of + + align:start position:0% +of x sub n converges to the square of + + + align:start position:0% +of x sub n converges to the square of +the limit and by induction you can show + + align:start position:0% +the limit and by induction you can show + + + align:start position:0% +the limit and by induction you can show +that the cube + + align:start position:0% +that the cube + + + align:start position:0% +that the cube +fourth power fifth power of x sub n + + align:start position:0% +fourth power fifth power of x sub n + + + align:start position:0% +fourth power fifth power of x sub n +converges to the fourth power fifth + + align:start position:0% +converges to the fourth power fifth + + + align:start position:0% +converges to the fourth power fifth +power of x okay + + align:start position:0% +power of x okay + + + align:start position:0% +power of x okay +and not only that you can also prove + + align:start position:0% +and not only that you can also prove + + + align:start position:0% +and not only that you can also prove +um + + align:start position:0% +um + + + align:start position:0% +um +so i'm not going to do this + + align:start position:0% +so i'm not going to do this + + + align:start position:0% +so i'm not going to do this +and i'm not going to force you to either + + align:start position:0% +and i'm not going to force you to either + + + align:start position:0% +and i'm not going to force you to either +but just know these as facts + + align:start position:0% +but just know these as facts + + + align:start position:0% +but just know these as facts +that i don't have to just take the + + align:start position:0% +that i don't have to just take the + + + align:start position:0% +that i don't have to just take the +square root i could take the kth root so + + align:start position:0% +square root i could take the kth root so + + + align:start position:0% +square root i could take the kth root so +um + + align:start position:0% +um + + + align:start position:0% +um +and this statement still is true that if + + align:start position:0% +and this statement still is true that if + + + align:start position:0% +and this statement still is true that if +x of n is bigger than or equal to 0 for + + align:start position:0% +x of n is bigger than or equal to 0 for + + + align:start position:0% +x of n is bigger than or equal to 0 for +all n + + align:start position:0% +all n + + + align:start position:0% +all n +and i have a + + align:start position:0% +and i have a + + + align:start position:0% +and i have a +a limit then the kth root of x of n + + align:start position:0% +a limit then the kth root of x of n + + + align:start position:0% +a limit then the kth root of x of n +converges to the kth root of x + + align:start position:0% + + + + align:start position:0% + +so the final + + align:start position:0% +so the final + + + align:start position:0% +so the final +theorem we'll prove for today which will + + align:start position:0% +theorem we'll prove for today which will + + + align:start position:0% +theorem we'll prove for today which will +conclude our + + align:start position:0% +conclude our + + + align:start position:0% +conclude our +facts about limits is + + align:start position:0% + + + + align:start position:0% + +you know we have um + + align:start position:0% +you know we have um + + + align:start position:0% +you know we have um +i mean we've been using this all along + + align:start position:0% +i mean we've been using this all along + + + align:start position:0% +i mean we've been using this all along +although i haven't made special + + align:start position:0% +although i haven't made special + + + align:start position:0% +although i haven't made special +attention about it you know the real + + align:start position:0% +attention about it you know the real + + + align:start position:0% +attention about it you know the real +numbers there this again like i said an + + align:start position:0% +numbers there this again like i said an + + + align:start position:0% +numbers there this again like i said an +ordered field with the least upper bound + + align:start position:0% +ordered field with the least upper bound + + + align:start position:0% +ordered field with the least upper bound +property + + align:start position:0% +property + + + align:start position:0% +property +so we've seen how + + align:start position:0% +so we've seen how + + + align:start position:0% +so we've seen how +uh limits interact with + + align:start position:0% +uh limits interact with + + + align:start position:0% +uh limits interact with +um + + align:start position:0% +um + + + align:start position:0% +um +you know this structure of the real + + align:start position:0% +you know this structure of the real + + + align:start position:0% +you know this structure of the real +numbers but they also have a distance + + align:start position:0% +numbers but they also have a distance + + + align:start position:0% +numbers but they also have a distance +associated to them right the absolute + + align:start position:0% +associated to them right the absolute + + + align:start position:0% +associated to them right the absolute +value the distance from two numbers a + + align:start position:0% +value the distance from two numbers a + + + align:start position:0% +value the distance from two numbers a +and b + + align:start position:0% +and b + + + align:start position:0% +and b +uh + + align:start position:0% +uh + + + align:start position:0% +uh +is the absolute value of a minus b + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +or the distance from a number + + align:start position:0% +or the distance from a number + + + align:start position:0% +or the distance from a number +to 0 is just the absolute value of that + + align:start position:0% +to 0 is just the absolute value of that + + + align:start position:0% +to 0 is just the absolute value of that +number + + align:start position:0% +number + + + align:start position:0% +number +so one could ask + + align:start position:0% +so one could ask + + + align:start position:0% +so one could ask +how does the limit + + align:start position:0% +how does the limit + + + align:start position:0% +how does the limit +interact with this additional structure + + align:start position:0% +interact with this additional structure + + + align:start position:0% +interact with this additional structure +of the absolute value + + align:start position:0% +of the absolute value + + + align:start position:0% +of the absolute value +okay and so + + align:start position:0% +okay and so + + + align:start position:0% +okay and so +just like everything's been good so far + + align:start position:0% +just like everything's been good so far + + + align:start position:0% +just like everything's been good so far +with limits + + align:start position:0% +with limits + + + align:start position:0% +with limits +uh it's the same with the absolute value + + align:start position:0% +uh it's the same with the absolute value + + + align:start position:0% +uh it's the same with the absolute value +namely that limits respect absolute + + align:start position:0% +namely that limits respect absolute + + + align:start position:0% +namely that limits respect absolute +value + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +if x of n is + + align:start position:0% + + + + align:start position:0% + +convergent sequence + + align:start position:0% + + + + align:start position:0% + +limit x + + align:start position:0% + + + + align:start position:0% + +then the sequence of absolute values is + + align:start position:0% +then the sequence of absolute values is + + + align:start position:0% +then the sequence of absolute values is +also a convergent sequence + + align:start position:0% + + + + align:start position:0% + +and the limit as n goes to infinity + + align:start position:0% +and the limit as n goes to infinity + + + align:start position:0% +and the limit as n goes to infinity +of + + align:start position:0% +of + + + align:start position:0% +of +the absolute values equals + + align:start position:0% +the absolute values equals + + + align:start position:0% +the absolute values equals +the absolute value of the limit okay now + + align:start position:0% +the absolute value of the limit okay now + + + align:start position:0% +the absolute value of the limit okay now +let me again let's let's um + + align:start position:0% +let me again let's let's um + + + align:start position:0% +let me again let's let's um +try to think a little more + + align:start position:0% +try to think a little more + + + align:start position:0% +try to think a little more +deeply about this real quick + + align:start position:0% +deeply about this real quick + + + align:start position:0% +deeply about this real quick +if i have a convergent sequence and the + + align:start position:0% +if i have a convergent sequence and the + + + align:start position:0% +if i have a convergent sequence and the +absolute values converge + + align:start position:0% +absolute values converge + + + align:start position:0% +absolute values converge +does the converse hold if the absolute + + align:start position:0% +does the converse hold if the absolute + + + align:start position:0% +does the converse hold if the absolute +values converge does this imply that the + + align:start position:0% +values converge does this imply that the + + + align:start position:0% +values converge does this imply that the +original sequence converges and the + + align:start position:0% +original sequence converges and the + + + align:start position:0% +original sequence converges and the +answer is of course no + + align:start position:0% +answer is of course no + + + align:start position:0% +answer is of course no +well not of course i didn't even give + + align:start position:0% +well not of course i didn't even give + + + align:start position:0% +well not of course i didn't even give +you a minute to think about it but + + align:start position:0% +you a minute to think about it but + + + align:start position:0% +you a minute to think about it but +why is the converse not true + + align:start position:0% + + + + align:start position:0% + +so let me make this a mark + + align:start position:0% + + + + align:start position:0% + +converse is not true + + align:start position:0% +converse is not true + + + align:start position:0% +converse is not true +because you could look at x sub n equals + + align:start position:0% +because you could look at x sub n equals + + + align:start position:0% +because you could look at x sub n equals +minus 1 to the n + + align:start position:0% +minus 1 to the n + + + align:start position:0% +minus 1 to the n +right + + align:start position:0% +right + + + align:start position:0% +right +then + + align:start position:0% + + + + align:start position:0% + +the absolute values of these guys + + align:start position:0% +the absolute values of these guys + + + align:start position:0% +the absolute values of these guys +converges but the original sequence does + + align:start position:0% +converges but the original sequence does + + + align:start position:0% +converges but the original sequence does +not converge + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +this is a one-way street uh + + align:start position:0% +this is a one-way street uh + + + align:start position:0% +this is a one-way street uh +for + + align:start position:0% +for + + + align:start position:0% +for +convergence and convergence of the + + align:start position:0% +convergence and convergence of the + + + align:start position:0% +convergence and convergence of the +absolute values + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +um so before i prove this theorem let me + + align:start position:0% +um so before i prove this theorem let me + + + align:start position:0% +um so before i prove this theorem let me +just prove a quick uh + + align:start position:0% +just prove a quick uh + + + align:start position:0% +just prove a quick uh +um + + align:start position:0% + + + + align:start position:0% + +inequality which i think i said i was + + align:start position:0% +inequality which i think i said i was + + + align:start position:0% +inequality which i think i said i was +going to put on the assignment and then + + align:start position:0% +going to put on the assignment and then + + + align:start position:0% +going to put on the assignment and then +forgot to put on the assignment but + + align:start position:0% +forgot to put on the assignment but + + + align:start position:0% +forgot to put on the assignment but +you should know it so this theorem is + + align:start position:0% +you should know it so this theorem is + + + align:start position:0% +you should know it so this theorem is +the reverse triangle inequality + + align:start position:0% + + + + align:start position:0% + +which states for all + + align:start position:0% +which states for all + + + align:start position:0% +which states for all +a b + + align:start position:0% +a b + + + align:start position:0% +a b +real number the absolute value of the + + align:start position:0% +real number the absolute value of the + + + align:start position:0% +real number the absolute value of the +difference in absolute values + + align:start position:0% +difference in absolute values + + + align:start position:0% +difference in absolute values +is less than or equal to + + align:start position:0% +is less than or equal to + + + align:start position:0% +is less than or equal to +the absolute value of the difference + + align:start position:0% +the absolute value of the difference + + + align:start position:0% +the absolute value of the difference +okay so the proof of + + align:start position:0% + + + + align:start position:0% + +this reverse triangle inequality + + align:start position:0% +this reverse triangle inequality + + + align:start position:0% +this reverse triangle inequality +just uses the the original triangle + + align:start position:0% +just uses the the original triangle + + + align:start position:0% +just uses the the original triangle +inequality + + align:start position:0% +inequality + + + align:start position:0% +inequality +so + + align:start position:0% + + + + align:start position:0% + +the absolute value of a + + align:start position:0% +the absolute value of a + + + align:start position:0% +the absolute value of a +this is equal to the absolute value of a + + align:start position:0% +this is equal to the absolute value of a + + + align:start position:0% +this is equal to the absolute value of a +minus b + + align:start position:0% +minus b + + + align:start position:0% +minus b +plus b and this is less than or equal to + + align:start position:0% +plus b and this is less than or equal to + + + align:start position:0% +plus b and this is less than or equal to +the absolute value of + + align:start position:0% +the absolute value of + + + align:start position:0% +the absolute value of +a minus b plus absolute value of b + + align:start position:0% +a minus b plus absolute value of b + + + align:start position:0% +a minus b plus absolute value of b +and thus + + align:start position:0% +and thus + + + align:start position:0% +and thus +the absolute value of + + align:start position:0% +the absolute value of + + + align:start position:0% +the absolute value of +a minus the absolute value of b is less + + align:start position:0% +a minus the absolute value of b is less + + + align:start position:0% +a minus the absolute value of b is less +than or equal to + + align:start position:0% +than or equal to + + + align:start position:0% +than or equal to +the absolute value of a minus b now + + align:start position:0% +the absolute value of a minus b now + + + align:start position:0% +the absolute value of a minus b now +these are just two numbers i mean two + + align:start position:0% +these are just two numbers i mean two + + + align:start position:0% +these are just two numbers i mean two +letters reverse the letters + + align:start position:0% + + + + align:start position:0% + +in this argument replace a with b + + align:start position:0% +in this argument replace a with b + + + align:start position:0% +in this argument replace a with b +and b with a so then + + align:start position:0% +and b with a so then + + + align:start position:0% +and b with a so then +i get b minus the absolute value + + align:start position:0% +i get b minus the absolute value + + + align:start position:0% +i get b minus the absolute value +the absolute value of b minus the + + align:start position:0% +the absolute value of b minus the + + + align:start position:0% +the absolute value of b minus the +absolute value of a is less than or + + align:start position:0% +absolute value of a is less than or + + + align:start position:0% +absolute value of a is less than or +equal to + + align:start position:0% + + + + align:start position:0% + +the absolute value of b minus a which is + + align:start position:0% +the absolute value of b minus a which is + + + align:start position:0% +the absolute value of b minus a which is +the same as this + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +therefore + + align:start position:0% +therefore + + + align:start position:0% +therefore +let me multiply through + + align:start position:0% +let me multiply through + + + align:start position:0% +let me multiply through +by minus 1 + + align:start position:0% +by minus 1 + + + align:start position:0% +by minus 1 +and that tells me + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +i have this is less than or equal to the + + align:start position:0% +i have this is less than or equal to the + + + align:start position:0% +i have this is less than or equal to the +absolute value of a minus b i also have + + align:start position:0% +absolute value of a minus b i also have + + + align:start position:0% +absolute value of a minus b i also have +it's bigger than or equal to minus the + + align:start position:0% +it's bigger than or equal to minus the + + + align:start position:0% +it's bigger than or equal to minus the +absolute value of a minus b + + align:start position:0% +absolute value of a minus b + + + align:start position:0% +absolute value of a minus b +[Applause] + + align:start position:0% + + + + align:start position:0% + +and therefore the absolute value of a + + align:start position:0% +and therefore the absolute value of a + + + align:start position:0% +and therefore the absolute value of a +minus the absolute value of b + + align:start position:0% +minus the absolute value of b + + + align:start position:0% +minus the absolute value of b +is less than or equal to + + align:start position:0% +is less than or equal to + + + align:start position:0% +is less than or equal to +absolute value of a minus b + + align:start position:0% + + + + align:start position:0% + +so i know it's taboo to write on the + + align:start position:0% +so i know it's taboo to write on the + + + align:start position:0% +so i know it's taboo to write on the +very back board but i'm going to do it + + align:start position:0% +very back board but i'm going to do it + + + align:start position:0% +very back board but i'm going to do it +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +so that was the proof of the reverse + + align:start position:0% +so that was the proof of the reverse + + + align:start position:0% +so that was the proof of the reverse +triangle inequality here's the proof of + + align:start position:0% +triangle inequality here's the proof of + + + align:start position:0% +triangle inequality here's the proof of +the theorem + + align:start position:0% +the theorem + + + align:start position:0% +the theorem +before it + + align:start position:0% +before it + + + align:start position:0% +before it +it just follows from the reverse + + align:start position:0% +it just follows from the reverse + + + align:start position:0% +it just follows from the reverse +triangle inequality and + + align:start position:0% +triangle inequality and + + + align:start position:0% +triangle inequality and +one in in that + + align:start position:0% +one in in that + + + align:start position:0% +one in in that +combination of those two theorems over + + align:start position:0% +combination of those two theorems over + + + align:start position:0% +combination of those two theorems over +there + + align:start position:0% + + + + align:start position:0% + +we have that the absolute value + + align:start position:0% +we have that the absolute value + + + align:start position:0% +we have that the absolute value +of x of n minus the absolute value + + align:start position:0% +of x of n minus the absolute value + + + align:start position:0% +of x of n minus the absolute value +of x + + align:start position:0% +of x + + + align:start position:0% +of x +this is less than or equal to by the + + align:start position:0% +this is less than or equal to by the + + + align:start position:0% +this is less than or equal to by the +reverse triangle inequality the absolute + + align:start position:0% +reverse triangle inequality the absolute + + + align:start position:0% +reverse triangle inequality the absolute +value of n x of n minus x + + align:start position:0% + + + + align:start position:0% + +so this is by + + align:start position:0% + + + + align:start position:0% + +reverse triangle + + align:start position:0% + + + + align:start position:0% + +inequality + + align:start position:0% +inequality + + + align:start position:0% +inequality +and by assumption + + align:start position:0% +and by assumption + + + align:start position:0% +and by assumption +this converges to 0 + + align:start position:0% +this converges to 0 + + + align:start position:0% +this converges to 0 +as n goes to infinity + + align:start position:0% +as n goes to infinity + + + align:start position:0% +as n goes to infinity +okay + + align:start position:0% + + + + align:start position:0% + +so by the squeeze theorem + + align:start position:0% + + + + align:start position:0% + +this goes to 0 and therefore + + align:start position:0% + + + + align:start position:0% + +the absolute value of x sub n converges + + align:start position:0% +the absolute value of x sub n converges + + + align:start position:0% +the absolute value of x sub n converges +to the absolute value of x + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +that's it for + + align:start position:0% +that's it for + + + align:start position:0% +that's it for +that proof for this lecture and for this + + align:start position:0% +that proof for this lecture and for this + + + align:start position:0% +that proof for this lecture and for this +week \ No newline at end of file diff --git a/pWHUGzxzPNk.txt b/pWHUGzxzPNk.txt new file mode 100644 index 0000000000000000000000000000000000000000..9a1e3302ee6d9199c7cacfd563221169deaee858 --- /dev/null +++ b/pWHUGzxzPNk.txt @@ -0,0 +1,12459 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let us start + + align:start position:0% + + + + align:start position:0% + +so first remind you + + align:start position:0% +so first remind you + + + align:start position:0% +so first remind you +the Master Formula will be derived + + align:start position:0% +the Master Formula will be derived + + + align:start position:0% +the Master Formula will be derived +before for past integral + + align:start position:0% + + + + align:start position:0% + +he said if we consider + + align:start position:0% +he said if we consider + + + align:start position:0% +he said if we consider +time ordered anything + + align:start position:0% +time ordered anything + + + align:start position:0% +time ordered anything +okay so let me just call it X will be + + align:start position:0% +okay so let me just call it X will be + + + align:start position:0% +okay so let me just call it X will be +say some product of operators + + align:start position:0% +say some product of operators + + + align:start position:0% +say some product of operators +and then this can be written as + + align:start position:0% +and then this can be written as + + + align:start position:0% +and then this can be written as +in the parking they've got formed + + align:start position:0% +in the parking they've got formed + + + align:start position:0% +in the parking they've got formed +so if I + + align:start position:0% +so if I + + + align:start position:0% +so if I +and then so X you just go into here + + align:start position:0% +and then so X you just go into here + + + align:start position:0% +and then so X you just go into here +and then you have is okay and then + + align:start position:0% +and then you have is okay and then + + + align:start position:0% +and then you have is okay and then +divided by + + align:start position:0% +divided by + + + align:start position:0% +divided by +defy just without X just i s okay + + align:start position:0% +defy just without X just i s okay + + + align:start position:0% +defy just without X just i s okay +so this is the last formula we derived + + align:start position:0% +so this is the last formula we derived + + + align:start position:0% +so this is the last formula we derived +before which applies to any series + + align:start position:0% +before which applies to any series + + + align:start position:0% +before which applies to any series +okay in principle any Theory and any X + + align:start position:0% +okay in principle any Theory and any X + + + align:start position:0% +okay in principle any Theory and any X +you want okay + + align:start position:0% +you want okay + + + align:start position:0% +you want okay +and uh so so so since inside this x + + align:start position:0% +and uh so so so since inside this x + + + align:start position:0% +and uh so so so since inside this x +should always be time ordered okay so + + align:start position:0% +should always be time ordered okay so + + + align:start position:0% +should always be time ordered okay so +this t means time volt + + align:start position:0% +this t means time volt + + + align:start position:0% +this t means time volt +so now we can apply this to an + + align:start position:0% +so now we can apply this to an + + + align:start position:0% +so now we can apply this to an +interacting Theory + + align:start position:0% + + + + align:start position:0% + +so for impacting Theory + + align:start position:0% +so for impacting Theory + + + align:start position:0% +so for impacting Theory +we have S + + align:start position:0% +we have S + + + align:start position:0% +we have S +let me write s so the action should be + + align:start position:0% +let me write s so the action should be + + + align:start position:0% +let me write s so the action should be +the 3C reaction plus the interaction + + align:start position:0% +the 3C reaction plus the interaction + + + align:start position:0% +the 3C reaction plus the interaction +part + + align:start position:0% +part + + + align:start position:0% +part +okay and the interaction part in terms + + align:start position:0% +okay and the interaction part in terms + + + align:start position:0% +okay and the interaction part in terms +can be written as say the integration + + align:start position:0% +can be written as say the integration + + + align:start position:0% +can be written as say the integration +over + + align:start position:0% +over + + + align:start position:0% +over +the interaction part of the lagonian + + align:start position:0% +the interaction part of the lagonian + + + align:start position:0% +the interaction part of the lagonian +density + + align:start position:0% +density + + + align:start position:0% +density +and it's also the same + + align:start position:0% +and it's also the same + + + align:start position:0% +and it's also the same +as the minus + + align:start position:0% + + + + align:start position:0% + +the interactive part of the hamiltonian + + align:start position:0% +the interactive part of the hamiltonian + + + align:start position:0% +the interactive part of the hamiltonian +integrated over time okay so the reason + + align:start position:0% +integrated over time okay so the reason + + + align:start position:0% +integrated over time okay so the reason +for this simple relation + + align:start position:0% +for this simple relation + + + align:start position:0% +for this simple relation +is because we assume the interacting + + align:start position:0% +is because we assume the interacting + + + align:start position:0% +is because we assume the interacting +part does not contain in the time time + + align:start position:0% +part does not contain in the time time + + + align:start position:0% +part does not contain in the time time +derivatives so the potential so so + + align:start position:0% +derivatives so the potential so so + + + align:start position:0% +derivatives so the potential so so +essentially interacting part + + align:start position:0% +essentially interacting part + + + align:start position:0% +essentially interacting part +corresponding to a potential in your in + + align:start position:0% +corresponding to a potential in your in + + + align:start position:0% +corresponding to a potential in your in +your electronic density and then the + + align:start position:0% +your electronic density and then the + + + align:start position:0% +your electronic density and then the +hamiltonian they just differ by minus + + align:start position:0% +hamiltonian they just differ by minus + + + align:start position:0% +hamiltonian they just differ by minus +sign okay + + align:start position:0% + + + + align:start position:0% + +so now we can just apply this to this + + align:start position:0% +so now we can just apply this to this + + + align:start position:0% +so now we can just apply this to this +case + + align:start position:0% +case + + + align:start position:0% +case +okay + + align:start position:0% +okay + + + align:start position:0% +okay +let's see so we can just write this + + align:start position:0% +let's see so we can just write this + + + align:start position:0% +let's see so we can just write this +object + + align:start position:0% +object + + + align:start position:0% +object +so now we can write it as + + align:start position:0% +so now we can write it as + + + align:start position:0% +so now we can write it as +also come here + + align:start position:0% + + + + align:start position:0% + +so so our goal is that we we assume the + + align:start position:0% +so so our goal is that we we assume the + + + align:start position:0% +so so our goal is that we we assume the +SI is small compared to s0 because we + + align:start position:0% +SI is small compared to s0 because we + + + align:start position:0% +SI is small compared to s0 because we +cannot solve this series exactly + + align:start position:0% +cannot solve this series exactly + + + align:start position:0% +cannot solve this series exactly +and so what we are going to do is we + + align:start position:0% +and so what we are going to do is we + + + align:start position:0% +and so what we are going to do is we +want to treat this eyes to be small and + + align:start position:0% +want to treat this eyes to be small and + + + align:start position:0% +want to treat this eyes to be small and +expand in the in the cautioning is I + + align:start position:0% +expand in the in the cautioning is I + + + align:start position:0% +expand in the in the cautioning is I +okay so example of s i is this Lambda 5 + + align:start position:0% +okay so example of s i is this Lambda 5 + + + align:start position:0% +okay so example of s i is this Lambda 5 +4 which we wrote down before + + align:start position:0% +4 which we wrote down before + + + align:start position:0% +4 which we wrote down before +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so uh so for this purpose then you + + align:start position:0% +so so uh so for this purpose then you + + + align:start position:0% +so so uh so for this purpose then you +can just write this more explicitly + + align:start position:0% +can just write this more explicitly + + + align:start position:0% +can just write this more explicitly +as 35 + + align:start position:0% +as 35 + + + align:start position:0% +as 35 +then you have X + + align:start position:0% +then you have X + + + align:start position:0% +then you have X +so you have is0 + + align:start position:0% + + + + align:start position:0% + +the expression isi okay + + align:start position:0% +the expression isi okay + + + align:start position:0% +the expression isi okay +and divide it by + + align:start position:0% +and divide it by + + + align:start position:0% +and divide it by +if I expansion is zero + + align:start position:0% + + + + align:start position:0% + +size okay + + align:start position:0% + + + + align:start position:0% + +and now + + align:start position:0% +and now + + + align:start position:0% +and now +so + + align:start position:0% +so + + + align:start position:0% +so +we cannot treat this + + align:start position:0% +we cannot treat this + + + align:start position:0% +we cannot treat this +as the integrand for the for the yeah so + + align:start position:0% +as the integrand for the for the yeah so + + + align:start position:0% +as the integrand for the for the yeah so +this is the integration for the free + + align:start position:0% +this is the integration for the free + + + align:start position:0% +this is the integration for the free +Theory okay so now we can interpret this + + align:start position:0% +Theory okay so now we can interpret this + + + align:start position:0% +Theory okay so now we can interpret this +just as a integrand for the free series + + align:start position:0% +just as a integrand for the free series + + + align:start position:0% +just as a integrand for the free series +as some say x Prime so so x times the + + align:start position:0% +as some say x Prime so so x times the + + + align:start position:0% +as some say x Prime so so x times the +expression isi as + + align:start position:0% +expression isi as + + + align:start position:0% +expression isi as +as a lot of X for the freezing and + + align:start position:0% +as a lot of X for the freezing and + + + align:start position:0% +as a lot of X for the freezing and +similarly here okay so we can write this + + align:start position:0% +similarly here okay so we can write this + + + align:start position:0% +similarly here okay so we can write this +as follows + + align:start position:0% +as follows + + + align:start position:0% +as follows +so we can write this + + align:start position:0% +so we can write this + + + align:start position:0% +so we can write this +as + + align:start position:0% +as + + + align:start position:0% +as +now in free Theory + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so upstairs should corresponding to zero + + align:start position:0% +so upstairs should corresponding to zero + + + align:start position:0% +so upstairs should corresponding to zero +uh uh yeah yeah let me just + + align:start position:0% +uh uh yeah yeah let me just + + + align:start position:0% +uh uh yeah yeah let me just +not worry about it at the moment so so + + align:start position:0% +not worry about it at the moment so so + + + align:start position:0% +not worry about it at the moment so so +now you can write it as + + align:start position:0% +now you can write it as + + + align:start position:0% +now you can write it as +in time order it + + align:start position:0% +in time order it + + + align:start position:0% +in time order it +X + + align:start position:0% +X + + + align:start position:0% +X +expression isi + + align:start position:0% + + + + align:start position:0% + +zero + + align:start position:0% +zero + + + align:start position:0% +zero +now this is in free series I put a + + align:start position:0% +now this is in free series I put a + + + align:start position:0% +now this is in free series I put a +subscript zero here means in pre-series + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +so in writing from here to here so so + + align:start position:0% +so in writing from here to here so so + + + align:start position:0% +so in writing from here to here so so +upstairs we we interpret it as a a a + + align:start position:0% +upstairs we we interpret it as a a a + + + align:start position:0% +upstairs we we interpret it as a a a +correlation function in the free Theory + + align:start position:0% +correlation function in the free Theory + + + align:start position:0% +correlation function in the free Theory +so here we should also divide + + align:start position:0% +so here we should also divide + + + align:start position:0% +so here we should also divide +by uh uh in order to write in terms of + + align:start position:0% +by uh uh in order to write in terms of + + + align:start position:0% +by uh uh in order to write in terms of +the expectation value in the three yeah + + align:start position:0% +the expectation value in the three yeah + + + align:start position:0% +the expectation value in the three yeah +so zero here is the free series vacuum + + align:start position:0% + + + + align:start position:0% + +so in writing the upstairs in the in + + align:start position:0% +so in writing the upstairs in the in + + + align:start position:0% +so in writing the upstairs in the in +this form we should divide this by a + + align:start position:0% +this form we should divide this by a + + + align:start position:0% +this form we should divide this by a +path integral just with exponential is + + align:start position:0% +path integral just with exponential is + + + align:start position:0% +path integral just with exponential is +zero but since upstairs and downstairs + + align:start position:0% +zero but since upstairs and downstairs + + + align:start position:0% +zero but since upstairs and downstairs +we need to divide by the same path + + align:start position:0% +we need to divide by the same path + + + align:start position:0% +we need to divide by the same path +integral they just cancel okay so I can + + align:start position:0% +integral they just cancel okay so I can + + + align:start position:0% +integral they just cancel okay so I can +just directly write down as the ratio of + + align:start position:0% +just directly write down as the ratio of + + + align:start position:0% +just directly write down as the ratio of +these two correlation functions + + align:start position:0% +these two correlation functions + + + align:start position:0% +these two correlation functions +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +so now + + align:start position:0% +so now + + + align:start position:0% +so now +this is a very nice form + + align:start position:0% +this is a very nice form + + + align:start position:0% +this is a very nice form +okay + + align:start position:0% +okay + + + align:start position:0% +okay +because the um so so this is a yeah let + + align:start position:0% +because the um so so this is a yeah let + + + align:start position:0% +because the um so so this is a yeah let +me call this equation star + + align:start position:0% +me call this equation star + + + align:start position:0% +me call this equation star +so this is the star is exact expression + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +which + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +correlation function + + align:start position:0% + + + + align:start position:0% + +of an interacting Theory + + align:start position:0% + + + + align:start position:0% + +in terms of + + align:start position:0% + + + + align:start position:0% + +notes of freeze here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now now these are just some + + align:start position:0% +so now now these are just some + + + align:start position:0% +so now now these are just some +correlation functions in the free Theory + + align:start position:0% +correlation functions in the free Theory + + + align:start position:0% +correlation functions in the free Theory +so both upstairs and downstairs they can + + align:start position:0% +so both upstairs and downstairs they can + + + align:start position:0% +so both upstairs and downstairs they can +in principle evaluate it as we discussed + + align:start position:0% +in principle evaluate it as we discussed + + + align:start position:0% +in principle evaluate it as we discussed +before in free series yes + + align:start position:0% + + + + align:start position:0% + +right right as we discussed before + + align:start position:0% +right right as we discussed before + + + align:start position:0% +right right as we discussed before +whenever you see time order the + + align:start position:0% +whenever you see time order the + + + align:start position:0% +whenever you see time order the +exponential you should always + + align:start position:0% +exponential you should always + + + align:start position:0% +exponential you should always +expand the exponential in power series + + align:start position:0% +expand the exponential in power series + + + align:start position:0% +expand the exponential in power series +and then and then you just yeah you just + + align:start position:0% +and then and then you just yeah you just + + + align:start position:0% +and then and then you just yeah you just +have a bunch of + + align:start position:0% +have a bunch of + + + align:start position:0% +have a bunch of +factors and you just time order them + + align:start position:0% + + + + align:start position:0% + +other questions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so uh yeah + + align:start position:0% +so uh yeah + + + align:start position:0% +so uh yeah +and this is precisely the expression + + align:start position:0% +and this is precisely the expression + + + align:start position:0% +and this is precisely the expression +Which derived the impact scheme okay so + + align:start position:0% +Which derived the impact scheme okay so + + + align:start position:0% +Which derived the impact scheme okay so +this is the so so this equation is the + + align:start position:0% +this is the so so this equation is the + + + align:start position:0% +this is the so so this equation is the +4.31 + + align:start position:0% +4.31 + + + align:start position:0% +4.31 +of + + align:start position:0% +of + + + align:start position:0% +of +asking shorter + + align:start position:0% + + + + align:start position:0% + +which they derived using the uh in + + align:start position:0% +which they derived using the uh in + + + align:start position:0% +which they derived using the uh in +action picture okay + + align:start position:0% +action picture okay + + + align:start position:0% +action picture okay +so so we see that for the past integral + + align:start position:0% +so so we see that for the past integral + + + align:start position:0% +so so we see that for the past integral +to derive this equation using part + + align:start position:0% +to derive this equation using part + + + align:start position:0% +to derive this equation using part +integral is just trivial okay + + align:start position:0% +integral is just trivial okay + + + align:start position:0% +integral is just trivial okay +essentially you just split + + align:start position:0% +essentially you just split + + + align:start position:0% +essentially you just split +the exponential for the for the full + + align:start position:0% +the exponential for the for the full + + + align:start position:0% +the exponential for the for the full +series into that of the free Theory and + + align:start position:0% +series into that of the free Theory and + + + align:start position:0% +series into that of the free Theory and +the interacting part and then + + align:start position:0% +the interacting part and then + + + align:start position:0% +the interacting part and then +automatically derive this equation okay + + align:start position:0% +automatically derive this equation okay + + + align:start position:0% +automatically derive this equation okay +so once you uh once you have understood + + align:start position:0% +so once you uh once you have understood + + + align:start position:0% +so once you uh once you have understood +how past integral works and then uh + + align:start position:0% +how past integral works and then uh + + + align:start position:0% +how past integral works and then uh +derive this equation become two + + align:start position:0% +derive this equation become two + + + align:start position:0% +derive this equation become two +and so this uh and this is actually + + align:start position:0% +and so this uh and this is actually + + + align:start position:0% +and so this uh and this is actually +General uh I'll be later the same + + align:start position:0% +General uh I'll be later the same + + + align:start position:0% +General uh I'll be later the same +expression we will be able to apply it + + align:start position:0% +expression we will be able to apply it + + + align:start position:0% +expression we will be able to apply it +for say when we include fermions and + + align:start position:0% +for say when we include fermions and + + + align:start position:0% +for say when we include fermions and +also photons Etc okay + + align:start position:0% + + + + align:start position:0% + +and now + + align:start position:0% +and now + + + align:start position:0% +and now +we will evaluate this this guy's Union + + align:start position:0% +we will evaluate this this guy's Union + + + align:start position:0% +we will evaluate this this guy's Union +perturbation Theory okay so we will + + align:start position:0% +perturbation Theory okay so we will + + + align:start position:0% +perturbation Theory okay so we will +expand + + align:start position:0% + + + + align:start position:0% + +star + + align:start position:0% +star + + + align:start position:0% +star +in power series + + align:start position:0% + + + + align:start position:0% + +of s i okay we choose SS + + align:start position:0% +of s i okay we choose SS + + + align:start position:0% +of s i okay we choose SS +a small + + align:start position:0% +a small + + + align:start position:0% +a small +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +um yeah just expanded in power series + + align:start position:0% +um yeah just expanded in power series + + + align:start position:0% +um yeah just expanded in power series +so go explicitly + + align:start position:0% + + + + align:start position:0% + +say we consider yeah + + align:start position:0% +say we consider yeah + + + align:start position:0% +say we consider yeah +GN + + align:start position:0% +GN + + + align:start position:0% +GN +so so this GM for the full series so let + + align:start position:0% +so so this GM for the full series so let + + + align:start position:0% +so so this GM for the full series so let +me call this TN just say + + align:start position:0% +me call this TN just say + + + align:start position:0% +me call this TN just say +we see some endpoint function + + align:start position:0% +we see some endpoint function + + + align:start position:0% +we see some endpoint function +okay so this is the end + + align:start position:0% +okay so this is the end + + + align:start position:0% +okay so this is the end +and then we can just explain we can just + + align:start position:0% +and then we can just explain we can just + + + align:start position:0% +and then we can just explain we can just +write GN that's so I have the zeros + + align:start position:0% +write GN that's so I have the zeros + + + align:start position:0% +write GN that's so I have the zeros +order + + align:start position:0% +order + + + align:start position:0% +order +you just have TX + + align:start position:0% + + + + align:start position:0% + +zero okay upstairs + + align:start position:0% +zero okay upstairs + + + align:start position:0% +zero okay upstairs +and uh and the next order would be I DT + + align:start position:0% +and uh and the next order would be I DT + + + align:start position:0% +and uh and the next order would be I DT +say 0 t + + align:start position:0% +say 0 t + + + align:start position:0% +say 0 t +x h i + + align:start position:0% +x h i + + + align:start position:0% +x h i +so I have expanded to the first order + + align:start position:0% +so I have expanded to the first order + + + align:start position:0% +so I have expanded to the first order +in in si the when I expand the s i then + + align:start position:0% +in in si the when I expand the s i then + + + align:start position:0% +in in si the when I expand the s i then +become DT times h i with the minus sign + + align:start position:0% +become DT times h i with the minus sign + + + align:start position:0% +become DT times h i with the minus sign +so so I just write it in terms like that + + align:start position:0% +so so I just write it in terms like that + + + align:start position:0% +so so I just write it in terms like that +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and uh and so so remember here you need + + align:start position:0% +and uh and so so remember here you need + + + align:start position:0% +and uh and so so remember here you need +to time all the them together because + + align:start position:0% +to time all the them together because + + + align:start position:0% +to time all the them together because +both of them are in the same integrand + + align:start position:0% +both of them are in the same integrand + + + align:start position:0% +both of them are in the same integrand +okay so we need to time all of them + + align:start position:0% +okay so we need to time all of them + + + align:start position:0% +okay so we need to time all of them +together + + align:start position:0% +together + + + align:start position:0% +together +and Etc + + align:start position:0% +and Etc + + + align:start position:0% +and Etc +okay so this is upstairs and downstairs + + align:start position:0% +okay so this is upstairs and downstairs + + + align:start position:0% +okay so this is upstairs and downstairs +you just explained this guy so + + align:start position:0% +you just explained this guy so + + + align:start position:0% +you just explained this guy so +essentially you have one minus I DT + + align:start position:0% +essentially you have one minus I DT + + + align:start position:0% +essentially you have one minus I DT +then in time order + + align:start position:0% +then in time order + + + align:start position:0% +then in time order +the hamiltonian + + align:start position:0% +the hamiltonian + + + align:start position:0% +the hamiltonian +inheriting part of the hamiltonian and + + align:start position:0% +inheriting part of the hamiltonian and + + + align:start position:0% +inheriting part of the hamiltonian and +then + + align:start position:0% +then + + + align:start position:0% +then +plus higher order + + align:start position:0% +plus higher order + + + align:start position:0% +plus higher order +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so you just now + + align:start position:0% +so so you just now + + + align:start position:0% +so so you just now +essentially do the Taylor series + + align:start position:0% +essentially do the Taylor series + + + align:start position:0% +essentially do the Taylor series +expansion + + align:start position:0% +expansion + + + align:start position:0% +expansion +and the uh + + align:start position:0% +and the uh + + + align:start position:0% +and the uh +um yeah + + align:start position:0% +um yeah + + + align:start position:0% +um yeah +and the first + + align:start position:0% +and the first + + + align:start position:0% +and the first +so so you always assume the interacting + + align:start position:0% +so so you always assume the interacting + + + align:start position:0% +so so you always assume the interacting +part is smooth so you can actually + + align:start position:0% +part is smooth so you can actually + + + align:start position:0% +part is smooth so you can actually +tightly expand the downstairs also + + align:start position:0% +tightly expand the downstairs also + + + align:start position:0% +tightly expand the downstairs also +so this will be reduced to say the first + + align:start position:0% +so this will be reduced to say the first + + + align:start position:0% +so this will be reduced to say the first +order so the zero solder just gives you + + align:start position:0% +order so the zero solder just gives you + + + align:start position:0% +order so the zero solder just gives you +the three Theory + + align:start position:0% +the three Theory + + + align:start position:0% +the three Theory +endpoint function okay so so I reload + + align:start position:0% +endpoint function okay so so I reload + + + align:start position:0% +endpoint function okay so so I reload +now with the subscript 0 means the free + + align:start position:0% +now with the subscript 0 means the free + + + align:start position:0% +now with the subscript 0 means the free +series correlation function + + align:start position:0% +series correlation function + + + align:start position:0% +series correlation function +okay and then + + align:start position:0% +okay and then + + + align:start position:0% +okay and then +um + + align:start position:0% +um + + + align:start position:0% +um +yeah and then you can add the rest Etc + + align:start position:0% +yeah and then you can add the rest Etc + + + align:start position:0% +yeah and then you can add the rest Etc +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so so the so the higher order the + + align:start position:0% +okay so so the so the higher order the + + + align:start position:0% +okay so so the so the higher order the +perturbations okay + + align:start position:0% +perturbations okay + + + align:start position:0% +perturbations okay +good + + align:start position:0% +good + + + align:start position:0% +good +any questions on this + + align:start position:0% + + + + align:start position:0% + +yeah actually for later purpose let me + + align:start position:0% +yeah actually for later purpose let me + + + align:start position:0% +yeah actually for later purpose let me +just write write one more term just + + align:start position:0% +just write write one more term just + + + align:start position:0% +just write write one more term just +explicitly let me just write it + + align:start position:0% +explicitly let me just write it + + + align:start position:0% +explicitly let me just write it +so so I bring this up + + align:start position:0% +so so I bring this up + + + align:start position:0% +so so I bring this up +so I when I bring this up and then this + + align:start position:0% +so I when I bring this up and then this + + + align:start position:0% +so I when I bring this up and then this +become I + + align:start position:0% +become I + + + align:start position:0% +become I +or zero + + align:start position:0% +or zero + + + align:start position:0% +or zero +TX + + align:start position:0% +TX + + + align:start position:0% +TX +zero + + align:start position:0% +zero + + + align:start position:0% +zero +then times DT + + align:start position:0% +then times DT + + + align:start position:0% +then times DT +zero + + align:start position:0% +zero + + + align:start position:0% +zero +t h i + + align:start position:0% + + + + align:start position:0% + +also so this is this term + + align:start position:0% +also so this is this term + + + align:start position:0% +also so this is this term +we bring up and then multiply that term + + align:start position:0% +we bring up and then multiply that term + + + align:start position:0% +we bring up and then multiply that term +that give you that and then there's + + align:start position:0% +that give you that and then there's + + + align:start position:0% +that give you that and then there's +another first order term + + align:start position:0% +another first order term + + + align:start position:0% +another first order term +is given by I + + align:start position:0% +is given by I + + + align:start position:0% +is given by I +DT + + align:start position:0% +DT + + + align:start position:0% +DT +zero + + align:start position:0% +zero + + + align:start position:0% +zero +t x h i + + align:start position:0% + + + + align:start position:0% + +zero + + align:start position:0% +zero + + + align:start position:0% +zero +and then + + align:start position:0% +and then + + + align:start position:0% +and then +so so these are the four first order + + align:start position:0% +so so these are the four first order + + + align:start position:0% +so so these are the four first order +terms okay so these are the full first + + align:start position:0% +terms okay so these are the full first + + + align:start position:0% +terms okay so these are the full first +order terms which is the correction to + + align:start position:0% +order terms which is the correction to + + + align:start position:0% +order terms which is the correction to +the free Theory + + align:start position:0% +the free Theory + + + align:start position:0% +the free Theory +endpoint functions and the uh ability to + + align:start position:0% +endpoint functions and the uh ability to + + + align:start position:0% +endpoint functions and the uh ability to +evaluate those quantities and all those + + align:start position:0% +evaluate those quantities and all those + + + align:start position:0% +evaluate those quantities and all those +quantities can be just evaluated using + + align:start position:0% +quantities can be just evaluated using + + + align:start position:0% +quantities can be just evaluated using +the weak theorem because we know how to + + align:start position:0% +the weak theorem because we know how to + + + align:start position:0% +the weak theorem because we know how to +because all correlation functions in + + align:start position:0% +because all correlation functions in + + + align:start position:0% +because all correlation functions in +free Theory just can be evaluated using + + align:start position:0% +free Theory just can be evaluated using + + + align:start position:0% +free Theory just can be evaluated using +big theorem just use the big theorem + + align:start position:0% +big theorem just use the big theorem + + + align:start position:0% +big theorem just use the big theorem +over and over + + align:start position:0% +over and over + + + align:start position:0% +over and over +okay + + align:start position:0% + + + + align:start position:0% + +so any questions on this + + align:start position:0% + + + + align:start position:0% + +so so now we will develop techniques to + + align:start position:0% +so so now we will develop techniques to + + + align:start position:0% +so so now we will develop techniques to +evaluate such kind of series okay + + align:start position:0% +evaluate such kind of series okay + + + align:start position:0% +evaluate such kind of series okay +still even though this is not too + + align:start position:0% +still even though this is not too + + + align:start position:0% +still even though this is not too +difficult to do now + + align:start position:0% +difficult to do now + + + align:start position:0% +difficult to do now +but still when you do it in practice + + align:start position:0% +but still when you do it in practice + + + align:start position:0% +but still when you do it in practice +it's pretty tedious + + align:start position:0% +it's pretty tedious + + + align:start position:0% +it's pretty tedious +so still worth making effort to actually + + align:start position:0% +so still worth making effort to actually + + + align:start position:0% +so still worth making effort to actually +simplify the process okay simplify the + + align:start position:0% +simplify the process okay simplify the + + + align:start position:0% +simplify the process okay simplify the +process + + align:start position:0% +process + + + align:start position:0% +process +and the and the technique to simplify is + + align:start position:0% +and the and the technique to simplify is + + + align:start position:0% +and the and the technique to simplify is +called environment diagrams + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now + + align:start position:0% +so now + + + align:start position:0% +so now +um so now we will consider + + align:start position:0% +um so now we will consider + + + align:start position:0% +um so now we will consider +so far those equations apply for any uh + + align:start position:0% +so far those equations apply for any uh + + + align:start position:0% +so far those equations apply for any uh +any series any kind of interaction okay + + align:start position:0% +any series any kind of interaction okay + + + align:start position:0% +any series any kind of interaction okay +so now let's work on for specific case + + align:start position:0% +so now let's work on for specific case + + + align:start position:0% +so now let's work on for specific case +so let's consider aoi + + align:start position:0% +so let's consider aoi + + + align:start position:0% +so let's consider aoi +equal to minus Lambda divided by 4 + + align:start position:0% +equal to minus Lambda divided by 4 + + + align:start position:0% +equal to minus Lambda divided by 4 +factorial + + align:start position:0% +factorial + + + align:start position:0% +factorial +5 to the power four okay + + align:start position:0% +5 to the power four okay + + + align:start position:0% +5 to the power four okay +so it means that h i + + align:start position:0% +so it means that h i + + + align:start position:0% +so it means that h i +would be you integrated over + + align:start position:0% +would be you integrated over + + + align:start position:0% +would be you integrated over +so h i + + align:start position:0% +so h i + + + align:start position:0% +so h i +yeah so + + align:start position:0% +yeah so + + + align:start position:0% +yeah so +yeah anyway uh yeah the others you can + + align:start position:0% +yeah anyway uh yeah the others you can + + + align:start position:0% +yeah anyway uh yeah the others you can +just directly right from here okay + + align:start position:0% +just directly right from here okay + + + align:start position:0% +just directly right from here okay +so let's consider this case okay + + align:start position:0% + + + + align:start position:0% + +and so + + align:start position:0% +and so + + + align:start position:0% +and so +um + + align:start position:0% +um + + + align:start position:0% +um +specific and now also let's consider + + align:start position:0% +specific and now also let's consider + + + align:start position:0% +specific and now also let's consider +just uh in the simplest + + align:start position:0% +just uh in the simplest + + + align:start position:0% +just uh in the simplest +correlation function let's just can see + + align:start position:0% +correlation function let's just can see + + + align:start position:0% +correlation function let's just can see +the two point function + + align:start position:0% +the two point function + + + align:start position:0% +the two point function +okay let's just consider two point + + align:start position:0% +okay let's just consider two point + + + align:start position:0% +okay let's just consider two point +function + + align:start position:0% +function + + + align:start position:0% +function +G2 + + align:start position:0% +G2 + + + align:start position:0% +G2 +so two point pong is also the fireman + + align:start position:0% +so two point pong is also the fireman + + + align:start position:0% +so two point pong is also the fireman +function but now this is the final + + align:start position:0% +function but now this is the final + + + align:start position:0% +function but now this is the final +function in the interacting Theory okay + + align:start position:0% +function in the interacting Theory okay + + + align:start position:0% +function in the interacting Theory okay +and so so now this is in the uh + + align:start position:0% +and so so now this is in the uh + + + align:start position:0% +and so so now this is in the uh +so so now we have two + + align:start position:0% +so so now we have two + + + align:start position:0% +so so now we have two +so imagine we have two coordinates and + + align:start position:0% +so imagine we have two coordinates and + + + align:start position:0% +so imagine we have two coordinates and +then + + align:start position:0% +then + + + align:start position:0% +then +is equal to now so let's consider this + + align:start position:0% +is equal to now so let's consider this + + + align:start position:0% +is equal to now so let's consider this +okay + + align:start position:0% + + + + align:start position:0% + +so now let's consider the family + + align:start position:0% +so now let's consider the family + + + align:start position:0% +so now let's consider the family +function + + align:start position:0% +function + + + align:start position:0% +function +at the uh in the full series okay + + align:start position:0% + + + + align:start position:0% + +and now we can just uh now apply this + + align:start position:0% +and now we can just uh now apply this + + + align:start position:0% +and now we can just uh now apply this +equation so let's try to let us try to + + align:start position:0% +equation so let's try to let us try to + + + align:start position:0% +equation so let's try to let us try to +calculate to the last order + + align:start position:0% +calculate to the last order + + + align:start position:0% +calculate to the last order +so the zeros order + + align:start position:0% + + + + align:start position:0% + +is given by the free Theory + + align:start position:0% +is given by the free Theory + + + align:start position:0% +is given by the free Theory +two point function + + align:start position:0% +two point function + + + align:start position:0% +two point function +so by translation symmetry it's always a + + align:start position:0% +so by translation symmetry it's always a + + + align:start position:0% +so by translation symmetry it's always a +function of X Y minus X2 okay so + + align:start position:0% +function of X Y minus X2 okay so + + + align:start position:0% +function of X Y minus X2 okay so +this does not depend on whether it's in + + align:start position:0% +this does not depend on whether it's in + + + align:start position:0% +this does not depend on whether it's in +the free series or intact in theory + + align:start position:0% +the free series or intact in theory + + + align:start position:0% +the free series or intact in theory +and now now let's just plug in here + + align:start position:0% +and now now let's just plug in here + + + align:start position:0% +and now now let's just plug in here +okay and it's just plugging here + + align:start position:0% +okay and it's just plugging here + + + align:start position:0% +okay and it's just plugging here +so so h i + + align:start position:0% + + + + align:start position:0% + +is integration of this over uh uh uh a + + align:start position:0% +is integration of this over uh uh uh a + + + align:start position:0% +is integration of this over uh uh uh a +three-dimensional a spatial and then + + align:start position:0% +three-dimensional a spatial and then + + + align:start position:0% +three-dimensional a spatial and then +combine this becomes just four + + align:start position:0% +combine this becomes just four + + + align:start position:0% +combine this becomes just four +dimensional space time integrals okay so + + align:start position:0% +dimensional space time integrals okay so + + + align:start position:0% +dimensional space time integrals okay so +so then you just get the + + align:start position:0% +so then you just get the + + + align:start position:0% +so then you just get the +um + + align:start position:0% +um + + + align:start position:0% +um +so this term becomes + + align:start position:0% +so this term becomes + + + align:start position:0% +so this term becomes +plus I Lambda divided by 4 factorial + + align:start position:0% +plus I Lambda divided by 4 factorial + + + align:start position:0% +plus I Lambda divided by 4 factorial +so we will assume this Lambda small okay + + align:start position:0% +so we will assume this Lambda small okay + + + align:start position:0% +so we will assume this Lambda small okay +so that we can expand this Lambda + + align:start position:0% + + + + align:start position:0% + +so and this term just again is the free + + align:start position:0% +so and this term just again is the free + + + align:start position:0% +so and this term just again is the free +Theory correlation function + + align:start position:0% +Theory correlation function + + + align:start position:0% +Theory correlation function +so we just have GF + + align:start position:0% +so we just have GF + + + align:start position:0% +so we just have GF +okay and zero x one minus X2 + + align:start position:0% +okay and zero x one minus X2 + + + align:start position:0% +okay and zero x one minus X2 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then times + + align:start position:0% + + + + align:start position:0% + +okay my board is a little bit so so we + + align:start position:0% +okay my board is a little bit so so we + + + align:start position:0% +okay my board is a little bit so so we +have to go to here + + align:start position:0% +have to go to here + + + align:start position:0% +have to go to here +times then you have d4x + + align:start position:0% +times then you have d4x + + + align:start position:0% +times then you have d4x +then + + align:start position:0% +then + + + align:start position:0% +then +0 t and five to the power 4 x + + align:start position:0% +0 t and five to the power 4 x + + + align:start position:0% +0 t and five to the power 4 x +here okay so so this is multiplied + + align:start position:0% +here okay so so this is multiplied + + + align:start position:0% +here okay so so this is multiplied +reset okay so that's the second term + + align:start position:0% +reset okay so that's the second term + + + align:start position:0% +reset okay so that's the second term +and the third term + + align:start position:0% +and the third term + + + align:start position:0% +and the third term +is minus I + + align:start position:0% +is minus I + + + align:start position:0% +is minus I +Lambda to the four factorial + + align:start position:0% + + + + align:start position:0% + +we have g4x + + align:start position:0% + + + + align:start position:0% + +you have zero t + + align:start position:0% +you have zero t + + + align:start position:0% +you have zero t +then you have to combine them together + + align:start position:0% +then you have to combine them together + + + align:start position:0% +then you have to combine them together +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this is 5x1 + + align:start position:0% +so this is 5x1 + + + align:start position:0% +so this is 5x1 +Phi X2 + + align:start position:0% +Phi X2 + + + align:start position:0% +Phi X2 +and 5 to the power 4 x and this x is + + align:start position:0% +and 5 to the power 4 x and this x is + + + align:start position:0% +and 5 to the power 4 x and this x is +integrated over okay + + align:start position:0% +integrated over okay + + + align:start position:0% +integrated over okay +and then zero + + align:start position:0% +and then zero + + + align:start position:0% +and then zero +okay and uh so so this is all time + + align:start position:0% +okay and uh so so this is all time + + + align:start position:0% +okay and uh so so this is all time +ordered and then the rest is all the + + align:start position:0% +ordered and then the rest is all the + + + align:start position:0% +ordered and then the rest is all the +time Lambda squared + + align:start position:0% +time Lambda squared + + + align:start position:0% +time Lambda squared +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +okay + + align:start position:0% + + + + align:start position:0% + +good any questions on this + + align:start position:0% + + + + align:start position:0% + +so yeah so let me just make a quick + + align:start position:0% +so yeah so let me just make a quick + + + align:start position:0% +so yeah so let me just make a quick +remark + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +so in the end + + align:start position:0% +so in the end + + + align:start position:0% +so in the end +so just note + + align:start position:0% + + + + align:start position:0% + +can be + + align:start position:0% +can be + + + align:start position:0% +can be +so uh + + align:start position:0% + + + + align:start position:0% + +yeah so + + align:start position:0% +yeah so + + + align:start position:0% +yeah so +so here even though we only write down + + align:start position:0% +so here even though we only write down + + + align:start position:0% +so here even though we only write down +the first order term but you can + + align:start position:0% +the first order term but you can + + + align:start position:0% +the first order term but you can +continue okay so so uh so all terms + + align:start position:0% + + + + align:start position:0% + +in the expansion + + align:start position:0% + + + + align:start position:0% + +can be + + align:start position:0% + + + + align:start position:0% + +evaluated + + align:start position:0% + + + + align:start position:0% + +by repeatedly apply + + align:start position:0% + + + + align:start position:0% + +the brick theorem + + align:start position:0% +the brick theorem + + + align:start position:0% +the brick theorem +so they're all yeah any such kind of + + align:start position:0% +so they're all yeah any such kind of + + + align:start position:0% +so they're all yeah any such kind of +functions they will factorized into two + + align:start position:0% +functions they will factorized into two + + + align:start position:0% +functions they will factorized into two +point functions + + align:start position:0% +point functions + + + align:start position:0% +point functions +and the two point functions essentially + + align:start position:0% +and the two point functions essentially + + + align:start position:0% +and the two point functions essentially +just given by + + align:start position:0% +just given by + + + align:start position:0% +just given by +gf0 okay this is the gf03 theory two + + align:start position:0% +gf0 okay this is the gf03 theory two + + + align:start position:0% +gf0 okay this is the gf03 theory two +point functions + + align:start position:0% +point functions + + + align:start position:0% +point functions +okay so the final result + + align:start position:0% + + + + align:start position:0% + +always have the form + + align:start position:0% + + + + align:start position:0% + +uh uh salary dot always have the form + + align:start position:0% +uh uh salary dot always have the form + + + align:start position:0% +uh uh salary dot always have the form +sum over + + align:start position:0% + + + + align:start position:0% + +products + + align:start position:0% + + + + align:start position:0% + +of GF zeros + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and the plus sum integration okay so sum + + align:start position:0% +and the plus sum integration okay so sum + + + align:start position:0% +and the plus sum integration okay so sum +of the + + align:start position:0% + + + + align:start position:0% + +transportable Integrations okay + + align:start position:0% +transportable Integrations okay + + + align:start position:0% +transportable Integrations okay +so the structure in general the + + align:start position:0% +so the structure in general the + + + align:start position:0% +so the structure in general the +structure is pretty simple they all just + + align:start position:0% +structure is pretty simple they all just + + + align:start position:0% +structure is pretty simple they all just +reduce to uh um the product of those two + + align:start position:0% +reduce to uh um the product of those two + + + align:start position:0% +reduce to uh um the product of those two +point functions okay + + align:start position:0% + + + + align:start position:0% + +so now let's just uh as an example let's + + align:start position:0% +so now let's just uh as an example let's + + + align:start position:0% +so now let's just uh as an example let's +just evaluate these two pieces okay uh + + align:start position:0% +just evaluate these two pieces okay uh + + + align:start position:0% +just evaluate these two pieces okay uh +evaluate these two pieces + + align:start position:0% +evaluate these two pieces + + + align:start position:0% +evaluate these two pieces +so let's continue + + align:start position:0% +so let's continue + + + align:start position:0% +so let's continue +so we find that g F X1 minus X2 + + align:start position:0% +so we find that g F X1 minus X2 + + + align:start position:0% +so we find that g F X1 minus X2 +yeah so GF is the same as G2 okay so so + + align:start position:0% +yeah so GF is the same as G2 okay so so + + + align:start position:0% +yeah so GF is the same as G2 okay so so +for two point function this is just the + + align:start position:0% +for two point function this is just the + + + align:start position:0% +for two point function this is just the +find my function for the interacting + + align:start position:0% +find my function for the interacting + + + align:start position:0% +find my function for the interacting +Theory + + align:start position:0% + + + + align:start position:0% + +so the leading term + + align:start position:0% +so the leading term + + + align:start position:0% +so the leading term +is just gf0 + + align:start position:0% +is just gf0 + + + align:start position:0% +is just gf0 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then now let's evaluate this term + + align:start position:0% +and then now let's evaluate this term + + + align:start position:0% +and then now let's evaluate this term +now the value is this + + align:start position:0% +now the value is this + + + align:start position:0% +now the value is this +so this is all Phi contracted on the + + align:start position:0% +so this is all Phi contracted on the + + + align:start position:0% +so this is all Phi contracted on the +same point + + align:start position:0% +same point + + + align:start position:0% +same point +okay so they are there are four files we + + align:start position:0% +okay so they are there are four files we + + + align:start position:0% +okay so they are there are four files we +can just contract them okay with the + + align:start position:0% +can just contract them okay with the + + + align:start position:0% +can just contract them okay with the +within themselves so we essentially get + + align:start position:0% +within themselves so we essentially get + + + align:start position:0% +within themselves so we essentially get +to the um + + align:start position:0% +to the um + + + align:start position:0% +to the um +so so you have GF + + align:start position:0% +so so you have GF + + + align:start position:0% +so so you have GF +and then the next term + + align:start position:0% +and then the next term + + + align:start position:0% +and then the next term +is I + + align:start position:0% + + + + align:start position:0% + +4 factorial + + align:start position:0% +4 factorial + + + align:start position:0% +4 factorial +I remember the four factorial and then + + align:start position:0% +I remember the four factorial and then + + + align:start position:0% +I remember the four factorial and then +you have gf0 + + align:start position:0% + + + + align:start position:0% + +so X12 so let me use X12 to denote the + + align:start position:0% +so X12 so let me use X12 to denote the + + + align:start position:0% +so X12 so let me use X12 to denote the +X1 minus X2 just to save a little bit + + align:start position:0% +X1 minus X2 just to save a little bit + + + align:start position:0% +X1 minus X2 just to save a little bit +effort + + align:start position:0% +effort + + + align:start position:0% +effort +and then we have this integration of the + + align:start position:0% +and then we have this integration of the + + + align:start position:0% +and then we have this integration of the +r 34x + + align:start position:0% +r 34x + + + align:start position:0% +r 34x +and then this evaluate this so this just + + align:start position:0% +and then this evaluate this so this just + + + align:start position:0% +and then this evaluate this so this just +reduced to two + + align:start position:0% +reduced to two + + + align:start position:0% +reduced to two +farming propagators + + align:start position:0% +farming propagators + + + align:start position:0% +farming propagators +but both of them have zero so + + align:start position:0% +but both of them have zero so + + + align:start position:0% +but both of them have zero so +essentially you just have + + align:start position:0% +essentially you just have + + + align:start position:0% +essentially you just have +GF + + align:start position:0% +GF + + + align:start position:0% +GF +zero zero is x minus X + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we just get that okay x minus X okay + + align:start position:0% +so we just get that okay x minus X okay + + + align:start position:0% +so we just get that okay x minus X okay +so let me just write one of them so that + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but we're actually missing fun factors + + align:start position:0% +but we're actually missing fun factors + + + align:start position:0% +but we're actually missing fun factors +because we have four files + + align:start position:0% +because we have four files + + + align:start position:0% +because we have four files +so when you contract the four files this + + align:start position:0% +so when you contract the four files this + + + align:start position:0% +so when you contract the four files this +there are three different ways to group + + align:start position:0% +there are three different ways to group + + + align:start position:0% +there are three different ways to group +them okay so so we should have a factor + + align:start position:0% +them okay so so we should have a factor + + + align:start position:0% +them okay so so we should have a factor +of three + + align:start position:0% + + + + align:start position:0% + +there's three different ways to group + + align:start position:0% +there's three different ways to group + + + align:start position:0% +there's three different ways to group +four five into two groups then we have a + + align:start position:0% +four five into two groups then we have a + + + align:start position:0% +four five into two groups then we have a +factor of three okay + + align:start position:0% + + + + align:start position:0% + +okay so now let's look at this term + + align:start position:0% +okay so now let's look at this term + + + align:start position:0% +okay so now let's look at this term +now let's look at this term + + align:start position:0% + + + + align:start position:0% + +so this term now I have now we have to + + align:start position:0% +so this term now I have now we have to + + + align:start position:0% +so this term now I have now we have to +contract six files okay so five x one + + align:start position:0% +contract six files okay so five x one + + + align:start position:0% +contract six files okay so five x one +five x two and then there are four fives + + align:start position:0% +five x two and then there are four fives + + + align:start position:0% +five x two and then there are four fives +here so we need to contract six files + + align:start position:0% +here so we need to contract six files + + + align:start position:0% +here so we need to contract six files +so we have we can have two possible + + align:start position:0% +so we have we can have two possible + + + align:start position:0% +so we have we can have two possible +patterns + + align:start position:0% +patterns + + + align:start position:0% +patterns +is that these two files contract with + + align:start position:0% +is that these two files contract with + + + align:start position:0% +is that these two files contract with +themselves + + align:start position:0% +themselves + + + align:start position:0% +themselves +okay these two files this five x y and + + align:start position:0% +okay these two files this five x y and + + + align:start position:0% +okay these two files this five x y and +the facts two contract with the same + + align:start position:0% +the facts two contract with the same + + + align:start position:0% +the facts two contract with the same +more sales and then four five then four + + align:start position:0% +more sales and then four five then four + + + align:start position:0% +more sales and then four five then four +five we have to contract with among + + align:start position:0% +five we have to contract with among + + + align:start position:0% +five we have to contract with among +themselves + + align:start position:0% +themselves + + + align:start position:0% +themselves +or five five x y in fact one contract + + align:start position:0% +or five five x y in fact one contract + + + align:start position:0% +or five five x y in fact one contract +with one of the five here then facts two + + align:start position:0% +with one of the five here then facts two + + + align:start position:0% +with one of the five here then facts two +also have to contract with one of the + + align:start position:0% +also have to contract with one of the + + + align:start position:0% +also have to contract with one of the +five here okay so you have two possible + + align:start position:0% +five here okay so you have two possible + + + align:start position:0% +five here okay so you have two possible +patterns for contraction okay so the + + align:start position:0% +patterns for contraction okay so the + + + align:start position:0% +patterns for contraction okay so the +first one is simple so let's just first + + align:start position:0% +first one is simple so let's just first + + + align:start position:0% +first one is simple so let's just first +contract five x one and the facts two + + align:start position:0% +contract five x one and the facts two + + + align:start position:0% +contract five x one and the facts two +so again so we have minus I + + align:start position:0% + + + + align:start position:0% + +minus I Lambda divided by four factorial + + align:start position:0% +minus I Lambda divided by four factorial + + + align:start position:0% +minus I Lambda divided by four factorial +so when we contract X1 and X2 + + align:start position:0% +so when we contract X1 and X2 + + + align:start position:0% +so when we contract X1 and X2 +then we just get GF + + align:start position:0% +then we just get GF + + + align:start position:0% +then we just get GF +0 x 1 2 + + align:start position:0% + + + + align:start position:0% + +and then we then we track a contract + + align:start position:0% +and then we then we track a contract + + + align:start position:0% +and then we then we track a contract +file form themselves that's what we did + + align:start position:0% +file form themselves that's what we did + + + align:start position:0% +file form themselves that's what we did +before it's the same thing as above so + + align:start position:0% +before it's the same thing as above so + + + align:start position:0% +before it's the same thing as above so +we just get a factor of three + + align:start position:0% +we just get a factor of three + + + align:start position:0% +we just get a factor of three +D four x + + align:start position:0% +D four x + + + align:start position:0% +D four x +and then G of f + + align:start position:0% +and then G of f + + + align:start position:0% +and then G of f +0 if we buy it at the zero squared okay + + align:start position:0% +0 if we buy it at the zero squared okay + + + align:start position:0% +0 if we buy it at the zero squared okay +just the same as it is okay + + align:start position:0% +just the same as it is okay + + + align:start position:0% +just the same as it is okay +but then then the other term Phi + + align:start position:0% +but then then the other term Phi + + + align:start position:0% +but then then the other term Phi +contracts with this so each of these uh + + align:start position:0% +contracts with this so each of these uh + + + align:start position:0% +contracts with this so each of these uh +X1 X2 contract with here okay so in this + + align:start position:0% +X1 X2 contract with here okay so in this + + + align:start position:0% +X1 X2 contract with here okay so in this +case + + align:start position:0% +case + + + align:start position:0% +case +so let's Imagine This + + align:start position:0% +so let's Imagine This + + + align:start position:0% +so let's Imagine This +contract with them then there are four + + align:start position:0% +contract with them then there are four + + + align:start position:0% +contract with them then there are four +possibilities + + align:start position:0% +possibilities + + + align:start position:0% +possibilities +so after this contract with one of them + + align:start position:0% +so after this contract with one of them + + + align:start position:0% +so after this contract with one of them +this contracts of that then I have three + + align:start position:0% +this contracts of that then I have three + + + align:start position:0% +this contracts of that then I have three +possibilities so you have four times + + align:start position:0% +possibilities so you have four times + + + align:start position:0% +possibilities so you have four times +three a combinatorical factors okay so + + align:start position:0% +three a combinatorical factors okay so + + + align:start position:0% +three a combinatorical factors okay so +you have I then the four factorial + + align:start position:0% +you have I then the four factorial + + + align:start position:0% +you have I then the four factorial +then you have four times three + + align:start position:0% +then you have four times three + + + align:start position:0% +then you have four times three +then you have d4x + + align:start position:0% + + + + align:start position:0% + +then we have here we have G four zero + + align:start position:0% +then we have here we have G four zero + + + align:start position:0% +then we have here we have G four zero +x minus X1 + + align:start position:0% +x minus X1 + + + align:start position:0% +x minus X1 +so X Y minus X it doesn't matter and GF + + align:start position:0% +so X Y minus X it doesn't matter and GF + + + align:start position:0% +so X Y minus X it doesn't matter and GF +0 x 2 minus X + + align:start position:0% +0 x 2 minus X + + + align:start position:0% +0 x 2 minus X +and then the last one just contract + + align:start position:0% +and then the last one just contract + + + align:start position:0% +and then the last one just contract +itself just again F 0 0 okay + + align:start position:0% + + + + align:start position:0% + +times + + align:start position:0% +times + + + align:start position:0% +times +and then and the other Lambda squared + + align:start position:0% +and then and the other Lambda squared + + + align:start position:0% +and then and the other Lambda squared +okay so so these are the explicit + + align:start position:0% +okay so so these are the explicit + + + align:start position:0% +okay so so these are the explicit +Expressions okay so so these are the + + align:start position:0% +Expressions okay so so these are the + + + align:start position:0% +Expressions okay so so these are the +experience expression + + align:start position:0% + + + + align:start position:0% + +so so now you can actually notice that + + align:start position:0% +so so now you can actually notice that + + + align:start position:0% +so so now you can actually notice that +these two terms actually are the same + + align:start position:0% +these two terms actually are the same + + + align:start position:0% +these two terms actually are the same +right + + align:start position:0% +right + + + align:start position:0% +right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so these two uh two terms actually are + + align:start position:0% +so these two uh two terms actually are + + + align:start position:0% +so these two uh two terms actually are +identical and they just differ by a sign + + align:start position:0% +identical and they just differ by a sign + + + align:start position:0% +identical and they just differ by a sign +so actually they cancel okay + + align:start position:0% +so actually they cancel okay + + + align:start position:0% +so actually they cancel okay +so this kind of so we just left with + + align:start position:0% +so this kind of so we just left with + + + align:start position:0% +so this kind of so we just left with +that and then this + + align:start position:0% +that and then this + + + align:start position:0% +that and then this +okay we just uh with this + + align:start position:0% +okay we just uh with this + + + align:start position:0% +okay we just uh with this +okay + + align:start position:0% + + + + align:start position:0% + +so so this procedure can actually + + align:start position:0% +so so this procedure can actually + + + align:start position:0% +so so this procedure can actually +be represented diagrammatically + + align:start position:0% +be represented diagrammatically + + + align:start position:0% +be represented diagrammatically +okay + + align:start position:0% +okay + + + align:start position:0% +okay +Representatives diagrammatically + + align:start position:0% +Representatives diagrammatically + + + align:start position:0% +Representatives diagrammatically +and I will just introduce a single line + + align:start position:0% + + + + align:start position:0% + +just introduce a single line + + align:start position:0% +just introduce a single line + + + align:start position:0% +just introduce a single line +for TF say X and Y + + align:start position:0% +for TF say X and Y + + + align:start position:0% +for TF say X and Y +for gf0 + + align:start position:0% + + + + align:start position:0% + +x minus y okay so so I will just + + align:start position:0% +x minus y okay so so I will just + + + align:start position:0% +x minus y okay so so I will just +represent the line like that okay + + align:start position:0% +represent the line like that okay + + + align:start position:0% +represent the line like that okay +so if I use that + + align:start position:0% +so if I use that + + + align:start position:0% +so if I use that +and then we can uh write them in the in + + align:start position:0% +and then we can uh write them in the in + + + align:start position:0% +and then we can uh write them in the in +the diagrammatic form then the first + + align:start position:0% +the diagrammatic form then the first + + + align:start position:0% +the diagrammatic form then the first +term is just + + align:start position:0% +term is just + + + align:start position:0% +term is just +X1 X2 okay + + align:start position:0% + + + + align:start position:0% + +and now the second term + + align:start position:0% +and now the second term + + + align:start position:0% +and now the second term +would be if 3 multiply 4 factorial so + + align:start position:0% +would be if 3 multiply 4 factorial so + + + align:start position:0% +would be if 3 multiply 4 factorial so +this is like I Lambda divided by eight + + align:start position:0% +this is like I Lambda divided by eight + + + align:start position:0% +this is like I Lambda divided by eight +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then you have X1 times x + + align:start position:0% +and then you have X1 times x + + + align:start position:0% +and then you have X1 times x +y x 2 + + align:start position:0% +y x 2 + + + align:start position:0% +y x 2 +then times this contracted with itself + + align:start position:0% +then times this contracted with itself + + + align:start position:0% +then times this contracted with itself +and so you have two propagated Y is + + align:start position:0% +and so you have two propagated Y is + + + align:start position:0% +and so you have two propagated Y is +contracted like that and one is + + align:start position:0% +contracted like that and one is + + + align:start position:0% +contracted like that and one is +contracted like that okay + + align:start position:0% +contracted like that okay + + + align:start position:0% +contracted like that okay +and this point is X + + align:start position:0% +and this point is X + + + align:start position:0% +and this point is X +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so you have a a you have a x but they + + align:start position:0% +so so you have a a you have a x but they + + + align:start position:0% +so so you have a a you have a x but they +all contract with itself so it's x minus + + align:start position:0% +all contract with itself so it's x minus + + + align:start position:0% +all contract with itself so it's x minus +X for this one and x minus X for that + + align:start position:0% +X for this one and x minus X for that + + + align:start position:0% +X for this one and x minus X for that +okay + + align:start position:0% + + + + align:start position:0% + +and similarly of course this is + + align:start position:0% +and similarly of course this is + + + align:start position:0% +and similarly of course this is +identical to that is I Lambda divided by + + align:start position:0% +identical to that is I Lambda divided by + + + align:start position:0% +identical to that is I Lambda divided by +eight + + align:start position:0% +eight + + + align:start position:0% +eight +so this is times + + align:start position:0% +so this is times + + + align:start position:0% +so this is times +so X1 X2 + + align:start position:0% + + + + align:start position:0% + +X okay + + align:start position:0% +X okay + + + align:start position:0% +X okay +and then the last one + + align:start position:0% +and then the last one + + + align:start position:0% +and then the last one +so this one corresponding to + + align:start position:0% +so this one corresponding to + + + align:start position:0% +so this one corresponding to +so now this is 12 divided by 24 this is + + align:start position:0% +so now this is 12 divided by 24 this is + + + align:start position:0% +so now this is 12 divided by 24 this is +minus I + + align:start position:0% +minus I + + + align:start position:0% +minus I +2 Lambda + + align:start position:0% +2 Lambda + + + align:start position:0% +2 Lambda +okay and I'm going to divide by 2 + + align:start position:0% +okay and I'm going to divide by 2 + + + align:start position:0% +okay and I'm going to divide by 2 +. so now so X Y is 2X x and X2 to X + + align:start position:0% +. so now so X Y is 2X x and X2 to X + + + align:start position:0% +. so now so X Y is 2X x and X2 to X +and then you have something like this + + align:start position:0% +and then you have something like this + + + align:start position:0% +and then you have something like this +X1 + + align:start position:0% +X1 + + + align:start position:0% +X1 +X2 + + align:start position:0% + + + + align:start position:0% + +okay so this here is X so if + + align:start position:0% +okay so this here is X so if + + + align:start position:0% +okay so this here is X so if +X1 x x 2 x and then x x between 0. + + align:start position:0% +X1 x x 2 x and then x x between 0. + + + align:start position:0% +X1 x x 2 x and then x x between 0. +okay and then then you have all the + + align:start position:0% +okay and then then you have all the + + + align:start position:0% +okay and then then you have all the +Lambda squared + + align:start position:0% +Lambda squared + + + align:start position:0% +Lambda squared +okay + + align:start position:0% + + + + align:start position:0% + +so so this again these two terms + + align:start position:0% +so so this again these two terms + + + align:start position:0% +so so this again these two terms +as we already said this two terms cancel + + align:start position:0% +as we already said this two terms cancel + + + align:start position:0% +as we already said this two terms cancel +and then you just get this tutor + + align:start position:0% +and then you just get this tutor + + + align:start position:0% +and then you just get this tutor +okay just get this tutor + + align:start position:0% + + + + align:start position:0% + +and we see that each + + align:start position:0% +and we see that each + + + align:start position:0% +and we see that each +factor of h i or each factor of s i you + + align:start position:0% +factor of h i or each factor of s i you + + + align:start position:0% +factor of h i or each factor of s i you +bring down okay so each fact of h i or + + align:start position:0% +bring down okay so each fact of h i or + + + align:start position:0% +bring down okay so each fact of h i or +each factor + + align:start position:0% +each factor + + + align:start position:0% +each factor +you've been done corresponding to an + + align:start position:0% +you've been done corresponding to an + + + align:start position:0% +you've been done corresponding to an +interacting vertex like this + + align:start position:0% +interacting vertex like this + + + align:start position:0% +interacting vertex like this +okay corresponding to interacting with + + align:start position:0% +okay corresponding to interacting with + + + align:start position:0% +okay corresponding to interacting with +act like this you have four legs or five + + align:start position:0% +act like this you have four legs or five + + + align:start position:0% +act like this you have four legs or five +okay and and so we call this interacting + + align:start position:0% +okay and and so we call this interacting + + + align:start position:0% +okay and and so we call this interacting +vertex okay + + align:start position:0% + + + + align:start position:0% + +okay so yeah + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so in practice + + align:start position:0% +so so in practice + + + align:start position:0% +so so in practice +so in practice it's actually much easier + + align:start position:0% +so in practice it's actually much easier + + + align:start position:0% +so in practice it's actually much easier +to just draw the diagram first + + align:start position:0% +to just draw the diagram first + + + align:start position:0% +to just draw the diagram first +and then from the diagram to write down + + align:start position:0% +and then from the diagram to write down + + + align:start position:0% +and then from the diagram to write down +the analytic expression + + align:start position:0% +the analytic expression + + + align:start position:0% +the analytic expression +because because the diagram is much more + + align:start position:0% +because because the diagram is much more + + + align:start position:0% +because because the diagram is much more +intuitive + + align:start position:0% +intuitive + + + align:start position:0% +intuitive +essentially What's Happening Here + + align:start position:0% +essentially What's Happening Here + + + align:start position:0% +essentially What's Happening Here +whatever terms here you just find the + + align:start position:0% +whatever terms here you just find the + + + align:start position:0% +whatever terms here you just find the +all possible way to contract them + + align:start position:0% +all possible way to contract them + + + align:start position:0% +all possible way to contract them +and diagrammatically you can we can just + + align:start position:0% +and diagrammatically you can we can just + + + align:start position:0% +and diagrammatically you can we can just +do it diagrammatically through all + + align:start position:0% +do it diagrammatically through all + + + align:start position:0% +do it diagrammatically through all +positive way to contract them that's + + align:start position:0% +positive way to contract them that's + + + align:start position:0% +positive way to contract them that's +much easier to do by doing a diagram + + align:start position:0% +much easier to do by doing a diagram + + + align:start position:0% +much easier to do by doing a diagram +than than by by doing the counting okay + + align:start position:0% +than than by by doing the counting okay + + + align:start position:0% +than than by by doing the counting okay +back to the content so so in practice + + align:start position:0% + + + + align:start position:0% + +much easier + + align:start position:0% + + + + align:start position:0% + +to draw the diagram first + + align:start position:0% + + + + align:start position:0% + +you just draw all possible diagrams okay + + align:start position:0% + + + + align:start position:0% + +and then from diagram + + align:start position:0% + + + + align:start position:0% + +right down + + align:start position:0% + + + + align:start position:0% + +the expressions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so so those diagrams I just call the + + align:start position:0% +so so those diagrams I just call the + + + align:start position:0% +so so those diagrams I just call the +Family diagrams + + align:start position:0% +Family diagrams + + + align:start position:0% +Family diagrams +okay so so we just do a portable + + align:start position:0% +okay so so we just do a portable + + + align:start position:0% +okay so so we just do a portable +diagrams and then from the diagrams we + + align:start position:0% +diagrams and then from the diagrams we + + + align:start position:0% +diagrams and then from the diagrams we +write down the expression that's called + + align:start position:0% +write down the expression that's called + + + align:start position:0% +write down the expression that's called +the five man rules okay I give you a + + align:start position:0% +the five man rules okay I give you a + + + align:start position:0% +the five man rules okay I give you a +diagram then there's a rule which you + + align:start position:0% +diagram then there's a rule which you + + + align:start position:0% +diagram then there's a rule which you +convert them into such kind of + + align:start position:0% +convert them into such kind of + + + align:start position:0% +convert them into such kind of +expression okay we can convert them into + + align:start position:0% +expression okay we can convert them into + + + align:start position:0% +expression okay we can convert them into +such an expression okay + + align:start position:0% +such an expression okay + + + align:start position:0% +such an expression okay +so so now let's give you an example okay + + align:start position:0% +so so now let's give you an example okay + + + align:start position:0% +so so now let's give you an example okay +so now let's give you example + + align:start position:0% +so now let's give you example + + + align:start position:0% +so now let's give you example +so now let's look at the example in the + + align:start position:0% +so now let's look at the example in the + + + align:start position:0% +so now let's look at the example in the +second order + + align:start position:0% +second order + + + align:start position:0% +second order +okay let's look at the example in the + + align:start position:0% +okay let's look at the example in the + + + align:start position:0% +okay let's look at the example in the +second order + + align:start position:0% + + + + align:start position:0% + +so let's consider + + align:start position:0% +so let's consider + + + align:start position:0% +so let's consider +yeah yes uh + + align:start position:0% + + + + align:start position:0% + +or the Lambda square example + + align:start position:0% + + + + align:start position:0% + +so at Lambda Square there there are many + + align:start position:0% +so at Lambda Square there there are many + + + align:start position:0% +so at Lambda Square there there are many +terms okay so so one of the term + + align:start position:0% +terms okay so so one of the term + + + align:start position:0% +terms okay so so one of the term +the one over the term is just to say you + + align:start position:0% +the one over the term is just to say you + + + align:start position:0% +the one over the term is just to say you +can now have h i squared here + + align:start position:0% +can now have h i squared here + + + align:start position:0% +can now have h i squared here +okay you also have downstairs Etc at the + + align:start position:0% +okay you also have downstairs Etc at the + + + align:start position:0% +okay you also have downstairs Etc at the +many times but but one of the term + + align:start position:0% +many times but but one of the term + + + align:start position:0% +many times but but one of the term +yeah so yeah right right yeah let me + + align:start position:0% +yeah so yeah right right yeah let me + + + align:start position:0% +yeah so yeah right right yeah let me +just say here so one of the term is just + + align:start position:0% +just say here so one of the term is just + + + align:start position:0% +just say here so one of the term is just +X and then you have h i Square here okay + + align:start position:0% +X and then you have h i Square here okay + + + align:start position:0% +X and then you have h i Square here okay +this is one over the term they also have + + align:start position:0% +this is one over the term they also have + + + align:start position:0% +this is one over the term they also have +other terms so let's now to look at just + + align:start position:0% +other terms so let's now to look at just + + + align:start position:0% +other terms so let's now to look at just +that okay + + align:start position:0% +that okay + + + align:start position:0% +that okay +a nice example + + align:start position:0% +a nice example + + + align:start position:0% +a nice example +so at the Lambda square example there's + + align:start position:0% +so at the Lambda square example there's + + + align:start position:0% +so at the Lambda square example there's +a term like this + + align:start position:0% + + + + align:start position:0% + +one factorial one factorial count when + + align:start position:0% +one factorial one factorial count when + + + align:start position:0% +one factorial one factorial count when +you expand this to the second order then + + align:start position:0% +you expand this to the second order then + + + align:start position:0% +you expand this to the second order then +this uh uh yeah uh uh uh one one half + + align:start position:0% +this uh uh yeah uh uh uh one one half + + + align:start position:0% +this uh uh yeah uh uh uh one one half +and then you have minus I Lambda 4 + + align:start position:0% +and then you have minus I Lambda 4 + + + align:start position:0% +and then you have minus I Lambda 4 +factorial Square because now this curve + + align:start position:0% +factorial Square because now this curve + + + align:start position:0% +factorial Square because now this curve +can also expand into second order + + align:start position:0% +can also expand into second order + + + align:start position:0% +can also expand into second order +and then you have d4x + + align:start position:0% +and then you have d4x + + + align:start position:0% +and then you have d4x +before y + + align:start position:0% + + + + align:start position:0% + +x one + + align:start position:0% +x one + + + align:start position:0% +x one +X2 + + align:start position:0% +X2 + + + align:start position:0% +X2 +by 4X + + align:start position:0% +by 4X + + + align:start position:0% +by 4X +54 y + + align:start position:0% +54 y + + + align:start position:0% +54 y +0 okay so now one of the term is like + + align:start position:0% +0 okay so now one of the term is like + + + align:start position:0% +0 okay so now one of the term is like +this + + align:start position:0% +this + + + align:start position:0% +this +okay + + align:start position:0% + + + + align:start position:0% + +so so later we don't even need to write + + align:start position:0% +so so later we don't even need to write + + + align:start position:0% +so so later we don't even need to write +down such a term we just immediately + + align:start position:0% +down such a term we just immediately + + + align:start position:0% +down such a term we just immediately +write down all the diagram okay just + + align:start position:0% +write down all the diagram okay just + + + align:start position:0% +write down all the diagram okay just +here uh uh to help you uh to uh to + + align:start position:0% +here uh uh to help you uh to uh to + + + align:start position:0% +here uh uh to help you uh to uh to +understand the process let's just say + + align:start position:0% +understand the process let's just say + + + align:start position:0% +understand the process let's just say +let's look at this particular term + + align:start position:0% +let's look at this particular term + + + align:start position:0% +let's look at this particular term +so now let's try to write down all + + align:start position:0% +so now let's try to write down all + + + align:start position:0% +so now let's try to write down all +possible contractions + + align:start position:0% +possible contractions + + + align:start position:0% +possible contractions +by just using diagrams okay just by + + align:start position:0% +by just using diagrams okay just by + + + align:start position:0% +by just using diagrams okay just by +using diagrams + + align:start position:0% +using diagrams + + + align:start position:0% +using diagrams +so now we have + + align:start position:0% +so now we have + + + align:start position:0% +so now we have +X1 X2 and and the four five four x and + + align:start position:0% +X1 X2 and and the four five four x and + + + align:start position:0% +X1 X2 and and the four five four x and +the four y's okay so essentially you + + align:start position:0% +the four y's okay so essentially you + + + align:start position:0% +the four y's okay so essentially you +have something like this you have X1 + + align:start position:0% + + + + align:start position:0% + +you have X2 so these are the two + + align:start position:0% +you have X2 so these are the two + + + align:start position:0% +you have X2 so these are the two +external points okay and then now you + + align:start position:0% +external points okay and then now you + + + align:start position:0% +external points okay and then now you +have four files + + align:start position:0% +have four files + + + align:start position:0% +have four files +coming from X and the four fives come + + align:start position:0% +coming from X and the four fives come + + + align:start position:0% +coming from X and the four fives come +from y + + align:start position:0% +from y + + + align:start position:0% +from y +okay so we need to connect find all + + align:start position:0% +okay so we need to connect find all + + + align:start position:0% +okay so we need to connect find all +possible ways to connect them + + align:start position:0% +possible ways to connect them + + + align:start position:0% +possible ways to connect them +okay we found all possible ways to + + align:start position:0% +okay we found all possible ways to + + + align:start position:0% +okay we found all possible ways to +connect okay so that's the uh uh uh uh + + align:start position:0% +connect okay so that's the uh uh uh uh + + + align:start position:0% +connect okay so that's the uh uh uh uh +uh that's the goal okay + + align:start position:0% +uh that's the goal okay + + + align:start position:0% +uh that's the goal okay +so uh yeah + + align:start position:0% +so uh yeah + + + align:start position:0% +so uh yeah +so so here are the all possible ways + + align:start position:0% + + + + align:start position:0% + +so here are the all possible ways + + align:start position:0% +so here are the all possible ways + + + align:start position:0% +so here are the all possible ways +so first + + align:start position:0% +so first + + + align:start position:0% +so first +yeah they're also there are actually + + align:start position:0% +yeah they're also there are actually + + + align:start position:0% +yeah they're also there are actually +five in equivalent way okay + + align:start position:0% +five in equivalent way okay + + + align:start position:0% +five in equivalent way okay +so so so so let me just write them down + + align:start position:0% +so so so so let me just write them down + + + align:start position:0% +so so so so let me just write them down +so the first one is you just connect one + + align:start position:0% +so the first one is you just connect one + + + align:start position:0% +so the first one is you just connect one +of them to X + + align:start position:0% +of them to X + + + align:start position:0% +of them to X +and one moves into X yeah one over the X + + align:start position:0% +and one moves into X yeah one over the X + + + align:start position:0% +and one moves into X yeah one over the X +yeah yeah yeah let me just throw them + + align:start position:0% +yeah yeah yeah let me just throw them + + + align:start position:0% +yeah yeah yeah let me just throw them +down okay + + align:start position:0% +down okay + + + align:start position:0% +down okay +so one of them is the following so you + + align:start position:0% +so one of them is the following so you + + + align:start position:0% +so one of them is the following so you +take one of the X + + align:start position:0% + + + + align:start position:0% + +so so there are five of them so let me + + align:start position:0% +so so there are five of them so let me + + + align:start position:0% +so so there are five of them so let me +write equal sign here + + align:start position:0% +write equal sign here + + + align:start position:0% +write equal sign here +so so each one of them let me give a + + align:start position:0% +so so each one of them let me give a + + + align:start position:0% +so so each one of them let me give a +label so for for later use + + align:start position:0% +label so for for later use + + + align:start position:0% +label so for for later use +so here you you can have say X1 and X2 + + align:start position:0% +so here you you can have say X1 and X2 + + + align:start position:0% +so here you you can have say X1 and X2 +then they can connect to + + align:start position:0% +then they can connect to + + + align:start position:0% +then they can connect to +to X + + align:start position:0% +to X + + + align:start position:0% +to X +and then X can connect to y + + align:start position:0% +and then X can connect to y + + + align:start position:0% +and then X can connect to y +okay so so this is one of them + + align:start position:0% +okay so so this is one of them + + + align:start position:0% +okay so so this is one of them +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and the second one possibility + + align:start position:0% +and the second one possibility + + + align:start position:0% +and the second one possibility +is you just uh X1 and connect to + + align:start position:0% +is you just uh X1 and connect to + + + align:start position:0% +is you just uh X1 and connect to +X + + align:start position:0% +X + + + align:start position:0% +X +and the X2 connect to y + + align:start position:0% +and the X2 connect to y + + + align:start position:0% +and the X2 connect to y +and now there are three another three uh + + align:start position:0% +and now there are three another three uh + + + align:start position:0% +and now there are three another three uh +uh uh between X and the Y we have to + + align:start position:0% +uh uh between X and the Y we have to + + + align:start position:0% +uh uh between X and the Y we have to +connect so we have something like that + + align:start position:0% +connect so we have something like that + + + align:start position:0% +connect so we have something like that +okay so this is the second + + align:start position:0% + + + + align:start position:0% + +so the Third + + align:start position:0% + + + + align:start position:0% + +and the Third Way + + align:start position:0% + + + + align:start position:0% + +is you connect X Y into X2 itself + + align:start position:0% + + + + align:start position:0% + +and then times + + align:start position:0% +and then times + + + align:start position:0% +and then times +and then you have to connect X and Y so + + align:start position:0% +and then you have to connect X and Y so + + + align:start position:0% +and then you have to connect X and Y so +there are four of them + + align:start position:0% +there are four of them + + + align:start position:0% +there are four of them +disconnect X and Y like this you can + + align:start position:0% +disconnect X and Y like this you can + + + align:start position:0% +disconnect X and Y like this you can +connect them at least + + align:start position:0% +connect them at least + + + align:start position:0% +connect them at least +and all + + align:start position:0% +and all + + + align:start position:0% +and all +you connect x y x 2 itself + + align:start position:0% +you connect x y x 2 itself + + + align:start position:0% +you connect x y x 2 itself +and then you can again have to connect + + align:start position:0% +and then you can again have to connect + + + align:start position:0% +and then you can again have to connect +with X and Y but you can connect then + + align:start position:0% +with X and Y but you can connect then + + + align:start position:0% +with X and Y but you can connect then +the Y not just between X and Y you can + + align:start position:0% +the Y not just between X and Y you can + + + align:start position:0% +the Y not just between X and Y you can +also have that + + align:start position:0% + + + + align:start position:0% + +so sum of X is contracted Y and sum of X + + align:start position:0% +so sum of X is contracted Y and sum of X + + + align:start position:0% +so sum of X is contracted Y and sum of X +is contract with itself okay + + align:start position:0% +is contract with itself okay + + + align:start position:0% +is contract with itself okay +and all you have the last possibility + + align:start position:0% +and all you have the last possibility + + + align:start position:0% +and all you have the last possibility +so you have X1 X2 + + align:start position:0% +so you have X1 X2 + + + align:start position:0% +so you have X1 X2 +but then the X just contract with the + + align:start position:0% +but then the X just contract with the + + + align:start position:0% +but then the X just contract with the +tail + + align:start position:0% +tail + + + align:start position:0% +tail +and the Y also contract with cell + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so any questions on this + + align:start position:0% +so any questions on this + + + align:start position:0% +so any questions on this +so these are essentially all possible + + align:start position:0% +so these are essentially all possible + + + align:start position:0% +so these are essentially all possible +contraptions + + align:start position:0% +contraptions + + + align:start position:0% +contraptions +you can have between them okay we just + + align:start position:0% +you can have between them okay we just + + + align:start position:0% +you can have between them okay we just +draw them diagrams + + align:start position:0% +draw them diagrams + + + align:start position:0% +draw them diagrams +but now we also have to + + align:start position:0% +but now we also have to + + + align:start position:0% +but now we also have to +calculate + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +so we also have to find the + + align:start position:0% +so we also have to find the + + + align:start position:0% +so we also have to find the +combinatorical factors between them + + align:start position:0% +combinatorical factors between them + + + align:start position:0% +combinatorical factors between them +okay we also have to find the communal + + align:start position:0% +okay we also have to find the communal + + + align:start position:0% +okay we also have to find the communal +rhetorical factors between them okay so + + align:start position:0% +rhetorical factors between them okay so + + + align:start position:0% +rhetorical factors between them okay so +now let's try to work out the + + align:start position:0% +now let's try to work out the + + + align:start position:0% +now let's try to work out the +combinatorical factors okay so so so let + + align:start position:0% +combinatorical factors okay so so so let + + + align:start position:0% +combinatorical factors okay so so so let +me just give you an example uh give you + + align:start position:0% +me just give you an example uh give you + + + align:start position:0% +me just give you an example uh give you +some examples and then the rest that we + + align:start position:0% +some examples and then the rest that we + + + align:start position:0% +some examples and then the rest that we +just write down the answer because uh it + + align:start position:0% +just write down the answer because uh it + + + align:start position:0% +just write down the answer because uh it +just takes too much time to do all the + + align:start position:0% +just takes too much time to do all the + + + align:start position:0% +just takes too much time to do all the +examples one by one okay + + align:start position:0% +examples one by one okay + + + align:start position:0% +examples one by one okay +so let's do this one as an example + + align:start position:0% +so let's do this one as an example + + + align:start position:0% +so let's do this one as an example +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so yeah let me just Erase here I made it + + align:start position:0% +so yeah let me just Erase here I made it + + + align:start position:0% +so yeah let me just Erase here I made it +space here + + align:start position:0% + + + + align:start position:0% + +so here actually there are two possible + + align:start position:0% +so here actually there are two possible + + + align:start position:0% +so here actually there are two possible +diagrams + + align:start position:0% +diagrams + + + align:start position:0% +diagrams +I can have X1 X2 connect to X I can also + + align:start position:0% +I can have X1 X2 connect to X I can also + + + align:start position:0% +I can have X1 X2 connect to X I can also +have X1 and X2 connected to Y okay and + + align:start position:0% +have X1 and X2 connected to Y okay and + + + align:start position:0% +have X1 and X2 connected to Y okay and +so this because X and the Y are + + align:start position:0% +so this because X and the Y are + + + align:start position:0% +so this because X and the Y are +symmetric so I only draw one of them + + align:start position:0% +symmetric so I only draw one of them + + + align:start position:0% +symmetric so I only draw one of them +okay so so that means there's a factor + + align:start position:0% +okay so so that means there's a factor + + + align:start position:0% +okay so so that means there's a factor +of two I can either connect to X or + + align:start position:0% +of two I can either connect to X or + + + align:start position:0% +of two I can either connect to X or +connect to Y so I have one half so let + + align:start position:0% +connect to Y so I have one half so let + + + align:start position:0% +connect to Y so I have one half so let +me close to copy this + + align:start position:0% +me close to copy this + + + align:start position:0% +me close to copy this +Lambda 4 factorial square and then I + + align:start position:0% +Lambda 4 factorial square and then I + + + align:start position:0% +Lambda 4 factorial square and then I +have a two Factor can either connect + + align:start position:0% +have a two Factor can either connect + + + align:start position:0% +have a two Factor can either connect +x y x 2 can either connect to X or + + align:start position:0% +x y x 2 can either connect to X or + + + align:start position:0% +x y x 2 can either connect to X or +connect to y + + align:start position:0% +connect to y + + + align:start position:0% +connect to y +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +so now so X1 have four possibilities to + + align:start position:0% +so now so X1 have four possibilities to + + + align:start position:0% +so now so X1 have four possibilities to +connect to X + + align:start position:0% +connect to X + + + align:start position:0% +connect to X +and the X2 have three plus b connect to + + align:start position:0% +and the X2 have three plus b connect to + + + align:start position:0% +and the X2 have three plus b connect to +X + + align:start position:0% +X + + + align:start position:0% +X +and then the remaining of Phi X then I + + align:start position:0% +and then the remaining of Phi X then I + + + align:start position:0% +and then the remaining of Phi X then I +have four points beta connected to y + + align:start position:0% +have four points beta connected to y + + + align:start position:0% +have four points beta connected to y +and the other remaining 5x have 4 is + + align:start position:0% +and the other remaining 5x have 4 is + + + align:start position:0% +and the other remaining 5x have 4 is +reports we connect to Y okay so + + align:start position:0% +reports we connect to Y okay so + + + align:start position:0% +reports we connect to Y okay so +essentially that's your + + align:start position:0% +essentially that's your + + + align:start position:0% +essentially that's your +pre-factors yeah combinatorical factors + + align:start position:0% +pre-factors yeah combinatorical factors + + + align:start position:0% +pre-factors yeah combinatorical factors +and uh so if you worked it out so let's + + align:start position:0% +and uh so if you worked it out so let's + + + align:start position:0% +and uh so if you worked it out so let's +give you + + align:start position:0% +give you + + + align:start position:0% +give you +minus Lambda Square + + align:start position:0% +minus Lambda Square + + + align:start position:0% +minus Lambda Square +around half Square okay + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +because the uh now you now you have two + + align:start position:0% +because the uh now you now you have two + + + align:start position:0% +because the uh now you now you have two +five remaining for q5x remaining + + align:start position:0% +five remaining for q5x remaining + + + align:start position:0% +five remaining for q5x remaining +so so 2 5 x when you have to connect + + align:start position:0% +so so 2 5 x when you have to connect + + + align:start position:0% +so so 2 5 x when you have to connect +with y + + align:start position:0% +with y + + + align:start position:0% +with y +so so the first five will have four + + align:start position:0% +so so the first five will have four + + + align:start position:0% +so so the first five will have four +possibility to connect y because there + + align:start position:0% +possibility to connect y because there + + + align:start position:0% +possibility to connect y because there +are four y's there so that's this factor + + align:start position:0% +are four y's there so that's this factor + + + align:start position:0% +are four y's there so that's this factor +four and then the other five acts have + + align:start position:0% +four and then the other five acts have + + + align:start position:0% +four and then the other five acts have +three possibilities connective Y and so + + align:start position:0% +three possibilities connective Y and so + + + align:start position:0% +three possibilities connective Y and so +that's factor of three and once you do + + align:start position:0% +that's factor of three and once you do + + + align:start position:0% +that's factor of three and once you do +that then there's y I just have to + + align:start position:0% +that then there's y I just have to + + + align:start position:0% +that then there's y I just have to +connect with yourself + + align:start position:0% +connect with yourself + + + align:start position:0% +connect with yourself +yes + + align:start position:0% + + + + align:start position:0% + +which one uh say it again + + align:start position:0% + + + + align:start position:0% + +x x y to X + + align:start position:0% + + + + align:start position:0% + +yeah X + + align:start position:0% +yeah X + + + align:start position:0% +yeah X +yeah + + align:start position:0% + + + + align:start position:0% + +and the y2x2 + + align:start position:0% +and the y2x2 + + + align:start position:0% +and the y2x2 +um + + align:start position:0% +um + + + align:start position:0% +um +yeah let me see + + align:start position:0% +yeah let me see + + + align:start position:0% +yeah let me see +um + + align:start position:0% +um + + + align:start position:0% +um +yes uh uh I should also have a diagram + + align:start position:0% +yes uh uh I should also have a diagram + + + align:start position:0% +yes uh uh I should also have a diagram +like this yeah it's possible I think I + + align:start position:0% +like this yeah it's possible I think I + + + align:start position:0% +like this yeah it's possible I think I +just forgot it + + align:start position:0% +just forgot it + + + align:start position:0% +just forgot it +uh let me see do I have something like + + align:start position:0% +uh let me see do I have something like + + + align:start position:0% +uh let me see do I have something like +this no actually yeah then I forgot it + + align:start position:0% +this no actually yeah then I forgot it + + + align:start position:0% +this no actually yeah then I forgot it +good good uh this diagram is here okay + + align:start position:0% +good good uh this diagram is here okay + + + align:start position:0% +good good uh this diagram is here okay +so so this is B Prime + + align:start position:0% +so so this is B Prime + + + align:start position:0% +so so this is B Prime +thank you thank you so so we can also + + align:start position:0% +thank you thank you so so we can also + + + align:start position:0% +thank you thank you so so we can also +have that okay so we can also yeah here + + align:start position:0% +have that okay so we can also yeah here + + + align:start position:0% +have that okay so we can also yeah here +is really for the illustration uh I + + align:start position:0% +is really for the illustration uh I + + + align:start position:0% +is really for the illustration uh I +don't actually I should claim at the + + align:start position:0% +don't actually I should claim at the + + + align:start position:0% +don't actually I should claim at the +beginning I didn't aim for complete this + + align:start position:0% +beginning I didn't aim for complete this + + + align:start position:0% +beginning I didn't aim for complete this +and just for for illustration because + + align:start position:0% +and just for for illustration because + + + align:start position:0% +and just for for illustration because +the uh if we try to be too complete then + + align:start position:0% +the uh if we try to be too complete then + + + align:start position:0% +the uh if we try to be too complete then +that may take too much time + + align:start position:0% +that may take too much time + + + align:start position:0% +that may take too much time +okay good good this is also possibility + + align:start position:0% +okay good good this is also possibility + + + align:start position:0% +okay good good this is also possibility +yeah yes a good job + + align:start position:0% + + + + align:start position:0% + +and the ah + + align:start position:0% +and the ah + + + align:start position:0% +and the ah +so so now let's look at this one + + align:start position:0% +so so now let's look at this one + + + align:start position:0% +so so now let's look at this one +okay so let's look at this one + + align:start position:0% +okay so let's look at this one + + + align:start position:0% +okay so let's look at this one +so so again let's copy this one half + + align:start position:0% +so so again let's copy this one half + + + align:start position:0% +so so again let's copy this one half +minus I divided by 4 factorial + + align:start position:0% +minus I divided by 4 factorial + + + align:start position:0% +minus I divided by 4 factorial +Square + + align:start position:0% +Square + + + align:start position:0% +Square +okay and then then the combinatorical + + align:start position:0% +okay and then then the combinatorical + + + align:start position:0% +okay and then then the combinatorical +factors + + align:start position:0% + + + + align:start position:0% + +again I can have the freedom so so X1 + + align:start position:0% +again I can have the freedom so so X1 + + + align:start position:0% +again I can have the freedom so so X1 +either connect to X or connect to Y uh + + align:start position:0% +either connect to X or connect to Y uh + + + align:start position:0% +either connect to X or connect to Y uh +that two diagram would be the same okay + + align:start position:0% +that two diagram would be the same okay + + + align:start position:0% +that two diagram would be the same okay +okay and so I have two possibilities + + align:start position:0% +okay and so I have two possibilities + + + align:start position:0% +okay and so I have two possibilities +here I only draw one of them a big + + align:start position:0% +here I only draw one of them a big + + + align:start position:0% +here I only draw one of them a big +because I just flip them + + align:start position:0% +because I just flip them + + + align:start position:0% +because I just flip them +X and Y is symmetric so I have a factor + + align:start position:0% +X and Y is symmetric so I have a factor + + + align:start position:0% +X and Y is symmetric so I have a factor +of two + + align:start position:0% +of two + + + align:start position:0% +of two +and then then the X Y I have four + + align:start position:0% +and then then the X Y I have four + + + align:start position:0% +and then then the X Y I have four +opportunities to connect with + + align:start position:0% +opportunities to connect with + + + align:start position:0% +opportunities to connect with +with the uh a four of X and X2 I have + + align:start position:0% +with the uh a four of X and X2 I have + + + align:start position:0% +with the uh a four of X and X2 I have +four possibility to connect four of Y + + align:start position:0% +four possibility to connect four of Y + + + align:start position:0% +four possibility to connect four of Y +because X2 connect with Y so I have two + + align:start position:0% +because X2 connect with Y so I have two + + + align:start position:0% +because X2 connect with Y so I have two +factors of four and four okay + + align:start position:0% + + + + align:start position:0% + +okay and so after that + + align:start position:0% +okay and so after that + + + align:start position:0% +okay and so after that +so 5x have three left and 5y I have + + align:start position:0% +so 5x have three left and 5y I have + + + align:start position:0% +so 5x have three left and 5y I have +three left and then take one of the a + + align:start position:0% +three left and then take one of the a + + + align:start position:0% +three left and then take one of the a +five then I have three possibilities you + + align:start position:0% +five then I have three possibilities you + + + align:start position:0% +five then I have three possibilities you +can connect y + + align:start position:0% +can connect y + + + align:start position:0% +can connect y +and then the other one have two + + align:start position:0% +and then the other one have two + + + align:start position:0% +and then the other one have two +okay and then that's it okay that's it + + align:start position:0% +okay and then that's it okay that's it + + + align:start position:0% +okay and then that's it okay that's it +so so that's all the possibilities and + + align:start position:0% +so so that's all the possibilities and + + + align:start position:0% +so so that's all the possibilities and +if you work it out so this gives you + + align:start position:0% +if you work it out so this gives you + + + align:start position:0% +if you work it out so this gives you +Lambda Square divided by three factorial + + align:start position:0% +Lambda Square divided by three factorial + + + align:start position:0% +Lambda Square divided by three factorial +and then so as exercise you should work + + align:start position:0% +and then so as exercise you should work + + + align:start position:0% +and then so as exercise you should work +out this one yourself + + align:start position:0% +out this one yourself + + + align:start position:0% +out this one yourself +okay and uh uh yeah which I didn't work + + align:start position:0% +okay and uh uh yeah which I didn't work + + + align:start position:0% +okay and uh uh yeah which I didn't work +out and uh but but I did work out this + + align:start position:0% +out and uh but but I did work out this + + + align:start position:0% +out and uh but but I did work out this +once + + align:start position:0% +once + + + align:start position:0% +once +so so these ones also give you as + + align:start position:0% +so so these ones also give you as + + + align:start position:0% +so so these ones also give you as +exercise so this is minus one half then + + align:start position:0% +exercise so this is minus one half then + + + align:start position:0% +exercise so this is minus one half then +the square four factorial Square + + align:start position:0% +the square four factorial Square + + + align:start position:0% +the square four factorial Square +times + + align:start position:0% +times + + + align:start position:0% +times +four times three times two + + align:start position:0% +four times three times two + + + align:start position:0% +four times three times two +equal to minus one half + + align:start position:0% +equal to minus one half + + + align:start position:0% +equal to minus one half +remember the square divided by 4 + + align:start position:0% +remember the square divided by 4 + + + align:start position:0% +remember the square divided by 4 +factorial + + align:start position:0% +factorial + + + align:start position:0% +factorial +and so this one is the + + align:start position:0% +and so this one is the + + + align:start position:0% +and so this one is the +again minus one half Lambda Square 4 + + align:start position:0% +again minus one half Lambda Square 4 + + + align:start position:0% +again minus one half Lambda Square 4 +factorial Square + + align:start position:0% +factorial Square + + + align:start position:0% +factorial Square +times two times three times two times + + align:start position:0% +times two times three times two times + + + align:start position:0% +times two times three times two times +three + + align:start position:0% +three + + + align:start position:0% +three +so that gives you + + align:start position:0% +so that gives you + + + align:start position:0% +so that gives you +minus Lambda squared divided by 16. + + align:start position:0% +minus Lambda squared divided by 16. + + + align:start position:0% +minus Lambda squared divided by 16. +so this will follow one is minus well + + align:start position:0% +so this will follow one is minus well + + + align:start position:0% +so this will follow one is minus well +half Lambda squared divided by 4 + + align:start position:0% +half Lambda squared divided by 4 + + + align:start position:0% +half Lambda squared divided by 4 +factorial Square + + align:start position:0% + + + + align:start position:0% + +times + + align:start position:0% +times + + + align:start position:0% +times +3 squared + + align:start position:0% + + + + align:start position:0% + +and then given by minus Lambda squared + + align:start position:0% +and then given by minus Lambda squared + + + align:start position:0% +and then given by minus Lambda squared +divided by two + + align:start position:0% +divided by two + + + align:start position:0% +divided by two +one over a squared + + align:start position:0% +one over a squared + + + align:start position:0% +one over a squared +okay + + align:start position:0% + + + + align:start position:0% + +good so uh yeah so I rather than done + + align:start position:0% +good so uh yeah so I rather than done + + + align:start position:0% +good so uh yeah so I rather than done +just for you to check yourself later + + align:start position:0% +just for you to check yourself later + + + align:start position:0% +just for you to check yourself later +okay so I urge you just as a exercise + + align:start position:0% +okay so I urge you just as a exercise + + + align:start position:0% +okay so I urge you just as a exercise +for yourself to to write them down later + + align:start position:0% +for yourself to to write them down later + + + align:start position:0% +for yourself to to write them down later +yourself okay and to do this exercise + + align:start position:0% +yourself okay and to do this exercise + + + align:start position:0% +yourself okay and to do this exercise +later yourself + + align:start position:0% +later yourself + + + align:start position:0% +later yourself +so so here we can already observe some + + align:start position:0% +so so here we can already observe some + + + align:start position:0% +so so here we can already observe some +patterns + + align:start position:0% +patterns + + + align:start position:0% +patterns +okay so so here we can observe some + + align:start position:0% +okay so so here we can observe some + + + align:start position:0% +okay so so here we can observe some +patterns + + align:start position:0% + + + + align:start position:0% + +and the so + + align:start position:0% +and the so + + + align:start position:0% +and the so +so you can do this for each individual + + align:start position:0% +so you can do this for each individual + + + align:start position:0% +so you can do this for each individual +diagrams okay you can do this interview + + align:start position:0% +diagrams okay you can do this interview + + + align:start position:0% +diagrams okay you can do this interview +okay but if you + + align:start position:0% +okay but if you + + + align:start position:0% +okay but if you +try to count this way + + align:start position:0% +try to count this way + + + align:start position:0% +try to count this way +okay if you try to counter this way as + + align:start position:0% +okay if you try to counter this way as + + + align:start position:0% +okay if you try to counter this way as +we are doing here + + align:start position:0% +we are doing here + + + align:start position:0% +we are doing here +even though it's not difficult to do + + align:start position:0% +even though it's not difficult to do + + + align:start position:0% +even though it's not difficult to do +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but it's still tedious okay still + + align:start position:0% +but it's still tedious okay still + + + align:start position:0% +but it's still tedious okay still +tedious but each Diagon have to count + + align:start position:0% +tedious but each Diagon have to count + + + align:start position:0% +tedious but each Diagon have to count +the factor four three Etc okay so it'd + + align:start position:0% +the factor four three Etc okay so it'd + + + align:start position:0% +the factor four three Etc okay so it'd +be nice if you find the better trick + + align:start position:0% +be nice if you find the better trick + + + align:start position:0% +be nice if you find the better trick +okay so now there's a better way to do + + align:start position:0% +okay so now there's a better way to do + + + align:start position:0% +okay so now there's a better way to do +it okay so the better way to do it + + align:start position:0% +it okay so the better way to do it + + + align:start position:0% +it okay so the better way to do it +so + + align:start position:0% +so + + + align:start position:0% +so +Factor trick + + align:start position:0% + + + + align:start position:0% + +so if I noticed the following + + align:start position:0% + + + + align:start position:0% + +so when you go to the Lambda ends order + + align:start position:0% +so when you go to the Lambda ends order + + + align:start position:0% +so when you go to the Lambda ends order +so there's always a there's a n + + align:start position:0% +so there's always a there's a n + + + align:start position:0% +so there's always a there's a n +factorial + + align:start position:0% +factorial + + + align:start position:0% +factorial +coming from expanding the exponential + + align:start position:0% +coming from expanding the exponential + + + align:start position:0% +coming from expanding the exponential +okay + + align:start position:0% + + + + align:start position:0% + +so because we are expanding the + + align:start position:0% +so because we are expanding the + + + align:start position:0% +so because we are expanding the +exponential uh and the uh + + align:start position:0% + + + + align:start position:0% + +okay so so there's always a factor of + + align:start position:0% +okay so so there's always a factor of + + + align:start position:0% +okay so so there's always a factor of +um + + align:start position:0% + + + + align:start position:0% + +uh or a factorial come from the + + align:start position:0% +uh or a factorial come from the + + + align:start position:0% +uh or a factorial come from the +expanding of uh + + align:start position:0% +expanding of uh + + + align:start position:0% +expanding of uh +so now + + align:start position:0% + + + + align:start position:0% + +at the end order + + align:start position:0% + + + + align:start position:0% + +yeah I think I erased my vertex so at + + align:start position:0% +yeah I think I erased my vertex so at + + + align:start position:0% +yeah I think I erased my vertex so at +the end's order + + align:start position:0% +the end's order + + + align:start position:0% +the end's order +you have a n factorial from expansion + + align:start position:0% +you have a n factorial from expansion + + + align:start position:0% +you have a n factorial from expansion +but you also have n vertices okay + + align:start position:0% +but you also have n vertices okay + + + align:start position:0% +but you also have n vertices okay +because each power each Lambda comes + + align:start position:0% +because each power each Lambda comes + + + align:start position:0% +because each power each Lambda comes +with a factor of these vertices + + align:start position:0% +with a factor of these vertices + + + align:start position:0% +with a factor of these vertices +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now + + align:start position:0% + + + + align:start position:0% + +you know when you permute all this and + + align:start position:0% +you know when you permute all this and + + + align:start position:0% +you know when you permute all this and +so when you permute the interacting + + align:start position:0% +so when you permute the interacting + + + align:start position:0% +so when you permute the interacting +vertices + + align:start position:0% + + + + align:start position:0% + +okay and you also get the factor of n + + align:start position:0% +okay and you also get the factor of n + + + align:start position:0% +okay and you also get the factor of n +factorial + + align:start position:0% +factorial + + + align:start position:0% +factorial +okay because you can okay because + + align:start position:0% +okay because you can okay because + + + align:start position:0% +okay because you can okay because +they're all symmetric okay they're all + + align:start position:0% +they're all symmetric okay they're all + + + align:start position:0% +they're all symmetric okay they're all +symmetric doing the contraction + + align:start position:0% +symmetric doing the contraction + + + align:start position:0% +symmetric doing the contraction +and if you have one way to contract and + + align:start position:0% +and if you have one way to contract and + + + align:start position:0% +and if you have one way to contract and +then you can have another way to + + align:start position:0% +then you can have another way to + + + align:start position:0% +then you can have another way to +contract by permuting all these + + align:start position:0% +contract by permuting all these + + + align:start position:0% +contract by permuting all these +different vertices okay + + align:start position:0% + + + + align:start position:0% + +so then these two factors cancel + + align:start position:0% + + + + align:start position:0% + +okay these two functions also modular + + align:start position:0% + + + + align:start position:0% + +modulo + + align:start position:0% +modulo + + + align:start position:0% +modulo +symmetries + + align:start position:0% + + + + align:start position:0% + +in permuting vertices + + align:start position:0% + + + + align:start position:0% + +okay if their symmetry is important a + + align:start position:0% +okay if their symmetry is important a + + + align:start position:0% +okay if their symmetry is important a +permuting vertices + + align:start position:0% +permuting vertices + + + align:start position:0% +permuting vertices +okay and then then of course you don't + + align:start position:0% +okay and then then of course you don't + + + align:start position:0% +okay and then then of course you don't +get in factorials because some of the + + align:start position:0% +get in factorials because some of the + + + align:start position:0% +get in factorials because some of the +permutations give you the same diagram + + align:start position:0% +permutations give you the same diagram + + + align:start position:0% +permutations give you the same diagram +okay and so so the modular symmetry is + + align:start position:0% +okay and so so the modular symmetry is + + + align:start position:0% +okay and so so the modular symmetry is +in permuting vertices and and you have + + align:start position:0% +in permuting vertices and and you have + + + align:start position:0% +in permuting vertices and and you have +this n factorial okay so this is the + + align:start position:0% +this n factorial okay so this is the + + + align:start position:0% +this n factorial okay so this is the +first observation + + align:start position:0% + + + + align:start position:0% + +so the second observation + + align:start position:0% + + + + align:start position:0% + +is that for each vertex + + align:start position:0% + + + + align:start position:0% + +which you have minus and Lambda divided + + align:start position:0% +which you have minus and Lambda divided + + + align:start position:0% +which you have minus and Lambda divided +by 4 factorial 5 4 + + align:start position:0% +by 4 factorial 5 4 + + + align:start position:0% +by 4 factorial 5 4 +okay + + align:start position:0% + + + + align:start position:0% + +so if each Phi + + align:start position:0% + + + + align:start position:0% + +in this 5 4 + + align:start position:0% + + + + align:start position:0% + +contracts differently + + align:start position:0% + + + + align:start position:0% + +contracts differently + + align:start position:0% + + + + align:start position:0% + +so all these four files are symmetric + + align:start position:0% +so all these four files are symmetric + + + align:start position:0% +so all these four files are symmetric +with each other okay there's no not any + + align:start position:0% +with each other okay there's no not any + + + align:start position:0% +with each other okay there's no not any +file which is special but if they uh but + + align:start position:0% +file which is special but if they uh but + + + align:start position:0% +file which is special but if they uh but +if each file contracts differently then + + align:start position:0% +if each file contracts differently then + + + align:start position:0% +if each file contracts differently then +again you permute the files or or it + + align:start position:0% +again you permute the files or or it + + + align:start position:0% +again you permute the files or or it +should be the same okay I should lead to + + align:start position:0% +should be the same okay I should lead to + + + align:start position:0% +should be the same okay I should lead to +uh uh that angle should also be included + + align:start position:0% +uh uh that angle should also be included + + + align:start position:0% +uh uh that angle should also be included +so so that's + + align:start position:0% +so so that's + + + align:start position:0% +so so that's +and then you can permute Phi + + align:start position:0% + + + + align:start position:0% + +permutation + + align:start position:0% +permutation + + + align:start position:0% +permutation +of four files + + align:start position:0% + + + + align:start position:0% + +then leads to four factorial + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +so again modular + + align:start position:0% + + + + align:start position:0% + +so so these facts four factorial again + + align:start position:0% +so so these facts four factorial again + + + align:start position:0% +so so these facts four factorial again +cancels with these four factorial + + align:start position:0% +cancels with these four factorial + + + align:start position:0% +cancels with these four factorial +so the two + + align:start position:0% + + + + align:start position:0% + +four factorial cancel + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +modular + + align:start position:0% + + + + align:start position:0% + +symmetries + + align:start position:0% + + + + align:start position:0% + +in permutating + + align:start position:0% +in permutating + + + align:start position:0% +in permutating +in permuting + + align:start position:0% + + + + align:start position:0% + +five + + align:start position:0% + + + + align:start position:0% + +coming from the same vertices + + align:start position:0% +coming from the same vertices + + + align:start position:0% +coming from the same vertices +coming from the same vertex okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so if these two files are contracted the + + align:start position:0% +so if these two files are contracted the + + + align:start position:0% +so if these two files are contracted the +same of course when you permute them you + + align:start position:0% +same of course when you permute them you + + + align:start position:0% +same of course when you permute them you +don't generate a new new diagram okay + + align:start position:0% +don't generate a new new diagram okay + + + align:start position:0% +don't generate a new new diagram okay +don't generate a new a new ways so so + + align:start position:0% +don't generate a new a new ways so so + + + align:start position:0% +don't generate a new a new ways so so +now we have two two different + + align:start position:0% +now we have two two different + + + align:start position:0% +now we have two two different +permutations + + align:start position:0% +permutations + + + align:start position:0% +permutations +why is the probability the vertices and + + align:start position:0% +why is the probability the vertices and + + + align:start position:0% +why is the probability the vertices and +the second is to permute the files + + align:start position:0% +the second is to permute the files + + + align:start position:0% +the second is to permute the files +within the within each vertex okay + + align:start position:0% +within the within each vertex okay + + + align:start position:0% +within the within each vertex okay +within each vertex + + align:start position:0% +within each vertex + + + align:start position:0% +within each vertex +so + + align:start position:0% +so + + + align:start position:0% +so +so that means both this n factorial + + align:start position:0% +so that means both this n factorial + + + align:start position:0% +so that means both this n factorial +and this four factorial the cancel okay + + align:start position:0% +and this four factorial the cancel okay + + + align:start position:0% +and this four factorial the cancel okay +so we can forget so this means + + align:start position:0% +so we can forget so this means + + + align:start position:0% +so we can forget so this means +forget about + + align:start position:0% + + + + align:start position:0% + +the N factorial Factor + + align:start position:0% + + + + align:start position:0% + +from exponential + + align:start position:0% + + + + align:start position:0% + +and the + + align:start position:0% +and the + + + align:start position:0% +and the +we also forget about this one over four + + align:start position:0% +we also forget about this one over four + + + align:start position:0% +we also forget about this one over four +factorial and then treat each vertex + + align:start position:0% + + + + align:start position:0% + +minus I Lambda okay just a coming from a + + align:start position:0% +minus I Lambda okay just a coming from a + + + align:start position:0% +minus I Lambda okay just a coming from a +factor of minus and + + align:start position:0% +factor of minus and + + + align:start position:0% +factor of minus and +but then this way we over count okay + + align:start position:0% + + + + align:start position:0% + +so this way we over count + + align:start position:0% +so this way we over count + + + align:start position:0% +so this way we over count +and then we need to divide + + align:start position:0% + + + + align:start position:0% + +so we need to divide + + align:start position:0% +so we need to divide + + + align:start position:0% +so we need to divide +and then + + align:start position:0% + + + + align:start position:0% + +divide + + align:start position:0% + + + + align:start position:0% + +now I see me two factors okay + + align:start position:0% + + + + align:start position:0% + +from + + align:start position:0% + + + + align:start position:0% + +from + + align:start position:0% +from + + + align:start position:0% +from +permuting + + align:start position:0% + + + + align:start position:0% + +vertices + + align:start position:0% + + + + align:start position:0% + +and relax + + align:start position:0% +and relax + + + align:start position:0% +and relax +okay + + align:start position:0% + + + + align:start position:0% + +okay so so now let's go back to this + + align:start position:0% +okay so so now let's go back to this + + + align:start position:0% +okay so so now let's go back to this +diagram + + align:start position:0% + + + + align:start position:0% + +okay so so now let's go back to this + + align:start position:0% +okay so so now let's go back to this + + + align:start position:0% +okay so so now let's go back to this +diagram + + align:start position:0% + + + + align:start position:0% + +so in this diagram + + align:start position:0% +so in this diagram + + + align:start position:0% +so in this diagram +there's no symmetry between X and Y + + align:start position:0% +there's no symmetry between X and Y + + + align:start position:0% +there's no symmetry between X and Y +so there's no uh scene yeah because X + + align:start position:0% +so there's no uh scene yeah because X + + + align:start position:0% +so there's no uh scene yeah because X +and Y they're not symmetric so so we + + align:start position:0% +and Y they're not symmetric so so we + + + align:start position:0% +and Y they're not symmetric so so we +don't need to divide so there's no + + align:start position:0% +don't need to divide so there's no + + + align:start position:0% +don't need to divide so there's no +symmetry Factor associated with the uh + + align:start position:0% +symmetry Factor associated with the uh + + + align:start position:0% +symmetry Factor associated with the uh +uh um + + align:start position:0% +uh um + + + align:start position:0% +uh um +a permuting the vertices + + align:start position:0% +a permuting the vertices + + + align:start position:0% +a permuting the vertices +but for the for the voters come from the + + align:start position:0% +but for the for the voters come from the + + + align:start position:0% +but for the for the voters come from the +X + + align:start position:0% +X + + + align:start position:0% +X +these two next are symmetric + + align:start position:0% +these two next are symmetric + + + align:start position:0% +these two next are symmetric +okay so there's a fact of two okay a + + align:start position:0% +okay so there's a fact of two okay a + + + align:start position:0% +okay so there's a fact of two okay a +permute them and for this + + align:start position:0% +permute them and for this + + + align:start position:0% +permute them and for this +thing comes from y again there are two + + align:start position:0% +thing comes from y again there are two + + + align:start position:0% +thing comes from y again there are two +of them are symmetric okay so that's why + + align:start position:0% +of them are symmetric okay so that's why + + + align:start position:0% +of them are symmetric okay so that's why +we divided by two symmetric factors so + + align:start position:0% +we divided by two symmetric factors so + + + align:start position:0% +we divided by two symmetric factors so +this one half okay + + align:start position:0% +this one half okay + + + align:start position:0% +this one half okay +and similarly from here + + align:start position:0% +and similarly from here + + + align:start position:0% +and similarly from here +again the X and the Y they are + + align:start position:0% +again the X and the Y they are + + + align:start position:0% +again the X and the Y they are +asymmetric + + align:start position:0% +asymmetric + + + align:start position:0% +asymmetric +because Y is contracted with x y and the + + align:start position:0% +because Y is contracted with x y and the + + + align:start position:0% +because Y is contracted with x y and the +Y is contract with uh + + align:start position:0% +Y is contract with uh + + + align:start position:0% +Y is contract with uh +X2 so there's no symmetry factors from + + align:start position:0% +X2 so there's no symmetry factors from + + + align:start position:0% +X2 so there's no symmetry factors from +commuting the uh uh um + + align:start position:0% +commuting the uh uh um + + + align:start position:0% +commuting the uh uh um +from Computing the uh uh the vertices + + align:start position:0% +from Computing the uh uh the vertices + + + align:start position:0% +from Computing the uh uh the vertices +but but between X and Y there are three + + align:start position:0% +but but between X and Y there are three + + + align:start position:0% +but but between X and Y there are three +next which are symmetric + + align:start position:0% +next which are symmetric + + + align:start position:0% +next which are symmetric +okay when we permute this relax and then + + align:start position:0% +okay when we permute this relax and then + + + align:start position:0% +okay when we permute this relax and then +we have three factorials + + align:start position:0% +we have three factorials + + + align:start position:0% +we have three factorials +okay so we have three factorials + + align:start position:0% +okay so we have three factorials + + + align:start position:0% +okay so we have three factorials +okay so and similarly uh a lever as an + + align:start position:0% +okay so and similarly uh a lever as an + + + align:start position:0% +okay so and similarly uh a lever as an +exercise for you to do the other + + align:start position:0% +exercise for you to do the other + + + align:start position:0% +exercise for you to do the other +diagrams okay to do the uh + + align:start position:0% +diagrams okay to do the uh + + + align:start position:0% +diagrams okay to do the uh +under diagrams + + align:start position:0% + + + + align:start position:0% + +so now + + align:start position:0% + + + + align:start position:0% + +we are ready to just uh uh uh uh to + + align:start position:0% +we are ready to just uh uh uh uh to + + + align:start position:0% +we are ready to just uh uh uh uh to +to write down our rule okay so so now so + + align:start position:0% +to write down our rule okay so so now so + + + align:start position:0% +to write down our rule okay so so now so +now we have shown the diagrams and now + + align:start position:0% +now we have shown the diagrams and now + + + align:start position:0% +now we have shown the diagrams and now +we can use the diagram to write down + + align:start position:0% +we can use the diagram to write down + + + align:start position:0% +we can use the diagram to write down +Expressions okay so so the rules + + align:start position:0% + + + + align:start position:0% + +of writing + + align:start position:0% + + + + align:start position:0% + +down expression + + align:start position:0% + + + + align:start position:0% + +from diagrams + + align:start position:0% + + + + align:start position:0% + +are called the fireman rules okay + + align:start position:0% + + + + align:start position:0% + +confinement rules + + align:start position:0% +confinement rules + + + align:start position:0% +confinement rules +so here is the family Rules + + align:start position:0% +so here is the family Rules + + + align:start position:0% +so here is the family Rules +so okay so here is the family Rules + + align:start position:0% + + + + align:start position:0% + +which you can + + align:start position:0% +which you can + + + align:start position:0% +which you can +so these are all very intuitive okay + + align:start position:0% + + + + align:start position:0% + +so so for each external point + + align:start position:0% + + + + align:start position:0% + +so here we have some external Point okay + + align:start position:0% +so here we have some external Point okay + + + align:start position:0% +so here we have some external Point okay +so each external point + + align:start position:0% + + + + align:start position:0% + +you associate this line okay so so here + + align:start position:0% +you associate this line okay so so here + + + align:start position:0% +you associate this line okay so so here +is the say for example X1 + + align:start position:0% +is the say for example X1 + + + align:start position:0% +is the say for example X1 +and then and then you just associate + + align:start position:0% +and then and then you just associate + + + align:start position:0% +and then and then you just associate +with the fact of one but there's always + + align:start position:0% +with the fact of one but there's always + + + align:start position:0% +with the fact of one but there's always +a line coming out of the uh external + + align:start position:0% +a line coming out of the uh external + + + align:start position:0% +a line coming out of the uh external +point because you have to contract with + + align:start position:0% +point because you have to contract with + + + align:start position:0% +point because you have to contract with +that one okay + + align:start position:0% + + + + align:start position:0% + +and then for each propagator + + align:start position:0% + + + + align:start position:0% + +to the propagator + + align:start position:0% +to the propagator + + + align:start position:0% +to the propagator +will write the row down + + align:start position:0% +will write the row down + + + align:start position:0% +will write the row down +you just have a say you have two + + align:start position:0% +you just have a say you have two + + + align:start position:0% +you just have a say you have two +endpoint then that's corresponding to + + align:start position:0% +endpoint then that's corresponding to + + + align:start position:0% +endpoint then that's corresponding to +gf0 + + align:start position:0% +gf0 + + + align:start position:0% +gf0 +x minus y + + align:start position:0% +x minus y + + + align:start position:0% +x minus y +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so each such a propagator you can just + + align:start position:0% +so each such a propagator you can just + + + align:start position:0% +so each such a propagator you can just +write down a factor + + align:start position:0% +write down a factor + + + align:start position:0% +write down a factor +equals 1 into GF + + align:start position:0% +equals 1 into GF + + + align:start position:0% +equals 1 into GF +y + + align:start position:0% + + + + align:start position:0% + +and then for each vertex + + align:start position:0% + + + + align:start position:0% + +erase them + + align:start position:0% + + + + align:start position:0% + +so for each vertex + + align:start position:0% + + + + align:start position:0% + +so point x + + align:start position:0% +so point x + + + align:start position:0% +so point x +so you associate with Lambda and the + + align:start position:0% +so you associate with Lambda and the + + + align:start position:0% +so you associate with Lambda and the +integration of X okay + + align:start position:0% + + + + align:start position:0% + +and then you the last step + + align:start position:0% +and then you the last step + + + align:start position:0% +and then you the last step +you divide by + + align:start position:0% + + + + align:start position:0% + +symmetry factors okay symmetry factors + + align:start position:0% +symmetry factors okay symmetry factors + + + align:start position:0% +symmetry factors okay symmetry factors +for diagram + + align:start position:0% +for diagram + + + align:start position:0% +for diagram +so for you so you just draw all possible + + align:start position:0% +so for you so you just draw all possible + + + align:start position:0% +so for you so you just draw all possible +diagrams + + align:start position:0% +diagrams + + + align:start position:0% +diagrams +using this kind of rule so for each + + align:start position:0% +using this kind of rule so for each + + + align:start position:0% +using this kind of rule so for each +probability we have line and then you + + align:start position:0% +probability we have line and then you + + + align:start position:0% +probability we have line and then you +have vertices + + align:start position:0% +have vertices + + + align:start position:0% +have vertices +and now so now from each diagram by + + align:start position:0% +and now so now from each diagram by + + + align:start position:0% +and now so now from each diagram by +applying this rule we can also write + + align:start position:0% +applying this rule we can also write + + + align:start position:0% +applying this rule we can also write +down the analytic expression + + align:start position:0% +down the analytic expression + + + align:start position:0% +down the analytic expression +okay we can write down analytic + + align:start position:0% +okay we can write down analytic + + + align:start position:0% +okay we can write down analytic +expression + + align:start position:0% + + + + align:start position:0% + +any questions on this + + align:start position:0% + + + + align:start position:0% + +so so exercise for yourself + + align:start position:0% +so so exercise for yourself + + + align:start position:0% +so so exercise for yourself +to write down an ending expression for + + align:start position:0% +to write down an ending expression for + + + align:start position:0% +to write down an ending expression for +each of them okay so uh uh yeah let me + + align:start position:0% +each of them okay so uh uh yeah let me + + + align:start position:0% +each of them okay so uh uh yeah let me +give you an example + + align:start position:0% +give you an example + + + align:start position:0% +give you an example +so for B + + align:start position:0% +so for B + + + align:start position:0% +so for B +so you should uh + + align:start position:0% + + + + align:start position:0% + +as exercise you should try to do + + align:start position:0% +as exercise you should try to do + + + align:start position:0% +as exercise you should try to do +yourself for each of them let me just + + align:start position:0% +yourself for each of them let me just + + + align:start position:0% +yourself for each of them let me just +give you one example for B + + align:start position:0% +give you one example for B + + + align:start position:0% +give you one example for B +and then you have + + align:start position:0% +and then you have + + + align:start position:0% +and then you have +first the symmetric factors Lambda + + align:start position:0% +first the symmetric factors Lambda + + + align:start position:0% +first the symmetric factors Lambda +squared divided by five three factorial + + align:start position:0% +squared divided by five three factorial + + + align:start position:0% +squared divided by five three factorial +and then you have the four + + align:start position:0% +and then you have the four + + + align:start position:0% +and then you have the four +X to 4y come from these two vertices + + align:start position:0% +X to 4y come from these two vertices + + + align:start position:0% +X to 4y come from these two vertices +okay yeah yeah I should just write it + + align:start position:0% +okay yeah yeah I should just write it + + + align:start position:0% +okay yeah yeah I should just write it +like this sorry I should yeah let me + + align:start position:0% +like this sorry I should yeah let me + + + align:start position:0% +like this sorry I should yeah let me +just strictly follow this rule okay so + + align:start position:0% +just strictly follow this rule okay so + + + align:start position:0% +just strictly follow this rule okay so +we have two vertices + + align:start position:0% +we have two vertices + + + align:start position:0% +we have two vertices +so each vertex we have I Lambda + + align:start position:0% +so each vertex we have I Lambda + + + align:start position:0% +so each vertex we have I Lambda +Square then you have D4 X and the D4 y + + align:start position:0% + + + + align:start position:0% + +and then for each propagator + + align:start position:0% +and then for each propagator + + + align:start position:0% +and then for each propagator +we associate this + + align:start position:0% +we associate this + + + align:start position:0% +we associate this +and then we have GF + + align:start position:0% +and then we have GF + + + align:start position:0% +and then we have GF +zero x minus y then Q + + align:start position:0% +zero x minus y then Q + + + align:start position:0% +zero x minus y then Q +and then finally we divide by symmetry + + align:start position:0% +and then finally we divide by symmetry + + + align:start position:0% +and then finally we divide by symmetry +factors because there's three + + align:start position:0% +factors because there's three + + + align:start position:0% +factors because there's three +permutation of them so we divide by + + align:start position:0% +permutation of them so we divide by + + + align:start position:0% +permutation of them so we divide by +three + + align:start position:0% +three + + + align:start position:0% +three +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so this is the analytics question + + align:start position:0% +so so this is the analytics question + + + align:start position:0% +so so this is the analytics question +corresponding to that diagram + + align:start position:0% +corresponding to that diagram + + + align:start position:0% +corresponding to that diagram +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so so now just + + align:start position:0% +so so so now just + + + align:start position:0% +so so so now just +naturally you don't even have to write + + align:start position:0% +naturally you don't even have to write + + + align:start position:0% +naturally you don't even have to write +down such expression in the Top Line + + align:start position:0% +down such expression in the Top Line + + + align:start position:0% +down such expression in the Top Line +wrote down there just add each order + + align:start position:0% +wrote down there just add each order + + + align:start position:0% +wrote down there just add each order +you have certain number external points + + align:start position:0% +you have certain number external points + + + align:start position:0% +you have certain number external points +and then just have number of vertices + + align:start position:0% +and then just have number of vertices + + + align:start position:0% +and then just have number of vertices +come from and so they just have em + + align:start position:0% +come from and so they just have em + + + align:start position:0% +come from and so they just have em +vertices you just try to connect all + + align:start position:0% +vertices you just try to connect all + + + align:start position:0% +vertices you just try to connect all +possible lines between them okay and + + align:start position:0% +possible lines between them okay and + + + align:start position:0% +possible lines between them okay and +then and then that's all possible + + align:start position:0% +then and then that's all possible + + + align:start position:0% +then and then that's all possible +contributions okay + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% +good + + + align:start position:0% +good +so this is the + + align:start position:0% +so this is the + + + align:start position:0% +so this is the +find my rule in coordinate space + + align:start position:0% + + + + align:start position:0% + +it's also convenient to go to the + + align:start position:0% +it's also convenient to go to the + + + align:start position:0% +it's also convenient to go to the +momentum space okay + + align:start position:0% +momentum space okay + + + align:start position:0% +momentum space okay +so it's also convenient to go to + + align:start position:0% +so it's also convenient to go to + + + align:start position:0% +so it's also convenient to go to +momentum space + + align:start position:0% +momentum space + + + align:start position:0% +momentum space +so Dakota momentum space is then we can + + align:start position:0% +so Dakota momentum space is then we can + + + align:start position:0% +so Dakota momentum space is then we can +Define the Fourier transform + + align:start position:0% + + + + align:start position:0% + +okay so so let's define the Fourier + + align:start position:0% +okay so so let's define the Fourier + + + align:start position:0% +okay so so let's define the Fourier +transform + + align:start position:0% +transform + + + align:start position:0% +transform +so suppose we have an endpoint function + + align:start position:0% +so suppose we have an endpoint function + + + align:start position:0% +so suppose we have an endpoint function +okay we have suppose we have endpoint + + align:start position:0% +okay we have suppose we have endpoint + + + align:start position:0% +okay we have suppose we have endpoint +function + + align:start position:0% + + + + align:start position:0% + +GN + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +suppose you have an endpoint function X1 + + align:start position:0% +suppose you have an endpoint function X1 + + + align:start position:0% +suppose you have an endpoint function X1 +x n okay + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% + + + + align:start position:0% + +so so so this is just the standard + + align:start position:0% +so so so this is just the standard + + + align:start position:0% +so so so this is just the standard +Fourier transform + + align:start position:0% + + + + align:start position:0% + +so because of the translation symmetry + + align:start position:0% +so because of the translation symmetry + + + align:start position:0% +so because of the translation symmetry +okay so we expect + + align:start position:0% + + + + align:start position:0% + +all the P's must be conserved okay + + align:start position:0% +all the P's must be conserved okay + + + align:start position:0% +all the P's must be conserved okay +just from the conversation uh I will + + align:start position:0% +just from the conversation uh I will + + + align:start position:0% +just from the conversation uh I will +derive it but but but you should also be + + align:start position:0% +derive it but but but you should also be + + + align:start position:0% +derive it but but but you should also be +able to expect on the general ground + + align:start position:0% +able to expect on the general ground + + + align:start position:0% +able to expect on the general ground +from the translation symmetry so we + + align:start position:0% +from the translation symmetry so we + + + align:start position:0% +from the translation symmetry so we +expect that there must be a factor + + align:start position:0% + + + + align:start position:0% + +of the momentum conversation + + align:start position:0% + + + + align:start position:0% + +coming from here okay + + align:start position:0% +coming from here okay + + + align:start position:0% +coming from here okay +and and then then we call that + + align:start position:0% +and and then then we call that + + + align:start position:0% +and and then then we call that +corruption GM + + align:start position:0% +corruption GM + + + align:start position:0% +corruption GM +p + + align:start position:0% + + + + align:start position:0% + +ok so so the momentum so so our + + align:start position:0% +ok so so the momentum so so our + + + align:start position:0% +ok so so the momentum so so our +convention is that for momentum momentum + + align:start position:0% +convention is that for momentum momentum + + + align:start position:0% +convention is that for momentum momentum +space uh correlation functions we + + align:start position:0% +space uh correlation functions we + + + align:start position:0% +space uh correlation functions we +defined without this Factor okay without + + align:start position:0% +defined without this Factor okay without + + + align:start position:0% +defined without this Factor okay without +this Factor yes + + align:start position:0% + + + + align:start position:0% + +trick to uh connected diagrams oh yeah + + align:start position:0% +trick to uh connected diagrams oh yeah + + + align:start position:0% +trick to uh connected diagrams oh yeah +yeah we will talk about that later yeah + + align:start position:0% + + + + align:start position:0% + +so here I'm just + + align:start position:0% +so here I'm just + + + align:start position:0% +so here I'm just +talk about the general rule and then we + + align:start position:0% +talk about the general rule and then we + + + align:start position:0% +talk about the general rule and then we +will talk about the uh more fine points + + align:start position:0% +will talk about the uh more fine points + + + align:start position:0% +will talk about the uh more fine points +uh how to stop how to enumerate all + + align:start position:0% +uh how to stop how to enumerate all + + + align:start position:0% +uh how to stop how to enumerate all +possible diagrams yeah thank you + + align:start position:0% +possible diagrams yeah thank you + + + align:start position:0% +possible diagrams yeah thank you +okay so so when we Define the momentum + + align:start position:0% +okay so so when we Define the momentum + + + align:start position:0% +okay so so when we Define the momentum +space correlation functions + + align:start position:0% +space correlation functions + + + align:start position:0% +space correlation functions +we uh we we extract out this Factor okay + + align:start position:0% +we uh we we extract out this Factor okay + + + align:start position:0% +we uh we we extract out this Factor okay +so the reason for to drag to extract + + align:start position:0% +so the reason for to drag to extract + + + align:start position:0% +so the reason for to drag to extract +this uh + + align:start position:0% +this uh + + + align:start position:0% +this uh +is from the uh a momentum conversation + + align:start position:0% +is from the uh a momentum conversation + + + align:start position:0% +is from the uh a momentum conversation +so to see this okay to see that there's + + align:start position:0% +so to see this okay to see that there's + + + align:start position:0% +so to see this okay to see that there's +a factor like this it's very easy + + align:start position:0% +a factor like this it's very easy + + + align:start position:0% +a factor like this it's very easy +okay so because the from the translation + + align:start position:0% +okay so because the from the translation + + + align:start position:0% +okay so because the from the translation +symmetry + + align:start position:0% + + + + align:start position:0% + +so the same argument + + align:start position:0% +so the same argument + + + align:start position:0% +so the same argument +that the two point function + + align:start position:0% +that the two point function + + + align:start position:0% +that the two point function +so x y x 2 + + align:start position:0% +so x y x 2 + + + align:start position:0% +so x y x 2 +should only be a function of X Y minus X + + align:start position:0% +should only be a function of X Y minus X + + + align:start position:0% +should only be a function of X Y minus X +cubed + + align:start position:0% +cubed + + + align:start position:0% +cubed +so for the endpoint function from the + + align:start position:0% +so for the endpoint function from the + + + align:start position:0% +so for the endpoint function from the +translation symmetry + + align:start position:0% + + + + align:start position:0% + +so this you can take + + align:start position:0% + + + + align:start position:0% + +you can just take one point to be the + + align:start position:0% +you can just take one point to be the + + + align:start position:0% +you can just take one point to be the +reference point you can subtract + + align:start position:0% + + + + align:start position:0% + +say + + align:start position:0% +say + + + align:start position:0% +say +all coordinate by the value of x n okay + + align:start position:0% +all coordinate by the value of x n okay + + + align:start position:0% +all coordinate by the value of x n okay +and and then the last the last argument + + align:start position:0% +and and then the last the last argument + + + align:start position:0% +and and then the last the last argument +becomes zero okay so so you can choose + + align:start position:0% +becomes zero okay so so you can choose + + + align:start position:0% +becomes zero okay so so you can choose +one point that's a reference point and + + align:start position:0% +one point that's a reference point and + + + align:start position:0% +one point that's a reference point and +subtract any other point from it and + + align:start position:0% +subtract any other point from it and + + + align:start position:0% +subtract any other point from it and +that should be equivalent okay because + + align:start position:0% +that should be equivalent okay because + + + align:start position:0% +that should be equivalent okay because +it doesn't matter where you choose the + + align:start position:0% +it doesn't matter where you choose the + + + align:start position:0% +it doesn't matter where you choose the +reference point so so here let's choose + + align:start position:0% +reference point so so here let's choose + + + align:start position:0% +reference point so so here let's choose +the reference point it to be x n so this + + align:start position:0% +the reference point it to be x n so this + + + align:start position:0% +the reference point it to be x n so this +should be equal to that okay + + align:start position:0% + + + + align:start position:0% + +so now when you do a free transform + + align:start position:0% + + + + align:start position:0% + +so now when you do a free transform so + + align:start position:0% +so now when you do a free transform so + + + align:start position:0% +so now when you do a free transform so +you can easily convince yourself okay so + + align:start position:0% +you can easily convince yourself okay so + + + align:start position:0% +you can easily convince yourself okay so +we need to a free transform of this + + align:start position:0% +we need to a free transform of this + + + align:start position:0% +we need to a free transform of this +object we plug this into here + + align:start position:0% + + + + align:start position:0% + +okay when you plug this into here and + + align:start position:0% +okay when you plug this into here and + + + align:start position:0% +okay when you plug this into here and +then you get the data function okay + + align:start position:0% +then you get the data function okay + + + align:start position:0% +then you get the data function okay +okay so uh so this is a simple exercise + + align:start position:0% +okay so uh so this is a simple exercise + + + align:start position:0% +okay so uh so this is a simple exercise +for yourself to do okay + + align:start position:0% +for yourself to do okay + + + align:start position:0% +for yourself to do okay +and so if you plug in here you find that + + align:start position:0% +and so if you plug in here you find that + + + align:start position:0% +and so if you plug in here you find that +there's always a data from here + + align:start position:0% + + + + align:start position:0% + +so now I recall that the momentum space + + align:start position:0% + + + + align:start position:0% + +the fireman propagator for the free + + align:start position:0% +the fireman propagator for the free + + + align:start position:0% +the fireman propagator for the free +theory in the momentum space if you say + + align:start position:0% +theory in the momentum space if you say + + + align:start position:0% +theory in the momentum space if you say +um + + align:start position:0% +um + + + align:start position:0% +um +k then it's given by minus I + + align:start position:0% +k then it's given by minus I + + + align:start position:0% +k then it's given by minus I +K square plus M Square minus I have zero + + align:start position:0% +K square plus M Square minus I have zero + + + align:start position:0% +K square plus M Square minus I have zero +so now you have a line but now it's + + align:start position:0% +so now you have a line but now it's + + + align:start position:0% +so now you have a line but now it's +labeled in the back momentum k okay + + align:start position:0% +labeled in the back momentum k okay + + + align:start position:0% +labeled in the back momentum k okay +okay so so this K denotes the flow of + + align:start position:0% +okay so so this K denotes the flow of + + + align:start position:0% +okay so so this K denotes the flow of +the direction of the momentum okay this + + align:start position:0% +the direction of the momentum okay this + + + align:start position:0% +the direction of the momentum okay this +Arrow + + align:start position:0% + + + + align:start position:0% + +okay so now with this rule + + align:start position:0% +okay so now with this rule + + + align:start position:0% +okay so now with this rule +you can easily write down + + align:start position:0% +you can easily write down + + + align:start position:0% +you can easily write down +what is the uh now you can just + + align:start position:0% +what is the uh now you can just + + + align:start position:0% +what is the uh now you can just +translate + + align:start position:0% + + + + align:start position:0% + +uh um + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +okay so so this is the one at one point + + align:start position:0% +okay so so this is the one at one point + + + align:start position:0% +okay so so this is the one at one point +and another point and the third point + + align:start position:0% +and another point and the third point + + + align:start position:0% +and another point and the third point +so let me just in order to go to + + align:start position:0% +so let me just in order to go to + + + align:start position:0% +so let me just in order to go to +momentum space let's just mention + + align:start position:0% +momentum space let's just mention + + + align:start position:0% +momentum space let's just mention +several points + + align:start position:0% +several points + + + align:start position:0% +several points +so yeah anyway so here is one point + + align:start position:0% +so yeah anyway so here is one point + + + align:start position:0% +so yeah anyway so here is one point +and then here is other point + + align:start position:0% +and then here is other point + + + align:start position:0% +and then here is other point +and also now let's look at the vertex + + align:start position:0% +and also now let's look at the vertex + + + align:start position:0% +and also now let's look at the vertex +okay + + align:start position:0% + + + + align:start position:0% + +so each vertex + + align:start position:0% + + + + align:start position:0% + +we have integration + + align:start position:0% + + + + align:start position:0% + +so suppose we have vertex like this + + align:start position:0% +so suppose we have vertex like this + + + align:start position:0% +so suppose we have vertex like this +so here is X and this is contracted with + + align:start position:0% +so here is X and this is contracted with + + + align:start position:0% +so here is X and this is contracted with +y1 by 2 by 3 by 4 okay so let's imagine + + align:start position:0% +y1 by 2 by 3 by 4 okay so let's imagine + + + align:start position:0% +y1 by 2 by 3 by 4 okay so let's imagine +so we have a voltage like this this four + + align:start position:0% +so we have a voltage like this this four + + + align:start position:0% +so we have a voltage like this this four +five is contracted with four different + + align:start position:0% +five is contracted with four different + + + align:start position:0% +five is contracted with four different +y's okay + + align:start position:0% +y's okay + + + align:start position:0% +y's okay +and then + + align:start position:0% +and then + + + align:start position:0% +and then +and then we will have expression at such + + align:start position:0% +and then we will have expression at such + + + align:start position:0% +and then we will have expression at such +a Vertex then we will have expressed + + align:start position:0% +a Vertex then we will have expressed + + + align:start position:0% +a Vertex then we will have expressed +like this gf0 + + align:start position:0% +like this gf0 + + + align:start position:0% +like this gf0 +x minus y1 + + align:start position:0% + + + + align:start position:0% + +GF + + align:start position:0% +GF + + + align:start position:0% +GF +0 x minus Y2 + + align:start position:0% +0 x minus Y2 + + + align:start position:0% +0 x minus Y2 +and G of 0. + + align:start position:0% +and G of 0. + + + align:start position:0% +and G of 0. +x minus Y3 + + align:start position:0% +x minus Y3 + + + align:start position:0% +x minus Y3 +hf0 + + align:start position:0% + + + + align:start position:0% + +x minus y4 okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and now again + + align:start position:0% +and now again + + + align:start position:0% +and now again +so now when you plug in the expression + + align:start position:0% +so now when you plug in the expression + + + align:start position:0% +so now when you plug in the expression +okay + + align:start position:0% + + + + align:start position:0% + +so now if you plug in the expression so + + align:start position:0% +so now if you plug in the expression so + + + align:start position:0% +so now if you plug in the expression so +uh so I will not write all the lines + + align:start position:0% +uh so I will not write all the lines + + + align:start position:0% +uh so I will not write all the lines +here I think you will just see the see + + align:start position:0% +here I think you will just see the see + + + align:start position:0% +here I think you will just see the see +the basic idea + + align:start position:0% + + + + align:start position:0% + +so this one if you write now that let's + + align:start position:0% +so this one if you write now that let's + + + align:start position:0% +so this one if you write now that let's +write each of them in terms of momentum + + align:start position:0% +write each of them in terms of momentum + + + align:start position:0% +write each of them in terms of momentum +space + + align:start position:0% +space + + + align:start position:0% +space +okay so so this if you write in terms of + + align:start position:0% +okay so so this if you write in terms of + + + align:start position:0% +okay so so this if you write in terms of +momentum space then you get a D4 K1 + + align:start position:0% +momentum space then you get a D4 K1 + + + align:start position:0% +momentum space then you get a D4 K1 +K1 + + align:start position:0% + + + + align:start position:0% + +times x minus y1 + + align:start position:0% +times x minus y1 + + + align:start position:0% +times x minus y1 +then GF + + align:start position:0% +then GF + + + align:start position:0% +then GF +zero K1 + + align:start position:0% +zero K1 + + + align:start position:0% +zero K1 +okay and similarly for that and for that + + align:start position:0% +okay and similarly for that and for that + + + align:start position:0% +okay and similarly for that and for that +for that okay + + align:start position:0% + + + + align:start position:0% + +so now you have + + align:start position:0% +so now you have + + + align:start position:0% +so now you have +and now these have expressed ik1 so this + + align:start position:0% +and now these have expressed ik1 so this + + + align:start position:0% +and now these have expressed ik1 so this +has explained to ik2 so this will + + align:start position:0% +has explained to ik2 so this will + + + align:start position:0% +has explained to ik2 so this will +explain your nk3x and this has k4x + + align:start position:0% +explain your nk3x and this has k4x + + + align:start position:0% +explain your nk3x and this has k4x +and there's no other X dependence + + align:start position:0% +and there's no other X dependence + + + align:start position:0% +and there's no other X dependence +and then you have a d4x here okay so + + align:start position:0% +and then you have a d4x here okay so + + + align:start position:0% +and then you have a d4x here okay so +what you get then you just get the data + + align:start position:0% +what you get then you just get the data + + + align:start position:0% +what you get then you just get the data +function + + align:start position:0% + + + + align:start position:0% + +so I just get the data function + + align:start position:0% +so I just get the data function + + + align:start position:0% +so I just get the data function +so into that first when you do that when + + align:start position:0% +so into that first when you do that when + + + align:start position:0% +so into that first when you do that when +you go to momentum space then you find + + align:start position:0% +you go to momentum space then you find + + + align:start position:0% +you go to momentum space then you find +that this should always be proportional + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that means momentum + + align:start position:0% + + + + align:start position:0% + +is conserved + + align:start position:0% + + + + align:start position:0% + +at each vertex + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so if I choose + + align:start position:0% + + + + align:start position:0% + +say K1 here + + align:start position:0% +say K1 here + + + align:start position:0% +say K1 here +K2 + + align:start position:0% +K2 + + + align:start position:0% +K2 +K3 + + align:start position:0% +K3 + + + align:start position:0% +K3 +so I use the same convention for all of + + align:start position:0% +so I use the same convention for all of + + + align:start position:0% +so I use the same convention for all of +them it doesn't matter whether you do it + + align:start position:0% +them it doesn't matter whether you do it + + + align:start position:0% +them it doesn't matter whether you do it +outgoing or in-going but but we draw the + + align:start position:0% +outgoing or in-going but but we draw the + + + align:start position:0% +outgoing or in-going but but we draw the +same commission for all of them and then + + align:start position:0% +same commission for all of them and then + + + align:start position:0% +same commission for all of them and then +then they should have to be + + align:start position:0% +then they should have to be + + + align:start position:0% +then they should have to be +then then there should be proponential + + align:start position:0% +then then there should be proponential + + + align:start position:0% +then then there should be proponential +to a factor of this okay + + align:start position:0% + + + + align:start position:0% + +and here it doesn't matter what is y1 + + align:start position:0% +and here it doesn't matter what is y1 + + + align:start position:0% +and here it doesn't matter what is y1 +okay y i so so y by two by three by four + + align:start position:0% +okay y i so so y by two by three by four + + + align:start position:0% +okay y i so so y by two by three by four +there can either be some external point + + align:start position:0% +there can either be some external point + + + align:start position:0% +there can either be some external point +or some other internal Point okay + + align:start position:0% + + + + align:start position:0% + +okay yes + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +expectation values of the momentum field + + align:start position:0% +expectation values of the momentum field + + + align:start position:0% +expectation values of the momentum field +operators + + align:start position:0% +operators + + + align:start position:0% +operators +like five + + align:start position:0% + + + + align:start position:0% + +yeah yeah you can yeah you can + + align:start position:0% + + + + align:start position:0% + +yeah you you yeah not yeah so this is + + align:start position:0% +yeah you you yeah not yeah so this is + + + align:start position:0% +yeah you you yeah not yeah so this is +strictly defined in terms of the uh uh + + align:start position:0% +strictly defined in terms of the uh uh + + + align:start position:0% +strictly defined in terms of the uh uh +um yeah so + + align:start position:0% +um yeah so + + + align:start position:0% +um yeah so +no you cannot write that way in the + + align:start position:0% +no you cannot write that way in the + + + align:start position:0% +no you cannot write that way in the +sense that the uh not as a whole + + align:start position:0% +sense that the uh not as a whole + + + align:start position:0% +sense that the uh not as a whole +momentum yeah yeah + + align:start position:0% + + + + align:start position:0% + +you really have to find the final + + align:start position:0% +you really have to find the final + + + align:start position:0% +you really have to find the final +expression and do the do the uh yeah + + align:start position:0% +expression and do the do the uh yeah + + + align:start position:0% +expression and do the do the uh yeah +yeah for the white function you can not + + align:start position:0% +yeah for the white function you can not + + + align:start position:0% +yeah for the white function you can not +for the time ordered + + align:start position:0% +for the time ordered + + + align:start position:0% +for the time ordered +function you can + + align:start position:0% + + + + align:start position:0% + +okay good + + align:start position:0% +okay good + + + align:start position:0% +okay good +so now we can write down + + align:start position:0% + + + + align:start position:0% + +the momentum Space by my rule + + align:start position:0% + + + + align:start position:0% + +and it will not we will not have time to + + align:start position:0% +and it will not we will not have time to + + + align:start position:0% +and it will not we will not have time to +to do it to do a example let me just + + align:start position:0% +to do it to do a example let me just + + + align:start position:0% +to do it to do a example let me just +write them down and then we will look at + + align:start position:0% +write them down and then we will look at + + + align:start position:0% +write them down and then we will look at +the example next time + + align:start position:0% +the example next time + + + align:start position:0% +the example next time +so um + + align:start position:0% + + + + align:start position:0% + +so yeah so here is the rule to compute + + align:start position:0% + + + + align:start position:0% + +this GM P1 + + align:start position:0% +this GM P1 + + + align:start position:0% +this GM P1 +PM okay + + align:start position:0% +PM okay + + + align:start position:0% +PM okay +we we use the following rule + + align:start position:0% + + + + align:start position:0% + +so first + + align:start position:0% +so first + + + align:start position:0% +so first +for each external point + + align:start position:0% + + + + align:start position:0% + +and now you just can associate + + align:start position:0% +and now you just can associate + + + align:start position:0% +and now you just can associate +say a momentum okay uh respect to that + + align:start position:0% +say a momentum okay uh respect to that + + + align:start position:0% +say a momentum okay uh respect to that +momentum and you you can associate with + + align:start position:0% +momentum and you you can associate with + + + align:start position:0% +momentum and you you can associate with +the factor one and then and then you + + align:start position:0% +the factor one and then and then you + + + align:start position:0% +the factor one and then and then you +draw a line okay still draw a line but + + align:start position:0% +draw a line okay still draw a line but + + + align:start position:0% +draw a line okay still draw a line but +now you associate the momentum with this + + align:start position:0% +now you associate the momentum with this + + + align:start position:0% +now you associate the momentum with this +line okay because when you free + + align:start position:0% +line okay because when you free + + + align:start position:0% +line okay because when you free +transform this line you will have + + align:start position:0% +transform this line you will have + + + align:start position:0% +transform this line you will have +movement so + + align:start position:0% +movement so + + + align:start position:0% +movement so +and for each propagator + + align:start position:0% + + + + align:start position:0% + +again the propagated is given by this so + + align:start position:0% +again the propagated is given by this so + + + align:start position:0% +again the propagated is given by this so +now you have a momentum + + align:start position:0% +now you have a momentum + + + align:start position:0% +now you have a momentum +and then this is equivalent by the + + align:start position:0% +and then this is equivalent by the + + + align:start position:0% +and then this is equivalent by the +momentum space + + align:start position:0% +momentum space + + + align:start position:0% +momentum space +p squared plus M Square minus Epsilon + + align:start position:0% +p squared plus M Square minus Epsilon + + + align:start position:0% +p squared plus M Square minus Epsilon +and then now for each + + align:start position:0% +and then now for each + + + align:start position:0% +and then now for each +vertex + + align:start position:0% + + + + align:start position:0% + +you have a + + align:start position:0% +you have a + + + align:start position:0% +you have a +factor of a Lambda + + align:start position:0% +factor of a Lambda + + + align:start position:0% +factor of a Lambda +and then you impose momentum + + align:start position:0% +and then you impose momentum + + + align:start position:0% +and then you impose momentum +conservation + + align:start position:0% + + + + align:start position:0% + +okay at each vertex + + align:start position:0% +okay at each vertex + + + align:start position:0% +okay at each vertex +okay + + align:start position:0% + + + + align:start position:0% + +so now remember + + align:start position:0% +so now remember + + + align:start position:0% +so now remember +when we do a three transform + + align:start position:0% +when we do a three transform + + + align:start position:0% +when we do a three transform +each propagator each line will have a + + align:start position:0% +each propagator each line will have a + + + align:start position:0% +each propagator each line will have a +momentum integration + + align:start position:0% +momentum integration + + + align:start position:0% +momentum integration +okay because because the uh each one of + + align:start position:0% +okay because because the uh each one of + + + align:start position:0% +okay because because the uh each one of +them is integrated over momentum okay so + + align:start position:0% +them is integrated over momentum okay so + + + align:start position:0% +them is integrated over momentum okay so +each one of them is associated with the + + align:start position:0% +each one of them is associated with the + + + align:start position:0% +each one of them is associated with the +momentum integration + + align:start position:0% +momentum integration + + + align:start position:0% +momentum integration +and now some of those momentum + + align:start position:0% +and now some of those momentum + + + align:start position:0% +and now some of those momentum +integration will can be get rid of by + + align:start position:0% +integration will can be get rid of by + + + align:start position:0% +integration will can be get rid of by +impose the data function at the vertex + + align:start position:0% +impose the data function at the vertex + + + align:start position:0% +impose the data function at the vertex +okay so you can get rid of some of them + + align:start position:0% +okay so you can get rid of some of them + + + align:start position:0% +okay so you can get rid of some of them +and by uh uh by momentum conservation at + + align:start position:0% +and by uh uh by momentum conservation at + + + align:start position:0% +and by uh uh by momentum conservation at +all times using the data functions + + align:start position:0% +all times using the data functions + + + align:start position:0% +all times using the data functions +so so but now you will have say a number + + align:start position:0% +so so but now you will have say a number + + + align:start position:0% +so so but now you will have say a number +of them left okay so so then you need to + + align:start position:0% +of them left okay so so then you need to + + + align:start position:0% +of them left okay so so then you need to +integrate over + + align:start position:0% + + + + align:start position:0% + +each on the each undetermined moment + + align:start position:0% + + + + align:start position:0% + +okay so each undeterminate momentum + + align:start position:0% +okay so each undeterminate momentum + + + align:start position:0% +okay so each undeterminate momentum +you need to integrate with this Factor + + align:start position:0% +you need to integrate with this Factor + + + align:start position:0% +you need to integrate with this Factor +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then the same thing you need to + + align:start position:0% +and then the same thing you need to + + + align:start position:0% +and then the same thing you need to +divide it by symmetry Factor + + align:start position:0% +divide it by symmetry Factor + + + align:start position:0% +divide it by symmetry Factor +so symmetry value is the same encoding + + align:start position:0% +so symmetry value is the same encoding + + + align:start position:0% +so symmetry value is the same encoding +that or or or in momentum space + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +okay so so this is the way which you uh + + align:start position:0% +okay so so this is the way which you uh + + + align:start position:0% +okay so so this is the way which you uh +uh I can write down the momentum space + + align:start position:0% +uh I can write down the momentum space + + + align:start position:0% +uh I can write down the momentum space +expression for each timer + + align:start position:0% +expression for each timer + + + align:start position:0% +expression for each timer +okay a momentum space expression for + + align:start position:0% +okay a momentum space expression for + + + align:start position:0% +okay a momentum space expression for +each step + + align:start position:0% +each step + + + align:start position:0% +each step +actually maybe we still have some time + + align:start position:0% +actually maybe we still have some time + + + align:start position:0% +actually maybe we still have some time +so so so we have a couple minutes + + align:start position:0% +so so so we have a couple minutes + + + align:start position:0% +so so so we have a couple minutes +so we can just do this example + + align:start position:0% + + + + align:start position:0% + +we can just do this example + + align:start position:0% +we can just do this example + + + align:start position:0% +we can just do this example +okay so this example let's see what it + + align:start position:0% +okay so this example let's see what it + + + align:start position:0% +okay so this example let's see what it +looks like in momentum space + + align:start position:0% +looks like in momentum space + + + align:start position:0% +looks like in momentum space +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so in momentum space + + align:start position:0% + + + + align:start position:0% + +we just + + align:start position:0% + + + + align:start position:0% + +could have erase the background + + align:start position:0% + + + + align:start position:0% + +so this diagram looks like this + + align:start position:0% +so this diagram looks like this + + + align:start position:0% +so this diagram looks like this +in coordinate space + + align:start position:0% +in coordinate space + + + align:start position:0% +in coordinate space +of X1 X2 and X and Y okay + + align:start position:0% +of X1 X2 and X and Y okay + + + align:start position:0% +of X1 X2 and X and Y okay +so now when we go to momentum space + + align:start position:0% + + + + align:start position:0% + +we just put the diagram is the same + + align:start position:0% +we just put the diagram is the same + + + align:start position:0% +we just put the diagram is the same +just now we label the momentum + + align:start position:0% +just now we label the momentum + + + align:start position:0% +just now we label the momentum +okay so so we have external line here + + align:start position:0% +okay so so we have external line here + + + align:start position:0% +okay so so we have external line here +internal Point here so here I have a + + align:start position:0% +internal Point here so here I have a + + + align:start position:0% +internal Point here so here I have a +momentum P1 + + align:start position:0% +momentum P1 + + + align:start position:0% +momentum P1 +here momentum P2 okay + + align:start position:0% +here momentum P2 okay + + + align:start position:0% +here momentum P2 okay +so now let's just call the say this K1 + + align:start position:0% +so now let's just call the say this K1 + + + align:start position:0% +so now let's just call the say this K1 +okay too you can assign momentum + + align:start position:0% +okay too you can assign momentum + + + align:start position:0% +okay too you can assign momentum +direction as you want okay say K3 okay + + align:start position:0% +direction as you want okay say K3 okay + + + align:start position:0% +direction as you want okay say K3 okay +so now we need to impose a momentum + + align:start position:0% +so now we need to impose a momentum + + + align:start position:0% +so now we need to impose a momentum +conversation + + align:start position:0% +conversation + + + align:start position:0% +conversation +so momentum flow like that so that means + + align:start position:0% +so momentum flow like that so that means + + + align:start position:0% +so momentum flow like that so that means +that the P1 should be equal to K1 plus + + align:start position:0% +that the P1 should be equal to K1 plus + + + align:start position:0% +that the P1 should be equal to K1 plus +K2 plus K3 + + align:start position:0% +K2 plus K3 + + + align:start position:0% +K2 plus K3 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh from the momentum conversation at + + align:start position:0% +uh from the momentum conversation at + + + align:start position:0% +uh from the momentum conversation at +this vertex + + align:start position:0% +this vertex + + + align:start position:0% +this vertex +and for momentum mode calibration at the + + align:start position:0% +and for momentum mode calibration at the + + + align:start position:0% +and for momentum mode calibration at the +boat this vertex they all go away from + + align:start position:0% +boat this vertex they all go away from + + + align:start position:0% +boat this vertex they all go away from +this vertex and then in this case then + + align:start position:0% +this vertex and then in this case then + + + align:start position:0% +this vertex and then in this case then +the P2 will be minus + + align:start position:0% +the P2 will be minus + + + align:start position:0% +the P2 will be minus +okay one plus K2 plus K3 + + align:start position:0% +okay one plus K2 plus K3 + + + align:start position:0% +okay one plus K2 plus K3 +okay so that means actually P2 should be + + align:start position:0% +okay so that means actually P2 should be + + + align:start position:0% +okay so that means actually P2 should be +equal to minus P1 + + align:start position:0% +equal to minus P1 + + + align:start position:0% +equal to minus P1 +so this makes perfect sense because here + + align:start position:0% +so this makes perfect sense because here + + + align:start position:0% +so this makes perfect sense because here +preserves momentum and preserves + + align:start position:0% +preserves momentum and preserves + + + align:start position:0% +preserves momentum and preserves +momentum so for momentum conversation if + + align:start position:0% +momentum so for momentum conversation if + + + align:start position:0% +momentum so for momentum conversation if +you have P1 here here it should also + + align:start position:0% +you have P1 here here it should also + + + align:start position:0% +you have P1 here here it should also +have P1 okay so so P2 by 2 will be + + align:start position:0% +have P1 okay so so P2 by 2 will be + + + align:start position:0% +have P1 okay so so P2 by 2 will be +selective sign and so we have electric + + align:start position:0% +selective sign and so we have electric + + + align:start position:0% +selective sign and so we have electric +P1 okay + + align:start position:0% + + + + align:start position:0% + +so and now we can yeah so so using this + + align:start position:0% +so and now we can yeah so so using this + + + align:start position:0% +so and now we can yeah so so using this +simplified notation + + align:start position:0% + + + + align:start position:0% + +a diagram like this + + align:start position:0% + + + + align:start position:0% + +okay so so here is p + + align:start position:0% +okay so so here is p + + + align:start position:0% +okay so so here is p +so this code is k1 + + align:start position:0% +so this code is k1 + + + align:start position:0% +so this code is k1 +K2 and in this case 3 can be solved in + + align:start position:0% +K2 and in this case 3 can be solved in + + + align:start position:0% +K2 and in this case 3 can be solved in +terms of the K1 K2 so this is just the P + + align:start position:0% +terms of the K1 K2 so this is just the P + + + align:start position:0% +terms of the K1 K2 so this is just the P +minus K1 T2 + + align:start position:0% +minus K1 T2 + + + align:start position:0% +minus K1 T2 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this is the P minus K1 K2 so now you + + align:start position:0% +so this is the P minus K1 K2 so now you + + + align:start position:0% +so this is the P minus K1 K2 so now you +can just write down the momentum series + + align:start position:0% +can just write down the momentum series + + + align:start position:0% +can just write down the momentum series +expression + + align:start position:0% + + + + align:start position:0% + +so we have minus cylinder we have two + + align:start position:0% +so we have minus cylinder we have two + + + align:start position:0% +so we have minus cylinder we have two +vertex we have two minus Lambda Square + + align:start position:0% +vertex we have two minus Lambda Square + + + align:start position:0% +vertex we have two minus Lambda Square +then we have two on the pelvic momentum + + align:start position:0% +then we have two on the pelvic momentum + + + align:start position:0% +then we have two on the pelvic momentum +K1 K2 because P1 and P and this P should + + align:start position:0% +K1 K2 because P1 and P and this P should + + + align:start position:0% +K1 K2 because P1 and P and this P should +be external momentum should be fixed + + align:start position:0% +be external momentum should be fixed + + + align:start position:0% +be external momentum should be fixed +okay so so we have + + align:start position:0% +okay so so we have + + + align:start position:0% +okay so so we have +okay one + + align:start position:0% + + + + align:start position:0% + +into K2 + + align:start position:0% + + + + align:start position:0% + +and then we just write down each of + + align:start position:0% +and then we just write down each of + + + align:start position:0% +and then we just write down each of +Greater okay so so we just write down + + align:start position:0% +Greater okay so so we just write down + + + align:start position:0% +Greater okay so so we just write down +each propagator so we just have + + align:start position:0% +each propagator so we just have + + + align:start position:0% +each propagator so we just have +minus I + + align:start position:0% +minus I + + + align:start position:0% +minus I +K 1 square plus M Square minus Epsilon + + align:start position:0% +K 1 square plus M Square minus Epsilon + + + align:start position:0% +K 1 square plus M Square minus Epsilon +corresponding to this one then I have + + align:start position:0% +corresponding to this one then I have + + + align:start position:0% +corresponding to this one then I have +minus I K1 K2 Square + + align:start position:0% +minus I K1 K2 Square + + + align:start position:0% +minus I K1 K2 Square +plus M Square + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +times + + align:start position:0% +times + + + align:start position:0% +times +minus I + + align:start position:0% +minus I + + + align:start position:0% +minus I +P minus K1 K2 Square + + align:start position:0% +P minus K1 K2 Square + + + align:start position:0% +P minus K1 K2 Square +plus N squared + + align:start position:0% +plus N squared + + + align:start position:0% +plus N squared +minus Epsilon + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then then this other depends on the + + align:start position:0% +and then then this other depends on the + + + align:start position:0% +and then then this other depends on the +k + + align:start position:0% +k + + + align:start position:0% +k +and then we have two factors + + align:start position:0% +and then we have two factors + + + align:start position:0% +and then we have two factors +so this + + align:start position:0% +so this + + + align:start position:0% +so this +times these two external factors + + align:start position:0% +times these two external factors + + + align:start position:0% +times these two external factors +so this is minus they have the same + + align:start position:0% +so this is minus they have the same + + + align:start position:0% +so this is minus they have the same +momentum so we have just have p square + + align:start position:0% +momentum so we have just have p square + + + align:start position:0% +momentum so we have just have p square +plus M Square minus Epsilon squared + + align:start position:0% +plus M Square minus Epsilon squared + + + align:start position:0% +plus M Square minus Epsilon squared +okay and then we divide it by three + + align:start position:0% +okay and then we divide it by three + + + align:start position:0% +okay and then we divide it by three +factorial corresponding to the symmetric + + align:start position:0% +factorial corresponding to the symmetric + + + align:start position:0% +factorial corresponding to the symmetric +Factor symmetry factors okay that's it + + align:start position:0% +Factor symmetry factors okay that's it + + + align:start position:0% +Factor symmetry factors okay that's it +so so this is the expression + + align:start position:0% +so so this is the expression + + + align:start position:0% +so so this is the expression +for this diagram in momentum space okay + + align:start position:0% + + + + align:start position:0% + +okay so let's uh stop here \ No newline at end of file diff --git a/pWXh5t-37Qg.txt b/pWXh5t-37Qg.txt new file mode 100644 index 0000000000000000000000000000000000000000..f2a69395641b4998118e6241199b610721efcf59 --- /dev/null +++ b/pWXh5t-37Qg.txt @@ -0,0 +1,2179 @@ +align:start position:0% + +Welcome back to recitation. In this + + align:start position:0% +Welcome back to recitation. In this + + + align:start position:0% +Welcome back to recitation. In this +video, I'd like us to practice + + align:start position:0% +video, I'd like us to practice + + + align:start position:0% +video, I'd like us to practice +integration by parts. Specifically, I'd + + align:start position:0% +integration by parts. Specifically, I'd + + + align:start position:0% +integration by parts. Specifically, I'd +like to solve the following four + + align:start position:0% +like to solve the following four + + + align:start position:0% +like to solve the following four +problems, or I'd like you to solve the + + align:start position:0% +problems, or I'd like you to solve the + + + align:start position:0% +problems, or I'd like you to solve the +following four + + align:start position:0% +following four + + + align:start position:0% +following four +problems. I'd like us to find + + align:start position:0% +problems. I'd like us to find + + + align:start position:0% +problems. I'd like us to find +anti-derivatives for each of these + + align:start position:0% +anti-derivatives for each of these + + + align:start position:0% +anti-derivatives for each of these +functions. x e minus x x cub over the + + align:start position:0% +functions. x e minus x x cub over the + + + align:start position:0% +functions. x e minus x x cub over the +quantity 1 + + + align:start position:0% +quantity 1 + + + + align:start position:0% +quantity 1 + +x^2 arc tan x and natural log + + align:start position:0% +x^2 arc tan x and natural log + + + align:start position:0% +x^2 arc tan x and natural log +x^2. And so the main goal because we're + + align:start position:0% +x^2. And so the main goal because we're + + + align:start position:0% +x^2. And so the main goal because we're +using integration by parts is to figure + + align:start position:0% +using integration by parts is to figure + + + align:start position:0% +using integration by parts is to figure +out what you should make u and what you + + align:start position:0% +out what you should make u and what you + + + align:start position:0% +out what you should make u and what you +should make v prime. And why don't you + + align:start position:0% +should make v prime. And why don't you + + + align:start position:0% +should make v prime. And why don't you +give it a shot, work on that for a + + align:start position:0% +give it a shot, work on that for a + + + align:start position:0% +give it a shot, work on that for a +little bit. I'm actually going to give + + align:start position:0% +little bit. I'm actually going to give + + + align:start position:0% +little bit. I'm actually going to give +you one hint, and that's that this one + + align:start position:0% +you one hint, and that's that this one + + + align:start position:0% +you one hint, and that's that this one +you may want to break up in a + + align:start position:0% +you may want to break up in a + + + align:start position:0% +you may want to break up in a +non-traditional way. You may not want to + + align:start position:0% +non-traditional way. You may not want to + + + align:start position:0% +non-traditional way. You may not want to +break it up as x cubed and one over this + + align:start position:0% +break it up as x cubed and one over this + + + align:start position:0% +break it up as x cubed and one over this +function. You're going to want to split + + align:start position:0% +function. You're going to want to split + + + align:start position:0% +function. You're going to want to split +up this function in the numerator. Part + + align:start position:0% +up this function in the numerator. Part + + + align:start position:0% +up this function in the numerator. Part +of it will be in u, part of it will be + + align:start position:0% +of it will be in u, part of it will be + + + align:start position:0% +of it will be in u, part of it will be +in v prime. So that's my hint on number + + align:start position:0% +in v prime. So that's my hint on number + + + align:start position:0% +in v prime. So that's my hint on number +two. So now with that information, I'd + + align:start position:0% +two. So now with that information, I'd + + + align:start position:0% +two. So now with that information, I'd +like you to give it a shot and then I'll + + align:start position:0% +like you to give it a shot and then I'll + + + align:start position:0% +like you to give it a shot and then I'll +come back and I'll show you how I do + + align:start position:0% + + + + align:start position:0% + +it. Okay, welcome back. So again, what + + align:start position:0% +it. Okay, welcome back. So again, what + + + align:start position:0% +it. Okay, welcome back. So again, what +we're looking for is anti-derivatives + + align:start position:0% +we're looking for is anti-derivatives + + + align:start position:0% +we're looking for is anti-derivatives +for each of these uh each of these four + + align:start position:0% +for each of these uh each of these four + + + align:start position:0% +for each of these uh each of these four +functions. And now what I'm going to do + + align:start position:0% +functions. And now what I'm going to do + + + align:start position:0% +functions. And now what I'm going to do +is I'm going to help you pick u and v + + align:start position:0% +is I'm going to help you pick u and v + + + align:start position:0% +is I'm going to help you pick u and v +prime. And then I'm going to show you + + align:start position:0% +prime. And then I'm going to show you + + + align:start position:0% +prime. And then I'm going to show you +what answer I got. And I'm going to let + + align:start position:0% +what answer I got. And I'm going to let + + + align:start position:0% +what answer I got. And I'm going to let +you do the work in the middle. So let's + + align:start position:0% +you do the work in the middle. So let's + + + align:start position:0% +you do the work in the middle. So let's +start off with number one. + + align:start position:0% + + + + align:start position:0% + +So if I have x e the minus x integral of + + align:start position:0% +So if I have x e the minus x integral of + + + align:start position:0% +So if I have x e the minus x integral of +x e minus x + + align:start position:0% +x e minus x + + + align:start position:0% +x e minus x +dx, it's very easy to do either to make + + align:start position:0% +dx, it's very easy to do either to make + + + align:start position:0% +dx, it's very easy to do either to make +e the minus x either u or v prime. + + align:start position:0% +e the minus x either u or v prime. + + + align:start position:0% +e the minus x either u or v prime. +Doesn't really matter because an + + align:start position:0% +Doesn't really matter because an + + + align:start position:0% +Doesn't really matter because an +integral of e to the minus x is going to + + align:start position:0% +integral of e to the minus x is going to + + + align:start position:0% +integral of e to the minus x is going to +have an e to the minus x again. And a + + align:start position:0% +have an e to the minus x again. And a + + + align:start position:0% +have an e to the minus x again. And a +derivative is going to have an e to the + + align:start position:0% +derivative is going to have an e to the + + + align:start position:0% +derivative is going to have an e to the +minus x again with a minus sign in front + + align:start position:0% +minus x again with a minus sign in front + + + align:start position:0% +minus x again with a minus sign in front +in both cases. But this doesn't really + + align:start position:0% +in both cases. But this doesn't really + + + align:start position:0% +in both cases. But this doesn't really +change. So we have a when we go up or + + align:start position:0% +change. So we have a when we go up or + + + align:start position:0% +change. So we have a when we go up or +down it doesn't really matter if we + + align:start position:0% +down it doesn't really matter if we + + + align:start position:0% +down it doesn't really matter if we +integrate up or take a derivative. So + + align:start position:0% +integrate up or take a derivative. So + + + align:start position:0% +integrate up or take a derivative. So +really it's we get to pick what we do + + align:start position:0% +really it's we get to pick what we do + + + align:start position:0% +really it's we get to pick what we do +with the c to the minus x based on what + + align:start position:0% +with the c to the minus x based on what + + + align:start position:0% +with the c to the minus x based on what +we want to do with the x. Well we like + + align:start position:0% +we want to do with the x. Well we like + + + align:start position:0% +we want to do with the x. Well we like +taking derivatives of things that don't + + align:start position:0% +taking derivatives of things that don't + + + align:start position:0% +taking derivatives of things that don't +have two functions of x. So it'd be nice + + align:start position:0% +have two functions of x. So it'd be nice + + + align:start position:0% +have two functions of x. So it'd be nice +if we chose our integration by parts + + align:start position:0% +if we chose our integration by parts + + + align:start position:0% +if we chose our integration by parts +pieces so that this thing wasn't there + + align:start position:0% +pieces so that this thing wasn't there + + + align:start position:0% +pieces so that this thing wasn't there +anymore. So let me write down actually + + align:start position:0% +anymore. So let me write down actually + + + align:start position:0% +anymore. So let me write down actually +before I even do number one maybe I + + align:start position:0% +before I even do number one maybe I + + + align:start position:0% +before I even do number one maybe I +should remind you what in the + + align:start position:0% +should remind you what in the + + + align:start position:0% +should remind you what in the +integration by parts formula is. So let + + align:start position:0% +integration by parts formula is. So let + + + align:start position:0% +integration by parts formula is. So let +me just I'll just just scratch that out + + align:start position:0% +me just I'll just just scratch that out + + + align:start position:0% +me just I'll just just scratch that out +for a second. And what we're doing is + + align:start position:0% +for a second. And what we're doing is + + + align:start position:0% +for a second. And what we're doing is +we're going to have integral of uv prime + + align:start position:0% +we're going to have integral of uv prime + + + align:start position:0% +we're going to have integral of uv prime +dx. And if you recall what you saw in + + align:start position:0% +dx. And if you recall what you saw in + + + align:start position:0% +dx. And if you recall what you saw in +lecture is this should be equal to uv + + align:start position:0% +lecture is this should be equal to uv + + + align:start position:0% +lecture is this should be equal to uv +minus the integral of v u prime dx. And + + align:start position:0% +minus the integral of v u prime dx. And + + + align:start position:0% +minus the integral of v u prime dx. And +we'll put that plus c because sometimes + + align:start position:0% +we'll put that plus c because sometimes + + + align:start position:0% +we'll put that plus c because sometimes +I forget to write it at the end. So I'll + + align:start position:0% +I forget to write it at the end. So I'll + + + align:start position:0% +I forget to write it at the end. So I'll +put it there so I don't forget. So + + align:start position:0% +put it there so I don't forget. So + + + align:start position:0% +put it there so I don't forget. So +really what we're trying to do right is + + align:start position:0% +really what we're trying to do right is + + + align:start position:0% +really what we're trying to do right is +pick the u and v prime. And so we want + + align:start position:0% +pick the u and v prime. And so we want + + + align:start position:0% +pick the u and v prime. And so we want +to make this this thing this v u prime + + align:start position:0% +to make this this thing this v u prime + + + align:start position:0% +to make this this thing this v u prime +as simple as possible. So what I was + + align:start position:0% +as simple as possible. So what I was + + + align:start position:0% +as simple as possible. So what I was +saying is if we make this V prime or + + align:start position:0% +saying is if we make this V prime or + + + align:start position:0% +saying is if we make this V prime or +this U, it doesn't matter. So let's pick + + align:start position:0% +this U, it doesn't matter. So let's pick + + + align:start position:0% +this U, it doesn't matter. So let's pick +this. Let's pick whether we want this to + + align:start position:0% +this. Let's pick whether we want this to + + + align:start position:0% +this. Let's pick whether we want this to +be U or V prime. Well, if I make this U, + + align:start position:0% +be U or V prime. Well, if I make this U, + + + align:start position:0% +be U or V prime. Well, if I make this U, +then U prime is one. That's good. If I + + align:start position:0% +then U prime is one. That's good. If I + + + align:start position:0% +then U prime is one. That's good. If I +make it V prime, then V is X^2 over two. + + align:start position:0% +make it V prime, then V is X^2 over two. + + + align:start position:0% +make it V prime, then V is X^2 over two. +That's more complicated. So we obviously + + align:start position:0% +That's more complicated. So we obviously + + + align:start position:0% +That's more complicated. So we obviously +want to make this U. So for number one, + + align:start position:0% +want to make this U. So for number one, + + + align:start position:0% +want to make this U. So for number one, +we're going to choose U is equal to X + + align:start position:0% +we're going to choose U is equal to X + + + align:start position:0% +we're going to choose U is equal to X +and V prime is equal to E minus X. + + align:start position:0% +and V prime is equal to E minus X. + + + align:start position:0% +and V prime is equal to E minus X. +And then you can proceed from there. And + + align:start position:0% +And then you can proceed from there. And + + + align:start position:0% +And then you can proceed from there. And +I I'll leave it at that. Well, actually, + + align:start position:0% +I I'll leave it at that. Well, actually, + + + align:start position:0% +I I'll leave it at that. Well, actually, +just to make sure we're okay, I'll even + + align:start position:0% +just to make sure we're okay, I'll even + + + align:start position:0% +just to make sure we're okay, I'll even +write u prime is equal to 1 and v is + + align:start position:0% +write u prime is equal to 1 and v is + + + align:start position:0% +write u prime is equal to 1 and v is +going to be equal to e to the minus x. + + align:start position:0% +going to be equal to e to the minus x. + + + align:start position:0% +going to be equal to e to the minus x. +So, we'd be able to proceed from there, + + align:start position:0% +So, we'd be able to proceed from there, + + + align:start position:0% +So, we'd be able to proceed from there, +right? We have all the pieces we + + align:start position:0% +right? We have all the pieces we + + + align:start position:0% +right? We have all the pieces we +need. Now, number two, I'll give you the + + align:start position:0% +need. Now, number two, I'll give you the + + + align:start position:0% +need. Now, number two, I'll give you the +final answers at the + + align:start position:0% +final answers at the + + + align:start position:0% +final answers at the +end. Number two, picking u and v prime + + align:start position:0% +end. Number two, picking u and v prime + + + align:start position:0% +end. Number two, picking u and v prime +is a little more complicated. And let's + + align:start position:0% +is a little more complicated. And let's + + + align:start position:0% +is a little more complicated. And let's +look at this + + align:start position:0% +look at this + + + align:start position:0% +look at this +function x cubed over 1 + + + align:start position:0% +function x cubed over 1 + + + + align:start position:0% +function x cubed over 1 + +x^2 + + align:start position:0% +x^2 + + + align:start position:0% +x^2 +squared. The problem with picking that + + align:start position:0% +squared. The problem with picking that + + + align:start position:0% +squared. The problem with picking that +does not look like a two. Sorry. The + + align:start position:0% +does not look like a two. Sorry. The + + + align:start position:0% +does not look like a two. Sorry. The +problem with picking uh u and v prime + + align:start position:0% +problem with picking uh u and v prime + + + align:start position:0% +problem with picking uh u and v prime +here is that it's hard to see what's + + align:start position:0% +here is that it's hard to see what's + + + align:start position:0% +here is that it's hard to see what's +going to be easy to integrate. So what + + align:start position:0% +going to be easy to integrate. So what + + + align:start position:0% +going to be easy to integrate. So what +we want to do is rewrite this as let's + + align:start position:0% +we want to do is rewrite this as let's + + + align:start position:0% +we want to do is rewrite this as let's +see x^2 + + align:start position:0% +see x^2 + + + align:start position:0% +see x^2 +* x over 1 + + + align:start position:0% +* x over 1 + + + + align:start position:0% +* x over 1 + +x^2 + + align:start position:0% +x^2 + + + align:start position:0% +x^2 +squared. And now why is this any better? + + align:start position:0% +squared. And now why is this any better? + + + align:start position:0% +squared. And now why is this any better? +Well, I mean it's the same thing, but + + align:start position:0% +Well, I mean it's the same thing, but + + + align:start position:0% +Well, I mean it's the same thing, but +why does this help us see what we want + + align:start position:0% +why does this help us see what we want + + + align:start position:0% +why does this help us see what we want +to do? Well, if you notice this thing + + align:start position:0% +to do? Well, if you notice this thing + + + align:start position:0% +to do? Well, if you notice this thing +right here, 1 plus x^2, what is its + + align:start position:0% +right here, 1 plus x^2, what is its + + + align:start position:0% +right here, 1 plus x^2, what is its +derivative? Its derivative is 2x. up + + align:start position:0% +derivative? Its derivative is 2x. up + + + align:start position:0% +derivative? Its derivative is 2x. up +here we have an x. So this piece right + + align:start position:0% +here we have an x. So this piece right + + + align:start position:0% +here we have an x. So this piece right +here looks like it could be much more + + align:start position:0% +here looks like it could be much more + + + align:start position:0% +here looks like it could be much more +easily integrated than this right here. + + align:start position:0% +easily integrated than this right here. + + + align:start position:0% +easily integrated than this right here. +So this might be a little + + align:start position:0% +So this might be a little + + + align:start position:0% +So this might be a little +counterintuitive + + align:start position:0% +counterintuitive + + + align:start position:0% +counterintuitive +uh because we're going to take the + + align:start position:0% +uh because we're going to take the + + + align:start position:0% +uh because we're going to take the +harder looking thing and make that our v + + align:start position:0% +harder looking thing and make that our v + + + align:start position:0% +harder looking thing and make that our v +prime. But the nice thing is that that + + align:start position:0% +prime. But the nice thing is that that + + + align:start position:0% +prime. But the nice thing is that that +we can actually integrate this quantity. + + align:start position:0% +we can actually integrate this quantity. + + + align:start position:0% +we can actually integrate this quantity. +So we choose in this case this is our + + align:start position:0% +So we choose in this case this is our + + + align:start position:0% +So we choose in this case this is our +u and this is our v prime. + + align:start position:0% +u and this is our v prime. + + + align:start position:0% +u and this is our v prime. +So how do I integrate this? Well, I + + align:start position:0% +So how do I integrate this? Well, I + + + align:start position:0% +So how do I integrate this? Well, I +integrate this by using a substitution + + align:start position:0% +integrate this by using a substitution + + + align:start position:0% +integrate this by using a substitution +and that will give me v. And the + + align:start position:0% +and that will give me v. And the + + + align:start position:0% +and that will give me v. And the +derivative of this is quite simple. It's + + align:start position:0% +derivative of this is quite simple. It's + + + align:start position:0% +derivative of this is quite simple. It's +just 2x, right? But this is the strategy + + align:start position:0% +just 2x, right? But this is the strategy + + + align:start position:0% +just 2x, right? But this is the strategy +we want here. Why did we even think to + + align:start position:0% +we want here. Why did we even think to + + + align:start position:0% +we want here. Why did we even think to +split that up like that? Well, we knew + + align:start position:0% +split that up like that? Well, we knew + + + align:start position:0% +split that up like that? Well, we knew +we had to deal with the denominator in + + align:start position:0% +we had to deal with the denominator in + + + align:start position:0% +we had to deal with the denominator in +some fashion. And taking a derivative + + align:start position:0% +some fashion. And taking a derivative + + + align:start position:0% +some fashion. And taking a derivative +with this in the denominator. So putting + + align:start position:0% +with this in the denominator. So putting + + + align:start position:0% +with this in the denominator. So putting +putting this part of the function in u + + align:start position:0% +putting this part of the function in u + + + align:start position:0% +putting this part of the function in u +when I look at u prime, it's going to be + + align:start position:0% +when I look at u prime, it's going to be + + + align:start position:0% +when I look at u prime, it's going to be +even worse. It's going to be at a higher + + align:start position:0% +even worse. It's going to be at a higher + + + align:start position:0% +even worse. It's going to be at a higher +power here. It's going to be a cubic in + + align:start position:0% +power here. It's going to be a cubic in + + + align:start position:0% +power here. It's going to be a cubic in +the denominator. That's just making + + align:start position:0% +the denominator. That's just making + + + align:start position:0% +the denominator. That's just making +things worse. So, we know we'd like to + + align:start position:0% +things worse. So, we know we'd like to + + + align:start position:0% +things worse. So, we know we'd like to +integrate this denominator. We'd like it + + align:start position:0% +integrate this denominator. We'd like it + + + align:start position:0% +integrate this denominator. We'd like it +to be a part of V prime. But the problem + + align:start position:0% +to be a part of V prime. But the problem + + + align:start position:0% +to be a part of V prime. But the problem +is that if I put all the x cubed in the + + align:start position:0% +is that if I put all the x cubed in the + + + align:start position:0% +is that if I put all the x cubed in the +u and if I just had a one here for my v + + align:start position:0% +u and if I just had a one here for my v + + + align:start position:0% +u and if I just had a one here for my v +prime, that's I can't really integrate + + align:start position:0% +prime, that's I can't really integrate + + + align:start position:0% +prime, that's I can't really integrate +that very well. But if I keep one of the + + align:start position:0% +that very well. But if I keep one of the + + + align:start position:0% +that very well. But if I keep one of the +x's, then I can integrate this quite + + align:start position:0% +x's, then I can integrate this quite + + + align:start position:0% +x's, then I can integrate this quite +simply with a substitution. So, that's + + align:start position:0% +simply with a substitution. So, that's + + + align:start position:0% +simply with a substitution. So, that's +the that's the sort of reasoning behind + + align:start position:0% +the that's the sort of reasoning behind + + + align:start position:0% +the that's the sort of reasoning behind +why we choose it that way. All right, + + align:start position:0% +why we choose it that way. All right, + + + align:start position:0% +why we choose it that way. All right, +we've got two more to look at and then + + align:start position:0% +we've got two more to look at and then + + + align:start position:0% +we've got two more to look at and then +I'll give you the + + align:start position:0% +I'll give you the + + + align:start position:0% +I'll give you the +answers. Three. Okay, three. You've seen + + align:start position:0% +answers. Three. Okay, three. You've seen + + + align:start position:0% +answers. Three. Okay, three. You've seen +this trick before. The function was arc + + align:start position:0% +this trick before. The function was arc + + + align:start position:0% +this trick before. The function was arc +tan + + align:start position:0% +tan + + + align:start position:0% +tan +x. Now, you've seen this trick I'm about + + align:start position:0% +x. Now, you've seen this trick I'm about + + + align:start position:0% +x. Now, you've seen this trick I'm about +to do with uh with natural log of x. The + + align:start position:0% +to do with uh with natural log of x. The + + + align:start position:0% +to do with uh with natural log of x. The +same kind of thing with natural log of + + align:start position:0% +same kind of thing with natural log of + + + align:start position:0% +same kind of thing with natural log of +x. You actually saw this in one of the + + align:start position:0% +x. You actually saw this in one of the + + + align:start position:0% +x. You actually saw this in one of the +lecture videos because there's only one + + align:start position:0% +lecture videos because there's only one + + + align:start position:0% +lecture videos because there's only one +function here. You might think, well, I + + align:start position:0% +function here. You might think, well, I + + + align:start position:0% +function here. You might think, well, I +have no idea what I'm supposed to pick + + align:start position:0% +have no idea what I'm supposed to pick + + + align:start position:0% +have no idea what I'm supposed to pick +for u and v prime. But remember, it's + + align:start position:0% +for u and v prime. But remember, it's + + + align:start position:0% +for u and v prime. But remember, it's +really arc tan x times 1. Now I have two + + align:start position:0% +really arc tan x times 1. Now I have two + + + align:start position:0% +really arc tan x times 1. Now I have two +functions. And what gives us a hint for + + align:start position:0% +functions. And what gives us a hint for + + + align:start position:0% +functions. And what gives us a hint for +why we would want to do this is that + + align:start position:0% +why we would want to do this is that + + + align:start position:0% +why we would want to do this is that +what's the derivative of arc tan x? Let + + align:start position:0% +what's the derivative of arc tan x? Let + + + align:start position:0% +what's the derivative of arc tan x? Let +me just remind + + align:start position:0% + + + + align:start position:0% + +you ddx of arc tan x is 1 over 1 plus + + align:start position:0% +you ddx of arc tan x is 1 over 1 plus + + + align:start position:0% +you ddx of arc tan x is 1 over 1 plus +x^2. Right? + + align:start position:0% +x^2. Right? + + + align:start position:0% +x^2. Right? +We're back to actually an almost similar + + align:start position:0% +We're back to actually an almost similar + + + align:start position:0% +We're back to actually an almost similar +situation to what we had in the previous + + align:start position:0% +situation to what we had in the previous + + + align:start position:0% +situation to what we had in the previous +thing. ddx of aran x is 1 over 1 plus + + align:start position:0% +thing. ddx of aran x is 1 over 1 plus + + + align:start position:0% +thing. ddx of aran x is 1 over 1 plus +x^2. So taking a derivative of this puts + + align:start position:0% +x^2. So taking a derivative of this puts + + + align:start position:0% +x^2. So taking a derivative of this puts +it in a form that almost looks easy to + + align:start position:0% +it in a form that almost looks easy to + + + align:start position:0% +it in a form that almost looks easy to +integrate. What would make this function + + align:start position:0% +integrate. What would make this function + + + align:start position:0% +integrate. What would make this function +easy to integrate? If there was an x up + + align:start position:0% +easy to integrate? If there was an x up + + + align:start position:0% +easy to integrate? If there was an x up +here instead of a one, then I could use + + align:start position:0% +here instead of a one, then I could use + + + align:start position:0% +here instead of a one, then I could use +substitution. Where do we get that x + + align:start position:0% +substitution. Where do we get that x + + + align:start position:0% +substitution. Where do we get that x +from when we're when we're solving this + + align:start position:0% +from when we're when we're solving this + + + align:start position:0% +from when we're when we're solving this +problem and we're actually taking + + align:start position:0% +problem and we're actually taking + + + align:start position:0% +problem and we're actually taking +finding an anti-derivative of arc tan x? + + align:start position:0% +finding an anti-derivative of arc tan x? + + + align:start position:0% +finding an anti-derivative of arc tan x? +Well, it's going to come from the fact + + align:start position:0% +Well, it's going to come from the fact + + + align:start position:0% +Well, it's going to come from the fact +that I make this U and I make one V + + align:start position:0% +that I make this U and I make one V + + + align:start position:0% +that I make this U and I make one V +prime. So, let me write that out + + align:start position:0% +prime. So, let me write that out + + + align:start position:0% +prime. So, let me write that out +explicitly. U I make arc tan + + align:start position:0% +explicitly. U I make arc tan + + + align:start position:0% +explicitly. U I make arc tan +X and V prime I make one. What does that + + align:start position:0% +X and V prime I make one. What does that + + + align:start position:0% +X and V prime I make one. What does that +do in our formula? Well, we're going to + + align:start position:0% +do in our formula? Well, we're going to + + + align:start position:0% +do in our formula? Well, we're going to +be we're going to be integrating + + align:start position:0% +be we're going to be integrating + + + align:start position:0% +be we're going to be integrating +something that is V u prime. Well, V is + + align:start position:0% +something that is V u prime. Well, V is + + + align:start position:0% +something that is V u prime. Well, V is +going to be X and U prime we see right + + align:start position:0% +going to be X and U prime we see right + + + align:start position:0% +going to be X and U prime we see right +here. So, it's going to be I'm going to + + align:start position:0% +here. So, it's going to be I'm going to + + + align:start position:0% +here. So, it's going to be I'm going to +be integrating x over 1 plus x^2 when I + + align:start position:0% +be integrating x over 1 plus x^2 when I + + + align:start position:0% +be integrating x over 1 plus x^2 when I +start doing the integration by parts + + align:start position:0% +start doing the integration by parts + + + align:start position:0% +start doing the integration by parts +method. That's much simpler as we talked + + align:start position:0% +method. That's much simpler as we talked + + + align:start position:0% +method. That's much simpler as we talked +about previously because the derivative + + align:start position:0% +about previously because the derivative + + + align:start position:0% +about previously because the derivative +of x^2 is 2x and you have an x in the + + align:start position:0% +of x^2 is 2x and you have an x in the + + + align:start position:0% +of x^2 is 2x and you have an x in the +numerator when you put in that v. So, + + align:start position:0% +numerator when you put in that v. So, + + + align:start position:0% +numerator when you put in that v. So, +this this is sort of the flavor of of + + align:start position:0% +this this is sort of the flavor of of + + + align:start position:0% +this this is sort of the flavor of of +how these things are actually working. + + align:start position:0% +how these things are actually working. + + + align:start position:0% +how these things are actually working. +So, let me do the final one + + align:start position:0% +So, let me do the final one + + + align:start position:0% +So, let me do the final one +here. We have ln + + align:start position:0% +here. We have ln + + + align:start position:0% +here. We have ln +x over x2. + + align:start position:0% +x over x2. + + + align:start position:0% +x over x2. +Okay, let me just tell you right now in + + align:start position:0% +Okay, let me just tell you right now in + + + align:start position:0% +Okay, let me just tell you right now in +integration by parts natural log x is + + align:start position:0% +integration by parts natural log x is + + + align:start position:0% +integration by parts natural log x is +not something you want to make the v + + align:start position:0% +not something you want to make the v + + + align:start position:0% +not something you want to make the v +prime. You don't want to try and take an + + align:start position:0% +prime. You don't want to try and take an + + + align:start position:0% +prime. You don't want to try and take an +anti-derivative. You know an you know an + + align:start position:0% +anti-derivative. You know an you know an + + + align:start position:0% +anti-derivative. You know an you know an +anti-derivative of natural log of x ln x + + align:start position:0% +anti-derivative of natural log of x ln x + + + align:start position:0% +anti-derivative of natural log of x ln x +- x but that's certainly not going to + + align:start position:0% +- x but that's certainly not going to + + + align:start position:0% +- x but that's certainly not going to +make things any easier, right? You're + + align:start position:0% +make things any easier, right? You're + + + align:start position:0% +make things any easier, right? You're +actually then you've got a a product of + + align:start position:0% +actually then you've got a a product of + + + align:start position:0% +actually then you've got a a product of +two functions. All of a sudden + + align:start position:0% +two functions. All of a sudden + + + align:start position:0% +two functions. All of a sudden +everything's getting more complicated. + + align:start position:0% +everything's getting more complicated. + + + align:start position:0% +everything's getting more complicated. +But natural log of x has a very nice + + align:start position:0% +But natural log of x has a very nice + + + align:start position:0% +But natural log of x has a very nice +derivative because you end up with + + align:start position:0% +derivative because you end up with + + + align:start position:0% +derivative because you end up with +something that has just a power of x. + + align:start position:0% +something that has just a power of x. + + + align:start position:0% +something that has just a power of x. +Derivative of natural log of x, it's + + align:start position:0% +Derivative of natural log of x, it's + + + align:start position:0% +Derivative of natural log of x, it's +just 1 /x. So that's probably the way + + align:start position:0% +just 1 /x. So that's probably the way + + + align:start position:0% +just 1 /x. So that's probably the way +you always want to go when you see + + align:start position:0% +you always want to go when you see + + + align:start position:0% +you always want to go when you see +natural log of x in these integration by + + align:start position:0% +natural log of x in these integration by + + + align:start position:0% +natural log of x in these integration by +parts uh techniques because if I choose + + align:start position:0% +parts uh techniques because if I choose + + + align:start position:0% +parts uh techniques because if I choose +u is equal to ln x and then v prime in + + align:start position:0% +u is equal to ln x and then v prime in + + + align:start position:0% +u is equal to ln x and then v prime in +this case, I'm going to write it as a + + align:start position:0% +this case, I'm going to write it as a + + + align:start position:0% +this case, I'm going to write it as a +power. Let's let's think about what + + align:start position:0% +power. Let's let's think about what + + + align:start position:0% +power. Let's let's think about what +happens. U prime is 1 /x, right? So u + + align:start position:0% +happens. U prime is 1 /x, right? So u + + + align:start position:0% +happens. U prime is 1 /x, right? So u +prime is x to the minus1. What's v? + + align:start position:0% +prime is x to the minus1. What's v? + + + align:start position:0% +prime is x to the minus1. What's v? +Well, if something like let's see x^ the + + align:start position:0% +Well, if something like let's see x^ the + + + align:start position:0% +Well, if something like let's see x^ the +minus1 something like that, right? Let's + + align:start position:0% +minus1 something like that, right? Let's + + + align:start position:0% +minus1 something like that, right? Let's +make sure I did that right. Yeah, I + + align:start position:0% +make sure I did that right. Yeah, I + + + align:start position:0% +make sure I did that right. Yeah, I +think I did that right. So all of a + + align:start position:0% +think I did that right. So all of a + + + align:start position:0% +think I did that right. So all of a +sudden if I integrate v u prime, that's + + align:start position:0% +sudden if I integrate v u prime, that's + + + align:start position:0% +sudden if I integrate v u prime, that's +just a power rule. It's x to the + + align:start position:0% +just a power rule. It's x to the + + + align:start position:0% +just a power rule. It's x to the +minus2xus 2. So that's quite easy to to + + align:start position:0% +minus2xus 2. So that's quite easy to to + + + align:start position:0% +minus2xus 2. So that's quite easy to to +to integrate. So again, when I see + + align:start position:0% +to integrate. So again, when I see + + + align:start position:0% +to integrate. So again, when I see +natural log of x in a in an integration + + align:start position:0% +natural log of x in a in an integration + + + align:start position:0% +natural log of x in a in an integration +by parts method, almost always, I hate + + align:start position:0% +by parts method, almost always, I hate + + + align:start position:0% +by parts method, almost always, I hate +to say always, but almost always almost + + align:start position:0% +to say always, but almost always almost + + + align:start position:0% +to say always, but almost always almost +a guarantee that you want to take a + + align:start position:0% +a guarantee that you want to take a + + + align:start position:0% +a guarantee that you want to take a +derivative. You want to make that the + + align:start position:0% +derivative. You want to make that the + + + align:start position:0% +derivative. You want to make that the +u. So hopefully that makes sense. Some + + align:start position:0% +u. So hopefully that makes sense. Some + + + align:start position:0% +u. So hopefully that makes sense. Some +of these strategies I tried to pick ones + + align:start position:0% +of these strategies I tried to pick ones + + + align:start position:0% +of these strategies I tried to pick ones +that were were somewhat different so you + + align:start position:0% +that were were somewhat different so you + + + align:start position:0% +that were were somewhat different so you +could see some different types of + + align:start position:0% +could see some different types of + + + align:start position:0% +could see some different types of +strategies we needed. And now I've I've + + align:start position:0% +strategies we needed. And now I've I've + + + align:start position:0% +strategies we needed. And now I've I've +done these earlier, so I'm just going to + + align:start position:0% +done these earlier, so I'm just going to + + + align:start position:0% +done these earlier, so I'm just going to +write down what the answers actually + + align:start position:0% +write down what the answers actually + + + align:start position:0% +write down what the answers actually +are, and you can you can compare to what + + align:start position:0% +are, and you can you can compare to what + + + align:start position:0% +are, and you can you can compare to what +uh what you got. So the answer to number + + align:start position:0% +uh what you got. So the answer to number + + + align:start position:0% +uh what you got. So the answer to number +one just to + + align:start position:0% + + + + align:start position:0% + +check. Number two, some of these are + + align:start position:0% +check. Number two, some of these are + + + align:start position:0% +check. Number two, some of these are +kind of long. + + align:start position:0% + + + + align:start position:0% + +Number + + align:start position:0% + + + + align:start position:0% + +three, number + + align:start position:0% +three, number + + + align:start position:0% +three, number +four. + + align:start position:0% + + + + align:start position:0% + +Oops. So, let's just go through. We get + + align:start position:0% +Oops. So, let's just go through. We get + + + align:start position:0% +Oops. So, let's just go through. We get +in number one we get x e - x - e - x + + + align:start position:0% +in number one we get x e - x - e - x + + + + align:start position:0% +in number one we get x e - x - e - x + +c. Number two we get x^2 / 2 * 1 + x^2 + + align:start position:0% +c. Number two we get x^2 / 2 * 1 + x^2 + + + align:start position:0% +c. Number two we get x^2 / 2 * 1 + x^2 +plus 12 natural log 1 + x^2 + c. 3 is x + + align:start position:0% +plus 12 natural log 1 + x^2 + c. 3 is x + + + align:start position:0% +plus 12 natural log 1 + x^2 + c. 3 is x +ar tan x - 12 natural log of the + + align:start position:0% +ar tan x - 12 natural log of the + + + align:start position:0% +ar tan x - 12 natural log of the +quantity 1 + x^2 + c and 4 is negative + + align:start position:0% +quantity 1 + x^2 + c and 4 is negative + + + align:start position:0% +quantity 1 + x^2 + c and 4 is negative +natural log x - 1x + + + align:start position:0% +natural log x - 1x + + + + align:start position:0% +natural log x - 1x + +c. So again, the whole point of this + + align:start position:0% +c. So again, the whole point of this + + + align:start position:0% +c. So again, the whole point of this +exercise in my mind is really to make + + align:start position:0% +exercise in my mind is really to make + + + align:start position:0% +exercise in my mind is really to make +sure we get a a good understanding of + + align:start position:0% +sure we get a a good understanding of + + + align:start position:0% +sure we get a a good understanding of +when we're doing integration by parts, + + align:start position:0% +when we're doing integration by parts, + + + align:start position:0% +when we're doing integration by parts, +which function makes the most sense to + + align:start position:0% +which function makes the most sense to + + + align:start position:0% +which function makes the most sense to +have as U and which function makes the + + align:start position:0% +have as U and which function makes the + + + align:start position:0% +have as U and which function makes the +most sense to have as V prime. So that + + align:start position:0% +most sense to have as V prime. So that + + + align:start position:0% +most sense to have as V prime. So that +was the main point of this exercise. + + align:start position:0% +was the main point of this exercise. + + + align:start position:0% +was the main point of this exercise. +Hopefully you're starting to get a + + align:start position:0% +Hopefully you're starting to get a + + + align:start position:0% +Hopefully you're starting to get a +flavor for how these problems actually + + align:start position:0% +flavor for how these problems actually + + + align:start position:0% +flavor for how these problems actually +work. And I think I will stop there. \ No newline at end of file diff --git a/pelPpuYUAho.txt b/pelPpuYUAho.txt new file mode 100644 index 0000000000000000000000000000000000000000..e66964eb5105abe3720f1fdee77db673eed471f9 --- /dev/null +++ b/pelPpuYUAho.txt @@ -0,0 +1,174 @@ +In the optimization +problem, we assumed + +the compatibility +scores were data + +that we could input directly +into the optimization model. + +But where do these +scores come from? + +In the words of the founder-- +Neil Clark Warren --opposites + +attract, then they attack. + +eHarmony's compatibility +match score + +is based on similarity +between users' answers + +to the questionnaire. + +Let us attempt to +demonstrate an approach + +to develop compatibility scores. + +We utilize public data from +eHarmony containing features + +for 275,000 users and +binary compatibility. + +Feature names and +exact values are + +masked to protect +users' privacy. + +Correspondingly we won't be +able to directly interpret + +which features are +important as we do not + +know the identity +of these features. + +We used logistic regression +on pairs of users' differences + +to predict compatibility. + +To reduce the size +of the problem, + +we filtered the data to include +only users in the Boston area + +who have compatibility scores +listed in the data set. + +We computed absolute difference +in features for these 1,475 + +pairs and trained a +logistic regression model + +on these differences. + +Let us observe the results +of this experiment. + +If we use a low threshold in +the logistic regression model, + +we predict more false +positives but also get + +more true positives. + +For example, the +classification matrix + +for threshold equal +to 0.2 is as follows. + +Note that we found 1,030 +pairs that are not compatible + +and 92 pairs that are +compatible correctly. + +Note that 92 out of 319-- +which is 227 plus 92 --of these + +were correctly identified. + +That is, 29% percent of +the matches we recommend + +would be successful, a very high +success rate for online dating. + +Clearly, there is a +potential for using + +many other analytic methods. + +Specifically trees, +which are especially + +useful for predicting +compatibility + +if there are nonlinear +relationships + +between variables. + +Clustering is another +potential approach + +with the idea of +segmenting the users. + +Finally, text analytics +is yet another approach + +with the idea of analyzing +the text of users' profiles. + +Of course, many other +techniques are possible. + +To give some intuition +of various features, + +let us see how the +probability of a match + +changes with the distance +between the two adults. + +It is interesting to note +that the probability drops + +with distance, and then +for a very long distance, + +the probability increases again. + +Also interesting +is this graph that + +shows that if the attractiveness +is too high or too low, + +the probability of a +successful match decreases. + +Finally, if the difference in +height is too high or too low, + +the probability of +the match also drops. + +It seems the sweet spot +is a difference in height + +between four and eight inches. \ No newline at end of file diff --git a/piFTZQywm2A.txt b/piFTZQywm2A.txt new file mode 100644 index 0000000000000000000000000000000000000000..43072803fbf30dbceded20a07751c1e5f3065ea7 --- /dev/null +++ b/piFTZQywm2A.txt @@ -0,0 +1,1395 @@ +align:start position:0% + +and so we have basically two topics for + + align:start position:0% +and so we have basically two topics for + + + align:start position:0% +and so we have basically two topics for +today and the first one is the concept + + align:start position:0% +today and the first one is the concept + + + align:start position:0% +today and the first one is the concept +of uh the value information and we're + + align:start position:0% +of uh the value information and we're + + + align:start position:0% +of uh the value information and we're +going to end up with two uh method two + + align:start position:0% +going to end up with two uh method two + + + align:start position:0% +going to end up with two uh method two +ways of thinking about it I am going to + + align:start position:0% +ways of thinking about it I am going to + + + align:start position:0% +ways of thinking about it I am going to +present in some detail the procedure for + + align:start position:0% +present in some detail the procedure for + + + align:start position:0% +present in some detail the procedure for +the definition of the upper and bound on + + align:start position:0% +the definition of the upper and bound on + + + align:start position:0% +the definition of the upper and bound on +the value of information the + + align:start position:0% +the value of information the + + + align:start position:0% +the value of information the +evpi which stands for expected value of + + align:start position:0% +evpi which stands for expected value of + + + align:start position:0% +evpi which stands for expected value of +perfect + + align:start position:0% +perfect + + + align:start position:0% +perfect +information at the end as a supplement + + align:start position:0% +information at the end as a supplement + + + align:start position:0% +information at the end as a supplement +for your interest if you're you want to + + align:start position:0% +for your interest if you're you want to + + + align:start position:0% +for your interest if you're you want to +is the calculation of the exact value of + + align:start position:0% +is the calculation of the exact value of + + + align:start position:0% +is the calculation of the exact value of +evsi which is a sort of + + align:start position:0% +evsi which is a sort of + + + align:start position:0% +evsi which is a sort of +uh interesting uh probabilistic exercise + + align:start position:0% +uh interesting uh probabilistic exercise + + + align:start position:0% +uh interesting uh probabilistic exercise +but I personally don't think that very + + align:start position:0% +but I personally don't think that very + + + align:start position:0% +but I personally don't think that very +valuable in practice but it's part of + + align:start position:0% +valuable in practice but it's part of + + + align:start position:0% +valuable in practice but it's part of +standard curricula and um uh it's there + + align:start position:0% +standard curricula and um uh it's there + + + align:start position:0% +standard curricula and um uh it's there +if you want to go for it it will not be + + align:start position:0% +if you want to go for it it will not be + + + align:start position:0% +if you want to go for it it will not be +a part of a quiz or anything like that I + + align:start position:0% +a part of a quiz or anything like that I + + + align:start position:0% +a part of a quiz or anything like that I +think you should know about it uh but I + + align:start position:0% +think you should know about it uh but I + + + align:start position:0% +think you should know about it uh but I +want to um so you can appreciate the + + align:start position:0% +want to um so you can appreciate the + + + align:start position:0% +want to um so you can appreciate the +other aspect I will be focusing on and + + align:start position:0% +other aspect I will be focusing on and + + + align:start position:0% +other aspect I will be focusing on and +uh so methods and then I want to sort of + + align:start position:0% +uh so methods and then I want to sort of + + + align:start position:0% +uh so methods and then I want to sort of +stand back from this and talk about in + + align:start position:0% +stand back from this and talk about in + + + align:start position:0% +stand back from this and talk about in +information gathering as a basis for + + align:start position:0% +information gathering as a basis for + + + align:start position:0% +information gathering as a basis for +having a flexible + + align:start position:0% + + + + align:start position:0% + +strategy so there is this notion that + + align:start position:0% +strategy so there is this notion that + + + align:start position:0% +strategy so there is this notion that +before you commit to almost anything you + + align:start position:0% +before you commit to almost anything you + + + align:start position:0% +before you commit to almost anything you +can reduce your uncertainty or you can + + align:start position:0% +can reduce your uncertainty or you can + + + align:start position:0% +can reduce your uncertainty or you can +hope to reduce your + + align:start position:0% +hope to reduce your + + + align:start position:0% +hope to reduce your +uncertainty uh by inserting some kind of + + align:start position:0% +uncertainty uh by inserting some kind of + + + align:start position:0% +uncertainty uh by inserting some kind of +information gathering which from a + + align:start position:0% +information gathering which from a + + + align:start position:0% +information gathering which from a +jargon point of view is called a test + + align:start position:0% +jargon point of view is called a test + + + align:start position:0% +jargon point of view is called a test +it's not an examination but it's a short + + align:start position:0% +it's not an examination but it's a short + + + align:start position:0% +it's not an examination but it's a short +way of referring to whatever you do to + + align:start position:0% +way of referring to whatever you do to + + + align:start position:0% +way of referring to whatever you do to +get information + + align:start position:0% +get information + + + align:start position:0% +get information +before your decision problem so in this + + align:start position:0% +before your decision problem so in this + + + align:start position:0% +before your decision problem so in this +diagram at the bottom of the page I have + + align:start position:0% +diagram at the bottom of the page I have + + + align:start position:0% +diagram at the bottom of the page I have +given you on you have your decision + + align:start position:0% +given you on you have your decision + + + align:start position:0% +given you on you have your decision +problem do I uh do this thing or not and + + align:start position:0% +problem do I uh do this thing or not and + + + align:start position:0% +problem do I uh do this thing or not and +you say okay I'm gonna have I'm going to + + align:start position:0% +you say okay I'm gonna have I'm going to + + + align:start position:0% +you say okay I'm gonna have I'm going to +go through a process of collecting some + + align:start position:0% +go through a process of collecting some + + + align:start position:0% +go through a process of collecting some +in relevant information or information I + + align:start position:0% +in relevant information or information I + + + align:start position:0% +in relevant information or information I +think is relevant get that information + + align:start position:0% +think is relevant get that information + + + align:start position:0% +think is relevant get that information +and then uh consider my decision problem + + align:start position:0% +and then uh consider my decision problem + + + align:start position:0% +and then uh consider my decision problem +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +in principle that's always available to + + align:start position:0% +in principle that's always available to + + + align:start position:0% +in principle that's always available to +you if only to say okay let me stop for + + align:start position:0% +you if only to say okay let me stop for + + + align:start position:0% +you if only to say okay let me stop for +a minute and think about it and remind + + align:start position:0% +a minute and think about it and remind + + + align:start position:0% +a minute and think about it and remind +myself from the back of my brains and so + + align:start position:0% +myself from the back of my brains and so + + + align:start position:0% +myself from the back of my brains and so +on what should I do now of course at + + align:start position:0% +on what should I do now of course at + + + align:start position:0% +on what should I do now of course at +some point uh you got to do something + + align:start position:0% +some point uh you got to do something + + + align:start position:0% +some point uh you got to do something +you got to react right away but in + + align:start position:0% +you got to react right away but in + + + align:start position:0% +you got to react right away but in +general you have the opportunity to do + + align:start position:0% +general you have the opportunity to do + + + align:start position:0% +general you have the opportunity to do +something and this can be an important + + align:start position:0% +something and this can be an important + + + align:start position:0% +something and this can be an important +has an can have an important effect on + + align:start position:0% +has an can have an important effect on + + + align:start position:0% +has an can have an important effect on +your value of your decision and your + + align:start position:0% +your value of your decision and your + + + align:start position:0% +your value of your decision and your +procedure + + align:start position:0% +procedure + + + align:start position:0% +procedure +so what does a test + + align:start position:0% +so what does a test + + + align:start position:0% +so what does a test +do so at the starting point any decision + + align:start position:0% +do so at the starting point any decision + + + align:start position:0% +do so at the starting point any decision +problem even though you might not think + + align:start position:0% +problem even though you might not think + + + align:start position:0% +problem even though you might not think +about it quite this way you're driving a + + align:start position:0% +about it quite this way you're driving a + + + align:start position:0% +about it quite this way you're driving a +car you turn left you may not think at + + align:start position:0% +car you turn left you may not think at + + + align:start position:0% +car you turn left you may not think at +all in terms of uh the probabilities but + + align:start position:0% +all in terms of uh the probabilities but + + + align:start position:0% +all in terms of uh the probabilities but +you have some uncertainties and you some + + align:start position:0% +you have some uncertainties and you some + + + align:start position:0% +you have some uncertainties and you some +assessment of them in principle and + + align:start position:0% +assessment of them in principle and + + + align:start position:0% +assessment of them in principle and +these are known as prior + + align:start position:0% +these are known as prior + + + align:start position:0% +these are known as prior +probabilities why prior because we want + + align:start position:0% +probabilities why prior because we want + + + align:start position:0% +probabilities why prior because we want +to distinguish them from um what you + + align:start position:0% +to distinguish them from um what you + + + align:start position:0% +to distinguish them from um what you +might have after a test so it assumes + + align:start position:0% +might have after a test so it assumes + + + align:start position:0% +might have after a test so it assumes +that these are what you your starting + + align:start position:0% +that these are what you your starting + + + align:start position:0% +that these are what you your starting +probabilities or assessment for example + + align:start position:0% +probabilities or assessment for example + + + align:start position:0% +probabilities or assessment for example +you're running a business or your group + + align:start position:0% +you're running a business or your group + + + align:start position:0% +you're running a business or your group +is running a business and you have some + + align:start position:0% +is running a business and you have some + + + align:start position:0% +is running a business and you have some +measure of the cost of production of + + align:start position:0% +measure of the cost of production of + + + align:start position:0% +measure of the cost of production of +unit you have some measure of the + + align:start position:0% +unit you have some measure of the + + + align:start position:0% +unit you have some measure of the +likelihood of sales uh and whatever + + align:start position:0% +likelihood of sales uh and whatever + + + align:start position:0% +likelihood of sales uh and whatever +other features uh that you might have so + + align:start position:0% +other features uh that you might have so + + + align:start position:0% +other features uh that you might have so +what does it test + + align:start position:0% +what does it test + + + align:start position:0% +what does it test +do well there are various forms of it + + align:start position:0% +do well there are various forms of it + + + align:start position:0% +do well there are various forms of it +but in general it gets information + + align:start position:0% +but in general it gets information + + + align:start position:0% +but in general it gets information +on these issues for example you can say + + align:start position:0% +on these issues for example you can say + + + align:start position:0% +on these issues for example you can say +well I think I know how it's going to + + align:start position:0% +well I think I know how it's going to + + + align:start position:0% +well I think I know how it's going to +produce uh in this plant I've run + + align:start position:0% +produce uh in this plant I've run + + + align:start position:0% +produce uh in this plant I've run +several of them back in the States but + + align:start position:0% +several of them back in the States but + + + align:start position:0% +several of them back in the States but +now I'm doing one in um South Africa say + + align:start position:0% +now I'm doing one in um South Africa say + + + align:start position:0% +now I'm doing one in um South Africa say +and situations might be different so you + + align:start position:0% +and situations might be different so you + + + align:start position:0% +and situations might be different so you +could run a test PL see how it works + + align:start position:0% +could run a test PL see how it works + + + align:start position:0% +could run a test PL see how it works +with the local materials see how it + + align:start position:0% +with the local materials see how it + + + align:start position:0% +with the local materials see how it +works with the local uh Engineers might + + align:start position:0% +works with the local uh Engineers might + + + align:start position:0% +works with the local uh Engineers might +work better they know things you didn't + + align:start position:0% +work better they know things you didn't + + + align:start position:0% +work better they know things you didn't +know whatever so uh you can run a test + + align:start position:0% +know whatever so uh you can run a test + + + align:start position:0% +know whatever so uh you can run a test +plant get more information + + align:start position:0% +plant get more information + + + align:start position:0% +plant get more information +so or for example you can run a market + + align:start position:0% +so or for example you can run a market + + + align:start position:0% +so or for example you can run a market +analysis you can say I'm going to take + + align:start position:0% +analysis you can say I'm going to take + + + align:start position:0% +analysis you can say I'm going to take +my new product and I'm going to test it + + align:start position:0% +my new product and I'm going to test it + + + align:start position:0% +my new product and I'm going to test it +in a in St Louis see how it picks up + + align:start position:0% +in a in St Louis see how it picks up + + + align:start position:0% +in a in St Louis see how it picks up +maybe I'll go for different demographic + + align:start position:0% +maybe I'll go for different demographic + + + align:start position:0% +maybe I'll go for different demographic +and also test it in San Francisco + + align:start position:0% +and also test it in San Francisco + + + align:start position:0% +and also test it in San Francisco +whatever you want but there are things + + align:start position:0% +whatever you want but there are things + + + align:start position:0% +whatever you want but there are things +that you could do individually as a + + align:start position:0% +that you could do individually as a + + + align:start position:0% +that you could do individually as a +company as an organization to get more + + align:start position:0% +company as an organization to get more + + + align:start position:0% +company as an organization to get more +information about something before you + + align:start position:0% +information about something before you + + + align:start position:0% +information about something before you +make a um a commit to a decision + + align:start position:0% +make a um a commit to a decision + + + align:start position:0% +make a um a commit to a decision +ision so the operational test is + + align:start position:0% +ision so the operational test is + + + align:start position:0% +ision so the operational test is +basically okay you get new information + + align:start position:0% +basically okay you get new information + + + align:start position:0% +basically okay you get new information +or you get the information from the + + align:start position:0% +or you get the information from the + + + align:start position:0% +or you get the information from the +thing that you're doing the test plant + + align:start position:0% +thing that you're doing the test plant + + + align:start position:0% +thing that you're doing the test plant +or the market survey or the test + + align:start position:0% +or the market survey or the test + + + align:start position:0% +or the market survey or the test +marketing or + + align:start position:0% +marketing or + + + align:start position:0% +marketing or +whatever and it says Ah I got the idea + + align:start position:0% +whatever and it says Ah I got the idea + + + align:start position:0% +whatever and it says Ah I got the idea +that this I thought I knew what was + + align:start position:0% +that this I thought I knew what was + + + align:start position:0% +that this I thought I knew what was +happening but gee this test market + + align:start position:0% +happening but gee this test market + + + align:start position:0% +happening but gee this test market +showed me that the product really stinks + + align:start position:0% +showed me that the product really stinks + + + align:start position:0% +showed me that the product really stinks +so maybe it isn't so good so maybe my + + align:start position:0% +so maybe it isn't so good so maybe my + + + align:start position:0% +so maybe it isn't so good so maybe my +probabilities are wrong or or it says + + align:start position:0% +probabilities are wrong or or it says + + + align:start position:0% +probabilities are wrong or or it says +wow it really took off like Gang Busters + + align:start position:0% +wow it really took off like Gang Busters + + + align:start position:0% +wow it really took off like Gang Busters +it's going to be wonderful so whatever + + align:start position:0% +it's going to be wonderful so whatever + + + align:start position:0% +it's going to be wonderful so whatever +it is you have the chance to give them + + align:start position:0% +it is you have the chance to give them + + + align:start position:0% +it is you have the chance to give them +new information to revise your prior + + align:start position:0% +new information to revise your prior + + + align:start position:0% +new information to revise your prior +probabilities known as posterior + + align:start position:0% +probabilities known as posterior + + + align:start position:0% +probabilities known as posterior +probabilities nothing to do with your + + align:start position:0% +probabilities nothing to do with your + + + align:start position:0% +probabilities nothing to do with your +tush or your posterior but just that + + align:start position:0% +tush or your posterior but just that + + + align:start position:0% +tush or your posterior but just that +they come afterwards it's a sort of a + + align:start position:0% +they come afterwards it's a sort of a + + + align:start position:0% +they come afterwards it's a sort of a +mouthful but it's the after + + align:start position:0% +mouthful but it's the after + + + align:start position:0% +mouthful but it's the after +probabilities and then you have new + + align:start position:0% +probabilities and then you have new + + + align:start position:0% +probabilities and then you have new +values for the decision so uh in general + + align:start position:0% +values for the decision so uh in general + + + align:start position:0% +values for the decision so uh in general +then you've had the original decision + + align:start position:0% +then you've had the original decision + + + align:start position:0% +then you've had the original decision +that um uh had a certain value that you + + align:start position:0% +that um uh had a certain value that you + + + align:start position:0% +that um uh had a certain value that you +could calculate as we've done before and + + align:start position:0% +could calculate as we've done before and + + + align:start position:0% +could calculate as we've done before and +then having with new probabilities you + + align:start position:0% +then having with new probabilities you + + + align:start position:0% +then having with new probabilities you +have a different + + align:start position:0% +have a different + + + align:start position:0% +have a different +value so the consequence of the test is + + align:start position:0% +value so the consequence of the test is + + + align:start position:0% +value so the consequence of the test is +that you have an expected value after + + align:start position:0% +that you have an expected value after + + + align:start position:0% +that you have an expected value after +the test and in general the expected + + align:start position:0% +the test and in general the expected + + + align:start position:0% +the test and in general the expected +value out of the test is greater than + + align:start position:0% +value out of the test is greater than + + + align:start position:0% +value out of the test is greater than +without the test why + + align:start position:0% +without the test why + + + align:start position:0% +without the test why +because you can avoid bad choices you + + align:start position:0% +because you can avoid bad choices you + + + align:start position:0% +because you can avoid bad choices you +say oh well I found out that my mar my + + align:start position:0% +say oh well I found out that my mar my + + + align:start position:0% +say oh well I found out that my mar my +sales estimate wasn't as good as I + + align:start position:0% +sales estimate wasn't as good as I + + + align:start position:0% +sales estimate wasn't as good as I +expected so really I shouldn't be so + + align:start position:0% +expected so really I shouldn't be so + + + align:start position:0% +expected so really I shouldn't be so +aggressive in in the production and I + + align:start position:0% +aggressive in in the production and I + + + align:start position:0% +aggressive in in the production and I +don't won't have all this stock I didn't + + align:start position:0% +don't won't have all this stock I didn't + + + align:start position:0% +don't won't have all this stock I didn't +use so I don't lose that + + align:start position:0% +use so I don't lose that + + + align:start position:0% +use so I don't lose that +money or on the other hand you can see + + align:start position:0% +money or on the other hand you can see + + + align:start position:0% +money or on the other hand you can see +oh it sold out really well maybe I + + align:start position:0% +oh it sold out really well maybe I + + + align:start position:0% +oh it sold out really well maybe I +should increase my production and do + + align:start position:0% +should increase my production and do + + + align:start position:0% +should increase my production and do +much better than I thought so um the + + align:start position:0% +much better than I thought so um the + + + align:start position:0% +much better than I thought so um the +general idea that the expected value + + align:start position:0% +general idea that the expected value + + + align:start position:0% +general idea that the expected value +after the test is greater than the + + align:start position:0% +after the test is greater than the + + + align:start position:0% +after the test is greater than the +expected value without the test in other + + align:start position:0% +expected value without the test in other + + + align:start position:0% +expected value without the test in other +words that you can do better by having + + align:start position:0% +words that you can do better by having + + + align:start position:0% +words that you can do better by having +the P some proper amount of information + + align:start position:0% +the P some proper amount of information + + + align:start position:0% +the P some proper amount of information +uh uh available to you now uh we'll take + + align:start position:0% +uh uh available to you now uh we'll take + + + align:start position:0% +uh uh available to you now uh we'll take +that as a given that's a useful starting + + align:start position:0% +that as a given that's a useful starting + + + align:start position:0% +that as a given that's a useful starting +point the question really is since a + + align:start position:0% +point the question really is since a + + + align:start position:0% +point the question really is since a +test has a cost is it worthwhile + + align:start position:0% +test has a cost is it worthwhile + + + align:start position:0% +test has a cost is it worthwhile +I mean it has a cost because if you're + + align:start position:0% +I mean it has a cost because if you're + + + align:start position:0% +I mean it has a cost because if you're +going to test marketing or set up a a + + align:start position:0% +going to test marketing or set up a a + + + align:start position:0% +going to test marketing or set up a a +pilot plan you have to spend some money + + align:start position:0% +pilot plan you have to spend some money + + + align:start position:0% +pilot plan you have to spend some money +on it you also have to spend some time + + align:start position:0% +on it you also have to spend some time + + + align:start position:0% +on it you also have to spend some time +the time you spend on that exercise May + + align:start position:0% +the time you spend on that exercise May + + + align:start position:0% +the time you spend on that exercise May +mean that you missed a market uh that + + align:start position:0% +mean that you missed a market uh that + + + align:start position:0% +mean that you missed a market uh that +you could have been making money instead + + align:start position:0% +you could have been making money instead + + + align:start position:0% +you could have been making money instead +of just delaying so the ultimate + + align:start position:0% +of just delaying so the ultimate + + + align:start position:0% +of just delaying so the ultimate +question is what is the value of the + + align:start position:0% +question is what is the value of the + + + align:start position:0% +question is what is the value of the +information and does this value is it + + align:start position:0% +information and does this value is it + + + align:start position:0% +information and does this value is it +greater than the cost of the test test + + align:start position:0% +greater than the cost of the test test + + + align:start position:0% +greater than the cost of the test test +or more precisely is it significantly + + align:start position:0% +or more precisely is it significantly + + + align:start position:0% +or more precisely is it significantly +greater than the cost of the test as is + + align:start position:0% +greater than the cost of the test as is + + + align:start position:0% +greater than the cost of the test as is +it really worthwhile to do if it's $10 + + align:start position:0% +it really worthwhile to do if it's $10 + + + align:start position:0% +it really worthwhile to do if it's $10 +better is doesn't seem like such a good + + align:start position:0% +better is doesn't seem like such a good + + + align:start position:0% +better is doesn't seem like such a good +deal but is it really a significant + + align:start position:0% +deal but is it really a significant + + + align:start position:0% +deal but is it really a significant +value that's the idea \ No newline at end of file diff --git a/q485E0u9Kjk.txt b/q485E0u9Kjk.txt new file mode 100644 index 0000000000000000000000000000000000000000..c733da8da57c19cc1370fe1fa87bea12bcf87eb6 --- /dev/null +++ b/q485E0u9Kjk.txt @@ -0,0 +1,8795 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Okay, enough about the knowledge of the + + align:start position:0% +Okay, enough about the knowledge of the + + + align:start position:0% +Okay, enough about the knowledge of the +past. Be it me, be it memory or + + align:start position:0% +past. Be it me, be it memory or + + + align:start position:0% +past. Be it me, be it memory or +history. We in + + align:start position:0% +history. We in + + + align:start position:0% +history. We in +a very + + align:start position:0% +a very + + + align:start position:0% +a very +interesting space-time capsule. We have + + align:start position:0% +interesting space-time capsule. We have + + + align:start position:0% +interesting space-time capsule. We have +the possibility of imagining the + + align:start position:0% +the possibility of imagining the + + + align:start position:0% +the possibility of imagining the +future or at least + + align:start position:0% +future or at least + + + align:start position:0% +future or at least +contemplating more and more about how + + align:start position:0% +contemplating more and more about how + + + align:start position:0% +contemplating more and more about how +one might use even geometry to associate + + align:start position:0% +one might use even geometry to associate + + + align:start position:0% +one might use even geometry to associate +with minimizing the obstacles of the + + align:start position:0% +with minimizing the obstacles of the + + + align:start position:0% +with minimizing the obstacles of the +future. And we also have the capacity to + + align:start position:0% +future. And we also have the capacity to + + + align:start position:0% +future. And we also have the capacity to +look backwards using many techniques as + + align:start position:0% +look backwards using many techniques as + + + align:start position:0% +look backwards using many techniques as +showed in these examples. + + align:start position:0% +showed in these examples. + + + align:start position:0% +showed in these examples. +This should produce a much richer set of + + align:start position:0% +This should produce a much richer set of + + + align:start position:0% +This should produce a much richer set of +ideas of urbanism than + + align:start position:0% +ideas of urbanism than + + + align:start position:0% +ideas of urbanism than +modernism. It will depend on the genius + + align:start position:0% +modernism. It will depend on the genius + + + align:start position:0% +modernism. It will depend on the genius +of individual interpreters given this + + align:start position:0% +of individual interpreters given this + + + align:start position:0% +of individual interpreters given this +new scale of + + align:start position:0% +new scale of + + + align:start position:0% +new scale of +things. What we're not + + align:start position:0% +things. What we're not + + + align:start position:0% +things. What we're not +seeing are overall theories of + + align:start position:0% +seeing are overall theories of + + + align:start position:0% +seeing are overall theories of +urbanism based on amalgamation of these + + align:start position:0% +urbanism based on amalgamation of these + + + align:start position:0% +urbanism based on amalgamation of these +two ideas. + + align:start position:0% +two ideas. + + + align:start position:0% +two ideas. +uh forwardlooking and backward + + align:start position:0% +uh forwardlooking and backward + + + align:start position:0% +uh forwardlooking and backward +looking. Maybe that'll + + align:start position:0% +looking. Maybe that'll + + + align:start position:0% +looking. Maybe that'll +happen. Maybe we're still too + + align:start position:0% + + + + align:start position:0% + +early. We switch now to a discussion of + + align:start position:0% +early. We switch now to a discussion of + + + align:start position:0% +early. We switch now to a discussion of +the relationship between public and + + align:start position:0% +the relationship between public and + + + align:start position:0% +the relationship between public and +private space. + + align:start position:0% + + + + align:start position:0% + +At first glance, the distinction between + + align:start position:0% +At first glance, the distinction between + + + align:start position:0% +At first glance, the distinction between +private and public space is simply a + + align:start position:0% +private and public space is simply a + + + align:start position:0% +private and public space is simply a +question of the difference between + + align:start position:0% +question of the difference between + + + align:start position:0% +question of the difference between +rights and + + align:start position:0% +rights and + + + align:start position:0% +rights and +obligations. You cannot park your car on + + align:start position:0% +obligations. You cannot park your car on + + + align:start position:0% +obligations. You cannot park your car on +my land because I have the right of + + align:start position:0% +my land because I have the right of + + + align:start position:0% +my land because I have the right of +ownership. + + align:start position:0% +ownership. + + + align:start position:0% +ownership. +But when we get to a parking lot on Mass + + align:start position:0% +But when we get to a parking lot on Mass + + + align:start position:0% +But when we get to a parking lot on Mass +Avenue, it's a contestation between two + + align:start position:0% +Avenue, it's a contestation between two + + + align:start position:0% +Avenue, it's a contestation between two +of us fighting for public use for the + + align:start position:0% +of us fighting for public use for the + + + align:start position:0% +of us fighting for public use for the +use of a publicly available space at any + + align:start position:0% +use of a publicly available space at any + + + align:start position:0% +use of a publicly available space at any +time. Sometimes we are very angry that + + align:start position:0% +time. Sometimes we are very angry that + + + align:start position:0% +time. Sometimes we are very angry that +we are beaten by a car which has gotten + + align:start position:0% +we are beaten by a car which has gotten + + + align:start position:0% +we are beaten by a car which has gotten +there first. But we have no rights. We + + align:start position:0% +there first. But we have no rights. We + + + align:start position:0% +there first. But we have no rights. We +only have rights to park if it's free. + + align:start position:0% + + + + align:start position:0% + +In the same way, we have rights of + + align:start position:0% +In the same way, we have rights of + + + align:start position:0% +In the same way, we have rights of +behavior in our private + + align:start position:0% +behavior in our private + + + align:start position:0% +behavior in our private +world which are + + align:start position:0% + + + + align:start position:0% + +not superintended by the + + align:start position:0% + + + + align:start position:0% + +law provided we don't hurt anybody or + + align:start position:0% +law provided we don't hurt anybody or + + + align:start position:0% +law provided we don't hurt anybody or +behave illegally. + + align:start position:0% + + + + align:start position:0% + +But if I grow marijuana in my garden, + + align:start position:0% +But if I grow marijuana in my garden, + + + align:start position:0% +But if I grow marijuana in my garden, +uh, and as long as it's seen as green + + align:start position:0% +uh, and as long as it's seen as green + + + align:start position:0% +uh, and as long as it's seen as green +space, it's okay. Um, there no rules in + + align:start position:0% +space, it's okay. Um, there no rules in + + + align:start position:0% +space, it's okay. Um, there no rules in +the Cambridge Historical Society's book, + + align:start position:0% +the Cambridge Historical Society's book, + + + align:start position:0% +the Cambridge Historical Society's book, +which says that you're not allowed to + + align:start position:0% +which says that you're not allowed to + + + align:start position:0% +which says that you're not allowed to +grow marijuana in your + + align:start position:0% +grow marijuana in your + + + align:start position:0% +grow marijuana in your +garden. There probably are other rules + + align:start position:0% +garden. There probably are other rules + + + align:start position:0% +garden. There probably are other rules +which prohibit that. + + align:start position:0% +which prohibit that. + + + align:start position:0% +which prohibit that. +Um there are a number of other + + align:start position:0% +Um there are a number of other + + + align:start position:0% +Um there are a number of other +distinction between between public and + + align:start position:0% +distinction between between public and + + + align:start position:0% +distinction between between public and +private and have been used at different + + align:start position:0% +private and have been used at different + + + align:start position:0% +private and have been used at different +times. I don't want to go into them. I + + align:start position:0% +times. I don't want to go into them. I + + + align:start position:0% +times. I don't want to go into them. I +simply want to look with you at a number + + align:start position:0% +simply want to look with you at a number + + + align:start position:0% +simply want to look with you at a number +of examples where the relationship + + align:start position:0% +of examples where the relationship + + + align:start position:0% +of examples where the relationship +between public and private is not so + + align:start position:0% +between public and private is not so + + + align:start position:0% +between public and private is not so +clear and + + align:start position:0% + + + + align:start position:0% + +where if you take a a matrix + + align:start position:0% +where if you take a a matrix + + + align:start position:0% +where if you take a a matrix +and have four headings to your vertical + + align:start position:0% +and have four headings to your vertical + + + align:start position:0% +and have four headings to your vertical +columns. The four headings are use, + + align:start position:0% +columns. The four headings are use, + + + align:start position:0% +columns. The four headings are use, +ownership, access and meaning. + + align:start position:0% + + + + align:start position:0% + +Let's look at each of these categories + + align:start position:0% +Let's look at each of these categories + + + align:start position:0% +Let's look at each of these categories +and see what examples come to + + align:start position:0% +and see what examples come to + + + align:start position:0% +and see what examples come to +mind. Under the first which is use, use, + + align:start position:0% +mind. Under the first which is use, use, + + + align:start position:0% +mind. Under the first which is use, use, +ownership, access and + + align:start position:0% + + + + align:start position:0% + +meaning. Richard Sennet gives an example + + align:start position:0% +meaning. Richard Sennet gives an example + + + align:start position:0% +meaning. Richard Sennet gives an example +in + + align:start position:0% +in + + + align:start position:0% +in +London in the 18th century. + + align:start position:0% + + + + align:start position:0% + +It was impossible for investors in + + align:start position:0% +It was impossible for investors in + + + align:start position:0% +It was impossible for investors in +shipping and in trade to know the + + align:start position:0% +shipping and in trade to know the + + + align:start position:0% +shipping and in trade to know the +outcome of the ex of a of a shipping + + align:start position:0% +outcome of the ex of a of a shipping + + + align:start position:0% +outcome of the ex of a of a shipping +trip that they've invested + + align:start position:0% +trip that they've invested + + + align:start position:0% +trip that they've invested +in. There was no electronic + + align:start position:0% +in. There was no electronic + + + align:start position:0% +in. There was no electronic +communication. It took too long to write + + align:start position:0% +communication. It took too long to write + + + align:start position:0% +communication. It took too long to write +letters. The letters had to come by ship + + align:start position:0% +letters. The letters had to come by ship + + + align:start position:0% +letters. The letters had to come by ship +anyway. So, you didn't know if the + + align:start position:0% +anyway. So, you didn't know if the + + + align:start position:0% +anyway. So, you didn't know if the +pirates had got hold of the ship that + + align:start position:0% +pirates had got hold of the ship that + + + align:start position:0% +pirates had got hold of the ship that +was carrying silver back to + + align:start position:0% +was carrying silver back to + + + align:start position:0% +was carrying silver back to +Spain + + align:start position:0% +Spain + + + align:start position:0% +Spain +or whether the ship had been sunk in a + + align:start position:0% +or whether the ship had been sunk in a + + + align:start position:0% +or whether the ship had been sunk in a +hurricane. This knowledge was only + + align:start position:0% +hurricane. This knowledge was only + + + align:start position:0% +hurricane. This knowledge was only +capable of being transmitted verbally + + align:start position:0% +capable of being transmitted verbally + + + align:start position:0% +capable of being transmitted verbally +through human beings. + + align:start position:0% + + + + align:start position:0% + +So near the docks in + + align:start position:0% +So near the docks in + + + align:start position:0% +So near the docks in +London, a coffee bar grew + + align:start position:0% +London, a coffee bar grew + + + align:start position:0% +London, a coffee bar grew +up. The coffee bar was a private + + align:start position:0% +up. The coffee bar was a private + + + align:start position:0% +up. The coffee bar was a private +entity. You paid a penny to enter and + + align:start position:0% +entity. You paid a penny to enter and + + + align:start position:0% +entity. You paid a penny to enter and +sit + + align:start position:0% +sit + + + align:start position:0% +sit +down. You weren't able + + align:start position:0% +down. You weren't able + + + align:start position:0% +down. You weren't able +to. You had to sit anywhere that space + + align:start position:0% +to. You had to sit anywhere that space + + + align:start position:0% +to. You had to sit anywhere that space +was available. You couldn't reserve + + align:start position:0% +was available. You couldn't reserve + + + align:start position:0% +was available. You couldn't reserve +space. + + align:start position:0% +space. + + + align:start position:0% +space. +It was frequented by sailors who had + + align:start position:0% +It was frequented by sailors who had + + + align:start position:0% +It was frequented by sailors who had +this important + + align:start position:0% + + + + align:start position:0% + +information about their + + align:start position:0% +information about their + + + align:start position:0% +information about their +ships. So the wealthy and the poor + + align:start position:0% +ships. So the wealthy and the poor + + + align:start position:0% +ships. So the wealthy and the poor +managed to occupy the same space because + + align:start position:0% +managed to occupy the same space because + + + align:start position:0% +managed to occupy the same space because +of the importance of the + + align:start position:0% + + + + align:start position:0% + +information. What became of this place? + + align:start position:0% + + + + align:start position:0% + +Lloyds of London grew out of this coffee + + align:start position:0% +Lloyds of London grew out of this coffee + + + align:start position:0% +Lloyds of London grew out of this coffee +shop. The important thing is that an + + align:start position:0% +shop. The important thing is that an + + + align:start position:0% +shop. The important thing is that an +important public set of + + align:start position:0% +important public set of + + + align:start position:0% +important public set of +transactions could take place but under + + align:start position:0% +transactions could take place but under + + + align:start position:0% +transactions could take place but under +the shelter of a private institution. + + align:start position:0% + + + + align:start position:0% + +If we wish to put our body into public + + align:start position:0% +If we wish to put our body into public + + + align:start position:0% +If we wish to put our body into public +space, we need + + align:start position:0% + + + + align:start position:0% + +security. Security is often provided + + align:start position:0% +security. Security is often provided + + + align:start position:0% +security. Security is often provided +more by private institutions than by + + align:start position:0% + + + + align:start position:0% + +public. 30,000 people on a summer's + + align:start position:0% +public. 30,000 people on a summer's + + + align:start position:0% +public. 30,000 people on a summer's +night occupy the center of Boston only + + align:start position:0% +night occupy the center of Boston only + + + align:start position:0% +night occupy the center of Boston only +if they go to the Red Sox game. The Red + + align:start position:0% +if they go to the Red Sox game. The Red + + + align:start position:0% +if they go to the Red Sox game. The Red +Sox are private + + align:start position:0% +Sox are private + + + align:start position:0% +Sox are private +corporation with private + + align:start position:0% +corporation with private + + + align:start position:0% +corporation with private +security. MIT has its own security + + align:start position:0% +security. MIT has its own security + + + align:start position:0% +security. MIT has its own security +force. Harvard has it. The Christian + + align:start position:0% +force. Harvard has it. The Christian + + + align:start position:0% +force. Harvard has it. The Christian +Science said just going down Mass + + align:start position:0% +Science said just going down Mass + + + align:start position:0% +Science said just going down Mass +Avenue, you + + align:start position:0% +Avenue, you + + + align:start position:0% +Avenue, you +transact transsect uh number of private + + align:start position:0% +transact transsect uh number of private + + + align:start position:0% +transact transsect uh number of private +authorities. + + align:start position:0% +authorities. + + + align:start position:0% +authorities. +So there's a + + align:start position:0% + + + + align:start position:0% + +principle that the private sector + + align:start position:0% +principle that the private sector + + + align:start position:0% +principle that the private sector +provides a kind of in + + align:start position:0% +provides a kind of in + + + align:start position:0% +provides a kind of in +phenomenological and actual security for + + align:start position:0% +phenomenological and actual security for + + + align:start position:0% +phenomenological and actual security for +the actions + + align:start position:0% +the actions + + + align:start position:0% +the actions +of + + align:start position:0% +of + + + align:start position:0% +of +public need such as putting your body + + align:start position:0% +public need such as putting your body + + + align:start position:0% +public need such as putting your body +into public + + align:start position:0% +into public + + + align:start position:0% +into public +space for those people who + + align:start position:0% +space for those people who + + + align:start position:0% +space for those people who +criticized and they're endless. Hana for + + align:start position:0% +criticized and they're endless. Hana for + + + align:start position:0% +criticized and they're endless. Hana for +instance, Richard + + align:start position:0% +instance, Richard + + + align:start position:0% +instance, Richard +Senate criticized the modern world + + align:start position:0% +Senate criticized the modern world + + + align:start position:0% +Senate criticized the modern world +as being promoting isolation from the + + align:start position:0% +as being promoting isolation from the + + + align:start position:0% +as being promoting isolation from the +public world. + + align:start position:0% +public world. + + + align:start position:0% +public world. +Nar, narcissism, self + + align:start position:0% +Nar, narcissism, self + + + align:start position:0% +Nar, narcissism, self +preoccupation, people locked up in their + + align:start position:0% +preoccupation, people locked up in their + + + align:start position:0% +preoccupation, people locked up in their +own + + align:start position:0% +own + + + align:start position:0% +own +private quarters, fed by television and + + align:start position:0% +private quarters, fed by television and + + + align:start position:0% +private quarters, fed by television and +electronic + + align:start position:0% +electronic + + + align:start position:0% +electronic +systems and not hazarding + + align:start position:0% +systems and not hazarding + + + align:start position:0% +systems and not hazarding +the danger, if you want to call it, but + + align:start position:0% +the danger, if you want to call it, but + + + align:start position:0% +the danger, if you want to call it, but +the + + align:start position:0% +the + + + align:start position:0% +the +adventure, which is a better word, of + + align:start position:0% +adventure, which is a better word, of + + + align:start position:0% +adventure, which is a better word, of +immersing yourself into public space. So + + align:start position:0% +immersing yourself into public space. So + + + align:start position:0% +immersing yourself into public space. So +public space doesn't + + align:start position:0% +public space doesn't + + + align:start position:0% +public space doesn't +exist except in Roger Scrutin the + + align:start position:0% +exist except in Roger Scrutin the + + + align:start position:0% +exist except in Roger Scrutin the +British critics's argument that public + + align:start position:0% +British critics's argument that public + + + align:start position:0% +British critics's argument that public +space only exists in the street. All the + + align:start position:0% +space only exists in the street. All the + + + align:start position:0% +space only exists in the street. All the +rest is an affectation and an + + align:start position:0% +rest is an affectation and an + + + align:start position:0% +rest is an affectation and an +unnecessary affectation. + + align:start position:0% +unnecessary affectation. + + + align:start position:0% +unnecessary affectation. +The idea of creating a public + + align:start position:0% +The idea of creating a public + + + align:start position:0% +The idea of creating a public +space as a + + align:start position:0% +space as a + + + align:start position:0% +space as a +plaza is an + + align:start position:0% + + + + align:start position:0% + +affectation. It's true + + align:start position:0% + + + + align:start position:0% + +of contemporary Tokyo for + + align:start position:0% + + + + align:start position:0% + +instance. Public world exists in the + + align:start position:0% +instance. Public world exists in the + + + align:start position:0% +instance. Public world exists in the +dense stream of connections between + + align:start position:0% +dense stream of connections between + + + align:start position:0% +dense stream of connections between +functions. + + align:start position:0% + + + + align:start position:0% + +There's no tradition + + align:start position:0% +There's no tradition + + + align:start position:0% +There's no tradition +of public meeting + + align:start position:0% +of public meeting + + + align:start position:0% +of public meeting +space where it's been tried in the in + + align:start position:0% +space where it's been tried in the in + + + align:start position:0% +space where it's been tried in the in +the in front of the tall new + + align:start position:0% +the in front of the tall new + + + align:start position:0% +the in front of the tall new +Metropolitan City Hall building. It's a + + align:start position:0% +Metropolitan City Hall building. It's a + + + align:start position:0% +Metropolitan City Hall building. It's a +waste of + + align:start position:0% + + + + align:start position:0% + +time. We'll go into the history of + + align:start position:0% +time. We'll go into the history of + + + align:start position:0% +time. We'll go into the history of +public space in a few minutes. + + align:start position:0% + + + + align:start position:0% + +We still have + + align:start position:0% + + + + align:start position:0% + +time. + + align:start position:0% + + + + align:start position:0% + +So if we see + + align:start position:0% +So if we see + + + align:start position:0% +So if we see +that public + + align:start position:0% +that public + + + align:start position:0% +that public +use can + + align:start position:0% +use can + + + align:start position:0% +use can +be advent made more + + align:start position:0% +be advent made more + + + align:start position:0% +be advent made more +appropriate by private + + align:start position:0% + + + + align:start position:0% + +endeavor. We + + align:start position:0% +endeavor. We + + + align:start position:0% +endeavor. We +have a notion of sharing of use which + + align:start position:0% +have a notion of sharing of use which + + + align:start position:0% +have a notion of sharing of use which +has always been true + + align:start position:0% + + + + align:start position:0% + +in in + + align:start position:0% + + + + align:start position:0% + +urbanism. The agura which most of our + + align:start position:0% +urbanism. The agura which most of our + + + align:start position:0% +urbanism. The agura which most of our +arguments for + + align:start position:0% +arguments for + + + align:start position:0% +arguments for +public communication space + + align:start position:0% +public communication space + + + align:start position:0% +public communication space +rests on was a 37 acre piece of messy + + align:start position:0% +rests on was a 37 acre piece of messy + + + align:start position:0% +rests on was a 37 acre piece of messy +mixtures of + + align:start position:0% +mixtures of + + + align:start position:0% +mixtures of +monuments, + + align:start position:0% +monuments, + + + align:start position:0% +monuments, +temples, shoe makers, stoas where + + align:start position:0% +temples, shoe makers, stoas where + + + align:start position:0% +temples, shoe makers, stoas where +philosophers like Socrates sat + + align:start position:0% +philosophers like Socrates sat + + + align:start position:0% +philosophers like Socrates sat +and engaged young men, not young women, + + align:start position:0% +and engaged young men, not young women, + + + align:start position:0% +and engaged young men, not young women, +young men in + + align:start position:0% +young men in + + + align:start position:0% +young men in +discourse. + + align:start position:0% +discourse. + + + align:start position:0% +discourse. +Um even + + align:start position:0% + + + + align:start position:0% + +housing this is the space of democracy. + + align:start position:0% + + + + align:start position:0% + +Witchery the historian writes about it + + align:start position:0% +Witchery the historian writes about it + + + align:start position:0% +Witchery the historian writes about it +in the same way that I've just mentioned + + align:start position:0% +in the same way that I've just mentioned + + + align:start position:0% +in the same way that I've just mentioned +it as an as a highly dense elomeration + + align:start position:0% +it as an as a highly dense elomeration + + + align:start position:0% +it as an as a highly dense elomeration +of shoe makers, temples, monuments, none + + align:start position:0% +of shoe makers, temples, monuments, none + + + align:start position:0% +of shoe makers, temples, monuments, none +of which fit any cardinal pattern. + + align:start position:0% + + + + align:start position:0% + +There's no assemb + + align:start position:0% +There's no assemb + + + align:start position:0% +There's no assemb +of items in the buildings which reset in + + align:start position:0% +of items in the buildings which reset in + + + align:start position:0% +of items in the buildings which reset in +relation to any + + align:start position:0% + + + + align:start position:0% + +other. This + + align:start position:0% +other. This + + + align:start position:0% +other. This +is in one thesis done here by a master's + + align:start position:0% +is in one thesis done here by a master's + + + align:start position:0% +is in one thesis done here by a master's +smark student the result of a kind of + + align:start position:0% +smark student the result of a kind of + + + align:start position:0% +smark student the result of a kind of +democratic form of rhetoric which only + + align:start position:0% +democratic form of rhetoric which only + + + align:start position:0% +democratic form of rhetoric which only +allowed people to speak that's males and + + align:start position:0% +allowed people to speak that's males and + + + align:start position:0% +allowed people to speak that's males and +not women and not slave to take part in + + align:start position:0% +not women and not slave to take part in + + + align:start position:0% +not women and not slave to take part in +discourse through the use of a + + align:start position:0% +discourse through the use of a + + + align:start position:0% +discourse through the use of a +particular language. + + align:start position:0% + + + + align:start position:0% + +When it became necessary for people to + + align:start position:0% +When it became necessary for people to + + + align:start position:0% +When it became necessary for people to +meet and debate propositions later + + align:start position:0% +meet and debate propositions later + + + align:start position:0% +meet and debate propositions later +on, + + align:start position:0% +on, + + + align:start position:0% +on, +a meeting place called the PNIX + + align:start position:0% +a meeting place called the PNIX + + + align:start position:0% +a meeting place called the PNIX +was created separate from the Agura. + + align:start position:0% +was created separate from the Agura. + + + align:start position:0% +was created separate from the Agura. +The agura was this mixed + + align:start position:0% + + + + align:start position:0% + +domain. + + align:start position:0% +domain. + + + align:start position:0% +domain. +Aristotle rejected that in image of the + + align:start position:0% +Aristotle rejected that in image of the + + + align:start position:0% +Aristotle rejected that in image of the +agura. For him a public plane public + + align:start position:0% +agura. For him a public plane public + + + align:start position:0% +agura. For him a public plane public +place of meeting was a clean + + align:start position:0% +place of meeting was a clean + + + align:start position:0% +place of meeting was a clean +absolutely minimized + + align:start position:0% +absolutely minimized + + + align:start position:0% +absolutely minimized +environment. Uh I + + align:start position:0% +environment. Uh I + + + align:start position:0% +environment. Uh I +should read you the quotation from + + align:start position:0% + + + + align:start position:0% + +Yeah. The agro in Athens, far from being + + align:start position:0% +Yeah. The agro in Athens, far from being + + + align:start position:0% +Yeah. The agro in Athens, far from being +architecturally impressive, was a jumble + + align:start position:0% +architecturally impressive, was a jumble + + + align:start position:0% +architecturally impressive, was a jumble +of crowded downtown streets and + + align:start position:0% +of crowded downtown streets and + + + align:start position:0% +of crowded downtown streets and +irregular open spaces where shrines and + + align:start position:0% +irregular open spaces where shrines and + + + align:start position:0% +irregular open spaces where shrines and +altars, public buildings, and monuments + + align:start position:0% +altars, public buildings, and monuments + + + align:start position:0% +altars, public buildings, and monuments +stood in the midst of workshops, market + + align:start position:0% +stood in the midst of workshops, market + + + align:start position:0% +stood in the midst of workshops, market +stalls, and + + align:start position:0% + + + + align:start position:0% + +taverns. Agra was the haunt of the dregs + + align:start position:0% +taverns. Agra was the haunt of the dregs + + + align:start position:0% +taverns. Agra was the haunt of the dregs +of the populace, the home of idleness, + + align:start position:0% +of the populace, the home of idleness, + + + align:start position:0% +of the populace, the home of idleness, +vulgarity, and gossip. + + align:start position:0% +vulgarity, and gossip. + + + align:start position:0% +vulgarity, and gossip. +For Aristotle, the ideal public square + + align:start position:0% +For Aristotle, the ideal public square + + + align:start position:0% +For Aristotle, the ideal public square +were that all commercial activities and + + align:start position:0% +were that all commercial activities and + + + align:start position:0% +were that all commercial activities and +all merchant and vendors were would be + + align:start position:0% +all merchant and vendors were would be + + + align:start position:0% +all merchant and vendors were would be +exported to another part of the town. + + align:start position:0% +exported to another part of the town. + + + align:start position:0% +exported to another part of the town. +Nothing in the aggra may be bought or + + align:start position:0% +Nothing in the aggra may be bought or + + + align:start position:0% +Nothing in the aggra may be bought or +sold. No member of the lower order may + + align:start position:0% +sold. No member of the lower order may + + + align:start position:0% +sold. No member of the lower order may +be admitted and is summoned by the and + + align:start position:0% +be admitted and is summoned by the and + + + align:start position:0% +be admitted and is summoned by the and +so on and so on. + + align:start position:0% + + + + align:start position:0% + +So much of Aristotle's view of the + + align:start position:0% +So much of Aristotle's view of the + + + align:start position:0% +So much of Aristotle's view of the +public meeting space as opposed to the + + align:start position:0% +public meeting space as opposed to the + + + align:start position:0% +public meeting space as opposed to the +agura the Athenian Agra has become part + + align:start position:0% +agura the Athenian Agra has become part + + + align:start position:0% +agura the Athenian Agra has become part +of architectural + + align:start position:0% + + + + align:start position:0% + +dogma city hall + + align:start position:0% +dogma city hall + + + align:start position:0% +dogma city hall +plaza rests on an aristoilian + + align:start position:0% +plaza rests on an aristoilian + + + align:start position:0% +plaza rests on an aristoilian +assumption that there's something + + align:start position:0% +assumption that there's something + + + align:start position:0% +assumption that there's something +absolute + + align:start position:0% +absolute + + + align:start position:0% +absolute +about p public space which is satisfied + + align:start position:0% +about p public space which is satisfied + + + align:start position:0% +about p public space which is satisfied +by whenever we wish to immerse ourself. + + align:start position:0% +by whenever we wish to immerse ourself. + + + align:start position:0% +by whenever we wish to immerse ourself. +But in our in our metaphysical + + align:start position:0% +But in our in our metaphysical + + + align:start position:0% +But in our in our metaphysical +condition, we think of it as depicting + + align:start position:0% +condition, we think of it as depicting + + + align:start position:0% +condition, we think of it as depicting +our public environment in gracious and + + align:start position:0% +our public environment in gracious and + + + align:start position:0% +our public environment in gracious and +whole terms. + + align:start position:0% +whole terms. + + + align:start position:0% +whole terms. +The curious thing is the pattern the + + align:start position:0% +The curious thing is the pattern the + + + align:start position:0% +The curious thing is the pattern the +bipolar relationship between city hall + + align:start position:0% +bipolar relationship between city hall + + + align:start position:0% +bipolar relationship between city hall +plaza and Faniel Lord + + align:start position:0% +plaza and Faniel Lord + + + align:start position:0% +plaza and Faniel Lord +marketplace. Faniel Lord marketplace + + align:start position:0% +marketplace. Faniel Lord marketplace + + + align:start position:0% +marketplace. Faniel Lord marketplace +would be the agura in the ideal + + align:start position:0% +would be the agura in the ideal + + + align:start position:0% +would be the agura in the ideal +connection between the two. However, + + align:start position:0% +connection between the two. However, + + + align:start position:0% +connection between the two. However, +it's + + align:start position:0% +it's + + + align:start position:0% +it's +not. It's a singular high up market + + align:start position:0% +not. It's a singular high up market + + + align:start position:0% +not. It's a singular high up market +phenomenon totally driven by market + + align:start position:0% +phenomenon totally driven by market + + + align:start position:0% +phenomenon totally driven by market +conditions up market conditions. + + align:start position:0% + + + + align:start position:0% + +Uh so we start off with a notion of + + align:start position:0% +Uh so we start off with a notion of + + + align:start position:0% +Uh so we start off with a notion of +the public meeting + + align:start position:0% + + + + align:start position:0% + +place which derives + + align:start position:0% + + + + align:start position:0% + +from a unique setting for democracy in + + align:start position:0% +from a unique setting for democracy in + + + align:start position:0% +from a unique setting for democracy in +fifth century Athens and has maintained + + align:start position:0% +fifth century Athens and has maintained + + + align:start position:0% +fifth century Athens and has maintained +itself + + align:start position:0% +itself + + + align:start position:0% +itself +through deviations in under the + + align:start position:0% + + + + align:start position:0% + +Romans. There were no elevated platforms + + align:start position:0% +Romans. There were no elevated platforms + + + align:start position:0% +Romans. There were no elevated platforms +in Niagara for people to make speeches. + + align:start position:0% +in Niagara for people to make speeches. + + + align:start position:0% +in Niagara for people to make speeches. +If you spoke, you spoke from the same + + align:start position:0% +If you spoke, you spoke from the same + + + align:start position:0% +If you spoke, you spoke from the same +plane as everybody + + align:start position:0% +plane as everybody + + + align:start position:0% +plane as everybody +else. The Romans introduced in the forum + + align:start position:0% +else. The Romans introduced in the forum + + + align:start position:0% +else. The Romans introduced in the forum +places for people who were spokesmen, + + align:start position:0% +places for people who were spokesmen, + + + align:start position:0% +places for people who were spokesmen, +people who had + + align:start position:0% +people who had + + + align:start position:0% +people who had +particular ability to make political + + align:start position:0% +particular ability to make political + + + align:start position:0% +particular ability to make political +speeches or speeches which are not + + align:start position:0% +speeches or speeches which are not + + + align:start position:0% +speeches or speeches which are not +political but of a specialized nature. + + align:start position:0% + + + + align:start position:0% + +In the examples I'll show in the slides + + align:start position:0% +In the examples I'll show in the slides + + + align:start position:0% +In the examples I'll show in the slides +at the beginning of next + + align:start position:0% +at the beginning of next + + + align:start position:0% +at the beginning of next +class, you will see that the + + align:start position:0% +class, you will see that the + + + align:start position:0% +class, you will see that the +traditional many of the traditional + + align:start position:0% +traditional many of the traditional + + + align:start position:0% +traditional many of the traditional +public squares in small towns in Italy + + align:start position:0% +public squares in small towns in Italy + + + align:start position:0% +public squares in small towns in Italy +were + + align:start position:0% +were + + + align:start position:0% +were +simply based upon passageways through + + align:start position:0% +simply based upon passageways through + + + align:start position:0% +simply based upon passageways through +space, not culdeacs of space at all. + + align:start position:0% +space, not culdeacs of space at all. + + + align:start position:0% +space, not culdeacs of space at all. +I spent a year in Ais living in Aisi + + align:start position:0% +I spent a year in Ais living in Aisi + + + align:start position:0% +I spent a year in Ais living in Aisi +documenting the town and measuring + + align:start position:0% +documenting the town and measuring + + + align:start position:0% +documenting the town and measuring +pedestrian + + align:start position:0% +pedestrian + + + align:start position:0% +pedestrian +volumes. The + + align:start position:0% +volumes. The + + + align:start position:0% +volumes. The +patune is exactly that space. I'll show + + align:start position:0% +patune is exactly that space. I'll show + + + align:start position:0% +patune is exactly that space. I'll show +you in some + + align:start position:0% +you in some + + + align:start position:0% +you in some +illustrations. + + align:start position:0% + + + + align:start position:0% + +Um, in the post telephone + + align:start position:0% +Um, in the post telephone + + + align:start position:0% +Um, in the post telephone +era, the need for people to obtain + + align:start position:0% +era, the need for people to obtain + + + align:start position:0% +era, the need for people to obtain +communication by machine interpost + + align:start position:0% +communication by machine interpost + + + align:start position:0% +communication by machine interpost +systems has become another + + align:start position:0% + + + + align:start position:0% + +variable. What is the most significant + + align:start position:0% +variable. What is the most significant + + + align:start position:0% +variable. What is the most significant +public place built since 1920? + + align:start position:0% + + + + align:start position:0% + +anywhere. This is a part of an urban + + align:start position:0% +anywhere. This is a part of an urban + + + align:start position:0% +anywhere. This is a part of an urban +tradition after all. Have we stopped? + + align:start position:0% +tradition after all. Have we stopped? + + + align:start position:0% +tradition after all. Have we stopped? +But it's really hard to h it's really + + align:start position:0% +But it's really hard to h it's really + + + align:start position:0% +But it's really hard to h it's really +hard to say. Well, say six. + + align:start position:0% + + + + align:start position:0% + +The + + align:start position:0% +The + + + align:start position:0% +The +Highline Highline is a water is a is a + + align:start position:0% +Highline Highline is a water is a is a + + + align:start position:0% +Highline Highline is a water is a is a +old train track. Um Oh, you mean from + + align:start position:0% +old train track. Um Oh, you mean from + + + align:start position:0% +old train track. Um Oh, you mean from +scratch? + + align:start position:0% +scratch? + + + align:start position:0% +scratch? +No, I don't. I mean just anything which + + align:start position:0% +No, I don't. I mean just anything which + + + align:start position:0% +No, I don't. I mean just anything which +resembles a public square. + + align:start position:0% + + + + align:start position:0% + +They built one in Columbia Heights in DC + + align:start position:0% +They built one in Columbia Heights in DC + + + align:start position:0% +They built one in Columbia Heights in DC +in the early + + align:start position:0% +in the early + + + align:start position:0% +in the early +2000s. That's been pretty successful. + + align:start position:0% +2000s. That's been pretty successful. + + + align:start position:0% +2000s. That's been pretty successful. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Rockefeller Center is by far the best + + align:start position:0% +Rockefeller Center is by far the best + + + align:start position:0% +Rockefeller Center is by far the best +universally. It contradicts all the + + align:start position:0% +universally. It contradicts all the + + + align:start position:0% +universally. It contradicts all the +argument about public. It's the largest + + align:start position:0% +argument about public. It's the largest + + + align:start position:0% +argument about public. It's the largest +private investment in a city in + + align:start position:0% + + + + align:start position:0% + +history. Let me give you a few details. + + align:start position:0% + + + + align:start position:0% + +It's the largest privately held complex + + align:start position:0% +It's the largest privately held complex + + + align:start position:0% +It's the largest privately held complex +of its kind in the + + align:start position:0% +of its kind in the + + + align:start position:0% +of its kind in the +world. It's the largest private building + + align:start position:0% +world. It's the largest private building + + + align:start position:0% +world. It's the largest private building +project ever undertaken in modern + + align:start position:0% +project ever undertaken in modern + + + align:start position:0% +project ever undertaken in modern +times. It was bought. It was leased by + + align:start position:0% +times. It was bought. It was leased by + + + align:start position:0% +times. It was bought. It was leased by +John D. Rockefeller from Colombia + + align:start position:0% +John D. Rockefeller from Colombia + + + align:start position:0% +John D. Rockefeller from Colombia +University in 1928. + + align:start position:0% + + + + align:start position:0% + +It was completed was built between 1930 + + align:start position:0% +It was completed was built between 1930 + + + align:start position:0% +It was completed was built between 1930 +and + + align:start position:0% +and + + + align:start position:0% +and +1939. In 1985, Colombia University sold + + align:start position:0% +1939. In 1985, Colombia University sold + + + align:start position:0% +1939. In 1985, Colombia University sold +the land beneath Rockefeller Center to + + align:start position:0% +the land beneath Rockefeller Center to + + + align:start position:0% +the land beneath Rockefeller Center to +the Rockefeller Group for $400 + + align:start position:0% +the Rockefeller Group for $400 + + + align:start position:0% +the Rockefeller Group for $400 +million. The entire complex was + + align:start position:0% +million. The entire complex was + + + align:start position:0% +million. The entire complex was +purchased by Mitubishi estate in 1989. + + align:start position:0% +purchased by Mitubishi estate in 1989. + + + align:start position:0% +purchased by Mitubishi estate in 1989. +In 2000, the current owner and so paid + + align:start position:0% +In 2000, the current owner and so paid + + + align:start position:0% +In 2000, the current owner and so paid +$1.85 billion dollars for the older + + align:start position:0% + + + + align:start position:0% + +buildings. This is an there could be + + align:start position:0% +buildings. This is an there could be + + + align:start position:0% +buildings. This is an there could be +nothing more + + align:start position:0% +nothing more + + + align:start position:0% +nothing more +private in ownership than Rockefeller + + align:start position:0% + + + + align:start position:0% + +Center. + + align:start position:0% +Center. + + + align:start position:0% +Center. +It provided the public with an open + + align:start position:0% +It provided the public with an open + + + align:start position:0% +It provided the public with an open +space. + + align:start position:0% +space. + + + align:start position:0% +space. +It provided the public with an + + align:start position:0% +It provided the public with an + + + align:start position:0% +It provided the public with an +underground concourse, shopping + + align:start position:0% +underground concourse, shopping + + + align:start position:0% +underground concourse, shopping +concourse. It added streets to the + + align:start position:0% +concourse. It added streets to the + + + align:start position:0% +concourse. It added streets to the +number of streets in the grid of + + align:start position:0% +number of streets in the grid of + + + align:start position:0% +number of streets in the grid of +Manhattan. And yet, it's a public + + align:start position:0% + + + + align:start position:0% + +space. So, does public space have to be + + align:start position:0% +space. So, does public space have to be + + + align:start position:0% +space. So, does public space have to be +owned by the + + align:start position:0% + + + + align:start position:0% + +public? I'm looking for examples of + + align:start position:0% +public? I'm looking for examples of + + + align:start position:0% +public? I'm looking for examples of +contradictions. + + align:start position:0% +contradictions. + + + align:start position:0% +contradictions. +simply to make our argument a little + + align:start position:0% +simply to make our argument a little + + + align:start position:0% +simply to make our argument a little +more interesting. + + align:start position:0% +more interesting. + + + align:start position:0% +more interesting. +Well, there's the famous court case, the + + align:start position:0% +Well, there's the famous court case, the + + + align:start position:0% +Well, there's the famous court case, the +Supreme Court case in the suburban mall + + align:start position:0% +Supreme Court case in the suburban mall + + + align:start position:0% +Supreme Court case in the suburban mall +in Portland, Oregon. I forget the + + align:start position:0% +in Portland, Oregon. I forget the + + + align:start position:0% +in Portland, Oregon. I forget the +details, but that's where I think you're + + align:start position:0% +details, but that's where I think you're + + + align:start position:0% +details, but that's where I think you're +not allowed to have a protest in the + + align:start position:0% +not allowed to have a protest in the + + + align:start position:0% +not allowed to have a protest in the +mall, even though it functions as a + + align:start position:0% +mall, even though it functions as a + + + align:start position:0% +mall, even though it functions as a +public + + align:start position:0% +public + + + align:start position:0% +public +space because it's private. So, you + + align:start position:0% +space because it's private. So, you + + + align:start position:0% +space because it's private. So, you +know, Rockefeller has more control over + + align:start position:0% +know, Rockefeller has more control over + + + align:start position:0% +know, Rockefeller has more control over +that space + + align:start position:0% +that space + + + align:start position:0% +that space +than a space that actually would be + + align:start position:0% +than a space that actually would be + + + align:start position:0% +than a space that actually would be +public. + + align:start position:0% +public. + + + align:start position:0% +public. +Yeah. I don't know about certainly Diego + + align:start position:0% +Yeah. I don't know about certainly Diego + + + align:start position:0% +Yeah. I don't know about certainly Diego +Rivera's mural + + align:start position:0% +Rivera's mural + + + align:start position:0% +Rivera's mural +was was + + align:start position:0% +was was + + + align:start position:0% +was was +removed uh and + + align:start position:0% +removed uh and + + + align:start position:0% +removed uh and +uh during the just before the 39 war + + align:start position:0% +uh during the just before the 39 war + + + align:start position:0% +uh during the just before the 39 war +Germany wanted to invest in Rockefeller + + align:start position:0% +Germany wanted to invest in Rockefeller + + + align:start position:0% +Germany wanted to invest in Rockefeller +center and built something called + + align:start position:0% +center and built something called + + + align:start position:0% +center and built something called +Deutsche House and that was turned down. + + align:start position:0% +Deutsche House and that was turned down. + + + align:start position:0% +Deutsche House and that was turned down. +Uh so the Rockefellers have played a + + align:start position:0% +Uh so the Rockefellers have played a + + + align:start position:0% +Uh so the Rockefellers have played a +very antiseptic attitude towards + + align:start position:0% +very antiseptic attitude towards + + + align:start position:0% +very antiseptic attitude towards +politics. I don't know what this present + + align:start position:0% +politics. I don't know what this present + + + align:start position:0% +politics. I don't know what this present +status would be. Security issues at the + + align:start position:0% +status would be. Security issues at the + + + align:start position:0% +status would be. Security issues at the +moment in America are probably so + + align:start position:0% +moment in America are probably so + + + align:start position:0% +moment in America are probably so +inflamed after Boston that uh you'd + + align:start position:0% +inflamed after Boston that uh you'd + + + align:start position:0% +inflamed after Boston that uh you'd +probably stop anybody carrying a + + align:start position:0% +probably stop anybody carrying a + + + align:start position:0% +probably stop anybody carrying a +knapsack for a while. Um, but to be more + + align:start position:0% +knapsack for a while. Um, but to be more + + + align:start position:0% +knapsack for a while. Um, but to be more +serious, I don't know about the + + align:start position:0% +serious, I don't know about the + + + align:start position:0% +serious, I don't know about the +limitations on public protest in New + + align:start position:0% +limitations on public protest in New + + + align:start position:0% +limitations on public protest in New +York. I should ask somebody. + + align:start position:0% +York. I should ask somebody. + + + align:start position:0% +York. I should ask somebody. +Um, I don't know of any history of the + + align:start position:0% +Um, I don't know of any history of the + + + align:start position:0% +Um, I don't know of any history of the +restriction of public protest in New + + align:start position:0% +restriction of public protest in New + + + align:start position:0% +restriction of public protest in New +York. It's a very open city. + + align:start position:0% +York. It's a very open city. + + + align:start position:0% +York. It's a very open city. +Well, with the + + align:start position:0% +Well, with the + + + align:start position:0% +Well, with the +protest, I mean, they started getting + + align:start position:0% +protest, I mean, they started getting + + + align:start position:0% +protest, I mean, they started getting +people in Iraq. + + align:start position:0% +people in Iraq. + + + align:start position:0% +people in Iraq. +Yeah, in that one too. I mean they would + + align:start position:0% +Yeah, in that one too. I mean they would + + + align:start position:0% +Yeah, in that one too. I mean they would +there was that famous that day before we + + align:start position:0% +there was that famous that day before we + + + align:start position:0% +there was that famous that day before we +invaded Iraq the second time there were + + align:start position:0% +invaded Iraq the second time there were + + + align:start position:0% +invaded Iraq the second time there were +protests all in cities all around the + + align:start position:0% +protests all in cities all around the + + + align:start position:0% +protests all in cities all around the +world and you saw you know most of that + + align:start position:0% +world and you saw you know most of that + + + align:start position:0% +world and you saw you know most of that +people gathered in plazas and in New + + align:start position:0% +people gathered in plazas and in New + + + align:start position:0% +people gathered in plazas and in New +York they had you pinned in you know + + align:start position:0% +York they had you pinned in you know + + + align:start position:0% +York they had you pinned in you know +they had all the streets blocked off + + align:start position:0% +they had all the streets blocked off + + + align:start position:0% +they had all the streets blocked off +with the um the popup fences + + align:start position:0% +with the um the popup fences + + + align:start position:0% +with the um the popup fences +didn't look very open. + + align:start position:0% + + + + align:start position:0% + +It raises + + align:start position:0% + + + + align:start position:0% + +another question which + + align:start position:0% +another question which + + + align:start position:0% +another question which +urbanistically is difficult to answer. + + align:start position:0% + + + + align:start position:0% + +Um we have city + + align:start position:0% +Um we have city + + + align:start position:0% +Um we have city +hall sitting on a + + align:start position:0% +hall sitting on a + + + align:start position:0% +hall sitting on a +plaza the mayor has said that he has + + align:start position:0% +plaza the mayor has said that he has + + + align:start position:0% +plaza the mayor has said that he has +actually thought of selling city hall + + align:start position:0% +actually thought of selling city hall + + + align:start position:0% +actually thought of selling city hall +plaza city hall not I don't know about + + align:start position:0% +plaza city hall not I don't know about + + + align:start position:0% +plaza city hall not I don't know about +the + + align:start position:0% +the + + + align:start position:0% +the +plaza do you feel more public when + + align:start position:0% +plaza do you feel more public when + + + align:start position:0% +plaza do you feel more public when +putting your body into space + + align:start position:0% +putting your body into space + + + align:start position:0% +putting your body into space +in Phileen's + + align:start position:0% +in Phileen's + + + align:start position:0% +in Phileen's +basement then you do in city hall + + align:start position:0% + + + + align:start position:0% + +plaza. If association with other people + + align:start position:0% +plaza. If association with other people + + + align:start position:0% +plaza. If association with other people +is the phenomenon which guides us from + + align:start position:0% +is the phenomenon which guides us from + + + align:start position:0% +is the phenomenon which guides us from +an self + + align:start position:0% +an self + + + align:start position:0% +an self +preoccupation to a sense of being or + + align:start position:0% +preoccupation to a sense of being or + + + align:start position:0% +preoccupation to a sense of being or +part of a human enlarged human race. + + align:start position:0% +part of a human enlarged human race. + + + align:start position:0% +part of a human enlarged human race. +part of the rhetoric of + + align:start position:0% +part of the rhetoric of + + + align:start position:0% +part of the rhetoric of +communication, + + align:start position:0% +communication, + + + align:start position:0% +communication, +stochastics and so on which Hana Arand + + align:start position:0% +stochastics and so on which Hana Arand + + + align:start position:0% +stochastics and so on which Hana Arand +makes a big fuss of in the human + + align:start position:0% +makes a big fuss of in the human + + + align:start position:0% +makes a big fuss of in the human +condition that we are different from + + align:start position:0% +condition that we are different from + + + align:start position:0% +condition that we are different from +animals. + + align:start position:0% +animals. + + + align:start position:0% +animals. +Uh I don't go to nor do I know anybody + + align:start position:0% +Uh I don't go to nor do I know anybody + + + align:start position:0% +Uh I don't go to nor do I know anybody +who goes to Boston City Hall or Plaza on + + align:start position:0% +who goes to Boston City Hall or Plaza on + + + align:start position:0% +who goes to Boston City Hall or Plaza on +a Sunday morning to negotiate with + + align:start position:0% +a Sunday morning to negotiate with + + + align:start position:0% +a Sunday morning to negotiate with +strangers. + + align:start position:0% + + + + align:start position:0% + +You do because you have too little else. + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +No, fair enough. + + align:start position:0% +No, fair enough. + + + align:start position:0% +No, fair enough. +You in a Cisi you will wander down to + + align:start position:0% +You in a Cisi you will wander down to + + + align:start position:0% +You in a Cisi you will wander down to +the patune because it's on your path + + align:start position:0% +the patune because it's on your path + + + align:start position:0% +the patune because it's on your path +somewhere else anyway. It's in the + + align:start position:0% +somewhere else anyway. It's in the + + + align:start position:0% +somewhere else anyway. It's in the +middle of a small town. Uh, and it's if + + align:start position:0% +middle of a small town. Uh, and it's if + + + align:start position:0% +middle of a small town. Uh, and it's if +there's any action. Secondly, the amount + + align:start position:0% +there's any action. Secondly, the amount + + + align:start position:0% +there's any action. Secondly, the amount +of private accommodation you've got is + + align:start position:0% +of private accommodation you've got is + + + align:start position:0% +of private accommodation you've got is +very + + align:start position:0% +very + + + align:start position:0% +very +small. Why do black kids in Baltimore + + align:start position:0% +small. Why do black kids in Baltimore + + + align:start position:0% +small. Why do black kids in Baltimore +play basketball in the + + align:start position:0% +play basketball in the + + + align:start position:0% +play basketball in the +street? Because they haven't got the + + align:start position:0% +street? Because they haven't got the + + + align:start position:0% +street? Because they haven't got the +space. They haven't got backyards to + + align:start position:0% +space. They haven't got backyards to + + + align:start position:0% +space. They haven't got backyards to +play basketball as you can in your own + + align:start position:0% +play basketball as you can in your own + + + align:start position:0% +play basketball as you can in your own +suburban garden. + + align:start position:0% +suburban garden. + + + align:start position:0% +suburban garden. +So there's all these connections. City + + align:start position:0% +So there's all these connections. City + + + align:start position:0% +So there's all these connections. City +or plaza should have been surrounded by + + align:start position:0% +or plaza should have been surrounded by + + + align:start position:0% +or plaza should have been surrounded by +dense housing. + + align:start position:0% + + + + align:start position:0% + +Most of + + align:start position:0% +Most of + + + align:start position:0% +Most of +the Rockefeller Center placed in De + + align:start position:0% +the Rockefeller Center placed in De + + + align:start position:0% +the Rockefeller Center placed in De +Moine, Iowa would not be the same as + + align:start position:0% +Moine, Iowa would not be the same as + + + align:start position:0% +Moine, Iowa would not be the same as +Rockefeller Center built on a grid of + + align:start position:0% +Rockefeller Center built on a grid of + + + align:start position:0% +Rockefeller Center built on a grid of +density plus + + align:start position:0% +density plus + + + align:start position:0% +density plus +income with Fifth Avenue right adjacent + + align:start position:0% +income with Fifth Avenue right adjacent + + + align:start position:0% +income with Fifth Avenue right adjacent +to it and part of a an extraordinary + + align:start position:0% +to it and part of a an extraordinary + + + align:start position:0% +to it and part of a an extraordinary +grid which pumps energy through all of + + align:start position:0% +grid which pumps energy through all of + + + align:start position:0% +grid which pumps energy through all of +the system much like your the the system + + align:start position:0% +the system much like your the the system + + + align:start position:0% +the system much like your the the system +of your articulation in your + + align:start position:0% + + + + align:start position:0% + +brain. Let's just look at some other + + align:start position:0% +brain. Let's just look at some other + + + align:start position:0% +brain. Let's just look at some other +examples. + + align:start position:0% + + + + align:start position:0% + +under the idea of control or + + align:start position:0% + + + + align:start position:0% + +axis. I pay taxes to maintain army + + align:start position:0% +axis. I pay taxes to maintain army + + + align:start position:0% +axis. I pay taxes to maintain army +camps and nuclear power stations and + + align:start position:0% +camps and nuclear power stations and + + + align:start position:0% +camps and nuclear power stations and +private domains which I don't claim + + align:start position:0% +private domains which I don't claim + + + align:start position:0% +private domains which I don't claim +access + + align:start position:0% +access + + + align:start position:0% +access +to but yet I own a fraction of it. + + align:start position:0% +to but yet I own a fraction of it. + + + align:start position:0% +to but yet I own a fraction of it. +What is public about + + align:start position:0% +What is public about + + + align:start position:0% +What is public about +me owning a part of the built + + align:start position:0% +me owning a part of the built + + + align:start position:0% +me owning a part of the built +environment but not being able to have + + align:start position:0% +environment but not being able to have + + + align:start position:0% +environment but not being able to have +access to + + align:start position:0% +access to + + + align:start position:0% +access to +it? I have much more access + + align:start position:0% + + + + align:start position:0% + +to shopping environments which are + + align:start position:0% +to shopping environments which are + + + align:start position:0% +to shopping environments which are +largely private. + + align:start position:0% +largely private. + + + align:start position:0% +largely private. +And I do + + align:start position:0% + + + + align:start position:0% + +too. Who guarantees access to all + + align:start position:0% + + + + align:start position:0% + +space? Independent of ownership. + + align:start position:0% + + + + align:start position:0% + +This is + + align:start position:0% +This is + + + align:start position:0% +This is +an a subject which Michael + + align:start position:0% +an a subject which Michael + + + align:start position:0% +an a subject which Michael +Soren tries to attack in his + + align:start position:0% +Soren tries to attack in his + + + align:start position:0% +Soren tries to attack in his +book. We terms shopping centers space to + + align:start position:0% +book. We terms shopping centers space to + + + align:start position:0% +book. We terms shopping centers space to +be a + + align:start position:0% +be a + + + align:start position:0% +be a +geographic + + align:start position:0% + + + + align:start position:0% + +where there's dissipation of stable + + align:start position:0% +where there's dissipation of stable + + + align:start position:0% +where there's dissipation of stable +relationships of loosening of ties to + + align:start position:0% +relationships of loosening of ties to + + + align:start position:0% +relationships of loosening of ties to +any specific place where there's nothing + + align:start position:0% +any specific place where there's nothing + + + align:start position:0% +any specific place where there's nothing +which is emanating from history. + + align:start position:0% +which is emanating from history. + + + align:start position:0% +which is emanating from history. +Everything is + + align:start position:0% + + + + align:start position:0% + +assets. A market doesn't produce any + + align:start position:0% +assets. A market doesn't produce any + + + align:start position:0% +assets. A market doesn't produce any +environment which has the + + align:start position:0% +environment which has the + + + align:start position:0% +environment which has the +resonance that is required + + align:start position:0% +resonance that is required + + + align:start position:0% +resonance that is required +for domain of public + + align:start position:0% + + + + align:start position:0% + +space. And lastly, the category of + + align:start position:0% + + + + align:start position:0% + +meaning. But just before we leave + + align:start position:0% +meaning. But just before we leave + + + align:start position:0% +meaning. But just before we leave +ownership, there's a category of + + align:start position:0% +ownership, there's a category of + + + align:start position:0% +ownership, there's a category of +psychological ownership which is very + + align:start position:0% +psychological ownership which is very + + + align:start position:0% +psychological ownership which is very +much part of the herabitation of your + + align:start position:0% + + + + align:start position:0% + +urbanism. If I had to ask you in + + align:start position:0% +urbanism. If I had to ask you in + + + align:start position:0% +urbanism. If I had to ask you in +Boston, what would be missed more? the + + align:start position:0% +Boston, what would be missed more? the + + + align:start position:0% +Boston, what would be missed more? the +Boston Celtics moving to + + align:start position:0% +Boston Celtics moving to + + + align:start position:0% +Boston Celtics moving to +Sacramento or City of Old Plaza being + + align:start position:0% + + + + align:start position:0% + +redeveloped. The one is an absolutely + + align:start position:0% +redeveloped. The one is an absolutely + + + align:start position:0% +redeveloped. The one is an absolutely +public + + align:start position:0% +public + + + align:start position:0% +public +phenomenon, + + align:start position:0% +phenomenon, + + + align:start position:0% +phenomenon, +especially the Celtics or private + + align:start position:0% +especially the Celtics or private + + + align:start position:0% +especially the Celtics or private +company. + + align:start position:0% + + + + align:start position:0% + +They they're only physical here in the + + align:start position:0% +They they're only physical here in the + + + align:start position:0% +They they're only physical here in the +sense they play 62 31 games a year in + + align:start position:0% +sense they play 62 31 games a year in + + + align:start position:0% +sense they play 62 31 games a year in +this in the + + align:start position:0% +this in the + + + align:start position:0% +this in the +town but the psychological + + align:start position:0% +town but the psychological + + + align:start position:0% +town but the psychological +ownership which is very again we go back + + align:start position:0% +ownership which is very again we go back + + + align:start position:0% +ownership which is very again we go back +to Rossi or not back to him necessarily + + align:start position:0% +to Rossi or not back to him necessarily + + + align:start position:0% +to Rossi or not back to him necessarily +but we get the sense that there + + align:start position:0% +but we get the sense that there + + + align:start position:0% +but we get the sense that there +are traces of understanding which we + + align:start position:0% +are traces of understanding which we + + + align:start position:0% +are traces of understanding which we +carry with us as human beings. + + align:start position:0% +carry with us as human beings. + + + align:start position:0% +carry with us as human beings. +which are not absolutely + + align:start position:0% + + + + align:start position:0% + +contingent. It's 5 + + align:start position:0% + + + + align:start position:0% + +to2. Let us talk a little bit about + + align:start position:0% + + + + align:start position:0% + +meaning. The federal courthouse in + + align:start position:0% +meaning. The federal courthouse in + + + align:start position:0% +meaning. The federal courthouse in +Boston is an interesting example. + + align:start position:0% +Boston is an interesting example. + + + align:start position:0% +Boston is an interesting example. +It faces the towards the + + align:start position:0% +It faces the towards the + + + align:start position:0% +It faces the towards the +sea which is a foodish kind of notion + + align:start position:0% +sea which is a foodish kind of notion + + + align:start position:0% +sea which is a foodish kind of notion +facing to lobstermen in the + + align:start position:0% +facing to lobstermen in the + + + align:start position:0% +facing to lobstermen in the +boats. The traditional courthouse in New + + align:start position:0% +boats. The traditional courthouse in New + + + align:start position:0% +boats. The traditional courthouse in New +England faces towards the town to a + + align:start position:0% +England faces towards the town to a + + + align:start position:0% +England faces towards the town to a +square opposed to a church or something + + align:start position:0% +square opposed to a church or something + + + align:start position:0% +square opposed to a church or something +of this kind. It's really weird because + + align:start position:0% +of this kind. It's really weird because + + + align:start position:0% +of this kind. It's really weird because +a courthouse here not only faces the + + align:start position:0% +a courthouse here not only faces the + + + align:start position:0% +a courthouse here not only faces the +seat, it has real good prime real estate + + align:start position:0% +seat, it has real good prime real estate + + + align:start position:0% +seat, it has real good prime real estate +that is off limits. It's heavily secured + + align:start position:0% +that is off limits. It's heavily secured + + + align:start position:0% +that is off limits. It's heavily secured +around as usual. Well, it has a + + align:start position:0% +around as usual. Well, it has a + + + align:start position:0% +around as usual. Well, it has a +McDonald's underneath it. Yeah. + + align:start position:0% +McDonald's underneath it. Yeah. + + + align:start position:0% +McDonald's underneath it. Yeah. +Underneath. Well, that's part of it. So, + + align:start position:0% +Underneath. Well, that's part of it. So, + + + align:start position:0% +Underneath. Well, that's part of it. So, +it's weird to stand in that little + + align:start position:0% +it's weird to stand in that little + + + align:start position:0% +it's weird to stand in that little +corner, that little tip, and look at + + align:start position:0% +corner, that little tip, and look at + + + align:start position:0% +corner, that little tip, and look at +what they have and then at the same time + + align:start position:0% +what they have and then at the same time + + + align:start position:0% +what they have and then at the same time +see nobody moving around because of the + + align:start position:0% +see nobody moving around because of the + + + align:start position:0% +see nobody moving around because of the +security around. Yeah. running places. + + align:start position:0% +security around. Yeah. running places. + + + align:start position:0% +security around. Yeah. running places. +It's it's badly configured in a number + + align:start position:0% +It's it's badly configured in a number + + + align:start position:0% +It's it's badly configured in a number +of ways, but there are there are private + + align:start position:0% +of ways, but there are there are private + + + align:start position:0% +of ways, but there are there are private +courouses in New England in Boston. In + + align:start position:0% +courouses in New England in Boston. In + + + align:start position:0% +courouses in New England in Boston. In +the State Street building, there are + + align:start position:0% +the State Street building, there are + + + align:start position:0% +the State Street building, there are +there are courouses which are purely + + align:start position:0% +there are courouses which are purely + + + align:start position:0% +there are courouses which are purely +private where you can settle civil suits + + align:start position:0% +private where you can settle civil suits + + + align:start position:0% +private where you can settle civil suits +by judges who are retired sitting in and + + align:start position:0% +by judges who are retired sitting in and + + + align:start position:0% +by judges who are retired sitting in and +you have to agree that you will. Now + + align:start position:0% +you have to agree that you will. Now + + + align:start position:0% +you have to agree that you will. Now +what is the difference between a public + + align:start position:0% +what is the difference between a public + + + align:start position:0% +what is the difference between a public +courthouse and a private courthouse? In + + align:start position:0% +courthouse and a private courthouse? In + + + align:start position:0% +courthouse and a private courthouse? In +contemporary + + align:start position:0% +contemporary + + + align:start position:0% +contemporary +s the private courthouse is lost in the + + align:start position:0% +s the private courthouse is lost in the + + + align:start position:0% +s the private courthouse is lost in the +build in the assemblage of this state + + align:start position:0% +build in the assemblage of this state + + + align:start position:0% +build in the assemblage of this state +street building. You could be going to + + align:start position:0% +street building. You could be going to + + + align:start position:0% +street building. You could be going to +visit your accountant instead of which + + align:start position:0% +visit your accountant instead of which + + + align:start position:0% +visit your accountant instead of which +you go to a + + align:start position:0% +you go to a + + + align:start position:0% +you go to a +courthouse which is not all you have to + + align:start position:0% +courthouse which is not all you have to + + + align:start position:0% +courthouse which is not all you have to +agree is to listen to take the judgment + + align:start position:0% +agree is to listen to take the judgment + + + align:start position:0% +agree is to listen to take the judgment +of you have it's a wonderfully beautiful + + align:start position:0% +of you have it's a wonderfully beautiful + + + align:start position:0% +of you have it's a wonderfully beautiful +environment he doesn't have the dsgs of + + align:start position:0% +environment he doesn't have the dsgs of + + + align:start position:0% +environment he doesn't have the dsgs of +the population have to go to a public + + align:start position:0% + + + + align:start position:0% + +courthouse I wonder how that would + + align:start position:0% +courthouse I wonder how that would + + + align:start position:0% +courthouse I wonder how that would +configure in + + align:start position:0% +configure in + + + align:start position:0% +configure in +cre's structure + + align:start position:0% + + + + align:start position:0% + +on. + + align:start position:0% + + + + align:start position:0% + +Okay. I've used the shorthand system of + + align:start position:0% +Okay. I've used the shorthand system of + + + align:start position:0% +Okay. I've used the shorthand system of +trying to connect us to some of the + + align:start position:0% +trying to connect us to some of the + + + align:start position:0% +trying to connect us to some of the +dilemmas of public and private life. + + align:start position:0% + + + + align:start position:0% + +The idea of solitude of removal + + align:start position:0% +The idea of solitude of removal + + + align:start position:0% +The idea of solitude of removal +from the + + align:start position:0% +from the + + + align:start position:0% +from the +public was considered + + align:start position:0% +public was considered + + + align:start position:0% +public was considered +madness in medieval + + align:start position:0% +madness in medieval + + + align:start position:0% +madness in medieval +society. You were + + align:start position:0% + + + + align:start position:0% + +you considered is insane or heroic. If + + align:start position:0% +you considered is insane or heroic. If + + + align:start position:0% +you considered is insane or heroic. If +you went on a + + align:start position:0% +you went on a + + + align:start position:0% +you went on a +trip without somebody else, without a + + align:start position:0% +trip without somebody else, without a + + + align:start position:0% +trip without somebody else, without a +group of + + align:start position:0% +group of + + + align:start position:0% +group of +people to build a to maintain your own + + align:start position:0% +people to build a to maintain your own + + + align:start position:0% +people to build a to maintain your own +private garden was considered as a + + align:start position:0% +private garden was considered as a + + + align:start position:0% +private garden was considered as a +very antisocial move. + + align:start position:0% + + + + align:start position:0% + +What caused + + align:start position:0% +What caused + + + align:start position:0% +What caused +us as a society to + + align:start position:0% +us as a society to + + + align:start position:0% +us as a society to +change from an extreme + + align:start position:0% +change from an extreme + + + align:start position:0% +change from an extreme +publicness and you read this book on + + align:start position:0% +publicness and you read this book on + + + align:start position:0% +publicness and you read this book on +Socrates in + + align:start position:0% +Socrates in + + + align:start position:0% +Socrates in +Athens, you are amazed at the sense of + + align:start position:0% +Athens, you are amazed at the sense of + + + align:start position:0% +Athens, you are amazed at the sense of +transparency. + + align:start position:0% + + + + align:start position:0% + +Socrates would be walking barefoot + + align:start position:0% +Socrates would be walking barefoot + + + align:start position:0% +Socrates would be walking barefoot +through the agura and a young man would + + align:start position:0% +through the agura and a young man would + + + align:start position:0% +through the agura and a young man would +come up to him and ask him something and + + align:start position:0% +come up to him and ask him something and + + + align:start position:0% +come up to him and ask him something and +he'd give a philosophical + + align:start position:0% +he'd give a philosophical + + + align:start position:0% +he'd give a philosophical +answer and the young man would be asking + + align:start position:0% +answer and the young man would be asking + + + align:start position:0% +answer and the young man would be asking +for where he could buy food. + + align:start position:0% +for where he could buy food. + + + align:start position:0% +for where he could buy food. +This intermering of the acceptance of + + align:start position:0% +This intermering of the acceptance of + + + align:start position:0% +This intermering of the acceptance of +remote speculation about life and + + align:start position:0% +remote speculation about life and + + + align:start position:0% +remote speculation about life and +everyday + + align:start position:0% +everyday + + + align:start position:0% +everyday +things is not part of our domain any + + align:start position:0% +things is not part of our domain any + + + align:start position:0% +things is not part of our domain any +longer. It may be in some + + align:start position:0% + + + + align:start position:0% + +places. Why did we invent solitude? + + align:start position:0% + + + + align:start position:0% + +Start with that question. Think about + + align:start position:0% +Start with that question. Think about + + + align:start position:0% +Start with that question. Think about +the answer to that + + align:start position:0% + + + + align:start position:0% + +question. We are blamed by Hana to + + align:start position:0% +question. We are blamed by Hana to + + + align:start position:0% +question. We are blamed by Hana to +Richard Senate and + + align:start position:0% +Richard Senate and + + + align:start position:0% +Richard Senate and +endless architects for not behaving more + + align:start position:0% +endless architects for not behaving more + + + align:start position:0% +endless architects for not behaving more +in public. + + align:start position:0% + + + + align:start position:0% + +I lived in a CC4 neck close to here + + align:start position:0% +I lived in a CC4 neck close to here + + + align:start position:0% +I lived in a CC4 neck close to here +measuring the whole + + align:start position:0% +measuring the whole + + + align:start position:0% +measuring the whole +town. This is a drawing an axonometric + + align:start position:0% +town. This is a drawing an axonometric + + + align:start position:0% +town. This is a drawing an axonometric +based on my measurements. + + align:start position:0% +based on my measurements. + + + align:start position:0% +based on my measurements. +That's some of the texture of part of + + align:start position:0% +That's some of the texture of part of + + + align:start position:0% +That's some of the texture of part of +the part of my purpose was + + align:start position:0% +the part of my purpose was + + + align:start position:0% +the part of my purpose was +after being at MIT as a student and + + align:start position:0% +after being at MIT as a student and + + + align:start position:0% +after being at MIT as a student and +teaching I got a Rome prize to study + + align:start position:0% +teaching I got a Rome prize to study + + + align:start position:0% +teaching I got a Rome prize to study +pedestrian movement in a small town. + + align:start position:0% + + + + align:start position:0% + +Next, this is the pat delun and those + + align:start position:0% +Next, this is the pat delun and those + + + align:start position:0% +Next, this is the pat delun and those +are the measurements of pedestrian flow + + align:start position:0% +are the measurements of pedestrian flow + + + align:start position:0% +are the measurements of pedestrian flow +at different times of the day. One of + + align:start position:0% +at different times of the day. One of + + + align:start position:0% +at different times of the day. One of +the things that is interesting was that + + align:start position:0% +the things that is interesting was that + + + align:start position:0% +the things that is interesting was that +there was always + + align:start position:0% +there was always + + + align:start position:0% +there was always +as the patun is the central plaza of the + + align:start position:0% +as the patun is the central plaza of the + + + align:start position:0% +as the patun is the central plaza of the +town. Aisi is a linear town. + + align:start position:0% + + + + align:start position:0% + +I just turn on the light for a + + align:start position:0% +I just turn on the light for a + + + align:start position:0% +I just turn on the light for a +second + + align:start position:0% + + + + align:start position:0% + +cuz I'm afraid you have to. It's got + + align:start position:0% +cuz I'm afraid you have to. It's got + + + align:start position:0% +cuz I'm afraid you have to. It's got +this mad system of turning it off in one + + align:start position:0% +this mad system of turning it off in one + + + align:start position:0% +this mad system of turning it off in one +place and turning it on in another + + align:start position:0% + + + + align:start position:0% + +place. He sees he's on the slope of a + + align:start position:0% +place. He sees he's on the slope of a + + + align:start position:0% +place. He sees he's on the slope of a +hill. + + align:start position:0% + + + + align:start position:0% + +The town consists of a set of public + + align:start position:0% +The town consists of a set of public + + + align:start position:0% +The town consists of a set of public +spaces + + align:start position:0% +spaces + + + align:start position:0% +spaces +linked across the grain and go along the + + align:start position:0% +linked across the grain and go along the + + + align:start position:0% +linked across the grain and go along the +contours with a major patzo or kimuna in + + align:start position:0% +contours with a major patzo or kimuna in + + + align:start position:0% +contours with a major patzo or kimuna in +the + + align:start position:0% +the + + + align:start position:0% +the +center because The land use is + + align:start position:0% +center because The land use is + + + align:start position:0% +center because The land use is +distributed throughout the town. There's + + align:start position:0% +distributed throughout the town. There's + + + align:start position:0% +distributed throughout the town. There's +as much chance of there being a + + align:start position:0% +as much chance of there being a + + + align:start position:0% +as much chance of there being a +destination here as a destination + + align:start position:0% + + + + align:start position:0% + +here. The volume of traffic moving this + + align:start position:0% +here. The volume of traffic moving this + + + align:start position:0% +here. The volume of traffic moving this +way through the center of the town is + + align:start position:0% +way through the center of the town is + + + align:start position:0% +way through the center of the town is +the same as the volume moving that way + + align:start position:0% +the same as the volume moving that way + + + align:start position:0% +the same as the volume moving that way +through the town. + + align:start position:0% +through the town. + + + align:start position:0% +through the town. +So the center of the + + align:start position:0% +So the center of the + + + align:start position:0% +So the center of the +town in a very + + align:start position:0% + + + + align:start position:0% + +dense non bulldozer kind of + + align:start position:0% +dense non bulldozer kind of + + + align:start position:0% +dense non bulldozer kind of +environment is a combination + + align:start position:0% +environment is a combination + + + align:start position:0% +environment is a combination +of + + align:start position:0% +of + + + align:start position:0% +of +platforms at + + align:start position:0% +platforms at + + + align:start position:0% +platforms at +different steepnesses. Patza with a San + + align:start position:0% +different steepnesses. Patza with a San + + + align:start position:0% +different steepnesses. Patza with a San +Rufino, Santa Kiara, San Francesco and + + align:start position:0% +Rufino, Santa Kiara, San Francesco and + + + align:start position:0% +Rufino, Santa Kiara, San Francesco and +so + + align:start position:0% +so + + + align:start position:0% +so +on forming the basis for the + + align:start position:0% +on forming the basis for the + + + align:start position:0% +on forming the basis for the +organization of the town into + + align:start position:0% +organization of the town into + + + align:start position:0% +organization of the town into +parishes and into + + align:start position:0% +parishes and into + + + align:start position:0% +parishes and into +neighborhoods. But essentially the + + align:start position:0% +neighborhoods. But essentially the + + + align:start position:0% +neighborhoods. But essentially the +meeting + + align:start position:0% +meeting + + + align:start position:0% +meeting +place is in a restricted town in the + + align:start position:0% +place is in a restricted town in the + + + align:start position:0% +place is in a restricted town in the +center and serves both as a pass through + + align:start position:0% +center and serves both as a pass through + + + align:start position:0% +center and serves both as a pass through +and as a place. + + align:start position:0% + + + + align:start position:0% + +The slide on the left is my crude + + align:start position:0% +The slide on the left is my crude + + + align:start position:0% +The slide on the left is my crude +attempt at lap timelapse + + align:start position:0% +attempt at lap timelapse + + + align:start position:0% +attempt at lap timelapse +photography of a burial of a + + align:start position:0% +photography of a burial of a + + + align:start position:0% +photography of a burial of a +soldier in the central plaza. + + align:start position:0% + + + + align:start position:0% + +Next, I stayed up in a tower above the + + align:start position:0% +Next, I stayed up in a tower above the + + + align:start position:0% +Next, I stayed up in a tower above the +plaza for many hours of the day and + + align:start position:0% +plaza for many hours of the day and + + + align:start position:0% +plaza for many hours of the day and +night and was struck by the fact that + + align:start position:0% +night and was struck by the fact that + + + align:start position:0% +night and was struck by the fact that +when there's nobody in the plaza, a + + align:start position:0% +when there's nobody in the plaza, a + + + align:start position:0% +when there's nobody in the plaza, a +small years of postman delivering mail, + + align:start position:0% +small years of postman delivering mail, + + + align:start position:0% +small years of postman delivering mail, +it still seems very well + + align:start position:0% +it still seems very well + + + align:start position:0% +it still seems very well +inhabited as opposed to when it was full + + align:start position:0% +inhabited as opposed to when it was full + + + align:start position:0% +inhabited as opposed to when it was full +with a crowd. It seemed appropriately + + align:start position:0% +with a crowd. It seemed appropriately + + + align:start position:0% +with a crowd. It seemed appropriately +sized. + + align:start position:0% + + + + align:start position:0% + +Next, traditionally the piaza, the + + align:start position:0% +Next, traditionally the piaza, the + + + align:start position:0% +Next, traditionally the piaza, the +Italian piaza + + align:start position:0% +Italian piaza + + + align:start position:0% +Italian piaza +um takes its form from a position of + + align:start position:0% +um takes its form from a position of + + + align:start position:0% +um takes its form from a position of +centrality or axis surrounded by dense + + align:start position:0% +centrality or axis surrounded by dense + + + align:start position:0% +centrality or axis surrounded by dense +in housing environments surrounded by a + + align:start position:0% +in housing environments surrounded by a + + + align:start position:0% +in housing environments surrounded by a +wall. This is a classic image of it + + align:start position:0% +wall. This is a classic image of it + + + align:start position:0% +wall. This is a classic image of it +plays out in different + + align:start position:0% +plays out in different + + + align:start position:0% +plays out in different +ways as the town is a bit bigger than + + align:start position:0% +ways as the town is a bit bigger than + + + align:start position:0% +ways as the town is a bit bigger than +this one. This is the paleio in + + align:start position:0% +this one. This is the paleio in + + + align:start position:0% +this one. This is the paleio in +Sienna. Um originally it is a place for + + align:start position:0% +Sienna. Um originally it is a place for + + + align:start position:0% +Sienna. Um originally it is a place for +festivals and for + + align:start position:0% +festivals and for + + + align:start position:0% +festivals and for +u + + align:start position:0% +u + + + align:start position:0% +u +animal games. + + align:start position:0% + + + + align:start position:0% + +Next, now it is a a large open space + + align:start position:0% +Next, now it is a a large open space + + + align:start position:0% +Next, now it is a a large open space +which twice a year hosts a paleio and a + + align:start position:0% +which twice a year hosts a paleio and a + + + align:start position:0% +which twice a year hosts a paleio and a +polio is a kind of medieval + + align:start position:0% +polio is a kind of medieval + + + align:start position:0% +polio is a kind of medieval +reconstruction of a ritual. It's a game + + align:start position:0% +reconstruction of a ritual. It's a game + + + align:start position:0% +reconstruction of a ritual. It's a game +in which the various components of the + + align:start position:0% +in which the various components of the + + + align:start position:0% +in which the various components of the +town + + align:start position:0% +town + + + align:start position:0% +town +compete in a race where a lot of money + + align:start position:0% +compete in a race where a lot of money + + + align:start position:0% +compete in a race where a lot of money +is now + + align:start position:0% +is now + + + align:start position:0% +is now +gambled. On the right is an example of + + align:start position:0% +gambled. On the right is an example of + + + align:start position:0% +gambled. On the right is an example of +the use of public space for private use. + + align:start position:0% +the use of public space for private use. + + + align:start position:0% +the use of public space for private use. +This is very typical in the Italian open + + align:start position:0% +This is very typical in the Italian open + + + align:start position:0% +This is very typical in the Italian open +space where land is leased from the + + align:start position:0% +space where land is leased from the + + + align:start position:0% +space where land is leased from the +public authority by the + + align:start position:0% + + + + align:start position:0% + +private in this case a restaurant. + + align:start position:0% + + + + align:start position:0% + +Next the + + align:start position:0% +Next the + + + align:start position:0% +Next the +paleio takes place in the pat delo. + + align:start position:0% + + + + align:start position:0% + +Here there are other significant places + + align:start position:0% +Here there are other significant places + + + align:start position:0% +Here there are other significant places +in the town. Just above it is + + align:start position:0% + + + + align:start position:0% + +the great + + align:start position:0% +the great + + + align:start position:0% +the great +cathedral and medieval hospital. + + align:start position:0% + + + + align:start position:0% + +People have fussed a lot about the + + align:start position:0% +People have fussed a lot about the + + + align:start position:0% +People have fussed a lot about the +emptiness + + align:start position:0% +emptiness + + + align:start position:0% +emptiness +of city hall or plaza and there are at + + align:start position:0% +of city hall or plaza and there are at + + + align:start position:0% +of city hall or plaza and there are at +least two thesis which have been written + + align:start position:0% +least two thesis which have been written + + + align:start position:0% +least two thesis which have been written +about + + align:start position:0% +about + + + align:start position:0% +about +it and two competitions to do something + + align:start position:0% +it and two competitions to do something + + + align:start position:0% +it and two competitions to do something +about + + align:start position:0% +about + + + align:start position:0% +about +it. What is wrong with Boston city hall + + align:start position:0% + + + + align:start position:0% + +plaza? Say something. It has no active. + + align:start position:0% +plaza? Say something. It has no active. + + + align:start position:0% +plaza? Say something. It has no active. +There's no active what? + + align:start position:0% + + + + align:start position:0% + +Okay. There's no reason + + align:start position:0% + + + + align:start position:0% + +the building. + + align:start position:0% +the building. + + + align:start position:0% +the building. +The building is the problem. Why is the + + align:start position:0% +The building is the problem. Why is the + + + align:start position:0% +The building is the problem. Why is the +building a problem? Is one part of the + + align:start position:0% +building a problem? Is one part of the + + + align:start position:0% +building a problem? Is one part of the +problem. + + align:start position:0% +problem. + + + align:start position:0% +problem. +Okay. So, we've got a couple of ideas. + + align:start position:0% +Okay. So, we've got a couple of ideas. + + + align:start position:0% +Okay. So, we've got a couple of ideas. +The one is there's not enough housing + + align:start position:0% +The one is there's not enough housing + + + align:start position:0% +The one is there's not enough housing +density around the + + align:start position:0% +density around the + + + align:start position:0% +density around the +square. It's probably a good + + align:start position:0% + + + + align:start position:0% + +observation. In a decentralized city, + + align:start position:0% +observation. In a decentralized city, + + + align:start position:0% +observation. In a decentralized city, +why do you need a central square? + + align:start position:0% + + + + align:start position:0% + +Stubbornness. + + align:start position:0% +Stubbornness. + + + align:start position:0% +Stubbornness. +Stubbornness. + + align:start position:0% + + + + align:start position:0% + +Yes. Archivalness. + + align:start position:0% +Yes. Archivalness. + + + align:start position:0% +Yes. Archivalness. +Yeah. It's that this was a good idea. + + align:start position:0% +Yeah. It's that this was a good idea. + + + align:start position:0% +Yeah. It's that this was a good idea. +historically, but it's + + align:start position:0% +historically, but it's + + + align:start position:0% +historically, but it's +misappropriated literally. It's taken + + align:start position:0% +misappropriated literally. It's taken + + + align:start position:0% +misappropriated literally. It's taken +out of another context and placed in one + + align:start position:0% +out of another context and placed in one + + + align:start position:0% +out of another context and placed in one +which doesn't serve + + align:start position:0% +which doesn't serve + + + align:start position:0% +which doesn't serve +it. + + align:start position:0% +it. + + + align:start position:0% +it. +[Music] + + align:start position:0% + + + + align:start position:0% + +Um there have been two attempts at + + align:start position:0% +Um there have been two attempts at + + + align:start position:0% +Um there have been two attempts at +solutions in competitions. The one is + + align:start position:0% +solutions in competitions. The one is + + + align:start position:0% +solutions in competitions. The one is +formal that is to do something formally. + + align:start position:0% +formal that is to do something formally. + + + align:start position:0% +formal that is to do something formally. +One of them was to + + align:start position:0% +One of them was to + + + align:start position:0% +One of them was to +continue Hannova Street from the north + + align:start position:0% +continue Hannova Street from the north + + + align:start position:0% +continue Hannova Street from the north +end through the plaza + + align:start position:0% +end through the plaza + + + align:start position:0% +end through the plaza +uh and to advocate some shopping along + + align:start position:0% +uh and to advocate some shopping along + + + align:start position:0% +uh and to advocate some shopping along +it. Uh others have proposed no formal + + align:start position:0% +it. Uh others have proposed no formal + + + align:start position:0% +it. Uh others have proposed no formal +intervention but only programmatic + + align:start position:0% +intervention but only programmatic + + + align:start position:0% +intervention but only programmatic +intervention. There's one famous one + + align:start position:0% +intervention. There's one famous one + + + align:start position:0% +intervention. There's one famous one +which puts a baseball diamond in the + + align:start position:0% +which puts a baseball diamond in the + + + align:start position:0% +which puts a baseball diamond in the +square. + + align:start position:0% +square. + + + align:start position:0% +square. +Um + + align:start position:0% + + + + align:start position:0% + +also I think the biggest difference is + + align:start position:0% +also I think the biggest difference is + + + align:start position:0% +also I think the biggest difference is +that uh in Sienna you the space it's + + align:start position:0% +that uh in Sienna you the space it's + + + align:start position:0% +that uh in Sienna you the space it's +like an interior space in an outdoor + + align:start position:0% +like an interior space in an outdoor + + + align:start position:0% +like an interior space in an outdoor +place because it's + + align:start position:0% +place because it's + + + align:start position:0% +place because it's +including and here the space just on the + + align:start position:0% +including and here the space just on the + + + align:start position:0% +including and here the space just on the +sides. + + align:start position:0% +sides. + + + align:start position:0% +sides. +Well, + + align:start position:0% + + + + align:start position:0% + +there there + + align:start position:0% + + + + align:start position:0% + +are city wall there's another tradition + + align:start position:0% +are city wall there's another tradition + + + align:start position:0% +are city wall there's another tradition +of open space which I'm not showing that + + align:start position:0% +of open space which I'm not showing that + + + align:start position:0% +of open space which I'm not showing that +is the creation of open space in front + + align:start position:0% +is the creation of open space in front + + + align:start position:0% +is the creation of open space in front +of important + + align:start position:0% +of important + + + align:start position:0% +of important +buildings. Uh in Aisi there they happen + + align:start position:0% +buildings. Uh in Aisi there they happen + + + align:start position:0% +buildings. Uh in Aisi there they happen +to be small open spaces plazas in front + + align:start position:0% +to be small open spaces plazas in front + + + align:start position:0% +to be small open spaces plazas in front +of each major + + align:start position:0% +of each major + + + align:start position:0% +of each major +church. + + align:start position:0% +church. + + + align:start position:0% +church. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +this depends very much on the quality of + + align:start position:0% +this depends very much on the quality of + + + align:start position:0% +this depends very much on the quality of +the building that is being + + align:start position:0% +the building that is being + + + align:start position:0% +the building that is being +addressed and whether there's any real + + align:start position:0% + + + + align:start position:0% + +significance in the comfort of Sienna. + + align:start position:0% +significance in the comfort of Sienna. + + + align:start position:0% +significance in the comfort of Sienna. +The municipality has paintings from + + align:start position:0% +The municipality has paintings from + + + align:start position:0% +The municipality has paintings from +medieval times of the kumune. There's a + + align:start position:0% +medieval times of the kumune. There's a + + + align:start position:0% +medieval times of the kumune. There's a +sense that the this place is somehow to + + align:start position:0% +sense that the this place is somehow to + + + align:start position:0% +sense that the this place is somehow to +use a word from our first class that + + align:start position:0% +use a word from our first class that + + + align:start position:0% +use a word from our first class that +it's somehow + + align:start position:0% +it's somehow + + + align:start position:0% +it's somehow +centered. I'm using a word from the + + align:start position:0% +centered. I'm using a word from the + + + align:start position:0% +centered. I'm using a word from the +cosmic + + align:start position:0% +cosmic + + + align:start position:0% +cosmic +model centeredness. + + align:start position:0% +model centeredness. + + + align:start position:0% +model centeredness. +It's + + align:start position:0% +It's + + + align:start position:0% +It's +a met + + align:start position:0% +a met + + + align:start position:0% +a met +metaphysical con + + align:start position:0% +metaphysical con + + + align:start position:0% +metaphysical con +concept. + + align:start position:0% + + + + align:start position:0% + +Um in the case of the compo it is both + + align:start position:0% +Um in the case of the compo it is both + + + align:start position:0% +Um in the case of the compo it is both +and a CC it is both I repeat myself it + + align:start position:0% +and a CC it is both I repeat myself it + + + align:start position:0% +and a CC it is both I repeat myself it +is both an important functional path to + + align:start position:0% +is both an important functional path to + + + align:start position:0% +is both an important functional path to +connect and also a place which can serve + + align:start position:0% +connect and also a place which can serve + + + align:start position:0% +connect and also a place which can serve +both small and large + + align:start position:0% + + + + align:start position:0% + +functions. Next + + align:start position:0% + + + + align:start position:0% + +This is + + align:start position:0% +This is + + + align:start position:0% +This is +the + + align:start position:0% +the + + + align:start position:0% +the +underground of Rockefeller Center with a + + align:start position:0% +underground of Rockefeller Center with a + + + align:start position:0% +underground of Rockefeller Center with a +shopping mall and elevators and new + + align:start position:0% +shopping mall and elevators and new + + + align:start position:0% +shopping mall and elevators and new +roads and the rooftop + + align:start position:0% +roads and the rooftop + + + align:start position:0% +roads and the rooftop +condition which was even considered to + + align:start position:0% +condition which was even considered to + + + align:start position:0% +condition which was even considered to +have aerial bridges above and recreation + + align:start position:0% +have aerial bridges above and recreation + + + align:start position:0% +have aerial bridges above and recreation +events on the roof. + + align:start position:0% +events on the roof. + + + align:start position:0% +events on the roof. +So in Rockefeller + + align:start position:0% + + + + align:start position:0% + +Center this is public space below and + + align:start position:0% + + + + align:start position:0% + +above. Next + + align:start position:0% + + + + align:start position:0% + +This is the + + align:start position:0% +This is the + + + align:start position:0% +This is the +largest probably at its time the largest + + align:start position:0% +largest probably at its time the largest + + + align:start position:0% +largest probably at its time the largest +private building development in + + align:start position:0% +private building development in + + + align:start position:0% +private building development in +history. I don't know about the + + align:start position:0% +history. I don't know about the + + + align:start position:0% +history. I don't know about the +comparing it to the pyramids or + + align:start position:0% +comparing it to the pyramids or + + + align:start position:0% +comparing it to the pyramids or +whatever, but in modern times + + align:start position:0% +whatever, but in modern times + + + align:start position:0% +whatever, but in modern times +certainly it's + + align:start position:0% +certainly it's + + + align:start position:0% +certainly it's +part it's like a + + align:start position:0% +part it's like a + + + align:start position:0% +part it's like a +Cisci the square is part of the + + align:start position:0% +Cisci the square is part of the + + + align:start position:0% +Cisci the square is part of the +structure the geometry of the whole + + align:start position:0% +structure the geometry of the whole + + + align:start position:0% +structure the geometry of the whole +town. In this + + align:start position:0% +town. In this + + + align:start position:0% +town. In this +case, it fits into a grid system which + + align:start position:0% +case, it fits into a grid system which + + + align:start position:0% +case, it fits into a grid system which +it doesn't try to destroy but actually + + align:start position:0% +it doesn't try to destroy but actually + + + align:start position:0% +it doesn't try to destroy but actually +adds + + align:start position:0% + + + + align:start position:0% + +roads. So its adjacency to fifth + + align:start position:0% +roads. So its adjacency to fifth + + + align:start position:0% +roads. So its adjacency to fifth +avenue plus its + + align:start position:0% +avenue plus its + + + align:start position:0% +avenue plus its +surrounding of a high density and high + + align:start position:0% +surrounding of a high density and high + + + align:start position:0% +surrounding of a high density and high +income + + align:start position:0% +income + + + align:start position:0% +income +area make this square again a + + align:start position:0% +area make this square again a + + + align:start position:0% +area make this square again a +functionally appropriate + + align:start position:0% +functionally appropriate + + + align:start position:0% +functionally appropriate +commodity not + + align:start position:0% +commodity not + + + align:start position:0% +commodity not +a an attempt to symbolize something. + + align:start position:0% + + + + align:start position:0% + +Next attempts + + align:start position:0% +Next attempts + + + align:start position:0% +Next attempts +to this + + align:start position:0% +to this + + + align:start position:0% +to this +is on the left a project called urban + + align:start position:0% +is on the left a project called urban + + + align:start position:0% +is on the left a project called urban +design Manhattan some 25 30 years ago by + + align:start position:0% +design Manhattan some 25 30 years ago by + + + align:start position:0% +design Manhattan some 25 30 years ago by +a group who tried to argue that the way + + align:start position:0% +a group who tried to argue that the way + + + align:start position:0% +a group who tried to argue that the way +to deal with Manhattan was to see it as + + align:start position:0% +to deal with Manhattan was to see it as + + + align:start position:0% +to deal with Manhattan was to see it as +a + + align:start position:0% +a + + + align:start position:0% +a +three-dimensional system with vertical + + align:start position:0% +three-dimensional system with vertical + + + align:start position:0% +three-dimensional system with vertical +connections. + + align:start position:0% +connections. + + + align:start position:0% +connections. +private and horizontal connections + + align:start position:0% + + + + align:start position:0% + +public. The slide on the right is what + + align:start position:0% +public. The slide on the right is what + + + align:start position:0% +public. The slide on the right is what +you see of the sky at intersections in + + align:start position:0% +you see of the sky at intersections in + + + align:start position:0% +you see of the sky at intersections in +the grid plan of + + align:start position:0% +the grid plan of + + + align:start position:0% +the grid plan of +Manhattan. It's an attempt to argue that + + align:start position:0% +Manhattan. It's an attempt to argue that + + + align:start position:0% +Manhattan. It's an attempt to argue that +you that there is a logic to what you + + align:start position:0% +you that there is a logic to what you + + + align:start position:0% +you that there is a logic to what you +see in the sky between tall buildings. + + align:start position:0% + + + + align:start position:0% + +Next, the muteness of the departed World + + align:start position:0% +Next, the muteness of the departed World + + + align:start position:0% +Next, the muteness of the departed World +Trade + + align:start position:0% +Trade + + + align:start position:0% +Trade +Center and the attempt in + + align:start position:0% + + + + align:start position:0% + +Shanghai to + + align:start position:0% +Shanghai to + + + align:start position:0% +Shanghai to +have completely private + + align:start position:0% +have completely private + + + align:start position:0% +have completely private +activity dominate the scene. + + align:start position:0% + + + + align:start position:0% + +despite all of the attempts in the + + align:start position:0% +despite all of the attempts in the + + + align:start position:0% +despite all of the attempts in the +competition and the procedures of + + align:start position:0% +competition and the procedures of + + + align:start position:0% +competition and the procedures of +participation to replace the buildings + + align:start position:0% +participation to replace the buildings + + + align:start position:0% +participation to replace the buildings +on the + + align:start position:0% +on the + + + align:start position:0% +on the +left. The building which is result is + + align:start position:0% +left. The building which is result is + + + align:start position:0% +left. The building which is result is +the purely the result of the wishes of + + align:start position:0% +the purely the result of the wishes of + + + align:start position:0% +the purely the result of the wishes of +the Mr. Silverstein the + + align:start position:0% +the Mr. Silverstein the + + + align:start position:0% +the Mr. Silverstein the +developer. + + align:start position:0% + + + + align:start position:0% + +Next, the tall building is a modern + + align:start position:0% +Next, the tall building is a modern + + + align:start position:0% +Next, the tall building is a modern +icon which has often been seen as having + + align:start position:0% +icon which has often been seen as having + + + align:start position:0% +icon which has often been seen as having +perceptual value much like a cathedral + + align:start position:0% +perceptual value much like a cathedral + + + align:start position:0% +perceptual value much like a cathedral +dominated a medieval town. the tall + + align:start position:0% +dominated a medieval town. the tall + + + align:start position:0% +dominated a medieval town. the tall +building is + + align:start position:0% +building is + + + align:start position:0% +building is +the and + + align:start position:0% +the and + + + align:start position:0% +the and +uh the attempts to make them taller and + + align:start position:0% +uh the attempts to make them taller and + + + align:start position:0% +uh the attempts to make them taller and +taller. On the left is the is a building + + align:start position:0% +taller. On the left is the is a building + + + align:start position:0% +taller. On the left is the is a building +in Shanghai. On the right is Louis + + align:start position:0% +in Shanghai. On the right is Louis + + + align:start position:0% +in Shanghai. On the right is Louis +Khan's attempt to design a much shor + + align:start position:0% +Khan's attempt to design a much shor + + + align:start position:0% +Khan's attempt to design a much shor +lower building in Philadelphia. + + align:start position:0% + + + + align:start position:0% + +Next, the Saudi bank building in Jedha + + align:start position:0% +Next, the Saudi bank building in Jedha + + + align:start position:0% +Next, the Saudi bank building in Jedha +on the left and the attempt to make a + + align:start position:0% +on the left and the attempt to make a + + + align:start position:0% +on the left and the attempt to make a +tall building in + + align:start position:0% +tall building in + + + align:start position:0% +tall building in +Quadalumpur on the left as an Islamic + + align:start position:0% +Quadalumpur on the left as an Islamic + + + align:start position:0% +Quadalumpur on the left as an Islamic +building. An Islamic skyscraper is a + + align:start position:0% +building. An Islamic skyscraper is a + + + align:start position:0% +building. An Islamic skyscraper is a +paradox. + + align:start position:0% + + + + align:start position:0% + +Next, you've seen + + align:start position:0% +Next, you've seen + + + align:start position:0% +Next, you've seen +this project on the left. It's + + align:start position:0% +this project on the left. It's + + + align:start position:0% +this project on the left. It's +Melnikov's the entry into the Pravda + + align:start position:0% +Melnikov's the entry into the Pravda + + + align:start position:0% +Melnikov's the entry into the Pravda +competition in St. Petersburg with a + + align:start position:0% +competition in St. Petersburg with a + + + align:start position:0% +competition in St. Petersburg with a +rotating + + align:start position:0% +rotating + + + align:start position:0% +rotating +system. Um, and on the right, the + + align:start position:0% +system. Um, and on the right, the + + + align:start position:0% +system. Um, and on the right, the +1922 Chicago Trivia Competition. This is + + align:start position:0% +1922 Chicago Trivia Competition. This is + + + align:start position:0% +1922 Chicago Trivia Competition. This is +the entry by Adolf Lewis. + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +where it's difficult to + + align:start position:0% +where it's difficult to + + + align:start position:0% +where it's difficult to +explain in simple terms but it's its + + align:start position:0% +explain in simple terms but it's its + + + align:start position:0% +explain in simple terms but it's its +obviousness is one of its powers. + + align:start position:0% + + + + align:start position:0% + +Next, there's no legislation or design + + align:start position:0% +Next, there's no legislation or design + + + align:start position:0% +Next, there's no legislation or design +of the periph of the vertical ends of + + align:start position:0% +of the periph of the vertical ends of + + + align:start position:0% +of the periph of the vertical ends of +tall buildings as a + + align:start position:0% +tall buildings as a + + + align:start position:0% +tall buildings as a +system. I know of no city in the world + + align:start position:0% +system. I know of no city in the world + + + align:start position:0% +system. I know of no city in the world +which has an + + align:start position:0% +which has an + + + align:start position:0% +which has an +inventory. This is Houston on the right, + + align:start position:0% +inventory. This is Houston on the right, + + + align:start position:0% +inventory. This is Houston on the right, +Constantinople on the left. + + align:start position:0% + + + + align:start position:0% + +One might have thought + + align:start position:0% +One might have thought + + + align:start position:0% +One might have thought +that somebody would have had the idea + + align:start position:0% +that somebody would have had the idea + + + align:start position:0% +that somebody would have had the idea +that the geometry + + align:start position:0% +that the geometry + + + align:start position:0% +that the geometry +of the system of tall buildings would + + align:start position:0% +of the system of tall buildings would + + + align:start position:0% +of the system of tall buildings would +have some significance but I don't know + + align:start position:0% +have some significance but I don't know + + + align:start position:0% +have some significance but I don't know +any if you know of a city tell me which + + align:start position:0% +any if you know of a city tell me which + + + align:start position:0% +any if you know of a city tell me which +controls the form of the system of tall + + align:start position:0% +controls the form of the system of tall + + + align:start position:0% +controls the form of the system of tall +buildings. It's + + align:start position:0% +buildings. It's + + + align:start position:0% +buildings. It's +seen as one of the things that is not + + align:start position:0% +seen as one of the things that is not + + + align:start position:0% +seen as one of the things that is not +necessary to + + align:start position:0% +necessary to + + + align:start position:0% +necessary to +control. It's + + align:start position:0% +control. It's + + + align:start position:0% +control. It's +interesting because it's seen in many + + align:start position:0% +interesting because it's seen in many + + + align:start position:0% +interesting because it's seen in many +respects. When you have a river and you + + align:start position:0% +respects. When you have a river and you + + + align:start position:0% +respects. When you have a river and you +have green space, you see the profile of + + align:start position:0% +have green space, you see the profile of + + + align:start position:0% +have green space, you see the profile of +the city from a distance. + + align:start position:0% + + + + align:start position:0% + +Next, tall buildings are often used to + + align:start position:0% +Next, tall buildings are often used to + + + align:start position:0% +Next, tall buildings are often used to +project futurism. + + align:start position:0% +project futurism. + + + align:start position:0% +project futurism. +This is in the cover of an + + align:start position:0% +This is in the cover of an + + + align:start position:0% +This is in the cover of an +arch booklet on the right and a wonder + + align:start position:0% +arch booklet on the right and a wonder + + + align:start position:0% +arch booklet on the right and a wonder +story book on the left where the + + align:start position:0% +story book on the left where the + + + align:start position:0% +story book on the left where the +synchronicity of the transportation + + align:start position:0% +synchronicity of the transportation + + + align:start position:0% +synchronicity of the transportation +system creates the dynamic of the city. + + align:start position:0% + + + + align:start position:0% + +Next, there's another aspect, concealed + + align:start position:0% +Next, there's another aspect, concealed + + + align:start position:0% +Next, there's another aspect, concealed +aspect of the city. Much though it's + + align:start position:0% +aspect of the city. Much though it's + + + align:start position:0% +aspect of the city. Much though it's +vertical + + align:start position:0% +vertical + + + align:start position:0% +vertical +shape is + + align:start position:0% +shape is + + + align:start position:0% +shape is +uncontrolled, so is the below + + align:start position:0% +uncontrolled, so is the below + + + align:start position:0% +uncontrolled, so is the below +the level of the platform. + + align:start position:0% +the level of the platform. + + + align:start position:0% +the level of the platform. +This + + align:start position:0% +This + + + align:start position:0% +This +is a part view + + align:start position:0% +is a part view + + + align:start position:0% +is a part view +of the + + align:start position:0% +of the + + + align:start position:0% +of the +the workings under Herald Square in New + + align:start position:0% +the workings under Herald Square in New + + + align:start position:0% +the workings under Herald Square in New +York. And on the right is a Diego Rivera + + align:start position:0% +York. And on the right is a Diego Rivera + + + align:start position:0% +York. And on the right is a Diego Rivera +drawing called frozen + + align:start position:0% +drawing called frozen + + + align:start position:0% +drawing called frozen +assets which + + align:start position:0% +assets which + + + align:start position:0% +assets which +argues that under every city there are + + align:start position:0% +argues that under every city there are + + + align:start position:0% +argues that under every city there are +bodies locked up and dead bodies giving + + align:start position:0% +bodies locked up and dead bodies giving + + + align:start position:0% +bodies locked up and dead bodies giving +a kind of macab + + align:start position:0% +a kind of macab + + + align:start position:0% +a kind of macab +picture of the use of the bottom. You'll + + align:start position:0% +picture of the use of the bottom. You'll + + + align:start position:0% +picture of the use of the bottom. You'll +remember a picture I showed you of + + align:start position:0% +remember a picture I showed you of + + + align:start position:0% +remember a picture I showed you of +travel in the sewers of New of + + align:start position:0% +travel in the sewers of New of + + + align:start position:0% +travel in the sewers of New of +Paris tourist trips. + + align:start position:0% + + + + align:start position:0% + +Next, here are two examples in from + + align:start position:0% +Next, here are two examples in from + + + align:start position:0% +Next, here are two examples in from +Manhattan of the attempt to + + align:start position:0% +Manhattan of the attempt to + + + align:start position:0% +Manhattan of the attempt to +buy new office buildings on the Lever + + align:start position:0% +buy new office buildings on the Lever + + + align:start position:0% +buy new office buildings on the Lever +Brothers on the left and the Ford + + align:start position:0% +Brothers on the left and the Ford + + + align:start position:0% +Brothers on the left and the Ford +Foundation on the right to give the + + align:start position:0% +Foundation on the right to give the + + + align:start position:0% +Foundation on the right to give the +impression that they're creating public + + align:start position:0% +impression that they're creating public + + + align:start position:0% +impression that they're creating public +space. + + align:start position:0% +space. + + + align:start position:0% +space. +There's no market for the space + + align:start position:0% +There's no market for the space + + + align:start position:0% +There's no market for the space +underneath as I try to show you in a + + align:start position:0% +underneath as I try to show you in a + + + align:start position:0% +underneath as I try to show you in a +comparison of Fifth Avenue in Madison or + + align:start position:0% +comparison of Fifth Avenue in Madison or + + + align:start position:0% +comparison of Fifth Avenue in Madison or +Fifth Avenue and Park. Um, so it's very + + align:start position:0% +Fifth Avenue and Park. Um, so it's very + + + align:start position:0% +Fifth Avenue and Park. Um, so it's very +easy to give up the ground floor space + + align:start position:0% +easy to give up the ground floor space + + + align:start position:0% +easy to give up the ground floor space +in an office building as it was easy for + + align:start position:0% +in an office building as it was easy for + + + align:start position:0% +in an office building as it was easy for +Seam's building to set back in return + + align:start position:0% +Seam's building to set back in return + + + align:start position:0% +Seam's building to set back in return +for higher bulk. + + align:start position:0% + + + + align:start position:0% + +There's no public space under a + + align:start position:0% + + + + align:start position:0% + +tower. Richard Senate has written very + + align:start position:0% +tower. Richard Senate has written very + + + align:start position:0% +tower. Richard Senate has written very +critically of this + + align:start position:0% +critically of this + + + align:start position:0% +critically of this +device. The Ford + + align:start position:0% +device. The Ford + + + align:start position:0% +device. The Ford +Foundation puts a garden inside the + + align:start position:0% +Foundation puts a garden inside the + + + align:start position:0% +Foundation puts a garden inside the +building as if it's a public + + align:start position:0% +building as if it's a public + + + align:start position:0% +building as if it's a public +park. In fact, it's very curtailed as to + + align:start position:0% +park. In fact, it's very curtailed as to + + + align:start position:0% +park. In fact, it's very curtailed as to +its entry. Next, + + align:start position:0% + + + + align:start position:0% + +bank in Hong Kong, of course, a famous + + align:start position:0% +bank in Hong Kong, of course, a famous + + + align:start position:0% +bank in Hong Kong, of course, a famous +bank where there's an attempt to give a + + align:start position:0% +bank where there's an attempt to give a + + + align:start position:0% +bank where there's an attempt to give a +sense of public in the + + align:start position:0% +sense of public in the + + + align:start position:0% +sense of public in the +interior and the access to the interior + + align:start position:0% +interior and the access to the interior + + + align:start position:0% +interior and the access to the interior +is tightly controlled by a single + + align:start position:0% +is tightly controlled by a single + + + align:start position:0% +is tightly controlled by a single +escalator. + + align:start position:0% +escalator. + + + align:start position:0% +escalator. +The whole idea of this + + align:start position:0% +The whole idea of this + + + align:start position:0% +The whole idea of this +insinuation is + + align:start position:0% + + + + align:start position:0% + +that this + + align:start position:0% +that this + + + align:start position:0% +that this +represents a unification of the + + align:start position:0% +represents a unification of the + + + align:start position:0% +represents a unification of the +work that's being done in this in this + + align:start position:0% +work that's being done in this in this + + + align:start position:0% +work that's being done in this in this +vertical space and + + align:start position:0% + + + + align:start position:0% + +yet each group works individually. + + align:start position:0% + + + + align:start position:0% + +Next, this is Herman + + align:start position:0% +Next, this is Herman + + + align:start position:0% +Next, this is Herman +Herzburgger's insurance company project + + align:start position:0% +Herzburgger's insurance company project + + + align:start position:0% +Herzburgger's insurance company project +in + + align:start position:0% +in + + + align:start position:0% +in +Amsterdam. No, no, sorry. It's in uh + + align:start position:0% +Amsterdam. No, no, sorry. It's in uh + + + align:start position:0% +Amsterdam. No, no, sorry. It's in uh +it's not in + + align:start position:0% +it's not in + + + align:start position:0% +it's not in +Amsterdam. It's in + + align:start position:0% +Amsterdam. It's in + + + align:start position:0% +Amsterdam. It's in +uh I'll think of the name. + + align:start position:0% +uh I'll think of the name. + + + align:start position:0% +uh I'll think of the name. +um + + align:start position:0% +um + + + align:start position:0% +um +where each of the workers in this + + align:start position:0% +where each of the workers in this + + + align:start position:0% +where each of the workers in this +insurance company is allowed to + + align:start position:0% +insurance company is allowed to + + + align:start position:0% +insurance company is allowed to +personalize their own space yet the + + align:start position:0% +personalize their own space yet the + + + align:start position:0% +personalize their own space yet the +openness of the whole structure depicts + + align:start position:0% +openness of the whole structure depicts + + + align:start position:0% +openness of the whole structure depicts +a sense of + + align:start position:0% +a sense of + + + align:start position:0% +a sense of +community. This is the exterior of the + + align:start position:0% +community. This is the exterior of the + + + align:start position:0% +community. This is the exterior of the +system whether whereby the system stops + + align:start position:0% +system whether whereby the system stops + + + align:start position:0% +system whether whereby the system stops +bluntly when it leaves the + + align:start position:0% +bluntly when it leaves the + + + align:start position:0% +bluntly when it leaves the +building. Next + + align:start position:0% + + + + align:start position:0% + +This is where the conjunction of public + + align:start position:0% +This is where the conjunction of public + + + align:start position:0% +This is where the conjunction of public +and private + + align:start position:0% +and private + + + align:start position:0% +and private +becomes somewhat + + align:start position:0% +becomes somewhat + + + align:start position:0% +becomes somewhat +meaningless. On the right is Trump + + align:start position:0% +meaningless. On the right is Trump + + + align:start position:0% +meaningless. On the right is Trump +Tower. On the left is City Corp, the + + align:start position:0% +Tower. On the left is City Corp, the + + + align:start position:0% +Tower. On the left is City Corp, the +ground floor of City Corp, which has 20 + + align:start position:0% +ground floor of City Corp, which has 20 + + + align:start position:0% +ground floor of City Corp, which has 20 +stores and enormous things going on. + + align:start position:0% +stores and enormous things going on. + + + align:start position:0% +stores and enormous things going on. +Do you feel public in these animated + + align:start position:0% +Do you feel public in these animated + + + align:start position:0% +Do you feel public in these animated +spaces which are intensely private + + align:start position:0% +spaces which are intensely private + + + align:start position:0% +spaces which are intensely private +ownership and + + align:start position:0% +ownership and + + + align:start position:0% +ownership and +you remember the + + align:start position:0% + + + + align:start position:0% + +matrix use + + align:start position:0% +matrix use + + + align:start position:0% +matrix use +ownership access and + + align:start position:0% +ownership access and + + + align:start position:0% +ownership access and +meaning and try always to use that + + align:start position:0% +meaning and try always to use that + + + align:start position:0% +meaning and try always to use that +matrix to test whether what is private + + align:start position:0% +matrix to test whether what is private + + + align:start position:0% +matrix to test whether what is private +and what is public about + + align:start position:0% +and what is public about + + + align:start position:0% +and what is public about +space in this case ownership is + + align:start position:0% +space in this case ownership is + + + align:start position:0% +space in this case ownership is +completely private. Access is + + align:start position:0% +completely private. Access is + + + align:start position:0% +completely private. Access is +public. Use + + align:start position:0% +public. Use + + + align:start position:0% +public. Use +is public but probably oriented + + align:start position:0% +is public but probably oriented + + + align:start position:0% +is public but probably oriented +absolutely to to private + + align:start position:0% +absolutely to to private + + + align:start position:0% +absolutely to to private +profit and meaning is whatever you want + + align:start position:0% +profit and meaning is whatever you want + + + align:start position:0% +profit and meaning is whatever you want +to make of + + align:start position:0% +to make of + + + align:start position:0% +to make of +it. You can feel more public + + align:start position:0% + + + + align:start position:0% + +in the base of City Core Plaza than you + + align:start position:0% +in the base of City Core Plaza than you + + + align:start position:0% +in the base of City Core Plaza than you +city core building than you can in city + + align:start position:0% +city core building than you can in city + + + align:start position:0% +city core building than you can in city +hall or plaza in Boston. + + align:start position:0% + + + + align:start position:0% + +Next, the attempt + + align:start position:0% +Next, the attempt + + + align:start position:0% +Next, the attempt +to shape tall buildings with elements of + + align:start position:0% +to shape tall buildings with elements of + + + align:start position:0% +to shape tall buildings with elements of +the decentralized + + align:start position:0% +the decentralized + + + align:start position:0% +the decentralized +city both ecologically + + align:start position:0% +city both ecologically + + + align:start position:0% +city both ecologically +and it's bit of a joke. + + align:start position:0% + + + + align:start position:0% + +Next from the Wonder magazine diagrams + + align:start position:0% +Next from the Wonder magazine diagrams + + + align:start position:0% +Next from the Wonder magazine diagrams +you get this + + align:start position:0% +you get this + + + align:start position:0% +you get this +intense there many visions of Manhattan + + align:start position:0% +intense there many visions of Manhattan + + + align:start position:0% +intense there many visions of Manhattan +which are multiplications of traffic + + align:start position:0% +which are multiplications of traffic + + + align:start position:0% +which are multiplications of traffic +uh suggesting that automobiles be on a + + align:start position:0% +uh suggesting that automobiles be on a + + + align:start position:0% +uh suggesting that automobiles be on a +different the trains on the lowest level + + align:start position:0% +different the trains on the lowest level + + + align:start position:0% +different the trains on the lowest level +automobiles above and including a rail + + align:start position:0% +automobiles above and including a rail + + + align:start position:0% +automobiles above and including a rail +system, public rail system, pedestrians + + align:start position:0% +system, public rail system, pedestrians + + + align:start position:0% +system, public rail system, pedestrians +on a level above and many levels above + + align:start position:0% +on a level above and many levels above + + + align:start position:0% +on a level above and many levels above +they are + + align:start position:0% +they are + + + align:start position:0% +they are +pedestrians. This is an image of the + + align:start position:0% +pedestrians. This is an image of the + + + align:start position:0% +pedestrians. This is an image of the +modern city which + + align:start position:0% +modern city which + + + align:start position:0% +modern city which +is closeted in a lot of people's + + align:start position:0% +is closeted in a lot of people's + + + align:start position:0% +is closeted in a lot of people's +minds. It just doesn't happen. + + align:start position:0% +minds. It just doesn't happen. + + + align:start position:0% +minds. It just doesn't happen. +was much visioned by + + align:start position:0% + + + + align:start position:0% + +a number of + + align:start position:0% + + + + align:start position:0% + +things. I think Moses King who did some + + align:start position:0% +things. I think Moses King who did some + + + align:start position:0% +things. I think Moses King who did some +of the most + + align:start position:0% +of the most + + + align:start position:0% +of the most +wonderful versions of this. These are + + align:start position:0% +wonderful versions of this. These are + + + align:start position:0% +wonderful versions of this. These are +not kings. + + align:start position:0% + + + + align:start position:0% + +Um portrayed a kind of utilitarian base + + align:start position:0% +Um portrayed a kind of utilitarian base + + + align:start position:0% +Um portrayed a kind of utilitarian base +to this. Manhattan was getting to be so + + align:start position:0% +to this. Manhattan was getting to be so + + + align:start position:0% +to this. Manhattan was getting to be so +dense and congested that the the + + align:start position:0% +dense and congested that the the + + + align:start position:0% +dense and congested that the the +reaction was let's use vertical space to + + align:start position:0% +reaction was let's use vertical space to + + + align:start position:0% +reaction was let's use vertical space to +distinguish + + align:start position:0% +distinguish + + + align:start position:0% +distinguish +between vertical and horizontal + + align:start position:0% +between vertical and horizontal + + + align:start position:0% +between vertical and horizontal +movement. Yes. + + align:start position:0% + + + + align:start position:0% + +Um, you can imagine movies being made. + + align:start position:0% +Um, you can imagine movies being made. + + + align:start position:0% +Um, you can imagine movies being made. +This is this is probably suitable for a + + align:start position:0% +This is this is probably suitable for a + + + align:start position:0% +This is this is probably suitable for a +Batman movie + + align:start position:0% +Batman movie + + + align:start position:0% +Batman movie +uh where extraordinary things are being + + align:start position:0% +uh where extraordinary things are being + + + align:start position:0% +uh where extraordinary things are being +supernatural events are taking place. + + align:start position:0% +supernatural events are taking place. + + + align:start position:0% +supernatural events are taking place. +There's something supernatural about + + align:start position:0% +There's something supernatural about + + + align:start position:0% +There's something supernatural about +people walking on the 20 up in the sky + + align:start position:0% +people walking on the 20 up in the sky + + + align:start position:0% +people walking on the 20 up in the sky +on the 20th floor across from two + + align:start position:0% +on the 20th floor across from two + + + align:start position:0% +on the 20th floor across from two +buildings. The basic rule, the basic + + align:start position:0% +buildings. The basic rule, the basic + + + align:start position:0% +buildings. The basic rule, the basic +rule is that people are where there is + + align:start position:0% +rule is that people are where there is + + + align:start position:0% +rule is that people are where there is +reason to + + align:start position:0% +reason to + + + align:start position:0% +reason to +be. The number of people on the 20th + + align:start position:0% +be. The number of people on the 20th + + + align:start position:0% +be. The number of people on the 20th +floor of two office buildings is too few + + align:start position:0% +floor of two office buildings is too few + + + align:start position:0% +floor of two office buildings is too few +to generate any need for connection at + + align:start position:0% +to generate any need for connection at + + + align:start position:0% +to generate any need for connection at +that time. You come down the elevator + + align:start position:0% +that time. You come down the elevator + + + align:start position:0% +that time. You come down the elevator +and you connect on the base. There are + + align:start position:0% +and you connect on the base. There are + + + align:start position:0% +and you connect on the base. There are +few cities in the world which have + + align:start position:0% +few cities in the world which have + + + align:start position:0% +few cities in the world which have +developed enough density. Nor do I I + + align:start position:0% +developed enough density. Nor do I I + + + align:start position:0% +developed enough density. Nor do I I +won't be around but I don't project that + + align:start position:0% +won't be around but I don't project that + + + align:start position:0% +won't be around but I don't project that +there will ever be cities which will + + align:start position:0% +there will ever be cities which will + + + align:start position:0% +there will ever be cities which will +develop significantly upper level + + align:start position:0% +develop significantly upper level + + + align:start position:0% +develop significantly upper level +pedestrian + + align:start position:0% + + + + align:start position:0% + +crossings. This contradicts many of the + + align:start position:0% +crossings. This contradicts many of the + + + align:start position:0% +crossings. This contradicts many of the +much of the romance for this kind of + + align:start position:0% +much of the romance for this kind of + + + align:start position:0% +much of the romance for this kind of +world of architects. Park was based on + + align:start position:0% +world of architects. Park was based on + + + align:start position:0% +world of architects. Park was based on +dense models of inter urban interaction + + align:start position:0% +dense models of inter urban interaction + + + align:start position:0% +dense models of inter urban interaction +which seldom take + + align:start position:0% +which seldom take + + + align:start position:0% +which seldom take +place. That's why architects hate + + align:start position:0% +place. That's why architects hate + + + align:start position:0% +place. That's why architects hate +suburbia so + + align:start position:0% +suburbia so + + + align:start position:0% +suburbia so +much. That's a Catholic + + align:start position:0% +much. That's a Catholic + + + align:start position:0% +much. That's a Catholic +statement. + + align:start position:0% +statement. + + + align:start position:0% +statement. +Next. + + align:start position:0% + + + + align:start position:0% + +Next. On the left is the marathon in New + + align:start position:0% +Next. On the left is the marathon in New + + + align:start position:0% +Next. On the left is the marathon in New +York and on the right are the + + align:start position:0% +York and on the right are the + + + align:start position:0% +York and on the right are the +celebrations after + + align:start position:0% +celebrations after + + + align:start position:0% +celebrations after +the hostages from Iran were released and + + align:start position:0% +the hostages from Iran were released and + + + align:start position:0% +the hostages from Iran were released and +returned. + + align:start position:0% + + + + align:start position:0% + +Um, archaic cities relied on spacetime + + align:start position:0% +Um, archaic cities relied on spacetime + + + align:start position:0% +Um, archaic cities relied on spacetime +inventions such as + + align:start position:0% +inventions such as + + + align:start position:0% +inventions such as +rituals, not only to mark space in + + align:start position:0% +rituals, not only to mark space in + + + align:start position:0% +rituals, not only to mark space in +particular ways as you saw in the in the + + align:start position:0% +particular ways as you saw in the in the + + + align:start position:0% +particular ways as you saw in the in the +example of Madurai in southern + + align:start position:0% +example of Madurai in southern + + + align:start position:0% +example of Madurai in southern +India but in crude form. This is the + + align:start position:0% +India but in crude form. This is the + + + align:start position:0% +India but in crude form. This is the +same + + align:start position:0% +same + + + align:start position:0% +same +phenomenon. The bringing together of + + align:start position:0% +phenomenon. The bringing together of + + + align:start position:0% +phenomenon. The bringing together of +people in public to celebrate a + + align:start position:0% +people in public to celebrate a + + + align:start position:0% +people in public to celebrate a +particular thing. In the case of race + + align:start position:0% +particular thing. In the case of race + + + align:start position:0% +particular thing. In the case of race +which has meaning which is meaningless. + + align:start position:0% +which has meaning which is meaningless. + + + align:start position:0% +which has meaning which is meaningless. +In the second a celebration to return + + align:start position:0% +In the second a celebration to return + + + align:start position:0% +In the second a celebration to return +people after being captured by a foreign + + align:start position:0% +people after being captured by a foreign + + + align:start position:0% +people after being captured by a foreign +nation. \ No newline at end of file diff --git a/qo-XkWeLWLs.txt b/qo-XkWeLWLs.txt new file mode 100644 index 0000000000000000000000000000000000000000..b24e54b55a49b18497a5c66b1ef9c29f67841ca2 --- /dev/null +++ b/qo-XkWeLWLs.txt @@ -0,0 +1,2402 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Okay. + +So this is our second +session with Phil + +[? Scarf, ?] please welcome him. + +So we're going to have +our presentations based + +on the design assignment +that Phil came up with. + +So who would like +to go for first? + +There you go. + +Thank you. + +PHIL SCARF: Can you +tell us your design? + +STUDENT 1: So we chose a raga. + +We decided on the notes +C, Db, F, G and Bb. + +And we went with a +more traditional, + +where you start out slow and +you slowly expand the range. + +And then you add in +more players and then + +you play a melody line together +and then alternate whoever + +is improvising. + +And then we did a little +bit of extrapolation + +halfway through by +changing one of the notes + +in the raga actually. + +And just for a little different +style and then we go back. + +[MUSIC PLAYING] + +PHIL SCARF: That +was very impressive. + +So let me just ask +the performers. + +Did that performance go the +way you envisioned it going? + +Since we're +improvising, you never + +know what's going to happen +when you improvise, right? + +So I'm just curious +if that's the way + +you had planned for it to go, +or you thought that anything + +might have been different. + +STUDENT 1: So when +I was describing it + +I said there was +a section where we + +change one of the +notes in the raga. + +That didn't happen. + +At the end, we had the option +of going into that or stopping. + +PHIL SCARF: Anything else? + +STUDENT 2: So we sort of knew +vaguely what different sections + +were going to be +like, and sort of what + +we would try and do with them. + +But that was completely +different -- like, we tried, + +we run through it a couple +of times before, today. + +That was kind of different +to what we'd done before. + +PHIL SCARF: That's +improvisation. + +It should be different. + +That's actually the point. + +It should be different. + +If you start doing the same +thing over and over again, + +it's no longer +improvisation, right? + +So that's great. + +Good. + +So any comments +from anybody else? + +Any thoughts? + +STUDENT 3: There were +a couple of times + +when you played in unison, +and I didn't really + +see any cues into +those sections. + +I was just wondering if you were +all improvising, how did you + +move from improvisational +section to unison section? + +STUDENT 4: We have this +one particular melody, + +so when one person started, we +could recognize that melody. + +Or one person began it, +we would go into it. + +And there was a couple +times we repeated it, + +so one person would +get to the end of it + +and then we'd go +straight into it again. + +PHIL SCARF: Any other comments? + +PROFESSOR: I'll +just say, I thought + +it worked very well as a +composed improvisation. + +I thought the framework +was well thought out. + +And the realization +through improvisation + +made a lot of sense. + +Very good. + +PHIL SCARF: I think you +really captured the frameworks + +very well. + +Why don't you want +to tell us about it? + +Because everybody needs to know. + +STUDENT 4: So basically we +came up with our own scale + +to base the improvisation on. + +And we decided to look into +the range and note density + +frameworks at first. + +So we're each starting +in different parts + +of our register, which is +maybe different than what + +would be done +traditionally, perhaps. + +But then we'll move +out and expand, + +which is pretty similar to some +of the stuff that happens with + +[INAUDIBLE]. + +And then we'll also be moving +from pretty simple melodies + +and pretty simple [INAUDIBLE] +to more complicated things + +that come up and we'll +try to then [INAUDIBLE]. + +It won't start with +a [INAUDIBLE] rhythm, + +but then we'll try to get into +a rhythmic groove later on. + +STUDENT 6: One more thing, I'm +going to start with a drone, + +to imitate the +tambura, and we're + +going to add ornamentation +to the melodies, + +to imitate [INAUDIBLE]. + +PHIL SCARF: OK, sounds good. + +[MUSIC PLAYING] + +PHIL SCARF: Nice. + +So any thoughts +about that piece? + +So did the performance +went the way you expected? + +Did you do anything different +that you were thinking about? + +STUDENT 6: I'd say in general, +the note density and range + +[INAUDIBLE]. + +We were hoping to get a motif +in there, but I don't think -- + +STUDENT 5: We were going to +just let it develop organically. + +But we just kind of +played off each other. + +STUDENT 6: And the rhythm wasn't +3-3-2 like we were predicting, + +it did settle. + +PHIL SCARF: Yeah, it did +become rhythmic, about halfway + +through. + +Yeah, good. + +Anything else? + +[INAUDIBLE] + +STUDENT 5: Yeah, a +little bit, yeah. + +PROFESSOR: And then +you jump right on. + +STUDENT 6: Well yeah, I +used the bass to really -- + +PROFESSOR: But that was +very good listening, + +because it didn't take +more than a second or two + +to really coalesce. + +And how about the ending? + +Had that been thought about? + +STUDENT 5: We +planned to just bring + +the range back in, +basically, to where + +we had been in the beginning. + +That fade-out, +literally fade out. + +PHIL SCARF: That +worked out great. + +Anybody else have any comments? + +Any thoughts, observations? + +Yeah. + +STUDENT 7: Well +in the beginning, + +I thought the piano +player was going + +to drone on for the entire song, +and just sort of be a drone. + +And I was waiting +for him to come in, + +and finally I felt +relieved when he + +came in and built on the violin. + +PHIL SCARF: Yeah + +STUDENT 6: Yeah, we didn't have +any unison melodies planned, + +so I didn't want it to be +really dense too early. + +PHIL SCARF: I mean, I thought +that was nice, you know? + +Because we had one solo voice +with a kind of accompaniment, + +and then it became +more of a duet. + +So there was an element +of progression there. + +STUDENT 6: Another thing +we didn't anticipate, + +Austin focused on the +mid-upper part of the scale, + +and I was just doing the +first three or four notes. + +PHIL SCARF: Anything else? + +Cool. + +OK. + +Next group. + +STUDENT 8: So I actually didn't +come up with my own scale. + +I just decided to use +the D Dorian mode. + +It's a little bit more humble +for me to play around with. + +My vision is around the piano to +form a sort of drone, in low D. + +And use that, and also drone, +and then as a little bit goes + +on, build up into a [INAUDIBLE] +[INAUDIBLE] necessary. + +It starts at +[INAUDIBLE] but then + +I do have a melodic motif that +I was going to center it around. + +PHIL SCARF: Can I just +ask, is the melodic thing + +a raga or scale idea? + +STUDENT 8: I just came up +with something on the guitar. + +PHIL SCARF: So are there +any specific frameworks + +from the set of 12 +that we're using here? + +STUDENT 8: I was looking +at -- I can't remember -- + +there were two [INAUDIBLE] +I was looking at. + +Looking at a little +bit no density. + +Kind of applying it towards the +[INAUDIBLE] notes, or the lower + +end. + +So the drone has a +little bit of freedom, + +in terms of picking up, +as he wants to [INAUDIBLE] + +tremolo, rhythmic +framework, I guess. + +PHIL SCARF: So is +the note density + +going to change +throughout the piece? + +Or not? + +Yes. + +Do you have a view of +how that would change? + +Or is that going +to be improvised? + +STUDENT 8: I envisioned it as +starting out slow, building up, + +more dense, little faster, +slowing down towards the end. + +And the other one I was looking +at was using the framework, + +the little melody, I guess, +and working that around -- + +I can't remember +what it was called -- + +PHIL SCARF: Oh, the +[INAUDIBLE] maybe? + +That's what you mean? + +Melodic motif. + +Yeah. + +Yeah. + +Good. + +[MUSIC PLAYING] + +PHIL SCARF: Yeah. + +That was good. + +I like that amp. + +That's pretty convenient. + +So any comments +from the performers? + +I'm particularly interested +in what the collaborators may + +think about this, +since they didn't have + +much notice before +playing the piece. + +STUDENT 9: I didn't +have any idea what + +it would be like going into it. + +But having the +framework really set + +an expectation of +gradually increasing + +note density and the range. + +And having the motif +definitely helps. + +PHIL SCARF: That motif was cool. + +And the way that it +was used was good. + +STUDENT 10: I think it +was just enough to provide + +a cool little phrase to work on. + +STUDENT 8: That was one +of the visions I had. + +PHIL SCARF: Yeah. + +That was great. + +The first group that's used +the [? chellan ?] framework, + +so that's good. + +Any other comments? + +What about the designer? + +Do you have any comments +about how this went? + +STUDENT 8: I just didn't know +what to expect going into it. + +Because again, I just sort of +did this myself, yesterday. + +And I didn't know +what the performers + +would think going into this. + +And from the outset, I +knew, I guess the piano + +sort of provided the +rhythmic background, I guess. + +And set the overall tone. + +And then I came in +with some free time + +before I settled into the motif. + +And then everybody settled +around that, as well. + +PHIL SCARF: Anybody +else have any thoughts? + +Observations, comments? + +STUDENT 7: I really +liked that motif. + +It really brought +it all together. + +And I think it gave +the collaborators + +a really solid +base to start from. + +And build off of. + +Seems like a cool way +improvise and make a framework. + +Just start with a tiny +motif and then see + +where you can take +it from there. + +PHIL SCARF: Exactly. + +And then, the listener also +gravitates towards that, + +as well. + +Every time it comes back, +it's familiar material. + +In fact, I think that +kind of illustrates one + +of the attractive elements +of Indian classical music + +is use of [? chellan ?]. + +Even if it's something +you haven't heard before, + +by the time you +finish hearing it, + +you've heard the [? chellan, ?] +some of the key phrases, you've + +heard them so many times, +it become familiar. + +So like this motif, by +the time we finished, + +it sounds like a familiar piece. + +Even though none of us +had heard it before, + +except perhaps, the composer. + +So it's nice. + +Any other thoughts? + +So what's your framework? + +Can you tell us +about your framework? + +STUDENT 11: OK, so basically, +we based off a [INAUDIBLE] + +in terms of -- we have a +motif that we start out with. + +And then we're going +late on build on it + +by adding some chords. + +And then while one +person plays the melody, + +the other person will +improvise on it, instead. + +STUDENT 12: We had +wanted a beat to feed us. + +He'll learn it. + +STUDENT 11: OK. + +You'll get the melody +after we play it. + +So basically, us +two will play it, + +and then you can come in +after four times or something. + +And then we'll take +turns improving + +while one person drones on a D. + +[MUSIC PLAYING] + +PHIL SCARF: So any thoughts? + +How did you think it went? + +STUDENT 11: I think +it went pretty well. + +I think originally we were +supposed to play the melody + +and then harmonize +a little bit to it. + +And then kind of stretch +up from that melody. + +But in the end, we just +started improvising instead + +so I guess that worked out. + +PHIL SCARF: But there +was harmony introduced + +as the improvisation +evolved, too. + +It's coo. + +Any other comments or thoughts? + +How about the flutist? + +STUDENT 1: I was playing +in F natural for too long. + +I was like there's probably +not an F# in this scale + +if there's a Bb, +[INAUDIBLE] really confused. + +[INAUDIBLE] + +PHIL SCARF: Anybody +else, have any comments? + +STUDENT 2: I thought +it was pretty cool how + +the rhythmic moment +of the melody + +became stronger +almost, throughout. + +It was like a little more +free in the beginning, + +maybe, when you +decided to push time. + +[INAUDIBLE] almost +like a very driving. + +PHIL SCARF: That's true. + +Good observation. + +It was very effective, too. + +PROFESSOR: So that's the +second one that did that. + +Where it evolved into +the rhythmic spectrum. + +It's an interesting +way to do it. + +STUDENT 13: So this +is D Mixolydian + +rather than picking a new scale. + +And [INAUDIBLE] Jamie +is going to set up + +a low drone at the beginning. + +And once Jamie has +this low drone, + +the flute and trumpet come +in on vibrato type lines. + +And then the flute +and trumpet explore + +the different [INAUDIBLE]. + +So I tried it in a low +range, [INAUDIBLE] Flute + +is going to start +with low note density + +and gradually increase density. + +Also Jamie is going to gradually +adopt a rhythmic progression + +and eventually start playing +[? jala. ?] And I think you + +said the [? jala ?] will be +in different rhythmic groups, + +so that we also have a +little bit of [? livhari ?], + +or rhythm play. + +And that will go on +for a minute or two. + +We don't really have +specifics of what's + +going to happen in there, +it's just to improvise. + +And at the end, I drop +out, flute drops out, + +and then Jamie just sort +of continues with the drone + +and fades out. + +[MUSIC PLAYING] + +PHIL SCARF: Nice. + +So do we have any thoughts +from the performers? + +STUDENT 7: I thought +it went pretty well. + +We just sort of set up +the framework last night + +and just ran through it once. + +We were like, alright, we'll +do something like that. + +So it turned out similar manner. + +Had sort of the same feel. + +I think it went well. + +STUDENT 13: I don't think it +sounded quite as Hindustani + +as a raja, but was totally +using the framework. + +Like it had the +same idea, and it + +was easy to communicate +with someone + +who just heard the +framework today, what to do. + +PROFESSOR: I like the +rhythmic of the banjo. + +You really sounded almost +like a mix between a tabla + +and something, I'm +not quite what else. + +STUDENT 7: Yeah, I almost +wanted to play it on my lap. + +PHIL SCARF: Maybe more +like a [? surod, ?] + +actually it's a little +like it's [? surod, ?] + +which is played with a pick +and it's got more of an attack. + +Cool. + +How about the flutist? + +Because this is +the first time you + +had been introduced +to the piece. + +Any comments? + +STUDENT 1: I liked it, +it was easy to follow. + +[INAUDIBLE] set up the +right image [INAUDIBLE] + +PROFESSOR: You're a +utility [INAUDIBLE], + +we bring you in +whenever we need it. + +Thank you for that. + +PHIL SCARF: I was +going to say, I thought + +it was cool because the way +you used the frameworks, + +you had assigned different +frameworks to different people, + +which was interesting. + +First time, I think, +we did that today. + +So that was cool. + +Good idea. + +STUDENT 7: I really +liked playing it + +because it sort of fit +my instrument very well. + +I could do like the +slower bluegrass picking, + +and just leave that D open +the entire time pretty much, + +and that leaves a nice drone. + +That makes it easy to play +around on the top three strings + +and it was a lot of fun. + +STUDENT 13: Actually, the +reason we split up frameworks + +is the first time we +decided what to do, Sarah + +and I were both just like, +yeah, we can both do range, + +we can both do note density. + +And then we ended up running +through the piece once, + +and I focused more on +range, and she focused more + +on the note density. + +So we said, well, why not +just make that the framework + +instead? + +PHIL SCARF: Yeah, +that's a great idea. + +That is a very cool idea. + +Excellent. + +STUDENT 10: At the risk +of overworking the flutes, + +can I ask one of you +guys to -- alright, cool. + +So like most of +the other groups, + +the frameworks we ended up +using are range and note density + +again. + +So I was going to start toward +the lower end of the range + +and then gradually work up. + +And then vice +versa for the oboe. + +So I guess rhythmic +progression is just + +like a natural part +of that, as well. + +So we are thinking of playing +in concert G natural minor. + +Yeah, so we're going to +start off just alternating, + +with one person doing a +drone on the concert G. + +And then the other person just +kind of soloing off of that. + +And then just +interchanging a few times. + +Maybe two or three +times or whatever. + +And then, just gradually +working into playing together. + +PHIL SCARF: That's cool. + +And did you have a specific idea +about the rhythmic progression + +and how that would work? + +STUDENT 10: Just in the vague +sense of gradually speeding up. + +Starting off with slower, +sustained whole notes + +and working to faster rhythms. + +We kind of wanted to work +some [? chellan ?] in there, + +as well. + +We don't have any kind of set +phrase we wanted to repeat. + +I guess it's something +we kind of wanted + +to figure out as we go. + +If we find something +worth holding on to, + +then we'll do that. + +[MUSIC PLAYING] + +PHIL SCARF: Yeah. + +Nice. + +PROFESSOR: So you're just +coming into this cold, right? + +So I noticed, you +were watching him. + +Had you determined that +you would watch each other + +and do those phrases toward +the end in synchrony? + +STUDENT 2: That was +just based off his -- + +he said that he wanted to do +something with [? chellan, ?] + +so I was trying to pick up +some very distinctive phrases + +and see whether I can put +them into different ranges. + +And so I picked out a +couple, and just tried + +to repeat them and then +put them in different notes + +with the same rhythm. + +But by and large, most +of it was just like, oh, + +that sounds nice. + +PROFESSOR: Well I personally +thought it was very good, + +the way it worked out, and +very interesting the way + +it all synchronized. + +I mean, it was like +you planned it. + +Which obviously, you didn't. + +STUDENT 10: Yeah, one problem +we ran into when Ben and I were + +rehearsing was just, when we +got toward the end each time, + +and we tried to make +the rhythm go faster, + +it kind of became more +difficult to play in synchrony. + +Because there's just so +much loudness going on. + +PHIL SCARF: Anybody +else have comments? + +STUDENT 7: You could +really tell you + +could find that +[? challen ?] motif, + +you repeated and played off of. + +I think it worked out nicely. + +PHIL SCARF: Anybody else? + +PROFESSOR: I was just thinking, +it would be interesting. + +We can do this through +the magic of taping, + +to play all these +exactly in sequence. + +And then hear them +as a unified suite. + +Which we could do through +the mystery of taping. + +[INAUDIBLE] It was +very interesting + +how we started with a slower +idea doing some things. + +Then we got more rhythmicized +as we got to the middle. + +Then we had this as the ending. + +Well, your thing just before +that and then this thing + +at the end, which +is very different. + +PHIL SCARF: Cool. + +Thank you. + +So what I thought is, +maybe, as a group, + +we can try some of +the frameworks that + +didn't get selected +for today's assignment. + +So I was thinking, +why don't we do -- + +I forget what I called +it, the constrained range. + +Confined range, OK. + +So there's one called +[? tans ?] confined range. + +And then we have the expanding +and contracting [? tans. ?] + +So maybe we can try those. + +And actually, why don't we as +a group figure out a a design? + +Why should I say +what the design is? + +Let's use those frameworks. + +And who wants to +volunteer, who wants + +to give us an idea +of how we can start? + +Or how to use the frameworks? + +I see an elbow going up. + +You got to be careful. + +It's like you're at +an auction, and if you + +do something like that, you +just bought it, you know? + +OK, well I know you +guys been thinking + +about these for a while. + +Yes, go ahead. + +STUDENT 7: Normally with range, +we start low and then go high, + +why don't we start high +and slowly incorporate + +the low notes? + +PHIL SCARF: That's fine. + +That's cool. + +And so that takes care of range. + +But who can think of what to do +with this confined range idea? + +And then expanding +and contracting. + +What could we do with +those two things? + +When you say start +high and move low, + +did you mean we have the +confined range times? + +OK. + +So the confined range +times, we'll start high. + +And then what are +we going to do? + +STUDENT 7: Expand +them slowly out? + +PHIL SCARF: So expanding. + +OK. + +Right. + +So expanding more down, because +we're going to start high. + +So expanding them down. + +And when we do the +expanding and contracting, + +these are more like linear. + +So you're kind of +going up and down, + +progressively up and down. + +So you would make the point, +if you're expanding downwards, + +you'll say you'll start here, +and go down and back up. + +And then go down, +farther and back up, + +and then farther and back up. + +Every time, you go progressively +farther and farther. + +And then, is that it? + +Or anybody else have +anything else to add? + +STUDENT 13: Maybe +when we contract, + +we can contract the top note, +so that the top end of the range + +is getting lower. + +And then we can track +down to the bottom tonic. + +PHIL SCARF: That +is a killer idea. + +I love that. + +OK. + +So that's good. + +And then, anything else? + +I think that's enough. + +So I think we can +play with that. + +So let's just review +this one more time, + +make sure I got this right, OK? + +I'm going to try to summarize +what I think we're doing. + +So we're starting with +a constrained range + +or confined range +[? tans, ?] which + +are fast lines, as opposed +to these slow lines which + +everybody's been starting with. + +So we're starting +something fast. + +But you've got to +pick just a few notes. + +Like three or four notes, and +just stick with those notes + +and just keep going fast +passages using those notes. + +And then after a +while, we're going + +to start doing expanding +and contracting, + +expanding [? tans. ?] +Expanding downwards, + +progressively farther downwards. + +And then start doing it +but reducing the upper part + +of the range, and then wind +up with some probably confined + +range, constrained range +[? tan ?] at the bottom. + +Yeah. + +OK. + +Great. + +So any questions +or anything about? + +Does that reflect what +you guys want to do? + +STUDENT 13: Do you want +to pick a mode or the key? + +PHIL SCARF: That's +a great question. + +I am tempted to say no. + +Because everybody's doing that. + +So I think we should +do something different. + +My two cents is no. + +No. + +That's just my two cents. + +Because everybody seems +to be still worrying + +about the modes and the scales. + +STUDENT 13: But there's +like a dozen of us. + +Won't it -- + +PHIL SCARF: OK. + +You guys, feel free +to override me. + +My two cents is I wouldn't +get too worried about it. + +But if you want to pick +a starting note maybe. + +That might be good. + +STUDENT 4: We can try both. + +We can try it twice. + +We could just try both. + +We could just try +it as you say first, + +and then see what +it sounds like. + +PHIL SCARF: Yeah. + +Because, hey, we can +always do it again. + +So let's try it without +overly defining this too much. + +And see how it goes. + +And then we can talk +about it, and see + +if it's something +we want to change. + +How about that? + +All right. + +So I'm going to let +you guys start -- + +maybe I won't even play. + +I'll let you guys play, +why do I need to play? + +Is everybody ready? + +OK. + +[MUSIC PLAYING] + +PHIL SCARF: Cool. + +OK. + +That was nice. + +So any thoughts about this? + +STUDENT 13: One thing I noticed, +is by the time we ended, + +I think, most people already +done the contracting, + +and I hadn't. + +And it was just very difficult +to listen to other people, + +to figure about what kind +of range they were in. + +Since everyone was in a +different part of their range. + +I couldn't just listen to +the sax and be like, oh yeah, + +he's in the low +part of his range. + +Because listening to the +flute or the banjo would like + +get me sort of confused about +what range everyone was in. + +PHIL SCARF: Well there's +so many people playing. + +It's pretty thick with +everybody playing. + +You know, the thing, in Indian +classical music, of course, + +normally there would +be one lead performer, + +one lead melodic performer. + +There might be two if it's +like a duel under your duet + +kind of program. + +There would typically be +an accompanist or even two, + +but they would be playing a much +more secondary role, usually. + +So we wouldn't have this +kind of size ensemble. + +Wouldn't happen. + +So these frameworks, +really, we can certainly + +apply them to a large ensemble. + +Traditionally, it +wouldn't be like this. + +Any other comments or thoughts? + +STUDENT 12: I felt like +we sort of ended up + +finding a modal +center, but we had + +some type of tonal +center of some sort. + +I don't know. + +PHIL SCARF: Yeah, I +think you're right. + +It's sort of emerged. + +PROFESSOR: I thought +you all started on one. + +Sounded to me like you were +all, I don't know what that note + +was, but -- anybody +else notice that? + +I mean, after all +that discussion. + +Everybody just intuitively said, +okay, we're going to do over, + +and that was pretty interesting. + +And again, I was the only +non-playing observer, + +but in addition to this concept, +of the range increasing and all + +that kind of thing, +contracting, you're + +also dealing with texture. + +So the whole thing +could be looked + +at as an exercise in texture. + +Particularly in the beginning +part and the last part, + +as I was hearing. + +Which is interesting. + +Which means that your +specific contributions, + +it's the overall +that's more important. + +To me, anyway. + +I don't know what +you think about that. + +PHIL SCARF: I don't know, +with so many people playing, + +everyone has their +own contribution. + +Everybody's listening. + +And there's so much +going on, it's hard -- + +some people are probably trying +to pick out maybe what one + +person is doing, or maybe others +are kind of trying to hear + +the overall sound. + +When you have so many +people improvising, + +it's challenging to +figure out how to fit in. + +Yes. + +STUDENT 12: I thought +speaking of fitting in. + +I think this was the +first time in this class, + +for me, at least, that I +wasn't trying to fill a space. + +I was just like, oh, +I'm just going to go. + +Because we had talked about +having that type of texture. + +And I think, most of the time +when you improvise, somebody + +starts something, and then +somebody else comes in and is + +trying to fill a +space that they left. + +And this was different +because we were just, like, + +who cares about +each other's space, + +and just went all over it. + +PHIL SCARF: Yeah. + +That's right. + +STUDENT 7: I think one thing +that really would have helped + +is if we'd trickled +in at the beginning, + +that way we could +have sort of set a -- + +STUDENT 12: I liked +it, I mean, we've + +never sounded like that before. + +PROFESSOR: The effect +was pretty strong. + +STUDENT 7: I feel like we did +sort of start funneling in. + +The beginning just +started as chaos, + +everyone was doing +something different. + +We did start to funnel +in towards the end. + +We might have been +funneling in to two or three + +different places, but +we were funneling. + +PHIL SCARF: Yeah. + +You know, part of +improvisation can be chaos. + +It doesn't have to be. + +But it can be. + +So that's part of +the game, you know? + +If it goes into chaos, then +where's it go from there, + +you know? + +Does something start to gel? + +Or come together? + +Improvisation, especially when +you're doing with a group, + +it has a life of +its own, you know? + +And everybody's kind +of going with that. + +Anything else? + +What else? + +OK. + +Cool. + +So let's try +something different. + +Let's try -- OK, +I'll take ideas. + +Ideas about how to set +up an improvisation. + +Let's say we want to use +the constrained range, + +I want to do this constrained +range, confined range. + +OK. + +We use the confined range idea. + +But this time we're +going to extrapolate it. + +And instead of picking notes +that are close together, + +pick three or four notes +that are far apart. + +And use that. + +But I also want to +change this density. + +So that's it's not continuous +high, like everybody + +playing all the time. + +So I want to solicit some ideas +about how we should do that. + +How can we make it thinner? + +STUDENT 7: We could +designate people + +who would be more drone, +lower, longer pitches. + +And who would be higher, +melodic type instruments. + +That way we can sort of +differentiate between that, + +and not everyone's +trying to do melody. + +PHIL SCARF: OK. + +That's a cool idea. + +So by default, people +would be droning. + +And then those who are going +to play the so-called lead part + +would emerge. + +OK. + +Yes? + +STUDENT 2: We could maybe have +a shifting window of maybe two + +or three people at a time, who +are out there trying to make + +a new motif, or kind of -- even +for the people who are just + +droning, they might +be playing something. + +But maybe designate a +moving group of people. + +Not any one, but like. + +You know, Ben can +experiment more, I guess. + +PHIL SCARF: Playing the lead -- +we'll call it lead and drone. + +Just to differentiate +the roles, right? + +So having small groups of +two or three people at a time + +playing the lead. + +Right. + +Yeah. + +That's a good idea. + +So any thoughts about +how do we implement that? + +How are we going +to know who's going + +to play the lead part +at any given time? + +Any ideas? + +STUDENT 2: You can just start +with first two or three, + +and then when one drops +out, the next person -- + +PHIL SCARF: OK, that's fine. + +Cool. + +So we'll start with three. + +When the first person drops +out, the next person adds in. + +That person drops out, +the next person adds in. + +And we work our way across +the room, how about that? + +OK. + +Great. + +This is for the lead part. + +By default, everyone's going +to be droning, more or less + +all the time. + +And then when it's your +turn to play the lead part, + +you jump out, you +emerge out of that, + +and you go into the lead part. + +And I was just +thinking also, maybe + +we should put in one +more element here. + +Like a note density element. + +Yeah. + +Everybody's going to pick like +three or four notes, which + +don't have to be the same notes. + +You can pick whatever +notes you want. + +And you could base it +on what the people are + +playing who played before you. + +Or not. + +It's up to you. + +But let's do this. + +Let's start it at a +very high density, + +and work our way +to a low density. + +OK? + +But still, the notes +should be rapid. + +So to achieve a low density +with rapid notes, what + +you have to do is maybe +play a few notes and stop. + +Play a few notes and stop. + +So that it's not as dense, +but when you play the notes, + +you're playing rapid lines. + +So let's not play sustained -- +the lead players should not be + +playing sustained notes. + +It's only the droners who +are playing sustained. + +And let's do the drone +-- let's pick a note. + +Who wants to pick a +note for the drone? + +A tonic? + +F. OK. + +Cool. + +So let's start. + +And we're going to start over +here and work our way around. + +Three people at a time. + +OK. + +Is everybody ready? + +[MUSIC PLAYING] + +PHIL SCARF: Right. + +Good. + +So comments? + +How well do you +think we followed + +the framework, or the design? + +STUDENT 7: We followed +it pretty well. + +It seemed like we were keeping +to the groups of three. + +PHIL SCARF: Yeah. + +We were keeping to +the groups of three. + +That's true. + +I was kind of +helping that along. + +Because sometimes +it was getting hazy. + +But yeah. + +STUDENT 13: I didn't hear +the change in note density, + +I guess? + +PHIL SCARF: Yeah. + +The change in note density +didn't really seem to happen. + +It wasn't too obvious. + +Maybe a little bit, but it +wasn't nearly as pronounced + +as I was hoping it would be. + +STUDENT 12: I +guess I wasn't sure + +exactly what that meant +when you described it. + +PHIL SCARF: Yeah. + +Well I'll try demonstrating +that with my reed -- aw man, + +I'll tell you, this weather. + +When it's cold and it's dry +in here, the reed dries up. + +While we're talking I'll +try to get this resolved. + +Picking three or four notes +and only playing those notes. + +I was hearing like scales and +different things going on, + +which wasn't really +part of the design. + +So that was the other +observation I had. + +STUDENT 7: I +thought we were just + +supposed to start with three +notes and then build out. + +PHIL SCARF: Oh. + +That's not what I had in mind. + +But that's certainly +a possibility. + +But it wasn't what I was +trying to communicate. + +PROFESSOR: If I +could just interject. + +It's almost the most difficult +thing, is just [INAUDIBLE] + +a reduced parameter. + +So three or four notes, +that's really hard. + +Because our inclination +always is to expand. + +So the idea of staying +with this limited + +whatever it is, range +or density or something, + +it's one of the +hardest things to do. + +So just something +to keep in mind. + +We'll probably try to work +on that as we go forward. + +PHIL SCARF: I agree. + +That's true. + +It's a very natural tendency. + +Once you start with +whatever the parameter is, + +you try to build something. + +OK. + +So for example, I'm +going to pick three notes + +and just play some rapid +lines with just three notes. + +So that's pretty high density. + +To go to lower density +without reducing the speed, + +you just leave space. + +So. + +And you could reduce the density +without changing the speed. + +So that's more like what +I was thinking about. + +So I don't know if we +want to try it again. + +Maybe try it again with that +in mind and see what we can do. + +PROFESSOR: So just time-wise, +we have room for one more. + +PHIL SCARF: OK. + +That's cool. + +So we'll do this. + +So we'll do the +same basic thing, + +with everybody +droning by default. + +And then we'll have +our window of three. + +And I may just do +the same thing. + +So let's just start. + +Yeah, still on the F. + +[MUSIC PLAYING] + +PHIL SCARF: Still have +a couple minutes, right? + +OK, any comments? + +That was much better. + +Much closer to what +we were trying to do. + +Yes. + +Good. + +So how did that feel? + +Start to compare the last two, +from the performer's point + +of view. + +How did it feel +the play those two? + +STUDENT 7: It's interesting. + +Because we look at +it on a micro scale. + +Each individual +person is playing + +this random, chaotic +assortment of just three notes. + +And when you look +on the macro level, + +when everyone was +playing together, + +it actually sort of made sense. + +I don't know. + +But if you just listen +to each individual part, + +it really didn't make sense, +it was just sort of random. + +PHIL SCARF: OK. + +Anything else? + +Other comments? + +STUDENT 1: I feel like +high density is also + +just as restricting +as like low density. + +There's only certain +things that you + +can play if you're +forced to play fast. + +There's certain things when +you're forced to play slow. + +But you're restricted +to those things. + +PHIL SCARF: As opposed +to having a full pallet, + +of all possibilities. + +STUDENT 1: I didn't mean +restricted as a bad thing. + +I meant, it's just +definitely more constraint + +than I expected. + +PHIL SCARF: Yeah. + +You have to work within +certain limitations, + +and it generates +a certain thing. + +And, you know, these +kind of concepts -- + +it's great to think +about it ahead of time. + +And have this design +worked out, and then try + +to implement the design. + +But you can also spontaneously +just play, and use these ideas + +as you go. + +And let the framework, +or let the whole design + +itself kind of +evolve spontaneously. + +It doesn't have to be +something that you've + +planned out before hand. + +PROFESSOR: The one +thing I would say + +is I thought everybody, +comparing the two, + +is the second one, +everybody was listening + +much more closely +than I thought. + +Which is why I think +it worked out better. + +Because you got to +listen as much as + +you make your individual +contributions. \ No newline at end of file diff --git a/quATCFNpM50.txt b/quATCFNpM50.txt new file mode 100644 index 0000000000000000000000000000000000000000..55efd2106c82621639f706fe9db313691066df26 --- /dev/null +++ b/quATCFNpM50.txt @@ -0,0 +1,3641 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So this is, as I +understand it, continuing the + +conversation you've already +started on education. + +And this is sort of the last +of the education lectures. + +So what I propose to do today is +to just kind of try to tell + +a story, a single story +that kind of fits some + +of the facts together. + +You've seen some of the broad +patterns of dysfunctionality + +already, as well as some +of the local success + +stories, if you like. + +I think the last lecture was +about this NGO [INAUDIBLE] + +and its many efforts to +improve education. + +So what I'm going to do today +is continue from there, but + +talk a little bit more +sort of big picture, + +focusing mostly on-- + +the goal is to tie things +together into a story that + +might make some sense, and help +us think forward about, + +if this is what's going on, +where should we act? + +That's always the ultimate +question we have in mind, + +which is to try to find a way to +an action point or a lever. + +And it's only by wrapping in +these facts into a narrative + +that we can find a lever. + +So what I want to do is +I want to go from + +the fact to a lever. + +And the way we will go there is +by talking about a specific + +interpretation of the facts. + +So that's what I want to do. + +And I'm hoping that you already +read some of this + +material and are sufficiently +engaged with it, that we'll + +have a lot of discussion along +the way about, is this a + +reasonable interpretation +of the facts or not? + +And I'm very much open to the +idea that you may think that + +this is not the right +interpretation. + +And we can definitely, you +should feel free to propose + +alternatives or whatever +you think. + +You think I'm going too fast, +or trying to push the logic + +too far, you should stop me, +or if you have questions. + +So I think that the first fact, +which is I think very, + +very widely accepted but somehow +not necessarily very + +widely documented, is that +education is actually + +beneficial for the people +who get it. + +And you would that this is +something that we would have + +seen tons and tons of reliable +evidence on. + +But in fact, the reliable +evidence, even on this very + +basic question, is +relatively weak. + +The reason why education +evidence tends to be weak is + +that, as you know, education's +not like taking a medicine. + +The nice thing about +taking medicine is + +that I take a medicine. + +A week later, I'm better. + +Education is something that +has action at a distance. + +It's like something that I get +educated today and tomorrow + +and day after, the +day after that. + +And then distant future, I get +a job, and that's where it + +benefits me. + +So that sort remoteness of it is +actually part of the reason + +why it's hard to find good +evidence for education. + +You need to have a data set +where you saw who got educated + +today, and what happened +to their + +salaries' 20 years later. + +And that's not always easy to +find, for obvious reasons. + +You might imagine that +you do need to track + +people in some way. + +So that's why there's +not much evidence. + +The evidence that there is, a +significant part of it comes + +from countries like +the US, where the + +evidence is very clear. + +Education seems to have a clear +and relatively high, + +stable rate of return. + +Hasn't changed very +much over time. + +And a few studies like the one +from Indonesia which also find + +the same thing, and actually +find, surprisingly, relatively + +similar rates of return +on education. + +The benefits of education in +Indonesia seem to be similar + +to that in the US. + +And that's something that, when +it came out, was rather + +surprising to people. + +Why would it be surprising? + +What would you have expected? + +AUDIENCE: I don't know, that +education here might be better + +or something. + +PROFESSOR: Right. + +So you could imagine +that it would be-- + +education in the US has higher +quality, so maybe the returns + +would be higher in the US. + +Anybody want to suggest a +reason for the opposite? + +AUDIENCE: Education in the +US is more expensive. + +PROFESSOR: That's an +excellent point. + +But primary education is what +we're talking about right now. + +So that's not very +expensive, right? + +It's mostly free. + +AUDIENCE: If everyone in the +US has an education, + +[INAUDIBLE]. + +PROFESSOR: Absolutely. + +The opposite view is +that education + +is scarce in Indonesia. + +And especially in the early +'70s, very few people had + +primary education. + +So you might imagine that +something that's scarce + +typically has a higher price. + +So you might imagine that it +would be more rewarding. + +So you could imagine it +going either way. + +Turns out, these two effects +seem to have cancelled out. + +And you get on net, roughly the +same rate on education in + +the US as you get +in Indonesia. + +But that's all to say that we +seem to think that there is-- + +it's not that there's a huge +amount of evidence. + +But what there is seems pretty +consistent and compelling. + +So I think most people accept +the idea that there is a + +benefit from education. + +And then the next question that +then arises is if there's + +a benefit from education, +why are people + +getting such lousy quality? + +Why isn't it the case that +education systems kind of + +stand up and deliver? + +If education's valuable, why +isn't there a system that + +supplies it? + +Why is it that you have all +these schools where kids are + +going and learning nothing? + +AUDIENCE: Unlike other +investments, one is it's not + +made by the primary +beneficiary. + +I mean, parents that +fundamentally pay for the + +investment or the government's +a case maybe. + +And the parents paid the +lost wages that that + +child could be earning. + +The other thing that, unlike +other investments, is the + +returns, like we talked about +earlier, are very long-term. + +PROFESSOR: So you're saying that +one reason why education + +might be different is the +connection between the cost + +you're paying and the returns +you're getting is weak. + +So maybe the government, +I don't really + +think about the returns. + +The government wants me to send +my children to school. + +So I send them. + +But I don't really +think about it. + +So I don't think of +all the returns. + +I don't make the investments +in it. + +I don't really care about it. + +It's just something the +government wants me to do. + +And therefore, I don't +get benefits. + +So I'm going to try to suggest +evidence that that's not + +what's going on. + +But that's exactly right. + +One very plausible hypothesis is +that this is something that + +people really, they're +not buying education + +like they buy machines. + +They're getting education +from the government + +as a kind of gift. + +And therefore, they don't +care about it. + +So that's one kind +of explanation. + +But that's exactly right. + +That's one possibility. + +Let's keep going a bit, +and we'll come-- + +go ahead. + +AUDIENCE: Well, one of the +things that was written was + +that they have this mistaken +impression that the first few + +years of schooling have very low +returns and that secondary + +education or university +education is where you + +actually get a meaningful +increase. + +So it gives the most incentive +to care about effective + +education [INAUDIBLE] it's +someone they're planning on + +funding later on. + +PROFESSOR: Right. + +And an alternative view, which +we'll come back to and spend + +some time on, is that people +actually don't-- + +it's not that people don't +believe education's valuable. + +They don't know which part +of education is valuable. + +And that's sort of what +you're suggesting. + +AUDIENCE: Question. + +So we just talked about how, +in Indonesia, we saw there + +were benefits to education. + +And now we're talking about the + +education being poor quality. + +So is the idea that even this +poor quality education is + +still incurring benefits that +people aren't realizing, that + +[INAUDIBLE]? + +PROFESSOR: So I think that goes +back to the conversation + +we had a little while ago, which +is that we would imagine + +that in Indonesia, education +would be a lot more valuable + +than in the US. + +Because there's so +much less of it. + +And you would think that when +I'm the first primary educated + +person in the village, that's +much more valuable than being + +the 2,000th. + +Never the less, we don't find +high returns in Indonesia. + +We find comparable to the US. + +So the idea is, implicitly, that +the returns to education + +are lower in Indonesia partly +because the quality is-- + +actually somebody suggested +exactly that, which is that + +one reason why you might +expect lower returns in + +Indonesia is that the +quality is lower. + +And so I think the concern is + +education is socially valuable. + +We want it because there's +not many educated people. + +On the other hand, maybe the +delivery systems are weak. + +And therefore, it's not +worth getting it. + +So that's a trade off. + +And the question, if you look at +the other evidence, you've + +already looked at it, it seems +like it's hard to imagine + +somebody who's in fifth grade +and can't really read having + +got much benefit +from education. + +So our presumption is that at +least a significant proportion + +of the people who are getting +to fifth grade without being + +able to read are not getting +anything out of education. + +They're just going through +the motions. + +So why is it that there are so +many people who are going + +through the motions rather than +saying look, why am I + +wasting my time with this +education thing, unless it's + +worth something to me? + +That's sort of the question. + +And a corollary to that question +comes from the fact + +that, in fact, the Pratham +experience suggests, is it's + +not even that hard to +improve quality. + +It may well be that you could +imagine that it's just + +impossible to improve quality, +because kids are very + +difficult to teach. + +But in fact, kids are not +difficult to teach. + +The whole Pratham experience is +that whenever you have an + +intervention which sort of +provides them with some little + +bit of extra help and some +focused help on what they + +need, the kids improve fast. + +So that makes it even +more positing. + +Because at some level, it's +easy to improve them. + +The kids' education, if you've +got a high quality education, + +that has value. + +So what's going on? + +Where's the pipeline broken? + +Yeah. + +AUDIENCE: [INAUDIBLE] education +focused on all + +levels of students, +[INAUDIBLE]. + +So it's not geared to +the basic needs that + +each student needs? + +PROFESSOR: Yeah. + +I think that that is part-- + +we're going to come and try to, +in a sense, develop that + +hypothesis and look at how that +can help us explain a + +whole bunch of different +things. + +So that's exactly the kind of +hypothesis that we'll come to. + +And it's good that we already +start hinting at it. + +But I just want to first frame +the question quite sharply. + +This seems like education is +something that, prima facie, + +is valuable. + +And it's not hard to deliver. + +Those two things are +what you've seen. + +You've seen that it +seems valuable. + +It seems very low quality. + +So many of you aren't getting +anything out of it. + +And it's easy to make +sure that they get + +something out of it. + +Those three facts, how are +they sitting together? + +That's the question. + +You would think that one of +these facts has to give. + +That's the puzzle. + +Why is it that this thing that's +easy to improve is not + +being improved, even though +improvements will generate + +large gains. + +Yeah. + +AUDIENCE: Maybe it's easy to +improve on a small scale, but + +not so much on a large +and consistent scale. + +PROFESSOR: That's another +possibility. + +Now, part of the reason we +emphasize some of the Pratham + +experience was that large +is a relative word. + +But Pratham operates +on a fairly-- + +like a state in India is often +larger than any five countries + +you would randomly name +in the world. + +So it's not small in any +obvious scale of small. + +That's why we were +emphasizing it. + +So if you take five countries +at random, the sum of the + +states, the way they work, would +be smaller than this. + +Because India has +so many people. + +OK. + +So this is sort of the story +that several of you have + +already hinted at, which is a +story that parents have the + +wrong view of which part of +an education is valuable. + +So starting point of +that is we call + +it an illusory s-shape. + +So you know the idea of +an s-shape, right? + +The idea of an s-shape is that +when you get a little bit of + +education that has very +little value. + +And then as I get more and more +education, the value of + +the education I'm getting +goes up for a while. + +And then at some point, +presumably, it flattens off. + +Once you've got your Ph.D., +presumably a second Ph.D. + +isn't worth that much, at +least in income terms. + +So at some point, it's +going to flatten out. + +So the returns go kind of like +that, then like that, + +and then like that. + +That's an s. + +Is that clear, why it's an s? + +So that idea. + +One of the hypothesis that +I think we've been most + +persuaded by is that parents +seem to believe that there is + +a real jackpot if you +get to the end of + +the education tunnel. + +So they think of education +as being this tunnel. + +Once you get into a tunnel, +there's nothing good happening + +for a long time. + +When you come out of the tunnel, +those who manage to + +come out of the tunnel, which +means you get through the + +whole school system and you +graduate from high school, + +then you get a government +job automatically. + +That's how they describe it. + +70% of them think that if my +child could only get through + +high school, he will actually +get a government job. + +In fact, the probability that +he would actually get a + +government job is less +than half of that. + +So they seem to, at the +top end, they seem + +to overvalue education. + +They think that if my child +could only get through this + +whole tunnel, there's a +job waiting for him. + +But in fact, that's not true. + +There are not enough government +jobs around. + +So you don't get these +good jobs. + +On the other end, and this is +the fact that's much harder to + +appreciate, you will find out +what the probability of + +getting a government job +is relatively easily. + +But what's really hard to find +out is what are the benefits? + +And especially if you are an +illiterate parent, what are + +the benefits of getting three +years of education? + +And if you think about it in +the US, the US actually, + +nobody gets three years +of education. + +Therefore, we can't even tell +what the benefits are. + +But I think what is surprising, +but maybe not + +surprising once you think about +it, is that the benefits + +of people who get three years of +education's insubstantial. + +Why are they substantial? + +There are a bunch of stuff that +it's hard to appreciate + +living from the perspective of +living in the US now, but are + +not automatic. + +So for example, many people +don't find out about + +government programs that are +available to help them. + +Why? + +Because we don't read any +newspapers or flyers or when + +the TV person say something, +they don't understand what is + +being said. + +So even a minimal understanding +of just how the + +system works actually gets +you large benefits. + +Or another example people often +give is that even if you + +go from first grade to third +grade and you learn to read, + +you can read the instructions +on your bag of fertilizer. + +And your bag of fertilizer +says, use one + +teaspoon, no more. + +You know you're to use one +teaspoon, no more. + +And put one cup of +water with it. + +Just being able to read that has +a large benefit in a world + +where people suddenly, lots of +evidence of people overusing + +and underusing fertilizer. + +So just the fact they can read +the instructions on the packet + +is very, very large, +has large benefits. + +So the reason why even getting +a third grade education has a + +benefit is because there are +lots of things in the world, + +lots of information that's +transmitted through reading, + +for example. + +Like what the government program +is, how to properly + +use fertilizer, what new +seeds have become + +available for planting. + +And that might be in +the newspaper. + +Somebody might have +taken an ad. + +But you don't read the ad, +and you never find out. + +So there are lots of benefits +even if you can read a little. + +You don't have to be able to do +calculus to be able to get + +benefits of education. + +I think that's the evidence. + +This picture that I'm going to +show you plots kind of actual + +and perceived returns in +Madagascar to the extent that + +they can be estimated. + +The actual returns are +pretty constant. + +The perceived returns come from +a survey where parents + +were asked what the +returns were. + +And the perceived returns +look more concave. + +This is to say, they are more +flat in the beginning, lower + +returns at the beginning. + +The beginning, you think +that you're not + +going to get much returns. + +And then as you go +up, they get-- + +they cross, and you think you +are going to get more returns + +than you actually get. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: What that is is +really the percentage increase + +in your earnings for an extra +year of education. + +When you go to 11, to 12, +what's your percentage + +increase in earnings? + +So this in some sense +is actually not-- + +this picture sort of +gets the idea. + +But in fact, it doesn't +actually tell you how + +big the effect is. + +The reason is that in fact, +there are some people who + +generally overestimate the +benefits for education. + +So some parents think +education's + +extraordinary valuable. + +And a lot of parents think that + +education's completely useless. + +So this yellow curve is +an average of very + +lows and very highs. + +So in some sense, the average +looks actually less wrong than + +the individual parents think. + +So some parents are +overestimating their returns. + +They're all sending their +children to school. + +Others just think education's +worthless, at + +least for their children. + +And their children is important +in that sentence, + +because a lot of people think +education is something that + +benefits those other children. + +People from rich families can +benefit from education. + +Our children don't benefit. + +So there's clearly a strong kind +of self-discrimination, + +which we'll come back +to in a bit. + +So that average actually masks +a lot of divergence. + +So what I want to do now is I'm +going to take this as a + +hypothesis, the fact that this +what I would call elite bias, + +the idea that people think +it's an s shape. + +Returns are at the high end, +no returns at the low end. + +Assume that that's true. + +And look at how that can +help us explain a + +bunch of other facts. + +So we're going to look at what +this does for the parents, the + +teachers, the students. + +You see where we're going? + +We're going to make +a hypothesis. + +We've made the hypothesis. + +Now we're going to look at what +that hypothesis does. + +Particularly, you know a bunch +of facts, and we'll try to fit + +together a bunch +of those facts. + +Then at the end, I'll tell you +some other facts that you + +probably don't know, which +also kind of fit this + +hypothesis. + +So it's sort of a way to +give it a bit more + +power, if you like. + +Try it out on things. + +So one implication is think of +the first implication of this. + +Imagine that, I believe that you +get benefits only if you + +get through high school. + +And you have three children. + +And you can't really afford to +put all three of them through + +high school. + +So in truth, as we saw, the +returns are pretty constant. + +So an extra year is +an extra year. + +If it were the case that an +extra year, an extra year, how + +should you spend the money? + +Equally. + +Since all the children, +there's no reason to + +discriminate. + +Why give one of them a chance +and not the others? + +Any bias towards equity will +make you just spend equal + +amounts over the children. + +Because they're all +your children. + +Why discriminate? + +One year of education is +one year of education. + +So there's no reason +to discriminate. + +Now, imagine we believed +something else. + +We believe that the +first years of + +education are worth much. + +But then the final years +are worth a lot. + +How would we spend our money? + +AUDIENCE: I'm assuming +you have two + +kids who are identical. + +You have [INAUDIBLE]. + +between the two. + +And you believe that the latter +is the most important + +[INAUDIBLE]. + +PROFESSOR: Right. + +You think of it as being-- + +you guess which of +your children + +will be good at education. + +And you're going to give all +your education to that child, + +and give the other +one nothing. + +That's one implication of this +view, is that you're going to + +discriminate among +your children. + +Now, the way you're going to +discriminate is probably, you + +probably don't believe your +children are identical. + +So you're going to +look for signs. + +Maybe in first grade, one of the +children was doing better + +than the other. + +It means nothing. + +Some children do well +in first grade. + +Some children do badly +in first grade. + +Many of you who are at MIT +were doing badly in first + +grade, and then ended +up at MIT. + +I'm sure some people +were doing very + +well in first grade. + +Didn't get to MIT. + +So it's a very poor predictor. + +Your first grade performance, a +very, very poor predictor of + +your long term performance. + +It's a predictor, but not +particularly a reliable one. + +But parents, what do +they have to go on? + +They're going to look at which +child is doing well in first + +grade, and then put their +money on that one. + +So you wouldn't probably +pick one at random. + +But you pick one based on +some very noisy signal. + +You observe whether they come +back from first grade with, + +they chewed up their pencils +in first grade + +more or less or something. + +And you decide, well, this +one's fit for education. + +This one's not. + +And then you're going to +put your money on that. + +You're going to find some way +of, since you can't spend + +equal amounts on both, you're +going to find some signal + +that's going to allow +you to discriminate. + +Right? + +That's what you'd expect. + +So actually, let me go back one +slide and just talk about + +discrimination a little bit more +before we get to this. + +So this is something that +if you do field work in + +developing countries, this +is something that + +jumps out at you. + +And something that you spend-- + +like me, I've spent all my +adult life in the US. + +So I'm kind of used +to the US now. + +So you go to somebody's house. + +What's the chance you'll hear +a parent with two children, + +one sitting here, the other +standing there, and he looks + +at the child who's sitting there +and says, oh, that one, + +he's an idiot. + +He's not capable of +study, literally. + +I don't mean metaphorically. + +I mean literally, that +one's an idiot. + +But this one, she's +really bright. + +And you hear that +all the time. + +It's something you'll never +hear in the US. + +You'll never hear parents +actually pointing to one of + +their children and saying, +this one's an idiot. + +That comes very much out of this +theory that in a sense, + +there are these, I have +the pick the winner. + +The pressure on the parents +is to pick the winner. + +Because if you don't pick the +winner, you wasted your money. + +So they're trying to +pick the winner. + +And in a sense, they are, in +fact, trying to persuade not + +just themselves, but also the +siblings to go along with it. + +And you see that very much. + +I've also seen, which is even +more touching, is one child + +saying, you ask him which +school you go to? + +He says, oh, I go to +this school, but I + +don't really go anymore. + +And I said, why? + +And he says, well, I'm stupid. + +I can't do it. + +But you know, my brother over +there, he's really smart. + +He's going to the private +school, and + +he's doing very well. + +And so everybody in the system +internalizes it. + +You see that very clear, every +word having internalized. + +And that's useful +for the family. + +Because the family doesn't want +to sustain a feeling of + +inequality. + +So if all children believe that +there's only one child + +who is smart among them, then +it's good for the family. + +The harmony in the +family remains. + +Because all the other children +are willing to not be + +educated, because they +think they are + +not fit to be educated. + +So everybody buys into +this idea that this + +one child is bright. + +And you see that all the time. + +Just prima facie, you +see it all the time. + +We'll also talk about +evidence. + +But I also wanted to say that +that's the shape of it, is + +often, you hear people pointing +to this child and + +saying, that one is an idiot. + +And that's very striking. + +If you come to the US, you never +hear a parent say that. + +And I don't think it comes out +of the fact that these are + +worse parents. + +They love their children. + +They'll do lots for +their children. + +But they really believe that +there is this sort of-- + +they need to be very good at +picking who's the winner. + +Because they need to justify +that to themselves. + +They need to justify that to +their other children, the fact + +that they pick the +right winner. + +That's very important to them. + +And you see that very much. + +So two studies. + +One is in Burkina Faso, they +found that if conditional on + +my cognitive score, in a simple +test score, if my + +brother is doing well, I'm less +likely to be in school. + +So if my brother's doing well, +or my sister's doing well, + +that hurts my chances of +getting investment. + +So that's exactly what +we're talking + +about, picking winners. + +Second, in Colombia, +they were given a + +conditional cash transfer. + +Conditional cash transfer is +like some money which you get + +if you child is in school. + +And the way it had been +implemented is that some + +children were eligible for it. + +So basically, when some children +were eligible for it, + +parents decided, well, we'll +invest in this child. + +That picked the child +to invest in. + +That meant you stopped investing +in the other one. + +The other child actually were +less likely to go to school, + +if your brother was +encouraged by the + +government to go to school. + +So the government was actually +kind of focused on one child. + +And you were getting some money +from sending one of the + +children to school. + +The other one was +then neglected. + +And so you see exactly this +pattern of parents trying-- + +yeah. + +AUDIENCE: How did they choose +the children to get the + +investment? + +PROFESSOR: In this particular +case, I think it was based on + +some age rule. + +I think only certain grades +were eligible, + +if I remember right. + +So it was like seventh graders +can get it, but sixth graders + +can't, or something. + +I think that was the rule. + +It was an age rule, age or +I think maybe a class. + +AUDIENCE: So they chose a class +at a particular level. + +And then they continued +that class throughout. + +PROFESSOR: Right. + +I think that's right. + +AUDIENCE: I have a question. + +Well, I have two questions. + +Does this pattern stay the +same if school is free? + +If it's still one child +that goes to school? + +And also, if it's conditional +cash transfer, wouldn't that + +increase the income +to the family? + +So they would have more +resources to spread around? + +PROFESSOR: Yeah. + +So both are excellent +questions. + +I think yes, it's still +true where it's free. + +Because one of the ways you +discriminate is by sending + +your bright child to +private school. + +You actually spend resources to +send him to private school. + +Or you get him a tutor. + +He gets special help. + +Or he doesn't have to +do the housework. + +He gets time to do his homework +in the evening, while + +all the other children are +like tying up the goat or + +whatever, giving food to +the cow, or whatever + +else they are doing. + +He's the one who gets +to do the homework. + +So that's one sense in which +you still have lots of + +discrimination. + +And to answer your other +question, it's true that I + +think that discrimination, +again, that's related. + +The answer I just gave is also +relevant for that, which is + +that part of the way to +operate is not just + +discrimination in money spent, +it's also in time. + +It's also in this, whose job +is to tie up the cow? + +Whose job is to take care +of the younger siblings? + +All of those get allocated +unequally. + +So the child who gets to go to +private school typically is + +also the one who doesn't +take care of the cow. + +So you get loaded on +benefits from that. + +Does that answer +your question? + +OK. + +So another implication of this +is that, this is a related + +point, which is that parents +will often-- + +another implication of this is +that if people associate + +education with particular forms +of getting a particular + +job, then when there are more of +those jobs, they might now + +start discriminating more +against the children. + +Why? + +Because now there is a valuable +opportunity available + +for my daughter. + +She can get this kind of job if +she only gets this degree. + +And I'm going to now try to, +therefore, find resources to + +make sure my daughter +can get that degree. + +That might mean that I'm going +to give up on my son entirely. + +So discrimination. + +Another related consequence of +this is that when a particular + +job appears which has high +returns, which you perceive + +generates high returns for +education, you would target + +money towards getting +that job. + +And that would increase +this tendency toward + +discrimination. + +So there's an experiment in +India, a very nice experiment. + +What this guy did is +there are all these + +call centers in India. + +You must have dealt with one. + +If you've ever had to call +United Airlines, for example. + +One of the things I love about +this is once they hear my + +name, their accent +quickly changes. + +And they stop trying to fake +an American accent. + +They figure that I don't +care so much. + +But so these call centers are +in this part of North India + +where this is actually +huge discrimination + +against girls, otherwise. + +But what he did in this +experiment is he went to these + +villages near the call center +and said, well, there's a call + +center right there. + +And if your daughter graduates +high school, she + +can get a job there. + +So that was the experiment. + +And he went and told-- + +and you immediately find parents +suddenly starting to + +discriminate against +their sons. + +They start to figure out, +my daughter can + +get this good job. + +Now I should just put all the +money in her education. + +And what happens to my son +doesn't matter anymore. + +So you get this pattern of once +parents decide that there + +is a jackpot to be had, it's +very easy to get into these + +patterns of massive + +discrimination within the family. + +So in particular, girls' +education went up? + +Why? + +Because call centers +like girls. + +Apparently, the view is, may +or may not be true, is that + +girls are easier to train to +be call center employees. + +They're more docile, +more, I don't know. + +They learn English faster. + +There are all kinds +of theories. + +But in any case, call centers +like girls, for some + +unspecified reason. + +So they found out that there +was a big demand for girls. + +The result was that you get +this effect on boys. + +On net, boys were +not affected. + +But parents already, the +baseline had said, this son, + +he's not really fit +for education. + +So those kids are really got +hurt when this happened. + +Because all of those kids who +the parents had decided were + +not fit for education, their +education actually dropped + +when their sisters started +getting these jobs. + +You started substituting away +from their education towards + +less education for them. + +So this is all to say that +parents are actually using all + +these cues to figure out which +child to put the money on. + +Because they believe that if I +put money on one child, I'll + +get much bigger benefits than +sharing it across children. + +And then all these cues +seem to matter. + +OK, let's go back to +a different fact. + +Another thing that of +course matters is + +information in this world. + +For parents, what matters is +their perceived returns. + +That's what we're talking. + +We're talking about +perceived returns. + +We're talking about the fact +that parents think their + +returns are higher when you get +12th grade education, and + +low if you get less than 12th +grade education, et cetera. + +So Madagascar, parents were +shown this particular picture. + +This picture's kind of +a way to capture + +the returns to education. + +So without any degree, you +get three kg of grain. + +If you get a few more +years, you get four. + +If you get more, you get +seven, et cetera. + +So this was roughly +the right scaling. + +So this is roughly how the +returns are in Madagascar. + +AUDIENCE: Is it [INAUDIBLE] +the political [INAUDIBLE]? + +PROFESSOR: Yeah. + +So that's the range. + +For females, it goes +from 34 to 163. + +For men, from 47 to 225. + +So this was what they +were shown. + +When they were shown this, +turned out-- so actually, + +before they did that, they +actually asked parents, what + +do you think are the returns +to education? + +Before they showed them, they +actually asked them, if your + +child got an education, +how much would his + +income go up by? + +So they had written that down. + +Then they showed them +this picture. + +And what's nice is that the +parents who already thought + +that children were going to +get high returns, their + +behavior didn't change +very much. + +Whose behavior has changed? + +The parents who thought that the +returns for the children + +were much lower than +they really are. + +And about 50% of the parents +had very low returns. + +And for those parents, +you get a very + +substantial improvement in-- + +no, that's not it. + +I don't know where-- + +OK. + +So it was a very substantial +improvement in the children's + +school attendance, to the point +where every intervention + +we have studied, the cheapest +way to improve school + +attendance that we found, +ever, is this one. + +This really is an +extraordinarily cheap + +intervention. + +It doesn't cost much money to +tell people the returns on + +education are higher +than you think. + +If you can do it in a credible +way, that improves education + +very cheaply. + +And it has a substantial +effect. + +This turns out to be the +cheapest single thing that + +Poverty Action's lab researchers +found for + +improving education. + +Obviously, it doesn't +do everything. + +You can't go very +far with this. + +Because it's not going +to distill all + +kinds of other things. + +If the education system's +broken, then people are not + +going to learn anything from +the school, et cetera. + +But to get them into school, +this is a very, very + +cheap way to do it. + +So there's lots of parents who +are clearly discriminating + +against their children and not +sending them to school because + +they think their children +are not going to get + +anything out of it. + +Why do they think that? + +Well, they think that their +children are never going to + +make it through the 12th grade, +or whatever it takes to + +get real money from education. + +So they'll already assume that, +my child is never going + +to make it 12th grade. + +Since he's never going +to make it to 12th + +grade, what's the point? + +And therefore, they don't +send children to school. + +You persuade them that even if +you went from third grade to + +fifth grade you get extra +returns, then they start + +sending children to school. + +So the returns to primary +education for many, many + +parents are massively +underestimated. + +Yeah. + +AUDIENCE: I have a +quick question. + +Is it distributed evenly across +the incoming classes? + +So for example, you were trying +to say education was + +for people who are +very wealthy. + +It could be 120% returns to +people-- it's education to + +people who are lower class to +be 0.5%, in which case, that + +progression will be tilted +towards the high end. + +[INAUDIBLE]? + +PROFESSOR: Yeah. + +So people have looked at that. + +Typically, it's difficult +to look at. + +Because you could imagine that +very few people who are + +wealthy families stop +at third grade. + +But to the extent that you can +look at it, you don't see big + +differences. + +There's some differences, but +not of the order of magnitude + +you're suggesting. + +AUDIENCE: I was wondering +if anyone has + +looked at the peer effects. + +Like you have a village. + +And there's several families. + +And some of them are sending +their kids to school, and + +others aren't. + +Are there any effects that just +one family sees how the + +other kids, look, they're +going to school. + +And they seem to be learning. + +And they seem to be +accomplishing something. + +Do they feel like they're +just wasting their time? + +Their parents always complain +[INAUDIBLE]. + +Are there any effects +between families? + +PROFESSOR: Probably. + +Nobody's looked. + +I mean, people look at this. + +But the problem is that when +you study peer effects, the + +first problem is that typically, +your peers are not + +randomly chosen. + +So you hang out with families +that are like yours. + +So therefore, the peer effects +tend to be over estimated. + +What looked like peer effects +could be just the effect of, + +who do you hang out with? + +So there's lots of evidence of +peer effects, but not so much + +at this level. + +Because it's hard to randomly +assign peers. + +The one place where you can +randomly assign peers turns + +out to be in college. + +So there is a nice set of +studies, like of Dartmouth, + +for example. + +In Dartmouth, there's +a college lottery. + +And you get different roommates + +based on your lottery. + +So if you get roommates who are +more inclined to study, + +you're more inclined to study. + +You get roommates who are more +inclined to drink, you are + +more inclined to drink. + +There seems to be clear +evidence of some + +kinds of peer effects. + +But it's hard to find because +of this reason. + +If you look at the data, +it looks like + +there's huge peer effects. + +If you look in the US, and you +look around Boston, you'll + +find that in Somerville, people +who live in Somerville + +seem to live with other +people who don't + +get much of an education. + +And people that live in +Lexington live with other + +people that get a lot +of education. + +That's not because of +large peer effects. + +It's because people who want +to get a lot of education, + +good education, go to +live in Lexington. + +Or other characteristics of +people who live in Lexington, + +rich people live in Lexington. + +It's not because of peer. + +So peer effects are +hard to detect. + +But I think that where people +have tried to look at it, like + +with this Dartmouth lotteries +and stuff, they find it. + +But it's hard to detect for the +reason we just discussed. + +OK. + +So now what I want to do is +switch to the teachers. + +So we talked about the effect +of this on the parents. + +The parents do two things. + +One is that they don't invest +in most of their children. + +I'll come back to the parents, +actually, later. + +And the second is that +they discriminate. + +Let's go to the teachers. + +Same hypothesis. + +Teachers also believe, and +maybe teachers don't + +intrinsically have to believe +this, if parents believe that + +the only goal of the school is +to get their children to 12th + +grade or whatever to get through +school, then teachers + +will have the same incentives. + +So the teachers will believe +what the parents believe. + +Because it doesn't matter +what the truth is. + +I'm going to get paid if +the parents like me. + +And the parents like +me if I have the + +belief that they have. + +So it's not clear that the +teachers even need to have the + +wrong beliefs. + +But I suspect parents, +teachers do + +have the wrong belief. + +I'll tell you why +in a little bit. + +So first thing that that implies +is that teachers will + +teach to the top of the class. + +If you believe that the goal of +this whole thing is to get + +children to complete 12th grade, +and in addition, you + +believe that you live in a +country where most people + +don't complete 12th grade, +then you're going to say, + +well, most people are +not capable of + +completing 12th grade. + +Because in fact, that's +what you see. + +Only 20% complete 12th grade. + +In Madagascar, maybe 10% +complete 12th grade. + +And you see that, you say that +most people are not going to + +complete 12th grade. + +So therefore, doesn't make any +sense to try to get the bottom + +of the class to-- + +if I believe A, that completing +12th grade is the + +only thing that I care about, +and B, that only a small + +fraction of these kids are +capable of reaching 12th + +grade, I think both of which +are probably false, but + +imagine I believe those +two things. + +How should I teach? + +I'll teach to the top +of the class. + +Because those are the +only people who are + +going to make it. + +So I might as well concentrate +my resources on that, and + +forget about the rest. + +The rest are here +as passengers. + +They're going to come. + +They're going to listen. + +They won't get anything. + +They'll leave. + +I don't really care, because +that's not the goal. + +And in particular, there's +a nice instance of this. + +I'll talk about an experiment +in a little bit where the + +school got an extra teacher, +let's say for eighth grade, or + +fourth grade. + +And in fourth grade, this +class was split up. + +And half the class was given +to the extra teacher. + +And half the class was given +to the original teacher. + +In some of the schools, it was +done so that the better + +performing children went to +one teacher, and the worst + +performing children go +to the other teacher. + +This was done by lottery. + +So there was a lottery. + +And one teacher got one, and +the other got the other. + +The teacher who got the +bottom half of the + +class was really upset. + +Because they really believe +this is pointless. + +They thought that this was just, +why am I teaching the + +bottom half of the class? + +There's no point in +teaching them. + +Because they, too, believe that +the bottom of the class + +can't learn. + +Because their whole goal is not +to get them from fourth + +grade to fifth grade, but to get +them from fourth grade to + +12th grade. + +So the goal of teaching, it's +pointless to teach people at + +the bottom of the class. + +Because people at the bottom +of the class can't learn. + +So once you believe that people +at the bottom of the + +class can't learn, then you +focus your effort at the top + +of the class. + +Now as you can imagine, what is +the consequence of that on + +the students? + +What would that do to students +at the bottom of the class? + +AUDIENCE: Well, they were +probably discouraged. + +They'd feel more discouraging if +the teacher is actively or + +subconsciously [INAUDIBLE]. + +PROFESSOR: Right. + +Is that what you were +going to say? + +Yeah. + +So they're going to +get discouraged. + +Now what happens when they +get discouraged? + +AUDIENCE: Poor performance. + +PROFESSOR: Sorry? + +AUDIENCE: I said poor +performance. + +PROFESSOR: They perform +poorly. + +What does the teacher think? + +AUDIENCE: Stupid. + +PROFESSOR: Yeah, +they're stupid. + +So it's a vicious cycle. + +Because once I believe the start +from this theory, that + +the bottom of the class +can't perform, then I + +give them no attention. + +They're all discouraged. + +They're not trying. + +They're doing badly. + +I think they're stupid. + +Then I feel like, you know, I +was right in focusing on the + +top of the class. + +So you get into this vicious +cycle of false beliefs. + +The other thing that this would +mean is that teachers + +also really-- + +so teachers also, in class, they +will look for the kids + +who can get to their view of +whatever the goal is, getting + +through high school. + +And if there are a few kids like +that in high school in + +this class, they're going to +stop putting in effort. + +You also expect why teachers +would not put in a lot of + +effort, because they'll think, +look, I got stuck with a bunch + +of dodos who can't learn. + +What am I doing here? + +So once teachers start believing +that children are + +unequal, then you get this +phenomenon that lots of + +teachers also give up. + +So the Pratham experience is, +I think, illuminating here. + +So one of the experiments you +must have talked about was the + +summer school experiment. + +The summer school was basically, +some villages + +randomly got a summer school. + +The teacher was given +some extra money to + +run a summer school. + +This is the same teacher who +teaches in school where the + +schools are very +low performing. + +Yet, when this teacher was given +a small amount of money + +and was asked to run a six weeks +summer school after a + +few days of training, that had +very large effects on the + +children's learning. + +The children who went to summer +school learned a lot. + +So why is it that this teacher +who can teach these children + +quite effectively in summer +school, why doesn't he teach + +them effectively during +the school year? + +What's going on? + +How can it be that the same +teacher, when he teaches + +summer school, he gets +large gains. + +But when he teaches regular +school, he does so badly? + +And one explanation is that in +summer school, his job is to + +attend to the worst performing +children. + +In the regular school, his +perception is that his job is + +to attend to the top +of the class. + +So in the regular year. + +he's not teaching +these children. + +He's teaching the top +of the class. + +When he's actually told, teach +these children, he actually + +can do it just fine. + +It's just that's not what the +system is telling him. + +His view of what his job is is +that I have to get the top of + +the class to learn the entire +curriculum, and be able to get + +into whatever, into a better +high school or something. + +He doesn't see his goal +as teaching the + +bottom of the class. + +When you actually ask him to +teach the bottom of the class, + +when that is his assigned +job, he does just fine. + +So that would also be consistent +with this view that + +the real problem is not that +the teachers don't have the + +incentive to teach, or they +don't want to teach. + +But they're being told to +teach the wrong thing. + +They're trying to teach these +children something that + +actually isn't. + +So here's the experiment +I talked about. + +This is very much +on this point. + +I already talked about this +experiment, 120 schools were + +cut into two, in 60 schools. + +All schools were given +extra teachers. + +And then half of those schools, +the extra teacher was + +assigned to, the class +was split at random. + +So every class, they used +to have one teacher. + +Now they have two teachers. + +Class was split at random. + +So half the class went to one, +half went to the other. + +In the other half of the +schools, they were + +not split at random. + +They were split by baseline +competency. + +So the better performing +children + +were sent to one teacher. + +The worst performing +children were sent + +to the other teacher. + +The teacher assigned +was random. + +So you didn't get a better +teacher or a worst teacher, + +but you got to be in +a classroom with + +children like you. + +What would our theory say about +what's going to happen? + +If you have any of the +top, what would + +happen in this setting? + +AUDIENCE: In both situations, +you teach to the top. + +What it means for the teacher in +the randomly assigned room + +is that the people who were +respectively at the top of the + +class one, they still +get taught to. + +But it means the people, when +it's divided into the high + +performer, low performer, is +you teach the top of that + +little [INAUDIBLE]. + +PROFESSOR: Exactly. + +So what this does is, I always +wanted to teach the best four + +people only in the classroom. + +But the best people in the +classroom have changed. + +When I divide the classroom in +this way, the best people in + +the low classroom is someone who +would have never got any + +attention in the original +classroom. + +Or if it was divided +at random, he would + +never be at the top. + +So it changes who +gets attention. + +Moreover, because I'm now paying +attention to somebody + +who's not at the top of the +class but in the middle of the + +class, the children who are at +the bottom of the class are + +more likely to get something +out of the class. + +Because what happens is that +the distance between-- + +imagine that this is a class +which has me and someone else. + +And I can't really read. + +And somebody else can +read Shakespeare. + +Now, if you teach to +the top of the + +class, I'll get nothing. + +But if I'm put it in the +classroom with somebody who + +can read a little better +than me, but not that + +much better, then. + +If you teach to him, I'll still +get something out of it + +because I'm closer to him. + +AUDIENCE: Do the teachers +know something? + +That they've got better-- + +PROFESSOR: Yeah. + +That's why they were +protesting. + +And I said this before. + +They were actually protesting. + +But once they found out, they +decided fine, we'll teach the + +best of this class. + +But the best of this class is +still much less different from + +the worst of this class, then +the difference between the + +best and the worst in +the original class. + +So even the worst in this class +gets something out of + +the teaching, where you would +have got nothing before. + +AUDIENCE: So do you think that +it'd be more effective to try + +to re-educate teachers such +that they don't have the + +attitude that they only teach +to the top of the class? + +Or is it better just to accept +that as a reality, sort of + +like in this survey. + +And then just trying to make +some circumstance to get a + +[INAUDIBLE]? + +PROFESSOR: That's an +excellent question. + +I guess my view is that it's +difficult to get the teachers + +to believe that they should have +a different attitude as + +long as parents have +that attitude. + +So you need to start +with the parents. + +Because after all, the +demand for education + +comes from the parents. + +So the parents are +the ones who are + +demanding this education. + +So in other words, to go back +to where we started, in this + +view, what's wrong with the +school system is that the + +parents think that there's no +point in educating their + +children unless the children +are good enough to graduate + +high school. + +Therefore, they want the entire +education system to + +focus on the few people in the +classroom who are high + +performing, and ignore +the rest. + +If that's what the parents +want, the teachers will + +deliver that. + +And it's going to get +too hard to get them + +to do anything else. + +You'll first have to start with +persuading parents that + +even if their child is not going +to get to high school, + +he still should be educated. + +I think that's sort of +the, I think, this-- + +so in fact, that's exactly +what they found. + +They found that when you do +this, when you divide this + +class up, everybody benefits. + +The top children benefit. + +Because they're now +being taught. + +The teacher is focusing +on them. + +The top children of the bottom +class benefit, because the + +teacher is benefiting +from them. + +The bottom children of the top +class benefit, because they + +are now closer to the top +of their own classroom. + +And the bottom children in the +bottom class benefit because + +they are closer to the top +of their classroom. + +So everybody is better +off in this outcome. + +Because as long as you can't +force the teachers to teach + +the bottom, then what you can +do, next best thing, is to + +bring the bottom closer +to the top. + +And this is what this does. + +If teachers are going to teach +to the top, then you should + +try to have classrooms +where the bottom is + +close to the stop. + +And that's what you see. + +The evidence is very clear, +everyone benefits from + +creating these tracks. + +This is the table. + +I won't go through it. + +Because we're going to +run out of time. + +This has already we've said. + +Who else gets hurt by this is +the children, obviously. + +The children get hurt because +they get discouraged. + +Most children get discouraged. + +Because they think education +is not for them. + +And this is especially true in +historically discriminated + +populations. + +So historically the +discriminated populations in + +many countries tend to be either +by race or in India, + +it's by caste, or girls, +depending on the particular + +structure of discrimination. + +Historically, discriminated +populations tend to already + +assume that since they have very +few people who have been + +educated, they assume that +that's perhaps because they + +have no talent for it. + +And then if you go and +tell them, look. + +So another way to put it is that +if you happen to be from + +a family who believe that you +can be educated, then if the + +teacher says, you're stupid, +they won't believe it. + +They're going to go and argue +with the teacher. + +And say, look, in my family, +everybody has a Ph.D. What do + +you mean, my son is stupid? + +Whereas if you're actually from +a family where no one has + +an education, it's much easier +to persuade them that their + +child is not fit +for education. + +So what you're going to do is +you're going to reinforce + +stereotypes in society. + +Because who's going to believe +you when you say + +your child is stupid? + +It's going to be the people +who have been told + +historically that they're +not fit for education. + +They're going to be the most +likely to believe you. + +So this kind of stereotype, the +existing stereotype will + +be reinforced by, if you give +people the message that their + +child is stupid, the existing +stereotype would get + +reinforced. + +So that's something that +you see a lot. + +You see that the parents in +these kind of very poor + +families tend to be more +likely to believe these + +negative stereotypes +of their children. + +Another thing that this would +explain is why children don't + +come to school. + +One thing that people don't +emphasize is how rarely + +children show up in school. + +A lot of children basically +completely don't believe that + +school is for them. + +And they may be enrolled +in school. + +So on a given day, up to 50% of +the children don't show up + +in a class. + +Now, that's also true at MIT, as +it turns out, but probably + +not for the same reasons. + +But many of these children +basically + +hate being in school. + +And they hate being in school +for the right reason, which is + +that they're constantly being +told that this is not for you. + +One interesting additional fact +that was, this goes back + +to the stereotype, this +is a nice experiment. + +So children were asked +to solve mazes. + +You know what mazes are? + +Like these things where you +have to draw a line, and + +there's a point of entry +and a point of exit. + +And you have to find +your way out of it. + +So they were given these mazes +and asked to solve them. + +I've done this, actually. + +It's fun to do. + +You can take a bunch of sheets +and get people in the village + +to give their kids, and get +them to solve them. + +And it's a very good +test of cognitive + +abilities, it turns out. + +So that's what people +usually do. + +Now, somebody has a good idea +of trying to follow it. + +They went to a village in India, +and they got together a + +group of historically low caste +people, people who were + +discriminated against. + +And combined them with people +from high castes, and put them + +in the same group. + +And one experiment, they just +asked them, play the maze. + +Do the maze. + +And they found no difference +between high + +caste and low caste. + +They got the exactly +same scores. + +Not everybody didn't get the +same score, obviously, but on + +average, there was +no difference. + +Second experiment, before they +play the game, everybody was + +asked their caste. + +So caste was made salient. + +And immediately, you see +a big difference. + +You see that the people +who were historically + +discriminated self-discriminate. + +They start playing badly. + +They believe that they can't +compete with the other guys. + +And they do much worse. + +So once you make caste salient, +it's exactly this + +fact that once you prime my +belief that I already am + +unsure whether I can do these +things, you prime my belief + +that I am from a particular +caste. + +I'm playing against these guys +from a superior caste. + +I'm just going to think +I'm going to lose. + +And it's very simple. + +You just have to get them to +remember what their caste is. + +And there's another experiment +which is also interesting. + +I'll just say that +and then move on. + +In another experiment, teachers +were asked to grade + +the same paper. + +And in some, they were told that +the paper was from a high + +caste person. + +And some, they were told that +the same paper was from a low + +caste person. + +Same paper, exact same paper, +photo copy of the same thing + +with the same answers, but +you're asked to grade it. + +And in one case, I said, this +is from Caste A, the other + +case, I say it's from Caste B. + +That was the experiment. + +Then the teachers themselves, +some of them were from a high + +caste, and some of them +were low caste. + +Who do you think +discriminated? + +What was the pattern +of discrimination? + +AUDIENCE: I'm guessing the +high class discriminated + +against the low class. + +PROFESSOR: Turns out +the opposite. + +The low class discriminated +against the low class. + +Low class were scoring their +own caste people lower. + +Because they also believe +that people from their + +caste cannot do it. + +So you have this underlying +stereotype. + +And now you prime that by +saying, this kid is stupid. + +What are they going to do? + +They're going to give +up very quickly. + +As they already believe that +they are not really + +capable of doing it. + +AUDIENCE: In the maze +experiment, did the results + +from the high caste +[INAUDIBLE] + +change [INAUDIBLE]? + +PROFESSOR: I think they went +down, if I remember correctly. + +They went down, but the +others went down. + +AUDIENCE: In the grade paper +example, did the high caste + +graders discriminate also +against the low caste? + +PROFESSOR: No. + +No discrimination from +the high caste. + +Only the low caste-- + +AUDIENCE: Did they grade the +high caste papers any higher? + +PROFESSOR: No. + +AUDIENCE: OK. + +PROFESSOR: Zero effect +of the high caste. + +Only the low caste teachers +discriminated against the low + +caste students. + +It was dramatically-- + +it's not what I expected. + +But it does show this + +self-discrimination is very powerful. + +The reason I emphasize that is +that that's the problem here. + +Once I have a classroom full +of kids who are being told + +they're stupid, the ones who +are from a high caste are + +going to say, look, I know my +grandfather was a religious + +teacher, and my father's +a religious teacher. + +I know I am fit for education. + +I'm going to continue. + +It's the people who have weak +self-belief who are going to + +be hurt by a system which +basically discriminates + +against them. \ No newline at end of file diff --git a/ra5yBfC9ztE.txt b/ra5yBfC9ztE.txt new file mode 100644 index 0000000000000000000000000000000000000000..73ca2f7fb7ae77050aece567f6cb95439e1500d6 --- /dev/null +++ b/ra5yBfC9ztE.txt @@ -0,0 +1,14131 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common license. Your support + + align:start position:0% +a Creative Common license. Your support + + + align:start position:0% +a Creative Common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Well, today I'm going to give the fourth + + align:start position:0% +Well, today I'm going to give the fourth + + + align:start position:0% +Well, today I'm going to give the fourth +and final case study of the of the + + align:start position:0% +and final case study of the of the + + + align:start position:0% +and final case study of the of the +course. And um everything I'm going to + + align:start position:0% +course. And um everything I'm going to + + + align:start position:0% +course. And um everything I'm going to +talk about is uh my thesis research uh + + align:start position:0% +talk about is uh my thesis research uh + + + align:start position:0% +talk about is uh my thesis research uh +in one form or another. Uh so this is + + align:start position:0% +in one form or another. Uh so this is + + + align:start position:0% +in one form or another. Uh so this is +work that's definitely in progress and + + align:start position:0% +work that's definitely in progress and + + + align:start position:0% +work that's definitely in progress and +in a lot of cases we haven't really + + align:start position:0% +in a lot of cases we haven't really + + + align:start position:0% +in a lot of cases we haven't really +drawn conclusions yet. So, it'll be + + align:start position:0% +drawn conclusions yet. So, it'll be + + + align:start position:0% +drawn conclusions yet. So, it'll be +quite rough and ready, but I hope it'll + + align:start position:0% +quite rough and ready, but I hope it'll + + + align:start position:0% +quite rough and ready, but I hope it'll +uh be informative and uh and raise some + + align:start position:0% +uh be informative and uh and raise some + + + align:start position:0% +uh be informative and uh and raise some +questions for you. Um the uh the focus + + align:start position:0% +questions for you. Um the uh the focus + + + align:start position:0% +questions for you. Um the uh the focus +of my thesis research is + + align:start position:0% +of my thesis research is + + + align:start position:0% +of my thesis research is +uh well, broadly speaking, finding + + align:start position:0% +uh well, broadly speaking, finding + + + align:start position:0% +uh well, broadly speaking, finding +approaches to manufacturing + + align:start position:0% +approaches to manufacturing + + + align:start position:0% +approaches to manufacturing +microffluidic devices using polymers. + + align:start position:0% +microffluidic devices using polymers. + + + align:start position:0% +microffluidic devices using polymers. +uh and uh for uh for many of you uh I + + align:start position:0% +uh and uh for uh for many of you uh I + + + align:start position:0% +uh and uh for uh for many of you uh I +think I think micrfluidics will be + + align:start position:0% +think I think micrfluidics will be + + + align:start position:0% +think I think micrfluidics will be +something you know at least a little + + align:start position:0% +something you know at least a little + + + align:start position:0% +something you know at least a little +about. Um essentially uh microchips that + + align:start position:0% +about. Um essentially uh microchips that + + + align:start position:0% +about. Um essentially uh microchips that +manipulate + + align:start position:0% +manipulate + + + align:start position:0% +manipulate +uh very small volumes of fluids to + + align:start position:0% +uh very small volumes of fluids to + + + align:start position:0% +uh very small volumes of fluids to +perform various experimental or + + align:start position:0% +perform various experimental or + + + align:start position:0% +perform various experimental or +diagnostic or uh or or or other + + align:start position:0% +diagnostic or uh or or or other + + + align:start position:0% +diagnostic or uh or or or other +engineering tasks. And um we're + + align:start position:0% +engineering tasks. And um we're + + + align:start position:0% +engineering tasks. And um we're +interested in developing processes and + + align:start position:0% +interested in developing processes and + + + align:start position:0% +interested in developing processes and +and and choosing materials that will + + align:start position:0% +and and choosing materials that will + + + align:start position:0% +and and choosing materials that will +help us make these things very cheaply + + align:start position:0% +help us make these things very cheaply + + + align:start position:0% +help us make these things very cheaply +so that they can be used uh at the point + + align:start position:0% +so that they can be used uh at the point + + + align:start position:0% +so that they can be used uh at the point +of care in the case of diagnostic + + align:start position:0% +of care in the case of diagnostic + + + align:start position:0% +of care in the case of diagnostic +devices and so forth. Now one particular + + align:start position:0% +devices and so forth. Now one particular + + + align:start position:0% +devices and so forth. Now one particular +process that's of great interest for + + align:start position:0% +process that's of great interest for + + + align:start position:0% +process that's of great interest for +this uh is the imprinting of + + align:start position:0% +this uh is the imprinting of + + + align:start position:0% +this uh is the imprinting of +thermoplastic polymer layers. uh hot + + align:start position:0% +thermoplastic polymer layers. uh hot + + + align:start position:0% +thermoplastic polymer layers. uh hot +embossing is uh is what we're going to + + align:start position:0% +embossing is uh is what we're going to + + + align:start position:0% +embossing is uh is what we're going to +call it. And + + align:start position:0% +call it. And + + + align:start position:0% +call it. And +uh for a start, let me say why polymers + + align:start position:0% +uh for a start, let me say why polymers + + + align:start position:0% +uh for a start, let me say why polymers +are interesting for making these sorts + + align:start position:0% +are interesting for making these sorts + + + align:start position:0% +are interesting for making these sorts +of devices. Uh I think I see three main + + align:start position:0% +of devices. Uh I think I see three main + + + align:start position:0% +of devices. Uh I think I see three main +reasons. Firstly, uh they're cheap + + align:start position:0% +reasons. Firstly, uh they're cheap + + + align:start position:0% +reasons. Firstly, uh they're cheap +compared to silicon or glass, which are + + align:start position:0% +compared to silicon or glass, which are + + + align:start position:0% +compared to silicon or glass, which are +other materials that you might think of + + align:start position:0% +other materials that you might think of + + + align:start position:0% +other materials that you might think of +as being obvious candidates to fabricate + + align:start position:0% +as being obvious candidates to fabricate + + + align:start position:0% +as being obvious candidates to fabricate +these these uh these microscopic fluidic + + align:start position:0% +these these uh these microscopic fluidic + + + align:start position:0% +these these uh these microscopic fluidic +channels and valves and pumps and so + + align:start position:0% +channels and valves and pumps and so + + + align:start position:0% +channels and valves and pumps and so +forth. So, polymers are polymers are + + align:start position:0% +forth. So, polymers are polymers are + + + align:start position:0% +forth. So, polymers are polymers are +cheap. Second thing is they're often + + align:start position:0% +cheap. Second thing is they're often + + + align:start position:0% +cheap. Second thing is they're often +transparent and that's really important + + align:start position:0% +transparent and that's really important + + + align:start position:0% +transparent and that's really important +when you have a biological sample inside + + align:start position:0% +when you have a biological sample inside + + + align:start position:0% +when you have a biological sample inside +this device and you're trying to look at + + align:start position:0% +this device and you're trying to look at + + + align:start position:0% +this device and you're trying to look at +how it behaves in response to certain + + align:start position:0% +how it behaves in response to certain + + + align:start position:0% +how it behaves in response to certain +stimuli. Either you're exposing it to a + + align:start position:0% +stimuli. Either you're exposing it to a + + + align:start position:0% +stimuli. Either you're exposing it to a +die that will make cells with certain + + align:start position:0% +die that will make cells with certain + + + align:start position:0% +die that will make cells with certain +properties fluores. You need to see that + + align:start position:0% +properties fluores. You need to see that + + + align:start position:0% +properties fluores. You need to see that +fluoresence or you're proddding a cell + + align:start position:0% +fluoresence or you're proddding a cell + + + align:start position:0% +fluoresence or you're proddding a cell +somehow to see whether its stiffness + + align:start position:0% +somehow to see whether its stiffness + + + align:start position:0% +somehow to see whether its stiffness +gives you information about its disease + + align:start position:0% +gives you information about its disease + + + align:start position:0% +gives you information about its disease +state. Something along these lines. + + align:start position:0% +state. Something along these lines. + + + align:start position:0% +state. Something along these lines. +Anyway, but transparency is an important + + align:start position:0% +Anyway, but transparency is an important + + + align:start position:0% +Anyway, but transparency is an important +property. And uh thirdly, uh a lot of + + align:start position:0% +property. And uh thirdly, uh a lot of + + + align:start position:0% +property. And uh thirdly, uh a lot of +plastics are mechanically tough which + + align:start position:0% +plastics are mechanically tough which + + + align:start position:0% +plastics are mechanically tough which +makes them highly suitable to use uh in + + align:start position:0% +makes them highly suitable to use uh in + + + align:start position:0% +makes them highly suitable to use uh in +the field at the point of care in + + align:start position:0% +the field at the point of care in + + + align:start position:0% +the field at the point of care in +doctor's surgeries and so forth. So + + align:start position:0% +doctor's surgeries and so forth. So + + + align:start position:0% +doctor's surgeries and so forth. So +these these are the three reasons why + + align:start position:0% +these these are the three reasons why + + + align:start position:0% +these these are the three reasons why +uh pol polymers are interesting and + + align:start position:0% +uh pol polymers are interesting and + + + align:start position:0% +uh pol polymers are interesting and +imprinting them is uh is interesting as + + align:start position:0% +imprinting them is uh is interesting as + + + align:start position:0% +imprinting them is uh is interesting as +a process because that itself has the + + align:start position:0% +a process because that itself has the + + + align:start position:0% +a process because that itself has the +potential to be uh to be quick and + + align:start position:0% +potential to be uh to be quick and + + + align:start position:0% +potential to be uh to be quick and +cheap. You + + align:start position:0% +cheap. You + + + align:start position:0% +cheap. You +can imagine a cycle imprinting a + + align:start position:0% +can imagine a cycle imprinting a + + + align:start position:0% +can imagine a cycle imprinting a +thermoplastic polymer occurring in + + align:start position:0% +thermoplastic polymer occurring in + + + align:start position:0% +thermoplastic polymer occurring in +around a minute and you can choose what + + align:start position:0% +around a minute and you can choose what + + + align:start position:0% +around a minute and you can choose what +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +size workpiece you you machine. You + + align:start position:0% +size workpiece you you machine. You + + + align:start position:0% +size workpiece you you machine. You +could machine anything from the size of + + align:start position:0% +could machine anything from the size of + + + align:start position:0% +could machine anything from the size of +a single microffluidic chip all the way + + align:start position:0% +a single microffluidic chip all the way + + + align:start position:0% +a single microffluidic chip all the way +up to continuous reels of polymer film. + + align:start position:0% +up to continuous reels of polymer film. + + + align:start position:0% +up to continuous reels of polymer film. +And uh indeed the the the realtore + + align:start position:0% +And uh indeed the the the realtore + + + align:start position:0% +And uh indeed the the the realtore +printing approach is something that's + + align:start position:0% +printing approach is something that's + + + align:start position:0% +printing approach is something that's +been used in industry already for for + + align:start position:0% +been used in industry already for for + + + align:start position:0% +been used in industry already for for +quite rudimentary devices. 3M has a + + align:start position:0% +quite rudimentary devices. 3M has a + + + align:start position:0% +quite rudimentary devices. 3M has a +patent on uh hot embossing reels of + + align:start position:0% +patent on uh hot embossing reels of + + + align:start position:0% +patent on uh hot embossing reels of +thermoplastic polymers and um so it's + + align:start position:0% +thermoplastic polymers and um so it's + + + align:start position:0% +thermoplastic polymers and um so it's +it's a pretty flexible process and + + align:start position:0% +it's a pretty flexible process and + + + align:start position:0% +it's a pretty flexible process and +micrfluidics aren't the only sorts of + + align:start position:0% +micrfluidics aren't the only sorts of + + + align:start position:0% +micrfluidics aren't the only sorts of +things you might think of uh think of + + align:start position:0% +things you might think of uh think of + + + align:start position:0% +things you might think of uh think of +making with it. Uh a lot of optical + + align:start position:0% +making with it. Uh a lot of optical + + + align:start position:0% +making with it. Uh a lot of optical +devices could be made this way. You + + align:start position:0% +devices could be made this way. You + + + align:start position:0% +devices could be made this way. You +could think of imprinting defractive + + align:start position:0% +could think of imprinting defractive + + + align:start position:0% +could think of imprinting defractive +elements um or uh in actually 3M's + + align:start position:0% +elements um or uh in actually 3M's + + + align:start position:0% +elements um or uh in actually 3M's +patent is is so that they can imprint um + + align:start position:0% +patent is is so that they can imprint um + + + align:start position:0% +patent is is so that they can imprint um +the reflective films that are laminated + + align:start position:0% +the reflective films that are laminated + + + align:start position:0% +the reflective films that are laminated +onto the front of road signs. Imprinted + + align:start position:0% +onto the front of road signs. Imprinted + + + align:start position:0% +onto the front of road signs. Imprinted +into those films are many parallel uh + + align:start position:0% +into those films are many parallel uh + + + align:start position:0% +into those films are many parallel uh +V-shaped grooves that act as corner cube + + align:start position:0% +V-shaped grooves that act as corner cube + + + align:start position:0% +V-shaped grooves that act as corner cube +reflectors so that the uh the street + + align:start position:0% +reflectors so that the uh the street + + + align:start position:0% +reflectors so that the uh the street +signs reflect light incident from any + + align:start position:0% +signs reflect light incident from any + + + align:start position:0% +signs reflect light incident from any +angle. And uh so that you know th those + + align:start position:0% +angle. And uh so that you know th those + + + align:start position:0% +angle. And uh so that you know th those +sorts of optical applications are also + + align:start position:0% +sorts of optical applications are also + + + align:start position:0% +sorts of optical applications are also +pretty uh pretty crucial. But anyway, + + align:start position:0% +pretty uh pretty crucial. But anyway, + + + align:start position:0% +pretty uh pretty crucial. But anyway, +let me just describe how the process + + align:start position:0% +let me just describe how the process + + + align:start position:0% +let me just describe how the process +works. What I'm illustrating here is not + + align:start position:0% +works. What I'm illustrating here is not + + + align:start position:0% +works. What I'm illustrating here is not +a roll-to-roll printing process, but + + align:start position:0% +a roll-to-roll printing process, but + + + align:start position:0% +a roll-to-roll printing process, but +something where the workpiece is about + + align:start position:0% +something where the workpiece is about + + + align:start position:0% +something where the workpiece is about +the size of a wafer. So tens of + + align:start position:0% +the size of a wafer. So tens of + + + align:start position:0% +the size of a wafer. So tens of +millimeters in + + align:start position:0% +millimeters in + + + align:start position:0% +millimeters in +diameter. And uh first thing we need is + + align:start position:0% +diameter. And uh first thing we need is + + + align:start position:0% +diameter. And uh first thing we need is +a is a hard stamp, a tool that's been + + align:start position:0% +a is a hard stamp, a tool that's been + + + align:start position:0% +a is a hard stamp, a tool that's been +microfabricated using uh some other + + align:start position:0% +microfabricated using uh some other + + + align:start position:0% +microfabricated using uh some other +process. This tool might have been + + align:start position:0% +process. This tool might have been + + + align:start position:0% +process. This tool might have been +etched from silicon. It might have been + + align:start position:0% +etched from silicon. It might have been + + + align:start position:0% +etched from silicon. It might have been +electroplated with nickel. Uh it might + + align:start position:0% +electroplated with nickel. Uh it might + + + align:start position:0% +electroplated with nickel. Uh it might +itself be a polymer but one that doesn't + + align:start position:0% +itself be a polymer but one that doesn't + + + align:start position:0% +itself be a polymer but one that doesn't +soften at the uh the processing + + align:start position:0% +soften at the uh the processing + + + align:start position:0% +soften at the uh the processing +temperatures. uh elastormas like PDMS + + align:start position:0% +temperatures. uh elastormas like PDMS + + + align:start position:0% +temperatures. uh elastormas like PDMS +poly dimethiles psylloxane are actually + + align:start position:0% +poly dimethiles psylloxane are actually + + + align:start position:0% +poly dimethiles psylloxane are actually +quite attractive as stamp + + align:start position:0% +quite attractive as stamp + + + align:start position:0% +quite attractive as stamp +materials. So we have this stamp we have + + align:start position:0% +materials. So we have this stamp we have + + + align:start position:0% +materials. So we have this stamp we have +uh two heated plates to heat the stamp + + align:start position:0% +uh two heated plates to heat the stamp + + + align:start position:0% +uh two heated plates to heat the stamp +and the workpiece and a means of + + align:start position:0% +and the workpiece and a means of + + + align:start position:0% +and the workpiece and a means of +applying a load uh normal to the surface + + align:start position:0% +applying a load uh normal to the surface + + + align:start position:0% +applying a load uh normal to the surface +of the + + align:start position:0% +of the + + + align:start position:0% +of the +workpiece. Usually what happens is the + + align:start position:0% +workpiece. Usually what happens is the + + + align:start position:0% +workpiece. Usually what happens is the +material is heated above what's called + + align:start position:0% +material is heated above what's called + + + align:start position:0% +material is heated above what's called +its glass transition temperature. And + + align:start position:0% +its glass transition temperature. And + + + align:start position:0% +its glass transition temperature. And +for anyone who isn't familiar with this, + + align:start position:0% +for anyone who isn't familiar with this, + + + align:start position:0% +for anyone who isn't familiar with this, +um, thermoplastics, + + align:start position:0% +um, thermoplastics, + + + align:start position:0% +um, thermoplastics, +uh, essentially are composed of, uh, an + + align:start position:0% +uh, essentially are composed of, uh, an + + + align:start position:0% +uh, essentially are composed of, uh, an +entangled network of, uh, polymer + + align:start position:0% +entangled network of, uh, polymer + + + align:start position:0% +entangled network of, uh, polymer +molecules. And, + + align:start position:0% +molecules. And, + + + align:start position:0% +molecules. And, +uh, there are one or more temperatures + + align:start position:0% +uh, there are one or more temperatures + + + align:start position:0% +uh, there are one or more temperatures +for a given polymer at which those + + align:start position:0% +for a given polymer at which those + + + align:start position:0% +for a given polymer at which those +entanglements loosen and, uh, and the + + align:start position:0% +entanglements loosen and, uh, and the + + + align:start position:0% +entanglements loosen and, uh, and the +chains can slide past one another. and + + align:start position:0% +chains can slide past one another. and + + + align:start position:0% +chains can slide past one another. and +the the stiffness and the effective + + align:start position:0% +the the stiffness and the effective + + + align:start position:0% +the the stiffness and the effective +viscosity of the material around that + + align:start position:0% +viscosity of the material around that + + + align:start position:0% +viscosity of the material around that +temperature falls by several orders of + + align:start position:0% +temperature falls by several orders of + + + align:start position:0% +temperature falls by several orders of +magnitude. So above that temperature, + + align:start position:0% +magnitude. So above that temperature, + + + align:start position:0% +magnitude. So above that temperature, +it's highly flexible, easily formed. + + align:start position:0% +it's highly flexible, easily formed. + + + align:start position:0% +it's highly flexible, easily formed. +Below that temperature, it's it's much + + align:start position:0% +Below that temperature, it's it's much + + + align:start position:0% +Below that temperature, it's it's much +stiffer and usable as a device. So we go + + align:start position:0% +stiffer and usable as a device. So we go + + + align:start position:0% +stiffer and usable as a device. So we go +above the glass transition temperature + + align:start position:0% +above the glass transition temperature + + + align:start position:0% +above the glass transition temperature +to soften it. How far we go above is is + + align:start position:0% +to soften it. How far we go above is is + + + align:start position:0% +to soften it. How far we go above is is +a is an important question to answer. + + align:start position:0% +a is an important question to answer. + + + align:start position:0% +a is an important question to answer. +That's a crucial parameter to choose. + + align:start position:0% +That's a crucial parameter to choose. + + + align:start position:0% +That's a crucial parameter to choose. +We then apply a load. That load is going + + align:start position:0% +We then apply a load. That load is going + + + align:start position:0% +We then apply a load. That load is going +to be ramped up over some time that we + + align:start position:0% +to be ramped up over some time that we + + + align:start position:0% +to be ramped up over some time that we +have a choice about. That might be an + + align:start position:0% +have a choice about. That might be an + + + align:start position:0% +have a choice about. That might be an +important parameter. We hold that load + + align:start position:0% +important parameter. We hold that load + + + align:start position:0% +important parameter. We hold that load +for some time to allow uh the material + + align:start position:0% +for some time to allow uh the material + + + align:start position:0% +for some time to allow uh the material +to flow to fill cavities in the stamp. + + align:start position:0% +to flow to fill cavities in the stamp. + + + align:start position:0% +to flow to fill cavities in the stamp. +And while the load is still applied, we + + align:start position:0% +And while the load is still applied, we + + + align:start position:0% +And while the load is still applied, we +cool down usually cool the material to + + align:start position:0% +cool down usually cool the material to + + + align:start position:0% +cool down usually cool the material to +below its glass transition temperature + + align:start position:0% +below its glass transition temperature + + + align:start position:0% +below its glass transition temperature +and finally remove the load. + + align:start position:0% +and finally remove the load. + + + align:start position:0% +and finally remove the load. +Um and often that removal step uh has + + align:start position:0% +Um and often that removal step uh has + + + align:start position:0% +Um and often that removal step uh has +has a lot of technical challenges + + align:start position:0% +has a lot of technical challenges + + + align:start position:0% +has a lot of technical challenges +involved in it because of differential + + align:start position:0% +involved in it because of differential + + + align:start position:0% +involved in it because of differential +thermal contraction of the workpiece and + + align:start position:0% +thermal contraction of the workpiece and + + + align:start position:0% +thermal contraction of the workpiece and +the + + align:start position:0% +the + + + align:start position:0% +the +tool. So that that gives you some idea + + align:start position:0% +tool. So that that gives you some idea + + + align:start position:0% +tool. So that that gives you some idea +that there are at least uh four + + align:start position:0% +that there are at least uh four + + + align:start position:0% +that there are at least uh four +parameters that that we need to decide + + align:start position:0% +parameters that that we need to decide + + + align:start position:0% +parameters that that we need to decide +upon um temperature a load and two times + + align:start position:0% +upon um temperature a load and two times + + + align:start position:0% +upon um temperature a load and two times +associated with that load. there there + + align:start position:0% +associated with that load. there there + + + align:start position:0% +associated with that load. there there +are probably more parameters that we + + align:start position:0% +are probably more parameters that we + + + align:start position:0% +are probably more parameters that we +we're interested + + align:start position:0% +we're interested + + + align:start position:0% +we're interested +in. Now at this point I should also + + align:start position:0% +in. Now at this point I should also + + + align:start position:0% +in. Now at this point I should also +mention uh a rather similar process that + + align:start position:0% +mention uh a rather similar process that + + + align:start position:0% +mention uh a rather similar process that +has quite different applications and + + align:start position:0% +has quite different applications and + + + align:start position:0% +has quite different applications and +that is uh thermal nano imprint + + align:start position:0% +that is uh thermal nano imprint + + + align:start position:0% +that is uh thermal nano imprint +lithography. + + align:start position:0% +lithography. + + + align:start position:0% +lithography. +This is essentially hot embossing but + + align:start position:0% +This is essentially hot embossing but + + + align:start position:0% +This is essentially hot embossing but +done on very thin layers of polymer uh + + align:start position:0% +done on very thin layers of polymer uh + + + align:start position:0% +done on very thin layers of polymer uh +thinner than a micron. And these these + + align:start position:0% +thinner than a micron. And these these + + + align:start position:0% +thinner than a micron. And these these +layers have been spun onto a much harder + + align:start position:0% +layers have been spun onto a much harder + + + align:start position:0% +layers have been spun onto a much harder +surface, usually a silicon wafer. And + + align:start position:0% +surface, usually a silicon wafer. And + + + align:start position:0% +surface, usually a silicon wafer. And +the the beauty of this process is that + + align:start position:0% +the the beauty of this process is that + + + align:start position:0% +the the beauty of this process is that +it allows uh submicron features to be + + align:start position:0% +it allows uh submicron features to be + + + align:start position:0% +it allows uh submicron features to be +transferred to the wafer. This is um I + + align:start position:0% +transferred to the wafer. This is um I + + + align:start position:0% +transferred to the wafer. This is um I +think a really exciting process. It has + + align:start position:0% +think a really exciting process. It has + + + align:start position:0% +think a really exciting process. It has +the potential to uh to revolutionize + + align:start position:0% +the potential to uh to revolutionize + + + align:start position:0% +the potential to uh to revolutionize +lithography and semiconductor + + align:start position:0% +lithography and semiconductor + + + align:start position:0% +lithography and semiconductor +manufacturing + + align:start position:0% +manufacturing + + + align:start position:0% +manufacturing +uh because the resolution with which + + align:start position:0% +uh because the resolution with which + + + align:start position:0% +uh because the resolution with which +with which features can be transferred + + align:start position:0% +with which features can be transferred + + + align:start position:0% +with which features can be transferred +is not uh is not limited by the + + align:start position:0% +is not uh is not limited by the + + + align:start position:0% +is not uh is not limited by the +wavelength of light. Usually you would + + align:start position:0% +wavelength of light. Usually you would + + + align:start position:0% +wavelength of light. Usually you would +pattern a photoresist layer with some + + align:start position:0% +pattern a photoresist layer with some + + + align:start position:0% +pattern a photoresist layer with some +kind of projection optical projection + + align:start position:0% +kind of projection optical projection + + + align:start position:0% +kind of projection optical projection +system and and we've really got to the + + align:start position:0% +system and and we've really got to the + + + align:start position:0% +system and and we've really got to the +stage where critical dimensions of of + + align:start position:0% +stage where critical dimensions of of + + + align:start position:0% +stage where critical dimensions of of +transistors are are are making that a + + align:start position:0% +transistors are are are making that a + + + align:start position:0% +transistors are are are making that a +big a big challenge making the optical + + align:start position:0% +big a big challenge making the optical + + + align:start position:0% +big a big challenge making the optical +lithography systems cost tens or + + align:start position:0% +lithography systems cost tens or + + + align:start position:0% +lithography systems cost tens or +hundreds of millions of dollars. So in + + align:start position:0% +hundreds of millions of dollars. So in + + + align:start position:0% +hundreds of millions of dollars. So in +this case we we have this spun spun on + + align:start position:0% +this case we we have this spun spun on + + + align:start position:0% +this case we we have this spun spun on +polymer layer. it it's dissolved in a in + + align:start position:0% +polymer layer. it it's dissolved in a in + + + align:start position:0% +polymer layer. it it's dissolved in a in +an organic solvent, spun on the solvent + + align:start position:0% +an organic solvent, spun on the solvent + + + align:start position:0% +an organic solvent, spun on the solvent +uh evaporates and then then the the spun + + align:start position:0% +uh evaporates and then then the the spun + + + align:start position:0% +uh evaporates and then then the the spun +on layer is a thermoplastic. It can be + + align:start position:0% +on layer is a thermoplastic. It can be + + + align:start position:0% +on layer is a thermoplastic. It can be +softened. You press the the the nanop + + align:start position:0% +softened. You press the the the nanop + + + align:start position:0% +softened. You press the the the nanop +fabricated stamp into the wafer and + + align:start position:0% +fabricated stamp into the wafer and + + + align:start position:0% +fabricated stamp into the wafer and +ideally uh squeeze all the material from + + align:start position:0% +ideally uh squeeze all the material from + + + align:start position:0% +ideally uh squeeze all the material from +below the individual features of the + + align:start position:0% +below the individual features of the + + + align:start position:0% +below the individual features of the +stamp. Now in reality that's not uh + + align:start position:0% +stamp. Now in reality that's not uh + + + align:start position:0% +stamp. Now in reality that's not uh +that's not possible and there is a small + + align:start position:0% +that's not possible and there is a small + + + align:start position:0% +that's not possible and there is a small +residual polymer layer that's left + + align:start position:0% +residual polymer layer that's left + + + align:start position:0% +residual polymer layer that's left +there. So you can imagine once we've + + align:start position:0% +there. So you can imagine once we've + + + align:start position:0% +there. So you can imagine once we've +removed the the stamp or the mold uh we + + align:start position:0% +removed the the stamp or the mold uh we + + + align:start position:0% +removed the the stamp or the mold uh we +have some extremely thin regions of + + align:start position:0% +have some extremely thin regions of + + + align:start position:0% +have some extremely thin regions of +polymer and uh then imagine that we want + + align:start position:0% +polymer and uh then imagine that we want + + + align:start position:0% +polymer and uh then imagine that we want +to pattern to etch away material in the + + align:start position:0% +to pattern to etch away material in the + + + align:start position:0% +to pattern to etch away material in the +wafer underneath the plasma or the + + align:start position:0% +wafer underneath the plasma or the + + + align:start position:0% +wafer underneath the plasma or the +etching uh the etching solution to which + + align:start position:0% +etching uh the etching solution to which + + + align:start position:0% +etching uh the etching solution to which +the wafer is exposed will quite readily + + align:start position:0% +the wafer is exposed will quite readily + + + align:start position:0% +the wafer is exposed will quite readily +break through that residual polymer + + align:start position:0% +break through that residual polymer + + + align:start position:0% +break through that residual polymer +layer and and remove the material. + + align:start position:0% +layer and and remove the material. + + + align:start position:0% +layer and and remove the material. +So these these processes are are similar + + align:start position:0% +So these these processes are are similar + + + align:start position:0% +So these these processes are are similar +uh in many ways. They actually often use + + align:start position:0% +uh in many ways. They actually often use + + + align:start position:0% +uh in many ways. They actually often use +the the same the same polymers uh but + + align:start position:0% +the the same the same polymers uh but + + + align:start position:0% +the the same the same polymers uh but +the uh the boundary conditions the the + + align:start position:0% +the uh the boundary conditions the the + + + align:start position:0% +the uh the boundary conditions the the +mechanics are rather different. And + + align:start position:0% +mechanics are rather different. And + + + align:start position:0% +mechanics are rather different. And +um so I'll I'll talk a little bit about + + align:start position:0% +um so I'll I'll talk a little bit about + + + align:start position:0% +um so I'll I'll talk a little bit about +uh about nano imprint, but mostly the + + align:start position:0% +uh about nano imprint, but mostly the + + + align:start position:0% +uh about nano imprint, but mostly the +results that I'm going to show you are + + align:start position:0% +results that I'm going to show you are + + + align:start position:0% +results that I'm going to show you are +to do with uh with micro hot embossing + + align:start position:0% +to do with uh with micro hot embossing + + + align:start position:0% +to do with uh with micro hot embossing +where the workpiece is substantially + + align:start position:0% +where the workpiece is substantially + + + align:start position:0% +where the workpiece is substantially +thicker than the diameters or the depths + + align:start position:0% +thicker than the diameters or the depths + + + align:start position:0% +thicker than the diameters or the depths +of the features that are being patent. + + align:start position:0% +of the features that are being patent. + + + align:start position:0% +of the features that are being patent. +Uh I'm not too familiar with the process + + align:start position:0% +Uh I'm not too familiar with the process + + + align:start position:0% +Uh I'm not too familiar with the process +but uh the uh deleting the mold during + + align:start position:0% +but uh the uh deleting the mold during + + + align:start position:0% +but uh the uh deleting the mold during +the mold removal process you have the uh + + align:start position:0% +the mold removal process you have the uh + + + align:start position:0% +the mold removal process you have the uh +the the mold walls getting dilated + + align:start position:0% +the the mold walls getting dilated + + + align:start position:0% +the the mold walls getting dilated +because uh the pattern is getting uh + + align:start position:0% +because uh the pattern is getting uh + + + align:start position:0% +because uh the pattern is getting uh +taken off and uh it might have + + align:start position:0% +taken off and uh it might have + + + align:start position:0% +taken off and uh it might have +dimensional constraints for it to Yeah, + + align:start position:0% +dimensional constraints for it to Yeah, + + + align:start position:0% +dimensional constraints for it to Yeah, +that's an excellent question. you've hit + + align:start position:0% +that's an excellent question. you've hit + + + align:start position:0% +that's an excellent question. you've hit +on one of the most important challenges + + align:start position:0% +on one of the most important challenges + + + align:start position:0% +on one of the most important challenges +of pot embossing and Siganth was asking + + align:start position:0% +of pot embossing and Siganth was asking + + + align:start position:0% +of pot embossing and Siganth was asking +are there are there problems with + + align:start position:0% +are there are there problems with + + + align:start position:0% +are there are there problems with +dimensional stability of of the walls + + align:start position:0% +dimensional stability of of the walls + + + align:start position:0% +dimensional stability of of the walls +the sidewalls during demolding and I'll + + align:start position:0% +the sidewalls during demolding and I'll + + + align:start position:0% +the sidewalls during demolding and I'll +show you some results that relate to + + align:start position:0% +show you some results that relate to + + + align:start position:0% +show you some results that relate to +that so yes good point anyhow as I as I + + align:start position:0% +that so yes good point anyhow as I as I + + + align:start position:0% +that so yes good point anyhow as I as I +already mentioned we there are several + + align:start position:0% +already mentioned we there are several + + + align:start position:0% +already mentioned we there are several +parameters to do with the the process uh + + align:start position:0% +parameters to do with the the process uh + + + align:start position:0% +parameters to do with the the process uh +that we need to pick temperatures + + align:start position:0% +that we need to pick temperatures + + + align:start position:0% +that we need to pick temperatures +uh loads times loading durations + + align:start position:0% +uh loads times loading durations + + + align:start position:0% +uh loads times loading durations +um the range that those parameters can + + align:start position:0% +um the range that those parameters can + + + align:start position:0% +um the range that those parameters can +take will be limited by the capabilities + + align:start position:0% +take will be limited by the capabilities + + + align:start position:0% +take will be limited by the capabilities +of the machine we have the physical + + align:start position:0% +of the machine we have the physical + + + align:start position:0% +of the machine we have the physical +properties of the polymer we're trying + + align:start position:0% +properties of the polymer we're trying + + + align:start position:0% +properties of the polymer we're trying +to pattern what temperature does it + + align:start position:0% +to pattern what temperature does it + + + align:start position:0% +to pattern what temperature does it +start to burn + + align:start position:0% +start to burn + + + align:start position:0% +start to burn +um and so forth what about the material + + align:start position:0% +um and so forth what about the material + + + align:start position:0% +um and so forth what about the material +underneath if we're doing nano imprint + + align:start position:0% +underneath if we're doing nano imprint + + + align:start position:0% +underneath if we're doing nano imprint +lithography are there temperature + + align:start position:0% +lithography are there temperature + + + align:start position:0% +lithography are there temperature +constraints that the that the wafer + + align:start position:0% +constraints that the that the wafer + + + align:start position:0% +constraints that the that the wafer +underneath has to observe + + align:start position:0% +underneath has to observe + + + align:start position:0% +underneath has to observe +so that's uh That's what constrains the + + align:start position:0% +so that's uh That's what constrains the + + + align:start position:0% +so that's uh That's what constrains the +process. And of course, um, we might + + align:start position:0% +process. And of course, um, we might + + + align:start position:0% +process. And of course, um, we might +also be making engineering decisions + + align:start position:0% +also be making engineering decisions + + + align:start position:0% +also be making engineering decisions +about what type of polymer we're going + + align:start position:0% +about what type of polymer we're going + + + align:start position:0% +about what type of polymer we're going +to use to achieve a certain, uh, end. + + align:start position:0% +to use to achieve a certain, uh, end. + + + align:start position:0% +to use to achieve a certain, uh, end. +And indeed, we might have some + + align:start position:0% +And indeed, we might have some + + + align:start position:0% +And indeed, we might have some +flexibility in the pattern that we're + + align:start position:0% +flexibility in the pattern that we're + + + align:start position:0% +flexibility in the pattern that we're +going to emboss. We might think about + + align:start position:0% +going to emboss. We might think about + + + align:start position:0% +going to emboss. We might think about +designing a pattern uh with an eye to + + align:start position:0% +designing a pattern uh with an eye to + + + align:start position:0% +designing a pattern uh with an eye to +manufacturability, something that will + + align:start position:0% +manufacturability, something that will + + + align:start position:0% +manufacturability, something that will +be easier to imprint with less + + align:start position:0% +be easier to imprint with less + + + align:start position:0% +be easier to imprint with less +variability. And that is uh one of the + + align:start position:0% +variability. And that is uh one of the + + + align:start position:0% +variability. And that is uh one of the +questions that I'm trying to answer. + + align:start position:0% +questions that I'm trying to answer. + + + align:start position:0% +questions that I'm trying to answer. +How do you make the SC? + + align:start position:0% +How do you make the SC? + + + align:start position:0% +How do you make the SC? +Right. Well, the the stamp can be made + + align:start position:0% +Right. Well, the the stamp can be made + + + align:start position:0% +Right. Well, the the stamp can be made +um in in in a variety of variety of ways + + align:start position:0% +um in in in a variety of variety of ways + + + align:start position:0% +um in in in a variety of variety of ways +um that are usually traditional micr + + align:start position:0% +um that are usually traditional micr + + + align:start position:0% +um that are usually traditional micr +fabrication. So um one particularly easy + + align:start position:0% +fabrication. So um one particularly easy + + + align:start position:0% +fabrication. So um one particularly easy +way of doing it would be to use a + + align:start position:0% +way of doing it would be to use a + + + align:start position:0% +way of doing it would be to use a +process called deep reactive ion + + align:start position:0% +process called deep reactive ion + + + align:start position:0% +process called deep reactive ion +etching. And and here I'm talking about + + align:start position:0% +etching. And and here I'm talking about + + + align:start position:0% +etching. And and here I'm talking about +micrombbossing where the features are + + align:start position:0% +micrombbossing where the features are + + + align:start position:0% +micrombbossing where the features are +you know several microns to many + + align:start position:0% +you know several microns to many + + + align:start position:0% +you know several microns to many +microns. And and and essentially this is + + align:start position:0% +microns. And and and essentially this is + + + align:start position:0% +microns. And and and essentially this is +just etching very deep trenches into a + + align:start position:0% +just etching very deep trenches into a + + + align:start position:0% +just etching very deep trenches into a +silicon wafer using a plasma process. + + align:start position:0% +silicon wafer using a plasma process. + + + align:start position:0% +silicon wafer using a plasma process. +Um, I could go into great detail about + + align:start position:0% +Um, I could go into great detail about + + + align:start position:0% +Um, I could go into great detail about +how that works, but essentially it's a + + align:start position:0% +how that works, but essentially it's a + + + align:start position:0% +how that works, but essentially it's a +florinebased chemistry. The precursor + + align:start position:0% +florinebased chemistry. The precursor + + + align:start position:0% +florinebased chemistry. The precursor +gas is uh + + align:start position:0% +gas is uh + + + align:start position:0% +gas is uh +SF6. And, uh, you build up these these + + align:start position:0% +SF6. And, uh, you build up these these + + + align:start position:0% +SF6. And, uh, you build up these these +very deep narrow trenches in the silicon + + align:start position:0% +very deep narrow trenches in the silicon + + + align:start position:0% +very deep narrow trenches in the silicon +wafer + + align:start position:0% +wafer + + + align:start position:0% +wafer +by a series of steps. So, um, in fact, + + align:start position:0% +by a series of steps. So, um, in fact, + + + align:start position:0% +by a series of steps. So, um, in fact, +you would start with you'd start with + + align:start position:0% +you would start with you'd start with + + + align:start position:0% +you would start with you'd start with +the silicon with a photoresist mask or + + align:start position:0% +the silicon with a photoresist mask or + + + align:start position:0% +the silicon with a photoresist mask or +something. + + align:start position:0% +something. + + + align:start position:0% +something. +you do a brief uh florine based plasma + + align:start position:0% +you do a brief uh florine based plasma + + + align:start position:0% +you do a brief uh florine based plasma +etch that would remove small amounts of + + align:start position:0% +etch that would remove small amounts of + + + align:start position:0% +etch that would remove small amounts of +material + + align:start position:0% +material + + + align:start position:0% +material +that's roughly isotropic. So if you want + + align:start position:0% +that's roughly isotropic. So if you want + + + align:start position:0% +that's roughly isotropic. So if you want +vertical side walls you got to do + + align:start position:0% +vertical side walls you got to do + + + align:start position:0% +vertical side walls you got to do +something else and the something else is + + align:start position:0% +something else and the something else is + + + align:start position:0% +something else and the something else is +depositing a polymer pivation layer. So + + align:start position:0% +depositing a polymer pivation layer. So + + + align:start position:0% +depositing a polymer pivation layer. So +you change the the gas in the chamber to + + align:start position:0% +you change the the gas in the chamber to + + + align:start position:0% +you change the the gas in the chamber to +um C4 F8 which creates what's + + align:start position:0% +um C4 F8 which creates what's + + + align:start position:0% +um C4 F8 which creates what's +essentially a teflon coating that + + align:start position:0% +essentially a teflon coating that + + + align:start position:0% +essentially a teflon coating that +passivates the sidewall of the trench + + align:start position:0% +passivates the sidewall of the trench + + + align:start position:0% +passivates the sidewall of the trench +that's developing. Then you go back to + + align:start position:0% +that's developing. Then you go back to + + + align:start position:0% +that's developing. Then you go back to +the SF6, you know, build up a new notch + + align:start position:0% +the SF6, you know, build up a new notch + + + align:start position:0% +the SF6, you know, build up a new notch +and do this many times, alternate many + + align:start position:0% +and do this many times, alternate many + + + align:start position:0% +and do this many times, alternate many +times. So, you know, whatever way you + + align:start position:0% +times. So, you know, whatever way you + + + align:start position:0% +times. So, you know, whatever way you +you pattern the the stamp, silicon + + align:start position:0% +you pattern the the stamp, silicon + + + align:start position:0% +you pattern the the stamp, silicon +actually, as as we'll see later, for for + + align:start position:0% +actually, as as we'll see later, for for + + + align:start position:0% +actually, as as we'll see later, for for +demolding reasons is is actually a lousy + + align:start position:0% +demolding reasons is is actually a lousy + + + align:start position:0% +demolding reasons is is actually a lousy +material to use for stamp. So, then you + + align:start position:0% +material to use for stamp. So, then you + + + align:start position:0% +material to use for stamp. So, then you +might go one step + + align:start position:0% +might go one step + + + align:start position:0% +might go one step +further, electroplate nickel into that + + align:start position:0% +further, electroplate nickel into that + + + align:start position:0% +further, electroplate nickel into that +etched wafer, peel off the nickel and + + align:start position:0% +etched wafer, peel off the nickel and + + + align:start position:0% +etched wafer, peel off the nickel and +use that as the stamp. Much tougher. or + + align:start position:0% +use that as the stamp. Much tougher. or + + + align:start position:0% +use that as the stamp. Much tougher. or +you might use uh more novel materials, + + align:start position:0% +you might use uh more novel materials, + + + align:start position:0% +you might use uh more novel materials, +things like metallic glasses, which are + + align:start position:0% +things like metallic glasses, which are + + + align:start position:0% +things like metallic glasses, which are +uh alloys with an + + align:start position:0% +uh alloys with an + + + align:start position:0% +uh alloys with an +amorphous structure that are both very + + align:start position:0% +amorphous structure that are both very + + + align:start position:0% +amorphous structure that are both very +hard and very tough. They would be great + + align:start position:0% +hard and very tough. They would be great + + + align:start position:0% +hard and very tough. They would be great +materials for a stamp. So, so what you + + align:start position:0% +materials for a stamp. So, so what you + + + align:start position:0% +materials for a stamp. So, so what you +mentioned, you said that you're not + + align:start position:0% +mentioned, you said that you're not + + + align:start position:0% +mentioned, you said that you're not +limited to wavelength of the light for + + align:start position:0% +limited to wavelength of the light for + + + align:start position:0% +limited to wavelength of the light for +this process, but however to make the + + align:start position:0% +this process, but however to make the + + + align:start position:0% +this process, but however to make the +stamp then you're limited to Yeah, + + align:start position:0% +stamp then you're limited to Yeah, + + + align:start position:0% +stamp then you're limited to Yeah, +you're well limitation exist. So what I + + align:start position:0% +you're well limitation exist. So what I + + + align:start position:0% +you're well limitation exist. So what I +just described here was for was for + + align:start position:0% +just described here was for was for + + + align:start position:0% +just described here was for was for +micro embossing. I'm sorry I'm sort of + + align:start position:0% +micro embossing. I'm sorry I'm sort of + + + align:start position:0% +micro embossing. I'm sorry I'm sort of +describing two processes in parallel + + align:start position:0% +describing two processes in parallel + + + align:start position:0% +describing two processes in parallel +that are you know have great + + align:start position:0% +that are you know have great + + + align:start position:0% +that are you know have great +similarities but not in terms of scale. + + align:start position:0% +similarities but not in terms of scale. + + + align:start position:0% +similarities but not in terms of scale. +So this would be for features that are + + align:start position:0% +So this would be for features that are + + + align:start position:0% +So this would be for features that are +you know a micron or larger. If you want + + align:start position:0% +you know a micron or larger. If you want + + + align:start position:0% +you know a micron or larger. If you want +to make submicron features then you're + + align:start position:0% +to make submicron features then you're + + + align:start position:0% +to make submicron features then you're +quite right. You need a process that + + align:start position:0% +quite right. You need a process that + + + align:start position:0% +quite right. You need a process that +will that will let you make a stamp with + + align:start position:0% +will that will let you make a stamp with + + + align:start position:0% +will that will let you make a stamp with +submicron features. And um you know + + align:start position:0% +submicron features. And um you know + + + align:start position:0% +submicron features. And um you know +electron beam lithography is a is a + + align:start position:0% +electron beam lithography is a is a + + + align:start position:0% +electron beam lithography is a is a +great candidate for that where you you + + align:start position:0% +great candidate for that where you you + + + align:start position:0% +great candidate for that where you you +actually would you know you would start + + align:start position:0% +actually would you know you would start + + + align:start position:0% +actually would you know you would start +with a silicon wafer with a 100 + + align:start position:0% +with a silicon wafer with a 100 + + + align:start position:0% +with a silicon wafer with a 100 +nanometer thick layer of + + align:start position:0% +nanometer thick layer of + + + align:start position:0% +nanometer thick layer of +uh a radiation sensitive resist. Then + + align:start position:0% +uh a radiation sensitive resist. Then + + + align:start position:0% +uh a radiation sensitive resist. Then +you would just actually steer a focused + + align:start position:0% +you would just actually steer a focused + + + align:start position:0% +you would just actually steer a focused +electron beam across the surface. scan + + align:start position:0% +electron beam across the surface. scan + + + align:start position:0% +electron beam across the surface. scan +it across the surface in the pattern + + align:start position:0% +it across the surface in the pattern + + + align:start position:0% +it across the surface in the pattern +that you wanted and that will give you, + + align:start position:0% +that you wanted and that will give you, + + + align:start position:0% +that you wanted and that will give you, +you know, 5 nanometer resolution or + + align:start position:0% +you know, 5 nanometer resolution or + + + align:start position:0% +you know, 5 nanometer resolution or +better. The trouble is it takes ages + + align:start position:0% +better. The trouble is it takes ages + + + align:start position:0% +better. The trouble is it takes ages +because it's a serial process. You're + + align:start position:0% +because it's a serial process. You're + + + align:start position:0% +because it's a serial process. You're +scanning the electrons over the surface. + + align:start position:0% +scanning the electrons over the surface. + + + align:start position:0% +scanning the electrons over the surface. +So once you've made the stamp, you've + + align:start position:0% +So once you've made the stamp, you've + + + align:start position:0% +So once you've made the stamp, you've +paid however many thousand dollars for + + align:start position:0% +paid however many thousand dollars for + + + align:start position:0% +paid however many thousand dollars for +the stamp. You know, you can stamp it in + + align:start position:0% +the stamp. You know, you can stamp it in + + + align:start position:0% +the stamp. You know, you can stamp it in +in a minute into as many substrates as + + align:start position:0% +in a minute into as many substrates as + + + align:start position:0% +in a minute into as many substrates as +you like. And that's really the the + + align:start position:0% +you like. And that's really the the + + + align:start position:0% +you like. And that's really the the +reason for nano + + align:start position:0% +reason for nano + + + align:start position:0% +reason for nano +imprint. Okay. But uh so keep keep both + + align:start position:0% +imprint. Okay. But uh so keep keep both + + + align:start position:0% +imprint. Okay. But uh so keep keep both +of those processes in mind. But a lot of + + align:start position:0% +of those processes in mind. But a lot of + + + align:start position:0% +of those processes in mind. But a lot of +the uh assertions I'm going to make from + + align:start position:0% +the uh assertions I'm going to make from + + + align:start position:0% +the uh assertions I'm going to make from +now on are all about the the micron + + align:start position:0% +now on are all about the the micron + + + align:start position:0% +now on are all about the the micron +scale + + align:start position:0% +scale + + + align:start position:0% +scale +embossing. So as I said we we there are + + align:start position:0% +embossing. So as I said we we there are + + + align:start position:0% +embossing. So as I said we we there are +lots of different parameters we can + + align:start position:0% +lots of different parameters we can + + + align:start position:0% +lots of different parameters we can +choose to do with the process to do with + + align:start position:0% +choose to do with the process to do with + + + align:start position:0% +choose to do with the process to do with +the material we're embossing to do with + + align:start position:0% +the material we're embossing to do with + + + align:start position:0% +the material we're embossing to do with +the pattern that we're embossing. And uh + + align:start position:0% +the pattern that we're embossing. And uh + + + align:start position:0% +the pattern that we're embossing. And uh +the overall mission that I suppose we + + align:start position:0% +the overall mission that I suppose we + + + align:start position:0% +the overall mission that I suppose we +have is to try to provide tools for + + align:start position:0% +have is to try to provide tools for + + + align:start position:0% +have is to try to provide tools for +people who are using this process to + + align:start position:0% +people who are using this process to + + + align:start position:0% +people who are using this process to +achieve the the desired structure micro + + align:start position:0% +achieve the the desired structure micro + + + align:start position:0% +achieve the the desired structure micro +structure uh with uh as little time, + + align:start position:0% +structure uh with uh as little time, + + + align:start position:0% +structure uh with uh as little time, +energy, cost as possible. So you if if + + align:start position:0% +energy, cost as possible. So you if if + + + align:start position:0% +energy, cost as possible. So you if if +you're processing a certain material, + + align:start position:0% +you're processing a certain material, + + + align:start position:0% +you're processing a certain material, +can you pick a pattern that will take 30 + + align:start position:0% +can you pick a pattern that will take 30 + + + align:start position:0% +can you pick a pattern that will take 30 +seconds to replicate instead of a minute + + align:start position:0% +seconds to replicate instead of a minute + + + align:start position:0% +seconds to replicate instead of a minute +at the available + + align:start position:0% +at the available + + + align:start position:0% +at the available +uh processing conditions. So + + align:start position:0% +uh processing conditions. So + + + align:start position:0% +uh processing conditions. So +there's that presupposes of course that + + align:start position:0% +there's that presupposes of course that + + + align:start position:0% +there's that presupposes of course that +we have some specification on what what + + align:start position:0% +we have some specification on what what + + + align:start position:0% +we have some specification on what what +satisfactory replication is. The most + + align:start position:0% +satisfactory replication is. The most + + + align:start position:0% +satisfactory replication is. The most +obvious specification would be that + + align:start position:0% +obvious specification would be that + + + align:start position:0% +obvious specification would be that +every cavity in the stamp has been + + align:start position:0% +every cavity in the stamp has been + + + align:start position:0% +every cavity in the stamp has been +filled with polymer, even the narrowest + + align:start position:0% +filled with polymer, even the narrowest + + + align:start position:0% +filled with polymer, even the narrowest +ones. That would be a good specification + + align:start position:0% +ones. That would be a good specification + + + align:start position:0% +ones. That would be a good specification +to use. Um, another good specification + + align:start position:0% +to use. Um, another good specification + + + align:start position:0% +to use. Um, another good specification +that's really important for nano imprint + + align:start position:0% +that's really important for nano imprint + + + align:start position:0% +that's really important for nano imprint +lithography is to make the thickness of + + align:start position:0% +lithography is to make the thickness of + + + align:start position:0% +lithography is to make the thickness of +those residual polymer layers very + + align:start position:0% +those residual polymer layers very + + + align:start position:0% +those residual polymer layers very +uniform. And that's that's important + + align:start position:0% +uniform. And that's that's important + + + align:start position:0% +uniform. And that's that's important +because it does take some time for the + + align:start position:0% +because it does take some time for the + + + align:start position:0% +because it does take some time for the +etching process to break through that + + align:start position:0% +etching process to break through that + + + align:start position:0% +etching process to break through that +residual + + align:start position:0% +residual + + + align:start position:0% +residual +layer. And if the residual layer varies + + align:start position:0% +layer. And if the residual layer varies + + + align:start position:0% +layer. And if the residual layer varies +in + + align:start position:0% +in + + + align:start position:0% +in +thickness, the time taken to break + + align:start position:0% +thickness, the time taken to break + + + align:start position:0% +thickness, the time taken to break +through it will be different. And then + + align:start position:0% +through it will be different. And then + + + align:start position:0% +through it will be different. And then +you'll get different properties of the + + align:start position:0% +you'll get different properties of the + + + align:start position:0% +you'll get different properties of the +underlying structure. So let's say + + align:start position:0% +underlying structure. So let's say + + + align:start position:0% +underlying structure. So let's say +you've got um you you've imprinted this + + align:start position:0% +you've got um you you've imprinted this + + + align:start position:0% +you've got um you you've imprinted this +100 nanometer thick polymer + + align:start position:0% +100 nanometer thick polymer + + + align:start position:0% +100 nanometer thick polymer +layer + + align:start position:0% +layer + + + align:start position:0% +layer +and on this side the residual layer is + + align:start position:0% +and on this side the residual layer is + + + align:start position:0% +and on this side the residual layer is +really thin and on this side it's twice + + align:start position:0% +really thin and on this side it's twice + + + align:start position:0% +really thin and on this side it's twice +as thick. You then expose it expose this + + align:start position:0% +as thick. You then expose it expose this + + + align:start position:0% +as thick. You then expose it expose this +with a a florine plasma. You're trying + + align:start position:0% +with a a florine plasma. You're trying + + + align:start position:0% +with a a florine plasma. You're trying +to etch the silicon underneath here. + + align:start position:0% +to etch the silicon underneath here. + + + align:start position:0% +to etch the silicon underneath here. +you're going to end up with a deeper + + align:start position:0% +you're going to end up with a deeper + + + align:start position:0% +you're going to end up with a deeper +trench here than you are here because of + + align:start position:0% +trench here than you are here because of + + + align:start position:0% +trench here than you are here because of +the time it took to get through that. + + align:start position:0% +the time it took to get through that. + + + align:start position:0% +the time it took to get through that. +So, coming up with ways of designing the + + align:start position:0% +So, coming up with ways of designing the + + + align:start position:0% +So, coming up with ways of designing the +stamp so that the residual layer ends up + + align:start position:0% +stamp so that the residual layer ends up + + + align:start position:0% +stamp so that the residual layer ends up +being as uniform as possible is is a a + + align:start position:0% +being as uniform as possible is is a a + + + align:start position:0% +being as uniform as possible is is a a +really uh pressing challenge actually + + align:start position:0% +really uh pressing challenge actually + + + align:start position:0% +really uh pressing challenge actually +for this uh lithography technique to be + + align:start position:0% + + + + align:start position:0% + +adopted. Anyhow, so what what we're all + + align:start position:0% +adopted. Anyhow, so what what we're all + + + align:start position:0% +adopted. Anyhow, so what what we're all +about + + align:start position:0% +about + + + align:start position:0% +about +is simplified modeling tools that can be + + align:start position:0% +is simplified modeling tools that can be + + + align:start position:0% +is simplified modeling tools that can be +used as part of the design loop that are + + align:start position:0% +used as part of the design loop that are + + + align:start position:0% +used as part of the design loop that are +that are computationally efficient + + align:start position:0% +that are computationally efficient + + + align:start position:0% +that are computationally efficient +enough to uh to give + + align:start position:0% +enough to uh to give + + + align:start position:0% +enough to uh to give +results in in in a reasonable amount of + + align:start position:0% +results in in in a reasonable amount of + + + align:start position:0% +results in in in a reasonable amount of +time and uh that represent reality well. + + align:start position:0% +time and uh that represent reality well. + + + align:start position:0% +time and uh that represent reality well. +So that implies that we need some way of + + align:start position:0% +So that implies that we need some way of + + + align:start position:0% +So that implies that we need some way of +characterizing the tool that we're + + align:start position:0% +characterizing the tool that we're + + + align:start position:0% +characterizing the tool that we're +using, the materials that we're using + + align:start position:0% +using, the materials that we're using + + + align:start position:0% +using, the materials that we're using +efficiently so that we we can get + + align:start position:0% +efficiently so that we we can get + + + align:start position:0% +efficiently so that we we can get +information about the physical + + align:start position:0% +information about the physical + + + align:start position:0% +information about the physical +properties of these things with a + + align:start position:0% +properties of these things with a + + + align:start position:0% +properties of these things with a +minimum of + + align:start position:0% +minimum of + + + align:start position:0% +minimum of +thus. Now I'm just going to + + align:start position:0% +thus. Now I'm just going to + + + align:start position:0% +thus. Now I'm just going to +uh split the problem up into into three + + align:start position:0% +uh split the problem up into into three + + + align:start position:0% +uh split the problem up into into three +notional length scales so that we can + + align:start position:0% +notional length scales so that we can + + + align:start position:0% +notional length scales so that we can +have a clearer picture of what's going + + align:start position:0% +have a clearer picture of what's going + + + align:start position:0% +have a clearer picture of what's going +on. And uh at the largest length + + align:start position:0% +on. And uh at the largest length + + + align:start position:0% +on. And uh at the largest length +scale, you can think of variations in + + align:start position:0% +scale, you can think of variations in + + + align:start position:0% +scale, you can think of variations in +the quality of the embossed features + + align:start position:0% +the quality of the embossed features + + + align:start position:0% +the quality of the embossed features +from one side of the substrate to the + + align:start position:0% +from one side of the substrate to the + + + align:start position:0% +from one side of the substrate to the +other. And that might occur because the + + align:start position:0% +other. And that might occur because the + + + align:start position:0% +other. And that might occur because the +two heated plates that are compressing + + align:start position:0% +two heated plates that are compressing + + + align:start position:0% +two heated plates that are compressing +the stamp and and the substrate are not + + align:start position:0% +the stamp and and the substrate are not + + + align:start position:0% +the stamp and and the substrate are not +perfectly parallel. So the pressure is + + align:start position:0% +perfectly parallel. So the pressure is + + + align:start position:0% +perfectly parallel. So the pressure is +greater on one side. It might be because + + align:start position:0% +greater on one side. It might be because + + + align:start position:0% +greater on one side. It might be because +one of the plates is bowed or wavy. uh + + align:start position:0% +one of the plates is bowed or wavy. uh + + + align:start position:0% +one of the plates is bowed or wavy. uh +or it might be to do with the simply the + + align:start position:0% +or it might be to do with the simply the + + + align:start position:0% +or it might be to do with the simply the +mechanics of the substrate itself. If + + align:start position:0% +mechanics of the substrate itself. If + + + align:start position:0% +mechanics of the substrate itself. If +that substrate is behaving uh as a + + align:start position:0% +that substrate is behaving uh as a + + + align:start position:0% +that substrate is behaving uh as a +viscous fluid say then as you compress + + align:start position:0% +viscous fluid say then as you compress + + + align:start position:0% +viscous fluid say then as you compress +that substrate that flat polymer + + align:start position:0% +that substrate that flat polymer + + + align:start position:0% +that substrate that flat polymer +substrate you're going to expect to see + + align:start position:0% +substrate you're going to expect to see + + + align:start position:0% +substrate you're going to expect to see +uh in fact a parabolic distribution of + + align:start position:0% +uh in fact a parabolic distribution of + + + align:start position:0% +uh in fact a parabolic distribution of +pressure across it. So there are various + + align:start position:0% +pressure across it. So there are various + + + align:start position:0% +pressure across it. So there are various +things to consider + + align:start position:0% +things to consider + + + align:start position:0% +things to consider +there. And then at the at the what I'm + + align:start position:0% +there. And then at the at the what I'm + + + align:start position:0% +there. And then at the at the what I'm +going to call the device scale, there + + align:start position:0% +going to call the device scale, there + + + align:start position:0% +going to call the device scale, there +are there are these pattern dependencies + + align:start position:0% +are there are these pattern dependencies + + + align:start position:0% +are there are these pattern dependencies +where the arrangement of features on the + + align:start position:0% +where the arrangement of features on the + + + align:start position:0% +where the arrangement of features on the +stamp can have a profound effect on uh + + align:start position:0% +stamp can have a profound effect on uh + + + align:start position:0% +stamp can have a profound effect on uh +how well- definfined the features end up + + align:start position:0% +how well- definfined the features end up + + + align:start position:0% +how well- definfined the features end up +being. And what I've sketched here, um, + + align:start position:0% +being. And what I've sketched here, um, + + + align:start position:0% +being. And what I've sketched here, um, +which which is, + + align:start position:0% +which which is, + + + align:start position:0% +which which is, +uh, really just a sketch, it it + + align:start position:0% +uh, really just a sketch, it it + + + align:start position:0% +uh, really just a sketch, it it +suggests, you know, if there are + + align:start position:0% +suggests, you know, if there are + + + align:start position:0% +suggests, you know, if there are +features that are slightly more closely + + align:start position:0% +features that are slightly more closely + + + align:start position:0% +features that are slightly more closely +packed together, then they may fill + + align:start position:0% +packed together, then they may fill + + + align:start position:0% +packed together, then they may fill +earlier or maybe sometimes later than + + align:start position:0% +earlier or maybe sometimes later than + + + align:start position:0% +earlier or maybe sometimes later than +regions that are less densely packed. + + align:start position:0% +regions that are less densely packed. + + + align:start position:0% +regions that are less densely packed. +And if that's the case, then maybe you + + align:start position:0% +And if that's the case, then maybe you + + + align:start position:0% +And if that's the case, then maybe you +want to put some design rules in place + + align:start position:0% +want to put some design rules in place + + + align:start position:0% +want to put some design rules in place +that will constrain the variation of + + align:start position:0% +that will constrain the variation of + + + align:start position:0% +that will constrain the variation of +density of features on the + + align:start position:0% +density of features on the + + + align:start position:0% +density of features on the +stamp. Finally, we've got at the + + align:start position:0% +stamp. Finally, we've got at the + + + align:start position:0% +stamp. Finally, we've got at the +smallest scale effects to do with + + align:start position:0% +smallest scale effects to do with + + + align:start position:0% +smallest scale effects to do with +individual features. So if an individual + + align:start position:0% +individual features. So if an individual + + + align:start position:0% +individual features. So if an individual +gap is too small, say, that's going to + + align:start position:0% +gap is too small, say, that's going to + + + align:start position:0% +gap is too small, say, that's going to +be very hard to force polymer into it + + align:start position:0% +be very hard to force polymer into it + + + align:start position:0% +be very hard to force polymer into it +and that could be could be a + + align:start position:0% +and that could be could be a + + + align:start position:0% +and that could be could be a +showstopper. So we've got these three + + align:start position:0% +showstopper. So we've got these three + + + align:start position:0% +showstopper. So we've got these three +different length scales. Um I I've + + align:start position:0% +different length scales. Um I I've + + + align:start position:0% +different length scales. Um I I've +alluded to these these sorts of + + align:start position:0% +alluded to these these sorts of + + + align:start position:0% +alluded to these these sorts of +problems. Boeing of the platens uh nonp + + align:start position:0% +problems. Boeing of the platens uh nonp + + + align:start position:0% +problems. Boeing of the platens uh nonp +parallelism of the platens um they + + align:start position:0% +parallelism of the platens um they + + + align:start position:0% +parallelism of the platens um they +relate to the substrate scale + + align:start position:0% +relate to the substrate scale + + + align:start position:0% +relate to the substrate scale +effects. Um this shows + + align:start position:0% +effects. Um this shows + + + align:start position:0% +effects. Um this shows +uh one + + align:start position:0% +uh one + + + align:start position:0% +uh one +uh particular substrate that we emboss. + + align:start position:0% +uh particular substrate that we emboss. + + + align:start position:0% +uh particular substrate that we emboss. +This is a a square of of uh Pmama which + + align:start position:0% +This is a a square of of uh Pmama which + + + align:start position:0% +This is a a square of of uh Pmama which +is acrylic which which is about 100 mm + + align:start position:0% +is acrylic which which is about 100 mm + + + align:start position:0% +is acrylic which which is about 100 mm +square we embossed with a a wafer that + + align:start position:0% +square we embossed with a a wafer that + + + align:start position:0% +square we embossed with a a wafer that +have been uniformly patented with some + + align:start position:0% +have been uniformly patented with some + + + align:start position:0% +have been uniformly patented with some +silicon posts um roughly 100 microns in + + align:start position:0% +silicon posts um roughly 100 microns in + + + align:start position:0% +silicon posts um roughly 100 microns in +diameter and we just use this as a probe + + align:start position:0% +diameter and we just use this as a probe + + + align:start position:0% +diameter and we just use this as a probe +to to look at our our embossing machine + + align:start position:0% +to to look at our our embossing machine + + + align:start position:0% +to to look at our our embossing machine +and see how uniform a pattern could be + + align:start position:0% +and see how uniform a pattern could be + + + align:start position:0% +and see how uniform a pattern could be +produced. Now, aside from the fact that + + align:start position:0% +produced. Now, aside from the fact that + + + align:start position:0% +produced. Now, aside from the fact that +huge chunks of the silicon wafer broke + + align:start position:0% +huge chunks of the silicon wafer broke + + + align:start position:0% +huge chunks of the silicon wafer broke +off during demolding, and that's a good + + align:start position:0% +off during demolding, and that's a good + + + align:start position:0% +off during demolding, and that's a good +illustration of some of the problems + + align:start position:0% +illustration of some of the problems + + + align:start position:0% +illustration of some of the problems +that we face, um we were able to look at + + align:start position:0% +that we face, um we were able to look at + + + align:start position:0% +that we face, um we were able to look at +uh at the topography of of the pattern + + align:start position:0% +uh at the topography of of the pattern + + + align:start position:0% +uh at the topography of of the pattern +at different locations on the wafer. We + + align:start position:0% +at different locations on the wafer. We + + + align:start position:0% +at different locations on the wafer. We +did that using uh an interpherometer + + align:start position:0% +did that using uh an interpherometer + + + align:start position:0% +did that using uh an interpherometer +scanning from above measuring the + + align:start position:0% +scanning from above measuring the + + + align:start position:0% +scanning from above measuring the +topography and um so we we were able to + + align:start position:0% +topography and um so we we were able to + + + align:start position:0% +topography and um so we we were able to +see various things that the embossed + + align:start position:0% +see various things that the embossed + + + align:start position:0% +see various things that the embossed +depth was higher on this side than on + + align:start position:0% +depth was higher on this side than on + + + align:start position:0% +depth was higher on this side than on +this side that near the edge of the + + align:start position:0% +this side that near the edge of the + + + align:start position:0% +this side that near the edge of the +wafer the embossed uh + + align:start position:0% +wafer the embossed uh + + + align:start position:0% +wafer the embossed uh +features tailed off in in in in height. + + align:start position:0% +features tailed off in in in in height. + + + align:start position:0% +features tailed off in in in in height. +And so these are the sorts of things + + align:start position:0% +And so these are the sorts of things + + + align:start position:0% +And so these are the sorts of things +that we need to come up with uh ways of + + align:start position:0% +that we need to come up with uh ways of + + + align:start position:0% +that we need to come up with uh ways of +predicting so that we can we can + + align:start position:0% +predicting so that we can we can + + + align:start position:0% +predicting so that we can we can +counteract + + align:start position:0% +counteract + + + align:start position:0% +counteract +them. Anyway, + + align:start position:0% + + + + align:start position:0% + +um what I'm going to concentrate on for + + align:start position:0% +um what I'm going to concentrate on for + + + align:start position:0% +um what I'm going to concentrate on for +the rest of this talk in fact is is + + align:start position:0% +the rest of this talk in fact is is + + + align:start position:0% +the rest of this talk in fact is is +patent dependent non-uniformity + + align:start position:0% +patent dependent non-uniformity + + + align:start position:0% +patent dependent non-uniformity +um which is is is in many ways + + align:start position:0% +um which is is is in many ways + + + align:start position:0% +um which is is is in many ways +um the uh the most challenging to deal + + align:start position:0% +um the uh the most challenging to deal + + + align:start position:0% +um the uh the most challenging to deal +with. You know, effects to do with the + + align:start position:0% +with. You know, effects to do with the + + + align:start position:0% +with. You know, effects to do with the +edge of the wafer become important when + + align:start position:0% +edge of the wafer become important when + + + align:start position:0% +edge of the wafer become important when +you're you're trying to eek out one or + + align:start position:0% +you're you're trying to eek out one or + + + align:start position:0% +you're you're trying to eek out one or +two extra devices. you're trying to save + + align:start position:0% +two extra devices. you're trying to save + + + align:start position:0% +two extra devices. you're trying to save +a little bit of material, but if the + + align:start position:0% +a little bit of material, but if the + + + align:start position:0% +a little bit of material, but if the +actual design of the of the device, + + align:start position:0% +actual design of the of the device, + + + align:start position:0% +actual design of the of the device, +there are maybe many devices across a + + align:start position:0% +there are maybe many devices across a + + + align:start position:0% +there are maybe many devices across a +wafer. If the design of the individual + + align:start position:0% +wafer. If the design of the individual + + + align:start position:0% +wafer. If the design of the individual +device is faulty and it will never + + align:start position:0% +device is faulty and it will never + + + align:start position:0% +device is faulty and it will never +replicate properly, then you're in real + + align:start position:0% +replicate properly, then you're in real + + + align:start position:0% +replicate properly, then you're in real +trouble. So trying to get an + + align:start position:0% +trouble. So trying to get an + + + align:start position:0% +trouble. So trying to get an +understanding of what patterns will form + + align:start position:0% +understanding of what patterns will form + + + align:start position:0% +understanding of what patterns will form +well and what patterns will not is + + align:start position:0% +well and what patterns will not is + + + align:start position:0% +well and what patterns will not is +crucial. + + align:start position:0% +crucial. + + + align:start position:0% +crucial. +And uh + + align:start position:0% +And uh + + + align:start position:0% +And uh +so although we we are working towards a + + align:start position:0% +so although we we are working towards a + + + align:start position:0% +so although we we are working towards a +unified way of dealing with this, I'm + + align:start position:0% +unified way of dealing with this, I'm + + + align:start position:0% +unified way of dealing with this, I'm +just going to talk mostly about the the + + align:start position:0% +just going to talk mostly about the the + + + align:start position:0% +just going to talk mostly about the the +pattern dependencies + + align:start position:0% +pattern dependencies + + + align:start position:0% +pattern dependencies +now. + + align:start position:0% + + + + align:start position:0% + +So I've mentioned all of these + + align:start position:0% +So I've mentioned all of these + + + align:start position:0% +So I've mentioned all of these +different questions that need to be + + align:start position:0% +different questions that need to be + + + align:start position:0% +different questions that need to be +answered, factors that need to be chosen + + align:start position:0% +answered, factors that need to be chosen + + + align:start position:0% +answered, factors that need to be chosen +when you're designing a new process. And + + align:start position:0% +when you're designing a new process. And + + + align:start position:0% +when you're designing a new process. And +um some of them are are going to be + + align:start position:0% +um some of them are are going to be + + + align:start position:0% +um some of them are are going to be +continuous variables and some of them + + align:start position:0% +continuous variables and some of them + + + align:start position:0% +continuous variables and some of them +will be discrete choices. And it's not + + align:start position:0% +will be discrete choices. And it's not + + + align:start position:0% +will be discrete choices. And it's not +absolutely clear which which will be + + align:start position:0% +absolutely clear which which will be + + + align:start position:0% +absolutely clear which which will be +which. Um I've really split the + + align:start position:0% +which. Um I've really split the + + + align:start position:0% +which. Um I've really split the +decisions up into three categories. + + align:start position:0% +decisions up into three categories. + + + align:start position:0% +decisions up into three categories. +Decisions you have to make about the + + align:start position:0% +Decisions you have to make about the + + + align:start position:0% +Decisions you have to make about the +pattern you're going to emboss. What are + + align:start position:0% +pattern you're going to emboss. What are + + + align:start position:0% +pattern you're going to emboss. What are +the shapes of the features? Rectangles, + + align:start position:0% +the shapes of the features? Rectangles, + + + align:start position:0% +the shapes of the features? Rectangles, +circles, triangles, how big they are, + + align:start position:0% +circles, triangles, how big they are, + + + align:start position:0% +circles, triangles, how big they are, +and uh how they are oriented on the + + align:start position:0% +and uh how they are oriented on the + + + align:start position:0% +and uh how they are oriented on the +stamp. um and and that that can be + + align:start position:0% +stamp. um and and that that can be + + + align:start position:0% +stamp. um and and that that can be +important when you're starting to think + + align:start position:0% +important when you're starting to think + + + align:start position:0% +important when you're starting to think +about radial thermal contraction of the + + align:start position:0% +about radial thermal contraction of the + + + align:start position:0% +about radial thermal contraction of the +parts or about anisotropic material + + align:start position:0% +parts or about anisotropic material + + + align:start position:0% +parts or about anisotropic material +properties. + + align:start position:0% +properties. + + + align:start position:0% +properties. +So there you've got, you know, sizes are + + align:start position:0% +So there you've got, you know, sizes are + + + align:start position:0% +So there you've got, you know, sizes are +a continuous variable and the feature + + align:start position:0% +a continuous variable and the feature + + + align:start position:0% +a continuous variable and the feature +shape you might think of as being a + + align:start position:0% +shape you might think of as being a + + + align:start position:0% +shape you might think of as being a +discrete choice. When it comes to the + + align:start position:0% +discrete choice. When it comes to the + + + align:start position:0% +discrete choice. When it comes to the +the substrate + + align:start position:0% +the substrate + + + align:start position:0% +the substrate +itself, then uh you've got to decide on + + align:start position:0% +itself, then uh you've got to decide on + + + align:start position:0% +itself, then uh you've got to decide on +a material. various materials soften at + + align:start position:0% +a material. various materials soften at + + + align:start position:0% +a material. various materials soften at +different temperatures. Uh some of them + + align:start position:0% +different temperatures. Uh some of them + + + align:start position:0% +different temperatures. Uh some of them +uh exhibit a range of temperatures over + + align:start position:0% +uh exhibit a range of temperatures over + + + align:start position:0% +uh exhibit a range of temperatures over +which they behave rather like a rubber. + + align:start position:0% +which they behave rather like a rubber. + + + align:start position:0% +which they behave rather like a rubber. +Others don't really have much of a + + align:start position:0% +Others don't really have much of a + + + align:start position:0% +Others don't really have much of a +rubbery region. They just flow very + + align:start position:0% +rubbery region. They just flow very + + + align:start position:0% +rubbery region. They just flow very +easily as soon as you're above the glass + + align:start position:0% +easily as soon as you're above the glass + + + align:start position:0% +easily as soon as you're above the glass +transition temperature. So that's a + + align:start position:0% +transition temperature. So that's a + + + align:start position:0% +transition temperature. So that's a +decision that has to be made. And in + + align:start position:0% +decision that has to be made. And in + + + align:start position:0% +decision that has to be made. And in +micrombbossing, often you're you're + + align:start position:0% +micrombbossing, often you're you're + + + align:start position:0% +micrombbossing, often you're you're +picking between a variety of of + + align:start position:0% +picking between a variety of of + + + align:start position:0% +picking between a variety of of +off-the-shelf substrates, you know, + + align:start position:0% +off-the-shelf substrates, you know, + + + align:start position:0% +off-the-shelf substrates, you know, +PMMA, plexiglass, + + align:start position:0% +PMMA, plexiglass, + + + align:start position:0% +PMMA, plexiglass, +polycarbonate, materials like this + + align:start position:0% +polycarbonate, materials like this + + + align:start position:0% +polycarbonate, materials like this +where, you know, these are technical + + align:start position:0% +where, you know, these are technical + + + align:start position:0% +where, you know, these are technical +grade materials. Their their molecular + + align:start position:0% +grade materials. Their their molecular + + + align:start position:0% +grade materials. Their their molecular +weight, in other words, the the average + + align:start position:0% +weight, in other words, the the average + + + align:start position:0% +weight, in other words, the the average +length of the polymer chains is not + + align:start position:0% +length of the polymer chains is not + + + align:start position:0% +length of the polymer chains is not +necessarily well documented or well + + align:start position:0% +necessarily well documented or well + + + align:start position:0% +necessarily well documented or well +defined. So in that sense, your material + + align:start position:0% +defined. So in that sense, your material + + + align:start position:0% +defined. So in that sense, your material +choice might be a discrete decision. On + + align:start position:0% +choice might be a discrete decision. On + + + align:start position:0% +choice might be a discrete decision. On +the other hand, if you're spinning the + + align:start position:0% +the other hand, if you're spinning the + + + align:start position:0% +the other hand, if you're spinning the +polymer onto the wafer and you're + + align:start position:0% +polymer onto the wafer and you're + + + align:start position:0% +polymer onto the wafer and you're +dissolving it, then you do you do have + + align:start position:0% +dissolving it, then you do you do have + + + align:start position:0% +dissolving it, then you do you do have +the option of choosing the the molecular + + align:start position:0% +the option of choosing the the molecular + + + align:start position:0% +the option of choosing the the molecular +weight and therefore defining the + + align:start position:0% +weight and therefore defining the + + + align:start position:0% +weight and therefore defining the +viscosity as as essentially a continuous + + align:start position:0% +viscosity as as essentially a continuous + + + align:start position:0% +viscosity as as essentially a continuous +variable. So those are things that might + + align:start position:0% +variable. So those are things that might + + + align:start position:0% +variable. So those are things that might +need to be thought about and of course + + align:start position:0% +need to be thought about and of course + + + align:start position:0% +need to be thought about and of course +there's the thickness either how thickly + + align:start position:0% +there's the thickness either how thickly + + + align:start position:0% +there's the thickness either how thickly +do you spin this uh this resist on and + + align:start position:0% +do you spin this uh this resist on and + + + align:start position:0% +do you spin this uh this resist on and +that a lot of research in the field you + + align:start position:0% +that a lot of research in the field you + + + align:start position:0% +that a lot of research in the field you +know demonstrates + + align:start position:0% +know demonstrates + + + align:start position:0% +know demonstrates +uh the optimal thickness is a strong + + align:start position:0% +uh the optimal thickness is a strong + + + align:start position:0% +uh the optimal thickness is a strong +function of what pattern you're trying + + align:start position:0% +function of what pattern you're trying + + + align:start position:0% +function of what pattern you're trying +to emboss how many voids there are in + + align:start position:0% +to emboss how many voids there are in + + + align:start position:0% +to emboss how many voids there are in +the stamp. So the thickness of that + + align:start position:0% +the stamp. So the thickness of that + + + align:start position:0% +the stamp. So the thickness of that +might be important and also the + + align:start position:0% +might be important and also the + + + align:start position:0% +might be important and also the +thickness of the of in micro embossing + + align:start position:0% +thickness of the of in micro embossing + + + align:start position:0% +thickness of the of in micro embossing +where where the substrate is a + + align:start position:0% +where where the substrate is a + + + align:start position:0% +where where the substrate is a +millimeter thick say that's also a + + align:start position:0% +millimeter thick say that's also a + + + align:start position:0% +millimeter thick say that's also a +decision that has to be made. So and the + + align:start position:0% +decision that has to be made. So and the + + + align:start position:0% +decision that has to be made. So and the +third category of course is the process + + align:start position:0% +third category of course is the process + + + align:start position:0% +third category of course is the process +parameters the temperature pressure hold + + align:start position:0% +parameters the temperature pressure hold + + + align:start position:0% +parameters the temperature pressure hold +time and and and so forth. + + align:start position:0% + + + + align:start position:0% + +Now there's an awful lot of variables + + align:start position:0% +Now there's an awful lot of variables + + + align:start position:0% +Now there's an awful lot of variables +there and uh if one was to just take a + + align:start position:0% +there and uh if one was to just take a + + + align:start position:0% +there and uh if one was to just take a +purely empirical approach and uh try + + align:start position:0% +purely empirical approach and uh try + + + align:start position:0% +purely empirical approach and uh try +doing a a full factorial or a fractional + + align:start position:0% +doing a a full factorial or a fractional + + + align:start position:0% +doing a a full factorial or a fractional +factorial exploration of the space, it + + align:start position:0% +factorial exploration of the space, it + + + align:start position:0% +factorial exploration of the space, it +would it would start to look pretty + + align:start position:0% +would it would start to look pretty + + + align:start position:0% +would it would start to look pretty +pretty much like a nightmare. And uh + + align:start position:0% +pretty much like a nightmare. And uh + + + align:start position:0% +pretty much like a nightmare. And uh +luckily we don't have to uh stumble + + align:start position:0% +luckily we don't have to uh stumble + + + align:start position:0% +luckily we don't have to uh stumble +around in the dark because we do already + + align:start position:0% +around in the dark because we do already + + + align:start position:0% +around in the dark because we do already +have uh some reasonably good physical + + align:start position:0% +have uh some reasonably good physical + + + align:start position:0% +have uh some reasonably good physical +intuition about how these materials + + align:start position:0% +intuition about how these materials + + + align:start position:0% +intuition about how these materials +behave. And of course there's a + + align:start position:0% +behave. And of course there's a + + + align:start position:0% +behave. And of course there's a +huge research field to do with + + align:start position:0% +huge research field to do with + + + align:start position:0% +huge research field to do with +characterizing these bulk materials, + + align:start position:0% +characterizing these bulk materials, + + + align:start position:0% +characterizing these bulk materials, +building theoretical models of how they + + align:start position:0% +building theoretical models of how they + + + align:start position:0% +building theoretical models of how they +behave, fitting data to those models. + + align:start position:0% +behave, fitting data to those models. + + + align:start position:0% +behave, fitting data to those models. +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and I'm sure mechanical engineers here + + align:start position:0% +and I'm sure mechanical engineers here + + + align:start position:0% +and I'm sure mechanical engineers here +will be familiar with uh with this sort + + align:start position:0% +will be familiar with uh with this sort + + + align:start position:0% +will be familiar with uh with this sort +of way of describing uh describing + + align:start position:0% +of way of describing uh describing + + + align:start position:0% +of way of describing uh describing +polymers in a simplified manner + + align:start position:0% +polymers in a simplified manner + + + align:start position:0% +polymers in a simplified manner +um where you + + align:start position:0% +um where you + + + align:start position:0% +um where you +uh you build up a model in this case + + align:start position:0% +uh you build up a model in this case + + + align:start position:0% +uh you build up a model in this case +this is a one-dimensional model that + + align:start position:0% +this is a one-dimensional model that + + + align:start position:0% +this is a one-dimensional model that +sums up the visco elastic behavior of + + align:start position:0% +sums up the visco elastic behavior of + + + align:start position:0% +sums up the visco elastic behavior of +the polymer using a combination of of + + align:start position:0% +the polymer using a combination of of + + + align:start position:0% +the polymer using a combination of of +springs, elastic non-disipative elements + + align:start position:0% +springs, elastic non-disipative elements + + + align:start position:0% +springs, elastic non-disipative elements +and and uh these these elements here + + align:start position:0% +and and uh these these elements here + + + align:start position:0% +and and uh these these elements here +dash pots which are essentially viscous + + align:start position:0% +dash pots which are essentially viscous + + + align:start position:0% +dash pots which are essentially viscous +components and damp. Yes, exactly. They + + align:start position:0% +components and damp. Yes, exactly. They + + + align:start position:0% +components and damp. Yes, exactly. They +dissipate they dissipate energy. So the + + align:start position:0% +dissipate they dissipate energy. So the + + + align:start position:0% +dissipate they dissipate energy. So the +the various stiffnesses and uh and and + + align:start position:0% +the various stiffnesses and uh and and + + + align:start position:0% +the various stiffnesses and uh and and +dissipation factors for the for the + + align:start position:0% +dissipation factors for the for the + + + align:start position:0% +dissipation factors for the for the +springs and dashbots um may be nonlinear + + align:start position:0% +springs and dashbots um may be nonlinear + + + align:start position:0% +springs and dashbots um may be nonlinear +functions of temperature. They may be + + align:start position:0% +functions of temperature. They may be + + + align:start position:0% +functions of temperature. They may be +nonlinear functions of strain rate and + + align:start position:0% +nonlinear functions of strain rate and + + + align:start position:0% +nonlinear functions of strain rate and +in fact almost always are and uh so you + + align:start position:0% +in fact almost always are and uh so you + + + align:start position:0% +in fact almost always are and uh so you +know there are many thesis that have + + align:start position:0% +know there are many thesis that have + + + align:start position:0% +know there are many thesis that have +been written trying to trying to + + align:start position:0% +been written trying to trying to + + + align:start position:0% +been written trying to trying to +characterize these materials. So and and + + align:start position:0% +characterize these materials. So and and + + + align:start position:0% +characterize these materials. So and and +and building on those uh those + + align:start position:0% +and building on those uh those + + + align:start position:0% +and building on those uh those +experimental approaches are simulation + + align:start position:0% +experimental approaches are simulation + + + align:start position:0% +experimental approaches are simulation +models. There are finite element + + align:start position:0% +models. There are finite element + + + align:start position:0% +models. There are finite element +uh models of these polymers that have + + align:start position:0% +uh models of these polymers that have + + + align:start position:0% +uh models of these polymers that have +been that have been lovingly built up. + + align:start position:0% +been that have been lovingly built up. + + + align:start position:0% +been that have been lovingly built up. +And so with enough information about the + + align:start position:0% +And so with enough information about the + + + align:start position:0% +And so with enough information about the +polymer uh with a detailed model of the + + align:start position:0% +polymer uh with a detailed model of the + + + align:start position:0% +polymer uh with a detailed model of the +stamp that you were thinking of + + align:start position:0% +stamp that you were thinking of + + + align:start position:0% +stamp that you were thinking of +embossing and knowing something about + + align:start position:0% +embossing and knowing something about + + + align:start position:0% +embossing and knowing something about +the dimensional tolerances of the + + align:start position:0% +the dimensional tolerances of the + + + align:start position:0% +the dimensional tolerances of the +machine you have, you could uh you could + + align:start position:0% +machine you have, you could uh you could + + + align:start position:0% +machine you have, you could uh you could +do a simulation and + + align:start position:0% +do a simulation and + + + align:start position:0% +do a simulation and +and perhaps predict what was going to + + align:start position:0% +and perhaps predict what was going to + + + align:start position:0% +and perhaps predict what was going to +happen. The trouble is it would probably + + align:start position:0% +happen. The trouble is it would probably + + + align:start position:0% +happen. The trouble is it would probably +take years + + align:start position:0% +take years + + + align:start position:0% +take years +because when you start having microscale + + align:start position:0% +because when you start having microscale + + + align:start position:0% +because when you start having microscale +patterns that you're trying to emboss + + align:start position:0% +patterns that you're trying to emboss + + + align:start position:0% +patterns that you're trying to emboss +um the computational burden of using + + align:start position:0% +um the computational burden of using + + + align:start position:0% +um the computational burden of using +these full nonlinear finite defamation + + align:start position:0% +these full nonlinear finite defamation + + + align:start position:0% +these full nonlinear finite defamation +polymer models becomes immense and + + align:start position:0% +polymer models becomes immense and + + + align:start position:0% +polymer models becomes immense and +that's great if you have one particular + + align:start position:0% +that's great if you have one particular + + + align:start position:0% +that's great if you have one particular +device that absolutely must be perfect. + + align:start position:0% +device that absolutely must be perfect. + + + align:start position:0% +device that absolutely must be perfect. +However, what we're interested in doing + + align:start position:0% +However, what we're interested in doing + + + align:start position:0% +However, what we're interested in doing +in our research is finding some sort of + + align:start position:0% +in our research is finding some sort of + + + align:start position:0% +in our research is finding some sort of +middle ground between the empirical + + align:start position:0% +middle ground between the empirical + + + align:start position:0% +middle ground between the empirical +approach and the really rigorous, + + align:start position:0% +approach and the really rigorous, + + + align:start position:0% +approach and the really rigorous, +thorough uh theoretical approach that's + + align:start position:0% +thorough uh theoretical approach that's + + + align:start position:0% +thorough uh theoretical approach that's +that's based on a on a highly controlled + + align:start position:0% +that's based on a on a highly controlled + + + align:start position:0% +that's based on a on a highly controlled +set of experiments. And um so the idea + + align:start position:0% +set of experiments. And um so the idea + + + align:start position:0% +set of experiments. And um so the idea +is to find approximate descriptions for + + align:start position:0% +is to find approximate descriptions for + + + align:start position:0% +is to find approximate descriptions for +the + + align:start position:0% +the + + + align:start position:0% +the +material that are efficient to to run + + align:start position:0% +material that are efficient to to run + + + align:start position:0% +material that are efficient to to run +efficient to + + align:start position:0% +efficient to + + + align:start position:0% +efficient to +simulate patterns wafers that have + + align:start position:0% +simulate patterns wafers that have + + + align:start position:0% +simulate patterns wafers that have +thousands of features across them. + + align:start position:0% +thousands of features across them. + + + align:start position:0% +thousands of features across them. +So um let's start to think about how we + + align:start position:0% +So um let's start to think about how we + + + align:start position:0% +So um let's start to think about how we +can uh how we can build out the bare + + align:start position:0% +can uh how we can build out the bare + + + align:start position:0% +can uh how we can build out the bare +bones of a model that are going to + + align:start position:0% +bones of a model that are going to + + + align:start position:0% +bones of a model that are going to +inform the experiments that we do about + + align:start position:0% +inform the experiments that we do about + + + align:start position:0% +inform the experiments that we do about +this uh about this embossing process. + + align:start position:0% +this uh about this embossing process. + + + align:start position:0% +this uh about this embossing process. +Now what I've done here and this uh I I + + align:start position:0% +Now what I've done here and this uh I I + + + align:start position:0% +Now what I've done here and this uh I I +I won't go into laborious detail about + + align:start position:0% +I won't go into laborious detail about + + + align:start position:0% +I won't go into laborious detail about +but essentially this is just building + + align:start position:0% +but essentially this is just building + + + align:start position:0% +but essentially this is just building +intuition about one particular polymer. + + align:start position:0% +intuition about one particular polymer. + + + align:start position:0% +intuition about one particular polymer. +This this is uh a model for polymethyl + + align:start position:0% +This this is uh a model for polymethyl + + + align:start position:0% +This this is uh a model for polymethyl +methacrylate plexiglass acrylic call it + + align:start position:0% +methacrylate plexiglass acrylic call it + + + align:start position:0% +methacrylate plexiglass acrylic call it +what you will which uh student at MIT + + align:start position:0% +what you will which uh student at MIT + + + align:start position:0% +what you will which uh student at MIT +has recently written a thesis about + + align:start position:0% +has recently written a thesis about + + + align:start position:0% +has recently written a thesis about +doing compression experiments of it + + align:start position:0% +doing compression experiments of it + + + align:start position:0% +doing compression experiments of it +building up a highly faithful model of + + align:start position:0% +building up a highly faithful model of + + + align:start position:0% +building up a highly faithful model of +it. But there's there's a there's a + + align:start position:0% +it. But there's there's a there's a + + + align:start position:0% +it. But there's there's a there's a +one-dimensional implementation of that + + align:start position:0% +one-dimensional implementation of that + + + align:start position:0% +one-dimensional implementation of that +model that we can run. we can look at + + align:start position:0% +model that we can run. we can look at + + + align:start position:0% +model that we can run. we can look at +what happens when you give it various + + align:start position:0% +what happens when you give it various + + + align:start position:0% +what happens when you give it various +load profiles over time and look at the + + align:start position:0% +load profiles over time and look at the + + + align:start position:0% +load profiles over time and look at the +uh the stresses and and the strains in + + align:start position:0% +uh the stresses and and the strains in + + + align:start position:0% +uh the stresses and and the strains in +each of those components of the model + + align:start position:0% +each of those components of the model + + + align:start position:0% +each of those components of the model +over + + align:start position:0% +over + + + align:start position:0% +over +time. + + align:start position:0% +time. + + + align:start position:0% +time. +So what I've done here is I've just done + + align:start position:0% +So what I've done here is I've just done + + + align:start position:0% +So what I've done here is I've just done +two well essentially thought + + align:start position:0% +two well essentially thought + + + align:start position:0% +two well essentially thought +experiments. The left hand column of + + align:start position:0% +experiments. The left hand column of + + + align:start position:0% +experiments. The left hand column of +um of graphs shows what happens if the + + align:start position:0% +um of graphs shows what happens if the + + + align:start position:0% +um of graphs shows what happens if the +material is heated above its glass + + align:start position:0% +material is heated above its glass + + + align:start position:0% +material is heated above its glass +transition temperature and then uh given + + align:start position:0% +transition temperature and then uh given + + + align:start position:0% +transition temperature and then uh given +uh 1 and a half megapascal compressive + + align:start position:0% +uh 1 and a half megapascal compressive + + + align:start position:0% +uh 1 and a half megapascal compressive +load which is held for 10 + + align:start position:0% +load which is held for 10 + + + align:start position:0% +load which is held for 10 +seconds that load is maintained while + + align:start position:0% +seconds that load is maintained while + + + align:start position:0% +seconds that load is maintained while +the temperature is reduced below glass + + align:start position:0% +the temperature is reduced below glass + + + align:start position:0% +the temperature is reduced below glass +transition. + + align:start position:0% +transition. + + + align:start position:0% +transition. +glass transition here is about 105 + + align:start position:0% +glass transition here is about 105 + + + align:start position:0% +glass transition here is about 105 +degrees C. + + align:start position:0% +degrees C. + + + align:start position:0% +degrees C. +So then we looked at how the model + + align:start position:0% +So then we looked at how the model + + + align:start position:0% +So then we looked at how the model +responded to that. There's a there's a + + align:start position:0% +responded to that. There's a there's a + + + align:start position:0% +responded to that. There's a there's a +compressive strain of course there are + + align:start position:0% +compressive strain of course there are + + + align:start position:0% +compressive strain of course there are +stresses built up in the left hand + + align:start position:0% +stresses built up in the left hand + + + align:start position:0% +stresses built up in the left hand +branch of that model this spring and + + align:start position:0% +branch of that model this spring and + + + align:start position:0% +branch of that model this spring and +this dashboard and there are stresses in + + align:start position:0% +this dashboard and there are stresses in + + + align:start position:0% +this dashboard and there are stresses in +the right hand side as well. And um + + align:start position:0% +the right hand side as well. And um + + + align:start position:0% +the right hand side as well. And um +essentially what this shows is that most + + align:start position:0% +essentially what this shows is that most + + + align:start position:0% +essentially what this shows is that most +of the defamation is frozen in place + + align:start position:0% +of the defamation is frozen in place + + + align:start position:0% +of the defamation is frozen in place +frozen by by this cooling below glass + + align:start position:0% +frozen by by this cooling below glass + + + align:start position:0% +frozen by by this cooling below glass +transition. So when the load is removed, + + align:start position:0% +transition. So when the load is removed, + + + align:start position:0% +transition. So when the load is removed, +this amount of strain remains this P + + align:start position:0% +this amount of strain remains this P + + + align:start position:0% +this amount of strain remains this P +amount here. + + align:start position:0% +amount here. + + + align:start position:0% +amount here. +However, if you uh if you don't cool + + align:start position:0% +However, if you uh if you don't cool + + + align:start position:0% +However, if you uh if you don't cool +down before you remove the load and + + align:start position:0% +down before you remove the load and + + + align:start position:0% +down before you remove the load and +that's what is shown on the right, then + + align:start position:0% +that's what is shown on the right, then + + + align:start position:0% +that's what is shown on the right, then +we see this recovery. We see we see the + + align:start position:0% +we see this recovery. We see we see the + + + align:start position:0% +we see this recovery. We see we see the +material springing back almost to its + + align:start position:0% +material springing back almost to its + + + align:start position:0% +material springing back almost to its +original shape. And uh so there's a very + + align:start position:0% +original shape. And uh so there's a very + + + align:start position:0% +original shape. And uh so there's a very +small residual compressive strain in + + align:start position:0% +small residual compressive strain in + + + align:start position:0% +small residual compressive strain in +that case. and just looking at a + + align:start position:0% +that case. and just looking at a + + + align:start position:0% +that case. and just looking at a +distance from a distance at at at this + + align:start position:0% +distance from a distance at at at this + + + align:start position:0% +distance from a distance at at at this +simulation which is done at a particular + + align:start position:0% +simulation which is done at a particular + + + align:start position:0% +simulation which is done at a particular +temperature 140° C. Um essentially that + + align:start position:0% +temperature 140° C. Um essentially that + + + align:start position:0% +temperature 140° C. Um essentially that +the material is behaving in a in in a + + align:start position:0% +the material is behaving in a in in a + + + align:start position:0% +the material is behaving in a in in a +spring-like way predominantly. Most of + + align:start position:0% +spring-like way predominantly. Most of + + + align:start position:0% +spring-like way predominantly. Most of +the defamation is recovered without + + align:start position:0% +the defamation is recovered without + + + align:start position:0% +the defamation is recovered without +cooling it to freeze that that + + align:start position:0% +cooling it to freeze that that + + + align:start position:0% +cooling it to freeze that that +defamation in place. And uh you could + + align:start position:0% +defamation in place. And uh you could + + + align:start position:0% +defamation in place. And uh you could +you could run similar thought + + align:start position:0% +you could run similar thought + + + align:start position:0% +you could run similar thought +experiments at different temperatures, + + align:start position:0% +experiments at different temperatures, + + + align:start position:0% +experiments at different temperatures, +different strain rates with the model + + align:start position:0% +different strain rates with the model + + + align:start position:0% +different strain rates with the model +and uh and get an impression of how much + + align:start position:0% +and uh and get an impression of how much + + + align:start position:0% +and uh and get an impression of how much +of that defamation is recovered uh when + + align:start position:0% +of that defamation is recovered uh when + + + align:start position:0% +of that defamation is recovered uh when +the temperature is kept at its elevated + + align:start position:0% +the temperature is kept at its elevated + + + align:start position:0% +the temperature is kept at its elevated +level when you remove the load. And so + + align:start position:0% +level when you remove the load. And so + + + align:start position:0% +level when you remove the load. And so +loosely + + align:start position:0% +loosely + + + align:start position:0% +loosely +speaking, if most of the defamation is + + align:start position:0% +speaking, if most of the defamation is + + + align:start position:0% +speaking, if most of the defamation is +recovered at high temperature, we would + + align:start position:0% +recovered at high temperature, we would + + + align:start position:0% +recovered at high temperature, we would +describe the material as being rubbery + + align:start position:0% +describe the material as being rubbery + + + align:start position:0% +describe the material as being rubbery +over here. This is a this is a plot + + align:start position:0% +over here. This is a this is a plot + + + align:start position:0% +over here. This is a this is a plot +essentially of the ratio of that strain + + align:start position:0% +essentially of the ratio of that strain + + + align:start position:0% +essentially of the ratio of that strain +to that strain P over Q. Uh as a + + align:start position:0% +to that strain P over Q. Uh as a + + + align:start position:0% +to that strain P over Q. Uh as a +function of temperature and peak + + align:start position:0% +function of temperature and peak + + + align:start position:0% +function of temperature and peak +compressive + + align:start position:0% +compressive + + + align:start position:0% +compressive +stress. If if that ratio is large, we + + align:start position:0% +stress. If if that ratio is large, we + + + align:start position:0% +stress. If if that ratio is large, we +call it rubbery. If the if the ratio is + + align:start position:0% +call it rubbery. If the if the ratio is + + + align:start position:0% +call it rubbery. If the if the ratio is +small, in other words, if there's been a + + align:start position:0% +small, in other words, if there's been a + + + align:start position:0% +small, in other words, if there's been a +lot of plastic defamation uh that + + align:start position:0% +lot of plastic defamation uh that + + + align:start position:0% +lot of plastic defamation uh that +doesn't spring back upon unloading, then + + align:start position:0% +doesn't spring back upon unloading, then + + + align:start position:0% +doesn't spring back upon unloading, then +we would we would we would sort of + + align:start position:0% +we would we would we would sort of + + + align:start position:0% +we would we would we would sort of +classify the material as as being in a + + align:start position:0% +classify the material as as being in a + + + align:start position:0% +classify the material as as being in a +glassy state. And sometimes glassy is + + align:start position:0% +glassy state. And sometimes glassy is + + + align:start position:0% +glassy state. And sometimes glassy is +useful to you, sometimes rubbery is + + align:start position:0% +useful to you, sometimes rubbery is + + + align:start position:0% +useful to you, sometimes rubbery is +preferable. So um in any case this sort + + align:start position:0% +preferable. So um in any case this sort + + + align:start position:0% +preferable. So um in any case this sort +of uh intuition building is helpful to + + align:start position:0% +of uh intuition building is helpful to + + + align:start position:0% +of uh intuition building is helpful to +us in that uh it it begins to give us a + + align:start position:0% +us in that uh it it begins to give us a + + + align:start position:0% +us in that uh it it begins to give us a +starting point for for a a physical + + align:start position:0% +starting point for for a a physical + + + align:start position:0% +starting point for for a a physical +model that that will let us choose what + + align:start position:0% +model that that will let us choose what + + + align:start position:0% +model that that will let us choose what +experiments we're going to do uh and + + align:start position:0% +experiments we're going to do uh and + + + align:start position:0% +experiments we're going to do uh and +will let us build quick efficient + + align:start position:0% +will let us build quick efficient + + + align:start position:0% +will let us build quick efficient +simulations. And and so for + + align:start position:0% +simulations. And and so for + + + align:start position:0% +simulations. And and so for +that particular temperature that that + + align:start position:0% +that particular temperature that that + + + align:start position:0% +that particular temperature that that +that I looked at in detail, if you + + align:start position:0% +that I looked at in detail, if you + + + align:start position:0% +that I looked at in detail, if you +wanted the simplest possible model of + + align:start position:0% +wanted the simplest possible model of + + + align:start position:0% +wanted the simplest possible model of +the polymer, you might just think of + + align:start position:0% +the polymer, you might just think of + + + align:start position:0% +the polymer, you might just think of +making making the model a linear elastic + + align:start position:0% +making making the model a linear elastic + + + align:start position:0% +making making the model a linear elastic +model that where the Young's modulus was + + align:start position:0% +model that where the Young's modulus was + + + align:start position:0% +model that where the Young's modulus was +a function of temperature. And there are + + align:start position:0% +a function of temperature. And there are + + + align:start position:0% +a function of temperature. And there are +many shortcomings of that. Um if you + + align:start position:0% +many shortcomings of that. Um if you + + + align:start position:0% +many shortcomings of that. Um if you +hold the load for long enough, then + + align:start position:0% +hold the load for long enough, then + + + align:start position:0% +hold the load for long enough, then +there will of course be plastic flow + + align:start position:0% +there will of course be plastic flow + + + align:start position:0% +there will of course be plastic flow +that's permanent. um and and uh the + + align:start position:0% +that's permanent. um and and uh the + + + align:start position:0% +that's permanent. um and and uh the +material is not linear elastic. It + + align:start position:0% +material is not linear elastic. It + + + align:start position:0% +material is not linear elastic. It +changes its stiffness as the strain + + align:start position:0% +changes its stiffness as the strain + + + align:start position:0% +changes its stiffness as the strain +increases. + + align:start position:0% +increases. + + + align:start position:0% +increases. +But we might as well start simple and + + align:start position:0% +But we might as well start simple and + + + align:start position:0% +But we might as well start simple and +see if it works. Gives us information + + align:start position:0% +see if it works. Gives us information + + + align:start position:0% +see if it works. Gives us information +about what types of features replicate + + align:start position:0% +about what types of features replicate + + + align:start position:0% +about what types of features replicate +and what do not. So that's what we uh we + + align:start position:0% +and what do not. So that's what we uh we + + + align:start position:0% +and what do not. So that's what we uh we +initially started with. And + + align:start position:0% +initially started with. And + + + align:start position:0% +initially started with. And +uh the idea is that increasing the + + align:start position:0% +uh the idea is that increasing the + + + align:start position:0% +uh the idea is that increasing the +temperature reduces that modulus by + + align:start position:0% +temperature reduces that modulus by + + + align:start position:0% +temperature reduces that modulus by +three or four orders of magnitude. + + align:start position:0% +three or four orders of magnitude. + + + align:start position:0% +three or four orders of magnitude. +uh we form the shape, then we cool down + + align:start position:0% +uh we form the shape, then we cool down + + + align:start position:0% +uh we form the shape, then we cool down +to freeze that topography in + + align:start position:0% +to freeze that topography in + + + align:start position:0% +to freeze that topography in +place. And + + align:start position:0% +place. And + + + align:start position:0% +place. And +uh what this is going to let us do is + + align:start position:0% +uh what this is going to let us do is + + + align:start position:0% +uh what this is going to let us do is +predict for an arbitrary stamp design uh + + align:start position:0% +predict for an arbitrary stamp design uh + + + align:start position:0% +predict for an arbitrary stamp design uh +what the shape of the uh the embossed + + align:start position:0% +what the shape of the uh the embossed + + + align:start position:0% +what the shape of the uh the embossed +part will be, what its surface + + align:start position:0% +part will be, what its surface + + + align:start position:0% +part will be, what its surface +topography will be for a chosen + + align:start position:0% +topography will be for a chosen + + + align:start position:0% +topography will be for a chosen +temperature and pressure. + + align:start position:0% +temperature and pressure. + + + align:start position:0% +temperature and pressure. +uh for embossing and + + align:start position:0% +uh for embossing and + + + align:start position:0% +uh for embossing and +uh here's the computational approach + + align:start position:0% +uh here's the computational approach + + + align:start position:0% +uh here's the computational approach +that we we decided upon and and this is + + align:start position:0% +that we we decided upon and and this is + + + align:start position:0% +that we we decided upon and and this is +um really quick to run. The idea is that + + align:start position:0% +um really quick to run. The idea is that + + + align:start position:0% +um really quick to run. The idea is that +we we want to describe how the surface + + align:start position:0% +we we want to describe how the surface + + + align:start position:0% +we we want to describe how the surface +of the material responds to a point + + align:start position:0% +of the material responds to a point + + + align:start position:0% +of the material responds to a point +load. And uh if the material were linear + + align:start position:0% +load. And uh if the material were linear + + + align:start position:0% +load. And uh if the material were linear +elastic and if it were uh substantially + + align:start position:0% +elastic and if it were uh substantially + + + align:start position:0% +elastic and if it were uh substantially +thicker than uh the uh the dimensions of + + align:start position:0% +thicker than uh the uh the dimensions of + + + align:start position:0% +thicker than uh the uh the dimensions of +the features of interest, then the + + align:start position:0% +the features of interest, then the + + + align:start position:0% +the features of interest, then the +topography in response to a point load + + align:start position:0% +topography in response to a point load + + + align:start position:0% +topography in response to a point load +would um effectively go as one over the + + align:start position:0% +would um effectively go as one over the + + + align:start position:0% +would um effectively go as one over the +radial distance from the the point where + + align:start position:0% +radial distance from the the point where + + + align:start position:0% +radial distance from the the point where +the load is applied. And that's a a + + align:start position:0% +the load is applied. And that's a a + + + align:start position:0% +the load is applied. And that's a a +standard contact mechanics result. + + align:start position:0% +standard contact mechanics result. + + + align:start position:0% +standard contact mechanics result. +But we're talking about computing uh + + align:start position:0% +But we're talking about computing uh + + + align:start position:0% +But we're talking about computing uh +computing + + align:start position:0% +computing + + + align:start position:0% +computing +approximate topographies and this is + + align:start position:0% +approximate topographies and this is + + + align:start position:0% +approximate topographies and this is +going to be done in a discretized way + + align:start position:0% +going to be done in a discretized way + + + align:start position:0% +going to be done in a discretized way +where we split the surface of the of the + + align:start position:0% +where we split the surface of the of the + + + align:start position:0% +where we split the surface of the of the +of the polymer into series of square + + align:start position:0% +of the polymer into series of square + + + align:start position:0% +of the polymer into series of square +elements. So we can uh we can translate + + align:start position:0% +elements. So we can uh we can translate + + + align:start position:0% +elements. So we can uh we can translate +this point load response into the + + align:start position:0% +this point load response into the + + + align:start position:0% +this point load response into the +response of the surface to unit pressure + + align:start position:0% +response of the surface to unit pressure + + + align:start position:0% +response of the surface to unit pressure +applied in a in over one element of our + + align:start position:0% +applied in a in over one element of our + + + align:start position:0% +applied in a in over one element of our +discretized surface. So this this is a + + align:start position:0% +discretized surface. So this this is a + + + align:start position:0% +discretized surface. So this this is a +the plane of the surface of the wafer, + + align:start position:0% +the plane of the surface of the wafer, + + + align:start position:0% +the plane of the surface of the wafer, +the surface of the the polymer, and + + align:start position:0% +the surface of the the polymer, and + + + align:start position:0% +the surface of the the polymer, and +we're trying to express how far that + + align:start position:0% +we're trying to express how far that + + + align:start position:0% +we're trying to express how far that +part of the surface goes down when you + + align:start position:0% +part of the surface goes down when you + + + align:start position:0% +part of the surface goes down when you +apply unit pressure here. And uh that's + + align:start position:0% +apply unit pressure here. And uh that's + + + align:start position:0% +apply unit pressure here. And uh that's +the + + align:start position:0% +the + + + align:start position:0% +the +answer. So we uh we tried this uh with + + align:start position:0% +answer. So we uh we tried this uh with + + + align:start position:0% +answer. So we uh we tried this uh with +some very simple geometries, lots of + + align:start position:0% +some very simple geometries, lots of + + + align:start position:0% +some very simple geometries, lots of +parallel channels that we had etched + + align:start position:0% +parallel channels that we had etched + + + align:start position:0% +parallel channels that we had etched +into into silicon. uh they they were + + align:start position:0% +into into silicon. uh they they were + + + align:start position:0% +into into silicon. uh they they were +about 20 microns deep and uh the these + + align:start position:0% +about 20 microns deep and uh the these + + + align:start position:0% +about 20 microns deep and uh the these +these silicon channels and on the order + + align:start position:0% +these silicon channels and on the order + + + align:start position:0% +these silicon channels and on the order +of 120 microns in in + + align:start position:0% +of 120 microns in in + + + align:start position:0% +of 120 microns in in +pitch. There are many channels going in + + align:start position:0% +pitch. There are many channels going in + + + align:start position:0% +pitch. There are many channels going in +uh AC across uh the screen. But what + + align:start position:0% +uh AC across uh the screen. But what + + + align:start position:0% +uh AC across uh the screen. But what +what we show here is on the left + + align:start position:0% +what we show here is on the left + + + align:start position:0% +what we show here is on the left +scanning electron microraphs of uh + + align:start position:0% +scanning electron microraphs of uh + + + align:start position:0% +scanning electron microraphs of uh +cross-sections through those embossed + + align:start position:0% +cross-sections through those embossed + + + align:start position:0% +cross-sections through those embossed +structures where a variety of different + + align:start position:0% +structures where a variety of different + + + align:start position:0% +structures where a variety of different +loads have been applied and the loads + + align:start position:0% +loads have been applied and the loads + + + align:start position:0% +loads have been applied and the loads +were held for less than a minute. So + + align:start position:0% +were held for less than a minute. So + + + align:start position:0% +were held for less than a minute. So +it's our working assumption here that + + align:start position:0% +it's our working assumption here that + + + align:start position:0% +it's our working assumption here that +all the defamation was to do with the + + align:start position:0% +all the defamation was to do with the + + + align:start position:0% +all the defamation was to do with the +with the rubbery behavior of the + + align:start position:0% +with the rubbery behavior of the + + + align:start position:0% +with the rubbery behavior of the +material and there wasn't really enough + + align:start position:0% +material and there wasn't really enough + + + align:start position:0% +material and there wasn't really enough +time for plastic flow to occur. So we're + + align:start position:0% +time for plastic flow to occur. So we're + + + align:start position:0% +time for plastic flow to occur. So we're +just using our zeroth order model to uh + + align:start position:0% +just using our zeroth order model to uh + + + align:start position:0% +just using our zeroth order model to uh +to to figure out what the Young's + + align:start position:0% +to to figure out what the Young's + + + align:start position:0% +to to figure out what the Young's +modulus of the material was. Essentially + + align:start position:0% +modulus of the material was. Essentially + + + align:start position:0% +modulus of the material was. Essentially +there's one parameter that we fit uh in + + align:start position:0% +there's one parameter that we fit uh in + + + align:start position:0% +there's one parameter that we fit uh in +doing the simulation and that is the + + align:start position:0% +doing the simulation and that is the + + + align:start position:0% +doing the simulation and that is the +Young's modulus. Here are simulations + + align:start position:0% +Young's modulus. Here are simulations + + + align:start position:0% +Young's modulus. Here are simulations +done using that model. So we're roughly + + align:start position:0% +done using that model. So we're roughly + + + align:start position:0% +done using that model. So we're roughly +capturing the uh the shape and it seems + + align:start position:0% +capturing the uh the shape and it seems + + + align:start position:0% +capturing the uh the shape and it seems +to all stack up if we choose this + + align:start position:0% +to all stack up if we choose this + + + align:start position:0% +to all stack up if we choose this +Young's modulus 5 megapascals at 130° + + align:start position:0% +Young's modulus 5 megapascals at 130° + + + align:start position:0% +Young's modulus 5 megapascals at 130° +C. So that's all very well but you know + + align:start position:0% +C. So that's all very well but you know + + + align:start position:0% +C. So that's all very well but you know +having these parallel channels doesn't + + align:start position:0% +having these parallel channels doesn't + + + align:start position:0% +having these parallel channels doesn't +give us too much information for a given + + align:start position:0% +give us too much information for a given + + + align:start position:0% +give us too much information for a given +experiment. So + + align:start position:0% +experiment. So + + + align:start position:0% +experiment. So +uh we had to think quite carefully about + + align:start position:0% +uh we had to think quite carefully about + + + align:start position:0% +uh we had to think quite carefully about +what type of characterization patterns + + align:start position:0% +what type of characterization patterns + + + align:start position:0% +what type of characterization patterns +to use in these these experiments. We're + + align:start position:0% +to use in these these experiments. We're + + + align:start position:0% +to use in these these experiments. We're +trying to think of ways of doing a + + align:start position:0% +trying to think of ways of doing a + + + align:start position:0% +trying to think of ways of doing a +minimal number of experiments that will + + align:start position:0% +minimal number of experiments that will + + + align:start position:0% +minimal number of experiments that will +give us as much physical information as + + align:start position:0% +give us as much physical information as + + + align:start position:0% +give us as much physical information as +possible. And and what we came up with + + align:start position:0% +possible. And and what we came up with + + + align:start position:0% +possible. And and what we came up with +with was this. Here is a a a plan of the + + align:start position:0% +with was this. Here is a a a plan of the + + + align:start position:0% +with was this. Here is a a a plan of the +surface of a silicon stamp that we + + align:start position:0% +surface of a silicon stamp that we + + + align:start position:0% +surface of a silicon stamp that we +etched. And + + align:start position:0% +etched. And + + + align:start position:0% +etched. And +uh it's a square array of uh various + + align:start position:0% +uh it's a square array of uh various + + + align:start position:0% +uh it's a square array of uh various +patches of features. Some of them are + + align:start position:0% +patches of features. Some of them are + + + align:start position:0% +patches of features. Some of them are +parallel channels, some of them are + + align:start position:0% +parallel channels, some of them are + + + align:start position:0% +parallel channels, some of them are +square holes. And uh we have parallel + + align:start position:0% +square holes. And uh we have parallel + + + align:start position:0% +square holes. And uh we have parallel +channels running in both directions. So + + align:start position:0% +channels running in both directions. So + + + align:start position:0% +channels running in both directions. So +for every line to space ratio of + + align:start position:0% +for every line to space ratio of + + + align:start position:0% +for every line to space ratio of +channels, there's one set running + + align:start position:0% +channels, there's one set running + + + align:start position:0% +channels, there's one set running +horizontally somewhere, one set running + + align:start position:0% +horizontally somewhere, one set running + + + align:start position:0% +horizontally somewhere, one set running +vertically. and that they they were + + align:start position:0% +vertically. and that they they were + + + align:start position:0% +vertically. and that they they were +arranged in a random order across the + + align:start position:0% +arranged in a random order across the + + + align:start position:0% +arranged in a random order across the +across the stamp. + + align:start position:0% + + + + align:start position:0% + +Now uh there's one twist to this which + + align:start position:0% +Now uh there's one twist to this which + + + align:start position:0% +Now uh there's one twist to this which +is + + align:start position:0% +is + + + align:start position:0% +is +that because we do our simulation using + + align:start position:0% +that because we do our simulation using + + + align:start position:0% +that because we do our simulation using +uh a discrete FA transform a fast fora + + align:start position:0% +uh a discrete FA transform a fast fora + + + align:start position:0% +uh a discrete FA transform a fast fora +transform the representation of + + align:start position:0% +transform the representation of + + + align:start position:0% +transform the representation of +the space that we're simulating is + + align:start position:0% +the space that we're simulating is + + + align:start position:0% +the space that we're simulating is +assumed to be periodic in space. Um + + align:start position:0% +assumed to be periodic in space. Um + + + align:start position:0% +assumed to be periodic in space. Um +so we uh accommodate that by actually + + align:start position:0% +so we uh accommodate that by actually + + + align:start position:0% +so we uh accommodate that by actually +making the pattern + + align:start position:0% + + + + align:start position:0% + +periodic. What I show here is uh is one + + align:start position:0% +periodic. What I show here is uh is one + + + align:start position:0% +periodic. What I show here is uh is one +one rep one one replicate of the pattern + + align:start position:0% +one rep one one replicate of the pattern + + + align:start position:0% +one rep one one replicate of the pattern +and this is about uh 4 mm in diameter. + + align:start position:0% +and this is about uh 4 mm in diameter. + + + align:start position:0% +and this is about uh 4 mm in diameter. +But in fact what we do is we + + align:start position:0% +But in fact what we do is we + + + align:start position:0% +But in fact what we do is we +have I suppose on the stamp we have a + + align:start position:0% +have I suppose on the stamp we have a + + + align:start position:0% +have I suppose on the stamp we have a +3x3 + + align:start position:0% +3x3 + + + align:start position:0% +3x3 +array where + + align:start position:0% +array where + + + align:start position:0% +array where +um where what I've shown on the screen + + align:start position:0% +um where what I've shown on the screen + + + align:start position:0% +um where what I've shown on the screen +is contained in this region. So it's + + align:start position:0% +is contained in this region. So it's + + + align:start position:0% +is contained in this region. So it's +pseudo periodic from the point of view + + align:start position:0% +pseudo periodic from the point of view + + + align:start position:0% +pseudo periodic from the point of view +of the material surrounding it. The + + align:start position:0% +of the material surrounding it. The + + + align:start position:0% +of the material surrounding it. The +material is a millimeter thick. This is + + align:start position:0% +material is a millimeter thick. This is + + + align:start position:0% +material is a millimeter thick. This is +4 mm. And uh so what's going on at the + + align:start position:0% +4 mm. And uh so what's going on at the + + + align:start position:0% +4 mm. And uh so what's going on at the +edge here uh looks exactly the same to + + align:start position:0% +edge here uh looks exactly the same to + + + align:start position:0% +edge here uh looks exactly the same to +the material as as this material sees + + align:start position:0% +the material as as this material sees + + + align:start position:0% +the material as as this material sees +over here. And that makes the simulation + + align:start position:0% +over here. And that makes the simulation + + + align:start position:0% +over here. And that makes the simulation +match up with the with the experiments + + align:start position:0% +match up with the with the experiments + + + align:start position:0% +match up with the with the experiments +nicely. So we etch this stamp, we choose + + align:start position:0% +nicely. So we etch this stamp, we choose + + + align:start position:0% +nicely. So we etch this stamp, we choose +some embossing conditions, press it into + + align:start position:0% +some embossing conditions, press it into + + + align:start position:0% +some embossing conditions, press it into +the substrate and use white light + + align:start position:0% +the substrate and use white light + + + align:start position:0% +the substrate and use white light +scanning interferometry to measure the + + align:start position:0% +scanning interferometry to measure the + + + align:start position:0% +scanning interferometry to measure the +surface topography. The smallest + + align:start position:0% +surface topography. The smallest + + + align:start position:0% +surface topography. The smallest +features in this particular stamp are + + align:start position:0% +features in this particular stamp are + + + align:start position:0% +features in this particular stamp are +five micron in diameter. Uh what we're + + align:start position:0% +five micron in diameter. Uh what we're + + + align:start position:0% +five micron in diameter. Uh what we're +also doing now actually is a set of + + align:start position:0% +also doing now actually is a set of + + + align:start position:0% +also doing now actually is a set of +experiments where we've scaled down this + + align:start position:0% +experiments where we've scaled down this + + + align:start position:0% +experiments where we've scaled down this +pattern a 100fold to make a nano imprint + + align:start position:0% +pattern a 100fold to make a nano imprint + + + align:start position:0% +pattern a 100fold to make a nano imprint +lithography stamp of the same pattern. + + align:start position:0% +lithography stamp of the same pattern. + + + align:start position:0% +lithography stamp of the same pattern. +And uh so we're we're trying to tie all + + align:start position:0% +And uh so we're we're trying to tie all + + + align:start position:0% +And uh so we're we're trying to tie all +the mechanics together and see if + + align:start position:0% +the mechanics together and see if + + + align:start position:0% +the mechanics together and see if +similar effects occur at the + + align:start position:0% +similar effects occur at the + + + align:start position:0% +similar effects occur at the +nanocale. + + align:start position:0% +nanocale. + + + align:start position:0% +nanocale. +Anyhow, in the bottom left here is uh is + + align:start position:0% +Anyhow, in the bottom left here is uh is + + + align:start position:0% +Anyhow, in the bottom left here is uh is +is a composite map of the surface where + + align:start position:0% +is a composite map of the surface where + + + align:start position:0% +is a composite map of the surface where +uh the the red colors show the the + + align:start position:0% +uh the the red colors show the the + + + align:start position:0% +uh the the red colors show the the +higher topographies where more material + + align:start position:0% +higher topographies where more material + + + align:start position:0% +higher topographies where more material +has penetrated further into the stamp + + align:start position:0% +has penetrated further into the stamp + + + align:start position:0% +has penetrated further into the stamp +cavities. And on the right here are + + align:start position:0% +cavities. And on the right here are + + + align:start position:0% +cavities. And on the right here are +eight cross-sections through that + + align:start position:0% +eight cross-sections through that + + + align:start position:0% +eight cross-sections through that +topography labeled 1 + + align:start position:0% +topography labeled 1 + + + align:start position:0% +topography labeled 1 +to8. The experimental data is shown in + + align:start position:0% +to8. The experimental data is shown in + + + align:start position:0% +to8. The experimental data is shown in +black underneath and and the and the + + align:start position:0% +black underneath and and the and the + + + align:start position:0% +black underneath and and the and the +prediction of the linear elastic model + + align:start position:0% +prediction of the linear elastic model + + + align:start position:0% +prediction of the linear elastic model +with only one fitted parameter the + + align:start position:0% +with only one fitted parameter the + + + align:start position:0% +with only one fitted parameter the +Young's modulus uh is shown in red and + + align:start position:0% +Young's modulus uh is shown in red and + + + align:start position:0% +Young's modulus uh is shown in red and +you can see that there's remarkable + + align:start position:0% +you can see that there's remarkable + + + align:start position:0% +you can see that there's remarkable +correspondence between the two. um we + + align:start position:0% +correspondence between the two. um we + + + align:start position:0% +correspondence between the two. um we +get both a prediction of + + align:start position:0% +get both a prediction of + + + align:start position:0% +get both a prediction of +how far on average material penetrates + + align:start position:0% +how far on average material penetrates + + + align:start position:0% +how far on average material penetrates +cavities of a given diameter and also we + + align:start position:0% +cavities of a given diameter and also we + + + align:start position:0% +cavities of a given diameter and also we +we do capture these interactions of + + align:start position:0% +we do capture these interactions of + + + align:start position:0% +we do capture these interactions of +patterns of different densities. You can + + align:start position:0% +patterns of different densities. You can + + + align:start position:0% +patterns of different densities. You can +see for example + + align:start position:0% +see for example + + + align:start position:0% +see for example +uh let's + + align:start position:0% +uh let's + + + align:start position:0% +uh let's +say well I guess this is a good this is + + align:start position:0% +say well I guess this is a good this is + + + align:start position:0% +say well I guess this is a good this is +a good example + + align:start position:0% +a good example + + + align:start position:0% +a good example +here you you're seeing many instances of + + align:start position:0% +here you you're seeing many instances of + + + align:start position:0% +here you you're seeing many instances of +a given trench diameter but trenches + + align:start position:0% +a given trench diameter but trenches + + + align:start position:0% +a given trench diameter but trenches +that are + + align:start position:0% +that are + + + align:start position:0% +that are +closer to different patterns fill less + + align:start position:0% +closer to different patterns fill less + + + align:start position:0% +closer to different patterns fill less +far than those that are in the center of + + align:start position:0% +far than those that are in the center of + + + align:start position:0% +far than those that are in the center of +the patch. And this is all this is all + + align:start position:0% +the patch. And this is all this is all + + + align:start position:0% +the patch. And this is all this is all +captured reasonably well by + + align:start position:0% +captured reasonably well by + + + align:start position:0% +captured reasonably well by +this rubbery model of of the polymer. + + align:start position:0% +this rubbery model of of the polymer. + + + align:start position:0% +this rubbery model of of the polymer. +So looks like we've got the basis here + + align:start position:0% +So looks like we've got the basis here + + + align:start position:0% +So looks like we've got the basis here +for + + align:start position:0% +for + + + align:start position:0% +for +uh for for for doing efficient + + align:start position:0% +uh for for for doing efficient + + + align:start position:0% +uh for for for doing efficient +simulations that you can run that + + align:start position:0% +simulations that you can run that + + + align:start position:0% +simulations that you can run that +simulation in 20 seconds in mat lab and + + align:start position:0% +simulation in 20 seconds in mat lab and + + + align:start position:0% +simulation in 20 seconds in mat lab and +it's uh it's giving you I think probably + + align:start position:0% +it's uh it's giving you I think probably + + + align:start position:0% +it's uh it's giving you I think probably +95% of the information a full finite + + align:start position:0% +95% of the information a full finite + + + align:start position:0% +95% of the information a full finite +element simulation would give you as far + + align:start position:0% +element simulation would give you as far + + + align:start position:0% +element simulation would give you as far +as topography is concerned. + + align:start position:0% + + + + align:start position:0% + +So we can also uh abstract our + + align:start position:0% +So we can also uh abstract our + + + align:start position:0% +So we can also uh abstract our +experimental results and and view them + + align:start position:0% +experimental results and and view them + + + align:start position:0% +experimental results and and view them +in simpler ways. Um and and and one way + + align:start position:0% +in simpler ways. Um and and and one way + + + align:start position:0% +in simpler ways. Um and and and one way +of doing that is to look within each + + align:start position:0% +of doing that is to look within each + + + align:start position:0% +of doing that is to look within each +region of features and uh measure the + + align:start position:0% +region of features and uh measure the + + + align:start position:0% +region of features and uh measure the +peak penetration of material into the + + align:start position:0% +peak penetration of material into the + + + align:start position:0% +peak penetration of material into the +cavity. So we we just measure the range + + align:start position:0% +cavity. So we we just measure the range + + + align:start position:0% +cavity. So we we just measure the range +of heights within the central 80% of the + + align:start position:0% +of heights within the central 80% of the + + + align:start position:0% +of heights within the central 80% of the +area of each patch of features and then + + align:start position:0% +area of each patch of features and then + + + align:start position:0% +area of each patch of features and then +plot that that peak penetration against + + align:start position:0% +plot that that peak penetration against + + + align:start position:0% +plot that that peak penetration against +uh against some some parameter. In this + + align:start position:0% +uh against some some parameter. In this + + + align:start position:0% +uh against some some parameter. In this +case I've plotted the pattern density + + align:start position:0% +case I've plotted the pattern density + + + align:start position:0% +case I've plotted the pattern density +which is the ratio of the cavity width + + align:start position:0% +which is the ratio of the cavity width + + + align:start position:0% +which is the ratio of the cavity width +to the cavity + + align:start position:0% +to the cavity + + + align:start position:0% +to the cavity +pitch and uh the different colors in + + align:start position:0% +pitch and uh the different colors in + + + align:start position:0% +pitch and uh the different colors in +this in this graph represent different + + align:start position:0% +this in this graph represent different + + + align:start position:0% +this in this graph represent different +feature pitches. So that the the pitch + + align:start position:0% +feature pitches. So that the the pitch + + + align:start position:0% +feature pitches. So that the the pitch +being the the distance from one cavity + + align:start position:0% +being the the distance from one cavity + + + align:start position:0% +being the the distance from one cavity +to the + + align:start position:0% +to the + + + align:start position:0% +to the +next. And + + align:start position:0% +next. And + + + align:start position:0% +next. And +uh what I what I show is the the the + + align:start position:0% +uh what I what I show is the the the + + + align:start position:0% +uh what I what I show is the the the +elastic model matching up pretty well + + align:start position:0% +elastic model matching up pretty well + + + align:start position:0% +elastic model matching up pretty well +with the with the experimental + + align:start position:0% + + + + align:start position:0% + +results. Of course, you might think that + + align:start position:0% +results. Of course, you might think that + + + align:start position:0% +results. Of course, you might think that +uh you know this this is leading towards + + align:start position:0% +uh you know this this is leading towards + + + align:start position:0% +uh you know this this is leading towards +the possibility of non-dimensional + + align:start position:0% +the possibility of non-dimensional + + + align:start position:0% +the possibility of non-dimensional +groups to describe features and how they + + align:start position:0% +groups to describe features and how they + + + align:start position:0% +groups to describe features and how they +fill and putting down design rules that + + align:start position:0% +fill and putting down design rules that + + + align:start position:0% +fill and putting down design rules that +would tell you how to scale the + + align:start position:0% +would tell you how to scale the + + + align:start position:0% +would tell you how to scale the +embossing pressure as your pattern + + align:start position:0% +embossing pressure as your pattern + + + align:start position:0% +embossing pressure as your pattern +scaled down and these sorts of things. + + align:start position:0% +scaled down and these sorts of things. + + + align:start position:0% +scaled down and these sorts of things. +So the this is a great way of of viewing + + align:start position:0% +So the this is a great way of of viewing + + + align:start position:0% +So the this is a great way of of viewing +the results and getting intuition about + + align:start position:0% +the results and getting intuition about + + + align:start position:0% +the results and getting intuition about +them. Of course, as you increase the + + align:start position:0% +them. Of course, as you increase the + + + align:start position:0% +them. Of course, as you increase the +pressure and material starts to touch + + align:start position:0% +pressure and material starts to touch + + + align:start position:0% +pressure and material starts to touch +the tops of the stamp cavities, this uh + + align:start position:0% +the tops of the stamp cavities, this uh + + + align:start position:0% +the tops of the stamp cavities, this uh +this straight line breaks down, of + + align:start position:0% +this straight line breaks down, of + + + align:start position:0% +this straight line breaks down, of +course, and and and the red the red + + align:start position:0% +course, and and and the red the red + + + align:start position:0% +course, and and and the red the red +symbols show what happens when the + + align:start position:0% +symbols show what happens when the + + + align:start position:0% +symbols show what happens when the +pressure is increased to a stage where + + align:start position:0% +pressure is increased to a stage where + + + align:start position:0% +pressure is increased to a stage where +where the larger cavities fill. + + align:start position:0% +where the larger cavities fill. + + + align:start position:0% +where the larger cavities fill. +What you can also do is use a series of + + align:start position:0% +What you can also do is use a series of + + + align:start position:0% +What you can also do is use a series of +these experiments to get material + + align:start position:0% +these experiments to get material + + + align:start position:0% +these experiments to get material +properties as a function of temperature + + align:start position:0% +properties as a function of temperature + + + align:start position:0% +properties as a function of temperature +or of some other parameter. And that's + + align:start position:0% +or of some other parameter. And that's + + + align:start position:0% +or of some other parameter. And that's +exactly what we did here by doing a + + align:start position:0% +exactly what we did here by doing a + + + align:start position:0% +exactly what we did here by doing a +series of embossing tests at different + + align:start position:0% +series of embossing tests at different + + + align:start position:0% +series of embossing tests at different +temperatures. And the gradient of that + + align:start position:0% +temperatures. And the gradient of that + + + align:start position:0% +temperatures. And the gradient of that +line penetration to pressure will be + + align:start position:0% +line penetration to pressure will be + + + align:start position:0% +line penetration to pressure will be +inversely proportional to the effective + + align:start position:0% +inversely proportional to the effective + + + align:start position:0% +inversely proportional to the effective +elastic modulus of the material. So we + + align:start position:0% +elastic modulus of the material. So we + + + align:start position:0% +elastic modulus of the material. So we +we did that. We uh got out these values + + align:start position:0% +we did that. We uh got out these values + + + align:start position:0% +we did that. We uh got out these values +for the Young's modulus against + + align:start position:0% +for the Young's modulus against + + + align:start position:0% +for the Young's modulus against +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +and luckily they match up really nicely + + align:start position:0% +and luckily they match up really nicely + + + align:start position:0% +and luckily they match up really nicely +with + + align:start position:0% +with + + + align:start position:0% +with +um a model for Young's modulus that was + + align:start position:0% +um a model for Young's modulus that was + + + align:start position:0% +um a model for Young's modulus that was +derived from bulk compression + + align:start position:0% +derived from bulk compression + + + align:start position:0% +derived from bulk compression +experiments that was just done in a big + + align:start position:0% +experiments that was just done in a big + + + align:start position:0% +experiments that was just done in a big +Instron load frame using bulk materials. + + align:start position:0% +Instron load frame using bulk materials. + + + align:start position:0% +Instron load frame using bulk materials. +So you could start to see how uh with + + align:start position:0% +So you could start to see how uh with + + + align:start position:0% +So you could start to see how uh with +careful choice of of of of test + + align:start position:0% +careful choice of of of of test + + + align:start position:0% +careful choice of of of of test +embossing patterns, we can get a lot of + + align:start position:0% +embossing patterns, we can get a lot of + + + align:start position:0% +embossing patterns, we can get a lot of +information out of a new material quite + + align:start position:0% +information out of a new material quite + + + align:start position:0% +information out of a new material quite +quickly. Uh scale information, strain + + align:start position:0% +quickly. Uh scale information, strain + + + align:start position:0% +quickly. Uh scale information, strain +rate information perhaps, temperature + + align:start position:0% +rate information perhaps, temperature + + + align:start position:0% +rate information perhaps, temperature +information. And uh really the one of + + align:start position:0% +information. And uh really the one of + + + align:start position:0% +information. And uh really the one of +the big challenges here is deciding what + + align:start position:0% +the big challenges here is deciding what + + + align:start position:0% +the big challenges here is deciding what +are the embossing tests you're going to + + align:start position:0% +are the embossing tests you're going to + + + align:start position:0% +are the embossing tests you're going to +do. What combination of temperatures and + + align:start position:0% +do. What combination of temperatures and + + + align:start position:0% +do. What combination of temperatures and +pressures are you going to go for first? + + align:start position:0% +pressures are you going to go for first? + + + align:start position:0% +pressures are you going to go for first? +That will give you the most + + align:start position:0% +That will give you the most + + + align:start position:0% +That will give you the most +information. Now, I said before that + + align:start position:0% +information. Now, I said before that + + + align:start position:0% +information. Now, I said before that +this rubbery model is really only useful + + align:start position:0% +this rubbery model is really only useful + + + align:start position:0% +this rubbery model is really only useful +if if the hold time is comparatively + + align:start position:0% +if if the hold time is comparatively + + + align:start position:0% +if if the hold time is comparatively +short. And uh you know, often + + align:start position:0% +short. And uh you know, often + + + align:start position:0% +short. And uh you know, often +that's that's the case. Um you you want + + align:start position:0% +that's that's the case. Um you you want + + + align:start position:0% +that's that's the case. Um you you want +the cycle time to be as short as + + align:start position:0% +the cycle time to be as short as + + + align:start position:0% +the cycle time to be as short as +possible. So if if you can uh get the + + align:start position:0% +possible. So if if you can uh get the + + + align:start position:0% +possible. So if if you can uh get the +material into a state where you press + + align:start position:0% +material into a state where you press + + + align:start position:0% +material into a state where you press +hard enough, you get the defamation + + align:start position:0% +hard enough, you get the defamation + + + align:start position:0% +hard enough, you get the defamation +almost instantaneously then that's + + align:start position:0% +almost instantaneously then that's + + + align:start position:0% +almost instantaneously then that's +great. But in a lot of cases you can't + + align:start position:0% +great. But in a lot of cases you can't + + + align:start position:0% +great. But in a lot of cases you can't +do that and uh you do get this plastic + + align:start position:0% +do that and uh you do get this plastic + + + align:start position:0% +do that and uh you do get this plastic +flow. So what I show here is uh the + + align:start position:0% +flow. So what I show here is uh the + + + align:start position:0% +flow. So what I show here is uh the +evolution of an embossed topography over + + align:start position:0% +evolution of an embossed topography over + + + align:start position:0% +evolution of an embossed topography over +time as we hold the load at high + + align:start position:0% +time as we hold the load at high + + + align:start position:0% +time as we hold the load at high +temperature. + + align:start position:0% +temperature. + + + align:start position:0% +temperature. +The black symbols down here show what + + align:start position:0% +The black symbols down here show what + + + align:start position:0% +The black symbols down here show what +happens if you start cooling the + + align:start position:0% +happens if you start cooling the + + + align:start position:0% +happens if you start cooling the +material down as soon as the load + + align:start position:0% +material down as soon as the load + + + align:start position:0% +material down as soon as the load +reaches its peak. So material is is + + align:start position:0% +reaches its peak. So material is is + + + align:start position:0% +reaches its peak. So material is is +boowing into the into the cavities but + + align:start position:0% +boowing into the into the cavities but + + + align:start position:0% +boowing into the into the cavities but +hasn't gone very far. And then right up + + align:start position:0% +hasn't gone very far. And then right up + + + align:start position:0% +hasn't gone very far. And then right up +here you you've waited for 10 minutes + + align:start position:0% +here you you've waited for 10 minutes + + + align:start position:0% +here you you've waited for 10 minutes +and uh all but the smallest features + + align:start position:0% +and uh all but the smallest features + + + align:start position:0% +and uh all but the smallest features +have at least touched the tops of the + + align:start position:0% +have at least touched the tops of the + + + align:start position:0% +have at least touched the tops of the +cavities. Of course this yaxis is + + align:start position:0% +cavities. Of course this yaxis is + + + align:start position:0% +cavities. Of course this yaxis is +showing the peak penetration. So it's + + align:start position:0% +showing the peak penetration. So it's + + + align:start position:0% +showing the peak penetration. So it's +the the distance from the top of the the + + align:start position:0% +the the distance from the top of the the + + + align:start position:0% +the the distance from the top of the the +the uh the feature to the bottom and it + + align:start position:0% +the uh the feature to the bottom and it + + + align:start position:0% +the uh the feature to the bottom and it +tells you nothing about whether the + + align:start position:0% +tells you nothing about whether the + + + align:start position:0% +tells you nothing about whether the +corners of the features have been + + align:start position:0% +corners of the features have been + + + align:start position:0% +corners of the features have been +filled. But this is a reasonably useful + + align:start position:0% +filled. But this is a reasonably useful + + + align:start position:0% +filled. But this is a reasonably useful +measurement. Now question is can we + + align:start position:0% +measurement. Now question is can we + + + align:start position:0% +measurement. Now question is can we +adapt our simple model to capture this + + align:start position:0% +adapt our simple model to capture this + + + align:start position:0% +adapt our simple model to capture this +visco elastic behavior without + + align:start position:0% +visco elastic behavior without + + + align:start position:0% +visco elastic behavior without +increasing the computational burden very + + align:start position:0% +increasing the computational burden very + + + align:start position:0% +increasing the computational burden very +much. And uh well the next thing you + + align:start position:0% +much. And uh well the next thing you + + + align:start position:0% +much. And uh well the next thing you +might think of doing is adding a linear + + align:start position:0% +might think of doing is adding a linear + + + align:start position:0% +might think of doing is adding a linear +dashboard into the system and uh maybe + + align:start position:0% +dashboard into the system and uh maybe + + + align:start position:0% +dashboard into the system and uh maybe +it's linear that would be the first + + align:start position:0% +it's linear that would be the first + + + align:start position:0% +it's linear that would be the first +thing to try. Maybe you do need to + + align:start position:0% +thing to try. Maybe you do need to + + + align:start position:0% +thing to try. Maybe you do need to +capture the idea of a yield stress as + + align:start position:0% +capture the idea of a yield stress as + + + align:start position:0% +capture the idea of a yield stress as +well. uh and maybe you need to capture + + align:start position:0% +well. uh and maybe you need to capture + + + align:start position:0% +well. uh and maybe you need to capture +the idea of a strain rate dependence + + align:start position:0% +the idea of a strain rate dependence + + + align:start position:0% +the idea of a strain rate dependence +which in PMMA is such that the that the + + align:start position:0% +which in PMMA is such that the that the + + + align:start position:0% +which in PMMA is such that the that the +yield stress uh increases substantially + + align:start position:0% +yield stress uh increases substantially + + + align:start position:0% +yield stress uh increases substantially +with strain rates above about 10 the + + align:start position:0% +with strain rates above about 10 the + + + align:start position:0% +with strain rates above about 10 the +minus2 per second. So + + align:start position:0% +minus2 per second. So + + + align:start position:0% +minus2 per second. So +uh in fact we just tried adding in a + + align:start position:0% +uh in fact we just tried adding in a + + + align:start position:0% +uh in fact we just tried adding in a +linear dash pot. So what this does in + + align:start position:0% +linear dash pot. So what this does in + + + align:start position:0% +linear dash pot. So what this does in +effect + + align:start position:0% +effect + + + align:start position:0% +effect +is takes + + align:start position:0% + + + + align:start position:0% + +the takes the point load response + + align:start position:0% +the takes the point load response + + + align:start position:0% +the takes the point load response +associated with purely rubbery purely + + align:start position:0% +associated with purely rubbery purely + + + align:start position:0% +associated with purely rubbery purely +linear elastic behavior which would be + + align:start position:0% +linear elastic behavior which would be + + + align:start position:0% +linear elastic behavior which would be +like + + align:start position:0% +like + + + align:start position:0% +like +this and uh scales it by a factor that's + + align:start position:0% +this and uh scales it by a factor that's + + + align:start position:0% +this and uh scales it by a factor that's +related to the time the load is applied + + align:start position:0% +related to the time the load is applied + + + align:start position:0% +related to the time the load is applied +and and all that's saying is imagine + + align:start position:0% +and and all that's saying is imagine + + + align:start position:0% +and and all that's saying is imagine +imagine this was visco elastic you + + align:start position:0% +imagine this was visco elastic you + + + align:start position:0% +imagine this was visco elastic you +applied a point load + + align:start position:0% +applied a point load + + + align:start position:0% +applied a point load +you get some instantaneous defamation, + + align:start position:0% +you get some instantaneous defamation, + + + align:start position:0% +you get some instantaneous defamation, +but over time I'm saying this this uh + + align:start position:0% +but over time I'm saying this this uh + + + align:start position:0% +but over time I'm saying this this uh +this surface is just scaling down. All + + align:start position:0% +this surface is just scaling down. All + + + align:start position:0% +this surface is just scaling down. All +the the points are staying in the same + + align:start position:0% +the the points are staying in the same + + + align:start position:0% +the the points are staying in the same +ratio of height, but it's just scaling + + align:start position:0% +ratio of height, but it's just scaling + + + align:start position:0% +ratio of height, but it's just scaling +down. And you you could + + align:start position:0% +down. And you you could + + + align:start position:0% +down. And you you could +um you know, we we assumed that that + + align:start position:0% +um you know, we we assumed that that + + + align:start position:0% +um you know, we we assumed that that +scale factor was proportional to the + + align:start position:0% +scale factor was proportional to the + + + align:start position:0% +scale factor was proportional to the +whole time, but you might not assume + + align:start position:0% +whole time, but you might not assume + + + align:start position:0% +whole time, but you might not assume +that. You might say, well, what if + + align:start position:0% +that. You might say, well, what if + + + align:start position:0% +that. You might say, well, what if +there's um there's actually a sort of + + align:start position:0% +there's um there's actually a sort of + + + align:start position:0% +there's um there's actually a sort of +limiting + + align:start position:0% +limiting + + + align:start position:0% +limiting +strain where the network the polymer + + align:start position:0% +strain where the network the polymer + + + align:start position:0% +strain where the network the polymer +network is as stretched out as it as it + + align:start position:0% +network is as stretched out as it as it + + + align:start position:0% +network is as stretched out as it as it +can be for a particular load and uh in + + align:start position:0% +can be for a particular load and uh in + + + align:start position:0% +can be for a particular load and uh in +that case you would have um I guess + + align:start position:0% +that case you would have um I guess + + + align:start position:0% +that case you would have um I guess +strain against time would be would + + align:start position:0% +strain against time would be would + + + align:start position:0% +strain against time would be would +asmtotically approach some limiting + + align:start position:0% +asmtotically approach some limiting + + + align:start position:0% +asmtotically approach some limiting +value that was related to that spring + + align:start position:0% +value that was related to that spring + + + align:start position:0% +value that was related to that spring +and that that would also be quite easy + + align:start position:0% +and that that would also be quite easy + + + align:start position:0% +and that that would also be quite easy +to compute. you computer a topography at + + align:start position:0% +to compute. you computer a topography at + + + align:start position:0% +to compute. you computer a topography at +the start of the holding, a topography + + align:start position:0% +the start of the holding, a topography + + + align:start position:0% +the start of the holding, a topography +that would be associated with infinite + + align:start position:0% +that would be associated with infinite + + + align:start position:0% +that would be associated with infinite +time and then maybe interpolate using an + + align:start position:0% +time and then maybe interpolate using an + + + align:start position:0% +time and then maybe interpolate using an +exponential function of whole time. But + + align:start position:0% +exponential function of whole time. But + + + align:start position:0% +exponential function of whole time. But +anyway, we just went with with a linear + + align:start position:0% +anyway, we just went with with a linear + + + align:start position:0% +anyway, we just went with with a linear +scaling and uh it seems to work + + align:start position:0% +scaling and uh it seems to work + + + align:start position:0% +scaling and uh it seems to work +remarkably + + align:start position:0% +remarkably + + + align:start position:0% +remarkably +well for these particular conditions, + + align:start position:0% +well for these particular conditions, + + + align:start position:0% +well for these particular conditions, +110 degrees C, which is a few degrees + + align:start position:0% +110 degrees C, which is a few degrees + + + align:start position:0% +110 degrees C, which is a few degrees +above glass transition. Um, so we're + + align:start position:0% +above glass transition. Um, so we're + + + align:start position:0% +above glass transition. Um, so we're +actually we're we're definitely in a + + align:start position:0% +actually we're we're definitely in a + + + align:start position:0% +actually we're we're definitely in a +uh in in a region where plastic flow is + + align:start position:0% +uh in in a region where plastic flow is + + + align:start position:0% +uh in in a region where plastic flow is +is is significant is important. Um and + + align:start position:0% +is is significant is important. Um and + + + align:start position:0% +is is significant is important. Um and +uh what we see uh the these are at the + + align:start position:0% +uh what we see uh the these are at the + + + align:start position:0% +uh what we see uh the these are at the +top experimental data 3D plot of the the + + align:start position:0% +top experimental data 3D plot of the the + + + align:start position:0% +top experimental data 3D plot of the the +measurements taken using optical + + align:start position:0% +measurements taken using optical + + + align:start position:0% +measurements taken using optical +interferometry on the left for less than + + align:start position:0% +interferometry on the left for less than + + + align:start position:0% +interferometry on the left for less than +a minute holding time loading duration + + align:start position:0% +a minute holding time loading duration + + + align:start position:0% +a minute holding time loading duration +and on the right when we left that load + + align:start position:0% +and on the right when we left that load + + + align:start position:0% +and on the right when we left that load +in place for 10 minutes. So you can see + + align:start position:0% +in place for 10 minutes. So you can see + + + align:start position:0% +in place for 10 minutes. So you can see +that obviously over time the narrower + + align:start position:0% +that obviously over time the narrower + + + align:start position:0% +that obviously over time the narrower +features start to fill and uh the + + align:start position:0% +features start to fill and uh the + + + align:start position:0% +features start to fill and uh the +simulation to a reasonable extent has + + align:start position:0% +simulation to a reasonable extent has + + + align:start position:0% +simulation to a reasonable extent has +has has captured that and in fact the + + align:start position:0% +has has captured that and in fact the + + + align:start position:0% +has has captured that and in fact the +shortcoming of the simulation is that it + + align:start position:0% +shortcoming of the simulation is that it + + + align:start position:0% +shortcoming of the simulation is that it +underestimates how quickly the narrower + + align:start position:0% +underestimates how quickly the narrower + + + align:start position:0% +underestimates how quickly the narrower +features fill for the for for the + + align:start position:0% +features fill for the for for the + + + align:start position:0% +features fill for the for for the +parameters that we fit. And + + align:start position:0% +parameters that we fit. And + + + align:start position:0% +parameters that we fit. And +um so that is is definitely an imperfect + + align:start position:0% +um so that is is definitely an imperfect + + + align:start position:0% +um so that is is definitely an imperfect +model, but it's pretty useful I think + + align:start position:0% +model, but it's pretty useful I think + + + align:start position:0% +model, but it's pretty useful I think +for for getting a first cut of of of + + align:start position:0% +for for getting a first cut of of of + + + align:start position:0% +for for getting a first cut of of of +uh of a simulation. + + align:start position:0% +uh of a simulation. + + + align:start position:0% +uh of a simulation. +So, of course, we can now that we've got + + align:start position:0% +So, of course, we can now that we've got + + + align:start position:0% +So, of course, we can now that we've got +this + + align:start position:0% +this + + + align:start position:0% +this +characterization idea, we can apply that + + align:start position:0% +characterization idea, we can apply that + + + align:start position:0% +characterization idea, we can apply that +to different materials. And we did it + + align:start position:0% +to different materials. And we did it + + + align:start position:0% +to different materials. And we did it +with this uh this cyclic olifin polymer + + align:start position:0% +with this uh this cyclic olifin polymer + + + align:start position:0% +with this uh this cyclic olifin polymer +xeon, which is um it's a thermoplastic. + + align:start position:0% +xeon, which is um it's a thermoplastic. + + + align:start position:0% +xeon, which is um it's a thermoplastic. +This one softens around 135 degrees C. + + align:start position:0% +This one softens around 135 degrees C. + + + align:start position:0% +This one softens around 135 degrees C. +Um has quite a few advantages over um + + align:start position:0% +Um has quite a few advantages over um + + + align:start position:0% +Um has quite a few advantages over um +over PMMA. uh although it's more + + align:start position:0% +over PMMA. uh although it's more + + + align:start position:0% +over PMMA. uh although it's more +expensive, it doesn't absorb water as + + align:start position:0% +expensive, it doesn't absorb water as + + + align:start position:0% +expensive, it doesn't absorb water as +readily, which is pretty relevant to uh + + align:start position:0% +readily, which is pretty relevant to uh + + + align:start position:0% +readily, which is pretty relevant to uh +microffluidic devices. Uh it transmits + + align:start position:0% +microffluidic devices. Uh it transmits + + + align:start position:0% +microffluidic devices. Uh it transmits +light to shorter wavelengths, which is + + align:start position:0% +light to shorter wavelengths, which is + + + align:start position:0% +light to shorter wavelengths, which is +relevant when you're exciting + + align:start position:0% +relevant when you're exciting + + + align:start position:0% +relevant when you're exciting +fluorescent tags inside the chip with UV + + align:start position:0% +fluorescent tags inside the chip with UV + + + align:start position:0% +fluorescent tags inside the chip with UV +light. And um so it's useful to be able + + align:start position:0% +light. And um so it's useful to be able + + + align:start position:0% +light. And um so it's useful to be able +to characterize these new materials as + + align:start position:0% +to characterize these new materials as + + + align:start position:0% +to characterize these new materials as +they come along and when you don't + + align:start position:0% +they come along and when you don't + + + align:start position:0% +they come along and when you don't +necessarily have an unlimited supply of + + align:start position:0% +necessarily have an unlimited supply of + + + align:start position:0% +necessarily have an unlimited supply of +the material. So + + align:start position:0% +the material. So + + + align:start position:0% +the material. So +uh again this is a plot of peak + + align:start position:0% +uh again this is a plot of peak + + + align:start position:0% +uh again this is a plot of peak +penetration against cavity diameter and + + align:start position:0% +penetration against cavity diameter and + + + align:start position:0% +penetration against cavity diameter and +um although most of the most of the data + + align:start position:0% +um although most of the most of the data + + + align:start position:0% +um although most of the most of the data +sit sit on a roughly straight line that + + align:start position:0% +sit sit on a roughly straight line that + + + align:start position:0% +sit sit on a roughly straight line that +when when you have cavity diameter being + + align:start position:0% +when when you have cavity diameter being + + + align:start position:0% +when when you have cavity diameter being +a large proportion of the pitch in other + + align:start position:0% +a large proportion of the pitch in other + + + align:start position:0% +a large proportion of the pitch in other +words there are very narrow + + align:start position:0% +words there are very narrow + + + align:start position:0% +words there are very narrow +uh hello um there are very narrow + + align:start position:0% +uh hello um there are very narrow + + + align:start position:0% +uh hello um there are very narrow +uh walls of of of the stamp material + + align:start position:0% +uh walls of of of the stamp material + + + align:start position:0% +uh walls of of of the stamp material +pressing into the pressing into the + + align:start position:0% +pressing into the pressing into the + + + align:start position:0% +pressing into the pressing into the +polymer. That's when the the penetration + + align:start position:0% +polymer. That's when the the penetration + + + align:start position:0% +polymer. That's when the the penetration +does does seem to deviate from this + + align:start position:0% +does does seem to deviate from this + + + align:start position:0% +does does seem to deviate from this +straight from this straight line. So + + align:start position:0% + + + + align:start position:0% + +anyway, now I've I've shown you results + + align:start position:0% +anyway, now I've I've shown you results + + + align:start position:0% +anyway, now I've I've shown you results +from a few carefully + + align:start position:0% +from a few carefully + + + align:start position:0% +from a few carefully +chosen operating points and you know I + + align:start position:0% +chosen operating points and you know I + + + align:start position:0% +chosen operating points and you know I +showed a set of results where only + + align:start position:0% +showed a set of results where only + + + align:start position:0% +showed a set of results where only +temperature was varied and I I showed um + + align:start position:0% +temperature was varied and I I showed um + + + align:start position:0% +temperature was varied and I I showed um +I showed some you know for Xeon there + + align:start position:0% +I showed some you know for Xeon there + + + align:start position:0% +I showed some you know for Xeon there +was only one temperature one whole time + + align:start position:0% +was only one temperature one whole time + + + align:start position:0% +was only one temperature one whole time +one uh one load and um we need to start + + align:start position:0% +one uh one load and um we need to start + + + align:start position:0% +one uh one load and um we need to start +thinking about what combination of + + align:start position:0% +thinking about what combination of + + + align:start position:0% +thinking about what combination of +operating parameters would we want to + + align:start position:0% +operating parameters would we want to + + + align:start position:0% +operating parameters would we want to +deploy if we knew nothing about a + + align:start position:0% +deploy if we knew nothing about a + + + align:start position:0% +deploy if we knew nothing about a +material uh except for its approximate + + align:start position:0% +material uh except for its approximate + + + align:start position:0% +material uh except for its approximate +glass transition temperature. What what + + align:start position:0% +glass transition temperature. What what + + + align:start position:0% +glass transition temperature. What what +would we uh want to vary first? And uh + + align:start position:0% +would we uh want to vary first? And uh + + + align:start position:0% +would we uh want to vary first? And uh +so you might think about doing some sort + + align:start position:0% +so you might think about doing some sort + + + align:start position:0% +so you might think about doing some sort +of fractional factorial experiment where + + align:start position:0% +of fractional factorial experiment where + + + align:start position:0% +of fractional factorial experiment where +your + + align:start position:0% +your + + + align:start position:0% +your +uh variables of interest were were those + + align:start position:0% +uh variables of interest were were those + + + align:start position:0% +uh variables of interest were were those +connected with the process. the + + align:start position:0% +connected with the process. the + + + align:start position:0% +connected with the process. the +temperature, the load, the hold time, + + align:start position:0% +temperature, the load, the hold time, + + + align:start position:0% +temperature, the load, the hold time, +the time over which the load is applied. + + align:start position:0% +the time over which the load is applied. + + + align:start position:0% +the time over which the load is applied. +And uh that indeed uh is is what what I + + align:start position:0% +And uh that indeed uh is is what what I + + + align:start position:0% +And uh that indeed uh is is what what I +what I did with a third material, + + align:start position:0% +what I did with a third material, + + + align:start position:0% +what I did with a third material, +another brand of cyclic olifin polymer + + align:start position:0% +another brand of cyclic olifin polymer + + + align:start position:0% +another brand of cyclic olifin polymer +called topaz. And this this is a + + align:start position:0% +called topaz. And this this is a + + + align:start position:0% +called topaz. And this this is a +material that + + align:start position:0% +material that + + + align:start position:0% +material that +uh softens around 85 degrees C. Um and + + align:start position:0% +uh softens around 85 degrees C. Um and + + + align:start position:0% +uh softens around 85 degrees C. Um and +so we we did a 2 to the 4 minus one + + align:start position:0% +so we we did a 2 to the 4 minus one + + + align:start position:0% +so we we did a 2 to the 4 minus one +fractional factorial uh where there were + + align:start position:0% +fractional factorial uh where there were + + + align:start position:0% +fractional factorial uh where there were +the four parameters were embossing + + align:start position:0% +the four parameters were embossing + + + align:start position:0% +the four parameters were embossing +temperature, peak embossing force, uh + + align:start position:0% +temperature, peak embossing force, uh + + + align:start position:0% +temperature, peak embossing force, uh +hold time and the time over which the + + align:start position:0% +hold time and the time over which the + + + align:start position:0% +hold time and the time over which the +load was was ramped up to its to its + + align:start position:0% +load was was ramped up to its to its + + + align:start position:0% +load was was ramped up to its to its +peak. And um the astute among you will + + align:start position:0% +peak. And um the astute among you will + + + align:start position:0% +peak. And um the astute among you will +will notice that these these variables + + align:start position:0% +will notice that these these variables + + + align:start position:0% +will notice that these these variables +are are not going to be independent + + align:start position:0% +are are not going to be independent + + + align:start position:0% +are are not going to be independent +because the the average load over the + + align:start position:0% +because the the average load over the + + + align:start position:0% +because the the average load over the +loading time will contribute to the uh + + align:start position:0% +loading time will contribute to the uh + + + align:start position:0% +loading time will contribute to the uh +to the hold time. So uh it's it's a it's + + align:start position:0% +to the hold time. So uh it's it's a it's + + + align:start position:0% +to the hold time. So uh it's it's a it's +a rough and ready uh set of experiments + + align:start position:0% +a rough and ready uh set of experiments + + + align:start position:0% +a rough and ready uh set of experiments +but nevertheless gives you gives you + + align:start position:0% +but nevertheless gives you gives you + + + align:start position:0% +but nevertheless gives you gives you +some idea of what we might do. And + + align:start position:0% +some idea of what we might do. And + + + align:start position:0% +some idea of what we might do. And +um here we have uh again cavity + + align:start position:0% +um here we have uh again cavity + + + align:start position:0% +um here we have uh again cavity +penetration results as a function of + + align:start position:0% +penetration results as a function of + + + align:start position:0% +penetration results as a function of +cavity width for different feature + + align:start position:0% +cavity width for different feature + + + align:start position:0% +cavity width for different feature +pitches. The top plot uh is for features + + align:start position:0% +pitches. The top plot uh is for features + + + align:start position:0% +pitches. The top plot uh is for features +of a pitch of 100 microns and this is + + align:start position:0% +of a pitch of 100 microns and this is + + + align:start position:0% +of a pitch of 100 microns and this is +for 50 and 25. And you you see that + + align:start position:0% +for 50 and 25. And you you see that + + + align:start position:0% +for 50 and 25. And you you see that +again we have this nice trend where the + + align:start position:0% +again we have this nice trend where the + + + align:start position:0% +again we have this nice trend where the +peak penetration + + align:start position:0% +peak penetration + + + align:start position:0% +peak penetration +uh increases up to uh up to a maximum + + align:start position:0% +uh increases up to uh up to a maximum + + + align:start position:0% +uh increases up to uh up to a maximum +value. That maximum value is the is the + + align:start position:0% +value. That maximum value is the is the + + + align:start position:0% +value. That maximum value is the is the +height of the the cavities in the stamp. + + align:start position:0% +height of the the cavities in the stamp. + + + align:start position:0% +height of the the cavities in the stamp. +And uh you'll also notice that I put + + align:start position:0% +And uh you'll also notice that I put + + + align:start position:0% +And uh you'll also notice that I put +these little black dots on the graph as + + align:start position:0% +these little black dots on the graph as + + + align:start position:0% +these little black dots on the graph as +well. And those are the measured heights + + align:start position:0% +well. And those are the measured heights + + + align:start position:0% +well. And those are the measured heights +of the stamp cavities. Um, so you can + + align:start position:0% +of the stamp cavities. Um, so you can + + + align:start position:0% +of the stamp cavities. Um, so you can +see that actually the heights of the + + align:start position:0% +see that actually the heights of the + + + align:start position:0% +see that actually the heights of the +stamp cavities fall off for the for the + + align:start position:0% +stamp cavities fall off for the for the + + + align:start position:0% +stamp cavities fall off for the for the +narrower for the narrower cavities and + + align:start position:0% +narrower for the narrower cavities and + + + align:start position:0% +narrower for the narrower cavities and +that's uh + + align:start position:0% +that's uh + + + align:start position:0% +that's uh +associated with um the uh the etching + + align:start position:0% +associated with um the uh the etching + + + align:start position:0% +associated with um the uh the etching +process that's used the the actual + + align:start position:0% +process that's used the the actual + + + align:start position:0% +process that's used the the actual +plasma etch that makes the trenches in + + align:start position:0% +plasma etch that makes the trenches in + + + align:start position:0% +plasma etch that makes the trenches in +the silicon stamp uh has a harder time + + align:start position:0% +the silicon stamp uh has a harder time + + + align:start position:0% +the silicon stamp uh has a harder time +etching the narrower trenches. + + align:start position:0% +etching the narrower trenches. + + + align:start position:0% +etching the narrower trenches. +you know, it's a good sanity check that + + align:start position:0% +you know, it's a good sanity check that + + + align:start position:0% +you know, it's a good sanity check that +we're actually measuring the uh the + + align:start position:0% +we're actually measuring the uh the + + + align:start position:0% +we're actually measuring the uh the +penetration of polymer into the + + align:start position:0% +penetration of polymer into the + + + align:start position:0% +penetration of polymer into the +cavities. Now, + + align:start position:0% +cavities. Now, + + + align:start position:0% +cavities. Now, +um here are some 3D plots of of results. + + align:start position:0% +um here are some 3D plots of of results. + + + align:start position:0% +um here are some 3D plots of of results. +This is in the top left. This is uh + + align:start position:0% +This is in the top left. This is uh + + + align:start position:0% +This is in the top left. This is uh +essentially our our standard our center + + align:start position:0% +essentially our our standard our center + + + align:start position:0% +essentially our our standard our center +point run set of parameters where for a + + align:start position:0% +point run set of parameters where for a + + + align:start position:0% +point run set of parameters where for a +4-minute hold time, you get reasonably + + align:start position:0% +4-minute hold time, you get reasonably + + + align:start position:0% +4-minute hold time, you get reasonably +good filling of most of the feature + + align:start position:0% +good filling of most of the feature + + + align:start position:0% +good filling of most of the feature +sizes, but it's not perfect. So we can + + align:start position:0% +sizes, but it's not perfect. So we can + + + align:start position:0% +sizes, but it's not perfect. So we can +get an idea of process variability. Uh + + align:start position:0% +get an idea of process variability. Uh + + + align:start position:0% +get an idea of process variability. Uh +this is a set of parameters that was + + align:start position:0% +this is a set of parameters that was + + + align:start position:0% +this is a set of parameters that was +really no use at all. Uh 100 newtons. We + + align:start position:0% +really no use at all. Uh 100 newtons. We + + + align:start position:0% +really no use at all. Uh 100 newtons. We +haven't even leveled out the uh the the + + align:start position:0% +haven't even leveled out the uh the the + + + align:start position:0% +haven't even leveled out the uh the the +nonp parallelis nonp parallelism in the + + align:start position:0% +nonp parallelis nonp parallelism in the + + + align:start position:0% +nonp parallelis nonp parallelism in the +machine and one side of the substrate + + align:start position:0% +machine and one side of the substrate + + + align:start position:0% +machine and one side of the substrate +was contacted with the stamp and the + + align:start position:0% +was contacted with the stamp and the + + + align:start position:0% +was contacted with the stamp and the +other was not. So there's a lot of + + align:start position:0% +other was not. So there's a lot of + + + align:start position:0% +other was not. So there's a lot of +missing data here. and at 100 100 C 900 + + align:start position:0% +missing data here. and at 100 100 C 900 + + + align:start position:0% +missing data here. and at 100 100 C 900 +newtons 8 minutes we pretty much got + + align:start position:0% +newtons 8 minutes we pretty much got + + + align:start position:0% +newtons 8 minutes we pretty much got +complete filling of of most of the + + align:start position:0% +complete filling of of most of the + + + align:start position:0% +complete filling of of most of the +features. So you know + + align:start position:0% + + + + align:start position:0% + +the what we + + align:start position:0% +the what we + + + align:start position:0% +the what we +um what we also did I I should should + + align:start position:0% +um what we also did I I should should + + + align:start position:0% +um what we also did I I should should +have mentioned that randomized the order + + align:start position:0% +have mentioned that randomized the order + + + align:start position:0% +have mentioned that randomized the order +of the samples and interspers these + + align:start position:0% +of the samples and interspers these + + + align:start position:0% +of the samples and interspers these +center point + + align:start position:0% +center point + + + align:start position:0% +center point +runs the feature size is very small for + + align:start position:0% +runs the feature size is very small for + + + align:start position:0% +runs the feature size is very small for +500 newton does damage the stamp + + align:start position:0% +500 newton does damage the stamp + + + align:start position:0% +500 newton does damage the stamp +uh in these experiments we haven't we + + align:start position:0% +uh in these experiments we haven't we + + + align:start position:0% +uh in these experiments we haven't we +haven't damaged the stamp um I mean + + align:start position:0% +haven't damaged the stamp um I mean + + + align:start position:0% +haven't damaged the stamp um I mean +the actually the + + align:start position:0% +the actually the + + + align:start position:0% +the actually the +compressive stresses experienced by the + + align:start position:0% +compressive stresses experienced by the + + + align:start position:0% +compressive stresses experienced by the +silicon are are nowhere nowhere near + + align:start position:0% +silicon are are nowhere nowhere near + + + align:start position:0% +silicon are are nowhere nowhere near +enough. I mean to to to break it the + + align:start position:0% +enough. I mean to to to break it the + + + align:start position:0% +enough. I mean to to to break it the +tensile strength of silicon is over 100 + + align:start position:0% +tensile strength of silicon is over 100 + + + align:start position:0% +tensile strength of silicon is over 100 +megapascals but actually where the + + align:start position:0% +megapascals but actually where the + + + align:start position:0% +megapascals but actually where the +danger arises when you're cooling the + + align:start position:0% +danger arises when you're cooling the + + + align:start position:0% +danger arises when you're cooling the +substrate and we'll we'll get we'll get + + align:start position:0% +substrate and we'll we'll get we'll get + + + align:start position:0% +substrate and we'll we'll get we'll get +on to that but um it's really the the + + align:start position:0% +on to that but um it's really the the + + + align:start position:0% +on to that but um it's really the the +lateral forces applied to the protruding + + align:start position:0% +lateral forces applied to the protruding + + + align:start position:0% +lateral forces applied to the protruding +stamp features that are dangerous + + align:start position:0% +stamp features that are dangerous + + + align:start position:0% +stamp features that are dangerous +because they they create moments on the + + align:start position:0% +because they they create moments on the + + + align:start position:0% +because they they create moments on the +features and can cause cracks at the at + + align:start position:0% +features and can cause cracks at the at + + + align:start position:0% +features and can cause cracks at the at +the base of the feature to propagate. So + + align:start position:0% +the base of the feature to propagate. So + + + align:start position:0% +the base of the feature to propagate. So +uh good question right? So anyway + + align:start position:0% +uh good question right? So anyway + + + align:start position:0% +uh good question right? So anyway +intersperse center point runs and then + + align:start position:0% +intersperse center point runs and then + + + align:start position:0% +intersperse center point runs and then +what what we've done to provide some + + align:start position:0% +what what we've done to provide some + + + align:start position:0% +what what we've done to provide some +basis for for a test of significance of + + align:start position:0% +basis for for a test of significance of + + + align:start position:0% +basis for for a test of significance of +the effects is is to take the average of + + align:start position:0% +the effects is is to take the average of + + + align:start position:0% +the effects is is to take the average of +these peak penetrations. So we've just + + align:start position:0% +these peak penetrations. So we've just + + + align:start position:0% +these peak penetrations. So we've just +taken the mean over all feature sizes + + align:start position:0% +taken the mean over all feature sizes + + + align:start position:0% +taken the mean over all feature sizes +and orientations and everything and uh + + align:start position:0% +and orientations and everything and uh + + + align:start position:0% +and orientations and everything and uh +put it put it down here. And so you know + + align:start position:0% +put it put it down here. And so you know + + + align:start position:0% +put it put it down here. And so you know +you can do an ANOVA and you can look at + + align:start position:0% +you can do an ANOVA and you can look at + + + align:start position:0% +you can do an ANOVA and you can look at +the significance of various effects. Um + + align:start position:0% +the significance of various effects. Um + + + align:start position:0% +the significance of various effects. Um +and and and actually + + align:start position:0% +and and and actually + + + align:start position:0% +and and and actually +um it we get we get the impression I + + align:start position:0% +um it we get we get the impression I + + + align:start position:0% +um it we get we get the impression I +mean certainly temperature and force and + + align:start position:0% +mean certainly temperature and force and + + + align:start position:0% +mean certainly temperature and force and +whole time is significant that you know + + align:start position:0% +whole time is significant that you know + + + align:start position:0% +whole time is significant that you know +is exactly what we expected. The + + align:start position:0% +is exactly what we expected. The + + + align:start position:0% +is exactly what we expected. The +question down + + align:start position:0% +question down + + + align:start position:0% +question down +here is um well at the 5% level load + + align:start position:0% +here is um well at the 5% level load + + + align:start position:0% +here is um well at the 5% level load +loading rate the time over which that + + align:start position:0% +loading rate the time over which that + + + align:start position:0% +loading rate the time over which that +load is ramped up uh is not appearing + + align:start position:0% +load is ramped up uh is not appearing + + + align:start position:0% +load is ramped up uh is not appearing +quite to be significant but you know + + align:start position:0% +quite to be significant but you know + + + align:start position:0% +quite to be significant but you know +even we we don't know because we we + + align:start position:0% +even we we don't know because we we + + + align:start position:0% +even we we don't know because we we +didn't make a very judicious choice of + + align:start position:0% +didn't make a very judicious choice of + + + align:start position:0% +didn't make a very judicious choice of +of of uh aliasing arrangements. um we we + + align:start position:0% +of of uh aliasing arrangements. um we we + + + align:start position:0% +of of uh aliasing arrangements. um we we +don't know whether that's + + align:start position:0% +don't know whether that's + + + align:start position:0% +don't know whether that's +really at the 7% level significant that + + align:start position:0% +really at the 7% level significant that + + + align:start position:0% +really at the 7% level significant that +loading time is is is a is is a relevant + + align:start position:0% +loading time is is is a is is a relevant + + + align:start position:0% +loading time is is is a is is a relevant +factor or whether it's the interaction + + align:start position:0% +factor or whether it's the interaction + + + align:start position:0% +factor or whether it's the interaction +of temperature, force and hold time. And + + align:start position:0% +of temperature, force and hold time. And + + + align:start position:0% +of temperature, force and hold time. And +you just thinking about this + + align:start position:0% +you just thinking about this + + + align:start position:0% +you just thinking about this +intuitively, you do expect the + + align:start position:0% +intuitively, you do expect the + + + align:start position:0% +intuitively, you do expect the +interactions to be important. You expect + + align:start position:0% +interactions to be important. You expect + + + align:start position:0% +interactions to be important. You expect +the product of temperature and force to + + align:start position:0% +the product of temperature and force to + + + align:start position:0% +the product of temperature and force to +be relevant or some + + align:start position:0% +be relevant or some + + + align:start position:0% +be relevant or some +nonlinear combination of of the two + + align:start position:0% +nonlinear combination of of the two + + + align:start position:0% +nonlinear combination of of the two +parameters. um just because a + + align:start position:0% +parameters. um just because a + + + align:start position:0% +parameters. um just because a +temperature imparts a strain rate for a + + align:start position:0% +temperature imparts a strain rate for a + + + align:start position:0% +temperature imparts a strain rate for a +given force. So increasing the force + + align:start position:0% +given force. So increasing the force + + + align:start position:0% +given force. So increasing the force +will increase the strain rate and so + + align:start position:0% +will increase the strain rate and so + + + align:start position:0% +will increase the strain rate and so +forth. So + + align:start position:0% + + + + align:start position:0% + +anyway and and also as you know as as we + + align:start position:0% +anyway and and also as you know as as we + + + align:start position:0% +anyway and and also as you know as as we +probably would have expected that + + align:start position:0% +probably would have expected that + + + align:start position:0% +probably would have expected that +there's significant curvature in the + + align:start position:0% +there's significant curvature in the + + + align:start position:0% +there's significant curvature in the +results and and you know harking back to + + align:start position:0% +results and and you know harking back to + + + align:start position:0% +results and and you know harking back to +that graph of uh modulus against + + align:start position:0% +that graph of uh modulus against + + + align:start position:0% +that graph of uh modulus against +temperature that's exactly what we would + + align:start position:0% +temperature that's exactly what we would + + + align:start position:0% +temperature that's exactly what we would +expect. + + align:start position:0% +expect. + + + align:start position:0% +expect. +I actually I should have highlighted + + align:start position:0% +I actually I should have highlighted + + + align:start position:0% +I actually I should have highlighted +when uh when I showed you this graph + + align:start position:0% +when uh when I showed you this graph + + + align:start position:0% +when uh when I showed you this graph +that + + align:start position:0% +that + + + align:start position:0% +that +uh there's there are trade-offs to be + + align:start position:0% +uh there's there are trade-offs to be + + + align:start position:0% +uh there's there are trade-offs to be +made in picking these operating + + align:start position:0% +made in picking these operating + + + align:start position:0% +made in picking these operating +parameters. On the one hand, you might + + align:start position:0% +parameters. On the one hand, you might + + + align:start position:0% +parameters. On the one hand, you might +say, I don't want to heat the material + + align:start position:0% +say, I don't want to heat the material + + + align:start position:0% +say, I don't want to heat the material +any hotter than is necessary. I'd rather + + align:start position:0% +any hotter than is necessary. I'd rather + + + align:start position:0% +any hotter than is necessary. I'd rather +just press press as hard as I need to + + align:start position:0% +just press press as hard as I need to + + + align:start position:0% +just press press as hard as I need to +and and operate maybe operate at 120 + + align:start position:0% +and and operate maybe operate at 120 + + + align:start position:0% +and and operate maybe operate at 120 +115° C. uh where I can deform material + + align:start position:0% +115° C. uh where I can deform material + + + align:start position:0% +115° C. uh where I can deform material +um and and then because I'm not at a + + align:start position:0% +um and and then because I'm not at a + + + align:start position:0% +um and and then because I'm not at a +very high temperature when I cool down + + align:start position:0% +very high temperature when I cool down + + + align:start position:0% +very high temperature when I cool down +there isn't going to be very much + + align:start position:0% +there isn't going to be very much + + + align:start position:0% +there isn't going to be very much +differential thermal contraction of the + + align:start position:0% +differential thermal contraction of the + + + align:start position:0% +differential thermal contraction of the +stamp and the substrate so I won't have + + align:start position:0% +stamp and the substrate so I won't have + + + align:start position:0% +stamp and the substrate so I won't have +big residual stresses and I won't risk + + align:start position:0% +big residual stresses and I won't risk + + + align:start position:0% +big residual stresses and I won't risk +breaking the stamp and that would be a + + align:start position:0% +breaking the stamp and that would be a + + + align:start position:0% +breaking the stamp and that would be a +re really logical thing to say um and + + align:start position:0% +re really logical thing to say um and + + + align:start position:0% +re really logical thing to say um and +from a process control perspective + + align:start position:0% +from a process control perspective + + + align:start position:0% +from a process control perspective +however you can see that this may not be + + align:start position:0% +however you can see that this may not be + + + align:start position:0% +however you can see that this may not be +a very good place to operate where + + align:start position:0% +a very good place to operate where + + + align:start position:0% +a very good place to operate where +modulus is highly sensitive to + + align:start position:0% +modulus is highly sensitive to + + + align:start position:0% +modulus is highly sensitive to +temperature and + + align:start position:0% +temperature and + + + align:start position:0% +temperature and +uh our personal experience with uh lab + + align:start position:0% +uh our personal experience with uh lab + + + align:start position:0% +uh our personal experience with uh lab +apparatus and this is probably different + + align:start position:0% +apparatus and this is probably different + + + align:start position:0% +apparatus and this is probably different +in industry but controlling the + + align:start position:0% +in industry but controlling the + + + align:start position:0% +in industry but controlling the +temperature is is is fairly difficult. I + + align:start position:0% +temperature is is is fairly difficult. I + + + align:start position:0% +temperature is is is fairly difficult. I +mean you you can this is quite an + + align:start position:0% +mean you you can this is quite an + + + align:start position:0% +mean you you can this is quite an +optimistic error bar in fact to put on + + align:start position:0% +optimistic error bar in fact to put on + + + align:start position:0% +optimistic error bar in fact to put on +the temperature. + + align:start position:0% +the temperature. + + + align:start position:0% +the temperature. +So that's I think a really relevant + + align:start position:0% +So that's I think a really relevant + + + align:start position:0% +So that's I think a really relevant +consideration um for for choosing hot + + align:start position:0% +consideration um for for choosing hot + + + align:start position:0% +consideration um for for choosing hot +embossing parameters how sensitive we + + align:start position:0% +embossing parameters how sensitive we + + + align:start position:0% +embossing parameters how sensitive we +are to temperature and um + + align:start position:0% +are to temperature and um + + + align:start position:0% +are to temperature and um +giving a temperature window of plusus + + align:start position:0% +giving a temperature window of plusus + + + align:start position:0% +giving a temperature window of plusus +one degree. That's what that's what I + + align:start position:0% +one degree. That's what that's what I + + + align:start position:0% +one degree. That's what that's what I +estimated for that particular machine. + + align:start position:0% +estimated for that particular machine. + + + align:start position:0% +estimated for that particular machine. +Yeah. Yeah. And I think um that there + + align:start position:0% +Yeah. Yeah. And I think um that there + + + align:start position:0% +Yeah. Yeah. And I think um that there +are also big challenges to do with + + align:start position:0% +are also big challenges to do with + + + align:start position:0% +are also big challenges to do with +temperature uniformity across chucks. + + align:start position:0% +temperature uniformity across chucks. + + + align:start position:0% +temperature uniformity across chucks. +Yeah. that's that's really uh something + + align:start position:0% +Yeah. that's that's really uh something + + + align:start position:0% +Yeah. that's that's really uh something +that people are looking at. + + align:start position:0% +that people are looking at. + + + align:start position:0% +that people are looking at. +So in in + + align:start position:0% +So in in + + + align:start position:0% +So in in +fact the uh the side of the industry + + align:start position:0% +fact the uh the side of the industry + + + align:start position:0% +fact the uh the side of the industry +that's more advanced is really the nano + + align:start position:0% +that's more advanced is really the nano + + + align:start position:0% +that's more advanced is really the nano +imprint lithography side more so than + + align:start position:0% +imprint lithography side more so than + + + align:start position:0% +imprint lithography side more so than +the the micrombbossing side and and in + + align:start position:0% +the the micrombbossing side and and in + + + align:start position:0% +the the micrombbossing side and and in +that case + + align:start position:0% +that case + + + align:start position:0% +that case +uh it's it's more attractive to go to + + align:start position:0% +uh it's it's more attractive to go to + + + align:start position:0% +uh it's it's more attractive to go to +very high temperatures to make the + + align:start position:0% +very high temperatures to make the + + + align:start position:0% +very high temperatures to make the +material behave more like a viscous + + align:start position:0% +material behave more like a viscous + + + align:start position:0% +material behave more like a viscous +fluid than like a a rubbery material or + + align:start position:0% +fluid than like a a rubbery material or + + + align:start position:0% +fluid than like a a rubbery material or +visco elastic. So then temperature + + align:start position:0% +visco elastic. So then temperature + + + align:start position:0% +visco elastic. So then temperature +variation isn't so much of of an issue. + + align:start position:0% +variation isn't so much of of an issue. + + + align:start position:0% +variation isn't so much of of an issue. +You're you're right down in the 4 + + align:start position:0% +You're you're right down in the 4 + + + align:start position:0% +You're you're right down in the 4 +megapascal range. So it's um but yes, + + align:start position:0% +megapascal range. So it's um but yes, + + + align:start position:0% +megapascal range. So it's um but yes, +good point. Absolutely. Now, + + align:start position:0% +good point. Absolutely. Now, + + + align:start position:0% +good point. Absolutely. Now, +um, yes, there's one really interesting + + align:start position:0% +um, yes, there's one really interesting + + + align:start position:0% +um, yes, there's one really interesting +thing about these results and, uh, I + + align:start position:0% +thing about these results and, uh, I + + + align:start position:0% +thing about these results and, uh, I +mentioned that I had two sets of each + + align:start position:0% +mentioned that I had two sets of each + + + align:start position:0% +mentioned that I had two sets of each +feature size and one was oriented + + align:start position:0% +feature size and one was oriented + + + align:start position:0% +feature size and one was oriented +vertically on the stamp and one + + align:start position:0% +vertically on the stamp and one + + + align:start position:0% +vertically on the stamp and one +horizontally. And I just put those on + + align:start position:0% +horizontally. And I just put those on + + + align:start position:0% +horizontally. And I just put those on +there on the off chance that there was + + align:start position:0% +there on the off chance that there was + + + align:start position:0% +there on the off chance that there was +anisotropy in in the materials. And it + + align:start position:0% +anisotropy in in the materials. And it + + + align:start position:0% +anisotropy in in the materials. And it +turns out with this topaz sample, which + + align:start position:0% +turns out with this topaz sample, which + + + align:start position:0% +turns out with this topaz sample, which +is a gift from the supplier, there is + + align:start position:0% +is a gift from the supplier, there is + + + align:start position:0% +is a gift from the supplier, there is +really strong anisotropy. And uh so you + + align:start position:0% +really strong anisotropy. And uh so you + + + align:start position:0% +really strong anisotropy. And uh so you +can see that the the filledin um the + + align:start position:0% +can see that the the filledin um the + + + align:start position:0% +can see that the the filledin um the +filledin + + align:start position:0% +filledin + + + align:start position:0% +filledin +symbols are uh for an arbitrary defined + + align:start position:0% +symbols are uh for an arbitrary defined + + + align:start position:0% +symbols are uh for an arbitrary defined +orientation 90° and and the open symbols + + align:start position:0% +orientation 90° and and the open symbols + + + align:start position:0% +orientation 90° and and the open symbols +for 0 degrees. So turning the feature + + align:start position:0% +for 0 degrees. So turning the feature + + + align:start position:0% +for 0 degrees. So turning the feature +through 90 degrees gives you this this + + align:start position:0% +through 90 degrees gives you this this + + + align:start position:0% +through 90 degrees gives you this this +really big difference in in in + + align:start position:0% +really big difference in in in + + + align:start position:0% +really big difference in in in +penetration. + + align:start position:0% +penetration. + + + align:start position:0% +penetration. +And these results are based on five + + align:start position:0% +And these results are based on five + + + align:start position:0% +And these results are based on five +replicates. You can see the error bars + + align:start position:0% +replicates. You can see the error bars + + + align:start position:0% +replicates. You can see the error bars +there. one standard deviation of of the + + align:start position:0% +there. one standard deviation of of the + + + align:start position:0% +there. one standard deviation of of the +five replica results. And uh there's + + align:start position:0% +five replica results. And uh there's + + + align:start position:0% +five replica results. And uh there's +definitely a + + align:start position:0% +definitely a + + + align:start position:0% +definitely a +significant an isotropy whether that's + + align:start position:0% +significant an isotropy whether that's + + + align:start position:0% +significant an isotropy whether that's +to do with residual stress in the in the + + align:start position:0% +to do with residual stress in the in the + + + align:start position:0% +to do with residual stress in the in the +cast + + align:start position:0% +cast + + + align:start position:0% +cast +uh in the cast sheets alignment of the + + align:start position:0% +uh in the cast sheets alignment of the + + + align:start position:0% +uh in the cast sheets alignment of the +polymer chains because of some some + + align:start position:0% +polymer chains because of some some + + + align:start position:0% +polymer chains because of some some +feature of its processing. I + + align:start position:0% +feature of its processing. I + + + align:start position:0% +feature of its processing. I +mean, you can start to see that if + + align:start position:0% +mean, you can start to see that if + + + align:start position:0% +mean, you can start to see that if +materials like this have such a big + + align:start position:0% +materials like this have such a big + + + align:start position:0% +materials like this have such a big +orientation dependence, um, and that is + + align:start position:0% +orientation dependence, um, and that is + + + align:start position:0% +orientation dependence, um, and that is +so dependent on how they've been + + align:start position:0% +so dependent on how they've been + + + align:start position:0% +so dependent on how they've been +processed, you can't necessarily know + + align:start position:0% +processed, you can't necessarily know + + + align:start position:0% +processed, you can't necessarily know +the whole processing history of what + + align:start position:0% +the whole processing history of what + + + align:start position:0% +the whole processing history of what +you're supplied. It will be useful to + + align:start position:0% +you're supplied. It will be useful to + + + align:start position:0% +you're supplied. It will be useful to +have these quick checks of of of the + + align:start position:0% +have these quick checks of of of the + + + align:start position:0% +have these quick checks of of of the +properties of materials that that are + + align:start position:0% +properties of materials that that are + + + align:start position:0% +properties of materials that that are +given to you. And they they wouldn't you + + align:start position:0% +given to you. And they they wouldn't you + + + align:start position:0% +given to you. And they they wouldn't you +wouldn't be able to get that information + + align:start position:0% +wouldn't be able to get that information + + + align:start position:0% +wouldn't be able to get that information +just by a bulk compression experiment. + + align:start position:0% +just by a bulk compression experiment. + + + align:start position:0% +just by a bulk compression experiment. +So these these carefully designed test + + align:start position:0% +So these these carefully designed test + + + align:start position:0% +So these these carefully designed test +patterns are really important. I should + + align:start position:0% +patterns are really important. I should + + + align:start position:0% +patterns are really important. I should +say that this is this is an in the + + align:start position:0% +say that this is this is an in the + + + align:start position:0% +say that this is this is an in the +material not in the stamp because if we + + align:start position:0% +material not in the stamp because if we + + + align:start position:0% +material not in the stamp because if we +rotate the stamp relative to the sample + + align:start position:0% +rotate the stamp relative to the sample + + + align:start position:0% +rotate the stamp relative to the sample +the uh the the results reverse. So it's + + align:start position:0% +the uh the the results reverse. So it's + + + align:start position:0% +the uh the the results reverse. So it's +definitely in the + + align:start position:0% +definitely in the + + + align:start position:0% +definitely in the +material. Uh anyhow, that was + + align:start position:0% +material. Uh anyhow, that was + + + align:start position:0% +material. Uh anyhow, that was +uh that was for Topaz and I I showed you + + align:start position:0% +uh that was for Topaz and I I showed you + + + align:start position:0% +uh that was for Topaz and I I showed you +a few slides ago what happens when uh + + align:start position:0% +a few slides ago what happens when uh + + + align:start position:0% +a few slides ago what happens when uh +when when hold time is relevant when + + align:start position:0% +when when hold time is relevant when + + + align:start position:0% +when when hold time is relevant when +you've got plastic flow and we saw that + + align:start position:0% +you've got plastic flow and we saw that + + + align:start position:0% +you've got plastic flow and we saw that +uh that that the introduction of this + + align:start position:0% +uh that that the introduction of this + + + align:start position:0% +uh that that the introduction of this +linear dash pot the scaling of the point + + align:start position:0% +linear dash pot the scaling of the point + + + align:start position:0% +linear dash pot the scaling of the point +load response function was a reasonably + + align:start position:0% +load response function was a reasonably + + + align:start position:0% +load response function was a reasonably +good way of capturing that. Uh what + + align:start position:0% +good way of capturing that. Uh what + + + align:start position:0% +good way of capturing that. Uh what +we're working on now is is this ability + + align:start position:0% +we're working on now is is this ability + + + align:start position:0% +we're working on now is is this ability +to capture yield stress to iron out some + + align:start position:0% +to capture yield stress to iron out some + + + align:start position:0% +to capture yield stress to iron out some +of the shortcomings of the model. The + + align:start position:0% +of the shortcomings of the model. The + + + align:start position:0% +of the shortcomings of the model. The +fact that those narrower features + + align:start position:0% +fact that those narrower features + + + align:start position:0% +fact that those narrower features +actually filled more than the model + + align:start position:0% +actually filled more than the model + + + align:start position:0% +actually filled more than the model +predicted. And + + align:start position:0% + + + + align:start position:0% + +uh the other thing that we're trying to + + align:start position:0% +uh the other thing that we're trying to + + + align:start position:0% +uh the other thing that we're trying to +do is extend this simulation approach to + + align:start position:0% +do is extend this simulation approach to + + + align:start position:0% +do is extend this simulation approach to +thin substrates for the nano imprint + + align:start position:0% +thin substrates for the nano imprint + + + align:start position:0% +thin substrates for the nano imprint +lithography case where this type of + + align:start position:0% +lithography case where this type of + + + align:start position:0% +lithography case where this type of +point load response function isn't + + align:start position:0% +point load response function isn't + + + align:start position:0% +point load response function isn't +correct. The features are the same size + + align:start position:0% +correct. The features are the same size + + + align:start position:0% +correct. The features are the same size +roughly as the thickness of the + + align:start position:0% +roughly as the thickness of the + + + align:start position:0% +roughly as the thickness of the +substrate. You have to start thinking + + align:start position:0% +substrate. You have to start thinking + + + align:start position:0% +substrate. You have to start thinking +about lateral transport of material and + + align:start position:0% +about lateral transport of material and + + + align:start position:0% +about lateral transport of material and +uh that's quite an exciting topic. + + align:start position:0% +uh that's quite an exciting topic. + + + align:start position:0% +uh that's quite an exciting topic. +Now, we had a couple of good questions + + align:start position:0% +Now, we had a couple of good questions + + + align:start position:0% +Now, we had a couple of good questions +about damage to the stamp and demolding + + align:start position:0% +about damage to the stamp and demolding + + + align:start position:0% +about damage to the stamp and demolding +issues. And this + + align:start position:0% + + + + align:start position:0% + +is perhaps the uh the biggest impediment + + align:start position:0% +is perhaps the uh the biggest impediment + + + align:start position:0% +is perhaps the uh the biggest impediment +to to the use of imprinting it + + align:start position:0% +to to the use of imprinting it + + + align:start position:0% +to to the use of imprinting it +microscale structures. It's not it's not + + align:start position:0% +microscale structures. It's not it's not + + + align:start position:0% +microscale structures. It's not it's not +that much of a problem for for nano + + align:start position:0% +that much of a problem for for nano + + + align:start position:0% +that much of a problem for for nano +imprint, but microscale structures, it's + + align:start position:0% +imprint, but microscale structures, it's + + + align:start position:0% +imprint, but microscale structures, it's +it's crucial. And you here are some + + align:start position:0% +it's crucial. And you here are some + + + align:start position:0% +it's crucial. And you here are some +examples of + + align:start position:0% +examples of + + + align:start position:0% +examples of +uh problems that that have occurred + + align:start position:0% +uh problems that that have occurred + + + align:start position:0% +uh problems that that have occurred +during cooling and demolding. This is an + + align:start position:0% +during cooling and demolding. This is an + + + align:start position:0% +during cooling and demolding. This is an +SEM picture of a PMA component that has + + align:start position:0% +SEM picture of a PMA component that has + + + align:start position:0% +SEM picture of a PMA component that has +been embossed with a a + + align:start position:0% +been embossed with a a + + + align:start position:0% +been embossed with a a +hexagonal post. This was this was made + + align:start position:0% +hexagonal post. This was this was made + + + align:start position:0% +hexagonal post. This was this was made +from silicon in fact. + + align:start position:0% +from silicon in fact. + + + align:start position:0% +from silicon in fact. +And if you imagine the uh the substrate + + align:start position:0% +And if you imagine the uh the substrate + + + align:start position:0% +And if you imagine the uh the substrate +being being mostly on this side of the + + align:start position:0% +being being mostly on this side of the + + + align:start position:0% +being being mostly on this side of the +feature cooled under load, the polymer + + align:start position:0% +feature cooled under load, the polymer + + + align:start position:0% +feature cooled under load, the polymer +having at least 10 times the thermal + + align:start position:0% +having at least 10 times the thermal + + + align:start position:0% +having at least 10 times the thermal +expansion coefficient as silicon uh + + align:start position:0% +expansion coefficient as silicon uh + + + align:start position:0% +expansion coefficient as silicon uh +has pushed itself against the sides of + + align:start position:0% +has pushed itself against the sides of + + + align:start position:0% +has pushed itself against the sides of +the features. And we when we demold we + + align:start position:0% +the features. And we when we demold we + + + align:start position:0% +the features. And we when we demold we +get these really substantial ridges. I + + align:start position:0% +get these really substantial ridges. I + + + align:start position:0% +get these really substantial ridges. I +think this was this was embossed at 130° + + align:start position:0% +think this was this was embossed at 130° + + + align:start position:0% +think this was this was embossed at 130° +C. So 20 20 degrees above glass + + align:start position:0% +C. So 20 20 degrees above glass + + + align:start position:0% +C. So 20 20 degrees above glass +transition. And uh + + align:start position:0% +transition. And uh + + + align:start position:0% +transition. And uh +so what we haven't yet worked out is + + align:start position:0% +so what we haven't yet worked out is + + + align:start position:0% +so what we haven't yet worked out is +whether these uh these contact stresses + + align:start position:0% +whether these uh these contact stresses + + + align:start position:0% +whether these uh these contact stresses +are large enough actually to push the + + align:start position:0% +are large enough actually to push the + + + align:start position:0% +are large enough actually to push the +stamp off the off the substrate or + + align:start position:0% +stamp off the off the substrate or + + + align:start position:0% +stamp off the off the substrate or +whether uh it's just + + align:start position:0% +whether uh it's just + + + align:start position:0% +whether uh it's just +uh + + align:start position:0% +uh + + + align:start position:0% +uh +elastic potential energy stored in the + + align:start position:0% +elastic potential energy stored in the + + + align:start position:0% +elastic potential energy stored in the +in the polymer that causes this ridge to + + align:start position:0% +in the polymer that causes this ridge to + + + align:start position:0% +in the polymer that causes this ridge to +spring up when you peel the the stamp + + align:start position:0% +spring up when you peel the the stamp + + + align:start position:0% +spring up when you peel the the stamp +off the substrate. + + align:start position:0% +off the substrate. + + + align:start position:0% +off the substrate. +Here are some optical microraphs showing + + align:start position:0% +Here are some optical microraphs showing + + + align:start position:0% +Here are some optical microraphs showing +similar problem. + + align:start position:0% +similar problem. + + + align:start position:0% +similar problem. +Triangular hole embossed into a polymer + + align:start position:0% +Triangular hole embossed into a polymer + + + align:start position:0% +Triangular hole embossed into a polymer +substrate. Uh the material has + + align:start position:0% +substrate. Uh the material has + + + align:start position:0% +substrate. Uh the material has +contracted from right to left relative + + align:start position:0% +contracted from right to left relative + + + align:start position:0% +contracted from right to left relative +to the stamp feature. And in fact, + + align:start position:0% +to the stamp feature. And in fact, + + + align:start position:0% +to the stamp feature. And in fact, +sometimes we see these shards of polymer + + align:start position:0% +sometimes we see these shards of polymer + + + align:start position:0% +sometimes we see these shards of polymer +being sheared off uh and and and again a + + align:start position:0% +being sheared off uh and and and again a + + + align:start position:0% +being sheared off uh and and and again a +hole where there's been a few tens of + + align:start position:0% +hole where there's been a few tens of + + + align:start position:0% +hole where there's been a few tens of +microns relative contraction. Go. I just + + align:start position:0% +microns relative contraction. Go. I just + + + align:start position:0% +microns relative contraction. Go. I just +I'm curious is there any some like + + align:start position:0% +I'm curious is there any some like + + + align:start position:0% +I'm curious is there any some like +lubricant that you can use to decrease + + align:start position:0% +lubricant that you can use to decrease + + + align:start position:0% +lubricant that you can use to decrease +the load you + + align:start position:0% +the load you + + + align:start position:0% +the load you +there are + + align:start position:0% +there are + + + align:start position:0% +there are +uh there are products you can get that + + align:start position:0% +uh there are products you can get that + + + align:start position:0% +uh there are products you can get that +you can spray onto the mold or indeed + + align:start position:0% +you can spray onto the mold or indeed + + + align:start position:0% +you can spray onto the mold or indeed +treatments that can be given to the mold + + align:start position:0% +treatments that can be given to the mold + + + align:start position:0% +treatments that can be given to the mold +to reduce the coefficient of friction + + align:start position:0% +to reduce the coefficient of friction + + + align:start position:0% +to reduce the coefficient of friction +between between the mold and the and the + + align:start position:0% +between between the mold and the and the + + + align:start position:0% +between between the mold and the and the +substrate. that + + align:start position:0% +substrate. that + + + align:start position:0% +substrate. that +won't that won't reduce the magnitude of + + align:start position:0% +won't that won't reduce the magnitude of + + + align:start position:0% +won't that won't reduce the magnitude of +the the lateral force. That's to do with + + align:start position:0% +the the lateral force. That's to do with + + + align:start position:0% +the the lateral force. That's to do with +Young's modulus and the coefficient of + + align:start position:0% +Young's modulus and the coefficient of + + + align:start position:0% +Young's modulus and the coefficient of +thermal expansion. But yes, it it will + + align:start position:0% +thermal expansion. But yes, it it will + + + align:start position:0% +thermal expansion. But yes, it it will +um it will potentially make it easier + + align:start position:0% +um it will potentially make it easier + + + align:start position:0% +um it will potentially make it easier +once that lateral force is exerted to + + align:start position:0% +once that lateral force is exerted to + + + align:start position:0% +once that lateral force is exerted to +pull the stamp + + align:start position:0% +pull the stamp + + + align:start position:0% +pull the stamp +out. However, it's not the problem isn't + + align:start position:0% +out. However, it's not the problem isn't + + + align:start position:0% +out. However, it's not the problem isn't +all to do with friction. Sometimes you + + align:start position:0% +all to do with friction. Sometimes you + + + align:start position:0% +all to do with friction. Sometimes you +have you either your stamp is + + align:start position:0% +have you either your stamp is + + + align:start position:0% +have you either your stamp is +imperfectly made and there's a a + + align:start position:0% +imperfectly made and there's a a + + + align:start position:0% +imperfectly made and there's a a +negative draft. I mean I exaggerate but + + align:start position:0% +negative draft. I mean I exaggerate but + + + align:start position:0% +negative draft. I mean I exaggerate but +you know that if that were a stamp and + + align:start position:0% +you know that if that were a stamp and + + + align:start position:0% +you know that if that were a stamp and +that were a polymer that's a problem + + align:start position:0% +that were a polymer that's a problem + + + align:start position:0% +that were a polymer that's a problem +that people run into quite a lot. And + + align:start position:0% +that people run into quite a lot. And + + + align:start position:0% +that people run into quite a lot. And +then if the stamp has been made by deep + + align:start position:0% +then if the stamp has been made by deep + + + align:start position:0% +then if the stamp has been made by deep +reactive ion etching where there's this + + align:start position:0% +reactive ion etching where there's this + + + align:start position:0% +reactive ion etching where there's this +uh cyclic etching process and there are + + align:start position:0% +uh cyclic etching process and there are + + + align:start position:0% +uh cyclic etching process and there are +there are these little submicron + + align:start position:0% +there are these little submicron + + + align:start position:0% +there are these little submicron +scallops. you're susceptible to + + align:start position:0% +scallops. you're susceptible to + + + align:start position:0% +scallops. you're susceptible to +mechanical locking and and and there's + + align:start position:0% +mechanical locking and and and there's + + + align:start position:0% +mechanical locking and and and there's +plastic defamation of the polymer as you + + align:start position:0% +plastic defamation of the polymer as you + + + align:start position:0% +plastic defamation of the polymer as you +pull it off. + + align:start position:0% +pull it off. + + + align:start position:0% +pull it off. +So, it's a good point. Yes. And and and + + align:start position:0% +So, it's a good point. Yes. And and and + + + align:start position:0% +So, it's a good point. Yes. And and and +actually one thing that does work quite + + align:start position:0% +actually one thing that does work quite + + + align:start position:0% +actually one thing that does work quite +well is to leave the uh the teflon + + align:start position:0% +well is to leave the uh the teflon + + + align:start position:0% +well is to leave the uh the teflon +polymer coating on the silicon after + + align:start position:0% +polymer coating on the silicon after + + + align:start position:0% +polymer coating on the silicon after +etching. And that that does do quite a + + align:start position:0% +etching. And that that does do quite a + + + align:start position:0% +etching. And that that does do quite a +lot. Has a very limited lifetime though. + + align:start position:0% + + + + align:start position:0% + +Anyway, uh the the points of saying all + + align:start position:0% +Anyway, uh the the points of saying all + + + align:start position:0% +Anyway, uh the the points of saying all +this is is um as as I alluded to a few + + align:start position:0% +this is is um as as I alluded to a few + + + align:start position:0% +this is is um as as I alluded to a few +minutes ago, you might you might think + + align:start position:0% +minutes ago, you might you might think + + + align:start position:0% +minutes ago, you might you might think +of + + align:start position:0% +of + + + align:start position:0% +of +uh reducing the temperature swing to as + + align:start position:0% +uh reducing the temperature swing to as + + + align:start position:0% +uh reducing the temperature swing to as +small a value as you can so that that + + align:start position:0% +small a value as you can so that that + + + align:start position:0% +small a value as you can so that that +amount of thermal contraction is is + + align:start position:0% +amount of thermal contraction is is + + + align:start position:0% +amount of thermal contraction is is +restricted. You might even think of + + align:start position:0% +restricted. You might even think of + + + align:start position:0% +restricted. You might even think of +removing the load slightly above the + + align:start position:0% +removing the load slightly above the + + + align:start position:0% +removing the load slightly above the +glass transition temperature. Um, if + + align:start position:0% +glass transition temperature. Um, if + + + align:start position:0% +glass transition temperature. Um, if +you're in a region where some of the + + align:start position:0% +you're in a region where some of the + + + align:start position:0% +you're in a region where some of the +defamation or most of the defamation is + + align:start position:0% +defamation or most of the defamation is + + + align:start position:0% +defamation or most of the defamation is +actually plastic, which is true in a + + align:start position:0% +actually plastic, which is true in a + + + align:start position:0% +actually plastic, which is true in a +region about 10 degrees above glass + + align:start position:0% +region about 10 degrees above glass + + + align:start position:0% +region about 10 degrees above glass +transition for Pmama, if you can exploit + + align:start position:0% +transition for Pmama, if you can exploit + + + align:start position:0% +transition for Pmama, if you can exploit +the material properties to to avoid + + align:start position:0% +the material properties to to avoid + + + align:start position:0% +the material properties to to avoid +having a big temperature swing, then + + align:start position:0% +having a big temperature swing, then + + + align:start position:0% +having a big temperature swing, then +that could potentially be very exciting. + + align:start position:0% +that could potentially be very exciting. + + + align:start position:0% +that could potentially be very exciting. +And uh together with with Matt Dirks + + align:start position:0% +And uh together with with Matt Dirks + + + align:start position:0% +And uh together with with Matt Dirks +who's in the lab for manufacturing and + + align:start position:0% +who's in the lab for manufacturing and + + + align:start position:0% +who's in the lab for manufacturing and +productivity um we we looked into this a + + align:start position:0% +productivity um we we looked into this a + + + align:start position:0% +productivity um we we looked into this a +couple of years ago and + + align:start position:0% +couple of years ago and + + + align:start position:0% +couple of years ago and +uh found that if we if we control the + + align:start position:0% +uh found that if we if we control the + + + align:start position:0% +uh found that if we if we control the +temperature really carefully um then + + align:start position:0% +temperature really carefully um then + + + align:start position:0% +temperature really carefully um then +then it was promising. uh you know if + + align:start position:0% +then it was promising. uh you know if + + + align:start position:0% +then it was promising. uh you know if +you + + align:start position:0% +you + + + align:start position:0% +you +demold at 50 degrees C so well below + + align:start position:0% +demold at 50 degrees C so well below + + + align:start position:0% +demold at 50 degrees C so well below +glass transition and then uh pull pull + + align:start position:0% +glass transition and then uh pull pull + + + align:start position:0% +glass transition and then uh pull pull +the stamp off this is a a cross-section + + align:start position:0% +the stamp off this is a a cross-section + + + align:start position:0% +the stamp off this is a a cross-section +through the through the part then you + + align:start position:0% +through the through the part then you + + + align:start position:0% +through the through the part then you +get this horrendous ridge on the side of + + align:start position:0% +get this horrendous ridge on the side of + + + align:start position:0% +get this horrendous ridge on the side of +the part near the edge the side of the + + align:start position:0% +the part near the edge the side of the + + + align:start position:0% +the part near the edge the side of the +the feature near the edge of the part if + + align:start position:0% +the feature near the edge of the part if + + + align:start position:0% +the feature near the edge of the part if +you go down to if you demold say well + + align:start position:0% +you go down to if you demold say well + + + align:start position:0% +you go down to if you demold say well +above d transition 120 you get this blue + + align:start position:0% +above d transition 120 you get this blue + + + align:start position:0% +above d transition 120 you get this blue +line so you get you get some boeing of + + align:start position:0% +line so you get you get some boeing of + + + align:start position:0% +line so you get you get some boeing of +the base of the feature where where + + align:start position:0% +the base of the feature where where + + + align:start position:0% +the base of the feature where where +material has sprung back and you get + + align:start position:0% +material has sprung back and you get + + + align:start position:0% +material has sprung back and you get +splaying of the sidewalls and that's and + + align:start position:0% +splaying of the sidewalls and that's and + + + align:start position:0% +splaying of the sidewalls and that's and +this was repeatable over over many + + align:start position:0% +this was repeatable over over many + + + align:start position:0% +this was repeatable over over many +samples. However, if we can hit 110 + + align:start position:0% +samples. However, if we can hit 110 + + + align:start position:0% +samples. However, if we can hit 110 +degrees C on the nose, we get a nice + + align:start position:0% +degrees C on the nose, we get a nice + + + align:start position:0% +degrees C on the nose, we get a nice +flat feature. We get nice flat sidewalls + + align:start position:0% +flat feature. We get nice flat sidewalls + + + align:start position:0% +flat feature. We get nice flat sidewalls +and we get no ridge at all. And that + + align:start position:0% +and we get no ridge at all. And that + + + align:start position:0% +and we get no ridge at all. And that +would be great. Um, but again, that's + + align:start position:0% +would be great. Um, but again, that's + + + align:start position:0% +would be great. Um, but again, that's +that's the thing. Can you in a + + align:start position:0% +that's the thing. Can you in a + + + align:start position:0% +that's the thing. Can you in a +production + + align:start position:0% +production + + + align:start position:0% +production +setting make it 110 and not 115 or 120 + + align:start position:0% +setting make it 110 and not 115 or 120 + + + align:start position:0% +setting make it 110 and not 115 or 120 +and and that and that I think + + align:start position:0% +and and that and that I think + + + align:start position:0% +and and that and that I think +is probably possible to achieve but + + align:start position:0% +is probably possible to achieve but + + + align:start position:0% +is probably possible to achieve but +would increase the cost of the + + align:start position:0% +would increase the cost of the + + + align:start position:0% +would increase the cost of the +apparatus. So this is + + align:start position:0% +apparatus. So this is + + + align:start position:0% +apparatus. So this is +uh this is definitely something to be + + align:start position:0% +uh this is definitely something to be + + + align:start position:0% +uh this is definitely something to be +aware of + + align:start position:0% +aware of + + + align:start position:0% +aware of +and another thing that is uh of + + align:start position:0% +and another thing that is uh of + + + align:start position:0% +and another thing that is uh of +importance is that the risk of the whole + + align:start position:0% +importance is that the risk of the whole + + + align:start position:0% +importance is that the risk of the whole +part boeing if the demolding temperature + + align:start position:0% +part boeing if the demolding temperature + + + align:start position:0% +part boeing if the demolding temperature +is too high. We've observed problems + + align:start position:0% +is too high. We've observed problems + + + align:start position:0% +is too high. We've observed problems +with with that. So, uh that needs to be + + align:start position:0% +with with that. So, uh that needs to be + + + align:start position:0% +with with that. So, uh that needs to be +thought of as well. Here we can + + align:start position:0% +thought of as well. Here we can + + + align:start position:0% +thought of as well. Here we can +see also that if you're going to remove + + align:start position:0% +see also that if you're going to remove + + + align:start position:0% +see also that if you're going to remove +the load at or above the glass + + align:start position:0% +the load at or above the glass + + + align:start position:0% +the load at or above the glass +transition temperature, you have to pull + + align:start position:0% +transition temperature, you have to pull + + + align:start position:0% +transition temperature, you have to pull +out the stamp and cool it down jolly + + align:start position:0% +out the stamp and cool it down jolly + + + align:start position:0% +out the stamp and cool it down jolly +quickly because otherwise the part will + + align:start position:0% +quickly because otherwise the part will + + + align:start position:0% +quickly because otherwise the part will +start to contract back to its original + + align:start position:0% +start to contract back to its original + + + align:start position:0% +start to contract back to its original +flat surface. and and and so you leave + + align:start position:0% +flat surface. and and and so you leave + + + align:start position:0% +flat surface. and and and so you leave +it for 10 minutes, things start to look + + align:start position:0% +it for 10 minutes, things start to look + + + align:start position:0% +it for 10 minutes, things start to look +pretty pretty + + align:start position:0% + + + + align:start position:0% + +poor. Okay, that is + + align:start position:0% +poor. Okay, that is + + + align:start position:0% +poor. Okay, that is +uh an overview of uh about half of my + + align:start position:0% +uh an overview of uh about half of my + + + align:start position:0% +uh an overview of uh about half of my +thesis. And since we're at half past 9, + + align:start position:0% +thesis. And since we're at half past 9, + + + align:start position:0% +thesis. And since we're at half past 9, +I think we should stop. But uh are there + + align:start position:0% +I think we should stop. But uh are there + + + align:start position:0% +I think we should stop. But uh are there +any + + align:start position:0% +any + + + align:start position:0% +any +questions from anyone? + + align:start position:0% +questions from anyone? + + + align:start position:0% +questions from anyone? +If not, uh, then I guess the floor is + + align:start position:0% +If not, uh, then I guess the floor is + + + align:start position:0% +If not, uh, then I guess the floor is +open + + align:start position:0% +open + + + align:start position:0% +open +for questions about the projects. + + align:start position:0% + + + + align:start position:0% + +Mention one thing. Yeah. + + align:start position:0% +Mention one thing. Yeah. + + + align:start position:0% +Mention one thing. Yeah. +I I think later today hopefully uh uh or + + align:start position:0% +I I think later today hopefully uh uh or + + + align:start position:0% +I I think later today hopefully uh uh or +by tomorrow at the latest I'll post the + + align:start position:0% +by tomorrow at the latest I'll post the + + + align:start position:0% +by tomorrow at the latest I'll post the +tentative schedule for what groups will + + align:start position:0% +tentative schedule for what groups will + + + align:start position:0% +tentative schedule for what groups will +be presenting uh on each of uh Tuesday + + align:start position:0% +be presenting uh on each of uh Tuesday + + + align:start position:0% +be presenting uh on each of uh Tuesday +and Thursday. It'll be in the normal + + align:start position:0% +and Thursday. It'll be in the normal + + + align:start position:0% +and Thursday. It'll be in the normal +class period. Uh so we'll we'll plan for + + align:start position:0% +class period. Uh so we'll we'll plan for + + + align:start position:0% +class period. Uh so we'll we'll plan for +that. I'll have some other instructions + + align:start position:0% +that. I'll have some other instructions + + + align:start position:0% +that. I'll have some other instructions +like uh it'll it'll be + + align:start position:0% +like uh it'll it'll be + + + align:start position:0% +like uh it'll it'll be +best if possible to send those + + align:start position:0% +best if possible to send those + + + align:start position:0% +best if possible to send those +presentations to me a little bit early. + + align:start position:0% +presentations to me a little bit early. + + + align:start position:0% +presentations to me a little bit early. +I see we do have a USB uh you know port + + align:start position:0% +I see we do have a USB uh you know port + + + align:start position:0% +I see we do have a USB uh you know port +so it's possible we can we uh add up the + + align:start position:0% +so it's possible we can we uh add up the + + + align:start position:0% +so it's possible we can we uh add up the +presentations on the fly. I don't know + + align:start position:0% +presentations on the fly. I don't know + + + align:start position:0% +presentations on the fly. I don't know +quite how well that works out in + + align:start position:0% +quite how well that works out in + + + align:start position:0% +quite how well that works out in +Singapore. We'll have to figure that out + + align:start position:0% +Singapore. We'll have to figure that out + + + align:start position:0% +Singapore. We'll have to figure that out +as well. But but be alert some of you + + align:start position:0% +as well. But but be alert some of you + + + align:start position:0% +as well. But but be alert some of you +based on random draw are will be doing + + align:start position:0% +based on random draw are will be doing + + + align:start position:0% +based on random draw are will be doing +uh presentations on Tuesday and some + + align:start position:0% +uh presentations on Tuesday and some + + + align:start position:0% +uh presentations on Tuesday and some +groups will be doing that on + + align:start position:0% +groups will be doing that on + + + align:start position:0% +groups will be doing that on +Thursday. Are there Yeah. questions? Is + + align:start position:0% +Thursday. Are there Yeah. questions? Is + + + align:start position:0% +Thursday. Are there Yeah. questions? Is +there a rough guideline for how long the + + align:start position:0% +there a rough guideline for how long the + + + align:start position:0% +there a rough guideline for how long the +IT e letter should be or oh of the e uh + + align:start position:0% +IT e letter should be or oh of the e uh + + + align:start position:0% +IT e letter should be or oh of the e uh +paper? Yeah. + + align:start position:0% +paper? Yeah. + + + align:start position:0% +paper? Yeah. +Um I think typically whatever what + + align:start position:0% +Um I think typically whatever what + + + align:start position:0% +Um I think typically whatever what +whatever it it takes to do a reasonable + + align:start position:0% +whatever it it takes to do a reasonable + + + align:start position:0% +whatever it it takes to do a reasonable +job. I think uh something typically on + + align:start position:0% +job. I think uh something typically on + + + align:start position:0% +job. I think uh something typically on +the order of six, seven, eight pages is + + align:start position:0% +the order of six, seven, eight pages is + + + align:start position:0% +the order of six, seven, eight pages is +is I I think what we often saw in the + + align:start position:0% +is I I think what we often saw in the + + + align:start position:0% +is I I think what we often saw in the +past. Sometimes it might be a little bit + + align:start position:0% +past. Sometimes it might be a little bit + + + align:start position:0% +past. Sometimes it might be a little bit +shorter depending on how much background + + align:start position:0% +shorter depending on how much background + + + align:start position:0% +shorter depending on how much background +you have. So I don't have a strict + + align:start position:0% +you have. So I don't have a strict + + + align:start position:0% +you have. So I don't have a strict +strict page guideline. + + align:start position:0% + + + + align:start position:0% + +Good. Any questions Singapore on on + + align:start position:0% +Good. Any questions Singapore on on + + + align:start position:0% +Good. Any questions Singapore on on +that? + + align:start position:0% +that? + + + align:start position:0% +that? +Okay, great. Professor, yes, we have a + + align:start position:0% +Okay, great. Professor, yes, we have a + + + align:start position:0% +Okay, great. Professor, yes, we have a +we have a question for our project. We + + align:start position:0% +we have a question for our project. We + + + align:start position:0% +we have a question for our project. We +have actually have two questions. + + align:start position:0% +have actually have two questions. + + + align:start position:0% +have actually have two questions. +So um one question is that uh we have + + align:start position:0% +So um one question is that uh we have + + + align:start position:0% +So um one question is that uh we have +two outputs in our Can can you hear me? + + align:start position:0% +two outputs in our Can can you hear me? + + + align:start position:0% +two outputs in our Can can you hear me? +Yeah, speak up a little bit. It's a + + align:start position:0% +Yeah, speak up a little bit. It's a + + + align:start position:0% +Yeah, speak up a little bit. It's a +little bit. Okay. So, um one question is + + align:start position:0% +little bit. Okay. So, um one question is + + + align:start position:0% +little bit. Okay. So, um one question is +that we have two outputs that we are + + align:start position:0% +that we have two outputs that we are + + + align:start position:0% +that we have two outputs that we are +measuring in the data but these two + + align:start position:0% +measuring in the data but these two + + + align:start position:0% +measuring in the data but these two +outputs they are negatively + + align:start position:0% +outputs they are negatively + + + align:start position:0% +outputs they are negatively +correlated and our objective is to + + align:start position:0% +correlated and our objective is to + + + align:start position:0% +correlated and our objective is to +maximize one output and minimize the + + align:start position:0% +maximize one output and minimize the + + + align:start position:0% +maximize one output and minimize the +other output. So we understand that we + + align:start position:0% +other output. So we understand that we + + + align:start position:0% +other output. So we understand that we +can do it separately in optimization but + + align:start position:0% +can do it separately in optimization but + + + align:start position:0% +can do it separately in optimization but +you know when we want to sort of create + + align:start position:0% +you know when we want to sort of create + + + align:start position:0% +you know when we want to sort of create +a combine objective function and + + align:start position:0% +a combine objective function and + + + align:start position:0% +a combine objective function and +optimize these two together as they they + + align:start position:0% +optimize these two together as they they + + + align:start position:0% +optimize these two together as they they +come from the same set of inputs how how + + align:start position:0% +come from the same set of inputs how how + + + align:start position:0% +come from the same set of inputs how how +can we do that? Yeah. So the classic + + align:start position:0% +can we do that? Yeah. So the classic + + + align:start position:0% +can we do that? Yeah. So the classic +approach there is is it's a trade-off + + align:start position:0% +approach there is is it's a trade-off + + + align:start position:0% +approach there is is it's a trade-off +right one or the other. And what you + + align:start position:0% +right one or the other. And what you + + + align:start position:0% +right one or the other. And what you +typically do is apply a weight to the + + align:start position:0% +typically do is apply a weight to the + + + align:start position:0% +typically do is apply a weight to the +two alternatives. So you have a + + align:start position:0% +two alternatives. So you have a + + + align:start position:0% +two alternatives. So you have a +different numeric weight based on your + + align:start position:0% +different numeric weight based on your + + + align:start position:0% +different numeric weight based on your +engineering importance or the you know + + align:start position:0% +engineering importance or the you know + + + align:start position:0% +engineering importance or the you know +the customer importance or whatever of + + align:start position:0% +the customer importance or whatever of + + + align:start position:0% +the customer importance or whatever of +the two two effects. So you have one + + align:start position:0% +the two two effects. So you have one + + + align:start position:0% +the two two effects. So you have one +function that combines say squared + + align:start position:0% +function that combines say squared + + + align:start position:0% +function that combines say squared +deviations in the two outputs but with a + + align:start position:0% +deviations in the two outputs but with a + + + align:start position:0% +deviations in the two outputs but with a +different weight on the two outputs. + + align:start position:0% +different weight on the two outputs. + + + align:start position:0% +different weight on the two outputs. +Okay. I see. + + align:start position:0% + + + + align:start position:0% + +Okay, you're all set. + + align:start position:0% +Okay, you're all set. + + + align:start position:0% +Okay, you're all set. +We have another question actually. Okay, + + align:start position:0% +We have another question actually. Okay, + + + align:start position:0% +We have another question actually. Okay, +I have one more question is regarding + + align:start position:0% +I have one more question is regarding + + + align:start position:0% +I have one more question is regarding +the email you sent us. So, uh we were + + align:start position:0% +the email you sent us. So, uh we were + + + align:start position:0% +the email you sent us. So, uh we were +told that we can explore some of the one + + align:start position:0% +told that we can explore some of the one + + + align:start position:0% +told that we can explore some of the one +factor at a time strategy. Um we are not + + align:start position:0% +factor at a time strategy. Um we are not + + + align:start position:0% +factor at a time strategy. Um we are not +quite sure what what the strategy are + + align:start position:0% +quite sure what what the strategy are + + + align:start position:0% +quite sure what what the strategy are +you referring to. Is it studying the + + align:start position:0% +you referring to. Is it studying the + + + align:start position:0% +you referring to. Is it studying the +output and one input at a time or is it + + align:start position:0% +output and one input at a time or is it + + + align:start position:0% +output and one input at a time or is it +more like a stepwise regression? No, I'm + + align:start position:0% +more like a stepwise regression? No, I'm + + + align:start position:0% +more like a stepwise regression? No, I'm +referring to the optimization approach + + align:start position:0% +referring to the optimization approach + + + align:start position:0% +referring to the optimization approach +uh the one factor at a time OFAT that uh + + align:start position:0% +uh the one factor at a time OFAT that uh + + + align:start position:0% +uh the one factor at a time OFAT that uh +professor Dan Frey talked about in his + + align:start position:0% +professor Dan Frey talked about in his + + + align:start position:0% +professor Dan Frey talked about in his +lecture. + + align:start position:0% +lecture. + + + align:start position:0% +lecture. +So where you explore the corners, you + + align:start position:0% +So where you explore the corners, you + + + align:start position:0% +So where you explore the corners, you +look and see if you've improved it or + + align:start position:0% +look and see if you've improved it or + + + align:start position:0% +look and see if you've improved it or +not to decide if you keep that move. And + + align:start position:0% +not to decide if you keep that move. And + + + align:start position:0% +not to decide if you keep that move. And +then once you do make a move, then you + + align:start position:0% +then once you do make a move, then you + + + align:start position:0% +then once you do make a move, then you +randomly decide which next corner to + + align:start position:0% +randomly decide which next corner to + + + align:start position:0% +randomly decide which next corner to +experimentally try. So you've actually + + align:start position:0% +experimentally try. So you've actually + + + align:start position:0% +experimentally try. So you've actually +got the data already done from an a DOE, + + align:start position:0% +got the data already done from an a DOE, + + + align:start position:0% +got the data already done from an a DOE, +but now you can pretend you were + + align:start position:0% +but now you can pretend you were + + + align:start position:0% +but now you can pretend you were +actually running the experiment just one + + align:start position:0% +actually running the experiment just one + + + align:start position:0% +actually running the experiment just one +experimental point at a time using the + + align:start position:0% +experimental point at a time using the + + + align:start position:0% +experimental point at a time using the +OFAT approach. And I think that would be + + align:start position:0% +OFAT approach. And I think that would be + + + align:start position:0% +OFAT approach. And I think that would be +interesting for online + + align:start position:0% +interesting for online + + + align:start position:0% +interesting for online +optimization to compare also to response + + align:start position:0% +optimization to compare also to response + + + align:start position:0% +optimization to compare also to response +surface modeling optimization. + + align:start position:0% +surface modeling optimization. + + + align:start position:0% +surface modeling optimization. +Okay. All right. Thanks. Great. + + align:start position:0% +Okay. All right. Thanks. Great. + + + align:start position:0% +Okay. All right. Thanks. Great. +All right, see you guys \ No newline at end of file diff --git a/rfgaLeHq5f0.txt b/rfgaLeHq5f0.txt new file mode 100644 index 0000000000000000000000000000000000000000..b94efa6c9bd4f404ed8bc4091330ca01ccb2622d --- /dev/null +++ b/rfgaLeHq5f0.txt @@ -0,0 +1,10883 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a creative common license. Your support + + align:start position:0% +a creative common license. Your support + + + align:start position:0% +a creative common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Okay. So, uh let's get started. Our a + + align:start position:0% +Okay. So, uh let's get started. Our a + + + align:start position:0% +Okay. So, uh let's get started. Our a +lot of stuff happened in the last + + align:start position:0% +lot of stuff happened in the last + + + align:start position:0% +lot of stuff happened in the last +lecture. So, I'll spend a little bit + + align:start position:0% +lecture. So, I'll spend a little bit + + + align:start position:0% +lecture. So, I'll spend a little bit +more time to review what we talked what + + align:start position:0% +more time to review what we talked what + + + align:start position:0% +more time to review what we talked what +are the key points here. Uh + + align:start position:0% +are the key points here. Uh + + + align:start position:0% +are the key points here. Uh +so what we + + align:start position:0% +so what we + + + align:start position:0% +so what we +did in the last lecture is to ask the + + align:start position:0% +did in the last lecture is to ask the + + + align:start position:0% +did in the last lecture is to ask the +question what are the electron energy + + align:start position:0% +question what are the electron energy + + + align:start position:0% +question what are the electron energy +levels uh in a periodic potential and + + align:start position:0% +levels uh in a periodic potential and + + + align:start position:0% +levels uh in a periodic potential and +that's uh really uh the periodic means + + align:start position:0% +that's uh really uh the periodic means + + + align:start position:0% +that's uh really uh the periodic means +we're start thinking about the crystals + + align:start position:0% +we're start thinking about the crystals + + + align:start position:0% +we're start thinking about the crystals +and we started with a onedimensional + + align:start position:0% +and we started with a onedimensional + + + align:start position:0% +and we started with a onedimensional +simple pictures where I have periodic + + align:start position:0% +simple pictures where I have periodic + + + align:start position:0% +simple pictures where I have periodic +arrangement of atoms + + align:start position:0% +arrangement of atoms + + + align:start position:0% +arrangement of atoms +And uh uh so if you recall uh before + + align:start position:0% +And uh uh so if you recall uh before + + + align:start position:0% +And uh uh so if you recall uh before +last lecture what we're considering + + align:start position:0% +last lecture what we're considering + + + align:start position:0% +last lecture what we're considering +really are confined states of a atom of + + align:start position:0% +really are confined states of a atom of + + + align:start position:0% +really are confined states of a atom of +a molecule where the wave function is + + align:start position:0% +a molecule where the wave function is + + + align:start position:0% +a molecule where the wave function is +specially just around the atom around + + align:start position:0% +specially just around the atom around + + + align:start position:0% +specially just around the atom around +the molecule right and uh uh in this + + align:start position:0% +the molecule right and uh uh in this + + + align:start position:0% +the molecule right and uh uh in this +periodic structure what could happen is + + align:start position:0% +periodic structure what could happen is + + + align:start position:0% +periodic structure what could happen is +the wave function that originally belong + + align:start position:0% +the wave function that originally belong + + + align:start position:0% +the wave function that originally belong +electron belong to a atom Now they have + + align:start position:0% +electron belong to a atom Now they have + + + align:start position:0% +electron belong to a atom Now they have +space to flex their wave function + + align:start position:0% +space to flex their wave function + + + align:start position:0% +space to flex their wave function +muscles right it go through the whole + + align:start position:0% +muscles right it go through the whole + + + align:start position:0% +muscles right it go through the whole +crystal and uh uh in that expression + + align:start position:0% +crystal and uh uh in that expression + + + align:start position:0% +crystal and uh uh in that expression +what we have is we use extended wave of + + align:start position:0% +what we have is we use extended wave of + + + align:start position:0% +what we have is we use extended wave of +different wave + + align:start position:0% +different wave + + + align:start position:0% +different wave +vectors right and uh and so this each of + + align:start position:0% +vectors right and uh and so this each of + + + align:start position:0% +vectors right and uh and so this each of +those wave vector represent uh say a + + align:start position:0% +those wave vector represent uh say a + + + align:start position:0% +those wave vector represent uh say a +wave function and uh if I have n atoms + + align:start position:0% +wave function and uh if I have n atoms + + + align:start position:0% +wave function and uh if I have n atoms +And the wave vector uh is every two pi k + + align:start position:0% +And the wave vector uh is every two pi k + + + align:start position:0% +And the wave vector uh is every two pi k +* a every two pi I have a repeating so + + align:start position:0% +* a every two pi I have a repeating so + + + align:start position:0% +* a every two pi I have a repeating so +at the end I'm drawing only two pi in + + align:start position:0% +at the end I'm drawing only two pi in + + + align:start position:0% +at the end I'm drawing only two pi in +fact I'm drawing from negative pi to + + align:start position:0% +fact I'm drawing from negative pi to + + + align:start position:0% +fact I'm drawing from negative pi to +plus pi and I'll give you the rational + + align:start position:0% +plus pi and I'll give you the rational + + + align:start position:0% +plus pi and I'll give you the rational +today why we draw this + + align:start position:0% +today why we draw this + + + align:start position:0% +today why we draw this +way and then it's important to recognize + + align:start position:0% +way and then it's important to recognize + + + align:start position:0% +way and then it's important to recognize +that between minus pi / a to plus pi / a + + align:start position:0% +that between minus pi / a to plus pi / a + + + align:start position:0% +that between minus pi / a to plus pi / a +we have a total of n points because I + + align:start position:0% +we have a total of n points because I + + + align:start position:0% +we have a total of n points because I +have n + + align:start position:0% +have n + + + align:start position:0% +have n +atoms in this uh periodic + + align:start position:0% +atoms in this uh periodic + + + align:start position:0% +atoms in this uh periodic +direction and uh each point of course + + align:start position:0% +direction and uh each point of course + + + align:start position:0% +direction and uh each point of course +represent a quantum state except I do + + align:start position:0% +represent a quantum state except I do + + + align:start position:0% +represent a quantum state except I do +not have the spin included so each so if + + align:start position:0% +not have the spin included so each so if + + + align:start position:0% +not have the spin included so each so if +I have n points in fact I have two n so + + align:start position:0% +I have n points in fact I have two n so + + + align:start position:0% +I have n points in fact I have two n so +it's a symmetric right from minus pi a + + align:start position:0% +it's a symmetric right from minus pi a + + + align:start position:0% +it's a symmetric right from minus pi a +to plus pi / a so I only draw you see I + + align:start position:0% +to plus pi / a so I only draw you see I + + + align:start position:0% +to plus pi / a so I only draw you see I +only draw the other the one half of it + + align:start position:0% +only draw the other the one half of it + + + align:start position:0% +only draw the other the one half of it +right and if I count from here to here + + align:start position:0% +right and if I count from here to here + + + align:start position:0% +right and if I count from here to here +there are really two end quantum + + align:start position:0% +there are really two end quantum + + + align:start position:0% +there are really two end quantum +states right and with that uh I say if I + + align:start position:0% +states right and with that uh I say if I + + + align:start position:0% +states right and with that uh I say if I +give hydrogen as example if I could + + align:start position:0% +give hydrogen as example if I could + + + align:start position:0% +give hydrogen as example if I could +arrange them in one dimensional + + align:start position:0% +arrange them in one dimensional + + + align:start position:0% +arrange them in one dimensional +periodical uh fashion then because each + + align:start position:0% +periodical uh fashion then because each + + + align:start position:0% +periodical uh fashion then because each +hydrogen has one electron and at the + + align:start position:0% +hydrogen has one electron and at the + + + align:start position:0% +hydrogen has one electron and at the +absolute zero temperature the lowest + + align:start position:0% +absolute zero temperature the lowest + + + align:start position:0% +absolute zero temperature the lowest +energy level feels + + align:start position:0% +energy level feels + + + align:start position:0% +energy level feels +And you will feel to the middle of the + + align:start position:0% +And you will feel to the middle of the + + + align:start position:0% +And you will feel to the middle of the +band, right? And if I have three + + align:start position:0% +band, right? And if I have three + + + align:start position:0% +band, right? And if I have three +electrons, lithium you'll feel to here. + + align:start position:0% +electrons, lithium you'll feel to here. + + + align:start position:0% +electrons, lithium you'll feel to here. +It feels to the middle of the band. And + + align:start position:0% +It feels to the middle of the band. And + + + align:start position:0% +It feels to the middle of the band. And +in that those are the metals where at + + align:start position:0% +in that those are the metals where at + + + align:start position:0% +in that those are the metals where at +the long zero temperature + + align:start position:0% +the long zero temperature + + + align:start position:0% +the long zero temperature +uh they uh there are some uh if there's + + align:start position:0% +uh they uh there are some uh if there's + + + align:start position:0% +uh they uh there are some uh if there's +very little energy you can move around + + align:start position:0% +very little energy you can move around + + + align:start position:0% +very little energy you can move around +those electrons near the top where the + + align:start position:0% +those electrons near the top where the + + + align:start position:0% +those electrons near the top where the +uppermost energy level that filled with + + align:start position:0% +uppermost energy level that filled with + + + align:start position:0% +uppermost energy level that filled with +electron this is called uh the firmy + + align:start position:0% +electron this is called uh the firmy + + + align:start position:0% +electron this is called uh the firmy +level right uh at the absolute t the + + align:start position:0% +level right uh at the absolute t the + + + align:start position:0% +level right uh at the absolute t the +upper most energy level where electrons + + align:start position:0% +upper most energy level where electrons + + + align:start position:0% +upper most energy level where electrons +are are the firmable and if you read the + + align:start position:0% +are are the firmable and if you read the + + + align:start position:0% +are are the firmable and if you read the +different + + align:start position:0% +different + + + align:start position:0% +different +books sometimes uh people uh will call + + align:start position:0% +books sometimes uh people uh will call + + + align:start position:0% +books sometimes uh people uh will call +at the long zero temperature they'll say + + align:start position:0% +at the long zero temperature they'll say + + + align:start position:0% +at the long zero temperature they'll say +that's also firm level but say a more uh + + align:start position:0% +that's also firm level but say a more uh + + + align:start position:0% +that's also firm level but say a more uh +um better way is at long zero + + align:start position:0% +um better way is at long zero + + + align:start position:0% +um better way is at long zero +temperature this one can shift a little + + align:start position:0% +temperature this one can shift a little + + + align:start position:0% +temperature this one can shift a little +bit around that position and that's uh + + align:start position:0% +bit around that position and that's uh + + + align:start position:0% +bit around that position and that's uh +say it's better call them camper + + align:start position:0% +say it's better call them camper + + + align:start position:0% +say it's better call them camper +potential okay so different books + + align:start position:0% +potential okay so different books + + + align:start position:0% +potential okay so different books +Sometimes they distinguish some times + + align:start position:0% +Sometimes they distinguish some times + + + align:start position:0% +Sometimes they distinguish some times +they do not. I had student came to me + + align:start position:0% +they do not. I had student came to me + + + align:start position:0% +they do not. I had student came to me +and say uh what is uh say in electrical + + align:start position:0% +and say uh what is uh say in electrical + + + align:start position:0% +and say uh what is uh say in electrical +engineering for example if you read + + align:start position:0% +engineering for example if you read + + + align:start position:0% +engineering for example if you read +electronics they'll always call that uh + + align:start position:0% +electronics they'll always call that uh + + + align:start position:0% +electronics they'll always call that uh +firmable non zero temperature is always + + align:start position:0% +firmable non zero temperature is always + + + align:start position:0% +firmable non zero temperature is always +called + + align:start position:0% +called + + + align:start position:0% +called +firmable. + + align:start position:0% +firmable. + + + align:start position:0% +firmable. +Okay. And uh so this is a uh of course + + align:start position:0% +Okay. And uh so this is a uh of course + + + align:start position:0% +Okay. And uh so this is a uh of course +it fills to the top then there is a gap + + align:start position:0% +it fills to the top then there is a gap + + + align:start position:0% +it fills to the top then there is a gap +uh in energy that means no electrons can + + align:start position:0% +uh in energy that means no electrons can + + + align:start position:0% +uh in energy that means no electrons can +exist with that specific energy in the + + align:start position:0% +exist with that specific energy in the + + + align:start position:0% +exist with that specific energy in the +crystal. So no waves + + align:start position:0% +crystal. So no waves + + + align:start position:0% +crystal. So no waves +allowed and so if I have two electrons + + align:start position:0% +allowed and so if I have two electrons + + + align:start position:0% +allowed and so if I have two electrons +uh then again at zero you will fill to + + align:start position:0% +uh then again at zero you will fill to + + + align:start position:0% +uh then again at zero you will fill to +the upper most + + align:start position:0% +the upper most + + + align:start position:0% +the upper most +uh of the lowest band there right and + + align:start position:0% +uh of the lowest band there right and + + + align:start position:0% +uh of the lowest band there right and +now because there's a gap electron does + + align:start position:0% +now because there's a gap electron does + + + align:start position:0% +now because there's a gap electron does +not have enough energy to go to the next + + align:start position:0% +not have enough energy to go to the next + + + align:start position:0% +not have enough energy to go to the next +level if that gap is + + align:start position:0% +level if that gap is + + + align:start position:0% +level if that gap is +large. So uh if we for large gap + + align:start position:0% +large. So uh if we for large gap + + + align:start position:0% +large. So uh if we for large gap +electron cannot move because there's no + + align:start position:0% +electron cannot move because there's no + + + align:start position:0% +electron cannot move because there's no +quantum + + align:start position:0% +quantum + + + align:start position:0% +quantum +state. Now everything is filled here. + + align:start position:0% +state. Now everything is filled here. + + + align:start position:0% +state. Now everything is filled here. +There's no more quantum state this + + align:start position:0% +There's no more quantum state this + + + align:start position:0% +There's no more quantum state this +electron can move to. So the firmy + + align:start position:0% +electron can move to. So the firmy + + + align:start position:0% +electron can move to. So the firmy +exclusion principle say you can't have + + align:start position:0% +exclusion principle say you can't have + + + align:start position:0% +exclusion principle say you can't have +more than one electron per quantum + + align:start position:0% +more than one electron per quantum + + + align:start position:0% +more than one electron per quantum +state. + + align:start position:0% +state. + + + align:start position:0% +state. +So this is the case where the there are + + align:start position:0% +So this is the case where the there are + + + align:start position:0% +So this is the case where the there are +electron in the material there always a + + align:start position:0% +electron in the material there always a + + + align:start position:0% +electron in the material there always a +charge right but you got the insulator + + align:start position:0% +charge right but you got the insulator + + + align:start position:0% +charge right but you got the insulator +there's low electric conduction so this + + align:start position:0% +there's low electric conduction so this + + + align:start position:0% +there's low electric conduction so this +is the + + align:start position:0% +is the + + + align:start position:0% +is the +insulator and of course uh uh we spend + + align:start position:0% +insulator and of course uh uh we spend + + + align:start position:0% +insulator and of course uh uh we spend +the uh most of time on this + + align:start position:0% +the uh most of time on this + + + align:start position:0% +the uh most of time on this +onedimensional + + align:start position:0% +onedimensional + + + align:start position:0% +onedimensional +uh uh say uh latice chair model and if + + align:start position:0% +uh uh say uh latice chair model and if + + + align:start position:0% +uh uh say uh latice chair model and if +you go to 3D which I'll talk more today + + align:start position:0% +you go to 3D which I'll talk more today + + + align:start position:0% +you go to 3D which I'll talk more today +you look At the each direction of the + + align:start position:0% +you look At the each direction of the + + + align:start position:0% +you look At the each direction of the +crystal you can say a different + + align:start position:0% +crystal you can say a different + + + align:start position:0% +crystal you can say a different +periodicity and different periodicity + + align:start position:0% +periodicity and different periodicity + + + align:start position:0% +periodicity and different periodicity +also means the bonding between the atoms + + align:start position:0% +also means the bonding between the atoms + + + align:start position:0% +also means the bonding between the atoms +in that specific direction the force is + + align:start position:0% +in that specific direction the force is + + + align:start position:0% +in that specific direction the force is +different right and so you'll see a + + align:start position:0% +different right and so you'll see a + + + align:start position:0% +different right and so you'll see a +different band + + align:start position:0% +different band + + + align:start position:0% +different band +structure I'm just handling drawing this + + align:start position:0% +structure I'm just handling drawing this + + + align:start position:0% +structure I'm just handling drawing this +right so this is the A1 is one specific + + align:start position:0% +right so this is the A1 is one specific + + + align:start position:0% +right so this is the A1 is one specific +direction with that periodicity A1 and + + align:start position:0% +direction with that periodicity A1 and + + + align:start position:0% +direction with that periodicity A1 and +Another crystalraphic direction could be + + align:start position:0% +Another crystalraphic direction could be + + + align:start position:0% +Another crystalraphic direction could be +A2 and in fact there are many + + align:start position:0% +A2 and in fact there are many + + + align:start position:0% +A2 and in fact there are many +crystalraphic direction in the crystal. + + align:start position:0% +crystalraphic direction in the crystal. + + + align:start position:0% +crystalraphic direction in the crystal. +So uh ideally you know everything you + + align:start position:0% +So uh ideally you know everything you + + + align:start position:0% +So uh ideally you know everything you +know each direction what are the energy + + align:start position:0% +know each direction what are the energy + + + align:start position:0% +know each direction what are the energy +uh diagram energy of the charge and here + + align:start position:0% +uh diagram energy of the charge and here + + + align:start position:0% +uh diagram energy of the charge and here +I'm drawing two + + align:start position:0% +I'm drawing two + + + align:start position:0% +I'm drawing two +direction and uh uh now say this is the + + align:start position:0% +direction and uh uh now say this is the + + + align:start position:0% +direction and uh uh now say this is the +minimum point here this is uh say the + + align:start position:0% +minimum point here this is uh say the + + + align:start position:0% +minimum point here this is uh say the +maximum point in the first band here and + + align:start position:0% +maximum point in the first band here and + + + align:start position:0% +maximum point in the first band here and +again the bank gap this is a gap here + + align:start position:0% +again the bank gap this is a gap here + + + align:start position:0% +again the bank gap this is a gap here +but when I talk about the semiconductor + + align:start position:0% +but when I talk about the semiconductor + + + align:start position:0% +but when I talk about the semiconductor +ctor I'm talking about the absolute + + align:start position:0% +ctor I'm talking about the absolute + + + align:start position:0% +ctor I'm talking about the absolute +gap meaning there this is the low at the + + align:start position:0% +gap meaning there this is the low at the + + + align:start position:0% +gap meaning there this is the low at the +highest point where the electron fails + + align:start position:0% +highest point where the electron fails + + + align:start position:0% +highest point where the electron fails +and lowest point that's empty and there + + align:start position:0% +and lowest point that's empty and there + + + align:start position:0% +and lowest point that's empty and there +is a separation energy. So in this + + align:start position:0% +is a separation energy. So in this + + + align:start position:0% +is a separation energy. So in this +region there's no uh in this region here + + align:start position:0% +region there's no uh in this region here + + + align:start position:0% +region there's no uh in this region here +there's no electron in the material in + + align:start position:0% +there's no electron in the material in + + + align:start position:0% +there's no electron in the material in +the crystal that has say could have + + align:start position:0% +the crystal that has say could have + + + align:start position:0% +the crystal that has say could have +those synergy that's quantum + + align:start position:0% +those synergy that's quantum + + + align:start position:0% +those synergy that's quantum +mechanically + + align:start position:0% +mechanically + + + align:start position:0% +mechanically +forbidden right that's what a real + + align:start position:0% +forbidden right that's what a real + + + align:start position:0% +forbidden right that's what a real +insulator like a + + align:start position:0% +insulator like a + + + align:start position:0% +insulator like a +glass or quartz if you think about + + align:start position:0% +glass or quartz if you think about + + + align:start position:0% +glass or quartz if you think about +crystalline form of glass right this is + + align:start position:0% +crystalline form of glass right this is + + + align:start position:0% +crystalline form of glass right this is +where electric insulator it has a very + + align:start position:0% +where electric insulator it has a very + + + align:start position:0% +where electric insulator it has a very +large band gap + + align:start position:0% +large band gap + + + align:start position:0% +large band gap +And if this band gap is small uh is not + + align:start position:0% +And if this band gap is small uh is not + + + align:start position:0% +And if this band gap is small uh is not +that large let's say silicon is 1.1 + + align:start position:0% +that large let's say silicon is 1.1 + + + align:start position:0% +that large let's say silicon is 1.1 +electron volt it becomes a + + align:start position:0% +electron volt it becomes a + + + align:start position:0% +electron volt it becomes a +semiconductor and uh uh uh for + + align:start position:0% +semiconductor and uh uh uh for + + + align:start position:0% +semiconductor and uh uh uh for +semiconductors we have different + + align:start position:0% +semiconductors we have different + + + align:start position:0% +semiconductors we have different +scenario where this + + align:start position:0% +scenario where this + + + align:start position:0% +scenario where this +uh noise energy point maximum energy + + align:start position:0% +uh noise energy point maximum energy + + + align:start position:0% +uh noise energy point maximum energy +point they do not align to the same wave + + align:start position:0% +point they do not align to the same wave + + + align:start position:0% +point they do not align to the same wave +vector. That's the case for silicon and + + align:start position:0% +vector. That's the case for silicon and + + + align:start position:0% +vector. That's the case for silicon and +that's a indirect gap + + align:start position:0% +that's a indirect gap + + + align:start position:0% +that's a indirect gap +semiconductor. So we have different type + + align:start position:0% +semiconductor. So we have different type + + + align:start position:0% +semiconductor. So we have different type +of + + align:start position:0% + + + + align:start position:0% + +semiconductors. We have uh uh direct + + align:start position:0% + + + + align:start position:0% + +gap. We have indirect gap. + + align:start position:0% + + + + align:start position:0% + +Right. Uh as direct gap is when the + + align:start position:0% +Right. Uh as direct gap is when the + + + align:start position:0% +Right. Uh as direct gap is when the +conduction and the valance band. So the + + align:start position:0% +conduction and the valance band. So the + + + align:start position:0% +conduction and the valance band. So the +upper band we say conduction and lower + + align:start position:0% +upper band we say conduction and lower + + + align:start position:0% +upper band we say conduction and lower +band is valance. So they are + + align:start position:0% +band is valance. So they are + + + align:start position:0% +band is valance. So they are +happening the minimum and maximum is at + + align:start position:0% +happening the minimum and maximum is at + + + align:start position:0% +happening the minimum and maximum is at +the same way vector while indirect is + + align:start position:0% +the same way vector while indirect is + + + align:start position:0% +the same way vector while indirect is +uh different. It could be + + align:start position:0% + + + + align:start position:0% + +uh here is the energy, here is the wave + + align:start position:0% +uh here is the energy, here is the wave + + + align:start position:0% +uh here is the energy, here is the wave +vector and they may happen at different + + align:start position:0% +vector and they may happen at different + + + align:start position:0% +vector and they may happen at different +wave + + align:start position:0% +wave + + + align:start position:0% +wave +vectors. Okay. And uh uh this uh makes + + align:start position:0% +vectors. Okay. And uh uh this uh makes + + + align:start position:0% +vectors. Okay. And uh uh this uh makes +an important distinction between gimmite + + align:start position:0% +an important distinction between gimmite + + + align:start position:0% +an important distinction between gimmite +which is direct gap semiconductor with a + + align:start position:0% +which is direct gap semiconductor with a + + + align:start position:0% +which is direct gap semiconductor with a +bang gap 1.4 electron volt and silicon + + align:start position:0% +bang gap 1.4 electron volt and silicon + + + align:start position:0% +bang gap 1.4 electron volt and silicon +which is indirect gap semiconductor with + + align:start position:0% +which is indirect gap semiconductor with + + + align:start position:0% +which is indirect gap semiconductor with +a bang gap 1.1. And you see most + + align:start position:0% +a bang gap 1.1. And you see most + + + align:start position:0% +a bang gap 1.1. And you see most +computer chips are made of silicon but + + align:start position:0% +computer chips are made of silicon but + + + align:start position:0% +computer chips are made of silicon but +most lasers pointers made of gyneite + + align:start position:0% +most lasers pointers made of gyneite + + + align:start position:0% +most lasers pointers made of gyneite +light uh say this one uh they when you + + align:start position:0% +light uh say this one uh they when you + + + align:start position:0% +light uh say this one uh they when you +want to make a light active device + + align:start position:0% +want to make a light active device + + + align:start position:0% +want to make a light active device +direct is usually better because you + + align:start position:0% +direct is usually better because you + + + align:start position:0% +direct is usually better because you +need a light light itself do not have + + align:start position:0% +need a light light itself do not have + + + align:start position:0% +need a light light itself do not have +much momentum. So here + + align:start position:0% +much momentum. So here + + + align:start position:0% +much momentum. So here +k is the momentum. So, h bar + + align:start position:0% + + + + align:start position:0% + +kar k is what do we call crystal + + align:start position:0% + + + + align:start position:0% + +momentum. it has uh some difference from + + align:start position:0% +momentum. it has uh some difference from + + + align:start position:0% +momentum. it has uh some difference from +the real momentum of the electrons but + + align:start position:0% +the real momentum of the electrons but + + + align:start position:0% +the real momentum of the electrons but +say we're not getting into that subtle + + align:start position:0% +say we're not getting into that subtle + + + align:start position:0% +say we're not getting into that subtle +difference in typical way you can think + + align:start position:0% +difference in typical way you can think + + + align:start position:0% +difference in typical way you can think +is this is when I think about momentum + + align:start position:0% +is this is when I think about momentum + + + align:start position:0% +is this is when I think about momentum +conservation of say a light comes in + + align:start position:0% +conservation of say a light comes in + + + align:start position:0% +conservation of say a light comes in +interact with electron I use h bar k of + + align:start position:0% +interact with electron I use h bar k of + + + align:start position:0% +interact with electron I use h bar k of +the electron in the crystal I'll h use + + align:start position:0% +the electron in the crystal I'll h use + + + align:start position:0% +the electron in the crystal I'll h use +use h bar k for the photon right um now + + align:start position:0% +use h bar k for the photon right um now + + + align:start position:0% +use h bar k for the photon right um now +the difference of course remember K is 2 + + align:start position:0% +the difference of course remember K is 2 + + + align:start position:0% +the difference of course remember K is 2 +pi lambda that's magnitude + + align:start position:0% +pi lambda that's magnitude + + + align:start position:0% +pi lambda that's magnitude +right so if you look at the uh uh here + + align:start position:0% +right so if you look at the uh uh here + + + align:start position:0% +right so if you look at the uh uh here +in crystal my latice + + align:start position:0% +in crystal my latice + + + align:start position:0% +in crystal my latice +constant this is pi / a that's + + align:start position:0% +constant this is pi / a that's + + + align:start position:0% +constant this is pi / a that's +unstrong in lambda wavelength and photon + + align:start position:0% +unstrong in lambda wavelength and photon + + + align:start position:0% +unstrong in lambda wavelength and photon +lambda is micron so the photon momentum + + align:start position:0% +lambda is micron so the photon momentum + + + align:start position:0% +lambda is micron so the photon momentum +is almost negligible very small and the + + align:start position:0% +is almost negligible very small and the + + + align:start position:0% +is almost negligible very small and the +electron momentum in this case if + + align:start position:0% +electron momentum in this case if + + + align:start position:0% +electron momentum in this case if +they're different they're very large + + align:start position:0% +they're different they're very large + + + align:start position:0% +they're different they're very large +that's why indirect semiconductor do not + + align:start position:0% +that's why indirect semiconductor do not + + + align:start position:0% +that's why indirect semiconductor do not +absorb + + align:start position:0% +absorb + + + align:start position:0% +absorb +well okay do not absorb light + + align:start position:0% +well okay do not absorb light + + + align:start position:0% +well okay do not absorb light +well that's the biggest problem when you + + align:start position:0% +well that's the biggest problem when you + + + align:start position:0% +well that's the biggest problem when you +make a silicon solar cells it doesn't + + align:start position:0% +make a silicon solar cells it doesn't + + + align:start position:0% +make a silicon solar cells it doesn't +you need a lot of materials to absorb + + align:start position:0% +you need a lot of materials to absorb + + + align:start position:0% +you need a lot of materials to absorb +this photon okay so this is the direct + + align:start position:0% +this photon okay so this is the direct + + + align:start position:0% +this photon okay so this is the direct +gap indirect gap and a little bit more + + align:start position:0% +gap indirect gap and a little bit more + + + align:start position:0% +gap indirect gap and a little bit more +terminology for + + align:start position:0% +terminology for + + + align:start position:0% +terminology for +semiconductors right and if I do not put + + align:start position:0% +semiconductors right and if I do not put + + + align:start position:0% +semiconductors right and if I do not put +impurities do not put say any uh say + + align:start position:0% +impurities do not put say any uh say + + + align:start position:0% +impurities do not put say any uh say +other atoms silicon for example at the + + align:start position:0% +other atoms silicon for example at the + + + align:start position:0% +other atoms silicon for example at the +absolute zero temperature the electrons + + align:start position:0% +absolute zero temperature the electrons + + + align:start position:0% +absolute zero temperature the electrons +will be here that's the uppermost energy + + align:start position:0% +will be here that's the uppermost energy + + + align:start position:0% +will be here that's the uppermost energy +level that's at the absolute zero + + align:start position:0% +level that's at the absolute zero + + + align:start position:0% +level that's at the absolute zero +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +uh uh the firm level where the firm + + align:start position:0% +uh uh the firm level where the firm + + + align:start position:0% +uh uh the firm level where the firm +level is okay And now at a long zero + + align:start position:0% +level is okay And now at a long zero + + + align:start position:0% +level is okay And now at a long zero +temperature some electron gain enough + + align:start position:0% +temperature some electron gain enough + + + align:start position:0% +temperature some electron gain enough +thermal energy because the boardsman + + align:start position:0% +thermal energy because the boardsman + + + align:start position:0% +thermal energy because the boardsman +statistics there always electron has a + + align:start position:0% +statistics there always electron has a + + + align:start position:0% +statistics there always electron has a +distribution and some electron move from + + align:start position:0% +distribution and some electron move from + + + align:start position:0% +distribution and some electron move from +here to + + align:start position:0% +here to + + + align:start position:0% +here to +here and that leave behind empty states + + align:start position:0% +here and that leave behind empty states + + + align:start position:0% +here and that leave behind empty states +and because empty states the electron + + align:start position:0% +and because empty states the electron + + + align:start position:0% +and because empty states the electron +here few electron here are very happy + + align:start position:0% +here few electron here are very happy + + + align:start position:0% +here few electron here are very happy +because there are a lot of empty + + align:start position:0% +because there are a lot of empty + + + align:start position:0% +because there are a lot of empty +states many electron here are also so + + align:start position:0% +states many electron here are also so + + + align:start position:0% +states many electron here are also so +happy because now they finally have a + + align:start position:0% +happy because now they finally have a + + + align:start position:0% +happy because now they finally have a +little bit of room to + + align:start position:0% +little bit of room to + + + align:start position:0% +little bit of room to +wiggle, right? So the ones on the bottom + + align:start position:0% +wiggle, right? So the ones on the bottom + + + align:start position:0% +wiggle, right? So the ones on the bottom +uh rather than describing the motion of + + align:start position:0% +uh rather than describing the motion of + + + align:start position:0% +uh rather than describing the motion of +all those + + align:start position:0% +all those + + + align:start position:0% +all those +electrons, right? feel the electron uh + + align:start position:0% +electrons, right? feel the electron uh + + + align:start position:0% +electrons, right? feel the electron uh +equivalent terminology is describe the + + align:start position:0% +equivalent terminology is describe the + + + align:start position:0% +equivalent terminology is describe the +motion of those amplitude states that's + + align:start position:0% +motion of those amplitude states that's + + + align:start position:0% +motion of those amplitude states that's +holes and holes when I think about holes + + align:start position:0% +holes and holes when I think about holes + + + align:start position:0% +holes and holes when I think about holes +energy is increasing this way because + + align:start position:0% +energy is increasing this way because + + + align:start position:0% +energy is increasing this way because +negative of the electron when I think + + align:start position:0% +negative of the electron when I think + + + align:start position:0% +negative of the electron when I think +about electrons the energy is increasing + + align:start position:0% +about electrons the energy is increasing + + + align:start position:0% +about electrons the energy is increasing +this way so when I look at this band + + align:start position:0% +this way so when I look at this band + + + align:start position:0% +this way so when I look at this band +diagram when I think about electron hole + + align:start position:0% +diagram when I think about electron hole + + + align:start position:0% +diagram when I think about electron hole +I actually say this direction is energy + + align:start position:0% +I actually say this direction is energy + + + align:start position:0% +I actually say this direction is energy +increasing + + align:start position:0% +increasing + + + align:start position:0% +increasing +for hole that's the energy increases for + + align:start position:0% +for hole that's the energy increases for + + + align:start position:0% +for hole that's the energy increases for +electron. So we have + + align:start position:0% + + + + align:start position:0% + +electrons, we have + + align:start position:0% + + + + align:start position:0% + +holes and here where the electron is the + + align:start position:0% +holes and here where the electron is the + + + align:start position:0% +holes and here where the electron is the +conduction + + align:start position:0% + + + + align:start position:0% + +band and where the home of this one is + + align:start position:0% +band and where the home of this one is + + + align:start position:0% +band and where the home of this one is +the valance + + align:start position:0% + + + + align:start position:0% + +then okay and if it's a uh true + + align:start position:0% +then okay and if it's a uh true + + + align:start position:0% +then okay and if it's a uh true +intrinsic semiconductor without doping a + + align:start position:0% +intrinsic semiconductor without doping a + + + align:start position:0% +intrinsic semiconductor without doping a +absolute zero it's a insulator because + + align:start position:0% +absolute zero it's a insulator because + + + align:start position:0% +absolute zero it's a insulator because +it's frozen all the charges here and + + align:start position:0% +it's frozen all the charges here and + + + align:start position:0% +it's frozen all the charges here and +there's no mobile charge uh say there + + align:start position:0% +there's no mobile charge uh say there + + + align:start position:0% +there's no mobile charge uh say there +are no empty states for the electron to + + align:start position:0% +are no empty states for the electron to + + + align:start position:0% +are no empty states for the electron to +move + + align:start position:0% +move + + + align:start position:0% +move +uh but say normally I do not deal with + + align:start position:0% +uh but say normally I do not deal with + + + align:start position:0% +uh but say normally I do not deal with +when use a semiconductor device. I want + + align:start position:0% +when use a semiconductor device. I want + + + align:start position:0% +when use a semiconductor device. I want +to have a specific either electron as a + + align:start position:0% +to have a specific either electron as a + + + align:start position:0% +to have a specific either electron as a +majority or hole as majority. So I do + + align:start position:0% +majority or hole as majority. So I do + + + align:start position:0% +majority or hole as majority. So I do +it. So that's uh uh intrinsic uh + + align:start position:0% +it. So that's uh uh intrinsic uh + + + align:start position:0% +it. So that's uh uh intrinsic uh +extrinsic semiconductor difference. So + + align:start position:0% +extrinsic semiconductor difference. So + + + align:start position:0% +extrinsic semiconductor difference. So +we have uh intrinsic that's when we do + + align:start position:0% +we have uh intrinsic that's when we do + + + align:start position:0% +we have uh intrinsic that's when we do +not do + + align:start position:0% +not do + + + align:start position:0% +not do +it and exttrinsic when we dope it. + + align:start position:0% + + + + align:start position:0% + +And when we do, we can do put the N + + align:start position:0% +And when we do, we can do put the N + + + align:start position:0% +And when we do, we can do put the N +type. When I put a phosphor or I do P + + align:start position:0% + + + + align:start position:0% + +type. So those are the uh um + + align:start position:0% +type. So those are the uh um + + + align:start position:0% +type. So those are the uh um +semiconductors. + + align:start position:0% +semiconductors. + + + align:start position:0% +semiconductors. +And uh one more thing I want to + + align:start position:0% +And uh one more thing I want to + + + align:start position:0% +And uh one more thing I want to +introduce this is uh if I look at uh the + + align:start position:0% +introduce this is uh if I look at uh the + + + align:start position:0% +introduce this is uh if I look at uh the +energy + + align:start position:0% +energy + + + align:start position:0% +energy +uh electron at the bottom or hole at the + + align:start position:0% +uh electron at the bottom or hole at the + + + align:start position:0% +uh electron at the bottom or hole at the +top right and in fact that's the bottom + + align:start position:0% +top right and in fact that's the bottom + + + align:start position:0% +top right and in fact that's the bottom +a hole + + align:start position:0% +a hole + + + align:start position:0% +a hole +right and when I do the uh because this + + align:start position:0% +right and when I do the uh because this + + + align:start position:0% +right and when I do the uh because this +is at a minimum maximum point so most of + + align:start position:0% +is at a minimum maximum point so most of + + + align:start position:0% +is at a minimum maximum point so most of +time the charge in semiconductor when + + align:start position:0% +time the charge in semiconductor when + + + align:start position:0% +time the charge in semiconductor when +you do not deal with the heavily dope + + align:start position:0% +you do not deal with the heavily dope + + + align:start position:0% +you do not deal with the heavily dope +they only at the bottom or top region + + align:start position:0% +they only at the bottom or top region + + + align:start position:0% +they only at the bottom or top region +there and because there's a minimum + + align:start position:0% +there and because there's a minimum + + + align:start position:0% +there and because there's a minimum +maximum so I can use approximation I can + + align:start position:0% +maximum so I can use approximation I can + + + align:start position:0% +maximum so I can use approximation I can +expand the potential electrical energy + + align:start position:0% +expand the potential electrical energy + + + align:start position:0% +expand the potential electrical energy +right around the minimum maximum so if I + + align:start position:0% +right around the minimum maximum so if I + + + align:start position:0% +right around the minimum maximum so if I +do a expansion typical + + align:start position:0% + + + + align:start position:0% + +expansion so energy as a function of K + + align:start position:0% +expansion so energy as a function of K + + + align:start position:0% +expansion so energy as a function of K +and I'm writing 1D you can say K in a + + align:start position:0% +and I'm writing 1D you can say K in a + + + align:start position:0% +and I'm writing 1D you can say K in a +real crystal in each crystal graphic + + align:start position:0% +real crystal in each crystal graphic + + + align:start position:0% +real crystal in each crystal graphic +direction has a k right so I'm not + + align:start position:0% +direction has a k right so I'm not + + + align:start position:0% +direction has a k right so I'm not +writing in vector form and but say I can + + align:start position:0% +writing in vector form and but say I can + + + align:start position:0% +writing in vector form and but say I can +expand that let's say + + align:start position:0% +expand that let's say + + + align:start position:0% +expand that let's say +here this is a uh e say conduction band + + align:start position:0% +here this is a uh e say conduction band + + + align:start position:0% +here this is a uh e say conduction band +edge this is a + + align:start position:0% +edge this is a + + + align:start position:0% +edge this is a +k0 right that's where the minimum + + align:start position:0% +k0 right that's where the minimum + + + align:start position:0% +k0 right that's where the minimum +happens so I'm going to expand this uh + + align:start position:0% +happens so I'm going to expand this uh + + + align:start position:0% +happens so I'm going to expand this uh +as a e say k0 That's the lowest the + + align:start position:0% +as a e say k0 That's the lowest the + + + align:start position:0% +as a e say k0 That's the lowest the +first term of the expansion and the + + align:start position:0% +first term of the expansion and the + + + align:start position:0% +first term of the expansion and the +second term + + align:start position:0% + + + + align:start position:0% + +DK + + align:start position:0% +DK + + + align:start position:0% +DK +K0 and K minus + + align:start position:0% +K0 and K minus + + + align:start position:0% +K0 and K minus +K0 and and the next term is D + + align:start position:0% +K0 and and the next term is D + + + align:start position:0% +K0 and and the next term is D +E D + + align:start position:0% +E D + + + align:start position:0% +E D +K² and K minus K0 square + + align:start position:0% +K² and K minus K0 square + + + align:start position:0% +K² and K minus K0 square +right okay So this term because the + + align:start position:0% +right okay So this term because the + + + align:start position:0% +right okay So this term because the +maximum + + align:start position:0% +maximum + + + align:start position:0% +maximum +minimum is zero as long as I do not have + + align:start position:0% +minimum is zero as long as I do not have + + + align:start position:0% +minimum is zero as long as I do not have +a sharp turn in right it's if it's a + + align:start position:0% +a sharp turn in right it's if it's a + + + align:start position:0% +a sharp turn in right it's if it's a +linear profile I'm I cannot make that + + align:start position:0% +linear profile I'm I cannot make that + + + align:start position:0% +linear profile I'm I cannot make that +approximation so normally this is + + align:start position:0% +approximation so normally this is + + + align:start position:0% +approximation so normally this is +zero and uh this one let me write into + + align:start position:0% +zero and uh this one let me write into + + + align:start position:0% +zero and uh this one let me write into +uh a form + + align:start position:0% +uh a form + + + align:start position:0% +uh a form +that's nicer so I could write this h² + + align:start position:0% +that's nicer so I could write this h² + + + align:start position:0% +that's nicer so I could write this h² +square k - k 0 squared and divided by uh + + align:start position:0% +square k - k 0 squared and divided by uh + + + align:start position:0% +square k - k 0 squared and divided by uh +uh say 2 m m as m star. So just a symbol + + align:start position:0% +uh say 2 m m as m star. So just a symbol + + + align:start position:0% +uh say 2 m m as m star. So just a symbol +right? So this + + align:start position:0% +right? So this + + + align:start position:0% +right? So this +mar because I have a h bar square. So I + + align:start position:0% +mar because I have a h bar square. So I + + + align:start position:0% +mar because I have a h bar square. So I +will have in the denominator I will add + + align:start position:0% +will have in the denominator I will add + + + align:start position:0% +will have in the denominator I will add +h bar square and the d e d + + align:start position:0% + + + + align:start position:0% + +k²h do + + align:start position:0% +k²h do + + + align:start position:0% +k²h do +I okay right? + + align:start position:0% + + + + align:start position:0% + +So uh you can say this + + align:start position:0% +So uh you can say this + + + align:start position:0% +So uh you can say this +mar is a second order der derivative of + + align:start position:0% +mar is a second order der derivative of + + + align:start position:0% +mar is a second order der derivative of +this curve at the bottom + + align:start position:0% +this curve at the bottom + + + align:start position:0% +this curve at the bottom +right. So uh if it's a uh the mar is + + align:start position:0% +right. So uh if it's a uh the mar is + + + align:start position:0% +right. So uh if it's a uh the mar is +large how is that shape looking + + align:start position:0% +large how is that shape looking + + + align:start position:0% +large how is that shape looking +like flat right? MAR is + + align:start position:0% +like flat right? MAR is + + + align:start position:0% +like flat right? MAR is +small that shape that parabola local + + align:start position:0% +small that shape that parabola local + + + align:start position:0% +small that shape that parabola local +parabola is Lar. M star is large the + + align:start position:0% +parabola is Lar. M star is large the + + + align:start position:0% +parabola is Lar. M star is large the +local parabola is a fat + + align:start position:0% +local parabola is a fat + + + align:start position:0% +local parabola is a fat +right. So this mass is like a in fact it + + align:start position:0% +right. So this mass is like a in fact it + + + align:start position:0% +right. So this mass is like a in fact it +has a unit of mass. If I write the free + + align:start position:0% +has a unit of mass. If I write the free + + + align:start position:0% +has a unit of mass. If I write the free +electron uh this is a h k is the + + align:start position:0% +electron uh this is a h k is the + + + align:start position:0% +electron uh this is a h k is the +momentum divide by 2m that's the kinetic + + align:start position:0% +momentum divide by 2m that's the kinetic + + + align:start position:0% +momentum divide by 2m that's the kinetic +energy right so by writing to this I + + align:start position:0% +energy right so by writing to this I + + + align:start position:0% +energy right so by writing to this I +introduce this m star as effective + + align:start position:0% + + + + align:start position:0% + +mass and uh I using this effective mass. + + align:start position:0% +mass and uh I using this effective mass. + + + align:start position:0% +mass and uh I using this effective mass. +This is HK. That's a more like a kinetic + + align:start position:0% +This is HK. That's a more like a kinetic + + + align:start position:0% +This is HK. That's a more like a kinetic +energy term and this is a pot potential + + align:start position:0% +energy term and this is a pot potential + + + align:start position:0% +energy term and this is a pot potential +energy term. So I can describe now the + + align:start position:0% +energy term. So I can describe now the + + + align:start position:0% +energy term. So I can describe now the +electron in this small band they + + align:start position:0% +electron in this small band they + + + align:start position:0% +electron in this small band they +transport as essentially inside a + + align:start position:0% +transport as essentially inside a + + + align:start position:0% +transport as essentially inside a +crystal as a free + + align:start position:0% +crystal as a free + + + align:start position:0% +crystal as a free +electron but with a different mass + + align:start position:0% +electron but with a different mass + + + align:start position:0% +electron but with a different mass +mar. And in fact now you can say because + + align:start position:0% +mar. And in fact now you can say because + + + align:start position:0% +mar. And in fact now you can say because +this K in a real crystal in different + + align:start position:0% +this K in a real crystal in different + + + align:start position:0% +this K in a real crystal in different +direction is different right so the mass + + align:start position:0% +direction is different right so the mass + + + align:start position:0% +direction is different right so the mass +in different direction is different. So + + align:start position:0% +in different direction is different. So + + + align:start position:0% +in different direction is different. So +in fact many times this M star is + + align:start position:0% +in fact many times this M star is + + + align:start position:0% +in fact many times this M star is +written as a + + align:start position:0% +written as a + + + align:start position:0% +written as a +tensor rather than just a single uh + + align:start position:0% +tensor rather than just a single uh + + + align:start position:0% +tensor rather than just a single uh +value there and that depends on + + align:start position:0% +value there and that depends on + + + align:start position:0% +value there and that depends on +different materials. + + align:start position:0% +different materials. + + + align:start position:0% +different materials. +So uh this is a uh both uh overview of + + align:start position:0% +So uh this is a uh both uh overview of + + + align:start position:0% +So uh this is a uh both uh overview of +last lecture and also some extension in + + align:start position:0% +last lecture and also some extension in + + + align:start position:0% +last lecture and also some extension in +terms of the uh effective mass and where + + align:start position:0% +terms of the uh effective mass and where + + + align:start position:0% +terms of the uh effective mass and where +I'm going today is continue this 3D + + align:start position:0% +I'm going today is continue this 3D + + + align:start position:0% +I'm going today is continue this 3D +picture. Now we have 1D picture. We're + + align:start position:0% +picture. Now we have 1D picture. We're + + + align:start position:0% +picture. Now we have 1D picture. We're +going 3D, right? So uh in the 3D I want + + align:start position:0% +going 3D, right? So uh in the 3D I want + + + align:start position:0% +going 3D, right? So uh in the 3D I want +to first talk about the crystal + + align:start position:0% +to first talk about the crystal + + + align:start position:0% +to first talk about the crystal +structure to get more + + align:start position:0% + + + + align:start position:0% + +familiar and and + + align:start position:0% +familiar and and + + + align:start position:0% +familiar and and +uh then I will talk about how what are + + align:start position:0% +uh then I will talk about how what are + + + align:start position:0% +uh then I will talk about how what are +the bonding between the atoms that hold + + align:start position:0% +the bonding between the atoms that hold + + + align:start position:0% +the bonding between the atoms that hold +the crystal together and finally we'll + + align:start position:0% +the crystal together and finally we'll + + + align:start position:0% +the crystal together and finally we'll +use uh uh a mathematical terminology + + align:start position:0% +use uh uh a mathematical terminology + + + align:start position:0% +use uh uh a mathematical terminology +ology is how we can um it's a periodic + + align:start position:0% +ology is how we can um it's a periodic + + + align:start position:0% +ology is how we can um it's a periodic +function in 3D and what's the + + align:start position:0% +function in 3D and what's the + + + align:start position:0% +function in 3D and what's the +corresponding fer transform right we did + + align:start position:0% +corresponding fer transform right we did + + + align:start position:0% +corresponding fer transform right we did +a onedimensional we say this k + + align:start position:0% +a onedimensional we say this k + + + align:start position:0% +a onedimensional we say this k +essentially the fal transform so this is + + align:start position:0% +essentially the fal transform so this is + + + align:start position:0% +essentially the fal transform so this is +where we're going today let's uh uh look + + align:start position:0% +where we're going today let's uh uh look + + + align:start position:0% +where we're going today let's uh uh look +at the crystal structures first and uh + + align:start position:0% +at the crystal structures first and uh + + + align:start position:0% +at the crystal structures first and uh +uh at the end of the lecture I'll show + + align:start position:0% +uh at the end of the lecture I'll show + + + align:start position:0% +uh at the end of the lecture I'll show +the best is by looking at the more + + align:start position:0% +the best is by looking at the more + + + align:start position:0% +the best is by looking at the more +visually I can't draw that well so I'll + + align:start position:0% +visually I can't draw that well so I'll + + + align:start position:0% +visually I can't draw that well so I'll +use a 2D D as a example but at the end + + align:start position:0% +use a 2D D as a example but at the end + + + align:start position:0% +use a 2D D as a example but at the end +we'll look at the 3D uh online. Okay. So + + align:start position:0% +we'll look at the 3D uh online. Okay. So + + + align:start position:0% +we'll look at the 3D uh online. Okay. So +crystals + + align:start position:0% +crystals + + + align:start position:0% +crystals +uh can be described the most important + + align:start position:0% +uh can be described the most important + + + align:start position:0% +uh can be described the most important +characteristics of crystal is + + align:start position:0% +characteristics of crystal is + + + align:start position:0% +characteristics of crystal is +periodicity periodical arrangement of + + align:start position:0% +periodicity periodical arrangement of + + + align:start position:0% +periodicity periodical arrangement of +atoms right and they have uh different + + align:start position:0% +atoms right and they have uh different + + + align:start position:0% +atoms right and they have uh different +atoms putting into same structure. So a + + align:start position:0% +atoms putting into same structure. So a + + + align:start position:0% +atoms putting into same structure. So a +crystal we can describe as a + + align:start position:0% +crystal we can describe as a + + + align:start position:0% +crystal we can describe as a +lattice which is a mathematical + + align:start position:0% +lattice which is a mathematical + + + align:start position:0% +lattice which is a mathematical +concept plus + + align:start position:0% +concept plus + + + align:start position:0% +concept plus +basis. So lattice is a periodical + + align:start position:0% +basis. So lattice is a periodical + + + align:start position:0% +basis. So lattice is a periodical +arrangement of points in space and it's + + align:start position:0% +arrangement of points in space and it's + + + align:start position:0% +arrangement of points in space and it's +mathematical concept no devoid of any + + align:start position:0% +mathematical concept no devoid of any + + + align:start position:0% +mathematical concept no devoid of any +real + + align:start position:0% +real + + + align:start position:0% +real +materials and by doing that you can + + align:start position:0% +materials and by doing that you can + + + align:start position:0% +materials and by doing that you can +actually uh classify different + + align:start position:0% +actually uh classify different + + + align:start position:0% +actually uh classify different +structures of this periodic points. So + + align:start position:0% +structures of this periodic points. So + + + align:start position:0% +structures of this periodic points. So +uh let's take a look at the a simple 2D + + align:start position:0% +uh let's take a look at the a simple 2D + + + align:start position:0% +uh let's take a look at the a simple 2D +like I + + align:start position:0% + + + + align:start position:0% + +said and 2D but there is a center + + align:start position:0% + + + + align:start position:0% + +point 2D structure periodic + + align:start position:0% +point 2D structure periodic + + + align:start position:0% +point 2D structure periodic +arrangement and uh we introduce a few uh + + align:start position:0% +arrangement and uh we introduce a few uh + + + align:start position:0% +arrangement and uh we introduce a few uh +basic terminology one is primitive + + align:start position:0% +basic terminology one is primitive + + + align:start position:0% +basic terminology one is primitive +latice vector + + align:start position:0% + + + + align:start position:0% + +There. So in 3D will be + + align:start position:0% +There. So in 3D will be + + + align:start position:0% +There. So in 3D will be +A1, A2, A3. In 2D of course you only + + align:start position:0% +A1, A2, A3. In 2D of course you only + + + align:start position:0% +A1, A2, A3. In 2D of course you only +have + + align:start position:0% +have + + + align:start position:0% +have +two. And what is a primitive lattice + + align:start position:0% +two. And what is a primitive lattice + + + align:start position:0% +two. And what is a primitive lattice +vector? It's a a set of vector with that + + align:start position:0% +vector? It's a a set of vector with that + + + align:start position:0% +vector? It's a a set of vector with that +I can use the linear combination to + + align:start position:0% +I can use the linear combination to + + + align:start position:0% +I can use the linear combination to +reach all other points by integers. So + + align:start position:0% +reach all other points by integers. So + + + align:start position:0% +reach all other points by integers. So +uh uh I can use this primitive latice + + align:start position:0% +uh uh I can use this primitive latice + + + align:start position:0% +uh uh I can use this primitive latice +vector to construct a translation vector + + align:start position:0% +vector to construct a translation vector + + + align:start position:0% +vector to construct a translation vector +uh n1 a1 plus n_sub_2 a2 plus n3 a3. + + align:start position:0% + + + + align:start position:0% + +Well, n1, n2, n3 are + + align:start position:0% + + + + align:start position:0% + +integers. Okay. So, this is uh the + + align:start position:0% +integers. Okay. So, this is uh the + + + align:start position:0% +integers. Okay. So, this is uh the +primitive lattice vector and uh the + + align:start position:0% +primitive lattice vector and uh the + + + align:start position:0% +primitive lattice vector and uh the +problem is if I look at this 2D, I have + + align:start position:0% +problem is if I look at this 2D, I have + + + align:start position:0% +problem is if I look at this 2D, I have +a different ways to choose the primitive + + align:start position:0% +a different ways to choose the primitive + + + align:start position:0% +a different ways to choose the primitive +lattice + + align:start position:0% +lattice + + + align:start position:0% +lattice +vector. Uh here is one way. If I have + + align:start position:0% +vector. Uh here is one way. If I have + + + align:start position:0% +vector. Uh here is one way. If I have +this one and this + + align:start position:0% +this one and this + + + align:start position:0% +this one and this +one, if you look at this, I can use this + + align:start position:0% +one, if you look at this, I can use this + + + align:start position:0% +one, if you look at this, I can use this +two and the linear combination of these + + align:start position:0% +two and the linear combination of these + + + align:start position:0% +two and the linear combination of these +two reach any other points. Right? So + + align:start position:0% +two reach any other points. Right? So + + + align:start position:0% +two reach any other points. Right? So +this is let's say a1 and this is + + align:start position:0% +this is let's say a1 and this is + + + align:start position:0% +this is let's say a1 and this is +a2 and of course you could also choose a + + align:start position:0% +a2 and of course you could also choose a + + + align:start position:0% +a2 and of course you could also choose a +different one. You can choose this one + + align:start position:0% +different one. You can choose this one + + + align:start position:0% +different one. You can choose this one +and this + + align:start position:0% +and this + + + align:start position:0% +and this +one. Right? + + align:start position:0% +one. Right? + + + align:start position:0% +one. Right? +So one of the challenge is how to narrow + + align:start position:0% +So one of the challenge is how to narrow + + + align:start position:0% +So one of the challenge is how to narrow +down our choice. How to uniquely define + + align:start position:0% +down our choice. How to uniquely define + + + align:start position:0% +down our choice. How to uniquely define +this choice of primitive lice + + align:start position:0% +this choice of primitive lice + + + align:start position:0% +this choice of primitive lice +vectors. The other is a + + align:start position:0% +vectors. The other is a + + + align:start position:0% +vectors. The other is a +conventional unit cell. So primitive + + align:start position:0% +conventional unit cell. So primitive + + + align:start position:0% +conventional unit cell. So primitive +lattice vector those vector will form a + + align:start position:0% +lattice vector those vector will form a + + + align:start position:0% +lattice vector those vector will form a +unit area or unit volume. Right? So in + + align:start position:0% +unit area or unit volume. Right? So in + + + align:start position:0% +unit area or unit volume. Right? So in +2D is by this unit area. If I choose + + align:start position:0% +2D is by this unit area. If I choose + + + align:start position:0% +2D is by this unit area. If I choose +this, this is + + align:start position:0% +this, this is + + + align:start position:0% +this, this is +my uni area and I just repeat it. I will + + align:start position:0% +my uni area and I just repeat it. I will + + + align:start position:0% +my uni area and I just repeat it. I will +pile up the 2D space without any + + align:start position:0% +pile up the 2D space without any + + + align:start position:0% +pile up the 2D space without any +voids. And similarly in 3D I choose my + + align:start position:0% +voids. And similarly in 3D I choose my + + + align:start position:0% +voids. And similarly in 3D I choose my +primitive this unit vector form volume + + align:start position:0% +primitive this unit vector form volume + + + align:start position:0% +primitive this unit vector form volume +that's a primitive unit cell. So this + + align:start position:0% +that's a primitive unit cell. So this + + + align:start position:0% +that's a primitive unit cell. So this +will + + align:start position:0% +will + + + align:start position:0% +will +form a primitive unit cell. + + align:start position:0% + + + + align:start position:0% + +Right. + + align:start position:0% +Right. + + + align:start position:0% +Right. +And so this is a uh uh the one choice of + + align:start position:0% +And so this is a uh uh the one choice of + + + align:start position:0% +And so this is a uh uh the one choice of +the + + align:start position:0% +the + + + align:start position:0% +the +vectors. And uh the other choice is a + + align:start position:0% +vectors. And uh the other choice is a + + + align:start position:0% +vectors. And uh the other choice is a +conventional you can say + + align:start position:0% + + + + align:start position:0% + +uh uh + + align:start position:0% + + + + align:start position:0% + +unis. Okay. And uh say if you look at + + align:start position:0% +unis. Okay. And uh say if you look at + + + align:start position:0% +unis. Okay. And uh say if you look at +this, it probably is much easier if you + + align:start position:0% +this, it probably is much easier if you + + + align:start position:0% +this, it probably is much easier if you +choose + + align:start position:0% +choose + + + align:start position:0% +choose +this as + + align:start position:0% +this as + + + align:start position:0% +this as +your unit cell, right? It looks more + + align:start position:0% +your unit cell, right? It looks more + + + align:start position:0% +your unit cell, right? It looks more +regular. And if you look at the + + align:start position:0% +regular. And if you look at the + + + align:start position:0% +regular. And if you look at the +difference of a primitive + + align:start position:0% + + + + align:start position:0% + +unlimit cell, each of the cell has only + + align:start position:0% +unlimit cell, each of the cell has only + + + align:start position:0% +unlimit cell, each of the cell has only +one lice + + align:start position:0% +one lice + + + align:start position:0% +one lice +point equivalently. This is because + + align:start position:0% +point equivalently. This is because + + + align:start position:0% +point equivalently. This is because +although this primitive unit cell has + + align:start position:0% +although this primitive unit cell has + + + align:start position:0% +although this primitive unit cell has +four lattice point each of this lattice + + align:start position:0% +four lattice point each of this lattice + + + align:start position:0% +four lattice point each of this lattice +point is sheared by four unit cells. So + + align:start position:0% +point is sheared by four unit cells. So + + + align:start position:0% +point is sheared by four unit cells. So +each the lattice point is one force you + + align:start position:0% +each the lattice point is one force you + + + align:start position:0% +each the lattice point is one force you +add up is one + + align:start position:0% +add up is one + + + align:start position:0% +add up is one +uh point one lattice point in one + + align:start position:0% +uh point one lattice point in one + + + align:start position:0% +uh point one lattice point in one +primitive unit cell but if I take this + + align:start position:0% +primitive unit cell but if I take this + + + align:start position:0% +primitive unit cell but if I take this +conventional one you can say this one is + + align:start position:0% +conventional one you can say this one is + + + align:start position:0% +conventional one you can say this one is +shared by four. So one force one force + + align:start position:0% +shared by four. So one force one force + + + align:start position:0% +shared by four. So one force one force +that's in my current drawing there are + + align:start position:0% +that's in my current drawing there are + + + align:start position:0% +that's in my current drawing there are +two points two lattice points. one in + + align:start position:0% +two points two lattice points. one in + + + align:start position:0% +two points two lattice points. one in +one conventional unit + + align:start position:0% +one conventional unit + + + align:start position:0% +one conventional unit +cell. + + align:start position:0% +cell. + + + align:start position:0% +cell. +Okay. And the uh so uh like I said one + + align:start position:0% +Okay. And the uh so uh like I said one + + + align:start position:0% +Okay. And the uh so uh like I said one +of the challenge is even if I take a + + align:start position:0% +of the challenge is even if I take a + + + align:start position:0% +of the challenge is even if I take a +primitive unit cell each of the cell has + + align:start position:0% +primitive unit cell each of the cell has + + + align:start position:0% +primitive unit cell each of the cell has +one at this point I do not have a unique + + align:start position:0% +one at this point I do not have a unique + + + align:start position:0% +one at this point I do not have a unique +way the way I have many + + align:start position:0% +way the way I have many + + + align:start position:0% +way the way I have many +choices. So there is a cuber + + align:start position:0% +choices. So there is a cuber + + + align:start position:0% +choices. So there is a cuber +sum but a unique way to do it to define + + align:start position:0% +sum but a unique way to do it to define + + + align:start position:0% +sum but a unique way to do it to define +uh primitive + + align:start position:0% +uh primitive + + + align:start position:0% +uh primitive +unisell and this is a uh vagner size + + align:start position:0% +unisell and this is a uh vagner size + + + align:start position:0% +unisell and this is a uh vagner size +construction. So let's let me extend + + align:start position:0% +construction. So let's let me extend + + + align:start position:0% +construction. So let's let me extend +this drawing + + align:start position:0% + + + + align:start position:0% + +here. I will extend to this side so to + + align:start position:0% +here. I will extend to this side so to + + + align:start position:0% +here. I will extend to this side so to +make it clear. + + align:start position:0% + + + + align:start position:0% + +Right. So one way to construct + + align:start position:0% +Right. So one way to construct + + + align:start position:0% +Right. So one way to construct +this is take any of this lattice + + align:start position:0% +this is take any of this lattice + + + align:start position:0% +this is take any of this lattice +point. Right. Here is a lattice point. I + + align:start position:0% +point. Right. Here is a lattice point. I + + + align:start position:0% +point. Right. Here is a lattice point. I +connect all the labor lattice + + align:start position:0% +connect all the labor lattice + + + align:start position:0% +connect all the labor lattice +points. So I connect to the all the + + align:start position:0% +points. So I connect to the all the + + + align:start position:0% +points. So I connect to the all the +laboring + + align:start position:0% + + + + align:start position:0% + +points right and then I take the + + align:start position:0% +points right and then I take the + + + align:start position:0% +points right and then I take the +bisect of this uh uh points here of this + + align:start position:0% +bisect of this uh uh points here of this + + + align:start position:0% +bisect of this uh uh points here of this +lines. So this is a bisct and here is a + + align:start position:0% +lines. So this is a bisct and here is a + + + align:start position:0% +lines. So this is a bisct and here is a +bisect and here is a + + align:start position:0% + + + + align:start position:0% + +bisct and you have another point + + align:start position:0% +bisct and you have another point + + + align:start position:0% +bisct and you have another point +here and it turns out this one is not a + + align:start position:0% +here and it turns out this one is not a + + + align:start position:0% +here and it turns out this one is not a +regular cell doesn't look very good + + align:start position:0% +regular cell doesn't look very good + + + align:start position:0% +regular cell doesn't look very good +right but it's + + align:start position:0% +right but it's + + + align:start position:0% +right but it's +unique because any crystal structure I + + align:start position:0% +unique because any crystal structure I + + + align:start position:0% +unique because any crystal structure I +can take latice point I collect all the + + align:start position:0% +can take latice point I collect all the + + + align:start position:0% +can take latice point I collect all the +liver points I take basex and the + + align:start position:0% +liver points I take basex and the + + + align:start position:0% +liver points I take basex and the +minimum volume In this case of area, the + + align:start position:0% +minimum volume In this case of area, the + + + align:start position:0% +minimum volume In this case of area, the +form is a primitive unisell and I can + + align:start position:0% +form is a primitive unisell and I can + + + align:start position:0% +form is a primitive unisell and I can +use that to stack together and form and + + align:start position:0% +use that to stack together and form and + + + align:start position:0% +use that to stack together and form and +fill the whole space without the + + align:start position:0% +fill the whole space without the + + + align:start position:0% +fill the whole space without the +voids. + + align:start position:0% +voids. + + + align:start position:0% +voids. +Right? So it's not the easiest + + align:start position:0% +Right? So it's not the easiest + + + align:start position:0% +Right? So it's not the easiest +construction but it's a unique con uh + + align:start position:0% +construction but it's a unique con uh + + + align:start position:0% +construction but it's a unique con uh +con construction and this is + + align:start position:0% +con construction and this is + + + align:start position:0% +con construction and this is +called wagner size uh construction. + + align:start position:0% + + + + align:start position:0% + +regular size unic wigler size seal + + align:start position:0% +regular size unic wigler size seal + + + align:start position:0% +regular size unic wigler size seal +because it's always this construction + + align:start position:0% +because it's always this construction + + + align:start position:0% +because it's always this construction +always give you + + align:start position:0% +always give you + + + align:start position:0% +always give you +unic. Okay. So uh uh this uh unic gives + + align:start position:0% +unic. Okay. So uh uh this uh unic gives + + + align:start position:0% +unic. Okay. So uh uh this uh unic gives +you now we have uh the primitive lattice + + align:start position:0% +you now we have uh the primitive lattice + + + align:start position:0% +you now we have uh the primitive lattice +vector the uh primitive unic and uh uh + + align:start position:0% +vector the uh primitive unic and uh uh + + + align:start position:0% +vector the uh primitive unic and uh uh +as I said this lattice is mathematical + + align:start position:0% +as I said this lattice is mathematical + + + align:start position:0% +as I said this lattice is mathematical +concept right. So there are different + + align:start position:0% +concept right. So there are different + + + align:start position:0% +concept right. So there are different +require different symmetry the most uh + + align:start position:0% +require different symmetry the most uh + + + align:start position:0% +require different symmetry the most uh +uh uh uh in 3D for example they use uh + + align:start position:0% +uh uh uh in 3D for example they use uh + + + align:start position:0% +uh uh uh in 3D for example they use uh +the uh easiest is uh uh tricinic + + align:start position:0% + + + + align:start position:0% + +unit cell that I can stack and form the + + align:start position:0% +unit cell that I can stack and form the + + + align:start position:0% +unit cell that I can stack and form the +whole uh uh to form the whole space I + + align:start position:0% +whole uh uh to form the whole space I + + + align:start position:0% +whole uh uh to form the whole space I +fill the whole space. So there's no + + align:start position:0% +fill the whole space. So there's no + + + align:start position:0% +fill the whole space. So there's no +symmetry the angle there's no 90 degree + + align:start position:0% +symmetry the angle there's no 90 degree + + + align:start position:0% +symmetry the angle there's no 90 degree +uh and the the lattice constant between + + align:start position:0% +uh and the the lattice constant between + + + align:start position:0% +uh and the the lattice constant between +here the unit cell of the lattice + + align:start position:0% +here the unit cell of the lattice + + + align:start position:0% +here the unit cell of the lattice +constant in each direction are + + align:start position:0% +constant in each direction are + + + align:start position:0% +constant in each direction are +different. So this is a general one, + + align:start position:0% +different. So this is a general one, + + + align:start position:0% +different. So this is a general one, +right? But then there are different + + align:start position:0% +right? But then there are different + + + align:start position:0% +right? But then there are different +symmetry. If you add the symmetries, it + + align:start position:0% +symmetry. If you add the symmetries, it + + + align:start position:0% +symmetry. If you add the symmetries, it +turns out there are only a total of 14 + + align:start position:0% + + + + align:start position:0% + +types of the uh crystal lattice. + + align:start position:0% + + + + align:start position:0% + +And uh I will defer this later on to + + align:start position:0% +And uh I will defer this later on to + + + align:start position:0% +And uh I will defer this later on to +show you uh on computer. And these are + + align:start position:0% +show you uh on computer. And these are + + + align:start position:0% +show you uh on computer. And these are +the 14 times also called the + + align:start position:0% + + + + align:start position:0% + +braas that + + align:start position:0% + + + + align:start position:0% + +is okay. So uh we'll look at this in + + align:start position:0% +is okay. So uh we'll look at this in + + + align:start position:0% +is okay. So uh we'll look at this in +computer later on. + + align:start position:0% +computer later on. + + + align:start position:0% +computer later on. +And uh one more convention of this uh uh + + align:start position:0% +And uh one more convention of this uh uh + + + align:start position:0% +And uh one more convention of this uh uh +lattice the mathematical description is + + align:start position:0% +lattice the mathematical description is + + + align:start position:0% +lattice the mathematical description is +a different crystal graphical plans + + align:start position:0% +a different crystal graphical plans + + + align:start position:0% +a different crystal graphical plans +right so if I take + + align:start position:0% + + + + align:start position:0% + +a a cubic + + align:start position:0% +a a cubic + + + align:start position:0% +a a cubic +structure a unisell that's made of + + align:start position:0% +structure a unisell that's made of + + + align:start position:0% +structure a unisell that's made of +cube right my question is how I would + + align:start position:0% +cube right my question is how I would + + + align:start position:0% +cube right my question is how I would +denote different + + align:start position:0% +denote different + + + align:start position:0% +denote different +faces different crystalographic + + align:start position:0% +faces different crystalographic + + + align:start position:0% +faces different crystalographic +directions, + + align:start position:0% + + + + align:start position:0% + +right? And the different crystalographic + + align:start position:0% +right? And the different crystalographic + + + align:start position:0% +right? And the different crystalographic +plans. And uh uh the convention that's + + align:start position:0% +plans. And uh uh the convention that's + + + align:start position:0% +plans. And uh uh the convention that's +usually used in define the crystalraphic + + align:start position:0% +usually used in define the crystalraphic + + + align:start position:0% +usually used in define the crystalraphic +plans is let's say this is a 3D I have + + align:start position:0% +plans is let's say this is a 3D I have + + + align:start position:0% +plans is let's say this is a 3D I have +a1 + + align:start position:0% +a1 + + + align:start position:0% +a1 +A2 + + align:start position:0% +A2 + + + align:start position:0% +A2 +A3 right and uh I have any + + align:start position:0% +A3 right and uh I have any + + + align:start position:0% +A3 right and uh I have any +crystalographic plan for example from + + align:start position:0% +crystalographic plan for example from + + + align:start position:0% +crystalographic plan for example from +here going here this is the middle point + + align:start position:0% +here going here this is the middle point + + + align:start position:0% +here going here this is the middle point +and uh I could have this point so this + + align:start position:0% +and uh I could have this point so this + + + align:start position:0% +and uh I could have this point so this +form a crystalographic + + align:start position:0% +form a crystalographic + + + align:start position:0% +form a crystalographic +plan right any any of + + align:start position:0% +plan right any any of + + + align:start position:0% +plan right any any of +those so if I have a plan that intersect + + align:start position:0% +those so if I have a plan that intersect + + + align:start position:0% +those so if I have a plan that intersect +this within the unit + + align:start position:0% +this within the unit + + + align:start position:0% +this within the unit +cell let's say at the one point uh A1 + + align:start position:0% +cell let's say at the one point uh A1 + + + align:start position:0% +cell let's say at the one point uh A1 +direction I have intersection point A2 + + align:start position:0% +direction I have intersection point A2 + + + align:start position:0% +direction I have intersection point A2 +A3 let me give you uh arbitrary lumber + + align:start position:0% +A3 let me give you uh arbitrary lumber + + + align:start position:0% +A3 let me give you uh arbitrary lumber +as example so this is a point 8 in terms + + align:start position:0% +as example so this is a point 8 in terms + + + align:start position:0% +as example so this is a point 8 in terms +of the total length of UNCL and here is + + align:start position:0% +of the total length of UNCL and here is + + + align:start position:0% +of the total length of UNCL and here is +a 0 four and here is + + align:start position:0% +a 0 four and here is + + + align:start position:0% +a 0 four and here is +6. Right? This is a + + align:start position:0% +6. Right? This is a + + + align:start position:0% +6. Right? This is a +plan within that cube there. + + align:start position:0% +plan within that cube there. + + + align:start position:0% +plan within that cube there. +And uh the way I label this plan is uh + + align:start position:0% +And uh the way I label this plan is uh + + + align:start position:0% +And uh the way I label this plan is uh +this uh uh Miller index + + align:start position:0% + + + + align:start position:0% + +method and and you take first step is + + align:start position:0% +method and and you take first step is + + + align:start position:0% +method and and you take first step is +you take a reciprocal of those numbers. + + align:start position:0% +you take a reciprocal of those numbers. + + + align:start position:0% +you take a reciprocal of those numbers. +uh the reciprocal + + align:start position:0% +uh the reciprocal + + + align:start position:0% +uh the reciprocal +is8 4 right and uh then say 6 + + align:start position:0% + + + + align:start position:0% + +uh uh you you take say inverse of those + + align:start position:0% +uh uh you you take say inverse of those + + + align:start position:0% +uh uh you you take say inverse of those +intersect and then you reduce this two + + align:start position:0% +intersect and then you reduce this two + + + align:start position:0% +intersect and then you reduce this two +uh integers uh the uh you multiply by + + align:start position:0% +uh integers uh the uh you multiply by + + + align:start position:0% +uh integers uh the uh you multiply by +the + + align:start position:0% +the + + + align:start position:0% +the +uh common the common factors right so if + + align:start position:0% +uh common the common factors right so if + + + align:start position:0% +uh common the common factors right so if +we multiply uh reduce this to integer I + + align:start position:0% +we multiply uh reduce this to integer I + + + align:start position:0% +we multiply uh reduce this to integer I +multiply by 2.4 and I got a + + align:start position:0% +multiply by 2.4 and I got a + + + align:start position:0% +multiply by 2.4 and I got a +36 4. So that's the crystalographic plan + + align:start position:0% +36 4. So that's the crystalographic plan + + + align:start position:0% +36 4. So that's the crystalographic plan +that we just draw. This is the + + align:start position:0% +that we just draw. This is the + + + align:start position:0% +that we just draw. This is the +convention. Okay. And you see that's a + + align:start position:0% +convention. Okay. And you see that's a + + + align:start position:0% +convention. Okay. And you see that's a +pretty cubism why you take a inverse, + + align:start position:0% +pretty cubism why you take a inverse, + + + align:start position:0% +pretty cubism why you take a inverse, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +uh uh that's a uh one way to think about + + align:start position:0% +uh uh that's a uh one way to think about + + + align:start position:0% +uh uh that's a uh one way to think about +this is if I look at this cube again for + + align:start position:0% +this is if I look at this cube again for + + + align:start position:0% +this is if I look at this cube again for +example this surface here + + align:start position:0% +example this surface here + + + align:start position:0% +example this surface here +right and uh if I do not take a inverse + + align:start position:0% +right and uh if I do not take a inverse + + + align:start position:0% +right and uh if I do not take a inverse +you see my intersect say this is a a1 + + align:start position:0% +you see my intersect say this is a a1 + + + align:start position:0% +you see my intersect say this is a a1 +this is a a2 and this is a a3 and if I + + align:start position:0% +this is a a2 and this is a a3 and if I + + + align:start position:0% +this is a a2 and this is a a3 and if I +look at this surface here that intersect + + align:start position:0% +look at this surface here that intersect + + + align:start position:0% +look at this surface here that intersect +here is a one and the other two + + align:start position:0% +here is a one and the other two + + + align:start position:0% +here is a one and the other two +direction is + + align:start position:0% +direction is + + + align:start position:0% +direction is +infinite + + align:start position:0% +infinite + + + align:start position:0% +infinite +right so this surface will be intersect + + align:start position:0% +right so this surface will be intersect + + + align:start position:0% +right so this surface will be intersect +is one infinite + + align:start position:0% +is one infinite + + + align:start position:0% +is one infinite +infinite okay and I guess people don't + + align:start position:0% +infinite okay and I guess people don't + + + align:start position:0% +infinite okay and I guess people don't +like infinite so you take a + + align:start position:0% +like infinite so you take a + + + align:start position:0% +like infinite so you take a +inverse and that + + align:start position:0% +inverse and that + + + align:start position:0% +inverse and that +becomes one 0 + + align:start position:0% +becomes one 0 + + + align:start position:0% +becomes one 0 +plan + + align:start position:0% +plan + + + align:start position:0% +plan +okay so that's uh just the convention of + + align:start position:0% +okay so that's uh just the convention of + + + align:start position:0% +okay so that's uh just the convention of +denoting specific crystalographic + + align:start position:0% + + + + align:start position:0% + +plans. Okay. Now here is so far is + + align:start position:0% +plans. Okay. Now here is so far is + + + align:start position:0% +plans. Okay. Now here is so far is +mathematics. We see the lattice point is + + align:start position:0% +mathematics. We see the lattice point is + + + align:start position:0% +mathematics. We see the lattice point is +abstract. There's no mass, right? Just + + align:start position:0% +abstract. There's no mass, right? Just + + + align:start position:0% +abstract. There's no mass, right? Just +periodic array and there are 14 types + + align:start position:0% +periodic array and there are 14 types + + + align:start position:0% +periodic array and there are 14 types +and uh but we have so many variations in + + align:start position:0% +and uh but we have so many variations in + + + align:start position:0% +and uh but we have so many variations in +real world different + + align:start position:0% +real world different + + + align:start position:0% +real world different +crystals right different + + align:start position:0% +crystals right different + + + align:start position:0% +crystals right different +materials. So + + align:start position:0% +materials. So + + + align:start position:0% +materials. So +structurally among this 14 type the + + align:start position:0% +structurally among this 14 type the + + + align:start position:0% +structurally among this 14 type the +difference is really at each lattice + + align:start position:0% +difference is really at each lattice + + + align:start position:0% +difference is really at each lattice +point what do you put + + align:start position:0% +point what do you put + + + align:start position:0% +point what do you put +there right what do you put there at + + align:start position:0% +there right what do you put there at + + + align:start position:0% +there right what do you put there at +each lattice point is a + + align:start position:0% + + + + align:start position:0% + +basis okay and you can put a single atom + + align:start position:0% +basis okay and you can put a single atom + + + align:start position:0% +basis okay and you can put a single atom +at each lattice + + align:start position:0% +at each lattice + + + align:start position:0% +at each lattice +point you can put a two atoms at each + + align:start position:0% +point you can put a two atoms at each + + + align:start position:0% +point you can put a two atoms at each +latin point or put a molecule at fish + + align:start position:0% +latin point or put a molecule at fish + + + align:start position:0% +latin point or put a molecule at fish +latice + + align:start position:0% +latice + + + align:start position:0% +latice +point right so uh uh salt is a common + + align:start position:0% +point right so uh uh salt is a common + + + align:start position:0% +point right so uh uh salt is a common +salt is among this 14 types later on is + + align:start position:0% +salt is among this 14 types later on is + + + align:start position:0% +salt is among this 14 types later on is +a face center cubic it's a cubic + + align:start position:0% +a face center cubic it's a cubic + + + align:start position:0% +a face center cubic it's a cubic +structure with one atom at the face but + + align:start position:0% +structure with one atom at the face but + + + align:start position:0% +structure with one atom at the face but +say at each of those lattice point you + + align:start position:0% +say at each of those lattice point you + + + align:start position:0% +say at each of those lattice point you +actually put a sodium and a + + align:start position:0% +actually put a sodium and a + + + align:start position:0% +actually put a sodium and a +chloride atom not well so okay each + + align:start position:0% +chloride atom not well so okay each + + + align:start position:0% +chloride atom not well so okay each +lattice point doesn't mean they occupy + + align:start position:0% +lattice point doesn't mean they occupy + + + align:start position:0% +lattice point doesn't mean they occupy +the same space. It's just a periodically + + align:start position:0% +the same space. It's just a periodically + + + align:start position:0% +the same space. It's just a periodically +you can say okay this is a sodium and + + align:start position:0% +you can say okay this is a sodium and + + + align:start position:0% +you can say okay this is a sodium and +then another direction you have chloride + + align:start position:0% +then another direction you have chloride + + + align:start position:0% +then another direction you have chloride +you just repeat that for the each + + align:start position:0% +you just repeat that for the each + + + align:start position:0% +you just repeat that for the each +lattice + + align:start position:0% +lattice + + + align:start position:0% +lattice +point this will become more clear later + + align:start position:0% +point this will become more clear later + + + align:start position:0% +point this will become more clear later +on as we look at the uh uh the computer + + align:start position:0% +on as we look at the uh uh the computer + + + align:start position:0% +on as we look at the uh uh the computer +okay uh I can't draw very well so I will + + align:start position:0% +okay uh I can't draw very well so I will + + + align:start position:0% +okay uh I can't draw very well so I will +rely on that and + + align:start position:0% +rely on that and + + + align:start position:0% +rely on that and +similarly silicon silicon crystal + + align:start position:0% +similarly silicon silicon crystal + + + align:start position:0% +similarly silicon silicon crystal +right and uh silicon crystal it turns + + align:start position:0% +right and uh silicon crystal it turns + + + align:start position:0% +right and uh silicon crystal it turns +out uh uh say at the each lattice + + align:start position:0% +out uh uh say at the each lattice + + + align:start position:0% +out uh uh say at the each lattice +point you put the two + + align:start position:0% +point you put the two + + + align:start position:0% +point you put the two +silicon and silicon and + + align:start position:0% + + + + align:start position:0% + +silicon. So again that's a uh uh even at + + align:start position:0% +silicon. So again that's a uh uh even at + + + align:start position:0% +silicon. So again that's a uh uh even at +say the same everywhere uh is a is a + + align:start position:0% +say the same everywhere uh is a is a + + + align:start position:0% +say the same everywhere uh is a is a +silicon atom but if you look at the + + align:start position:0% +silicon atom but if you look at the + + + align:start position:0% +silicon atom but if you look at the +crystal itself you actually put two + + align:start position:0% +crystal itself you actually put two + + + align:start position:0% +crystal itself you actually put two +silicon atoms in specific direction with + + align:start position:0% +silicon atoms in specific direction with + + + align:start position:0% +silicon atoms in specific direction with +specific angle that form the silicon + + align:start position:0% +specific angle that form the silicon + + + align:start position:0% +specific angle that form the silicon +crystal. So those are the bases uh for + + align:start position:0% +crystal. So those are the bases uh for + + + align:start position:0% +crystal. So those are the bases uh for +what we call lice plus bases together to + + align:start position:0% +what we call lice plus bases together to + + + align:start position:0% +what we call lice plus bases together to +form the crystals. + + align:start position:0% + + + + align:start position:0% + +Okay. Uh let's hold that we'll look come + + align:start position:0% +Okay. Uh let's hold that we'll look come + + + align:start position:0% +Okay. Uh let's hold that we'll look come +back to look at + + align:start position:0% +back to look at + + + align:start position:0% +back to look at +it. What uh we want to talk next. So + + align:start position:0% +it. What uh we want to talk next. So + + + align:start position:0% +it. What uh we want to talk next. So +here is a description for the crystal + + align:start position:0% +here is a description for the crystal + + + align:start position:0% +here is a description for the crystal +structure. Right? And next we want to + + align:start position:0% +structure. Right? And next we want to + + + align:start position:0% +structure. Right? And next we want to +answer what is the uh bonding between + + align:start position:0% +answer what is the uh bonding between + + + align:start position:0% +answer what is the uh bonding between +the crystals. + + align:start position:0% + + + + align:start position:0% + +So bounding potentials and uh + + align:start position:0% +So bounding potentials and uh + + + align:start position:0% +So bounding potentials and uh +um what really hold the material + + align:start position:0% +um what really hold the material + + + align:start position:0% +um what really hold the material +together I think I said this before are + + align:start position:0% +together I think I said this before are + + + align:start position:0% +together I think I said this before are +charge right it's the electron so I say + + align:start position:0% +charge right it's the electron so I say + + + align:start position:0% +charge right it's the electron so I say +electron is the glue for all the + + align:start position:0% +electron is the glue for all the + + + align:start position:0% +electron is the glue for all the +materials + + align:start position:0% + + + + align:start position:0% + +Okay. And uh uh uh when we have uh the + + align:start position:0% +Okay. And uh uh uh when we have uh the + + + align:start position:0% +Okay. And uh uh uh when we have uh the +typical potential when I have two atoms + + align:start position:0% +typical potential when I have two atoms + + + align:start position:0% +typical potential when I have two atoms +putting close together. So typical + + align:start position:0% +putting close together. So typical + + + align:start position:0% +putting close together. So typical +potential curve is this is the + + align:start position:0% +potential curve is this is the + + + align:start position:0% +potential curve is this is the +separation and this is the potential + + align:start position:0% +separation and this is the potential + + + align:start position:0% +separation and this is the potential +interatomical + + align:start position:0% +interatomical + + + align:start position:0% +interatomical +potential and they always look like + + align:start position:0% +potential and they always look like + + + align:start position:0% +potential and they always look like +this. Right? when they are far apart + + align:start position:0% +this. Right? when they are far apart + + + align:start position:0% +this. Right? when they are far apart +they're + + align:start position:0% +they're + + + align:start position:0% +they're +attractive and uh when they are close to + + align:start position:0% +attractive and uh when they are close to + + + align:start position:0% +attractive and uh when they are close to +each other they are + + align:start position:0% +each other they are + + + align:start position:0% +each other they are +repulsive that's a typical inter + + align:start position:0% +repulsive that's a typical inter + + + align:start position:0% +repulsive that's a typical inter +interatomic potential and the minimal + + align:start position:0% +interatomic potential and the minimal + + + align:start position:0% +interatomic potential and the minimal +energy point is where the separation + + align:start position:0% +energy point is where the separation + + + align:start position:0% +energy point is where the separation +will be most + + align:start position:0% +will be most + + + align:start position:0% +will be most +stable right so uh it turns out this + + align:start position:0% +stable right so uh it turns out this + + + align:start position:0% +stable right so uh it turns out this +what's the why you have repulsive that's + + align:start position:0% +what's the why you have repulsive that's + + + align:start position:0% +what's the why you have repulsive that's +when the for example the nucleus + + align:start position:0% +when the for example the nucleus + + + align:start position:0% +when the for example the nucleus +of the two atom positive + + align:start position:0% +of the two atom positive + + + align:start position:0% +of the two atom positive +charge start to overlap influence each + + align:start position:0% +charge start to overlap influence each + + + align:start position:0% +charge start to overlap influence each +other and that's always uh that's what's + + align:start position:0% +other and that's always uh that's what's + + + align:start position:0% +other and that's always uh that's what's +the cause of repulsive and nuclear of + + align:start position:0% +the cause of repulsive and nuclear of + + + align:start position:0% +the cause of repulsive and nuclear of +course that's when they get really + + align:start position:0% +course that's when they get really + + + align:start position:0% +course that's when they get really +close right so uh repulsive part is + + align:start position:0% +close right so uh repulsive part is + + + align:start position:0% +close right so uh repulsive part is +actually uh easier uh to describe + + align:start position:0% + + + + align:start position:0% + +repulsive and uh uh typical potential + + align:start position:0% +repulsive and uh uh typical potential + + + align:start position:0% +repulsive and uh uh typical potential +form + + align:start position:0% +form + + + align:start position:0% +form +uh for the repulsive part as a function + + align:start position:0% +uh for the repulsive part as a function + + + align:start position:0% +uh for the repulsive part as a function +of separation. + + align:start position:0% +of separation. + + + align:start position:0% +of separation. +One is people often use is the 12th's + + align:start position:0% +One is people often use is the 12th's + + + align:start position:0% +One is people often use is the 12th's +power law. Very sharp function 12's + + align:start position:0% +power law. Very sharp function 12's + + + align:start position:0% +power law. Very sharp function 12's +power. Right? This is a Linda John's + + align:start position:0% + + + + align:start position:0% + +type and uh uh the other is using + + align:start position:0% +type and uh uh the other is using + + + align:start position:0% +type and uh uh the other is using +exponential function + + align:start position:0% +exponential function + + + align:start position:0% +exponential function +u0 exponential minus r c and cass is a + + align:start position:0% +u0 exponential minus r c and cass is a + + + align:start position:0% +u0 exponential minus r c and cass is a +caristic length and this is a + + align:start position:0% +caristic length and this is a + + + align:start position:0% +caristic length and this is a +b born meer + + align:start position:0% + + + + align:start position:0% + +So repulsive that's the typical form + + align:start position:0% +So repulsive that's the typical form + + + align:start position:0% +So repulsive that's the typical form +that people use to describe repulsive + + align:start position:0% +that people use to describe repulsive + + + align:start position:0% +that people use to describe repulsive +potential and what really differ between + + align:start position:0% +potential and what really differ between + + + align:start position:0% +potential and what really differ between +different crystals is the attractive + + align:start position:0% +different crystals is the attractive + + + align:start position:0% +different crystals is the attractive +part. Okay. So attractive + + align:start position:0% + + + + align:start position:0% + +potential and uh I said the electron is + + align:start position:0% +potential and uh I said the electron is + + + align:start position:0% +potential and uh I said the electron is +the + + align:start position:0% +the + + + align:start position:0% +the +glue right so even for the least say u + + align:start position:0% +glue right so even for the least say u + + + align:start position:0% +glue right so even for the least say u +uh strongly bonded the crystal is still + + align:start position:0% +uh strongly bonded the crystal is still + + + align:start position:0% +uh strongly bonded the crystal is still +due to electron these are the crystal + + align:start position:0% +due to electron these are the crystal + + + align:start position:0% +due to electron these are the crystal +formed by alert atoms argon crystal + + align:start position:0% +formed by alert atoms argon crystal + + + align:start position:0% +formed by alert atoms argon crystal +Argon is a gas right but if you cool to + + align:start position:0% +Argon is a gas right but if you cool to + + + align:start position:0% +Argon is a gas right but if you cool to +low temperature it actually form + + align:start position:0% +low temperature it actually form + + + align:start position:0% +low temperature it actually form +crystal. So uh we already learned before + + align:start position:0% +crystal. So uh we already learned before + + + align:start position:0% +crystal. So uh we already learned before +argon why is stable because the time say + + align:start position:0% +argon why is stable because the time say + + + align:start position:0% +argon why is stable because the time say +electron field to the uh close to the + + align:start position:0% +electron field to the uh close to the + + + align:start position:0% +electron field to the uh close to the +let's say um n equals which which which + + align:start position:0% +let's say um n equals which which which + + + align:start position:0% +let's say um n equals which which which +line it is there I forgot n= three right + + align:start position:0% +line it is there I forgot n= three right + + + align:start position:0% +line it is there I forgot n= three right +um uh three or four okay right so it + + align:start position:0% +um uh three or four okay right so it + + + align:start position:0% +um uh three or four okay right so it +fails closed shell and there's no so + + align:start position:0% +fails closed shell and there's no so + + + align:start position:0% +fails closed shell and there's no so +each l atom is + + align:start position:0% +each l atom is + + + align:start position:0% +each l atom is +neutral right so even in this uh neutral + + align:start position:0% +neutral right so even in this uh neutral + + + align:start position:0% +neutral right so even in this uh neutral +atom. Remember that atom always have + + align:start position:0% +atom. Remember that atom always have + + + align:start position:0% +atom. Remember that atom always have +nuclei and the + + align:start position:0% +nuclei and the + + + align:start position:0% +nuclei and the +electrons right? So when you put them + + align:start position:0% +electrons right? So when you put them + + + align:start position:0% +electrons right? So when you put them +together what for what what what's the + + align:start position:0% +together what for what what what's the + + + align:start position:0% +together what for what what what's the +interaction why they could have + + align:start position:0% +interaction why they could have + + + align:start position:0% +interaction why they could have +attractive is this possible nucleate + + align:start position:0% +attractive is this possible nucleate + + + align:start position:0% +attractive is this possible nucleate +will attract the electrons in the labor + + align:start position:0% +will attract the electrons in the labor + + + align:start position:0% +will attract the electrons in the labor +atom and similarly the electron of this + + align:start position:0% +atom and similarly the electron of this + + + align:start position:0% +atom and similarly the electron of this +atom will attract the nucleate in the + + align:start position:0% +atom will attract the nucleate in the + + + align:start position:0% +atom will attract the nucleate in the +labor atom. Right? So these are the + + align:start position:0% +labor atom. Right? So these are the + + + align:start position:0% +labor atom. Right? So these are the +dipole dipole interaction. So you will + + align:start position:0% +dipole dipole interaction. So you will + + + align:start position:0% +dipole dipole interaction. So you will +polarize mutual polarize each + + align:start position:0% +polarize mutual polarize each + + + align:start position:0% +polarize mutual polarize each +other and that create attractive + + align:start position:0% +other and that create attractive + + + align:start position:0% +other and that create attractive +force. Okay. So this uh uh attractive + + align:start position:0% +force. Okay. So this uh uh attractive + + + align:start position:0% +force. Okay. So this uh uh attractive +force is a + + align:start position:0% + + + + align:start position:0% + +vender and uh uh the + + align:start position:0% +vender and uh uh the + + + align:start position:0% +vender and uh uh the +attractive + + align:start position:0% +attractive + + + align:start position:0% +attractive +is a to the separation six + + align:start position:0% +is a to the separation six + + + align:start position:0% +is a to the separation six +power and repulsive is positive, + + align:start position:0% +power and repulsive is positive, + + + align:start position:0% +power and repulsive is positive, +attractive is negative and uh so by + + align:start position:0% +attractive is negative and uh so by + + + align:start position:0% +attractive is negative and uh so by +putting the crystal together forming + + align:start position:0% +putting the crystal together forming + + + align:start position:0% +putting the crystal together forming +argon crystal what we have is when they + + align:start position:0% +argon crystal what we have is when they + + + align:start position:0% +argon crystal what we have is when they +are very close is repulsive. When + + align:start position:0% +are very close is repulsive. When + + + align:start position:0% +are very close is repulsive. When +they're uh far apart they attractive but + + align:start position:0% +they're uh far apart they attractive but + + + align:start position:0% +they're uh far apart they attractive but +of course a real crystal has many atoms + + align:start position:0% +of course a real crystal has many atoms + + + align:start position:0% +of course a real crystal has many atoms +periodic + + align:start position:0% +periodic + + + align:start position:0% +periodic +arrangement. So we want to a stable + + align:start position:0% +arrangement. So we want to a stable + + + align:start position:0% +arrangement. So we want to a stable +crystal is when the total energy is + + align:start position:0% +crystal is when the total energy is + + + align:start position:0% +crystal is when the total energy is +minimized + + align:start position:0% +minimized + + + align:start position:0% +minimized +right. So if I have many atoms together + + align:start position:0% +right. So if I have many atoms together + + + align:start position:0% +right. So if I have many atoms together +I minimize the total energy. + + align:start position:0% + + + + align:start position:0% + +So if I have um uh the total energy of + + align:start position:0% +So if I have um uh the total energy of + + + align:start position:0% +So if I have um uh the total energy of +the crystal if I denote the atoms as I + + align:start position:0% +the crystal if I denote the atoms as I + + + align:start position:0% +the crystal if I denote the atoms as I +say uh uh I sum i / j right pair wise + + align:start position:0% +say uh uh I sum i / j right pair wise + + + align:start position:0% +say uh uh I sum i / j right pair wise +because what I have here is between two + + align:start position:0% +because what I have here is between two + + + align:start position:0% +because what I have here is between two +atoms. So atom I and atom + + align:start position:0% +atoms. So atom I and atom + + + align:start position:0% +atoms. So atom I and atom +J and sum up all the atoms and I does + + align:start position:0% +J and sum up all the atoms and I does + + + align:start position:0% +J and sum up all the atoms and I does +not equal to J because I'm look at the + + align:start position:0% +not equal to J because I'm look at the + + + align:start position:0% +not equal to J because I'm look at the +inter mutual interactions and I have + + align:start position:0% +inter mutual interactions and I have + + + align:start position:0% +inter mutual interactions and I have +here uh the uh Lena Johns that's a B R I + + align:start position:0% +here uh the uh Lena Johns that's a B R I + + + align:start position:0% +here uh the uh Lena Johns that's a B R I +J 12 IG is separation between the two + + align:start position:0% +J 12 IG is separation between the two + + + align:start position:0% +J 12 IG is separation between the two +crystals. If it's a cubic you can + + align:start position:0% +crystals. If it's a cubic you can + + + align:start position:0% +crystals. If it's a cubic you can +calculate no matter how far apart in + + align:start position:0% +calculate no matter how far apart in + + + align:start position:0% +calculate no matter how far apart in +terms of unit + + align:start position:0% +terms of unit + + + align:start position:0% +terms of unit +constant and then minus b a r i j6 + + align:start position:0% +constant and then minus b a r i j6 + + + align:start position:0% +constant and then minus b a r i j6 +power right so you uh this is total + + align:start position:0% +power right so you uh this is total + + + align:start position:0% +power right so you uh this is total +energy and when the crystal is stable is + + align:start position:0% +energy and when the crystal is stable is + + + align:start position:0% +energy and when the crystal is stable is +you uh take the um uh r uh one two for + + align:start position:0% +you uh take the um uh r uh one two for + + + align:start position:0% +you uh take the um uh r uh one two for +example one two is the unit constant the + + align:start position:0% +example one two is the unit constant the + + + align:start position:0% +example one two is the unit constant the +constant between two labor + + align:start position:0% +constant between two labor + + + align:start position:0% +constant between two labor +atoms. So you can always express ri + + align:start position:0% +atoms. So you can always express ri + + + align:start position:0% +atoms. So you can always express ri +between further away in terms of if you + + align:start position:0% +between further away in terms of if you + + + align:start position:0% +between further away in terms of if you +have a + + align:start position:0% +have a + + + align:start position:0% +have a +cube, + + align:start position:0% +cube, + + + align:start position:0% +cube, +right? You can express any further + + align:start position:0% +right? You can express any further + + + align:start position:0% +right? You can express any further +points in terms of the smallest lattice + + align:start position:0% +points in terms of the smallest lattice + + + align:start position:0% +points in terms of the smallest lattice +constant and you can take the derivative + + align:start position:0% +constant and you can take the derivative + + + align:start position:0% +constant and you can take the derivative +of that in terms of lattice constant and + + align:start position:0% +of that in terms of lattice constant and + + + align:start position:0% +of that in terms of lattice constant and +that give you where the crystal is + + align:start position:0% +that give you where the crystal is + + + align:start position:0% +that give you where the crystal is +stable. What's the corresponding lattice + + align:start position:0% +stable. What's the corresponding lattice + + + align:start position:0% +stable. What's the corresponding lattice +constant? So this is the u uh uh uh + + align:start position:0% +constant? So this is the u uh uh uh + + + align:start position:0% +constant? So this is the u uh uh uh +simplest uh potential uh that's the wand + + align:start position:0% +simplest uh potential uh that's the wand + + + align:start position:0% +simplest uh potential uh that's the wand +potential and correspondingly those kind + + align:start position:0% +potential and correspondingly those kind + + + align:start position:0% +potential and correspondingly those kind +of crystal is called wand crystal argon + + align:start position:0% +of crystal is called wand crystal argon + + + align:start position:0% +of crystal is called wand crystal argon +and krypton those crystals wonder so uh + + align:start position:0% +and krypton those crystals wonder so uh + + + align:start position:0% +and krypton those crystals wonder so uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh I I remember + + align:start position:0% +uh I I remember + + + align:start position:0% +uh I I remember +uh you see the superman There's this cry + + align:start position:0% +uh you see the superman There's this cry + + + align:start position:0% +uh you see the superman There's this cry +cry uh krypton right I don't know what's + + align:start position:0% +cry uh krypton right I don't know what's + + + align:start position:0% +cry uh krypton right I don't know what's +the say condensity or the temperature I + + align:start position:0% +the say condensity or the temperature I + + + align:start position:0% +the say condensity or the temperature I +haven't checked what's the temperature + + align:start position:0% +haven't checked what's the temperature + + + align:start position:0% +haven't checked what's the temperature +and uh it's not a very strong + + align:start position:0% +and uh it's not a very strong + + + align:start position:0% +and uh it's not a very strong +bonding + + align:start position:0% +bonding + + + align:start position:0% +bonding +okay and uh + + align:start position:0% +okay and uh + + + align:start position:0% +okay and uh +uh secondly what I say let's look at + + align:start position:0% +uh secondly what I say let's look at + + + align:start position:0% +uh secondly what I say let's look at +that this is where it's really the one + + align:start position:0% +that this is where it's really the one + + + align:start position:0% +that this is where it's really the one +attraction and the next type of + + align:start position:0% +attraction and the next type of + + + align:start position:0% +attraction and the next type of +attraction that's easier to deal with is + + align:start position:0% +attraction that's easier to deal with is + + + align:start position:0% +attraction that's easier to deal with is +if you of salt, right? And uh in the + + align:start position:0% +if you of salt, right? And uh in the + + + align:start position:0% +if you of salt, right? And uh in the +case of salt, sodium chloride, what + + align:start position:0% +case of salt, sodium chloride, what + + + align:start position:0% +case of salt, sodium chloride, what +happens is the sodium the electron has a + + align:start position:0% +happens is the sodium the electron has a + + + align:start position:0% +happens is the sodium the electron has a +one sodium has say one outer electron. + + align:start position:0% +one sodium has say one outer electron. + + + align:start position:0% +one sodium has say one outer electron. +It completely lose it to the chloride. + + align:start position:0% +It completely lose it to the chloride. + + + align:start position:0% +It completely lose it to the chloride. +So sodium is a positive charge and + + align:start position:0% +So sodium is a positive charge and + + + align:start position:0% +So sodium is a positive charge and +chloride is a negative charge. Right? + + align:start position:0% +chloride is a negative charge. Right? + + + align:start position:0% +chloride is a negative charge. Right? +And uh in this kind of periodic + + align:start position:0% +And uh in this kind of periodic + + + align:start position:0% +And uh in this kind of periodic +arrangement you have attraction. If it's + + align:start position:0% +arrangement you have attraction. If it's + + + align:start position:0% +arrangement you have attraction. If it's +a if sodium say sodium atom is is + + align:start position:0% +a if sodium say sodium atom is is + + + align:start position:0% +a if sodium say sodium atom is is +positive or positive is repulsion. It + + align:start position:0% +positive or positive is repulsion. It + + + align:start position:0% +positive or positive is repulsion. It +says a chloride atom is attraction + + align:start position:0% +says a chloride atom is attraction + + + align:start position:0% +says a chloride atom is attraction +right. So at the end whether you have a + + align:start position:0% +right. So at the end whether you have a + + + align:start position:0% +right. So at the end whether you have a +stable crystal is you put all those + + align:start position:0% +stable crystal is you put all those + + + align:start position:0% +stable crystal is you put all those +energy together you minimize them + + align:start position:0% +energy together you minimize them + + + align:start position:0% +energy together you minimize them +together uh and in addition to the + + align:start position:0% +together uh and in addition to the + + + align:start position:0% +together uh and in addition to the +repulsive we can't put them too close + + align:start position:0% +repulsive we can't put them too close + + + align:start position:0% +repulsive we can't put them too close +right. So uh in a ionic + + align:start position:0% + + + + align:start position:0% + +crystal and the uh attractive potential + + align:start position:0% +crystal and the uh attractive potential + + + align:start position:0% +crystal and the uh attractive potential +for any atom I attractive part is uh uh + + align:start position:0% +for any atom I attractive part is uh uh + + + align:start position:0% +for any atom I attractive part is uh uh +it has to be attractive the lead effect + + align:start position:0% +it has to be attractive the lead effect + + + align:start position:0% +it has to be attractive the lead effect +has to be attractive otherwise + + align:start position:0% +has to be attractive otherwise + + + align:start position:0% +has to be attractive otherwise +everything is repulsive you don't have a + + align:start position:0% +everything is repulsive you don't have a + + + align:start position:0% +everything is repulsive you don't have a +crystal right so this atom I you look at + + align:start position:0% +crystal right so this atom I you look at + + + align:start position:0% +crystal right so this atom I you look at +the surrounding sodium you look at the + + align:start position:0% +the surrounding sodium you look at the + + + align:start position:0% +the surrounding sodium you look at the +surrounding Lex atom could be chloride + + align:start position:0% +surrounding Lex atom could be chloride + + + align:start position:0% +surrounding Lex atom could be chloride +right so you sum them up and you look at + + align:start position:0% +right so you sum them up and you look at + + + align:start position:0% +right so you sum them up and you look at +le shell that be sodium again that's a + + align:start position:0% +le shell that be sodium again that's a + + + align:start position:0% +le shell that be sodium again that's a +repulsive and you do all the summation + + align:start position:0% +repulsive and you do all the summation + + + align:start position:0% +repulsive and you do all the summation +so we have this + + align:start position:0% +so we have this + + + align:start position:0% +so we have this +summation of all other + + align:start position:0% +summation of all other + + + align:start position:0% +summation of all other +atoms and if uh they are say charged + + align:start position:0% +atoms and if uh they are say charged + + + align:start position:0% +atoms and if uh they are say charged +each atom is with charge q so plus minus + + align:start position:0% +each atom is with charge q so plus minus + + + align:start position:0% +each atom is with charge q so plus minus +to represent it's repulsive or + + align:start position:0% +to represent it's repulsive or + + + align:start position:0% +to represent it's repulsive or +attractive due to electron to a coolum + + align:start position:0% +attractive due to electron to a coolum + + + align:start position:0% +attractive due to electron to a coolum +interaction + + align:start position:0% +interaction + + + align:start position:0% +interaction +RI right so this is the uh coolum + + align:start position:0% +RI right so this is the uh coolum + + + align:start position:0% +RI right so this is the uh coolum +interaction and uh uh it's a very simple + + align:start position:0% +interaction and uh uh it's a very simple + + + align:start position:0% +interaction and uh uh it's a very simple +uh analytically and again you can + + align:start position:0% +uh analytically and again you can + + + align:start position:0% +uh analytically and again you can +express further atoms say in other + + align:start position:0% +express further atoms say in other + + + align:start position:0% +express further atoms say in other +locations if this is the one you're + + align:start position:0% +locations if this is the one you're + + + align:start position:0% +locations if this is the one you're +considering uh other any other location + + align:start position:0% +considering uh other any other location + + + align:start position:0% +considering uh other any other location +in terms of unit constant and so they uh + + align:start position:0% +in terms of unit constant and so they uh + + + align:start position:0% +in terms of unit constant and so they uh +this one in fact sometimes people write + + align:start position:0% +this one in fact sometimes people write + + + align:start position:0% +this one in fact sometimes people write +into alpha squar alpha q ² 4 pi + + align:start position:0% +into alpha squar alpha q ² 4 pi + + + align:start position:0% +into alpha squar alpha q ² 4 pi +epsilon0 and r0 r0 is the nearest labor + + align:start position:0% + + + + align:start position:0% + +distance. So that's a le labor distance + + align:start position:0% +distance. So that's a le labor distance + + + align:start position:0% +distance. So that's a le labor distance +and this alpha is a constant for uh + + align:start position:0% +and this alpha is a constant for uh + + + align:start position:0% +and this alpha is a constant for uh +different crystals. uh you do your s uh + + align:start position:0% +different crystals. uh you do your s uh + + + align:start position:0% +different crystals. uh you do your s uh +structures you sum it up it becomes a uh + + align:start position:0% +structures you sum it up it becomes a uh + + + align:start position:0% +structures you sum it up it becomes a uh +just dependent on crystal structure and + + align:start position:0% +just dependent on crystal structure and + + + align:start position:0% +just dependent on crystal structure and +this is a uh meline + + align:start position:0% + + + + align:start position:0% + +constant + + align:start position:0% + + + + align:start position:0% + +constant okay so with this and also with + + align:start position:0% +constant okay so with this and also with + + + align:start position:0% +constant okay so with this and also with +the uh repulsive part you add them + + align:start position:0% +the uh repulsive part you add them + + + align:start position:0% +the uh repulsive part you add them +together the whole crystal you find out + + align:start position:0% +together the whole crystal you find out + + + align:start position:0% +together the whole crystal you find out +what's the le's labor separation that + + align:start position:0% +what's the le's labor separation that + + + align:start position:0% +what's the le's labor separation that +minimize total ionic crystal energy and + + align:start position:0% +minimize total ionic crystal energy and + + + align:start position:0% +minimize total ionic crystal energy and +that uh uh that's the stable crystal + + align:start position:0% + + + + align:start position:0% + +structure. Okay. So um having said this + + align:start position:0% +structure. Okay. So um having said this + + + align:start position:0% +structure. Okay. So um having said this +if you do your uh this is this is of + + align:start position:0% +if you do your uh this is this is of + + + align:start position:0% +if you do your uh this is this is of +course the minimum this is a zero point + + align:start position:0% +course the minimum this is a zero point + + + align:start position:0% +course the minimum this is a zero point +it doesn't include temperature right + + align:start position:0% +it doesn't include temperature right + + + align:start position:0% +it doesn't include temperature right +some of you may do molecular dynamic + + align:start position:0% +some of you may do molecular dynamic + + + align:start position:0% +some of you may do molecular dynamic +simulation for example and in that case + + align:start position:0% +simulation for example and in that case + + + align:start position:0% +simulation for example and in that case +long zero temperature you write F= MA + + align:start position:0% +long zero temperature you write F= MA + + + align:start position:0% +long zero temperature you write F= MA +and then your F is this kind of + + align:start position:0% +and then your F is this kind of + + + align:start position:0% +and then your F is this kind of +potential interaction and that + + align:start position:0% +potential interaction and that + + + align:start position:0% +potential interaction and that +separation now is not ideal lattice + + align:start position:0% +separation now is not ideal lattice + + + align:start position:0% +separation now is not ideal lattice +constant because the atoms jiggle around + + align:start position:0% +constant because the atoms jiggle around + + + align:start position:0% +constant because the atoms jiggle around +So this separation was a function of + + align:start position:0% +So this separation was a function of + + + align:start position:0% +So this separation was a function of +time right and dealing with ionic force + + align:start position:0% +time right and dealing with ionic force + + + align:start position:0% +time right and dealing with ionic force +become more + + align:start position:0% +become more + + + align:start position:0% +become more +challenging in fact that's more + + align:start position:0% +challenging in fact that's more + + + align:start position:0% +challenging in fact that's more +challenging than coalent in certain uh + + align:start position:0% +challenging than coalent in certain uh + + + align:start position:0% +challenging than coalent in certain uh +uh sense because this dies out very + + align:start position:0% +uh sense because this dies out very + + + align:start position:0% +uh sense because this dies out very +slowly right one / r dice out very + + align:start position:0% +slowly right one / r dice out very + + + align:start position:0% +slowly right one / r dice out very +slowly and that means you need to + + align:start position:0% +slowly and that means you need to + + + align:start position:0% +slowly and that means you need to +include a lot of atoms together to do + + align:start position:0% +include a lot of atoms together to do + + + align:start position:0% +include a lot of atoms together to do +your simulation + + align:start position:0% +your simulation + + + align:start position:0% +your simulation +increase your domain size when you do a + + align:start position:0% +increase your domain size when you do a + + + align:start position:0% +increase your domain size when you do a +simulation. If the force is short range, + + align:start position:0% +simulation. If the force is short range, + + + align:start position:0% +simulation. If the force is short range, +it's much easier to + + align:start position:0% +it's much easier to + + + align:start position:0% +it's much easier to +simulate. + + align:start position:0% +simulate. + + + align:start position:0% +simulate. +Okay. So, + + align:start position:0% +Okay. So, + + + align:start position:0% +Okay. So, +uh now we have + + align:start position:0% +uh now we have + + + align:start position:0% +uh now we have +ionic and next is uh + + align:start position:0% + + + + align:start position:0% + +coalent coalent. + + align:start position:0% + + + + align:start position:0% + +So I have given a coalent example + + align:start position:0% +So I have given a coalent example + + + align:start position:0% +So I have given a coalent example +before and this is a when two hydrogen + + align:start position:0% +before and this is a when two hydrogen + + + align:start position:0% +before and this is a when two hydrogen +atoms form a hydrogen molecule right. So + + align:start position:0% +atoms form a hydrogen molecule right. So + + + align:start position:0% +atoms form a hydrogen molecule right. So +when we have two hydrogen atoms form + + align:start position:0% +when we have two hydrogen atoms form + + + align:start position:0% +when we have two hydrogen atoms form +hydrogen molecule and with the lower + + align:start position:0% +hydrogen molecule and with the lower + + + align:start position:0% +hydrogen molecule and with the lower +energy states is when now electron + + align:start position:0% +energy states is when now electron + + + align:start position:0% +energy states is when now electron +because the poly exclusion the hydrogen + + align:start position:0% +because the poly exclusion the hydrogen + + + align:start position:0% +because the poly exclusion the hydrogen +atom energy level split into sigma and + + align:start position:0% +atom energy level split into sigma and + + + align:start position:0% +atom energy level split into sigma and +sigma star right sigma bonds the lower + + align:start position:0% +sigma star right sigma bonds the lower + + + align:start position:0% +sigma star right sigma bonds the lower +bound one is when the electron orbital + + align:start position:0% +bound one is when the electron orbital + + + align:start position:0% +bound one is when the electron orbital +is like what I draw here and you can say + + align:start position:0% +is like what I draw here and you can say + + + align:start position:0% +is like what I draw here and you can say +the electron is orbited + + align:start position:0% +the electron is orbited + + + align:start position:0% +the electron is orbited +between two hydrogen and has + + align:start position:0% +between two hydrogen and has + + + align:start position:0% +between two hydrogen and has +directionalities + + align:start position:0% +directionalities + + + align:start position:0% +directionalities +right and those are the uh coalent + + align:start position:0% +right and those are the uh coalent + + + align:start position:0% +right and those are the uh coalent +bonds and uh if you form a crystal + + align:start position:0% +bonds and uh if you form a crystal + + + align:start position:0% +bonds and uh if you form a crystal +so again 2D for simplicity so you have + + align:start position:0% +so again 2D for simplicity so you have + + + align:start position:0% +so again 2D for simplicity so you have +directionality in this one you have + + align:start position:0% +directionality in this one you have + + + align:start position:0% +directionality in this one you have +directionality in here directionality + + align:start position:0% +directionality in here directionality + + + align:start position:0% +directionality in here directionality +here so those are the regions where most + + align:start position:0% +here so those are the regions where most + + + align:start position:0% +here so those are the regions where most +likely you find electrons + + align:start position:0% + + + + align:start position:0% + +Right? And in this + + align:start position:0% +Right? And in this + + + align:start position:0% +Right? And in this +region you don't find the probability + + align:start position:0% +region you don't find the probability + + + align:start position:0% +region you don't find the probability +find the electron is small. So the bonds + + align:start position:0% +find the electron is small. So the bonds + + + align:start position:0% +find the electron is small. So the bonds +has + + align:start position:0% +has + + + align:start position:0% +has +directionality right those are the + + align:start position:0% +directionality right those are the + + + align:start position:0% +directionality right those are the +coalent + + align:start position:0% +coalent + + + align:start position:0% +coalent +bond and now uh the next one is if this + + align:start position:0% +bond and now uh the next one is if this + + + align:start position:0% +bond and now uh the next one is if this +expand start to overlap and fill the + + align:start position:0% +expand start to overlap and fill the + + + align:start position:0% +expand start to overlap and fill the +whole space those + + align:start position:0% +whole space those + + + align:start position:0% +whole space those +coalent right the electron can go + + align:start position:0% +coalent right the electron can go + + + align:start position:0% +coalent right the electron can go +anywhere that becomes under that picture + + align:start position:0% +anywhere that becomes under that picture + + + align:start position:0% +anywhere that becomes under that picture +I come to the metallic bonds + + align:start position:0% + + + + align:start position:0% + +electron become + + align:start position:0% +electron become + + + align:start position:0% +electron become +free. It's a metallic + + align:start position:0% +free. It's a metallic + + + align:start position:0% +free. It's a metallic +bonding. So coalent is strongest + + align:start position:0% +bonding. So coalent is strongest + + + align:start position:0% +bonding. So coalent is strongest +uh bonding uh uh among the uh say for + + align:start position:0% +uh bonding uh uh among the uh say for + + + align:start position:0% +uh bonding uh uh among the uh say for +the + + align:start position:0% +the + + + align:start position:0% +the +crystals. Okay. + + align:start position:0% +crystals. Okay. + + + align:start position:0% +crystals. Okay. +And uh uh in passen uh uh when we deal + + align:start position:0% +And uh uh in passen uh uh when we deal + + + align:start position:0% +And uh uh in passen uh uh when we deal +with water liquid there's also hydrogen + + align:start position:0% +with water liquid there's also hydrogen + + + align:start position:0% +with water liquid there's also hydrogen +bond right what is hydrogen + + align:start position:0% +bond right what is hydrogen + + + align:start position:0% +bond right what is hydrogen +bond and uh I I think you you all know + + align:start position:0% +bond and uh I I think you you all know + + + align:start position:0% +bond and uh I I think you you all know +so if I have H2O right so I have say + + align:start position:0% +so if I have H2O right so I have say + + + align:start position:0% +so if I have H2O right so I have say +this is a hydrogen this is a hydrogen + + align:start position:0% +this is a hydrogen this is a hydrogen + + + align:start position:0% +this is a hydrogen this is a hydrogen +this oxygen and uh uh it has some + + align:start position:0% +this oxygen and uh uh it has some + + + align:start position:0% +this oxygen and uh uh it has some +directionality in bond angle + + align:start position:0% +directionality in bond angle + + + align:start position:0% +directionality in bond angle +That's a single hydro uh water molecule. + + align:start position:0% +That's a single hydro uh water molecule. + + + align:start position:0% +That's a single hydro uh water molecule. +And now when you bring your lex molecule + + align:start position:0% +And now when you bring your lex molecule + + + align:start position:0% +And now when you bring your lex molecule +oxygen will form some bonding rather + + align:start position:0% +oxygen will form some bonding rather + + + align:start position:0% +oxygen will form some bonding rather +than just now electron is shared between + + align:start position:0% +than just now electron is shared between + + + align:start position:0% +than just now electron is shared between +one hydrogen say H2O molecule there + + align:start position:0% +one hydrogen say H2O molecule there + + + align:start position:0% +one hydrogen say H2O molecule there +start bond between this oxygen and next + + align:start position:0% +start bond between this oxygen and next + + + align:start position:0% +start bond between this oxygen and next +hydrogen. That's your hydrogen + + align:start position:0% + + + + align:start position:0% + +bond. Okay. So what I have talked so far + + align:start position:0% +bond. Okay. So what I have talked so far + + + align:start position:0% +bond. Okay. So what I have talked so far +is uh uh the periodic structure + + align:start position:0% +is uh uh the periodic structure + + + align:start position:0% +is uh uh the periodic structure +crystal and the basic notation of + + align:start position:0% +crystal and the basic notation of + + + align:start position:0% +crystal and the basic notation of +periodic structure and then we talked + + align:start position:0% +periodic structure and then we talked + + + align:start position:0% +periodic structure and then we talked +about the bonding what holds the atoms + + align:start position:0% +about the bonding what holds the atoms + + + align:start position:0% +about the bonding what holds the atoms +together different forms of + + align:start position:0% +together different forms of + + + align:start position:0% +together different forms of +bonds and next I want come back to this + + align:start position:0% +bonds and next I want come back to this + + + align:start position:0% +bonds and next I want come back to this +periodical structure I'm going to talk + + align:start position:0% +periodical structure I'm going to talk + + + align:start position:0% +periodical structure I'm going to talk +you to you + + align:start position:0% +you to you + + + align:start position:0% +you to you +uh very mathematical concept + + align:start position:0% +uh very mathematical concept + + + align:start position:0% +uh very mathematical concept +And this is a fer + + align:start position:0% +And this is a fer + + + align:start position:0% +And this is a fer +transform and uh uh if you're electric + + align:start position:0% +transform and uh uh if you're electric + + + align:start position:0% +transform and uh uh if you're electric +engineer you're familiar with the uh + + align:start position:0% +engineer you're familiar with the uh + + + align:start position:0% +engineer you're familiar with the uh +frequency domain right and uh the + + align:start position:0% +frequency domain right and uh the + + + align:start position:0% +frequency domain right and uh the +question is we we we mentioned this in + + align:start position:0% +question is we we we mentioned this in + + + align:start position:0% +question is we we we mentioned this in +different occasions like last time when + + align:start position:0% +different occasions like last time when + + + align:start position:0% +different occasions like last time when +we talk about the + + align:start position:0% +we talk about the + + + align:start position:0% +we talk about the +uh fun common periodic boundary + + align:start position:0% +uh fun common periodic boundary + + + align:start position:0% +uh fun common periodic boundary +condition right so up. + + align:start position:0% + + + + align:start position:0% + +And uh um last time when we talk about + + align:start position:0% +And uh um last time when we talk about + + + align:start position:0% +And uh um last time when we talk about +from common periodic boundary condition + + align:start position:0% +from common periodic boundary condition + + + align:start position:0% +from common periodic boundary condition +we say a one-dimensional lattice ch of + + align:start position:0% +we say a one-dimensional lattice ch of + + + align:start position:0% +we say a one-dimensional lattice ch of +length l right has n + + align:start position:0% +length l right has n + + + align:start position:0% +length l right has n +atoms and from common per periodic + + align:start position:0% +atoms and from common per periodic + + + align:start position:0% +atoms and from common per periodic +boundary condition say uh x + l equals + + align:start position:0% +boundary condition say uh x + l equals + + + align:start position:0% +boundary condition say uh x + l equals +cosine x and from Here uh we use the uh + + align:start position:0% +cosine x and from Here uh we use the uh + + + align:start position:0% +cosine x and from Here uh we use the uh +block theorem because this one is x + + align:start position:0% +block theorem because this one is x + + + align:start position:0% +block theorem because this one is x +exponential minus i k which is the wave + + align:start position:0% +exponential minus i k which is the wave + + + align:start position:0% +exponential minus i k which is the wave +through the whole lattice l is n a and + + align:start position:0% +through the whole lattice l is n a and + + + align:start position:0% +through the whole lattice l is n a and +that equals cosine x. So this is a block + + align:start position:0% +that equals cosine x. So this is a block + + + align:start position:0% +that equals cosine x. So this is a block +theorem from he this this equals so this + + align:start position:0% +theorem from he this this equals so this + + + align:start position:0% +theorem from he this this equals so this +one equals one that's why we get a k + + align:start position:0% +one equals one that's why we get a k + + + align:start position:0% +one equals one that's why we get a k +equals plus mass 2 n uh 2 n pi / by + + align:start position:0% +equals plus mass 2 n uh 2 n pi / by + + + align:start position:0% +equals plus mass 2 n uh 2 n pi / by +capital n a so this is how we got one + + align:start position:0% +capital n a so this is how we got one + + + align:start position:0% +capital n a so this is how we got one +way we got it right from block theorem + + align:start position:0% +way we got it right from block theorem + + + align:start position:0% +way we got it right from block theorem +allowable v vector k and the other way + + align:start position:0% +allowable v vector k and the other way + + + align:start position:0% +allowable v vector k and the other way +we got it we we explain it is uh I just + + align:start position:0% +we got it we we explain it is uh I just + + + align:start position:0% +we got it we we explain it is uh I just +have a w function Here I want to expand + + align:start position:0% +have a w function Here I want to expand + + + align:start position:0% +have a w function Here I want to expand +in fial space right in in fial + + align:start position:0% +in fial space right in in fial + + + align:start position:0% +in fial space right in in fial +series. So uh this are equivalent + + align:start position:0% +series. So uh this are equivalent + + + align:start position:0% +series. So uh this are equivalent +essentially they say I have periodic + + align:start position:0% +essentially they say I have periodic + + + align:start position:0% +essentially they say I have periodic +function I want to use uh here is + + align:start position:0% +function I want to use uh here is + + + align:start position:0% +function I want to use uh here is +extended wave uh uh in in in block block + + align:start position:0% +extended wave uh uh in in in block block + + + align:start position:0% +extended wave uh uh in in in block block +wave the other one once you expand into + + align:start position:0% +wave the other one once you expand into + + + align:start position:0% +wave the other one once you expand into +fial series you still got a wave vector + + align:start position:0% +fial series you still got a wave vector + + + align:start position:0% +fial series you still got a wave vector +you got the extended wave through the + + align:start position:0% +you got the extended wave through the + + + align:start position:0% +you got the extended wave through the +whole + + align:start position:0% +whole + + + align:start position:0% +whole +region right this is a + + align:start position:0% +region right this is a + + + align:start position:0% +region right this is a +1D 1D I think you're all probably + + align:start position:0% +1D 1D I think you're all probably + + + align:start position:0% +1D 1D I think you're all probably +comfortable because it's just a + + align:start position:0% +comfortable because it's just a + + + align:start position:0% +comfortable because it's just a +corresponding time right time into 1D + + align:start position:0% +corresponding time right time into 1D + + + align:start position:0% +corresponding time right time into 1D +space. Now I'm asking you to construct a + + align:start position:0% +space. Now I'm asking you to construct a + + + align:start position:0% +space. Now I'm asking you to construct a +3D because crystal is periodically in + + align:start position:0% +3D because crystal is periodically in + + + align:start position:0% +3D because crystal is periodically in +3D. my wave + + align:start position:0% +3D. my wave + + + align:start position:0% +3D. my wave +function I'm going to write in general + + align:start position:0% +function I'm going to write in general + + + align:start position:0% +function I'm going to write in general +case a wave function and any + + align:start position:0% +case a wave function and any + + + align:start position:0% +case a wave function and any +location plus any translation of wave + + align:start position:0% +location plus any translation of wave + + + align:start position:0% +location plus any translation of wave +vector that's periodic right or unit say + + align:start position:0% +vector that's periodic right or unit say + + + align:start position:0% +vector that's periodic right or unit say +primitive lice vector and that + + align:start position:0% + + + + align:start position:0% + +equals so now I have a 3D rather than + + align:start position:0% +equals so now I have a 3D rather than + + + align:start position:0% +equals so now I have a 3D rather than +writing 1D can you do the full + + align:start position:0% + + + + align:start position:0% + +representation, right? + + align:start position:0% +representation, right? + + + align:start position:0% +representation, right? +So this is uh uh uh uh where why we + + align:start position:0% +So this is uh uh uh uh where why we + + + align:start position:0% +So this is uh uh uh uh where why we +introduce the reciprocal lice and turns + + align:start position:0% +introduce the reciprocal lice and turns + + + align:start position:0% +introduce the reciprocal lice and turns +out if you look at the uh 1D uh the here + + align:start position:0% +out if you look at the uh 1D uh the here + + + align:start position:0% +out if you look at the uh 1D uh the here +the period is a right and then in your + + align:start position:0% +the period is a right and then in your + + + align:start position:0% +the period is a right and then in your +denominator you have a so it's a inverse + + align:start position:0% +denominator you have a so it's a inverse + + + align:start position:0% +denominator you have a so it's a inverse +of that + + align:start position:0% +of that + + + align:start position:0% +of that +pure + + align:start position:0% +pure + + + align:start position:0% +pure +okay so the way I do 3D construction of + + align:start position:0% +okay so the way I do 3D construction of + + + align:start position:0% +okay so the way I do 3D construction of +that period uni vector because the 3D. + + align:start position:0% +that period uni vector because the 3D. + + + align:start position:0% +that period uni vector because the 3D. +So a real space 3D is inverted into F + + align:start position:0% +So a real space 3D is inverted into F + + + align:start position:0% +So a real space 3D is inverted into F +real space + + align:start position:0% +real space + + + align:start position:0% +real space +3D and the F real space I also + + align:start position:0% +3D and the F real space I also + + + align:start position:0% +3D and the F real space I also +correspondingly have a primitive unit + + align:start position:0% +correspondingly have a primitive unit + + + align:start position:0% +correspondingly have a primitive unit +vector a primitive unit cell and vner + + align:start position:0% +vector a primitive unit cell and vner + + + align:start position:0% +vector a primitive unit cell and vner +size + + align:start position:0% + + + + align:start position:0% + +construction. Okay. And the way I + + align:start position:0% +construction. Okay. And the way I + + + align:start position:0% +construction. Okay. And the way I +construct this reciprocal + + align:start position:0% +construct this reciprocal + + + align:start position:0% +construct this reciprocal +uh uh primitive lattice vector is if I + + align:start position:0% +uh uh primitive lattice vector is if I + + + align:start position:0% +uh uh primitive lattice vector is if I +have the uh + + align:start position:0% +have the uh + + + align:start position:0% +have the uh +a1 + + align:start position:0% +a1 + + + align:start position:0% +a1 +a2 + + align:start position:0% +a2 + + + align:start position:0% +a2 +a3 as the real space primitive lice + + align:start position:0% +a3 as the real space primitive lice + + + align:start position:0% +a3 as the real space primitive lice +vector and then the reciprocal space is + + align:start position:0% +vector and then the reciprocal space is + + + align:start position:0% +vector and then the reciprocal space is +b1 equals 2 pi. So that's my 2 pi. + + align:start position:0% +b1 equals 2 pi. So that's my 2 pi. + + + align:start position:0% +b1 equals 2 pi. So that's my 2 pi. +Okay, length becomes a volume. So length + + align:start position:0% +Okay, length becomes a volume. So length + + + align:start position:0% +Okay, length becomes a volume. So length +become + + align:start position:0% +become + + + align:start position:0% +become +volume and uh uh here I have a2 * + + align:start position:0% + + + + align:start position:0% + +a3 and then permute the subscript then I + + align:start position:0% +a3 and then permute the subscript then I + + + align:start position:0% +a3 and then permute the subscript then I +have + + align:start position:0% +have + + + align:start position:0% +have +b2 is 2 pi volume a3 * + + align:start position:0% +b2 is 2 pi volume a3 * + + + align:start position:0% +b2 is 2 pi volume a3 * +a1 this is a cross the vector + + align:start position:0% +a1 this is a cross the vector + + + align:start position:0% +a1 this is a cross the vector +product and 2 + + align:start position:0% +product and 2 + + + align:start position:0% +product and 2 +pi we a1 * A2 and this ensure me the + + align:start position:0% +pi we a1 * A2 and this ensure me the + + + align:start position:0% +pi we a1 * A2 and this ensure me the +that's the corresponding + + align:start position:0% +that's the corresponding + + + align:start position:0% +that's the corresponding +uh vector uh in the fuller space of this + + align:start position:0% +uh vector uh in the fuller space of this + + + align:start position:0% +uh vector uh in the fuller space of this +3D periodic space real + + align:start position:0% +3D periodic space real + + + align:start position:0% +3D periodic space real +space. + + align:start position:0% +space. + + + align:start position:0% +space. +Okay. Uh uh you will see + + align:start position:0% +Okay. Uh uh you will see + + + align:start position:0% +Okay. Uh uh you will see +why. Let me + + align:start position:0% +why. Let me + + + align:start position:0% +why. Let me +uh give a a few + + align:start position:0% +uh give a a few + + + align:start position:0% +uh give a a few +more points. + + align:start position:0% + + + + align:start position:0% + +here and uh uh so with that I can + + align:start position:0% +here and uh uh so with that I can + + + align:start position:0% +here and uh uh so with that I can +construct this is my + + align:start position:0% +construct this is my + + + align:start position:0% +construct this is my +primitive unit vector uh in the + + align:start position:0% +primitive unit vector uh in the + + + align:start position:0% +primitive unit vector uh in the +reciprocal space. So the translational + + align:start position:0% +reciprocal space. So the translational + + + align:start position:0% +reciprocal space. So the translational +vector uh so any of this m_sub_1 b1 and + + align:start position:0% +vector uh so any of this m_sub_1 b1 and + + + align:start position:0% +vector uh so any of this m_sub_1 b1 and +m_sub_2 b2 plus m3 b3 any of this + + align:start position:0% +m_sub_2 b2 plus m3 b3 any of this + + + align:start position:0% +m_sub_2 b2 plus m3 b3 any of this +combination give me one point the + + align:start position:0% +combination give me one point the + + + align:start position:0% +combination give me one point the +lattice point in the reciprocal space. + + align:start position:0% +lattice point in the reciprocal space. + + + align:start position:0% +lattice point in the reciprocal space. +So this will make a periodical space + + align:start position:0% + + + + align:start position:0% + +reciprocal + + align:start position:0% + + + + align:start position:0% + +space and uh that's reciprocal of real + + align:start position:0% +space and uh that's reciprocal of real + + + align:start position:0% +space and uh that's reciprocal of real +space. It turns out sometimes I joke + + align:start position:0% +space. It turns out sometimes I joke + + + align:start position:0% +space. It turns out sometimes I joke +physicist live in the not in the real + + align:start position:0% +physicist live in the not in the real + + + align:start position:0% +physicist live in the not in the real +world they live in the reciprocal world. + + align:start position:0% +world they live in the reciprocal world. + + + align:start position:0% +world they live in the reciprocal world. +Okay, that's because most of time you + + align:start position:0% +Okay, that's because most of time you + + + align:start position:0% +Okay, that's because most of time you +see everything is draw in terms of the + + align:start position:0% +see everything is draw in terms of the + + + align:start position:0% +see everything is draw in terms of the +uh wave + + align:start position:0% +uh wave + + + align:start position:0% +uh wave +vectors and uh you can of course + + align:start position:0% +vectors and uh you can of course + + + align:start position:0% +vectors and uh you can of course +construct your uh unisell primitive unl + + align:start position:0% +construct your uh unisell primitive unl + + + align:start position:0% +construct your uh unisell primitive unl +cell based on this latice + + align:start position:0% +cell based on this latice + + + align:start position:0% +cell based on this latice +points and uh now if you have your uh + + align:start position:0% +points and uh now if you have your uh + + + align:start position:0% +points and uh now if you have your uh +for example you have your function + + align:start position:0% +for example you have your function + + + align:start position:0% +for example you have your function +that's a periodic any function that's a + + align:start position:0% +that's a periodic any function that's a + + + align:start position:0% +that's a periodic any function that's a +periodic + + align:start position:0% +periodic + + + align:start position:0% +periodic +R + uh + + align:start position:0% +R + uh + + + align:start position:0% +R + uh +T and the way you do your FIA transform + + align:start position:0% +T and the way you do your FIA transform + + + align:start position:0% +T and the way you do your FIA transform +if this is due to this periodicity you + + align:start position:0% +if this is due to this periodicity you + + + align:start position:0% +if this is due to this periodicity you +can write write this function in FI + + align:start position:0% +can write write this function in FI + + + align:start position:0% +can write write this function in FI +series + + align:start position:0% +series + + + align:start position:0% +series +right 3D rather than 1D F series now you + + align:start position:0% +right 3D rather than 1D F series now you + + + align:start position:0% +right 3D rather than 1D F series now you +write 3D FI series and the FI series is + + align:start position:0% +write 3D FI series and the FI series is + + + align:start position:0% +write 3D FI series and the FI series is +your R + + align:start position:0% +your R + + + align:start position:0% +your R +equals and uh here is the for a constant + + align:start position:0% +equals and uh here is the for a constant + + + align:start position:0% +equals and uh here is the for a constant +u g + + align:start position:0% +u g + + + align:start position:0% +u g +exponential I r * + + align:start position:0% +exponential I r * + + + align:start position:0% +exponential I r * +g so like r * k and uh uh this is a sum + + align:start position:0% +g so like r * k and uh uh this is a sum + + + align:start position:0% +g so like r * k and uh uh this is a sum +up over all uh + + align:start position:0% +up over all uh + + + align:start position:0% +up over all uh +g's over all those latice + + align:start position:0% +g's over all those latice + + + align:start position:0% +g's over all those latice +points + + align:start position:0% +points + + + align:start position:0% +points +okay and uh uh I will not I I will not + + align:start position:0% +okay and uh uh I will not I I will not + + + align:start position:0% +okay and uh uh I will not I I will not +say prove but I will use that I'll do + + align:start position:0% +say prove but I will use that I'll do + + + align:start position:0% +say prove but I will use that I'll do +that proof in the next lecture. uh the + + align:start position:0% +that proof in the next lecture. uh the + + + align:start position:0% +that proof in the next lecture. uh the +point of this reciprocal space the + + align:start position:0% +point of this reciprocal space the + + + align:start position:0% +point of this reciprocal space the +the what you could use it's very easy + + align:start position:0% +the what you could use it's very easy + + + align:start position:0% +the what you could use it's very easy +actually doing when you do an + + align:start position:0% +actually doing when you do an + + + align:start position:0% +actually doing when you do an +experiment when you do a transmission + + align:start position:0% +experiment when you do a transmission + + + align:start position:0% +experiment when you do a transmission +electron micro uh uh say defraction + + align:start position:0% +electron micro uh uh say defraction + + + align:start position:0% +electron micro uh uh say defraction +pattern it turns out that what you map + + align:start position:0% +pattern it turns out that what you map + + + align:start position:0% +pattern it turns out that what you map +out are the reciprocal space you can + + align:start position:0% +out are the reciprocal space you can + + + align:start position:0% +out are the reciprocal space you can +actually + + align:start position:0% +actually + + + align:start position:0% +actually +uh easily map out this reciprocal space + + align:start position:0% +uh easily map out this reciprocal space + + + align:start position:0% +uh easily map out this reciprocal space +and uh uh so if you + + align:start position:0% +and uh uh so if you + + + align:start position:0% +and uh uh so if you +have a object crystal periodic + + align:start position:0% +have a object crystal periodic + + + align:start position:0% +have a object crystal periodic +structure, right? You shoot a wave + + align:start position:0% +structure, right? You shoot a wave + + + align:start position:0% +structure, right? You shoot a wave +coming in and you have + + align:start position:0% +coming in and you have + + + align:start position:0% +coming in and you have +defraction, right? And some of you have + + align:start position:0% +defraction, right? And some of you have + + + align:start position:0% +defraction, right? And some of you have +seen gradients. How many of of you have + + align:start position:0% +seen gradients. How many of of you have + + + align:start position:0% +seen gradients. How many of of you have +seen + + align:start position:0% +seen + + + align:start position:0% +seen +gradients? Gradient structure. So it + + align:start position:0% +gradients? Gradient structure. So it + + + align:start position:0% +gradients? Gradient structure. So it +turns out that any periodic structure I + + align:start position:0% +turns out that any periodic structure I + + + align:start position:0% +turns out that any periodic structure I +next time I'll bring one. Okay. you + + align:start position:0% +next time I'll bring one. Okay. you + + + align:start position:0% +next time I'll bring one. Okay. you +should uh say uh uh light onto a a + + align:start position:0% +should uh say uh uh light onto a a + + + align:start position:0% +should uh say uh uh light onto a a +gradient you only see the defraction uh + + align:start position:0% +gradient you only see the defraction uh + + + align:start position:0% +gradient you only see the defraction uh +the light in the reflected in any say + + align:start position:0% +the light in the reflected in any say + + + align:start position:0% +the light in the reflected in any say +any in discrete + + align:start position:0% +any in discrete + + + align:start position:0% +any in discrete +spots okay so again if I have a + + align:start position:0% +spots okay so again if I have a + + + align:start position:0% +spots okay so again if I have a +periodical range of atoms and what + + align:start position:0% +periodical range of atoms and what + + + align:start position:0% +periodical range of atoms and what +they'll say is only in certain + + align:start position:0% +they'll say is only in certain + + + align:start position:0% +they'll say is only in certain +directions you'll see the light come out + + align:start position:0% +directions you'll see the light come out + + + align:start position:0% +directions you'll see the light come out +or this is not light this could be + + align:start position:0% +or this is not light this could be + + + align:start position:0% +or this is not light this could be +electron beam when you do transmission + + align:start position:0% +electron beam when you do transmission + + + align:start position:0% +electron beam when you do transmission +electron micro graph uh or it could be + + align:start position:0% +electron micro graph uh or it could be + + + align:start position:0% +electron micro graph uh or it could be +X-ray right why you use X-ray because + + align:start position:0% +X-ray right why you use X-ray because + + + align:start position:0% +X-ray right why you use X-ray because +X-ray wavelengths can be very short + + align:start position:0% +X-ray wavelengths can be very short + + + align:start position:0% +X-ray wavelengths can be very short +comparable to the lattice + + align:start position:0% +comparable to the lattice + + + align:start position:0% +comparable to the lattice +constant and in that case in uh say if + + align:start position:0% +constant and in that case in uh say if + + + align:start position:0% +constant and in that case in uh say if +you m satisfy this gradient say + + align:start position:0% +you m satisfy this gradient say + + + align:start position:0% +you m satisfy this gradient say +condition let me write down the + + align:start position:0% +condition let me write down the + + + align:start position:0% +condition let me write down the +condition I'll prove it uh in the uh + + align:start position:0% +condition I'll prove it uh in the uh + + + align:start position:0% +condition I'll prove it uh in the uh +next lecture so your condition is if + + align:start position:0% +next lecture so your condition is if + + + align:start position:0% +next lecture so your condition is if +this is the wave vector of incident wave + + align:start position:0% +this is the wave vector of incident wave + + + align:start position:0% +this is the wave vector of incident wave +this V vector of the reflective wave and + + align:start position:0% +this V vector of the reflective wave and + + + align:start position:0% +this V vector of the reflective wave and +uh you will have K I minus + + align:start position:0% +uh you will have K I minus + + + align:start position:0% +uh you will have K I minus +KF equals plus G equals zero. So the you + + align:start position:0% +KF equals plus G equals zero. So the you + + + align:start position:0% +KF equals plus G equals zero. So the you +say G is the uh latice point point in + + align:start position:0% +say G is the uh latice point point in + + + align:start position:0% +say G is the uh latice point point in +the reciprocal + + align:start position:0% +the reciprocal + + + align:start position:0% +the reciprocal +space. Okay. And uh say this is incident + + align:start position:0% +space. Okay. And uh say this is incident + + + align:start position:0% +space. Okay. And uh say this is incident +reflected. And coming back to why at the + + align:start position:0% +reflected. And coming back to why at the + + + align:start position:0% +reflected. And coming back to why at the +beginning we + + align:start position:0% + + + + align:start position:0% + +draw the uh uh electron energy + + align:start position:0% +draw the uh uh electron energy + + + align:start position:0% +draw the uh uh electron energy +dispersion. This is pi / a right and we + + align:start position:0% +dispersion. This is pi / a right and we + + + align:start position:0% +dispersion. This is pi / a right and we +only draw uh over pi / a. And this pi / + + align:start position:0% +only draw uh over pi / a. And this pi / + + + align:start position:0% +only draw uh over pi / a. And this pi / +a turns out that's the wagner side seal + + align:start position:0% +a turns out that's the wagner side seal + + + align:start position:0% +a turns out that's the wagner side seal +boundary in the reciprocal + + align:start position:0% +boundary in the reciprocal + + + align:start position:0% +boundary in the reciprocal +space. + + align:start position:0% +space. + + + align:start position:0% +space. +Okay. So uh having said all this I think + + align:start position:0% +Okay. So uh having said all this I think + + + align:start position:0% +Okay. So uh having said all this I think +we really need to look at some + + align:start position:0% +we really need to look at some + + + align:start position:0% +we really need to look at some +pictures. Let's look at the + + align:start position:0% + + + + align:start position:0% + +So uh this Google image is be a + + align:start position:0% +So uh this Google image is be a + + + align:start position:0% +So uh this Google image is be a +wonderful + + align:start position:0% +wonderful + + + align:start position:0% +wonderful +I don't need to draw anything. Let's + + align:start position:0% +I don't need to draw anything. Let's + + + align:start position:0% +I don't need to draw anything. Let's +first look at the uh the uh bravis + + align:start position:0% +first look at the uh the uh bravis + + + align:start position:0% +first look at the uh the uh bravis +lattice, + + align:start position:0% + + + + align:start position:0% + +right? And uh uh you can say there are + + align:start position:0% +right? And uh uh you can say there are + + + align:start position:0% +right? And uh uh you can say there are +uh 14 + + align:start position:0% +uh 14 + + + align:start position:0% +uh 14 +type right. Uh here is a uh tri + + align:start position:0% +type right. Uh here is a uh tri + + + align:start position:0% +type right. Uh here is a uh tri +clinic right different angle different + + align:start position:0% +clinic right different angle different + + + align:start position:0% +clinic right different angle different +latice + + align:start position:0% +latice + + + align:start position:0% +latice +constant and here the simplest is a + + align:start position:0% +constant and here the simplest is a + + + align:start position:0% +constant and here the simplest is a +simple + + align:start position:0% +simple + + + align:start position:0% +simple +cube this is a conventional cell. So if + + align:start position:0% +cube this is a conventional cell. So if + + + align:start position:0% +cube this is a conventional cell. So if +I put uh say a center here, put a a + + align:start position:0% +I put uh say a center here, put a a + + + align:start position:0% +I put uh say a center here, put a a +lattice point at the center, then this + + align:start position:0% +lattice point at the center, then this + + + align:start position:0% +lattice point at the center, then this +simple cube, I got a body + + align:start position:0% +simple cube, I got a body + + + align:start position:0% +simple cube, I got a body +center, + + align:start position:0% +center, + + + align:start position:0% +center, +right? And then if I put a lattice point + + align:start position:0% +right? And then if I put a lattice point + + + align:start position:0% +right? And then if I put a lattice point +at every face, I got a face center. In + + align:start position:0% +at every face, I got a face center. In + + + align:start position:0% +at every face, I got a face center. In +this conventional UNC cell, you can have + + align:start position:0% +this conventional UNC cell, you can have + + + align:start position:0% +this conventional UNC cell, you can have +more than one lattice point. In + + align:start position:0% +more than one lattice point. In + + + align:start position:0% +more than one lattice point. In +primitive unic, you can only have one + + align:start position:0% +primitive unic, you can only have one + + + align:start position:0% +primitive unic, you can only have one +lattice point. So if you look at the + + align:start position:0% +lattice point. So if you look at the + + + align:start position:0% +lattice point. So if you look at the +body center how many last points I have + + align:start position:0% +body center how many last points I have + + + align:start position:0% +body center how many last points I have +equivalent + + align:start position:0% +equivalent + + + align:start position:0% +equivalent +two right because each of this corner is + + align:start position:0% +two right because each of this corner is + + + align:start position:0% +two right because each of this corner is +shared by a uh say eight right so that's + + align:start position:0% +shared by a uh say eight right so that's + + + align:start position:0% +shared by a uh say eight right so that's +1/8 so simple cubic I have one body + + align:start position:0% +1/8 so simple cubic I have one body + + + align:start position:0% +1/8 so simple cubic I have one body +center I have two how about f + + align:start position:0% +center I have two how about f + + + align:start position:0% +center I have two how about f +center four right because say every face + + align:start position:0% +center four right because say every face + + + align:start position:0% +center four right because say every face +you have six face and air face is shared + + align:start position:0% +you have six face and air face is shared + + + align:start position:0% +you have six face and air face is shared +by two so that's one half and that's + + align:start position:0% +by two so that's one half and that's + + + align:start position:0% +by two so that's one half and that's +three + one of the eight corners. So, uh + + align:start position:0% +three + one of the eight corners. So, uh + + + align:start position:0% +three + one of the eight corners. So, uh +gives you u so this is um uh if you look + + align:start position:0% +gives you u so this is um uh if you look + + + align:start position:0% +gives you u so this is um uh if you look +at the + + align:start position:0% +at the + + + align:start position:0% +at the +uh they they form a total of uh 14 type + + align:start position:0% +uh they they form a total of uh 14 type + + + align:start position:0% +uh they they form a total of uh 14 type +and hexagonal is also interesting + + align:start position:0% +and hexagonal is also interesting + + + align:start position:0% +and hexagonal is also interesting +because a lot of people interested in + + align:start position:0% +because a lot of people interested in + + + align:start position:0% +because a lot of people interested in +graphite right and graphite is a + + align:start position:0% +graphite right and graphite is a + + + align:start position:0% +graphite right and graphite is a +hexagonal + + align:start position:0% +hexagonal + + + align:start position:0% +hexagonal +structure. So let's look at the so this + + align:start position:0% +structure. So let's look at the so this + + + align:start position:0% +structure. So let's look at the so this +is the bravid latis let's look at + + align:start position:0% +is the bravid latis let's look at + + + align:start position:0% +is the bravid latis let's look at +the some real crystal + + align:start position:0% +the some real crystal + + + align:start position:0% +the some real crystal +structures. So starting with uh uh + + align:start position:0% +structures. So starting with uh uh + + + align:start position:0% +structures. So starting with uh uh +sodium + + align:start position:0% + + + + align:start position:0% + +chloride so probably + + align:start position:0% + + + + align:start position:0% + +zero let's still look at this + + align:start position:0% +zero let's still look at this + + + align:start position:0% +zero let's still look at this +here right uh if you say uh sodium + + align:start position:0% +here right uh if you say uh sodium + + + align:start position:0% +here right uh if you say uh sodium +chloride and uh here is uh if If we look + + align:start position:0% +chloride and uh here is uh if If we look + + + align:start position:0% +chloride and uh here is uh if If we look +at sodium atom right this is a uh here + + align:start position:0% +at sodium atom right this is a uh here + + + align:start position:0% +at sodium atom right this is a uh here +at the center you have sodium right so a + + align:start position:0% +at the center you have sodium right so a + + + align:start position:0% +at the center you have sodium right so a +basis is between here and here that's a + + align:start position:0% +basis is between here and here that's a + + + align:start position:0% +basis is between here and here that's a +say molecule you put a sodium chloride + + align:start position:0% +say molecule you put a sodium chloride + + + align:start position:0% +say molecule you put a sodium chloride +and every point you can look at that + + align:start position:0% +and every point you can look at that + + + align:start position:0% +and every point you can look at that +same sodium chloride you repeat that + + align:start position:0% +same sodium chloride you repeat that + + + align:start position:0% +same sodium chloride you repeat that +basis at each lattice + + align:start position:0% +basis at each lattice + + + align:start position:0% +basis at each lattice +point + + align:start position:0% +point + + + align:start position:0% +point +right and look at the crystal + + align:start position:0% +right and look at the crystal + + + align:start position:0% +right and look at the crystal +silicon structure + + align:start position:0% + + + + align:start position:0% + +silicon, right? If you look at silicon + + align:start position:0% +silicon, right? If you look at silicon + + + align:start position:0% +silicon, right? If you look at silicon +crystal, the uh what do you have here? + + align:start position:0% +crystal, the uh what do you have here? + + + align:start position:0% +crystal, the uh what do you have here? +Again, this is a uh face + + align:start position:0% +Again, this is a uh face + + + align:start position:0% +Again, this is a uh face +center, right? There is a one point here + + align:start position:0% +center, right? There is a one point here + + + align:start position:0% +center, right? There is a one point here +but you have each point you actually put + + align:start position:0% +but you have each point you actually put + + + align:start position:0% +but you have each point you actually put +a two atoms silicon this point and this + + align:start position:0% +a two atoms silicon this point and this + + + align:start position:0% +a two atoms silicon this point and this +point this is not in any of this is + + align:start position:0% +point this is not in any of this is + + + align:start position:0% +point this is not in any of this is +1/4 point right. So between 0 0 and + + align:start position:0% +1/4 point right. So between 0 0 and + + + align:start position:0% +1/4 point right. So between 0 0 and +1/4 you repeating that structure to each + + align:start position:0% +1/4 you repeating that structure to each + + + align:start position:0% +1/4 you repeating that structure to each +lattice point. So it turns out this + + align:start position:0% +lattice point. So it turns out this + + + align:start position:0% +lattice point. So it turns out this +atoms there is more like a tetraula. It + + align:start position:0% +atoms there is more like a tetraula. It + + + align:start position:0% +atoms there is more like a tetraula. It +form it's equidistant between this and + + align:start position:0% +form it's equidistant between this and + + + align:start position:0% +form it's equidistant between this and +this center and this + + align:start position:0% +this center and this + + + align:start position:0% +this center and this +center. Right? So it's at each lattice + + align:start position:0% +center. Right? So it's at each lattice + + + align:start position:0% +center. Right? So it's at each lattice +point you put a basis you put a say a + + align:start position:0% +point you put a basis you put a say a + + + align:start position:0% +point you put a basis you put a say a +molecule or atoms say or two atoms of + + align:start position:0% +molecule or atoms say or two atoms of + + + align:start position:0% +molecule or atoms say or two atoms of +three atoms many atoms you you you can + + align:start position:0% +three atoms many atoms you you you can + + + align:start position:0% +three atoms many atoms you you you can +have polymers form crystal and that + + align:start position:0% +have polymers form crystal and that + + + align:start position:0% +have polymers form crystal and that +could be very long uh a very large + + align:start position:0% +could be very long uh a very large + + + align:start position:0% +could be very long uh a very large +basis. Okay. + + align:start position:0% +basis. Okay. + + + align:start position:0% +basis. Okay. +uh reciprocal + + align:start position:0% + + + + align:start position:0% + +space. Let's + + align:start position:0% +space. Let's + + + align:start position:0% +space. Let's +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +say I don't like + + align:start position:0% + + + + align:start position:0% + +this regular size. + + align:start position:0% +this regular size. + + + align:start position:0% +this regular size. +Okay. So, + + align:start position:0% +Okay. So, + + + align:start position:0% +Okay. So, +uh you can see this is a + + align:start position:0% +uh you can see this is a + + + align:start position:0% +uh you can see this is a +construction of wigler sides unis. So, + + align:start position:0% +construction of wigler sides unis. So, + + + align:start position:0% +construction of wigler sides unis. So, +you have a point in the center. If you + + align:start position:0% +you have a point in the center. If you + + + align:start position:0% +you have a point in the center. If you +from center to this direction, you take + + align:start position:0% +from center to this direction, you take + + + align:start position:0% +from center to this direction, you take +the uh midpoint, you cut the I think you + + align:start position:0% +the uh midpoint, you cut the I think you + + + align:start position:0% +the uh midpoint, you cut the I think you +cut this plan, right? So, the wigler + + align:start position:0% +cut this plan, right? So, the wigler + + + align:start position:0% +cut this plan, right? So, the wigler +size seal looks in 3D. could be very uh + + align:start position:0% +size seal looks in 3D. could be very uh + + + align:start position:0% +size seal looks in 3D. could be very uh +irregular but that's a unique way uh for + + align:start position:0% +irregular but that's a unique way uh for + + + align:start position:0% +irregular but that's a unique way uh for +constructing there's no + + align:start position:0% +constructing there's no + + + align:start position:0% +constructing there's no +ambiguity and each lice uh type uh uh + + align:start position:0% +ambiguity and each lice uh type uh uh + + + align:start position:0% +ambiguity and each lice uh type uh uh +you you construct uh you can construct a + + align:start position:0% +you you construct uh you can construct a + + + align:start position:0% +you you construct uh you can construct a +corresponding wigler sites uh unl Oh, so + + align:start position:0% +corresponding wigler sites uh unl Oh, so + + + align:start position:0% +corresponding wigler sites uh unl Oh, so +uh we see pretty cool. I still on + + align:start position:0% + + + + align:start position:0% + +Google unit still. Let's see + + align:start position:0% +Google unit still. Let's see + + + align:start position:0% +Google unit still. Let's see +this. Ah, + + align:start position:0% + + + + align:start position:0% + +no. Let's get + + align:start position:0% +no. Let's get + + + align:start position:0% +no. Let's get +Do I + + align:start position:0% +Do I + + + align:start position:0% +Do I +have a + + align:start position:0% + + + + align:start position:0% + +simpler? Okay. So this is a this is now + + align:start position:0% +simpler? Okay. So this is a this is now + + + align:start position:0% +simpler? Okay. So this is a this is now +getting more to uh what people uh + + align:start position:0% +getting more to uh what people uh + + + align:start position:0% +getting more to uh what people uh +usually draw FCC structure face center + + align:start position:0% +usually draw FCC structure face center + + + align:start position:0% +usually draw FCC structure face center +cubic uh uh they will say okay they + + align:start position:0% +cubic uh uh they will say okay they + + + align:start position:0% +cubic uh uh they will say okay they +actually have specific location from + + align:start position:0% +actually have specific location from + + + align:start position:0% +actually have specific location from +gamma to L that's 111 + + align:start position:0% +gamma to L that's 111 + + + align:start position:0% +gamma to L that's 111 +direction okay and the way I look at + + align:start position:0% +direction okay and the way I look at + + + align:start position:0% +direction okay and the way I look at +this the shortest + + align:start position:0% +this the shortest + + + align:start position:0% +this the shortest +distance is say because um 111 is the + + align:start position:0% +distance is say because um 111 is the + + + align:start position:0% +distance is say because um 111 is the +longer distance in real face and inverse + + align:start position:0% +longer distance in real face and inverse + + + align:start position:0% +longer distance in real face and inverse +is the shortest distance. So I'll say + + align:start position:0% +is the shortest distance. So I'll say + + + align:start position:0% +is the shortest distance. So I'll say +that's the one one direction. This is a + + align:start position:0% +that's the one one direction. This is a + + + align:start position:0% +that's the one one direction. This is a +one z direction longest distance right + + align:start position:0% +one z direction longest distance right + + + align:start position:0% +one z direction longest distance right +and uh so those are the uh very + + align:start position:0% +and uh so those are the uh very + + + align:start position:0% +and uh so those are the uh very +complicated reciprocal + + align:start position:0% +complicated reciprocal + + + align:start position:0% +complicated reciprocal +space and uh coming back to here + + align:start position:0% +space and uh coming back to here + + + align:start position:0% +space and uh coming back to here +uh this is the broad + + align:start position:0% + + + + align:start position:0% + +condition we'll prove it next time. + + align:start position:0% +condition we'll prove it next time. + + + align:start position:0% +condition we'll prove it next time. +I don't actually know whether it's a 1g + + align:start position:0% +I don't actually know whether it's a 1g + + + align:start position:0% +I don't actually know whether it's a 1g +or 2 + + align:start position:0% +or 2 + + + align:start position:0% +or 2 +G. 2 G's. Let's see. Okay. So, if you do + + align:start position:0% +G. 2 G's. Let's see. Okay. So, if you do + + + align:start position:0% +G. 2 G's. Let's see. Okay. So, if you do +your uh you can map this out. So, TM + + align:start position:0% + + + + align:start position:0% + +defraction. So if you do uh uh + + align:start position:0% +defraction. So if you do uh uh + + + align:start position:0% +defraction. So if you do uh uh +transmission electron microraph uh micro + + align:start position:0% +transmission electron microraph uh micro + + + align:start position:0% +transmission electron microraph uh micro +microscopy we mentioned the TM is you + + align:start position:0% +microscopy we mentioned the TM is you + + + align:start position:0% +microscopy we mentioned the TM is you +actually electron to very high uh uh + + align:start position:0% +actually electron to very high uh uh + + + align:start position:0% +actually electron to very high uh uh +velocity and under that high velocity + + align:start position:0% +velocity and under that high velocity + + + align:start position:0% +velocity and under that high velocity +the electron wavelength is short + + align:start position:0% +the electron wavelength is short + + + align:start position:0% +the electron wavelength is short +comparable to the uh uh lattice + + align:start position:0% +comparable to the uh uh lattice + + + align:start position:0% +comparable to the uh uh lattice +constant. So now it goes through a thin + + align:start position:0% +constant. So now it goes through a thin + + + align:start position:0% +constant. So now it goes through a thin +specimen typically 1,00 2,000 Armstrong + + align:start position:0% +specimen typically 1,00 2,000 Armstrong + + + align:start position:0% +specimen typically 1,00 2,000 Armstrong +maximum right it go through there and + + align:start position:0% +maximum right it go through there and + + + align:start position:0% +maximum right it go through there and +even though it's 1,000 + + align:start position:0% +even though it's 1,000 + + + align:start position:0% +even though it's 1,000 +Armstrong remember the latch constant is + + align:start position:0% +Armstrong remember the latch constant is + + + align:start position:0% +Armstrong remember the latch constant is +a few Armstrongs so you got a thousand + + align:start position:0% +a few Armstrongs so you got a thousand + + + align:start position:0% +a few Armstrongs so you got a thousand +period and so it's a periodical + + align:start position:0% +period and so it's a periodical + + + align:start position:0% +period and so it's a periodical +structure and depend on so you rotate + + align:start position:0% +structure and depend on so you rotate + + + align:start position:0% +structure and depend on so you rotate +your crystals you can look at a + + align:start position:0% +your crystals you can look at a + + + align:start position:0% +your crystals you can look at a +different uh uh uh defraction spot + + align:start position:0% +different uh uh uh defraction spot + + + align:start position:0% +different uh uh uh defraction spot +Right? In this dark region, you don't + + align:start position:0% +Right? In this dark region, you don't + + + align:start position:0% +Right? In this dark region, you don't +say the electron going there. That's a + + align:start position:0% +say the electron going there. That's a + + + align:start position:0% +say the electron going there. That's a +result of the wave defraction. And uh uh + + align:start position:0% +result of the wave defraction. And uh uh + + + align:start position:0% +result of the wave defraction. And uh uh +the uh um we again we'll show this uh + + align:start position:0% +the uh um we again we'll show this uh + + + align:start position:0% +the uh um we again we'll show this uh +we'll prove this later on. And that's + + align:start position:0% +we'll prove this later on. And that's + + + align:start position:0% +we'll prove this later on. And that's +the electron defraction. Let's look at + + align:start position:0% +the electron defraction. Let's look at + + + align:start position:0% +the electron defraction. Let's look at +the X-ray + + align:start position:0% +the X-ray + + + align:start position:0% +the X-ray +uh + + align:start position:0% + + + + align:start position:0% + +defraction, right? Uh so X-ray + + align:start position:0% +defraction, right? Uh so X-ray + + + align:start position:0% +defraction, right? Uh so X-ray +defraction again is a is a optical wave + + align:start position:0% +defraction again is a is a optical wave + + + align:start position:0% +defraction again is a is a optical wave +and what you show what you people say is + + align:start position:0% +and what you show what you people say is + + + align:start position:0% +and what you show what you people say is +people + + align:start position:0% +people + + + align:start position:0% +people +uh they don't uh the image the detector + + align:start position:0% +uh they don't uh the image the detector + + + align:start position:0% +uh they don't uh the image the detector +is typically a line. So by rotating the + + align:start position:0% +is typically a line. So by rotating the + + + align:start position:0% +is typically a line. So by rotating the +angle of X-ray incidence you see the + + align:start position:0% +angle of X-ray incidence you see the + + + align:start position:0% +angle of X-ray incidence you see the +picss right again that's the uh uh say + + align:start position:0% +picss right again that's the uh uh say + + + align:start position:0% +picss right again that's the uh uh say +um B condition + + align:start position:0% +um B condition + + + align:start position:0% +um B condition +requirement and uh let's see whether + + align:start position:0% +requirement and uh let's see whether + + + align:start position:0% +requirement and uh let's see whether +they're uh the clean + + align:start position:0% +they're uh the clean + + + align:start position:0% +they're uh the clean +ones right you some of those clean + + align:start position:0% +ones right you some of those clean + + + align:start position:0% +ones right you some of those clean +pick + + align:start position:0% + + + + align:start position:0% + +what oh like this + + align:start position:0% + + + + align:start position:0% + +H doesn't look like I can show this one. + + align:start position:0% +H doesn't look like I can show this one. + + + align:start position:0% +H doesn't look like I can show this one. +Okay. So you can say some so basically + + align:start position:0% +Okay. So you can say some so basically + + + align:start position:0% +Okay. So you can say some so basically +people have built + + align:start position:0% +people have built + + + align:start position:0% +people have built +libraries and uh sometimes you don't + + align:start position:0% +libraries and uh sometimes you don't + + + align:start position:0% +libraries and uh sometimes you don't +even know what you have. You got all + + align:start position:0% +even know what you have. You got all + + + align:start position:0% +even know what you have. You got all +those picss you search library and you + + align:start position:0% +those picss you search library and you + + + align:start position:0% +those picss you search library and you +find out what the materials you + + align:start position:0% +find out what the materials you + + + align:start position:0% +find out what the materials you +have. Okay. And uh one more time going + + align:start position:0% +have. Okay. And uh one more time going + + + align:start position:0% +have. Okay. And uh one more time going +to uh next time I'm not going to go + + align:start position:0% +to uh next time I'm not going to go + + + align:start position:0% +to uh next time I'm not going to go +through this here, right? It's no longer + + align:start position:0% +through this here, right? It's no longer + + + align:start position:0% +through this here, right? It's no longer +single spot. Why? That's because it's + + align:start position:0% +single spot. Why? That's because it's + + + align:start position:0% +single spot. Why? That's because it's +not a single crystal. It's a poly + + align:start position:0% +not a single crystal. It's a poly + + + align:start position:0% +not a single crystal. It's a poly +crystal. Okay? So you got + + align:start position:0% +crystal. Okay? So you got + + + align:start position:0% +crystal. Okay? So you got +rins. So uh uh this is all coming back + + align:start position:0% +rins. So uh uh this is all coming back + + + align:start position:0% +rins. So uh uh this is all coming back +to the uh reciprocal space. You can + + align:start position:0% +to the uh reciprocal space. You can + + + align:start position:0% +to the uh reciprocal space. You can +rotate your crystal, rotate your angle + + align:start position:0% +rotate your crystal, rotate your angle + + + align:start position:0% +rotate your crystal, rotate your angle +of incidence in X-ray uh change your + + align:start position:0% +of incidence in X-ray uh change your + + + align:start position:0% +of incidence in X-ray uh change your +angle of incidence. So you can map out + + align:start position:0% +angle of incidence. So you can map out + + + align:start position:0% +angle of incidence. So you can map out +the what's the latice constant? What are + + align:start position:0% +the what's the latice constant? What are + + + align:start position:0% +the what's the latice constant? What are +the arrange of arrangement of atoms? + + align:start position:0% +the arrange of arrangement of atoms? + + + align:start position:0% +the arrange of arrangement of atoms? +Okay, I'll stop here. \ No newline at end of file diff --git a/s9r4mLOQJuo.txt b/s9r4mLOQJuo.txt new file mode 100644 index 0000000000000000000000000000000000000000..47027fbb33268bf84058e8c383254b7b42f4345b --- /dev/null +++ b/s9r4mLOQJuo.txt @@ -0,0 +1,579 @@ +align:start position:0% + +This insulating cylinder is free to + + align:start position:0% +This insulating cylinder is free to + + + align:start position:0% +This insulating cylinder is free to +rotate. + + align:start position:0% + + + + align:start position:0% + +It's centered between these + + align:start position:0% +It's centered between these + + + align:start position:0% +It's centered between these +electrodes which will be used to impose + + align:start position:0% +electrodes which will be used to impose + + + align:start position:0% +electrodes which will be used to impose +an electric + + align:start position:0% +an electric + + + align:start position:0% +an electric +field transverse to the axis of + + align:start position:0% + + + + align:start position:0% + +rotation. The electrodes and cylinder + + align:start position:0% +rotation. The electrodes and cylinder + + + align:start position:0% +rotation. The electrodes and cylinder +are immersed in slightly conducting corn + + align:start position:0% +are immersed in slightly conducting corn + + + align:start position:0% +are immersed in slightly conducting corn +oil. As we apply the potential to the + + align:start position:0% +oil. As we apply the potential to the + + + align:start position:0% +oil. As we apply the potential to the +plates, the threshold of about 20 kov + + align:start position:0% +plates, the threshold of about 20 kov + + + align:start position:0% +plates, the threshold of about 20 kov +volts is reached and the cylinder begins + + align:start position:0% +volts is reached and the cylinder begins + + + align:start position:0% +volts is reached and the cylinder begins +to + + align:start position:0% + + + + align:start position:0% + +rotate. Which direction is a matter of + + align:start position:0% +rotate. Which direction is a matter of + + + align:start position:0% +rotate. Which direction is a matter of +chance? + + align:start position:0% + + + + align:start position:0% + +You need two more pieces of information + + align:start position:0% +You need two more pieces of information + + + align:start position:0% +You need two more pieces of information +to explain this experiment. The Teflon + + align:start position:0% +to explain this experiment. The Teflon + + + align:start position:0% +to explain this experiment. The Teflon +rotor is a very good insulator compared + + align:start position:0% +rotor is a very good insulator compared + + + align:start position:0% +rotor is a very good insulator compared +to the corn oil and the oil has a + + align:start position:0% +to the corn oil and the oil has a + + + align:start position:0% +to the corn oil and the oil has a +relaxation time on the same order as the + + align:start position:0% +relaxation time on the same order as the + + + align:start position:0% +relaxation time on the same order as the +period of rotation. + + align:start position:0% +period of rotation. + + + align:start position:0% +period of rotation. +The rotor acts as an insulator in series + + align:start position:0% +The rotor acts as an insulator in series + + + align:start position:0% +The rotor acts as an insulator in series +with the regions of conducting liquid + + align:start position:0% +with the regions of conducting liquid + + + align:start position:0% +with the regions of conducting liquid +adjacent to the + + align:start position:0% +adjacent to the + + + align:start position:0% +adjacent to the +electrodes. As surface charges build up + + align:start position:0% +electrodes. As surface charges build up + + + align:start position:0% +electrodes. As surface charges build up +on the electrodes, they induce + + align:start position:0% +on the electrodes, they induce + + + align:start position:0% +on the electrodes, they induce +neighboring surface charges of the same + + align:start position:0% +neighboring surface charges of the same + + + align:start position:0% +neighboring surface charges of the same +sign on the rotor liquid + + align:start position:0% +sign on the rotor liquid + + + align:start position:0% +sign on the rotor liquid +interface. A perturbation of the static + + align:start position:0% +interface. A perturbation of the static + + + align:start position:0% +interface. A perturbation of the static +cylinder carries these charges + + align:start position:0% +cylinder carries these charges + + + align:start position:0% +cylinder carries these charges +along. The motion affects the field. + + align:start position:0% +along. The motion affects the field. + + + align:start position:0% +along. The motion affects the field. +In return, there is a repulsion of the + + align:start position:0% +In return, there is a repulsion of the + + + align:start position:0% +In return, there is a repulsion of the +light charges that tends to sustain the + + align:start position:0% +light charges that tends to sustain the + + + align:start position:0% +light charges that tends to sustain the +rotation. The field affects the + + align:start position:0% + + + + align:start position:0% + +motion. Steady rotation is maintained + + align:start position:0% +motion. Steady rotation is maintained + + + align:start position:0% +motion. Steady rotation is maintained +because the convection of the surface + + align:start position:0% +because the convection of the surface + + + align:start position:0% +because the convection of the surface +charge is just compensated by its + + align:start position:0% +charge is just compensated by its + + + align:start position:0% +charge is just compensated by its +relaxation through conduction in the + + align:start position:0% +relaxation through conduction in the + + + align:start position:0% +relaxation through conduction in the +corn oil. + + align:start position:0% +corn oil. + + + align:start position:0% +corn oil. +The cylinder begins to rotate only + + align:start position:0% +The cylinder begins to rotate only + + + align:start position:0% +The cylinder begins to rotate only +because there is both an effect of the + + align:start position:0% +because there is both an effect of the + + + align:start position:0% +because there is both an effect of the +field on the motion and of the motion on + + align:start position:0% +field on the motion and of the motion on + + + align:start position:0% +field on the motion and of the motion on +the + + align:start position:0% + + + + align:start position:0% + +field. The rotation alters the charge + + align:start position:0% +field. The rotation alters the charge + + + align:start position:0% +field. The rotation alters the charge +distribution because the ratio of + + align:start position:0% +distribution because the ratio of + + + align:start position:0% +distribution because the ratio of +relaxation time in the oil to the time + + align:start position:0% +relaxation time in the oil to the time + + + align:start position:0% +relaxation time in the oil to the time +required for a point on the cylinder + + align:start position:0% +required for a point on the cylinder + + + align:start position:0% +required for a point on the cylinder +surface to make one revolution is about + + align:start position:0% +surface to make one revolution is about + + + align:start position:0% +surface to make one revolution is about +unity. + + align:start position:0% + + + + align:start position:0% + +The field induced rotations of the + + align:start position:0% +The field induced rotations of the + + + align:start position:0% +The field induced rotations of the +cylinder also are responsible for this + + align:start position:0% + + + + align:start position:0% + +motion. These cells of fluid are + + align:start position:0% +motion. These cells of fluid are + + + align:start position:0% +motion. These cells of fluid are +spinning on the free surface of corn + + align:start position:0% +spinning on the free surface of corn + + + align:start position:0% +spinning on the free surface of corn +oil. + + align:start position:0% + + + + align:start position:0% + +The fluid is contained in this box which + + align:start position:0% +The fluid is contained in this box which + + + align:start position:0% +The fluid is contained in this box which +has two electrodes lying flat on its + + align:start position:0% + + + + align:start position:0% + +bottom. They're separated by about 1/4 + + align:start position:0% +bottom. They're separated by about 1/4 + + + align:start position:0% +bottom. They're separated by about 1/4 +in. + + align:start position:0% + + + + align:start position:0% + +Bubbles injected on the surface show how + + align:start position:0% +Bubbles injected on the surface show how + + + align:start position:0% +Bubbles injected on the surface show how +the rotations + + align:start position:0% + + + + align:start position:0% + +develop. Passage of current through the + + align:start position:0% +develop. Passage of current through the + + + align:start position:0% +develop. Passage of current through the +oil results in a potential drop along + + align:start position:0% +oil results in a potential drop along + + + align:start position:0% +oil results in a potential drop along +the + + align:start position:0% + + + + align:start position:0% + +interface. From above, we see the + + align:start position:0% +interface. From above, we see the + + + align:start position:0% +interface. From above, we see the +charges on the + + align:start position:0% +charges on the + + + align:start position:0% +charges on the +electrodes and on the + + align:start position:0% +electrodes and on the + + + align:start position:0% +electrodes and on the +interface. + + align:start position:0% +interface. + + + align:start position:0% +interface. +Any slight fluid rotation results in + + align:start position:0% +Any slight fluid rotation results in + + + align:start position:0% +Any slight fluid rotation results in +charge redistribution which encourages + + align:start position:0% +charge redistribution which encourages + + + align:start position:0% +charge redistribution which encourages +further rotation. + + align:start position:0% +further rotation. + + + align:start position:0% +further rotation. +The interface is unstable to cellular + + align:start position:0% +The interface is unstable to cellular + + + align:start position:0% +The interface is unstable to cellular +motions in its own plane and the + + align:start position:0% +motions in its own plane and the + + + align:start position:0% +motions in its own plane and the +resulting cell pattern is one which + + align:start position:0% +resulting cell pattern is one which + + + align:start position:0% +resulting cell pattern is one which +reduces viscous drag to a minimum. \ No newline at end of file diff --git a/sAD1Xr3-rmI.txt b/sAD1Xr3-rmI.txt new file mode 100644 index 0000000000000000000000000000000000000000..1799f5da95fb81f5609c24edceaf08aea8fee719 --- /dev/null +++ b/sAD1Xr3-rmI.txt @@ -0,0 +1,759 @@ +PROFESSOR: So now I have this. + +And what I need to do is +I need to transform. + +So I need to take E.coli +growing in a test tube. + +And I need to put into it a +whole collection of zillions + +and zillions of plasmid +molecules, plasmid circles + +that all have different +pieces of human DNA. + +One of these things might +have ARG1, one ARG2, + +one ARG3, et cetera. + +Or if it's human DNA, one of +them your hemoglobin, one of + +them your collagen, whatever. + +I have to throw the DNA on +top of the bacteria. + +And then I need to come up with +some engineering trick to + +make the bacteria take up this +DNA across their cell + +membranes and use it. + +Why should I be able to +persuade bacteria + +to take up my DNA? + +AUDIENCE: They do it anyway. + +PROFESSOR: They do it anyway. + +Remember, we said they +like to exchange DNA. + +That's kind of their +thing, right? + +They pick up DNA from their +environment anyway. + +See, as usual, we haven't really +invented something. + +What we've done is we have +used the natural property + +that's out there. + +The natural properties, bacteria +like to slurp up DNA. + +Now in fairness, some pretty +cool protocols were developed + +that improve the ability +to do it. + +You treat the DNA, +a little nastily. + +You give it certain ions. + +You heat shock it in +a certain way. + +And then it encourages it +to slurp up DNA better. + +But the ability to slurp +up DNA was there + +in the first place. + +We couldn't have given it the +ability to slurp up DNA if it + +wasn't there. + +But we can always goose it up, +improve it in certain ways. + +And there are great protocols +that were developed in order + +to be able to increase the +efficiency of such + +transformation. + +So now we now have our E.coli. + +Here's an E.coli. + +Some of the E.coli have acquired +a plasmid containing + +human DNA or maybe, if we +used yeast, yeast DNA. + +Some of them have it, right? + +Because it's kind of +a random process. + +Some slurp it up, +some haven't. + +So I might have, I don't know, +maybe one in 100 of my cells + +will have slurped up DNA. + +But 99 in 100 won't have +slurped up DNA. + +I want to plate these out on a +Petri plate and grow them up + +into individual colonies. + +But I would like it to be the +case, please, that the + +individual colonies that grow up +are only the ones that got + +my plasmid. + +I really don't want to see +all these guys who + +didn't get my plasmid. + +So what do I do? + +Do I go in there with a +microscope and try to figure + +out which ones got my +human DNA plasmid? + +So I would love to plate it out +and only have the guys who + +got my plasmid grow. + +How do I arrange that only +the guys who got my + +plasmid will grow? + +Sorry? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: For something. + +I got to put in a gene into that +plasmid so that only the + +guys who get that will grow. + +Any ideas for what gene +might go in there? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Sorry? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: How about a gene +conferring resistance to an + +antibiotic. + +And then what could I do? + +Well, I could plate. + +I'm going to select-- + +see this E.coli here, +it had my plasmid. + +And it's going to have a +drug resistance gene. + +And it will grow up. + +This guy over here, he didn't +get a drug resistance gene. + +He doesn't grow up. + +The only ones who grow up +have a drug resistant-- + +wait a second. + +Why doesn't this guy grow up? + +AUDIENCE: You add the drug. + +PROFESSOR: Oh, I got to add +the drug, good point. + +So what I'm going to do is I +add my drug to the plate. + +I add my drug to the medium, +to the Petri plate here. + +And now my Petri plate is say +a penicillin plate or a + +streptomycin plate or a +ampicillin plate or a + +kanamycin plate or whatever. + +And then the only things that +could grow up are the ones + +that have resistance to whatever +antibiotic I used. + +So I grow them up +on that plate. + +And they grew up just fine. + +The ones who didn't get-- now +how did I get that antibiotic + +gene into the plasmid? + +It actually comes that way +in nature, sort of. + +Now when I get good, +I can move them + +around from one to another. + +But nature thought +of it first. + +Nature gave us something that +had an origin of replication + +and an antibiotic +resistance gene. + +And we could just add +things to it. + +It had everything we needed. + +It had the ability +to slurp up DNA. + +It had the ability to confer a +new property on the cells like + +resistance to antibiotics. + +And when we're done, we +have a library here. + +And we call this a library of +cells or colonies, each one of + +which has a distinct piece of +human DNA, each one of which + +has a different piece +of human DNA. + +Let me stop and ask, +any questions? + +This is like one of the coolest + +new procedures invented. + +Yes? + +AUDIENCE: Is it possible that +the same E.coli takes in two + +of the things? + +PROFESSOR: Is it possible that +same E.coli takes in two? + +Yes, turns out we do this at a +dilution in a way so that most + +take up zero, some take up one, +and a couple take up two. + +And what we say there +is, oh well. + +It's not so common. + +And we live with it. + +What else? + +AUDIENCE: You need to make sure +the bacteria that doesn't + +already have a resistance +to it? + +PROFESSOR: I better use a +bacteria that's not already + +resistant to this antibiotic, +good point. + +That's right. + +And I can do that. + +Yes? + +AUDIENCE: When making those +vectors, how do you make sure + +it only cuts once so you can put +one piece of human DNA and + +it doesn't break apart? + +PROFESSOR: Oh, so what if the +vector had five EcoR1 sites? + +People have engineered them +to just have one. + +In fact, what they've really +done now is they engineer them + +so that within the vector +there's a little region, + +called a polylinker, that has +many different sites for many + +different restriction enzymes, +depending on which one you + +might want to use. + +And they're all right over +here in the same place. + +And they go around and +they fix the vector. + +So it doesn't have any +of the others. + +You could, for example cut it +open and change the sequence a + +little bit. + +All these tools are +available to us. + +And rather than you +having to do it, + +they're all in the catalog. + +The catalog has vectors that +have polylinkers, don't have + +any other cut sites, et cetera. + +Yes? + +AUDIENCE: How do you isolate the +sequence you want if the + +cutting sequence +is so frequent? + +PROFESSOR: Oh, so you're +asking two questions. + +One is you're asking how do I +find the particular thing I'm + +looking for on the plate +amongst the millions of + +colonies that might grow up? + +Or are you asking if the +cutting sequence is so + +frequent, how do I avoid cutting +in the middle of the + +sequence I want? + +AUDIENCE: Well both, I guess. + +If you want to replicate human +genes, if you have a bunch of + +DNA, how can you make +it so that you + +isolate only that gene? + +PROFESSOR: OK, so now there +are really two questions + +you're asking. + +They're both really +good questions. + +One, I take my human DNA. + +And let's say we're trying +to clone the gene for + +beta-globin. + +Beta-globin is a part +of hemoglobin. + +It's one of the two proteins +in hemoglobin. + +And let's say the beta-globin +gene is a certain length. + +And suppose the beta-globin +gene actually has several + +EcoR1 sites. + +I'm going to chop it up +into multiple pieces. + +That's bad, right? + +That's step one bad. + +How do I avoid that? + +Sorry? + +AUDIENCE: Paste it. + +PROFESSOR: Paste it again. + +Oh no, once I cut it, all the +pieces of human DNA are + +floating around. + +How do I know what +to paste to what? + +AUDIENCE: Methylate it. + +PROFESSOR: Methylate it. + +So first I could take +my human DNA. + +And I could methylate it. + +Then it won't get cut +up by the enzyme. + +But what's the problem +with that? + +None of it will get cut +up with the enzyme. + +Suppose I did something that +was a compromise though. + +Suppose I added a little +methylase and a little + +restriction enzyme. + +And the methylase went around +randomly and put some + +methyl groups on. + +Then these wouldn't get cut. + +And sometimes it might +put on that. + +And those wouldn't get cut. + +And it would just +get cut here. + +I would call such a thing +a partial digestion. + +It can be done one +of two ways. + +I could just add a little bit of +restriction enzyme and not + +give it too long. + +Or I could add a mixture of a +little restriction enzyme, a + +little methylation enzyme, +and let them have at it. + +And if I had the right balance, +I could cut on + +average every second restriction +site or on average + +every fourth restriction site. + +Or if I use a different ratio, +every tenth restriction site. + +So I actually can play a +stochastic, a probabilistic + +game of cutting every second, +fourth, tenth site and + +obviously get a mix. + +I'll get a mixture of +different cuts. + +But in terms of cutting in the +middle of my gene, I no longer + +care because I can do +partial digestions. + +Now that means that in my +library I might not just have + +the Eco fragments. + +But because I did a partial +digestion, I might have two + +consecutive or five consecutive +Eco fragments, if + +I've done a partial digestion. + +But your question +still stands. + +How do I find my right gene? + +How do I figure out which +is the right gene? + +So I've got this. + +I've got my plate. + +I've done this amazing +purification. + +Every one of these guys has a +chunk of human DNA that might + +be just one EcoR1 fragment. + +Or if I happen to have done a +partial digestion, it might be + +two EcoR1 fragments. + +But it turns out that this +guy here is beta-globin. + +How do I know? + +I've purified beta-globin. + +I get points, right? + +I purified beta-globin. + +Somewhere on my plate is a pure + +beta-globin sitting there. + +But the problem is I don't +know where it is. + +How am I going to find it? + +They all still look the same. + +They look like bacteria. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: To do what? + +AUDIENCE: Well, in this case +find some way to determine + +whether or not a certain certain +has beta-globin. + +PROFESSOR: Whether a +certain colony-- + +AUDIENCE: Has beta-globin. + +PROFESSOR: Has the beta-globin +gene in it. + +So I somehow have to test each +colony to figure out whether + +it's got the beta-globin +gene in it. + +How do you propose to do that? + +AUDIENCE: There's some +observation you can make. + +PROFESSOR: Talk loud. + +AUDIENCE: There's some +observation you can make. + +PROFESSOR: And you make +that observation. + +Right, so-- + +I'm with you. + +Yeah? + +AUDIENCE: You basically +want some ribosomes + +to create the proteins. + +PROFESSOR: Oh, oh, oh, so maybe +I can make that thing + +make beta-globin. + +Oh, and then look +for the protein. + +Problem with that is E.coli +doesn't read human + +instructions. + +So E.coli's polymerase +won't read. + +But it's a great idea. + +Maybe we can do that. + +Any other ideas? + +How are we going to +find our gene? + +We've made a library. + +We have a library. + +It's a bigger library +than MIT. + +It's got more volumes +than MIT. + +How are we're going +to find our book? + +AUDIENCE: Put it in a medium +without beta-globin. + +PROFESSOR: Put a medium +without beta-globin. + +AUDIENCE: See if it +grows or not. + +PROFESSOR: See if it grows up. + +E.coli couldn't care less +about beta-globin. + +It doesn't need beta-globin. + +And in addition, it won't +produce beta-globin because it + +doesn't read the human +instructions. + +All right, so we've gone +to all this trouble. + +We've made a library with all +the possible books in the + +human genome. + +And we don't know how +to use the library. + +Friday's lecture let us discuss + +how to use the library. \ No newline at end of file diff --git a/sJalJ1A9NDg.txt b/sJalJ1A9NDg.txt new file mode 100644 index 0000000000000000000000000000000000000000..21cf50c78440365073556d6f46a86b47f2b5b213 --- /dev/null +++ b/sJalJ1A9NDg.txt @@ -0,0 +1,563 @@ +align:start position:0% + +recommendation systems are used in many + + align:start position:0% +recommendation systems are used in many + + + align:start position:0% +recommendation systems are used in many +different areas other than movies jeff + + align:start position:0% +different areas other than movies jeff + + + align:start position:0% +different areas other than movies jeff +bezos + + align:start position:0% +bezos + + + align:start position:0% +bezos +the CEO of Amazon said that if I have + + align:start position:0% +the CEO of Amazon said that if I have + + + align:start position:0% +the CEO of Amazon said that if I have +three million customers on the web I + + align:start position:0% +three million customers on the web I + + + align:start position:0% +three million customers on the web I +should have three million stores on the + + align:start position:0% +should have three million stores on the + + + align:start position:0% +should have three million stores on the +web the Internet allows for mass + + align:start position:0% +web the Internet allows for mass + + + align:start position:0% +web the Internet allows for mass +personalization and recommendation + + align:start position:0% +personalization and recommendation + + + align:start position:0% +personalization and recommendation +systems are a key part of that + + align:start position:0% +systems are a key part of that + + + align:start position:0% +systems are a key part of that +recommendation systems build models + + align:start position:0% +recommendation systems build models + + + align:start position:0% +recommendation systems build models +about users preferences to personalise + + align:start position:0% +about users preferences to personalise + + + align:start position:0% +about users preferences to personalise +the user experience this helps users + + align:start position:0% +the user experience this helps users + + + align:start position:0% +the user experience this helps users +find items they might not have searched + + align:start position:0% +find items they might not have searched + + + align:start position:0% +find items they might not have searched +for like a new favorite band + + align:start position:0% +for like a new favorite band + + + align:start position:0% +for like a new favorite band +an old friend who uses the same social + + align:start position:0% +an old friend who uses the same social + + + align:start position:0% +an old friend who uses the same social +media network or a book or song that + + align:start position:0% +media network or a book or song that + + + align:start position:0% +media network or a book or song that +they're likely to enjoy recommendation + + align:start position:0% +they're likely to enjoy recommendation + + + align:start position:0% +they're likely to enjoy recommendation +systems are a cornerstone of these top + + align:start position:0% +systems are a cornerstone of these top + + + align:start position:0% +systems are a cornerstone of these top +business's social networking sites like + + align:start position:0% +business's social networking sites like + + + align:start position:0% +business's social networking sites like +Facebook music streaming sites like + + align:start position:0% +Facebook music streaming sites like + + + align:start position:0% +Facebook music streaming sites like +Pandora and retail companies like Amazon + + align:start position:0% +Pandora and retail companies like Amazon + + + align:start position:0% +Pandora and retail companies like Amazon +all provide recommendation systems for + + align:start position:0% +all provide recommendation systems for + + + align:start position:0% +all provide recommendation systems for +their users both collaborative filtering + + align:start position:0% +their users both collaborative filtering + + + align:start position:0% +their users both collaborative filtering +and content filtering are used in + + align:start position:0% +and content filtering are used in + + + align:start position:0% +and content filtering are used in +practice collaborative filtering is used + + align:start position:0% +practice collaborative filtering is used + + + align:start position:0% +practice collaborative filtering is used +by companies like Amazon Facebook and + + align:start position:0% +by companies like Amazon Facebook and + + + align:start position:0% +by companies like Amazon Facebook and +Google News content filtering is used by + + align:start position:0% +Google News content filtering is used by + + + align:start position:0% +Google News content filtering is used by +companies like Pandora Rotten Tomatoes + + align:start position:0% +companies like Pandora Rotten Tomatoes + + + align:start position:0% +companies like Pandora Rotten Tomatoes +and see this next and Netflix uses both + + align:start position:0% +and see this next and Netflix uses both + + + align:start position:0% +and see this next and Netflix uses both +collaborative filtering and content + + align:start position:0% +collaborative filtering and content + + + align:start position:0% +collaborative filtering and content +filtering so now let's go back to the + + align:start position:0% +filtering so now let's go back to the + + + align:start position:0% +filtering so now let's go back to the +Netflix prize twenty nine days after + + align:start position:0% +Netflix prize twenty nine days after + + + align:start position:0% +Netflix prize twenty nine days after +last call was announced on July 25th + + align:start position:0% +last call was announced on July 25th + + + align:start position:0% +last call was announced on July 25th +2009 the team the ensemble submitted a + + align:start position:0% +2009 the team the ensemble submitted a + + + align:start position:0% +2009 the team the ensemble submitted a +ten point oh nine percent improvement + + align:start position:0% +ten point oh nine percent improvement + + + align:start position:0% +ten point oh nine percent improvement +beating the ten point oh five percent + + align:start position:0% +beating the ten point oh five percent + + + align:start position:0% +beating the ten point oh five percent +improvement that was submitted by + + align:start position:0% +improvement that was submitted by + + + align:start position:0% +improvement that was submitted by +bellcore's pragmatic chaos to signal + + align:start position:0% +bellcore's pragmatic chaos to signal + + + align:start position:0% +bellcore's pragmatic chaos to signal +last call but by the time Netflix + + align:start position:0% +last call but by the time Netflix + + + align:start position:0% +last call but by the time Netflix +stopped accepting submissions the next + + align:start position:0% +stopped accepting submissions the next + + + align:start position:0% +stopped accepting submissions the next +day bellcore's pragmatic chaos had also + + align:start position:0% +day bellcore's pragmatic chaos had also + + + align:start position:0% +day bellcore's pragmatic chaos had also +submitted a ten point oh nine percent + + align:start position:0% +submitted a ten point oh nine percent + + + align:start position:0% +submitted a ten point oh nine percent +improvement and the ensemble had + + align:start position:0% +improvement and the ensemble had + + + align:start position:0% +improvement and the ensemble had +submitted a ten point ten percent + + align:start position:0% +submitted a ten point ten percent + + + align:start position:0% +submitted a ten point ten percent +improvement to really test the + + align:start position:0% +improvement to really test the + + + align:start position:0% +improvement to really test the +algorithms Netflix tested them on a + + align:start position:0% +algorithms Netflix tested them on a + + + align:start position:0% +algorithms Netflix tested them on a +private test set that the teams had + + align:start position:0% +private test set that the teams had + + + align:start position:0% +private test set that the teams had +never seen before + + align:start position:0% +never seen before + + + align:start position:0% +never seen before +this is the true test of predictive + + align:start position:0% +this is the true test of predictive + + + align:start position:0% +this is the true test of predictive +ability + + align:start position:0% +ability + + + align:start position:0% +ability +on September 18 2009 Netflix announced + + align:start position:0% +on September 18 2009 Netflix announced + + + align:start position:0% +on September 18 2009 Netflix announced +that the winning team was bellcore's + + align:start position:0% +that the winning team was bellcore's + + + align:start position:0% +that the winning team was bellcore's +pragmatic chaos they won the competition + + align:start position:0% +pragmatic chaos they won the competition + + + align:start position:0% +pragmatic chaos they won the competition +and the 1 million dollar grand prize + + align:start position:0% +and the 1 million dollar grand prize + + + align:start position:0% +and the 1 million dollar grand prize +recommendation systems provide a + + align:start position:0% +recommendation systems provide a + + + align:start position:0% +recommendation systems provide a +significant edge to many companies in + + align:start position:0% +significant edge to many companies in + + + align:start position:0% +significant edge to many companies in +today's digital age businesses often + + align:start position:0% +today's digital age businesses often + + + align:start position:0% +today's digital age businesses often +have hundreds of thousands of items to + + align:start position:0% +have hundreds of thousands of items to + + + align:start position:0% +have hundreds of thousands of items to +offer their customers whether their + + align:start position:0% +offer their customers whether their + + + align:start position:0% +offer their customers whether their +movies songs or people they might know + + align:start position:0% +movies songs or people they might know + + + align:start position:0% +movies songs or people they might know +on Facebook excellent recommendation + + align:start position:0% +on Facebook excellent recommendation + + + align:start position:0% +on Facebook excellent recommendation +systems can make or break these + + align:start position:0% +systems can make or break these + + + align:start position:0% +systems can make or break these +businesses clustering algorithms which + + align:start position:0% +businesses clustering algorithms which + + + align:start position:0% +businesses clustering algorithms which +are tailored to find similar customers + + align:start position:0% +are tailored to find similar customers + + + align:start position:0% +are tailored to find similar customers +or similar items form the backbone of + + align:start position:0% +or similar items form the backbone of + + + align:start position:0% +or similar items form the backbone of +many of these recommendation systems + + align:start position:0% +many of these recommendation systems + + + align:start position:0% +many of these recommendation systems +clustering also has many other + + align:start position:0% +clustering also has many other + + + align:start position:0% +clustering also has many other +interesting applications in the next + + align:start position:0% +interesting applications in the next + + + align:start position:0% +interesting applications in the next +lecture we'll see how clustering can be + + align:start position:0% +lecture we'll see how clustering can be + + + align:start position:0% +lecture we'll see how clustering can be +used to improve the predictive ability + + align:start position:0% +used to improve the predictive ability + + + align:start position:0% +used to improve the predictive ability +of classification methods \ No newline at end of file diff --git a/sxzFpOsvfgU.txt b/sxzFpOsvfgU.txt new file mode 100644 index 0000000000000000000000000000000000000000..e0b018456ab1ab53146eb3317a55a8baa00653f8 --- /dev/null +++ b/sxzFpOsvfgU.txt @@ -0,0 +1,2003 @@ +align:start position:0% + +simple harmonic oscillator so what is + + align:start position:0% +simple harmonic oscillator so what is + + + align:start position:0% +simple harmonic oscillator so what is +there about the simple harmonic + + align:start position:0% +there about the simple harmonic + + + align:start position:0% +there about the simple harmonic +oscillator well it's a classical system + + align:start position:0% +oscillator well it's a classical system + + + align:start position:0% +oscillator well it's a classical system +that you understand perfectly well + + align:start position:0% +that you understand perfectly well + + + align:start position:0% +that you understand perfectly well +oscillator spring with a mass oscillates + + align:start position:0% +oscillator spring with a mass oscillates + + + align:start position:0% +oscillator spring with a mass oscillates +and has an energy which is the kinetic + + align:start position:0% +and has an energy which is the kinetic + + + align:start position:0% +and has an energy which is the kinetic +energy plus the potential energy and + + align:start position:0% +energy plus the potential energy and + + + align:start position:0% +energy plus the potential energy and +that's P squared over 2m plus 1/2 M + + align:start position:0% +that's P squared over 2m plus 1/2 M + + + align:start position:0% +that's P squared over 2m plus 1/2 M +Omega squared x squared and this may be + + align:start position:0% +Omega squared x squared and this may be + + + align:start position:0% +Omega squared x squared and this may be +a tiny bit unfamiliar this way of + + align:start position:0% +a tiny bit unfamiliar this way of + + + align:start position:0% +a tiny bit unfamiliar this way of +writing it but you may recall that Omega + + align:start position:0% +writing it but you may recall that Omega + + + align:start position:0% +writing it but you may recall that Omega +is equal to square root of K over m the + + align:start position:0% +is equal to square root of K over m the + + + align:start position:0% +is equal to square root of K over m the +so-called spring constant in which the + + align:start position:0% +so-called spring constant in which the + + + align:start position:0% +so-called spring constant in which the +potential in terms of K would be + + align:start position:0% +potential in terms of K would be + + + align:start position:0% +potential in terms of K would be +one-half K x squared and that's the + + align:start position:0% +one-half K x squared and that's the + + + align:start position:0% +one-half K x squared and that's the +potential energy stored in a spring that + + align:start position:0% +potential energy stored in a spring that + + + align:start position:0% +potential energy stored in a spring that +you've stretch a distance X that's the + + align:start position:0% +you've stretch a distance X that's the + + + align:start position:0% +you've stretch a distance X that's the +total energy of a harmonic oscillator so + + align:start position:0% +total energy of a harmonic oscillator so + + + align:start position:0% +total energy of a harmonic oscillator so +when physicists starting with quantum + + align:start position:0% +when physicists starting with quantum + + + align:start position:0% +when physicists starting with quantum +mechanics in the twenties decided let's + + align:start position:0% +mechanics in the twenties decided let's + + + align:start position:0% +mechanics in the twenties decided let's +do a harmonic oscillator a quantum + + align:start position:0% +do a harmonic oscillator a quantum + + + align:start position:0% +do a harmonic oscillator a quantum +harmonic oscillator they had to invent a + + align:start position:0% +harmonic oscillator they had to invent a + + + align:start position:0% +harmonic oscillator they had to invent a +Hamiltonian and Hamiltonian they + + align:start position:0% +Hamiltonian and Hamiltonian they + + + align:start position:0% +Hamiltonian and Hamiltonian they +invented was a simple one they looked at + + align:start position:0% +invented was a simple one they looked at + + + align:start position:0% +invented was a simple one they looked at +that and said H is gonna be P hat + + align:start position:0% +that and said H is gonna be P hat + + + align:start position:0% +that and said H is gonna be P hat +squared over 2m plus 1/2 M Omega square + + align:start position:0% +squared over 2m plus 1/2 M Omega square + + + align:start position:0% +squared over 2m plus 1/2 M Omega square +X hat squared and now the difference is + + align:start position:0% +X hat squared and now the difference is + + + align:start position:0% +X hat squared and now the difference is +going to be that X with P are operators + + align:start position:0% +going to be that X with P are operators + + + align:start position:0% +going to be that X with P are operators +and this is IH bar and that's going to + + align:start position:0% +and this is IH bar and that's going to + + + align:start position:0% +and this is IH bar and that's going to +be my quantum system so this is a + + align:start position:0% +be my quantum system so this is a + + + align:start position:0% +be my quantum system so this is a +quantum system that is inspired by + + align:start position:0% +quantum system that is inspired by + + + align:start position:0% +quantum system that is inspired by +classical mechanics in the purest and + + align:start position:0% +classical mechanics in the purest and + + + align:start position:0% +classical mechanics in the purest and +simple way anyone could have invented + + align:start position:0% +simple way anyone could have invented + + + align:start position:0% +simple way anyone could have invented +quantum system it was very natural + + align:start position:0% +quantum system it was very natural + + + align:start position:0% +quantum system it was very natural +still the result of the quantization is + + align:start position:0% +still the result of the quantization is + + + align:start position:0% +still the result of the quantization is +very surprising because while this + + align:start position:0% +very surprising because while this + + + align:start position:0% +very surprising because while this +postulator of mechanical oscillator can + + align:start position:0% +postulator of mechanical oscillator can + + + align:start position:0% +postulator of mechanical oscillator can +oscillate with any amplitude the quantum + + align:start position:0% +oscillate with any amplitude the quantum + + + align:start position:0% +oscillate with any amplitude the quantum +oscillator has quantized amplitudes and + + align:start position:0% +oscillator has quantized amplitudes and + + + align:start position:0% +oscillator has quantized amplitudes and +quantized energy is therefore so all + + align:start position:0% +quantized energy is therefore so all + + + align:start position:0% +quantized energy is therefore so all +kinds of interesting things happen with + + align:start position:0% +kinds of interesting things happen with + + + align:start position:0% +kinds of interesting things happen with +this oscillator now the reason this is + + align:start position:0% +this oscillator now the reason this is + + + align:start position:0% +this oscillator now the reason this is +also very new big latest is that this + + align:start position:0% +also very new big latest is that this + + + align:start position:0% +also very new big latest is that this +potential this exactly a quadratic + + align:start position:0% +potential this exactly a quadratic + + + align:start position:0% +potential this exactly a quadratic +potential V of X V of X is 1/2 M Omega + + align:start position:0% +potential V of X V of X is 1/2 M Omega + + + align:start position:0% +potential V of X V of X is 1/2 M Omega +squared x squared V of X without the + + align:start position:0% +squared x squared V of X without the + + + align:start position:0% +squared x squared V of X without the +heart but this is a good approximation + + align:start position:0% +heart but this is a good approximation + + + align:start position:0% +heart but this is a good approximation +to almost any system you consider in + + align:start position:0% +to almost any system you consider in + + + align:start position:0% +to almost any system you consider in +nature any oscillating system because + + align:start position:0% +nature any oscillating system because + + + align:start position:0% +nature any oscillating system because +for any potential that has a minimum + + align:start position:0% +for any potential that has a minimum + + + align:start position:0% +for any potential that has a minimum +there is some parabolic approximation at + + align:start position:0% +there is some parabolic approximation at + + + align:start position:0% +there is some parabolic approximation at +the bottom at the bottom the derivative + + align:start position:0% +the bottom at the bottom the derivative + + + align:start position:0% +the bottom at the bottom the derivative +vanishes so the Taylor series says that + + align:start position:0% +vanishes so the Taylor series says that + + + align:start position:0% +vanishes so the Taylor series says that +approximately at the bottom is a + + align:start position:0% +approximately at the bottom is a + + + align:start position:0% +approximately at the bottom is a +quadratic potential and therefore this + + align:start position:0% +quadratic potential and therefore this + + + align:start position:0% +quadratic potential and therefore this +quadratic potential will govern the + + align:start position:0% +quadratic potential will govern the + + + align:start position:0% +quadratic potential will govern the +quantum oscillations of a diatomic + + align:start position:0% +quantum oscillations of a diatomic + + + align:start position:0% +quantum oscillations of a diatomic +molecule the quantum oscillations of a + + align:start position:0% +molecule the quantum oscillations of a + + + align:start position:0% +molecule the quantum oscillations of a +periodic system all kind of quantum + + align:start position:0% +periodic system all kind of quantum + + + align:start position:0% +periodic system all kind of quantum +oscillations will be approximately + + align:start position:0% +oscillations will be approximately + + + align:start position:0% +oscillations will be approximately +governed by a harmonic oscillator light + + align:start position:0% +governed by a harmonic oscillator light + + + align:start position:0% +governed by a harmonic oscillator light +has a harmonic oscillator description + + align:start position:0% +has a harmonic oscillator description + + + align:start position:0% +has a harmonic oscillator description +for its photons this Hamiltonian is the + + align:start position:0% +for its photons this Hamiltonian is the + + + align:start position:0% +for its photons this Hamiltonian is the +most famous final tone e'en there is it + + align:start position:0% +most famous final tone e'en there is it + + + align:start position:0% +most famous final tone e'en there is it +in fact when you have electrons in a + + align:start position:0% +in fact when you have electrons in a + + + align:start position:0% +in fact when you have electrons in a +magnetic field + + align:start position:0% +magnetic field + + + align:start position:0% +magnetic field +somehow this shows up and this becomes + + align:start position:0% +somehow this shows up and this becomes + + + align:start position:0% +somehow this shows up and this becomes +some sort of problem that you solve very + + align:start position:0% +some sort of problem that you solve very + + + align:start position:0% +some sort of problem that you solve very +well understand very well and suddenly + + align:start position:0% +well understand very well and suddenly + + + align:start position:0% +well understand very well and suddenly +it pops up in all kinds of contexts so + + align:start position:0% +it pops up in all kinds of contexts so + + + align:start position:0% +it pops up in all kinds of contexts so +we need to understand it and let's go + + align:start position:0% +we need to understand it and let's go + + + align:start position:0% +we need to understand it and let's go +directly to the + + align:start position:0% +directly to the + + + align:start position:0% +directly to the +- of solving this problem because it has + + align:start position:0% +- of solving this problem because it has + + + align:start position:0% +- of solving this problem because it has +many important lessons so there's two + + align:start position:0% +many important lessons so there's two + + + align:start position:0% +many important lessons so there's two +ways to solve this problem of the + + align:start position:0% +ways to solve this problem of the + + + align:start position:0% +ways to solve this problem of the +finding the bound States on the energy + + align:start position:0% +finding the bound States on the energy + + + align:start position:0% +finding the bound States on the energy +eigenstates of the harmonic oscillator + + align:start position:0% +eigenstates of the harmonic oscillator + + + align:start position:0% +eigenstates of the harmonic oscillator +this is a very interesting potential + + align:start position:0% +this is a very interesting potential + + + align:start position:0% +this is a very interesting potential +because all its energy eigenstates are + + align:start position:0% +because all its energy eigenstates are + + + align:start position:0% +because all its energy eigenstates are +bound States that's not the case for the + + align:start position:0% +bound States that's not the case for the + + + align:start position:0% +bound States that's not the case for the +Delta function potential in the Delta + + align:start position:0% +Delta function potential in the Delta + + + align:start position:0% +Delta function potential in the Delta +function potential we found one bound + + align:start position:0% +function potential we found one bound + + + align:start position:0% +function potential we found one bound +state but they're all kind of unbound + + align:start position:0% +state but they're all kind of unbound + + + align:start position:0% +state but they're all kind of unbound +states with positive energy but this + + align:start position:0% +states with positive energy but this + + + align:start position:0% +states with positive energy but this +potential grows forever never stops + + align:start position:0% +potential grows forever never stops + + + align:start position:0% +potential grows forever never stops +growing so whatever energy you have it + + align:start position:0% +growing so whatever energy you have it + + + align:start position:0% +growing so whatever energy you have it +is a bound state it will decay it will + + align:start position:0% +is a bound state it will decay it will + + + align:start position:0% +is a bound state it will decay it will +be localized so you just have bound + + align:start position:0% +be localized so you just have bound + + + align:start position:0% +be localized so you just have bound +States + + align:start position:0% +States + + + align:start position:0% +States +it's marvelously nice because of that + + align:start position:0% +it's marvelously nice because of that + + + align:start position:0% +it's marvelously nice because of that +property much simpler than anything you + + align:start position:0% +property much simpler than anything you + + + align:start position:0% +property much simpler than anything you +can imagine so what do we have to do we + + align:start position:0% +can imagine so what do we have to do we + + + align:start position:0% +can imagine so what do we have to do we +want to find the energy eigenstate so + + align:start position:0% +want to find the energy eigenstate so + + + align:start position:0% +want to find the energy eigenstate so +we'll write H and I will write five + + align:start position:0% +we'll write H and I will write five + + + align:start position:0% +we'll write H and I will write five +people right sometimes five five n of X + + align:start position:0% +people right sometimes five five n of X + + + align:start position:0% +people right sometimes five five n of X +is equal to e Phi n of X and we don't + + align:start position:0% +is equal to e Phi n of X and we don't + + + align:start position:0% +is equal to e Phi n of X and we don't +know the energy eigenstates you know + + align:start position:0% +know the energy eigenstates you know + + + align:start position:0% +know the energy eigenstates you know +it's a symmetric potential it's a real + + align:start position:0% +it's a symmetric potential it's a real + + + align:start position:0% +it's a symmetric potential it's a real +potential this we used to go up science + + align:start position:0% +potential this we used to go up science + + + align:start position:0% +potential this we used to go up science +but I will write them as faience as many + + align:start position:0% +but I will write them as faience as many + + + align:start position:0% +but I will write them as faience as many +people do because they are the harmonic + + align:start position:0% +people do because they are the harmonic + + + align:start position:0% +people do because they are the harmonic +oscillator ones they're very famous and + + align:start position:0% +oscillator ones they're very famous and + + + align:start position:0% +oscillator ones they're very famous and +we don't know this could be an energy of + + align:start position:0% +we don't know this could be an energy of + + + align:start position:0% +we don't know this could be an energy of +the end state and we don't know what are + + align:start position:0% +the end state and we don't know what are + + + align:start position:0% +the end state and we don't know what are +the energies know how the wave functions + + align:start position:0% +the energies know how the wave functions + + + align:start position:0% +the energies know how the wave functions +look and we have to solve the + + align:start position:0% +look and we have to solve the + + + align:start position:0% +look and we have to solve the +differential equation as I was saying + + align:start position:0% +differential equation as I was saying + + + align:start position:0% +differential equation as I was saying +there are two ways of solving this + + align:start position:0% +there are two ways of solving this + + + align:start position:0% +there are two ways of solving this +differential equation one treating this + + align:start position:0% +differential equation one treating this + + + align:start position:0% +differential equation one treating this +as a differential equation and + + align:start position:0% +as a differential equation and + + + align:start position:0% +as a differential equation and +understanding why the energy + + align:start position:0% +understanding why the energy + + + align:start position:0% +understanding why the energy +quantized from the differential equation + + align:start position:0% +quantized from the differential equation + + + align:start position:0% +quantized from the differential equation +this actually gives you a lot of insight + + align:start position:0% +this actually gives you a lot of insight + + + align:start position:0% +this actually gives you a lot of insight +as to what's going on and it will relate + + align:start position:0% +as to what's going on and it will relate + + + align:start position:0% +as to what's going on and it will relate +to the kind of things you're doing in + + align:start position:0% +to the kind of things you're doing in + + + align:start position:0% +to the kind of things you're doing in +the homework this week the other way is + + align:start position:0% +the homework this week the other way is + + + align:start position:0% +the homework this week the other way is +to be very clever and invent what are + + align:start position:0% +to be very clever and invent what are + + + align:start position:0% +to be very clever and invent what are +called raising and lowering operators + + align:start position:0% +called raising and lowering operators + + + align:start position:0% +called raising and lowering operators +and sort of solve this whole system + + align:start position:0% +and sort of solve this whole system + + + align:start position:0% +and sort of solve this whole system +without solving the general differential + + align:start position:0% +without solving the general differential + + + align:start position:0% +without solving the general differential +equation but solving a first-order very + + align:start position:0% +equation but solving a first-order very + + + align:start position:0% +equation but solving a first-order very +simple differential equation and then + + align:start position:0% +simple differential equation and then + + + align:start position:0% +simple differential equation and then +doing everything else algebraically with + + align:start position:0% +doing everything else algebraically with + + + align:start position:0% +doing everything else algebraically with +creation and halation operators we will + + align:start position:0% +creation and halation operators we will + + + align:start position:0% +creation and halation operators we will +also do that but we will not develop + + align:start position:0% +also do that but we will not develop + + + align:start position:0% +also do that but we will not develop +that too far + + align:start position:0% +that too far + + + align:start position:0% +that too far +that's the applications of that method + + align:start position:0% +that's the applications of that method + + + align:start position:0% +that's the applications of that method +are mostly for 805 so we'll introduce + + align:start position:0% +are mostly for 805 so we'll introduce + + + align:start position:0% +are mostly for 805 so we'll introduce +creation and halation operators which + + align:start position:0% +creation and halation operators which + + + align:start position:0% +creation and halation operators which +are very nice and very useful but we'll + + align:start position:0% +are very nice and very useful but we'll + + + align:start position:0% +are very nice and very useful but we'll +leave some of the applications to + + align:start position:0% +leave some of the applications to + + + align:start position:0% +leave some of the applications to +coherent states of harmonic oscillators + + align:start position:0% +coherent states of harmonic oscillators + + + align:start position:0% +coherent states of harmonic oscillators +the squeezed states of harmonic + + align:start position:0% +the squeezed states of harmonic + + + align:start position:0% +the squeezed states of harmonic +oscillators for later so this is what we + + align:start position:0% +oscillators for later so this is what we + + + align:start position:0% +oscillators for later so this is what we +want to solve so we have minus h squared + + align:start position:0% +want to solve so we have minus h squared + + + align:start position:0% +want to solve so we have minus h squared +over 2m v ii psy phi n the x squared and + + align:start position:0% +over 2m v ii psy phi n the x squared and + + + align:start position:0% +over 2m v ii psy phi n the x squared and +I will probably forget about the labels + + align:start position:0% +I will probably forget about the labels + + + align:start position:0% +I will probably forget about the labels +the labels will come later as we solve + + align:start position:0% +the labels will come later as we solve + + + align:start position:0% +the labels will come later as we solve +the equation plus V of X 1/2 M Omega + + align:start position:0% +the equation plus V of X 1/2 M Omega + + + align:start position:0% +the equation plus V of X 1/2 M Omega +squared x squared Phi of X is equal to e + + align:start position:0% +squared x squared Phi of X is equal to e + + + align:start position:0% +squared x squared Phi of X is equal to e +Phi of X ok this is the equation we want + + align:start position:0% +Phi of X ok this is the equation we want + + + align:start position:0% +Phi of X ok this is the equation we want +to solve now we're going to do one thing + + align:start position:0% +to solve now we're going to do one thing + + + align:start position:0% +to solve now we're going to do one thing +first with this differential equation we + + align:start position:0% +first with this differential equation we + + + align:start position:0% +first with this differential equation we +don't like all these dimensional + + align:start position:0% +don't like all these dimensional + + + align:start position:0% +don't like all these dimensional +constants if you had to put it in the + + align:start position:0% +constants if you had to put it in the + + + align:start position:0% +constants if you had to put it in the +computer what are you gonna put six + + align:start position:0% +computer what are you gonna put six + + + align:start position:0% +computer what are you gonna put six +times ten to the minus twenty-three over + + align:start position:0% +times ten to the minus twenty-three over + + + align:start position:0% +times ten to the minus twenty-three over +m + + align:start position:0% +m + + + align:start position:0% +m +you won't solve a differential equation + + align:start position:0% +you won't solve a differential equation + + + align:start position:0% +you won't solve a differential equation +we have to clean this up to clean this + + align:start position:0% +we have to clean this up to clean this + + + align:start position:0% +we have to clean this up to clean this +up there's a procedure that warrant this + + align:start position:0% +up there's a procedure that warrant this + + + align:start position:0% +up there's a procedure that warrant this +warranty to do the job for you and the + + align:start position:0% +warranty to do the job for you and the + + + align:start position:0% +warranty to do the job for you and the +procedure is to change the X variable + + align:start position:0% +procedure is to change the X variable + + + align:start position:0% +procedure is to change the X variable +into a variable that has no units + + align:start position:0% +into a variable that has no units + + + align:start position:0% +into a variable that has no units +this is warranty to lead you to the way + + align:start position:0% +this is warranty to lead you to the way + + + align:start position:0% +this is warranty to lead you to the way +to solve this differential equation you + + align:start position:0% +to solve this differential equation you + + + align:start position:0% +to solve this differential equation you +will be using this throughout this + + align:start position:0% +will be using this throughout this + + + align:start position:0% +will be using this throughout this +semester cleaning differential equations + + align:start position:0% +semester cleaning differential equations + + + align:start position:0% +semester cleaning differential equations +is a nice skill and the fact is that + + align:start position:0% +is a nice skill and the fact is that + + + align:start position:0% +is a nice skill and the fact is that +it's a it there's a method and the + + align:start position:0% +it's a it there's a method and the + + + align:start position:0% +it's a it there's a method and the +method always proceeds by first writing + + align:start position:0% +method always proceeds by first writing + + + align:start position:0% +method always proceeds by first writing +x equals a you where this will be unit + + align:start position:0% +x equals a you where this will be unit + + + align:start position:0% +x equals a you where this will be unit +free this quantity you so this will + + align:start position:0% +free this quantity you so this will + + + align:start position:0% +free this quantity you so this will +become a differential equation on a unit + + align:start position:0% +become a differential equation on a unit + + + align:start position:0% +become a differential equation on a unit +free constant which is ideal for your + + align:start position:0% +free constant which is ideal for your + + + align:start position:0% +free constant which is ideal for your +numerical solution and it's much nicer + + align:start position:0% +numerical solution and it's much nicer + + + align:start position:0% +numerical solution and it's much nicer +but then this a has to have units of + + align:start position:0% +but then this a has to have units of + + + align:start position:0% +but then this a has to have units of +length so the first thing you have to do + + align:start position:0% +length so the first thing you have to do + + + align:start position:0% +length so the first thing you have to do +is look up in your problem + + align:start position:0% +is look up in your problem + + + align:start position:0% +is look up in your problem +what are your constants and you have a + + align:start position:0% +what are your constants and you have a + + + align:start position:0% +what are your constants and you have a +mass M a frequency Omega and H bar and + + align:start position:0% +mass M a frequency Omega and H bar and + + + align:start position:0% +mass M a frequency Omega and H bar and +you need to find a constant with units + + align:start position:0% +you need to find a constant with units + + + align:start position:0% +you need to find a constant with units +of length wasn't that in your test I + + align:start position:0% +of length wasn't that in your test I + + + align:start position:0% +of length wasn't that in your test I +think so how do you find a concept with + + align:start position:0% +think so how do you find a concept with + + + align:start position:0% +think so how do you find a concept with +units of length here well energy is + + align:start position:0% +units of length here well energy is + + + align:start position:0% +units of length here well energy is +equal to you can write it in two ways + + align:start position:0% +equal to you can write it in two ways + + + align:start position:0% +equal to you can write it in two ways +the energy can be written as P squared + + align:start position:0% +the energy can be written as P squared + + + align:start position:0% +the energy can be written as P squared +over m so it will be H squared over m + + align:start position:0% +over m so it will be H squared over m + + + align:start position:0% +over m so it will be H squared over m +times a length squared but from the + + align:start position:0% +times a length squared but from the + + + align:start position:0% +times a length squared but from the +potential it also has the units of M + + align:start position:0% +potential it also has the units of M + + + align:start position:0% +potential it also has the units of M +Omega squared a squared those these are + + align:start position:0% +Omega squared a squared those these are + + + align:start position:0% +Omega squared a squared those these are +units equations for units the units of + + align:start position:0% +units equations for units the units of + + + align:start position:0% +units equations for units the units of +energy are this and the units of energy + + align:start position:0% +energy are this and the units of energy + + + align:start position:0% +energy are this and the units of energy +from the second term in the Hamiltonian + + align:start position:0% +from the second term in the Hamiltonian + + + align:start position:0% +from the second term in the Hamiltonian +are those from where you get that a + + align:start position:0% +are those from where you get that a + + + align:start position:0% +are those from where you get that a +squared is equal to H over m Omega so + + align:start position:0% +squared is equal to H over m Omega so + + + align:start position:0% +squared is equal to H over m Omega so +that's the constant that you need if you + + align:start position:0% +that's the constant that you need if you + + + align:start position:0% +that's the constant that you need if you +have that constant your differential + + align:start position:0% +have that constant your differential + + + align:start position:0% +have that constant your differential +equation becomes what well it becomes + + align:start position:0% +equation becomes what well it becomes + + + align:start position:0% +equation becomes what well it becomes +the following let's write it out it's + + align:start position:0% +the following let's write it out it's + + + align:start position:0% +the following let's write it out it's +very simple because X is equal to a U + + align:start position:0% +very simple because X is equal to a U + + + align:start position:0% +very simple because X is equal to a U +and therefore you get minus H squared + + align:start position:0% +and therefore you get minus H squared + + + align:start position:0% +and therefore you get minus H squared +over 2m a squared D second Phi the U + + align:start position:0% +over 2m a squared D second Phi the U + + + align:start position:0% +over 2m a squared D second Phi the U +squared X is equal 8u so it basically + + align:start position:0% +squared X is equal 8u so it basically + + + align:start position:0% +squared X is equal 8u so it basically +just shows up here plus 1/2 M Omega + + align:start position:0% +just shows up here plus 1/2 M Omega + + + align:start position:0% +just shows up here plus 1/2 M Omega +squared a squared u squared Phi is equal + + align:start position:0% +squared a squared u squared Phi is equal + + + align:start position:0% +squared a squared u squared Phi is equal +to e Phi now things have to work nicely + + align:start position:0% +to e Phi now things have to work nicely + + + align:start position:0% +to e Phi now things have to work nicely +if you did the job well they have to + + align:start position:0% +if you did the job well they have to + + + align:start position:0% +if you did the job well they have to +work nicely you see let's think of the + + align:start position:0% +work nicely you see let's think of the + + + align:start position:0% +work nicely you see let's think of the +unit of this equation Phi is here 5 here + + align:start position:0% +unit of this equation Phi is here 5 here + + + align:start position:0% +unit of this equation Phi is here 5 here +5 years of Phi is not an issue + + align:start position:0% +5 years of Phi is not an issue + + + align:start position:0% +5 years of Phi is not an issue +the units of Phi are irrelevant here is + + align:start position:0% +the units of Phi are irrelevant here is + + + align:start position:0% +the units of Phi are irrelevant here is +units of energy but you has no units so + + align:start position:0% +units of energy but you has no units so + + + align:start position:0% +units of energy but you has no units so +this has no unit so this must have units + + align:start position:0% +this has no unit so this must have units + + + align:start position:0% +this has no unit so this must have units +of energy and since you has no units + + align:start position:0% +of energy and since you has no units + + + align:start position:0% +of energy and since you has no units +this derivative has no units and this + + align:start position:0% +this derivative has no units and this + + + align:start position:0% +this derivative has no units and this +must have units of energy and these two + + align:start position:0% +must have units of energy and these two + + + align:start position:0% +must have units of energy and these two +numbers must be something nice if you + + align:start position:0% +numbers must be something nice if you + + + align:start position:0% +numbers must be something nice if you +substitute a squared and indeed if you + + align:start position:0% +substitute a squared and indeed if you + + + align:start position:0% +substitute a squared and indeed if you +set as substitute a square + + align:start position:0% +set as substitute a square + + + align:start position:0% +set as substitute a square +here this whole number becomes H bar + + align:start position:0% +here this whole number becomes H bar + + + align:start position:0% +here this whole number becomes H bar +Omega and this number becomes H bar + + align:start position:0% +Omega and this number becomes H bar + + + align:start position:0% +Omega and this number becomes H bar +Omega as well which is very nice so this + + align:start position:0% +Omega as well which is very nice so this + + + align:start position:0% +Omega as well which is very nice so this +whole equation has become minus one half + + align:start position:0% +whole equation has become minus one half + + + align:start position:0% +whole equation has become minus one half +one all times H bar Omega the second Phi + + align:start position:0% +one all times H bar Omega the second Phi + + + align:start position:0% +one all times H bar Omega the second Phi +the U squared plus one-half H bar Omega + + align:start position:0% +the U squared plus one-half H bar Omega + + + align:start position:0% +the U squared plus one-half H bar Omega +u squared v equal e Phi the next step is + + align:start position:0% +u squared v equal e Phi the next step is + + + align:start position:0% +u squared v equal e Phi the next step is +to say you don't even want this energy + + align:start position:0% +to say you don't even want this energy + + + align:start position:0% +to say you don't even want this energy +units even though they don't look that + + align:start position:0% +units even though they don't look that + + + align:start position:0% +units even though they don't look that +bad this equation looks much nicer than + + align:start position:0% +bad this equation looks much nicer than + + + align:start position:0% +bad this equation looks much nicer than +the original equation which had all kind + + align:start position:0% +the original equation which had all kind + + + align:start position:0% +the original equation which had all kind +of strange units so I will multiply this + + align:start position:0% +of strange units so I will multiply this + + + align:start position:0% +of strange units so I will multiply this +equation by 2 over H Omega to cancel it + + align:start position:0% +equation by 2 over H Omega to cancel it + + + align:start position:0% +equation by 2 over H Omega to cancel it +so I get minus ii v the u squared plus u + + align:start position:0% +so I get minus ii v the u squared plus u + + + align:start position:0% +so I get minus ii v the u squared plus u +squared v is equal to 2 e over H bar + + align:start position:0% +squared v is equal to 2 e over H bar + + + align:start position:0% +squared v is equal to 2 e over H bar +Omega Phi + + align:start position:0% + + + + align:start position:0% + +so look at this the equation is now + + align:start position:0% +so look at this the equation is now + + + align:start position:0% +so look at this the equation is now +almost in perfect form and in order to + + align:start position:0% +almost in perfect form and in order to + + + align:start position:0% +almost in perfect form and in order to +make it perfect I would say that the + + align:start position:0% +make it perfect I would say that the + + + align:start position:0% +make it perfect I would say that the +right-hand side now see again by + + align:start position:0% +right-hand side now see again by + + + align:start position:0% +right-hand side now see again by +whatever units it has it doesn't matter + + align:start position:0% +whatever units it has it doesn't matter + + + align:start position:0% +whatever units it has it doesn't matter +it's all over the place but this has no + + align:start position:0% +it's all over the place but this has no + + + align:start position:0% +it's all over the place but this has no +units is derivatives and this has no + + align:start position:0% +units is derivatives and this has no + + + align:start position:0% +units is derivatives and this has no +units this multiplication so this must + + align:start position:0% +units this multiplication so this must + + + align:start position:0% +units this multiplication so this must +have no units and indeed you know that H + + align:start position:0% +have no units and indeed you know that H + + + align:start position:0% +have no units and indeed you know that H +Omega has units of energy in that energy + + align:start position:0% +Omega has units of energy in that energy + + + align:start position:0% +Omega has units of energy in that energy +so it suggests that you define a unit + + align:start position:0% +so it suggests that you define a unit + + + align:start position:0% +so it suggests that you define a unit +free energy free energy which is 2 e + + align:start position:0% +free energy free energy which is 2 e + + + align:start position:0% +free energy free energy which is 2 e +over H Omega and calculating chrome mu + + align:start position:0% +over H Omega and calculating chrome mu + + + align:start position:0% +over H Omega and calculating chrome mu +is the same thing as calculating the + + align:start position:0% +is the same thing as calculating the + + + align:start position:0% +is the same thing as calculating the +energy because if you know this number + + align:start position:0% +energy because if you know this number + + + align:start position:0% +energy because if you know this number +you know the energy the energy is H bar + + align:start position:0% +you know the energy the energy is H bar + + + align:start position:0% +you know the energy the energy is H bar +Omega over 2 times curly e the advantage + + align:start position:0% +Omega over 2 times curly e the advantage + + + align:start position:0% +Omega over 2 times curly e the advantage +is that curly e will be either 1/2 1/2 a + + align:start position:0% +is that curly e will be either 1/2 1/2 a + + + align:start position:0% +is that curly e will be either 1/2 1/2 a +nice number well is some 0.87 eveer + + align:start position:0% +nice number well is some 0.87 eveer + + + align:start position:0% +nice number well is some 0.87 eveer +things like that so all of this equation + + align:start position:0% +things like that so all of this equation + + + align:start position:0% +things like that so all of this equation +has been removed to this very nice + + align:start position:0% +has been removed to this very nice + + + align:start position:0% +has been removed to this very nice +equation this minus the second Phi the u + + align:start position:0% +equation this minus the second Phi the u + + + align:start position:0% +equation this minus the second Phi the u +squared plus u squared Phi is equal to e + + align:start position:0% +squared plus u squared Phi is equal to e + + + align:start position:0% +squared plus u squared Phi is equal to e +Phi or the second Phi D u squared is + + align:start position:0% +Phi or the second Phi D u squared is + + + align:start position:0% +Phi or the second Phi D u squared is +equal to u squared minus E Phi \ No newline at end of file diff --git a/t5Wxk96QjUk.txt b/t5Wxk96QjUk.txt new file mode 100644 index 0000000000000000000000000000000000000000..82e571706404096720f67b6d1244a20872124c3c --- /dev/null +++ b/t5Wxk96QjUk.txt @@ -0,0 +1,2481 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: +Computational complexity + +is basically about how +hard is a problem, right? + +There are some problems +that are really easy + +and some problems +that are really hard. + +And Eric drew this +line on the board + +where you have really +easy on the left + +and really hard on the right. + +What's the hardest problem +that we can possibly have? + +AUDIENCE: It was chess, right? + +Or something like that? + +PROFESSOR: No, there's +something beyond chess. + +AUDIENCE: A halting problem? + +PROFESSOR: Halting problem. + +AUDIENCE: Yeah. + +PROFESSOR: Yep. + +Halting problem +is somewhere here. + +So what's the best solution +for the halting problem? + +Running time. + +AUDIENCE: It is +exponential, or something? + +PROFESSOR: You'd wish. + +AUDIENCE: Oh really? + +It's not even exponential? + +AUDIENCE: I think +there's like no solution. + +PROFESSOR: There is no solution +for the halting problem. + +No matter how much time, +computers, and money you have, + +you cannot solve +the halting problem. + +It's undesignable. + +So this is the worst kind of +problem you can come up with. + +AUDIENCE: What exactly +is the halting problem? + +PROFESSOR: So halting +problem is given + +a program in any representation +that makes sense to you, + +machine language, CE, assembly, +parsing tree, whatever + +you want, decide if +it terminates or not. + +Sounds really simple, right? + +Turns out there's a proof that +says it's impossible to solve. + +So you can't say will terminate +or will not terminate. + +AUDIENCE: Well, but for some +programs, it's like while true, + +but there's no break. + +PROFESSOR: So Turing Machine. + +Yeah. + +If you have a machine where +you're not allowed loops, + +then it's easy to know +what's going to happen. + +So you need to have a +Turing machine, something + +that allows loops. + +So some instances +are easy, right? + +But for the general +case of you have + +to write a program that gets +another program and outputs + +this bit, we don't +know how to do that. + +But we've proven that nobody +will know how to do that, + +so we're OK with it. + +So this means undecidable. + +We know that nobody will +ever be able to solve this. + +So if you're given the halting +problem on an interview, + +it's safe to laugh in the +guy's face and tell them, + +why don't you show +me how to do it? + +So what is better +than undecidable? + +There are these problems here +that are outright impossible. + +What's the next best thing? + +AUDIENCE: Chess? + +I know chess is in +there somewhere. + +PROFESSOR: Chess is still here. + +There's something +harder than that. + +AUDIENCE: Is it R, or +something like that? + +PROFESSOR: Yup. + +So this is the boundary +for R and this whole thing + +is R. What R? + +R is-- so if these +are undecidable, + +R means decidable, right? + +So you can write an algorithm +that will compute the answer + +and do that in a +finite amount of time. + +Will the world end before +the algorithm ends? + +Maybe, who knows. + +But at least there's a +finite amount of time, + +so the problem can +be solved somehow. + +That means R. + +AUDIENCE: R is like, +real, like it's not. + +PROFESSOR: Real, OK. + +AUDIENCE: So like numbers, +like, you know, real numbers-- + +PROFESSOR: So you know it +actually comes from recursive, + +because some old people +decided that recursive + +means it terminates +at some point. + +This is really old +school stuff, 1940. + +So R actually stands +for recursive. + +Just know that R +means decidable. + +Weird abbreviation, but oh well. + +AUDIENCE: I'll go with real. + +PROFESSOR: OK. + +What's next? + +So some problems are +in R. All the ones + +that we care about are in r. + +So what's better than r? + +R means it's going to +terminate at some point, + +there is a running +time for the problem. + +What's the better than that? + +Exponential, OK. + +What does exponential mean? + +AUDIENCE: Exponential? + +PROFESSOR: Yup. + +So the running time +looks like what? + +AUDIENCE: 2 to the 10, or +something constant to the n? + +2 to the n of the C? + +PROFESSOR: For some +constant C, right? + +So it's not just 2 to the n. + +The moment you +have a 2 to the n, + +we're like, OK, +if you're already + +in this bad of a +situation, I don't + +care if this is a polynomial. + +I don't care if it's +an n or n to the 100, + +you're already +pretty much screwed, + +you're not going to solve +this before the world ends. + +So that's what +exponential means. + +Going to solve it, but +not before the world + +ends for most +practical problems. + +What's better than exponential? + +AUDIENCE: NP. + +PROFESSOR: OK, and +before we talk about NP, + +let's talk about the +easy case, the problems + +that we've talked about all +the time in the semester. + +AUDIENCE: May I ask +you a stupid question? + +What does NP stand for? + +PROFESSOR: It's not +a stupid question. + +It has a really hard to answer. + +So the one-sentence +answer is NP stands + +for non deterministic binomial. + +And we're going to go +over that at some point + +in the next few minutes. + +OK, so what problems +have we talked about? + +All the terms, except +for one problem, + +for the knapsack +problem, the entire term + +we talked about some +sort of problems. + +Polynomial. + +These are the +reasonably easy ones. + +So polynomial problems are those +where t of n is n to the C, + +so it's a binomial. + +The running time is a binomial +in terms of the input sites. + +Why does this matter? + +If you have a +polynomial algorithm, + +than if you double the +input, then the running time + +is going to be 2 to +the C times n to the C. + +So every time you +double the input, + +the running time will +increase by a constant factor. + +And you know what that is. + +If your problem is exponential, +then if you double the input, + +then the running time +increases quadratically. + +It's not a linear increase. + +Here it's a linear increase. + +The factor isn't 2, but it's +still a linear increase. + +Make sense? + +So that's why we like +these problems, at least + +we like them more +than anything else. + +So polynomial problems +are the nice and easy ones + +that we've talked about so far. + +What does NP stand for? + +Give me a practical definition. + +AUDIENCE: You can +check it [INAUDIBLE]. + +PROFESSOR: OK, so NP means +that we can write the verifier. + +I'm going to say exactly what +you said with different words. + +That takes a solution +to the problem. + +And of course, it has to +think the input to the problem + +and tells us is it correct +or is it not correct. + +And this very fire is NP. + +So the very fire runs +in polynomial time. + +Yes. + +So if the verifier runs +in polynomial time, + +what's the solution size +and what's the input size? + +AUDIENCE: I think the-- I mean, +the solution said it's like 01, + +right? + +PROFESSOR: If we have +decision problems. + +An algorithm that +solves an NP problem. + +If you run it +against the verifier, + +also has to convince you +that its answer is correct. + +So the problems that we +talked about in class + +were decidability problems +where you have to say, + +is it possible to do this? + +Yes or no. + +When you have a +verifier with you, + +then you have to output a string +that convinces the verifier + +that your answer is correct. + +So like if you +have a problem that + +says-- if you have three +sets, for example-- that says, + +given a logical expression, can +you assign variable values such + +that the expression is true? + +If I say yes, what +does that mean? + +That means nothing. + +How do I convince you +that my answer is correct? + +I will have to give you +the assignment, right? + +And then you can verify +in polynomial time + +if my answer is right or not. + +So the input to the +verifier, this solution, + +is not necessarily the decision. + +It's not just the +bit, yes or no. + +So if the verifier runs +in polynomial time, + +what's true about +the problem input + +and what's true about +the problem output which + +becomes an input +to the verifier? + +They have to be +polynomial in size. + +Otherwise, my +algorithm wouldn't be + +able to consume +them fast enough. + +So actually, polynomial +means that the running time + +is polynomial in the input size. + +So the input size is +automatically all set. + +But the solution has to be +polynomial in the input size + +as well. + +And if you're thinking +decision problems, + +you can be more rigorous +and call this a proof. + +So if this proof is +binomial in the input size, + +then if I'm really, +really lucky, + +I can take the +input to a problem, + +and I can flip coins and use +the corn results as bits, + +and put them together, +and create the proof. + +If I'm really, really lucky, +I'll get the right proof. + +Chances of that +happening almost zero, + +but if I'm really, really lucky, +conceptually I can get a proof. + +This is what a non-deterministic +polynomial means. + +It means that if you have +a magical machine where + +you can flip a coin, and +it will always be lucky, + +then you can output the +proof in polynomial time. + +So far so good? + +So this definition of a machine +that can flip random bits + +is really useful, because we can +use it to build a common sense + +proof that P is not NP. + +There is no real rigorous +math proof that P's not NP. + +That's worth a million dollars. + +There is no proof +that P equals NP. + +If you have proof +that P equals NP, then + +that's worth a lot more. + +And I will use that in +the common sense proof + +that I'm going to show you now. + +So we don't know if P is NP-- +get it right-- if P is NP + +or if P is not NP. + +This is an open problem, and +there's at least $1 million + +worth of prize money for it. + +Let's talk about +an algorithm where + +if you would know-- +so if you would + +be able to solve NP +problems in polynomial time, + +you would be able to +make a lot of money. + +A million dollars +is nothing compared + +to what you could make +if you could do that. + +So I'm going to use +that to convince you + +that nobody knows how to +solve NP problems in P time. + +Suppose you want to do +something really bad. + +Suppose you want to +impersonate a bank. + +So you guys probably +imagine that banks nowadays + +don't transfer +money to each other + +by sending trucks +with gold bars. + +They do that every once in +awhile, but most of the time + +the transfers happen very +quickly over the internet. + +So banks have a +secure connection, + +and they say, yo, give +me a billion dollars. + +I'll give it back to +you in a few days. + +Sure. + +Done deal. + +Now imagine what +you could do if you + +could impersonate +one of those banks. + +Sweet happy life in some +faraway place, right? + +What would it take to +impersonate another bank? + +It turns out that the +encryption algorithm that + +use to secure this links +is an algorithm called RSA. + +Do you guys remember that? + +Heard about it? + +So in RSA, each +party-- so each bank + +has a secret key that +consists of two numbers-- + +P and Q-- big prime numbers. + +And say each of these +are N-bit prime numbers. + +And then they have +a probably key. + +So they have a +number that announce + +that is N equals +P times Q. So this + +is announced to +the entire world. + +This is public. + +We went through this +[INAUDIBLE] set, right? + +So this rings a bell. + +They have to announce this +so that the other people can + +encrypt messages for them. + +If you want someone else to +be able to send you a message, + +you have to tell them your n. + +Now if you know P and Q, +you can decrypt messages. + +So you can pretend +you're the bank. + +Now let's set up a +problem in this way. + +Given a verifier that +does long division-- + +so we have a verifier that +the verifiers input is N, + +and some guess P, +P guess, right? + +So the verifier will +compute N modulo P. + +And if N modulo P is 0, +then it will say happy. + +Actually, it will say, +you're rich as hell. + +If it's not 0, then well, +tough luck, try again. + +So if you could make +this verifier happy, + +you could get P. So +given public information, + +you could get the +private information that + +would allow you to +impersonate the bank. + +This is called a factoring +problem by the way. + +So P and N are +usually 1024 bits. + +So the chances of doing +that with a coin flip, no. + +The chances of guessing it +are one in two to the 1024-- + +it's basically worse +than having to pick + +a random atom in the universe +and choosing the right one. + +So not going to happen. + +But if you had an algorithm +that takes a verifier + +and produces an input +that makes it happy, + +then you would +solve this problem, + +and you would +impersonate the bank, + +and you would +become really rich, + +and then the whole +world's economic system + +would be in a +terrible situation. + +AUDIENCE: P and Q +are primes, right? + +So couldn't you just +find all the primes? + +PROFESSOR: Well, so look at +it from this perspective, + +the economic system +still functions. + +It's not like everyone's +money disappeared somewhere. + +Therefore, nobody was +able to pull this off. + +AUDIENCE: Isn't there a +quantum algorithm to do it + +or that's something different? + +PROFESSOR: So this +assumes Turing machines. + +We're assuming regular +Turing machines. + +A quantum computer +breaks that abstraction. + +For practical purposes, if +you had a quantum computer + +that can manipulate +this many bits. + +Then you would break RSA, and +the world would go to hell. + +So hopefully by the time quantum +computers get this powerful, + +we'll invent new security +algorithms that replace them. + +But the fact that eCommerce +works now and that banks work + +means that nobody +is able to solve + +NP problems in polynomial time. + +So by the way, factoring is not +the hardest type of NP problem. + +Factoring is somewhere here. + +OK. + +Any questions about this part? + +AUDIENCE: So factoring +is not an NP problem? + +PROFESSOR: Factoring +is NP, but it's not + +the most difficult +type of NP problem. + +We'll get to those right now. + +So this is a common sense +proof not the math proof + +that NP is not P-- +that at least nobody + +knows how to solve NP +problems in polynomial time. + +So there are these NP problems +that if you think about it, + +the solution is +polynomial in size. + +We can write a verifier +in polynomial time. + +So why can't we write the +solver in polynomial time? + +If you're a very high picture +guy like managerial type, + +then you might think, +yeah why, can't you guys + +just figure this out? + +Like come up with an algorithm. + +Isn't that what you guys do? + +Well, so theory people +have been thinking + +about this for 40 years or more. + +So what do you do when +you think about something + +and you can't come +up with a solution? + +AUDIENCE: Say it's impossible? + +PROFESSOR: You try to +say that it's impossible. + +So you try to prove +that P is not NP. + +But if you fail to do that +too, what do you do next? + +AUDIENCE: Offer +a million dollars + +to someone who can do it. + +PROFESSOR: That too. + +That might help. + +That might help. + +Well, you complain that it's +really, really hard, right? + +You want to go back +to your boss or you + +want to go back to the world, +and say, we thought about this. + +It is true that with thought +about it for four years, + +but it's a really, +really hard problem. + +Well, so for +undecidable problems-- + +so for the whole +thing problems, they + +are able to convince the world +that nobody can solve this, + +so we're all good. + +So we couldn't come up with a +solution, because nobody can. + +Here, we can't prove +that P is not NP yet. + +So instead the next best +thing that theory people + +could come up with +is-- they saw, + +what are the hardest +kind of NP problems? + +Let's look at them and let's +see if we can solve them + +in some way. + +And they found +some problems here + +that are the +hardest NP problems. + +And they called them +NP-complete problems. + +And we'll see why +complete in a bit. + +So these are the hardest NP +problems that you can have. + +Factoring is not one of them. + +Factoring is not +with the cool kids, + +even though it +would make you rich. + +There are some problems +that are harder than that. + +OK so for these +NP-complete problems, + +turns out there are a +few hundred of them that + +would have practical +implications. + +So you wouldn't be able +to get rich right away, + +but still you'd be able to +solved the important problems + +that would save +companies a lot of money. + +So you think, if +there's a solution + +someone would come up with it. + +It also turns out that +they're all interrelated. + +So if you can solve one problem, +you can solve all of them. + +And you do that +through reductions, + +which we'll go over in a bit. + +But the bottom line +is there are hundreds + +of NP-complete problems. + +And if you solve one, then +you solved everything. + +For now theory people +are trying to say, + +look there are all +these problems. + +If anyone would solve +any of them, all of them + +would go away. + +Nobody was able to +solve any of them, + +so they must be +really, really hard. + +This is the best they +could come up with. + +This is NP complete. + +AUDIENCE: This is same lecture +that you-- any problem that's + +already [INAUDIBLE] transform +it into a different problem? + +PROFESSOR: Yeah. + +So if you have the +solution for one of them, + +you could transform all the +other ones into that problem + +just like we do with +graph transformations, + +solve it, use the solution for +it to solve all the other ones. + +So if anyone could solve any +of those hundreds of problems, + +we'd have the solution to +all of them in an instant. + +The fact that we don't +have a solution to them + +means that nobody was +able to solve any of them. + +AUDIENCE: Like there are some +problems like the chess problem + +that can be solved +exponential time. + +PROFESSOR: Those are different. + +Chess is here. + +AUDIENCE: So we can solve +chess though, right? + +It's just exponential time. + +Right? + +PROFESSOR: As far as I know, +because it's exponential time, + +there's no algorithm +that can actually + +look at the entire configuration +space, and tell if you can win + +or not. + +So solving chess, what's chess? + +Chess has given a board. + +Can I win or not +from this board? + +This would be very +useful in playing chess, + +because you start with +the initial board, + +and then for every +move you can make, + +you look at the +resulting board, and you + +say can I win or +not from that board. + +If you're in a board +configuration in which you + +can win, you don't want +to go to a configuration + +where you won't be +able to win anymore. + +So if you keep doing +this you eventually win. + +So it would be really nice +to have this algorithm. + +Yeah, we don't have it. + +We don't have it and +chess is unsolved. + +Wait. + +AUDIENCE: So only things +that are below P-- + +but there are some algorithms +that run in exponential time. + +They just take longer. + +PROFESSOR: So the problem +is what's the input size? + +Exponential in what? + +If it's going to be-- if the +running time is 2 to the n, + +and it's 10, then that's fine. + +But for chess its exponential +in the board configuration. + +And it turns out that there's +so many board configurations + +that we don't have +computers fast + +enough to solve the whole thing. + +So deep blue goes to +a level-- to a depth + +I think of somewhere around +15 and can barely competes + +with humans, but it's not +guaranteed to win all the time. + +So we don't have something that +has completely solved chess. + +AUDIENCE: So we can only +solve things below P then. + +PROFESSOR: We can only +solve things below P + +fast, reasonably fast. + +So what we care +about in this class + +is how do our algorithm scale. + +So do we have this or not? + +Does your algorithm +scale or not? + +The reason we don't like +algorithms that are after this + +is that for problem sizes that +are really small like 8, 10, + +or something small, +they're going to work. + +But the moment the problem +gets bigger and bigger, + +you're going to run +into a dead end. + +AUDIENCE: Well, can +you use DP on chess? + +PROFESSOR: You can +use DP until you + +get to an exponential algorithm. + +You might get to an +exponential algorithm + +where the exponent is better. + +So far all the smart +algorithms for chess + +have reduced the +c here, but they + +haven't been able to get +away from 2 to the n part. + +If you make c smaller, sure +it's going to run faster, + +and you can explore a +bigger part of the board. + +But you're still not +going to be able to run + +through the whole thing +before the world ends. + +That's a good thing +to think about. + +Will we solve chess +before the world + +ends with the current +algorithms and machines? + +No. + +AUDIENCE: I guess. + +Remember the Rubik's cube? + +Wasn't that bordering +exponential or something? + +I think Eric said that there +is order one solution where + +the constant factor +is really high. + +So that's different. + +raises I think Tetris is +here, but the Rubik's cube-- + +AUDIENCE: It's in +the P, isn't it? + +Yeah. + +PROFESSOR: There's +a solution that's + +order one with a high +constant [INAUDIBLE]. + +AUDIENCE: But our +brains can play chess. + +PROFESSOR: Sorry? + +Our brains-- + +AUDIENCE: We can play chess. + +PROFESSOR: Well, we can +play reasonably well, + +but if someone could +play optimally, + +they'd probably beat you. + +Yeah. + +AUDIENCE: Can someone +play optimally? + +[INAUDIBLE] + +AUDIENCE: What about +machine learning? + +PROFESSOR: Machine learning +problems are usually here. + +That's why they don't +scale, and that's + +why we've seen a lot of +interesting machine learning, + +but so far I can't talk +to my computer right. + +They can't make a +lot of progress, + +because they have these really +hard problems that they're + +working on. + +AUDIENCE: There's Siri, right. + +You can talk to Siri. + +PROFESSOR: Yeah OK. + +Sure. + +I think I've seen +on the Internet + +that it says some +awful things sometimes. + +So I wouldn't +consider that solved. + +So what does NP mean to +us like practical terms? + +Here's how I see it, you're +on an exam or in an interview, + +you start out with a problem. + +Suppose all the +possible problems + +are a graph, because +we work with graphs. + +You have your starting problem. + +This Is the problem that +you're trying to solve now. + +Then you have a few +destination nodes. + +Say you have merge sort. + +We know how to solve. + +If you can reduce your +problem to merge sort, + +then you're in a good position. + +You're writing your solution. + +You're out of the room. + +If you can reduce your problem +to a graph search algorithm, + +so to BFS or DFS, you're done. + +If you can reduce it to +shortest path, you're happy. + +You're done. + +If you can reduce it to a +dynamic programming problem + +that we understand, you're done. + +If you can somehow use hashing +or use divide and conquer + +with an algorithm that we +studied, you're also happy. + +So we have all these +destination points. + +And what you're +trying to do is you're + +trying to get from here all +the way to here via reductions. + +So suppose you see +three reductions + +that you could possibly do. + +You don't have time to +work on all three of them, + +so let's say you +choose the middle one, + +because this one seems +like it's the easiest one. + +So I'm going to +guess that this is + +the easiest one I can tackle. + +So now I'm going +to work on this. + +I'm going to put the +original problem aside. + +And I'm going to say if I can +solve this, then I'm happy. + +Now say this turns into +three more reductions. + +And this one looks promising. + +it's a hard problem. + +You have to do a few reductions. + +It doesn't work right away. + +But say I take this one +which looks promising, + +and I'm able to reduce +it to a happy problem. + +Reduction, reduction, reduction. + +I write this up. + +I'm done. + +Exam solved or interview +question solved. + +Now the problem +is what if instead + +of going on this path which +is reasonably happy, what if I + +go on a path that +looks like this? + +All the reductions that +I can see from there + +go really, really far +away from the problems + +that I know how to solve. + +Well you're going to +try some reductions, + +and eventually you're +going to run out of time. + +And this other interviewer +is going to say, yeah, + +do you have any +questions about us? + +Or the exam people will be like, +hey, can we have the exam back? + +We want to go home now. + +So this is a bad outcome. + +Up until now, all you had +was good destination points. + +So this is where +you want to reach. + +Now we have these NP-complete +problems that we know are hard. + +I've convinced you +hopefully that their hard. + +So if you know some +NP-complete problems, + +you also have some landmines. + +You have some places +where if you got there + +via reductions, not a good path. + +You want to backtrack and +think of something else. + +So for example if this +was an NP-complete problem + +like if this reduction +then was, oh yeah, + +solve [INAUDIBLE] +in polynomial time. + +Let's see. + +I don't know how to do that. + +The world tried really hard. + +Maybe I shouldn't try +this avenue on the exam. + +So if you know that +this is NP-complete. + +You stop right there. + +You don't waste anymore time. + +So this isn't time wasted. + +If you understand NP-complete, +and you read the CLRS chapter + +on NP-complete problems. + +Then you also have +some sad faces here. + +You have some land mines and +you know not to go there. + +So now your space that +you're looking through + +is a lot more bonded. + +Hopefully, you're going to +have better chances of finding + +a happy path, because not only +you have some destinations, + +but you have some places that +you know you shouldn't go to. + +So this is the point +of NP-complete. + +You're probably really +busy at the end of the term + +as we all are, so I'm +guessing you're not + +going to have time to read +CLRS beyond what we really + +ask you to read now. + +But after you're done, +do yourself a favor. + +For the sake of your +future interviews + +and general happy +programming life, + +read the NP-complete +chapter in CLRS. + +Read the problem statements +and understand them. + +Don't worry about the proofs. + +Don't worry about the reductions +that say their NP-complete. + +Read the statements. + +Believe CLRS that +it's NP-complete. + +And remember that whenever +you solve a problem, + +you want to stay +away from those. + +So those will be your landmines. + +Those will be your sad spots. + +Guaranteed, after you +do that, your interviews + +will go a lot better, +because you'll + +be faster at solving problems. + +And that's what we +really care about. + +So that's why NP-complete +is relevant in real life. + +It gives us these data points. + +Makes sense? + +All right, I want to talk about +one NP complete problem that's + +really important. + +And that is SAT. + +So SAT means satisfiability. + +So given the logical +expression, find some values + +for the variables +that make it true. + +Let me grab an +example from here. + +So in SAT your +expressions come out + +in a really nice form, so +parsing isn't a big deal. + +The way they come +out is there a bunch + +of terms separated by AND. + +So your expressions +look like this-- and, + +and, and-- say we +have four terms. + +These look good. + +So you have some +terms, say n terms, + +and they're all +separated by ANDs. + +This is a term. + +In a term you have +variables separated by ORs. + +Nothing else. + +Just either the +variable or a variable + +with a NOT in front of it. + +So say x1 OR NOT x2, NOT x1 OR +x4, NOT x3 or x4, and X2 OR X4. + +So this is called the +Conjuntive Normal Form, CNF. + +The reason this is really +nice to work with is-- OK, + +you just have some +variables here. + +You know that these +are all joined by AND, + +so you're going to have to +make all these terms true. + +And then you have ORs inside. + +So you know that for +every term, at least one + +of the things inside +the term has to be true. + +And that's it. + +This is the problem. + +This is SAT. + +You have n terms. + +And then the number of variables +that you have inside is k. + +So you have at most k +variables in a term. + +This k looks like +a constant factor. + +But it's so important +that in fact it + +shows up in the +name of the problem. + +The problem is called k-SAT. + +And there are two +values of k for which + +the problem is important. + +There's 2-SAT, +and there's 3-SAT. + +2-SAT is polynomial. + +We have a solution that runs +in order and time in fact. + +Really good. + +AUDIENCE: But you're +saying that to make-- + +you're actually rearranging +things or you're just-- + +PROFESSOR: So I have to come +up with values for x1, x2, x3, + +and four, so that the +whole thing is true. + +And the expression +is already arranged + +in this nice form for you. + +AUDIENCE: It's just-- +it seems like order + +and, because you're just +evaluating to block, right? + +PROFESSOR: Well, no, you have +to come up with the values. + +AUDIENCE: Oh, I know. + +I know. + +But like-- + +PROFESSOR: OK and this +seems really easy, right? + +Well, wait for it. + +Wait for it. + +2-SAT is polynomial. + +3-SAT is NP-complete. + +So if you solve it, you're +in turn for a Turing reward, + +or you can become +really, really rich. + +So n-SAT can be +reduced to 3-SAT. + +So for anything +bigger than three, + +n-SAT can be reduced to 3-SAT +using reasonable reduction. + +So the input size +won't explode too much. + +So why is this important. + +This basically shows us +that 3-SAT is NP-complete. + +And I can make a +three-minute proof + +that 3-SAT is NP-complete. + +Let's take that verifier +guy that we have there. + +A verifier wants the +input, which already have + +and the proof. + +Let's write the +verifier as a circuit + +that takes the input +and the proof as bits. + +Those are input to the circuit. + +The circuit is going to +evaluate to true or false. + +Now that we have a circuit, +it's easy to turn that + +into a logical expression. + +Turn AND gate and OR gate +into-- and ANDs and ORs, + +and then reduce N-SAT to +3-SAT and get one of these. + +If you can solve +3-SAT, then you can + +compute values for +the proof bits. + +Bam. + +That's it. + +So I take the verifier and +I turn it into a circuit. + +The circuit is all logic gates. + +And then it has some inputs, +the original problem input + +and the proof. + +These are represented +as a series of bits, + +and they're all +inputs in the circuit. + +If the algorithm +is polynomial time, + +then the circuit also has to be +polynomial in the input size. + +Proof already has to be +polynomial in the input size, + +so we're all good. + +We're all in polynomial world. + +Now we take this +circuit, and we turn it + +into a logical expression. + +Sorry not logical, logic, also +known as a Boolean expression. + +So the input bits become +Boolean variables, + +and then we express gates as +Boolean functions-- AND, OR, + +NOT, whatever we want. + +And this is going to +give us some expression. + +That expression is going to map +to N-SAT for some value of n. + +So then we're going to +take this expression, + +and we're going to +reduce it to 3-SAT. + +So actually we're going to +reduce the expression to 3-CNF + +and then run 3-SAT on it. + +The expression will +be reduced to 3-CNF. + +So to something that +looks like this, + +except you have three +variables inside everything. + +Once it's in 3-CNF, you +can run 3-SAT on it. + +If it is satisfiable, +then 3-SAT has + +to give us some values +here for the variables. + +Some of the variables are +the problem input-- Sorry + +the problem input gets +hard coded in the circuit. + +Sorry. + +Not thinking here-- +hard coded in circuit, + +because we don't want it to +tell us what the input is. + +And then the proof is +encoded as a series + +of bits, which are +inputs in the circuit. + +OK. + +So problem hard coded, proofs +are inputs in the circuit. + +We've taken the circuits, turned +it into an input for 3-SAT. + +If 3-SAT says there is a +valid variable assignment, + +then that assignment tells me +what the bits are in the proof. + +So that means I can take the +proof, feed it to the verifier. + +The verifier will +say it's happy, + +so we solved the problem. + +And this is true for +any NP-complete problem. + +NP-complete means it has +to have a verifier that + +runs in polynomial time. + +So I have to be able +to follow this process. + +So for the factoring +problem, for example, I + +would take this +modulo algorithm, + +I would express it as a circuit. + +The bits of P +would be the input. + +I take that circuit and I turn +into a 3-CNF formula, run it + +on 3-SAT. + +The variable values for +which the circuit happy + +are the bits of P that make up. + +So they're the bits of P. +They make up a factor of n. + +So if I can run 3-SAT fast +enough to get an answer, + +then I have P and +I have factor of n. + +And I've become really, really +rich, and bye guys, I'm gone. + +AUDIENCE: For each +of those expressions, + +you said you make +that circuit n. + +You've got all +these inputs, which + +are x1, x2, +everything like that. + +Could you just go through +every possible combination? + +PROFESSOR: That's +exponential, right? + +That's two to the n, where +n is number of variables. + +And the number of +variables can be + +proportional to the +number of terms. + +AUDIENCE: Yeah. + +That would be fine with it. + +PROFESSOR: So that +means you have + +an exponential running time. + +It's not polynomial, +which is reassuring, + +because otherwise it would mean +that the whole world has been + +spinning their wheels around +nothing all this time, right? + +So it's reassuring +that you can't + +find the solution in two +minutes to this problem. + +In fact, so far I've been +trying to convince you + +that you should not +attempt to solve + +this problem in real +time, so not on exam time, + +not on [INAUDIBLE] time, +nor anywhere else where time + +actually matters. + +You guys bored? + +Maybe. + +Well, so there's +this proof that's + +not too hard to follow that +says that if you solve 3-SAT + +you have solved any +NP-complete problem by turning + +the verifier into a +logical expression. + +That's what it comes down to. + +Now 2-SAT is polynomial. + +And if you guys want, we +can go through the solution. + +If not, we can skip that. + +But this tiny difference +here, how many variables + +you're allowed +inside, which looks + +like it might be a constant +factor in an algorithm + +actually makes the difference +between a very easy problem, + +a problem that's in P, and +the hardest problem in NP. + +So 2-SAT is order n, +so it's somewhere here. + +3-SAT is all the way here. + +Small difference how +many variables you're + +allowed, two or three. + +Makes all the +difference in the world. + +AUDIENCE: There are logic +reductions you can make, right? + +PROFESSOR: There are +optimizations that you + +can make. + +And there are some +people who do research + +on how to solve 3-SAT in +a reasonably fast time. + +Because if you solve +3-SAT, any problem + +can be reduced to 3-SAT. + +All right, we have a feeling +that we're not going to be able + +to solve this in +polynomial time, + +because a lot of people tried, +but some researchers are hoping + +that well maybe you can solve +3-SAT in order of 2 to the n + +to the power of 0.00001, +which exponential, right? + +But you can solve many +problems with this. + +Active research, so far I don't +think they've come very far. + +Actually, I shouldn't +say that, because if you + +apply the brute +force algorithm, then + +you die at about 20 variables. + +State of the art 3-SAT +solving algorithms, + +I think it can handle +1,000 to 10,000 variables + +in a reasonable time, +like a few hours. + +There progress. + +And that is all by doing the +reductions that you said. + +You see some optimizations that +you can make in the expression. + +You draw some +inferences, and you + +explore the possible +configurations, + +taking us part way. + +So there's a lot of active +research going in that area + +too. + +So far, they didn't get here. + +AUDIENCE: That's almost solving +NP-complete problem then, + +right? + +PROFESSOR: Well, +yeah, the thing is + +in the end we care about +practical solutions, right? + +So they're hoping to get +to a practical solution. + +AUDIENCE: Well, a few +hours is pretty practical. + +So that's for some problems. + +Obviously they didn't +solve factoring, right? + +If they would have solved +1,000-bit factoring in a few + +hours, then we +would have noticed. + +AUDIENCE: Maybe. + +Seriously, OK. + +PROFESSOR: We +would have noticed. + +So far so good? + +Any questions on this stuff? + +So I want to reemphasize in +two minutes, the reduction + +part of this. + +So the reason why we +can solve, once we solve + +one NP-complete problem, +we solve all the other ones + +is reductions. + +So we've done a lot of graph +transformations in this class. + +We had three recitations and two +or three exam problems on that, + +and I think we had some +homework problems on it + +too-- a lot of graph +transformations. + +Graph transformations +are just reductions. + +You take some problem that looks +hard, and you do some magic, + +and you build a graph that +represents that problem, + +and you run shortest path on it. + +Then you take the output for +the shortest path algorithm, + +and you turn it into a solution +to the initial problem. + +This means that we've +reduced those problems + +to shortest path. + +Well, you don't have to +reduce to shortest path. + +If you have a problem that +you know how to solve, + +you can take any other +problem and reduce to it, + +and you've solved +that other problem. + +So basically, here, if you +have your starting problem, + +shortest path is +just one smiley face. + +As long as you arrive +to any smiley face, + +you're in good shape. + +Of course, you +have to be careful + +that while you're +doing you're reduction, + +your problem size +doesn't explode. + +So for example, if you take this +problem-- if you take 3-SAT-- + +if you take a 3-CNF +expression, and you reduce it + +to the graph that has +3 to the n vertices, + +and then you try to +run [INAUDIBLE] on it, + +it was the running +time, 3 to the n. + +Now I've got a new +polynomial, right? + +So when you do the +reductions, you + +have to be careful about what +happens to your input size. + +And that's about it. + +This is complexity theory. + +It's basically one +big excuse for why + +we can't solve some +problems that are hard. \ No newline at end of file diff --git a/tHttGDNmgKI.txt b/tHttGDNmgKI.txt new file mode 100644 index 0000000000000000000000000000000000000000..08967a3b65b3c3413bfd26725e9f404ec75a4478 --- /dev/null +++ b/tHttGDNmgKI.txt @@ -0,0 +1,11931 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Um, I want to continue our discourse + + align:start position:0% +Um, I want to continue our discourse + + + align:start position:0% +Um, I want to continue our discourse +about u musicals especially as a way of + + align:start position:0% +about u musicals especially as a way of + + + align:start position:0% +about u musicals especially as a way of +trying to lead into the two remarkable + + align:start position:0% +trying to lead into the two remarkable + + + align:start position:0% +trying to lead into the two remarkable +in many ways landmark films we're going + + align:start position:0% +in many ways landmark films we're going + + + align:start position:0% +in many ways landmark films we're going +to juxtapose this evening. Remember that + + align:start position:0% +to juxtapose this evening. Remember that + + + align:start position:0% +to juxtapose this evening. Remember that +our plan here is to juxtapose one film, + + align:start position:0% +our plan here is to juxtapose one film, + + + align:start position:0% +our plan here is to juxtapose one film, +a classic instance, even a culminating + + align:start position:0% +a classic instance, even a culminating + + + align:start position:0% +a classic instance, even a culminating +instance of the studio era and of the mu + + align:start position:0% +instance of the studio era and of the mu + + + align:start position:0% +instance of the studio era and of the mu +tradition of the musical in the studio + + align:start position:0% +tradition of the musical in the studio + + + align:start position:0% +tradition of the musical in the studio +era against another kind of musical that + + align:start position:0% +era against another kind of musical that + + + align:start position:0% +era against another kind of musical that +appears after the advent of television + + align:start position:0% +appears after the advent of television + + + align:start position:0% +appears after the advent of television +and after the studio system has begun to + + align:start position:0% +and after the studio system has begun to + + + align:start position:0% +and after the studio system has begun to +break apart in and especially a uh after + + align:start position:0% +break apart in and especially a uh after + + + align:start position:0% +break apart in and especially a uh after +the uh the the uh fundamental + + align:start position:0% +the uh the the uh fundamental + + + align:start position:0% +the uh the the uh fundamental +transformation that the audience + + align:start position:0% +transformation that the audience + + + align:start position:0% +transformation that the audience +underwent. + + align:start position:0% +underwent. + + + align:start position:0% +underwent. +migrating from an habitual, a regular, a + + align:start position:0% +migrating from an habitual, a regular, a + + + align:start position:0% +migrating from an habitual, a regular, a +weekly relationship to Hollywood films + + align:start position:0% +weekly relationship to Hollywood films + + + align:start position:0% +weekly relationship to Hollywood films +to essentially a blockbuster + + align:start position:0% +to essentially a blockbuster + + + align:start position:0% +to essentially a blockbuster +relationship in which they would attend + + align:start position:0% +relationship in which they would attend + + + align:start position:0% +relationship in which they would attend +the movies. The vast majority of + + align:start position:0% +the movies. The vast majority of + + + align:start position:0% +the movies. The vast majority of +Americans would attend the movies only + + align:start position:0% +Americans would attend the movies only + + + align:start position:0% +Americans would attend the movies only +once or twice a year. And if you think + + align:start position:0% +once or twice a year. And if you think + + + align:start position:0% +once or twice a year. And if you think +about the implications of that, that + + align:start position:0% +about the implications of that, that + + + align:start position:0% +about the implications of that, that +fact alone will explain how profoundly + + align:start position:0% +fact alone will explain how profoundly + + + align:start position:0% +fact alone will explain how profoundly +the movie industry was transformed. + + align:start position:0% +the movie industry was transformed. + + + align:start position:0% +the movie industry was transformed. +Incidentally, I should mention to you + + align:start position:0% +Incidentally, I should mention to you + + + align:start position:0% +Incidentally, I should mention to you +that this is still not an idea that has + + align:start position:0% +that this is still not an idea that has + + + align:start position:0% +that this is still not an idea that has +been fully understood by what I'll call + + align:start position:0% +been fully understood by what I'll call + + + align:start position:0% +been fully understood by what I'll call +traditional film historians who are so + + align:start position:0% +traditional film historians who are so + + + align:start position:0% +traditional film historians who are so +locked into an idea that film must + + align:start position:0% +locked into an idea that film must + + + align:start position:0% +locked into an idea that film must +resemble the kind of thing that I that I + + align:start position:0% +resemble the kind of thing that I that I + + + align:start position:0% +resemble the kind of thing that I that I +uh learned that I watched when I grew up + + align:start position:0% +uh learned that I watched when I grew up + + + align:start position:0% +uh learned that I watched when I grew up +as a boy or as a as or as a young as a + + align:start position:0% +as a boy or as a as or as a young as a + + + align:start position:0% +as a boy or as a as or as a young as a +young girl. And now that a tradition of + + align:start position:0% +young girl. And now that a tradition of + + + align:start position:0% +young girl. And now that a tradition of +scholarship has talked about that is to + + align:start position:0% +scholarship has talked about that is to + + + align:start position:0% +scholarship has talked about that is to +say those films that never were shown on + + align:start position:0% +say those films that never were shown on + + + align:start position:0% +say those films that never were shown on +television or were never made for + + align:start position:0% +television or were never made for + + + align:start position:0% +television or were never made for +television uh uh it causes a problem + + align:start position:0% +television uh uh it causes a problem + + + align:start position:0% +television uh uh it causes a problem +because what these what these scholars + + align:start position:0% +because what these what these scholars + + + align:start position:0% +because what these what these scholars +tend to do is they ignore the social + + align:start position:0% +tend to do is they ignore the social + + + align:start position:0% +tend to do is they ignore the social +context within which the function of the + + align:start position:0% +context within which the function of the + + + align:start position:0% +context within which the function of the +movies began to be transformed. Partly + + align:start position:0% +movies began to be transformed. Partly + + + align:start position:0% +movies began to be transformed. Partly +there was a kind of hostility on on the + + align:start position:0% +there was a kind of hostility on on the + + + align:start position:0% +there was a kind of hostility on on the +on the part of many older film scholars + + align:start position:0% +on the part of many older film scholars + + + align:start position:0% +on the part of many older film scholars +toward the notion that television might + + align:start position:0% +toward the notion that television might + + + align:start position:0% +toward the notion that television might +be a worthy place to look for uh a + + align:start position:0% +be a worthy place to look for uh a + + + align:start position:0% +be a worthy place to look for uh a +valuable cinematic narrative. And it + + align:start position:0% +valuable cinematic narrative. And it + + + align:start position:0% +valuable cinematic narrative. And it +took a long time before the film scholar + + align:start position:0% +took a long time before the film scholar + + + align:start position:0% +took a long time before the film scholar +the film scholarly the com the the + + align:start position:0% +the film scholarly the com the the + + + align:start position:0% +the film scholarly the com the the +community of film scholars even a part + + align:start position:0% +community of film scholars even a part + + + align:start position:0% +community of film scholars even a part +of it was ready to acknowledge that + + align:start position:0% +of it was ready to acknowledge that + + + align:start position:0% +of it was ready to acknowledge that +television was also an environment in + + align:start position:0% +television was also an environment in + + + align:start position:0% +television was also an environment in +which in which cinema what we might call + + align:start position:0% +which in which cinema what we might call + + + align:start position:0% +which in which cinema what we might call +cinema audiovisisual narrative uh could + + align:start position:0% +cinema audiovisisual narrative uh could + + + align:start position:0% +cinema audiovisisual narrative uh could +be uh looked at taken seriously and so + + align:start position:0% +be uh looked at taken seriously and so + + + align:start position:0% +be uh looked at taken seriously and so +forth and of course today it's taken for + + align:start position:0% +forth and of course today it's taken for + + + align:start position:0% +forth and of course today it's taken for +granted by many commentators many of + + align:start position:0% +granted by many commentators many of + + + align:start position:0% +granted by many commentators many of +them no longer even with a cultural + + align:start position:0% +them no longer even with a cultural + + + align:start position:0% +them no longer even with a cultural +memory of the studio era that what goes + + align:start position:0% +memory of the studio era that what goes + + + align:start position:0% +memory of the studio era that what goes +on on television that shows like + + align:start position:0% +on on television that shows like + + + align:start position:0% +on on television that shows like +Breaking Bad or The Sopranos are the + + align:start position:0% +Breaking Bad or The Sopranos are the + + + align:start position:0% +Breaking Bad or The Sopranos are the +supreme forms of audiovisisual uh + + align:start position:0% +supreme forms of audiovisisual uh + + + align:start position:0% +supreme forms of audiovisisual uh +entertainment in our society. This too + + align:start position:0% +entertainment in our society. This too + + + align:start position:0% +entertainment in our society. This too +is a little uh oversimpl radically + + align:start position:0% +is a little uh oversimpl radically + + + align:start position:0% +is a little uh oversimpl radically +oversimplified and I will return to + + align:start position:0% +oversimplified and I will return to + + + align:start position:0% +oversimplified and I will return to +these questions a bit later when we when + + align:start position:0% +these questions a bit later when we when + + + align:start position:0% +these questions a bit later when we when +I when we talk when I talk about the + + align:start position:0% +I when we talk when I talk about the + + + align:start position:0% +I when we talk when I talk about the +westerns uh in uh and about and about + + align:start position:0% +westerns uh in uh and about and about + + + align:start position:0% +westerns uh in uh and about and about +film in the 70s uh in two weeks. I want + + align:start position:0% +film in the 70s uh in two weeks. I want + + + align:start position:0% +film in the 70s uh in two weeks. I want +to continue our discourse about uh about + + align:start position:0% +to continue our discourse about uh about + + + align:start position:0% +to continue our discourse about uh about +the musical then first by giving you a + + align:start position:0% +the musical then first by giving you a + + + align:start position:0% +the musical then first by giving you a +very brief uh uh perspective drawn from + + align:start position:0% +very brief uh uh perspective drawn from + + + align:start position:0% +very brief uh uh perspective drawn from +the film scholar Leo Brody whose essay + + align:start position:0% +the film scholar Leo Brody whose essay + + + align:start position:0% +the film scholar Leo Brody whose essay +the aesthetics of connection uh is + + align:start position:0% +the aesthetics of connection uh is + + + align:start position:0% +the aesthetics of connection uh is +required reading I think for this week + + align:start position:0% +required reading I think for this week + + + align:start position:0% +required reading I think for this week +in any case for this week or next week + + align:start position:0% +in any case for this week or next week + + + align:start position:0% +in any case for this week or next week +uh and he talks in that essay among + + align:start position:0% +uh and he talks in that essay among + + + align:start position:0% +uh and he talks in that essay among +other things very richly about the + + align:start position:0% +other things very richly about the + + + align:start position:0% +other things very richly about the +musical and about ways of thinking about + + align:start position:0% +musical and about ways of thinking about + + + align:start position:0% +musical and about ways of thinking about +the musical and I'm I'm borrowing from + + align:start position:0% +the musical and I'm I'm borrowing from + + + align:start position:0% +the musical and I'm I'm borrowing from +an argument he makes in that in that + + align:start position:0% +an argument he makes in that in that + + + align:start position:0% +an argument he makes in that in that +remarkable essay he makes a distinction + + align:start position:0% +remarkable essay he makes a distinction + + + align:start position:0% +remarkable essay he makes a distinction +in that essay or a or a a series of + + align:start position:0% +in that essay or a or a a series of + + + align:start position:0% +in that essay or a or a a series of +comparisons between a stair and Kelly, + + align:start position:0% +comparisons between a stair and Kelly, + + + align:start position:0% +comparisons between a stair and Kelly, +the two great male leads we associate + + align:start position:0% +the two great male leads we associate + + + align:start position:0% +the two great male leads we associate +with the American film musical. And he + + align:start position:0% +with the American film musical. And he + + + align:start position:0% +with the American film musical. And he +sees them very helpfully as contrasting + + align:start position:0% +sees them very helpfully as contrasting + + + align:start position:0% +sees them very helpfully as contrasting +figures illustrating what we might call + + align:start position:0% +figures illustrating what we might call + + + align:start position:0% +figures illustrating what we might call +contrasting elements or contrasting + + align:start position:0% +contrasting elements or contrasting + + + align:start position:0% +contrasting elements or contrasting +tendencies within the musical form. Uh + + align:start position:0% +tendencies within the musical form. Uh + + + align:start position:0% +tendencies within the musical form. Uh +think if you think about a stare and you + + align:start position:0% +think if you think about a stare and you + + + align:start position:0% +think if you think about a stare and you +saw him in one of his classic + + align:start position:0% +saw him in one of his classic + + + align:start position:0% +saw him in one of his classic +performances at the end of our last + + align:start position:0% +performances at the end of our last + + + align:start position:0% +performances at the end of our last +lecture in that sequence cheek to cheek. + + align:start position:0% +lecture in that sequence cheek to cheek. + + + align:start position:0% +lecture in that sequence cheek to cheek. +If you think about a stare in this way, + + align:start position:0% +If you think about a stare in this way, + + + align:start position:0% +If you think about a stare in this way, +you can get uh from that sequence, you + + align:start position:0% +you can get uh from that sequence, you + + + align:start position:0% +you can get uh from that sequence, you +can get something of what uh we Brody + + align:start position:0% +can get something of what uh we Brody + + + align:start position:0% +can get something of what uh we Brody +had in mind. He talks about he reminds + + align:start position:0% +had in mind. He talks about he reminds + + + align:start position:0% +had in mind. He talks about he reminds +us that a stare often dances um almost + + align:start position:0% +us that a stare often dances um almost + + + align:start position:0% +us that a stare often dances um almost +always dances and this is a partial ex a + + align:start position:0% +always dances and this is a partial ex a + + + align:start position:0% +always dances and this is a partial ex a +partial exception in the film you saw + + align:start position:0% +partial exception in the film you saw + + + align:start position:0% +partial exception in the film you saw +tonight, only a partial one, but but + + align:start position:0% +tonight, only a partial one, but but + + + align:start position:0% +tonight, only a partial one, but but +almost always we see a stair dancing in + + align:start position:0% +almost always we see a stair dancing in + + + align:start position:0% +almost always we see a stair dancing in +places that seem intended for + + align:start position:0% +places that seem intended for + + + align:start position:0% +places that seem intended for +performance. to say we won't see + + align:start position:0% +performance. to say we won't see + + + align:start position:0% +performance. to say we won't see +uh a stair dancing in the middle of a + + align:start position:0% +uh a stair dancing in the middle of a + + + align:start position:0% +uh a stair dancing in the middle of a +cornfield or dancing up the side of the + + align:start position:0% +cornfield or dancing up the side of the + + + align:start position:0% +cornfield or dancing up the side of the +Empire State Building as Frank Sinatra + + align:start position:0% +Empire State Building as Frank Sinatra + + + align:start position:0% +Empire State Building as Frank Sinatra +and Jean Kelly do in a in a in a + + align:start position:0% +and Jean Kelly do in a in a in a + + + align:start position:0% +and Jean Kelly do in a in a in a +musical. It's called On the Town. Uh and + + align:start position:0% +musical. It's called On the Town. Uh and + + + align:start position:0% +musical. It's called On the Town. Uh and +it's one it's one of the wonderful MGM + + align:start position:0% +it's one it's one of the wonderful MGM + + + align:start position:0% +it's one it's one of the wonderful MGM +musicals. Uh Kelly and Sinatra are + + align:start position:0% +musicals. Uh Kelly and Sinatra are + + + align:start position:0% +musicals. Uh Kelly and Sinatra are +dancing in spaces that are inappropriate + + align:start position:0% +dancing in spaces that are inappropriate + + + align:start position:0% +dancing in spaces that are inappropriate +for dance. But almost all of stairs + + align:start position:0% +for dance. But almost all of stairs + + + align:start position:0% +for dance. But almost all of stairs +dances take place either in literal + + align:start position:0% +dances take place either in literal + + + align:start position:0% +dances take place either in literal +performance spaces or in public + + align:start position:0% +performance spaces or in public + + + align:start position:0% +performance spaces or in public +environments that seem as if they're + + align:start position:0% +environments that seem as if they're + + + align:start position:0% +environments that seem as if they're +quai stage or or or dance environments. + + align:start position:0% +quai stage or or or dance environments. + + + align:start position:0% +quai stage or or or dance environments. +Uh in other words, he's he dances in + + align:start position:0% +Uh in other words, he's he dances in + + + align:start position:0% +Uh in other words, he's he dances in +spaces that we expect for dance and and + + align:start position:0% +spaces that we expect for dance and and + + + align:start position:0% +spaces that we expect for dance and and +he doesn't violate those spaces in some + + align:start position:0% +he doesn't violate those spaces in some + + + align:start position:0% +he doesn't violate those spaces in some +way. Uh he often in his films plays + + align:start position:0% +way. Uh he often in his films plays + + + align:start position:0% +way. Uh he often in his films plays +either a professional dancer or a + + align:start position:0% +either a professional dancer or a + + + align:start position:0% +either a professional dancer or a +professional performer of some kind. So + + align:start position:0% +professional performer of some kind. So + + + align:start position:0% +professional performer of some kind. So +when he segways into his performances + + align:start position:0% +when he segways into his performances + + + align:start position:0% +when he segways into his performances +there's a kind of natural connection. Um + + align:start position:0% +there's a kind of natural connection. Um + + + align:start position:0% +there's a kind of natural connection. Um +uh he's almost always very fancily + + align:start position:0% +uh he's almost always very fancily + + + align:start position:0% +uh he's almost always very fancily +dressed as you saw in tonight's + + align:start position:0% +dressed as you saw in tonight's + + + align:start position:0% +dressed as you saw in tonight's +sequence. Sometimes very often dancing + + align:start position:0% +sequence. Sometimes very often dancing + + + align:start position:0% +sequence. Sometimes very often dancing +in tux and tails uh but in any case in + + align:start position:0% +in tux and tails uh but in any case in + + + align:start position:0% +in tux and tails uh but in any case in +formal dress of some kind. Uh so he + + align:start position:0% +formal dress of some kind. Uh so he + + + align:start position:0% +formal dress of some kind. Uh so he +dances in spaces appropriate for dance + + align:start position:0% +dances in spaces appropriate for dance + + + align:start position:0% +dances in spaces appropriate for dance +dressed up in a kind of in a kind of + + align:start position:0% +dressed up in a kind of in a kind of + + + align:start position:0% +dressed up in a kind of in a kind of +formal way play uh in often playing a + + align:start position:0% +formal way play uh in often playing a + + + align:start position:0% +formal way play uh in often playing a +professional dancer or performer. Um but + + align:start position:0% +professional dancer or performer. Um but + + + align:start position:0% +professional dancer or performer. Um but +there's an immense grace and energy in + + align:start position:0% +there's an immense grace and energy in + + + align:start position:0% +there's an immense grace and energy in +his in his dancing. He's one of the + + align:start position:0% +his in his dancing. He's one of the + + + align:start position:0% +his in his dancing. He's one of the +great dancers in in as many would say + + align:start position:0% +great dancers in in as many would say + + + align:start position:0% +great dancers in in as many would say +the greatest dancer who ever performed + + align:start position:0% +the greatest dancer who ever performed + + + align:start position:0% +the greatest dancer who ever performed +in American movies. Uh and uh one way to + + align:start position:0% +in American movies. Uh and uh one way to + + + align:start position:0% +in American movies. Uh and uh one way to +talk about what the attractions of what + + align:start position:0% +talk about what the attractions of what + + + align:start position:0% +talk about what the attractions of what +he's doing is we can say that what he + + align:start position:0% +he's doing is we can say that what he + + + align:start position:0% +he's doing is we can say that what he +embodies is a is the principle of grace + + align:start position:0% +embodies is a is the principle of grace + + + align:start position:0% +embodies is a is the principle of grace +under constraint. Like a great baseball + + align:start position:0% +under constraint. Like a great baseball + + + align:start position:0% +under constraint. Like a great baseball +pitcher. Look, a lot of people can throw + + align:start position:0% +pitcher. Look, a lot of people can throw + + + align:start position:0% +pitcher. Look, a lot of people can throw +the ball 97 miles an hour, but only a + + align:start position:0% +the ball 97 miles an hour, but only a + + + align:start position:0% +the ball 97 miles an hour, but only a +very small number of people of pitchers + + align:start position:0% +very small number of people of pitchers + + + align:start position:0% +very small number of people of pitchers +who make a lot of money can throw a ball + + align:start position:0% +who make a lot of money can throw a ball + + + align:start position:0% +who make a lot of money can throw a ball +97 miles an hour and control where it + + align:start position:0% +97 miles an hour and control where it + + + align:start position:0% +97 miles an hour and control where it +goes. And we can say that that kind of + + align:start position:0% +goes. And we can say that that kind of + + + align:start position:0% +goes. And we can say that that kind of +athletic power to a lot of athletics + + align:start position:0% +athletic power to a lot of athletics + + + align:start position:0% +athletic power to a lot of athletics +involves this where you're where you're + + align:start position:0% +involves this where you're where you're + + + align:start position:0% +involves this where you're where you're +trying to control um uh tremendous + + align:start position:0% +trying to control um uh tremendous + + + align:start position:0% +trying to control um uh tremendous +physical energy and the physical energy + + align:start position:0% +physical energy and the physical energy + + + align:start position:0% +physical energy and the physical energy +has to be constrained in certain ways + + align:start position:0% +has to be constrained in certain ways + + + align:start position:0% +has to be constrained in certain ways +and part of what we admire about the + + align:start position:0% +and part of what we admire about the + + + align:start position:0% +and part of what we admire about the +expression of that physical energy is + + align:start position:0% +expression of that physical energy is + + + align:start position:0% +expression of that physical energy is +how constrained or graceful it could be + + align:start position:0% +how constrained or graceful it could be + + + align:start position:0% +how constrained or graceful it could be +it can become. There are many people who + + align:start position:0% +it can become. There are many people who + + + align:start position:0% +it can become. There are many people who +make who have made analogies between a + + align:start position:0% +make who have made analogies between a + + + align:start position:0% +make who have made analogies between a +stairs dancing and what great basketball + + align:start position:0% +stairs dancing and what great basketball + + + align:start position:0% +stairs dancing and what great basketball +players do showing showing tremendous + + align:start position:0% +players do showing showing tremendous + + + align:start position:0% +players do showing showing tremendous +physical energy but also a kind of + + align:start position:0% +physical energy but also a kind of + + + align:start position:0% +physical energy but also a kind of +gracefulness uh uh within the + + align:start position:0% +gracefulness uh uh within the + + + align:start position:0% +gracefulness uh uh within the +constraints that are imposed upon them + + align:start position:0% +constraints that are imposed upon them + + + align:start position:0% +constraints that are imposed upon them +by the lines on the court by the demands + + align:start position:0% +by the lines on the court by the demands + + + align:start position:0% +by the lines on the court by the demands +of the basket and and so by the claims + + align:start position:0% +of the basket and and so by the claims + + + align:start position:0% +of the basket and and so by the claims +of gravity when they jump and so forth + + align:start position:0% +of gravity when they jump and so forth + + + align:start position:0% +of gravity when they jump and so forth +uh and I I make illusion to these uh + + align:start position:0% +uh and I I make illusion to these uh + + + align:start position:0% +uh and I I make illusion to these uh +non-dance analogies because so so many + + align:start position:0% +non-dance analogies because so so many + + + align:start position:0% +non-dance analogies because so so many +people seem to respond more fully to + + align:start position:0% +people seem to respond more fully to + + + align:start position:0% +people seem to respond more fully to +those than to dance them itself. Even + + align:start position:0% +those than to dance them itself. Even + + + align:start position:0% +those than to dance them itself. Even +though those of you who have danced or + + align:start position:0% +though those of you who have danced or + + + align:start position:0% +though those of you who have danced or +are dancers or know serious dancers will + + align:start position:0% +are dancers or know serious dancers will + + + align:start position:0% +are dancers or know serious dancers will +understand that uh dancers themselves + + align:start position:0% +understand that uh dancers themselves + + + align:start position:0% +understand that uh dancers themselves +are much greater athletes than most + + align:start position:0% +are much greater athletes than most + + + align:start position:0% +are much greater athletes than most +athletes and that and that there is a + + align:start position:0% +athletes and that and that there is a + + + align:start position:0% +athletes and that and that there is a +profound form of athleticism of physical + + align:start position:0% +profound form of athleticism of physical + + + align:start position:0% +profound form of athleticism of physical +energy grace and physical control + + align:start position:0% +energy grace and physical control + + + align:start position:0% +energy grace and physical control +involved in dance. And we see that in + + align:start position:0% +involved in dance. And we see that in + + + align:start position:0% +involved in dance. And we see that in +Estair's performances. It's as if he + + align:start position:0% +Estair's performances. It's as if he + + + align:start position:0% +Estair's performances. It's as if he +stands for a form of grace under + + align:start position:0% +stands for a form of grace under + + + align:start position:0% +stands for a form of grace under +constraint of strength and power + + align:start position:0% +constraint of strength and power + + + align:start position:0% +constraint of strength and power +constrained but not but not uh u uh + + align:start position:0% +constrained but not but not uh u uh + + + align:start position:0% +constrained but not but not uh u uh +undermined by the by the rules and + + align:start position:0% +undermined by the by the rules and + + + align:start position:0% +undermined by the by the rules and +boundaries within which it must operate. + + align:start position:0% +boundaries within which it must operate. + + + align:start position:0% +boundaries within which it must operate. +It's a form of classical art. And what + + align:start position:0% +It's a form of classical art. And what + + + align:start position:0% +It's a form of classical art. And what +we can say is that Kelly stands for + + align:start position:0% +we can say is that Kelly stands for + + + align:start position:0% +we can say is that Kelly stands for +classicism. Um uh I'm sorry a stair + + align:start position:0% +classicism. Um uh I'm sorry a stair + + + align:start position:0% +classicism. Um uh I'm sorry a stair +stands for the classic for the cl for + + align:start position:0% +stands for the classic for the cl for + + + align:start position:0% +stands for the classic for the cl for +classicism and Jean Kelly who is a kind + + align:start position:0% +classicism and Jean Kelly who is a kind + + + align:start position:0% +classicism and Jean Kelly who is a kind +of opposite in this way in his dances + + align:start position:0% +of opposite in this way in his dances + + + align:start position:0% +of opposite in this way in his dances +stands for the romantic right the + + align:start position:0% +stands for the romantic right the + + + align:start position:0% +stands for the romantic right the +classic and the romantic tendencies or + + align:start position:0% +classic and the romantic tendencies or + + + align:start position:0% +classic and the romantic tendencies or +energies. I'm oversimplifying here as + + align:start position:0% +energies. I'm oversimplifying here as + + + align:start position:0% +energies. I'm oversimplifying here as +Brody does, but it again it's a useful + + align:start position:0% +Brody does, but it again it's a useful + + + align:start position:0% +Brody does, but it again it's a useful +and illuminating simplification because + + align:start position:0% +and illuminating simplification because + + + align:start position:0% +and illuminating simplification because +we see Kelly for example mostly he + + align:start position:0% +we see Kelly for example mostly he + + + align:start position:0% +we see Kelly for example mostly he +doesn't play professional performers or + + align:start position:0% +doesn't play professional performers or + + + align:start position:0% +doesn't play professional performers or +professional dancers. He almost he + + align:start position:0% +professional dancers. He almost he + + + align:start position:0% +professional dancers. He almost he +almost always wears ordinary casual + + align:start position:0% +almost always wears ordinary casual + + + align:start position:0% +almost always wears ordinary casual +clothing, open shirts, uh jeans. Uh um + + align:start position:0% +clothing, open shirts, uh jeans. Uh um + + + align:start position:0% +clothing, open shirts, uh jeans. Uh um +he + + align:start position:0% +he + + + align:start position:0% +he +um a and um this casualness of + + align:start position:0% +um a and um this casualness of + + + align:start position:0% +um a and um this casualness of +appearance is matched by the fact that + + align:start position:0% +appearance is matched by the fact that + + + align:start position:0% +appearance is matched by the fact that +the dances he engages in often take + + align:start position:0% +the dances he engages in often take + + + align:start position:0% +the dances he engages in often take +place in spaces that are not appropriate + + align:start position:0% +place in spaces that are not appropriate + + + align:start position:0% +place in spaces that are not appropriate +for dance or almost hostile to dance. + + align:start position:0% +for dance or almost hostile to dance. + + + align:start position:0% +for dance or almost hostile to dance. +And one of the deepest principles of + + align:start position:0% +And one of the deepest principles of + + + align:start position:0% +And one of the deepest principles of +Kelly's performances of Kelly's dances + + align:start position:0% +Kelly's performances of Kelly's dances + + + align:start position:0% +Kelly's performances of Kelly's dances +are this is this in a certain sense is + + align:start position:0% +are this is this in a certain sense is + + + align:start position:0% +are this is this in a certain sense is +this contest between his exuberance and + + align:start position:0% +this contest between his exuberance and + + + align:start position:0% +this contest between his exuberance and +the and energy and the constraints that + + align:start position:0% +the and energy and the constraints that + + + align:start position:0% +the and energy and the constraints that +surround him. But unlike unlike a stare + + align:start position:0% +surround him. But unlike unlike a stare + + + align:start position:0% +surround him. But unlike unlike a stare +he does not reveal the power and grace + + align:start position:0% +he does not reveal the power and grace + + + align:start position:0% +he does not reveal the power and grace +of his dance by acknowledging the + + align:start position:0% +of his dance by acknowledging the + + + align:start position:0% +of his dance by acknowledging the +constraints and living within them. He + + align:start position:0% +constraints and living within them. He + + + align:start position:0% +constraints and living within them. He +the the energy of his dance expresses + + align:start position:0% +the the energy of his dance expresses + + + align:start position:0% +the the energy of his dance expresses +itself in the moments when he overgoes + + align:start position:0% +itself in the moments when he overgoes + + + align:start position:0% +itself in the moments when he overgoes +boundaries when he violates uh uh + + align:start position:0% +boundaries when he violates uh uh + + + align:start position:0% +boundaries when he violates uh uh +borders of various kinds and there are + + align:start position:0% +borders of various kinds and there are + + + align:start position:0% +borders of various kinds and there are +numerous examples of this in singing in + + align:start position:0% +numerous examples of this in singing in + + + align:start position:0% +numerous examples of this in singing in +the rain. I'll give you them. I I'll + + align:start position:0% +the rain. I'll give you them. I I'll + + + align:start position:0% +the rain. I'll give you them. I I'll +mention some of them in a little while. + + align:start position:0% +mention some of them in a little while. + + + align:start position:0% +mention some of them in a little while. +So, so the contrast between Kelly and a + + align:start position:0% +So, so the contrast between Kelly and a + + + align:start position:0% +So, so the contrast between Kelly and a +stair in this way both and and look in + + align:start position:0% +stair in this way both and and look in + + + align:start position:0% +stair in this way both and and look in +in both cases I've simplified because + + align:start position:0% +in both cases I've simplified because + + + align:start position:0% +in both cases I've simplified because +they also resemble each other in certain + + align:start position:0% +they also resemble each other in certain + + + align:start position:0% +they also resemble each other in certain +ways but these tendencies distill + + align:start position:0% +ways but these tendencies distill + + + align:start position:0% +ways but these tendencies distill +quality the these this argument distills + + align:start position:0% +quality the these this argument distills + + + align:start position:0% +quality the these this argument distills +qualities in them that clarify certain + + align:start position:0% +qualities in them that clarify certain + + + align:start position:0% +qualities in them that clarify certain +energies or tensions that can be said to + + align:start position:0% +energies or tensions that can be said to + + + align:start position:0% +energies or tensions that can be said to +be characteristic not only of their the + + align:start position:0% +be characteristic not only of their the + + + align:start position:0% +be characteristic not only of their the +two dance styles the kinds of movies + + align:start position:0% +two dance styles the kinds of movies + + + align:start position:0% +two dance styles the kinds of movies +these two stars are in but also in the + + align:start position:0% +these two stars are in but also in the + + + align:start position:0% +these two stars are in but also in the +musical genre as a whole. + + align:start position:0% +musical genre as a whole. + + + align:start position:0% +musical genre as a whole. +I'd like to say a couple of things about + + align:start position:0% +I'd like to say a couple of things about + + + align:start position:0% +I'd like to say a couple of things about +each of the two films we're going to see + + align:start position:0% +each of the two films we're going to see + + + align:start position:0% +each of the two films we're going to see +tonight by by way of uh uh framing some + + align:start position:0% +tonight by by way of uh uh framing some + + + align:start position:0% +tonight by by way of uh uh framing some +of the most important issues for you to + + align:start position:0% +of the most important issues for you to + + + align:start position:0% +of the most important issues for you to +think about. And I think without trying + + align:start position:0% +think about. And I think without trying + + + align:start position:0% +think about. And I think without trying +to anticipate too much and I have to + + align:start position:0% +to anticipate too much and I have to + + + align:start position:0% +to anticipate too much and I have to +these are very rich complex texts and uh + + align:start position:0% +these are very rich complex texts and uh + + + align:start position:0% +these are very rich complex texts and uh +20 minutes of conversation uh no matter + + align:start position:0% +20 minutes of conversation uh no matter + + + align:start position:0% +20 minutes of conversation uh no matter +how pointed can never do full justice to + + align:start position:0% +how pointed can never do full justice to + + + align:start position:0% +how pointed can never do full justice to +them. I don't intend to do full justice + + align:start position:0% +them. I don't intend to do full justice + + + align:start position:0% +them. I don't intend to do full justice +to them but I want to suggest some ways + + align:start position:0% +to them but I want to suggest some ways + + + align:start position:0% +to them but I want to suggest some ways +for you to think about aspects of these + + align:start position:0% +for you to think about aspects of these + + + align:start position:0% +for you to think about aspects of these +films as you're viewing them. And my + + align:start position:0% +films as you're viewing them. And my + + + align:start position:0% +films as you're viewing them. And my +hope and expectation is that these + + align:start position:0% +hope and expectation is that these + + + align:start position:0% +hope and expectation is that these +perspectives will energize and enliven + + align:start position:0% +perspectives will energize and enliven + + + align:start position:0% +perspectives will energize and enliven +the film for you and clue cue you in to + + align:start position:0% +the film for you and clue cue you in to + + + align:start position:0% +the film for you and clue cue you in to +aspects of the film that you might + + align:start position:0% +aspects of the film that you might + + + align:start position:0% +aspects of the film that you might +otherwise not see as deeply or might not + + align:start position:0% +otherwise not see as deeply or might not + + + align:start position:0% +otherwise not see as deeply or might not +occur to you until you reflected on the + + align:start position:0% +occur to you until you reflected on the + + + align:start position:0% +occur to you until you reflected on the +film after the case. One way to think + + align:start position:0% +film after the case. One way to think + + + align:start position:0% +film after the case. One way to think +about singing in the rain then uh our + + align:start position:0% +about singing in the rain then uh our + + + align:start position:0% +about singing in the rain then uh our +our classic H our example of a of of a + + align:start position:0% +our classic H our example of a of of a + + + align:start position:0% +our classic H our example of a of of a +Hollywood musical our a culminating + + align:start position:0% +Hollywood musical our a culminating + + + align:start position:0% +Hollywood musical our a culminating +instance of a Hollywood musical is to + + align:start position:0% +instance of a Hollywood musical is to + + + align:start position:0% +instance of a Hollywood musical is to +recognize that it belongs to a + + align:start position:0% +recognize that it belongs to a + + + align:start position:0% +recognize that it belongs to a +subcategory of musicals to several + + align:start position:0% +subcategory of musicals to several + + + align:start position:0% +subcategory of musicals to several +subcategories of musicals one of which + + align:start position:0% +subcategories of musicals one of which + + + align:start position:0% +subcategories of musicals one of which +I've already mentioned the putting on + + align:start position:0% +I've already mentioned the putting on + + + align:start position:0% +I've already mentioned the putting on +the show the backstage story but here + + align:start position:0% +the show the backstage story but here + + + align:start position:0% +the show the backstage story but here +the backstage story is the story of a + + align:start position:0% +the backstage story is the story of a + + + align:start position:0% +the backstage story is the story of a +movie instead of a play but it's the + + align:start position:0% +movie instead of a play but it's the + + + align:start position:0% +movie instead of a play but it's the +same basic uh uh the same basic + + align:start position:0% +same basic uh uh the same basic + + + align:start position:0% +same basic uh uh the same basic +situation + + align:start position:0% +situation + + + align:start position:0% +situation +Uh but it is also sometimes called uh a + + align:start position:0% +Uh but it is also sometimes called uh a + + + align:start position:0% +Uh but it is also sometimes called uh a +song catalog movie because there's so + + align:start position:0% +song catalog movie because there's so + + + align:start position:0% +song catalog movie because there's so +many songs in it and it's kind of a kind + + align:start position:0% +many songs in it and it's kind of a kind + + + align:start position:0% +many songs in it and it's kind of a kind +of catalog or or an encyclopedic uh um + + align:start position:0% +of catalog or or an encyclopedic uh um + + + align:start position:0% +of catalog or or an encyclopedic uh um +uh uh object and an encyclopedia of film + + align:start position:0% +uh uh object and an encyclopedia of film + + + align:start position:0% +uh uh object and an encyclopedia of film +of of of of mu of music and of song. Uh + + align:start position:0% +of of of of mu of music and of song. Uh + + + align:start position:0% +of of of of mu of music and of song. Uh +and uh this is almost literally true of + + align:start position:0% +and uh this is almost literally true of + + + align:start position:0% +and uh this is almost literally true of +Singing in the Rain. Arthur Freed, the + + align:start position:0% +Singing in the Rain. Arthur Freed, the + + + align:start position:0% +Singing in the Rain. Arthur Freed, the +the the u uh executive producer of so + + align:start position:0% +the the u uh executive producer of so + + + align:start position:0% +the the u uh executive producer of so +many of uh major films, over 40 MGM + + align:start position:0% +many of uh major films, over 40 MGM + + + align:start position:0% +many of uh major films, over 40 MGM +musicals between + + align:start position:0% +musicals between + + + align:start position:0% +musicals between +um uh something like + + align:start position:0% +um uh something like + + + align:start position:0% +um uh something like +1939. What was the great musical in + + align:start position:0% +1939. What was the great musical in + + + align:start position:0% +1939. What was the great musical in +1939? The Wizard of Oz. The first + + align:start position:0% +1939? The Wizard of Oz. The first + + + align:start position:0% +1939? The Wizard of Oz. The first +musical that is thought to be a a + + align:start position:0% +musical that is thought to be a a + + + align:start position:0% +musical that is thought to be a a +musical in color. And think how + + align:start position:0% +musical in color. And think how + + + align:start position:0% +musical in color. And think how +organically The Wizard of Oz uses color. + + align:start position:0% +organically The Wizard of Oz uses color. + + + align:start position:0% +organically The Wizard of Oz uses color. +Arthur Freed was the executive producer + + align:start position:0% +Arthur Freed was the executive producer + + + align:start position:0% +Arthur Freed was the executive producer +of that film. From that point until + + align:start position:0% +of that film. From that point until + + + align:start position:0% +of that film. From that point until +sometime in the 1960s, he was the + + align:start position:0% +sometime in the 1960s, he was the + + + align:start position:0% +sometime in the 1960s, he was the +executive producer or the supervisor of + + align:start position:0% +executive producer or the supervisor of + + + align:start position:0% +executive producer or the supervisor of +something like 40 plus MGM musicals of + + align:start position:0% +something like 40 plus MGM musicals of + + + align:start position:0% +something like 40 plus MGM musicals of +which Singing in the Rain is a classic + + align:start position:0% +which Singing in the Rain is a classic + + + align:start position:0% +which Singing in the Rain is a classic +is a classic instance. Uh and uh uh so + + align:start position:0% +is a classic instance. Uh and uh uh so + + + align:start position:0% +is a classic instance. Uh and uh uh so +Frerieded had worked as a lyricist, + + align:start position:0% +Frerieded had worked as a lyricist, + + + align:start position:0% +Frerieded had worked as a lyricist, +Arthur Freed had worked as a lyricist at + + align:start position:0% +Arthur Freed had worked as a lyricist at + + + align:start position:0% +Arthur Freed had worked as a lyricist at +MGM with Nasio Herb Brown, the + + align:start position:0% +MGM with Nasio Herb Brown, the + + + align:start position:0% +MGM with Nasio Herb Brown, the +songwriter, uh many years earlier and + + align:start position:0% +songwriter, uh many years earlier and + + + align:start position:0% +songwriter, uh many years earlier and +most of the songs in Singing in the Rain + + align:start position:0% +most of the songs in Singing in the Rain + + + align:start position:0% +most of the songs in Singing in the Rain +1952 had been introduced in MGM musicals + + align:start position:0% +1952 had been introduced in MGM musicals + + + align:start position:0% +1952 had been introduced in MGM musicals +from 1929 on. So in a literal sense, the + + align:start position:0% +from 1929 on. So in a literal sense, the + + + align:start position:0% +from 1929 on. So in a literal sense, the +film is a kind of encyclopedia of older + + align:start position:0% +film is a kind of encyclopedia of older + + + align:start position:0% +film is a kind of encyclopedia of older +songs. us and especially two key songs + + align:start position:0% +songs. us and especially two key songs + + + align:start position:0% +songs. us and especially two key songs +in the film, Broadway Melody and You + + align:start position:0% +in the film, Broadway Melody and You + + + align:start position:0% +in the film, Broadway Melody and You +Were Meant for Me, were both featured in + + align:start position:0% +Were Meant for Me, were both featured in + + + align:start position:0% +Were Meant for Me, were both featured in +that early uh and and and signature + + align:start position:0% +that early uh and and and signature + + + align:start position:0% +that early uh and and and signature +musical that founding musical that I + + align:start position:0% +musical that founding musical that I + + + align:start position:0% +musical that founding musical that I +mentioned this afternoon, The Broadway + + align:start position:0% +mentioned this afternoon, The Broadway + + + align:start position:0% +mentioned this afternoon, The Broadway +Melody of 1929. So part of the pleasure + + align:start position:0% +Melody of 1929. So part of the pleasure + + + align:start position:0% +Melody of 1929. So part of the pleasure +for older members of the audience in + + align:start position:0% +for older members of the audience in + + + align:start position:0% +for older members of the audience in +1952 would have been to hear and see + + align:start position:0% +1952 would have been to hear and see + + + align:start position:0% +1952 would have been to hear and see +these numbers in the new souped-up + + align:start position:0% +these numbers in the new souped-up + + + align:start position:0% +these numbers in the new souped-up +arrangements that were created for this + + align:start position:0% +arrangements that were created for this + + + align:start position:0% +arrangements that were created for this +film in such and in such artful + + align:start position:0% +film in such and in such artful + + + align:start position:0% +film in such and in such artful +performances. There's one song in the + + align:start position:0% +performances. There's one song in the + + + align:start position:0% +performances. There's one song in the +film that my colleague Martin Marx M A R + + align:start position:0% +film that my colleague Martin Marx M A R + + + align:start position:0% +film that my colleague Martin Marx M A R +KS he sometimes teaches this course in + + align:start position:0% +KS he sometimes teaches this course in + + + align:start position:0% +KS he sometimes teaches this course in +the spring. He's a professor of music + + align:start position:0% +the spring. He's a professor of music + + + align:start position:0% +the spring. He's a professor of music +and he a and he sometimes and I + + align:start position:0% +and he a and he sometimes and I + + + align:start position:0% +and he a and he sometimes and I +encourage all of you to consider taking + + align:start position:0% +encourage all of you to consider taking + + + align:start position:0% +encourage all of you to consider taking +it teaches us an advanced course in the + + align:start position:0% +it teaches us an advanced course in the + + + align:start position:0% +it teaches us an advanced course in the +American musical. It's a wonderfully + + align:start position:0% +American musical. It's a wonderfully + + + align:start position:0% +American musical. It's a wonderfully +interesting course and he knows more + + align:start position:0% +interesting course and he knows more + + + align:start position:0% +interesting course and he knows more +about the musical I think than almost + + align:start position:0% +about the musical I think than almost + + + align:start position:0% +about the musical I think than almost +any living human being. Uh and I'm + + align:start position:0% +any living human being. Uh and I'm + + + align:start position:0% +any living human being. Uh and I'm +stealing from some of his teaching notes + + align:start position:0% +stealing from some of his teaching notes + + + align:start position:0% +stealing from some of his teaching notes +here when I when I say this. He says one + + align:start position:0% +here when I when I say this. He says one + + + align:start position:0% +here when I when I say this. He says one +song that Marty Marx loves to talk about + + align:start position:0% +song that Marty Marx loves to talk about + + + align:start position:0% +song that Marty Marx loves to talk about +is one a minor song in the film and I'm + + align:start position:0% +is one a minor song in the film and I'm + + + align:start position:0% +is one a minor song in the film and I'm +mentioning it because you might miss it + + align:start position:0% +mentioning it because you might miss it + + + align:start position:0% +mentioning it because you might miss it +otherwise. It's called Would You and + + align:start position:0% +otherwise. It's called Would You and + + + align:start position:0% +otherwise. It's called Would You and +it's a It's a song about it's it's a + + align:start position:0% +it's a It's a song about it's it's a + + + align:start position:0% +it's a It's a song about it's it's a +song that shows the process of dubbing, + + align:start position:0% +song that shows the process of dubbing, + + + align:start position:0% +song that shows the process of dubbing, +right? And it's a it's a it's a song + + align:start position:0% +right? And it's a it's a it's a song + + + align:start position:0% +right? And it's a it's a it's a song +that actually has a kind of a uh plot + + align:start position:0% +that actually has a kind of a uh plot + + + align:start position:0% +that actually has a kind of a uh plot +and historical function within the film. + + align:start position:0% +and historical function within the film. + + + align:start position:0% +and historical function within the film. +It it comes near the end of the film. + + align:start position:0% +It it comes near the end of the film. + + + align:start position:0% +It it comes near the end of the film. +When it was sung in this moment, it it + + align:start position:0% +When it was sung in this moment, it it + + + align:start position:0% +When it was sung in this moment, it it +was all well, it was already + + align:start position:0% +was all well, it was already + + + align:start position:0% +was all well, it was already +old-fashioned in its original day when + + align:start position:0% +old-fashioned in its original day when + + + align:start position:0% +old-fashioned in its original day when +it was first when it was first uh uh um + + align:start position:0% +it was first when it was first uh uh um + + + align:start position:0% +it was first when it was first uh uh um +written and sung. And by 1952, it's much + + align:start position:0% +written and sung. And by 1952, it's much + + + align:start position:0% +written and sung. And by 1952, it's much +more outmoded. Professor Marx tells us + + align:start position:0% +more outmoded. Professor Marx tells us + + + align:start position:0% +more outmoded. Professor Marx tells us +um uh although it's a simple and + + align:start position:0% +um uh although it's a simple and + + + align:start position:0% +um uh although it's a simple and +graceful waltz, it uses an antiquated + + align:start position:0% +graceful waltz, it uses an antiquated + + + align:start position:0% +graceful waltz, it uses an antiquated +diction for example uh and and there are + + align:start position:0% +diction for example uh and and there are + + + align:start position:0% +diction for example uh and and there are +other signals that even the fact that + + align:start position:0% +other signals that even the fact that + + + align:start position:0% +other signals that even the fact that +it's a waltz that show it to be kind of + + align:start position:0% +it's a waltz that show it to be kind of + + + align:start position:0% +it's a waltz that show it to be kind of +old-fashioned in a way. But in singing + + align:start position:0% +old-fashioned in a way. But in singing + + + align:start position:0% +old-fashioned in a way. But in singing +in the rain, this old-fashioned song is + + align:start position:0% +in the rain, this old-fashioned song is + + + align:start position:0% +in the rain, this old-fashioned song is +used to telescope the process of + + align:start position:0% +used to telescope the process of + + + align:start position:0% +used to telescope the process of +recording for films shot by shot. Watch + + align:start position:0% +recording for films shot by shot. Watch + + + align:start position:0% +recording for films shot by shot. Watch +how it happens. It's a very exciting + + align:start position:0% +how it happens. It's a very exciting + + + align:start position:0% +how it happens. It's a very exciting +moment. uh uh because u um uh uh uh and + + align:start position:0% +moment. uh uh because u um uh uh uh and + + + align:start position:0% +moment. uh uh because u um uh uh uh and +so what happens then is that the + + align:start position:0% +so what happens then is that the + + + align:start position:0% +so what happens then is that the +old-fashioned song becomes the + + align:start position:0% +old-fashioned song becomes the + + + align:start position:0% +old-fashioned song becomes the +cornerstone of the new technology of + + align:start position:0% +cornerstone of the new technology of + + + align:start position:0% +cornerstone of the new technology of +sound recording. Watch how it happens in + + align:start position:0% +sound recording. Watch how it happens in + + + align:start position:0% +sound recording. Watch how it happens in +the film. And what this calls our + + align:start position:0% +the film. And what this calls our + + + align:start position:0% +the film. And what this calls our +attention to is something I I I uh uh is + + align:start position:0% +attention to is something I I I uh uh is + + + align:start position:0% +attention to is something I I I uh uh is +is is something I've talked about + + align:start position:0% +is is something I've talked about + + + align:start position:0% +is is something I've talked about +earlier and we'll return to in a moment. + + align:start position:0% +earlier and we'll return to in a moment. + + + align:start position:0% +earlier and we'll return to in a moment. +The whole the idea that in certain in + + align:start position:0% +The whole the idea that in certain in + + + align:start position:0% +The whole the idea that in certain in +the most remarkable works of art, we are + + align:start position:0% +the most remarkable works of art, we are + + + align:start position:0% +the most remarkable works of art, we are +surely aware of the fact that we're in + + align:start position:0% +surely aware of the fact that we're in + + + align:start position:0% +surely aware of the fact that we're in +the presence of what the literary + + align:start position:0% +the presence of what the literary + + + align:start position:0% +the presence of what the literary +critics and the art critics sometimes + + align:start position:0% +critics and the art critics sometimes + + + align:start position:0% +critics and the art critics sometimes +call organic form. In which the form of + + align:start position:0% +call organic form. In which the form of + + + align:start position:0% +call organic form. In which the form of +the text contributes to its meaning, in + + align:start position:0% +the text contributes to its meaning, in + + + align:start position:0% +the text contributes to its meaning, in +which form and content are married, are + + align:start position:0% +which form and content are married, are + + + align:start position:0% +which form and content are married, are +hard to can't really be separated. that + + align:start position:0% +hard to can't really be separated. that + + + align:start position:0% +hard to can't really be separated. that +the formal behavior of the text enacts + + align:start position:0% +the formal behavior of the text enacts + + + align:start position:0% +the formal behavior of the text enacts +or embodies or articulates or dramatizes + + align:start position:0% +or embodies or articulates or dramatizes + + + align:start position:0% +or embodies or articulates or dramatizes +what the film is about, what the text + + align:start position:0% +what the film is about, what the text + + + align:start position:0% +what the film is about, what the text +means. I'll come back to this point in a + + align:start position:0% +means. I'll come back to this point in a + + + align:start position:0% +means. I'll come back to this point in a +in a minute with even more dramatic + + align:start position:0% +in a minute with even more dramatic + + + align:start position:0% +in a minute with even more dramatic +examples. I I I I hope um um so and an + + align:start position:0% +examples. I I I I hope um um so and an + + + align:start position:0% +examples. I I I I hope um um so and an +added point about about this would song + + align:start position:0% +added point about about this would song + + + align:start position:0% +added point about about this would song +just this one sort of minor sequence. + + align:start position:0% +just this one sort of minor sequence. + + + align:start position:0% +just this one sort of minor sequence. +I'm mentioning this partly to show you + + align:start position:0% +I'm mentioning this partly to show you + + + align:start position:0% +I'm mentioning this partly to show you +how deeply you could actually dig into + + align:start position:0% +how deeply you could actually dig into + + + align:start position:0% +how deeply you could actually dig into +particular sequences and particular + + align:start position:0% +particular sequences and particular + + + align:start position:0% +particular sequences and particular +songs in the film and find meaning, + + align:start position:0% +songs in the film and find meaning, + + + align:start position:0% +songs in the film and find meaning, +relevance, and complexity there. When + + align:start position:0% +relevance, and complexity there. When + + + align:start position:0% +relevance, and complexity there. When +Debbie Reynolds, who sings the song, + + align:start position:0% +Debbie Reynolds, who sings the song, + + + align:start position:0% +Debbie Reynolds, who sings the song, +looks point blank at Jean Kelly as she + + align:start position:0% +looks point blank at Jean Kelly as she + + + align:start position:0% +looks point blank at Jean Kelly as she +sings it, she drives home the question + + align:start position:0% +sings it, she drives home the question + + + align:start position:0% +sings it, she drives home the question +of whether he'll be brave enough to love + + align:start position:0% +of whether he'll be brave enough to love + + + align:start position:0% +of whether he'll be brave enough to love +her. Right? So, it even implicates + + align:start position:0% +her. Right? So, it even implicates + + + align:start position:0% +her. Right? So, it even implicates +implicates itself in the love story + + align:start position:0% +implicates itself in the love story + + + align:start position:0% +implicates itself in the love story +that's at the heart of the film. Uh um + + align:start position:0% +that's at the heart of the film. Uh um + + + align:start position:0% +that's at the heart of the film. Uh um +her singing voice, we might note + + align:start position:0% +her singing voice, we might note + + + align:start position:0% +her singing voice, we might note +ironically and comically in this scene + + align:start position:0% +ironically and comically in this scene + + + align:start position:0% +ironically and comically in this scene +is actually dubbed for this song. And + + align:start position:0% +is actually dubbed for this song. And + + + align:start position:0% +is actually dubbed for this song. And +you'll understand if you haven't seen + + align:start position:0% +you'll understand if you haven't seen + + + align:start position:0% +you'll understand if you haven't seen +the film why that's a comic and ironic + + align:start position:0% +the film why that's a comic and ironic + + + align:start position:0% +the film why that's a comic and ironic +commentary. Uh she had the wrong kind of + + align:start position:0% +commentary. Uh she had the wrong kind of + + + align:start position:0% +commentary. Uh she had the wrong kind of +voice. It was too flat and nasal for + + align:start position:0% +voice. It was too flat and nasal for + + + align:start position:0% +voice. It was too flat and nasal for +this opereta-like number. So they dubbed + + align:start position:0% +this opereta-like number. So they dubbed + + + align:start position:0% +this opereta-like number. So they dubbed +her voice. Uh so there's a double iron + + align:start position:0% +her voice. Uh so there's a double iron + + + align:start position:0% +her voice. Uh so there's a double iron +here because she's playing a dubbber + + align:start position:0% +here because she's playing a dubbber + + + align:start position:0% +here because she's playing a dubbber +when she's sing when she's singing the + + align:start position:0% +when she's sing when she's singing the + + + align:start position:0% +when she's sing when she's singing the +song. And you might compare the voice in + + align:start position:0% +song. And you might compare the voice in + + + align:start position:0% +song. And you might compare the voice in +Good Morning another number in the fil + + align:start position:0% +Good Morning another number in the fil + + + align:start position:0% +Good Morning another number in the fil +where Debbie Reynolds is really singing + + align:start position:0% +where Debbie Reynolds is really singing + + + align:start position:0% +where Debbie Reynolds is really singing +and and you can see the difference + + align:start position:0% +and and you can see the difference + + + align:start position:0% +and and you can see the difference +between the between the two voices. + + align:start position:0% +between the between the two voices. + + + align:start position:0% +between the between the two voices. +Okay. Um so so uh the the point I've the + + align:start position:0% +Okay. Um so so uh the the point I've the + + + align:start position:0% +Okay. Um so so uh the the point I've the +point I've made the implicit point that + + align:start position:0% +point I've made the implicit point that + + + align:start position:0% +point I've made the implicit point that +I made uh in talking about this one this + + align:start position:0% +I made uh in talking about this one this + + + align:start position:0% +I made uh in talking about this one this +one number the would you number uh it + + align:start position:0% +one number the would you number uh it + + + align:start position:0% +one number the would you number uh it +has to do with what we might call a + + align:start position:0% +has to do with what we might call a + + + align:start position:0% +has to do with what we might call a +central element or feature of singing in + + align:start position:0% +central element or feature of singing in + + + align:start position:0% +central element or feature of singing in +the rain. its profound + + align:start position:0% +the rain. its profound + + + align:start position:0% +the rain. its profound +self-consciousness. The profound way in + + align:start position:0% +self-consciousness. The profound way in + + + align:start position:0% +self-consciousness. The profound way in +which in which it shows itself to be + + align:start position:0% +which in which it shows itself to be + + + align:start position:0% +which in which it shows itself to be +aware of itself to be aware of itself as + + align:start position:0% +aware of itself to be aware of itself as + + + align:start position:0% +aware of itself to be aware of itself as +a movie to be aware of itself as a + + align:start position:0% +a movie to be aware of itself as a + + + align:start position:0% +a movie to be aware of itself as a +bearer of diff of of a of traditions of + + align:start position:0% +bearer of diff of of a of traditions of + + + align:start position:0% +bearer of diff of of a of traditions of +singing of dancing and performance. Uh + + align:start position:0% +singing of dancing and performance. Uh + + + align:start position:0% +singing of dancing and performance. Uh +uh and it's uh that makes it so it isn't + + align:start position:0% +uh and it's uh that makes it so it isn't + + + align:start position:0% +uh and it's uh that makes it so it isn't +simply an encyclopedia of musical + + align:start position:0% +simply an encyclopedia of musical + + + align:start position:0% +simply an encyclopedia of musical +history. It's almost an encyclopedia of + + align:start position:0% +history. It's almost an encyclopedia of + + + align:start position:0% +history. It's almost an encyclopedia of +different forms of of almost all forms + + align:start position:0% +different forms of of almost all forms + + + align:start position:0% +different forms of of almost all forms +of performance. I don't want to go too + + align:start position:0% +of performance. I don't want to go too + + + align:start position:0% +of performance. I don't want to go too +far but there many many forms of + + align:start position:0% +far but there many many forms of + + + align:start position:0% +far but there many many forms of +performance are incorporated in the in + + align:start position:0% +performance are incorporated in the in + + + align:start position:0% +performance are incorporated in the in +the film's in the film's grasp in the + + align:start position:0% +the film's in the film's grasp in the + + + align:start position:0% +the film's in the film's grasp in the +film's embrace. All right. Uh we can one + + align:start position:0% +film's embrace. All right. Uh we can one + + + align:start position:0% +film's embrace. All right. Uh we can one +way we can think of it is as an + + align:start position:0% +way we can think of it is as an + + + align:start position:0% +way we can think of it is as an +encyclopedic recapitulation of the + + align:start position:0% +encyclopedic recapitulation of the + + + align:start position:0% +encyclopedic recapitulation of the +history of m of of of musicals uh and of + + align:start position:0% +history of m of of of musicals uh and of + + + align:start position:0% +history of m of of of musicals uh and of +films in general. But as you'll notice + + align:start position:0% +films in general. But as you'll notice + + + align:start position:0% +films in general. But as you'll notice +when you look at the film there the uh + + align:start position:0% +when you look at the film there the uh + + + align:start position:0% +when you look at the film there the uh +singing in the rain has uh begins by + + align:start position:0% +singing in the rain has uh begins by + + + align:start position:0% +singing in the rain has uh begins by +being about the problem of trans of + + align:start position:0% +being about the problem of trans of + + + align:start position:0% +being about the problem of trans of +changing a silent film into a sound film + + align:start position:0% +changing a silent film into a sound film + + + align:start position:0% +changing a silent film into a sound film +because the silent the silent film has + + align:start position:0% +because the silent the silent film has + + + align:start position:0% +because the silent the silent film has +been made just at that cusp moment when + + align:start position:0% +been made just at that cusp moment when + + + align:start position:0% +been made just at that cusp moment when +the transition to sound is occurring and + + align:start position:0% +the transition to sound is occurring and + + + align:start position:0% +the transition to sound is occurring and +the film in that sense is also a + + align:start position:0% +the film in that sense is also a + + + align:start position:0% +the film in that sense is also a +wonderful sort of historical repreeze + + align:start position:0% +wonderful sort of historical repreeze + + + align:start position:0% +wonderful sort of historical repreeze +for members of our for our course even + + align:start position:0% +for members of our for our course even + + + align:start position:0% +for members of our for our course even +though it wasn't made for that purpose + + align:start position:0% +though it wasn't made for that purpose + + + align:start position:0% +though it wasn't made for that purpose +alas. Um and and uh um uh so so in the + + align:start position:0% +alas. Um and and uh um uh so so in the + + + align:start position:0% +alas. Um and and uh um uh so so in the +film then we also get an illusion to and + + align:start position:0% +film then we also get an illusion to and + + + align:start position:0% +film then we also get an illusion to and +a representation of silent movies but + + align:start position:0% +a representation of silent movies but + + + align:start position:0% +a representation of silent movies but +not just any not just some generic idea + + align:start position:0% +not just any not just some generic idea + + + align:start position:0% +not just any not just some generic idea +of silent movies. A very particular kind + + align:start position:0% +of silent movies. A very particular kind + + + align:start position:0% +of silent movies. A very particular kind +of swashbuckler adventure film is + + align:start position:0% +of swashbuckler adventure film is + + + align:start position:0% +of swashbuckler adventure film is +dramatized there. And then later in a + + align:start position:0% +dramatized there. And then later in a + + + align:start position:0% +dramatized there. And then later in a +scene I mentioned earlier today in the + + align:start position:0% +scene I mentioned earlier today in the + + + align:start position:0% +scene I mentioned earlier today in the +audition scene, the beautiful girls + + align:start position:0% +audition scene, the beautiful girls + + + align:start position:0% +audition scene, the beautiful girls +sequence in Singing in the Rain where a + + align:start position:0% +sequence in Singing in the Rain where a + + + align:start position:0% +sequence in Singing in the Rain where a +megaphone suddenly turns into a circle + + align:start position:0% +megaphone suddenly turns into a circle + + + align:start position:0% +megaphone suddenly turns into a circle +of dancers alluding to the Busby + + align:start position:0% +of dancers alluding to the Busby + + + align:start position:0% +of dancers alluding to the Busby +Berkeley tradition. Uh we have uh a very + + align:start position:0% +Berkeley tradition. Uh we have uh a very + + + align:start position:0% +Berkeley tradition. Uh we have uh a very +specific reference to another kind of + + align:start position:0% +specific reference to another kind of + + + align:start position:0% +specific reference to another kind of +movie musical. Right? So juxtaposed + + align:start position:0% +movie musical. Right? So juxtaposed + + + align:start position:0% +movie musical. Right? So juxtaposed +against each other are two different + + align:start position:0% +against each other are two different + + + align:start position:0% +against each other are two different +kinds of movies. Right? And I've only + + align:start position:0% +kinds of movies. Right? And I've only + + + align:start position:0% +kinds of movies. Right? And I've only +mentioned a couple of examples. As you + + align:start position:0% +mentioned a couple of examples. As you + + + align:start position:0% +mentioned a couple of examples. As you +watch the film, you'll see dozens and + + align:start position:0% +watch the film, you'll see dozens and + + + align:start position:0% +watch the film, you'll see dozens and +dozens of instances in which the film + + align:start position:0% +dozens of instances in which the film + + + align:start position:0% +dozens of instances in which the film +capaciously reaches back to older forms + + align:start position:0% +capaciously reaches back to older forms + + + align:start position:0% +capaciously reaches back to older forms +of performance and tries to incorporate + + align:start position:0% +of performance and tries to incorporate + + + align:start position:0% +of performance and tries to incorporate +them in some sense into its own + + align:start position:0% +them in some sense into its own + + + align:start position:0% +them in some sense into its own +structure, into its own energies. Um, + + align:start position:0% +structure, into its own energies. Um, + + + align:start position:0% +structure, into its own energies. Um, +and there are many older performance + + align:start position:0% +and there are many older performance + + + align:start position:0% +and there are many older performance +forms in the film. There are forms of + + align:start position:0% +forms in the film. There are forms of + + + align:start position:0% +forms in the film. There are forms of +slip, slapstick, and katon katon-like + + align:start position:0% +slip, slapstick, and katon katon-like + + + align:start position:0% +slip, slapstick, and katon katon-like +comedy, especially in Donald O' Conor's + + align:start position:0% +comedy, especially in Donald O' Conor's + + + align:start position:0% +comedy, especially in Donald O' Conor's +wonderful dance and song sequence, Make + + align:start position:0% +wonderful dance and song sequence, Make + + + align:start position:0% +wonderful dance and song sequence, Make +The Him Laugh. There are illusions and + + align:start position:0% +The Him Laugh. There are illusions and + + + align:start position:0% +The Him Laugh. There are illusions and +references and dramatized scenes from + + align:start position:0% +references and dramatized scenes from + + + align:start position:0% +references and dramatized scenes from +vaudeville, from jazz, from what we + + align:start position:0% +vaudeville, from jazz, from what we + + + align:start position:0% +vaudeville, from jazz, from what we +might call forms of love melodrama uh + + align:start position:0% +might call forms of love melodrama uh + + + align:start position:0% +might call forms of love melodrama uh +all the way through the film. And so the + + align:start position:0% +all the way through the film. And so the + + + align:start position:0% +all the way through the film. And so the +what and I've hardly exhausted the I + + align:start position:0% +what and I've hardly exhausted the I + + + align:start position:0% +what and I've hardly exhausted the I +haven't really cataloged even remotely + + align:start position:0% +haven't really cataloged even remotely + + + align:start position:0% +haven't really cataloged even remotely +all the kinds of performance spaces and + + align:start position:0% +all the kinds of performance spaces and + + + align:start position:0% +all the kinds of performance spaces and +performance uh uh types that the film + + align:start position:0% +performance uh uh types that the film + + + align:start position:0% +performance uh uh types that the film +incorporates and utilizes in the course + + align:start position:0% +incorporates and utilizes in the course + + + align:start position:0% +incorporates and utilizes in the course +of its uh uh uh length. uh nor have I + + align:start position:0% +of its uh uh uh length. uh nor have I + + + align:start position:0% +of its uh uh uh length. uh nor have I +even begun to list the number of musical + + align:start position:0% +even begun to list the number of musical + + + align:start position:0% +even begun to list the number of musical +styles, particular particular songs and + + align:start position:0% +styles, particular particular songs and + + + align:start position:0% +styles, particular particular songs and +particular dance styles that are also + + align:start position:0% +particular dance styles that are also + + + align:start position:0% +particular dance styles that are also +incorporated into the film. But I've + + align:start position:0% +incorporated into the film. But I've + + + align:start position:0% +incorporated into the film. But I've +said enough to suggest that the singing + + align:start position:0% +said enough to suggest that the singing + + + align:start position:0% +said enough to suggest that the singing +in the rain has what might be called a + + align:start position:0% +in the rain has what might be called a + + + align:start position:0% +in the rain has what might be called a +structural or a + + align:start position:0% +structural or a + + + align:start position:0% +structural or a +formal exuberance, a kind of excitement + + align:start position:0% +formal exuberance, a kind of excitement + + + align:start position:0% +formal exuberance, a kind of excitement +as if it as if it uh as if it every time + + align:start position:0% +as if it as if it uh as if it every time + + + align:start position:0% +as if it as if it uh as if it every time +it turns it wants to make an illusion to + + align:start position:0% +it turns it wants to make an illusion to + + + align:start position:0% +it turns it wants to make an illusion to +another kind of text. as if it feels + + align:start position:0% +another kind of text. as if it feels + + + align:start position:0% +another kind of text. as if it feels +itself in some sense with a kind of + + align:start position:0% +itself in some sense with a kind of + + + align:start position:0% +itself in some sense with a kind of +excitement and exuberant energy, + + align:start position:0% +excitement and exuberant energy, + + + align:start position:0% +excitement and exuberant energy, +constantly in touch with its ancestry + + align:start position:0% +constantly in touch with its ancestry + + + align:start position:0% +constantly in touch with its ancestry +and with an ancestry that it tries to + + align:start position:0% +and with an ancestry that it tries to + + + align:start position:0% +and with an ancestry that it tries to +define very generously and broadly. And + + align:start position:0% +define very generously and broadly. And + + + align:start position:0% +define very generously and broadly. And +so what we're saying is that formally, + + align:start position:0% +so what we're saying is that formally, + + + align:start position:0% +so what we're saying is that formally, +structurally, the film is the film is + + align:start position:0% +structurally, the film is the film is + + + align:start position:0% +structurally, the film is the film is +expressing a special kind of + + align:start position:0% +expressing a special kind of + + + align:start position:0% +expressing a special kind of +intellectual energy, excitement, + + align:start position:0% +intellectual energy, excitement, + + + align:start position:0% +intellectual energy, excitement, +exuberance, right? Uh and and of course + + align:start position:0% +exuberance, right? Uh and and of course + + + align:start position:0% +exuberance, right? Uh and and of course +what's interesting and fundamental about + + align:start position:0% +what's interesting and fundamental about + + + align:start position:0% +what's interesting and fundamental about +that is that those energies are also + + align:start position:0% +that is that those energies are also + + + align:start position:0% +that is that those energies are also +replicated centrally reenacted in the + + align:start position:0% +replicated centrally reenacted in the + + + align:start position:0% +replicated centrally reenacted in the +actual dance sequences that we see in + + align:start position:0% +actual dance sequences that we see in + + + align:start position:0% +actual dance sequences that we see in +the in the in the uh in the film. It's + + align:start position:0% +the in the in the uh in the film. It's + + + align:start position:0% +the in the in the uh in the film. It's +an a profoundly rich example of what I + + align:start position:0% +an a profoundly rich example of what I + + + align:start position:0% +an a profoundly rich example of what I +called a moment ago organic form. The + + align:start position:0% +called a moment ago organic form. The + + + align:start position:0% +called a moment ago organic form. The +structure or the shape of the film + + align:start position:0% +structure or the shape of the film + + + align:start position:0% +structure or the shape of the film +contributes to our sense not only that + + align:start position:0% +contributes to our sense not only that + + + align:start position:0% +contributes to our sense not only that +it has a kind of encyclopedic + + align:start position:0% +it has a kind of encyclopedic + + + align:start position:0% +it has a kind of encyclopedic +self-reflective interest in its own + + align:start position:0% +self-reflective interest in its own + + + align:start position:0% +self-reflective interest in its own +history and that it's recapitulating its + + align:start position:0% +history and that it's recapitulating its + + + align:start position:0% +history and that it's recapitulating its +own history for us as it as it proceeds. + + align:start position:0% +own history for us as it as it proceeds. + + + align:start position:0% +own history for us as it as it proceeds. +We also have a deep sense, a deep sense + + align:start position:0% +We also have a deep sense, a deep sense + + + align:start position:0% +We also have a deep sense, a deep sense +of the extent to which the film + + align:start position:0% +of the extent to which the film + + + align:start position:0% +of the extent to which the film +understands that many of the older forms + + align:start position:0% +understands that many of the older forms + + + align:start position:0% +understands that many of the older forms +it dramatizes are now simply being + + align:start position:0% +it dramatizes are now simply being + + + align:start position:0% +it dramatizes are now simply being +archived as if the film understands + + align:start position:0% +archived as if the film understands + + + align:start position:0% +archived as if the film understands +itself not only as a as a as a dramatic + + align:start position:0% +itself not only as a as a as a dramatic + + + align:start position:0% +itself not only as a as a as a dramatic +as a dramatic entertainment, but also as + + align:start position:0% +as a dramatic entertainment, but also as + + + align:start position:0% +as a dramatic entertainment, but also as +a kind of history book or a kind of + + align:start position:0% +a kind of history book or a kind of + + + align:start position:0% +a kind of history book or a kind of +encyclopedia, literally a kind of + + align:start position:0% +encyclopedia, literally a kind of + + + align:start position:0% +encyclopedia, literally a kind of +archive of all the forms of performance + + align:start position:0% +archive of all the forms of performance + + + align:start position:0% +archive of all the forms of performance +and song and dance that lie behind the + + align:start position:0% +and song and dance that lie behind the + + + align:start position:0% +and song and dance that lie behind the +making of such of such a film. And of + + align:start position:0% +making of such of such a film. And of + + + align:start position:0% +making of such of such a film. And of +course the this formal exuberance as I + + align:start position:0% +course the this formal exuberance as I + + + align:start position:0% +course the this formal exuberance as I +said is repeated again and again uh in a + + align:start position:0% +said is repeated again and again uh in a + + + align:start position:0% +said is repeated again and again uh in a +in a in an actualized and concrete way + + align:start position:0% +in a in an actualized and concrete way + + + align:start position:0% +in a in an actualized and concrete way +in the story in the plot every time the + + align:start position:0% +in the story in the plot every time the + + + align:start position:0% +in the story in the plot every time the +character starts singing or dancing. And + + align:start position:0% +character starts singing or dancing. And + + + align:start position:0% +character starts singing or dancing. And +as you'll see there's a particular kind + + align:start position:0% +as you'll see there's a particular kind + + + align:start position:0% +as you'll see there's a particular kind +of exuberance and energy in many of the + + align:start position:0% +of exuberance and energy in many of the + + + align:start position:0% +of exuberance and energy in many of the +dances key themes. Well I've already + + align:start position:0% +dances key themes. Well I've already + + + align:start position:0% +dances key themes. Well I've already +implicitly been talking about some of + + align:start position:0% +implicitly been talking about some of + + + align:start position:0% +implicitly been talking about some of +the themes. uh but let me mention just + + align:start position:0% +the themes. uh but let me mention just + + + align:start position:0% +the themes. uh but let me mention just +two that are seem to me especially + + align:start position:0% +two that are seem to me especially + + + align:start position:0% +two that are seem to me especially +significance significant one I've + + align:start position:0% +significance significant one I've + + + align:start position:0% +significance significant one I've +mentioned much earlier and I simply want + + align:start position:0% +mentioned much earlier and I simply want + + + align:start position:0% +mentioned much earlier and I simply want +to remind you again that this tension + + align:start position:0% +to remind you again that this tension + + + align:start position:0% +to remind you again that this tension +between what might be called high art + + align:start position:0% +between what might be called high art + + + align:start position:0% +between what might be called high art +and the pretentious expectations of a of + + align:start position:0% +and the pretentious expectations of a of + + + align:start position:0% +and the pretentious expectations of a of +a cultural establishment are set up for + + align:start position:0% +a cultural establishment are set up for + + + align:start position:0% +a cultural establishment are set up for +parody and mockery in this film + + align:start position:0% +parody and mockery in this film + + + align:start position:0% +parody and mockery in this film +repeatedly the film is on the side of + + align:start position:0% +repeatedly the film is on the side of + + + align:start position:0% +repeatedly the film is on the side of +the of the of the popular and the + + align:start position:0% +the of the of the popular and the + + + align:start position:0% +the of the of the popular and the +energetic and the ex and the and the uh + + align:start position:0% +energetic and the ex and the and the uh + + + align:start position:0% +energetic and the ex and the and the uh +unpretentious uh and and and and and one + + align:start position:0% +unpretentious uh and and and and and one + + + align:start position:0% +unpretentious uh and and and and and one +can feel that tension again and again in + + align:start position:0% +can feel that tension again and again in + + + align:start position:0% +can feel that tension again and again in +many many of the sequences in the movie + + align:start position:0% +many many of the sequences in the movie + + + align:start position:0% +many many of the sequences in the movie +in in in in the in the film. + + align:start position:0% +in in in in the in the film. + + + align:start position:0% +in in in in the in the film. +Uh just one obvious let me give you just + + align:start position:0% +Uh just one obvious let me give you just + + + align:start position:0% +Uh just one obvious let me give you just +two obvious examples. one um uh in the + + align:start position:0% +two obvious examples. one um uh in the + + + align:start position:0% +two obvious examples. one um uh in the +very opening sequence of the film, one + + align:start position:0% +very opening sequence of the film, one + + + align:start position:0% +very opening sequence of the film, one +of the classic moments in the history of + + align:start position:0% +of the classic moments in the history of + + + align:start position:0% +of the classic moments in the history of +American movies, re replayed again and + + align:start position:0% +American movies, re replayed again and + + + align:start position:0% +American movies, re replayed again and +again in in compilation anthologies of + + align:start position:0% +again in in compilation anthologies of + + + align:start position:0% +again in in compilation anthologies of +the great of great moments in uh in + + align:start position:0% +the great of great moments in uh in + + + align:start position:0% +the great of great moments in uh in +Hollywood, great moments of Hollywood + + align:start position:0% +Hollywood, great moments of Hollywood + + + align:start position:0% +Hollywood, great moments of Hollywood +film, uh is the introduction to the film + + align:start position:0% +film, uh is the introduction to the film + + + align:start position:0% +film, uh is the introduction to the film +and uh the the the introduction to + + align:start position:0% +and uh the the the introduction to + + + align:start position:0% +and uh the the the introduction to +Singing in the Rain recreates uh a a + + align:start position:0% +Singing in the Rain recreates uh a a + + + align:start position:0% +Singing in the Rain recreates uh a a +historical actuality that I need to + + align:start position:0% +historical actuality that I need to + + + align:start position:0% +historical actuality that I need to +remind today's audiences of. shows you + + align:start position:0% +remind today's audiences of. shows you + + + align:start position:0% +remind today's audiences of. shows you +how old this course is because when I + + align:start position:0% +how old this course is because when I + + + align:start position:0% +how old this course is because when I +first began to teach this course, these + + align:start position:0% +first began to teach this course, these + + + align:start position:0% +first began to teach this course, these +practices were still going on and the + + align:start position:0% +practices were still going on and the + + + align:start position:0% +practices were still going on and the +students still still understood and in + + align:start position:0% +students still still understood and in + + + align:start position:0% +students still still understood and in +fact had their own experience of + + align:start position:0% +fact had their own experience of + + + align:start position:0% +fact had their own experience of +exhibition movies in a way that most of + + align:start position:0% +exhibition movies in a way that most of + + + align:start position:0% +exhibition movies in a way that most of +and of and of of uh going to theaters + + align:start position:0% +and of and of of uh going to theaters + + + align:start position:0% +and of and of of uh going to theaters +that that uh were very lavish and and + + align:start position:0% +that that uh were very lavish and and + + + align:start position:0% +that that uh were very lavish and and +and and uh uh um in many ways even even + + align:start position:0% +and and uh uh um in many ways even even + + + align:start position:0% +and and uh uh um in many ways even even +pretentious. And what they were + + align:start position:0% +pretentious. And what they were + + + align:start position:0% +pretentious. And what they were +especially aware of is something I have + + align:start position:0% +especially aware of is something I have + + + align:start position:0% +especially aware of is something I have +to remind you of now, which is that very + + align:start position:0% +to remind you of now, which is that very + + + align:start position:0% +to remind you of now, which is that very +often Hollywood had a strategy of + + align:start position:0% +often Hollywood had a strategy of + + + align:start position:0% +often Hollywood had a strategy of +rolling out its great blockbuster, what + + align:start position:0% +rolling out its great blockbuster, what + + + align:start position:0% +rolling out its great blockbuster, what +it had hoped would be great blockbuster + + align:start position:0% +it had hoped would be great blockbuster + + + align:start position:0% +it had hoped would be great blockbuster +films with very elaborate uh um + + align:start position:0% +films with very elaborate uh um + + + align:start position:0% +films with very elaborate uh um +inaugural events, right? The debut of a + + align:start position:0% +inaugural events, right? The debut of a + + + align:start position:0% +inaugural events, right? The debut of a +film was often a major event and it + + align:start position:0% +film was often a major event and it + + + align:start position:0% +film was often a major event and it +would be covered by newspapers and and + + align:start position:0% +would be covered by newspapers and and + + + align:start position:0% +would be covered by newspapers and and +uh uh many Hollywood stars would be + + align:start position:0% +uh uh many Hollywood stars would be + + + align:start position:0% +uh uh many Hollywood stars would be +would would come and attend and they + + align:start position:0% +would would come and attend and they + + + align:start position:0% +would would come and attend and they +they would turn they would turn the + + align:start position:0% +they would turn they would turn the + + + align:start position:0% +they would turn they would turn the +event into a publicity event partly in + + align:start position:0% +event into a publicity event partly in + + + align:start position:0% +event into a publicity event partly in +order to get publicity for the for the + + align:start position:0% +order to get publicity for the for the + + + align:start position:0% +order to get publicity for the for the +uh release of the film, right? And + + align:start position:0% +uh release of the film, right? And + + + align:start position:0% +uh release of the film, right? And +Singing in the Rain opens with with such + + align:start position:0% +Singing in the Rain opens with with such + + + align:start position:0% +Singing in the Rain opens with with such +a moment in which a film is opening and + + align:start position:0% +a moment in which a film is opening and + + + align:start position:0% +a moment in which a film is opening and +and it dramatizes the the uh the the uh + + align:start position:0% +and it dramatizes the the uh the the uh + + + align:start position:0% +and it dramatizes the the uh the the uh +the comic hypocrisies that attend such + + align:start position:0% +the comic hypocrisies that attend such + + + align:start position:0% +the comic hypocrisies that attend such +uh such publicity gestures. And as the + + align:start position:0% +uh such publicity gestures. And as the + + + align:start position:0% +uh such publicity gestures. And as the +film opens, then we have a we we see a + + align:start position:0% +film opens, then we have a we we see a + + + align:start position:0% +film opens, then we have a we we see a +sequence in which the star of the the + + align:start position:0% +sequence in which the star of the the + + + align:start position:0% +sequence in which the star of the the +stars of the of the film we're about to + + align:start position:0% +stars of the of the film we're about to + + + align:start position:0% +stars of the of the film we're about to +see, Jean Kelly, is interviewed the star + + align:start position:0% +see, Jean Kelly, is interviewed the star + + + align:start position:0% +see, Jean Kelly, is interviewed the star +of the film is interviewed by a + + align:start position:0% +of the film is interviewed by a + + + align:start position:0% +of the film is interviewed by a +reporter. And he then tells sort of the + + align:start position:0% +reporter. And he then tells sort of the + + + align:start position:0% +reporter. And he then tells sort of the +story of his of of his career. Uh but + + align:start position:0% +story of his of of his career. Uh but + + + align:start position:0% +story of his of of his career. Uh but +the story of that he tells is fake is a + + align:start position:0% +the story of that he tells is fake is a + + + align:start position:0% +the story of that he tells is fake is a +lie. It's very pretentious. Oh, we went + + align:start position:0% +lie. It's very pretentious. Oh, we went + + + align:start position:0% +lie. It's very pretentious. Oh, we went +to the best conservatories. We were + + align:start position:0% +to the best conservatories. We were + + + align:start position:0% +to the best conservatories. We were +trained by classical musicians and + + align:start position:0% +trained by classical musicians and + + + align:start position:0% +trained by classical musicians and +classical actors, actors, right? And he + + align:start position:0% +classical actors, actors, right? And he + + + align:start position:0% +classical actors, actors, right? And he +acts very pretent, but what that's what + + align:start position:0% +acts very pretent, but what that's what + + + align:start position:0% +acts very pretent, but what that's what +he says. But what we see, what is shown + + align:start position:0% +he says. But what we see, what is shown + + + align:start position:0% +he says. But what we see, what is shown +to us is the actual history of how Don + + align:start position:0% +to us is the actual history of how Don + + + align:start position:0% +to us is the actual history of how Don +Lockwood and his partner um his sidekick + + align:start position:0% +Lockwood and his partner um his sidekick + + + align:start position:0% +Lockwood and his partner um his sidekick +uh um played by the brilliant performer + + align:start position:0% +uh um played by the brilliant performer + + + align:start position:0% +uh um played by the brilliant performer +Donald O' Conor uh uh uh really got + + align:start position:0% +Donald O' Conor uh uh uh really got + + + align:start position:0% +Donald O' Conor uh uh uh really got +their start. And so that while he says + + align:start position:0% +their start. And so that while he says + + + align:start position:0% +their start. And so that while he says +we were trained in the best uh + + align:start position:0% +we were trained in the best uh + + + align:start position:0% +we were trained in the best uh +conservatories, what we see are Donald + + align:start position:0% +conservatories, what we see are Donald + + + align:start position:0% +conservatories, what we see are Donald +O' Conor and Jean Kelly dancing in a + + align:start position:0% +O' Conor and Jean Kelly dancing in a + + + align:start position:0% +O' Conor and Jean Kelly dancing in a +burles show. and and so the so there's + + align:start position:0% +burles show. and and so the so there's + + + align:start position:0% +burles show. and and so the so there's +this there's this constant very obvious + + align:start position:0% +this there's this constant very obvious + + + align:start position:0% +this there's this constant very obvious +even in some ways crude uh mockery or + + align:start position:0% +even in some ways crude uh mockery or + + + align:start position:0% +even in some ways crude uh mockery or +laughter at the hypocrisies of of of of + + align:start position:0% +laughter at the hypocrisies of of of of + + + align:start position:0% +laughter at the hypocrisies of of of of +Hollywood and part of what's being + + align:start position:0% +Hollywood and part of what's being + + + align:start position:0% +Hollywood and part of what's being +celebrated there is the exuberance and + + align:start position:0% +celebrated there is the exuberance and + + + align:start position:0% +celebrated there is the exuberance and +energy of of unsanctioned forms of + + align:start position:0% +energy of of unsanctioned forms of + + + align:start position:0% +energy of of unsanctioned forms of +performance like the dances that people + + align:start position:0% +performance like the dances that people + + + align:start position:0% +performance like the dances that people +do in burlesque shows right uh as + + align:start position:0% +do in burlesque shows right uh as + + + align:start position:0% +do in burlesque shows right uh as +against what you do when you go to the + + align:start position:0% +against what you do when you go to the + + + align:start position:0% +against what you do when you go to the +museum or when you come to the + + align:start position:0% +museum or when you come to the + + + align:start position:0% +museum or when you come to the +university and have your professor + + align:start position:0% +university and have your professor + + + align:start position:0% +university and have your professor +declaim ancient Greek to you in + + align:start position:0% +declaim ancient Greek to you in + + + align:start position:0% +declaim ancient Greek to you in +syllables you have no understanding of. + + align:start position:0% +syllables you have no understanding of. + + + align:start position:0% +syllables you have no understanding of. +Right? So, uh uh so there's one example + + align:start position:0% +Right? So, uh uh so there's one example + + + align:start position:0% +Right? So, uh uh so there's one example +of how that theme plays out, but you can + + align:start position:0% +of how that theme plays out, but you can + + + align:start position:0% +of how that theme plays out, but you can +find it in dozens and dozens of other + + align:start position:0% +find it in dozens and dozens of other + + + align:start position:0% +find it in dozens and dozens of other +places in the film, and I hope you'll + + align:start position:0% +places in the film, and I hope you'll + + + align:start position:0% +places in the film, and I hope you'll +watch watch for them. Um uh for such + + align:start position:0% +watch watch for them. Um uh for such + + + align:start position:0% +watch watch for them. Um uh for such +moments. So, I so I won't give you my + + align:start position:0% +moments. So, I so I won't give you my + + + align:start position:0% +moments. So, I so I won't give you my +second example. I'm running out of time. + + align:start position:0% +second example. I'm running out of time. + + + align:start position:0% +second example. I'm running out of time. +I'll let me turn to a next to to the + + align:start position:0% +I'll let me turn to a next to to the + + + align:start position:0% +I'll let me turn to a next to to the +next large theme I want you to be aware + + align:start position:0% +next large theme I want you to be aware + + + align:start position:0% +next large theme I want you to be aware +of. I call it the theme of outer versus + + align:start position:0% +of. I call it the theme of outer versus + + + align:start position:0% +of. I call it the theme of outer versus +inner. It's really a variation on or or + + align:start position:0% +inner. It's really a variation on or or + + + align:start position:0% +inner. It's really a variation on or or +or a or or an extension uh um of the + + align:start position:0% +or a or or an extension uh um of the + + + align:start position:0% +or a or or an extension uh um of the +theme of high versus popular art in the + + align:start position:0% +theme of high versus popular art in the + + + align:start position:0% +theme of high versus popular art in the +sense that it's also about the + + align:start position:0% +sense that it's also about the + + + align:start position:0% +sense that it's also about the +difference between a kind of pretentious + + align:start position:0% +difference between a kind of pretentious + + + align:start position:0% +difference between a kind of pretentious +and constraining and old-fashioned view + + align:start position:0% +and constraining and old-fashioned view + + + align:start position:0% +and constraining and old-fashioned view +of things and a more spontaneous uh um u + + align:start position:0% +of things and a more spontaneous uh um u + + + align:start position:0% +of things and a more spontaneous uh um u +and and and uh I we might even say a + + align:start position:0% +and and and uh I we might even say a + + + align:start position:0% +and and and uh I we might even say a +more spontaneous and popular or + + align:start position:0% +more spontaneous and popular or + + + align:start position:0% +more spontaneous and popular or +democratic view view of things. this + + align:start position:0% +democratic view view of things. this + + + align:start position:0% +democratic view view of things. this +when I so and the term I give it is the + + align:start position:0% +when I so and the term I give it is the + + + align:start position:0% +when I so and the term I give it is the +difference between outer and inner or + + align:start position:0% +difference between outer and inner or + + + align:start position:0% +difference between outer and inner or +the difference between appearance and + + align:start position:0% +the difference between appearance and + + + align:start position:0% +the difference between appearance and +reality and in in fact the example I + + align:start position:0% +reality and in in fact the example I + + + align:start position:0% +reality and in in fact the example I +just gave you in which we have Don + + align:start position:0% +just gave you in which we have Don + + + align:start position:0% +just gave you in which we have Don +Lockwood telling the reporter that he + + align:start position:0% +Lockwood telling the reporter that he + + + align:start position:0% +Lockwood telling the reporter that he +was educated in the best conservatories + + align:start position:0% +was educated in the best conservatories + + + align:start position:0% +was educated in the best conservatories +while we see that he's dancing in a + + align:start position:0% +while we see that he's dancing in a + + + align:start position:0% +while we see that he's dancing in a +burles show uh is an example of that + + align:start position:0% +burles show uh is an example of that + + + align:start position:0% +burles show uh is an example of that +kind of thing as well but there are many + + align:start position:0% +kind of thing as well but there are many + + + align:start position:0% +kind of thing as well but there are many +other very dramatic examples and I want + + align:start position:0% +other very dramatic examples and I want + + + align:start position:0% +other very dramatic examples and I want +to mention u one of them now uh the uh + + align:start position:0% +to mention u one of them now uh the uh + + + align:start position:0% +to mention u one of them now uh the uh +the uh when when uh when the Debbie + + align:start position:0% +the uh when when uh when the Debbie + + + align:start position:0% +the uh when when uh when the Debbie +Reynolds character the love interest of + + align:start position:0% +Reynolds character the love interest of + + + align:start position:0% +Reynolds character the love interest of +of of the of our protagonist first meets + + align:start position:0% +of of the of our protagonist first meets + + + align:start position:0% +of of the of our protagonist first meets +the Don Lockwood character, the + + align:start position:0% +the Don Lockwood character, the + + + align:start position:0% +the Don Lockwood character, the +character played by Jean Kelly. Uh she + + align:start position:0% +character played by Jean Kelly. Uh she + + + align:start position:0% +character played by Jean Kelly. Uh she +pretends not to recognize him even + + align:start position:0% +pretends not to recognize him even + + + align:start position:0% +pretends not to recognize him even +though he's a famous movie star. And she + + align:start position:0% +though he's a famous movie star. And she + + + align:start position:0% +though he's a famous movie star. And she +says and she and and she says, "Oh, she + + align:start position:0% +says and she and and she says, "Oh, she + + + align:start position:0% +says and she and and she says, "Oh, she +spends her time watching Shakespeare, + + align:start position:0% +spends her time watching Shakespeare, + + + align:start position:0% +spends her time watching Shakespeare, +but she doesn't spend much time watching + + align:start position:0% +but she doesn't spend much time watching + + + align:start position:0% +but she doesn't spend much time watching +the movies." And Don Lockwood is kind of + + align:start position:0% +the movies." And Don Lockwood is kind of + + + align:start position:0% +the movies." And Don Lockwood is kind of +offended by this. It later turns out, + + align:start position:0% +offended by this. It later turns out, + + + align:start position:0% +offended by this. It later turns out, +not even that much later, that of course + + align:start position:0% +not even that much later, that of course + + + align:start position:0% +not even that much later, that of course +Debbie Reynolds character herself is + + align:start position:0% +Debbie Reynolds character herself is + + + align:start position:0% +Debbie Reynolds character herself is +deeply immersed in the popular culture. + + align:start position:0% +deeply immersed in the popular culture. + + + align:start position:0% +deeply immersed in the popular culture. +Right after she makes this comment to + + align:start position:0% +Right after she makes this comment to + + + align:start position:0% +Right after she makes this comment to +Don Lockwood, a few a few minutes after + + align:start position:0% +Don Lockwood, a few a few minutes after + + + align:start position:0% +Don Lockwood, a few a few minutes after +that, we find her jumping out of a cake + + align:start position:0% +that, we find her jumping out of a cake + + + align:start position:0% +that, we find her jumping out of a cake +as a dancer in a in a uh at a party. Uh + + align:start position:0% +as a dancer in a in a uh at a party. Uh + + + align:start position:0% +as a dancer in a in a uh at a party. Uh +and and and and what we + + align:start position:0% + + + + align:start position:0% + +recognize, of course, that that of she + + align:start position:0% +recognize, of course, that that of she + + + align:start position:0% +recognize, of course, that that of she +knows a great deal about Don Lockwood. + + align:start position:0% +knows a great deal about Don Lockwood. + + + align:start position:0% +knows a great deal about Don Lockwood. +She's always been a tremendous fan of + + align:start position:0% +She's always been a tremendous fan of + + + align:start position:0% +She's always been a tremendous fan of +the movies, but she's been covering it + + align:start position:0% +the movies, but she's been covering it + + + align:start position:0% +the movies, but she's been covering it +up. And again and again in the in the + + align:start position:0% +up. And again and again in the in the + + + align:start position:0% +up. And again and again in the in the +film, uh, we see this kind of tension + + align:start position:0% +film, uh, we see this kind of tension + + + align:start position:0% +film, uh, we see this kind of tension +playing itself out. This tension between + + align:start position:0% +playing itself out. This tension between + + + align:start position:0% +playing itself out. This tension between +a kind of uh outer facade, a kind of a + + align:start position:0% +a kind of uh outer facade, a kind of a + + + align:start position:0% +a kind of uh outer facade, a kind of a +kind of and the notion is that what what + + align:start position:0% +kind of and the notion is that what what + + + align:start position:0% +kind of and the notion is that what what +is shown on the outside, what the + + align:start position:0% +is shown on the outside, what the + + + align:start position:0% +is shown on the outside, what the +exterior of things is often fake, a a + + align:start position:0% +exterior of things is often fake, a a + + + align:start position:0% +exterior of things is often fake, a a +mere a mere cover for what is authentic + + align:start position:0% +mere a mere cover for what is authentic + + + align:start position:0% +mere a mere cover for what is authentic +and within, right? And you can + + align:start position:0% +and within, right? And you can + + + align:start position:0% +and within, right? And you can +understand this in a number of ways. But + + align:start position:0% +understand this in a number of ways. But + + + align:start position:0% +understand this in a number of ways. But +if you think uh one of the ways it plays + + align:start position:0% +if you think uh one of the ways it plays + + + align:start position:0% +if you think uh one of the ways it plays +out in the movie is the question of the + + align:start position:0% +out in the movie is the question of the + + + align:start position:0% +out in the movie is the question of the +person who is who is in front of the + + align:start position:0% +person who is who is in front of the + + + align:start position:0% +person who is who is in front of the +audience and singing, but but it's not + + align:start position:0% +audience and singing, but but it's not + + + align:start position:0% +audience and singing, but but it's not +really her voice. It's the voice of + + align:start position:0% +really her voice. It's the voice of + + + align:start position:0% +really her voice. It's the voice of +Debbie Reynolds who's behind the + + align:start position:0% +Debbie Reynolds who's behind the + + + align:start position:0% +Debbie Reynolds who's behind the +curtain, right? And uh that so that so + + align:start position:0% +curtain, right? And uh that so that so + + + align:start position:0% +curtain, right? And uh that so that so +that again this theme of of of the + + align:start position:0% +that again this theme of of of the + + + align:start position:0% +that again this theme of of of the +artificial versus the authentic or the + + align:start position:0% +artificial versus the authentic or the + + + align:start position:0% +artificial versus the authentic or the +outer versus the inner plays itself out + + align:start position:0% +outer versus the inner plays itself out + + + align:start position:0% +outer versus the inner plays itself out +in many many ways in the film. That's + + align:start position:0% +in many many ways in the film. That's + + + align:start position:0% +in many many ways in the film. That's +part of what makes the film so coherent, + + align:start position:0% +part of what makes the film so coherent, + + + align:start position:0% +part of what makes the film so coherent, +so so so uh so dramatically effective + + align:start position:0% +so so so uh so dramatically effective + + + align:start position:0% +so so so uh so dramatically effective +and energetic. Um uh and so another way + + align:start position:0% +and energetic. Um uh and so another way + + + align:start position:0% +and energetic. Um uh and so another way +of thinking about this sequence, this + + align:start position:0% +of thinking about this sequence, this + + + align:start position:0% +of thinking about this sequence, this +idea of the outer versus the outer + + align:start position:0% +idea of the outer versus the outer + + + align:start position:0% +idea of the outer versus the outer +person versus the inner authentic + + align:start position:0% +person versus the inner authentic + + + align:start position:0% +person versus the inner authentic +person. Uh the the outer appearance, the + + align:start position:0% +person. Uh the the outer appearance, the + + + align:start position:0% +person. Uh the the outer appearance, the +illusion that film makes, but what + + align:start position:0% +illusion that film makes, but what + + + align:start position:0% +illusion that film makes, but what +really goes on behind the scenes. And as + + align:start position:0% +really goes on behind the scenes. And as + + + align:start position:0% +really goes on behind the scenes. And as +you'll discover, Singing in the Rain + + align:start position:0% +you'll discover, Singing in the Rain + + + align:start position:0% +you'll discover, Singing in the Rain +constantly takes us behind the scenes to + + align:start position:0% +constantly takes us behind the scenes to + + + align:start position:0% +constantly takes us behind the scenes to +show us how the illusion of movies is + + align:start position:0% +show us how the illusion of movies is + + + align:start position:0% +show us how the illusion of movies is +put together. Right. And that's a part + + align:start position:0% +put together. Right. And that's a part + + + align:start position:0% +put together. Right. And that's a part +of this same theme. So, one of the + + align:start position:0% +of this same theme. So, one of the + + + align:start position:0% +of this same theme. So, one of the +things I'm trying to call your attention + + align:start position:0% +things I'm trying to call your attention + + + align:start position:0% +things I'm trying to call your attention +to again is the way in which the the bas + + align:start position:0% +to again is the way in which the the bas + + + align:start position:0% +to again is the way in which the the bas +the central ideas of the film permeate + + align:start position:0% +the central ideas of the film permeate + + + align:start position:0% +the central ideas of the film permeate +both its form and its content in ways + + align:start position:0% +both its form and its content in ways + + + align:start position:0% +both its form and its content in ways +that make it very difficult to separate. + + align:start position:0% +that make it very difficult to separate. + + + align:start position:0% +that make it very difficult to separate. +Right. Uh, finally, one last fundamental + + align:start position:0% +Right. Uh, finally, one last fundamental + + + align:start position:0% +Right. Uh, finally, one last fundamental +issue connected to what I've been saying + + align:start position:0% +issue connected to what I've been saying + + + align:start position:0% +issue connected to what I've been saying +before, the way the film meditates on or + + align:start position:0% +before, the way the film meditates on or + + + align:start position:0% +before, the way the film meditates on or +dramatizes an idea about the place of + + align:start position:0% +dramatizes an idea about the place of + + + align:start position:0% +dramatizes an idea about the place of +song and dance in human life. You will + + align:start position:0% +song and dance in human life. You will + + + align:start position:0% +song and dance in human life. You will +have noticed of course uh uh that I + + align:start position:0% +have noticed of course uh uh that I + + + align:start position:0% +have noticed of course uh uh that I +myself feel and uh if you've seen any of + + align:start position:0% +myself feel and uh if you've seen any of + + + align:start position:0% +myself feel and uh if you've seen any of +the performances uh in this film you'll + + align:start position:0% +the performances uh in this film you'll + + + align:start position:0% +the performances uh in this film you'll +know yourselves that a principle of + + align:start position:0% +know yourselves that a principle of + + + align:start position:0% +know yourselves that a principle of +energy, vitality, playfulness, + + align:start position:0% +energy, vitality, playfulness, + + + align:start position:0% +energy, vitality, playfulness, +exuberance is almost always present in + + align:start position:0% +exuberance is almost always present in + + + align:start position:0% +exuberance is almost always present in +the dances in singing in the rain. Song + + align:start position:0% +the dances in singing in the rain. Song + + + align:start position:0% +the dances in singing in the rain. Song +and dance is seen in singing in the rain + + align:start position:0% +and dance is seen in singing in the rain + + + align:start position:0% +and dance is seen in singing in the rain +as a morally and psychologically + + align:start position:0% +as a morally and psychologically + + + align:start position:0% +as a morally and psychologically +revolutionary experience. I think and I + + align:start position:0% +revolutionary experience. I think and I + + + align:start position:0% +revolutionary experience. I think and I +use the word revolution in a dangerous + + align:start position:0% +use the word revolution in a dangerous + + + align:start position:0% +use the word revolution in a dangerous +way. I don't mean a politically + + align:start position:0% +way. I don't mean a politically + + + align:start position:0% +way. I don't mean a politically +revolutionary way, but I mean in a + + align:start position:0% +revolutionary way, but I mean in a + + + align:start position:0% +revolutionary way, but I mean in a +morally, a psychologically revolutionary + + align:start position:0% +morally, a psychologically revolutionary + + + align:start position:0% +morally, a psychologically revolutionary +way. And over uh so what's going on in + + align:start position:0% +way. And over uh so what's going on in + + + align:start position:0% +way. And over uh so what's going on in +some sense is the sense that constraint + + align:start position:0% +some sense is the sense that constraint + + + align:start position:0% +some sense is the sense that constraint +and convention are constantly threatened + + align:start position:0% +and convention are constantly threatened + + + align:start position:0% +and convention are constantly threatened +by the exuberance, spontaneity, energy, + + align:start position:0% +by the exuberance, spontaneity, energy, + + + align:start position:0% +by the exuberance, spontaneity, energy, +excitement, vitality of the dance, + + align:start position:0% +excitement, vitality of the dance, + + + align:start position:0% +excitement, vitality of the dance, +right? And this expresses itself in all + + align:start position:0% +right? And this expresses itself in all + + + align:start position:0% +right? And this expresses itself in all +kinds of ways in the film. Let me just + + align:start position:0% +kinds of ways in the film. Let me just + + + align:start position:0% +kinds of ways in the film. Let me just +mention a couple to call your attention + + align:start position:0% +mention a couple to call your attention + + + align:start position:0% +mention a couple to call your attention +to. You'll you'll discover many many + + align:start position:0% +to. You'll you'll discover many many + + + align:start position:0% +to. You'll you'll discover many many +other examples. One is the wonderful + + align:start position:0% +other examples. One is the wonderful + + + align:start position:0% +other examples. One is the wonderful +sequence, the Moses suppososes sequence. + + align:start position:0% +sequence, the Moses suppososes sequence. + + + align:start position:0% +sequence, the Moses suppososes sequence. +This is a sequence in which Don Lockwood + + align:start position:0% +This is a sequence in which Don Lockwood + + + align:start position:0% +This is a sequence in which Don Lockwood +and his partner Donald O' Conor have to + + align:start position:0% +and his partner Donald O' Conor have to + + + align:start position:0% +and his partner Donald O' Conor have to +be trained because they're making the + + align:start position:0% +be trained because they're making the + + + align:start position:0% +be trained because they're making the +transition to sound and the studio calls + + align:start position:0% +transition to sound and the studio calls + + + align:start position:0% +transition to sound and the studio calls +in an elecution expert who's a very + + align:start position:0% +in an elecution expert who's a very + + + align:start position:0% +in an elecution expert who's a very +who's dressed up like a very pretentious + + align:start position:0% +who's dressed up like a very pretentious + + + align:start position:0% +who's dressed up like a very pretentious +oldline professor, right? Uh and he's + + align:start position:0% +oldline professor, right? Uh and he's + + + align:start position:0% +oldline professor, right? Uh and he's +he's going to teach them how to + + align:start position:0% +he's going to teach them how to + + + align:start position:0% +he's going to teach them how to +pronounce things correctly. So he comes + + align:start position:0% +pronounce things correctly. So he comes + + + align:start position:0% +pronounce things correctly. So he comes +in and and he says, "I want you to + + align:start position:0% +in and and he says, "I want you to + + + align:start position:0% +in and and he says, "I want you to +repeat after me. Moses supposes his toes + + align:start position:0% +repeat after me. Moses supposes his toes + + + align:start position:0% +repeat after me. Moses supposes his toes +are + + align:start position:0% +are + + + align:start position:0% +are +roses, but Moses supposes + + align:start position:0% +roses, but Moses supposes + + + align:start position:0% +roses, but Moses supposes +erroneously, right? He's also ugly. His + + align:start position:0% +erroneously, right? He's also ugly. His + + + align:start position:0% +erroneously, right? He's also ugly. His +teeth are disgusting. And so you're + + align:start position:0% +teeth are disgusting. And so you're + + + align:start position:0% +teeth are disgusting. And so you're +already offended by the guy before Dawn + + align:start position:0% +already offended by the guy before Dawn + + + align:start position:0% +already offended by the guy before Dawn +and his comrade begin to respond. But + + align:start position:0% +and his comrade begin to respond. But + + + align:start position:0% +and his comrade begin to respond. But +and also, of course, what's ridiculous + + align:start position:0% +and also, of course, what's ridiculous + + + align:start position:0% +and also, of course, what's ridiculous +about this? It's meaningless talk, + + align:start position:0% +about this? It's meaningless talk, + + + align:start position:0% +about this? It's meaningless talk, +right? Or he's so interested in making + + align:start position:0% +right? Or he's so interested in making + + + align:start position:0% +right? Or he's so interested in making +him pronounce the the O vowel properly + + align:start position:0% +him pronounce the the O vowel properly + + + align:start position:0% +him pronounce the the O vowel properly +that he creates meaning meaningless uh + + align:start position:0% +that he creates meaning meaningless uh + + + align:start position:0% +that he creates meaning meaningless uh +sentences. But but their meaninglessness + + align:start position:0% +sentences. But but their meaninglessness + + + align:start position:0% +sentences. But but their meaninglessness +uh amuses Don Lockwood and his partner. + + align:start position:0% +uh amuses Don Lockwood and his partner. + + + align:start position:0% +uh amuses Don Lockwood and his partner. +And what they essentially what they do + + align:start position:0% +And what they essentially what they do + + + align:start position:0% +And what they essentially what they do +is they take the Moses supposes uh lines + + align:start position:0% +is they take the Moses supposes uh lines + + + align:start position:0% +is they take the Moses supposes uh lines +and they begin to sort of make fun of + + align:start position:0% +and they begin to sort of make fun of + + + align:start position:0% +and they begin to sort of make fun of +them and they begin to make fun of their + + align:start position:0% +them and they begin to make fun of their + + + align:start position:0% +them and they begin to make fun of their +of their interlocator their teacher. + + align:start position:0% +of their interlocator their teacher. + + + align:start position:0% +of their interlocator their teacher. +They end up taking a garbage can and + + align:start position:0% +They end up taking a garbage can and + + + align:start position:0% +They end up taking a garbage can and +emptying it out just as paper and + + align:start position:0% +emptying it out just as paper and + + + align:start position:0% +emptying it out just as paper and +putting it on his head. They end up + + align:start position:0% +putting it on his head. They end up + + + align:start position:0% +putting it on his head. They end up +dancing in a ridiculous way. So they end + + align:start position:0% +dancing in a ridiculous way. So they end + + + align:start position:0% +dancing in a ridiculous way. So they end +up dancing on top of desks or up the + + align:start position:0% +up dancing on top of desks or up the + + + align:start position:0% +up dancing on top of desks or up the +side of walls. Again, what are they + + align:start position:0% +side of walls. Again, what are they + + + align:start position:0% +side of walls. Again, what are they +doing? their dances are violating the + + align:start position:0% +doing? their dances are violating the + + + align:start position:0% +doing? their dances are violating the +normal spaces in which we expect people + + align:start position:0% +normal spaces in which we expect people + + + align:start position:0% +normal spaces in which we expect people +to be walking or standing upright. The + + align:start position:0% +to be walking or standing upright. The + + + align:start position:0% +to be walking or standing upright. The +very way in which the dance violates + + align:start position:0% +very way in which the dance violates + + + align:start position:0% +very way in which the dance violates +normal boundaries creates this sense of + + align:start position:0% +normal boundaries creates this sense of + + + align:start position:0% +normal boundaries creates this sense of +exuberance and of freedom. So what + + align:start position:0% +exuberance and of freedom. So what + + + align:start position:0% +exuberance and of freedom. So what +they're doing is they're rebelling + + align:start position:0% +they're doing is they're rebelling + + + align:start position:0% +they're doing is they're rebelling +against the pretentiousness um uh the + + align:start position:0% +against the pretentiousness um uh the + + + align:start position:0% +against the pretentiousness um uh the +constraints of these of this kind of of + + align:start position:0% +constraints of these of this kind of of + + + align:start position:0% +constraints of these of this kind of of +this kind of uh uh high culture + + align:start position:0% +this kind of uh uh high culture + + + align:start position:0% +this kind of uh uh high culture +expectation uh and and and the song song + + align:start position:0% +expectation uh and and and the song song + + + align:start position:0% +expectation uh and and and the song song +and dance uh uh in the Moses sequence + + align:start position:0% +and dance uh uh in the Moses sequence + + + align:start position:0% +and dance uh uh in the Moses sequence +create a kind of exuberant chaos in + + align:start position:0% +create a kind of exuberant chaos in + + + align:start position:0% +create a kind of exuberant chaos in +which they dance on the tables and make + + align:start position:0% +which they dance on the tables and make + + + align:start position:0% +which they dance on the tables and make +fun of the very elements that they're + + align:start position:0% +fun of the very elements that they're + + + align:start position:0% +fun of the very elements that they're +supposed to be learning. The good + + align:start position:0% +supposed to be learning. The good + + + align:start position:0% +supposed to be learning. The good +morning sequence, one of the great + + align:start position:0% +morning sequence, one of the great + + + align:start position:0% +morning sequence, one of the great +sequences in the history of movies, I + + align:start position:0% +sequences in the history of movies, I + + + align:start position:0% +sequences in the history of movies, I +think, shows the same thing which it + + align:start position:0% +think, shows the same thing which it + + + align:start position:0% +think, shows the same thing which it +takes place at breakfast in an ordinary + + align:start position:0% +takes place at breakfast in an ordinary + + + align:start position:0% +takes place at breakfast in an ordinary +domestic space which is transfigured or + + align:start position:0% +domestic space which is transfigured or + + + align:start position:0% +domestic space which is transfigured or +transformed including the props in + + align:start position:0% +transformed including the props in + + + align:start position:0% +transformed including the props in +something of that we might imagine + + align:start position:0% +something of that we might imagine + + + align:start position:0% +something of that we might imagine +chaplain doing such imaginative things + + align:start position:0% +chaplain doing such imaginative things + + + align:start position:0% +chaplain doing such imaginative things +in which in which the ordinary props of + + align:start position:0% +in which in which the ordinary props of + + + align:start position:0% +in which in which the ordinary props of +the kitchen uh turning be become + + align:start position:0% +the kitchen uh turning be become + + + align:start position:0% +the kitchen uh turning be become +partners in the dance become elements in + + align:start position:0% +partners in the dance become elements in + + + align:start position:0% +partners in the dance become elements in +a dance. What we feel is the imaginative + + align:start position:0% +a dance. What we feel is the imaginative + + + align:start position:0% +a dance. What we feel is the imaginative +power of love and and of performance + + align:start position:0% +power of love and and of performance + + + align:start position:0% +power of love and and of performance +transforming an ordinary space. And we + + align:start position:0% +transforming an ordinary space. And we + + + align:start position:0% +transforming an ordinary space. And we +can see this principle operating in with + + align:start position:0% +can see this principle operating in with + + + align:start position:0% +can see this principle operating in with +an even greater force in the title + + align:start position:0% +an even greater force in the title + + + align:start position:0% +an even greater force in the title +sequence of the film. Probably the most + + align:start position:0% +sequence of the film. Probably the most + + + align:start position:0% +sequence of the film. Probably the most +famous sequence of dance in the in in + + align:start position:0% +famous sequence of dance in the in in + + + align:start position:0% +famous sequence of dance in the in in +the history of Hollywood. The singing in + + align:start position:0% +the history of Hollywood. The singing in + + + align:start position:0% +the history of Hollywood. The singing in +the rain sequence itself. Uh we see the + + align:start position:0% +the rain sequence itself. Uh we see the + + + align:start position:0% +the rain sequence itself. Uh we see the +rain itself. What a funny place to be + + align:start position:0% +rain itself. What a funny place to be + + + align:start position:0% +rain itself. What a funny place to be +dancing, right? There's a contradiction. + + align:start position:0% +dancing, right? There's a contradiction. + + + align:start position:0% +dancing, right? There's a contradiction. +But your exuberance, your energy, your + + align:start position:0% +But your exuberance, your energy, your + + + align:start position:0% +But your exuberance, your energy, your +sense of love is so great that even rain + + align:start position:0% +sense of love is so great that even rain + + + align:start position:0% +sense of love is so great that even rain +doesn't matter. Uh, and watch what + + align:start position:0% +doesn't matter. Uh, and watch what + + + align:start position:0% +doesn't matter. Uh, and watch what +happens. He has an umbrella, but he + + align:start position:0% +happens. He has an umbrella, but he + + + align:start position:0% +happens. He has an umbrella, but he +doesn't use the umbrella to protect him + + align:start position:0% +doesn't use the umbrella to protect him + + + align:start position:0% +doesn't use the umbrella to protect him +from the rain, violating our + + align:start position:0% +from the rain, violating our + + + align:start position:0% +from the rain, violating our +expectations. There's a one wonderful + + align:start position:0% +expectations. There's a one wonderful + + + align:start position:0% +expectations. There's a one wonderful +moment in the film where he hands the + + align:start position:0% +moment in the film where he hands the + + + align:start position:0% +moment in the film where he hands the +umbrella in the midst of pouring rain to + + align:start position:0% +umbrella in the midst of pouring rain to + + + align:start position:0% +umbrella in the midst of pouring rain to +someone else who goes by to a pedestrian + + align:start position:0% +someone else who goes by to a pedestrian + + + align:start position:0% +someone else who goes by to a pedestrian +who goes by, right? Uh there's a moment + + align:start position:0% +who goes by, right? Uh there's a moment + + + align:start position:0% +who goes by, right? Uh there's a moment +when he's dancing in the rain. He take + + align:start position:0% +when he's dancing in the rain. He take + + + align:start position:0% +when he's dancing in the rain. He take +puts the umbrella down. The rain's come, + + align:start position:0% +puts the umbrella down. The rain's come, + + + align:start position:0% +puts the umbrella down. The rain's come, +but he doesn't have enough rain pouring + + align:start position:0% +but he doesn't have enough rain pouring + + + align:start position:0% +but he doesn't have enough rain pouring +on him. steps under a downspout to have + + align:start position:0% +on him. steps under a downspout to have + + + align:start position:0% +on him. steps under a downspout to have +the even more rain come down on. And + + align:start position:0% +the even more rain come down on. And + + + align:start position:0% +the even more rain come down on. And +when we experience this, what we feel is + + align:start position:0% +when we experience this, what we feel is + + + align:start position:0% +when we experience this, what we feel is +not what one of the reasons we + + align:start position:0% +not what one of the reasons we + + + align:start position:0% +not what one of the reasons we +experience this as joyful and as + + align:start position:0% +experience this as joyful and as + + + align:start position:0% +experience this as joyful and as +assertive and as individualizing is the + + align:start position:0% +assertive and as individualizing is the + + + align:start position:0% +assertive and as individualizing is the +sense we have that these are exactly not + + align:start position:0% +sense we have that these are exactly not + + + align:start position:0% +sense we have that these are exactly not +things that people normally do. He's + + align:start position:0% +things that people normally do. He's + + + align:start position:0% +things that people normally do. He's +overgoing or violating certain + + align:start position:0% +overgoing or violating certain + + + align:start position:0% +overgoing or violating certain +conventions or literal boundaries. And + + align:start position:0% +conventions or literal boundaries. And + + + align:start position:0% +conventions or literal boundaries. And +there's one moment in the dance very + + align:start position:0% +there's one moment in the dance very + + + align:start position:0% +there's one moment in the dance very +dramatic. I know this incidentally not + + align:start position:0% +dramatic. I know this incidentally not + + + align:start position:0% +dramatic. I know this incidentally not +because I've discovered it myself but + + align:start position:0% +because I've discovered it myself but + + + align:start position:0% +because I've discovered it myself but +because 20 years ago or 15 years ago in + + align:start position:0% +because 20 years ago or 15 years ago in + + + align:start position:0% +because 20 years ago or 15 years ago in +this course a student who later went on + + align:start position:0% +this course a student who later went on + + + align:start position:0% +this course a student who later went on +to work in Hollywood and he still works + + align:start position:0% +to work in Hollywood and he still works + + + align:start position:0% +to work in Hollywood and he still works +there. He's a sound genius. He was an + + align:start position:0% +there. He's a sound genius. He was an + + + align:start position:0% +there. He's a sound genius. He was an +MIT engineer who loved this course and + + align:start position:0% +MIT engineer who loved this course and + + + align:start position:0% +MIT engineer who loved this course and +was a musician as well. He wrote a paper + + align:start position:0% +was a musician as well. He wrote a paper + + + align:start position:0% +was a musician as well. He wrote a paper +for me uh uh about that sequence and he + + align:start position:0% +for me uh uh about that sequence and he + + + align:start position:0% +for me uh uh about that sequence and he +showed me this and uh I'm sure that some + + align:start position:0% +showed me this and uh I'm sure that some + + + align:start position:0% +showed me this and uh I'm sure that some +smart critics also saw it but I learned + + align:start position:0% +smart critics also saw it but I learned + + + align:start position:0% +smart critics also saw it but I learned +this from an MIT student in this course + + align:start position:0% +this from an MIT student in this course + + + align:start position:0% +this from an MIT student in this course +about 15 years ago. He analyzed the + + align:start position:0% +about 15 years ago. He analyzed the + + + align:start position:0% +about 15 years ago. He analyzed the +dance sequence very closely. And one of + + align:start position:0% +dance sequence very closely. And one of + + + align:start position:0% +dance sequence very closely. And one of +the things he showed was that the + + align:start position:0% +the things he showed was that the + + + align:start position:0% +the things he showed was that the +decisive moment in the dance occurs when + + align:start position:0% +decisive moment in the dance occurs when + + + align:start position:0% +decisive moment in the dance occurs when +the ordecisive moment in the dance + + align:start position:0% +the ordecisive moment in the dance + + + align:start position:0% +the ordecisive moment in the dance +occurs when the Kelly character suddenly + + align:start position:0% +occurs when the Kelly character suddenly + + + align:start position:0% +occurs when the Kelly character suddenly +is dancing on the sidewalk jumps off the + + align:start position:0% +is dancing on the sidewalk jumps off the + + + align:start position:0% +is dancing on the sidewalk jumps off the +sidewalk across the curb into the + + align:start position:0% +sidewalk across the curb into the + + + align:start position:0% +sidewalk across the curb into the +street. And psychologically it has a + + align:start position:0% +street. And psychologically it has a + + + align:start position:0% +street. And psychologically it has a +tremendously profound effect because you + + align:start position:0% +tremendously profound effect because you + + + align:start position:0% +tremendously profound effect because you +don't walk in the street much less dance + + align:start position:0% +don't walk in the street much less dance + + + align:start position:0% +don't walk in the street much less dance +in the street. The streets for this the + + align:start position:0% +in the street. The streets for this the + + + align:start position:0% +in the street. The streets for this the +street is for cars. But that violation + + align:start position:0% +street is for cars. But that violation + + + align:start position:0% +street is for cars. But that violation +of the boundary expresses the sense of + + align:start position:0% +of the boundary expresses the sense of + + + align:start position:0% +of the boundary expresses the sense of +exuberance of freedom that is supposed + + align:start position:0% +exuberance of freedom that is supposed + + + align:start position:0% +exuberance of freedom that is supposed +to be pre that is that is the that is + + align:start position:0% +to be pre that is that is the that is + + + align:start position:0% +to be pre that is that is the that is +the the essential meaning of of what + + align:start position:0% +the the essential meaning of of what + + + align:start position:0% +the the essential meaning of of what +these dances represent. So energy, + + align:start position:0% +these dances represent. So energy, + + + align:start position:0% +these dances represent. So energy, +spontaneous feeling, performing and + + align:start position:0% +spontaneous feeling, performing and + + + align:start position:0% +spontaneous feeling, performing and +overgoing limits is one of the things + + align:start position:0% +overgoing limits is one of the things + + + align:start position:0% +overgoing limits is one of the things +that's being expressed in the in the in + + align:start position:0% +that's being expressed in the in the in + + + align:start position:0% +that's being expressed in the in the in +the exuberance of the film's formal + + align:start position:0% +the exuberance of the film's formal + + + align:start position:0% +the exuberance of the film's formal +structure in its encyclopedic reaching + + align:start position:0% +structure in its encyclopedic reaching + + + align:start position:0% +structure in its encyclopedic reaching +out to other forms which it wants to + + align:start position:0% +out to other forms which it wants to + + + align:start position:0% +out to other forms which it wants to +incorporate into itself and in its + + align:start position:0% +incorporate into itself and in its + + + align:start position:0% +incorporate into itself and in its +particular dance and song sequences. And + + align:start position:0% +particular dance and song sequences. And + + + align:start position:0% +particular dance and song sequences. And +this energy, this celebration of + + align:start position:0% +this energy, this celebration of + + + align:start position:0% +this energy, this celebration of +transformative energy, of the overgoing + + align:start position:0% +transformative energy, of the overgoing + + + align:start position:0% +transformative energy, of the overgoing +of boundaries, strikes me as + + align:start position:0% +of boundaries, strikes me as + + + align:start position:0% +of boundaries, strikes me as +particularly American as a as a as a + + align:start position:0% +particularly American as a as a as a + + + align:start position:0% +particularly American as a as a as a +uniquely interesting expression of what + + align:start position:0% +uniquely interesting expression of what + + + align:start position:0% +uniquely interesting expression of what +people have sometimes called American + + align:start position:0% +people have sometimes called American + + + align:start position:0% +people have sometimes called American +optimism. Uh, and even of the democratic + + align:start position:0% +optimism. Uh, and even of the democratic + + + align:start position:0% +optimism. Uh, and even of the democratic +spirit of the openness that we associate + + align:start position:0% +spirit of the openness that we associate + + + align:start position:0% +spirit of the openness that we associate +with democratic that we associate with + + align:start position:0% +with democratic that we associate with + + + align:start position:0% +with democratic that we associate with +our ideals, not the reality, but our + + align:start position:0% +our ideals, not the reality, but our + + + align:start position:0% +our ideals, not the reality, but our +ideals of democratic society. What these + + align:start position:0% +ideals of democratic society. What these + + + align:start position:0% +ideals of democratic society. What these +dances and songs tell us then about the + + align:start position:0% +dances and songs tell us then about the + + + align:start position:0% +dances and songs tell us then about the +place of dance and song in our lives. + + align:start position:0% +place of dance and song in our lives. + + + align:start position:0% +place of dance and song in our lives. +The idea that you would begin to dance + + align:start position:0% +The idea that you would begin to dance + + + align:start position:0% +The idea that you would begin to dance +in a space unused to dance, hostile to + + align:start position:0% +in a space unused to dance, hostile to + + + align:start position:0% +in a space unused to dance, hostile to +dance transforms the space. Right? So + + align:start position:0% +dance transforms the space. Right? So + + + align:start position:0% +dance transforms the space. Right? So +what this film then says about these + + align:start position:0% +what this film then says about these + + + align:start position:0% +what this film then says about these +things is that our speech can be nudged + + align:start position:0% +things is that our speech can be nudged + + + align:start position:0% +things is that our speech can be nudged +into song. our way of walking can be + + align:start position:0% +into song. our way of walking can be + + + align:start position:0% +into song. our way of walking can be +edged into a dance and that the ordinary + + align:start position:0% +edged into a dance and that the ordinary + + + align:start position:0% +edged into a dance and that the ordinary +objects in our domestic and public + + align:start position:0% +objects in our domestic and public + + + align:start position:0% +objects in our domestic and public +spaces can become + + align:start position:0% +spaces can become + + + align:start position:0% +spaces can become +props can become props in an improvised + + align:start position:0% +props can become props in an improvised + + + align:start position:0% +props can become props in an improvised +valet. When we turn to cabaret, we're + + align:start position:0% +valet. When we turn to cabaret, we're + + + align:start position:0% +valet. When we turn to cabaret, we're +looking at a very different kind of + + align:start position:0% +looking at a very different kind of + + + align:start position:0% +looking at a very different kind of +object. Uh and it's important to + + align:start position:0% +object. Uh and it's important to + + + align:start position:0% +object. Uh and it's important to +recognize uh what I mentioned earlier + + align:start position:0% +recognize uh what I mentioned earlier + + + align:start position:0% +recognize uh what I mentioned earlier +and I will develop more fully in a + + align:start position:0% +and I will develop more fully in a + + + align:start position:0% +and I will develop more fully in a +couple of weeks. The fact that now we + + align:start position:0% +couple of weeks. The fact that now we + + + align:start position:0% +couple of weeks. The fact that now we +have gone almost beyond genre. There are + + align:start position:0% +have gone almost beyond genre. There are + + + align:start position:0% +have gone almost beyond genre. There are +people who would argue and there are + + align:start position:0% +people who would argue and there are + + + align:start position:0% +people who would argue and there are +purists of the music m scholars of the + + align:start position:0% +purists of the music m scholars of the + + + align:start position:0% +purists of the music m scholars of the +musical film who want to argue that well + + align:start position:0% +musical film who want to argue that well + + + align:start position:0% +musical film who want to argue that well +cabaret really isn't a musical for a + + align:start position:0% +cabaret really isn't a musical for a + + + align:start position:0% +cabaret really isn't a musical for a +variety of reasons. It seems to me a + + align:start position:0% +variety of reasons. It seems to me a + + + align:start position:0% +variety of reasons. It seems to me a +very strange and unhelpful argument. But + + align:start position:0% +very strange and unhelpful argument. But + + + align:start position:0% +very strange and unhelpful argument. But +I think if you watch the film closely, + + align:start position:0% +I think if you watch the film closely, + + + align:start position:0% +I think if you watch the film closely, +you'll understand why people who are + + align:start position:0% +you'll understand why people who are + + + align:start position:0% +you'll understand why people who are +partisans of the great Hollywood musical + + align:start position:0% +partisans of the great Hollywood musical + + + align:start position:0% +partisans of the great Hollywood musical +tradition or even the older opereta + + align:start position:0% +tradition or even the older opereta + + + align:start position:0% +tradition or even the older opereta +tradition represented by by uh directors + + align:start position:0% +tradition represented by by uh directors + + + align:start position:0% +tradition represented by by uh directors +like Ruben Mamoan would have problems + + align:start position:0% +like Ruben Mamoan would have problems + + + align:start position:0% +like Ruben Mamoan would have problems +fitting Cabaret into the category of + + align:start position:0% +fitting Cabaret into the category of + + + align:start position:0% +fitting Cabaret into the category of +musical. I I think it's a + + align:start position:0% +musical. I I think it's a + + + align:start position:0% +musical. I I think it's a +misunderstanding of how we should think + + align:start position:0% +misunderstanding of how we should think + + + align:start position:0% +misunderstanding of how we should think +about musicals. But uh uh uh for the + + align:start position:0% +about musicals. But uh uh uh for the + + + align:start position:0% +about musicals. But uh uh uh for the +moment, let's just let let me just + + align:start position:0% +moment, let's just let let me just + + + align:start position:0% +moment, let's just let let me just +encourage you to watch the film and + + align:start position:0% +encourage you to watch the film and + + + align:start position:0% +encourage you to watch the film and +think about how different it is from + + align:start position:0% +think about how different it is from + + + align:start position:0% +think about how different it is from +traditional musicals and especially its + + align:start position:0% +traditional musicals and especially its + + + align:start position:0% +traditional musicals and especially its +tone, its moral its moral perspective. + + align:start position:0% +tone, its moral its moral perspective. + + + align:start position:0% +tone, its moral its moral perspective. +Uh u uh but but also it's it it it's its + + align:start position:0% +Uh u uh but but also it's it it it's its + + + align:start position:0% +Uh u uh but but also it's it it it's its +structure. Uh uh think about that and + + align:start position:0% +structure. Uh uh think about that and + + + align:start position:0% +structure. Uh uh think about that and +you'll understand more fully why it's + + align:start position:0% +you'll understand more fully why it's + + + align:start position:0% +you'll understand more fully why it's +easy to see that this film could not + + align:start position:0% +easy to see that this film could not + + + align:start position:0% +easy to see that this film could not +would not have would be very unlikely to + + align:start position:0% +would not have would be very unlikely to + + + align:start position:0% +would not have would be very unlikely to +have been made in the Hollywood era that + + align:start position:0% +have been made in the Hollywood era that + + + align:start position:0% +have been made in the Hollywood era that +it required the kind of freedom that + + align:start position:0% +it required the kind of freedom that + + + align:start position:0% +it required the kind of freedom that +came to film after film was no longer + + align:start position:0% +came to film after film was no longer + + + align:start position:0% +came to film after film was no longer +constrained by the necessity to speak to + + align:start position:0% +constrained by the necessity to speak to + + + align:start position:0% +constrained by the necessity to speak to +a in a consensus voice. And as I said, + + align:start position:0% +a in a consensus voice. And as I said, + + + align:start position:0% +a in a consensus voice. And as I said, +these are matters I will try to clarify + + align:start position:0% +these are matters I will try to clarify + + + align:start position:0% +these are matters I will try to clarify +and conclude with when in two weeks when + + align:start position:0% +and conclude with when in two weeks when + + + align:start position:0% +and conclude with when in two weeks when +I return to this question when we talk + + align:start position:0% +I return to this question when we talk + + + align:start position:0% +I return to this question when we talk +about film in the 70s and the great 70s + + align:start position:0% +about film in the 70s and the great 70s + + + align:start position:0% +about film in the 70s and the great 70s +western almost contemporary with + + align:start position:0% +western almost contemporary with + + + align:start position:0% +western almost contemporary with +cabaret Robert Alman's McCabe and Mrs. + + align:start position:0% +cabaret Robert Alman's McCabe and Mrs. + + + align:start position:0% +cabaret Robert Alman's McCabe and Mrs. +Miller. I had hoped to say a number of + + align:start position:0% +Miller. I had hoped to say a number of + + + align:start position:0% +Miller. I had hoped to say a number of +things about Falsy's career but I don't + + align:start position:0% +things about Falsy's career but I don't + + + align:start position:0% +things about Falsy's career but I don't +have time and I'm just going to + + align:start position:0% +have time and I'm just going to + + + align:start position:0% +have time and I'm just going to +encourage you look him up. He's a very + + align:start position:0% +encourage you look him up. He's a very + + + align:start position:0% +encourage you look him up. He's a very +very remarkable figure uh in some I call + + align:start position:0% +very remarkable figure uh in some I call + + + align:start position:0% +very remarkable figure uh in some I call +him the inheritor because he began his + + align:start position:0% +him the inheritor because he began his + + + align:start position:0% +him the inheritor because he began his +career in connection he be he was both a + + align:start position:0% +career in connection he be he was both a + + + align:start position:0% +career in connection he be he was both a +Broadway director and choreographer and + + align:start position:0% +Broadway director and choreographer and + + + align:start position:0% +Broadway director and choreographer and +a dancer both on Broadway and in films + + align:start position:0% +a dancer both on Broadway and in films + + + align:start position:0% +a dancer both on Broadway and in films +and he uh uh performed and directed both + + align:start position:0% +and he uh uh performed and directed both + + + align:start position:0% +and he uh uh performed and directed both +on Broadway and in films. uh he was a + + align:start position:0% +on Broadway and in films. uh he was a + + + align:start position:0% +on Broadway and in films. uh he was a +first a choreographer in films before he + + align:start position:0% +first a choreographer in films before he + + + align:start position:0% +first a choreographer in films before he +became a director and in his career as a + + align:start position:0% +became a director and in his career as a + + + align:start position:0% +became a director and in his career as a +performer and choreographer he linked up + + align:start position:0% +performer and choreographer he linked up + + + align:start position:0% +performer and choreographer he linked up +with almost all the other great names of + + align:start position:0% +with almost all the other great names of + + + align:start position:0% +with almost all the other great names of +the American musical stage both the + + align:start position:0% +the American musical stage both the + + + align:start position:0% +the American musical stage both the +Broadway stage and the Hollywood + + align:start position:0% +Broadway stage and the Hollywood + + + align:start position:0% +Broadway stage and the Hollywood +tradition and in that sense we can say + + align:start position:0% +tradition and in that sense we can say + + + align:start position:0% +tradition and in that sense we can say +that that that uh uh Bob FSY is the + + align:start position:0% +that that that uh uh Bob FSY is the + + + align:start position:0% +that that that uh uh Bob FSY is the +inheritor of the great tradition of of + + align:start position:0% +inheritor of the great tradition of of + + + align:start position:0% +inheritor of the great tradition of of +the American musical and I I wish I + + align:start position:0% +the American musical and I I wish I + + + align:start position:0% +the American musical and I I wish I +could go into detail about this and show + + align:start position:0% +could go into detail about this and show + + + align:start position:0% +could go into detail about this and show +you how many affiliations and specific + + align:start position:0% +you how many affiliations and specific + + + align:start position:0% +you how many affiliations and specific +connection ictions he has with the great + + align:start position:0% +connection ictions he has with the great + + + align:start position:0% +connection ictions he has with the great +figures of the classical age of American + + align:start position:0% +figures of the classical age of American + + + align:start position:0% +figures of the classical age of American +movies and especially the classical age + + align:start position:0% +movies and especially the classical age + + + align:start position:0% +movies and especially the classical age +of of the of the American musical. Uh + + align:start position:0% +of of the of the American musical. Uh + + + align:start position:0% +of of the of the American musical. Uh +but but suffice it to say that it's a + + align:start position:0% +but but suffice it to say that it's a + + + align:start position:0% +but but suffice it to say that it's a +very rich set of connections and his + + align:start position:0% +very rich set of connections and his + + + align:start position:0% +very rich set of connections and his +career is a very remarkable career a + + align:start position:0% +career is a very remarkable career a + + + align:start position:0% +career is a very remarkable career a +very a very honored career. Uh let me + + align:start position:0% +very a very honored career. Uh let me + + + align:start position:0% +very a very honored career. Uh let me +mention one fact about his career + + align:start position:0% +mention one fact about his career + + + align:start position:0% +mention one fact about his career +perhaps most the most remarkable one + + align:start position:0% +perhaps most the most remarkable one + + + align:start position:0% +perhaps most the most remarkable one +easy to remember tells you something + + align:start position:0% +easy to remember tells you something + + + align:start position:0% +easy to remember tells you something +about his his diversity his as a + + align:start position:0% +about his his diversity his as a + + + align:start position:0% +about his his diversity his as a +director his gifts his ambition. In + + align:start position:0% +director his gifts his ambition. In + + + align:start position:0% +director his gifts his ambition. In +1973 Bob FSY I think became the only man + + align:start position:0% +1973 Bob FSY I think became the only man + + + align:start position:0% +1973 Bob FSY I think became the only man +in history to win an Oscar, a + + align:start position:0% +in history to win an Oscar, a + + + align:start position:0% +in history to win an Oscar, a +Tony and an Emmy. an Oscar for for uh um + + align:start position:0% +Tony and an Emmy. an Oscar for for uh um + + + align:start position:0% +Tony and an Emmy. an Oscar for for uh um +Cabaret as best director. Uh and uh a a + + align:start position:0% +Cabaret as best director. Uh and uh a a + + + align:start position:0% +Cabaret as best director. Uh and uh a a +Tony for as best d or maybe he won as + + align:start position:0% +Tony for as best d or maybe he won as + + + align:start position:0% +Tony for as best d or maybe he won as +best director or the play that he + + align:start position:0% +best director or the play that he + + + align:start position:0% +best director or the play that he +directed on Broadway. Pippen won as best + + align:start position:0% +directed on Broadway. Pippen won as best + + + align:start position:0% +directed on Broadway. Pippen won as best +play on Broadway and he also won a + + align:start position:0% +play on Broadway and he also won a + + + align:start position:0% +play on Broadway and he also won a +television Emmy for a show starring Liza + + align:start position:0% +television Emmy for a show starring Liza + + + align:start position:0% +television Emmy for a show starring Liza +Manelli, the star in Cabaret called Liza + + align:start position:0% +Manelli, the star in Cabaret called Liza + + + align:start position:0% +Manelli, the star in Cabaret called Liza +with a Z. uh so and I think he's the + + align:start position:0% +with a Z. uh so and I think he's the + + + align:start position:0% +with a Z. uh so and I think he's the +only man in history for whom those three + + align:start position:0% +only man in history for whom those three + + + align:start position:0% +only man in history for whom those three +awards came in the in in in in the same + + align:start position:0% +awards came in the in in in in the same + + + align:start position:0% +awards came in the in in in in the same +year for three different for three + + align:start position:0% +year for three different for three + + + align:start position:0% +year for three different for three +different texts um uh uh he he directed + + align:start position:0% +different texts um uh uh he he directed + + + align:start position:0% +different texts um uh uh he he directed +one two three four five films of which + + align:start position:0% +one two three four five films of which + + + align:start position:0% +one two three four five films of which +of cabaret was the second they are all + + align:start position:0% +of cabaret was the second they are all + + + align:start position:0% +of cabaret was the second they are all +well the the the last four uh are are + + align:start position:0% +well the the the last four uh are are + + + align:start position:0% +well the the the last four uh are are +all very remarkable and interesting uh + + align:start position:0% +all very remarkable and interesting uh + + + align:start position:0% +all very remarkable and interesting uh +uh texts I I I won't talk about them + + align:start position:0% +uh texts I I I won't talk about them + + + align:start position:0% +uh texts I I I won't talk about them +here except to encourage you to look + + align:start position:0% +here except to encourage you to look + + + align:start position:0% +here except to encourage you to look +them up and think about them the theme + + align:start position:0% +them up and think about them the theme + + + align:start position:0% +them up and think about them the theme +of performance and the idea of the + + align:start position:0% +of performance and the idea of the + + + align:start position:0% +of performance and the idea of the +charact characters who who are + + align:start position:0% +charact characters who who are + + + align:start position:0% +charact characters who who are +characters who are themselves performer + + align:start position:0% +characters who are themselves performer + + + align:start position:0% +characters who are themselves performer +performers uh are always at the center + + align:start position:0% +performers uh are always at the center + + + align:start position:0% +performers uh are always at the center +of his films even film not all of his + + align:start position:0% +of his films even film not all of his + + + align:start position:0% +of his films even film not all of his +films involve dance he made a film about + + align:start position:0% +films involve dance he made a film about + + + align:start position:0% +films involve dance he made a film about +the life of Lenny Bruce called Lenny + + align:start position:0% +the life of Lenny Bruce called Lenny + + + align:start position:0% +the life of Lenny Bruce called Lenny +starring Dustin Hoffman for example uh + + align:start position:0% +starring Dustin Hoffman for example uh + + + align:start position:0% +starring Dustin Hoffman for example uh +that doesn't have musical numbers in it + + align:start position:0% +that doesn't have musical numbers in it + + + align:start position:0% +that doesn't have musical numbers in it +but it has many performance numbers in + + align:start position:0% +but it has many performance numbers in + + + align:start position:0% +but it has many performance numbers in +it and it's a very rich complex uh + + align:start position:0% +it and it's a very rich complex uh + + + align:start position:0% +it and it's a very rich complex uh +sophisticated film uh um So for an + + align:start position:0% +sophisticated film uh um So for an + + + align:start position:0% +sophisticated film uh um So for an +interesting and and and and profoundly + + align:start position:0% +interesting and and and and profoundly + + + align:start position:0% +interesting and and and and profoundly +serious director + + align:start position:0% +serious director + + + align:start position:0% +serious director +um I wish I could say more about his + + align:start position:0% +um I wish I could say more about his + + + align:start position:0% +um I wish I could say more about his +career. I want to say a word about the + + align:start position:0% +career. I want to say a word about the + + + align:start position:0% +career. I want to say a word about the +context of cabaret so you'll understand + + align:start position:0% +context of cabaret so you'll understand + + + align:start position:0% +context of cabaret so you'll understand +that aspect of the film more fully too. + + align:start position:0% +that aspect of the film more fully too. + + + align:start position:0% +that aspect of the film more fully too. +It's set in Vimar Germany that curious + + align:start position:0% +It's set in Vimar Germany that curious + + + align:start position:0% +It's set in Vimar Germany that curious +time in the 1920s before the during the + + align:start position:0% +time in the 1920s before the during the + + + align:start position:0% +time in the 1920s before the during the +rise of Nazism but before Hitler has + + align:start position:0% +rise of Nazism but before Hitler has + + + align:start position:0% +rise of Nazism but before Hitler has +come long before Hitler has come to + + align:start position:0% +come long before Hitler has come to + + + align:start position:0% +come long before Hitler has come to +power in which the the VHimar Republic + + align:start position:0% +power in which the the VHimar Republic + + + align:start position:0% +power in which the the VHimar Republic +uh a vulnerable and and and unstable + + align:start position:0% +uh a vulnerable and and and unstable + + + align:start position:0% +uh a vulnerable and and and unstable +democracy uh but a but a democracy in + + align:start position:0% +democracy uh but a but a democracy in + + + align:start position:0% +democracy uh but a but a democracy in +which an enormous amount of of of of uh + + align:start position:0% +which an enormous amount of of of of uh + + + align:start position:0% +which an enormous amount of of of of uh +artistic and literary experimentation + + align:start position:0% +artistic and literary experimentation + + + align:start position:0% +artistic and literary experimentation +was taking place. It's the period of + + align:start position:0% +was taking place. It's the period of + + + align:start position:0% +was taking place. It's the period of +German expressionism. It's the period of + + align:start position:0% +German expressionism. It's the period of + + + align:start position:0% +German expressionism. It's the period of +the great German silent films that we + + align:start position:0% +the great German silent films that we + + + align:start position:0% +the great German silent films that we +talked about earlier. And so our film + + align:start position:0% +talked about earlier. And so our film + + + align:start position:0% +talked about earlier. And so our film +Cabaret is set in that era and in that + + align:start position:0% +Cabaret is set in that era and in that + + + align:start position:0% +Cabaret is set in that era and in that +driven era in uh uh in that divided era + + align:start position:0% +driven era in uh uh in that divided era + + + align:start position:0% +driven era in uh uh in that divided era +in which the rise of Nazism was coupled + + align:start position:0% +in which the rise of Nazism was coupled + + + align:start position:0% +in which the rise of Nazism was coupled +with was or joined to and connected to + + align:start position:0% +with was or joined to and connected to + + + align:start position:0% +with was or joined to and connected to +the uh uh the the fact that German + + align:start position:0% +the uh uh the the fact that German + + + align:start position:0% +the uh uh the the fact that German +society was was was under immense + + align:start position:0% +society was was was under immense + + + align:start position:0% +society was was was under immense +constraints because it had lost the + + align:start position:0% +constraints because it had lost the + + + align:start position:0% +constraints because it had lost the +first world war. The conditions on under + + align:start position:0% +first world war. The conditions on under + + + align:start position:0% +first world war. The conditions on under +which they had been forced to surrender + + align:start position:0% +which they had been forced to surrender + + + align:start position:0% +which they had been forced to surrender +were very ownorous. Uh there was very + + align:start position:0% +were very ownorous. Uh there was very + + + align:start position:0% +were very ownorous. Uh there was very +high levels of unemployment. It was a it + + align:start position:0% +high levels of unemployment. It was a it + + + align:start position:0% +high levels of unemployment. It was a it +was a society it was a schizophrenically + + align:start position:0% +was a society it was a schizophrenically + + + align:start position:0% +was a society it was a schizophrenically +divid divided society. A society of + + align:start position:0% +divid divided society. A society of + + + align:start position:0% +divid divided society. A society of +great artistic energies but of great + + align:start position:0% +great artistic energies but of great + + + align:start position:0% +great artistic energies but of great +political divisions and and and + + align:start position:0% +political divisions and and and + + + align:start position:0% +political divisions and and and +difficulties and and uh nightmare + + align:start position:0% +difficulties and and uh nightmare + + + align:start position:0% +difficulties and and uh nightmare +possibilities that were lurking in its + + align:start position:0% +possibilities that were lurking in its + + + align:start position:0% +possibilities that were lurking in its +in it in it in in in many of its + + align:start position:0% +in it in it in in in many of its + + + align:start position:0% +in it in it in in in many of its +practices. And there's a link or a or at + + align:start position:0% +practices. And there's a link or a or at + + + align:start position:0% +practices. And there's a link or a or at +least a partial link between the + + align:start position:0% +least a partial link between the + + + align:start position:0% +least a partial link between the +instability and the excitement but also + + align:start position:0% +instability and the excitement but also + + + align:start position:0% +instability and the excitement but also +the dividedness of Vimar Germany and the + + align:start position:0% +the dividedness of Vimar Germany and the + + + align:start position:0% +the dividedness of Vimar Germany and the +actual condition of the United States in + + align:start position:0% +actual condition of the United States in + + + align:start position:0% +actual condition of the United States in +the era when the movie came out. Right? + + align:start position:0% +the era when the movie came out. Right? + + + align:start position:0% +the era when the movie came out. Right? +Because this is the period at the end of + + align:start position:0% +Because this is the period at the end of + + + align:start position:0% +Because this is the period at the end of +the 60s after the late 60s and early 70s + + align:start position:0% +the 60s after the late 60s and early 70s + + + align:start position:0% +the 60s after the late 60s and early 70s +probably the most divided time in + + align:start position:0% +probably the most divided time in + + + align:start position:0% +probably the most divided time in +American history after the second world + + align:start position:0% +American history after the second world + + + align:start position:0% +American history after the second world +war before our current moment. Right? + + align:start position:0% +war before our current moment. Right? + + + align:start position:0% +war before our current moment. Right? +And in fact the divisions then were more + + align:start position:0% +And in fact the divisions then were more + + + align:start position:0% +And in fact the divisions then were more +legitimate. That is by more legitimate I + + align:start position:0% +legitimate. That is by more legitimate I + + + align:start position:0% +legitimate. That is by more legitimate I +mean they they had a more sensible + + align:start position:0% +mean they they had a more sensible + + + align:start position:0% +mean they they had a more sensible +cause. There was a ter there were + + align:start position:0% +cause. There was a ter there were + + + align:start position:0% +cause. There was a ter there were +terrible wars going on. Uh there were + + align:start position:0% +terrible wars going on. Uh there were + + + align:start position:0% +terrible wars going on. Uh there were +there were there were there were better + + align:start position:0% +there were there were there were better + + + align:start position:0% +there were there were there were better +reasons for the for the partisanship + + align:start position:0% +reasons for the for the partisanship + + + align:start position:0% +reasons for the for the partisanship +that occurred in the 19 in the late 60s + + align:start position:0% +that occurred in the 19 in the late 60s + + + align:start position:0% +that occurred in the 19 in the late 60s +and early 70s than there are for the + + align:start position:0% +and early 70s than there are for the + + + align:start position:0% +and early 70s than there are for the +weird partisanship we're suffering in + + align:start position:0% +weird partisanship we're suffering in + + + align:start position:0% +weird partisanship we're suffering in +the United States in the United States + + align:start position:0% +the United States in the United States + + + align:start position:0% +the United States in the United States +today. And and in any case there was a + + align:start position:0% +today. And and in any case there was a + + + align:start position:0% +today. And and in any case there was a +much greater sense in the late 60s and + + align:start position:0% +much greater sense in the late 60s and + + + align:start position:0% +much greater sense in the late 60s and +early 70s that the fabric of American + + align:start position:0% +early 70s that the fabric of American + + + align:start position:0% +early 70s that the fabric of American +society was under attack that it was + + align:start position:0% +society was under attack that it was + + + align:start position:0% +society was under attack that it was +imperfect. not only because the Vietnam + + align:start position:0% +imperfect. not only because the Vietnam + + + align:start position:0% +imperfect. not only because the Vietnam +War had so divided the country against + + align:start position:0% +War had so divided the country against + + + align:start position:0% +War had so divided the country against +itself, but because of other other uh uh + + align:start position:0% +itself, but because of other other uh uh + + + align:start position:0% +itself, but because of other other uh uh +matters as well, including the + + align:start position:0% +matters as well, including the + + + align:start position:0% +matters as well, including the +increasing militancy of of the civil + + align:start position:0% +increasing militancy of of the civil + + + align:start position:0% +increasing militancy of of the civil +rights movement, which had w- which had + + align:start position:0% +rights movement, which had w- which had + + + align:start position:0% +rights movement, which had w- which had +which had gone from a sort of Martin + + align:start position:0% +which had gone from a sort of Martin + + + align:start position:0% +which had gone from a sort of Martin +Luther King type uh uh um uh commitment + + align:start position:0% +Luther King type uh uh um uh commitment + + + align:start position:0% +Luther King type uh uh um uh commitment +to to to nonviolent protest uh into much + + align:start position:0% +to to to nonviolent protest uh into much + + + align:start position:0% +to to to nonviolent protest uh into much +more disturbing and sometime and + + align:start position:0% +more disturbing and sometime and + + + align:start position:0% +more disturbing and sometime and +sometimes violent confrontations with + + align:start position:0% +sometimes violent confrontations with + + + align:start position:0% +sometimes violent confrontations with +authorities. and with some theorists and + + align:start position:0% +authorities. and with some theorists and + + + align:start position:0% +authorities. and with some theorists and +speakers actually calling for for uh uh + + align:start position:0% +speakers actually calling for for uh uh + + + align:start position:0% +speakers actually calling for for uh uh +violence and this racial tension was + + align:start position:0% +violence and this racial tension was + + + align:start position:0% +violence and this racial tension was +then coupled by another kind of + + align:start position:0% +then coupled by another kind of + + + align:start position:0% +then coupled by another kind of +political tension coming from the people + + align:start position:0% +political tension coming from the people + + + align:start position:0% +political tension coming from the people +from the young men and women who were + + align:start position:0% +from the young men and women who were + + + align:start position:0% +from the young men and women who were +mostly young men and women who were + + align:start position:0% +mostly young men and women who were + + + align:start position:0% +mostly young men and women who were +opposed to the Vietnam war. So it was a + + align:start position:0% +opposed to the Vietnam war. So it was a + + + align:start position:0% +opposed to the Vietnam war. So it was a +very driven and disturbed time. There + + align:start position:0% +very driven and disturbed time. There + + + align:start position:0% +very driven and disturbed time. There +were then parallels between the + + align:start position:0% +were then parallels between the + + + align:start position:0% +were then parallels between the +instability and the uh disturbance of + + align:start position:0% +instability and the uh disturbance of + + + align:start position:0% +instability and the uh disturbance of +the Vhimar period and the period uh in + + align:start position:0% +the Vhimar period and the period uh in + + + align:start position:0% +the Vhimar period and the period uh in +which the film appeared and the original + + align:start position:0% +which the film appeared and the original + + + align:start position:0% +which the film appeared and the original +audiences I think would have been highly + + align:start position:0% +audiences I think would have been highly + + + align:start position:0% +audiences I think would have been highly +aware of this of this connection would + + align:start position:0% +aware of this of this connection would + + + align:start position:0% +aware of this of this connection would +have seen that although the film was set + + align:start position:0% +have seen that although the film was set + + + align:start position:0% +have seen that although the film was set +in the past it it spoke to the + + align:start position:0% +in the past it it spoke to the + + + align:start position:0% +in the past it it spoke to the +contemporary moment in a very powerful + + align:start position:0% +contemporary moment in a very powerful + + + align:start position:0% +contemporary moment in a very powerful +way. I want to also uh remind you uh + + align:start position:0% +way. I want to also uh remind you uh + + + align:start position:0% +way. I want to also uh remind you uh +that that there are certain aspects + + align:start position:0% +that that there are certain aspects + + + align:start position:0% +that that there are certain aspects +there are certain aspects of the style + + align:start position:0% +there are certain aspects of the style + + + align:start position:0% +there are certain aspects of the style +of of + + align:start position:0% +of of + + + align:start position:0% +of of +uh cabaret that are worth keeping in + + align:start position:0% +uh cabaret that are worth keeping in + + + align:start position:0% +uh cabaret that are worth keeping in +mind. And one way to think about this is + + align:start position:0% +mind. And one way to think about this is + + + align:start position:0% +mind. And one way to think about this is +to recognize that both misan sen style + + align:start position:0% +to recognize that both misan sen style + + + align:start position:0% +to recognize that both misan sen style +and montage style re are are are + + align:start position:0% +and montage style re are are are + + + align:start position:0% +and montage style re are are are +are embodied at in the film and and and + + align:start position:0% +are embodied at in the film and and and + + + align:start position:0% +are embodied at in the film and and and +are carried to extremes in certain + + align:start position:0% +are carried to extremes in certain + + + align:start position:0% +are carried to extremes in certain +moments of the film. That is to say, in + + align:start position:0% +moments of the film. That is to say, in + + + align:start position:0% +moments of the film. That is to say, in +many of the performance sequences in the + + align:start position:0% +many of the performance sequences in the + + + align:start position:0% +many of the performance sequences in the +film, the camera behaves in an + + align:start position:0% +film, the camera behaves in an + + + align:start position:0% +film, the camera behaves in an +unbelievably frenetic and frantic way, + + align:start position:0% +unbelievably frenetic and frantic way, + + + align:start position:0% +unbelievably frenetic and frantic way, +changes your eye uh angle, uh jumps + + align:start position:0% +changes your eye uh angle, uh jumps + + + align:start position:0% +changes your eye uh angle, uh jumps +around a lot, dis disorients you + + align:start position:0% +around a lot, dis disorients you + + + align:start position:0% +around a lot, dis disorients you +sometime, almost disorients you in the + + align:start position:0% +sometime, almost disorients you in the + + + align:start position:0% +sometime, almost disorients you in the +style of a Hitchcock. Uh uh and yet in + + align:start position:0% +style of a Hitchcock. Uh uh and yet in + + + align:start position:0% +style of a Hitchcock. Uh uh and yet in +other sequences in the film, especially + + align:start position:0% +other sequences in the film, especially + + + align:start position:0% +other sequences in the film, especially +those outside the cabaret that take + + align:start position:0% +those outside the cabaret that take + + + align:start position:0% +those outside the cabaret that take +place in ordinary life, not in a + + align:start position:0% +place in ordinary life, not in a + + + align:start position:0% +place in ordinary life, not in a +performance space, the the camera and + + align:start position:0% +performance space, the the camera and + + + align:start position:0% +performance space, the the camera and +the editing slow down and become more + + align:start position:0% +the editing slow down and become more + + + align:start position:0% +the editing slow down and become more +like a kind of misison style. And the + + align:start position:0% +like a kind of misison style. And the + + + align:start position:0% +like a kind of misison style. And the +combination of the two is especially + + align:start position:0% +combination of the two is especially + + + align:start position:0% +combination of the two is especially +rich and interesting. You might want to + + align:start position:0% +rich and interesting. You might want to + + + align:start position:0% +rich and interesting. You might want to +watch for the way these rhythms alter + + align:start position:0% +watch for the way these rhythms alter + + + align:start position:0% +watch for the way these rhythms alter +your sense of what's happening in the + + align:start position:0% +your sense of what's happening in the + + + align:start position:0% +your sense of what's happening in the +film. The way the film slows down and + + align:start position:0% +film. The way the film slows down and + + + align:start position:0% +film. The way the film slows down and +speeds up at certain points. And I mean + + align:start position:0% +speeds up at certain points. And I mean + + + align:start position:0% +speeds up at certain points. And I mean +I I mean this literally in terms of the + + align:start position:0% +I I mean this literally in terms of the + + + align:start position:0% +I I mean this literally in terms of the +number of images that go by quickly, but + + align:start position:0% +number of images that go by quickly, but + + + align:start position:0% +number of images that go by quickly, but +also in terms of the way the physical + + align:start position:0% +also in terms of the way the physical + + + align:start position:0% +also in terms of the way the physical +bodies of the performers move across the + + align:start position:0% +bodies of the performers move across the + + + align:start position:0% +bodies of the performers move across the +screen and of course the way in which + + align:start position:0% +screen and of course the way in which + + + align:start position:0% +screen and of course the way in which +the camera itself behaves, whether it's + + align:start position:0% +the camera itself behaves, whether it's + + + align:start position:0% +the camera itself behaves, whether it's +jittery and movement all or oriented + + align:start position:0% +jittery and movement all or oriented + + + align:start position:0% +jittery and movement all or oriented +toward constant movement or whether it's + + align:start position:0% +toward constant movement or whether it's + + + align:start position:0% +toward constant movement or whether it's +more stable and and gives you a chance + + align:start position:0% +more stable and and gives you a chance + + + align:start position:0% +more stable and and gives you a chance +to look at the environment your your uh + + align:start position:0% +to look at the environment your your uh + + + align:start position:0% +to look at the environment your your uh +um this scene is set in. + + align:start position:0% +um this scene is set in. + + + align:start position:0% +um this scene is set in. +Um, one way I can give you a sense of + + align:start position:0% +Um, one way I can give you a sense of + + + align:start position:0% +Um, one way I can give you a sense of +the richness of of the film is to remind + + align:start position:0% +the richness of of the film is to remind + + + align:start position:0% +the richness of of the film is to remind +you that there's a kind of texture or + + align:start position:0% +you that there's a kind of texture or + + + align:start position:0% +you that there's a kind of texture or +multiplicity in cabaret in almost every + + align:start position:0% +multiplicity in cabaret in almost every + + + align:start position:0% +multiplicity in cabaret in almost every +moment that if you watch for it and + + align:start position:0% +moment that if you watch for it and + + + align:start position:0% +moment that if you watch for it and +you're attentive to it, you will always + + align:start position:0% +you're attentive to it, you will always + + + align:start position:0% +you're attentive to it, you will always +be rewarded. Let me just give you two + + align:start position:0% +be rewarded. Let me just give you two + + + align:start position:0% +be rewarded. Let me just give you two +very quick examples of what I mean by + + align:start position:0% +very quick examples of what I mean by + + + align:start position:0% +very quick examples of what I mean by +this. Remember I suggested to you that + + align:start position:0% +this. Remember I suggested to you that + + + align:start position:0% +this. Remember I suggested to you that +this principle of multiplicity is one of + + align:start position:0% +this principle of multiplicity is one of + + + align:start position:0% +this principle of multiplicity is one of +the principles we turn to if we want to + + align:start position:0% +the principles we turn to if we want to + + + align:start position:0% +the principles we turn to if we want to +recognize a work of art, right? The + + align:start position:0% +recognize a work of art, right? The + + + align:start position:0% +recognize a work of art, right? The +difference between a work of art and an + + align:start position:0% +difference between a work of art and an + + + align:start position:0% +difference between a work of art and an +entertainment in my terms is that a work + + align:start position:0% +entertainment in my terms is that a work + + + align:start position:0% +entertainment in my terms is that a work +of art is just more intelligent. That is + + align:start position:0% +of art is just more intelligent. That is + + + align:start position:0% +of art is just more intelligent. That is +to say, it makes more complex use of its + + align:start position:0% +to say, it makes more complex use of its + + + align:start position:0% +to say, it makes more complex use of its +materials. So that in a entertainment, a + + align:start position:0% +materials. So that in a entertainment, a + + + align:start position:0% +materials. So that in a entertainment, a +particular event or gesture may have + + align:start position:0% +particular event or gesture may have + + + align:start position:0% +particular event or gesture may have +only one function, but in a work of art, + + align:start position:0% +only one function, but in a work of art, + + + align:start position:0% +only one function, but in a work of art, +it will have multiple functions. It will + + align:start position:0% +it will have multiple functions. It will + + + align:start position:0% +it will have multiple functions. It will +perform several jobs simultaneously. And + + align:start position:0% +perform several jobs simultaneously. And + + + align:start position:0% +perform several jobs simultaneously. And +if you I'll give you two examples of + + align:start position:0% +if you I'll give you two examples of + + + align:start position:0% +if you I'll give you two examples of +this. Um, think about what takes place + + align:start position:0% +this. Um, think about what takes place + + + align:start position:0% +this. Um, think about what takes place +on the periphery of what you're watching + + align:start position:0% +on the periphery of what you're watching + + + align:start position:0% +on the periphery of what you're watching +and you'll begin to get some sense of + + align:start position:0% +and you'll begin to get some sense of + + + align:start position:0% +and you'll begin to get some sense of +one way in which the texture of this + + align:start position:0% +one way in which the texture of this + + + align:start position:0% +one way in which the texture of this +film come brings the material alive. + + align:start position:0% +film come brings the material alive. + + + align:start position:0% +film come brings the material alive. +There's one moment, I think, fairly + + align:start position:0% +There's one moment, I think, fairly + + + align:start position:0% +There's one moment, I think, fairly +early in the film. It's a street scene. + + align:start position:0% +early in the film. It's a street scene. + + + align:start position:0% +early in the film. It's a street scene. +We're not paying much attention to + + align:start position:0% +We're not paying much attention to + + + align:start position:0% +We're not paying much attention to +what's going on. We see we see, I think, + + align:start position:0% +what's going on. We see we see, I think, + + + align:start position:0% +what's going on. We see we see, I think, +uh, the the protagonist walking in the + + align:start position:0% +uh, the the protagonist walking in the + + + align:start position:0% +uh, the the protagonist walking in the +street and around on the periphery of + + align:start position:0% +street and around on the periphery of + + + align:start position:0% +street and around on the periphery of +them or or or sort of not certainly not + + align:start position:0% +them or or or sort of not certainly not + + + align:start position:0% +them or or or sort of not certainly not +in the center of the frame. nothing that + + align:start position:0% +in the center of the frame. nothing that + + + align:start position:0% +in the center of the frame. nothing that +is commented on by the characters. Uh, a + + align:start position:0% +is commented on by the characters. Uh, a + + + align:start position:0% +is commented on by the characters. Uh, a + slides by on one of those + + align:start position:0% + slides by on one of those + + + align:start position:0% + slides by on one of those +wheeled platforms that people without + + align:start position:0% +wheeled platforms that people without + + + align:start position:0% +wheeled platforms that people without +legs sometimes used in major cities + + align:start position:0% +legs sometimes used in major cities + + + align:start position:0% +legs sometimes used in major cities +before. Maybe they still happen, but + + align:start position:0% +before. Maybe they still happen, but + + + align:start position:0% +before. Maybe they still happen, but +they but but but they're but but they + + align:start position:0% +they but but but they're but but they + + + align:start position:0% +they but but but they're but but they +were very common in the in the first + + align:start position:0% +were very common in the in the first + + + align:start position:0% +were very common in the in the first +half of the 20th century. And we see + + align:start position:0% +half of the 20th century. And we see + + + align:start position:0% +half of the 20th century. And we see +this guy who's obviously he's a wounded + + align:start position:0% +this guy who's obviously he's a wounded + + + align:start position:0% +this guy who's obviously he's a wounded +veteran and he's he's he's an amputee + + align:start position:0% +veteran and he's he's he's an amputee + + + align:start position:0% +veteran and he's he's he's an amputee +and he pushes himself along on this cart + + align:start position:0% +and he pushes himself along on this cart + + + align:start position:0% +and he pushes himself along on this cart +and and we just see him go by. But + + align:start position:0% +and and we just see him go by. But + + + align:start position:0% +and and we just see him go by. But +what's interesting about that is that + + align:start position:0% +what's interesting about that is that + + + align:start position:0% +what's interesting about that is that +he's this on the platform has a + + align:start position:0% +he's this on the platform has a + + + align:start position:0% +he's this on the platform has a +little flag on his platform. Guess what + + align:start position:0% +little flag on his platform. Guess what + + + align:start position:0% +little flag on his platform. Guess what +kind of a flag it is? It's a Nazi + + align:start position:0% +kind of a flag it is? It's a Nazi + + + align:start position:0% +kind of a flag it is? It's a Nazi +flag, right? And this is early in the + + align:start position:0% +flag, right? And this is early in the + + + align:start position:0% +flag, right? And this is early in the +film before the Nazis have become a + + align:start position:0% +film before the Nazis have become a + + + align:start position:0% +film before the Nazis have become a +powerful force. The rise of Nazism is in + + align:start position:0% +powerful force. The rise of Nazism is in + + + align:start position:0% +powerful force. The rise of Nazism is in +the background of the film. As you'll + + align:start position:0% +the background of the film. As you'll + + + align:start position:0% +the background of the film. As you'll +see, come the the Nazis move from the + + align:start position:0% +see, come the the Nazis move from the + + + align:start position:0% +see, come the the Nazis move from the +periphery to the center of the frame + + align:start position:0% +periphery to the center of the frame + + + align:start position:0% +periphery to the center of the frame +before the film is over. And that's the + + align:start position:0% +before the film is over. And that's the + + + align:start position:0% +before the film is over. And that's the +fundamental historical motion of the + + align:start position:0% +fundamental historical motion of the + + + align:start position:0% +fundamental historical motion of the +film. But all of that's taking place in + + align:start position:0% +film. But all of that's taking place in + + + align:start position:0% +film. But all of that's taking place in +the background. The foreground are the + + align:start position:0% +the background. The foreground are the + + + align:start position:0% +the background. The foreground are the +central characters and the the the comic + + align:start position:0% +central characters and the the the comic + + + align:start position:0% +central characters and the the the comic +and innocent and and ultimately not so + + align:start position:0% +and innocent and and ultimately not so + + + align:start position:0% +and innocent and and ultimately not so +comic disturbing love affairs and + + align:start position:0% +comic disturbing love affairs and + + + align:start position:0% +comic disturbing love affairs and +difficulties that they encounter in this + + align:start position:0% +difficulties that they encounter in this + + + align:start position:0% +difficulties that they encounter in this +environment. They're too naive or + + align:start position:0% +environment. They're too naive or + + + align:start position:0% +environment. They're too naive or +innocent to understand the historical + + align:start position:0% +innocent to understand the historical + + + align:start position:0% +innocent to understand the historical +forces that are surrounding them. Uh so + + align:start position:0% +forces that are surrounding them. Uh so + + + align:start position:0% +forces that are surrounding them. Uh so +that example of the Nazi flag and this + + align:start position:0% +that example of the Nazi flag and this + + + align:start position:0% +that example of the Nazi flag and this +crippled figure because the crippled + + align:start position:0% +crippled figure because the crippled + + + align:start position:0% +crippled figure because the crippled +figure is in fact an illusion to the + + align:start position:0% +figure is in fact an illusion to the + + + align:start position:0% +figure is in fact an illusion to the +ownerous uh uh u uh u uh demands that + + align:start position:0% +ownerous uh uh u uh u uh demands that + + + align:start position:0% +ownerous uh uh u uh u uh demands that +were put upon Germany by by France and + + align:start position:0% +were put upon Germany by by France and + + + align:start position:0% +were put upon Germany by by France and +the other allies at the end of the war. + + align:start position:0% +the other allies at the end of the war. + + + align:start position:0% +the other allies at the end of the war. +And this is in some sense this + + align:start position:0% +And this is in some sense this + + + align:start position:0% +And this is in some sense this +crippled. So the the assumption is he's + + align:start position:0% +crippled. So the the assumption is he's + + + align:start position:0% +crippled. So the the assumption is he's +probably a war veteran. I don't remember + + align:start position:0% +probably a war veteran. I don't remember + + + align:start position:0% +probably a war veteran. I don't remember +if he's actually wearing a uniform which + + align:start position:0% +if he's actually wearing a uniform which + + + align:start position:0% +if he's actually wearing a uniform which +would confirm this. It would be helpful + + align:start position:0% +would confirm this. It would be helpful + + + align:start position:0% +would confirm this. It would be helpful +if he would, but I don't remember. watch + + align:start position:0% +if he would, but I don't remember. watch + + + align:start position:0% +if he would, but I don't remember. watch +for it and you'll see. But in any case, + + align:start position:0% +for it and you'll see. But in any case, + + + align:start position:0% +for it and you'll see. But in any case, +he's he refers to that and now anyone + + align:start position:0% +he's he refers to that and now anyone + + + align:start position:0% +he's he refers to that and now anyone +attentive to the film can recognize that + + align:start position:0% +attentive to the film can recognize that + + + align:start position:0% +attentive to the film can recognize that +the the historical texture of the of of + + align:start position:0% +the the historical texture of the of of + + + align:start position:0% +the the historical texture of the of of +of the film is is carried by such + + align:start position:0% +of the film is is carried by such + + + align:start position:0% +of the film is is carried by such +moments. There's another such moment + + align:start position:0% +moments. There's another such moment + + + align:start position:0% +moments. There's another such moment +also so minor that you might not notice + + align:start position:0% +also so minor that you might not notice + + + align:start position:0% +also so minor that you might not notice +it. It the foreground is the love + + align:start position:0% +it. It the foreground is the love + + + align:start position:0% +it. It the foreground is the love +affair. What or not yet a love affair + + align:start position:0% +affair. What or not yet a love affair + + + align:start position:0% +affair. What or not yet a love affair +but the acquaintance the deepening + + align:start position:0% +but the acquaintance the deepening + + + align:start position:0% +but the acquaintance the deepening +friendship between the two protagonists + + align:start position:0% +friendship between the two protagonists + + + align:start position:0% +friendship between the two protagonists +Sally BS and her boyfriend. And uh they + + align:start position:0% +Sally BS and her boyfriend. And uh they + + + align:start position:0% +Sally BS and her boyfriend. And uh they +go out they go out for a walk in Berlin + + align:start position:0% +go out they go out for a walk in Berlin + + + align:start position:0% +go out they go out for a walk in Berlin +and Sally pretends that she's this + + align:start position:0% +and Sally pretends that she's this + + + align:start position:0% +and Sally pretends that she's this +immensely sophisticated woman. Turns out + + align:start position:0% +immensely sophisticated woman. Turns out + + + align:start position:0% +immensely sophisticated woman. Turns out +that she's fooling herself and fooling + + align:start position:0% +that she's fooling herself and fooling + + + align:start position:0% +that she's fooling herself and fooling +us. Uh uh she's not at all even though + + align:start position:0% +us. Uh uh she's not at all even though + + + align:start position:0% +us. Uh uh she's not at all even though +she pretends to a great kind of + + align:start position:0% +she pretends to a great kind of + + + align:start position:0% +she pretends to a great kind of +sophistication. And she sings dirty + + align:start position:0% +sophistication. And she sings dirty + + + align:start position:0% +sophistication. And she sings dirty +songs in a cabaret and she performs in a + + align:start position:0% +songs in a cabaret and she performs in a + + + align:start position:0% +songs in a cabaret and she performs in a +cabaret where they make jokes about + + align:start position:0% +cabaret where they make jokes about + + + align:start position:0% +cabaret where they make jokes about +everything including all forms of sexual + + align:start position:0% +everything including all forms of sexual + + + align:start position:0% +everything including all forms of sexual +perversion. Nonetheless, she's an + + align:start position:0% +perversion. Nonetheless, she's an + + + align:start position:0% +perversion. Nonetheless, she's an +innocent. She has no way of recognizing + + align:start position:0% +innocent. She has no way of recognizing + + + align:start position:0% +innocent. She has no way of recognizing +the depth and complexity of the evil + + align:start position:0% +the depth and complexity of the evil + + + align:start position:0% +the depth and complexity of the evil +that's built, the moral evil and moral + + align:start position:0% +that's built, the moral evil and moral + + + align:start position:0% +that's built, the moral evil and moral +terror that's building around her. And + + align:start position:0% +terror that's building around her. And + + + align:start position:0% +terror that's building around her. And +she's not alone in this. Most of the + + align:start position:0% +she's not alone in this. Most of the + + + align:start position:0% +she's not alone in this. Most of the +other characters in the foreground of + + align:start position:0% +other characters in the foreground of + + + align:start position:0% +other characters in the foreground of +the film perform this same naive ballet. + + align:start position:0% +the film perform this same naive ballet. + + + align:start position:0% +the film perform this same naive ballet. +Although Sally BS is the most powerful + + align:start position:0% +Although Sally BS is the most powerful + + + align:start position:0% +Although Sally BS is the most powerful +instance of it, it is certainly Liza + + align:start position:0% +instance of it, it is certainly Liza + + + align:start position:0% +instance of it, it is certainly Liza +Minnelli's greatest role. Certainly the + + align:start position:0% +Minnelli's greatest role. Certainly the + + + align:start position:0% +Minnelli's greatest role. Certainly the +role that she'll be remembered for long + + align:start position:0% +role that she'll be remembered for long + + + align:start position:0% +role that she'll be remembered for long +after she's dead, long after we're all + + align:start position:0% +after she's dead, long after we're all + + + align:start position:0% +after she's dead, long after we're all +in the in the ground. Liza Minnelli's + + align:start position:0% +in the in the ground. Liza Minnelli's + + + align:start position:0% +in the in the ground. Liza Minnelli's +performance in this film will still be + + align:start position:0% +performance in this film will still be + + + align:start position:0% +performance in this film will still be +treasured and savored, I think. Um, so + + align:start position:0% +treasured and savored, I think. Um, so + + + align:start position:0% +treasured and savored, I think. Um, so +another instance of the multiplicity + + align:start position:0% +another instance of the multiplicity + + + align:start position:0% +another instance of the multiplicity +when when when we find u uh uh the two + + align:start position:0% +when when when we find u uh uh the two + + + align:start position:0% +when when when we find u uh uh the two +two characters are walking in the street + + align:start position:0% +two characters are walking in the street + + + align:start position:0% +two characters are walking in the street +and Sally says, "Oh, I want to show you + + align:start position:0% +and Sally says, "Oh, I want to show you + + + align:start position:0% +and Sally says, "Oh, I want to show you +something that I do." And she pulls this + + align:start position:0% +something that I do." And she pulls this + + + align:start position:0% +something that I do." And she pulls this +guy along. She leans up against the side + + align:start position:0% +guy along. She leans up against the side + + + align:start position:0% +guy along. She leans up against the side +of an elevated train station, right? And + + align:start position:0% +of an elevated train station, right? And + + + align:start position:0% +of an elevated train station, right? And +she waits until the train comes by. And + + align:start position:0% +she waits until the train comes by. And + + + align:start position:0% +she waits until the train comes by. And +as the train comes by, she screams and + + align:start position:0% +as the train comes by, she screams and + + + align:start position:0% +as the train comes by, she screams and +she says, "See, if you wait for the + + align:start position:0% +she says, "See, if you wait for the + + + align:start position:0% +she says, "See, if you wait for the +noise, nobody will hear you scream." And + + align:start position:0% +noise, nobody will hear you scream." And + + + align:start position:0% +noise, nobody will hear you scream." And +she's just expressing her exuberance, + + align:start position:0% +she's just expressing her exuberance, + + + align:start position:0% +she's just expressing her exuberance, +showing her, she's showing him how she + + align:start position:0% +showing her, she's showing him how she + + + align:start position:0% +showing her, she's showing him how she +commands this space, how she knows how + + align:start position:0% +commands this space, how she knows how + + + align:start position:0% +commands this space, how she knows how +to use this urban space, right? But + + align:start position:0% +to use this urban space, right? But + + + align:start position:0% +to use this urban space, right? But +there's an irony she's unaware of. When + + align:start position:0% +there's an irony she's unaware of. When + + + align:start position:0% +there's an irony she's unaware of. When +she leans up against the wall, behind + + align:start position:0% +she leans up against the wall, behind + + + align:start position:0% +she leans up against the wall, behind +her, what we see are political posters. + + align:start position:0% +her, what we see are political posters. + + + align:start position:0% +her, what we see are political posters. +And the political posters behind her are + + align:start position:0% +And the political posters behind her are + + + align:start position:0% +And the political posters behind her are +defaced. They're both Nazi and communist + + align:start position:0% +defaced. They're both Nazi and communist + + + align:start position:0% +defaced. They're both Nazi and communist +posters. And the communists and the + + align:start position:0% +posters. And the communists and the + + + align:start position:0% +posters. And the communists and the +Nazis are defacing one another's + + align:start position:0% +Nazis are defacing one another's + + + align:start position:0% +Nazis are defacing one another's +posters. And what is implicit then again + + align:start position:0% +posters. And what is implicit then again + + + align:start position:0% +posters. And what is implicit then again +in the background against the against + + align:start position:0% +in the background against the against + + + align:start position:0% +in the background against the against +the foreground of these of these two + + align:start position:0% +the foreground of these of these two + + + align:start position:0% +the foreground of these of these two +relatively naive characters carrying on + + align:start position:0% +relatively naive characters carrying on + + + align:start position:0% +relatively naive characters carrying on +is the historical reality that's + + align:start position:0% +is the historical reality that's + + + align:start position:0% +is the historical reality that's +building behind them. Another example of + + align:start position:0% +building behind them. Another example of + + + align:start position:0% +building behind them. Another example of +what I mean by the multiplicity the + + align:start position:0% +what I mean by the multiplicity the + + + align:start position:0% +what I mean by the multiplicity the +texture of this film right. Uh finally + + align:start position:0% +texture of this film right. Uh finally + + + align:start position:0% +texture of this film right. Uh finally +the music all next to finally the + + align:start position:0% +the music all next to finally the + + + align:start position:0% +the music all next to finally the +musical numbers. Uh penultimately uh the + + align:start position:0% +musical numbers. Uh penultimately uh the + + + align:start position:0% +musical numbers. Uh penultimately uh the +musical numbers another kind of + + align:start position:0% +musical numbers another kind of + + + align:start position:0% +musical numbers another kind of +integration is going on in this film. + + align:start position:0% +integration is going on in this film. + + + align:start position:0% +integration is going on in this film. +Right when we talk about the integrated + + align:start position:0% +Right when we talk about the integrated + + + align:start position:0% +Right when we talk about the integrated +musical as Arthur Freed and his comrades + + align:start position:0% +musical as Arthur Freed and his comrades + + + align:start position:0% +musical as Arthur Freed and his comrades +during the studio era articulated this + + align:start position:0% +during the studio era articulated this + + + align:start position:0% +during the studio era articulated this +idea we're not talking about the form of + + align:start position:0% +idea we're not talking about the form of + + + align:start position:0% +idea we're not talking about the form of +integration that we see in Cabaret. And + + align:start position:0% +integration that we see in Cabaret. And + + + align:start position:0% +integration that we see in Cabaret. And +this in fact is one of the reasons that + + align:start position:0% +this in fact is one of the reasons that + + + align:start position:0% +this in fact is one of the reasons that +some people argue that Cabaret is not a + + align:start position:0% +some people argue that Cabaret is not a + + + align:start position:0% +some people argue that Cabaret is not a +musical because with one exception none + + align:start position:0% +musical because with one exception none + + + align:start position:0% +musical because with one exception none +of the musical performances in Cabaret + + align:start position:0% +of the musical performances in Cabaret + + + align:start position:0% +of the musical performances in Cabaret +take place out of a performance + + align:start position:0% +take place out of a performance + + + align:start position:0% +take place out of a performance +environment. They all take place in the + + align:start position:0% +environment. They all take place in the + + + align:start position:0% +environment. They all take place in the +cabaret. The film is about a cabaret + + align:start position:0% +cabaret. The film is about a cabaret + + + align:start position:0% +cabaret. The film is about a cabaret +performer and we see many performances + + align:start position:0% +performer and we see many performances + + + align:start position:0% +performer and we see many performances +in the cabaret. Now, when we watch those + + align:start position:0% +in the cabaret. Now, when we watch those + + + align:start position:0% +in the cabaret. Now, when we watch those +performances, we see them from angles + + align:start position:0% +performances, we see them from angles + + + align:start position:0% +performances, we see them from angles +that no one in the audience could ever + + align:start position:0% +that no one in the audience could ever + + + align:start position:0% +that no one in the audience could ever +see because FSY is a genius with the + + align:start position:0% +see because FSY is a genius with the + + + align:start position:0% +see because FSY is a genius with the +camera and creates visual effects + + align:start position:0% +camera and creates visual effects + + + align:start position:0% +camera and creates visual effects +drawing on the tradition of the + + align:start position:0% +drawing on the tradition of the + + + align:start position:0% +drawing on the tradition of the +Hollywood musical that could never be + + align:start position:0% +Hollywood musical that could never be + + + align:start position:0% +Hollywood musical that could never be +replicated in a theater. Nonetheless, + + align:start position:0% +replicated in a theater. Nonetheless, + + + align:start position:0% +replicated in a theater. Nonetheless, +the performances themselves are + + align:start position:0% +the performances themselves are + + + align:start position:0% +the performances themselves are +theatrical performances. They all are + + align:start position:0% +theatrical performances. They all are + + + align:start position:0% +theatrical performances. They all are +real performances. And when we see the + + align:start position:0% +real performances. And when we see the + + + align:start position:0% +real performances. And when we see the +characters behaving like real + + align:start position:0% +characters behaving like real + + + align:start position:0% +characters behaving like real +characters, they don't suddenly burst + + align:start position:0% +characters, they don't suddenly burst + + + align:start position:0% +characters, they don't suddenly burst +into song and dance, right? Because + + align:start position:0% +into song and dance, right? Because + + + align:start position:0% +into song and dance, right? Because +there's something theoretically so + + align:start position:0% +there's something theoretically so + + + align:start position:0% +there's something theoretically so +implausible about that that cabaret + + align:start position:0% +implausible about that that cabaret + + + align:start position:0% +implausible about that that cabaret +refuses that convention, right? It + + align:start position:0% +refuses that convention, right? It + + + align:start position:0% +refuses that convention, right? It +refuses to embrace that basic convention + + align:start position:0% +refuses to embrace that basic convention + + + align:start position:0% +refuses to embrace that basic convention +of the American musical, which is that + + align:start position:0% +of the American musical, which is that + + + align:start position:0% +of the American musical, which is that +one way that people express their + + align:start position:0% +one way that people express their + + + align:start position:0% +one way that people express their +exuberance, I love you. I love you. Now, + + align:start position:0% +exuberance, I love you. I love you. Now, + + + align:start position:0% +exuberance, I love you. I love you. Now, +let me sing a song telling you how much + + align:start position:0% +let me sing a song telling you how much + + + align:start position:0% +let me sing a song telling you how much +I love you. Right? Whereas in real life, + + align:start position:0% +I love you. Right? Whereas in real life, + + + align:start position:0% +I love you. Right? Whereas in real life, +we don't do that. Now, I don't think + + align:start position:0% +we don't do that. Now, I don't think + + + align:start position:0% +we don't do that. Now, I don't think +that this convention is really a bad con + + align:start position:0% +that this convention is really a bad con + + + align:start position:0% +that this convention is really a bad con +is a convention that undermines the + + align:start position:0% +is a convention that undermines the + + + align:start position:0% +is a convention that undermines the +music. It's a convention or a rule or a + + align:start position:0% +music. It's a convention or a rule or a + + + align:start position:0% +music. It's a convention or a rule or a +habit, a protocol you need to embrace in + + align:start position:0% +habit, a protocol you need to embrace in + + + align:start position:0% +habit, a protocol you need to embrace in +order to experience these films + + align:start position:0% +order to experience these films + + + align:start position:0% +order to experience these films +appropriately. And it's no more + + align:start position:0% +appropriately. And it's no more + + + align:start position:0% +appropriately. And it's no more +implausible in one sense than the + + align:start position:0% +implausible in one sense than the + + + align:start position:0% +implausible in one sense than the +implausibility of opera singers bursting + + align:start position:0% +implausibility of opera singers bursting + + + align:start position:0% +implausibility of opera singers bursting +into song at moments of great passion. + + align:start position:0% +into song at moments of great passion. + + + align:start position:0% +into song at moments of great passion. +Right? It's the the convention requires + + align:start position:0% +Right? It's the the convention requires + + + align:start position:0% +Right? It's the the convention requires +it. It's as if it's as if we're in a + + align:start position:0% +it. It's as if it's as if we're in a + + + align:start position:0% +it. It's as if it's as if we're in a +form of of of artistic experience in + + align:start position:0% +form of of of artistic experience in + + + align:start position:0% +form of of of artistic experience in +which in which art is crystallizing + + align:start position:0% +which in which art is crystallizing + + + align:start position:0% +which in which art is crystallizing +experience for us. So, I don't mean to + + align:start position:0% +experience for us. So, I don't mean to + + + align:start position:0% +experience for us. So, I don't mean to +undermine this convention at all or cast + + align:start position:0% +undermine this convention at all or cast + + + align:start position:0% +undermine this convention at all or cast +out on it, but Cabaret refuses that + + align:start position:0% +out on it, but Cabaret refuses that + + + align:start position:0% +out on it, but Cabaret refuses that +convention. Cabaret says every time with + + align:start position:0% +convention. Cabaret says every time with + + + align:start position:0% +convention. Cabaret says every time with +one exception, uh there and I'm calling + + align:start position:0% +one exception, uh there and I'm calling + + + align:start position:0% +one exception, uh there and I'm calling +attention to that exception. I'm not + + align:start position:0% +attention to that exception. I'm not + + + align:start position:0% +attention to that exception. I'm not +going to tell you what it is, but I want + + align:start position:0% +going to tell you what it is, but I want + + + align:start position:0% +going to tell you what it is, but I want +you to watch for it. There's one moment + + align:start position:0% +you to watch for it. There's one moment + + + align:start position:0% +you to watch for it. There's one moment +in the film when there is a song sung + + align:start position:0% +in the film when there is a song sung + + + align:start position:0% +in the film when there is a song sung +outside by ordinary people. It happens + + align:start position:0% +outside by ordinary people. It happens + + + align:start position:0% +outside by ordinary people. It happens +spontaneously. It may be the most + + align:start position:0% +spontaneously. It may be the most + + + align:start position:0% +spontaneously. It may be the most +morally and historically frightening + + align:start position:0% +morally and historically frightening + + + align:start position:0% +morally and historically frightening +moment in the whole of the film. + + align:start position:0% +moment in the whole of the film. + + + align:start position:0% +moment in the whole of the film. +And it's completely believable just as + + align:start position:0% +And it's completely believable just as + + + align:start position:0% +And it's completely believable just as +this pl totally plausible that it would + + align:start position:0% +this pl totally plausible that it would + + + align:start position:0% +this pl totally plausible that it would +happen. But that's the only moment in + + align:start position:0% +happen. But that's the only moment in + + + align:start position:0% +happen. But that's the only moment in +the film when there's any singing that + + align:start position:0% +the film when there's any singing that + + + align:start position:0% +the film when there's any singing that +doesn't take place inside a space + + align:start position:0% +doesn't take place inside a space + + + align:start position:0% +doesn't take place inside a space +intended for singing and dancing. So one + + align:start position:0% +intended for singing and dancing. So one + + + align:start position:0% +intended for singing and dancing. So one +of the interesting things about cabaret + + align:start position:0% +of the interesting things about cabaret + + + align:start position:0% +of the interesting things about cabaret +is that there is a kind of true + + align:start position:0% +is that there is a kind of true + + + align:start position:0% +is that there is a kind of true +integration of song and dance because + + align:start position:0% +integration of song and dance because + + + align:start position:0% +integration of song and dance because +none of that happens except in spaces + + align:start position:0% +none of that happens except in spaces + + + align:start position:0% +none of that happens except in spaces +where it's appropriate, right? Uh + + align:start position:0% +where it's appropriate, right? Uh + + + align:start position:0% +where it's appropriate, right? Uh +realistically appropriate, right? And so + + align:start position:0% +realistically appropriate, right? And so + + + align:start position:0% +realistically appropriate, right? And so +you might watch for that and and and the + + align:start position:0% +you might watch for that and and and the + + + align:start position:0% +you might watch for that and and and the +the the complexity that this decision on + + align:start position:0% +the the complexity that this decision on + + + align:start position:0% +the the complexity that this decision on +the part of Bob FSY and the people + + align:start position:0% +the part of Bob FSY and the people + + + align:start position:0% +the part of Bob FSY and the people +making the film uh uh uh the the impact + + align:start position:0% +making the film uh uh uh the the impact + + + align:start position:0% +making the film uh uh uh the the impact +of that of that decision on on your + + align:start position:0% +of that of that decision on on your + + + align:start position:0% +of that of that decision on on your +understanding of the movie as a whole. + + align:start position:0% +understanding of the movie as a whole. + + + align:start position:0% +understanding of the movie as a whole. +Finally, the central themes of the film. + + align:start position:0% +Finally, the central themes of the film. + + + align:start position:0% +Finally, the central themes of the film. +I've already talked about them. The + + align:start position:0% +I've already talked about them. The + + + align:start position:0% +I've already talked about them. The +theme of innocence, the way the central + + align:start position:0% +theme of innocence, the way the central + + + align:start position:0% +theme of innocence, the way the central +characters in the film are too innocent + + align:start position:0% +characters in the film are too innocent + + + align:start position:0% +characters in the film are too innocent +to understand the historical forces + + align:start position:0% +to understand the historical forces + + + align:start position:0% +to understand the historical forces +around them, underestimate them. This + + align:start position:0% +around them, underestimate them. This + + + align:start position:0% +around them, underestimate them. This +isn't just true of the central figures. + + align:start position:0% +isn't just true of the central figures. + + + align:start position:0% +isn't just true of the central figures. +It's true of the secondary characters as + + align:start position:0% +It's true of the secondary characters as + + + align:start position:0% +It's true of the secondary characters as +well. Some of whom are even more + + align:start position:0% +well. Some of whom are even more + + + align:start position:0% +well. Some of whom are even more +poignantly uh uh uh more who some of + + align:start position:0% +poignantly uh uh uh more who some of + + + align:start position:0% +poignantly uh uh uh more who some of +whom even more poignantly embody uh this + + align:start position:0% +whom even more poignantly embody uh this + + + align:start position:0% +whom even more poignantly embody uh this +theme. Uh and then the theme of history. + + align:start position:0% +theme. Uh and then the theme of history. + + + align:start position:0% +theme. Uh and then the theme of history. +What history is what how how how how the + + align:start position:0% +What history is what how how how how the + + + align:start position:0% +What history is what how how how how the +power how the force of history can + + align:start position:0% +power how the force of history can + + + align:start position:0% +power how the force of history can +overwhelm individual desires, individual + + align:start position:0% +overwhelm individual desires, individual + + + align:start position:0% +overwhelm individual desires, individual +hopes uh love itself and of course also + + align:start position:0% +hopes uh love itself and of course also + + + align:start position:0% +hopes uh love itself and of course also +the limits of satire. The cabaret is a + + align:start position:0% +the limits of satire. The cabaret is a + + + align:start position:0% +the limits of satire. The cabaret is a +space of satire, a space of mockery, a + + align:start position:0% +space of satire, a space of mockery, a + + + align:start position:0% +space of satire, a space of mockery, a +space of exuberant intellectual distance + + align:start position:0% +space of exuberant intellectual distance + + + align:start position:0% +space of exuberant intellectual distance +and disdain. Much of the energy of the + + align:start position:0% +and disdain. Much of the energy of the + + + align:start position:0% +and disdain. Much of the energy of the +cabaret comes from an impulse of parody, + + align:start position:0% +cabaret comes from an impulse of parody, + + + align:start position:0% +cabaret comes from an impulse of parody, +mockery, satire, right? And in the very + + align:start position:0% +mockery, satire, right? And in the very + + + align:start position:0% +mockery, satire, right? And in the very +beginning of the film, there's actually + + align:start position:0% +beginning of the film, there's actually + + + align:start position:0% +beginning of the film, there's actually +a moment where you can see the Joel Gray + + align:start position:0% +a moment where you can see the Joel Gray + + + align:start position:0% +a moment where you can see the Joel Gray +character who plays this ominous strange + + align:start position:0% +character who plays this ominous strange + + + align:start position:0% +character who plays this ominous strange +uh figure of the MC, the interlocator, + + align:start position:0% +uh figure of the MC, the interlocator, + + + align:start position:0% +uh figure of the MC, the interlocator, +right? Uh at in the cabaret. He sort of + + align:start position:0% +right? Uh at in the cabaret. He sort of + + + align:start position:0% +right? Uh at in the cabaret. He sort of +is the is the master of ceremonies. Uh, + + align:start position:0% +is the is the master of ceremonies. Uh, + + + align:start position:0% +is the is the master of ceremonies. Uh, +and there's one moment early in the film + + align:start position:0% +and there's one moment early in the film + + + align:start position:0% +and there's one moment early in the film +when he when when he uh um in a rather + + align:start position:0% +when he when when he uh um in a rather + + + align:start position:0% +when he when when he uh um in a rather +disgusting scene in which they have a + + align:start position:0% +disgusting scene in which they have a + + + align:start position:0% +disgusting scene in which they have a +sort of they replicate a scene of mud + + align:start position:0% +sort of they replicate a scene of mud + + + align:start position:0% +sort of they replicate a scene of mud +wrestling and and he's mcing it and he + + align:start position:0% +wrestling and and he's mcing it and he + + + align:start position:0% +wrestling and and he's mcing it and he +reaches down, he picks up a piece of + + align:start position:0% +reaches down, he picks up a piece of + + + align:start position:0% +reaches down, he picks up a piece of +mud, he rubs it on his upper lip and he + + align:start position:0% +mud, he rubs it on his upper lip and he + + + align:start position:0% +mud, he rubs it on his upper lip and he +makes himself look like Hitler and he's + + align:start position:0% +makes himself look like Hitler and he's + + + align:start position:0% +makes himself look like Hitler and he's +mocking Hitler in that, right? Well, if + + align:start position:0% +mocking Hitler in that, right? Well, if + + + align:start position:0% +mocking Hitler in that, right? Well, if +you compare that early moment in which + + align:start position:0% +you compare that early moment in which + + + align:start position:0% +you compare that early moment in which +Hitler and Nazism are objects of + + align:start position:0% +Hitler and Nazism are objects of + + + align:start position:0% +Hitler and Nazism are objects of +mockery, there's also an early scene in + + align:start position:0% +mockery, there's also an early scene in + + + align:start position:0% +mockery, there's also an early scene in +which we see a Nazi being pulled out of + + align:start position:0% +which we see a Nazi being pulled out of + + + align:start position:0% +which we see a Nazi being pulled out of +the audience of the cabaret and pushed + + align:start position:0% +the audience of the cabaret and pushed + + + align:start position:0% +the audience of the cabaret and pushed +outside, right? Kicked out of the + + align:start position:0% +outside, right? Kicked out of the + + + align:start position:0% +outside, right? Kicked out of the +cabaret because Nazis are thought to be + + align:start position:0% +cabaret because Nazis are thought to be + + + align:start position:0% +cabaret because Nazis are thought to be +uh unacceptable. They're thought to be + + align:start position:0% +uh unacceptable. They're thought to be + + + align:start position:0% +uh unacceptable. They're thought to be +vulgarians, right? This is early in the + + align:start position:0% +vulgarians, right? This is early in the + + + align:start position:0% +vulgarians, right? This is early in the +by the time the film is over. By the by + + align:start position:0% +by the time the film is over. By the by + + + align:start position:0% +by the time the film is over. By the by +the time you come to the very end of the + + align:start position:0% +the time you come to the very end of the + + + align:start position:0% +the time you come to the very end of the +film, one of the very final images of + + align:start position:0% +film, one of the very final images of + + + align:start position:0% +film, one of the very final images of +the film shows us the audience of the + + align:start position:0% +the film shows us the audience of the + + + align:start position:0% +the film shows us the audience of the +cabaret filled with Nazi officers, + + align:start position:0% +cabaret filled with Nazi officers, + + + align:start position:0% +cabaret filled with Nazi officers, +filled with Nazi uniforms. The Nazis + + align:start position:0% +filled with Nazi uniforms. The Nazis + + + align:start position:0% +filled with Nazi uniforms. The Nazis +have moved from the periphery to the + + align:start position:0% +have moved from the periphery to the + + + align:start position:0% +have moved from the periphery to the +center of the movie. And that's part of + + align:start position:0% +center of the movie. And that's part of + + + align:start position:0% +center of the movie. And that's part of +the terror uh and that that the film + + align:start position:0% +the terror uh and that that the film + + + align:start position:0% +the terror uh and that that the film +dramatizes. And it also therefore of + + align:start position:0% +dramatizes. And it also therefore of + + + align:start position:0% +dramatizes. And it also therefore of +course dramatizes the limits of satire + + align:start position:0% +course dramatizes the limits of satire + + + align:start position:0% +course dramatizes the limits of satire +because the cabaret itself like the + + align:start position:0% +because the cabaret itself like the + + + align:start position:0% +because the cabaret itself like the +characters imagines itself to be + + align:start position:0% +characters imagines itself to be + + + align:start position:0% +characters imagines itself to be +exempted from or apart from history. It + + align:start position:0% +exempted from or apart from history. It + + + align:start position:0% +exempted from or apart from history. It +can maintain its mockery, its distance. + + align:start position:0% +can maintain its mockery, its distance. + + + align:start position:0% +can maintain its mockery, its distance. +Satire can protect me from all the And + + align:start position:0% +Satire can protect me from all the And + + + align:start position:0% +Satire can protect me from all the And +of course, the cabaret is just as naive + + align:start position:0% +of course, the cabaret is just as naive + + + align:start position:0% +of course, the cabaret is just as naive +as the characters themselves. It's + + align:start position:0% +as the characters themselves. It's + + + align:start position:0% +as the characters themselves. It's +overwhelmed by the forces of history in + + align:start position:0% +overwhelmed by the forces of history in + + + align:start position:0% +overwhelmed by the forces of history in +a way in a way that the characters + + align:start position:0% +a way in a way that the characters + + + align:start position:0% +a way in a way that the characters +themselves also are. Both of these films + + align:start position:0% +themselves also are. Both of these films + + + align:start position:0% +themselves also are. Both of these films +in their own way have generated a + + align:start position:0% +in their own way have generated a + + + align:start position:0% +in their own way have generated a +tremendously interesting and serious + + align:start position:0% +tremendously interesting and serious + + + align:start position:0% +tremendously interesting and serious +volume of discourse both uh uh in terms + + align:start position:0% +volume of discourse both uh uh in terms + + + align:start position:0% +volume of discourse both uh uh in terms +of their musical qualities and their and + + align:start position:0% +of their musical qualities and their and + + + align:start position:0% +of their musical qualities and their and +the qualities of their of their + + align:start position:0% +the qualities of their of their + + + align:start position:0% +the qualities of their of their +choreography and in terms of their + + align:start position:0% +choreography and in terms of their + + + align:start position:0% +choreography and in terms of their +content. They're really such complex + + align:start position:0% +content. They're really such complex + + + align:start position:0% +content. They're really such complex +films that watching them together makes + + align:start position:0% +films that watching them together makes + + + align:start position:0% +films that watching them together makes +an immense intellectual demand on + + align:start position:0% +an immense intellectual demand on + + + align:start position:0% +an immense intellectual demand on +everyone. I know you're capable of that, + + align:start position:0% +everyone. I know you're capable of that, + + + align:start position:0% +everyone. I know you're capable of that, +but I hope that you'll take the time to + + align:start position:0% +but I hope that you'll take the time to + + + align:start position:0% +but I hope that you'll take the time to +let the implications of these films + + align:start position:0% +let the implications of these films + + + align:start position:0% +let the implications of these films +settle into your mind for days and maybe + + align:start position:0% +settle into your mind for days and maybe + + + align:start position:0% +settle into your mind for days and maybe +even weeks after you've watched them. + + align:start position:0% +even weeks after you've watched them. + + + align:start position:0% +even weeks after you've watched them. +And I hope, of course, that this first + + align:start position:0% +And I hope, of course, that this first + + + align:start position:0% +And I hope, of course, that this first +viewing will only be the first of many. + + align:start position:0% +viewing will only be the first of many. + + + align:start position:0% +viewing will only be the first of many. +I wish you the joy of these wonderful + + align:start position:0% +I wish you the joy of these wonderful + + + align:start position:0% +I wish you the joy of these wonderful +movies. \ No newline at end of file diff --git a/te6Mplq3DCU.txt b/te6Mplq3DCU.txt new file mode 100644 index 0000000000000000000000000000000000000000..f2a0d53ff3262760a91174ba8ec6dbc2e79cc2ac --- /dev/null +++ b/te6Mplq3DCU.txt @@ -0,0 +1,1934 @@ +Today, once again, +a day of solving no + +differential equations +whatsoever. + +The topic is a special kind of +differential equation, + +which occurs a lot. +It's one in which the + +right-hand side doesn't have any +independent variable in it. + +Now, since I'm going to use as +the independent variable, + +t for time, maybe it would be +better to write the left-hand + +side to let you know, +since you won't be able to + +figure out any other way what it +is, dy dt. + +We will write it this time. +dy dt is equal to, + +and the point is that there is +no t on the right hand side. + +So, there's no t. +There's a name for such an + +equation. +Now, some people call it time + +independent. +The only problem with that is + +that sometimes the independent +variable is a time. + +It's something else. +We need a generic word for + +there being no independent +variable on the right-hand side. + +So, the word that's used for +that is autonomous. + +So, that means no independent +variable on the right-hand side. + +It's a function of y alone, +the dependent variable. + +Now, your first reaction should +be, oh, well, + +big deal. +Big deal. + +If there's no t on the right +hand side, then we can solve + +this by separating variables. +So, why has he been talking + +about it in the first place? +So, I admit that. + +We can separate variables, +and what I'm going to talk + +about today is how to get useful +information out of the equation + +about how its solutions look +without solving the equation. + +The reason for wanting to do +that is, A, it's fast. + +It gives you a lot of insight, +and the actual solution, + +I'll illustrate one, +in the first place, + +take you quite a while. +You may not be able to actually + +do the integrations, +the required and separation of + +variables to get an explicit +solution, or it might simply not + +be worth the effort of doing if +you only want certain kinds of + +separations about the solution. +So, the thing is, + +the problem is, +therefore, to get qualitative + +information about the solutions +without actually solving -- + +Without actually having to +solve the equation. + +Now, to do that, +let's take a quick look at how + +the direction fields of such an +equation, after all, + +it's the direction field is our +principal tool for getting + +qualitative information about +solutions without actually + +solving. +So, how does the direction + +field look? +Well, think about it for just a + +second, and you will see that +every horizontal line is an + +isocline. +So, the horizontal lines, + +what are their equations? +This is the t axis. + +And, here's the y axis. +The horizontal lines have the + +formula y equals a constant. +Let's make it y equals a y zero + +for different values of the +constant y zero. + +Those are the horizontal lines. +And, the point is they are + +isoclines. +Why? + +Well, because along any one of +these horizontal lines, + +I'll draw one in, +what are the slopes of the line + +elements? +The slopes are dy / dt is equal + +to f of y zero, +but that's a constant because + +there's no t to change as you +move in the horizontal + +direction. +The slope is a constant. + +So, if I draw in that isocline, +I guess I've forgotten, + +as our convention, +isoclines are in dashed lines, + +but if you have color, +you are allowed to put them in + +living yellow. +Well, I guess I could make them + +solid, in that case. +I don't have to make a dash. + +Then, all the line elements, +you put them in at will because + +they will all have, +they are all the same, + +and they have slope, +that, f of y0. + +And, similarly down here, +they'll have some other slope. + +This one will have some other +slope. + +Whatever, this is the y zero, +the value of it, + +and whatever that happens to +be. + +I'll put it one more. +That's the x-axis. + +I can use the x-axis. +That's an isocline, + +too. +Now, what do you deduce about + +how the solutions must look? +Well, let's draw one solution. + +Suppose one solution looks like +this. + +Well, that's an integral curve, +in other words. + +Its graph is a solution. +Now, as I slide along, + +these slope elements stay +exactly the same, + +I can slide this curb along +horizontally, + +and it will still be an +integral curve everywhere. + +So, in other words, +they integral curves are + +invariant under translation for +an equation of this type. + +They all look exactly the same, +and you get them all by taking + +one, and just pushing it along. +Well, that's so simple it's + +almost uninteresting, +except in that these equations + +occur a lot in practice. +They are often hard to + +integrate directly. +And, therefore, + +it's important to be able to +get information about them. + +Now, how does one do that? +There's one critical idea, + +and that is the notion of a +critical point. + +These equations have what are +called critical points. + +And, what it is is very simple. +There are three ways of looking + +at it: critical point, +y zero; + +what does it mean for y0 to be +a critical point? + +It means, another way of saying +it is that it should be a zero + +of the right-hand side. +So, if I ask you to find the + +critical points for the +equation, what you will do is + +solve the equation f of y equals +zero. + +Now, what's interesting about +them? + +Well, for a critical point, +what would be the slope of the + +line element along, +if this is at a critical level, + +if that's a critical point? +Look at that isocline. + +What's the slope of the line +elements along it? + +It is zero. +And therefore, + +for these guys, +these are, in other words, + +our solution curves. +But let's prove it formally. + +So, there are three ways of +saying it. + +y zero is a critical point. + +It's a zero of the right-hand +side, or, y equals y0 is a + +solution to the equation. +Now, that's perfectly easy to + +verify. +If y zero makes this + +right-hand side zero, +it's certainly also y equals y0 + +makes the left-hand +side zero because you're + +differentiating a constant. +So, the reasoning, + +if you want reasoning, +is proof. + +Maybe we can make one line out +of a proof. + +To say that it's a solution, +what does it mean to say that + +it's a solution? +It means to say that when you + +plug it in, plug in this +constant function, + +y0, the dy0 dt is equal to f of +y0. + +Is that true? +Yeah. + +Both sides are zero. +It's true. + +Now, y0 is not a number. +Well, it is. + +It's a number on this side, +but on this side, + +what I mean is a constant +function whose constant value is + +y zero, this function, + +and its derivatives are zero +because it has slope zero + +everywhere. +So, this guy is a constant + +function, has slope zero. +This is a number which makes + +the right-hand side zero. +Well, that's nice. + +So, in other words, +what we found are, + +by finding these critical +points, solving that equation, + +we found all the horizontal +solutions. + +But, what's so good about +those? + +Surely, they must be the most +interesting solutions there are. + +Well, think of how the picture +goes. + +Let's draw in one of those +horizontal solutions. + +So, here's a horizontal +solution. + +That's a solution. +So, this is my y0. + +That's the height at which it +is. + +And, I'm assuming that f of y0 +equals zero. + +So, that's a solution. +Now, the significance of that + +is, because it's a solution, +in other words, + +it's an integral curve, +remember what's true about + +integral curves. +Other curves are not allowed to + +cross them. +And therefore, + +these things are the absolute +barriers. + +So, for example, +suppose I have two of them is + +y0, and let's say here's another +one, another constant solution. + +I want to know what the curves +in between those can do. + +Well, I do know that whatever +those red curves do, + +the other integral curves, +they cannot cross this, + +and they cannot cross that. +And, you must be able to + +translate them along each other +without ever having two of them + +intersect. +Now, that really limits their + +behavior, but I'm going to nail +it down even more. + +So, other curves can't cross +these. + +Other integral curves can't +cross these yellow curves, + +these yellow lines, +these horizontal lines. + +But, I'm going to show you +more, and namely, + +so what I'm after is deciding, +without solving the equation, + +what those curves must look +like in between. + +Now, the way to do that is you +draw, so if we want to make + +steps, everybody likes steps, +okay, so step one is going to + +be, find these. +Find the critical points. + +And, you're going to do that by +solving this equation, + +finding out where it's zero. +Once you have done that, + +you are going to draw the graph +of f of y. + +And, the interest is going to +be, where is it positive? + +Where is it negative? +You've already found where it's + +zero. +Everywhere else, + +therefore, it must be either +positive or negative. + +Now, once you have found that +out, why am I interested in + +that? +Well, because dy / dt is equal + +to f of y, right? + +That's what the differential +equation says. + +Therefore, if this, +for example, + +is positive, +that means this must be + +positive. +It means that y must be + +increasing. +It means the solution must be + +increasing. +Where it's negative, + +the solution will be +decreasing. + +And, that tells me how it's +behaving in between these yellow + +lines, or on top of them, +or on the bottom. + +Now, at this point, +I'm going to stop, + +or not stop, +I mean, I'm going to stop + +talking generally. +And everything in the rest of + +the period will be done by +examples which will get + +increasingly complicated, +not terribly complicated by the + +end. +But, let's do one that's super + +simple to begin with. +Sorry, I shouldn't say that + +because some of you may be +baffled even by here because + +after all I'm going to be doing +the analysis not in the usual + +way, but by using new ideas. +That's the way you make + +progress. +All right, so, + +let's do our bank account. +So, y is money in the bank + +account. +r is the interest rate. + +Let's assume it's a continuous +interest rate. + +All banks nowadays pay interest +continuously, + +the continuous interest rate. +So, if that's all there is, + +and money is growing, +you know the differential + +equation says that the rate at +which it grows is equal to r, + +the interest rate times a +principle, the amount that's in + +the bank at that time. +So, that's the differential + +equation that governs that. +Now, that's, + +of course, the solution is +simply an exponential curve. + +There's nothing more to say +about it. + +Now, let's make it more +interesting. + +Let's suppose there is a shifty +teller at the bank, + +and your money is being +embezzled from your account at a + +constant rate. +So, let's let w equal, + +or maybe e, but e has so many +other uses in mathematics, + +w is relatively unused, +w is the rate of embezzlement, + +thought of as continuous. +So, every day a little bit of + +money is sneaked out of your +account because you are not + +paying any attention to it. +You're off skiing somewhere, + +and not noticing what's +happening to your bank account. + +So, since it's the rate, +the time rate of embezzlement, + +I simply subtract it from this. +It's not w times y because the + +embezzler isn't stealing a +certain fraction of your + +account. +It's simply stealing a certain + +number of dollars every day, +the same number of dollars + +being withdrawn for the count. +Okay, now, of course, + +you could solve this. +This separates variables + +immediately. +You get the answer, + +and there's no problem with +that. + +Let's analyze the behavior of +the solutions without solving + +the equation by using these two +points. + +So, I want to analyze this +equation using the method of + +critical points. +So, the first thing I should do + +is, so, here's our equation, +is find the critical points. + +Notice it's an autonomous +equation all right, + +because there's no t on the +right-hand side. + +Okay, so, the critical points, +well, that's where ry minus w + +equals zero. +In other words, + +there's only one critical +point, and that occurs when y is + +equal to w over r. +So, that's the only critical + +point. +Now, I want to know what's + +happening to the solution. +So, in other words, + +if I plot, I can write away, +of course, negative values + +aren't of particularly +interesting here, + +there is definitely a +horizontal solution, + +and it has the value, +it's at the height, + +w over r. +That's a solution. + +The question is, +what do the other solutions + +look like? +Now, watch how I make the + +analysis because I'm going to +use two now. + +So, this is step one, +then step two. + +What do I do? Well, +I'm going to graph f of y. + +Well, f of y is ry minus w. + +What does that look like? + +Okay, so, here is the y-axis. +Notice the y-axis is going + +horizontally because what I'm +interested in is the graph of + +this function. +What do I call the other axis? + +I'm going to use the same +terminology that is used on the + +little visual that describes +this. + +And, that's dy. +You could call this other axis + +the f of y axis. +That's not a good name for it. + +You could call it the dy / dt +axis because it's, + +so to speak, +the other variable. + +That's not great either. +But, worst of all would be + +introducing yet another letter +for which we would have no use + +whatsoever. +So, let's think of it. + +We are plotting, +now, the graph of f of y. + +f of y is this function, + +ry minus w. +Well, that's a line. + +Its intercept is down here at +w, and so the graph looks + +something like this. +It's a line. + +This is the line, +ry minus w. + +It has slope r. +Well, what am I going to get + +out of that line? +Just exactly this. + +What am I interested in about +that line? + +Nothing other than where is it +above the axis, + +and where is it below? +This function is positive over + +here, and therefore, +I'm going to indicate that + +symbolically, +this, by putting an arrow here. + +The meeting of this arrow is +that y of t is + +increasing. +See where it's the right-hand + +side of that last board? +y of t is increasing when f of + +y is positive. +f of y is positive here, + +and therefore, +to the right of this point, + +it's increasing. +Here to the left of it, + +f of y is negative, +and therefore over here it's + +going to be decreasing. +What point is this, + +in fact? +Well, that's where it crosses + +the axis. +That's exactly the critical + +point, w over r. +Therefore, what this says is + +that a solution, +once it's bigger than y over r, + +it increases, +and it increases faster and + +faster because this function is +higher and higher. + +And, that represents the rate +of change. + +So, in other words, +once the solution, + +let's say a solution starts +over here at time zero. + +So, this is the t axis. +And, here is the y axis. + +So, now, I'm plotting +solutions. + +If it starts at t equals zero, +above this line, + +that is, starts with the value +w over r, + +which is bigger than zero, +a value bigger than w over r, + +then it increases, +and increases faster and + +faster. +If it starts below that, + +it decreases and decreases +faster and faster. + +Now, in fact, +I only have to draw two of + +those because what do all the +others look like? + +They are translations. +All the other curves look + +exactly like those. +They are just translations of + +them. +This guy, if I start closer, + +it's still going to decrease. +Well, that's supposed to be a + +translation. +Maybe it is. + +So, these guys look like that. +Let's do just a tiny bit more + +interpretation of that. +Well, I think I better leave it + +there because we've got harder +things to do, + +and I want to make sure we've +got time for it. + +Sorry. +Okay, next example, + +a logistic equation. +Some of you have already solved + +this in recitation, +and some of you haven't. + +This is a population equation. +This is the one that section + +7.1 and section 1.7 is most +heavily concerned with, + +this particular equation. +The derivation of it is a + +little vague. +It's an equation which + +describes how population +increases. + +And one minute, +the population behavior of some + +population, -- +-- let's call it, + +y is the only thing I know to +call anything today, + +but of course your book uses +capital P for population, + +to get you used to different +variables. + +Now, the basic population +equation runs dy / dt. + +There's a certain growth rate. +Let's call it k y. + +So, k is what's called the +growth rate. + +It's actually, +sometimes it's talked about in + +terms of birthrate. +But, it's the net birth rate. + +It's the rate at which people, +or bacteria, + +or whatever are being born +minus the rate at which they are + +dying. +So, it's a net birthrate. + +But, let's just call it the +growth rate. + +Now, if this is the equation, +we can think of this, + +if k is constant, +that's what's called simple + +population growth. +And you are all familiar with + +that. +Logistical growth allows for + +slightly more complex +situations. + +Logistic growth says that +calling k a constant is + +unrealistic because the Earth is +not filled entirely with people. + +What stops it from having +unlimited growth? + +Well, the fact that the +resources, the food, + +the organism has to live on +gets depleted. + +And, in other words, +the growth rate declines as y + +increases. +As the population increases, + +one expects the growth rate to +decline because resources are + +being used up, +and they are not indefinitely + +available. +Well, in other words, + +we should replace k by a +function with this behavior. + +What's the simplest function +that declines as y increases? + +The simplest choice, +and if you are ignorant about + +what else to do, +stick with the simplest, + +at least you won't work any +harder than you have to, + +would be to take k equal to the +simplest declining function of y + +there is, which is simply a +linear function, + +A minus BY. +So, if I use that as the choice + +of the declining growth rate, +the new equation is dy / dt + +equals, here's my new k. +The y stays the same, + +so the equation becomes a minus +by, the quantity times y, + +or in other words, + +ay minus b y squared. + +This equation is what's called +the logistic equation. + +It has many applications, +not just to population growth. + +It's applied to the spread of +disease, the spread of a rumor, + +the spread of many things. +Yeah, a couple pieces of chalk + +here. + +Okay, now, those of you who +have solved it know that the + +explicit solution involves, +well, you separate variables, + +but you will have to use +partial fractions, + +ugh, I hope you love partial +fractions. + +You're going to need them later +in the term. + +But, I could avoid them now by +not solving the equation + +explicitly. +But anyway, you get a solution, + +which I was going to write on +the board for you, + +but you could look it up in +your book. + +It's unpleasant enough looking +to make you feel that there must + +be an easier way at least to get +the basic information out. + +Okay, let's see if we can get +the basic information out. + +What are the critical points? +Well, this is pretty easy. + +A, I want to set the right-hand +side equal to zero. + +So, I'm going to solve the +equation. + +I can factor out a y. +It's going to be y times a + +minus by equals zero. + +And therefore, +the critical points are where y + +equals zero. That's one. + +And, the other factor is when +this factor is zero, + +and that happens when y is +equal to a over b. + +So, there are my two critical +points. + +Okay, what does, +let's start drawing pictures of + +solutions. +Let's put it in those right + +away. +Okay, the critical point, + +zero, gives me a solution that +looks like this. + +And, the critical point, +a over b, + +those are positive numbers. +So, that's somewhere up here. + +So, those are two solutions, +constant solutions. + +In other words, +if the population by dumb luck + +started at zero, +it would stay at zero for all + +time. +That's not terribly surprising. + +But, it's a little less obvious +that if it starts at that magic + +number, a over b, +it will also stay at that magic + +number for all time without +moving up or down or away from + +it. +Now, the question is, + +therefore, what happens in +between? + +So, for the in between, +I'm going to make that same + +analysis that I made before. +And, it's really not very hard. + +Look, so here's my dy/dt-axis. +I'll call that y prime, + +okay? +And, here's the y-axis. + +So, I'm now doing step two. +This was step one. + +Okay, the function that I want +to graph is this one, + +ay minus b y squared, +or in factor form, + +y times a minus by. + +Now, this function, +we know, has a zero. + +It has a zero here, +and it has a zero at the point + +a over b. +At these two critical points, + +it has a zero. +What is it doing in between? + +Well, in between, +it's a parabola. + +It's a quadratic function. +It's a parabola. + +Does it go up or does it go +down? + +Well, when y is very large, +it's very negative. + +That means it must be a +downward-opening parabola. + +And therefore, +this curve looks like this. + +So, I'm interested in knowing, +where is it positive, + +and where is it negative? +Well, it's positive, + +here, for this range of values +of y. + +Since it's positive there, +it will be increasing there. + +Here, it's negative, +and therefore it will be + +decreasing. +Here, it's negative, + +and therefore, +dy / dt will be negative also, + +and therefore the function, +y, will be decreasing here. + +So, how do these other +solutions look? + +Well, we can put them in. +I'll put them in in white, + +okay, because this has got to +last until the end of the term. + +So, how are they doing? +They are increasing between the + +two curves. +They are not allowed to cross + +either of these yellow curves. +But, they are always + +increasing. +Well, if they're always + +increasing, they must start here +and increase, + +and not allowed to cross. +It must do something like that. + +This must be a translation of +it. + +In other words, +the curves must look like that. + +Those are supposed to be +translations of each other. + +I know they aren't, +but use your imaginations. + +But what's happening above? +So in other words, + +if I start with a population +anywhere bigger than zero but + +less than a over b, +it increases asymptotically to + +the level a over b. +What happens if I start above + +that? +Well, then it decreases to it + +because, this way, +for the values of y bigger than + +a over b, +it decreases as time increases. + +So, these guys up here are +doing this. + +And, how about the ones below +the axis? + +Well, they have no physical +significance. + +But let's put them in anyway. +Whether they doing? + +They are decreasing away from +zero. + +So, these guys don't mean +anything physically, + +but mathematically they exist. +Their solutions, + +they're going down like that. +Now, you notice from this + +picture that there are, +even though both of these are + +constant solutions, +they have dramatically + +different behavior. +This one, this solution, + +is the one that all other +solutions try to approach as + +time goes to infinity. +This one, the solution zero, + +is repulsive, +as it were. + +Any solution that starts near +zero, if it starts at zero, + +of course, it stays there for +all time, but if it starts just + +a little bit above zero, +it increases to a over b. + +This is called a stable + +solution because everybody tries +to get closer and closer to it. + +This is called, +zero is also a constant + +solution, but this is an +unstable solution. + +And now, usually, +solution is too general a word. + +I think it's better to call it +a stable critical point, + +and an unstable critical point. +But, of course, + +it also corresponds to a +solution. + +So, critical points are not all +the same. + +Some are stable, +and some are unstable. + +And, you can see which is which +just by looking at this picture. + +If the arrows point towards +them, you've got a stable + +critical point. +If it arrows point away from + +them, you've got an unstable +critical point. + +Now, there is a third +possibility. + +Okay, I think we'd better +address it because otherwise + +you're going to sit there +wondering, hey, + +what did he do? +Suppose it looks like this. + +Suppose it were just tangent. +Well, this is the picture of + +that curve, the pink curve. +What would the arrows look like + +then? +What would the arrows look like + +then? +Well, since they are positive, + +it's always positive, +the arrow goes like this. + +And then on the side, +it also goes in the same + +direction. +So, is this critical point + +stable or unstable? +It's stable if you approach it + +from the left. +So, how, in fact, + +do the curves, +how would the corresponding + +curves look? +Well, there's our long-term + +solution. +This corresponds to that point. + +Let's call this a, +and then this will be the + +value, a. +If I start below it, + +I rise to it. +If I start above it, + +I increase. +So, if I start above it, + +I do this. +Well, now, that's stable on one + +side, and unstable on the other. +And, that's indicated by saying + +it's semi-stable. +That's a brilliant word. + +I wonder how long it to do +think that one up, + +semi-stable critical point: +stable on one side, + +unstable on the other depending +on whether you start below it. + +And, of course, +it could be reversed if I had + +drawn the picture the other way. +I could have approached it from + +the top, and left it from below. +You get the idea of the + +behavior. +Okay, let's now take, + +I'm going to soup up this +logistic equation just a little + +bit more. +So, let's talk about the + +logistic equation. +But, I'm going to add to it + +harvesting, with harvesting. +So, this is a very late 20th + +century concept. +So, we imagine, + +for example, +a bunch of formerly free range + +Atlantic salmon penned in one of +these huge factory farms off the + +coast of Maine or someplace. +They've made salmon much + +cheaper than it used to be, +but at a certain cost to the + +salmon, and possibly to our +environment. + +So, what happens? +Well, the salmon grow, + +and grow, and do what salmon +do. + +And, they are harvested. +That's a word somewhere in the + +category of ethnic cleansing in +my opinion. + +But, it's, again, +a very 20th-century word. + +I think it was Hitler who +discovered that, + +that all you had to do was call +something by a sanitary name, + +and no matter how horrible it +was, good bourgeois people would + +accept it. +So, the harvesting, + +which means, +of course, picking them up and + +killing them, +and putting them in cans and + +stuff like that, +okay, so what's the equation? + +I'm going to assume that the +harvest is at a constant time + +rate. +In other words, + +it's not a certain fraction of +all the salmon that are being + +caught each day and canned. +The factory has a certain + +capacity, so, +400 pounds of salmon each day + +are pulled out and canned. +So, it's a constant time rate. + +That means that the equation is +now going to be dy/dt is equal + +to, well, salmon grow +logistically. + +ay minus b y squared, +so, that part of the + +equation is the same. +But, I need a term to take care + +of this constant harvesting +rate, and that will be h. + +Let's call it h, +not h times y. + +Then, I would be harvesting a +certain fraction of all the + +salmon there, +which is not what I'm doing. + +Okay: our equation. +Now, I want to analyze what the + +critical points of this look +like. + +Now, this is a little more +subtle because there's now a new + +parameter, there. +And, what I want to see is how + +that varies with the new +parameter. + +The best thing to do is, +I mean, the thing not to do is + +make this equal to zero, +fiddle around with the + +quadratic formula, +get some massive expression, + +and then spend the next half +hour scratching your head trying + +to figure out what it means, +and what information you are + +supposed to be getting out of +it. + +Draw pictures instead. +Draw pictures. + +If h is zero, +that's the smallest harvesting + +rate I could have. +The picture looks like our old + +one. +So, if h is zero, + +the picture looks like, +what color did I, + +okay, pink. +Yellow. + +Yellow is the cheapest, +but I can't find it. + +Okay, yellow is commercially +available. + +These are precious. +All right, purple if it's okay, + +purple. +So, this is the one, + +our original one corresponding +to h equals zero. + +Or, in other words, +it's the equation ay minus b y + +squared. h is zero. + +Now, if I want to find, +I now want to increase the + +value of h, well, +if I increase the value of h, + +in other words, +harvest more and more, + +what's happening? +Well, I simply lower this + +function by h. +So, if I lower h somewhat, + +it will come to here. +So, this is some value, + +ay minus b y squared minus h1, + +let's say. +That's this curve. + +If I lower it a lot, +it will look like this. + +So, ay minus b y squared minus +h a lot, h twenty. + +This doesn't mean anything. + +Two. +Obviously, there's one + +interesting value to lower it +by. + +It's a value which would lower +it exactly by this amount. + +Let me put that in special. +If I lower it by just that + +amount, the curve always looks +the same. + +It's just been lowered. +I'm going to say this one is, + +so this one is the same thing, +except that I've subtracted h + +sub m. Where is h sub m on + +the picture? +Well, I lowered it by this + +amount. +So, this height is h sub m. + +In other words, +if I find the maximum height + +here, which is easy to do +because it's a parabola, + +and lower it by exactly that +amount, I will have lowered it + +to this point. +This will be a critical point. + +Now, the question is, +what's happened to the critical + +point as I did this? +I started with the critical + +points here and here. +As I lower h, + +the critical point changed to +this and that. + +And now, it changed to this one +when I got to the purple line. + +And, as I went still further +down, there were no critical + +points. +So, this curve has no critical + +points attached to it. +What are the corresponding + +pictures? +Well, the corresponding + +pictures, well, +we've already drawn, + +the picture for h equals zero +is drawn already. + +The pictures that I'm talking +about are how the solutions + +look. +How would the solution look + +like for this one for h one? + +For h1, the solutions look +like, here is a over b. + +Here is a over b, +but the critical points aren't + +at zero and a over b anymore. +They've moved in a little bit. + +So, they are here and here. +And, otherwise, + +the solutions look just like +they did before, + +and the analysis is the same. +And, similarly, + +if h two goes very far, +if h2 is very large, + +there are no critical points. +h, too large, + +no critical points. +Are the solutions decreasing + +all the time or increasing? +Well, they are always + +decreasing because the function +is always negative. + +Solutions always go down, +always. + +The interesting one is this +last one, where I decreased it + +just to (h)m. +And, what happens there is + +there is this certain, +magic critical point whose + +value we could calculate. +There's one constant solution. + +So, this is one that has the +value. + +Sorry, I'm calculating the +solutions out. + +So, y here and t here, +so here it is value, + +(h)m is the value by which it +has been lowered. + +So, this is the picture for +(h)m. + +And, how do the solutions look? +Well, to the right of that, + +they are decreasing. +And, to the left they are also + +decreasing because this function +is always negative. + +So, the solutions look like +this, if you start above, + +and if you start below, +they decrease. + +And, of course, +they can't get lower than zero + +because these are salmon. +What is the significance of + +(h)m? +(h)m is the maximum rate of + +harvesting. +It's an extremely important + +number for this industry. +If the maximum time rate at + +which you can pull the salmon +daily out of the water, + +and can them without what +happening? + +Without the salmon going to +zero. + +As long as you start above, +and don't harvest it more than + +this rate, it will be following +these curves. + +You will be following these +curves, and you will still have + +salmon. +If you harvest just a little + +bit more, you will be on this +curve that has no critical + +points, and the salmon in the +tank will decrease to zero. \ No newline at end of file diff --git a/tkU8_LJGCvE.txt b/tkU8_LJGCvE.txt new file mode 100644 index 0000000000000000000000000000000000000000..1f3da50c76c5ef435a73cbf5df0daba1dc91de7c --- /dev/null +++ b/tkU8_LJGCvE.txt @@ -0,0 +1,203 @@ +align:start position:0% + +I mean, I was really happy with how the + + align:start position:0% +I mean, I was really happy with how the + + + align:start position:0% +I mean, I was really happy with how the +class came out. Um, even though I was + + align:start position:0% +class came out. Um, even though I was + + + align:start position:0% +class came out. Um, even though I was +learning the material as I went, uh, + + align:start position:0% +learning the material as I went, uh, + + + align:start position:0% +learning the material as I went, uh, +thing things came together pretty well. + + align:start position:0% +thing things came together pretty well. + + + align:start position:0% +thing things came together pretty well. +Uh, there are a couple of the topics + + align:start position:0% +Uh, there are a couple of the topics + + + align:start position:0% +Uh, there are a couple of the topics +where because I was just learning as I + + align:start position:0% +where because I was just learning as I + + + align:start position:0% +where because I was just learning as I +was teaching it. I might have selected + + align:start position:0% +was teaching it. I might have selected + + + align:start position:0% +was teaching it. I might have selected +the topics a little differently. Um uh + + align:start position:0% +the topics a little differently. Um uh + + + align:start position:0% +the topics a little differently. Um uh +now that I have a bigger sense of the + + align:start position:0% +now that I have a bigger sense of the + + + align:start position:0% +now that I have a bigger sense of the +picture, I would maybe focus in on some + + align:start position:0% +picture, I would maybe focus in on some + + + align:start position:0% +picture, I would maybe focus in on some +of the more interesting subtopics within + + align:start position:0% +of the more interesting subtopics within + + + align:start position:0% +of the more interesting subtopics within +approximation algorithms was one where + + align:start position:0% +approximation algorithms was one where + + + align:start position:0% +approximation algorithms was one where +it's it's such a huge field, it was hard + + align:start position:0% +it's it's such a huge field, it was hard + + + align:start position:0% +it's it's such a huge field, it was hard +for me to learn all of it and then pick + + align:start position:0% +for me to learn all of it and then pick + + + align:start position:0% +for me to learn all of it and then pick +out the best examples. So I learned a + + align:start position:0% +out the best examples. So I learned a + + + align:start position:0% +out the best examples. So I learned a +big part of it and then picked out some + + align:start position:0% +big part of it and then picked out some + + + align:start position:0% +big part of it and then picked out some +examples. But I would + + align:start position:0% +examples. But I would + + + align:start position:0% +examples. But I would +probably now that I have more experience + + align:start position:0% +probably now that I have more experience + + + align:start position:0% +probably now that I have more experience +with it, I would I would do it a little + + align:start position:0% +with it, I would I would do it a little + + + align:start position:0% +with it, I would I would do it a little +differently. Um and of course there are + + align:start position:0% +differently. Um and of course there are + + + align:start position:0% +differently. Um and of course there are +more topics that I didn't get to. So, + + align:start position:0% +more topics that I didn't get to. So, + + + align:start position:0% +more topics that I didn't get to. So, +next time I teach the class, I'd + + align:start position:0% +next time I teach the class, I'd + + + align:start position:0% +next time I teach the class, I'd +probably add in a few more uh additional + + align:start position:0% +probably add in a few more uh additional + + + align:start position:0% +probably add in a few more uh additional +topics and kick out a few others which + + align:start position:0% +topics and kick out a few others which + + + align:start position:0% +topics and kick out a few others which +are still available in video form. So, + + align:start position:0% +are still available in video form. So, + + + align:start position:0% +are still available in video form. So, +they're they're not gone. \ No newline at end of file diff --git a/tuRYbBvOMRo.txt b/tuRYbBvOMRo.txt new file mode 100644 index 0000000000000000000000000000000000000000..9bb8acd4a7a7935e32fd6ff32ae707112ef1e011 --- /dev/null +++ b/tuRYbBvOMRo.txt @@ -0,0 +1,2386 @@ +ANNOUNCER: Open content is +provided under a creative + +commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation, or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu . + +PROFESSOR JOHN GUTTAG: OK. + +I finished up last time +talking about lists. + +And I pointed out that lists are +mutable, showed you some + +examples of mutation. + +We can look at it here; we +looked at append, which added + +things to lists, we looked at +delete, deleting things from a + +list. You can also assign to a +list, or to an element of a + +list. So ivy sub 1, for example, +could be assigned + +minus 15, and that will actually +mutate the list. + +So heretofore, when we wrote +assignment, what we always + +meant, was changing the binding +of a variable to a + +different object. + +Here, we are overloading the +notation to say, no, no, ivys + +is still bound to the same +object, but an element of ivys + +is bound to a different +object. + +If you think about it, that +makes sense, because when we + +have a list, what a list is, +is a sequence of objects. + +And what this says is, is the +object named by the expression + +ivys sub 1, is now bound to the +object, if you will, named + +by the constant minus 15. + +So we can watch this run here. + +Idle can-- that's exciting. + +I hadn't expected that answer. + +All right, your question. + +STUDENT: [INAUDIBLE] four +elements to ivys, and you tell + +it to change the fifth element +of ivys to negative 15, will + +it add it or [INAUDIBLE] + +PROFESSOR JOHN GUTTAG: Well, +I'll tell you how ol-- let's + +answer that the easy way. + +We'll start up a shell +and we'll try it. + +All right, we'll just get out +of what we were doing here. + +And so, we now have some things, +so we, for example, + +have ivys, I can print ivys +, and it's only got three + +elements but your question +probably is just as good for + +adding the fourth as adding +the fifth, so what would + +happen if we say ivys sub 3-- +because that of course is the + +fourth element, right? + +Let's find out. + +OK. + +Because what that does is, it's +changing the binding of + +the name ivys, in this +case, sub 1. + +What it looked at here, with the +name ivys sub 3, and said + +that name doesn't-- isn't +bound, right? + +That isn't there. + +So it couldn't do it, so instead +that's what append is + +for, is to stick things on to +the end of the list. But a + +very good question. + +So we can see what we did here, +and, but of course I can + +now, if I choose, say something +like, ivys sub 1 is + +assigned minus 15, and now if +I print ivys, there it is. + +And again, this points out +something I wanted to me-- + +I mentioned last time, list can +be heterogeneous, in the + +sense that the elements can be +multiple different types. + +As you see here, some of the +elements are strings and some + +of the elements are integers. + +Let's look at another example. + +Let's suppose, we'll start +with the list, + +I'll call it l 1. + +This, by the way, is a really +bad thing I just did. + +What was-- what's really bad +about calling a list l 1? + +STUDENT: [INAUDIBLE] + +PROFESSOR JOHN GUTTAG: Is it l +1, or is it 11, or is it l l? + +It's a bad habit to get into +when you write programs, so I + +never use lowercase L except +when I'm spelling the word + +where it's obvious, because +otherwise I get all sorts of + +crazy things going on. + +All right, so let's make +it the list 123. + +All right? + +Now, I'll say L 2 equals L 1. + +Now I'll print L 2. + +Kind of what you'd guess, but +here's the interesting + +question: if I say L 1 is +assigned 0, L 1 sub 0 is + +assigned 4, I'll print L 1. + +That's what you expect, but +what's going to happen + +if I print L 2? + +423 as well, and that's because +what happened is I had + +this model, which we looked at +last time, where I had the + +list L 1, which was bound to +an object, and then the + +assignment L 2 gets L 1, bound +the name L 2 to the same + +object, so when I mutated this +object, which I reached + +through the name L 1 to make +that 4, since this name was + +bound to the same object, when +I print it, I got 423. + +So that's the key thing to-- +to realize; that what the + +assignment did was +have two separate + +paths to the same object. + +So I could get to that object +either through this path or + +through that path, it didn't +matter which path I use to + +modify it, I would see it when +I looked at the other. + +Yes. + +STUDENT: [INAUDIBLE] + +PROFESSOR JOHN GUTTAG: So the +question, if I said a is + +assigned 2, b is assigned a, +and then a is assigned 3. + +Is that your question? + +So the question is, a is +assigned 1, b is assigned a, a + +is assigned 2, and then if +I print b, I'll get 1. + +Because these are not mutable, +this is going to be assigned + +to an object in the store, so +we'll draw the picture over + +here, that we had initially a +is bound to an object with 1 + +in it, and then b got bound to +the same object, but then when + +I did the assignment, what that +did was it broke this + +connection, and now had a +assigned to a different + +object, with the number, +in this case, 2 in it. + +Whereas the list assignment you +see here did not rebind + +the object l 1, it +changed this. + +OK? + +Now formally I could have had +this pointing off to another + +object containing 4, but that +just seemed excessive, right? + +But you see the difference. + +Great question, and a very +important thing to understand, + +and that's why I'm belaboring +this point, since this is + +where people tend to get pretty +confused, and this is + +why mutation is very important +to understand. + +Yeah. + +STUDENT: [UNINTELLIGIBLE] + +PROFESSOR JOHN GUTTAG: +I'm just assuming + +it'll be a great question. + +STUDENT: [INAUDIBLE] + +PROFESSOR JOHN GUTTAG: +Exactly. + +So if-- very good question-- so, +for example, we can just + +do it here. + +The question was, suppose I now +type L 1 equals the empty + +list. I can print L 1, and I can +print L 2, because again, + +that's analogous to this +example, where I just swung + +the binding of the identifier. + +So this is important, it's a +little bit subtle, but if you + +don't really understand this +deeply, you'll find yourself + +getting confused a lot. + +All right? + +OK. + +Let me move on, and I want to +talk about one more type. + +By the way, if you look at the +handout from last time, you'll + +see that there's some other +examples of mutation, + +including a function +that does mutation. + +It's kind of interesting, but I +don't think we need-- think + +we've probably done +enough here that I + +hope it now make sense. + +That one type I want to talk +about still is dictionaries. + +Like lists, dictionaries are +mutable, like lists, they can + +be heterogeneous, but unlike +lists, they're not ordered. + +The elements in them don't +have an order, and + +furthermore, we have generalized +the indexing. + +So lists and strings, we can +only get at elements by + +numbers, by integers, really. + +Here what we use is, think +of every element of the + +dictionary as a key value pair, +where the keys are used + +as the indices. + +So we can have an example, +let's look at it. + +So, if you look at the function +show dics here, + +you'll see I've declared a +variable called e to f, ah, + +think of that as English to +French, and I've defined a + +dictionary to do translations. + +And so, we see that the string +one corresponds the-- the key + +one corresponds to the value un +the key soccer corresponds + +to the French word football, +et cetera. + +It's kind of bizarre, but the +French call soccer football. + +And then I can index in it. + +So if I print e to f of soccer, +it will print the + +string football. + +So you can imagine that this is +a very powerful mechanism. + +So let's look what happens +when I run-- + +start to run this. + +All right. + +So, it says not defined-- and +why did it say not defined, + +there's an interesting +question. + +Let's just make sure we get this +right, and we start the + +show up again-- + +All right, so, I run +it, and sure + +enough, it shows football. + +What happens if I +go e to f of 0? + +I get a key error. + +Because, remember, these +things are not ordered. + +There is no 0th element. + +0 is not a key of this +particular object. + +Now I could have made 0 a key, +keys don't have to be strings, + +but as it happened, I didn't. + +So let's comment that out, so +we don't get stuck again. + +Where we were before, I've +printed it here, you might be + +a little surprised +of the order. + +Why is soccer first? + +Because the order of this +doesn't matter. + +That's why it's using +set braces, so + +don't worry about that. + +The next thing I'm doing is-- +so that's that, and then-- + +I'm now going to create another +one, n to s, for + +numbers to strings, where my +keys are numbers, in this case + +the number 1 corresponds +to the word one, and + +interestingly enough, I'm also +going to have the word one + +corresponding to the number 1. + +I can use anything I want for +keys, I can use anything I + +want for values. + +And now if we look at this, +we see, I can get this. + +All right. + +So these are extremely +valuable. + +I can do lots of things with +these, and you'll see that as + +we get to future assignments, +we'll make heavy use of + +dictionaries. + +Yeah. + +Question. + +STUDENT: [INAUDIBLE] + +PROFESSOR JOHN GUTTAG: You can, +but you don't know what + +order you'll get them in. + +What you can do is you can +iterate keys, which gives you + +the keys in the dictionary, and +then you can choose them, + +but there's no guarantee +in the order in + +which you get keys. + +Now you might wonder, why +do we have dictionaries? + +It would be pretty easy to +implement them with lists, + +because you could have a list +where each element of the list + +was a key value pair, and if +I wanted to find the value + +corresponding to a key, I could +say for e in the list, + +if the first element of e is the +key, then I get the value, + +otherwise I look at the next +element in the list. + +So adding dictionaries, as +Professor Grimson said with so + +many other things, doesn't +give you any more + +computational power. + +It gives you a lot of expressive +convenience, you + +can write the programs much +more cleanly, but most + +importantly, it's fast. + +Because if you did what I +suggested with the list, the + +time to look up the key would be +linear in the length of the + +list. You'd have to look +at each element until + +you found the key. + +Dictionaries are implemented +using a magic technique called + +hashing, which we'll look at a +little bit later in the term, + +which allows us to retrieve +keys in constant time. + +So it doesn't matter how big +the dictionary is, you can + +instantaneously retrieve the +value associated with the key. + +Extremely powerful. + +Not in the next problems set but +in the problem set after + +that, we'll be exploiting that +facility of dictionaries. + +All right. + +Any questions about this? + +If not, I will turn the podium +over to Professor Grimson. + +PROFESSOR ERIC GRIMSON: +I've stolen it. + +This is like tag team +wrestling, right? + +Professor Guttag has you +on the ropes, I get + +to finish you off. + +Try this again. + +OK. + +We wanted to finish up that +section, we're now going to + +start on a new section, and I +want to try and do one and a + +half things in the +remaining time. + +I'm going to introduce one topic +that we're going to deal + +with fairly quickly, and then +we tackle the second topic, + +it's going to start today, and +we're going to carry on. + +So let me tell the two +things I want to do. + +I want to talk a little bit +about how you use the things + +we've been building in terms +of functions to help you + +structure and organize +your code. + +It's a valuable tool that you +want to have as a programmer. + +And then we're going to turn to +the question of efficiency. + +How do we measure efficiency +of algorithms? + +Which is going to be a really +important thing that we want + +to deal with, and we'll start +it today, it's undoubtedly + +going to take us a couple more +lectures to finish it off. + +Right, so how do you +use the idea of + +functions to organize code? + +We've been doing it implicitly, +ever since we + +introduced functions. + +I want to make it a little more +explicit, and I want to + +show you a tool for +doing that. + +And I think the easy way +to do is-- is to + +do it with an example. + +So let's take a really +simple example. + +I want to compute the +length of the + +hypotenuse of a right triangle. + +And yeah, I know you know how +to do it, but let's think + +about what might happen if +I wanted to do that. + +And in particular, if I think +about that problem-- actually + +I want to do this-- if I think +about that problem, I'm going + +to write a little piece +of pseudo code. + +Just to think about how I would +break that problem up. + +Pseudo code. + +Now, you're all linguistic +majors, pseudo means false, + +this sounds like code that ain't +going to run, and that's + +not the intent of the term. + +When I say pseudo code, what I +mean is, I'm going to write a + +description of the steps, +but not in a particular + +programming language. + +I'm going to simply write +a description of what + +do I want to do. + +So if I were to solve this +problem, here's the way I + +would do it. + +I would say, first thing I want +to do, is I want to input + +a value for the base +as a float. + +Need to get the base in. + +Second thing I want to do, I +need to get the height, so I'm + +going to input a value for the +height, also as a float, a + +floating point. + +OK. + +I get the two values in, what +do I need to do, well, you + +sort of know that, right? + +I want to then do, I need to +find the square root-- b + +squared plus h squared, right? + +The base plus the height, that's +the thing I want for + +the hypotenuse-- and I'm going +to save that as a float in + +hyp, for hypotenuse. + +And then finally I need to print +something out, using the + +value in hyp. + +OK. + +Whoop-dee-doo, right? + +Come on. + +We know how to do this. + +But notice what I did. + +First of all, I've used the +notion of modularity. + +I've listed a sequence of +modules, the things that I + +want to do. + +Second thing to notice, is that +little piece of pseudo + +code is telling me things +about values. + +I need to have a float. + +I need to have another float +here, it's giving me some + +information. + +Third thing to notice is, +there's a flow of control. + +The order which these things +are going to happen. + +And the fourth thing to notice +is, I've used abstraction. + +I've said nothing about how I'm +going to make square root. + +I'm using it as an abstraction, +saying I'm going + +to have square root from +somewhere, maybe I'll build it + +myself, maybe somebody gives it +to me as part of a library, + +so I'm burying the details +inside of it. + +I know this is a simple example, +but when you mature + +as a programmer, one of the +first things you should do + +when you sit down to tackle +some problem is write + +something like this +pseudo code. + +I know Professor Guttag +does it all the time. + +I know, for a lot of +you, it's like, OK, + +I got a heavy problem. + +Let's see, def Foobar open +paren, a bunch of parameters. + +Wrong way to start. + +Start by thinking about what +are the sequences. + +This also, by the way, in some +sense, gives me the beginnings + +of my comments for what +the structure of my + +code is going to be. + +OK. + +If we do that, if you look at +the handout then, I can now + +start implementing this. + +I wanted to show you that, so, +first thing I'm going to do is + +say, all right, I know I'm going +to need square root in + +here, so I'm going to, +in fact, import math. + +That's a little different from +other import statements. + +This says I'm going to get the +entire math library and bring + +it in so I can use it. + +And then, what's the first +thing I wanted to do? + +I need to get a value +for base as a float. + +Well OK, and that sounds like +I'm going to need to do input + +of something, you can see that +statement there, it's-- got + +the wrong glasses on +but right there-- + +I'm going to do an input with +a little message, and I'm + +going to store it in base. + +But here's where I'm going to +practice a little bit of + +defensive programming. + +I can't rely on Professor Guttag +if I give this-- if + +this code to him, I can't rely +on him to type in a float. + +Actually I can, because he's a +smart guy, but in general, I + +can't rely on the user-- + +PROFESSOR JOHN GUTTAG: I +wouldn't do it right + +to see if you did. + +PROFESSOR ERIC GRIMSON: +Actually, + +he's right, you know. + +He would not do it, just to +see if I'm doing it right. + +I can't rely on the user. + +I want to make sure I +get a float in it, + +so how do I do that? + +Well, here's one nice +little trick. + +First of all, having read in +that value, I can check to + +see, is it of the right type? + +Now, this is not the nicest way +to do it but it'll work. + +I can look at the type of the +value of base and compare it + +to the type of an actual float +and see, are they the same? + +Is this a real or a float? + +If it is, I'm done. + +How do I go back if it isn't? + +Well, I'm going to create +a little infinite loop. + +Not normally a good idea. + +I set up a variable here, +called input OK. + +Initially it's false, because +I have no input. + +And then I run a loop in which +I read something in, I check + +to see if it's the right type, +if it is, I change that + +variable to say it's now the +correct type, which means the + +next time through the loop, I'm +going to say I'm all set + +and I'm going to bounce out. + +But if it is not, it's going +to print out a message here + +saying, you screwed up, somewhat +politely, and it's + +going to go back around. + +So it'll just cycle until +I get something + +of the right type. + +Nice way of doing it. + +Right, what's the second +thing I do? + +Well, I get the same sort of +thing to read in the height, + +once I have that I'm going to +take base squared plus height + +squared, and there's a form +that we've just seen once + +before, and it's going to repeat +it, that is math.SQRT + +and it says the following: it +says, take from the math + +library the function +called sqrt. + +OK. + +We're going to come back to this +when we get to objects, + +it's basically picking up that +object and it's applying that, + +putting that value into hype, +and then just printing + +something out. + +And again, if I just run this, +just to show that it's going + +to do the right thing, it says +enter base, I'm obnoxious, it + +says oops, wasn't a float, so +we'll be nice about it, and I + +enter a height, and it prints +out what I expected. + +I just concatenated those +strings together, by the way, + +at the end. + +All right. + +Notice what I did. + +OK. + +I went from this description, +it gives me [UNINTELLIGIBLE] + +some information. + +I need to have a particular +type. + +I made sure I had the +particular type. + +I've used some abstraction to +suppress some details here. + +Now if you look at that list, +there is actually something I + +didn't seem to check, which is, +I said I wanted a float + +stored in hyp. + +How do I know I've got +a float in hyp? + +Well I'm relying on the +contract, if you like, that + +the manufacturer of square root +put together, which is, + +if I know I'm giving it two +floats, which I do because I + +make sure they're floats, the +contract, if you like, of + +square root says I'll give +you back a float. + +So I can guarantee I've got +something of the right type. + +OK. + +I know this is boring +as whatever. + +But there's an important +point here. + +Having now used this pseudo code +to line things up, I can + +start putting some additional +structure on this. + +And in particular, I'm sure +you're looking at this going-- + +will look at it if we look +at the right piece-- + +going, wait a minute. + +This chunk of code and this +chunk of code, they're really + +doing the same thing. + +And this is something +I want to use. + +If I look at those two pieces +of computation, I can see a + +pattern there. + +It's an obvious pattern +of what I'm doing. + +And in particular, I can then +ask the following question, + +which is, what's different +between those + +two pieces of code? + +And I suggest two +things, right? + +One is, what's the thing +I print out when + +I ask for the input? + +The second thing is, what do I +print out if I actually don't + +get the right input in? + +And so the only two differences +are, right there, + +and there versus +here and here. + +So this is a good place to +think about, OK, let me + +capture that. + +Let me write a function, in fact +the literal thing I would + +do is to say, identify the +things that change, give each + +of them a variable name because +I want to refer to + +them, and then write a function +that captures the + +rest of that computation +just with those + +variable names inside. + +And in fact, if you look down-- +and I'm just going to + +highlight this portion, I'm not +going to run it-- but if + +you look down here, that's +exactly what that does. + +I happen to have it commented +out, right? + +What does it do? + +It has height, it says, I've got +two names of things: the + +request message and +the error message. + +The body of that function +looks exactly like the + +computation up above, except +I'm simply using those in + +place of the specific message +I had before. + +And then the only other +difference is obviously, it's + +a function I need to +return a value. + +So when I'm done, I'm going to +give the value back out. + +All right? + +And that then let's me get +to, basically, this code. + +Having done that, I simply call +base with get float, I + +call height with get float, and +do the rest of the work. + +All right. + +What's the point +of doing this? + +Well, notice again. + +What have I done? + +I've captured a module +inside of a function. + +And even though it's a simple +little thing here, there's + +some a couple of really nice +advantages to this. + +All right? + +First one is there's +less code to read. + +It's easier to debug. + +I don't have as much +to deal with. + +But the more important thing +is, I've now separated out + +implementation from +functionality, or + +implementation from use. + +What does that mean? + +It means anybody using that +little function get float + +doesn't have to worry about +what's inside of it. + +So for example, I decide I want +to change the message I + +print out, I don't have to +change the function, I just + +pass in a different parameter. + +Well if I-- you know, with +[UNINTELLIGIBLE PHRASE sorry, + +let me say it differently. + +I don't need to worry about +how checking is done, it's + +handled inside of +that function. + +If I decide there's a better +way to get input, and there + +is, then I can make it to change +what I don't have to + +change the code that +uses the input. + +So, if you like, I've built a +separation between the user + +and the implementer. + +And that's exactly one of the +reasons why I want to have the + +functions, because I've +separated those out. + +Another way of saying it is, +anything that uses get float + +doesn't care what the details +are inside or shouldn't, and + +if I change that definition, I +don't have to change anything + +elsewhere in my code, whereas if +I just have the raw code in + +there, I have to go +off and do it. + +Right, so the things we want +you to take away from this + +are, get into the habit of using +pseudo code when you sit + +down to start a problem, write +out what are the steps. + +I will tell you that a good +programmer, at least in my + +mind, may actually go back and +modify the pseudo code as they + +realize they're missing things, +but it's easier to do + +that when you're looking at a +simple set of steps, than when + +you're in the middle +of a pile of code. + +And get into the habit of using +it to help you define + +what is the flow of control. + +What are the basic modules, what +information needs to be + +passed between those +modules in order to + +make the code work. + +OK. + +That was the short topic. + +I will come back to this some +more and you're going to get + +lots of practice with this. + +What I want to do is +to start talking + +about a different topic. + +Which is efficiency. + +And this is going to sound +like a weird topic, we're + +going to see why it's of +value in a second. + +I want to talk about efficiency, +and we're going + +to, or at least I'm going to, at +times also refer to this as + +orders of growth, for reasons +that you'll see over the next + +few minutes. + +Now, efficiency is obviously +an important consideration + +when you're designing code, +although I have to admit, at + +least for me, I usually want +to at least start initially + +with code that works, and then +worry about how I might go + +back and come up with more +efficient implementation. + +I like to have something I +can rely on, but it is an + +important issue. + +And our goal over the next +couple of lectures, is + +basically to give you +a sense of this. + +So we're not going to turn +you into an expert on + +computational efficiency. + +That's, there are whole courses +on that, there's some + +great courses here on that, +it takes some mathematical + +sophistication, we're going to +push that off a little bit. + +But what we-- what we do want +to do, is to give you some + +intuition about how to +approach questions of + +efficiency. + +We want you to have a sense of +why some programs complete + +almost before you're +done typing it. + +Some programs run overnight. + +Some programs won't stop +until I'm old and gray. + +Some programs won't stop until +you're old and gray. + +And these are really different +efficiencies, and we want to + +give you a sense of how do you +reason about those different + +kinds of programs. + +And part of it is we want you +to learn how to have a + +catalog, if you like, of +different classes of + +algorithms, so that when you get +a problem, you try and map + +it into an appropriate class, +and use the leverage, if you + +like, of that class + +of algorithms. Now. + +It's a quick sidebar, I've got +to say, I'm sure talking about + +efficiency to folks like you +probably seems really strange. + +I mean, you grew up in an age +when computers were blazingly + +fast, and have tons of memory, +so why in the world do you + +care about efficiency? + +Some of us were not so lucky. + +So I'll admit, my first computer +I program was a PDP6, + +only Professor Guttag even knows +what PDP stands for, it + +was made by Digital Equipment +Company, which does not exist + +anymore, is now long gone. + +It had, I know, this is +old guy stories, but + +it had 160k of memory. + +Yeah. + +160k. + +160 kilobits of memory. + +I mean, your flash cards have +more than that, right? + +It had a processor speed +of one megahertz. + +It did a million operations +per second. + +So let's think about it. + +This sucker, what's +it got in there? + +That Air Mac, it's, see, it's +got, its go-- my Air Mac, I + +don't know about John's, his is +probably better, mine has + +1.8 gigahertz speed. + +That's 1800 times faster. + +But the real one that blows me +away is, it has 2 gig of + +memory inside of it. + +That's 12 thousand times +more memory. + +Oh, and by the way? + +The PDP6, it was in a rack +about this tall. + +From the floor, not +from the table. + +All right, so you didn't grow +up in the late 1800s like I + +did, you don't have to +worry about this + +sort of stuff, right? + +But a point I'm trying to make +is, it sounds like anymore + +computers have gotten so +blazingly fast, why should you + +worry about it? + +Let me give you one other +anecdote that I can't resist. + +This is the kind of thing you +can use at cocktail parties to + +impress your friends +from Harvard. + +OK. + +Imagine I have a little lamp, a +little goose-- one of those + +little gooseneck lamps, I'd put +it on the table here, I'd + +put the height about a f-- about +a foot off the table. + +And if I was really good, I +could hit, or time it so that + +when I hurt-- yeah, try again. + +When I turn this on switch on +in the lamp, at exactly the + +same time, I'm going to hit a +key on my computer and start + +it running. + +OK. + +In the length of time it takes +for the light to get from that + +bulb to the table, this +machine processes two + +operations. + +Oh come on, that's amazing. + +Two operations. + +You know, you can do the +simple numbers, right? + +[UNINTELLIGIBLE PHRASE] + +Light travels basically a +foot in a nanosecond. + +Simple rule of thumb. + +Now, the nanosecond is what, +10 to the minus 9 seconds. + +This thing does 2 gig +worth of operations. + +A gig is 10 to the 9, so it +does two operations in the + +length of time it takes light +to get from one foot off the + +table down to the table. + +That's amazing. + +So why in the world do you +care about efficiency? + +Well the problem is that the +problems grow faster than the + +computers speed up. + +I'll give you two examples. + +I happen to work in +medical imaging. + +Actually, so does Professor +Guttag. + +In my in my area of research, +it's common for us to want to + +process about 100 images a +second in order to get real + +time display. + +Each image has about a million +elements in it. + +I've got to process about a half +a gig of data a second in + +order to get anything +out of it. + +Second example. + +Maybe one that'll hit a little +more home to you. + +I'm sure you all use Google, I'm +sure it's a verb in your + +vocabulary, right? + +Now, Google processes-- +ten million? + +Ten billion pages? + +John? + +I think ten billion was the +last number I heard. + +Does that sound about right? + +PROFESSOR JOHN GUTTAG: +I think it might + +actually be more by now. + +PROFESSOR ERIC GRIMSON: +Maybe more by now. + +But let's, for the sake of +argument, ten billion pages. + +Imagine you want to search +through Google to find a + +particular page. + +You want to do it in a second. + +And you're going to just do it +the brute force way, assuming + +you could even reach all of +those pages in that time. + +Well, if you're going to do +that, you've got to be able to + +find what you're looking for +in a page in two steps. + +Where a step is a comparison +or an arithmetic operation. + +Ain't going to happen, right? + +You just can't do it. + +So again, part of the point here +is that things grow-- or + +to rephrase it, interesting +things grow at + +an incredible rate. + +And as a consequence, brute +force methods are typically + +not going to work. + +OK. + +So that then leads to the +question about what should we + +do about this? + +And probably the obvious thing +you'll think about is, we'll + +come up with a clever +algorithm. + +And I want to disabuse +you of that notion. + +It's a great idea if +you can do it, + +The guy who-- + +I think I'm going to say this +right, John, right? + +Sanjay? + +Ghemawat?-- with a guy who was +a graduate of our department, + +who is the heart and soul behind +Google's really fast + +search, is an incredibly smart +guy, and he did come up with a + +really clever algorithm about +how you structure that search, + +in order to make it happen. + +And he probably made a lot +of money along the way. + +So if you have a great idea, +you know, talk to a good + +patent attorney and get +it locked away. + +But in general, it's hard +to come up with the + +really clever algorithm. + +What you're much better at doing +is saying how do I take + +the problem I've got and map it +into a class of algorithms + +about which I know and use the +efficiencies of those to try + +and figure out how +to make it work. + +So what we want to do, is, I +guess another way of saying it + +is, efficiency is really about +choice of algorithm. + +And we want to help you learn +how to map a problem into a + +class of algorithms of +some efficiency. + +That's our goal. + +OK. + +So to do this, we need a little +more abstract way of + +talking about efficiency, and +so, the question is, how do we + +think about efficiency? + +Typically there's two things +we want to measure. + +Space and time. + +Sounds like an astrophysics +course, right? + +Now, space usually we-- +ach, try it again. + +When we talk about space, what +we usually refer to is, how + +much computer memory does it +take to complete a computation + +of a particular size? + +So let me write that down, it's +how much memory do I need + +to complete a computation. + +And by that, I mean, not how +much memory do I need to store + +the size of the input, it's +really how much internal + +memory do I use up as I go +through the computation? + +I've got some internal variables +I have to store, + +what kinds of things do I +have to keep track of? + +You're going to see the +arguments about space if you + +take some of the courses that +follow on, and again, some + +nice courses about that. + +For this course, we're +not going to worry + +about space that much. + +What we're really going +to focus on is time. + +OK. + +So we're going to focus here. + +And the obvious question I +could start with is, and + +suppose I ask you, how long does +the algorithm implemented + +by this program take to run? + +How might I answer +that question? + +Any thoughts? + +Yeah. + +STUDENT: [INAUDIBLE] + +PROFESSOR ERIC GRIMSON: +Ah, you're jumping + +ahead of me, great. + +The answer was, find a +mathematical expression + +depending on the number +of inputs. + +It was exactly where +I want to go. + +Thank you. + +I was hoping for a simpler +answer, which is, just run it. + +Which is, yeah I know, +seems like a dumb + +thing to say, right? + +One of the things you could +imagine is just try it on and + +input, see how long it takes. + +You're all cleverer than that, +but I want to point out why + +that's not a great idea. + +First of all, that depends on +which input I've picked. + +All right? + +Obviously the algorithm is +likely to depend on the size + +of the input, so this +is not a great idea. + +Second one is, it depends on +which machine I'm running on. + +If I'm using a PDP6, it's going +to take a whole lot + +longer than if I'm +using an Air Mac. + +All right? + +Third one is, it may depend +on which version + +of Python I'm running. + +Depends on how clever the +implementer of Python was. + +Fourth one is, it may depend on +which programming language + +I'm doing it in. + +So I could do it empirically, +but I don't want to do that + +typically, it's just not a +great way to get at it. + +And so in fact, what we +want is exactly what + +the young lady said. + +I'm going to ask the following +question, which is-- let me + +write it down-- what is the +number of the basic steps + +needed as a function +of the input size? + +That's the question we're going +to try and address. + +If we can do this, this is good, +because first of all, it + +removes any questions about what +machine I'm running on, + +it's talking about +fundamentally, how hard is + +this problem, and the second +thing is, it is going to do it + +specifically in terms +of the input. + +Which is one of the things +that I was worried about. + +OK. + +So to do this, we're going to +have to do a couple of things. + +All right, the first one is, +what do we mean by input size? + +And unfortunately, this depends +on the problem. + +It could be what's the size of +the integer I pass in as an + +argument, if that's what +I'm passing in. + +It could be, how long is the +list, if I'm processing a list + +or a tuple It could +be, how many bits + +are there in something. + +So it-- that is something where +we have to simply be + +clear about specifying what +we're using as input size. + +And we want to characterize it +mathematically as some number, + +or some variable rather, the +length of the list, the size + +of the integer, would be the +thing we'd want to do. + +Second thing we've got +to worry about is, + +what's a basic step? + +All right, if I bury a whole lot +of computation inside of + +something, I can say, wow, this +program, you know, runs + +in one step. + +Unfortunately, that one step +calls the Oracle at Delphi and + +gets an answer back. + +Maybe not quite what you want. + +We're typically going to use +as basic steps the built-in + +primitives that a machine +comes with. + +Or another way of saying it is, +we're going to use as the + +basic steps, those operations +that run in constant time, so + +arithmetic operations. + +Comparisons. + +Memory access, and in fact one +of the things we're going to + +do here, is we're going to +assume a particular model, + +called a random access model, +which basically says, we're + +going to assume that the length +of time it takes me to + +get to any location in +memory is constant. + +It's not true, by the way, of +all programming languages. + +In fact, Professor Guttag +already talked about that, in + +some languages lists take +a time linear with the + +length to get to it. + +So we're to assume we can get +to any piece of data, any + +instruction in constant time, +and the second assumption + +we're going to make is that the +basic primitive steps take + +constant time, same amount +of time to compute. + +Again, not completely true, +but it's a good model, so + +arithmetic operations, +comparisons, things of that + +sort, we're all going to assume +are basically in that + +in that particular model. + +OK. + +Having done that, then, there +are three things that we're + +going to look at. + +As I said, what we want to do +is, we want to count the + +number of basic steps it takes +to compute a computation as a + +function of input size. + +And the question is, what +do we want to count? + +Now, one possibility +is to do best case. + +Over all possible inputs to +this function, what's the + +fastest it runs? + +The fewest, so the minimum, +if you like. + +It's nice, but not particularly +helpful. + +The other obvious one to +do would be worst case. + +Again, over all possible inputs +to this function, + +what's the most number of +steps it takes to do the + +computation? + +And the third possibility, is +to do the expected case. + +The average. + +I'm going to think +of it that way. + +In general, people focus +on worst case. + +For a couple of reasons. + +In some ways, this would be +nicer, do expected cases, it's + +going to tell you on average how +much you expect to take, + +but it tends to be hard to +compute, because to compute + +that, you have to know a +distribution on input. + +How likely are all the inputs, +are they all equally likely, + +or are they going to depend +on other things? + +And that may depend on the +user, so you can't + +kind of get at that. + +We're, as a consequence, going +to focus on worst case. + +This is handy for a +couple of reasons. + +One, it means there +are no surprises. + +All right? + +If you run it, you have a sense +of the upper bound, + +about how much time it's going +to take to do this + +computation, so you're not +going to get surprised by + +something showing up. + +The second one is, a lot of the +time, the worst case is + +the one that happens. + +Professor Guttag used an example +of looking in the + +dictionary for something. + +Now, imagine that dictionary +actually has something that's + +a linear search to go through +it, as opposed to the hashing + +he did, so it's a list, +for example. + +If it's in there, you'll find +it perhaps very quickly. + +If it's not there, you've got +to go through everything to + +say it's not there. + +And so the worst case often +is the one that shows up, + +especially in things +like search. + +So, as a consequence, we're +going to stick with the worst + +case analysis. + +Now, I've got two +minutes left. + +I was going to start showing +you some examples, but I + +think, rather than doing that, +I'm going to stop here, I'm + +going to give you two minutes +back of time, but I want to + +just point out to you that we +are going to have fun next + +week, because I'm going to show +you what in the world + +that has to do with +efficiency. + +So with that, we'll +see you next time. \ No newline at end of file diff --git a/u6s_jy0n6vI.txt b/u6s_jy0n6vI.txt new file mode 100644 index 0000000000000000000000000000000000000000..b9c24461e5e4289cdbafdbaffcedffc21ae24b81 --- /dev/null +++ b/u6s_jy0n6vI.txt @@ -0,0 +1,2009 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Last time, under the +tutelage of Professor Blendi, + +you started to see some +of the consequences, + +the more immediate consequences, +of some of the properties + +we've been discussing +over the last few lectures + +of binary liquid mixtures. + +And in particular he +started showing you + +some of the colligative +properties by which you + +see changes in the vapor +pressure and the boiling point + +and so forth, that arise because +you've got liquids in mixtures + +and this affects their +chemical potentials. + +And today I want +to start by going + +through the fourth colligative +property that's commonly seen, + +what called osmotic pressure. + +And I mentioned this before. + +Today we'll go through a +quantitative calculation + +of its effects. + +And then we'll start in on a +different unit of the course. + +We'll start in on +statistical mechanics. + +So let's continue with the +colligative properties. + +And osmotic pressure plays a +super-important role, certainly + +in all of biology, because of +course inside biological cells + +you have solutions. + +Water is in there, +along with a whole bunch + +of other components. + +And so the chemical +potential of the water + +is strongly affected by +all the other constituents. + +And this has profound +effects on what's + +involved in maintaining an +equilibrium between what + +goes on inside and +outside of the cell. + +And this is the case +in all organisms. + +And it's also +exploited of course + +in all sorts of other contexts. + +So what's happening with +osmotic pressure is, + +you've got some +situation where there's + +a semi-permeable membrane. + +It allows one of +the constituents + +but not others to pass through. + +And typically that's water. + +Although, of course, +it could be anything. + +So, in the lab the way +this typically looks + +is something like this. + +Here's your +semi-permeable membrane. + +Outside, we can +imagine that there's + +pure liquid A. Could be water, +could be something else. + +Inside, you've got +A mixed with B, + +one or more other constituents. + +And then there's some +level of the liquid + +outside the container. + +Of course, A can pass between, +pass through, the membrane. + +And so what ends up +happening is, if you just + +look at the situation, +what you immediately + +notice is that +the liquid in here + +goes up higher than +the liquid around it. + +It's at a higher level. + +It seems counterintuitive +at first. + +And in fact it can +be enormously higher. + +But that's what happens. + +So there's extra height, h, +of liquid inside the container + +relative to what's outside it. + +And what that means is +the pressure inside here + +must be higher, right? + +Of course, the +weight of this liquid + +is pushing down on +what's down here. + +So the pressure +inside here is higher + +than the pressure outside. + +But of course, from +what you know already + +about liquid mixtures, this +should in fact make sense. + +Because what's happening +is that if these things are + +at the same pressure, you know +that the chemical potential + +of A is going to be +lower in the mixture. + +It's always lower in the +mixture than it is in pure A. + +So there's nothing to +stop A from rushing in. + +So A does rush in. + +If the liquid level goes up, it +raises the pressure down here. + +But as the pressure rises, +now the chemical potential + +changes and goes up. + +So eventually, equilibrium +is reestablished. + +Because these aren't +at the same pressure. + +The additional pressure means +the chemical potential of A + +goes up. + +Of course, it goes down by +virtue of being in the mixture. + +And those two things will +eventually reach an equilibrium + +where the chemical +potential of A + +is the same everywhere, +as it has to be. + +So what we'll +calculate now is, OK, + +how much does the +pressure go up. + +When that happens. + +So let's take a look. + +And so of course, there +are all kinds of examples. + +In a typical one, +A would be water. + +And B would be one +or more sugars. + +All sorts of other +potential constituents also. + +OK, so let's just +consider the pressure + +at two places that +are the same level. + +The same height. + +We'll label this +one point alpha. + +Let's put some color in here. + +We'll have points +alpha and beta. + +And we'll make this distance l. + +So now let's just +first calculate + +what the pressure +is at both points. + +It's going to be +higher here, because of + +this additional liquid on top. + +So, if we look at +point alpha, well, + +let's start at point +beta, actually. + +That's the simpler +one since it doesn't + +have the additional liquid. + +And first of all, there's +just atmospheric pressure. + +So there's an external pressure. + +Certainly, typically, it would +just be atmosphere pressure. + +It's pushing down here. + +It's also there. + +So that has to factor in. + +So there's our +external pressure. + +And then there is the +product of this height + +times the density +of the solution. + +Times the gravitational +force constant. + +And I'll work through +that momentarily + +so you see that that +indeed is the pressure. + +That's exerted by +the amount of liquid + +that's up above this level. + +But before I do that, let's put +the pressure at point alpha. + +So p alpha. + +And that's p external +plus l rho g. + +But now, there's this additional +height on top of that. + +So there's also h rho g. + +There's an extra pressure. + +We'll label this pi. + +So we can write p alpha is +equals to p beta plus h rho g. + +Which we'll say is +equal to p beta plus pi. + +Now, just to make sure +we're all on the same page + +about these quantities +being the pressure that's + +exerted by the liquid, +let's just look at that. + +So l times rho times g. + +It should be a pressure which +is a force per unit area. + +And in particular, this is going +to be a weight per unit area. + +Remember the weight is the +force that a mass exerts. + +And it exerts it because of +the gravitational constant. + +So what happens? + +Well, this is just a length. + +Rho is a density, right? + +So it's mass per unit volume. + +And of course, g is just our +gravitational force constant. + +So it'll be in units of +meters per second squared. + +So what's going to happen? + +If we multiply l +times rho together, + +this is units of length. + +This is units of volume. + +What we're going to get +then is mass per unit area. + +And that's what +it is, of course. + +It's distributing across +the area of that surface + +where point alpha is. + +So these two +together, l times rho, + +give us mass per unit area. + +So it could be in +units of kilograms. + +Per unit area, per +meters squared. + +And now we're going to multiply +that by the gravitational force + +constant. + +So now we're going +to have all together + +kilograms per meter +second squared. + +In other words, it's +force per unit area. + +And so that's what we have. + +And now, of course, we have +the additional component. + +Due to the height here. + +Now, what do we know about +the chemical potential + +in both parts? + +The chemical potential +has to be equal + +outside and inside +the container. + +So mu A at point +alpha is just mu A + +of the liquid at pressure p +plus pi and temperature T. + +And that has to be equal +to mu A at point beta. + +But point beta is just +in the pure liquid. + +So that's just mu A +star of the liquid + +at pressure p and +temperature T. So here's + +the chemical potential +at point beta. + +Here it is at point alpha. + +Those two have to be +equal to each other. + +And now we're just going +to use Raoult's law. + +And what does that tell us? + +We have RT log of xA plus mu A +star of the liquid at pressure + +p plus pi and T So there +is our chemical potential + +inside the container. + +And that's equal to mu A star of +the pure liquid at point beta. + +And so we can just +rewrite this as RT log xA. + +Plus mu A star liquid +at pressure p plus pi + +of T minus mu A star at +pressure p is equal to zero. + +OK., now we need the +pressure dependence + +of the chemical potential. + +But we certainly have +an expression for that. + +So we know that dG +is S dT plus V dp. + +The temperature is the +same on both sides. + +But we need to worry about what +happens at different pressures. + +So at constant T, dG is V dp. + +So now if we look at the +chemical potential, which + +is just the Gibbs +free energy per mole, + +then d mu A star is +VA star molar dp. + +In other words, the difference +in the chemical potential + +is, this changes as a +function of pressure. + +Is going to be given by +the molar volume of a + +under these conditions +in the pure liquid dp. + +It's just the potential, +the pressure dependence + +of G. It's not the kind of +topic I would have thought + +would drive away +a lot of people. + +But, you never know. + +OK. + +For the rest of you who are +willing to bear with me, + +let's continue. + +So now let's just integrate. + +We need to know the change in mu +A at a finite jump in pressure + +from inside to +outside the container. + +So we're just +going to integrate. + +So if I want mu A +star at pressure p + +plus pi minus mu A +star at pressure p, + +then I just have to integrate +from p to p plus pi VA bar star + +dp. + +And now I'm going to assume, +and this is certainly + +a safe assumption, that this +quantity this, molar volume, + +isn't going to change. + +In other words, the +molar volume of liquid A + +isn't going to +change significantly, + +going from the pressure out +here to the pressure in here. + +On the grand scale of things +it's a small pressure change. + +We can assume that the +liquid is incompressible + +over that small pressure change. + +Which means that this +is constant, since all + +we have then is simply +VA bar star times pi. + +So then, substituting +back here, so now + +we've calculated +this difference, + +it's a simple result. + +So then we simply have +that RT log xA plus VA bar + +star pi is equal to zero. + +Now, you saw last time, +and I'll work through this + +quickly again, +that the log of xA + +can be written approximately +as minus nB over nA + +if you remember, this +came from writing + +that this is equal to +the log of one minus xB. + +But we're assuming that B is +the minor constituent here. + +So xB is a small number. + +So that this is roughly +equal to minus xB. + +And that's just minus +nB over nA plus nB. + +And since nB is much +smaller than nA, + +this is approximately +equal to minus nB over nA. + +So we're going to make +this substitution. + +Also, this quantity, +this molar volume + +of A over the pure liquid, since +the concentration of B is low, + +we can assume that +this is just the molar + +volume of A in general. + +So, in other words, we +can write VA bar star. + +We can just write it as VA bar. + +That is, we're +not going to worry + +about changes in +the molar volume, + +either as a function of pressure +or a function of concentration + +at the low concentrations +that we're working. + +And then, note that +nA times VA per mole + +is just the total volume. + +Oops, not bar. + +Not the molar quantity. + +This is the molar +quantity multiplied + +by the number of moles. + +So it just gives us VA, the +total volume, occupied by A. + +And using these two results, +then we have that RT times + +negative nB over nA, +that's this result. + +Plus VA over nA times pi is +equal to zero. nA will cancel. + +And finally, since almost +all the volume is due to A, + +again because B is +the minor constituent, + +we can approximate further that +VA is approximately equal to V. + +So finally getting rid of +the nA on the denominators, + +we're left with a +simple expression. + +pi times V is RT nB. + +So we have a very +simple expression + +which is called the +van't Hoff expression, + +and look at how it +resembles the ideal gas law. + +This is the pressure +times the volume equals + +the number of moles times RT. + +Of course, really it's +a change in pressure. + +And this number of +moles is the number + +of moles of a guest +constituent in a solution. + +But it has the same form +that you're familiar with. + +We also, sometimes it's +convenient to substitute, + +since nB over V, that's +just the concentration. + +That's the number of +moles over the volume. + +And in that case, +the expression is + +rewritten as pi is RT times c, +where it's understood that this + +is the concentration +of the solute. + +OK, any questions? + +Let's work through +a numerical problem. + +These things can seem a little +bit, they can seem simple, + +but sometimes when +confronted with a problem, + +sometimes it may seem less +than obvious what to do. + +And also the results can +seem a little bit surprising. + +So I just want to work through +a simple numerical example + +to see how these play out. + +So let's try, let's imagine we +have 10 grams of unknown solid. + +Dissolved in 1000 +grams of water. + +The vapor pressure is +25.195 torr at 27 degrees C. + +And the pure water vapor +pressure is 25.000. + +No, .200 torr at the +same temperature. + +So first, let's just +calculate the molecular weight + +of the solid. + +Now, this you I think, +saw from last time. + +So this is straightforward. + +It's going to come from +the vapor pressure lowering + +not from the osmotic +pressure, which we'll do next. + +So the delta p of H2O is +minus xB times p star of H2O. + +Alright, this is from last time. + +The expression for the +vapor pressure reduction. + +Due to the concentration +of the mole fraction of B. + +And then xB is 0.005 +torr over 25.2 torr. + +Right? + +And that's 1.98 times +10 to the minus 4. + +So that's our mole +fraction of B. + +And then xB is nB +over nA plus nB. + +So, now we have +this, it's 10 grams + +divided by the molecular weight, +which is in grams per mole, + +over 1000 grams of water. + +Divided by 18 grams +per mole plus 10 grams + +divided by the molecular +weight in grams per mole. + +But since the solution +is overwhelmingly water, + +we can get rid of this term +and make the math simple. + +Can you see that? + +I guess barely. + +So this turns out to be about +1.98 time 10 to the minus 4. + +And if we solve for +molecular weight, + +then we wind up with +907 grams per mole. + +So that's using one of +the colligative properties + +that you saw last time. + +Now let's, though, +finish up by calculating + +the additional pressure +that we'll find. + +So what's the osmotic +pressure of the solution. + +So now we're going to assume +that we have that solution + +inside, in a situation +like this where there's + +pure water outside +that can go in. + +And there's going to be +excess pressure because + +of the water rushing +into the solution. + +So what happens? + +And let's use a +value of the density. + +0.995 grams per +centimeters cubed. + +So, pi is RT times c. + +That's 0.08314 bar +per Kelvin mole. + +Times 300 K times +c. c is nB over V. + +So it's 10 grams divided +by 907 grams per mole, + +over 1010 grams over 0.995 +grams per milliliter, + +I'm equating with +centimeter cubed. + +And that turns out +to be 1.09 times 10 + +to the minus 5th +mole per millileter. + +Let's get that into liters. + +So we'll multiply by 1000 +milliliters per liter. + +So it's 1.09 times 10 to +the 5th moles per liter. + +OK, yeah. + +STUDENT: [INAUDIBLE] + +PROFESSOR: Let's see. + +Oh, don't forget that, right. + +STUDENT: [INAUDIBLE] + +PROFESSOR: Ah, yes, yes, yes. + +And I think that's the +case in the notes also. + +Yep. + +Thank you. + +OK, so the concentration, +just to calibrate us here, + +it's a pretty low +concentration, right? + +It's about 10 to the +minus 5 moles per liter. + +The excess pressure is 0.27 bar. + +In other words, about a +quarter of an atmosphere. + +Uh-oh, what's happening? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Where are we? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Sorry, where exactly? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Oh, yes. + +Yes, sorry. + +Yeah. + +10 to the minus 2 +moles per liter. + +All right. + +And so the pressure that results +is a modest pressure, right? + +It's about a quarter of an +atmosphere of excess pressure. + +2.7 time 10 to the 4 pascals. + +So let's just calculate, given +this small additional pressure, + +how high is the +liquid going to go, + +above the level of the solution. + +Anybody want to guess? + +You know, a centimeter. + +10 centimeters. + +100 centimeters? + +Give me an order of magnitude. + +Who guesses one centimeter? + +You got three choices. + +One, 10 and 100, and +you have to make one. + +Who guesses one centimeter? + +Who guesses 10 centimeters? + +Who guesses 100 centimeters? + +OK. + +Now, fortunately we +don't do problem sets. + +Or other scientific +problems by popular vote. + +Rather, we just solve them. + +Whenever possible. + +So, what's the height +of a column of solution? + +Well, that pi, remember, that's +equal to rho times g times h, + +right? + +And we know pi now. + +So h is pi over rho times g. + +So it's 2.7 times +10 to the 4 pascal + +over rho, that's 0.995 +grams per centimeters cubed. + +Times 1 kilogram over 1000 grams +times 100 centimeters per meter + +cubed. + +I'm just getting +this into units that + +will give me, that +will be in meters, + +times 9.8 meter per +a second squared. + +And when I multiply all +that out, it's 2.8 meters. + +So that puny little pressure +ends up being meters high. + +Taller than any of us, by far. + +Sorry, it's up to there. + +And that's actually +pretty typical. + +And what that means is, it +actually makes osmotic pressure + +a very, very sensitive +measurement method. + +If you want to determine a +molecular weight, for example. + +Because it's so +high, that means, + +and of course you can measure +that height pretty accurately. + +Certainly within +about a millimeter. + +And so even relatively +modest concentrations, + +it's still easy to see the +effect and measure the impact. + +And use that to calculate +the properties of the solute. + +OK, any questions? + +Alright. + +Now we're going to +start something new. + +So, so far what you've seen, +and I hope come to appreciate, + +is the whole structure +of thermodynamics + +is built on empirical +macroscopic observation + +and deduction. + +We observe things. + +We formulate these broad +thermodynamic laws. + +All macroscopic. + +It doesn't depend on any +microscopic model at all. + +And in fact much of +it was formulated + +before there was a good +microscopic model of matter. + +Before the atomic theory +of matter, and molecules, + +and so forth was +well worked out. + +And it's incredible how powerful +that whole formalism is, right? + +In some sense, +although it may seem + +like neglecting what +we now know to be + +an important part of nature, +actually part of its power + +is its empiricism. + +Right? + +There are these +very small number + +of fundamental laws from +which everything else follows. + +And at this point, +of course, there's + +just enormous confidence in +that small number of laws. + +Because of their being +verified in so many context. + +But, at the same +time, we do know + +about the atomic +theory of matter. + +We know there are +atoms and molecules. + +So it ought to be possible, +at least in principle, + +to start from a purely +microscopic approach to nature. + +And just based on figuring out +the microscopic properties. + +And then saying, well, +OK, my macroscopic stuff + +is just a collection of +those microscopic entities. + +I should also be able to figure +out macroscopic thermodynamics. + +I should be able to start +from my microscopic picture + +and get to macroscopic +thermodynamic results. + +And in fact, that is possible. + +And the theoretical +formulation for it + +is what's called +statistical mechanics. + +Called that because, +of course, you + +won't be surprised +to learn that it's + +going to require a +statistical treatment. + +We're going to be dealing +with moles of material. + +But now we're going +to be trying to think + +about their +microscopic properties. + +And so we'll be dealing not with +n number of moles, but with 10 + +to the 24th number of +molecules or atoms. + +And you know we won't +be able to keep track + +of every one of their +individual states, all the time. + +We may be able to do a terrific +calculation of the quantum + +mechanics or the +classical mechanics that + +describe the states +that they could be in. + +But there's no way in +practice that we're either + +going to experimentally +or theoretically keep + +track of all of that. + +So we're going +to, at some point, + +have to introduce statistics. + +To take what we know about +the microscopic properties + +and try to go from there +to the macroscopic results. + +The thermodynamics +that we've seen so far. + +And that's what statistical +mechanics is all about. + +So let's try to +introduce a little bit + +of statistical mechanics. + +Where we're going +to go from what + +we know about +microscopic properties + +all the way to macroscopic +thermodynamics. + +That's our objective. + +So let's start by just +trying to calculate + +energies of +individual molecules, + +or individual particles. + +And what's the probability +that some molecule, one + +of the oxygen molecules +somewhere in this room, + +is in a certain energy state. + +Right? + +And what our strategy +is going to be, + +is to determine what are the +probabilities that molecules + +are in certain states +with certain energies. + +And if we can determine that +for all the possible states, + +then we can average over those. + +So without keeping track of +every individual molecule, + +we could then calculate, +an average energy, + +which is what you would +measure thermodynamically + +when you look at the whole +collection and measure what + +we call u, right? + +Of course, we're +really averaging + +over disparate energies +of lots of different atoms + +or molecules. + +They don't all have the +same molecular energy. + +And we don't try to measure +their individual energies. + +So that's what we'd +like to calculate. + +And so we'd like +to be able to know + +what are all these probabilities +of different energy states. + +And then from +that, statistically + +averaging, what are the +macroscopic average energies. + +And other macroscopic +quantities. + +So, let's start there. + +Probability that a +molecule, must be specific + +as possible is in +state i with energy Ei. + +And right now we're +not even going + +to specify the +nature of the state. + +We could be worrying about +translational energy. + +What state it is, how fast +it's whizzing around the room. + +We could worry about its +vibrational or rotational + +energy, or electronic state. + +For now, let's not +even specify it. + +Let's just say the +only thing we're really + +specifying about +the state is it has + +some energy that +we presumably know. + +Now, what we'd like is +to know a functional + +form for the probability. + +And we don't know one a priori. + +But let's just think +about two molecules. + +And the probability +that one of them + +has energy i, and another +one has energy Ej. + +It also, let me say, would be +sufficient to think about even + +one molecule and +say, we'll let's + +think about independent +parts of its energy. + +Let's say, translational +energy in this direction. + +And in an orthogonal direction. + +What matters is, we're thinking +about two independent energies. + +Could be separate molecules +that aren't interacting. + +Or independent degrees of +freedom on the same molecule. + +But let's just consider it. + +So a molecule is in state +i, and that another molecule + +is in state j, with energy Ej. + +So what we're going to calculate +is the joint probability + +that the two molecules +are in those states. + +So we want a probability. + +This one, we'll call Pi(Ei). + +This would be Pj of Ej. + +And this probability together +will be Pij(Ei + Ej). + +I could just write Ei comma +Ej, but the energy's add. + +And that's crucial. + +Now, since the molecules +are completely independent, + +this should just be the product +of the separate probabilities. + +Two completely +independent events, + +or things whose probability +we want to determine together. + +So, that suggests a really +simple functional form. + +Because what we're saying here +is we want a function of a plus + +b, which is equal to the same +sort of function of a times + +the same sort of function of b. + +In other words, when we +multiply these functions, + +we get a function of the +sum of those arguments. + +What functional form does that? + +Exponential. + +Sure. + +So in other words, +e to the a plus + +b power equals e to +the a times e to the b. + +So it suggests that there's +an exponential probability. + +Suggests it. + +Now, there's also +some physical insight + +that we can apply +to the problem. + +First of all, we +expect that states + +with higher energy +in general are + +going to be less probable +than states with lower energy. + +If it's cold, not much +thermal energy around, + +and you say, how +much energy does + +a particle in an equilibrium +collection of particles have, + +at thermal equilibrium, if +there's not much thermal energy + +around, you don't expect +it to be very likely + +that a particle has a +huge amount of energy. + +That one individual +particle has it. + +Could happen, right? + +From some random +collisions that just + +happened to bulk up the +energy of that one particle. + +But on a balance it's not +going to be very probable. + +Lower energies will +be more probable. + +And the other thing is, even +in thinking about something + +like that, temperature comes in. + +Immediately. + +Right? + +If you raise the +temperature a lot, + +surely we have to expect +many more molecules will + +start to become energized. + +Will have more energy. + +So, lower probability +for higher energy. + +But the probability +of higher energy + +should go up if the +temperature goes up. + +In other words, the ratio +of energy to temperature + +should be involved here. + +So, P of Ei should go +down as Ei goes up. + +And should depend +on Ei over T. Right? + +So, we can start with +this functional form. + +And by the way, there's +no reason we can't have, + +in general we would have +some constants here, right? + +We haven't changed +anything to do that. + +And now let's just +use the little bit + +of physical intuition that +we're thinking about here, + +to refine this +just a little bit. + +Let's write, we +expect that Pi of Ei + +is some exponential to +the minus C Ei over T, + +where C is some constant +greater than zero. + +So this will have the property, +then, that as energy goes up, + +the probability goes down. + +But it's scaled by temperature. + +If I raise the temperature, that +makes the higher energy states + +get more and more likely. + +Well, this is our +functional form + +for probability of a +molecule being in a state + +with energy Ei. + +And the only difference +between this and what's + +written conventionally is the +way the constant is labeled. + +So really what we +have is Pi of Ei + +is proportional to e to the +minus Ei over kB T, or just k + +T, where kB is called +the Boltzmann constant. + +And it's just equal to R +over Avogadro's number. + +It's the gas constant per +molecule, rather than per mole. + +One way to try to rationalize +this is, you've probably seen, + +you've all seen Arrhenius +kinetics, right? + +Arrhenius rate laws? + +If you remember what +that looks like, + +you get this rate constant. + +Arrhenius rate constant +is some constant A times e + +to the minus Ea over RT. + +Remember that? + +You've all seen that before? + +And so what's +happening here, Ea is + +what is an activation energy. + +Remember, the idea +is that you've + +got reactants and +products, and there's + +some barrier you've +got to get over. + +The activation energy, +before you can have reaction. + +So the rate depends on +surmounting that activation + +barrier. + +This is really coming +from the same idea + +as this, which is the +probability of one + +of the molecules having +this much energy. + +Depends on e to the +minus energy over RT. + +This is per mole, +so this is per mole. + +The exact same relation. + +So the idea in the +context of kinetics + +is that the rate depends on how +many molecules can get up here. + +And what the probability is +of their getting enough energy + +to go over the barrier. + +And that energy, +that probability, + +is given by this expression. + +So in this form you've seen +this kind of dependence + +before in a very explicit way. + +Let me just take it one small +but important step farther. + +Which is that +proportionality constant. + +Couldn't we do better? + +Couldn't we say, couldn't we +figure out what exactly it is, + +not just what it's +proportional to? + +Well, let's try. + +So as we've written +it, we've got Pi of Ei + +is proportional to e to +the minus Ei over kT. + +We could write that as equals +A e to the minus Ei over kT. + +This is just some +proportionality constant. + +But we can determine +what that constant is, + +because we know that if we sum +over all the possible states, + +the molecule has to be +in some state, right? + +So that sum of all those +probabilities has to equal one. + +So sum over i of Pi of +Ei, is equal to one. + +Because the molecule must +be in one of the states. + +OK, now this is our expression +for all those p i's. + +So let's just write that way. +a is just a constant times + +the sum over all the i's of +e to the minus Ei over kT. + +And so there it is. a is equal +to one over the sum over i, e + +to the minus Ei over kT. + +So now we can +rewrite Pi of Ei is + +equal to e to the minus Ei +over kT over, the sum over i, e + +to the minus Ei over kT. + +Now, just so you're not +confused, this i matters. + +That's the i we're +talking about. + +What's the probability of it +being in some particular state + +i with energy e i. + +This i is just a dummy variable. + +So just to be explicit, +we could write this just + +as well as e to the +minus Ei over kT + +times the sum over j, e +to the minus Ej over kT. + +It could be confusing, but +this is usually the way + +that it's written. + +Even though this +dummy variable here + +has nothing to do with +the particular choice + +that's made here. + +So now we know. + +And we can calculate what the +probability is for a molecule + +to be in any +particular state if we + +know the energy of that state. + +Now, notice we need to know +all the energies of all + +the other states, too. + +Because this thing, +in other words, + +this a, right, depends on +summing over all of those. + +But if we know those, +then we can do it. + +We can do the whole calculation. + +And for a good number of +cases, we realistically + +do know it all. + +So from the proportionality +relationship alone, + +of course, we can tell +the ratio of chances + +that you're in one +state or another. + +Even without this a +constant, we already + +could've said well, if +what's the ratio of, + +the probability of being in +state i with energy Ei to state + +j with energy Ej. + +Well, it's just e to the +minus Ei over kT over e + +to the minus Ej over kT. + +It's e to the minus +Ei minus Ej over kT. + +But apart from just being +able to get the ratio, + +we can get the absolute number. + +What's the absolute +probability that a molecule + +is in any particular +state of a given energy. + +Next time what +you'll see is what + +can be calculated based on +the results that you've seen, + +just the results +you've seen so far. + +From these quantities +alone, it turns out + +you'll be able to calculate +every single macroscopic + +thermodynamic quantity. + +So you'll see some +of that next time. \ No newline at end of file diff --git a/vFmdogFFcko.txt b/vFmdogFFcko.txt new file mode 100644 index 0000000000000000000000000000000000000000..a66c7a11f879d8bf127ac5e7c0dcc98569133569 --- /dev/null +++ b/vFmdogFFcko.txt @@ -0,0 +1,3807 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation, or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: I apologize +for the delay. + +But we are ready +for multimedia show + +with three different +applications. + +One of them are the clickers. + +I hope you all took a clicker. + +It's just two questions today, +but really good questions. + +[LAUGHTER] + +So today's actually +very nice topic. + +I think almost every lecture +we have a nice topic, + +but today's especially nice. + +It's called Unraveling +Open Quantum System. + +That may not tell you so much. + +Well unravelling means we +want to sort of untangle it, + +We want to understand +what is inside. + +And so we want to develop +a better understanding what + +is inside a density matrix. + +How can we think about +the quantum system + +in an even more microscopic +way than the density + +matrix tell us? + +And again, this finds +applications in atomic physics, + +because one application of it +is spontaneous emission optical + +block equations. + +On the other hand, +actually, this class + +will also teach you +something very general + +about quantum physics. + +So today's lecture is this part. + +We'll have three topics. + +One is I want to provide a +motivation for single quantum + +systems. + +And you should appreciate this. + +A single quantum system is not +what Schrodinger and Heisenberg + +told us about. + +Quantum mechanics was formulated +as an ensemble average. + +But today we want to talk about, +is there something in addition? + +About single quantum systems. + +Part two is-- addresses the +derivation of the quantum Monte + +Carlo wave function method. + +And this is a formalism, +which is really + +simulating in quite general +terms, quantum physics + +by following-- using quantum +Monte Carlo simulations-- + +trajectories of individual +quantum systems. + +So here the individual +quantum system-- + +even if you have one, even +if you don't have one-- + +becomes a computational tool. + +And eventually in +part two I want + +to give you another example +for unraveling open quantum + +system, which differ from +the models for dephasing. + +And if you remember that this +was on one of your homework + +assignment that's correct. + +I sort of want to here +take your homework + +into the classroom discussion. + +Well I think it's nice to start +this lecture with the quote + +by Erwin Schrodinger. + +Where he said, "We +never experiment + +with just one electron, +or atom, or molecule. + +In thought experiments, we +sometimes assume that we do; + +this inevitably entails +ridiculous consequences." + +Well today we want to talk about +those ridiculous consequences, + +because many people +in our field trap, + +address, and observe single +electrons and single atoms. + +Now this is related +to quantum jumps. + +Quantum jumps has even made +it into the popular realm. + +You can find lots and lots of +references on quantum jumping, + +but I warn you this +is about quantum + +jumping into different worlds. + +It's about broadening +your horizon. + +And those authors, +those people actually, + +sell you something by claiming +that people like Einstein + +and Stephen Hawking would +support the idea that you can + +jump into different universe, +experience another version + +of yourself-- probably a +better version of yourself-- + +and this will +inspire you to change + +your life in the world you live. + +But-- So this is +quantum jumping. + +I'm not talking about +quantum jumping, + +I will only talk +about quantum chunks. + +So what you see here is +really a classic experiment. + +One of three +experiments which were + +done almost simultaneously. + +There have always been +races for, you know, + +the first observation +of something. + +And there was the [? Hamburg ?] +group by [? Toshak ?], + +the Seattle group +by Hunt [INAUDIBLE], + +and the Boulder +Group by Dave Wylen, + +who observed the phenomenon +of quantum jumps for the first + +time. + +Let me just tell you +what it is, because it's + +exactly what you're +going to describe. + +Here in this situation +you have a system. + +It's a trapped barium +ion with a p and s state. + +And there is very +fast transition + +where you can rapidly +scatter light, and get + +lots of fluorescence, +at 493 nanometer. + +But what happened is, +every once in a while, + +the particle has a branching +ratio to decay to d state, + +and, well, d to s 2 units +of angular momentum. + +The transition here down to +the ground state is very slow. + +It's slow because +it's forbidden. + +It's even slower +because it happens + +at longer wavelengths +of 1,600 nanometer. + +And this is slow. + +And it has a lifetime +of about 50 second. + +So you-- If you think +about it naively + +and that's probably +the correct approach-- + +you would say the +particles in the s state, + +it's like a light bulb. + +It scatters many, many +photons, but then it + +branches to the d state. + +And for 50 seconds +the light bulb + +is switched off, until +the particle spontaneously + +goes down to the s state, +and then the light bulb + +is switched on. + +And this is exactly +what people observed. + +But I mean I was-- This was '86. + +That was the time I +was a graduate student, + +and I talked with +theorists in the field, + +and respectable +theorists told me + +that there was a +controversy-- probably + +not among experimentalists, +who use the naive + +approach-- but theorists +who believed too much + +in what they calculate. + +Because if you solve it +quantum mechanically, + +and look what you get. + +It's a steady state solution. + +Atom in steady state. + +Laser in steady state. + +And if you calculate the quantum +mechanical expectation value, + +the expectation value is +constant as a function of time. + +So a simple quantum +calculation would + +say the fluorescence +is on average. + +Well just the time +average and his constant, + +and his time independent. + +So there were some +serious doubts + +whether you would observe +this, or something + +which looks more like +the ensemble average. + +Well made all of the theorists +soon realize you cannot + +calculate the steady +state average. + +You have to calculate +the correlation function + +in steady state. + +And the steady state +correlation function + +has structure exactly +at 50 seconds. + +So in a steady state +system, if you're + +interested in fluctuations +and temporal behavior, + +you can't just +calculate quantities, + +you have to calculate +correlation functions + +of quantities. + +So anyway-- But then +of course, if you now + +average over many, +many realizations, + +you find exactly an exponential +decay of 50 seconds. + +And this is sort +of what you would + +get for an ensemble average. + +So this is what +quantum jumps are. + +This is what you +should always imagine + +when we talk about quantum jumps +in the rest of this lecture. + +But I also want to show +you more recent example + +from Serge Haroche, +in Paris, where + +they observed quantum jumps. + +Recording a single +photon in a cavity. + +So what happens is there's a +single photon in this cavity, + +and they can read +out whether there + +is a photon or not by sending +Rydberg atoms through. + +And a single photon +is never observed, + +but it causes a phase +shift, an AC-Stark shift, + +on the Rydberg atom. + +And then they can read out +with a Ramsey interferometer + +the AC-Stark shift. + +So every atom which +passes through the cavity + +will tell you whether +there is a photon or not. + +And-- And this is shown here. + +Blue means no, +there is no photon. + +Red means there is a photon. + +So here you repeatedly figure +out again there is no photon. + +And suddenly there +is a quantum jump + +when the cavity has +absorbed a photon, + +or when a thermal +photon was released. + +You may say, what happened here? + +Well no measurement is perfect. + +There is some noise. + +But by seeing that +these are outliers, + +you clearly see that here +is a photon in the cavity, + +and here where the red +read out of the atom + +overwhelms the blue readout +here you have no photon. + +And then as time goes by, you +can observe the death and birth + +of micro-cavity photons. + +So these are now quantum +jumps in the-- not + +in atomic population, but +quantum jumps in the photon + +number in a cavity. + +AUDIENCE:What's the +time scale on that? + +Seconds? + +PROFESSOR: Yeah, time is second. + +So what is shown here is-- I +think what is shown is here + +are 300 milliseconds, and +this is 2.5 second element. + +AUDIENCE: What was the +density of each line mean? + +PROFESSOR: Each line +is a Rydberg atom, + +which has been readout with +a Ramsey interferometer. + +And-- + +AUDIENCE: So that +means that they're + +leaving no, like between-- + +PROFESSOR: I think +that means there + +was a Rydberg atom in state e, +which means there is a photon. + +And blue means, the +blue bar means, there + +was a Rydberg atom in state g. + +These are two highlighting +states of the rubidium atom. + +Sort of each spike +here is one readout + +of the microchannel plate. + +So these are detector clicks. + +You can say, yes. + +You can sort of say, blue +is yes, and red is no. + +And these are the two clicks. + +AUDIENCE: Yeah, but, like the +separation between two clicks + +is not uniform. + +PROFESSOR: No, because +if you're an atomic beam + +the atoms come not +equally spaced out. + +There's a randomness +when the atom comes. + +I think it's posed only in +statistics in this experiment. + +It's a real experiment. + +It's amazing. + +Other questions? + +Team One. + +AUDIENCE: So one more question. + +So the, for example, +the first bit of blue + +is all measurements for the +same state of the cavity. + +I know blue means +photon or no photon, + +but if it does mean +photon, that means + +it's the same photon +interacting with-- + +PROFESSOR: Yes. + +AUDIENCE: OK. + +PROFESSOR: Yes, because, I +mean, this is something people + +know that the photon +number in this cavity + +only changes over +very long time scales. + +And you sort of see, +kind of, exactly + +hear how-- You see +here two quantum jumps. + +One from blue to +red, and one from red + +to blue in this cavity. + +Yes? + +AUDIENCE: I don't if +this is maybe just + +my accent's not very good, +but in the bottom left graph-- + +Right? + +Or on the bottom graph, in +sort of the left corner, + +it looks like +there's some overlap + +between the dark blue +and the dark red. + +Yeah. + +PROFESSOR: You mean here? + +AUDIENCE: Yeah, +like right there. + +Is that like sort of there is +a photon in that [INAUDIBLE] + +simultaneously? + +PROFESSOR: I think, to +the best of my knowledge, + +I haven't really +looked-- I've heard + +wonderful talks about it.You +can go back and read the paper, + +but this probably means in +the atom number in the cavity, + +and the algorithm they have +used to analyze the data + +says that here the photon +number was 0, jumped to 1, + +and jumped back again. + +So you-- If you see +here, for instance, + +there is some overlap, +but you would still + +say, since either there is +a photon or not a photon, + +as long as you have a-- +as you have a higher + +number of red clicks +than blue clicks, + +you would say there is a photon. + +And the little overlap, there +is maybe a little bit of time + +where you don't know whether +there is a photon or not. + +But this really-- This is +real, because every measurement + +takes a certain amount of time. + +Since you have a +few random clicks, + +if they are a few +random clicks, you + +do not know yet if +the system has jumped, + +you have to wait a little bit. + +But this is really +also showing how + +our knowledge about the +quantum system comes with time. + +And therefore, +the wave function, + +or the statistical +operator changes with time, + +because of wave function +and statistical operator + +are simply a description of +our knowledge about the quantum + +system. + +AUDIENCE: [INAUDIBLE] +is too dense + +PROFESSOR: You could have +a situation, for instance, + +you could prepare +the cavity, that it + +has an equal probability +foreseeable in one. + +And then what you would read out +may just be completely random. + +So that may be possible, +but in their experiment, + +I think, the nature +here is that you + +have most of the +time stable photons, + +because the cavity is cooled +to very low temperature, + +and only occasionally does +the thermal distribution, + +the Bose-Einstein distribution +of photons in the cavity + +have a one. + +And what we observe are +the thermal fluctuations + +between mainly 0 and +occasionally a 1. + +If you would make the cavity +and little bit hotter, + +it would have maybe +half of the time a 1 + +and half of the time 0. + +But that wouldn't mean that +you have completely randomness + +in your results, because +there is a thermal relaxation + +time over which a +photon is created, + +and a photon goes back. + +The photon would not jump +back and forth from the cavity + +to the walls of the +cavity in microseconds. + +It would probably +have an exchange time, + +and you could sort of measure +the thermal correlation + +time of photons in a cavity. + +It's a really good experiment. + +OK. + +So in that sense I +think I showed you + +that what Schrodinger said +is ridiculous is real, + +is the subject of +current research, + +and since for +quantum information + +processing in +quantum computers, we + +need single quantum system +is at the heart of quantum + +information processing. + +So therefore, we +want to now describe + +single quantum systems. + +But when I do that, +I-- come very -- + +It will become clear at +the end of this unit, + +but I want to give you +the warning right away. + +The way how I describe now +a single quantum system + +may not be unique. + +There will be, +there is actually, + +an infinite number of ways. + +And I've already +mentioned that to you, + +that there is an +infinite number of ways + +to unravel a density matrix. + +I mentioned that you can +write every density matrix + +as a probability of pure states. + +Weighted probability of +being in pure states, + +but there's always +different choices. + +You can get an infinite number +of different combinations + +of pure states, and construct +your density matrix. + +So, so this was sort of in +at the level of the density + +matrix, but similarly-- +and this will come out + +of this discussion today-- +there is also an infinite number + +of ways to unravel the +dynamics-- the dynamics + +involved in the evolution +of an open quantum system. + +So-- so with that I want to +describe the quantum Monte + +Carlo wave function method. + +So in the quantum Monte +Carlo wave function method, + +we perform-- We don't +need an experiment. + +We don't need +sophisticated experiments + +to observe a single +quantum system. + +It's a theoretical +method, but we + +perform thought, or +gedanken experiments. + +So our gedanken experiments is +that we perform measurements. + +So we assume-- we +have-- When we want + +to describe an +ensemble of atoms, + +we assume we have a single atom. + +We assume it emits +photon, and then we + +assume that the +photon is detected. + +And the mom-- So the +moment the photon + +is detected we +know, for instance, + +that the atom is in +the ground state. + +And so our quantum Monte +Carlo simulation follows now + +the trajectory of the single +quantum system by saying, + +I toss a coin, there's +a certain probability + +for detecting the photon. + +If I detect the photon, +the system I know + +is in the ground state. + +If I don't detect +the photon, it's + +not in the ground +state, and such. + +And these probabilistic +approach is just simulated + +in the quantum +Monte Carlo sense. + +So-- So what is +in essence-- what + +is the essence of the +quantum Monte Carlo + +method is that we allow a +small time step delta t. + +It's a real time simulation. + +And there is a small +probability that the system + +has decayed in that time. + +So we may now toss a coin-- use +a random function generator-- + +and ask, has spontaneous +emission taken place? + +And then the two +possibilities are yes, + +and we continue +whatever the outcome, + +whatever the quantum state is. + +Or we say no, and then with +the probability-- with a-- so + +with a probability, +p, we say yes. + +With a probability +1 minus p we say no, + +and then we continue the +simulation accordingly. + +So this will become +much, much clearer + +when I write down the +formalism for you, + +but there is one important +aspect, which I really + +want to discuss with you. + +And this is the +essence of the method. + +Namely, how does +the wave function + +change by your measurement? + +So-- so this is the essential, +the only conceptional part + +for the quantum Monte +Carlo wave function. + +Afterwards I just show you. + +Once you have this, +once we have cleared up + +this conceptional part, the +rest is just a few equations. + +And we immediately show that +the quantum Monte Carlo wave + +function method is equivalent +to the optical block equation. + +But let's really feature +and take some time + +for discussing the concept, +namely, the change over wave + +function by a +quantum measurement. + +And maybe what this +carries home to you + +is that the nature of an open +system-- we have a quantum + +system, which interacts +with the environment-- + +is, actually, that the +environment permanently + +performs measurements. + +And you will actually see +that the idea of performing + +measurements, formalized in +the quantum Monte Carlo sense, + +gives us an equation for +the density matrix, which + +is identical to the +optical block equation. + +So in other words, you +can say I am re-deriving + +for you master equation now, +but from a very, very different + +perspective. + +From the perspective +of an environment + +which constantly +performs measurement. + +OK. + +So let's go through that. + +How-- What happens +in a measurement? + +Well if our initial state is +the ground state-- starting + +very in trivial ways-- well +there is no measurement, + +because the particle will stay +in the ground state forever. + +OK. + +Now let's go to +the next situation + +that our atom starts out +in the excited state. + +Now in a time step delta t, +we have two possibilities. + +A photon can be observed, +or nor photon is observed. + +When the photon is +observed, we know for sure + +that the system is now +projected into the ground state. + +If no photon is +observed, well the system + +is still in the excited state. + +OK. + +So we've discussed what happens +when the system is initially + +in the ground, and when +the system is initially + +in the excited state. + +But now comes the +following question. + +We prepare the system +in a superposition + +of ground and excited state. + +And we want to +discuss what happens + +when the photon is observed? + +What happens when no +photon is observed? + +I think if you observe +the photon it's + +pretty clear we have to +assume after photon emission + +the system is in +the ground state. + +But if no photon is observed, I +want to give you three choices, + +and you should address +them with the clicker. + +One choice is that the particle +stays in the same state. + +The second choice is +that the particle stays + +in a superposition state, +but the probability + +to be in the excited +state decays. + +Also no photon +has being emitted, + +or no photon has been observed. + +And the third possibility +is something else. + +So in other words, assume +you're an observer, + +and you know with 100% +detection probability-- + +let's not discuss technical +issues-- you have completely + +surrounded your system +with perfect detectors. + +And you know in the time +step delta t, in the time t, + +no photon was observed. + +And now you should +make a prediction + +what happens next to +the quantum system. + +And you make the +prediction by assuming + +that the system is described +by a wave function or density + +matrix. + +And I'm asking you, which +of the three choices + +correctly describes what the +system will do afterwards? + +What the system will do next? + +Is the question very clear? + +Good. + +[TAPPING] + +OK. + +All right. + +Pretty good. + +A lot of people when I taught +the class before said it's A, + +the wave function +is not changing, + +because no photon +has been emitted. + +Now in-- For those people, but +there only few among those, + +I would have now asked +the next question. + +If you have-- If you have +a 50-50 superposition, + +of ground and excited +state-- And let's + +say the spot time for +spontaneous emission + +is 10 nanoseconds-- But +now you wait one second, + +and after 1 second, no +photon has been observed. + +What is your prediction? + +In what state is the +system at this point? + +Is the system in +the ground state? + +Or is the system in, +still in, a superposition + +of ground and excited state? + +Well since we have to +clicker, you can tell me. + +Is it-- Is it still a +superposition state, + +or is the system in +the ground state? + +OK. + +So now you have to help me out, +because the people who said B, + +if they would go back to +here-- And most people said + +it is B. If you put in gamma 10 +nanoseconds, the inverse of 10 + +nanosecond, and the +time is 1 second, + +the excited state amplitude, +the excited stated mixture, + +is 10 to the minus nothing. + +So-- OK. + +If you want to be a +mathematician and say-- + +[LAUGHING] + +--there is epsilon 10 +to the minus 10, yes. + +Then you can say there is +still a small admixture + +to the excited state. + +But by making it so +extreme-- 10 nanoseconds + +versus a second-- at least +in all practical terms, + +the system is in +the ground state. + +And I think this +should teach you + +what it means if you +have a system which + +is in the superposition of +ground and excited state, + +and after 1 second it +has not emitted a photon. + +I mean-- + +Then you would say, +it had its chance. + +It had plenty of +chances to emit, + +but it decided it +doesn't want to emit. + +And that would mean +your 50/50 superposition + +of ground and +excited state means + +the atom decided that +it's in the ground state. + +You should also realize +a 50% superposition + +of ground and +excited state means + +in half, in 50% of the +cases there will never + +be a photon emitted. + +So in other words, +what you should realize + +is if your 50-50% superposition +of ground and excited state, + +that the quantum +evolution of this system + +is-- after a long +time the system + +is definitely positively, +absolutely in the ground state. + +It's always in the ground +state after a long time. + +In 50% of the cases with +emission of a photon, + +in 50% of the cases without +emission of a photon. + +If you have a +radioactive-- ensemble + +of radioactive nuclei-- and +let's say half of the atoms + +are in the excited state +and [INAUDIBLE] and half are + +in the ground state-- and you +send the sample to your friend, + +and your friend waits many, +many, many half times, + +common sense tells you that +all the particles are now + +in the ground state. + +Also only half of them have +decayed, because the other half + +were in the ground +state to begin with. + +I mean this is what +quantum physics tells us. + +This is what a 50/50 +superposition is. + +But quantitatively +this is, of course, + +included in this +result-- which magically + +that almost all of you +got right-- namely there + +is a superposition of +ground and excited state, + +but the excited state +amplitude decays. + +And to the limit, in the limit +that the time is much longer + +than the decay time, no matter +what the coefficient initially + +was in front of +the excited state, + +this coefficient +has decayed to 0. + +Any question about that? + +Let me just +emphasize that, again + +in giving you also an example in +the reference, a 0 measurement. + +A 0 measurement modifies +the wave function. + +You can also put it like this, +what the wave function is + +is the best knowledge you +would have about this system. + +The wave function is a way +to predict what happens next, + +and it's the most precise +way to predict it. + +More accurate predictions than +the wave function always cannot + +be made, because of Heisenberg's +uncertainty relation. + +But what happens is, +if you have a 50/50% + +superposition of ground +and excited state, + +and the system has not emitted, +then you would say initially + +my guess was half of the atoms +were excited, half of the atoms + +are in the ground state. + +But if none of them +has decayed for awhile, + +you would say I revise +my estimate now. + +Now I have to assume that +more are in the ground state. + +Because having not decayed means +there is a higher probability + +that the system has actually-- +is in the ground state + +to begin with. + +So this is how this way of +dealing with a wave function + +automatically adjusts +for the knowledge + +you have gained +about the system. + +Let me give you another +example which carries home + +the same message, and I take +it from a pedagogical paper + +from Dickey, from American +Journal of Physics, 49, 926, + +1981. + +And what he discussed +is the following. + +You have a box and originally +your atomic wave function + +is completely localized. + +Your Bose-Einstein condensate +if you want in this box, + +or let's just assume one +atom to be more precise, + +and it's completely delocalized. + +But now you focus a laser +beam into the system. + +And the laser beam +would ionize your atom, + +and you could count the +ion with 100% probability. + +And for a short moment, +you flash on the laser + +and the result is +yes, you count. + +You get a count. + +In that moment you +would say my wave + +function is more localized. + +I revise my estimate. + +Well maybe I +shouldn't say ionized. + +If it's ionized you +destroy the atom. + +Let's just say you observe +fluorescence so the atom is + +still alive. + +But now you have to +say that the atom is + +localized in that region. + +However, if you don't +observe anything, + +you would say, well +now it's actually + +more probable that +the atom is outside. + +Because if it had been +in the laser beam, + +with a certain probability, I +would have detected a photon. + +But the non-detection +of a photon + +means that I revise my estimate. + +And I say it's +much more probable + +that the atom is +outside the laser beam + +than inside the laser beam. + +So this here is exactly how a +non-observation of anything, + +a 0 measurement, modifies +your wave function. + +And the formalism +to incorporate that + +is what we have +discussed before. + +Yes? + +Cody? + +AUDIENCE: So your arguments +here so far work the same way + +as if it's in a +wave function, you + +have just an entire +Pascal probability, + +and we're updating our +understanding of probability. + +Like you haven't +included anything + +about the relative phase +between these two-- + +PROFESSOR: I want +to do that now. + +I mean, I-- This is sort of just +to address the basic concepts + +about what does a +measurement mean, + +what does a 0 measurement mean. + +But now I want to write +down everything for you + +in amplitudes. + +We want to do exactly the +time evolution of the system. + +Nancy? + +AUDIENCE: Is this, +like, inconsistent + +with [INAUDIBLE] +quantum equation? + +Like especially the [INAUDIBLE], +because when you are saying + +that it is admixture of the +ground and excited state, + +and we did not observe-- + +PROFESSOR: Then +the superposition + +say that ground +and excited state. + +We are not starting out in +an energy heightened state, + +so therefore, we-- +what we have is not + +a sharp value of the energy, +but an expectation value. + +And also if you repeat +the measurement many, + +many times, the average +energy is conserved, + +and this is exactly what energy +conservation in quantum physics + +says. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Well if your +particle, if your system, + +is not in an eigenstate +of the Hamiltonian. + +It doesn't have a sharp energy. + +And that would mean that when +you measure the energy now, + +you have fluctuations. + +Sometimes you measure higher, +sometimes you measure lower. + +It's only when +you're in eigenstate + +that you measure a sharp value. + +And therefore you know +from the beginning + +that you will measure +an energy distribution. + +And sometimes you +measure higher, + +and sometimes you measure +lower than the average value. + +There's nothing wrong +about it, but your question + +is a very good one. + +You should-- I +mean those examples + +are really-- On the one +hand they are trivial, + +but on the other hand, it's +very profound what they tell us + +about quantum physics +and how to apply + +conservation laws and such. + +OK. + +I think-- Let's-- Let me now +formalize exactly how this is + +done with all the +bells and whistles. + +We assume we have an initial +wave function, which is now + +an arbitrary superposition state +of ground and excited state. + +And we have the environment, +which, in this case, + +we assume is the 0 photon state. + +It's a vacuum. + +And we want to exactly +solve the Schrodinger + +equation for that system. + +But we restrict +ourselves too much, + +to a very small time step. + +The small time step is smaller +than, you know, anything else. + +Than the natural decay time. + +Maybe the inverse +[INAUDIBLE] frequency + +if you drive the system. + +You're not doing it +here, but I will later + +show how you can add a laser +beam and drive the system. + +Or it should also be smaller +than the inverse tuning. + +So what is very important here +is that we want to deal only + +with simple cases, +namely one photon + +has been emitted or not photon. + +So you want to make +sure that there + +is, at most, one +spontaneous emission event + +during the time delta t. + +So what I'm writing down now +is the total wave function + +of the system plus +the environment. + +And now we can evolve it. + +We can ask what happens? + +What is the wave +function time later? + +This can be exactly done by +time-dependent perturbation + +theory. + +And the result is +that the system + +will be in a superposition +of ground and excited state. + +And we want to calculate +the coefficients + +alpha prime and beta prime. + +And we still have +the vacuum state. + +But then we have the possibility +that a photon has been emitted. + +In that case we are +in the ground state. + +And the direct product +with the environment + +involves now the photon emitted +into a certain direction + +with wave vector k, with +the polarization epsilon. + +And we have coefficients +beta, k epsilon, + +and we have to sum over all +possibilities for the photon + +to be emitted. + +So we call this-- So the wave +function of the total system + +has now two parts. + +It's a wave function, +which I call psi 0. + +This is a wave +function which involves + +no photon in the environment. + +And the wave function +psi 1 involves + +one photon in the environment. + +So this is the [INAUDIBLE], +which seems very natural, + +but it's also-- you +could immediately + +prove that these are the +only possibilities, how + +the system can evolve. + +And we can verify this by using +time-dependent perturbation + +theory. + +It's actually almost +everyone of you + +has seen it in either 8.21 or in +a more basic course on quantum + +physics. + +It's time-dependent +perturbation theory + +for the emission of a photon. + +But usually when you see +those treatments there + +reservoir, the environment, +is not treated as explicitly + +as we do it here. + +The theory where this +is treated exactly + +in this way, how we need it, +is the Viegener Biscoff theory. + +Which is nothing else in +the perturbative approach, + +but it's really a +perturbation theory. + +Not just for the atomic system-- +how we sometimes present it + +in a simplified version-- +it's perturbation theory + +for the total wave function +of the complete system. + +Philmore? + +AUDIENCE: So you mentioned +the time interval [INAUDIBLE] + +is much smaller than +a lot of things. + +But you were ignoring, I take +it, the counter rotating terms? + +In which case we're still +at a large enough time + +step that's average +out, so to speak? + +I simply say this, +because I expected + +to be an e with a photon term. + +From the g going +up, so to speak. + +PROFESSOR: Yes. + +Well-- The counter +rotating term-- + +The first answer I +wanted to give you, + +no this is exact +perturbation theory. + +But I think I get +myself in trouble + +if I would allow-- I would get +myself in trouble if I would + +allow the time step to be +extremely short, because then + +I'm in shorter +than 1 over omega. + +Because during the +time 1 over omega, + +we have-- you can say we +have counter rotating terms. + +Or in other words, this +particle in the ground + +state during a +time 1 over omega, + +particle in the ground state can +emit a photon and reabsorb it. + +These are where +those weird diagrams + +with virtual states, +which we discussed earlier + +in this course. + +So I think I want to assume +here, which I haven't done, + +that the time step is larger +than omega to the minus 1. + +And as you know the +counter rotating term + +has a detuning delta, +which is 2 omega, + +so therefore it is excluded. + +Or in other words, when +we talk about photons + +sent into the +environment, we want + +to talk about real photons, +and not virtual photons. + +Yes, good point. + +OK. + +So if you do simple lowest order +time dependent perturbation + +theory, in the Viegener +Biscoff approach, + +you get an exact +result for beta prime. + +You find that beta prime +in this superposition + +is the original amplitude +beta, but it has decayed with e + +to the minus gamma over 2dt. + +And since we are only +interested in small time steps, + +we can do a linear +expansion of that. + +The probability, dp, that +a photon has been emitted + +is the norm of this +wave function psi 1. + +And this, using Viegener +Biscoff perturbation theory, + +is gamma dt times the +amplitude squared, + +that the system was +excited to begin with. + +And because of the conservation +of the norm, the wave function, + +the norm of the wave +function psi 0-- which + +is a wave function without +a photon being emitted-- + +is 1 minus dp. + +So what I'm telling +you here is that this + +is an exact result of +time-dependent perturbation + +theory. + +Often when this-- when textbooks +treat spontaneous emission, + +they're more interested +in getting Fermi's gold + +rule at this rate. + +But the same approach-- if +you just write it down-- + +tells you how the amplitude +in the excited state evolves. + +So therefore, what we learn +from perturbation theory, + +that alpha prime and beta prime, +the wave, the coefficients + +of the wave function, +without emission of a photon, + +this evolution of +the wave function + +occurs with a +non-emission Hamiltonian. + +And this non-emission +Hamiltonian + +is our Hamiltonian +for the atomic system. + +But then we have to account +for spontaneous decay, + +and this is done by +this non-emission part. + +So occasionally +you may have heard + +that people wave +their hands and say, + +your system is described +by a Hamiltonian, which + +has an imaginary part for decay. + +And this is sort of +phenomenological. + +This is definitely not +the case, because, even + +if you have a +Hamiltonian like this, + +a pure state would simply +decay and remain a pure state. + +What we are doing +here explicitly + +is we deal with probability +in the correct way. + +Every time the +system can branch out + +into different possibilities, +two different dimensions + +of the density matrix-- one +has probability delta p, + +one has probability +1 minus delta p-- + +and it is only the wave +function associated + +with probability 1 +minus delta p, which + +evolves with this Hamiltonian. + +So what I'm telling you +is the exact solution + +for the evolution +of the total system, + +in terms of a density matrix +for the atomic system. + +And this is exact. + +So that means we +can now-- write down + +the-- Just get some extra space. + +Oops. + +How does it do it? + +Nope So we have to +insert new page. + +Yep. + +OK. + +OK. + +So the procedure, how we +implement this exact solution + +of perturbation theory, +is the following. + +We have a time step delta t. + +We compute what +is the probability + +that a photon will be emitted. + +Then we need a ran-- Then we +need a random number generator. + +So we need a number +epsilon, which + +is a random number chosen +in the interval 0 and 1. + +If this random number turns +out to be smaller than delta p, + +then we continue our time +evolution on the computer. + +That psi is now in +the ground state, + +and maybe there is a laser +beam which excites it again. + +And such I will add a few +bells and whistles later. + +Otherwise psi, +our wave function, + +is now the wave function +which is the time evolution + +with a non-emission operator of +the original wave function psi. + +And since we have a +real wave function now + +with probability 1, we have to +re-normalize the wave function + +by this denominator. + +And then we execute +the next time step. + +This means go to 2 and +do the next time step. + +And then you have, so to speak, +if you do it many, many times, + +you get a time direct +trajectory of, so to speak, + +one experiment. + +And then you start again with +your system in a wave function + +psi, and you accumulate +a second experiment. + +And maybe you do it 10,000 +times to get enough statistics. + +And then you sum up, +you know, everything + +you want and calculate +all the expectation + +values you want to know +about your quantum system. + +So the claim is that this +method, called quantum Monte + +Carlo wave function +method, is fully + +equivalent to the +optical block equations. + +And I want to prove +it to you by showing + +that, if I take a density +matrix, which is an ensemble + +average, over many +realizations of those quantum + +Monte Carlo trajectories. + +That then this density matrix +follows the differential + +equation, which is your +optical block equation. + +And the proof is shown here. + +So what I told you is the +density matrix after time delta + +t, has now two matrix elements. + +One with probability +delta p, and this + +is-- photon has been emitted. + +System is in the ground state, +with probability 1 minus delta + +p. + +We evolve the quantum state +with a non-emission Hamiltonian. + +And then all what is done +in the next few steps we + +assume that delta t is small. + +We do a Taylor expansion +of the exponent. + +We neglect quadratic +terms in delta t, + +and then we come to this line. + +And if we write this as +rho of t plus delta t, + +minus the original +rho of t, we find + +that this follows differential +equation, which is exactly + +the optical block equations. + +So therefore what we +sort of implemented + +as a form of doing many, +many quantum measurements + +in the environment +is a procedure, + +which is rigorously the +same as the optical block + +equations, which we derived +using a master equation + +approach. + +OK. + +This method is very powerful +for the following reasons. + +If you simulate a density +matrix with, you know, + +an internal states, or external, +internal states-- I should've + +said with in quantum +states, you need + +n times n matrix elements, +which can become quite a memory + +hog for your computer. + +The wave function, at any given +moment, as only n components. + +So therefore there is a +computational advantage + +in using a stochastic +wave function + +approach over simulation +of the density matrix. + +The second thing is that a +lot of people, especially + +experimentalists, like +sort of this approach, + +because it reflects directly +what they do in the experiment. + +And I think it's pretty +clear that with this approach + +you can deal with a great +variety of situations. + +Let me just mention +two obvious extensions. + +One is polarization. + +A photon is detected. + +That means your random number +produced a number epsilon, + +which was smaller than delta p. + +At that point you can create +a second random number, + +which determines if your pull-- +if the photon has been detected + +with sigma plus, sigma +minus, or pi polarization. + +Or you can discuss recoil. + +If the photon is-- If +the photon is detected, + +you use-- you throw on +another random function + +generator, which determines what +the k vector of the photon is. + +So what direction each part +k the photon has taken, + +and this determines +now what is the recoil, + +the change in +momentum of your atom. + +So you see, kind +of, you can start + +with an atom at 0 momentum. + +You can see it emits +a photon, and then + +your computer always +makes a choice + +based on the random number. + +And then you say, +OK my photon has now + +received a recoil +kick at 45 degrees. + +Now your wave function of +the photon is such and such, + +and if you add a laser +to the Hamiltonian, + +the recoil may have kicked-- +may have Doppler shifted + +the resonance, but everything +is easily taken into account. + +So you see this quantum +Monte Carlo wave function + +method can easily be +extended to describe + +external degrees of freedom, +multiple laser fields, and all + +that. + +Any questions? + +OK. + +Let me now just +generalize the thought, + +but I think you know +already everything about it. + +We talked about the +master equation. + +We talked about the most +general master equation + +in the [INAUDIBLE] platform, +where those operators L + +are the jump operators. + +And the prominent +example for jump operator + +was the signal minus +operator, which + +takes a particle from the +excited state to the ground + +state. + +And this is the jump operator +for spontaneous emission. + +But you may have +many jump operators. + +May be spontaneous emission +of different photons + +with different +polarization and such. + +Or the cavity may lose +a photon, and then we + +have a jump operator +for the cavity. + +We went through that. + +Well that means +now in an exact way + +that the non-emission +Hamiltonian is + +the original Hamiltonian +with an imaginary part, which + +comes because of +those jump operators. + +And the general quantum Monte +Carlo wave function procedure + +is that first you ask, +has something happened? + +Has any jump happened? + +And this gives you the +probability delta p. + +And if-- If no +jump has happened, + +you just do a time +evolution with + +a non-emission Hamiltonian. + +But if a jump has +happened, then the jump + +is now-- the wave function is +projected by the jump operator. + +If you have a sigma +minus operator, + +it takes a particle +to the ground state. + +If you have several operators, +a different jump operator + +may take your particle +to another state. + +And you-- And you then +have a branching ratio + +that you know first +a jump has happened. + +And then the question is, +which jump has happened? + +And you just play the +probabilities game. + +So that you see that the quantum +Monte Carlo wave function + +method can be immediately +be generalized. + +So let me come back +to the special case + +of spontaneous emission. + +In that case, we have +only one jump operator, + +which is sigma minus. + +And the normalization is +the square root of gamma. + +And that actually means that +our quantum trajectory ground + +state, excited state, +is very simple. + +If you start with the system +100% in the excited state, + +it's very trivial what happens. + +Nothing happens. + +But if then the jump +occurs, the particle + +is in the ground state. + +Then nothing happens +then until infinite time. + +You then have to start-- +The next trajectory + +you start in the excited state. + +And this time, by chance of +the random number generator, + +the jump happens later. + +Another time the +jump happens earlier. + +And what you then have to +do is, you have to average, + +over all of those +realizations, what + +is the probability +for the particle + +to be in the excited state. + +And this is now your estimator +for the excited state diagonal + +matrix element of +the density matrix. + +And if you-- If you've +written your code correctly, + +you will find that you get a +wonderful exponential decay + +exactly as you have expected. + +Questions? + +Now-- Yes? + +Let-- Let me now +talk about dephasing. + +What I've shown you so far is +how we can unravel the density + +matrix in many +microscopic realizations. + +And I've given you +a specific example. + +We assume probability +for spontaneous emission, + +and with that we propagate +our wave function. + +But now I come to, sort of, +the nitty gritty details, + +or the dirty truth, that what +we have assumed is by no means + +unique. + +And I want to explain it to +you first by reminding you + +of a very, very nice homework +assignment you have solved. + +And this was about we have +optical block equations + +for the density matrix, +and the dense -- + +and the solution of the optical +block equation is that we have + +population damping +with a damping time t1. + +And the off diagonal +matrix elements + +are damped with a time t2. + +Remember if you've only +spontaneous emission t2 + +is 2 times t1. + +But we can have a lot of +other processes, which + +can lead to much, +much faster defacing + +time than the population, than +the time of population changes. + +And in your homework, you have +discussed three possibilities. + +One is, well, spontaneous +emission is energy loss. + +But you have discussed three +different possibilities for t2. + +One-- Three different +possibilities + +how dephasing, loss of +coherence, and phase damping + +can happen. + +And in this homework +assignment, you assumed either + +that there is a random phase, +that the elastic collision + +which project onto +the excited state, + +and then you got the most +crazy and artificial model. + +That every time, randomly, +the phase of the excited state + +flips form plus to minus. + +So if I would implement that +now, with a quantum Monte Carlo + +method, it would have +the following affect. + +And I hope you enjoy, sort of, +the graphical representation. + +You can really think about +it, that this is what happens. + +That this is what inside-- +what is inside the density + +matrices described +by this process. + +So let's assume we +have a system, which + +would be in a superposition +of ground and excited state. + +And that would mean +that in the left frame + +the dipole moment would +just rotate at the resonance + +frequency. + +It rotates, and it is a +rotating dipole moment, + +which emits coherent light. + +But now you assume that +you have a random phase. + +So if you add +random phases to it, + +maybe because you're +fluctuating magnetic fields, + +then the line becomes sort +of-- That doesn't look random, + +but you know what I mean. + +It becomes sort of jagged. + +The phase distribution +is still sort of there, + +but there is a +jitter on top of it. + +And as a result, the light +emitted by this dipole + +is spectrally broadened + +Well in your second +model you assumed + +that-- with a +certain randomness, + +with a certain time +constant-- there's + +an elastic collision in +the excited state, which + +projects the system +into the excited state. + +At this moment there is no +superposition state anymore, + +and the dipole moment is 0. + +So that's what you assume. + +Or when you have +random phase flips, + +you assumed that +suddenly this kind + +of data to data +ministic sine function + +suddenly jumps corresponding +to a minus sign in the excited + +state. + +And depending where +you are in the cycle, + +it creates jumps +at random places. + +And the question of course is, +if all those three processes-- + +and that's what you showed +in your homework-- lead + +to the same density matrix, +which one is correct? + +Which one is real-- +is really realized + +in an experiment on a +system which is described + +by this kind of damping, or +by the optical block equation? + +So you can say all or none. + +Well you can assume +what you want, + +it doesn't make a difference. + +And the reason is +actually profound. + +The reason-- The reason +is profound in that sense + +that the way-- our goal +was to have an open quantum + +system, which is the +atomic system, interacting + +with a reservoir. + +But the way, how we +phrase the question, + +we are only interested in +what the atomic system does. + +We didn't do extra measurements +on the environment. + +The environment was just a dump +for photons; a dump for energy; + +a dump for whatever we assumed +in our dephasing mechanism. + +So let me just take the +example of putting photons + +into the environment. + +And this is described by +a certain damping term, + +but there is an ambiguity. + +And this is shown here. + +If you evolve the system-- our, +our atomic system, the density + +matrix evolves, but the +environment sort of also + +evolves. + +And for instance here, +the unitary time evolution + +has taken the excitation +from the atom, + +and we have emitted a +photon into the environment. + +And you remember we got +the optical block equation + +by doing the partial trace +here, and just focusing + +on the atomic part. + +But now wait a moment. + +If we trace out +the environment, we + +can trace it out in a +different basis set. + +Remember, I showed you the +quantum Monte Carlo wave + +function, we emit a photon. + +But we can, for instance, +detect the photon + +in our gedanken experiment. + +We can detect it with +linear polarization + +or with circular polarization. + +If you have a situation where +you have a-- an s state, which + +decays to a p state, sigma plus +takes you to m equals plus 1, + +sigma minus takes you +to m equals minus 1. + +So therefore, if photon is +emitted in you quantum Monte + +Carlo procedure, you would +say, now the atom mean + +is in the plus 1 +state, or now the atom + +is in the minus 1 state. + +But if you detect +linearly polarized light, + +by just putting a +polarizer here-- + +and this is a unitary +transformation in front + +of your detector-- you +would no longer project + +the atomic system on +plus 1 at minus 1, + +you would project +it on m equals 0 + +or whatever is connected +to the linear polarization + +of the measurement. + +So therefore, if +you simply assume + +that something has been +dumped in the environment, + +and can be used for +measurement, there + +are many ways, many +unitary transformations, + +what you can do to the +information, to the energy, + +to the photons, which have been +dumped into the environment. + +And each of them will lead to +a very different trajectory + +in your quantum +Monte Carlo system. + +So therefore if you +just dump the photons + +and not measure them, +you have equal rights + +to assume that your quantum +Monte Carlo wave function jumps + +to states which correspond +to a circular basis, + +or jump to states which +correspond to linear basis. + +And there's many, +many possibilities. + +But each of those possibilities +is 100% correct unravelling + +of the density matrix. + +And if you just do it right, +assume that the measurement is + +done in a certain basis, and +you're consistent with it, + +you will 100% correctly +describe the time evolution + +of your atomic system. + +Any questions? + +Philmore? + +AUDIENCE: Again with the dt. + +I'm just curious that we take +a [INAUDIBLE] very short, + +but why don't you +run into something + +like the quantum Zeno effect? + +Where if every evolution +is initially quadratic, + +like the [INAUDIBLE] frequency, +you take very short dt-- + +short measuring system-- +Shouldn't for a choice + +of sufficiently short dt you, +you know the simulation would + +give you strange +results, because of-- + +PROFESSOR: [SIGHS] + +AUDIENCE: --some sort of +quantum Zeno effect there? + +PROFESSOR: That's a very +deep question, Philmore. + +And I, I want to +think about it more, + +but I think I've +excluded that by saying + +that the time step, dt, is +larger than the correlation + +time of the environment. + +So I'm doing some kind +of Markov approximation + +with the environment, where +s-- the quadratic part + +of the behavior +is a coherent time + +evolution, for very short time +steps a wave function evolves + +quadratically, but this part +is a coherent evolution. + +And that's related to the fact +that an atom can emit a photon, + +but in the very first +moment, before the vacuum + +has transported it away, it +can take the photon back. + +And the result of that is +that at very short times + +the exponential decay doesn't +start out exponentially, + +it starts out a +little bit flatter. + +We get the exponential decay, +we get Fermi's golden rule, + +and we get optical blocks +equations only if your time + +step is larger than +the correlation + +time of the reservoir. + +And the fact, you remember +when we derived the master + +equation we had to say we do +a step, which is sufficiently + +small for the dynamics +of the atomic system, + +but sufficiently large, that we +are not getting into any memory + +affects of the reservoir. + +And we've done the +same assumption here. + +Other questions? + +Nicky? + +AUDIENCE: Just confused. + +We are not always say +the environment measures + +the system in range at +time intervals, delta t, + +which are large compared +to the correlation time? + +What's more [INAUDIBLE] +the evolution of the atom. + +But now everyone isn't +that defected the Markov + +approximation we've made when +we derived the master equation? + +And I was just wondering +for just-- [INAUDIBLE] + +did you derive it by +making the master equation? + +Maybe we don't +actually need-- Maybe + +we don't need the idea +of constantly measuring. + +Maybe a physical interpretation +of the Markov approximation. + +PROFESSOR: Oh yes, +exactly, Nicky. + +I still think you said it +really very, very nicely. + +We derived a master +equation just + +by assuming that the system, +you know, takes a photon. + +And past the correlation +time, the photon + +is taken for good +by the environment. + +And with a Markov +approximation, we formalized + +that there is no memory +affect, the photon + +is not stored like in a cavity. + +The photon has disappeared. + +And by saying that this +time is very short, + +this was a Markov approximation +in the derivation of the master + +equation. + +But that also means, if +the photon has disappeared, + +has separated from +the atomic system, + +we are now free to +make a measurement. + +And of course it +shouldn't matter + +whether we make the +measurement or not. + +But what I was able +to do today is, + +I was making now the +assumption, let's assume + +we make a measurement. + +We measure all the photons +which have been emitted, + +and the measurement +is probabilistic. + +And we fold this +probabilistic evolution + +into our quantum system. + +And what we obtained was +exactly the same time evolution + +for the density matrix as we +got from the master equation. + +So in other words, +this should you + +that interactions +with an open quantum + +system, where irreversibly +energy, photons, angular + +momentum, or whatever-- +flows into the environment. + +Once it has flown +into the environment, + +you can measure it. + +And you get all the stochastics +from the measurement. + +But even if you +don't measure it, + +you get exactly the +same stochastics as + +if you had measured it. + +It's all the same. + +Jenny? + +AUDIENCE: Now that +I think about it, + +it seems sort of weird to me +that we've-- that we're making + +these measurements, or +lack of measurements, + +these interactions, +at regular intervals. + +And not-- + +PROFESSOR: It doesn't +really matter. + +All we-- All we +have to make is-- + +You could actually make +delta t a random variable. + +It wouldn't change anything. + +The only thing we +have to make sure + +is we have to make the +time interval short enough + +that we don't have, maybe, two +photons emitted in that time. + +We just want to +make sure that it's + +a simple probabilistic +branching, yes or no. + +And that's the only +requirement here. + +AUDIENCE: Is this a formula +or is it based on time? + +You say that would +be the wave function + +evolving and then collapse. + +And that's-- This is what-- +Where the measurement comes in. + +The equivalent, so now +say, the equivalent + +is a wave function +evolved in a collapse, + +when you make a measurement +you say that after it evolves. + +So is it possible +that it could also + +have-- like evolves +some kind of formalism? + +Like this? + +Where there is an operator? + +Because still like even though +the density matrix operator, + +maybe it is kind of like-- +[INAUDIBLE] describes a state. + +PROFESSOR: I haven't +seen it, Mark, + +but I'm absolutely certain +that you could describe + +the same physics in +the Heisenberg picture, + +where the time evolution +is with operators. + +Because what we have here is, +we have a time step, delta t, + +where the system evolves as +an isolated quantum system, + +and then we measure again. + +And so, I think if you +would use operator equation, + +you would have an +evolution of the operator + +with the same Hamiltonian, which +is non-emission Hamiltonian. + +And then the measurement would +do some form of projection. + +I have to think about it, +what the projection would + +be in terms of operators. + +But my gut feeling is, you can +always take the transformation + +where you put the time +dependence into the operators, + +and not in the wave function. + +On the other hand, I have +some little bit misgivings + +about that, because the quantum +Monte Carlo wave function + +was really developed in order +not to deal with matrices, + +not to deal with something +which is dimension n times in, + +if n is the number of +components of the wave function. + +It was specifically formulated +to have the simpler description + +with n coefficients +for the wave function. + +But conceptually, I +think, it is evolution + +with a Hamiltonian measurement. + +Evolution with a +Hamiltonian measurement. + +And I assume this could +also be done with operators. + +Nancy? + +AUDIENCE: Suddenly like +[INAUDIBLE] but when + +we've-- these simulations +are actively done, + +how important is the randomness? + +Like up to epsilon [INAUDIBLE] +because no computer is actually + +emitting random numbers. + +PROFESSOR: Well I think how +random a random number has + +to be is really dealt +with in computer science + +and mathematics. + +AUDIENCE: But due +to our reserves + +we always get this +exponential behavior? + +PROFESSOR: I don't +know the answer. + +I mean here, +conceptionally, it should + +be completely random number. + +And I think that algorithms, +which even which produce + +pseudo random numbers, but if +the pseudo is close enough, + +if there is a recurrence +time of your random number-- + +if your random number-- +your series of random number + +repeat itself after several +billion random numbers, + +this gives you a +small error bar. + +And if you don't-- If you'd +only do a limited sampling, + +a limited number of +time trajectories, + +I don't think it matters. + +Of course if you want to +have ultimate precision, + +then also the precision +of the random number + +may enter through the +backdoor at some point. + +AUDIENCE: [INAUDIBLE] +lack of simulation + +of the photons emitted? + +But if we know the +photons emitted, + +if we have that information, +then we can decide [INAUDIBLE]. + +PROFESSOR: That's correct. + +If we-- If we would know-- +If we would know more + +about the environment, +if we would + +say we measured the +photons in a certain basis, + +or when energy is dumped +in the environment + +by a dephasing mechanism, +we look at the environment. + +Then, of course, we would +add extra information to it, + +and then certain +quantum trajectories + +would reflect the extra +knowledge we have. + +And of course, we would +then describe everything + +in this basis. + +On the other hand, +what you should + +learn from this is once the +information, once the photon + +has escaped, it doesn't +matter for the time evolution + +of your atomic system, in which +basis you measure the photon. + +So the evolution of the +atomic system itself-- + +at least when you averaged-- +is unaffected by the basis. + +However if you make a +coincidence measurement, + +that you say your atoms +which has emitted, + +is still flying through +your vacuum chamber, + +and now you figure +out the photon + +is emitted as circularly +polarized light. + +Then of course you know that +this atom, which is still + +available, has emitted +circularly polarized light. + +And then you have actually +obtained extra information + +about your atom. + +In other words, the +photon in the atom + +was entangled, like a Bell pair. + +And if you now do a measurement +on one part of the Bell pair, + +you know more about +the other part. + +But this is just how +quantum physics works. + +If you don't use this +information for anything, + +then you could have-- you +could have as well not measured + +the polarization. + +And it would have no effect +on the atomic density matrix. + +OK that's it for today. + +We have class at the +usual time on Wednesday. \ No newline at end of file diff --git a/w-zdunIsHUU.txt b/w-zdunIsHUU.txt new file mode 100644 index 0000000000000000000000000000000000000000..9abac0798aa2068b7a17dae40a911f087204046e --- /dev/null +++ b/w-zdunIsHUU.txt @@ -0,0 +1,275 @@ +align:start position:0% + +um the advice I would give to Educators + + align:start position:0% +um the advice I would give to Educators + + + align:start position:0% +um the advice I would give to Educators +who are teaching this course would be to + + align:start position:0% +who are teaching this course would be to + + + align:start position:0% +who are teaching this course would be to +um first the class had a very technical + + align:start position:0% +um first the class had a very technical + + + align:start position:0% +um first the class had a very technical +component in terms of the readings uh + + align:start position:0% +component in terms of the readings uh + + + align:start position:0% +component in terms of the readings uh +maybe not it had a + + align:start position:0% +maybe not it had a + + + align:start position:0% +maybe not it had a +very one of the components of the class + + align:start position:0% +very one of the components of the class + + + align:start position:0% +very one of the components of the class +was very focused on having greeings that + + align:start position:0% +was very focused on having greeings that + + + align:start position:0% +was very focused on having greeings that +really opened up the discussions uh a + + align:start position:0% +really opened up the discussions uh a + + + align:start position:0% +really opened up the discussions uh a +lot of these were taken from different + + align:start position:0% +lot of these were taken from different + + + align:start position:0% +lot of these were taken from different +sources different some from theoretical + + align:start position:0% +sources different some from theoretical + + + align:start position:0% +sources different some from theoretical +Linguistics to just General readings + + align:start position:0% +Linguistics to just General readings + + + align:start position:0% +Linguistics to just General readings +from like things like James Baldwin uh + + align:start position:0% +from like things like James Baldwin uh + + + align:start position:0% +from like things like James Baldwin uh +or uh open up ads from newspapers um I + + align:start position:0% +or uh open up ads from newspapers um I + + + align:start position:0% +or uh open up ads from newspapers um I +think having like a strong uh I think + + align:start position:0% +think having like a strong uh I think + + + align:start position:0% +think having like a strong uh I think +having a lot of reading material that + + align:start position:0% +having a lot of reading material that + + + align:start position:0% +having a lot of reading material that +can exract from different places but + + align:start position:0% +can exract from different places but + + + align:start position:0% +can exract from different places but +that also is like very good or that + + align:start position:0% +that also is like very good or that + + + align:start position:0% +that also is like very good or that +gives to a lot of thinking I think + + align:start position:0% +gives to a lot of thinking I think + + + align:start position:0% +gives to a lot of thinking I think +that's something that really was one of + + align:start position:0% +that's something that really was one of + + + align:start position:0% +that's something that really was one of +the best things I like of this course + + align:start position:0% +the best things I like of this course + + + align:start position:0% +the best things I like of this course +the second was is how this course is + + align:start position:0% +the second was is how this course is + + + align:start position:0% +the second was is how this course is +also a place for dialogue to examine + + align:start position:0% +also a place for dialogue to examine + + + align:start position:0% +also a place for dialogue to examine +ourselves we all speak a language uh we + + align:start position:0% +ourselves we all speak a language uh we + + + align:start position:0% +ourselves we all speak a language uh we +all have a sense of identity + + align:start position:0% +all have a sense of identity + + + align:start position:0% +all have a sense of identity +so thinking about all these things with + + align:start position:0% +so thinking about all these things with + + + align:start position:0% +so thinking about all these things with +from from our point of view or from our + + align:start position:0% +from from our point of view or from our + + + align:start position:0% +from from our point of view or from our +lives um is very important so being able + + align:start position:0% +lives um is very important so being able + + + align:start position:0% +lives um is very important so being able +to have a space of discussion a space in + + align:start position:0% +to have a space of discussion a space in + + + align:start position:0% +to have a space of discussion a space in +which people can tell their own stories + + align:start position:0% +which people can tell their own stories + + + align:start position:0% +which people can tell their own stories +probably for like most a good part of + + align:start position:0% +probably for like most a good part of + + + align:start position:0% +probably for like most a good part of +the class I think that's one of the + + align:start position:0% +the class I think that's one of the + + + align:start position:0% +the class I think that's one of the +essential parts to making this a truly + + align:start position:0% +essential parts to making this a truly + + + align:start position:0% +essential parts to making this a truly +learning experience that helps you read + + align:start position:0% +learning experience that helps you read + + + align:start position:0% +learning experience that helps you read +the word and read the world and not just + + align:start position:0% +the word and read the world and not just + + + align:start position:0% +the word and read the world and not just +the word \ No newline at end of file diff --git a/w6vrSsNPE00.txt b/w6vrSsNPE00.txt new file mode 100644 index 0000000000000000000000000000000000000000..b9150176bde74b2e5c0547a7c37d9667c98efa37 --- /dev/null +++ b/w6vrSsNPE00.txt @@ -0,0 +1,7171 @@ +align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +down. + + align:start position:0% +down. + + + align:start position:0% +down. +Hey + + align:start position:0% +Hey + + + align:start position:0% +Hey +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% + + + + align:start position:0% + +Hi, in our last session we considered + + align:start position:0% +Hi, in our last session we considered + + + align:start position:0% +Hi, in our last session we considered +one technique for the analysis of + + align:start position:0% +one technique for the analysis of + + + align:start position:0% +one technique for the analysis of +nonlinear systems that of linearization. + + align:start position:0% +nonlinear systems that of linearization. + + + align:start position:0% +nonlinear systems that of linearization. +Linearization basically involves + + align:start position:0% +Linearization basically involves + + + align:start position:0% +Linearization basically involves +approximating a nonlinear system by a + + align:start position:0% +approximating a nonlinear system by a + + + align:start position:0% +approximating a nonlinear system by a +linear one that's valid with the + + align:start position:0% +linear one that's valid with the + + + align:start position:0% +linear one that's valid with the +approximation valid over some restricted + + align:start position:0% +approximation valid over some restricted + + + align:start position:0% +approximation valid over some restricted +range of operating conditions. Today I'd + + align:start position:0% +range of operating conditions. Today I'd + + + align:start position:0% +range of operating conditions. Today I'd +like to look at another technique for + + align:start position:0% +like to look at another technique for + + + align:start position:0% +like to look at another technique for +the analysis of of nonlinear systems + + align:start position:0% +the analysis of of nonlinear systems + + + align:start position:0% +the analysis of of nonlinear systems +that of describing functions. + + align:start position:0% +that of describing functions. + + + align:start position:0% +that of describing functions. +Describing functions are an outgrowth of + + align:start position:0% +Describing functions are an outgrowth of + + + align:start position:0% +Describing functions are an outgrowth of +an attempt to apply the familiar + + align:start position:0% +an attempt to apply the familiar + + + align:start position:0% +an attempt to apply the familiar +frequency domain techniques that work so + + align:start position:0% +frequency domain techniques that work so + + + align:start position:0% +frequency domain techniques that work so +well for linear systems to nonlinear + + align:start position:0% +well for linear systems to nonlinear + + + align:start position:0% +well for linear systems to nonlinear +systems to find extensions that work for + + align:start position:0% +systems to find extensions that work for + + + align:start position:0% +systems to find extensions that work for +at least certain classes of nonlinear + + align:start position:0% +at least certain classes of nonlinear + + + align:start position:0% +at least certain classes of nonlinear +systems. + + align:start position:0% + + + + align:start position:0% + +Describing functions can in fact be used + + align:start position:0% +Describing functions can in fact be used + + + align:start position:0% +Describing functions can in fact be used +to predict behavior under syosoidal + + align:start position:0% +to predict behavior under syosoidal + + + align:start position:0% +to predict behavior under syosoidal +steady state conditions. And we can + + align:start position:0% +steady state conditions. And we can + + + align:start position:0% +steady state conditions. And we can +determine things like the gain, the + + align:start position:0% +determine things like the gain, the + + + align:start position:0% +determine things like the gain, the +closed loop gain of a nonlinear system + + align:start position:0% +closed loop gain of a nonlinear system + + + align:start position:0% +closed loop gain of a nonlinear system +as a function of frequency and as we'll + + align:start position:0% +as a function of frequency and as we'll + + + align:start position:0% +as a function of frequency and as we'll +see as a function of the input + + align:start position:0% +see as a function of the input + + + align:start position:0% +see as a function of the input +amplitude, the driving amplitude applied + + align:start position:0% +amplitude, the driving amplitude applied + + + align:start position:0% +amplitude, the driving amplitude applied +to the system. However, that sort of an + + align:start position:0% +to the system. However, that sort of an + + + align:start position:0% +to the system. However, that sort of an +analysis is quite difficult by + + align:start position:0% +analysis is quite difficult by + + + align:start position:0% +analysis is quite difficult by +describing functions. In fact, generally + + align:start position:0% +describing functions. In fact, generally + + + align:start position:0% +describing functions. In fact, generally +it leads to rather involved numerical + + align:start position:0% +it leads to rather involved numerical + + + align:start position:0% +it leads to rather involved numerical +calculations. I guess my own feeling is + + align:start position:0% +calculations. I guess my own feeling is + + + align:start position:0% +calculations. I guess my own feeling is +that we probably ought to avoid + + align:start position:0% +that we probably ought to avoid + + + align:start position:0% +that we probably ought to avoid +approximate techniques that involve very + + align:start position:0% +approximate techniques that involve very + + + align:start position:0% +approximate techniques that involve very +difficult numerical manipulations. If + + align:start position:0% +difficult numerical manipulations. If + + + align:start position:0% +difficult numerical manipulations. If +we're going to go to a machine for + + align:start position:0% +we're going to go to a machine for + + + align:start position:0% +we're going to go to a machine for +computation anyway, we can really get an + + align:start position:0% +computation anyway, we can really get an + + + align:start position:0% +computation anyway, we can really get an +exact numerical solution to the problem. + + align:start position:0% +exact numerical solution to the problem. + + + align:start position:0% +exact numerical solution to the problem. +So there's no need for approximations. + + align:start position:0% +So there's no need for approximations. + + + align:start position:0% +So there's no need for approximations. +However, one case of interest for which + + align:start position:0% +However, one case of interest for which + + + align:start position:0% +However, one case of interest for which +describing functions work very very well + + align:start position:0% +describing functions work very very well + + + align:start position:0% +describing functions work very very well +is that of the oscillator. We can look + + align:start position:0% +is that of the oscillator. We can look + + + align:start position:0% +is that of the oscillator. We can look +at a feedback system and we can find out + + align:start position:0% +at a feedback system and we can find out + + + align:start position:0% +at a feedback system and we can find out +if the system is going to oscillate and + + align:start position:0% +if the system is going to oscillate and + + + align:start position:0% +if the system is going to oscillate and +if it is going to oscillate we can + + align:start position:0% +if it is going to oscillate we can + + + align:start position:0% +if it is going to oscillate we can +discover the amplitude of the + + align:start position:0% +discover the amplitude of the + + + align:start position:0% +discover the amplitude of the +oscillation and the frequency of the + + align:start position:0% +oscillation and the frequency of the + + + align:start position:0% +oscillation and the frequency of the +oscillation and generally the place that + + align:start position:0% +oscillation and generally the place that + + + align:start position:0% +oscillation and generally the place that +I have used describing functions in my + + align:start position:0% +I have used describing functions in my + + + align:start position:0% +I have used describing functions in my +own work is for this sort of analysis + + align:start position:0% +own work is for this sort of analysis + + + align:start position:0% +own work is for this sort of analysis +for looking at the behavior of + + align:start position:0% +for looking at the behavior of + + + align:start position:0% +for looking at the behavior of +oscillators and I think the examples + + align:start position:0% +oscillators and I think the examples + + + align:start position:0% +oscillators and I think the examples +that we'll do later on will demonstrate + + align:start position:0% +that we'll do later on will demonstrate + + + align:start position:0% +that we'll do later on will demonstrate +this aspect of the use of describing + + align:start position:0% +this aspect of the use of describing + + + align:start position:0% +this aspect of the use of describing +functions. + + align:start position:0% +functions. + + + align:start position:0% +functions. +Let's see how describing functions are + + align:start position:0% +Let's see how describing functions are + + + align:start position:0% +Let's see how describing functions are +developed. + + align:start position:0% +developed. + + + align:start position:0% +developed. +Remember how we define the transfer + + align:start position:0% +Remember how we define the transfer + + + align:start position:0% +Remember how we define the transfer +function of a linear system. Suppose we + + align:start position:0% +function of a linear system. Suppose we + + + align:start position:0% +function of a linear system. Suppose we +excite a linear system with an input + + align:start position:0% +excite a linear system with an input + + + align:start position:0% +excite a linear system with an input +syosoid vi sin omega t and we allow the + + align:start position:0% +syosoid vi sin omega t and we allow the + + + align:start position:0% +syosoid vi sin omega t and we allow the +system to reach steady state. In other + + align:start position:0% +system to reach steady state. In other + + + align:start position:0% +system to reach steady state. In other +words, we wait until all of the startup + + align:start position:0% +words, we wait until all of the startup + + + align:start position:0% +words, we wait until all of the startup +transients have died out. And under + + align:start position:0% +transients have died out. And under + + + align:start position:0% +transients have died out. And under +those conditions, of course, if the + + align:start position:0% +those conditions, of course, if the + + + align:start position:0% +those conditions, of course, if the +system is linear, the output again will + + align:start position:0% +system is linear, the output again will + + + align:start position:0% +system is linear, the output again will +be a syosoid at the same frequency as + + align:start position:0% +be a syosoid at the same frequency as + + + align:start position:0% +be a syosoid at the same frequency as +the input. And the only difference + + align:start position:0% +the input. And the only difference + + + align:start position:0% +the input. And the only difference +between the input and the output will be + + align:start position:0% +between the input and the output will be + + + align:start position:0% +between the input and the output will be +first of all a possible scaling VO may + + align:start position:0% +first of all a possible scaling VO may + + + align:start position:0% +first of all a possible scaling VO may +be different than the amplitude VI. And + + align:start position:0% +be different than the amplitude VI. And + + + align:start position:0% +be different than the amplitude VI. And +a phase shift between the output and the + + align:start position:0% +a phase shift between the output and the + + + align:start position:0% +a phase shift between the output and the +input. In other words, the output + + align:start position:0% +input. In other words, the output + + + align:start position:0% +input. In other words, the output +syosoid may be displaced by some amount + + align:start position:0% +syosoid may be displaced by some amount + + + align:start position:0% +syosoid may be displaced by some amount +theta relative to the input syosoid. + + align:start position:0% +theta relative to the input syosoid. + + + align:start position:0% +theta relative to the input syosoid. +If we characterize the linear element by + + align:start position:0% +If we characterize the linear element by + + + align:start position:0% +If we characterize the linear element by +its transfer function G of S and + + align:start position:0% +its transfer function G of S and + + + align:start position:0% +its transfer function G of S and +evaluate that for S= J omega, we recall + + align:start position:0% +evaluate that for S= J omega, we recall + + + align:start position:0% +evaluate that for S= J omega, we recall +that the ratio of the output magnitude + + align:start position:0% +that the ratio of the output magnitude + + + align:start position:0% +that the ratio of the output magnitude +to the input magnitude, the quantity VO + + align:start position:0% +to the input magnitude, the quantity VO + + + align:start position:0% +to the input magnitude, the quantity VO +over VI in our notation is equal to the + + align:start position:0% +over VI in our notation is equal to the + + + align:start position:0% +over VI in our notation is equal to the +magnitude of the complex variable G of J + + align:start position:0% +magnitude of the complex variable G of J + + + align:start position:0% +magnitude of the complex variable G of J +omega. + + align:start position:0% +omega. + + + align:start position:0% +omega. +And the angle between the output and the + + align:start position:0% +And the angle between the output and the + + + align:start position:0% +And the angle between the output and the +input syocides is simply equal to the + + align:start position:0% +input syocides is simply equal to the + + + align:start position:0% +input syocides is simply equal to the +angle of the complex variable g of j + + align:start position:0% +angle of the complex variable g of j + + + align:start position:0% +angle of the complex variable g of j +omega. + + align:start position:0% +omega. + + + align:start position:0% +omega. +Now let's see what happens if we have a + + align:start position:0% +Now let's see what happens if we have a + + + align:start position:0% +Now let's see what happens if we have a +nonlinear system. Let's first consider + + align:start position:0% +nonlinear system. Let's first consider + + + align:start position:0% +nonlinear system. Let's first consider +systems which don't rectify. So when we + + align:start position:0% +systems which don't rectify. So when we + + + align:start position:0% +systems which don't rectify. So when we +put in a a syosoidal signal the output + + align:start position:0% +put in a a syosoidal signal the output + + + align:start position:0% +put in a a syosoidal signal the output +remains zero mean. + + align:start position:0% +remains zero mean. + + + align:start position:0% +remains zero mean. +And let's also assume that we introduce + + align:start position:0% +And let's also assume that we introduce + + + align:start position:0% +And let's also assume that we introduce +no subharmonics + + align:start position:0% +no subharmonics + + + align:start position:0% +no subharmonics +from our our system. + + align:start position:0% +from our our system. + + + align:start position:0% +from our our system. +If that's the case and we apply a test + + align:start position:0% +If that's the case and we apply a test + + + align:start position:0% +If that's the case and we apply a test +signal to a nonlinear element where the + + align:start position:0% +signal to a nonlinear element where the + + + align:start position:0% +signal to a nonlinear element where the +test signal is a sinosoid at frequency + + align:start position:0% +test signal is a sinosoid at frequency + + + align:start position:0% +test signal is a sinosoid at frequency +omega with amplitude capital E, we + + align:start position:0% +omega with amplitude capital E, we + + + align:start position:0% +omega with amplitude capital E, we +obtain an output and we're able to + + align:start position:0% +obtain an output and we're able to + + + align:start position:0% +obtain an output and we're able to +represent that output by a forier + + align:start position:0% +represent that output by a forier + + + align:start position:0% +represent that output by a forier +series. I've said that the element does + + align:start position:0% +series. I've said that the element does + + + align:start position:0% +series. I've said that the element does +not rectify. So the output contains no + + align:start position:0% +not rectify. So the output contains no + + + align:start position:0% +not rectify. So the output contains no +DC term and similarly there's no + + align:start position:0% +DC term and similarly there's no + + + align:start position:0% +DC term and similarly there's no +subharmonic generation. Consequently the + + align:start position:0% +subharmonic generation. Consequently the + + + align:start position:0% +subharmonic generation. Consequently the +first term in the forier series for the + + align:start position:0% +first term in the forier series for the + + + align:start position:0% +first term in the forier series for the +output signal is at omega and + + align:start position:0% +output signal is at omega and + + + align:start position:0% +output signal is at omega and +consequently we can express the output + + align:start position:0% +consequently we can express the output + + + align:start position:0% +consequently we can express the output +signal as some constant b1 * sin omega t + + align:start position:0% +signal as some constant b1 * sin omega t + + + align:start position:0% +signal as some constant b1 * sin omega t +plus another constant a1 * cosine omega + + align:start position:0% +plus another constant a1 * cosine omega + + + align:start position:0% +plus another constant a1 * cosine omega +t. And then we get all the higher order + + align:start position:0% +t. And then we get all the higher order + + + align:start position:0% +t. And then we get all the higher order +terms in the forier series. Uh b2 sin 2 + + align:start position:0% +terms in the forier series. Uh b2 sin 2 + + + align:start position:0% +terms in the forier series. Uh b2 sin 2 +omega t plus a2 cosine 2 omega t and so + + align:start position:0% +omega t plus a2 cosine 2 omega t and so + + + align:start position:0% +omega t plus a2 cosine 2 omega t and so +forth. + + align:start position:0% +forth. + + + align:start position:0% +forth. +And what we do is define a describing + + align:start position:0% +And what we do is define a describing + + + align:start position:0% +And what we do is define a describing +function which is in general a function + + align:start position:0% +function which is in general a function + + + align:start position:0% +function which is in general a function +now of e and omega uh as being equal to + + align:start position:0% +now of e and omega uh as being equal to + + + align:start position:0% +now of e and omega uh as being equal to +the gain and the angle of the + + align:start position:0% +the gain and the angle of the + + + align:start position:0% +the gain and the angle of the +fundamental component of the output + + align:start position:0% +fundamental component of the output + + + align:start position:0% +fundamental component of the output +relative to the input. So we define our + + align:start position:0% +relative to the input. So we define our + + + align:start position:0% +relative to the input. So we define our +magnitude the magnitude of the + + align:start position:0% +magnitude the magnitude of the + + + align:start position:0% +magnitude the magnitude of the +describing function g subd which may of + + align:start position:0% +describing function g subd which may of + + + align:start position:0% +describing function g subd which may of +course be a function of both e and omega + + align:start position:0% +course be a function of both e and omega + + + align:start position:0% +course be a function of both e and omega +as simply being equal to the amplitude + + align:start position:0% +as simply being equal to the amplitude + + + align:start position:0% +as simply being equal to the amplitude +of the fundamental component of the + + align:start position:0% +of the fundamental component of the + + + align:start position:0% +of the fundamental component of the +output. That's a1^ 2 + b1^ 2 to the 1/2 + + align:start position:0% +output. That's a1^ 2 + b1^ 2 to the 1/2 + + + align:start position:0% +output. That's a1^ 2 + b1^ 2 to the 1/2 +uh that's the magnitude of the + + align:start position:0% +uh that's the magnitude of the + + + align:start position:0% +uh that's the magnitude of the +fundamental component of the output + + align:start position:0% +fundamental component of the output + + + align:start position:0% +fundamental component of the output +divided by the magnitude of the input. + + align:start position:0% +divided by the magnitude of the input. + + + align:start position:0% +divided by the magnitude of the input. +So the physical significance of the + + align:start position:0% +So the physical significance of the + + + align:start position:0% +So the physical significance of the +magnitude of the describing function is + + align:start position:0% +magnitude of the describing function is + + + align:start position:0% +magnitude of the describing function is +it that it's the gain from the input + + align:start position:0% +it that it's the gain from the input + + + align:start position:0% +it that it's the gain from the input +amplitude to the fundamental component + + align:start position:0% +amplitude to the fundamental component + + + align:start position:0% +amplitude to the fundamental component +of the output. Again let me emphasize + + align:start position:0% +of the output. Again let me emphasize + + + align:start position:0% +of the output. Again let me emphasize +that for a nonlinear system or a + + align:start position:0% +that for a nonlinear system or a + + + align:start position:0% +that for a nonlinear system or a +nonlinear element the quote gain in a + + align:start position:0% +nonlinear element the quote gain in a + + + align:start position:0% +nonlinear element the quote gain in a +describing function sense of course may + + align:start position:0% +describing function sense of course may + + + align:start position:0% +describing function sense of course may +be dependent on the amplitude of the + + align:start position:0% +be dependent on the amplitude of the + + + align:start position:0% +be dependent on the amplitude of the +signal that we apply to the + + align:start position:0% +signal that we apply to the + + + align:start position:0% +signal that we apply to the +nonlinearity. We recognize that for a + + align:start position:0% +nonlinearity. We recognize that for a + + + align:start position:0% +nonlinearity. We recognize that for a +linear element that's not possible. The + + align:start position:0% +linear element that's not possible. The + + + align:start position:0% +linear element that's not possible. The +gain of the linear element is only a + + align:start position:0% +gain of the linear element is only a + + + align:start position:0% +gain of the linear element is only a +function of frequency. + + align:start position:0% +function of frequency. + + + align:start position:0% +function of frequency. +Similarly, we define the angle of our + + align:start position:0% +Similarly, we define the angle of our + + + align:start position:0% +Similarly, we define the angle of our +describing function in direct parallel + + align:start position:0% +describing function in direct parallel + + + align:start position:0% +describing function in direct parallel +to the angle of a linear transfer + + align:start position:0% +to the angle of a linear transfer + + + align:start position:0% +to the angle of a linear transfer +function as simply being equal to the + + align:start position:0% +function as simply being equal to the + + + align:start position:0% +function as simply being equal to the +arc tangent of a1 over b1. If we look at + + align:start position:0% +arc tangent of a1 over b1. If we look at + + + align:start position:0% +arc tangent of a1 over b1. If we look at +that, that's the relative sh phase shift + + align:start position:0% +that, that's the relative sh phase shift + + + align:start position:0% +that, that's the relative sh phase shift +of the fundamental component of the + + align:start position:0% +of the fundamental component of the + + + align:start position:0% +of the fundamental component of the +output uh compared to the input. So uh + + align:start position:0% +output uh compared to the input. So uh + + + align:start position:0% +output uh compared to the input. So uh +the angle of the describing function + + align:start position:0% +the angle of the describing function + + + align:start position:0% +the angle of the describing function +exactly as the angle of our linear + + align:start position:0% +exactly as the angle of our linear + + + align:start position:0% +exactly as the angle of our linear +transfer function uh simply reflects the + + align:start position:0% +transfer function uh simply reflects the + + + align:start position:0% +transfer function uh simply reflects the +relative phase shift between the + + align:start position:0% +relative phase shift between the + + + align:start position:0% +relative phase shift between the +fundamental component of the output and + + align:start position:0% +fundamental component of the output and + + + align:start position:0% +fundamental component of the output and +the input signal. + + align:start position:0% +the input signal. + + + align:start position:0% +the input signal. +Usually we don't have to calculate + + align:start position:0% +Usually we don't have to calculate + + + align:start position:0% +Usually we don't have to calculate +describing functions. There are + + align:start position:0% +describing functions. There are + + + align:start position:0% +describing functions. There are +excellent tables. I provide an example + + align:start position:0% +excellent tables. I provide an example + + + align:start position:0% +excellent tables. I provide an example +of several describing functions in in + + align:start position:0% +of several describing functions in in + + + align:start position:0% +of several describing functions in in +the book. But there are also much more + + align:start position:0% +the book. But there are also much more + + + align:start position:0% +the book. But there are also much more +extensive tables of describing functions + + align:start position:0% +extensive tables of describing functions + + + align:start position:0% +extensive tables of describing functions +for many commonly encountered nonlinear + + align:start position:0% +for many commonly encountered nonlinear + + + align:start position:0% +for many commonly encountered nonlinear +elements. However, since we're starting + + align:start position:0% +elements. However, since we're starting + + + align:start position:0% +elements. However, since we're starting +now, let's go through the development of + + align:start position:0% +now, let's go through the development of + + + align:start position:0% +now, let's go through the development of +at least one describing function so we + + align:start position:0% +at least one describing function so we + + + align:start position:0% +at least one describing function so we +see how this works. + + align:start position:0% +see how this works. + + + align:start position:0% +see how this works. +And for an example, I'll use the + + align:start position:0% +And for an example, I'll use the + + + align:start position:0% +And for an example, I'll use the +so-called infinite gain limiter. Uh in + + align:start position:0% +so-called infinite gain limiter. Uh in + + + align:start position:0% +so-called infinite gain limiter. Uh in +other words, we have an element whose + + align:start position:0% +other words, we have an element whose + + + align:start position:0% +other words, we have an element whose +input output characteristics are such + + align:start position:0% +input output characteristics are such + + + align:start position:0% +input output characteristics are such +that the output is + one for any + + align:start position:0% +that the output is + one for any + + + align:start position:0% +that the output is + one for any +positive input. The output is minus one + + align:start position:0% +positive input. The output is minus one + + + align:start position:0% +positive input. The output is minus one +for any negative input. + + align:start position:0% + + + + align:start position:0% + +Let's now test our system. And recall + + align:start position:0% +Let's now test our system. And recall + + + align:start position:0% +Let's now test our system. And recall +that what we do is apply a syosoid to + + align:start position:0% +that what we do is apply a syosoid to + + + align:start position:0% +that what we do is apply a syosoid to +the input of our nonlinear element. And + + align:start position:0% +the input of our nonlinear element. And + + + align:start position:0% +the input of our nonlinear element. And +the amplitude of that syosoid + + align:start position:0% +the amplitude of that syosoid + + + align:start position:0% +the amplitude of that syosoid +will be E. That's the amplitude of the + + align:start position:0% +will be E. That's the amplitude of the + + + align:start position:0% +will be E. That's the amplitude of the +syosoidal test signal that we apply to + + align:start position:0% +syosoidal test signal that we apply to + + + align:start position:0% +syosoidal test signal that we apply to +our nonlinearity. + + align:start position:0% +our nonlinearity. + + + align:start position:0% +our nonlinearity. +In response to that input, the infinite + + align:start position:0% +In response to that input, the infinite + + + align:start position:0% +In response to that input, the infinite +gain limiter gives us an output that's + + align:start position:0% +gain limiter gives us an output that's + + + align:start position:0% +gain limiter gives us an output that's +plus one whenever the input is positive, + + align:start position:0% +plus one whenever the input is positive, + + + align:start position:0% +plus one whenever the input is positive, +an output that's minus one whenever the + + align:start position:0% +an output that's minus one whenever the + + + align:start position:0% +an output that's minus one whenever the +input is negative. So we simply get a + + align:start position:0% +input is negative. So we simply get a + + + align:start position:0% +input is negative. So we simply get a +square wave, + + align:start position:0% +square wave, + + + align:start position:0% +square wave, +the figure shown in white here, uh a + + align:start position:0% +the figure shown in white here, uh a + + + align:start position:0% +the figure shown in white here, uh a +square wave for the output wave form + + align:start position:0% +square wave for the output wave form + + + align:start position:0% +square wave for the output wave form +from the infinite gain limiter. And the + + align:start position:0% +from the infinite gain limiter. And the + + + align:start position:0% +from the infinite gain limiter. And the +zero crossings of the square wave are of + + align:start position:0% +zero crossings of the square wave are of + + + align:start position:0% +zero crossings of the square wave are of +course synchronized with those of the + + align:start position:0% +course synchronized with those of the + + + align:start position:0% +course synchronized with those of the +sine wave. + + align:start position:0% +sine wave. + + + align:start position:0% +sine wave. +You recall that the forier series for a + + align:start position:0% +You recall that the forier series for a + + + align:start position:0% +You recall that the forier series for a +square wave is 4 over<unk> * the + + align:start position:0% +square wave is 4 over<unk> * the + + + align:start position:0% +square wave is 4 over<unk> * the +fundamental plus a third of the third + + align:start position:0% +fundamental plus a third of the third + + + align:start position:0% +fundamental plus a third of the third +harmonic plus 1/5 of the fifth fifth + + align:start position:0% +harmonic plus 1/5 of the fifth fifth + + + align:start position:0% +harmonic plus 1/5 of the fifth fifth +harmonic and so forth. Only odd + + align:start position:0% +harmonic and so forth. Only odd + + + align:start position:0% +harmonic and so forth. Only odd +harmonics are present. And the magnitude + + align:start position:0% +harmonics are present. And the magnitude + + + align:start position:0% +harmonics are present. And the magnitude +of relative harmonics drops off as the + + align:start position:0% +of relative harmonics drops off as the + + + align:start position:0% +of relative harmonics drops off as the +order of the harmonic. And so the we've + + align:start position:0% +order of the harmonic. And so the we've + + + align:start position:0% +order of the harmonic. And so the we've +sketched here the fundamental component + + align:start position:0% +sketched here the fundamental component + + + align:start position:0% +sketched here the fundamental component +of the output signoid. Uh it's of course + + align:start position:0% +of the output signoid. Uh it's of course + + + align:start position:0% +of the output signoid. Uh it's of course +inphase with the input signal. This is a + + align:start position:0% +inphase with the input signal. This is a + + + align:start position:0% +inphase with the input signal. This is a +describing function that has no relative + + align:start position:0% +describing function that has no relative + + + align:start position:0% +describing function that has no relative +phase shift. And the peak magn or the + + align:start position:0% +phase shift. And the peak magn or the + + + align:start position:0% +phase shift. And the peak magn or the +magnitude of the fundamental component + + align:start position:0% +magnitude of the fundamental component + + + align:start position:0% +magnitude of the fundamental component +of the output is simply four over pi. + + align:start position:0% +of the output is simply four over pi. + + + align:start position:0% +of the output is simply four over pi. +Consequently the describing function in + + align:start position:0% +Consequently the describing function in + + + align:start position:0% +Consequently the describing function in +this case is only a function of input + + align:start position:0% +this case is only a function of input + + + align:start position:0% +this case is only a function of input +amplitude. It's not a function of + + align:start position:0% +amplitude. It's not a function of + + + align:start position:0% +amplitude. It's not a function of +frequency. It's the magnitude of the + + align:start position:0% +frequency. It's the magnitude of the + + + align:start position:0% +frequency. It's the magnitude of the +output, the fundamental component of the + + align:start position:0% +output, the fundamental component of the + + + align:start position:0% +output, the fundamental component of the +output which is 4 over pi divided by the + + align:start position:0% +output which is 4 over pi divided by the + + + align:start position:0% +output which is 4 over pi divided by the +amplitude of the input signal which is + + align:start position:0% +amplitude of the input signal which is + + + align:start position:0% +amplitude of the input signal which is +e. And of course the angle associated + + align:start position:0% +e. And of course the angle associated + + + align:start position:0% +e. And of course the angle associated +with our describing function is 0 + + align:start position:0% +with our describing function is 0 + + + align:start position:0% +with our describing function is 0 +degrees since the fundamental component + + align:start position:0% +degrees since the fundamental component + + + align:start position:0% +degrees since the fundamental component +of the output is in phase with the input + + align:start position:0% +of the output is in phase with the input + + + align:start position:0% +of the output is in phase with the input +signal. + + align:start position:0% +signal. + + + align:start position:0% +signal. +If we plot the magnitude of G subd of E + + align:start position:0% +If we plot the magnitude of G subd of E + + + align:start position:0% +If we plot the magnitude of G subd of E +as a function now of E since it's not a + + align:start position:0% +as a function now of E since it's not a + + + align:start position:0% +as a function now of E since it's not a +function of omega again for this + + align:start position:0% +function of omega again for this + + + align:start position:0% +function of omega again for this +particular case, we simply get a + + align:start position:0% +particular case, we simply get a + + + align:start position:0% +particular case, we simply get a +hyperola. + + align:start position:0% +hyperola. + + + align:start position:0% +hyperola. +Well, how do we use describing functions + + align:start position:0% +Well, how do we use describing functions + + + align:start position:0% +Well, how do we use describing functions +to analyze the stability of nonlinear + + align:start position:0% +to analyze the stability of nonlinear + + + align:start position:0% +to analyze the stability of nonlinear +systems? + + align:start position:0% +systems? + + + align:start position:0% +systems? +What we attempt to do is arrange our + + align:start position:0% +What we attempt to do is arrange our + + + align:start position:0% +What we attempt to do is arrange our +nonlinear system in the form shown. We + + align:start position:0% +nonlinear system in the form shown. We + + + align:start position:0% +nonlinear system in the form shown. We +hope that we can break up the system so + + align:start position:0% +hope that we can break up the system so + + + align:start position:0% +hope that we can break up the system so +that it we lump all of the linear + + align:start position:0% +that it we lump all of the linear + + + align:start position:0% +that it we lump all of the linear +components in one path here. This may be + + align:start position:0% +components in one path here. This may be + + + align:start position:0% +components in one path here. This may be +the reduction of some far more complex + + align:start position:0% +the reduction of some far more complex + + + align:start position:0% +the reduction of some far more complex +multiloop system. But the hope is that + + align:start position:0% +multiloop system. But the hope is that + + + align:start position:0% +multiloop system. But the hope is that +we can break up the system as shown. We + + align:start position:0% +we can break up the system as shown. We + + + align:start position:0% +we can break up the system as shown. We +get all of our linear elements in one + + align:start position:0% +get all of our linear elements in one + + + align:start position:0% +get all of our linear elements in one +path. Here we + + align:start position:0% +path. Here we + + + align:start position:0% +path. Here we +have a a single nonlinearity or a + + align:start position:0% +have a a single nonlinearity or a + + + align:start position:0% +have a a single nonlinearity or a +collection of nonlinearities that can be + + align:start position:0% +collection of nonlinearities that can be + + + align:start position:0% +collection of nonlinearities that can be +represented by a single describing + + align:start position:0% +represented by a single describing + + + align:start position:0% +represented by a single describing +function. And we specifically indicate + + align:start position:0% +function. And we specifically indicate + + + align:start position:0% +function. And we specifically indicate +that we're considering a negative + + align:start position:0% +that we're considering a negative + + + align:start position:0% +that we're considering a negative +feedback system by including a minus one + + align:start position:0% +feedback system by including a minus one + + + align:start position:0% +feedback system by including a minus one +here in the loop. Notice that the loop + + align:start position:0% +here in the loop. Notice that the loop + + + align:start position:0% +here in the loop. Notice that the loop +as shown has no input and no output. I + + align:start position:0% +as shown has no input and no output. I + + + align:start position:0% +as shown has no input and no output. I +mentioned earlier that my own personal + + align:start position:0% +mentioned earlier that my own personal + + + align:start position:0% +mentioned earlier that my own personal +experience shows that the use of + + align:start position:0% +experience shows that the use of + + + align:start position:0% +experience shows that the use of +describing functions is most valuable + + align:start position:0% +describing functions is most valuable + + + align:start position:0% +describing functions is most valuable +for oscillators. Uh it certainly is + + align:start position:0% +for oscillators. Uh it certainly is + + + align:start position:0% +for oscillators. Uh it certainly is +valid to determine whether a system + + align:start position:0% +valid to determine whether a system + + + align:start position:0% +valid to determine whether a system +that's intended to have some given input + + align:start position:0% +that's intended to have some given input + + + align:start position:0% +that's intended to have some given input +output relationship will oscillate. But + + align:start position:0% +output relationship will oscillate. But + + + align:start position:0% +output relationship will oscillate. But +when we're looking for oscillations, we + + align:start position:0% +when we're looking for oscillations, we + + + align:start position:0% +when we're looking for oscillations, we +can ignore the input and output and + + align:start position:0% +can ignore the input and output and + + + align:start position:0% +can ignore the input and output and +simply end up with a loop as shown. So + + align:start position:0% +simply end up with a loop as shown. So + + + align:start position:0% +simply end up with a loop as shown. So +one of the constraints or one of the + + align:start position:0% +one of the constraints or one of the + + + align:start position:0% +one of the constraints or one of the +things that certainly makes describing + + align:start position:0% +things that certainly makes describing + + + align:start position:0% +things that certainly makes describing +function analysis practical uh is that + + align:start position:0% +function analysis practical uh is that + + + align:start position:0% +function analysis practical uh is that +we are able to break up the loop as + + align:start position:0% +we are able to break up the loop as + + + align:start position:0% +we are able to break up the loop as +shown get all of the linear elements in + + align:start position:0% +shown get all of the linear elements in + + + align:start position:0% +shown get all of the linear elements in +one location combined with a single + + align:start position:0% +one location combined with a single + + + align:start position:0% +one location combined with a single +nonlinearity. + + align:start position:0% +nonlinearity. + + + align:start position:0% +nonlinearity. +Uh if we assume that the amplitude of + + align:start position:0% +Uh if we assume that the amplitude of + + + align:start position:0% +Uh if we assume that the amplitude of +the assumed syosoidal signal in the loop + + align:start position:0% +the assumed syosoidal signal in the loop + + + align:start position:0% +the assumed syosoidal signal in the loop +at this point is E. In other words, the + + align:start position:0% +at this point is E. In other words, the + + + align:start position:0% +at this point is E. In other words, the +signal here under steady state + + align:start position:0% +signal here under steady state + + + align:start position:0% +signal here under steady state +conditions has the form e sin omega t. + + align:start position:0% +conditions has the form e sin omega t. + + + align:start position:0% +conditions has the form e sin omega t. +Then the describing function analysis + + align:start position:0% +Then the describing function analysis + + + align:start position:0% +Then the describing function analysis +says that oscillations may be possible + + align:start position:0% +says that oscillations may be possible + + + align:start position:0% +says that oscillations may be possible +and we'll have to explain a little bit + + align:start position:0% +and we'll have to explain a little bit + + + align:start position:0% +and we'll have to explain a little bit +later on exactly what the hedge is with + + align:start position:0% +later on exactly what the hedge is with + + + align:start position:0% +later on exactly what the hedge is with +may be possible. But oscillations may be + + align:start position:0% +may be possible. But oscillations may be + + + align:start position:0% +may be possible. But oscillations may be +possible for combinations of amplitude e + + align:start position:0% +possible for combinations of amplitude e + + + align:start position:0% +possible for combinations of amplitude e +and frequency omega such that a of j + + align:start position:0% +and frequency omega such that a of j + + + align:start position:0% +and frequency omega such that a of j +omega time g subd of e omega e and + + align:start position:0% +omega time g subd of e omega e and + + + align:start position:0% +omega time g subd of e omega e and +frequency of amplitude and frequency uh + + align:start position:0% +frequency of amplitude and frequency uh + + + align:start position:0% +frequency of amplitude and frequency uh +that product is equal to minus1. + + align:start position:0% +that product is equal to minus1. + + + align:start position:0% +that product is equal to minus1. +This is of course exactly the describing + + align:start position:0% +This is of course exactly the describing + + + align:start position:0% +This is of course exactly the describing +function parallel of positive loop + + align:start position:0% +function parallel of positive loop + + + align:start position:0% +function parallel of positive loop +transmission with a magnitude of one. + + align:start position:0% +transmission with a magnitude of one. + + + align:start position:0% +transmission with a magnitude of one. +Here we have a loop. Uh we explicitly + + align:start position:0% +Here we have a loop. Uh we explicitly + + + align:start position:0% +Here we have a loop. Uh we explicitly +show the inversion that may occur at a + + align:start position:0% +show the inversion that may occur at a + + + align:start position:0% +show the inversion that may occur at a +summing point. Uh if the a of j omega + + align:start position:0% +summing point. Uh if the a of j omega + + + align:start position:0% +summing point. Uh if the a of j omega +time g subd of e omega it product is + + align:start position:0% +time g subd of e omega it product is + + + align:start position:0% +time g subd of e omega it product is +equal to minus1 that minus1 combined + + align:start position:0% +equal to minus1 that minus1 combined + + + align:start position:0% +equal to minus1 that minus1 combined +with the inversion gives us positive + + align:start position:0% +with the inversion gives us positive + + + align:start position:0% +with the inversion gives us positive +loop transmission with a magnitude of + + align:start position:0% +loop transmission with a magnitude of + + + align:start position:0% +loop transmission with a magnitude of +one and that's of course the parallel of + + align:start position:0% +one and that's of course the parallel of + + + align:start position:0% +one and that's of course the parallel of +the condition or at least a possible + + align:start position:0% +the condition or at least a possible + + + align:start position:0% +the condition or at least a possible +condition for oscillation in linear + + align:start position:0% +condition for oscillation in linear + + + align:start position:0% +condition for oscillation in linear +systems. + + align:start position:0% + + + + align:start position:0% + +The uh assumptions in describing + + align:start position:0% +The uh assumptions in describing + + + align:start position:0% +The uh assumptions in describing +function an analysis are now beginning + + align:start position:0% +function an analysis are now beginning + + + align:start position:0% +function an analysis are now beginning +to emerge. We assume that the signal at + + align:start position:0% +to emerge. We assume that the signal at + + + align:start position:0% +to emerge. We assume that the signal at +this point contains no harmonics. In + + align:start position:0% +this point contains no harmonics. In + + + align:start position:0% +this point contains no harmonics. In +other words, our test signal, our + + align:start position:0% +other words, our test signal, our + + + align:start position:0% +other words, our test signal, our +assumed test signal is a pure syosoid. + + align:start position:0% +assumed test signal is a pure syosoid. + + + align:start position:0% +assumed test signal is a pure syosoid. +Consequently, we'd expect that if there + + align:start position:0% +Consequently, we'd expect that if there + + + align:start position:0% +Consequently, we'd expect that if there +were a large harmonic content associated + + align:start position:0% +were a large harmonic content associated + + + align:start position:0% +were a large harmonic content associated +with this signal that the analysis might + + align:start position:0% +with this signal that the analysis might + + + align:start position:0% +with this signal that the analysis might +be suspect and might have relatively + + align:start position:0% +be suspect and might have relatively + + + align:start position:0% +be suspect and might have relatively +large errors. So, what we might hope is + + align:start position:0% +large errors. So, what we might hope is + + + align:start position:0% +large errors. So, what we might hope is +that first of all, the nonlinearity + + align:start position:0% +that first of all, the nonlinearity + + + align:start position:0% +that first of all, the nonlinearity +itself is of of a type that introduces + + align:start position:0% +itself is of of a type that introduces + + + align:start position:0% +itself is of of a type that introduces +relatively small harmonics relative to + + align:start position:0% +relatively small harmonics relative to + + + align:start position:0% +relatively small harmonics relative to +the fundamental. Uh so we might hope + + align:start position:0% +the fundamental. Uh so we might hope + + + align:start position:0% +the fundamental. Uh so we might hope +that the signal at this point uh that + + align:start position:0% +that the signal at this point uh that + + + align:start position:0% +that the signal at this point uh that +the fundamental component of the signal + + align:start position:0% +the fundamental component of the signal + + + align:start position:0% +the fundamental component of the signal +at this point dominated and that higher + + align:start position:0% +at this point dominated and that higher + + + align:start position:0% +at this point dominated and that higher +harmonics were relatively smaller in + + align:start position:0% +harmonics were relatively smaller in + + + align:start position:0% +harmonics were relatively smaller in +amplitude. + + align:start position:0% +amplitude. + + + align:start position:0% +amplitude. +Further we'd anticipate that the + + align:start position:0% +Further we'd anticipate that the + + + align:start position:0% +Further we'd anticipate that the +technique would work better for systems + + align:start position:0% +technique would work better for systems + + + align:start position:0% +technique would work better for systems +that are lowass in nature. If a of j + + align:start position:0% +that are lowass in nature. If a of j + + + align:start position:0% +that are lowass in nature. If a of j +omega is lowass in nature then harmonics + + align:start position:0% +omega is lowass in nature then harmonics + + + align:start position:0% +omega is lowass in nature then harmonics +in this signal will be filtered to a + + align:start position:0% +in this signal will be filtered to a + + + align:start position:0% +in this signal will be filtered to a +greater extent than the fundamental. In + + align:start position:0% +greater extent than the fundamental. In + + + align:start position:0% +greater extent than the fundamental. In +other words, the linear elements will + + align:start position:0% +other words, the linear elements will + + + align:start position:0% +other words, the linear elements will +then provide a gain that's greater for + + align:start position:0% +then provide a gain that's greater for + + + align:start position:0% +then provide a gain that's greater for +the fundamental than it is for higher + + align:start position:0% +the fundamental than it is for higher + + + align:start position:0% +the fundamental than it is for higher +harmonics. And consequently, the signal + + align:start position:0% +harmonics. And consequently, the signal + + + align:start position:0% +harmonics. And consequently, the signal +here will be pure in a harmonic sense + + align:start position:0% +here will be pure in a harmonic sense + + + align:start position:0% +here will be pure in a harmonic sense +than is the signal going in to the + + align:start position:0% +than is the signal going in to the + + + align:start position:0% +than is the signal going in to the +linear element. And if those two + + align:start position:0% +linear element. And if those two + + + align:start position:0% +linear element. And if those two +conditions are are satisfied in some + + align:start position:0% +conditions are are satisfied in some + + + align:start position:0% +conditions are are satisfied in some +way, if there's relatively small + + align:start position:0% +way, if there's relatively small + + + align:start position:0% +way, if there's relatively small +harmonic generation by the nonlinearity + + align:start position:0% +harmonic generation by the nonlinearity + + + align:start position:0% +harmonic generation by the nonlinearity +and if further those harmonics are are + + align:start position:0% +and if further those harmonics are are + + + align:start position:0% +and if further those harmonics are are +attenuated well by the uh linear portion + + align:start position:0% +attenuated well by the uh linear portion + + + align:start position:0% +attenuated well by the uh linear portion +of the loop, then we can be reasonably + + align:start position:0% +of the loop, then we can be reasonably + + + align:start position:0% +of the loop, then we can be reasonably +certain that the describing function + + align:start position:0% +certain that the describing function + + + align:start position:0% +certain that the describing function +analysis will well predict the behavior + + align:start position:0% +analysis will well predict the behavior + + + align:start position:0% +analysis will well predict the behavior +of the system. + + align:start position:0% + + + + align:start position:0% + +Let's consider uh another special case + + align:start position:0% +Let's consider uh another special case + + + align:start position:0% +Let's consider uh another special case +which is really necessary again to make + + align:start position:0% +which is really necessary again to make + + + align:start position:0% +which is really necessary again to make +describing function analysis practical. + + align:start position:0% +describing function analysis practical. + + + align:start position:0% +describing function analysis practical. +As I describe the limitations of the + + align:start position:0% +As I describe the limitations of the + + + align:start position:0% +As I describe the limitations of the +method, it seems as though uh there are + + align:start position:0% +method, it seems as though uh there are + + + align:start position:0% +method, it seems as though uh there are +very few cases that that this is can + + align:start position:0% +very few cases that that this is can + + + align:start position:0% +very few cases that that this is can +where this technique can be used. But + + align:start position:0% +where this technique can be used. But + + + align:start position:0% +where this technique can be used. But +that's that's really not true. say there + + align:start position:0% +that's that's really not true. say there + + + align:start position:0% +that's that's really not true. say there +are a number of of examples of practical + + align:start position:0% +are a number of of examples of practical + + + align:start position:0% +are a number of of examples of practical +interest and we'll see some of them + + align:start position:0% +interest and we'll see some of them + + + align:start position:0% +interest and we'll see some of them +where describing function analysis gives + + align:start position:0% +where describing function analysis gives + + + align:start position:0% +where describing function analysis gives +us a very good indication of the + + align:start position:0% +us a very good indication of the + + + align:start position:0% +us a very good indication of the +behavior of a nonlinear system u while + + align:start position:0% +behavior of a nonlinear system u while + + + align:start position:0% +behavior of a nonlinear system u while +it does have limitations we recognize + + align:start position:0% +it does have limitations we recognize + + + align:start position:0% +it does have limitations we recognize +that getting any insight into the + + align:start position:0% +that getting any insight into the + + + align:start position:0% +that getting any insight into the +operation of a nonlinear system is a + + align:start position:0% +operation of a nonlinear system is a + + + align:start position:0% +operation of a nonlinear system is a +very very difficult task anyway and I + + align:start position:0% +very very difficult task anyway and I + + + align:start position:0% +very very difficult task anyway and I +think we're willing to settle for + + align:start position:0% +think we're willing to settle for + + + align:start position:0% +think we're willing to settle for +approximations that are a little bit + + align:start position:0% +approximations that are a little bit + + + align:start position:0% +approximations that are a little bit +crude and that that have somewhat + + align:start position:0% +crude and that that have somewhat + + + align:start position:0% +crude and that that have somewhat +limited applicability because they do + + align:start position:0% +limited applicability because they do + + + align:start position:0% +limited applicability because they do +give us at least one technique techique + + align:start position:0% +give us at least one technique techique + + + align:start position:0% +give us at least one technique techique +for gaining insight into certain classes + + align:start position:0% +for gaining insight into certain classes + + + align:start position:0% +for gaining insight into certain classes +of nonlinear systems. Well, anyway, + + align:start position:0% +of nonlinear systems. Well, anyway, + + + align:start position:0% +of nonlinear systems. Well, anyway, +let's consider a nonlinearity which is + + align:start position:0% +let's consider a nonlinearity which is + + + align:start position:0% +let's consider a nonlinearity which is +in fact frequency independent. And + + align:start position:0% +in fact frequency independent. And + + + align:start position:0% +in fact frequency independent. And +again, I think this is necessary really + + align:start position:0% +again, I think this is necessary really + + + align:start position:0% +again, I think this is necessary really +to make the kinds of manipulations that + + align:start position:0% +to make the kinds of manipulations that + + + align:start position:0% +to make the kinds of manipulations that +we have to do practical. Uh it's not a a + + align:start position:0% +we have to do practical. Uh it's not a a + + + align:start position:0% +we have to do practical. Uh it's not a a +an absolute restriction. We can still + + align:start position:0% +an absolute restriction. We can still + + + align:start position:0% +an absolute restriction. We can still +use describing function analysis for + + align:start position:0% +use describing function analysis for + + + align:start position:0% +use describing function analysis for +elements which in fact are frequency + + align:start position:0% +elements which in fact are frequency + + + align:start position:0% +elements which in fact are frequency +dependent. But we find out when we do + + align:start position:0% +dependent. But we find out when we do + + + align:start position:0% +dependent. But we find out when we do +that that that uh again the numerical + + align:start position:0% +that that that uh again the numerical + + + align:start position:0% +that that that uh again the numerical +effort involved is considerable. We + + align:start position:0% +effort involved is considerable. We + + + align:start position:0% +effort involved is considerable. We +begin to to wonder if if maybe we + + align:start position:0% +begin to to wonder if if maybe we + + + align:start position:0% +begin to to wonder if if maybe we +wouldn't be better off actually doing a + + align:start position:0% +wouldn't be better off actually doing a + + + align:start position:0% +wouldn't be better off actually doing a +a numerical simulation of the system. + + align:start position:0% +a numerical simulation of the system. + + + align:start position:0% +a numerical simulation of the system. +However, if the nonlinearity is in fact + + align:start position:0% +However, if the nonlinearity is in fact + + + align:start position:0% +However, if the nonlinearity is in fact +frequency independent, our condition + + align:start position:0% +frequency independent, our condition + + + align:start position:0% +frequency independent, our condition +then reduces uh to the constraint that + + align:start position:0% +then reduces uh to the constraint that + + + align:start position:0% +then reduces uh to the constraint that +oscillations may be possible if the + + align:start position:0% +oscillations may be possible if the + + + align:start position:0% +oscillations may be possible if the +product a of j omega times g subd of e + + align:start position:0% +product a of j omega times g subd of e + + + align:start position:0% +product a of j omega times g subd of e +equals minus1. E is now independent of + + align:start position:0% +equals minus1. E is now independent of + + + align:start position:0% +equals minus1. E is now independent of +of frequency or g subd is independent of + + align:start position:0% +of frequency or g subd is independent of + + + align:start position:0% +of frequency or g subd is independent of +frequency. It's dependent only on the + + align:start position:0% +frequency. It's dependent only on the + + + align:start position:0% +frequency. It's dependent only on the +assumed amplitude of the signal at this + + align:start position:0% +assumed amplitude of the signal at this + + + align:start position:0% +assumed amplitude of the signal at this +point in the loop. + + align:start position:0% +point in the loop. + + + align:start position:0% +point in the loop. +We can rearrange that again in a form + + align:start position:0% +We can rearrange that again in a form + + + align:start position:0% +We can rearrange that again in a form +very reminiscent of some of our linear + + align:start position:0% +very reminiscent of some of our linear + + + align:start position:0% +very reminiscent of some of our linear +system manipulations + + align:start position:0% +system manipulations + + + align:start position:0% +system manipulations +uh and get the relationship a of j omega + + align:start position:0% +uh and get the relationship a of j omega + + + align:start position:0% +uh and get the relationship a of j omega +equals minus 1 / g subd of e. And a + + align:start position:0% +equals minus 1 / g subd of e. And a + + + align:start position:0% +equals minus 1 / g subd of e. And a +convenient way to look for equalities in + + align:start position:0% +convenient way to look for equalities in + + + align:start position:0% +convenient way to look for equalities in +that relationship is to plot both of the + + align:start position:0% +that relationship is to plot both of the + + + align:start position:0% +that relationship is to plot both of the +indicated functions in a gain phase + + align:start position:0% +indicated functions in a gain phase + + + align:start position:0% +indicated functions in a gain phase +plane. So let's consider a gain phase + + align:start position:0% +plane. So let's consider a gain phase + + + align:start position:0% +plane. So let's consider a gain phase +plane. Here we have the magnitude of + + align:start position:0% +plane. Here we have the magnitude of + + + align:start position:0% +plane. Here we have the magnitude of +both a of j omega and 1 / g subd of e. + + align:start position:0% +both a of j omega and 1 / g subd of e. + + + align:start position:0% +both a of j omega and 1 / g subd of e. +And along this axis we have the angle of + + align:start position:0% +And along this axis we have the angle of + + + align:start position:0% +And along this axis we have the angle of +a of j omega and simultaneously the + + align:start position:0% +a of j omega and simultaneously the + + + align:start position:0% +a of j omega and simultaneously the +angle of minus one over g subd of e. And + + align:start position:0% +angle of minus one over g subd of e. And + + + align:start position:0% +angle of minus one over g subd of e. And +then in those gain phase coordinates + + align:start position:0% +then in those gain phase coordinates + + + align:start position:0% +then in those gain phase coordinates +we'll plot the transfer function of our + + align:start position:0% +we'll plot the transfer function of our + + + align:start position:0% +we'll plot the transfer function of our +linear system a of j omega. And so in + + align:start position:0% +linear system a of j omega. And so in + + + align:start position:0% +linear system a of j omega. And so in +this curve we of course are representing + + align:start position:0% +this curve we of course are representing + + + align:start position:0% +this curve we of course are representing +the magnitude and the angle of a of j + + align:start position:0% +the magnitude and the angle of a of j + + + align:start position:0% +the magnitude and the angle of a of j +omega. The magnitude and angle of a of j + + align:start position:0% +omega. The magnitude and angle of a of j + + + align:start position:0% +omega. The magnitude and angle of a of j +omega. And in general omega is a + + align:start position:0% +omega. And in general omega is a + + + align:start position:0% +omega. And in general omega is a +parameter running along that curve. + + align:start position:0% +parameter running along that curve. + + + align:start position:0% +parameter running along that curve. +And similarly similarly we'll plot the + + align:start position:0% +And similarly similarly we'll plot the + + + align:start position:0% +And similarly similarly we'll plot the +magnitude and the angle of minus1 / g + + align:start position:0% +magnitude and the angle of minus1 / g + + + align:start position:0% +magnitude and the angle of minus1 / g +subd of e. Again recall that our in this + + align:start position:0% +subd of e. Again recall that our in this + + + align:start position:0% +subd of e. Again recall that our in this +case we're considering describing + + align:start position:0% +case we're considering describing + + + align:start position:0% +case we're considering describing +functions that are frequency + + align:start position:0% +functions that are frequency + + + align:start position:0% +functions that are frequency +independent. So we only have to consider + + align:start position:0% +independent. So we only have to consider + + + align:start position:0% +independent. So we only have to consider +them as a function of amplitude e. And + + align:start position:0% +them as a function of amplitude e. And + + + align:start position:0% +them as a function of amplitude e. And +presumably E is a parameter along this + + align:start position:0% +presumably E is a parameter along this + + + align:start position:0% +presumably E is a parameter along this +minus one over GD of E curve. + + align:start position:0% +minus one over GD of E curve. + + + align:start position:0% +minus one over GD of E curve. +If there is an intersection, + + align:start position:0% +If there is an intersection, + + + align:start position:0% +If there is an intersection, +Y, + + align:start position:0% +Y, + + + align:start position:0% +Y, +that intersection is of course a + + align:start position:0% +that intersection is of course a + + + align:start position:0% +that intersection is of course a +solution of the equation A of J omega + + align:start position:0% +solution of the equation A of J omega + + + align:start position:0% +solution of the equation A of J omega +equals minus 1 / GD of E. We plotted A + + align:start position:0% +equals minus 1 / GD of E. We plotted A + + + align:start position:0% +equals minus 1 / GD of E. We plotted A +of J omega. We've plotted minus one over + + align:start position:0% +of J omega. We've plotted minus one over + + + align:start position:0% +of J omega. We've plotted minus one over +GD of E on the same coordinates. If + + align:start position:0% +GD of E on the same coordinates. If + + + align:start position:0% +GD of E on the same coordinates. If +there's intersection of those two + + align:start position:0% +there's intersection of those two + + + align:start position:0% +there's intersection of those two +curves, we've solved this equality. + + align:start position:0% +curves, we've solved this equality. + + + align:start position:0% +curves, we've solved this equality. +So that's one way of looking for + + align:start position:0% +So that's one way of looking for + + + align:start position:0% +So that's one way of looking for +combinations of omega and e that will + + align:start position:0% +combinations of omega and e that will + + + align:start position:0% +combinations of omega and e that will +solve this equation that that give us + + align:start position:0% +solve this equation that that give us + + + align:start position:0% +solve this equation that that give us +equality between a of j omega and minus + + align:start position:0% +equality between a of j omega and minus + + + align:start position:0% +equality between a of j omega and minus +one over g d of e. We would find the + + align:start position:0% +one over g d of e. We would find the + + + align:start position:0% +one over g d of e. We would find the +combination of omega and e necessary by + + align:start position:0% +combination of omega and e necessary by + + + align:start position:0% +combination of omega and e necessary by +looking + + align:start position:0% +looking + + + align:start position:0% +looking +along the a of j omega curve and + + align:start position:0% +along the a of j omega curve and + + + align:start position:0% +along the a of j omega curve and +determining the value of omega at this + + align:start position:0% +determining the value of omega at this + + + align:start position:0% +determining the value of omega at this +point from the a of j a of j omega + + align:start position:0% +point from the a of j a of j omega + + + align:start position:0% +point from the a of j a of j omega +curve. Similarly, we'd find the + + align:start position:0% +curve. Similarly, we'd find the + + + align:start position:0% +curve. Similarly, we'd find the +amplitude necessary to force the + + align:start position:0% +amplitude necessary to force the + + + align:start position:0% +amplitude necessary to force the +intersection by looking along the minus1 + + align:start position:0% +intersection by looking along the minus1 + + + align:start position:0% +intersection by looking along the minus1 +over gd of e curve. e is of course a a + + align:start position:0% +over gd of e curve. e is of course a a + + + align:start position:0% +over gd of e curve. e is of course a a +parameter running along this curve. And + + align:start position:0% +parameter running along this curve. And + + + align:start position:0% +parameter running along this curve. And +so we can find the value of E that + + align:start position:0% +so we can find the value of E that + + + align:start position:0% +so we can find the value of E that +creates the intersection by looking at + + align:start position:0% +creates the intersection by looking at + + + align:start position:0% +creates the intersection by looking at +at how this curve changes as a function + + align:start position:0% +at how this curve changes as a function + + + align:start position:0% +at how this curve changes as a function +of E. + + align:start position:0% +of E. + + + align:start position:0% +of E. +Well, let's apply this kind of analysis + + align:start position:0% +Well, let's apply this kind of analysis + + + align:start position:0% +Well, let's apply this kind of analysis +to one system. As I mentioned earlier, + + align:start position:0% +to one system. As I mentioned earlier, + + + align:start position:0% +to one system. As I mentioned earlier, +this uh is I find most useful for the + + align:start position:0% +this uh is I find most useful for the + + + align:start position:0% +this uh is I find most useful for the +analysis of oscillators. And of course + + align:start position:0% +analysis of oscillators. And of course + + + align:start position:0% +analysis of oscillators. And of course +following along with that why we'll look + + align:start position:0% +following along with that why we'll look + + + align:start position:0% +following along with that why we'll look +at an oscillator. + + align:start position:0% +at an oscillator. + + + align:start position:0% +at an oscillator. +And let's now consider a loop where the + + align:start position:0% +And let's now consider a loop where the + + + align:start position:0% +And let's now consider a loop where the +linear elements uh or the linear element + + align:start position:0% +linear elements uh or the linear element + + + align:start position:0% +linear elements uh or the linear element +consists of three real axis poles. I'll + + align:start position:0% +consists of three real axis poles. I'll + + + align:start position:0% +consists of three real axis poles. I'll +drop the minus one out here and include + + align:start position:0% +drop the minus one out here and include + + + align:start position:0% +drop the minus one out here and include +it in the linear transfer function. Uh + + align:start position:0% +it in the linear transfer function. Uh + + + align:start position:0% +it in the linear transfer function. Uh +and let's assume that the the poles are + + align:start position:0% +and let's assume that the the poles are + + + align:start position:0% +and let's assume that the the poles are +normalized to unit frequency. So the + + align:start position:0% +normalized to unit frequency. So the + + + align:start position:0% +normalized to unit frequency. So the +transfer function of our linear element + + align:start position:0% +transfer function of our linear element + + + align:start position:0% +transfer function of our linear element +is then simply 1 over s + one quantity + + align:start position:0% +is then simply 1 over s + one quantity + + + align:start position:0% +is then simply 1 over s + one quantity +cubed. + + align:start position:0% +cubed. + + + align:start position:0% +cubed. +And since to this point we have a very + + align:start position:0% +And since to this point we have a very + + + align:start position:0% +And since to this point we have a very +limited collection of describing + + align:start position:0% +limited collection of describing + + + align:start position:0% +limited collection of describing +functions we know in particular we know + + align:start position:0% +functions we know in particular we know + + + align:start position:0% +functions we know in particular we know +one the one we've worked out let's + + align:start position:0% +one the one we've worked out let's + + + align:start position:0% +one the one we've worked out let's +consider that nonlinearity included in + + align:start position:0% +consider that nonlinearity included in + + + align:start position:0% +consider that nonlinearity included in +the loop. So here we have our infinite + + align:start position:0% +the loop. So here we have our infinite + + + align:start position:0% +the loop. So here we have our infinite +gain limiter. Again, let's assume that + + align:start position:0% +gain limiter. Again, let's assume that + + + align:start position:0% +gain limiter. Again, let's assume that +it's normalized to unit amplitude. And + + align:start position:0% +it's normalized to unit amplitude. And + + + align:start position:0% +it's normalized to unit amplitude. And +we saw earlier that the describing + + align:start position:0% +we saw earlier that the describing + + + align:start position:0% +we saw earlier that the describing +function for that infinite gain limiter + + align:start position:0% +function for that infinite gain limiter + + + align:start position:0% +function for that infinite gain limiter +G subd of E is simply the magnitude of + + align:start position:0% +G subd of E is simply the magnitude of + + + align:start position:0% +G subd of E is simply the magnitude of +the fundamental component of the output + + align:start position:0% +the fundamental component of the output + + + align:start position:0% +the fundamental component of the output +4 over pi divided by the magnitude of + + align:start position:0% +4 over pi divided by the magnitude of + + + align:start position:0% +4 over pi divided by the magnitude of +the assumed test signal applied to the + + align:start position:0% +the assumed test signal applied to the + + + align:start position:0% +the assumed test signal applied to the +limiter E. And the angle associated with + + align:start position:0% +limiter E. And the angle associated with + + + align:start position:0% +limiter E. And the angle associated with +the infinite gain limiter is 0 degrees. + + align:start position:0% +the infinite gain limiter is 0 degrees. + + + align:start position:0% +the infinite gain limiter is 0 degrees. +Well, following along then, minus 1 / g + + align:start position:0% +Well, following along then, minus 1 / g + + + align:start position:0% +Well, following along then, minus 1 / g +subd of e is simply equal to the + + align:start position:0% +subd of e is simply equal to the + + + align:start position:0% +subd of e is simply equal to the +reciprocal of this quantity pi e / 4. + + align:start position:0% +reciprocal of this quantity pi e / 4. + + + align:start position:0% +reciprocal of this quantity pi e / 4. +Since the angle of gd of e itself is 0°, + + align:start position:0% +Since the angle of gd of e itself is 0°, + + + align:start position:0% +Since the angle of gd of e itself is 0°, +the angle of minus1 / g d of e is simply + + align:start position:0% +the angle of minus1 / g d of e is simply + + + align:start position:0% +the angle of minus1 / g d of e is simply +minus 180°. + + align:start position:0% +minus 180°. + + + align:start position:0% +minus 180°. +We've looked at at the transfer function + + align:start position:0% +We've looked at at the transfer function + + + align:start position:0% +We've looked at at the transfer function +associated with this kind of linear + + align:start position:0% +associated with this kind of linear + + + align:start position:0% +associated with this kind of linear +element earlier. uh we did look uh at at + + align:start position:0% +element earlier. uh we did look uh at at + + + align:start position:0% +element earlier. uh we did look uh at at +sort of the the phase shift oscillator, + + align:start position:0% +sort of the the phase shift oscillator, + + + align:start position:0% +sort of the the phase shift oscillator, +the case of three coincident poles on + + align:start position:0% +the case of three coincident poles on + + + align:start position:0% +the case of three coincident poles on +the negative real axis when we + + align:start position:0% +the negative real axis when we + + + align:start position:0% +the negative real axis when we +introduced the idea of stability and + + align:start position:0% +introduced the idea of stability and + + + align:start position:0% +introduced the idea of stability and +showed that that that configuration was + + align:start position:0% +showed that that that configuration was + + + align:start position:0% +showed that that that configuration was +at least capable of of oscillation for + + align:start position:0% +at least capable of of oscillation for + + + align:start position:0% +at least capable of of oscillation for +certain combinations of loop + + align:start position:0% +certain combinations of loop + + + align:start position:0% +certain combinations of loop +transmission magnitude. And if we + + align:start position:0% +transmission magnitude. And if we + + + align:start position:0% +transmission magnitude. And if we +recall, the magnitude of this transfer + + align:start position:0% +recall, the magnitude of this transfer + + + align:start position:0% +recall, the magnitude of this transfer +function starts of course at one at + + align:start position:0% +function starts of course at one at + + + align:start position:0% +function starts of course at one at +sufficiently low frequencies and then + + align:start position:0% +sufficiently low frequencies and then + + + align:start position:0% +sufficiently low frequencies and then +drops off past one radian per second. Uh + + align:start position:0% +drops off past one radian per second. Uh + + + align:start position:0% +drops off past one radian per second. Uh +basically falling off as frequency cubed + + align:start position:0% +basically falling off as frequency cubed + + + align:start position:0% +basically falling off as frequency cubed +past that break frequency. The angle of + + align:start position:0% +past that break frequency. The angle of + + + align:start position:0% +past that break frequency. The angle of +1 / s + 1 cubed, ignoring the minus + + align:start position:0% +1 / s + 1 cubed, ignoring the minus + + + align:start position:0% +1 / s + 1 cubed, ignoring the minus +sign, which really simply represents the + + align:start position:0% +sign, which really simply represents the + + + align:start position:0% +sign, which really simply represents the +inversion in the loop. uh the angle of 1 + + align:start position:0% +inversion in the loop. uh the angle of 1 + + + align:start position:0% +inversion in the loop. uh the angle of 1 +over s+1 cubed starts at 0 degrees at + + align:start position:0% +over s+1 cubed starts at 0 degrees at + + + align:start position:0% +over s+1 cubed starts at 0 degrees at +very low frequencies and eventually + + align:start position:0% +very low frequencies and eventually + + + align:start position:0% +very low frequencies and eventually +reaches minus270 + + align:start position:0% +reaches minus270 + + + align:start position:0% +reaches minus270 +degrees at very high frequencies. + + align:start position:0% +degrees at very high frequencies. + + + align:start position:0% +degrees at very high frequencies. +So here in gain phase coordinates + + align:start position:0% +So here in gain phase coordinates + + + align:start position:0% +So here in gain phase coordinates +running from 0° through - 180° + + align:start position:0% +running from 0° through - 180° + + + align:start position:0% +running from 0° through - 180° +eventually to minus 270 I've plotted the + + align:start position:0% +eventually to minus 270 I've plotted the + + + align:start position:0% +eventually to minus 270 I've plotted the +transfer function of our linear element + + align:start position:0% +transfer function of our linear element + + + align:start position:0% +transfer function of our linear element +a of j omega. Uh this is a a function + + align:start position:0% +a of j omega. Uh this is a a function + + + align:start position:0% +a of j omega. Uh this is a a function +that starts at one for omega equals 0 of + + align:start position:0% +that starts at one for omega equals 0 of + + + align:start position:0% +that starts at one for omega equals 0 of +course a magnitude of one and an angle + + align:start position:0% +course a magnitude of one and an angle + + + align:start position:0% +course a magnitude of one and an angle +of 0 degrees for omega equals 0 drops + + align:start position:0% +of 0 degrees for omega equals 0 drops + + + align:start position:0% +of 0 degrees for omega equals 0 drops +off uh eventually heading asmtoically + + align:start position:0% +off uh eventually heading asmtoically + + + align:start position:0% +off uh eventually heading asmtoically +toward -270°. + + align:start position:0% + + + + align:start position:0% + +If you recall from our earlier + + align:start position:0% +If you recall from our earlier + + + align:start position:0% +If you recall from our earlier +development the angle associated with + + align:start position:0% +development the angle associated with + + + align:start position:0% +development the angle associated with +the three pole three coincident pole + + align:start position:0% +the three pole three coincident pole + + + align:start position:0% +the three pole three coincident pole +transfer function reaches minus 180° at + + align:start position:0% +transfer function reaches minus 180° at + + + align:start position:0% +transfer function reaches minus 180° at +a frequency that's radle 3 times the + + align:start position:0% +a frequency that's radle 3 times the + + + align:start position:0% +a frequency that's radle 3 times the +break frequency. So in our case where we + + align:start position:0% +break frequency. So in our case where we + + + align:start position:0% +break frequency. So in our case where we +have uh the poles located at 1 radian + + align:start position:0% +have uh the poles located at 1 radian + + + align:start position:0% +have uh the poles located at 1 radian +per second at omega= radical 3 radians/s + + align:start position:0% +per second at omega= radical 3 radians/s + + + align:start position:0% +per second at omega= radical 3 radians/s +the angle of the linear portion of our + + align:start position:0% +the angle of the linear portion of our + + + align:start position:0% +the angle of the linear portion of our +system goes through minus 180°. + + align:start position:0% +system goes through minus 180°. + + + align:start position:0% +system goes through minus 180°. +also recall from the development done + + align:start position:0% +also recall from the development done + + + align:start position:0% +also recall from the development done +earlier that the magnitude of the + + align:start position:0% +earlier that the magnitude of the + + + align:start position:0% +earlier that the magnitude of the +transfer function at the frequency where + + align:start position:0% +transfer function at the frequency where + + + align:start position:0% +transfer function at the frequency where +its angle is minus 180 degrees is 0.125. + + align:start position:0% +its angle is minus 180 degrees is 0.125. + + + align:start position:0% +its angle is minus 180 degrees is 0.125. +So here we have the important point as + + align:start position:0% +So here we have the important point as + + + align:start position:0% +So here we have the important point as +we'll see for describing function + + align:start position:0% +we'll see for describing function + + + align:start position:0% +we'll see for describing function +analysis. The point where this curve or + + align:start position:0% +analysis. The point where this curve or + + + align:start position:0% +analysis. The point where this curve or +for this describing function analysis + + align:start position:0% +for this describing function analysis + + + align:start position:0% +for this describing function analysis +anyway the point where the linear curve + + align:start position:0% +anyway the point where the linear curve + + + align:start position:0% +anyway the point where the linear curve +goes through - 180° because that's the + + align:start position:0% +goes through - 180° because that's the + + + align:start position:0% +goes through - 180° because that's the +point where it intersects the minus1 + + align:start position:0% +point where it intersects the minus1 + + + align:start position:0% +point where it intersects the minus1 +over GD of E curve. + + align:start position:0% +over GD of E curve. + + + align:start position:0% +over GD of E curve. +Uh minus1 over GD of E is pi E / 4 at an + + align:start position:0% +Uh minus1 over GD of E is pi E / 4 at an + + + align:start position:0% +Uh minus1 over GD of E is pi E / 4 at an +angle of - 180°. So it lies directly + + align:start position:0% +angle of - 180°. So it lies directly + + + align:start position:0% +angle of - 180°. So it lies directly +along the minus 180 degree line. + + align:start position:0% +along the minus 180 degree line. + + + align:start position:0% +along the minus 180 degree line. +And this then is the direction of + + align:start position:0% +And this then is the direction of + + + align:start position:0% +And this then is the direction of +increasing E on our minus1 over GD of E + + align:start position:0% +increasing E on our minus1 over GD of E + + + align:start position:0% +increasing E on our minus1 over GD of E +curve. As E gets larger, minus1 over GD + + align:start position:0% +curve. As E gets larger, minus1 over GD + + + align:start position:0% +curve. As E gets larger, minus1 over GD +of E gets larger. Consequently, this is + + align:start position:0% +of E gets larger. Consequently, this is + + + align:start position:0% +of E gets larger. Consequently, this is +the direction of increasing E. And that + + align:start position:0% +the direction of increasing E. And that + + + align:start position:0% +the direction of increasing E. And that +curve is is simply a straight line along + + align:start position:0% +curve is is simply a straight line along + + + align:start position:0% +curve is is simply a straight line along +the minus 180° line in our gain phase + + align:start position:0% +the minus 180° line in our gain phase + + + align:start position:0% +the minus 180° line in our gain phase +plane. + + align:start position:0% +plane. + + + align:start position:0% +plane. +It encompasses all values along that + + align:start position:0% +It encompasses all values along that + + + align:start position:0% +It encompasses all values along that +line because uh certainly it goes from + + align:start position:0% +line because uh certainly it goes from + + + align:start position:0% +line because uh certainly it goes from +zero for very small values of E to to + + align:start position:0% +zero for very small values of E to to + + + align:start position:0% +zero for very small values of E to to +infinity for or approaches infinity for + + align:start position:0% +infinity for or approaches infinity for + + + align:start position:0% +infinity for or approaches infinity for +very large values of E. So uh this line + + align:start position:0% +very large values of E. So uh this line + + + align:start position:0% +very large values of E. So uh this line +runs across the entire + + align:start position:0% +runs across the entire + + + align:start position:0% +runs across the entire +uh gain phase plane. + + align:start position:0% +uh gain phase plane. + + + align:start position:0% +uh gain phase plane. +We can solve for the amplitude E the + + align:start position:0% +We can solve for the amplitude E the + + + align:start position:0% +We can solve for the amplitude E the +assumed the amplitude of the assumed + + align:start position:0% +assumed the amplitude of the assumed + + + align:start position:0% +assumed the amplitude of the assumed +syosoidal signal at this point in the + + align:start position:0% +syosoidal signal at this point in the + + + align:start position:0% +syosoidal signal at this point in the +loop necessary to satisfy that + + align:start position:0% +loop necessary to satisfy that + + + align:start position:0% +loop necessary to satisfy that +condition. The condition of course is + + align:start position:0% +condition. The condition of course is + + + align:start position:0% +condition. The condition of course is +the intersection between the minus1 over + + align:start position:0% +the intersection between the minus1 over + + + align:start position:0% +the intersection between the minus1 over +GD of E curve and the A of J omega + + align:start position:0% +GD of E curve and the A of J omega + + + align:start position:0% +GD of E curve and the A of J omega +curve. We've already found out that at + + align:start position:0% +curve. We've already found out that at + + + align:start position:0% +curve. We've already found out that at +that intersection the magnitude of a of + + align:start position:0% +that intersection the magnitude of a of + + + align:start position:0% +that intersection the magnitude of a of +j omega is.125 + + align:start position:0% +j omega is.125 + + + align:start position:0% +j omega is.125 +and that must of course be also the + + align:start position:0% +and that must of course be also the + + + align:start position:0% +and that must of course be also the +magnitude of the minus 1 / g d of e + + align:start position:0% +magnitude of the minus 1 / g d of e + + + align:start position:0% +magnitude of the minus 1 / g d of e +curve and consequently pi e over4 which + + align:start position:0% +curve and consequently pi e over4 which + + + align:start position:0% +curve and consequently pi e over4 which +is the magnitude of 1 / gd of e must be + + align:start position:0% +is the magnitude of 1 / gd of e must be + + + align:start position:0% +is the magnitude of 1 / gd of e must be +equal to.125. + + align:start position:0% + + + + align:start position:0% + +If we solve that for the amplitude of + + align:start position:0% +If we solve that for the amplitude of + + + align:start position:0% +If we solve that for the amplitude of +the signal E that creates the + + align:start position:0% +the signal E that creates the + + + align:start position:0% +the signal E that creates the +intersection, we find out that E is + + align:start position:0% +intersection, we find out that E is + + + align:start position:0% +intersection, we find out that E is +simply equal uh to 4 over 8 pi or 1 over + + align:start position:0% +simply equal uh to 4 over 8 pi or 1 over + + + align:start position:0% +simply equal uh to 4 over 8 pi or 1 over +2 pi. + + align:start position:0% +2 pi. + + + align:start position:0% +2 pi. +So our describing function analysis + + align:start position:0% +So our describing function analysis + + + align:start position:0% +So our describing function analysis +tells us that an oscillation may be + + align:start position:0% +tells us that an oscillation may be + + + align:start position:0% +tells us that an oscillation may be +possible + + align:start position:0% +possible + + + align:start position:0% +possible +with a signal amplitude at this point + + align:start position:0% +with a signal amplitude at this point + + + align:start position:0% +with a signal amplitude at this point +uh that's 1 / 2 pi and the frequency of + + align:start position:0% +uh that's 1 / 2 pi and the frequency of + + + align:start position:0% +uh that's 1 / 2 pi and the frequency of +that signal is simply equal to radle 3. + + align:start position:0% +that signal is simply equal to radle 3. + + + align:start position:0% +that signal is simply equal to radle 3. +So we'd have 1 over 2 pi * sin radle 3 + + align:start position:0% +So we'd have 1 over 2 pi * sin radle 3 + + + align:start position:0% +So we'd have 1 over 2 pi * sin radle 3 +t. + + align:start position:0% +t. + + + align:start position:0% +t. +And under those conditions, uh, if we + + align:start position:0% +And under those conditions, uh, if we + + + align:start position:0% +And under those conditions, uh, if we +conducted a a loop transmission test in + + align:start position:0% +conducted a a loop transmission test in + + + align:start position:0% +conducted a a loop transmission test in +a describing function sense, if we, for + + align:start position:0% +a describing function sense, if we, for + + + align:start position:0% +a describing function sense, if we, for +example, broke the loop, drove this + + align:start position:0% +example, broke the loop, drove this + + + align:start position:0% +example, broke the loop, drove this +point with a signal 1 over 2 pi sin + + align:start position:0% +point with a signal 1 over 2 pi sin + + + align:start position:0% +point with a signal 1 over 2 pi sin +radle 3 t, uh, we would find that the + + align:start position:0% +radle 3 t, uh, we would find that the + + + align:start position:0% +radle 3 t, uh, we would find that the +signal that came back would have a + + align:start position:0% +signal that came back would have a + + + align:start position:0% +signal that came back would have a +fundamental component that was exactly + + align:start position:0% +fundamental component that was exactly + + + align:start position:0% +fundamental component that was exactly +identical to the signal we had applied. + + align:start position:0% +identical to the signal we had applied. + + + align:start position:0% +identical to the signal we had applied. +Now, we have to look at the hedge that I + + align:start position:0% +Now, we have to look at the hedge that I + + + align:start position:0% +Now, we have to look at the hedge that I +mentioned earlier. And the issue really + + align:start position:0% +mentioned earlier. And the issue really + + + align:start position:0% +mentioned earlier. And the issue really +revolves around whether the oscillation + + align:start position:0% +revolves around whether the oscillation + + + align:start position:0% +revolves around whether the oscillation +predicted by by that intersection is + + align:start position:0% +predicted by by that intersection is + + + align:start position:0% +predicted by by that intersection is +stable in amplitude. In other words, we + + align:start position:0% +stable in amplitude. In other words, we + + + align:start position:0% +stable in amplitude. In other words, we +have to look at a a funny kind of + + align:start position:0% +have to look at a a funny kind of + + + align:start position:0% +have to look at a a funny kind of +stability analysis. Now we we think that + + align:start position:0% +stability analysis. Now we we think that + + + align:start position:0% +stability analysis. Now we we think that +the system may be oscillating. But what + + align:start position:0% +the system may be oscillating. But what + + + align:start position:0% +the system may be oscillating. But what +we have to do is is see what happens if + + align:start position:0% +we have to do is is see what happens if + + + align:start position:0% +we have to do is is see what happens if +we perturb the amplitude of the + + align:start position:0% +we perturb the amplitude of the + + + align:start position:0% +we perturb the amplitude of the +oscillation a little bit. Is the system + + align:start position:0% +oscillation a little bit. Is the system + + + align:start position:0% +oscillation a little bit. Is the system +restorative? In other words, if we + + align:start position:0% +restorative? In other words, if we + + + align:start position:0% +restorative? In other words, if we +somehow consider a perturbation that + + align:start position:0% +somehow consider a perturbation that + + + align:start position:0% +somehow consider a perturbation that +forces a slightly larger amplitude, does + + align:start position:0% +forces a slightly larger amplitude, does + + + align:start position:0% +forces a slightly larger amplitude, does +the system tend to react to squeeze the + + align:start position:0% +the system tend to react to squeeze the + + + align:start position:0% +the system tend to react to squeeze the +amplitude down to its original + + align:start position:0% +amplitude down to its original + + + align:start position:0% +amplitude down to its original +value? Conversely, if if we envision a + + align:start position:0% +value? Conversely, if if we envision a + + + align:start position:0% +value? Conversely, if if we envision a +perturbation where the amplitude of the + + align:start position:0% +perturbation where the amplitude of the + + + align:start position:0% +perturbation where the amplitude of the +oscillation, the amplitude of the signal + + align:start position:0% +oscillation, the amplitude of the signal + + + align:start position:0% +oscillation, the amplitude of the signal +at this point shrinks a little bit, + + align:start position:0% +at this point shrinks a little bit, + + + align:start position:0% +at this point shrinks a little bit, +again, is the system restored? Does the + + align:start position:0% +again, is the system restored? Does the + + + align:start position:0% +again, is the system restored? Does the +system work in a direction such as to + + align:start position:0% +system work in a direction such as to + + + align:start position:0% +system work in a direction such as to +increase the amplitude back to its + + align:start position:0% +increase the amplitude back to its + + + align:start position:0% +increase the amplitude back to its +original value? If that's the case, then + + align:start position:0% +original value? If that's the case, then + + + align:start position:0% +original value? If that's the case, then +in fact the system will oscillate at the + + align:start position:0% +in fact the system will oscillate at the + + + align:start position:0% +in fact the system will oscillate at the +intersection predicted by this analysis. + + align:start position:0% +intersection predicted by this analysis. + + + align:start position:0% +intersection predicted by this analysis. +Uh we have a a stable amplitude + + align:start position:0% +Uh we have a a stable amplitude + + + align:start position:0% +Uh we have a a stable amplitude +oscillation that's called the limit + + align:start position:0% +oscillation that's called the limit + + + align:start position:0% +oscillation that's called the limit +cycle. + + align:start position:0% +cycle. + + + align:start position:0% +cycle. +The converse is also possible and we'll + + align:start position:0% +The converse is also possible and we'll + + + align:start position:0% +The converse is also possible and we'll +see an example of that next time where + + align:start position:0% +see an example of that next time where + + + align:start position:0% +see an example of that next time where +when we envision a perturbation about + + align:start position:0% +when we envision a perturbation about + + + align:start position:0% +when we envision a perturbation about +this operating point and describing + + align:start position:0% +this operating point and describing + + + align:start position:0% +this operating point and describing +function analysis is really a kind of + + align:start position:0% +function analysis is really a kind of + + + align:start position:0% +function analysis is really a kind of +linearization about an operating point + + align:start position:0% +linearization about an operating point + + + align:start position:0% +linearization about an operating point +defined by a syosidal amplitude. When we + + align:start position:0% +defined by a syosidal amplitude. When we + + + align:start position:0% +defined by a syosidal amplitude. When we +consider a perturbation about that + + align:start position:0% +consider a perturbation about that + + + align:start position:0% +consider a perturbation about that +operating point, why suppose once again + + align:start position:0% +operating point, why suppose once again + + + align:start position:0% +operating point, why suppose once again +we envision a a slight increase in the + + align:start position:0% +we envision a a slight increase in the + + + align:start position:0% +we envision a a slight increase in the +amplitude, the system might work to + + align:start position:0% +amplitude, the system might work to + + + align:start position:0% +amplitude, the system might work to +force the the amplitude still to be + + align:start position:0% +force the the amplitude still to be + + + align:start position:0% +force the the amplitude still to be +still larger. If that's the case, the + + align:start position:0% +still larger. If that's the case, the + + + align:start position:0% +still larger. If that's the case, the +oscillation predicted by the + + align:start position:0% +oscillation predicted by the + + + align:start position:0% +oscillation predicted by the +intersection will be divergent. There's + + align:start position:0% +intersection will be divergent. There's + + + align:start position:0% +intersection will be divergent. There's +a parallel here, of course, in in linear + + align:start position:0% +a parallel here, of course, in in linear + + + align:start position:0% +a parallel here, of course, in in linear +systems, the stable equilibrium versus + + align:start position:0% +systems, the stable equilibrium versus + + + align:start position:0% +systems, the stable equilibrium versus +the unstable equilibrium. uh the uh + + align:start position:0% +the unstable equilibrium. uh the uh + + + align:start position:0% +the unstable equilibrium. uh the uh +pendulum hanging in this direction where + + align:start position:0% +pendulum hanging in this direction where + + + align:start position:0% +pendulum hanging in this direction where +a perturbation is restorative uh versus + + align:start position:0% +a perturbation is restorative uh versus + + + align:start position:0% +a perturbation is restorative uh versus +the inverted pendulum where a slight + + align:start position:0% +the inverted pendulum where a slight + + + align:start position:0% +the inverted pendulum where a slight +perturbation from the equilibrium point + + align:start position:0% +perturbation from the equilibrium point + + + align:start position:0% +perturbation from the equilibrium point +results in the pendulum falling over or + + align:start position:0% +results in the pendulum falling over or + + + align:start position:0% +results in the pendulum falling over or +the example we had last time where we + + align:start position:0% +the example we had last time where we + + + align:start position:0% +the example we had last time where we +had a ball in a magnetic field. We found + + align:start position:0% +had a ball in a magnetic field. We found + + + align:start position:0% +had a ball in a magnetic field. We found +out that there was an equilibrium point. + + align:start position:0% +out that there was an equilibrium point. + + + align:start position:0% +out that there was an equilibrium point. +It happened to be an unstable + + align:start position:0% +It happened to be an unstable + + + align:start position:0% +It happened to be an unstable +equilibrium if the magnetic field is + + align:start position:0% +equilibrium if the magnetic field is + + + align:start position:0% +equilibrium if the magnetic field is +constant. + + align:start position:0% +constant. + + + align:start position:0% +constant. +Well, let's see how we might argue uh + + align:start position:0% +Well, let's see how we might argue uh + + + align:start position:0% +Well, let's see how we might argue uh +stability of amplitude for this + + align:start position:0% +stability of amplitude for this + + + align:start position:0% +stability of amplitude for this +particular case. There's rules uh that + + align:start position:0% +particular case. There's rules uh that + + + align:start position:0% +particular case. There's rules uh that +allow you to get this in a sort of blind + + align:start position:0% +allow you to get this in a sort of blind + + + align:start position:0% +allow you to get this in a sort of blind +way. And I I list them in the book, but + + align:start position:0% +way. And I I list them in the book, but + + + align:start position:0% +way. And I I list them in the book, but +somehow I always forget them. And we can + + align:start position:0% +somehow I always forget them. And we can + + + align:start position:0% +somehow I always forget them. And we can +argue it physically and I think that's + + align:start position:0% +argue it physically and I think that's + + + align:start position:0% +argue it physically and I think that's +probably a better way to determine the + + align:start position:0% +probably a better way to determine the + + + align:start position:0% +probably a better way to determine the +question of whether the amplitude + + align:start position:0% +question of whether the amplitude + + + align:start position:0% +question of whether the amplitude +predicted by the intersection is stable + + align:start position:0% +predicted by the intersection is stable + + + align:start position:0% +predicted by the intersection is stable +or not. + + align:start position:0% +or not. + + + align:start position:0% +or not. +Let's consider uh drawing a loop + + align:start position:0% +Let's consider uh drawing a loop + + + align:start position:0% +Let's consider uh drawing a loop +transmission or a bodie plot for the + + align:start position:0% +transmission or a bodie plot for the + + + align:start position:0% +transmission or a bodie plot for the +actually the negative of the loop + + align:start position:0% +actually the negative of the loop + + + align:start position:0% +actually the negative of the loop +transmission. Um when we've linearized + + align:start position:0% +transmission. Um when we've linearized + + + align:start position:0% +transmission. Um when we've linearized +our system in a describing function + + align:start position:0% +our system in a describing function + + + align:start position:0% +our system in a describing function +sense we're predicting an oscillation + + align:start position:0% +sense we're predicting an oscillation + + + align:start position:0% +sense we're predicting an oscillation +with an amplitude of 1 / 2 pi + + align:start position:0% +with an amplitude of 1 / 2 pi + + + align:start position:0% +with an amplitude of 1 / 2 pi +and so for the signal at this point. So + + align:start position:0% +and so for the signal at this point. So + + + align:start position:0% +and so for the signal at this point. So +let's draw a loop transmission or the + + align:start position:0% +let's draw a loop transmission or the + + + align:start position:0% +let's draw a loop transmission or the +negative of the loop transmission. The + + align:start position:0% +negative of the loop transmission. The + + + align:start position:0% +negative of the loop transmission. The +equivalent of the AF plot for a linear + + align:start position:0% +equivalent of the AF plot for a linear + + + align:start position:0% +equivalent of the AF plot for a linear +system. Let's draw an A of J omega times + + align:start position:0% +system. Let's draw an A of J omega times + + + align:start position:0% +system. Let's draw an A of J omega times +G subd of 1 / 2 pi. That's the uh + + align:start position:0% +G subd of 1 / 2 pi. That's the uh + + + align:start position:0% +G subd of 1 / 2 pi. That's the uh +amplitude that we assume for the + + align:start position:0% +amplitude that we assume for the + + + align:start position:0% +amplitude that we assume for the +oscillation at this point or that our + + align:start position:0% +oscillation at this point or that our + + + align:start position:0% +oscillation at this point or that our +analysis predicts will be the amplitude + + align:start position:0% +analysis predicts will be the amplitude + + + align:start position:0% +analysis predicts will be the amplitude +of the oscillation. And so let's go + + align:start position:0% +of the oscillation. And so let's go + + + align:start position:0% +of the oscillation. And so let's go +ahead and and draw the negative of the + + align:start position:0% +ahead and and draw the negative of the + + + align:start position:0% +ahead and and draw the negative of the +loop transmission for our system as a + + align:start position:0% +loop transmission for our system as a + + + align:start position:0% +loop transmission for our system as a +function of frequency assuming that the + + align:start position:0% +function of frequency assuming that the + + + align:start position:0% +function of frequency assuming that the +test signal has the amplitude 1 / 2 pi + + align:start position:0% +test signal has the amplitude 1 / 2 pi + + + align:start position:0% +test signal has the amplitude 1 / 2 pi +and is applied at this point. + + align:start position:0% +and is applied at this point. + + + align:start position:0% +and is applied at this point. +Well, the gain of our describing + + align:start position:0% +Well, the gain of our describing + + + align:start position:0% +Well, the gain of our describing +function, the magnitude of the + + align:start position:0% +function, the magnitude of the + + + align:start position:0% +function, the magnitude of the +describing function, the gain of our + + align:start position:0% +describing function, the gain of our + + + align:start position:0% +describing function, the gain of our +nonlinear nonlinear element for uh e is + + align:start position:0% +nonlinear nonlinear element for uh e is + + + align:start position:0% +nonlinear nonlinear element for uh e is +equal to 1 over 2 pi, we can get from + + align:start position:0% +equal to 1 over 2 pi, we can get from + + + align:start position:0% +equal to 1 over 2 pi, we can get from +this expression and that gain will be + + align:start position:0% +this expression and that gain will be + + + align:start position:0% +this expression and that gain will be +simply 8. When we substitute in E= 1 + + align:start position:0% +simply 8. When we substitute in E= 1 + + + align:start position:0% +simply 8. When we substitute in E= 1 +over 2 pi, the pies cancel out and we + + align:start position:0% +over 2 pi, the pies cancel out and we + + + align:start position:0% +over 2 pi, the pies cancel out and we +get simply eight for the magnitude of + + align:start position:0% +get simply eight for the magnitude of + + + align:start position:0% +get simply eight for the magnitude of +our describing function. We've already + + align:start position:0% +our describing function. We've already + + + align:start position:0% +our describing function. We've already +found at sufficiently low frequencies, + + align:start position:0% +found at sufficiently low frequencies, + + + align:start position:0% +found at sufficiently low frequencies, +the magnitude of the linear portion of + + align:start position:0% +the magnitude of the linear portion of + + + align:start position:0% +the magnitude of the linear portion of +our transfer function is unity. + + align:start position:0% +our transfer function is unity. + + + align:start position:0% +our transfer function is unity. +Consequently, the indicated magnitude A + + align:start position:0% +Consequently, the indicated magnitude A + + + align:start position:0% +Consequently, the indicated magnitude A +of J omega* G subd of 1 / 2 pi has a low + + align:start position:0% +of J omega* G subd of 1 / 2 pi has a low + + + align:start position:0% +of J omega* G subd of 1 / 2 pi has a low +frequency value of 8. It has a corner + + align:start position:0% +frequency value of 8. It has a corner + + + align:start position:0% +frequency value of 8. It has a corner +frequency of 1 radian per second. It + + align:start position:0% +frequency of 1 radian per second. It + + + align:start position:0% +frequency of 1 radian per second. It +rolls off to unit magnitude by radical 3 + + align:start position:0% +rolls off to unit magnitude by radical 3 + + + align:start position:0% +rolls off to unit magnitude by radical 3 +radians per second. Uh because a of + + align:start position:0% +radians per second. Uh because a of + + + align:start position:0% +radians per second. Uh because a of +jalle 3 is equal to 1/8. That combines + + align:start position:0% +jalle 3 is equal to 1/8. That combines + + + align:start position:0% +jalle 3 is equal to 1/8. That combines +with the magnitude g subd of 1 / 2 pi of + + align:start position:0% +with the magnitude g subd of 1 / 2 pi of + + + align:start position:0% +with the magnitude g subd of 1 / 2 pi of +8 to give us a unit magnitude for the + + align:start position:0% +8 to give us a unit magnitude for the + + + align:start position:0% +8 to give us a unit magnitude for the +product at radical 3 radians/s. + + align:start position:0% +product at radical 3 radians/s. + + + align:start position:0% +product at radical 3 radians/s. +In the meantime, the angle associated + + align:start position:0% +In the meantime, the angle associated + + + align:start position:0% +In the meantime, the angle associated +with that, of course, is with the same + + align:start position:0% +with that, of course, is with the same + + + align:start position:0% +with that, of course, is with the same +quantity is one that starts at 0 degrees + + align:start position:0% +quantity is one that starts at 0 degrees + + + align:start position:0% +quantity is one that starts at 0 degrees +uh heads toward minus 270°. + + align:start position:0% +uh heads toward minus 270°. + + + align:start position:0% +uh heads toward minus 270°. +For our purpose, it's only necessary + + align:start position:0% +For our purpose, it's only necessary + + + align:start position:0% +For our purpose, it's only necessary +that we look at the angle in the + + align:start position:0% +that we look at the angle in the + + + align:start position:0% +that we look at the angle in the +vicinity of the crossover frequency out + + align:start position:0% +vicinity of the crossover frequency out + + + align:start position:0% +vicinity of the crossover frequency out +here. So I haven't drawn the complete + + align:start position:0% +here. So I haven't drawn the complete + + + align:start position:0% +here. So I haven't drawn the complete +angle curve but uh we we can find out + + align:start position:0% +angle curve but uh we we can find out + + + align:start position:0% +angle curve but uh we we can find out +what we need to by simply looking at the + + align:start position:0% +what we need to by simply looking at the + + + align:start position:0% +what we need to by simply looking at the +angle the behavior of the angle in the + + align:start position:0% +angle the behavior of the angle in the + + + align:start position:0% +angle the behavior of the angle in the +vicinity of the crossover frequency. + + align:start position:0% +vicinity of the crossover frequency. + + + align:start position:0% +vicinity of the crossover frequency. +Let's consider what happens if uh for + + align:start position:0% +Let's consider what happens if uh for + + + align:start position:0% +Let's consider what happens if uh for +example we assume that the amplitude at + + align:start position:0% +example we assume that the amplitude at + + + align:start position:0% +example we assume that the amplitude at +this point increases a little bit. Our + + align:start position:0% +this point increases a little bit. Our + + + align:start position:0% +this point increases a little bit. Our +describing function operating point is + + align:start position:0% +describing function operating point is + + + align:start position:0% +describing function operating point is +an amplitude of 1 / 2 pi. Let's assume + + align:start position:0% +an amplitude of 1 / 2 pi. Let's assume + + + align:start position:0% +an amplitude of 1 / 2 pi. Let's assume +that that amplitude increases just a + + align:start position:0% +that that amplitude increases just a + + + align:start position:0% +that that amplitude increases just a +little bit. + + align:start position:0% +little bit. + + + align:start position:0% +little bit. +Well, g subd of e is inversely + + align:start position:0% +Well, g subd of e is inversely + + + align:start position:0% +Well, g subd of e is inversely +proportional to e. Consequently, if e + + align:start position:0% +proportional to e. Consequently, if e + + + align:start position:0% +proportional to e. Consequently, if e +increases, the gain of our describing + + align:start position:0% +increases, the gain of our describing + + + align:start position:0% +increases, the gain of our describing +function, the magnitude of g subd of e + + align:start position:0% +function, the magnitude of g subd of e + + + align:start position:0% +function, the magnitude of g subd of e +will decrease. + + align:start position:0% +will decrease. + + + align:start position:0% +will decrease. +We now have a somewhat perturbed + + align:start position:0% +We now have a somewhat perturbed + + + align:start position:0% +We now have a somewhat perturbed +operating point. We've changed the + + align:start position:0% +operating point. We've changed the + + + align:start position:0% +operating point. We've changed the +magnitude to be slightly larger than 1 + + align:start position:0% +magnitude to be slightly larger than 1 + + + align:start position:0% +magnitude to be slightly larger than 1 +over 2 pi uh or the test amplitude to be + + align:start position:0% +over 2 pi uh or the test amplitude to be + + + align:start position:0% +over 2 pi uh or the test amplitude to be +slightly larger than 1 over 2 pi. And + + align:start position:0% +slightly larger than 1 over 2 pi. And + + + align:start position:0% +slightly larger than 1 over 2 pi. And +consequently, the magnitude g subd has + + align:start position:0% +consequently, the magnitude g subd has + + + align:start position:0% +consequently, the magnitude g subd has +decreased a little bit. + + align:start position:0% +decreased a little bit. + + + align:start position:0% +decreased a little bit. +And that tells us that our new curve + + align:start position:0% +And that tells us that our new curve + + + align:start position:0% +And that tells us that our new curve +parallels the original one and lies + + align:start position:0% +parallels the original one and lies + + + align:start position:0% +parallels the original one and lies +below it + + align:start position:0% +below it + + + align:start position:0% +below it +by some small amount like so. So in + + align:start position:0% +by some small amount like so. So in + + + align:start position:0% +by some small amount like so. So in +other words, this is the uh resultant + + align:start position:0% +other words, this is the uh resultant + + + align:start position:0% +other words, this is the uh resultant +negative of the loop transmission plot + + align:start position:0% +negative of the loop transmission plot + + + align:start position:0% +negative of the loop transmission plot +for a somewhat increased value of E. + + align:start position:0% + + + + align:start position:0% + +Uh if we decreased E slightly, we'd get + + align:start position:0% +Uh if we decreased E slightly, we'd get + + + align:start position:0% +Uh if we decreased E slightly, we'd get +a higher plot + + align:start position:0% + + + + align:start position:0% + +like so because a decreased value for E, + + align:start position:0% +like so because a decreased value for E, + + + align:start position:0% +like so because a decreased value for E, +a smaller value of E would result in a + + align:start position:0% +a smaller value of E would result in a + + + align:start position:0% +a smaller value of E would result in a +larger magnitude for G subd of E. + + align:start position:0% + + + + align:start position:0% + +So this is the sort of curve that + + align:start position:0% +So this is the sort of curve that + + + align:start position:0% +So this is the sort of curve that +results for a smaller test signal. Or if + + align:start position:0% +results for a smaller test signal. Or if + + + align:start position:0% +results for a smaller test signal. Or if +we assume that the amplitude of the + + align:start position:0% +we assume that the amplitude of the + + + align:start position:0% +we assume that the amplitude of the +oscillation that existed had decreased + + align:start position:0% +oscillation that existed had decreased + + + align:start position:0% +oscillation that existed had decreased +slightly. + + align:start position:0% +slightly. + + + align:start position:0% +slightly. +Well, now let's look at at the magnitude + + align:start position:0% +Well, now let's look at at the magnitude + + + align:start position:0% +Well, now let's look at at the magnitude +plot in conjunction with the angle plot. + + align:start position:0% +plot in conjunction with the angle plot. + + + align:start position:0% +plot in conjunction with the angle plot. +If we assume that the amplitude of of + + align:start position:0% +If we assume that the amplitude of of + + + align:start position:0% +If we assume that the amplitude of of +the signal at this point has increased + + align:start position:0% +the signal at this point has increased + + + align:start position:0% +the signal at this point has increased +slightly, + + align:start position:0% + + + + align:start position:0% + +we notice that the system crosses over + + align:start position:0% +we notice that the system crosses over + + + align:start position:0% +we notice that the system crosses over +in a region with positive phase margin. + + align:start position:0% +in a region with positive phase margin. + + + align:start position:0% +in a region with positive phase margin. +We cross over where the angle associated + + align:start position:0% +We cross over where the angle associated + + + align:start position:0% +We cross over where the angle associated +with the negative of the loop + + align:start position:0% +with the negative of the loop + + + align:start position:0% +with the negative of the loop +transmission is more positive than minus + + align:start position:0% +transmission is more positive than minus + + + align:start position:0% +transmission is more positive than minus +180°. In other words, the st the system + + align:start position:0% +180°. In other words, the st the system + + + align:start position:0% +180°. In other words, the st the system +is stable under those conditions at + + align:start position:0% +is stable under those conditions at + + + align:start position:0% +is stable under those conditions at +least in an absolute sense. It has small + + align:start position:0% +least in an absolute sense. It has small + + + align:start position:0% +least in an absolute sense. It has small +phase margin but nonetheless a positive + + align:start position:0% +phase margin but nonetheless a positive + + + align:start position:0% +phase margin but nonetheless a positive +phase margin. Well, we assume that that + + align:start position:0% +phase margin. Well, we assume that that + + + align:start position:0% +phase margin. Well, we assume that that +E increased a small amount and our + + align:start position:0% +E increased a small amount and our + + + align:start position:0% +E increased a small amount and our +system becomes stable in an absolute + + align:start position:0% +system becomes stable in an absolute + + + align:start position:0% +system becomes stable in an absolute +sense which means that the amplitude E + + align:start position:0% +sense which means that the amplitude E + + + align:start position:0% +sense which means that the amplitude E +would shrink tending back toward its + + align:start position:0% +would shrink tending back toward its + + + align:start position:0% +would shrink tending back toward its +original value. We assume that it it + + align:start position:0% +original value. We assume that it it + + + align:start position:0% +original value. We assume that it it +increased. We found the system becomes + + align:start position:0% +increased. We found the system becomes + + + align:start position:0% +increased. We found the system becomes +stable. The amplitude would shrink back + + align:start position:0% +stable. The amplitude would shrink back + + + align:start position:0% +stable. The amplitude would shrink back +down to its original value. Consequently + + align:start position:0% +down to its original value. Consequently + + + align:start position:0% +down to its original value. Consequently +uh or similarly uh if we assume that we + + align:start position:0% +uh or similarly uh if we assume that we + + + align:start position:0% +uh or similarly uh if we assume that we +had a smaller value for E, + + align:start position:0% + + + + align:start position:0% + +the system crossover now occurs in a + + align:start position:0% +the system crossover now occurs in a + + + align:start position:0% +the system crossover now occurs in a +region of negative phase margin. We have + + align:start position:0% +region of negative phase margin. We have + + + align:start position:0% +region of negative phase margin. We have +an an unstable system. We get + + align:start position:0% +an an unstable system. We get + + + align:start position:0% +an an unstable system. We get +exponentially growing responses that + + align:start position:0% +exponentially growing responses that + + + align:start position:0% +exponentially growing responses that +tend us tend once again to increase the + + align:start position:0% +tend us tend once again to increase the + + + align:start position:0% +tend us tend once again to increase the +magnitude of E, restore us to the + + align:start position:0% +magnitude of E, restore us to the + + + align:start position:0% +magnitude of E, restore us to the +original operating point. So here's an + + align:start position:0% +original operating point. So here's an + + + align:start position:0% +original operating point. So here's an +example of a system where there is an + + align:start position:0% +example of a system where there is an + + + align:start position:0% +example of a system where there is an +intersection in the gain phase plane and + + align:start position:0% +intersection in the gain phase plane and + + + align:start position:0% +intersection in the gain phase plane and +we find that the intersection represents + + align:start position:0% +we find that the intersection represents + + + align:start position:0% +we find that the intersection represents +a stable amplitude oscillation. We'd + + align:start position:0% +a stable amplitude oscillation. We'd + + + align:start position:0% +a stable amplitude oscillation. We'd +conclude that if we built this system uh + + align:start position:0% +conclude that if we built this system uh + + + align:start position:0% +conclude that if we built this system uh +that we should find it oscillating at + + align:start position:0% +that we should find it oscillating at + + + align:start position:0% +that we should find it oscillating at +radical 3 radians per second and that + + align:start position:0% +radical 3 radians per second and that + + + align:start position:0% +radical 3 radians per second and that +the amplitude of the signal at this + + align:start position:0% +the amplitude of the signal at this + + + align:start position:0% +the amplitude of the signal at this +point should be about 1 over 2 pi. And + + align:start position:0% +point should be about 1 over 2 pi. And + + + align:start position:0% +point should be about 1 over 2 pi. And +in fact, if we if we did that, we'd find + + align:start position:0% +in fact, if we if we did that, we'd find + + + align:start position:0% +in fact, if we if we did that, we'd find +out that that those numbers were very + + align:start position:0% +out that that those numbers were very + + + align:start position:0% +out that that those numbers were very +very nearly satisfied by the system. + + align:start position:0% +very nearly satisfied by the system. + + + align:start position:0% +very nearly satisfied by the system. +Uh we might want to go back and check uh + + align:start position:0% +Uh we might want to go back and check uh + + + align:start position:0% +Uh we might want to go back and check uh +we mentioned that one of the assumptions + + align:start position:0% +we mentioned that one of the assumptions + + + align:start position:0% +we mentioned that one of the assumptions +in describing function analysis is that + + align:start position:0% +in describing function analysis is that + + + align:start position:0% +in describing function analysis is that +the signal at the input to the + + align:start position:0% +the signal at the input to the + + + align:start position:0% +the signal at the input to the +nonlinearity is harmonically pure. And + + align:start position:0% +nonlinearity is harmonically pure. And + + + align:start position:0% +nonlinearity is harmonically pure. And +let's look at how well that assumption + + align:start position:0% +let's look at how well that assumption + + + align:start position:0% +let's look at how well that assumption +is satisfied for this particular + + align:start position:0% +is satisfied for this particular + + + align:start position:0% +is satisfied for this particular +example. + + align:start position:0% +example. + + + align:start position:0% +example. +We of course recognize that we'll have a + + align:start position:0% +We of course recognize that we'll have a + + + align:start position:0% +We of course recognize that we'll have a +square wave at this point in the loop. + + align:start position:0% +square wave at this point in the loop. + + + align:start position:0% +square wave at this point in the loop. +Our assumption is that the signal at + + align:start position:0% +Our assumption is that the signal at + + + align:start position:0% +Our assumption is that the signal at +this point is syosoidal. And so what we + + align:start position:0% +this point is syosoidal. And so what we + + + align:start position:0% +this point is syosoidal. And so what we +want to do is is look at the harmonic + + align:start position:0% +want to do is is look at the harmonic + + + align:start position:0% +want to do is is look at the harmonic +content of the square wave, chase it + + align:start position:0% +content of the square wave, chase it + + + align:start position:0% +content of the square wave, chase it +through the loop and see how much + + align:start position:0% +through the loop and see how much + + + align:start position:0% +through the loop and see how much +remains at this point. + + align:start position:0% +remains at this point. + + + align:start position:0% +remains at this point. +Well, let's look at that calculation. At + + align:start position:0% +Well, let's look at that calculation. At + + + align:start position:0% +Well, let's look at that calculation. At +the output of the nonlinearity, + + align:start position:0% +the output of the nonlinearity, + + + align:start position:0% +the output of the nonlinearity, +the ratio of the third harmonic to the + + align:start position:0% +the ratio of the third harmonic to the + + + align:start position:0% +the ratio of the third harmonic to the +first to the fundamental is simply 1/3. + + align:start position:0% +first to the fundamental is simply 1/3. + + + align:start position:0% +first to the fundamental is simply 1/3. +Uh the forier expansion for a square + + align:start position:0% +Uh the forier expansion for a square + + + align:start position:0% +Uh the forier expansion for a square +wave of course is 4 over pi times the + + align:start position:0% +wave of course is 4 over pi times the + + + align:start position:0% +wave of course is 4 over pi times the +sum of the odd harmonics where the + + align:start position:0% +sum of the odd harmonics where the + + + align:start position:0% +sum of the odd harmonics where the +amplitude of of the various harmonics is + + align:start position:0% +amplitude of of the various harmonics is + + + align:start position:0% +amplitude of of the various harmonics is +inversely proportional to the order of + + align:start position:0% +inversely proportional to the order of + + + align:start position:0% +inversely proportional to the order of +the harmonic. So the at least the third + + align:start position:0% +the harmonic. So the at least the third + + + align:start position:0% +the harmonic. So the at least the third +harmonic relative to the fundamental has + + align:start position:0% +harmonic relative to the fundamental has + + + align:start position:0% +harmonic relative to the fundamental has +an amplitude of 1/3. + + align:start position:0% +an amplitude of 1/3. + + + align:start position:0% +an amplitude of 1/3. +Similarly, we can evaluate the gain of + + align:start position:0% +Similarly, we can evaluate the gain of + + + align:start position:0% +Similarly, we can evaluate the gain of +the linear portion of our system uh to + + align:start position:0% +the linear portion of our system uh to + + + align:start position:0% +the linear portion of our system uh to +the third harmonic and compare that with + + align:start position:0% +the third harmonic and compare that with + + + align:start position:0% +the third harmonic and compare that with +the gain uh to the fundamental uh + + align:start position:0% +the gain uh to the fundamental uh + + + align:start position:0% +the gain uh to the fundamental uh +component. And when we do that, the gain + + align:start position:0% +component. And when we do that, the gain + + + align:start position:0% +component. And when we do that, the gain +to the fundamental component of course + + align:start position:0% +to the fundamental component of course + + + align:start position:0% +to the fundamental component of course +is simply equal to uh a evaluated at J + + align:start position:0% +is simply equal to uh a evaluated at J + + + align:start position:0% +is simply equal to uh a evaluated at J +radical 3. That's the fundamental uh the + + align:start position:0% +radical 3. That's the fundamental uh the + + + align:start position:0% +radical 3. That's the fundamental uh the +fundamental frequency. And we divide + + align:start position:0% +fundamental frequency. And we divide + + + align:start position:0% +fundamental frequency. And we divide +that by a evaluated at J * 3 radical 3. + + align:start position:0% +that by a evaluated at J * 3 radical 3. + + + align:start position:0% +that by a evaluated at J * 3 radical 3. +That's the third harmonic. If we perform + + align:start position:0% +That's the third harmonic. If we perform + + + align:start position:0% +That's the third harmonic. If we perform +that calculation, we find out that the + + align:start position:0% +that calculation, we find out that the + + + align:start position:0% +that calculation, we find out that the +ratio of the gain at the uh at the third + + align:start position:0% +ratio of the gain at the uh at the third + + + align:start position:0% +ratio of the gain at the uh at the third +harmonic uh to the um I have an inverse + + align:start position:0% +harmonic uh to the um I have an inverse + + + align:start position:0% +harmonic uh to the um I have an inverse +here. Uh + + align:start position:0% +here. Uh + + + align:start position:0% +here. Uh +the gain at the third harmonic is of + + align:start position:0% +the gain at the third harmonic is of + + + align:start position:0% +the gain at the third harmonic is of +course smaller. So this equation really + + align:start position:0% +course smaller. So this equation really + + + align:start position:0% +course smaller. So this equation really +should be flipped over. + + align:start position:0% +should be flipped over. + + + align:start position:0% +should be flipped over. +Uh the ratio of the gain at the third + + align:start position:0% +Uh the ratio of the gain at the third + + + align:start position:0% +Uh the ratio of the gain at the third +harmonic to that at the fundamental is + + align:start position:0% +harmonic to that at the fundamental is + + + align:start position:0% +harmonic to that at the fundamental is +simply 0.057. 057. + + align:start position:0% +simply 0.057. 057. + + + align:start position:0% +simply 0.057. 057. +Uh the + + align:start position:0% +Uh the + + + align:start position:0% +Uh the +non the linear elements attenuate the + + align:start position:0% +non the linear elements attenuate the + + + align:start position:0% +non the linear elements attenuate the +third harmonic by a factor of of nearly + + align:start position:0% +third harmonic by a factor of of nearly + + + align:start position:0% +third harmonic by a factor of of nearly +20 compared to the fundamental. + + align:start position:0% +20 compared to the fundamental. + + + align:start position:0% +20 compared to the fundamental. +Uh since we already since we started out + + align:start position:0% +Uh since we already since we started out + + + align:start position:0% +Uh since we already since we started out +with the third harmonic being only 1/3 + + align:start position:0% +with the third harmonic being only 1/3 + + + align:start position:0% +with the third harmonic being only 1/3 +of the amplitude of the fundamental the + + align:start position:0% +of the amplitude of the fundamental the + + + align:start position:0% +of the amplitude of the fundamental the +net result of that original lower + + align:start position:0% +net result of that original lower + + + align:start position:0% +net result of that original lower +harmonic amplitude and the much greater + + align:start position:0% +harmonic amplitude and the much greater + + + align:start position:0% +harmonic amplitude and the much greater +attenuation applied to the third + + align:start position:0% +attenuation applied to the third + + + align:start position:0% +attenuation applied to the third +harmonic is that the distortion or at + + align:start position:0% +harmonic is that the distortion or at + + + align:start position:0% +harmonic is that the distortion or at +least the third harmonic distortion in + + align:start position:0% +least the third harmonic distortion in + + + align:start position:0% +least the third harmonic distortion in +the signal is about 2%. + + align:start position:0% +the signal is about 2%. + + + align:start position:0% +the signal is about 2%. +uh the ratio 0.057 + + align:start position:0% +uh the ratio 0.057 + + + align:start position:0% +uh the ratio 0.057 +divided by 3. + + align:start position:0% +divided by 3. + + + align:start position:0% +divided by 3. +So we'd have about 2% + + align:start position:0% +So we'd have about 2% + + + align:start position:0% +So we'd have about 2% +uh third harmonic content in the signal + + align:start position:0% +uh third harmonic content in the signal + + + align:start position:0% +uh third harmonic content in the signal +at this point. Uh higher harmonics are + + align:start position:0% +at this point. Uh higher harmonics are + + + align:start position:0% +at this point. Uh higher harmonics are +attenuated even further. The uh fifth + + align:start position:0% +attenuated even further. The uh fifth + + + align:start position:0% +attenuated even further. The uh fifth +harmonic is first of all down relative + + align:start position:0% +harmonic is first of all down relative + + + align:start position:0% +harmonic is first of all down relative +to the third. It's its relative + + align:start position:0% +to the third. It's its relative + + + align:start position:0% +to the third. It's its relative +amplitude is 1/5 rather than 1/3. Uh + + align:start position:0% +amplitude is 1/5 rather than 1/3. Uh + + + align:start position:0% +amplitude is 1/5 rather than 1/3. Uh +furthermore, the linear portion of the + + align:start position:0% +furthermore, the linear portion of the + + + align:start position:0% +furthermore, the linear portion of the +loop attenuates the fifth harmonic even + + align:start position:0% +loop attenuates the fifth harmonic even + + + align:start position:0% +loop attenuates the fifth harmonic even +to an even greater extent than it + + align:start position:0% +to an even greater extent than it + + + align:start position:0% +to an even greater extent than it +attenuates the third harmonic. And so + + align:start position:0% +attenuates the third harmonic. And so + + + align:start position:0% +attenuates the third harmonic. And so +that uh uh fifth harmonic is is + + align:start position:0% +that uh uh fifth harmonic is is + + + align:start position:0% +that uh uh fifth harmonic is is +attenuated even to a much larger extent. + + align:start position:0% +attenuated even to a much larger extent. + + + align:start position:0% +attenuated even to a much larger extent. +Uh the net result is that the total + + align:start position:0% +Uh the net result is that the total + + + align:start position:0% +Uh the net result is that the total +harmonic distortion for this particular + + align:start position:0% +harmonic distortion for this particular + + + align:start position:0% +harmonic distortion for this particular +system at the input to the nonlinearity + + align:start position:0% +system at the input to the nonlinearity + + + align:start position:0% +system at the input to the nonlinearity +is about 2%. Say under these conditions + + align:start position:0% +is about 2%. Say under these conditions + + + align:start position:0% +is about 2%. Say under these conditions +uh the describing function analysis + + align:start position:0% +uh the describing function analysis + + + align:start position:0% +uh the describing function analysis +works very well. uh we find out that uh + + align:start position:0% +works very well. uh we find out that uh + + + align:start position:0% +works very well. uh we find out that uh +if we actually tested a system like + + align:start position:0% +if we actually tested a system like + + + align:start position:0% +if we actually tested a system like +this, constructed a system like this and + + align:start position:0% +this, constructed a system like this and + + + align:start position:0% +this, constructed a system like this and +tested it, we'd find out that the + + align:start position:0% +tested it, we'd find out that the + + + align:start position:0% +tested it, we'd find out that the +frequency of oscillation and the + + align:start position:0% +frequency of oscillation and the + + + align:start position:0% +frequency of oscillation and the +amplitude of the signal at this point uh + + align:start position:0% +amplitude of the signal at this point uh + + + align:start position:0% +amplitude of the signal at this point uh +were very nearly the values predicted by + + align:start position:0% +were very nearly the values predicted by + + + align:start position:0% +were very nearly the values predicted by +the describing function analysis. + + align:start position:0% +the describing function analysis. + + + align:start position:0% +the describing function analysis. +Next time we'll look at how we apply + + align:start position:0% +Next time we'll look at how we apply + + + align:start position:0% +Next time we'll look at how we apply +this analysis to several other systems + + align:start position:0% +this analysis to several other systems + + + align:start position:0% +this analysis to several other systems +of interest. Thank you. \ No newline at end of file diff --git a/wIq4CssPoO0.txt b/wIq4CssPoO0.txt new file mode 100644 index 0000000000000000000000000000000000000000..7aaf79f8efdb3e4b47c90a4735b7342c4bfc98c1 --- /dev/null +++ b/wIq4CssPoO0.txt @@ -0,0 +1,451 @@ +align:start position:0% + +This is mathematics for computer science + + align:start position:0% +This is mathematics for computer science + + + align:start position:0% +This is mathematics for computer science +6042J18062J + + align:start position:0% + + + + align:start position:0% + +a joint subject between electrical + + align:start position:0% +a joint subject between electrical + + + align:start position:0% +a joint subject between electrical +engineering and computer science and + + align:start position:0% +engineering and computer science and + + + align:start position:0% +engineering and computer science and +mathematics. + + align:start position:0% +mathematics. + + + align:start position:0% +mathematics. +Welcome. The instructors are professor + + align:start position:0% +Welcome. The instructors are professor + + + align:start position:0% +Welcome. The instructors are professor +Adam Chapala and professor Albert Ryer + + align:start position:0% +Adam Chapala and professor Albert Ryer + + + align:start position:0% +Adam Chapala and professor Albert Ryer +and I'm Albert Haya. + + align:start position:0% +and I'm Albert Haya. + + + align:start position:0% +and I'm Albert Haya. +Quickly summarizing what this course is + + align:start position:0% +Quickly summarizing what this course is + + + align:start position:0% +Quickly summarizing what this course is +about. It's about the uh math that + + align:start position:0% +about. It's about the uh math that + + + align:start position:0% +about. It's about the uh math that +computer scientists almost all need + + align:start position:0% +computer scientists almost all need + + + align:start position:0% +computer scientists almost all need +regularly and which you're not likely to + + align:start position:0% +regularly and which you're not likely to + + + align:start position:0% +regularly and which you're not likely to +have come across in your standard + + align:start position:0% +have come across in your standard + + + align:start position:0% +have come across in your standard +calculus classes. You may have seen some + + align:start position:0% +calculus classes. You may have seen some + + + align:start position:0% +calculus classes. You may have seen some +of this stuff in high school. For + + align:start position:0% +of this stuff in high school. For + + + align:start position:0% +of this stuff in high school. For +example, uh in calculus courses, people + + align:start position:0% +example, uh in calculus courses, people + + + align:start position:0% +example, uh in calculus courses, people +talk about functions on the real numbers + + align:start position:0% +talk about functions on the real numbers + + + align:start position:0% +talk about functions on the real numbers +and sometimes they'll talk about + + align:start position:0% +and sometimes they'll talk about + + + align:start position:0% +and sometimes they'll talk about +functions on the complex numbers. But + + align:start position:0% +functions on the complex numbers. But + + + align:start position:0% +functions on the complex numbers. But +computer scientists are usually dealing + + align:start position:0% +computer scientists are usually dealing + + + align:start position:0% +computer scientists are usually dealing +with much more abstract functions on + + align:start position:0% +with much more abstract functions on + + + align:start position:0% +with much more abstract functions on +data types and even functions on + + align:start position:0% +data types and even functions on + + + align:start position:0% +data types and even functions on +functions. And uh I wonder how many of + + align:start position:0% +functions. And uh I wonder how many of + + + align:start position:0% +functions. And uh I wonder how many of +you if I ask you to define abstractly + + align:start position:0% +you if I ask you to define abstractly + + + align:start position:0% +you if I ask you to define abstractly +what a function was could give that + + align:start position:0% +what a function was could give that + + + align:start position:0% +what a function was could give that +definition. In a couple of weeks uh in + + align:start position:0% +definition. In a couple of weeks uh in + + + align:start position:0% +definition. In a couple of weeks uh in +this class you'll be able to do that + + align:start position:0% +this class you'll be able to do that + + + align:start position:0% +this class you'll be able to do that +with facility. + + align:start position:0% +with facility. + + + align:start position:0% +with facility. +Um we will also be talking about a + + align:start position:0% +Um we will also be talking about a + + + align:start position:0% +Um we will also be talking about a +variety of standard discrete structures + + align:start position:0% +variety of standard discrete structures + + + align:start position:0% +variety of standard discrete structures +starting with the numbers which we think + + align:start position:0% +starting with the numbers which we think + + + align:start position:0% +starting with the numbers which we think +of as a structure because it's the + + align:start position:0% +of as a structure because it's the + + + align:start position:0% +of as a structure because it's the +numbers packaged with the operations on + + align:start position:0% +numbers packaged with the operations on + + + align:start position:0% +numbers packaged with the operations on +them like plus and times and + + align:start position:0% +them like plus and times and + + + align:start position:0% +them like plus and times and +exponentiation. We'll also talk about uh + + align:start position:0% +exponentiation. We'll also talk about uh + + + align:start position:0% +exponentiation. We'll also talk about uh +various other standard graphical uh data + + align:start position:0% +various other standard graphical uh data + + + align:start position:0% +various other standard graphical uh data +structures like graphs and trees. And + + align:start position:0% +structures like graphs and trees. And + + + align:start position:0% +structures like graphs and trees. And +we'll look at uh methods for counting + + align:start position:0% +we'll look at uh methods for counting + + + align:start position:0% +we'll look at uh methods for counting +the numbers of these different kinds of + + align:start position:0% +the numbers of these different kinds of + + + align:start position:0% +the numbers of these different kinds of +data structures as a typical fundamental + + align:start position:0% +data structures as a typical fundamental + + + align:start position:0% +data structures as a typical fundamental +problem in computer science where you + + align:start position:0% +problem in computer science where you + + + align:start position:0% +problem in computer science where you +typically want to know how big is the + + align:start position:0% +typically want to know how big is the + + + align:start position:0% +typically want to know how big is the +search space. For example, the search + + align:start position:0% +search space. For example, the search + + + align:start position:0% +search space. For example, the search +space of passwords had better be large + + align:start position:0% +space of passwords had better be large + + + align:start position:0% +space of passwords had better be large +or a cracker can just search through + + align:start position:0% +or a cracker can just search through + + + align:start position:0% +or a cracker can just search through +them all to find one that works. And + + align:start position:0% +them all to find one that works. And + + + align:start position:0% +them all to find one that works. And +finally, we'll talk about discrete + + align:start position:0% +finally, we'll talk about discrete + + + align:start position:0% +finally, we'll talk about discrete +probability theory, which is simply a + + align:start position:0% +probability theory, which is simply a + + + align:start position:0% +probability theory, which is simply a +version of probability theory where we + + align:start position:0% +version of probability theory where we + + + align:start position:0% +version of probability theory where we +can get by with sums instead of getting + + align:start position:0% +can get by with sums instead of getting + + + align:start position:0% +can get by with sums instead of getting +into the complications of integrals. + + align:start position:0% +into the complications of integrals. + + + align:start position:0% +into the complications of integrals. +So, here's a quick sanity check or + + align:start position:0% +So, here's a quick sanity check or + + + align:start position:0% +So, here's a quick sanity check or +vocabulary check. Do you know what + + align:start position:0% +vocabulary check. Do you know what + + + align:start position:0% +vocabulary check. Do you know what +discreet means? And I'll give you a + + align:start position:0% +discreet means? And I'll give you a + + + align:start position:0% +discreet means? And I'll give you a +hint. It doesn't mean discreet. If you + + align:start position:0% +hint. It doesn't mean discreet. If you + + + align:start position:0% +hint. It doesn't mean discreet. If you +don't know, this is a good moment to + + align:start position:0% +don't know, this is a good moment to + + + align:start position:0% +don't know, this is a good moment to +stop the video and look it up. \ No newline at end of file diff --git a/wKhhpELFyZo.txt b/wKhhpELFyZo.txt new file mode 100644 index 0000000000000000000000000000000000000000..c4efff632593b4991816a18e654c406839f402a3 --- /dev/null +++ b/wKhhpELFyZo.txt @@ -0,0 +1,12547 @@ +align:start position:0% + +the following content is provided by mit + + align:start position:0% +the following content is provided by mit + + + align:start position:0% +the following content is provided by mit +opencourseware under a creative commons + + align:start position:0% +opencourseware under a creative commons + + + align:start position:0% +opencourseware under a creative commons +license + + align:start position:0% +license + + + align:start position:0% +license +additional information about our license + + align:start position:0% +additional information about our license + + + align:start position:0% +additional information about our license +and mit opencourseware in general is + + align:start position:0% +and mit opencourseware in general is + + + align:start position:0% +and mit opencourseware in general is +available at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +comments + + align:start position:0% + + + + align:start position:0% + +questions anything about + + align:start position:0% +questions anything about + + + align:start position:0% +questions anything about +thursday + + align:start position:0% + + + + align:start position:0% + +on + + align:start position:0% +on + + + align:start position:0% +on +narrative ethics yeah + + align:start position:0% +narrative ethics yeah + + + align:start position:0% +narrative ethics yeah +yeah you all didn't get a chance to + + align:start position:0% +yeah you all didn't get a chance to + + + align:start position:0% +yeah you all didn't get a chance to +do your + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +and um that was + + align:start position:0% + + + + align:start position:0% + +that there is always someone + + align:start position:0% + + + + align:start position:0% + +uh what he said was something that i did + + align:start position:0% +uh what he said was something that i did + + + align:start position:0% +uh what he said was something that i did +not know + + align:start position:0% +not know + + + align:start position:0% +not know +but if i was taking the test would + + align:start position:0% +but if i was taking the test would + + + align:start position:0% +but if i was taking the test would +probably guess it + + align:start position:0% +probably guess it + + + align:start position:0% +probably guess it +that you do have + + align:start position:0% +that you do have + + + align:start position:0% +that you do have +a um + + align:start position:0% + + + + align:start position:0% + +cultural building and monitoring + + align:start position:0% +cultural building and monitoring + + + align:start position:0% +cultural building and monitoring +mechanism + + align:start position:0% +mechanism + + + align:start position:0% +mechanism +in all cultures they just don't people + + align:start position:0% +in all cultures they just don't people + + + align:start position:0% +in all cultures they just don't people +just don't go around doing what they're + + align:start position:0% +just don't go around doing what they're + + + align:start position:0% +just don't go around doing what they're +going to do + + align:start position:0% +going to do + + + align:start position:0% +going to do +i mean somebody is sitting down watching + + align:start position:0% +i mean somebody is sitting down watching + + + align:start position:0% +i mean somebody is sitting down watching +and talking about it + + align:start position:0% +and talking about it + + + align:start position:0% +and talking about it +and then passing it down + + align:start position:0% +and then passing it down + + + align:start position:0% +and then passing it down +but i did not + + align:start position:0% +but i did not + + + align:start position:0% +but i did not +know that you that that was a universal + + align:start position:0% +know that you that that was a universal + + + align:start position:0% +know that you that that was a universal +phenomenon + + align:start position:0% +phenomenon + + + align:start position:0% +phenomenon +yeah + + align:start position:0% + + + + align:start position:0% + +yeah that was a sweeping statement it + + align:start position:0% +yeah that was a sweeping statement it + + + align:start position:0% +yeah that was a sweeping statement it +see i had this picture that at least + + align:start position:0% +see i had this picture that at least + + + align:start position:0% +see i had this picture that at least +wherever you go there's a tradition and + + align:start position:0% +wherever you go there's a tradition and + + + align:start position:0% +wherever you go there's a tradition and +the tradition is known and is handed + + align:start position:0% +the tradition is known and is handed + + + align:start position:0% +the tradition is known and is handed +down + + align:start position:0% +down + + + align:start position:0% +down +i didn't know that it was discussed + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +then that people are always + + align:start position:0% +then that people are always + + + align:start position:0% +then that people are always +having a subject matter to i don't know + + align:start position:0% +having a subject matter to i don't know + + + align:start position:0% +having a subject matter to i don't know +if they're changing it + + align:start position:0% +if they're changing it + + + align:start position:0% +if they're changing it +but it's more than just handing it down + + align:start position:0% +but it's more than just handing it down + + + align:start position:0% +but it's more than just handing it down +it's more than just having one person + + align:start position:0% +it's more than just having one person + + + align:start position:0% +it's more than just having one person +who knows it + + align:start position:0% +who knows it + + + align:start position:0% +who knows it +and + + align:start position:0% +and + + + align:start position:0% +and +everybody hands it down and you just go + + align:start position:0% +everybody hands it down and you just go + + + align:start position:0% +everybody hands it down and you just go +from day to day + + align:start position:0% +from day to day + + + align:start position:0% +from day to day +that's more than that what they actually + + align:start position:0% +that's more than that what they actually + + + align:start position:0% +that's more than that what they actually +do + + align:start position:0% +do + + + align:start position:0% +do +have + + align:start position:0% +have + + + align:start position:0% +have +is + + align:start position:0% + + + + align:start position:0% + +an academic community a community that + + align:start position:0% +an academic community a community that + + + align:start position:0% +an academic community a community that +not only + + align:start position:0% +not only + + + align:start position:0% +not only +transmits culture + + align:start position:0% +transmits culture + + + align:start position:0% +transmits culture +but advances and preserves it + + align:start position:0% + + + + align:start position:0% + +now they probably don't do research on + + align:start position:0% +now they probably don't do research on + + + align:start position:0% +now they probably don't do research on +it but they're talking about it in terms + + align:start position:0% +it but they're talking about it in terms + + + align:start position:0% +it but they're talking about it in terms +of in in terms of + + align:start position:0% +of in in terms of + + + align:start position:0% +of in in terms of +of + + align:start position:0% + + + + align:start position:0% + +current problems right + + align:start position:0% +current problems right + + + align:start position:0% +current problems right +well and he suggested that + + align:start position:0% +well and he suggested that + + + align:start position:0% +well and he suggested that +sort of + + align:start position:0% + + + + align:start position:0% + +the way they evaluate the way in all + + align:start position:0% +the way they evaluate the way in all + + + align:start position:0% +the way they evaluate the way in all +cultures + + align:start position:0% +cultures + + + align:start position:0% +cultures +that those critics evaluate + + align:start position:0% +that those critics evaluate + + + align:start position:0% +that those critics evaluate +the norm + + align:start position:0% + + + + align:start position:0% + +he said + + align:start position:0% +he said + + + align:start position:0% +he said +is whether or not it promotes human + + align:start position:0% +is whether or not it promotes human + + + align:start position:0% +is whether or not it promotes human +flourishing + + align:start position:0% +flourishing + + + align:start position:0% +flourishing +yes + + align:start position:0% +yes + + + align:start position:0% +yes +and that's where he quoted thomas pogue + + align:start position:0% +and that's where he quoted thomas pogue + + + align:start position:0% +and that's where he quoted thomas pogue +that + + align:start position:0% + + + + align:start position:0% + +well flourishing comes + + align:start position:0% +well flourishing comes + + + align:start position:0% +well flourishing comes +out of of out of plato + + align:start position:0% +out of of out of plato + + + align:start position:0% +out of of out of plato +and it's still very popular + + align:start position:0% +and it's still very popular + + + align:start position:0% +and it's still very popular +uh but in different at different terms + + align:start position:0% +uh but in different at different terms + + + align:start position:0% +uh but in different at different terms +um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i'll tell you i'll tell you what i think + + align:start position:0% +i'll tell you i'll tell you what i think + + + align:start position:0% +i'll tell you i'll tell you what i think +i tell you what i think is pr is the + + align:start position:0% +i tell you what i think is pr is the + + + align:start position:0% +i tell you what i think is pr is the +best way to describe + + align:start position:0% +best way to describe + + + align:start position:0% +best way to describe +human flourishing and that is um + + align:start position:0% +human flourishing and that is um + + + align:start position:0% +human flourishing and that is um +the advertisement of the of the united + + align:start position:0% +the advertisement of the of the united + + + align:start position:0% +the advertisement of the of the united +states marine corps be all that you can + + align:start position:0% +states marine corps be all that you can + + + align:start position:0% +states marine corps be all that you can +be + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh it's not exactly destiny that i talk + + align:start position:0% +uh it's not exactly destiny that i talk + + + align:start position:0% +uh it's not exactly destiny that i talk +about + + align:start position:0% +about + + + align:start position:0% +about +but destiny is being all that you can be + + align:start position:0% +but destiny is being all that you can be + + + align:start position:0% +but destiny is being all that you can be +too + + align:start position:0% +too + + + align:start position:0% +too +so human flourishing + + align:start position:0% +so human flourishing + + + align:start position:0% +so human flourishing +you got to have a community where each + + align:start position:0% +you got to have a community where each + + + align:start position:0% +you got to have a community where each +individual can be all that they can be + + align:start position:0% +individual can be all that they can be + + + align:start position:0% +individual can be all that they can be +without + + align:start position:0% +without + + + align:start position:0% +without +a and without breaking the community up + + align:start position:0% +a and without breaking the community up + + + align:start position:0% +a and without breaking the community up +in the pieces + + align:start position:0% +in the pieces + + + align:start position:0% +in the pieces +so the balance of the individual and the + + align:start position:0% +so the balance of the individual and the + + + align:start position:0% +so the balance of the individual and the +community flourishing yeah + + align:start position:0% +community flourishing yeah + + + align:start position:0% +community flourishing yeah +so there's an individual definition + + align:start position:0% +so there's an individual definition + + + align:start position:0% +so there's an individual definition +there's a collective definition and + + align:start position:0% +there's a collective definition and + + + align:start position:0% +there's a collective definition and +there's + + align:start position:0% +there's + + + align:start position:0% +there's +some kind of uh not presumption but um + + align:start position:0% +some kind of uh not presumption but um + + + align:start position:0% +some kind of uh not presumption but um +presumption that harmony can exist + + align:start position:0% +presumption that harmony can exist + + + align:start position:0% +presumption that harmony can exist +between individual and society + + align:start position:0% +between individual and society + + + align:start position:0% +between individual and society +and um + + align:start position:0% +and um + + + align:start position:0% +and um +but i think you ought to get your own + + align:start position:0% +but i think you ought to get your own + + + align:start position:0% +but i think you ought to get your own +perspective on human flourishing and i + + align:start position:0% +perspective on human flourishing and i + + + align:start position:0% +perspective on human flourishing and i +think a good place to start is with + + align:start position:0% +think a good place to start is with + + + align:start position:0% +think a good place to start is with +plato + + align:start position:0% + + + + align:start position:0% + +okay um + + align:start position:0% + + + + align:start position:0% + +any other observations comments + + align:start position:0% +any other observations comments + + + align:start position:0% +any other observations comments +criticisms critiques + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +which is maybe the con the one + + align:start position:0% +which is maybe the con the one + + + align:start position:0% +which is maybe the con the one +possibility for + + align:start position:0% +possibility for + + + align:start position:0% +possibility for +for a weakness in combativation + + align:start position:0% +for a weakness in combativation + + + align:start position:0% +for a weakness in combativation +argument + + align:start position:0% +argument + + + align:start position:0% +argument +he says + + align:start position:0% +he says + + + align:start position:0% +he says +the critique of a culture + + align:start position:0% +the critique of a culture + + + align:start position:0% +the critique of a culture +insofar as how it allows for human + + align:start position:0% +insofar as how it allows for human + + + align:start position:0% +insofar as how it allows for human +flourishing is common across all + + align:start position:0% +flourishing is common across all + + + align:start position:0% +flourishing is common across all +cultures + + align:start position:0% +cultures + + + align:start position:0% +cultures +but what if human flourishing is + + align:start position:0% +but what if human flourishing is + + + align:start position:0% +but what if human flourishing is +different across all cultures + + align:start position:0% + + + + align:start position:0% + +yeah uh + + align:start position:0% + + + + align:start position:0% + +anyway go ahead + + align:start position:0% +anyway go ahead + + + align:start position:0% +anyway go ahead +ask me + + align:start position:0% +ask me + + + align:start position:0% +ask me +well i had some question about that + + align:start position:0% +well i had some question about that + + + align:start position:0% +well i had some question about that +well no i did not have questions about + + align:start position:0% +well no i did not have questions about + + + align:start position:0% +well no i did not have questions about +it i wanted to think more about that + + align:start position:0% +it i wanted to think more about that + + + align:start position:0% +it i wanted to think more about that +uh because + + align:start position:0% +uh because + + + align:start position:0% +uh because +i don't that's just one view on a goal + + align:start position:0% +i don't that's just one view on a goal + + + align:start position:0% +i don't that's just one view on a goal +for morocco + + align:start position:0% +for morocco + + + align:start position:0% +for morocco +it's just one + + align:start position:0% +it's just one + + + align:start position:0% +it's just one +view and the other view + + align:start position:0% +view and the other view + + + align:start position:0% +view and the other view +and what i really had problems with i'll + + align:start position:0% +and what i really had problems with i'll + + + align:start position:0% +and what i really had problems with i'll +tell you what really gave me some pause + + align:start position:0% +tell you what really gave me some pause + + + align:start position:0% +tell you what really gave me some pause +about that + + align:start position:0% +about that + + + align:start position:0% +about that +was that um + + align:start position:0% + + + + align:start position:0% + +see i have these three ways of life that + + align:start position:0% +see i have these three ways of life that + + + align:start position:0% +see i have these three ways of life that +that i learned from joseph campbell that + + align:start position:0% +that i learned from joseph campbell that + + + align:start position:0% +that i learned from joseph campbell that +and i added a little something to it + + align:start position:0% +and i added a little something to it + + + align:start position:0% +and i added a little something to it +that seemed to make a lot of sense to me + + align:start position:0% +that seemed to make a lot of sense to me + + + align:start position:0% +that seemed to make a lot of sense to me +and one of them is this way of the + + align:start position:0% +and one of them is this way of the + + + align:start position:0% +and one of them is this way of the +primary mask where you give up your + + align:start position:0% +primary mask where you give up your + + + align:start position:0% +primary mask where you give up your +personality + + align:start position:0% +personality + + + align:start position:0% +personality +better stated you give up your + + align:start position:0% +better stated you give up your + + + align:start position:0% +better stated you give up your +individuality + + align:start position:0% +individuality + + + align:start position:0% +individuality +in order to assume a particular kind of + + align:start position:0% +in order to assume a particular kind of + + + align:start position:0% +in order to assume a particular kind of +role + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% + + + + align:start position:0% + +it's not + + align:start position:0% +it's not + + + align:start position:0% +it's not +i know that the greeks + + align:start position:0% + + + + align:start position:0% + +i don't think that the greeks had a + + align:start position:0% +i don't think that the greeks had a + + + align:start position:0% +i don't think that the greeks had a +whole lot of respect for them + + align:start position:0% + + + + align:start position:0% + +and so when when you start talking about + + align:start position:0% +and so when when you start talking about + + + align:start position:0% +and so when when you start talking about +the greeks talking about + + align:start position:0% +the greeks talking about + + + align:start position:0% +the greeks talking about +human flourishing + + align:start position:0% +human flourishing + + + align:start position:0% +human flourishing +i don't think they're talking about + + align:start position:0% +i don't think they're talking about + + + align:start position:0% +i don't think they're talking about +the way the primary mask and i think + + align:start position:0% +the way the primary mask and i think + + + align:start position:0% +the way the primary mask and i think +that the where the primary mask is very + + align:start position:0% +that the where the primary mask is very + + + align:start position:0% +that the where the primary mask is very +popular east of greece + + align:start position:0% +popular east of greece + + + align:start position:0% +popular east of greece +in those days + + align:start position:0% +in those days + + + align:start position:0% +in those days +persians + + align:start position:0% +persians + + + align:start position:0% +persians +going out to chinese and others + + align:start position:0% +going out to chinese and others + + + align:start position:0% +going out to chinese and others +and the + + align:start position:0% +and the + + + align:start position:0% +and the +greek when we start talking about greek + + align:start position:0% +greek when we start talking about greek + + + align:start position:0% +greek when we start talking about greek +philosophy + + align:start position:0% +philosophy + + + align:start position:0% +philosophy +um + + align:start position:0% +um + + + align:start position:0% +um +you may disagree with this but i think + + align:start position:0% +you may disagree with this but i think + + + align:start position:0% +you may disagree with this but i think +that we have to remember when we talk + + align:start position:0% +that we have to remember when we talk + + + align:start position:0% +that we have to remember when we talk +about greek philosophy we're talking + + align:start position:0% +about greek philosophy we're talking + + + align:start position:0% +about greek philosophy we're talking +about the people who invented democracy + + align:start position:0% +about the people who invented democracy + + + align:start position:0% +about the people who invented democracy +so we're talking about the primacy of + + align:start position:0% +so we're talking about the primacy of + + + align:start position:0% +so we're talking about the primacy of +the individual + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +when you go outside of that kind of a + + align:start position:0% +when you go outside of that kind of a + + + align:start position:0% +when you go outside of that kind of a +culture and the primacy is not the + + align:start position:0% +culture and the primacy is not the + + + align:start position:0% +culture and the primacy is not the +individual the promise is a role in + + align:start position:0% +individual the promise is a role in + + + align:start position:0% +individual the promise is a role in +society + + align:start position:0% +society + + + align:start position:0% +society +then i think you got a con a conflict + + align:start position:0% +then i think you got a con a conflict + + + align:start position:0% +then i think you got a con a conflict +and i + + align:start position:0% +and i + + + align:start position:0% +and i +think that the conflict is um + + align:start position:0% + + + + align:start position:0% + +conflict is not bad i mean i well i i + + align:start position:0% +conflict is not bad i mean i well i i + + + align:start position:0% +conflict is not bad i mean i well i i +think that people just have different + + align:start position:0% +think that people just have different + + + align:start position:0% +think that people just have different +ways of fitting + + align:start position:0% +ways of fitting + + + align:start position:0% +ways of fitting +okay and there are probably ways for + + align:start position:0% +okay and there are probably ways for + + + align:start position:0% +okay and there are probably ways for +them to be + + align:start position:0% +them to be + + + align:start position:0% +them to be +worked out when people have to live + + align:start position:0% +worked out when people have to live + + + align:start position:0% +worked out when people have to live +together + + align:start position:0% +together + + + align:start position:0% +together +but i don't think that people should be + + align:start position:0% +but i don't think that people should be + + + align:start position:0% +but i don't think that people should be +forced to think one way or another + + align:start position:0% +forced to think one way or another + + + align:start position:0% +forced to think one way or another +it's good to know what other people + + align:start position:0% +it's good to know what other people + + + align:start position:0% +it's good to know what other people +think + + align:start position:0% +think + + + align:start position:0% +think +and if if their thoughts are um + + align:start position:0% +and if if their thoughts are um + + + align:start position:0% +and if if their thoughts are um +defensible then there should be value + + align:start position:0% +defensible then there should be value + + + align:start position:0% +defensible then there should be value +and you should look for ways to get + + align:start position:0% +and you should look for ways to get + + + align:start position:0% +and you should look for ways to get +along but + + align:start position:0% +along but + + + align:start position:0% +along but +i don't think that people should walk + + align:start position:0% +i don't think that people should walk + + + align:start position:0% +i don't think that people should walk +around the world without + + align:start position:0% +around the world without + + + align:start position:0% +around the world without +debate + + align:start position:0% +debate + + + align:start position:0% +debate +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and so i am so when he mentioned the + + align:start position:0% +and so i am so when he mentioned the + + + align:start position:0% +and so i am so when he mentioned the +flourishing part he talked to he went + + align:start position:0% +flourishing part he talked to he went + + + align:start position:0% +flourishing part he talked to he went +just went from something universal to + + align:start position:0% +just went from something universal to + + + align:start position:0% +just went from something universal to +something that was not universal + + align:start position:0% +something that was not universal + + + align:start position:0% +something that was not universal +so the observations + + align:start position:0% +so the observations + + + align:start position:0% +so the observations +the scientific more or less observations + + align:start position:0% +the scientific more or less observations + + + align:start position:0% +the scientific more or less observations +the um + + align:start position:0% +the um + + + align:start position:0% +the um +the um + + align:start position:0% + + + + align:start position:0% + +the um + + align:start position:0% +the um + + + align:start position:0% +the um +descriptive ethics + + align:start position:0% + + + + align:start position:0% + +he found universal themes + + align:start position:0% +he found universal themes + + + align:start position:0% +he found universal themes +but then when he started talking about + + align:start position:0% +but then when he started talking about + + + align:start position:0% +but then when he started talking about +normative + + align:start position:0% +normative + + + align:start position:0% +normative +ethics + + align:start position:0% +ethics + + + align:start position:0% +ethics +what should be the goal what constitutes + + align:start position:0% +what should be the goal what constitutes + + + align:start position:0% +what should be the goal what constitutes +then i am not so sure + + align:start position:0% +then i am not so sure + + + align:start position:0% +then i am not so sure +i need to think about it more but i'm + + align:start position:0% +i need to think about it more but i'm + + + align:start position:0% +i need to think about it more but i'm +not so sure that + + align:start position:0% +not so sure that + + + align:start position:0% +not so sure that +that has the power that the other part + + align:start position:0% +that has the power that the other part + + + align:start position:0% +that has the power that the other part +had in terms of universality + + align:start position:0% + + + + align:start position:0% + +you know that that's interesting + + align:start position:0% +you know that that's interesting + + + align:start position:0% +you know that that's interesting +that + + align:start position:0% +that + + + align:start position:0% +that +you say that's what + + align:start position:0% +you say that's what + + + align:start position:0% +you say that's what +gave you pause because what i was going + + align:start position:0% +gave you pause because what i was going + + + align:start position:0% +gave you pause because what i was going +to say was most surprising to me was his + + align:start position:0% +to say was most surprising to me was his + + + align:start position:0% +to say was most surprising to me was his +willingness + + align:start position:0% +willingness + + + align:start position:0% +willingness +in fact his insistence on + + align:start position:0% + + + + align:start position:0% + +not being morally relative + + align:start position:0% +not being morally relative + + + align:start position:0% +not being morally relative +morally + + align:start position:0% +morally + + + align:start position:0% +morally +one of the first things he told me when + + align:start position:0% +one of the first things he told me when + + + align:start position:0% +one of the first things he told me when +i was talking to him is i don't think we + + align:start position:0% +i was talking to him is i don't think we + + + align:start position:0% +i was talking to him is i don't think we +have to be morally relative i think + + align:start position:0% +have to be morally relative i think + + + align:start position:0% +have to be morally relative i think +there are + + align:start position:0% +there are + + + align:start position:0% +there are +universal ways to evaluate + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +um on thursday we had a + + align:start position:0% + + + + align:start position:0% + +so i was just surprised to hear a + + align:start position:0% +so i was just surprised to hear a + + + align:start position:0% +so i was just surprised to hear a +scholar + + align:start position:0% +scholar + + + align:start position:0% +scholar +come from a starting point of really + + align:start position:0% +come from a starting point of really + + + align:start position:0% +come from a starting point of really +wanting to have a hierarchy + + align:start position:0% +wanting to have a hierarchy + + + align:start position:0% +wanting to have a hierarchy +um + + align:start position:0% + + + + align:start position:0% + +one thing that i've heard him speak + + align:start position:0% +one thing that i've heard him speak + + + align:start position:0% +one thing that i've heard him speak +about before + + align:start position:0% + + + + align:start position:0% + +and we're not just talking about him you + + align:start position:0% +and we're not just talking about him you + + + align:start position:0% +and we're not just talking about him you +can criticize me and you can criticize + + align:start position:0% +can criticize me and you can criticize + + + align:start position:0% +can criticize me and you can criticize +what i said about winston + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +one thing he didn't have time to talk + + align:start position:0% +one thing he didn't have time to talk + + + align:start position:0% +one thing he didn't have time to talk +about + + align:start position:0% +about + + + align:start position:0% +about +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and if he had more time i'm sure he + + align:start position:0% +and if he had more time i'm sure he + + + align:start position:0% +and if he had more time i'm sure he +would have talked about but he's uh + + align:start position:0% +would have talked about but he's uh + + + align:start position:0% +would have talked about but he's uh +he is a he's an activist + + align:start position:0% +he is a he's an activist + + + align:start position:0% +he is a he's an activist +um + + align:start position:0% +um + + + align:start position:0% +um +with nigerian issues + + align:start position:0% +with nigerian issues + + + align:start position:0% +with nigerian issues +uh so uh the the things he talks about + + align:start position:0% +uh so uh the the things he talks about + + + align:start position:0% +uh so uh the the things he talks about +are not purely theoretical + + align:start position:0% + + + + align:start position:0% + +yeah he yeah he he applies + + align:start position:0% +yeah he yeah he he applies + + + align:start position:0% +yeah he yeah he he applies +what he does he's quite serious + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +if you have time + + align:start position:0% +if you have time + + + align:start position:0% +if you have time +well it's a good review it won't take a + + align:start position:0% +well it's a good review it won't take a + + + align:start position:0% +well it's a good review it won't take a +minute + + align:start position:0% +minute + + + align:start position:0% +minute +um + + align:start position:0% + + + + align:start position:0% + +mythology talks about three different + + align:start position:0% +mythology talks about three different + + + align:start position:0% +mythology talks about three different +ways of uh a way a person conducts one + + align:start position:0% +ways of uh a way a person conducts one + + + align:start position:0% +ways of uh a way a person conducts one +one's life + + align:start position:0% + + + + align:start position:0% + +um is called the + + align:start position:0% +um is called the + + + align:start position:0% +um is called the +individual way + + align:start position:0% +individual way + + + align:start position:0% +individual way +and that's where a person + + align:start position:0% +and that's where a person + + + align:start position:0% +and that's where a person +has to + + align:start position:0% +has to + + + align:start position:0% +has to +grow up by separating oneself out from + + align:start position:0% +grow up by separating oneself out from + + + align:start position:0% +grow up by separating oneself out from +the group finding + + align:start position:0% +the group finding + + + align:start position:0% +the group finding +one's own destiny + + align:start position:0% +one's own destiny + + + align:start position:0% +one's own destiny +by going out into the world + + align:start position:0% +by going out into the world + + + align:start position:0% +by going out into the world +and literally you know fighting dragons + + align:start position:0% +and literally you know fighting dragons + + + align:start position:0% +and literally you know fighting dragons +winning the holy grail so to speak + + align:start position:0% +winning the holy grail so to speak + + + align:start position:0% +winning the holy grail so to speak +and bringing it back and sharing it with + + align:start position:0% +and bringing it back and sharing it with + + + align:start position:0% +and bringing it back and sharing it with +everybody + + align:start position:0% +everybody + + + align:start position:0% +everybody +and one of the lessons of all of that it + + align:start position:0% +and one of the lessons of all of that it + + + align:start position:0% +and one of the lessons of all of that it +seems to me that from mythology is + + align:start position:0% +seems to me that from mythology is + + + align:start position:0% +seems to me that from mythology is +that if you have a leader + + align:start position:0% +that if you have a leader + + + align:start position:0% +that if you have a leader +that has power + + align:start position:0% +that has power + + + align:start position:0% +that has power +like a king + + align:start position:0% +like a king + + + align:start position:0% +like a king +then you want a person who has gone the + + align:start position:0% +then you want a person who has gone the + + + align:start position:0% +then you want a person who has gone the +individual way because that's a person + + align:start position:0% +individual way because that's a person + + + align:start position:0% +individual way because that's a person +who not only knows how to use power has + + align:start position:0% +who not only knows how to use power has + + + align:start position:0% +who not only knows how to use power has +fought dragon but will do it in your + + align:start position:0% +fought dragon but will do it in your + + + align:start position:0% +fought dragon but will do it in your +interest not for his own + + align:start position:0% +interest not for his own + + + align:start position:0% +interest not for his own +okay so that's called the individual way + + align:start position:0% +okay so that's called the individual way + + + align:start position:0% +okay so that's called the individual way +there's one called the way of the + + align:start position:0% +there's one called the way of the + + + align:start position:0% +there's one called the way of the +primary mask + + align:start position:0% +primary mask + + + align:start position:0% +primary mask +where a person + + align:start position:0% +where a person + + + align:start position:0% +where a person +comes to a point in one's life + + align:start position:0% +comes to a point in one's life + + + align:start position:0% +comes to a point in one's life +where they give up + + align:start position:0% +where they give up + + + align:start position:0% +where they give up +their individuality + + align:start position:0% +their individuality + + + align:start position:0% +their individuality +and become mother + + align:start position:0% +and become mother + + + align:start position:0% +and become mother +or father + + align:start position:0% +or father + + + align:start position:0% +or father +or king + + align:start position:0% +or king + + + align:start position:0% +or king +or + + align:start position:0% +or + + + align:start position:0% +or +whomever and and they define their lives + + align:start position:0% +whomever and and they define their lives + + + align:start position:0% +whomever and and they define their lives +first in terms of their role in role + + align:start position:0% +first in terms of their role in role + + + align:start position:0% +first in terms of their role in role +responsibilities + + align:start position:0% + + + + align:start position:0% + +that's called the way of the primary + + align:start position:0% +that's called the way of the primary + + + align:start position:0% +that's called the way of the primary +mask + + align:start position:0% +mask + + + align:start position:0% +mask +just the name + + align:start position:0% +just the name + + + align:start position:0% +just the name +um + + align:start position:0% +um + + + align:start position:0% +um +and then there is another way + + align:start position:0% +and then there is another way + + + align:start position:0% +and then there is another way +that i give a name to + + align:start position:0% +that i give a name to + + + align:start position:0% +that i give a name to +every people talk about it i didn't + + align:start position:0% +every people talk about it i didn't + + + align:start position:0% +every people talk about it i didn't +invent it but i just + + align:start position:0% +invent it but i just + + + align:start position:0% +invent it but i just +thought didn't see where anybody gave it + + align:start position:0% +thought didn't see where anybody gave it + + + align:start position:0% +thought didn't see where anybody gave it +a name + + align:start position:0% +a name + + + align:start position:0% +a name +uh and that's called i give it call it + + align:start position:0% +uh and that's called i give it call it + + + align:start position:0% +uh and that's called i give it call it +the popular way + + align:start position:0% +the popular way + + + align:start position:0% +the popular way +and that's the way a person + + align:start position:0% +and that's the way a person + + + align:start position:0% +and that's the way a person +uh does not go out does not assume a + + align:start position:0% +uh does not go out does not assume a + + + align:start position:0% +uh does not go out does not assume a +role + + align:start position:0% +role + + + align:start position:0% +role +uh but just demonstrates how to be a + + align:start position:0% +uh but just demonstrates how to be a + + + align:start position:0% +uh but just demonstrates how to be a +good citizen + + align:start position:0% +good citizen + + + align:start position:0% +good citizen +and the exam i've used some examples and + + align:start position:0% +and the exam i've used some examples and + + + align:start position:0% +and the exam i've used some examples and +one example of that is socrates + + align:start position:0% +one example of that is socrates + + + align:start position:0% +one example of that is socrates +socrates was not a leader + + align:start position:0% +socrates was not a leader + + + align:start position:0% +socrates was not a leader +socrates was one of the popul + + align:start position:0% +socrates was one of the popul + + + align:start position:0% +socrates was one of the popul +populists + + align:start position:0% +populists + + + align:start position:0% +populists +but uh he was he was a model at being a + + align:start position:0% +but uh he was he was a model at being a + + + align:start position:0% +but uh he was he was a model at being a +good uh + + align:start position:0% +good uh + + + align:start position:0% +good uh +since + + align:start position:0% +since + + + align:start position:0% +since +a good ordinary person + + align:start position:0% +a good ordinary person + + + align:start position:0% +a good ordinary person +now + + align:start position:0% +now + + + align:start position:0% +now +you can go different places + + align:start position:0% +you can go different places + + + align:start position:0% +you can go different places +uh in the academy and find the same + + align:start position:0% +uh in the academy and find the same + + + align:start position:0% +uh in the academy and find the same +lesson + + align:start position:0% +lesson + + + align:start position:0% +lesson +now one place i want to i just want that + + align:start position:0% +now one place i want to i just want that + + + align:start position:0% +now one place i want to i just want that +i've mentioned in this class + + align:start position:0% +i've mentioned in this class + + + align:start position:0% +i've mentioned in this class +um + + align:start position:0% +um + + + align:start position:0% +um +which is uh what religion does + + align:start position:0% +which is uh what religion does + + + align:start position:0% +which is uh what religion does +religion tries to + + align:start position:0% +religion tries to + + + align:start position:0% +religion tries to +give an example in + + align:start position:0% +give an example in + + + align:start position:0% +give an example in +the spiritual world + + align:start position:0% +the spiritual world + + + align:start position:0% +the spiritual world +of how to conduct our lives on + + align:start position:0% +of how to conduct our lives on + + + align:start position:0% +of how to conduct our lives on +in the material world + + align:start position:0% +in the material world + + + align:start position:0% +in the material world +and one of those examples they try to + + align:start position:0% +and one of those examples they try to + + + align:start position:0% +and one of those examples they try to +give us is an example of the family + + align:start position:0% +give us is an example of the family + + + align:start position:0% +give us is an example of the family +in christian religion that example is + + align:start position:0% +in christian religion that example is + + + align:start position:0% +in christian religion that example is +called the trinity + + align:start position:0% +called the trinity + + + align:start position:0% +called the trinity +father the son father the + + align:start position:0% +father the son father the + + + align:start position:0% +father the son father the +no no god the son god the father god the + + align:start position:0% +no no god the son god the father god the + + + align:start position:0% +no no god the son god the father god the +holy spirit okay so one is so the son is + + align:start position:0% +holy spirit okay so one is so the son is + + + align:start position:0% +holy spirit okay so one is so the son is +supposed to demonstrate how to be + + align:start position:0% +supposed to demonstrate how to be + + + align:start position:0% +supposed to demonstrate how to be +a good child in the family + + align:start position:0% +a good child in the family + + + align:start position:0% +a good child in the family +the father is supposed to show what the + + align:start position:0% +the father is supposed to show what the + + + align:start position:0% +the father is supposed to show what the +father's role is and the holy spirit is + + align:start position:0% +father's role is and the holy spirit is + + + align:start position:0% +father's role is and the holy spirit is +supposed to show what the mother's role + + align:start position:0% +supposed to show what the mother's role + + + align:start position:0% +supposed to show what the mother's role +is + + align:start position:0% +is + + + align:start position:0% +is +and you suppose if you understand that + + align:start position:0% +and you suppose if you understand that + + + align:start position:0% +and you suppose if you understand that +and and use it as authority + + align:start position:0% +and and use it as authority + + + align:start position:0% +and and use it as authority +for the same structure in other um + + align:start position:0% +for the same structure in other um + + + align:start position:0% +for the same structure in other um +and + + align:start position:0% +and + + + align:start position:0% +and +and other + + align:start position:0% + + + + align:start position:0% + +divisions of society the family + + align:start position:0% +divisions of society the family + + + align:start position:0% +divisions of society the family +community work in different places then + + align:start position:0% +community work in different places then + + + align:start position:0% +community work in different places then +that's supposed to make harmony for the + + align:start position:0% +that's supposed to make harmony for the + + + align:start position:0% +that's supposed to make harmony for the +whole society + + align:start position:0% +whole society + + + align:start position:0% +whole society +so + + align:start position:0% +so + + + align:start position:0% +so +so there's a good engineering word for + + align:start position:0% +so there's a good engineering word for + + + align:start position:0% +so there's a good engineering word for +all of this called fractal + + align:start position:0% +all of this called fractal + + + align:start position:0% +all of this called fractal +you have the whole + + align:start position:0% +you have the whole + + + align:start position:0% +you have the whole +and then when you look at the parts you + + align:start position:0% +and then when you look at the parts you + + + align:start position:0% +and then when you look at the parts you +see the whole rep is + + align:start position:0% +see the whole rep is + + + align:start position:0% +see the whole rep is +repeated when you look at the smaller + + align:start position:0% +repeated when you look at the smaller + + + align:start position:0% +repeated when you look at the smaller +part you see the whole repeat of the + + align:start position:0% +part you see the whole repeat of the + + + align:start position:0% +part you see the whole repeat of the +game + + align:start position:0% +game + + + align:start position:0% +game +and that that concept uh + + align:start position:0% +and that that concept uh + + + align:start position:0% +and that that concept uh +goes across different religions you + + align:start position:0% +goes across different religions you + + + align:start position:0% +goes across different religions you +might want to talk about that + + align:start position:0% +might want to talk about that + + + align:start position:0% +might want to talk about that +uh but um it uh seems to be very + + align:start position:0% +uh but um it uh seems to be very + + + align:start position:0% +uh but um it uh seems to be very +effective that if you learn how + + align:start position:0% +effective that if you learn how + + + align:start position:0% +effective that if you learn how +to be a good citizen of the family then + + align:start position:0% +to be a good citizen of the family then + + + align:start position:0% +to be a good citizen of the family then +it doesn't take a whole lot more to be a + + align:start position:0% +it doesn't take a whole lot more to be a + + + align:start position:0% +it doesn't take a whole lot more to be a +good citizen of the community + + align:start position:0% +good citizen of the community + + + align:start position:0% +good citizen of the community +and of these other + + align:start position:0% +and of these other + + + align:start position:0% +and of these other +social institutions + + align:start position:0% +social institutions + + + align:start position:0% +social institutions +so that's what i was talking about and + + align:start position:0% +so that's what i was talking about and + + + align:start position:0% +so that's what i was talking about and +that in um + + align:start position:0% +that in um + + + align:start position:0% +that in um +and that uh + + align:start position:0% +and that uh + + + align:start position:0% +and that uh +in a democracy + + align:start position:0% +in a democracy + + + align:start position:0% +in a democracy +the way of the individual way is + + align:start position:0% +the way of the individual way is + + + align:start position:0% +the way of the individual way is +respected a lot the way of the primary + + align:start position:0% +respected a lot the way of the primary + + + align:start position:0% +respected a lot the way of the primary +mask is now + + align:start position:0% +mask is now + + + align:start position:0% +mask is now +you're supposed to you're supposed to + + align:start position:0% +you're supposed to you're supposed to + + + align:start position:0% +you're supposed to you're supposed to +hold on to your individuality in a + + align:start position:0% +hold on to your individuality in a + + + align:start position:0% +hold on to your individuality in a +democracy + + align:start position:0% +democracy + + + align:start position:0% +democracy +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +communism + + align:start position:0% +communism + + + align:start position:0% +communism +the individual way is not respected the + + align:start position:0% +the individual way is not respected the + + + align:start position:0% +the individual way is not respected the +way the primary mask is respected + + align:start position:0% + + + + align:start position:0% + +you know you're supposed to come to the + + align:start position:0% +you know you're supposed to come to the + + + align:start position:0% +you know you're supposed to come to the +realization somewhere early in your life + + align:start position:0% +realization somewhere early in your life + + + align:start position:0% +realization somewhere early in your life +where the state is more important than + + align:start position:0% +where the state is more important than + + + align:start position:0% +where the state is more important than +the individual + + align:start position:0% +the individual + + + align:start position:0% +the individual +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so as the world it + + align:start position:0% +and so as the world it + + + align:start position:0% +and so as the world it +becomes more a global society + + align:start position:0% +becomes more a global society + + + align:start position:0% +becomes more a global society +then the stresses of trying to make all + + align:start position:0% +then the stresses of trying to make all + + + align:start position:0% +then the stresses of trying to make all +three of these ways work + + align:start position:0% +three of these ways work + + + align:start position:0% +three of these ways work +uh + + align:start position:0% +uh + + + align:start position:0% +uh +become stronger and we just have to find + + align:start position:0% +become stronger and we just have to find + + + align:start position:0% +become stronger and we just have to find +ways to deal with it + + align:start position:0% + + + + align:start position:0% + +i see a conflict between + + align:start position:0% +i see a conflict between + + + align:start position:0% +i see a conflict between +human flourishing + + align:start position:0% +human flourishing + + + align:start position:0% +human flourishing +and um + + align:start position:0% +and um + + + align:start position:0% +and um +the way of the primary mass that's what + + align:start position:0% +the way of the primary mass that's what + + + align:start position:0% +the way of the primary mass that's what +i see + + align:start position:0% +i see + + + align:start position:0% +i see +okay it's worthy of debate + + align:start position:0% +okay it's worthy of debate + + + align:start position:0% +okay it's worthy of debate +but i've had to get i've had i've given + + align:start position:0% +but i've had to get i've had i've given + + + align:start position:0% +but i've had to get i've had i've given +that some thought over the last couple + + align:start position:0% +that some thought over the last couple + + + align:start position:0% +that some thought over the last couple +of years and um + + align:start position:0% + + + + align:start position:0% + +but i think the way of the primary i'm + + align:start position:0% +but i think the way of the primary i'm + + + align:start position:0% +but i think the way of the primary i'm +sorry i think + + align:start position:0% +sorry i think + + + align:start position:0% +sorry i think +the concept of human flourishing as a + + align:start position:0% +the concept of human flourishing as a + + + align:start position:0% +the concept of human flourishing as a +goal + + align:start position:0% +goal + + + align:start position:0% +goal +uh is as justifiable as any other + + align:start position:0% +uh is as justifiable as any other + + + align:start position:0% +uh is as justifiable as any other +what i would call great concept okay i'm + + align:start position:0% +what i would call great concept okay i'm + + + align:start position:0% +what i would call great concept okay i'm +not talking about something that + + align:start position:0% +not talking about something that + + + align:start position:0% +not talking about something that +somebody thought of yesterday + + align:start position:0% +somebody thought of yesterday + + + align:start position:0% +somebody thought of yesterday +something that's been tested + + align:start position:0% + + + + align:start position:0% + +so any other view that i come up with + + align:start position:0% +so any other view that i come up with + + + align:start position:0% +so any other view that i come up with +will have + + align:start position:0% +will have + + + align:start position:0% +will have +will exhibit some of the same weaknesses + + align:start position:0% +will exhibit some of the same weaknesses + + + align:start position:0% +will exhibit some of the same weaknesses +okay + + align:start position:0% +okay + + + align:start position:0% +okay +it's just that i don't see that one + + align:start position:0% +it's just that i don't see that one + + + align:start position:0% +it's just that i don't see that one +fitting in as as as as a global + + align:start position:0% +fitting in as as as as a global + + + align:start position:0% +fitting in as as as as a global +as a global concept like the other + + align:start position:0% +as a global concept like the other + + + align:start position:0% +as a global concept like the other +concepts that the bodyguaran was talking + + align:start position:0% +concepts that the bodyguaran was talking + + + align:start position:0% +concepts that the bodyguaran was talking +about that were that i thought were + + align:start position:0% +about that were that i thought were + + + align:start position:0% +about that were that i thought were +global i would see them as global + + align:start position:0% +global i would see them as global + + + align:start position:0% +global i would see them as global +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in ways that i didn't describe uh + + align:start position:0% +in ways that i didn't describe uh + + + align:start position:0% +in ways that i didn't describe uh +earlier um + + align:start position:0% +earlier um + + + align:start position:0% +earlier um +joseph campbell does the same thing + + align:start position:0% +joseph campbell does the same thing + + + align:start position:0% +joseph campbell does the same thing +see joseph campbell + + align:start position:0% +see joseph campbell + + + align:start position:0% +see joseph campbell +depending on which lecture you're + + align:start position:0% +depending on which lecture you're + + + align:start position:0% +depending on which lecture you're +listening to can drift off into + + align:start position:0% +listening to can drift off into + + + align:start position:0% +listening to can drift off into +cultural anthropology and stay there + + align:start position:0% +cultural anthropology and stay there + + + align:start position:0% +cultural anthropology and stay there +he can get very much involved in + + align:start position:0% +he can get very much involved in + + + align:start position:0% +he can get very much involved in +and + + align:start position:0% +and + + + align:start position:0% +and +then he'll start talking about how those + + align:start position:0% +then he'll start talking about how those + + + align:start position:0% +then he'll start talking about how those +how you'll find the same + + align:start position:0% +how you'll find the same + + + align:start position:0% +how you'll find the same +rituals + + align:start position:0% +rituals + + + align:start position:0% +rituals +uh in all societies + + align:start position:0% + + + + align:start position:0% + +and uh for example there's one ritual + + align:start position:0% +and uh for example there's one ritual + + + align:start position:0% +and uh for example there's one ritual +where it's in + + align:start position:0% +where it's in + + + align:start position:0% +where it's in +it's in where + + align:start position:0% +it's in where + + + align:start position:0% +it's in where +uh + + align:start position:0% + + + + align:start position:0% + +it's in um + + align:start position:0% + + + + align:start position:0% + +it's in i can see the island in my head + + align:start position:0% +it's in i can see the island in my head + + + align:start position:0% +it's in i can see the island in my head +it's in southeast asia + + align:start position:0% + + + + align:start position:0% + +i can't think of the country but when + + align:start position:0% +i can't think of the country but when + + + align:start position:0% +i can't think of the country but when +two people get married + + align:start position:0% + + + + align:start position:0% + +okay then there's this big celebration + + align:start position:0% +okay then there's this big celebration + + + align:start position:0% +okay then there's this big celebration +where there is this where they build + + align:start position:0% +where there is this where they build + + + align:start position:0% +where there is this where they build +this um + + align:start position:0% +this um + + + align:start position:0% +this um +tunnel + + align:start position:0% +tunnel + + + align:start position:0% +tunnel +out of grasses + + align:start position:0% +out of grasses + + + align:start position:0% +out of grasses +weeds and + + align:start position:0% +weeds and + + + align:start position:0% +weeds and +and then there's this bulge at the end + + align:start position:0% +and then there's this bulge at the end + + + align:start position:0% +and then there's this bulge at the end +and the two people + + align:start position:0% +and the two people + + + align:start position:0% +and the two people +come into the tunnel from different + + align:start position:0% +come into the tunnel from different + + + align:start position:0% +come into the tunnel from different +sides + + align:start position:0% +sides + + + align:start position:0% +sides +and they crawl through it + + align:start position:0% +and they crawl through it + + + align:start position:0% +and they crawl through it +and when they come out at the other end + + align:start position:0% +and when they come out at the other end + + + align:start position:0% +and when they come out at the other end +everybody goes berserk + + align:start position:0% +everybody goes berserk + + + align:start position:0% +everybody goes berserk +oh it's a great thing well what it is is + + align:start position:0% +oh it's a great thing well what it is is + + + align:start position:0% +oh it's a great thing well what it is is +that it's really born again that's the + + align:start position:0% +that it's really born again that's the + + + align:start position:0% +that it's really born again that's the +fallopian tube + + align:start position:0% +fallopian tube + + + align:start position:0% +fallopian tube +that the two now the two eggs + + align:start position:0% +that the two now the two eggs + + + align:start position:0% +that the two now the two eggs +parts of the egg have come together and + + align:start position:0% +parts of the egg have come together and + + + align:start position:0% +parts of the egg have come together and +they've come out as one + + align:start position:0% +they've come out as one + + + align:start position:0% +they've come out as one +and + + align:start position:0% +and + + + align:start position:0% +and +whoever the person was + + align:start position:0% +whoever the person was + + + align:start position:0% +whoever the person was +because jim in that society and the + + align:start position:0% +because jim in that society and the + + + align:start position:0% +because jim in that society and the +reigning + + align:start position:0% +reigning + + + align:start position:0% +reigning +they come out their different names you + + align:start position:0% +they come out their different names you + + + align:start position:0% +they come out their different names you +know and they're they've come out as one + + align:start position:0% +know and they're they've come out as one + + + align:start position:0% +know and they're they've come out as one +and uh the whole + + align:start position:0% +and uh the whole + + + align:start position:0% +and uh the whole +village + + align:start position:0% +village + + + align:start position:0% +village +you know goes berserk + + align:start position:0% +you know goes berserk + + + align:start position:0% +you know goes berserk +well i mean doesn't that sound familiar + + align:start position:0% +well i mean doesn't that sound familiar + + + align:start position:0% +well i mean doesn't that sound familiar +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you can find different expressions of + + align:start position:0% +so you can find different expressions of + + + align:start position:0% +so you can find different expressions of +the same thing + + align:start position:0% +the same thing + + + align:start position:0% +the same thing +in a lot of different places + + align:start position:0% +in a lot of different places + + + align:start position:0% +in a lot of different places +so um + + align:start position:0% +so um + + + align:start position:0% +so um +so i think that's + + align:start position:0% +so i think that's + + + align:start position:0% +so i think that's +that is what uh + + align:start position:0% +that is what uh + + + align:start position:0% +that is what uh +one of the lessons we learned + + align:start position:0% +one of the lessons we learned + + + align:start position:0% +one of the lessons we learned +about gays + + align:start position:0% + + + + align:start position:0% + +that was just brought up here just + + align:start position:0% +that was just brought up here just + + + align:start position:0% +that was just brought up here just +before you came in and i assigned it as + + align:start position:0% +before you came in and i assigned it as + + + align:start position:0% +before you came in and i assigned it as +homework + + align:start position:0% +homework + + + align:start position:0% +homework +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +yeah well no i sanded this homework + + align:start position:0% +yeah well no i sanded this homework + + + align:start position:0% +yeah well no i sanded this homework +today + + align:start position:0% +today + + + align:start position:0% +today +because i wasn't prepared to give a + + align:start position:0% +because i wasn't prepared to give a + + + align:start position:0% +because i wasn't prepared to give a +lecture on it + + align:start position:0% +lecture on it + + + align:start position:0% +lecture on it +uh frankly all right so uh start with + + align:start position:0% +uh frankly all right so uh start with + + + align:start position:0% +uh frankly all right so uh start with +plate hold and go through with some + + align:start position:0% +plate hold and go through with some + + + align:start position:0% +plate hold and go through with some +with + + align:start position:0% +with + + + align:start position:0% +with +some of the things people have said + + align:start position:0% +some of the things people have said + + + align:start position:0% +some of the things people have said +about human flourishing + + align:start position:0% +about human flourishing + + + align:start position:0% +about human flourishing +and see if you can't pick out one idea + + align:start position:0% +and see if you can't pick out one idea + + + align:start position:0% +and see if you can't pick out one idea +that appeals to you + + align:start position:0% +that appeals to you + + + align:start position:0% +that appeals to you +and um + + align:start position:0% +and um + + + align:start position:0% +and um +you might find ways to live with that + + align:start position:0% +you might find ways to live with that + + + align:start position:0% +you might find ways to live with that +that's a good tool + + align:start position:0% + + + + align:start position:0% + +i said a few things that i hadn't said + + align:start position:0% +i said a few things that i hadn't said + + + align:start position:0% +i said a few things that i hadn't said +before + + align:start position:0% +before + + + align:start position:0% +before +in this class + + align:start position:0% +in this class + + + align:start position:0% +in this class +and got a few noses turned up + + align:start position:0% + + + + align:start position:0% + +any comments on any of that + + align:start position:0% + + + + align:start position:0% + +let's give them a chance to + + align:start position:0% + + + + align:start position:0% + +say what they think + + align:start position:0% +say what they think + + + align:start position:0% +say what they think +because this is i mean this is a + + align:start position:0% +because this is i mean this is a + + + align:start position:0% +because this is i mean this is a +university isn't it + + align:start position:0% + + + + align:start position:0% + +no presentation today presentation on + + align:start position:0% +no presentation today presentation on + + + align:start position:0% +no presentation today presentation on +thursday + + align:start position:0% + + + + align:start position:0% + +want to talk about it more + + align:start position:0% + + + + align:start position:0% + +yeah i mean i guess + + align:start position:0% +yeah i mean i guess + + + align:start position:0% +yeah i mean i guess +what i recall + + align:start position:0% +what i recall + + + align:start position:0% +what i recall +is the new things had to do with + + align:start position:0% +is the new things had to do with + + + align:start position:0% +is the new things had to do with +defining learning disciplines + + align:start position:0% +defining learning disciplines + + + align:start position:0% +defining learning disciplines +um + + align:start position:0% +um + + + align:start position:0% +um +as a specialty of knowledge and + + align:start position:0% +as a specialty of knowledge and + + + align:start position:0% +as a specialty of knowledge and +a special claim on + + align:start position:0% +a special claim on + + + align:start position:0% +a special claim on +some cognitive process + + align:start position:0% +some cognitive process + + + align:start position:0% +some cognitive process +or mental progness process underlying + + align:start position:0% +or mental progness process underlying + + + align:start position:0% +or mental progness process underlying +the specialty + + align:start position:0% +the specialty + + + align:start position:0% +the specialty +okay that empowers the specialist okay + + align:start position:0% + + + + align:start position:0% + +so yeah i don't know + + align:start position:0% + + + + align:start position:0% + +let's go through that yeah + + align:start position:0% +let's go through that yeah + + + align:start position:0% +let's go through that yeah +okay um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +yes let's go through that um we've got + + align:start position:0% +yes let's go through that um we've got + + + align:start position:0% +yes let's go through that um we've got +time + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +okay um + + align:start position:0% + + + + align:start position:0% + +what i'm going to talk about now is + + align:start position:0% +what i'm going to talk about now is + + + align:start position:0% +what i'm going to talk about now is +comes from my own researchers + + align:start position:0% + + + + align:start position:0% + +but 99 of it is not new + + align:start position:0% + + + + align:start position:0% + +i'll let you know what i spent new spin + + align:start position:0% +i'll let you know what i spent new spin + + + align:start position:0% +i'll let you know what i spent new spin +out + + align:start position:0% +out + + + align:start position:0% +out +okay + + align:start position:0% + + + + align:start position:0% + +i shouldn't say 90 amps + + align:start position:0% +i shouldn't say 90 amps + + + align:start position:0% +i shouldn't say 90 amps +10 percent of it + + align:start position:0% + + + + align:start position:0% + +but i'll let you know + + align:start position:0% +but i'll let you know + + + align:start position:0% +but i'll let you know +where my uh + + align:start position:0% + + + + align:start position:0% + +spin comes in + + align:start position:0% +spin comes in + + + align:start position:0% +spin comes in +okay um + + align:start position:0% + + + + align:start position:0% + +there is discussion about what is called + + align:start position:0% +there is discussion about what is called + + + align:start position:0% +there is discussion about what is called +learning + + align:start position:0% +learning + + + align:start position:0% +learning +in psychology better stated educational + + align:start position:0% +in psychology better stated educational + + + align:start position:0% +in psychology better stated educational +psychology + + align:start position:0% +psychology + + + align:start position:0% +psychology +and there are discussions about + + align:start position:0% + + + + align:start position:0% + +four categories of learning + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% +one + + + align:start position:0% +one +two + + align:start position:0% +two + + + align:start position:0% +two +three + + align:start position:0% +three + + + align:start position:0% +three +four + + align:start position:0% + + + + align:start position:0% + +one category of learning is knowledge + + align:start position:0% + + + + align:start position:0% + +another category is values + + align:start position:0% + + + + align:start position:0% + +and let's stop for a second + + align:start position:0% +and let's stop for a second + + + align:start position:0% +and let's stop for a second +here + + align:start position:0% + + + + align:start position:0% + +uh because what i'm going to put up over + + align:start position:0% +uh because what i'm going to put up over + + + align:start position:0% +uh because what i'm going to put up over +here is + + align:start position:0% +here is + + + align:start position:0% +here is +um + + align:start position:0% +um + + + align:start position:0% +um +this is + + align:start position:0% +this is + + + align:start position:0% +this is +but i'm going to use words to describe + + align:start position:0% +but i'm going to use words to describe + + + align:start position:0% +but i'm going to use words to describe +something that a lot of people talk + + align:start position:0% +something that a lot of people talk + + + align:start position:0% +something that a lot of people talk +about + + align:start position:0% +about + + + align:start position:0% +about +but they have not + + align:start position:0% +but they have not + + + align:start position:0% +but they have not +used these same words + + align:start position:0% + + + + align:start position:0% + +and that is + + align:start position:0% +and that is + + + align:start position:0% +and that is +on this side + + align:start position:0% + + + + align:start position:0% + +what i have called already + + align:start position:0% + + + + align:start position:0% + +praxis and practice + + align:start position:0% +praxis and practice + + + align:start position:0% +praxis and practice +and + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i've talked about what a knowledge + + align:start position:0% +i've talked about what a knowledge + + + align:start position:0% +i've talked about what a knowledge +statement looks like + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i've talked about two kinds of knowledge + + align:start position:0% +i've talked about two kinds of knowledge + + + align:start position:0% +i've talked about two kinds of knowledge +statements rational and empirical + + align:start position:0% + + + + align:start position:0% + +we've talked about value judgments + + align:start position:0% +we've talked about value judgments + + + align:start position:0% +we've talked about value judgments +uh and one kind of value judgment is a + + align:start position:0% +uh and one kind of value judgment is a + + + align:start position:0% +uh and one kind of value judgment is a +moral or ethical value of judgment + + align:start position:0% +moral or ethical value of judgment + + + align:start position:0% +moral or ethical value of judgment +you're talking about now good and bad + + align:start position:0% + + + + align:start position:0% + +right and wrong + + align:start position:0% + + + + align:start position:0% + +another kind of value judgment is an + + align:start position:0% +another kind of value judgment is an + + + align:start position:0% +another kind of value judgment is an +aesthetic value judgment + + align:start position:0% + + + + align:start position:0% + +then we talked a little bit about + + align:start position:0% + + + + align:start position:0% + +action + + align:start position:0% + + + + align:start position:0% + +and theory + + align:start position:0% + + + + align:start position:0% + +praxis being not a theory of what action + + align:start position:0% +praxis being not a theory of what action + + + align:start position:0% +praxis being not a theory of what action +is + + align:start position:0% +is + + + align:start position:0% +is +but a theory of how to perform a certain + + align:start position:0% +but a theory of how to perform a certain + + + align:start position:0% +but a theory of how to perform a certain +kind of an action + + align:start position:0% +kind of an action + + + align:start position:0% +kind of an action +it's the it's the kind of theoretical + + align:start position:0% +it's the it's the kind of theoretical + + + align:start position:0% +it's the it's the kind of theoretical +thought you do just before you act + + align:start position:0% +thought you do just before you act + + + align:start position:0% +thought you do just before you act +and + + align:start position:0% +and + + + align:start position:0% +and +to understand this + + align:start position:0% +to understand this + + + align:start position:0% +to understand this +part + + align:start position:0% +part + + + align:start position:0% +part +here uh what i do is add this little + + align:start position:0% +here uh what i do is add this little + + + align:start position:0% +here uh what i do is add this little +piece here + + align:start position:0% +piece here + + + align:start position:0% +piece here +and it's called the commitment pathway + + align:start position:0% +and it's called the commitment pathway + + + align:start position:0% +and it's called the commitment pathway +from wishes + + align:start position:0% + + + + align:start position:0% + +to + + align:start position:0% +to + + + align:start position:0% +to +wants + + align:start position:0% + + + + align:start position:0% + +to + + align:start position:0% +to + + + align:start position:0% +to +intentions + + align:start position:0% + + + + align:start position:0% + +to action + + align:start position:0% + + + + align:start position:0% + +this this is called the commitment + + align:start position:0% +this this is called the commitment + + + align:start position:0% +this this is called the commitment +pathway + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +praxis + + align:start position:0% +praxis + + + align:start position:0% +praxis +is a theory for getting through this + + align:start position:0% +is a theory for getting through this + + + align:start position:0% +is a theory for getting through this +thing and practice is actually what you + + align:start position:0% +thing and practice is actually what you + + + align:start position:0% +thing and practice is actually what you +do to get through it how do you go from + + align:start position:0% +do to get through it how do you go from + + + align:start position:0% +do to get through it how do you go from +a wish to a want to an intention + + align:start position:0% +a wish to a want to an intention + + + align:start position:0% +a wish to a want to an intention +to action that you think will bring + + align:start position:0% +to action that you think will bring + + + align:start position:0% +to action that you think will bring +about the wish + + align:start position:0% +about the wish + + + align:start position:0% +about the wish +or will fulfill the wish + + align:start position:0% +or will fulfill the wish + + + align:start position:0% +or will fulfill the wish +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now what's the difference between a wish + + align:start position:0% +now what's the difference between a wish + + + align:start position:0% +now what's the difference between a wish +and a want i want an intention tension + + align:start position:0% +and a want i want an intention tension + + + align:start position:0% +and a want i want an intention tension +and action + + align:start position:0% +and action + + + align:start position:0% +and action +all right + + align:start position:0% + + + + align:start position:0% + +i've got another role to talk about that + + align:start position:0% +i've got another role to talk about that + + + align:start position:0% +i've got another role to talk about that +under the psychological capacity to know + + align:start position:0% +under the psychological capacity to know + + + align:start position:0% +under the psychological capacity to know +is called the cognition + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +there is + + align:start position:0% +there is + + + align:start position:0% +there is +in psychology + + align:start position:0% +in psychology + + + align:start position:0% +in psychology +there is a + + align:start position:0% +there is a + + + align:start position:0% +there is a +and in brain science + + align:start position:0% + + + + align:start position:0% + +there + + align:start position:0% +there + + + align:start position:0% +there +a considerable proportion of the + + align:start position:0% +a considerable proportion of the + + + align:start position:0% +a considerable proportion of the +research and discussion is on the + + align:start position:0% +research and discussion is on the + + + align:start position:0% +research and discussion is on the +cognition + + align:start position:0% +cognition + + + align:start position:0% +cognition +now + + align:start position:0% +now + + + align:start position:0% +now +i will not hazard a percentage + + align:start position:0% +i will not hazard a percentage + + + align:start position:0% +i will not hazard a percentage +um + + align:start position:0% +um + + + align:start position:0% +um +i will say offhand maybe 80 + + align:start position:0% + + + + align:start position:0% + +all the research that's done on brain + + align:start position:0% +all the research that's done on brain + + + align:start position:0% +all the research that's done on brain +and cognitive sciences in the learning + + align:start position:0% +and cognitive sciences in the learning + + + align:start position:0% +and cognitive sciences in the learning +areas + + align:start position:0% +areas + + + align:start position:0% +areas +is on the cognition + + align:start position:0% +is on the cognition + + + align:start position:0% +is on the cognition +now + + align:start position:0% +now + + + align:start position:0% +now +i've heard brain and cognitive + + align:start position:0% +i've heard brain and cognitive + + + align:start position:0% +i've heard brain and cognitive +scientists say that okay + + align:start position:0% +scientists say that okay + + + align:start position:0% +scientists say that okay +but + + align:start position:0% +but + + + align:start position:0% +but +the point is that at least in the united + + align:start position:0% +the point is that at least in the united + + + align:start position:0% +the point is that at least in the united +states + + align:start position:0% +states + + + align:start position:0% +states +almost all of it's on the cognition + + align:start position:0% +almost all of it's on the cognition + + + align:start position:0% +almost all of it's on the cognition +and this goes into the um + + align:start position:0% +and this goes into the um + + + align:start position:0% +and this goes into the um +significance of knowledge + + align:start position:0% +significance of knowledge + + + align:start position:0% +significance of knowledge +because as we'll see in a minute + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +sciences have specialties in knowledge + + align:start position:0% +sciences have specialties in knowledge + + + align:start position:0% +sciences have specialties in knowledge +so if you really want to advance science + + align:start position:0% +so if you really want to advance science + + + align:start position:0% +so if you really want to advance science +uh in the brain and in the mind + + align:start position:0% +uh in the brain and in the mind + + + align:start position:0% +uh in the brain and in the mind +using great scholarship you gotta have + + align:start position:0% +using great scholarship you gotta have + + + align:start position:0% +using great scholarship you gotta have +to talk about knowledge in the cognition + + align:start position:0% + + + + align:start position:0% + +now following this same role + + align:start position:0% +now following this same role + + + align:start position:0% +now following this same role +you get something called the affect + + align:start position:0% + + + + align:start position:0% + +which is has feelings of good and bad + + align:start position:0% +which is has feelings of good and bad + + + align:start position:0% +which is has feelings of good and bad +but it also has some other feelings + + align:start position:0% +but it also has some other feelings + + + align:start position:0% +but it also has some other feelings +in it + + align:start position:0% +in it + + + align:start position:0% +in it +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i've read whereas uh + + align:start position:0% +i've read whereas uh + + + align:start position:0% +i've read whereas uh +psychologists will say this is more + + align:start position:0% +psychologists will say this is more + + + align:start position:0% +psychologists will say this is more +difficult to study + + align:start position:0% +difficult to study + + + align:start position:0% +difficult to study +than this + + align:start position:0% +than this + + + align:start position:0% +than this +uh but underlying + + align:start position:0% +uh but underlying + + + align:start position:0% +uh but underlying +this is called the conation + + align:start position:0% + + + + align:start position:0% + +and underlying this + + align:start position:0% +and underlying this + + + align:start position:0% +and underlying this +is called + + align:start position:0% + + + + align:start position:0% + +psychomotor skill + + align:start position:0% + + + + align:start position:0% + +and so what you are talking about in + + align:start position:0% +and so what you are talking about in + + + align:start position:0% +and so what you are talking about in +terms of the learned disciplines + + align:start position:0% +terms of the learned disciplines + + + align:start position:0% +terms of the learned disciplines +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and when if i'll define that in a minute + + align:start position:0% +and when if i'll define that in a minute + + + align:start position:0% +and when if i'll define that in a minute +but it's good to just talk about this + + align:start position:0% +but it's good to just talk about this + + + align:start position:0% +but it's good to just talk about this +chart first + + align:start position:0% + + + + align:start position:0% + +what you're talking about when it comes + + align:start position:0% +what you're talking about when it comes + + + align:start position:0% +what you're talking about when it comes +to the learned disciplines + + align:start position:0% +to the learned disciplines + + + align:start position:0% +to the learned disciplines +are what are two words that i use + + align:start position:0% +are what are two words that i use + + + align:start position:0% +are what are two words that i use +one word i did not invent + + align:start position:0% +one word i did not invent + + + align:start position:0% +one word i did not invent +the other one i didn't invent but i mean + + align:start position:0% +the other one i didn't invent but i mean + + + align:start position:0% +the other one i didn't invent but i mean +i don't know if how many people use + + align:start position:0% +i don't know if how many people use + + + align:start position:0% +i don't know if how many people use +talk about the subject so i need needed + + align:start position:0% +talk about the subject so i need needed + + + align:start position:0% +talk about the subject so i need needed +a word + + align:start position:0% +a word + + + align:start position:0% +a word +and the first word is specialty in + + align:start position:0% +and the first word is specialty in + + + align:start position:0% +and the first word is specialty in +element word is + + align:start position:0% +element word is + + + align:start position:0% +element word is +forte + + align:start position:0% +forte + + + align:start position:0% +forte +so + + align:start position:0% +so + + + align:start position:0% +so +you'll find the word specialty being + + align:start position:0% +you'll find the word specialty being + + + align:start position:0% +you'll find the word specialty being +used when people say that a learner + + align:start position:0% +used when people say that a learner + + + align:start position:0% +used when people say that a learner +discipline has a specialty that is + + align:start position:0% +discipline has a specialty that is + + + align:start position:0% +discipline has a specialty that is +deep penetration + + align:start position:0% +deep penetration + + + align:start position:0% +deep penetration +of learning into one of these categories + + align:start position:0% +of learning into one of these categories + + + align:start position:0% +of learning into one of these categories +so a specialty of science is deep + + align:start position:0% +so a specialty of science is deep + + + align:start position:0% +so a specialty of science is deep +penetration into the into the category + + align:start position:0% +penetration into the into the category + + + align:start position:0% +penetration into the into the category +of knowledge + + align:start position:0% +of knowledge + + + align:start position:0% +of knowledge +particularly knowledge about the + + align:start position:0% +particularly knowledge about the + + + align:start position:0% +particularly knowledge about the +material world + + align:start position:0% + + + + align:start position:0% + +and you can break the material world up + + align:start position:0% +and you can break the material world up + + + align:start position:0% +and you can break the material world up +into two kinds + + align:start position:0% +into two kinds + + + align:start position:0% +into two kinds +the physical and the social + + align:start position:0% +the physical and the social + + + align:start position:0% +the physical and the social +from which you get the physical sciences + + align:start position:0% +from which you get the physical sciences + + + align:start position:0% +from which you get the physical sciences +and the social science + + align:start position:0% + + + + align:start position:0% + +a specialty in values can be ethics or + + align:start position:0% +a specialty in values can be ethics or + + + align:start position:0% +a specialty in values can be ethics or +aesthetics + + align:start position:0% +aesthetics + + + align:start position:0% +aesthetics +and there and if you want to put ethics + + align:start position:0% +and there and if you want to put ethics + + + align:start position:0% +and there and if you want to put ethics +and aesthetics together i've got another + + align:start position:0% +and aesthetics together i've got another + + + align:start position:0% +and aesthetics together i've got another +word for you called axiology + + align:start position:0% + + + + align:start position:0% + +and aesthetics is usually best + + align:start position:0% +and aesthetics is usually best + + + align:start position:0% +and aesthetics is usually best +understood at the + + align:start position:0% +understood at the + + + align:start position:0% +understood at the +at the at the + + align:start position:0% +at the at the + + + align:start position:0% +at the at the +fundamental level in terms of the senses + + align:start position:0% + + + + align:start position:0% + +so if you + + align:start position:0% +so if you + + + align:start position:0% +so if you +did i say aesthetics + + align:start position:0% +did i say aesthetics + + + align:start position:0% +did i say aesthetics +so if you're talking about the good as + + align:start position:0% +so if you're talking about the good as + + + align:start position:0% +so if you're talking about the good as +applied to uh + + align:start position:0% +applied to uh + + + align:start position:0% +applied to uh +to the visual senses + + align:start position:0% +to the visual senses + + + align:start position:0% +to the visual senses +then art is one + + align:start position:0% +then art is one + + + align:start position:0% +then art is one +of the um + + align:start position:0% + + + + align:start position:0% + +learning disciplines that has a + + align:start position:0% +learning disciplines that has a + + + align:start position:0% +learning disciplines that has a +specialty and values + + align:start position:0% +specialty and values + + + align:start position:0% +specialty and values +the way i put it + + align:start position:0% +the way i put it + + + align:start position:0% +the way i put it +if you're talking about the auditory + + align:start position:0% +if you're talking about the auditory + + + align:start position:0% +if you're talking about the auditory +senses + + align:start position:0% +senses + + + align:start position:0% +senses +then music + + align:start position:0% +then music + + + align:start position:0% +then music +is a + + align:start position:0% + + + + align:start position:0% + +learner discipline + + align:start position:0% +learner discipline + + + align:start position:0% +learner discipline +uh if you're talking about the gustatory + + align:start position:0% + + + + align:start position:0% + +taste + + align:start position:0% +taste + + + align:start position:0% +taste +then you're talking about um + + align:start position:0% +then you're talking about um + + + align:start position:0% +then you're talking about um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +food you're talking about food + + align:start position:0% +food you're talking about food + + + align:start position:0% +food you're talking about food +preparation you talk about something be + + align:start position:0% +preparation you talk about something be + + + align:start position:0% +preparation you talk about something be +prepared better than another + + align:start position:0% +prepared better than another + + + align:start position:0% +prepared better than another +um + + align:start position:0% +um + + + align:start position:0% +um +can and let me see did i miss any old + + align:start position:0% +can and let me see did i miss any old + + + align:start position:0% +can and let me see did i miss any old +factory + + align:start position:0% +factory + + + align:start position:0% +factory +that's that can be food too for + + align:start position:0% +that's that can be food too for + + + align:start position:0% +that's that can be food too for +us uh + + align:start position:0% +us uh + + + align:start position:0% +us uh +and tactile that's the physical + + align:start position:0% +and tactile that's the physical + + + align:start position:0% +and tactile that's the physical +feeling of things um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +on this side + + align:start position:0% +on this side + + + align:start position:0% +on this side +over here + + align:start position:0% +over here + + + align:start position:0% +over here +uh i claim that you'll find the + + align:start position:0% +uh i claim that you'll find the + + + align:start position:0% +uh i claim that you'll find the +practical learned disciplines + + align:start position:0% +practical learned disciplines + + + align:start position:0% +practical learned disciplines +engineering + + align:start position:0% +engineering + + + align:start position:0% +engineering +medicine + + align:start position:0% +medicine + + + align:start position:0% +medicine +law + + align:start position:0% +law + + + align:start position:0% +law +and the rest of them + + align:start position:0% +and the rest of them + + + align:start position:0% +and the rest of them +all right + + align:start position:0% +all right + + + align:start position:0% +all right +now + + align:start position:0% +now + + + align:start position:0% +now +so + + align:start position:0% +so + + + align:start position:0% +so +engineering is going to have a specialty + + align:start position:0% +engineering is going to have a specialty + + + align:start position:0% +engineering is going to have a specialty +in both of these + + align:start position:0% + + + + align:start position:0% + +and when you start talking about what we + + align:start position:0% +and when you start talking about what we + + + align:start position:0% +and when you start talking about what we +call engineering theories that's mostly + + align:start position:0% +call engineering theories that's mostly + + + align:start position:0% +call engineering theories that's mostly +practice + + align:start position:0% + + + + align:start position:0% + +praxis and when you talk about + + align:start position:0% +praxis and when you talk about + + + align:start position:0% +praxis and when you talk about +how you actually put the theories into + + align:start position:0% +how you actually put the theories into + + + align:start position:0% +how you actually put the theories into +action + + align:start position:0% +action + + + align:start position:0% +action +you're talking about practice + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +now in all learned disciplines all + + align:start position:0% +now in all learned disciplines all + + + align:start position:0% +now in all learned disciplines all +you'll find all four of these areas + + align:start position:0% +you'll find all four of these areas + + + align:start position:0% +you'll find all four of these areas +but the specialty is the question + + align:start position:0% +but the specialty is the question + + + align:start position:0% +but the specialty is the question +so in engineering + + align:start position:0% +so in engineering + + + align:start position:0% +so in engineering +in other words most most engineering + + align:start position:0% +in other words most most engineering + + + align:start position:0% +in other words most most engineering +professors are specialties in + + align:start position:0% +professors are specialties in + + + align:start position:0% +professors are specialties in +engineering practice + + align:start position:0% +engineering practice + + + align:start position:0% +engineering practice +and when you go out and somebody's + + align:start position:0% +and when you go out and somebody's + + + align:start position:0% +and when you go out and somebody's +actually building the building up and as + + align:start position:0% +actually building the building up and as + + + align:start position:0% +actually building the building up and as +chief of the project as a specialty in + + align:start position:0% +chief of the project as a specialty in + + + align:start position:0% +chief of the project as a specialty in +practice + + align:start position:0% +practice + + + align:start position:0% +practice +uh in universities um + + align:start position:0% + + + + align:start position:0% + +if you go to uh + + align:start position:0% + + + + align:start position:0% + +well you can go to some universities um + + align:start position:0% +well you can go to some universities um + + + align:start position:0% +well you can go to some universities um +and the students will have a very solid + + align:start position:0% +and the students will have a very solid + + + align:start position:0% +and the students will have a 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howard + + + align:start position:0% +undergraduate education at howard +because howard's educational program was + + align:start position:0% +because howard's educational program was + + + align:start position:0% +because howard's educational program was +built up as a as an imitation of mit's + + align:start position:0% +built up as a as an imitation of mit's + + + align:start position:0% +built up as a as an imitation of mit's +program + + align:start position:0% +program + + + align:start position:0% +program +because the first dean of engineering + + align:start position:0% +because the first dean of engineering + + + align:start position:0% +because the first dean of engineering +and dean for 30 years was an mit + + align:start position:0% +and dean for 30 years was an mit + + + align:start position:0% +and dean for 30 years was an mit +graduate + + align:start position:0% + + + + align:start position:0% + +our graduates various have never come + + align:start position:0% +our graduates various have never come + + + align:start position:0% +our graduates various have never come +right out of school the first day + + align:start position:0% +right out of school the first day + + + align:start position:0% +right out of school the first day +and went right on a construction job and + + align:start position:0% +and went right on a construction job and + + + align:start position:0% +and went right on a construction job and +knew what to do + + align:start position:0% +knew what to do + + + align:start position:0% +knew what to do +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you have to sit there and learn it for a + + align:start position:0% +you have to sit there and learn it for a + + + align:start position:0% +you have to sit there and learn it for a +while but + + align:start position:0% +while but + + + align:start position:0% +while but +we knew what to do the first day when we + + align:start position:0% +we knew what to do the first day when we + + + align:start position:0% +we knew what to do the first day when we +got to graduate school + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so in other words you can stress + + align:start position:0% +so in other words you can stress + + + align:start position:0% +so in other words you can stress +practice as opposed to practice + + align:start position:0% +practice as opposed to practice + + + align:start position:0% +practice as opposed to practice +in some educational systems and you can + + align:start position:0% +in some educational systems and you can + + + align:start position:0% +in some educational systems and you can +stress practice in terms of practice in + + align:start position:0% +stress practice in terms of practice in + + + align:start position:0% +stress practice in terms of practice in +some educational system + + align:start position:0% +some educational system + + + align:start position:0% +some educational system +so um + + align:start position:0% +so um + + + align:start position:0% +so um +a friend of mine who graduated from + + align:start position:0% +a friend of mine who graduated from + + + align:start position:0% +a friend of mine who graduated from +texas a m said + + align:start position:0% +texas a m said + + + align:start position:0% +texas a m said +when we walk out of the ivory tower we + + align:start position:0% +when we walk out of the ivory tower we + + + align:start position:0% +when we walk out of the ivory tower we +can go on a construction project and we + + align:start position:0% +can go on a construction project and we + + + align:start position:0% +can go on a construction project and we +know what to do first day + + align:start position:0% +know what to do first day + + + align:start position:0% +know what to do first day +stanford + + align:start position:0% +stanford + + + align:start position:0% +stanford +you come out got a good education + + align:start position:0% +you come out got a good education + + + align:start position:0% +you come out got a good education +you have to stand around for a little + + align:start position:0% +you have to stand around for a little + + + align:start position:0% +you have to stand around for a little +while + + align:start position:0% +while + + + align:start position:0% +while +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so that's basically these + + align:start position:0% +all right so that's basically these + + + align:start position:0% +all right so that's basically these +differences + + align:start position:0% +differences + + + align:start position:0% +differences +now here's + + align:start position:0% + + + + align:start position:0% + +now here's what inevitably comes into + + align:start position:0% +now here's what inevitably comes into + + + align:start position:0% +now here's what inevitably comes into +a discussion about all of this that i + + align:start position:0% +a discussion about all of this that i + + + align:start position:0% +a discussion about all of this that i +think describes more about the culture + + align:start position:0% +think describes more about the culture + + + align:start position:0% +think describes more about the culture +of higher education + + align:start position:0% +of higher education + + + align:start position:0% +of higher education +than any of this + + align:start position:0% +than any of this + + + align:start position:0% +than any of this +and that is + + align:start position:0% +and that is + + + align:start position:0% +and that is +on what basis if you're a scientist do + + align:start position:0% +on what basis if you're a scientist do + + + align:start position:0% +on what basis if you're a scientist do +you say + + align:start position:0% +you say + + + align:start position:0% +you say +you have the ability + + align:start position:0% +you have the ability + + + align:start position:0% +you have the ability +to know all of these scientific things + + align:start position:0% +to know all of these scientific things + + + align:start position:0% +to know all of these scientific things +or that you have an inclination to be a + + align:start position:0% +or that you have an inclination to be a + + + align:start position:0% +or that you have an inclination to be a +scientist + + align:start position:0% +scientist + + + align:start position:0% +scientist +well what people will say is + + align:start position:0% +well what people will say is + + + align:start position:0% +well what people will say is +that they have a very well developed + + align:start position:0% +that they have a very well developed + + + align:start position:0% +that they have a very well developed +cognition + + align:start position:0% + + + + align:start position:0% + +they make a special claim + + align:start position:0% +they make a special claim + + + align:start position:0% +they make a special claim +on their innate ability + + align:start position:0% +on their innate ability + + + align:start position:0% +on their innate ability +to know + + align:start position:0% + + + + align:start position:0% + +or they will make a special claim on how + + align:start position:0% +or they will make a special claim on how + + + align:start position:0% +or they will make a special claim on how +that innate ability has been cultivated + + align:start position:0% +that innate ability has been cultivated + + + align:start position:0% +that innate ability has been cultivated +to know + + align:start position:0% +to know + + + align:start position:0% +to know +and that's what i call the forte + + align:start position:0% + + + + align:start position:0% + +so the specialty and the forte go + + align:start position:0% +so the specialty and the forte go + + + align:start position:0% +so the specialty and the forte go +together + + align:start position:0% +together + + + align:start position:0% +together +but specialty + + align:start position:0% + + + + align:start position:0% + +is understood in this row and forte is + + align:start position:0% +is understood in this row and forte is + + + align:start position:0% +is understood in this row and forte is +understood in this room + + align:start position:0% + + + + align:start position:0% + +and uh that is important + + align:start position:0% +and uh that is important + + + align:start position:0% +and uh that is important +because um + + align:start position:0% + + + + align:start position:0% + +as i discussed at the end of the + + align:start position:0% +as i discussed at the end of the + + + align:start position:0% +as i discussed at the end of the +seminar + + align:start position:0% +seminar + + + align:start position:0% +seminar +or when when people started asking me + + align:start position:0% +or when when people started asking me + + + align:start position:0% +or when when people started asking me +some questions about what does it mean + + align:start position:0% +some questions about what does it mean + + + align:start position:0% +some questions about what does it mean +when + + align:start position:0% +when + + + align:start position:0% +when +you engage two learned disciplines + + align:start position:0% +you engage two learned disciplines + + + align:start position:0% +you engage two learned disciplines +and + + align:start position:0% +and + + + align:start position:0% +and +does that mean that you engage the + + align:start position:0% +does that mean that you engage the + + + align:start position:0% +does that mean that you engage the +practitioners or the or the scholars of + + align:start position:0% +practitioners or the or the scholars of + + + align:start position:0% +practitioners or the or the scholars of +the two learning disciplines and the + + align:start position:0% +the two learning disciplines and the + + + align:start position:0% +the two learning disciplines and the +answer is no not necessarily and so the + + align:start position:0% +answer is no not necessarily and so the + + + align:start position:0% +answer is no not necessarily and so the +question is why and one of one of the + + align:start position:0% +question is why and one of one of the + + + align:start position:0% +question is why and one of one of the +reasons is not just that + + align:start position:0% +reasons is not just that + + + align:start position:0% +reasons is not just that +you're talking about uh + + align:start position:0% +you're talking about uh + + + align:start position:0% +you're talking about uh +tradition as being a conflict you're + + align:start position:0% +tradition as being a conflict you're + + + align:start position:0% +tradition as being a conflict you're +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +an arrogance that's built up in scholars + + align:start position:0% +an arrogance that's built up in scholars + + + align:start position:0% +an arrogance that's built up in scholars +because of this forte + + align:start position:0% +because of this forte + + + align:start position:0% +because of this forte +we make this and and the arrogance is + + align:start position:0% +we make this and and the arrogance is + + + align:start position:0% +we make this and and the arrogance is +not unjustified i mean maybe the word + + align:start position:0% +not unjustified i mean maybe the word + + + align:start position:0% +not unjustified i mean maybe the word +arrogance means unjustified that's not + + align:start position:0% +arrogance means unjustified that's not + + + align:start position:0% +arrogance means unjustified that's not +the way i'm using it + + align:start position:0% +the way i'm using it + + + align:start position:0% +the way i'm using it +i'm using it as a uh + + align:start position:0% +i'm using it as a uh + + + align:start position:0% +i'm using it as a uh +particularly acute self-esteem + + align:start position:0% +particularly acute self-esteem + + + align:start position:0% +particularly acute self-esteem +that once + + align:start position:0% +that once + + + align:start position:0% +that once +you have a once you have gained a lot of + + align:start position:0% +you have a once you have gained a lot of + + + align:start position:0% +you have a once you have gained a lot of +scientific knowledge you believe that + + align:start position:0% +scientific knowledge you believe that + + + align:start position:0% +scientific knowledge you believe that +you have abilities + + align:start position:0% +you have abilities + + + align:start position:0% +you have abilities +to gain knowledge + + align:start position:0% +to gain knowledge + + + align:start position:0% +to gain knowledge +in certain ways that other people don't + + align:start position:0% +in certain ways that other people don't + + + align:start position:0% +in certain ways that other people don't +have those abilities + + align:start position:0% + + + + align:start position:0% + +innately no + + align:start position:0% +innately no + + + align:start position:0% +innately no +in cultivation probably yes you've been + + align:start position:0% +in cultivation probably yes you've been + + + align:start position:0% +in cultivation probably yes you've been +cultivated to use your knowledge in a + + align:start position:0% +cultivated to use your knowledge in a + + + align:start position:0% +cultivated to use your knowledge in a +certain way systematic way that's what + + align:start position:0% +certain way systematic way that's what + + + align:start position:0% +certain way systematic way that's what +we've been doing with + + align:start position:0% +we've been doing with + + + align:start position:0% +we've been doing with +ethics in here + + align:start position:0% +ethics in here + + + align:start position:0% +ethics in here +your effective abilities + + align:start position:0% +your effective abilities + + + align:start position:0% +your effective abilities +are the same + + align:start position:0% +are the same + + + align:start position:0% +are the same +but all of this + + align:start position:0% +but all of this + + + align:start position:0% +but all of this +talking about well let's talk about the + + align:start position:0% +talking about well let's talk about the + + + align:start position:0% +talking about well let's talk about the +principle as opposed to the consequence + + align:start position:0% +principle as opposed to the consequence + + + align:start position:0% +principle as opposed to the consequence +now that's cultivating the effort so now + + align:start position:0% +now that's cultivating the effort so now + + + align:start position:0% +now that's cultivating the effort so now +you look back and say well i know how to + + align:start position:0% +you look back and say well i know how to + + + align:start position:0% +you look back and say well i know how to +do these things + + align:start position:0% +do these things + + + align:start position:0% +do these things +so + + align:start position:0% +so + + + align:start position:0% +so +people are not willing people are + + align:start position:0% +people are not willing people are + + + align:start position:0% +people are not willing people are +willing to make compromises when it + + align:start position:0% +willing to make compromises when it + + + align:start position:0% +willing to make compromises when it +comes to their specialties + + align:start position:0% +comes to their specialties + + + align:start position:0% +comes to their specialties +they are not willing to make compromise + + align:start position:0% +they are not willing to make compromise + + + align:start position:0% +they are not willing to make compromise +when it comes to their forte + + align:start position:0% + + + + align:start position:0% + +and they will tell you you have to do + + align:start position:0% +and they will tell you you have to do + + + align:start position:0% +and they will tell you you have to do +things to my way + + align:start position:0% + + + + align:start position:0% + +and when you get somebody in one field + + align:start position:0% +and when you get somebody in one field + + + align:start position:0% +and when you get somebody in one field +like an ethicist and somebody in another + + align:start position:0% +like an ethicist and somebody in another + + + align:start position:0% +like an ethicist and somebody in another +field like an engineer + + align:start position:0% +field like an engineer + + + align:start position:0% +field like an engineer +and they're gonna work together + + align:start position:0% +and they're gonna work together + + + align:start position:0% +and they're gonna work together +you're gonna have to make compromises + + align:start position:0% +you're gonna have to make compromises + + + align:start position:0% +you're gonna have to make compromises +both in the specialty and in the forte + + align:start position:0% + + + + align:start position:0% + +you're going to have to say well let's + + align:start position:0% +you're going to have to say well let's + + + align:start position:0% +you're going to have to say well let's +let the effect drive the + + align:start position:0% +let the effect drive the + + + align:start position:0% +let the effect drive the +discussion + + align:start position:0% + + + + align:start position:0% + +right so that's the argument that i was + + align:start position:0% +right so that's the argument that i was + + + align:start position:0% +right so that's the argument that i was +making about + + align:start position:0% + + + + align:start position:0% + +that lean more towards one of the other + + align:start position:0% +that lean more towards one of the other + + + align:start position:0% +that lean more towards one of the other +fortes so like + + align:start position:0% +fortes so like + + + align:start position:0% +fortes so like +an engineer who actually + + align:start position:0% +an engineer who actually + + + align:start position:0% +an engineer who actually +faces a lot of decisions or actions on + + align:start position:0% +faces a lot of decisions or actions on + + + align:start position:0% +faces a lot of decisions or actions on +affect or + + align:start position:0% +affect or + + + align:start position:0% +affect or +a scientist who's really good at science + + align:start position:0% +a scientist who's really good at science + + + align:start position:0% +a scientist who's really good at science +because of his or her psychomotor skills + + align:start position:0% +because of his or her psychomotor skills + + + align:start position:0% +because of his or her psychomotor skills +in the lab + + align:start position:0% +in the lab + + + align:start position:0% +in the lab +yes how do you deal with that i don't + + align:start position:0% +yes how do you deal with that i don't + + + align:start position:0% +yes how do you deal with that i don't +deal with that i say + + align:start position:0% +deal with that i say + + + align:start position:0% +deal with that i say +that + + align:start position:0% +that + + + align:start position:0% +that +all of this is a structure that gets us + + align:start position:0% +all of this is a structure that gets us + + + align:start position:0% +all of this is a structure that gets us +started on the indiv and it applies in + + align:start position:0% +started on the indiv and it applies in + + + align:start position:0% +started on the indiv and it applies in +the general case applying it to + + align:start position:0% +the general case applying it to + + + align:start position:0% +the general case applying it to +individuals is hard + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% + + + + align:start position:0% + +it's like ethics i mean we can get the + + align:start position:0% +it's like ethics i mean we can get the + + + align:start position:0% +it's like ethics i mean we can get the +general principle + + align:start position:0% +general principle + + + align:start position:0% +general principle +but applying it to a specific case + + align:start position:0% +but applying it to a specific case + + + align:start position:0% +but applying it to a specific case +uh is not always a straightforward + + align:start position:0% +uh is not always a straightforward + + + align:start position:0% +uh is not always a straightforward +matter + + align:start position:0% +matter + + + align:start position:0% +matter +and yes um + + align:start position:0% +and yes um + + + align:start position:0% +and yes um +uh + + align:start position:0% + + + + align:start position:0% + +you can be a mathematician + + align:start position:0% +you can be a mathematician + + + align:start position:0% +you can be a mathematician +that they call an intuitive + + align:start position:0% +that they call an intuitive + + + align:start position:0% +that they call an intuitive +mathematician + + align:start position:0% +mathematician + + + align:start position:0% +mathematician +you haven't figured anything out you + + align:start position:0% +you haven't figured anything out you + + + align:start position:0% +you haven't figured anything out you +just seem to know + + align:start position:0% +just seem to know + + + align:start position:0% +just seem to know +see the pattern with these numbers + + align:start position:0% +see the pattern with these numbers + + + align:start position:0% +see the pattern with these numbers +there's this guy named ever heard of + + align:start position:0% +there's this guy named ever heard of + + + align:start position:0% +there's this guy named ever heard of +ramanujan + + align:start position:0% +ramanujan + + + align:start position:0% +ramanujan +yeah sort of ramanujan wasn't wasn't was + + align:start position:0% +yeah sort of ramanujan wasn't wasn't was + + + align:start position:0% +yeah sort of ramanujan wasn't wasn't was +an intuitive mathematician + + align:start position:0% +an intuitive mathematician + + + align:start position:0% +an intuitive mathematician +i might have talked about him in here + + align:start position:0% +i might have talked about him in here + + + align:start position:0% +i might have talked about him in here +um + + align:start position:0% +um + + + align:start position:0% +um +we talked about + + align:start position:0% +we talked about + + + align:start position:0% +we talked about +how he uh + + align:start position:0% +how he uh + + + align:start position:0% +how he uh +got came with came up with this method + + align:start position:0% +got came with came up with this method + + + align:start position:0% +got came with came up with this method +of + + align:start position:0% +of + + + align:start position:0% +of +determining whether a number was a prime + + align:start position:0% +determining whether a number was a prime + + + align:start position:0% +determining whether a number was a prime +number or not + + align:start position:0% +number or not + + + align:start position:0% +number or not +using hand calculations + + align:start position:0% +using hand calculations + + + align:start position:0% +using hand calculations +long + + align:start position:0% +long + + + align:start position:0% +long +long you know 30 digit numbers + + align:start position:0% + + + + align:start position:0% + +and he couldn't prove to you that his + + align:start position:0% +and he couldn't prove to you that his + + + align:start position:0% +and he couldn't prove to you that his +method was right + + align:start position:0% +method was right + + + align:start position:0% +method was right +somebody else 20 years later proved it + + align:start position:0% +somebody else 20 years later proved it + + + align:start position:0% +somebody else 20 years later proved it +but + + align:start position:0% +but + + + align:start position:0% +but +yeah uh the human capacity to + + align:start position:0% +yeah uh the human capacity to + + + align:start position:0% +yeah uh the human capacity to +manipulate this chart is + + align:start position:0% +manipulate this chart is + + + align:start position:0% +manipulate this chart is +extraordinary + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +uh we want to talk a lot about + + align:start position:0% +uh we want to talk a lot about + + + align:start position:0% +uh we want to talk a lot about +psychomotor skill when it comes to + + align:start position:0% +psychomotor skill when it comes to + + + align:start position:0% +psychomotor skill when it comes to +ballet + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so yeah the whole for so all of this is + + align:start position:0% +so yeah the whole for so all of this is + + + align:start position:0% +so yeah the whole for so all of this is +in all of the disciplines + + align:start position:0% +in all of the disciplines + + + align:start position:0% +in all of the disciplines +but we want to talk about the + + align:start position:0% +but we want to talk about the + + + align:start position:0% +but we want to talk about the +disciplines being + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +distinct + + align:start position:0% +distinct + + + align:start position:0% +distinct +in terms of specialties in forte and + + align:start position:0% +in terms of specialties in forte and + + + align:start position:0% +in terms of specialties in forte and +that's the usual way we do it and if we + + align:start position:0% +that's the usual way we do it and if we + + + align:start position:0% +that's the usual way we do it and if we +apply this to every to on an individual + + align:start position:0% +apply this to every to on an individual + + + align:start position:0% +apply this to every to on an individual +basis it's very has + + align:start position:0% +basis it's very has + + + align:start position:0% +basis it's very has +uh another thing is to separate out + + align:start position:0% + + + + align:start position:0% + +what's going on + + align:start position:0% + + + + align:start position:0% + +as a brain + + align:start position:0% + + + + align:start position:0% + +going on in the brain + + align:start position:0% +going on in the brain + + + align:start position:0% +going on in the brain +and in the mind + + align:start position:0% +and in the mind + + + align:start position:0% +and in the mind +from what is actually written down in a + + align:start position:0% +from what is actually written down in a + + + align:start position:0% +from what is actually written down in a +manuscript + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +because what will what will happen with + + align:start position:0% +because what will what will happen with + + + align:start position:0% +because what will what will happen with +your um + + align:start position:0% + + + + align:start position:0% + +your your rigorous mathematicians + + align:start position:0% +your your rigorous mathematicians + + + align:start position:0% +your your rigorous mathematicians +uh is that many of them will get a + + align:start position:0% +uh is that many of them will get a + + + align:start position:0% +uh is that many of them will get a +formula + + align:start position:0% +formula + + + align:start position:0% +formula +or something + + align:start position:0% +or something + + + align:start position:0% +or something +uh + + align:start position:0% +uh + + + align:start position:0% +uh +through intuition first + + align:start position:0% +through intuition first + + + align:start position:0% +through intuition first +and then spend the next two years trying + + align:start position:0% +and then spend the next two years trying + + + align:start position:0% +and then spend the next two years trying +to make it try to prove it + + align:start position:0% +to make it try to prove it + + + align:start position:0% +to make it try to prove it +but they got it already + + align:start position:0% + + + + align:start position:0% + +uh and so + + align:start position:0% +uh and so + + + align:start position:0% +uh and so +what you and i get in the end is the + + align:start position:0% +what you and i get in the end is the + + + align:start position:0% +what you and i get in the end is the +manuscript where it's nice and rigorous + + align:start position:0% +manuscript where it's nice and rigorous + + + align:start position:0% +manuscript where it's nice and rigorous +and laid out systematically uh but what + + align:start position:0% +and laid out systematically uh but what + + + align:start position:0% +and laid out systematically uh but what +went on in the person's brain is + + align:start position:0% +went on in the person's brain is + + + align:start position:0% +went on in the person's brain is +something different a lot more + + align:start position:0% +something different a lot more + + + align:start position:0% +something different a lot more +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +and people are beginning to understand + + align:start position:0% +and people are beginning to understand + + + align:start position:0% +and people are beginning to understand +that a lot now + + align:start position:0% +that a lot now + + + align:start position:0% +that a lot now +but it's very important to us as + + align:start position:0% +but it's very important to us as + + + align:start position:0% +but it's very important to us as +teachers + + align:start position:0% +teachers + + + align:start position:0% +teachers +to give + + align:start position:0% +to give + + + align:start position:0% +to give +the manuscript + + align:start position:0% +the manuscript + + + align:start position:0% +the manuscript +to the students + + align:start position:0% +to the students + + + align:start position:0% +to the students +and do the guessing about what's + + align:start position:0% +and do the guessing about what's + + + align:start position:0% +and do the guessing about what's +actually going on in the mind over here + + align:start position:0% +actually going on in the mind over here + + + align:start position:0% +actually going on in the mind over here +as a separate kind of discussion + + align:start position:0% +as a separate kind of discussion + + + align:start position:0% +as a separate kind of discussion +because otherwise the student is not + + align:start position:0% +because otherwise the student is not + + + align:start position:0% +because otherwise the student is not +what we call liberated + + align:start position:0% +what we call liberated + + + align:start position:0% +what we call liberated +you really don't know + + align:start position:0% +you really don't know + + + align:start position:0% +you really don't know +where to go on your own + + align:start position:0% +where to go on your own + + + align:start position:0% +where to go on your own +so if i give you this + + align:start position:0% +so if i give you this + + + align:start position:0% +so if i give you this +learn that + + align:start position:0% +learn that + + + align:start position:0% +learn that +and take the author add his or her word + + align:start position:0% +and take the author add his or her word + + + align:start position:0% +and take the author add his or her word +then we can start talking about + + align:start position:0% +then we can start talking about + + + align:start position:0% +then we can start talking about +well i can tell you what einstein told + + align:start position:0% +well i can tell you what einstein told + + + align:start position:0% +well i can tell you what einstein told +my grandfather + + align:start position:0% +my grandfather + + + align:start position:0% +my grandfather +he didn't figure this stuff out it came + + align:start position:0% +he didn't figure this stuff out it came + + + align:start position:0% +he didn't figure this stuff out it came +to him in the night okay + + align:start position:0% +to him in the night okay + + + align:start position:0% +to him in the night okay +all right that's a separate discussion + + align:start position:0% +all right that's a separate discussion + + + align:start position:0% +all right that's a separate discussion +now you're liberated you can do what you + + align:start position:0% +now you're liberated you can do what you + + + align:start position:0% +now you're liberated you can do what you +want + + align:start position:0% +want + + + align:start position:0% +want +but i am not going to teach from the + + align:start position:0% +but i am not going to teach from the + + + align:start position:0% +but i am not going to teach from the +standpoint of teach + + align:start position:0% +standpoint of teach + + + align:start position:0% +standpoint of teach +let's say + + align:start position:0% + + + + align:start position:0% + +relativity from the standpoint of what + + align:start position:0% +relativity from the standpoint of what + + + align:start position:0% +relativity from the standpoint of what +went on in einstein's mind + + align:start position:0% +went on in einstein's mind + + + align:start position:0% +went on in einstein's mind +i'm going to look at the manuscript + + align:start position:0% +i'm going to look at the manuscript + + + align:start position:0% +i'm going to look at the manuscript +and try to induct back what + + align:start position:0% +and try to induct back what + + + align:start position:0% +and try to induct back what +systematically went on in his mind and + + align:start position:0% +systematically went on in his mind and + + + align:start position:0% +systematically went on in his mind and +then make the other argument separate + + align:start position:0% +then make the other argument separate + + + align:start position:0% +then make the other argument separate +because it will not be systematic + + align:start position:0% + + + + align:start position:0% + +okay but it will be what you do when you + + align:start position:0% +okay but it will be what you do when you + + + align:start position:0% +okay but it will be what you do when you +try to do something great + + align:start position:0% + + + + align:start position:0% + +okay so um + + align:start position:0% + + + + align:start position:0% + +i guess the last thing i want to say is + + align:start position:0% +i guess the last thing i want to say is + + + align:start position:0% +i guess the last thing i want to say is +that + + align:start position:0% + + + + align:start position:0% + +these two are what most people refer to + + align:start position:0% +these two are what most people refer to + + + align:start position:0% +these two are what most people refer to +when they use the word intellect + + align:start position:0% +when they use the word intellect + + + align:start position:0% +when they use the word intellect +and call you an intellectual + + align:start position:0% +and call you an intellectual + + + align:start position:0% +and call you an intellectual +it means that your cognition and your + + align:start position:0% +it means that your cognition and your + + + align:start position:0% +it means that your cognition and your +affect cognition and or your affect has + + align:start position:0% +affect cognition and or your affect has + + + align:start position:0% +affect cognition and or your affect has +been cultivated by great study + + align:start position:0% +been cultivated by great study + + + align:start position:0% +been cultivated by great study +great study meaning a specialty + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh what i argue and uh i've already + + align:start position:0% +uh what i argue and uh i've already + + + align:start position:0% +uh what i argue and uh i've already +gotten + + align:start position:0% +gotten + + + align:start position:0% +gotten +unhappiness expressed + + align:start position:0% +unhappiness expressed + + + align:start position:0% +unhappiness expressed +from engineers is that + + align:start position:0% +from engineers is that + + + align:start position:0% +from engineers is that +that's the intellect we've got to give + + align:start position:0% +that's the intellect we've got to give + + + align:start position:0% +that's the intellect we've got to give +another name to this this is not + + align:start position:0% +another name to this this is not + + + align:start position:0% +another name to this this is not +intellectual + + align:start position:0% +intellectual + + + align:start position:0% +intellectual +okay the reason is that + + align:start position:0% +okay the reason is that + + + align:start position:0% +okay the reason is that +it just goes to show just the power + + align:start position:0% +it just goes to show just the power + + + align:start position:0% +it just goes to show just the power +of + + align:start position:0% +of + + + align:start position:0% +of +of science and + + align:start position:0% +of science and + + + align:start position:0% +of science and +ethics in our educational system over + + align:start position:0% +ethics in our educational system over + + + align:start position:0% +ethics in our educational system over +what engineers do when we're really + + align:start position:0% +what engineers do when we're really + + + align:start position:0% +what engineers do when we're really +doing engineering and i think that's + + align:start position:0% +doing engineering and i think that's + + + align:start position:0% +doing engineering and i think that's +unfortunate + + align:start position:0% +unfortunate + + + align:start position:0% +unfortunate +i don't think we get enough preps + + align:start position:0% +i don't think we get enough preps + + + align:start position:0% +i don't think we get enough preps +or because we don't get the press right + + align:start position:0% +or because we don't get the press right + + + align:start position:0% +or because we don't get the press right +so i've given this a name + + align:start position:0% + + + + align:start position:0% + +i'll put it in quotes to remind you that + + align:start position:0% +i'll put it in quotes to remind you that + + + align:start position:0% +i'll put it in quotes to remind you that +that's that was my word + + align:start position:0% + + + + align:start position:0% + +okay i call it the practitioner + + align:start position:0% + + + + align:start position:0% + +and so i find no problems in letting the + + align:start position:0% +and so i find no problems in letting the + + + align:start position:0% +and so i find no problems in letting the +intellectuals have their intellect + + align:start position:0% +intellectuals have their intellect + + + align:start position:0% +intellectuals have their intellect +and what i want to say is that the + + align:start position:0% +and what i want to say is that the + + + align:start position:0% +and what i want to say is that the +practitioner is a higher order function + + align:start position:0% +practitioner is a higher order function + + + align:start position:0% +practitioner is a higher order function +of the mind just like the intellect is + + align:start position:0% +of the mind just like the intellect is + + + align:start position:0% +of the mind just like the intellect is +and what i also want to say is that when + + align:start position:0% +and what i also want to say is that when + + + align:start position:0% +and what i also want to say is that when +you get out of the united states and go + + align:start position:0% +you get out of the united states and go + + + align:start position:0% +you get out of the united states and go +to some other philosophy philosophies + + align:start position:0% +to some other philosophy philosophies + + + align:start position:0% +to some other philosophy philosophies +as a matter of fact existentialism is + + align:start position:0% +as a matter of fact existentialism is + + + align:start position:0% +as a matter of fact existentialism is +one of them + + align:start position:0% +one of them + + + align:start position:0% +one of them +what they really say is that this is the + + align:start position:0% +what they really say is that this is the + + + align:start position:0% +what they really say is that this is the +highest order function of the mind + + align:start position:0% + + + + align:start position:0% + +because you don't need a whole lot of + + align:start position:0% +because you don't need a whole lot of + + + align:start position:0% +because you don't need a whole lot of +knowledge to do what you got to do + + align:start position:0% + + + + align:start position:0% + +or better stated what they're really + + align:start position:0% +or better stated what they're really + + + align:start position:0% +or better stated what they're really +saying is we can trans we can transcend + + align:start position:0% +saying is we can trans we can transcend + + + align:start position:0% +saying is we can trans we can transcend +the intellect + + align:start position:0% +the intellect + + + align:start position:0% +the intellect +the intellect confines you + + align:start position:0% +the intellect confines you + + + align:start position:0% +the intellect confines you +the practitioner liberates you + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so uh that's the way a lot of that + + align:start position:0% +so uh that's the way a lot of that + + + align:start position:0% +so uh that's the way a lot of that +argument goes + + align:start position:0% +argument goes + + + align:start position:0% +argument goes +and + + align:start position:0% + + + + align:start position:0% + +but engineers + + align:start position:0% +but engineers + + + align:start position:0% +but engineers +for partly for this reason probably for + + align:start position:0% +for partly for this reason probably for + + + align:start position:0% +for partly for this reason probably for +other reasons + + align:start position:0% +other reasons + + + align:start position:0% +other reasons +do not + + align:start position:0% +do not + + + align:start position:0% +do not +and engineering just does not have + + align:start position:0% +and engineering just does not have + + + align:start position:0% +and engineering just does not have +the learned status as the scientists + + align:start position:0% +the learned status as the scientists + + + align:start position:0% +the learned status as the scientists +and the humanities in the united states + + align:start position:0% + + + + align:start position:0% + +and i think that the intellect and the + + align:start position:0% +and i think that the intellect and the + + + align:start position:0% +and i think that the intellect and the +practitioner are equally high + + align:start position:0% +practitioner are equally high + + + align:start position:0% +practitioner are equally high +what they call higher order functions of + + align:start position:0% +what they call higher order functions of + + + align:start position:0% +what they call higher order functions of +the mind + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +we've got uh + + align:start position:0% +we've got uh + + + align:start position:0% +we've got uh +20 minutes + + align:start position:0% + + + + align:start position:0% + +okay self + + align:start position:0% + + + + align:start position:0% + +esteem + + align:start position:0% + + + + align:start position:0% + +now that's a psychological term + + align:start position:0% +now that's a psychological term + + + align:start position:0% +now that's a psychological term +but i'm not going to use it as a + + align:start position:0% +but i'm not going to use it as a + + + align:start position:0% +but i'm not going to use it as a +psychological term + + align:start position:0% +psychological term + + + align:start position:0% +psychological term +uh there is a + + align:start position:0% +uh there is a + + + align:start position:0% +uh there is a +scholar of jurisprudence by the name of + + align:start position:0% +scholar of jurisprudence by the name of + + + align:start position:0% +scholar of jurisprudence by the name of +john rose + + align:start position:0% + + + + align:start position:0% + +who + + align:start position:0% + + + + align:start position:0% + +wrote this book called a theory of + + align:start position:0% +wrote this book called a theory of + + + align:start position:0% +wrote this book called a theory of +justice + + align:start position:0% +justice + + + align:start position:0% +justice +and what he was really trying to do + + align:start position:0% +and what he was really trying to do + + + align:start position:0% +and what he was really trying to do +now + + align:start position:0% +now + + + align:start position:0% +now +to understand + + align:start position:0% +to understand + + + align:start position:0% +to understand +raw's + + align:start position:0% +raw's + + + align:start position:0% +raw's +one of the things you have to understand + + align:start position:0% +one of the things you have to understand + + + align:start position:0% +one of the things you have to understand +is what he was trying to do + + align:start position:0% +is what he was trying to do + + + align:start position:0% +is what he was trying to do +with a theory of justice + + align:start position:0% +with a theory of justice + + + align:start position:0% +with a theory of justice +he was trying to do the same thing + + align:start position:0% +he was trying to do the same thing + + + align:start position:0% +he was trying to do the same thing +that + + align:start position:0% +that + + + align:start position:0% +that +uh what they call social he's a social + + align:start position:0% +uh what they call social he's a social + + + align:start position:0% +uh what they call social he's a social +contractaria + + align:start position:0% +contractaria + + + align:start position:0% +contractaria +he was trying to do the same thing that + + align:start position:0% +he was trying to do the same thing that + + + align:start position:0% +he was trying to do the same thing that +other social contractarians i'm going to + + align:start position:0% +other social contractarians i'm going to + + + align:start position:0% +other social contractarians i'm going to +name + + align:start position:0% +name + + + align:start position:0% +name +big names + + align:start position:0% +big names + + + align:start position:0% +big names +in + + align:start position:0% +in + + + align:start position:0% +in +western uh philosophical and + + align:start position:0% +western uh philosophical and + + + align:start position:0% +western uh philosophical and +learned thought + + align:start position:0% +learned thought + + + align:start position:0% +learned thought +hobbs with leviathan + + align:start position:0% +hobbs with leviathan + + + align:start position:0% +hobbs with leviathan +rousseau + + align:start position:0% +rousseau + + + align:start position:0% +rousseau +with the second treatise on + + align:start position:0% +with the second treatise on + + + align:start position:0% +with the second treatise on +government + + align:start position:0% +government + + + align:start position:0% +government +um um + + align:start position:0% +um um + + + align:start position:0% +um um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +machiavelli the prince + + align:start position:0% +machiavelli the prince + + + align:start position:0% +machiavelli the prince +all of these people + + align:start position:0% +all of these people + + + align:start position:0% +all of these people +were working at a time when there was a + + align:start position:0% +were working at a time when there was a + + + align:start position:0% +were working at a time when there was a +revolution of some sort + + align:start position:0% +revolution of some sort + + + align:start position:0% +revolution of some sort +and they wanted to replace it with a + + align:start position:0% +and they wanted to replace it with a + + + align:start position:0% +and they wanted to replace it with a +whole new idea of government so you're + + align:start position:0% +whole new idea of government so you're + + + align:start position:0% +whole new idea of government so you're +talking about the russo with the french + + align:start position:0% +talking about the russo with the french + + + align:start position:0% +talking about the russo with the french +revolution + + align:start position:0% +revolution + + + align:start position:0% +revolution +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and all of these people were trying to + + align:start position:0% +and all of these people were trying to + + + align:start position:0% +and all of these people were trying to +figure out how do you just start out a + + align:start position:0% +figure out how do you just start out a + + + align:start position:0% +figure out how do you just start out a +whole new kind of government + + align:start position:0% +whole new kind of government + + + align:start position:0% +whole new kind of government +and what they did was they came up with + + align:start position:0% +and what they did was they came up with + + + align:start position:0% +and what they did was they came up with +what was called social contract theory + + align:start position:0% +what was called social contract theory + + + align:start position:0% +what was called social contract theory +actually it was social contractarian + + align:start position:0% +actually it was social contractarian + + + align:start position:0% +actually it was social contractarian +approach you'd be surprised it was a + + align:start position:0% +approach you'd be surprised it was a + + + align:start position:0% +approach you'd be surprised it was a +narrative approach + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and what they did was they said all + + align:start position:0% +and what they did was they said all + + + align:start position:0% +and what they did was they said all +right + + align:start position:0% + + + + align:start position:0% + +how are we gonna just think about it + + align:start position:0% +how are we gonna just think about it + + + align:start position:0% +how are we gonna just think about it +suppose there's some big revolution in + + align:start position:0% +suppose there's some big revolution in + + + align:start position:0% +suppose there's some big revolution in +the united states + + align:start position:0% +the united states + + + align:start position:0% +the united states +okay people running up + + align:start position:0% +okay people running up + + + align:start position:0% +okay people running up +i remember this + + align:start position:0% +i remember this + + + align:start position:0% +i remember this +they called it the 1960s people running + + align:start position:0% +they called it the 1960s people running + + + align:start position:0% +they called it the 1960s people running +up and down the streets + + align:start position:0% +up and down the streets + + + align:start position:0% +up and down the streets +all sorts of things falling apart + + align:start position:0% +all sorts of things falling apart + + + align:start position:0% +all sorts of things falling apart +and you sit down and you say now + + align:start position:0% +and you sit down and you say now + + + align:start position:0% +and you sit down and you say now +this whole thing is going to fall apart + + align:start position:0% +this whole thing is going to fall apart + + + align:start position:0% +this whole thing is going to fall apart +how are we going to build a whole new + + align:start position:0% +how are we going to build a whole new + + + align:start position:0% +how are we going to build a whole new +government how are we going to do that + + align:start position:0% +government how are we going to do that + + + align:start position:0% +government how are we going to do that +right + + align:start position:0% +right + + + align:start position:0% +right +so what they did was the social + + align:start position:0% +so what they did was the social + + + align:start position:0% +so what they did was the social +contractarians did was they came up with + + align:start position:0% +contractarians did was they came up with + + + align:start position:0% +contractarians did was they came up with +a fictional situation + + align:start position:0% +a fictional situation + + + align:start position:0% +a fictional situation +where + + align:start position:0% +where + + + align:start position:0% +where +uh uh people are going to build a whole + + align:start position:0% +uh uh people are going to build a whole + + + align:start position:0% +uh uh people are going to build a whole +new government + + align:start position:0% +new government + + + align:start position:0% +new government +and how would they do it + + align:start position:0% +and how would they do it + + + align:start position:0% +and how would they do it +and you how would you populate this + + align:start position:0% +and you how would you populate this + + + align:start position:0% +and you how would you populate this +group you're only going to have a small + + align:start position:0% +group you're only going to have a small + + + align:start position:0% +group you're only going to have a small +number of people 20 40 50. okay + + align:start position:0% +number of people 20 40 50. okay + + + align:start position:0% +number of people 20 40 50. okay +and what do they know are they experts + + align:start position:0% +and what do they know are they experts + + + align:start position:0% +and what do they know are they experts +are they ordinary people + + align:start position:0% +are they ordinary people + + + align:start position:0% +are they ordinary people +okay and how do they work their way + + align:start position:0% +okay and how do they work their way + + + align:start position:0% +okay and how do they work their way +through this thing that's called social + + align:start position:0% +through this thing that's called social + + + align:start position:0% +through this thing that's called social +contract theory + + align:start position:0% +contract theory + + + align:start position:0% +contract theory +uh and um + + align:start position:0% +uh and um + + + align:start position:0% +uh and um +uh + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +even the man + + align:start position:0% +even the man + + + align:start position:0% +even the man +who gave the lecture on the internet + + align:start position:0% +who gave the lecture on the internet + + + align:start position:0% +who gave the lecture on the internet +a couple weeks ago referred to hobbes + + align:start position:0% +a couple weeks ago referred to hobbes + + + align:start position:0% +a couple weeks ago referred to hobbes +when he talked about + + align:start position:0% +when he talked about + + + align:start position:0% +when he talked about +life can be + + align:start position:0% +life can be + + + align:start position:0% +life can be +nasty brutish and short + + align:start position:0% +nasty brutish and short + + + align:start position:0% +nasty brutish and short +yeah hobbes that's one of hobbs + + align:start position:0% +yeah hobbes that's one of hobbs + + + align:start position:0% +yeah hobbes that's one of hobbs +statement in leviathan it's called + + align:start position:0% +statement in leviathan it's called + + + align:start position:0% +statement in leviathan it's called +and rawl sat down + + align:start position:0% +and rawl sat down + + + align:start position:0% +and rawl sat down +and he was concerned about all that was + + align:start position:0% +and he was concerned about all that was + + + align:start position:0% +and he was concerned about all that was +happening in the 1960s here in the + + align:start position:0% +happening in the 1960s here in the + + + align:start position:0% +happening in the 1960s here in the +united states + + align:start position:0% +united states + + + align:start position:0% +united states +and he said how can we build a whole new + + align:start position:0% +and he said how can we build a whole new + + + align:start position:0% +and he said how can we build a whole new +society where we can solve all these + + align:start position:0% +society where we can solve all these + + + align:start position:0% +society where we can solve all these +problems + + align:start position:0% +problems + + + align:start position:0% +problems +okay + + align:start position:0% +okay + + + align:start position:0% +okay +one of the things he started with was + + align:start position:0% +one of the things he started with was + + + align:start position:0% +one of the things he started with was +with + + align:start position:0% +with + + + align:start position:0% +with +uh was what he called um + + align:start position:0% +uh was what he called um + + + align:start position:0% +uh was what he called um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the + + align:start position:0% +the + + + align:start position:0% +the +um + + align:start position:0% +um + + + align:start position:0% +um +i forget what he called him but the + + align:start position:0% +i forget what he called him but the + + + align:start position:0% +i forget what he called him but the +things that people need to live what are + + align:start position:0% +things that people need to live what are + + + align:start position:0% +things that people need to live what are +the basic things + + align:start position:0% +the basic things + + + align:start position:0% +the basic things +primary needs that's what he called them + + align:start position:0% +primary needs that's what he called them + + + align:start position:0% +primary needs that's what he called them +those were his that's a form of for him + + align:start position:0% +those were his that's a form of for him + + + align:start position:0% +those were his that's a form of for him +that's a term of heart what are the + + align:start position:0% +that's a term of heart what are the + + + align:start position:0% +that's a term of heart what are the +primary needs food + + align:start position:0% +primary needs food + + + align:start position:0% +primary needs food +okay + + align:start position:0% +okay + + + align:start position:0% +okay +shelter + + align:start position:0% +shelter + + + align:start position:0% +shelter +all that + + align:start position:0% +all that + + + align:start position:0% +all that +he named about + + align:start position:0% +he named about + + + align:start position:0% +he named about +half a dozen of them + + align:start position:0% +half a dozen of them + + + align:start position:0% +half a dozen of them +and he justified them + + align:start position:0% +and he justified them + + + align:start position:0% +and he justified them +okay he justified his list + + align:start position:0% +okay he justified his list + + + align:start position:0% +okay he justified his list +and + + align:start position:0% +and + + + align:start position:0% +and +self-esteem was one of them + + align:start position:0% + + + + align:start position:0% + +and he said + + align:start position:0% +and he said + + + align:start position:0% +and he said +self-esteem was the most important one + + align:start position:0% + + + + align:start position:0% + +because if you don't have high + + align:start position:0% +because if you don't have high + + + align:start position:0% +because if you don't have high +self-esteem + + align:start position:0% +self-esteem + + + align:start position:0% +self-esteem +you will never see the point in putting + + align:start position:0% +you will never see the point in putting + + + align:start position:0% +you will never see the point in putting +your time and energy in the rest of them + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +he talked about self-esteem and + + align:start position:0% + + + + align:start position:0% + +when i was + + align:start position:0% +when i was + + + align:start position:0% +when i was +studying him in a course + + align:start position:0% +studying him in a course + + + align:start position:0% +studying him in a course +that i was taking for well + + align:start position:0% +that i was taking for well + + + align:start position:0% +that i was taking for well +this book was the textbook for the + + align:start position:0% +this book was the textbook for the + + + align:start position:0% +this book was the textbook for the +course and i had to get a grade + + align:start position:0% +course and i had to get a grade + + + align:start position:0% +course and i had to get a grade +this chart worked out for me + + align:start position:0% +this chart worked out for me + + + align:start position:0% +this chart worked out for me +and that was um i put internal + + align:start position:0% +and that was um i put internal + + + align:start position:0% +and that was um i put internal +here + + align:start position:0% +here + + + align:start position:0% +here +i put external here + + align:start position:0% + + + + align:start position:0% + +and what that meant was that one kind of + + align:start position:0% +and what that meant was that one kind of + + + align:start position:0% +and what that meant was that one kind of +self-esteem + + align:start position:0% +self-esteem + + + align:start position:0% +self-esteem +is a judgment that you make a value + + align:start position:0% +is a judgment that you make a value + + + align:start position:0% +is a judgment that you make a value +judgment that you make about yourself + + align:start position:0% + + + + align:start position:0% + +so that's the internal + + align:start position:0% +so that's the internal + + + align:start position:0% +so that's the internal +the external is one that you may make + + align:start position:0% +the external is one that you may make + + + align:start position:0% +the external is one that you may make +but is what you think everybody else + + align:start position:0% +but is what you think everybody else + + + align:start position:0% +but is what you think everybody else +thinks about you + + align:start position:0% +thinks about you + + + align:start position:0% +thinks about you +that's the x term + + align:start position:0% +that's the x term + + + align:start position:0% +that's the x term +so it is possible to have a very high + + align:start position:0% +so it is possible to have a very high + + + align:start position:0% +so it is possible to have a very high +internal + + align:start position:0% +internal + + + align:start position:0% +internal +self-esteem and a very low external + + align:start position:0% +self-esteem and a very low external + + + align:start position:0% +self-esteem and a very low external +self-esteem you can think very highly of + + align:start position:0% +self-esteem you can think very highly of + + + align:start position:0% +self-esteem you can think very highly of +yourself but you think that nobody else + + align:start position:0% +yourself but you think that nobody else + + + align:start position:0% +yourself but you think that nobody else +thinks highly of you + + align:start position:0% +thinks highly of you + + + align:start position:0% +thinks highly of you +and that's important + + align:start position:0% +and that's important + + + align:start position:0% +and that's important +because if you think if your external + + align:start position:0% +because if you think if your external + + + align:start position:0% +because if you think if your external +self-esteem is low + + align:start position:0% +self-esteem is low + + + align:start position:0% +self-esteem is low +then you're going to find it difficult + + align:start position:0% +then you're going to find it difficult + + + align:start position:0% +then you're going to find it difficult +to get people to join you + + align:start position:0% +to get people to join you + + + align:start position:0% +to get people to join you +in the things that you want to do to + + align:start position:0% +in the things that you want to do to + + + align:start position:0% +in the things that you want to do to +help you out getting the things that you + + align:start position:0% +help you out getting the things that you + + + align:start position:0% +help you out getting the things that you +want to do + + align:start position:0% +want to do + + + align:start position:0% +want to do +the other side was + + align:start position:0% +the other side was + + + align:start position:0% +the other side was +called + + align:start position:0% +called + + + align:start position:0% +called +self-confidence + + align:start position:0% + + + + align:start position:0% + +and self-worth + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +in other words you're saying that it's + + align:start position:0% +in other words you're saying that it's + + + align:start position:0% +in other words you're saying that it's +the same thing as this + + align:start position:0% + + + + align:start position:0% + +oh all of these are the dimensions of + + align:start position:0% +oh all of these are the dimensions of + + + align:start position:0% +oh all of these are the dimensions of +self-esteem + + align:start position:0% +self-esteem + + + align:start position:0% +self-esteem +all of them + + align:start position:0% +all of them + + + align:start position:0% +all of them +all of them are different kinds or + + align:start position:0% +all of them are different kinds or + + + align:start position:0% +all of them are different kinds or +facets of self-esteem yeah + + align:start position:0% +facets of self-esteem yeah + + + align:start position:0% +facets of self-esteem yeah +so this one was the one this internal + + align:start position:0% +so this one was the one this internal + + + align:start position:0% +so this one was the one this internal +judgment + + align:start position:0% +judgment + + + align:start position:0% +judgment +not only of + + align:start position:0% +not only of + + + align:start position:0% +not only of +uh yourself but whether or not + + align:start position:0% +uh yourself but whether or not + + + align:start position:0% +uh yourself but whether or not +uh you you put all + + align:start position:0% +uh you you put all + + + align:start position:0% +uh you you put all +sort of like a number on it + + align:start position:0% +sort of like a number on it + + + align:start position:0% +sort of like a number on it +that if you think yourself as not being + + align:start position:0% +that if you think yourself as not being + + + align:start position:0% +that if you think yourself as not being +worthy + + align:start position:0% + + + + align:start position:0% + +then you probably + + align:start position:0% +then you probably + + + align:start position:0% +then you probably +will not + + align:start position:0% +will not + + + align:start position:0% +will not +um succeed + + align:start position:0% +um succeed + + + align:start position:0% +um succeed +uh in the things you set out to do + + align:start position:0% +uh in the things you set out to do + + + align:start position:0% +uh in the things you set out to do +because you're unconscious + + align:start position:0% +because you're unconscious + + + align:start position:0% +because you're unconscious +just not come up with a picture of you + + align:start position:0% +just not come up with a picture of you + + + align:start position:0% +just not come up with a picture of you +being the king + + align:start position:0% +being the king + + + align:start position:0% +being the king +how can you + + align:start position:0% +how can you + + + align:start position:0% +how can you +be the king + + align:start position:0% +be the king + + + align:start position:0% +be the king +so it's + + align:start position:0% +so it's + + + align:start position:0% +so it's +so when when rawls begins to talk about + + align:start position:0% +so when when rawls begins to talk about + + + align:start position:0% +so when when rawls begins to talk about +all of these things i could put them in + + align:start position:0% +all of these things i could put them in + + + align:start position:0% +all of these things i could put them in +one of these boxes + + align:start position:0% +one of these boxes + + + align:start position:0% +one of these boxes +and find out and follow what he's saying + + align:start position:0% +and find out and follow what he's saying + + + align:start position:0% +and find out and follow what he's saying +okay so that's what this chart was about + + align:start position:0% +okay so that's what this chart was about + + + align:start position:0% +okay so that's what this chart was about +and self-esteem + + align:start position:0% +and self-esteem + + + align:start position:0% +and self-esteem +is what is needed + + align:start position:0% +is what is needed + + + align:start position:0% +is what is needed +to go + + align:start position:0% +to go + + + align:start position:0% +to go +from wants to intentions + + align:start position:0% +from wants to intentions + + + align:start position:0% +from wants to intentions +low self-esteem you'll sit around + + align:start position:0% +low self-esteem you'll sit around + + + align:start position:0% +low self-esteem you'll sit around +wanting things and being in pain all day + + align:start position:0% +wanting things and being in pain all day + + + align:start position:0% +wanting things and being in pain all day +but you will never get to the point + + align:start position:0% +but you will never get to the point + + + align:start position:0% +but you will never get to the point +where you + + align:start position:0% +where you + + + align:start position:0% +where you +intend to do something about them + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +what about if you think that um + + align:start position:0% +what about if you think that um + + + align:start position:0% +what about if you think that um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +let's say the let's say okay there are + + align:start position:0% +let's say the let's say okay there are + + + align:start position:0% +let's say the let's say okay there are +uh five others here in the room + + align:start position:0% +uh five others here in the room + + + align:start position:0% +uh five others here in the room +uh let's say that we want to uh + + align:start position:0% +uh let's say that we want to uh + + + align:start position:0% +uh let's say that we want to uh +build a car and put it in competition + + align:start position:0% +build a car and put it in competition + + + align:start position:0% +build a car and put it in competition +that's the best gas saving car + + align:start position:0% +that's the best gas saving car + + + align:start position:0% +that's the best gas saving car +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now suppose you look around and + + align:start position:0% +now suppose you look around and + + + align:start position:0% +now suppose you look around and +everybody has a different job to do + + align:start position:0% +everybody has a different job to do + + + align:start position:0% +everybody has a different job to do +suppose you know that you can do your + + align:start position:0% +suppose you know that you can do your + + + align:start position:0% +suppose you know that you can do your +job + + align:start position:0% +job + + + align:start position:0% +job +but the rest of us think you cannot do + + align:start position:0% +but the rest of us think you cannot do + + + align:start position:0% +but the rest of us think you cannot do +your job + + align:start position:0% + + + + align:start position:0% + +that means that your external judgment + + align:start position:0% +that means that your external judgment + + + align:start position:0% +that means that your external judgment +of your self-account self-confidence is + + align:start position:0% +of your self-account self-confidence is + + + align:start position:0% +of your self-account self-confidence is +low because you think that the rest of + + align:start position:0% +low because you think that the rest of + + + align:start position:0% +low because you think that the rest of +us don't think that don't have any + + align:start position:0% +us don't think that don't have any + + + align:start position:0% +us don't think that don't have any +confidence in you + + align:start position:0% +confidence in you + + + align:start position:0% +confidence in you +and that's not + + align:start position:0% + + + + align:start position:0% + +right that's complicated but that's the + + align:start position:0% +right that's complicated but that's the + + + align:start position:0% +right that's complicated but that's the +way it goes it's what you think about + + align:start position:0% +way it goes it's what you think about + + + align:start position:0% +way it goes it's what you think about +what we think about you + + align:start position:0% +what we think about you + + + align:start position:0% +what we think about you +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +i don't know of any better way that's + + align:start position:0% +i don't know of any better way that's + + + align:start position:0% +i don't know of any better way that's +what it is so so you so + + align:start position:0% +what it is so so you so + + + align:start position:0% +what it is so so you so +how many times have you ever been been + + align:start position:0% +how many times have you ever been been + + + align:start position:0% +how many times have you ever been been +in a group and somebody says well y'all + + align:start position:0% +in a group and somebody says well y'all + + + align:start position:0% +in a group and somebody says well y'all +just don't have any confidence in me + + align:start position:0% +just don't have any confidence in me + + + align:start position:0% +just don't have any confidence in me +that's what it is + + align:start position:0% +that's what it is + + + align:start position:0% +that's what it is +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +that has to do with the prosecution of + + align:start position:0% +that has to do with the prosecution of + + + align:start position:0% +that has to do with the prosecution of +this commitment pathway from wants to + + align:start position:0% +this commitment pathway from wants to + + + align:start position:0% +this commitment pathway from wants to +intentions + + align:start position:0% +intentions + + + align:start position:0% +intentions +so uh what you've got to do is um + + align:start position:0% +so uh what you've got to do is um + + + align:start position:0% +so uh what you've got to do is um +to be able to convince your customers + + align:start position:0% +to be able to convince your customers + + + align:start position:0% +to be able to convince your customers +that you can do it + + align:start position:0% +that you can do it + + + align:start position:0% +that you can do it +you've got to think convince yourself + + align:start position:0% +you've got to think convince yourself + + + align:start position:0% +you've got to think convince yourself +you can do it + + align:start position:0% +you can do it + + + align:start position:0% +you can do it +those things that's where that came + + align:start position:0% + + + + align:start position:0% + +all right and um + + align:start position:0% + + + + align:start position:0% + +so i really think that the basic idea of + + align:start position:0% +so i really think that the basic idea of + + + align:start position:0% +so i really think that the basic idea of +engineering and all the practical + + align:start position:0% +engineering and all the practical + + + align:start position:0% +engineering and all the practical +disciplines + + align:start position:0% +disciplines + + + align:start position:0% +disciplines +has to do with this commitment pathway + + align:start position:0% +has to do with this commitment pathway + + + align:start position:0% +has to do with this commitment pathway +and this ability this innate ability + + align:start position:0% +and this ability this innate ability + + + align:start position:0% +and this ability this innate ability +that we all have + + align:start position:0% +that we all have + + + align:start position:0% +that we all have +and i make the uh + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +our prior assumption that we all have it + + align:start position:0% +our prior assumption that we all have it + + + align:start position:0% +our prior assumption that we all have it +at the same degree + + align:start position:0% + + + + align:start position:0% + +uh what i will say is that it's possible + + align:start position:0% +uh what i will say is that it's possible + + + align:start position:0% +uh what i will say is that it's possible +to study + + align:start position:0% +to study + + + align:start position:0% +to study +and debate + + align:start position:0% +and debate + + + align:start position:0% +and debate +and to read + + align:start position:0% +and to read + + + align:start position:0% +and to read +and develop this + + align:start position:0% +and develop this + + + align:start position:0% +and develop this +so that you can do more in the area of + + align:start position:0% +so that you can do more in the area of + + + align:start position:0% +so that you can do more in the area of +this + + align:start position:0% + + + + align:start position:0% + +and your development of it is what i + + align:start position:0% +and your development of it is what i + + + align:start position:0% +and your development of it is what i +call the forte + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +you want to write it down + + align:start position:0% + + + + align:start position:0% + +just write it down because i mean + + align:start position:0% +just write it down because i mean + + + align:start position:0% +just write it down because i mean +this isn't uh + + align:start position:0% + + + + align:start position:0% + +or you're going to make a matrix out of + + align:start position:0% +or you're going to make a matrix out of + + + align:start position:0% +or you're going to make a matrix out of +that the cognition + + align:start position:0% + + + + align:start position:0% + +i don't know it might be look there's a + + align:start position:0% +i don't know it might be look there's a + + + align:start position:0% +i don't know it might be look there's a +way to think about all of this + + align:start position:0% +way to think about all of this + + + align:start position:0% +way to think about all of this +depends on which how you want to use it + + align:start position:0% +depends on which how you want to use it + + + align:start position:0% +depends on which how you want to use it +make your arguments this is good for me + + align:start position:0% + + + + align:start position:0% + +there's different permutations of the + + align:start position:0% +there's different permutations of the + + + align:start position:0% +there's different permutations of the +speciality + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +yes + + align:start position:0% + + + + align:start position:0% + +sure uh so this matrix would be best for + + align:start position:0% +sure uh so this matrix would be best for + + + align:start position:0% +sure uh so this matrix would be best for +that kind of thinking + + align:start position:0% +that kind of thinking + + + align:start position:0% +that kind of thinking +and this would be best for + + align:start position:0% +and this would be best for + + + align:start position:0% +and this would be best for +the established learning discipline like + + align:start position:0% +the established learning discipline like + + + align:start position:0% +the established learning discipline like +this perhaps but this is the way i think + + align:start position:0% +this perhaps but this is the way i think + + + align:start position:0% +this perhaps but this is the way i think +about it + + align:start position:0% + + + + align:start position:0% + +no that's right um + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +there's a word that i did use over here + + align:start position:0% +there's a word that i did use over here + + + align:start position:0% +there's a word that i did use over here +not now + + align:start position:0% +not now + + + align:start position:0% +not now +first of all + + align:start position:0% +first of all + + + align:start position:0% +first of all +i'm applying the whole chart to every + + align:start position:0% +i'm applying the whole chart to every + + + align:start position:0% +i'm applying the whole chart to every +learning discipline + + align:start position:0% + + + + align:start position:0% + +what i do not apply to everyone in the + + align:start position:0% +what i do not apply to everyone in the + + + align:start position:0% +what i do not apply to everyone in the +discipline is the same specialty and the + + align:start position:0% +discipline is the same specialty and the + + + align:start position:0% +discipline is the same specialty and the +same form + + align:start position:0% +same form + + + align:start position:0% +same form +in other words what do you spend your + + align:start position:0% +in other words what do you spend your + + + align:start position:0% +in other words what do you spend your +time learning the most on + + align:start position:0% + + + + align:start position:0% + +we already said that there's a + + align:start position:0% +we already said that there's a + + + align:start position:0% +we already said that there's a +difference between the way you think + + align:start position:0% +difference between the way you think + + + align:start position:0% +difference between the way you think +about this matter and what you write + + align:start position:0% +about this matter and what you write + + + align:start position:0% +about this matter and what you write +down and pass on to others and how you + + align:start position:0% +down and pass on to others and how you + + + align:start position:0% +down and pass on to others and how you +argue + + align:start position:0% +argue + + + align:start position:0% +argue +the matter + + align:start position:0% +the matter + + + align:start position:0% +the matter +and these are what you have called when + + align:start position:0% +and these are what you have called when + + + align:start position:0% +and these are what you have called when +we talked about learning disciplines and + + align:start position:0% +we talked about learning disciplines and + + + align:start position:0% +we talked about learning disciplines and +what i call + + align:start position:0% +what i call + + + align:start position:0% +what i call +the body of knowledge + + align:start position:0% +the body of knowledge + + + align:start position:0% +the body of knowledge +that's what that is + + align:start position:0% +that's what that is + + + align:start position:0% +that's what that is +the real value of the body body of + + align:start position:0% +the real value of the body body of + + + align:start position:0% +the real value of the body body of +knowledge is really not that is set down + + align:start position:0% +knowledge is really not that is set down + + + align:start position:0% +knowledge is really not that is set down +here and that you can argue from it the + + align:start position:0% +here and that you can argue from it the + + + align:start position:0% +here and that you can argue from it the +real body is that when we're dead we can + + align:start position:0% +real body is that when we're dead we can + + + align:start position:0% +real body is that when we're dead we can +give it to somebody else's living + + align:start position:0% +give it to somebody else's living + + + align:start position:0% +give it to somebody else's living +that's the real value of it it can go + + align:start position:0% +that's the real value of it it can go + + + align:start position:0% +that's the real value of it it can go +from generation to generation + + align:start position:0% +from generation to generation + + + align:start position:0% +from generation to generation +you can preserve it + + align:start position:0% +you can preserve it + + + align:start position:0% +you can preserve it +a lot of these thoughts about what's + + align:start position:0% +a lot of these thoughts about what's + + + align:start position:0% +a lot of these thoughts about what's +coming to me in the night + + align:start position:0% +coming to me in the night + + + align:start position:0% +coming to me in the night +are gone when i'm gone + + align:start position:0% +are gone when i'm gone + + + align:start position:0% +are gone when i'm gone +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +when we talk about the body of learning + + align:start position:0% +when we talk about the body of learning + + + align:start position:0% +when we talk about the body of learning +knowledge we're talking about something + + align:start position:0% +knowledge we're talking about something + + + align:start position:0% +knowledge we're talking about something +that's transmittable + + align:start position:0% +that's transmittable + + + align:start position:0% +that's transmittable +through the generations + + align:start position:0% +through the generations + + + align:start position:0% +through the generations +which makes ballet hard + + align:start position:0% +which makes ballet hard + + + align:start position:0% +which makes ballet hard +so you have to transmit it + + align:start position:0% +so you have to transmit it + + + align:start position:0% +so you have to transmit it +through um + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +what's the word i'm looking for the word + + align:start position:0% +what's the word i'm looking for the word + + + align:start position:0% +what's the word i'm looking for the word +um + + align:start position:0% + + + + align:start position:0% + +apprenticeship + + align:start position:0% +apprenticeship + + + align:start position:0% +apprenticeship +yeah so you get it clear and then you + + align:start position:0% +yeah so you get it clear and then you + + + align:start position:0% +yeah so you get it clear and then you +pass it to somebody what and they + + align:start position:0% +pass it to somebody what and they + + + align:start position:0% +pass it to somebody what and they +and hopefully the line is not broken + + align:start position:0% + + + + align:start position:0% + +uh in philosophy they have such a thing + + align:start position:0% +uh in philosophy they have such a thing + + + align:start position:0% +uh in philosophy they have such a thing +as uh since we got five more minutes + + align:start position:0% +as uh since we got five more minutes + + + align:start position:0% +as uh since we got five more minutes +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +i think is uh + + align:start position:0% +i think is uh + + + align:start position:0% +i think is uh +remarkable + + align:start position:0% +remarkable + + + align:start position:0% +remarkable +believe it not they have it in + + align:start position:0% +believe it not they have it in + + + align:start position:0% +believe it not they have it in +philosophy when you think about it they + + align:start position:0% +philosophy when you think about it they + + + align:start position:0% +philosophy when you think about it they +have it in + + align:start position:0% +have it in + + + align:start position:0% +have it in +theology too in philosophy there's such + + align:start position:0% +theology too in philosophy there's such + + + align:start position:0% +theology too in philosophy there's such +a thing as um + + align:start position:0% +a thing as um + + + align:start position:0% +a thing as um +kantian scholar + + align:start position:0% + + + + align:start position:0% + +now a kantian scholar is not merely a + + align:start position:0% +now a kantian scholar is not merely a + + + align:start position:0% +now a kantian scholar is not merely a +person who + + align:start position:0% +person who + + + align:start position:0% +person who +did his or her dissertation on immanuel + + align:start position:0% +did his or her dissertation on immanuel + + + align:start position:0% +did his or her dissertation on immanuel +kant + + align:start position:0% +kant + + + align:start position:0% +kant +a kantian scholar is a person + + align:start position:0% +a kantian scholar is a person + + + align:start position:0% +a kantian scholar is a person +who has been cultivated by somebody + + align:start position:0% +who has been cultivated by somebody + + + align:start position:0% +who has been cultivated by somebody +who was cultivated by somebody + + align:start position:0% +who was cultivated by somebody + + + align:start position:0% +who was cultivated by somebody +who was cultivated by somebody who was + + align:start position:0% +who was cultivated by somebody who was + + + align:start position:0% +who was cultivated by somebody who was +cultivated by immanuel kant + + align:start position:0% +cultivated by immanuel kant + + + align:start position:0% +cultivated by immanuel kant +there's an intellectual lineage + + align:start position:0% +there's an intellectual lineage + + + align:start position:0% +there's an intellectual lineage +that + + align:start position:0% +that + + + align:start position:0% +that +that comes straight from the person + + align:start position:0% +that comes straight from the person + + + align:start position:0% +that comes straight from the person +straight down + + align:start position:0% +straight down + + + align:start position:0% +straight down +and that person's + + align:start position:0% +and that person's + + + align:start position:0% +and that person's +duty in life + + align:start position:0% +duty in life + + + align:start position:0% +duty in life +is to be emanuel kant + + align:start position:0% +is to be emanuel kant + + + align:start position:0% +is to be emanuel kant +in our generation + + align:start position:0% + + + + align:start position:0% + +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +there was a philosopher an + + align:start position:0% +there was a philosopher an + + + align:start position:0% +there was a philosopher an +african-american who was + + align:start position:0% +african-american who was + + + align:start position:0% +african-american who was +um chair of the philosophy department at + + align:start position:0% +um chair of the philosophy department at + + + align:start position:0% +um chair of the philosophy department at +howard named alain locke for 40 years 35 + + align:start position:0% +howard named alain locke for 40 years 35 + + + align:start position:0% +howard named alain locke for 40 years 35 +years + + align:start position:0% +years + + + align:start position:0% +years +they've got still lock they're still + + align:start position:0% +they've got still lock they're still + + + align:start position:0% +they've got still lock they're still +making lockheed scholars + + align:start position:0% + + + + align:start position:0% + +they got that lineage coming straight + + align:start position:0% +they got that lineage coming straight + + + align:start position:0% +they got that lineage coming straight +now + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +i don't know any of them + + align:start position:0% +i don't know any of them + + + align:start position:0% +i don't know any of them +and it would be a nightmare but i'll + + align:start position:0% +and it would be a nightmare but i'll + + + align:start position:0% +and it would be a nightmare but i'll +tell you this it would be a nightmare + + align:start position:0% +tell you this it would be a nightmare + + + align:start position:0% +tell you this it would be a nightmare +for me to learn that the line was broken + + align:start position:0% + + + + align:start position:0% + +it would be nice if i don't even know i + + align:start position:0% +it would be nice if i don't even know i + + + align:start position:0% +it would be nice if i don't even know i +don't even know how much this stuff is + + align:start position:0% +don't even know how much this stuff is + + + align:start position:0% +don't even know how much this stuff is +cherished uh today + + align:start position:0% + + + + align:start position:0% + +but um the idea was as a matter of fact + + align:start position:0% +but um the idea was as a matter of fact + + + align:start position:0% +but um the idea was as a matter of fact +the idea can you think of where where + + align:start position:0% +the idea can you think of where where + + + align:start position:0% +the idea can you think of where where +this idea + + align:start position:0% +this idea + + + align:start position:0% +this idea +we got three more minutes it's kept + + align:start position:0% +we got three more minutes it's kept + + + align:start position:0% +we got three more minutes it's kept +alive or has been kept alive for a long + + align:start position:0% +alive or has been kept alive for a long + + + align:start position:0% +alive or has been kept alive for a long +time + + align:start position:0% + + + + align:start position:0% + +i understand that the pope + + align:start position:0% +i understand that the pope + + + align:start position:0% +i understand that the pope +had to be cultivated by somebody who was + + align:start position:0% +had to be cultivated by somebody who was + + + align:start position:0% +had to be cultivated by somebody who was +cultivated by somebody who was + + align:start position:0% +cultivated by somebody who was + + + align:start position:0% +cultivated by somebody who was +cultivated all the way back to the + + align:start position:0% +cultivated all the way back to the + + + align:start position:0% +cultivated all the way back to the +apostles + + align:start position:0% + + + + align:start position:0% + +they tried to keep it going + + align:start position:0% + + + + align:start position:0% + +they tried to keep it going i think they + + align:start position:0% +they tried to keep it going i think they + + + align:start position:0% +they tried to keep it going i think they +broke it down + + align:start position:0% +broke it down + + + align:start position:0% +broke it down +well i don't want to get into all that + + align:start position:0% +well i don't want to get into all that + + + align:start position:0% +well i don't want to get into all that +but + + align:start position:0% +but + + + align:start position:0% +but +but uh philosophers did try to they + + align:start position:0% +but uh philosophers did try to they + + + align:start position:0% +but uh philosophers did try to they +still they still have to do it with some + + align:start position:0% +still they still have to do it with some + + + align:start position:0% +still they still have to do it with some +philosophical + + align:start position:0% +philosophical + + + align:start position:0% +philosophical +be nice if engineers did it wouldn't it + + align:start position:0% + + + + align:start position:0% + +the question is who would we start with + + align:start position:0% + + + + align:start position:0% + +but uh + + align:start position:0% +but uh + + + align:start position:0% +but uh +yeah the idea is to have that person + + align:start position:0% +yeah the idea is to have that person + + + align:start position:0% +yeah the idea is to have that person +with us in this generation what would + + align:start position:0% +with us in this generation what would + + + align:start position:0% +with us in this generation what would +that person say and would we be better + + align:start position:0% +that person say and would we be better + + + align:start position:0% +that person say and would we be better +off + + align:start position:0% +off + + + align:start position:0% +off +uh if we had that point of view straight + + align:start position:0% +uh if we had that point of view straight + + + align:start position:0% +uh if we had that point of view straight +out of uh + + align:start position:0% +out of uh + + + align:start position:0% +out of uh +as close as we can get it that person's + + align:start position:0% +as close as we can get it that person's + + + align:start position:0% +as close as we can get it that person's +mine + + align:start position:0% + + + + align:start position:0% + +i know that game + + align:start position:0% + + + + align:start position:0% + +it was you can't take it too seriously + + align:start position:0% +it was you can't take it too seriously + + + align:start position:0% +it was you can't take it too seriously +but there's something in it + + align:start position:0% + + + + align:start position:0% + +because the person is not supposed to + + align:start position:0% +because the person is not supposed to + + + align:start position:0% +because the person is not supposed to +just learn the methods supposed to learn + + align:start position:0% +just learn the methods supposed to learn + + + align:start position:0% +just learn the methods supposed to learn +the person's + + align:start position:0% +the person's + + + align:start position:0% +the person's +habits you know and personal views on + + align:start position:0% +habits you know and personal views on + + + align:start position:0% +habits you know and personal views on +this that and the other + + align:start position:0% +this that and the other + + + align:start position:0% +this that and the other +uh supposed to be a biographer + + align:start position:0% + + + + align:start position:0% + +and you're supposed to be + + align:start position:0% +and you're supposed to be + + + align:start position:0% +and you're supposed to be +that person emmanuel kant in this life + + align:start position:0% +that person emmanuel kant in this life + + + align:start position:0% +that person emmanuel kant in this life +today \ No newline at end of file diff --git a/xIOQ0O90DjI.txt b/xIOQ0O90DjI.txt new file mode 100644 index 0000000000000000000000000000000000000000..93c2a96114a9bcc4f6e6367c527cb3fbeeeb7f0d --- /dev/null +++ b/xIOQ0O90DjI.txt @@ -0,0 +1,14667 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +So today what what I want to do is as as + + align:start position:0% +So today what what I want to do is as as + + + align:start position:0% +So today what what I want to do is as as +as pro as requested and and uh promised + + align:start position:0% +as pro as requested and and uh promised + + + align:start position:0% +as pro as requested and and uh promised +uh uh last week today we'll spend some + + align:start position:0% +uh uh last week today we'll spend some + + + align:start position:0% +uh uh last week today we'll spend some +time just reviewing some of the things + + align:start position:0% +time just reviewing some of the things + + + align:start position:0% +time just reviewing some of the things +we've talked about up until now and some + + align:start position:0% +we've talked about up until now and some + + + align:start position:0% +we've talked about up until now and some +of the concepts that you might find uh + + align:start position:0% +of the concepts that you might find uh + + + align:start position:0% +of the concepts that you might find uh +questions around on the quiz. Okay. So + + align:start position:0% +questions around on the quiz. Okay. So + + + align:start position:0% +questions around on the quiz. Okay. So +maybe I'll I'll I'll ask you guys just + + align:start position:0% +maybe I'll I'll I'll ask you guys just + + + align:start position:0% +maybe I'll I'll I'll ask you guys just +to make sure you understand each of the + + align:start position:0% +to make sure you understand each of the + + + align:start position:0% +to make sure you understand each of the +the kind of key concepts. Um I'll also + + align:start position:0% +the kind of key concepts. Um I'll also + + + align:start position:0% +the kind of key concepts. Um I'll also +as part of this review, we'll we'll look + + align:start position:0% +as part of this review, we'll we'll look + + + align:start position:0% +as part of this review, we'll we'll look +at a couple of questions a couple more + + align:start position:0% +at a couple of questions a couple more + + + align:start position:0% +at a couple of questions a couple more +questions from last year. Okay. Uh from + + align:start position:0% +questions from last year. Okay. Uh from + + + align:start position:0% +questions from last year. Okay. Uh from +the quiz last year. Um you have a + + align:start position:0% +the quiz last year. Um you have a + + + align:start position:0% +the quiz last year. Um you have a +practice quiz and in solutions and that + + align:start position:0% +practice quiz and in solutions and that + + + align:start position:0% +practice quiz and in solutions and that +would be a good idea to look at. Those + + align:start position:0% +would be a good idea to look at. Those + + + align:start position:0% +would be a good idea to look at. Those +are posted on stellar as well. That's + + align:start position:0% +are posted on stellar as well. That's + + + align:start position:0% +are posted on stellar as well. That's +not uh to say that that's exactly what + + align:start position:0% +not uh to say that that's exactly what + + + align:start position:0% +not uh to say that that's exactly what +you're going to get, but you might get, + + align:start position:0% +you're going to get, but you might get, + + + align:start position:0% +you're going to get, but you might get, +you know, in terms of topics, those are + + align:start position:0% +you know, in terms of topics, those are + + + align:start position:0% +you know, in terms of topics, those are +good ones. + + align:start position:0% +good ones. + + + align:start position:0% +good ones. +But what's not in the practice quiz are + + align:start position:0% +But what's not in the practice quiz are + + + align:start position:0% +But what's not in the practice quiz are +is sort of any pictures of a density of + + align:start position:0% +is sort of any pictures of a density of + + + align:start position:0% +is sort of any pictures of a density of +states or a band structure. Um I I can + + align:start position:0% +states or a band structure. Um I I can + + + align:start position:0% +states or a band structure. Um I I can +almost guarantee you you'll have sort of + + align:start position:0% +almost guarantee you you'll have sort of + + + align:start position:0% +almost guarantee you you'll have sort of +one of each of those, right, on the real + + align:start position:0% +one of each of those, right, on the real + + + align:start position:0% +one of each of those, right, on the real +quiz. So you'll have a a band structure + + align:start position:0% +quiz. So you'll have a a band structure + + + align:start position:0% +quiz. So you'll have a a band structure +that we'll ask I'll ask you some + + align:start position:0% +that we'll ask I'll ask you some + + + align:start position:0% +that we'll ask I'll ask you some +questions about as well as a doss plot. + + align:start position:0% +questions about as well as a doss plot. + + + align:start position:0% +questions about as well as a doss plot. +All right? All + + align:start position:0% +All right? All + + + align:start position:0% +All right? All +right. So, so, so we're sort of supposed + + align:start position:0% +right. So, so, so we're sort of supposed + + + align:start position:0% +right. So, so, so we're sort of supposed +to be here, but we're and I still hope + + align:start position:0% +to be here, but we're and I still hope + + + align:start position:0% +to be here, but we're and I still hope +to get to solar cells and, uh, we have + + align:start position:0% +to get to solar cells and, uh, we have + + + align:start position:0% +to get to solar cells and, uh, we have +time. Uh, so, so we're going to talk + + align:start position:0% +time. Uh, so, so we're going to talk + + + align:start position:0% +time. Uh, so, so we're going to talk +about solar cells. Um, + + align:start position:0% +about solar cells. Um, + + + align:start position:0% +about solar cells. Um, +but I know that since the quiz is + + align:start position:0% +but I know that since the quiz is + + + align:start position:0% +but I know that since the quiz is +Thursday, we want to take a good chunk + + align:start position:0% +Thursday, we want to take a good chunk + + + align:start position:0% +Thursday, we want to take a good chunk +of today and just make sure that we, uh, + + align:start position:0% +of today and just make sure that we, uh, + + + align:start position:0% +of today and just make sure that we, uh, +have a good sense of what to expect and + + align:start position:0% +have a good sense of what to expect and + + + align:start position:0% +have a good sense of what to expect and +and and do do a review. But I hope to + + align:start position:0% +and and do do a review. But I hope to + + + align:start position:0% +and and do do a review. But I hope to +get to our beginning of talking about + + align:start position:0% +get to our beginning of talking about + + + align:start position:0% +get to our beginning of talking about +modeling solar cells today as well. + + align:start position:0% +modeling solar cells today as well. + + + align:start position:0% +modeling solar cells today as well. +Okay? and we'll pick up on that after + + align:start position:0% +Okay? and we'll pick up on that after + + + align:start position:0% +Okay? and we'll pick up on that after +the quiz. Are there any questions just + + align:start position:0% +the quiz. Are there any questions just + + + align:start position:0% +the quiz. Are there any questions just +about the quiz which is Thursday? + + align:start position:0% +about the quiz which is Thursday? + + + align:start position:0% +about the quiz which is Thursday? +It's open book, open notes, + + align:start position:0% + + + + align:start position:0% + +no phones, PDAs. Yeah. + + align:start position:0% +no phones, PDAs. Yeah. + + + align:start position:0% +no phones, PDAs. Yeah. +Somewhere like definitely no more than a + + align:start position:0% +Somewhere like definitely no more than a + + + align:start position:0% +Somewhere like definitely no more than a +hundred and + + align:start position:0% +hundred and + + + align:start position:0% +hundred and +kidding. Uh + + align:start position:0% + + + + align:start position:0% + +10. I don't know. Does that sound about + + align:start position:0% +10. I don't know. Does that sound about + + + align:start position:0% +10. I don't know. Does that sound about +right? Something like that. + + align:start position:0% +right? Something like that. + + + align:start position:0% +right? Something like that. +Yeah. + + align:start position:0% + + + + align:start position:0% + +12. + + align:start position:0% + + + + align:start position:0% + +Okay. So, there we are. Now, I I I do + + align:start position:0% +Okay. So, there we are. Now, I I I do + + + align:start position:0% +Okay. So, there we are. Now, I I I do +want to since since Lynn already made a + + align:start position:0% +want to since since Lynn already made a + + + align:start position:0% +want to since since Lynn already made a +little announcements about part two, I + + align:start position:0% +little announcements about part two, I + + + align:start position:0% +little announcements about part two, I +wanted to start today. Um so, that's + + align:start position:0% +wanted to start today. Um so, that's + + + align:start position:0% +wanted to start today. Um so, that's +what we're going to do. I wanted to just + + align:start position:0% +what we're going to do. I wanted to just + + + align:start position:0% +what we're going to do. I wanted to just +even though I just postponed the piece. + + align:start position:0% +even though I just postponed the piece. + + + align:start position:0% +even though I just postponed the piece. +Oh, that was I'm gonna have an office + + align:start position:0% +Oh, that was I'm gonna have an office + + + align:start position:0% +Oh, that was I'm gonna have an office +hour tomorrow + + align:start position:0% +hour tomorrow + + + align:start position:0% +hour tomorrow +um at 4. + + align:start position:0% +um at 4. + + + align:start position:0% +um at 4. +Is that what I said? Four to five or did + + align:start position:0% +Is that what I said? Four to five or did + + + align:start position:0% +Is that what I said? Four to five or did +I say 5 to 6? 4 to 5, I think. And but + + align:start position:0% +I say 5 to 6? 4 to 5, I think. And but + + + align:start position:0% +I say 5 to 6? 4 to 5, I think. And but +if anybody has questions, as always, + + align:start position:0% +if anybody has questions, as always, + + + align:start position:0% +if anybody has questions, as always, +send me an email and I'm happy to answer + + align:start position:0% +send me an email and I'm happy to answer + + + align:start position:0% +send me an email and I'm happy to answer +electronically or set up a time to meet + + align:start position:0% +electronically or set up a time to meet + + + align:start position:0% +electronically or set up a time to meet +that um works uh you know, on on your + + align:start position:0% +that um works uh you know, on on your + + + align:start position:0% +that um works uh you know, on on your +side. Okay. So that that's that's very + + align:start position:0% +side. Okay. So that that's that's very + + + align:start position:0% +side. Okay. So that that's that's very +good. And how many of you have looked at + + align:start position:0% +good. And how many of you have looked at + + + align:start position:0% +good. And how many of you have looked at +problem three? + + align:start position:0% +problem three? + + + align:start position:0% +problem three? +Couple of you. Okay. + + align:start position:0% +Couple of you. Okay. + + + align:start position:0% +Couple of you. Okay. +So um + + align:start position:0% +So um + + + align:start position:0% +So um +so are there any questions that anybody + + align:start position:0% +so are there any questions that anybody + + + align:start position:0% +so are there any questions that anybody +has about problem three right now who've + + align:start position:0% +has about problem three right now who've + + + align:start position:0% +has about problem three right now who've +who've looked at it? Go ahead. + + align:start position:0% + + + + align:start position:0% + +That's a good question. That's a really + + align:start position:0% +That's a good question. That's a really + + + align:start position:0% +That's a good question. That's a really +good question. Um, anything more + + align:start position:0% +good question. Um, anything more + + + align:start position:0% +good question. Um, anything more +specific? + + align:start position:0% +specific? + + + align:start position:0% +specific? +Like you know that maximum efficiency is + + align:start position:0% +Like you know that maximum efficiency is + + + align:start position:0% +Like you know that maximum efficiency is +going to be related to the energy going + + align:start position:0% +going to be related to the energy going + + + align:start position:0% +going to be related to the energy going +in versus the energy going out. + + align:start position:0% +in versus the energy going out. + + + align:start position:0% +in versus the energy going out. +But how do you determine I guess the + + align:start position:0% +But how do you determine I guess the + + + align:start position:0% +But how do you determine I guess the +energy going out? + + align:start position:0% +energy going out? + + + align:start position:0% +energy going out? +Yeah. Yeah. Okay. So, so let me let me + + align:start position:0% +Yeah. Yeah. Okay. So, so let me let me + + + align:start position:0% +Yeah. Yeah. Okay. So, so let me let me +talk a little bit about this problem to + + align:start position:0% +talk a little bit about this problem to + + + align:start position:0% +talk a little bit about this problem to +make sure that we kind of know where to + + align:start position:0% +make sure that we kind of know where to + + + align:start position:0% +make sure that we kind of know where to +go with it. Okay. Um, and the key the + + align:start position:0% +go with it. Okay. Um, and the key the + + + align:start position:0% +go with it. Okay. Um, and the key the +key setup here is actually really part A + + align:start position:0% +key setup here is actually really part A + + + align:start position:0% +key setup here is actually really part A +in a way. It seems pretty simple. Um, + + align:start position:0% +in a way. It seems pretty simple. Um, + + + align:start position:0% +in a way. It seems pretty simple. Um, +but it's kind of the core piece of + + align:start position:0% +but it's kind of the core piece of + + + align:start position:0% +but it's kind of the core piece of +information that that you need to + + align:start position:0% +information that that you need to + + + align:start position:0% +information that that you need to +understand. Okay. And I'm going to use + + align:start position:0% +understand. Okay. And I'm going to use + + + align:start position:0% +understand. Okay. And I'm going to use +this yellow chalk that's actually white + + align:start position:0% +this yellow chalk that's actually white + + + align:start position:0% +this yellow chalk that's actually white +to draw. + + align:start position:0% +to draw. + + + align:start position:0% +to draw. +Let's let's not forget what it is that + + align:start position:0% +Let's let's not forget what it is that + + + align:start position:0% +Let's let's not forget what it is that +we're talking about, which is um + + align:start position:0% +we're talking about, which is um + + + align:start position:0% +we're talking about, which is um +basically an energy landscape. Remember, + + align:start position:0% +basically an energy landscape. Remember, + + + align:start position:0% +basically an energy landscape. Remember, +in in capturing the sun's energy, what + + align:start position:0% +in in capturing the sun's energy, what + + + align:start position:0% +in in capturing the sun's energy, what +we're trying to what we're doing and in + + align:start position:0% +we're trying to what we're doing and in + + + align:start position:0% +we're trying to what we're doing and in +in many energy technologies, what we're + + align:start position:0% +in many energy technologies, what we're + + + align:start position:0% +in many energy technologies, what we're +doing is we're pumping something up an + + align:start position:0% +doing is we're pumping something up an + + + align:start position:0% +doing is we're pumping something up an +energy hill, right? Um, and in this + + align:start position:0% +energy hill, right? Um, and in this + + + align:start position:0% +energy hill, right? Um, and in this +case, we pump an electron, we shine + + align:start position:0% +case, we pump an electron, we shine + + + align:start position:0% +case, we pump an electron, we shine +light on it, + + align:start position:0% +light on it, + + + align:start position:0% +light on it, +okay? and the the molecule is in the + + align:start position:0% +okay? and the the molecule is in the + + + align:start position:0% +okay? and the the molecule is in the +trans state + + align:start position:0% +trans state + + + align:start position:0% +trans state +and then it gets excited + + align:start position:0% +and then it gets excited + + + align:start position:0% +and then it gets excited +because the light the electrons from the + + align:start position:0% +because the light the electrons from the + + + align:start position:0% +because the light the electrons from the +the photons from the light excite + + align:start position:0% +the photons from the light excite + + + align:start position:0% +the photons from the light excite +electrons in the molecule. So that's + + align:start position:0% +electrons in the molecule. So that's + + + align:start position:0% +electrons in the molecule. So that's +that pumping action that's happening. + + align:start position:0% +that pumping action that's happening. + + + align:start position:0% +that pumping action that's happening. +You're pumping electrons within this + + align:start position:0% +You're pumping electrons within this + + + align:start position:0% +You're pumping electrons within this +molecule up to a higher level. When you + + align:start position:0% +molecule up to a higher level. When you + + + align:start position:0% +molecule up to a higher level. When you +do that, the molecule is allowed to go + + align:start position:0% +do that, the molecule is allowed to go + + + align:start position:0% +do that, the molecule is allowed to go +to here just from that energy from the + + align:start position:0% +to here just from that energy from the + + + align:start position:0% +to here just from that energy from the +light. Okay? So the light's energy is + + align:start position:0% +light. Okay? So the light's energy is + + + align:start position:0% +light. Okay? So the light's energy is +being converted into creating electrons + + align:start position:0% +being converted into creating electrons + + + align:start position:0% +being converted into creating electrons +that are higher in energy and that + + align:start position:0% +that are higher in energy and that + + + align:start position:0% +that are higher in energy and that +allows the molecule to go from this + + align:start position:0% +allows the molecule to go from this + + + align:start position:0% +allows the molecule to go from this +structure to this structure and that's + + align:start position:0% +structure to this structure and that's + + + align:start position:0% +structure to this structure and that's +allowing you to store this much energy. + + align:start position:0% +allowing you to store this much energy. + + + align:start position:0% +allowing you to store this much energy. +So don't forget this picture as you + + align:start position:0% +So don't forget this picture as you + + + align:start position:0% +So don't forget this picture as you +think about you know this homework + + align:start position:0% +think about you know this homework + + + align:start position:0% +think about you know this homework +because that's really this homework is + + align:start position:0% +because that's really this homework is + + + align:start position:0% +because that's really this homework is +all about this um this picture. + + align:start position:0% +all about this um this picture. + + + align:start position:0% +all about this um this picture. +Now, um, + + align:start position:0% +Now, um, + + + align:start position:0% +Now, um, +who can tell me, we we talked about this + + align:start position:0% +who can tell me, we we talked about this + + + align:start position:0% +who can tell me, we we talked about this +in in in class already when we talked + + align:start position:0% +in in in class already when we talked + + + align:start position:0% +in in in class already when we talked +about this, uh, this whole solar thermal + + align:start position:0% +about this, uh, this whole solar thermal + + + align:start position:0% +about this, uh, this whole solar thermal +fuel concept. Who can tell me + + align:start position:0% +fuel concept. Who can tell me + + + align:start position:0% +fuel concept. Who can tell me +why? Who can tell me the answer to part + + align:start position:0% +why? Who can tell me the answer to part + + + align:start position:0% +why? Who can tell me the answer to part +A? Let's just see if we can do that + + align:start position:0% +A? Let's just see if we can do that + + + align:start position:0% +A? Let's just see if we can do that +together. + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% + + + + align:start position:0% + +energy + + align:start position:0% +energy + + + align:start position:0% +energy +between the transis + + align:start position:0% + + + + align:start position:0% + +energy. + + align:start position:0% +energy. + + + align:start position:0% +energy. +Okay. So, so, so here I'm going I'm + + align:start position:0% +Okay. So, so, so here I'm going I'm + + + align:start position:0% +Okay. So, so, so here I'm going I'm +shining light and I I shined light of + + align:start position:0% +shining light and I I shined light of + + + align:start position:0% +shining light and I I shined light of +this energy or if you want to think + + align:start position:0% +this energy or if you want to think + + + align:start position:0% +this energy or if you want to think +about it as HC over lambda, right, of + + align:start position:0% +about it as HC over lambda, right, of + + + align:start position:0% +about it as HC over lambda, right, of +that amount of energy just going between + + align:start position:0% +that amount of energy just going between + + + align:start position:0% +that amount of energy just going between +wavelength and frequency. And I I shine + + align:start position:0% +wavelength and frequency. And I I shine + + + align:start position:0% +wavelength and frequency. And I I shine +light on this trans state and I only + + align:start position:0% +light on this trans state and I only + + + align:start position:0% +light on this trans state and I only +shine light with this amount kentite of + + align:start position:0% +shine light with this amount kentite of + + + align:start position:0% +shine light with this amount kentite of +energy. + + align:start position:0% +energy. + + + align:start position:0% +energy. +Can it possibly be converted to here? + + align:start position:0% +Can it possibly be converted to here? + + + align:start position:0% +Can it possibly be converted to here? +Right? It can't because you you got to + + align:start position:0% +Right? It can't because you you got to + + + align:start position:0% +Right? It can't because you you got to +you don't we can't now some of you took + + align:start position:0% +you don't we can't now some of you took + + + align:start position:0% +you don't we can't now some of you took +3012 and you know we don't violate the + + align:start position:0% +3012 and you know we don't violate the + + + align:start position:0% +3012 and you know we don't violate the +laws of thermodynamics. Those are + + align:start position:0% +laws of thermodynamics. Those are + + + align:start position:0% +laws of thermodynamics. Those are +untouchable. + + align:start position:0% +untouchable. + + + align:start position:0% +untouchable. +You can't get something for nothing, + + align:start position:0% +You can't get something for nothing, + + + align:start position:0% +You can't get something for nothing, +right? So, you're not going to get + + align:start position:0% +right? So, you're not going to get + + + align:start position:0% +right? So, you're not going to get +to store this much energy if you only + + align:start position:0% +to store this much energy if you only + + + align:start position:0% +to store this much energy if you only +put in this much, right? I That kind of + + align:start position:0% +put in this much, right? I That kind of + + + align:start position:0% +put in this much, right? I That kind of +makes sense, right? You can't put it up + + align:start position:0% +makes sense, right? You can't put it up + + + align:start position:0% +makes sense, right? You can't put it up +in some shelf of energy, some chemical + + align:start position:0% +in some shelf of energy, some chemical + + + align:start position:0% +in some shelf of energy, some chemical +shelf, which is a way of thinking about + + align:start position:0% +shelf, which is a way of thinking about + + + align:start position:0% +shelf, which is a way of thinking about +this if you haven't given it enough to + + align:start position:0% +this if you haven't given it enough to + + + align:start position:0% +this if you haven't given it enough to +get up there, right? Unless you use a + + align:start position:0% +get up there, right? Unless you use a + + + align:start position:0% +get up there, right? Unless you use a +lot of thermal vibrations, but that's + + align:start position:0% +lot of thermal vibrations, but that's + + + align:start position:0% +lot of thermal vibrations, but that's +not what we're doing here. You could use + + align:start position:0% +not what we're doing here. You could use + + + align:start position:0% +not what we're doing here. You could use +heat you, but you can't get it with just + + align:start position:0% +heat you, but you can't get it with just + + + align:start position:0% +heat you, but you can't get it with just +input less than output. Okay, so that's + + align:start position:0% +input less than output. Okay, so that's + + + align:start position:0% +input less than output. Okay, so that's +sort of what part A is asking. Does + + align:start position:0% +sort of what part A is asking. Does + + + align:start position:0% +sort of what part A is asking. Does +everybody see that? Ah, now here comes + + align:start position:0% +everybody see that? Ah, now here comes + + + align:start position:0% +everybody see that? Ah, now here comes +the fun part. + + align:start position:0% +the fun part. + + + align:start position:0% +the fun part. +But you see, it's not just this is the + + align:start position:0% +But you see, it's not just this is the + + + align:start position:0% +But you see, it's not just this is the +molecule sort of going about its + + align:start position:0% +molecule sort of going about its + + + align:start position:0% +molecule sort of going about its +business. This is the happygo + + align:start position:0% +business. This is the happygo + + + align:start position:0% +business. This is the happygo +lucky molecule. But then we have the + + align:start position:0% +lucky molecule. But then we have the + + + align:start position:0% +lucky molecule. But then we have the +sun. We have this part. Where did this + + align:start position:0% +sun. We have this part. Where did this + + + align:start position:0% +sun. We have this part. Where did this +come from? Right? Well, this is the sun, + + align:start position:0% +come from? Right? Well, this is the sun, + + + align:start position:0% +come from? Right? Well, this is the sun, +you see? And that has its thing that it + + align:start position:0% +you see? And that has its thing that it + + + align:start position:0% +you see? And that has its thing that it +does. And its thing that it does is it + + align:start position:0% +does. And its thing that it does is it + + + align:start position:0% +does. And its thing that it does is it +has intensity + + align:start position:0% +has intensity + + + align:start position:0% +has intensity +that comes in + + align:start position:0% +that comes in + + + align:start position:0% +that comes in +as a function of this has probably + + align:start position:0% +as a function of this has probably + + + align:start position:0% +as a function of this has probably +nothing to do with the real curve but + + align:start position:0% +nothing to do with the real curve but + + + align:start position:0% +nothing to do with the real curve but +it's my I draw the sun's intensity + + align:start position:0% +it's my I draw the sun's intensity + + + align:start position:0% +it's my I draw the sun's intensity +different every time I draw it but this + + align:start position:0% +different every time I draw it but this + + + align:start position:0% +different every time I draw it but this +would be say well this could be energy + + align:start position:0% +would be say well this could be energy + + + align:start position:0% +would be say well this could be energy +or wavelength or frequency + + align:start position:0% +or wavelength or frequency + + + align:start position:0% +or wavelength or frequency +let's call it energy + + align:start position:0% +let's call it energy + + + align:start position:0% +let's call it energy +and so you have a dependence of + + align:start position:0% +and so you have a dependence of + + + align:start position:0% +and so you have a dependence of +intensity of the sunlight that strikes + + align:start position:0% +intensity of the sunlight that strikes + + + align:start position:0% +intensity of the sunlight that strikes +the Earth or the atmosphere, those are + + align:start position:0% +the Earth or the atmosphere, those are + + + align:start position:0% +the Earth or the atmosphere, those are +different on the energy that you get. + + align:start position:0% +different on the energy that you get. + + + align:start position:0% +different on the energy that you get. +Okay? So, there's some energies of light + + align:start position:0% +Okay? So, there's some energies of light + + + align:start position:0% +Okay? So, there's some energies of light +that are have a lot of intensity and + + align:start position:0% +that are have a lot of intensity and + + + align:start position:0% +that are have a lot of intensity and +some that have very little. Now, what's + + align:start position:0% +some that have very little. Now, what's + + + align:start position:0% +some that have very little. Now, what's +the key connection here between these + + align:start position:0% +the key connection here between these + + + align:start position:0% +the key connection here between these +two? + + align:start position:0% + + + + align:start position:0% + +Who remembers + + align:start position:0% + + + + align:start position:0% + +which is really what part two is about, + + align:start position:0% +which is really what part two is about, + + + align:start position:0% +which is really what part two is about, +question two is about. What's the key + + align:start position:0% +question two is about. What's the key + + + align:start position:0% +question two is about. What's the key +connection here between this curve and + + align:start position:0% +connection here between this curve and + + + align:start position:0% +connection here between this curve and +this picture? + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +So only photons with a sufficient energy + + align:start position:0% +So only photons with a sufficient energy + + + align:start position:0% +So only photons with a sufficient energy +will be able to excite your molecule + + align:start position:0% +will be able to excite your molecule + + + align:start position:0% +will be able to excite your molecule +from the trans to cy states. So only + + align:start position:0% +from the trans to cy states. So only + + + align:start position:0% +from the trans to cy states. So only +some part of that curve with energy + + align:start position:0% +some part of that curve with energy + + + align:start position:0% +some part of that curve with energy +greater than or equal to delta h will be + + align:start position:0% +greater than or equal to delta h will be + + + align:start position:0% +greater than or equal to delta h will be +able to uh to do that. So it can only + + align:start position:0% +able to uh to do that. So it can only + + + align:start position:0% +able to uh to do that. So it can only +capture that much of the sun's total + + align:start position:0% +capture that much of the sun's total + + + align:start position:0% +capture that much of the sun's total +energy. + + align:start position:0% +energy. + + + align:start position:0% +energy. +Yeah. Exactly right. So so there and and + + align:start position:0% +Yeah. Exactly right. So so there and and + + + align:start position:0% +Yeah. Exactly right. So so there and and +there's something else too. But that's + + align:start position:0% +there's something else too. But that's + + + align:start position:0% +there's something else too. But that's +exactly what we need for problem three. + + align:start position:0% +exactly what we need for problem three. + + + align:start position:0% +exactly what we need for problem three. +That's exactly it. Okay. So, what I've + + align:start position:0% +That's exactly it. Okay. So, what I've + + + align:start position:0% +That's exactly it. Okay. So, what I've +told you, what we did in in what we did + + align:start position:0% +told you, what we did in in what we did + + + align:start position:0% +told you, what we did in in what we did +already is we said, well, + + align:start position:0% +already is we said, well, + + + align:start position:0% +already is we said, well, +you can't get more energy out than you + + align:start position:0% +you can't get more energy out than you + + + align:start position:0% +you can't get more energy out than you +put in. So, you got to have at least + + align:start position:0% +put in. So, you got to have at least + + + align:start position:0% +put in. So, you got to have at least +delta H minimum + + align:start position:0% + + + + align:start position:0% + +of sun's energy + + align:start position:0% + + + + align:start position:0% + +is delta H. That's the absolute minimum + + align:start position:0% +is delta H. That's the absolute minimum + + + align:start position:0% +is delta H. That's the absolute minimum +you have to put into this to get delta H + + align:start position:0% +you have to put into this to get delta H + + + align:start position:0% +you have to put into this to get delta H +stored, right? So, uh, sorry, that's + + align:start position:0% +stored, right? So, uh, sorry, that's + + + align:start position:0% +stored, right? So, uh, sorry, that's +kind of hard to read. I'm not liking + + align:start position:0% +kind of hard to read. I'm not liking + + + align:start position:0% +kind of hard to read. I'm not liking +this yellow colored white chalk because + + align:start position:0% +this yellow colored white chalk because + + + align:start position:0% +this yellow colored white chalk because +it's too thick. + + align:start position:0% +it's too thick. + + + align:start position:0% +it's too thick. +So, the minimum sun's energy is that's + + align:start position:0% +So, the minimum sun's energy is that's + + + align:start position:0% +So, the minimum sun's energy is that's +better. Okay, is delta H. + + align:start position:0% +better. Okay, is delta H. + + + align:start position:0% +better. Okay, is delta H. +But you see there's also now what + + align:start position:0% +But you see there's also now what + + + align:start position:0% +But you see there's also now what +happens is so let's say I can + + align:start position:0% +happens is so let's say I can + + + align:start position:0% +happens is so let's say I can +uh let's say that delta H is somewhere + + align:start position:0% +uh let's say that delta H is somewhere + + + align:start position:0% +uh let's say that delta H is somewhere +here I don't know call it one electron + + align:start position:0% +here I don't know call it one electron + + + align:start position:0% +here I don't know call it one electron +volt + + align:start position:0% +volt + + + align:start position:0% +volt +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well what I've just said in part a is + + align:start position:0% +well what I've just said in part a is + + + align:start position:0% +well what I've just said in part a is +that anything below that anything below + + align:start position:0% +that anything below that anything below + + + align:start position:0% +that anything below that anything below +one electron volt cannot be + + align:start position:0% +one electron volt cannot be + + + align:start position:0% +one electron volt cannot be +used to store energy. So any sunlight + + align:start position:0% +used to store energy. So any sunlight + + + align:start position:0% +used to store energy. So any sunlight +energy that's below that is is is + + align:start position:0% +energy that's below that is is is + + + align:start position:0% +energy that's below that is is is +wasted, right? It's not going to do + + align:start position:0% +wasted, right? It's not going to do + + + align:start position:0% +wasted, right? It's not going to do +anything to charge that fuel because + + align:start position:0% +anything to charge that fuel because + + + align:start position:0% +anything to charge that fuel because +it's below this amount. + + align:start position:0% +it's below this amount. + + + align:start position:0% +it's below this amount. +On the other hand, everything above that + + align:start position:0% + + + + align:start position:0% + +will charge the fuel. Okay. + + align:start position:0% + + + + align:start position:0% + +But is it it but now here's where the + + align:start position:0% +But is it it but now here's where the + + + align:start position:0% +But is it it but now here's where the +this question of efficiency comes in + + align:start position:0% +this question of efficiency comes in + + + align:start position:0% +this question of efficiency comes in +because is it really I mean what what + + align:start position:0% +because is it really I mean what what + + + align:start position:0% +because is it really I mean what what +would I really like to do here in terms + + align:start position:0% +would I really like to do here in terms + + + align:start position:0% +would I really like to do here in terms +of charging this fuel? + + align:start position:0% +of charging this fuel? + + + align:start position:0% +of charging this fuel? +Somebody tell me the difference between + + align:start position:0% +Somebody tell me the difference between + + + align:start position:0% +Somebody tell me the difference between +a photon of sunlight energy that's here + + align:start position:0% +a photon of sunlight energy that's here + + + align:start position:0% +a photon of sunlight energy that's here +that charges the fuel versus one that's + + align:start position:0% +that charges the fuel versus one that's + + + align:start position:0% +that charges the fuel versus one that's +out here that also charges the fuel. + + align:start position:0% +out here that also charges the fuel. + + + align:start position:0% +out here that also charges the fuel. +Somebody tell me what's different or + + align:start position:0% +Somebody tell me what's different or + + + align:start position:0% +Somebody tell me what's different or +similar between those two parts of the + + align:start position:0% +similar between those two parts of the + + + align:start position:0% +similar between those two parts of the +spectrum. Both of which convert my fuel. + + align:start position:0% +spectrum. Both of which convert my fuel. + + + align:start position:0% +spectrum. Both of which convert my fuel. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Like the one that's higher energy, it + + align:start position:0% +Like the one that's higher energy, it + + + align:start position:0% +Like the one that's higher energy, it +just has like less part of that energy + + align:start position:0% +just has like less part of that energy + + + align:start position:0% +just has like less part of that energy +be wasted. It's not like delta H is + + align:start position:0% +be wasted. It's not like delta H is + + + align:start position:0% +be wasted. It's not like delta H is +constant. So once you get above it, the + + align:start position:0% +constant. So once you get above it, the + + + align:start position:0% +constant. So once you get above it, the +more above it you get the less. + + align:start position:0% +more above it you get the less. + + + align:start position:0% +more above it you get the less. +Exactly. Exactly. So, I I can charge the + + align:start position:0% +Exactly. Exactly. So, I I can charge the + + + align:start position:0% +Exactly. Exactly. So, I I can charge the +fuel now because I said I can't have + + align:start position:0% +fuel now because I said I can't have + + + align:start position:0% +fuel now because I said I can't have +less than how much I'm storing. That's a + + align:start position:0% +less than how much I'm storing. That's a + + + align:start position:0% +less than how much I'm storing. That's a +rule. Um, but I can charge it with + + align:start position:0% +rule. Um, but I can charge it with + + + align:start position:0% +rule. Um, but I can charge it with +anything above that except for one thing + + align:start position:0% +anything above that except for one thing + + + align:start position:0% +anything above that except for one thing +that I'm going to tell you about in a + + align:start position:0% +that I'm going to tell you about in a + + + align:start position:0% +that I'm going to tell you about in a +second or you're going to tell me + + align:start position:0% +second or you're going to tell me + + + align:start position:0% +second or you're going to tell me +because I know somebody knows this. But, + + align:start position:0% +because I know somebody knows this. But, + + + align:start position:0% +because I know somebody knows this. But, +but if I use this amount of energy from + + align:start position:0% +but if I use this amount of energy from + + + align:start position:0% +but if I use this amount of energy from +the sun, well, I still only stored that. + + align:start position:0% +the sun, well, I still only stored that. + + + align:start position:0% +the sun, well, I still only stored that. +That's my delta H. + + align:start position:0% +That's my delta H. + + + align:start position:0% +That's my delta H. +So, that means I wasted a whole lot. And + + align:start position:0% +So, that means I wasted a whole lot. And + + + align:start position:0% +So, that means I wasted a whole lot. And +that's where that's what I want you to + + align:start position:0% +that's where that's what I want you to + + + align:start position:0% +that's where that's what I want you to +to tell me. What's the efficiency? + + align:start position:0% +to tell me. What's the efficiency? + + + align:start position:0% +to tell me. What's the efficiency? +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +You know, so if I if I'm all the way + + align:start position:0% +You know, so if I if I'm all the way + + + align:start position:0% +You know, so if I if I'm all the way +down here, you can say, well, this is + + align:start position:0% +down here, you can say, well, this is + + + align:start position:0% +down here, you can say, well, this is +what we talked about in the lecture. If + + align:start position:0% +what we talked about in the lecture. If + + + align:start position:0% +what we talked about in the lecture. If +I'm all the way down here, then I can + + align:start position:0% +I'm all the way down here, then I can + + + align:start position:0% +I'm all the way down here, then I can +absorb all this light and use it to + + align:start position:0% +absorb all this light and use it to + + + align:start position:0% +absorb all this light and use it to +convert. But light up here is really + + align:start position:0% +convert. But light up here is really + + + align:start position:0% +convert. But light up here is really +wasted. It's super wasted, + + align:start position:0% +wasted. It's super wasted, + + + align:start position:0% +wasted. It's super wasted, +right? The further you get up in energy. + + align:start position:0% +right? The further you get up in energy. + + + align:start position:0% +right? The further you get up in energy. +So, where is the sweet spot? Right? + + align:start position:0% +So, where is the sweet spot? Right? + + + align:start position:0% +So, where is the sweet spot? Right? +There's going to be a sweet spot. And I' + + align:start position:0% +There's going to be a sweet spot. And I' + + + align:start position:0% +There's going to be a sweet spot. And I' +I'd like that's what I want you to tell + + align:start position:0% +I'd like that's what I want you to tell + + + align:start position:0% +I'd like that's what I want you to tell +me in part B. Okay? Now, there's + + align:start position:0% +me in part B. Okay? Now, there's + + + align:start position:0% +me in part B. Okay? Now, there's +something I'm not telling you which is + + align:start position:0% +something I'm not telling you which is + + + align:start position:0% +something I'm not telling you which is +really important here that's not part of + + align:start position:0% +really important here that's not part of + + + align:start position:0% +really important here that's not part of +that question. Okay? But there's + + align:start position:0% +that question. Okay? But there's + + + align:start position:0% +that question. Okay? But there's +something else that matters a lot that's + + align:start position:0% +something else that matters a lot that's + + + align:start position:0% +something else that matters a lot that's +part of part B. Uh part number two, + + align:start position:0% +part of part B. Uh part number two, + + + align:start position:0% +part of part B. Uh part number two, +question number two. What am what have + + align:start position:0% +question number two. What am what have + + + align:start position:0% +question number two. What am what have +we not considered yet? + + align:start position:0% +we not considered yet? + + + align:start position:0% +we not considered yet? +And in particular, what about it? + + align:start position:0% +And in particular, what about it? + + + align:start position:0% +And in particular, what about it? +The band gap, the gap or the gap of the + + align:start position:0% +The band gap, the gap or the gap of the + + + align:start position:0% +The band gap, the gap or the gap of the +molecule. And you see because that's the + + align:start position:0% +molecule. And you see because that's the + + + align:start position:0% +molecule. And you see because that's the +other component here, + + align:start position:0% +other component here, + + + align:start position:0% +other component here, +right? So these are problem three is + + align:start position:0% +right? So these are problem three is + + + align:start position:0% +right? So these are problem three is +talking about theoretical limits based + + align:start position:0% +talking about theoretical limits based + + + align:start position:0% +talking about theoretical limits based +on how much the molecule stores and how + + align:start position:0% +on how much the molecule stores and how + + + align:start position:0% +on how much the molecule stores and how +much sunlight shines on it. But there's + + align:start position:0% +much sunlight shines on it. But there's + + + align:start position:0% +much sunlight shines on it. But there's +this other thing that problem two talks + + align:start position:0% +this other thing that problem two talks + + + align:start position:0% +this other thing that problem two talks +about which is the fact that the + + align:start position:0% +about which is the fact that the + + + align:start position:0% +about which is the fact that the +molecule will not absorb any light lower + + align:start position:0% +molecule will not absorb any light lower + + + align:start position:0% +molecule will not absorb any light lower +than its gap. + + align:start position:0% +than its gap. + + + align:start position:0% +than its gap. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +And that's why those two problems are + + align:start position:0% +And that's why those two problems are + + + align:start position:0% +And that's why those two problems are +very I think complimentary to one + + align:start position:0% +very I think complimentary to one + + + align:start position:0% +very I think complimentary to one +another. Right? So all of that comes + + align:start position:0% +another. Right? So all of that comes + + + align:start position:0% +another. Right? So all of that comes +into play. So even if I say, well, it + + align:start position:0% +into play. So even if I say, well, it + + + align:start position:0% +into play. So even if I say, well, it +stores an EV, so theoretically it could + + align:start position:0% +stores an EV, so theoretically it could + + + align:start position:0% +stores an EV, so theoretically it could +absorb all of this, actually if its gap + + align:start position:0% +absorb all of this, actually if its gap + + + align:start position:0% +absorb all of this, actually if its gap +is 2 EV, it's only absorbing this, + + align:start position:0% +is 2 EV, it's only absorbing this, + + + align:start position:0% +is 2 EV, it's only absorbing this, +right? But we're not talking about the + + align:start position:0% +right? But we're not talking about the + + + align:start position:0% +right? But we're not talking about the +gap in problem number three. Okay. All + + align:start position:0% +gap in problem number three. Okay. All + + + align:start position:0% +gap in problem number three. Okay. All +right. + + align:start position:0% + + + + align:start position:0% + +It's fun. This is fun, right? Any + + align:start position:0% +It's fun. This is fun, right? Any + + + align:start position:0% +It's fun. This is fun, right? Any +questions? + + align:start position:0% +questions? + + + align:start position:0% +questions? +We're integrating the sun. Any + + align:start position:0% +We're integrating the sun. Any + + + align:start position:0% +We're integrating the sun. Any +questions about that uh problem? Yeah. + + align:start position:0% + + + + align:start position:0% + +Well, + + align:start position:0% + + + + align:start position:0% + +yeah. I mean it seems to me like so you + + align:start position:0% +yeah. I mean it seems to me like so you + + + align:start position:0% +yeah. I mean it seems to me like so you +you figured out in um the earlier + + align:start position:0% +you figured out in um the earlier + + + align:start position:0% +you figured out in um the earlier +problem how to figure out right that if + + align:start position:0% +problem how to figure out right that if + + + align:start position:0% +problem how to figure out right that if +you integrated this you would get like + + align:start position:0% +you integrated this you would get like + + + align:start position:0% +you integrated this you would get like +how much of the sun's energy that + + align:start position:0% +how much of the sun's energy that + + + align:start position:0% +how much of the sun's energy that +molecule is absorbing and you use the + + align:start position:0% +molecule is absorbing and you use the + + + align:start position:0% +molecule is absorbing and you use the +band gap as the cutoff but now it seems + + align:start position:0% +band gap as the cutoff but now it seems + + + align:start position:0% +band gap as the cutoff but now it seems +like maybe you want to use delta h as in + + align:start position:0% +like maybe you want to use delta h as in + + + align:start position:0% +like maybe you want to use delta h as in +a similar way because you're looking at + + align:start position:0% +a similar way because you're looking at + + + align:start position:0% +a similar way because you're looking at +sort of a a theoretical efficiency and + + align:start position:0% +sort of a a theoretical efficiency and + + + align:start position:0% +sort of a a theoretical efficiency and +ignoring the gap okay now then what what + + align:start position:0% +ignoring the gap okay now then what what + + + align:start position:0% +ignoring the gap okay now then what what +is the efficiency Well, it's how much + + align:start position:0% +is the efficiency Well, it's how much + + + align:start position:0% +is the efficiency Well, it's how much +energy that molecule + + align:start position:0% +energy that molecule + + + align:start position:0% +energy that molecule +can take in from the sun, + + align:start position:0% +can take in from the sun, + + + align:start position:0% +can take in from the sun, +right? Um, + + align:start position:0% +right? Um, + + + align:start position:0% +right? Um, +you know, divided by that the amount + + align:start position:0% +you know, divided by that the amount + + + align:start position:0% +you know, divided by that the amount +that is stored. + + align:start position:0% +that is stored. + + + align:start position:0% +that is stored. +Did I answer your question or did I + + align:start position:0% +Did I answer your question or did I + + + align:start position:0% +Did I answer your question or did I +dance around it? + + align:start position:0% + + + + align:start position:0% + +Was that good? Was that helpful? + + align:start position:0% + + + + align:start position:0% + +Ah, but that's what you you chose it. + + align:start position:0% +Ah, but that's what you you chose it. + + + align:start position:0% +Ah, but that's what you you chose it. +You just picked it. You said, "I'm going + + align:start position:0% +You just picked it. You said, "I'm going + + + align:start position:0% +You just picked it. You said, "I'm going +to say it stores one EV because that was + + align:start position:0% +to say it stores one EV because that was + + + align:start position:0% +to say it stores one EV because that was +delta + + align:start position:0% +delta + + + align:start position:0% +delta +H + + align:start position:0% +H + + + align:start position:0% +H +per molecule + + align:start position:0% + + + + align:start position:0% + +per + + align:start position:0% +per + + + align:start position:0% +per +per molecule is the way to think about + + align:start position:0% +per molecule is the way to think about + + + align:start position:0% +per molecule is the way to think about +it, right? So then there's and then + + align:start position:0% +it, right? So then there's and then + + + align:start position:0% +it, right? So then there's and then +there's um so that's how much energy + + align:start position:0% +there's um so that's how much energy + + + align:start position:0% +there's um so that's how much energy +you're storing in each molecule and then + + align:start position:0% +you're storing in each molecule and then + + + align:start position:0% +you're storing in each molecule and then +each molecule is getting how much energy + + align:start position:0% +each molecule is getting how much energy + + + align:start position:0% +each molecule is getting how much energy +from the sun, + + align:start position:0% +from the sun, + + + align:start position:0% +from the sun, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +And between those you have an + + align:start position:0% +And between those you have an + + + align:start position:0% +And between those you have an +efficiency. It's basically one divided + + align:start position:0% +efficiency. It's basically one divided + + + align:start position:0% +efficiency. It's basically one divided +by the other + + align:start position:0% + + + + align:start position:0% + +and you know which one to divide by the + + align:start position:0% +and you know which one to divide by the + + + align:start position:0% +and you know which one to divide by the +other because if you divide it and it's + + align:start position:0% +other because if you divide it and it's + + + align:start position:0% +other because if you divide it and it's +more than one, you should do it the + + align:start position:0% +more than one, you should do it the + + + align:start position:0% +more than one, you should do it the +other way. + + align:start position:0% +other way. + + + align:start position:0% +other way. +That's a hint. But um no, but seriously, + + align:start position:0% +That's a hint. But um no, but seriously, + + + align:start position:0% +That's a hint. But um no, but seriously, +I mean, are there does that make sense + + align:start position:0% +I mean, are there does that make sense + + + align:start position:0% +I mean, are there does that make sense +enough? Okay. Now question C is a little + + align:start position:0% +enough? Okay. Now question C is a little + + + align:start position:0% +enough? Okay. Now question C is a little +bit taking that a little bit further. + + align:start position:0% +bit taking that a little bit further. + + + align:start position:0% +bit taking that a little bit further. +Okay. But if you have u but it's that + + align:start position:0% +Okay. But if you have u but it's that + + + align:start position:0% +Okay. But if you have u but it's that +same exact concept that + + align:start position:0% +same exact concept that + + + align:start position:0% +same exact concept that +you know. Yeah. Okay. + + align:start position:0% +you know. Yeah. Okay. + + + align:start position:0% +you know. Yeah. Okay. +Any questions? + + align:start position:0% +Any questions? + + + align:start position:0% +Any questions? +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +I'm just a little confused like um so + + align:start position:0% +I'm just a little confused like um so + + + align:start position:0% +I'm just a little confused like um so +when we calculate the band gap that's + + align:start position:0% +when we calculate the band gap that's + + + align:start position:0% +when we calculate the band gap that's +like the amount of energy needed for it + + align:start position:0% +like the amount of energy needed for it + + + align:start position:0% +like the amount of energy needed for it +to absorb energy from the sun + + align:start position:0% +to absorb energy from the sun + + + align:start position:0% +to absorb energy from the sun +but then how does that relate to the + + align:start position:0% +but then how does that relate to the + + + align:start position:0% +but then how does that relate to the +delta H are those + + align:start position:0% +delta H are those + + + align:start position:0% +delta H are those +yeah that's a great great question and + + align:start position:0% +yeah that's a great great question and + + + align:start position:0% +yeah that's a great great question and +that really is you know it it it's + + align:start position:0% + + + + align:start position:0% + +I want you to think about them + + align:start position:0% +I want you to think about them + + + align:start position:0% +I want you to think about them +separately okay uh for this problem So + + align:start position:0% +separately okay uh for this problem So + + + align:start position:0% +separately okay uh for this problem So +they they really are of course + + align:start position:0% +they they really are of course + + + align:start position:0% +they they really are of course +intertwined in in fairly complicated + + align:start position:0% +intertwined in in fairly complicated + + + align:start position:0% +intertwined in in fairly complicated +ways. Um but here what I want you to do + + align:start position:0% +ways. Um but here what I want you to do + + + align:start position:0% +ways. Um but here what I want you to do +is + + align:start position:0% +is + + + align:start position:0% +is +suppose you could just make the gap at + + align:start position:0% +suppose you could just make the gap at + + + align:start position:0% +suppose you could just make the gap at +any delta h you could just make it equal + + align:start position:0% +any delta h you could just make it equal + + + align:start position:0% +any delta h you could just make it equal +to delta h. That's really what you're + + align:start position:0% +to delta h. That's really what you're + + + align:start position:0% +to delta h. That's really what you're +doing here because you're taking a kind + + align:start position:0% +doing here because you're taking a kind + + + align:start position:0% +doing here because you're taking a kind +of theoretical limit exercise in this. + + align:start position:0% +of theoretical limit exercise in this. + + + align:start position:0% +of theoretical limit exercise in this. +Um that's not the case. It's not as + + align:start position:0% +Um that's not the case. It's not as + + + align:start position:0% +Um that's not the case. It's not as +tunable as that. Although you can tune + + align:start position:0% +tunable as that. Although you can tune + + + align:start position:0% +tunable as that. Although you can tune +the gap in these materials to quite an + + align:start position:0% +the gap in these materials to quite an + + + align:start position:0% +the gap in these materials to quite an +extent. But here I'm saying suppose that + + align:start position:0% +extent. But here I'm saying suppose that + + + align:start position:0% +extent. But here I'm saying suppose that +the amount it absorbs is in fact set not + + align:start position:0% +the amount it absorbs is in fact set not + + + align:start position:0% +the amount it absorbs is in fact set not +by the gap but by this other constraint + + align:start position:0% +by the gap but by this other constraint + + + align:start position:0% +by the gap but by this other constraint +that is part a of this question which is + + align:start position:0% +that is part a of this question which is + + + align:start position:0% +that is part a of this question which is +that you just can't convert it unless + + align:start position:0% +that you just can't convert it unless + + + align:start position:0% +that you just can't convert it unless +you have as much as delta H. That's just + + align:start position:0% +you have as much as delta H. That's just + + + align:start position:0% +you have as much as delta H. That's just +you know that there's no way around + + align:start position:0% +you know that there's no way around + + + align:start position:0% +you know that there's no way around +right you can't tune around that. That's + + align:start position:0% +right you can't tune around that. That's + + + align:start position:0% +right you can't tune around that. That's +just it. You can't get to here unless + + align:start position:0% +just it. You can't get to here unless + + + align:start position:0% +just it. You can't get to here unless +enough energy from the sun is is this or + + align:start position:0% +enough energy from the sun is is this or + + + align:start position:0% +enough energy from the sun is is this or +more. Right? So that's really ignoring + + align:start position:0% +more. Right? So that's really ignoring + + + align:start position:0% +more. Right? So that's really ignoring +the gap. + + align:start position:0% + + + + align:start position:0% + +But in reality, um it's going to only + + align:start position:0% +But in reality, um it's going to only + + + align:start position:0% +But in reality, um it's going to only +absorb photons at the gap or higher. But + + align:start position:0% +absorb photons at the gap or higher. But + + + align:start position:0% +absorb photons at the gap or higher. But +if you found it, now if you were h if + + align:start position:0% +if you found it, now if you were h if + + + align:start position:0% +if you found it, now if you were h if +you were to happen to do 3B and get a + + align:start position:0% +you were to happen to do 3B and get a + + + align:start position:0% +you were to happen to do 3B and get a +maximum in a curve, let's suppose, + + align:start position:0% +maximum in a curve, let's suppose, + + + align:start position:0% +maximum in a curve, let's suppose, +right? and that maximum occurred at a + + align:start position:0% +right? and that maximum occurred at a + + + align:start position:0% +right? and that maximum occurred at a +certain delta H, then you might say, + + align:start position:0% +certain delta H, then you might say, + + + align:start position:0% +certain delta H, then you might say, +well, that's where I I should try to get + + align:start position:0% +well, that's where I I should try to get + + + align:start position:0% +well, that's where I I should try to get +my gap to that point. Okay, that might + + align:start position:0% +my gap to that point. Okay, that might + + + align:start position:0% +my gap to that point. Okay, that might +be some guidance. Of course, that's not + + align:start position:0% +be some guidance. Of course, that's not + + + align:start position:0% +be some guidance. Of course, that's not +actually what you want to do. But as we + + align:start position:0% +actually what you want to do. But as we + + + align:start position:0% +actually what you want to do. But as we +ignore the gap, you know, you can think + + align:start position:0% +ignore the gap, you know, you can think + + + align:start position:0% +ignore the gap, you know, you can think +about it that way. It provides some + + align:start position:0% +about it that way. It provides some + + + align:start position:0% +about it that way. It provides some +guidance into where you might, you know, + + align:start position:0% +guidance into where you might, you know, + + + align:start position:0% +guidance into where you might, you know, +look at, you know, these kinds of + + align:start position:0% +look at, you know, these kinds of + + + align:start position:0% +look at, you know, these kinds of +exercises in in theoretical efficiencies + + align:start position:0% +exercises in in theoretical efficiencies + + + align:start position:0% +exercises in in theoretical efficiencies +can always be useful for those reasons. + + align:start position:0% +can always be useful for those reasons. + + + align:start position:0% +can always be useful for those reasons. +Okay. Um, does that answer your + + align:start position:0% +Okay. Um, does that answer your + + + align:start position:0% +Okay. Um, does that answer your +question? + + align:start position:0% + + + + align:start position:0% + +Definitely. I I'm very happy to talk + + align:start position:0% +Definitely. I I'm very happy to talk + + + align:start position:0% +Definitely. I I'm very happy to talk +about this more. Office hours tomorrow + + align:start position:0% +about this more. Office hours tomorrow + + + align:start position:0% +about this more. Office hours tomorrow +at 4. Um, and also by request. So, just + + align:start position:0% +at 4. Um, and also by request. So, just + + + align:start position:0% +at 4. Um, and also by request. So, just +send me an email or if you I think a lot + + align:start position:0% +send me an email or if you I think a lot + + + align:start position:0% +send me an email or if you I think a lot +of you know if you send me an email, + + align:start position:0% +of you know if you send me an email, + + + align:start position:0% +of you know if you send me an email, +I'll try to write back, you know, pretty + + align:start position:0% +I'll try to write back, you know, pretty + + + align:start position:0% +I'll try to write back, you know, pretty +quickly. So, if you have questions, I'm + + align:start position:0% +quickly. So, if you have questions, I'm + + + align:start position:0% +quickly. So, if you have questions, I'm +happy to answer. + + align:start position:0% +happy to answer. + + + align:start position:0% +happy to answer. +We feeling good. + + align:start position:0% +We feeling good. + + + align:start position:0% +We feeling good. +Yeah. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +No, we're not going to look at a + + align:start position:0% +No, we're not going to look at a + + + align:start position:0% +No, we're not going to look at a +recommendation letter together. + + align:start position:0% +recommendation letter together. + + + align:start position:0% +recommendation letter together. +Um, that wouldn't be appropriate. Uh, + + align:start position:0% +Um, that wouldn't be appropriate. Uh, + + + align:start position:0% +Um, that wouldn't be appropriate. Uh, +so + + align:start position:0% +so + + + align:start position:0% +so +wait a second. There was but there was + + align:start position:0% +wait a second. There was but there was + + + align:start position:0% +wait a second. There was but there was +Yeah, let's get that out of there. And + + align:start position:0% +Yeah, let's get that out of there. And + + + align:start position:0% +Yeah, let's get that out of there. And +there was a uh Aha. Here we go. Ah, what + + align:start position:0% +there was a uh Aha. Here we go. Ah, what + + + align:start position:0% +there was a uh Aha. Here we go. Ah, what +did you do? + + align:start position:0% +did you do? + + + align:start position:0% +did you do? +Now, this is not this year's quiz. + + align:start position:0% +Now, this is not this year's quiz. + + + align:start position:0% +Now, this is not this year's quiz. +Um, but this is last year's quiz and + + align:start position:0% +Um, but this is last year's quiz and + + + align:start position:0% +Um, but this is last year's quiz and +I'll do this first because then then we + + align:start position:0% +I'll do this first because then then we + + + align:start position:0% +I'll do this first because then then we +can review. So, here's a couple of + + align:start position:0% +can review. So, here's a couple of + + + align:start position:0% +can review. So, here's a couple of +questions from last year's quiz. Let's + + align:start position:0% +questions from last year's quiz. Let's + + + align:start position:0% +questions from last year's quiz. Let's +just focus on this one. + + align:start position:0% +just focus on this one. + + + align:start position:0% +just focus on this one. +Okay. + + align:start position:0% + + + + align:start position:0% + +Oh, what are basis functions and how do + + align:start position:0% +Oh, what are basis functions and how do + + + align:start position:0% +Oh, what are basis functions and how do +you know if you have enough of them? + + align:start position:0% +you know if you have enough of them? + + + align:start position:0% +you know if you have enough of them? +Somebody answer that for me first. What + + align:start position:0% +Somebody answer that for me first. What + + + align:start position:0% +Somebody answer that for me first. What +are basis functions and how do you know + + align:start position:0% +are basis functions and how do you know + + + align:start position:0% +are basis functions and how do you know +if you have enough? + + align:start position:0% +if you have enough? + + + align:start position:0% +if you have enough? +Yeah. So basis functions are a set of + + align:start position:0% +Yeah. So basis functions are a set of + + + align:start position:0% +Yeah. So basis functions are a set of +functions which you can take + + align:start position:0% +functions which you can take + + + align:start position:0% +functions which you can take +combinations of to create an + + align:start position:0% +combinations of to create an + + + align:start position:0% +combinations of to create an +approximation what the exactly function + + align:start position:0% +approximation what the exactly function + + + align:start position:0% +approximation what the exactly function +should be and you know you have enough + + align:start position:0% +should be and you know you have enough + + + align:start position:0% +should be and you know you have enough +of them if whatever you're trying to + + align:start position:0% +of them if whatever you're trying to + + + align:start position:0% +of them if whatever you're trying to +calculate you use a basis set and then a + + align:start position:0% +calculate you use a basis set and then a + + + align:start position:0% +calculate you use a basis set and then a +uh I guess more refined basis set you + + align:start position:0% +uh I guess more refined basis set you + + + align:start position:0% +uh I guess more refined basis set you +know and do this a little bit and it + + align:start position:0% +know and do this a little bit and it + + + align:start position:0% +know and do this a little bit and it +sort of you know converges to some value + + align:start position:0% +sort of you know converges to some value + + + align:start position:0% +sort of you know converges to some value +right exactly now and and and + + align:start position:0% +right exactly now and and and + + + align:start position:0% +right exactly now and and and +there's a really important part of that. + + align:start position:0% +there's a really important part of that. + + + align:start position:0% +there's a really important part of that. +So that that is basis functions are + + align:start position:0% +So that that is basis functions are + + + align:start position:0% +So that that is basis functions are +mathematical functions. Gaussians, + + align:start position:0% +mathematical functions. Gaussians, + + + align:start position:0% +mathematical functions. Gaussians, +exponents, + + align:start position:0% +exponents, + + + align:start position:0% +exponents, +plane waves, wavelets. Don't use + + align:start position:0% +plane waves, wavelets. Don't use + + + align:start position:0% +plane waves, wavelets. Don't use +wavelets, but they're kind of funny. + + align:start position:0% +wavelets, but they're kind of funny. + + + align:start position:0% +wavelets, but they're kind of funny. +They're neat functions, but it can be + + align:start position:0% +They're neat functions, but it can be + + + align:start position:0% +They're neat functions, but it can be +anything. Uh it's just a function. Yeah. + + align:start position:0% +anything. Uh it's just a function. Yeah. + + + align:start position:0% +anything. Uh it's just a function. Yeah. +And um and you just use them. You use a + + align:start position:0% +And um and you just use them. You use a + + + align:start position:0% +And um and you just use them. You use a +series of them, usually a sequence of + + align:start position:0% +series of them, usually a sequence of + + + align:start position:0% +series of them, usually a sequence of +them that you add together to make up + + align:start position:0% +them that you add together to make up + + + align:start position:0% +them that you add together to make up +the complexity that is Sai, which is the + + align:start position:0% +the complexity that is Sai, which is the + + + align:start position:0% +the complexity that is Sai, which is the +wave function, the wave function that + + align:start position:0% +wave function, the wave function that + + + align:start position:0% +wave function, the wave function that +we're after in this part of the course. + + align:start position:0% +we're after in this part of the course. + + + align:start position:0% +we're after in this part of the course. +Okay? So, it's just a representation, + + align:start position:0% +Okay? So, it's just a representation, + + + align:start position:0% +Okay? So, it's just a representation, +but it's one that you don't find in + + align:start position:0% +but it's one that you don't find in + + + align:start position:0% +but it's one that you don't find in +classical simulations that you did in + + align:start position:0% +classical simulations that you did in + + + align:start position:0% +classical simulations that you did in +the first part, but you do find it here. + + align:start position:0% +the first part, but you do find it here. + + + align:start position:0% +the first part, but you do find it here. +And it's really important to know when + + align:start position:0% +And it's really important to know when + + + align:start position:0% +And it's really important to know when +you're converged. And say that part + + align:start position:0% +you're converged. And say that part + + + align:start position:0% +you're converged. And say that part +again. When are you converged? + + align:start position:0% +again. When are you converged? + + + align:start position:0% +again. When are you converged? +Uh, when you + + align:start position:0% +Uh, when you + + + align:start position:0% +Uh, when you +uh use when when you know you take + + align:start position:0% +uh use when when you know you take + + + align:start position:0% +uh use when when you know you take +whatever you're trying to calculate. + + align:start position:0% +whatever you're trying to calculate. + + + align:start position:0% +whatever you're trying to calculate. +Stop right there. That's it. Whatever + + align:start position:0% +Stop right there. That's it. Whatever + + + align:start position:0% +Stop right there. That's it. Whatever +you're trying to calculate, + + align:start position:0% +you're trying to calculate, + + + align:start position:0% +you're trying to calculate, +what are you trying to calculate? + + align:start position:0% +what are you trying to calculate? + + + align:start position:0% +what are you trying to calculate? +Give me an example. + + align:start position:0% +Give me an example. + + + align:start position:0% +Give me an example. +Um total energy of a system. + + align:start position:0% +Um total energy of a system. + + + align:start position:0% +Um total energy of a system. +Total energy of the system. Now give me + + align:start position:0% +Total energy of the system. Now give me + + + align:start position:0% +Total energy of the system. Now give me +another example. + + align:start position:0% +another example. + + + align:start position:0% +another example. +Uh homolyo gap. + + align:start position:0% +Uh homolyo gap. + + + align:start position:0% +Uh homolyo gap. +Homolimo gap. I love it. We could go on + + align:start position:0% +Homolimo gap. I love it. We could go on + + + align:start position:0% +Homolimo gap. I love it. We could go on +like this, but I won't. But now are the + + align:start position:0% +like this, but I won't. But now are the + + + align:start position:0% +like this, but I won't. But now are the +number of basis functions you need to + + align:start position:0% +number of basis functions you need to + + + align:start position:0% +number of basis functions you need to +converge the the representation of your + + align:start position:0% +converge the the representation of your + + + align:start position:0% +converge the the representation of your +wave function the same for the total + + align:start position:0% +wave function the same for the total + + + align:start position:0% +wave function the same for the total +energy or the homolumo gap + + align:start position:0% + + + + align:start position:0% + +it depends is always a good answer you + + align:start position:0% +it depends is always a good answer you + + + align:start position:0% +it depends is always a good answer you +can always write that don't put it for + + align:start position:0% +can always write that don't put it for + + + align:start position:0% +can always write that don't put it for +your name but you can put it for + + align:start position:0% +your name but you can put it for + + + align:start position:0% +your name but you can put it for +but well I don't know maybe you do need + + align:start position:0% +but well I don't know maybe you do need + + + align:start position:0% +but well I don't know maybe you do need +the same number of functions for those + + align:start position:0% +the same number of functions for those + + + align:start position:0% +the same number of functions for those +properties but you need to look at them + + align:start position:0% +properties but you need to look at them + + + align:start position:0% +properties but you need to look at them +on a property by property uh basis, no + + align:start position:0% +on a property by property uh basis, no + + + align:start position:0% +on a property by property uh basis, no +pun intended. + + align:start position:0% +pun intended. + + + align:start position:0% +pun intended. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +so very good. Now, without solving any + + align:start position:0% +so very good. Now, without solving any + + + align:start position:0% +so very good. Now, without solving any +equations, which electron do you think + + align:start position:0% +equations, which electron do you think + + + align:start position:0% +equations, which electron do you think +would require more basis functions to + + align:start position:0% +would require more basis functions to + + + align:start position:0% +would require more basis functions to +describe well the 2p electron in carbon + + align:start position:0% +describe well the 2p electron in carbon + + + align:start position:0% +describe well the 2p electron in carbon +or the 3p electron in silicon? Who can + + align:start position:0% +or the 3p electron in silicon? Who can + + + align:start position:0% +or the 3p electron in silicon? Who can +tell me what they think? + + align:start position:0% +tell me what they think? + + + align:start position:0% +tell me what they think? +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Well, you need now hang on. You'd need + + align:start position:0% +Well, you need now hang on. You'd need + + + align:start position:0% +Well, you need now hang on. You'd need +more basis functions for 3p. Tell me + + align:start position:0% +more basis functions for 3p. Tell me + + + align:start position:0% +more basis functions for 3p. Tell me +why. + + align:start position:0% + + + + align:start position:0% + +Well, what is it that makes you need + + align:start position:0% +Well, what is it that makes you need + + + align:start position:0% +Well, what is it that makes you need +more basis functions? What is it that + + align:start position:0% +more basis functions? What is it that + + + align:start position:0% +more basis functions? What is it that +makes you need more basis functions? + + align:start position:0% +makes you need more basis functions? + + + align:start position:0% +makes you need more basis functions? +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Okay. So if the wave function, + + align:start position:0% + + + + align:start position:0% + +if the wave function is + + align:start position:0% +if the wave function is + + + align:start position:0% +if the wave function is +looks like this + + align:start position:0% +looks like this + + + align:start position:0% +looks like this +versus say a wave function + + align:start position:0% +versus say a wave function + + + align:start position:0% +versus say a wave function +that looks like that, + + align:start position:0% +that looks like that, + + + align:start position:0% +that looks like that, +which one do you think I'm going to need + + align:start position:0% +which one do you think I'm going to need + + + align:start position:0% +which one do you think I'm going to need +more functions for? I'm going to need + + align:start position:0% +more functions for? I'm going to need + + + align:start position:0% +more functions for? I'm going to need +more basis functions, + + align:start position:0% +more basis functions, + + + align:start position:0% +more basis functions, +right? for this one, right? + + align:start position:0% + + + + align:start position:0% + +Does everybody see that now? And then + + align:start position:0% +Does everybody see that now? And then + + + align:start position:0% +Does everybody see that now? And then +the question is, okay, so that if you + + align:start position:0% +the question is, okay, so that if you + + + align:start position:0% +the question is, okay, so that if you +put that down, you're already doing + + align:start position:0% +put that down, you're already doing + + + align:start position:0% +put that down, you're already doing +really well, right? because that you + + align:start position:0% +really well, right? because that you + + + align:start position:0% +really well, right? because that you +know on these questions what I'm looking + + align:start position:0% +know on these questions what I'm looking + + + align:start position:0% +know on these questions what I'm looking +for + + align:start position:0% +for + + + align:start position:0% +for +isn't even if you didn't know the answer + + align:start position:0% +isn't even if you didn't know the answer + + + align:start position:0% +isn't even if you didn't know the answer +to what 2P carbon or 3P silicon which + + align:start position:0% +to what 2P carbon or 3P silicon which + + + align:start position:0% +to what 2P carbon or 3P silicon which +one is more wiggly but you knew that you + + align:start position:0% +one is more wiggly but you knew that you + + + align:start position:0% +one is more wiggly but you knew that you +needed to know that to answer the + + align:start position:0% +needed to know that to answer the + + + align:start position:0% +needed to know that to answer the +question that's already you know that's + + align:start position:0% +question that's already you know that's + + + align:start position:0% +question that's already you know that's +in my opinion four out of five points + + align:start position:0% +in my opinion four out of five points + + + align:start position:0% +in my opinion four out of five points +okay u because that's the key the key is + + align:start position:0% +okay u because that's the key the key is + + + align:start position:0% +okay u because that's the key the key is +what I'm trying to just get at you know + + align:start position:0% +what I'm trying to just get at you know + + + align:start position:0% +what I'm trying to just get at you know +the key things you need to know in + + align:start position:0% +the key things you need to know in + + + align:start position:0% +the key things you need to know in +computational quantum mechanics some of + + align:start position:0% +computational quantum mechanics some of + + + align:start position:0% +computational quantum mechanics some of +key ingredients. And that's the key is + + align:start position:0% +key ingredients. And that's the key is + + + align:start position:0% +key ingredients. And that's the key is +that you need more basis functions if + + align:start position:0% +that you need more basis functions if + + + align:start position:0% +that you need more basis functions if +the if the electrons wave function + + align:start position:0% +the if the electrons wave function + + + align:start position:0% +the if the electrons wave function +wiggles more, right? Or wiggles more + + align:start position:0% +wiggles more, right? Or wiggles more + + + align:start position:0% +wiggles more, right? Or wiggles more +quickly. + + align:start position:0% +quickly. + + + align:start position:0% +quickly. +Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +wiggle's more for carbon + + align:start position:0% +wiggle's more for carbon + + + align:start position:0% +wiggle's more for carbon +because the um you see you it's what you + + align:start position:0% +because the um you see you it's what you + + + align:start position:0% +because the um you see you it's what you +said actually you have more screening in + + align:start position:0% +said actually you have more screening in + + + align:start position:0% +said actually you have more screening in +silicon and so the outer electrons um + + align:start position:0% +silicon and so the outer electrons um + + + align:start position:0% +silicon and so the outer electrons um +they're further out and they actually uh + + align:start position:0% +they're further out and they actually uh + + + align:start position:0% +they're further out and they actually uh +wiggle less. They're more smooth. Now + + align:start position:0% +wiggle less. They're more smooth. Now + + + align:start position:0% +wiggle less. They're more smooth. Now +that's not always true but between + + align:start position:0% +that's not always true but between + + + align:start position:0% +that's not always true but between +silicon and carbon that's true. I think + + align:start position:0% +silicon and carbon that's true. I think + + + align:start position:0% +silicon and carbon that's true. I think +I talked about that in lecture two. Um + + align:start position:0% +I talked about that in lecture two. Um + + + align:start position:0% +I talked about that in lecture two. Um +and and it's part of why carbon can make + + align:start position:0% +and and it's part of why carbon can make + + + align:start position:0% +and and it's part of why carbon can make +such strong bonds. So carbon has no p + + align:start position:0% +such strong bonds. So carbon has no p + + + align:start position:0% +such strong bonds. So carbon has no p +electrons in the core. Silicon does. So + + align:start position:0% +electrons in the core. Silicon does. So + + + align:start position:0% +electrons in the core. Silicon does. So +the screening is very different. A p + + align:start position:0% +the screening is very different. A p + + + align:start position:0% +the screening is very different. A p +electron in carbon sees no p electrons + + align:start position:0% +electron in carbon sees no p electrons + + + align:start position:0% +electron in carbon sees no p electrons +in the core. But a p electron in silicon + + align:start position:0% +in the core. But a p electron in silicon + + + align:start position:0% +in the core. But a p electron in silicon +does sees two p electrons in the core. + + align:start position:0% +does sees two p electrons in the core. + + + align:start position:0% +does sees two p electrons in the core. +So that that screening that shielding + + align:start position:0% +So that that screening that shielding + + + align:start position:0% +So that that screening that shielding +makes a huge difference in the kind of + + align:start position:0% +makes a huge difference in the kind of + + + align:start position:0% +makes a huge difference in the kind of +bonding that these two atoms can do. + + align:start position:0% +bonding that these two atoms can do. + + + align:start position:0% +bonding that these two atoms can do. +Okay? It's why we're made of carbon and + + align:start position:0% +Okay? It's why we're made of carbon and + + + align:start position:0% +Okay? It's why we're made of carbon and +not silicon. But that's not that's not + + align:start position:0% +not silicon. But that's not that's not + + + align:start position:0% +not silicon. But that's not that's not +the question. And let's do another one. + + align:start position:0% +the question. And let's do another one. + + + align:start position:0% +the question. And let's do another one. +Materials are composed of nuclei and + + align:start position:0% +Materials are composed of nuclei and + + + align:start position:0% +Materials are composed of nuclei and +electrons. When the cone sham equation + + align:start position:0% +electrons. When the cone sham equation + + + align:start position:0% +electrons. When the cone sham equation +is solved, solutions only for electrons + + align:start position:0% +is solved, solutions only for electrons + + + align:start position:0% +is solved, solutions only for electrons +are obtained. Why do we not care about + + align:start position:0% +are obtained. Why do we not care about + + + align:start position:0% +are obtained. Why do we not care about +nuclei? Come on. That's a good one, + + align:start position:0% +nuclei? Come on. That's a good one, + + + align:start position:0% +nuclei? Come on. That's a good one, +right Sam? + + align:start position:0% + + + + align:start position:0% + +Right. + + align:start position:0% + + + + align:start position:0% + +And do do you remember what that's + + align:start position:0% +And do do you remember what that's + + + align:start position:0% +And do do you remember what that's +called? + + align:start position:0% +called? + + + align:start position:0% +called? +It's that guy's back. The tattoo + + align:start position:0% +It's that guy's back. The tattoo + + + align:start position:0% +It's that guy's back. The tattoo +born openenheimer. See, that's going to + + align:start position:0% +born openenheimer. See, that's going to + + + align:start position:0% +born openenheimer. See, that's going to +be it. You're always going to remember + + align:start position:0% +be it. You're always going to remember + + + align:start position:0% +be it. You're always going to remember +that guy's tattoo on his back. You're + + align:start position:0% +that guy's tattoo on his back. You're + + + align:start position:0% +that guy's tattoo on his back. You're +going to think Borne Openheimer. It's + + align:start position:0% +going to think Borne Openheimer. It's + + + align:start position:0% +going to think Borne Openheimer. It's +effective. + + align:start position:0% +effective. + + + align:start position:0% +effective. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +okay. And then we'll do one more. Um, + + align:start position:0% +okay. And then we'll do one more. Um, + + + align:start position:0% +okay. And then we'll do one more. Um, +what does kpoint sampling refer to? + + align:start position:0% +what does kpoint sampling refer to? + + + align:start position:0% +what does kpoint sampling refer to? +Below are the band structures computed + + align:start position:0% +Below are the band structures computed + + + align:start position:0% +Below are the band structures computed +for two different materials. Which one + + align:start position:0% +for two different materials. Which one + + + align:start position:0% +for two different materials. Which one +requires more K points to converge? And + + align:start position:0% +requires more K points to converge? And + + + align:start position:0% +requires more K points to converge? And +you know what I'm looking for here is + + align:start position:0% +you know what I'm looking for here is + + + align:start position:0% +you know what I'm looking for here is +not a long essay. It's really just a + + align:start position:0% +not a long essay. It's really just a + + + align:start position:0% +not a long essay. It's really just a +sentence, right, to explain the + + align:start position:0% +sentence, right, to explain the + + + align:start position:0% +sentence, right, to explain the +reasoning. So somebody tell me which of + + align:start position:0% +reasoning. So somebody tell me which of + + + align:start position:0% +reasoning. So somebody tell me which of +these might need more K points. Which + + align:start position:0% +these might need more K points. Which + + + align:start position:0% +these might need more K points. Which +band structure would need more K points? + + align:start position:0% +band structure would need more K points? + + + align:start position:0% +band structure would need more K points? +Uh I see this. Yes. Why? + + align:start position:0% +Uh I see this. Yes. Why? + + + align:start position:0% +Uh I see this. Yes. Why? +There's more variations, more wiggles + + align:start position:0% +There's more variations, more wiggles + + + align:start position:0% +There's more variations, more wiggles +within it. So you need more points to + + align:start position:0% +within it. So you need more points to + + + align:start position:0% +within it. So you need more points to +get capture those changes. + + align:start position:0% + + + + align:start position:0% + +Okay, it's the same. You see these are + + align:start position:0% +Okay, it's the same. You see these are + + + align:start position:0% +Okay, it's the same. You see these are +uh same this also just a convergence + + align:start position:0% +uh same this also just a convergence + + + align:start position:0% +uh same this also just a convergence +question. Okay. Um + + align:start position:0% +question. Okay. Um + + + align:start position:0% +question. Okay. Um +does everybody see that? It's another + + align:start position:0% +does everybody see that? It's another + + + align:start position:0% +does everybody see that? It's another +convergence question. I mean you're not + + align:start position:0% +convergence question. I mean you're not + + + align:start position:0% +convergence question. I mean you're not +going to just get convergence questions, + + align:start position:0% +going to just get convergence questions, + + + align:start position:0% +going to just get convergence questions, +but those two those two were + + align:start position:0% +but those two those two were + + + align:start position:0% +but those two those two were +okay. And then we did this one. Does + + align:start position:0% +okay. And then we did this one. Does + + + align:start position:0% +okay. And then we did this one. Does +anybody is did everybody see this last + + align:start position:0% +anybody is did everybody see this last + + + align:start position:0% +anybody is did everybody see this last +time? Okay. This is that band structure + + align:start position:0% +time? Okay. This is that band structure + + + align:start position:0% +time? Okay. This is that band structure +that you got, but your your advisor + + align:start position:0% +that you got, but your your advisor + + + align:start position:0% +that you got, but your your advisor +spilled coffee on it and this is the + + align:start position:0% +spilled coffee on it and this is the + + + align:start position:0% +spilled coffee on it and this is the +only copy you have. And so I'm not you + + align:start position:0% +only copy you have. And so I'm not you + + + align:start position:0% +only copy you have. And so I'm not you +won't have a coffee spilled. Well, you + + align:start position:0% +won't have a coffee spilled. Well, you + + + align:start position:0% +won't have a coffee spilled. Well, you +might have a coffee spilled band + + align:start position:0% +might have a coffee spilled band + + + align:start position:0% +might have a coffee spilled band +structure because it's kind of a fun way + + align:start position:0% +structure because it's kind of a fun way + + + align:start position:0% +structure because it's kind of a fun way +to ask questions, but you you'll + + align:start position:0% +to ask questions, but you you'll + + + align:start position:0% +to ask questions, but you you'll +definitely have a question about band + + align:start position:0% +definitely have a question about band + + + align:start position:0% +definitely have a question about band +structures. Okay? And so don't don't you + + align:start position:0% +structures. Okay? And so don't don't you + + + align:start position:0% +structures. Okay? And so don't don't you +know um so make sure you kind of are + + align:start position:0% +know um so make sure you kind of are + + + align:start position:0% +know um so make sure you kind of are +comfortable with the concepts that I'm + + align:start position:0% +comfortable with the concepts that I'm + + + align:start position:0% +comfortable with the concepts that I'm +going to we'll review right now with + + align:start position:0% +going to we'll review right now with + + + align:start position:0% +going to we'll review right now with +band structures. Okay. So those are a + + align:start position:0% +band structures. Okay. So those are a + + + align:start position:0% +band structures. Okay. So those are a +couple nice uh examples of the kinds of + + align:start position:0% +couple nice uh examples of the kinds of + + + align:start position:0% +couple nice uh examples of the kinds of +problems you might get. + + align:start position:0% +problems you might get. + + + align:start position:0% +problems you might get. +You can see a coffee stand in the + + align:start position:0% +You can see a coffee stand in the + + + align:start position:0% +You can see a coffee stand in the +example. Don't ask for because you put + + align:start position:0% +example. Don't ask for because you put + + + align:start position:0% +example. Don't ask for because you put +in there. + + align:start position:0% +in there. + + + align:start position:0% +in there. +Yeah. We're gonna actually use real + + align:start position:0% +Yeah. We're gonna actually use real + + + align:start position:0% +Yeah. We're gonna actually use real +coffee this time. + + align:start position:0% +coffee this time. + + + align:start position:0% +coffee this time. +Okay. Uh okay. Okay. Good. + + align:start position:0% +Okay. Uh okay. Okay. Good. + + + align:start position:0% +Okay. Uh okay. Okay. Good. +So, what we're going to do now, + + align:start position:0% +So, what we're going to do now, + + + align:start position:0% +So, what we're going to do now, +so any questions? The questions are + + align:start position:0% +so any questions? The questions are + + + align:start position:0% +so any questions? The questions are +great. It's really helpful. Questions on + + align:start position:0% +great. It's really helpful. Questions on + + + align:start position:0% +great. It's really helpful. Questions on +the pet, questions on um + + align:start position:0% +the pet, questions on um + + + align:start position:0% +the pet, questions on um +those those questions. Questions on the + + align:start position:0% +those those questions. Questions on the + + + align:start position:0% +those those questions. Questions on the +questions? + + align:start position:0% +questions? + + + align:start position:0% +questions? +Questions about + + align:start position:0% +Questions about + + + align:start position:0% +Questions about +what is that? The Celtics. They're going + + align:start position:0% +what is that? The Celtics. They're going + + + align:start position:0% +what is that? The Celtics. They're going +to wrap it up. Yeah. Tonight. + + align:start position:0% +to wrap it up. Yeah. Tonight. + + + align:start position:0% +to wrap it up. Yeah. Tonight. +Anyway. Um + + align:start position:0% +Anyway. Um + + + align:start position:0% +Anyway. Um +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +I just like sharing a little something + + align:start position:0% +I just like sharing a little something + + + align:start position:0% +I just like sharing a little something +like this each time. Everybody seen this + + align:start position:0% +like this each time. Everybody seen this + + + align:start position:0% +like this each time. Everybody seen this +one? With great power comes great + + align:start position:0% +one? With great power comes great + + + align:start position:0% +one? With great power comes great +responsibility. Vision without action is + + align:start position:0% +responsibility. Vision without action is + + + align:start position:0% +responsibility. Vision without action is +a dream. Action without vision is a + + align:start position:0% +a dream. Action without vision is a + + + align:start position:0% +a dream. Action without vision is a +nightmare. So this is uh you know when + + align:start position:0% +nightmare. So this is uh you know when + + + align:start position:0% +nightmare. So this is uh you know when +you do calc this is my my reminder. When + + align:start position:0% +you do calc this is my my reminder. When + + + align:start position:0% +you do calc this is my my reminder. When +you do calculations + + align:start position:0% +you do calculations + + + align:start position:0% +you do calculations +you this is what counts most, right? + + align:start position:0% +you this is what counts most, right? + + + align:start position:0% +you this is what counts most, right? +Okay. Don't just start computing. + + align:start position:0% +Okay. Don't just start computing. + + + align:start position:0% +Okay. Don't just start computing. +Think about what you're doing. Okay, + + align:start position:0% +Think about what you're doing. Okay, + + + align:start position:0% +Think about what you're doing. Okay, +I'm going to take you through a little + + align:start position:0% +I'm going to take you through a little + + + align:start position:0% +I'm going to take you through a little +bit of uh a tour of some of the key + + align:start position:0% +bit of uh a tour of some of the key + + + align:start position:0% +bit of uh a tour of some of the key +concepts that I think would be important + + align:start position:0% +concepts that I think would be important + + + align:start position:0% +concepts that I think would be important +to know about that you might get + + align:start position:0% +to know about that you might get + + + align:start position:0% +to know about that you might get +questions on. Okay. Um you might get a + + align:start position:0% +questions on. Okay. Um you might get a + + + align:start position:0% +questions on. Okay. Um you might get a +question on and I think there's a + + align:start position:0% +question on and I think there's a + + + align:start position:0% +question on and I think there's a +practice quiz question or two on some of + + align:start position:0% +practice quiz question or two on some of + + + align:start position:0% +practice quiz question or two on some of +these um you know concepts of what led + + align:start position:0% +these um you know concepts of what led + + + align:start position:0% +these um you know concepts of what led +to uh you know quantum mechanics which + + align:start position:0% +to uh you know quantum mechanics which + + + align:start position:0% +to uh you know quantum mechanics which +we talked about in the first lecture. So + + align:start position:0% +we talked about in the first lecture. So + + + align:start position:0% +we talked about in the first lecture. So +why did we need a new physics? Why did + + align:start position:0% +why did we need a new physics? Why did + + + align:start position:0% +why did we need a new physics? Why did +we need something new? + + align:start position:0% +we need something new? + + + align:start position:0% +we need something new? +Um + + align:start position:0% +Um + + + align:start position:0% +Um +and uh you know the the fact that you + + align:start position:0% +and uh you know the the fact that you + + + align:start position:0% +and uh you know the the fact that you +have um uh you know as a result of of of + + align:start position:0% +have um uh you know as a result of of of + + + align:start position:0% +have um uh you know as a result of of of +a lot of research in that time what came + + align:start position:0% +a lot of research in that time what came + + + align:start position:0% +a lot of research in that time what came +out of it was that matter has both wave + + align:start position:0% +out of it was that matter has both wave + + + align:start position:0% +out of it was that matter has both wave +and particle character. Okay. And so + + align:start position:0% +and particle character. Okay. And so + + + align:start position:0% +and particle character. Okay. And so +we've talked about this experiment we've + + align:start position:0% +we've talked about this experiment we've + + + align:start position:0% +we've talked about this experiment we've +talked about that experiment. So you + + align:start position:0% +talked about that experiment. So you + + + align:start position:0% +talked about that experiment. So you +would know like if I asked a question + + align:start position:0% +would know like if I asked a question + + + align:start position:0% +would know like if I asked a question +about those experiments maybe um one of + + align:start position:0% +about those experiments maybe um one of + + + align:start position:0% +about those experiments maybe um one of +them and and we found that um that uh + + align:start position:0% +them and and we found that um that uh + + + align:start position:0% +them and and we found that um that uh +actually + + align:start position:0% +actually + + + align:start position:0% +actually +uh light can behave like a particle and + + align:start position:0% +uh light can behave like a particle and + + + align:start position:0% +uh light can behave like a particle and +matter can behave like a wave and it it + + align:start position:0% +matter can behave like a wave and it it + + + align:start position:0% +matter can behave like a wave and it it +would have a wave vector K that's + + align:start position:0% +would have a wave vector K that's + + + align:start position:0% +would have a wave vector K that's +related to its momentum and uh a + + align:start position:0% +related to its momentum and uh a + + + align:start position:0% +related to its momentum and uh a +frequency and and that's kind of really + + align:start position:0% +frequency and and that's kind of really + + + align:start position:0% +frequency and and that's kind of really +cool. And so if I asked you what the + + align:start position:0% +cool. And so if I asked you what the + + + align:start position:0% +cool. And so if I asked you what the +wavelength of a baseball was, right? I + + align:start position:0% +wavelength of a baseball was, right? I + + + align:start position:0% +wavelength of a baseball was, right? I +don't know. I think that might have been + + align:start position:0% +don't know. I think that might have been + + + align:start position:0% +don't know. I think that might have been +on the practice quiz, then that's + + align:start position:0% +on the practice quiz, then that's + + + align:start position:0% +on the practice quiz, then that's +something you could compute, right? For + + align:start position:0% +something you could compute, right? For + + + align:start position:0% +something you could compute, right? For +example, + + align:start position:0% +example, + + + align:start position:0% +example, +um I won't ask you that, but you kind of + + align:start position:0% +um I won't ask you that, but you kind of + + + align:start position:0% +um I won't ask you that, but you kind of +could could compute the wavelength of + + align:start position:0% +could could compute the wavelength of + + + align:start position:0% +could could compute the wavelength of +something. + + align:start position:0% +something. + + + align:start position:0% +something. +And then that took us to um + + align:start position:0% +And then that took us to um + + + align:start position:0% +And then that took us to um +uh well, okay, so you have to represent + + align:start position:0% +uh well, okay, so you have to represent + + + align:start position:0% +uh well, okay, so you have to represent +matter now with waves. So we're going to + + align:start position:0% +matter now with waves. So we're going to + + + align:start position:0% +matter now with waves. So we're going to +have this function to do that. Okay. So + + align:start position:0% +have this function to do that. Okay. So + + + align:start position:0% +have this function to do that. Okay. So +that took us to this function. We said + + align:start position:0% +that took us to this function. We said + + + align:start position:0% +that took us to this function. We said +there's going to be this function. It's + + align:start position:0% +there's going to be this function. It's + + + align:start position:0% +there's going to be this function. It's +a wave function. Well, that's a creative + + align:start position:0% +a wave function. Well, that's a creative + + + align:start position:0% +a wave function. Well, that's a creative +name. It's a function that represents + + align:start position:0% +name. It's a function that represents + + + align:start position:0% +name. It's a function that represents +waves, right? Okay, that's good. And we + + align:start position:0% +waves, right? Okay, that's good. And we + + + align:start position:0% +waves, right? Okay, that's good. And we +also said we didn't really explain this + + align:start position:0% +also said we didn't really explain this + + + align:start position:0% +also said we didn't really explain this +much but we said but you know you can't + + align:start position:0% +much but we said but you know you can't + + + align:start position:0% +much but we said but you know you can't +we don't actually know much about the + + align:start position:0% +we don't actually know much about the + + + align:start position:0% +we don't actually know much about the +physical meaning of this function but we + + align:start position:0% +physical meaning of this function but we + + + align:start position:0% +physical meaning of this function but we +do know that when you square it or since + + align:start position:0% +do know that when you square it or since + + + align:start position:0% +do know that when you square it or since +it's complex you multiply it by its + + align:start position:0% +it's complex you multiply it by its + + + align:start position:0% +it's complex you multiply it by its +complex conjugate that you get the + + align:start position:0% +complex conjugate that you get the + + + align:start position:0% +complex conjugate that you get the +density of this quantum mechanical + + align:start position:0% +density of this quantum mechanical + + + align:start position:0% +density of this quantum mechanical +particle. Right? And we we said this is + + align:start position:0% +particle. Right? And we we said this is + + + align:start position:0% +particle. Right? And we we said this is +it. This is what we need. We need this + + align:start position:0% +it. This is what we need. We need this + + + align:start position:0% +it. This is what we need. We need this +function because in quantum mechanics + + align:start position:0% +function because in quantum mechanics + + + align:start position:0% +function because in quantum mechanics +that function tells you where uh + + align:start position:0% +that function tells you where uh + + + align:start position:0% +that function tells you where uh +electrons are right the probability + + align:start position:0% +electrons are right the probability + + + align:start position:0% +electrons are right the probability +density of the electrons and so that's + + align:start position:0% +density of the electrons and so that's + + + align:start position:0% +density of the electrons and so that's +the thing we need because if you know + + align:start position:0% +the thing we need because if you know + + + align:start position:0% +the thing we need because if you know +that then you get all these other + + align:start position:0% +that then you get all these other + + + align:start position:0% +that then you get all these other +properties see once you have this that's + + align:start position:0% +properties see once you have this that's + + + align:start position:0% +properties see once you have this that's +what the doss comes from that's what the + + align:start position:0% +what the doss comes from that's what the + + + align:start position:0% +what the doss comes from that's what the +band structure comes from right it came + + align:start position:0% +band structure comes from right it came + + + align:start position:0% +band structure comes from right it came +from solving for that + + align:start position:0% +from solving for that + + + align:start position:0% +from solving for that +okay and then the question is well what + + align:start position:0% +okay and then the question is well what + + + align:start position:0% +okay and then the question is well what +are you solving and so what we needed + + align:start position:0% +are you solving and so what we needed + + + align:start position:0% +are you solving and so what we needed +there was the f equals ma of quantum + + align:start position:0% +there was the f equals ma of quantum + + + align:start position:0% +there was the f equals ma of quantum +mechanics, right? We needed the equation + + align:start position:0% +mechanics, right? We needed the equation + + + align:start position:0% +mechanics, right? We needed the equation +that governs the behavior of this wave + + align:start position:0% +that governs the behavior of this wave + + + align:start position:0% +that governs the behavior of this wave +function. + + align:start position:0% +function. + + + align:start position:0% +function. +And that's the shortinger equation. + + align:start position:0% +And that's the shortinger equation. + + + align:start position:0% +And that's the shortinger equation. +That's it. Okay. And um + + align:start position:0% +That's it. Okay. And um + + + align:start position:0% +That's it. Okay. And um +and we this is it, right? So we have the + + align:start position:0% +and we this is it, right? So we have the + + + align:start position:0% +and we this is it, right? So we have the +function that we need which when we + + align:start position:0% +function that we need which when we + + + align:start position:0% +function that we need which when we +solve it, we get all these properties + + align:start position:0% +solve it, we get all these properties + + + align:start position:0% +solve it, we get all these properties +that we really care about that we can + + align:start position:0% +that we really care about that we can + + + align:start position:0% +that we really care about that we can +use to make solar cells and solar fuels + + align:start position:0% +use to make solar cells and solar fuels + + + align:start position:0% +use to make solar cells and solar fuels +and lots of other things. Um there is an + + align:start position:0% +and lots of other things. Um there is an + + + align:start position:0% +and lots of other things. Um there is an +equation we need to solve to get that + + align:start position:0% +equation we need to solve to get that + + + align:start position:0% +equation we need to solve to get that +wave function and that equation is a + + align:start position:0% +wave function and that equation is a + + + align:start position:0% +wave function and that equation is a +shortinger equation and we took time out + + align:start position:0% +shortinger equation and we took time out + + + align:start position:0% +shortinger equation and we took time out +because we don't like time just + + align:start position:0% +because we don't like time just + + + align:start position:0% +because we don't like time just +complicates things and so we uh we we + + align:start position:0% +complicates things and so we uh we we + + + align:start position:0% +complicates things and so we uh we we +did it for the stationary solution. Um + + align:start position:0% +did it for the stationary solution. Um + + + align:start position:0% +did it for the stationary solution. Um +and the shortinger equation is hi equals + + align:start position:0% +and the shortinger equation is hi equals + + + align:start position:0% +and the shortinger equation is hi equals +ei where h is the the total energy right + + align:start position:0% +ei where h is the the total energy right + + + align:start position:0% +ei where h is the the total energy right +so it's the kinetic energy plus the + + align:start position:0% +so it's the kinetic energy plus the + + + align:start position:0% +so it's the kinetic energy plus the +potential energy + + align:start position:0% +potential energy + + + align:start position:0% +potential energy +um and when you write these out uh you + + align:start position:0% +um and when you write these out uh you + + + align:start position:0% +um and when you write these out uh you +you write out the kinetic energy as + + align:start position:0% +you write out the kinetic energy as + + + align:start position:0% +you write out the kinetic energy as +this second derivative and the potential + + align:start position:0% +this second derivative and the potential + + + align:start position:0% +this second derivative and the potential +well okay that depends on what we're + + align:start position:0% +well okay that depends on what we're + + + align:start position:0% +well okay that depends on what we're +talking about but if we're talking about + + align:start position:0% +talking about but if we're talking about + + + align:start position:0% +talking about but if we're talking about +say an electron + + align:start position:0% +say an electron + + + align:start position:0% +say an electron +uh in a hydrogen atom then it's it's E^2 + + align:start position:0% +uh in a hydrogen atom then it's it's E^2 + + + align:start position:0% +uh in a hydrogen atom then it's it's E^2 +R that's your potential the potential + + align:start position:0% +R that's your potential the potential + + + align:start position:0% +R that's your potential the potential +that that charge particle feels + + align:start position:0% + + + + align:start position:0% + +so that's the hydrogen atom right that's + + align:start position:0% +so that's the hydrogen atom right that's + + + align:start position:0% +so that's the hydrogen atom right that's +the electron in the hydrogen atom + + align:start position:0% +the electron in the hydrogen atom + + + align:start position:0% +the electron in the hydrogen atom +um + + align:start position:0% +um + + + align:start position:0% +um +okay I'm going through this quickly + + align:start position:0% +okay I'm going through this quickly + + + align:start position:0% +okay I'm going through this quickly +because I think we kind of are all + + align:start position:0% +because I think we kind of are all + + + align:start position:0% +because I think we kind of are all +feeling okay about this but if anyone + + align:start position:0% +feeling okay about this but if anyone + + + align:start position:0% +feeling okay about this but if anyone +has questions please raise your hand + + align:start position:0% +has questions please raise your hand + + + align:start position:0% +has questions please raise your hand +please because you know if you have a + + align:start position:0% +please because you know if you have a + + + align:start position:0% +please because you know if you have a +question it's very likely someone else + + align:start position:0% +question it's very likely someone else + + + align:start position:0% +question it's very likely someone else +has the same question. + + align:start position:0% +has the same question. + + + align:start position:0% +has the same question. +Any questions? + + align:start position:0% +Any questions? + + + align:start position:0% +Any questions? +Okay. Now you can solve this equation um + + align:start position:0% +Okay. Now you can solve this equation um + + + align:start position:0% +Okay. Now you can solve this equation um +actually very easily. Uh we did this I + + align:start position:0% +actually very easily. Uh we did this I + + + align:start position:0% +actually very easily. Uh we did this I +think in the second lecture maybe and uh + + align:start position:0% +think in the second lecture maybe and uh + + + align:start position:0% +think in the second lecture maybe and uh +um and you get solutions for that wave + + align:start position:0% +um and you get solutions for that wave + + + align:start position:0% +um and you get solutions for that wave +function and we talked about how the one + + align:start position:0% +function and we talked about how the one + + + align:start position:0% +function and we talked about how the one +of the key results here is that you get + + align:start position:0% +of the key results here is that you get + + + align:start position:0% +of the key results here is that you get +um quantization of the energies of the + + align:start position:0% +um quantization of the energies of the + + + align:start position:0% +um quantization of the energies of the +wave function. And what that means is + + align:start position:0% +wave function. And what that means is + + + align:start position:0% +wave function. And what that means is +that the energies can only have certain + + align:start position:0% +that the energies can only have certain + + + align:start position:0% +that the energies can only have certain +values, nothing in between. And we + + align:start position:0% +values, nothing in between. And we + + + align:start position:0% +values, nothing in between. And we +talked about the magic of that + + align:start position:0% +talked about the magic of that + + + align:start position:0% +talked about the magic of that +and and why and how that that explains + + align:start position:0% +and and why and how that that explains + + + align:start position:0% +and and why and how that that explains +these spectral lines that were observed + + align:start position:0% +these spectral lines that were observed + + + align:start position:0% +these spectral lines that were observed +long before + + align:start position:0% +long before + + + align:start position:0% +long before +um it finally explained those, right? So + + align:start position:0% +um it finally explained those, right? So + + + align:start position:0% +um it finally explained those, right? So +I don't know like calculating the energy + + align:start position:0% +I don't know like calculating the energy + + + align:start position:0% +I don't know like calculating the energy +differences here or how much energy it + + align:start position:0% +differences here or how much energy it + + + align:start position:0% +differences here or how much energy it +takes for an electron to move from one + + align:start position:0% +takes for an electron to move from one + + + align:start position:0% +takes for an electron to move from one +level to another. That sounds like a + + align:start position:0% +level to another. That sounds like a + + + align:start position:0% +level to another. That sounds like a +good problem to me. Um right okay okay + + align:start position:0% +good problem to me. Um right okay okay + + + align:start position:0% +good problem to me. Um right okay okay +now okay and units so forth now the + + align:start position:0% +now okay and units so forth now the + + + align:start position:0% +now okay and units so forth now the +other piece of ingredient that was + + align:start position:0% +other piece of ingredient that was + + + align:start position:0% +other piece of ingredient that was +really important is that actually + + align:start position:0% +really important is that actually + + + align:start position:0% +really important is that actually +electrons are they have this angular + + align:start position:0% +electrons are they have this angular + + + align:start position:0% +electrons are they have this angular +moment they have this spin okay and it + + align:start position:0% +moment they have this spin okay and it + + + align:start position:0% +moment they have this spin okay and it +was observed by putting them shooting + + align:start position:0% +was observed by putting them shooting + + + align:start position:0% +was observed by putting them shooting +them through a big magnet + + align:start position:0% +them through a big magnet + + + align:start position:0% +them through a big magnet +and basically finding that so so what + + align:start position:0% +and basically finding that so so what + + + align:start position:0% +and basically finding that so so what +was observed what was observed wasn't + + align:start position:0% +was observed what was observed wasn't + + + align:start position:0% +was observed what was observed wasn't +just that they had spin but that they + + align:start position:0% +just that they had spin but that they + + + align:start position:0% +just that they had spin but that they +only had one of two kinds of spin. So + + align:start position:0% +only had one of two kinds of spin. So + + + align:start position:0% +only had one of two kinds of spin. So +instead of getting a spread, you would + + align:start position:0% +instead of getting a spread, you would + + + align:start position:0% +instead of getting a spread, you would +think you would be applying a force on + + align:start position:0% +think you would be applying a force on + + + align:start position:0% +think you would be applying a force on +these electrons which are magnetic um + + align:start position:0% +these electrons which are magnetic um + + + align:start position:0% +these electrons which are magnetic um +since they're spinning, you would you + + align:start position:0% +since they're spinning, you would you + + + align:start position:0% +since they're spinning, you would you +would but they're not. But that's how we + + align:start position:0% +would but they're not. But that's how we + + + align:start position:0% +would but they're not. But that's how we +like to think of them in our classical + + align:start position:0% +like to think of them in our classical + + + align:start position:0% +like to think of them in our classical +minds. Um you would think that you would + + align:start position:0% +minds. Um you would think that you would + + + align:start position:0% +minds. Um you would think that you would +get a a nice continuous spread of of + + align:start position:0% +get a a nice continuous spread of of + + + align:start position:0% +get a a nice continuous spread of of +force acting on them causing them to + + align:start position:0% +force acting on them causing them to + + + align:start position:0% +force acting on them causing them to +separate, but instead you only get two + + align:start position:0% +separate, but instead you only get two + + + align:start position:0% +separate, but instead you only get two +spots, right? Those are that was really + + align:start position:0% +spots, right? Those are that was really + + + align:start position:0% +spots, right? Those are that was really +important because it told us that these + + align:start position:0% +important because it told us that these + + + align:start position:0% +important because it told us that these +uh there's another kind of quantum + + align:start position:0% +uh there's another kind of quantum + + + align:start position:0% +uh there's another kind of quantum +mechanical um number which is the spin + + align:start position:0% +mechanical um number which is the spin + + + align:start position:0% +mechanical um number which is the spin +number which can be up or down right + + align:start position:0% +number which can be up or down right + + + align:start position:0% +number which can be up or down right +only up or down. Okay. + + align:start position:0% +only up or down. Okay. + + + align:start position:0% +only up or down. Okay. +And then um you put that together and + + align:start position:0% +And then um you put that together and + + + align:start position:0% +And then um you put that together and +you put together your solution for the + + align:start position:0% +you put together your solution for the + + + align:start position:0% +you put together your solution for the +shortinger equation and uh voila you get + + align:start position:0% +shortinger equation and uh voila you get + + + align:start position:0% +shortinger equation and uh voila you get +essentially uh uh oh you add on a little + + align:start position:0% +essentially uh uh oh you add on a little + + + align:start position:0% +essentially uh uh oh you add on a little +bit of pi you put in some pi exclusion + + align:start position:0% +bit of pi you put in some pi exclusion + + + align:start position:0% +bit of pi you put in some pi exclusion +just a little bit you don't want to over + + align:start position:0% +just a little bit you don't want to over + + + align:start position:0% +just a little bit you don't want to over +pi anyway never mind um which just says + + align:start position:0% +pi anyway never mind um which just says + + + align:start position:0% +pi anyway never mind um which just says +that okay we got these quantum numbers + + align:start position:0% +that okay we got these quantum numbers + + + align:start position:0% +that okay we got these quantum numbers +you know n l mm and now the spin and no + + align:start position:0% +you know n l mm and now the spin and no + + + align:start position:0% +you know n l mm and now the spin and no +two electrons can have the same set, + + align:start position:0% +two electrons can have the same set, + + + align:start position:0% +two electrons can have the same set, +which results in the fact that you + + align:start position:0% +which results in the fact that you + + + align:start position:0% +which results in the fact that you +cannot put more than two electrons in + + align:start position:0% +cannot put more than two electrons in + + + align:start position:0% +cannot put more than two electrons in +one of these energy levels. And + + align:start position:0% +one of these energy levels. And + + + align:start position:0% +one of these energy levels. And +remember, these energy levels are kind + + align:start position:0% +remember, these energy levels are kind + + + align:start position:0% +remember, these energy levels are kind +of like the key ingredient we're after + + align:start position:0% +of like the key ingredient we're after + + + align:start position:0% +of like the key ingredient we're after +in in this class. Okay, it's really one + + align:start position:0% +in in this class. Okay, it's really one + + + align:start position:0% +in in this class. Okay, it's really one +of the key ingredients we're after. + + align:start position:0% +of the key ingredients we're after. + + + align:start position:0% +of the key ingredients we're after. +Where do those electrons want to sit? + + align:start position:0% +Where do those electrons want to sit? + + + align:start position:0% +Where do those electrons want to sit? +Because it tells us so much about um + + align:start position:0% +Because it tells us so much about um + + + align:start position:0% +Because it tells us so much about um +properties of materials that that are + + align:start position:0% +properties of materials that that are + + + align:start position:0% +properties of materials that that are +interesting. Okay, now that it really + + align:start position:0% +interesting. Okay, now that it really + + + align:start position:0% +interesting. Okay, now that it really +allows you to go to a description of of + + align:start position:0% +allows you to go to a description of of + + + align:start position:0% +allows you to go to a description of of +the whole periodic table. The problem is + + align:start position:0% +the whole periodic table. The problem is + + + align:start position:0% +the whole periodic table. The problem is +that that was a a description based on + + align:start position:0% +that that was a a description based on + + + align:start position:0% +that that was a a description based on +one electron and one proton. We solved + + align:start position:0% +one electron and one proton. We solved + + + align:start position:0% +one electron and one proton. We solved +for that. We could solve for that. And + + align:start position:0% +for that. We could solve for that. And + + + align:start position:0% +for that. We could solve for that. And +so we did and we got the levels and that + + align:start position:0% +so we did and we got the levels and that + + + align:start position:0% +so we did and we got the levels and that +was really neat. And then we had rules + + align:start position:0% +was really neat. And then we had rules + + + align:start position:0% +was really neat. And then we had rules +about how to fill them and that was + + align:start position:0% +about how to fill them and that was + + + align:start position:0% +about how to fill them and that was +really neat. And then you can actually + + align:start position:0% +really neat. And then you can actually + + + align:start position:0% +really neat. And then you can actually +explain a lot of chemistry that way, + + align:start position:0% +explain a lot of chemistry that way, + + + align:start position:0% +explain a lot of chemistry that way, +right? you get your S and your P and + + align:start position:0% +right? you get your S and your P and + + + align:start position:0% +right? you get your S and your P and +your D orbitals and you fill them. The + + align:start position:0% +your D orbitals and you fill them. The + + + align:start position:0% +your D orbitals and you fill them. The +problem is that actually when you have + + align:start position:0% +problem is that actually when you have + + + align:start position:0% +problem is that actually when you have +anything but hydrogen, you have more + + align:start position:0% +anything but hydrogen, you have more + + + align:start position:0% +anything but hydrogen, you have more +than one electron. Okay? + + align:start position:0% +than one electron. Okay? + + + align:start position:0% +than one electron. Okay? +And so that really requires going back + + align:start position:0% +And so that really requires going back + + + align:start position:0% +And so that really requires going back +to the shortinger equation and adding in + + align:start position:0% +to the shortinger equation and adding in + + + align:start position:0% +to the shortinger equation and adding in +the interactions between electrons that + + align:start position:0% +the interactions between electrons that + + + align:start position:0% +the interactions between electrons that +was not in the original hydrogen atom. + + align:start position:0% +was not in the original hydrogen atom. + + + align:start position:0% +was not in the original hydrogen atom. +And that's hard. That's the hard part. + + align:start position:0% +And that's hard. That's the hard part. + + + align:start position:0% +And that's hard. That's the hard part. +Hard stuff. + + align:start position:0% +Hard stuff. + + + align:start position:0% +Hard stuff. +And so we turn to computation. Okay, + + align:start position:0% +And so we turn to computation. Okay, + + + align:start position:0% +And so we turn to computation. Okay, +that's really hard to do analytically + + align:start position:0% +that's really hard to do analytically + + + align:start position:0% +that's really hard to do analytically +and it gets much much worse the more + + align:start position:0% +and it gets much much worse the more + + + align:start position:0% +and it gets much much worse the more +electrons you have. Okay, any questions + + align:start position:0% +electrons you have. Okay, any questions + + + align:start position:0% +electrons you have. Okay, any questions +up to this point, right? So how do we do + + align:start position:0% +up to this point, right? So how do we do + + + align:start position:0% +up to this point, right? So how do we do +that? Well, you got to So we're using + + align:start position:0% +that? Well, you got to So we're using + + + align:start position:0% +that? Well, you got to So we're using +computation, but you can't just throw + + align:start position:0% +computation, but you can't just throw + + + align:start position:0% +computation, but you can't just throw +this onto a grid or throw this into mat + + align:start position:0% +this onto a grid or throw this into mat + + + align:start position:0% +this onto a grid or throw this into mat +lab. It still isn't isn't doable. And so + + align:start position:0% +lab. It still isn't isn't doable. And so + + + align:start position:0% +lab. It still isn't isn't doable. And so +there's sort of two branches in + + align:start position:0% +there's sort of two branches in + + + align:start position:0% +there's sort of two branches in +computational quantum mechanics. One + + align:start position:0% +computational quantum mechanics. One + + + align:start position:0% +computational quantum mechanics. One +that loosely is labeled quantum + + align:start position:0% +that loosely is labeled quantum + + + align:start position:0% +that loosely is labeled quantum +chemistry and the other kind of more + + align:start position:0% +chemistry and the other kind of more + + + align:start position:0% +chemistry and the other kind of more +solid state physics density functional + + align:start position:0% +solid state physics density functional + + + align:start position:0% +solid state physics density functional +theory. And both of them make + + align:start position:0% +theory. And both of them make + + + align:start position:0% +theory. And both of them make +approximations. We talked about those + + align:start position:0% +approximations. We talked about those + + + align:start position:0% +approximations. We talked about those +approximations. What they're + + align:start position:0% +approximations. What they're + + + align:start position:0% +approximations. What they're +approximating is the shortinger + + align:start position:0% +approximating is the shortinger + + + align:start position:0% +approximating is the shortinger +equation. They're simplifying it because + + align:start position:0% +equation. They're simplifying it because + + + align:start position:0% +equation. They're simplifying it because +even as simple as that may look, just + + align:start position:0% +even as simple as that may look, just + + + align:start position:0% +even as simple as that may look, just +throw that into mat lab. It doesn't + + align:start position:0% +throw that into mat lab. It doesn't + + + align:start position:0% +throw that into mat lab. It doesn't +happen. You can't solve it when you have + + align:start position:0% +happen. You can't solve it when you have + + + align:start position:0% +happen. You can't solve it when you have +more than a couple of electrons. + + align:start position:0% +more than a couple of electrons. + + + align:start position:0% +more than a couple of electrons. +Five + + align:start position:0% +Five + + + align:start position:0% +Five +electrons, I don't know, six, that won't + + align:start position:0% +electrons, I don't know, six, that won't + + + align:start position:0% +electrons, I don't know, six, that won't +be on the quiz, but you just can't solve + + align:start position:0% +be on the quiz, but you just can't solve + + + align:start position:0% +be on the quiz, but you just can't solve +it exactly on a computer unless you have + + align:start position:0% +it exactly on a computer unless you have + + + align:start position:0% +it exactly on a computer unless you have +the age of the universe. And even then, + + align:start position:0% +the age of the universe. And even then, + + + align:start position:0% +the age of the universe. And even then, +it's too hard. So, we got to simplify + + align:start position:0% +it's too hard. So, we got to simplify + + + align:start position:0% +it's too hard. So, we got to simplify +this equation. And you know, mostly in + + align:start position:0% +this equation. And you know, mostly in + + + align:start position:0% +this equation. And you know, mostly in +the quantum chemistry world, what you do + + align:start position:0% +the quantum chemistry world, what you do + + + align:start position:0% +the quantum chemistry world, what you do +is you simplify this. We talked about + + align:start position:0% +is you simplify this. We talked about + + + align:start position:0% +is you simplify this. We talked about +using basis sets, right? Basis functions + + align:start position:0% +using basis sets, right? Basis functions + + + align:start position:0% +using basis sets, right? Basis functions +to represent this. Well, you can + + align:start position:0% +to represent this. Well, you can + + + align:start position:0% +to represent this. Well, you can +restrict + + align:start position:0% +restrict + + + align:start position:0% +restrict +the degrees of freedom in that function + + align:start position:0% +the degrees of freedom in that function + + + align:start position:0% +the degrees of freedom in that function +as well, + + align:start position:0% +as well, + + + align:start position:0% +as well, +right? And that makes that equation much + + align:start position:0% +right? And that makes that equation much + + + align:start position:0% +right? And that makes that equation much +easier. And the other thing you can do + + align:start position:0% +easier. And the other thing you can do + + + align:start position:0% +easier. And the other thing you can do +is you can actually change so that's + + align:start position:0% +is you can actually change so that's + + + align:start position:0% +is you can actually change so that's +changing this part. And the other thing + + align:start position:0% +changing this part. And the other thing + + + align:start position:0% +changing this part. And the other thing +is you could change this part, right? + + align:start position:0% +is you could change this part, right? + + + align:start position:0% +is you could change this part, right? +And that's what that's what uh + + align:start position:0% +And that's what that's what uh + + + align:start position:0% +And that's what that's what uh +physicists mostly did. And now everyone + + align:start position:0% +physicists mostly did. And now everyone + + + align:start position:0% +physicists mostly did. And now everyone +holds hands and sings kumbaya and + + align:start position:0% +holds hands and sings kumbaya and + + + align:start position:0% +holds hands and sings kumbaya and +everyone's happy. Back then there was a + + align:start position:0% +everyone's happy. Back then there was a + + + align:start position:0% +everyone's happy. Back then there was a +lot of uh two fields, you know, + + align:start position:0% +lot of uh two fields, you know, + + + align:start position:0% +lot of uh two fields, you know, +physicists versus chemists, all that. + + align:start position:0% +physicists versus chemists, all that. + + + align:start position:0% +physicists versus chemists, all that. +But it's we're all happy together now. + + align:start position:0% +But it's we're all happy together now. + + + align:start position:0% +But it's we're all happy together now. +Everyone's and so so chemists do density + + align:start position:0% +Everyone's and so so chemists do density + + + align:start position:0% +Everyone's and so so chemists do density +functional theory. Physicists don't mind + + align:start position:0% +functional theory. Physicists don't mind + + + align:start position:0% +functional theory. Physicists don't mind +wave functionbased methods as they're + + align:start position:0% +wave functionbased methods as they're + + + align:start position:0% +wave functionbased methods as they're +called. Okay. The result and this is a + + align:start position:0% +called. Okay. The result and this is a + + + align:start position:0% +called. Okay. The result and this is a +this is this was one of my sort of red + + align:start position:0% +this is this was one of my sort of red + + + align:start position:0% +this is this was one of my sort of red +flag key results here is that what + + align:start position:0% +flag key results here is that what + + + align:start position:0% +flag key results here is that what +you've done + + align:start position:0% +you've done + + + align:start position:0% +you've done +when you do this is you you have taken a + + align:start position:0% +when you do this is you you have taken a + + + align:start position:0% +when you do this is you you have taken a +problem that involved all of these + + align:start position:0% +problem that involved all of these + + + align:start position:0% +problem that involved all of these +interactions remember one over r12 meant + + align:start position:0% +interactions remember one over r12 meant + + + align:start position:0% +interactions remember one over r12 meant +taking into account the interaction + + align:start position:0% +taking into account the interaction + + + align:start position:0% +taking into account the interaction +between electron one and electron 2 and + + align:start position:0% +between electron one and electron 2 and + + + align:start position:0% +between electron one and electron 2 and +that just gets really painful and hard + + align:start position:0% +that just gets really painful and hard + + + align:start position:0% +that just gets really painful and hard +and so what you've done in both sense + + align:start position:0% +and so what you've done in both sense + + + align:start position:0% +and so what you've done in both sense +both categories is you've completely + + align:start position:0% +both categories is you've completely + + + align:start position:0% +both categories is you've completely +changed the picture into what's called a + + align:start position:0% +changed the picture into what's called a + + + align:start position:0% +changed the picture into what's called a +meanfield picture So each electron is + + align:start position:0% +meanfield picture So each electron is + + + align:start position:0% +meanfield picture So each electron is +only now really solved in the context of + + align:start position:0% +only now really solved in the context of + + + align:start position:0% +only now really solved in the context of +a an average field of the other + + align:start position:0% +a an average field of the other + + + align:start position:0% +a an average field of the other +electrons. Okay, that's the + + align:start position:0% +electrons. Okay, that's the + + + align:start position:0% +electrons. Okay, that's the +simplification key. That's the key + + align:start position:0% +simplification key. That's the key + + + align:start position:0% +simplification key. That's the key +simplification. So the the mean field + + align:start position:0% +simplification. So the the mean field + + + align:start position:0% +simplification. So the the mean field +methods are really what enable us to do + + align:start position:0% +methods are really what enable us to do + + + align:start position:0% +methods are really what enable us to do +computational quantum mechanics for + + align:start position:0% +computational quantum mechanics for + + + align:start position:0% +computational quantum mechanics for +large systems, right? + + align:start position:0% +large systems, right? + + + align:start position:0% +large systems, right? +Um I don't really think I need to review + + align:start position:0% +Um I don't really think I need to review + + + align:start position:0% +Um I don't really think I need to review +this too much, but uh because I I did + + align:start position:0% +this too much, but uh because I I did + + + align:start position:0% +this too much, but uh because I I did +just review this I think a week ago. Um + + align:start position:0% +just review this I think a week ago. Um + + + align:start position:0% +just review this I think a week ago. Um +but the density uh is a nice thing to + + align:start position:0% +but the density uh is a nice thing to + + + align:start position:0% +but the density uh is a nice thing to +work with because unlike the wave + + align:start position:0% +work with because unlike the wave + + + align:start position:0% +work with because unlike the wave +function with sort of if you wanted a + + align:start position:0% +function with sort of if you wanted a + + + align:start position:0% +function with sort of if you wanted a +grid to represent each a grid of points + + align:start position:0% +grid to represent each a grid of points + + + align:start position:0% +grid to represent each a grid of points +um even as the number of atoms in the + + align:start position:0% +um even as the number of atoms in the + + + align:start position:0% +um even as the number of atoms in the +system grows the density grid is is just + + align:start position:0% +system grows the density grid is is just + + + align:start position:0% +system grows the density grid is is just +the same. So the number of points you + + align:start position:0% +the same. So the number of points you + + + align:start position:0% +the same. So the number of points you +need to represent the density is + + align:start position:0% +need to represent the density is + + + align:start position:0% +need to represent the density is +constant while the number of points you + + align:start position:0% +constant while the number of points you + + + align:start position:0% +constant while the number of points you +would need to represent SI grows + + align:start position:0% +would need to represent SI grows + + + align:start position:0% +would need to represent SI grows +exponentially. So it's a really hard + + align:start position:0% +exponentially. So it's a really hard + + + align:start position:0% +exponentially. So it's a really hard +problem in in in in in + + align:start position:0% +problem in in in in in + + + align:start position:0% +problem in in in in in +the context of scaling with size for the + + align:start position:0% +the context of scaling with size for the + + + align:start position:0% +the context of scaling with size for the +wave function, but the density offers + + align:start position:0% +wave function, but the density offers + + + align:start position:0% +wave function, but the density offers +this really nice + + align:start position:0% +this really nice + + + align:start position:0% +this really nice +scaling. + + align:start position:0% +scaling. + + + align:start position:0% +scaling. +And so that's what density functional + + align:start position:0% +And so that's what density functional + + + align:start position:0% +And so that's what density functional +theory is. Is it's it's a it's a method + + align:start position:0% +theory is. Is it's it's a it's a method + + + align:start position:0% +theory is. Is it's it's a it's a method +that relates it it shows that the + + align:start position:0% +that relates it it shows that the + + + align:start position:0% +that relates it it shows that the +density can be related um to the wave + + align:start position:0% +density can be related um to the wave + + + align:start position:0% +density can be related um to the wave +function and then you just work with the + + align:start position:0% +function and then you just work with the + + + align:start position:0% +function and then you just work with the +density and you throw out the wave + + align:start position:0% +density and you throw out the wave + + + align:start position:0% +density and you throw out the wave +function. You bring it back in later. + + align:start position:0% +function. You bring it back in later. + + + align:start position:0% +function. You bring it back in later. +But that's basically what the theory + + align:start position:0% +But that's basically what the theory + + + align:start position:0% +But that's basically what the theory +does. Um the problem is that it pushes + + align:start position:0% +does. Um the problem is that it pushes + + + align:start position:0% +does. Um the problem is that it pushes +out it has this sort of term + + align:start position:0% +out it has this sort of term + + + align:start position:0% +out it has this sort of term +uh that you you talked about in lecture + + align:start position:0% +uh that you you talked about in lecture + + + align:start position:0% +uh that you you talked about in lecture +three or four um + + align:start position:0% +three or four um + + + align:start position:0% +three or four um +that you have to kind of approximate + + align:start position:0% +that you have to kind of approximate + + + align:start position:0% +that you have to kind of approximate +this exchange correlation potential and + + align:start position:0% +this exchange correlation potential and + + + align:start position:0% +this exchange correlation potential and +um we talked about that + + align:start position:0% +um we talked about that + + + align:start position:0% +um we talked about that +uh and the exchange correlation + + align:start position:0% +uh and the exchange correlation + + + align:start position:0% +uh and the exchange correlation +potential let's get to that is not + + align:start position:0% +potential let's get to that is not + + + align:start position:0% +potential let's get to that is not +known. If you knew it, it would be + + align:start position:0% +known. If you knew it, it would be + + + align:start position:0% +known. If you knew it, it would be +actually an exact method, but it's not. + + align:start position:0% +actually an exact method, but it's not. + + + align:start position:0% +actually an exact method, but it's not. +And so you make approximations. And + + align:start position:0% +And so you make approximations. And + + + align:start position:0% +And so you make approximations. And +these are actually two of the + + align:start position:0% +these are actually two of the + + + align:start position:0% +these are actually two of the +approximations that you have as um as as + + align:start position:0% +approximations that you have as um as as + + + align:start position:0% +approximations that you have as um as as +options in the nano hub tools. Now what + + align:start position:0% +options in the nano hub tools. Now what + + + align:start position:0% +options in the nano hub tools. Now what +these approximations are is not part of + + align:start position:0% +these approximations are is not part of + + + align:start position:0% +these approximations are is not part of +this class. Okay? That gets into kind + + align:start position:0% +this class. Okay? That gets into kind + + + align:start position:0% +this class. Okay? That gets into kind +of, you know, more complicated um you + + align:start position:0% +of, you know, more complicated um you + + + align:start position:0% +of, you know, more complicated um you +know, more complicated equations that we + + align:start position:0% +know, more complicated equations that we + + + align:start position:0% +know, more complicated equations that we +would have to cover that I don't want to + + align:start position:0% +would have to cover that I don't want to + + + align:start position:0% +would have to cover that I don't want to +do. But what I want you to pull out from + + align:start position:0% +do. But what I want you to pull out from + + + align:start position:0% +do. But what I want you to pull out from +this is that + + align:start position:0% +this is that + + + align:start position:0% +this is that +we are still we are not solving the + + align:start position:0% +we are still we are not solving the + + + align:start position:0% +we are still we are not solving the +shortinger equation exactly + + align:start position:0% +shortinger equation exactly + + + align:start position:0% +shortinger equation exactly +right we are making approximations and + + align:start position:0% +right we are making approximations and + + + align:start position:0% +right we are making approximations and +those approximations need to be checked + + align:start position:0% +those approximations need to be checked + + + align:start position:0% +those approximations need to be checked +so you see there's two kinds of + + align:start position:0% +so you see there's two kinds of + + + align:start position:0% +so you see there's two kinds of +convergence here + + align:start position:0% +convergence here + + + align:start position:0% +convergence here +that's the key right and and this is + + align:start position:0% +that's the key right and and this is + + + align:start position:0% +that's the key right and and this is +where I come with responsibility + + align:start position:0% +where I come with responsibility + + + align:start position:0% +where I come with responsibility +right one kind of convergence is + + align:start position:0% +right one kind of convergence is + + + align:start position:0% +right one kind of convergence is +is k points basis sets right but another + + align:start position:0% +is k points basis sets right but another + + + align:start position:0% +is k points basis sets right but another +kind of convergence is where are you in + + align:start position:0% +kind of convergence is where are you in + + + align:start position:0% +kind of convergence is where are you in +accuracy space where are you do you know + + align:start position:0% +accuracy space where are you do you know + + + align:start position:0% +accuracy space where are you do you know +right because you are making + + align:start position:0% +right because you are making + + + align:start position:0% +right because you are making +approximations when you pull down that + + align:start position:0% +approximations when you pull down that + + + align:start position:0% +approximations when you pull down that +option on the toolkit to say gg or lda + + align:start position:0% +option on the toolkit to say gg or lda + + + align:start position:0% +option on the toolkit to say gg or lda +what you're doing is you're changing the + + align:start position:0% +what you're doing is you're changing the + + + align:start position:0% +what you're doing is you're changing the +form of this which one is right you're + + align:start position:0% +form of this which one is right you're + + + align:start position:0% +form of this which one is right you're +still not solving the equations exactly + + align:start position:0% +still not solving the equations exactly + + + align:start position:0% +still not solving the equations exactly +so how do you know if you're right. + + align:start position:0% +so how do you know if you're right. + + + align:start position:0% +so how do you know if you're right. +Throw that out there as a question. + + align:start position:0% + + + + align:start position:0% + +Find an experimentalist. + + align:start position:0% +Find an experimentalist. + + + align:start position:0% +Find an experimentalist. +Find an experimentalist. Father them. + + align:start position:0% +Find an experimentalist. Father them. + + + align:start position:0% +Find an experimentalist. Father them. +Say, "Can you measure this?" And they + + align:start position:0% +Say, "Can you measure this?" And they + + + align:start position:0% +Say, "Can you measure this?" And they +say, "No. Are you crazy? My my adviser + + align:start position:0% +say, "No. Are you crazy? My my adviser + + + align:start position:0% +say, "No. Are you crazy? My my adviser +just told me to work 90 hours a week on + + align:start position:0% +just told me to work 90 hours a week on + + + align:start position:0% +just told me to work 90 hours a week on +something else." So then what do you do? + + align:start position:0% +something else." So then what do you do? + + + align:start position:0% +something else." So then what do you do? +Because it's not in the literature. + + align:start position:0% +Because it's not in the literature. + + + align:start position:0% +Because it's not in the literature. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Try a bunch of different approximations. + + align:start position:0% +Try a bunch of different approximations. + + + align:start position:0% +Try a bunch of different approximations. +Okay. Any of them are great. see if any + + align:start position:0% +Okay. Any of them are great. see if any + + + align:start position:0% +Okay. Any of them are great. see if any +of them agree. Let's suppose half of + + align:start position:0% +of them agree. Let's suppose half of + + + align:start position:0% +of them agree. Let's suppose half of +them agree and half of them disagree. + + align:start position:0% +them agree and half of them disagree. + + + align:start position:0% +them agree and half of them disagree. +Say I had 10 functionals to choose from. + + align:start position:0% +Say I had 10 functionals to choose from. + + + align:start position:0% +Say I had 10 functionals to choose from. +What else could you do? Or or are you + + align:start position:0% +What else could you do? Or or are you + + + align:start position:0% +What else could you do? Or or are you +done? Is that good enough? + + align:start position:0% + + + + align:start position:0% + +Run one more. The tiebreaker. I love it. + + align:start position:0% + + + + align:start position:0% + +Sadly, there are papers in the + + align:start position:0% +Sadly, there are papers in the + + + align:start position:0% +Sadly, there are papers in the +literature that kind of take that + + align:start position:0% +literature that kind of take that + + + align:start position:0% +literature that kind of take that +approach. Um, it's a little too loosey + + align:start position:0% +approach. Um, it's a little too loosey + + + align:start position:0% +approach. Um, it's a little too loosey +goosey, but it's it was a good idea. + + align:start position:0% +goosey, but it's it was a good idea. + + + align:start position:0% +goosey, but it's it was a good idea. +Okay, what else? What? Well, is it good + + align:start position:0% +Okay, what else? What? Well, is it good + + + align:start position:0% +Okay, what else? What? Well, is it good +enough? I mean, if if I had 10 + + align:start position:0% +enough? I mean, if if I had 10 + + + align:start position:0% +enough? I mean, if if I had 10 +functionals, + + align:start position:0% +functionals, + + + align:start position:0% +functionals, +by the way, there are hundreds of + + align:start position:0% +by the way, there are hundreds of + + + align:start position:0% +by the way, there are hundreds of +functionals now to choose from in + + align:start position:0% +functionals now to choose from in + + + align:start position:0% +functionals now to choose from in +density functional theory. If I had 10 + + align:start position:0% +density functional theory. If I had 10 + + + align:start position:0% +density functional theory. If I had 10 +and half of them agreed, but the other + + align:start position:0% +and half of them agreed, but the other + + + align:start position:0% +and half of them agreed, but the other +half didn't, what do I do? + + align:start position:0% + + + + align:start position:0% + +Okay. Why? + + align:start position:0% +Okay. Why? + + + align:start position:0% +Okay. Why? +like a whole different + + align:start position:0% +like a whole different + + + align:start position:0% +like a whole different +whole different theory. Good. Okay. Go + + align:start position:0% +whole different theory. Good. Okay. Go + + + align:start position:0% +whole different theory. Good. Okay. Go +to a different theory for quantum + + align:start position:0% +to a different theory for quantum + + + align:start position:0% +to a different theory for quantum +mechanics. See what that agrees with. + + align:start position:0% +mechanics. See what that agrees with. + + + align:start position:0% +mechanics. See what that agrees with. +But see, that may have its own whole it + + align:start position:0% +But see, that may have its own whole it + + + align:start position:0% +But see, that may have its own whole it +does have its own own whole world of + + align:start position:0% +does have its own own whole world of + + + align:start position:0% +does have its own own whole world of +approximations, + + align:start position:0% +approximations, + + + align:start position:0% +approximations, +right? But that's the right that's sort + + align:start position:0% +right? But that's the right that's sort + + + align:start position:0% +right? But that's the right that's sort +of the right, you know, way to think + + align:start position:0% +of the right, you know, way to think + + + align:start position:0% +of the right, you know, way to think +about it because there are theories that + + align:start position:0% +about it because there are theories that + + + align:start position:0% +about it because there are theories that +are more accurate and less accurate in + + align:start position:0% +are more accurate and less accurate in + + + align:start position:0% +are more accurate and less accurate in +how they solve for how they simplify the + + align:start position:0% +how they solve for how they simplify the + + + align:start position:0% +how they solve for how they simplify the +shinger equation. So you can try to go + + align:start position:0% +shinger equation. So you can try to go + + + align:start position:0% +shinger equation. So you can try to go +to more accurate or what are known to be + + align:start position:0% +to more accurate or what are known to be + + + align:start position:0% +to more accurate or what are known to be +better accurate theories. Now there's + + align:start position:0% +better accurate theories. Now there's + + + align:start position:0% +better accurate theories. Now there's +one other thing to do. I told you that + + align:start position:0% +one other thing to do. I told you that + + + align:start position:0% +one other thing to do. I told you that +um + + align:start position:0% +um + + + align:start position:0% +um +in this particular case it's a solar + + align:start position:0% +in this particular case it's a solar + + + align:start position:0% +in this particular case it's a solar +fuel that you just calculated. + + align:start position:0% +fuel that you just calculated. + + + align:start position:0% +fuel that you just calculated. +You think it's going to be + + align:start position:0% +You think it's going to be + + + align:start position:0% +You think it's going to be +revolutionary, + + align:start position:0% +revolutionary, + + + align:start position:0% +revolutionary, +right? Um + + align:start position:0% +right? Um + + + align:start position:0% +right? Um +but only only by one functional. The + + align:start position:0% +but only only by one functional. The + + + align:start position:0% +but only only by one functional. The +other functional says it's really bad. + + align:start position:0% +other functional says it's really bad. + + + align:start position:0% +other functional says it's really bad. +Um, you went to an experimentalist, they + + align:start position:0% +Um, you went to an experimentalist, they + + + align:start position:0% +Um, you went to an experimentalist, they +said no and you can't do higher level + + align:start position:0% +said no and you can't do higher level + + + align:start position:0% +said no and you can't do higher level +theory. + + align:start position:0% +theory. + + + align:start position:0% +theory. +Anything else you can do? + + align:start position:0% + + + + align:start position:0% + +Take a poll of your like your group + + align:start position:0% +Take a poll of your like your group + + + align:start position:0% +Take a poll of your like your group +members. + + align:start position:0% +members. + + + align:start position:0% +members. +That's good. I like that. Computational + + align:start position:0% +That's good. I like that. Computational + + + align:start position:0% +That's good. I like that. Computational +people people computing. What else? + + align:start position:0% + + + + align:start position:0% + +What is that? + + align:start position:0% +What is that? + + + align:start position:0% +What is that? +I said request more funding. + + align:start position:0% +I said request more funding. + + + align:start position:0% +I said request more funding. +Request more funding. You're talking + + align:start position:0% +Request more funding. You're talking + + + align:start position:0% +Request more funding. You're talking +like a like a professor. So um what + + align:start position:0% +like a like a professor. So um what + + + align:start position:0% +like a like a professor. So um what +else? Anything else? There is something + + align:start position:0% +else? Anything else? There is something + + + align:start position:0% +else? Anything else? There is something +else you can do. So the key is I said + + align:start position:0% +else you can do. So the key is I said + + + align:start position:0% +else you can do. So the key is I said +that the experiment for that fuel hasn't + + align:start position:0% +that the experiment for that fuel hasn't + + + align:start position:0% +that the experiment for that fuel hasn't +been done but okay + + align:start position:0% +been done but okay + + + align:start position:0% +been done but okay +use the same level of theory on a system + + align:start position:0% +use the same level of theory on a system + + + align:start position:0% +use the same level of theory on a system +that has been done that's related that's + + align:start position:0% +that has been done that's related that's + + + align:start position:0% +that has been done that's related that's +closely related. + + align:start position:0% +closely related. + + + align:start position:0% +closely related. +Right? Well, I modified aobenzene to + + align:start position:0% +Right? Well, I modified aobenzene to + + + align:start position:0% +Right? Well, I modified aobenzene to +make a good fuel. + + align:start position:0% +make a good fuel. + + + align:start position:0% +make a good fuel. +That hasn't been made yet, but a benzene + + align:start position:0% +That hasn't been made yet, but a benzene + + + align:start position:0% +That hasn't been made yet, but a benzene +has. Did my theory work well for all of + + align:start position:0% +has. Did my theory work well for all of + + + align:start position:0% +has. Did my theory work well for all of +the data I can get my hands on that's + + align:start position:0% +the data I can get my hands on that's + + + align:start position:0% +the data I can get my hands on that's +relevant to what I'm simulating for that + + align:start position:0% +relevant to what I'm simulating for that + + + align:start position:0% +relevant to what I'm simulating for that +material? This is validation. Okay, this + + align:start position:0% +material? This is validation. Okay, this + + + align:start position:0% +material? This is validation. Okay, this +is validation. It's it's it's not the + + align:start position:0% +is validation. It's it's it's not the + + + align:start position:0% +is validation. It's it's it's not the +same as convergence. I said, you know, + + align:start position:0% +same as convergence. I said, you know, + + + align:start position:0% +same as convergence. I said, you know, +sort of two kinds of convergence. This + + align:start position:0% +sort of two kinds of convergence. This + + + align:start position:0% +sort of two kinds of convergence. This +kind is called validation and it is + + align:start position:0% +kind is called validation and it is + + + align:start position:0% +kind is called validation and it is +critical in computation. It is a + + align:start position:0% +critical in computation. It is a + + + align:start position:0% +critical in computation. It is a +critical part of computation. + + align:start position:0% +critical part of computation. + + + align:start position:0% +critical part of computation. +Please uh don't go away from this class + + align:start position:0% +Please uh don't go away from this class + + + align:start position:0% +Please uh don't go away from this class +without you know remembering that part. + + align:start position:0% +without you know remembering that part. + + + align:start position:0% +without you know remembering that part. +Know where you are. Test your test your + + align:start position:0% +Know where you are. Test your test your + + + align:start position:0% +Know where you are. Test your test your +calculations. Be confident in them + + align:start position:0% +calculations. Be confident in them + + + align:start position:0% +calculations. Be confident in them +because you validated them. Okay. + + align:start position:0% +because you validated them. Okay. + + + align:start position:0% +because you validated them. Okay. +All right. Too much computation goes on + + align:start position:0% +All right. Too much computation goes on + + + align:start position:0% +All right. Too much computation goes on +that's uh that doesn't have that and and + + align:start position:0% +that's uh that doesn't have that and and + + + align:start position:0% +that's uh that doesn't have that and and +and it's a lot of wasted time. Okay. + + align:start position:0% +and it's a lot of wasted time. Okay. + + + align:start position:0% +and it's a lot of wasted time. Okay. +Computer time but also people time. All + + align:start position:0% +Computer time but also people time. All + + + align:start position:0% +Computer time but also people time. All +right. + + align:start position:0% +right. + + + align:start position:0% +right. +Okay. Now um you know so we can get a + + align:start position:0% +Okay. Now um you know so we can get a + + + align:start position:0% +Okay. Now um you know so we can get a +lot of properties um we can get + + align:start position:0% +lot of properties um we can get + + + align:start position:0% +lot of properties um we can get +properties of uh you know I've talked + + align:start position:0% +properties of uh you know I've talked + + + align:start position:0% +properties of uh you know I've talked +about lots of different properties you + + align:start position:0% +about lots of different properties you + + + align:start position:0% +about lots of different properties you +can get I won't ask you anything on the + + align:start position:0% +can get I won't ask you anything on the + + + align:start position:0% +can get I won't ask you anything on the +test about properties you haven't we + + align:start position:0% +test about properties you haven't we + + + align:start position:0% +test about properties you haven't we +haven't actually really talked about in + + align:start position:0% +haven't actually really talked about in + + + align:start position:0% +haven't actually really talked about in +class okay so um but you can you can + + align:start position:0% +class okay so um but you can you can + + + align:start position:0% +class okay so um but you can you can +calculate a lot of things we just talked + + align:start position:0% +calculate a lot of things we just talked + + + align:start position:0% +calculate a lot of things we just talked +about this the one thing okay did you + + align:start position:0% +about this the one thing okay did you + + + align:start position:0% +about this the one thing okay did you +exit the SCF at the right loop + + align:start position:0% +exit the SCF at the right loop + + + align:start position:0% +exit the SCF at the right loop +don't worry about that because the code + + align:start position:0% +don't worry about that because the code + + + align:start position:0% +don't worry about that because the code +just sort of does that for you was my + + align:start position:0% +just sort of does that for you was my + + + align:start position:0% +just sort of does that for you was my +basis big enough we talked about That + + align:start position:0% +basis big enough we talked about That + + + align:start position:0% +basis big enough we talked about That +right. Convergence for molecules. Was my + + align:start position:0% +right. Convergence for molecules. Was my + + + align:start position:0% +right. Convergence for molecules. Was my +box big enough? Now, why do I have a box + + align:start position:0% +box big enough? Now, why do I have a box + + + align:start position:0% +box big enough? Now, why do I have a box +for molecules? What does that even mean? + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah. Exactly. Exactly. So if I have so + + align:start position:0% +Yeah. Exactly. Exactly. So if I have so + + + align:start position:0% +Yeah. Exactly. Exactly. So if I have so +you know a lot of these codes especially + + align:start position:0% +you know a lot of these codes especially + + + align:start position:0% +you know a lot of these codes especially +plane wave codes were originally + + align:start position:0% +plane wave codes were originally + + + align:start position:0% +plane wave codes were originally +developed for solids but they work fine + + align:start position:0% +developed for solids but they work fine + + + align:start position:0% +developed for solids but they work fine +for molecules. Okay actually siesta is + + align:start position:0% +for molecules. Okay actually siesta is + + + align:start position:0% +for molecules. Okay actually siesta is +not even a plane wave code. It uses a + + align:start position:0% +not even a plane wave code. It uses a + + + align:start position:0% +not even a plane wave code. It uses a +different kind of basis. Okay. It uses a + + align:start position:0% +different kind of basis. Okay. It uses a + + + align:start position:0% +different kind of basis. Okay. It uses a +more Gaussian like localized functions + + align:start position:0% +more Gaussian like localized functions + + + align:start position:0% +more Gaussian like localized functions +basis but it's still a a periodic box. + + align:start position:0% +basis but it's still a a periodic box. + + + align:start position:0% +basis but it's still a a periodic box. +It's based on a periodic box. And so + + align:start position:0% +It's based on a periodic box. And so + + + align:start position:0% +It's based on a periodic box. And so +that means that when you input + + align:start position:0% +that means that when you input + + + align:start position:0% +that means that when you input +right when you input something like an + + align:start position:0% +right when you input something like an + + + align:start position:0% +right when you input something like an +atom if I want to simulate that one atom + + align:start position:0% +atom if I want to simulate that one atom + + + align:start position:0% +atom if I want to simulate that one atom +then uh I need to make sure that I leave + + align:start position:0% +then uh I need to make sure that I leave + + + align:start position:0% +then uh I need to make sure that I leave +enough space + + align:start position:0% +enough space + + + align:start position:0% +enough space +so that it's um not going to feel its + + align:start position:0% +so that it's um not going to feel its + + + align:start position:0% +so that it's um not going to feel its +periodic image in all directions. Right? + + align:start position:0% +periodic image in all directions. Right? + + + align:start position:0% +periodic image in all directions. Right? +one new molecule. Is my box big enough + + align:start position:0% +one new molecule. Is my box big enough + + + align:start position:0% +one new molecule. Is my box big enough +means leaving vacuum between the the + + align:start position:0% +means leaving vacuum between the the + + + align:start position:0% +means leaving vacuum between the the +molecules. + + align:start position:0% + + + + align:start position:0% + +Okay. Um and then we talked about solids + + align:start position:0% +Okay. Um and then we talked about solids + + + align:start position:0% +Okay. Um and then we talked about solids +and that's certainly fair game for the + + align:start position:0% +and that's certainly fair game for the + + + align:start position:0% +and that's certainly fair game for the +quiz even though we haven't had a + + align:start position:0% +quiz even though we haven't had a + + + align:start position:0% +quiz even though we haven't had a +homework problem on the solar cells. + + align:start position:0% +homework problem on the solar cells. + + + align:start position:0% +homework problem on the solar cells. +Certainly, you know, I wouldn't talk + + align:start position:0% +Certainly, you know, I wouldn't talk + + + align:start position:0% +Certainly, you know, I wouldn't talk +about that. I won't talk about solar + + align:start position:0% +about that. I won't talk about solar + + + align:start position:0% +about that. I won't talk about solar +cells on the quiz or I should rephrase + + align:start position:0% +cells on the quiz or I should rephrase + + + align:start position:0% +cells on the quiz or I should rephrase +that. I won't I won't ask you questions + + align:start position:0% +that. I won't I won't ask you questions + + + align:start position:0% +that. I won't I won't ask you questions +that we haven't talked about in lecture + + align:start position:0% + + + + align:start position:0% + +but like I mean you know the band + + align:start position:0% +but like I mean you know the band + + + align:start position:0% +but like I mean you know the band +structure of a solar cell well I mean + + align:start position:0% +structure of a solar cell well I mean + + + align:start position:0% +structure of a solar cell well I mean +you know band structures we've talked + + align:start position:0% +you know band structures we've talked + + + align:start position:0% +you know band structures we've talked +about a lot right so um + + align:start position:0% +about a lot right so um + + + align:start position:0% +about a lot right so um +now the way we built up our + + align:start position:0% +now the way we built up our + + + align:start position:0% +now the way we built up our +our solids part is we said well okay now + + align:start position:0% +our solids part is we said well okay now + + + align:start position:0% +our solids part is we said well okay now +we're talking not about some molecule + + align:start position:0% +we're talking not about some molecule + + + align:start position:0% +we're talking not about some molecule +that can have some shape and then gets + + align:start position:0% +that can have some shape and then gets + + + align:start position:0% +that can have some shape and then gets +repeated heated like this. But we're + + align:start position:0% +repeated heated like this. But we're + + + align:start position:0% +repeated heated like this. But we're +actually talking now about a crystal + + align:start position:0% +actually talking now about a crystal + + + align:start position:0% +actually talking now about a crystal +that goes on forever and ever. And so it + + align:start position:0% +that goes on forever and ever. And so it + + + align:start position:0% +that goes on forever and ever. And so it +needs to have, you know, a kind of + + align:start position:0% +needs to have, you know, a kind of + + + align:start position:0% +needs to have, you know, a kind of +lattice. And + + align:start position:0% +lattice. And + + + align:start position:0% +lattice. And +you know, we talked about how you can + + align:start position:0% +you know, we talked about how you can + + + align:start position:0% +you know, we talked about how you can +define that just like you we defined it + + align:start position:0% +define that just like you we defined it + + + align:start position:0% +define that just like you we defined it +in uh class uh and you seen it in other + + align:start position:0% +in uh class uh and you seen it in other + + + align:start position:0% +in uh class uh and you seen it in other +classes. You define it in a computer. + + align:start position:0% +classes. You define it in a computer. + + + align:start position:0% +classes. You define it in a computer. +Okay. And then we talked about the + + align:start position:0% +Okay. And then we talked about the + + + align:start position:0% +Okay. And then we talked about the +inverse lattice. And I'm not going to go + + align:start position:0% +inverse lattice. And I'm not going to go + + + align:start position:0% +inverse lattice. And I'm not going to go +through this again, but we built this + + align:start position:0% +through this again, but we built this + + + align:start position:0% +through this again, but we built this +up. Why did we build up the inverse + + align:start position:0% +up. Why did we build up the inverse + + + align:start position:0% +up. Why did we build up the inverse +lattice? The understanding of that + + align:start position:0% + + + + align:start position:0% + +where does that come in? Why do you need + + align:start position:0% +where does that come in? Why do you need + + + align:start position:0% +where does that come in? Why do you need +to know about inverse size? Yeah. + + align:start position:0% + + + + align:start position:0% + +Good. Okay. And why does K space matter? + + align:start position:0% + + + + align:start position:0% + +Yeah. So, so that's exactly right. So + + align:start position:0% +Yeah. So, so that's exactly right. So + + + align:start position:0% +Yeah. So, so that's exactly right. So +the inverse lattice is a is the + + align:start position:0% +the inverse lattice is a is the + + + align:start position:0% +the inverse lattice is a is the +reciprocal lattice of our real lattice. + + align:start position:0% +reciprocal lattice of our real lattice. + + + align:start position:0% +reciprocal lattice of our real lattice. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +you know it's really important in + + align:start position:0% +you know it's really important in + + + align:start position:0% +you know it's really important in +crystalallography. So I think a lot of + + align:start position:0% +crystalallography. So I think a lot of + + + align:start position:0% +crystalallography. So I think a lot of +you have seen this. Um and and you can + + align:start position:0% +you have seen this. Um and and you can + + + align:start position:0% +you have seen this. Um and and you can +define by just drawing these + + align:start position:0% +define by just drawing these + + + align:start position:0% +define by just drawing these +perpendiculars to the nearest neighbors. + + align:start position:0% +perpendiculars to the nearest neighbors. + + + align:start position:0% +perpendiculars to the nearest neighbors. +You define the first broan zone which is + + align:start position:0% +You define the first broan zone which is + + + align:start position:0% +You define the first broan zone which is +where + + align:start position:0% +where + + + align:start position:0% +where +the energy levels those precious energy + + align:start position:0% +the energy levels those precious energy + + + align:start position:0% +the energy levels those precious energy +levels of this molecule that I want that + + align:start position:0% +levels of this molecule that I want that + + + align:start position:0% +levels of this molecule that I want that +first bruan zone is is where in the + + align:start position:0% +first bruan zone is is where in the + + + align:start position:0% +first bruan zone is is where in the +inverse lattice see this now becomes + + align:start position:0% +inverse lattice see this now becomes + + + align:start position:0% +inverse lattice see this now becomes +inverse + + align:start position:0% +inverse + + + align:start position:0% +inverse +space + + align:start position:0% +space + + + align:start position:0% +space +also known as + + align:start position:0% +also known as + + + align:start position:0% +also known as +ksp case + + align:start position:0% +ksp case + + + align:start position:0% +ksp case +that becomes a degree of freedom. And so + + align:start position:0% +that becomes a degree of freedom. And so + + + align:start position:0% +that becomes a degree of freedom. And so +that makes these guys move. They can + + align:start position:0% +that makes these guys move. They can + + + align:start position:0% +that makes these guys move. They can +even move and cross one another, + + align:start position:0% +even move and cross one another, + + + align:start position:0% +even move and cross one another, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +And that is the difference between a + + align:start position:0% +And that is the difference between a + + + align:start position:0% +And that is the difference between a +solid computational quantum mechanics on + + align:start position:0% +solid computational quantum mechanics on + + + align:start position:0% +solid computational quantum mechanics on +a solid what you can get out in a + + align:start position:0% +a solid what you can get out in a + + + align:start position:0% +a solid what you can get out in a +molecule. Um and the brewan zone is the + + align:start position:0% +molecule. Um and the brewan zone is the + + + align:start position:0% +molecule. Um and the brewan zone is the +playground of this space that matters. + + align:start position:0% +playground of this space that matters. + + + align:start position:0% +playground of this space that matters. +See, because as we showed from blocks + + align:start position:0% +See, because as we showed from blocks + + + align:start position:0% +See, because as we showed from blocks +theorem, if you go outside of the bruan + + align:start position:0% +theorem, if you go outside of the bruan + + + align:start position:0% +theorem, if you go outside of the bruan +zone, you can just wrap it and get back + + align:start position:0% +zone, you can just wrap it and get back + + + align:start position:0% +zone, you can just wrap it and get back +exactly to where you were. So your wave + + align:start position:0% +exactly to where you were. So your wave + + + align:start position:0% +exactly to where you were. So your wave +function and your energies won't change. + + align:start position:0% +function and your energies won't change. + + + align:start position:0% +function and your energies won't change. +So all that matters is to know and + + align:start position:0% +So all that matters is to know and + + + align:start position:0% +So all that matters is to know and +understand and compute, which is what + + align:start position:0% +understand and compute, which is what + + + align:start position:0% +understand and compute, which is what +the code does, the variation inside this + + align:start position:0% +the code does, the variation inside this + + + align:start position:0% +the code does, the variation inside this +brillan zone. That's why we defined it + + align:start position:0% +brillan zone. That's why we defined it + + + align:start position:0% +brillan zone. That's why we defined it +because we just don't need any other + + align:start position:0% +because we just don't need any other + + + align:start position:0% +because we just don't need any other +zone. Okay. + + align:start position:0% +zone. Okay. + + + align:start position:0% +zone. Okay. +And you know we got here by looking at + + align:start position:0% +And you know we got here by looking at + + + align:start position:0% +And you know we got here by looking at +uh periodic potential and the result of + + align:start position:0% +uh periodic potential and the result of + + + align:start position:0% +uh periodic potential and the result of +solving the Schroinger equation in the + + align:start position:0% +solving the Schroinger equation in the + + + align:start position:0% +solving the Schroinger equation in the +presence of a periodic potential is that + + align:start position:0% +presence of a periodic potential is that + + + align:start position:0% +presence of a periodic potential is that +you get this new constraint on the wave + + align:start position:0% +you get this new constraint on the wave + + + align:start position:0% +you get this new constraint on the wave +function. + + align:start position:0% +function. + + + align:start position:0% +function. +And the key here + + align:start position:0% +And the key here + + + align:start position:0% +And the key here +the key here is that okay so this is + + align:start position:0% +the key here is that okay so this is + + + align:start position:0% +the key here is that okay so this is +just saying you can go one lattice + + align:start position:0% +just saying you can go one lattice + + + align:start position:0% +just saying you can go one lattice +vector away and get back the same thing. + + align:start position:0% +vector away and get back the same thing. + + + align:start position:0% +vector away and get back the same thing. +That's what I just said about only the + + align:start position:0% +That's what I just said about only the + + + align:start position:0% +That's what I just said about only the +buran zone mattering. But the key result + + align:start position:0% +buran zone mattering. But the key result + + + align:start position:0% +buran zone mattering. But the key result +of blocks theorem + + align:start position:0% +of blocks theorem + + + align:start position:0% +of blocks theorem +is not here. Huh? But the key result of + + align:start position:0% +is not here. Huh? But the key result of + + + align:start position:0% +is not here. Huh? But the key result of +blocks theorem is that you have this K + + align:start position:0% +blocks theorem is that you have this K + + + align:start position:0% +blocks theorem is that you have this K +in the first place. The key result is + + align:start position:0% +in the first place. The key result is + + + align:start position:0% +in the first place. The key result is +that you have a new index just like the + + align:start position:0% +that you have a new index just like the + + + align:start position:0% +that you have a new index just like the +quantum numbers came out of the hydrogen + + align:start position:0% +quantum numbers came out of the hydrogen + + + align:start position:0% +quantum numbers came out of the hydrogen +atom. You have a new index that can + + align:start position:0% +atom. You have a new index that can + + + align:start position:0% +atom. You have a new index that can +vary. + + align:start position:0% +vary. + + + align:start position:0% +vary. +And as it varies, it changes your + + align:start position:0% +And as it varies, it changes your + + + align:start position:0% +And as it varies, it changes your +levels. And we spent some time talking + + align:start position:0% +levels. And we spent some time talking + + + align:start position:0% +levels. And we spent some time talking +about this. So, please let me know if + + align:start position:0% +about this. So, please let me know if + + + align:start position:0% +about this. So, please let me know if +you have any questions about this. + + align:start position:0% +you have any questions about this. + + + align:start position:0% +you have any questions about this. +I just talked right into the mic. + + align:start position:0% +I just talked right into the mic. + + + align:start position:0% +I just talked right into the mic. +Let me know if you have any Oh, sorry. + + align:start position:0% +Let me know if you have any Oh, sorry. + + + align:start position:0% +Let me know if you have any Oh, sorry. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +any uh So, does everybody understand + + align:start position:0% +any uh So, does everybody understand + + + align:start position:0% +any uh So, does everybody understand +that + + align:start position:0% +that + + + align:start position:0% +that +by putting + + align:start position:0% +by putting + + + align:start position:0% +by putting +by mapping quantum mechanics and all of + + align:start position:0% +by mapping quantum mechanics and all of + + + align:start position:0% +by mapping quantum mechanics and all of +our machinery Schroinger equation + + align:start position:0% +our machinery Schroinger equation + + + align:start position:0% +our machinery Schroinger equation +approximations to it? But remember, HSI + + align:start position:0% +approximations to it? But remember, HSI + + + align:start position:0% +approximations to it? But remember, HSI +equals EI. H has V and by having V be + + align:start position:0% +equals EI. H has V and by having V be + + + align:start position:0% +equals EI. H has V and by having V be +the same everywhere in space we got this + + align:start position:0% +the same everywhere in space we got this + + + align:start position:0% +the same everywhere in space we got this +new degree of freedom this new thing + + align:start position:0% +new degree of freedom this new thing + + + align:start position:0% +new degree of freedom this new thing +that's critical okay and this new thing + + align:start position:0% +that's critical okay and this new thing + + + align:start position:0% +that's critical okay and this new thing +is what is what makes a band structure + + align:start position:0% +is what is what makes a band structure + + + align:start position:0% +is what is what makes a band structure +so if I you know so if I showed you a + + align:start position:0% +so if I you know so if I showed you a + + + align:start position:0% +so if I you know so if I showed you a +band structure like this + + align:start position:0% + + + + align:start position:0% + +what am I simulating + + align:start position:0% + + + + align:start position:0% + +What is that? Forget these other ones. + + align:start position:0% +What is that? Forget these other ones. + + + align:start position:0% +What is that? Forget these other ones. +Just look at those. + + align:start position:0% + + + + align:start position:0% + +Yeah, it's a non-periodic system, + + align:start position:0% +Yeah, it's a non-periodic system, + + + align:start position:0% +Yeah, it's a non-periodic system, +right? If it's if the bands are flat, + + align:start position:0% +right? If it's if the bands are flat, + + + align:start position:0% +right? If it's if the bands are flat, +you don't have this variation in Kspace. + + align:start position:0% +you don't have this variation in Kspace. + + + align:start position:0% +you don't have this variation in Kspace. +And if you don't have the variation in + + align:start position:0% +And if you don't have the variation in + + + align:start position:0% +And if you don't have the variation in +kspace, well, at least to within what + + align:start position:0% +kspace, well, at least to within what + + + align:start position:0% +kspace, well, at least to within what +the system can feel, it's not a crystal. + + align:start position:0% +the system can feel, it's not a crystal. + + + align:start position:0% +the system can feel, it's not a crystal. +It's not a periodic periodically + + align:start position:0% +It's not a periodic periodically + + + align:start position:0% +It's not a periodic periodically +repeating potential. It may be, right? + + align:start position:0% +repeating potential. It may be, right? + + + align:start position:0% +repeating potential. It may be, right? +Or it may be really close like what if + + align:start position:0% +Or it may be really close like what if + + + align:start position:0% +Or it may be really close like what if +you had a molecular crystal, right, + + align:start position:0% +you had a molecular crystal, right, + + + align:start position:0% +you had a molecular crystal, right, +which exists many there are many + + align:start position:0% +which exists many there are many + + + align:start position:0% +which exists many there are many +molecular crystals, but they're really + + align:start position:0% +molecular crystals, but they're really + + + align:start position:0% +molecular crystals, but they're really +far spaced apart. These molecules are + + align:start position:0% +far spaced apart. These molecules are + + + align:start position:0% +far spaced apart. These molecules are +weakly interacting. Well, you might get + + align:start position:0% +weakly interacting. Well, you might get + + + align:start position:0% +weakly interacting. Well, you might get +then something, you know, you might just + + align:start position:0% +then something, you know, you might just + + + align:start position:0% +then something, you know, you might just +start to see this, and we played with + + align:start position:0% +start to see this, and we played with + + + align:start position:0% +start to see this, and we played with +this in the computer. You might just + + align:start position:0% +this in the computer. You might just + + + align:start position:0% +this in the computer. You might just +start to see some little wiggles, + + align:start position:0% +start to see some little wiggles, + + + align:start position:0% +start to see some little wiggles, +feeling that effect of the variation in + + align:start position:0% +feeling that effect of the variation in + + + align:start position:0% +feeling that effect of the variation in +case, but you won't see very much, + + align:start position:0% +case, but you won't see very much, + + + align:start position:0% +case, but you won't see very much, +right? And then as the interactions or + + align:start position:0% +right? And then as the interactions or + + + align:start position:0% +right? And then as the interactions or +as the potential that's periodic gets + + align:start position:0% +as the potential that's periodic gets + + + align:start position:0% +as the potential that's periodic gets +stronger, well, then this variation can + + align:start position:0% +stronger, well, then this variation can + + + align:start position:0% +stronger, well, then this variation can +get very high, right? + + align:start position:0% +get very high, right? + + + align:start position:0% +get very high, right? +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +any questions about any of that. + + align:start position:0% +any questions about any of that. + + + align:start position:0% +any questions about any of that. +So that's that's kind of the key the key + + align:start position:0% +So that's that's kind of the key the key + + + align:start position:0% +So that's that's kind of the key the key +point there. And we talked about the + + align:start position:0% +point there. And we talked about the + + + align:start position:0% +point there. And we talked about the +kinds of things you can get. And we also + + align:start position:0% +kinds of things you can get. And we also + + + align:start position:0% +kinds of things you can get. And we also +talked about how + + align:start position:0% +talked about how + + + align:start position:0% +talked about how +what so this is density functional + + align:start position:0% +what so this is density functional + + + align:start position:0% +what so this is density functional +theory. We talked about how when you + + align:start position:0% +theory. We talked about how when you + + + align:start position:0% +theory. We talked about how when you +solve for the band structure, you first + + align:start position:0% +solve for the band structure, you first + + + align:start position:0% +solve for the band structure, you first +converge the density. That's a separate + + align:start position:0% +converge the density. That's a separate + + + align:start position:0% +converge the density. That's a separate +calculation. + + align:start position:0% + + + + align:start position:0% + +And then what am I doing here? How do I + + align:start position:0% +And then what am I doing here? How do I + + + align:start position:0% +And then what am I doing here? How do I +get this? I mean the the third point is + + align:start position:0% +get this? I mean the the third point is + + + align:start position:0% +get this? I mean the the third point is +sort of silly. You plot but point two. + + align:start position:0% +sort of silly. You plot but point two. + + + align:start position:0% +sort of silly. You plot but point two. +What am I doing? Somebody explain point + + align:start position:0% +What am I doing? Somebody explain point + + + align:start position:0% +What am I doing? Somebody explain point +2. + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah. you well you find yeah you find + + align:start position:0% +Yeah. you well you find yeah you find + + + align:start position:0% +Yeah. you well you find yeah you find +the band gaps you find the energy levels + + align:start position:0% +the band gaps you find the energy levels + + + align:start position:0% +the band gaps you find the energy levels +at each point now but as we said as you + + align:start position:0% +at each point now but as we said as you + + + align:start position:0% +at each point now but as we said as you +just said + + align:start position:0% +just said + + + align:start position:0% +just said +you're doing this for lines in the buran + + align:start position:0% +you're doing this for lines in the buran + + + align:start position:0% +you're doing this for lines in the buran +zone how do you choose which lines + + align:start position:0% +zone how do you choose which lines + + + align:start position:0% +zone how do you choose which lines +my choice but I need to choose + + align:start position:0% + + + + align:start position:0% + +Sam + + align:start position:0% +Sam + + + align:start position:0% +Sam +highm + + align:start position:0% +highm + + + align:start position:0% +highm +yeah it's the high symmetry parts Right. + + align:start position:0% +yeah it's the high symmetry parts Right. + + + align:start position:0% +yeah it's the high symmetry parts Right. +We talked about that + + align:start position:0% +We talked about that + + + align:start position:0% +We talked about that +because why + + align:start position:0% + + + + align:start position:0% + +nature likes symmetry? + + align:start position:0% +nature likes symmetry? + + + align:start position:0% +nature likes symmetry? +Well, that's a good answer. This is + + align:start position:0% +Well, that's a good answer. This is + + + align:start position:0% +Well, that's a good answer. This is +always a good answer. Nature does like + + align:start position:0% +always a good answer. Nature does like + + + align:start position:0% +always a good answer. Nature does like +symmetry. It's a beautiful thing. + + align:start position:0% +symmetry. It's a beautiful thing. + + + align:start position:0% +symmetry. It's a beautiful thing. +But does that but is that really why + + align:start position:0% +But does that but is that really why + + + align:start position:0% +But does that but is that really why +that's what I do for my band structure? + + align:start position:0% +that's what I do for my band structure? + + + align:start position:0% +that's what I do for my band structure? +What does that mean? + + align:start position:0% + + + + align:start position:0% + +pretty much that's where the variation + + align:start position:0% +pretty much that's where the variation + + + align:start position:0% +pretty much that's where the variation +that could happen in the energy levels + + align:start position:0% +that could happen in the energy levels + + + align:start position:0% +that could happen in the energy levels +is going to happen and that's what you + + align:start position:0% +is going to happen and that's what you + + + align:start position:0% +is going to happen and that's what you +want to capture. Right? So a band + + align:start position:0% +want to capture. Right? So a band + + + align:start position:0% +want to capture. Right? So a band +structure is a is a simple + + align:start position:0% +structure is a is a simple + + + align:start position:0% +structure is a is a simple +two-dimensional way of of cruising + + align:start position:0% +two-dimensional way of of cruising + + + align:start position:0% +two-dimensional way of of cruising +through this kind of complex + + align:start position:0% +through this kind of complex + + + align:start position:0% +through this kind of complex +three-dimensional bruan zone where + + align:start position:0% +three-dimensional bruan zone where + + + align:start position:0% +three-dimensional bruan zone where +things are varying any point I go. But + + align:start position:0% +things are varying any point I go. But + + + align:start position:0% +things are varying any point I go. But +if I go just along the high symmetry + + align:start position:0% +if I go just along the high symmetry + + + align:start position:0% +if I go just along the high symmetry +points, then I get the variation that's + + align:start position:0% +points, then I get the variation that's + + + align:start position:0% +points, then I get the variation that's +usually most important. Okay. Okay. You + + align:start position:0% +usually most important. Okay. Okay. You + + + align:start position:0% +usually most important. Okay. Okay. You +know, we talked about how you fill these + + align:start position:0% +know, we talked about how you fill these + + + align:start position:0% +know, we talked about how you fill these +up to the firmy energy. Um, is the firmy + + align:start position:0% +up to the firmy energy. Um, is the firmy + + + align:start position:0% +up to the firmy energy. Um, is the firmy +energy always at zero? + + align:start position:0% + + + + align:start position:0% + +Yeah. So if I if I didn't tell you where + + align:start position:0% +Yeah. So if I if I didn't tell you where + + + align:start position:0% +Yeah. So if I if I didn't tell you where +the firmy energy is and I asked you to + + align:start position:0% +the firmy energy is and I asked you to + + + align:start position:0% +the firmy energy is and I asked you to +tell me if it's a metal or an insulator, + + align:start position:0% +tell me if it's a metal or an insulator, + + + align:start position:0% +tell me if it's a metal or an insulator, +could you + + align:start position:0% +could you + + + align:start position:0% +could you +would it even be possible? + + align:start position:0% + + + + align:start position:0% + +Why why or why not? + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Yeah. And so if I leave that piece of + + align:start position:0% +Yeah. And so if I leave that piece of + + + align:start position:0% +Yeah. And so if I leave that piece of +information out, which I did last year, + + align:start position:0% +information out, which I did last year, + + + align:start position:0% +information out, which I did last year, +then and I give you a a band structure + + align:start position:0% +then and I give you a a band structure + + + align:start position:0% +then and I give you a a band structure +that you know looks like this. + + align:start position:0% + + + + align:start position:0% + +And then let's say you have bands up + + align:start position:0% +And then let's say you have bands up + + + align:start position:0% +And then let's say you have bands up +here. Well, everybody is really excited + + align:start position:0% +here. Well, everybody is really excited + + + align:start position:0% +here. Well, everybody is really excited +to call this an insulator. I'd be I'm + + align:start position:0% +to call this an insulator. I'd be I'm + + + align:start position:0% +to call this an insulator. I'd be I'm +excited to do it. I can hardly hold + + align:start position:0% +excited to do it. I can hardly hold + + + align:start position:0% +excited to do it. I can hardly hold +back. + + align:start position:0% +back. + + + align:start position:0% +back. +This is an insulator. But hang on. If I + + align:start position:0% +This is an insulator. But hang on. If I + + + align:start position:0% +This is an insulator. But hang on. If I +didn't tell you where the firmy energy + + align:start position:0% +didn't tell you where the firmy energy + + + align:start position:0% +didn't tell you where the firmy energy +is, what if the firmy energy is here? + + align:start position:0% +is, what if the firmy energy is here? + + + align:start position:0% +is, what if the firmy energy is here? +You got to have all the information to + + align:start position:0% +You got to have all the information to + + + align:start position:0% +You got to have all the information to +answer the questions, right? Um, so know + + align:start position:0% +answer the questions, right? Um, so know + + + align:start position:0% +answer the questions, right? Um, so know +what information you need if you're + + align:start position:0% +what information you need if you're + + + align:start position:0% +what information you need if you're +asked a question about a metal + + align:start position:0% +asked a question about a metal + + + align:start position:0% +asked a question about a metal +insulator, right? And you know, yeah, + + align:start position:0% +insulator, right? And you know, yeah, + + + align:start position:0% +insulator, right? And you know, yeah, +typically + + align:start position:0% +typically + + + align:start position:0% +typically +at zero, + + align:start position:0% +at zero, + + + align:start position:0% +at zero, +it's only because + + align:start position:0% +it's only because + + + align:start position:0% +it's only because +it's sort of uh there's there's no good + + align:start position:0% +it's sort of uh there's there's no good + + + align:start position:0% +it's sort of uh there's there's no good +reason except that it's convenient. + + align:start position:0% +reason except that it's convenient. + + + align:start position:0% +reason except that it's convenient. +you know. + + align:start position:0% +you know. + + + align:start position:0% +you know. +Okay. So, usually it's just like + + align:start position:0% +Okay. So, usually it's just like + + + align:start position:0% +Okay. So, usually it's just like +it's just nice to shift them so they're + + align:start position:0% +it's just nice to shift them so they're + + + align:start position:0% +it's just nice to shift them so they're +always at the same place. + + align:start position:0% +always at the same place. + + + align:start position:0% +always at the same place. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Right. And then we can compare things + + align:start position:0% +Right. And then we can compare things + + + align:start position:0% +Right. And then we can compare things +more easily. Yeah. + + align:start position:0% +more easily. Yeah. + + + align:start position:0% +more easily. Yeah. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +the um why is this definitely going to + + align:start position:0% +the um why is this definitely going to + + + align:start position:0% +the um why is this definitely going to +be a metal if I have an odd number of + + align:start position:0% +be a metal if I have an odd number of + + + align:start position:0% +be a metal if I have an odd number of +electrons. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +there's a little discussion there. I + + align:start position:0% +there's a little discussion there. I + + + align:start position:0% +there's a little discussion there. I +want to know what you guys are saying. + + align:start position:0% +want to know what you guys are saying. + + + align:start position:0% +want to know what you guys are saying. +Confirming. + + align:start position:0% +Confirming. + + + align:start position:0% +Confirming. +Confirming. + + align:start position:0% +Confirming. + + + align:start position:0% +Confirming. +You're validating. I love it. Using the + + align:start position:0% +You're validating. I love it. Using the + + + align:start position:0% +You're validating. I love it. Using the +group uh consensus. + + align:start position:0% +group uh consensus. + + + align:start position:0% +group uh consensus. +Yeah, crowd sourcing is very powerful. + + align:start position:0% +Yeah, crowd sourcing is very powerful. + + + align:start position:0% +Yeah, crowd sourcing is very powerful. +Anyway, don't use it for computing. + + align:start position:0% + + + + align:start position:0% + +Why? That's exactly right. Why? + + align:start position:0% + + + + align:start position:0% + +That's it. Do everybody get that? + + align:start position:0% +That's it. Do everybody get that? + + + align:start position:0% +That's it. Do everybody get that? +Firmeni energy is the energy that you + + align:start position:0% +Firmeni energy is the energy that you + + + align:start position:0% +Firmeni energy is the energy that you +fill the electrons to. So if the if you + + align:start position:0% +fill the electrons to. So if the if you + + + align:start position:0% +fill the electrons to. So if the if you +have an odd number of electrons, well, + + align:start position:0% +have an odd number of electrons, well, + + + align:start position:0% +have an odd number of electrons, well, +how many electrons go in each one of + + align:start position:0% +how many electrons go in each one of + + + align:start position:0% +how many electrons go in each one of +these bands? + + align:start position:0% +these bands? + + + align:start position:0% +these bands? +Two. So if I have an odd number of + + align:start position:0% +Two. So if I have an odd number of + + + align:start position:0% +Two. So if I have an odd number of +electrons, one of them is only going to + + align:start position:0% +electrons, one of them is only going to + + + align:start position:0% +electrons, one of them is only going to +be half filled. That means my firmy + + align:start position:0% +be half filled. That means my firmy + + + align:start position:0% +be half filled. That means my firmy +energy has to cut it. + + align:start position:0% +energy has to cut it. + + + align:start position:0% +energy has to cut it. +It's got to cut it somewhere, which + + align:start position:0% +It's got to cut it somewhere, which + + + align:start position:0% +It's got to cut it somewhere, which +means I have a band crossing the firmy + + align:start position:0% +means I have a band crossing the firmy + + + align:start position:0% +means I have a band crossing the firmy +energy, which means it's a metal, right? + + align:start position:0% +energy, which means it's a metal, right? + + + align:start position:0% +energy, which means it's a metal, right? +Has to be. + + align:start position:0% +Has to be. + + + align:start position:0% +Has to be. +So you you know I mean you could think + + align:start position:0% +So you you know I mean you could think + + + align:start position:0% +So you you know I mean you could think +about the same for an atom except that + + align:start position:0% +about the same for an atom except that + + + align:start position:0% +about the same for an atom except that +atoms aren't metals. But most atoms have + + align:start position:0% +atoms aren't metals. But most atoms have + + + align:start position:0% +atoms aren't metals. But most atoms have +that case. They have half or partially + + align:start position:0% +that case. They have half or partially + + + align:start position:0% +that case. They have half or partially +filled levels, right? you don't fill all + + align:start position:0% +filled levels, right? you don't fill all + + + align:start position:0% +filled levels, right? you don't fill all +the p electrons in carbon. Um but we + + align:start position:0% +the p electrons in carbon. Um but we + + + align:start position:0% +the p electrons in carbon. Um but we +don't think of the carbon atom as a + + align:start position:0% +don't think of the carbon atom as a + + + align:start position:0% +don't think of the carbon atom as a +metal because atoms and molecules don't + + align:start position:0% +metal because atoms and molecules don't + + + align:start position:0% +metal because atoms and molecules don't +really have this kind of behavior, + + align:start position:0% +really have this kind of behavior, + + + align:start position:0% +really have this kind of behavior, +right? Okay. But it's the same idea. + + align:start position:0% +right? Okay. But it's the same idea. + + + align:start position:0% +right? Okay. But it's the same idea. +You're partially filling levels. + + align:start position:0% +You're partially filling levels. + + + align:start position:0% +You're partially filling levels. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +We talked about um how how are we + + align:start position:0% +We talked about um how how are we + + + align:start position:0% +We talked about um how how are we +feeling about direct versus indirect + + align:start position:0% +feeling about direct versus indirect + + + align:start position:0% +feeling about direct versus indirect +gaps? + + align:start position:0% +gaps? + + + align:start position:0% +gaps? +Good. Okay. Talked about that. Yeah, + + align:start position:0% +Good. Okay. Talked about that. Yeah, + + + align:start position:0% +Good. Okay. Talked about that. Yeah, +liking that. That could be a good + + align:start position:0% +liking that. That could be a good + + + align:start position:0% +liking that. That could be a good +question. And we talked about other + + align:start position:0% +question. And we talked about other + + + align:start position:0% +question. And we talked about other +things um + + align:start position:0% +things um + + + align:start position:0% +things um +uh that you can calculate vibrational + + align:start position:0% +uh that you can calculate vibrational + + + align:start position:0% +uh that you can calculate vibrational +properties. Um we did talk about + + align:start position:0% +properties. Um we did talk about + + + align:start position:0% +properties. Um we did talk about +magnetization, + + align:start position:0% +magnetization, + + + align:start position:0% +magnetization, +right? Now, this is not uh sorry, this + + align:start position:0% +right? Now, this is not uh sorry, this + + + align:start position:0% +right? Now, this is not uh sorry, this +is actually from a um + + align:start position:0% +is actually from a um + + + align:start position:0% +is actually from a um +a different code we used to use. Um so + + align:start position:0% +a different code we used to use. Um so + + + align:start position:0% +a different code we used to use. Um so +just ignore this. We used to use a + + align:start position:0% +just ignore this. We used to use a + + + align:start position:0% +just ignore this. We used to use a +different code than Siesta, but um and + + align:start position:0% +different code than Siesta, but um and + + + align:start position:0% +different code than Siesta, but um and +and that was the input for it. But um + + align:start position:0% +and that was the input for it. But um + + + align:start position:0% +and that was the input for it. But um +but you know and this is showing that + + align:start position:0% +but you know and this is showing that + + + align:start position:0% +but you know and this is showing that +you know you can do uh calculations of + + align:start position:0% +you know you can do uh calculations of + + + align:start position:0% +you know you can do uh calculations of +say different phases of a magnetic + + align:start position:0% +say different phases of a magnetic + + + align:start position:0% +say different phases of a magnetic +material like iron. + + align:start position:0% +material like iron. + + + align:start position:0% +material like iron. +And how would I calculate the + + align:start position:0% +And how would I calculate the + + + align:start position:0% +And how would I calculate the +magnetization of those materials? + + align:start position:0% +magnetization of those materials? + + + align:start position:0% +magnetization of those materials? +This was in uh lecture something + + align:start position:0% + + + + align:start position:0% + +number of days ago. Yeah. + + align:start position:0% +number of days ago. Yeah. + + + align:start position:0% +number of days ago. Yeah. +magnetic field. + + align:start position:0% +magnetic field. + + + align:start position:0% +magnetic field. +You absolutely could and that would be + + align:start position:0% +You absolutely could and that would be + + + align:start position:0% +You absolutely could and that would be +really hard there. But you could do that + + align:start position:0% +really hard there. But you could do that + + + align:start position:0% +really hard there. But you could do that +actually and we do do that but um that's + + align:start position:0% +actually and we do do that but um that's + + + align:start position:0% +actually and we do do that but um that's +a hard calculation. + + align:start position:0% + + + + align:start position:0% + +What is the magnetization of a material? + + align:start position:0% +What is the magnetization of a material? + + + align:start position:0% +What is the magnetization of a material? +What's it due to anyway? + + align:start position:0% +What's it due to anyway? + + + align:start position:0% +What's it due to anyway? +What part of the material is it due to? + + align:start position:0% +What part of the material is it due to? + + + align:start position:0% +What part of the material is it due to? +Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah. Yeah. It's due to electrons. It's + + align:start position:0% +Yeah. Yeah. It's due to electrons. It's + + + align:start position:0% +Yeah. Yeah. It's due to electrons. It's +due to the spin of the electrons, right? + + align:start position:0% +due to the spin of the electrons, right? + + + align:start position:0% +due to the spin of the electrons, right? +And that's what gave us the Stern + + align:start position:0% +And that's what gave us the Stern + + + align:start position:0% +And that's what gave us the Stern +Gorlock experiments. It was the + + align:start position:0% +Gorlock experiments. It was the + + + align:start position:0% +Gorlock experiments. It was the +magnetization + + align:start position:0% +magnetization + + + align:start position:0% +magnetization +possible of the spins of the electrons, + + align:start position:0% +possible of the spins of the electrons, + + + align:start position:0% +possible of the spins of the electrons, +right? It was the the fact that a + + align:start position:0% +right? It was the the fact that a + + + align:start position:0% +right? It was the the fact that a +magnetic field could exert a force on + + align:start position:0% +magnetic field could exert a force on + + + align:start position:0% +magnetic field could exert a force on +those. + + align:start position:0% +those. + + + align:start position:0% +those. +Now we said that in your material + + align:start position:0% + + + + align:start position:0% + +you have you know spin up electrons and + + align:start position:0% +you have you know spin up electrons and + + + align:start position:0% +you have you know spin up electrons and +spin down electrons the precious things + + align:start position:0% +spin down electrons the precious things + + + align:start position:0% +spin down electrons the precious things +that we're computing this whole second + + align:start position:0% +that we're computing this whole second + + + align:start position:0% +that we're computing this whole second +half right and you fill those up and you + + align:start position:0% +half right and you fill those up and you + + + align:start position:0% +half right and you fill those up and you +fill them up according to the pi + + align:start position:0% +fill them up according to the pi + + + align:start position:0% +fill them up according to the pi +exclusion principle you fill the levels + + align:start position:0% +exclusion principle you fill the levels + + + align:start position:0% +exclusion principle you fill the levels +up with these electrons right + + align:start position:0% +up with these electrons right + + + align:start position:0% +up with these electrons right +um + + align:start position:0% +um + + + align:start position:0% +um +but when you get to a solid or even in + + align:start position:0% +but when you get to a solid or even in + + + align:start position:0% +but when you get to a solid or even in +atoms um you don't always necessarily + + align:start position:0% +atoms um you don't always necessarily + + + align:start position:0% +atoms um you don't always necessarily +have the same uh up and down electrons. + + align:start position:0% +have the same uh up and down electrons. + + + align:start position:0% +have the same uh up and down electrons. +You can have differences. Okay? And when + + align:start position:0% +You can have differences. Okay? And when + + + align:start position:0% +You can have differences. Okay? And when +you have differences between them, you + + align:start position:0% +you have differences between them, you + + + align:start position:0% +you have differences between them, you +can have a net magnetic moment. + + align:start position:0% +can have a net magnetic moment. + + + align:start position:0% +can have a net magnetic moment. +And we talked about that + + align:start position:0% +And we talked about that + + + align:start position:0% +And we talked about that +before. And then we say, well, okay, if + + align:start position:0% +before. And then we say, well, okay, if + + + align:start position:0% +before. And then we say, well, okay, if +I if I had an atom, then you can have a + + align:start position:0% +I if I had an atom, then you can have a + + + align:start position:0% +I if I had an atom, then you can have a +net magnetic moment just count the + + align:start position:0% +net magnetic moment just count the + + + align:start position:0% +net magnetic moment just count the +number of up electrons minus the number + + align:start position:0% +number of up electrons minus the number + + + align:start position:0% +number of up electrons minus the number +of down electrons. But in a solid + + align:start position:0% +of down electrons. But in a solid + + + align:start position:0% +of down electrons. But in a solid +you in in a crystal you don't you know + + align:start position:0% +you in in a crystal you don't you know + + + align:start position:0% +you in in a crystal you don't you know +you you now have these electrons in + + align:start position:0% +you you now have these electrons in + + + align:start position:0% +you you now have these electrons in +these in these bands you need to use + + align:start position:0% +these in these bands you need to use + + + align:start position:0% +these in these bands you need to use +something else and that's where you need + + align:start position:0% +something else and that's where you need + + + align:start position:0% +something else and that's where you need +to use the density of states + + align:start position:0% +to use the density of states + + + align:start position:0% +to use the density of states +and so + + align:start position:0% +and so + + + align:start position:0% +and so +right and so if you have sort of the + + align:start position:0% +right and so if you have sort of the + + + align:start position:0% +right and so if you have sort of the +density of states + + align:start position:0% +density of states + + + align:start position:0% +density of states +now remember + + align:start position:0% +now remember + + + align:start position:0% +now remember +versus say energy and this is something + + align:start position:0% +versus say energy and this is something + + + align:start position:0% +versus say energy and this is something +you're all now familiar with from the + + align:start position:0% +you're all now familiar with from the + + + align:start position:0% +you're all now familiar with from the +the homework but we talked about this + + align:start position:0% +the homework but we talked about this + + + align:start position:0% +the homework but we talked about this +also how it relates to magnetism + + align:start position:0% +also how it relates to magnetism + + + align:start position:0% +also how it relates to magnetism +Right? And that in the Siesta tool, you + + align:start position:0% +Right? And that in the Siesta tool, you + + + align:start position:0% +Right? And that in the Siesta tool, you +could plot, for example, the spin up + + align:start position:0% +could plot, for example, the spin up + + + align:start position:0% +could plot, for example, the spin up +electrons. So let's say these are the + + align:start position:0% +electrons. So let's say these are the + + + align:start position:0% +electrons. So let's say these are the +spin up electrons. + + align:start position:0% +spin up electrons. + + + align:start position:0% +spin up electrons. +And then you could plot the spin down + + align:start position:0% +And then you could plot the spin down + + + align:start position:0% +And then you could plot the spin down +electrons. + + align:start position:0% +electrons. + + + align:start position:0% +electrons. +And that's a little hard to see because + + align:start position:0% +And that's a little hard to see because + + + align:start position:0% +And that's a little hard to see because +there's three curves with one color. But + + align:start position:0% +there's three curves with one color. But + + + align:start position:0% +there's three curves with one color. But +the main point is that the up electrons + + align:start position:0% +the main point is that the up electrons + + + align:start position:0% +the main point is that the up electrons +and down electrons could be very + + align:start position:0% +and down electrons could be very + + + align:start position:0% +and down electrons could be very +different in in where they are in + + align:start position:0% +different in in where they are in + + + align:start position:0% +different in in where they are in +energy, which translates into what where + + align:start position:0% +energy, which translates into what where + + + align:start position:0% +energy, which translates into what where +the peaks are in the doss. + + align:start position:0% + + + + align:start position:0% + +Now + + align:start position:0% +Now + + + align:start position:0% +Now +you see what matters though + + align:start position:0% +you see what matters though + + + align:start position:0% +you see what matters though +is is not the difference across the + + align:start position:0% +is is not the difference across the + + + align:start position:0% +is is not the difference across the +whole DOSs curve. What's going to + + align:start position:0% +whole DOSs curve. What's going to + + + align:start position:0% +whole DOSs curve. What's going to +matter? + + align:start position:0% + + + + align:start position:0% + +It's not the whole DOSs that matters. + + align:start position:0% +It's not the whole DOSs that matters. + + + align:start position:0% +It's not the whole DOSs that matters. +It's only part of it. Which part? + + align:start position:0% +It's only part of it. Which part? + + + align:start position:0% +It's only part of it. Which part? +Yeah, it's the part up until + + align:start position:0% + + + + align:start position:0% + +up until the firmy level. What are the + + align:start position:0% +up until the firmy level. What are the + + + align:start position:0% +up until the firmy level. What are the +differences in where I filled the + + align:start position:0% +differences in where I filled the + + + align:start position:0% +differences in where I filled the +electrons between the ones that would be + + align:start position:0% +electrons between the ones that would be + + + align:start position:0% +electrons between the ones that would be +up and the ones that would be down? + + align:start position:0% +up and the ones that would be down? + + + align:start position:0% +up and the ones that would be down? +Right? So, um, now and that got us to + + align:start position:0% +Right? So, um, now and that got us to + + + align:start position:0% +Right? So, um, now and that got us to +talking about this spin polarized thing + + align:start position:0% +talking about this spin polarized thing + + + align:start position:0% +talking about this spin polarized thing +that we talked about last time. Okay. + + align:start position:0% +that we talked about last time. Okay. + + + align:start position:0% +that we talked about last time. Okay. +What's so and and that's a little button + + align:start position:0% +What's so and and that's a little button + + + align:start position:0% +What's so and and that's a little button +on your on your simulation tool that you + + align:start position:0% +on your on your simulation tool that you + + + align:start position:0% +on your on your simulation tool that you +can check or uncheck. So if something + + align:start position:0% +can check or uncheck. So if something + + + align:start position:0% +can check or uncheck. So if something +has spin + + align:start position:0% +has spin + + + align:start position:0% +has spin +polarized, + + align:start position:0% +polarized, + + + align:start position:0% +polarized, +it allows the up and down electrons to + + align:start position:0% +it allows the up and down electrons to + + + align:start position:0% +it allows the up and down electrons to +be different to have different energies. + + align:start position:0% +be different to have different energies. + + + align:start position:0% +be different to have different energies. +So you know I just I just told you that + + align:start position:0% +So you know I just I just told you that + + + align:start position:0% +So you know I just I just told you that +that difference is what gives you + + align:start position:0% +that difference is what gives you + + + align:start position:0% +that difference is what gives you +magnetization. So if you don't allow + + align:start position:0% +magnetization. So if you don't allow + + + align:start position:0% +magnetization. So if you don't allow +it to be spin polarized, + + align:start position:0% +it to be spin polarized, + + + align:start position:0% +it to be spin polarized, +then you won't get magnetization, right? + + align:start position:0% +then you won't get magnetization, right? + + + align:start position:0% +then you won't get magnetization, right? +Yeah. + + align:start position:0% + + + + align:start position:0% + +Ah very good question and + + align:start position:0% +Ah very good question and + + + align:start position:0% +Ah very good question and +um + + align:start position:0% + + + + align:start position:0% + +that is exactly what spin polarized + + align:start position:0% +that is exactly what spin polarized + + + align:start position:0% +that is exactly what spin polarized +does. You see, so this is what you're + + align:start position:0% +does. You see, so this is what you're + + + align:start position:0% +does. You see, so this is what you're +talking about. You're saying, well, + + align:start position:0% +talking about. You're saying, well, + + + align:start position:0% +talking about. You're saying, well, +aren't these don't these aren't this + + align:start position:0% +aren't these don't these aren't this + + + align:start position:0% +aren't these don't these aren't this +isn't this just in one level, right? But + + align:start position:0% +isn't this just in one level, right? But + + + align:start position:0% +isn't this just in one level, right? But +it actually, it turns out that that's + + align:start position:0% +it actually, it turns out that that's + + + align:start position:0% +it actually, it turns out that that's +what's called um a restricted + + align:start position:0% +what's called um a restricted + + + align:start position:0% +what's called um a restricted +uh uh you can say restricted closed + + align:start position:0% +uh uh you can say restricted closed + + + align:start position:0% +uh uh you can say restricted closed +shell or restricted open shell formalism + + align:start position:0% +shell or restricted open shell formalism + + + align:start position:0% +shell or restricted open shell formalism +that is valid for many many materials + + align:start position:0% +that is valid for many many materials + + + align:start position:0% +that is valid for many many materials +and molecules where in fact there's no + + align:start position:0% +and molecules where in fact there's no + + + align:start position:0% +and molecules where in fact there's no +difference. But in reality, in reality, + + align:start position:0% +difference. But in reality, in reality, + + + align:start position:0% +difference. But in reality, in reality, +even when it's restricted, you still + + align:start position:0% +even when it's restricted, you still + + + align:start position:0% +even when it's restricted, you still +should write these as a sort of one spin + + align:start position:0% +should write these as a sort of one spin + + + align:start position:0% +should write these as a sort of one spin +channel and another. You could call it + + align:start position:0% +channel and another. You could call it + + + align:start position:0% +channel and another. You could call it +like alpha is spin up and beta spin + + align:start position:0% +like alpha is spin up and beta spin + + + align:start position:0% +like alpha is spin up and beta spin +down. And each one of those has its own + + align:start position:0% +down. And each one of those has its own + + + align:start position:0% +down. And each one of those has its own +set of orbitals and wave functions. + + align:start position:0% +set of orbitals and wave functions. + + + align:start position:0% +set of orbitals and wave functions. +Okay? So in reality, that's what that's + + align:start position:0% +Okay? So in reality, that's what that's + + + align:start position:0% +Okay? So in reality, that's what that's +what you solve for. Now in many + + align:start position:0% +what you solve for. Now in many + + + align:start position:0% +what you solve for. Now in many +materials it turns out alpha and beta + + align:start position:0% +materials it turns out alpha and beta + + + align:start position:0% +materials it turns out alpha and beta +electrons do have the exact same energy + + align:start position:0% +electrons do have the exact same energy + + + align:start position:0% +electrons do have the exact same energy +level but not always and and actually um + + align:start position:0% +level but not always and and actually um + + + align:start position:0% +level but not always and and actually um +in in exactly what you were talking + + align:start position:0% +in in exactly what you were talking + + + align:start position:0% +in in exactly what you were talking +about when I apply a magnetic field even + + align:start position:0% +about when I apply a magnetic field even + + + align:start position:0% +about when I apply a magnetic field even +to a material that's not very magnetic + + align:start position:0% +to a material that's not very magnetic + + + align:start position:0% +to a material that's not very magnetic +you can cause big shifts in these okay + + align:start position:0% +you can cause big shifts in these okay + + + align:start position:0% +you can cause big shifts in these okay +you can depends + + align:start position:0% +you can depends + + + align:start position:0% +you can depends +yeah it depends on the material but when + + align:start position:0% +yeah it depends on the material but when + + + align:start position:0% +yeah it depends on the material but when +you apply external perturbations to the + + align:start position:0% +you apply external perturbations to the + + + align:start position:0% +you apply external perturbations to the +system you can split these so that + + align:start position:0% +system you can split these so that + + + align:start position:0% +system you can split these so that +Actually, you do have this picture + + align:start position:0% +Actually, you do have this picture + + + align:start position:0% +Actually, you do have this picture +where the energy of the spin up channel + + align:start position:0% +where the energy of the spin up channel + + + align:start position:0% +where the energy of the spin up channel +for that um you know for that energy + + align:start position:0% +for that um you know for that energy + + + align:start position:0% +for that um you know for that energy +level is different than the spin down + + align:start position:0% +level is different than the spin down + + + align:start position:0% +level is different than the spin down +channel. And that's exactly what spin + + align:start position:0% +channel. And that's exactly what spin + + + align:start position:0% +channel. And that's exactly what spin +polarized does. It allows those energies + + align:start position:0% +polarized does. It allows those energies + + + align:start position:0% +polarized does. It allows those energies +to be different. Without that you you + + align:start position:0% +to be different. Without that you you + + + align:start position:0% +to be different. Without that you you +can't really um + + align:start position:0% +can't really um + + + align:start position:0% +can't really um +study magnetism correctly. Okay. + + align:start position:0% +study magnetism correctly. Okay. + + + align:start position:0% +study magnetism correctly. Okay. +It's a good question. Okay. And so we + + align:start position:0% +It's a good question. Okay. And so we + + + align:start position:0% +It's a good question. Okay. And so we +talked about uh some other things. We + + align:start position:0% +talked about uh some other things. We + + + align:start position:0% +talked about uh some other things. We +did talk about how you could calculate + + align:start position:0% +did talk about how you could calculate + + + align:start position:0% +did talk about how you could calculate +um + + align:start position:0% +um + + + align:start position:0% +um +electrical connectivity. So that's fair + + align:start position:0% +electrical connectivity. So that's fair + + + align:start position:0% +electrical connectivity. So that's fair +game, right? From the band structure. + + align:start position:0% +game, right? From the band structure. + + + align:start position:0% +game, right? From the band structure. +There's an equation in the lecture uh + + align:start position:0% +There's an equation in the lecture uh + + + align:start position:0% +There's an equation in the lecture uh +from last week on that. + + align:start position:0% +from last week on that. + + + align:start position:0% +from last week on that. +We didn't talk about thermal + + align:start position:0% +We didn't talk about thermal + + + align:start position:0% +We didn't talk about thermal +conductivity. We've talked about optical + + align:start position:0% +conductivity. We've talked about optical + + + align:start position:0% +conductivity. We've talked about optical +properties and magnetization. + + align:start position:0% +properties and magnetization. + + + align:start position:0% +properties and magnetization. +That looks like it's just repeating the + + align:start position:0% +That looks like it's just repeating the + + + align:start position:0% +That looks like it's just repeating the +first and fourth bullets which is + + align:start position:0% +first and fourth bullets which is + + + align:start position:0% +first and fourth bullets which is +interesting to me. Um uh but these are + + align:start position:0% +interesting to me. Um uh but these are + + + align:start position:0% +interesting to me. Um uh but these are +the kinds of things we can calculate + + align:start position:0% +the kinds of things we can calculate + + + align:start position:0% +the kinds of things we can calculate +using the band structure and the doss. + + align:start position:0% +using the band structure and the doss. + + + align:start position:0% +using the band structure and the doss. +Okay. Which is what we've focused on a + + align:start position:0% +Okay. Which is what we've focused on a + + + align:start position:0% +Okay. Which is what we've focused on a +lot in the last three four lectures. + + align:start position:0% +lot in the last three four lectures. + + + align:start position:0% +lot in the last three four lectures. +Okay. So, so that that's certainly what + + align:start position:0% +Okay. So, so that that's certainly what + + + align:start position:0% +Okay. So, so that that's certainly what +I would think you you should know about + + align:start position:0% +I would think you you should know about + + + align:start position:0% +I would think you you should know about +you know how to get just you know some + + align:start position:0% +you know how to get just you know some + + + align:start position:0% +you know how to get just you know some +of the key properties from the band + + align:start position:0% +of the key properties from the band + + + align:start position:0% +of the key properties from the band +structure and dos from uh in these first + + align:start position:0% +structure and dos from uh in these first + + + align:start position:0% +structure and dos from uh in these first +four excluding thermal which we didn't + + align:start position:0% +four excluding thermal which we didn't + + + align:start position:0% +four excluding thermal which we didn't +talk about. Okay. + + align:start position:0% +talk about. Okay. + + + align:start position:0% +talk about. Okay. +any uh + + align:start position:0% + + + + align:start position:0% + +okay and with the with the convergence + + align:start position:0% +okay and with the with the convergence + + + align:start position:0% +okay and with the with the convergence +questions + + align:start position:0% +questions + + + align:start position:0% +questions +we got to have a convergence question + + align:start position:0% +we got to have a convergence question + + + align:start position:0% +we got to have a convergence question +right you just you got to you would feel + + align:start position:0% +right you just you got to you would feel + + + align:start position:0% +right you just you got to you would feel +you would feel cheated if you didn't + + align:start position:0% +you would feel cheated if you didn't + + + align:start position:0% +you would feel cheated if you didn't +have one right and I don't want you to + + align:start position:0% +have one right and I don't want you to + + + align:start position:0% +have one right and I don't want you to +have that feeling um you know when you + + align:start position:0% +have that feeling um you know when you + + + align:start position:0% +have that feeling um you know when you +have a solid k points now becomes a + + align:start position:0% +have a solid k points now becomes a + + + align:start position:0% +have a solid k points now becomes a +convergence parameter Okay, so that's + + align:start position:0% +convergence parameter Okay, so that's + + + align:start position:0% +convergence parameter Okay, so that's +kind of our review. Um, any any + + align:start position:0% +kind of our review. Um, any any + + + align:start position:0% +kind of our review. Um, any any +questions? Any questions about that at + + align:start position:0% +questions? Any questions about that at + + + align:start position:0% +questions? Any questions about that at +all? + + align:start position:0% + + + + align:start position:0% + +Any thoughts or + + align:start position:0% +Any thoughts or + + + align:start position:0% +Any thoughts or +um comments? Any other questions? We're + + align:start position:0% +um comments? Any other questions? We're + + + align:start position:0% +um comments? Any other questions? We're +good. Any questions about the the quiz? + + align:start position:0% + + + + align:start position:0% + +Okay, let let me just take five minutes + + align:start position:0% +Okay, let let me just take five minutes + + + align:start position:0% +Okay, let let me just take five minutes +to do a little stuff. Get it out of the + + align:start position:0% +to do a little stuff. Get it out of the + + + align:start position:0% +to do a little stuff. Get it out of the +way so that after the quiz we can dive + + align:start position:0% +way so that after the quiz we can dive + + + align:start position:0% +way so that after the quiz we can dive +into um or do or do you guys just kind + + align:start position:0% +into um or do or do you guys just kind + + + align:start position:0% +into um or do or do you guys just kind +of want to maybe we stop here, huh? + + align:start position:0% +of want to maybe we stop here, huh? + + + align:start position:0% +of want to maybe we stop here, huh? +Should we stop here? Have five minutes + + align:start position:0% +Should we stop here? Have five minutes + + + align:start position:0% +Should we stop here? Have five minutes +on solar right before a + + align:start position:0% +on solar right before a + + + align:start position:0% +on solar right before a +right before a quiz. Yeah. I'll tell you + + align:start position:0% +right before a quiz. Yeah. I'll tell you + + + align:start position:0% +right before a quiz. Yeah. I'll tell you +what. I'll do I'll do my little my + + align:start position:0% +what. I'll do I'll do my little my + + + align:start position:0% +what. I'll do I'll do my little my +little energy slides and then we'll + + align:start position:0% +little energy slides and then we'll + + + align:start position:0% +little energy slides and then we'll +start solar because this isn't really uh + + align:start position:0% +start solar because this isn't really uh + + + align:start position:0% +start solar because this isn't really uh +solar but it's related and I don't think + + align:start position:0% +solar but it's related and I don't think + + + align:start position:0% +solar but it's related and I don't think +I showed these before. Did I show these + + align:start position:0% +I showed these before. Did I show these + + + align:start position:0% +I showed these before. Did I show these +before when I was motivating research + + align:start position:0% +before when I was motivating research + + + align:start position:0% +before when I was motivating research +and energy? You know, I I really like + + align:start position:0% +and energy? You know, I I really like + + + align:start position:0% +and energy? You know, I I really like +this. You know, we talk a lot about + + align:start position:0% +this. You know, we talk a lot about + + + align:start position:0% +this. You know, we talk a lot about +global warming + + align:start position:0% +global warming + + + align:start position:0% +global warming +and um + + align:start position:0% +and um + + + align:start position:0% +and um +and I I think that's a really important + + align:start position:0% +and I I think that's a really important + + + align:start position:0% +and I I think that's a really important +topic. Um and and I you know there's + + align:start position:0% +topic. Um and and I you know there's + + + align:start position:0% +topic. Um and and I you know there's +some really great um work and and + + align:start position:0% +some really great um work and and + + + align:start position:0% +some really great um work and and +unfortunately not enough understanding I + + align:start position:0% +unfortunately not enough understanding I + + + align:start position:0% +unfortunately not enough understanding I +think um but uh on + + align:start position:0% +think um but uh on + + + align:start position:0% +think um but uh on +I don't even know where to begin. You + + align:start position:0% +I don't even know where to begin. You + + + align:start position:0% +I don't even know where to begin. You +know the polls show that half of this + + align:start position:0% +know the polls show that half of this + + + align:start position:0% +know the polls show that half of this +country still doesn't uh think that + + align:start position:0% +country still doesn't uh think that + + + align:start position:0% +country still doesn't uh think that +there's any um evidence uh that it's + + align:start position:0% +there's any um evidence uh that it's + + + align:start position:0% +there's any um evidence uh that it's +anthropogenically linked. But anyway um + + align:start position:0% +anthropogenically linked. But anyway um + + + align:start position:0% +anthropogenically linked. But anyway um +uh okay. So, let's say we don't talk + + align:start position:0% +uh okay. So, let's say we don't talk + + + align:start position:0% +uh okay. So, let's say we don't talk +about that and we and we ignore these + + align:start position:0% +about that and we and we ignore these + + + align:start position:0% +about that and we and we ignore these +sort of really hard scientific facts. + + align:start position:0% +sort of really hard scientific facts. + + + align:start position:0% +sort of really hard scientific facts. +Um, there are other reasons other + + align:start position:0% +Um, there are other reasons other + + + align:start position:0% +Um, there are other reasons other +reasons to think about renewable energy. + + align:start position:0% +reasons to think about renewable energy. + + + align:start position:0% +reasons to think about renewable energy. +Okay. Um, + + align:start position:0% +Okay. Um, + + + align:start position:0% +Okay. Um, +and and I like this one. I mean, I I + + align:start position:0% +and and I like this one. I mean, I I + + + align:start position:0% +and and I like this one. I mean, I I +don't know how many of you have seen + + align:start position:0% +don't know how many of you have seen + + + align:start position:0% +don't know how many of you have seen +something like this, but this is the the + + align:start position:0% +something like this, but this is the the + + + align:start position:0% +something like this, but this is the the +United Nations puts these out. This is + + align:start position:0% +United Nations puts these out. This is + + + align:start position:0% +United Nations puts these out. This is +the human development index, right? What + + align:start position:0% +the human development index, right? What + + + align:start position:0% +the human development index, right? What +does that mean? Well, I feel pretty + + align:start position:0% +does that mean? Well, I feel pretty + + + align:start position:0% +does that mean? Well, I feel pretty +developed. I mean, does that just mean I + + align:start position:0% +developed. I mean, does that just mean I + + + align:start position:0% +developed. I mean, does that just mean I +can go to like Starbucks and get a + + align:start position:0% +can go to like Starbucks and get a + + + align:start position:0% +can go to like Starbucks and get a +latte, right, when I want? No. Right. + + align:start position:0% +latte, right, when I want? No. Right. + + + align:start position:0% +latte, right, when I want? No. Right. +This means healthcare, education, you + + align:start position:0% +This means healthcare, education, you + + + align:start position:0% +This means healthcare, education, you +know, it means I can read. Um, it means + + align:start position:0% +know, it means I can read. Um, it means + + + align:start position:0% +know, it means I can read. Um, it means +I could maybe have a light on at night + + align:start position:0% +I could maybe have a light on at night + + + align:start position:0% +I could maybe have a light on at night +to read, but it's primarily some sort of + + align:start position:0% +to read, but it's primarily some sort of + + + align:start position:0% +to read, but it's primarily some sort of +key indices um that that talk about sort + + align:start position:0% +key indices um that that talk about sort + + + align:start position:0% +key indices um that that talk about sort +of the well-being of a person. And that + + align:start position:0% +of the well-being of a person. And that + + + align:start position:0% +of the well-being of a person. And that +you can see is incredibly uh strongly + + align:start position:0% +you can see is incredibly uh strongly + + + align:start position:0% +you can see is incredibly uh strongly +correlated with how much energy a + + align:start position:0% +correlated with how much energy a + + + align:start position:0% +correlated with how much energy a +country gets. Right? So this is the + + align:start position:0% +country gets. Right? So this is the + + + align:start position:0% +country gets. Right? So this is the +amount of per capita electricity use and + + align:start position:0% +amount of per capita electricity use and + + + align:start position:0% +amount of per capita electricity use and +that's this human development. It's + + align:start position:0% +that's this human development. It's + + + align:start position:0% +that's this human development. It's +basically a well-being index. Okay? As + + align:start position:0% +basically a well-being index. Okay? As + + + align:start position:0% +basically a well-being index. Okay? As +you can see some people get surprised + + align:start position:0% +you can see some people get surprised + + + align:start position:0% +you can see some people get surprised +that Canada beats us. So how did they + + align:start position:0% +that Canada beats us. So how did they + + + align:start position:0% +that Canada beats us. So how did they +beat us? + + align:start position:0% +beat us? + + + align:start position:0% +beat us? +It's cold. + + align:start position:0% +It's cold. + + + align:start position:0% +It's cold. +It's cold. It's really cold up there, + + align:start position:0% +It's cold. It's really cold up there, + + + align:start position:0% +It's cold. It's really cold up there, +right? Um and but you know you can just + + align:start position:0% +right? Um and but you know you can just + + + align:start position:0% +right? Um and but you know you can just +see the strong correlation. Okay. Um + + align:start position:0% +see the strong correlation. Okay. Um + + + align:start position:0% +see the strong correlation. Okay. Um +you know the question is when they turn + + align:start position:0% +you know the question is when they turn + + + align:start position:0% +you know the question is when they turn +see there's enough fossil fuels for + + align:start position:0% +see there's enough fossil fuels for + + + align:start position:0% +see there's enough fossil fuels for +everybody here probably certainly if you + + align:start position:0% +everybody here probably certainly if you + + + align:start position:0% +everybody here probably certainly if you +if you go with coal + + align:start position:0% +if you go with coal + + + align:start position:0% +if you go with coal +um there's a whole lot of energy in + + align:start position:0% +um there's a whole lot of energy in + + + align:start position:0% +um there's a whole lot of energy in +fossil fuels and we could lift a lot of + + align:start position:0% +fossil fuels and we could lift a lot of + + + align:start position:0% +fossil fuels and we could lift a lot of +these people up the curve. Question is + + align:start position:0% +these people up the curve. Question is + + + align:start position:0% +these people up the curve. Question is +is that really how we want to do it? + + align:start position:0% +is that really how we want to do it? + + + align:start position:0% +is that really how we want to do it? +Okay. Um, now the other point I want to + + align:start position:0% +Okay. Um, now the other point I want to + + + align:start position:0% +Okay. Um, now the other point I want to +make and this will be, you know, the + + align:start position:0% +make and this will be, you know, the + + + align:start position:0% +make and this will be, you know, the +other intro point just so you have in + + align:start position:0% +other intro point just so you have in + + + align:start position:0% +other intro point just so you have in +your minds when you're talking to people + + align:start position:0% +your minds when you're talking to people + + + align:start position:0% +your minds when you're talking to people +about energy. It's not just about global + + align:start position:0% +about energy. It's not just about global + + + align:start position:0% +about energy. It's not just about global +warming, + + align:start position:0% +warming, + + + align:start position:0% +warming, +right? Um, and this is a this was a + + align:start position:0% +right? Um, and this is a this was a + + + align:start position:0% +right? Um, and this is a this was a +great experiment that was run + + align:start position:0% +great experiment that was run + + + align:start position:0% +great experiment that was run +accidentally when 256 power plants went + + align:start position:0% +accidentally when 256 power plants went + + + align:start position:0% +accidentally when 256 power plants went +offline in the Eastern Corridor. This is + + align:start position:0% +offline in the Eastern Corridor. This is + + + align:start position:0% +offline in the Eastern Corridor. This is +one of these stories where, you know, + + align:start position:0% +one of these stories where, you know, + + + align:start position:0% +one of these stories where, you know, +one plant goes off because a mouse + + align:start position:0% +one plant goes off because a mouse + + + align:start position:0% +one plant goes off because a mouse +chewed through a wire or something and + + align:start position:0% +chewed through a wire or something and + + + align:start position:0% +chewed through a wire or something and +then the whole country feels it. But it + + align:start position:0% +then the whole country feels it. But it + + + align:start position:0% +then the whole country feels it. But it +was a great test bed because they were + + align:start position:0% +was a great test bed because they were + + + align:start position:0% +was a great test bed because they were +offline for quite a lot. All these + + align:start position:0% +offline for quite a lot. All these + + + align:start position:0% +offline for quite a lot. All these +things shut down. Everything had to shut + + align:start position:0% +things shut down. Everything had to shut + + + align:start position:0% +things shut down. Everything had to shut +down. And so people took planes up and + + align:start position:0% +down. And so people took planes up and + + + align:start position:0% +down. And so people took planes up and +and did testing and published these + + align:start position:0% +and did testing and published these + + + align:start position:0% +and did testing and published these +results, right, of the air quality. And + + align:start position:0% +results, right, of the air quality. And + + + align:start position:0% +results, right, of the air quality. And +it's incredible to look at the data, + + align:start position:0% +it's incredible to look at the data, + + + align:start position:0% +it's incredible to look at the data, +right? You look at all kinds of stuff + + align:start position:0% +right? You look at all kinds of stuff + + + align:start position:0% +right? You look at all kinds of stuff +that affect what we breathe, what we + + align:start position:0% +that affect what we breathe, what we + + + align:start position:0% +that affect what we breathe, what we +see, how we live, who has asthma, right? + + align:start position:0% +see, how we live, who has asthma, right? + + + align:start position:0% +see, how we live, who has asthma, right? +A lot of that stuff goes down instantly, + + align:start position:0% +A lot of that stuff goes down instantly, + + + align:start position:0% +A lot of that stuff goes down instantly, +right? Um, so, you know, there there + + align:start position:0% +right? Um, so, you know, there there + + + align:start position:0% +right? Um, so, you know, there there +there are different reasons than just + + align:start position:0% +there are different reasons than just + + + align:start position:0% +there are different reasons than just +global warming. Um, + + align:start position:0% +global warming. Um, + + + align:start position:0% +global warming. Um, +and and I like this map. I don't know if + + align:start position:0% +and and I like this map. I don't know if + + + align:start position:0% +and and I like this map. I don't know if +I showed this to you, but this is how + + align:start position:0% +I showed this to you, but this is how + + + align:start position:0% +I showed this to you, but this is how +much we consume scaled by scaled by + + align:start position:0% +much we consume scaled by scaled by + + + align:start position:0% +much we consume scaled by scaled by +consumption. This is the country, the + + align:start position:0% +consumption. This is the country, the + + + align:start position:0% +consumption. This is the country, the +world map. + + align:start position:0% +world map. + + + align:start position:0% +world map. +We're pretty big. + + align:start position:0% +We're pretty big. + + + align:start position:0% +We're pretty big. +right? Pretty big. There are some places + + align:start position:0% +right? Pretty big. There are some places + + + align:start position:0% +right? Pretty big. There are some places +that are pretty small. Okay. So, you + + align:start position:0% +that are pretty small. Okay. So, you + + + align:start position:0% +that are pretty small. Okay. So, you +scale it by by country. Um, + + align:start position:0% +scale it by by country. Um, + + + align:start position:0% +scale it by by country. Um, +yeah. I mean, one question that comes up + + align:start position:0% +yeah. I mean, one question that comes up + + + align:start position:0% +yeah. I mean, one question that comes up +and gets modified is, you know, how much + + align:start position:0% +and gets modified is, you know, how much + + + align:start position:0% +and gets modified is, you know, how much +energy do we really need, right? Um, or + + align:start position:0% +energy do we really need, right? Um, or + + + align:start position:0% +energy do we really need, right? Um, or +power. In 2002, we burned energy at a + + align:start position:0% +power. In 2002, we burned energy at a + + + align:start position:0% +power. In 2002, we burned energy at a +rate of three and a half terowatts. + + align:start position:0% +rate of three and a half terowatts. + + + align:start position:0% +rate of three and a half terowatts. +What's it going to be in 2050? Well, if + + align:start position:0% +What's it going to be in 2050? Well, if + + + align:start position:0% +What's it going to be in 2050? Well, if +you make some assumptions about how many + + align:start position:0% +you make some assumptions about how many + + + align:start position:0% +you make some assumptions about how many +people there are + + align:start position:0% +people there are + + + align:start position:0% +people there are +um and if you use if everybody use + + align:start position:0% +um and if you use if everybody use + + + align:start position:0% +um and if you use if everybody use +energy like us, which is really + + align:start position:0% +energy like us, which is really + + + align:start position:0% +energy like us, which is really +inefficiently, + + align:start position:0% +inefficiently, + + + align:start position:0% +inefficiently, +then we'd need a 100 terowatts in 2050. + + align:start position:0% +then we'd need a 100 terowatts in 2050. + + + align:start position:0% +then we'd need a 100 terowatts in 2050. +Okay, we only have 13 now, 14 now. We + + align:start position:0% +Okay, we only have 13 now, 14 now. We + + + align:start position:0% +Okay, we only have 13 now, 14 now. We +need a whole lot. And we like to think + + align:start position:0% +need a whole lot. And we like to think + + + align:start position:0% +need a whole lot. And we like to think +that people are going to be more + + align:start position:0% +that people are going to be more + + + align:start position:0% +that people are going to be more +efficient. Um and so that becomes the + + align:start position:0% +efficient. Um and so that becomes the + + + align:start position:0% +efficient. Um and so that becomes the +target. You know, 30 terowatts, 30 to 50 + + align:start position:0% +target. You know, 30 terowatts, 30 to 50 + + + align:start position:0% +target. You know, 30 terowatts, 30 to 50 +terowatts is what we're going to need. + + align:start position:0% +terowatts is what we're going to need. + + + align:start position:0% +terowatts is what we're going to need. +How do we generate that? Well, this is + + align:start position:0% +How do we generate that? Well, this is + + + align:start position:0% +How do we generate that? Well, this is +um you know, and this is all just again + + align:start position:0% +um you know, and this is all just again + + + align:start position:0% +um you know, and this is all just again +building up to solar, which we'll start + + align:start position:0% +building up to solar, which we'll start + + + align:start position:0% +building up to solar, which we'll start +next week. This is how we've generated + + align:start position:0% +next week. This is how we've generated + + + align:start position:0% +next week. This is how we've generated +it so far. + + align:start position:0% +it so far. + + + align:start position:0% +it so far. +Okay, you know, we we burned a lot of + + align:start position:0% +Okay, you know, we we burned a lot of + + + align:start position:0% +Okay, you know, we we burned a lot of +wood and that was kind of dirty. So, we + + align:start position:0% +wood and that was kind of dirty. So, we + + + align:start position:0% +wood and that was kind of dirty. So, we +burned coal that was really dirty. Um + + align:start position:0% +burned coal that was really dirty. Um + + + align:start position:0% +burned coal that was really dirty. Um +but there's so much coal and it's so + + align:start position:0% +but there's so much coal and it's so + + + align:start position:0% +but there's so much coal and it's so +cheap, right? Um and then we found oil, + + align:start position:0% +cheap, right? Um and then we found oil, + + + align:start position:0% +cheap, right? Um and then we found oil, +which is this magnificent energy + + align:start position:0% +which is this magnificent energy + + + align:start position:0% +which is this magnificent energy +carrier. It's a solar resource, right? + + align:start position:0% +carrier. It's a solar resource, right? + + + align:start position:0% +carrier. It's a solar resource, right? +All of these are solar resources by the + + align:start position:0% +All of these are solar resources by the + + + align:start position:0% +All of these are solar resources by the +way, right? Including hydro. Um + + align:start position:0% +way, right? Including hydro. Um + + + align:start position:0% +way, right? Including hydro. Um +uh and uh um now + + align:start position:0% +uh and uh um now + + + align:start position:0% +uh and uh um now +uh natural gas, you know, with fracking, + + align:start position:0% +uh natural gas, you know, with fracking, + + + align:start position:0% +uh natural gas, you know, with fracking, +this is going to go from this, it's + + align:start position:0% +this is going to go from this, it's + + + align:start position:0% +this is going to go from this, it's +going to go like this and just sort of + + align:start position:0% +going to go like this and just sort of + + + align:start position:0% +going to go like this and just sort of +take over this this chart, right? + + align:start position:0% +take over this this chart, right? + + + align:start position:0% +take over this this chart, right? +Natural gas is is fracking in the last + + align:start position:0% +Natural gas is is fracking in the last + + + align:start position:0% +Natural gas is is fracking in the last +few years has done more for energy than + + align:start position:0% +few years has done more for energy than + + + align:start position:0% +few years has done more for energy than +anything has in in many decades. Okay. + + align:start position:0% +anything has in in many decades. Okay. + + + align:start position:0% +anything has in in many decades. Okay. +Um, but that's not that's not what I'm + + align:start position:0% +Um, but that's not that's not what I'm + + + align:start position:0% +Um, but that's not that's not what I'm +talking about. I'm talking about this + + align:start position:0% +talking about. I'm talking about this + + + align:start position:0% +talking about. I'm talking about this +green sliver, which is what where I like + + align:start position:0% +green sliver, which is what where I like + + + align:start position:0% +green sliver, which is what where I like +to sit. Um, and uh we separate out hydro + + align:start position:0% +to sit. Um, and uh we separate out hydro + + + align:start position:0% +to sit. Um, and uh we separate out hydro +because uh at least onshore hydro is is + + align:start position:0% +because uh at least onshore hydro is is + + + align:start position:0% +because uh at least onshore hydro is is +fairly tapped out. Um, + + align:start position:0% +fairly tapped out. Um, + + + align:start position:0% +fairly tapped out. Um, +and then you've got that green sliver. + + align:start position:0% +and then you've got that green sliver. + + + align:start position:0% +and then you've got that green sliver. +And you know the thing is that if you + + align:start position:0% +And you know the thing is that if you + + + align:start position:0% +And you know the thing is that if you +want you know if you look at global + + align:start position:0% +want you know if you look at global + + + align:start position:0% +want you know if you look at global +warming curve CO2 emissions people talk + + align:start position:0% +warming curve CO2 emissions people talk + + + align:start position:0% +warming curve CO2 emissions people talk +about wanting half of all the energy to + + align:start position:0% +about wanting half of all the energy to + + + align:start position:0% +about wanting half of all the energy to +come from that green sliver by 2050. So + + align:start position:0% +come from that green sliver by 2050. So + + + align:start position:0% +come from that green sliver by 2050. So +you back the numbers out. We need 30 + + align:start position:0% +you back the numbers out. We need 30 + + + align:start position:0% +you back the numbers out. We need 30 +terowatts in 2050. Right? That's how + + align:start position:0% +terowatts in 2050. Right? That's how + + + align:start position:0% +terowatts in 2050. Right? That's how +much the world needs if we're really + + align:start position:0% +much the world needs if we're really + + + align:start position:0% +much the world needs if we're really +good at how we use it. 100 if we're like + + align:start position:0% +good at how we use it. 100 if we're like + + + align:start position:0% +good at how we use it. 100 if we're like +us. And you want half of that to come + + align:start position:0% +us. And you want half of that to come + + + align:start position:0% +us. And you want half of that to come +from a green sliver which isn't really + + align:start position:0% +from a green sliver which isn't really + + + align:start position:0% +from a green sliver which isn't really +expanding much. And notice it's sitting + + align:start position:0% +expanding much. And notice it's sitting + + + align:start position:0% +expanding much. And notice it's sitting +on a slope like this. Right? this slope + + align:start position:0% +on a slope like this. Right? this slope + + + align:start position:0% +on a slope like this. Right? this slope +is still, you know, could go even much + + align:start position:0% +is still, you know, could go even much + + + align:start position:0% +is still, you know, could go even much +higher, much faster. So, it's a really + + align:start position:0% +higher, much faster. So, it's a really + + + align:start position:0% +higher, much faster. So, it's a really +tall challenge. This is the the the + + align:start position:0% +tall challenge. This is the the the + + + align:start position:0% +tall challenge. This is the the the +challenge that um that that I like to + + align:start position:0% +challenge that um that that I like to + + + align:start position:0% +challenge that um that that I like to +think about is how how can we actually + + align:start position:0% +think about is how how can we actually + + + align:start position:0% +think about is how how can we actually +do that? And solar PV, I think, is is a + + align:start position:0% +do that? And solar PV, I think, is is a + + + align:start position:0% +do that? And solar PV, I think, is is a +a and and I I'll end on this slide. + + align:start position:0% +a and and I I'll end on this slide. + + + align:start position:0% +a and and I I'll end on this slide. +Okay. Um so, we'll start we'll we'll + + align:start position:0% +Okay. Um so, we'll start we'll we'll + + + align:start position:0% +Okay. Um so, we'll start we'll we'll +pick up from here on the technology part + + align:start position:0% +pick up from here on the technology part + + + align:start position:0% +pick up from here on the technology part +and the science part next week. Um, you + + align:start position:0% +and the science part next week. Um, you + + + align:start position:0% +and the science part next week. Um, you +know, + + align:start position:0% +know, + + + align:start position:0% +know, +we we use about 15 terowatts today. Does + + align:start position:0% +we we use about 15 terowatts today. Does + + + align:start position:0% +we we use about 15 terowatts today. Does +anybody know how much we get from the + + align:start position:0% +anybody know how much we get from the + + + align:start position:0% +anybody know how much we get from the +sun? I think I did talk about that. + + align:start position:0% +sun? I think I did talk about that. + + + align:start position:0% +sun? I think I did talk about that. +What's the number we get from the sun? + + align:start position:0% +What's the number we get from the sun? + + + align:start position:0% +What's the number we get from the sun? +We use 15 terowatts a year, right? How + + align:start position:0% +We use 15 terowatts a year, right? How + + + align:start position:0% +We use 15 terowatts a year, right? How +much do we get from the sun per year? + + align:start position:0% + + + + align:start position:0% + +40,000. Roughly 40,000, right? So, it's + + align:start position:0% +40,000. Roughly 40,000, right? So, it's + + + align:start position:0% +40,000. Roughly 40,000, right? So, it's +just a whole lot of energy that comes + + align:start position:0% +just a whole lot of energy that comes + + + align:start position:0% +just a whole lot of energy that comes +from the sun. Um, right. The energy + + align:start position:0% +from the sun. Um, right. The energy + + + align:start position:0% +from the sun. Um, right. The energy +released by an earthquake is we get from + + align:start position:0% +released by an earthquake is we get from + + + align:start position:0% +released by an earthquake is we get from +that from the sun in a second. You've + + align:start position:0% +that from the sun in a second. You've + + + align:start position:0% +that from the sun in a second. You've +probably heard this. Every year we get + + align:start position:0% +probably heard this. Every year we get + + + align:start position:0% +probably heard this. Every year we get +that amount of energy in an hour from + + align:start position:0% +that amount of energy in an hour from + + + align:start position:0% +that amount of energy in an hour from +the sun. Here's one I like. You may not + + align:start position:0% +the sun. Here's one I like. You may not + + + align:start position:0% +the sun. Here's one I like. You may not +have heard the total resource of of oil + + align:start position:0% +have heard the total resource of of oil + + + align:start position:0% +have heard the total resource of of oil +including the two trillion we barrels + + align:start position:0% +including the two trillion we barrels + + + align:start position:0% +including the two trillion we barrels +we've used roughly, right? And the + + align:start position:0% +we've used roughly, right? And the + + + align:start position:0% +we've used roughly, right? And the +trillion more that we're going to use + + align:start position:0% +trillion more that we're going to use + + + align:start position:0% +trillion more that we're going to use +for sure. Um that amount of energy + + align:start position:0% +for sure. Um that amount of energy + + + align:start position:0% +for sure. Um that amount of energy +resource you get from the sun in two + + align:start position:0% +resource you get from the sun in two + + + align:start position:0% +resource you get from the sun in two +days, right? So, you know, it's an + + align:start position:0% +days, right? So, you know, it's an + + + align:start position:0% +days, right? So, you know, it's an +incredible resource, right? And but, you + + align:start position:0% +incredible resource, right? And but, you + + + align:start position:0% +incredible resource, right? And but, you +know, apart from just painting a barrel + + align:start position:0% +know, apart from just painting a barrel + + + align:start position:0% +know, apart from just painting a barrel +black and heating water with it, we + + align:start position:0% +black and heating water with it, we + + + align:start position:0% +black and heating water with it, we +really don't use it much. And even + + align:start position:0% +really don't use it much. And even + + + align:start position:0% +really don't use it much. And even +there, we don't use it much at all. Um, + + align:start position:0% +there, we don't use it much at all. Um, + + + align:start position:0% +there, we don't use it much at all. Um, +solar photovoltaics + + align:start position:0% +solar photovoltaics + + + align:start position:0% +solar photovoltaics +is an extremely appealing way of trying + + align:start position:0% +is an extremely appealing way of trying + + + align:start position:0% +is an extremely appealing way of trying +to capture this resource and and really + + align:start position:0% +to capture this resource and and really + + + align:start position:0% +to capture this resource and and really +change that that green sliver. Okay? And + + align:start position:0% +change that that green sliver. Okay? And + + + align:start position:0% +change that that green sliver. Okay? And +so, that's that's what I want to talk + + align:start position:0% +so, that's that's what I want to talk + + + align:start position:0% +so, that's that's what I want to talk +about next um after the quiz. Okay? So, + + align:start position:0% +about next um after the quiz. Okay? So, + + + align:start position:0% +about next um after the quiz. Okay? So, +uh, see you all Thursday. Office hours + + align:start position:0% +uh, see you all Thursday. Office hours + + + align:start position:0% +uh, see you all Thursday. Office hours +tomorrow. Any questions at all, please + + align:start position:0% +tomorrow. Any questions at all, please + + + align:start position:0% +tomorrow. Any questions at all, please +send me an email. \ No newline at end of file diff --git a/xKnBPAcwx4I.txt b/xKnBPAcwx4I.txt new file mode 100644 index 0000000000000000000000000000000000000000..e91db5b2e0712537866ac7a84662459f7d1e44ee --- /dev/null +++ b/xKnBPAcwx4I.txt @@ -0,0 +1,939 @@ +align:start position:0% + +hi this is richard denifeld again and + + align:start position:0% +hi this is richard denifeld again and + + + align:start position:0% +hi this is richard denifeld again and +now we're switching gears to think not + + align:start position:0% +now we're switching gears to think not + + + align:start position:0% +now we're switching gears to think not +just about + + align:start position:0% +just about + + + align:start position:0% +just about +the evidence that we don't forecast + + align:start position:0% +the evidence that we don't forecast + + + align:start position:0% +the evidence that we don't forecast +correctly but let's peer underneath the + + align:start position:0% +correctly but let's peer underneath the + + + align:start position:0% +correctly but let's peer underneath the +cover bit + + align:start position:0% +cover bit + + + align:start position:0% +cover bit +underneath the hood if you want of this + + align:start position:0% +underneath the hood if you want of this + + + align:start position:0% +underneath the hood if you want of this +engine that's driving the forecast to + + align:start position:0% +engine that's driving the forecast to + + + align:start position:0% +engine that's driving the forecast to +think about what the forecasting process + + align:start position:0% +think about what the forecasting process + + + align:start position:0% +think about what the forecasting process +is and why + + align:start position:0% +is and why + + + align:start position:0% +is and why +it has difficulties + + align:start position:0% +it has difficulties + + + align:start position:0% +it has difficulties +so the natural thing when you are + + align:start position:0% +so the natural thing when you are + + + align:start position:0% +so the natural thing when you are +creating when anybody's creating a + + align:start position:0% +creating when anybody's creating a + + + align:start position:0% +creating when anybody's creating a +forecast is to look to the past to see + + align:start position:0% +forecast is to look to the past to see + + + align:start position:0% +forecast is to look to the past to see +what has been happening this is step one + + align:start position:0% +what has been happening this is step one + + + align:start position:0% +what has been happening this is step one +is what's at field + + align:start position:0% +is what's at field + + + align:start position:0% +is what's at field +so you look to the past see what's been + + align:start position:0% +so you look to the past see what's been + + + align:start position:0% +so you look to the past see what's been +moving up or down whatever the trend is + + align:start position:0% +moving up or down whatever the trend is + + + align:start position:0% +moving up or down whatever the trend is +going to be and you project us ahead in + + align:start position:0% +going to be and you project us ahead in + + + align:start position:0% +going to be and you project us ahead in +some ways now of course you want to + + align:start position:0% +some ways now of course you want to + + + align:start position:0% +some ways now of course you want to +project it ahead to take into account + + align:start position:0% +project it ahead to take into account + + + align:start position:0% +project it ahead to take into account +some adjustments so that you project to + + align:start position:0% +some adjustments so that you project to + + + align:start position:0% +some adjustments so that you project to +get ahead but you see there's some + + align:start position:0% +get ahead but you see there's some + + + align:start position:0% +get ahead but you see there's some +changes that people are using more of it + + align:start position:0% +changes that people are using more of it + + + align:start position:0% +changes that people are using more of it +or less of it so you just don't uh + + align:start position:0% +or less of it so you just don't uh + + + align:start position:0% +or less of it so you just don't uh +project ahead in a straight line or an + + align:start position:0% +project ahead in a straight line or an + + + align:start position:0% +project ahead in a straight line or an +exponential line you adjust it some way + + align:start position:0% +exponential line you adjust it some way + + + align:start position:0% +exponential line you adjust it some way +that's the common activity + + align:start position:0% +that's the common activity + + + align:start position:0% +that's the common activity +but now what then happens let's take a + + align:start position:0% +but now what then happens let's take a + + + align:start position:0% +but now what then happens let's take a +look at + + align:start position:0% +look at + + + align:start position:0% +look at +some example here i'm choosing now some + + align:start position:0% +some example here i'm choosing now some + + + align:start position:0% +some example here i'm choosing now some +of some data from the forecast for + + align:start position:0% +of some data from the forecast for + + + align:start position:0% +of some data from the forecast for +international travel from japan + + align:start position:0% +international travel from japan + + + align:start position:0% +international travel from japan +so this is the data and the important + + align:start position:0% +so this is the data and the important + + + align:start position:0% +so this is the data and the important +thing is here our 10-year forecast + + align:start position:0% +thing is here our 10-year forecast + + + align:start position:0% +thing is here our 10-year forecast +which is the kind of thing you need if + + align:start position:0% +which is the kind of thing you need if + + + align:start position:0% +which is the kind of thing you need if +you're planning major investments in an + + align:start position:0% +you're planning major investments in an + + + align:start position:0% +you're planning major investments in an +airport so what is the traffic going to + + align:start position:0% +airport so what is the traffic going to + + + align:start position:0% +airport so what is the traffic going to +be + + align:start position:0% +be + + + align:start position:0% +be +and + + align:start position:0% +and + + + align:start position:0% +and +what you want to see is on the far right + + align:start position:0% +what you want to see is on the far right + + + align:start position:0% +what you want to see is on the far right +hand side here that the percent error + + align:start position:0% +hand side here that the percent error + + + align:start position:0% +hand side here that the percent error +how big was the difference between what + + align:start position:0% +how big was the difference between what + + + align:start position:0% +how big was the difference between what +was forecast 10 years earlier and what + + align:start position:0% +was forecast 10 years earlier and what + + + align:start position:0% +was forecast 10 years earlier and what +came out and the numbers here are 65 53 + + align:start position:0% +came out and the numbers here are 65 53 + + + align:start position:0% +came out and the numbers here are 65 53 +27 minus 13 that's what the brackets + + align:start position:0% +27 minus 13 that's what the brackets + + + align:start position:0% +27 minus 13 that's what the brackets +mean so + + align:start position:0% +mean so + + + align:start position:0% +mean so +not too bad in the last year really + + align:start position:0% +not too bad in the last year really + + + align:start position:0% +not too bad in the last year really +terrible in the first one that this is + + align:start position:0% +terrible in the first one that this is + + + align:start position:0% +terrible in the first one that this is +the kind of error that happens + + align:start position:0% +the kind of error that happens + + + align:start position:0% +the kind of error that happens +so + + align:start position:0% +so + + + align:start position:0% +so +there weren't accurate + + align:start position:0% +there weren't accurate + + + align:start position:0% +there weren't accurate +why weren't they accurate let's look at + + align:start position:0% +why weren't they accurate let's look at + + + align:start position:0% +why weren't they accurate let's look at +the evolution of traffic + + align:start position:0% +the evolution of traffic + + + align:start position:0% +the evolution of traffic +for this uh + + align:start position:0% +for this uh + + + align:start position:0% +for this uh +situation + + align:start position:0% +situation + + + align:start position:0% +situation +so the thick blue line with all the dots + + align:start position:0% +so the thick blue line with all the dots + + + align:start position:0% +so the thick blue line with all the dots +on it that's what actually happened + + align:start position:0% +on it that's what actually happened + + + align:start position:0% +on it that's what actually happened +and the little dots here underneath and + + align:start position:0% +and the little dots here underneath and + + + align:start position:0% +and the little dots here underneath and +above and at the end on the right hand + + align:start position:0% +above and at the end on the right hand + + + align:start position:0% +above and at the end on the right hand +side audit are the projections + + align:start position:0% +side audit are the projections + + + align:start position:0% +side audit are the projections +so + + align:start position:0% +so + + + align:start position:0% +so +what do we observe when the traffic was + + align:start position:0% +what do we observe when the traffic was + + + align:start position:0% +what do we observe when the traffic was +increasing slowly + + align:start position:0% +increasing slowly + + + align:start position:0% +increasing slowly +naturally you projected + + align:start position:0% +naturally you projected + + + align:start position:0% +naturally you projected +low amounts so that you got to under + + align:start position:0% +low amounts so that you got to under + + + align:start position:0% +low amounts so that you got to under +project + + align:start position:0% +project + + + align:start position:0% +project +okay so then they said okay when the + + align:start position:0% +okay so then they said okay when the + + + align:start position:0% +okay so then they said okay when the +traffic is increasing quickly we will + + align:start position:0% +traffic is increasing quickly we will + + + align:start position:0% +traffic is increasing quickly we will +project above + + align:start position:0% +project above + + + align:start position:0% +project above +so you get over the forecast + + align:start position:0% +so you get over the forecast + + + align:start position:0% +so you get over the forecast +so that whenever there is + + align:start position:0% +so that whenever there is + + + align:start position:0% +so that whenever there is +something that is + + align:start position:0% +something that is + + + align:start position:0% +something that is +starting off slowly and then + + align:start position:0% +starting off slowly and then + + + align:start position:0% +starting off slowly and then +going faster you tend to have these + + align:start position:0% +going faster you tend to have these + + + align:start position:0% +going faster you tend to have these +kinds of act + + align:start position:0% +kinds of act + + + align:start position:0% +kinds of act +events happening you under project + + align:start position:0% +events happening you under project + + + align:start position:0% +events happening you under project +overproject so unless the thing is + + align:start position:0% +overproject so unless the thing is + + + align:start position:0% +overproject so unless the thing is +really steady as in the case of japan it + + align:start position:0% +really steady as in the case of japan it + + + align:start position:0% +really steady as in the case of japan it +was later on and it was fairly even it's + + align:start position:0% +was later on and it was fairly even it's + + + align:start position:0% +was later on and it was fairly even it's +only in those circumstances that you + + align:start position:0% +only in those circumstances that you + + + align:start position:0% +only in those circumstances that you +tend to get answers that are right on + + align:start position:0% +tend to get answers that are right on + + + align:start position:0% +tend to get answers that are right on +otherwise when you're dealing with new + + align:start position:0% +otherwise when you're dealing with new + + + align:start position:0% +otherwise when you're dealing with new +situations introduction of new + + align:start position:0% +situations introduction of new + + + align:start position:0% +situations introduction of new +technologies as was a case for + + align:start position:0% +technologies as was a case for + + + align:start position:0% +technologies as was a case for +international travel from japan in the + + align:start position:0% +international travel from japan in the + + + align:start position:0% +international travel from japan in the +70s and 80s and 90s + + align:start position:0% +70s and 80s and 90s + + + align:start position:0% +70s and 80s and 90s +when you're having introduction of new + + align:start position:0% +when you're having introduction of new + + + align:start position:0% +when you're having introduction of new +technologies you basically + + align:start position:0% +technologies you basically + + + align:start position:0% +technologies you basically +have this undershoot and then overshoot + + align:start position:0% +have this undershoot and then overshoot + + + align:start position:0% +have this undershoot and then overshoot +so + + align:start position:0% +so + + + align:start position:0% +so +what's the pattern + + align:start position:0% +what's the pattern + + + align:start position:0% +what's the pattern +forecasting projects for the past in the + + align:start position:0% +forecasting projects for the past in the + + + align:start position:0% +forecasting projects for the past in the +future + + align:start position:0% +future + + + align:start position:0% +future +is like steering a car by looking in the + + align:start position:0% +is like steering a car by looking in the + + + align:start position:0% +is like steering a car by looking in the +rear view mirror that's what you're + + align:start position:0% +rear view mirror that's what you're + + + align:start position:0% +rear view mirror that's what you're +doing you're looking at the past and + + align:start position:0% +doing you're looking at the past and + + + align:start position:0% +doing you're looking at the past and +imagining the future + + align:start position:0% +imagining the future + + + align:start position:0% +imagining the future +and what would happen to you if you + + align:start position:0% +and what would happen to you if you + + + align:start position:0% +and what would happen to you if you +drove a car like that + + align:start position:0% +drove a car like that + + + align:start position:0% +drove a car like that +if the if it's low growth you + + align:start position:0% +if the if it's low growth you + + + align:start position:0% +if the if it's low growth you +underestimate it's high growth you + + align:start position:0% +underestimate it's high growth you + + + align:start position:0% +underestimate it's high growth you +overestimate and in general it's never + + align:start position:0% +overestimate and in general it's never + + + align:start position:0% +overestimate and in general it's never +right and in general if you actually + + align:start position:0% +right and in general if you actually + + + align:start position:0% +right and in general if you actually +drove by looking at the rear view mirror + + align:start position:0% +drove by looking at the rear view mirror + + + align:start position:0% +drove by looking at the rear view mirror +what would you do you'd run off the road + + align:start position:0% +what would you do you'd run off the road + + + align:start position:0% +what would you do you'd run off the road +so + + align:start position:0% +so + + + align:start position:0% +so +one of the issues is that + + align:start position:0% +one of the issues is that + + + align:start position:0% +one of the issues is that +just by + + align:start position:0% +just by + + + align:start position:0% +just by +the natural processes of what we do we + + align:start position:0% +the natural processes of what we do we + + + align:start position:0% +the natural processes of what we do we +have to do in the forecasting that is + + align:start position:0% +have to do in the forecasting that is + + + align:start position:0% +have to do in the forecasting that is +look to the past to somehow project the + + align:start position:0% +look to the past to somehow project the + + + align:start position:0% +look to the past to somehow project the +future there is that tendency to run off + + align:start position:0% +future there is that tendency to run off + + + align:start position:0% +future there is that tendency to run off +the road whether it is under forecast in + + align:start position:0% +the road whether it is under forecast in + + + align:start position:0% +the road whether it is under forecast in +some situations overforecast in some + + align:start position:0% +some situations overforecast in some + + + align:start position:0% +some situations overforecast in some +other situations and again never quite + + align:start position:0% +other situations and again never quite + + + align:start position:0% +other situations and again never quite +get it right this is the common uh + + align:start position:0% +get it right this is the common uh + + + align:start position:0% +get it right this is the common uh +experience \ No newline at end of file diff --git a/xQANWfUYeNg.txt b/xQANWfUYeNg.txt new file mode 100644 index 0000000000000000000000000000000000000000..f4ee68baff3e789753792c18972dc5561227ce21 --- /dev/null +++ b/xQANWfUYeNg.txt @@ -0,0 +1,18571 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Okay. Um, welcome to class. + + align:start position:0% +Okay. Um, welcome to class. + + + align:start position:0% +Okay. Um, welcome to class. +Um the theme the theme of today's + + align:start position:0% +Um the theme the theme of today's + + + align:start position:0% +Um the theme the theme of today's +lectures is all about testing. So I'm + + align:start position:0% +lectures is all about testing. So I'm + + + align:start position:0% +lectures is all about testing. So I'm +going to give I'm going to give the + + align:start position:0% +going to give I'm going to give the + + + align:start position:0% +going to give I'm going to give the +intro to testing lecture where I talk + + align:start position:0% +intro to testing lecture where I talk + + + align:start position:0% +intro to testing lecture where I talk +about testing and how what it is and why + + align:start position:0% +about testing and how what it is and why + + + align:start position:0% +about testing and how what it is and why +we do it. Give you some basic testing + + align:start position:0% +we do it. Give you some basic testing + + + align:start position:0% +we do it. Give you some basic testing +tips and let you know what we expect you + + align:start position:0% +tips and let you know what we expect you + + + align:start position:0% +tips and let you know what we expect you +to be doing in terms of testing for your + + align:start position:0% +to be doing in terms of testing for your + + + align:start position:0% +to be doing in terms of testing for your +projects. And I'll spend a little more + + align:start position:0% +projects. And I'll spend a little more + + + align:start position:0% +projects. And I'll spend a little more +time on focus testing because that's the + + align:start position:0% +time on focus testing because that's the + + + align:start position:0% +time on focus testing because that's the +part people are frequently least + + align:start position:0% +part people are frequently least + + + align:start position:0% +part people are frequently least +familiar with. Um, we have Jenny Jenny + + align:start position:0% +familiar with. Um, we have Jenny Jenny + + + align:start position:0% +familiar with. Um, we have Jenny Jenny +Connley from Riot and she's going to + + align:start position:0% +Connley from Riot and she's going to + + + align:start position:0% +Connley from Riot and she's going to +give a a lecture related to testing, but + + align:start position:0% +give a a lecture related to testing, but + + + align:start position:0% +give a a lecture related to testing, but +um, more about what Riot's doing and + + align:start position:0% +um, more about what Riot's doing and + + + align:start position:0% +um, more about what Riot's doing and +stuff like that. So, hopefully that will + + align:start position:0% +stuff like that. So, hopefully that will + + + align:start position:0% +stuff like that. So, hopefully that will +be fun. Um, we'll take a break and then + + align:start position:0% +be fun. Um, we'll take a break and then + + + align:start position:0% +be fun. Um, we'll take a break and then +since we just told you all about testing + + align:start position:0% +since we just told you all about testing + + + align:start position:0% +since we just told you all about testing +and how important it is, we will go + + align:start position:0% +and how important it is, we will go + + + align:start position:0% +and how important it is, we will go +ahead and run a focus test in class. Um, + + align:start position:0% +ahead and run a focus test in class. Um, + + + align:start position:0% +ahead and run a focus test in class. Um, +we'll give you some time to get things + + align:start position:0% +we'll give you some time to get things + + + align:start position:0% +we'll give you some time to get things +set up, probably about 10 minutes to + + align:start position:0% +set up, probably about 10 minutes to + + + align:start position:0% +set up, probably about 10 minutes to +plan your test. Then we'll set things up + + align:start position:0% +plan your test. Then we'll set things up + + + align:start position:0% +plan your test. Then we'll set things up +and we will run testing. We're going to + + align:start position:0% +and we will run testing. We're going to + + + align:start position:0% +and we will run testing. We're going to +ask that everyone on your team test at + + align:start position:0% +ask that everyone on your team test at + + + align:start position:0% +ask that everyone on your team test at +least two games and that + + align:start position:0% +least two games and that + + + align:start position:0% +least two games and that +everyone on your team observe at least + + align:start position:0% +everyone on your team observe at least + + + align:start position:0% +everyone on your team observe at least +one person playing a game. How exactly + + align:start position:0% +one person playing a game. How exactly + + + align:start position:0% +one person playing a game. How exactly +you're going to make all of that happen + + align:start position:0% +you're going to make all of that happen + + + align:start position:0% +you're going to make all of that happen +in flow is your problem. + + align:start position:0% +in flow is your problem. + + + align:start position:0% +in flow is your problem. +Um yeah and then we will come down we'll + + align:start position:0% +Um yeah and then we will come down we'll + + + align:start position:0% +Um yeah and then we will come down we'll +give you some time to talk about let + + align:start position:0% +give you some time to talk about let + + + align:start position:0% +give you some time to talk about let +your team compare observations and talk + + align:start position:0% +your team compare observations and talk + + + align:start position:0% +your team compare observations and talk +about results and then we'll ask you to + + align:start position:0% +about results and then we'll ask you to + + + align:start position:0% +about results and then we'll ask you to +come down for a sort of standard inclass + + align:start position:0% +come down for a sort of standard inclass + + + align:start position:0% +come down for a sort of standard inclass +twominut no visuals presentation. + + align:start position:0% +twominut no visuals presentation. + + + align:start position:0% +twominut no visuals presentation. +Um, Monday, project two is due. Um, + + align:start position:0% +Um, Monday, project two is due. Um, + + + align:start position:0% +Um, Monday, project two is due. Um, +along with your design change log and + + align:start position:0% +along with your design change log and + + + align:start position:0% +along with your design change log and +focus test reports, um, and your + + align:start position:0% +focus test reports, um, and your + + + align:start position:0% +focus test reports, um, and your +individual writeups. Um, and the project + + align:start position:0% +individual writeups. Um, and the project + + + align:start position:0% +individual writeups. Um, and the project +2 presentation. This is a five-minute + + align:start position:0% +2 presentation. This is a five-minute + + + align:start position:0% +2 presentation. This is a five-minute +presentation. There are presentation + + align:start position:0% +presentation. There are presentation + + + align:start position:0% +presentation. There are presentation +guidelines on Stellar. You can download + + align:start position:0% +guidelines on Stellar. You can download + + + align:start position:0% +guidelines on Stellar. You can download +and look at them. Um, once again, we're + + align:start position:0% +and look at them. Um, once again, we're + + + align:start position:0% +and look at them. Um, once again, we're +primarily looking for post-mortem and + + align:start position:0% +primarily looking for post-mortem and + + + align:start position:0% +primarily looking for post-mortem and +reflection. We want to hear about your + + align:start position:0% +reflection. We want to hear about your + + + align:start position:0% +reflection. We want to hear about your +process. We want to know what you + + align:start position:0% +process. We want to know what you + + + align:start position:0% +process. We want to know what you +learned. We'll know what you did right, + + align:start position:0% +learned. We'll know what you did right, + + + align:start position:0% +learned. We'll know what you did right, +what you did wrong, and what you're + + align:start position:0% +what you did wrong, and what you're + + + align:start position:0% +what you did wrong, and what you're +going to do in the future. And we want + + align:start position:0% +going to do in the future. And we want + + + align:start position:0% +going to do in the future. And we want +in five minutes. Um, + + align:start position:0% +in five minutes. Um, + + + align:start position:0% +in five minutes. Um, +grades for project one are up along with + + align:start position:0% +grades for project one are up along with + + + align:start position:0% +grades for project one are up along with +um comments about your individual + + align:start position:0% +um comments about your individual + + + align:start position:0% +um comments about your individual +postmortems and some comments about um + + align:start position:0% +postmortems and some comments about um + + + align:start position:0% +postmortems and some comments about um +the overall project stuff. Overall, we + + align:start position:0% +the overall project stuff. Overall, we + + + align:start position:0% +the overall project stuff. Overall, we +were really impressed with the quality + + align:start position:0% +were really impressed with the quality + + + align:start position:0% +were really impressed with the quality +of project one. So, keep it up. Um, but + + align:start position:0% +of project one. So, keep it up. Um, but + + + align:start position:0% +of project one. So, keep it up. Um, but +do stop and read the comments so that + + align:start position:0% +do stop and read the comments so that + + + align:start position:0% +do stop and read the comments so that +you guys can make sure to do good jobs + + align:start position:0% +you guys can make sure to do good jobs + + + align:start position:0% +you guys can make sure to do good jobs +on your individual postmortems going + + align:start position:0% +on your individual postmortems going + + + align:start position:0% +on your individual postmortems going +forward. + + align:start position:0% +forward. + + + align:start position:0% +forward. +Anything to add? + + align:start position:0% +Anything to add? + + + align:start position:0% +Anything to add? +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +Okay. So, um, + + align:start position:0% +Okay. So, um, + + + align:start position:0% +Okay. So, um, +people say testing, people say quality + + align:start position:0% +people say testing, people say quality + + + align:start position:0% +people say testing, people say quality +assurance. What are they? Quality + + align:start position:0% +assurance. What are they? Quality + + + align:start position:0% +assurance. What are they? Quality +assurance is actually just it's a whole + + align:start position:0% +assurance is actually just it's a whole + + + align:start position:0% +assurance is actually just it's a whole +process that involves a whole lot of + + align:start position:0% +process that involves a whole lot of + + + align:start position:0% +process that involves a whole lot of +different types of testing, but in + + align:start position:0% +different types of testing, but in + + + align:start position:0% +different types of testing, but in +general + + align:start position:0% +general + + + align:start position:0% +general +it's the systematic process um checking + + align:start position:0% +it's the systematic process um checking + + + align:start position:0% +it's the systematic process um checking +to see whether a product or service + + align:start position:0% +to see whether a product or service + + + align:start position:0% +to see whether a product or service +being developed is meeting its specified + + align:start position:0% +being developed is meeting its specified + + + align:start position:0% +being developed is meeting its specified +requirements. Uh the most important part + + align:start position:0% +requirements. Uh the most important part + + + align:start position:0% +requirements. Uh the most important part +of that definition really is systemic + + align:start position:0% +of that definition really is systemic + + + align:start position:0% +of that definition really is systemic +which means you're doing regular + + align:start position:0% +which means you're doing regular + + + align:start position:0% +which means you're doing regular +repeatable testing. Looking at making + + align:start position:0% +repeatable testing. Looking at making + + + align:start position:0% +repeatable testing. Looking at making +sure that all the section all the + + align:start position:0% +sure that all the section all the + + + align:start position:0% +sure that all the section all the +portions of your game or project are + + align:start position:0% +portions of your game or project are + + + align:start position:0% +portions of your game or project are +working and requirements making sure + + align:start position:0% +working and requirements making sure + + + align:start position:0% +working and requirements making sure +you're meeting that it doesn't just work + + align:start position:0% +you're meeting that it doesn't just work + + + align:start position:0% +you're meeting that it doesn't just work +as far as you think it as far as you + + align:start position:0% +as far as you think it as far as you + + + align:start position:0% +as far as you think it as far as you +think it does. It works according to the + + align:start position:0% +think it does. It works according to the + + + align:start position:0% +think it does. It works according to the +requirements of the game of the project + + align:start position:0% +requirements of the game of the project + + + align:start position:0% +requirements of the game of the project +of whoever you're shipping to and etc + + align:start position:0% +of whoever you're shipping to and etc + + + align:start position:0% +of whoever you're shipping to and etc +and so forth. So you sort of need to + + align:start position:0% +and so forth. So you sort of need to + + + align:start position:0% +and so forth. So you sort of need to +know what your standards are to be doing + + align:start position:0% +know what your standards are to be doing + + + align:start position:0% +know what your standards are to be doing +good quality assurance. + + align:start position:0% +good quality assurance. + + + align:start position:0% +good quality assurance. +Um + + align:start position:0% + + + + align:start position:0% + +without testing your project will fail + + align:start position:0% +without testing your project will fail + + + align:start position:0% +without testing your project will fail +and will take more time and will take a + + align:start position:0% +and will take more time and will take a + + + align:start position:0% +and will take more time and will take a +lot more effort. You can make games + + align:start position:0% +lot more effort. You can make games + + + align:start position:0% +lot more effort. You can make games +without programmers. Um there's a lot of + + align:start position:0% +without programmers. Um there's a lot of + + + align:start position:0% +without programmers. Um there's a lot of +graphical user interface engines out + + align:start position:0% +graphical user interface engines out + + + align:start position:0% +graphical user interface engines out +there. Some of they're getting older and + + align:start position:0% +there. Some of they're getting older and + + + align:start position:0% +there. Some of they're getting older and +older, but they're out there and you can + + align:start position:0% +older, but they're out there and you can + + + align:start position:0% +older, but they're out there and you can +use them. Game Maker, for example. You + + align:start position:0% +use them. Game Maker, for example. You + + + align:start position:0% +use them. Game Maker, for example. You +can make games without artists. I bet + + align:start position:0% +can make games without artists. I bet + + + align:start position:0% +can make games without artists. I bet +several of you are figuring out how to + + align:start position:0% +several of you are figuring out how to + + + align:start position:0% +several of you are figuring out how to +do that right now. But um you can also + + align:start position:0% +do that right now. But um you can also + + + align:start position:0% +do that right now. But um you can also +make games completely without assets + + align:start position:0% +make games completely without assets + + + align:start position:0% +make games completely without assets +using text engines like in form 7. Um + + align:start position:0% +using text engines like in form 7. Um + + + align:start position:0% +using text engines like in form 7. Um +you don't really need a designated + + align:start position:0% +you don't really need a designated + + + align:start position:0% +you don't really need a designated +producer or distinct game designer on a + + align:start position:0% +producer or distinct game designer on a + + + align:start position:0% +producer or distinct game designer on a +small team. One person can really do it + + align:start position:0% +small team. One person can really do it + + + align:start position:0% +small team. One person can really do it +alone. But you're never going to make a + + align:start position:0% +alone. But you're never going to make a + + + align:start position:0% +alone. But you're never going to make a +good game without testing. Um and the + + align:start position:0% +good game without testing. Um and the + + + align:start position:0% +good game without testing. Um and the +more systemic and planned your testing + + align:start position:0% +more systemic and planned your testing + + + align:start position:0% +more systemic and planned your testing +is, the more results you'll get from + + align:start position:0% +is, the more results you'll get from + + + align:start position:0% +is, the more results you'll get from +less effort. + + align:start position:0% + + + + align:start position:0% + +So, who gets to do all this testing? Um, + + align:start position:0% +So, who gets to do all this testing? Um, + + + align:start position:0% +So, who gets to do all this testing? Um, +that's really everyone involved in the + + align:start position:0% +that's really everyone involved in the + + + align:start position:0% +that's really everyone involved in the +project. Um, do not assume that because + + align:start position:0% +project. Um, do not assume that because + + + align:start position:0% +project. Um, do not assume that because +you are the key programmer or the key + + align:start position:0% +you are the key programmer or the key + + + align:start position:0% +you are the key programmer or the key +designer or the key whatever that + + align:start position:0% +designer or the key whatever that + + + align:start position:0% +designer or the key whatever that +someone else will check your code and + + align:start position:0% +someone else will check your code and + + + align:start position:0% +someone else will check your code and +make sure it's working after you've + + align:start position:0% +make sure it's working after you've + + + align:start position:0% +make sure it's working after you've +integrated it. Um, you really want + + align:start position:0% +integrated it. Um, you really want + + + align:start position:0% +integrated it. Um, you really want +everyone on the team to consider it to + + align:start position:0% +everyone on the team to consider it to + + + align:start position:0% +everyone on the team to consider it to +be their responsibility to keep the game + + align:start position:0% +be their responsibility to keep the game + + + align:start position:0% +be their responsibility to keep the game +working as well as possible all the way + + align:start position:0% +working as well as possible all the way + + + align:start position:0% +working as well as possible all the way +through and also to take the time to go + + align:start position:0% +through and also to take the time to go + + + align:start position:0% +through and also to take the time to go +in and check other people's stuff to + + align:start position:0% +in and check other people's stuff to + + + align:start position:0% +in and check other people's stuff to +make sure that it went in. Um, remember + + align:start position:0% +make sure that it went in. Um, remember + + + align:start position:0% +make sure that it went in. Um, remember +that this is this is one of sort of the + + align:start position:0% +that this is this is one of sort of the + + + align:start position:0% +that this is this is one of sort of the +cornerstones of using Scrum as well + + align:start position:0% +cornerstones of using Scrum as well + + + align:start position:0% +cornerstones of using Scrum as well +where before a task is actually done, + + align:start position:0% +where before a task is actually done, + + + align:start position:0% +where before a task is actually done, +someone else has gone in and verified. + + align:start position:0% +someone else has gone in and verified. + + + align:start position:0% +someone else has gone in and verified. +Well, someone else is going to be + + align:start position:0% +Well, someone else is going to be + + + align:start position:0% +Well, someone else is going to be +someone on the team, which means you're + + align:start position:0% +someone on the team, which means you're + + + align:start position:0% +someone on the team, which means you're +all going to have to all lot some time + + align:start position:0% +all going to have to all lot some time + + + align:start position:0% +all going to have to all lot some time +to doing it, and you're going to have to + + align:start position:0% +to doing it, and you're going to have to + + + align:start position:0% +to doing it, and you're going to have to +think about that. Speaking of which, + + align:start position:0% +think about that. Speaking of which, + + + align:start position:0% +think about that. Speaking of which, +anybody have testing as one of your + + align:start position:0% +anybody have testing as one of your + + + align:start position:0% +anybody have testing as one of your +tasks on your sprint task list? + + align:start position:0% + + + + align:start position:0% + +Anybody? + + align:start position:0% +Anybody? + + + align:start position:0% +Anybody? +Woo! You win. Um, it's going to take + + align:start position:0% +Woo! You win. Um, it's going to take + + + align:start position:0% +Woo! You win. Um, it's going to take +some time and it's going to take some + + align:start position:0% +some time and it's going to take some + + + align:start position:0% +some time and it's going to take some +time that will probably otherwise could + + align:start position:0% +time that will probably otherwise could + + + align:start position:0% +time that will probably otherwise could +be used for making code. So go ahead and + + align:start position:0% +be used for making code. So go ahead and + + + align:start position:0% +be used for making code. So go ahead and +remember that now and think about that + + align:start position:0% +remember that now and think about that + + + align:start position:0% +remember that now and think about that +as you're going into your last kind of + + align:start position:0% +as you're going into your last kind of + + + align:start position:0% +as you're going into your last kind of +week of work that you need to all lot + + align:start position:0% +week of work that you need to all lot + + + align:start position:0% +week of work that you need to all lot +some time for testing. + + align:start position:0% +some time for testing. + + + align:start position:0% +some time for testing. +So types of testing, what is the + + align:start position:0% +So types of testing, what is the + + + align:start position:0% +So types of testing, what is the +terminology I'm going to use so that we + + align:start position:0% +terminology I'm going to use so that we + + + align:start position:0% +terminology I'm going to use so that we +all understand what I'm saying when I + + align:start position:0% +all understand what I'm saying when I + + + align:start position:0% +all understand what I'm saying when I +say it. Um I divide testing up into + + align:start position:0% +say it. Um I divide testing up into + + + align:start position:0% +say it. Um I divide testing up into +three major areas. Um and that's really + + align:start position:0% +three major areas. Um and that's really + + + align:start position:0% +three major areas. Um and that's really +there isn't a lot of formal methodology + + align:start position:0% +there isn't a lot of formal methodology + + + align:start position:0% +there isn't a lot of formal methodology +on this especially not in the game + + align:start position:0% +on this especially not in the game + + + align:start position:0% +on this especially not in the game +industry. So, I tend to talk about + + align:start position:0% +industry. So, I tend to talk about + + + align:start position:0% +industry. So, I tend to talk about +technical testing, play testing, and + + align:start position:0% +technical testing, play testing, and + + + align:start position:0% +technical testing, play testing, and +user testing. When I say technical + + align:start position:0% +user testing. When I say technical + + + align:start position:0% +user testing. When I say technical +testing, I mean getting your game to + + align:start position:0% +testing, I mean getting your game to + + + align:start position:0% +testing, I mean getting your game to +run. + + align:start position:0% +run. + + + align:start position:0% +run. +Specifically, I often mean getting your + + align:start position:0% +Specifically, I often mean getting your + + + align:start position:0% +Specifically, I often mean getting your +game to run exactly as how you intended + + align:start position:0% +game to run exactly as how you intended + + + align:start position:0% +game to run exactly as how you intended +it to run. + + align:start position:0% +it to run. + + + align:start position:0% +it to run. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +so if the designer claims that the + + align:start position:0% +so if the designer claims that the + + + align:start position:0% +so if the designer claims that the +Peachmobile should go up to 30 miles per + + align:start position:0% +Peachmobile should go up to 30 miles per + + + align:start position:0% +Peachmobile should go up to 30 miles per +hour and fire eight peaches per second, + + align:start position:0% +hour and fire eight peaches per second, + + + align:start position:0% +hour and fire eight peaches per second, +if you go into the game and you discover + + align:start position:0% +if you go into the game and you discover + + + align:start position:0% +if you go into the game and you discover +that it goes 70 miles per hour and fires + + align:start position:0% +that it goes 70 miles per hour and fires + + + align:start position:0% +that it goes 70 miles per hour and fires +two peaches per second, that's not + + align:start position:0% +two peaches per second, that's not + + + align:start position:0% +two peaches per second, that's not +working. Even if it makes the game + + align:start position:0% +working. Even if it makes the game + + + align:start position:0% +working. Even if it makes the game +awfully fun with it like that. Um, + + align:start position:0% +awfully fun with it like that. Um, + + + align:start position:0% +awfully fun with it like that. Um, +when you start thinking about whether + + align:start position:0% +when you start thinking about whether + + + align:start position:0% +when you start thinking about whether +it's fun or not as a developer, then + + align:start position:0% +it's fun or not as a developer, then + + + align:start position:0% +it's fun or not as a developer, then +you're moving into the area of play + + align:start position:0% +you're moving into the area of play + + + align:start position:0% +you're moving into the area of play +testing, which is where you, the team, + + align:start position:0% +testing, which is where you, the team, + + + align:start position:0% +testing, which is where you, the team, +are playing your game trying to figure + + align:start position:0% +are playing your game trying to figure + + + align:start position:0% +are playing your game trying to figure +out, hey, all those requirements and + + align:start position:0% +out, hey, all those requirements and + + + align:start position:0% +out, hey, all those requirements and +constraints and and and plans we made, + + align:start position:0% +constraints and and and plans we made, + + + align:start position:0% +constraints and and and plans we made, +are they working and are they working + + align:start position:0% +are they working and are they working + + + align:start position:0% +are they working and are they working +well and is a player going to enjoy it? + + align:start position:0% +well and is a player going to enjoy it? + + + align:start position:0% +well and is a player going to enjoy it? +Um, you're play testing your game as a + + align:start position:0% +Um, you're play testing your game as a + + + align:start position:0% +Um, you're play testing your game as a +developer, you're checking to make sure + + align:start position:0% +developer, you're checking to make sure + + + align:start position:0% +developer, you're checking to make sure +it works. In that case, yes. The fact + + align:start position:0% +it works. In that case, yes. The fact + + + align:start position:0% +it works. In that case, yes. The fact +that the peak mobile is currently going + + align:start position:0% +that the peak mobile is currently going + + + align:start position:0% +that the peak mobile is currently going +70 is currently going 30 miles per hour + + align:start position:0% +70 is currently going 30 miles per hour + + + align:start position:0% +70 is currently going 30 miles per hour +and it's so slow that no player is ever + + align:start position:0% +and it's so slow that no player is ever + + + align:start position:0% +and it's so slow that no player is ever +going to want to use it. That's a bug. + + align:start position:0% +going to want to use it. That's a bug. + + + align:start position:0% +going to want to use it. That's a bug. +That's a really big bug. But it's a play + + align:start position:0% +That's a really big bug. But it's a play + + + align:start position:0% +That's a really big bug. But it's a play +testing bug if your specs say it should + + align:start position:0% +testing bug if your specs say it should + + + align:start position:0% +testing bug if your specs say it should +be going 30 miles per hour. Not a + + align:start position:0% +be going 30 miles per hour. Not a + + + align:start position:0% +be going 30 miles per hour. Not a +technical testing bug. And it's it is + + align:start position:0% +technical testing bug. And it's it is + + + align:start position:0% +technical testing bug. And it's it is +good to know the differences so that you + + align:start position:0% +good to know the differences so that you + + + align:start position:0% +good to know the differences so that you +can know what you're talking about and + + align:start position:0% +can know what you're talking about and + + + align:start position:0% +can know what you're talking about and +why you're talking about it. Finally, um + + align:start position:0% +why you're talking about it. Finally, um + + + align:start position:0% +why you're talking about it. Finally, um +there's user testing, which is getting + + align:start position:0% +there's user testing, which is getting + + + align:start position:0% +there's user testing, which is getting +someone who is not on your team to play + + align:start position:0% +someone who is not on your team to play + + + align:start position:0% +someone who is not on your team to play +your game. + + align:start position:0% +your game. + + + align:start position:0% +your game. +Um, you the developer while you do play + + align:start position:0% +Um, you the developer while you do play + + + align:start position:0% +Um, you the developer while you do play +testing can pretend to be an actual + + align:start position:0% +testing can pretend to be an actual + + + align:start position:0% +testing can pretend to be an actual +player, but you are not an actual + + align:start position:0% +player, but you are not an actual + + + align:start position:0% +player, but you are not an actual +player. You will never be an actual + + align:start position:0% +player. You will never be an actual + + + align:start position:0% +player. You will never be an actual +player for your game. You know it too + + align:start position:0% +player for your game. You know it too + + + align:start position:0% +player for your game. You know it too +well. You are too close to it. You have + + align:start position:0% +well. You are too close to it. You have + + + align:start position:0% +well. You are too close to it. You have +spent too many hours playing it. Um, + + align:start position:0% +spent too many hours playing it. Um, + + + align:start position:0% +spent too many hours playing it. Um, +so you really need to get someone who + + align:start position:0% +so you really need to get someone who + + + align:start position:0% +so you really need to get someone who +has never seen your game before, ideally + + align:start position:0% +has never seen your game before, ideally + + + align:start position:0% +has never seen your game before, ideally +to come in and sit down in front of your + + align:start position:0% +to come in and sit down in front of your + + + align:start position:0% +to come in and sit down in front of your +game and play it. We're going to make + + align:start position:0% +game and play it. We're going to make + + + align:start position:0% +game and play it. We're going to make +pretend when we run our focus testing + + align:start position:0% +pretend when we run our focus testing + + + align:start position:0% +pretend when we run our focus testing +workshop. We're going to pretend that + + align:start position:0% +workshop. We're going to pretend that + + + align:start position:0% +workshop. We're going to pretend that +the your classmates here are actually + + align:start position:0% +the your classmates here are actually + + + align:start position:0% +the your classmates here are actually +good testers. Tell you a secret, they're + + align:start position:0% +good testers. Tell you a secret, they're + + + align:start position:0% +good testers. Tell you a secret, they're +not. They've seen your game because they + + align:start position:0% +not. They've seen your game because they + + + align:start position:0% +not. They've seen your game because they +tested it before. They've heard you talk + + align:start position:0% +tested it before. They've heard you talk + + + align:start position:0% +tested it before. They've heard you talk +about it. They heard you pitch it. They + + align:start position:0% +about it. They heard you pitch it. They + + + align:start position:0% +about it. They heard you pitch it. They +might even have worked on it if they + + align:start position:0% +might even have worked on it if they + + + align:start position:0% +might even have worked on it if they +switched teams. So, they're not actually + + align:start position:0% +switched teams. So, they're not actually + + + align:start position:0% +switched teams. So, they're not actually +your ideal testers, but they are very + + align:start position:0% +your ideal testers, but they are very + + + align:start position:0% +your ideal testers, but they are very +convenient testers. So, we're going to + + align:start position:0% +convenient testers. So, we're going to + + + align:start position:0% +convenient testers. So, we're going to +use them today. And for your next + + align:start position:0% +use them today. And for your next + + + align:start position:0% +use them today. And for your next +projects, we're going to encourage you + + align:start position:0% +projects, we're going to encourage you + + + align:start position:0% +projects, we're going to encourage you +and in fact require you to go out into + + align:start position:0% +and in fact require you to go out into + + + align:start position:0% +and in fact require you to go out into +the cold, cold world and find actual + + align:start position:0% +the cold, cold world and find actual + + + align:start position:0% +the cold, cold world and find actual +testers who haven't seen your game. + + align:start position:0% +testers who haven't seen your game. + + + align:start position:0% +testers who haven't seen your game. +people in your dorms, people in your + + align:start position:0% +people in your dorms, people in your + + + align:start position:0% +people in your dorms, people in your +other classes, friends, people at the + + align:start position:0% +other classes, friends, people at the + + + align:start position:0% +other classes, friends, people at the +coffee shop, whoever you think will do + + align:start position:0% +coffee shop, whoever you think will do + + + align:start position:0% +coffee shop, whoever you think will do +the best job of giving you the + + align:start position:0% +the best job of giving you the + + + align:start position:0% +the best job of giving you the +information you need. Um, user testing, + + align:start position:0% +information you need. Um, user testing, + + + align:start position:0% +information you need. Um, user testing, +user testing is another one of those + + align:start position:0% +user testing is another one of those + + + align:start position:0% +user testing is another one of those +term terminologies that means a whole + + align:start position:0% +term terminologies that means a whole + + + align:start position:0% +term terminologies that means a whole +lot. So, for my convenience, I tend to + + align:start position:0% +lot. So, for my convenience, I tend to + + + align:start position:0% +lot. So, for my convenience, I tend to +divide it up into two kinds of things. + + align:start position:0% +divide it up into two kinds of things. + + + align:start position:0% +divide it up into two kinds of things. +Focus testing and user testing. Um, + + align:start position:0% +Focus testing and user testing. Um, + + + align:start position:0% +Focus testing and user testing. Um, +where focus testing is specifically when + + align:start position:0% +where focus testing is specifically when + + + align:start position:0% +where focus testing is specifically when +you're sitting down and you're playing + + align:start position:0% +you're sitting down and you're playing + + + align:start position:0% +you're sitting down and you're playing +the game, looking at how it plays. Is it + + align:start position:0% +the game, looking at how it plays. Is it + + + align:start position:0% +the game, looking at how it plays. Is it +fun? Are people enjoying it? Is it + + align:start position:0% +fun? Are people enjoying it? Is it + + + align:start position:0% +fun? Are people enjoying it? Is it +challenging enough? Are the mechanics + + align:start position:0% +challenging enough? Are the mechanics + + + align:start position:0% +challenging enough? Are the mechanics +interesting? Um, does is your game a + + align:start position:0% +interesting? Um, does is your game a + + + align:start position:0% +interesting? Um, does is your game a +good game? And getting that information + + align:start position:0% +good game? And getting that information + + + align:start position:0% +good game? And getting that information +back from your players. When user + + align:start position:0% +back from your players. When user + + + align:start position:0% +back from your players. When user +testing, I tend to use more for looking + + align:start position:0% +testing, I tend to use more for looking + + + align:start position:0% +testing, I tend to use more for looking +at the usability of your game. You may + + align:start position:0% +at the usability of your game. You may + + + align:start position:0% +at the usability of your game. You may +have a really, really fun game, but if + + align:start position:0% +have a really, really fun game, but if + + + align:start position:0% +have a really, really fun game, but if +it takes your players 12 minutes to get + + align:start position:0% +it takes your players 12 minutes to get + + + align:start position:0% +it takes your players 12 minutes to get +off your starting page because they + + align:start position:0% +off your starting page because they + + + align:start position:0% +off your starting page because they +can't figure out what they're doing or + + align:start position:0% +can't figure out what they're doing or + + + align:start position:0% +can't figure out what they're doing or +how to do it, that's a pretty serious + + align:start position:0% +how to do it, that's a pretty serious + + + align:start position:0% +how to do it, that's a pretty serious +usability issue and you need to you need + + align:start position:0% +usability issue and you need to you need + + + align:start position:0% +usability issue and you need to you need +to figure that out as well. So just so + + align:start position:0% +to figure that out as well. So just so + + + align:start position:0% +to figure that out as well. So just so +you know that those are sort of those + + align:start position:0% +you know that those are sort of those + + + align:start position:0% +you know that those are sort of those +two two user types. It's all user + + align:start position:0% +two two user types. It's all user + + + align:start position:0% +two two user types. It's all user +testing but having some granularity to + + align:start position:0% +testing but having some granularity to + + + align:start position:0% +testing but having some granularity to +find define the difference is a little + + align:start position:0% +find define the difference is a little + + + align:start position:0% +find define the difference is a little +useful. Um so the basics for technical + + align:start position:0% +useful. Um so the basics for technical + + + align:start position:0% +useful. Um so the basics for technical +testing which hopefully we can go + + align:start position:0% +testing which hopefully we can go + + + align:start position:0% +testing which hopefully we can go +through um pretty quickly. Um I suspect + + align:start position:0% +through um pretty quickly. Um I suspect + + + align:start position:0% +through um pretty quickly. Um I suspect +that you guys if you guys have done + + align:start position:0% +that you guys if you guys have done + + + align:start position:0% +that you guys if you guys have done +programming you've done this before. If + + align:start position:0% +programming you've done this before. If + + + align:start position:0% +programming you've done this before. If +you've had classes that wanted code that + + align:start position:0% +you've had classes that wanted code that + + + align:start position:0% +you've had classes that wanted code that +worked hopefully they've helped teach + + align:start position:0% +worked hopefully they've helped teach + + + align:start position:0% +worked hopefully they've helped teach +you what the good things to do are. Um, + + align:start position:0% +you what the good things to do are. Um, + + + align:start position:0% +you what the good things to do are. Um, +a lot of this sounds an awful lot like + + align:start position:0% +a lot of this sounds an awful lot like + + + align:start position:0% +a lot of this sounds an awful lot like +good software practices lecture that + + align:start position:0% +good software practices lecture that + + + align:start position:0% +good software practices lecture that +Andrew gave because a lot of good + + align:start position:0% +Andrew gave because a lot of good + + + align:start position:0% +Andrew gave because a lot of good +testing is in fact a good software + + align:start position:0% +testing is in fact a good software + + + align:start position:0% +testing is in fact a good software +practice. So have some technical + + align:start position:0% +practice. So have some technical + + + align:start position:0% +practice. So have some technical +standards. Um, have a bug database or + + align:start position:0% +standards. Um, have a bug database or + + + align:start position:0% +standards. Um, have a bug database or +given the size of these projects at + + align:start position:0% +given the size of these projects at + + + align:start position:0% +given the size of these projects at +least a bug Excel spreadsheet with a + + align:start position:0% +least a bug Excel spreadsheet with a + + + align:start position:0% +least a bug Excel spreadsheet with a +list of everything that you've noticed. + + align:start position:0% +list of everything that you've noticed. + + + align:start position:0% +list of everything that you've noticed. +Um, build and test before checking it + + align:start position:0% +Um, build and test before checking it + + + align:start position:0% +Um, build and test before checking it +in. Have daily builds. Have a daily + + align:start position:0% +in. Have daily builds. Have a daily + + + align:start position:0% +in. Have daily builds. Have a daily +playthrough. Um, plan feature cuts, + + align:start position:0% +playthrough. Um, plan feature cuts, + + + align:start position:0% +playthrough. Um, plan feature cuts, +scope. When you realize that you're not + + align:start position:0% +scope. When you realize that you're not + + + align:start position:0% +scope. When you realize that you're not +getting everything done on Friday night + + align:start position:0% +getting everything done on Friday night + + + align:start position:0% +getting everything done on Friday night +as you're working on your game, start + + align:start position:0% +as you're working on your game, start + + + align:start position:0% +as you're working on your game, start +cutting then. Don't wait until Sunday + + align:start position:0% +cutting then. Don't wait until Sunday + + + align:start position:0% +cutting then. Don't wait until Sunday +night to decide what you're going to + + align:start position:0% +night to decide what you're going to + + + align:start position:0% +night to decide what you're going to +cut. Cut as soon as you realize that + + align:start position:0% +cut. Cut as soon as you realize that + + + align:start position:0% +cut. Cut as soon as you realize that +you're blowing your estimates. That will + + align:start position:0% +you're blowing your estimates. That will + + + align:start position:0% +you're blowing your estimates. That will +allow you to choose what you cut and to + + align:start position:0% +allow you to choose what you cut and to + + + align:start position:0% +allow you to choose what you cut and to +adjust changes in your game to reflect + + align:start position:0% +adjust changes in your game to reflect + + + align:start position:0% +adjust changes in your game to reflect +the things you cut. It will also mean + + align:start position:0% +the things you cut. It will also mean + + + align:start position:0% +the things you cut. It will also mean +that testing your game to make sure it + + align:start position:0% +that testing your game to make sure it + + + align:start position:0% +that testing your game to make sure it +all it will introduce a lot fewer bugs + + align:start position:0% +all it will introduce a lot fewer bugs + + + align:start position:0% +all it will introduce a lot fewer bugs +when you do it in a controlled manner + + align:start position:0% +when you do it in a controlled manner + + + align:start position:0% +when you do it in a controlled manner +than when you do it in desperation, + + align:start position:0% +than when you do it in desperation, + + + align:start position:0% +than when you do it in desperation, +which is why I put it under testing. + + align:start position:0% +which is why I put it under testing. + + + align:start position:0% +which is why I put it under testing. +Um, finally, code freezes and asset + + align:start position:0% +Um, finally, code freezes and asset + + + align:start position:0% +Um, finally, code freezes and asset +freezes. These are great and no one + + align:start position:0% +freezes. These are great and no one + + + align:start position:0% +freezes. These are great and no one +likes to use them because it means + + align:start position:0% +likes to use them because it means + + + align:start position:0% +likes to use them because it means +you're going to waste an entire day not + + align:start position:0% +you're going to waste an entire day not + + + align:start position:0% +you're going to waste an entire day not +working on your game. Who wants to do + + align:start position:0% +working on your game. Who wants to do + + + align:start position:0% +working on your game. Who wants to do +that? On the other hand, has anybody + + align:start position:0% +that? On the other hand, has anybody + + + align:start position:0% +that? On the other hand, has anybody +here turned in a project that they've + + align:start position:0% +here turned in a project that they've + + + align:start position:0% +here turned in a project that they've +made a lastm minute change to Sunday + + align:start position:0% +made a lastm minute change to Sunday + + + align:start position:0% +made a lastm minute change to Sunday +night? It was due Monday morning and + + align:start position:0% +night? It was due Monday morning and + + + align:start position:0% +night? It was due Monday morning and +then it didn't run at all. + + align:start position:0% + + + + align:start position:0% + +I got some honest people out there. + + align:start position:0% +I got some honest people out there. + + + align:start position:0% +I got some honest people out there. +Good. Um, yeah. The advantage of taking + + align:start position:0% +Good. Um, yeah. The advantage of taking + + + align:start position:0% +Good. Um, yeah. The advantage of taking +that whole day to test your game is you + + align:start position:0% +that whole day to test your game is you + + + align:start position:0% +that whole day to test your game is you +turn something in that works on Monday. + + align:start position:0% +turn something in that works on Monday. + + + align:start position:0% +turn something in that works on Monday. +Um, often you turn in something that + + align:start position:0% +Um, often you turn in something that + + + align:start position:0% +Um, often you turn in something that +works a lot better on Monday because + + align:start position:0% +works a lot better on Monday because + + + align:start position:0% +works a lot better on Monday because +you've taken the time to test it. You + + align:start position:0% +you've taken the time to test it. You + + + align:start position:0% +you've taken the time to test it. You +found the bugs. You've had a friend help + + align:start position:0% +found the bugs. You've had a friend help + + + align:start position:0% +found the bugs. You've had a friend help +you review your code changes and you + + align:start position:0% +you review your code changes and you + + + align:start position:0% +you review your code changes and you +really got it working. Um, if you want + + align:start position:0% +really got it working. Um, if you want + + + align:start position:0% +really got it working. Um, if you want +to make a good, polished, solid game, + + align:start position:0% +to make a good, polished, solid game, + + + align:start position:0% +to make a good, polished, solid game, +you will think about it and give + + align:start position:0% +you will think about it and give + + + align:start position:0% +you will think about it and give +yourself a cushion. Um, for project two, + + align:start position:0% +yourself a cushion. Um, for project two, + + + align:start position:0% +yourself a cushion. Um, for project two, +that's probably maybe a day. It's a + + align:start position:0% +that's probably maybe a day. It's a + + + align:start position:0% +that's probably maybe a day. It's a +two-eek project. If you give yourself + + align:start position:0% +two-eek project. If you give yourself + + + align:start position:0% +two-eek project. If you give yourself +much more cushion than that, you're not + + align:start position:0% +much more cushion than that, you're not + + + align:start position:0% +much more cushion than that, you're not +actually working on it. Um, but actively + + align:start position:0% +actually working on it. Um, but actively + + + align:start position:0% +actually working on it. Um, but actively +give yourself that deadline and give + + align:start position:0% +give yourself that deadline and give + + + align:start position:0% +give yourself that deadline and give +yourself some time to play your game. + + align:start position:0% +yourself some time to play your game. + + + align:start position:0% +yourself some time to play your game. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +so that's sort of the basics. Some + + align:start position:0% +so that's sort of the basics. Some + + + align:start position:0% +so that's sort of the basics. Some +advanced tips. Um, it's all pretty + + align:start position:0% +advanced tips. Um, it's all pretty + + + align:start position:0% +advanced tips. Um, it's all pretty +simple. I think you've all heard this + + align:start position:0% +simple. I think you've all heard this + + + align:start position:0% +simple. I think you've all heard this +all have we maintain your feature lists. + + align:start position:0% +all have we maintain your feature lists. + + + align:start position:0% +all have we maintain your feature lists. +Agree on how features are going to work. + + align:start position:0% +Agree on how features are going to work. + + + align:start position:0% +Agree on how features are going to work. +So, talk with each other. Um, test those + + align:start position:0% +So, talk with each other. Um, test those + + + align:start position:0% +So, talk with each other. Um, test those +features as soon as they go in. Um, and + + align:start position:0% +features as soon as they go in. Um, and + + + align:start position:0% +features as soon as they go in. Um, and +think about, this may not be worth it on + + align:start position:0% +think about, this may not be worth it on + + + align:start position:0% +think about, this may not be worth it on +these games because they're small. When + + align:start position:0% +these games because they're small. When + + + align:start position:0% +these games because they're small. When +you hit your project 4 game, you may + + align:start position:0% +you hit your project 4 game, you may + + + align:start position:0% +you hit your project 4 game, you may +want to have one of these. Think about + + align:start position:0% +want to have one of these. Think about + + + align:start position:0% +want to have one of these. Think about +having a sort of standardized test plan + + align:start position:0% +having a sort of standardized test plan + + + align:start position:0% +having a sort of standardized test plan +that runs through all the buttons and + + align:start position:0% +that runs through all the buttons and + + + align:start position:0% +that runs through all the buttons and +the branches and the pages and the + + align:start position:0% +the branches and the pages and the + + + align:start position:0% +the branches and the pages and the +options of your game. Um, I realize that + + align:start position:0% +options of your game. Um, I realize that + + + align:start position:0% +options of your game. Um, I realize that +when you've got randomness as one of + + align:start position:0% +when you've got randomness as one of + + + align:start position:0% +when you've got randomness as one of +your core design goals, you can't + + align:start position:0% +your core design goals, you can't + + + align:start position:0% +your core design goals, you can't +predict how your game is going to play. + + align:start position:0% +predict how your game is going to play. + + + align:start position:0% +predict how your game is going to play. +But you should be able to take a look at + + align:start position:0% +But you should be able to take a look at + + + align:start position:0% +But you should be able to take a look at +your game and know most of the states + + align:start position:0% +your game and know most of the states + + + align:start position:0% +your game and know most of the states +that it's going to get in. And you can + + align:start position:0% +that it's going to get in. And you can + + + align:start position:0% +that it's going to get in. And you can +create sort of a checklist that says, + + align:start position:0% +create sort of a checklist that says, + + + align:start position:0% +create sort of a checklist that says, +"Hey, have we sort of exhausted all the + + align:start position:0% +"Hey, have we sort of exhausted all the + + + align:start position:0% +"Hey, have we sort of exhausted all the +possibilities that a player will will + + align:start position:0% +possibilities that a player will will + + + align:start position:0% +possibilities that a player will will +will encounter? Have we tested them all + + align:start position:0% +will encounter? Have we tested them all + + + align:start position:0% +will encounter? Have we tested them all +in the last two builds? Yes or no?" And + + align:start position:0% +in the last two builds? Yes or no?" And + + + align:start position:0% +in the last two builds? Yes or no?" And +the answer should probably there be yes. + + align:start position:0% +the answer should probably there be yes. + + + align:start position:0% +the answer should probably there be yes. +Because one of the things that's very + + align:start position:0% +Because one of the things that's very + + + align:start position:0% +Because one of the things that's very +common with projects that have a lot of + + align:start position:0% +common with projects that have a lot of + + + align:start position:0% +common with projects that have a lot of +highly integrated systems working + + align:start position:0% +highly integrated systems working + + + align:start position:0% +highly integrated systems working +together and depend on emergent + + align:start position:0% +together and depend on emergent + + + align:start position:0% +together and depend on emergent +behavior, which is most games, is you + + align:start position:0% +behavior, which is most games, is you + + + align:start position:0% +behavior, which is most games, is you +can introduce a feature over here that + + align:start position:0% +can introduce a feature over here that + + + align:start position:0% +can introduce a feature over here that +changes the way that a feature that you + + align:start position:0% +changes the way that a feature that you + + + align:start position:0% +changes the way that a feature that you +implemented two weeks ago works. And + + align:start position:0% +implemented two weeks ago works. And + + + align:start position:0% +implemented two weeks ago works. And +you'll never know that it did that until + + align:start position:0% +you'll never know that it did that until + + + align:start position:0% +you'll never know that it did that until +you go through and you test and you find + + align:start position:0% +you go through and you test and you find + + + align:start position:0% +you go through and you test and you find +that something that was working is now + + align:start position:0% +that something that was working is now + + + align:start position:0% +that something that was working is now +broken. So, it is worth it to take the + + align:start position:0% +broken. So, it is worth it to take the + + + align:start position:0% +broken. So, it is worth it to take the +time to go back and check those + + align:start position:0% +time to go back and check those + + + align:start position:0% +time to go back and check those +features, you know, nobody touched + + align:start position:0% + + + + align:start position:0% + +um bug reporting because so many people + + align:start position:0% +um bug reporting because so many people + + + align:start position:0% +um bug reporting because so many people +are so bad at this. I'm going to take my + + align:start position:0% +are so bad at this. I'm going to take my + + + align:start position:0% +are so bad at this. I'm going to take my +I'm going to take the time with a + + align:start position:0% +I'm going to take the time with a + + + align:start position:0% +I'm going to take the time with a +captured audience to tell you how to do + + align:start position:0% +captured audience to tell you how to do + + + align:start position:0% +captured audience to tell you how to do +it. + + align:start position:0% +it. + + + align:start position:0% +it. +Um, be kind to your fellow engineers. Be + + align:start position:0% +Um, be kind to your fellow engineers. Be + + + align:start position:0% +Um, be kind to your fellow engineers. Be +kind to yourself if you end up getting + + align:start position:0% +kind to yourself if you end up getting + + + align:start position:0% +kind to yourself if you end up getting +your own bugs. Write good defect reports + + align:start position:0% +your own bugs. Write good defect reports + + + align:start position:0% +your own bugs. Write good defect reports +and not bad ones. Good bugs include what + + align:start position:0% +and not bad ones. Good bugs include what + + + align:start position:0% +and not bad ones. Good bugs include what +happened, what should have happened, + + align:start position:0% +happened, what should have happened, + + + align:start position:0% +happened, what should have happened, +because it doesn't do me a lot of good + + align:start position:0% +because it doesn't do me a lot of good + + + align:start position:0% +because it doesn't do me a lot of good +if you tell me that the peach mobile is + + align:start position:0% +if you tell me that the peach mobile is + + + align:start position:0% +if you tell me that the peach mobile is +going 30 miles per hour. If I don't know + + align:start position:0% +going 30 miles per hour. If I don't know + + + align:start position:0% +going 30 miles per hour. If I don't know +why that's a problem, um + + align:start position:0% +why that's a problem, um + + + align:start position:0% +why that's a problem, um +how how do I reproduce it? If it's + + align:start position:0% +how how do I reproduce it? If it's + + + align:start position:0% +how how do I reproduce it? If it's +obvious to reproduce, you don't need to + + align:start position:0% +obvious to reproduce, you don't need to + + + align:start position:0% +obvious to reproduce, you don't need to +include it. But if it took 38 steps, + + align:start position:0% +include it. But if it took 38 steps, + + + align:start position:0% +include it. But if it took 38 steps, +include a text file. + + align:start position:0% +include a text file. + + + align:start position:0% +include a text file. +How common is the bug? How serious is + + align:start position:0% +How common is the bug? How serious is + + + align:start position:0% +How common is the bug? How serious is +the bug? Is this something that the team + + align:start position:0% +the bug? Is this something that the team + + + align:start position:0% +the bug? Is this something that the team +needs to jump on right now? or is this + + align:start position:0% +needs to jump on right now? or is this + + + align:start position:0% +needs to jump on right now? or is this +something that Sunday afternoon you're + + align:start position:0% +something that Sunday afternoon you're + + + align:start position:0% +something that Sunday afternoon you're +gonna look at and say, "Eh, ship it." + + align:start position:0% +gonna look at and say, "Eh, ship it." + + + align:start position:0% +gonna look at and say, "Eh, ship it." +Because some bugs you look at and you + + align:start position:0% +Because some bugs you look at and you + + + align:start position:0% +Because some bugs you look at and you +say, "Eh, ship it." But you want to know + + align:start position:0% +say, "Eh, ship it." But you want to know + + + align:start position:0% +say, "Eh, ship it." But you want to know +that it's there and you want to know how + + align:start position:0% +that it's there and you want to know how + + + align:start position:0% +that it's there and you want to know how +it's going to affect your game before + + align:start position:0% +it's going to affect your game before + + + align:start position:0% +it's going to affect your game before +you just decide to ship it. Um, include + + align:start position:0% +you just decide to ship it. Um, include + + + align:start position:0% +you just decide to ship it. Um, include +some supporting data if it's going to be + + align:start position:0% +some supporting data if it's going to be + + + align:start position:0% +some supporting data if it's going to be +helpful, and it often is. If you're + + align:start position:0% +helpful, and it often is. If you're + + + align:start position:0% +helpful, and it often is. If you're +trying to describe something visually, + + align:start position:0% +trying to describe something visually, + + + align:start position:0% +trying to describe something visually, +give them a screenshot. Um, if you can + + align:start position:0% +give them a screenshot. Um, if you can + + + align:start position:0% +give them a screenshot. Um, if you can +run it in the debugger and catch some + + align:start position:0% +run it in the debugger and catch some + + + align:start position:0% +run it in the debugger and catch some +debugging code, great. + + align:start position:0% +debugging code, great. + + + align:start position:0% +debugging code, great. +Um, save the files, know the version of + + align:start position:0% +Um, save the files, know the version of + + + align:start position:0% +Um, save the files, know the version of +the game you were using. Um, be ready to + + align:start position:0% +the game you were using. Um, be ready to + + + align:start position:0% +the game you were using. Um, be ready to +help your team member who has to fix + + align:start position:0% +help your team member who has to fix + + + align:start position:0% +help your team member who has to fix +your horrible, awful crash that happens + + align:start position:0% +your horrible, awful crash that happens + + + align:start position:0% +your horrible, awful crash that happens +one out of every four times. Um, and + + align:start position:0% +one out of every four times. Um, and + + + align:start position:0% +one out of every four times. Um, and +you're not sure how you made it. Be + + align:start position:0% +you're not sure how you made it. Be + + + align:start position:0% +you're not sure how you made it. Be +willing to help them recreate it because + + align:start position:0% +willing to help them recreate it because + + + align:start position:0% +willing to help them recreate it because +it can be really hard to recreate bugs. + + align:start position:0% +it can be really hard to recreate bugs. + + + align:start position:0% +it can be really hard to recreate bugs. +Finally, + + align:start position:0% +Finally, + + + align:start position:0% +Finally, +um, know the difference between a + + align:start position:0% +um, know the difference between a + + + align:start position:0% +um, know the difference between a +criticism and a critique and make sure + + align:start position:0% +criticism and a critique and make sure + + + align:start position:0% +criticism and a critique and make sure +that your reports are critiques of the + + align:start position:0% +that your reports are critiques of the + + + align:start position:0% +that your reports are critiques of the +game and the bugs and not criticisms of + + align:start position:0% +game and the bugs and not criticisms of + + + align:start position:0% +game and the bugs and not criticisms of +your fellow developers and their ideas. + + align:start position:0% +your fellow developers and their ideas. + + + align:start position:0% +your fellow developers and their ideas. +And when I say criticism, what I mean + + align:start position:0% +And when I say criticism, what I mean + + + align:start position:0% +And when I say criticism, what I mean +here is an unsupported opinion, usually + + align:start position:0% +here is an unsupported opinion, usually + + + align:start position:0% +here is an unsupported opinion, usually +delivered in an unprofessional tone. + + align:start position:0% +delivered in an unprofessional tone. + + + align:start position:0% +delivered in an unprofessional tone. +These purple elephants are junk and it's + + align:start position:0% +These purple elephants are junk and it's + + + align:start position:0% +These purple elephants are junk and it's +totally stupid that they fly. + + align:start position:0% +totally stupid that they fly. + + + align:start position:0% +totally stupid that they fly. +Um, a critique is a statement of opinion + + align:start position:0% +Um, a critique is a statement of opinion + + + align:start position:0% +Um, a critique is a statement of opinion +about the game backed up by examples and + + align:start position:0% +about the game backed up by examples and + + + align:start position:0% +about the game backed up by examples and +hopefully facts. The purple elephants + + align:start position:0% +hopefully facts. The purple elephants + + + align:start position:0% +hopefully facts. The purple elephants +make the game too easy because they can + + align:start position:0% +make the game too easy because they can + + + align:start position:0% +make the game too easy because they can +fly. I can skip almost a third of the + + align:start position:0% +fly. I can skip almost a third of the + + + align:start position:0% +fly. I can skip almost a third of the +gameplay in the bottom area of the + + align:start position:0% +gameplay in the bottom area of the + + + align:start position:0% +gameplay in the bottom area of the +screen. There's a problem. There's a + + align:start position:0% +screen. There's a problem. There's a + + + align:start position:0% +screen. There's a problem. There's a +reason why it's a problem. And there's a + + align:start position:0% +reason why it's a problem. And there's a + + + align:start position:0% +reason why it's a problem. And there's a +fact that you can talk about. You can + + align:start position:0% +fact that you can talk about. You can + + + align:start position:0% +fact that you can talk about. You can +have opinions. And it doesn't matter + + align:start position:0% +have opinions. And it doesn't matter + + + align:start position:0% +have opinions. And it doesn't matter +that the purple elephants go in the game + + align:start position:0% +that the purple elephants go in the game + + + align:start position:0% +that the purple elephants go in the game +or not. You can just talk about what + + align:start position:0% +or not. You can just talk about what + + + align:start position:0% +or not. You can just talk about what +they're doing in the game. You don't + + align:start position:0% +they're doing in the game. You don't + + + align:start position:0% +they're doing in the game. You don't +have to talk about the person who put + + align:start position:0% +have to talk about the person who put + + + align:start position:0% +have to talk about the person who put +the purple elephants in the game at all. + + align:start position:0% +the purple elephants in the game at all. + + + align:start position:0% +the purple elephants in the game at all. +Okay, so user testing. I think we've + + align:start position:0% +Okay, so user testing. I think we've + + + align:start position:0% +Okay, so user testing. I think we've +actually covered this one to death. But + + align:start position:0% +actually covered this one to death. But + + + align:start position:0% +actually covered this one to death. But +if I did a slide, if I did a lecture + + align:start position:0% +if I did a slide, if I did a lecture + + + align:start position:0% +if I did a slide, if I did a lecture +about testing, I didn't stop and talk + + align:start position:0% +about testing, I didn't stop and talk + + + align:start position:0% +about testing, I didn't stop and talk +about why you're doing it. It would be a + + align:start position:0% +about why you're doing it. It would be a + + + align:start position:0% +about why you're doing it. It would be a +little odd. Um, once again, every time + + align:start position:0% +little odd. Um, once again, every time + + + align:start position:0% +little odd. Um, once again, every time +we say iterative design, that means you + + align:start position:0% +we say iterative design, that means you + + + align:start position:0% +we say iterative design, that means you +make a design, you test it, you get the + + align:start position:0% +make a design, you test it, you get the + + + align:start position:0% +make a design, you test it, you get the +data, you move on. Without actually + + align:start position:0% +data, you move on. Without actually + + + align:start position:0% +data, you move on. Without actually +testing it with users, you don't get + + align:start position:0% +testing it with users, you don't get + + + align:start position:0% +testing it with users, you don't get +real data. + + align:start position:0% +real data. + + + align:start position:0% +real data. +um etc and so forth. So I think that + + align:start position:0% +um etc and so forth. So I think that + + + align:start position:0% +um etc and so forth. So I think that +drum has been well and truly beaten. But + + align:start position:0% +drum has been well and truly beaten. But + + + align:start position:0% +drum has been well and truly beaten. But +um here's a warning we haven't really + + align:start position:0% +um here's a warning we haven't really + + + align:start position:0% +um here's a warning we haven't really +talked about yet, which is testdriven + + align:start position:0% +talked about yet, which is testdriven + + + align:start position:0% +talked about yet, which is testdriven +design + + align:start position:0% +design + + + align:start position:0% +design +does not mean do what your testers tell + + align:start position:0% +does not mean do what your testers tell + + + align:start position:0% +does not mean do what your testers tell +you to do. Testd driven design means + + align:start position:0% +you to do. Testd driven design means + + + align:start position:0% +you to do. Testd driven design means +gather data from your testers, analyze + + align:start position:0% +gather data from your testers, analyze + + + align:start position:0% +gather data from your testers, analyze +it, and act on it. Um 90% of all MIT + + align:start position:0% +it, and act on it. Um 90% of all MIT + + + align:start position:0% +it, and act on it. Um 90% of all MIT +students will tell you that your game is + + align:start position:0% +students will tell you that your game is + + + align:start position:0% +students will tell you that your game is +too easy. + + align:start position:0% +too easy. + + + align:start position:0% +too easy. +They're wrong. + + align:start position:0% +They're wrong. + + + align:start position:0% +They're wrong. +90% of all people who like to play + + align:start position:0% +90% of all people who like to play + + + align:start position:0% +90% of all people who like to play +first-person shooters will tell you that + + align:start position:0% +first-person shooters will tell you that + + + align:start position:0% +first-person shooters will tell you that +your game needs a gun. + + align:start position:0% +your game needs a gun. + + + align:start position:0% +your game needs a gun. +If you didn't plan on having a gun in + + align:start position:0% +If you didn't plan on having a gun in + + + align:start position:0% +If you didn't plan on having a gun in +your game, it probably really doesn't + + align:start position:0% +your game, it probably really doesn't + + + align:start position:0% +your game, it probably really doesn't +need a gun. Um, testers are often full + + align:start position:0% +need a gun. Um, testers are often full + + + align:start position:0% +need a gun. Um, testers are often full +of solutions and suggestions to make + + align:start position:0% +of solutions and suggestions to make + + + align:start position:0% +of solutions and suggestions to make +your game just like the game they wish + + align:start position:0% +your game just like the game they wish + + + align:start position:0% +your game just like the game they wish +they were playing. But you're not trying + + align:start position:0% +they were playing. But you're not trying + + + align:start position:0% +they were playing. But you're not trying +to make that game. You're trying to make + + align:start position:0% +to make that game. You're trying to make + + + align:start position:0% +to make that game. You're trying to make +the game you're trying to make. So when + + align:start position:0% +the game you're trying to make. So when + + + align:start position:0% +the game you're trying to make. So when +you gather your data, put it through the + + align:start position:0% +you gather your data, put it through the + + + align:start position:0% +you gather your data, put it through the +filter of what your vision of the game + + align:start position:0% +filter of what your vision of the game + + + align:start position:0% +filter of what your vision of the game +is and what you intend your game to do. + + align:start position:0% +is and what you intend your game to do. + + + align:start position:0% +is and what you intend your game to do. +And don't let your testers drive your + + align:start position:0% +And don't let your testers drive your + + + align:start position:0% +And don't let your testers drive your +game. Let your vision and your data + + align:start position:0% +game. Let your vision and your data + + + align:start position:0% +game. Let your vision and your data +drive it. + + align:start position:0% +drive it. + + + align:start position:0% +drive it. +So how how do you get ideas from testers + + align:start position:0% +So how how do you get ideas from testers + + + align:start position:0% +So how how do you get ideas from testers +and how do you actually turn them into + + align:start position:0% +and how do you actually turn them into + + + align:start position:0% +and how do you actually turn them into +something useful? + + align:start position:0% +something useful? + + + align:start position:0% +something useful? +Um so you all remember the experimental + + align:start position:0% +Um so you all remember the experimental + + + align:start position:0% +Um so you all remember the experimental +method. It's actually really pretty + + align:start position:0% +method. It's actually really pretty + + + align:start position:0% +method. It's actually really pretty +similar. going to form a hypothesis or + + align:start position:0% +similar. going to form a hypothesis or + + + align:start position:0% +similar. going to form a hypothesis or +ask a question. Um figure out how to get + + align:start position:0% +ask a question. Um figure out how to get + + + align:start position:0% +ask a question. Um figure out how to get +the data to that question, collect it + + align:start position:0% +the data to that question, collect it + + + align:start position:0% +the data to that question, collect it +and analyze it. So forming a question, + + align:start position:0% +and analyze it. So forming a question, + + + align:start position:0% +and analyze it. So forming a question, +what do you need to know about your game + + align:start position:0% +what do you need to know about your game + + + align:start position:0% +what do you need to know about your game +that your team can't answer? Um the more + + align:start position:0% +that your team can't answer? Um the more + + + align:start position:0% +that your team can't answer? Um the more +specific you can be, the more the easier + + align:start position:0% +specific you can be, the more the easier + + + align:start position:0% +specific you can be, the more the easier +it is. Sometimes it is kind of hard to + + align:start position:0% +it is. Sometimes it is kind of hard to + + + align:start position:0% +it is. Sometimes it is kind of hard to +get specific because you've got a game + + align:start position:0% +get specific because you've got a game + + + align:start position:0% +get specific because you've got a game +and you've got a whole lot of + + align:start position:0% +and you've got a whole lot of + + + align:start position:0% +and you've got a whole lot of +interlinking systems and it's hard to + + align:start position:0% +interlinking systems and it's hard to + + + align:start position:0% +interlinking systems and it's hard to +figure out which one is making things + + align:start position:0% +figure out which one is making things + + + align:start position:0% +figure out which one is making things +not quite right. But do your best. Um is + + align:start position:0% +not quite right. But do your best. Um is + + + align:start position:0% +not quite right. But do your best. Um is +there a particular mechanic? Are people + + align:start position:0% +there a particular mechanic? Are people + + + align:start position:0% +there a particular mechanic? Are people +having a hard time or an easy time + + align:start position:0% +having a hard time or an easy time + + + align:start position:0% +having a hard time or an easy time +getting started on your game? Um, how + + align:start position:0% +getting started on your game? Um, how + + + align:start position:0% +getting started on your game? Um, how +engaged are people in your gameplay? Are + + align:start position:0% +engaged are people in your gameplay? Are + + + align:start position:0% +engaged are people in your gameplay? Are +they playing the game and grinning or + + align:start position:0% +they playing the game and grinning or + + + align:start position:0% +they playing the game and grinning or +they just sort of sitting there and and + + align:start position:0% +they just sort of sitting there and and + + + align:start position:0% +they just sort of sitting there and and +hitting the keys? Um, how many of your + + align:start position:0% +hitting the keys? Um, how many of your + + + align:start position:0% +hitting the keys? Um, how many of your +players complete your game in about the + + align:start position:0% +players complete your game in about the + + + align:start position:0% +players complete your game in about the +time you expected them to? How many of + + align:start position:0% +time you expected them to? How many of + + + align:start position:0% +time you expected them to? How many of +them complete it too quickly or take too + + align:start position:0% +them complete it too quickly or take too + + + align:start position:0% +them complete it too quickly or take too +long? Um, so when you're running + + align:start position:0% +long? Um, so when you're running + + + align:start position:0% +long? Um, so when you're running +scientific experiments, you kind of try + + align:start position:0% +scientific experiments, you kind of try + + + align:start position:0% +scientific experiments, you kind of try +to standardize your conditions as much + + align:start position:0% +to standardize your conditions as much + + + align:start position:0% +to standardize your conditions as much +as possible to get data that can be + + align:start position:0% +as possible to get data that can be + + + align:start position:0% +as possible to get data that can be +compared with it with with each other. + + align:start position:0% +compared with it with with each other. + + + align:start position:0% +compared with it with with each other. +when you're when you're collecting + + align:start position:0% +when you're when you're collecting + + + align:start position:0% +when you're when you're collecting +qualitative data, which is what most + + align:start position:0% +qualitative data, which is what most + + + align:start position:0% +qualitative data, which is what most +focus testing data is, this is actually + + align:start position:0% +focus testing data is, this is actually + + + align:start position:0% +focus testing data is, this is actually +pretty hard to do, but you want to try + + align:start position:0% +pretty hard to do, but you want to try + + + align:start position:0% +pretty hard to do, but you want to try +to do it anyway. So, um, some of the + + align:start position:0% +to do it anyway. So, um, some of the + + + align:start position:0% +to do it anyway. So, um, some of the +ways you can do that is by make sure + + align:start position:0% +ways you can do that is by make sure + + + align:start position:0% +ways you can do that is by make sure +you're giving each player the same set + + align:start position:0% +you're giving each player the same set + + + align:start position:0% +you're giving each player the same set +of starting information, by having a + + align:start position:0% +of starting information, by having a + + + align:start position:0% +of starting information, by having a +script to introduce your game, to give + + align:start position:0% +script to introduce your game, to give + + + align:start position:0% +script to introduce your game, to give +them any information about the game + + align:start position:0% +them any information about the game + + + align:start position:0% +them any information about the game +they're going to need, because your game + + align:start position:0% +they're going to need, because your game + + + align:start position:0% +they're going to need, because your game +isn't too early to have a UI. Games + + align:start position:0% +isn't too early to have a UI. Games + + + align:start position:0% +isn't too early to have a UI. Games +often don't have UIs that are + + align:start position:0% +often don't have UIs that are + + + align:start position:0% +often don't have UIs that are +particularly useful while they're while + + align:start position:0% +particularly useful while they're while + + + align:start position:0% +particularly useful while they're while +they want to be tested early. That's + + align:start position:0% +they want to be tested early. That's + + + align:start position:0% +they want to be tested early. That's +okay. Just tell your players what your + + align:start position:0% +okay. Just tell your players what your + + + align:start position:0% +okay. Just tell your players what your +UI should tell them. Um, you can double + + align:start position:0% +UI should tell them. Um, you can double + + + align:start position:0% +UI should tell them. Um, you can double +this up with user testing by giving them + + align:start position:0% +this up with user testing by giving them + + + align:start position:0% +this up with user testing by giving them +pictures of the intended UI and they can + + align:start position:0% +pictures of the intended UI and they can + + + align:start position:0% +pictures of the intended UI and they can +you can see if they can figure it out + + align:start position:0% +you can see if they can figure it out + + + align:start position:0% +you can see if they can figure it out +from there or not. But that's kind of + + align:start position:0% +from there or not. But that's kind of + + + align:start position:0% +from there or not. But that's kind of +advanced testing tricks. Um, have a + + align:start position:0% +advanced testing tricks. Um, have a + + + align:start position:0% +advanced testing tricks. Um, have a +dedicated observer. Don't depend on + + align:start position:0% +dedicated observer. Don't depend on + + + align:start position:0% +dedicated observer. Don't depend on +their memory for what they're looking + + align:start position:0% +their memory for what they're looking + + + align:start position:0% +their memory for what they're looking +for or what they see. Um, give them a + + align:start position:0% +for or what they see. Um, give them a + + + align:start position:0% +for or what they see. Um, give them a +list of specific things to look for that + + align:start position:0% +list of specific things to look for that + + + align:start position:0% +list of specific things to look for that +you think will answer the questions you + + align:start position:0% +you think will answer the questions you + + + align:start position:0% +you think will answer the questions you +need to answer. Give them space to write + + align:start position:0% +need to answer. Give them space to write + + + align:start position:0% +need to answer. Give them space to write +it down with and give them sort of the + + align:start position:0% +it down with and give them sort of the + + + align:start position:0% +it down with and give them sort of the +autonomy to stand back and just take + + align:start position:0% +autonomy to stand back and just take + + + align:start position:0% +autonomy to stand back and just take +notes while someone else offers your + + align:start position:0% +notes while someone else offers your + + + align:start position:0% +notes while someone else offers your +player assistance or introduces them to + + align:start position:0% +player assistance or introduces them to + + + align:start position:0% +player assistance or introduces them to +the game. And finally, you really can't + + align:start position:0% +the game. And finally, you really can't + + + align:start position:0% +the game. And finally, you really can't +observe everything. Um, think about what + + align:start position:0% +observe everything. Um, think about what + + + align:start position:0% +observe everything. Um, think about what +your players might be able to tell you + + align:start position:0% +your players might be able to tell you + + + align:start position:0% +your players might be able to tell you +um that you can't see. Write down a few + + align:start position:0% +um that you can't see. Write down a few + + + align:start position:0% +um that you can't see. Write down a few +questions for them to answer afterwards + + align:start position:0% +questions for them to answer afterwards + + + align:start position:0% +questions for them to answer afterwards +if you need to. Keep it short. You don't + + align:start position:0% +if you need to. Keep it short. You don't + + + align:start position:0% +if you need to. Keep it short. You don't +really want to make somebody write an + + align:start position:0% +really want to make somebody write an + + + align:start position:0% +really want to make somebody write an +essay while they do your testing. Um, if + + align:start position:0% +essay while they do your testing. Um, if + + + align:start position:0% +essay while they do your testing. Um, if +you can encourage your players to talk + + align:start position:0% +you can encourage your players to talk + + + align:start position:0% +you can encourage your players to talk +to the game or to talk out loud while + + align:start position:0% +to the game or to talk out loud while + + + align:start position:0% +to the game or to talk out loud while +they play, that's the greatest thing + + align:start position:0% +they play, that's the greatest thing + + + align:start position:0% +they play, that's the greatest thing +ever. Um, + + align:start position:0% +ever. Um, + + + align:start position:0% +ever. Um, +the best people I've ever heard played + + align:start position:0% +the best people I've ever heard played + + + align:start position:0% +the best people I've ever heard played +games are middle schoolers because they + + align:start position:0% +games are middle schoolers because they + + + align:start position:0% +games are middle schoolers because they +they connect their they kind of connect + + align:start position:0% +they connect their they kind of connect + + + align:start position:0% +they connect their they kind of connect +their brain straight to their mouth + + align:start position:0% +their brain straight to their mouth + + + align:start position:0% +their brain straight to their mouth +without any filter and they're just + + align:start position:0% +without any filter and they're just + + + align:start position:0% +without any filter and they're just +they're just there. They're telling you + + align:start position:0% +they're just there. They're telling you + + + align:start position:0% +they're just there. They're telling you +what they're doing. They're telling you + + align:start position:0% +what they're doing. They're telling you + + + align:start position:0% +what they're doing. They're telling you +why they're doing it. They're telling + + align:start position:0% +why they're doing it. They're telling + + + align:start position:0% +why they're doing it. They're telling +you why this particular aspect of your + + align:start position:0% +you why this particular aspect of your + + + align:start position:0% +you why this particular aspect of your +game is the worst thing ever or why this + + align:start position:0% +game is the worst thing ever or why this + + + align:start position:0% +game is the worst thing ever or why this +particular aspect of your game is the + + align:start position:0% +particular aspect of your game is the + + + align:start position:0% +particular aspect of your game is the +greatest thing ever. Um, and you can + + align:start position:0% +greatest thing ever. Um, and you can + + + align:start position:0% +greatest thing ever. Um, and you can +just sit there and listen to them and + + align:start position:0% +just sit there and listen to them and + + + align:start position:0% +just sit there and listen to them and +you know why they're doing things. + + align:start position:0% +you know why they're doing things. + + + align:start position:0% +you know why they're doing things. +Adults are a lot quieter. We often don't + + align:start position:0% +Adults are a lot quieter. We often don't + + + align:start position:0% +Adults are a lot quieter. We often don't +want to explain why we're doing + + align:start position:0% +want to explain why we're doing + + + align:start position:0% +want to explain why we're doing +something because often it's because we + + align:start position:0% +something because often it's because we + + + align:start position:0% +something because often it's because we +don't know what we're supposed to be + + align:start position:0% +don't know what we're supposed to be + + + align:start position:0% +don't know what we're supposed to be +doing and we don't want to admit that I + + align:start position:0% +doing and we don't want to admit that I + + + align:start position:0% +doing and we don't want to admit that I +don't know what I'm doing. I'm just + + align:start position:0% +don't know what I'm doing. I'm just + + + align:start position:0% +don't know what I'm doing. I'm just +going to poke stuff until I figure out + + align:start position:0% +going to poke stuff until I figure out + + + align:start position:0% +going to poke stuff until I figure out +what's going on. Um so that's where you + + align:start position:0% +what's going on. Um so that's where you + + + align:start position:0% +what's going on. Um so that's where you +kind of want to watch people and you + + align:start position:0% +kind of want to watch people and you + + + align:start position:0% +kind of want to watch people and you +know if you really need to you can lean + + align:start position:0% +know if you really need to you can lean + + + align:start position:0% +know if you really need to you can lean +in and say why did you do that thing or + + align:start position:0% +in and say why did you do that thing or + + + align:start position:0% +in and say why did you do that thing or +even better what are you thinking? + + align:start position:0% +even better what are you thinking? + + + align:start position:0% +even better what are you thinking? +People will often answer those questions + + align:start position:0% +People will often answer those questions + + + align:start position:0% +People will often answer those questions +but you really want to keep those + + align:start position:0% +but you really want to keep those + + + align:start position:0% +but you really want to keep those +proddding questions neutral. Don't say, + + align:start position:0% +proddding questions neutral. Don't say, + + + align:start position:0% +proddding questions neutral. Don't say, +"Why did you do that crazy thing?" or + + align:start position:0% +"Why did you do that crazy thing?" or + + + align:start position:0% +"Why did you do that crazy thing?" or +"What are you looking for back there?" + + align:start position:0% +"What are you looking for back there?" + + + align:start position:0% +"What are you looking for back there?" +Like just what are you thinking? What + + align:start position:0% +Like just what are you thinking? What + + + align:start position:0% +Like just what are you thinking? What +are you doing? + + align:start position:0% +are you doing? + + + align:start position:0% +are you doing? +What's your plan? + + align:start position:0% +What's your plan? + + + align:start position:0% +What's your plan? +Um that sort of thing. Once you've got + + align:start position:0% +Um that sort of thing. Once you've got + + + align:start position:0% +Um that sort of thing. Once you've got +your data, the team can review it + + align:start position:0% +your data, the team can review it + + + align:start position:0% +your data, the team can review it +together to kind of notice trends, spot + + align:start position:0% +together to kind of notice trends, spot + + + align:start position:0% +together to kind of notice trends, spot +common problems, and so on. And that's + + align:start position:0% +common problems, and so on. And that's + + + align:start position:0% +common problems, and so on. And that's +where the things that four or five or a + + align:start position:0% +where the things that four or five or a + + + align:start position:0% +where the things that four or five or a +majority of your testers did or said or + + align:start position:0% +majority of your testers did or said or + + + align:start position:0% +majority of your testers did or said or +or ran into, that's what you're going to + + align:start position:0% +or ran into, that's what you're going to + + + align:start position:0% +or ran into, that's what you're going to +be pulling out. and using to think about + + align:start position:0% +be pulling out. and using to think about + + + align:start position:0% +be pulling out. and using to think about +how you're going to fix those problems. + + align:start position:0% +how you're going to fix those problems. + + + align:start position:0% +how you're going to fix those problems. +Or if you noticed a trend that you + + align:start position:0% +Or if you noticed a trend that you + + + align:start position:0% +Or if you noticed a trend that you +hadn't noticed before that people were + + align:start position:0% +hadn't noticed before that people were + + + align:start position:0% +hadn't noticed before that people were +really liking the aspect of your game + + align:start position:0% +really liking the aspect of your game + + + align:start position:0% +really liking the aspect of your game +you hadn't thought about, it's something + + align:start position:0% +you hadn't thought about, it's something + + + align:start position:0% +you hadn't thought about, it's something +you can work on magnifying so that you + + align:start position:0% +you can work on magnifying so that you + + + align:start position:0% +you can work on magnifying so that you +can share it with everyone. + + align:start position:0% +can share it with everyone. + + + align:start position:0% +can share it with everyone. +Um, so for those of you who fell asleep + + align:start position:0% +Um, so for those of you who fell asleep + + + align:start position:0% +Um, so for those of you who fell asleep +while I was talking, the too long didn't + + align:start position:0% +while I was talking, the too long didn't + + + align:start position:0% +while I was talking, the too long didn't +read version really is who are you + + align:start position:0% +read version really is who are you + + + align:start position:0% +read version really is who are you +testing with because your audience will + + align:start position:0% +testing with because your audience will + + + align:start position:0% +testing with because your audience will +affect your data. what are you testing + + align:start position:0% +affect your data. what are you testing + + + align:start position:0% +affect your data. what are you testing +with? The state of your game will affect + + align:start position:0% +with? The state of your game will affect + + + align:start position:0% +with? The state of your game will affect +your data. That shouldn't stop you from + + align:start position:0% +your data. That shouldn't stop you from + + + align:start position:0% +your data. That shouldn't stop you from +testing with early builds. Um, but it + + align:start position:0% +testing with early builds. Um, but it + + + align:start position:0% +testing with early builds. Um, but it +does mean you need to adjust your + + align:start position:0% +does mean you need to adjust your + + + align:start position:0% +does mean you need to adjust your +expectations and make sure your players + + align:start position:0% +expectations and make sure your players + + + align:start position:0% +expectations and make sure your players +are ready to play with it. Um, + + align:start position:0% +are ready to play with it. Um, + + + align:start position:0% +are ready to play with it. Um, +and finally, why are you testing? Only + + align:start position:0% +and finally, why are you testing? Only + + + align:start position:0% +and finally, why are you testing? Only +you can answer that question. We can + + align:start position:0% +you can answer that question. We can + + + align:start position:0% +you can answer that question. We can +give you a lot of reasons or + + align:start position:0% +give you a lot of reasons or + + + align:start position:0% +give you a lot of reasons or +suggestions, but if you're running a + + align:start position:0% +suggestions, but if you're running a + + + align:start position:0% +suggestions, but if you're running a +focus test, it really needs to be + + align:start position:0% +focus test, it really needs to be + + + align:start position:0% +focus test, it really needs to be +because you're looking for data that + + align:start position:0% +because you're looking for data that + + + align:start position:0% +because you're looking for data that +your team intends to use. Um, and you + + align:start position:0% +your team intends to use. Um, and you + + + align:start position:0% +your team intends to use. Um, and you +can always use data to support your + + align:start position:0% +can always use data to support your + + + align:start position:0% +can always use data to support your +game. You really can. Even if you don't + + align:start position:0% +game. You really can. Even if you don't + + + align:start position:0% +game. You really can. Even if you don't +realize that you need it, you do. + + align:start position:0% +realize that you need it, you do. + + + align:start position:0% +realize that you need it, you do. +Okay? And I keep saying and gather data. + + align:start position:0% +Okay? And I keep saying and gather data. + + + align:start position:0% +Okay? And I keep saying and gather data. +And I talked about observations, I + + align:start position:0% +And I talked about observations, I + + + align:start position:0% +And I talked about observations, I +talked about surveys, um, I talked about + + align:start position:0% +talked about surveys, um, I talked about + + + align:start position:0% +talked about surveys, um, I talked about +interviews, which are kind of our our + + align:start position:0% +interviews, which are kind of our our + + + align:start position:0% +interviews, which are kind of our our +three major tools. Unless you are going + + align:start position:0% +three major tools. Unless you are going + + + align:start position:0% +three major tools. Unless you are going +to go to all the work of videotaping + + align:start position:0% +to go to all the work of videotaping + + + align:start position:0% +to go to all the work of videotaping +your videotaping and audio recording and + + align:start position:0% +your videotaping and audio recording and + + + align:start position:0% +your videotaping and audio recording and +getting releases from your testers, + + align:start position:0% +getting releases from your testers, + + + align:start position:0% +getting releases from your testers, +which I I I really don't recommend. + + align:start position:0% +which I I I really don't recommend. + + + align:start position:0% +which I I I really don't recommend. +That's that's more work than you should + + align:start position:0% +That's that's more work than you should + + + align:start position:0% +That's that's more work than you should +be doing. But but the three major tools + + align:start position:0% +be doing. But but the three major tools + + + align:start position:0% +be doing. But but the three major tools +really are observing people and taking + + align:start position:0% +really are observing people and taking + + + align:start position:0% +really are observing people and taking +notes, asking them a standard set of + + align:start position:0% +notes, asking them a standard set of + + + align:start position:0% +notes, asking them a standard set of +questions afterwards, either on paper or + + align:start position:0% +questions afterwards, either on paper or + + + align:start position:0% +questions afterwards, either on paper or +in person, and thinking about what kind + + align:start position:0% +in person, and thinking about what kind + + + align:start position:0% +in person, and thinking about what kind +of data you could gather with each of + + align:start position:0% +of data you could gather with each of + + + align:start position:0% +of data you could gather with each of +those you gather best with each of those + + align:start position:0% +those you gather best with each of those + + + align:start position:0% +those you gather best with each of those +methods. Um, if you have 20 different + + align:start position:0% +methods. Um, if you have 20 different + + + align:start position:0% +methods. Um, if you have 20 different +levels you want someone to rate on a one + + align:start position:0% +levels you want someone to rate on a one + + + align:start position:0% +levels you want someone to rate on a one +to five as to whether it's good or not, + + align:start position:0% +to five as to whether it's good or not, + + + align:start position:0% +to five as to whether it's good or not, +you should just give them a piece of + + align:start position:0% +you should just give them a piece of + + + align:start position:0% +you should just give them a piece of +paper and when they finish each level, + + align:start position:0% +paper and when they finish each level, + + + align:start position:0% +paper and when they finish each level, +they can check a number between one and + + align:start position:0% +they can check a number between one and + + + align:start position:0% +they can check a number between one and +five. Um, if you want to see how long it + + align:start position:0% +five. Um, if you want to see how long it + + + align:start position:0% +five. Um, if you want to see how long it +takes someone to get started playing the + + align:start position:0% +takes someone to get started playing the + + + align:start position:0% +takes someone to get started playing the +game, you probably just want to watch + + align:start position:0% +game, you probably just want to watch + + + align:start position:0% +game, you probably just want to watch +them with a timer. How long does it take + + align:start position:0% +them with a timer. How long does it take + + + align:start position:0% +them with a timer. How long does it take +them to get from that first screen to + + align:start position:0% +them to get from that first screen to + + + align:start position:0% +them to get from that first screen to +the the to the to this to getting into + + align:start position:0% +the the to the to this to getting into + + + align:start position:0% +the the to the to this to getting into +the game? Um, and finally, if you want + + align:start position:0% +the game? Um, and finally, if you want + + + align:start position:0% +the game? Um, and finally, if you want +to get sort of a general impression, + + align:start position:0% +to get sort of a general impression, + + + align:start position:0% +to get sort of a general impression, +sometimes talking with people helps + + align:start position:0% +sometimes talking with people helps + + + align:start position:0% +sometimes talking with people helps +bring out things that you didn't think + + align:start position:0% +bring out things that you didn't think + + + align:start position:0% +bring out things that you didn't think +of. You can get some some insights you + + align:start position:0% +of. You can get some some insights you + + + align:start position:0% +of. You can get some some insights you +wouldn't have thought to ask for by + + align:start position:0% +wouldn't have thought to ask for by + + + align:start position:0% +wouldn't have thought to ask for by +talking with people. But be a little + + align:start position:0% +talking with people. But be a little + + + align:start position:0% +talking with people. But be a little +careful talking with people because + + align:start position:0% +careful talking with people because + + + align:start position:0% +careful talking with people because +people don't want to tell you bad things + + align:start position:0% +people don't want to tell you bad things + + + align:start position:0% +people don't want to tell you bad things +to your face. They'd rather write the + + align:start position:0% +to your face. They'd rather write the + + + align:start position:0% +to your face. They'd rather write the +bad things down on a piece of paper + + align:start position:0% +bad things down on a piece of paper + + + align:start position:0% +bad things down on a piece of paper +where they don't have to admit that they + + align:start position:0% +where they don't have to admit that they + + + align:start position:0% +where they don't have to admit that they +said bad things about this game. um that + + align:start position:0% +said bad things about this game. um that + + + align:start position:0% +said bad things about this game. um that +that covers less for middle school + + align:start position:0% +that covers less for middle school + + + align:start position:0% +that covers less for middle school +students as I mentioned earlier, but um + + align:start position:0% +students as I mentioned earlier, but um + + + align:start position:0% +students as I mentioned earlier, but um +but most people don't really want to say + + align:start position:0% +but most people don't really want to say + + + align:start position:0% +but most people don't really want to say +mean things to the person who made the + + align:start position:0% +mean things to the person who made the + + + align:start position:0% +mean things to the person who made the +game because we don't want to make + + align:start position:0% +game because we don't want to make + + + align:start position:0% +game because we don't want to make +people feel bad. So, you kind of need to + + align:start position:0% +people feel bad. So, you kind of need to + + + align:start position:0% +people feel bad. So, you kind of need to +balance that out when you're asking + + align:start position:0% +balance that out when you're asking + + + align:start position:0% +balance that out when you're asking +people questions about, well, how did + + align:start position:0% +people questions about, well, how did + + + align:start position:0% +people questions about, well, how did +you like the game? + + align:start position:0% +you like the game? + + + align:start position:0% +you like the game? +The answer is usually, oh, it's great. + + align:start position:0% +The answer is usually, oh, it's great. + + + align:start position:0% +The answer is usually, oh, it's great. +Yeah. + + align:start position:0% + + + + align:start position:0% + +Okay. So, having kind of run through all + + align:start position:0% +Okay. So, having kind of run through all + + + align:start position:0% +Okay. So, having kind of run through all +of that, let me show you. Let me fight + + align:start position:0% +of that, let me show you. Let me fight + + + align:start position:0% +of that, let me show you. Let me fight +with my computer and bring up a couple + + align:start position:0% +with my computer and bring up a couple + + + align:start position:0% +with my computer and bring up a couple +of examples. Um, + + align:start position:0% +of examples. Um, + + + align:start position:0% +of examples. Um, +this is that's not the right form yet. + + align:start position:0% +this is that's not the right form yet. + + + align:start position:0% +this is that's not the right form yet. +All right. So, this is a script created + + align:start position:0% +All right. So, this is a script created + + + align:start position:0% +All right. So, this is a script created +by students by a team that had a + + align:start position:0% +by students by a team that had a + + + align:start position:0% +by students by a team that had a +dedicated QA lead person. Don't expect + + align:start position:0% +dedicated QA lead person. Don't expect + + + align:start position:0% +dedicated QA lead person. Don't expect +your don't I do not expect your your + + align:start position:0% +your don't I do not expect your your + + + align:start position:0% +your don't I do not expect your your +sheets to look anything like this, but I + + align:start position:0% +sheets to look anything like this, but I + + + align:start position:0% +sheets to look anything like this, but I +wanted to see sort of an example of what + + align:start position:0% +wanted to see sort of an example of what + + + align:start position:0% +wanted to see sort of an example of what +someone did when it was their job and + + align:start position:0% +someone did when it was their job and + + + align:start position:0% +someone did when it was their job and +they were taking time to get things + + align:start position:0% +they were taking time to get things + + + align:start position:0% +they were taking time to get things +ready. So, you can see how serious we + + align:start position:0% +ready. So, you can see how serious we + + + align:start position:0% +ready. So, you can see how serious we +are. And so, you've got sort of your + + align:start position:0% +are. And so, you've got sort of your + + + align:start position:0% +are. And so, you've got sort of your +your observer instructions. And what's + + align:start position:0% +your observer instructions. And what's + + + align:start position:0% +your observer instructions. And what's +day's goal? + + align:start position:0% +day's goal? + + + align:start position:0% +day's goal? +Finding out if the feedback in the game + + align:start position:0% +Finding out if the feedback in the game + + + align:start position:0% +Finding out if the feedback in the game +works along with a couple of other + + align:start position:0% +works along with a couple of other + + + align:start position:0% +works along with a couple of other +things. Um, and there's a testing script + + align:start position:0% +things. Um, and there's a testing script + + + align:start position:0% +things. Um, and there's a testing script +kind of read out written out pretty + + align:start position:0% +kind of read out written out pretty + + + align:start position:0% +kind of read out written out pretty +clearly along with some basic + + align:start position:0% +clearly along with some basic + + + align:start position:0% +clearly along with some basic +instructions. Um, since these teams had + + align:start position:0% +instructions. Um, since these teams had + + + align:start position:0% +instructions. Um, since these teams had +a dedicated focus lead, focus test lead, + + align:start position:0% +a dedicated focus lead, focus test lead, + + + align:start position:0% +a dedicated focus lead, focus test lead, +they had someone who'd spent a lot of + + align:start position:0% +they had someone who'd spent a lot of + + + align:start position:0% +they had someone who'd spent a lot of +time thinking about testing and a lot of + + align:start position:0% +time thinking about testing and a lot of + + + align:start position:0% +time thinking about testing and a lot of +people had spent a lot of time working + + align:start position:0% +people had spent a lot of time working + + + align:start position:0% +people had spent a lot of time working +on the game. So, the lead tester was in + + align:start position:0% +on the game. So, the lead tester was in + + + align:start position:0% +on the game. So, the lead tester was in +the position of trying to make sure that + + align:start position:0% +the position of trying to make sure that + + + align:start position:0% +the position of trying to make sure that +the team understood how to run tests + + align:start position:0% +the team understood how to run tests + + + align:start position:0% +the team understood how to run tests +because they weren't experts at it + + align:start position:0% +because they weren't experts at it + + + align:start position:0% +because they weren't experts at it +either. So, they just sort of embedded + + align:start position:0% +either. So, they just sort of embedded + + + align:start position:0% +either. So, they just sort of embedded +all of the good advice right into the + + align:start position:0% +all of the good advice right into the + + + align:start position:0% +all of the good advice right into the +script. + + align:start position:0% +script. + + + align:start position:0% +script. +Um, and there you have it. And then + + align:start position:0% +Um, and there you have it. And then + + + align:start position:0% +Um, and there you have it. And then +there's a sheet to write notes down. + + align:start position:0% +there's a sheet to write notes down. + + + align:start position:0% +there's a sheet to write notes down. +um they've got sort of the big questions + + align:start position:0% +um they've got sort of the big questions + + + align:start position:0% +um they've got sort of the big questions +that they're worried about + + align:start position:0% +that they're worried about + + + align:start position:0% +that they're worried about +so they can write down they've got space + + align:start position:0% +so they can write down they've got space + + + align:start position:0% +so they can write down they've got space +for other notes and it means that + + align:start position:0% +for other notes and it means that + + + align:start position:0% +for other notes and it means that +whatever they've got they've got and + + align:start position:0% +whatever they've got they've got and + + + align:start position:0% +whatever they've got they've got and +then finally it follows up with a fairly + + align:start position:0% +then finally it follows up with a fairly + + + align:start position:0% +then finally it follows up with a fairly +short questionnaire + + align:start position:0% +short questionnaire + + + align:start position:0% +short questionnaire +um trying to to get some answers to + + align:start position:0% +um trying to to get some answers to + + + align:start position:0% +um trying to to get some answers to +questions they're wondering about and + + align:start position:0% +questions they're wondering about and + + + align:start position:0% +questions they're wondering about and +the specific I mean the specifics are + + align:start position:0% +the specific I mean the specifics are + + + align:start position:0% +the specific I mean the specifics are +always going to vary from game to game. + + align:start position:0% +always going to vary from game to game. + + + align:start position:0% +always going to vary from game to game. +looking at the focus test sheet for one + + align:start position:0% +looking at the focus test sheet for one + + + align:start position:0% +looking at the focus test sheet for one +game isn't going to help you wildly with + + align:start position:0% +game isn't going to help you wildly with + + + align:start position:0% +game isn't going to help you wildly with +yours, but you can take a look at the + + align:start position:0% +yours, but you can take a look at the + + + align:start position:0% +yours, but you can take a look at the +way you can think about the way the + + align:start position:0% +way you can think about the way the + + + align:start position:0% +way you can think about the way the +questions are worded and the number of + + align:start position:0% +questions are worded and the number of + + + align:start position:0% +questions are worded and the number of +questions + + align:start position:0% +questions + + + align:start position:0% +questions +um so that you're not overloading + + align:start position:0% +um so that you're not overloading + + + align:start position:0% +um so that you're not overloading +people. I believe these are up on + + align:start position:0% +people. I believe these are up on + + + align:start position:0% +people. I believe these are up on +stellar as as a sample if you want to + + align:start position:0% +stellar as as a sample if you want to + + + align:start position:0% +stellar as as a sample if you want to +download it and look at it as an + + align:start position:0% +download it and look at it as an + + + align:start position:0% +download it and look at it as an +example. + + align:start position:0% +example. + + + align:start position:0% +example. +Um finally, the the paper we expect you + + align:start position:0% +Um finally, the the paper we expect you + + + align:start position:0% +Um finally, the the paper we expect you +to do. Um so this is the focus test + + align:start position:0% +to do. Um so this is the focus test + + + align:start position:0% +to do. Um so this is the focus test +report + + align:start position:0% +report + + + align:start position:0% +report +um which is also downloadable on stellar + + align:start position:0% +um which is also downloadable on stellar + + + align:start position:0% +um which is also downloadable on stellar +I think in either word or rich text + + align:start position:0% +I think in either word or rich text + + + align:start position:0% +I think in either word or rich text +format so you can use it. This is what + + align:start position:0% +format so you can use it. This is what + + + align:start position:0% +format so you can use it. This is what +we when we say when we expect you to + + align:start position:0% +we when we say when we expect you to + + + align:start position:0% +we when we say when we expect you to +turn in a focus test report this is what + + align:start position:0% +turn in a focus test report this is what + + + align:start position:0% +turn in a focus test report this is what +we're expecting you to turn in. If you + + align:start position:0% +we're expecting you to turn in. If you + + + align:start position:0% +we're expecting you to turn in. If you +take a look at it it's actually got most + + align:start position:0% +take a look at it it's actually got most + + + align:start position:0% +take a look at it it's actually got most +it sort of walks you through the whole + + align:start position:0% +it sort of walks you through the whole + + + align:start position:0% +it sort of walks you through the whole +process and there's a space for most of + + align:start position:0% +process and there's a space for most of + + + align:start position:0% +process and there's a space for most of +the stuff. So what's the goal of the + + align:start position:0% +the stuff. So what's the goal of the + + + align:start position:0% +the stuff. So what's the goal of the +focus test? + + align:start position:0% +focus test? + + + align:start position:0% +focus test? +Record what happened at the focus test + + align:start position:0% +Record what happened at the focus test + + + align:start position:0% +Record what happened at the focus test +and what are you going to do afterwards. + + align:start position:0% +and what are you going to do afterwards. + + + align:start position:0% +and what are you going to do afterwards. +Um, when you are planning your focus + + align:start position:0% +Um, when you are planning your focus + + + align:start position:0% +Um, when you are planning your focus +tests for this afternoon later in class, + + align:start position:0% +tests for this afternoon later in class, + + + align:start position:0% +tests for this afternoon later in class, +I recommend you download this and sort + + align:start position:0% +I recommend you download this and sort + + + align:start position:0% +I recommend you download this and sort +of use it as your sheet to record notes + + align:start position:0% +of use it as your sheet to record notes + + + align:start position:0% +of use it as your sheet to record notes +on because it'll it'll help keep you + + align:start position:0% +on because it'll it'll help keep you + + + align:start position:0% +on because it'll it'll help keep you +it'll help make sure that you get the + + align:start position:0% +it'll help make sure that you get the + + + align:start position:0% +it'll help make sure that you get the +data that we are asking you to get. + + align:start position:0% +data that we are asking you to get. + + + align:start position:0% +data that we are asking you to get. +Um, and I think that's actually most + + align:start position:0% +Um, and I think that's actually most + + + align:start position:0% +Um, and I think that's actually most +about most of what I have to say about + + align:start position:0% +about most of what I have to say about + + + align:start position:0% +about most of what I have to say about +testing. Are there any questions? + + align:start position:0% + + + + align:start position:0% + +question. + + align:start position:0% +question. + + + align:start position:0% +question. +Who's currently using some sort of bug + + align:start position:0% +Who's currently using some sort of bug + + + align:start position:0% +Who's currently using some sort of bug +database? + + align:start position:0% +database? + + + align:start position:0% +database? +And if so, what are you what are folks + + align:start position:0% +And if so, what are you what are folks + + + align:start position:0% +And if so, what are you what are folks +currently using? Oh, who let me rephrase + + align:start position:0% +currently using? Oh, who let me rephrase + + + align:start position:0% +currently using? Oh, who let me rephrase +that. Who who has used a bug data + + align:start position:0% +that. Who who has used a bug data + + + align:start position:0% +that. Who who has used a bug data +before? But what are some of the ones + + align:start position:0% +before? But what are some of the ones + + + align:start position:0% +before? But what are some of the ones +that you're familiar with? + + align:start position:0% +that you're familiar with? + + + align:start position:0% +that you're familiar with? +Jira. Jira. + + align:start position:0% +Jira. Jira. + + + align:start position:0% +Jira. Jira. +Bug. + + align:start position:0% +Bug. + + + align:start position:0% +Bug. +Which one? + + align:start position:0% +Which one? + + + align:start position:0% +Which one? +Bug. + + align:start position:0% +Bug. + + + align:start position:0% +Bug. +Oh, Bugzilla. Yeah. Bugganizer. + + align:start position:0% +Oh, Bugzilla. Yeah. Bugganizer. + + + align:start position:0% +Oh, Bugzilla. Yeah. Bugganizer. +Morganizer. + + align:start position:0% +Morganizer. + + + align:start position:0% +Morganizer. +Modernizer. + + align:start position:0% +Modernizer. + + + align:start position:0% +Modernizer. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Huh. Google. + + align:start position:0% +Huh. Google. + + + align:start position:0% +Huh. Google. +Oh, the the the Google Cloud database. + + align:start position:0% +Oh, the the the Google Cloud database. + + + align:start position:0% +Oh, the the the Google Cloud database. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Mhm. + + align:start position:0% +Mhm. + + + align:start position:0% +Mhm. +And you know, as Sarah mentioned, you + + align:start position:0% +And you know, as Sarah mentioned, you + + + align:start position:0% +And you know, as Sarah mentioned, you +can also just use like a Google + + align:start position:0% +can also just use like a Google + + + align:start position:0% +can also just use like a Google +spreadsheet or something. + + align:start position:0% +spreadsheet or something. + + + align:start position:0% +spreadsheet or something. +Integrate database too. + + align:start position:0% +Integrate database too. + + + align:start position:0% +Integrate database too. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +You you can there is always this + + align:start position:0% +You you can there is always this + + + align:start position:0% +You you can there is always this +intermediate step between someone + + align:start position:0% +intermediate step between someone + + + align:start position:0% +intermediate step between someone +entering a bug into a bug database and + + align:start position:0% +entering a bug into a bug database and + + + align:start position:0% +entering a bug into a bug database and +then deciding that they're going to fix + + align:start position:0% +then deciding that they're going to fix + + + align:start position:0% +then deciding that they're going to fix +it, right? You know, there's a priority. + + align:start position:0% +it, right? You know, there's a priority. + + + align:start position:0% +it, right? You know, there's a priority. +Somebody actually says, "I, you know, I + + align:start position:0% +Somebody actually says, "I, you know, I + + + align:start position:0% +Somebody actually says, "I, you know, I +think it's a bug that the characters, + + align:start position:0% +think it's a bug that the characters, + + + align:start position:0% +think it's a bug that the characters, +you know, are too short or something." + + align:start position:0% +you know, are too short or something." + + + align:start position:0% +you know, are too short or something." +And then the art director says, "Nope, + + align:start position:0% +And then the art director says, "Nope, + + + align:start position:0% +And then the art director says, "Nope, +not a bug. Will not fix that." Um, + + align:start position:0% +not a bug. Will not fix that." Um, + + + align:start position:0% +not a bug. Will not fix that." Um, +so, uh, just because you're entering + + align:start position:0% +so, uh, just because you're entering + + + align:start position:0% +so, uh, just because you're entering +something in a bug database doesn't + + align:start position:0% +something in a bug database doesn't + + + align:start position:0% +something in a bug database doesn't +necessarily mean that your team's + + align:start position:0% +necessarily mean that your team's + + + align:start position:0% +necessarily mean that your team's +committed to actually spending time on + + align:start position:0% +committed to actually spending time on + + + align:start position:0% +committed to actually spending time on +that. But when the team does decide that + + align:start position:0% +that. But when the team does decide that + + + align:start position:0% +that. But when the team does decide that +okay this is a problem maybe because it + + align:start position:0% +okay this is a problem maybe because it + + + align:start position:0% +okay this is a problem maybe because it +crashes the game maybe because it's + + align:start position:0% +crashes the game maybe because it's + + + align:start position:0% +crashes the game maybe because it's +actually some not how we want the game + + align:start position:0% +actually some not how we want the game + + + align:start position:0% +actually some not how we want the game +to perform uh it needs to be entered + + align:start position:0% +to perform uh it needs to be entered + + + align:start position:0% +to perform uh it needs to be entered +into your task list. So that means your + + align:start position:0% +into your task list. So that means your + + + align:start position:0% +into your task list. So that means your +task list is changing uh you need to be + + align:start position:0% +task list is changing uh you need to be + + + align:start position:0% +task list is changing uh you need to be +able to to to put that in a priority. + + align:start position:0% +able to to to put that in a priority. + + + align:start position:0% +able to to to put that in a priority. +Possibly this bug is more serious than + + align:start position:0% +Possibly this bug is more serious than + + + align:start position:0% +Possibly this bug is more serious than +some of the planned tasks that you + + align:start position:0% +some of the planned tasks that you + + + align:start position:0% +some of the planned tasks that you +already had on. So you need to re you + + align:start position:0% +already had on. So you need to re you + + + align:start position:0% +already had on. So you need to re you +need to rearrange them so that they fix. + + align:start position:0% +need to rearrange them so that they fix. + + + align:start position:0% +need to rearrange them so that they fix. +Um, something else that Sarah mentioned + + align:start position:0% +Um, something else that Sarah mentioned + + + align:start position:0% +Um, something else that Sarah mentioned +very briefly, but I want to stress MIT + + align:start position:0% +very briefly, but I want to stress MIT + + + align:start position:0% +very briefly, but I want to stress MIT +students are actually horrible testers. + + align:start position:0% +students are actually horrible testers. + + + align:start position:0% +students are actually horrible testers. +Um, I've heard this many times from many + + align:start position:0% +Um, I've heard this many times from many + + + align:start position:0% +Um, I've heard this many times from many +different uh, companies here in in MIT + + align:start position:0% +different uh, companies here in in MIT + + + align:start position:0% +different uh, companies here in in MIT +students are are not a representative + + align:start position:0% +students are are not a representative + + + align:start position:0% +students are are not a representative +population of the general public. You + + align:start position:0% +population of the general public. You + + + align:start position:0% +population of the general public. You +look at systems differently. You look at + + align:start position:0% +look at systems differently. You look at + + + align:start position:0% +look at systems differently. You look at +screens differently. Um, so even though + + align:start position:0% +screens differently. Um, so even though + + + align:start position:0% +screens differently. Um, so even though +most of our testing that we're going to + + align:start position:0% +most of our testing that we're going to + + + align:start position:0% +most of our testing that we're going to +be doing this semester, I imagine that a + + align:start position:0% +be doing this semester, I imagine that a + + + align:start position:0% +be doing this semester, I imagine that a +lot of the testing you're going to do on + + align:start position:0% +lot of the testing you're going to do on + + + align:start position:0% +lot of the testing you're going to do on +your own is going to be with other + + align:start position:0% +your own is going to be with other + + + align:start position:0% +your own is going to be with other +people in your dorms, for instance. Uh, + + align:start position:0% +people in your dorms, for instance. Uh, + + + align:start position:0% +people in your dorms, for instance. Uh, +and that's that's fine for this class, + + align:start position:0% +and that's that's fine for this class, + + + align:start position:0% +and that's that's fine for this class, +but don't think that it's normal to use + + align:start position:0% +but don't think that it's normal to use + + + align:start position:0% +but don't think that it's normal to use +even like university students as your + + align:start position:0% +even like university students as your + + + align:start position:0% +even like university students as your +only test audience. That's that's really + + align:start position:0% +only test audience. That's that's really + + + align:start position:0% +only test audience. That's that's really +not representative of general public. + + align:start position:0% +not representative of general public. + + + align:start position:0% +not representative of general public. +MIT students in particular + + align:start position:0% +MIT students in particular + + + align:start position:0% +MIT students in particular +students final thing is um Sarah + + align:start position:0% +students final thing is um Sarah + + + align:start position:0% +students final thing is um Sarah +mentioned user testing in two contexts + + align:start position:0% +mentioned user testing in two contexts + + + align:start position:0% +mentioned user testing in two contexts +one for sort of an overall category of + + align:start position:0% +one for sort of an overall category of + + + align:start position:0% +one for sort of an overall category of +you are testing with users and then you + + align:start position:0% +you are testing with users and then you + + + align:start position:0% +you are testing with users and then you +broken down to more specifically focus + + align:start position:0% +broken down to more specifically focus + + + align:start position:0% +broken down to more specifically focus +testing and user testing + + align:start position:0% +testing and user testing + + + align:start position:0% +testing and user testing +and you may be wondering why user + + align:start position:0% +and you may be wondering why user + + + align:start position:0% +and you may be wondering why user +testing is used in that that way for two + + align:start position:0% +testing is used in that that way for two + + + align:start position:0% +testing is used in that that way for two +different things uh uh as Sarah said + + align:start position:0% +different things uh uh as Sarah said + + + align:start position:0% +different things uh uh as Sarah said +it's good to be more granular what we + + align:start position:0% +it's good to be more granular what we + + + align:start position:0% +it's good to be more granular what we +normally refer to as usability testing + + align:start position:0% +normally refer to as usability testing + + + align:start position:0% +normally refer to as usability testing +as as S mentioned earlier earlier has + + align:start position:0% +as as S mentioned earlier earlier has + + + align:start position:0% +as as S mentioned earlier earlier has +only like fairly recently become like + + align:start position:0% +only like fairly recently become like + + + align:start position:0% +only like fairly recently become like +the standard name for it. + + align:start position:0% +the standard name for it. + + + align:start position:0% +the standard name for it. +Yes. + + align:start position:0% +Yes. + + + align:start position:0% +Yes. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Back in the 90s and even the early 2000s + + align:start position:0% +Back in the 90s and even the early 2000s + + + align:start position:0% +Back in the 90s and even the early 2000s +user testing and usability testing were + + align:start position:0% +user testing and usability testing were + + + align:start position:0% +user testing and usability testing were +basically the same thing because we were + + align:start position:0% +basically the same thing because we were + + + align:start position:0% +basically the same thing because we were +talking about websites and enterprise + + align:start position:0% +talking about websites and enterprise + + + align:start position:0% +talking about websites and enterprise +software. We were not talking about + + align:start position:0% +software. We were not talking about + + + align:start position:0% +software. We were not talking about +games. So the only kind of user testing + + align:start position:0% +games. So the only kind of user testing + + + align:start position:0% +games. So the only kind of user testing +that you'll be doing putting piece of + + align:start position:0% +that you'll be doing putting piece of + + + align:start position:0% +that you'll be doing putting piece of +software in front of somebody getting + + align:start position:0% +software in front of somebody getting + + + align:start position:0% +software in front of somebody getting +feedback was usability testing. That's + + align:start position:0% +feedback was usability testing. That's + + + align:start position:0% +feedback was usability testing. That's +why it's had the same name for so long. + + align:start position:0% +why it's had the same name for so long. + + + align:start position:0% +why it's had the same name for so long. +But now there's focus testing which is + + align:start position:0% +But now there's focus testing which is + + + align:start position:0% +But now there's focus testing which is +very very applicable not just for games + + align:start position:0% +very very applicable not just for games + + + align:start position:0% +very very applicable not just for games +but also for things like user + + align:start position:0% +but also for things like user + + + align:start position:0% +but also for things like user +experience. Anyone heard that term user + + align:start position:0% +experience. Anyone heard that term user + + + align:start position:0% +experience. Anyone heard that term user +experience design? + + align:start position:0% +experience design? + + + align:start position:0% +experience design? +Yeah. So where it's not just can the + + align:start position:0% +Yeah. So where it's not just can the + + + align:start position:0% +Yeah. So where it's not just can the +person figure out what to do but is the + + align:start position:0% +person figure out what to do but is the + + + align:start position:0% +person figure out what to do but is the +person actually having the desired + + align:start position:0% +person actually having the desired + + + align:start position:0% +person actually having the desired +experience from the game. + + align:start position:0% +experience from the game. + + + align:start position:0% +experience from the game. +That's why now there's multiple for + + align:start position:0% +That's why now there's multiple for + + + align:start position:0% +That's why now there's multiple for +that. + + align:start position:0% +that. + + + align:start position:0% +that. +Thank you. Okay. Um then I think I'm out + + align:start position:0% +Thank you. Okay. Um then I think I'm out + + + align:start position:0% +Thank you. Okay. Um then I think I'm out +of here. I'm going to sneak off with my + + align:start position:0% +of here. I'm going to sneak off with my + + + align:start position:0% +of here. I'm going to sneak off with my +computer. + + align:start position:0% +computer. + + + align:start position:0% +computer. +All right. Hi guys. My name is Genevieve + + align:start position:0% +All right. Hi guys. My name is Genevieve + + + align:start position:0% +All right. Hi guys. My name is Genevieve +Connley. I'm a researcher at Riot. And + + align:start position:0% +Connley. I'm a researcher at Riot. And + + + align:start position:0% +Connley. I'm a researcher at Riot. And +um some other terms that you might have + + align:start position:0% +um some other terms that you might have + + + align:start position:0% +um some other terms that you might have +heard for that, user experience + + align:start position:0% +heard for that, user experience + + + align:start position:0% +heard for that, user experience +researcher, user researcher, or kind of + + align:start position:0% +researcher, user researcher, or kind of + + + align:start position:0% +researcher, user researcher, or kind of +the way we were just talking about like + + align:start position:0% +the way we were just talking about like + + + align:start position:0% +the way we were just talking about like +a user tester basically. Um and a little + + align:start position:0% +a user tester basically. Um and a little + + + align:start position:0% +a user tester basically. Um and a little +bit about me, I graduated from MIT in + + align:start position:0% +bit about me, I graduated from MIT in + + + align:start position:0% +bit about me, I graduated from MIT in +2010. Um I got my degree in course 9. + + align:start position:0% +2010. Um I got my degree in course 9. + + + align:start position:0% +2010. Um I got my degree in course 9. +And uh I actually worked at the MIT + + align:start position:0% +And uh I actually worked at the MIT + + + align:start position:0% +And uh I actually worked at the MIT +Gambit Game Lab um on a couple games + + align:start position:0% +Gambit Game Lab um on a couple games + + + align:start position:0% +Gambit Game Lab um on a couple games +there. So that's actually where I got my + + align:start position:0% +there. So that's actually where I got my + + + align:start position:0% +there. So that's actually where I got my +start doing user testing was in the + + align:start position:0% +start doing user testing was in the + + + align:start position:0% +start doing user testing was in the +summer projects. Um, we would run play + + align:start position:0% +summer projects. Um, we would run play + + + align:start position:0% +summer projects. Um, we would run play +tests with local community members, have + + align:start position:0% +tests with local community members, have + + + align:start position:0% +tests with local community members, have +them come in, and that's where I + + align:start position:0% +them come in, and that's where I + + + align:start position:0% +them come in, and that's where I +actually did my first user tests. + + align:start position:0% +actually did my first user tests. + + + align:start position:0% +actually did my first user tests. +So, I work at Riot Games. Uh, how many + + align:start position:0% +So, I work at Riot Games. Uh, how many + + + align:start position:0% +So, I work at Riot Games. Uh, how many +of you guys have heard of League of + + align:start position:0% +of you guys have heard of League of + + + align:start position:0% +of you guys have heard of League of +Legends before? + + align:start position:0% +Legends before? + + + align:start position:0% +Legends before? +Okay. How many How many of you actively + + align:start position:0% +Okay. How many How many of you actively + + + align:start position:0% +Okay. How many How many of you actively +play League of Legends? Okay, good. So, + + align:start position:0% +play League of Legends? Okay, good. So, + + + align:start position:0% +play League of Legends? Okay, good. So, +I'll give I'll give a little bit of + + align:start position:0% +I'll give I'll give a little bit of + + + align:start position:0% +I'll give I'll give a little bit of +context on the game just so I'm not + + align:start position:0% +context on the game just so I'm not + + + align:start position:0% +context on the game just so I'm not +losing anybody and I'll try to make sure + + align:start position:0% +losing anybody and I'll try to make sure + + + align:start position:0% +losing anybody and I'll try to make sure +I explain all of our jargon because + + align:start position:0% +I explain all of our jargon because + + + align:start position:0% +I explain all of our jargon because +sometimes when you're in a game company, + + align:start position:0% +sometimes when you're in a game company, + + + align:start position:0% +sometimes when you're in a game company, +you just kind of start using the + + align:start position:0% +you just kind of start using the + + + align:start position:0% +you just kind of start using the +language like everybody speaks that + + align:start position:0% +language like everybody speaks that + + + align:start position:0% +language like everybody speaks that +language. But a little bit about Riot is + + align:start position:0% +language. But a little bit about Riot is + + + align:start position:0% +language. But a little bit about Riot is +we make League of Legends and our kind + + align:start position:0% +we make League of Legends and our kind + + + align:start position:0% +we make League of Legends and our kind +of core mission is that we aspire to be + + align:start position:0% +of core mission is that we aspire to be + + + align:start position:0% +of core mission is that we aspire to be +the most player focused game company in + + align:start position:0% +the most player focused game company in + + + align:start position:0% +the most player focused game company in +the world. And this is going to be + + align:start position:0% +the world. And this is going to be + + + align:start position:0% +the world. And this is going to be +pretty relevant to what I'm talking + + align:start position:0% +pretty relevant to what I'm talking + + + align:start position:0% +pretty relevant to what I'm talking +about today because you can't really be + + align:start position:0% +about today because you can't really be + + + align:start position:0% +about today because you can't really be +player focused if you don't talk to your + + align:start position:0% +player focused if you don't talk to your + + + align:start position:0% +player focused if you don't talk to your +players. So what this means at Wright is + + align:start position:0% +players. So what this means at Wright is + + + align:start position:0% +players. So what this means at Wright is +we think about all of our decisions in + + align:start position:0% +we think about all of our decisions in + + + align:start position:0% +we think about all of our decisions in +terms of how much player value it adds + + align:start position:0% +terms of how much player value it adds + + + align:start position:0% +terms of how much player value it adds +or how much player pain something + + align:start position:0% +or how much player pain something + + + align:start position:0% +or how much player pain something +negative causes. Uh, so this is like I + + align:start position:0% +negative causes. Uh, so this is like I + + + align:start position:0% +negative causes. Uh, so this is like I +don't know if any of you are familiar, + + align:start position:0% +don't know if any of you are familiar, + + + align:start position:0% +don't know if any of you are familiar, +we have an esports scene and right now + + align:start position:0% +we have an esports scene and right now + + + align:start position:0% +we have an esports scene and right now +we're in the middle of our world + + align:start position:0% +we're in the middle of our world + + + align:start position:0% +we're in the middle of our world +championships and we created a video and + + align:start position:0% +championships and we created a video and + + + align:start position:0% +championships and we created a video and +a song that would basically we hope to + + align:start position:0% +a song that would basically we hope to + + + align:start position:0% +a song that would basically we hope to +be kind of the anthem of the world + + align:start position:0% +be kind of the anthem of the world + + + align:start position:0% +be kind of the anthem of the world +championship. And this is kind of + + align:start position:0% +championship. And this is kind of + + + align:start position:0% +championship. And this is kind of +something that a couple of people at the + + align:start position:0% +something that a couple of people at the + + + align:start position:0% +something that a couple of people at the +studio thought was really important. So + + align:start position:0% +studio thought was really important. So + + + align:start position:0% +studio thought was really important. So +they just went out and made it and the + + align:start position:0% +they just went out and made it and the + + + align:start position:0% +they just went out and made it and the +point was just make players pumped up + + align:start position:0% +point was just make players pumped up + + + align:start position:0% +point was just make players pumped up +about worlds and to give them a song + + align:start position:0% +about worlds and to give them a song + + + align:start position:0% +about worlds and to give them a song +that kind of represented how they feel. + + align:start position:0% +that kind of represented how they feel. + + + align:start position:0% +that kind of represented how they feel. +And this is just a small example of + + align:start position:0% +And this is just a small example of + + + align:start position:0% +And this is just a small example of +something that happens at Riot where we + + align:start position:0% +something that happens at Riot where we + + + align:start position:0% +something that happens at Riot where we +really just want to do something that we + + align:start position:0% +really just want to do something that we + + + align:start position:0% +really just want to do something that we +think players will think is cool. And + + align:start position:0% +think players will think is cool. And + + + align:start position:0% +think players will think is cool. And +one of the ways that we do that is + + align:start position:0% +one of the ways that we do that is + + + align:start position:0% +one of the ways that we do that is +through play testing and user testing. + + align:start position:0% +through play testing and user testing. + + + align:start position:0% +through play testing and user testing. +And I'm going to use a little bit + + align:start position:0% +And I'm going to use a little bit + + + align:start position:0% +And I'm going to use a little bit +different terminology. So I'll make sure + + align:start position:0% +different terminology. So I'll make sure + + + align:start position:0% +different terminology. So I'll make sure +that I kind of tie it back into the way + + align:start position:0% +that I kind of tie it back into the way + + + align:start position:0% +that I kind of tie it back into the way +that Sarah's been talking about it as we + + align:start position:0% +that Sarah's been talking about it as we + + + align:start position:0% +that Sarah's been talking about it as we +go. So a little bit League of Legends, + + align:start position:0% +go. So a little bit League of Legends, + + + align:start position:0% +go. So a little bit League of Legends, +it's a generally a 5v5 game. It's a team + + align:start position:0% +it's a generally a 5v5 game. It's a team + + + align:start position:0% +it's a generally a 5v5 game. It's a team +oriented game. So you play as a member + + align:start position:0% +oriented game. So you play as a member + + + align:start position:0% +oriented game. So you play as a member +of a team and you usually play a + + align:start position:0% +of a team and you usually play a + + + align:start position:0% +of a team and you usually play a +specific role or position on that team + + align:start position:0% +specific role or position on that team + + + align:start position:0% +specific role or position on that team +just like kind of basketball. Um, and + + align:start position:0% +just like kind of basketball. Um, and + + + align:start position:0% +just like kind of basketball. Um, and +you play as one of many champions and + + align:start position:0% +you play as one of many champions and + + + align:start position:0% +you play as one of many champions and +it's online and it's competitive. So, + + align:start position:0% +it's online and it's competitive. So, + + + align:start position:0% +it's online and it's competitive. So, +like I said, we have an esports scene, + + align:start position:0% +like I said, we have an esports scene, + + + align:start position:0% +like I said, we have an esports scene, +but you play against another team and + + align:start position:0% +but you play against another team and + + + align:start position:0% +but you play against another team and +you go basically across this map, try to + + align:start position:0% +you go basically across this map, try to + + + align:start position:0% +you go basically across this map, try to +take in objectives and ultimately blow + + align:start position:0% +take in objectives and ultimately blow + + + align:start position:0% +take in objectives and ultimately blow +up this thing called the Nexus, which is + + align:start position:0% +up this thing called the Nexus, which is + + + align:start position:0% +up this thing called the Nexus, which is +like a giant crystal on the other side + + align:start position:0% +like a giant crystal on the other side + + + align:start position:0% +like a giant crystal on the other side +of the map + + align:start position:0% +of the map + + + align:start position:0% +of the map +and you play as a champion. And these + + align:start position:0% +and you play as a champion. And these + + + align:start position:0% +and you play as a champion. And these +are player characters that each have + + align:start position:0% +are player characters that each have + + + align:start position:0% +are player characters that each have +kind of an individual set of skills, + + align:start position:0% +kind of an individual set of skills, + + + align:start position:0% +kind of an individual set of skills, +different play styles, and there's over + + align:start position:0% +different play styles, and there's over + + + align:start position:0% +different play styles, and there's over +120 of them in our game. So even though + + align:start position:0% +120 of them in our game. So even though + + + align:start position:0% +120 of them in our game. So even though +the each game is session based, you + + align:start position:0% +the each game is session based, you + + + align:start position:0% +the each game is session based, you +don't kind of level up your character + + align:start position:0% +don't kind of level up your character + + + align:start position:0% +don't kind of level up your character +necessarily over the lifetime of playing + + align:start position:0% +necessarily over the lifetime of playing + + + align:start position:0% +necessarily over the lifetime of playing +the game. Each session is a new session. + + align:start position:0% +the game. Each session is a new session. + + + align:start position:0% +the game. Each session is a new session. +There's lots of different ways to play + + align:start position:0% +There's lots of different ways to play + + + align:start position:0% +There's lots of different ways to play +because we have lots of different + + align:start position:0% +because we have lots of different + + + align:start position:0% +because we have lots of different +characters, which I'll talk to in a + + align:start position:0% +characters, which I'll talk to in a + + + align:start position:0% +characters, which I'll talk to in a +little bit. + + align:start position:0% + + + + align:start position:0% + +So one of the things that I talked about + + align:start position:0% +So one of the things that I talked about + + + align:start position:0% +So one of the things that I talked about +is it's really hard to be player focused + + align:start position:0% +is it's really hard to be player focused + + + align:start position:0% +is it's really hard to be player focused +if you don't talk to your players. And + + align:start position:0% +if you don't talk to your players. And + + + align:start position:0% +if you don't talk to your players. And +one of the things at Riot is that we all + + align:start position:0% +one of the things at Riot is that we all + + + align:start position:0% +one of the things at Riot is that we all +play League of Legends. In fact, some of + + align:start position:0% +play League of Legends. In fact, some of + + + align:start position:0% +play League of Legends. In fact, some of +us play it a lot. Um some of us play a + + align:start position:0% +us play it a lot. Um some of us play a + + + align:start position:0% +us play it a lot. Um some of us play a +lot at work. But just because you play + + align:start position:0% +lot at work. But just because you play + + + align:start position:0% +lot at work. But just because you play +your own game doesn't mean that you + + align:start position:0% +your own game doesn't mean that you + + + align:start position:0% +your own game doesn't mean that you +actually know what it's like for all of + + align:start position:0% +actually know what it's like for all of + + + align:start position:0% +actually know what it's like for all of +your players. And using MIT students as + + align:start position:0% +your players. And using MIT students as + + + align:start position:0% +your players. And using MIT students as +a great example, if you guys just play + + align:start position:0% +a great example, if you guys just play + + + align:start position:0% +a great example, if you guys just play +with MIT students, you might not know + + align:start position:0% +with MIT students, you might not know + + + align:start position:0% +with MIT students, you might not know +what it's like for people in other + + align:start position:0% +what it's like for people in other + + + align:start position:0% +what it's like for people in other +countries, for example. Um, so one of + + align:start position:0% +countries, for example. Um, so one of + + + align:start position:0% +countries, for example. Um, so one of +the things we try to do is make sure + + align:start position:0% +the things we try to do is make sure + + + align:start position:0% +the things we try to do is make sure +that we understand our players broadly + + align:start position:0% +that we understand our players broadly + + + align:start position:0% +that we understand our players broadly +and know that we are our players, but we + + align:start position:0% +and know that we are our players, but we + + + align:start position:0% +and know that we are our players, but we +are a small subsegment of our players. + + align:start position:0% +are a small subsegment of our players. + + + align:start position:0% +are a small subsegment of our players. +The way we use research is it equips us + + align:start position:0% +The way we use research is it equips us + + + align:start position:0% +The way we use research is it equips us +to understand player beliefs, their + + align:start position:0% +to understand player beliefs, their + + + align:start position:0% +to understand player beliefs, their +needs, their desires, and their + + align:start position:0% +needs, their desires, and their + + + align:start position:0% +needs, their desires, and their +relationship with the game and with + + align:start position:0% +relationship with the game and with + + + align:start position:0% +relationship with the game and with +other people in the game. And what this + + align:start position:0% +other people in the game. And what this + + + align:start position:0% +other people in the game. And what this +allows us to do is design experiences. + + align:start position:0% +allows us to do is design experiences. + + + align:start position:0% +allows us to do is design experiences. +So there's specific, you know, + + align:start position:0% +So there's specific, you know, + + + align:start position:0% +So there's specific, you know, +experiences, um, interactions that we're + + align:start position:0% +experiences, um, interactions that we're + + + align:start position:0% +experiences, um, interactions that we're +hoping to design. So in general, when + + align:start position:0% +hoping to design. So in general, when + + + align:start position:0% +hoping to design. So in general, when +we're creating a feature, we have a set + + align:start position:0% +we're creating a feature, we have a set + + + align:start position:0% +we're creating a feature, we have a set +of goals that we're trying to achieve. + + align:start position:0% +of goals that we're trying to achieve. + + + align:start position:0% +of goals that we're trying to achieve. +And what we want to do is we want to + + align:start position:0% +And what we want to do is we want to + + + align:start position:0% +And what we want to do is we want to +help designers, developers, QA, artists, + + align:start position:0% +help designers, developers, QA, artists, + + + align:start position:0% +help designers, developers, QA, artists, +we want to help them achieve these + + align:start position:0% +we want to help them achieve these + + + align:start position:0% +we want to help them achieve these +goals. So, we want to know exactly what + + align:start position:0% +goals. So, we want to know exactly what + + + align:start position:0% +goals. So, we want to know exactly what +they're trying to do and then get them + + align:start position:0% +they're trying to do and then get them + + + align:start position:0% +they're trying to do and then get them +feedback on how well those goals are + + align:start position:0% +feedback on how well those goals are + + + align:start position:0% +feedback on how well those goals are +being communicated to players, how well + + align:start position:0% +being communicated to players, how well + + + align:start position:0% +being communicated to players, how well +they're actually able to interact with + + align:start position:0% +they're actually able to interact with + + + align:start position:0% +they're actually able to interact with +those, and then what their reception is + + align:start position:0% +those, and then what their reception is + + + align:start position:0% +those, and then what their reception is +as a result. + + align:start position:0% +as a result. + + + align:start position:0% +as a result. +So, the way I'm going to break break + + align:start position:0% +So, the way I'm going to break break + + + align:start position:0% +So, the way I'm going to break break +this down is play tests and user labs, + + align:start position:0% +this down is play tests and user labs, + + + align:start position:0% +this down is play tests and user labs, +which is essentially the way we were + + align:start position:0% +which is essentially the way we were + + + align:start position:0% +which is essentially the way we were +talking about it before is play tests + + align:start position:0% +talking about it before is play tests + + + align:start position:0% +talking about it before is play tests +and user tests. + + align:start position:0% +and user tests. + + + align:start position:0% +and user tests. +So, play test is the kind of the + + align:start position:0% +So, play test is the kind of the + + + align:start position:0% +So, play test is the kind of the +backbone of creating your game. Uh, it's + + align:start position:0% +backbone of creating your game. Uh, it's + + + align:start position:0% +backbone of creating your game. Uh, it's +really, really difficult to create a + + align:start position:0% +really, really difficult to create a + + + align:start position:0% +really, really difficult to create a +game without play testing it. So, I'm + + align:start position:0% +game without play testing it. So, I'm + + + align:start position:0% +game without play testing it. So, I'm +glad that's really part of how you guys + + align:start position:0% +glad that's really part of how you guys + + + align:start position:0% +glad that's really part of how you guys +are designing your games. And play test + + align:start position:0% +are designing your games. And play test + + + align:start position:0% +are designing your games. And play test +basically allows to quickly gather + + align:start position:0% +basically allows to quickly gather + + + align:start position:0% +basically allows to quickly gather +information about a game or a feature to + + align:start position:0% +information about a game or a feature to + + + align:start position:0% +information about a game or a feature to +see how it's working. And typically, + + align:start position:0% +see how it's working. And typically, + + + align:start position:0% +see how it's working. And typically, +this is done with resources that are + + align:start position:0% +this is done with resources that are + + + align:start position:0% +this is done with resources that are +readily available. So, people in your + + align:start position:0% +readily available. So, people in your + + + align:start position:0% +readily available. So, people in your +dorms, people in your class, um, or at + + align:start position:0% +dorms, people in your class, um, or at + + + align:start position:0% +dorms, people in your class, um, or at +Riot, we often do it with other riers + + align:start position:0% +Riot, we often do it with other riers + + + align:start position:0% +Riot, we often do it with other riers +and even on the team. And some of the + + align:start position:0% +and even on the team. And some of the + + + align:start position:0% +and even on the team. And some of the +benefits we can get of this is we can + + align:start position:0% +benefits we can get of this is we can + + + align:start position:0% +benefits we can get of this is we can +identify technical issues. Now, Sarah + + align:start position:0% +identify technical issues. Now, Sarah + + + align:start position:0% +identify technical issues. Now, Sarah +talked about a specific type of this, + + align:start position:0% +talked about a specific type of this, + + + align:start position:0% +talked about a specific type of this, +which is like quality assurance testing, + + align:start position:0% +which is like quality assurance testing, + + + align:start position:0% +which is like quality assurance testing, +which is less what I'm talking about. + + align:start position:0% +which is less what I'm talking about. + + + align:start position:0% +which is less what I'm talking about. +I'm more talking about testing with your + + align:start position:0% +I'm more talking about testing with your + + + align:start position:0% +I'm more talking about testing with your +team to just quickly identify technical + + align:start position:0% +team to just quickly identify technical + + + align:start position:0% +team to just quickly identify technical +issues that might prevent you from + + align:start position:0% +issues that might prevent you from + + + align:start position:0% +issues that might prevent you from +playing that game. You can also look at + + align:start position:0% +playing that game. You can also look at + + + align:start position:0% +playing that game. You can also look at +things like balance. So, in a + + align:start position:0% +things like balance. So, in a + + + align:start position:0% +things like balance. So, in a +competitive game like League of Legends, + + align:start position:0% +competitive game like League of Legends, + + + align:start position:0% +competitive game like League of Legends, +you play against other players. And if + + align:start position:0% +you play against other players. And if + + + align:start position:0% +you play against other players. And if +one type of character is really + + align:start position:0% +one type of character is really + + + align:start position:0% +one type of character is really +overpowered or has a significant + + align:start position:0% +overpowered or has a significant + + + align:start position:0% +overpowered or has a significant +advantage over another type of + + align:start position:0% +advantage over another type of + + + align:start position:0% +advantage over another type of +character, we can quickly identify that + + align:start position:0% +character, we can quickly identify that + + + align:start position:0% +character, we can quickly identify that +through play testing. So for instance, + + align:start position:0% +through play testing. So for instance, + + + align:start position:0% +through play testing. So for instance, +our designers have two play tests a day + + align:start position:0% +our designers have two play tests a day + + + align:start position:0% +our designers have two play tests a day +where they test their inrogress + + align:start position:0% +where they test their inrogress + + + align:start position:0% +where they test their inrogress +champions to see if there's anything + + align:start position:0% +champions to see if there's anything + + + align:start position:0% +champions to see if there's anything +basically game-breaking like that that + + align:start position:0% +basically game-breaking like that that + + + align:start position:0% +basically game-breaking like that that +they can quickly identify and iterate + + align:start position:0% +they can quickly identify and iterate + + + align:start position:0% +they can quickly identify and iterate +on. We can also look at things for fun. + + align:start position:0% +on. We can also look at things for fun. + + + align:start position:0% +on. We can also look at things for fun. +So I mean this is kind of the most + + align:start position:0% +So I mean this is kind of the most + + + align:start position:0% +So I mean this is kind of the most +obvious one, but it's really important + + align:start position:0% +obvious one, but it's really important + + + align:start position:0% +obvious one, but it's really important +that when you're making a game, if the + + align:start position:0% +that when you're making a game, if the + + + align:start position:0% +that when you're making a game, if the +game is supposed to be fun, that it is + + align:start position:0% +game is supposed to be fun, that it is + + + align:start position:0% +game is supposed to be fun, that it is +actually fun. And in our case, we do + + align:start position:0% +actually fun. And in our case, we do + + + align:start position:0% +actually fun. And in our case, we do +want to have a fun game. So we have a + + align:start position:0% +want to have a fun game. So we have a + + + align:start position:0% +want to have a fun game. So we have a +whole group of designers and developers + + align:start position:0% +whole group of designers and developers + + + align:start position:0% +whole group of designers and developers +that have a team which is known as the + + align:start position:0% +that have a team which is known as the + + + align:start position:0% +that have a team which is known as the +play team. And they make um temporary + + align:start position:0% +play team. And they make um temporary + + + align:start position:0% +play team. And they make um temporary +game modes. So, I don't know if anybody + + align:start position:0% +game modes. So, I don't know if anybody + + + align:start position:0% +game modes. So, I don't know if anybody +played recently, but we had a big game + + align:start position:0% +played recently, but we had a big game + + + align:start position:0% +played recently, but we had a big game +in-game event called Shrea. And we had + + align:start position:0% +in-game event called Shrea. And we had + + + align:start position:0% +in-game event called Shrea. And we had +this game mode called Ascension. And + + align:start position:0% +this game mode called Ascension. And + + + align:start position:0% +this game mode called Ascension. And +when they were developing that, they + + align:start position:0% +when they were developing that, they + + + align:start position:0% +when they were developing that, they +were often, you know, several times a + + align:start position:0% +were often, you know, several times a + + + align:start position:0% +were often, you know, several times a +day, many, many times a day in some + + align:start position:0% +day, many, many times a day in some + + + align:start position:0% +day, many, many times a day in some +cases, testing every iteration they made + + align:start position:0% +cases, testing every iteration they made + + + align:start position:0% +cases, testing every iteration they made +to that game mode to make sure that it + + align:start position:0% +to that game mode to make sure that it + + + align:start position:0% +to that game mode to make sure that it +was actually fun. And a lot of times + + align:start position:0% +was actually fun. And a lot of times + + + align:start position:0% +was actually fun. And a lot of times +what you find is that your game isn't + + align:start position:0% +what you find is that your game isn't + + + align:start position:0% +what you find is that your game isn't +necessarily fun sometimes. And that's + + align:start position:0% +necessarily fun sometimes. And that's + + + align:start position:0% +necessarily fun sometimes. And that's +okay because each time you make a + + align:start position:0% +okay because each time you make a + + + align:start position:0% +okay because each time you make a +change, you're getting closer to that + + align:start position:0% +change, you're getting closer to that + + + align:start position:0% +change, you're getting closer to that +fun experience. One day you'll be + + align:start position:0% +fun experience. One day you'll be + + + align:start position:0% +fun experience. One day you'll be +playing your game and like, "Oh my gosh, + + align:start position:0% +playing your game and like, "Oh my gosh, + + + align:start position:0% +playing your game and like, "Oh my gosh, +it's actually fun now. This is great. + + align:start position:0% +it's actually fun now. This is great. + + + align:start position:0% +it's actually fun now. This is great. +Let's do this." So, it's a really good + + align:start position:0% +Let's do this." So, it's a really good + + + align:start position:0% +Let's do this." So, it's a really good +way to get that feedback. And another + + align:start position:0% +way to get that feedback. And another + + + align:start position:0% +way to get that feedback. And another +kind of specific area that we're looking + + align:start position:0% +kind of specific area that we're looking + + + align:start position:0% +kind of specific area that we're looking +for a lot when we play test is clarity. + + align:start position:0% +for a lot when we play test is clarity. + + + align:start position:0% +for a lot when we play test is clarity. +And clarity is a word that we use to + + align:start position:0% +And clarity is a word that we use to + + + align:start position:0% +And clarity is a word that we use to +mean basically how clear is the + + align:start position:0% +mean basically how clear is the + + + align:start position:0% +mean basically how clear is the +information, either the visual + + align:start position:0% +information, either the visual + + + align:start position:0% +information, either the visual +information or the mechanical + + align:start position:0% +information or the mechanical + + + align:start position:0% +information or the mechanical +information. How well is that being + + align:start position:0% +information. How well is that being + + + align:start position:0% +information. How well is that being +communicated to players? So, this could + + align:start position:0% +communicated to players? So, this could + + + align:start position:0% +communicated to players? So, this could +be something like with UI, if you just + + align:start position:0% +be something like with UI, if you just + + + align:start position:0% +be something like with UI, if you just +have a picture and you show it to + + align:start position:0% +have a picture and you show it to + + + align:start position:0% +have a picture and you show it to +players or to, you know, your doormates, + + align:start position:0% +players or to, you know, your doormates, + + + align:start position:0% +players or to, you know, your doormates, +your classmates, how easily are they + + align:start position:0% +your classmates, how easily are they + + + align:start position:0% +your classmates, how easily are they +able to identify what a button means, + + align:start position:0% +able to identify what a button means, + + + align:start position:0% +able to identify what a button means, +right? Or which things are clickable and + + align:start position:0% +right? Or which things are clickable and + + + align:start position:0% +right? Or which things are clickable and +not clickable? Um, those things are all + + align:start position:0% +not clickable? Um, those things are all + + + align:start position:0% +not clickable? Um, those things are all +really, really important in a game like + + align:start position:0% +really, really important in a game like + + + align:start position:0% +really, really important in a game like +ours where we have five people on a + + align:start position:0% +ours where we have five people on a + + + align:start position:0% +ours where we have five people on a +team, 10 people on the map, each with + + align:start position:0% +team, 10 people on the map, each with + + + align:start position:0% +team, 10 people on the map, each with +their own set of abilities and visual + + align:start position:0% +their own set of abilities and visual + + + align:start position:0% +their own set of abilities and visual +effects. And there could be a lot of + + align:start position:0% +effects. And there could be a lot of + + + align:start position:0% +effects. And there could be a lot of +visual clutter if we didn't think about + + align:start position:0% +visual clutter if we didn't think about + + + align:start position:0% +visual clutter if we didn't think about +this type of thing. And then the way we + + align:start position:0% +this type of thing. And then the way we + + + align:start position:0% +this type of thing. And then the way we +typically get these, at least at Riot, + + align:start position:0% +typically get these, at least at Riot, + + + align:start position:0% +typically get these, at least at Riot, +is like I said, team tests. That's the + + align:start position:0% +is like I said, team tests. That's the + + + align:start position:0% +is like I said, team tests. That's the +example I use with the designers and the + + align:start position:0% +example I use with the designers and the + + + align:start position:0% +example I use with the designers and the +play team. They're just playing within + + align:start position:0% +play team. They're just playing within + + + align:start position:0% +play team. They're just playing within +their team frequently to make sure that + + align:start position:0% +their team frequently to make sure that + + + align:start position:0% +their team frequently to make sure that +they can e quickly and easily give each + + align:start position:0% +they can e quickly and easily give each + + + align:start position:0% +they can e quickly and easily give each +other feedback. Quality assurance test + + align:start position:0% +other feedback. Quality assurance test + + + align:start position:0% +other feedback. Quality assurance test +is another type that's a very specific + + align:start position:0% +is another type that's a very specific + + + align:start position:0% +is another type that's a very specific +implementation of this which Sarah spoke + + align:start position:0% +implementation of this which Sarah spoke + + + align:start position:0% +implementation of this which Sarah spoke +to and in-house gorilla test and I + + align:start position:0% +to and in-house gorilla test and I + + + align:start position:0% +to and in-house gorilla test and I +always have to be careful how I say + + align:start position:0% +always have to be careful how I say + + + align:start position:0% +always have to be careful how I say +gorilla not gorilla gorilla this is when + + align:start position:0% +gorilla not gorilla gorilla this is when + + + align:start position:0% +gorilla not gorilla gorilla this is when +we bring other riers who aren't part of + + align:start position:0% +we bring other riers who aren't part of + + + align:start position:0% +we bring other riers who aren't part of +a team who maybe haven't had exposure to + + align:start position:0% +a team who maybe haven't had exposure to + + + align:start position:0% +a team who maybe haven't had exposure to +that particular feature this is + + align:start position:0% +that particular feature this is + + + align:start position:0% +that particular feature this is +particularly useful for things like + + align:start position:0% +particularly useful for things like + + + align:start position:0% +particularly useful for things like +clarity or usability tests because we + + align:start position:0% +clarity or usability tests because we + + + align:start position:0% +clarity or usability tests because we +don't necessarily need to have that that + + align:start position:0% +don't necessarily need to have that that + + + align:start position:0% +don't necessarily need to have that that +perception or that sentiment that is + + align:start position:0% +perception or that sentiment that is + + + align:start position:0% +perception or that sentiment that is +really unique to players all what we + + align:start position:0% +really unique to players all what we + + + align:start position:0% +really unique to players all what we +need here instead is for just see hey + + align:start position:0% +need here instead is for just see hey + + + align:start position:0% +need here instead is for just see hey +how easily is this usable for a + + align:start position:0% +how easily is this usable for a + + + align:start position:0% +how easily is this usable for a +reasonably tech-savvy person, but even + + align:start position:0% +reasonably tech-savvy person, but even + + + align:start position:0% +reasonably tech-savvy person, but even +then, of course, there are some cultural + + align:start position:0% +then, of course, there are some cultural + + + align:start position:0% +then, of course, there are some cultural +differences. There's some hardware + + align:start position:0% +differences. There's some hardware + + + align:start position:0% +differences. There's some hardware +differences. So, it's kind of a first + + align:start position:0% +differences. So, it's kind of a first + + + align:start position:0% +differences. So, it's kind of a first +phase when you do them as guerilla + + align:start position:0% +phase when you do them as guerilla + + + align:start position:0% +phase when you do them as guerilla +testing, and you always want to make + + align:start position:0% +testing, and you always want to make + + + align:start position:0% +testing, and you always want to make +sure that you follow up with with real + + align:start position:0% +sure that you follow up with with real + + + align:start position:0% +sure that you follow up with with real +players after the fact. + + align:start position:0% +players after the fact. + + + align:start position:0% +players after the fact. +So, user labs, this is what I really + + align:start position:0% +So, user labs, this is what I really + + + align:start position:0% +So, user labs, this is what I really +focus in. So, I use a lot of different + + align:start position:0% +focus in. So, I use a lot of different + + + align:start position:0% +focus in. So, I use a lot of different +methods at Riot, but one of the key ways + + align:start position:0% +methods at Riot, but one of the key ways + + + align:start position:0% +methods at Riot, but one of the key ways +that we're able to get player feedback + + align:start position:0% +that we're able to get player feedback + + + align:start position:0% +that we're able to get player feedback +is by bringing players to Riot to have + + align:start position:0% +is by bringing players to Riot to have + + + align:start position:0% +is by bringing players to Riot to have +them play the game. So this is a way to + + align:start position:0% +them play the game. So this is a way to + + + align:start position:0% +them play the game. So this is a way to +help us understand how real players will + + align:start position:0% +help us understand how real players will + + + align:start position:0% +help us understand how real players will +actually approach a feature. So the way + + align:start position:0% +actually approach a feature. So the way + + + align:start position:0% +actually approach a feature. So the way +we get this, what we get out of this is + + align:start position:0% +we get this, what we get out of this is + + + align:start position:0% +we get this, what we get out of this is +really really important. We get + + align:start position:0% +really really important. We get + + + align:start position:0% +really really important. We get +reception and interest like how stoked + + align:start position:0% +reception and interest like how stoked + + + align:start position:0% +reception and interest like how stoked +are players going to be about something + + align:start position:0% +are players going to be about something + + + align:start position:0% +are players going to be about something +or what we call the table flip reaction + + align:start position:0% +or what we call the table flip reaction + + + align:start position:0% +or what we call the table flip reaction +which is uh you know like we're working + + align:start position:0% +which is uh you know like we're working + + + align:start position:0% +which is uh you know like we're working +on an update to Summoner's Rift right + + align:start position:0% +on an update to Summoner's Rift right + + + align:start position:0% +on an update to Summoner's Rift right +now and it was early on it was really + + align:start position:0% +now and it was early on it was really + + + align:start position:0% +now and it was early on it was really +important for us to know were players + + align:start position:0% +important for us to know were players + + + align:start position:0% +important for us to know were players +going to be really upset that we were + + align:start position:0% +going to be really upset that we were + + + align:start position:0% +going to be really upset that we were +changing something that's so key to the + + align:start position:0% +changing something that's so key to the + + + align:start position:0% +changing something that's so key to the +game. So, we made sure to loop them on + + align:start position:0% +game. So, we made sure to loop them on + + + align:start position:0% +game. So, we made sure to loop them on +very early in in the process to see how + + align:start position:0% +very early in in the process to see how + + + align:start position:0% +very early in in the process to see how +they were responding to changes we were + + align:start position:0% +they were responding to changes we were + + + align:start position:0% +they were responding to changes we were +going to make. We also look for things + + align:start position:0% +going to make. We also look for things + + + align:start position:0% +going to make. We also look for things +like usage patterns and errors. And this + + align:start position:0% +like usage patterns and errors. And this + + + align:start position:0% +like usage patterns and errors. And this +is important that we get a broad swath + + align:start position:0% +is important that we get a broad swath + + + align:start position:0% +is important that we get a broad swath +of different types of players to look at + + align:start position:0% +of different types of players to look at + + + align:start position:0% +of different types of players to look at +this type of things, especially with + + align:start position:0% +this type of things, especially with + + + align:start position:0% +this type of things, especially with +things like we just updated the client. + + align:start position:0% +things like we just updated the client. + + + align:start position:0% +things like we just updated the client. +Making sure that the changes we made to + + align:start position:0% +Making sure that the changes we made to + + + align:start position:0% +Making sure that the changes we made to +the interface weren't going to confuse + + align:start position:0% +the interface weren't going to confuse + + + align:start position:0% +the interface weren't going to confuse +players, experienced players who are + + align:start position:0% +players, experienced players who are + + + align:start position:0% +players, experienced players who are +used to our old version and new players + + align:start position:0% +used to our old version and new players + + + align:start position:0% +used to our old version and new players +who' be coming into our game for the + + align:start position:0% +who' be coming into our game for the + + + align:start position:0% +who' be coming into our game for the +first time. We also look at needs and + + align:start position:0% +first time. We also look at needs and + + + align:start position:0% +first time. We also look at needs and +desires. And this is not like Maz + + align:start position:0% +desires. And this is not like Maz + + + align:start position:0% +desires. And this is not like Maz +Maslo's Maslo's hierarchy of needs. It's + + align:start position:0% +Maslo's Maslo's hierarchy of needs. It's + + + align:start position:0% +Maslo's Maslo's hierarchy of needs. It's +more like what are things that players + + align:start position:0% +more like what are things that players + + + align:start position:0% +more like what are things that players +really want from our game, right? And + + align:start position:0% +really want from our game, right? And + + + align:start position:0% +really want from our game, right? And +and understanding that uh can be + + align:start position:0% +and understanding that uh can be + + + align:start position:0% +and understanding that uh can be +difficult sometimes because like I said, + + align:start position:0% +difficult sometimes because like I said, + + + align:start position:0% +difficult sometimes because like I said, +we all play our game. We're very + + align:start position:0% +we all play our game. We're very + + + align:start position:0% +we all play our game. We're very +entrenched in this experience. We have + + align:start position:0% +entrenched in this experience. We have + + + align:start position:0% +entrenched in this experience. We have +our own experience in the game that we + + align:start position:0% +our own experience in the game that we + + + align:start position:0% +our own experience in the game that we +feel very strongly about. But + + align:start position:0% +feel very strongly about. But + + + align:start position:0% +feel very strongly about. But +understanding that other players might + + align:start position:0% +understanding that other players might + + + align:start position:0% +understanding that other players might +have different needs and desires and + + align:start position:0% +have different needs and desires and + + + align:start position:0% +have different needs and desires and +understanding what proportion that + + align:start position:0% +understanding what proportion that + + + align:start position:0% +understanding what proportion that +represents within our broader player + + align:start position:0% +represents within our broader player + + + align:start position:0% +represents within our broader player +base. These are really important things + + align:start position:0% +base. These are really important things + + + align:start position:0% +base. These are really important things +to understand. How we get this is a lot + + align:start position:0% +to understand. How we get this is a lot + + + align:start position:0% +to understand. How we get this is a lot +of different ways that I'm actually + + align:start position:0% +of different ways that I'm actually + + + align:start position:0% +of different ways that I'm actually +going to go into in a little bit more + + align:start position:0% +going to go into in a little bit more + + + align:start position:0% +going to go into in a little bit more +detail. And each one has a kind of a + + align:start position:0% +detail. And each one has a kind of a + + + align:start position:0% +detail. And each one has a kind of a +specific application, but there are a + + align:start position:0% +specific application, but there are a + + + align:start position:0% +specific application, but there are a +few that we use pretty much in every + + align:start position:0% +few that we use pretty much in every + + + align:start position:0% +few that we use pretty much in every +user lab, which I'm going to go through + + align:start position:0% +user lab, which I'm going to go through + + + align:start position:0% +user lab, which I'm going to go through +right now. + + align:start position:0% +right now. + + + align:start position:0% +right now. +So, the first is something we just + + align:start position:0% +So, the first is something we just + + + align:start position:0% +So, the first is something we just +talked about, which is just observation. + + align:start position:0% +talked about, which is just observation. + + + align:start position:0% +talked about, which is just observation. +And I bring this up because it's + + align:start position:0% +And I bring this up because it's + + + align:start position:0% +And I bring this up because it's +something that anybody can do. You don't + + align:start position:0% +something that anybody can do. You don't + + + align:start position:0% +something that anybody can do. You don't +need a dedicated researcher like myself. + + align:start position:0% +need a dedicated researcher like myself. + + + align:start position:0% +need a dedicated researcher like myself. +You guys should and will be doing this, + + align:start position:0% +You guys should and will be doing this, + + + align:start position:0% +You guys should and will be doing this, +right? And so, in this case, I have + + align:start position:0% +right? And so, in this case, I have + + + align:start position:0% +right? And so, in this case, I have +Chris, who is a developer at Riot, + + align:start position:0% +Chris, who is a developer at Riot, + + + align:start position:0% +Chris, who is a developer at Riot, +sitting in for a player. and I have Jan + + align:start position:0% +sitting in for a player. and I have Jan + + + align:start position:0% +sitting in for a player. and I have Jan +who is another researcher at Riot + + align:start position:0% +who is another researcher at Riot + + + align:start position:0% +who is another researcher at Riot +sitting over his shoulder watching him + + align:start position:0% +sitting over his shoulder watching him + + + align:start position:0% +sitting over his shoulder watching him +play. Um in our case we typically just + + align:start position:0% +play. Um in our case we typically just + + + align:start position:0% +play. Um in our case we typically just +have one researcher in the room both + + align:start position:0% +have one researcher in the room both + + + align:start position:0% +have one researcher in the room both +taking the notes and doing the + + align:start position:0% +taking the notes and doing the + + + align:start position:0% +taking the notes and doing the +observation just because of resource + + align:start position:0% +observation just because of resource + + + align:start position:0% +observation just because of resource +limitations and because we've done this + + align:start position:0% +limitations and because we've done this + + + align:start position:0% +limitations and because we've done this +a lot and it's our full-time job. So in + + align:start position:0% +a lot and it's our full-time job. So in + + + align:start position:0% +a lot and it's our full-time job. So in +this case uh Jan is watching Chris + + align:start position:0% +this case uh Jan is watching Chris + + + align:start position:0% +this case uh Jan is watching Chris +interact with the client and you can see + + align:start position:0% +interact with the client and you can see + + + align:start position:0% +interact with the client and you can see +in his hand he's actually got the script + + align:start position:0% +in his hand he's actually got the script + + + align:start position:0% +in his hand he's actually got the script +or we call protocol in his hands so he + + align:start position:0% +or we call protocol in his hands so he + + + align:start position:0% +or we call protocol in his hands so he +can remember what things he should be + + align:start position:0% +can remember what things he should be + + + align:start position:0% +can remember what things he should be +looking for what things he wants to say. + + align:start position:0% +looking for what things he wants to say. + + + align:start position:0% +looking for what things he wants to say. +In this case, we don't generally try to + + align:start position:0% +In this case, we don't generally try to + + + align:start position:0% +In this case, we don't generally try to +use it as a script. We try to use it as + + align:start position:0% +use it as a script. We try to use it as + + + align:start position:0% +use it as a script. We try to use it as +kind of a memory refresher. That way, + + align:start position:0% +kind of a memory refresher. That way, + + + align:start position:0% +kind of a memory refresher. That way, +players can feel really comfortable with + + align:start position:0% +players can feel really comfortable with + + + align:start position:0% +players can feel really comfortable with +us and feel like they have a + + align:start position:0% +us and feel like they have a + + + align:start position:0% +us and feel like they have a +relationship and can have a comfortable + + align:start position:0% +relationship and can have a comfortable + + + align:start position:0% +relationship and can have a comfortable +conversation. + + align:start position:0% +conversation. + + + align:start position:0% +conversation. +One of the ways we achieve this is + + align:start position:0% +One of the ways we achieve this is + + + align:start position:0% +One of the ways we achieve this is +through what we call the thinkaloud + + align:start position:0% +through what we call the thinkaloud + + + align:start position:0% +through what we call the thinkaloud +protocol, which is what Sarah was + + align:start position:0% +protocol, which is what Sarah was + + + align:start position:0% +protocol, which is what Sarah was +referencing, which is basically we try + + align:start position:0% +referencing, which is basically we try + + + align:start position:0% +referencing, which is basically we try +to make sure that they have this direct + + align:start position:0% +to make sure that they have this direct + + + align:start position:0% +to make sure that they have this direct +link from their mind to their mouth. And + + align:start position:0% +link from their mind to their mouth. And + + + align:start position:0% +link from their mind to their mouth. And +there's a couple ways to achieve this + + align:start position:0% +there's a couple ways to achieve this + + + align:start position:0% +there's a couple ways to achieve this +that I'll speak to, but the goal of this + + align:start position:0% +that I'll speak to, but the goal of this + + + align:start position:0% +that I'll speak to, but the goal of this +is we want to know exactly what the game + + align:start position:0% +is we want to know exactly what the game + + + align:start position:0% +is we want to know exactly what the game +is communicating to players and then how + + align:start position:0% +is communicating to players and then how + + + align:start position:0% +is communicating to players and then how +players are processing that and creating + + align:start position:0% +players are processing that and creating + + + align:start position:0% +players are processing that and creating +an internal model. And the best way to + + align:start position:0% +an internal model. And the best way to + + + align:start position:0% +an internal model. And the best way to +do that is just to step back and let + + align:start position:0% +do that is just to step back and let + + + align:start position:0% +do that is just to step back and let +them tell you exactly what they're + + align:start position:0% +them tell you exactly what they're + + + align:start position:0% +them tell you exactly what they're +seeing. And if you aren't quite sure + + align:start position:0% +seeing. And if you aren't quite sure + + + align:start position:0% +seeing. And if you aren't quite sure +what they're seeing, then you can follow + + align:start position:0% +what they're seeing, then you can follow + + + align:start position:0% +what they're seeing, then you can follow +up, which I'll get to in a second. So + + align:start position:0% +up, which I'll get to in a second. So + + + align:start position:0% +up, which I'll get to in a second. So +here's an example of a player who's + + align:start position:0% +here's an example of a player who's + + + align:start position:0% +here's an example of a player who's +seeing our character Lucian, who is a + + align:start position:0% +seeing our character Lucian, who is a + + + align:start position:0% +seeing our character Lucian, who is a +champion who was released fairly + + align:start position:0% +champion who was released fairly + + + align:start position:0% +champion who was released fairly +recently in the game. She's seeing him + + align:start position:0% +recently in the game. She's seeing him + + + align:start position:0% +recently in the game. She's seeing him +as before he had been released in a work + + align:start position:0% +as before he had been released in a work + + + align:start position:0% +as before he had been released in a work +in progress state and giving us feedback + + align:start position:0% +in progress state and giving us feedback + + + align:start position:0% +in progress state and giving us feedback +on what she sees. + + align:start position:0% +on what she sees. + + + align:start position:0% +on what she sees. +I can see that he + + align:start position:0% +I can see that he + + + align:start position:0% +I can see that he +walks faster than normal. + + align:start position:0% +walks faster than normal. + + + align:start position:0% +walks faster than normal. +Sorry, we forgot to plug in the audio. + + align:start position:0% +Sorry, we forgot to plug in the audio. + + + align:start position:0% +Sorry, we forgot to plug in the audio. +I think you guys could hear it. All + + align:start position:0% +I think you guys could hear it. All + + + align:start position:0% +I think you guys could hear it. All +right. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +Oops. + + align:start position:0% + + + + align:start position:0% + +I can see that he walks faster than a + + align:start position:0% +I can see that he walks faster than a + + + align:start position:0% +I can see that he walks faster than a +normal um character, but his animation + + align:start position:0% +normal um character, but his animation + + + align:start position:0% +normal um character, but his animation +doesn't make it seem so. Um it seems + + align:start position:0% +doesn't make it seem so. Um it seems + + + align:start position:0% +doesn't make it seem so. Um it seems +like it takes a really big stride, but I + + align:start position:0% +like it takes a really big stride, but I + + + align:start position:0% +like it takes a really big stride, but I +was imagining to walk really fast, but + + align:start position:0% +was imagining to walk really fast, but + + + align:start position:0% +was imagining to walk really fast, but +it just like it looks like that way. + + align:start position:0% +it just like it looks like that way. + + + align:start position:0% +it just like it looks like that way. +This is an example where the the player + + align:start position:0% +This is an example where the the player + + + align:start position:0% +This is an example where the the player +has just kind of brought this up to us + + align:start position:0% +has just kind of brought this up to us + + + align:start position:0% +has just kind of brought this up to us +that she expected him to move one way + + align:start position:0% +that she expected him to move one way + + + align:start position:0% +that she expected him to move one way +and he's actually operating in a + + align:start position:0% +and he's actually operating in a + + + align:start position:0% +and he's actually operating in a +different way. Um, you can think of this + + align:start position:0% +different way. Um, you can think of this + + + align:start position:0% +different way. Um, you can think of this +as like basically a violation of + + align:start position:0% +as like basically a violation of + + + align:start position:0% +as like basically a violation of +expectations, which is often what we're + + align:start position:0% +expectations, which is often what we're + + + align:start position:0% +expectations, which is often what we're +looking for, especially with our + + align:start position:0% +looking for, especially with our + + + align:start position:0% +looking for, especially with our +characters. Does what you see and what + + align:start position:0% +characters. Does what you see and what + + + align:start position:0% +characters. Does what you see and what +you hear about a champion match with how + + align:start position:0% +you hear about a champion match with how + + + align:start position:0% +you hear about a champion match with how +they actually play. So, one way you can + + align:start position:0% +they actually play. So, one way you can + + + align:start position:0% +they actually play. So, one way you can +do this is just let them talk. And it it + + align:start position:0% +do this is just let them talk. And it it + + + align:start position:0% +do this is just let them talk. And it it +is really important not to be giving um + + align:start position:0% +is really important not to be giving um + + + align:start position:0% +is really important not to be giving um +feedback on whether or not you think + + align:start position:0% +feedback on whether or not you think + + + align:start position:0% +feedback on whether or not you think +they're correct. Um, especially if they + + align:start position:0% +they're correct. Um, especially if they + + + align:start position:0% +they're correct. Um, especially if they +do have a question. It's also really + + align:start position:0% +do have a question. It's also really + + + align:start position:0% +do have a question. It's also really +important not to be judgmental, right? + + align:start position:0% +important not to be judgmental, right? + + + align:start position:0% +important not to be judgmental, right? +So, the way you phrase your questions, + + align:start position:0% +So, the way you phrase your questions, + + + align:start position:0% +So, the way you phrase your questions, +even if you aren't actually being + + align:start position:0% +even if you aren't actually being + + + align:start position:0% +even if you aren't actually being +judgmental, sometimes players might + + align:start position:0% +judgmental, sometimes players might + + + align:start position:0% +judgmental, sometimes players might +think that you're judging them. So, one + + align:start position:0% +think that you're judging them. So, one + + + align:start position:0% +think that you're judging them. So, one +of the kind of contexts we give players + + align:start position:0% +of the kind of contexts we give players + + + align:start position:0% +of the kind of contexts we give players +up front is always um for us since we + + align:start position:0% +up front is always um for us since we + + + align:start position:0% +up front is always um for us since we +actually didn't work on the game or the + + align:start position:0% +actually didn't work on the game or the + + + align:start position:0% +actually didn't work on the game or the +feature that they're seeing, we can say, + + align:start position:0% +feature that they're seeing, we can say, + + + align:start position:0% +feature that they're seeing, we can say, +you know, we didn't work on this, it's + + align:start position:0% +you know, we didn't work on this, it's + + + align:start position:0% +you know, we didn't work on this, it's +really important that you give us honest + + align:start position:0% +really important that you give us honest + + + align:start position:0% +really important that you give us honest +feedback. I'm not going to go home and + + align:start position:0% +feedback. I'm not going to go home and + + + align:start position:0% +feedback. I'm not going to go home and +cry at night. So, I want you to give me + + align:start position:0% +cry at night. So, I want you to give me + + + align:start position:0% +cry at night. So, I want you to give me +totally honest feedback. And we also let + + align:start position:0% +totally honest feedback. And we also let + + + align:start position:0% +totally honest feedback. And we also let +them know that sometimes we're going to + + align:start position:0% +them know that sometimes we're going to + + + align:start position:0% +them know that sometimes we're going to +ask them questions. And we're asking it + + align:start position:0% +ask them questions. And we're asking it + + + align:start position:0% +ask them questions. And we're asking it +so that we can understand what they're + + align:start position:0% +so that we can understand what they're + + + align:start position:0% +so that we can understand what they're +thinking because that's what we're + + align:start position:0% +thinking because that's what we're + + + align:start position:0% +thinking because that's what we're +interested in understanding. We're not + + align:start position:0% +interested in understanding. We're not + + + align:start position:0% +interested in understanding. We're not +asking it because there is a right or + + align:start position:0% +asking it because there is a right or + + + align:start position:0% +asking it because there is a right or +wrong answer. + + align:start position:0% +wrong answer. + + + align:start position:0% +wrong answer. +So, one of the ways that makes it easier + + align:start position:0% +So, one of the ways that makes it easier + + + align:start position:0% +So, one of the ways that makes it easier +to kind of make sure that we understand + + align:start position:0% +to kind of make sure that we understand + + + align:start position:0% +to kind of make sure that we understand +what their mental model of the game is + + align:start position:0% +what their mental model of the game is + + + align:start position:0% +what their mental model of the game is +is to follow up with some probing + + align:start position:0% +is to follow up with some probing + + + align:start position:0% +is to follow up with some probing +questions. So, the player in the + + align:start position:0% +questions. So, the player in the + + + align:start position:0% +questions. So, the player in the +previous example was pretty clear about + + align:start position:0% +previous example was pretty clear about + + + align:start position:0% +previous example was pretty clear about +what she was seeing and why it violated + + align:start position:0% +what she was seeing and why it violated + + + align:start position:0% +what she was seeing and why it violated +her expectations. But sometimes players + + align:start position:0% +her expectations. But sometimes players + + + align:start position:0% +her expectations. But sometimes players +don't necessarily know why it doesn't + + align:start position:0% +don't necessarily know why it doesn't + + + align:start position:0% +don't necessarily know why it doesn't +actually fit what they expected. Or they + + align:start position:0% +actually fit what they expected. Or they + + + align:start position:0% +actually fit what they expected. Or they +might know that something's frustrating, + + align:start position:0% +might know that something's frustrating, + + + align:start position:0% +might know that something's frustrating, +but they're not necessarily giving you + + align:start position:0% +but they're not necessarily giving you + + + align:start position:0% +but they're not necessarily giving you +the answer why. So, one of the ways you + + align:start position:0% +the answer why. So, one of the ways you + + + align:start position:0% +the answer why. So, one of the ways you +can follow it up is either with probing + + align:start position:0% +can follow it up is either with probing + + + align:start position:0% +can follow it up is either with probing +questions, which you ask in the moment, + + align:start position:0% +questions, which you ask in the moment, + + + align:start position:0% +questions, which you ask in the moment, +or you can follow up with interviews + + align:start position:0% +or you can follow up with interviews + + + align:start position:0% +or you can follow up with interviews +after the fact. So, here's an example of + + align:start position:0% +after the fact. So, here's an example of + + + align:start position:0% +after the fact. So, here's an example of +Jan following up with a player who just + + align:start position:0% +Jan following up with a player who just + + + align:start position:0% +Jan following up with a player who just +saw Lucian for the first time. + + align:start position:0% + + + + align:start position:0% + +What makes + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +he uh instead of the I guess normal + + align:start position:0% +he uh instead of the I guess normal + + + align:start position:0% +he uh instead of the I guess normal +uh like one skill to just increase the + + align:start position:0% +uh like one skill to just increase the + + + align:start position:0% +uh like one skill to just increase the +attack speed, he has a lot of his skills + + align:start position:0% +attack speed, he has a lot of his skills + + + align:start position:0% +attack speed, he has a lot of his skills +like based off speed and that speed and + + align:start position:0% +like based off speed and that speed and + + + align:start position:0% +like based off speed and that speed and +um I guess it feels kind. + + align:start position:0% +um I guess it feels kind. + + + align:start position:0% +um I guess it feels kind. +So as an example, a lot of times you'll + + align:start position:0% +So as an example, a lot of times you'll + + + align:start position:0% +So as an example, a lot of times you'll +find this is that when you ask that + + align:start position:0% +find this is that when you ask that + + + align:start position:0% +find this is that when you ask that +initial question, you get kind of a + + align:start position:0% +initial question, you get kind of a + + + align:start position:0% +initial question, you get kind of a +short response, right? And like what + + align:start position:0% +short response, right? And like what + + + align:start position:0% +short response, right? And like what +we're always trying to do as researchers + + align:start position:0% +we're always trying to do as researchers + + + align:start position:0% +we're always trying to do as researchers +is invite a conversation where they're + + align:start position:0% +is invite a conversation where they're + + + align:start position:0% +is invite a conversation where they're +just really comfortable telling us + + align:start position:0% +just really comfortable telling us + + + align:start position:0% +just really comfortable telling us +exactly what they feel and giving us a + + align:start position:0% +exactly what they feel and giving us a + + + align:start position:0% +exactly what they feel and giving us a +lot of detail. So in the first question, + + align:start position:0% +lot of detail. So in the first question, + + + align:start position:0% +lot of detail. So in the first question, +he asked a really broad opening question + + align:start position:0% +he asked a really broad opening question + + + align:start position:0% +he asked a really broad opening question +which was how was that? He didn't even + + align:start position:0% +which was how was that? He didn't even + + + align:start position:0% +which was how was that? He didn't even +ask how did that feel, which might lead + + align:start position:0% +ask how did that feel, which might lead + + + align:start position:0% +ask how did that feel, which might lead +in a certain direction, although that + + align:start position:0% +in a certain direction, although that + + + align:start position:0% +in a certain direction, although that +would be an appropriate question as + + align:start position:0% +would be an appropriate question as + + + align:start position:0% +would be an appropriate question as +well. He left it wide open for the + + align:start position:0% +well. He left it wide open for the + + + align:start position:0% +well. He left it wide open for the +player to take us where they wanted to + + align:start position:0% +player to take us where they wanted to + + + align:start position:0% +player to take us where they wanted to +talk about it. So, the player mentioned + + align:start position:0% +talk about it. So, the player mentioned + + + align:start position:0% +talk about it. So, the player mentioned +that it was fun and something different. + + align:start position:0% +that it was fun and something different. + + + align:start position:0% +that it was fun and something different. +So, Jam wanted to get more depth into + + align:start position:0% +So, Jam wanted to get more depth into + + + align:start position:0% +So, Jam wanted to get more depth into +what does that actually mean because + + align:start position:0% +what does that actually mean because + + + align:start position:0% +what does that actually mean because +that alone doesn't give us enough + + align:start position:0% +that alone doesn't give us enough + + + align:start position:0% +that alone doesn't give us enough +direction to be able to provide to our + + align:start position:0% +direction to be able to provide to our + + + align:start position:0% +direction to be able to provide to our +designers to say what was good, what was + + align:start position:0% +designers to say what was good, what was + + + align:start position:0% +designers to say what was good, what was +working. So, he mirrored exactly what + + align:start position:0% +working. So, he mirrored exactly what + + + align:start position:0% +working. So, he mirrored exactly what +the player said back at him. He said, + + align:start position:0% +the player said back at him. He said, + + + align:start position:0% +the player said back at him. He said, +"Oh, what was fun and what was the thing + + align:start position:0% +"Oh, what was fun and what was the thing + + + align:start position:0% +"Oh, what was fun and what was the thing +that made it feel different?" and then + + align:start position:0% +that made it feel different?" and then + + + align:start position:0% +that made it feel different?" and then +the player. That way, we're not actually + + align:start position:0% +the player. That way, we're not actually + + + align:start position:0% +the player. That way, we're not actually +putting our own spin on interpreting + + align:start position:0% +putting our own spin on interpreting + + + align:start position:0% +putting our own spin on interpreting +what we think they're saying is fun or + + align:start position:0% +what we think they're saying is fun or + + + align:start position:0% +what we think they're saying is fun or +maybe what's different. We're just + + align:start position:0% +maybe what's different. We're just + + + align:start position:0% +maybe what's different. We're just +mirroring exactly back what they said so + + align:start position:0% +mirroring exactly back what they said so + + + align:start position:0% +mirroring exactly back what they said so +that they can give us more detail. You + + align:start position:0% +that they can give us more detail. You + + + align:start position:0% +that they can give us more detail. You +have to be kind of careful with that + + align:start position:0% +have to be kind of careful with that + + + align:start position:0% +have to be kind of careful with that +because you also don't want to sound + + align:start position:0% +because you also don't want to sound + + + align:start position:0% +because you also don't want to sound +cold and clinical like you're, you know, + + align:start position:0% +cold and clinical like you're, you know, + + + align:start position:0% +cold and clinical like you're, you know, +sitting in an office somewhere writing + + align:start position:0% +sitting in an office somewhere writing + + + align:start position:0% +sitting in an office somewhere writing +down everything they say, which you will + + align:start position:0% +down everything they say, which you will + + + align:start position:0% +down everything they say, which you will +be. You want to make it feel like it's a + + align:start position:0% +be. You want to make it feel like it's a + + + align:start position:0% +be. You want to make it feel like it's a +natural conversation. So, we're really + + align:start position:0% +natural conversation. So, we're really + + + align:start position:0% +natural conversation. So, we're really +lucky because we get to work with League + + align:start position:0% +lucky because we get to work with League + + + align:start position:0% +lucky because we get to work with League +of Legends players. So, we already have + + align:start position:0% +of Legends players. So, we already have + + + align:start position:0% +of Legends players. So, we already have +a connection built up with them where we + + align:start position:0% +a connection built up with them where we + + + align:start position:0% +a connection built up with them where we +can talk about it. But it's really + + align:start position:0% +can talk about it. But it's really + + + align:start position:0% +can talk about it. But it's really +important that you kind of make that as, + + align:start position:0% +important that you kind of make that as, + + + align:start position:0% +important that you kind of make that as, +hey, you know, I want to know what you + + align:start position:0% +hey, you know, I want to know what you + + + align:start position:0% +hey, you know, I want to know what you +think. You're really valuable. Let's + + align:start position:0% +think. You're really valuable. Let's + + + align:start position:0% +think. You're really valuable. Let's +just have a conversation about it. And + + align:start position:0% +just have a conversation about it. And + + + align:start position:0% +just have a conversation about it. And +it can be really challenging sometimes. + + align:start position:0% +it can be really challenging sometimes. + + + align:start position:0% +it can be really challenging sometimes. +So, this is one that you guys are + + align:start position:0% +So, this is one that you guys are + + + align:start position:0% +So, this is one that you guys are +already pretty familiar with, too, is + + align:start position:0% +already pretty familiar with, too, is + + + align:start position:0% +already pretty familiar with, too, is +part of interviews that I've clumped in + + align:start position:0% +part of interviews that I've clumped in + + + align:start position:0% +part of interviews that I've clumped in +here is basically the questionnaire. Um + + align:start position:0% +here is basically the questionnaire. Um + + + align:start position:0% +here is basically the questionnaire. Um +Sarah gave you guys some great context + + align:start position:0% +Sarah gave you guys some great context + + + align:start position:0% +Sarah gave you guys some great context +about when this might be useful. Here's + + align:start position:0% +about when this might be useful. Here's + + + align:start position:0% +about when this might be useful. Here's +an example of when we use it in um + + align:start position:0% +an example of when we use it in um + + + align:start position:0% +an example of when we use it in um +League of Legends research. So, this is + + align:start position:0% +League of Legends research. So, this is + + + align:start position:0% +League of Legends research. So, this is +an example with Azir, who's a character + + align:start position:0% +an example with Azir, who's a character + + + align:start position:0% +an example with Azir, who's a character +who just came out in League of Legends. + + align:start position:0% +who just came out in League of Legends. + + + align:start position:0% +who just came out in League of Legends. +This is actually from quite a long time + + align:start position:0% +This is actually from quite a long time + + + align:start position:0% +This is actually from quite a long time +ago when he was in the concept phase. + + align:start position:0% +ago when he was in the concept phase. + + + align:start position:0% +ago when he was in the concept phase. +And this is something we do actually + + align:start position:0% +And this is something we do actually + + + align:start position:0% +And this is something we do actually +with most of our concepts is we put them + + align:start position:0% +with most of our concepts is we put them + + + align:start position:0% +with most of our concepts is we put them +in front of players before they go into + + align:start position:0% +in front of players before they go into + + + align:start position:0% +in front of players before they go into +development to see, hey, is this + + align:start position:0% +development to see, hey, is this + + + align:start position:0% +development to see, hey, is this +something that feels like it fits in the + + align:start position:0% +something that feels like it fits in the + + + align:start position:0% +something that feels like it fits in the +world of League of Legends? Is it clear + + align:start position:0% +world of League of Legends? Is it clear + + + align:start position:0% +world of League of Legends? Is it clear +where maybe the source of power is and + + align:start position:0% +where maybe the source of power is and + + + align:start position:0% +where maybe the source of power is and +does this look like a champion you would + + align:start position:0% +does this look like a champion you would + + + align:start position:0% +does this look like a champion you would +actually want to play? Now, we don't use + + align:start position:0% +actually want to play? Now, we don't use + + + align:start position:0% +actually want to play? Now, we don't use +data to drive decisions at Riot. I want + + align:start position:0% +data to drive decisions at Riot. I want + + + align:start position:0% +data to drive decisions at Riot. I want +to make that really clear. We use it to + + align:start position:0% +to make that really clear. We use it to + + + align:start position:0% +to make that really clear. We use it to +inform. So, just because something + + align:start position:0% +inform. So, just because something + + + align:start position:0% +inform. So, just because something +wasn't resonating with players in our + + align:start position:0% +wasn't resonating with players in our + + + align:start position:0% +wasn't resonating with players in our +labs wouldn't mean that we would like + + align:start position:0% +labs wouldn't mean that we would like + + + align:start position:0% +labs wouldn't mean that we would like +cancel a character. It's just a way for + + align:start position:0% +cancel a character. It's just a way for + + + align:start position:0% +cancel a character. It's just a way for +us to get feedback for our designers who + + align:start position:0% +us to get feedback for our designers who + + + align:start position:0% +us to get feedback for our designers who +already have their experience and their + + align:start position:0% +already have their experience and their + + + align:start position:0% +already have their experience and their +uh experience testing with other riders + + align:start position:0% +uh experience testing with other riders + + + align:start position:0% +uh experience testing with other riders +to help them kind of make informed + + align:start position:0% +to help them kind of make informed + + + align:start position:0% +to help them kind of make informed +decisions. So, what's useful about a + + align:start position:0% +decisions. So, what's useful about a + + + align:start position:0% +decisions. So, what's useful about a +questionnaire in this case is that we + + align:start position:0% +questionnaire in this case is that we + + + align:start position:0% +questionnaire in this case is that we +can compare across champions over time + + align:start position:0% +can compare across champions over time + + + align:start position:0% +can compare across champions over time +and across different roles or positions + + align:start position:0% +and across different roles or positions + + + align:start position:0% +and across different roles or positions +and see what is resonating and what does + + align:start position:0% +and see what is resonating and what does + + + align:start position:0% +and see what is resonating and what does +good look like. We also use this as a + + align:start position:0% +good look like. We also use this as a + + + align:start position:0% +good look like. We also use this as a +jumping off point. So we start with a + + align:start position:0% +jumping off point. So we start with a + + + align:start position:0% +jumping off point. So we start with a +questionnaire and then we go into a more + + align:start position:0% +questionnaire and then we go into a more + + + align:start position:0% +questionnaire and then we go into a more +detailed interview about it to make sure + + align:start position:0% +detailed interview about it to make sure + + + align:start position:0% +detailed interview about it to make sure +that we're getting enough detail to be + + align:start position:0% +that we're getting enough detail to be + + + align:start position:0% +that we're getting enough detail to be +able to provide useful information to + + align:start position:0% +able to provide useful information to + + + align:start position:0% +able to provide useful information to +the designers. + + align:start position:0% +the designers. + + + align:start position:0% +the designers. +So you guys are also probably pretty + + align:start position:0% +So you guys are also probably pretty + + + align:start position:0% +So you guys are also probably pretty +familiar with the idea of experiments in + + align:start position:0% +familiar with the idea of experiments in + + + align:start position:0% +familiar with the idea of experiments in +general, but part of research testing + + align:start position:0% +general, but part of research testing + + + align:start position:0% +general, but part of research testing +can be devising experiments. So we often + + align:start position:0% +can be devising experiments. So we often + + + align:start position:0% +can be devising experiments. So we often +hire people from psychology backgrounds + + align:start position:0% +hire people from psychology backgrounds + + + align:start position:0% +hire people from psychology backgrounds +or research backgrounds in academia + + align:start position:0% +or research backgrounds in academia + + + align:start position:0% +or research backgrounds in academia +because they have experience setting up + + align:start position:0% +because they have experience setting up + + + align:start position:0% +because they have experience setting up +experiments. So this is like the classic + + align:start position:0% +experiments. So this is like the classic + + + align:start position:0% +experiments. So this is like the classic +one. I don't know if you guys have + + align:start position:0% +one. I don't know if you guys have + + + align:start position:0% +one. I don't know if you guys have +already covered this, the Angelbart + + align:start position:0% +already covered this, the Angelbart + + + align:start position:0% +already covered this, the Angelbart +experiment. Okay, so this is like + + align:start position:0% +experiment. Okay, so this is like + + + align:start position:0% +experiment. Okay, so this is like +foundational human computer interaction. + + align:start position:0% +foundational human computer interaction. + + + align:start position:0% +foundational human computer interaction. +It's one of the like most cited studies + + align:start position:0% +It's one of the like most cited studies + + + align:start position:0% +It's one of the like most cited studies +and it's uh Englishbart and Burman + + align:start position:0% +and it's uh Englishbart and Burman + + + align:start position:0% +and it's uh Englishbart and Burman +basically were looking for a way to + + align:start position:0% +basically were looking for a way to + + + align:start position:0% +basically were looking for a way to +improve uh a way to interact with the + + align:start position:0% +improve uh a way to interact with the + + + align:start position:0% +improve uh a way to interact with the +screen or text manipulation and what + + align:start position:0% +screen or text manipulation and what + + + align:start position:0% +screen or text manipulation and what +they proposed was something that was + + align:start position:0% +they proposed was something that was + + + align:start position:0% +they proposed was something that was +radical and was called the mouse. Maybe + + align:start position:0% +radical and was called the mouse. Maybe + + + align:start position:0% +radical and was called the mouse. Maybe +you've heard of it. So that thing in the + + align:start position:0% +you've heard of it. So that thing in the + + + align:start position:0% +you've heard of it. So that thing in the +right, I know it's not a a really clear + + align:start position:0% +right, I know it's not a a really clear + + + align:start position:0% +right, I know it's not a a really clear +photo, but that is um one of the first + + align:start position:0% +photo, but that is um one of the first + + + align:start position:0% +photo, but that is um one of the first +early prototypes of a mouse. And what + + align:start position:0% +early prototypes of a mouse. And what + + + align:start position:0% +early prototypes of a mouse. And what +they wanted to do is they wanted to see + + align:start position:0% +they wanted to do is they wanted to see + + + align:start position:0% +they wanted to do is they wanted to see +is this better than some of these other + + align:start position:0% +is this better than some of these other + + + align:start position:0% +is this better than some of these other +interactions out there. But you can't + + align:start position:0% +interactions out there. But you can't + + + align:start position:0% +interactions out there. But you can't +just kind of maybe qualitative + + align:start position:0% +just kind of maybe qualitative + + + align:start position:0% +just kind of maybe qualitative +experience alone might not be a very + + align:start position:0% +experience alone might not be a very + + + align:start position:0% +experience alone might not be a very +strong way to prove it in this case + + align:start position:0% +strong way to prove it in this case + + + align:start position:0% +strong way to prove it in this case +especially when you can collect + + align:start position:0% +especially when you can collect + + + align:start position:0% +especially when you can collect +quantitative data to back it up. So what + + align:start position:0% +quantitative data to back it up. So what + + + align:start position:0% +quantitative data to back it up. So what +they did is they used uh the time that + + align:start position:0% +they did is they used uh the time that + + + align:start position:0% +they did is they used uh the time that +it took to complete a task very specific + + align:start position:0% +it took to complete a task very specific + + + align:start position:0% +it took to complete a task very specific +task that was given across all these + + align:start position:0% +task that was given across all these + + + align:start position:0% +task that was given across all these +different ways of manipulating text and + + align:start position:0% +different ways of manipulating text and + + + align:start position:0% +different ways of manipulating text and +they saw how many errors the the user + + align:start position:0% +they saw how many errors the the user + + + align:start position:0% +they saw how many errors the the user +made in this case. So you can see that + + align:start position:0% +made in this case. So you can see that + + + align:start position:0% +made in this case. So you can see that +the mouse did pretty well in terms of + + align:start position:0% +the mouse did pretty well in terms of + + + align:start position:0% +the mouse did pretty well in terms of +time overall. It didn't take the + + align:start position:0% +time overall. It didn't take the + + + align:start position:0% +time overall. It didn't take the +participants very long to be able to + + align:start position:0% +participants very long to be able to + + + align:start position:0% +participants very long to be able to +complete the task, but it had very few + + align:start position:0% +complete the task, but it had very few + + + align:start position:0% +complete the task, but it had very few +errors, which made it overall the best + + align:start position:0% +errors, which made it overall the best + + + align:start position:0% +errors, which made it overall the best +out of these different ways to select + + align:start position:0% +out of these different ways to select + + + align:start position:0% +out of these different ways to select +text. And you can see some of the other + + align:start position:0% +text. And you can see some of the other + + + align:start position:0% +text. And you can see some of the other +ones on here were things like knee + + align:start position:0% +ones on here were things like knee + + + align:start position:0% +ones on here were things like knee +control, joystick, uh a graphicon, which + + align:start position:0% +control, joystick, uh a graphicon, which + + + align:start position:0% +control, joystick, uh a graphicon, which +is kind of like a an arc drawer, um a + + align:start position:0% +is kind of like a an arc drawer, um a + + + align:start position:0% +is kind of like a an arc drawer, um a +light pen, and a joystick. And all of + + align:start position:0% +light pen, and a joystick. And all of + + + align:start position:0% +light pen, and a joystick. And all of +these were ways that we could have gone + + align:start position:0% +these were ways that we could have gone + + + align:start position:0% +these were ways that we could have gone +instead of the mouse. Um but based on + + align:start position:0% +instead of the mouse. Um but based on + + + align:start position:0% +instead of the mouse. Um but based on +some of this research, they were able to + + align:start position:0% +some of this research, they were able to + + + align:start position:0% +some of this research, they were able to +improve their design. And now you can + + align:start position:0% +improve their design. And now you can + + + align:start position:0% +improve their design. And now you can +see I'm using one right now. So, + + align:start position:0% + + + + align:start position:0% + +and as part of the experimental + + align:start position:0% +and as part of the experimental + + + align:start position:0% +and as part of the experimental +approach, I broke it out, but there's a + + align:start position:0% +approach, I broke it out, but there's a + + + align:start position:0% +approach, I broke it out, but there's a +specific way you can look at it, which + + align:start position:0% +specific way you can look at it, which + + + align:start position:0% +specific way you can look at it, which +is using physiological techniques, and + + align:start position:0% +is using physiological techniques, and + + + align:start position:0% +is using physiological techniques, and +there are many, and I'm just going to + + align:start position:0% +there are many, and I'm just going to + + + align:start position:0% +there are many, and I'm just going to +cover two. Um, and typically these are + + align:start position:0% +cover two. Um, and typically these are + + + align:start position:0% +cover two. Um, and typically these are +used for very specific types of + + align:start position:0% +used for very specific types of + + + align:start position:0% +used for very specific types of +research. They're very exciting. So, + + align:start position:0% +research. They're very exciting. So, + + + align:start position:0% +research. They're very exciting. So, +oftentimes you'll see people want to use + + align:start position:0% +oftentimes you'll see people want to use + + + align:start position:0% +oftentimes you'll see people want to use +them on everything, but they do they're + + align:start position:0% +them on everything, but they do they're + + + align:start position:0% +them on everything, but they do they're +very particularly useful for certain + + align:start position:0% +very particularly useful for certain + + + align:start position:0% +very particularly useful for certain +cases. So this is an example of eye + + align:start position:0% +cases. So this is an example of eye + + + align:start position:0% +cases. So this is an example of eye +tracking which is you know basically + + align:start position:0% +tracking which is you know basically + + + align:start position:0% +tracking which is you know basically +fundamentally we put a camera up that's + + align:start position:0% +fundamentally we put a camera up that's + + + align:start position:0% +fundamentally we put a camera up that's +able to specially track where eye + + align:start position:0% +able to specially track where eye + + + align:start position:0% +able to specially track where eye +movements are and there are more + + align:start position:0% +movements are and there are more + + + align:start position:0% +movements are and there are more +sophisticated ways you can look at this + + align:start position:0% +sophisticated ways you can look at this + + + align:start position:0% +sophisticated ways you can look at this +and I'm sure a bunch of researchers at + + align:start position:0% +and I'm sure a bunch of researchers at + + + align:start position:0% +and I'm sure a bunch of researchers at +MIT could tell you a lot more about it + + align:start position:0% +MIT could tell you a lot more about it + + + align:start position:0% +MIT could tell you a lot more about it +but in this case it was pretty simple we + + align:start position:0% +but in this case it was pretty simple we + + + align:start position:0% +but in this case it was pretty simple we +were just looking at where people were + + align:start position:0% +were just looking at where people were + + + align:start position:0% +were just looking at where people were +looking on the screen and how often and + + align:start position:0% +looking on the screen and how often and + + + align:start position:0% +looking on the screen and how often and +how long they were looking there. So you + + align:start position:0% +how long they were looking there. So you + + + align:start position:0% +how long they were looking there. So you +can see the red parts of the map here + + align:start position:0% +can see the red parts of the map here + + + align:start position:0% +can see the red parts of the map here +are the parts where there are more + + align:start position:0% +are the parts where there are more + + + align:start position:0% +are the parts where there are more +intense gazes or more gazes overall. So, + + align:start position:0% +intense gazes or more gazes overall. So, + + + align:start position:0% +intense gazes or more gazes overall. So, +unsurprisingly to probably most of the + + align:start position:0% +unsurprisingly to probably most of the + + + align:start position:0% +unsurprisingly to probably most of the +League of Legends players in here or you + + align:start position:0% +League of Legends players in here or you + + + align:start position:0% +League of Legends players in here or you +guys as gamers in general, the mini map + + align:start position:0% +guys as gamers in general, the mini map + + + align:start position:0% +guys as gamers in general, the mini map +has a lot of gaze. The bottom part, + + align:start position:0% +has a lot of gaze. The bottom part, + + + align:start position:0% +has a lot of gaze. The bottom part, +which is where the abilities are + + align:start position:0% +which is where the abilities are + + + align:start position:0% +which is where the abilities are +displayed, also has a lot of gauge. + + align:start position:0% +displayed, also has a lot of gauge. + + + align:start position:0% +displayed, also has a lot of gauge. +Those that has a lot of information + + align:start position:0% +Those that has a lot of information + + + align:start position:0% +Those that has a lot of information +that's really relevant to players, like + + align:start position:0% +that's really relevant to players, like + + + align:start position:0% +that's really relevant to players, like +the cooldown, timer, basically when the + + align:start position:0% +the cooldown, timer, basically when the + + + align:start position:0% +the cooldown, timer, basically when the +ability is going to be ready again. And + + align:start position:0% +ability is going to be ready again. And + + + align:start position:0% +ability is going to be ready again. And +the center of the screen is where most + + align:start position:0% +the center of the screen is where most + + + align:start position:0% +the center of the screen is where most +of the action happens. So, this type of + + align:start position:0% +of the action happens. So, this type of + + + align:start position:0% +of the action happens. So, this type of +information is helpful for us if we want + + align:start position:0% +information is helpful for us if we want + + + align:start position:0% +information is helpful for us if we want +to, for instance, introduce new + + align:start position:0% +to, for instance, introduce new + + + align:start position:0% +to, for instance, introduce new +information on the screen. We'd want to + + align:start position:0% +information on the screen. We'd want to + + + align:start position:0% +information on the screen. We'd want to +know, hey, are we going to introduce + + align:start position:0% +know, hey, are we going to introduce + + + align:start position:0% +know, hey, are we going to introduce +this in a place that's going to get a + + align:start position:0% +this in a place that's going to get a + + + align:start position:0% +this in a place that's going to get a +lot of traffic naturally, but also is it + + align:start position:0% +lot of traffic naturally, but also is it + + + align:start position:0% +lot of traffic naturally, but also is it +going to interrupt things that need that + + align:start position:0% +going to interrupt things that need that + + + align:start position:0% +going to interrupt things that need that +that that gaze is there for a very + + align:start position:0% +that that gaze is there for a very + + + align:start position:0% +that that gaze is there for a very +important reason and maybe we shouldn't + + align:start position:0% +important reason and maybe we shouldn't + + + align:start position:0% +important reason and maybe we shouldn't +interrupt that. So, we can help this to + + align:start position:0% +interrupt that. So, we can help this to + + + align:start position:0% +interrupt that. So, we can help this to +inform those types of decisions. + + align:start position:0% +inform those types of decisions. + + + align:start position:0% +inform those types of decisions. +There's also many other types of + + align:start position:0% +There's also many other types of + + + align:start position:0% +There's also many other types of +physiological, and I'll just kind of + + align:start position:0% +physiological, and I'll just kind of + + + align:start position:0% +physiological, and I'll just kind of +hint at one right now, which is things + + align:start position:0% +hint at one right now, which is things + + + align:start position:0% +hint at one right now, which is things +like um you know, galvanic skin + + align:start position:0% +like um you know, galvanic skin + + + align:start position:0% +like um you know, galvanic skin +response, anything that has to do with + + align:start position:0% +response, anything that has to do with + + + align:start position:0% +response, anything that has to do with +like physiological arousal, I either for + + align:start position:0% +like physiological arousal, I either for + + + align:start position:0% +like physiological arousal, I either for +stress or excitement. These can help + + align:start position:0% +stress or excitement. These can help + + + align:start position:0% +stress or excitement. These can help +with situations where maybe players + + align:start position:0% +with situations where maybe players + + + align:start position:0% +with situations where maybe players +wouldn't be able to vocalize why + + align:start position:0% +wouldn't be able to vocalize why + + + align:start position:0% +wouldn't be able to vocalize why +something was frustrating or exciting. + + align:start position:0% +something was frustrating or exciting. + + + align:start position:0% +something was frustrating or exciting. +Um, or it can also combat some biases + + align:start position:0% +Um, or it can also combat some biases + + + align:start position:0% +Um, or it can also combat some biases +like recency effects where, you know, if + + align:start position:0% +like recency effects where, you know, if + + + align:start position:0% +like recency effects where, you know, if +you ask a player at the end of a lab or + + align:start position:0% +you ask a player at the end of a lab or + + + align:start position:0% +you ask a player at the end of a lab or +at the end of a play test what was + + align:start position:0% +at the end of a play test what was + + + align:start position:0% +at the end of a play test what was +interesting or what was frustrating, + + align:start position:0% +interesting or what was frustrating, + + + align:start position:0% +interesting or what was frustrating, +they might preference things that were + + align:start position:0% +they might preference things that were + + + align:start position:0% +they might preference things that were +at the end or they might preference + + align:start position:0% +at the end or they might preference + + + align:start position:0% +at the end or they might preference +things that were really emotionally um, + + align:start position:0% +things that were really emotionally um, + + + align:start position:0% +things that were really emotionally um, +significant for them, but might forget + + align:start position:0% +significant for them, but might forget + + + align:start position:0% +significant for them, but might forget +smaller things that are still, you know, + + align:start position:0% +smaller things that are still, you know, + + + align:start position:0% +smaller things that are still, you know, +very maybe small frustrating things that + + align:start position:0% +very maybe small frustrating things that + + + align:start position:0% +very maybe small frustrating things that +build up over time. + + align:start position:0% +build up over time. + + + align:start position:0% +build up over time. +Okay. So, none of this is really that + + align:start position:0% +Okay. So, none of this is really that + + + align:start position:0% +Okay. So, none of this is really that +interesting if I don't give you an + + align:start position:0% +interesting if I don't give you an + + + align:start position:0% +interesting if I don't give you an +example of how we actually do it at + + align:start position:0% +example of how we actually do it at + + + align:start position:0% +example of how we actually do it at +Riot. So, here's a case study. And I + + align:start position:0% +Riot. So, here's a case study. And I + + + align:start position:0% +Riot. So, here's a case study. And I +actually presented this last year um as + + align:start position:0% +actually presented this last year um as + + + align:start position:0% +actually presented this last year um as +part of my uh as part of a talk that we + + align:start position:0% +part of my uh as part of a talk that we + + + align:start position:0% +part of my uh as part of a talk that we +did at MIT. So, I apologize if a little + + align:start position:0% +did at MIT. So, I apologize if a little + + + align:start position:0% +did at MIT. So, I apologize if a little +bit is um rerun for you guys. I'll try + + align:start position:0% +bit is um rerun for you guys. I'll try + + + align:start position:0% +bit is um rerun for you guys. I'll try +to spice it up a little bit as I go. So, + + align:start position:0% +to spice it up a little bit as I go. So, + + + align:start position:0% +to spice it up a little bit as I go. So, +I'm going to be talking about Lucian um + + align:start position:0% +I'm going to be talking about Lucian um + + + align:start position:0% +I'm going to be talking about Lucian um +who I introduced to you guys earlier. He + + align:start position:0% +who I introduced to you guys earlier. He + + + align:start position:0% +who I introduced to you guys earlier. He +is one of the player characters or + + align:start position:0% +is one of the player characters or + + + align:start position:0% +is one of the player characters or +champions in League of Legends. + + align:start position:0% +champions in League of Legends. + + + align:start position:0% +champions in League of Legends. +So where we always start as researchers + + align:start position:0% +So where we always start as researchers + + + align:start position:0% +So where we always start as researchers +and part of the job that I haven't + + align:start position:0% +and part of the job that I haven't + + + align:start position:0% +and part of the job that I haven't +really alluded to yet is we spend a lot + + align:start position:0% +really alluded to yet is we spend a lot + + + align:start position:0% +really alluded to yet is we spend a lot +of time talking to our designers, to our + + align:start position:0% +of time talking to our designers, to our + + + align:start position:0% +of time talking to our designers, to our +developers, to our artists, to our + + align:start position:0% +developers, to our artists, to our + + + align:start position:0% +developers, to our artists, to our +producers to make sure we understand the + + align:start position:0% +producers to make sure we understand the + + + align:start position:0% +producers to make sure we understand the +goals they're trying to achieve. And I + + align:start position:0% +goals they're trying to achieve. And I + + + align:start position:0% +goals they're trying to achieve. And I +don't know how many of you guys got to + + align:start position:0% +don't know how many of you guys got to + + + align:start position:0% +don't know how many of you guys got to +catch August Browning's talk last night, + + align:start position:0% +catch August Browning's talk last night, + + + align:start position:0% +catch August Browning's talk last night, +but for the champion designers, they + + align:start position:0% +but for the champion designers, they + + + align:start position:0% +but for the champion designers, they +start with a very specific idea of what + + align:start position:0% +start with a very specific idea of what + + + align:start position:0% +start with a very specific idea of what +goals they're trying to achieve. What is + + align:start position:0% +goals they're trying to achieve. What is + + + align:start position:0% +goals they're trying to achieve. What is +this player character going to feel + + align:start position:0% +this player character going to feel + + + align:start position:0% +this player character going to feel +like? What are you going to feel like + + align:start position:0% +like? What are you going to feel like + + + align:start position:0% +like? What are you going to feel like +when you play it? What is the mechanic + + align:start position:0% +when you play it? What is the mechanic + + + align:start position:0% +when you play it? What is the mechanic +supposed to feel like? What is the theme + + align:start position:0% +supposed to feel like? What is the theme + + + align:start position:0% +supposed to feel like? What is the theme +supposed to feel like? How does this + + align:start position:0% +supposed to feel like? How does this + + + align:start position:0% +supposed to feel like? How does this +resonate with players? How does it fit + + align:start position:0% +resonate with players? How does it fit + + + align:start position:0% +resonate with players? How does it fit +in League of Legends? These are all + + align:start position:0% +in League of Legends? These are all + + + align:start position:0% +in League of Legends? These are all +really important questions for them that + + align:start position:0% +really important questions for them that + + + align:start position:0% +really important questions for them that +they're constantly asking themselves. + + align:start position:0% +they're constantly asking themselves. + + + align:start position:0% +they're constantly asking themselves. +And in the case of Lucian, he was + + align:start position:0% +And in the case of Lucian, he was + + + align:start position:0% +And in the case of Lucian, he was +supposed to feel fast, sleek, speedy. + + align:start position:0% +supposed to feel fast, sleek, speedy. + + + align:start position:0% +supposed to feel fast, sleek, speedy. +He's like a gun ninja, like pew pew. No. + + align:start position:0% +He's like a gun ninja, like pew pew. No. + + + align:start position:0% +He's like a gun ninja, like pew pew. No. +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +Just trying to see if you guys were + + align:start position:0% +Just trying to see if you guys were + + + align:start position:0% +Just trying to see if you guys were +awake there. And he's a range damage + + align:start position:0% +awake there. And he's a range damage + + + align:start position:0% +awake there. And he's a range damage +character with finesse gameplay. And he + + align:start position:0% +character with finesse gameplay. And he + + + align:start position:0% +character with finesse gameplay. And he +basically has a high ceiling uh like a + + align:start position:0% +basically has a high ceiling uh like a + + + align:start position:0% +basically has a high ceiling uh like a +high skill ceiling. Um, and what that + + align:start position:0% +high skill ceiling. Um, and what that + + + align:start position:0% +high skill ceiling. Um, and what that +means is basically he's harder to pick + + align:start position:0% +means is basically he's harder to pick + + + align:start position:0% +means is basically he's harder to pick +up, but when you master him, it's a + + align:start position:0% +up, but when you master him, it's a + + + align:start position:0% +up, but when you master him, it's a +really rewarding feeling. So, that's + + align:start position:0% +really rewarding feeling. So, that's + + + align:start position:0% +really rewarding feeling. So, that's +kind of a trade-off between + + align:start position:0% +kind of a trade-off between + + + align:start position:0% +kind of a trade-off between +accessibility, like maybe how quickly a + + align:start position:0% +accessibility, like maybe how quickly a + + + align:start position:0% +accessibility, like maybe how quickly a +player can pick him up or what level a + + align:start position:0% +player can pick him up or what level a + + + align:start position:0% +player can pick him up or what level a +player can pick him up for a reward of + + align:start position:0% +player can pick him up for a reward of + + + align:start position:0% +player can pick him up for a reward of +how rewarding that feels when you do + + align:start position:0% +how rewarding that feels when you do + + + align:start position:0% +how rewarding that feels when you do +master that champion. And some of the + + align:start position:0% +master that champion. And some of the + + + align:start position:0% +master that champion. And some of the +challenges in this were this guy, his + + align:start position:0% +challenges in this were this guy, his + + + align:start position:0% +challenges in this were this guy, his +theme is pretty different. He's like + + align:start position:0% +theme is pretty different. He's like + + + align:start position:0% +theme is pretty different. He's like +equilibrium style, if you've ever seen + + align:start position:0% +equilibrium style, if you've ever seen + + + align:start position:0% +equilibrium style, if you've ever seen +that movie. Um, and that's not something + + align:start position:0% +that movie. Um, and that's not something + + + align:start position:0% +that movie. Um, and that's not something +we had necessarily done that much in + + align:start position:0% +we had necessarily done that much in + + + align:start position:0% +we had necessarily done that much in +League of Legends before. We wanted to + + align:start position:0% +League of Legends before. We wanted to + + + align:start position:0% +League of Legends before. We wanted to +make sure does he even fit and we also + + align:start position:0% +make sure does he even fit and we also + + + align:start position:0% +make sure does he even fit and we also +wanted to know how do you let a player + + align:start position:0% +wanted to know how do you let a player + + + align:start position:0% +wanted to know how do you let a player +feel super fast and speedy what is it + + align:start position:0% +feel super fast and speedy what is it + + + align:start position:0% +feel super fast and speedy what is it +what in what is essentially an RTS style + + align:start position:0% +what in what is essentially an RTS style + + + align:start position:0% +what in what is essentially an RTS style +game. It's kind of a challenge. + + align:start position:0% +game. It's kind of a challenge. + + + align:start position:0% +game. It's kind of a challenge. +So this is what the test plan eventually + + align:start position:0% +So this is what the test plan eventually + + + align:start position:0% +So this is what the test plan eventually +looked like. It's not necessarily where + + align:start position:0% +looked like. It's not necessarily where + + + align:start position:0% +looked like. It's not necessarily where +we started from but we started with + + align:start position:0% +we started from but we started with + + + align:start position:0% +we started from but we started with +concept testing and then we went through + + align:start position:0% +concept testing and then we went through + + + align:start position:0% +concept testing and then we went through +actually three lab studies with + + align:start position:0% +actually three lab studies with + + + align:start position:0% +actually three lab studies with +iteration in between based on the + + align:start position:0% +iteration in between based on the + + + align:start position:0% +iteration in between based on the +feedback we got from players. And after + + align:start position:0% +feedback we got from players. And after + + + align:start position:0% +feedback we got from players. And after +he launched, we did some post test + + align:start position:0% +he launched, we did some post test + + + align:start position:0% +he launched, we did some post test +post-launch evaluation. + + align:start position:0% +post-launch evaluation. + + + align:start position:0% +post-launch evaluation. +So step one, just like I showed you + + align:start position:0% +So step one, just like I showed you + + + align:start position:0% +So step one, just like I showed you +earlier, was to do this concept testing. + + align:start position:0% +earlier, was to do this concept testing. + + + align:start position:0% +earlier, was to do this concept testing. +And we got some pretty good feedback + + align:start position:0% +And we got some pretty good feedback + + + align:start position:0% +And we got some pretty good feedback +based on that. He felt fast. I mean, + + align:start position:0% +based on that. He felt fast. I mean, + + + align:start position:0% +based on that. He felt fast. I mean, +sorry, he was his fantasy was good with + + align:start position:0% +sorry, he was his fantasy was good with + + + align:start position:0% +sorry, he was his fantasy was good with +players. They like the mood. They felt + + align:start position:0% +players. They like the mood. They felt + + + align:start position:0% +players. They like the mood. They felt +like he fit. Are you all right? + + align:start position:0% +like he fit. Are you all right? + + + align:start position:0% +like he fit. Are you all right? +Um, and he made sense for the role of an + + align:start position:0% +Um, and he made sense for the role of an + + + align:start position:0% +Um, and he made sense for the role of an +AD carry, which again is like a range + + align:start position:0% +AD carry, which again is like a range + + + align:start position:0% +AD carry, which again is like a range +damage dealer in this case. So he had + + align:start position:0% +damage dealer in this case. So he had + + + align:start position:0% +damage dealer in this case. So he had +high appeal scores and the theme felt + + align:start position:0% +high appeal scores and the theme felt + + + align:start position:0% +high appeal scores and the theme felt +really strong. But one thing we very + + align:start position:0% +really strong. But one thing we very + + + align:start position:0% +really strong. But one thing we very +quickly identified, it's a little hard + + align:start position:0% +quickly identified, it's a little hard + + + align:start position:0% +quickly identified, it's a little hard +to see on this one, but his guns were + + align:start position:0% +to see on this one, but his guns were + + + align:start position:0% +to see on this one, but his guns were +different colors. So players expected + + align:start position:0% +different colors. So players expected + + + align:start position:0% +different colors. So players expected +the guns to do different things based on + + align:start position:0% +the guns to do different things based on + + + align:start position:0% +the guns to do different things based on +their colors, which was not what we were + + align:start position:0% +their colors, which was not what we were + + + align:start position:0% +their colors, which was not what we were +planning. So this is very good early + + align:start position:0% +planning. So this is very good early + + + align:start position:0% +planning. So this is very good early +feedback before we got very far into + + align:start position:0% +feedback before we got very far into + + + align:start position:0% +feedback before we got very far into +development where we could pivot and + + align:start position:0% +development where we could pivot and + + + align:start position:0% +development where we could pivot and +make sure that the idea of the two guns + + align:start position:0% +make sure that the idea of the two guns + + + align:start position:0% +make sure that the idea of the two guns +doing the same thing was conveyed. + + align:start position:0% +doing the same thing was conveyed. + + + align:start position:0% +doing the same thing was conveyed. +So based on the feedback we got, we were + + align:start position:0% +So based on the feedback we got, we were + + + align:start position:0% +So based on the feedback we got, we were +able to give that to the designers and + + align:start position:0% +able to give that to the designers and + + + align:start position:0% +able to give that to the designers and +they continued their development. And + + align:start position:0% +they continued their development. And + + + align:start position:0% +they continued their development. And +then after a little bit of time, we were + + align:start position:0% +then after a little bit of time, we were + + + align:start position:0% +then after a little bit of time, we were +able to take it into the lab. So, we + + align:start position:0% +able to take it into the lab. So, we + + + align:start position:0% +able to take it into the lab. So, we +started with the Lucian that was + + align:start position:0% +started with the Lucian that was + + + align:start position:0% +started with the Lucian that was +designed to be a speedy ranged assassin. + + align:start position:0% +designed to be a speedy ranged assassin. + + + align:start position:0% +designed to be a speedy ranged assassin. +He had a double shot and a utility kit. + + align:start position:0% +He had a double shot and a utility kit. + + + align:start position:0% +He had a double shot and a utility kit. +And when I refer to kit, just to be + + align:start position:0% +And when I refer to kit, just to be + + + align:start position:0% +And when I refer to kit, just to be +clear, that means this is a set of + + align:start position:0% +clear, that means this is a set of + + + align:start position:0% +clear, that means this is a set of +abilities. And characters in League of + + align:start position:0% +abilities. And characters in League of + + + align:start position:0% +abilities. And characters in League of +Legends generally have three abilities + + align:start position:0% +Legends generally have three abilities + + + align:start position:0% +Legends generally have three abilities +and then an ultimate ability where the + + align:start position:0% +and then an ultimate ability where the + + + align:start position:0% +and then an ultimate ability where the +ultimate is kind of like the super big + + align:start position:0% +ultimate is kind of like the super big + + + align:start position:0% +ultimate is kind of like the super big +bad power that you get after some some + + align:start position:0% +bad power that you get after some some + + + align:start position:0% +bad power that you get after some some +leveling of the character. So, I kind of + + align:start position:0% +leveling of the character. So, I kind of + + + align:start position:0% +leveling of the character. So, I kind of +I kind of blew the reveal here, but in + + align:start position:0% +I kind of blew the reveal here, but in + + + align:start position:0% +I kind of blew the reveal here, but in +the first lab, we found out that he + + align:start position:0% +the first lab, we found out that he + + + align:start position:0% +the first lab, we found out that he +didn't really feel that sleek and fast. + + align:start position:0% +didn't really feel that sleek and fast. + + + align:start position:0% +didn't really feel that sleek and fast. +He felt stiff. He kind of planted and + + align:start position:0% +He felt stiff. He kind of planted and + + + align:start position:0% +He felt stiff. He kind of planted and +then fired his double shot, which made + + align:start position:0% +then fired his double shot, which made + + + align:start position:0% +then fired his double shot, which made +him feel kind of like a turret. And + + align:start position:0% +him feel kind of like a turret. And + + + align:start position:0% +him feel kind of like a turret. And +people did like his visual theme. They + + align:start position:0% +people did like his visual theme. They + + + align:start position:0% +people did like his visual theme. They +thought it was compelling, but it just + + align:start position:0% +thought it was compelling, but it just + + + align:start position:0% +thought it was compelling, but it just +didn't match his play style. So, we took + + align:start position:0% +didn't match his play style. So, we took + + + align:start position:0% +didn't match his play style. So, we took +this back to the designers. We said, + + align:start position:0% +this back to the designers. We said, + + + align:start position:0% +this back to the designers. We said, +"Hey guys, here's the videos. Here's the + + align:start position:0% +"Hey guys, here's the videos. Here's the + + + align:start position:0% +"Hey guys, here's the videos. Here's the +notes." Um, we usually make a highlight + + align:start position:0% +notes." Um, we usually make a highlight + + + align:start position:0% +notes." Um, we usually make a highlight +reel based on what we see to kind of + + align:start position:0% +reel based on what we see to kind of + + + align:start position:0% +reel based on what we see to kind of +support our evidence so that the + + align:start position:0% +support our evidence so that the + + + align:start position:0% +support our evidence so that the +designers can get enough feedback from + + align:start position:0% +designers can get enough feedback from + + + align:start position:0% +designers can get enough feedback from +that as they are subject matter experts + + align:start position:0% +that as they are subject matter experts + + + align:start position:0% +that as they are subject matter experts +and really know how to interpret what + + align:start position:0% +and really know how to interpret what + + + align:start position:0% +and really know how to interpret what +they see. And we said, "Okay, let's go + + align:start position:0% +they see. And we said, "Okay, let's go + + + align:start position:0% +they see. And we said, "Okay, let's go +back. You guys take some time, do some + + align:start position:0% +back. You guys take some time, do some + + + align:start position:0% +back. You guys take some time, do some +changes. we'll take you into the lab + + align:start position:0% +changes. we'll take you into the lab + + + align:start position:0% +changes. we'll take you into the lab +again. So, we did lab study two and this + + align:start position:0% +again. So, we did lab study two and this + + + align:start position:0% +again. So, we did lab study two and this +time we had a different Lucian to bring + + align:start position:0% +time we had a different Lucian to bring + + + align:start position:0% +time we had a different Lucian to bring +in. This time he was more mobile. He was + + align:start position:0% +in. This time he was more mobile. He was + + + align:start position:0% +in. This time he was more mobile. He was +basically a range carrier running and + + align:start position:0% +basically a range carrier running and + + + align:start position:0% +basically a range carrier running and +gun double shot guy. + + align:start position:0% +gun double shot guy. + + + align:start position:0% +gun double shot guy. +Well, so we had a little bit of a mixed + + align:start position:0% +Well, so we had a little bit of a mixed + + + align:start position:0% +Well, so we had a little bit of a mixed +bag of results here. He did feel a + + align:start position:0% +bag of results here. He did feel a + + + align:start position:0% +bag of results here. He did feel a +little bit faster, but some poses and + + align:start position:0% +little bit faster, but some poses and + + + align:start position:0% +little bit faster, but some poses and +animations felt awkward. And he was high + + align:start position:0% +animations felt awkward. And he was high + + + align:start position:0% +animations felt awkward. And he was high +speed in the numbers, which I'll talk + + align:start position:0% +speed in the numbers, which I'll talk + + + align:start position:0% +speed in the numbers, which I'll talk +about in a second, but he still felt + + align:start position:0% +about in a second, but he still felt + + + align:start position:0% +about in a second, but he still felt +slow for some reason. But kind of worst + + align:start position:0% +slow for some reason. But kind of worst + + + align:start position:0% +slow for some reason. But kind of worst +of all, we got quotes like this one, + + align:start position:0% +of all, we got quotes like this one, + + + align:start position:0% +of all, we got quotes like this one, +which about the ultimate, which was, "It + + align:start position:0% +which about the ultimate, which was, "It + + + align:start position:0% +which about the ultimate, which was, "It +worked in the way I did not want it to + + align:start position:0% +worked in the way I did not want it to + + + align:start position:0% +worked in the way I did not want it to +work, which is a pretty good sign that + + align:start position:0% +work, which is a pretty good sign that + + + align:start position:0% +work, which is a pretty good sign that +something's wrong." + + align:start position:0% +something's wrong." + + + align:start position:0% +something's wrong." +So, we took all this back designers + + align:start position:0% +So, we took all this back designers + + + align:start position:0% +So, we took all this back designers +again. We said, "Hey guys," and the + + align:start position:0% +again. We said, "Hey guys," and the + + + align:start position:0% +again. We said, "Hey guys," and the +animators and the artists in this case, + + align:start position:0% +animators and the artists in this case, + + + align:start position:0% +animators and the artists in this case, +of course, and we said, "He feels slow. + + align:start position:0% +of course, and we said, "He feels slow. + + + align:start position:0% +of course, and we said, "He feels slow. +His ultimate doesn't really have the + + align:start position:0% +His ultimate doesn't really have the + + + align:start position:0% +His ultimate doesn't really have the +usability that people expect, but the + + align:start position:0% +usability that people expect, but the + + + align:start position:0% +usability that people expect, but the +double shot theme is working. So, we're + + align:start position:0% +double shot theme is working. So, we're + + + align:start position:0% +double shot theme is working. So, we're +definitely on the right track, and + + align:start position:0% +definitely on the right track, and + + + align:start position:0% +definitely on the right track, and +players are still very excited about + + align:start position:0% +players are still very excited about + + + align:start position:0% +players are still very excited about +this champion." + + align:start position:0% +this champion." + + + align:start position:0% +this champion." +So now we're in kind of a bind and this + + align:start position:0% +So now we're in kind of a bind and this + + + align:start position:0% +So now we're in kind of a bind and this +is often the case when you are working + + align:start position:0% +is often the case when you are working + + + align:start position:0% +is often the case when you are working +with research from players because + + align:start position:0% +with research from players because + + + align:start position:0% +with research from players because +they're not always able to articulate + + align:start position:0% +they're not always able to articulate + + + align:start position:0% +they're not always able to articulate +exactly what's wrong because they don't + + align:start position:0% +exactly what's wrong because they don't + + + align:start position:0% +exactly what's wrong because they don't +have the context that you do. So this is + + align:start position:0% +have the context that you do. So this is + + + align:start position:0% +have the context that you do. So this is +why it's so important for us as + + align:start position:0% +why it's so important for us as + + + align:start position:0% +why it's so important for us as +researchers to pair with our designers, + + align:start position:0% +researchers to pair with our designers, + + + align:start position:0% +researchers to pair with our designers, +our artists, our producers, and our + + align:start position:0% +our artists, our producers, and our + + + align:start position:0% +our artists, our producers, and our +players to be able to get the right kind + + align:start position:0% +players to be able to get the right kind + + + align:start position:0% +players to be able to get the right kind +of data to make informed decisions. So + + align:start position:0% +of data to make informed decisions. So + + + align:start position:0% +of data to make informed decisions. So +here was our problem. The frame delay + + align:start position:0% +here was our problem. The frame delay + + + align:start position:0% +here was our problem. The frame delay +between his basic attacks was actually + + align:start position:0% +between his basic attacks was actually + + + align:start position:0% +between his basic attacks was actually +very very low in this last lab. Usually + + align:start position:0% +very very low in this last lab. Usually + + + align:start position:0% +very very low in this last lab. Usually +that means things feel fast. It's a + + align:start position:0% +that means things feel fast. It's a + + + align:start position:0% +that means things feel fast. It's a +pretty like standard way when we're + + align:start position:0% +pretty like standard way when we're + + + align:start position:0% +pretty like standard way when we're +developing characters to be like, "Okay, + + align:start position:0% +developing characters to be like, "Okay, + + + align:start position:0% +developing characters to be like, "Okay, +this will feel faster." He also had a + + align:start position:0% +this will feel faster." He also had a + + + align:start position:0% +this will feel faster." He also had a +very high base movement speed, which + + align:start position:0% +very high base movement speed, which + + + align:start position:0% +very high base movement speed, which +means that like the time it took him to + + align:start position:0% +means that like the time it took him to + + + align:start position:0% +means that like the time it took him to +get to run from point A to point B was + + align:start position:0% +get to run from point A to point B was + + + align:start position:0% +get to run from point A to point B was +pretty high relative to the rest of our + + align:start position:0% +pretty high relative to the rest of our + + + align:start position:0% +pretty high relative to the rest of our +champions. And if that weren't enough, + + align:start position:0% +champions. And if that weren't enough, + + + align:start position:0% +champions. And if that weren't enough, +he actually had a dash ability, which + + align:start position:0% +he actually had a dash ability, which + + + align:start position:0% +he actually had a dash ability, which +means that he could just jump basically + + align:start position:0% +means that he could just jump basically + + + align:start position:0% +means that he could just jump basically +from one point to another. All of these + + align:start position:0% +from one point to another. All of these + + + align:start position:0% +from one point to another. All of these +things should have made him feel fast, + + align:start position:0% +things should have made him feel fast, + + + align:start position:0% +things should have made him feel fast, +but players were saying he didn't feel + + align:start position:0% +but players were saying he didn't feel + + + align:start position:0% +but players were saying he didn't feel +fast. So there was something wrong. + + align:start position:0% +fast. So there was something wrong. + + + align:start position:0% +fast. So there was something wrong. +So our designers and our artists and our + + align:start position:0% +So our designers and our artists and our + + + align:start position:0% +So our designers and our artists and our +producers took all of this information + + align:start position:0% +producers took all of this information + + + align:start position:0% +producers took all of this information +back, looked at the videos, play tested + + align:start position:0% +back, looked at the videos, play tested + + + align:start position:0% +back, looked at the videos, play tested +the heck out of it, and came to this + + align:start position:0% +the heck out of it, and came to this + + + align:start position:0% +the heck out of it, and came to this +conclusion. + + align:start position:0% +conclusion. + + + align:start position:0% +conclusion. +They increased the ability + + align:start position:0% +They increased the ability + + + align:start position:0% +They increased the ability +responsiveness, and they uh they changed + + align:start position:0% +responsiveness, and they uh they changed + + + align:start position:0% +responsiveness, and they uh they changed +how animation flowed from one state to + + align:start position:0% +how animation flowed from one state to + + + align:start position:0% +how animation flowed from one state to +another. So, I'm not an artist, but what + + align:start position:0% +another. So, I'm not an artist, but what + + + align:start position:0% +another. So, I'm not an artist, but what +this means to me is that they are + + align:start position:0% +this means to me is that they are + + + align:start position:0% +this means to me is that they are +basically able to make the transitions + + align:start position:0% +basically able to make the transitions + + + align:start position:0% +basically able to make the transitions +from animation A, animation B or ability + + align:start position:0% +from animation A, animation B or ability + + + align:start position:0% +from animation A, animation B or ability +A to ability B and make those feel more + + align:start position:0% +A to ability B and make those feel more + + + align:start position:0% +A to ability B and make those feel more +natural, not like me. And they're also + + align:start position:0% +natural, not like me. And they're also + + + align:start position:0% +natural, not like me. And they're also +they also gave more feedback to the + + align:start position:0% +they also gave more feedback to the + + + align:start position:0% +they also gave more feedback to the +double shot. And again, this is where + + align:start position:0% +double shot. And again, this is where + + + align:start position:0% +double shot. And again, this is where +subject matter expertise is so important + + align:start position:0% +subject matter expertise is so important + + + align:start position:0% +subject matter expertise is so important +because our animators, our visual + + align:start position:0% +because our animators, our visual + + + align:start position:0% +because our animators, our visual +artists, our designers kind of knew this + + align:start position:0% +artists, our designers kind of knew this + + + align:start position:0% +artists, our designers kind of knew this +bag of tricks to be able to apply to it. + + align:start position:0% +bag of tricks to be able to apply to it. + + + align:start position:0% +bag of tricks to be able to apply to it. +And finally, they were able to make the + + align:start position:0% +And finally, they were able to make the + + + align:start position:0% +And finally, they were able to make the +ultimate ability clearer. So they were + + align:start position:0% +ultimate ability clearer. So they were + + + align:start position:0% +ultimate ability clearer. So they were +able to telegraph better what it was + + align:start position:0% +able to telegraph better what it was + + + align:start position:0% +able to telegraph better what it was +actually supposed to do so that players + + align:start position:0% +actually supposed to do so that players + + + align:start position:0% +actually supposed to do so that players +would have more accurate expectations. + + align:start position:0% +would have more accurate expectations. + + + align:start position:0% +would have more accurate expectations. +So we took it to lab study number three. + + align:start position:0% +So we took it to lab study number three. + + + align:start position:0% +So we took it to lab study number three. +We put it in and finally the gameplay + + align:start position:0% +We put it in and finally the gameplay + + + align:start position:0% +We put it in and finally the gameplay +and aesthetics fit the concept and + + align:start position:0% +and aesthetics fit the concept and + + + align:start position:0% +and aesthetics fit the concept and +players were quite happy. But not + + align:start position:0% +players were quite happy. But not + + + align:start position:0% +players were quite happy. But not +everything is always happy ending. + + align:start position:0% +everything is always happy ending. + + + align:start position:0% +everything is always happy ending. +Everything is perfect. There was still + + align:start position:0% +Everything is perfect. There was still + + + align:start position:0% +Everything is perfect. There was still +some confusion about how the ultimate + + align:start position:0% +some confusion about how the ultimate + + + align:start position:0% +some confusion about how the ultimate +was supposed to work. We found that + + align:start position:0% +was supposed to work. We found that + + + align:start position:0% +was supposed to work. We found that +players wanted more control of it. + + align:start position:0% +players wanted more control of it. + + + align:start position:0% +players wanted more control of it. +Basically, how the ultimate currently + + align:start position:0% +Basically, how the ultimate currently + + + align:start position:0% +Basically, how the ultimate currently +works is he locks his arms forward and + + align:start position:0% +works is he locks his arms forward and + + + align:start position:0% +works is he locks his arms forward and +shoots in that direction. So, if you + + align:start position:0% +shoots in that direction. So, if you + + + align:start position:0% +shoots in that direction. So, if you +strafe left or right, he continues + + align:start position:0% +strafe left or right, he continues + + + align:start position:0% +strafe left or right, he continues +shooting in that direction, which for + + align:start position:0% +shooting in that direction, which for + + + align:start position:0% +shooting in that direction, which for +some players was pretty confusing, not + + align:start position:0% +some players was pretty confusing, not + + + align:start position:0% +some players was pretty confusing, not +what they expected based on some of our + + align:start position:0% +what they expected based on some of our + + + align:start position:0% +what they expected based on some of our +other champions. And it wasn't able for + + align:start position:0% +other champions. And it wasn't able for + + + align:start position:0% +other champions. And it wasn't able for +them to like learn it in one session. + + align:start position:0% +them to like learn it in one session. + + + align:start position:0% +them to like learn it in one session. +So, one of the things that we have to + + align:start position:0% +So, one of the things that we have to + + + align:start position:0% +So, one of the things that we have to +take away from that is labs are have + + align:start position:0% +take away from that is labs are have + + + align:start position:0% +take away from that is labs are have +some external validity problems, which + + align:start position:0% +some external validity problems, which + + + align:start position:0% +some external validity problems, which +basically means that, you know, we're + + align:start position:0% +basically means that, you know, we're + + + align:start position:0% +basically means that, you know, we're +sitting in a lab, there's not other + + align:start position:0% +sitting in a lab, there's not other + + + align:start position:0% +sitting in a lab, there's not other +players around. They're often not + + align:start position:0% +players around. They're often not + + + align:start position:0% +players around. They're often not +playing on live. You know, there's a lot + + align:start position:0% +playing on live. You know, there's a lot + + + align:start position:0% +playing on live. You know, there's a lot +of things that are different in our test + + align:start position:0% +of things that are different in our test + + + align:start position:0% +of things that are different in our test +situations than real life. Usually, you + + align:start position:0% +situations than real life. Usually, you + + + align:start position:0% +situations than real life. Usually, you +wouldn't try to master a champion in one + + align:start position:0% +wouldn't try to master a champion in one + + + align:start position:0% +wouldn't try to master a champion in one +session. So, this is one of those cases + + align:start position:0% +session. So, this is one of those cases + + + align:start position:0% +session. So, this is one of those cases +where we kind of put it out to our + + align:start position:0% +where we kind of put it out to our + + + align:start position:0% +where we kind of put it out to our +designers and we and they decided and we + + align:start position:0% +designers and we and they decided and we + + + align:start position:0% +designers and we and they decided and we +supported that, you know, he was going + + align:start position:0% +supported that, you know, he was going + + + align:start position:0% +supported that, you know, he was going +to be a high skill ceiling champion, + + align:start position:0% +to be a high skill ceiling champion, + + + align:start position:0% +to be a high skill ceiling champion, +which meant that players were going to + + align:start position:0% +which meant that players were going to + + + align:start position:0% +which meant that players were going to +need some time to learn how to play him + + align:start position:0% +need some time to learn how to play him + + + align:start position:0% +need some time to learn how to play him +and that just because they didn't learn + + align:start position:0% +and that just because they didn't learn + + + align:start position:0% +and that just because they didn't learn +him in one session didn't mean that they + + align:start position:0% +him in one session didn't mean that they + + + align:start position:0% +him in one session didn't mean that they +wouldn't learn him over time. + + align:start position:0% + + + + align:start position:0% + +So, this is what Lucian looked like when + + align:start position:0% +So, this is what Lucian looked like when + + + align:start position:0% +So, this is what Lucian looked like when +he did go live. + + align:start position:0% +he did go live. + + + align:start position:0% +he did go live. +And it helps if I play the video. + + align:start position:0% + + + + align:start position:0% + +So he's in the top there. + + align:start position:0% + + + + align:start position:0% + +So you can see his dash there. + + align:start position:0% +So you can see his dash there. + + + align:start position:0% +So you can see his dash there. +[Music] + + align:start position:0% + + + + align:start position:0% + +So yeah, a little sometimes a little + + align:start position:0% +So yeah, a little sometimes a little + + + align:start position:0% +So yeah, a little sometimes a little +confusing if you don't play the game to + + align:start position:0% +confusing if you don't play the game to + + + align:start position:0% +confusing if you don't play the game to +have to watch 10 champions all in one + + align:start position:0% +have to watch 10 champions all in one + + + align:start position:0% +have to watch 10 champions all in one +little team fight like that. But + + align:start position:0% +little team fight like that. But + + + align:start position:0% +little team fight like that. But +ultimately the important parts there. + + align:start position:0% +ultimately the important parts there. + + + align:start position:0% +ultimately the important parts there. +He's using his ultimate and he dashed at + + align:start position:0% +He's using his ultimate and he dashed at + + + align:start position:0% +He's using his ultimate and he dashed at +the end. Ultimately ended up actually + + align:start position:0% +the end. Ultimately ended up actually + + + align:start position:0% +the end. Ultimately ended up actually +delivering on player expectations for + + align:start position:0% +delivering on player expectations for + + + align:start position:0% +delivering on player expectations for +this champion. + + align:start position:0% +this champion. + + + align:start position:0% +this champion. +We don't need to watch that again. + + align:start position:0% +We don't need to watch that again. + + + align:start position:0% +We don't need to watch that again. +So what did we learn? Well, we knew + + align:start position:0% +So what did we learn? Well, we knew + + + align:start position:0% +So what did we learn? Well, we knew +going into it that Lucian was going to + + align:start position:0% +going into it that Lucian was going to + + + align:start position:0% +going into it that Lucian was going to +be a difficult champion to get right. + + align:start position:0% +be a difficult champion to get right. + + + align:start position:0% +be a difficult champion to get right. +And we also learned that, you know what, + + align:start position:0% +And we also learned that, you know what, + + + align:start position:0% +And we also learned that, you know what, +it's okay to take a champion back to the + + align:start position:0% +it's okay to take a champion back to the + + + align:start position:0% +it's okay to take a champion back to the +lab multiple times if we really feel + + align:start position:0% +lab multiple times if we really feel + + + align:start position:0% +lab multiple times if we really feel +that it's worth the effort. + + align:start position:0% +that it's worth the effort. + + + align:start position:0% +that it's worth the effort. +We knew that his theme was compelling, + + align:start position:0% +We knew that his theme was compelling, + + + align:start position:0% +We knew that his theme was compelling, +but there was something that wasn't just + + align:start position:0% +but there was something that wasn't just + + + align:start position:0% +but there was something that wasn't just +matching up between his mechanics, his + + align:start position:0% +matching up between his mechanics, his + + + align:start position:0% +matching up between his mechanics, his +visuals, and his theme. And this is one + + align:start position:0% +visuals, and his theme. And this is one + + + align:start position:0% +visuals, and his theme. And this is one +of those things is that everything on + + align:start position:0% +of those things is that everything on + + + align:start position:0% +of those things is that everything on +paper can be totally 100% right, but if + + align:start position:0% +paper can be totally 100% right, but if + + + align:start position:0% +paper can be totally 100% right, but if +players don't agree with it or players + + align:start position:0% +players don't agree with it or players + + + align:start position:0% +players don't agree with it or players +aren't feeling those goals that you're + + align:start position:0% +aren't feeling those goals that you're + + + align:start position:0% +aren't feeling those goals that you're +trying to hit, there's going to be a + + align:start position:0% +trying to hit, there's going to be a + + + align:start position:0% +trying to hit, there's going to be a +problem. So, we're able to collaborate + + align:start position:0% +problem. So, we're able to collaborate + + + align:start position:0% +problem. So, we're able to collaborate +with our subject matter experts, with + + align:start position:0% +with our subject matter experts, with + + + align:start position:0% +with our subject matter experts, with +our players in order to get the + + align:start position:0% +our players in order to get the + + + align:start position:0% +our players in order to get the +experience right. + + align:start position:0% +experience right. + + + align:start position:0% +experience right. +And so, I mean, that's kind of like I'll + + align:start position:0% +And so, I mean, that's kind of like I'll + + + align:start position:0% +And so, I mean, that's kind of like I'll +say it again, like just because the + + align:start position:0% +say it again, like just because the + + + align:start position:0% +say it again, like just because the +mechanics stack up correctly does not + + align:start position:0% +mechanics stack up correctly does not + + + align:start position:0% +mechanics stack up correctly does not +mean that it necessarily will in the + + align:start position:0% +mean that it necessarily will in the + + + align:start position:0% +mean that it necessarily will in the +feeling, which is why you play test it + + align:start position:0% +feeling, which is why you play test it + + + align:start position:0% +feeling, which is why you play test it +in-house, why you play test it with + + align:start position:0% +in-house, why you play test it with + + + align:start position:0% +in-house, why you play test it with +other people at your studio or at your + + align:start position:0% +other people at your studio or at your + + + align:start position:0% +other people at your studio or at your +school, and ideally why you test it with + + align:start position:0% +school, and ideally why you test it with + + + align:start position:0% +school, and ideally why you test it with +the people who are actually going to + + align:start position:0% +the people who are actually going to + + + align:start position:0% +the people who are actually going to +play your game. And then we also learned + + align:start position:0% +play your game. And then we also learned + + + align:start position:0% +play your game. And then we also learned +that, you know, you can sometimes have + + align:start position:0% +that, you know, you can sometimes have + + + align:start position:0% +that, you know, you can sometimes have +these trade-offs, right? It's kind of + + align:start position:0% +these trade-offs, right? It's kind of + + + align:start position:0% +these trade-offs, right? It's kind of +goes back to what you hear from players. + + align:start position:0% +goes back to what you hear from players. + + + align:start position:0% +goes back to what you hear from players. +Sometimes they're going to make + + align:start position:0% +Sometimes they're going to make + + + align:start position:0% +Sometimes they're going to make +suggestions and you have to kind of look + + align:start position:0% +suggestions and you have to kind of look + + + align:start position:0% +suggestions and you have to kind of look +for the note behind the note, right? + + align:start position:0% +for the note behind the note, right? + + + align:start position:0% +for the note behind the note, right? +It's like what is actually the problem? + + align:start position:0% +It's like what is actually the problem? + + + align:start position:0% +It's like what is actually the problem? +You guys are the subject matter experts. + + align:start position:0% +You guys are the subject matter experts. + + + align:start position:0% +You guys are the subject matter experts. +You're going to be able to look at what + + align:start position:0% +You're going to be able to look at what + + + align:start position:0% +You're going to be able to look at what +they're saying and never take it as from + + align:start position:0% +they're saying and never take it as from + + + align:start position:0% +they're saying and never take it as from +players a criticism. Always think about + + align:start position:0% +players a criticism. Always think about + + + align:start position:0% +players a criticism. Always think about +it as if they said something wrong. + + align:start position:0% +it as if they said something wrong. + + + align:start position:0% +it as if they said something wrong. +There's something that has to be causing + + align:start position:0% +There's something that has to be causing + + + align:start position:0% +There's something that has to be causing +the problem. What is it underneath their + + align:start position:0% +the problem. What is it underneath their + + + align:start position:0% +the problem. What is it underneath their +note that's actually causing that + + align:start position:0% +note that's actually causing that + + + align:start position:0% +note that's actually causing that +problem? Let's look for that thing. + + align:start position:0% + + + + align:start position:0% + +And we're still iterating after launch. + + align:start position:0% +And we're still iterating after launch. + + + align:start position:0% +And we're still iterating after launch. +That's one thing that's typical with our + + align:start position:0% +That's one thing that's typical with our + + + align:start position:0% +That's one thing that's typical with our +champions is that yes, we do play tests + + align:start position:0% +champions is that yes, we do play tests + + + align:start position:0% +champions is that yes, we do play tests +with players. Yes, we do play tests in + + align:start position:0% +with players. Yes, we do play tests in + + + align:start position:0% +with players. Yes, we do play tests in +house. But once we launch the champion, + + align:start position:0% +house. But once we launch the champion, + + + align:start position:0% +house. But once we launch the champion, +there are thousands and thousands of + + align:start position:0% +there are thousands and thousands of + + + align:start position:0% +there are thousands and thousands of +play tests with real players on live. + + align:start position:0% +play tests with real players on live. + + + align:start position:0% +play tests with real players on live. +And that's when we learn about things + + align:start position:0% +And that's when we learn about things + + + align:start position:0% +And that's when we learn about things +that happen maybe at scale or under very + + align:start position:0% +that happen maybe at scale or under very + + + align:start position:0% +that happen maybe at scale or under very +specific situations or for things that + + align:start position:0% +specific situations or for things that + + + align:start position:0% +specific situations or for things that +we didn't account for with these + + align:start position:0% +we didn't account for with these + + + align:start position:0% +we didn't account for with these +external validity concerns. So we keep + + align:start position:0% +external validity concerns. So we keep + + + align:start position:0% +external validity concerns. So we keep +iterating and in the case of Lucian, we + + align:start position:0% +iterating and in the case of Lucian, we + + + align:start position:0% +iterating and in the case of Lucian, we +actually continued to collect metrics + + align:start position:0% +actually continued to collect metrics + + + align:start position:0% +actually continued to collect metrics +and user sentiment through things like + + align:start position:0% +and user sentiment through things like + + + align:start position:0% +and user sentiment through things like +surveys and through game data to + + align:start position:0% +surveys and through game data to + + + align:start position:0% +surveys and through game data to +understand how he was doing. And based + + align:start position:0% +understand how he was doing. And based + + + align:start position:0% +understand how he was doing. And based +on this, we were able to make more + + align:start position:0% +on this, we were able to make more + + + align:start position:0% +on this, we were able to make more +iterations, fine-tune, and hopefully + + align:start position:0% +iterations, fine-tune, and hopefully + + + align:start position:0% +iterations, fine-tune, and hopefully +make him a little bit more accessible. + + align:start position:0% +make him a little bit more accessible. + + + align:start position:0% +make him a little bit more accessible. +And today, Lucian is well regarded, + + align:start position:0% +And today, Lucian is well regarded, + + + align:start position:0% +And today, Lucian is well regarded, +widely played, and if you watch the + + align:start position:0% +widely played, and if you watch the + + + align:start position:0% +widely played, and if you watch the +professional matches in the world + + align:start position:0% +professional matches in the world + + + align:start position:0% +professional matches in the world +championship, he's used quite + + align:start position:0% +championship, he's used quite + + + align:start position:0% +championship, he's used quite +frequently. + + align:start position:0% +frequently. + + + align:start position:0% +frequently. +All right, guys. I hope I didn't bore + + align:start position:0% +All right, guys. I hope I didn't bore + + + align:start position:0% +All right, guys. I hope I didn't bore +you. My name is Genevie again. If you + + align:start position:0% +you. My name is Genevie again. If you + + + align:start position:0% +you. My name is Genevie again. If you +guys ever have any questions, you can + + align:start position:0% +guys ever have any questions, you can + + + align:start position:0% +guys ever have any questions, you can +feel free to reach out to me at gcon + + align:start position:0% +feel free to reach out to me at gcon + + + align:start position:0% +feel free to reach out to me at gcon +conleys.com. + + align:start position:0% +conleys.com. + + + align:start position:0% +conleys.com. +My summoner name and game if you play is + + align:start position:0% +My summoner name and game if you play is + + + align:start position:0% +My summoner name and game if you play is +Riot Capro and you can also find me on + + align:start position:0% +Riot Capro and you can also find me on + + + align:start position:0% +Riot Capro and you can also find me on +Twitter there. I'm always happy to + + align:start position:0% +Twitter there. I'm always happy to + + + align:start position:0% +Twitter there. I'm always happy to +answer questions. Thank you guys. + + align:start position:0% + + + + align:start position:0% + +So, um 10 minute break. Um come back at + + align:start position:0% +So, um 10 minute break. Um come back at + + + align:start position:0% +So, um 10 minute break. Um come back at +2:20 and be ready to start working on + + align:start position:0% +2:20 and be ready to start working on + + + align:start position:0% +2:20 and be ready to start working on +your focus test stuff. + + align:start position:0% +your focus test stuff. + + + align:start position:0% +your focus test stuff. +Okay. Welcome, welcome back to class. + + align:start position:0% +Okay. Welcome, welcome back to class. + + + align:start position:0% +Okay. Welcome, welcome back to class. +Um now that you've had a chance to be + + align:start position:0% +Um now that you've had a chance to be + + + align:start position:0% +Um now that you've had a chance to be +talked at a whole lot, we're going to go + + align:start position:0% +talked at a whole lot, we're going to go + + + align:start position:0% +talked at a whole lot, we're going to go +ahead and ask you to actually do the + + align:start position:0% +ahead and ask you to actually do the + + + align:start position:0% +ahead and ask you to actually do the +plan. The plan is is to give you about + + align:start position:0% +plan. The plan is is to give you about + + + align:start position:0% +plan. The plan is is to give you about +10 minutes to meet in your groups. Plan + + align:start position:0% +10 minutes to meet in your groups. Plan + + + align:start position:0% +10 minutes to meet in your groups. Plan +your test. Go ahead and get a I I I + + align:start position:0% +your test. Go ahead and get a I I I + + + align:start position:0% +your test. Go ahead and get a I I I +actually strongly recommend you just + + align:start position:0% +actually strongly recommend you just + + + align:start position:0% +actually strongly recommend you just +grab a copy of the focus test either in + + align:start position:0% +grab a copy of the focus test either in + + + align:start position:0% +grab a copy of the focus test either in +the Word version or the RTF version off + + align:start position:0% +the Word version or the RTF version off + + + align:start position:0% +the Word version or the RTF version off +of Stellar so you've got that as a + + align:start position:0% +of Stellar so you've got that as a + + + align:start position:0% +of Stellar so you've got that as a +guide. Um sit down, plan your test and + + align:start position:0% +guide. Um sit down, plan your test and + + + align:start position:0% +guide. Um sit down, plan your test and +how you're going to run it. Um we'll + + align:start position:0% +how you're going to run it. Um we'll + + + align:start position:0% +how you're going to run it. Um we'll +give you 10 minutes for that. Then we'll + + align:start position:0% +give you 10 minutes for that. Then we'll + + + align:start position:0% +give you 10 minutes for that. Then we'll +have about 45 minutes for people to + + align:start position:0% +have about 45 minutes for people to + + + align:start position:0% +have about 45 minutes for people to +circulate and test. And one of the + + align:start position:0% +circulate and test. And one of the + + + align:start position:0% +circulate and test. And one of the +things you should also be planning is + + align:start position:0% +things you should also be planning is + + + align:start position:0% +things you should also be planning is +when your team members will be out + + align:start position:0% +when your team members will be out + + + align:start position:0% +when your team members will be out +testing other people's games, and when + + align:start position:0% +testing other people's games, and when + + + align:start position:0% +testing other people's games, and when +your team members will be observing. Um, + + align:start position:0% +your team members will be observing. Um, + + + align:start position:0% +your team members will be observing. Um, +just sort of given the number of people + + align:start position:0% +just sort of given the number of people + + + align:start position:0% +just sort of given the number of people +in class, the number of games we have, + + align:start position:0% +in class, the number of games we have, + + + align:start position:0% +in class, the number of games we have, +and the number of people's on the team. + + align:start position:0% +and the number of people's on the team. + + + align:start position:0% +and the number of people's on the team. +Um, chances are good that you aren't + + align:start position:0% +Um, chances are good that you aren't + + + align:start position:0% +Um, chances are good that you aren't +going to be either observing or testing + + align:start position:0% +going to be either observing or testing + + + align:start position:0% +going to be either observing or testing +all the time, you're probably going to + + align:start position:0% +all the time, you're probably going to + + + align:start position:0% +all the time, you're probably going to +have to wait. Um, but go ahead and + + align:start position:0% +have to wait. Um, but go ahead and + + + align:start position:0% +have to wait. Um, but go ahead and +circulate. Take the time to watch other + + align:start position:0% +circulate. Take the time to watch other + + + align:start position:0% +circulate. Take the time to watch other +teams doing focus testing. Try not to + + align:start position:0% +teams doing focus testing. Try not to + + + align:start position:0% +teams doing focus testing. Try not to +watch a game in progress that you are + + align:start position:0% +watch a game in progress that you are + + + align:start position:0% +watch a game in progress that you are +going to focus test. Um, if you realize + + align:start position:0% +going to focus test. Um, if you realize + + + align:start position:0% +going to focus test. Um, if you realize +that you're just sort of sitting around + + align:start position:0% +that you're just sort of sitting around + + + align:start position:0% +that you're just sort of sitting around +waiting for a chance to focus test, let + + align:start position:0% +waiting for a chance to focus test, let + + + align:start position:0% +waiting for a chance to focus test, let +the team know that you're in line next. + + align:start position:0% +the team know that you're in line next. + + + align:start position:0% +the team know that you're in line next. +I'd rather you pulled out a book and + + align:start position:0% +I'd rather you pulled out a book and + + + align:start position:0% +I'd rather you pulled out a book and +read it than watched someone else play a + + align:start position:0% +read it than watched someone else play a + + + align:start position:0% +read it than watched someone else play a +game you're about to focus test. It will + + align:start position:0% +game you're about to focus test. It will + + + align:start position:0% +game you're about to focus test. It will +be more useful for the poor people who + + align:start position:0% +be more useful for the poor people who + + + align:start position:0% +be more useful for the poor people who +you're testing for if you haven't + + align:start position:0% +you're testing for if you haven't + + + align:start position:0% +you're testing for if you haven't +already seen somebody do all those + + align:start position:0% +already seen somebody do all those + + + align:start position:0% +already seen somebody do all those +things. Um, that doesn't mean hide in + + align:start position:0% +things. Um, that doesn't mean hide in + + + align:start position:0% +things. Um, that doesn't mean hide in +the corner and read a book because um, + + align:start position:0% +the corner and read a book because um, + + + align:start position:0% +the corner and read a book because um, +there's too many people wandering around + + align:start position:0% +there's too many people wandering around + + + align:start position:0% +there's too many people wandering around +testing games. We do expect everybody to + + align:start position:0% +testing games. We do expect everybody to + + + align:start position:0% +testing games. We do expect everybody to +both to participate both sides, observe + + align:start position:0% +both to participate both sides, observe + + + align:start position:0% +both to participate both sides, observe +and test. So, so try to balance that out + + align:start position:0% +and test. So, so try to balance that out + + + align:start position:0% +and test. So, so try to balance that out +a bit. Um, we'll kind of we'll kind of + + align:start position:0% +a bit. Um, we'll kind of we'll kind of + + + align:start position:0% +a bit. Um, we'll kind of we'll kind of +circulate and keep an eye on things and + + align:start position:0% +circulate and keep an eye on things and + + + align:start position:0% +circulate and keep an eye on things and +if it looks like at some point nobody's + + align:start position:0% +if it looks like at some point nobody's + + + align:start position:0% +if it looks like at some point nobody's +actually testing, you're all kind of + + align:start position:0% +actually testing, you're all kind of + + + align:start position:0% +actually testing, you're all kind of +sitting around twiddling your thumbs, + + align:start position:0% +sitting around twiddling your thumbs, + + + align:start position:0% +sitting around twiddling your thumbs, +we'll end it early. I don't know how + + align:start position:0% +we'll end it early. I don't know how + + + align:start position:0% +we'll end it early. I don't know how +long this testing session will take + + align:start position:0% +long this testing session will take + + + align:start position:0% +long this testing session will take +because we haven't had such large teams + + align:start position:0% +because we haven't had such large teams + + + align:start position:0% +because we haven't had such large teams +on this project before. So, it's a + + align:start position:0% +on this project before. So, it's a + + + align:start position:0% +on this project before. So, it's a +little harder for me to know what the + + align:start position:0% +little harder for me to know what the + + + align:start position:0% +little harder for me to know what the +amount of time is. Um, after that, we'll + + align:start position:0% +amount of time is. Um, after that, we'll + + + align:start position:0% +amount of time is. Um, after that, we'll +give you some more time to talk in your + + align:start position:0% +give you some more time to talk in your + + + align:start position:0% +give you some more time to talk in your +own teams and sort of come up with the + + align:start position:0% +own teams and sort of come up with the + + + align:start position:0% +own teams and sort of come up with the +what are the results of your test to + + align:start position:0% +what are the results of your test to + + + align:start position:0% +what are the results of your test to +analyze your data and then we'll ask + + align:start position:0% +analyze your data and then we'll ask + + + align:start position:0% +analyze your data and then we'll ask +somebody to come down and for each team + + align:start position:0% +somebody to come down and for each team + + + align:start position:0% +somebody to come down and for each team +give us sort of a summary of your focus + + align:start position:0% +give us sort of a summary of your focus + + + align:start position:0% +give us sort of a summary of your focus +test report. You know, how did your + + align:start position:0% +test report. You know, how did your + + + align:start position:0% +test report. You know, how did your +focus test turn out? What did you learn? + + align:start position:0% +focus test turn out? What did you learn? + + + align:start position:0% +focus test turn out? What did you learn? +Do you have a plan for what you're going + + align:start position:0% +Do you have a plan for what you're going + + + align:start position:0% +Do you have a plan for what you're going +to do with it or are you still kind of + + align:start position:0% +to do with it or are you still kind of + + + align:start position:0% +to do with it or are you still kind of +figuring out how you'll deal with it? + + align:start position:0% +figuring out how you'll deal with it? + + + align:start position:0% +figuring out how you'll deal with it? +Those are all reasonable things given + + align:start position:0% +Those are all reasonable things given + + + align:start position:0% +Those are all reasonable things given +you only had 10 minutes to look at your + + align:start position:0% +you only had 10 minutes to look at your + + + align:start position:0% +you only had 10 minutes to look at your +data. Okay, thank you. It is 2:23. + + align:start position:0% +data. Okay, thank you. It is 2:23. + + + align:start position:0% +data. Okay, thank you. It is 2:23. +Um at uh 2:33, we'll go ahead and start + + align:start position:0% +Um at uh 2:33, we'll go ahead and start + + + align:start position:0% +Um at uh 2:33, we'll go ahead and start +focus testing. + + align:start position:0% +focus testing. + + + align:start position:0% +focus testing. +Actually, I'm going to give you 15 + + align:start position:0% +Actually, I'm going to give you 15 + + + align:start position:0% +Actually, I'm going to give you 15 +minutes to get set up because I just + + align:start position:0% +minutes to get set up because I just + + + align:start position:0% +minutes to get set up because I just +realized you probably need 10 minutes to + + align:start position:0% +realized you probably need 10 minutes to + + + align:start position:0% +realized you probably need 10 minutes to +talk and then probably five minutes to + + align:start position:0% +talk and then probably five minutes to + + + align:start position:0% +talk and then probably five minutes to +make sure you have a machine up and + + align:start position:0% +make sure you have a machine up and + + + align:start position:0% +make sure you have a machine up and +running. So, I apologize. It's going to + + align:start position:0% +running. So, I apologize. It's going to + + + align:start position:0% +running. So, I apologize. It's going to +be 15 minutes to plan and prepare for + + align:start position:0% +be 15 minutes to plan and prepare for + + + align:start position:0% +be 15 minutes to plan and prepare for +your test. So that's 330 238 at this + + align:start position:0% +your test. So that's 330 238 at this + + + align:start position:0% +your test. So that's 330 238 at this +point. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +Yeah, I think he just wants it. + + align:start position:0% +Yeah, I think he just wants it. + + + align:start position:0% +Yeah, I think he just wants it. +Okay, you should be ready to go now. I + + align:start position:0% +Okay, you should be ready to go now. I + + + align:start position:0% +Okay, you should be ready to go now. I +hope. + + align:start position:0% +hope. + + + align:start position:0% +hope. +Um, and actively go ahead. Um, you + + align:start position:0% +Um, and actively go ahead. Um, you + + + align:start position:0% +Um, and actively go ahead. Um, you +should have a computer ideally set up to + + align:start position:0% +should have a computer ideally set up to + + + align:start position:0% +should have a computer ideally set up to +run your game. + + align:start position:0% +run your game. + + + align:start position:0% +run your game. +Um, who is actually ready to run a focus + + align:start position:0% +Um, who is actually ready to run a focus + + + align:start position:0% +Um, who is actually ready to run a focus +test? + + align:start position:0% +test? + + + align:start position:0% +test? +Everyone who's managing like a demo + + align:start position:0% +Everyone who's managing like a demo + + + align:start position:0% +Everyone who's managing like a demo +computer, a computer ready to run the + + align:start position:0% +computer, a computer ready to run the + + + align:start position:0% +computer, a computer ready to run the +game, put your hand up. + + align:start position:0% +game, put your hand up. + + + align:start position:0% +game, put your hand up. +Yeah. or or stand up so that we can see + + align:start position:0% +Yeah. or or stand up so that we can see + + + align:start position:0% +Yeah. or or stand up so that we can see +you. + + align:start position:0% +you. + + + align:start position:0% +you. +Yeah. Go ahead and stand up so we can + + align:start position:0% +Yeah. Go ahead and stand up so we can + + + align:start position:0% +Yeah. Go ahead and stand up so we can +see where you are. Um + + align:start position:0% +see where you are. Um + + + align:start position:0% +see where you are. Um +I'm not seeing any hands from these + + align:start position:0% +I'm not seeing any hands from these + + + align:start position:0% +I'm not seeing any hands from these +teams over here. Okay. All right. All + + align:start position:0% +teams over here. Okay. All right. All + + + align:start position:0% +teams over here. Okay. All right. All +right. All right. That there's someone + + align:start position:0% +right. All right. That there's someone + + + align:start position:0% +right. All right. That there's someone +standing up back there. + + align:start position:0% +standing up back there. + + + align:start position:0% +standing up back there. +How about the Sparkly Redemption team? + + align:start position:0% +How about the Sparkly Redemption team? + + + align:start position:0% +How about the Sparkly Redemption team? +Okay. All right. There's someone there + + align:start position:0% +Okay. All right. There's someone there + + + align:start position:0% +Okay. All right. There's someone there +to run the game. All right. + + align:start position:0% +to run the game. All right. + + + align:start position:0% +to run the game. All right. +So, close all the laptops that are not + + align:start position:0% +So, close all the laptops that are not + + + align:start position:0% +So, close all the laptops that are not +actually running the game would be my + + align:start position:0% +actually running the game would be my + + + align:start position:0% +actually running the game would be my +advice. + + align:start position:0% +advice. + + + align:start position:0% +advice. +And then let's go ahead and get started. + + align:start position:0% +And then let's go ahead and get started. + + + align:start position:0% +And then let's go ahead and get started. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +All right. Start start playing each + + align:start position:0% +All right. Start start playing each + + + align:start position:0% +All right. Start start playing each +other's games. Go. + + align:start position:0% +other's games. Go. + + + align:start position:0% +other's games. Go. +Yep. + + align:start position:0% + + + + align:start position:0% + +Next time we'll ask them to have two or + + align:start position:0% +Next time we'll ask them to have two or + + + align:start position:0% +Next time we'll ask them to have two or +three. + + align:start position:0% +three. + + + align:start position:0% +three. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Um as part of the stellar thing he he + + align:start position:0% +Um as part of the stellar thing he he + + + align:start position:0% +Um as part of the stellar thing he he +got he was talking about. + + align:start position:0% + + + + align:start position:0% + +Okay. Um, + + align:start position:0% + + + + align:start position:0% + +it's okay if you don't have a plan of + + align:start position:0% +it's okay if you don't have a plan of + + + align:start position:0% +it's okay if you don't have a plan of +action as you're looking at your results + + align:start position:0% +action as you're looking at your results + + + align:start position:0% +action as you're looking at your results +as long as you've sort of gotten ideas + + align:start position:0% +as long as you've sort of gotten ideas + + + align:start position:0% +as long as you've sort of gotten ideas +as to what you're what you're seeing out + + align:start position:0% +as to what you're what you're seeing out + + + align:start position:0% +as to what you're what you're seeing out +of your data. Um, it's kind of hard to + + align:start position:0% +of your data. Um, it's kind of hard to + + + align:start position:0% +of your data. Um, it's kind of hard to +come up with look at your data, get it + + align:start position:0% +come up with look at your data, get it + + + align:start position:0% +come up with look at your data, get it +evaluated, talk about it, and figure out + + align:start position:0% +evaluated, talk about it, and figure out + + + align:start position:0% +evaluated, talk about it, and figure out +what you're going to do about it all in + + align:start position:0% +what you're going to do about it all in + + + align:start position:0% +what you're going to do about it all in +10 minutes. We are giving you a short + + align:start position:0% +10 minutes. We are giving you a short + + + align:start position:0% +10 minutes. We are giving you a short +amount of time because because we're + + align:start position:0% +amount of time because because we're + + + align:start position:0% +amount of time because because we're +running out of time. Um, that said, + + align:start position:0% +running out of time. Um, that said, + + + align:start position:0% +running out of time. Um, that said, +let's get started with Sparkly + + align:start position:0% +let's get started with Sparkly + + + align:start position:0% +let's get started with Sparkly +Redemption. + + align:start position:0% + + + + align:start position:0% + +So, we had a small hiccup when we + + align:start position:0% +So, we had a small hiccup when we + + + align:start position:0% +So, we had a small hiccup when we +started where we didn't have uh part of + + align:start position:0% +started where we didn't have uh part of + + + align:start position:0% +started where we didn't have uh part of +our core game is collecting sparklies + + align:start position:0% +our core game is collecting sparklies + + + align:start position:0% +our core game is collecting sparklies +and we didn't have a version with that + + align:start position:0% +and we didn't have a version with that + + + align:start position:0% +and we didn't have a version with that +when we started play testing. So, we + + align:start position:0% +when we started play testing. So, we + + + align:start position:0% +when we started play testing. So, we +actually got to test out some different + + align:start position:0% +actually got to test out some different + + + align:start position:0% +actually got to test out some different +movement controls that we were trying + + align:start position:0% +movement controls that we were trying + + + align:start position:0% +movement controls that we were trying +out which actually turned out to be good + + align:start position:0% +out which actually turned out to be good + + + align:start position:0% +out which actually turned out to be good +because the controls that we liked which + + align:start position:0% +because the controls that we liked which + + + align:start position:0% +because the controls that we liked which +was uh right clicking with the mouse and + + align:start position:0% +was uh right clicking with the mouse and + + + align:start position:0% +was uh right clicking with the mouse and +then left clicking to shoot. A lot of + + align:start position:0% +then left clicking to shoot. A lot of + + + align:start position:0% +then left clicking to shoot. A lot of +people had a lot of trouble with that. + + align:start position:0% +people had a lot of trouble with that. + + + align:start position:0% +people had a lot of trouble with that. +So, it was a good thing that we kind of + + align:start position:0% +So, it was a good thing that we kind of + + + align:start position:0% +So, it was a good thing that we kind of +messed up and then got some information + + align:start position:0% +messed up and then got some information + + + align:start position:0% +messed up and then got some information +from that. Then, we got a version with + + align:start position:0% +from that. Then, we got a version with + + + align:start position:0% +from that. Then, we got a version with +the sparkly working and there was a big + + align:start position:0% +the sparkly working and there was a big + + + align:start position:0% +the sparkly working and there was a big +bug where if you killed all the + + align:start position:0% +bug where if you killed all the + + + align:start position:0% +bug where if you killed all the +monsters, they never respond. So, that + + align:start position:0% +monsters, they never respond. So, that + + + align:start position:0% +monsters, they never respond. So, that +bug has now been fixed in the last 10 + + align:start position:0% +bug has now been fixed in the last 10 + + + align:start position:0% +bug has now been fixed in the last 10 +minutes. So, that was good. Um, other + + align:start position:0% +minutes. So, that was good. Um, other + + + align:start position:0% +minutes. So, that was good. Um, other +than that, we got uh just random things + + align:start position:0% +than that, we got uh just random things + + + align:start position:0% +than that, we got uh just random things +like people staying in a corner and just + + align:start position:0% +like people staying in a corner and just + + + align:start position:0% +like people staying in a corner and just +shooting as opposed to just moving + + align:start position:0% +shooting as opposed to just moving + + + align:start position:0% +shooting as opposed to just moving +around the map like we want them to. So, + + align:start position:0% +around the map like we want them to. So, + + + align:start position:0% +around the map like we want them to. So, +we have a few problems that we have to + + align:start position:0% +we have a few problems that we have to + + + align:start position:0% +we have a few problems that we have to +figure out that right now we + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Hi, I'm with Lost Underground. As a + + align:start position:0% +Hi, I'm with Lost Underground. As a + + + align:start position:0% +Hi, I'm with Lost Underground. As a +refresher on our game, the idea is that + + align:start position:0% +refresher on our game, the idea is that + + + align:start position:0% +refresher on our game, the idea is that +you're lost underground in darkness + + align:start position:0% +you're lost underground in darkness + + + align:start position:0% +you're lost underground in darkness +trying to find an exit. And so, as part + + align:start position:0% +trying to find an exit. And so, as part + + + align:start position:0% +trying to find an exit. And so, as part +of our game, uh, we have this sphere of + + align:start position:0% +of our game, uh, we have this sphere of + + + align:start position:0% +of our game, uh, we have this sphere of +visibility around you. And as we play + + align:start position:0% +visibility around you. And as we play + + + align:start position:0% +visibility around you. And as we play +tested, we got a lot of good feedback on + + align:start position:0% +tested, we got a lot of good feedback on + + + align:start position:0% +tested, we got a lot of good feedback on +what that visibility means to people and + + align:start position:0% +what that visibility means to people and + + + align:start position:0% +what that visibility means to people and +how we can actually use it to uh make + + align:start position:0% +how we can actually use it to uh make + + + align:start position:0% +how we can actually use it to uh make +our our mechanics and our level design + + align:start position:0% +our our mechanics and our level design + + + align:start position:0% +our our mechanics and our level design +more compelling. Another big issue we + + align:start position:0% +more compelling. Another big issue we + + + align:start position:0% +more compelling. Another big issue we +ran into with people play testing was + + align:start position:0% +ran into with people play testing was + + + align:start position:0% +ran into with people play testing was +our our collision boxes are basically + + align:start position:0% +our our collision boxes are basically + + + align:start position:0% +our our collision boxes are basically +pixel perfect and so people would get + + align:start position:0% +pixel perfect and so people would get + + + align:start position:0% +pixel perfect and so people would get +caught trying to go through the map + + align:start position:0% +caught trying to go through the map + + + align:start position:0% +caught trying to go through the map +which was really helpful uh for us + + align:start position:0% +which was really helpful uh for us + + + align:start position:0% +which was really helpful uh for us +because although we already knew that + + align:start position:0% +because although we already knew that + + + align:start position:0% +because although we already knew that +this problem existed, we actually + + align:start position:0% +this problem existed, we actually + + + align:start position:0% +this problem existed, we actually +learned a lot about how people were + + align:start position:0% +learned a lot about how people were + + + align:start position:0% +learned a lot about how people were +actually trying to make these decisions. + + align:start position:0% +actually trying to make these decisions. + + + align:start position:0% +actually trying to make these decisions. +And we learned that instead of using the + + align:start position:0% +And we learned that instead of using the + + + align:start position:0% +And we learned that instead of using the +idea of like the entire player shape, a + + align:start position:0% +idea of like the entire player shape, a + + + align:start position:0% +idea of like the entire player shape, a +lot of players were actually looking at + + align:start position:0% +lot of players were actually looking at + + + align:start position:0% +lot of players were actually looking at +where the feet were planted and trying + + align:start position:0% +where the feet were planted and trying + + + align:start position:0% +where the feet were planted and trying +to move based on that. So when we go and + + align:start position:0% +to move based on that. So when we go and + + + align:start position:0% +to move based on that. So when we go and +fix it, we'll make sure to put the + + align:start position:0% +fix it, we'll make sure to put the + + + align:start position:0% +fix it, we'll make sure to put the +collision box around where their feet + + align:start position:0% +collision box around where their feet + + + align:start position:0% +collision box around where their feet +are. Uh we also got a lot of good + + align:start position:0% +are. Uh we also got a lot of good + + + align:start position:0% +are. Uh we also got a lot of good +feedback on uh the items that we had in + + align:start position:0% +feedback on uh the items that we had in + + + align:start position:0% +feedback on uh the items that we had in +our game and where people are actually + + align:start position:0% +our game and where people are actually + + + align:start position:0% +our game and where people are actually +focusing their attention. + + align:start position:0% +focusing their attention. + + + align:start position:0% +focusing their attention. +[Applause] + + align:start position:0% + + + + align:start position:0% + +Oh, you're coming down. + + align:start position:0% +Oh, you're coming down. + + + align:start position:0% +Oh, you're coming down. +Oh, Flender wins. + + align:start position:0% +Oh, Flender wins. + + + align:start position:0% +Oh, Flender wins. +Yeah. + + align:start position:0% + + + + align:start position:0% + +Um, so our game involves uh moving + + align:start position:0% +Um, so our game involves uh moving + + + align:start position:0% +Um, so our game involves uh moving +around a grid and uh running into random + + align:start position:0% +around a grid and uh running into random + + + align:start position:0% +around a grid and uh running into random +encounters which are indicated to the + + align:start position:0% +encounters which are indicated to the + + + align:start position:0% +encounters which are indicated to the +player. Um, the favorability of the + + align:start position:0% +player. Um, the favorability of the + + + align:start position:0% +player. Um, the favorability of the +random encounters are indicated to the + + align:start position:0% +random encounters are indicated to the + + + align:start position:0% +random encounters are indicated to the +player by numbers and colors on the + + align:start position:0% +player by numbers and colors on the + + + align:start position:0% +player by numbers and colors on the +board. Um, so one of the biggest things + + align:start position:0% +board. Um, so one of the biggest things + + + align:start position:0% +board. Um, so one of the biggest things +that uh we got from testing was that + + align:start position:0% +that uh we got from testing was that + + + align:start position:0% +that uh we got from testing was that +people didn't understand the role that + + align:start position:0% +people didn't understand the role that + + + align:start position:0% +people didn't understand the role that +the numbers and colors played or how + + align:start position:0% +the numbers and colors played or how + + + align:start position:0% +the numbers and colors played or how +they were related or if they were + + align:start position:0% +they were related or if they were + + + align:start position:0% +they were related or if they were +related and uh they began by like moving + + align:start position:0% +related and uh they began by like moving + + + align:start position:0% +related and uh they began by like moving +around kind of randomly and just waiting + + align:start position:0% +around kind of randomly and just waiting + + + align:start position:0% +around kind of randomly and just waiting +for things to happen to them. Um, + + align:start position:0% +for things to happen to them. Um, + + + align:start position:0% +for things to happen to them. Um, +there's also a mechanic in our game that + + align:start position:0% +there's also a mechanic in our game that + + + align:start position:0% +there's also a mechanic in our game that +involves uh moving with the wind and + + align:start position:0% +involves uh moving with the wind and + + + align:start position:0% +involves uh moving with the wind and +against the wind. And so moving with the + + align:start position:0% +against the wind. And so moving with the + + + align:start position:0% +against the wind. And so moving with the +wind doesn't cost stamina. Moving + + align:start position:0% +wind doesn't cost stamina. Moving + + + align:start position:0% +wind doesn't cost stamina. Moving +against the wind does. And or moving + + align:start position:0% +against the wind does. And or moving + + + align:start position:0% +against the wind does. And or moving +sideways the wind does moving against + + align:start position:0% +sideways the wind does moving against + + + align:start position:0% +sideways the wind does moving against +the wind is not possible. People had + + align:start position:0% +the wind is not possible. People had + + + align:start position:0% +the wind is not possible. People had +trouble figuring that out as well. So, + + align:start position:0% +trouble figuring that out as well. So, + + + align:start position:0% +trouble figuring that out as well. So, +one of the biggest things we're going to + + align:start position:0% +one of the biggest things we're going to + + + align:start position:0% +one of the biggest things we're going to +try and do is uh more visual feedback uh + + align:start position:0% +try and do is uh more visual feedback uh + + + align:start position:0% +try and do is uh more visual feedback uh +to the player, help them figure things + + align:start position:0% +to the player, help them figure things + + + align:start position:0% +to the player, help them figure things +out as it goes. Um, also people felt + + align:start position:0% +out as it goes. Um, also people felt + + + align:start position:0% +out as it goes. Um, also people felt +like there should be more long-term + + align:start position:0% +like there should be more long-term + + + align:start position:0% +like there should be more long-term +consequences instead of just planning + + align:start position:0% +consequences instead of just planning + + + align:start position:0% +consequences instead of just planning +for the next move or two. And so, we're + + align:start position:0% +for the next move or two. And so, we're + + + align:start position:0% +for the next move or two. And so, we're +going to see how we can integrate that + + align:start position:0% +going to see how we can integrate that + + + align:start position:0% +going to see how we can integrate that +into our game. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Hi blind aliens. So we got a lot of + + align:start position:0% +Hi blind aliens. So we got a lot of + + + align:start position:0% +Hi blind aliens. So we got a lot of +great feedback uh from the user play + + align:start position:0% +great feedback uh from the user play + + + align:start position:0% +great feedback uh from the user play +testing. So one of the main things we + + align:start position:0% +testing. So one of the main things we + + + align:start position:0% +testing. So one of the main things we +realized is we needed more clear goals + + align:start position:0% +realized is we needed more clear goals + + + align:start position:0% +realized is we needed more clear goals +and more long-term goals. So for + + align:start position:0% +and more long-term goals. So for + + + align:start position:0% +and more long-term goals. So for +example, our bot automatically reloads + + align:start position:0% +example, our bot automatically reloads + + + align:start position:0% +example, our bot automatically reloads +and that was a little confusing for + + align:start position:0% +and that was a little confusing for + + + align:start position:0% +and that was a little confusing for +people because they didn't really see + + align:start position:0% +people because they didn't really see + + + align:start position:0% +people because they didn't really see +that it was reloading. But instead of + + align:start position:0% +that it was reloading. But instead of + + + align:start position:0% +that it was reloading. But instead of +doing something like + + align:start position:0% +doing something like + + + align:start position:0% +doing something like +your loads. We're thinking of adding + + align:start position:0% +your loads. We're thinking of adding + + + align:start position:0% +your loads. We're thinking of adding +like bullets around that you have to go + + align:start position:0% +like bullets around that you have to go + + + align:start position:0% +like bullets around that you have to go +and collect. So, it's more short-term + + align:start position:0% +and collect. So, it's more short-term + + + align:start position:0% +and collect. So, it's more short-term +goals and also long-term strategy. How + + align:start position:0% +goals and also long-term strategy. How + + + align:start position:0% +goals and also long-term strategy. How +do you save your bullets up when you use + + align:start position:0% +do you save your bullets up when you use + + + align:start position:0% +do you save your bullets up when you use +them all? Um, another thing we noticed + + align:start position:0% +them all? Um, another thing we noticed + + + align:start position:0% +them all? Um, another thing we noticed +was that our game was way too hard at + + align:start position:0% +was that our game was way too hard at + + + align:start position:0% +was that our game was way too hard at +first and way too easy after 5 minutes. + + align:start position:0% +first and way too easy after 5 minutes. + + + align:start position:0% +first and way too easy after 5 minutes. +Uh, so we decided we could focus on + + align:start position:0% +Uh, so we decided we could focus on + + + align:start position:0% +Uh, so we decided we could focus on +ramping up the difficulty. Instead of + + align:start position:0% +ramping up the difficulty. Instead of + + + align:start position:0% +ramping up the difficulty. Instead of +starting with three aliens attacking + + align:start position:0% +starting with three aliens attacking + + + align:start position:0% +starting with three aliens attacking +you, maybe only one. And then maybe + + align:start position:0% +you, maybe only one. And then maybe + + + align:start position:0% +you, maybe only one. And then maybe +after five minutes, instead of only + + align:start position:0% +after five minutes, instead of only + + + align:start position:0% +after five minutes, instead of only +having three aliens, maybe 10. But + + align:start position:0% +having three aliens, maybe 10. But + + + align:start position:0% +having three aliens, maybe 10. But +that'd be a bit difficult. + + align:start position:0% +that'd be a bit difficult. + + + align:start position:0% +that'd be a bit difficult. +Uh, so another thing we focused on was + + align:start position:0% +Uh, so another thing we focused on was + + + align:start position:0% +Uh, so another thing we focused on was +uh our AI. So I talked about not AI, + + align:start position:0% +uh our AI. So I talked about not AI, + + + align:start position:0% +uh our AI. So I talked about not AI, +user interface. So I talked about how + + align:start position:0% +user interface. So I talked about how + + + align:start position:0% +user interface. So I talked about how +there was a reloading thing. It was + + align:start position:0% +there was a reloading thing. It was + + + align:start position:0% +there was a reloading thing. It was +flashing in the corner, but no one saw + + align:start position:0% +flashing in the corner, but no one saw + + + align:start position:0% +flashing in the corner, but no one saw +it. So no one knew that their gun was + + align:start position:0% +it. So no one knew that their gun was + + + align:start position:0% +it. So no one knew that their gun was +reloading. They thought it just wasn't + + align:start position:0% +reloading. They thought it just wasn't + + + align:start position:0% +reloading. They thought it just wasn't +working and they were frustrated that it + + align:start position:0% +working and they were frustrated that it + + + align:start position:0% +working and they were frustrated that it +wasn't. They were clicking and nothing + + align:start position:0% +wasn't. They were clicking and nothing + + + align:start position:0% +wasn't. They were clicking and nothing +was happening. So we need to make that + + align:start position:0% +was happening. So we need to make that + + + align:start position:0% +was happening. So we need to make that +more visual. along with our aliens when + + align:start position:0% +more visual. along with our aliens when + + + align:start position:0% +more visual. along with our aliens when +they're half dead or like they're still + + align:start position:0% +they're half dead or like they're still + + + align:start position:0% +they're half dead or like they're still +attacking you. People thought they were + + align:start position:0% +attacking you. People thought they were + + + align:start position:0% +attacking you. People thought they were +dead, but they run into them and they + + align:start position:0% +dead, but they run into them and they + + + align:start position:0% +dead, but they run into them and they +died and be frustrated. So, instead of + + align:start position:0% +died and be frustrated. So, instead of + + + align:start position:0% +died and be frustrated. So, instead of +maybe turning them more darker, maybe + + align:start position:0% +maybe turning them more darker, maybe + + + align:start position:0% +maybe turning them more darker, maybe +turn them red, something like that to + + align:start position:0% +turn them red, something like that to + + + align:start position:0% +turn them red, something like that to +make that clearer. So, thank you guys + + align:start position:0% +make that clearer. So, thank you guys + + + align:start position:0% +make that clearer. So, thank you guys +for all the feedback. + + align:start position:0% +for all the feedback. + + + align:start position:0% +for all the feedback. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Majice, + + align:start position:0% + + + + align:start position:0% + +hi, we're Majice. So, a lot of the + + align:start position:0% +hi, we're Majice. So, a lot of the + + + align:start position:0% +hi, we're Majice. So, a lot of the +feedback we got was really based on our + + align:start position:0% +feedback we got was really based on our + + + align:start position:0% +feedback we got was really based on our +UI and it's because we're sort of + + align:start position:0% +UI and it's because we're sort of + + + align:start position:0% +UI and it's because we're sort of +modeling a 3D die using 2D graphics. So, + + align:start position:0% +modeling a 3D die using 2D graphics. So, + + + align:start position:0% +modeling a 3D die using 2D graphics. So, +a lot of people have different opinions + + align:start position:0% +a lot of people have different opinions + + + align:start position:0% +a lot of people have different opinions +about how that should look and no one + + align:start position:0% +about how that should look and no one + + + align:start position:0% +about how that should look and no one +thought that the way it does look is + + align:start position:0% +thought that the way it does look is + + + align:start position:0% +thought that the way it does look is +okay. + + align:start position:0% +okay. + + + align:start position:0% +okay. +And so, like it's we've really gotten a + + align:start position:0% +And so, like it's we've really gotten a + + + align:start position:0% +And so, like it's we've really gotten a +lot of opinions like May could do it + + align:start position:0% +lot of opinions like May could do it + + + align:start position:0% +lot of opinions like May could do it +this way, May could do it this way. And + + align:start position:0% +this way, May could do it this way. And + + + align:start position:0% +this way, May could do it this way. And +that really like helps because now we + + align:start position:0% +that really like helps because now we + + + align:start position:0% +that really like helps because now we +can really build up a discussion of how + + align:start position:0% +can really build up a discussion of how + + + align:start position:0% +can really build up a discussion of how +it should look, how we can make this + + align:start position:0% +it should look, how we can make this + + + align:start position:0% +it should look, how we can make this +mental model in people's heads match + + align:start position:0% +mental model in people's heads match + + + align:start position:0% +mental model in people's heads match +what they're seeing on the screen, which + + align:start position:0% +what they're seeing on the screen, which + + + align:start position:0% +what they're seeing on the screen, which +is the real like hard challenge that + + align:start position:0% +is the real like hard challenge that + + + align:start position:0% +is the real like hard challenge that +we're facing. So thanks for the feedback + + align:start position:0% + + + + align:start position:0% + +beaver evolution. + + align:start position:0% + + + + align:start position:0% + +It's going to be a problem several days + + align:start position:0% +It's going to be a problem several days + + + align:start position:0% +It's going to be a problem several days +ago. + + align:start position:0% +ago. + + + align:start position:0% +ago. +All right. So, I guess through play + + align:start position:0% +All right. So, I guess through play + + + align:start position:0% +All right. So, I guess through play +testing, we really realized that we + + align:start position:0% +testing, we really realized that we + + + align:start position:0% +testing, we really realized that we +weren't conveying to the user um exactly + + align:start position:0% +weren't conveying to the user um exactly + + + align:start position:0% +weren't conveying to the user um exactly +what all the instructions were clearly + + align:start position:0% +what all the instructions were clearly + + + align:start position:0% +what all the instructions were clearly +and you know what was happening at each + + align:start position:0% +and you know what was happening at each + + + align:start position:0% +and you know what was happening at each +turn. Um but otherwise, like the game + + align:start position:0% +turn. Um but otherwise, like the game + + + align:start position:0% +turn. Um but otherwise, like the game +mechanics worked pretty well. So, um + + align:start position:0% +mechanics worked pretty well. So, um + + + align:start position:0% +mechanics worked pretty well. So, um +like in M Revolution, you can choose + + align:start position:0% +like in M Revolution, you can choose + + + align:start position:0% +like in M Revolution, you can choose +whether to build, populate, or evolve, + + align:start position:0% +whether to build, populate, or evolve, + + + align:start position:0% +whether to build, populate, or evolve, +but it wasn't clear to the player like + + align:start position:0% +but it wasn't clear to the player like + + + align:start position:0% +but it wasn't clear to the player like +exactly how many beirds you could + + align:start position:0% +exactly how many beirds you could + + + align:start position:0% +exactly how many beirds you could +populate or like how many dams you could + + align:start position:0% +populate or like how many dams you could + + + align:start position:0% +populate or like how many dams you could +build or like what natural disaster + + align:start position:0% +build or like what natural disaster + + + align:start position:0% +build or like what natural disaster +could happen. Um and then like between + + align:start position:0% +could happen. Um and then like between + + + align:start position:0% +could happen. Um and then like between +each turn if natural dis happened. Um + + align:start position:0% +each turn if natural dis happened. Um + + + align:start position:0% +each turn if natural dis happened. Um +there wasn't that much engagement + + align:start position:0% +there wasn't that much engagement + + + align:start position:0% +there wasn't that much engagement +between the player and the game being + + align:start position:0% +between the player and the game being + + + align:start position:0% +between the player and the game being +like, oh, you know, this drought + + align:start position:0% +like, oh, you know, this drought + + + align:start position:0% +like, oh, you know, this drought +happened this and then this is a + + align:start position:0% +happened this and then this is a + + + align:start position:0% +happened this and then this is a +consequence of that. Um so I think like + + align:start position:0% +consequence of that. Um so I think like + + + align:start position:0% +consequence of that. Um so I think like +going forward, we're going to really try + + align:start position:0% +going forward, we're going to really try + + + align:start position:0% +going forward, we're going to really try +to um make it easier for players to + + align:start position:0% +to um make it easier for players to + + + align:start position:0% +to um make it easier for players to +understand what happened during that + + align:start position:0% +understand what happened during that + + + align:start position:0% +understand what happened during that +turn and then what their choices are um + + align:start position:0% +turn and then what their choices are um + + + align:start position:0% +turn and then what their choices are um +in terms of picking it. So a lot of it + + align:start position:0% +in terms of picking it. So a lot of it + + + align:start position:0% +in terms of picking it. So a lot of it +is like um clarifying what the + + align:start position:0% +is like um clarifying what the + + + align:start position:0% +is like um clarifying what the +instructions are, what the game + + align:start position:0% +instructions are, what the game + + + align:start position:0% +instructions are, what the game +mechanics are. + + align:start position:0% + + + + align:start position:0% + +And finally, Comcastic. + + align:start position:0% + + + + align:start position:0% + +Okay. Well, the two main pieces of + + align:start position:0% +Okay. Well, the two main pieces of + + + align:start position:0% +Okay. Well, the two main pieces of +feedback that we got from players were + + align:start position:0% +feedback that we got from players were + + + align:start position:0% +feedback that we got from players were +about the UI of the game, and we had + + align:start position:0% +about the UI of the game, and we had + + + align:start position:0% +about the UI of the game, and we had +some issues with that because our game + + align:start position:0% +some issues with that because our game + + + align:start position:0% +some issues with that because our game +has a lot of like kind of sort of + + align:start position:0% +has a lot of like kind of sort of + + + align:start position:0% +has a lot of like kind of sort of +complex UI requirements, and we didn't + + align:start position:0% +complex UI requirements, and we didn't + + + align:start position:0% +complex UI requirements, and we didn't +have time to implement a lot of those + + align:start position:0% +have time to implement a lot of those + + + align:start position:0% +have time to implement a lot of those +prior to this test session, but we did + + align:start position:0% +prior to this test session, but we did + + + align:start position:0% +prior to this test session, but we did +get a lot of feedback about um UI + + align:start position:0% +get a lot of feedback about um UI + + + align:start position:0% +get a lot of feedback about um UI +improvements that would make it easier + + align:start position:0% +improvements that would make it easier + + + align:start position:0% +improvements that would make it easier +for players to see what was going on + + align:start position:0% +for players to see what was going on + + + align:start position:0% +for players to see what was going on +with the game. For example, highlighting + + align:start position:0% +with the game. For example, highlighting + + + align:start position:0% +with the game. For example, highlighting +how those that are currently being + + align:start position:0% +how those that are currently being + + + align:start position:0% +how those that are currently being +served by our center. Um the other main + + align:start position:0% +served by our center. Um the other main + + + align:start position:0% +served by our center. Um the other main +complaint that we got was that uh the + + align:start position:0% +complaint that we got was that uh the + + + align:start position:0% +complaint that we got was that uh the +game is sort of uh nebulous right now. + + align:start position:0% +game is sort of uh nebulous right now. + + + align:start position:0% +game is sort of uh nebulous right now. +there's not a whole lot of challenge or + + align:start position:0% +there's not a whole lot of challenge or + + + align:start position:0% +there's not a whole lot of challenge or +a clearly defined goal. It's something + + align:start position:0% +a clearly defined goal. It's something + + + align:start position:0% +a clearly defined goal. It's something +that we're really going to look at going + + align:start position:0% +that we're really going to look at going + + + align:start position:0% +that we're really going to look at going +forward is uh like uh tightening the + + align:start position:0% +forward is uh like uh tightening the + + + align:start position:0% +forward is uh like uh tightening the +focus of a game, adding more uh tension + + align:start position:0% +focus of a game, adding more uh tension + + + align:start position:0% +focus of a game, adding more uh tension +and making the goal of the game more + + align:start position:0% +and making the goal of the game more + + + align:start position:0% +and making the goal of the game more +concrete. And since um we it's not it + + align:start position:0% +concrete. And since um we it's not it + + + align:start position:0% +concrete. And since um we it's not it +doesn't fit very well into an + + align:start position:0% +doesn't fit very well into an + + + align:start position:0% +doesn't fit very well into an +established armor, we had some more like + + align:start position:0% +established armor, we had some more like + + + align:start position:0% +established armor, we had some more like +sort of complex design decisions to + + align:start position:0% +sort of complex design decisions to + + + align:start position:0% +sort of complex design decisions to +figure out like how to make this a fun + + align:start position:0% +figure out like how to make this a fun + + + align:start position:0% +figure out like how to make this a fun +and engaging game. And so that's uh + + align:start position:0% +and engaging game. And so that's uh + + + align:start position:0% +and engaging game. And so that's uh +pretty much what we're going to be + + align:start position:0% +pretty much what we're going to be + + + align:start position:0% +pretty much what we're going to be +focusing on going forward be UI and + + align:start position:0% +focusing on going forward be UI and + + + align:start position:0% +focusing on going forward be UI and +adding more like challenge and tension + + align:start position:0% +adding more like challenge and tension + + + align:start position:0% +adding more like challenge and tension +to the game. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Do you have anything to say? + + align:start position:0% +Do you have anything to say? + + + align:start position:0% +Do you have anything to say? +Okay. So I just want to remind everybody + + align:start position:0% +Okay. So I just want to remind everybody + + + align:start position:0% +Okay. So I just want to remind everybody +that you started on this project less + + align:start position:0% +that you started on this project less + + + align:start position:0% +that you started on this project less +than 10 days ago. Okay. So and you just + + align:start position:0% +than 10 days ago. Okay. So and you just + + + align:start position:0% +than 10 days ago. Okay. So and you just +finished your first playable prototype. + + align:start position:0% +finished your first playable prototype. + + + align:start position:0% +finished your first playable prototype. +So and and and you did a good test. So + + align:start position:0% +So and and and you did a good test. So + + + align:start position:0% +So and and and you did a good test. So +give yourself a hand. + + align:start position:0% + + + + align:start position:0% + +Um, let's see. Things to keep in mind. + + align:start position:0% +Um, let's see. Things to keep in mind. + + + align:start position:0% +Um, let's see. Things to keep in mind. +Uh, for those of you who are making + + align:start position:0% +Uh, for those of you who are making + + + align:start position:0% +Uh, for those of you who are making +moused driven games, you want to make + + align:start position:0% +moused driven games, you want to make + + + align:start position:0% +moused driven games, you want to make +sure that you have enough mice to to + + align:start position:0% +sure that you have enough mice to to + + + align:start position:0% +sure that you have enough mice to to +have uh + + align:start position:0% +have uh + + + align:start position:0% +have uh +uh for your next play play test, which + + align:start position:0% +uh for your next play play test, which + + + align:start position:0% +uh for your next play play test, which +will be probably project three, right? + + align:start position:0% +will be probably project three, right? + + + align:start position:0% +will be probably project three, right? +Um, and uh you've only got like another + + align:start position:0% +Um, and uh you've only got like another + + + align:start position:0% +Um, and uh you've only got like another +five days if I'm not mistaken till the + + align:start position:0% +five days if I'm not mistaken till the + + + align:start position:0% +five days if I'm not mistaken till the +uh when when when this when this is + + align:start position:0% +uh when when when this when this is + + + align:start position:0% +uh when when when this when this is +done. This is exactly two weeks uh pro + + align:start position:0% +done. This is exactly two weeks uh pro + + + align:start position:0% +done. This is exactly two weeks uh pro +project. So if you haven't started + + align:start position:0% +project. So if you haven't started + + + align:start position:0% +project. So if you haven't started +cutting features, this is probably the + + align:start position:0% +cutting features, this is probably the + + + align:start position:0% +cutting features, this is probably the +time to do it. Let's see what else. Um + + align:start position:0% +time to do it. Let's see what else. Um + + + align:start position:0% +time to do it. Let's see what else. Um +something that of course we did notice + + align:start position:0% +something that of course we did notice + + + align:start position:0% +something that of course we did notice +and you all felt it was that there + + align:start position:0% +and you all felt it was that there + + + align:start position:0% +and you all felt it was that there +weren't enough uh stations for playing + + align:start position:0% +weren't enough uh stations for playing + + + align:start position:0% +weren't enough uh stations for playing +the games uh for future play tests for + + align:start position:0% +the games uh for future play tests for + + + align:start position:0% +the games uh for future play tests for +project 3 onwards. uh we are going to + + align:start position:0% +project 3 onwards. uh we are going to + + + align:start position:0% +project 3 onwards. uh we are going to +expect at least half as many uh game + + align:start position:0% +expect at least half as many uh game + + + align:start position:0% +expect at least half as many uh game +computers as you have uh at the average + + align:start position:0% +computers as you have uh at the average + + + align:start position:0% +computers as you have uh at the average +team size. So I I I'm not sure whether + + align:start position:0% +team size. So I I I'm not sure whether + + + align:start position:0% +team size. So I I I'm not sure whether +we're doing teams of six or teams of + + align:start position:0% +we're doing teams of six or teams of + + + align:start position:0% +we're doing teams of six or teams of +eight. Uh we're doing teams of six for + + align:start position:0% +eight. Uh we're doing teams of six for + + + align:start position:0% +eight. Uh we're doing teams of six for +for for project three which means each + + align:start position:0% +for for project three which means each + + + align:start position:0% +for for project three which means each +team should be prepared to have at least + + align:start position:0% +team should be prepared to have at least + + + align:start position:0% +team should be prepared to have at least +three computers running uh with the + + align:start position:0% +three computers running uh with the + + + align:start position:0% +three computers running uh with the +games. Something else that we're also + + align:start position:0% +games. Something else that we're also + + + align:start position:0% +games. Something else that we're also +going to en uh to to to make it a lot + + align:start position:0% +going to en uh to to to make it a lot + + + align:start position:0% +going to en uh to to to make it a lot +clearer where the game stations are is + + align:start position:0% +clearer where the game stations are is + + + align:start position:0% +clearer where the game stations are is +that the computers that are not being + + align:start position:0% +that the computers that are not being + + + align:start position:0% +that the computers that are not being +used for gameplay should actually just + + align:start position:0% +used for gameplay should actually just + + + align:start position:0% +used for gameplay should actually just +be closed. Take notes using paper + + align:start position:0% +be closed. Take notes using paper + + + align:start position:0% +be closed. Take notes using paper +because it gets confusing to figure out + + align:start position:0% +because it gets confusing to figure out + + + align:start position:0% +because it gets confusing to figure out +which are the game stations and which + + align:start position:0% +which are the game stations and which + + + align:start position:0% +which are the game stations and which +ones are just like people taking notes + + align:start position:0% +ones are just like people taking notes + + + align:start position:0% +ones are just like people taking notes +and which ones are the ones where uh + + align:start position:0% +and which ones are the ones where uh + + + align:start position:0% +and which ones are the ones where uh +people are actually like coding on the + + align:start position:0% +people are actually like coding on the + + + align:start position:0% +people are actually like coding on the +slide trying to fix last minute + + align:start position:0% +slide trying to fix last minute + + + align:start position:0% +slide trying to fix last minute +problems. You really should have all + + align:start position:0% +problems. You really should have all + + + align:start position:0% +problems. You really should have all +that sorted out before the play test, + + align:start position:0% +that sorted out before the play test, + + + align:start position:0% +that sorted out before the play test, +not during the play test. All right. So, + + align:start position:0% +not during the play test. All right. So, + + + align:start position:0% +not during the play test. All right. So, +um, next time when we're doing a play + + align:start position:0% +um, next time when we're doing a play + + + align:start position:0% +um, next time when we're doing a play +test, just make sure that, you know, + + align:start position:0% +test, just make sure that, you know, + + + align:start position:0% +test, just make sure that, you know, +half your team basically is, uh, is is + + align:start position:0% +half your team basically is, uh, is is + + + align:start position:0% +half your team basically is, uh, is is +ready to go with with the game. And I + + align:start position:0% +ready to go with with the game. And I + + + align:start position:0% +ready to go with with the game. And I +would suggest more than half your team + + align:start position:0% +would suggest more than half your team + + + align:start position:0% +would suggest more than half your team +should be able to run the code just in + + align:start position:0% +should be able to run the code just in + + + align:start position:0% +should be able to run the code just in +case someone falls sick, right? You + + align:start position:0% +case someone falls sick, right? You + + + align:start position:0% +case someone falls sick, right? You +know, and doesn't and and doesn't bring + + align:start position:0% +know, and doesn't and and doesn't bring + + + align:start position:0% +know, and doesn't and and doesn't bring +their computer or their mouse. Rest of + + align:start position:0% +their computer or their mouse. Rest of + + + align:start position:0% +their computer or their mouse. Rest of +the class is for you to work on with + + align:start position:0% +the class is for you to work on with + + + align:start position:0% +the class is for you to work on with +your on your own team. I if anyone + + align:start position:0% +your on your own team. I if anyone + + + align:start position:0% +your on your own team. I if anyone +hasn't signed in to the attendance + + align:start position:0% +hasn't signed in to the attendance + + + align:start position:0% +hasn't signed in to the attendance +sheet, uh, we still have it up here. And + + align:start position:0% +sheet, uh, we still have it up here. And + + + align:start position:0% +sheet, uh, we still have it up here. And +uh I want to have uh uh everyone give + + align:start position:0% +uh I want to have uh uh everyone give + + + align:start position:0% +uh I want to have uh uh everyone give +the folks from Riot a big hand for + + align:start position:0% +the folks from Riot a big hand for + + + align:start position:0% +the folks from Riot a big hand for +coming and giving their feedback. + + align:start position:0% + + + + align:start position:0% + +Thank you. + + align:start position:0% + + + + align:start position:0% + +Oh yes, they have lots of information + + align:start position:0% +Oh yes, they have lots of information + + + align:start position:0% +Oh yes, they have lots of information +about internships. Oops. Whoa. Whoa. A + + align:start position:0% +about internships. Oops. Whoa. Whoa. A + + + align:start position:0% +about internships. Oops. Whoa. Whoa. A +very very large stack of documents and + + align:start position:0% +very very large stack of documents and + + + align:start position:0% +very very large stack of documents and +positions that they're uh that are + + align:start position:0% +positions that they're uh that are + + + align:start position:0% +positions that they're uh that are +available and a deadline October 15th + + align:start position:0% +available and a deadline October 15th + + + align:start position:0% +available and a deadline October 15th +which is not that long uh not that long + + align:start position:0% +which is not that long uh not that long + + + align:start position:0% +which is not that long uh not that long +from from from now. So, um, definitely + + align:start position:0% +from from from now. So, um, definitely + + + align:start position:0% +from from from now. So, um, definitely +check this out as soon as you can. Uh, + + align:start position:0% +check this out as soon as you can. Uh, + + + align:start position:0% +check this out as soon as you can. Uh, +let's see. Actually, while while we're + + align:start position:0% +let's see. Actually, while while we're + + + align:start position:0% +let's see. Actually, while while we're +on internships, there's one other thing + + align:start position:0% +on internships, there's one other thing + + + align:start position:0% +on internships, there's one other thing +that I want to mention. Uh, there was I + + align:start position:0% +that I want to mention. Uh, there was I + + + align:start position:0% +that I want to mention. Uh, there was I +sent out a a message for a Europe over + + align:start position:0% +sent out a a message for a Europe over + + + align:start position:0% +sent out a a message for a Europe over +in Arrow Astro. They are looking for + + align:start position:0% +in Arrow Astro. They are looking for + + + align:start position:0% +in Arrow Astro. They are looking for +game developers. Uh, specific uh even + + align:start position:0% +game developers. Uh, specific uh even + + + align:start position:0% +game developers. Uh, specific uh even +better if you also know Mat Lab, but + + align:start position:0% +better if you also know Mat Lab, but + + + align:start position:0% +better if you also know Mat Lab, but +they just want game developers um for a + + align:start position:0% +they just want game developers um for a + + + align:start position:0% +they just want game developers um for a +high school science competition that uh + + align:start position:0% +high school science competition that uh + + + align:start position:0% +high school science competition that uh +that they're running. It's like it's + + align:start position:0% +that they're running. It's like it's + + + align:start position:0% +that they're running. It's like it's +like first robotics. is a robotics + + align:start position:0% +like first robotics. is a robotics + + + align:start position:0% +like first robotics. is a robotics +competition only in zero gravity. So if + + align:start position:0% +competition only in zero gravity. So if + + + align:start position:0% +competition only in zero gravity. So if +that sounds cool, uh you should uh + + align:start position:0% +that sounds cool, uh you should uh + + + align:start position:0% +that sounds cool, uh you should uh +definitely respond to them quickly + + align:start position:0% +definitely respond to them quickly + + + align:start position:0% +definitely respond to them quickly +because your update lines are coming up. + + align:start position:0% +because your update lines are coming up. + + + align:start position:0% +because your update lines are coming up. +And + + align:start position:0% +And + + + align:start position:0% +And +that's it. Yeah. See you on Monday. \ No newline at end of file diff --git a/xvTYUnqn2wY.txt b/xvTYUnqn2wY.txt new file mode 100644 index 0000000000000000000000000000000000000000..077984c86e55160b3428ccff5d2f73f4acc4d677 --- /dev/null +++ b/xvTYUnqn2wY.txt @@ -0,0 +1,3048 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high-quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: This week is my +second pair of lectures. + +Last week the two lectures were +about first order differential + +equations, and this +week second order. + +Those are the two big topics +in differential equations. + +Let me start with most +basic second order equation. + +We see the second derivative +and the function itself, + +and we don't see yet the +first derivative term. + +This is the nice case, when I +just have y double prime and y. + +In general, I-- I'm taking +constant coefficients today. + +Because if the coefficients +depend on time, + +the problem gets +much, much harder now. + +So let's stay with +constant coefficients, + +meaning we have a mass, for +example, we have a spring. + +The stiffness of the +spring is k, the mass is m, + +and the y, the +unknown displacement, + +tells us the +movement of the mass. + +The classical problem. + +You will have seen it before. + +Because you have an +exam this afternoon, + +I wanted to start with +things that-- they + +are about second +order equations, + +but they're still close to +the exam idea, particularly + +the idea of exponentials. + +With constant coefficients, +that's the fundamental message. + +Exponentials in, +exponentials out. + +But it's not quite +so clear when we + +had first order, +y prime equal ay, + +we knew that the exponent was a. + +The solution was e to the at. + +Now we've got second +derivatives coming in, + +and it won't be so much +e to the at type thing. + +Either the at was growth for a +positive, decay for a negative. + +Now we're going to +see oscillation. + +It's still exponentials, +but oscillation. + +Things going up and down, +things going around. + +Harmonic motion, you call it. + +Sines and cosines. + +And sines and cosines connect +to complex exponentials. + +So that instead of e to the +at-- so now oscillations-- + +they're going to be coming +from e to the i omega t. + +In other words, instead of an a, +we're going to have an i omega. + +Or, if we like to +stay real, we can + +stay with cos-- +cosine-- and sine. + +And actually, I've written +two real guys there, + +so I better have +two complex ones. + +And it will turn out +to be plus or minus. + +There are two frequencies there. + +Plus i omega, minus i omega, and +they turn into cosine and sine. + +So in this case, +with no damping term, + +we can stay entirely real +without creating any problems. + +We can work with +cosines and sines. + +The first question +is, what's omega. + +What is the frequency +of oscillation. + +And of course, another +similar picture + +would be a pendulum, +a linear pendulum, + +swinging side to +side, keeping time, + +because that frequency +will stay constant. + +Always I'll start with zero +on the right hand side. + +Just look at these equations. + +Constants there. + +I'm looking for solutions. + +And I'm looking +for null solutions, + +looking for the natural motion +of this spring, the natural up + +and down motion of this spring. + +Classical problem. + +Won't be brand new, but +it's the right starting + +point for the full +second order equation. + +It'll get a little +complicated on Wednesday, + +when damping gets in there. + +The formula got a little +messy, because you've + +got a mass-- you've got +an m-- and a k, still, + +but you also will have +a damping constant. + +Then complex numbers +really come in. + +Here they're optional. + +So this is my equation to solve. + +Because we don't have +a first derivative, + +a cosine will solve that. + +So let me look for-- I +could look for exponentials. + +Maybe I should do +that first, look + +for an exponential solution. + +Yeah, that's a good idea. + +And let me not +jump ahead to know + +that the exponent has +that i omega form. + +Let me discover it. + +So I look for no +solutions-- because I + +have that zero there-- +no solutions of the form + +e to the st, some exponent. + +Plug it in. + +That's the message with +constant coefficients. + +Look for exponentials, +substitute them in, + +discover what s will be. + +So let's just do that. + +This is the most basic step. + +For null solutions +will be exponentials, + +I substitute into the equation. + +I get ms squared +from two derivatives. + +It will bring s down twice. + +This is just ke to the st, and +I'm looking for null solutions. + +Zero. + +No forcing. + +So this is undamped, unforced. + +Undamped, unforced. + +Natural motion. + +What do I do now? + +Plugged in an exponential, +got this equation. + +And the beauty is that +the exponentials cancel. + +An exponential is never zero, +so I can safely divide by it. + +So I cancel those, and I get +ms squared plus k equals zero. + +The key equation-- and +it's so simple-- it's + +just we're doing algebra now. + +The calculus, the derivative +we took when we plugged it in, + +but now it's an +algebra question. + +And of course, solving +that system is easy. + +There's no s term, +no damping term. + +So the frequency, s, is-- put k +on the other side, divide by n. + +s is-- s squared, let's say-- +is k over m-- is minus k over m. + +Critical point. + +That tells me, with +that minus sign there, + +that s is an imaginary number. + +A complex number has a real +part and an imaginary part. + +In this case, all imaginary. + +No real part at all. + +It's natural to think-- s +is the square root of that, + +so I'm going to write-- +everybody writes-- s, + +the frequency s, is i omega. + +So if I plug that in, I have +omega squared equal k over m. + +i squared and the minus +1 deal with each other. + +So the frequency omega-- here +is the great fact-- square + +root of k over m. + +That's-- yes? + +AUDIENCE: What +difference does having + +imaginary parts to answer +affect the oscillation? + +PROFESSOR: To-- OK. + +Oscillation, just +pure oscillation-- + +which is what we would +see here with no damping-- + +is the frequency, e to the-- +the solution-- the displacement, + +I could write-- the +displacement up and down, + +y, will involve e to the i +omega t, and e to the minus i + +omega t. + +We've got second order equation. + +Let me just go back +to that key point. + +When we have second +order equations, + +we look for two-- we +expect and we want + +and we need two-- solutions. + +There will be two. + +I didn't put it +here, and I should. + +s, the frequency, is +plus or minus i omega, + +because in both cases when we +square, it comes out right. + +So we get two frequencies, +and here they are. + +So let's see how to +answer your question. + +The presence of this +i is only telling me + +that, essentially, I've +got sines and cosines. + +That's really what-- when it's a +pure imaginary number-- I would + +call that a pure +imaginary number, + +there's no real part at +all-- then equally cos omega + +t and sine omega t. + +I can now, if I want, go real. + +I can say, OK, these were +the general null solutions. + +Let me put this down, then. + +The null solution-- I'm +looking only right now + +at null solutions-- is +some combination of e + +to the i omega t and e +to the minus i omega t. + +That's what we got from +plugging in e to the st, + +discovering that s was +an imaginary number, + +and we got these guys. + +But equally-- equally-- +yn is a combination + +of cos omega t and sine omega t. + +And maybe you'll +like those better. + +I think everybody practically +likes those better. + +Do you see that these guys +are the same as these guys? + +The c's are a little +different because, well, we + +know that we can switch +from one to the other. + +We remember that basic fact +that e to the i omega t + +is cos omega t plus +i times sine omega t. + +You're used to maybe seeing that +omega t as theta, e to the i + +theta is cos theta +plus i sine theta. + +And e to the minus i +omega t, of course, + +is cos omega t minus +i sine omega t. + +I hope you won't think +I'm filling the blackboard + +with formulas, because I'm +really just writing down-- + +well anyway, they're +beautiful formulas. + +So if I have these guys, then +I have these and vice versa. + +If I have cos-- +how would you write + +cos omega t using +the exponentials? + +I want to just see +totally clearly + +that I can go back and forth +between complex imaginary + +exponentials and +cosines and sines. + +So how would I, I want to +go in the opposite direction + +and write the cosine and the +sine as combinations of these, + +just to show if I've +got combinations of one, + +I've got combinations +of the other. + +Combinations of these are the +same as combinations of those. + +So what is cos omega t +in terms of these guys? + +AUDIENCE: [INAUDIBLE] +some of them divided by 2? + +PROFESSOR: Exactly. + +If I add those two, +this part cancels. + +I've got two of these, so I +have to divide by 2, as you say. + +It's a half of the first +plus a half of the second. + +And how about sine omega t? + +Sine omega t is always +slightly more annoying, + +because it's the one-- it's +the imaginary part that + +brings in an i. + +What would be the same formula? + +How could I produce sine +omega t out of that? + +Yes? + +AUDIENCE: The difference +divided by 2i. + +PROFESSOR: Yes. + +If I take the difference, +that'll cancel the cosines. + +So I'm going to take +e to the i omega + +t minus e-- minus e to +the minus i omega t. + +Take the difference. + +But then I've got 2i +multiplying this sine. + +Up here I had a 2, but now I've +got-- when I take the subtract, + +these i's are in there, +so I divide by 2i. + +So this just tells me +that I can go either way. + +Next time, we'll see what +happens when there is damping + +and there are complex numbers +instead of pure i omegas. + +We're golden here. + +We've found the great +quantity with the right units. + +The right units of +omega are 1 over time. + +Actually the units are +radians per second, + +would be the typical +appropriate unit. + +Radians per second. + +I'll use the word +frequency for that, + +but there's another +definition of frequency, + +cycles per second. + +I just want to think about +steady motion around a circle. + +So this tells me how +many radians per second. + +And if this is 2pi-- if +omega happened to be 2pi-- + +then I would go once +around the circle. + +If omega was 2pi, then +when t reached one, + +I would be around the circle. + +Let me draw a +circle in a minute. + +So there's a 2pi here hiding +behind the word radians. + +And in many cases, +you'll want also + +a definition in +cycles per second. + +So f is omega +divided by the 2pi, + +and that's in cycles per second. + +Full revolutions per second. + +And that's hertz. + +I think I misspoke last +time in confusing these two, + +so let's get them straight here. + +There's no complicated math in +here, it's just a factor 2pi, + +but of course that +factor is important. + +So a typical frequency +in everyday life + +would be like f, 60 cycles +per second, 120pi radians + +per second. + +So I'm going around in a circle. + +Now I'm ready to have +initial conditions. + +This connects, again, +to the afternoon exam. + +We found the general solution +with some constants, like here. + +Let's keep that real form. + +And now those constants +get determined + +by the initial conditions. + +Conditions plural, because +we have an initial position, + +like I stretch it-- maybe +I stretch it and let go. + +Maybe I stretch the +spring and then I let go. + +What happens? + +By stretching it, I'm giving +it an initial displacement. + +And I'm giving it +zero initial velocity, + +because I stretched +it and just let go. + +Another possibility +would be to strike it. + +If I hit that +mass, that would be + +a different initial condition. + +What would be the +initial condition + +if it's sitting there in +equilibrium quietly minding + +its own business and I hit it? + +Then I've given it +an initial velocity, + +with initial displacement zero. + +So those would be the two +extreme possibilities. + +Pull it down, let +go, or strike it + +when it's sitting +in equilibrium. + +Anyway, we've got two +initial conditions. + +You see why-- y double +prime is showing up + +because essentially +we've got Newton's Law. + +This is Newton's Law. + +Mass times acceleration is +equal to minus ky-- that's + +the, with the minus sign, +and the all-important minus + +sign, that's the acceleration. + +That's a force, sorry. + +Mass, acceleration, this thing +with a minus sign is the force, + +and the force is pulling back. + +If y is stretching, +the force is restoring. + +Let me just go ahead +with what you know. + +The initial conditions. + +And I want to solve my double +prime plus ky equals 0. + +So I'm still talking about +the unforced with given + +y of 0 and y prime of 0. + +Just think for a moment. + +Could you do that? + +This is the most basic +second order equation. + +We know what the +solutions look like. + +Let's do this one in a +box, cosines and sines. + +We know what omega is. + +Omega had to be square +root of k over m. + +Then the equation was solved. + +All I've got left +is to get c1 and c2. + +All I have left is to +match-- choose c1 and c2 + +to match the two +initial conditions. + +So let me just do that. + +What are c2 and c2? + +At time zero, I have to match +an initial displacement. + +So at time zero, this is a +1, cosine of zero is a one, + +and that's a zero. + +So at t equals 0, I have y of 0. + +The displacement +matches c1 times cosine + +of omega t, which is +a 1, plus c2 times 0. + +I'll put it in there +plus c2 times 0. + +C1 cos 0 plus c2 sine 0. + +I've learned c1. + +And also-- what do I do next? + +I want to get c2. + +And where is c2 coming from? + +Now I would like to know +what's the coefficient + +of the-- the initial +conditions are supposed + +to determine that coefficient. + +It'll be that initial +condition that determines it. + +y prime of 0. + +The initial velocity should +match the derivative. + +OK, so what's the derivative? + +y prime. + +So the derivative of the +cosine will be a sine. + +And that will disappear +at t equals 0. + +The derivative of +this sine will be + +a cosine with a factor omega. + +So I'll have y prime of 0 +will be the c2 omega cos of 0. + +Which is what? + +That tells me c2. + +You could do all this +without my pointing the way. + +I'm solving this equation. + +I have the solution in general +form with two constants. + +Now I'm determining +those constants, + +and cosine and sine just +determine them perfectly + +because cosine is 1 and +sine is 0 at the start. + +So we've got the answer. + +The solution is y of t is +c1 is y of 0 cos omega t, + +and c2 is-- now +you'll notice, c2 + +is y prime at 0 +divided by omega. + +y prime of 0 divided +by omega sine omega t. + +There we go. + +Finished. + +Finished. + +Unforced problem solved. + +Everybody in this room +could get to that point. + +Let me make some +comments about that. + +It's a combination +of cosine and sine. + +They're both running at +the same frequency, omega. + +I'm going to give a special +name to that frequency, omega, + +this famous formula, +all-important. + +Lots of physics in that formula. + +I call that the +natural frequency, + +because the next step will be +to drive the system by a driving + +frequency, which would +be different from omega. + +So we need to-- +we've got 2 omegas. + +Actually when I first +wrote the book I thought, + +we've got to keep +these two separate. + +Everybody has to +keep them separate. + +My first attempt was to use +little omega and big omega + +for the two. + +I concluded after +looking at it for a while + +that it was better to +be more conventional. + +People had figured out +a good way to do it. + +And the good way is to call +this the natural frequency + +and put a subscript, m. + +So all the omegas that +you see on this board + +should be omega n. + +I can change them all, but +let me just change it here. + +I'll change omega n. + +So that's omega n. + +We've only got that +one omega right now, + +because we don't have +a driving term yet. + +So natural frequency +has the advantage, + +which kind of made me smile, +that the n stands for natural, + +and everybody calls it +the natural frequency. + +And n also stands +for null, and we're + +talking here about +the null solution, + +because there's no forcing. + +So I could have +subscripts on all the y's. + +Eventually I'll need +subscripts on the y + +to separate what we've done. + +This is really yn of +t, the null solution. + +Good? + +Now we could take one more step. + +This is a combination +of cosine and sine. + +And we learned +last time that that + +could be put in a polar form, +but I don't plan to do this. + +Let me just say I could do it. + +This would be some +amplitude, some gain-- + +maybe g for gain-- +no, a for amplitude + +is good-- times-- what is this +second optional form, which I'm + +just going to write here, +say that we could do it, + +remember a little about it, +but not make a big deal-- what + +is it I'm after here? + +I'm looking to write this +combination of cosine and sine, + +which is two oscillations, a +cosine curve and a sine curve, + +but with the same frequency. + +Then I can combine them +into a single cosine, + +a single cosine of omega nt. + +But now what else have +I got in this form? + +There's a phase +shift, minus phi. + +Thanks. + +So there's an a phi, two +constants, or there's y of 0, + +y prime of 0, two constants. + +Let me not write again the +formula for a or for phi, + +I don't plan to do +anything with it. + +It just could be done. + +In other words, what +we've done so far + +is just to see that the +single spring oscillates + +with the frequency omega n. + +That's really what we've done. + +A single spring oscillates +with a frequency omega n. + +Saying that makes me +think, let me look ahead + +to the linear algebra +part of the course. + +So where is linear +algebra going to come in? + +It's going to come in +for a system of springs. + +When I have another spring. + +Can I draw another +spring and another mass + +and another spring? + +Say six springs, six masses. + +Then-- and they could be +different k's, different m's, + +or not. + +Then we've got six +displacements-- + +six differential equations-- +coupled together, + +because the whole system +is coupled together. + +So what happens at that point? + +That's the point where linear +algebra, where matrices + +are coming in. + +You want to see what's +the point of matrices. + +It's not a separate +course by any means. + +It's a most necessary part, +because a single spring happens + +in reality but also +systems today are coupled. + +Big, actually, there +are many, many things. + +You have an electric +circuit with thousands + +or tens of thousands +of elements. + +You have a coupled +system with many gears, + +many oscillations going on. + +So we need matrices +at that point. + +Can I even just add one more +word about the language? + +When we had-- here +we have a frequency + +of motion for one spring. + +What are we going to have for +two springs or six springs? + +The motion will be a combination +of six different frequencies. + +And so you'll see that it's +a much more interesting, + +much more not so simple motion. + +A combination of six +pure frequencies. + +And those frequencies +are determined + +from the six eigenvalues +of the matrix. + +I'm just using that +word looking ahead. + +We will have a 6x6 matrix to +describe the coupled system. + +That matrix will +have six eigenvalues. + +It will tell us six +natural frequencies, + +and our solution will be +a combination of all six + +oscillations. + +Here, it's 1. + +Here it's 1. + +That spring is not there. + +So the problem +we've solved now is + +the fundamental, basic problem, +and I have to-- next step + +is forcing. + +I now want to add a force +that drives the motion. + +In general, it could be +any function of time. + +Calling it f of t. + +So that's what I'm +going to put in now. + +But in reality, very, +very, very often f of t + +is also a simple +harmonic motion. + +It's also a cosine. + +But at a different frequency, +at a driving frequency. + +So I'm going to-- +the next equation + +to solve is to put in cosine-- +let's stay real for now-- + +at another, driving frequency. + +At a driving frequency. + +And of course, it could +have an amplitude. + +But let me take that amplitude +as 1 to keep things simple. + +So now I'm talking +about forced motion. + +Can we solve it? + +How can we solve this equation? + +Let me take out the 0 or-- take +out the 0-- equals cosine omega + +t. + +With a different omega. + +If the two omegas were the same, +if the driving frequency is + +the same as the +natural frequency, + +the formulas have to +be slightly adjusted. + +There's still an answer, +but it's a case of resonance + +and you have to look separately. + +But let's say, no. + +Let's say omega d is +different from omega n. + +How are you going to solve this? + +I have to think myself. + +How do I solve that. + +Let's start a fresh board. + +my double prime plus +ky equals cosine + +of omega dt-- or often, +I won't put the d. + +I don't have to +put the d anymore. + +Omega will now represent +the driving frequency, + +because I've got omega +n, the natural frequency, + +as the square root of k over m. + +What am I looking for now? + +I found the null solution. + +I'm looking for a +particular solution. + +I'm trying to keep the +whole thing systematic. + +Null solutions are +now dealt with. + +Took a little more +time than just ce + +to the at for first +order equations, + +because we've now got a +two-dimensional collection + +of null solutions, +but we've got them. + +Now I'm taking a forcing term. + +So I'm looking for a +particular solution. + +I'm looking for any +solution to this equation. + +I'm looking for +a particular guy. + +What do you suggest? + +Again, it's a neat +problem because + +of that particular forcing +term, a cosine, an oscillation. + +So I'm going to look for yp is +some gain times [INAUDIBLE]. + +This is the next and, +fortunately, a highly, highly + +important case, in which +the particular solution has + +the same form as +the forcing term. + +It's just a multiple +of the forcing term. + +That's best possible. + +That's best possible, is to have +the forcing term reveal to me-- + +the forcing term immediately +reveals a particular solution. + +Once I know what I'm +looking for, what do I do? + +Substitute it in. + +So I substitute that +particular solution in here. + +And notice everything +is going to be + +a cosine, mgy double prime. + +So what do I get when I +plug this in for that guy? + +I want to-- you can do +it quickly, but let's + +stay together and do it +together, because we can + +with this case. + +What happens when I plug that in +and take its second derivative? + +I get the g. + +And then what's the +second derivative? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: We have a negative, +because two derivatives + +of the cosine bring out a minus +omega d, will come out twice. + +And I'll keep writing +omega d for a moment, + +but then I'll give up on the d. + +Cosine of omega dt. + +And then k times this, +g cosine of omega dt, + +equals the forcing term, +cosine of omega dt. + +It worked. + +This is one of that small +family of nice functions + +where the solution has the +same form as the function. + +Actually that list of what +you could call best possible + +forcing functions, where the +form of the forcing function + +tells you the form +of the solution. + +That's a small family. + +But it's fortunately +a very important one. + +Cosines, sines are +included, and we'll + +see all the other guys +that are included. + +Most forcing functions +we couldn't just + +assume that the solution +had the same form. + +It's only these nice ones. + +But cosines are nice. + +So what do I do now? + +Everything is +multiplying cosines, + +so I just look at-- +I have minus m omega + +squared g-- g is going to factor +out-- minus m omega squared + +and a k times g. + +Let me remove that +off for the moment. + +I'm canceling cosine omega, +so my right hand side is 1. + +That's it. + +We looked for a solution +with that simple format, + +and we found it. + +Now we know g, the gain. + +So the solution is-- this +is g is 1 over k minus m + +omega squared times +cosine of omega t. + +And omega is omega d. + +Omega is omega d now. + +Does that look good to you? + +This is the periodic solution +going at the driving. + +This is what the-- this g is +the gain, the driving force. + +The driving force is 1 +times cosine omega d, + +then that 1 gets +multiplied by this number. + +This is, you could say, +the amplifying factor. + +I guess frequency response +would be the right word. + +Can I bring in that +word, response, again? + +Response is a word +for a solution. + +It's what comes out. + +When the input is +this, a pure frequency, + +the output, the response, +is a pure frequency-- + +same frequency, of course-- +multiplied by that. + +That is the frequency +response factor. + +Notice we could write that +a cool way, by remembering + +that omega squared-- +that's wrong as it stands. + +What have I forgotten +in writing k + +minus m omega squared +in that denominator? + +I forgot a subscript, +which is n. + +Which is n. + +This is n. + +This is-- is that right? + +No. + +Is it? + +Or is it d? + +Maybe I didn't make a mistake. + +Is it d? + +You're seeing a kind +of critical moment. + +Which is it? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: It's d, isn't it? + +Yeah. + +It's d. + +Sorry. + +It's d. + +But when I see this and remember +what omega n squared is-- + +omega n squared is +k over m-- I can + +see that I can get an omega-- +I can use this in here + +to make it even +more interesting. + +So it'll be equals-- let me +get this box ready-- cosine + +of omega dt divided by-- now +I just want to rewrite that. + +I want to take out an m. + +I'm going to write this +as m times k over m. + +m times k over m. + +Safe to do that. + +Now I have a factor, m, +that I can bring out. + +And what is m multiplying? + +That's the neat thing. + +What is m multiplying? + +k over m is-- omega n squared. + +And this is minus +m omega d squared. + +Minus omega d squared. + +That's pretty terrific. + +The gain is this multiplier, +1 over m, times that. + +And we see that the gain +is bigger and bigger when + +the frequency is near +the natural frequency. + +And of course everybody has seen +the pictures of that bridge-- + +wherever the heck +was that bridge? + +Somewhere in the +Northwest, I think. + +You know the bridge +I'm talking about? + +AUDIENCE: [INAUDIBLE] +Tacoma, Washington. + +PROFESSOR: Yeah, I think +Tacoma, that's right. + +The Tacoma Narrows Bridge. + +Right. + +Tacoma, Washington. + +Where the natural-- +when you build a bridge, + +you've built in a +natural frequency. + +And then when traffic comes, +it's doing a driving frequency. + +And if you haven't got +those two well-separated, + +you're in trouble, +as this shows. + +Or similarly, when an +architect designs a skyscraper, + +there's going to be a +frequency of oscillation, + +a natural frequency, at +which that skyscraper swings. + +And then there's wind. + +Actually I talked yesterday +to the-- by chance, + +the math department is not a +very party-going department, + +but once a year we let it out. + +And so we had our party +at Endicott house out + +in the suburbs, and +all the usual people-- + +that's all the professors +I know-- came, of course. + +But also, there was +a really cool person. + +He's the key architect +for Building 2. + +You've noticed that +Building 2 is under wraps + +and we're moved out. + +And we move back +in January 2016. + +So we've been out a +year and a quarter + +and we have another year +and a quarter to go. + +It's going to be cool. + +And you may say, +well, who cares. + +But the key point is +Building 1 is next, + +and Building 1 is going to +have the same cool addition + +of a fourth floor. + +We're putting in a fourth floor, +which all the-- Buildings 3, 4, + +5, 6 go up to four, but +Buildings 2 and 1 stopped + +at the third floor. + +But there's a lot of space +up there under the roof. + +And they've +discovered they could + +put a fourth floor up there. + +Here was one interesting +thing, though. + +These buildings that we're +sitting in are sinking. + +You know that MIT was built +on marshy land, just the way + +the Back Bay-- which +is like the greatest + +idea in the history of Boston, +the Back Bay and the dam + +that makes the Charles +River beautiful-- + +was built by bringing +in trainloads of earth + +from Needham. + +So whole mountains and hills in +Needham have come into Boston + +and come here. + +So anyway, we're sinking. + +You may say something like +3/16 of an inch a year + +is not something to +worry about, but now it's + +been more than 100 years that +these buildings have been here. + +Anyway, not good to sink faster. + +So the weight had +to be controlled. + +So by putting in a +fourth floor, that + +put in a lot a new weight, +and faster sinking, + +probably by some formula here. + +Probably there. + +So the weight had to +get subtracted out. + +It turns out that +the ceiling, the roof + +to Building 1-- Building 2 +and no doubt to Building 1-- + +was more than a foot +thick of concrete. + +Really heavy. + +And some more asbestos +probably, which we don't want + +to think about. + +That's much reduced. + +A whole lot of weight +came out of the roof. + +I think they probably did +the calculation right, + +so we won't get +rain coming through, + +but it won't weigh as much and +the fourth floor is acceptable. + +All this was a big decision +by MIT to pay for that, + +or to raise money and pay +for the new fourth floor. + +But it's going to be fantastic. + +And it'll be fantastic +in Building 1 also. + +So all that is discussion +of that formula. + +That's the frequency response, +this factor to frequency, + +omega d, or omega, +is this factor. + +I guess I should say +something about resonance. + +What happens when that +formula breaks down? + +When the driving force +equals the natural frequency, + +then we're dividing by 0, +and something is different. + +The formula isn't right anymore. + +What enters in the formula-- let +me just tell you what enters, + +and then we'll see it +in a simple example. + +When I have this repeated +thing, two things are equal, + +what tends to +happen is a factor, + +an extra factor, t, appears. + +So an extra factor, t, will +appear in the case omega n + +equal omega d. + +The solution, y, +will be some factor, + +I'll still call it g-- no, +I don't want to call it g, + +let me call it a. + +There'll be a factor, t, +times cosine of omega t. + +So in this case, there's +really only one frequency. + +We're driving it. + +So the oscillation grows. + +As you know, when you +push a child on a swing, + +the whole point of +pushing that child + +is to push at the +natural frequency. + +You wait for this swing +to swing back naturally + +and you drive it again +with that-- at that-- + +maintain that frequency. + +And of course you +see the amplitude-- + +the child swing +higher and higher. + +Presumably you stop pushing +before disaster for that child. + +But that's a case of resonance. + +And it's what happened in +the Tacoma Narrows Bridge, + +and there was nothing +to-- nobody stopped, + +traffic just kept coming. + +The movie is amazing, +because there's + +one car that shows up after +it's already swinging wildly, + +some crazy person +still driving across. + +And you might think, OK, +that's ancient history. + +But you know the +bridge in London, + +the pedestrian bridge, the +Millennium Bridge-- it's just + +a walking bridge +across the Thames-- + +a big feature of modern London, +and it had the same problem. + +It was swaying. + +People could not walk across. + +They couldn't keep +their balance. + +So they had change it. + +So it's not trivial +to anticipate. + +So now we've solved it-- we've +solved the the null equation + +with no force, and +we've solved the driving + +force equal to a cosine. + +And of course, we +could do a sine. + +What other driving +force should we do? + +I think we should +do a delta function. + +I think we have to understand +the fundamental solution is + +the case when, if +we can solve it-- + +there's always this general +rule, if we can solve + +with a delta function, +that will give us + +a formula for every +driving force, + +because every function is some +combination of delta functions. + +So if we could do +it with a delta-- + +really the great +right hand sides + +are-- well, cosines +and sines I'll + +include as great +right hand sides. + +Those are the +exponentials in disguise. + +So the great right +hand sides are + +really exponentials at +different frequencies and delta + +functions. + +Delta of impulses. + +So now I want to find +the impulse response. + +That's the next-- +that's really a job. + +At this point, in these +last 20 minutes when + +I solve my double prime plus ky +equal a delta function-- well, + +what I was going to say was +I'm now taking you to something + +that you won't see on +the exam this afternoon. + +But maybe you will. + +Delta function, right hand side. + +I haven't seen it yet. + +Or I haven't looked recently. + +You won't see second +derivatives, I guess. + +So what is it? + +So now this is of the +form with an f of t, + +a very special f of t. + +And that very special f of +t makes that extremely easy + +to solve. + +That's really my +point here, is it + +it's going to be a +cinch to solve that, + +and we practically +have done it already + +to solve that with +a delta function. + +And the reason is +sort of physical. + +We have here our spring. + +And what am I doing +with that force? + +I'm hitting the mass. + +I'm striking the mass. + +Let me say, and I'll write +it on the board, the point I + +want to make about this. + +That point is that this +equation with a delta function + +force starting from 0-- say, +y of 0 equal y prime of 0 + +equals 0, let's give +it starting from rest-- + +it starts from +rest by hitting it. + +And that hit, that impulse, +is in no time at all. + +It's not stretched out. + +It's hit over one second. + +So this has the same solution. + +This is the beauty. + +This is why we can +solve it so easily. + +Same solution as-- let me write +it and see what you think-- + +as my double prime +plus ky equal 0. + +We know how to solve those. + +With-- it's still, when +I hit it-- when I hit it, + +what happens in +that split second? + +In that split second, it +doesn't have time to move. + +It doesn't move. + +It still has y of 0 equals 0. + +But in that split second, +we've given it a velocity. + +We've given it a velocity. + +And that velocity +will be y prime. + +The initial velocity is 1-- +because here I had a 1-- + +over an m. + +We have to have the units right. + +So here's a point, and +we will stay with it. + +We'll come back to +this point next time. + +Maybe the first thing +for you to take in + +is the fact that it's +such a nice thing. + +We have this equation with +this mysterious delta function, + +and I'm saying that +the solution is + +the same as this +equation with no force, + +but starting from a mass. + +I'm tempted to take an +example to make this point. + +Let me take an example where the +whole thing is a lot simpler. + +y double prime equal delta of t. + +I've taken the spring away, so +the k is gone, the mass is 1. + +What's the solution to y +double prime equal delta of t? + +If we concentrate on this +example, we're good for today. + +So my point is the +same solution as-- now, + +what's the other problem? + +I'm just repeating here, but +making it simple by taking k + +equals 0 and m equal 1. + +So the same solution as y double +prime equals 0, with y of 0 + +equal what, and y +prime of 0 equal what. + +I just wanted to repeat +here what I've said there, + +and then we'll solve it and +we'll see that it's all true. + +If I look for a solution to +y double prime equal delta + +starting from 0-- this +was starting from 0-- + +if I say that's the same +as this, what should y of 0 + +be here? + +AUDIENCE: Zero. + +PROFESSOR: Zero, right. + +It hasn't had time to move. + +It hasn't had time to move. + +But in that instant, +what happened to y prime? + +It jumped to 1. + +That's right. + +That's right. + +Exactly. + +Now just solve that +equation for me. + +Solve this example for me. + +Suppose y double prime-- yeah. + +Here we go. + +What's the solution if +y double prime is 0? + +What are the solutions to +y double prime equals 0? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Constant and linear. + +a plus bt, right, have +second derivative 0. + +Now what's the solution that +starts from 0 that kills the a + +and has slope 1? + +What's the answer +to that question? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: t. + +t. + +The solution to this +equation is a ramp. + +It's zero everything in this +course, is zero up until time + +0. + +At time 0, in this example, +all the action happens. + +Everything happens. + +And what happens is it +gets a velocity of 1, + +and the solution +is y equal to t. + +y is 0 here, of course. + +At that point, that's the +key point, t equals 0, + +right there-- it gets a slope. + +We don't have a step function. + +There's no jump in y. + +The jump is in y prime, the +y prime the velocity jumped + +from 0 to 1. + +That's exactly-- I think when +I introduced delta functions + +and drew a picture. + +What is the derivative, the +first derivative, y prime, + +for that guy? + +Let's just review, because this +is what we've seen already. + +The first derivative is-- + +AUDIENCE: [INAUDIBLE] step. + +PROFESSOR: A step. + +And the second +derivative is delta. + +The second derivative of this is +the first derivative of a step. + +The derivative of a step is 0 +everywhere except at the step, + +at the jump when it jumps to 1. + +So that's the solution +in this example. + +And now to end the lecture, +let's solve it in this example. + +Again, let me just say-- why +do I like this forcing term? + +Mathematically, I +like it because, if I + +can solve that guy-- +as we're doing, + +we are solving it-- if +I can solve that one, + +I can solve all forces. + +Over here, I could solve when +I had a very happy f of t, + +a perfect f of t, where +I could guess the answer + +and push through. + +Now with a delta, I can +build everything out + +of delta functions. + +That's why I like +it mathematically. + +Why do I like it physically? + +Because it's a very physical +thing to have an impulse. + +That happens in real +time, in real things. + +And by the way, let's just, +before I write down any more + +formula, what +would-- I would like + +to be able to solve it +for a step function. + +[? Heavy thud. ?] I would like +to be able to do that one. + +I'm going to have +to erase something, + +or I'll write it right +above just for the moment. + +I would also like to +solve my double prime plus + +ky equal a step function. + +So I would call the solution, +y, the step response. + +And what would be a +step function start? + +A step function start would +be like turning a switch. + +Suddenly things happen. + +That's forcing by a step, so I'm +looking for the step response. + +And how do you think +these two are related? + +I look at the relation +at the right hand sides. + +What's the relation of +this step to the delta? + +Yeah? + +AUDIENCE: One's a derivative. + +PROFESSOR: One's a +derivative of the other. + +And we've got linear equations. + +So the right hand sides. + +The step response, y step, +and the delta response, + +y delta-- I'll use a +different letter for this + +because it's so important. + +One is the derivative +of the other. + +The great thing about +linear equations + +is we have linear equations, +differentiation, integration. + +Those are linear operations. + +The step function is just +like a steady-- anyway. + +I was going to-- I won't-- +is the integral of the delta. + +Step function is the +integral of the delta, + +so the step response is the +integral of the delta response. + +I guess to finish the +lecture, why don't we + +solve this problem, +which looks tricky + +because it's got a delta. + +Instead, we'll +solve this problem, + +which doesn't look +tricky at all. + +It's exactly what we +started the lecture with. + +Zero forcing and some +initial conditions. + +So let me just +finally make space + +for the big deal +from today's lecture, + +which would be the fundamental +solution with a force + +by a delta. + +I'm just going to write +down the answer when + +you tell me what it is. + +What's the answer to that? + +What's the solution +to this second order + +constant coefficient +unforced equation + +with those initial conditions? + +We probably had it here. + +I may just have erased it. + +But now let's get it. + +So y is y delta. + +This is the impulse response. + +y of t-- and I'll give +it later another name. + +So here's a perfect +review question. + +What's the solution +to this problem? + +Everybody remembers-- what +are the solutions, what's + +the general form for the +solution to the equation? + +I'm reviewing today's lecture. + +The solution to that +equation looks like what? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: It's a cosine +and a sine, right. + +And then how much of a cosine do +we have and how much of a sine + +do we have? + +The initial condition will +tell me how much of a cosine + +we have. + +And what's the answer? + +None? + +No cosine. + +This condition, this +initial velocity, + +will tell me how much +of a sine we have, + +because the sines are the things +that have initial velocities. + +So it would be a sine +of-- the sine of what? + +Square root of k over m, right? + +omega nt, right? + +And what's the number? + +What's the number so +this has the right-- let + +me write again what I want. + +I want y prime at +0 to be 1 over m. + +What's the number +that I put in there? + +I've got something, its +derivative, at zero. + +This is some number-- I'll call +it little a for the moment, + +but I want to find +out what it is. + +Are we right? + +Yeah? + +I think we're right. + +Yeah. + +The derivative is at zero, so +I just plug that into here, + +take the derivative at zero-- +of course that makes it + +a cosine, which will be 1-- but +it also brings out that factor. + +So a times-- well, that +factor will be 1 over m, + +and that tells me +what a has to be. + +Well, this is omega. + +So a is-- this is +omega a equal m. + +This is 1 over m omega. + +And that's omega. + +Sorry I'm erasing +stuff which I-- this is + +the formula I'm after. + +Sine omega t over omega. + +I think we're good. + +Are we? + +Yeah? + +Yeah. + +I'll come back to +this in-- Wednesday + +is my day to move +to damping terms. + +I've intentionally stayed +with undamped equations + +here, because you're thinking +about that level of equation. + +Damping is going to +bring in new stuff, + +and that should +wait till Wednesday. + +Shall I recap today? + +I'll just recap today, +and then we're done. + +Today started with +the unforced equation. + +We solved it by assuming-- +by not thinking ahead, + +just assume I have +an exponential, + +because the beauty +of exponentials + +is, when I plug it in, +the exponential cancels. + +And that told me that +s was pure imaginary. + +It told me that it had this +form, e to the i omega t. + +And there were two s's. + +Two possible s's, +plus and minus. + +I get to make a little comment +about this example here. + +What was omega? + +What's the natural +frequency in this problem? + +What's the natural +frequency here? + +I guess this is a case where-- +what's the natural frequency? + +I guess this is a case where m +is 1 and k is 0, is that right? + +This does fit into that pattern, +but it's a little special. + +This is a case where +m is 1 and k is 0. + +So what's the natural +frequency in this? + +AUDIENCE: Zero. + +PROFESSOR: Zero. + +Zero. + +This is a crazy +case of resonance. + +It's a case in which the natural +frequency and the driving + +frequency, say in this-- +I'll have to do it here-- + +this simplest of all equations +is, in a way, special. + +It's a case when the +natural frequency is zero + +and the driving frequency +is zero and they're equal. + +And what happens with resonance? + +What's the new +formula, the new term + +that comes in with resonance? + +It's t. + +You saw it happen +for this example, + +and we didn't have to +use the word resonance. + +We knew that we had a ramp. + +We just used the word +ramp, not resonance. + +But this is a case of resonance. + +When omega n is zero +and omega d is zero. + +And the factor t up here. + +Anyway. + +Just that small comment there. + +And now, just going +back to the recap. + +The recap was, we +tried exponentials. + +We learned that they +were pure oscillations. + +We realized that we could do +cosines and sines instead, + +and we did. + +And we took off. + +We got the formula. + +Then of course the-- so this +is section 2.1 of the book. + +And it goes through all +those steps carefully. + +Section 2.2 of the book tells +us about complex numbers, + +and section 2.3 +brings damping in. + +So that's what's +coming next time. + +So the recap again. + +We found the null solution, we +found a particular solution-- + +oh there's just one +comment I want to make, + +and then I'm done. + +Where was our +particular solution? + +Yeah. + +This was our +particular solution. + +Here's my comment. + +Here's my comment. + +Suppose I want to solve +this basic equation starting + +from a given y of 0 +and a y prime of 0. + +I'm going to do it in +two parts, I think. + +I've got the null +solution, and I've + +got this particular solution. + +Now here's my point. + +If I want to get y of +0-- how shall I say this. + +You can't just put together-- +it's an easy mistake + +to make-- solve +the null equation + +with the initial +conditions and then + +add in the particular solution. + +You'd think, I just +followed all the rules. + +But this particular solution +that you added in has a-- at t + +equals 0, it's not zero. + +So you have to change. + +So the correct thing, +the correct yp plus yn-- + +let me make that point. + +Just a warning. + +So in words the +warning is, remember + +that the particular solution +has some initial condition-- + +in that case, g-- and +then that is going + +to affect the right +null solution. + +So again, y is y null +plus y particular-- plus y + +of particular-- so it's some c1 +cos omega nt plus some c2 sine + +omega nt plus this particular +guy, g, cosine of omega dt. + +All correct. + +All correct. + +But now, put in the +initial conditions. + +y of 0 is given. + +And what do I get on +the right hand side + +when I put in t equals 0? + +I get c1 here. + +What do I get when I +put t equals 0 in there? + +Nothing. + +What do I get when I +put t equals 0 in here? + +g. + +So it's not c1 equal +y of 0 anymore. + +That's the easy mistake +that I'm correcting. + +When you put in this +particular solution, + +it has an initial value. + +That initial value is +going to come in here. + +So c1, then, the correct +c1 is y of 0 minus g. + +End of story. + +Just don't be too quick to just +add the two pieces and think + +you can do them +completely separately, + +because you're +putting them together. + +And then you have +to put them together + +in the initial condition. \ No newline at end of file diff --git a/yWIQCewgfwY.txt b/yWIQCewgfwY.txt new file mode 100644 index 0000000000000000000000000000000000000000..96ea53bc6bb9c92649882730ca77fdc08abde01d --- /dev/null +++ b/yWIQCewgfwY.txt @@ -0,0 +1,1283 @@ +align:start position:0% + +we've mentioned the P equals and P + + align:start position:0% +we've mentioned the P equals and P + + + align:start position:0% +we've mentioned the P equals and P +question a number of times now as as the + + align:start position:0% +question a number of times now as as the + + + align:start position:0% +question a number of times now as as the +most important question in theoretical + + align:start position:0% +most important question in theoretical + + + align:start position:0% +most important question in theoretical +computer science and we've said that one + + align:start position:0% +computer science and we've said that one + + + align:start position:0% +computer science and we've said that one +way to formulate it is exactly to ask + + align:start position:0% +way to formulate it is exactly to ask + + + align:start position:0% +way to formulate it is exactly to ask +whether there's an efficient that is + + align:start position:0% +whether there's an efficient that is + + + align:start position:0% +whether there's an efficient that is +polynomial time procedure to test + + align:start position:0% +polynomial time procedure to test + + + align:start position:0% +polynomial time procedure to test +whether or not a formula in + + align:start position:0% +whether or not a formula in + + + align:start position:0% +whether or not a formula in +propositional logic is satisfiable now + + align:start position:0% +propositional logic is satisfiable now + + + align:start position:0% +propositional logic is satisfiable now +why is that such an important problem I + + align:start position:0% +why is that such an important problem I + + + align:start position:0% +why is that such an important problem I +mean you know we're not just logicians + + align:start position:0% +mean you know we're not just logicians + + + align:start position:0% +mean you know we're not just logicians +and we want to know whether or not some + + align:start position:0% +and we want to know whether or not some + + + align:start position:0% +and we want to know whether or not some +formulas satisfiable how did it take on + + align:start position:0% +formulas satisfiable how did it take on + + + align:start position:0% +formulas satisfiable how did it take on +this enormous importance and apply to so + + align:start position:0% +this enormous importance and apply to so + + + align:start position:0% +this enormous importance and apply to so +many fields and illustrating how you + + align:start position:0% +many fields and illustrating how you + + + align:start position:0% +many fields and illustrating how you +could use a satisfiability tester to + + align:start position:0% +could use a satisfiability tester to + + + align:start position:0% +could use a satisfiability tester to +factor efficiently is a good hint about + + align:start position:0% +factor efficiently is a good hint about + + + align:start position:0% +factor efficiently is a good hint about +why it is that all sorts of things + + align:start position:0% +why it is that all sorts of things + + + align:start position:0% +why it is that all sorts of things +reduced to Sat and why it in fact is + + align:start position:0% +reduced to Sat and why it in fact is + + + align:start position:0% +reduced to Sat and why it in fact is +such a centrally important problem so + + align:start position:0% +such a centrally important problem so + + + align:start position:0% +such a centrally important problem so +let's suppose that we have a + + align:start position:0% +let's suppose that we have a + + + align:start position:0% +let's suppose that we have a +satisfiability tester and use it to find + + align:start position:0% +satisfiability tester and use it to find + + + align:start position:0% +satisfiability tester and use it to find +the factor a number n now the + + align:start position:0% +the factor a number n now the + + + align:start position:0% +the factor a number n now the +observation begins with how you use a + + align:start position:0% +observation begins with how you use a + + + align:start position:0% +observation begins with how you use a +Sat solver is that you can begin by + + align:start position:0% +Sat solver is that you can begin by + + + align:start position:0% +Sat solver is that you can begin by +writing a or observing that it's easy + + align:start position:0% +writing a or observing that it's easy + + + align:start position:0% +writing a or observing that it's easy +enough to design a digital circuit that + + align:start position:0% +enough to design a digital circuit that + + + align:start position:0% +enough to design a digital circuit that +multiplies that does arithmetic + + align:start position:0% +multiplies that does arithmetic + + + align:start position:0% +multiplies that does arithmetic +multiplications in other words it's got + + align:start position:0% +multiplications in other words it's got + + + align:start position:0% +multiplications in other words it's got +some number of bits reserved for an + + align:start position:0% +some number of bits reserved for an + + + align:start position:0% +some number of bits reserved for an +input X say K bits and another K bits + + align:start position:0% +input X say K bits and another K bits + + + align:start position:0% +input X say K bits and another K bits +for an input Y and it's got two K output + + align:start position:0% +for an input Y and it's got two K output + + + align:start position:0% +for an input Y and it's got two K output +lines that produce the digits of x times + + align:start position:0% +lines that produce the digits of x times + + + align:start position:0% +lines that produce the digits of x times +y you might need one extra digit but + + align:start position:0% +y you might need one extra digit but + + + align:start position:0% +y you might need one extra digit but +never mind that + + align:start position:0% +never mind that + + + align:start position:0% +never mind that +okay so this is a multiplier circuit + + align:start position:0% +okay so this is a multiplier circuit + + + align:start position:0% +okay so this is a multiplier circuit +takes an X at a bit X in and a what K + + align:start position:0% +takes an X at a bit X in and a what K + + + align:start position:0% +takes an X at a bit X in and a what K +bit Y in and it spits out the product + + align:start position:0% +bit Y in and it spits out the product + + + align:start position:0% +bit Y in and it spits out the product +which is another 2k bit number and this + + align:start position:0% +which is another 2k bit number and this + + + align:start position:0% +which is another 2k bit number and this +is not a terribly big circuit the naive + + align:start position:0% +is not a terribly big circuit the naive + + + align:start position:0% +is not a terribly big circuit the naive +way to design it would use a number of + + align:start position:0% +way to design it would use a number of + + + align:start position:0% +way to design it would use a number of +gates that was about and a number of + + align:start position:0% +gates that was about and a number of + + + align:start position:0% +gates that was about and a number of +wires that was about quadratic in the + + align:start position:0% +wires that was about quadratic in the + + + align:start position:0% +wires that was about quadratic in the +number K the it's easy enough to design + + align:start position:0% +number K the it's easy enough to design + + + align:start position:0% +number K the it's easy enough to design +one of these things where the size is + + align:start position:0% +one of these things where the size is + + + align:start position:0% +one of these things where the size is +literally bounded by five times K + + align:start position:0% +literally bounded by five times K + + + align:start position:0% +literally bounded by five times K +squared maybe plus a constant and so + + align:start position:0% +squared maybe plus a constant and so + + + align:start position:0% +squared maybe plus a constant and so +there's definitely a small polynomial we + + align:start position:0% +there's definitely a small polynomial we + + + align:start position:0% +there's definitely a small polynomial we +can given the number of bits that I'm + + align:start position:0% +can given the number of bits that I'm + + + align:start position:0% +can given the number of bits that I'm +working with it's easy enough to build + + align:start position:0% +working with it's easy enough to build + + + align:start position:0% +working with it's easy enough to build +this multiplier circuit + + align:start position:0% +this multiplier circuit + + + align:start position:0% +this multiplier circuit +now suppose that I have a way to test + + align:start position:0% +now suppose that I have a way to test + + + align:start position:0% +now suppose that I have a way to test +satisfiability of circuits how am I + + align:start position:0% +satisfiability of circuits how am I + + + align:start position:0% +satisfiability of circuits how am I +gonna use this multiplier circuit to + + align:start position:0% +gonna use this multiplier circuit to + + + align:start position:0% +gonna use this multiplier circuit to +factor well the first thing I'm going to + + align:start position:0% +factor well the first thing I'm going to + + + align:start position:0% +factor well the first thing I'm going to +do is let's suppose the number that I'm + + align:start position:0% +do is let's suppose the number that I'm + + + align:start position:0% +do is let's suppose the number that I'm +factoring scroll is N and it's the + + align:start position:0% +factoring scroll is N and it's the + + + align:start position:0% +factoring scroll is N and it's the +product of two primes P and Q those are + + align:start position:0% +product of two primes P and Q those are + + + align:start position:0% +product of two primes P and Q those are +the kinds of ends that we've been using + + align:start position:0% +the kinds of ends that we've been using + + + align:start position:0% +the kinds of ends that we've been using +in RSA and let me also observe that it's + + align:start position:0% +in RSA and let me also observe that it's + + + align:start position:0% +in RSA and let me also observe that it's +very easy to design an end tester that + + align:start position:0% +very easy to design an end tester that + + + align:start position:0% +very easy to design an end tester that +is a little digital circuit that has 2k + + align:start position:0% +is a little digital circuit that has 2k + + + align:start position:0% +is a little digital circuit that has 2k +o input lines and produces a 1 on its 1 + + align:start position:0% +o input lines and produces a 1 on its 1 + + + align:start position:0% +o input lines and produces a 1 on its 1 +output line precisely when the input is + + align:start position:0% +output line precisely when the input is + + + align:start position:0% +output line precisely when the input is +the binary representation of n so let's + + align:start position:0% +the binary representation of n so let's + + + align:start position:0% +the binary representation of n so let's +attach this equality tester that does + + align:start position:0% +attach this equality tester that does + + + align:start position:0% +attach this equality tester that does +nothing but ask whether it's being fed + + align:start position:0% +nothing but ask whether it's being fed + + + align:start position:0% +nothing but ask whether it's being fed +the digits of n as input and it produces + + align:start position:0% +the digits of n as input and it produces + + + align:start position:0% +the digits of n as input and it produces +an output yes for 1 for N and 0 if the + + align:start position:0% +an output yes for 1 for N and 0 if the + + + align:start position:0% +an output yes for 1 for N and 0 if the +input pattern is an the digital + + align:start position:0% +input pattern is an the digital + + + align:start position:0% +input pattern is an the digital +representation a binary representation + + align:start position:0% +representation a binary representation + + + align:start position:0% +representation a binary representation +of anything other than and that's + + align:start position:0% +of anything other than and that's + + + align:start position:0% +of anything other than and that's +another trivial circuit to build so we + + align:start position:0% +another trivial circuit to build so we + + + align:start position:0% +another trivial circuit to build so we +put those two together and now watch + + align:start position:0% +put those two together and now watch + + + align:start position:0% +put those two together and now watch +what happens um I'm gonna take the + + align:start position:0% +what happens um I'm gonna take the + + + align:start position:0% +what happens um I'm gonna take the +circuit and set the first of the input + + align:start position:0% +circuit and set the first of the input + + + align:start position:0% +circuit and set the first of the input +bits to 0 and then I'm gonna ask the Sat + + align:start position:0% +bits to 0 and then I'm gonna ask the Sat + + + align:start position:0% +bits to 0 and then I'm gonna ask the Sat +solver the following question is there a + + align:start position:0% +solver the following question is there a + + + align:start position:0% +solver the following question is there a +way to set the remaining input bits + + align:start position:0% +way to set the remaining input bits + + + align:start position:0% +way to set the remaining input bits +other than 0 so I've set the first one + + align:start position:0% +other than 0 so I've set the first one + + + align:start position:0% +other than 0 so I've set the first one +to 0 what about these other bits I mean + + align:start position:0% +to 0 what about these other bits I mean + + + align:start position:0% +to 0 what about these other bits I mean +the Sat solver can tell me whether or + + align:start position:0% +the Sat solver can tell me whether or + + + align:start position:0% +the Sat solver can tell me whether or +not it's possible to get a 1 out of this + + align:start position:0% +not it's possible to get a 1 out of this + + + align:start position:0% +not it's possible to get a 1 out of this +circuit with the 0 there fixed so let's + + align:start position:0% +circuit with the 0 there fixed so let's + + + align:start position:0% +circuit with the 0 there fixed so let's +ask the Sat solver what happens and the + + align:start position:0% +ask the Sat solver what happens and the + + + align:start position:0% +ask the Sat solver what happens and the +Sat solver says hey yes there is a way + + align:start position:0% +Sat solver says hey yes there is a way + + + align:start position:0% +Sat solver says hey yes there is a way +to fill in the remaining digits and get + + align:start position:0% +to fill in the remaining digits and get + + + align:start position:0% +to fill in the remaining digits and get +an output one well what does that tell + + align:start position:0% +an output one well what does that tell + + + align:start position:0% +an output one well what does that tell +me what tells me that there there is a + + align:start position:0% +me what tells me that there there is a + + + align:start position:0% +me what tells me that there there is a +factor that starts with zero so let's + + align:start position:0% +factor that starts with zero so let's + + + align:start position:0% +factor that starts with zero so let's +fix the zero based on the fact that um + + align:start position:0% +fix the zero based on the fact that um + + + align:start position:0% +fix the zero based on the fact that um +it's possible for me to fill in the + + align:start position:0% +it's possible for me to fill in the + + + align:start position:0% +it's possible for me to fill in the +remaining digits with the bits of + + align:start position:0% +remaining digits with the bits of + + + align:start position:0% +remaining digits with the bits of +factors x and y that equal n okay let's + + align:start position:0% +factors x and y that equal n okay let's + + + align:start position:0% +factors x and y that equal n okay let's +try to set the second input bit to zero + + align:start position:0% +try to set the second input bit to zero + + + align:start position:0% +try to set the second input bit to zero +and see what happens well well as the + + align:start position:0% +and see what happens well well as the + + + align:start position:0% +and see what happens well well as the +sat tester is it possible now to fill in + + align:start position:0% +sat tester is it possible now to fill in + + + align:start position:0% +sat tester is it possible now to fill in +the remaining digits to get the two + + align:start position:0% +the remaining digits to get the two + + + align:start position:0% +the remaining digits to get the two +numbers x and y that multiply and + + align:start position:0% +numbers x and y that multiply and + + + align:start position:0% +numbers x and y that multiply and +produce + + align:start position:0% +produce + + + align:start position:0% +produce +and therefore output one and a set set + + align:start position:0% +and therefore output one and a set set + + + align:start position:0% +and therefore output one and a set set +the set tester says no this is an + + align:start position:0% +the set tester says no this is an + + + align:start position:0% +the set tester says no this is an +unsatisfiable circuit you can't get a 1 + + align:start position:0% +unsatisfiable circuit you can't get a 1 + + + align:start position:0% +unsatisfiable circuit you can't get a 1 +out of it anymore that tells me that I'm + + align:start position:0% +out of it anymore that tells me that I'm + + + align:start position:0% +out of it anymore that tells me that I'm +have to set the second bit to 1 in order + + align:start position:0% +have to set the second bit to 1 in order + + + align:start position:0% +have to set the second bit to 1 in order +to have a factor that of n where the x + + align:start position:0% +to have a factor that of n where the x + + + align:start position:0% +to have a factor that of n where the x +and y will multiply together to be in + + align:start position:0% +and y will multiply together to be in + + + align:start position:0% +and y will multiply together to be in +all right fine go to the third bit ask + + align:start position:0% +all right fine go to the third bit ask + + + align:start position:0% +all right fine go to the third bit ask +whether or not zero works the sat set + + align:start position:0% +whether or not zero works the sat set + + + align:start position:0% +whether or not zero works the sat set +fester says let's say yes so then I can + + align:start position:0% +fester says let's say yes so then I can + + + align:start position:0% +fester says let's say yes so then I can +fix here oh I now know the first three + + align:start position:0% +fix here oh I now know the first three + + + align:start position:0% +fix here oh I now know the first three +bits of X and of course I go on and in + + align:start position:0% +bits of X and of course I go on and in + + + align:start position:0% +bits of X and of course I go on and in +two case at tests I know exactly what P + + align:start position:0% +two case at tests I know exactly what P + + + align:start position:0% +two case at tests I know exactly what P +and Q are and I have in fact found the + + align:start position:0% +and Q are and I have in fact found the + + + align:start position:0% +and Q are and I have in fact found the +factors P and Q so that's wraps that one + + align:start position:0% +factors P and Q so that's wraps that one + + + align:start position:0% +factors P and Q so that's wraps that one +up that's how you use a Sat tester you + + align:start position:0% +up that's how you use a Sat tester you + + + align:start position:0% +up that's how you use a Sat tester you +just do this at tests to K times and + + align:start position:0% +just do this at tests to K times and + + + align:start position:0% +just do this at tests to K times and +you've factored this to K bit number um + + align:start position:0% +you've factored this to K bit number um + + + align:start position:0% +you've factored this to K bit number um +and of course if the Sat test is + + align:start position:0% +and of course if the Sat test is + + + align:start position:0% +and of course if the Sat test is +polynomial and K then doing it to K + + align:start position:0% +polynomial and K then doing it to K + + + align:start position:0% +polynomial and K then doing it to K +times just is also polynomial and K with + + align:start position:0% +times just is also polynomial and K with + + + align:start position:0% +times just is also polynomial and K with +one degree higher higher + + align:start position:0% +one degree higher higher + + + align:start position:0% +one degree higher higher +okay now the this has five bility + + align:start position:0% +okay now the this has five bility + + + align:start position:0% +okay now the this has five bility +problem as we formulated was a problem + + align:start position:0% +problem as we formulated was a problem + + + align:start position:0% +problem as we formulated was a problem +about formulas that as you wrote out a + + align:start position:0% +about formulas that as you wrote out a + + + align:start position:0% +about formulas that as you wrote out a +propositional formula and asked whether + + align:start position:0% +propositional formula and asked whether + + + align:start position:0% +propositional formula and asked whether +or not it was satisfiable and i'm + + align:start position:0% +or not it was satisfiable and i'm + + + align:start position:0% +or not it was satisfiable and i'm +instead asking about satisfiability of + + align:start position:0% +instead asking about satisfiability of + + + align:start position:0% +instead asking about satisfiability of +binary circuits but in fact as we did in + + align:start position:0% +binary circuits but in fact as we did in + + + align:start position:0% +binary circuits but in fact as we did in +some early exercises you can describe a + + align:start position:0% +some early exercises you can describe a + + + align:start position:0% +some early exercises you can describe a +binary circuit by assigning a fresh + + align:start position:0% +binary circuit by assigning a fresh + + + align:start position:0% +binary circuit by assigning a fresh +variable to every wire in the circuit + + align:start position:0% +variable to every wire in the circuit + + + align:start position:0% +variable to every wire in the circuit +and then writing a little formula around + + align:start position:0% +and then writing a little formula around + + + align:start position:0% +and then writing a little formula around +each gate which explains how the input + + align:start position:0% +each gate which explains how the input + + + align:start position:0% +each gate which explains how the input +wires to that gate are related to the + + align:start position:0% +wires to that gate are related to the + + + align:start position:0% +wires to that gate are related to the +output wire of that gate and that little + + align:start position:0% +output wire of that gate and that little + + + align:start position:0% +output wire of that gate and that little +formula explains that wiring of that + + align:start position:0% +formula explains that wiring of that + + + align:start position:0% +formula explains that wiring of that +gate and you take the end of all those + + align:start position:0% +gate and you take the end of all those + + + align:start position:0% +gate and you take the end of all those +formulas and you have a formula that is + + align:start position:0% +formulas and you have a formula that is + + + align:start position:0% +formulas and you have a formula that is +describing the structure of the of the + + align:start position:0% +describing the structure of the of the + + + align:start position:0% +describing the structure of the of the +circuitry and in fact the formula is + + align:start position:0% +circuitry and in fact the formula is + + + align:start position:0% +circuitry and in fact the formula is +satisfiable if and only if the circuit + + align:start position:0% +satisfiable if and only if the circuit + + + align:start position:0% +satisfiable if and only if the circuit +can produce an output one so we really + + align:start position:0% +can produce an output one so we really + + + align:start position:0% +can produce an output one so we really +have by assuming that I could test + + align:start position:0% +have by assuming that I could test + + + align:start position:0% +have by assuming that I could test +satisfiability of formulas I can + + align:start position:0% +satisfiability of formulas I can + + + align:start position:0% +satisfiability of formulas I can +therefore test satisfiability of + + align:start position:0% +therefore test satisfiability of + + + align:start position:0% +therefore test satisfiability of +circuits and therefore I can factor so + + align:start position:0% +circuits and therefore I can factor so + + + align:start position:0% +circuits and therefore I can factor so +this is if that's a simple trick to find + + align:start position:0% +this is if that's a simple trick to find + + + align:start position:0% +this is if that's a simple trick to find +a propositional formula that's equally + + align:start position:0% +a propositional formula that's equally + + + align:start position:0% +a propositional formula that's equally +satisfying + + align:start position:0% +satisfying + + + align:start position:0% +satisfying +both to the circuit if the circuit + + align:start position:0% +both to the circuit if the circuit + + + align:start position:0% +both to the circuit if the circuit +produces output one if and only if this + + align:start position:0% +produces output one if and only if this + + + align:start position:0% +produces output one if and only if this +formula of about the same size as the + + align:start position:0% +formula of about the same size as the + + + align:start position:0% +formula of about the same size as the +circuit in satisfiable and that's the + + align:start position:0% +circuit in satisfiable and that's the + + + align:start position:0% +circuit in satisfiable and that's the +last piece that I needed in order to + + align:start position:0% +last piece that I needed in order to + + + align:start position:0% +last piece that I needed in order to +completely reduce satisfiability the + + align:start position:0% +completely reduce satisfiability the + + + align:start position:0% +completely reduce satisfiability the +factoring rather to the satisfiability + + align:start position:0% +factoring rather to the satisfiability + + + align:start position:0% +factoring rather to the satisfiability +problem and you can see that this is + + align:start position:0% +problem and you can see that this is + + + align:start position:0% +problem and you can see that this is +actually a general method that will + + align:start position:0% +actually a general method that will + + + align:start position:0% +actually a general method that will +enable you to reduce most any kind of + + align:start position:0% +enable you to reduce most any kind of + + + align:start position:0% +enable you to reduce most any kind of +one-way function to a few sad tests \ No newline at end of file diff --git a/yiQTHtvszJ8.txt b/yiQTHtvszJ8.txt new file mode 100644 index 0000000000000000000000000000000000000000..43b42f24892e7b95962ddd0e7e7a087099f48f9f --- /dev/null +++ b/yiQTHtvszJ8.txt @@ -0,0 +1,12651 @@ +align:start position:0% + +we're going to kind of slightly rewind + + align:start position:0% +we're going to kind of slightly rewind + + + align:start position:0% +we're going to kind of slightly rewind +since the end of yesterday was a little + + align:start position:0% +since the end of yesterday was a little + + + align:start position:0% +since the end of yesterday was a little +quick on the carel and assume we are + + align:start position:0% +quick on the carel and assume we are + + + align:start position:0% +quick on the carel and assume we are +finishing with carel with histograms and + + align:start position:0% +finishing with carel with histograms and + + + align:start position:0% +finishing with carel with histograms and +now I'm going + + align:start position:0% +now I'm going + + + align:start position:0% +now I'm going +to uh talk about canel again so given + + align:start position:0% +to uh talk about canel again so given + + + align:start position:0% +to uh talk about canel again so given +that yesterday was a little + + align:start position:0% +that yesterday was a little + + + align:start position:0% +that yesterday was a little +um uh we spent more there was more disc + + align:start position:0% +um uh we spent more there was more disc + + + align:start position:0% +um uh we spent more there was more disc +we spend more time uh than I originally + + align:start position:0% +we spend more time uh than I originally + + + align:start position:0% +we spend more time uh than I originally +anticipated I think most of today will + + align:start position:0% +anticipated I think most of today will + + + align:start position:0% +anticipated I think most of today will +be uh + + align:start position:0% +be uh + + + align:start position:0% +be uh +uh my material looking at distributions + + align:start position:0% +uh my material looking at distributions + + + align:start position:0% +uh my material looking at distributions +Etc and then uh we'll go back to um + + align:start position:0% +Etc and then uh we'll go back to um + + + align:start position:0% +Etc and then uh we'll go back to um +discussing conditional hund variable and + + align:start position:0% +discussing conditional hund variable and + + + align:start position:0% +discussing conditional hund variable and +marginal distribution Etc um next + + align:start position:0% +marginal distribution Etc um next + + + align:start position:0% +marginal distribution Etc um next +week so this is what's going to happen + + align:start position:0% +week so this is what's going to happen + + + align:start position:0% +week so this is what's going to happen +and then after that with all that behind + + align:start position:0% +and then after that with all that behind + + + align:start position:0% +and then after that with all that behind +us we'll be able to talk about + + align:start position:0% +us we'll be able to talk about + + + align:start position:0% +us we'll be able to talk about +expectation bar and Central limit + + align:start position:0% +expectation bar and Central limit + + + align:start position:0% +expectation bar and Central limit +theorum and all that all that good stuff + + align:start position:0% +theorum and all that all that good stuff + + + align:start position:0% +theorum and all that all that good stuff +which should Place Us in turn in a very + + align:start position:0% +which should Place Us in turn in a very + + + align:start position:0% +which should Place Us in turn in a very +good position to start analyzing data in + + align:start position:0% +good position to start analyzing data in + + + align:start position:0% +good position to start analyzing data in +a way that uh we won't be confined to + + align:start position:0% +a way that uh we won't be confined to + + + align:start position:0% +a way that uh we won't be confined to +one or maybe two variables uh and very + + align:start position:0% +one or maybe two variables uh and very + + + align:start position:0% +one or maybe two variables uh and very +simple distributions so that's sort of + + align:start position:0% +simple distributions so that's sort of + + + align:start position:0% +simple distributions so that's sort of +the game + + align:start position:0% +the game + + + align:start position:0% +the game +plans all right so we were there at + + align:start position:0% +plans all right so we were there at + + + align:start position:0% +plans all right so we were there at +playing with + + align:start position:0% +playing with + + + align:start position:0% +playing with +beans and uh you can see that uh the + + align:start position:0% +beans and uh you can see that uh the + + + align:start position:0% +beans and uh you can see that uh the +number of beIN that I I put on the on + + align:start position:0% +number of beIN that I I put on the on + + + align:start position:0% +number of beIN that I I put on the on +the shape of the distribution might + + align:start position:0% +the shape of the distribution might + + + align:start position:0% +the shape of the distribution might +influence what I have to to say about it + + align:start position:0% +influence what I have to to say about it + + + align:start position:0% +influence what I have to to say about it +for example with only very few beans + + align:start position:0% +for example with only very few beans + + + align:start position:0% +for example with only very few beans +over at the top I might think that uh uh + + align:start position:0% +over at the top I might think that uh uh + + + align:start position:0% +over at the top I might think that uh uh +the the distribution seems to have some + + align:start position:0% +the the distribution seems to have some + + + align:start position:0% +the the distribution seems to have some +like uh skewing to the left maybe uh but + + align:start position:0% +like uh skewing to the left maybe uh but + + + align:start position:0% +like uh skewing to the left maybe uh but +then when I move to a few more beans + + align:start position:0% +then when I move to a few more beans + + + align:start position:0% +then when I move to a few more beans +that starts going away and then even + + align:start position:0% +that starts going away and then even + + + align:start position:0% +that starts going away and then even +more beans that start going away and + + align:start position:0% +more beans that start going away and + + + align:start position:0% +more beans that start going away and +then with the most uh beans it start + + align:start position:0% +then with the most uh beans it start + + + align:start position:0% +then with the most uh beans it start +looking quite symmetrical and not skewed + + align:start position:0% +looking quite symmetrical and not skewed + + + align:start position:0% +looking quite symmetrical and not skewed +and kind of b b Bell shaping Bel shapy + + align:start position:0% +and kind of b b Bell shaping Bel shapy + + + align:start position:0% +and kind of b b Bell shaping Bel shapy +so it seems that we would gain in our + + align:start position:0% +so it seems that we would gain in our + + + align:start position:0% +so it seems that we would gain in our +understanding of the distribution of the + + align:start position:0% +understanding of the distribution of the + + + align:start position:0% +understanding of the distribution of the +underlying random variable if we had a a + + align:start position:0% +underlying random variable if we had a a + + + align:start position:0% +underlying random variable if we had a a +smoother more continuous way of + + align:start position:0% +smoother more continuous way of + + + align:start position:0% +smoother more continuous way of +describing it and that's what the kernel + + align:start position:0% +describing it and that's what the kernel + + + align:start position:0% +describing it and that's what the kernel +does so the kernel density is in a sense + + align:start position:0% +does so the kernel density is in a sense + + + align:start position:0% +does so the kernel density is in a sense +an extension of the + + align:start position:0% +an extension of the + + + align:start position:0% +an extension of the +histogram except that for the histogram + + align:start position:0% +histogram except that for the histogram + + + align:start position:0% +histogram except that for the histogram +we the histogram draws a a bin at + + align:start position:0% +we the histogram draws a a bin at + + + align:start position:0% +we the histogram draws a a bin at +several points we have to decide where + + align:start position:0% +several points we have to decide where + + + align:start position:0% +several points we have to decide where +the bins are and then we estimate the + + align:start position:0% +the bins are and then we estimate the + + + align:start position:0% +the bins are and then we estimate the +value for that bin + + align:start position:0% +value for that bin + + + align:start position:0% +value for that bin +and the Kel is continuous it's it's + + align:start position:0% +and the Kel is continuous it's it's + + + align:start position:0% +and the Kel is continuous it's it's +looking at a function it's looking at + + align:start position:0% +looking at a function it's looking at + + + align:start position:0% +looking at a function it's looking at +drawing a function which is going to be + + align:start position:0% +drawing a function which is going to be + + + align:start position:0% +drawing a function which is going to be +I guess the histogram is a function too + + align:start position:0% +I guess the histogram is a function too + + + align:start position:0% +I guess the histogram is a function too +but it's a discrete function evaluated + + align:start position:0% +but it's a discrete function evaluated + + + align:start position:0% +but it's a discrete function evaluated +at different intervals the histogram the + + align:start position:0% +at different intervals the histogram the + + + align:start position:0% +at different intervals the histogram the +the Kel is is a continuous + + align:start position:0% +the Kel is is a continuous + + + align:start position:0% +the Kel is is a continuous +function uh so formally for a sample we + + align:start position:0% +function uh so formally for a sample we + + + align:start position:0% +function uh so formally for a sample we +have a sample which has a given number + + align:start position:0% +have a sample which has a given number + + + align:start position:0% +have a sample which has a given number +of observation in in this case n + + align:start position:0% +of observation in in this case n + + + align:start position:0% +of observation in in this case n +observation X1 X2 xn uh and we want to + + align:start position:0% +observation X1 X2 xn uh and we want to + + + align:start position:0% +observation X1 X2 xn uh and we want to +draw a function uh based on this on this + + align:start position:0% +draw a function uh based on this on this + + + align:start position:0% +draw a function uh based on this on this +X's we we might have very many sample + + align:start position:0% +X's we we might have very many sample + + + align:start position:0% +X's we we might have very many sample +points uh many many more than we could + + align:start position:0% +points uh many many more than we could + + + align:start position:0% +points uh many many more than we could +see in if they are plotted slowly or we + + align:start position:0% +see in if they are plotted slowly or we + + + align:start position:0% +see in if they are plotted slowly or we +may have very few of sample points + + align:start position:0% +may have very few of sample points + + + align:start position:0% +may have very few of sample points +regardless we want a continuous + + align:start position:0% +regardless we want a continuous + + + align:start position:0% +regardless we want a continuous +distribution so the caral density + + align:start position:0% +distribution so the caral density + + + align:start position:0% +distribution so the caral density +estimator what it does it's um it's it's + + align:start position:0% +estimator what it does it's um it's it's + + + align:start position:0% +estimator what it does it's um it's it's +a little bit like a count like an + + align:start position:0% +a little bit like a count like an + + + align:start position:0% +a little bit like a count like an +histogram except it's not going to + + align:start position:0% +histogram except it's not going to + + + align:start position:0% +histogram except it's not going to +assign the same weight to every + + align:start position:0% +assign the same weight to every + + + align:start position:0% +assign the same weight to every +observation we count so in fact it is + + align:start position:0% +observation we count so in fact it is + + + align:start position:0% +observation we count so in fact it is +not a count it is a weighted average of + + align:start position:0% +not a count it is a weighted average of + + + align:start position:0% +not a count it is a weighted average of +frequencies so what it does is that it + + align:start position:0% +frequencies so what it does is that it + + + align:start position:0% +frequencies so what it does is that it +looks uh if we want to estimate it at + + align:start position:0% +looks uh if we want to estimate it at + + + align:start position:0% +looks uh if we want to estimate it at +point x I want to evaluate it at point x + + align:start position:0% +point x I want to evaluate it at point x + + + align:start position:0% +point x I want to evaluate it at point x +it says well at point x I'm going to + + align:start position:0% +it says well at point x I'm going to + + + align:start position:0% +it says well at point x I'm going to +apply a function which is going to be a + + align:start position:0% +apply a function which is going to be a + + + align:start position:0% +apply a function which is going to be a +sort of filter and I'm going to look at + + align:start position:0% +sort of filter and I'm going to look at + + + align:start position:0% +sort of filter and I'm going to look at +uh um the the value of this function for + + align:start position:0% +uh um the the value of this function for + + + align:start position:0% +uh um the the value of this function for +uh for uh points that are ad various + + align:start position:0% +uh for uh points that are ad various + + + align:start position:0% +uh for uh points that are ad various +distance from + + align:start position:0% +distance from + + + align:start position:0% +distance from +X uh within a particular Bond WID which + + align:start position:0% +X uh within a particular Bond WID which + + + align:start position:0% +X uh within a particular Bond WID which +we are going to called the + + align:start position:0% +we are going to called the + + + align:start position:0% +we are going to called the +H and I'm going to uh take the average + + align:start position:0% +H and I'm going to uh take the average + + + align:start position:0% +H and I'm going to uh take the average +of this function over the entire sample + + align:start position:0% +of this function over the entire sample + + + align:start position:0% +of this function over the entire sample +so in practice how does it work in + + align:start position:0% +so in practice how does it work in + + + align:start position:0% +so in practice how does it work in +practice suppose that you have a a few a + + align:start position:0% +practice suppose that you have a a few a + + + align:start position:0% +practice suppose that you have a a few a +sample with a few + + align:start position:0% +sample with a few + + + align:start position:0% +sample with a few +observations uh how many do we have what + + align:start position:0% +observations uh how many do we have what + + + align:start position:0% +observations uh how many do we have what +one two three four five like about a + + align:start position:0% +one two three four five like about a + + + align:start position:0% +one two three four five like about a +dozen + + align:start position:0% +dozen + + + align:start position:0% +dozen +maybe for each + + align:start position:0% +maybe for each + + + align:start position:0% +maybe for each +observation that I have I'm going to + + align:start position:0% +observation that I have I'm going to + + + align:start position:0% +observation that I have I'm going to +draw the function uh the function K so + + align:start position:0% +draw the function uh the function K so + + + align:start position:0% +draw the function uh the function K so +here it's of looking like a so what is + + align:start position:0% +here it's of looking like a so what is + + + align:start position:0% +here it's of looking like a so what is +the function K I'm going to come in a + + align:start position:0% +the function K I'm going to come in a + + + align:start position:0% +the function K I'm going to come in a +minute it could be something flat that + + align:start position:0% +minute it could be something flat that + + + align:start position:0% +minute it could be something flat that +would be what we call a uniform + + align:start position:0% +would be what we call a uniform + + + align:start position:0% +would be what we call a uniform +Kel typically we use something Bell + + align:start position:0% +Kel typically we use something Bell + + + align:start position:0% +Kel typically we use something Bell +shape to give it a bit more nice + + align:start position:0% +shape to give it a bit more nice + + + align:start position:0% +shape to give it a bit more nice +continuity and I'm going to draw at each + + align:start position:0% +continuity and I'm going to draw at each + + + align:start position:0% +continuity and I'm going to draw at each +X point I'm going to draw my + + align:start position:0% +X point I'm going to draw my + + + align:start position:0% +X point I'm going to draw my +kernel so I'm going to draw my kernel + + align:start position:0% +kernel so I'm going to draw my kernel + + + align:start position:0% +kernel so I'm going to draw my kernel +function uh the width of this is uh is + + align:start position:0% +function uh the width of this is uh is + + + align:start position:0% +function uh the width of this is uh is +the width here is the bond withd H so + + align:start position:0% +the width here is the bond withd H so + + + align:start position:0% +the width here is the bond withd H so +the function the Kel function is zero + + align:start position:0% +the function the Kel function is zero + + + align:start position:0% +the function the Kel function is zero +until you are at some distance from X H + + align:start position:0% +until you are at some distance from X H + + + align:start position:0% +until you are at some distance from X H +over two uh or H depending on how H is + + align:start position:0% +over two uh or H depending on how H is + + + align:start position:0% +over two uh or H depending on how H is +defined and then it's uh it's it's + + align:start position:0% +defined and then it's uh it's it's + + + align:start position:0% +defined and then it's uh it's it's +increasing as you getting closer to X + + align:start position:0% +increasing as you getting closer to X + + + align:start position:0% +increasing as you getting closer to X +and then it's decreasing again as you + + align:start position:0% +and then it's decreasing again as you + + + align:start position:0% +and then it's decreasing again as you +get further away and it goes back to uh + + align:start position:0% +get further away and it goes back to uh + + + align:start position:0% +get further away and it goes back to uh +to then it doesn't have there's no + + align:start position:0% +to then it doesn't have there's no + + + align:start position:0% +to then it doesn't have there's no +requirement that the canel be belt + + align:start position:0% +requirement that the canel be belt + + + align:start position:0% +requirement that the canel be belt +shaped it has to be uh symmetrical it + + align:start position:0% +shaped it has to be uh symmetrical it + + + align:start position:0% +shaped it has to be uh symmetrical it +has to integrate to to one and to have + + align:start position:0% +has to integrate to to one and to have + + + align:start position:0% +has to integrate to to one and to have +mean zero if it's symmetric across so + + align:start position:0% +mean zero if it's symmetric across so + + + align:start position:0% +mean zero if it's symmetric across so +you it takes NE negative value and + + align:start position:0% +you it takes NE negative value and + + + align:start position:0% +you it takes NE negative value and +positive value it integrates to one has + + align:start position:0% +positive value it integrates to one has + + + align:start position:0% +positive value it integrates to one has +mean + + align:start position:0% +mean + + + align:start position:0% +mean +Zer so that's the kernel so then for + + align:start position:0% +Zer so that's the kernel so then for + + + align:start position:0% +Zer so that's the kernel so then for +example if I want to know the the + + align:start position:0% +example if I want to know the the + + + align:start position:0% +example if I want to know the the +density for a point that is over here + + align:start position:0% +density for a point that is over here + + + align:start position:0% +density for a point that is over here +I'm going to I have just one kernel here + + align:start position:0% +I'm going to I have just one kernel here + + + align:start position:0% +I'm going to I have just one kernel here +so I'm going to put it it's it's is + + align:start position:0% +so I'm going to put it it's it's is + + + align:start position:0% +so I'm going to put it it's it's is +going to be that point if I want to uh + + align:start position:0% +going to be that point if I want to uh + + + align:start position:0% +going to be that point if I want to uh +if I want to integrate if I want to to + + align:start position:0% +if I want to integrate if I want to to + + + align:start position:0% +if I want to integrate if I want to to +to take the kernel at a larger function + + align:start position:0% +to take the kernel at a larger function + + + align:start position:0% +to take the kernel at a larger function +I'm going to sum them up basically sum + + align:start position:0% +I'm going to sum them up basically sum + + + align:start position:0% +I'm going to sum them up basically sum +up the the vertical distance until I + + align:start position:0% +up the the vertical distance until I + + + align:start position:0% +up the the vertical distance until I +have the point uh and that's what it + + align:start position:0% +have the point uh and that's what it + + + align:start position:0% +have the point uh and that's what it +does so what it does in practice is some + + align:start position:0% +does so what it does in practice is some + + + align:start position:0% +does so what it does in practice is some +counting except the count that it gives + + align:start position:0% +counting except the count that it gives + + + align:start position:0% +counting except the count that it gives +is uh it counts only the observation + + align:start position:0% +is uh it counts only the observation + + + align:start position:0% +is uh it counts only the observation +that are closed by like a histogram and + + align:start position:0% +that are closed by like a histogram and + + + align:start position:0% +that are closed by like a histogram and +it changes the and it also gives less + + align:start position:0% +it changes the and it also gives less + + + align:start position:0% +it changes the and it also gives less +weight to the observation that are it + + align:start position:0% +weight to the observation that are it + + + align:start position:0% +weight to the observation that are it +gives more and more weight as the + + align:start position:0% +gives more and more weight as the + + + align:start position:0% +gives more and more weight as the +observation are closer and closer from + + align:start position:0% +observation are closer and closer from + + + align:start position:0% +observation are closer and closer from +each other yeah why if you're just + + align:start position:0% +each other yeah why if you're just + + + align:start position:0% +each other yeah why if you're just +summing vertically don't the right and + + align:start position:0% +summing vertically don't the right and + + + align:start position:0% +summing vertically don't the right and +left edges overlap yeah I think they + + align:start position:0% +left edges overlap yeah I think they + + + align:start position:0% +left edges overlap yeah I think they +should I think they should be like this + + align:start position:0% +should I think they should be like this + + + align:start position:0% +should I think they should be like this +I think as I was think was like there is + + align:start position:0% +I think as I was think was like there is + + + align:start position:0% +I think as I was think was like there is +an issue with that I think it should + + align:start position:0% +an issue with that I think it should + + + align:start position:0% +an issue with that I think it should +they should they should be like they + + align:start position:0% +they should they should be like they + + + align:start position:0% +they should they should be like they +should go like + + align:start position:0% +should go like + + + align:start position:0% +should go like +this and then same thing over here as + + align:start position:0% +this and then same thing over here as + + + align:start position:0% +this and then same thing over here as +well yeah is it only for uh continuous + + align:start position:0% +well yeah is it only for uh continuous + + + align:start position:0% +well yeah is it only for uh continuous +uh variables that we so for I no no look + + align:start position:0% +uh variables that we so for I no no look + + + align:start position:0% +uh variables that we so for I no no look +here we have very + + align:start position:0% +here we have very + + + align:start position:0% +here we have very +few uh so we could oh is the is the + + align:start position:0% +few uh so we could oh is the is the + + + align:start position:0% +few uh so we could oh is the is the +function itself is not uh youing if the + + align:start position:0% +function itself is not uh youing if the + + + align:start position:0% +function itself is not uh youing if the +function itself the underlying fun prob + + align:start position:0% +function itself the underlying fun prob + + + align:start position:0% +function itself the underlying fun prob +function is not is not continuous then + + align:start position:0% +function is not is not continuous then + + + align:start position:0% +function is not is not continuous then +it would be odd to draw + + align:start position:0% +it would be odd to draw + + + align:start position:0% +it would be odd to draw +a + + align:start position:0% +a + + + align:start position:0% +a +would do you mind explaining or if it if + + align:start position:0% +would do you mind explaining or if it if + + + align:start position:0% +would do you mind explaining or if it if +it is at all useful to or important to + + align:start position:0% +it is at all useful to or important to + + + align:start position:0% +it is at all useful to or important to +know the the height or the altitude of + + align:start position:0% +know the the height or the altitude of + + + align:start position:0% +know the the height or the altitude of +these kernels like how do you actually + + align:start position:0% +these kernels like how do you actually + + + align:start position:0% +these kernels like how do you actually +determine does that + + align:start position:0% +determine does that + + + align:start position:0% +determine does that +matter it's uh so the height is going to + + align:start position:0% +matter it's uh so the height is going to + + + align:start position:0% +matter it's uh so the height is going to +be determined by by by the bond width + + align:start position:0% +be determined by by by the bond width + + + align:start position:0% +be determined by by by the bond width +basically because they have to integrate + + align:start position:0% +basically because they have to integrate + + + align:start position:0% +basically because they have to integrate +to one so + + align:start position:0% +to one so + + + align:start position:0% +to one so +they will they become flatter if the + + align:start position:0% +they will they become flatter if the + + + align:start position:0% +they will they become flatter if the +bond WID is larger or they become higher + + align:start position:0% +bond WID is larger or they become higher + + + align:start position:0% +bond WID is larger or they become higher +if the bond WID is smaller so that they + + align:start position:0% +if the bond WID is smaller so that they + + + align:start position:0% +if the bond WID is smaller so that they +integrate to one yeah so when we are + + align:start position:0% +integrate to one yeah so when we are + + + align:start position:0% +integrate to one yeah so when we are +determining the function of and we're + + align:start position:0% +determining the function of and we're + + + align:start position:0% +determining the function of and we're +deciding between uniform normal + + align:start position:0% + + + + align:start position:0% + +or um how are we deciding which one of + + align:start position:0% +or um how are we deciding which one of + + + align:start position:0% +or um how are we deciding which one of +those functional forms we want to use in + + align:start position:0% +those functional forms we want to use in + + + align:start position:0% +those functional forms we want to use in +similarly with bandwidth how are we what + + align:start position:0% +similarly with bandwidth how are we what + + + align:start position:0% +similarly with bandwidth how are we what +rule of come are we using to determine + + align:start position:0% +rule of come are we using to determine + + + align:start position:0% +rule of come are we using to determine +so honestly the the choice of carel I + + align:start position:0% +so honestly the the choice of carel I + + + align:start position:0% +so honestly the the choice of carel I +don't think matter a huge amount as long + + align:start position:0% +don't think matter a huge amount as long + + + align:start position:0% +don't think matter a huge amount as long +as the kernel is some B shaped looking a + + align:start position:0% +as the kernel is some B shaped looking a + + + align:start position:0% +as the kernel is some B shaped looking a +lot of people for um for computational + + align:start position:0% +lot of people for um for computational + + + align:start position:0% +lot of people for um for computational +reason people prefer the epine cof than + + align:start position:0% +reason people prefer the epine cof than + + + align:start position:0% +reason people prefer the epine cof than +you know over a normal kernel because + + align:start position:0% +you know over a normal kernel because + + + align:start position:0% +you know over a normal kernel because +the normal kernel has positive + + align:start position:0% +the normal kernel has positive + + + align:start position:0% +the normal kernel has positive +probability + + align:start position:0% +probability + + + align:start position:0% +probability +everywhere yeah so computationally it's + + align:start position:0% +everywhere yeah so computationally it's + + + align:start position:0% +everywhere yeah so computationally it's +just more intensive than the epen C it + + align:start position:0% +just more intensive than the epen C it + + + align:start position:0% +just more intensive than the epen C it +because it's waiting the the closer no + + align:start position:0% +because it's waiting the the closer no + + + align:start position:0% +because it's waiting the the closer no +all of them in any case weigh the closer + + align:start position:0% +all of them in any case weigh the closer + + + align:start position:0% +all of them in any case weigh the closer +more but the normal is the normal is not + + align:start position:0% +more but the normal is the normal is not + + + align:start position:0% +more but the normal is the normal is not +bound that is trying to go all the way + + align:start position:0% +bound that is trying to go all the way + + + align:start position:0% +bound that is trying to go all the way +to + + align:start position:0% +to + + + align:start position:0% +to +the to the end so either you need to do + + align:start position:0% +the to the end so either you need to do + + + align:start position:0% +the to the end so either you need to do +something like that that is going to + + align:start position:0% +something like that that is going to + + + align:start position:0% +something like that that is going to +truncate it above your bandwidth it + + align:start position:0% +truncate it above your bandwidth it + + + align:start position:0% +truncate it above your bandwidth it +still has some little Mass here so it's + + align:start position:0% +still has some little Mass here so it's + + + align:start position:0% +still has some little Mass here so it's +going to be like that it's still going + + align:start position:0% +going to be like that it's still going + + + align:start position:0% +going to be like that it's still going +to have some little Mass here that's + + align:start position:0% +to have some little Mass here that's + + + align:start position:0% +to have some little Mass here that's +left where thean nikov is exactly zero + + align:start position:0% +left where thean nikov is exactly zero + + + align:start position:0% +left where thean nikov is exactly zero +at the kernel and then it's Bell shipped + + align:start position:0% +at the kernel and then it's Bell shipped + + + align:start position:0% +at the kernel and then it's Bell shipped +it's also optimal in some sort of stat + + align:start position:0% +it's also optimal in some sort of stat + + + align:start position:0% +it's also optimal in some sort of stat +statistical sense that's too involved + + align:start position:0% +statistical sense that's too involved + + + align:start position:0% +statistical sense that's too involved +for me to be fair uh so the car you will + + align:start position:0% +for me to be fair uh so the car you will + + + align:start position:0% +for me to be fair uh so the car you will +typically go a pish + + align:start position:0% +typically go a pish + + + align:start position:0% +typically go a pish +nikov the bandwidth is a much + + align:start position:0% +nikov the bandwidth is a much + + + align:start position:0% +nikov the bandwidth is a much +more uh relevant choice in a sense much + + align:start position:0% +more uh relevant choice in a sense much + + + align:start position:0% +more uh relevant choice in a sense much +more sensitive and relevant let me show + + align:start position:0% +more sensitive and relevant let me show + + + align:start position:0% +more sensitive and relevant let me show +you what happened with + + align:start position:0% +you what happened with + + + align:start position:0% +you what happened with +bandwidth in fact I'll SCP something I + + align:start position:0% +bandwidth in fact I'll SCP something I + + + align:start position:0% +bandwidth in fact I'll SCP something I +I'll come back I I'll show you a picture + + align:start position:0% +I'll come back I I'll show you a picture + + + align:start position:0% +I'll come back I I'll show you a picture +where it matters a lot I'm not telling + + align:start position:0% +where it matters a lot I'm not telling + + + align:start position:0% +where it matters a lot I'm not telling +you what's the what the picture is for + + align:start position:0% +you what's the what the picture is for + + + align:start position:0% +you what's the what the picture is for +the moment we'll get back to the nature + + align:start position:0% +the moment we'll get back to the nature + + + align:start position:0% +the moment we'll get back to the nature +of the picture but um so here is an + + align:start position:0% +of the picture but um so here is an + + + align:start position:0% +of the picture but um so here is an +histogram this is our this is our friend + + align:start position:0% +histogram this is our this is our friend + + + align:start position:0% +histogram this is our this is our friend +Steph Curry and this is the the short + + align:start position:0% +Steph Curry and this is the the short + + + align:start position:0% +Steph Curry and this is the the short +distance from the midline of court is + + align:start position:0% +distance from the midline of court is + + + align:start position:0% +distance from the midline of court is +taking so doesn't matter how why this is + + align:start position:0% +taking so doesn't matter how why this is + + + align:start position:0% +taking so doesn't matter how why this is +like that but it turns out that's the + + align:start position:0% +like that but it turns out that's the + + + align:start position:0% +like that but it turns out that's the +shape of the histogram you see it has + + align:start position:0% +shape of the histogram you see it has + + + align:start position:0% +shape of the histogram you see it has +this slight peek at the at the end and a + + align:start position:0% +this slight peek at the at the end and a + + + align:start position:0% +this slight peek at the at the end and a +big peek in the bottom and that's uh + + align:start position:0% +big peek in the bottom and that's uh + + + align:start position:0% +big peek in the bottom and that's uh +that's the that's one first Bond WID you + + align:start position:0% +that's the that's one first Bond WID you + + + align:start position:0% +that's the that's one first Bond WID you +could you could use which turns out to + + align:start position:0% +could you could use which turns out to + + + align:start position:0% +could you could use which turns out to +be the default Bond WID I'll explain to + + align:start position:0% +be the default Bond WID I'll explain to + + + align:start position:0% +be the default Bond WID I'll explain to +you in a minute what the default is + + align:start position:0% +you in a minute what the default is + + + align:start position:0% +you in a minute what the default is +trying to do and here is what you would + + align:start position:0% +trying to do and here is what you would + + + align:start position:0% +trying to do and here is what you would +get if you try to use a bond width that + + align:start position:0% +get if you try to use a bond width that + + + align:start position:0% +get if you try to use a bond width that +is uh much wider + + align:start position:0% +is uh much wider + + + align:start position:0% +is uh much wider +so you would completely lose if you had + + align:start position:0% +so you would completely lose if you had + + + align:start position:0% +so you would completely lose if you had +not plotted the data and you start with + + align:start position:0% +not plotted the data and you start with + + + align:start position:0% +not plotted the data and you start with +a big bandwidth you would completely + + align:start position:0% +a big bandwidth you would completely + + + align:start position:0% +a big bandwidth you would completely +lose what this distribution is looking + + align:start position:0% +lose what this distribution is looking + + + align:start position:0% +lose what this distribution is looking +like it might be looking to you like + + align:start position:0% +like it might be looking to you like + + + align:start position:0% +like it might be looking to you like +it's you know kind of almost bell-shaped + + align:start position:0% +it's you know kind of almost bell-shaped + + + align:start position:0% +it's you know kind of almost bell-shaped +when in fact just plotting the histogram + + align:start position:0% +when in fact just plotting the histogram + + + align:start position:0% +when in fact just plotting the histogram +would have convinced you that it's not + + align:start position:0% +would have convinced you that it's not + + + align:start position:0% +would have convinced you that it's not +Bell shape + + align:start position:0% +Bell shape + + + align:start position:0% +Bell shape +whatsoever so uh that illustrates the + + align:start position:0% +whatsoever so uh that illustrates the + + + align:start position:0% +whatsoever so uh that illustrates the +ideally I would have plotted one more + + align:start position:0% +ideally I would have plotted one more + + + align:start position:0% +ideally I would have plotted one more +where we have a very small + + align:start position:0% +where we have a very small + + + align:start position:0% +where we have a very small +bandwidth so much shorter than that and + + align:start position:0% +bandwidth so much shorter than that and + + + align:start position:0% +bandwidth so much shorter than that and +what you would get is like it Go + + align:start position:0% +what you would get is like it Go + + + align:start position:0% +what you would get is like it Go +squiggle squiggle squiggle squiggle and + + align:start position:0% +squiggle squiggle squiggle squiggle and + + + align:start position:0% +squiggle squiggle squiggle squiggle and +then top squiggle squiggle squiggle + + align:start position:0% +then top squiggle squiggle squiggle + + + align:start position:0% +then top squiggle squiggle squiggle +squiggle so it' be very uh variable and + + align:start position:0% +squiggle so it' be very uh variable and + + + align:start position:0% +squiggle so it' be very uh variable and +not very nice to look at uh and that + + align:start position:0% +not very nice to look at uh and that + + + align:start position:0% +not very nice to look at uh and that +sort of illustrate the issue if we go + + align:start position:0% +sort of illustrate the issue if we go + + + align:start position:0% +sort of illustrate the issue if we go +with a bandwidth that very + + align:start position:0% +with a bandwidth that very + + + align:start position:0% +with a bandwidth that very +wide we might get the shape altogether + + align:start position:0% +wide we might get the shape altogether + + + align:start position:0% +wide we might get the shape altogether +wrong a technical way to say that and + + align:start position:0% +wrong a technical way to say that and + + + align:start position:0% +wrong a technical way to say that and +much more accurate way to say that is + + align:start position:0% +much more accurate way to say that is + + + align:start position:0% +much more accurate way to say that is +that we might get + + align:start position:0% +that we might get + + + align:start position:0% +that we might get +biased because basically our comp starts + + align:start position:0% +biased because basically our comp starts + + + align:start position:0% +biased because basically our comp starts +getting + + align:start position:0% +getting + + + align:start position:0% +getting +wrong and not not estimating the right + + align:start position:0% +wrong and not not estimating the right + + + align:start position:0% +wrong and not not estimating the right +uh it's not converging towards the right + + align:start position:0% +uh it's not converging towards the right + + + align:start position:0% +uh it's not converging towards the right +function at the end of the day as I if I + + align:start position:0% +function at the end of the day as I if I + + + align:start position:0% +function at the end of the day as I if I +start with a very large Bond WID as I + + align:start position:0% +start with a very large Bond WID as I + + + align:start position:0% +start with a very large Bond WID as I +add more and more and more observation + + align:start position:0% +add more and more and more observation + + + align:start position:0% +add more and more and more observation +this is still never going to go to the + + align:start position:0% +this is still never going to go to the + + + align:start position:0% +this is still never going to go to the +right shape so this is + + align:start position:0% +right shape so this is + + + align:start position:0% +right shape so this is +bias if I have a too small Bond width + + align:start position:0% +bias if I have a too small Bond width + + + align:start position:0% +bias if I have a too small Bond width +and I don't have that many observation + + align:start position:0% +and I don't have that many observation + + + align:start position:0% +and I don't have that many observation +it's going to look much more uh bumpy + + align:start position:0% +it's going to look much more uh bumpy + + + align:start position:0% +it's going to look much more uh bumpy +than it really is but in this situation + + align:start position:0% +than it really is but in this situation + + + align:start position:0% +than it really is but in this situation +with a very small Bond if I continue to + + align:start position:0% +with a very small Bond if I continue to + + + align:start position:0% +with a very small Bond if I continue to +add observation it will eventually + + align:start position:0% +add observation it will eventually + + + align:start position:0% +add observation it will eventually +smooth itself out so for a given sample + + align:start position:0% +smooth itself out so for a given sample + + + align:start position:0% +smooth itself out so for a given sample +size that is + + align:start position:0% +size that is + + + align:start position:0% +size that is +variance so the choice of bandwidth in + + align:start position:0% +variance so the choice of bandwidth in + + + align:start position:0% +variance so the choice of bandwidth in +kernel density approximation and by the + + align:start position:0% +kernel density approximation and by the + + + align:start position:0% +kernel density approximation and by the +way in kernel regression which we are + + align:start position:0% +way in kernel regression which we are + + + align:start position:0% +way in kernel regression which we are +going to see little bit further along + + align:start position:0% +going to see little bit further along + + + align:start position:0% +going to see little bit further along +the way is trying to uh balance these + + align:start position:0% +the way is trying to uh balance these + + + align:start position:0% +the way is trying to uh balance these +two sources of error the bias and the + + align:start position:0% +two sources of error the bias and the + + + align:start position:0% +two sources of error the bias and the +variance so what it does is basically + + align:start position:0% +variance so what it does is basically + + + align:start position:0% +variance so what it does is basically +trying to optimiz so you can choose you + + align:start position:0% +trying to optimiz so you can choose you + + + align:start position:0% +trying to optimiz so you can choose you +can think of of it as a minimization + + align:start position:0% +can think of of it as a minimization + + + align:start position:0% +can think of of it as a minimization +problem where you're trying to minimize + + align:start position:0% +problem where you're trying to minimize + + + align:start position:0% +problem where you're trying to minimize +some function of the two a natural uh uh + + align:start position:0% +some function of the two a natural uh uh + + + align:start position:0% +some function of the two a natural uh uh +object that summarizes the two is mean + + align:start position:0% +object that summarizes the two is mean + + + align:start position:0% +object that summarizes the two is mean +square error which is how far away are + + align:start position:0% +square error which is how far away are + + + align:start position:0% +square error which is how far away are +you for how far away is each of your + + align:start position:0% +you for how far away is each of your + + + align:start position:0% +you for how far away is each of your +observation from the truth which is a + + align:start position:0% +observation from the truth which is a + + + align:start position:0% +observation from the truth which is a +combination of variance and bias so the + + align:start position:0% +combination of variance and bias so the + + + align:start position:0% +combination of variance and bias so the +optimal Bond width is + + align:start position:0% +optimal Bond width is + + + align:start position:0% +optimal Bond width is +a solution to this mean square error uh + + align:start position:0% +a solution to this mean square error uh + + + align:start position:0% +a solution to this mean square error uh +minimization problem uh there are + + align:start position:0% +minimization problem uh there are + + + align:start position:0% +minimization problem uh there are +various solutions to the mid square + + align:start position:0% +various solutions to the mid square + + + align:start position:0% +various solutions to the mid square +error uh uh minimization problem that + + align:start position:0% +error uh uh minimization problem that + + + align:start position:0% +error uh uh minimization problem that +people have + + align:start position:0% +people have + + + align:start position:0% +people have +suggested uh the one that is implemented + + align:start position:0% +suggested uh the one that is implemented + + + align:start position:0% +suggested uh the one that is implemented +in in R is one of the most common one uh + + align:start position:0% +in in R is one of the most common one uh + + + align:start position:0% +in in R is one of the most common one uh +so in a lot of cases you can sort of I + + align:start position:0% +so in a lot of cases you can sort of I + + + align:start position:0% +so in a lot of cases you can sort of I +think go with the r default which if you + + align:start position:0% +think go with the r default which if you + + + align:start position:0% +think go with the r default which if you +type nothing this is what can come or if + + align:start position:0% +type nothing this is what can come or if + + + align:start position:0% +type nothing this is what can come or if +you type if you type an RD zero is going + + align:start position:0% +you type if you type an RD zero is going + + + align:start position:0% +you type if you type an RD zero is going +to uh uh to be the default and then you + + align:start position:0% +to uh uh to be the default and then you + + + align:start position:0% +to uh uh to be the default and then you +can you know play with making it smaller + + align:start position:0% +can you know play with making it smaller + + + align:start position:0% +can you know play with making it smaller +making it B big f with respect to ND Z + + align:start position:0% +making it B big f with respect to ND Z + + + align:start position:0% +making it B big f with respect to ND Z +and see what happens um there is no harm + + align:start position:0% +and see what happens um there is no harm + + + align:start position:0% +and see what happens um there is no harm +in trying trying it out uh + + align:start position:0% +in trying trying it out uh + + + align:start position:0% +in trying trying it out uh +the you can see what the there is good + + align:start position:0% +the you can see what the there is good + + + align:start position:0% +the you can see what the there is good +reasons to refer rever to the default + + align:start position:0% +reasons to refer rever to the default + + + align:start position:0% +reasons to refer rever to the default +not only because someone assumed that it + + align:start position:0% +not only because someone assumed that it + + + align:start position:0% +not only because someone assumed that it +was optimal in some ways but also + + align:start position:0% +was optimal in some ways but also + + + align:start position:0% +was optimal in some ways but also +because it's it's a number that is that + + align:start position:0% +because it's it's a number that is that + + + align:start position:0% +because it's it's a number that is that +at least you've not manipulated in some + + align:start position:0% +at least you've not manipulated in some + + + align:start position:0% +at least you've not manipulated in some +ways to to to get the shape you wanted + + align:start position:0% +ways to to to get the shape you wanted + + + align:start position:0% +ways to to to get the shape you wanted +for example someone who in like this + + align:start position:0% +for example someone who in like this + + + align:start position:0% +for example someone who in like this +shape say no I really think it has to be + + align:start position:0% +shape say no I really think it has to be + + + align:start position:0% +shape say no I really think it has to be +B shaped would eventually be able to get + + align:start position:0% +B shaped would eventually be able to get + + + align:start position:0% +B shaped would eventually be able to get +it by just manipulating the sample a bit + + align:start position:0% +it by just manipulating the sample a bit + + + align:start position:0% +it by just manipulating the sample a bit +more or alternatively someone who had a + + align:start position:0% +more or alternatively someone who had a + + + align:start position:0% +more or alternatively someone who had a +prior that the highight distribution in + + align:start position:0% +prior that the highight distribution in + + + align:start position:0% +prior that the highight distribution in +Bear is really uh + + align:start position:0% + + + + align:start position:0% + +um we go back to very few Kel is very + + align:start position:0% +um we go back to very few Kel is very + + + align:start position:0% +um we go back to very few Kel is very +shap it's really in fact skewed towards + + align:start position:0% +shap it's really in fact skewed towards + + + align:start position:0% +shap it's really in fact skewed towards +the left might have said well I'm going + + align:start position:0% +the left might have said well I'm going + + + align:start position:0% +the left might have said well I'm going +to try and espouse it in some way uh + + align:start position:0% +to try and espouse it in some way uh + + + align:start position:0% +to try and espouse it in some way uh +that's going to be difficult but uh you + + align:start position:0% +that's going to be difficult but uh you + + + align:start position:0% +that's going to be difficult but uh you +could for example try to someone might + + align:start position:0% +could for example try to someone might + + + align:start position:0% +could for example try to someone might +want might show this histogram and + + align:start position:0% +want might show this histogram and + + + align:start position:0% +want might show this histogram and +convince themsel that there is bunching + + align:start position:0% +convince themsel that there is bunching + + + align:start position:0% +convince themsel that there is bunching +at a meter + + align:start position:0% +at a meter + + + align:start position:0% +at a meter +50 uh which is plaus simply because + + align:start position:0% +50 uh which is plaus simply because + + + align:start position:0% +50 uh which is plaus simply because +people might round there you know the + + align:start position:0% +people might round there you know the + + + align:start position:0% +people might round there you know the +people who are measuring the height + + align:start position:0% +people who are measuring the height + + + align:start position:0% +people who are measuring the height +might be rounding at a m 50 uh and then + + align:start position:0% +might be rounding at a m 50 uh and then + + + align:start position:0% +might be rounding at a m 50 uh and then +they they try and you know with enough + + align:start position:0% +they they try and you know with enough + + + align:start position:0% +they they try and you know with enough +with enough squiggling you might + + align:start position:0% +with enough squiggling you might + + + align:start position:0% +with enough squiggling you might +actually be able to find it even in with + + align:start position:0% +actually be able to find it even in with + + + align:start position:0% +actually be able to find it even in with +the continuous carel which of course + + align:start position:0% +the continuous carel which of course + + + align:start position:0% +the continuous carel which of course +might not in fact be there in the data + + align:start position:0% +might not in fact be there in the data + + + align:start position:0% +might not in fact be there in the data +so for all of these + + align:start position:0% +so for all of these + + + align:start position:0% +so for all of these +reason um if we're a little bit worried + + align:start position:0% +reason um if we're a little bit worried + + + align:start position:0% +reason um if we're a little bit worried +about specification searching default is + + align:start position:0% +about specification searching default is + + + align:start position:0% +about specification searching default is +a good thing to go for over and above + + align:start position:0% +a good thing to go for over and above + + + align:start position:0% +a good thing to go for over and above +the fact that it is in fact optimal in + + align:start position:0% +the fact that it is in fact optimal in + + + align:start position:0% +the fact that it is in fact optimal in +some ways so I would always show some + + align:start position:0% +some ways so I would always show some + + + align:start position:0% +some ways so I would always show some +default boundaries and then I would also + + align:start position:0% +default boundaries and then I would also + + + align:start position:0% +default boundaries and then I would also +play uh going back and forth to see + + align:start position:0% +play uh going back and forth to see + + + align:start position:0% +play uh going back and forth to see +whether you're actually not missing + + align:start position:0% + + + + align:start position:0% + +something + + align:start position:0% +something + + + align:start position:0% +something +um if you play with the Kel you will see + + align:start position:0% +um if you play with the Kel you will see + + + align:start position:0% +um if you play with the Kel you will see +that with the exception of the uniform + + align:start position:0% +that with the exception of the uniform + + + align:start position:0% +that with the exception of the uniform +canel that can give you slightly + + align:start position:0% +canel that can give you slightly + + + align:start position:0% +canel that can give you slightly +different shapes the the whatever canel + + align:start position:0% +different shapes the the whatever canel + + + align:start position:0% +different shapes the the whatever canel +you use is going to to look + + align:start position:0% +you use is going to to look + + + align:start position:0% +you use is going to to look +pretty okay so now that we've plotted it + + align:start position:0% +pretty okay so now that we've plotted it + + + align:start position:0% +pretty okay so now that we've plotted it +uh let's um let's look at the uh uh + + align:start position:0% +uh let's um let's look at the uh uh + + + align:start position:0% +uh let's um let's look at the uh uh +let's talk a bit about you know + + align:start position:0% +let's talk a bit about you know + + + align:start position:0% +let's talk a bit about you know +substance let's talk a bit about the + + align:start position:0% +substance let's talk a bit about the + + + align:start position:0% +substance let's talk a bit about the +shape of this um let me show you one + + align:start position:0% +shape of this um let me show you one + + + align:start position:0% +shape of this um let me show you one +where we don't have a we we don't have + + align:start position:0% +where we don't have a we we don't have + + + align:start position:0% +where we don't have a we we don't have +just one uh what + + align:start position:0% +just one uh what + + + align:start position:0% +just one uh what +what do you think about this the shape + + align:start position:0% +what do you think about this the shape + + + align:start position:0% +what do you think about this the shape +of this of this + + align:start position:0% +of this of this + + + align:start position:0% +of this of this +distribution what how can we + + align:start position:0% +distribution what how can we + + + align:start position:0% +distribution what how can we +characterize this distribution in term + + align:start position:0% +characterize this distribution in term + + + align:start position:0% +characterize this distribution in term +of its physical shape yeah you can look + + align:start position:0% +of its physical shape yeah you can look + + + align:start position:0% +of its physical shape yeah you can look +at its mean and standard deviation oh + + align:start position:0% +at its mean and standard deviation oh + + + align:start position:0% +at its mean and standard deviation oh +yeah we could do that we could look at + + align:start position:0% +yeah we could do that we could look at + + + align:start position:0% +yeah we could do that we could look at +it mean and standard devation I was just + + align:start position:0% +it mean and standard devation I was just + + + align:start position:0% +it mean and standard devation I was just +asking you just uh to look at the the + + align:start position:0% +asking you just uh to look at the the + + + align:start position:0% +asking you just uh to look at the the +the shape it hasi sorrys it looks + + align:start position:0% +the shape it hasi sorrys it looks + + + align:start position:0% +the shape it hasi sorrys it looks +gausian what what makes you think it + + align:start position:0% +gausian what what makes you think it + + + align:start position:0% +gausian what what makes you think it +looks + + align:start position:0% +looks + + + align:start position:0% +looks +Gan it's symmetrical it's bell shaped uh + + align:start position:0% +Gan it's symmetrical it's bell shaped uh + + + align:start position:0% +Gan it's symmetrical it's bell shaped uh +it doesn't seem to have thick Tails uh + + align:start position:0% +it doesn't seem to have thick Tails uh + + + align:start position:0% +it doesn't seem to have thick Tails uh +so that uh remind him of a gaussian + + align:start position:0% +so that uh remind him of a gaussian + + + align:start position:0% +so that uh remind him of a gaussian +curve or what we also call a normal + + align:start position:0% +curve or what we also call a normal + + + align:start position:0% +curve or what we also call a normal +distribution uh what does it remind you + + align:start position:0% +distribution uh what does it remind you + + + align:start position:0% +distribution uh what does it remind you +of things we've seen actually before + + align:start position:0% +of things we've seen actually before + + + align:start position:0% +of things we've seen actually before +we've already plotted uh curves looking + + align:start position:0% +we've already plotted uh curves looking + + + align:start position:0% +we've already plotted uh curves looking +very much like that uh a couple of + + align:start position:0% +very much like that uh a couple of + + + align:start position:0% +very much like that uh a couple of +lectures ago bomal exactly it looks very + + align:start position:0% +lectures ago bomal exactly it looks very + + + align:start position:0% +lectures ago bomal exactly it looks very +much like a binomial as you increase the + + align:start position:0% +much like a binomial as you increase the + + + align:start position:0% +much like a binomial as you increase the +number of uh of attempts uh and that + + align:start position:0% +number of uh of attempts uh and that + + + align:start position:0% +number of uh of attempts uh and that +makes sense that it should look like + + align:start position:0% +makes sense that it should look like + + + align:start position:0% +makes sense that it should look like +both because uh uh the binomial + + align:start position:0% +both because uh uh the binomial + + + align:start position:0% +both because uh uh the binomial +distribution is approximately normal uh + + align:start position:0% +distribution is approximately normal uh + + + align:start position:0% +distribution is approximately normal uh +with mean NP and variance n p * 1 minus + + align:start position:0% +with mean NP and variance n p * 1 minus + + + align:start position:0% +with mean NP and variance n p * 1 minus +P for large n and p not too close to + + align:start position:0% +P for large n and p not too close to + + + align:start position:0% +P for large n and p not too close to +zero or one so this curve is actually a + + align:start position:0% +zero or one so this curve is actually a + + + align:start position:0% +zero or one so this curve is actually a +quite normal looking I don't want to say + + align:start position:0% +quite normal looking I don't want to say + + + align:start position:0% +quite normal looking I don't want to say +it is normal because how would I know I + + align:start position:0% +it is normal because how would I know I + + + align:start position:0% +it is normal because how would I know I +haven't estimated it I haven't tried to + + align:start position:0% +haven't estimated it I haven't tried to + + + align:start position:0% +haven't estimated it I haven't tried to +reject to reject it but it looks quite + + align:start position:0% +reject to reject it but it looks quite + + + align:start position:0% +reject to reject it but it looks quite +normal looking and uh and and in fact + + align:start position:0% +normal looking and uh and and in fact + + + align:start position:0% +normal looking and uh and and in fact +you you will be able to show very soon + + align:start position:0% +you you will be able to show very soon + + + align:start position:0% +you you will be able to show very soon +uh that it makes sense that it also + + align:start position:0% +uh that it makes sense that it also + + + align:start position:0% +uh that it makes sense that it also +looks like the binomial since the + + align:start position:0% +looks like the binomial since the + + + align:start position:0% +looks like the binomial since the +binomial is quite normal looking after + + align:start position:0% +binomial is quite normal looking after + + + align:start position:0% +binomial is quite normal looking after +uh for uh for + + align:start position:0% +uh for uh for + + + align:start position:0% +uh for uh for +lend we will come back to our friend the + + align:start position:0% +lend we will come back to our friend the + + + align:start position:0% +lend we will come back to our friend the +normal distribution in great detail + + align:start position:0% +normal distribution in great detail + + + align:start position:0% +normal distribution in great detail +because it will turn out for a very good + + align:start position:0% +because it will turn out for a very good + + + align:start position:0% +because it will turn out for a very good +reason that not only it's the limit of + + align:start position:0% +reason that not only it's the limit of + + + align:start position:0% +reason that not only it's the limit of +the binomial as n becomes large but many + + align:start position:0% +the binomial as n becomes large but many + + + align:start position:0% +the binomial as n becomes large but many +random variables we will we will uh play + + align:start position:0% +random variables we will we will uh play + + + align:start position:0% +random variables we will we will uh play +with uh in economic application and + + align:start position:0% +with uh in economic application and + + + align:start position:0% +with uh in economic application and +other applications can conveniently uh + + align:start position:0% +other applications can conveniently uh + + + align:start position:0% +other applications can conveniently uh +be assumed to have a normal + + align:start position:0% +be assumed to have a normal + + + align:start position:0% +be assumed to have a normal +distribution and in fact if you open any + + align:start position:0% +distribution and in fact if you open any + + + align:start position:0% +distribution and in fact if you open any +statistics textbooks height is a + + align:start position:0% +statistics textbooks height is a + + + align:start position:0% +statistics textbooks height is a +canonical example of uh of something + + align:start position:0% +canonical example of uh of something + + + align:start position:0% +canonical example of uh of something +that's normally + + align:start position:0% +that's normally + + + align:start position:0% +that's normally +distributed so some some exercise that + + align:start position:0% +distributed so some some exercise that + + + align:start position:0% +distributed so some some exercise that +I've been uh doing is uh asking myself + + align:start position:0% +I've been uh doing is uh asking myself + + + align:start position:0% +I've been uh doing is uh asking myself +why on Earth should height be normally + + align:start position:0% +why on Earth should height be normally + + + align:start position:0% +why on Earth should height be normally +distributed uh actually not completely + + align:start position:0% +distributed uh actually not completely + + + align:start position:0% +distributed uh actually not completely +obvious to me that height should be + + align:start position:0% +obvious to me that height should be + + + align:start position:0% +obvious to me that height should be +normally distributed even now so when we + + align:start position:0% +normally distributed even now so when we + + + align:start position:0% +normally distributed even now so when we +know a bit more about where the normal + + align:start position:0% +know a bit more about where the normal + + + align:start position:0% +know a bit more about where the normal +distribution is coming from uh we will + + align:start position:0% +distribution is coming from uh we will + + + align:start position:0% +distribution is coming from uh we will +come back to whether there is a good + + align:start position:0% +come back to whether there is a good + + + align:start position:0% +come back to whether there is a good +reason for height to be normally + + align:start position:0% +reason for height to be normally + + + align:start position:0% +reason for height to be normally +distributed or not in a particular + + align:start position:0% +distributed or not in a particular + + + align:start position:0% +distributed or not in a particular +population um so I want to get back to + + align:start position:0% +population um so I want to get back to + + + align:start position:0% +population um so I want to get back to +that at some point we will do + + align:start position:0% +that at some point we will do + + + align:start position:0% +that at some point we will do +it so here is one reason why it should + + align:start position:0% +it so here is one reason why it should + + + align:start position:0% +it so here is one reason why it should +not be normally distributed is is for + + align:start position:0% +not be normally distributed is is for + + + align:start position:0% +not be normally distributed is is for +some reason uh there was a bunch of + + align:start position:0% +some reason uh there was a bunch of + + + align:start position:0% +some reason uh there was a bunch of +Peace score volunteer in your data set + + align:start position:0% +Peace score volunteer in your data set + + + align:start position:0% +Peace score volunteer in your data set +and um and they they all came from + + align:start position:0% +and um and they they all came from + + + align:start position:0% +and um and they they all came from +America then uh you would have a very + + align:start position:0% +America then uh you would have a very + + + align:start position:0% +America then uh you would have a very +different shape of uh you know if by + + align:start position:0% +different shape of uh you know if by + + + align:start position:0% +different shape of uh you know if by +mistakes we would have to we would also + + align:start position:0% +mistakes we would have to we would also + + + align:start position:0% +mistakes we would have to we would also +have taken the height of all of the all + + align:start position:0% +have taken the height of all of the all + + + align:start position:0% +have taken the height of all of the all +of the peace car volunteer in the same + + align:start position:0% +of the peace car volunteer in the same + + + align:start position:0% +of the peace car volunteer in the same +area beha uh we might not have the + + align:start position:0% +area beha uh we might not have the + + + align:start position:0% +area beha uh we might not have the +distribution might not not have been + + align:start position:0% +distribution might not not have been + + + align:start position:0% +distribution might not not have been +looked so much uh uh the same + + align:start position:0% +looked so much uh uh the same + + + align:start position:0% +looked so much uh uh the same +way the reason being that here I've not + + align:start position:0% +way the reason being that here I've not + + + align:start position:0% +way the reason being that here I've not +plotted the the the distribution of a + + align:start position:0% +plotted the the the distribution of a + + + align:start position:0% +plotted the the the distribution of a +sample which has both I've ploted two + + align:start position:0% +sample which has both I've ploted two + + + align:start position:0% +sample which has both I've ploted two +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +separately uh and the distribution of + + align:start position:0% +separately uh and the distribution of + + + align:start position:0% +separately uh and the distribution of +height in the United States look quite + + align:start position:0% +height in the United States look quite + + + align:start position:0% +height in the United States look quite +different from the distribution of + + align:start position:0% +different from the distribution of + + + align:start position:0% +different from the distribution of +height and be so if I had put both in + + align:start position:0% +height and be so if I had put both in + + + align:start position:0% +height and be so if I had put both in +the data + + align:start position:0% +the data + + + align:start position:0% +the data +set uh which what would have been the + + align:start position:0% +set uh which what would have been the + + + align:start position:0% +set uh which what would have been the +distribution in the overall sample which + + align:start position:0% +distribution in the overall sample which + + + align:start position:0% +distribution in the overall sample which +shape would it would it have had it + + align:start position:0% +shape would it would it have had it + + + align:start position:0% +shape would it would it have had it +might not I've had a whole right because + + align:start position:0% +might not I've had a whole right because + + + align:start position:0% +might not I've had a whole right because +I'm going to I need to add them up but + + align:start position:0% +I'm going to I need to add them up but + + + align:start position:0% +I'm going to I need to add them up but +it's going to have like kind of an + + align:start position:0% +it's going to have like kind of an + + + align:start position:0% +it's going to have like kind of an +elephant looking shape a little bit + + align:start position:0% +elephant looking shape a little bit + + + align:start position:0% +elephant looking shape a little bit +the sum of the two + + align:start position:0% +the sum of the two + + + align:start position:0% +the sum of the two +uh so while looking at these two is sort + + align:start position:0% +uh so while looking at these two is sort + + + align:start position:0% +uh so while looking at these two is sort +of interesting we can see that what can + + align:start position:0% +of interesting we can see that what can + + + align:start position:0% +of interesting we can see that what can +we see from I already told you the big + + align:start position:0% +we see from I already told you the big + + + align:start position:0% +we see from I already told you the big +fact but what can we see from this uh + + align:start position:0% +fact but what can we see from this uh + + + align:start position:0% +fact but what can we see from this uh +what makes me think what why can I see + + align:start position:0% +what makes me think what why can I see + + + align:start position:0% +what makes me think what why can I see +why can I see almost intuitively that + + align:start position:0% +why can I see almost intuitively that + + + align:start position:0% +why can I see almost intuitively that +that or very quickly just by plotting + + align:start position:0% +that or very quickly just by plotting + + + align:start position:0% +that or very quickly just by plotting +these two that uh woman in the US tends + + align:start position:0% +these two that uh woman in the US tends + + + align:start position:0% +these two that uh woman in the US tends +to be uh be taller than women in in + + align:start position:0% +to be uh be taller than women in in + + + align:start position:0% +to be uh be taller than women in in +India + + align:start position:0% + + + + align:start position:0% + +yeah nutrition oh no I'm just that that + + align:start position:0% +yeah nutrition oh no I'm just that that + + + align:start position:0% +yeah nutrition oh no I'm just that that +is certainly a part of the explanation + + align:start position:0% +is certainly a part of the explanation + + + align:start position:0% +is certainly a part of the explanation +uh I I'll I'll get to the explanation or + + align:start position:0% +uh I I'll I'll get to the explanation or + + + align:start position:0% +uh I I'll I'll get to the explanation or +some explanations in a minute if you + + align:start position:0% +some explanations in a minute if you + + + align:start position:0% +some explanations in a minute if you +want but just as a matter of uh looking + + align:start position:0% +want but just as a matter of uh looking + + + align:start position:0% +want but just as a matter of uh looking +at the graphs why can we say immediately + + align:start position:0% +at the graphs why can we say immediately + + + align:start position:0% +at the graphs why can we say immediately +that woman yes the mean is for for us + + align:start position:0% +that woman yes the mean is for for us + + + align:start position:0% +that woman yes the mean is for for us +women is shifted towards the right + + align:start position:0% +women is shifted towards the right + + + align:start position:0% +women is shifted towards the right +exactly so so in this with with + + align:start position:0% +exactly so so in this with with + + + align:start position:0% +exactly so so in this with with +distribution that are B shaped like that + + align:start position:0% +distribution that are B shaped like that + + + align:start position:0% +distribution that are B shaped like that +the mean the mood and the median are all + + align:start position:0% +the mean the mood and the median are all + + + align:start position:0% +the mean the mood and the median are all +in the same place so we can uh uh so + + align:start position:0% +in the same place so we can uh uh so + + + align:start position:0% +in the same place so we can uh uh so +that's kind of the peak of the discri is + + align:start position:0% +that's kind of the peak of the discri is + + + align:start position:0% +that's kind of the peak of the discri is +very easy to see and we can see that it + + align:start position:0% +very easy to see and we can see that it + + + align:start position:0% +very easy to see and we can see that it +clearly has moved moved + + align:start position:0% +clearly has moved moved + + + align:start position:0% +clearly has moved moved +right + + align:start position:0% +right + + + align:start position:0% +right +um what might be a little bit uh harder + + align:start position:0% +um what might be a little bit uh harder + + + align:start position:0% +um what might be a little bit uh harder +to see from this picture is whether uh + + align:start position:0% +to see from this picture is whether uh + + + align:start position:0% +to see from this picture is whether uh +this is true at all level of the + + align:start position:0% +this is true at all level of the + + + align:start position:0% +this is true at all level of the +distribution or maybe uh or not yes I + + align:start position:0% +distribution or maybe uh or not yes I + + + align:start position:0% +distribution or maybe uh or not yes I +think in + + align:start position:0% + + + + align:start position:0% + +every called distribution + + align:start position:0% +every called distribution + + + align:start position:0% +every called distribution +us yes what what make you think + + align:start position:0% +us yes what what make you think + + + align:start position:0% +us yes what what make you think +that and and how do you to make this + + align:start position:0% +that and and how do you to make this + + + align:start position:0% +that and and how do you to make this +statement what did you need to look + + align:start position:0% +statement what did you need to look + + + align:start position:0% +statement what did you need to look +at with of the distribution and about + + align:start position:0% +at with of the distribution and about + + + align:start position:0% +at with of the distribution and about +how every away from the uh the average + + align:start position:0% +how every away from the uh the average + + + align:start position:0% +how every away from the uh the average +it's towards the right exactly so to to + + align:start position:0% +it's towards the right exactly so to to + + + align:start position:0% +it's towards the right exactly so to to +to to make the statement what you had to + + align:start position:0% +to to make the statement what you had to + + + align:start position:0% +to to make the statement what you had to +do was to look at surfaces it's a little + + align:start position:0% +do was to look at surfaces it's a little + + + align:start position:0% +do was to look at surfaces it's a little +bit hard but it's possible you know you + + align:start position:0% +bit hard but it's possible you know you + + + align:start position:0% +bit hard but it's possible you know you +kind of look at for every possible + + align:start position:0% +kind of look at for every possible + + + align:start position:0% +kind of look at for every possible +quantal um the probability that a woman + + align:start position:0% +quantal um the probability that a woman + + + align:start position:0% +quantal um the probability that a woman +is smaller than that quantal is given by + + align:start position:0% +is smaller than that quantal is given by + + + align:start position:0% +is smaller than that quantal is given by +the by the surface still here and it is + + align:start position:0% +the by the surface still here and it is + + + align:start position:0% +the by the surface still here and it is +true I think and one can given that the + + align:start position:0% +true I think and one can given that the + + + align:start position:0% +true I think and one can given that the +distribution the way the distribution + + align:start position:0% +distribution the way the distribution + + + align:start position:0% +distribution the way the distribution +are you can probably convince yourself + + align:start position:0% +are you can probably convince yourself + + + align:start position:0% +are you can probably convince yourself +here that all the triangles here are + + align:start position:0% +here that all the triangles here are + + + align:start position:0% +here that all the triangles here are +um um different than all the triangle on + + align:start position:0% +um um different than all the triangle on + + + align:start position:0% +um um different than all the triangle on +the red + + align:start position:0% +the red + + + align:start position:0% +the red +line uh but comparing triangle is not + + align:start position:0% +line uh but comparing triangle is not + + + align:start position:0% +line uh but comparing triangle is not +very easy so there would be a another if + + align:start position:0% +very easy so there would be a another if + + + align:start position:0% +very easy so there would be a another if +I had given you the data in another form + + align:start position:0% +I had given you the data in another form + + + align:start position:0% +I had given you the data in another form +it might have been a little bit easier + + align:start position:0% +it might have been a little bit easier + + + align:start position:0% +it might have been a little bit easier +for you to make this exact uh point + + align:start position:0% +for you to make this exact uh point + + + align:start position:0% +for you to make this exact uh point +which way would you like to have seen + + align:start position:0% +which way would you like to have seen + + + align:start position:0% +which way would you like to have seen +the the data which form would you like + + align:start position:0% +the the data which form would you like + + + align:start position:0% +the the data which form would you like +to see the data to really to to be able + + align:start position:0% +to see the data to really to to be able + + + align:start position:0% +to see the data to really to to be able +to make this this point that you made + + align:start position:0% +to make this this point that you made + + + align:start position:0% +to make this this point that you made +which is at every quantile uh the we + + align:start position:0% +which is at every quantile uh the we + + + align:start position:0% +which is at every quantile uh the we +seem to have fewer uh American women + + align:start position:0% +seem to have fewer uh American women + + + align:start position:0% +seem to have fewer uh American women +that are shorter to that uh to a + + align:start position:0% +that are shorter to that uh to a + + + align:start position:0% +that are shorter to that uh to a +particular uh level than others yeah s + + align:start position:0% +particular uh level than others yeah s + + + align:start position:0% +particular uh level than others yeah s +of use Z score for standard + + align:start position:0% +of use Z score for standard + + + align:start position:0% +of use Z score for standard +devation well then if you use if you + + align:start position:0% +devation well then if you use if you + + + align:start position:0% +devation well then if you use if you +standardize you're going to miss + + align:start position:0% +standardize you're going to miss + + + align:start position:0% +standardize you're going to miss +everything about levels so I think + + align:start position:0% +everything about levels so I think + + + align:start position:0% +everything about levels so I think +you're going to get if we were to + + align:start position:0% +you're going to get if we were to + + + align:start position:0% +you're going to get if we were to +standardize the data with so that they + + align:start position:0% +standardize the data with so that they + + + align:start position:0% +standardize the data with so that they +have the same mean and the same standard + + align:start position:0% +have the same mean and the same standard + + + align:start position:0% +have the same mean and the same standard +deviation I think you might find them to + + align:start position:0% +deviation I think you might find them to + + + align:start position:0% +deviation I think you might find them to +be similar because you would have + + align:start position:0% +be similar because you would have + + + align:start position:0% +be similar because you would have +removed what is different about them may + + align:start position:0% +removed what is different about them may + + + align:start position:0% +removed what is different about them may +a box plot box and whiskers oh so if we + + align:start position:0% +a box plot box and whiskers oh so if we + + + align:start position:0% +a box plot box and whiskers oh so if we +did a box and whisker plots what would + + align:start position:0% +did a box and whisker plots what would + + + align:start position:0% +did a box and whisker plots what would +we get from a box and whisker plots just + + align:start position:0% +we get from a box and whisker plots just + + + align:start position:0% +we get from a box and whisker plots just +to summarize for people who hav't will + + align:start position:0% +to summarize for people who hav't will + + + align:start position:0% +to summarize for people who hav't will +will see them we would see what is in + + align:start position:0% +will see them we would see what is in + + + align:start position:0% +will see them we would see what is in +the box and we tell us we see for the US + + align:start position:0% +the box and we tell us we see for the US + + + align:start position:0% +the box and we tell us we see for the US +women that it's it's again shifted + + align:start position:0% +women that it's it's again shifted + + + align:start position:0% +women that it's it's again shifted +towards the right and there are + + align:start position:0% +towards the right and there are + + + align:start position:0% +towards the right and there are +more so yeah I think it will be shifted + + align:start position:0% +more so yeah I think it will be shifted + + + align:start position:0% +more so yeah I think it will be shifted +towards the right exactly so that + + align:start position:0% +towards the right exactly so that + + + align:start position:0% +towards the right exactly so that +something is going to be true because + + align:start position:0% +something is going to be true because + + + align:start position:0% +something is going to be true because +the mean is shifted towards the right + + align:start position:0% +the mean is shifted towards the right + + + align:start position:0% +the mean is shifted towards the right +but with a box and whisker plot what + + align:start position:0% +but with a box and whisker plot what + + + align:start position:0% +but with a box and whisker plot what +would we had the the mean yes it would + + align:start position:0% +would we had the the mean yes it would + + + align:start position:0% +would we had the the mean yes it would +also the mean would be shifted also to + + align:start position:0% +also the mean would be shifted also to + + + align:start position:0% +also the mean would be shifted also to +the right for the United States women + + align:start position:0% +the right for the United States women + + + align:start position:0% +the right for the United States women +but also the would be larger and what is + + align:start position:0% +but also the would be larger and what is + + + align:start position:0% +but also the would be larger and what is +the box in the box and whisker the box + + align:start position:0% +the box in the box and whisker the box + + + align:start position:0% +the box in the box and whisker the box +is is the middle 50% yes and what are + + align:start position:0% +is is the middle 50% yes and what are + + + align:start position:0% +is is the middle 50% yes and what are +the whiskers are the outlier 25% each uh + + align:start position:0% +the whiskers are the outlier 25% each uh + + + align:start position:0% +the whiskers are the outlier 25% each uh +depending on on on your whiskers and + + align:start position:0% +depending on on on your whiskers and + + + align:start position:0% +depending on on on your whiskers and +sometimes the 95% Etc so it's it's + + align:start position:0% +sometimes the 95% Etc so it's it's + + + align:start position:0% +sometimes the 95% Etc so it's it's +already some data but it's not all the + + align:start position:0% +already some data but it's not all the + + + align:start position:0% +already some data but it's not all the +data so by write by plotting a box and + + align:start position:0% +data so by write by plotting a box and + + + align:start position:0% +data so by write by plotting a box and +whisker plots compared to that I'm still + + align:start position:0% +whisker plots compared to that I'm still + + + align:start position:0% +whisker plots compared to that I'm still +losing some of the I still cannot answer + + align:start position:0% +losing some of the I still cannot answer + + + align:start position:0% +losing some of the I still cannot answer +this question that is true at every + + align:start position:0% +this question that is true at every + + + align:start position:0% +this question that is true at every +Quant time yeah um the CDF yes we can + + align:start position:0% +Quant time yeah um the CDF yes we can + + + align:start position:0% +Quant time yeah um the CDF yes we can +also decide that okay from the PDF I can + + align:start position:0% +also decide that okay from the PDF I can + + + align:start position:0% +also decide that okay from the PDF I can +write I can instead I could plot the the + + align:start position:0% +write I can instead I could plot the the + + + align:start position:0% +write I can instead I could plot the the +PDF it's no different information it's a + + align:start position:0% +PDF it's no different information it's a + + + align:start position:0% +PDF it's no different information it's a +way of plotting it differently that will + + align:start position:0% +way of plotting it differently that will + + + align:start position:0% +way of plotting it differently that will +directly bring us to this fact um so you + + align:start position:0% +directly bring us to this fact um so you + + + align:start position:0% +directly bring us to this fact um so you +can do it in an histogram which is + + align:start position:0% +can do it in an histogram which is + + + align:start position:0% +can do it in an histogram which is +instead of plotting U instead of + + align:start position:0% +instead of plotting U instead of + + + align:start position:0% +instead of plotting U instead of +plotting an histogram you can plot a + + align:start position:0% +plotting an histogram you can plot a + + + align:start position:0% +plotting an histogram you can plot a +cumulative histogram which is at every + + align:start position:0% +cumulative histogram which is at every + + + align:start position:0% +cumulative histogram which is at every +bin you're not counting the number of + + align:start position:0% +bin you're not counting the number of + + + align:start position:0% +bin you're not counting the number of +cases that falls in that bin but you're + + align:start position:0% +cases that falls in that bin but you're + + + align:start position:0% +cases that falls in that bin but you're +counting the number of cases that falls + + align:start position:0% +counting the number of cases that falls + + + align:start position:0% +counting the number of cases that falls +in that in or below so the histogram is + + align:start position:0% +in that in or below so the histogram is + + + align:start position:0% +in that in or below so the histogram is +going to be non decreasing and uh till + + align:start position:0% +going to be non decreasing and uh till + + + align:start position:0% +going to be non decreasing and uh till +it gets to + + align:start position:0% +it gets to + + + align:start position:0% +it gets to +one or you can could I just just to + + align:start position:0% +one or you can could I just just to + + + align:start position:0% +one or you can could I just just to +clarify so if we think about a histogram + + align:start position:0% +clarify so if we think about a histogram + + + align:start position:0% +clarify so if we think about a histogram +for instance as an empirical counterpart + + align:start position:0% +for instance as an empirical counterpart + + + align:start position:0% +for instance as an empirical counterpart +for of a probability density function + + align:start position:0% +for of a probability density function + + + align:start position:0% +for of a probability density function +then what Esther's going to talk about + + align:start position:0% +then what Esther's going to talk about + + + align:start position:0% +then what Esther's going to talk about +is the empirical counterpart for a + + align:start position:0% +is the empirical counterpart for a + + + align:start position:0% +is the empirical counterpart for a +cumulative distribution exactly it's the + + align:start position:0% +cumulative distribution exactly it's the + + + align:start position:0% +cumulative distribution exactly it's the +CDF is a cumulative distribution + + align:start position:0% +CDF is a cumulative distribution + + + align:start position:0% +CDF is a cumulative distribution +function so the histogram will tell us + + align:start position:0% +function so the histogram will tell us + + + align:start position:0% +function so the histogram will tell us +the cumulative histogram will give us + + align:start position:0% +the cumulative histogram will give us + + + align:start position:0% +the cumulative histogram will give us +something that will look like a CDF but + + align:start position:0% +something that will look like a CDF but + + + align:start position:0% +something that will look like a CDF but +jigged or we can do it in a similar + + align:start position:0% +jigged or we can do it in a similar + + + align:start position:0% +jigged or we can do it in a similar +technique to a to a Kel using again R + + align:start position:0% +technique to a to a Kel using again R + + + align:start position:0% +technique to a to a Kel using again R +gives that to us for for free and we get + + align:start position:0% +gives that to us for for free and we get + + + align:start position:0% +gives that to us for for free and we get +our um descriptive representation or we + + align:start position:0% +our um descriptive representation or we + + + align:start position:0% +our um descriptive representation or we +get estimation of the cumulative + + align:start position:0% +get estimation of the cumulative + + + align:start position:0% +get estimation of the cumulative +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +function and there we can answer you we + + align:start position:0% +function and there we can answer you we + + + align:start position:0% +function and there we can answer you we +can immediately see the point that we + + align:start position:0% +can immediately see the point that we + + + align:start position:0% +can immediately see the point that we +saw with surfaces which is uh what can + + align:start position:0% +saw with surfaces which is uh what can + + + align:start position:0% +saw with surfaces which is uh what can +you say about the the US regard um + + align:start position:0% +you say about the the US regard um + + + align:start position:0% +you say about the the US regard um +compared to the bear + + align:start position:0% + + + + align:start position:0% + +curve so the US curve looks shifted to + + align:start position:0% +curve so the US curve looks shifted to + + + align:start position:0% +curve so the US curve looks shifted to +the right regarding regardless compared + + align:start position:0% +the right regarding regardless compared + + + align:start position:0% +the right regarding regardless compared +to the be be curve so what does it tell + + align:start position:0% +to the be be curve so what does it tell + + + align:start position:0% +to the be be curve so what does it tell +us it tells us that whatever the + + align:start position:0% +us it tells us that whatever the + + + align:start position:0% +us it tells us that whatever the +threshold that we + + align:start position:0% +threshold that we + + + align:start position:0% +threshold that we +pick there are more wom that are below + + align:start position:0% +pick there are more wom that are below + + + align:start position:0% +pick there are more wom that are below +this threshold in the in biha than they + + align:start position:0% +this threshold in the in biha than they + + + align:start position:0% +this threshold in the in biha than they +are in the US for example EX at a meter + + align:start position:0% +are in the US for example EX at a meter + + + align:start position:0% +are in the US for example EX at a meter +50 we have uh we have about uh let's + + align:start position:0% +50 we have uh we have about uh let's + + + align:start position:0% +50 we have uh we have about uh let's +say would what would you say 22 I'm + + align:start position:0% +say would what would you say 22 I'm + + + align:start position:0% +say would what would you say 22 I'm +making that up uh 22 uh women who are + + align:start position:0% +making that up uh 22 uh women who are + + + align:start position:0% +making that up uh 22 uh women who are +below uh in biha and we have uh less + + align:start position:0% +below uh in biha and we have uh less + + + align:start position:0% +below uh in biha and we have uh less +than 10% women who are below in uh in + + align:start position:0% +than 10% women who are below in uh in + + + align:start position:0% +than 10% women who are below in uh in +the US and we can repeat that exercise + + align:start position:0% +the US and we can repeat that exercise + + + align:start position:0% +the US and we can repeat that exercise +many times so it looks like of course + + align:start position:0% +many times so it looks like of course + + + align:start position:0% +many times so it looks like of course +eventually we will want to make to have + + align:start position:0% +eventually we will want to make to have + + + align:start position:0% +eventually we will want to make to have +a formal test of that uh but visually it + + align:start position:0% +a formal test of that uh but visually it + + + align:start position:0% +a formal test of that uh but visually it +does look like the the bear distribution + + align:start position:0% +does look like the the bear distribution + + + align:start position:0% +does look like the the bear distribution +is uh pushed to the right sorry the the + + align:start position:0% +is uh pushed to the right sorry the the + + + align:start position:0% +is uh pushed to the right sorry the the +Us distribution is pushed to the right + + align:start position:0% +Us distribution is pushed to the right + + + align:start position:0% +Us distribution is pushed to the right +compared to the be distribution and + + align:start position:0% +compared to the be distribution and + + + align:start position:0% +compared to the be distribution and +hence that what we would might might + + align:start position:0% +hence that what we would might might + + + align:start position:0% +hence that what we would might might +want to test is whether the be distribu + + align:start position:0% +want to test is whether the be distribu + + + align:start position:0% +want to test is whether the be distribu +the Us distribution first order + + align:start position:0% +the Us distribution first order + + + align:start position:0% +the Us distribution first order +stochastically dominate the um be + + align:start position:0% +stochastically dominate the um be + + + align:start position:0% +stochastically dominate the um be +distribution that is formally we we will + + align:start position:0% +distribution that is formally we we will + + + align:start position:0% +distribution that is formally we we will +want to test and we'll give you a test + + align:start position:0% +want to test and we'll give you a test + + + align:start position:0% +want to test and we'll give you a test +statistics for that when we come to that + + align:start position:0% +statistics for that when we come to that + + + align:start position:0% +statistics for that when we come to that +point uh that at every point in the + + align:start position:0% +point uh that at every point in the + + + align:start position:0% +point uh that at every point in the +distribution for every value of height + + align:start position:0% +distribution for every value of height + + + align:start position:0% +distribution for every value of height +there is more + + align:start position:0% +there is more + + + align:start position:0% +there is more +people in bead that are smaller to this + + align:start position:0% +people in bead that are smaller to this + + + align:start position:0% +people in bead that are smaller to this +value than they are in in the + + align:start position:0% +value than they are in in the + + + align:start position:0% +value than they are in in the +US so when might we prefer to plot CDF + + align:start position:0% +US so when might we prefer to plot CDF + + + align:start position:0% +US so when might we prefer to plot CDF +versus + + align:start position:0% +versus + + + align:start position:0% +versus +pdf Ling uh information is is is similar + + align:start position:0% +pdf Ling uh information is is is similar + + + align:start position:0% +pdf Ling uh information is is is similar +uh but uh when you're interested in + + align:start position:0% +uh but uh when you're interested in + + + align:start position:0% +uh but uh when you're interested in +probabilities for example when you're + + align:start position:0% +probabilities for example when you're + + + align:start position:0% +probabilities for example when you're +interested in making this type of + + align:start position:0% +interested in making this type of + + + align:start position:0% +interested in making this type of +statement representing uh the distrib + + align:start position:0% +statement representing uh the distrib + + + align:start position:0% +statement representing uh the distrib +the distribu the plotting the CDF or + + align:start position:0% +the distribu the plotting the CDF or + + + align:start position:0% +the distribu the plotting the CDF or +plotting an estimate of the CDF of the + + align:start position:0% +plotting an estimate of the CDF of the + + + align:start position:0% +plotting an estimate of the CDF of the +of the uh distribution is more + + align:start position:0% +of the uh distribution is more + + + align:start position:0% +of the uh distribution is more +conventional than plotting PDF often + + align:start position:0% +conventional than plotting PDF often + + + align:start position:0% +conventional than plotting PDF often +although people do both uh but you will + + align:start position:0% +although people do both uh but you will + + + align:start position:0% +although people do both uh but you will +see more often when people make try to + + align:start position:0% +see more often when people make try to + + + align:start position:0% +see more often when people make try to +make the argument try to argue exactly + + align:start position:0% +make the argument try to argue exactly + + + align:start position:0% +make the argument try to argue exactly +your point uh although you were able to + + align:start position:0% +your point uh although you were able to + + + align:start position:0% +your point uh although you were able to +do it with a PDF most people will do it + + align:start position:0% +do it with a PDF most people will do it + + + align:start position:0% +do it with a PDF most people will do it +with + + align:start position:0% +with + + + align:start position:0% +with +CDF there is a reason statistical reason + + align:start position:0% +CDF there is a reason statistical reason + + + align:start position:0% +CDF there is a reason statistical reason +which is the test that we are going to + + align:start position:0% +which is the test that we are going to + + + align:start position:0% +which is the test that we are going to +talk about is expressed in term of + + align:start position:0% +talk about is expressed in term of + + + align:start position:0% +talk about is expressed in term of +cumulative distribution function but + + align:start position:0% +cumulative distribution function but + + + align:start position:0% +cumulative distribution function but +there is also I think a more sort of uh + + align:start position:0% +there is also I think a more sort of uh + + + align:start position:0% +there is also I think a more sort of uh +something that has more to do with + + align:start position:0% +something that has more to do with + + + align:start position:0% +something that has more to do with +cognition and how we perceive things + + align:start position:0% +cognition and how we perceive things + + + align:start position:0% +cognition and how we perceive things +which is the the PDF represent + + align:start position:0% +which is the the PDF represent + + + align:start position:0% +which is the the PDF represent +probabilities to be in a particular + + align:start position:0% +probabilities to be in a particular + + + align:start position:0% +probabilities to be in a particular +interval to be smaller than a number or + + align:start position:0% +interval to be smaller than a number or + + + align:start position:0% +interval to be smaller than a number or +in a particular range or whatever you're + + align:start position:0% +in a particular range or whatever you're + + + align:start position:0% +in a particular range or whatever you're +interested with areas we had to look at + + align:start position:0% +interested with areas we had to look at + + + align:start position:0% +interested with areas we had to look at +triangles where the the PDF does it with + + align:start position:0% +triangles where the the PDF does it with + + + align:start position:0% +triangles where the the PDF does it with +vertical distance and it's a bit easier + + align:start position:0% +vertical distance and it's a bit easier + + + align:start position:0% +vertical distance and it's a bit easier +for the human eye to uh to compare + + align:start position:0% +for the human eye to uh to compare + + + align:start position:0% +for the human eye to uh to compare +distances than to compare areas we don't + + align:start position:0% +distances than to compare areas we don't + + + align:start position:0% +distances than to compare areas we don't +have to do we don't have to do the + + align:start position:0% +have to do we don't have to do the + + + align:start position:0% +have to do we don't have to do the +counting we don't have to integrate in + + align:start position:0% +counting we don't have to integrate in + + + align:start position:0% +counting we don't have to integrate in +our brain so if we're interested in + + align:start position:0% +our brain so if we're interested in + + + align:start position:0% +our brain so if we're interested in +areas then we might as well just it's + + align:start position:0% +areas then we might as well just it's + + + align:start position:0% +areas then we might as well just it's +it's much easier to do it uh with the + + align:start position:0% +it's much easier to do it uh with the + + + align:start position:0% +it's much easier to do it uh with the +CDF we can see that it is true + + align:start position:0% +CDF we can see that it is true + + + align:start position:0% +CDF we can see that it is true +everywhere that the the CDF of the US is + + align:start position:0% +everywhere that the the CDF of the US is + + + align:start position:0% +everywhere that the the CDF of the US is +below CDF of the beha so that's uh I + + align:start position:0% +below CDF of the beha so that's uh I + + + align:start position:0% +below CDF of the beha so that's uh I +think that's kind of a reason why uh um + + align:start position:0% +think that's kind of a reason why uh um + + + align:start position:0% +think that's kind of a reason why uh um +I at least personally much prefer to see + + align:start position:0% +I at least personally much prefer to see + + + align:start position:0% +I at least personally much prefer to see +CDF than PDF when this type of question + + align:start position:0% +CDF than PDF when this type of question + + + align:start position:0% +CDF than PDF when this type of question +are being asked on the other hand + + align:start position:0% +are being asked on the other hand + + + align:start position:0% +are being asked on the other hand +sometimes you might be interested in + + align:start position:0% +sometimes you might be interested in + + + align:start position:0% +sometimes you might be interested in +densities not um not uh probabilities + + align:start position:0% +densities not um not uh probabilities + + + align:start position:0% +densities not um not uh probabilities +but both the CDF and the PDF shows + + align:start position:0% +but both the CDF and the PDF shows + + + align:start position:0% +but both the CDF and the PDF shows +density but to get the density from a + + align:start position:0% +density but to get the density from a + + + align:start position:0% +density but to get the density from a +CDF you you need to take the slope so + + align:start position:0% +CDF you you need to take the slope so + + + align:start position:0% +CDF you you need to take the slope so +you need to take derivative in your in + + align:start position:0% +you need to take derivative in your in + + + align:start position:0% +you need to take derivative in your in +your head which you can do but it's a + + align:start position:0% +your head which you can do but it's a + + + align:start position:0% +your head which you can do but it's a +little bit unintuitive where the the the + + align:start position:0% +little bit unintuitive where the the the + + + align:start position:0% +little bit unintuitive where the the the +PDF the gives it to you by distance + + align:start position:0% +PDF the gives it to you by distance + + + align:start position:0% +PDF the gives it to you by distance +which is easier for us to look at so if + + align:start position:0% +which is easier for us to look at so if + + + align:start position:0% +which is easier for us to look at so if +you're interested for example in knowing + + align:start position:0% +you're interested for example in knowing + + + align:start position:0% +you're interested for example in knowing +where the mode of the distribution is uh + + align:start position:0% +where the mode of the distribution is uh + + + align:start position:0% +where the mode of the distribution is uh +whether the distribution looks + + align:start position:0% +whether the distribution looks + + + align:start position:0% +whether the distribution looks +symmetrical or not whether it looks hu + + align:start position:0% +symmetrical or not whether it looks hu + + + align:start position:0% +symmetrical or not whether it looks hu +or not or stuff like that it is possible + + align:start position:0% +or not or stuff like that it is possible + + + align:start position:0% +or not or stuff like that it is possible +to to do it from a PDF but it's much + + align:start position:0% +to to do it from a PDF but it's much + + + align:start position:0% +to to do it from a PDF but it's much +less good from a CDF but it's much less + + align:start position:0% +less good from a CDF but it's much less + + + align:start position:0% +less good from a CDF but it's much less +good so typically you're going to plot a + + align:start position:0% +good so typically you're going to plot a + + + align:start position:0% +good so typically you're going to plot a +PDF okay uh so that's the and then + + align:start position:0% +PDF okay uh so that's the and then + + + align:start position:0% +PDF okay uh so that's the and then +generally you of course for at least for + + align:start position:0% +generally you of course for at least for + + + align:start position:0% +generally you of course for at least for +your own eyes you need to be able to go + + align:start position:0% +your own eyes you need to be able to go + + + align:start position:0% +your own eyes you need to be able to go +from one to the other and uh and then + + align:start position:0% +from one to the other and uh and then + + + align:start position:0% +from one to the other and uh and then +you're going to choose uh depending on + + align:start position:0% +you're going to choose uh depending on + + + align:start position:0% +you're going to choose uh depending on +the argument you're trying to make what + + align:start position:0% +the argument you're trying to make what + + + align:start position:0% +the argument you're trying to make what +is going to be visually represented in + + align:start position:0% +is going to be visually represented in + + + align:start position:0% +is going to be visually represented in +your presentations at the end of the day + + align:start position:0% +your presentations at the end of the day + + + align:start position:0% +your presentations at the end of the day +okay so I hope you are super excited + + align:start position:0% +okay so I hope you are super excited + + + align:start position:0% +okay so I hope you are super excited +because I've given you a very new novel + + align:start position:0% +because I've given you a very new novel + + + align:start position:0% +because I've given you a very new novel +fact that American women are taller than + + align:start position:0% +fact that American women are taller than + + + align:start position:0% +fact that American women are taller than +Indian women so it was worth three + + align:start position:0% +Indian women so it was worth three + + + align:start position:0% +Indian women so it was worth three +lectures of probability and statistic to + + align:start position:0% +lectures of probability and statistic to + + + align:start position:0% +lectures of probability and statistic to +get to that + + align:start position:0% +get to that + + + align:start position:0% +get to that +point + + align:start position:0% +point + + + align:start position:0% +point +uh okay uh we even have an explanation + + align:start position:0% +uh okay uh we even have an explanation + + + align:start position:0% +uh okay uh we even have an explanation +for it it might be + + align:start position:0% +for it it might be + + + align:start position:0% +for it it might be +nutrition although some people have + + align:start position:0% +nutrition although some people have + + + align:start position:0% +nutrition although some people have +argued this about jeans little aside + + align:start position:0% +argued this about jeans little aside + + + align:start position:0% +argued this about jeans little aside +while we are + + align:start position:0% +while we are + + + align:start position:0% +while we are +it uh what would be an empirical + + align:start position:0% +it uh what would be an empirical + + + align:start position:0% +it uh what would be an empirical +strategy to uh distinguish between the + + align:start position:0% +strategy to uh distinguish between the + + + align:start position:0% +strategy to uh distinguish between the +two I found somebody who's genetically + + align:start position:0% +two I found somebody who's genetically + + + align:start position:0% +two I found somebody who's genetically +Indian but grew up in terms of like the + + align:start position:0% +Indian but grew up in terms of like the + + + align:start position:0% +Indian but grew up in terms of like the +same nutrition as the United States yes + + align:start position:0% +same nutrition as the United States yes + + + align:start position:0% +same nutrition as the United States yes +so for example myself + + align:start position:0% +so for example myself + + + align:start position:0% +so for example myself +yourself you're pretty + + align:start position:0% +yourself you're pretty + + + align:start position:0% +yourself you're pretty +tall uh + + align:start position:0% +tall uh + + + align:start position:0% +tall uh +so + + align:start position:0% + + + + align:start position:0% + +uh so that would be a good so if we did + + align:start position:0% +uh so that would be a good so if we did + + + align:start position:0% +uh so that would be a good so if we did +that + + align:start position:0% +that + + + align:start position:0% +that +if we plotted that we would have the + + align:start position:0% +if we plotted that we would have the + + + align:start position:0% +if we plotted that we would have the +first generation the children of uh of + + align:start position:0% +first generation the children of uh of + + + align:start position:0% +first generation the children of uh of +Indian + + align:start position:0% +Indian + + + align:start position:0% +Indian +immigrant said take Indian immigrants + + align:start position:0% +immigrant said take Indian immigrants + + + align:start position:0% +immigrant said take Indian immigrants +were your parents born in India so uh + + align:start position:0% +were your parents born in India so uh + + + align:start position:0% +were your parents born in India so uh +and your name is k say it again kotan so + + align:start position:0% +and your name is k say it again kotan so + + + align:start position:0% +and your name is k say it again kotan so +kyan's SP were born and brought up in + + align:start position:0% +kyan's SP were born and brought up in + + + align:start position:0% +kyan's SP were born and brought up in +India and he was born here uh uh and of + + align:start position:0% +India and he was born here uh uh and of + + + align:start position:0% +India and he was born here uh uh and of +course he's a male which sort of screws + + align:start position:0% +course he's a male which sort of screws + + + align:start position:0% +course he's a male which sort of screws +a bit example but if if he had been a + + align:start position:0% +a bit example but if if he had been a + + + align:start position:0% +a bit example but if if he had been a +female uh he the distribution actually + + align:start position:0% +female uh he the distribution actually + + + align:start position:0% +female uh he the distribution actually +of uh of people like him who are female + + align:start position:0% +of uh of people like him who are female + + + align:start position:0% +of uh of people like him who are female +instead uh is exactly in between the two + + align:start position:0% +instead uh is exactly in between the two + + + align:start position:0% +instead uh is exactly in between the two +so it's first order stochastically + + align:start position:0% +so it's first order stochastically + + + align:start position:0% +so it's first order stochastically +dominates the uh Indian uh woman and + + align:start position:0% +dominates the uh Indian uh woman and + + + align:start position:0% +dominates the uh Indian uh woman and +it's uh and the US kids first all St + + align:start position:0% +it's uh and the US kids first all St + + + align:start position:0% +it's uh and the US kids first all St +stochastically dominate first generation + + align:start position:0% +stochastically dominate first generation + + + align:start position:0% +stochastically dominate first generation +immigrant uh does that tell us we are + + align:start position:0% +immigrant uh does that tell us we are + + + align:start position:0% +immigrant uh does that tell us we are +about half half half Gene half + + align:start position:0% + + + + align:start position:0% + +nutrition why because we're only because + + align:start position:0% +nutrition why because we're only because + + + align:start position:0% +nutrition why because we're only because +it still didn't give us any cause we + + align:start position:0% +it still didn't give us any cause we + + + align:start position:0% +it still didn't give us any cause we +just changed one yes so we don't know + + align:start position:0% +just changed one yes so we don't know + + + align:start position:0% +just changed one yes so we don't know +that specifically genetics that causes + + align:start position:0% +that specifically genetics that causes + + + align:start position:0% +that specifically genetics that causes +the that difference yes so that's that's + + align:start position:0% +the that difference yes so that's that's + + + align:start position:0% +the that difference yes so that's that's +one thing yes there's also other omed + + align:start position:0% +one thing yes there's also other omed + + + align:start position:0% +one thing yes there's also other omed +variables altitude could be one the + + align:start position:0% +variables altitude could be one the + + + align:start position:0% +variables altitude could be one the +amount of oxygen you're growing up yes + + align:start position:0% +amount of oxygen you're growing up yes + + + align:start position:0% +amount of oxygen you're growing up yes +so that is all the other stuff going up + + align:start position:0% +so that is all the other stuff going up + + + align:start position:0% +so that is all the other stuff going up +and + + align:start position:0% +and + + + align:start position:0% +and +uh is another reason yes maybe it would + + align:start position:0% +uh is another reason yes maybe it would + + + align:start position:0% +uh is another reason yes maybe it would +also be worth looking at more than just + + align:start position:0% +also be worth looking at more than just + + + align:start position:0% +also be worth looking at more than just +one generation exactly so what if we + + align:start position:0% +one generation exactly so what if we + + + align:start position:0% +one generation exactly so what if we +looked at grandchildren is there do we + + align:start position:0% +looked at grandchildren is there do we + + + align:start position:0% +looked at grandchildren is there do we +have grandchilden + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% +here + + + align:start position:0% +here +yes so if we looked at + + align:start position:0% +yes so if we looked at + + + align:start position:0% +yes so if we looked at +grandchildren would you have a guess + + align:start position:0% +grandchildren would you have a guess + + + align:start position:0% +grandchildren would you have a guess +where we would + + align:start position:0% + + + + align:start position:0% + +be yeah be back toward the US yes + + align:start position:0% +be yeah be back toward the US yes + + + align:start position:0% +be yeah be back toward the US yes +they're pretty much in the same + + align:start position:0% +they're pretty much in the same + + + align:start position:0% +they're pretty much in the same +place so the grandchildren are pretty + + align:start position:0% +place so the grandchildren are pretty + + + align:start position:0% +place so the grandchildren are pretty +much in the same place so the the + + align:start position:0% +much in the same place so the the + + + align:start position:0% +much in the same place so the the +problem with children is that uh um I + + align:start position:0% +problem with children is that uh um I + + + align:start position:0% +problem with children is that uh um I +don't know if it's a problem but the + + align:start position:0% +don't know if it's a problem but the + + + align:start position:0% +don't know if it's a problem but the +fact we still learn is that uh so it it + + align:start position:0% +fact we still learn is that uh so it it + + + align:start position:0% +fact we still learn is that uh so it it +turns out that when you grow up in a in + + align:start position:0% +turns out that when you grow up in a in + + + align:start position:0% +turns out that when you grow up in a in +a with poor + + align:start position:0% +a with poor + + + align:start position:0% +a with poor +nutrition your uh uh your + + align:start position:0% +nutrition your uh uh your + + + align:start position:0% +nutrition your uh uh your +your your entire body gets affected + + align:start position:0% +your your entire body gets affected + + + align:start position:0% +your your entire body gets affected +including your reproductive cells such + + align:start position:0% +including your reproductive cells such + + + align:start position:0% +including your reproductive cells such +that uh your parents probably uh got + + align:start position:0% +that uh your parents probably uh got + + + align:start position:0% +that uh your parents probably uh got +assuming they the uh they didn't that + + align:start position:0% +assuming they the uh they didn't that + + + align:start position:0% +assuming they the uh they didn't that +they grew up or the parents the of the + + align:start position:0% +they grew up or the parents the of the + + + align:start position:0% +they grew up or the parents the of the +average immigrant person I I know + + align:start position:0% +average immigrant person I I know + + + align:start position:0% +average immigrant person I I know +nothing about your parents but if your + + align:start position:0% +nothing about your parents but if your + + + align:start position:0% +nothing about your parents but if your +parents grew up in a place where they + + align:start position:0% +parents grew up in a place where they + + + align:start position:0% +parents grew up in a place where they +didn't get very good + + align:start position:0% +didn't get very good + + + align:start position:0% +didn't get very good +nutrition uh there is what they call EP + + align:start position:0% +nutrition uh there is what they call EP + + + align:start position:0% +nutrition uh there is what they call EP +EP epigenetic modification of the uh of + + align:start position:0% +EP epigenetic modification of the uh of + + + align:start position:0% +EP epigenetic modification of the uh of +the reproductive cells which means that + + align:start position:0% +the reproductive cells which means that + + + align:start position:0% +the reproductive cells which means that +the children of people who are + + align:start position:0% +the children of people who are + + + align:start position:0% +the children of people who are +themselves uh not po not properly + + align:start position:0% +themselves uh not po not properly + + + align:start position:0% +themselves uh not po not properly +nourished will not reach their will also + + align:start position:0% +nourished will not reach their will also + + + align:start position:0% +nourished will not reach their will also +be + + align:start position:0% +be + + + align:start position:0% +be +smaller but meaning they will not reach + + align:start position:0% +smaller but meaning they will not reach + + + align:start position:0% +smaller but meaning they will not reach +their gen potential but Grand the + + align:start position:0% +their gen potential but Grand the + + + align:start position:0% +their gen potential but Grand the +children of these people because there + + align:start position:0% +children of these people because there + + + align:start position:0% +children of these people because there +is no epigenetic modification of these + + align:start position:0% +is no epigenetic modification of these + + + align:start position:0% +is no epigenetic modification of these +guys because they were perfectly well + + align:start position:0% +guys because they were perfectly well + + + align:start position:0% +guys because they were perfectly well +nourished from the beginning the + + align:start position:0% +nourished from the beginning the + + + align:start position:0% +nourished from the beginning the +children of these people so the + + align:start position:0% +children of these people so the + + + align:start position:0% +children of these people so the +grandchildren of the Immigrant will be + + align:start position:0% +grandchildren of the Immigrant will be + + + align:start position:0% +grandchildren of the Immigrant will be +back to uh full possibility so in order + + align:start position:0% +back to uh full possibility so in order + + + align:start position:0% +back to uh full possibility so in order +to look at the genetic things we need to + + align:start position:0% +to look at the genetic things we need to + + + align:start position:0% +to look at the genetic things we need to +look at more than one + + align:start position:0% +look at more than one + + + align:start position:0% +look at more than one +generation um in the same way like so + + align:start position:0% +generation um in the same way like so + + + align:start position:0% +generation um in the same way like so +you we had one question here I just want + + align:start position:0% +you we had one question here I just want + + + align:start position:0% +you we had one question here I just want +to understand how do you use the word + + align:start position:0% +to understand how do you use the word + + + align:start position:0% +to understand how do you use the word +first order first order stochastic + + align:start position:0% +first order first order stochastic + + + align:start position:0% +first order first order stochastic +dominance why first order first order + + align:start position:0% +dominance why first order first order + + + align:start position:0% +dominance why first order first order +stasic dominance is about uh uh um the + + align:start position:0% +stasic dominance is about uh uh um the + + + align:start position:0% +stasic dominance is about uh uh um the +the fraction of people who are below a + + align:start position:0% +the fraction of people who are below a + + + align:start position:0% +the fraction of people who are below a +certain height uh so first order + + align:start position:0% +certain height uh so first order + + + align:start position:0% +certain height uh so first order +distribution first order St stas + + align:start position:0% +distribution first order St stas + + + align:start position:0% +distribution first order St stas +dominate another one if the probability + + align:start position:0% +dominate another one if the probability + + + align:start position:0% +dominate another one if the probability +to be below a certain height is uh + + align:start position:0% +to be below a certain height is uh + + + align:start position:0% +to be below a certain height is uh +smaller regardless of the of the + + align:start position:0% +smaller regardless of the of the + + + align:start position:0% +smaller regardless of the of the +threshold second order stochastic + + align:start position:0% +threshold second order stochastic + + + align:start position:0% +threshold second order stochastic +dominance is if maybe it doesn't but the + + align:start position:0% +dominance is if maybe it doesn't but the + + + align:start position:0% +dominance is if maybe it doesn't but the +variance is smaller at each of these + + align:start position:0% +variance is smaller at each of these + + + align:start position:0% +variance is smaller at each of these +point so we'll we'll get back and write + + align:start position:0% +point so we'll we'll get back and write + + + align:start position:0% +point so we'll we'll get back and write +down formally those distribution as we + + align:start position:0% +down formally those distribution as we + + + align:start position:0% +down formally those distribution as we +go to as we move to statistics but + + align:start position:0% +go to as we move to statistics but + + + align:start position:0% +go to as we move to statistics but +that's the that's the reason okay this + + align:start position:0% +that's the that's the reason okay this + + + align:start position:0% +that's the that's the reason okay this +was an aside in order to make that graph + + align:start position:0% +was an aside in order to make that graph + + + align:start position:0% +was an aside in order to make that graph +interesting for for five minutes uh but + + align:start position:0% +interesting for for five minutes uh but + + + align:start position:0% +interesting for for five minutes uh but +much more interesting we can go back to + + align:start position:0% +much more interesting we can go back to + + + align:start position:0% +much more interesting we can go back to +Mr Steph Curry and uh and and plot uh uh + + align:start position:0% +Mr Steph Curry and uh and and plot uh uh + + + align:start position:0% +Mr Steph Curry and uh and and plot uh uh +CDF commited distribution of uh so + + align:start position:0% +CDF commited distribution of uh so + + + align:start position:0% +CDF commited distribution of uh so +someone make I think it's kotan actually + + align:start position:0% +someone make I think it's kotan actually + + + align:start position:0% +someone make I think it's kotan actually +made the claim someone made the claim + + align:start position:0% +made the claim someone made the claim + + + align:start position:0% +made the claim someone made the claim +the Bold claim that he might have been + + align:start position:0% +the Bold claim that he might have been + + + align:start position:0% +the Bold claim that he might have been +the best um three-point shooter is that + + align:start position:0% +the best um three-point shooter is that + + + align:start position:0% +the best um three-point shooter is that +the point shooter absolute shooter in in + + align:start position:0% +the point shooter absolute shooter in in + + + align:start position:0% +the point shooter absolute shooter in in +the history of uh of + + align:start position:0% +the history of uh of + + + align:start position:0% +the history of uh of +basketball so in order + + align:start position:0% +basketball so in order + + + align:start position:0% +basketball so in order +to check this claim we should have given + + align:start position:0% +to check this claim we should have given + + + align:start position:0% +to check this claim we should have given +you more data than that but uh this are + + align:start position:0% +you more data than that but uh this are + + + align:start position:0% +you more data than that but uh this are +at least him compared to a couple of + + align:start position:0% +at least him compared to a couple of + + + align:start position:0% +at least him compared to a couple of +other Contender for that title according + + align:start position:0% +other Contender for that title according + + + align:start position:0% +other Contender for that title according +to knowledge I don't have so you don't + + align:start position:0% +to knowledge I don't have so you don't + + + align:start position:0% +to knowledge I don't have so you don't +ask questions on that oh if you ask them + + align:start position:0% +ask questions on that oh if you ask them + + + align:start position:0% +ask questions on that oh if you ask them +you direct them to Sarah over here uh it + + align:start position:0% +you direct them to Sarah over here uh it + + + align:start position:0% +you direct them to Sarah over here uh it +looks in fact that the the colors are + + align:start position:0% +looks in fact that the the colors are + + + align:start position:0% +looks in fact that the the colors are +all a little bit blue but uh uh Steph + + align:start position:0% +all a little bit blue but uh uh Steph + + + align:start position:0% +all a little bit blue but uh uh Steph +Curry is the darker here and it looks in + + align:start position:0% +Curry is the darker here and it looks in + + + align:start position:0% +Curry is the darker here and it looks in +fact that the distribution of the um the + + align:start position:0% +fact that the distribution of the um the + + + align:start position:0% +fact that the distribution of the um the +distribution of his shots in term of + + align:start position:0% +distribution of his shots in term of + + + align:start position:0% +distribution of his shots in term of +where he took the where he took the shot + + align:start position:0% +where he took the where he took the shot + + + align:start position:0% +where he took the where he took the shot +from distance to the basket + + align:start position:0% +from distance to the basket + + + align:start position:0% +from distance to the basket +stochastically dominates are LeBron + + align:start position:0% +stochastically dominates are LeBron + + + align:start position:0% +stochastically dominates are LeBron +James and Kevin Kevin + + align:start position:0% +James and Kevin Kevin + + + align:start position:0% +James and Kevin Kevin +Durant uh so you might say well it's + + align:start position:0% +Durant uh so you might say well it's + + + align:start position:0% +Durant uh so you might say well it's +easier because you can try but in fact + + align:start position:0% +easier because you can try but in fact + + + align:start position:0% +easier because you can try but in fact +when you look at successes successful + + align:start position:0% +when you look at successes successful + + + align:start position:0% +when you look at successes successful +shots it's it's true as well so Steph + + align:start position:0% +shots it's it's true as well so Steph + + + align:start position:0% +shots it's it's true as well so Steph +Curry is in fact maybe the best shooter + + align:start position:0% +Curry is in fact maybe the best shooter + + + align:start position:0% +Curry is in fact maybe the best shooter +in NBA history uh there's SM data to + + align:start position:0% +in NBA history uh there's SM data to + + + align:start position:0% +in NBA history uh there's SM data to +make that Pro to prove that point if + + align:start position:0% +make that Pro to prove that point if + + + align:start position:0% +make that Pro to prove that point if +you're interested uh but that's not the + + align:start position:0% +you're interested uh but that's not the + + + align:start position:0% +you're interested uh but that's not the +only thing we might be interested about + + align:start position:0% +only thing we might be interested about + + + align:start position:0% +only thing we might be interested about +him about with him in fact one thing we + + align:start position:0% +him about with him in fact one thing we + + + align:start position:0% +him about with him in fact one thing we +might be interested in is where he + + align:start position:0% +might be interested in is where he + + + align:start position:0% +might be interested in is where he +shoots + + align:start position:0% +shoots + + + align:start position:0% +shoots +from um and + + align:start position:0% +from um and + + + align:start position:0% +from um and +uh there are two places to consider + + align:start position:0% +uh there are two places to consider + + + align:start position:0% +uh there are two places to consider +since the basketball court is a plane is + + align:start position:0% +since the basketball court is a plane is + + + align:start position:0% +since the basketball court is a plane is +uh the distance from the the the + + align:start position:0% +uh the distance from the the the + + + align:start position:0% +uh the distance from the the the +horizontal distance from the basket the + + align:start position:0% +horizontal distance from the basket the + + + align:start position:0% +horizontal distance from the basket the +distance like from the where is to the + + align:start position:0% +distance like from the where is to the + + + align:start position:0% +distance like from the where is to the +basket in this way and then if he on the + + align:start position:0% +basket in this way and then if he on the + + + align:start position:0% +basket in this way and then if he on the +side or not on the side so distance to + + align:start position:0% +side or not on the side so distance to + + + align:start position:0% +side or not on the side so distance to +the Bas line and distance from the + + align:start position:0% +the Bas line and distance from the + + + align:start position:0% +the Bas line and distance from the +sideline or I'm going to do it with + + align:start position:0% +sideline or I'm going to do it with + + + align:start position:0% +sideline or I'm going to do it with +respect to the midline of the court so + + align:start position:0% +respect to the midline of the court so + + + align:start position:0% +respect to the midline of the court so +if I plot each of them separated see + + align:start position:0% +if I plot each of them separated see + + + align:start position:0% +if I plot each of them separated see +here is the basketball + + align:start position:0% +here is the basketball + + + align:start position:0% +here is the basketball +court uh so I'm going to call the + + align:start position:0% +court uh so I'm going to call the + + + align:start position:0% +court uh so I'm going to call the +midline line that's not uh that's not + + align:start position:0% +midline line that's not uh that's not + + + align:start position:0% +midline line that's not uh that's not +this design here but it goes from 0 to + + align:start position:0% +this design here but it goes from 0 to + + + align:start position:0% +this design here but it goes from 0 to +minus 25 and then the distance from Bas + + align:start position:0% +minus 25 and then the distance from Bas + + + align:start position:0% +minus 25 and then the distance from Bas +line is uh you know suppose this is zero + + align:start position:0% +line is uh you know suppose this is zero + + + align:start position:0% +line is uh you know suppose this is zero +till 94 + + align:start position:0% +till 94 + + + align:start position:0% +till 94 +principle uh you can shut from anywhere + + align:start position:0% +principle uh you can shut from anywhere + + + align:start position:0% +principle uh you can shut from anywhere +you want but you'll get more points if + + align:start position:0% +you want but you'll get more points if + + + align:start position:0% +you want but you'll get more points if +you shoot from here and of course it's + + align:start position:0% +you shoot from here and of course it's + + + align:start position:0% +you shoot from here and of course it's +going to be much much easier if you are + + align:start position:0% +going to be much much easier if you are + + + align:start position:0% +going to be much much easier if you are +right below the basket so uh so what if + + align:start position:0% +right below the basket so uh so what if + + + align:start position:0% +right below the basket so uh so what if +I so if I were to plot uh either uh + + align:start position:0% +I so if I were to plot uh either uh + + + align:start position:0% +I so if I were to plot uh either uh +distribution so I could be interested in + + align:start position:0% +distribution so I could be interested in + + + align:start position:0% +distribution so I could be interested in +distance from the Baseline of Court + + align:start position:0% +distance from the Baseline of Court + + + align:start position:0% +distance from the Baseline of Court +what's interesting here I FL the + + align:start position:0% +what's interesting here I FL the + + + align:start position:0% +what's interesting here I FL the +histogram and and the canel with the + + align:start position:0% +histogram and and the canel with the + + + align:start position:0% +histogram and and the canel with the +optimal bway what what's what comes out + + align:start position:0% +optimal bway what what's what comes out + + + align:start position:0% +optimal bway what what's what comes out +of + + align:start position:0% + + + + align:start position:0% + +this yeah that huge Peak yes could be + + align:start position:0% +this yeah that huge Peak yes could be + + + align:start position:0% +this yeah that huge Peak yes could be +due to free throw shots maybe uh that um + + align:start position:0% +due to free throw shots maybe uh that um + + + align:start position:0% +due to free throw shots maybe uh that um +shots are not in the + + align:start position:0% + + + + align:start position:0% + +data so what's a huge speak even I would + + align:start position:0% +data so what's a huge speak even I would + + + align:start position:0% +data so what's a huge speak even I would +know that yeah would it be that you know + + align:start position:0% +know that yeah would it be that you know + + + align:start position:0% +know that yeah would it be that you know +say like five 5 ft away is like where + + align:start position:0% +say like five 5 ft away is like where + + + align:start position:0% +say like five 5 ft away is like where +they start jumping to junk yeah you can + + align:start position:0% +they start jumping to junk yeah you can + + + align:start position:0% +they start jumping to junk yeah you can +just junk and exactly so that's we have + + align:start position:0% +just junk and exactly so that's we have + + + align:start position:0% +just junk and exactly so that's we have +a peak there and then we seem to have + + align:start position:0% +a peak there and then we seem to have + + + align:start position:0% +a peak there and then we seem to have +something over here so as we go they + + align:start position:0% +something over here so as we go they + + + align:start position:0% +something over here so as we go they +seem to be kind of the further is then + + align:start position:0% +seem to be kind of the further is then + + + align:start position:0% +seem to be kind of the further is then +there's not too many shots within a + + align:start position:0% +there's not too many shots within a + + + align:start position:0% +there's not too many shots within a +close distance then it start kind of + + align:start position:0% +close distance then it start kind of + + + align:start position:0% +close distance then it start kind of +going up but in a smooth way maybe + + align:start position:0% +going up but in a smooth way maybe + + + align:start position:0% +going up but in a smooth way maybe +nothing very I mean it's it's kind of + + align:start position:0% +nothing very I mean it's it's kind of + + + align:start position:0% +nothing very I mean it's it's kind of +hard to interpret exactly what's going + + align:start position:0% +hard to interpret exactly what's going + + + align:start position:0% +hard to interpret exactly what's going +on here so the peak we understand quite + + align:start position:0% +on here so the peak we understand quite + + + align:start position:0% +on here so the peak we understand quite +well well but then the throw and why it + + align:start position:0% +well well but then the throw and why it + + + align:start position:0% +well well but then the throw and why it +goes slowly not fully + + align:start position:0% +goes slowly not fully + + + align:start position:0% +goes slowly not fully +clear uh and if I did that we already we + + align:start position:0% +clear uh and if I did that we already we + + + align:start position:0% +clear uh and if I did that we already we +already you already saw this + + align:start position:0% +already you already saw this + + + align:start position:0% +already you already saw this +picture uh from the midline of Court + + align:start position:0% +picture uh from the midline of Court + + + align:start position:0% +picture uh from the midline of Court +likewise we have a big peek at zero + + align:start position:0% +likewise we have a big peek at zero + + + align:start position:0% +likewise we have a big peek at zero +because they are right under the the + + align:start position:0% +because they are right under the the + + + align:start position:0% +because they are right under the the +basket but then at the then it's kind of + + align:start position:0% +basket but then at the then it's kind of + + + align:start position:0% +basket but then at the then it's kind of +slows is really maybe it's trying to go + + align:start position:0% +slows is really maybe it's trying to go + + + align:start position:0% +slows is really maybe it's trying to go +up again we might miss it if we if we + + align:start position:0% +up again we might miss it if we if we + + + align:start position:0% +up again we might miss it if we if we +have to smooth bound that we discuss but + + align:start position:0% +have to smooth bound that we discuss but + + + align:start position:0% +have to smooth bound that we discuss but +it seem seems to be a bit so what's + + align:start position:0% +it seem seems to be a bit so what's + + + align:start position:0% +it seem seems to be a bit so what's +going on here what am I missing by + + align:start position:0% +going on here what am I missing by + + + align:start position:0% +going on here what am I missing by +plotting them the distance to midline + + align:start position:0% +plotting them the distance to midline + + + align:start position:0% +plotting them the distance to midline +and distance to to Bas line + + align:start position:0% + + + + align:start position:0% + +separately yeah since it's like radio it + + align:start position:0% +separately yeah since it's like radio it + + + align:start position:0% +separately yeah since it's like radio it +might be that he was you can interpret + + align:start position:0% +might be that he was you can interpret + + + align:start position:0% +might be that he was you can interpret +that oh he's better at shooting fre like + + align:start position:0% +that oh he's better at shooting fre like + + + align:start position:0% +that oh he's better at shooting fre like +symmetrically or you can interpret it as + + align:start position:0% +symmetrically or you can interpret it as + + + align:start position:0% +symmetrically or you can interpret it as +like oh he's better when he's + + align:start position:0% +like oh he's better when he's + + + align:start position:0% +like oh he's better when he's +closer near the basket so you can really + + align:start position:0% +closer near the basket so you can really + + + align:start position:0% +closer near the basket so you can really +it's like that he prefers to sho from + + align:start position:0% +it's like that he prefers to sho from + + + align:start position:0% +it's like that he prefers to sho from +the metal or if he's + + align:start position:0% +the metal or if he's + + + align:start position:0% +the metal or if he's +actually yeah and in particular because + + align:start position:0% +actually yeah and in particular because + + + align:start position:0% +actually yeah and in particular because +it's radial just showing it the distance + + align:start position:0% +it's radial just showing it the distance + + + align:start position:0% +it's radial just showing it the distance +to the Baseline is going to change + + align:start position:0% +to the Baseline is going to change + + + align:start position:0% +to the Baseline is going to change +depending on where on the suppose that + + align:start position:0% +depending on where on the suppose that + + + align:start position:0% +depending on where on the suppose that +the what he was trying to do is to try + + align:start position:0% +the what he was trying to do is to try + + + align:start position:0% +the what he was trying to do is to try +to not go past the the the three-point + + align:start position:0% +to not go past the the the three-point + + + align:start position:0% +to not go past the the the three-point +line but yet be as close as possible for + + align:start position:0% +line but yet be as close as possible for + + + align:start position:0% +line but yet be as close as possible for +me because closer it easier then that's + + align:start position:0% +me because closer it easier then that's + + + align:start position:0% +me because closer it easier then that's +going to the that's going to depend on + + align:start position:0% +going to the that's going to depend on + + + align:start position:0% +going to the that's going to depend on +the distance from the midline is going + + align:start position:0% +the distance from the midline is going + + + align:start position:0% +the distance from the midline is going +to depend that he's going to shoot from + + align:start position:0% +to depend that he's going to shoot from + + + align:start position:0% +to depend that he's going to shoot from +is going to depend on where he is with + + align:start position:0% +is going to depend on where he is with + + + align:start position:0% +is going to depend on where he is with +respect to the Baseline + + align:start position:0% +respect to the Baseline + + + align:start position:0% +respect to the Baseline +and vice versa which means that in order + + align:start position:0% +and vice versa which means that in order + + + align:start position:0% +and vice versa which means that in order +to understand whether there is in fact a + + align:start position:0% +to understand whether there is in fact a + + + align:start position:0% +to understand whether there is in fact a +pattern to uh the way that is throwing + + align:start position:0% +pattern to uh the way that is throwing + + + align:start position:0% +pattern to uh the way that is throwing +in particular to test my hypothesis that + + align:start position:0% +in particular to test my hypothesis that + + + align:start position:0% +in particular to test my hypothesis that +the he's going to try to be as close as + + align:start position:0% +the he's going to try to be as close as + + + align:start position:0% +the he's going to try to be as close as +possible to the three-point line what do + + align:start position:0% +possible to the three-point line what do + + + align:start position:0% +possible to the three-point line what do +I need to show you instead of showing + + align:start position:0% +I need to show you instead of showing + + + align:start position:0% +I need to show you instead of showing +you these data separately could you make + + align:start position:0% +you these data separately could you make + + + align:start position:0% +you these data separately could you make +the three-point line zero and then just + + align:start position:0% +the three-point line zero and then just + + + align:start position:0% +the three-point line zero and then just +somehow come the new coordinate to give + + align:start position:0% +somehow come the new coordinate to give + + + align:start position:0% +somehow come the new coordinate to give +you dist yes so we could re normalize + + align:start position:0% +you dist yes so we could re normalize + + + align:start position:0% +you dist yes so we could re normalize +the data everything with respect to the + + align:start position:0% +the data everything with respect to the + + + align:start position:0% +the data everything with respect to the +three-point line and in order to even + + align:start position:0% +three-point line and in order to even + + + align:start position:0% +three-point line and in order to even +know whether it's kind of this wor doing + + align:start position:0% +know whether it's kind of this wor doing + + + align:start position:0% +know whether it's kind of this wor doing +one possibility could be to draw it on + + align:start position:0% +one possibility could be to draw it on + + + align:start position:0% +one possibility could be to draw it on +the x-axis and the Y AIS sideline the + + align:start position:0% +the x-axis and the Y AIS sideline the + + + align:start position:0% +the x-axis and the Y AIS sideline the +mid line exactly the point somehow + + align:start position:0% +mid line exactly the point somehow + + + align:start position:0% +mid line exactly the point somehow +through another like the radius of the + + align:start position:0% +through another like the radius of the + + + align:start position:0% +through another like the radius of the +circle or something that then determines + + align:start position:0% +circle or something that then determines + + + align:start position:0% +circle or something that then determines +the number of + + align:start position:0% +the number of + + + align:start position:0% +the number of +successes at that coordinate t + + align:start position:0% +successes at that coordinate t + + + align:start position:0% +successes at that coordinate t +um uh we can in fact do that looks + + align:start position:0% +um uh we can in fact do that looks + + + align:start position:0% +um uh we can in fact do that looks +better on my screen this is a three uh + + align:start position:0% +better on my screen this is a three uh + + + align:start position:0% +better on my screen this is a three uh +dimensional graph that does exactly that + + align:start position:0% +dimensional graph that does exactly that + + + align:start position:0% +dimensional graph that does exactly that +so now I am drawing something which uh + + align:start position:0% +so now I am drawing something which uh + + + align:start position:0% +so now I am drawing something which uh +which basically what you all saying is + + align:start position:0% +which basically what you all saying is + + + align:start position:0% +which basically what you all saying is +that look the distance to the Baseline + + align:start position:0% +that look the distance to the Baseline + + + align:start position:0% +that look the distance to the Baseline +distance to the midline are not + + align:start position:0% +distance to the midline are not + + + align:start position:0% +distance to the midline are not +independent distri they're not + + align:start position:0% +independent distri they're not + + + align:start position:0% +independent distri they're not +independent I don't want to be drawing + + align:start position:0% +independent I don't want to be drawing + + + align:start position:0% +independent I don't want to be drawing +them separate so either I force the + + align:start position:0% +them separate so either I force the + + + align:start position:0% +them separate so either I force the +functional form and transform it back + + align:start position:0% +functional form and transform it back + + + align:start position:0% +functional form and transform it back +into one variable we could do that or I + + align:start position:0% +into one variable we could do that or I + + + align:start position:0% +into one variable we could do that or I +could uh and then we should be able to + + align:start position:0% +could uh and then we should be able to + + + align:start position:0% +could uh and then we should be able to +see bunching at the three-point line uh + + align:start position:0% +see bunching at the three-point line uh + + + align:start position:0% +see bunching at the three-point line uh +or I um I drew it uh on the in in three + + align:start position:0% +or I um I drew it uh on the in in three + + + align:start position:0% +or I um I drew it uh on the in in three +dimension which is uh uh which is + + align:start position:0% +dimension which is uh uh which is + + + align:start position:0% +dimension which is uh uh which is +something like we get here so and it + + align:start position:0% +something like we get here so and it + + + align:start position:0% +something like we get here so and it +looks better on my screen uh but this is + + align:start position:0% +looks better on my screen uh but this is + + + align:start position:0% +looks better on my screen uh but this is +kind of a heat map with the where we + + align:start position:0% +kind of a heat map with the where we + + + align:start position:0% +kind of a heat map with the where we +both use there is both a heat map and + + align:start position:0% +both use there is both a heat map and + + + align:start position:0% +both use there is both a heat map and +and the height of the graph this is done + + align:start position:0% +and the height of the graph this is done + + + align:start position:0% +and the height of the graph this is done +in R you got VAR ious ways to represent + + align:start position:0% +in R you got VAR ious ways to represent + + + align:start position:0% +in R you got VAR ious ways to represent +threedimensional objects in r one of + + align:start position:0% +threedimensional objects in r one of + + + align:start position:0% +threedimensional objects in r one of +them is this that gives you both the + + align:start position:0% +them is this that gives you both the + + + align:start position:0% +them is this that gives you both the +height of the bar and the colors another + + align:start position:0% +height of the bar and the colors another + + + align:start position:0% +height of the bar and the colors another +one is just the heat map which has which + + align:start position:0% +one is just the heat map which has which + + + align:start position:0% +one is just the heat map which has which +has just uh which will just just use the + + align:start position:0% +has just uh which will just just use the + + + align:start position:0% +has just uh which will just just use the +colors to tell us and otherwise you can + + align:start position:0% +colors to tell us and otherwise you can + + + align:start position:0% +colors to tell us and otherwise you can +have a just just a relief whatever you + + align:start position:0% +have a just just a relief whatever you + + + align:start position:0% +have a just just a relief whatever you +prefer I thought this would be the best + + align:start position:0% +prefer I thought this would be the best + + + align:start position:0% +prefer I thought this would be the best +looking one but it's actually not that + + align:start position:0% +looking one but it's actually not that + + + align:start position:0% +looking one but it's actually not that +great so what + + align:start position:0% +great so what + + + align:start position:0% +great so what +you what you see now is that clearly at + + align:start position:0% +you what you see now is that clearly at + + + align:start position:0% +you what you see now is that clearly at +something it looks like the map it looks + + align:start position:0% +something it looks like the map it looks + + + align:start position:0% +something it looks like the map it looks +like + + align:start position:0% +like + + + align:start position:0% +like +the basketball court viewed from above + + align:start position:0% +the basketball court viewed from above + + + align:start position:0% +the basketball court viewed from above +uh where the the height of each of the + + align:start position:0% +uh where the the height of each of the + + + align:start position:0% +uh where the the height of each of the +bars in fact draws very nicely the + + align:start position:0% +bars in fact draws very nicely the + + + align:start position:0% +bars in fact draws very nicely the +three-point the three-point line and + + align:start position:0% +three-point the three-point line and + + + align:start position:0% +three-point the three-point line and +then we also have a huge speak at the + + align:start position:0% +then we also have a huge speak at the + + + align:start position:0% +then we also have a huge speak at the +where they can dunk where he can dunk + + align:start position:0% +where they can dunk where he can dunk + + + align:start position:0% +where they can dunk where he can dunk +and then now we have something that + + align:start position:0% +and then now we have something that + + + align:start position:0% +and then now we have something that +looks uh interesting so from then on we + + align:start position:0% +looks uh interesting so from then on we + + + align:start position:0% +looks uh interesting so from then on we +could say well clearly there is + + align:start position:0% +could say well clearly there is + + + align:start position:0% +could say well clearly there is +something we could we could now have a + + align:start position:0% +something we could we could now have a + + + align:start position:0% +something we could we could now have a +functional form that expresses + + align:start position:0% +functional form that expresses + + + align:start position:0% +functional form that expresses +everything with distance to with two + + align:start position:0% +everything with distance to with two + + + align:start position:0% +everything with distance to with two +kind of summary variable is distance to + + align:start position:0% +kind of summary variable is distance to + + + align:start position:0% +kind of summary variable is distance to +the basket and distance to the 3PO + + align:start position:0% +the basket and distance to the 3PO + + + align:start position:0% +the basket and distance to the 3PO +line and that could be put in a in a in + + align:start position:0% +line and that could be put in a in a in + + + align:start position:0% +line and that could be put in a in a in +a in + + align:start position:0% +a in + + + align:start position:0% +a in +a um in know two dimensional + + align:start position:0% + + + + align:start position:0% + +graph okay so these are kind of type of + + align:start position:0% +graph okay so these are kind of type of + + + align:start position:0% +graph okay so these are kind of type of +things you can do as soon as you get + + align:start position:0% +things you can do as soon as you get + + + align:start position:0% +things you can do as soon as you get +your hands on some data putting them up + + align:start position:0% +your hands on some data putting them up + + + align:start position:0% +your hands on some data putting them up +but something that uh I want to give you + + align:start position:0% +but something that uh I want to give you + + + align:start position:0% +but something that uh I want to give you +another very specific example of what we + + align:start position:0% +another very specific example of what we + + + align:start position:0% +another very specific example of what we +do why it's really useful to understand + + align:start position:0% +do why it's really useful to understand + + + align:start position:0% +do why it's really useful to understand +the underlying distribution of our + + align:start position:0% +the underlying distribution of our + + + align:start position:0% +the underlying distribution of our +variables we're going to see plenty of + + align:start position:0% +variables we're going to see plenty of + + + align:start position:0% +variables we're going to see plenty of +example of that but before we do any + + align:start position:0% +example of that but before we do any + + + align:start position:0% +example of that but before we do any +statistic or econometrics already the + + align:start position:0% +statistic or econometrics already the + + + align:start position:0% +statistic or econometrics already the +power of understanding + + align:start position:0% +power of understanding + + + align:start position:0% +power of understanding +probability uh and this is about top + + align:start position:0% +probability uh and this is about top + + + align:start position:0% +probability uh and this is about top +income distribution you might be + + align:start position:0% +income distribution you might be + + + align:start position:0% +income distribution you might be +interested in the distribution of top + + align:start position:0% +interested in the distribution of top + + + align:start position:0% +interested in the distribution of top +income so how are uh so first let's look + + align:start position:0% +income so how are uh so first let's look + + + align:start position:0% +income so how are uh so first let's look +at distribution of wages here is + + align:start position:0% +at distribution of wages here is + + + align:start position:0% +at distribution of wages here is +California uh CPS year + + align:start position:0% +California uh CPS year + + + align:start position:0% +California uh CPS year +2014 data that you could download of the + + align:start position:0% +2014 data that you could download of the + + + align:start position:0% +2014 data that you could download of the +the + + align:start position:0% +the + + + align:start position:0% +the +internet um does it look + + align:start position:0% +internet um does it look + + + align:start position:0% +internet um does it look +gaussian just when I was telling you + + align:start position:0% +gaussian just when I was telling you + + + align:start position:0% +gaussian just when I was telling you +that lots of stuff in E Comics look go + + align:start position:0% +that lots of stuff in E Comics look go + + + align:start position:0% +that lots of stuff in E Comics look go +in and there it doesn't look Goen + + align:start position:0% +in and there it doesn't look Goen + + + align:start position:0% +in and there it doesn't look Goen +whatsoever uh so forget that little guy + + align:start position:0% +whatsoever uh so forget that little guy + + + align:start position:0% +whatsoever uh so forget that little guy +for a while will come back to him uh it + + align:start position:0% +for a while will come back to him uh it + + + align:start position:0% +for a while will come back to him uh it +looks it does look pretty uh skewed to + + align:start position:0% +looks it does look pretty uh skewed to + + + align:start position:0% +looks it does look pretty uh skewed to +the left so in fact it turns out wages + + align:start position:0% +the left so in fact it turns out wages + + + align:start position:0% +the left so in fact it turns out wages +are not at all normal um but uh their + + align:start position:0% +are not at all normal um but uh their + + + align:start position:0% +are not at all normal um but uh their +log is a little + + align:start position:0% +log is a little + + + align:start position:0% +log is a little +better uh so the log is actually I I + + align:start position:0% +better uh so the log is actually I I + + + align:start position:0% +better uh so the log is actually I I +before we plotted that I would have + + align:start position:0% +before we plotted that I would have + + + align:start position:0% +before we plotted that I would have +thought it would be more bell shaped + + align:start position:0% +thought it would be more bell shaped + + + align:start position:0% +thought it would be more bell shaped +once it's logged wages are frequently + + align:start position:0% +once it's logged wages are frequently + + + align:start position:0% +once it's logged wages are frequently +assumed to be loged normal as a little + + align:start position:0% +assumed to be loged normal as a little + + + align:start position:0% +assumed to be loged normal as a little +surprise that in the log it still + + align:start position:0% +surprise that in the log it still + + + align:start position:0% +surprise that in the log it still +doesn't look very symmetrical but so + + align:start position:0% +doesn't look very symmetrical but so + + + align:start position:0% +doesn't look very symmetrical but so +um so it is useful to plot the data when + + align:start position:0% +um so it is useful to plot the data when + + + align:start position:0% +um so it is useful to plot the data when +you get some data it is very useful to + + align:start position:0% +you get some data it is very useful to + + + align:start position:0% +you get some data it is very useful to +plot the histogram to see how it looks + + align:start position:0% +plot the histogram to see how it looks + + + align:start position:0% +plot the histogram to see how it looks +like when you see a shape like that you + + align:start position:0% +like when you see a shape like that you + + + align:start position:0% +like when you see a shape like that you +feel you might think that it worth uh uh + + align:start position:0% +feel you might think that it worth uh uh + + + align:start position:0% +feel you might think that it worth uh uh +taking the logs and that the log would + + align:start position:0% +taking the logs and that the log would + + + align:start position:0% +taking the logs and that the log would +look a little bit better + + align:start position:0% +look a little bit better + + + align:start position:0% +look a little bit better +but even once we've done that I've done + + align:start position:0% +but even once we've done that I've done + + + align:start position:0% +but even once we've done that I've done +that uh kind of getting rid of the + + align:start position:0% +that uh kind of getting rid of the + + + align:start position:0% +that uh kind of getting rid of the +little guy to the + + align:start position:0% +little guy to the + + + align:start position:0% +little guy to the +end uh but what is that PE like what's + + align:start position:0% +end uh but what is that PE like what's + + + align:start position:0% +end uh but what is that PE like what's +that it looks like there is a mass of + + align:start position:0% +that it looks like there is a mass of + + + align:start position:0% +that it looks like there is a mass of +wages + + align:start position:0% +wages + + + align:start position:0% +wages +at outside of the range but what is + + align:start position:0% +at outside of the range but what is + + + align:start position:0% +at outside of the range but what is +going on + + align:start position:0% +going on + + + align:start position:0% +going on +here lots of people with exactly the + + align:start position:0% +here lots of people with exactly the + + + align:start position:0% +here lots of people with exactly the +same income seems unusual because we + + align:start position:0% +same income seems unusual because we + + + align:start position:0% +same income seems unusual because we +might think that wages are actually a + + align:start position:0% +might think that wages are actually a + + + align:start position:0% +might think that wages are actually a +continuous random variable so we + + align:start position:0% +continuous random variable so we + + + align:start position:0% +continuous random variable so we +shouldn't expect a mass point + + align:start position:0% +shouldn't expect a mass point + + + align:start position:0% +shouldn't expect a mass point +CEOs yes but you think CEOs on all + + align:start position:0% +CEOs yes but you think CEOs on all + + + align:start position:0% +CEOs yes but you think CEOs on all +exactly the same + + align:start position:0% +exactly the same + + + align:start position:0% +exactly the same +amount depends on how big the buiness + + align:start position:0% +amount depends on how big the buiness + + + align:start position:0% +amount depends on how big the buiness +right so what's what's the range of the + + align:start position:0% +right so what's what's the range of the + + + align:start position:0% +right so what's what's the range of the +buiness I tell you you make it as little + + align:start position:0% +buiness I tell you you make it as little + + + align:start position:0% +buiness I tell you you make it as little +as you can and it's still going to be + + align:start position:0% +as you can and it's still going to be + + + align:start position:0% +as you can and it's still going to be +this yeah it could it could have a legal + + align:start position:0% +this yeah it could it could have a legal + + + align:start position:0% +this yeah it could it could have a legal +basis there may be an accounting reason + + align:start position:0% +basis there may be an accounting reason + + + align:start position:0% +basis there may be an accounting reason +why to only have so much income at a + + align:start position:0% +why to only have so much income at a + + + align:start position:0% +why to only have so much income at a +specified value tax reasons rest okay so + + align:start position:0% +specified value tax reasons rest okay so + + + align:start position:0% +specified value tax reasons rest okay so +it could be it could be that so it's not + + align:start position:0% +it could be it could be that so it's not + + + align:start position:0% +it could be it could be that so it's not +we know know that cosos make all sorts + + align:start position:0% +we know know that cosos make all sorts + + + align:start position:0% +we know know that cosos make all sorts +of different wages yes about that is of + + align:start position:0% +of different wages yes about that is of + + + align:start position:0% +of different wages yes about that is of +that because if you + + align:start position:0% +that because if you + + + align:start position:0% +that because if you +can that it makes EAS + + align:start position:0% +can that it makes EAS + + + align:start position:0% +can that it makes EAS +for have exactly wages are top coded in + + align:start position:0% +for have exactly wages are top coded in + + + align:start position:0% +for have exactly wages are top coded in +the + + align:start position:0% +the + + + align:start position:0% +the +CPS + + align:start position:0% +CPS + + + align:start position:0% +CPS +so wages are top coded in the + + align:start position:0% + + + + align:start position:0% + +CPS I think we have it in the slide Wes + + align:start position:0% +CPS I think we have it in the slide Wes + + + align:start position:0% +CPS I think we have it in the slide Wes +are top coded in the census and the CPS + + align:start position:0% +are top coded in the census and the CPS + + + align:start position:0% +are top coded in the census and the CPS +to protect priv what does top coded mean + + align:start position:0% +to protect priv what does top coded mean + + + align:start position:0% +to protect priv what does top coded mean +anyone who makes more than that is going + + align:start position:0% +anyone who makes more than that is going + + + align:start position:0% +anyone who makes more than that is going +to be brought back to that so anyone who + + align:start position:0% +to be brought back to that so anyone who + + + align:start position:0% +to be brought back to that so anyone who +makes I don't know what that is but it's + + align:start position:0% +makes I don't know what that is but it's + + + align:start position:0% +makes I don't know what that is but it's +not that high and anyone who make more + + align:start position:0% +not that high and anyone who make more + + + align:start position:0% +not that high and anyone who make more +than that amount is just uh brought back + + align:start position:0% +than that amount is just uh brought back + + + align:start position:0% +than that amount is just uh brought back +to that level the do codes vary from + + align:start position:0% +to that level the do codes vary from + + + align:start position:0% +to that level the do codes vary from +year to year Etc and this is exactly for + + align:start position:0% +year to year Etc and this is exactly for + + + align:start position:0% +year to year Etc and this is exactly for +privacy reason you don't want to + + align:start position:0% +privacy reason you don't want to + + + align:start position:0% +privacy reason you don't want to +identify you know there are not that + + align:start position:0% +identify you know there are not that + + + align:start position:0% +identify you know there are not that +many people who make if you if you wrote + + align:start position:0% +many people who make if you if you wrote + + + align:start position:0% +many people who make if you if you wrote +down every single piece wages of people + + align:start position:0% +down every single piece wages of people + + + align:start position:0% +down every single piece wages of people +who are interviewed in the CPS it would + + align:start position:0% +who are interviewed in the CPS it would + + + align:start position:0% +who are interviewed in the CPS it would +not be very very difficult to find uh to + + align:start position:0% +not be very very difficult to find uh to + + + align:start position:0% +not be very very difficult to find uh to +find + + align:start position:0% +find + + + align:start position:0% +find +them ah so that's fine if you're + + align:start position:0% +them ah so that's fine if you're + + + align:start position:0% +them ah so that's fine if you're +interested in the impact of minimum wage + + align:start position:0% +interested in the impact of minimum wage + + + align:start position:0% +interested in the impact of minimum wage +on uh on people's lives because there + + align:start position:0% +on uh on people's lives because there + + + align:start position:0% +on uh on people's lives because there +are not very many people who are the top + + align:start position:0% +are not very many people who are the top + + + align:start position:0% +are not very many people who are the top +Cod top coded people are unlikely to be + + align:start position:0% +Cod top coded people are unlikely to be + + + align:start position:0% +Cod top coded people are unlikely to be +affected by that but what if we're + + align:start position:0% +affected by that but what if we're + + + align:start position:0% +affected by that but what if we're +interested in see paying Silicon Valley + + align:start position:0% +interested in see paying Silicon Valley + + + align:start position:0% +interested in see paying Silicon Valley +then that's not going to be the right + + align:start position:0% +then that's not going to be the right + + + align:start position:0% +then that's not going to be the right +data and the right data might be a + + align:start position:0% +data and the right data might be a + + + align:start position:0% +data and the right data might be a +little bit uh difficult to get hold of + + align:start position:0% +little bit uh difficult to get hold of + + + align:start position:0% +little bit uh difficult to get hold of +in fact there is for of data forbs + + align:start position:0% +in fact there is for of data forbs + + + align:start position:0% +in fact there is for of data forbs +publishes some data Etc you can look for + + align:start position:0% +publishes some data Etc you can look for + + + align:start position:0% +publishes some data Etc you can look for +it uh but it's generally not that easy + + align:start position:0% +it uh but it's generally not that easy + + + align:start position:0% +it uh but it's generally not that easy +to to to find data certainly not uh if + + align:start position:0% +to to to find data certainly not uh if + + + align:start position:0% +to to to find data certainly not uh if +you are interested in the history of + + align:start position:0% +you are interested in the history of + + + align:start position:0% +you are interested in the history of +very top wages uh uh you you will find + + align:start position:0% +very top wages uh uh you you will find + + + align:start position:0% +very top wages uh uh you you will find +some data that that is published on cop + + align:start position:0% +some data that that is published on cop + + + align:start position:0% +some data that that is published on cop +um But for recent years and if you + + align:start position:0% +um But for recent years and if you + + + align:start position:0% +um But for recent years and if you +wanted a continuous time series going + + align:start position:0% +wanted a continuous time series going + + + align:start position:0% +wanted a continuous time series going +back a long time to see how things + + align:start position:0% +back a long time to see how things + + + align:start position:0% +back a long time to see how things +changed over time you would not be able + + align:start position:0% +changed over time you would not be able + + + align:start position:0% +changed over time you would not be able +to um to do + + align:start position:0% +to um to do + + + align:start position:0% +to um to do +it and uh we could be + + align:start position:0% +it and uh we could be + + + align:start position:0% +it and uh we could be +yes if one wants to get + + align:start position:0% +yes if one wants to get + + + align:start position:0% +yes if one wants to get +uh the real wages of cosos in that one + + align:start position:0% +uh the real wages of cosos in that one + + + align:start position:0% +uh the real wages of cosos in that one +corner yeah would it still be having + + align:start position:0% +corner yeah would it still be having + + + align:start position:0% +corner yeah would it still be having +this fun because I'm just thinking of + + align:start position:0% +this fun because I'm just thinking of + + + align:start position:0% +this fun because I'm just thinking of +people who had some of the big + + align:start position:0% +people who had some of the big + + + align:start position:0% +people who had some of the big +technology platform + + align:start position:0% +technology platform + + + align:start position:0% +technology platform +companies they basically are sort of + + align:start position:0% +companies they basically are sort of + + + align:start position:0% +companies they basically are sort of +consolidating a lot of the weth so would + + align:start position:0% +consolidating a lot of the weth so would + + + align:start position:0% +consolidating a lot of the weth so would +it still be like a nice degradation + + align:start position:0% +it still be like a nice degradation + + + align:start position:0% +it still be like a nice degradation +would be that's a very good that's a + + align:start position:0% +would be that's a very good that's a + + + align:start position:0% +would be that's a very good that's a +very good question and we are going to + + align:start position:0% +very good question and we are going to + + + align:start position:0% +very good question and we are going to +answer it right + + align:start position:0% +answer it right + + + align:start position:0% +answer it right +now um so some people are interested in + + align:start position:0% +now um so some people are interested in + + + align:start position:0% +now um so some people are interested in +the in the in top one person in + + align:start position:0% +the in the in top one person in + + + align:start position:0% +the in the in top one person in +particular uh the rest of us uh uh um + + align:start position:0% +particular uh the rest of us uh uh um + + + align:start position:0% +particular uh the rest of us uh uh um +there was a lot of discussion this + + align:start position:0% +there was a lot of discussion this + + + align:start position:0% +there was a lot of discussion this +one% captured imagination right we are + + align:start position:0% +one% captured imagination right we are + + + align:start position:0% +one% captured imagination right we are +the one% how much income do the 1% + + align:start position:0% +the one% how much income do the 1% + + + align:start position:0% +the one% how much income do the 1% +richest people capture it got embodied + + align:start position:0% +richest people capture it got embodied + + + align:start position:0% +richest people capture it got embodied +in this + + align:start position:0% +in this + + + align:start position:0% +in this +idea of we are the 99% that the that now + + align:start position:0% +idea of we are the 99% that the that now + + + align:start position:0% +idea of we are the 99% that the that now +you can people discuss one person 99% + + align:start position:0% +you can people discuss one person 99% + + + align:start position:0% +you can people discuss one person 99% +it's just part of the part of the uh + + align:start position:0% +it's just part of the part of the uh + + + align:start position:0% +it's just part of the part of the uh +language uh uh thanks to the Occupy well + + align:start position:0% +language uh uh thanks to the Occupy well + + + align:start position:0% +language uh uh thanks to the Occupy well +streate movement but where did they get + + align:start position:0% +streate movement but where did they get + + + align:start position:0% +streate movement but where did they get +it from we've been talking a lot about + + align:start position:0% +it from we've been talking a lot about + + + align:start position:0% +it from we've been talking a lot about +Republican uh presidential candidates so + + align:start position:0% +Republican uh presidential candidates so + + + align:start position:0% +Republican uh presidential candidates so +let's let's you know even the balance + + align:start position:0% +let's let's you know even the balance + + + align:start position:0% +let's let's you know even the balance +and talk a bit about the Democrats so it + + align:start position:0% +and talk a bit about the Democrats so it + + + align:start position:0% +and talk a bit about the Democrats so it +I think it turns out uh so I was trying + + align:start position:0% +I think it turns out uh so I was trying + + + align:start position:0% +I think it turns out uh so I was trying +to trace the the 99% U history my best + + align:start position:0% +to trace the the 99% U history my best + + + align:start position:0% +to trace the the 99% U history my best +guess my best answer at the woman is + + align:start position:0% +guess my best answer at the woman is + + + align:start position:0% +guess my best answer at the woman is +that it comes from this one + + align:start position:0% +that it comes from this one + + + align:start position:0% +that it comes from this one +speech our friend Bernie Sanders uh + + align:start position:0% +speech our friend Bernie Sanders uh + + + align:start position:0% +speech our friend Bernie Sanders uh +December 10 2010 uh made himself well he + + align:start position:0% +December 10 2010 uh made himself well he + + + align:start position:0% +December 10 2010 uh made himself well he +was kind of famous already but made the + + align:start position:0% +was kind of famous already but made the + + + align:start position:0% +was kind of famous already but made the +one person famous with his famous Philly + + align:start position:0% +one person famous with his famous Philly + + + align:start position:0% +one person famous with his famous Philly +bery which was a eight hour speech on uh + + align:start position:0% +bery which was a eight hour speech on uh + + + align:start position:0% +bery which was a eight hour speech on uh +on uh on these issues uh uh you know + + align:start position:0% +on uh on these issues uh uh you know + + + align:start position:0% +on uh on these issues uh uh you know +opposing uh opposing uh uh further um + + align:start position:0% +opposing uh opposing uh uh further um + + + align:start position:0% +opposing uh opposing uh uh further um +tax relief etc for for the + + align:start position:0% +tax relief etc for for the + + + align:start position:0% +tax relief etc for for the +rich and uh here is what he said we + + align:start position:0% +rich and uh here is what he said we + + + align:start position:0% +rich and uh here is what he said we +cannot give tax breaks to the rich when + + align:start position:0% +cannot give tax breaks to the rich when + + + align:start position:0% +cannot give tax breaks to the rich when +we already have the most unequal + + align:start position:0% +we already have the most unequal + + + align:start position:0% +we already have the most unequal +distribution of income of any major + + align:start position:0% +distribution of income of any major + + + align:start position:0% +distribution of income of any major +country on Earth the percentage of + + align:start position:0% +country on Earth the percentage of + + + align:start position:0% +country on Earth the percentage of +income going to the top one% nearly + + align:start position:0% +income going to the top one% nearly + + + align:start position:0% +income going to the top one% nearly +tripled since the 1970s the top 1% now + + align:start position:0% +tripled since the 1970s the top 1% now + + + align:start position:0% +tripled since the 1970s the top 1% now +owns more wealth than the bottom 90% + + align:start position:0% +owns more wealth than the bottom 90% + + + align:start position:0% +owns more wealth than the bottom 90% +that's not the foundation of a + + align:start position:0% +that's not the foundation of a + + + align:start position:0% +that's not the foundation of a +Democratic Society the fact is 80% of + + align:start position:0% +Democratic Society the fact is 80% of + + + align:start position:0% +Democratic Society the fact is 80% of +all all new income on from 1980 to 2005 + + align:start position:0% +all all new income on from 1980 to 2005 + + + align:start position:0% +all all new income on from 1980 to 2005 +has gone to the top 1% people should be + + align:start position:0% +has gone to the top 1% people should be + + + align:start position:0% +has gone to the top 1% people should be +mindful of this fact the last time that + + align:start position:0% +mindful of this fact the last time that + + + align:start position:0% +mindful of this fact the last time that +type of income disparity took place was + + align:start position:0% +type of income disparity took place was + + + align:start position:0% +type of income disparity took place was +1928 I think we all know what happened + + align:start position:0% +1928 I think we all know what happened + + + align:start position:0% +1928 I think we all know what happened +in + + align:start position:0% +in + + + align:start position:0% +in +1929 you have to agree that compared to + + align:start position:0% +1929 you have to agree that compared to + + + align:start position:0% +1929 you have to agree that compared to +most political speeches this is Chuck + + align:start position:0% +most political speeches this is Chuck + + + align:start position:0% +most political speeches this is Chuck +full with + + align:start position:0% +full with + + + align:start position:0% +full with +facts even better if you wanted to to + + align:start position:0% +facts even better if you wanted to to + + + align:start position:0% +facts even better if you wanted to to +prove to to fact check this fact you + + align:start position:0% +prove to to fact check this fact you + + + align:start position:0% +prove to to fact check this fact you +could they come back to These + + align:start position:0% +could they come back to These + + + align:start position:0% +could they come back to These +Guys these facts come ver te from a + + align:start position:0% +Guys these facts come ver te from a + + + align:start position:0% +Guys these facts come ver te from a +research that Pik and Emanuel s wrote + + align:start position:0% +research that Pik and Emanuel s wrote + + + align:start position:0% +research that Pik and Emanuel s wrote +some years before their first article + + align:start position:0% +some years before their first article + + + align:start position:0% +some years before their first article +was for the late 1990s for the US you + + align:start position:0% +was for the late 1990s for the US you + + + align:start position:0% +was for the late 1990s for the US you +know building on a lot of tomap pik's + + align:start position:0% +know building on a lot of tomap pik's + + + align:start position:0% +know building on a lot of tomap pik's +work for France in uh uh uh done in + + align:start position:0% +work for France in uh uh uh done in + + + align:start position:0% +work for France in uh uh uh done in +1998 by the way Toma was a faculty + + align:start position:0% +1998 by the way Toma was a faculty + + + align:start position:0% +1998 by the way Toma was a faculty +member here at MIT and Emanuel was a PhD + + align:start position:0% +member here at MIT and Emanuel was a PhD + + + align:start position:0% +member here at MIT and Emanuel was a PhD +student + + align:start position:0% +student + + + align:start position:0% +student +here and uh how did they do it so they + + align:start position:0% +here and uh how did they do it so they + + + align:start position:0% +here and uh how did they do it so they +were interested exactly in your question + + align:start position:0% +were interested exactly in your question + + + align:start position:0% +were interested exactly in your question +what's the what's the the shape of the + + align:start position:0% +what's the what's the the shape of the + + + align:start position:0% +what's the what's the the shape of the +distribution of the income distribution + + align:start position:0% +distribution of the income distribution + + + align:start position:0% +distribution of the income distribution +past the line does it still look very + + align:start position:0% +past the line does it still look very + + + align:start position:0% +past the line does it still look very +Bunch or what does it look like and the + + align:start position:0% +Bunch or what does it look like and the + + + align:start position:0% +Bunch or what does it look like and the +issue and and that's and they calculated + + align:start position:0% +issue and and that's and they calculated + + + align:start position:0% +issue and and that's and they calculated +it for many years and you can go back to + + align:start position:0% +it for many years and you can go back to + + + align:start position:0% +it for many years and you can go back to +Mr sers speech and I assume and I hope + + align:start position:0% +Mr sers speech and I assume and I hope + + + align:start position:0% +Mr sers speech and I assume and I hope +you will be impressed by the fact that + + align:start position:0% +you will be impressed by the fact that + + + align:start position:0% +you will be impressed by the fact that +everything he said actually is + + align:start position:0% +everything he said actually is + + + align:start position:0% +everything he said actually is +Faithfully taken from that one graph uh + + align:start position:0% +Faithfully taken from that one graph uh + + + align:start position:0% +Faithfully taken from that one graph uh +which tells us the top in 1% income + + align:start position:0% +which tells us the top in 1% income + + + align:start position:0% +which tells us the top in 1% income +share uh in fact Emanuel recently EXT + + align:start position:0% +share uh in fact Emanuel recently EXT + + + align:start position:0% +share uh in fact Emanuel recently EXT +ended the the graph the original paper I + + align:start position:0% +ended the the graph the original paper I + + + align:start position:0% +ended the the graph the original paper I +think went in 1998 Emanuel extended + + align:start position:0% +think went in 1998 Emanuel extended + + + align:start position:0% +think went in 1998 Emanuel extended +keeps extending every year he adds more + + align:start position:0% +keeps extending every year he adds more + + + align:start position:0% +keeps extending every year he adds more +data it goes now till + + align:start position:0% +data it goes now till + + + align:start position:0% +data it goes now till +2014 and uh the the black line is the + + align:start position:0% +2014 and uh the the black line is the + + + align:start position:0% +2014 and uh the the black line is the +top is the one the share of income that + + align:start position:0% +top is the one the share of income that + + + align:start position:0% +top is the one the share of income that +goes to the top + + align:start position:0% +goes to the top + + + align:start position:0% +goes to the top +1% of the of + + align:start position:0% +1% of the of + + + align:start position:0% +1% of the of +the of the US population uh and you can + + align:start position:0% +the of the US population uh and you can + + + align:start position:0% +the of the US population uh and you can +see that his right which is in + + align:start position:0% +see that his right which is in + + + align:start position:0% +see that his right which is in +1928 uh it took a huge beating with the + + align:start position:0% +1928 uh it took a huge beating with the + + + align:start position:0% +1928 uh it took a huge beating with the +29 crisis and then there was it + + align:start position:0% +29 crisis and then there was it + + + align:start position:0% +29 crisis and then there was it +recovered a little bit then there was + + align:start position:0% +recovered a little bit then there was + + + align:start position:0% +recovered a little bit then there was +the war and then it was flat for a long + + align:start position:0% +the war and then it was flat for a long + + + align:start position:0% +the war and then it was flat for a long +time and since the + + align:start position:0% +time and since the + + + align:start position:0% +time and since the +1980s really it's been steadily + + align:start position:0% +1980s really it's been steadily + + + align:start position:0% +1980s really it's been steadily +increasing you can see the impact of + + align:start position:0% +increasing you can see the impact of + + + align:start position:0% +increasing you can see the impact of +the.com bubble and the 2008 crisis where + + align:start position:0% +the.com bubble and the 2008 crisis where + + + align:start position:0% +the.com bubble and the 2008 crisis where +it falls down and then it goes it went + + align:start position:0% +it falls down and then it goes it went + + + align:start position:0% +it falls down and then it goes it went +back up again in fact between 2009 and + + align:start position:0% +back up again in fact between 2009 and + + + align:start position:0% +back up again in fact between 2009 and +2014 so this is a lot of + + align:start position:0% +2014 so this is a lot of + + + align:start position:0% +2014 so this is a lot of +data and uh you might ask yourself how + + align:start position:0% +data and uh you might ask yourself how + + + align:start position:0% +data and uh you might ask yourself how +did they they you know where is that + + align:start position:0% +did they they you know where is that + + + align:start position:0% +did they they you know where is that +data coming from how did they find out + + align:start position:0% +data coming from how did they find out + + + align:start position:0% +data coming from how did they find out +since there are no places there is no + + align:start position:0% +since there are no places there is no + + + align:start position:0% +since there are no places there is no +data set that tells + + align:start position:0% +data set that tells + + + align:start position:0% +data set that tells +you line by line in fact now in for + + align:start position:0% +you line by line in fact now in for + + + align:start position:0% +you line by line in fact now in for +recent year the the the IRS makes + + align:start position:0% +recent year the the the IRS makes + + + align:start position:0% +recent year the the the IRS makes +available to the P size team and people + + align:start position:0% +available to the P size team and people + + + align:start position:0% +available to the P size team and people +who work with them in very spec very uh + + align:start position:0% +who work with them in very spec very uh + + + align:start position:0% +who work with them in very spec very uh +uh very very uh controll situation + + align:start position:0% +uh very very uh controll situation + + + align:start position:0% +uh very very uh controll situation +access to the individual tax data but + + align:start position:0% +access to the individual tax data but + + + align:start position:0% +access to the individual tax data but +this is recent and and this is this way + + align:start position:0% +this is recent and and this is this way + + + align:start position:0% +this is recent and and this is this way +is not available for a longer time + + align:start position:0% +is not available for a longer time + + + align:start position:0% +is not available for a longer time +period so how do we how could they do + + align:start position:0% +period so how do we how could they do + + + align:start position:0% +period so how do we how could they do +this + + align:start position:0% +this + + + align:start position:0% +this +graphs so the only source of data on the + + align:start position:0% +graphs so the only source of data on the + + + align:start position:0% +graphs so the only source of data on the +distribution of income that's con + + align:start position:0% +distribution of income that's con + + + align:start position:0% +distribution of income that's con +consistently available over a long + + align:start position:0% +consistently available over a long + + + align:start position:0% +consistently available over a long +period of time is the tax + + align:start position:0% +period of time is the tax + + + align:start position:0% +period of time is the tax +data uh and the tax data doesn't tell + + align:start position:0% +data uh and the tax data doesn't tell + + + align:start position:0% +data uh and the tax data doesn't tell +you uh which person pays what taxes uh + + align:start position:0% +you uh which person pays what taxes uh + + + align:start position:0% +you uh which person pays what taxes uh +thank goodness and there would be a lot + + align:start position:0% +thank goodness and there would be a lot + + + align:start position:0% +thank goodness and there would be a lot +of uh private information devolved on us + + align:start position:0% +of uh private information devolved on us + + + align:start position:0% +of uh private information devolved on us +but it's available in the form of + + align:start position:0% +but it's available in the form of + + + align:start position:0% +but it's available in the form of +tabulations so what are a tabulation + + align:start position:0% +tabulations so what are a tabulation + + + align:start position:0% +tabulations so what are a tabulation +basically it tells you for bracket for + + align:start position:0% +basically it tells you for bracket for + + + align:start position:0% +basically it tells you for bracket for +for bracket of income it tells you how + + align:start position:0% +for bracket of income it tells you how + + + align:start position:0% +for bracket of income it tells you how +many people are in this bracket + + align:start position:0% +many people are in this bracket + + + align:start position:0% +many people are in this bracket +correspond to a tax bracket or how many + + align:start position:0% +correspond to a tax bracket or how many + + + align:start position:0% +correspond to a tax bracket or how many +people in this income bracket and how + + align:start position:0% +people in this income bracket and how + + + align:start position:0% +people in this income bracket and how +what's obviously a bracket is defined by + + align:start position:0% +what's obviously a bracket is defined by + + + align:start position:0% +what's obviously a bracket is defined by +a minimum and a maximum amount that + + align:start position:0% +a minimum and a maximum amount that + + + align:start position:0% +a minimum and a maximum amount that +defines the bracket and the uh tax data + + align:start position:0% +defines the bracket and the uh tax data + + + align:start position:0% +defines the bracket and the uh tax data +also tell you the average income of + + align:start position:0% +also tell you the average income of + + + align:start position:0% +also tell you the average income of +people in the + + align:start position:0% +people in the + + + align:start position:0% +people in the +bracket so this uh data comes from + + align:start position:0% +bracket so this uh data comes from + + + align:start position:0% +bracket so this uh data comes from +combining this data with population + + align:start position:0% +combining this data with population + + + align:start position:0% +combining this data with population +census data and aggregate income to + + align:start position:0% +census data and aggregate income to + + + align:start position:0% +census data and aggregate income to +calculate the share of total personal + + align:start position:0% +calculate the share of total personal + + + align:start position:0% +calculate the share of total personal +income acing to various top income group + + align:start position:0% +income acing to various top income group + + + align:start position:0% +income acing to various top income group +that you would be interested in the top + + align:start position:0% +that you would be interested in the top + + + align:start position:0% +that you would be interested in the top +10% the top 1% fact the top 0000 one% if + + align:start position:0% +10% the top 1% fact the top 0000 one% if + + + align:start position:0% +10% the top 1% fact the top 0000 one% if +that's what you're interested + + align:start position:0% +that's what you're interested + + + align:start position:0% +that's what you're interested +in how do they do that uh they exploit + + align:start position:0% +in how do they do that uh they exploit + + + align:start position:0% +in how do they do that uh they exploit +that by they do that by exploiting a + + align:start position:0% +that by they do that by exploiting a + + + align:start position:0% +that by they do that by exploiting a +known fact about distribution of top + + align:start position:0% +known fact about distribution of top + + + align:start position:0% +known fact about distribution of top +incomes which we can actually verify in + + align:start position:0% +incomes which we can actually verify in + + + align:start position:0% +incomes which we can actually verify in +the data which is that it tends to be + + align:start position:0% +the data which is that it tends to be + + + align:start position:0% +the data which is that it tends to be +well approximated by a Paro distribution + + align:start position:0% +well approximated by a Paro distribution + + + align:start position:0% +well approximated by a Paro distribution +so it's not a bunch it's a Paro + + align:start position:0% +so it's not a bunch it's a Paro + + + align:start position:0% +so it's not a bunch it's a Paro +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +what's sear + + align:start position:0% +what's sear + + + align:start position:0% +what's sear +distribution uh that's uh in technical + + align:start position:0% +distribution uh that's uh in technical + + + align:start position:0% +distribution uh that's uh in technical +term that's the density or one minus the + + align:start position:0% +term that's the density or one minus the + + + align:start position:0% +term that's the density or one minus the +density one minus the density that's the + + align:start position:0% +density one minus the density that's the + + + align:start position:0% +density one minus the density that's the +probability that um um any U that X is + + align:start position:0% +probability that um um any U that X is + + + align:start position:0% +probability that um um any U that X is +bigger than any number X is XM /x to the + + align:start position:0% +bigger than any number X is XM /x to the + + + align:start position:0% +bigger than any number X is XM /x to the +power + + align:start position:0% +power + + + align:start position:0% +power +Lambda for any X bigger than XM and one + + align:start position:0% +Lambda for any X bigger than XM and one + + + align:start position:0% +Lambda for any X bigger than XM and one +over otherwise so if I drew the in order + + align:start position:0% +over otherwise so if I drew the in order + + + align:start position:0% +over otherwise so if I drew the in order +to draw the the PDF the PDF looks + + align:start position:0% +to draw the the PDF the PDF looks + + + align:start position:0% +to draw the the PDF the PDF looks +something like that so say if XM is + + align:start position:0% +something like that so say if XM is + + + align:start position:0% +something like that so say if XM is +one uh it looks like this and then like + + align:start position:0% +one uh it looks like this and then like + + + align:start position:0% +one uh it looks like this and then like +this + + align:start position:0% +this + + + align:start position:0% +this +um that's this we're typically not + + align:start position:0% +um that's this we're typically not + + + align:start position:0% +um that's this we're typically not +interested in income close to XM but we + + align:start position:0% +interested in income close to XM but we + + + align:start position:0% +interested in income close to XM but we +need to this is gives us the scale + + align:start position:0% +need to this is gives us the scale + + + align:start position:0% +need to this is gives us the scale +parameter and then Lambda gives us it's + + align:start position:0% +parameter and then Lambda gives us it's + + + align:start position:0% +parameter and then Lambda gives us it's +called the shape shape + + align:start position:0% +called the shape shape + + + align:start position:0% +called the shape shape +parameter so what it what it reflects is + + align:start position:0% +parameter so what it what it reflects is + + + align:start position:0% +parameter so what it what it reflects is +something it's more intuitive to see + + align:start position:0% +something it's more intuitive to see + + + align:start position:0% +something it's more intuitive to see +this that way it's the the average + + align:start position:0% +this that way it's the the average + + + align:start position:0% +this that way it's the the average +income of those whose income is greater + + align:start position:0% +income of those whose income is greater + + + align:start position:0% +income of those whose income is greater +than some line Y is y times the constant + + align:start position:0% +than some line Y is y times the constant + + + align:start position:0% +than some line Y is y times the constant +Lambda over Lambda minus one so for + + align:start position:0% +Lambda over Lambda minus one so for + + + align:start position:0% +Lambda over Lambda minus one so for +example suppose Lambda is equal to two + + align:start position:0% +example suppose Lambda is equal to two + + + align:start position:0% +example suppose Lambda is equal to two +what's the average income of people + + align:start position:0% +what's the average income of people + + + align:start position:0% +what's the average income of people +whose income is larger than + + align:start position:0% + + + + align:start position:0% + +100,000 200,000 uh if Lambda is equal to + + align:start position:0% +100,000 200,000 uh if Lambda is equal to + + + align:start position:0% +100,000 200,000 uh if Lambda is equal to +four + + align:start position:0% + + + + align:start position:0% + +exactly which is bigger or smaller than + + align:start position:0% +exactly which is bigger or smaller than + + + align:start position:0% +exactly which is bigger or smaller than +200 smaller so the the smaller Lambda uh + + align:start position:0% +200 smaller so the the smaller Lambda uh + + + align:start position:0% +200 smaller so the the smaller Lambda uh +the more inequality there is at the top + + align:start position:0% +the more inequality there is at the top + + + align:start position:0% +the more inequality there is at the top +of the distribution in the sense that + + align:start position:0% +of the distribution in the sense that + + + align:start position:0% +of the distribution in the sense that +the bigger the share of the of the + + align:start position:0% +the bigger the share of the of the + + + align:start position:0% +the bigger the share of the of the +income that that goes the bigger the + + align:start position:0% +income that that goes the bigger the + + + align:start position:0% +income that that goes the bigger the +larger is the average income that that + + align:start position:0% +larger is the average income that that + + + align:start position:0% +larger is the average income that that +goes above any given line uh this this + + align:start position:0% +goes above any given line uh this this + + + align:start position:0% +goes above any given line uh this this +of course doesn't this is for Lambda + + align:start position:0% +of course doesn't this is for Lambda + + + align:start position:0% +of course doesn't this is for Lambda +greater than one uh otherwise that's not + + align:start position:0% +greater than one uh otherwise that's not + + + align:start position:0% +greater than one uh otherwise that's not +true the if if Lambda is greater than + + align:start position:0% +true the if if Lambda is greater than + + + align:start position:0% +true the if if Lambda is greater than +one the the average distribution the + + align:start position:0% +one the the average distribution the + + + align:start position:0% +one the the average distribution the +average of the above any given threshold + + align:start position:0% +average of the above any given threshold + + + align:start position:0% +average of the above any given threshold +is + + align:start position:0% +is + + + align:start position:0% +is +infinity so this is the that's kind of + + align:start position:0% +infinity so this is the that's kind of + + + align:start position:0% +infinity so this is the that's kind of +what's you know the known property of + + align:start position:0% +what's you know the known property of + + + align:start position:0% +what's you know the known property of +the Paro distribution is and it's very + + align:start position:0% +the Paro distribution is and it's very + + + align:start position:0% +the Paro distribution is and it's very +useful property because once you know + + align:start position:0% +useful property because once you know + + + align:start position:0% +useful property because once you know +that uh then you can it's very easy to + + align:start position:0% +that uh then you can it's very easy to + + + align:start position:0% +that uh then you can it's very easy to +calculate the coefficient of the Paro + + align:start position:0% +calculate the coefficient of the Paro + + + align:start position:0% +calculate the coefficient of the Paro +distribution and the XM parameter I'll + + align:start position:0% +distribution and the XM parameter I'll + + + align:start position:0% +distribution and the XM parameter I'll +show it how they do it in a minute and + + align:start position:0% +show it how they do it in a minute and + + + align:start position:0% +show it how they do it in a minute and +then once you have that then you can do + + align:start position:0% +then once you have that then you can do + + + align:start position:0% +then once you have that then you can do +it for any quantal you're interested in + + align:start position:0% +it for any quantal you're interested in + + + align:start position:0% +it for any quantal you're interested in +uh before we get that + + align:start position:0% +uh before we get that + + + align:start position:0% +uh before we get that +um little aside the zip distribution is + + align:start position:0% +um little aside the zip distribution is + + + align:start position:0% +um little aside the zip distribution is +special is so income are not zip + + align:start position:0% +special is so income are not zip + + + align:start position:0% +special is so income are not zip +distributed but it's a special case with + + align:start position:0% +distributed but it's a special case with + + + align:start position:0% +distributed but it's a special case with +Lambda equal one and one way that zip + + align:start position:0% +Lambda equal one and one way that zip + + + align:start position:0% +Lambda equal one and one way that zip +distribution is described is in term of + + align:start position:0% +distribution is described is in term of + + + align:start position:0% +distribution is described is in term of +the rank and it says that the log the + + align:start position:0% +the rank and it says that the log the + + + align:start position:0% +the rank and it says that the log the +way you can uh you can write the zip + + align:start position:0% +way you can uh you can write the zip + + + align:start position:0% +way you can uh you can write the zip +distribution is that the the + + align:start position:0% +distribution is that the the + + + align:start position:0% +distribution is that the the +relationship between the log Rank and + + align:start position:0% +relationship between the log Rank and + + + align:start position:0% +relationship between the log Rank and +the log size is one so I'll show it to + + align:start position:0% +the log size is one so I'll show it to + + + align:start position:0% +the log size is one so I'll show it to +you for + + align:start position:0% +you for + + + align:start position:0% +you for +City uh the log population plotted + + align:start position:0% +City uh the log population plotted + + + align:start position:0% +City uh the log population plotted +against the log of the rank uh is + + align:start position:0% +against the log of the rank uh is + + + align:start position:0% +against the log of the rank uh is +exactly minus one that means the um + + align:start position:0% +exactly minus one that means the um + + + align:start position:0% +exactly minus one that means the um +the say for example the word that is it + + align:start position:0% +the say for example the word that is it + + + align:start position:0% +the say for example the word that is it +also works for words in the English + + align:start position:0% +also works for words in the English + + + align:start position:0% +also works for words in the English +language anyway so the word that is + + align:start position:0% +language anyway so the word that is + + + align:start position:0% +language anyway so the word that is +spoken the most in the English language + + align:start position:0% +spoken the most in the English language + + + align:start position:0% +spoken the most in the English language +is what you + + align:start position:0% + + + + align:start position:0% + +think it is the the word the and it's + + align:start position:0% +think it is the the word the and it's + + + align:start position:0% +think it is the the word the and it's +spoken about 7% of the + + align:start position:0% +spoken about 7% of the + + + align:start position:0% +spoken about 7% of the +time the next most frequent is + + align:start position:0% +time the next most frequent is + + + align:start position:0% +time the next most frequent is +off and it's it follows the zip flow so + + align:start position:0% +off and it's it follows the zip flow so + + + align:start position:0% +off and it's it follows the zip flow so +you can tell me how often number two + + align:start position:0% +you can tell me how often number two + + + align:start position:0% +you can tell me how often number two +given that I I I uncarded it at 7% for + + align:start position:0% +given that I I I uncarded it at 7% for + + + align:start position:0% +given that I I I uncarded it at 7% for +the how frequently is of + + align:start position:0% +the how frequently is of + + + align:start position:0% +the how frequently is of +spoken it's rank + + align:start position:0% +spoken it's rank + + + align:start position:0% +spoken it's rank +two 3.5 exactly and then so and it + + align:start position:0% +two 3.5 exactly and then so and it + + + align:start position:0% +two 3.5 exactly and then so and it +continues like that so many phenomenon + + align:start position:0% +continues like that so many phenomenon + + + align:start position:0% +continues like that so many phenomenon +are approximately approximated by zip + + align:start position:0% +are approximately approximated by zip + + + align:start position:0% +are approximately approximated by zip +flow and people like to give explanation + + align:start position:0% +flow and people like to give explanation + + + align:start position:0% +flow and people like to give explanation +for these things uh maybe if we have + + align:start position:0% +for these things uh maybe if we have + + + align:start position:0% +for these things uh maybe if we have +time down the line we will give you the + + align:start position:0% +time down the line we will give you the + + + align:start position:0% +time down the line we will give you the +one for City but it's more economics + + align:start position:0% +one for City but it's more economics + + + align:start position:0% +one for City but it's more economics +than statistics so we might not have + + align:start position:0% +than statistics so we might not have + + + align:start position:0% +than statistics so we might not have +time to get there but you can see the + + align:start position:0% +time to get there but you can see the + + + align:start position:0% +time to get there but you can see the +zip flow follow cities the farm size + + align:start position:0% +zip flow follow cities the farm size + + + align:start position:0% +zip flow follow cities the farm size +also is quite well approximated by + + align:start position:0% +also is quite well approximated by + + + align:start position:0% +also is quite well approximated by +something like a zip + + align:start position:0% +something like a zip + + + align:start position:0% +something like a zip +flow uh an income it turns out uh follow + + align:start position:0% +flow uh an income it turns out uh follow + + + align:start position:0% +flow uh an income it turns out uh follow +Paro + + align:start position:0% +Paro + + + align:start position:0% +Paro +distribution and what you can uh do is + + align:start position:0% +distribution and what you can uh do is + + + align:start position:0% +distribution and what you can uh do is +estimate estimate them so if come it's + + align:start position:0% +estimate estimate them so if come it's + + + align:start position:0% +estimate estimate them so if come it's +at the top top income tend to be par to + + align:start position:0% +at the top top income tend to be par to + + + align:start position:0% +at the top top income tend to be par to +distribution which is consistent with + + align:start position:0% +distribution which is consistent with + + + align:start position:0% +distribution which is consistent with +the fact that the rest of the income + + align:start position:0% +the fact that the rest of the income + + + align:start position:0% +the fact that the rest of the income +tend to be log normal because at the + + align:start position:0% +tend to be log normal because at the + + + align:start position:0% +tend to be log normal because at the +tail it's very disting difficult to + + align:start position:0% +tail it's very disting difficult to + + + align:start position:0% +tail it's very disting difficult to +distinguish a log normal distribution + + align:start position:0% +distinguish a log normal distribution + + + align:start position:0% +distinguish a log normal distribution +from a Paro + + align:start position:0% +from a Paro + + + align:start position:0% +from a Paro +distribution so if income distribution + + align:start position:0% +distribution so if income distribution + + + align:start position:0% +distribution so if income distribution +is Paro at the top then you can derive + + align:start position:0% +is Paro at the top then you can derive + + + align:start position:0% +is Paro at the top then you can derive +simple expressions for the share of the + + align:start position:0% +simple expressions for the share of the + + + align:start position:0% +simple expressions for the share of the +top 1% so I'm going to let you do this + + align:start position:0% +top 1% so I'm going to let you do this + + + align:start position:0% +top 1% so I'm going to let you do this +calculation and in your home is very + + align:start position:0% +calculation and in your home is very + + + align:start position:0% +calculation and in your home is very +simple integration of the we take the + + align:start position:0% +simple integration of the we take the + + + align:start position:0% +simple integration of the we take the +derivative of the of the of the from + + align:start position:0% +derivative of the of the of the from + + + align:start position:0% +derivative of the of the of the from +this you can get of course the PDF take + + align:start position:0% +this you can get of course the PDF take + + + align:start position:0% +this you can get of course the PDF take +the derivative of the PDF and + + align:start position:0% +the derivative of the PDF and + + + align:start position:0% +the derivative of the PDF and +reintegrate over whatever you're + + align:start position:0% +reintegrate over whatever you're + + + align:start position:0% +reintegrate over whatever you're +interested in you can convince yourself + + align:start position:0% +interested in you can convince yourself + + + align:start position:0% +interested in you can convince yourself +very easily that the top uh the qest + + align:start position:0% +very easily that the top uh the qest + + + align:start position:0% +very easily that the top uh the qest +percenti share of income can be derived + + align:start position:0% +percenti share of income can be derived + + + align:start position:0% +percenti share of income can be derived +as Q over 100 to the power of Lambda + + align:start position:0% +as Q over 100 to the power of Lambda + + + align:start position:0% +as Q over 100 to the power of Lambda +minus one over + + align:start position:0% +minus one over + + + align:start position:0% +minus one over +Lambda so that for example with Lambda + + align:start position:0% +Lambda so that for example with Lambda + + + align:start position:0% +Lambda so that for example with Lambda +equal to the top 1% share is 10% with + + align:start position:0% +equal to the top 1% share is 10% with + + + align:start position:0% +equal to the top 1% share is 10% with +Lambda equal three it's 4% so the + + align:start position:0% +Lambda equal three it's 4% so the + + + align:start position:0% +Lambda equal three it's 4% so the +smaller the Lambda the more inequality + + align:start position:0% +smaller the Lambda the more inequality + + + align:start position:0% +smaller the Lambda the more inequality +there is at the + + align:start position:0% +there is at the + + + align:start position:0% +there is at the +top so all we have to do now is to use + + align:start position:0% +top so all we have to do now is to use + + + align:start position:0% +top so all we have to do now is to use +available data to estimate the parameter + + align:start position:0% +available data to estimate the parameter + + + align:start position:0% +available data to estimate the parameter +lamb the shape parameter Lambda and the + + align:start position:0% +lamb the shape parameter Lambda and the + + + align:start position:0% +lamb the shape parameter Lambda and the +scale parameter XM and uh that's what uh + + align:start position:0% +scale parameter XM and uh that's what uh + + + align:start position:0% +scale parameter XM and uh that's what uh +P started doing for uh uh France by the + + align:start position:0% +P started doing for uh uh France by the + + + align:start position:0% +P started doing for uh uh France by the +way it's not he's not the first to have + + align:start position:0% +way it's not he's not the first to have + + + align:start position:0% +way it's not he's not the first to have +observed that uh um Jim poterba who is + + align:start position:0% +observed that uh um Jim poterba who is + + + align:start position:0% +observed that uh um Jim poterba who is +here is one of the first person person + + align:start position:0% +here is one of the first person person + + + align:start position:0% +here is one of the first person person +who have done it and he did it he + + align:start position:0% +who have done it and he did it he + + + align:start position:0% +who have done it and he did it he +started doing it for for p first wrote a + + align:start position:0% +started doing it for for p first wrote a + + + align:start position:0% +started doing it for for p first wrote a +big book on France and started doing + + align:start position:0% +big book on France and started doing + + + align:start position:0% +big book on France and started doing +systematically a little bit differently + + align:start position:0% +systematically a little bit differently + + + align:start position:0% +systematically a little bit differently +than jimba had done but very much same + + align:start position:0% +than jimba had done but very much same + + + align:start position:0% +than jimba had done but very much same +principle and then p and say did it for + + align:start position:0% +principle and then p and say did it for + + + align:start position:0% +principle and then p and say did it for +the US and then they did it again for + + align:start position:0% +the US and then they did it again for + + + align:start position:0% +the US and then they did it again for +wealth distribution + + align:start position:0% +wealth distribution + + + align:start position:0% +wealth distribution +Etc um so in PR the top so when you well + + align:start position:0% +Etc um so in PR the top so when you well + + + align:start position:0% +Etc um so in PR the top so when you well +well it is true that the top + + align:start position:0% +well it is true that the top + + + align:start position:0% +well it is true that the top +distribution is approximately Paro and + + align:start position:0% +distribution is approximately Paro and + + + align:start position:0% +distribution is approximately Paro and +you can check that because we can + + align:start position:0% +you can check that because we can + + + align:start position:0% +you can check that because we can +calculate calculate the B for various + + align:start position:0% +calculate calculate the B for various + + + align:start position:0% +calculate calculate the B for various +brackets + + align:start position:0% +brackets + + + align:start position:0% +brackets +that you would get at various brackets + + align:start position:0% +that you would get at various brackets + + + align:start position:0% +that you would get at various brackets +and for you can calculate the B above + + align:start position:0% +and for you can calculate the B above + + + align:start position:0% +and for you can calculate the B above +100,000 above 200,000 above 300,000 + + align:start position:0% +100,000 above 200,000 above 300,000 + + + align:start position:0% +100,000 above 200,000 above 300,000 +whatever you're interested in and you + + align:start position:0% +whatever you're interested in and you + + + align:start position:0% +whatever you're interested in and you +can see that the B does look + + align:start position:0% +can see that the B does look + + + align:start position:0% +can see that the B does look +approximately constant As you move up + + align:start position:0% +approximately constant As you move up + + + align:start position:0% +approximately constant As you move up +but it's not exactly constant so it is + + align:start position:0% +but it's not exactly constant so it is + + + align:start position:0% +but it's not exactly constant so it is +best to use the B that is the closest to + + align:start position:0% +best to use the B that is the closest to + + + align:start position:0% +best to use the B that is the closest to +the quantal that you're interested + + align:start position:0% +the quantal that you're interested + + + align:start position:0% +the quantal that you're interested +in so how do you do that well the table + + align:start position:0% +in so how do you do that well the table + + + align:start position:0% +in so how do you do that well the table +give you for each TX tax bracket the + + align:start position:0% +give you for each TX tax bracket the + + + align:start position:0% +give you for each TX tax bracket the +number of people in the + + align:start position:0% +number of people in the + + + align:start position:0% +number of people in the +bracket and the sum of the income of + + align:start position:0% +bracket and the sum of the income of + + + align:start position:0% +bracket and the sum of the income of +people in this bracket so if you divide + + align:start position:0% +people in this bracket so if you divide + + + align:start position:0% +people in this bracket so if you divide +the sum of the income of people in this + + align:start position:0% +the sum of the income of people in this + + + align:start position:0% +the sum of the income of people in this +bracket by the uh overall income of the + + align:start position:0% +bracket by the uh overall income of the + + + align:start position:0% +bracket by the uh overall income of the +economy you get the average income of + + align:start position:0% +economy you get the average income of + + + align:start position:0% +economy you get the average income of +people in this bracket uh and as we if + + align:start position:0% +people in this bracket uh and as we if + + + align:start position:0% +people in this bracket uh and as we if +you remember the average income of + + align:start position:0% +you remember the average income of + + + align:start position:0% +you remember the average income of +people in in a bracket is is the + + align:start position:0% +people in in a bracket is is the + + + align:start position:0% +people in in a bracket is is the +multiplicative Factor times the minimum + + align:start position:0% +multiplicative Factor times the minimum + + + align:start position:0% +multiplicative Factor times the minimum +income of people and in the line so that + + align:start position:0% +income of people and in the line so that + + + align:start position:0% +income of people and in the line so that +allows us to calculate the + + align:start position:0% +allows us to calculate the + + + align:start position:0% +allows us to calculate the +Paro coefficient B B is B over B minus + + align:start position:0% +Paro coefficient B B is B over B minus + + + align:start position:0% +Paro coefficient B B is B over B minus +one um as the average people of income + + align:start position:0% +one um as the average people of income + + + align:start position:0% +one um as the average people of income +in the bracket divided by the lower + + align:start position:0% +in the bracket divided by the lower + + + align:start position:0% +in the bracket divided by the lower +bound of the bracket the average people + + align:start position:0% +bound of the bracket the average people + + + align:start position:0% +bound of the bracket the average people +sorry above a particular line divided by + + align:start position:0% +sorry above a particular line divided by + + + align:start position:0% +sorry above a particular line divided by +the + + align:start position:0% +the + + + align:start position:0% +the +line from B we can calculate Lambda and + + align:start position:0% +line from B we can calculate Lambda and + + + align:start position:0% +line from B we can calculate Lambda and +from Lambda we can calculate uh the the + + align:start position:0% +from Lambda we can calculate uh the the + + + align:start position:0% +from Lambda we can calculate uh the the +scale parameter and then we have + + align:start position:0% +scale parameter and then we have + + + align:start position:0% +scale parameter and then we have +everything now that describe we have an + + align:start position:0% +everything now that describe we have an + + + align:start position:0% +everything now that describe we have an +entire description of the distribution + + align:start position:0% +entire description of the distribution + + + align:start position:0% +entire description of the distribution +at the top we have everything we need we + + align:start position:0% +at the top we have everything we need we + + + align:start position:0% +at the top we have everything we need we +take the share going to the relevant + + align:start position:0% +take the share going to the relevant + + + align:start position:0% +take the share going to the relevant +percentile using the closest uh tax + + align:start position:0% +percentile using the closest uh tax + + + align:start position:0% +percentile using the closest uh tax +bracket that gives us the closest line S + + align:start position:0% +bracket that gives us the closest line S + + + align:start position:0% +bracket that gives us the closest line S +and we we calculate the top income of + + align:start position:0% +and we we calculate the top income of + + + align:start position:0% +and we we calculate the top income of +everybody above divided by average by + + align:start position:0% +everybody above divided by average by + + + align:start position:0% +everybody above divided by average by +total income to obtain the average + + align:start position:0% +total income to obtain the average + + + align:start position:0% +total income to obtain the average +income obtain the coefficient B obtain + + align:start position:0% +income obtain the coefficient B obtain + + + align:start position:0% +income obtain the coefficient B obtain +Lambda and then applies this to to the + + align:start position:0% +Lambda and then applies this to to the + + + align:start position:0% +Lambda and then applies this to to the +quanti we are interested in so that's + + align:start position:0% +quanti we are interested in so that's + + + align:start position:0% +quanti we are interested in so that's +what they do in a systematic way and + + align:start position:0% +what they do in a systematic way and + + + align:start position:0% +what they do in a systematic way and +then you know once you know that you can + + align:start position:0% +then you know once you know that you can + + + align:start position:0% +then you know once you know that you can +just do whatever you're interested in uh + + align:start position:0% +just do whatever you're interested in uh + + + align:start position:0% +just do whatever you're interested in uh +and that's how we get this nice graph + + align:start position:0% +and that's how we get this nice graph + + + align:start position:0% +and that's how we get this nice graph +which have had I think pretty altering + + align:start position:0% +which have had I think pretty altering + + + align:start position:0% +which have had I think pretty altering +consequences on at least on the + + align:start position:0% +consequences on at least on the + + + align:start position:0% +consequences on at least on the +political debates of the last few years + + align:start position:0% +political debates of the last few years + + + align:start position:0% +political debates of the last few years +yes I was just curious if the slope of + + align:start position:0% +yes I was just curious if the slope of + + + align:start position:0% +yes I was just curious if the slope of +the parator is changing as the years are + + align:start position:0% +the parator is changing as the years are + + + align:start position:0% +the parator is changing as the years are +progressing well especially like in ter + + align:start position:0% +progressing well especially like in ter + + + align:start position:0% +progressing well especially like in ter +of getting more more and more intense + + align:start position:0% +of getting more more and more intense + + + align:start position:0% +of getting more more and more intense +because my assumption would be not + + align:start position:0% +because my assumption would be not + + + align:start position:0% +because my assumption would be not +coming from economics background that + + align:start position:0% +coming from economics background that + + + align:start position:0% +coming from economics background that +Technologies allowing more and platforms + + align:start position:0% +Technologies allowing more and platforms + + + align:start position:0% +Technologies allowing more and platforms +to consolidate things then in a way the + + align:start position:0% +to consolidate things then in a way the + + + align:start position:0% +to consolidate things then in a way the +inequality stretch also keep on + + align:start position:0% +inequality stretch also keep on + + + align:start position:0% +inequality stretch also keep on +increasing so there is a lot in your + + align:start position:0% +increasing so there is a lot in your + + + align:start position:0% +increasing so there is a lot in your +question the first point is an empirical + + align:start position:0% +question the first point is an empirical + + + align:start position:0% +question the first point is an empirical +fact you're asking if the Baro + + align:start position:0% +fact you're asking if the Baro + + + align:start position:0% +fact you're asking if the Baro +coefficient changes + + align:start position:0% +coefficient changes + + + align:start position:0% +coefficient changes +uh you can almost see there like by + + align:start position:0% +uh you can almost see there like by + + + align:start position:0% +uh you can almost see there like by +definition it does this is why this is + + align:start position:0% +definition it does this is why this is + + + align:start position:0% +definition it does this is why this is +telling us in a sense the top one person + + align:start position:0% +telling us in a sense the top one person + + + align:start position:0% +telling us in a sense the top one person +is getting a larger and larger share of + + align:start position:0% +is getting a larger and larger share of + + + align:start position:0% +is getting a larger and larger share of +the income that means B is becoming + + align:start position:0% +the income that means B is becoming + + + align:start position:0% +the income that means B is becoming +smaller and smaller at least since the + + align:start position:0% +smaller and smaller at least since the + + + align:start position:0% +smaller and smaller at least since the +since the 80s and it was higher before + + align:start position:0% +since the 80s and it was higher before + + + align:start position:0% +since the 80s and it was higher before +the second thing is you're providing an + + align:start position:0% +the second thing is you're providing an + + + align:start position:0% +the second thing is you're providing an +explanation for this fact which is + + align:start position:0% +explanation for this fact which is + + + align:start position:0% +explanation for this fact which is +technology uh there is an actually very + + align:start position:0% +technology uh there is an actually very + + + align:start position:0% +technology uh there is an actually very +interesting paper by gabex about cop + + align:start position:0% +interesting paper by gabex about cop + + + align:start position:0% +interesting paper by gabex about cop +which very much makes this assumption in + + align:start position:0% +which very much makes this assumption in + + + align:start position:0% +which very much makes this assumption in +the sense that the technology means that + + align:start position:0% +the sense that the technology means that + + + align:start position:0% +the sense that the technology means that +cop will be we sort of derive the reason + + align:start position:0% +cop will be we sort of derive the reason + + + align:start position:0% +cop will be we sort of derive the reason +why C would be Paro distributed and that + + align:start position:0% +why C would be Paro distributed and that + + + align:start position:0% +why C would be Paro distributed and that +and that the the coefficient might + + align:start position:0% +and that the the coefficient might + + + align:start position:0% +and that the the coefficient might +change as a response of how much + + align:start position:0% +change as a response of how much + + + align:start position:0% +change as a response of how much +leverage there is in the in the economy + + align:start position:0% +leverage there is in the in the economy + + + align:start position:0% +leverage there is in the in the economy +yeah is this all before after taxes + + align:start position:0% +yeah is this all before after taxes + + + align:start position:0% +yeah is this all before after taxes +uh so this is before + + align:start position:0% +uh so this is before + + + align:start position:0% +uh so this is before +taxes and then uh after taxes + + align:start position:0% +taxes and then uh after taxes + + + align:start position:0% +taxes and then uh after taxes +is the same shape because because our + + align:start position:0% +is the same shape because because our + + + align:start position:0% +is the same shape because because our +tax rates are not hugely of course it's + + align:start position:0% +tax rates are not hugely of course it's + + + align:start position:0% +tax rates are not hugely of course it's +flattened a bit but our tax rates are + + align:start position:0% +flattened a bit but our tax rates are + + + align:start position:0% +flattened a bit but our tax rates are +not extraordinary Progressive not + + align:start position:0% +not extraordinary Progressive not + + + align:start position:0% +not extraordinary Progressive not +Progressive enough to undo that so the + + align:start position:0% +Progressive enough to undo that so the + + + align:start position:0% +Progressive enough to undo that so the +shape is similar and the levels are + + align:start position:0% + + + + align:start position:0% + +different and you you're asking a very + + align:start position:0% +different and you you're asking a very + + + align:start position:0% +different and you you're asking a very +good question which is for some uh uh + + align:start position:0% +good question which is for some uh uh + + + align:start position:0% +good question which is for some uh uh +for some problems we're interested in + + align:start position:0% +for some problems we're interested in + + + align:start position:0% +for some problems we're interested in +before for example where if we're + + align:start position:0% +before for example where if we're + + + align:start position:0% +before for example where if we're +interested in testing his hypothesis + + align:start position:0% +interested in testing his hypothesis + + + align:start position:0% +interested in testing his hypothesis +that the technology development of + + align:start position:0% +that the technology development of + + + align:start position:0% +that the technology development of +Technology will lead to uh uh + + align:start position:0% +Technology will lead to uh uh + + + align:start position:0% +Technology will lead to uh uh +concentration of the + + align:start position:0% +concentration of the + + + align:start position:0% +concentration of the +income uh uh to towards few people by + + align:start position:0% +income uh uh to towards few people by + + + align:start position:0% +income uh uh to towards few people by +through a changing of the Paro + + align:start position:0% +through a changing of the Paro + + + align:start position:0% +through a changing of the Paro +distribution we are interested in pre- + + align:start position:0% +distribution we are interested in pre- + + + align:start position:0% +distribution we are interested in pre- +taxes if we're interested in uh whether + + align:start position:0% +taxes if we're interested in uh whether + + + align:start position:0% +taxes if we're interested in uh whether +uh in in how how much inequality there + + align:start position:0% +uh in in how how much inequality there + + + align:start position:0% +uh in in how how much inequality there +is in actual spending power we're + + align:start position:0% +is in actual spending power we're + + + align:start position:0% +is in actual spending power we're +interested in post taxes so depending on + + align:start position:0% +interested in post taxes so depending on + + + align:start position:0% +interested in post taxes so depending on +the on depending on + + align:start position:0% +the on depending on + + + align:start position:0% +the on depending on +the on what we're interested in we we're + + align:start position:0% +the on what we're interested in we we're + + + align:start position:0% +the on what we're interested in we we're +going to be interested in both um I + + align:start position:0% +going to be interested in both um I + + + align:start position:0% +going to be interested in both um I +should say that the you know the sort of + + align:start position:0% +should say that the you know the sort of + + + align:start position:0% +should say that the you know the sort of +the big sort of competing explanation + + align:start position:0% +the big sort of competing explanation + + + align:start position:0% +the big sort of competing explanation +for this type of phenomenon one is uh + + align:start position:0% +for this type of phenomenon one is uh + + + align:start position:0% +for this type of phenomenon one is uh +the what you're talking about technology + + align:start position:0% +the what you're talking about technology + + + align:start position:0% +the what you're talking about technology +lead explanation the other institution + + align:start position:0% +lead explanation the other institution + + + align:start position:0% +lead explanation the other institution +Le explanation in the sense you know how + + align:start position:0% +Le explanation in the sense you know how + + + align:start position:0% +Le explanation in the sense you know how +cop are set by board and stuff like that + + align:start position:0% +cop are set by board and stuff like that + + + align:start position:0% +cop are set by board and stuff like that +um um there was a very interesting NPR + + align:start position:0% +um um there was a very interesting NPR + + + align:start position:0% +um um there was a very interesting NPR +plan money episode a few days ago about + + align:start position:0% +plan money episode a few days ago about + + + align:start position:0% +plan money episode a few days ago about +cop that was very much leaning in the + + align:start position:0% +cop that was very much leaning in the + + + align:start position:0% +cop that was very much leaning in the +institutional Direction uh which is and + + align:start position:0% +institutional Direction uh which is and + + + align:start position:0% +institutional Direction uh which is and +the P says do thing do do do favor the + + align:start position:0% +the P says do thing do do do favor the + + + align:start position:0% +the P says do thing do do do favor the +institutional Direction but there there + + align:start position:0% +institutional Direction but there there + + + align:start position:0% +institutional Direction but there there +are there's lots of good work in both + + align:start position:0% +are there's lots of good work in both + + + align:start position:0% +are there's lots of good work in both +sense once you have the facts you can + + align:start position:0% +sense once you have the facts you can + + + align:start position:0% +sense once you have the facts you can +start playing a lot to try and explain + + align:start position:0% +start playing a lot to try and explain + + + align:start position:0% +start playing a lot to try and explain +them yep no + + align:start position:0% +them yep no + + + align:start position:0% +them yep no +you criticism of like assuming the CR + + align:start position:0% +you criticism of like assuming the CR + + + align:start position:0% +you criticism of like assuming the CR +distribution or is it sort of generally + + align:start position:0% +distribution or is it sort of generally + + + align:start position:0% +distribution or is it sort of generally +accepted well you can verify it because + + align:start position:0% +accepted well you can verify it because + + + align:start position:0% +accepted well you can verify it because +uh so first it's quite generally + + align:start position:0% +uh so first it's quite generally + + + align:start position:0% +uh so first it's quite generally +accepted uh uh second you can verify + + align:start position:0% +accepted uh uh second you can verify + + + align:start position:0% +accepted uh uh second you can verify +it's very easy to check because you have + + align:start position:0% +it's very easy to check because you have + + + align:start position:0% +it's very easy to check because you have +several tax bracket at the top so what + + align:start position:0% +several tax bracket at the top so what + + + align:start position:0% +several tax bracket at the top so what +you can do is to calculate the Paro + + align:start position:0% +you can do is to calculate the Paro + + + align:start position:0% +you can do is to calculate the Paro +coefficient for for several lines and + + align:start position:0% +coefficient for for several lines and + + + align:start position:0% +coefficient for for several lines and +you can see if in fact they look roughly + + align:start position:0% +you can see if in fact they look roughly + + + align:start position:0% +you can see if in fact they look roughly +constant and what you do is that what + + align:start position:0% +constant and what you do is that what + + + align:start position:0% +constant and what you do is that what +you see is that for a given year they + + align:start position:0% +you see is that for a given year they + + + align:start position:0% +you see is that for a given year they +look roughly constant but then they + + align:start position:0% +look roughly constant but then they + + + align:start position:0% +look roughly constant but then they +change after a certain income after it's + + align:start position:0% +change after a certain income after it's + + + align:start position:0% +change after a certain income after it's +only true at the top this + + align:start position:0% +only true at the top this + + + align:start position:0% +only true at the top this +solution all right so I think we can + + align:start position:0% +solution all right so I think we can + + + align:start position:0% +solution all right so I think we can +stop here no point starting something + + align:start position:0% +stop here no point starting something + + + align:start position:0% +stop here no point starting something +new uh and uh we will start again on + + align:start position:0% +new uh and uh we will start again on + + + align:start position:0% +new uh and uh we will start again on +Monday with uh first deepening our + + align:start position:0% +Monday with uh first deepening our + + + align:start position:0% +Monday with uh first deepening our +knowledge of uh uh joint distribution + + align:start position:0% +knowledge of uh uh joint distribution + + + align:start position:0% +knowledge of uh uh joint distribution +and how we play with them and then + + align:start position:0% +and how we play with them and then + + + align:start position:0% +and how we play with them and then +function of random variable and the + + align:start position:0% + + + + align:start position:0% + +like \ No newline at end of file diff --git a/zWxhmBCdvFs.txt b/zWxhmBCdvFs.txt new file mode 100644 index 0000000000000000000000000000000000000000..83ac70390a71bb84e6624d55d15433587333e7e4 --- /dev/null +++ b/zWxhmBCdvFs.txt @@ -0,0 +1,1027 @@ +align:start position:0% + +hi there my name is Anna welcome to + + align:start position:0% +hi there my name is Anna welcome to + + + align:start position:0% +hi there my name is Anna welcome to +recitation in lecture you've been + + align:start position:0% +recitation in lecture you've been + + + align:start position:0% +recitation in lecture you've been +learning about how to multiply matrices + + align:start position:0% +learning about how to multiply matrices + + + align:start position:0% +learning about how to multiply matrices +and how to think about that + + align:start position:0% +and how to think about that + + + align:start position:0% +and how to think about that +multiplication in different ways and + + align:start position:0% +multiplication in different ways and + + + align:start position:0% +multiplication in different ways and +also about when a matrix is invertible + + align:start position:0% +also about when a matrix is invertible + + + align:start position:0% +also about when a matrix is invertible +not or not and how to compute the + + align:start position:0% +not or not and how to compute the + + + align:start position:0% +not or not and how to compute the +inverse when it is invertible and that's + + align:start position:0% +inverse when it is invertible and that's + + + align:start position:0% +inverse when it is invertible and that's +what today's problem is about we have a + + align:start position:0% +what today's problem is about we have a + + + align:start position:0% +what today's problem is about we have a +matrix a that has variables a and B + + align:start position:0% +matrix a that has variables a and B + + + align:start position:0% +matrix a that has variables a and B +instead of numbers and the question is + + align:start position:0% +instead of numbers and the question is + + + align:start position:0% +instead of numbers and the question is +what are the conditions on a and B that + + align:start position:0% +what are the conditions on a and B that + + + align:start position:0% +what are the conditions on a and B that +made that mean that make that matrix + + align:start position:0% +made that mean that make that matrix + + + align:start position:0% +made that mean that make that matrix +invertible and when it is invertible + + align:start position:0% +invertible and when it is invertible + + + align:start position:0% +invertible and when it is invertible +what is a inverse why don't you hit + + align:start position:0% +what is a inverse why don't you hit + + + align:start position:0% +what is a inverse why don't you hit +pause and work on it for a little while + + align:start position:0% +pause and work on it for a little while + + + align:start position:0% +pause and work on it for a little while +and then we'll come back and work on it + + align:start position:0% +and then we'll come back and work on it + + + align:start position:0% +and then we'll come back and work on it +together and we're back I hope you had + + align:start position:0% +together and we're back I hope you had + + + align:start position:0% +together and we're back I hope you had +success in solving that let's do it + + align:start position:0% +success in solving that let's do it + + + align:start position:0% +success in solving that let's do it +ourselves + + align:start position:0% +ourselves + + + align:start position:0% +ourselves +alright so remember from lecture we + + align:start position:0% +alright so remember from lecture we + + + align:start position:0% +alright so remember from lecture we +talked about well professor Strang + + align:start position:0% +talked about well professor Strang + + + align:start position:0% +talked about well professor Strang +talked about how it's easy to spot some + + align:start position:0% +talked about how it's easy to spot some + + + align:start position:0% +talked about how it's easy to spot some +easy tests to spot when a matrix is not + + align:start position:0% +easy tests to spot when a matrix is not + + + align:start position:0% +easy tests to spot when a matrix is not +invertible those were if you have a + + align:start position:0% +invertible those were if you have a + + + align:start position:0% +invertible those were if you have a +column of zeros or a row of zeros then + + align:start position:0% +column of zeros or a row of zeros then + + + align:start position:0% +column of zeros or a row of zeros then +the matrix is not invertible or if you + + align:start position:0% +the matrix is not invertible or if you + + + align:start position:0% +the matrix is not invertible or if you +have two columns that are the same or + + align:start position:0% +have two columns that are the same or + + + align:start position:0% +have two columns that are the same or +two rows that are the same the matrix is + + align:start position:0% +two rows that are the same the matrix is + + + align:start position:0% +two rows that are the same the matrix is +also not invertible so let's see if we + + align:start position:0% +also not invertible so let's see if we + + + align:start position:0% +also not invertible so let's see if we +can if this matrix satisfies any of + + align:start position:0% +can if this matrix satisfies any of + + + align:start position:0% +can if this matrix satisfies any of +those easy conditions well here you have + + align:start position:0% +those easy conditions well here you have + + + align:start position:0% +those easy conditions well here you have +a row of s if a is equal to 0 you have a + + align:start position:0% +a row of s if a is equal to 0 you have a + + + align:start position:0% +a row of s if a is equal to 0 you have a +row of zeros the matrix is not + + align:start position:0% +row of zeros the matrix is not + + + align:start position:0% +row of zeros the matrix is not +invertible so is what was the other one + + align:start position:0% +invertible so is what was the other one + + + align:start position:0% +invertible so is what was the other one +two of the same column or the same row + + align:start position:0% +two of the same column or the same row + + + align:start position:0% +two of the same column or the same row +well if a is equal to B then all the + + align:start position:0% +well if a is equal to B then all the + + + align:start position:0% +well if a is equal to B then all the +entries in the matrix are the same so + + align:start position:0% +entries in the matrix are the same so + + + align:start position:0% +entries in the matrix are the same so +all the rows are the same or the columns + + align:start position:0% +all the rows are the same or the columns + + + align:start position:0% +all the rows are the same or the columns +are the same the matrix is not + + align:start position:0% +are the same the matrix is not + + + align:start position:0% +are the same the matrix is not +invertible so that's the other easy + + align:start position:0% +invertible so that's the other easy + + + align:start position:0% +invertible so that's the other easy +condition it's not invertible if a is + + align:start position:0% +condition it's not invertible if a is + + + align:start position:0% +condition it's not invertible if a is +equal to 0 or a equals to B there is not + + align:start position:0% +equal to 0 or a equals to B there is not + + + align:start position:0% +equal to 0 or a equals to B there is not +any other easy condition that I can spot + + align:start position:0% +any other easy condition that I can spot + + + align:start position:0% +any other easy condition that I can spot +so we have to do it in a more systematic + + align:start position:0% +so we have to do it in a more systematic + + + align:start position:0% +so we have to do it in a more systematic +way + + align:start position:0% +way + + + align:start position:0% +way +so to do that actually what we do is we + + align:start position:0% +so to do that actually what we do is we + + + align:start position:0% +so to do that actually what we do is we +start with a we tried to find it since + + align:start position:0% +start with a we tried to find it since + + + align:start position:0% +start with a we tried to find it since +its inverse and if in the process we run + + align:start position:0% +its inverse and if in the process we run + + + align:start position:0% +its inverse and if in the process we run +into something fishy those are our + + align:start position:0% +into something fishy those are our + + + align:start position:0% +into something fishy those are our +conditions so remember how to find the + + align:start position:0% +conditions so remember how to find the + + + align:start position:0% +conditions so remember how to find the +inverse of a matrix you start by writing + + align:start position:0% +inverse of a matrix you start by writing + + + align:start position:0% +inverse of a matrix you start by writing +a giant matrix that has a and the + + align:start position:0% +a giant matrix that has a and the + + + align:start position:0% +a giant matrix that has a and the +identity next to it and then you perform + + align:start position:0% +identity next to it and then you perform + + + align:start position:0% +identity next to it and then you perform +elimination steps until let's put dots + + align:start position:0% +elimination steps until let's put dots + + + align:start position:0% +elimination steps until let's put dots +here because there's lots of steps and + + align:start position:0% +here because there's lots of steps and + + + align:start position:0% +here because there's lots of steps and +you stop once you've reached the + + align:start position:0% +you stop once you've reached the + + + align:start position:0% +you stop once you've reached the +identity matrix on the left side and + + align:start position:0% +identity matrix on the left side and + + + align:start position:0% +identity matrix on the left side and +when you do that what you have on the + + align:start position:0% +when you do that what you have on the + + + align:start position:0% +when you do that what you have on the +right side will be your a inverse easy + + align:start position:0% +right side will be your a inverse easy + + + align:start position:0% +right side will be your a inverse easy +enough so let's do the computations my + + align:start position:0% +enough so let's do the computations my + + + align:start position:0% +enough so let's do the computations my +identity matrix next to it and now I + + align:start position:0% +identity matrix next to it and now I + + + align:start position:0% +identity matrix next to it and now I +know you learned about elimination in + + align:start position:0% +know you learned about elimination in + + + align:start position:0% +know you learned about elimination in +the past recitation so I'll do the first + + align:start position:0% +the past recitation so I'll do the first + + + align:start position:0% +the past recitation so I'll do the first +few steps slowly and then I'll just + + align:start position:0% +few steps slowly and then I'll just + + + align:start position:0% +few steps slowly and then I'll just +write the solution for the last steps + + align:start position:0% +write the solution for the last steps + + + align:start position:0% +write the solution for the last steps +all right so we want to eliminate this a + + align:start position:0% +all right so we want to eliminate this a + + + align:start position:0% +all right so we want to eliminate this a +we want to turn it into zero so let's + + align:start position:0% +we want to turn it into zero so let's + + + align:start position:0% +we want to turn it into zero so let's +subtract the first row from the second + + align:start position:0% +subtract the first row from the second + + + align:start position:0% +subtract the first row from the second +let's do Row 2 minus Row 1 and write it + + align:start position:0% +let's do Row 2 minus Row 1 and write it + + + align:start position:0% +let's do Row 2 minus Row 1 and write it +instead of Row 2 so a B be 1 0 0 0 a + + align:start position:0% +instead of Row 2 so a B be 1 0 0 0 a + + + align:start position:0% +instead of Row 2 so a B be 1 0 0 0 a +minus ay ay minus V B minus B 0 0 minus + + align:start position:0% +minus ay ay minus V B minus B 0 0 minus + + + align:start position:0% +minus ay ay minus V B minus B 0 0 minus +1 1 minus 0 0 minus 0 and then we want + + align:start position:0% +1 1 minus 0 0 minus 0 and then we want + + + align:start position:0% +1 1 minus 0 0 minus 0 and then we want +to do the same with the third row so + + align:start position:0% +to do the same with the third row so + + + align:start position:0% +to do the same with the third row so +let's do Row 3 minus Row 1 0 a minus B + + align:start position:0% +let's do Row 3 minus Row 1 0 a minus B + + + align:start position:0% +let's do Row 3 minus Row 1 0 a minus B +it doesn't fit a minus B you understand + + align:start position:0% +it doesn't fit a minus B you understand + + + align:start position:0% +it doesn't fit a minus B you understand +that and then 0 minus 1 0 minus 0 1 + + align:start position:0% +that and then 0 minus 1 0 minus 0 1 + + + align:start position:0% +that and then 0 minus 1 0 minus 0 1 +minus 0 all right let's continue up here + + align:start position:0% + + + + align:start position:0% + +right now I want to eliminate this a - B + + align:start position:0% +right now I want to eliminate this a - B + + + align:start position:0% +right now I want to eliminate this a - B +I want to turn it into a zero so the + + align:start position:0% +I want to turn it into a zero so the + + + align:start position:0% +I want to turn it into a zero so the +first row stays the same + + align:start position:0% +first row stays the same + + + align:start position:0% +first row stays the same +maybe B 1 0 0 0 a minus B 0 minus 1 1 0 + + align:start position:0% +maybe B 1 0 0 0 a minus B 0 minus 1 1 0 + + + align:start position:0% +maybe B 1 0 0 0 a minus B 0 minus 1 1 0 +and now 0 minus 0 a minus B minus a + + align:start position:0% +and now 0 minus 0 a minus B minus a + + + align:start position:0% +and now 0 minus 0 a minus B minus a +minus B 0 a minus B minus 0 that's easy + + align:start position:0% +minus B 0 a minus B minus 0 that's easy + + + align:start position:0% +minus B 0 a minus B minus 0 that's easy +minus 1 minus minus 1 0 again minus 1 + + align:start position:0% +minus 1 minus minus 1 0 again minus 1 + + + align:start position:0% +minus 1 minus minus 1 0 again minus 1 +and 1 almost there we already have zeros + + align:start position:0% +and 1 almost there we already have zeros + + + align:start position:0% +and 1 almost there we already have zeros +down here it's looking more and more + + align:start position:0% +down here it's looking more and more + + + align:start position:0% +down here it's looking more and more +like the identity matrix so we have to + + align:start position:0% +like the identity matrix so we have to + + + align:start position:0% +like the identity matrix so we have to +turn all these diagonal entries into 1 + + align:start position:0% +turn all these diagonal entries into 1 + + + align:start position:0% +turn all these diagonal entries into 1 +so let's do that now mm 1 B over a bo oh + + align:start position:0% +so let's do that now mm 1 B over a bo oh + + + align:start position:0% +so let's do that now mm 1 B over a bo oh +I'm dividing by a they better not be 0 + + align:start position:0% +I'm dividing by a they better not be 0 + + + align:start position:0% +I'm dividing by a they better not be 0 +let me signal that here hey different + + align:start position:0% +let me signal that here hey different + + + align:start position:0% +let me signal that here hey different +from 0 1 over a 0 0 0 I want to make + + align:start position:0% +from 0 1 over a 0 0 0 I want to make + + + align:start position:0% +from 0 1 over a 0 0 0 I want to make +that into a 1 so 1 over a minus B and + + align:start position:0% +that into a 1 so 1 over a minus B and + + + align:start position:0% +that into a 1 so 1 over a minus B and +you guessed it a minus B has to be + + align:start position:0% +you guessed it a minus B has to be + + + align:start position:0% +you guessed it a minus B has to be +different from 0 0 minus minus 1 over a + + align:start position:0% +different from 0 0 minus minus 1 over a + + + align:start position:0% +different from 0 0 minus minus 1 over a +minus B 1 over a minus B 0 0 0 1 0 minus + + align:start position:0% +minus B 1 over a minus B 0 0 0 1 0 minus + + + align:start position:0% +minus B 1 over a minus B 0 0 0 1 0 minus +1 over a minus B 1 over a minus B + + align:start position:0% + + + + align:start position:0% + +someone's pointing a mistake oh you're + + align:start position:0% +someone's pointing a mistake oh you're + + + align:start position:0% +someone's pointing a mistake oh you're +absolutely right + + align:start position:0% + + + + align:start position:0% + +thank you all right so not much left to + + align:start position:0% +thank you all right so not much left to + + + align:start position:0% +thank you all right so not much left to +do we only have to eliminate B over a + + align:start position:0% +do we only have to eliminate B over a + + + align:start position:0% +do we only have to eliminate B over a +and B over a that's a little bit + + align:start position:0% +and B over a that's a little bit + + + align:start position:0% +and B over a that's a little bit +computationally heavy so what do you + + align:start position:0% +computationally heavy so what do you + + + align:start position:0% +computationally heavy so what do you +have to do and just have to basically + + align:start position:0% +have to do and just have to basically + + + align:start position:0% +have to do and just have to basically +subtract replace Rho 1 by Rho 1 minus B + + align:start position:0% +subtract replace Rho 1 by Rho 1 minus B + + + align:start position:0% +subtract replace Rho 1 by Rho 1 minus B +over a times Row 2 plus Row 3 let me + + align:start position:0% +over a times Row 2 plus Row 3 let me + + + align:start position:0% +over a times Row 2 plus Row 3 let me +write that down + + align:start position:0% +write that down + + + align:start position:0% +write that down +Rho 1 minus V over a times Row 2 plus + + align:start position:0% +Rho 1 minus V over a times Row 2 plus + + + align:start position:0% +Rho 1 minus V over a times Row 2 plus +Row 3 you want that to go into your Row + + align:start position:0% +Row 3 you want that to go into your Row + + + align:start position:0% +Row 3 you want that to go into your Row +1 these stay the same once 1 over a + + align:start position:0% +1 these stay the same once 1 over a + + + align:start position:0% +1 these stay the same once 1 over a +minus B 1 over a minus B all right this + + align:start position:0% +minus B 1 over a minus B all right this + + + align:start position:0% +minus B 1 over a minus B all right this +is where I'm gonna go to my notes tell + + align:start position:0% +is where I'm gonna go to my notes tell + + + align:start position:0% +is where I'm gonna go to my notes tell +you that these numbers are 1 over a + + align:start position:0% +you that these numbers are 1 over a + + + align:start position:0% +you that these numbers are 1 over a +minus B 0 minus B over a a minus B that + + align:start position:0% +minus B 0 minus B over a a minus B that + + + align:start position:0% +minus B 0 minus B over a a minus B that +looks pretty awful but that is a inverse + + align:start position:0% +looks pretty awful but that is a inverse + + + align:start position:0% +looks pretty awful but that is a inverse +and we're done except it looks terrible + + align:start position:0% +and we're done except it looks terrible + + + align:start position:0% +and we're done except it looks terrible +so let me just write it in a nicer way a + + align:start position:0% +so let me just write it in a nicer way a + + + align:start position:0% +so let me just write it in a nicer way a +inverse equals C you're dividing + + align:start position:0% +inverse equals C you're dividing + + + align:start position:0% +inverse equals C you're dividing +everything by a minus B so pull out that + + align:start position:0% +everything by a minus B so pull out that + + + align:start position:0% +everything by a minus B so pull out that +factor 1 0 minus B over a minus 1 1 0 0 + + align:start position:0% +factor 1 0 minus B over a minus 1 1 0 0 + + + align:start position:0% +factor 1 0 minus B over a minus 1 1 0 0 +minus 1 1 looks much better now so + + align:start position:0% +minus 1 1 looks much better now so + + + align:start position:0% +minus 1 1 looks much better now so +here's your a inverse and the other + + align:start position:0% +here's your a inverse and the other + + + align:start position:0% +here's your a inverse and the other +question was what are the conditions on + + align:start position:0% +question was what are the conditions on + + + align:start position:0% +question was what are the conditions on +a and B for the in matrix a to be + + align:start position:0% +a and B for the in matrix a to be + + + align:start position:0% +a and B for the in matrix a to be +invertible well it has to be nonzero and + + align:start position:0% +invertible well it has to be nonzero and + + + align:start position:0% +invertible well it has to be nonzero and +a has to be different from B and we're + + align:start position:0% +a has to be different from B and we're + + + align:start position:0% +a has to be different from B and we're +done that's it for today see you next + + align:start position:0% +done that's it for today see you next + + + align:start position:0% +done that's it for today see you next +time \ No newline at end of file